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b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/entry_points.txt @@ -0,0 +1,51 @@ +[distutils.commands] +alias = setuptools.command.alias:alias +bdist_egg = setuptools.command.bdist_egg:bdist_egg +bdist_rpm = setuptools.command.bdist_rpm:bdist_rpm +bdist_wheel = setuptools.command.bdist_wheel:bdist_wheel +build = setuptools.command.build:build +build_clib = setuptools.command.build_clib:build_clib +build_ext = setuptools.command.build_ext:build_ext +build_py = setuptools.command.build_py:build_py +develop = setuptools.command.develop:develop +dist_info = setuptools.command.dist_info:dist_info +easy_install = setuptools.command.easy_install:easy_install +editable_wheel = setuptools.command.editable_wheel:editable_wheel +egg_info = setuptools.command.egg_info:egg_info +install = setuptools.command.install:install +install_egg_info = setuptools.command.install_egg_info:install_egg_info +install_lib = setuptools.command.install_lib:install_lib +install_scripts = setuptools.command.install_scripts:install_scripts +rotate = setuptools.command.rotate:rotate +saveopts = setuptools.command.saveopts:saveopts +sdist = setuptools.command.sdist:sdist +setopt = setuptools.command.setopt:setopt + +[distutils.setup_keywords] +dependency_links = setuptools.dist:assert_string_list +eager_resources = setuptools.dist:assert_string_list +entry_points = setuptools.dist:check_entry_points +exclude_package_data = setuptools.dist:check_package_data +extras_require = setuptools.dist:check_extras +include_package_data = setuptools.dist:assert_bool +install_requires = setuptools.dist:check_requirements +namespace_packages = setuptools.dist:check_nsp +package_data = setuptools.dist:check_package_data +packages = setuptools.dist:check_packages +python_requires = setuptools.dist:check_specifier +setup_requires = setuptools.dist:check_requirements +use_2to3 = setuptools.dist:invalid_unless_false +zip_safe = setuptools.dist:assert_bool + +[egg_info.writers] +PKG-INFO = setuptools.command.egg_info:write_pkg_info +dependency_links.txt = setuptools.command.egg_info:overwrite_arg +eager_resources.txt = setuptools.command.egg_info:overwrite_arg +entry_points.txt = setuptools.command.egg_info:write_entries +namespace_packages.txt = setuptools.command.egg_info:overwrite_arg +requires.txt = setuptools.command.egg_info:write_requirements +top_level.txt = setuptools.command.egg_info:write_toplevel_names + +[setuptools.finalize_distribution_options] +keywords = setuptools.dist:Distribution._finalize_setup_keywords +parent_finalize = setuptools.dist:_Distribution.finalize_options diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/licenses/LICENSE b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/licenses/LICENSE new file mode 100644 index 0000000000000000000000000000000000000000..1bb5a44356f00884a71ceeefd24ded6caaba2418 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/licenses/LICENSE @@ -0,0 +1,17 @@ +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to +deal in the Software without restriction, including without limitation the +rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +sell copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS +IN THE SOFTWARE. diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/top_level.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/top_level.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5ac1070294b478b7cc2ce677207ee08813bfa37 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools-79.0.1.dist-info/top_level.txt @@ -0,0 +1,3 @@ +_distutils_hack +pkg_resources +setuptools diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/INSTALLER b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/INSTALLER new file mode 100644 index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/INSTALLER @@ -0,0 +1 @@ +pip diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/LICENSE.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/LICENSE.txt new file mode 100644 index 0000000000000000000000000000000000000000..a31470f14c5978d5fcc3bc173b8399b6c9a6443f --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/LICENSE.txt @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2012 Daniel Holth and contributors + +Permission is hereby granted, free of charge, to any person obtaining a +copy of this software and associated documentation files (the "Software"), +to deal in the Software without restriction, including without limitation +the rights to use, copy, modify, merge, publish, distribute, sublicense, +and/or sell copies of the Software, and to permit persons to whom the +Software is furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included +in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +OTHER DEALINGS IN THE SOFTWARE. diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/METADATA b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/METADATA new file mode 100644 index 0000000000000000000000000000000000000000..f645dcb673aaa7e3e7e054d57af5e8c0992b70e8 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/METADATA @@ -0,0 +1,66 @@ +Metadata-Version: 2.3 +Name: wheel +Version: 0.45.1 +Summary: A built-package format for Python +Keywords: wheel,packaging +Author-email: Daniel Holth +Maintainer-email: Alex Grönholm +Requires-Python: >=3.8 +Description-Content-Type: text/x-rst +Classifier: Development Status :: 5 - Production/Stable +Classifier: Intended Audience :: Developers +Classifier: Topic :: System :: Archiving :: Packaging +Classifier: License :: OSI Approved :: MIT License +Classifier: Programming Language :: Python +Classifier: Programming Language :: Python :: 3 :: Only +Classifier: Programming Language :: Python :: 3.8 +Classifier: Programming Language :: Python :: 3.9 +Classifier: Programming Language :: Python :: 3.10 +Classifier: Programming Language :: Python :: 3.11 +Classifier: Programming Language :: Python :: 3.12 +Requires-Dist: pytest >= 6.0.0 ; extra == "test" +Requires-Dist: setuptools >= 65 ; extra == "test" +Project-URL: Changelog, https://wheel.readthedocs.io/en/stable/news.html +Project-URL: Documentation, https://wheel.readthedocs.io/ +Project-URL: Issue Tracker, https://github.com/pypa/wheel/issues +Project-URL: Source, https://github.com/pypa/wheel +Provides-Extra: test + +wheel +===== + +This is a command line tool for manipulating Python wheel files, as defined in +`PEP 427`_. It contains the following functionality: + +* Convert ``.egg`` archives into ``.whl`` +* Unpack wheel archives +* Repack wheel archives +* Add or remove tags in existing wheel archives + +.. _PEP 427: https://www.python.org/dev/peps/pep-0427/ + +Historical note +--------------- + +This project used to contain the implementation of the setuptools_ ``bdist_wheel`` +command, but as of setuptools v70.1, it no longer needs ``wheel`` installed for that to +work. Thus, you should install this **only** if you intend to use the ``wheel`` command +line tool! + +.. _setuptools: https://pypi.org/project/setuptools/ + +Documentation +------------- + +The documentation_ can be found on Read The Docs. + +.. _documentation: https://wheel.readthedocs.io/ + +Code of Conduct +--------------- + +Everyone interacting in the wheel project's codebases, issue trackers, chat +rooms, and mailing lists is expected to follow the `PSF Code of Conduct`_. + +.. _PSF Code of Conduct: https://github.com/pypa/.github/blob/main/CODE_OF_CONDUCT.md + diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/RECORD b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/RECORD new file mode 100644 index 0000000000000000000000000000000000000000..c1535b697f8dd60212541f637c69c9dfb4f1c8f1 --- /dev/null +++ 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b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/WHEEL new file mode 100644 index 0000000000000000000000000000000000000000..e3c6feefa22927866e3fd5575379ea972b432aaf --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/WHEEL @@ -0,0 +1,4 @@ +Wheel-Version: 1.0 +Generator: flit 3.10.1 +Root-Is-Purelib: true +Tag: py3-none-any diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/entry_points.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/entry_points.txt new file mode 100644 index 0000000000000000000000000000000000000000..06c9f69debd05e53c3b6053a905805e616c61fad --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel-0.45.1.dist-info/entry_points.txt @@ -0,0 +1,6 @@ +[console_scripts] +wheel=wheel.cli:main + +[distutils.commands] +bdist_wheel=wheel.bdist_wheel:bdist_wheel + diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_elffile.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_elffile.py new file mode 100644 index 0000000000000000000000000000000000000000..6fb19b30bb53c18f38a9ef02dd7c4478670fb962 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_elffile.py @@ -0,0 +1,108 @@ +""" +ELF file parser. + +This provides a class ``ELFFile`` that parses an ELF executable in a similar +interface to ``ZipFile``. Only the read interface is implemented. + +Based on: https://gist.github.com/lyssdod/f51579ae8d93c8657a5564aefc2ffbca +ELF header: https://refspecs.linuxfoundation.org/elf/gabi4+/ch4.eheader.html +""" + +import enum +import os +import struct +from typing import IO, Optional, Tuple + + +class ELFInvalid(ValueError): + pass + + +class EIClass(enum.IntEnum): + C32 = 1 + C64 = 2 + + +class EIData(enum.IntEnum): + Lsb = 1 + Msb = 2 + + +class EMachine(enum.IntEnum): + I386 = 3 + S390 = 22 + Arm = 40 + X8664 = 62 + AArc64 = 183 + + +class ELFFile: + """ + Representation of an ELF executable. + """ + + def __init__(self, f: IO[bytes]) -> None: + self._f = f + + try: + ident = self._read("16B") + except struct.error: + raise ELFInvalid("unable to parse identification") + magic = bytes(ident[:4]) + if magic != b"\x7fELF": + raise ELFInvalid(f"invalid magic: {magic!r}") + + self.capacity = ident[4] # Format for program header (bitness). + self.encoding = ident[5] # Data structure encoding (endianness). + + try: + # e_fmt: Format for program header. + # p_fmt: Format for section header. + # p_idx: Indexes to find p_type, p_offset, and p_filesz. + e_fmt, self._p_fmt, self._p_idx = { + (1, 1): ("HHIIIIIHHH", ">IIIIIIII", (0, 1, 4)), # 32-bit MSB. + (2, 1): ("HHIQQQIHHH", ">IIQQQQQQ", (0, 2, 5)), # 64-bit MSB. + }[(self.capacity, self.encoding)] + except KeyError: + raise ELFInvalid( + f"unrecognized capacity ({self.capacity}) or " + f"encoding ({self.encoding})" + ) + + try: + ( + _, + self.machine, # Architecture type. + _, + _, + self._e_phoff, # Offset of program header. + _, + self.flags, # Processor-specific flags. + _, + self._e_phentsize, # Size of section. + self._e_phnum, # Number of sections. + ) = self._read(e_fmt) + except struct.error as e: + raise ELFInvalid("unable to parse machine and section information") from e + + def _read(self, fmt: str) -> Tuple[int, ...]: + return struct.unpack(fmt, self._f.read(struct.calcsize(fmt))) + + @property + def interpreter(self) -> Optional[str]: + """ + The path recorded in the ``PT_INTERP`` section header. + """ + for index in range(self._e_phnum): + self._f.seek(self._e_phoff + self._e_phentsize * index) + try: + data = self._read(self._p_fmt) + except struct.error: + continue + if data[self._p_idx[0]] != 3: # Not PT_INTERP. + continue + self._f.seek(data[self._p_idx[1]]) + return os.fsdecode(self._f.read(data[self._p_idx[2]])).strip("\0") + return None diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_manylinux.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_manylinux.py new file mode 100644 index 0000000000000000000000000000000000000000..1f5f4ab3e514d1846d3bd189bf081fdb1528ba08 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_manylinux.py @@ -0,0 +1,260 @@ +import collections +import contextlib +import functools +import os +import re +import sys +import warnings +from typing import Dict, Generator, Iterator, NamedTuple, Optional, Sequence, Tuple + +from ._elffile import EIClass, EIData, ELFFile, EMachine + +EF_ARM_ABIMASK = 0xFF000000 +EF_ARM_ABI_VER5 = 0x05000000 +EF_ARM_ABI_FLOAT_HARD = 0x00000400 + + +# `os.PathLike` not a generic type until Python 3.9, so sticking with `str` +# as the type for `path` until then. +@contextlib.contextmanager +def _parse_elf(path: str) -> Generator[Optional[ELFFile], None, None]: + try: + with open(path, "rb") as f: + yield ELFFile(f) + except (OSError, TypeError, ValueError): + yield None + + +def _is_linux_armhf(executable: str) -> bool: + # hard-float ABI can be detected from the ELF header of the running + # process + # https://static.docs.arm.com/ihi0044/g/aaelf32.pdf + with _parse_elf(executable) as f: + return ( + f is not None + and f.capacity == EIClass.C32 + and f.encoding == EIData.Lsb + and f.machine == EMachine.Arm + and f.flags & EF_ARM_ABIMASK == EF_ARM_ABI_VER5 + and f.flags & EF_ARM_ABI_FLOAT_HARD == EF_ARM_ABI_FLOAT_HARD + ) + + +def _is_linux_i686(executable: str) -> bool: + with _parse_elf(executable) as f: + return ( + f is not None + and f.capacity == EIClass.C32 + and f.encoding == EIData.Lsb + and f.machine == EMachine.I386 + ) + + +def _have_compatible_abi(executable: str, archs: Sequence[str]) -> bool: + if "armv7l" in archs: + return _is_linux_armhf(executable) + if "i686" in archs: + return _is_linux_i686(executable) + allowed_archs = { + "x86_64", + "aarch64", + "ppc64", + "ppc64le", + "s390x", + "loongarch64", + "riscv64", + } + return any(arch in allowed_archs for arch in archs) + + +# If glibc ever changes its major version, we need to know what the last +# minor version was, so we can build the complete list of all versions. +# For now, guess what the highest minor version might be, assume it will +# be 50 for testing. Once this actually happens, update the dictionary +# with the actual value. +_LAST_GLIBC_MINOR: Dict[int, int] = collections.defaultdict(lambda: 50) + + +class _GLibCVersion(NamedTuple): + major: int + minor: int + + +def _glibc_version_string_confstr() -> Optional[str]: + """ + Primary implementation of glibc_version_string using os.confstr. + """ + # os.confstr is quite a bit faster than ctypes.DLL. It's also less likely + # to be broken or missing. This strategy is used in the standard library + # platform module. + # https://github.com/python/cpython/blob/fcf1d003bf4f0100c/Lib/platform.py#L175-L183 + try: + # Should be a string like "glibc 2.17". + version_string: Optional[str] = os.confstr("CS_GNU_LIBC_VERSION") + assert version_string is not None + _, version = version_string.rsplit() + except (AssertionError, AttributeError, OSError, ValueError): + # os.confstr() or CS_GNU_LIBC_VERSION not available (or a bad value)... + return None + return version + + +def _glibc_version_string_ctypes() -> Optional[str]: + """ + Fallback implementation of glibc_version_string using ctypes. + """ + try: + import ctypes + except ImportError: + return None + + # ctypes.CDLL(None) internally calls dlopen(NULL), and as the dlopen + # manpage says, "If filename is NULL, then the returned handle is for the + # main program". This way we can let the linker do the work to figure out + # which libc our process is actually using. + # + # We must also handle the special case where the executable is not a + # dynamically linked executable. This can occur when using musl libc, + # for example. In this situation, dlopen() will error, leading to an + # OSError. Interestingly, at least in the case of musl, there is no + # errno set on the OSError. The single string argument used to construct + # OSError comes from libc itself and is therefore not portable to + # hard code here. In any case, failure to call dlopen() means we + # can proceed, so we bail on our attempt. + try: + process_namespace = ctypes.CDLL(None) + except OSError: + return None + + try: + gnu_get_libc_version = process_namespace.gnu_get_libc_version + except AttributeError: + # Symbol doesn't exist -> therefore, we are not linked to + # glibc. + return None + + # Call gnu_get_libc_version, which returns a string like "2.5" + gnu_get_libc_version.restype = ctypes.c_char_p + version_str: str = gnu_get_libc_version() + # py2 / py3 compatibility: + if not isinstance(version_str, str): + version_str = version_str.decode("ascii") + + return version_str + + +def _glibc_version_string() -> Optional[str]: + """Returns glibc version string, or None if not using glibc.""" + return _glibc_version_string_confstr() or _glibc_version_string_ctypes() + + +def _parse_glibc_version(version_str: str) -> Tuple[int, int]: + """Parse glibc version. + + We use a regexp instead of str.split because we want to discard any + random junk that might come after the minor version -- this might happen + in patched/forked versions of glibc (e.g. Linaro's version of glibc + uses version strings like "2.20-2014.11"). See gh-3588. + """ + m = re.match(r"(?P[0-9]+)\.(?P[0-9]+)", version_str) + if not m: + warnings.warn( + f"Expected glibc version with 2 components major.minor," + f" got: {version_str}", + RuntimeWarning, + ) + return -1, -1 + return int(m.group("major")), int(m.group("minor")) + + +@functools.lru_cache +def _get_glibc_version() -> Tuple[int, int]: + version_str = _glibc_version_string() + if version_str is None: + return (-1, -1) + return _parse_glibc_version(version_str) + + +# From PEP 513, PEP 600 +def _is_compatible(arch: str, version: _GLibCVersion) -> bool: + sys_glibc = _get_glibc_version() + if sys_glibc < version: + return False + # Check for presence of _manylinux module. + try: + import _manylinux + except ImportError: + return True + if hasattr(_manylinux, "manylinux_compatible"): + result = _manylinux.manylinux_compatible(version[0], version[1], arch) + if result is not None: + return bool(result) + return True + if version == _GLibCVersion(2, 5): + if hasattr(_manylinux, "manylinux1_compatible"): + return bool(_manylinux.manylinux1_compatible) + if version == _GLibCVersion(2, 12): + if hasattr(_manylinux, "manylinux2010_compatible"): + return bool(_manylinux.manylinux2010_compatible) + if version == _GLibCVersion(2, 17): + if hasattr(_manylinux, "manylinux2014_compatible"): + return bool(_manylinux.manylinux2014_compatible) + return True + + +_LEGACY_MANYLINUX_MAP = { + # CentOS 7 w/ glibc 2.17 (PEP 599) + (2, 17): "manylinux2014", + # CentOS 6 w/ glibc 2.12 (PEP 571) + (2, 12): "manylinux2010", + # CentOS 5 w/ glibc 2.5 (PEP 513) + (2, 5): "manylinux1", +} + + +def platform_tags(archs: Sequence[str]) -> Iterator[str]: + """Generate manylinux tags compatible to the current platform. + + :param archs: Sequence of compatible architectures. + The first one shall be the closest to the actual architecture and be the part of + platform tag after the ``linux_`` prefix, e.g. ``x86_64``. + The ``linux_`` prefix is assumed as a prerequisite for the current platform to + be manylinux-compatible. + + :returns: An iterator of compatible manylinux tags. + """ + if not _have_compatible_abi(sys.executable, archs): + return + # Oldest glibc to be supported regardless of architecture is (2, 17). + too_old_glibc2 = _GLibCVersion(2, 16) + if set(archs) & {"x86_64", "i686"}: + # On x86/i686 also oldest glibc to be supported is (2, 5). + too_old_glibc2 = _GLibCVersion(2, 4) + current_glibc = _GLibCVersion(*_get_glibc_version()) + glibc_max_list = [current_glibc] + # We can assume compatibility across glibc major versions. + # https://sourceware.org/bugzilla/show_bug.cgi?id=24636 + # + # Build a list of maximum glibc versions so that we can + # output the canonical list of all glibc from current_glibc + # down to too_old_glibc2, including all intermediary versions. + for glibc_major in range(current_glibc.major - 1, 1, -1): + glibc_minor = _LAST_GLIBC_MINOR[glibc_major] + glibc_max_list.append(_GLibCVersion(glibc_major, glibc_minor)) + for arch in archs: + for glibc_max in glibc_max_list: + if glibc_max.major == too_old_glibc2.major: + min_minor = too_old_glibc2.minor + else: + # For other glibc major versions oldest supported is (x, 0). + min_minor = -1 + for glibc_minor in range(glibc_max.minor, min_minor, -1): + glibc_version = _GLibCVersion(glibc_max.major, glibc_minor) + tag = "manylinux_{}_{}".format(*glibc_version) + if _is_compatible(arch, glibc_version): + yield f"{tag}_{arch}" + # Handle the legacy manylinux1, manylinux2010, manylinux2014 tags. + if glibc_version in _LEGACY_MANYLINUX_MAP: + legacy_tag = _LEGACY_MANYLINUX_MAP[glibc_version] + if _is_compatible(arch, glibc_version): + yield f"{legacy_tag}_{arch}" diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_musllinux.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_musllinux.py new file mode 100644 index 0000000000000000000000000000000000000000..eb4251b5c1e82772b2b0ea539943da5141fd55ec --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_musllinux.py @@ -0,0 +1,83 @@ +"""PEP 656 support. + +This module implements logic to detect if the currently running Python is +linked against musl, and what musl version is used. +""" + +import functools +import re +import subprocess +import sys +from typing import Iterator, NamedTuple, Optional, Sequence + +from ._elffile import ELFFile + + +class _MuslVersion(NamedTuple): + major: int + minor: int + + +def _parse_musl_version(output: str) -> Optional[_MuslVersion]: + lines = [n for n in (n.strip() for n in output.splitlines()) if n] + if len(lines) < 2 or lines[0][:4] != "musl": + return None + m = re.match(r"Version (\d+)\.(\d+)", lines[1]) + if not m: + return None + return _MuslVersion(major=int(m.group(1)), minor=int(m.group(2))) + + +@functools.lru_cache +def _get_musl_version(executable: str) -> Optional[_MuslVersion]: + """Detect currently-running musl runtime version. + + This is done by checking the specified executable's dynamic linking + information, and invoking the loader to parse its output for a version + string. If the loader is musl, the output would be something like:: + + musl libc (x86_64) + Version 1.2.2 + Dynamic Program Loader + """ + try: + with open(executable, "rb") as f: + ld = ELFFile(f).interpreter + except (OSError, TypeError, ValueError): + return None + if ld is None or "musl" not in ld: + return None + proc = subprocess.run([ld], stderr=subprocess.PIPE, text=True) + return _parse_musl_version(proc.stderr) + + +def platform_tags(archs: Sequence[str]) -> Iterator[str]: + """Generate musllinux tags compatible to the current platform. + + :param archs: Sequence of compatible architectures. + The first one shall be the closest to the actual architecture and be the part of + platform tag after the ``linux_`` prefix, e.g. ``x86_64``. + The ``linux_`` prefix is assumed as a prerequisite for the current platform to + be musllinux-compatible. + + :returns: An iterator of compatible musllinux tags. + """ + sys_musl = _get_musl_version(sys.executable) + if sys_musl is None: # Python not dynamically linked against musl. + return + for arch in archs: + for minor in range(sys_musl.minor, -1, -1): + yield f"musllinux_{sys_musl.major}_{minor}_{arch}" + + +if __name__ == "__main__": # pragma: no cover + import sysconfig + + plat = sysconfig.get_platform() + assert plat.startswith("linux-"), "not linux" + + print("plat:", plat) + print("musl:", _get_musl_version(sys.executable)) + print("tags:", end=" ") + for t in platform_tags(re.sub(r"[.-]", "_", plat.split("-", 1)[-1])): + print(t, end="\n ") diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_parser.py new file mode 100644 index 0000000000000000000000000000000000000000..513686a2190f9911c08ca1ca263f37b799f44702 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_parser.py @@ -0,0 +1,356 @@ +"""Handwritten parser of dependency specifiers. + +The docstring for each __parse_* function contains EBNF-inspired grammar representing +the implementation. +""" + +import ast +from typing import Any, List, NamedTuple, Optional, Tuple, Union + +from ._tokenizer import DEFAULT_RULES, Tokenizer + + +class Node: + def __init__(self, value: str) -> None: + self.value = value + + def __str__(self) -> str: + return self.value + + def __repr__(self) -> str: + return f"<{self.__class__.__name__}('{self}')>" + + def serialize(self) -> str: + raise NotImplementedError + + +class Variable(Node): + def serialize(self) -> str: + return str(self) + + +class Value(Node): + def serialize(self) -> str: + return f'"{self}"' + + +class Op(Node): + def serialize(self) -> str: + return str(self) + + +MarkerVar = Union[Variable, Value] +MarkerItem = Tuple[MarkerVar, Op, MarkerVar] +# MarkerAtom = Union[MarkerItem, List["MarkerAtom"]] +# MarkerList = List[Union["MarkerList", MarkerAtom, str]] +# mypy does not support recursive type definition +# https://github.com/python/mypy/issues/731 +MarkerAtom = Any +MarkerList = List[Any] + + +class ParsedRequirement(NamedTuple): + name: str + url: str + extras: List[str] + specifier: str + marker: Optional[MarkerList] + + +# -------------------------------------------------------------------------------------- +# Recursive descent parser for dependency specifier +# -------------------------------------------------------------------------------------- +def parse_requirement(source: str) -> ParsedRequirement: + return _parse_requirement(Tokenizer(source, rules=DEFAULT_RULES)) + + +def _parse_requirement(tokenizer: Tokenizer) -> ParsedRequirement: + """ + requirement = WS? IDENTIFIER WS? extras WS? requirement_details + """ + tokenizer.consume("WS") + + name_token = tokenizer.expect( + "IDENTIFIER", expected="package name at the start of dependency specifier" + ) + name = name_token.text + tokenizer.consume("WS") + + extras = _parse_extras(tokenizer) + tokenizer.consume("WS") + + url, specifier, marker = _parse_requirement_details(tokenizer) + tokenizer.expect("END", expected="end of dependency specifier") + + return ParsedRequirement(name, url, extras, specifier, marker) + + +def _parse_requirement_details( + tokenizer: Tokenizer, +) -> Tuple[str, str, Optional[MarkerList]]: + """ + requirement_details = AT URL (WS requirement_marker?)? + | specifier WS? (requirement_marker)? + """ + + specifier = "" + url = "" + marker = None + + if tokenizer.check("AT"): + tokenizer.read() + tokenizer.consume("WS") + + url_start = tokenizer.position + url = tokenizer.expect("URL", expected="URL after @").text + if tokenizer.check("END", peek=True): + return (url, specifier, marker) + + tokenizer.expect("WS", expected="whitespace after URL") + + # The input might end after whitespace. + if tokenizer.check("END", peek=True): + return (url, specifier, marker) + + marker = _parse_requirement_marker( + tokenizer, span_start=url_start, after="URL and whitespace" + ) + else: + specifier_start = tokenizer.position + specifier = _parse_specifier(tokenizer) + tokenizer.consume("WS") + + if tokenizer.check("END", peek=True): + return (url, specifier, marker) + + marker = _parse_requirement_marker( + tokenizer, + span_start=specifier_start, + after=( + "version specifier" + if specifier + else "name and no valid version specifier" + ), + ) + + return (url, specifier, marker) + + +def _parse_requirement_marker( + tokenizer: Tokenizer, *, span_start: int, after: str +) -> MarkerList: + """ + requirement_marker = SEMICOLON marker WS? + """ + + if not tokenizer.check("SEMICOLON"): + tokenizer.raise_syntax_error( + f"Expected end or semicolon (after {after})", + span_start=span_start, + ) + tokenizer.read() + + marker = _parse_marker(tokenizer) + tokenizer.consume("WS") + + return marker + + +def _parse_extras(tokenizer: Tokenizer) -> List[str]: + """ + extras = (LEFT_BRACKET wsp* extras_list? wsp* RIGHT_BRACKET)? + """ + if not tokenizer.check("LEFT_BRACKET", peek=True): + return [] + + with tokenizer.enclosing_tokens( + "LEFT_BRACKET", + "RIGHT_BRACKET", + around="extras", + ): + tokenizer.consume("WS") + extras = _parse_extras_list(tokenizer) + tokenizer.consume("WS") + + return extras + + +def _parse_extras_list(tokenizer: Tokenizer) -> List[str]: + """ + extras_list = identifier (wsp* ',' wsp* identifier)* + """ + extras: List[str] = [] + + if not tokenizer.check("IDENTIFIER"): + return extras + + extras.append(tokenizer.read().text) + + while True: + tokenizer.consume("WS") + if tokenizer.check("IDENTIFIER", peek=True): + tokenizer.raise_syntax_error("Expected comma between extra names") + elif not tokenizer.check("COMMA"): + break + + tokenizer.read() + tokenizer.consume("WS") + + extra_token = tokenizer.expect("IDENTIFIER", expected="extra name after comma") + extras.append(extra_token.text) + + return extras + + +def _parse_specifier(tokenizer: Tokenizer) -> str: + """ + specifier = LEFT_PARENTHESIS WS? version_many WS? RIGHT_PARENTHESIS + | WS? version_many WS? + """ + with tokenizer.enclosing_tokens( + "LEFT_PARENTHESIS", + "RIGHT_PARENTHESIS", + around="version specifier", + ): + tokenizer.consume("WS") + parsed_specifiers = _parse_version_many(tokenizer) + tokenizer.consume("WS") + + return parsed_specifiers + + +def _parse_version_many(tokenizer: Tokenizer) -> str: + """ + version_many = (SPECIFIER (WS? COMMA WS? SPECIFIER)*)? + """ + parsed_specifiers = "" + while tokenizer.check("SPECIFIER"): + span_start = tokenizer.position + parsed_specifiers += tokenizer.read().text + if tokenizer.check("VERSION_PREFIX_TRAIL", peek=True): + tokenizer.raise_syntax_error( + ".* suffix can only be used with `==` or `!=` operators", + span_start=span_start, + span_end=tokenizer.position + 1, + ) + if tokenizer.check("VERSION_LOCAL_LABEL_TRAIL", peek=True): + tokenizer.raise_syntax_error( + "Local version label can only be used with `==` or `!=` operators", + span_start=span_start, + span_end=tokenizer.position, + ) + tokenizer.consume("WS") + if not tokenizer.check("COMMA"): + break + parsed_specifiers += tokenizer.read().text + tokenizer.consume("WS") + + return parsed_specifiers + + +# -------------------------------------------------------------------------------------- +# Recursive descent parser for marker expression +# -------------------------------------------------------------------------------------- +def parse_marker(source: str) -> MarkerList: + return _parse_full_marker(Tokenizer(source, rules=DEFAULT_RULES)) + + +def _parse_full_marker(tokenizer: Tokenizer) -> MarkerList: + retval = _parse_marker(tokenizer) + tokenizer.expect("END", expected="end of marker expression") + return retval + + +def _parse_marker(tokenizer: Tokenizer) -> MarkerList: + """ + marker = marker_atom (BOOLOP marker_atom)+ + """ + expression = [_parse_marker_atom(tokenizer)] + while tokenizer.check("BOOLOP"): + token = tokenizer.read() + expr_right = _parse_marker_atom(tokenizer) + expression.extend((token.text, expr_right)) + return expression + + +def _parse_marker_atom(tokenizer: Tokenizer) -> MarkerAtom: + """ + marker_atom = WS? LEFT_PARENTHESIS WS? marker WS? RIGHT_PARENTHESIS WS? + | WS? marker_item WS? + """ + + tokenizer.consume("WS") + if tokenizer.check("LEFT_PARENTHESIS", peek=True): + with tokenizer.enclosing_tokens( + "LEFT_PARENTHESIS", + "RIGHT_PARENTHESIS", + around="marker expression", + ): + tokenizer.consume("WS") + marker: MarkerAtom = _parse_marker(tokenizer) + tokenizer.consume("WS") + else: + marker = _parse_marker_item(tokenizer) + tokenizer.consume("WS") + return marker + + +def _parse_marker_item(tokenizer: Tokenizer) -> MarkerItem: + """ + marker_item = WS? marker_var WS? marker_op WS? marker_var WS? + """ + tokenizer.consume("WS") + marker_var_left = _parse_marker_var(tokenizer) + tokenizer.consume("WS") + marker_op = _parse_marker_op(tokenizer) + tokenizer.consume("WS") + marker_var_right = _parse_marker_var(tokenizer) + tokenizer.consume("WS") + return (marker_var_left, marker_op, marker_var_right) + + +def _parse_marker_var(tokenizer: Tokenizer) -> MarkerVar: + """ + marker_var = VARIABLE | QUOTED_STRING + """ + if tokenizer.check("VARIABLE"): + return process_env_var(tokenizer.read().text.replace(".", "_")) + elif tokenizer.check("QUOTED_STRING"): + return process_python_str(tokenizer.read().text) + else: + tokenizer.raise_syntax_error( + message="Expected a marker variable or quoted string" + ) + + +def process_env_var(env_var: str) -> Variable: + if env_var in ("platform_python_implementation", "python_implementation"): + return Variable("platform_python_implementation") + else: + return Variable(env_var) + + +def process_python_str(python_str: str) -> Value: + value = ast.literal_eval(python_str) + return Value(str(value)) + + +def _parse_marker_op(tokenizer: Tokenizer) -> Op: + """ + marker_op = IN | NOT IN | OP + """ + if tokenizer.check("IN"): + tokenizer.read() + return Op("in") + elif tokenizer.check("NOT"): + tokenizer.read() + tokenizer.expect("WS", expected="whitespace after 'not'") + tokenizer.expect("IN", expected="'in' after 'not'") + return Op("not in") + elif tokenizer.check("OP"): + return Op(tokenizer.read().text) + else: + return tokenizer.raise_syntax_error( + "Expected marker operator, one of " + "<=, <, !=, ==, >=, >, ~=, ===, in, not in" + ) diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_structures.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_structures.py new file mode 100644 index 0000000000000000000000000000000000000000..90a6465f9682c886363eea5327dac64bf623a6ff --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_structures.py @@ -0,0 +1,61 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + + +class InfinityType: + def __repr__(self) -> str: + return "Infinity" + + def __hash__(self) -> int: + return hash(repr(self)) + + def __lt__(self, other: object) -> bool: + return False + + def __le__(self, other: object) -> bool: + return False + + def __eq__(self, other: object) -> bool: + return isinstance(other, self.__class__) + + def __gt__(self, other: object) -> bool: + return True + + def __ge__(self, other: object) -> bool: + return True + + def __neg__(self: object) -> "NegativeInfinityType": + return NegativeInfinity + + +Infinity = InfinityType() + + +class NegativeInfinityType: + def __repr__(self) -> str: + return "-Infinity" + + def __hash__(self) -> int: + return hash(repr(self)) + + def __lt__(self, other: object) -> bool: + return True + + def __le__(self, other: object) -> bool: + return True + + def __eq__(self, other: object) -> bool: + return isinstance(other, self.__class__) + + def __gt__(self, other: object) -> bool: + return False + + def __ge__(self, other: object) -> bool: + return False + + def __neg__(self: object) -> InfinityType: + return Infinity + + +NegativeInfinity = NegativeInfinityType() diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_tokenizer.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_tokenizer.py new file mode 100644 index 0000000000000000000000000000000000000000..dd0d648d49a7c1a62d25ce5c9107aa448a8a22d1 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/_tokenizer.py @@ -0,0 +1,192 @@ +import contextlib +import re +from dataclasses import dataclass +from typing import Dict, Iterator, NoReturn, Optional, Tuple, Union + +from .specifiers import Specifier + + +@dataclass +class Token: + name: str + text: str + position: int + + +class ParserSyntaxError(Exception): + """The provided source text could not be parsed correctly.""" + + def __init__( + self, + message: str, + *, + source: str, + span: Tuple[int, int], + ) -> None: + self.span = span + self.message = message + self.source = source + + super().__init__() + + def __str__(self) -> str: + marker = " " * self.span[0] + "~" * (self.span[1] - self.span[0]) + "^" + return "\n ".join([self.message, self.source, marker]) + + +DEFAULT_RULES: "Dict[str, Union[str, re.Pattern[str]]]" = { + "LEFT_PARENTHESIS": r"\(", + "RIGHT_PARENTHESIS": r"\)", + "LEFT_BRACKET": r"\[", + "RIGHT_BRACKET": r"\]", + "SEMICOLON": r";", + "COMMA": r",", + "QUOTED_STRING": re.compile( + r""" + ( + ('[^']*') + | + ("[^"]*") + ) + """, + re.VERBOSE, + ), + "OP": r"(===|==|~=|!=|<=|>=|<|>)", + "BOOLOP": r"\b(or|and)\b", + "IN": r"\bin\b", + "NOT": r"\bnot\b", + "VARIABLE": re.compile( + r""" + \b( + python_version + |python_full_version + |os[._]name + |sys[._]platform + |platform_(release|system) + |platform[._](version|machine|python_implementation) + |python_implementation + |implementation_(name|version) + |extra + )\b + """, + re.VERBOSE, + ), + "SPECIFIER": re.compile( + Specifier._operator_regex_str + Specifier._version_regex_str, + re.VERBOSE | re.IGNORECASE, + ), + "AT": r"\@", + "URL": r"[^ \t]+", + "IDENTIFIER": r"\b[a-zA-Z0-9][a-zA-Z0-9._-]*\b", + "VERSION_PREFIX_TRAIL": r"\.\*", + "VERSION_LOCAL_LABEL_TRAIL": r"\+[a-z0-9]+(?:[-_\.][a-z0-9]+)*", + "WS": r"[ \t]+", + "END": r"$", +} + + +class Tokenizer: + """Context-sensitive token parsing. + + Provides methods to examine the input stream to check whether the next token + matches. + """ + + def __init__( + self, + source: str, + *, + rules: "Dict[str, Union[str, re.Pattern[str]]]", + ) -> None: + self.source = source + self.rules: Dict[str, re.Pattern[str]] = { + name: re.compile(pattern) for name, pattern in rules.items() + } + self.next_token: Optional[Token] = None + self.position = 0 + + def consume(self, name: str) -> None: + """Move beyond provided token name, if at current position.""" + if self.check(name): + self.read() + + def check(self, name: str, *, peek: bool = False) -> bool: + """Check whether the next token has the provided name. + + By default, if the check succeeds, the token *must* be read before + another check. If `peek` is set to `True`, the token is not loaded and + would need to be checked again. + """ + assert ( + self.next_token is None + ), f"Cannot check for {name!r}, already have {self.next_token!r}" + assert name in self.rules, f"Unknown token name: {name!r}" + + expression = self.rules[name] + + match = expression.match(self.source, self.position) + if match is None: + return False + if not peek: + self.next_token = Token(name, match[0], self.position) + return True + + def expect(self, name: str, *, expected: str) -> Token: + """Expect a certain token name next, failing with a syntax error otherwise. + + The token is *not* read. + """ + if not self.check(name): + raise self.raise_syntax_error(f"Expected {expected}") + return self.read() + + def read(self) -> Token: + """Consume the next token and return it.""" + token = self.next_token + assert token is not None + + self.position += len(token.text) + self.next_token = None + + return token + + def raise_syntax_error( + self, + message: str, + *, + span_start: Optional[int] = None, + span_end: Optional[int] = None, + ) -> NoReturn: + """Raise ParserSyntaxError at the given position.""" + span = ( + self.position if span_start is None else span_start, + self.position if span_end is None else span_end, + ) + raise ParserSyntaxError( + message, + source=self.source, + span=span, + ) + + @contextlib.contextmanager + def enclosing_tokens( + self, open_token: str, close_token: str, *, around: str + ) -> Iterator[None]: + if self.check(open_token): + open_position = self.position + self.read() + else: + open_position = None + + yield + + if open_position is None: + return + + if not self.check(close_token): + self.raise_syntax_error( + f"Expected matching {close_token} for {open_token}, after {around}", + span_start=open_position, + ) + + self.read() diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/markers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/markers.py new file mode 100644 index 0000000000000000000000000000000000000000..c96d22a5a445e7353cd2454dec4255d3785c07b3 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/markers.py @@ -0,0 +1,253 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import operator +import os +import platform +import sys +from typing import Any, Callable, Dict, List, Optional, Tuple, Union + +from ._parser import ( + MarkerAtom, + MarkerList, + Op, + Value, + Variable, +) +from ._parser import ( + parse_marker as _parse_marker, +) +from ._tokenizer import ParserSyntaxError +from .specifiers import InvalidSpecifier, Specifier +from .utils import canonicalize_name + +__all__ = [ + "InvalidMarker", + "UndefinedComparison", + "UndefinedEnvironmentName", + "Marker", + "default_environment", +] + +Operator = Callable[[str, str], bool] + + +class InvalidMarker(ValueError): + """ + An invalid marker was found, users should refer to PEP 508. + """ + + +class UndefinedComparison(ValueError): + """ + An invalid operation was attempted on a value that doesn't support it. + """ + + +class UndefinedEnvironmentName(ValueError): + """ + A name was attempted to be used that does not exist inside of the + environment. + """ + + +def _normalize_extra_values(results: Any) -> Any: + """ + Normalize extra values. + """ + if isinstance(results[0], tuple): + lhs, op, rhs = results[0] + if isinstance(lhs, Variable) and lhs.value == "extra": + normalized_extra = canonicalize_name(rhs.value) + rhs = Value(normalized_extra) + elif isinstance(rhs, Variable) and rhs.value == "extra": + normalized_extra = canonicalize_name(lhs.value) + lhs = Value(normalized_extra) + results[0] = lhs, op, rhs + return results + + +def _format_marker( + marker: Union[List[str], MarkerAtom, str], first: Optional[bool] = True +) -> str: + assert isinstance(marker, (list, tuple, str)) + + # Sometimes we have a structure like [[...]] which is a single item list + # where the single item is itself it's own list. In that case we want skip + # the rest of this function so that we don't get extraneous () on the + # outside. + if ( + isinstance(marker, list) + and len(marker) == 1 + and isinstance(marker[0], (list, tuple)) + ): + return _format_marker(marker[0]) + + if isinstance(marker, list): + inner = (_format_marker(m, first=False) for m in marker) + if first: + return " ".join(inner) + else: + return "(" + " ".join(inner) + ")" + elif isinstance(marker, tuple): + return " ".join([m.serialize() for m in marker]) + else: + return marker + + +_operators: Dict[str, Operator] = { + "in": lambda lhs, rhs: lhs in rhs, + "not in": lambda lhs, rhs: lhs not in rhs, + "<": operator.lt, + "<=": operator.le, + "==": operator.eq, + "!=": operator.ne, + ">=": operator.ge, + ">": operator.gt, +} + + +def _eval_op(lhs: str, op: Op, rhs: str) -> bool: + try: + spec = Specifier("".join([op.serialize(), rhs])) + except InvalidSpecifier: + pass + else: + return spec.contains(lhs, prereleases=True) + + oper: Optional[Operator] = _operators.get(op.serialize()) + if oper is None: + raise UndefinedComparison(f"Undefined {op!r} on {lhs!r} and {rhs!r}.") + + return oper(lhs, rhs) + + +def _normalize(*values: str, key: str) -> Tuple[str, ...]: + # PEP 685 – Comparison of extra names for optional distribution dependencies + # https://peps.python.org/pep-0685/ + # > When comparing extra names, tools MUST normalize the names being + # > compared using the semantics outlined in PEP 503 for names + if key == "extra": + return tuple(canonicalize_name(v) for v in values) + + # other environment markers don't have such standards + return values + + +def _evaluate_markers(markers: MarkerList, environment: Dict[str, str]) -> bool: + groups: List[List[bool]] = [[]] + + for marker in markers: + assert isinstance(marker, (list, tuple, str)) + + if isinstance(marker, list): + groups[-1].append(_evaluate_markers(marker, environment)) + elif isinstance(marker, tuple): + lhs, op, rhs = marker + + if isinstance(lhs, Variable): + environment_key = lhs.value + lhs_value = environment[environment_key] + rhs_value = rhs.value + else: + lhs_value = lhs.value + environment_key = rhs.value + rhs_value = environment[environment_key] + + lhs_value, rhs_value = _normalize(lhs_value, rhs_value, key=environment_key) + groups[-1].append(_eval_op(lhs_value, op, rhs_value)) + else: + assert marker in ["and", "or"] + if marker == "or": + groups.append([]) + + return any(all(item) for item in groups) + + +def format_full_version(info: "sys._version_info") -> str: + version = "{0.major}.{0.minor}.{0.micro}".format(info) + kind = info.releaselevel + if kind != "final": + version += kind[0] + str(info.serial) + return version + + +def default_environment() -> Dict[str, str]: + iver = format_full_version(sys.implementation.version) + implementation_name = sys.implementation.name + return { + "implementation_name": implementation_name, + "implementation_version": iver, + "os_name": os.name, + "platform_machine": platform.machine(), + "platform_release": platform.release(), + "platform_system": platform.system(), + "platform_version": platform.version(), + "python_full_version": platform.python_version(), + "platform_python_implementation": platform.python_implementation(), + "python_version": ".".join(platform.python_version_tuple()[:2]), + "sys_platform": sys.platform, + } + + +class Marker: + def __init__(self, marker: str) -> None: + # Note: We create a Marker object without calling this constructor in + # packaging.requirements.Requirement. If any additional logic is + # added here, make sure to mirror/adapt Requirement. + try: + self._markers = _normalize_extra_values(_parse_marker(marker)) + # The attribute `_markers` can be described in terms of a recursive type: + # MarkerList = List[Union[Tuple[Node, ...], str, MarkerList]] + # + # For example, the following expression: + # python_version > "3.6" or (python_version == "3.6" and os_name == "unix") + # + # is parsed into: + # [ + # (, ')>, ), + # 'and', + # [ + # (, , ), + # 'or', + # (, , ) + # ] + # ] + except ParserSyntaxError as e: + raise InvalidMarker(str(e)) from e + + def __str__(self) -> str: + return _format_marker(self._markers) + + def __repr__(self) -> str: + return f"" + + def __hash__(self) -> int: + return hash((self.__class__.__name__, str(self))) + + def __eq__(self, other: Any) -> bool: + if not isinstance(other, Marker): + return NotImplemented + + return str(self) == str(other) + + def evaluate(self, environment: Optional[Dict[str, str]] = None) -> bool: + """Evaluate a marker. + + Return the boolean from evaluating the given marker against the + environment. environment is an optional argument to override all or + part of the determined environment. + + The environment is determined from the current Python process. + """ + current_environment = default_environment() + current_environment["extra"] = "" + if environment is not None: + current_environment.update(environment) + # The API used to allow setting extra to None. We need to handle this + # case for backwards compatibility. + if current_environment["extra"] is None: + current_environment["extra"] = "" + + return _evaluate_markers(self._markers, current_environment) diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/requirements.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/requirements.py new file mode 100644 index 0000000000000000000000000000000000000000..bdc43a7e98d87dba0c2069bfb4554f71d228cad4 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/requirements.py @@ -0,0 +1,90 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +from typing import Any, Iterator, Optional, Set + +from ._parser import parse_requirement as _parse_requirement +from ._tokenizer import ParserSyntaxError +from .markers import Marker, _normalize_extra_values +from .specifiers import SpecifierSet +from .utils import canonicalize_name + + +class InvalidRequirement(ValueError): + """ + An invalid requirement was found, users should refer to PEP 508. + """ + + +class Requirement: + """Parse a requirement. + + Parse a given requirement string into its parts, such as name, specifier, + URL, and extras. Raises InvalidRequirement on a badly-formed requirement + string. + """ + + # TODO: Can we test whether something is contained within a requirement? + # If so how do we do that? Do we need to test against the _name_ of + # the thing as well as the version? What about the markers? + # TODO: Can we normalize the name and extra name? + + def __init__(self, requirement_string: str) -> None: + try: + parsed = _parse_requirement(requirement_string) + except ParserSyntaxError as e: + raise InvalidRequirement(str(e)) from e + + self.name: str = parsed.name + self.url: Optional[str] = parsed.url or None + self.extras: Set[str] = set(parsed.extras or []) + self.specifier: SpecifierSet = SpecifierSet(parsed.specifier) + self.marker: Optional[Marker] = None + if parsed.marker is not None: + self.marker = Marker.__new__(Marker) + self.marker._markers = _normalize_extra_values(parsed.marker) + + def _iter_parts(self, name: str) -> Iterator[str]: + yield name + + if self.extras: + formatted_extras = ",".join(sorted(self.extras)) + yield f"[{formatted_extras}]" + + if self.specifier: + yield str(self.specifier) + + if self.url: + yield f"@ {self.url}" + if self.marker: + yield " " + + if self.marker: + yield f"; {self.marker}" + + def __str__(self) -> str: + return "".join(self._iter_parts(self.name)) + + def __repr__(self) -> str: + return f"" + + def __hash__(self) -> int: + return hash( + ( + self.__class__.__name__, + *self._iter_parts(canonicalize_name(self.name)), + ) + ) + + def __eq__(self, other: Any) -> bool: + if not isinstance(other, Requirement): + return NotImplemented + + return ( + canonicalize_name(self.name) == canonicalize_name(other.name) + and self.extras == other.extras + and self.specifier == other.specifier + and self.url == other.url + and self.marker == other.marker + ) diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/specifiers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/specifiers.py new file mode 100644 index 0000000000000000000000000000000000000000..6d4066ae2770a3112f37d0e30d9a98fe59c4861f --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/specifiers.py @@ -0,0 +1,1011 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. +""" +.. testsetup:: + + from packaging.specifiers import Specifier, SpecifierSet, InvalidSpecifier + from packaging.version import Version +""" + +import abc +import itertools +import re +from typing import Callable, Iterable, Iterator, List, Optional, Tuple, TypeVar, Union + +from .utils import canonicalize_version +from .version import Version + +UnparsedVersion = Union[Version, str] +UnparsedVersionVar = TypeVar("UnparsedVersionVar", bound=UnparsedVersion) +CallableOperator = Callable[[Version, str], bool] + + +def _coerce_version(version: UnparsedVersion) -> Version: + if not isinstance(version, Version): + version = Version(version) + return version + + +class InvalidSpecifier(ValueError): + """ + Raised when attempting to create a :class:`Specifier` with a specifier + string that is invalid. + + >>> Specifier("lolwat") + Traceback (most recent call last): + ... + packaging.specifiers.InvalidSpecifier: Invalid specifier: 'lolwat' + """ + + +class BaseSpecifier(metaclass=abc.ABCMeta): + @abc.abstractmethod + def __str__(self) -> str: + """ + Returns the str representation of this Specifier-like object. This + should be representative of the Specifier itself. + """ + + @abc.abstractmethod + def __hash__(self) -> int: + """ + Returns a hash value for this Specifier-like object. + """ + + @abc.abstractmethod + def __eq__(self, other: object) -> bool: + """ + Returns a boolean representing whether or not the two Specifier-like + objects are equal. + + :param other: The other object to check against. + """ + + @property + @abc.abstractmethod + def prereleases(self) -> Optional[bool]: + """Whether or not pre-releases as a whole are allowed. + + This can be set to either ``True`` or ``False`` to explicitly enable or disable + prereleases or it can be set to ``None`` (the default) to use default semantics. + """ + + @prereleases.setter + def prereleases(self, value: bool) -> None: + """Setter for :attr:`prereleases`. + + :param value: The value to set. + """ + + @abc.abstractmethod + def contains(self, item: str, prereleases: Optional[bool] = None) -> bool: + """ + Determines if the given item is contained within this specifier. + """ + + @abc.abstractmethod + def filter( + self, iterable: Iterable[UnparsedVersionVar], prereleases: Optional[bool] = None + ) -> Iterator[UnparsedVersionVar]: + """ + Takes an iterable of items and filters them so that only items which + are contained within this specifier are allowed in it. + """ + + +class Specifier(BaseSpecifier): + """This class abstracts handling of version specifiers. + + .. tip:: + + It is generally not required to instantiate this manually. You should instead + prefer to work with :class:`SpecifierSet` instead, which can parse + comma-separated version specifiers (which is what package metadata contains). + """ + + _operator_regex_str = r""" + (?P(~=|==|!=|<=|>=|<|>|===)) + """ + _version_regex_str = r""" + (?P + (?: + # The identity operators allow for an escape hatch that will + # do an exact string match of the version you wish to install. + # This will not be parsed by PEP 440 and we cannot determine + # any semantic meaning from it. This operator is discouraged + # but included entirely as an escape hatch. + (?<====) # Only match for the identity operator + \s* + [^\s;)]* # The arbitrary version can be just about anything, + # we match everything except for whitespace, a + # semi-colon for marker support, and a closing paren + # since versions can be enclosed in them. + ) + | + (?: + # The (non)equality operators allow for wild card and local + # versions to be specified so we have to define these two + # operators separately to enable that. + (?<===|!=) # Only match for equals and not equals + + \s* + v? + (?:[0-9]+!)? # epoch + [0-9]+(?:\.[0-9]+)* # release + + # You cannot use a wild card and a pre-release, post-release, a dev or + # local version together so group them with a | and make them optional. + (?: + \.\* # Wild card syntax of .* + | + (?: # pre release + [-_\.]? + (alpha|beta|preview|pre|a|b|c|rc) + [-_\.]? + [0-9]* + )? + (?: # post release + (?:-[0-9]+)|(?:[-_\.]?(post|rev|r)[-_\.]?[0-9]*) + )? + (?:[-_\.]?dev[-_\.]?[0-9]*)? # dev release + (?:\+[a-z0-9]+(?:[-_\.][a-z0-9]+)*)? # local + )? + ) + | + (?: + # The compatible operator requires at least two digits in the + # release segment. + (?<=~=) # Only match for the compatible operator + + \s* + v? + (?:[0-9]+!)? # epoch + [0-9]+(?:\.[0-9]+)+ # release (We have a + instead of a *) + (?: # pre release + [-_\.]? + (alpha|beta|preview|pre|a|b|c|rc) + [-_\.]? + [0-9]* + )? + (?: # post release + (?:-[0-9]+)|(?:[-_\.]?(post|rev|r)[-_\.]?[0-9]*) + )? + (?:[-_\.]?dev[-_\.]?[0-9]*)? # dev release + ) + | + (?: + # All other operators only allow a sub set of what the + # (non)equality operators do. Specifically they do not allow + # local versions to be specified nor do they allow the prefix + # matching wild cards. + (?=": "greater_than_equal", + "<": "less_than", + ">": "greater_than", + "===": "arbitrary", + } + + def __init__(self, spec: str = "", prereleases: Optional[bool] = None) -> None: + """Initialize a Specifier instance. + + :param spec: + The string representation of a specifier which will be parsed and + normalized before use. + :param prereleases: + This tells the specifier if it should accept prerelease versions if + applicable or not. The default of ``None`` will autodetect it from the + given specifiers. + :raises InvalidSpecifier: + If the given specifier is invalid (i.e. bad syntax). + """ + match = self._regex.search(spec) + if not match: + raise InvalidSpecifier(f"Invalid specifier: '{spec}'") + + self._spec: Tuple[str, str] = ( + match.group("operator").strip(), + match.group("version").strip(), + ) + + # Store whether or not this Specifier should accept prereleases + self._prereleases = prereleases + + # https://github.com/python/mypy/pull/13475#pullrequestreview-1079784515 + @property # type: ignore[override] + def prereleases(self) -> bool: + # If there is an explicit prereleases set for this, then we'll just + # blindly use that. + if self._prereleases is not None: + return self._prereleases + + # Look at all of our specifiers and determine if they are inclusive + # operators, and if they are if they are including an explicit + # prerelease. + operator, version = self._spec + if operator in ["==", ">=", "<=", "~=", "==="]: + # The == specifier can include a trailing .*, if it does we + # want to remove before parsing. + if operator == "==" and version.endswith(".*"): + version = version[:-2] + + # Parse the version, and if it is a pre-release than this + # specifier allows pre-releases. + if Version(version).is_prerelease: + return True + + return False + + @prereleases.setter + def prereleases(self, value: bool) -> None: + self._prereleases = value + + @property + def operator(self) -> str: + """The operator of this specifier. + + >>> Specifier("==1.2.3").operator + '==' + """ + return self._spec[0] + + @property + def version(self) -> str: + """The version of this specifier. + + >>> Specifier("==1.2.3").version + '1.2.3' + """ + return self._spec[1] + + def __repr__(self) -> str: + """A representation of the Specifier that shows all internal state. + + >>> Specifier('>=1.0.0') + =1.0.0')> + >>> Specifier('>=1.0.0', prereleases=False) + =1.0.0', prereleases=False)> + >>> Specifier('>=1.0.0', prereleases=True) + =1.0.0', prereleases=True)> + """ + pre = ( + f", prereleases={self.prereleases!r}" + if self._prereleases is not None + else "" + ) + + return f"<{self.__class__.__name__}({str(self)!r}{pre})>" + + def __str__(self) -> str: + """A string representation of the Specifier that can be round-tripped. + + >>> str(Specifier('>=1.0.0')) + '>=1.0.0' + >>> str(Specifier('>=1.0.0', prereleases=False)) + '>=1.0.0' + """ + return "{}{}".format(*self._spec) + + @property + def _canonical_spec(self) -> Tuple[str, str]: + canonical_version = canonicalize_version( + self._spec[1], + strip_trailing_zero=(self._spec[0] != "~="), + ) + return self._spec[0], canonical_version + + def __hash__(self) -> int: + return hash(self._canonical_spec) + + def __eq__(self, other: object) -> bool: + """Whether or not the two Specifier-like objects are equal. + + :param other: The other object to check against. + + The value of :attr:`prereleases` is ignored. + + >>> Specifier("==1.2.3") == Specifier("== 1.2.3.0") + True + >>> (Specifier("==1.2.3", prereleases=False) == + ... Specifier("==1.2.3", prereleases=True)) + True + >>> Specifier("==1.2.3") == "==1.2.3" + True + >>> Specifier("==1.2.3") == Specifier("==1.2.4") + False + >>> Specifier("==1.2.3") == Specifier("~=1.2.3") + False + """ + if isinstance(other, str): + try: + other = self.__class__(str(other)) + except InvalidSpecifier: + return NotImplemented + elif not isinstance(other, self.__class__): + return NotImplemented + + return self._canonical_spec == other._canonical_spec + + def _get_operator(self, op: str) -> CallableOperator: + operator_callable: CallableOperator = getattr( + self, f"_compare_{self._operators[op]}" + ) + return operator_callable + + def _compare_compatible(self, prospective: Version, spec: str) -> bool: + # Compatible releases have an equivalent combination of >= and ==. That + # is that ~=2.2 is equivalent to >=2.2,==2.*. This allows us to + # implement this in terms of the other specifiers instead of + # implementing it ourselves. The only thing we need to do is construct + # the other specifiers. + + # We want everything but the last item in the version, but we want to + # ignore suffix segments. + prefix = _version_join( + list(itertools.takewhile(_is_not_suffix, _version_split(spec)))[:-1] + ) + + # Add the prefix notation to the end of our string + prefix += ".*" + + return self._get_operator(">=")(prospective, spec) and self._get_operator("==")( + prospective, prefix + ) + + def _compare_equal(self, prospective: Version, spec: str) -> bool: + # We need special logic to handle prefix matching + if spec.endswith(".*"): + # In the case of prefix matching we want to ignore local segment. + normalized_prospective = canonicalize_version( + prospective.public, strip_trailing_zero=False + ) + # Get the normalized version string ignoring the trailing .* + normalized_spec = canonicalize_version(spec[:-2], strip_trailing_zero=False) + # Split the spec out by bangs and dots, and pretend that there is + # an implicit dot in between a release segment and a pre-release segment. + split_spec = _version_split(normalized_spec) + + # Split the prospective version out by bangs and dots, and pretend + # that there is an implicit dot in between a release segment and + # a pre-release segment. + split_prospective = _version_split(normalized_prospective) + + # 0-pad the prospective version before shortening it to get the correct + # shortened version. + padded_prospective, _ = _pad_version(split_prospective, split_spec) + + # Shorten the prospective version to be the same length as the spec + # so that we can determine if the specifier is a prefix of the + # prospective version or not. + shortened_prospective = padded_prospective[: len(split_spec)] + + return shortened_prospective == split_spec + else: + # Convert our spec string into a Version + spec_version = Version(spec) + + # If the specifier does not have a local segment, then we want to + # act as if the prospective version also does not have a local + # segment. + if not spec_version.local: + prospective = Version(prospective.public) + + return prospective == spec_version + + def _compare_not_equal(self, prospective: Version, spec: str) -> bool: + return not self._compare_equal(prospective, spec) + + def _compare_less_than_equal(self, prospective: Version, spec: str) -> bool: + # NB: Local version identifiers are NOT permitted in the version + # specifier, so local version labels can be universally removed from + # the prospective version. + return Version(prospective.public) <= Version(spec) + + def _compare_greater_than_equal(self, prospective: Version, spec: str) -> bool: + # NB: Local version identifiers are NOT permitted in the version + # specifier, so local version labels can be universally removed from + # the prospective version. + return Version(prospective.public) >= Version(spec) + + def _compare_less_than(self, prospective: Version, spec_str: str) -> bool: + # Convert our spec to a Version instance, since we'll want to work with + # it as a version. + spec = Version(spec_str) + + # Check to see if the prospective version is less than the spec + # version. If it's not we can short circuit and just return False now + # instead of doing extra unneeded work. + if not prospective < spec: + return False + + # This special case is here so that, unless the specifier itself + # includes is a pre-release version, that we do not accept pre-release + # versions for the version mentioned in the specifier (e.g. <3.1 should + # not match 3.1.dev0, but should match 3.0.dev0). + if not spec.is_prerelease and prospective.is_prerelease: + if Version(prospective.base_version) == Version(spec.base_version): + return False + + # If we've gotten to here, it means that prospective version is both + # less than the spec version *and* it's not a pre-release of the same + # version in the spec. + return True + + def _compare_greater_than(self, prospective: Version, spec_str: str) -> bool: + # Convert our spec to a Version instance, since we'll want to work with + # it as a version. + spec = Version(spec_str) + + # Check to see if the prospective version is greater than the spec + # version. If it's not we can short circuit and just return False now + # instead of doing extra unneeded work. + if not prospective > spec: + return False + + # This special case is here so that, unless the specifier itself + # includes is a post-release version, that we do not accept + # post-release versions for the version mentioned in the specifier + # (e.g. >3.1 should not match 3.0.post0, but should match 3.2.post0). + if not spec.is_postrelease and prospective.is_postrelease: + if Version(prospective.base_version) == Version(spec.base_version): + return False + + # Ensure that we do not allow a local version of the version mentioned + # in the specifier, which is technically greater than, to match. + if prospective.local is not None: + if Version(prospective.base_version) == Version(spec.base_version): + return False + + # If we've gotten to here, it means that prospective version is both + # greater than the spec version *and* it's not a pre-release of the + # same version in the spec. + return True + + def _compare_arbitrary(self, prospective: Version, spec: str) -> bool: + return str(prospective).lower() == str(spec).lower() + + def __contains__(self, item: Union[str, Version]) -> bool: + """Return whether or not the item is contained in this specifier. + + :param item: The item to check for. + + This is used for the ``in`` operator and behaves the same as + :meth:`contains` with no ``prereleases`` argument passed. + + >>> "1.2.3" in Specifier(">=1.2.3") + True + >>> Version("1.2.3") in Specifier(">=1.2.3") + True + >>> "1.0.0" in Specifier(">=1.2.3") + False + >>> "1.3.0a1" in Specifier(">=1.2.3") + False + >>> "1.3.0a1" in Specifier(">=1.2.3", prereleases=True) + True + """ + return self.contains(item) + + def contains( + self, item: UnparsedVersion, prereleases: Optional[bool] = None + ) -> bool: + """Return whether or not the item is contained in this specifier. + + :param item: + The item to check for, which can be a version string or a + :class:`Version` instance. + :param prereleases: + Whether or not to match prereleases with this Specifier. If set to + ``None`` (the default), it uses :attr:`prereleases` to determine + whether or not prereleases are allowed. + + >>> Specifier(">=1.2.3").contains("1.2.3") + True + >>> Specifier(">=1.2.3").contains(Version("1.2.3")) + True + >>> Specifier(">=1.2.3").contains("1.0.0") + False + >>> Specifier(">=1.2.3").contains("1.3.0a1") + False + >>> Specifier(">=1.2.3", prereleases=True).contains("1.3.0a1") + True + >>> Specifier(">=1.2.3").contains("1.3.0a1", prereleases=True) + True + """ + + # Determine if prereleases are to be allowed or not. + if prereleases is None: + prereleases = self.prereleases + + # Normalize item to a Version, this allows us to have a shortcut for + # "2.0" in Specifier(">=2") + normalized_item = _coerce_version(item) + + # Determine if we should be supporting prereleases in this specifier + # or not, if we do not support prereleases than we can short circuit + # logic if this version is a prereleases. + if normalized_item.is_prerelease and not prereleases: + return False + + # Actually do the comparison to determine if this item is contained + # within this Specifier or not. + operator_callable: CallableOperator = self._get_operator(self.operator) + return operator_callable(normalized_item, self.version) + + def filter( + self, iterable: Iterable[UnparsedVersionVar], prereleases: Optional[bool] = None + ) -> Iterator[UnparsedVersionVar]: + """Filter items in the given iterable, that match the specifier. + + :param iterable: + An iterable that can contain version strings and :class:`Version` instances. + The items in the iterable will be filtered according to the specifier. + :param prereleases: + Whether or not to allow prereleases in the returned iterator. If set to + ``None`` (the default), it will be intelligently decide whether to allow + prereleases or not (based on the :attr:`prereleases` attribute, and + whether the only versions matching are prereleases). + + This method is smarter than just ``filter(Specifier().contains, [...])`` + because it implements the rule from :pep:`440` that a prerelease item + SHOULD be accepted if no other versions match the given specifier. + + >>> list(Specifier(">=1.2.3").filter(["1.2", "1.3", "1.5a1"])) + ['1.3'] + >>> list(Specifier(">=1.2.3").filter(["1.2", "1.2.3", "1.3", Version("1.4")])) + ['1.2.3', '1.3', ] + >>> list(Specifier(">=1.2.3").filter(["1.2", "1.5a1"])) + ['1.5a1'] + >>> list(Specifier(">=1.2.3").filter(["1.3", "1.5a1"], prereleases=True)) + ['1.3', '1.5a1'] + >>> list(Specifier(">=1.2.3", prereleases=True).filter(["1.3", "1.5a1"])) + ['1.3', '1.5a1'] + """ + + yielded = False + found_prereleases = [] + + kw = {"prereleases": prereleases if prereleases is not None else True} + + # Attempt to iterate over all the values in the iterable and if any of + # them match, yield them. + for version in iterable: + parsed_version = _coerce_version(version) + + if self.contains(parsed_version, **kw): + # If our version is a prerelease, and we were not set to allow + # prereleases, then we'll store it for later in case nothing + # else matches this specifier. + if parsed_version.is_prerelease and not ( + prereleases or self.prereleases + ): + found_prereleases.append(version) + # Either this is not a prerelease, or we should have been + # accepting prereleases from the beginning. + else: + yielded = True + yield version + + # Now that we've iterated over everything, determine if we've yielded + # any values, and if we have not and we have any prereleases stored up + # then we will go ahead and yield the prereleases. + if not yielded and found_prereleases: + for version in found_prereleases: + yield version + + +_prefix_regex = re.compile(r"^([0-9]+)((?:a|b|c|rc)[0-9]+)$") + + +def _version_split(version: str) -> List[str]: + """Split version into components. + + The split components are intended for version comparison. The logic does + not attempt to retain the original version string, so joining the + components back with :func:`_version_join` may not produce the original + version string. + """ + result: List[str] = [] + + epoch, _, rest = version.rpartition("!") + result.append(epoch or "0") + + for item in rest.split("."): + match = _prefix_regex.search(item) + if match: + result.extend(match.groups()) + else: + result.append(item) + return result + + +def _version_join(components: List[str]) -> str: + """Join split version components into a version string. + + This function assumes the input came from :func:`_version_split`, where the + first component must be the epoch (either empty or numeric), and all other + components numeric. + """ + epoch, *rest = components + return f"{epoch}!{'.'.join(rest)}" + + +def _is_not_suffix(segment: str) -> bool: + return not any( + segment.startswith(prefix) for prefix in ("dev", "a", "b", "rc", "post") + ) + + +def _pad_version(left: List[str], right: List[str]) -> Tuple[List[str], List[str]]: + left_split, right_split = [], [] + + # Get the release segment of our versions + left_split.append(list(itertools.takewhile(lambda x: x.isdigit(), left))) + right_split.append(list(itertools.takewhile(lambda x: x.isdigit(), right))) + + # Get the rest of our versions + left_split.append(left[len(left_split[0]) :]) + right_split.append(right[len(right_split[0]) :]) + + # Insert our padding + left_split.insert(1, ["0"] * max(0, len(right_split[0]) - len(left_split[0]))) + right_split.insert(1, ["0"] * max(0, len(left_split[0]) - len(right_split[0]))) + + return ( + list(itertools.chain.from_iterable(left_split)), + list(itertools.chain.from_iterable(right_split)), + ) + + +class SpecifierSet(BaseSpecifier): + """This class abstracts handling of a set of version specifiers. + + It can be passed a single specifier (``>=3.0``), a comma-separated list of + specifiers (``>=3.0,!=3.1``), or no specifier at all. + """ + + def __init__( + self, specifiers: str = "", prereleases: Optional[bool] = None + ) -> None: + """Initialize a SpecifierSet instance. + + :param specifiers: + The string representation of a specifier or a comma-separated list of + specifiers which will be parsed and normalized before use. + :param prereleases: + This tells the SpecifierSet if it should accept prerelease versions if + applicable or not. The default of ``None`` will autodetect it from the + given specifiers. + + :raises InvalidSpecifier: + If the given ``specifiers`` are not parseable than this exception will be + raised. + """ + + # Split on `,` to break each individual specifier into it's own item, and + # strip each item to remove leading/trailing whitespace. + split_specifiers = [s.strip() for s in specifiers.split(",") if s.strip()] + + # Make each individual specifier a Specifier and save in a frozen set for later. + self._specs = frozenset(map(Specifier, split_specifiers)) + + # Store our prereleases value so we can use it later to determine if + # we accept prereleases or not. + self._prereleases = prereleases + + @property + def prereleases(self) -> Optional[bool]: + # If we have been given an explicit prerelease modifier, then we'll + # pass that through here. + if self._prereleases is not None: + return self._prereleases + + # If we don't have any specifiers, and we don't have a forced value, + # then we'll just return None since we don't know if this should have + # pre-releases or not. + if not self._specs: + return None + + # Otherwise we'll see if any of the given specifiers accept + # prereleases, if any of them do we'll return True, otherwise False. + return any(s.prereleases for s in self._specs) + + @prereleases.setter + def prereleases(self, value: bool) -> None: + self._prereleases = value + + def __repr__(self) -> str: + """A representation of the specifier set that shows all internal state. + + Note that the ordering of the individual specifiers within the set may not + match the input string. + + >>> SpecifierSet('>=1.0.0,!=2.0.0') + =1.0.0')> + >>> SpecifierSet('>=1.0.0,!=2.0.0', prereleases=False) + =1.0.0', prereleases=False)> + >>> SpecifierSet('>=1.0.0,!=2.0.0', prereleases=True) + =1.0.0', prereleases=True)> + """ + pre = ( + f", prereleases={self.prereleases!r}" + if self._prereleases is not None + else "" + ) + + return f"" + + def __str__(self) -> str: + """A string representation of the specifier set that can be round-tripped. + + Note that the ordering of the individual specifiers within the set may not + match the input string. + + >>> str(SpecifierSet(">=1.0.0,!=1.0.1")) + '!=1.0.1,>=1.0.0' + >>> str(SpecifierSet(">=1.0.0,!=1.0.1", prereleases=False)) + '!=1.0.1,>=1.0.0' + """ + return ",".join(sorted(str(s) for s in self._specs)) + + def __hash__(self) -> int: + return hash(self._specs) + + def __and__(self, other: Union["SpecifierSet", str]) -> "SpecifierSet": + """Return a SpecifierSet which is a combination of the two sets. + + :param other: The other object to combine with. + + >>> SpecifierSet(">=1.0.0,!=1.0.1") & '<=2.0.0,!=2.0.1' + =1.0.0')> + >>> SpecifierSet(">=1.0.0,!=1.0.1") & SpecifierSet('<=2.0.0,!=2.0.1') + =1.0.0')> + """ + if isinstance(other, str): + other = SpecifierSet(other) + elif not isinstance(other, SpecifierSet): + return NotImplemented + + specifier = SpecifierSet() + specifier._specs = frozenset(self._specs | other._specs) + + if self._prereleases is None and other._prereleases is not None: + specifier._prereleases = other._prereleases + elif self._prereleases is not None and other._prereleases is None: + specifier._prereleases = self._prereleases + elif self._prereleases == other._prereleases: + specifier._prereleases = self._prereleases + else: + raise ValueError( + "Cannot combine SpecifierSets with True and False prerelease " + "overrides." + ) + + return specifier + + def __eq__(self, other: object) -> bool: + """Whether or not the two SpecifierSet-like objects are equal. + + :param other: The other object to check against. + + The value of :attr:`prereleases` is ignored. + + >>> SpecifierSet(">=1.0.0,!=1.0.1") == SpecifierSet(">=1.0.0,!=1.0.1") + True + >>> (SpecifierSet(">=1.0.0,!=1.0.1", prereleases=False) == + ... SpecifierSet(">=1.0.0,!=1.0.1", prereleases=True)) + True + >>> SpecifierSet(">=1.0.0,!=1.0.1") == ">=1.0.0,!=1.0.1" + True + >>> SpecifierSet(">=1.0.0,!=1.0.1") == SpecifierSet(">=1.0.0") + False + >>> SpecifierSet(">=1.0.0,!=1.0.1") == SpecifierSet(">=1.0.0,!=1.0.2") + False + """ + if isinstance(other, (str, Specifier)): + other = SpecifierSet(str(other)) + elif not isinstance(other, SpecifierSet): + return NotImplemented + + return self._specs == other._specs + + def __len__(self) -> int: + """Returns the number of specifiers in this specifier set.""" + return len(self._specs) + + def __iter__(self) -> Iterator[Specifier]: + """ + Returns an iterator over all the underlying :class:`Specifier` instances + in this specifier set. + + >>> sorted(SpecifierSet(">=1.0.0,!=1.0.1"), key=str) + [, =1.0.0')>] + """ + return iter(self._specs) + + def __contains__(self, item: UnparsedVersion) -> bool: + """Return whether or not the item is contained in this specifier. + + :param item: The item to check for. + + This is used for the ``in`` operator and behaves the same as + :meth:`contains` with no ``prereleases`` argument passed. + + >>> "1.2.3" in SpecifierSet(">=1.0.0,!=1.0.1") + True + >>> Version("1.2.3") in SpecifierSet(">=1.0.0,!=1.0.1") + True + >>> "1.0.1" in SpecifierSet(">=1.0.0,!=1.0.1") + False + >>> "1.3.0a1" in SpecifierSet(">=1.0.0,!=1.0.1") + False + >>> "1.3.0a1" in SpecifierSet(">=1.0.0,!=1.0.1", prereleases=True) + True + """ + return self.contains(item) + + def contains( + self, + item: UnparsedVersion, + prereleases: Optional[bool] = None, + installed: Optional[bool] = None, + ) -> bool: + """Return whether or not the item is contained in this SpecifierSet. + + :param item: + The item to check for, which can be a version string or a + :class:`Version` instance. + :param prereleases: + Whether or not to match prereleases with this SpecifierSet. If set to + ``None`` (the default), it uses :attr:`prereleases` to determine + whether or not prereleases are allowed. + + >>> SpecifierSet(">=1.0.0,!=1.0.1").contains("1.2.3") + True + >>> SpecifierSet(">=1.0.0,!=1.0.1").contains(Version("1.2.3")) + True + >>> SpecifierSet(">=1.0.0,!=1.0.1").contains("1.0.1") + False + >>> SpecifierSet(">=1.0.0,!=1.0.1").contains("1.3.0a1") + False + >>> SpecifierSet(">=1.0.0,!=1.0.1", prereleases=True).contains("1.3.0a1") + True + >>> SpecifierSet(">=1.0.0,!=1.0.1").contains("1.3.0a1", prereleases=True) + True + """ + # Ensure that our item is a Version instance. + if not isinstance(item, Version): + item = Version(item) + + # Determine if we're forcing a prerelease or not, if we're not forcing + # one for this particular filter call, then we'll use whatever the + # SpecifierSet thinks for whether or not we should support prereleases. + if prereleases is None: + prereleases = self.prereleases + + # We can determine if we're going to allow pre-releases by looking to + # see if any of the underlying items supports them. If none of them do + # and this item is a pre-release then we do not allow it and we can + # short circuit that here. + # Note: This means that 1.0.dev1 would not be contained in something + # like >=1.0.devabc however it would be in >=1.0.debabc,>0.0.dev0 + if not prereleases and item.is_prerelease: + return False + + if installed and item.is_prerelease: + item = Version(item.base_version) + + # We simply dispatch to the underlying specs here to make sure that the + # given version is contained within all of them. + # Note: This use of all() here means that an empty set of specifiers + # will always return True, this is an explicit design decision. + return all(s.contains(item, prereleases=prereleases) for s in self._specs) + + def filter( + self, iterable: Iterable[UnparsedVersionVar], prereleases: Optional[bool] = None + ) -> Iterator[UnparsedVersionVar]: + """Filter items in the given iterable, that match the specifiers in this set. + + :param iterable: + An iterable that can contain version strings and :class:`Version` instances. + The items in the iterable will be filtered according to the specifier. + :param prereleases: + Whether or not to allow prereleases in the returned iterator. If set to + ``None`` (the default), it will be intelligently decide whether to allow + prereleases or not (based on the :attr:`prereleases` attribute, and + whether the only versions matching are prereleases). + + This method is smarter than just ``filter(SpecifierSet(...).contains, [...])`` + because it implements the rule from :pep:`440` that a prerelease item + SHOULD be accepted if no other versions match the given specifier. + + >>> list(SpecifierSet(">=1.2.3").filter(["1.2", "1.3", "1.5a1"])) + ['1.3'] + >>> list(SpecifierSet(">=1.2.3").filter(["1.2", "1.3", Version("1.4")])) + ['1.3', ] + >>> list(SpecifierSet(">=1.2.3").filter(["1.2", "1.5a1"])) + [] + >>> list(SpecifierSet(">=1.2.3").filter(["1.3", "1.5a1"], prereleases=True)) + ['1.3', '1.5a1'] + >>> list(SpecifierSet(">=1.2.3", prereleases=True).filter(["1.3", "1.5a1"])) + ['1.3', '1.5a1'] + + An "empty" SpecifierSet will filter items based on the presence of prerelease + versions in the set. + + >>> list(SpecifierSet("").filter(["1.3", "1.5a1"])) + ['1.3'] + >>> list(SpecifierSet("").filter(["1.5a1"])) + ['1.5a1'] + >>> list(SpecifierSet("", prereleases=True).filter(["1.3", "1.5a1"])) + ['1.3', '1.5a1'] + >>> list(SpecifierSet("").filter(["1.3", "1.5a1"], prereleases=True)) + ['1.3', '1.5a1'] + """ + # Determine if we're forcing a prerelease or not, if we're not forcing + # one for this particular filter call, then we'll use whatever the + # SpecifierSet thinks for whether or not we should support prereleases. + if prereleases is None: + prereleases = self.prereleases + + # If we have any specifiers, then we want to wrap our iterable in the + # filter method for each one, this will act as a logical AND amongst + # each specifier. + if self._specs: + for spec in self._specs: + iterable = spec.filter(iterable, prereleases=bool(prereleases)) + return iter(iterable) + # If we do not have any specifiers, then we need to have a rough filter + # which will filter out any pre-releases, unless there are no final + # releases. + else: + filtered: List[UnparsedVersionVar] = [] + found_prereleases: List[UnparsedVersionVar] = [] + + for item in iterable: + parsed_version = _coerce_version(item) + + # Store any item which is a pre-release for later unless we've + # already found a final version or we are accepting prereleases + if parsed_version.is_prerelease and not prereleases: + if not filtered: + found_prereleases.append(item) + else: + filtered.append(item) + + # If we've found no items except for pre-releases, then we'll go + # ahead and use the pre-releases + if not filtered and found_prereleases and prereleases is None: + return iter(found_prereleases) + + return iter(filtered) diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/tags.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/tags.py new file mode 100644 index 0000000000000000000000000000000000000000..89f1926137dd2d2a6bd63616bf5b9f722fc8d584 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/tags.py @@ -0,0 +1,571 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import logging +import platform +import re +import struct +import subprocess +import sys +import sysconfig +from importlib.machinery import EXTENSION_SUFFIXES +from typing import ( + Dict, + FrozenSet, + Iterable, + Iterator, + List, + Optional, + Sequence, + Tuple, + Union, + cast, +) + +from . import _manylinux, _musllinux + +logger = logging.getLogger(__name__) + +PythonVersion = Sequence[int] +MacVersion = Tuple[int, int] + +INTERPRETER_SHORT_NAMES: Dict[str, str] = { + "python": "py", # Generic. + "cpython": "cp", + "pypy": "pp", + "ironpython": "ip", + "jython": "jy", +} + + +_32_BIT_INTERPRETER = struct.calcsize("P") == 4 + + +class Tag: + """ + A representation of the tag triple for a wheel. + + Instances are considered immutable and thus are hashable. Equality checking + is also supported. + """ + + __slots__ = ["_interpreter", "_abi", "_platform", "_hash"] + + def __init__(self, interpreter: str, abi: str, platform: str) -> None: + self._interpreter = interpreter.lower() + self._abi = abi.lower() + self._platform = platform.lower() + # The __hash__ of every single element in a Set[Tag] will be evaluated each time + # that a set calls its `.disjoint()` method, which may be called hundreds of + # times when scanning a page of links for packages with tags matching that + # Set[Tag]. Pre-computing the value here produces significant speedups for + # downstream consumers. + self._hash = hash((self._interpreter, self._abi, self._platform)) + + @property + def interpreter(self) -> str: + return self._interpreter + + @property + def abi(self) -> str: + return self._abi + + @property + def platform(self) -> str: + return self._platform + + def __eq__(self, other: object) -> bool: + if not isinstance(other, Tag): + return NotImplemented + + return ( + (self._hash == other._hash) # Short-circuit ASAP for perf reasons. + and (self._platform == other._platform) + and (self._abi == other._abi) + and (self._interpreter == other._interpreter) + ) + + def __hash__(self) -> int: + return self._hash + + def __str__(self) -> str: + return f"{self._interpreter}-{self._abi}-{self._platform}" + + def __repr__(self) -> str: + return f"<{self} @ {id(self)}>" + + +def parse_tag(tag: str) -> FrozenSet[Tag]: + """ + Parses the provided tag (e.g. `py3-none-any`) into a frozenset of Tag instances. + + Returning a set is required due to the possibility that the tag is a + compressed tag set. + """ + tags = set() + interpreters, abis, platforms = tag.split("-") + for interpreter in interpreters.split("."): + for abi in abis.split("."): + for platform_ in platforms.split("."): + tags.add(Tag(interpreter, abi, platform_)) + return frozenset(tags) + + +def _get_config_var(name: str, warn: bool = False) -> Union[int, str, None]: + value: Union[int, str, None] = sysconfig.get_config_var(name) + if value is None and warn: + logger.debug( + "Config variable '%s' is unset, Python ABI tag may be incorrect", name + ) + return value + + +def _normalize_string(string: str) -> str: + return string.replace(".", "_").replace("-", "_").replace(" ", "_") + + +def _is_threaded_cpython(abis: List[str]) -> bool: + """ + Determine if the ABI corresponds to a threaded (`--disable-gil`) build. + + The threaded builds are indicated by a "t" in the abiflags. + """ + if len(abis) == 0: + return False + # expect e.g., cp313 + m = re.match(r"cp\d+(.*)", abis[0]) + if not m: + return False + abiflags = m.group(1) + return "t" in abiflags + + +def _abi3_applies(python_version: PythonVersion, threading: bool) -> bool: + """ + Determine if the Python version supports abi3. + + PEP 384 was first implemented in Python 3.2. The threaded (`--disable-gil`) + builds do not support abi3. + """ + return len(python_version) > 1 and tuple(python_version) >= (3, 2) and not threading + + +def _cpython_abis(py_version: PythonVersion, warn: bool = False) -> List[str]: + py_version = tuple(py_version) # To allow for version comparison. + abis = [] + version = _version_nodot(py_version[:2]) + threading = debug = pymalloc = ucs4 = "" + with_debug = _get_config_var("Py_DEBUG", warn) + has_refcount = hasattr(sys, "gettotalrefcount") + # Windows doesn't set Py_DEBUG, so checking for support of debug-compiled + # extension modules is the best option. + # https://github.com/pypa/pip/issues/3383#issuecomment-173267692 + has_ext = "_d.pyd" in EXTENSION_SUFFIXES + if with_debug or (with_debug is None and (has_refcount or has_ext)): + debug = "d" + if py_version >= (3, 13) and _get_config_var("Py_GIL_DISABLED", warn): + threading = "t" + if py_version < (3, 8): + with_pymalloc = _get_config_var("WITH_PYMALLOC", warn) + if with_pymalloc or with_pymalloc is None: + pymalloc = "m" + if py_version < (3, 3): + unicode_size = _get_config_var("Py_UNICODE_SIZE", warn) + if unicode_size == 4 or ( + unicode_size is None and sys.maxunicode == 0x10FFFF + ): + ucs4 = "u" + elif debug: + # Debug builds can also load "normal" extension modules. + # We can also assume no UCS-4 or pymalloc requirement. + abis.append(f"cp{version}{threading}") + abis.insert(0, f"cp{version}{threading}{debug}{pymalloc}{ucs4}") + return abis + + +def cpython_tags( + python_version: Optional[PythonVersion] = None, + abis: Optional[Iterable[str]] = None, + platforms: Optional[Iterable[str]] = None, + *, + warn: bool = False, +) -> Iterator[Tag]: + """ + Yields the tags for a CPython interpreter. + + The tags consist of: + - cp-- + - cp-abi3- + - cp-none- + - cp-abi3- # Older Python versions down to 3.2. + + If python_version only specifies a major version then user-provided ABIs and + the 'none' ABItag will be used. + + If 'abi3' or 'none' are specified in 'abis' then they will be yielded at + their normal position and not at the beginning. + """ + if not python_version: + python_version = sys.version_info[:2] + + interpreter = f"cp{_version_nodot(python_version[:2])}" + + if abis is None: + if len(python_version) > 1: + abis = _cpython_abis(python_version, warn) + else: + abis = [] + abis = list(abis) + # 'abi3' and 'none' are explicitly handled later. + for explicit_abi in ("abi3", "none"): + try: + abis.remove(explicit_abi) + except ValueError: + pass + + platforms = list(platforms or platform_tags()) + for abi in abis: + for platform_ in platforms: + yield Tag(interpreter, abi, platform_) + + threading = _is_threaded_cpython(abis) + use_abi3 = _abi3_applies(python_version, threading) + if use_abi3: + yield from (Tag(interpreter, "abi3", platform_) for platform_ in platforms) + yield from (Tag(interpreter, "none", platform_) for platform_ in platforms) + + if use_abi3: + for minor_version in range(python_version[1] - 1, 1, -1): + for platform_ in platforms: + interpreter = "cp{version}".format( + version=_version_nodot((python_version[0], minor_version)) + ) + yield Tag(interpreter, "abi3", platform_) + + +def _generic_abi() -> List[str]: + """ + Return the ABI tag based on EXT_SUFFIX. + """ + # The following are examples of `EXT_SUFFIX`. + # We want to keep the parts which are related to the ABI and remove the + # parts which are related to the platform: + # - linux: '.cpython-310-x86_64-linux-gnu.so' => cp310 + # - mac: '.cpython-310-darwin.so' => cp310 + # - win: '.cp310-win_amd64.pyd' => cp310 + # - win: '.pyd' => cp37 (uses _cpython_abis()) + # - pypy: '.pypy38-pp73-x86_64-linux-gnu.so' => pypy38_pp73 + # - graalpy: '.graalpy-38-native-x86_64-darwin.dylib' + # => graalpy_38_native + + ext_suffix = _get_config_var("EXT_SUFFIX", warn=True) + if not isinstance(ext_suffix, str) or ext_suffix[0] != ".": + raise SystemError("invalid sysconfig.get_config_var('EXT_SUFFIX')") + parts = ext_suffix.split(".") + if len(parts) < 3: + # CPython3.7 and earlier uses ".pyd" on Windows. + return _cpython_abis(sys.version_info[:2]) + soabi = parts[1] + if soabi.startswith("cpython"): + # non-windows + abi = "cp" + soabi.split("-")[1] + elif soabi.startswith("cp"): + # windows + abi = soabi.split("-")[0] + elif soabi.startswith("pypy"): + abi = "-".join(soabi.split("-")[:2]) + elif soabi.startswith("graalpy"): + abi = "-".join(soabi.split("-")[:3]) + elif soabi: + # pyston, ironpython, others? + abi = soabi + else: + return [] + return [_normalize_string(abi)] + + +def generic_tags( + interpreter: Optional[str] = None, + abis: Optional[Iterable[str]] = None, + platforms: Optional[Iterable[str]] = None, + *, + warn: bool = False, +) -> Iterator[Tag]: + """ + Yields the tags for a generic interpreter. + + The tags consist of: + - -- + + The "none" ABI will be added if it was not explicitly provided. + """ + if not interpreter: + interp_name = interpreter_name() + interp_version = interpreter_version(warn=warn) + interpreter = "".join([interp_name, interp_version]) + if abis is None: + abis = _generic_abi() + else: + abis = list(abis) + platforms = list(platforms or platform_tags()) + if "none" not in abis: + abis.append("none") + for abi in abis: + for platform_ in platforms: + yield Tag(interpreter, abi, platform_) + + +def _py_interpreter_range(py_version: PythonVersion) -> Iterator[str]: + """ + Yields Python versions in descending order. + + After the latest version, the major-only version will be yielded, and then + all previous versions of that major version. + """ + if len(py_version) > 1: + yield f"py{_version_nodot(py_version[:2])}" + yield f"py{py_version[0]}" + if len(py_version) > 1: + for minor in range(py_version[1] - 1, -1, -1): + yield f"py{_version_nodot((py_version[0], minor))}" + + +def compatible_tags( + python_version: Optional[PythonVersion] = None, + interpreter: Optional[str] = None, + platforms: Optional[Iterable[str]] = None, +) -> Iterator[Tag]: + """ + Yields the sequence of tags that are compatible with a specific version of Python. + + The tags consist of: + - py*-none- + - -none-any # ... if `interpreter` is provided. + - py*-none-any + """ + if not python_version: + python_version = sys.version_info[:2] + platforms = list(platforms or platform_tags()) + for version in _py_interpreter_range(python_version): + for platform_ in platforms: + yield Tag(version, "none", platform_) + if interpreter: + yield Tag(interpreter, "none", "any") + for version in _py_interpreter_range(python_version): + yield Tag(version, "none", "any") + + +def _mac_arch(arch: str, is_32bit: bool = _32_BIT_INTERPRETER) -> str: + if not is_32bit: + return arch + + if arch.startswith("ppc"): + return "ppc" + + return "i386" + + +def _mac_binary_formats(version: MacVersion, cpu_arch: str) -> List[str]: + formats = [cpu_arch] + if cpu_arch == "x86_64": + if version < (10, 4): + return [] + formats.extend(["intel", "fat64", "fat32"]) + + elif cpu_arch == "i386": + if version < (10, 4): + return [] + formats.extend(["intel", "fat32", "fat"]) + + elif cpu_arch == "ppc64": + # TODO: Need to care about 32-bit PPC for ppc64 through 10.2? + if version > (10, 5) or version < (10, 4): + return [] + formats.append("fat64") + + elif cpu_arch == "ppc": + if version > (10, 6): + return [] + formats.extend(["fat32", "fat"]) + + if cpu_arch in {"arm64", "x86_64"}: + formats.append("universal2") + + if cpu_arch in {"x86_64", "i386", "ppc64", "ppc", "intel"}: + formats.append("universal") + + return formats + + +def mac_platforms( + version: Optional[MacVersion] = None, arch: Optional[str] = None +) -> Iterator[str]: + """ + Yields the platform tags for a macOS system. + + The `version` parameter is a two-item tuple specifying the macOS version to + generate platform tags for. The `arch` parameter is the CPU architecture to + generate platform tags for. Both parameters default to the appropriate value + for the current system. + """ + version_str, _, cpu_arch = platform.mac_ver() + if version is None: + version = cast("MacVersion", tuple(map(int, version_str.split(".")[:2]))) + if version == (10, 16): + # When built against an older macOS SDK, Python will report macOS 10.16 + # instead of the real version. + version_str = subprocess.run( + [ + sys.executable, + "-sS", + "-c", + "import platform; print(platform.mac_ver()[0])", + ], + check=True, + env={"SYSTEM_VERSION_COMPAT": "0"}, + stdout=subprocess.PIPE, + text=True, + ).stdout + version = cast("MacVersion", tuple(map(int, version_str.split(".")[:2]))) + else: + version = version + if arch is None: + arch = _mac_arch(cpu_arch) + else: + arch = arch + + if (10, 0) <= version and version < (11, 0): + # Prior to Mac OS 11, each yearly release of Mac OS bumped the + # "minor" version number. The major version was always 10. + for minor_version in range(version[1], -1, -1): + compat_version = 10, minor_version + binary_formats = _mac_binary_formats(compat_version, arch) + for binary_format in binary_formats: + yield "macosx_{major}_{minor}_{binary_format}".format( + major=10, minor=minor_version, binary_format=binary_format + ) + + if version >= (11, 0): + # Starting with Mac OS 11, each yearly release bumps the major version + # number. The minor versions are now the midyear updates. + for major_version in range(version[0], 10, -1): + compat_version = major_version, 0 + binary_formats = _mac_binary_formats(compat_version, arch) + for binary_format in binary_formats: + yield "macosx_{major}_{minor}_{binary_format}".format( + major=major_version, minor=0, binary_format=binary_format + ) + + if version >= (11, 0): + # Mac OS 11 on x86_64 is compatible with binaries from previous releases. + # Arm64 support was introduced in 11.0, so no Arm binaries from previous + # releases exist. + # + # However, the "universal2" binary format can have a + # macOS version earlier than 11.0 when the x86_64 part of the binary supports + # that version of macOS. + if arch == "x86_64": + for minor_version in range(16, 3, -1): + compat_version = 10, minor_version + binary_formats = _mac_binary_formats(compat_version, arch) + for binary_format in binary_formats: + yield "macosx_{major}_{minor}_{binary_format}".format( + major=compat_version[0], + minor=compat_version[1], + binary_format=binary_format, + ) + else: + for minor_version in range(16, 3, -1): + compat_version = 10, minor_version + binary_format = "universal2" + yield "macosx_{major}_{minor}_{binary_format}".format( + major=compat_version[0], + minor=compat_version[1], + binary_format=binary_format, + ) + + +def _linux_platforms(is_32bit: bool = _32_BIT_INTERPRETER) -> Iterator[str]: + linux = _normalize_string(sysconfig.get_platform()) + if not linux.startswith("linux_"): + # we should never be here, just yield the sysconfig one and return + yield linux + return + if is_32bit: + if linux == "linux_x86_64": + linux = "linux_i686" + elif linux == "linux_aarch64": + linux = "linux_armv8l" + _, arch = linux.split("_", 1) + archs = {"armv8l": ["armv8l", "armv7l"]}.get(arch, [arch]) + yield from _manylinux.platform_tags(archs) + yield from _musllinux.platform_tags(archs) + for arch in archs: + yield f"linux_{arch}" + + +def _generic_platforms() -> Iterator[str]: + yield _normalize_string(sysconfig.get_platform()) + + +def platform_tags() -> Iterator[str]: + """ + Provides the platform tags for this installation. + """ + if platform.system() == "Darwin": + return mac_platforms() + elif platform.system() == "Linux": + return _linux_platforms() + else: + return _generic_platforms() + + +def interpreter_name() -> str: + """ + Returns the name of the running interpreter. + + Some implementations have a reserved, two-letter abbreviation which will + be returned when appropriate. + """ + name = sys.implementation.name + return INTERPRETER_SHORT_NAMES.get(name) or name + + +def interpreter_version(*, warn: bool = False) -> str: + """ + Returns the version of the running interpreter. + """ + version = _get_config_var("py_version_nodot", warn=warn) + if version: + version = str(version) + else: + version = _version_nodot(sys.version_info[:2]) + return version + + +def _version_nodot(version: PythonVersion) -> str: + return "".join(map(str, version)) + + +def sys_tags(*, warn: bool = False) -> Iterator[Tag]: + """ + Returns the sequence of tag triples for the running interpreter. + + The order of the sequence corresponds to priority order for the + interpreter, from most to least important. + """ + + interp_name = interpreter_name() + if interp_name == "cp": + yield from cpython_tags(warn=warn) + else: + yield from generic_tags() + + if interp_name == "pp": + interp = "pp3" + elif interp_name == "cp": + interp = "cp" + interpreter_version(warn=warn) + else: + interp = None + yield from compatible_tags(interpreter=interp) diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/utils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/utils.py new file mode 100644 index 0000000000000000000000000000000000000000..c2c2f75aa806282d322c76c2117c0f0fdfb09d25 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/utils.py @@ -0,0 +1,172 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import re +from typing import FrozenSet, NewType, Tuple, Union, cast + +from .tags import Tag, parse_tag +from .version import InvalidVersion, Version + +BuildTag = Union[Tuple[()], Tuple[int, str]] +NormalizedName = NewType("NormalizedName", str) + + +class InvalidName(ValueError): + """ + An invalid distribution name; users should refer to the packaging user guide. + """ + + +class InvalidWheelFilename(ValueError): + """ + An invalid wheel filename was found, users should refer to PEP 427. + """ + + +class InvalidSdistFilename(ValueError): + """ + An invalid sdist filename was found, users should refer to the packaging user guide. + """ + + +# Core metadata spec for `Name` +_validate_regex = re.compile( + r"^([A-Z0-9]|[A-Z0-9][A-Z0-9._-]*[A-Z0-9])$", re.IGNORECASE +) +_canonicalize_regex = re.compile(r"[-_.]+") +_normalized_regex = re.compile(r"^([a-z0-9]|[a-z0-9]([a-z0-9-](?!--))*[a-z0-9])$") +# PEP 427: The build number must start with a digit. +_build_tag_regex = re.compile(r"(\d+)(.*)") + + +def canonicalize_name(name: str, *, validate: bool = False) -> NormalizedName: + if validate and not _validate_regex.match(name): + raise InvalidName(f"name is invalid: {name!r}") + # This is taken from PEP 503. + value = _canonicalize_regex.sub("-", name).lower() + return cast(NormalizedName, value) + + +def is_normalized_name(name: str) -> bool: + return _normalized_regex.match(name) is not None + + +def canonicalize_version( + version: Union[Version, str], *, strip_trailing_zero: bool = True +) -> str: + """ + This is very similar to Version.__str__, but has one subtle difference + with the way it handles the release segment. + """ + if isinstance(version, str): + try: + parsed = Version(version) + except InvalidVersion: + # Legacy versions cannot be normalized + return version + else: + parsed = version + + parts = [] + + # Epoch + if parsed.epoch != 0: + parts.append(f"{parsed.epoch}!") + + # Release segment + release_segment = ".".join(str(x) for x in parsed.release) + if strip_trailing_zero: + # NB: This strips trailing '.0's to normalize + release_segment = re.sub(r"(\.0)+$", "", release_segment) + parts.append(release_segment) + + # Pre-release + if parsed.pre is not None: + parts.append("".join(str(x) for x in parsed.pre)) + + # Post-release + if parsed.post is not None: + parts.append(f".post{parsed.post}") + + # Development release + if parsed.dev is not None: + parts.append(f".dev{parsed.dev}") + + # Local version segment + if parsed.local is not None: + parts.append(f"+{parsed.local}") + + return "".join(parts) + + +def parse_wheel_filename( + filename: str, +) -> Tuple[NormalizedName, Version, BuildTag, FrozenSet[Tag]]: + if not filename.endswith(".whl"): + raise InvalidWheelFilename( + f"Invalid wheel filename (extension must be '.whl'): {filename}" + ) + + filename = filename[:-4] + dashes = filename.count("-") + if dashes not in (4, 5): + raise InvalidWheelFilename( + f"Invalid wheel filename (wrong number of parts): {filename}" + ) + + parts = filename.split("-", dashes - 2) + name_part = parts[0] + # See PEP 427 for the rules on escaping the project name. + if "__" in name_part or re.match(r"^[\w\d._]*$", name_part, re.UNICODE) is None: + raise InvalidWheelFilename(f"Invalid project name: {filename}") + name = canonicalize_name(name_part) + + try: + version = Version(parts[1]) + except InvalidVersion as e: + raise InvalidWheelFilename( + f"Invalid wheel filename (invalid version): {filename}" + ) from e + + if dashes == 5: + build_part = parts[2] + build_match = _build_tag_regex.match(build_part) + if build_match is None: + raise InvalidWheelFilename( + f"Invalid build number: {build_part} in '{filename}'" + ) + build = cast(BuildTag, (int(build_match.group(1)), build_match.group(2))) + else: + build = () + tags = parse_tag(parts[-1]) + return (name, version, build, tags) + + +def parse_sdist_filename(filename: str) -> Tuple[NormalizedName, Version]: + if filename.endswith(".tar.gz"): + file_stem = filename[: -len(".tar.gz")] + elif filename.endswith(".zip"): + file_stem = filename[: -len(".zip")] + else: + raise InvalidSdistFilename( + f"Invalid sdist filename (extension must be '.tar.gz' or '.zip'):" + f" {filename}" + ) + + # We are requiring a PEP 440 version, which cannot contain dashes, + # so we split on the last dash. + name_part, sep, version_part = file_stem.rpartition("-") + if not sep: + raise InvalidSdistFilename(f"Invalid sdist filename: {filename}") + + name = canonicalize_name(name_part) + + try: + version = Version(version_part) + except InvalidVersion as e: + raise InvalidSdistFilename( + f"Invalid sdist filename (invalid version): {filename}" + ) from e + + return (name, version) diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/version.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/version.py new file mode 100644 index 0000000000000000000000000000000000000000..cda8e99935c8d92010b84437ae83d75031245d61 --- /dev/null +++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/wheel/vendored/packaging/version.py @@ -0,0 +1,561 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. +""" +.. testsetup:: + + from packaging.version import parse, Version +""" + +import itertools +import re +from typing import Any, Callable, NamedTuple, Optional, SupportsInt, Tuple, Union + +from ._structures import Infinity, InfinityType, NegativeInfinity, NegativeInfinityType + +__all__ = ["VERSION_PATTERN", "parse", "Version", "InvalidVersion"] + +LocalType = Tuple[Union[int, str], ...] + +CmpPrePostDevType = Union[InfinityType, NegativeInfinityType, Tuple[str, int]] +CmpLocalType = Union[ + NegativeInfinityType, + Tuple[Union[Tuple[int, str], Tuple[NegativeInfinityType, Union[int, str]]], ...], +] +CmpKey = Tuple[ + int, + Tuple[int, ...], + CmpPrePostDevType, + CmpPrePostDevType, + CmpPrePostDevType, + CmpLocalType, +] +VersionComparisonMethod = Callable[[CmpKey, CmpKey], bool] + + +class _Version(NamedTuple): + epoch: int + release: Tuple[int, ...] + dev: Optional[Tuple[str, int]] + pre: Optional[Tuple[str, int]] + post: Optional[Tuple[str, int]] + local: Optional[LocalType] + + +def parse(version: str) -> "Version": + """Parse the given version string. + + >>> parse('1.0.dev1') + + + :param version: The version string to parse. + :raises InvalidVersion: When the version string is not a valid version. + """ + return Version(version) + + +class InvalidVersion(ValueError): + """Raised when a version string is not a valid version. + + >>> Version("invalid") + Traceback (most recent call last): + ... + packaging.version.InvalidVersion: Invalid version: 'invalid' + """ + + +class _BaseVersion: + _key: Tuple[Any, ...] + + def __hash__(self) -> int: + return hash(self._key) + + # Please keep the duplicated `isinstance` check + # in the six comparisons hereunder + # unless you find a way to avoid adding overhead function calls. + def __lt__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key < other._key + + def __le__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key <= other._key + + def __eq__(self, other: object) -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key == other._key + + def __ge__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key >= other._key + + def __gt__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key > other._key + + def __ne__(self, other: object) -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key != other._key + + +# Deliberately not anchored to the start and end of the string, to make it +# easier for 3rd party code to reuse +_VERSION_PATTERN = r""" + v? + (?: + (?:(?P[0-9]+)!)? # epoch + (?P[0-9]+(?:\.[0-9]+)*) # release segment + (?P
                                          # pre-release
+            [-_\.]?
+            (?Palpha|a|beta|b|preview|pre|c|rc)
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+        (?P                                         # post release
+            (?:-(?P[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?Ppost|rev|r)
+                [-_\.]?
+                (?P[0-9]+)?
+            )
+        )?
+        (?P                                          # dev release
+            [-_\.]?
+            (?Pdev)
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+    )
+    (?:\+(?P[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+VERSION_PATTERN = _VERSION_PATTERN
+"""
+A string containing the regular expression used to match a valid version.
+
+The pattern is not anchored at either end, and is intended for embedding in larger
+expressions (for example, matching a version number as part of a file name). The
+regular expression should be compiled with the ``re.VERBOSE`` and ``re.IGNORECASE``
+flags set.
+
+:meta hide-value:
+"""
+
+
+class Version(_BaseVersion):
+    """This class abstracts handling of a project's versions.
+
+    A :class:`Version` instance is comparison aware and can be compared and
+    sorted using the standard Python interfaces.
+
+    >>> v1 = Version("1.0a5")
+    >>> v2 = Version("1.0")
+    >>> v1
+    
+    >>> v2
+    
+    >>> v1 < v2
+    True
+    >>> v1 == v2
+    False
+    >>> v1 > v2
+    False
+    >>> v1 >= v2
+    False
+    >>> v1 <= v2
+    True
+    """
+
+    _regex = re.compile(r"^\s*" + VERSION_PATTERN + r"\s*$", re.VERBOSE | re.IGNORECASE)
+    _key: CmpKey
+
+    def __init__(self, version: str) -> None:
+        """Initialize a Version object.
+
+        :param version:
+            The string representation of a version which will be parsed and normalized
+            before use.
+        :raises InvalidVersion:
+            If the ``version`` does not conform to PEP 440 in any way then this
+            exception will be raised.
+        """
+
+        # Validate the version and parse it into pieces
+        match = self._regex.search(version)
+        if not match:
+            raise InvalidVersion(f"Invalid version: '{version}'")
+
+        # Store the parsed out pieces of the version
+        self._version = _Version(
+            epoch=int(match.group("epoch")) if match.group("epoch") else 0,
+            release=tuple(int(i) for i in match.group("release").split(".")),
+            pre=_parse_letter_version(match.group("pre_l"), match.group("pre_n")),
+            post=_parse_letter_version(
+                match.group("post_l"), match.group("post_n1") or match.group("post_n2")
+            ),
+            dev=_parse_letter_version(match.group("dev_l"), match.group("dev_n")),
+            local=_parse_local_version(match.group("local")),
+        )
+
+        # Generate a key which will be used for sorting
+        self._key = _cmpkey(
+            self._version.epoch,
+            self._version.release,
+            self._version.pre,
+            self._version.post,
+            self._version.dev,
+            self._version.local,
+        )
+
+    def __repr__(self) -> str:
+        """A representation of the Version that shows all internal state.
+
+        >>> Version('1.0.0')
+        
+        """
+        return f""
+
+    def __str__(self) -> str:
+        """A string representation of the version that can be rounded-tripped.
+
+        >>> str(Version("1.0a5"))
+        '1.0a5'
+        """
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append(f"{self.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        # Pre-release
+        if self.pre is not None:
+            parts.append("".join(str(x) for x in self.pre))
+
+        # Post-release
+        if self.post is not None:
+            parts.append(f".post{self.post}")
+
+        # Development release
+        if self.dev is not None:
+            parts.append(f".dev{self.dev}")
+
+        # Local version segment
+        if self.local is not None:
+            parts.append(f"+{self.local}")
+
+        return "".join(parts)
+
+    @property
+    def epoch(self) -> int:
+        """The epoch of the version.
+
+        >>> Version("2.0.0").epoch
+        0
+        >>> Version("1!2.0.0").epoch
+        1
+        """
+        return self._version.epoch
+
+    @property
+    def release(self) -> Tuple[int, ...]:
+        """The components of the "release" segment of the version.
+
+        >>> Version("1.2.3").release
+        (1, 2, 3)
+        >>> Version("2.0.0").release
+        (2, 0, 0)
+        >>> Version("1!2.0.0.post0").release
+        (2, 0, 0)
+
+        Includes trailing zeroes but not the epoch or any pre-release / development /
+        post-release suffixes.
+        """
+        return self._version.release
+
+    @property
+    def pre(self) -> Optional[Tuple[str, int]]:
+        """The pre-release segment of the version.
+
+        >>> print(Version("1.2.3").pre)
+        None
+        >>> Version("1.2.3a1").pre
+        ('a', 1)
+        >>> Version("1.2.3b1").pre
+        ('b', 1)
+        >>> Version("1.2.3rc1").pre
+        ('rc', 1)
+        """
+        return self._version.pre
+
+    @property
+    def post(self) -> Optional[int]:
+        """The post-release number of the version.
+
+        >>> print(Version("1.2.3").post)
+        None
+        >>> Version("1.2.3.post1").post
+        1
+        """
+        return self._version.post[1] if self._version.post else None
+
+    @property
+    def dev(self) -> Optional[int]:
+        """The development number of the version.
+
+        >>> print(Version("1.2.3").dev)
+        None
+        >>> Version("1.2.3.dev1").dev
+        1
+        """
+        return self._version.dev[1] if self._version.dev else None
+
+    @property
+    def local(self) -> Optional[str]:
+        """The local version segment of the version.
+
+        >>> print(Version("1.2.3").local)
+        None
+        >>> Version("1.2.3+abc").local
+        'abc'
+        """
+        if self._version.local:
+            return ".".join(str(x) for x in self._version.local)
+        else:
+            return None
+
+    @property
+    def public(self) -> str:
+        """The public portion of the version.
+
+        >>> Version("1.2.3").public
+        '1.2.3'
+        >>> Version("1.2.3+abc").public
+        '1.2.3'
+        >>> Version("1.2.3+abc.dev1").public
+        '1.2.3'
+        """
+        return str(self).split("+", 1)[0]
+
+    @property
+    def base_version(self) -> str:
+        """The "base version" of the version.
+
+        >>> Version("1.2.3").base_version
+        '1.2.3'
+        >>> Version("1.2.3+abc").base_version
+        '1.2.3'
+        >>> Version("1!1.2.3+abc.dev1").base_version
+        '1!1.2.3'
+
+        The "base version" is the public version of the project without any pre or post
+        release markers.
+        """
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append(f"{self.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        return "".join(parts)
+
+    @property
+    def is_prerelease(self) -> bool:
+        """Whether this version is a pre-release.
+
+        >>> Version("1.2.3").is_prerelease
+        False
+        >>> Version("1.2.3a1").is_prerelease
+        True
+        >>> Version("1.2.3b1").is_prerelease
+        True
+        >>> Version("1.2.3rc1").is_prerelease
+        True
+        >>> Version("1.2.3dev1").is_prerelease
+        True
+        """
+        return self.dev is not None or self.pre is not None
+
+    @property
+    def is_postrelease(self) -> bool:
+        """Whether this version is a post-release.
+
+        >>> Version("1.2.3").is_postrelease
+        False
+        >>> Version("1.2.3.post1").is_postrelease
+        True
+        """
+        return self.post is not None
+
+    @property
+    def is_devrelease(self) -> bool:
+        """Whether this version is a development release.
+
+        >>> Version("1.2.3").is_devrelease
+        False
+        >>> Version("1.2.3.dev1").is_devrelease
+        True
+        """
+        return self.dev is not None
+
+    @property
+    def major(self) -> int:
+        """The first item of :attr:`release` or ``0`` if unavailable.
+
+        >>> Version("1.2.3").major
+        1
+        """
+        return self.release[0] if len(self.release) >= 1 else 0
+
+    @property
+    def minor(self) -> int:
+        """The second item of :attr:`release` or ``0`` if unavailable.
+
+        >>> Version("1.2.3").minor
+        2
+        >>> Version("1").minor
+        0
+        """
+        return self.release[1] if len(self.release) >= 2 else 0
+
+    @property
+    def micro(self) -> int:
+        """The third item of :attr:`release` or ``0`` if unavailable.
+
+        >>> Version("1.2.3").micro
+        3
+        >>> Version("1").micro
+        0
+        """
+        return self.release[2] if len(self.release) >= 3 else 0
+
+
+def _parse_letter_version(
+    letter: Optional[str], number: Union[str, bytes, SupportsInt, None]
+) -> Optional[Tuple[str, int]]:
+    if letter:
+        # We consider there to be an implicit 0 in a pre-release if there is
+        # not a numeral associated with it.
+        if number is None:
+            number = 0
+
+        # We normalize any letters to their lower case form
+        letter = letter.lower()
+
+        # We consider some words to be alternate spellings of other words and
+        # in those cases we want to normalize the spellings to our preferred
+        # spelling.
+        if letter == "alpha":
+            letter = "a"
+        elif letter == "beta":
+            letter = "b"
+        elif letter in ["c", "pre", "preview"]:
+            letter = "rc"
+        elif letter in ["rev", "r"]:
+            letter = "post"
+
+        return letter, int(number)
+    if not letter and number:
+        # We assume if we are given a number, but we are not given a letter
+        # then this is using the implicit post release syntax (e.g. 1.0-1)
+        letter = "post"
+
+        return letter, int(number)
+
+    return None
+
+
+_local_version_separators = re.compile(r"[\._-]")
+
+
+def _parse_local_version(local: Optional[str]) -> Optional[LocalType]:
+    """
+    Takes a string like abc.1.twelve and turns it into ("abc", 1, "twelve").
+    """
+    if local is not None:
+        return tuple(
+            part.lower() if not part.isdigit() else int(part)
+            for part in _local_version_separators.split(local)
+        )
+    return None
+
+
+def _cmpkey(
+    epoch: int,
+    release: Tuple[int, ...],
+    pre: Optional[Tuple[str, int]],
+    post: Optional[Tuple[str, int]],
+    dev: Optional[Tuple[str, int]],
+    local: Optional[LocalType],
+) -> CmpKey:
+    # When we compare a release version, we want to compare it with all of the
+    # trailing zeros removed. So we'll use a reverse the list, drop all the now
+    # leading zeros until we come to something non zero, then take the rest
+    # re-reverse it back into the correct order and make it a tuple and use
+    # that for our sorting key.
+    _release = tuple(
+        reversed(list(itertools.dropwhile(lambda x: x == 0, reversed(release))))
+    )
+
+    # We need to "trick" the sorting algorithm to put 1.0.dev0 before 1.0a0.
+    # We'll do this by abusing the pre segment, but we _only_ want to do this
+    # if there is not a pre or a post segment. If we have one of those then
+    # the normal sorting rules will handle this case correctly.
+    if pre is None and post is None and dev is not None:
+        _pre: CmpPrePostDevType = NegativeInfinity
+    # Versions without a pre-release (except as noted above) should sort after
+    # those with one.
+    elif pre is None:
+        _pre = Infinity
+    else:
+        _pre = pre
+
+    # Versions without a post segment should sort before those with one.
+    if post is None:
+        _post: CmpPrePostDevType = NegativeInfinity
+
+    else:
+        _post = post
+
+    # Versions without a development segment should sort after those with one.
+    if dev is None:
+        _dev: CmpPrePostDevType = Infinity
+
+    else:
+        _dev = dev
+
+    if local is None:
+        # Versions without a local segment should sort before those with one.
+        _local: CmpLocalType = NegativeInfinity
+    else:
+        # Versions with a local segment need that segment parsed to implement
+        # the sorting rules in PEP440.
+        # - Alpha numeric segments sort before numeric segments
+        # - Alpha numeric segments sort lexicographically
+        # - Numeric segments sort numerically
+        # - Shorter versions sort before longer versions when the prefixes
+        #   match exactly
+        _local = tuple(
+            (i, "") if isinstance(i, int) else (NegativeInfinity, i) for i in local
+        )
+
+    return epoch, _release, _pre, _post, _dev, _local
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/INSTALLER b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/LICENSE b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..1bb5a44356f00884a71ceeefd24ded6caaba2418
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/LICENSE
@@ -0,0 +1,17 @@
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to
+deal in the Software without restriction, including without limitation the
+rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+sell copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+IN THE SOFTWARE.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/METADATA b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..1399281717f23d7a37cb8c56153afedf0c73c860
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/METADATA
@@ -0,0 +1,102 @@
+Metadata-Version: 2.1
+Name: zipp
+Version: 3.19.2
+Summary: Backport of pathlib-compatible object wrapper for zip files
+Author-email: "Jason R. Coombs" 
+Project-URL: Homepage, https://github.com/jaraco/zipp
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: MIT License
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Requires-Python: >=3.8
+Description-Content-Type: text/x-rst
+License-File: LICENSE
+Provides-Extra: doc
+Requires-Dist: sphinx >=3.5 ; extra == 'doc'
+Requires-Dist: jaraco.packaging >=9.3 ; extra == 'doc'
+Requires-Dist: rst.linker >=1.9 ; extra == 'doc'
+Requires-Dist: furo ; extra == 'doc'
+Requires-Dist: sphinx-lint ; extra == 'doc'
+Requires-Dist: jaraco.tidelift >=1.4 ; extra == 'doc'
+Provides-Extra: test
+Requires-Dist: pytest !=8.1.*,>=6 ; extra == 'test'
+Requires-Dist: pytest-checkdocs >=2.4 ; extra == 'test'
+Requires-Dist: pytest-cov ; extra == 'test'
+Requires-Dist: pytest-mypy ; extra == 'test'
+Requires-Dist: pytest-enabler >=2.2 ; extra == 'test'
+Requires-Dist: pytest-ruff >=0.2.1 ; extra == 'test'
+Requires-Dist: jaraco.itertools ; extra == 'test'
+Requires-Dist: jaraco.functools ; extra == 'test'
+Requires-Dist: more-itertools ; extra == 'test'
+Requires-Dist: big-O ; extra == 'test'
+Requires-Dist: pytest-ignore-flaky ; extra == 'test'
+Requires-Dist: jaraco.test ; extra == 'test'
+Requires-Dist: importlib-resources ; (python_version < "3.9") and extra == 'test'
+
+.. image:: https://img.shields.io/pypi/v/zipp.svg
+   :target: https://pypi.org/project/zipp
+
+.. image:: https://img.shields.io/pypi/pyversions/zipp.svg
+
+.. image:: https://github.com/jaraco/zipp/actions/workflows/main.yml/badge.svg
+   :target: https://github.com/jaraco/zipp/actions?query=workflow%3A%22tests%22
+   :alt: tests
+
+.. image:: https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/charliermarsh/ruff/main/assets/badge/v2.json
+    :target: https://github.com/astral-sh/ruff
+    :alt: Ruff
+
+.. .. image:: https://readthedocs.org/projects/PROJECT_RTD/badge/?version=latest
+..    :target: https://PROJECT_RTD.readthedocs.io/en/latest/?badge=latest
+
+.. image:: https://img.shields.io/badge/skeleton-2024-informational
+   :target: https://blog.jaraco.com/skeleton
+
+.. image:: https://tidelift.com/badges/package/pypi/zipp
+   :target: https://tidelift.com/subscription/pkg/pypi-zipp?utm_source=pypi-zipp&utm_medium=readme
+
+
+A pathlib-compatible Zipfile object wrapper. Official backport of the standard library
+`Path object `_.
+
+
+Compatibility
+=============
+
+New features are introduced in this third-party library and later merged
+into CPython. The following table indicates which versions of this library
+were contributed to different versions in the standard library:
+
+.. list-table::
+   :header-rows: 1
+
+   * - zipp
+     - stdlib
+   * - 3.18
+     - 3.13
+   * - 3.16
+     - 3.12
+   * - 3.5
+     - 3.11
+   * - 3.2
+     - 3.10
+   * - 3.3 ??
+     - 3.9
+   * - 1.0
+     - 3.8
+
+
+Usage
+=====
+
+Use ``zipp.Path`` in place of ``zipfile.Path`` on any Python.
+
+For Enterprise
+==============
+
+Available as part of the Tidelift Subscription.
+
+This project and the maintainers of thousands of other packages are working with Tidelift to deliver one enterprise subscription that covers all of the open source you use.
+
+`Learn more `_.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/RECORD b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..77c02835d891989ded4fbb04d1fdbdb92c208c10
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/RECORD
@@ -0,0 +1,15 @@
+zipp-3.19.2.dist-info/INSTALLER,sha256=zuuue4knoyJ-UwPPXg8fezS7VCrXJQrAP7zeNuwvFQg,4
+zipp-3.19.2.dist-info/LICENSE,sha256=htoPAa6uRjSKPD1GUZXcHOzN55956HdppkuNoEsqR0E,1023
+zipp-3.19.2.dist-info/METADATA,sha256=UIrk_kMIHGSwsKKChYizqMw0MMZpPRZ2ZiVpQAsN_bE,3575
+zipp-3.19.2.dist-info/RECORD,,
+zipp-3.19.2.dist-info/REQUESTED,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+zipp-3.19.2.dist-info/WHEEL,sha256=GJ7t_kWBFywbagK5eo9IoUwLW6oyOeTKmQ-9iHFVNxQ,92
+zipp-3.19.2.dist-info/top_level.txt,sha256=iAbdoSHfaGqBfVb2XuR9JqSQHCoOsOtG6y9C_LSpqFw,5
+zipp/__init__.py,sha256=QuI1g00G4fRAcGt-HqbV0oWIkmSgedCGGYsHHYzNa8A,13412
+zipp/__pycache__/__init__.cpython-312.pyc,,
+zipp/__pycache__/glob.cpython-312.pyc,,
+zipp/compat/__init__.py,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+zipp/compat/__pycache__/__init__.cpython-312.pyc,,
+zipp/compat/__pycache__/py310.cpython-312.pyc,,
+zipp/compat/py310.py,sha256=eZpkW0zRtunkhEh8jjX3gCGe22emoKCBJw72Zt4RkhA,219
+zipp/glob.py,sha256=etWpnfEoRyfUvrUsi6sTiGmErvPwe6HzY6pT8jg_lUI,3082
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/REQUESTED b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/REQUESTED
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/WHEEL b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..bab98d675883cc7567a79df485cd7b4f015e376f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/WHEEL
@@ -0,0 +1,5 @@
+Wheel-Version: 1.0
+Generator: bdist_wheel (0.43.0)
+Root-Is-Purelib: true
+Tag: py3-none-any
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/top_level.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/top_level.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e82f676f82a3381fa909d1e6578c7a22044fafca
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp-3.19.2.dist-info/top_level.txt
@@ -0,0 +1 @@
+zipp
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..d65297b8354b934f687de1ab79c1f8cdf30050ff
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/__init__.py
@@ -0,0 +1,501 @@
+import io
+import posixpath
+import zipfile
+import itertools
+import contextlib
+import pathlib
+import re
+import stat
+import sys
+
+from .compat.py310 import text_encoding
+from .glob import Translator
+
+
+__all__ = ['Path']
+
+
+def _parents(path):
+    """
+    Given a path with elements separated by
+    posixpath.sep, generate all parents of that path.
+
+    >>> list(_parents('b/d'))
+    ['b']
+    >>> list(_parents('/b/d/'))
+    ['/b']
+    >>> list(_parents('b/d/f/'))
+    ['b/d', 'b']
+    >>> list(_parents('b'))
+    []
+    >>> list(_parents(''))
+    []
+    """
+    return itertools.islice(_ancestry(path), 1, None)
+
+
+def _ancestry(path):
+    """
+    Given a path with elements separated by
+    posixpath.sep, generate all elements of that path
+
+    >>> list(_ancestry('b/d'))
+    ['b/d', 'b']
+    >>> list(_ancestry('/b/d/'))
+    ['/b/d', '/b']
+    >>> list(_ancestry('b/d/f/'))
+    ['b/d/f', 'b/d', 'b']
+    >>> list(_ancestry('b'))
+    ['b']
+    >>> list(_ancestry(''))
+    []
+    """
+    path = path.rstrip(posixpath.sep)
+    while path and path != posixpath.sep:
+        yield path
+        path, tail = posixpath.split(path)
+
+
+_dedupe = dict.fromkeys
+"""Deduplicate an iterable in original order"""
+
+
+def _difference(minuend, subtrahend):
+    """
+    Return items in minuend not in subtrahend, retaining order
+    with O(1) lookup.
+    """
+    return itertools.filterfalse(set(subtrahend).__contains__, minuend)
+
+
+class InitializedState:
+    """
+    Mix-in to save the initialization state for pickling.
+    """
+
+    def __init__(self, *args, **kwargs):
+        self.__args = args
+        self.__kwargs = kwargs
+        super().__init__(*args, **kwargs)
+
+    def __getstate__(self):
+        return self.__args, self.__kwargs
+
+    def __setstate__(self, state):
+        args, kwargs = state
+        super().__init__(*args, **kwargs)
+
+
+class SanitizedNames:
+    """
+    ZipFile mix-in to ensure names are sanitized.
+    """
+
+    def namelist(self):
+        return list(map(self._sanitize, super().namelist()))
+
+    @staticmethod
+    def _sanitize(name):
+        r"""
+        Ensure a relative path with posix separators and no dot names.
+
+        Modeled after
+        https://github.com/python/cpython/blob/bcc1be39cb1d04ad9fc0bd1b9193d3972835a57c/Lib/zipfile/__init__.py#L1799-L1813
+        but provides consistent cross-platform behavior.
+
+        >>> san = SanitizedNames._sanitize
+        >>> san('/foo/bar')
+        'foo/bar'
+        >>> san('//foo.txt')
+        'foo.txt'
+        >>> san('foo/.././bar.txt')
+        'foo/bar.txt'
+        >>> san('foo../.bar.txt')
+        'foo../.bar.txt'
+        >>> san('\\foo\\bar.txt')
+        'foo/bar.txt'
+        >>> san('D:\\foo.txt')
+        'D/foo.txt'
+        >>> san('\\\\server\\share\\file.txt')
+        'server/share/file.txt'
+        >>> san('\\\\?\\GLOBALROOT\\Volume3')
+        '?/GLOBALROOT/Volume3'
+        >>> san('\\\\.\\PhysicalDrive1\\root')
+        'PhysicalDrive1/root'
+
+        Retain any trailing slash.
+        >>> san('abc/')
+        'abc/'
+
+        Raises a ValueError if the result is empty.
+        >>> san('../..')
+        Traceback (most recent call last):
+        ...
+        ValueError: Empty filename
+        """
+
+        def allowed(part):
+            return part and part not in {'..', '.'}
+
+        # Remove the drive letter.
+        # Don't use ntpath.splitdrive, because that also strips UNC paths
+        bare = re.sub('^([A-Z]):', r'\1', name, flags=re.IGNORECASE)
+        clean = bare.replace('\\', '/')
+        parts = clean.split('/')
+        joined = '/'.join(filter(allowed, parts))
+        if not joined:
+            raise ValueError("Empty filename")
+        return joined + '/' * name.endswith('/')
+
+
+class CompleteDirs(InitializedState, SanitizedNames, zipfile.ZipFile):
+    """
+    A ZipFile subclass that ensures that implied directories
+    are always included in the namelist.
+
+    >>> list(CompleteDirs._implied_dirs(['foo/bar.txt', 'foo/bar/baz.txt']))
+    ['foo/', 'foo/bar/']
+    >>> list(CompleteDirs._implied_dirs(['foo/bar.txt', 'foo/bar/baz.txt', 'foo/bar/']))
+    ['foo/']
+    """
+
+    @staticmethod
+    def _implied_dirs(names):
+        parents = itertools.chain.from_iterable(map(_parents, names))
+        as_dirs = (p + posixpath.sep for p in parents)
+        return _dedupe(_difference(as_dirs, names))
+
+    def namelist(self):
+        names = super().namelist()
+        return names + list(self._implied_dirs(names))
+
+    def _name_set(self):
+        return set(self.namelist())
+
+    def resolve_dir(self, name):
+        """
+        If the name represents a directory, return that name
+        as a directory (with the trailing slash).
+        """
+        names = self._name_set()
+        dirname = name + '/'
+        dir_match = name not in names and dirname in names
+        return dirname if dir_match else name
+
+    def getinfo(self, name):
+        """
+        Supplement getinfo for implied dirs.
+        """
+        try:
+            return super().getinfo(name)
+        except KeyError:
+            if not name.endswith('/') or name not in self._name_set():
+                raise
+            return zipfile.ZipInfo(filename=name)
+
+    @classmethod
+    def make(cls, source):
+        """
+        Given a source (filename or zipfile), return an
+        appropriate CompleteDirs subclass.
+        """
+        if isinstance(source, CompleteDirs):
+            return source
+
+        if not isinstance(source, zipfile.ZipFile):
+            return cls(source)
+
+        # Only allow for FastLookup when supplied zipfile is read-only
+        if 'r' not in source.mode:
+            cls = CompleteDirs
+
+        source.__class__ = cls
+        return source
+
+    @classmethod
+    def inject(cls, zf: zipfile.ZipFile) -> zipfile.ZipFile:
+        """
+        Given a writable zip file zf, inject directory entries for
+        any directories implied by the presence of children.
+        """
+        for name in cls._implied_dirs(zf.namelist()):
+            zf.writestr(name, b"")
+        return zf
+
+
+class FastLookup(CompleteDirs):
+    """
+    ZipFile subclass to ensure implicit
+    dirs exist and are resolved rapidly.
+    """
+
+    def namelist(self):
+        with contextlib.suppress(AttributeError):
+            return self.__names
+        self.__names = super().namelist()
+        return self.__names
+
+    def _name_set(self):
+        with contextlib.suppress(AttributeError):
+            return self.__lookup
+        self.__lookup = super()._name_set()
+        return self.__lookup
+
+
+def _extract_text_encoding(encoding=None, *args, **kwargs):
+    # compute stack level so that the caller of the caller sees any warning.
+    is_pypy = sys.implementation.name == 'pypy'
+    stack_level = 3 + is_pypy
+    return text_encoding(encoding, stack_level), args, kwargs
+
+
+class Path:
+    """
+    A :class:`importlib.resources.abc.Traversable` interface for zip files.
+
+    Implements many of the features users enjoy from
+    :class:`pathlib.Path`.
+
+    Consider a zip file with this structure::
+
+        .
+        ├── a.txt
+        └── b
+            ├── c.txt
+            └── d
+                └── e.txt
+
+    >>> data = io.BytesIO()
+    >>> zf = zipfile.ZipFile(data, 'w')
+    >>> zf.writestr('a.txt', 'content of a')
+    >>> zf.writestr('b/c.txt', 'content of c')
+    >>> zf.writestr('b/d/e.txt', 'content of e')
+    >>> zf.filename = 'mem/abcde.zip'
+
+    Path accepts the zipfile object itself or a filename
+
+    >>> path = Path(zf)
+
+    From there, several path operations are available.
+
+    Directory iteration (including the zip file itself):
+
+    >>> a, b = path.iterdir()
+    >>> a
+    Path('mem/abcde.zip', 'a.txt')
+    >>> b
+    Path('mem/abcde.zip', 'b/')
+
+    name property:
+
+    >>> b.name
+    'b'
+
+    join with divide operator:
+
+    >>> c = b / 'c.txt'
+    >>> c
+    Path('mem/abcde.zip', 'b/c.txt')
+    >>> c.name
+    'c.txt'
+
+    Read text:
+
+    >>> c.read_text(encoding='utf-8')
+    'content of c'
+
+    existence:
+
+    >>> c.exists()
+    True
+    >>> (b / 'missing.txt').exists()
+    False
+
+    Coercion to string:
+
+    >>> import os
+    >>> str(c).replace(os.sep, posixpath.sep)
+    'mem/abcde.zip/b/c.txt'
+
+    At the root, ``name``, ``filename``, and ``parent``
+    resolve to the zipfile.
+
+    >>> str(path)
+    'mem/abcde.zip/'
+    >>> path.name
+    'abcde.zip'
+    >>> path.filename == pathlib.Path('mem/abcde.zip')
+    True
+    >>> str(path.parent)
+    'mem'
+
+    If the zipfile has no filename, such attributes are not
+    valid and accessing them will raise an Exception.
+
+    >>> zf.filename = None
+    >>> path.name
+    Traceback (most recent call last):
+    ...
+    TypeError: ...
+
+    >>> path.filename
+    Traceback (most recent call last):
+    ...
+    TypeError: ...
+
+    >>> path.parent
+    Traceback (most recent call last):
+    ...
+    TypeError: ...
+
+    # workaround python/cpython#106763
+    >>> pass
+    """
+
+    __repr = "{self.__class__.__name__}({self.root.filename!r}, {self.at!r})"
+
+    def __init__(self, root, at=""):
+        """
+        Construct a Path from a ZipFile or filename.
+
+        Note: When the source is an existing ZipFile object,
+        its type (__class__) will be mutated to a
+        specialized type. If the caller wishes to retain the
+        original type, the caller should either create a
+        separate ZipFile object or pass a filename.
+        """
+        self.root = FastLookup.make(root)
+        self.at = at
+
+    def __eq__(self, other):
+        """
+        >>> Path(zipfile.ZipFile(io.BytesIO(), 'w')) == 'foo'
+        False
+        """
+        if self.__class__ is not other.__class__:
+            return NotImplemented
+        return (self.root, self.at) == (other.root, other.at)
+
+    def __hash__(self):
+        return hash((self.root, self.at))
+
+    def open(self, mode='r', *args, pwd=None, **kwargs):
+        """
+        Open this entry as text or binary following the semantics
+        of ``pathlib.Path.open()`` by passing arguments through
+        to io.TextIOWrapper().
+        """
+        if self.is_dir():
+            raise IsADirectoryError(self)
+        zip_mode = mode[0]
+        if not self.exists() and zip_mode == 'r':
+            raise FileNotFoundError(self)
+        stream = self.root.open(self.at, zip_mode, pwd=pwd)
+        if 'b' in mode:
+            if args or kwargs:
+                raise ValueError("encoding args invalid for binary operation")
+            return stream
+        # Text mode:
+        encoding, args, kwargs = _extract_text_encoding(*args, **kwargs)
+        return io.TextIOWrapper(stream, encoding, *args, **kwargs)
+
+    def _base(self):
+        return pathlib.PurePosixPath(self.at or self.root.filename)
+
+    @property
+    def name(self):
+        return self._base().name
+
+    @property
+    def suffix(self):
+        return self._base().suffix
+
+    @property
+    def suffixes(self):
+        return self._base().suffixes
+
+    @property
+    def stem(self):
+        return self._base().stem
+
+    @property
+    def filename(self):
+        return pathlib.Path(self.root.filename).joinpath(self.at)
+
+    def read_text(self, *args, **kwargs):
+        encoding, args, kwargs = _extract_text_encoding(*args, **kwargs)
+        with self.open('r', encoding, *args, **kwargs) as strm:
+            return strm.read()
+
+    def read_bytes(self):
+        with self.open('rb') as strm:
+            return strm.read()
+
+    def _is_child(self, path):
+        return posixpath.dirname(path.at.rstrip("/")) == self.at.rstrip("/")
+
+    def _next(self, at):
+        return self.__class__(self.root, at)
+
+    def is_dir(self):
+        return not self.at or self.at.endswith("/")
+
+    def is_file(self):
+        return self.exists() and not self.is_dir()
+
+    def exists(self):
+        return self.at in self.root._name_set()
+
+    def iterdir(self):
+        if not self.is_dir():
+            raise ValueError("Can't listdir a file")
+        subs = map(self._next, self.root.namelist())
+        return filter(self._is_child, subs)
+
+    def match(self, path_pattern):
+        return pathlib.PurePosixPath(self.at).match(path_pattern)
+
+    def is_symlink(self):
+        """
+        Return whether this path is a symlink.
+        """
+        info = self.root.getinfo(self.at)
+        mode = info.external_attr >> 16
+        return stat.S_ISLNK(mode)
+
+    def glob(self, pattern):
+        if not pattern:
+            raise ValueError(f"Unacceptable pattern: {pattern!r}")
+
+        prefix = re.escape(self.at)
+        tr = Translator(seps='/')
+        matches = re.compile(prefix + tr.translate(pattern)).fullmatch
+        names = (data.filename for data in self.root.filelist)
+        return map(self._next, filter(matches, names))
+
+    def rglob(self, pattern):
+        return self.glob(f'**/{pattern}')
+
+    def relative_to(self, other, *extra):
+        return posixpath.relpath(str(self), str(other.joinpath(*extra)))
+
+    def __str__(self):
+        return posixpath.join(self.root.filename, self.at)
+
+    def __repr__(self):
+        return self.__repr.format(self=self)
+
+    def joinpath(self, *other):
+        next = posixpath.join(self.at, *other)
+        return self._next(self.root.resolve_dir(next))
+
+    __truediv__ = joinpath
+
+    @property
+    def parent(self):
+        if not self.at:
+            return self.filename.parent
+        parent_at = posixpath.dirname(self.at.rstrip('/'))
+        if parent_at:
+            parent_at += '/'
+        return self._next(parent_at)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/compat/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/compat/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/compat/py310.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/compat/py310.py
new file mode 100644
index 0000000000000000000000000000000000000000..d5ca53e037b267ff1b196b3b208dea0acdebe4c5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/compat/py310.py
@@ -0,0 +1,11 @@
+import sys
+import io
+
+
+def _text_encoding(encoding, stacklevel=2, /):  # pragma: no cover
+    return encoding
+
+
+text_encoding = (
+    io.text_encoding if sys.version_info > (3, 10) else _text_encoding  # type: ignore
+)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/glob.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/glob.py
new file mode 100644
index 0000000000000000000000000000000000000000..69c41d77c3f6549bd58d778dfe978a6ed728ede5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/_vendor/zipp/glob.py
@@ -0,0 +1,106 @@
+import os
+import re
+
+
+_default_seps = os.sep + str(os.altsep) * bool(os.altsep)
+
+
+class Translator:
+    """
+    >>> Translator('xyz')
+    Traceback (most recent call last):
+    ...
+    AssertionError: Invalid separators
+
+    >>> Translator('')
+    Traceback (most recent call last):
+    ...
+    AssertionError: Invalid separators
+    """
+
+    seps: str
+
+    def __init__(self, seps: str = _default_seps):
+        assert seps and set(seps) <= set(_default_seps), "Invalid separators"
+        self.seps = seps
+
+    def translate(self, pattern):
+        """
+        Given a glob pattern, produce a regex that matches it.
+        """
+        return self.extend(self.translate_core(pattern))
+
+    def extend(self, pattern):
+        r"""
+        Extend regex for pattern-wide concerns.
+
+        Apply '(?s:)' to create a non-matching group that
+        matches newlines (valid on Unix).
+
+        Append '\Z' to imply fullmatch even when match is used.
+        """
+        return rf'(?s:{pattern})\Z'
+
+    def translate_core(self, pattern):
+        r"""
+        Given a glob pattern, produce a regex that matches it.
+
+        >>> t = Translator()
+        >>> t.translate_core('*.txt').replace('\\\\', '')
+        '[^/]*\\.txt'
+        >>> t.translate_core('a?txt')
+        'a[^/]txt'
+        >>> t.translate_core('**/*').replace('\\\\', '')
+        '.*/[^/][^/]*'
+        """
+        self.restrict_rglob(pattern)
+        return ''.join(map(self.replace, separate(self.star_not_empty(pattern))))
+
+    def replace(self, match):
+        """
+        Perform the replacements for a match from :func:`separate`.
+        """
+        return match.group('set') or (
+            re.escape(match.group(0))
+            .replace('\\*\\*', r'.*')
+            .replace('\\*', rf'[^{re.escape(self.seps)}]*')
+            .replace('\\?', r'[^/]')
+        )
+
+    def restrict_rglob(self, pattern):
+        """
+        Raise ValueError if ** appears in anything but a full path segment.
+
+        >>> Translator().translate('**foo')
+        Traceback (most recent call last):
+        ...
+        ValueError: ** must appear alone in a path segment
+        """
+        seps_pattern = rf'[{re.escape(self.seps)}]+'
+        segments = re.split(seps_pattern, pattern)
+        if any('**' in segment and segment != '**' for segment in segments):
+            raise ValueError("** must appear alone in a path segment")
+
+    def star_not_empty(self, pattern):
+        """
+        Ensure that * will not match an empty segment.
+        """
+
+        def handle_segment(match):
+            segment = match.group(0)
+            return '?*' if segment == '*' else segment
+
+        not_seps_pattern = rf'[^{re.escape(self.seps)}]+'
+        return re.sub(not_seps_pattern, handle_segment, pattern)
+
+
+def separate(pattern):
+    """
+    Separate out character sets to avoid translating their contents.
+
+    >>> [m.group(0) for m in separate('*.txt')]
+    ['*.txt']
+    >>> [m.group(0) for m in separate('a[?]txt')]
+    ['a', '[?]', 'txt']
+    """
+    return re.finditer(r'([^\[]+)|(?P[\[].*?[\]])|([\[][^\]]*$)', pattern)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..50e6c2f54f38db5bf5175a7a4db219815785f1bc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/__init__.py
@@ -0,0 +1,21 @@
+# mypy: disable_error_code=call-overload
+# pyright: reportCallIssue=false, reportArgumentType=false
+# Can't disable on the exact line because distutils doesn't exists on Python 3.12
+# and type-checkers aren't aware of distutils_hack,
+# causing distutils.command.bdist.bdist.format_commands to be Any.
+
+import sys
+
+from distutils.command.bdist import bdist
+
+if 'egg' not in bdist.format_commands:
+    try:
+        # format_commands is a dict in vendored distutils
+        # It used to be a list in older (stdlib) distutils
+        # We support both for backwards compatibility
+        bdist.format_commands['egg'] = ('bdist_egg', "Python .egg file")
+    except TypeError:
+        bdist.format_command['egg'] = ('bdist_egg', "Python .egg file")
+        bdist.format_commands.append('egg')
+
+del bdist, sys
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/_requirestxt.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/_requirestxt.py
new file mode 100644
index 0000000000000000000000000000000000000000..9029b125141158d4b12de1db8215819ce6ccf437
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/_requirestxt.py
@@ -0,0 +1,131 @@
+"""Helper code used to generate ``requires.txt`` files in the egg-info directory.
+
+The ``requires.txt`` file has an specific format:
+    - Environment markers need to be part of the section headers and
+      should not be part of the requirement spec itself.
+
+See https://setuptools.pypa.io/en/latest/deprecated/python_eggs.html#requires-txt
+"""
+
+from __future__ import annotations
+
+import io
+from collections import defaultdict
+from collections.abc import Mapping
+from itertools import filterfalse
+from typing import TypeVar
+
+from jaraco.text import yield_lines
+from packaging.requirements import Requirement
+
+from .. import _reqs
+from .._reqs import _StrOrIter
+
+# dict can work as an ordered set
+_T = TypeVar("_T")
+_Ordered = dict[_T, None]
+
+
+def _prepare(
+    install_requires: _StrOrIter, extras_require: Mapping[str, _StrOrIter]
+) -> tuple[list[str], dict[str, list[str]]]:
+    """Given values for ``install_requires`` and ``extras_require``
+    create modified versions in a way that can be written in ``requires.txt``
+    """
+    extras = _convert_extras_requirements(extras_require)
+    return _move_install_requirements_markers(install_requires, extras)
+
+
+def _convert_extras_requirements(
+    extras_require: Mapping[str, _StrOrIter],
+) -> defaultdict[str, _Ordered[Requirement]]:
+    """
+    Convert requirements in `extras_require` of the form
+    `"extra": ["barbazquux; {marker}"]` to
+    `"extra:{marker}": ["barbazquux"]`.
+    """
+    output = defaultdict[str, _Ordered[Requirement]](dict)
+    for section, v in extras_require.items():
+        # Do not strip empty sections.
+        output[section]
+        for r in _reqs.parse(v):
+            output[section + _suffix_for(r)].setdefault(r)
+
+    return output
+
+
+def _move_install_requirements_markers(
+    install_requires: _StrOrIter, extras_require: Mapping[str, _Ordered[Requirement]]
+) -> tuple[list[str], dict[str, list[str]]]:
+    """
+    The ``requires.txt`` file has an specific format:
+        - Environment markers need to be part of the section headers and
+          should not be part of the requirement spec itself.
+
+    Move requirements in ``install_requires`` that are using environment
+    markers ``extras_require``.
+    """
+
+    # divide the install_requires into two sets, simple ones still
+    # handled by install_requires and more complex ones handled by extras_require.
+
+    inst_reqs = list(_reqs.parse(install_requires))
+    simple_reqs = filter(_no_marker, inst_reqs)
+    complex_reqs = filterfalse(_no_marker, inst_reqs)
+    simple_install_requires = list(map(str, simple_reqs))
+
+    for r in complex_reqs:
+        extras_require[':' + str(r.marker)].setdefault(r)
+
+    expanded_extras = dict(
+        # list(dict.fromkeys(...))  ensures a list of unique strings
+        (k, list(dict.fromkeys(str(r) for r in map(_clean_req, v))))
+        for k, v in extras_require.items()
+    )
+
+    return simple_install_requires, expanded_extras
+
+
+def _suffix_for(req):
+    """Return the 'extras_require' suffix for a given requirement."""
+    return ':' + str(req.marker) if req.marker else ''
+
+
+def _clean_req(req):
+    """Given a Requirement, remove environment markers and return it"""
+    r = Requirement(str(req))  # create a copy before modifying
+    r.marker = None
+    return r
+
+
+def _no_marker(req):
+    return not req.marker
+
+
+def _write_requirements(stream, reqs):
+    lines = yield_lines(reqs or ())
+
+    def append_cr(line):
+        return line + '\n'
+
+    lines = map(append_cr, lines)
+    stream.writelines(lines)
+
+
+def write_requirements(cmd, basename, filename):
+    dist = cmd.distribution
+    data = io.StringIO()
+    install_requires, extras_require = _prepare(
+        dist.install_requires or (), dist.extras_require or {}
+    )
+    _write_requirements(data, install_requires)
+    for extra in sorted(extras_require):
+        data.write('\n[{extra}]\n'.format(**vars()))
+        _write_requirements(data, extras_require[extra])
+    cmd.write_or_delete_file("requirements", filename, data.getvalue())
+
+
+def write_setup_requirements(cmd, basename, filename):
+    data = io.StringIO()
+    _write_requirements(data, cmd.distribution.setup_requires)
+    cmd.write_or_delete_file("setup-requirements", filename, data.getvalue())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/alias.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/alias.py
new file mode 100644
index 0000000000000000000000000000000000000000..b8d74af71d4464abf899b9f872b5741f23167165
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/alias.py
@@ -0,0 +1,77 @@
+from setuptools.command.setopt import config_file, edit_config, option_base
+
+from distutils.errors import DistutilsOptionError
+
+
+def shquote(arg):
+    """Quote an argument for later parsing by shlex.split()"""
+    for c in '"', "'", "\\", "#":
+        if c in arg:
+            return repr(arg)
+    if arg.split() != [arg]:
+        return repr(arg)
+    return arg
+
+
+class alias(option_base):
+    """Define a shortcut that invokes one or more commands"""
+
+    description = "define a shortcut to invoke one or more commands"
+    command_consumes_arguments = True
+
+    user_options = [
+        ('remove', 'r', 'remove (unset) the alias'),
+    ] + option_base.user_options
+
+    boolean_options = option_base.boolean_options + ['remove']
+
+    def initialize_options(self):
+        option_base.initialize_options(self)
+        self.args = None
+        self.remove = None
+
+    def finalize_options(self) -> None:
+        option_base.finalize_options(self)
+        if self.remove and len(self.args) != 1:
+            raise DistutilsOptionError(
+                "Must specify exactly one argument (the alias name) when using --remove"
+            )
+
+    def run(self) -> None:
+        aliases = self.distribution.get_option_dict('aliases')
+
+        if not self.args:
+            print("Command Aliases")
+            print("---------------")
+            for alias in aliases:
+                print("setup.py alias", format_alias(alias, aliases))
+            return
+
+        elif len(self.args) == 1:
+            (alias,) = self.args
+            if self.remove:
+                command = None
+            elif alias in aliases:
+                print("setup.py alias", format_alias(alias, aliases))
+                return
+            else:
+                print(f"No alias definition found for {alias!r}")
+                return
+        else:
+            alias = self.args[0]
+            command = ' '.join(map(shquote, self.args[1:]))
+
+        edit_config(self.filename, {'aliases': {alias: command}}, self.dry_run)
+
+
+def format_alias(name, aliases):
+    source, command = aliases[name]
+    if source == config_file('global'):
+        source = '--global-config '
+    elif source == config_file('user'):
+        source = '--user-config '
+    elif source == config_file('local'):
+        source = ''
+    else:
+        source = f'--filename={source!r}'
+    return source + name + ' ' + command
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_egg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_egg.py
new file mode 100644
index 0000000000000000000000000000000000000000..7f66c3ba6a7f554e910800a21c5ccc3733abf07d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_egg.py
@@ -0,0 +1,479 @@
+"""setuptools.command.bdist_egg
+
+Build .egg distributions"""
+
+from __future__ import annotations
+
+import marshal
+import os
+import re
+import sys
+import textwrap
+from sysconfig import get_path, get_python_version
+from types import CodeType
+from typing import TYPE_CHECKING, Literal
+
+from setuptools import Command
+from setuptools.extension import Library
+
+from .._path import StrPathT, ensure_directory
+
+from distutils import log
+from distutils.dir_util import mkpath, remove_tree
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeAlias
+
+# Same as zipfile._ZipFileMode from typeshed
+_ZipFileMode: TypeAlias = Literal["r", "w", "x", "a"]
+
+
+def _get_purelib():
+    return get_path("purelib")
+
+
+def strip_module(filename):
+    if '.' in filename:
+        filename = os.path.splitext(filename)[0]
+    if filename.endswith('module'):
+        filename = filename[:-6]
+    return filename
+
+
+def sorted_walk(dir):
+    """Do os.walk in a reproducible way,
+    independent of indeterministic filesystem readdir order
+    """
+    for base, dirs, files in os.walk(dir):
+        dirs.sort()
+        files.sort()
+        yield base, dirs, files
+
+
+def write_stub(resource, pyfile) -> None:
+    _stub_template = textwrap.dedent(
+        """
+        def __bootstrap__():
+            global __bootstrap__, __loader__, __file__
+            import sys, pkg_resources, importlib.util
+            __file__ = pkg_resources.resource_filename(__name__, %r)
+            __loader__ = None; del __bootstrap__, __loader__
+            spec = importlib.util.spec_from_file_location(__name__,__file__)
+            mod = importlib.util.module_from_spec(spec)
+            spec.loader.exec_module(mod)
+        __bootstrap__()
+        """
+    ).lstrip()
+    with open(pyfile, 'w', encoding="utf-8") as f:
+        f.write(_stub_template % resource)
+
+
+class bdist_egg(Command):
+    description = 'create an "egg" distribution'
+
+    user_options = [
+        ('bdist-dir=', 'b', "temporary directory for creating the distribution"),
+        (
+            'plat-name=',
+            'p',
+            "platform name to embed in generated filenames "
+            "(by default uses `pkg_resources.get_build_platform()`)",
+        ),
+        ('exclude-source-files', None, "remove all .py files from the generated egg"),
+        (
+            'keep-temp',
+            'k',
+            "keep the pseudo-installation tree around after "
+            "creating the distribution archive",
+        ),
+        ('dist-dir=', 'd', "directory to put final built distributions in"),
+        ('skip-build', None, "skip rebuilding everything (for testing/debugging)"),
+    ]
+
+    boolean_options = ['keep-temp', 'skip-build', 'exclude-source-files']
+
+    def initialize_options(self):
+        self.bdist_dir = None
+        self.plat_name = None
+        self.keep_temp = False
+        self.dist_dir = None
+        self.skip_build = False
+        self.egg_output = None
+        self.exclude_source_files = None
+
+    def finalize_options(self) -> None:
+        ei_cmd = self.ei_cmd = self.get_finalized_command("egg_info")
+        self.egg_info = ei_cmd.egg_info
+
+        if self.bdist_dir is None:
+            bdist_base = self.get_finalized_command('bdist').bdist_base
+            self.bdist_dir = os.path.join(bdist_base, 'egg')
+
+        if self.plat_name is None:
+            from pkg_resources import get_build_platform
+
+            self.plat_name = get_build_platform()
+
+        self.set_undefined_options('bdist', ('dist_dir', 'dist_dir'))
+
+        if self.egg_output is None:
+            # Compute filename of the output egg
+            basename = ei_cmd._get_egg_basename(
+                py_version=get_python_version(),
+                platform=self.distribution.has_ext_modules() and self.plat_name,
+            )
+
+            self.egg_output = os.path.join(self.dist_dir, basename + '.egg')
+
+    def do_install_data(self) -> None:
+        # Hack for packages that install data to install's --install-lib
+        self.get_finalized_command('install').install_lib = self.bdist_dir
+
+        site_packages = os.path.normcase(os.path.realpath(_get_purelib()))
+        old, self.distribution.data_files = self.distribution.data_files, []
+
+        for item in old:
+            if isinstance(item, tuple) and len(item) == 2:
+                if os.path.isabs(item[0]):
+                    realpath = os.path.realpath(item[0])
+                    normalized = os.path.normcase(realpath)
+                    if normalized == site_packages or normalized.startswith(
+                        site_packages + os.sep
+                    ):
+                        item = realpath[len(site_packages) + 1 :], item[1]
+                        # XXX else: raise ???
+            self.distribution.data_files.append(item)
+
+        try:
+            log.info("installing package data to %s", self.bdist_dir)
+            self.call_command('install_data', force=False, root=None)
+        finally:
+            self.distribution.data_files = old
+
+    def get_outputs(self):
+        return [self.egg_output]
+
+    def call_command(self, cmdname, **kw):
+        """Invoke reinitialized command `cmdname` with keyword args"""
+        for dirname in INSTALL_DIRECTORY_ATTRS:
+            kw.setdefault(dirname, self.bdist_dir)
+        kw.setdefault('skip_build', self.skip_build)
+        kw.setdefault('dry_run', self.dry_run)
+        cmd = self.reinitialize_command(cmdname, **kw)
+        self.run_command(cmdname)
+        return cmd
+
+    def run(self):  # noqa: C901  # is too complex (14)  # FIXME
+        # Generate metadata first
+        self.run_command("egg_info")
+        # We run install_lib before install_data, because some data hacks
+        # pull their data path from the install_lib command.
+        log.info("installing library code to %s", self.bdist_dir)
+        instcmd = self.get_finalized_command('install')
+        old_root = instcmd.root
+        instcmd.root = None
+        if self.distribution.has_c_libraries() and not self.skip_build:
+            self.run_command('build_clib')
+        cmd = self.call_command('install_lib', warn_dir=False)
+        instcmd.root = old_root
+
+        all_outputs, ext_outputs = self.get_ext_outputs()
+        self.stubs = []
+        to_compile = []
+        for p, ext_name in enumerate(ext_outputs):
+            filename, _ext = os.path.splitext(ext_name)
+            pyfile = os.path.join(self.bdist_dir, strip_module(filename) + '.py')
+            self.stubs.append(pyfile)
+            log.info("creating stub loader for %s", ext_name)
+            if not self.dry_run:
+                write_stub(os.path.basename(ext_name), pyfile)
+            to_compile.append(pyfile)
+            ext_outputs[p] = ext_name.replace(os.sep, '/')
+
+        if to_compile:
+            cmd.byte_compile(to_compile)
+        if self.distribution.data_files:
+            self.do_install_data()
+
+        # Make the EGG-INFO directory
+        archive_root = self.bdist_dir
+        egg_info = os.path.join(archive_root, 'EGG-INFO')
+        self.mkpath(egg_info)
+        if self.distribution.scripts:
+            script_dir = os.path.join(egg_info, 'scripts')
+            log.info("installing scripts to %s", script_dir)
+            self.call_command('install_scripts', install_dir=script_dir, no_ep=True)
+
+        self.copy_metadata_to(egg_info)
+        native_libs = os.path.join(egg_info, "native_libs.txt")
+        if all_outputs:
+            log.info("writing %s", native_libs)
+            if not self.dry_run:
+                ensure_directory(native_libs)
+                with open(native_libs, 'wt', encoding="utf-8") as libs_file:
+                    libs_file.write('\n'.join(all_outputs))
+                    libs_file.write('\n')
+        elif os.path.isfile(native_libs):
+            log.info("removing %s", native_libs)
+            if not self.dry_run:
+                os.unlink(native_libs)
+
+        write_safety_flag(os.path.join(archive_root, 'EGG-INFO'), self.zip_safe())
+
+        if os.path.exists(os.path.join(self.egg_info, 'depends.txt')):
+            log.warn(
+                "WARNING: 'depends.txt' will not be used by setuptools 0.6!\n"
+                "Use the install_requires/extras_require setup() args instead."
+            )
+
+        if self.exclude_source_files:
+            self.zap_pyfiles()
+
+        # Make the archive
+        make_zipfile(
+            self.egg_output,
+            archive_root,
+            verbose=self.verbose,
+            dry_run=self.dry_run,
+            mode=self.gen_header(),
+        )
+        if not self.keep_temp:
+            remove_tree(self.bdist_dir, dry_run=self.dry_run)
+
+        # Add to 'Distribution.dist_files' so that the "upload" command works
+        getattr(self.distribution, 'dist_files', []).append((
+            'bdist_egg',
+            get_python_version(),
+            self.egg_output,
+        ))
+
+    def zap_pyfiles(self):
+        log.info("Removing .py files from temporary directory")
+        for base, dirs, files in walk_egg(self.bdist_dir):
+            for name in files:
+                path = os.path.join(base, name)
+
+                if name.endswith('.py'):
+                    log.debug("Deleting %s", path)
+                    os.unlink(path)
+
+                if base.endswith('__pycache__'):
+                    path_old = path
+
+                    pattern = r'(?P.+)\.(?P[^.]+)\.pyc'
+                    m = re.match(pattern, name)
+                    path_new = os.path.join(base, os.pardir, m.group('name') + '.pyc')
+                    log.info(f"Renaming file from [{path_old}] to [{path_new}]")
+                    try:
+                        os.remove(path_new)
+                    except OSError:
+                        pass
+                    os.rename(path_old, path_new)
+
+    def zip_safe(self):
+        safe = getattr(self.distribution, 'zip_safe', None)
+        if safe is not None:
+            return safe
+        log.warn("zip_safe flag not set; analyzing archive contents...")
+        return analyze_egg(self.bdist_dir, self.stubs)
+
+    def gen_header(self) -> Literal["w"]:
+        return 'w'
+
+    def copy_metadata_to(self, target_dir) -> None:
+        "Copy metadata (egg info) to the target_dir"
+        # normalize the path (so that a forward-slash in egg_info will
+        # match using startswith below)
+        norm_egg_info = os.path.normpath(self.egg_info)
+        prefix = os.path.join(norm_egg_info, '')
+        for path in self.ei_cmd.filelist.files:
+            if path.startswith(prefix):
+                target = os.path.join(target_dir, path[len(prefix) :])
+                ensure_directory(target)
+                self.copy_file(path, target)
+
+    def get_ext_outputs(self):
+        """Get a list of relative paths to C extensions in the output distro"""
+
+        all_outputs = []
+        ext_outputs = []
+
+        paths = {self.bdist_dir: ''}
+        for base, dirs, files in sorted_walk(self.bdist_dir):
+            all_outputs.extend(
+                paths[base] + filename
+                for filename in files
+                if os.path.splitext(filename)[1].lower() in NATIVE_EXTENSIONS
+            )
+            for filename in dirs:
+                paths[os.path.join(base, filename)] = paths[base] + filename + '/'
+
+        if self.distribution.has_ext_modules():
+            build_cmd = self.get_finalized_command('build_ext')
+            for ext in build_cmd.extensions:
+                if isinstance(ext, Library):
+                    continue
+                fullname = build_cmd.get_ext_fullname(ext.name)
+                filename = build_cmd.get_ext_filename(fullname)
+                if not os.path.basename(filename).startswith('dl-'):
+                    if os.path.exists(os.path.join(self.bdist_dir, filename)):
+                        ext_outputs.append(filename)
+
+        return all_outputs, ext_outputs
+
+
+NATIVE_EXTENSIONS: dict[str, None] = dict.fromkeys('.dll .so .dylib .pyd'.split())
+
+
+def walk_egg(egg_dir):
+    """Walk an unpacked egg's contents, skipping the metadata directory"""
+    walker = sorted_walk(egg_dir)
+    base, dirs, files = next(walker)
+    if 'EGG-INFO' in dirs:
+        dirs.remove('EGG-INFO')
+    yield base, dirs, files
+    yield from walker
+
+
+def analyze_egg(egg_dir, stubs):
+    # check for existing flag in EGG-INFO
+    for flag, fn in safety_flags.items():
+        if os.path.exists(os.path.join(egg_dir, 'EGG-INFO', fn)):
+            return flag
+    if not can_scan():
+        return False
+    safe = True
+    for base, dirs, files in walk_egg(egg_dir):
+        for name in files:
+            if name.endswith('.py') or name.endswith('.pyw'):
+                continue
+            elif name.endswith('.pyc') or name.endswith('.pyo'):
+                # always scan, even if we already know we're not safe
+                safe = scan_module(egg_dir, base, name, stubs) and safe
+    return safe
+
+
+def write_safety_flag(egg_dir, safe) -> None:
+    # Write or remove zip safety flag file(s)
+    for flag, fn in safety_flags.items():
+        fn = os.path.join(egg_dir, fn)
+        if os.path.exists(fn):
+            if safe is None or bool(safe) != flag:
+                os.unlink(fn)
+        elif safe is not None and bool(safe) == flag:
+            with open(fn, 'wt', encoding="utf-8") as f:
+                f.write('\n')
+
+
+safety_flags = {
+    True: 'zip-safe',
+    False: 'not-zip-safe',
+}
+
+
+def scan_module(egg_dir, base, name, stubs):
+    """Check whether module possibly uses unsafe-for-zipfile stuff"""
+
+    filename = os.path.join(base, name)
+    if filename[:-1] in stubs:
+        return True  # Extension module
+    pkg = base[len(egg_dir) + 1 :].replace(os.sep, '.')
+    module = pkg + (pkg and '.' or '') + os.path.splitext(name)[0]
+    skip = 16  # skip magic & reserved? & date & file size
+    f = open(filename, 'rb')
+    f.read(skip)
+    code = marshal.load(f)
+    f.close()
+    safe = True
+    symbols = dict.fromkeys(iter_symbols(code))
+    for bad in ['__file__', '__path__']:
+        if bad in symbols:
+            log.warn("%s: module references %s", module, bad)
+            safe = False
+    if 'inspect' in symbols:
+        for bad in [
+            'getsource',
+            'getabsfile',
+            'getfile',
+            'getsourcefile',
+            'getsourcelines',
+            'findsource',
+            'getcomments',
+            'getframeinfo',
+            'getinnerframes',
+            'getouterframes',
+            'stack',
+            'trace',
+        ]:
+            if bad in symbols:
+                log.warn("%s: module MAY be using inspect.%s", module, bad)
+                safe = False
+    return safe
+
+
+def iter_symbols(code):
+    """Yield names and strings used by `code` and its nested code objects"""
+    yield from code.co_names
+    for const in code.co_consts:
+        if isinstance(const, str):
+            yield const
+        elif isinstance(const, CodeType):
+            yield from iter_symbols(const)
+
+
+def can_scan() -> bool:
+    if not sys.platform.startswith('java') and sys.platform != 'cli':
+        # CPython, PyPy, etc.
+        return True
+    log.warn("Unable to analyze compiled code on this platform.")
+    log.warn(
+        "Please ask the author to include a 'zip_safe'"
+        " setting (either True or False) in the package's setup.py"
+    )
+    return False
+
+
+# Attribute names of options for commands that might need to be convinced to
+# install to the egg build directory
+
+INSTALL_DIRECTORY_ATTRS = ['install_lib', 'install_dir', 'install_data', 'install_base']
+
+
+def make_zipfile(
+    zip_filename: StrPathT,
+    base_dir,
+    verbose: bool = False,
+    dry_run: bool = False,
+    compress=True,
+    mode: _ZipFileMode = 'w',
+) -> StrPathT:
+    """Create a zip file from all the files under 'base_dir'.  The output
+    zip file will be named 'base_dir' + ".zip".  Uses either the "zipfile"
+    Python module (if available) or the InfoZIP "zip" utility (if installed
+    and found on the default search path).  If neither tool is available,
+    raises DistutilsExecError.  Returns the name of the output zip file.
+    """
+    import zipfile
+
+    mkpath(os.path.dirname(zip_filename), dry_run=dry_run)  # type: ignore[arg-type] # python/mypy#18075
+    log.info("creating '%s' and adding '%s' to it", zip_filename, base_dir)
+
+    def visit(z, dirname, names):
+        for name in names:
+            path = os.path.normpath(os.path.join(dirname, name))
+            if os.path.isfile(path):
+                p = path[len(base_dir) + 1 :]
+                if not dry_run:
+                    z.write(path, p)
+                log.debug("adding '%s'", p)
+
+    compression = zipfile.ZIP_DEFLATED if compress else zipfile.ZIP_STORED
+    if not dry_run:
+        z = zipfile.ZipFile(zip_filename, mode, compression=compression)
+        for dirname, dirs, files in sorted_walk(base_dir):
+            visit(z, dirname, files)
+        z.close()
+    else:
+        for dirname, dirs, files in sorted_walk(base_dir):
+            visit(None, dirname, files)
+    return zip_filename
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_rpm.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_rpm.py
new file mode 100644
index 0000000000000000000000000000000000000000..6dbb27002a8cc7f1cafd4f5cbb75ba39aa7430e2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_rpm.py
@@ -0,0 +1,42 @@
+from ..dist import Distribution
+from ..warnings import SetuptoolsDeprecationWarning
+
+import distutils.command.bdist_rpm as orig
+
+
+class bdist_rpm(orig.bdist_rpm):
+    """
+    Override the default bdist_rpm behavior to do the following:
+
+    1. Run egg_info to ensure the name and version are properly calculated.
+    2. Always run 'install' using --single-version-externally-managed to
+       disable eggs in RPM distributions.
+    """
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    def run(self) -> None:
+        SetuptoolsDeprecationWarning.emit(
+            "Deprecated command",
+            """
+            bdist_rpm is deprecated and will be removed in a future version.
+            Use bdist_wheel (wheel packages) instead.
+            """,
+            see_url="https://github.com/pypa/setuptools/issues/1988",
+            due_date=(2023, 10, 30),  # Deprecation introduced in 22 Oct 2021.
+        )
+
+        # ensure distro name is up-to-date
+        self.run_command('egg_info')
+
+        orig.bdist_rpm.run(self)
+
+    def _make_spec_file(self):
+        spec = orig.bdist_rpm._make_spec_file(self)
+        return [
+            line.replace(
+                "setup.py install ",
+                "setup.py install --single-version-externally-managed ",
+            ).replace("%setup", "%setup -n %{name}-%{unmangled_version}")
+            for line in spec
+        ]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_wheel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_wheel.py
new file mode 100644
index 0000000000000000000000000000000000000000..1e3f637bcc31e6b49f2f9415934f553e9cf55c4a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/bdist_wheel.py
@@ -0,0 +1,604 @@
+"""
+Create a wheel (.whl) distribution.
+
+A wheel is a built archive format.
+"""
+
+from __future__ import annotations
+
+import os
+import re
+import shutil
+import struct
+import sys
+import sysconfig
+import warnings
+from collections.abc import Iterable, Sequence
+from email.generator import BytesGenerator
+from glob import iglob
+from typing import Literal, cast
+from zipfile import ZIP_DEFLATED, ZIP_STORED
+
+from packaging import tags, version as _packaging_version
+from wheel.wheelfile import WheelFile
+
+from .. import Command, __version__, _shutil
+from .._core_metadata import _safe_license_file
+from .._normalization import safer_name
+from ..warnings import SetuptoolsDeprecationWarning
+from .egg_info import egg_info as egg_info_cls
+
+from distutils import log
+
+
+def safe_version(version: str) -> str:
+    """
+    Convert an arbitrary string to a standard version string
+    """
+    try:
+        # normalize the version
+        return str(_packaging_version.Version(version))
+    except _packaging_version.InvalidVersion:
+        version = version.replace(" ", ".")
+        return re.sub("[^A-Za-z0-9.]+", "-", version)
+
+
+setuptools_major_version = int(__version__.split(".")[0])
+
+PY_LIMITED_API_PATTERN = r"cp3\d"
+
+
+def _is_32bit_interpreter() -> bool:
+    return struct.calcsize("P") == 4
+
+
+def python_tag() -> str:
+    return f"py{sys.version_info.major}"
+
+
+def get_platform(archive_root: str | None) -> str:
+    """Return our platform name 'win32', 'linux_x86_64'"""
+    result = sysconfig.get_platform()
+    if result.startswith("macosx") and archive_root is not None:  # pragma: no cover
+        from wheel.macosx_libfile import calculate_macosx_platform_tag
+
+        result = calculate_macosx_platform_tag(archive_root, result)
+    elif _is_32bit_interpreter():
+        if result == "linux-x86_64":
+            # pip pull request #3497
+            result = "linux-i686"
+        elif result == "linux-aarch64":
+            # packaging pull request #234
+            # TODO armv8l, packaging pull request #690 => this did not land
+            # in pip/packaging yet
+            result = "linux-armv7l"
+
+    return result.replace("-", "_")
+
+
+def get_flag(
+    var: str, fallback: bool, expected: bool = True, warn: bool = True
+) -> bool:
+    """Use a fallback value for determining SOABI flags if the needed config
+    var is unset or unavailable."""
+    val = sysconfig.get_config_var(var)
+    if val is None:
+        if warn:
+            warnings.warn(
+                f"Config variable '{var}' is unset, Python ABI tag may be incorrect",
+                RuntimeWarning,
+                stacklevel=2,
+            )
+        return fallback
+    return val == expected
+
+
+def get_abi_tag() -> str | None:
+    """Return the ABI tag based on SOABI (if available) or emulate SOABI (PyPy2)."""
+    soabi: str = sysconfig.get_config_var("SOABI")
+    impl = tags.interpreter_name()
+    if not soabi and impl in ("cp", "pp") and hasattr(sys, "maxunicode"):
+        d = ""
+        u = ""
+        if get_flag("Py_DEBUG", hasattr(sys, "gettotalrefcount"), warn=(impl == "cp")):
+            d = "d"
+
+        abi = f"{impl}{tags.interpreter_version()}{d}{u}"
+    elif soabi and impl == "cp" and soabi.startswith("cpython"):
+        # non-Windows
+        abi = "cp" + soabi.split("-")[1]
+    elif soabi and impl == "cp" and soabi.startswith("cp"):
+        # Windows
+        abi = soabi.split("-")[0]
+        if hasattr(sys, "gettotalrefcount"):
+            # using debug build; append "d" flag
+            abi += "d"
+    elif soabi and impl == "pp":
+        # we want something like pypy36-pp73
+        abi = "-".join(soabi.split("-")[:2])
+        abi = abi.replace(".", "_").replace("-", "_")
+    elif soabi and impl == "graalpy":
+        abi = "-".join(soabi.split("-")[:3])
+        abi = abi.replace(".", "_").replace("-", "_")
+    elif soabi:
+        abi = soabi.replace(".", "_").replace("-", "_")
+    else:
+        abi = None
+
+    return abi
+
+
+def safer_version(version: str) -> str:
+    return safe_version(version).replace("-", "_")
+
+
+class bdist_wheel(Command):
+    description = "create a wheel distribution"
+
+    supported_compressions = {
+        "stored": ZIP_STORED,
+        "deflated": ZIP_DEFLATED,
+    }
+
+    user_options = [
+        ("bdist-dir=", "b", "temporary directory for creating the distribution"),
+        (
+            "plat-name=",
+            "p",
+            "platform name to embed in generated filenames "
+            f"[default: {get_platform(None)}]",
+        ),
+        (
+            "keep-temp",
+            "k",
+            "keep the pseudo-installation tree around after "
+            "creating the distribution archive",
+        ),
+        ("dist-dir=", "d", "directory to put final built distributions in"),
+        ("skip-build", None, "skip rebuilding everything (for testing/debugging)"),
+        (
+            "relative",
+            None,
+            "build the archive using relative paths [default: false]",
+        ),
+        (
+            "owner=",
+            "u",
+            "Owner name used when creating a tar file [default: current user]",
+        ),
+        (
+            "group=",
+            "g",
+            "Group name used when creating a tar file [default: current group]",
+        ),
+        ("universal", None, "*DEPRECATED* make a universal wheel [default: false]"),
+        (
+            "compression=",
+            None,
+            f"zipfile compression (one of: {', '.join(supported_compressions)}) [default: 'deflated']",
+        ),
+        (
+            "python-tag=",
+            None,
+            f"Python implementation compatibility tag [default: '{python_tag()}']",
+        ),
+        (
+            "build-number=",
+            None,
+            "Build number for this particular version. "
+            "As specified in PEP-0427, this must start with a digit. "
+            "[default: None]",
+        ),
+        (
+            "py-limited-api=",
+            None,
+            "Python tag (cp32|cp33|cpNN) for abi3 wheel tag [default: false]",
+        ),
+        (
+            "dist-info-dir=",
+            None,
+            "directory where a pre-generated dist-info can be found (e.g. as a "
+            "result of calling the PEP517 'prepare_metadata_for_build_wheel' "
+            "method)",
+        ),
+    ]
+
+    boolean_options = ["keep-temp", "skip-build", "relative", "universal"]
+
+    def initialize_options(self) -> None:
+        self.bdist_dir: str | None = None
+        self.data_dir = ""
+        self.plat_name: str | None = None
+        self.plat_tag: str | None = None
+        self.format = "zip"
+        self.keep_temp = False
+        self.dist_dir: str | None = None
+        self.dist_info_dir = None
+        self.egginfo_dir: str | None = None
+        self.root_is_pure: bool | None = None
+        self.skip_build = False
+        self.relative = False
+        self.owner = None
+        self.group = None
+        self.universal = False
+        self.compression: str | int = "deflated"
+        self.python_tag = python_tag()
+        self.build_number: str | None = None
+        self.py_limited_api: str | Literal[False] = False
+        self.plat_name_supplied = False
+
+    def finalize_options(self) -> None:
+        if not self.bdist_dir:
+            bdist_base = self.get_finalized_command("bdist").bdist_base
+            self.bdist_dir = os.path.join(bdist_base, "wheel")
+
+        if self.dist_info_dir is None:
+            egg_info = cast(egg_info_cls, self.distribution.get_command_obj("egg_info"))
+            egg_info.ensure_finalized()  # needed for correct `wheel_dist_name`
+
+        self.data_dir = self.wheel_dist_name + ".data"
+        self.plat_name_supplied = bool(self.plat_name)
+
+        need_options = ("dist_dir", "plat_name", "skip_build")
+
+        self.set_undefined_options("bdist", *zip(need_options, need_options))
+
+        self.root_is_pure = not (
+            self.distribution.has_ext_modules() or self.distribution.has_c_libraries()
+        )
+
+        self._validate_py_limited_api()
+
+        # Support legacy [wheel] section for setting universal
+        wheel = self.distribution.get_option_dict("wheel")
+        if "universal" in wheel:  # pragma: no cover
+            # please don't define this in your global configs
+            log.warn("The [wheel] section is deprecated. Use [bdist_wheel] instead.")
+            val = wheel["universal"][1].strip()
+            if val.lower() in ("1", "true", "yes"):
+                self.universal = True
+
+        if self.universal:
+            SetuptoolsDeprecationWarning.emit(
+                "bdist_wheel.universal is deprecated",
+                """
+                With Python 2.7 end-of-life, support for building universal wheels
+                (i.e., wheels that support both Python 2 and Python 3)
+                is being obviated.
+                Please discontinue using this option, or if you still need it,
+                file an issue with pypa/setuptools describing your use case.
+                """,
+                due_date=(2025, 8, 30),  # Introduced in 2024-08-30
+            )
+
+        if self.build_number is not None and not self.build_number[:1].isdigit():
+            raise ValueError("Build tag (build-number) must start with a digit.")
+
+    def _validate_py_limited_api(self) -> None:
+        if not self.py_limited_api:
+            return
+
+        if not re.match(PY_LIMITED_API_PATTERN, self.py_limited_api):
+            raise ValueError(f"py-limited-api must match '{PY_LIMITED_API_PATTERN}'")
+
+        if sysconfig.get_config_var("Py_GIL_DISABLED"):
+            raise ValueError(
+                f"`py_limited_api={self.py_limited_api!r}` not supported. "
+                "`Py_LIMITED_API` is currently incompatible with "
+                "`Py_GIL_DISABLED`."
+                "See https://github.com/python/cpython/issues/111506."
+            )
+
+    @property
+    def wheel_dist_name(self) -> str:
+        """Return distribution full name with - replaced with _"""
+        components = [
+            safer_name(self.distribution.get_name()),
+            safer_version(self.distribution.get_version()),
+        ]
+        if self.build_number:
+            components.append(self.build_number)
+        return "-".join(components)
+
+    def get_tag(self) -> tuple[str, str, str]:
+        # bdist sets self.plat_name if unset, we should only use it for purepy
+        # wheels if the user supplied it.
+        if self.plat_name_supplied and self.plat_name:
+            plat_name = self.plat_name
+        elif self.root_is_pure:
+            plat_name = "any"
+        else:
+            # macosx contains system version in platform name so need special handle
+            if self.plat_name and not self.plat_name.startswith("macosx"):
+                plat_name = self.plat_name
+            else:
+                # on macosx always limit the platform name to comply with any
+                # c-extension modules in bdist_dir, since the user can specify
+                # a higher MACOSX_DEPLOYMENT_TARGET via tools like CMake
+
+                # on other platforms, and on macosx if there are no c-extension
+                # modules, use the default platform name.
+                plat_name = get_platform(self.bdist_dir)
+
+            if _is_32bit_interpreter():
+                if plat_name in ("linux-x86_64", "linux_x86_64"):
+                    plat_name = "linux_i686"
+                if plat_name in ("linux-aarch64", "linux_aarch64"):
+                    # TODO armv8l, packaging pull request #690 => this did not land
+                    # in pip/packaging yet
+                    plat_name = "linux_armv7l"
+
+        plat_name = (
+            plat_name.lower().replace("-", "_").replace(".", "_").replace(" ", "_")
+        )
+
+        if self.root_is_pure:
+            if self.universal:
+                impl = "py2.py3"
+            else:
+                impl = self.python_tag
+            tag = (impl, "none", plat_name)
+        else:
+            impl_name = tags.interpreter_name()
+            impl_ver = tags.interpreter_version()
+            impl = impl_name + impl_ver
+            # We don't work on CPython 3.1, 3.0.
+            if self.py_limited_api and (impl_name + impl_ver).startswith("cp3"):
+                impl = self.py_limited_api
+                abi_tag = "abi3"
+            else:
+                abi_tag = str(get_abi_tag()).lower()
+            tag = (impl, abi_tag, plat_name)
+            # issue gh-374: allow overriding plat_name
+            supported_tags = [
+                (t.interpreter, t.abi, plat_name) for t in tags.sys_tags()
+            ]
+            assert tag in supported_tags, (
+                f"would build wheel with unsupported tag {tag}"
+            )
+        return tag
+
+    def run(self):
+        build_scripts = self.reinitialize_command("build_scripts")
+        build_scripts.executable = "python"
+        build_scripts.force = True
+
+        build_ext = self.reinitialize_command("build_ext")
+        build_ext.inplace = False
+
+        if not self.skip_build:
+            self.run_command("build")
+
+        install = self.reinitialize_command("install", reinit_subcommands=True)
+        install.root = self.bdist_dir
+        install.compile = False
+        install.skip_build = self.skip_build
+        install.warn_dir = False
+
+        # A wheel without setuptools scripts is more cross-platform.
+        # Use the (undocumented) `no_ep` option to setuptools'
+        # install_scripts command to avoid creating entry point scripts.
+        install_scripts = self.reinitialize_command("install_scripts")
+        install_scripts.no_ep = True
+
+        # Use a custom scheme for the archive, because we have to decide
+        # at installation time which scheme to use.
+        for key in ("headers", "scripts", "data", "purelib", "platlib"):
+            setattr(install, "install_" + key, os.path.join(self.data_dir, key))
+
+        basedir_observed = ""
+
+        if os.name == "nt":
+            # win32 barfs if any of these are ''; could be '.'?
+            # (distutils.command.install:change_roots bug)
+            basedir_observed = os.path.normpath(os.path.join(self.data_dir, ".."))
+            self.install_libbase = self.install_lib = basedir_observed
+
+        setattr(
+            install,
+            "install_purelib" if self.root_is_pure else "install_platlib",
+            basedir_observed,
+        )
+
+        log.info(f"installing to {self.bdist_dir}")
+
+        self.run_command("install")
+
+        impl_tag, abi_tag, plat_tag = self.get_tag()
+        archive_basename = f"{self.wheel_dist_name}-{impl_tag}-{abi_tag}-{plat_tag}"
+        if not self.relative:
+            archive_root = self.bdist_dir
+        else:
+            archive_root = os.path.join(
+                self.bdist_dir, self._ensure_relative(install.install_base)
+            )
+
+        self.set_undefined_options("install_egg_info", ("target", "egginfo_dir"))
+        distinfo_dirname = (
+            f"{safer_name(self.distribution.get_name())}-"
+            f"{safer_version(self.distribution.get_version())}.dist-info"
+        )
+        distinfo_dir = os.path.join(self.bdist_dir, distinfo_dirname)
+        if self.dist_info_dir:
+            # Use the given dist-info directly.
+            log.debug(f"reusing {self.dist_info_dir}")
+            shutil.copytree(self.dist_info_dir, distinfo_dir)
+            # Egg info is still generated, so remove it now to avoid it getting
+            # copied into the wheel.
+            _shutil.rmtree(self.egginfo_dir)
+        else:
+            # Convert the generated egg-info into dist-info.
+            self.egg2dist(self.egginfo_dir, distinfo_dir)
+
+        self.write_wheelfile(distinfo_dir)
+
+        # Make the archive
+        if not os.path.exists(self.dist_dir):
+            os.makedirs(self.dist_dir)
+
+        wheel_path = os.path.join(self.dist_dir, archive_basename + ".whl")
+        with WheelFile(wheel_path, "w", self._zip_compression()) as wf:
+            wf.write_files(archive_root)
+
+        # Add to 'Distribution.dist_files' so that the "upload" command works
+        getattr(self.distribution, "dist_files", []).append((
+            "bdist_wheel",
+            f"{sys.version_info.major}.{sys.version_info.minor}",
+            wheel_path,
+        ))
+
+        if not self.keep_temp:
+            log.info(f"removing {self.bdist_dir}")
+            if not self.dry_run:
+                _shutil.rmtree(self.bdist_dir)
+
+    def write_wheelfile(
+        self, wheelfile_base: str, generator: str = f"setuptools ({__version__})"
+    ) -> None:
+        from email.message import Message
+
+        msg = Message()
+        msg["Wheel-Version"] = "1.0"  # of the spec
+        msg["Generator"] = generator
+        msg["Root-Is-Purelib"] = str(self.root_is_pure).lower()
+        if self.build_number is not None:
+            msg["Build"] = self.build_number
+
+        # Doesn't work for bdist_wininst
+        impl_tag, abi_tag, plat_tag = self.get_tag()
+        for impl in impl_tag.split("."):
+            for abi in abi_tag.split("."):
+                for plat in plat_tag.split("."):
+                    msg["Tag"] = "-".join((impl, abi, plat))
+
+        wheelfile_path = os.path.join(wheelfile_base, "WHEEL")
+        log.info(f"creating {wheelfile_path}")
+        with open(wheelfile_path, "wb") as f:
+            BytesGenerator(f, maxheaderlen=0).flatten(msg)
+
+    def _ensure_relative(self, path: str) -> str:
+        # copied from dir_util, deleted
+        drive, path = os.path.splitdrive(path)
+        if path[0:1] == os.sep:
+            path = drive + path[1:]
+        return path
+
+    @property
+    def license_paths(self) -> Iterable[str]:
+        if setuptools_major_version >= 57:
+            # Setuptools has resolved any patterns to actual file names
+            return self.distribution.metadata.license_files or ()
+
+        files = set[str]()
+        metadata = self.distribution.get_option_dict("metadata")
+        if setuptools_major_version >= 42:
+            # Setuptools recognizes the license_files option but does not do globbing
+            patterns = cast(Sequence[str], self.distribution.metadata.license_files)
+        else:
+            # Prior to those, wheel is entirely responsible for handling license files
+            if "license_files" in metadata:
+                patterns = metadata["license_files"][1].split()
+            else:
+                patterns = ()
+
+        if "license_file" in metadata:
+            warnings.warn(
+                'The "license_file" option is deprecated. Use "license_files" instead.',
+                DeprecationWarning,
+                stacklevel=2,
+            )
+            files.add(metadata["license_file"][1])
+
+        if not files and not patterns and not isinstance(patterns, list):
+            patterns = ("LICEN[CS]E*", "COPYING*", "NOTICE*", "AUTHORS*")
+
+        for pattern in patterns:
+            for path in iglob(pattern):
+                if path.endswith("~"):
+                    log.debug(
+                        f'ignoring license file "{path}" as it looks like a backup'
+                    )
+                    continue
+
+                if path not in files and os.path.isfile(path):
+                    log.info(
+                        f'adding license file "{path}" (matched pattern "{pattern}")'
+                    )
+                    files.add(path)
+
+        return files
+
+    def egg2dist(self, egginfo_path: str, distinfo_path: str) -> None:
+        """Convert an .egg-info directory into a .dist-info directory"""
+
+        def adios(p: str) -> None:
+            """Appropriately delete directory, file or link."""
+            if os.path.exists(p) and not os.path.islink(p) and os.path.isdir(p):
+                _shutil.rmtree(p)
+            elif os.path.exists(p):
+                os.unlink(p)
+
+        adios(distinfo_path)
+
+        if not os.path.exists(egginfo_path):
+            # There is no egg-info. This is probably because the egg-info
+            # file/directory is not named matching the distribution name used
+            # to name the archive file. Check for this case and report
+            # accordingly.
+            import glob
+
+            pat = os.path.join(os.path.dirname(egginfo_path), "*.egg-info")
+            possible = glob.glob(pat)
+            err = f"Egg metadata expected at {egginfo_path} but not found"
+            if possible:
+                alt = os.path.basename(possible[0])
+                err += f" ({alt} found - possible misnamed archive file?)"
+
+            raise ValueError(err)
+
+        # .egg-info is a directory
+        pkginfo_path = os.path.join(egginfo_path, "PKG-INFO")
+
+        # ignore common egg metadata that is useless to wheel
+        shutil.copytree(
+            egginfo_path,
+            distinfo_path,
+            ignore=lambda x, y: {
+                "PKG-INFO",
+                "requires.txt",
+                "SOURCES.txt",
+                "not-zip-safe",
+            },
+        )
+
+        # delete dependency_links if it is only whitespace
+        dependency_links_path = os.path.join(distinfo_path, "dependency_links.txt")
+        with open(dependency_links_path, encoding="utf-8") as dependency_links_file:
+            dependency_links = dependency_links_file.read().strip()
+        if not dependency_links:
+            adios(dependency_links_path)
+
+        metadata_path = os.path.join(distinfo_path, "METADATA")
+        shutil.copy(pkginfo_path, metadata_path)
+
+        licenses_folder_path = os.path.join(distinfo_path, "licenses")
+        for license_path in self.license_paths:
+            safe_path = _safe_license_file(license_path)
+            dist_info_license_path = os.path.join(licenses_folder_path, safe_path)
+            os.makedirs(os.path.dirname(dist_info_license_path), exist_ok=True)
+            shutil.copy(license_path, dist_info_license_path)
+
+        adios(egginfo_path)
+
+    def _zip_compression(self) -> int:
+        if (
+            isinstance(self.compression, int)
+            and self.compression in self.supported_compressions.values()
+        ):
+            return self.compression
+
+        compression = self.supported_compressions.get(str(self.compression))
+        if compression is not None:
+            return compression
+
+        raise ValueError(f"Unsupported compression: {self.compression!r}")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build.py
new file mode 100644
index 0000000000000000000000000000000000000000..54cbb8d2e7bf41de4e187613718879f2a4c3d8d3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build.py
@@ -0,0 +1,135 @@
+from __future__ import annotations
+
+from typing import Protocol
+
+from ..dist import Distribution
+
+from distutils.command.build import build as _build
+
+_ORIGINAL_SUBCOMMANDS = {"build_py", "build_clib", "build_ext", "build_scripts"}
+
+
+class build(_build):
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    # copy to avoid sharing the object with parent class
+    sub_commands = _build.sub_commands[:]
+
+
+class SubCommand(Protocol):
+    """In order to support editable installations (see :pep:`660`) all
+    build subcommands **SHOULD** implement this protocol. They also **MUST** inherit
+    from ``setuptools.Command``.
+
+    When creating an :pep:`editable wheel <660>`, ``setuptools`` will try to evaluate
+    custom ``build`` subcommands using the following procedure:
+
+    1. ``setuptools`` will set the ``editable_mode`` attribute to ``True``
+    2. ``setuptools`` will execute the ``run()`` command.
+
+       .. important::
+          Subcommands **SHOULD** take advantage of ``editable_mode=True`` to adequate
+          its behaviour or perform optimisations.
+
+          For example, if a subcommand doesn't need to generate an extra file and
+          all it does is to copy a source file into the build directory,
+          ``run()`` **SHOULD** simply "early return".
+
+          Similarly, if the subcommand creates files that would be placed alongside
+          Python files in the final distribution, during an editable install
+          the command **SHOULD** generate these files "in place" (i.e. write them to
+          the original source directory, instead of using the build directory).
+          Note that ``get_output_mapping()`` should reflect that and include mappings
+          for "in place" builds accordingly.
+
+    3. ``setuptools`` use any knowledge it can derive from the return values of
+       ``get_outputs()`` and ``get_output_mapping()`` to create an editable wheel.
+       When relevant ``setuptools`` **MAY** attempt to use file links based on the value
+       of ``get_output_mapping()``. Alternatively, ``setuptools`` **MAY** attempt to use
+       :doc:`import hooks ` to redirect any attempt to import
+       to the directory with the original source code and other files built in place.
+
+    Please note that custom sub-commands **SHOULD NOT** rely on ``run()`` being
+    executed (or not) to provide correct return values for ``get_outputs()``,
+    ``get_output_mapping()`` or ``get_source_files()``. The ``get_*`` methods should
+    work independently of ``run()``.
+    """
+
+    editable_mode: bool = False
+    """Boolean flag that will be set to ``True`` when setuptools is used for an
+    editable installation (see :pep:`660`).
+    Implementations **SHOULD** explicitly set the default value of this attribute to
+    ``False``.
+    When subcommands run, they can use this flag to perform optimizations or change
+    their behaviour accordingly.
+    """
+
+    build_lib: str
+    """String representing the directory where the build artifacts should be stored,
+    e.g. ``build/lib``.
+    For example, if a distribution wants to provide a Python module named ``pkg.mod``,
+    then a corresponding file should be written to ``{build_lib}/package/module.py``.
+    A way of thinking about this is that the files saved under ``build_lib``
+    would be eventually copied to one of the directories in :obj:`site.PREFIXES`
+    upon installation.
+
+    A command that produces platform-independent files (e.g. compiling text templates
+    into Python functions), **CAN** initialize ``build_lib`` by copying its value from
+    the ``build_py`` command. On the other hand, a command that produces
+    platform-specific files **CAN** initialize ``build_lib`` by copying its value from
+    the ``build_ext`` command. In general this is done inside the ``finalize_options``
+    method with the help of the ``set_undefined_options`` command::
+
+        def finalize_options(self):
+            self.set_undefined_options("build_py", ("build_lib", "build_lib"))
+            ...
+    """
+
+    def initialize_options(self) -> None:
+        """(Required by the original :class:`setuptools.Command` interface)"""
+        ...
+
+    def finalize_options(self) -> None:
+        """(Required by the original :class:`setuptools.Command` interface)"""
+        ...
+
+    def run(self) -> None:
+        """(Required by the original :class:`setuptools.Command` interface)"""
+        ...
+
+    def get_source_files(self) -> list[str]:
+        """
+        Return a list of all files that are used by the command to create the expected
+        outputs.
+        For example, if your build command transpiles Java files into Python, you should
+        list here all the Java files.
+        The primary purpose of this function is to help populating the ``sdist``
+        with all the files necessary to build the distribution.
+        All files should be strings relative to the project root directory.
+        """
+        ...
+
+    def get_outputs(self) -> list[str]:
+        """
+        Return a list of files intended for distribution as they would have been
+        produced by the build.
+        These files should be strings in the form of
+        ``"{build_lib}/destination/file/path"``.
+
+        .. note::
+           The return value of ``get_output()`` should include all files used as keys
+           in ``get_output_mapping()`` plus files that are generated during the build
+           and don't correspond to any source file already present in the project.
+        """
+        ...
+
+    def get_output_mapping(self) -> dict[str, str]:
+        """
+        Return a mapping between destination files as they would be produced by the
+        build (dict keys) into the respective existing (source) files (dict values).
+        Existing (source) files should be represented as strings relative to the project
+        root directory.
+        Destination files should be strings in the form of
+        ``"{build_lib}/destination/file/path"``.
+        """
+        ...
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_clib.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_clib.py
new file mode 100644
index 0000000000000000000000000000000000000000..f376f4ce4d2afc4a58f1fa0e85624136edc93835
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_clib.py
@@ -0,0 +1,103 @@
+from ..dist import Distribution
+from ..modified import newer_pairwise_group
+
+import distutils.command.build_clib as orig
+from distutils import log
+from distutils.errors import DistutilsSetupError
+
+
+class build_clib(orig.build_clib):
+    """
+    Override the default build_clib behaviour to do the following:
+
+    1. Implement a rudimentary timestamp-based dependency system
+       so 'compile()' doesn't run every time.
+    2. Add more keys to the 'build_info' dictionary:
+        * obj_deps - specify dependencies for each object compiled.
+                     this should be a dictionary mapping a key
+                     with the source filename to a list of
+                     dependencies. Use an empty string for global
+                     dependencies.
+        * cflags   - specify a list of additional flags to pass to
+                     the compiler.
+    """
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    def build_libraries(self, libraries) -> None:
+        for lib_name, build_info in libraries:
+            sources = build_info.get('sources')
+            if sources is None or not isinstance(sources, (list, tuple)):
+                raise DistutilsSetupError(
+                    f"in 'libraries' option (library '{lib_name}'), "
+                    "'sources' must be present and must be "
+                    "a list of source filenames"
+                )
+            sources = sorted(list(sources))
+
+            log.info("building '%s' library", lib_name)
+
+            # Make sure everything is the correct type.
+            # obj_deps should be a dictionary of keys as sources
+            # and a list/tuple of files that are its dependencies.
+            obj_deps = build_info.get('obj_deps', dict())
+            if not isinstance(obj_deps, dict):
+                raise DistutilsSetupError(
+                    f"in 'libraries' option (library '{lib_name}'), "
+                    "'obj_deps' must be a dictionary of "
+                    "type 'source: list'"
+                )
+            dependencies = []
+
+            # Get the global dependencies that are specified by the '' key.
+            # These will go into every source's dependency list.
+            global_deps = obj_deps.get('', list())
+            if not isinstance(global_deps, (list, tuple)):
+                raise DistutilsSetupError(
+                    f"in 'libraries' option (library '{lib_name}'), "
+                    "'obj_deps' must be a dictionary of "
+                    "type 'source: list'"
+                )
+
+            # Build the list to be used by newer_pairwise_group
+            # each source will be auto-added to its dependencies.
+            for source in sources:
+                src_deps = [source]
+                src_deps.extend(global_deps)
+                extra_deps = obj_deps.get(source, list())
+                if not isinstance(extra_deps, (list, tuple)):
+                    raise DistutilsSetupError(
+                        f"in 'libraries' option (library '{lib_name}'), "
+                        "'obj_deps' must be a dictionary of "
+                        "type 'source: list'"
+                    )
+                src_deps.extend(extra_deps)
+                dependencies.append(src_deps)
+
+            expected_objects = self.compiler.object_filenames(
+                sources,
+                output_dir=self.build_temp,
+            )
+
+            if newer_pairwise_group(dependencies, expected_objects) != ([], []):
+                # First, compile the source code to object files in the library
+                # directory.  (This should probably change to putting object
+                # files in a temporary build directory.)
+                macros = build_info.get('macros')
+                include_dirs = build_info.get('include_dirs')
+                cflags = build_info.get('cflags')
+                self.compiler.compile(
+                    sources,
+                    output_dir=self.build_temp,
+                    macros=macros,
+                    include_dirs=include_dirs,
+                    extra_postargs=cflags,
+                    debug=self.debug,
+                )
+
+            # Now "link" the object files together into a static library.
+            # (On Unix at least, this isn't really linking -- it just
+            # builds an archive.  Whatever.)
+            self.compiler.create_static_lib(
+                expected_objects, lib_name, output_dir=self.build_clib, debug=self.debug
+            )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_ext.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_ext.py
new file mode 100644
index 0000000000000000000000000000000000000000..be833a379c71c3a6b1a85a89f8e9703c66d79824
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_ext.py
@@ -0,0 +1,469 @@
+from __future__ import annotations
+
+import itertools
+import os
+import sys
+from collections.abc import Iterator
+from importlib.machinery import EXTENSION_SUFFIXES
+from importlib.util import cache_from_source as _compiled_file_name
+from pathlib import Path
+from typing import TYPE_CHECKING
+
+from setuptools.dist import Distribution
+from setuptools.errors import BaseError
+from setuptools.extension import Extension, Library
+
+from distutils import log
+from distutils.ccompiler import new_compiler
+from distutils.sysconfig import customize_compiler, get_config_var
+
+if TYPE_CHECKING:
+    # Cython not installed on CI tests, causing _build_ext to be `Any`
+    from distutils.command.build_ext import build_ext as _build_ext
+else:
+    try:
+        # Attempt to use Cython for building extensions, if available
+        from Cython.Distutils.build_ext import build_ext as _build_ext
+
+        # Additionally, assert that the compiler module will load
+        # also. Ref #1229.
+        __import__('Cython.Compiler.Main')
+    except ImportError:
+        from distutils.command.build_ext import build_ext as _build_ext
+
+# make sure _config_vars is initialized
+get_config_var("LDSHARED")
+# Not publicly exposed in typeshed distutils stubs, but this is done on purpose
+# See https://github.com/pypa/setuptools/pull/4228#issuecomment-1959856400
+from distutils.sysconfig import _config_vars as _CONFIG_VARS  # noqa: E402
+
+
+def _customize_compiler_for_shlib(compiler):
+    if sys.platform == "darwin":
+        # building .dylib requires additional compiler flags on OSX; here we
+        # temporarily substitute the pyconfig.h variables so that distutils'
+        # 'customize_compiler' uses them before we build the shared libraries.
+        tmp = _CONFIG_VARS.copy()
+        try:
+            # XXX Help!  I don't have any idea whether these are right...
+            _CONFIG_VARS['LDSHARED'] = (
+                "gcc -Wl,-x -dynamiclib -undefined dynamic_lookup"
+            )
+            _CONFIG_VARS['CCSHARED'] = " -dynamiclib"
+            _CONFIG_VARS['SO'] = ".dylib"
+            customize_compiler(compiler)
+        finally:
+            _CONFIG_VARS.clear()
+            _CONFIG_VARS.update(tmp)
+    else:
+        customize_compiler(compiler)
+
+
+have_rtld = False
+use_stubs = False
+libtype = 'shared'
+
+if sys.platform == "darwin":
+    use_stubs = True
+elif os.name != 'nt':
+    try:
+        import dl  # type: ignore[import-not-found] # https://github.com/python/mypy/issues/13002
+
+        use_stubs = have_rtld = hasattr(dl, 'RTLD_NOW')
+    except ImportError:
+        pass
+
+
+def if_dl(s):
+    return s if have_rtld else ''
+
+
+def get_abi3_suffix():
+    """Return the file extension for an abi3-compliant Extension()"""
+    for suffix in EXTENSION_SUFFIXES:
+        if '.abi3' in suffix:  # Unix
+            return suffix
+        elif suffix == '.pyd':  # Windows
+            return suffix
+    return None
+
+
+class build_ext(_build_ext):
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+    editable_mode = False
+    inplace = False
+
+    def run(self):
+        """Build extensions in build directory, then copy if --inplace"""
+        old_inplace, self.inplace = self.inplace, False
+        _build_ext.run(self)
+        self.inplace = old_inplace
+        if old_inplace:
+            self.copy_extensions_to_source()
+
+    def _get_inplace_equivalent(self, build_py, ext: Extension) -> tuple[str, str]:
+        fullname = self.get_ext_fullname(ext.name)
+        filename = self.get_ext_filename(fullname)
+        modpath = fullname.split('.')
+        package = '.'.join(modpath[:-1])
+        package_dir = build_py.get_package_dir(package)
+        inplace_file = os.path.join(package_dir, os.path.basename(filename))
+        regular_file = os.path.join(self.build_lib, filename)
+        return (inplace_file, regular_file)
+
+    def copy_extensions_to_source(self) -> None:
+        build_py = self.get_finalized_command('build_py')
+        for ext in self.extensions:
+            inplace_file, regular_file = self._get_inplace_equivalent(build_py, ext)
+
+            # Always copy, even if source is older than destination, to ensure
+            # that the right extensions for the current Python/platform are
+            # used.
+            if os.path.exists(regular_file) or not ext.optional:
+                self.copy_file(regular_file, inplace_file, level=self.verbose)
+
+            if ext._needs_stub:
+                inplace_stub = self._get_equivalent_stub(ext, inplace_file)
+                self._write_stub_file(inplace_stub, ext, compile=True)
+                # Always compile stub and remove the original (leave the cache behind)
+                # (this behaviour was observed in previous iterations of the code)
+
+    def _get_equivalent_stub(self, ext: Extension, output_file: str) -> str:
+        dir_ = os.path.dirname(output_file)
+        _, _, name = ext.name.rpartition(".")
+        return f"{os.path.join(dir_, name)}.py"
+
+    def _get_output_mapping(self) -> Iterator[tuple[str, str]]:
+        if not self.inplace:
+            return
+
+        build_py = self.get_finalized_command('build_py')
+        opt = self.get_finalized_command('install_lib').optimize or ""
+
+        for ext in self.extensions:
+            inplace_file, regular_file = self._get_inplace_equivalent(build_py, ext)
+            yield (regular_file, inplace_file)
+
+            if ext._needs_stub:
+                # This version of `build_ext` always builds artifacts in another dir,
+                # when "inplace=True" is given it just copies them back.
+                # This is done in the `copy_extensions_to_source` function, which
+                # always compile stub files via `_compile_and_remove_stub`.
+                # At the end of the process, a `.pyc` stub file is created without the
+                # corresponding `.py`.
+
+                inplace_stub = self._get_equivalent_stub(ext, inplace_file)
+                regular_stub = self._get_equivalent_stub(ext, regular_file)
+                inplace_cache = _compiled_file_name(inplace_stub, optimization=opt)
+                output_cache = _compiled_file_name(regular_stub, optimization=opt)
+                yield (output_cache, inplace_cache)
+
+    def get_ext_filename(self, fullname: str) -> str:
+        so_ext = os.getenv('SETUPTOOLS_EXT_SUFFIX')
+        if so_ext:
+            filename = os.path.join(*fullname.split('.')) + so_ext
+        else:
+            filename = _build_ext.get_ext_filename(self, fullname)
+            ext_suffix = get_config_var('EXT_SUFFIX')
+            if not isinstance(ext_suffix, str):
+                raise OSError(
+                    "Configuration variable EXT_SUFFIX not found for this platform "
+                    "and environment variable SETUPTOOLS_EXT_SUFFIX is missing"
+                )
+            so_ext = ext_suffix
+
+        if fullname in self.ext_map:
+            ext = self.ext_map[fullname]
+            abi3_suffix = get_abi3_suffix()
+            if ext.py_limited_api and abi3_suffix:  # Use abi3
+                filename = filename[: -len(so_ext)] + abi3_suffix
+            if isinstance(ext, Library):
+                fn, ext = os.path.splitext(filename)
+                return self.shlib_compiler.library_filename(fn, libtype)
+            elif use_stubs and ext._links_to_dynamic:
+                d, fn = os.path.split(filename)
+                return os.path.join(d, 'dl-' + fn)
+        return filename
+
+    def initialize_options(self):
+        _build_ext.initialize_options(self)
+        self.shlib_compiler = None
+        self.shlibs = []
+        self.ext_map = {}
+        self.editable_mode = False
+
+    def finalize_options(self) -> None:
+        _build_ext.finalize_options(self)
+        self.extensions = self.extensions or []
+        self.check_extensions_list(self.extensions)
+        self.shlibs = [ext for ext in self.extensions if isinstance(ext, Library)]
+        if self.shlibs:
+            self.setup_shlib_compiler()
+        for ext in self.extensions:
+            ext._full_name = self.get_ext_fullname(ext.name)
+        for ext in self.extensions:
+            fullname = ext._full_name
+            self.ext_map[fullname] = ext
+
+            # distutils 3.1 will also ask for module names
+            # XXX what to do with conflicts?
+            self.ext_map[fullname.split('.')[-1]] = ext
+
+            ltd = self.shlibs and self.links_to_dynamic(ext) or False
+            ns = ltd and use_stubs and not isinstance(ext, Library)
+            ext._links_to_dynamic = ltd
+            ext._needs_stub = ns
+            filename = ext._file_name = self.get_ext_filename(fullname)
+            libdir = os.path.dirname(os.path.join(self.build_lib, filename))
+            if ltd and libdir not in ext.library_dirs:
+                ext.library_dirs.append(libdir)
+            if ltd and use_stubs and os.curdir not in ext.runtime_library_dirs:
+                ext.runtime_library_dirs.append(os.curdir)
+
+        if self.editable_mode:
+            self.inplace = True
+
+    def setup_shlib_compiler(self):
+        compiler = self.shlib_compiler = new_compiler(
+            compiler=self.compiler, dry_run=self.dry_run, force=self.force
+        )
+        _customize_compiler_for_shlib(compiler)
+
+        if self.include_dirs is not None:
+            compiler.set_include_dirs(self.include_dirs)
+        if self.define is not None:
+            # 'define' option is a list of (name,value) tuples
+            for name, value in self.define:
+                compiler.define_macro(name, value)
+        if self.undef is not None:
+            for macro in self.undef:
+                compiler.undefine_macro(macro)
+        if self.libraries is not None:
+            compiler.set_libraries(self.libraries)
+        if self.library_dirs is not None:
+            compiler.set_library_dirs(self.library_dirs)
+        if self.rpath is not None:
+            compiler.set_runtime_library_dirs(self.rpath)
+        if self.link_objects is not None:
+            compiler.set_link_objects(self.link_objects)
+
+        # hack so distutils' build_extension() builds a library instead
+        compiler.link_shared_object = link_shared_object.__get__(compiler)  # type: ignore[method-assign]
+
+    def get_export_symbols(self, ext):
+        if isinstance(ext, Library):
+            return ext.export_symbols
+        return _build_ext.get_export_symbols(self, ext)
+
+    def build_extension(self, ext) -> None:
+        ext._convert_pyx_sources_to_lang()
+        _compiler = self.compiler
+        try:
+            if isinstance(ext, Library):
+                self.compiler = self.shlib_compiler
+            _build_ext.build_extension(self, ext)
+            if ext._needs_stub:
+                build_lib = self.get_finalized_command('build_py').build_lib
+                self.write_stub(build_lib, ext)
+        finally:
+            self.compiler = _compiler
+
+    def links_to_dynamic(self, ext):
+        """Return true if 'ext' links to a dynamic lib in the same package"""
+        # XXX this should check to ensure the lib is actually being built
+        # XXX as dynamic, and not just using a locally-found version or a
+        # XXX static-compiled version
+        libnames = dict.fromkeys([lib._full_name for lib in self.shlibs])
+        pkg = '.'.join(ext._full_name.split('.')[:-1] + [''])
+        return any(pkg + libname in libnames for libname in ext.libraries)
+
+    def get_source_files(self) -> list[str]:
+        return [*_build_ext.get_source_files(self), *self._get_internal_depends()]
+
+    def _get_internal_depends(self) -> Iterator[str]:
+        """Yield ``ext.depends`` that are contained by the project directory"""
+        project_root = Path(self.distribution.src_root or os.curdir).resolve()
+        depends = (dep for ext in self.extensions for dep in ext.depends)
+
+        def skip(orig_path: str, reason: str) -> None:
+            log.info(
+                "dependency %s won't be automatically "
+                "included in the manifest: the path %s",
+                orig_path,
+                reason,
+            )
+
+        for dep in depends:
+            path = Path(dep)
+
+            if path.is_absolute():
+                skip(dep, "must be relative")
+                continue
+
+            if ".." in path.parts:
+                skip(dep, "can't have `..` segments")
+                continue
+
+            try:
+                resolved = (project_root / path).resolve(strict=True)
+            except OSError:
+                skip(dep, "doesn't exist")
+                continue
+
+            try:
+                resolved.relative_to(project_root)
+            except ValueError:
+                skip(dep, "must be inside the project root")
+                continue
+
+            yield path.as_posix()
+
+    def get_outputs(self) -> list[str]:
+        if self.inplace:
+            return list(self.get_output_mapping().keys())
+        return sorted(_build_ext.get_outputs(self) + self.__get_stubs_outputs())
+
+    def get_output_mapping(self) -> dict[str, str]:
+        """See :class:`setuptools.commands.build.SubCommand`"""
+        mapping = self._get_output_mapping()
+        return dict(sorted(mapping, key=lambda x: x[0]))
+
+    def __get_stubs_outputs(self):
+        # assemble the base name for each extension that needs a stub
+        ns_ext_bases = (
+            os.path.join(self.build_lib, *ext._full_name.split('.'))
+            for ext in self.extensions
+            if ext._needs_stub
+        )
+        # pair each base with the extension
+        pairs = itertools.product(ns_ext_bases, self.__get_output_extensions())
+        return list(base + fnext for base, fnext in pairs)
+
+    def __get_output_extensions(self):
+        yield '.py'
+        yield '.pyc'
+        if self.get_finalized_command('build_py').optimize:
+            yield '.pyo'
+
+    def write_stub(self, output_dir, ext, compile=False) -> None:
+        stub_file = os.path.join(output_dir, *ext._full_name.split('.')) + '.py'
+        self._write_stub_file(stub_file, ext, compile)
+
+    def _write_stub_file(self, stub_file: str, ext: Extension, compile=False):
+        log.info("writing stub loader for %s to %s", ext._full_name, stub_file)
+        if compile and os.path.exists(stub_file):
+            raise BaseError(stub_file + " already exists! Please delete.")
+        if not self.dry_run:
+            with open(stub_file, 'w', encoding="utf-8") as f:
+                content = '\n'.join([
+                    "def __bootstrap__():",
+                    "   global __bootstrap__, __file__, __loader__",
+                    "   import sys, os, pkg_resources, importlib.util" + if_dl(", dl"),
+                    "   __file__ = pkg_resources.resource_filename"
+                    f"(__name__,{os.path.basename(ext._file_name)!r})",
+                    "   del __bootstrap__",
+                    "   if '__loader__' in globals():",
+                    "       del __loader__",
+                    if_dl("   old_flags = sys.getdlopenflags()"),
+                    "   old_dir = os.getcwd()",
+                    "   try:",
+                    "     os.chdir(os.path.dirname(__file__))",
+                    if_dl("     sys.setdlopenflags(dl.RTLD_NOW)"),
+                    "     spec = importlib.util.spec_from_file_location(",
+                    "                __name__, __file__)",
+                    "     mod = importlib.util.module_from_spec(spec)",
+                    "     spec.loader.exec_module(mod)",
+                    "   finally:",
+                    if_dl("     sys.setdlopenflags(old_flags)"),
+                    "     os.chdir(old_dir)",
+                    "__bootstrap__()",
+                    "",  # terminal \n
+                ])
+                f.write(content)
+        if compile:
+            self._compile_and_remove_stub(stub_file)
+
+    def _compile_and_remove_stub(self, stub_file: str):
+        from distutils.util import byte_compile
+
+        byte_compile([stub_file], optimize=0, force=True, dry_run=self.dry_run)
+        optimize = self.get_finalized_command('install_lib').optimize
+        if optimize > 0:
+            byte_compile(
+                [stub_file],
+                optimize=optimize,
+                force=True,
+                dry_run=self.dry_run,
+            )
+        if os.path.exists(stub_file) and not self.dry_run:
+            os.unlink(stub_file)
+
+
+if use_stubs or os.name == 'nt':
+    # Build shared libraries
+    #
+    def link_shared_object(
+        self,
+        objects,
+        output_libname,
+        output_dir=None,
+        libraries=None,
+        library_dirs=None,
+        runtime_library_dirs=None,
+        export_symbols=None,
+        debug: bool = False,
+        extra_preargs=None,
+        extra_postargs=None,
+        build_temp=None,
+        target_lang=None,
+    ) -> None:
+        self.link(
+            self.SHARED_LIBRARY,
+            objects,
+            output_libname,
+            output_dir,
+            libraries,
+            library_dirs,
+            runtime_library_dirs,
+            export_symbols,
+            debug,
+            extra_preargs,
+            extra_postargs,
+            build_temp,
+            target_lang,
+        )
+
+else:
+    # Build static libraries everywhere else
+    libtype = 'static'
+
+    def link_shared_object(
+        self,
+        objects,
+        output_libname,
+        output_dir=None,
+        libraries=None,
+        library_dirs=None,
+        runtime_library_dirs=None,
+        export_symbols=None,
+        debug: bool = False,
+        extra_preargs=None,
+        extra_postargs=None,
+        build_temp=None,
+        target_lang=None,
+    ) -> None:
+        # XXX we need to either disallow these attrs on Library instances,
+        # or warn/abort here if set, or something...
+        # libraries=None, library_dirs=None, runtime_library_dirs=None,
+        # export_symbols=None, extra_preargs=None, extra_postargs=None,
+        # build_temp=None
+
+        assert output_dir is None  # distutils build_ext doesn't pass this
+        output_dir, filename = os.path.split(output_libname)
+        basename, _ext = os.path.splitext(filename)
+        if self.library_filename("x").startswith('lib'):
+            # strip 'lib' prefix; this is kludgy if some platform uses
+            # a different prefix
+            basename = basename[3:]
+
+        self.create_static_lib(objects, basename, output_dir, debug, target_lang)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_py.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..2f6fcb7cdcb39a61007acbb399c84125cce93c9f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/build_py.py
@@ -0,0 +1,400 @@
+from __future__ import annotations
+
+import fnmatch
+import itertools
+import os
+import stat
+import textwrap
+from collections.abc import Iterable, Iterator
+from functools import partial
+from glob import glob
+from pathlib import Path
+
+from more_itertools import unique_everseen
+
+from .._path import StrPath, StrPathT
+from ..dist import Distribution
+from ..warnings import SetuptoolsDeprecationWarning
+
+import distutils.command.build_py as orig
+import distutils.errors
+from distutils.util import convert_path
+
+_IMPLICIT_DATA_FILES = ('*.pyi', 'py.typed')
+
+
+def make_writable(target) -> None:
+    os.chmod(target, os.stat(target).st_mode | stat.S_IWRITE)
+
+
+class build_py(orig.build_py):
+    """Enhanced 'build_py' command that includes data files with packages
+
+    The data files are specified via a 'package_data' argument to 'setup()'.
+    See 'setuptools.dist.Distribution' for more details.
+
+    Also, this version of the 'build_py' command allows you to specify both
+    'py_modules' and 'packages' in the same setup operation.
+    """
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+    editable_mode: bool = False
+    existing_egg_info_dir: StrPath | None = None  #: Private API, internal use only.
+
+    def finalize_options(self):
+        orig.build_py.finalize_options(self)
+        self.package_data = self.distribution.package_data
+        self.exclude_package_data = self.distribution.exclude_package_data or {}
+        if 'data_files' in self.__dict__:
+            del self.__dict__['data_files']
+
+    def copy_file(  # type: ignore[override] # No overload, no bytes support
+        self,
+        infile: StrPath,
+        outfile: StrPathT,
+        preserve_mode: bool = True,
+        preserve_times: bool = True,
+        link: str | None = None,
+        level: object = 1,
+    ) -> tuple[StrPathT | str, bool]:
+        # Overwrite base class to allow using links
+        if link:
+            infile = str(Path(infile).resolve())
+            outfile = str(Path(outfile).resolve())  # type: ignore[assignment] # Re-assigning a str when outfile is StrPath is ok
+        return super().copy_file(  # pyright: ignore[reportReturnType] # pypa/distutils#309
+            infile, outfile, preserve_mode, preserve_times, link, level
+        )
+
+    def run(self) -> None:
+        """Build modules, packages, and copy data files to build directory"""
+        if not (self.py_modules or self.packages) or self.editable_mode:
+            return
+
+        if self.py_modules:
+            self.build_modules()
+
+        if self.packages:
+            self.build_packages()
+            self.build_package_data()
+
+        # Only compile actual .py files, using our base class' idea of what our
+        # output files are.
+        self.byte_compile(orig.build_py.get_outputs(self, include_bytecode=False))
+
+    def __getattr__(self, attr: str):
+        "lazily compute data files"
+        if attr == 'data_files':
+            self.data_files = self._get_data_files()
+            return self.data_files
+        return orig.build_py.__getattr__(self, attr)
+
+    def _get_data_files(self):
+        """Generate list of '(package,src_dir,build_dir,filenames)' tuples"""
+        self.analyze_manifest()
+        return list(map(self._get_pkg_data_files, self.packages or ()))
+
+    def get_data_files_without_manifest(self):
+        """
+        Generate list of ``(package,src_dir,build_dir,filenames)`` tuples,
+        but without triggering any attempt to analyze or build the manifest.
+        """
+        # Prevent eventual errors from unset `manifest_files`
+        # (that would otherwise be set by `analyze_manifest`)
+        self.__dict__.setdefault('manifest_files', {})
+        return list(map(self._get_pkg_data_files, self.packages or ()))
+
+    def _get_pkg_data_files(self, package):
+        # Locate package source directory
+        src_dir = self.get_package_dir(package)
+
+        # Compute package build directory
+        build_dir = os.path.join(*([self.build_lib] + package.split('.')))
+
+        # Strip directory from globbed filenames
+        filenames = [
+            os.path.relpath(file, src_dir)
+            for file in self.find_data_files(package, src_dir)
+        ]
+        return package, src_dir, build_dir, filenames
+
+    def find_data_files(self, package, src_dir):
+        """Return filenames for package's data files in 'src_dir'"""
+        patterns = self._get_platform_patterns(
+            self.package_data,
+            package,
+            src_dir,
+            extra_patterns=_IMPLICIT_DATA_FILES,
+        )
+        globs_expanded = map(partial(glob, recursive=True), patterns)
+        # flatten the expanded globs into an iterable of matches
+        globs_matches = itertools.chain.from_iterable(globs_expanded)
+        glob_files = filter(os.path.isfile, globs_matches)
+        files = itertools.chain(
+            self.manifest_files.get(package, []),
+            glob_files,
+        )
+        return self.exclude_data_files(package, src_dir, files)
+
+    def get_outputs(self, include_bytecode: bool = True) -> list[str]:  # type: ignore[override] # Using a real boolean instead of 0|1
+        """See :class:`setuptools.commands.build.SubCommand`"""
+        if self.editable_mode:
+            return list(self.get_output_mapping().keys())
+        return super().get_outputs(include_bytecode)
+
+    def get_output_mapping(self) -> dict[str, str]:
+        """See :class:`setuptools.commands.build.SubCommand`"""
+        mapping = itertools.chain(
+            self._get_package_data_output_mapping(),
+            self._get_module_mapping(),
+        )
+        return dict(sorted(mapping, key=lambda x: x[0]))
+
+    def _get_module_mapping(self) -> Iterator[tuple[str, str]]:
+        """Iterate over all modules producing (dest, src) pairs."""
+        for package, module, module_file in self.find_all_modules():
+            package = package.split('.')
+            filename = self.get_module_outfile(self.build_lib, package, module)
+            yield (filename, module_file)
+
+    def _get_package_data_output_mapping(self) -> Iterator[tuple[str, str]]:
+        """Iterate over package data producing (dest, src) pairs."""
+        for package, src_dir, build_dir, filenames in self.data_files:
+            for filename in filenames:
+                target = os.path.join(build_dir, filename)
+                srcfile = os.path.join(src_dir, filename)
+                yield (target, srcfile)
+
+    def build_package_data(self) -> None:
+        """Copy data files into build directory"""
+        for target, srcfile in self._get_package_data_output_mapping():
+            self.mkpath(os.path.dirname(target))
+            _outf, _copied = self.copy_file(srcfile, target)
+            make_writable(target)
+
+    def analyze_manifest(self) -> None:
+        self.manifest_files: dict[str, list[str]] = {}
+        if not self.distribution.include_package_data:
+            return
+        src_dirs: dict[str, str] = {}
+        for package in self.packages or ():
+            # Locate package source directory
+            src_dirs[assert_relative(self.get_package_dir(package))] = package
+
+        if (
+            self.existing_egg_info_dir
+            and Path(self.existing_egg_info_dir, "SOURCES.txt").exists()
+        ):
+            egg_info_dir = self.existing_egg_info_dir
+            manifest = Path(egg_info_dir, "SOURCES.txt")
+            files = manifest.read_text(encoding="utf-8").splitlines()
+        else:
+            self.run_command('egg_info')
+            ei_cmd = self.get_finalized_command('egg_info')
+            egg_info_dir = ei_cmd.egg_info
+            files = ei_cmd.filelist.files
+
+        check = _IncludePackageDataAbuse()
+        for path in self._filter_build_files(files, egg_info_dir):
+            d, f = os.path.split(assert_relative(path))
+            prev = None
+            oldf = f
+            while d and d != prev and d not in src_dirs:
+                prev = d
+                d, df = os.path.split(d)
+                f = os.path.join(df, f)
+            if d in src_dirs:
+                if f == oldf:
+                    if check.is_module(f):
+                        continue  # it's a module, not data
+                else:
+                    importable = check.importable_subpackage(src_dirs[d], f)
+                    if importable:
+                        check.warn(importable)
+                self.manifest_files.setdefault(src_dirs[d], []).append(path)
+
+    def _filter_build_files(
+        self, files: Iterable[str], egg_info: StrPath
+    ) -> Iterator[str]:
+        """
+        ``build_meta`` may try to create egg_info outside of the project directory,
+        and this can be problematic for certain plugins (reported in issue #3500).
+
+        Extensions might also include between their sources files created on the
+        ``build_lib`` and ``build_temp`` directories.
+
+        This function should filter this case of invalid files out.
+        """
+        build = self.get_finalized_command("build")
+        build_dirs = (egg_info, self.build_lib, build.build_temp, build.build_base)
+        norm_dirs = [os.path.normpath(p) for p in build_dirs if p]
+
+        for file in files:
+            norm_path = os.path.normpath(file)
+            if not os.path.isabs(file) or all(d not in norm_path for d in norm_dirs):
+                yield file
+
+    def get_data_files(self) -> None:
+        pass  # Lazily compute data files in _get_data_files() function.
+
+    def check_package(self, package, package_dir):
+        """Check namespace packages' __init__ for declare_namespace"""
+        try:
+            return self.packages_checked[package]
+        except KeyError:
+            pass
+
+        init_py = orig.build_py.check_package(self, package, package_dir)
+        self.packages_checked[package] = init_py
+
+        if not init_py or not self.distribution.namespace_packages:
+            return init_py
+
+        for pkg in self.distribution.namespace_packages:
+            if pkg == package or pkg.startswith(package + '.'):
+                break
+        else:
+            return init_py
+
+        with open(init_py, 'rb') as f:
+            contents = f.read()
+        if b'declare_namespace' not in contents:
+            raise distutils.errors.DistutilsError(
+                f"Namespace package problem: {package} is a namespace package, but "
+                "its\n__init__.py does not call declare_namespace()! Please "
+                'fix it.\n(See the setuptools manual under '
+                '"Namespace Packages" for details.)\n"'
+            )
+        return init_py
+
+    def initialize_options(self):
+        self.packages_checked = {}
+        orig.build_py.initialize_options(self)
+        self.editable_mode = False
+        self.existing_egg_info_dir = None
+
+    def get_package_dir(self, package):
+        res = orig.build_py.get_package_dir(self, package)
+        if self.distribution.src_root is not None:
+            return os.path.join(self.distribution.src_root, res)
+        return res
+
+    def exclude_data_files(self, package, src_dir, files):
+        """Filter filenames for package's data files in 'src_dir'"""
+        files = list(files)
+        patterns = self._get_platform_patterns(
+            self.exclude_package_data,
+            package,
+            src_dir,
+        )
+        match_groups = (fnmatch.filter(files, pattern) for pattern in patterns)
+        # flatten the groups of matches into an iterable of matches
+        matches = itertools.chain.from_iterable(match_groups)
+        bad = set(matches)
+        keepers = (fn for fn in files if fn not in bad)
+        # ditch dupes
+        return list(unique_everseen(keepers))
+
+    @staticmethod
+    def _get_platform_patterns(spec, package, src_dir, extra_patterns=()):
+        """
+        yield platform-specific path patterns (suitable for glob
+        or fn_match) from a glob-based spec (such as
+        self.package_data or self.exclude_package_data)
+        matching package in src_dir.
+        """
+        raw_patterns = itertools.chain(
+            extra_patterns,
+            spec.get('', []),
+            spec.get(package, []),
+        )
+        return (
+            # Each pattern has to be converted to a platform-specific path
+            os.path.join(src_dir, convert_path(pattern))
+            for pattern in raw_patterns
+        )
+
+
+def assert_relative(path):
+    if not os.path.isabs(path):
+        return path
+    from distutils.errors import DistutilsSetupError
+
+    msg = (
+        textwrap.dedent(
+            """
+        Error: setup script specifies an absolute path:
+
+            %s
+
+        setup() arguments must *always* be /-separated paths relative to the
+        setup.py directory, *never* absolute paths.
+        """
+        ).lstrip()
+        % path
+    )
+    raise DistutilsSetupError(msg)
+
+
+class _IncludePackageDataAbuse:
+    """Inform users that package or module is included as 'data file'"""
+
+    class _Warning(SetuptoolsDeprecationWarning):
+        _SUMMARY = """
+        Package {importable!r} is absent from the `packages` configuration.
+        """
+
+        _DETAILS = """
+        ############################
+        # Package would be ignored #
+        ############################
+        Python recognizes {importable!r} as an importable package[^1],
+        but it is absent from setuptools' `packages` configuration.
+
+        This leads to an ambiguous overall configuration. If you want to distribute this
+        package, please make sure that {importable!r} is explicitly added
+        to the `packages` configuration field.
+
+        Alternatively, you can also rely on setuptools' discovery methods
+        (for example by using `find_namespace_packages(...)`/`find_namespace:`
+        instead of `find_packages(...)`/`find:`).
+
+        You can read more about "package discovery" on setuptools documentation page:
+
+        - https://setuptools.pypa.io/en/latest/userguide/package_discovery.html
+
+        If you don't want {importable!r} to be distributed and are
+        already explicitly excluding {importable!r} via
+        `find_namespace_packages(...)/find_namespace` or `find_packages(...)/find`,
+        you can try to use `exclude_package_data`, or `include-package-data=False` in
+        combination with a more fine grained `package-data` configuration.
+
+        You can read more about "package data files" on setuptools documentation page:
+
+        - https://setuptools.pypa.io/en/latest/userguide/datafiles.html
+
+
+        [^1]: For Python, any directory (with suitable naming) can be imported,
+              even if it does not contain any `.py` files.
+              On the other hand, currently there is no concept of package data
+              directory, all directories are treated like packages.
+        """
+        # _DUE_DATE: still not defined as this is particularly controversial.
+        # Warning initially introduced in May 2022. See issue #3340 for discussion.
+
+    def __init__(self):
+        self._already_warned = set()
+
+    def is_module(self, file):
+        return file.endswith(".py") and file[: -len(".py")].isidentifier()
+
+    def importable_subpackage(self, parent, file):
+        pkg = Path(file).parent
+        parts = list(itertools.takewhile(str.isidentifier, pkg.parts))
+        if parts:
+            return ".".join([parent, *parts])
+        return None
+
+    def warn(self, importable):
+        if importable not in self._already_warned:
+            self._Warning.emit(importable=importable)
+            self._already_warned.add(importable)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/develop.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/develop.py
new file mode 100644
index 0000000000000000000000000000000000000000..7eee29d491f72d8b0869493013a781d88c0aa3cd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/develop.py
@@ -0,0 +1,195 @@
+import glob
+import os
+
+import setuptools
+from setuptools import _normalization, _path, namespaces
+from setuptools.command.easy_install import easy_install
+
+from ..unicode_utils import _read_utf8_with_fallback
+
+from distutils import log
+from distutils.errors import DistutilsOptionError
+from distutils.util import convert_path
+
+
+class develop(namespaces.DevelopInstaller, easy_install):
+    """Set up package for development"""
+
+    description = "install package in 'development mode'"
+
+    user_options = easy_install.user_options + [
+        ("uninstall", "u", "Uninstall this source package"),
+        ("egg-path=", None, "Set the path to be used in the .egg-link file"),
+    ]
+
+    boolean_options = easy_install.boolean_options + ['uninstall']
+
+    command_consumes_arguments = False  # override base
+
+    def run(self):
+        if self.uninstall:
+            self.multi_version = True
+            self.uninstall_link()
+            self.uninstall_namespaces()
+        else:
+            self.install_for_development()
+        self.warn_deprecated_options()
+
+    def initialize_options(self):
+        self.uninstall = None
+        self.egg_path = None
+        easy_install.initialize_options(self)
+        self.setup_path = None
+        self.always_copy_from = '.'  # always copy eggs installed in curdir
+
+    def finalize_options(self) -> None:
+        import pkg_resources
+
+        ei = self.get_finalized_command("egg_info")
+        self.args = [ei.egg_name]
+
+        easy_install.finalize_options(self)
+        self.expand_basedirs()
+        self.expand_dirs()
+        # pick up setup-dir .egg files only: no .egg-info
+        self.package_index.scan(glob.glob('*.egg'))
+
+        egg_link_fn = (
+            _normalization.filename_component_broken(ei.egg_name) + '.egg-link'
+        )
+        self.egg_link = os.path.join(self.install_dir, egg_link_fn)
+        self.egg_base = ei.egg_base
+        if self.egg_path is None:
+            self.egg_path = os.path.abspath(ei.egg_base)
+
+        target = _path.normpath(self.egg_base)
+        egg_path = _path.normpath(os.path.join(self.install_dir, self.egg_path))
+        if egg_path != target:
+            raise DistutilsOptionError(
+                "--egg-path must be a relative path from the install"
+                " directory to " + target
+            )
+
+        # Make a distribution for the package's source
+        self.dist = pkg_resources.Distribution(
+            target,
+            pkg_resources.PathMetadata(target, os.path.abspath(ei.egg_info)),
+            project_name=ei.egg_name,
+        )
+
+        self.setup_path = self._resolve_setup_path(
+            self.egg_base,
+            self.install_dir,
+            self.egg_path,
+        )
+
+    @staticmethod
+    def _resolve_setup_path(egg_base, install_dir, egg_path):
+        """
+        Generate a path from egg_base back to '.' where the
+        setup script resides and ensure that path points to the
+        setup path from $install_dir/$egg_path.
+        """
+        path_to_setup = egg_base.replace(os.sep, '/').rstrip('/')
+        if path_to_setup != os.curdir:
+            path_to_setup = '../' * (path_to_setup.count('/') + 1)
+        resolved = _path.normpath(os.path.join(install_dir, egg_path, path_to_setup))
+        curdir = _path.normpath(os.curdir)
+        if resolved != curdir:
+            raise DistutilsOptionError(
+                "Can't get a consistent path to setup script from"
+                " installation directory",
+                resolved,
+                curdir,
+            )
+        return path_to_setup
+
+    def install_for_development(self) -> None:
+        self.run_command('egg_info')
+
+        # Build extensions in-place
+        self.reinitialize_command('build_ext', inplace=True)
+        self.run_command('build_ext')
+
+        if setuptools.bootstrap_install_from:
+            self.easy_install(setuptools.bootstrap_install_from)
+            setuptools.bootstrap_install_from = None
+
+        self.install_namespaces()
+
+        # create an .egg-link in the installation dir, pointing to our egg
+        log.info("Creating %s (link to %s)", self.egg_link, self.egg_base)
+        if not self.dry_run:
+            with open(self.egg_link, "w", encoding="utf-8") as f:
+                f.write(self.egg_path + "\n" + self.setup_path)
+        # postprocess the installed distro, fixing up .pth, installing scripts,
+        # and handling requirements
+        self.process_distribution(None, self.dist, not self.no_deps)
+
+    def uninstall_link(self) -> None:
+        if os.path.exists(self.egg_link):
+            log.info("Removing %s (link to %s)", self.egg_link, self.egg_base)
+
+            contents = [
+                line.rstrip()
+                for line in _read_utf8_with_fallback(self.egg_link).splitlines()
+            ]
+
+            if contents not in ([self.egg_path], [self.egg_path, self.setup_path]):
+                log.warn("Link points to %s: uninstall aborted", contents)
+                return
+            if not self.dry_run:
+                os.unlink(self.egg_link)
+        if not self.dry_run:
+            self.update_pth(self.dist)  # remove any .pth link to us
+        if self.distribution.scripts:
+            # XXX should also check for entry point scripts!
+            log.warn("Note: you must uninstall or replace scripts manually!")
+
+    def install_egg_scripts(self, dist):
+        if dist is not self.dist:
+            # Installing a dependency, so fall back to normal behavior
+            return easy_install.install_egg_scripts(self, dist)
+
+        # create wrapper scripts in the script dir, pointing to dist.scripts
+
+        # new-style...
+        self.install_wrapper_scripts(dist)
+
+        # ...and old-style
+        for script_name in self.distribution.scripts or []:
+            script_path = os.path.abspath(convert_path(script_name))
+            script_name = os.path.basename(script_path)
+            script_text = _read_utf8_with_fallback(script_path)
+            self.install_script(dist, script_name, script_text, script_path)
+
+        return None
+
+    def install_wrapper_scripts(self, dist):
+        dist = VersionlessRequirement(dist)
+        return easy_install.install_wrapper_scripts(self, dist)
+
+
+class VersionlessRequirement:
+    """
+    Adapt a pkg_resources.Distribution to simply return the project
+    name as the 'requirement' so that scripts will work across
+    multiple versions.
+
+    >>> from pkg_resources import Distribution
+    >>> dist = Distribution(project_name='foo', version='1.0')
+    >>> str(dist.as_requirement())
+    'foo==1.0'
+    >>> adapted_dist = VersionlessRequirement(dist)
+    >>> str(adapted_dist.as_requirement())
+    'foo'
+    """
+
+    def __init__(self, dist) -> None:
+        self.__dist = dist
+
+    def __getattr__(self, name: str):
+        return getattr(self.__dist, name)
+
+    def as_requirement(self):
+        return self.project_name
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/dist_info.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/dist_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..dca01ff0ce355dfd375512e4a06b05b909ee41b6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/dist_info.py
@@ -0,0 +1,103 @@
+"""
+Create a dist_info directory
+As defined in the wheel specification
+"""
+
+import os
+import shutil
+from contextlib import contextmanager
+from pathlib import Path
+from typing import cast
+
+from .. import _normalization
+from .._shutil import rmdir as _rm
+from .egg_info import egg_info as egg_info_cls
+
+from distutils import log
+from distutils.core import Command
+
+
+class dist_info(Command):
+    """
+    This command is private and reserved for internal use of setuptools,
+    users should rely on ``setuptools.build_meta`` APIs.
+    """
+
+    description = "DO NOT CALL DIRECTLY, INTERNAL ONLY: create .dist-info directory"
+
+    user_options = [
+        (
+            'output-dir=',
+            'o',
+            "directory inside of which the .dist-info will be"
+            "created [default: top of the source tree]",
+        ),
+        ('tag-date', 'd', "Add date stamp (e.g. 20050528) to version number"),
+        ('tag-build=', 'b', "Specify explicit tag to add to version number"),
+        ('no-date', 'D', "Don't include date stamp [default]"),
+        ('keep-egg-info', None, "*TRANSITIONAL* will be removed in the future"),
+    ]
+
+    boolean_options = ['tag-date', 'keep-egg-info']
+    negative_opt = {'no-date': 'tag-date'}
+
+    def initialize_options(self):
+        self.output_dir = None
+        self.name = None
+        self.dist_info_dir = None
+        self.tag_date = None
+        self.tag_build = None
+        self.keep_egg_info = False
+
+    def finalize_options(self) -> None:
+        dist = self.distribution
+        project_dir = dist.src_root or os.curdir
+        self.output_dir = Path(self.output_dir or project_dir)
+
+        egg_info = cast(egg_info_cls, self.reinitialize_command("egg_info"))
+        egg_info.egg_base = str(self.output_dir)
+
+        if self.tag_date:
+            egg_info.tag_date = self.tag_date
+        else:
+            self.tag_date = egg_info.tag_date
+
+        if self.tag_build:
+            egg_info.tag_build = self.tag_build
+        else:
+            self.tag_build = egg_info.tag_build
+
+        egg_info.finalize_options()
+        self.egg_info = egg_info
+
+        name = _normalization.safer_name(dist.get_name())
+        version = _normalization.safer_best_effort_version(dist.get_version())
+        self.name = f"{name}-{version}"
+        self.dist_info_dir = os.path.join(self.output_dir, f"{self.name}.dist-info")
+
+    @contextmanager
+    def _maybe_bkp_dir(self, dir_path: str, requires_bkp: bool):
+        if requires_bkp:
+            bkp_name = f"{dir_path}.__bkp__"
+            _rm(bkp_name, ignore_errors=True)
+            shutil.copytree(dir_path, bkp_name, dirs_exist_ok=True, symlinks=True)
+            try:
+                yield
+            finally:
+                _rm(dir_path, ignore_errors=True)
+                shutil.move(bkp_name, dir_path)
+        else:
+            yield
+
+    def run(self) -> None:
+        self.output_dir.mkdir(parents=True, exist_ok=True)
+        self.egg_info.run()
+        egg_info_dir = self.egg_info.egg_info
+        assert os.path.isdir(egg_info_dir), ".egg-info dir should have been created"
+
+        log.info(f"creating '{os.path.abspath(self.dist_info_dir)}'")
+        bdist_wheel = self.get_finalized_command('bdist_wheel')
+
+        # TODO: if bdist_wheel if merged into setuptools, just add "keep_egg_info" there
+        with self._maybe_bkp_dir(egg_info_dir, self.keep_egg_info):
+            bdist_wheel.egg2dist(egg_info_dir, self.dist_info_dir)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/easy_install.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/easy_install.py
new file mode 100644
index 0000000000000000000000000000000000000000..eb1b4c1fcc21dbebf23b5669913a59aaf3ce104a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/easy_install.py
@@ -0,0 +1,2365 @@
+"""
+Easy Install
+------------
+
+A tool for doing automatic download/extract/build of distutils-based Python
+packages.  For detailed documentation, see the accompanying EasyInstall.txt
+file, or visit the `EasyInstall home page`__.
+
+__ https://setuptools.pypa.io/en/latest/deprecated/easy_install.html
+
+"""
+
+from __future__ import annotations
+
+import configparser
+import contextlib
+import io
+import os
+import random
+import re
+import shlex
+import shutil
+import site
+import stat
+import struct
+import subprocess
+import sys
+import sysconfig
+import tempfile
+import textwrap
+import warnings
+import zipfile
+import zipimport
+from collections.abc import Iterable
+from glob import glob
+from sysconfig import get_path
+from typing import TYPE_CHECKING, NoReturn, TypedDict
+
+from jaraco.text import yield_lines
+
+import pkg_resources
+from pkg_resources import (
+    DEVELOP_DIST,
+    Distribution,
+    DistributionNotFound,
+    EggMetadata,
+    Environment,
+    PathMetadata,
+    Requirement,
+    VersionConflict,
+    WorkingSet,
+    find_distributions,
+    get_distribution,
+    normalize_path,
+    resource_string,
+)
+from setuptools import Command
+from setuptools.archive_util import unpack_archive
+from setuptools.command import bdist_egg, egg_info, setopt
+from setuptools.package_index import URL_SCHEME, PackageIndex, parse_requirement_arg
+from setuptools.sandbox import run_setup
+from setuptools.warnings import SetuptoolsDeprecationWarning, SetuptoolsWarning
+from setuptools.wheel import Wheel
+
+from .._path import ensure_directory
+from .._shutil import attempt_chmod_verbose as chmod, rmtree as _rmtree
+from ..compat import py39, py312
+
+from distutils import dir_util, log
+from distutils.command import install
+from distutils.command.build_scripts import first_line_re
+from distutils.errors import (
+    DistutilsArgError,
+    DistutilsError,
+    DistutilsOptionError,
+    DistutilsPlatformError,
+)
+from distutils.util import convert_path, get_platform, subst_vars
+
+if TYPE_CHECKING:
+    from typing_extensions import Self
+
+# Turn on PEP440Warnings
+warnings.filterwarnings("default", category=pkg_resources.PEP440Warning)
+
+__all__ = [
+    'easy_install',
+    'PthDistributions',
+    'extract_wininst_cfg',
+    'get_exe_prefixes',
+]
+
+
+def is_64bit():
+    return struct.calcsize("P") == 8
+
+
+def _to_bytes(s):
+    return s.encode('utf8')
+
+
+def isascii(s):
+    try:
+        s.encode('ascii')
+    except UnicodeError:
+        return False
+    return True
+
+
+def _one_liner(text):
+    return textwrap.dedent(text).strip().replace('\n', '; ')
+
+
+class easy_install(Command):
+    """Manage a download/build/install process"""
+
+    description = "Find/get/install Python packages"
+    command_consumes_arguments = True
+
+    user_options = [
+        ('prefix=', None, "installation prefix"),
+        ("zip-ok", "z", "install package as a zipfile"),
+        ("multi-version", "m", "make apps have to require() a version"),
+        ("upgrade", "U", "force upgrade (searches PyPI for latest versions)"),
+        ("install-dir=", "d", "install package to DIR"),
+        ("script-dir=", "s", "install scripts to DIR"),
+        ("exclude-scripts", "x", "Don't install scripts"),
+        ("always-copy", "a", "Copy all needed packages to install dir"),
+        ("index-url=", "i", "base URL of Python Package Index"),
+        ("find-links=", "f", "additional URL(s) to search for packages"),
+        ("build-directory=", "b", "download/extract/build in DIR; keep the results"),
+        (
+            'optimize=',
+            'O',
+            'also compile with optimization: -O1 for "python -O", '
+            '-O2 for "python -OO", and -O0 to disable [default: -O0]',
+        ),
+        ('record=', None, "filename in which to record list of installed files"),
+        ('always-unzip', 'Z', "don't install as a zipfile, no matter what"),
+        ('site-dirs=', 'S', "list of directories where .pth files work"),
+        ('editable', 'e', "Install specified packages in editable form"),
+        ('no-deps', 'N', "don't install dependencies"),
+        ('allow-hosts=', 'H', "pattern(s) that hostnames must match"),
+        ('local-snapshots-ok', 'l', "allow building eggs from local checkouts"),
+        ('version', None, "print version information and exit"),
+        (
+            'no-find-links',
+            None,
+            "Don't load find-links defined in packages being installed",
+        ),
+        ('user', None, f"install in user site-package '{site.USER_SITE}'"),
+    ]
+    boolean_options = [
+        'zip-ok',
+        'multi-version',
+        'exclude-scripts',
+        'upgrade',
+        'always-copy',
+        'editable',
+        'no-deps',
+        'local-snapshots-ok',
+        'version',
+        'user',
+    ]
+
+    negative_opt = {'always-unzip': 'zip-ok'}
+    create_index = PackageIndex
+
+    def initialize_options(self):
+        EasyInstallDeprecationWarning.emit()
+
+        # the --user option seems to be an opt-in one,
+        # so the default should be False.
+        self.user = False
+        self.zip_ok = self.local_snapshots_ok = None
+        self.install_dir = self.script_dir = self.exclude_scripts = None
+        self.index_url = None
+        self.find_links = None
+        self.build_directory = None
+        self.args = None
+        self.optimize = self.record = None
+        self.upgrade = self.always_copy = self.multi_version = None
+        self.editable = self.no_deps = self.allow_hosts = None
+        self.root = self.prefix = self.no_report = None
+        self.version = None
+        self.install_purelib = None  # for pure module distributions
+        self.install_platlib = None  # non-pure (dists w/ extensions)
+        self.install_headers = None  # for C/C++ headers
+        self.install_lib = None  # set to either purelib or platlib
+        self.install_scripts = None
+        self.install_data = None
+        self.install_base = None
+        self.install_platbase = None
+        self.install_userbase = site.USER_BASE
+        self.install_usersite = site.USER_SITE
+        self.no_find_links = None
+
+        # Options not specifiable via command line
+        self.package_index = None
+        self.pth_file = self.always_copy_from = None
+        self.site_dirs = None
+        self.installed_projects = {}
+        # Always read easy_install options, even if we are subclassed, or have
+        # an independent instance created.  This ensures that defaults will
+        # always come from the standard configuration file(s)' "easy_install"
+        # section, even if this is a "develop" or "install" command, or some
+        # other embedding.
+        self._dry_run = None
+        self.verbose = self.distribution.verbose
+        self.distribution._set_command_options(
+            self, self.distribution.get_option_dict('easy_install')
+        )
+
+    def delete_blockers(self, blockers) -> None:
+        extant_blockers = (
+            filename
+            for filename in blockers
+            if os.path.exists(filename) or os.path.islink(filename)
+        )
+        list(map(self._delete_path, extant_blockers))
+
+    def _delete_path(self, path):
+        log.info("Deleting %s", path)
+        if self.dry_run:
+            return
+
+        is_tree = os.path.isdir(path) and not os.path.islink(path)
+        remover = _rmtree if is_tree else os.unlink
+        remover(path)
+
+    @staticmethod
+    def _render_version():
+        """
+        Render the Setuptools version and installation details, then exit.
+        """
+        ver = f'{sys.version_info.major}.{sys.version_info.minor}'
+        dist = get_distribution('setuptools')
+        print(f'setuptools {dist.version} from {dist.location} (Python {ver})')
+        raise SystemExit
+
+    def finalize_options(self) -> None:  # noqa: C901  # is too complex (25)  # FIXME
+        self.version and self._render_version()
+
+        py_version = sys.version.split()[0]
+
+        self.config_vars = dict(sysconfig.get_config_vars())
+
+        self.config_vars.update({
+            'dist_name': self.distribution.get_name(),
+            'dist_version': self.distribution.get_version(),
+            'dist_fullname': self.distribution.get_fullname(),
+            'py_version': py_version,
+            'py_version_short': f'{sys.version_info.major}.{sys.version_info.minor}',
+            'py_version_nodot': f'{sys.version_info.major}{sys.version_info.minor}',
+            'sys_prefix': self.config_vars['prefix'],
+            'sys_exec_prefix': self.config_vars['exec_prefix'],
+            # Only POSIX systems have abiflags
+            'abiflags': getattr(sys, 'abiflags', ''),
+            # Only python 3.9+ has platlibdir
+            'platlibdir': getattr(sys, 'platlibdir', 'lib'),
+        })
+        with contextlib.suppress(AttributeError):
+            # only for distutils outside stdlib
+            self.config_vars.update({
+                'implementation_lower': install._get_implementation().lower(),
+                'implementation': install._get_implementation(),
+            })
+
+        # pypa/distutils#113 Python 3.9 compat
+        self.config_vars.setdefault(
+            'py_version_nodot_plat',
+            getattr(sys, 'windir', '').replace('.', ''),
+        )
+
+        self.config_vars['userbase'] = self.install_userbase
+        self.config_vars['usersite'] = self.install_usersite
+        if self.user and not site.ENABLE_USER_SITE:
+            log.warn("WARNING: The user site-packages directory is disabled.")
+
+        self._fix_install_dir_for_user_site()
+
+        self.expand_basedirs()
+        self.expand_dirs()
+
+        self._expand(
+            'install_dir',
+            'script_dir',
+            'build_directory',
+            'site_dirs',
+        )
+        # If a non-default installation directory was specified, default the
+        # script directory to match it.
+        if self.script_dir is None:
+            self.script_dir = self.install_dir
+
+        if self.no_find_links is None:
+            self.no_find_links = False
+
+        # Let install_dir get set by install_lib command, which in turn
+        # gets its info from the install command, and takes into account
+        # --prefix and --home and all that other crud.
+        self.set_undefined_options('install_lib', ('install_dir', 'install_dir'))
+        # Likewise, set default script_dir from 'install_scripts.install_dir'
+        self.set_undefined_options('install_scripts', ('install_dir', 'script_dir'))
+
+        if self.user and self.install_purelib:
+            self.install_dir = self.install_purelib
+            self.script_dir = self.install_scripts
+        # default --record from the install command
+        self.set_undefined_options('install', ('record', 'record'))
+        self.all_site_dirs = get_site_dirs()
+        self.all_site_dirs.extend(self._process_site_dirs(self.site_dirs))
+
+        if not self.editable:
+            self.check_site_dir()
+        default_index = os.getenv("__EASYINSTALL_INDEX", "https://pypi.org/simple/")
+        # ^ Private API for testing purposes only
+        self.index_url = self.index_url or default_index
+        self.shadow_path = self.all_site_dirs[:]
+        for path_item in self.install_dir, normalize_path(self.script_dir):
+            if path_item not in self.shadow_path:
+                self.shadow_path.insert(0, path_item)
+
+        if self.allow_hosts is not None:
+            hosts = [s.strip() for s in self.allow_hosts.split(',')]
+        else:
+            hosts = ['*']
+        if self.package_index is None:
+            self.package_index = self.create_index(
+                self.index_url,
+                search_path=self.shadow_path,
+                hosts=hosts,
+            )
+        self.local_index = Environment(self.shadow_path + sys.path)
+
+        if self.find_links is not None:
+            if isinstance(self.find_links, str):
+                self.find_links = self.find_links.split()
+        else:
+            self.find_links = []
+        if self.local_snapshots_ok:
+            self.package_index.scan_egg_links(self.shadow_path + sys.path)
+        if not self.no_find_links:
+            self.package_index.add_find_links(self.find_links)
+        self.set_undefined_options('install_lib', ('optimize', 'optimize'))
+        self.optimize = self._validate_optimize(self.optimize)
+
+        if self.editable and not self.build_directory:
+            raise DistutilsArgError(
+                "Must specify a build directory (-b) when using --editable"
+            )
+        if not self.args:
+            raise DistutilsArgError(
+                "No urls, filenames, or requirements specified (see --help)"
+            )
+
+        self.outputs: list[str] = []
+
+    @staticmethod
+    def _process_site_dirs(site_dirs):
+        if site_dirs is None:
+            return
+
+        normpath = map(normalize_path, sys.path)
+        site_dirs = [os.path.expanduser(s.strip()) for s in site_dirs.split(',')]
+        for d in site_dirs:
+            if not os.path.isdir(d):
+                log.warn("%s (in --site-dirs) does not exist", d)
+            elif normalize_path(d) not in normpath:
+                raise DistutilsOptionError(d + " (in --site-dirs) is not on sys.path")
+            else:
+                yield normalize_path(d)
+
+    @staticmethod
+    def _validate_optimize(value):
+        try:
+            value = int(value)
+            if value not in range(3):
+                raise ValueError
+        except ValueError as e:
+            raise DistutilsOptionError("--optimize must be 0, 1, or 2") from e
+
+        return value
+
+    def _fix_install_dir_for_user_site(self):
+        """
+        Fix the install_dir if "--user" was used.
+        """
+        if not self.user:
+            return
+
+        self.create_home_path()
+        if self.install_userbase is None:
+            msg = "User base directory is not specified"
+            raise DistutilsPlatformError(msg)
+        self.install_base = self.install_platbase = self.install_userbase
+        scheme_name = f'{os.name}_user'
+        self.select_scheme(scheme_name)
+
+    def _expand_attrs(self, attrs):
+        for attr in attrs:
+            val = getattr(self, attr)
+            if val is not None:
+                if os.name == 'posix' or os.name == 'nt':
+                    val = os.path.expanduser(val)
+                val = subst_vars(val, self.config_vars)
+                setattr(self, attr, val)
+
+    def expand_basedirs(self) -> None:
+        """Calls `os.path.expanduser` on install_base, install_platbase and
+        root."""
+        self._expand_attrs(['install_base', 'install_platbase', 'root'])
+
+    def expand_dirs(self) -> None:
+        """Calls `os.path.expanduser` on install dirs."""
+        dirs = [
+            'install_purelib',
+            'install_platlib',
+            'install_lib',
+            'install_headers',
+            'install_scripts',
+            'install_data',
+        ]
+        self._expand_attrs(dirs)
+
+    def run(self, show_deprecation: bool = True) -> None:
+        if show_deprecation:
+            self.announce(
+                "WARNING: The easy_install command is deprecated "
+                "and will be removed in a future version.",
+                log.WARN,
+            )
+        if self.verbose != self.distribution.verbose:
+            log.set_verbosity(self.verbose)
+        try:
+            for spec in self.args:
+                self.easy_install(spec, not self.no_deps)
+            if self.record:
+                outputs = self.outputs
+                if self.root:  # strip any package prefix
+                    root_len = len(self.root)
+                    for counter in range(len(outputs)):
+                        outputs[counter] = outputs[counter][root_len:]
+                from distutils import file_util
+
+                self.execute(
+                    file_util.write_file,
+                    (self.record, outputs),
+                    f"writing list of installed files to '{self.record}'",
+                )
+            self.warn_deprecated_options()
+        finally:
+            log.set_verbosity(self.distribution.verbose)
+
+    def pseudo_tempname(self):
+        """Return a pseudo-tempname base in the install directory.
+        This code is intentionally naive; if a malicious party can write to
+        the target directory you're already in deep doodoo.
+        """
+        try:
+            pid = os.getpid()
+        except Exception:
+            pid = random.randint(0, sys.maxsize)
+        return os.path.join(self.install_dir, f"test-easy-install-{pid}")
+
+    def warn_deprecated_options(self) -> None:
+        pass
+
+    def check_site_dir(self) -> None:  # is too complex (12)  # FIXME
+        """Verify that self.install_dir is .pth-capable dir, if needed"""
+
+        instdir = normalize_path(self.install_dir)
+        pth_file = os.path.join(instdir, 'easy-install.pth')
+
+        if not os.path.exists(instdir):
+            try:
+                os.makedirs(instdir)
+            except OSError:
+                self.cant_write_to_target()
+
+        # Is it a configured, PYTHONPATH, implicit, or explicit site dir?
+        is_site_dir = instdir in self.all_site_dirs
+
+        if not is_site_dir and not self.multi_version:
+            # No?  Then directly test whether it does .pth file processing
+            is_site_dir = self.check_pth_processing()
+        else:
+            # make sure we can write to target dir
+            testfile = self.pseudo_tempname() + '.write-test'
+            test_exists = os.path.exists(testfile)
+            try:
+                if test_exists:
+                    os.unlink(testfile)
+                open(testfile, 'wb').close()
+                os.unlink(testfile)
+            except OSError:
+                self.cant_write_to_target()
+
+        if not is_site_dir and not self.multi_version:
+            # Can't install non-multi to non-site dir with easy_install
+            pythonpath = os.environ.get('PYTHONPATH', '')
+            log.warn(self.__no_default_msg, self.install_dir, pythonpath)
+
+        if is_site_dir:
+            if self.pth_file is None:
+                self.pth_file = PthDistributions(pth_file, self.all_site_dirs)
+        else:
+            self.pth_file = None
+
+        if self.multi_version and not os.path.exists(pth_file):
+            self.pth_file = None  # don't create a .pth file
+        self.install_dir = instdir
+
+    __cant_write_msg = textwrap.dedent(
+        """
+        can't create or remove files in install directory
+
+        The following error occurred while trying to add or remove files in the
+        installation directory:
+
+            %s
+
+        The installation directory you specified (via --install-dir, --prefix, or
+        the distutils default setting) was:
+
+            %s
+        """
+    ).lstrip()
+
+    __not_exists_id = textwrap.dedent(
+        """
+        This directory does not currently exist.  Please create it and try again, or
+        choose a different installation directory (using the -d or --install-dir
+        option).
+        """
+    ).lstrip()
+
+    __access_msg = textwrap.dedent(
+        """
+        Perhaps your account does not have write access to this directory?  If the
+        installation directory is a system-owned directory, you may need to sign in
+        as the administrator or "root" account.  If you do not have administrative
+        access to this machine, you may wish to choose a different installation
+        directory, preferably one that is listed in your PYTHONPATH environment
+        variable.
+
+        For information on other options, you may wish to consult the
+        documentation at:
+
+          https://setuptools.pypa.io/en/latest/deprecated/easy_install.html
+
+        Please make the appropriate changes for your system and try again.
+        """
+    ).lstrip()
+
+    def cant_write_to_target(self) -> NoReturn:
+        msg = self.__cant_write_msg % (
+            sys.exc_info()[1],
+            self.install_dir,
+        )
+
+        if not os.path.exists(self.install_dir):
+            msg += '\n' + self.__not_exists_id
+        else:
+            msg += '\n' + self.__access_msg
+        raise DistutilsError(msg)
+
+    def check_pth_processing(self):  # noqa: C901
+        """Empirically verify whether .pth files are supported in inst. dir"""
+        instdir = self.install_dir
+        log.info("Checking .pth file support in %s", instdir)
+        pth_file = self.pseudo_tempname() + ".pth"
+        ok_file = pth_file + '.ok'
+        ok_exists = os.path.exists(ok_file)
+        tmpl = (
+            _one_liner(
+                """
+            import os
+            f = open({ok_file!r}, 'w', encoding="utf-8")
+            f.write('OK')
+            f.close()
+            """
+            )
+            + '\n'
+        )
+        try:
+            if ok_exists:
+                os.unlink(ok_file)
+            dirname = os.path.dirname(ok_file)
+            os.makedirs(dirname, exist_ok=True)
+            f = open(pth_file, 'w', encoding=py312.PTH_ENCODING)
+            # ^-- Python<3.13 require encoding="locale" instead of "utf-8",
+            #     see python/cpython#77102.
+        except OSError:
+            self.cant_write_to_target()
+        else:
+            try:
+                f.write(tmpl.format(**locals()))
+                f.close()
+                f = None
+                executable = sys.executable
+                if os.name == 'nt':
+                    dirname, basename = os.path.split(executable)
+                    alt = os.path.join(dirname, 'pythonw.exe')
+                    use_alt = basename.lower() == 'python.exe' and os.path.exists(alt)
+                    if use_alt:
+                        # use pythonw.exe to avoid opening a console window
+                        executable = alt
+
+                from distutils.spawn import spawn
+
+                spawn([executable, '-E', '-c', 'pass'], 0)
+
+                if os.path.exists(ok_file):
+                    log.info("TEST PASSED: %s appears to support .pth files", instdir)
+                    return True
+            finally:
+                if f:
+                    f.close()
+                if os.path.exists(ok_file):
+                    os.unlink(ok_file)
+                if os.path.exists(pth_file):
+                    os.unlink(pth_file)
+        if not self.multi_version:
+            log.warn("TEST FAILED: %s does NOT support .pth files", instdir)
+        return False
+
+    def install_egg_scripts(self, dist) -> None:
+        """Write all the scripts for `dist`, unless scripts are excluded"""
+        if not self.exclude_scripts and dist.metadata_isdir('scripts'):
+            for script_name in dist.metadata_listdir('scripts'):
+                if dist.metadata_isdir('scripts/' + script_name):
+                    # The "script" is a directory, likely a Python 3
+                    # __pycache__ directory, so skip it.
+                    continue
+                self.install_script(
+                    dist, script_name, dist.get_metadata('scripts/' + script_name)
+                )
+        self.install_wrapper_scripts(dist)
+
+    def add_output(self, path) -> None:
+        if os.path.isdir(path):
+            for base, dirs, files in os.walk(path):
+                for filename in files:
+                    self.outputs.append(os.path.join(base, filename))
+        else:
+            self.outputs.append(path)
+
+    def not_editable(self, spec) -> None:
+        if self.editable:
+            raise DistutilsArgError(
+                f"Invalid argument {spec!r}: you can't use filenames or URLs "
+                "with --editable (except via the --find-links option)."
+            )
+
+    def check_editable(self, spec) -> None:
+        if not self.editable:
+            return
+
+        if os.path.exists(os.path.join(self.build_directory, spec.key)):
+            raise DistutilsArgError(
+                f"{spec.key!r} already exists in {self.build_directory}; can't do a checkout there"
+            )
+
+    @contextlib.contextmanager
+    def _tmpdir(self):
+        tmpdir = tempfile.mkdtemp(prefix="easy_install-")
+        try:
+            # cast to str as workaround for #709 and #710 and #712
+            yield str(tmpdir)
+        finally:
+            os.path.exists(tmpdir) and _rmtree(tmpdir)
+
+    def easy_install(self, spec, deps: bool = False) -> Distribution | None:
+        with self._tmpdir() as tmpdir:
+            if not isinstance(spec, Requirement):
+                if URL_SCHEME(spec):
+                    # It's a url, download it to tmpdir and process
+                    self.not_editable(spec)
+                    dl = self.package_index.download(spec, tmpdir)
+                    return self.install_item(None, dl, tmpdir, deps, True)
+
+                elif os.path.exists(spec):
+                    # Existing file or directory, just process it directly
+                    self.not_editable(spec)
+                    return self.install_item(None, spec, tmpdir, deps, True)
+                else:
+                    spec = parse_requirement_arg(spec)
+
+            self.check_editable(spec)
+            dist = self.package_index.fetch_distribution(
+                spec,
+                tmpdir,
+                self.upgrade,
+                self.editable,
+                not self.always_copy,
+                self.local_index,
+            )
+            if dist is None:
+                msg = f"Could not find suitable distribution for {spec!r}"
+                if self.always_copy:
+                    msg += " (--always-copy skips system and development eggs)"
+                raise DistutilsError(msg)
+            elif dist.precedence == DEVELOP_DIST:
+                # .egg-info dists don't need installing, just process deps
+                self.process_distribution(spec, dist, deps, "Using")
+                return dist
+            else:
+                return self.install_item(spec, dist.location, tmpdir, deps)
+
+    def install_item(
+        self, spec, download, tmpdir, deps, install_needed: bool = False
+    ) -> Distribution | None:
+        # Installation is also needed if file in tmpdir or is not an egg
+        install_needed = install_needed or bool(self.always_copy)
+        install_needed = install_needed or os.path.dirname(download) == tmpdir
+        install_needed = install_needed or not download.endswith('.egg')
+        install_needed = install_needed or (
+            self.always_copy_from is not None
+            and os.path.dirname(normalize_path(download))
+            == normalize_path(self.always_copy_from)
+        )
+
+        if spec and not install_needed:
+            # at this point, we know it's a local .egg, we just don't know if
+            # it's already installed.
+            for dist in self.local_index[spec.project_name]:
+                if dist.location == download:
+                    break
+            else:
+                install_needed = True  # it's not in the local index
+
+        log.info("Processing %s", os.path.basename(download))
+
+        if install_needed:
+            dists = self.install_eggs(spec, download, tmpdir)
+            for dist in dists:
+                self.process_distribution(spec, dist, deps)
+        else:
+            dists = [self.egg_distribution(download)]
+            self.process_distribution(spec, dists[0], deps, "Using")
+
+        if spec is not None:
+            for dist in dists:
+                if dist in spec:
+                    return dist
+        return None
+
+    def select_scheme(self, name):
+        try:
+            install._select_scheme(self, name)
+        except AttributeError:
+            # stdlib distutils
+            install.install.select_scheme(self, name.replace('posix', 'unix'))
+
+    # FIXME: 'easy_install.process_distribution' is too complex (12)
+    def process_distribution(  # noqa: C901
+        self,
+        requirement,
+        dist,
+        deps: bool = True,
+        *info,
+    ) -> None:
+        self.update_pth(dist)
+        self.package_index.add(dist)
+        if dist in self.local_index[dist.key]:
+            self.local_index.remove(dist)
+        self.local_index.add(dist)
+        self.install_egg_scripts(dist)
+        self.installed_projects[dist.key] = dist
+        log.info(self.installation_report(requirement, dist, *info))
+        if dist.has_metadata('dependency_links.txt') and not self.no_find_links:
+            self.package_index.add_find_links(
+                dist.get_metadata_lines('dependency_links.txt')
+            )
+        if not deps and not self.always_copy:
+            return
+        elif requirement is not None and dist.key != requirement.key:
+            log.warn("Skipping dependencies for %s", dist)
+            return  # XXX this is not the distribution we were looking for
+        elif requirement is None or dist not in requirement:
+            # if we wound up with a different version, resolve what we've got
+            distreq = dist.as_requirement()
+            requirement = Requirement(str(distreq))
+        log.info("Processing dependencies for %s", requirement)
+        try:
+            distros = WorkingSet([]).resolve(
+                [requirement], self.local_index, self.easy_install
+            )
+        except DistributionNotFound as e:
+            raise DistutilsError(str(e)) from e
+        except VersionConflict as e:
+            raise DistutilsError(e.report()) from e
+        if self.always_copy or self.always_copy_from:
+            # Force all the relevant distros to be copied or activated
+            for dist in distros:
+                if dist.key not in self.installed_projects:
+                    self.easy_install(dist.as_requirement())
+        log.info("Finished processing dependencies for %s", requirement)
+
+    def should_unzip(self, dist) -> bool:
+        if self.zip_ok is not None:
+            return not self.zip_ok
+        if dist.has_metadata('not-zip-safe'):
+            return True
+        if not dist.has_metadata('zip-safe'):
+            return True
+        return False
+
+    def maybe_move(self, spec, dist_filename, setup_base):
+        dst = os.path.join(self.build_directory, spec.key)
+        if os.path.exists(dst):
+            msg = "%r already exists in %s; build directory %s will not be kept"
+            log.warn(msg, spec.key, self.build_directory, setup_base)
+            return setup_base
+        if os.path.isdir(dist_filename):
+            setup_base = dist_filename
+        else:
+            if os.path.dirname(dist_filename) == setup_base:
+                os.unlink(dist_filename)  # get it out of the tmp dir
+            contents = os.listdir(setup_base)
+            if len(contents) == 1:
+                dist_filename = os.path.join(setup_base, contents[0])
+                if os.path.isdir(dist_filename):
+                    # if the only thing there is a directory, move it instead
+                    setup_base = dist_filename
+        ensure_directory(dst)
+        shutil.move(setup_base, dst)
+        return dst
+
+    def install_wrapper_scripts(self, dist) -> None:
+        if self.exclude_scripts:
+            return
+        for args in ScriptWriter.best().get_args(dist):
+            self.write_script(*args)
+
+    def install_script(self, dist, script_name, script_text, dev_path=None) -> None:
+        """Generate a legacy script wrapper and install it"""
+        spec = str(dist.as_requirement())
+        is_script = is_python_script(script_text, script_name)
+
+        if is_script:
+            body = self._load_template(dev_path) % locals()
+            script_text = ScriptWriter.get_header(script_text) + body
+        self.write_script(script_name, _to_bytes(script_text), 'b')
+
+    @staticmethod
+    def _load_template(dev_path):
+        """
+        There are a couple of template scripts in the package. This
+        function loads one of them and prepares it for use.
+        """
+        # See https://github.com/pypa/setuptools/issues/134 for info
+        # on script file naming and downstream issues with SVR4
+        name = 'script.tmpl'
+        if dev_path:
+            name = name.replace('.tmpl', ' (dev).tmpl')
+
+        raw_bytes = resource_string('setuptools', name)
+        return raw_bytes.decode('utf-8')
+
+    def write_script(self, script_name, contents, mode: str = "t", blockers=()) -> None:
+        """Write an executable file to the scripts directory"""
+        self.delete_blockers(  # clean up old .py/.pyw w/o a script
+            [os.path.join(self.script_dir, x) for x in blockers]
+        )
+        log.info("Installing %s script to %s", script_name, self.script_dir)
+        target = os.path.join(self.script_dir, script_name)
+        self.add_output(target)
+
+        if self.dry_run:
+            return
+
+        mask = current_umask()
+        ensure_directory(target)
+        if os.path.exists(target):
+            os.unlink(target)
+
+        encoding = None if "b" in mode else "utf-8"
+        with open(target, "w" + mode, encoding=encoding) as f:
+            f.write(contents)
+        chmod(target, 0o777 - mask)
+
+    def install_eggs(self, spec, dist_filename, tmpdir) -> list[Distribution]:
+        # .egg dirs or files are already built, so just return them
+        installer_map = {
+            '.egg': self.install_egg,
+            '.exe': self.install_exe,
+            '.whl': self.install_wheel,
+        }
+        try:
+            install_dist = installer_map[dist_filename.lower()[-4:]]
+        except KeyError:
+            pass
+        else:
+            return [install_dist(dist_filename, tmpdir)]
+
+        # Anything else, try to extract and build
+        setup_base = tmpdir
+        if os.path.isfile(dist_filename) and not dist_filename.endswith('.py'):
+            unpack_archive(dist_filename, tmpdir, self.unpack_progress)
+        elif os.path.isdir(dist_filename):
+            setup_base = os.path.abspath(dist_filename)
+
+        if (
+            setup_base.startswith(tmpdir)  # something we downloaded
+            and self.build_directory
+            and spec is not None
+        ):
+            setup_base = self.maybe_move(spec, dist_filename, setup_base)
+
+        # Find the setup.py file
+        setup_script = os.path.join(setup_base, 'setup.py')
+
+        if not os.path.exists(setup_script):
+            setups = glob(os.path.join(setup_base, '*', 'setup.py'))
+            if not setups:
+                raise DistutilsError(
+                    f"Couldn't find a setup script in {os.path.abspath(dist_filename)}"
+                )
+            if len(setups) > 1:
+                raise DistutilsError(
+                    f"Multiple setup scripts in {os.path.abspath(dist_filename)}"
+                )
+            setup_script = setups[0]
+
+        # Now run it, and return the result
+        if self.editable:
+            log.info(self.report_editable(spec, setup_script))
+            return []
+        else:
+            return self.build_and_install(setup_script, setup_base)
+
+    def egg_distribution(self, egg_path):
+        if os.path.isdir(egg_path):
+            metadata = PathMetadata(egg_path, os.path.join(egg_path, 'EGG-INFO'))
+        else:
+            metadata = EggMetadata(zipimport.zipimporter(egg_path))
+        return Distribution.from_filename(egg_path, metadata=metadata)
+
+    # FIXME: 'easy_install.install_egg' is too complex (11)
+    def install_egg(self, egg_path, tmpdir):
+        destination = os.path.join(
+            self.install_dir,
+            os.path.basename(egg_path),
+        )
+        destination = os.path.abspath(destination)
+        if not self.dry_run:
+            ensure_directory(destination)
+
+        dist = self.egg_distribution(egg_path)
+        if not (
+            os.path.exists(destination) and os.path.samefile(egg_path, destination)
+        ):
+            if os.path.isdir(destination) and not os.path.islink(destination):
+                dir_util.remove_tree(destination, dry_run=self.dry_run)
+            elif os.path.exists(destination):
+                self.execute(
+                    os.unlink,
+                    (destination,),
+                    "Removing " + destination,
+                )
+            try:
+                new_dist_is_zipped = False
+                if os.path.isdir(egg_path):
+                    if egg_path.startswith(tmpdir):
+                        f, m = shutil.move, "Moving"
+                    else:
+                        f, m = shutil.copytree, "Copying"
+                elif self.should_unzip(dist):
+                    self.mkpath(destination)
+                    f, m = self.unpack_and_compile, "Extracting"
+                else:
+                    new_dist_is_zipped = True
+                    if egg_path.startswith(tmpdir):
+                        f, m = shutil.move, "Moving"
+                    else:
+                        f, m = shutil.copy2, "Copying"
+                self.execute(
+                    f,
+                    (egg_path, destination),
+                    (m + " %s to %s")
+                    % (os.path.basename(egg_path), os.path.dirname(destination)),
+                )
+                update_dist_caches(
+                    destination,
+                    fix_zipimporter_caches=new_dist_is_zipped,
+                )
+            except Exception:
+                update_dist_caches(destination, fix_zipimporter_caches=False)
+                raise
+
+        self.add_output(destination)
+        return self.egg_distribution(destination)
+
+    def install_exe(self, dist_filename, tmpdir):
+        # See if it's valid, get data
+        cfg = extract_wininst_cfg(dist_filename)
+        if cfg is None:
+            raise DistutilsError(
+                f"{dist_filename} is not a valid distutils Windows .exe"
+            )
+        # Create a dummy distribution object until we build the real distro
+        dist = Distribution(
+            None,
+            project_name=cfg.get('metadata', 'name'),
+            version=cfg.get('metadata', 'version'),
+            platform=get_platform(),
+        )
+
+        # Convert the .exe to an unpacked egg
+        egg_path = os.path.join(tmpdir, dist.egg_name() + '.egg')
+        dist.location = egg_path
+        egg_tmp = egg_path + '.tmp'
+        _egg_info = os.path.join(egg_tmp, 'EGG-INFO')
+        pkg_inf = os.path.join(_egg_info, 'PKG-INFO')
+        ensure_directory(pkg_inf)  # make sure EGG-INFO dir exists
+        dist._provider = PathMetadata(egg_tmp, _egg_info)  # XXX
+        self.exe_to_egg(dist_filename, egg_tmp)
+
+        # Write EGG-INFO/PKG-INFO
+        if not os.path.exists(pkg_inf):
+            with open(pkg_inf, 'w', encoding="utf-8") as f:
+                f.write('Metadata-Version: 1.0\n')
+                for k, v in cfg.items('metadata'):
+                    if k != 'target_version':
+                        k = k.replace('_', '-').title()
+                        f.write(f'{k}: {v}\n')
+        script_dir = os.path.join(_egg_info, 'scripts')
+        # delete entry-point scripts to avoid duping
+        self.delete_blockers([
+            os.path.join(script_dir, args[0]) for args in ScriptWriter.get_args(dist)
+        ])
+        # Build .egg file from tmpdir
+        bdist_egg.make_zipfile(
+            egg_path,
+            egg_tmp,
+            verbose=self.verbose,
+            dry_run=self.dry_run,
+        )
+        # install the .egg
+        return self.install_egg(egg_path, tmpdir)
+
+    # FIXME: 'easy_install.exe_to_egg' is too complex (12)
+    def exe_to_egg(self, dist_filename, egg_tmp) -> None:  # noqa: C901
+        """Extract a bdist_wininst to the directories an egg would use"""
+        # Check for .pth file and set up prefix translations
+        prefixes = get_exe_prefixes(dist_filename)
+        to_compile = []
+        native_libs = []
+        top_level = set()
+
+        def process(src, dst):
+            s = src.lower()
+            for old, new in prefixes:
+                if s.startswith(old):
+                    src = new + src[len(old) :]
+                    parts = src.split('/')
+                    dst = os.path.join(egg_tmp, *parts)
+                    dl = dst.lower()
+                    if dl.endswith('.pyd') or dl.endswith('.dll'):
+                        parts[-1] = bdist_egg.strip_module(parts[-1])
+                        top_level.add([os.path.splitext(parts[0])[0]])
+                        native_libs.append(src)
+                    elif dl.endswith('.py') and old != 'SCRIPTS/':
+                        top_level.add([os.path.splitext(parts[0])[0]])
+                        to_compile.append(dst)
+                    return dst
+            if not src.endswith('.pth'):
+                log.warn("WARNING: can't process %s", src)
+            return None
+
+        # extract, tracking .pyd/.dll->native_libs and .py -> to_compile
+        unpack_archive(dist_filename, egg_tmp, process)
+        stubs = []
+        for res in native_libs:
+            if res.lower().endswith('.pyd'):  # create stubs for .pyd's
+                parts = res.split('/')
+                resource = parts[-1]
+                parts[-1] = bdist_egg.strip_module(parts[-1]) + '.py'
+                pyfile = os.path.join(egg_tmp, *parts)
+                to_compile.append(pyfile)
+                stubs.append(pyfile)
+                bdist_egg.write_stub(resource, pyfile)
+        self.byte_compile(to_compile)  # compile .py's
+        bdist_egg.write_safety_flag(
+            os.path.join(egg_tmp, 'EGG-INFO'), bdist_egg.analyze_egg(egg_tmp, stubs)
+        )  # write zip-safety flag
+
+        for name in 'top_level', 'native_libs':
+            if locals()[name]:
+                txt = os.path.join(egg_tmp, 'EGG-INFO', name + '.txt')
+                if not os.path.exists(txt):
+                    with open(txt, 'w', encoding="utf-8") as f:
+                        f.write('\n'.join(locals()[name]) + '\n')
+
+    def install_wheel(self, wheel_path, tmpdir):
+        wheel = Wheel(wheel_path)
+        assert wheel.is_compatible()
+        destination = os.path.join(self.install_dir, wheel.egg_name())
+        destination = os.path.abspath(destination)
+        if not self.dry_run:
+            ensure_directory(destination)
+        if os.path.isdir(destination) and not os.path.islink(destination):
+            dir_util.remove_tree(destination, dry_run=self.dry_run)
+        elif os.path.exists(destination):
+            self.execute(
+                os.unlink,
+                (destination,),
+                "Removing " + destination,
+            )
+        try:
+            self.execute(
+                wheel.install_as_egg,
+                (destination,),
+                (
+                    f"Installing {os.path.basename(wheel_path)} to {os.path.dirname(destination)}"
+                ),
+            )
+        finally:
+            update_dist_caches(destination, fix_zipimporter_caches=False)
+        self.add_output(destination)
+        return self.egg_distribution(destination)
+
+    __mv_warning = textwrap.dedent(
+        """
+        Because this distribution was installed --multi-version, before you can
+        import modules from this package in an application, you will need to
+        'import pkg_resources' and then use a 'require()' call similar to one of
+        these examples, in order to select the desired version:
+
+            pkg_resources.require("%(name)s")  # latest installed version
+            pkg_resources.require("%(name)s==%(version)s")  # this exact version
+            pkg_resources.require("%(name)s>=%(version)s")  # this version or higher
+        """
+    ).lstrip()
+
+    __id_warning = textwrap.dedent(
+        """
+        Note also that the installation directory must be on sys.path at runtime for
+        this to work.  (e.g. by being the application's script directory, by being on
+        PYTHONPATH, or by being added to sys.path by your code.)
+        """
+    )
+
+    def installation_report(self, req, dist, what: str = "Installed") -> str:
+        """Helpful installation message for display to package users"""
+        msg = "\n%(what)s %(eggloc)s%(extras)s"
+        if self.multi_version and not self.no_report:
+            msg += '\n' + self.__mv_warning
+            if self.install_dir not in map(normalize_path, sys.path):
+                msg += '\n' + self.__id_warning
+
+        eggloc = dist.location
+        name = dist.project_name
+        version = dist.version
+        extras = ''  # TODO: self.report_extras(req, dist)
+        return msg % locals()
+
+    __editable_msg = textwrap.dedent(
+        """
+        Extracted editable version of %(spec)s to %(dirname)s
+
+        If it uses setuptools in its setup script, you can activate it in
+        "development" mode by going to that directory and running::
+
+            %(python)s setup.py develop
+
+        See the setuptools documentation for the "develop" command for more info.
+        """
+    ).lstrip()
+
+    def report_editable(self, spec, setup_script):
+        dirname = os.path.dirname(setup_script)
+        python = sys.executable
+        return '\n' + self.__editable_msg % locals()
+
+    def run_setup(self, setup_script, setup_base, args) -> None:
+        sys.modules.setdefault('distutils.command.bdist_egg', bdist_egg)
+        sys.modules.setdefault('distutils.command.egg_info', egg_info)
+
+        args = list(args)
+        if self.verbose > 2:
+            v = 'v' * (self.verbose - 1)
+            args.insert(0, '-' + v)
+        elif self.verbose < 2:
+            args.insert(0, '-q')
+        if self.dry_run:
+            args.insert(0, '-n')
+        log.info("Running %s %s", setup_script[len(setup_base) + 1 :], ' '.join(args))
+        try:
+            run_setup(setup_script, args)
+        except SystemExit as v:
+            raise DistutilsError(f"Setup script exited with {v.args[0]}") from v
+
+    def build_and_install(self, setup_script, setup_base):
+        args = ['bdist_egg', '--dist-dir']
+
+        dist_dir = tempfile.mkdtemp(
+            prefix='egg-dist-tmp-', dir=os.path.dirname(setup_script)
+        )
+        try:
+            self._set_fetcher_options(os.path.dirname(setup_script))
+            args.append(dist_dir)
+
+            self.run_setup(setup_script, setup_base, args)
+            all_eggs = Environment([dist_dir])
+            eggs = [
+                self.install_egg(dist.location, setup_base)
+                for key in all_eggs
+                for dist in all_eggs[key]
+            ]
+            if not eggs and not self.dry_run:
+                log.warn("No eggs found in %s (setup script problem?)", dist_dir)
+            return eggs
+        finally:
+            _rmtree(dist_dir)
+            log.set_verbosity(self.verbose)  # restore our log verbosity
+
+    def _set_fetcher_options(self, base):
+        """
+        When easy_install is about to run bdist_egg on a source dist, that
+        source dist might have 'setup_requires' directives, requiring
+        additional fetching. Ensure the fetcher options given to easy_install
+        are available to that command as well.
+        """
+        # find the fetch options from easy_install and write them out
+        # to the setup.cfg file.
+        ei_opts = self.distribution.get_option_dict('easy_install').copy()
+        fetch_directives = (
+            'find_links',
+            'site_dirs',
+            'index_url',
+            'optimize',
+            'allow_hosts',
+        )
+        fetch_options = {}
+        for key, val in ei_opts.items():
+            if key not in fetch_directives:
+                continue
+            fetch_options[key] = val[1]
+        # create a settings dictionary suitable for `edit_config`
+        settings = dict(easy_install=fetch_options)
+        cfg_filename = os.path.join(base, 'setup.cfg')
+        setopt.edit_config(cfg_filename, settings)
+
+    def update_pth(self, dist) -> None:  # noqa: C901  # is too complex (11)  # FIXME
+        if self.pth_file is None:
+            return
+
+        for d in self.pth_file[dist.key]:  # drop old entries
+            if not self.multi_version and d.location == dist.location:
+                continue
+
+            log.info("Removing %s from easy-install.pth file", d)
+            self.pth_file.remove(d)
+            if d.location in self.shadow_path:
+                self.shadow_path.remove(d.location)
+
+        if not self.multi_version:
+            if dist.location in self.pth_file.paths:
+                log.info(
+                    "%s is already the active version in easy-install.pth",
+                    dist,
+                )
+            else:
+                log.info("Adding %s to easy-install.pth file", dist)
+                self.pth_file.add(dist)  # add new entry
+                if dist.location not in self.shadow_path:
+                    self.shadow_path.append(dist.location)
+
+        if self.dry_run:
+            return
+
+        self.pth_file.save()
+
+        if dist.key != 'setuptools':
+            return
+
+        # Ensure that setuptools itself never becomes unavailable!
+        # XXX should this check for latest version?
+        filename = os.path.join(self.install_dir, 'setuptools.pth')
+        if os.path.islink(filename):
+            os.unlink(filename)
+
+        with open(filename, 'wt', encoding=py312.PTH_ENCODING) as f:
+            # ^-- Python<3.13 require encoding="locale" instead of "utf-8",
+            #     see python/cpython#77102.
+            f.write(self.pth_file.make_relative(dist.location) + '\n')
+
+    def unpack_progress(self, src, dst):
+        # Progress filter for unpacking
+        log.debug("Unpacking %s to %s", src, dst)
+        return dst  # only unpack-and-compile skips files for dry run
+
+    def unpack_and_compile(self, egg_path, destination) -> None:
+        to_compile = []
+        to_chmod = []
+
+        def pf(src, dst):
+            if dst.endswith('.py') and not src.startswith('EGG-INFO/'):
+                to_compile.append(dst)
+            elif dst.endswith('.dll') or dst.endswith('.so'):
+                to_chmod.append(dst)
+            self.unpack_progress(src, dst)
+            return not self.dry_run and dst or None
+
+        unpack_archive(egg_path, destination, pf)
+        self.byte_compile(to_compile)
+        if not self.dry_run:
+            for f in to_chmod:
+                mode = ((os.stat(f)[stat.ST_MODE]) | 0o555) & 0o7755
+                chmod(f, mode)
+
+    def byte_compile(self, to_compile) -> None:
+        if sys.dont_write_bytecode:
+            return
+
+        from distutils.util import byte_compile
+
+        try:
+            # try to make the byte compile messages quieter
+            log.set_verbosity(self.verbose - 1)
+
+            byte_compile(to_compile, optimize=0, force=True, dry_run=self.dry_run)
+            if self.optimize:
+                byte_compile(
+                    to_compile,
+                    optimize=self.optimize,
+                    force=True,
+                    dry_run=self.dry_run,
+                )
+        finally:
+            log.set_verbosity(self.verbose)  # restore original verbosity
+
+    __no_default_msg = textwrap.dedent(
+        """
+        bad install directory or PYTHONPATH
+
+        You are attempting to install a package to a directory that is not
+        on PYTHONPATH and which Python does not read ".pth" files from.  The
+        installation directory you specified (via --install-dir, --prefix, or
+        the distutils default setting) was:
+
+            %s
+
+        and your PYTHONPATH environment variable currently contains:
+
+            %r
+
+        Here are some of your options for correcting the problem:
+
+        * You can choose a different installation directory, i.e., one that is
+          on PYTHONPATH or supports .pth files
+
+        * You can add the installation directory to the PYTHONPATH environment
+          variable.  (It must then also be on PYTHONPATH whenever you run
+          Python and want to use the package(s) you are installing.)
+
+        * You can set up the installation directory to support ".pth" files by
+          using one of the approaches described here:
+
+          https://setuptools.pypa.io/en/latest/deprecated/easy_install.html#custom-installation-locations
+
+
+        Please make the appropriate changes for your system and try again.
+        """
+    ).strip()
+
+    def create_home_path(self) -> None:
+        """Create directories under ~."""
+        if not self.user:
+            return
+        home = convert_path(os.path.expanduser("~"))
+        for path in only_strs(self.config_vars.values()):
+            if path.startswith(home) and not os.path.isdir(path):
+                self.debug_print(f"os.makedirs('{path}', 0o700)")
+                os.makedirs(path, 0o700)
+
+    INSTALL_SCHEMES = dict(
+        posix=dict(
+            install_dir='$base/lib/python$py_version_short/site-packages',
+            script_dir='$base/bin',
+        ),
+    )
+
+    DEFAULT_SCHEME = dict(
+        install_dir='$base/Lib/site-packages',
+        script_dir='$base/Scripts',
+    )
+
+    def _expand(self, *attrs):
+        config_vars = self.get_finalized_command('install').config_vars
+
+        if self.prefix:
+            # Set default install_dir/scripts from --prefix
+            config_vars = dict(config_vars)
+            config_vars['base'] = self.prefix
+            scheme = self.INSTALL_SCHEMES.get(os.name, self.DEFAULT_SCHEME)
+            for attr, val in scheme.items():
+                if getattr(self, attr, None) is None:
+                    setattr(self, attr, val)
+
+        from distutils.util import subst_vars
+
+        for attr in attrs:
+            val = getattr(self, attr)
+            if val is not None:
+                val = subst_vars(val, config_vars)
+                if os.name == 'posix':
+                    val = os.path.expanduser(val)
+                setattr(self, attr, val)
+
+
+def _pythonpath():
+    items = os.environ.get('PYTHONPATH', '').split(os.pathsep)
+    return filter(None, items)
+
+
+def get_site_dirs():
+    """
+    Return a list of 'site' dirs
+    """
+
+    sitedirs = []
+
+    # start with PYTHONPATH
+    sitedirs.extend(_pythonpath())
+
+    prefixes = [sys.prefix]
+    if sys.exec_prefix != sys.prefix:
+        prefixes.append(sys.exec_prefix)
+    for prefix in prefixes:
+        if not prefix:
+            continue
+
+        if sys.platform in ('os2emx', 'riscos'):
+            sitedirs.append(os.path.join(prefix, "Lib", "site-packages"))
+        elif os.sep == '/':
+            sitedirs.extend([
+                os.path.join(
+                    prefix,
+                    "lib",
+                    f"python{sys.version_info.major}.{sys.version_info.minor}",
+                    "site-packages",
+                ),
+                os.path.join(prefix, "lib", "site-python"),
+            ])
+        else:
+            sitedirs.extend([
+                prefix,
+                os.path.join(prefix, "lib", "site-packages"),
+            ])
+        if sys.platform != 'darwin':
+            continue
+
+        # for framework builds *only* we add the standard Apple
+        # locations. Currently only per-user, but /Library and
+        # /Network/Library could be added too
+        if 'Python.framework' not in prefix:
+            continue
+
+        home = os.environ.get('HOME')
+        if not home:
+            continue
+
+        home_sp = os.path.join(
+            home,
+            'Library',
+            'Python',
+            f'{sys.version_info.major}.{sys.version_info.minor}',
+            'site-packages',
+        )
+        sitedirs.append(home_sp)
+    lib_paths = get_path('purelib'), get_path('platlib')
+
+    sitedirs.extend(s for s in lib_paths if s not in sitedirs)
+
+    if site.ENABLE_USER_SITE:
+        sitedirs.append(site.USER_SITE)
+
+    with contextlib.suppress(AttributeError):
+        sitedirs.extend(site.getsitepackages())
+
+    return list(map(normalize_path, sitedirs))
+
+
+def expand_paths(inputs):  # noqa: C901  # is too complex (11)  # FIXME
+    """Yield sys.path directories that might contain "old-style" packages"""
+
+    seen = set()
+
+    for dirname in inputs:
+        dirname = normalize_path(dirname)
+        if dirname in seen:
+            continue
+
+        seen.add(dirname)
+        if not os.path.isdir(dirname):
+            continue
+
+        files = os.listdir(dirname)
+        yield dirname, files
+
+        for name in files:
+            if not name.endswith('.pth'):
+                # We only care about the .pth files
+                continue
+            if name in ('easy-install.pth', 'setuptools.pth'):
+                # Ignore .pth files that we control
+                continue
+
+            # Read the .pth file
+            content = _read_pth(os.path.join(dirname, name))
+            lines = list(yield_lines(content))
+
+            # Yield existing non-dupe, non-import directory lines from it
+            for line in lines:
+                if line.startswith("import"):
+                    continue
+
+                line = normalize_path(line.rstrip())
+                if line in seen:
+                    continue
+
+                seen.add(line)
+                if not os.path.isdir(line):
+                    continue
+
+                yield line, os.listdir(line)
+
+
+def extract_wininst_cfg(dist_filename):
+    """Extract configuration data from a bdist_wininst .exe
+
+    Returns a configparser.RawConfigParser, or None
+    """
+    f = open(dist_filename, 'rb')
+    try:
+        endrec = zipfile._EndRecData(f)
+        if endrec is None:
+            return None
+
+        prepended = (endrec[9] - endrec[5]) - endrec[6]
+        if prepended < 12:  # no wininst data here
+            return None
+        f.seek(prepended - 12)
+
+        tag, cfglen, _bmlen = struct.unpack("egg path translations for a given .exe file"""
+
+    prefixes = [
+        ('PURELIB/', ''),
+        ('PLATLIB/pywin32_system32', ''),
+        ('PLATLIB/', ''),
+        ('SCRIPTS/', 'EGG-INFO/scripts/'),
+        ('DATA/lib/site-packages', ''),
+    ]
+    z = zipfile.ZipFile(exe_filename)
+    try:
+        for info in z.infolist():
+            name = info.filename
+            parts = name.split('/')
+            if len(parts) == 3 and parts[2] == 'PKG-INFO':
+                if parts[1].endswith('.egg-info'):
+                    prefixes.insert(0, ('/'.join(parts[:2]), 'EGG-INFO/'))
+                    break
+            if len(parts) != 2 or not name.endswith('.pth'):
+                continue
+            if name.endswith('-nspkg.pth'):
+                continue
+            if parts[0].upper() in ('PURELIB', 'PLATLIB'):
+                contents = z.read(name).decode()
+                for pth in yield_lines(contents):
+                    pth = pth.strip().replace('\\', '/')
+                    if not pth.startswith('import'):
+                        prefixes.append(((f'{parts[0]}/{pth}/'), ''))
+    finally:
+        z.close()
+    prefixes = [(x.lower(), y) for x, y in prefixes]
+    prefixes.sort()
+    prefixes.reverse()
+    return prefixes
+
+
+class PthDistributions(Environment):
+    """A .pth file with Distribution paths in it"""
+
+    def __init__(self, filename, sitedirs=()) -> None:
+        self.filename = filename
+        self.sitedirs = list(map(normalize_path, sitedirs))
+        self.basedir = normalize_path(os.path.dirname(self.filename))
+        self.paths, self.dirty = self._load()
+        # keep a copy if someone manually updates the paths attribute on the instance
+        self._init_paths = self.paths[:]
+        super().__init__([], None, None)
+        for path in yield_lines(self.paths):
+            list(map(self.add, find_distributions(path, True)))
+
+    def _load_raw(self):
+        paths = []
+        dirty = saw_import = False
+        seen = set(self.sitedirs)
+        content = _read_pth(self.filename)
+        for line in content.splitlines():
+            path = line.rstrip()
+            # still keep imports and empty/commented lines for formatting
+            paths.append(path)
+            if line.startswith(('import ', 'from ')):
+                saw_import = True
+                continue
+            stripped_path = path.strip()
+            if not stripped_path or stripped_path.startswith('#'):
+                continue
+            # skip non-existent paths, in case somebody deleted a package
+            # manually, and duplicate paths as well
+            normalized_path = normalize_path(os.path.join(self.basedir, path))
+            if normalized_path in seen or not os.path.exists(normalized_path):
+                log.debug("cleaned up dirty or duplicated %r", path)
+                dirty = True
+                paths.pop()
+                continue
+            seen.add(normalized_path)
+        # remove any trailing empty/blank line
+        while paths and not paths[-1].strip():
+            paths.pop()
+            dirty = True
+        return paths, dirty or (paths and saw_import)
+
+    def _load(self):
+        if os.path.isfile(self.filename):
+            return self._load_raw()
+        return [], False
+
+    def save(self) -> None:
+        """Write changed .pth file back to disk"""
+        # first reload the file
+        last_paths, last_dirty = self._load()
+        # and check that there are no difference with what we have.
+        # there can be difference if someone else has written to the file
+        # since we first loaded it.
+        # we don't want to lose the eventual new paths added since then.
+        for path in last_paths[:]:
+            if path not in self.paths:
+                self.paths.append(path)
+                log.info("detected new path %r", path)
+                last_dirty = True
+            else:
+                last_paths.remove(path)
+        # also, re-check that all paths are still valid before saving them
+        for path in self.paths[:]:
+            if path not in last_paths and not path.startswith((
+                'import ',
+                'from ',
+                '#',
+            )):
+                absolute_path = os.path.join(self.basedir, path)
+                if not os.path.exists(absolute_path):
+                    self.paths.remove(path)
+                    log.info("removing now non-existent path %r", path)
+                    last_dirty = True
+
+        self.dirty |= last_dirty or self.paths != self._init_paths
+        if not self.dirty:
+            return
+
+        rel_paths = list(map(self.make_relative, self.paths))
+        if rel_paths:
+            log.debug("Saving %s", self.filename)
+            lines = self._wrap_lines(rel_paths)
+            data = '\n'.join(lines) + '\n'
+            if os.path.islink(self.filename):
+                os.unlink(self.filename)
+            with open(self.filename, 'wt', encoding=py312.PTH_ENCODING) as f:
+                # ^-- Python<3.13 require encoding="locale" instead of "utf-8",
+                #     see python/cpython#77102.
+                f.write(data)
+        elif os.path.exists(self.filename):
+            log.debug("Deleting empty %s", self.filename)
+            os.unlink(self.filename)
+
+        self.dirty = False
+        self._init_paths[:] = self.paths[:]
+
+    @staticmethod
+    def _wrap_lines(lines):
+        return lines
+
+    def add(self, dist) -> None:
+        """Add `dist` to the distribution map"""
+        new_path = dist.location not in self.paths and (
+            dist.location not in self.sitedirs
+            or
+            # account for '.' being in PYTHONPATH
+            dist.location == os.getcwd()
+        )
+        if new_path:
+            self.paths.append(dist.location)
+            self.dirty = True
+        super().add(dist)
+
+    def remove(self, dist) -> None:
+        """Remove `dist` from the distribution map"""
+        while dist.location in self.paths:
+            self.paths.remove(dist.location)
+            self.dirty = True
+        super().remove(dist)
+
+    def make_relative(self, path):
+        npath, last = os.path.split(normalize_path(path))
+        baselen = len(self.basedir)
+        parts = [last]
+        sep = os.altsep == '/' and '/' or os.sep
+        while len(npath) >= baselen:
+            if npath == self.basedir:
+                parts.append(os.curdir)
+                parts.reverse()
+                return sep.join(parts)
+            npath, last = os.path.split(npath)
+            parts.append(last)
+        else:
+            return path
+
+
+class RewritePthDistributions(PthDistributions):
+    @classmethod
+    def _wrap_lines(cls, lines):
+        yield cls.prelude
+        yield from lines
+        yield cls.postlude
+
+    prelude = _one_liner(
+        """
+        import sys
+        sys.__plen = len(sys.path)
+        """
+    )
+    postlude = _one_liner(
+        """
+        import sys
+        new = sys.path[sys.__plen:]
+        del sys.path[sys.__plen:]
+        p = getattr(sys, '__egginsert', 0)
+        sys.path[p:p] = new
+        sys.__egginsert = p + len(new)
+        """
+    )
+
+
+if os.environ.get('SETUPTOOLS_SYS_PATH_TECHNIQUE', 'raw') == 'rewrite':
+    PthDistributions = RewritePthDistributions  # type: ignore[misc]  # Overwriting type
+
+
+def _first_line_re():
+    """
+    Return a regular expression based on first_line_re suitable for matching
+    strings.
+    """
+    if isinstance(first_line_re.pattern, str):
+        return first_line_re
+
+    # first_line_re in Python >=3.1.4 and >=3.2.1 is a bytes pattern.
+    return re.compile(first_line_re.pattern.decode())
+
+
+def update_dist_caches(dist_path, fix_zipimporter_caches):
+    """
+    Fix any globally cached `dist_path` related data
+
+    `dist_path` should be a path of a newly installed egg distribution (zipped
+    or unzipped).
+
+    sys.path_importer_cache contains finder objects that have been cached when
+    importing data from the original distribution. Any such finders need to be
+    cleared since the replacement distribution might be packaged differently,
+    e.g. a zipped egg distribution might get replaced with an unzipped egg
+    folder or vice versa. Having the old finders cached may then cause Python
+    to attempt loading modules from the replacement distribution using an
+    incorrect loader.
+
+    zipimport.zipimporter objects are Python loaders charged with importing
+    data packaged inside zip archives. If stale loaders referencing the
+    original distribution, are left behind, they can fail to load modules from
+    the replacement distribution. E.g. if an old zipimport.zipimporter instance
+    is used to load data from a new zipped egg archive, it may cause the
+    operation to attempt to locate the requested data in the wrong location -
+    one indicated by the original distribution's zip archive directory
+    information. Such an operation may then fail outright, e.g. report having
+    read a 'bad local file header', or even worse, it may fail silently &
+    return invalid data.
+
+    zipimport._zip_directory_cache contains cached zip archive directory
+    information for all existing zipimport.zipimporter instances and all such
+    instances connected to the same archive share the same cached directory
+    information.
+
+    If asked, and the underlying Python implementation allows it, we can fix
+    all existing zipimport.zipimporter instances instead of having to track
+    them down and remove them one by one, by updating their shared cached zip
+    archive directory information. This, of course, assumes that the
+    replacement distribution is packaged as a zipped egg.
+
+    If not asked to fix existing zipimport.zipimporter instances, we still do
+    our best to clear any remaining zipimport.zipimporter related cached data
+    that might somehow later get used when attempting to load data from the new
+    distribution and thus cause such load operations to fail. Note that when
+    tracking down such remaining stale data, we can not catch every conceivable
+    usage from here, and we clear only those that we know of and have found to
+    cause problems if left alive. Any remaining caches should be updated by
+    whomever is in charge of maintaining them, i.e. they should be ready to
+    handle us replacing their zip archives with new distributions at runtime.
+
+    """
+    # There are several other known sources of stale zipimport.zipimporter
+    # instances that we do not clear here, but might if ever given a reason to
+    # do so:
+    # * Global setuptools pkg_resources.working_set (a.k.a. 'master working
+    # set') may contain distributions which may in turn contain their
+    #   zipimport.zipimporter loaders.
+    # * Several zipimport.zipimporter loaders held by local variables further
+    #   up the function call stack when running the setuptools installation.
+    # * Already loaded modules may have their __loader__ attribute set to the
+    #   exact loader instance used when importing them. Python 3.4 docs state
+    #   that this information is intended mostly for introspection and so is
+    #   not expected to cause us problems.
+    normalized_path = normalize_path(dist_path)
+    _uncache(normalized_path, sys.path_importer_cache)
+    if fix_zipimporter_caches:
+        _replace_zip_directory_cache_data(normalized_path)
+    else:
+        # Here, even though we do not want to fix existing and now stale
+        # zipimporter cache information, we still want to remove it. Related to
+        # Python's zip archive directory information cache, we clear each of
+        # its stale entries in two phases:
+        #   1. Clear the entry so attempting to access zip archive information
+        #      via any existing stale zipimport.zipimporter instances fails.
+        #   2. Remove the entry from the cache so any newly constructed
+        #      zipimport.zipimporter instances do not end up using old stale
+        #      zip archive directory information.
+        # This whole stale data removal step does not seem strictly necessary,
+        # but has been left in because it was done before we started replacing
+        # the zip archive directory information cache content if possible, and
+        # there are no relevant unit tests that we can depend on to tell us if
+        # this is really needed.
+        _remove_and_clear_zip_directory_cache_data(normalized_path)
+
+
+def _collect_zipimporter_cache_entries(normalized_path, cache):
+    """
+    Return zipimporter cache entry keys related to a given normalized path.
+
+    Alternative path spellings (e.g. those using different character case or
+    those using alternative path separators) related to the same path are
+    included. Any sub-path entries are included as well, i.e. those
+    corresponding to zip archives embedded in other zip archives.
+
+    """
+    result = []
+    prefix_len = len(normalized_path)
+    for p in cache:
+        np = normalize_path(p)
+        if np.startswith(normalized_path) and np[prefix_len : prefix_len + 1] in (
+            os.sep,
+            '',
+        ):
+            result.append(p)
+    return result
+
+
+def _update_zipimporter_cache(normalized_path, cache, updater=None):
+    """
+    Update zipimporter cache data for a given normalized path.
+
+    Any sub-path entries are processed as well, i.e. those corresponding to zip
+    archives embedded in other zip archives.
+
+    Given updater is a callable taking a cache entry key and the original entry
+    (after already removing the entry from the cache), and expected to update
+    the entry and possibly return a new one to be inserted in its place.
+    Returning None indicates that the entry should not be replaced with a new
+    one. If no updater is given, the cache entries are simply removed without
+    any additional processing, the same as if the updater simply returned None.
+
+    """
+    for p in _collect_zipimporter_cache_entries(normalized_path, cache):
+        # N.B. pypy's custom zipimport._zip_directory_cache implementation does
+        # not support the complete dict interface:
+        # * Does not support item assignment, thus not allowing this function
+        #    to be used only for removing existing cache entries.
+        #  * Does not support the dict.pop() method, forcing us to use the
+        #    get/del patterns instead. For more detailed information see the
+        #    following links:
+        #      https://github.com/pypa/setuptools/issues/202#issuecomment-202913420
+        #      https://foss.heptapod.net/pypy/pypy/-/blob/144c4e65cb6accb8e592f3a7584ea38265d1873c/pypy/module/zipimport/interp_zipimport.py
+        old_entry = cache[p]
+        del cache[p]
+        new_entry = updater and updater(p, old_entry)
+        if new_entry is not None:
+            cache[p] = new_entry
+
+
+def _uncache(normalized_path, cache):
+    _update_zipimporter_cache(normalized_path, cache)
+
+
+def _remove_and_clear_zip_directory_cache_data(normalized_path):
+    def clear_and_remove_cached_zip_archive_directory_data(path, old_entry):
+        old_entry.clear()
+
+    _update_zipimporter_cache(
+        normalized_path,
+        zipimport._zip_directory_cache,
+        updater=clear_and_remove_cached_zip_archive_directory_data,
+    )
+
+
+# PyPy Python implementation does not allow directly writing to the
+# zipimport._zip_directory_cache and so prevents us from attempting to correct
+# its content. The best we can do there is clear the problematic cache content
+# and have PyPy repopulate it as needed. The downside is that if there are any
+# stale zipimport.zipimporter instances laying around, attempting to use them
+# will fail due to not having its zip archive directory information available
+# instead of being automatically corrected to use the new correct zip archive
+# directory information.
+if '__pypy__' in sys.builtin_module_names:
+    _replace_zip_directory_cache_data = _remove_and_clear_zip_directory_cache_data
+else:
+
+    def _replace_zip_directory_cache_data(normalized_path):
+        def replace_cached_zip_archive_directory_data(path, old_entry):
+            # N.B. In theory, we could load the zip directory information just
+            # once for all updated path spellings, and then copy it locally and
+            # update its contained path strings to contain the correct
+            # spelling, but that seems like a way too invasive move (this cache
+            # structure is not officially documented anywhere and could in
+            # theory change with new Python releases) for no significant
+            # benefit.
+            old_entry.clear()
+            zipimport.zipimporter(path)
+            old_entry.update(zipimport._zip_directory_cache[path])
+            return old_entry
+
+        _update_zipimporter_cache(
+            normalized_path,
+            zipimport._zip_directory_cache,
+            updater=replace_cached_zip_archive_directory_data,
+        )
+
+
+def is_python(text, filename=''):
+    "Is this string a valid Python script?"
+    try:
+        compile(text, filename, 'exec')
+    except (SyntaxError, TypeError):
+        return False
+    else:
+        return True
+
+
+def is_sh(executable):
+    """Determine if the specified executable is a .sh (contains a #! line)"""
+    try:
+        with open(executable, encoding='latin-1') as fp:
+            magic = fp.read(2)
+    except OSError:
+        return executable
+    return magic == '#!'
+
+
+def nt_quote_arg(arg):
+    """Quote a command line argument according to Windows parsing rules"""
+    return subprocess.list2cmdline([arg])
+
+
+def is_python_script(script_text, filename):
+    """Is this text, as a whole, a Python script? (as opposed to shell/bat/etc."""
+    if filename.endswith('.py') or filename.endswith('.pyw'):
+        return True  # extension says it's Python
+    if is_python(script_text, filename):
+        return True  # it's syntactically valid Python
+    if script_text.startswith('#!'):
+        # It begins with a '#!' line, so check if 'python' is in it somewhere
+        return 'python' in script_text.splitlines()[0].lower()
+
+    return False  # Not any Python I can recognize
+
+
+class _SplitArgs(TypedDict, total=False):
+    comments: bool
+    posix: bool
+
+
+class CommandSpec(list):
+    """
+    A command spec for a #! header, specified as a list of arguments akin to
+    those passed to Popen.
+    """
+
+    options: list[str] = []
+    split_args = _SplitArgs()
+
+    @classmethod
+    def best(cls):
+        """
+        Choose the best CommandSpec class based on environmental conditions.
+        """
+        return cls
+
+    @classmethod
+    def _sys_executable(cls):
+        _default = os.path.normpath(sys.executable)
+        return os.environ.get('__PYVENV_LAUNCHER__', _default)
+
+    @classmethod
+    def from_param(cls, param: Self | str | Iterable[str] | None) -> Self:
+        """
+        Construct a CommandSpec from a parameter to build_scripts, which may
+        be None.
+        """
+        if isinstance(param, cls):
+            return param
+        if isinstance(param, str):
+            return cls.from_string(param)
+        if isinstance(param, Iterable):
+            return cls(param)
+        if param is None:
+            return cls.from_environment()
+        raise TypeError(f"Argument has an unsupported type {type(param)}")
+
+    @classmethod
+    def from_environment(cls):
+        return cls([cls._sys_executable()])
+
+    @classmethod
+    def from_string(cls, string: str) -> Self:
+        """
+        Construct a command spec from a simple string representing a command
+        line parseable by shlex.split.
+        """
+        items = shlex.split(string, **cls.split_args)
+        return cls(items)
+
+    def install_options(self, script_text: str):
+        self.options = shlex.split(self._extract_options(script_text))
+        cmdline = subprocess.list2cmdline(self)
+        if not isascii(cmdline):
+            self.options[:0] = ['-x']
+
+    @staticmethod
+    def _extract_options(orig_script):
+        """
+        Extract any options from the first line of the script.
+        """
+        first = (orig_script + '\n').splitlines()[0]
+        match = _first_line_re().match(first)
+        options = match.group(1) or '' if match else ''
+        return options.strip()
+
+    def as_header(self):
+        return self._render(self + list(self.options))
+
+    @staticmethod
+    def _strip_quotes(item):
+        _QUOTES = '"\''
+        for q in _QUOTES:
+            if item.startswith(q) and item.endswith(q):
+                return item[1:-1]
+        return item
+
+    @staticmethod
+    def _render(items):
+        cmdline = subprocess.list2cmdline(
+            CommandSpec._strip_quotes(item.strip()) for item in items
+        )
+        return '#!' + cmdline + '\n'
+
+
+# For pbr compat; will be removed in a future version.
+sys_executable = CommandSpec._sys_executable()
+
+
+class WindowsCommandSpec(CommandSpec):
+    split_args = _SplitArgs(posix=False)
+
+
+class ScriptWriter:
+    """
+    Encapsulates behavior around writing entry point scripts for console and
+    gui apps.
+    """
+
+    template = textwrap.dedent(
+        r"""
+        # EASY-INSTALL-ENTRY-SCRIPT: %(spec)r,%(group)r,%(name)r
+        import re
+        import sys
+
+        # for compatibility with easy_install; see #2198
+        __requires__ = %(spec)r
+
+        try:
+            from importlib.metadata import distribution
+        except ImportError:
+            try:
+                from importlib_metadata import distribution
+            except ImportError:
+                from pkg_resources import load_entry_point
+
+
+        def importlib_load_entry_point(spec, group, name):
+            dist_name, _, _ = spec.partition('==')
+            matches = (
+                entry_point
+                for entry_point in distribution(dist_name).entry_points
+                if entry_point.group == group and entry_point.name == name
+            )
+            return next(matches).load()
+
+
+        globals().setdefault('load_entry_point', importlib_load_entry_point)
+
+
+        if __name__ == '__main__':
+            sys.argv[0] = re.sub(r'(-script\.pyw?|\.exe)?$', '', sys.argv[0])
+            sys.exit(load_entry_point(%(spec)r, %(group)r, %(name)r)())
+        """
+    ).lstrip()
+
+    command_spec_class = CommandSpec
+
+    @classmethod
+    def get_args(cls, dist, header=None):
+        """
+        Yield write_script() argument tuples for a distribution's
+        console_scripts and gui_scripts entry points.
+        """
+        if header is None:
+            header = cls.get_header()
+        spec = str(dist.as_requirement())
+        for type_ in 'console', 'gui':
+            group = type_ + '_scripts'
+            for name in dist.get_entry_map(group).keys():
+                cls._ensure_safe_name(name)
+                script_text = cls.template % locals()
+                args = cls._get_script_args(type_, name, header, script_text)
+                yield from args
+
+    @staticmethod
+    def _ensure_safe_name(name):
+        """
+        Prevent paths in *_scripts entry point names.
+        """
+        has_path_sep = re.search(r'[\\/]', name)
+        if has_path_sep:
+            raise ValueError("Path separators not allowed in script names")
+
+    @classmethod
+    def best(cls):
+        """
+        Select the best ScriptWriter for this environment.
+        """
+        if sys.platform == 'win32' or (os.name == 'java' and os._name == 'nt'):
+            return WindowsScriptWriter.best()
+        else:
+            return cls
+
+    @classmethod
+    def _get_script_args(cls, type_, name, header, script_text):
+        # Simply write the stub with no extension.
+        yield (name, header + script_text)
+
+    @classmethod
+    def get_header(
+        cls,
+        script_text: str = "",
+        executable: str | CommandSpec | Iterable[str] | None = None,
+    ) -> str:
+        """Create a #! line, getting options (if any) from script_text"""
+        cmd = cls.command_spec_class.best().from_param(executable)
+        cmd.install_options(script_text)
+        return cmd.as_header()
+
+
+class WindowsScriptWriter(ScriptWriter):
+    command_spec_class = WindowsCommandSpec
+
+    @classmethod
+    def best(cls):
+        """
+        Select the best ScriptWriter suitable for Windows
+        """
+        writer_lookup = dict(
+            executable=WindowsExecutableLauncherWriter,
+            natural=cls,
+        )
+        # for compatibility, use the executable launcher by default
+        launcher = os.environ.get('SETUPTOOLS_LAUNCHER', 'executable')
+        return writer_lookup[launcher]
+
+    @classmethod
+    def _get_script_args(cls, type_, name, header, script_text):
+        "For Windows, add a .py extension"
+        ext = dict(console='.pya', gui='.pyw')[type_]
+        if ext not in os.environ['PATHEXT'].lower().split(';'):
+            msg = (
+                "{ext} not listed in PATHEXT; scripts will not be "
+                "recognized as executables."
+            ).format(**locals())
+            SetuptoolsWarning.emit(msg)
+        old = ['.pya', '.py', '-script.py', '.pyc', '.pyo', '.pyw', '.exe']
+        old.remove(ext)
+        header = cls._adjust_header(type_, header)
+        blockers = [name + x for x in old]
+        yield name + ext, header + script_text, 't', blockers
+
+    @classmethod
+    def _adjust_header(cls, type_, orig_header):
+        """
+        Make sure 'pythonw' is used for gui and 'python' is used for
+        console (regardless of what sys.executable is).
+        """
+        pattern = 'pythonw.exe'
+        repl = 'python.exe'
+        if type_ == 'gui':
+            pattern, repl = repl, pattern
+        pattern_ob = re.compile(re.escape(pattern), re.IGNORECASE)
+        new_header = pattern_ob.sub(string=orig_header, repl=repl)
+        return new_header if cls._use_header(new_header) else orig_header
+
+    @staticmethod
+    def _use_header(new_header):
+        """
+        Should _adjust_header use the replaced header?
+
+        On non-windows systems, always use. On
+        Windows systems, only use the replaced header if it resolves
+        to an executable on the system.
+        """
+        clean_header = new_header[2:-1].strip('"')
+        return sys.platform != 'win32' or shutil.which(clean_header)
+
+
+class WindowsExecutableLauncherWriter(WindowsScriptWriter):
+    @classmethod
+    def _get_script_args(cls, type_, name, header, script_text):
+        """
+        For Windows, add a .py extension and an .exe launcher
+        """
+        if type_ == 'gui':
+            launcher_type = 'gui'
+            ext = '-script.pyw'
+            old = ['.pyw']
+        else:
+            launcher_type = 'cli'
+            ext = '-script.py'
+            old = ['.py', '.pyc', '.pyo']
+        hdr = cls._adjust_header(type_, header)
+        blockers = [name + x for x in old]
+        yield (name + ext, hdr + script_text, 't', blockers)
+        yield (
+            name + '.exe',
+            get_win_launcher(launcher_type),
+            'b',  # write in binary mode
+        )
+        if not is_64bit():
+            # install a manifest for the launcher to prevent Windows
+            # from detecting it as an installer (which it will for
+            #  launchers like easy_install.exe). Consider only
+            #  adding a manifest for launchers detected as installers.
+            #  See Distribute #143 for details.
+            m_name = name + '.exe.manifest'
+            yield (m_name, load_launcher_manifest(name), 't')
+
+
+def get_win_launcher(type):
+    """
+    Load the Windows launcher (executable) suitable for launching a script.
+
+    `type` should be either 'cli' or 'gui'
+
+    Returns the executable as a byte string.
+    """
+    launcher_fn = f'{type}.exe'
+    if is_64bit():
+        if get_platform() == "win-arm64":
+            launcher_fn = launcher_fn.replace(".", "-arm64.")
+        else:
+            launcher_fn = launcher_fn.replace(".", "-64.")
+    else:
+        launcher_fn = launcher_fn.replace(".", "-32.")
+    return resource_string('setuptools', launcher_fn)
+
+
+def load_launcher_manifest(name):
+    manifest = pkg_resources.resource_string(__name__, 'launcher manifest.xml')
+    return manifest.decode('utf-8') % vars()
+
+
+def current_umask():
+    tmp = os.umask(0o022)
+    os.umask(tmp)
+    return tmp
+
+
+def only_strs(values):
+    """
+    Exclude non-str values. Ref #3063.
+    """
+    return filter(lambda val: isinstance(val, str), values)
+
+
+def _read_pth(fullname: str) -> str:
+    # Python<3.13 require encoding="locale" instead of "utf-8", see python/cpython#77102
+    # In the case old versions of setuptools are producing `pth` files with
+    # different encodings that might be problematic... So we fallback to "locale".
+
+    try:
+        with open(fullname, encoding=py312.PTH_ENCODING) as f:
+            return f.read()
+    except UnicodeDecodeError:  # pragma: no cover
+        # This error may only happen for Python >= 3.13
+        # TODO: Possible deprecation warnings to be added in the future:
+        #       ``.pth file {fullname!r} is not UTF-8.``
+        #       Your environment contain {fullname!r} that cannot be read as UTF-8.
+        #       This is likely to have been produced with an old version of setuptools.
+        #       Please be mindful that this is deprecated and in the future, non-utf8
+        #       .pth files may cause setuptools to fail.
+        with open(fullname, encoding=py39.LOCALE_ENCODING) as f:
+            return f.read()
+
+
+class EasyInstallDeprecationWarning(SetuptoolsDeprecationWarning):
+    _SUMMARY = "easy_install command is deprecated."
+    _DETAILS = """
+    Please avoid running ``setup.py`` and ``easy_install``.
+    Instead, use pypa/build, pypa/installer or other
+    standards-based tools.
+    """
+    _SEE_URL = "https://github.com/pypa/setuptools/issues/917"
+    # _DUE_DATE not defined yet
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/editable_wheel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/editable_wheel.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a544ec258196616a4242b679c20b061c1c4010d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/editable_wheel.py
@@ -0,0 +1,925 @@
+"""
+Create a wheel that, when installed, will make the source package 'editable'
+(add it to the interpreter's path, including metadata) per PEP 660. Replaces
+'setup.py develop'.
+
+.. note::
+   One of the mechanisms briefly mentioned in PEP 660 to implement editable installs is
+   to create a separated directory inside ``build`` and use a .pth file to point to that
+   directory. In the context of this file such directory is referred as
+   *auxiliary build directory* or ``auxiliary_dir``.
+"""
+
+from __future__ import annotations
+
+import io
+import logging
+import os
+import shutil
+import traceback
+from collections.abc import Iterable, Iterator, Mapping
+from contextlib import suppress
+from enum import Enum
+from inspect import cleandoc
+from itertools import chain, starmap
+from pathlib import Path
+from tempfile import TemporaryDirectory
+from types import TracebackType
+from typing import TYPE_CHECKING, Protocol, TypeVar, cast
+
+from .. import Command, _normalization, _path, _shutil, errors, namespaces
+from .._path import StrPath
+from ..compat import py312
+from ..discovery import find_package_path
+from ..dist import Distribution
+from ..warnings import InformationOnly, SetuptoolsDeprecationWarning, SetuptoolsWarning
+from .build import build as build_cls
+from .build_py import build_py as build_py_cls
+from .dist_info import dist_info as dist_info_cls
+from .egg_info import egg_info as egg_info_cls
+from .install import install as install_cls
+from .install_scripts import install_scripts as install_scripts_cls
+
+if TYPE_CHECKING:
+    from typing_extensions import Self
+
+    from .._vendor.wheel.wheelfile import WheelFile
+
+_P = TypeVar("_P", bound=StrPath)
+_logger = logging.getLogger(__name__)
+
+
+class _EditableMode(Enum):
+    """
+    Possible editable installation modes:
+    `lenient` (new files automatically added to the package - DEFAULT);
+    `strict` (requires a new installation when files are added/removed); or
+    `compat` (attempts to emulate `python setup.py develop` - DEPRECATED).
+    """
+
+    STRICT = "strict"
+    LENIENT = "lenient"
+    COMPAT = "compat"  # TODO: Remove `compat` after Dec/2022.
+
+    @classmethod
+    def convert(cls, mode: str | None) -> _EditableMode:
+        if not mode:
+            return _EditableMode.LENIENT  # default
+
+        _mode = mode.upper()
+        if _mode not in _EditableMode.__members__:
+            raise errors.OptionError(f"Invalid editable mode: {mode!r}. Try: 'strict'.")
+
+        if _mode == "COMPAT":
+            SetuptoolsDeprecationWarning.emit(
+                "Compat editable installs",
+                """
+                The 'compat' editable mode is transitional and will be removed
+                in future versions of `setuptools`.
+                Please adapt your code accordingly to use either the 'strict' or the
+                'lenient' modes.
+                """,
+                see_docs="userguide/development_mode.html",
+                # TODO: define due_date
+                # There is a series of shortcomings with the available editable install
+                # methods, and they are very controversial. This is something that still
+                # needs work.
+                # Moreover, `pip` is still hiding this warning, so users are not aware.
+            )
+
+        return _EditableMode[_mode]
+
+
+_STRICT_WARNING = """
+New or renamed files may not be automatically picked up without a new installation.
+"""
+
+_LENIENT_WARNING = """
+Options like `package-data`, `include/exclude-package-data` or
+`packages.find.exclude/include` may have no effect.
+"""
+
+
+class editable_wheel(Command):
+    """Build 'editable' wheel for development.
+    This command is private and reserved for internal use of setuptools,
+    users should rely on ``setuptools.build_meta`` APIs.
+    """
+
+    description = "DO NOT CALL DIRECTLY, INTERNAL ONLY: create PEP 660 editable wheel"
+
+    user_options = [
+        ("dist-dir=", "d", "directory to put final built distributions in"),
+        ("dist-info-dir=", "I", "path to a pre-build .dist-info directory"),
+        ("mode=", None, cleandoc(_EditableMode.__doc__ or "")),
+    ]
+
+    def initialize_options(self):
+        self.dist_dir = None
+        self.dist_info_dir = None
+        self.project_dir = None
+        self.mode = None
+
+    def finalize_options(self) -> None:
+        dist = self.distribution
+        self.project_dir = dist.src_root or os.curdir
+        self.package_dir = dist.package_dir or {}
+        self.dist_dir = Path(self.dist_dir or os.path.join(self.project_dir, "dist"))
+
+    def run(self) -> None:
+        try:
+            self.dist_dir.mkdir(exist_ok=True)
+            self._ensure_dist_info()
+
+            # Add missing dist_info files
+            self.reinitialize_command("bdist_wheel")
+            bdist_wheel = self.get_finalized_command("bdist_wheel")
+            bdist_wheel.write_wheelfile(self.dist_info_dir)
+
+            self._create_wheel_file(bdist_wheel)
+        except Exception:
+            traceback.print_exc()
+            project = self.distribution.name or self.distribution.get_name()
+            _DebuggingTips.emit(project=project)
+            raise
+
+    def _ensure_dist_info(self):
+        if self.dist_info_dir is None:
+            dist_info = cast(dist_info_cls, self.reinitialize_command("dist_info"))
+            dist_info.output_dir = self.dist_dir
+            dist_info.ensure_finalized()
+            dist_info.run()
+            self.dist_info_dir = dist_info.dist_info_dir
+        else:
+            assert str(self.dist_info_dir).endswith(".dist-info")
+            assert Path(self.dist_info_dir, "METADATA").exists()
+
+    def _install_namespaces(self, installation_dir, pth_prefix):
+        # XXX: Only required to support the deprecated namespace practice
+        dist = self.distribution
+        if not dist.namespace_packages:
+            return
+
+        src_root = Path(self.project_dir, self.package_dir.get("", ".")).resolve()
+        installer = _NamespaceInstaller(dist, installation_dir, pth_prefix, src_root)
+        installer.install_namespaces()
+
+    def _find_egg_info_dir(self) -> str | None:
+        parent_dir = Path(self.dist_info_dir).parent if self.dist_info_dir else Path()
+        candidates = map(str, parent_dir.glob("*.egg-info"))
+        return next(candidates, None)
+
+    def _configure_build(
+        self, name: str, unpacked_wheel: StrPath, build_lib: StrPath, tmp_dir: StrPath
+    ):
+        """Configure commands to behave in the following ways:
+
+        - Build commands can write to ``build_lib`` if they really want to...
+          (but this folder is expected to be ignored and modules are expected to live
+          in the project directory...)
+        - Binary extensions should be built in-place (editable_mode = True)
+        - Data/header/script files are not part of the "editable" specification
+          so they are written directly to the unpacked_wheel directory.
+        """
+        # Non-editable files (data, headers, scripts) are written directly to the
+        # unpacked_wheel
+
+        dist = self.distribution
+        wheel = str(unpacked_wheel)
+        build_lib = str(build_lib)
+        data = str(Path(unpacked_wheel, f"{name}.data", "data"))
+        headers = str(Path(unpacked_wheel, f"{name}.data", "headers"))
+        scripts = str(Path(unpacked_wheel, f"{name}.data", "scripts"))
+
+        # egg-info may be generated again to create a manifest (used for package data)
+        egg_info = cast(
+            egg_info_cls, dist.reinitialize_command("egg_info", reinit_subcommands=True)
+        )
+        egg_info.egg_base = str(tmp_dir)
+        egg_info.ignore_egg_info_in_manifest = True
+
+        build = cast(
+            build_cls, dist.reinitialize_command("build", reinit_subcommands=True)
+        )
+        install = cast(
+            install_cls, dist.reinitialize_command("install", reinit_subcommands=True)
+        )
+
+        build.build_platlib = build.build_purelib = build.build_lib = build_lib
+        install.install_purelib = install.install_platlib = install.install_lib = wheel
+        install.install_scripts = build.build_scripts = scripts
+        install.install_headers = headers
+        install.install_data = data
+
+        install_scripts = cast(
+            install_scripts_cls, dist.get_command_obj("install_scripts")
+        )
+        install_scripts.no_ep = True
+
+        build.build_temp = str(tmp_dir)
+
+        build_py = cast(build_py_cls, dist.get_command_obj("build_py"))
+        build_py.compile = False
+        build_py.existing_egg_info_dir = self._find_egg_info_dir()
+
+        self._set_editable_mode()
+
+        build.ensure_finalized()
+        install.ensure_finalized()
+
+    def _set_editable_mode(self):
+        """Set the ``editable_mode`` flag in the build sub-commands"""
+        dist = self.distribution
+        build = dist.get_command_obj("build")
+        for cmd_name in build.get_sub_commands():
+            cmd = dist.get_command_obj(cmd_name)
+            if hasattr(cmd, "editable_mode"):
+                cmd.editable_mode = True
+            elif hasattr(cmd, "inplace"):
+                cmd.inplace = True  # backward compatibility with distutils
+
+    def _collect_build_outputs(self) -> tuple[list[str], dict[str, str]]:
+        files: list[str] = []
+        mapping: dict[str, str] = {}
+        build = self.get_finalized_command("build")
+
+        for cmd_name in build.get_sub_commands():
+            cmd = self.get_finalized_command(cmd_name)
+            if hasattr(cmd, "get_outputs"):
+                files.extend(cmd.get_outputs() or [])
+            if hasattr(cmd, "get_output_mapping"):
+                mapping.update(cmd.get_output_mapping() or {})
+
+        return files, mapping
+
+    def _run_build_commands(
+        self,
+        dist_name: str,
+        unpacked_wheel: StrPath,
+        build_lib: StrPath,
+        tmp_dir: StrPath,
+    ) -> tuple[list[str], dict[str, str]]:
+        self._configure_build(dist_name, unpacked_wheel, build_lib, tmp_dir)
+        self._run_build_subcommands()
+        files, mapping = self._collect_build_outputs()
+        self._run_install("headers")
+        self._run_install("scripts")
+        self._run_install("data")
+        return files, mapping
+
+    def _run_build_subcommands(self) -> None:
+        """
+        Issue #3501 indicates that some plugins/customizations might rely on:
+
+        1. ``build_py`` not running
+        2. ``build_py`` always copying files to ``build_lib``
+
+        However both these assumptions may be false in editable_wheel.
+        This method implements a temporary workaround to support the ecosystem
+        while the implementations catch up.
+        """
+        # TODO: Once plugins/customizations had the chance to catch up, replace
+        #       `self._run_build_subcommands()` with `self.run_command("build")`.
+        #       Also remove _safely_run, TestCustomBuildPy. Suggested date: Aug/2023.
+        build = self.get_finalized_command("build")
+        for name in build.get_sub_commands():
+            cmd = self.get_finalized_command(name)
+            if name == "build_py" and type(cmd) is not build_py_cls:
+                self._safely_run(name)
+            else:
+                self.run_command(name)
+
+    def _safely_run(self, cmd_name: str):
+        try:
+            return self.run_command(cmd_name)
+        except Exception:
+            SetuptoolsDeprecationWarning.emit(
+                "Customization incompatible with editable install",
+                f"""
+                {traceback.format_exc()}
+
+                If you are seeing this warning it is very likely that a setuptools
+                plugin or customization overrides the `{cmd_name}` command, without
+                taking into consideration how editable installs run build steps
+                starting from setuptools v64.0.0.
+
+                Plugin authors and developers relying on custom build steps are
+                encouraged to update their `{cmd_name}` implementation considering the
+                information about editable installs in
+                https://setuptools.pypa.io/en/latest/userguide/extension.html.
+
+                For the time being `setuptools` will silence this error and ignore
+                the faulty command, but this behavior will change in future versions.
+                """,
+                # TODO: define due_date
+                # There is a series of shortcomings with the available editable install
+                # methods, and they are very controversial. This is something that still
+                # needs work.
+            )
+
+    def _create_wheel_file(self, bdist_wheel):
+        from wheel.wheelfile import WheelFile
+
+        dist_info = self.get_finalized_command("dist_info")
+        dist_name = dist_info.name
+        tag = "-".join(bdist_wheel.get_tag())
+        build_tag = "0.editable"  # According to PEP 427 needs to start with digit
+        archive_name = f"{dist_name}-{build_tag}-{tag}.whl"
+        wheel_path = Path(self.dist_dir, archive_name)
+        if wheel_path.exists():
+            wheel_path.unlink()
+
+        unpacked_wheel = TemporaryDirectory(suffix=archive_name)
+        build_lib = TemporaryDirectory(suffix=".build-lib")
+        build_tmp = TemporaryDirectory(suffix=".build-temp")
+
+        with unpacked_wheel as unpacked, build_lib as lib, build_tmp as tmp:
+            unpacked_dist_info = Path(unpacked, Path(self.dist_info_dir).name)
+            shutil.copytree(self.dist_info_dir, unpacked_dist_info)
+            self._install_namespaces(unpacked, dist_name)
+            files, mapping = self._run_build_commands(dist_name, unpacked, lib, tmp)
+            strategy = self._select_strategy(dist_name, tag, lib)
+            with strategy, WheelFile(wheel_path, "w") as wheel_obj:
+                strategy(wheel_obj, files, mapping)
+                wheel_obj.write_files(unpacked)
+
+        return wheel_path
+
+    def _run_install(self, category: str):
+        has_category = getattr(self.distribution, f"has_{category}", None)
+        if has_category and has_category():
+            _logger.info(f"Installing {category} as non editable")
+            self.run_command(f"install_{category}")
+
+    def _select_strategy(
+        self,
+        name: str,
+        tag: str,
+        build_lib: StrPath,
+    ) -> EditableStrategy:
+        """Decides which strategy to use to implement an editable installation."""
+        build_name = f"__editable__.{name}-{tag}"
+        project_dir = Path(self.project_dir)
+        mode = _EditableMode.convert(self.mode)
+
+        if mode is _EditableMode.STRICT:
+            auxiliary_dir = _empty_dir(Path(self.project_dir, "build", build_name))
+            return _LinkTree(self.distribution, name, auxiliary_dir, build_lib)
+
+        packages = _find_packages(self.distribution)
+        has_simple_layout = _simple_layout(packages, self.package_dir, project_dir)
+        is_compat_mode = mode is _EditableMode.COMPAT
+        if set(self.package_dir) == {""} and has_simple_layout or is_compat_mode:
+            # src-layout(ish) is relatively safe for a simple pth file
+            src_dir = self.package_dir.get("", ".")
+            return _StaticPth(self.distribution, name, [Path(project_dir, src_dir)])
+
+        # Use a MetaPathFinder to avoid adding accidental top-level packages/modules
+        return _TopLevelFinder(self.distribution, name)
+
+
+class EditableStrategy(Protocol):
+    def __call__(
+        self, wheel: WheelFile, files: list[str], mapping: Mapping[str, str]
+    ) -> object: ...
+    def __enter__(self) -> Self: ...
+    def __exit__(
+        self,
+        _exc_type: type[BaseException] | None,
+        _exc_value: BaseException | None,
+        _traceback: TracebackType | None,
+    ) -> object: ...
+
+
+class _StaticPth:
+    def __init__(self, dist: Distribution, name: str, path_entries: list[Path]) -> None:
+        self.dist = dist
+        self.name = name
+        self.path_entries = path_entries
+
+    def __call__(self, wheel: WheelFile, files: list[str], mapping: Mapping[str, str]):
+        entries = "\n".join(str(p.resolve()) for p in self.path_entries)
+        contents = _encode_pth(f"{entries}\n")
+        wheel.writestr(f"__editable__.{self.name}.pth", contents)
+
+    def __enter__(self) -> Self:
+        msg = f"""
+        Editable install will be performed using .pth file to extend `sys.path` with:
+        {list(map(os.fspath, self.path_entries))!r}
+        """
+        _logger.warning(msg + _LENIENT_WARNING)
+        return self
+
+    def __exit__(
+        self,
+        _exc_type: object,
+        _exc_value: object,
+        _traceback: object,
+    ) -> None:
+        pass
+
+
+class _LinkTree(_StaticPth):
+    """
+    Creates a ``.pth`` file that points to a link tree in the ``auxiliary_dir``.
+
+    This strategy will only link files (not dirs), so it can be implemented in
+    any OS, even if that means using hardlinks instead of symlinks.
+
+    By collocating ``auxiliary_dir`` and the original source code, limitations
+    with hardlinks should be avoided.
+    """
+
+    def __init__(
+        self,
+        dist: Distribution,
+        name: str,
+        auxiliary_dir: StrPath,
+        build_lib: StrPath,
+    ) -> None:
+        self.auxiliary_dir = Path(auxiliary_dir)
+        self.build_lib = Path(build_lib).resolve()
+        self._file = dist.get_command_obj("build_py").copy_file
+        super().__init__(dist, name, [self.auxiliary_dir])
+
+    def __call__(self, wheel: WheelFile, files: list[str], mapping: Mapping[str, str]):
+        self._create_links(files, mapping)
+        super().__call__(wheel, files, mapping)
+
+    def _normalize_output(self, file: str) -> str | None:
+        # Files relative to build_lib will be normalized to None
+        with suppress(ValueError):
+            path = Path(file).resolve().relative_to(self.build_lib)
+            return str(path).replace(os.sep, '/')
+        return None
+
+    def _create_file(self, relative_output: str, src_file: str, link=None):
+        dest = self.auxiliary_dir / relative_output
+        if not dest.parent.is_dir():
+            dest.parent.mkdir(parents=True)
+        self._file(src_file, dest, link=link)
+
+    def _create_links(self, outputs, output_mapping: Mapping[str, str]):
+        self.auxiliary_dir.mkdir(parents=True, exist_ok=True)
+        link_type = "sym" if _can_symlink_files(self.auxiliary_dir) else "hard"
+        normalised = ((self._normalize_output(k), v) for k, v in output_mapping.items())
+        # remove files that are not relative to build_lib
+        mappings = {k: v for k, v in normalised if k is not None}
+
+        for output in outputs:
+            relative = self._normalize_output(output)
+            if relative and relative not in mappings:
+                self._create_file(relative, output)
+
+        for relative, src in mappings.items():
+            self._create_file(relative, src, link=link_type)
+
+    def __enter__(self) -> Self:
+        msg = "Strict editable install will be performed using a link tree.\n"
+        _logger.warning(msg + _STRICT_WARNING)
+        return self
+
+    def __exit__(
+        self,
+        _exc_type: object,
+        _exc_value: object,
+        _traceback: object,
+    ) -> None:
+        msg = f"""\n
+        Strict editable installation performed using the auxiliary directory:
+            {self.auxiliary_dir}
+
+        Please be careful to not remove this directory, otherwise you might not be able
+        to import/use your package.
+        """
+        InformationOnly.emit("Editable installation.", msg)
+
+
+class _TopLevelFinder:
+    def __init__(self, dist: Distribution, name: str) -> None:
+        self.dist = dist
+        self.name = name
+
+    def template_vars(self) -> tuple[str, str, dict[str, str], dict[str, list[str]]]:
+        src_root = self.dist.src_root or os.curdir
+        top_level = chain(_find_packages(self.dist), _find_top_level_modules(self.dist))
+        package_dir = self.dist.package_dir or {}
+        roots = _find_package_roots(top_level, package_dir, src_root)
+
+        namespaces_ = dict(
+            chain(
+                _find_namespaces(self.dist.packages or [], roots),
+                ((ns, []) for ns in _find_virtual_namespaces(roots)),
+            )
+        )
+
+        legacy_namespaces = {
+            pkg: find_package_path(pkg, roots, self.dist.src_root or "")
+            for pkg in self.dist.namespace_packages or []
+        }
+
+        mapping = {**roots, **legacy_namespaces}
+        # ^-- We need to explicitly add the legacy_namespaces to the mapping to be
+        #     able to import their modules even if another package sharing the same
+        #     namespace is installed in a conventional (non-editable) way.
+
+        name = f"__editable__.{self.name}.finder"
+        finder = _normalization.safe_identifier(name)
+        return finder, name, mapping, namespaces_
+
+    def get_implementation(self) -> Iterator[tuple[str, bytes]]:
+        finder, name, mapping, namespaces_ = self.template_vars()
+
+        content = bytes(_finder_template(name, mapping, namespaces_), "utf-8")
+        yield (f"{finder}.py", content)
+
+        content = _encode_pth(f"import {finder}; {finder}.install()")
+        yield (f"__editable__.{self.name}.pth", content)
+
+    def __call__(self, wheel: WheelFile, files: list[str], mapping: Mapping[str, str]):
+        for file, content in self.get_implementation():
+            wheel.writestr(file, content)
+
+    def __enter__(self) -> Self:
+        msg = "Editable install will be performed using a meta path finder.\n"
+        _logger.warning(msg + _LENIENT_WARNING)
+        return self
+
+    def __exit__(
+        self,
+        _exc_type: object,
+        _exc_value: object,
+        _traceback: object,
+    ) -> None:
+        msg = """\n
+        Please be careful with folders in your working directory with the same
+        name as your package as they may take precedence during imports.
+        """
+        InformationOnly.emit("Editable installation.", msg)
+
+
+def _encode_pth(content: str) -> bytes:
+    """
+    Prior to Python 3.13 (see https://github.com/python/cpython/issues/77102),
+    .pth files are always read with 'locale' encoding, the recommendation
+    from the cpython core developers is to write them as ``open(path, "w")``
+    and ignore warnings (see python/cpython#77102, pypa/setuptools#3937).
+    This function tries to simulate this behavior without having to create an
+    actual file, in a way that supports a range of active Python versions.
+    (There seems to be some variety in the way different version of Python handle
+    ``encoding=None``, not all of them use ``locale.getpreferredencoding(False)``
+    or ``locale.getencoding()``).
+    """
+    with io.BytesIO() as buffer:
+        wrapper = io.TextIOWrapper(buffer, encoding=py312.PTH_ENCODING)
+        # TODO: Python 3.13 replace the whole function with `bytes(content, "utf-8")`
+        wrapper.write(content)
+        wrapper.flush()
+        buffer.seek(0)
+        return buffer.read()
+
+
+def _can_symlink_files(base_dir: Path) -> bool:
+    with TemporaryDirectory(dir=str(base_dir.resolve())) as tmp:
+        path1, path2 = Path(tmp, "file1.txt"), Path(tmp, "file2.txt")
+        path1.write_text("file1", encoding="utf-8")
+        with suppress(AttributeError, NotImplementedError, OSError):
+            os.symlink(path1, path2)
+            if path2.is_symlink() and path2.read_text(encoding="utf-8") == "file1":
+                return True
+
+        try:
+            os.link(path1, path2)  # Ensure hard links can be created
+        except Exception as ex:
+            msg = (
+                "File system does not seem to support either symlinks or hard links. "
+                "Strict editable installs require one of them to be supported."
+            )
+            raise LinksNotSupported(msg) from ex
+        return False
+
+
+def _simple_layout(
+    packages: Iterable[str], package_dir: dict[str, str], project_dir: StrPath
+) -> bool:
+    """Return ``True`` if:
+    - all packages are contained by the same parent directory, **and**
+    - all packages become importable if the parent directory is added to ``sys.path``.
+
+    >>> _simple_layout(['a'], {"": "src"}, "/tmp/myproj")
+    True
+    >>> _simple_layout(['a', 'a.b'], {"": "src"}, "/tmp/myproj")
+    True
+    >>> _simple_layout(['a', 'a.b'], {}, "/tmp/myproj")
+    True
+    >>> _simple_layout(['a', 'a.a1', 'a.a1.a2', 'b'], {"": "src"}, "/tmp/myproj")
+    True
+    >>> _simple_layout(['a', 'a.a1', 'a.a1.a2', 'b'], {"a": "a", "b": "b"}, ".")
+    True
+    >>> _simple_layout(['a', 'a.a1', 'a.a1.a2', 'b'], {"a": "_a", "b": "_b"}, ".")
+    False
+    >>> _simple_layout(['a', 'a.a1', 'a.a1.a2', 'b'], {"a": "_a"}, "/tmp/myproj")
+    False
+    >>> _simple_layout(['a', 'a.a1', 'a.a1.a2', 'b'], {"a.a1.a2": "_a2"}, ".")
+    False
+    >>> _simple_layout(['a', 'a.b'], {"": "src", "a.b": "_ab"}, "/tmp/myproj")
+    False
+    >>> # Special cases, no packages yet:
+    >>> _simple_layout([], {"": "src"}, "/tmp/myproj")
+    True
+    >>> _simple_layout([], {"a": "_a", "": "src"}, "/tmp/myproj")
+    False
+    """
+    layout = {pkg: find_package_path(pkg, package_dir, project_dir) for pkg in packages}
+    if not layout:
+        return set(package_dir) in ({}, {""})
+    parent = os.path.commonpath(starmap(_parent_path, layout.items()))
+    return all(
+        _path.same_path(Path(parent, *key.split('.')), value)
+        for key, value in layout.items()
+    )
+
+
+def _parent_path(pkg, pkg_path):
+    """Infer the parent path containing a package, that if added to ``sys.path`` would
+    allow importing that package.
+    When ``pkg`` is directly mapped into a directory with a different name, return its
+    own path.
+    >>> _parent_path("a", "src/a")
+    'src'
+    >>> _parent_path("b", "src/c")
+    'src/c'
+    """
+    parent = pkg_path[: -len(pkg)] if pkg_path.endswith(pkg) else pkg_path
+    return parent.rstrip("/" + os.sep)
+
+
+def _find_packages(dist: Distribution) -> Iterator[str]:
+    yield from iter(dist.packages or [])
+
+    py_modules = dist.py_modules or []
+    nested_modules = [mod for mod in py_modules if "." in mod]
+    if dist.ext_package:
+        yield dist.ext_package
+    else:
+        ext_modules = dist.ext_modules or []
+        nested_modules += [x.name for x in ext_modules if "." in x.name]
+
+    for module in nested_modules:
+        package, _, _ = module.rpartition(".")
+        yield package
+
+
+def _find_top_level_modules(dist: Distribution) -> Iterator[str]:
+    py_modules = dist.py_modules or []
+    yield from (mod for mod in py_modules if "." not in mod)
+
+    if not dist.ext_package:
+        ext_modules = dist.ext_modules or []
+        yield from (x.name for x in ext_modules if "." not in x.name)
+
+
+def _find_package_roots(
+    packages: Iterable[str],
+    package_dir: Mapping[str, str],
+    src_root: StrPath,
+) -> dict[str, str]:
+    pkg_roots: dict[str, str] = {
+        pkg: _absolute_root(find_package_path(pkg, package_dir, src_root))
+        for pkg in sorted(packages)
+    }
+
+    return _remove_nested(pkg_roots)
+
+
+def _absolute_root(path: StrPath) -> str:
+    """Works for packages and top-level modules"""
+    path_ = Path(path)
+    parent = path_.parent
+
+    if path_.exists():
+        return str(path_.resolve())
+    else:
+        return str(parent.resolve() / path_.name)
+
+
+def _find_virtual_namespaces(pkg_roots: dict[str, str]) -> Iterator[str]:
+    """By carefully designing ``package_dir``, it is possible to implement the logical
+    structure of PEP 420 in a package without the corresponding directories.
+
+    Moreover a parent package can be purposefully/accidentally skipped in the discovery
+    phase (e.g. ``find_packages(include=["mypkg.*"])``, when ``mypkg.foo`` is included
+    by ``mypkg`` itself is not).
+    We consider this case to also be a virtual namespace (ignoring the original
+    directory) to emulate a non-editable installation.
+
+    This function will try to find these kinds of namespaces.
+    """
+    for pkg in pkg_roots:
+        if "." not in pkg:
+            continue
+        parts = pkg.split(".")
+        for i in range(len(parts) - 1, 0, -1):
+            partial_name = ".".join(parts[:i])
+            path = Path(find_package_path(partial_name, pkg_roots, ""))
+            if not path.exists() or partial_name not in pkg_roots:
+                # partial_name not in pkg_roots ==> purposefully/accidentally skipped
+                yield partial_name
+
+
+def _find_namespaces(
+    packages: list[str], pkg_roots: dict[str, str]
+) -> Iterator[tuple[str, list[str]]]:
+    for pkg in packages:
+        path = find_package_path(pkg, pkg_roots, "")
+        if Path(path).exists() and not Path(path, "__init__.py").exists():
+            yield (pkg, [path])
+
+
+def _remove_nested(pkg_roots: dict[str, str]) -> dict[str, str]:
+    output = dict(pkg_roots.copy())
+
+    for pkg, path in reversed(list(pkg_roots.items())):
+        if any(
+            pkg != other and _is_nested(pkg, path, other, other_path)
+            for other, other_path in pkg_roots.items()
+        ):
+            output.pop(pkg)
+
+    return output
+
+
+def _is_nested(pkg: str, pkg_path: str, parent: str, parent_path: str) -> bool:
+    """
+    Return ``True`` if ``pkg`` is nested inside ``parent`` both logically and in the
+    file system.
+    >>> _is_nested("a.b", "path/a/b", "a", "path/a")
+    True
+    >>> _is_nested("a.b", "path/a/b", "a", "otherpath/a")
+    False
+    >>> _is_nested("a.b", "path/a/b", "c", "path/c")
+    False
+    >>> _is_nested("a.a", "path/a/a", "a", "path/a")
+    True
+    >>> _is_nested("b.a", "path/b/a", "a", "path/a")
+    False
+    """
+    norm_pkg_path = _path.normpath(pkg_path)
+    rest = pkg.replace(parent, "", 1).strip(".").split(".")
+    return pkg.startswith(parent) and norm_pkg_path == _path.normpath(
+        Path(parent_path, *rest)
+    )
+
+
+def _empty_dir(dir_: _P) -> _P:
+    """Create a directory ensured to be empty. Existing files may be removed."""
+    _shutil.rmtree(dir_, ignore_errors=True)
+    os.makedirs(dir_)
+    return dir_
+
+
+class _NamespaceInstaller(namespaces.Installer):
+    def __init__(self, distribution, installation_dir, editable_name, src_root) -> None:
+        self.distribution = distribution
+        self.src_root = src_root
+        self.installation_dir = installation_dir
+        self.editable_name = editable_name
+        self.outputs: list[str] = []
+        self.dry_run = False
+
+    def _get_nspkg_file(self):
+        """Installation target."""
+        return os.path.join(self.installation_dir, self.editable_name + self.nspkg_ext)
+
+    def _get_root(self):
+        """Where the modules/packages should be loaded from."""
+        return repr(str(self.src_root))
+
+
+_FINDER_TEMPLATE = """\
+from __future__ import annotations
+import sys
+from importlib.machinery import ModuleSpec, PathFinder
+from importlib.machinery import all_suffixes as module_suffixes
+from importlib.util import spec_from_file_location
+from itertools import chain
+from pathlib import Path
+
+MAPPING: dict[str, str] = {mapping!r}
+NAMESPACES: dict[str, list[str]] = {namespaces!r}
+PATH_PLACEHOLDER = {name!r} + ".__path_hook__"
+
+
+class _EditableFinder:  # MetaPathFinder
+    @classmethod
+    def find_spec(cls, fullname: str, path=None, target=None) -> ModuleSpec | None:  # type: ignore
+        # Top-level packages and modules (we know these exist in the FS)
+        if fullname in MAPPING:
+            pkg_path = MAPPING[fullname]
+            return cls._find_spec(fullname, Path(pkg_path))
+
+        # Handle immediate children modules (required for namespaces to work)
+        # To avoid problems with case sensitivity in the file system we delegate
+        # to the importlib.machinery implementation.
+        parent, _, child = fullname.rpartition(".")
+        if parent and parent in MAPPING:
+            return PathFinder.find_spec(fullname, path=[MAPPING[parent]])
+
+        # Other levels of nesting should be handled automatically by importlib
+        # using the parent path.
+        return None
+
+    @classmethod
+    def _find_spec(cls, fullname: str, candidate_path: Path) -> ModuleSpec | None:
+        init = candidate_path / "__init__.py"
+        candidates = (candidate_path.with_suffix(x) for x in module_suffixes())
+        for candidate in chain([init], candidates):
+            if candidate.exists():
+                return spec_from_file_location(fullname, candidate)
+        return None
+
+
+class _EditableNamespaceFinder:  # PathEntryFinder
+    @classmethod
+    def _path_hook(cls, path) -> type[_EditableNamespaceFinder]:
+        if path == PATH_PLACEHOLDER:
+            return cls
+        raise ImportError
+
+    @classmethod
+    def _paths(cls, fullname: str) -> list[str]:
+        paths = NAMESPACES[fullname]
+        if not paths and fullname in MAPPING:
+            paths = [MAPPING[fullname]]
+        # Always add placeholder, for 2 reasons:
+        # 1. __path__ cannot be empty for the spec to be considered namespace.
+        # 2. In the case of nested namespaces, we need to force
+        #    import machinery to query _EditableNamespaceFinder again.
+        return [*paths, PATH_PLACEHOLDER]
+
+    @classmethod
+    def find_spec(cls, fullname: str, target=None) -> ModuleSpec | None:  # type: ignore
+        if fullname in NAMESPACES:
+            spec = ModuleSpec(fullname, None, is_package=True)
+            spec.submodule_search_locations = cls._paths(fullname)
+            return spec
+        return None
+
+    @classmethod
+    def find_module(cls, _fullname) -> None:
+        return None
+
+
+def install():
+    if not any(finder == _EditableFinder for finder in sys.meta_path):
+        sys.meta_path.append(_EditableFinder)
+
+    if not NAMESPACES:
+        return
+
+    if not any(hook == _EditableNamespaceFinder._path_hook for hook in sys.path_hooks):
+        # PathEntryFinder is needed to create NamespaceSpec without private APIS
+        sys.path_hooks.append(_EditableNamespaceFinder._path_hook)
+    if PATH_PLACEHOLDER not in sys.path:
+        sys.path.append(PATH_PLACEHOLDER)  # Used just to trigger the path hook
+"""
+
+
+def _finder_template(
+    name: str, mapping: Mapping[str, str], namespaces: dict[str, list[str]]
+) -> str:
+    """Create a string containing the code for the``MetaPathFinder`` and
+    ``PathEntryFinder``.
+    """
+    mapping = dict(sorted(mapping.items(), key=lambda p: p[0]))
+    return _FINDER_TEMPLATE.format(name=name, mapping=mapping, namespaces=namespaces)
+
+
+class LinksNotSupported(errors.FileError):
+    """File system does not seem to support either symlinks or hard links."""
+
+
+class _DebuggingTips(SetuptoolsWarning):
+    _SUMMARY = "Problem in editable installation."
+    _DETAILS = """
+    An error happened while installing `{project}` in editable mode.
+
+    The following steps are recommended to help debug this problem:
+
+    - Try to install the project normally, without using the editable mode.
+      Does the error still persist?
+      (If it does, try fixing the problem before attempting the editable mode).
+    - If you are using binary extensions, make sure you have all OS-level
+      dependencies installed (e.g. compilers, toolchains, binary libraries, ...).
+    - Try the latest version of setuptools (maybe the error was already fixed).
+    - If you (or your project dependencies) are using any setuptools extension
+      or customization, make sure they support the editable mode.
+
+    After following the steps above, if the problem still persists and
+    you think this is related to how setuptools handles editable installations,
+    please submit a reproducible example
+    (see https://stackoverflow.com/help/minimal-reproducible-example) to:
+
+        https://github.com/pypa/setuptools/issues
+    """
+    _SEE_DOCS = "userguide/development_mode.html"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/egg_info.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/egg_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..f77631168fcdb60e14ddd757e18b4c301473aa82
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/egg_info.py
@@ -0,0 +1,720 @@
+"""setuptools.command.egg_info
+
+Create a distribution's .egg-info directory and contents"""
+
+import functools
+import os
+import re
+import sys
+import time
+from collections.abc import Callable
+
+import packaging
+import packaging.requirements
+import packaging.version
+
+import setuptools.unicode_utils as unicode_utils
+from setuptools import Command
+from setuptools.command import bdist_egg
+from setuptools.command.sdist import sdist, walk_revctrl
+from setuptools.command.setopt import edit_config
+from setuptools.glob import glob
+
+from .. import _entry_points, _normalization
+from .._importlib import metadata
+from ..warnings import SetuptoolsDeprecationWarning
+from . import _requirestxt
+
+import distutils.errors
+import distutils.filelist
+from distutils import log
+from distutils.errors import DistutilsInternalError
+from distutils.filelist import FileList as _FileList
+from distutils.util import convert_path
+
+PY_MAJOR = f'{sys.version_info.major}.{sys.version_info.minor}'
+
+
+def translate_pattern(glob):  # noqa: C901  # is too complex (14)  # FIXME
+    """
+    Translate a file path glob like '*.txt' in to a regular expression.
+    This differs from fnmatch.translate which allows wildcards to match
+    directory separators. It also knows about '**/' which matches any number of
+    directories.
+    """
+    pat = ''
+
+    # This will split on '/' within [character classes]. This is deliberate.
+    chunks = glob.split(os.path.sep)
+
+    sep = re.escape(os.sep)
+    valid_char = f'[^{sep}]'
+
+    for c, chunk in enumerate(chunks):
+        last_chunk = c == len(chunks) - 1
+
+        # Chunks that are a literal ** are globstars. They match anything.
+        if chunk == '**':
+            if last_chunk:
+                # Match anything if this is the last component
+                pat += '.*'
+            else:
+                # Match '(name/)*'
+                pat += f'(?:{valid_char}+{sep})*'
+            continue  # Break here as the whole path component has been handled
+
+        # Find any special characters in the remainder
+        i = 0
+        chunk_len = len(chunk)
+        while i < chunk_len:
+            char = chunk[i]
+            if char == '*':
+                # Match any number of name characters
+                pat += valid_char + '*'
+            elif char == '?':
+                # Match a name character
+                pat += valid_char
+            elif char == '[':
+                # Character class
+                inner_i = i + 1
+                # Skip initial !/] chars
+                if inner_i < chunk_len and chunk[inner_i] == '!':
+                    inner_i = inner_i + 1
+                if inner_i < chunk_len and chunk[inner_i] == ']':
+                    inner_i = inner_i + 1
+
+                # Loop till the closing ] is found
+                while inner_i < chunk_len and chunk[inner_i] != ']':
+                    inner_i = inner_i + 1
+
+                if inner_i >= chunk_len:
+                    # Got to the end of the string without finding a closing ]
+                    # Do not treat this as a matching group, but as a literal [
+                    pat += re.escape(char)
+                else:
+                    # Grab the insides of the [brackets]
+                    inner = chunk[i + 1 : inner_i]
+                    char_class = ''
+
+                    # Class negation
+                    if inner[0] == '!':
+                        char_class = '^'
+                        inner = inner[1:]
+
+                    char_class += re.escape(inner)
+                    pat += f'[{char_class}]'
+
+                    # Skip to the end ]
+                    i = inner_i
+            else:
+                pat += re.escape(char)
+            i += 1
+
+        # Join each chunk with the dir separator
+        if not last_chunk:
+            pat += sep
+
+    pat += r'\Z'
+    return re.compile(pat, flags=re.MULTILINE | re.DOTALL)
+
+
+class InfoCommon:
+    tag_build = None
+    tag_date = None
+
+    @property
+    def name(self):
+        return _normalization.safe_name(self.distribution.get_name())
+
+    def tagged_version(self):
+        tagged = self._maybe_tag(self.distribution.get_version())
+        return _normalization.safe_version(tagged)
+
+    def _maybe_tag(self, version):
+        """
+        egg_info may be called more than once for a distribution,
+        in which case the version string already contains all tags.
+        """
+        return (
+            version
+            if self.vtags and self._already_tagged(version)
+            else version + self.vtags
+        )
+
+    def _already_tagged(self, version: str) -> bool:
+        # Depending on their format, tags may change with version normalization.
+        # So in addition the regular tags, we have to search for the normalized ones.
+        return version.endswith(self.vtags) or version.endswith(self._safe_tags())
+
+    def _safe_tags(self) -> str:
+        # To implement this we can rely on `safe_version` pretending to be version 0
+        # followed by tags. Then we simply discard the starting 0 (fake version number)
+        try:
+            return _normalization.safe_version(f"0{self.vtags}")[1:]
+        except packaging.version.InvalidVersion:
+            return _normalization.safe_name(self.vtags.replace(' ', '.'))
+
+    def tags(self) -> str:
+        version = ''
+        if self.tag_build:
+            version += self.tag_build
+        if self.tag_date:
+            version += time.strftime("%Y%m%d")
+        return version
+
+    vtags = property(tags)
+
+
+class egg_info(InfoCommon, Command):
+    description = "create a distribution's .egg-info directory"
+
+    user_options = [
+        (
+            'egg-base=',
+            'e',
+            "directory containing .egg-info directories"
+            " [default: top of the source tree]",
+        ),
+        ('tag-date', 'd', "Add date stamp (e.g. 20050528) to version number"),
+        ('tag-build=', 'b', "Specify explicit tag to add to version number"),
+        ('no-date', 'D', "Don't include date stamp [default]"),
+    ]
+
+    boolean_options = ['tag-date']
+    negative_opt = {
+        'no-date': 'tag-date',
+    }
+
+    def initialize_options(self):
+        self.egg_base = None
+        self.egg_name = None
+        self.egg_info = None
+        self.egg_version = None
+        self.ignore_egg_info_in_manifest = False
+
+    ####################################
+    # allow the 'tag_svn_revision' to be detected and
+    # set, supporting sdists built on older Setuptools.
+    @property
+    def tag_svn_revision(self) -> None:
+        pass
+
+    @tag_svn_revision.setter
+    def tag_svn_revision(self, value):
+        pass
+
+    ####################################
+
+    def save_version_info(self, filename) -> None:
+        """
+        Materialize the value of date into the
+        build tag. Install build keys in a deterministic order
+        to avoid arbitrary reordering on subsequent builds.
+        """
+        # follow the order these keys would have been added
+        # when PYTHONHASHSEED=0
+        egg_info = dict(tag_build=self.tags(), tag_date=0)
+        edit_config(filename, dict(egg_info=egg_info))
+
+    def finalize_options(self) -> None:
+        # Note: we need to capture the current value returned
+        # by `self.tagged_version()`, so we can later update
+        # `self.distribution.metadata.version` without
+        # repercussions.
+        self.egg_name = self.name
+        self.egg_version = self.tagged_version()
+        parsed_version = packaging.version.Version(self.egg_version)
+
+        try:
+            is_version = isinstance(parsed_version, packaging.version.Version)
+            spec = "%s==%s" if is_version else "%s===%s"
+            packaging.requirements.Requirement(spec % (self.egg_name, self.egg_version))
+        except ValueError as e:
+            raise distutils.errors.DistutilsOptionError(
+                f"Invalid distribution name or version syntax: {self.egg_name}-{self.egg_version}"
+            ) from e
+
+        if self.egg_base is None:
+            dirs = self.distribution.package_dir
+            self.egg_base = (dirs or {}).get('', os.curdir)
+
+        self.ensure_dirname('egg_base')
+        self.egg_info = _normalization.filename_component(self.egg_name) + '.egg-info'
+        if self.egg_base != os.curdir:
+            self.egg_info = os.path.join(self.egg_base, self.egg_info)
+
+        # Set package version for the benefit of dumber commands
+        # (e.g. sdist, bdist_wininst, etc.)
+        #
+        self.distribution.metadata.version = self.egg_version
+
+    def _get_egg_basename(self, py_version=PY_MAJOR, platform=None):
+        """Compute filename of the output egg. Private API."""
+        return _egg_basename(self.egg_name, self.egg_version, py_version, platform)
+
+    def write_or_delete_file(self, what, filename, data, force: bool = False) -> None:
+        """Write `data` to `filename` or delete if empty
+
+        If `data` is non-empty, this routine is the same as ``write_file()``.
+        If `data` is empty but not ``None``, this is the same as calling
+        ``delete_file(filename)`.  If `data` is ``None``, then this is a no-op
+        unless `filename` exists, in which case a warning is issued about the
+        orphaned file (if `force` is false), or deleted (if `force` is true).
+        """
+        if data:
+            self.write_file(what, filename, data)
+        elif os.path.exists(filename):
+            if data is None and not force:
+                log.warn("%s not set in setup(), but %s exists", what, filename)
+                return
+            else:
+                self.delete_file(filename)
+
+    def write_file(self, what, filename, data) -> None:
+        """Write `data` to `filename` (if not a dry run) after announcing it
+
+        `what` is used in a log message to identify what is being written
+        to the file.
+        """
+        log.info("writing %s to %s", what, filename)
+        data = data.encode("utf-8")
+        if not self.dry_run:
+            f = open(filename, 'wb')
+            f.write(data)
+            f.close()
+
+    def delete_file(self, filename) -> None:
+        """Delete `filename` (if not a dry run) after announcing it"""
+        log.info("deleting %s", filename)
+        if not self.dry_run:
+            os.unlink(filename)
+
+    def run(self) -> None:
+        # Pre-load to avoid iterating over entry-points while an empty .egg-info
+        # exists in sys.path. See pypa/pyproject-hooks#206
+        writers = list(metadata.entry_points(group='egg_info.writers'))
+
+        self.mkpath(self.egg_info)
+        try:
+            os.utime(self.egg_info, None)
+        except OSError as e:
+            msg = f"Cannot update time stamp of directory '{self.egg_info}'"
+            raise distutils.errors.DistutilsFileError(msg) from e
+        for ep in writers:
+            writer = ep.load()
+            writer(self, ep.name, os.path.join(self.egg_info, ep.name))
+
+        # Get rid of native_libs.txt if it was put there by older bdist_egg
+        nl = os.path.join(self.egg_info, "native_libs.txt")
+        if os.path.exists(nl):
+            self.delete_file(nl)
+
+        self.find_sources()
+
+    def find_sources(self) -> None:
+        """Generate SOURCES.txt manifest file"""
+        manifest_filename = os.path.join(self.egg_info, "SOURCES.txt")
+        mm = manifest_maker(self.distribution)
+        mm.ignore_egg_info_dir = self.ignore_egg_info_in_manifest
+        mm.manifest = manifest_filename
+        mm.run()
+        self.filelist = mm.filelist
+
+
+class FileList(_FileList):
+    # Implementations of the various MANIFEST.in commands
+
+    def __init__(
+        self, warn=None, debug_print=None, ignore_egg_info_dir: bool = False
+    ) -> None:
+        super().__init__(warn, debug_print)
+        self.ignore_egg_info_dir = ignore_egg_info_dir
+
+    def process_template_line(self, line) -> None:
+        # Parse the line: split it up, make sure the right number of words
+        # is there, and return the relevant words.  'action' is always
+        # defined: it's the first word of the line.  Which of the other
+        # three are defined depends on the action; it'll be either
+        # patterns, (dir and patterns), or (dir_pattern).
+        (action, patterns, dir, dir_pattern) = self._parse_template_line(line)
+
+        action_map: dict[str, Callable] = {
+            'include': self.include,
+            'exclude': self.exclude,
+            'global-include': self.global_include,
+            'global-exclude': self.global_exclude,
+            'recursive-include': functools.partial(
+                self.recursive_include,
+                dir,
+            ),
+            'recursive-exclude': functools.partial(
+                self.recursive_exclude,
+                dir,
+            ),
+            'graft': self.graft,
+            'prune': self.prune,
+        }
+        log_map = {
+            'include': "warning: no files found matching '%s'",
+            'exclude': ("warning: no previously-included files found matching '%s'"),
+            'global-include': (
+                "warning: no files found matching '%s' anywhere in distribution"
+            ),
+            'global-exclude': (
+                "warning: no previously-included files matching "
+                "'%s' found anywhere in distribution"
+            ),
+            'recursive-include': (
+                "warning: no files found matching '%s' under directory '%s'"
+            ),
+            'recursive-exclude': (
+                "warning: no previously-included files matching "
+                "'%s' found under directory '%s'"
+            ),
+            'graft': "warning: no directories found matching '%s'",
+            'prune': "no previously-included directories found matching '%s'",
+        }
+
+        try:
+            process_action = action_map[action]
+        except KeyError:
+            msg = f"Invalid MANIFEST.in: unknown action {action!r} in {line!r}"
+            raise DistutilsInternalError(msg) from None
+
+        # OK, now we know that the action is valid and we have the
+        # right number of words on the line for that action -- so we
+        # can proceed with minimal error-checking.
+
+        action_is_recursive = action.startswith('recursive-')
+        if action in {'graft', 'prune'}:
+            patterns = [dir_pattern]
+        extra_log_args = (dir,) if action_is_recursive else ()
+        log_tmpl = log_map[action]
+
+        self.debug_print(
+            ' '.join(
+                [action] + ([dir] if action_is_recursive else []) + patterns,
+            )
+        )
+        for pattern in patterns:
+            if not process_action(pattern):
+                log.warn(log_tmpl, pattern, *extra_log_args)
+
+    def _remove_files(self, predicate):
+        """
+        Remove all files from the file list that match the predicate.
+        Return True if any matching files were removed
+        """
+        found = False
+        for i in range(len(self.files) - 1, -1, -1):
+            if predicate(self.files[i]):
+                self.debug_print(" removing " + self.files[i])
+                del self.files[i]
+                found = True
+        return found
+
+    def include(self, pattern):
+        """Include files that match 'pattern'."""
+        found = [f for f in glob(pattern) if not os.path.isdir(f)]
+        self.extend(found)
+        return bool(found)
+
+    def exclude(self, pattern):
+        """Exclude files that match 'pattern'."""
+        match = translate_pattern(pattern)
+        return self._remove_files(match.match)
+
+    def recursive_include(self, dir, pattern):
+        """
+        Include all files anywhere in 'dir/' that match the pattern.
+        """
+        full_pattern = os.path.join(dir, '**', pattern)
+        found = [f for f in glob(full_pattern, recursive=True) if not os.path.isdir(f)]
+        self.extend(found)
+        return bool(found)
+
+    def recursive_exclude(self, dir, pattern):
+        """
+        Exclude any file anywhere in 'dir/' that match the pattern.
+        """
+        match = translate_pattern(os.path.join(dir, '**', pattern))
+        return self._remove_files(match.match)
+
+    def graft(self, dir):
+        """Include all files from 'dir/'."""
+        found = [
+            item
+            for match_dir in glob(dir)
+            for item in distutils.filelist.findall(match_dir)
+        ]
+        self.extend(found)
+        return bool(found)
+
+    def prune(self, dir):
+        """Filter out files from 'dir/'."""
+        match = translate_pattern(os.path.join(dir, '**'))
+        return self._remove_files(match.match)
+
+    def global_include(self, pattern):
+        """
+        Include all files anywhere in the current directory that match the
+        pattern. This is very inefficient on large file trees.
+        """
+        if self.allfiles is None:
+            self.findall()
+        match = translate_pattern(os.path.join('**', pattern))
+        found = [f for f in self.allfiles if match.match(f)]
+        self.extend(found)
+        return bool(found)
+
+    def global_exclude(self, pattern):
+        """
+        Exclude all files anywhere that match the pattern.
+        """
+        match = translate_pattern(os.path.join('**', pattern))
+        return self._remove_files(match.match)
+
+    def append(self, item) -> None:
+        if item.endswith('\r'):  # Fix older sdists built on Windows
+            item = item[:-1]
+        path = convert_path(item)
+
+        if self._safe_path(path):
+            self.files.append(path)
+
+    def extend(self, paths) -> None:
+        self.files.extend(filter(self._safe_path, paths))
+
+    def _repair(self):
+        """
+        Replace self.files with only safe paths
+
+        Because some owners of FileList manipulate the underlying
+        ``files`` attribute directly, this method must be called to
+        repair those paths.
+        """
+        self.files = list(filter(self._safe_path, self.files))
+
+    def _safe_path(self, path):
+        enc_warn = "'%s' not %s encodable -- skipping"
+
+        # To avoid accidental trans-codings errors, first to unicode
+        u_path = unicode_utils.filesys_decode(path)
+        if u_path is None:
+            log.warn(f"'{path}' in unexpected encoding -- skipping")
+            return False
+
+        # Must ensure utf-8 encodability
+        utf8_path = unicode_utils.try_encode(u_path, "utf-8")
+        if utf8_path is None:
+            log.warn(enc_warn, path, 'utf-8')
+            return False
+
+        try:
+            # ignore egg-info paths
+            is_egg_info = ".egg-info" in u_path or b".egg-info" in utf8_path
+            if self.ignore_egg_info_dir and is_egg_info:
+                return False
+            # accept is either way checks out
+            if os.path.exists(u_path) or os.path.exists(utf8_path):
+                return True
+        # this will catch any encode errors decoding u_path
+        except UnicodeEncodeError:
+            log.warn(enc_warn, path, sys.getfilesystemencoding())
+
+
+class manifest_maker(sdist):
+    template = "MANIFEST.in"
+
+    def initialize_options(self) -> None:
+        self.use_defaults = True
+        self.prune = True
+        self.manifest_only = True
+        self.force_manifest = True
+        self.ignore_egg_info_dir = False
+
+    def finalize_options(self) -> None:
+        pass
+
+    def run(self) -> None:
+        self.filelist = FileList(ignore_egg_info_dir=self.ignore_egg_info_dir)
+        if not os.path.exists(self.manifest):
+            self.write_manifest()  # it must exist so it'll get in the list
+        self.add_defaults()
+        if os.path.exists(self.template):
+            self.read_template()
+        self.add_license_files()
+        self._add_referenced_files()
+        self.prune_file_list()
+        self.filelist.sort()
+        self.filelist.remove_duplicates()
+        self.write_manifest()
+
+    def _manifest_normalize(self, path):
+        path = unicode_utils.filesys_decode(path)
+        return path.replace(os.sep, '/')
+
+    def write_manifest(self) -> None:
+        """
+        Write the file list in 'self.filelist' to the manifest file
+        named by 'self.manifest'.
+        """
+        self.filelist._repair()
+
+        # Now _repairs should encodability, but not unicode
+        files = [self._manifest_normalize(f) for f in self.filelist.files]
+        msg = f"writing manifest file '{self.manifest}'"
+        self.execute(write_file, (self.manifest, files), msg)
+
+    def warn(self, msg) -> None:
+        if not self._should_suppress_warning(msg):
+            sdist.warn(self, msg)
+
+    @staticmethod
+    def _should_suppress_warning(msg):
+        """
+        suppress missing-file warnings from sdist
+        """
+        return re.match(r"standard file .*not found", msg)
+
+    def add_defaults(self) -> None:
+        sdist.add_defaults(self)
+        self.filelist.append(self.template)
+        self.filelist.append(self.manifest)
+        rcfiles = list(walk_revctrl())
+        if rcfiles:
+            self.filelist.extend(rcfiles)
+        elif os.path.exists(self.manifest):
+            self.read_manifest()
+
+        if os.path.exists("setup.py"):
+            # setup.py should be included by default, even if it's not
+            # the script called to create the sdist
+            self.filelist.append("setup.py")
+
+        ei_cmd = self.get_finalized_command('egg_info')
+        self.filelist.graft(ei_cmd.egg_info)
+
+    def add_license_files(self) -> None:
+        license_files = self.distribution.metadata.license_files or []
+        for lf in license_files:
+            log.info("adding license file '%s'", lf)
+        self.filelist.extend(license_files)
+
+    def _add_referenced_files(self):
+        """Add files referenced by the config (e.g. `file:` directive) to filelist"""
+        referenced = getattr(self.distribution, '_referenced_files', [])
+        # ^-- fallback if dist comes from distutils or is a custom class
+        for rf in referenced:
+            log.debug("adding file referenced by config '%s'", rf)
+        self.filelist.extend(referenced)
+
+    def _safe_data_files(self, build_py):
+        """
+        The parent class implementation of this method
+        (``sdist``) will try to include data files, which
+        might cause recursion problems when
+        ``include_package_data=True``.
+
+        Therefore, avoid triggering any attempt of
+        analyzing/building the manifest again.
+        """
+        if hasattr(build_py, 'get_data_files_without_manifest'):
+            return build_py.get_data_files_without_manifest()
+
+        SetuptoolsDeprecationWarning.emit(
+            "`build_py` command does not inherit from setuptools' `build_py`.",
+            """
+            Custom 'build_py' does not implement 'get_data_files_without_manifest'.
+            Please extend command classes from setuptools instead of distutils.
+            """,
+            see_url="https://peps.python.org/pep-0632/",
+            # due_date not defined yet, old projects might still do it?
+        )
+        return build_py.get_data_files()
+
+
+def write_file(filename, contents) -> None:
+    """Create a file with the specified name and write 'contents' (a
+    sequence of strings without line terminators) to it.
+    """
+    contents = "\n".join(contents)
+
+    # assuming the contents has been vetted for utf-8 encoding
+    contents = contents.encode("utf-8")
+
+    with open(filename, "wb") as f:  # always write POSIX-style manifest
+        f.write(contents)
+
+
+def write_pkg_info(cmd, basename, filename) -> None:
+    log.info("writing %s", filename)
+    if not cmd.dry_run:
+        metadata = cmd.distribution.metadata
+        metadata.version, oldver = cmd.egg_version, metadata.version
+        metadata.name, oldname = cmd.egg_name, metadata.name
+
+        try:
+            # write unescaped data to PKG-INFO, so older pkg_resources
+            # can still parse it
+            metadata.write_pkg_info(cmd.egg_info)
+        finally:
+            metadata.name, metadata.version = oldname, oldver
+
+        safe = getattr(cmd.distribution, 'zip_safe', None)
+
+        bdist_egg.write_safety_flag(cmd.egg_info, safe)
+
+
+def warn_depends_obsolete(cmd, basename, filename) -> None:
+    """
+    Unused: left to avoid errors when updating (from source) from <= 67.8.
+    Old installations have a .dist-info directory with the entry-point
+    ``depends.txt = setuptools.command.egg_info:warn_depends_obsolete``.
+    This may trigger errors when running the first egg_info in build_meta.
+    TODO: Remove this function in a version sufficiently > 68.
+    """
+
+
+# Export API used in entry_points
+write_requirements = _requirestxt.write_requirements
+write_setup_requirements = _requirestxt.write_setup_requirements
+
+
+def write_toplevel_names(cmd, basename, filename) -> None:
+    pkgs = dict.fromkeys([
+        k.split('.', 1)[0] for k in cmd.distribution.iter_distribution_names()
+    ])
+    cmd.write_file("top-level names", filename, '\n'.join(sorted(pkgs)) + '\n')
+
+
+def overwrite_arg(cmd, basename, filename) -> None:
+    write_arg(cmd, basename, filename, True)
+
+
+def write_arg(cmd, basename, filename, force: bool = False) -> None:
+    argname = os.path.splitext(basename)[0]
+    value = getattr(cmd.distribution, argname, None)
+    if value is not None:
+        value = '\n'.join(value) + '\n'
+    cmd.write_or_delete_file(argname, filename, value, force)
+
+
+def write_entries(cmd, basename, filename) -> None:
+    eps = _entry_points.load(cmd.distribution.entry_points)
+    defn = _entry_points.render(eps)
+    cmd.write_or_delete_file('entry points', filename, defn, True)
+
+
+def _egg_basename(egg_name, egg_version, py_version=None, platform=None):
+    """Compute filename of the output egg. Private API."""
+    name = _normalization.filename_component(egg_name)
+    version = _normalization.filename_component(egg_version)
+    egg = f"{name}-{version}-py{py_version or PY_MAJOR}"
+    if platform:
+        egg += f"-{platform}"
+    return egg
+
+
+class EggInfoDeprecationWarning(SetuptoolsDeprecationWarning):
+    """Deprecated behavior warning for EggInfo, bypassing suppression."""
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install.py
new file mode 100644
index 0000000000000000000000000000000000000000..15ef36468889d55718711edbe9c4e061c48ee6e8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install.py
@@ -0,0 +1,183 @@
+from __future__ import annotations
+
+import glob
+import inspect
+import platform
+from collections.abc import Callable
+from typing import TYPE_CHECKING, Any, ClassVar, cast
+
+import setuptools
+
+from ..dist import Distribution
+from ..warnings import SetuptoolsDeprecationWarning, SetuptoolsWarning
+from .bdist_egg import bdist_egg as bdist_egg_cls
+
+import distutils.command.install as orig
+from distutils.errors import DistutilsArgError
+
+if TYPE_CHECKING:
+    # This is only used for a type-cast, don't import at runtime or it'll cause deprecation warnings
+    from .easy_install import easy_install as easy_install_cls
+else:
+    easy_install_cls = None
+
+
+def __getattr__(name: str):  # pragma: no cover
+    if name == "_install":
+        SetuptoolsDeprecationWarning.emit(
+            "`setuptools.command._install` was an internal implementation detail "
+            + "that was left in for numpy<1.9 support.",
+            due_date=(2025, 5, 2),  # Originally added on 2024-11-01
+        )
+        return orig.install
+    raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
+
+
+class install(orig.install):
+    """Use easy_install to install the package, w/dependencies"""
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    user_options = orig.install.user_options + [
+        ('old-and-unmanageable', None, "Try not to use this!"),
+        (
+            'single-version-externally-managed',
+            None,
+            "used by system package builders to create 'flat' eggs",
+        ),
+    ]
+    boolean_options = orig.install.boolean_options + [
+        'old-and-unmanageable',
+        'single-version-externally-managed',
+    ]
+    # Type the same as distutils.command.install.install.sub_commands
+    # Must keep the second tuple item potentially None due to invariance
+    new_commands: ClassVar[list[tuple[str, Callable[[Any], bool] | None]]] = [
+        ('install_egg_info', lambda self: True),
+        ('install_scripts', lambda self: True),
+    ]
+    _nc = dict(new_commands)
+
+    def initialize_options(self):
+        SetuptoolsDeprecationWarning.emit(
+            "setup.py install is deprecated.",
+            """
+            Please avoid running ``setup.py`` directly.
+            Instead, use pypa/build, pypa/installer or other
+            standards-based tools.
+            """,
+            see_url="https://blog.ganssle.io/articles/2021/10/setup-py-deprecated.html",
+            # TODO: Document how to bootstrap setuptools without install
+            #       (e.g. by unzipping the wheel file)
+            #       and then add a due_date to this warning.
+        )
+
+        super().initialize_options()
+        self.old_and_unmanageable = None
+        self.single_version_externally_managed = None
+
+    def finalize_options(self) -> None:
+        super().finalize_options()
+        if self.root:
+            self.single_version_externally_managed = True
+        elif self.single_version_externally_managed:
+            if not self.root and not self.record:
+                raise DistutilsArgError(
+                    "You must specify --record or --root when building system packages"
+                )
+
+    def handle_extra_path(self):
+        if self.root or self.single_version_externally_managed:
+            # explicit backward-compatibility mode, allow extra_path to work
+            return orig.install.handle_extra_path(self)
+
+        # Ignore extra_path when installing an egg (or being run by another
+        # command without --root or --single-version-externally-managed
+        self.path_file = None
+        self.extra_dirs = ''
+        return None
+
+    def run(self):
+        # Explicit request for old-style install?  Just do it
+        if self.old_and_unmanageable or self.single_version_externally_managed:
+            return super().run()
+
+        if not self._called_from_setup(inspect.currentframe()):
+            # Run in backward-compatibility mode to support bdist_* commands.
+            super().run()
+        else:
+            self.do_egg_install()
+
+        return None
+
+    @staticmethod
+    def _called_from_setup(run_frame):
+        """
+        Attempt to detect whether run() was called from setup() or by another
+        command.  If called by setup(), the parent caller will be the
+        'run_command' method in 'distutils.dist', and *its* caller will be
+        the 'run_commands' method.  If called any other way, the
+        immediate caller *might* be 'run_command', but it won't have been
+        called by 'run_commands'. Return True in that case or if a call stack
+        is unavailable. Return False otherwise.
+        """
+        if run_frame is None:
+            msg = "Call stack not available. bdist_* commands may fail."
+            SetuptoolsWarning.emit(msg)
+            if platform.python_implementation() == 'IronPython':
+                msg = "For best results, pass -X:Frames to enable call stack."
+                SetuptoolsWarning.emit(msg)
+            return True
+
+        frames = inspect.getouterframes(run_frame)
+        for frame in frames[2:4]:
+            (caller,) = frame[:1]
+            info = inspect.getframeinfo(caller)
+            caller_module = caller.f_globals.get('__name__', '')
+
+            if caller_module == "setuptools.dist" and info.function == "run_command":
+                # Starting from v61.0.0 setuptools overwrites dist.run_command
+                continue
+
+            return caller_module == 'distutils.dist' and info.function == 'run_commands'
+
+        return False
+
+    def do_egg_install(self) -> None:
+        easy_install = self.distribution.get_command_class('easy_install')
+
+        cmd = cast(
+            # We'd want to cast easy_install as type[easy_install_cls] but a bug in
+            # mypy makes it think easy_install() returns a Command on Python 3.12+
+            # https://github.com/python/mypy/issues/18088
+            easy_install_cls,
+            easy_install(  # type: ignore[call-arg]
+                self.distribution,
+                args="x",
+                root=self.root,
+                record=self.record,
+            ),
+        )
+        cmd.ensure_finalized()  # finalize before bdist_egg munges install cmd
+        cmd.always_copy_from = '.'  # make sure local-dir eggs get installed
+
+        # pick up setup-dir .egg files only: no .egg-info
+        cmd.package_index.scan(glob.glob('*.egg'))
+
+        self.run_command('bdist_egg')
+        bdist_egg = cast(bdist_egg_cls, self.distribution.get_command_obj('bdist_egg'))
+        args = [bdist_egg.egg_output]
+
+        if setuptools.bootstrap_install_from:
+            # Bootstrap self-installation of setuptools
+            args.insert(0, setuptools.bootstrap_install_from)
+
+        cmd.args = args
+        cmd.run(show_deprecation=False)
+        setuptools.bootstrap_install_from = None
+
+
+# XXX Python 3.1 doesn't see _nc if this is inside the class
+install.sub_commands = [
+    cmd for cmd in orig.install.sub_commands if cmd[0] not in install._nc
+] + install.new_commands
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_egg_info.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_egg_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..44f22ccf51cc3fb1662b326c3150845356d77fc3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_egg_info.py
@@ -0,0 +1,58 @@
+import os
+
+from setuptools import Command, namespaces
+from setuptools.archive_util import unpack_archive
+
+from .._path import ensure_directory
+
+from distutils import dir_util, log
+
+
+class install_egg_info(namespaces.Installer, Command):
+    """Install an .egg-info directory for the package"""
+
+    description = "Install an .egg-info directory for the package"
+
+    user_options = [
+        ('install-dir=', 'd', "directory to install to"),
+    ]
+
+    def initialize_options(self):
+        self.install_dir = None
+
+    def finalize_options(self) -> None:
+        self.set_undefined_options('install_lib', ('install_dir', 'install_dir'))
+        ei_cmd = self.get_finalized_command("egg_info")
+        basename = f"{ei_cmd._get_egg_basename()}.egg-info"
+        self.source = ei_cmd.egg_info
+        self.target = os.path.join(self.install_dir, basename)
+        self.outputs: list[str] = []
+
+    def run(self) -> None:
+        self.run_command('egg_info')
+        if os.path.isdir(self.target) and not os.path.islink(self.target):
+            dir_util.remove_tree(self.target, dry_run=self.dry_run)
+        elif os.path.exists(self.target):
+            self.execute(os.unlink, (self.target,), "Removing " + self.target)
+        if not self.dry_run:
+            ensure_directory(self.target)
+        self.execute(self.copytree, (), f"Copying {self.source} to {self.target}")
+        self.install_namespaces()
+
+    def get_outputs(self):
+        return self.outputs
+
+    def copytree(self) -> None:
+        # Copy the .egg-info tree to site-packages
+        def skimmer(src, dst):
+            # filter out source-control directories; note that 'src' is always
+            # a '/'-separated path, regardless of platform.  'dst' is a
+            # platform-specific path.
+            for skip in '.svn/', 'CVS/':
+                if src.startswith(skip) or '/' + skip in src:
+                    return None
+            self.outputs.append(dst)
+            log.debug("Copying %s to %s", src, dst)
+            return dst
+
+        unpack_archive(self.source, self.target, skimmer)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_lib.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_lib.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e1e07271028386e138585cac7619ab0338017cc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_lib.py
@@ -0,0 +1,137 @@
+from __future__ import annotations
+
+import os
+import sys
+from itertools import product, starmap
+
+from .._path import StrPath
+from ..dist import Distribution
+
+import distutils.command.install_lib as orig
+
+
+class install_lib(orig.install_lib):
+    """Don't add compiled flags to filenames of non-Python files"""
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    def run(self) -> None:
+        self.build()
+        outfiles = self.install()
+        if outfiles is not None:
+            # always compile, in case we have any extension stubs to deal with
+            self.byte_compile(outfiles)
+
+    def get_exclusions(self):
+        """
+        Return a collections.Sized collections.Container of paths to be
+        excluded for single_version_externally_managed installations.
+        """
+        all_packages = (
+            pkg
+            for ns_pkg in self._get_SVEM_NSPs()
+            for pkg in self._all_packages(ns_pkg)
+        )
+
+        excl_specs = product(all_packages, self._gen_exclusion_paths())
+        return set(starmap(self._exclude_pkg_path, excl_specs))
+
+    def _exclude_pkg_path(self, pkg, exclusion_path):
+        """
+        Given a package name and exclusion path within that package,
+        compute the full exclusion path.
+        """
+        parts = pkg.split('.') + [exclusion_path]
+        return os.path.join(self.install_dir, *parts)
+
+    @staticmethod
+    def _all_packages(pkg_name):
+        """
+        >>> list(install_lib._all_packages('foo.bar.baz'))
+        ['foo.bar.baz', 'foo.bar', 'foo']
+        """
+        while pkg_name:
+            yield pkg_name
+            pkg_name, _sep, _child = pkg_name.rpartition('.')
+
+    def _get_SVEM_NSPs(self):
+        """
+        Get namespace packages (list) but only for
+        single_version_externally_managed installations and empty otherwise.
+        """
+        # TODO: is it necessary to short-circuit here? i.e. what's the cost
+        # if get_finalized_command is called even when namespace_packages is
+        # False?
+        if not self.distribution.namespace_packages:
+            return []
+
+        install_cmd = self.get_finalized_command('install')
+        svem = install_cmd.single_version_externally_managed
+
+        return self.distribution.namespace_packages if svem else []
+
+    @staticmethod
+    def _gen_exclusion_paths():
+        """
+        Generate file paths to be excluded for namespace packages (bytecode
+        cache files).
+        """
+        # always exclude the package module itself
+        yield '__init__.py'
+
+        yield '__init__.pyc'
+        yield '__init__.pyo'
+
+        if not hasattr(sys, 'implementation'):
+            return
+
+        base = os.path.join('__pycache__', '__init__.' + sys.implementation.cache_tag)
+        yield base + '.pyc'
+        yield base + '.pyo'
+        yield base + '.opt-1.pyc'
+        yield base + '.opt-2.pyc'
+
+    def copy_tree(
+        self,
+        infile: StrPath,
+        outfile: str,
+        # override: Using actual booleans
+        preserve_mode: bool = True,  # type: ignore[override]
+        preserve_times: bool = True,  # type: ignore[override]
+        preserve_symlinks: bool = False,  # type: ignore[override]
+        level: object = 1,
+    ) -> list[str]:
+        assert preserve_mode
+        assert preserve_times
+        assert not preserve_symlinks
+        exclude = self.get_exclusions()
+
+        if not exclude:
+            return orig.install_lib.copy_tree(self, infile, outfile)
+
+        # Exclude namespace package __init__.py* files from the output
+
+        from setuptools.archive_util import unpack_directory
+
+        from distutils import log
+
+        outfiles: list[str] = []
+
+        def pf(src: str, dst: str):
+            if dst in exclude:
+                log.warn("Skipping installation of %s (namespace package)", dst)
+                return False
+
+            log.info("copying %s -> %s", src, os.path.dirname(dst))
+            outfiles.append(dst)
+            return dst
+
+        unpack_directory(infile, outfile, pf)
+        return outfiles
+
+    def get_outputs(self):
+        outputs = orig.install_lib.get_outputs(self)
+        exclude = self.get_exclusions()
+        if exclude:
+            return [f for f in outputs if f not in exclude]
+        return outputs
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_scripts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..4401cf693d2642abce449dee238c037038633fec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/install_scripts.py
@@ -0,0 +1,73 @@
+from __future__ import annotations
+
+import os
+import sys
+
+from .._path import ensure_directory
+from ..dist import Distribution
+
+import distutils.command.install_scripts as orig
+from distutils import log
+
+
+class install_scripts(orig.install_scripts):
+    """Do normal script install, plus any egg_info wrapper scripts"""
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    def initialize_options(self) -> None:
+        orig.install_scripts.initialize_options(self)
+        self.no_ep = False
+
+    def run(self) -> None:
+        self.run_command("egg_info")
+        if self.distribution.scripts:
+            orig.install_scripts.run(self)  # run first to set up self.outfiles
+        else:
+            self.outfiles: list[str] = []
+        if self.no_ep:
+            # don't install entry point scripts into .egg file!
+            return
+        self._install_ep_scripts()
+
+    def _install_ep_scripts(self):
+        # Delay import side-effects
+        from pkg_resources import Distribution, PathMetadata
+
+        from . import easy_install as ei
+
+        ei_cmd = self.get_finalized_command("egg_info")
+        dist = Distribution(
+            ei_cmd.egg_base,
+            PathMetadata(ei_cmd.egg_base, ei_cmd.egg_info),
+            ei_cmd.egg_name,
+            ei_cmd.egg_version,
+        )
+        bs_cmd = self.get_finalized_command('build_scripts')
+        exec_param = getattr(bs_cmd, 'executable', None)
+        writer = ei.ScriptWriter
+        if exec_param == sys.executable:
+            # In case the path to the Python executable contains a space, wrap
+            # it so it's not split up.
+            exec_param = [exec_param]
+        # resolve the writer to the environment
+        writer = writer.best()
+        cmd = writer.command_spec_class.best().from_param(exec_param)
+        for args in writer.get_args(dist, cmd.as_header()):
+            self.write_script(*args)
+
+    def write_script(self, script_name, contents, mode: str = "t", *ignored) -> None:
+        """Write an executable file to the scripts directory"""
+        from setuptools.command.easy_install import chmod, current_umask
+
+        log.info("Installing %s script to %s", script_name, self.install_dir)
+        target = os.path.join(self.install_dir, script_name)
+        self.outfiles.append(target)
+
+        encoding = None if "b" in mode else "utf-8"
+        mask = current_umask()
+        if not self.dry_run:
+            ensure_directory(target)
+            with open(target, "w" + mode, encoding=encoding) as f:
+                f.write(contents)
+            chmod(target, 0o777 - mask)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/launcher manifest.xml b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/launcher manifest.xml
new file mode 100644
index 0000000000000000000000000000000000000000..5972a96d8ded85cc14147ffc1400ec67c3b5a578
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/launcher manifest.xml	
@@ -0,0 +1,15 @@
+
+
+    
+    
+    
+        
+            
+                
+            
+        
+    
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/rotate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/rotate.py
new file mode 100644
index 0000000000000000000000000000000000000000..acdce07baaf3e4fc87552c39d7ee6e0271fe2a72
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/rotate.py
@@ -0,0 +1,65 @@
+from __future__ import annotations
+
+import os
+from typing import ClassVar
+
+from .. import Command, _shutil
+
+from distutils import log
+from distutils.errors import DistutilsOptionError
+from distutils.util import convert_path
+
+
+class rotate(Command):
+    """Delete older distributions"""
+
+    description = "delete older distributions, keeping N newest files"
+    user_options = [
+        ('match=', 'm', "patterns to match (required)"),
+        ('dist-dir=', 'd', "directory where the distributions are"),
+        ('keep=', 'k', "number of matching distributions to keep"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = []
+
+    def initialize_options(self):
+        self.match = None
+        self.dist_dir = None
+        self.keep = None
+
+    def finalize_options(self) -> None:
+        if self.match is None:
+            raise DistutilsOptionError(
+                "Must specify one or more (comma-separated) match patterns "
+                "(e.g. '.zip' or '.egg')"
+            )
+        if self.keep is None:
+            raise DistutilsOptionError("Must specify number of files to keep")
+        try:
+            self.keep = int(self.keep)
+        except ValueError as e:
+            raise DistutilsOptionError("--keep must be an integer") from e
+        if isinstance(self.match, str):
+            self.match = [convert_path(p.strip()) for p in self.match.split(',')]
+        self.set_undefined_options('bdist', ('dist_dir', 'dist_dir'))
+
+    def run(self) -> None:
+        self.run_command("egg_info")
+        from glob import glob
+
+        for pattern in self.match:
+            pattern = self.distribution.get_name() + '*' + pattern
+            files = glob(os.path.join(self.dist_dir, pattern))
+            files = [(os.path.getmtime(f), f) for f in files]
+            files.sort()
+            files.reverse()
+
+            log.info("%d file(s) matching %s", len(files), pattern)
+            files = files[self.keep :]
+            for t, f in files:
+                log.info("Deleting %s", f)
+                if not self.dry_run:
+                    if os.path.isdir(f):
+                        _shutil.rmtree(f)
+                    else:
+                        os.unlink(f)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/saveopts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/saveopts.py
new file mode 100644
index 0000000000000000000000000000000000000000..2a2cbce6e2aad396f4a5ee9788d53387237df96d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/saveopts.py
@@ -0,0 +1,21 @@
+from setuptools.command.setopt import edit_config, option_base
+
+
+class saveopts(option_base):
+    """Save command-line options to a file"""
+
+    description = "save supplied options to setup.cfg or other config file"
+
+    def run(self) -> None:
+        dist = self.distribution
+        settings: dict[str, dict[str, str]] = {}
+
+        for cmd in dist.command_options:
+            if cmd == 'saveopts':
+                continue  # don't save our own options!
+
+            for opt, (src, val) in dist.get_option_dict(cmd).items():
+                if src == "command line":
+                    settings.setdefault(cmd, {})[opt] = val
+
+        edit_config(self.filename, settings, self.dry_run)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/sdist.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/sdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..9631cf3114778a8865917d02878525fc0127a253
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/sdist.py
@@ -0,0 +1,217 @@
+from __future__ import annotations
+
+import contextlib
+import os
+import re
+from itertools import chain
+from typing import ClassVar
+
+from .._importlib import metadata
+from ..dist import Distribution
+from .build import _ORIGINAL_SUBCOMMANDS
+
+import distutils.command.sdist as orig
+from distutils import log
+
+_default_revctrl = list
+
+
+def walk_revctrl(dirname=''):
+    """Find all files under revision control"""
+    for ep in metadata.entry_points(group='setuptools.file_finders'):
+        yield from ep.load()(dirname)
+
+
+class sdist(orig.sdist):
+    """Smart sdist that finds anything supported by revision control"""
+
+    user_options = [
+        ('formats=', None, "formats for source distribution (comma-separated list)"),
+        (
+            'keep-temp',
+            'k',
+            "keep the distribution tree around after creating " + "archive file(s)",
+        ),
+        (
+            'dist-dir=',
+            'd',
+            "directory to put the source distribution archive(s) in [default: dist]",
+        ),
+        (
+            'owner=',
+            'u',
+            "Owner name used when creating a tar file [default: current user]",
+        ),
+        (
+            'group=',
+            'g',
+            "Group name used when creating a tar file [default: current group]",
+        ),
+    ]
+
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+    negative_opt: ClassVar[dict[str, str]] = {}
+
+    README_EXTENSIONS = ['', '.rst', '.txt', '.md']
+    READMES = tuple(f'README{ext}' for ext in README_EXTENSIONS)
+
+    def run(self) -> None:
+        self.run_command('egg_info')
+        ei_cmd = self.get_finalized_command('egg_info')
+        self.filelist = ei_cmd.filelist
+        self.filelist.append(os.path.join(ei_cmd.egg_info, 'SOURCES.txt'))
+        self.check_readme()
+
+        # Run sub commands
+        for cmd_name in self.get_sub_commands():
+            self.run_command(cmd_name)
+
+        self.make_distribution()
+
+        dist_files = getattr(self.distribution, 'dist_files', [])
+        for file in self.archive_files:
+            data = ('sdist', '', file)
+            if data not in dist_files:
+                dist_files.append(data)
+
+    def initialize_options(self) -> None:
+        orig.sdist.initialize_options(self)
+
+    def make_distribution(self) -> None:
+        """
+        Workaround for #516
+        """
+        with self._remove_os_link():
+            orig.sdist.make_distribution(self)
+
+    @staticmethod
+    @contextlib.contextmanager
+    def _remove_os_link():
+        """
+        In a context, remove and restore os.link if it exists
+        """
+
+        class NoValue:
+            pass
+
+        orig_val = getattr(os, 'link', NoValue)
+        try:
+            del os.link
+        except Exception:
+            pass
+        try:
+            yield
+        finally:
+            if orig_val is not NoValue:
+                os.link = orig_val
+
+    def add_defaults(self) -> None:
+        super().add_defaults()
+        self._add_defaults_build_sub_commands()
+
+    def _add_defaults_optional(self):
+        super()._add_defaults_optional()
+        if os.path.isfile('pyproject.toml'):
+            self.filelist.append('pyproject.toml')
+
+    def _add_defaults_python(self):
+        """getting python files"""
+        if self.distribution.has_pure_modules():
+            build_py = self.get_finalized_command('build_py')
+            self.filelist.extend(build_py.get_source_files())
+            self._add_data_files(self._safe_data_files(build_py))
+
+    def _add_defaults_build_sub_commands(self):
+        build = self.get_finalized_command("build")
+        missing_cmds = set(build.get_sub_commands()) - _ORIGINAL_SUBCOMMANDS
+        # ^-- the original built-in sub-commands are already handled by default.
+        cmds = (self.get_finalized_command(c) for c in missing_cmds)
+        files = (c.get_source_files() for c in cmds if hasattr(c, "get_source_files"))
+        self.filelist.extend(chain.from_iterable(files))
+
+    def _safe_data_files(self, build_py):
+        """
+        Since the ``sdist`` class is also used to compute the MANIFEST
+        (via :obj:`setuptools.command.egg_info.manifest_maker`),
+        there might be recursion problems when trying to obtain the list of
+        data_files and ``include_package_data=True`` (which in turn depends on
+        the files included in the MANIFEST).
+
+        To avoid that, ``manifest_maker`` should be able to overwrite this
+        method and avoid recursive attempts to build/analyze the MANIFEST.
+        """
+        return build_py.data_files
+
+    def _add_data_files(self, data_files):
+        """
+        Add data files as found in build_py.data_files.
+        """
+        self.filelist.extend(
+            os.path.join(src_dir, name)
+            for _, src_dir, _, filenames in data_files
+            for name in filenames
+        )
+
+    def _add_defaults_data_files(self):
+        try:
+            super()._add_defaults_data_files()
+        except TypeError:
+            log.warn("data_files contains unexpected objects")
+
+    def prune_file_list(self) -> None:
+        super().prune_file_list()
+        # Prevent accidental inclusion of test-related cache dirs at the project root
+        sep = re.escape(os.sep)
+        self.filelist.exclude_pattern(r"^(\.tox|\.nox|\.venv)" + sep, is_regex=True)
+
+    def check_readme(self) -> None:
+        for f in self.READMES:
+            if os.path.exists(f):
+                return
+        else:
+            self.warn(
+                "standard file not found: should have one of " + ', '.join(self.READMES)
+            )
+
+    def make_release_tree(self, base_dir, files) -> None:
+        orig.sdist.make_release_tree(self, base_dir, files)
+
+        # Save any egg_info command line options used to create this sdist
+        dest = os.path.join(base_dir, 'setup.cfg')
+        if hasattr(os, 'link') and os.path.exists(dest):
+            # unlink and re-copy, since it might be hard-linked, and
+            # we don't want to change the source version
+            os.unlink(dest)
+            self.copy_file('setup.cfg', dest)
+
+        self.get_finalized_command('egg_info').save_version_info(dest)
+
+    def _manifest_is_not_generated(self):
+        # check for special comment used in 2.7.1 and higher
+        if not os.path.isfile(self.manifest):
+            return False
+
+        with open(self.manifest, 'rb') as fp:
+            first_line = fp.readline()
+        return first_line != b'# file GENERATED by distutils, do NOT edit\n'
+
+    def read_manifest(self):
+        """Read the manifest file (named by 'self.manifest') and use it to
+        fill in 'self.filelist', the list of files to include in the source
+        distribution.
+        """
+        log.info("reading manifest file '%s'", self.manifest)
+        manifest = open(self.manifest, 'rb')
+        for bytes_line in manifest:
+            # The manifest must contain UTF-8. See #303.
+            try:
+                line = bytes_line.decode('UTF-8')
+            except UnicodeDecodeError:
+                log.warn(f"{line!r} not UTF-8 decodable -- skipping")
+                continue
+            # ignore comments and blank lines
+            line = line.strip()
+            if line.startswith('#') or not line:
+                continue
+            self.filelist.append(line)
+        manifest.close()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/setopt.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/setopt.py
new file mode 100644
index 0000000000000000000000000000000000000000..678a0593d6739db316bd4008860a613b59892f1f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/setopt.py
@@ -0,0 +1,141 @@
+import configparser
+import os
+
+from .. import Command
+from ..unicode_utils import _cfg_read_utf8_with_fallback
+
+import distutils
+from distutils import log
+from distutils.errors import DistutilsOptionError
+from distutils.util import convert_path
+
+__all__ = ['config_file', 'edit_config', 'option_base', 'setopt']
+
+
+def config_file(kind="local"):
+    """Get the filename of the distutils, local, global, or per-user config
+
+    `kind` must be one of "local", "global", or "user"
+    """
+    if kind == 'local':
+        return 'setup.cfg'
+    if kind == 'global':
+        return os.path.join(os.path.dirname(distutils.__file__), 'distutils.cfg')
+    if kind == 'user':
+        dot = os.name == 'posix' and '.' or ''
+        return os.path.expanduser(convert_path(f"~/{dot}pydistutils.cfg"))
+    raise ValueError("config_file() type must be 'local', 'global', or 'user'", kind)
+
+
+def edit_config(filename, settings, dry_run=False):
+    """Edit a configuration file to include `settings`
+
+    `settings` is a dictionary of dictionaries or ``None`` values, keyed by
+    command/section name.  A ``None`` value means to delete the entire section,
+    while a dictionary lists settings to be changed or deleted in that section.
+    A setting of ``None`` means to delete that setting.
+    """
+    log.debug("Reading configuration from %s", filename)
+    opts = configparser.RawConfigParser()
+    opts.optionxform = lambda optionstr: optionstr  # type: ignore[method-assign] # overriding method
+    _cfg_read_utf8_with_fallback(opts, filename)
+
+    for section, options in settings.items():
+        if options is None:
+            log.info("Deleting section [%s] from %s", section, filename)
+            opts.remove_section(section)
+        else:
+            if not opts.has_section(section):
+                log.debug("Adding new section [%s] to %s", section, filename)
+                opts.add_section(section)
+            for option, value in options.items():
+                if value is None:
+                    log.debug("Deleting %s.%s from %s", section, option, filename)
+                    opts.remove_option(section, option)
+                    if not opts.options(section):
+                        log.info(
+                            "Deleting empty [%s] section from %s", section, filename
+                        )
+                        opts.remove_section(section)
+                else:
+                    log.debug(
+                        "Setting %s.%s to %r in %s", section, option, value, filename
+                    )
+                    opts.set(section, option, value)
+
+    log.info("Writing %s", filename)
+    if not dry_run:
+        with open(filename, 'w', encoding="utf-8") as f:
+            opts.write(f)
+
+
+class option_base(Command):
+    """Abstract base class for commands that mess with config files"""
+
+    user_options = [
+        ('global-config', 'g', "save options to the site-wide distutils.cfg file"),
+        ('user-config', 'u', "save options to the current user's pydistutils.cfg file"),
+        ('filename=', 'f', "configuration file to use (default=setup.cfg)"),
+    ]
+
+    boolean_options = [
+        'global-config',
+        'user-config',
+    ]
+
+    def initialize_options(self):
+        self.global_config = None
+        self.user_config = None
+        self.filename = None
+
+    def finalize_options(self):
+        filenames = []
+        if self.global_config:
+            filenames.append(config_file('global'))
+        if self.user_config:
+            filenames.append(config_file('user'))
+        if self.filename is not None:
+            filenames.append(self.filename)
+        if not filenames:
+            filenames.append(config_file('local'))
+        if len(filenames) > 1:
+            raise DistutilsOptionError(
+                "Must specify only one configuration file option", filenames
+            )
+        (self.filename,) = filenames
+
+
+class setopt(option_base):
+    """Save command-line options to a file"""
+
+    description = "set an option in setup.cfg or another config file"
+
+    user_options = [
+        ('command=', 'c', 'command to set an option for'),
+        ('option=', 'o', 'option to set'),
+        ('set-value=', 's', 'value of the option'),
+        ('remove', 'r', 'remove (unset) the value'),
+    ] + option_base.user_options
+
+    boolean_options = option_base.boolean_options + ['remove']
+
+    def initialize_options(self):
+        option_base.initialize_options(self)
+        self.command = None
+        self.option = None
+        self.set_value = None
+        self.remove = None
+
+    def finalize_options(self) -> None:
+        option_base.finalize_options(self)
+        if self.command is None or self.option is None:
+            raise DistutilsOptionError("Must specify --command *and* --option")
+        if self.set_value is None and not self.remove:
+            raise DistutilsOptionError("Must specify --set-value or --remove")
+
+    def run(self) -> None:
+        edit_config(
+            self.filename,
+            {self.command: {self.option.replace('-', '_'): self.set_value}},
+            self.dry_run,
+        )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/test.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/test.py
new file mode 100644
index 0000000000000000000000000000000000000000..341b11a20eb2cce98cdeeebea9ba2de0282d5d38
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/command/test.py
@@ -0,0 +1,45 @@
+from __future__ import annotations
+
+from setuptools import Command
+from setuptools.warnings import SetuptoolsDeprecationWarning
+
+
+# Would restrict to Literal["test"], but mypy doesn't support it: https://github.com/python/mypy/issues/8203
+def __getattr__(name: str) -> type[_test]:
+    if name == 'test':
+        SetuptoolsDeprecationWarning.emit(
+            "The test command is disabled and references to it are deprecated.",
+            "Please remove any references to `setuptools.command.test` in all "
+            "supported versions of the affected package.",
+            due_date=(2024, 11, 15),
+            stacklevel=2,
+        )
+        return _test
+    raise AttributeError(name)
+
+
+class _test(Command):
+    """
+    Stub to warn when test command is referenced or used.
+    """
+
+    description = "stub for old test command (do not use)"
+
+    user_options = [
+        ('test-module=', 'm', "Run 'test_suite' in specified module"),
+        (
+            'test-suite=',
+            's',
+            "Run single test, case or suite (e.g. 'module.test_suite')",
+        ),
+        ('test-runner=', 'r', "Test runner to use"),
+    ]
+
+    def initialize_options(self):
+        pass
+
+    def finalize_options(self):
+        pass
+
+    def run(self):
+        raise RuntimeError("Support for the test command was removed in Setuptools 72")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py310.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py310.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3912f8e02a57a5b9ba738673a21a596e94c1122
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py310.py
@@ -0,0 +1,9 @@
+import sys
+
+__all__ = ['tomllib']
+
+
+if sys.version_info >= (3, 11):
+    import tomllib
+else:  # pragma: no cover
+    import tomli as tomllib
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py311.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py311.py
new file mode 100644
index 0000000000000000000000000000000000000000..52b58af32a28817deeaf592cc795f311434e39e7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py311.py
@@ -0,0 +1,27 @@
+from __future__ import annotations
+
+import shutil
+import sys
+from typing import TYPE_CHECKING, Any, Callable
+
+if TYPE_CHECKING:
+    from _typeshed import ExcInfo, StrOrBytesPath
+    from typing_extensions import TypeAlias
+
+# Same as shutil._OnExcCallback from typeshed
+_OnExcCallback: TypeAlias = Callable[[Callable[..., Any], str, BaseException], object]
+
+
+def shutil_rmtree(
+    path: StrOrBytesPath,
+    ignore_errors: bool = False,
+    onexc: _OnExcCallback | None = None,
+) -> None:
+    if sys.version_info >= (3, 12):
+        return shutil.rmtree(path, ignore_errors, onexc=onexc)
+
+    def _handler(fn: Callable[..., Any], path: str, excinfo: ExcInfo) -> None:
+        if onexc:
+            onexc(fn, path, excinfo[1])
+
+    return shutil.rmtree(path, ignore_errors, onerror=_handler)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py312.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py312.py
new file mode 100644
index 0000000000000000000000000000000000000000..b20c5f697a861a680c4a747baf9ca9c901e72978
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py312.py
@@ -0,0 +1,13 @@
+from __future__ import annotations
+
+import sys
+
+if sys.version_info >= (3, 12, 4):
+    # Python 3.13 should support `.pth` files encoded in UTF-8
+    # See discussion in https://github.com/python/cpython/issues/77102
+    PTH_ENCODING: str | None = "utf-8"
+else:
+    from .py39 import LOCALE_ENCODING
+
+    # PTH_ENCODING = "locale"
+    PTH_ENCODING = LOCALE_ENCODING
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py39.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py39.py
new file mode 100644
index 0000000000000000000000000000000000000000..04a4abe5a9e61596f97dc3d1b0b3da93a558158f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/compat/py39.py
@@ -0,0 +1,9 @@
+import sys
+
+# Explicitly use the ``"locale"`` encoding in versions that support it,
+# otherwise just rely on the implicit handling of ``encoding=None``.
+# Since all platforms that support ``EncodingWarning`` also support
+# ``encoding="locale"``, this can be used to suppress the warning.
+# However, please try to use UTF-8 when possible
+# (.pth files are the notorious exception: python/cpython#77102, pypa/setuptools#3937).
+LOCALE_ENCODING = "locale" if sys.version_info >= (3, 10) else None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/NOTICE b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/NOTICE
new file mode 100644
index 0000000000000000000000000000000000000000..01864511b0f52a6bf944f70b5e15b75364791935
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/NOTICE
@@ -0,0 +1,10 @@
+The following files include code from opensource projects
+(either as direct copies or modified versions):
+
+- `setuptools.schema.json`, `distutils.schema.json`:
+    - project: `validate-pyproject` - licensed under MPL-2.0
+      (https://github.com/abravalheri/validate-pyproject):
+
+      This Source Code Form is subject to the terms of the Mozilla Public
+      License, v. 2.0. If a copy of the MPL was not distributed with this file,
+      You can obtain one at https://mozilla.org/MPL/2.0/.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..fcc7d008d6c9b3ab2610f2a1b05c4c1eeb5e1416
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/__init__.py
@@ -0,0 +1,43 @@
+"""For backward compatibility, expose main functions from
+``setuptools.config.setupcfg``
+"""
+
+from functools import wraps
+from typing import Callable, TypeVar, cast
+
+from ..warnings import SetuptoolsDeprecationWarning
+from . import setupcfg
+
+Fn = TypeVar("Fn", bound=Callable)
+
+__all__ = ('parse_configuration', 'read_configuration')
+
+
+def _deprecation_notice(fn: Fn) -> Fn:
+    @wraps(fn)
+    def _wrapper(*args, **kwargs):
+        SetuptoolsDeprecationWarning.emit(
+            "Deprecated API usage.",
+            f"""
+            As setuptools moves its configuration towards `pyproject.toml`,
+            `{__name__}.{fn.__name__}` became deprecated.
+
+            For the time being, you can use the `{setupcfg.__name__}` module
+            to access a backward compatible API, but this module is provisional
+            and might be removed in the future.
+
+            To read project metadata, consider using
+            ``build.util.project_wheel_metadata`` (https://pypi.org/project/build/).
+            For simple scenarios, you can also try parsing the file directly
+            with the help of ``configparser``.
+            """,
+            # due_date not defined yet, because the community still heavily relies on it
+            # Warning introduced in 24 Mar 2022
+        )
+        return fn(*args, **kwargs)
+
+    return cast(Fn, _wrapper)
+
+
+read_configuration = _deprecation_notice(setupcfg.read_configuration)
+parse_configuration = _deprecation_notice(setupcfg.parse_configuration)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_apply_pyprojecttoml.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_apply_pyprojecttoml.py
new file mode 100644
index 0000000000000000000000000000000000000000..9088bc1383c87d3ed62a5a4dc44481ffafa1e35e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_apply_pyprojecttoml.py
@@ -0,0 +1,526 @@
+"""Translation layer between pyproject config and setuptools distribution and
+metadata objects.
+
+The distribution and metadata objects are modeled after (an old version of)
+core metadata, therefore configs in the format specified for ``pyproject.toml``
+need to be processed before being applied.
+
+**PRIVATE MODULE**: API reserved for setuptools internal usage only.
+"""
+
+from __future__ import annotations
+
+import logging
+import os
+from collections.abc import Mapping
+from email.headerregistry import Address
+from functools import partial, reduce
+from inspect import cleandoc
+from itertools import chain
+from types import MappingProxyType
+from typing import TYPE_CHECKING, Any, Callable, TypeVar, Union
+
+from .. import _static
+from .._path import StrPath
+from ..errors import InvalidConfigError, RemovedConfigError
+from ..extension import Extension
+from ..warnings import SetuptoolsDeprecationWarning, SetuptoolsWarning
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeAlias
+
+    from setuptools._importlib import metadata
+    from setuptools.dist import Distribution
+
+    from distutils.dist import _OptionsList  # Comes from typeshed
+
+
+EMPTY: Mapping = MappingProxyType({})  # Immutable dict-like
+_ProjectReadmeValue: TypeAlias = Union[str, dict[str, str]]
+_Correspondence: TypeAlias = Callable[["Distribution", Any, Union[StrPath, None]], None]
+_T = TypeVar("_T")
+
+_logger = logging.getLogger(__name__)
+
+
+def apply(dist: Distribution, config: dict, filename: StrPath) -> Distribution:
+    """Apply configuration dict read with :func:`read_configuration`"""
+
+    if not config:
+        return dist  # short-circuit unrelated pyproject.toml file
+
+    root_dir = os.path.dirname(filename) or "."
+
+    _apply_project_table(dist, config, root_dir)
+    _apply_tool_table(dist, config, filename)
+
+    current_directory = os.getcwd()
+    os.chdir(root_dir)
+    try:
+        dist._finalize_requires()
+        dist._finalize_license_expression()
+        dist._finalize_license_files()
+    finally:
+        os.chdir(current_directory)
+
+    return dist
+
+
+def _apply_project_table(dist: Distribution, config: dict, root_dir: StrPath):
+    orig_config = config.get("project", {})
+    if not orig_config:
+        return  # short-circuit
+
+    project_table = {k: _static.attempt_conversion(v) for k, v in orig_config.items()}
+    _handle_missing_dynamic(dist, project_table)
+    _unify_entry_points(project_table)
+
+    for field, value in project_table.items():
+        norm_key = json_compatible_key(field)
+        corresp = PYPROJECT_CORRESPONDENCE.get(norm_key, norm_key)
+        if callable(corresp):
+            corresp(dist, value, root_dir)
+        else:
+            _set_config(dist, corresp, value)
+
+
+def _apply_tool_table(dist: Distribution, config: dict, filename: StrPath):
+    tool_table = config.get("tool", {}).get("setuptools", {})
+    if not tool_table:
+        return  # short-circuit
+
+    if "license-files" in tool_table:
+        if "license-files" in config.get("project", {}):
+            # https://github.com/pypa/setuptools/pull/4837#discussion_r2004983349
+            raise InvalidConfigError(
+                "'project.license-files' is defined already. "
+                "Remove 'tool.setuptools.license-files'."
+            )
+
+        pypa_guides = "guides/writing-pyproject-toml/#license-files"
+        SetuptoolsDeprecationWarning.emit(
+            "'tool.setuptools.license-files' is deprecated in favor of "
+            "'project.license-files' (available on setuptools>=77.0.0).",
+            see_url=f"https://packaging.python.org/en/latest/{pypa_guides}",
+            due_date=(2026, 2, 18),  # Warning introduced on 2025-02-18
+        )
+
+    for field, value in tool_table.items():
+        norm_key = json_compatible_key(field)
+
+        if norm_key in TOOL_TABLE_REMOVALS:
+            suggestion = cleandoc(TOOL_TABLE_REMOVALS[norm_key])
+            msg = f"""
+            The parameter `tool.setuptools.{field}` was long deprecated
+            and has been removed from `pyproject.toml`.
+            """
+            raise RemovedConfigError("\n".join([cleandoc(msg), suggestion]))
+
+        norm_key = TOOL_TABLE_RENAMES.get(norm_key, norm_key)
+        corresp = TOOL_TABLE_CORRESPONDENCE.get(norm_key, norm_key)
+        if callable(corresp):
+            corresp(dist, value)
+        else:
+            _set_config(dist, corresp, value)
+
+    _copy_command_options(config, dist, filename)
+
+
+def _handle_missing_dynamic(dist: Distribution, project_table: dict):
+    """Be temporarily forgiving with ``dynamic`` fields not listed in ``dynamic``"""
+    dynamic = set(project_table.get("dynamic", []))
+    for field, getter in _PREVIOUSLY_DEFINED.items():
+        if not (field in project_table or field in dynamic):
+            value = getter(dist)
+            if value:
+                _MissingDynamic.emit(field=field, value=value)
+                project_table[field] = _RESET_PREVIOUSLY_DEFINED.get(field)
+
+
+def json_compatible_key(key: str) -> str:
+    """As defined in :pep:`566#json-compatible-metadata`"""
+    return key.lower().replace("-", "_")
+
+
+def _set_config(dist: Distribution, field: str, value: Any):
+    val = _PREPROCESS.get(field, _noop)(dist, value)
+    setter = getattr(dist.metadata, f"set_{field}", None)
+    if setter:
+        setter(val)
+    elif hasattr(dist.metadata, field) or field in SETUPTOOLS_PATCHES:
+        setattr(dist.metadata, field, val)
+    else:
+        setattr(dist, field, val)
+
+
+_CONTENT_TYPES = {
+    ".md": "text/markdown",
+    ".rst": "text/x-rst",
+    ".txt": "text/plain",
+}
+
+
+def _guess_content_type(file: str) -> str | None:
+    _, ext = os.path.splitext(file.lower())
+    if not ext:
+        return None
+
+    if ext in _CONTENT_TYPES:
+        return _static.Str(_CONTENT_TYPES[ext])
+
+    valid = ", ".join(f"{k} ({v})" for k, v in _CONTENT_TYPES.items())
+    msg = f"only the following file extensions are recognized: {valid}."
+    raise ValueError(f"Undefined content type for {file}, {msg}")
+
+
+def _long_description(
+    dist: Distribution, val: _ProjectReadmeValue, root_dir: StrPath | None
+):
+    from setuptools.config import expand
+
+    file: str | tuple[()]
+    if isinstance(val, str):
+        file = val
+        text = expand.read_files(file, root_dir)
+        ctype = _guess_content_type(file)
+    else:
+        file = val.get("file") or ()
+        text = val.get("text") or expand.read_files(file, root_dir)
+        ctype = val["content-type"]
+
+    # XXX: Is it completely safe to assume static?
+    _set_config(dist, "long_description", _static.Str(text))
+
+    if ctype:
+        _set_config(dist, "long_description_content_type", _static.Str(ctype))
+
+    if file:
+        dist._referenced_files.add(file)
+
+
+def _license(dist: Distribution, val: str | dict, root_dir: StrPath | None):
+    from setuptools.config import expand
+
+    if isinstance(val, str):
+        if getattr(dist.metadata, "license", None):
+            SetuptoolsWarning.emit("`license` overwritten by `pyproject.toml`")
+            dist.metadata.license = None
+        _set_config(dist, "license_expression", _static.Str(val))
+    else:
+        pypa_guides = "guides/writing-pyproject-toml/#license"
+        SetuptoolsDeprecationWarning.emit(
+            "`project.license` as a TOML table is deprecated",
+            "Please use a simple string containing a SPDX expression for "
+            "`project.license`. You can also use `project.license-files`. "
+            "(Both options available on setuptools>=77.0.0).",
+            see_url=f"https://packaging.python.org/en/latest/{pypa_guides}",
+            due_date=(2026, 2, 18),  # Introduced on 2025-02-18
+        )
+        if "file" in val:
+            # XXX: Is it completely safe to assume static?
+            value = expand.read_files([val["file"]], root_dir)
+            _set_config(dist, "license", _static.Str(value))
+            dist._referenced_files.add(val["file"])
+        else:
+            _set_config(dist, "license", _static.Str(val["text"]))
+
+
+def _people(dist: Distribution, val: list[dict], _root_dir: StrPath | None, kind: str):
+    field = []
+    email_field = []
+    for person in val:
+        if "name" not in person:
+            email_field.append(person["email"])
+        elif "email" not in person:
+            field.append(person["name"])
+        else:
+            addr = Address(display_name=person["name"], addr_spec=person["email"])
+            email_field.append(str(addr))
+
+    if field:
+        _set_config(dist, kind, _static.Str(", ".join(field)))
+    if email_field:
+        _set_config(dist, f"{kind}_email", _static.Str(", ".join(email_field)))
+
+
+def _project_urls(dist: Distribution, val: dict, _root_dir: StrPath | None):
+    _set_config(dist, "project_urls", val)
+
+
+def _python_requires(dist: Distribution, val: str, _root_dir: StrPath | None):
+    _set_config(dist, "python_requires", _static.SpecifierSet(val))
+
+
+def _dependencies(dist: Distribution, val: list, _root_dir: StrPath | None):
+    if getattr(dist, "install_requires", []):
+        msg = "`install_requires` overwritten in `pyproject.toml` (dependencies)"
+        SetuptoolsWarning.emit(msg)
+    dist.install_requires = val
+
+
+def _optional_dependencies(dist: Distribution, val: dict, _root_dir: StrPath | None):
+    if getattr(dist, "extras_require", None):
+        msg = "`extras_require` overwritten in `pyproject.toml` (optional-dependencies)"
+        SetuptoolsWarning.emit(msg)
+    dist.extras_require = val
+
+
+def _ext_modules(dist: Distribution, val: list[dict]) -> list[Extension]:
+    existing = dist.ext_modules or []
+    args = ({k.replace("-", "_"): v for k, v in x.items()} for x in val)
+    new = [Extension(**kw) for kw in args]
+    return [*existing, *new]
+
+
+def _noop(_dist: Distribution, val: _T) -> _T:
+    return val
+
+
+def _identity(val: _T) -> _T:
+    return val
+
+
+def _unify_entry_points(project_table: dict):
+    project = project_table
+    given = project.pop("entry-points", project.pop("entry_points", {}))
+    entry_points = dict(given)  # Avoid problems with static
+    renaming = {"scripts": "console_scripts", "gui_scripts": "gui_scripts"}
+    for key, value in list(project.items()):  # eager to allow modifications
+        norm_key = json_compatible_key(key)
+        if norm_key in renaming:
+            # Don't skip even if value is empty (reason: reset missing `dynamic`)
+            entry_points[renaming[norm_key]] = project.pop(key)
+
+    if entry_points:
+        project["entry-points"] = {
+            name: [f"{k} = {v}" for k, v in group.items()]
+            for name, group in entry_points.items()
+            if group  # now we can skip empty groups
+        }
+        # Sometimes this will set `project["entry-points"] = {}`, and that is
+        # intentional (for resetting configurations that are missing `dynamic`).
+
+
+def _copy_command_options(pyproject: dict, dist: Distribution, filename: StrPath):
+    tool_table = pyproject.get("tool", {})
+    cmdclass = tool_table.get("setuptools", {}).get("cmdclass", {})
+    valid_options = _valid_command_options(cmdclass)
+
+    cmd_opts = dist.command_options
+    for cmd, config in pyproject.get("tool", {}).get("distutils", {}).items():
+        cmd = json_compatible_key(cmd)
+        valid = valid_options.get(cmd, set())
+        cmd_opts.setdefault(cmd, {})
+        for key, value in config.items():
+            key = json_compatible_key(key)
+            cmd_opts[cmd][key] = (str(filename), value)
+            if key not in valid:
+                # To avoid removing options that are specified dynamically we
+                # just log a warn...
+                _logger.warning(f"Command option {cmd}.{key} is not defined")
+
+
+def _valid_command_options(cmdclass: Mapping = EMPTY) -> dict[str, set[str]]:
+    from setuptools.dist import Distribution
+
+    from .._importlib import metadata
+
+    valid_options = {"global": _normalise_cmd_options(Distribution.global_options)}
+
+    unloaded_entry_points = metadata.entry_points(group='distutils.commands')
+    loaded_entry_points = (_load_ep(ep) for ep in unloaded_entry_points)
+    entry_points = (ep for ep in loaded_entry_points if ep)
+    for cmd, cmd_class in chain(entry_points, cmdclass.items()):
+        opts = valid_options.get(cmd, set())
+        opts = opts | _normalise_cmd_options(getattr(cmd_class, "user_options", []))
+        valid_options[cmd] = opts
+
+    return valid_options
+
+
+def _load_ep(ep: metadata.EntryPoint) -> tuple[str, type] | None:
+    if ep.value.startswith("wheel.bdist_wheel"):
+        # Ignore deprecated entrypoint from wheel and avoid warning pypa/wheel#631
+        # TODO: remove check when `bdist_wheel` has been fully removed from pypa/wheel
+        return None
+
+    # Ignore all the errors
+    try:
+        return (ep.name, ep.load())
+    except Exception as ex:
+        msg = f"{ex.__class__.__name__} while trying to load entry-point {ep.name}"
+        _logger.warning(f"{msg}: {ex}")
+        return None
+
+
+def _normalise_cmd_option_key(name: str) -> str:
+    return json_compatible_key(name).strip("_=")
+
+
+def _normalise_cmd_options(desc: _OptionsList) -> set[str]:
+    return {_normalise_cmd_option_key(fancy_option[0]) for fancy_option in desc}
+
+
+def _get_previous_entrypoints(dist: Distribution) -> dict[str, list]:
+    ignore = ("console_scripts", "gui_scripts")
+    value = getattr(dist, "entry_points", None) or {}
+    return {k: v for k, v in value.items() if k not in ignore}
+
+
+def _get_previous_scripts(dist: Distribution) -> list | None:
+    value = getattr(dist, "entry_points", None) or {}
+    return value.get("console_scripts")
+
+
+def _get_previous_gui_scripts(dist: Distribution) -> list | None:
+    value = getattr(dist, "entry_points", None) or {}
+    return value.get("gui_scripts")
+
+
+def _set_static_list_metadata(attr: str, dist: Distribution, val: list) -> None:
+    """Apply distutils metadata validation but preserve "static" behaviour"""
+    meta = dist.metadata
+    setter, getter = getattr(meta, f"set_{attr}"), getattr(meta, f"get_{attr}")
+    setter(val)
+    setattr(meta, attr, _static.List(getter()))
+
+
+def _attrgetter(attr):
+    """
+    Similar to ``operator.attrgetter`` but returns None if ``attr`` is not found
+    >>> from types import SimpleNamespace
+    >>> obj = SimpleNamespace(a=42, b=SimpleNamespace(c=13))
+    >>> _attrgetter("a")(obj)
+    42
+    >>> _attrgetter("b.c")(obj)
+    13
+    >>> _attrgetter("d")(obj) is None
+    True
+    """
+    return partial(reduce, lambda acc, x: getattr(acc, x, None), attr.split("."))
+
+
+def _some_attrgetter(*items):
+    """
+    Return the first "truth-y" attribute or None
+    >>> from types import SimpleNamespace
+    >>> obj = SimpleNamespace(a=42, b=SimpleNamespace(c=13))
+    >>> _some_attrgetter("d", "a", "b.c")(obj)
+    42
+    >>> _some_attrgetter("d", "e", "b.c", "a")(obj)
+    13
+    >>> _some_attrgetter("d", "e", "f")(obj) is None
+    True
+    """
+
+    def _acessor(obj):
+        values = (_attrgetter(i)(obj) for i in items)
+        return next((i for i in values if i is not None), None)
+
+    return _acessor
+
+
+PYPROJECT_CORRESPONDENCE: dict[str, _Correspondence] = {
+    "readme": _long_description,
+    "license": _license,
+    "authors": partial(_people, kind="author"),
+    "maintainers": partial(_people, kind="maintainer"),
+    "urls": _project_urls,
+    "dependencies": _dependencies,
+    "optional_dependencies": _optional_dependencies,
+    "requires_python": _python_requires,
+}
+
+TOOL_TABLE_RENAMES = {"script_files": "scripts"}
+TOOL_TABLE_REMOVALS = {
+    "namespace_packages": """
+        Please migrate to implicit native namespaces instead.
+        See https://packaging.python.org/en/latest/guides/packaging-namespace-packages/.
+        """,
+}
+TOOL_TABLE_CORRESPONDENCE = {
+    # Fields with corresponding core metadata need to be marked as static:
+    "obsoletes": partial(_set_static_list_metadata, "obsoletes"),
+    "provides": partial(_set_static_list_metadata, "provides"),
+    "platforms": partial(_set_static_list_metadata, "platforms"),
+}
+
+SETUPTOOLS_PATCHES = {
+    "long_description_content_type",
+    "project_urls",
+    "provides_extras",
+    "license_file",
+    "license_files",
+    "license_expression",
+}
+
+_PREPROCESS = {
+    "ext_modules": _ext_modules,
+}
+
+_PREVIOUSLY_DEFINED = {
+    "name": _attrgetter("metadata.name"),
+    "version": _attrgetter("metadata.version"),
+    "description": _attrgetter("metadata.description"),
+    "readme": _attrgetter("metadata.long_description"),
+    "requires-python": _some_attrgetter("python_requires", "metadata.python_requires"),
+    "license": _some_attrgetter("metadata.license_expression", "metadata.license"),
+    # XXX: `license-file` is currently not considered in the context of `dynamic`.
+    #      See TestPresetField.test_license_files_exempt_from_dynamic
+    "authors": _some_attrgetter("metadata.author", "metadata.author_email"),
+    "maintainers": _some_attrgetter("metadata.maintainer", "metadata.maintainer_email"),
+    "keywords": _attrgetter("metadata.keywords"),
+    "classifiers": _attrgetter("metadata.classifiers"),
+    "urls": _attrgetter("metadata.project_urls"),
+    "entry-points": _get_previous_entrypoints,
+    "scripts": _get_previous_scripts,
+    "gui-scripts": _get_previous_gui_scripts,
+    "dependencies": _attrgetter("install_requires"),
+    "optional-dependencies": _attrgetter("extras_require"),
+}
+
+
+_RESET_PREVIOUSLY_DEFINED: dict = {
+    # Fix improper setting: given in `setup.py`, but not listed in `dynamic`
+    # Use "immutable" data structures to avoid in-place modification.
+    # dict: pyproject name => value to which reset
+    "license": "",
+    # XXX: `license-file` is currently not considered in the context of `dynamic`.
+    #      See TestPresetField.test_license_files_exempt_from_dynamic
+    "authors": _static.EMPTY_LIST,
+    "maintainers": _static.EMPTY_LIST,
+    "keywords": _static.EMPTY_LIST,
+    "classifiers": _static.EMPTY_LIST,
+    "urls": _static.EMPTY_DICT,
+    "entry-points": _static.EMPTY_DICT,
+    "scripts": _static.EMPTY_DICT,
+    "gui-scripts": _static.EMPTY_DICT,
+    "dependencies": _static.EMPTY_LIST,
+    "optional-dependencies": _static.EMPTY_DICT,
+}
+
+
+class _MissingDynamic(SetuptoolsWarning):
+    _SUMMARY = "`{field}` defined outside of `pyproject.toml` is ignored."
+
+    _DETAILS = """
+    The following seems to be defined outside of `pyproject.toml`:
+
+    `{field} = {value!r}`
+
+    According to the spec (see the link below), however, setuptools CANNOT
+    consider this value unless `{field}` is listed as `dynamic`.
+
+    https://packaging.python.org/en/latest/specifications/pyproject-toml/#declaring-project-metadata-the-project-table
+
+    To prevent this problem, you can list `{field}` under `dynamic` or alternatively
+    remove the `[project]` table from your file and rely entirely on other means of
+    configuration.
+    """
+    # TODO: Consider removing this check in the future?
+    #       There is a trade-off here between improving "debug-ability" and the cost
+    #       of running/testing/maintaining these unnecessary checks...
+
+    @classmethod
+    def details(cls, field: str, value: Any) -> str:
+        return cls._DETAILS.format(field=field, value=value)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/NOTICE b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/NOTICE
new file mode 100644
index 0000000000000000000000000000000000000000..ac5464d88c6f071c18d8eceb1e81d2550573599b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/NOTICE
@@ -0,0 +1,438 @@
+The code contained in this directory was automatically generated using the
+following command:
+
+    python -m validate_pyproject.pre_compile --output-dir=setuptools/config/_validate_pyproject --enable-plugins setuptools distutils --very-verbose -t setuptools=setuptools/config/setuptools.schema.json -t distutils=setuptools/config/distutils.schema.json
+
+Please avoid changing it manually.
+
+
+You can report issues or suggest changes directly to `validate-pyproject`
+(or to the relevant plugin repository)
+
+- https://github.com/abravalheri/validate-pyproject/issues
+
+
+***
+
+The following files include code from opensource projects
+(either as direct copies or modified versions):
+
+- `fastjsonschema_exceptions.py`:
+    - project: `fastjsonschema` - licensed under BSD-3-Clause
+      (https://github.com/horejsek/python-fastjsonschema)
+- `extra_validations.py` and `format.py`, `error_reporting.py`:
+    - project: `validate-pyproject` - licensed under MPL-2.0
+      (https://github.com/abravalheri/validate-pyproject)
+
+
+Additionally the following files are automatically generated by tools provided
+by the same projects:
+
+- `__init__.py`
+- `fastjsonschema_validations.py`
+
+The relevant copyright notes and licenses are included below.
+
+
+***
+
+`fastjsonschema`
+================
+
+Copyright (c) 2018, Michal Horejsek
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification,
+are permitted provided that the following conditions are met:
+
+  Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+  Redistributions in binary form must reproduce the above copyright notice, this
+  list of conditions and the following disclaimer in the documentation and/or
+  other materials provided with the distribution.
+
+  Neither the name of the {organization} nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+
+***
+
+`validate-pyproject`
+====================
+
+Mozilla Public License, version 2.0
+
+1. Definitions
+
+1.1. "Contributor"
+
+     means each individual or legal entity that creates, contributes to the
+     creation of, or owns Covered Software.
+
+1.2. "Contributor Version"
+
+     means the combination of the Contributions of others (if any) used by a
+     Contributor and that particular Contributor's Contribution.
+
+1.3. "Contribution"
+
+     means Covered Software of a particular Contributor.
+
+1.4. "Covered Software"
+
+     means Source Code Form to which the initial Contributor has attached the
+     notice in Exhibit A, the Executable Form of such Source Code Form, and
+     Modifications of such Source Code Form, in each case including portions
+     thereof.
+
+1.5. "Incompatible With Secondary Licenses"
+     means
+
+     a. that the initial Contributor has attached the notice described in
+        Exhibit B to the Covered Software; or
+
+     b. that the Covered Software was made available under the terms of
+        version 1.1 or earlier of the License, but not also under the terms of
+        a Secondary License.
+
+1.6. "Executable Form"
+
+     means any form of the work other than Source Code Form.
+
+1.7. "Larger Work"
+
+     means a work that combines Covered Software with other material, in a
+     separate file or files, that is not Covered Software.
+
+1.8. "License"
+
+     means this document.
+
+1.9. "Licensable"
+
+     means having the right to grant, to the maximum extent possible, whether
+     at the time of the initial grant or subsequently, any and all of the
+     rights conveyed by this License.
+
+1.10. "Modifications"
+
+     means any of the following:
+
+     a. any file in Source Code Form that results from an addition to,
+        deletion from, or modification of the contents of Covered Software; or
+
+     b. any new file in Source Code Form that contains any Covered Software.
+
+1.11. "Patent Claims" of a Contributor
+
+      means any patent claim(s), including without limitation, method,
+      process, and apparatus claims, in any patent Licensable by such
+      Contributor that would be infringed, but for the grant of the License,
+      by the making, using, selling, offering for sale, having made, import,
+      or transfer of either its Contributions or its Contributor Version.
+
+1.12. "Secondary License"
+
+      means either the GNU General Public License, Version 2.0, the GNU Lesser
+      General Public License, Version 2.1, the GNU Affero General Public
+      License, Version 3.0, or any later versions of those licenses.
+
+1.13. "Source Code Form"
+
+      means the form of the work preferred for making modifications.
+
+1.14. "You" (or "Your")
+
+      means an individual or a legal entity exercising rights under this
+      License. For legal entities, "You" includes any entity that controls, is
+      controlled by, or is under common control with You. For purposes of this
+      definition, "control" means (a) the power, direct or indirect, to cause
+      the direction or management of such entity, whether by contract or
+      otherwise, or (b) ownership of more than fifty percent (50%) of the
+      outstanding shares or beneficial ownership of such entity.
+
+
+2. License Grants and Conditions
+
+2.1. Grants
+
+     Each Contributor hereby grants You a world-wide, royalty-free,
+     non-exclusive license:
+
+     a. under intellectual property rights (other than patent or trademark)
+        Licensable by such Contributor to use, reproduce, make available,
+        modify, display, perform, distribute, and otherwise exploit its
+        Contributions, either on an unmodified basis, with Modifications, or
+        as part of a Larger Work; and
+
+     b. under Patent Claims of such Contributor to make, use, sell, offer for
+        sale, have made, import, and otherwise transfer either its
+        Contributions or its Contributor Version.
+
+2.2. Effective Date
+
+     The licenses granted in Section 2.1 with respect to any Contribution
+     become effective for each Contribution on the date the Contributor first
+     distributes such Contribution.
+
+2.3. Limitations on Grant Scope
+
+     The licenses granted in this Section 2 are the only rights granted under
+     this License. No additional rights or licenses will be implied from the
+     distribution or licensing of Covered Software under this License.
+     Notwithstanding Section 2.1(b) above, no patent license is granted by a
+     Contributor:
+
+     a. for any code that a Contributor has removed from Covered Software; or
+
+     b. for infringements caused by: (i) Your and any other third party's
+        modifications of Covered Software, or (ii) the combination of its
+        Contributions with other software (except as part of its Contributor
+        Version); or
+
+     c. under Patent Claims infringed by Covered Software in the absence of
+        its Contributions.
+
+     This License does not grant any rights in the trademarks, service marks,
+     or logos of any Contributor (except as may be necessary to comply with
+     the notice requirements in Section 3.4).
+
+2.4. Subsequent Licenses
+
+     No Contributor makes additional grants as a result of Your choice to
+     distribute the Covered Software under a subsequent version of this
+     License (see Section 10.2) or under the terms of a Secondary License (if
+     permitted under the terms of Section 3.3).
+
+2.5. Representation
+
+     Each Contributor represents that the Contributor believes its
+     Contributions are its original creation(s) or it has sufficient rights to
+     grant the rights to its Contributions conveyed by this License.
+
+2.6. Fair Use
+
+     This License is not intended to limit any rights You have under
+     applicable copyright doctrines of fair use, fair dealing, or other
+     equivalents.
+
+2.7. Conditions
+
+     Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted in
+     Section 2.1.
+
+
+3. Responsibilities
+
+3.1. Distribution of Source Form
+
+     All distribution of Covered Software in Source Code Form, including any
+     Modifications that You create or to which You contribute, must be under
+     the terms of this License. You must inform recipients that the Source
+     Code Form of the Covered Software is governed by the terms of this
+     License, and how they can obtain a copy of this License. You may not
+     attempt to alter or restrict the recipients' rights in the Source Code
+     Form.
+
+3.2. Distribution of Executable Form
+
+     If You distribute Covered Software in Executable Form then:
+
+     a. such Covered Software must also be made available in Source Code Form,
+        as described in Section 3.1, and You must inform recipients of the
+        Executable Form how they can obtain a copy of such Source Code Form by
+        reasonable means in a timely manner, at a charge no more than the cost
+        of distribution to the recipient; and
+
+     b. You may distribute such Executable Form under the terms of this
+        License, or sublicense it under different terms, provided that the
+        license for the Executable Form does not attempt to limit or alter the
+        recipients' rights in the Source Code Form under this License.
+
+3.3. Distribution of a Larger Work
+
+     You may create and distribute a Larger Work under terms of Your choice,
+     provided that You also comply with the requirements of this License for
+     the Covered Software. If the Larger Work is a combination of Covered
+     Software with a work governed by one or more Secondary Licenses, and the
+     Covered Software is not Incompatible With Secondary Licenses, this
+     License permits You to additionally distribute such Covered Software
+     under the terms of such Secondary License(s), so that the recipient of
+     the Larger Work may, at their option, further distribute the Covered
+     Software under the terms of either this License or such Secondary
+     License(s).
+
+3.4. Notices
+
+     You may not remove or alter the substance of any license notices
+     (including copyright notices, patent notices, disclaimers of warranty, or
+     limitations of liability) contained within the Source Code Form of the
+     Covered Software, except that You may alter any license notices to the
+     extent required to remedy known factual inaccuracies.
+
+3.5. Application of Additional Terms
+
+     You may choose to offer, and to charge a fee for, warranty, support,
+     indemnity or liability obligations to one or more recipients of Covered
+     Software. However, You may do so only on Your own behalf, and not on
+     behalf of any Contributor. You must make it absolutely clear that any
+     such warranty, support, indemnity, or liability obligation is offered by
+     You alone, and You hereby agree to indemnify every Contributor for any
+     liability incurred by such Contributor as a result of warranty, support,
+     indemnity or liability terms You offer. You may include additional
+     disclaimers of warranty and limitations of liability specific to any
+     jurisdiction.
+
+4. Inability to Comply Due to Statute or Regulation
+
+   If it is impossible for You to comply with any of the terms of this License
+   with respect to some or all of the Covered Software due to statute,
+   judicial order, or regulation then You must: (a) comply with the terms of
+   this License to the maximum extent possible; and (b) describe the
+   limitations and the code they affect. Such description must be placed in a
+   text file included with all distributions of the Covered Software under
+   this License. Except to the extent prohibited by statute or regulation,
+   such description must be sufficiently detailed for a recipient of ordinary
+   skill to be able to understand it.
+
+5. Termination
+
+5.1. The rights granted under this License will terminate automatically if You
+     fail to comply with any of its terms. However, if You become compliant,
+     then the rights granted under this License from a particular Contributor
+     are reinstated (a) provisionally, unless and until such Contributor
+     explicitly and finally terminates Your grants, and (b) on an ongoing
+     basis, if such Contributor fails to notify You of the non-compliance by
+     some reasonable means prior to 60 days after You have come back into
+     compliance. Moreover, Your grants from a particular Contributor are
+     reinstated on an ongoing basis if such Contributor notifies You of the
+     non-compliance by some reasonable means, this is the first time You have
+     received notice of non-compliance with this License from such
+     Contributor, and You become compliant prior to 30 days after Your receipt
+     of the notice.
+
+5.2. If You initiate litigation against any entity by asserting a patent
+     infringement claim (excluding declaratory judgment actions,
+     counter-claims, and cross-claims) alleging that a Contributor Version
+     directly or indirectly infringes any patent, then the rights granted to
+     You by any and all Contributors for the Covered Software under Section
+     2.1 of this License shall terminate.
+
+5.3. In the event of termination under Sections 5.1 or 5.2 above, all end user
+     license agreements (excluding distributors and resellers) which have been
+     validly granted by You or Your distributors under this License prior to
+     termination shall survive termination.
+
+6. Disclaimer of Warranty
+
+   Covered Software is provided under this License on an "as is" basis,
+   without warranty of any kind, either expressed, implied, or statutory,
+   including, without limitation, warranties that the Covered Software is free
+   of defects, merchantable, fit for a particular purpose or non-infringing.
+   The entire risk as to the quality and performance of the Covered Software
+   is with You. Should any Covered Software prove defective in any respect,
+   You (not any Contributor) assume the cost of any necessary servicing,
+   repair, or correction. This disclaimer of warranty constitutes an essential
+   part of this License. No use of  any Covered Software is authorized under
+   this License except under this disclaimer.
+
+7. Limitation of Liability
+
+   Under no circumstances and under no legal theory, whether tort (including
+   negligence), contract, or otherwise, shall any Contributor, or anyone who
+   distributes Covered Software as permitted above, be liable to You for any
+   direct, indirect, special, incidental, or consequential damages of any
+   character including, without limitation, damages for lost profits, loss of
+   goodwill, work stoppage, computer failure or malfunction, or any and all
+   other commercial damages or losses, even if such party shall have been
+   informed of the possibility of such damages. This limitation of liability
+   shall not apply to liability for death or personal injury resulting from
+   such party's negligence to the extent applicable law prohibits such
+   limitation. Some jurisdictions do not allow the exclusion or limitation of
+   incidental or consequential damages, so this exclusion and limitation may
+   not apply to You.
+
+8. Litigation
+
+   Any litigation relating to this License may be brought only in the courts
+   of a jurisdiction where the defendant maintains its principal place of
+   business and such litigation shall be governed by laws of that
+   jurisdiction, without reference to its conflict-of-law provisions. Nothing
+   in this Section shall prevent a party's ability to bring cross-claims or
+   counter-claims.
+
+9. Miscellaneous
+
+   This License represents the complete agreement concerning the subject
+   matter hereof. If any provision of this License is held to be
+   unenforceable, such provision shall be reformed only to the extent
+   necessary to make it enforceable. Any law or regulation which provides that
+   the language of a contract shall be construed against the drafter shall not
+   be used to construe this License against a Contributor.
+
+
+10. Versions of the License
+
+10.1. New Versions
+
+      Mozilla Foundation is the license steward. Except as provided in Section
+      10.3, no one other than the license steward has the right to modify or
+      publish new versions of this License. Each version will be given a
+      distinguishing version number.
+
+10.2. Effect of New Versions
+
+      You may distribute the Covered Software under the terms of the version
+      of the License under which You originally received the Covered Software,
+      or under the terms of any subsequent version published by the license
+      steward.
+
+10.3. Modified Versions
+
+      If you create software not governed by this License, and you want to
+      create a new license for such software, you may create and use a
+      modified version of this License if you rename the license and remove
+      any references to the name of the license steward (except to note that
+      such modified license differs from this License).
+
+10.4. Distributing Source Code Form that is Incompatible With Secondary
+      Licenses If You choose to distribute Source Code Form that is
+      Incompatible With Secondary Licenses under the terms of this version of
+      the License, the notice described in Exhibit B of this License must be
+      attached.
+
+Exhibit A - Source Code Form License Notice
+
+      This Source Code Form is subject to the
+      terms of the Mozilla Public License, v.
+      2.0. If a copy of the MPL was not
+      distributed with this file, You can
+      obtain one at
+      https://mozilla.org/MPL/2.0/.
+
+If it is not possible or desirable to put the notice in a particular file,
+then You may include the notice in a location (such as a LICENSE file in a
+relevant directory) where a recipient would be likely to look for such a
+notice.
+
+You may add additional accurate notices of copyright ownership.
+
+Exhibit B - "Incompatible With Secondary Licenses" Notice
+
+      This Source Code Form is "Incompatible
+      With Secondary Licenses", as defined by
+      the Mozilla Public License, v. 2.0.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..4f612bd51c4ac1d272318ed6fb96e4aeb57e3e27
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/__init__.py
@@ -0,0 +1,34 @@
+from functools import reduce
+from typing import Any, Callable, Dict
+
+from . import formats
+from .error_reporting import detailed_errors, ValidationError
+from .extra_validations import EXTRA_VALIDATIONS
+from .fastjsonschema_exceptions import JsonSchemaException, JsonSchemaValueException
+from .fastjsonschema_validations import validate as _validate
+
+__all__ = [
+    "validate",
+    "FORMAT_FUNCTIONS",
+    "EXTRA_VALIDATIONS",
+    "ValidationError",
+    "JsonSchemaException",
+    "JsonSchemaValueException",
+]
+
+
+FORMAT_FUNCTIONS: Dict[str, Callable[[str], bool]] = {
+    fn.__name__.replace("_", "-"): fn
+    for fn in formats.__dict__.values()
+    if callable(fn) and not fn.__name__.startswith("_")
+}
+
+
+def validate(data: Any) -> bool:
+    """Validate the given ``data`` object using JSON Schema
+    This function raises ``ValidationError`` if ``data`` is invalid.
+    """
+    with detailed_errors():
+        _validate(data, custom_formats=FORMAT_FUNCTIONS)
+        reduce(lambda acc, fn: fn(acc), EXTRA_VALIDATIONS, data)
+    return True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/error_reporting.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/error_reporting.py
new file mode 100644
index 0000000000000000000000000000000000000000..3591231c09f56494eb46119f9794053439b3fe8c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/error_reporting.py
@@ -0,0 +1,336 @@
+import io
+import json
+import logging
+import os
+import re
+import typing
+from contextlib import contextmanager
+from textwrap import indent, wrap
+from typing import Any, Dict, Generator, Iterator, List, Optional, Sequence, Union
+
+from .fastjsonschema_exceptions import JsonSchemaValueException
+
+if typing.TYPE_CHECKING:
+    import sys
+
+    if sys.version_info < (3, 11):
+        from typing_extensions import Self
+    else:
+        from typing import Self
+
+_logger = logging.getLogger(__name__)
+
+_MESSAGE_REPLACEMENTS = {
+    "must be named by propertyName definition": "keys must be named by",
+    "one of contains definition": "at least one item that matches",
+    " same as const definition:": "",
+    "only specified items": "only items matching the definition",
+}
+
+_SKIP_DETAILS = (
+    "must not be empty",
+    "is always invalid",
+    "must not be there",
+)
+
+_NEED_DETAILS = {"anyOf", "oneOf", "allOf", "contains", "propertyNames", "not", "items"}
+
+_CAMEL_CASE_SPLITTER = re.compile(r"\W+|([A-Z][^A-Z\W]*)")
+_IDENTIFIER = re.compile(r"^[\w_]+$", re.I)
+
+_TOML_JARGON = {
+    "object": "table",
+    "property": "key",
+    "properties": "keys",
+    "property names": "keys",
+}
+
+_FORMATS_HELP = """
+For more details about `format` see
+https://validate-pyproject.readthedocs.io/en/latest/api/validate_pyproject.formats.html
+"""
+
+
+class ValidationError(JsonSchemaValueException):
+    """Report violations of a given JSON schema.
+
+    This class extends :exc:`~fastjsonschema.JsonSchemaValueException`
+    by adding the following properties:
+
+    - ``summary``: an improved version of the ``JsonSchemaValueException`` error message
+      with only the necessary information)
+
+    - ``details``: more contextual information about the error like the failing schema
+      itself and the value that violates the schema.
+
+    Depending on the level of the verbosity of the ``logging`` configuration
+    the exception message will be only ``summary`` (default) or a combination of
+    ``summary`` and ``details`` (when the logging level is set to :obj:`logging.DEBUG`).
+    """
+
+    summary = ""
+    details = ""
+    _original_message = ""
+
+    @classmethod
+    def _from_jsonschema(cls, ex: JsonSchemaValueException) -> "Self":
+        formatter = _ErrorFormatting(ex)
+        obj = cls(str(formatter), ex.value, formatter.name, ex.definition, ex.rule)
+        debug_code = os.getenv("JSONSCHEMA_DEBUG_CODE_GENERATION", "false").lower()
+        if debug_code != "false":  # pragma: no cover
+            obj.__cause__, obj.__traceback__ = ex.__cause__, ex.__traceback__
+        obj._original_message = ex.message
+        obj.summary = formatter.summary
+        obj.details = formatter.details
+        return obj
+
+
+@contextmanager
+def detailed_errors() -> Generator[None, None, None]:
+    try:
+        yield
+    except JsonSchemaValueException as ex:
+        raise ValidationError._from_jsonschema(ex) from None
+
+
+class _ErrorFormatting:
+    def __init__(self, ex: JsonSchemaValueException):
+        self.ex = ex
+        self.name = f"`{self._simplify_name(ex.name)}`"
+        self._original_message: str = self.ex.message.replace(ex.name, self.name)
+        self._summary = ""
+        self._details = ""
+
+    def __str__(self) -> str:
+        if _logger.getEffectiveLevel() <= logging.DEBUG and self.details:
+            return f"{self.summary}\n\n{self.details}"
+
+        return self.summary
+
+    @property
+    def summary(self) -> str:
+        if not self._summary:
+            self._summary = self._expand_summary()
+
+        return self._summary
+
+    @property
+    def details(self) -> str:
+        if not self._details:
+            self._details = self._expand_details()
+
+        return self._details
+
+    @staticmethod
+    def _simplify_name(name: str) -> str:
+        x = len("data.")
+        return name[x:] if name.startswith("data.") else name
+
+    def _expand_summary(self) -> str:
+        msg = self._original_message
+
+        for bad, repl in _MESSAGE_REPLACEMENTS.items():
+            msg = msg.replace(bad, repl)
+
+        if any(substring in msg for substring in _SKIP_DETAILS):
+            return msg
+
+        schema = self.ex.rule_definition
+        if self.ex.rule in _NEED_DETAILS and schema:
+            summary = _SummaryWriter(_TOML_JARGON)
+            return f"{msg}:\n\n{indent(summary(schema), '    ')}"
+
+        return msg
+
+    def _expand_details(self) -> str:
+        optional = []
+        definition = self.ex.definition or {}
+        desc_lines = definition.pop("$$description", [])
+        desc = definition.pop("description", None) or " ".join(desc_lines)
+        if desc:
+            description = "\n".join(
+                wrap(
+                    desc,
+                    width=80,
+                    initial_indent="    ",
+                    subsequent_indent="    ",
+                    break_long_words=False,
+                )
+            )
+            optional.append(f"DESCRIPTION:\n{description}")
+        schema = json.dumps(definition, indent=4)
+        value = json.dumps(self.ex.value, indent=4)
+        defaults = [
+            f"GIVEN VALUE:\n{indent(value, '    ')}",
+            f"OFFENDING RULE: {self.ex.rule!r}",
+            f"DEFINITION:\n{indent(schema, '    ')}",
+        ]
+        msg = "\n\n".join(optional + defaults)
+        epilog = f"\n{_FORMATS_HELP}" if "format" in msg.lower() else ""
+        return msg + epilog
+
+
+class _SummaryWriter:
+    _IGNORE = frozenset(("description", "default", "title", "examples"))
+
+    def __init__(self, jargon: Optional[Dict[str, str]] = None):
+        self.jargon: Dict[str, str] = jargon or {}
+        # Clarify confusing terms
+        self._terms = {
+            "anyOf": "at least one of the following",
+            "oneOf": "exactly one of the following",
+            "allOf": "all of the following",
+            "not": "(*NOT* the following)",
+            "prefixItems": f"{self._jargon('items')} (in order)",
+            "items": "items",
+            "contains": "contains at least one of",
+            "propertyNames": (
+                f"non-predefined acceptable {self._jargon('property names')}"
+            ),
+            "patternProperties": f"{self._jargon('properties')} named via pattern",
+            "const": "predefined value",
+            "enum": "one of",
+        }
+        # Attributes that indicate that the definition is easy and can be done
+        # inline (e.g. string and number)
+        self._guess_inline_defs = [
+            "enum",
+            "const",
+            "maxLength",
+            "minLength",
+            "pattern",
+            "format",
+            "minimum",
+            "maximum",
+            "exclusiveMinimum",
+            "exclusiveMaximum",
+            "multipleOf",
+        ]
+
+    def _jargon(self, term: Union[str, List[str]]) -> Union[str, List[str]]:
+        if isinstance(term, list):
+            return [self.jargon.get(t, t) for t in term]
+        return self.jargon.get(term, term)
+
+    def __call__(
+        self,
+        schema: Union[dict, List[dict]],
+        prefix: str = "",
+        *,
+        _path: Sequence[str] = (),
+    ) -> str:
+        if isinstance(schema, list):
+            return self._handle_list(schema, prefix, _path)
+
+        filtered = self._filter_unecessary(schema, _path)
+        simple = self._handle_simple_dict(filtered, _path)
+        if simple:
+            return f"{prefix}{simple}"
+
+        child_prefix = self._child_prefix(prefix, "  ")
+        item_prefix = self._child_prefix(prefix, "- ")
+        indent = len(prefix) * " "
+        with io.StringIO() as buffer:
+            for i, (key, value) in enumerate(filtered.items()):
+                child_path = [*_path, key]
+                line_prefix = prefix if i == 0 else indent
+                buffer.write(f"{line_prefix}{self._label(child_path)}:")
+                # ^  just the first item should receive the complete prefix
+                if isinstance(value, dict):
+                    filtered = self._filter_unecessary(value, child_path)
+                    simple = self._handle_simple_dict(filtered, child_path)
+                    buffer.write(
+                        f" {simple}"
+                        if simple
+                        else f"\n{self(value, child_prefix, _path=child_path)}"
+                    )
+                elif isinstance(value, list) and (
+                    key != "type" or self._is_property(child_path)
+                ):
+                    children = self._handle_list(value, item_prefix, child_path)
+                    sep = " " if children.startswith("[") else "\n"
+                    buffer.write(f"{sep}{children}")
+                else:
+                    buffer.write(f" {self._value(value, child_path)}\n")
+            return buffer.getvalue()
+
+    def _is_unecessary(self, path: Sequence[str]) -> bool:
+        if self._is_property(path) or not path:  # empty path => instruction @ root
+            return False
+        key = path[-1]
+        return any(key.startswith(k) for k in "$_") or key in self._IGNORE
+
+    def _filter_unecessary(
+        self, schema: Dict[str, Any], path: Sequence[str]
+    ) -> Dict[str, Any]:
+        return {
+            key: value
+            for key, value in schema.items()
+            if not self._is_unecessary([*path, key])
+        }
+
+    def _handle_simple_dict(self, value: dict, path: Sequence[str]) -> Optional[str]:
+        inline = any(p in value for p in self._guess_inline_defs)
+        simple = not any(isinstance(v, (list, dict)) for v in value.values())
+        if inline or simple:
+            return f"{{{', '.join(self._inline_attrs(value, path))}}}\n"
+        return None
+
+    def _handle_list(
+        self, schemas: list, prefix: str = "", path: Sequence[str] = ()
+    ) -> str:
+        if self._is_unecessary(path):
+            return ""
+
+        repr_ = repr(schemas)
+        if all(not isinstance(e, (dict, list)) for e in schemas) and len(repr_) < 60:
+            return f"{repr_}\n"
+
+        item_prefix = self._child_prefix(prefix, "- ")
+        return "".join(
+            self(v, item_prefix, _path=[*path, f"[{i}]"]) for i, v in enumerate(schemas)
+        )
+
+    def _is_property(self, path: Sequence[str]) -> bool:
+        """Check if the given path can correspond to an arbitrarily named property"""
+        counter = 0
+        for key in path[-2::-1]:
+            if key not in {"properties", "patternProperties"}:
+                break
+            counter += 1
+
+        # If the counter if even, the path correspond to a JSON Schema keyword
+        # otherwise it can be any arbitrary string naming a property
+        return counter % 2 == 1
+
+    def _label(self, path: Sequence[str]) -> str:
+        *parents, key = path
+        if not self._is_property(path):
+            norm_key = _separate_terms(key)
+            return self._terms.get(key) or " ".join(self._jargon(norm_key))
+
+        if parents[-1] == "patternProperties":
+            return f"(regex {key!r})"
+        return repr(key)  # property name
+
+    def _value(self, value: Any, path: Sequence[str]) -> str:
+        if path[-1] == "type" and not self._is_property(path):
+            type_ = self._jargon(value)
+            return f"[{', '.join(type_)}]" if isinstance(type_, list) else type_
+        return repr(value)
+
+    def _inline_attrs(self, schema: dict, path: Sequence[str]) -> Iterator[str]:
+        for key, value in schema.items():
+            child_path = [*path, key]
+            yield f"{self._label(child_path)}: {self._value(value, child_path)}"
+
+    def _child_prefix(self, parent_prefix: str, child_prefix: str) -> str:
+        return len(parent_prefix) * " " + child_prefix
+
+
+def _separate_terms(word: str) -> List[str]:
+    """
+    >>> _separate_terms("FooBar-foo")
+    ['foo', 'bar', 'foo']
+    """
+    return [w.lower() for w in _CAMEL_CASE_SPLITTER.split(word) if w]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/extra_validations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/extra_validations.py
new file mode 100644
index 0000000000000000000000000000000000000000..789411d0ff397041f87a834e634bac8488024326
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/extra_validations.py
@@ -0,0 +1,82 @@
+"""The purpose of this module is implement PEP 621 validations that are
+difficult to express as a JSON Schema (or that are not supported by the current
+JSON Schema library).
+"""
+
+from inspect import cleandoc
+from typing import Mapping, TypeVar
+
+from .error_reporting import ValidationError
+
+T = TypeVar("T", bound=Mapping)
+
+
+class RedefiningStaticFieldAsDynamic(ValidationError):
+    _DESC = """According to PEP 621:
+
+    Build back-ends MUST raise an error if the metadata specifies a field
+    statically as well as being listed in dynamic.
+    """
+    __doc__ = _DESC
+    _URL = (
+        "https://packaging.python.org/en/latest/specifications/"
+        "pyproject-toml/#dynamic"
+    )
+
+
+class IncludedDependencyGroupMustExist(ValidationError):
+    _DESC = """An included dependency group must exist and must not be cyclic.
+    """
+    __doc__ = _DESC
+    _URL = "https://peps.python.org/pep-0735/"
+
+
+def validate_project_dynamic(pyproject: T) -> T:
+    project_table = pyproject.get("project", {})
+    dynamic = project_table.get("dynamic", [])
+
+    for field in dynamic:
+        if field in project_table:
+            raise RedefiningStaticFieldAsDynamic(
+                message=f"You cannot provide a value for `project.{field}` and "
+                "list it under `project.dynamic` at the same time",
+                value={
+                    field: project_table[field],
+                    "...": " # ...",
+                    "dynamic": dynamic,
+                },
+                name=f"data.project.{field}",
+                definition={
+                    "description": cleandoc(RedefiningStaticFieldAsDynamic._DESC),
+                    "see": RedefiningStaticFieldAsDynamic._URL,
+                },
+                rule="PEP 621",
+            )
+
+    return pyproject
+
+
+def validate_include_depenency(pyproject: T) -> T:
+    dependency_groups = pyproject.get("dependency-groups", {})
+    for key, value in dependency_groups.items():
+        for each in value:
+            if (
+                isinstance(each, dict)
+                and (include_group := each.get("include-group"))
+                and include_group not in dependency_groups
+            ):
+                raise IncludedDependencyGroupMustExist(
+                    message=f"The included dependency group {include_group} doesn't exist",
+                    value=each,
+                    name=f"data.dependency_groups.{key}",
+                    definition={
+                        "description": cleandoc(IncludedDependencyGroupMustExist._DESC),
+                        "see": IncludedDependencyGroupMustExist._URL,
+                    },
+                    rule="PEP 735",
+                )
+    # TODO: check for `include-group` cycles (can be conditional to graphlib)
+    return pyproject
+
+
+EXTRA_VALIDATIONS = (validate_project_dynamic, validate_include_depenency)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/fastjsonschema_exceptions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/fastjsonschema_exceptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2dddd6a106f021a4723c1e8f5953ccc09e55e1f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/fastjsonschema_exceptions.py
@@ -0,0 +1,51 @@
+import re
+
+
+SPLIT_RE = re.compile(r'[\.\[\]]+')
+
+
+class JsonSchemaException(ValueError):
+    """
+    Base exception of ``fastjsonschema`` library.
+    """
+
+
+class JsonSchemaValueException(JsonSchemaException):
+    """
+    Exception raised by validation function. Available properties:
+
+     * ``message`` containing human-readable information what is wrong (e.g. ``data.property[index] must be smaller than or equal to 42``),
+     * invalid ``value`` (e.g. ``60``),
+     * ``name`` of a path in the data structure (e.g. ``data.property[index]``),
+     * ``path`` as an array in the data structure (e.g. ``['data', 'property', 'index']``),
+     * the whole ``definition`` which the ``value`` has to fulfil (e.g. ``{'type': 'number', 'maximum': 42}``),
+     * ``rule`` which the ``value`` is breaking (e.g. ``maximum``)
+     * and ``rule_definition`` (e.g. ``42``).
+
+    .. versionchanged:: 2.14.0
+        Added all extra properties.
+    """
+
+    def __init__(self, message, value=None, name=None, definition=None, rule=None):
+        super().__init__(message)
+        self.message = message
+        self.value = value
+        self.name = name
+        self.definition = definition
+        self.rule = rule
+
+    @property
+    def path(self):
+        return [item for item in SPLIT_RE.split(self.name) if item != '']
+
+    @property
+    def rule_definition(self):
+        if not self.rule or not self.definition:
+            return None
+        return self.definition.get(self.rule)
+
+
+class JsonSchemaDefinitionException(JsonSchemaException):
+    """
+    Exception raised by generator of validation function.
+    """
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/fastjsonschema_validations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/fastjsonschema_validations.py
new file mode 100644
index 0000000000000000000000000000000000000000..c69368a83ff1bdb89cf4853e00429f0125ca3dce
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/fastjsonschema_validations.py
@@ -0,0 +1,1412 @@
+# noqa
+# ruff: noqa
+# flake8: noqa
+# pylint: skip-file
+# mypy: ignore-errors
+# yapf: disable
+# pylama:skip=1
+
+
+# *** PLEASE DO NOT MODIFY DIRECTLY: Automatically generated code *** 
+
+
+VERSION = "2.20.0"
+from decimal import Decimal
+import re
+from .fastjsonschema_exceptions import JsonSchemaValueException
+
+
+REGEX_PATTERNS = {
+    '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$': re.compile('^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])\\Z'),
+    '^.*$': re.compile('^.*$'),
+    '.+': re.compile('.+'),
+    '^.+$': re.compile('^.+$'),
+    'idn-email_re_pattern': re.compile('^[^@]+@[^@]+\\.[^@]+\\Z')
+}
+
+NoneType = type(None)
+
+def validate(data, custom_formats={}, name_prefix=None):
+    validate_https___packaging_python_org_en_latest_specifications_declaring_build_dependencies(data, custom_formats, (name_prefix or "data") + "")
+    return data
+
+def validate_https___packaging_python_org_en_latest_specifications_declaring_build_dependencies(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/declaring-build-dependencies/', 'title': 'Data structure for ``pyproject.toml`` files', '$$description': ['File format containing build-time configurations for the Python ecosystem. ', ':pep:`517` initially defined a build-system independent format for source trees', 'which was complemented by :pep:`518` to provide a way of specifying dependencies ', 'for building Python projects.', 'Please notice the ``project`` table (as initially defined in  :pep:`621`) is not included', 'in this schema and should be considered separately.'], 'type': 'object', 'additionalProperties': False, 'properties': {'build-system': {'type': 'object', 'description': 'Table used to store build-related data', 'additionalProperties': False, 'properties': {'requires': {'type': 'array', '$$description': ['List of dependencies in the :pep:`508` format required to execute the build', 'system. Please notice that the resulting dependency graph', '**MUST NOT contain cycles**'], 'items': {'type': 'string'}}, 'build-backend': {'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, 'backend-path': {'type': 'array', '$$description': ['List of directories to be prepended to ``sys.path`` when loading the', 'back-end, and running its hooks'], 'items': {'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}}}, 'required': ['requires']}, 'project': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create command-line wrappers for the given', '`entry points `_.']}, 'gui-scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create GUI wrappers for the given', '`entry points `_.', 'The difference between ``scripts`` and ``gui-scripts`` is only relevant in', 'Windows.']}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$ref': '#/definitions/entry-point-group'}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$ref': '#/definitions/dependency'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$ref': '#/definitions/dependency'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}, 'tool': {'type': 'object', 'properties': {'distutils': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/deprecated/distutils/configfile.html', 'title': '``tool.distutils`` table', '$$description': ['**EXPERIMENTAL** (NOT OFFICIALLY SUPPORTED): Use ``tool.distutils``', 'subtables to configure arguments for ``distutils`` commands.', 'Originally, ``distutils`` allowed developers to configure arguments for', '``setup.py`` commands via `distutils configuration files', '`_.', 'See also `the old Python docs _`.'], 'type': 'object', 'properties': {'global': {'type': 'object', 'description': 'Global options applied to all ``distutils`` commands'}}, 'patternProperties': {'.+': {'type': 'object'}}, '$comment': 'TODO: Is there a practical way of making this schema more specific?'}, 'setuptools': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/userguide/pyproject_config.html', 'title': '``tool.setuptools`` table', '$$description': ['``setuptools``-specific configurations that can be set by users that require', 'customization.', 'These configurations are completely optional and probably can be skipped when', 'creating simple packages. They are equivalent to some of the `Keywords', '`_', 'used by the ``setup.py`` file, and can be set via the ``tool.setuptools`` table.', 'It considers only ``setuptools`` `parameters', '`_', 'that are not covered by :pep:`621`; and intentionally excludes ``dependency_links``', 'and ``setup_requires`` (incompatible with modern workflows/standards).'], 'type': 'object', 'additionalProperties': False, 'properties': {'platforms': {'type': 'array', 'items': {'type': 'string'}}, 'provides': {'$$description': ['Package and virtual package names contained within this package', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'obsoletes': {'$$description': ['Packages which this package renders obsolete', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'zip-safe': {'$$description': ['Whether the project can be safely installed and run from a zip file.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'boolean'}, 'script-files': {'$$description': ['Legacy way of defining scripts (entry-points are preferred).', 'Equivalent to the ``script`` keyword in ``setup.py``', '(it was renamed to avoid confusion with entry-point based ``project.scripts``', 'defined in :pep:`621`).', '**DISCOURAGED**: generic script wrappers are tricky and may not work properly.', 'Whenever possible, please use ``project.scripts`` instead.'], 'type': 'array', 'items': {'type': 'string'}, '$comment': 'TODO: is this field deprecated/should be removed?'}, 'eager-resources': {'$$description': ['Resources that should be extracted together, if any of them is needed,', 'or if any C extensions included in the project are imported.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'array', 'items': {'type': 'string'}}, 'packages': {'$$description': ['Packages that should be included in the distribution.', 'It can be given either as a list of package identifiers', 'or as a ``dict``-like structure with a single key ``find``', 'which corresponds to a dynamic call to', '``setuptools.config.expand.find_packages`` function.', 'The ``find`` key is associated with a nested ``dict``-like structure that can', 'contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,', 'mimicking the keyword arguments of the associated function.'], 'oneOf': [{'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$ref': '#/definitions/package-name'}}, {'$ref': '#/definitions/find-directive'}]}, 'package-dir': {'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$ref': '#/definitions/package-name'}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, 'package-data': {'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'include-package-data': {'$$description': ['Automatically include any data files inside the package directories', 'that are specified by ``MANIFEST.in``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'boolean'}, 'exclude-package-data': {'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'namespace-packages': {'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'https://setuptools.pypa.io/en/latest/userguide/package_discovery.html', 'description': '**DEPRECATED**: use implicit namespaces instead (:pep:`420`).'}, 'py-modules': {'description': 'Modules that setuptools will manipulate', 'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'TODO: clarify the relationship with ``packages``'}, 'ext-modules': {'description': 'Extension modules to be compiled by setuptools', 'type': 'array', 'items': {'$ref': '#/definitions/ext-module'}}, 'data-files': {'$$description': ['``dict``-like structure where each key represents a directory and', 'the value is a list of glob patterns that should be installed in them.', '**DISCOURAGED**: please notice this might not work as expected with wheels.', 'Whenever possible, consider using data files inside the package directories', '(or create a new namespace package that only contains data files).', 'See `data files support', '`_.'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'cmdclass': {'$$description': ['Mapping of distutils-style command names to ``setuptools.Command`` subclasses', 'which in turn should be represented by strings with a qualified class name', '(i.e., "dotted" form with module), e.g.::\n\n', '    cmdclass = {mycmd = "pkg.subpkg.module.CommandClass"}\n\n', 'The command class should be a directly defined at the top-level of the', 'containing module (no class nesting).'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'string', 'format': 'python-qualified-identifier'}}}, 'license-files': {'type': 'array', 'items': {'type': 'string'}, '$$description': ['**PROVISIONAL**: list of glob patterns for all license files being distributed.', '(likely to become standard with :pep:`639`).', "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"], '$comment': 'TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?'}, 'dynamic': {'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'$ref': '#/definitions/attr-directive'}, {'$ref': '#/definitions/file-directive'}]}, 'classifiers': {'$ref': '#/definitions/file-directive'}, 'description': {'$ref': '#/definitions/file-directive'}, 'entry-points': {'$ref': '#/definitions/file-directive'}, 'dependencies': {'$ref': '#/definitions/file-directive-for-dependencies'}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'$ref': '#/definitions/file-directive-for-dependencies'}}}, 'readme': {'type': 'object', 'anyOf': [{'$ref': '#/definitions/file-directive'}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'$ref': '#/definitions/file-directive/properties/file'}}, 'additionalProperties': False}], 'required': ['file']}}}}, 'definitions': {'package-name': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, 'ext-module': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, 'file-directive': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'file-directive-for-dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'attr-directive': {'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, 'find-directive': {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}}}}}, 'dependency-groups': {'type': 'object', 'description': 'Dependency groups following PEP 735', 'additionalProperties': False, 'patternProperties': {'^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$': {'type': 'array', 'items': {'oneOf': [{'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, {'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}]}}}}}, 'project': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create command-line wrappers for the given', '`entry points `_.']}, 'gui-scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create GUI wrappers for the given', '`entry points `_.', 'The difference between ``scripts`` and ``gui-scripts`` is only relevant in', 'Windows.']}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$ref': '#/definitions/entry-point-group'}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$ref': '#/definitions/dependency'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$ref': '#/definitions/dependency'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data_keys = set(data.keys())
+        if "build-system" in data_keys:
+            data_keys.remove("build-system")
+            data__buildsystem = data["build-system"]
+            if not isinstance(data__buildsystem, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system must be object", value=data__buildsystem, name="" + (name_prefix or "data") + ".build-system", definition={'type': 'object', 'description': 'Table used to store build-related data', 'additionalProperties': False, 'properties': {'requires': {'type': 'array', '$$description': ['List of dependencies in the :pep:`508` format required to execute the build', 'system. Please notice that the resulting dependency graph', '**MUST NOT contain cycles**'], 'items': {'type': 'string'}}, 'build-backend': {'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, 'backend-path': {'type': 'array', '$$description': ['List of directories to be prepended to ``sys.path`` when loading the', 'back-end, and running its hooks'], 'items': {'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}}}, 'required': ['requires']}, rule='type')
+            data__buildsystem_is_dict = isinstance(data__buildsystem, dict)
+            if data__buildsystem_is_dict:
+                data__buildsystem__missing_keys = set(['requires']) - data__buildsystem.keys()
+                if data__buildsystem__missing_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system must contain " + (str(sorted(data__buildsystem__missing_keys)) + " properties"), value=data__buildsystem, name="" + (name_prefix or "data") + ".build-system", definition={'type': 'object', 'description': 'Table used to store build-related data', 'additionalProperties': False, 'properties': {'requires': {'type': 'array', '$$description': ['List of dependencies in the :pep:`508` format required to execute the build', 'system. Please notice that the resulting dependency graph', '**MUST NOT contain cycles**'], 'items': {'type': 'string'}}, 'build-backend': {'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, 'backend-path': {'type': 'array', '$$description': ['List of directories to be prepended to ``sys.path`` when loading the', 'back-end, and running its hooks'], 'items': {'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}}}, 'required': ['requires']}, rule='required')
+                data__buildsystem_keys = set(data__buildsystem.keys())
+                if "requires" in data__buildsystem_keys:
+                    data__buildsystem_keys.remove("requires")
+                    data__buildsystem__requires = data__buildsystem["requires"]
+                    if not isinstance(data__buildsystem__requires, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system.requires must be array", value=data__buildsystem__requires, name="" + (name_prefix or "data") + ".build-system.requires", definition={'type': 'array', '$$description': ['List of dependencies in the :pep:`508` format required to execute the build', 'system. Please notice that the resulting dependency graph', '**MUST NOT contain cycles**'], 'items': {'type': 'string'}}, rule='type')
+                    data__buildsystem__requires_is_list = isinstance(data__buildsystem__requires, (list, tuple))
+                    if data__buildsystem__requires_is_list:
+                        data__buildsystem__requires_len = len(data__buildsystem__requires)
+                        for data__buildsystem__requires_x, data__buildsystem__requires_item in enumerate(data__buildsystem__requires):
+                            if not isinstance(data__buildsystem__requires_item, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system.requires[{data__buildsystem__requires_x}]".format(**locals()) + " must be string", value=data__buildsystem__requires_item, name="" + (name_prefix or "data") + ".build-system.requires[{data__buildsystem__requires_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if "build-backend" in data__buildsystem_keys:
+                    data__buildsystem_keys.remove("build-backend")
+                    data__buildsystem__buildbackend = data__buildsystem["build-backend"]
+                    if not isinstance(data__buildsystem__buildbackend, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system.build-backend must be string", value=data__buildsystem__buildbackend, name="" + (name_prefix or "data") + ".build-system.build-backend", definition={'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, rule='type')
+                    if isinstance(data__buildsystem__buildbackend, str):
+                        if not custom_formats["pep517-backend-reference"](data__buildsystem__buildbackend):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system.build-backend must be pep517-backend-reference", value=data__buildsystem__buildbackend, name="" + (name_prefix or "data") + ".build-system.build-backend", definition={'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, rule='format')
+                if "backend-path" in data__buildsystem_keys:
+                    data__buildsystem_keys.remove("backend-path")
+                    data__buildsystem__backendpath = data__buildsystem["backend-path"]
+                    if not isinstance(data__buildsystem__backendpath, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system.backend-path must be array", value=data__buildsystem__backendpath, name="" + (name_prefix or "data") + ".build-system.backend-path", definition={'type': 'array', '$$description': ['List of directories to be prepended to ``sys.path`` when loading the', 'back-end, and running its hooks'], 'items': {'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}}, rule='type')
+                    data__buildsystem__backendpath_is_list = isinstance(data__buildsystem__backendpath, (list, tuple))
+                    if data__buildsystem__backendpath_is_list:
+                        data__buildsystem__backendpath_len = len(data__buildsystem__backendpath)
+                        for data__buildsystem__backendpath_x, data__buildsystem__backendpath_item in enumerate(data__buildsystem__backendpath):
+                            if not isinstance(data__buildsystem__backendpath_item, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system.backend-path[{data__buildsystem__backendpath_x}]".format(**locals()) + " must be string", value=data__buildsystem__backendpath_item, name="" + (name_prefix or "data") + ".build-system.backend-path[{data__buildsystem__backendpath_x}]".format(**locals()) + "", definition={'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}, rule='type')
+                if data__buildsystem_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".build-system must not contain "+str(data__buildsystem_keys)+" properties", value=data__buildsystem, name="" + (name_prefix or "data") + ".build-system", definition={'type': 'object', 'description': 'Table used to store build-related data', 'additionalProperties': False, 'properties': {'requires': {'type': 'array', '$$description': ['List of dependencies in the :pep:`508` format required to execute the build', 'system. Please notice that the resulting dependency graph', '**MUST NOT contain cycles**'], 'items': {'type': 'string'}}, 'build-backend': {'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, 'backend-path': {'type': 'array', '$$description': ['List of directories to be prepended to ``sys.path`` when loading the', 'back-end, and running its hooks'], 'items': {'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}}}, 'required': ['requires']}, rule='additionalProperties')
+        if "project" in data_keys:
+            data_keys.remove("project")
+            data__project = data["project"]
+            validate_https___packaging_python_org_en_latest_specifications_pyproject_toml(data__project, custom_formats, (name_prefix or "data") + ".project")
+        if "tool" in data_keys:
+            data_keys.remove("tool")
+            data__tool = data["tool"]
+            if not isinstance(data__tool, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".tool must be object", value=data__tool, name="" + (name_prefix or "data") + ".tool", definition={'type': 'object', 'properties': {'distutils': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/deprecated/distutils/configfile.html', 'title': '``tool.distutils`` table', '$$description': ['**EXPERIMENTAL** (NOT OFFICIALLY SUPPORTED): Use ``tool.distutils``', 'subtables to configure arguments for ``distutils`` commands.', 'Originally, ``distutils`` allowed developers to configure arguments for', '``setup.py`` commands via `distutils configuration files', '`_.', 'See also `the old Python docs _`.'], 'type': 'object', 'properties': {'global': {'type': 'object', 'description': 'Global options applied to all ``distutils`` commands'}}, 'patternProperties': {'.+': {'type': 'object'}}, '$comment': 'TODO: Is there a practical way of making this schema more specific?'}, 'setuptools': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/userguide/pyproject_config.html', 'title': '``tool.setuptools`` table', '$$description': ['``setuptools``-specific configurations that can be set by users that require', 'customization.', 'These configurations are completely optional and probably can be skipped when', 'creating simple packages. They are equivalent to some of the `Keywords', '`_', 'used by the ``setup.py`` file, and can be set via the ``tool.setuptools`` table.', 'It considers only ``setuptools`` `parameters', '`_', 'that are not covered by :pep:`621`; and intentionally excludes ``dependency_links``', 'and ``setup_requires`` (incompatible with modern workflows/standards).'], 'type': 'object', 'additionalProperties': False, 'properties': {'platforms': {'type': 'array', 'items': {'type': 'string'}}, 'provides': {'$$description': ['Package and virtual package names contained within this package', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'obsoletes': {'$$description': ['Packages which this package renders obsolete', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'zip-safe': {'$$description': ['Whether the project can be safely installed and run from a zip file.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'boolean'}, 'script-files': {'$$description': ['Legacy way of defining scripts (entry-points are preferred).', 'Equivalent to the ``script`` keyword in ``setup.py``', '(it was renamed to avoid confusion with entry-point based ``project.scripts``', 'defined in :pep:`621`).', '**DISCOURAGED**: generic script wrappers are tricky and may not work properly.', 'Whenever possible, please use ``project.scripts`` instead.'], 'type': 'array', 'items': {'type': 'string'}, '$comment': 'TODO: is this field deprecated/should be removed?'}, 'eager-resources': {'$$description': ['Resources that should be extracted together, if any of them is needed,', 'or if any C extensions included in the project are imported.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'array', 'items': {'type': 'string'}}, 'packages': {'$$description': ['Packages that should be included in the distribution.', 'It can be given either as a list of package identifiers', 'or as a ``dict``-like structure with a single key ``find``', 'which corresponds to a dynamic call to', '``setuptools.config.expand.find_packages`` function.', 'The ``find`` key is associated with a nested ``dict``-like structure that can', 'contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,', 'mimicking the keyword arguments of the associated function.'], 'oneOf': [{'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$ref': '#/definitions/package-name'}}, {'$ref': '#/definitions/find-directive'}]}, 'package-dir': {'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$ref': '#/definitions/package-name'}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, 'package-data': {'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'include-package-data': {'$$description': ['Automatically include any data files inside the package directories', 'that are specified by ``MANIFEST.in``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'boolean'}, 'exclude-package-data': {'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'namespace-packages': {'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'https://setuptools.pypa.io/en/latest/userguide/package_discovery.html', 'description': '**DEPRECATED**: use implicit namespaces instead (:pep:`420`).'}, 'py-modules': {'description': 'Modules that setuptools will manipulate', 'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'TODO: clarify the relationship with ``packages``'}, 'ext-modules': {'description': 'Extension modules to be compiled by setuptools', 'type': 'array', 'items': {'$ref': '#/definitions/ext-module'}}, 'data-files': {'$$description': ['``dict``-like structure where each key represents a directory and', 'the value is a list of glob patterns that should be installed in them.', '**DISCOURAGED**: please notice this might not work as expected with wheels.', 'Whenever possible, consider using data files inside the package directories', '(or create a new namespace package that only contains data files).', 'See `data files support', '`_.'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'cmdclass': {'$$description': ['Mapping of distutils-style command names to ``setuptools.Command`` subclasses', 'which in turn should be represented by strings with a qualified class name', '(i.e., "dotted" form with module), e.g.::\n\n', '    cmdclass = {mycmd = "pkg.subpkg.module.CommandClass"}\n\n', 'The command class should be a directly defined at the top-level of the', 'containing module (no class nesting).'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'string', 'format': 'python-qualified-identifier'}}}, 'license-files': {'type': 'array', 'items': {'type': 'string'}, '$$description': ['**PROVISIONAL**: list of glob patterns for all license files being distributed.', '(likely to become standard with :pep:`639`).', "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"], '$comment': 'TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?'}, 'dynamic': {'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'$ref': '#/definitions/attr-directive'}, {'$ref': '#/definitions/file-directive'}]}, 'classifiers': {'$ref': '#/definitions/file-directive'}, 'description': {'$ref': '#/definitions/file-directive'}, 'entry-points': {'$ref': '#/definitions/file-directive'}, 'dependencies': {'$ref': '#/definitions/file-directive-for-dependencies'}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'$ref': '#/definitions/file-directive-for-dependencies'}}}, 'readme': {'type': 'object', 'anyOf': [{'$ref': '#/definitions/file-directive'}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'$ref': '#/definitions/file-directive/properties/file'}}, 'additionalProperties': False}], 'required': ['file']}}}}, 'definitions': {'package-name': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, 'ext-module': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, 'file-directive': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'file-directive-for-dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'attr-directive': {'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, 'find-directive': {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}}}}}, rule='type')
+            data__tool_is_dict = isinstance(data__tool, dict)
+            if data__tool_is_dict:
+                data__tool_keys = set(data__tool.keys())
+                if "distutils" in data__tool_keys:
+                    data__tool_keys.remove("distutils")
+                    data__tool__distutils = data__tool["distutils"]
+                    validate_https___setuptools_pypa_io_en_latest_deprecated_distutils_configfile_html(data__tool__distutils, custom_formats, (name_prefix or "data") + ".tool.distutils")
+                if "setuptools" in data__tool_keys:
+                    data__tool_keys.remove("setuptools")
+                    data__tool__setuptools = data__tool["setuptools"]
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html(data__tool__setuptools, custom_formats, (name_prefix or "data") + ".tool.setuptools")
+        if "dependency-groups" in data_keys:
+            data_keys.remove("dependency-groups")
+            data__dependencygroups = data["dependency-groups"]
+            if not isinstance(data__dependencygroups, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups must be object", value=data__dependencygroups, name="" + (name_prefix or "data") + ".dependency-groups", definition={'type': 'object', 'description': 'Dependency groups following PEP 735', 'additionalProperties': False, 'patternProperties': {'^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$': {'type': 'array', 'items': {'oneOf': [{'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, {'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}]}}}}, rule='type')
+            data__dependencygroups_is_dict = isinstance(data__dependencygroups, dict)
+            if data__dependencygroups_is_dict:
+                data__dependencygroups_keys = set(data__dependencygroups.keys())
+                for data__dependencygroups_key, data__dependencygroups_val in data__dependencygroups.items():
+                    if REGEX_PATTERNS['^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'].search(data__dependencygroups_key):
+                        if data__dependencygroups_key in data__dependencygroups_keys:
+                            data__dependencygroups_keys.remove(data__dependencygroups_key)
+                        if not isinstance(data__dependencygroups_val, (list, tuple)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}".format(**locals()) + " must be array", value=data__dependencygroups_val, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}".format(**locals()) + "", definition={'type': 'array', 'items': {'oneOf': [{'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, {'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}]}}, rule='type')
+                        data__dependencygroups_val_is_list = isinstance(data__dependencygroups_val, (list, tuple))
+                        if data__dependencygroups_val_is_list:
+                            data__dependencygroups_val_len = len(data__dependencygroups_val)
+                            for data__dependencygroups_val_x, data__dependencygroups_val_item in enumerate(data__dependencygroups_val):
+                                data__dependencygroups_val_item_one_of_count1 = 0
+                                if data__dependencygroups_val_item_one_of_count1 < 2:
+                                    try:
+                                        if not isinstance(data__dependencygroups_val_item, (str)):
+                                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + " must be string", value=data__dependencygroups_val_item, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + "", definition={'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, rule='type')
+                                        if isinstance(data__dependencygroups_val_item, str):
+                                            if not custom_formats["pep508"](data__dependencygroups_val_item):
+                                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + " must be pep508", value=data__dependencygroups_val_item, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + "", definition={'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, rule='format')
+                                        data__dependencygroups_val_item_one_of_count1 += 1
+                                    except JsonSchemaValueException: pass
+                                if data__dependencygroups_val_item_one_of_count1 < 2:
+                                    try:
+                                        if not isinstance(data__dependencygroups_val_item, (dict)):
+                                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + " must be object", value=data__dependencygroups_val_item, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + "", definition={'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}, rule='type')
+                                        data__dependencygroups_val_item_is_dict = isinstance(data__dependencygroups_val_item, dict)
+                                        if data__dependencygroups_val_item_is_dict:
+                                            data__dependencygroups_val_item_keys = set(data__dependencygroups_val_item.keys())
+                                            if "include-group" in data__dependencygroups_val_item_keys:
+                                                data__dependencygroups_val_item_keys.remove("include-group")
+                                                data__dependencygroups_val_item__includegroup = data__dependencygroups_val_item["include-group"]
+                                                if not isinstance(data__dependencygroups_val_item__includegroup, (str)):
+                                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}].include-group".format(**locals()) + " must be string", value=data__dependencygroups_val_item__includegroup, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}].include-group".format(**locals()) + "", definition={'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}, rule='type')
+                                                if isinstance(data__dependencygroups_val_item__includegroup, str):
+                                                    if not REGEX_PATTERNS['^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'].search(data__dependencygroups_val_item__includegroup):
+                                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}].include-group".format(**locals()) + " must match pattern ^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$", value=data__dependencygroups_val_item__includegroup, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}].include-group".format(**locals()) + "", definition={'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}, rule='pattern')
+                                            if data__dependencygroups_val_item_keys:
+                                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + " must not contain "+str(data__dependencygroups_val_item_keys)+" properties", value=data__dependencygroups_val_item, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + "", definition={'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}, rule='additionalProperties')
+                                        data__dependencygroups_val_item_one_of_count1 += 1
+                                    except JsonSchemaValueException: pass
+                                if data__dependencygroups_val_item_one_of_count1 != 1:
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + " must be valid exactly by one definition" + (" (" + str(data__dependencygroups_val_item_one_of_count1) + " matches found)"), value=data__dependencygroups_val_item, name="" + (name_prefix or "data") + ".dependency-groups.{data__dependencygroups_key}[{data__dependencygroups_val_x}]".format(**locals()) + "", definition={'oneOf': [{'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, {'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}]}, rule='oneOf')
+                if data__dependencygroups_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependency-groups must not contain "+str(data__dependencygroups_keys)+" properties", value=data__dependencygroups, name="" + (name_prefix or "data") + ".dependency-groups", definition={'type': 'object', 'description': 'Dependency groups following PEP 735', 'additionalProperties': False, 'patternProperties': {'^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$': {'type': 'array', 'items': {'oneOf': [{'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, {'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}]}}}}, rule='additionalProperties')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/declaring-build-dependencies/', 'title': 'Data structure for ``pyproject.toml`` files', '$$description': ['File format containing build-time configurations for the Python ecosystem. ', ':pep:`517` initially defined a build-system independent format for source trees', 'which was complemented by :pep:`518` to provide a way of specifying dependencies ', 'for building Python projects.', 'Please notice the ``project`` table (as initially defined in  :pep:`621`) is not included', 'in this schema and should be considered separately.'], 'type': 'object', 'additionalProperties': False, 'properties': {'build-system': {'type': 'object', 'description': 'Table used to store build-related data', 'additionalProperties': False, 'properties': {'requires': {'type': 'array', '$$description': ['List of dependencies in the :pep:`508` format required to execute the build', 'system. Please notice that the resulting dependency graph', '**MUST NOT contain cycles**'], 'items': {'type': 'string'}}, 'build-backend': {'type': 'string', 'description': 'Python object that will be used to perform the build according to :pep:`517`', 'format': 'pep517-backend-reference'}, 'backend-path': {'type': 'array', '$$description': ['List of directories to be prepended to ``sys.path`` when loading the', 'back-end, and running its hooks'], 'items': {'type': 'string', '$comment': 'Should be a path (TODO: enforce it with format?)'}}}, 'required': ['requires']}, 'project': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create command-line wrappers for the given', '`entry points `_.']}, 'gui-scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create GUI wrappers for the given', '`entry points `_.', 'The difference between ``scripts`` and ``gui-scripts`` is only relevant in', 'Windows.']}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$ref': '#/definitions/entry-point-group'}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$ref': '#/definitions/dependency'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$ref': '#/definitions/dependency'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}, 'tool': {'type': 'object', 'properties': {'distutils': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/deprecated/distutils/configfile.html', 'title': '``tool.distutils`` table', '$$description': ['**EXPERIMENTAL** (NOT OFFICIALLY SUPPORTED): Use ``tool.distutils``', 'subtables to configure arguments for ``distutils`` commands.', 'Originally, ``distutils`` allowed developers to configure arguments for', '``setup.py`` commands via `distutils configuration files', '`_.', 'See also `the old Python docs _`.'], 'type': 'object', 'properties': {'global': {'type': 'object', 'description': 'Global options applied to all ``distutils`` commands'}}, 'patternProperties': {'.+': {'type': 'object'}}, '$comment': 'TODO: Is there a practical way of making this schema more specific?'}, 'setuptools': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/userguide/pyproject_config.html', 'title': '``tool.setuptools`` table', '$$description': ['``setuptools``-specific configurations that can be set by users that require', 'customization.', 'These configurations are completely optional and probably can be skipped when', 'creating simple packages. They are equivalent to some of the `Keywords', '`_', 'used by the ``setup.py`` file, and can be set via the ``tool.setuptools`` table.', 'It considers only ``setuptools`` `parameters', '`_', 'that are not covered by :pep:`621`; and intentionally excludes ``dependency_links``', 'and ``setup_requires`` (incompatible with modern workflows/standards).'], 'type': 'object', 'additionalProperties': False, 'properties': {'platforms': {'type': 'array', 'items': {'type': 'string'}}, 'provides': {'$$description': ['Package and virtual package names contained within this package', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'obsoletes': {'$$description': ['Packages which this package renders obsolete', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'zip-safe': {'$$description': ['Whether the project can be safely installed and run from a zip file.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'boolean'}, 'script-files': {'$$description': ['Legacy way of defining scripts (entry-points are preferred).', 'Equivalent to the ``script`` keyword in ``setup.py``', '(it was renamed to avoid confusion with entry-point based ``project.scripts``', 'defined in :pep:`621`).', '**DISCOURAGED**: generic script wrappers are tricky and may not work properly.', 'Whenever possible, please use ``project.scripts`` instead.'], 'type': 'array', 'items': {'type': 'string'}, '$comment': 'TODO: is this field deprecated/should be removed?'}, 'eager-resources': {'$$description': ['Resources that should be extracted together, if any of them is needed,', 'or if any C extensions included in the project are imported.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'array', 'items': {'type': 'string'}}, 'packages': {'$$description': ['Packages that should be included in the distribution.', 'It can be given either as a list of package identifiers', 'or as a ``dict``-like structure with a single key ``find``', 'which corresponds to a dynamic call to', '``setuptools.config.expand.find_packages`` function.', 'The ``find`` key is associated with a nested ``dict``-like structure that can', 'contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,', 'mimicking the keyword arguments of the associated function.'], 'oneOf': [{'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$ref': '#/definitions/package-name'}}, {'$ref': '#/definitions/find-directive'}]}, 'package-dir': {'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$ref': '#/definitions/package-name'}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, 'package-data': {'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'include-package-data': {'$$description': ['Automatically include any data files inside the package directories', 'that are specified by ``MANIFEST.in``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'boolean'}, 'exclude-package-data': {'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'namespace-packages': {'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'https://setuptools.pypa.io/en/latest/userguide/package_discovery.html', 'description': '**DEPRECATED**: use implicit namespaces instead (:pep:`420`).'}, 'py-modules': {'description': 'Modules that setuptools will manipulate', 'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'TODO: clarify the relationship with ``packages``'}, 'ext-modules': {'description': 'Extension modules to be compiled by setuptools', 'type': 'array', 'items': {'$ref': '#/definitions/ext-module'}}, 'data-files': {'$$description': ['``dict``-like structure where each key represents a directory and', 'the value is a list of glob patterns that should be installed in them.', '**DISCOURAGED**: please notice this might not work as expected with wheels.', 'Whenever possible, consider using data files inside the package directories', '(or create a new namespace package that only contains data files).', 'See `data files support', '`_.'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'cmdclass': {'$$description': ['Mapping of distutils-style command names to ``setuptools.Command`` subclasses', 'which in turn should be represented by strings with a qualified class name', '(i.e., "dotted" form with module), e.g.::\n\n', '    cmdclass = {mycmd = "pkg.subpkg.module.CommandClass"}\n\n', 'The command class should be a directly defined at the top-level of the', 'containing module (no class nesting).'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'string', 'format': 'python-qualified-identifier'}}}, 'license-files': {'type': 'array', 'items': {'type': 'string'}, '$$description': ['**PROVISIONAL**: list of glob patterns for all license files being distributed.', '(likely to become standard with :pep:`639`).', "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"], '$comment': 'TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?'}, 'dynamic': {'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'$ref': '#/definitions/attr-directive'}, {'$ref': '#/definitions/file-directive'}]}, 'classifiers': {'$ref': '#/definitions/file-directive'}, 'description': {'$ref': '#/definitions/file-directive'}, 'entry-points': {'$ref': '#/definitions/file-directive'}, 'dependencies': {'$ref': '#/definitions/file-directive-for-dependencies'}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'$ref': '#/definitions/file-directive-for-dependencies'}}}, 'readme': {'type': 'object', 'anyOf': [{'$ref': '#/definitions/file-directive'}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'$ref': '#/definitions/file-directive/properties/file'}}, 'additionalProperties': False}], 'required': ['file']}}}}, 'definitions': {'package-name': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, 'ext-module': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, 'file-directive': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'file-directive-for-dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'attr-directive': {'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, 'find-directive': {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}}}}}, 'dependency-groups': {'type': 'object', 'description': 'Dependency groups following PEP 735', 'additionalProperties': False, 'patternProperties': {'^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$': {'type': 'array', 'items': {'oneOf': [{'type': 'string', 'description': 'Python package specifiers following PEP 508', 'format': 'pep508'}, {'type': 'object', 'additionalProperties': False, 'properties': {'include-group': {'description': 'Another dependency group to include in this one', 'type': 'string', 'pattern': '^([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9._-]*[a-zA-Z0-9])$'}}}]}}}}}, 'project': {'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$ref': '#/definitions/author'}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create command-line wrappers for the given', '`entry points `_.']}, 'gui-scripts': {'$ref': '#/definitions/entry-point-group', '$$description': ['Instruct the installer to create GUI wrappers for the given', '`entry points `_.', 'The difference between ``scripts`` and ``gui-scripts`` is only relevant in', 'Windows.']}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$ref': '#/definitions/entry-point-group'}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$ref': '#/definitions/dependency'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$ref': '#/definitions/dependency'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, rule='additionalProperties')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/userguide/pyproject_config.html', 'title': '``tool.setuptools`` table', '$$description': ['``setuptools``-specific configurations that can be set by users that require', 'customization.', 'These configurations are completely optional and probably can be skipped when', 'creating simple packages. They are equivalent to some of the `Keywords', '`_', 'used by the ``setup.py`` file, and can be set via the ``tool.setuptools`` table.', 'It considers only ``setuptools`` `parameters', '`_', 'that are not covered by :pep:`621`; and intentionally excludes ``dependency_links``', 'and ``setup_requires`` (incompatible with modern workflows/standards).'], 'type': 'object', 'additionalProperties': False, 'properties': {'platforms': {'type': 'array', 'items': {'type': 'string'}}, 'provides': {'$$description': ['Package and virtual package names contained within this package', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'obsoletes': {'$$description': ['Packages which this package renders obsolete', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'zip-safe': {'$$description': ['Whether the project can be safely installed and run from a zip file.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'boolean'}, 'script-files': {'$$description': ['Legacy way of defining scripts (entry-points are preferred).', 'Equivalent to the ``script`` keyword in ``setup.py``', '(it was renamed to avoid confusion with entry-point based ``project.scripts``', 'defined in :pep:`621`).', '**DISCOURAGED**: generic script wrappers are tricky and may not work properly.', 'Whenever possible, please use ``project.scripts`` instead.'], 'type': 'array', 'items': {'type': 'string'}, '$comment': 'TODO: is this field deprecated/should be removed?'}, 'eager-resources': {'$$description': ['Resources that should be extracted together, if any of them is needed,', 'or if any C extensions included in the project are imported.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'array', 'items': {'type': 'string'}}, 'packages': {'$$description': ['Packages that should be included in the distribution.', 'It can be given either as a list of package identifiers', 'or as a ``dict``-like structure with a single key ``find``', 'which corresponds to a dynamic call to', '``setuptools.config.expand.find_packages`` function.', 'The ``find`` key is associated with a nested ``dict``-like structure that can', 'contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,', 'mimicking the keyword arguments of the associated function.'], 'oneOf': [{'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}}, {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}]}, 'package-dir': {'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, 'package-data': {'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'include-package-data': {'$$description': ['Automatically include any data files inside the package directories', 'that are specified by ``MANIFEST.in``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'boolean'}, 'exclude-package-data': {'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'namespace-packages': {'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'https://setuptools.pypa.io/en/latest/userguide/package_discovery.html', 'description': '**DEPRECATED**: use implicit namespaces instead (:pep:`420`).'}, 'py-modules': {'description': 'Modules that setuptools will manipulate', 'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'TODO: clarify the relationship with ``packages``'}, 'ext-modules': {'description': 'Extension modules to be compiled by setuptools', 'type': 'array', 'items': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}}, 'data-files': {'$$description': ['``dict``-like structure where each key represents a directory and', 'the value is a list of glob patterns that should be installed in them.', '**DISCOURAGED**: please notice this might not work as expected with wheels.', 'Whenever possible, consider using data files inside the package directories', '(or create a new namespace package that only contains data files).', 'See `data files support', '`_.'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'cmdclass': {'$$description': ['Mapping of distutils-style command names to ``setuptools.Command`` subclasses', 'which in turn should be represented by strings with a qualified class name', '(i.e., "dotted" form with module), e.g.::\n\n', '    cmdclass = {mycmd = "pkg.subpkg.module.CommandClass"}\n\n', 'The command class should be a directly defined at the top-level of the', 'containing module (no class nesting).'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'string', 'format': 'python-qualified-identifier'}}}, 'license-files': {'type': 'array', 'items': {'type': 'string'}, '$$description': ['**PROVISIONAL**: list of glob patterns for all license files being distributed.', '(likely to become standard with :pep:`639`).', "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"], '$comment': 'TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?'}, 'dynamic': {'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, 'classifiers': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'description': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'entry-points': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, 'readme': {'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}}}}, 'definitions': {'package-name': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, 'ext-module': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, 'file-directive': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'file-directive-for-dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, 'attr-directive': {'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, 'find-directive': {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}}}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data_keys = set(data.keys())
+        if "platforms" in data_keys:
+            data_keys.remove("platforms")
+            data__platforms = data["platforms"]
+            if not isinstance(data__platforms, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".platforms must be array", value=data__platforms, name="" + (name_prefix or "data") + ".platforms", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__platforms_is_list = isinstance(data__platforms, (list, tuple))
+            if data__platforms_is_list:
+                data__platforms_len = len(data__platforms)
+                for data__platforms_x, data__platforms_item in enumerate(data__platforms):
+                    if not isinstance(data__platforms_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".platforms[{data__platforms_x}]".format(**locals()) + " must be string", value=data__platforms_item, name="" + (name_prefix or "data") + ".platforms[{data__platforms_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "provides" in data_keys:
+            data_keys.remove("provides")
+            data__provides = data["provides"]
+            if not isinstance(data__provides, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".provides must be array", value=data__provides, name="" + (name_prefix or "data") + ".provides", definition={'$$description': ['Package and virtual package names contained within this package', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, rule='type')
+            data__provides_is_list = isinstance(data__provides, (list, tuple))
+            if data__provides_is_list:
+                data__provides_len = len(data__provides)
+                for data__provides_x, data__provides_item in enumerate(data__provides):
+                    if not isinstance(data__provides_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".provides[{data__provides_x}]".format(**locals()) + " must be string", value=data__provides_item, name="" + (name_prefix or "data") + ".provides[{data__provides_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'pep508-identifier'}, rule='type')
+                    if isinstance(data__provides_item, str):
+                        if not custom_formats["pep508-identifier"](data__provides_item):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".provides[{data__provides_x}]".format(**locals()) + " must be pep508-identifier", value=data__provides_item, name="" + (name_prefix or "data") + ".provides[{data__provides_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'pep508-identifier'}, rule='format')
+        if "obsoletes" in data_keys:
+            data_keys.remove("obsoletes")
+            data__obsoletes = data["obsoletes"]
+            if not isinstance(data__obsoletes, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".obsoletes must be array", value=data__obsoletes, name="" + (name_prefix or "data") + ".obsoletes", definition={'$$description': ['Packages which this package renders obsolete', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, rule='type')
+            data__obsoletes_is_list = isinstance(data__obsoletes, (list, tuple))
+            if data__obsoletes_is_list:
+                data__obsoletes_len = len(data__obsoletes)
+                for data__obsoletes_x, data__obsoletes_item in enumerate(data__obsoletes):
+                    if not isinstance(data__obsoletes_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".obsoletes[{data__obsoletes_x}]".format(**locals()) + " must be string", value=data__obsoletes_item, name="" + (name_prefix or "data") + ".obsoletes[{data__obsoletes_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'pep508-identifier'}, rule='type')
+                    if isinstance(data__obsoletes_item, str):
+                        if not custom_formats["pep508-identifier"](data__obsoletes_item):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".obsoletes[{data__obsoletes_x}]".format(**locals()) + " must be pep508-identifier", value=data__obsoletes_item, name="" + (name_prefix or "data") + ".obsoletes[{data__obsoletes_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'pep508-identifier'}, rule='format')
+        if "zip-safe" in data_keys:
+            data_keys.remove("zip-safe")
+            data__zipsafe = data["zip-safe"]
+            if not isinstance(data__zipsafe, (bool)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".zip-safe must be boolean", value=data__zipsafe, name="" + (name_prefix or "data") + ".zip-safe", definition={'$$description': ['Whether the project can be safely installed and run from a zip file.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'boolean'}, rule='type')
+        if "script-files" in data_keys:
+            data_keys.remove("script-files")
+            data__scriptfiles = data["script-files"]
+            if not isinstance(data__scriptfiles, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".script-files must be array", value=data__scriptfiles, name="" + (name_prefix or "data") + ".script-files", definition={'$$description': ['Legacy way of defining scripts (entry-points are preferred).', 'Equivalent to the ``script`` keyword in ``setup.py``', '(it was renamed to avoid confusion with entry-point based ``project.scripts``', 'defined in :pep:`621`).', '**DISCOURAGED**: generic script wrappers are tricky and may not work properly.', 'Whenever possible, please use ``project.scripts`` instead.'], 'type': 'array', 'items': {'type': 'string'}, '$comment': 'TODO: is this field deprecated/should be removed?'}, rule='type')
+            data__scriptfiles_is_list = isinstance(data__scriptfiles, (list, tuple))
+            if data__scriptfiles_is_list:
+                data__scriptfiles_len = len(data__scriptfiles)
+                for data__scriptfiles_x, data__scriptfiles_item in enumerate(data__scriptfiles):
+                    if not isinstance(data__scriptfiles_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".script-files[{data__scriptfiles_x}]".format(**locals()) + " must be string", value=data__scriptfiles_item, name="" + (name_prefix or "data") + ".script-files[{data__scriptfiles_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "eager-resources" in data_keys:
+            data_keys.remove("eager-resources")
+            data__eagerresources = data["eager-resources"]
+            if not isinstance(data__eagerresources, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".eager-resources must be array", value=data__eagerresources, name="" + (name_prefix or "data") + ".eager-resources", definition={'$$description': ['Resources that should be extracted together, if any of them is needed,', 'or if any C extensions included in the project are imported.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__eagerresources_is_list = isinstance(data__eagerresources, (list, tuple))
+            if data__eagerresources_is_list:
+                data__eagerresources_len = len(data__eagerresources)
+                for data__eagerresources_x, data__eagerresources_item in enumerate(data__eagerresources):
+                    if not isinstance(data__eagerresources_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".eager-resources[{data__eagerresources_x}]".format(**locals()) + " must be string", value=data__eagerresources_item, name="" + (name_prefix or "data") + ".eager-resources[{data__eagerresources_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "packages" in data_keys:
+            data_keys.remove("packages")
+            data__packages = data["packages"]
+            data__packages_one_of_count2 = 0
+            if data__packages_one_of_count2 < 2:
+                try:
+                    if not isinstance(data__packages, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".packages must be array", value=data__packages, name="" + (name_prefix or "data") + ".packages", definition={'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}}, rule='type')
+                    data__packages_is_list = isinstance(data__packages, (list, tuple))
+                    if data__packages_is_list:
+                        data__packages_len = len(data__packages)
+                        for data__packages_x, data__packages_item in enumerate(data__packages):
+                            validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_package_name(data__packages_item, custom_formats, (name_prefix or "data") + ".packages[{data__packages_x}]".format(**locals()))
+                    data__packages_one_of_count2 += 1
+                except JsonSchemaValueException: pass
+            if data__packages_one_of_count2 < 2:
+                try:
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_find_directive(data__packages, custom_formats, (name_prefix or "data") + ".packages")
+                    data__packages_one_of_count2 += 1
+                except JsonSchemaValueException: pass
+            if data__packages_one_of_count2 != 1:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".packages must be valid exactly by one definition" + (" (" + str(data__packages_one_of_count2) + " matches found)"), value=data__packages, name="" + (name_prefix or "data") + ".packages", definition={'$$description': ['Packages that should be included in the distribution.', 'It can be given either as a list of package identifiers', 'or as a ``dict``-like structure with a single key ``find``', 'which corresponds to a dynamic call to', '``setuptools.config.expand.find_packages`` function.', 'The ``find`` key is associated with a nested ``dict``-like structure that can', 'contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,', 'mimicking the keyword arguments of the associated function.'], 'oneOf': [{'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}}, {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}]}, rule='oneOf')
+        if "package-dir" in data_keys:
+            data_keys.remove("package-dir")
+            data__packagedir = data["package-dir"]
+            if not isinstance(data__packagedir, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-dir must be object", value=data__packagedir, name="" + (name_prefix or "data") + ".package-dir", definition={'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, rule='type')
+            data__packagedir_is_dict = isinstance(data__packagedir, dict)
+            if data__packagedir_is_dict:
+                data__packagedir_keys = set(data__packagedir.keys())
+                for data__packagedir_key, data__packagedir_val in data__packagedir.items():
+                    if REGEX_PATTERNS['^.*$'].search(data__packagedir_key):
+                        if data__packagedir_key in data__packagedir_keys:
+                            data__packagedir_keys.remove(data__packagedir_key)
+                        if not isinstance(data__packagedir_val, (str)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-dir.{data__packagedir_key}".format(**locals()) + " must be string", value=data__packagedir_val, name="" + (name_prefix or "data") + ".package-dir.{data__packagedir_key}".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if data__packagedir_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-dir must not contain "+str(data__packagedir_keys)+" properties", value=data__packagedir, name="" + (name_prefix or "data") + ".package-dir", definition={'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, rule='additionalProperties')
+                data__packagedir_len = len(data__packagedir)
+                if data__packagedir_len != 0:
+                    data__packagedir_property_names = True
+                    for data__packagedir_key in data__packagedir:
+                        try:
+                            data__packagedir_key_any_of_count3 = 0
+                            if not data__packagedir_key_any_of_count3:
+                                try:
+                                    if data__packagedir_key != "":
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-dir must be same as const definition: ", value=data__packagedir_key, name="" + (name_prefix or "data") + ".package-dir", definition={'const': ''}, rule='const')
+                                    data__packagedir_key_any_of_count3 += 1
+                                except JsonSchemaValueException: pass
+                            if not data__packagedir_key_any_of_count3:
+                                try:
+                                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_package_name(data__packagedir_key, custom_formats, (name_prefix or "data") + ".package-dir")
+                                    data__packagedir_key_any_of_count3 += 1
+                                except JsonSchemaValueException: pass
+                            if not data__packagedir_key_any_of_count3:
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-dir cannot be validated by any definition", value=data__packagedir_key, name="" + (name_prefix or "data") + ".package-dir", definition={'anyOf': [{'const': ''}, {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}]}, rule='anyOf')
+                        except JsonSchemaValueException:
+                            data__packagedir_property_names = False
+                    if not data__packagedir_property_names:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-dir must be named by propertyName definition", value=data__packagedir, name="" + (name_prefix or "data") + ".package-dir", definition={'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, rule='propertyNames')
+        if "package-data" in data_keys:
+            data_keys.remove("package-data")
+            data__packagedata = data["package-data"]
+            if not isinstance(data__packagedata, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data must be object", value=data__packagedata, name="" + (name_prefix or "data") + ".package-data", definition={'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='type')
+            data__packagedata_is_dict = isinstance(data__packagedata, dict)
+            if data__packagedata_is_dict:
+                data__packagedata_keys = set(data__packagedata.keys())
+                for data__packagedata_key, data__packagedata_val in data__packagedata.items():
+                    if REGEX_PATTERNS['^.*$'].search(data__packagedata_key):
+                        if data__packagedata_key in data__packagedata_keys:
+                            data__packagedata_keys.remove(data__packagedata_key)
+                        if not isinstance(data__packagedata_val, (list, tuple)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data.{data__packagedata_key}".format(**locals()) + " must be array", value=data__packagedata_val, name="" + (name_prefix or "data") + ".package-data.{data__packagedata_key}".format(**locals()) + "", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+                        data__packagedata_val_is_list = isinstance(data__packagedata_val, (list, tuple))
+                        if data__packagedata_val_is_list:
+                            data__packagedata_val_len = len(data__packagedata_val)
+                            for data__packagedata_val_x, data__packagedata_val_item in enumerate(data__packagedata_val):
+                                if not isinstance(data__packagedata_val_item, (str)):
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data.{data__packagedata_key}[{data__packagedata_val_x}]".format(**locals()) + " must be string", value=data__packagedata_val_item, name="" + (name_prefix or "data") + ".package-data.{data__packagedata_key}[{data__packagedata_val_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if data__packagedata_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data must not contain "+str(data__packagedata_keys)+" properties", value=data__packagedata, name="" + (name_prefix or "data") + ".package-data", definition={'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='additionalProperties')
+                data__packagedata_len = len(data__packagedata)
+                if data__packagedata_len != 0:
+                    data__packagedata_property_names = True
+                    for data__packagedata_key in data__packagedata:
+                        try:
+                            data__packagedata_key_any_of_count4 = 0
+                            if not data__packagedata_key_any_of_count4:
+                                try:
+                                    if not isinstance(data__packagedata_key, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data must be string", value=data__packagedata_key, name="" + (name_prefix or "data") + ".package-data", definition={'type': 'string', 'format': 'python-module-name'}, rule='type')
+                                    if isinstance(data__packagedata_key, str):
+                                        if not custom_formats["python-module-name"](data__packagedata_key):
+                                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data must be python-module-name", value=data__packagedata_key, name="" + (name_prefix or "data") + ".package-data", definition={'type': 'string', 'format': 'python-module-name'}, rule='format')
+                                    data__packagedata_key_any_of_count4 += 1
+                                except JsonSchemaValueException: pass
+                            if not data__packagedata_key_any_of_count4:
+                                try:
+                                    if data__packagedata_key != "*":
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data must be same as const definition: *", value=data__packagedata_key, name="" + (name_prefix or "data") + ".package-data", definition={'const': '*'}, rule='const')
+                                    data__packagedata_key_any_of_count4 += 1
+                                except JsonSchemaValueException: pass
+                            if not data__packagedata_key_any_of_count4:
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data cannot be validated by any definition", value=data__packagedata_key, name="" + (name_prefix or "data") + ".package-data", definition={'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, rule='anyOf')
+                        except JsonSchemaValueException:
+                            data__packagedata_property_names = False
+                    if not data__packagedata_property_names:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".package-data must be named by propertyName definition", value=data__packagedata, name="" + (name_prefix or "data") + ".package-data", definition={'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='propertyNames')
+        if "include-package-data" in data_keys:
+            data_keys.remove("include-package-data")
+            data__includepackagedata = data["include-package-data"]
+            if not isinstance(data__includepackagedata, (bool)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".include-package-data must be boolean", value=data__includepackagedata, name="" + (name_prefix or "data") + ".include-package-data", definition={'$$description': ['Automatically include any data files inside the package directories', 'that are specified by ``MANIFEST.in``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'boolean'}, rule='type')
+        if "exclude-package-data" in data_keys:
+            data_keys.remove("exclude-package-data")
+            data__excludepackagedata = data["exclude-package-data"]
+            if not isinstance(data__excludepackagedata, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data must be object", value=data__excludepackagedata, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='type')
+            data__excludepackagedata_is_dict = isinstance(data__excludepackagedata, dict)
+            if data__excludepackagedata_is_dict:
+                data__excludepackagedata_keys = set(data__excludepackagedata.keys())
+                for data__excludepackagedata_key, data__excludepackagedata_val in data__excludepackagedata.items():
+                    if REGEX_PATTERNS['^.*$'].search(data__excludepackagedata_key):
+                        if data__excludepackagedata_key in data__excludepackagedata_keys:
+                            data__excludepackagedata_keys.remove(data__excludepackagedata_key)
+                        if not isinstance(data__excludepackagedata_val, (list, tuple)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data.{data__excludepackagedata_key}".format(**locals()) + " must be array", value=data__excludepackagedata_val, name="" + (name_prefix or "data") + ".exclude-package-data.{data__excludepackagedata_key}".format(**locals()) + "", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+                        data__excludepackagedata_val_is_list = isinstance(data__excludepackagedata_val, (list, tuple))
+                        if data__excludepackagedata_val_is_list:
+                            data__excludepackagedata_val_len = len(data__excludepackagedata_val)
+                            for data__excludepackagedata_val_x, data__excludepackagedata_val_item in enumerate(data__excludepackagedata_val):
+                                if not isinstance(data__excludepackagedata_val_item, (str)):
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data.{data__excludepackagedata_key}[{data__excludepackagedata_val_x}]".format(**locals()) + " must be string", value=data__excludepackagedata_val_item, name="" + (name_prefix or "data") + ".exclude-package-data.{data__excludepackagedata_key}[{data__excludepackagedata_val_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if data__excludepackagedata_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data must not contain "+str(data__excludepackagedata_keys)+" properties", value=data__excludepackagedata, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='additionalProperties')
+                data__excludepackagedata_len = len(data__excludepackagedata)
+                if data__excludepackagedata_len != 0:
+                    data__excludepackagedata_property_names = True
+                    for data__excludepackagedata_key in data__excludepackagedata:
+                        try:
+                            data__excludepackagedata_key_any_of_count5 = 0
+                            if not data__excludepackagedata_key_any_of_count5:
+                                try:
+                                    if not isinstance(data__excludepackagedata_key, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data must be string", value=data__excludepackagedata_key, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'type': 'string', 'format': 'python-module-name'}, rule='type')
+                                    if isinstance(data__excludepackagedata_key, str):
+                                        if not custom_formats["python-module-name"](data__excludepackagedata_key):
+                                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data must be python-module-name", value=data__excludepackagedata_key, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'type': 'string', 'format': 'python-module-name'}, rule='format')
+                                    data__excludepackagedata_key_any_of_count5 += 1
+                                except JsonSchemaValueException: pass
+                            if not data__excludepackagedata_key_any_of_count5:
+                                try:
+                                    if data__excludepackagedata_key != "*":
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data must be same as const definition: *", value=data__excludepackagedata_key, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'const': '*'}, rule='const')
+                                    data__excludepackagedata_key_any_of_count5 += 1
+                                except JsonSchemaValueException: pass
+                            if not data__excludepackagedata_key_any_of_count5:
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data cannot be validated by any definition", value=data__excludepackagedata_key, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, rule='anyOf')
+                        except JsonSchemaValueException:
+                            data__excludepackagedata_property_names = False
+                    if not data__excludepackagedata_property_names:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".exclude-package-data must be named by propertyName definition", value=data__excludepackagedata, name="" + (name_prefix or "data") + ".exclude-package-data", definition={'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='propertyNames')
+        if "namespace-packages" in data_keys:
+            data_keys.remove("namespace-packages")
+            data__namespacepackages = data["namespace-packages"]
+            if not isinstance(data__namespacepackages, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".namespace-packages must be array", value=data__namespacepackages, name="" + (name_prefix or "data") + ".namespace-packages", definition={'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'https://setuptools.pypa.io/en/latest/userguide/package_discovery.html', 'description': '**DEPRECATED**: use implicit namespaces instead (:pep:`420`).'}, rule='type')
+            data__namespacepackages_is_list = isinstance(data__namespacepackages, (list, tuple))
+            if data__namespacepackages_is_list:
+                data__namespacepackages_len = len(data__namespacepackages)
+                for data__namespacepackages_x, data__namespacepackages_item in enumerate(data__namespacepackages):
+                    if not isinstance(data__namespacepackages_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".namespace-packages[{data__namespacepackages_x}]".format(**locals()) + " must be string", value=data__namespacepackages_item, name="" + (name_prefix or "data") + ".namespace-packages[{data__namespacepackages_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='type')
+                    if isinstance(data__namespacepackages_item, str):
+                        if not custom_formats["python-module-name-relaxed"](data__namespacepackages_item):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".namespace-packages[{data__namespacepackages_x}]".format(**locals()) + " must be python-module-name-relaxed", value=data__namespacepackages_item, name="" + (name_prefix or "data") + ".namespace-packages[{data__namespacepackages_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='format')
+        if "py-modules" in data_keys:
+            data_keys.remove("py-modules")
+            data__pymodules = data["py-modules"]
+            if not isinstance(data__pymodules, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".py-modules must be array", value=data__pymodules, name="" + (name_prefix or "data") + ".py-modules", definition={'description': 'Modules that setuptools will manipulate', 'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'TODO: clarify the relationship with ``packages``'}, rule='type')
+            data__pymodules_is_list = isinstance(data__pymodules, (list, tuple))
+            if data__pymodules_is_list:
+                data__pymodules_len = len(data__pymodules)
+                for data__pymodules_x, data__pymodules_item in enumerate(data__pymodules):
+                    if not isinstance(data__pymodules_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".py-modules[{data__pymodules_x}]".format(**locals()) + " must be string", value=data__pymodules_item, name="" + (name_prefix or "data") + ".py-modules[{data__pymodules_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='type')
+                    if isinstance(data__pymodules_item, str):
+                        if not custom_formats["python-module-name-relaxed"](data__pymodules_item):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".py-modules[{data__pymodules_x}]".format(**locals()) + " must be python-module-name-relaxed", value=data__pymodules_item, name="" + (name_prefix or "data") + ".py-modules[{data__pymodules_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='format')
+        if "ext-modules" in data_keys:
+            data_keys.remove("ext-modules")
+            data__extmodules = data["ext-modules"]
+            if not isinstance(data__extmodules, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".ext-modules must be array", value=data__extmodules, name="" + (name_prefix or "data") + ".ext-modules", definition={'description': 'Extension modules to be compiled by setuptools', 'type': 'array', 'items': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}}, rule='type')
+            data__extmodules_is_list = isinstance(data__extmodules, (list, tuple))
+            if data__extmodules_is_list:
+                data__extmodules_len = len(data__extmodules)
+                for data__extmodules_x, data__extmodules_item in enumerate(data__extmodules):
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_ext_module(data__extmodules_item, custom_formats, (name_prefix or "data") + ".ext-modules[{data__extmodules_x}]".format(**locals()))
+        if "data-files" in data_keys:
+            data_keys.remove("data-files")
+            data__datafiles = data["data-files"]
+            if not isinstance(data__datafiles, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".data-files must be object", value=data__datafiles, name="" + (name_prefix or "data") + ".data-files", definition={'$$description': ['``dict``-like structure where each key represents a directory and', 'the value is a list of glob patterns that should be installed in them.', '**DISCOURAGED**: please notice this might not work as expected with wheels.', 'Whenever possible, consider using data files inside the package directories', '(or create a new namespace package that only contains data files).', 'See `data files support', '`_.'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, rule='type')
+            data__datafiles_is_dict = isinstance(data__datafiles, dict)
+            if data__datafiles_is_dict:
+                data__datafiles_keys = set(data__datafiles.keys())
+                for data__datafiles_key, data__datafiles_val in data__datafiles.items():
+                    if REGEX_PATTERNS['^.*$'].search(data__datafiles_key):
+                        if data__datafiles_key in data__datafiles_keys:
+                            data__datafiles_keys.remove(data__datafiles_key)
+                        if not isinstance(data__datafiles_val, (list, tuple)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".data-files.{data__datafiles_key}".format(**locals()) + " must be array", value=data__datafiles_val, name="" + (name_prefix or "data") + ".data-files.{data__datafiles_key}".format(**locals()) + "", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+                        data__datafiles_val_is_list = isinstance(data__datafiles_val, (list, tuple))
+                        if data__datafiles_val_is_list:
+                            data__datafiles_val_len = len(data__datafiles_val)
+                            for data__datafiles_val_x, data__datafiles_val_item in enumerate(data__datafiles_val):
+                                if not isinstance(data__datafiles_val_item, (str)):
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".data-files.{data__datafiles_key}[{data__datafiles_val_x}]".format(**locals()) + " must be string", value=data__datafiles_val_item, name="" + (name_prefix or "data") + ".data-files.{data__datafiles_key}[{data__datafiles_val_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "cmdclass" in data_keys:
+            data_keys.remove("cmdclass")
+            data__cmdclass = data["cmdclass"]
+            if not isinstance(data__cmdclass, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".cmdclass must be object", value=data__cmdclass, name="" + (name_prefix or "data") + ".cmdclass", definition={'$$description': ['Mapping of distutils-style command names to ``setuptools.Command`` subclasses', 'which in turn should be represented by strings with a qualified class name', '(i.e., "dotted" form with module), e.g.::\n\n', '    cmdclass = {mycmd = "pkg.subpkg.module.CommandClass"}\n\n', 'The command class should be a directly defined at the top-level of the', 'containing module (no class nesting).'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'string', 'format': 'python-qualified-identifier'}}}, rule='type')
+            data__cmdclass_is_dict = isinstance(data__cmdclass, dict)
+            if data__cmdclass_is_dict:
+                data__cmdclass_keys = set(data__cmdclass.keys())
+                for data__cmdclass_key, data__cmdclass_val in data__cmdclass.items():
+                    if REGEX_PATTERNS['^.*$'].search(data__cmdclass_key):
+                        if data__cmdclass_key in data__cmdclass_keys:
+                            data__cmdclass_keys.remove(data__cmdclass_key)
+                        if not isinstance(data__cmdclass_val, (str)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".cmdclass.{data__cmdclass_key}".format(**locals()) + " must be string", value=data__cmdclass_val, name="" + (name_prefix or "data") + ".cmdclass.{data__cmdclass_key}".format(**locals()) + "", definition={'type': 'string', 'format': 'python-qualified-identifier'}, rule='type')
+                        if isinstance(data__cmdclass_val, str):
+                            if not custom_formats["python-qualified-identifier"](data__cmdclass_val):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".cmdclass.{data__cmdclass_key}".format(**locals()) + " must be python-qualified-identifier", value=data__cmdclass_val, name="" + (name_prefix or "data") + ".cmdclass.{data__cmdclass_key}".format(**locals()) + "", definition={'type': 'string', 'format': 'python-qualified-identifier'}, rule='format')
+        if "license-files" in data_keys:
+            data_keys.remove("license-files")
+            data__licensefiles = data["license-files"]
+            if not isinstance(data__licensefiles, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".license-files must be array", value=data__licensefiles, name="" + (name_prefix or "data") + ".license-files", definition={'type': 'array', 'items': {'type': 'string'}, '$$description': ['**PROVISIONAL**: list of glob patterns for all license files being distributed.', '(likely to become standard with :pep:`639`).', "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"], '$comment': 'TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?'}, rule='type')
+            data__licensefiles_is_list = isinstance(data__licensefiles, (list, tuple))
+            if data__licensefiles_is_list:
+                data__licensefiles_len = len(data__licensefiles)
+                for data__licensefiles_x, data__licensefiles_item in enumerate(data__licensefiles):
+                    if not isinstance(data__licensefiles_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".license-files[{data__licensefiles_x}]".format(**locals()) + " must be string", value=data__licensefiles_item, name="" + (name_prefix or "data") + ".license-files[{data__licensefiles_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "dynamic" in data_keys:
+            data_keys.remove("dynamic")
+            data__dynamic = data["dynamic"]
+            if not isinstance(data__dynamic, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic must be object", value=data__dynamic, name="" + (name_prefix or "data") + ".dynamic", definition={'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, 'classifiers': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'description': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'entry-points': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, 'readme': {'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}}}, rule='type')
+            data__dynamic_is_dict = isinstance(data__dynamic, dict)
+            if data__dynamic_is_dict:
+                data__dynamic_keys = set(data__dynamic.keys())
+                if "version" in data__dynamic_keys:
+                    data__dynamic_keys.remove("version")
+                    data__dynamic__version = data__dynamic["version"]
+                    data__dynamic__version_one_of_count6 = 0
+                    if data__dynamic__version_one_of_count6 < 2:
+                        try:
+                            validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_attr_directive(data__dynamic__version, custom_formats, (name_prefix or "data") + ".dynamic.version")
+                            data__dynamic__version_one_of_count6 += 1
+                        except JsonSchemaValueException: pass
+                    if data__dynamic__version_one_of_count6 < 2:
+                        try:
+                            validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data__dynamic__version, custom_formats, (name_prefix or "data") + ".dynamic.version")
+                            data__dynamic__version_one_of_count6 += 1
+                        except JsonSchemaValueException: pass
+                    if data__dynamic__version_one_of_count6 != 1:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.version must be valid exactly by one definition" + (" (" + str(data__dynamic__version_one_of_count6) + " matches found)"), value=data__dynamic__version, name="" + (name_prefix or "data") + ".dynamic.version", definition={'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, rule='oneOf')
+                if "classifiers" in data__dynamic_keys:
+                    data__dynamic_keys.remove("classifiers")
+                    data__dynamic__classifiers = data__dynamic["classifiers"]
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data__dynamic__classifiers, custom_formats, (name_prefix or "data") + ".dynamic.classifiers")
+                if "description" in data__dynamic_keys:
+                    data__dynamic_keys.remove("description")
+                    data__dynamic__description = data__dynamic["description"]
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data__dynamic__description, custom_formats, (name_prefix or "data") + ".dynamic.description")
+                if "entry-points" in data__dynamic_keys:
+                    data__dynamic_keys.remove("entry-points")
+                    data__dynamic__entrypoints = data__dynamic["entry-points"]
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data__dynamic__entrypoints, custom_formats, (name_prefix or "data") + ".dynamic.entry-points")
+                if "dependencies" in data__dynamic_keys:
+                    data__dynamic_keys.remove("dependencies")
+                    data__dynamic__dependencies = data__dynamic["dependencies"]
+                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive_for_dependencies(data__dynamic__dependencies, custom_formats, (name_prefix or "data") + ".dynamic.dependencies")
+                if "optional-dependencies" in data__dynamic_keys:
+                    data__dynamic_keys.remove("optional-dependencies")
+                    data__dynamic__optionaldependencies = data__dynamic["optional-dependencies"]
+                    if not isinstance(data__dynamic__optionaldependencies, (dict)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.optional-dependencies must be object", value=data__dynamic__optionaldependencies, name="" + (name_prefix or "data") + ".dynamic.optional-dependencies", definition={'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, rule='type')
+                    data__dynamic__optionaldependencies_is_dict = isinstance(data__dynamic__optionaldependencies, dict)
+                    if data__dynamic__optionaldependencies_is_dict:
+                        data__dynamic__optionaldependencies_keys = set(data__dynamic__optionaldependencies.keys())
+                        for data__dynamic__optionaldependencies_key, data__dynamic__optionaldependencies_val in data__dynamic__optionaldependencies.items():
+                            if REGEX_PATTERNS['.+'].search(data__dynamic__optionaldependencies_key):
+                                if data__dynamic__optionaldependencies_key in data__dynamic__optionaldependencies_keys:
+                                    data__dynamic__optionaldependencies_keys.remove(data__dynamic__optionaldependencies_key)
+                                validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive_for_dependencies(data__dynamic__optionaldependencies_val, custom_formats, (name_prefix or "data") + ".dynamic.optional-dependencies.{data__dynamic__optionaldependencies_key}".format(**locals()))
+                        if data__dynamic__optionaldependencies_keys:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.optional-dependencies must not contain "+str(data__dynamic__optionaldependencies_keys)+" properties", value=data__dynamic__optionaldependencies, name="" + (name_prefix or "data") + ".dynamic.optional-dependencies", definition={'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, rule='additionalProperties')
+                        data__dynamic__optionaldependencies_len = len(data__dynamic__optionaldependencies)
+                        if data__dynamic__optionaldependencies_len != 0:
+                            data__dynamic__optionaldependencies_property_names = True
+                            for data__dynamic__optionaldependencies_key in data__dynamic__optionaldependencies:
+                                try:
+                                    if not isinstance(data__dynamic__optionaldependencies_key, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.optional-dependencies must be string", value=data__dynamic__optionaldependencies_key, name="" + (name_prefix or "data") + ".dynamic.optional-dependencies", definition={'type': 'string', 'format': 'pep508-identifier'}, rule='type')
+                                    if isinstance(data__dynamic__optionaldependencies_key, str):
+                                        if not custom_formats["pep508-identifier"](data__dynamic__optionaldependencies_key):
+                                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.optional-dependencies must be pep508-identifier", value=data__dynamic__optionaldependencies_key, name="" + (name_prefix or "data") + ".dynamic.optional-dependencies", definition={'type': 'string', 'format': 'pep508-identifier'}, rule='format')
+                                except JsonSchemaValueException:
+                                    data__dynamic__optionaldependencies_property_names = False
+                            if not data__dynamic__optionaldependencies_property_names:
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.optional-dependencies must be named by propertyName definition", value=data__dynamic__optionaldependencies, name="" + (name_prefix or "data") + ".dynamic.optional-dependencies", definition={'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, rule='propertyNames')
+                if "readme" in data__dynamic_keys:
+                    data__dynamic_keys.remove("readme")
+                    data__dynamic__readme = data__dynamic["readme"]
+                    if not isinstance(data__dynamic__readme, (dict)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.readme must be object", value=data__dynamic__readme, name="" + (name_prefix or "data") + ".dynamic.readme", definition={'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}, rule='type')
+                    data__dynamic__readme_any_of_count7 = 0
+                    if not data__dynamic__readme_any_of_count7:
+                        try:
+                            validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data__dynamic__readme, custom_formats, (name_prefix or "data") + ".dynamic.readme")
+                            data__dynamic__readme_any_of_count7 += 1
+                        except JsonSchemaValueException: pass
+                    if not data__dynamic__readme_any_of_count7:
+                        try:
+                            if not isinstance(data__dynamic__readme, (dict)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.readme must be object", value=data__dynamic__readme, name="" + (name_prefix or "data") + ".dynamic.readme", definition={'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}, rule='type')
+                            data__dynamic__readme_is_dict = isinstance(data__dynamic__readme, dict)
+                            if data__dynamic__readme_is_dict:
+                                data__dynamic__readme_keys = set(data__dynamic__readme.keys())
+                                if "content-type" in data__dynamic__readme_keys:
+                                    data__dynamic__readme_keys.remove("content-type")
+                                    data__dynamic__readme__contenttype = data__dynamic__readme["content-type"]
+                                    if not isinstance(data__dynamic__readme__contenttype, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.readme.content-type must be string", value=data__dynamic__readme__contenttype, name="" + (name_prefix or "data") + ".dynamic.readme.content-type", definition={'type': 'string'}, rule='type')
+                                if "file" in data__dynamic__readme_keys:
+                                    data__dynamic__readme_keys.remove("file")
+                                    data__dynamic__readme__file = data__dynamic__readme["file"]
+                                    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive_properties_file(data__dynamic__readme__file, custom_formats, (name_prefix or "data") + ".dynamic.readme.file")
+                                if data__dynamic__readme_keys:
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.readme must not contain "+str(data__dynamic__readme_keys)+" properties", value=data__dynamic__readme, name="" + (name_prefix or "data") + ".dynamic.readme", definition={'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}, rule='additionalProperties')
+                            data__dynamic__readme_any_of_count7 += 1
+                        except JsonSchemaValueException: pass
+                    if not data__dynamic__readme_any_of_count7:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.readme cannot be validated by any definition", value=data__dynamic__readme, name="" + (name_prefix or "data") + ".dynamic.readme", definition={'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}, rule='anyOf')
+                    data__dynamic__readme_is_dict = isinstance(data__dynamic__readme, dict)
+                    if data__dynamic__readme_is_dict:
+                        data__dynamic__readme__missing_keys = set(['file']) - data__dynamic__readme.keys()
+                        if data__dynamic__readme__missing_keys:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic.readme must contain " + (str(sorted(data__dynamic__readme__missing_keys)) + " properties"), value=data__dynamic__readme, name="" + (name_prefix or "data") + ".dynamic.readme", definition={'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}, rule='required')
+                if data__dynamic_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic must not contain "+str(data__dynamic_keys)+" properties", value=data__dynamic, name="" + (name_prefix or "data") + ".dynamic", definition={'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, 'classifiers': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'description': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'entry-points': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, 'readme': {'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}}}, rule='additionalProperties')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/userguide/pyproject_config.html', 'title': '``tool.setuptools`` table', '$$description': ['``setuptools``-specific configurations that can be set by users that require', 'customization.', 'These configurations are completely optional and probably can be skipped when', 'creating simple packages. They are equivalent to some of the `Keywords', '`_', 'used by the ``setup.py`` file, and can be set via the ``tool.setuptools`` table.', 'It considers only ``setuptools`` `parameters', '`_', 'that are not covered by :pep:`621`; and intentionally excludes ``dependency_links``', 'and ``setup_requires`` (incompatible with modern workflows/standards).'], 'type': 'object', 'additionalProperties': False, 'properties': {'platforms': {'type': 'array', 'items': {'type': 'string'}}, 'provides': {'$$description': ['Package and virtual package names contained within this package', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'obsoletes': {'$$description': ['Packages which this package renders obsolete', '**(not supported by pip)**'], 'type': 'array', 'items': {'type': 'string', 'format': 'pep508-identifier'}}, 'zip-safe': {'$$description': ['Whether the project can be safely installed and run from a zip file.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'boolean'}, 'script-files': {'$$description': ['Legacy way of defining scripts (entry-points are preferred).', 'Equivalent to the ``script`` keyword in ``setup.py``', '(it was renamed to avoid confusion with entry-point based ``project.scripts``', 'defined in :pep:`621`).', '**DISCOURAGED**: generic script wrappers are tricky and may not work properly.', 'Whenever possible, please use ``project.scripts`` instead.'], 'type': 'array', 'items': {'type': 'string'}, '$comment': 'TODO: is this field deprecated/should be removed?'}, 'eager-resources': {'$$description': ['Resources that should be extracted together, if any of them is needed,', 'or if any C extensions included in the project are imported.', '**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and', '``setup.py install`` in the context of ``eggs`` (**DEPRECATED**).'], 'type': 'array', 'items': {'type': 'string'}}, 'packages': {'$$description': ['Packages that should be included in the distribution.', 'It can be given either as a list of package identifiers', 'or as a ``dict``-like structure with a single key ``find``', 'which corresponds to a dynamic call to', '``setuptools.config.expand.find_packages`` function.', 'The ``find`` key is associated with a nested ``dict``-like structure that can', 'contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,', 'mimicking the keyword arguments of the associated function.'], 'oneOf': [{'title': 'Array of Python package identifiers', 'type': 'array', 'items': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}}, {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}]}, 'package-dir': {'$$description': [':class:`dict`-like structure mapping from package names to directories where their', 'code can be found.', 'The empty string (as key) means that all packages are contained inside', 'the given directory will be included in the distribution.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'const': ''}, {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}]}, 'patternProperties': {'^.*$': {'type': 'string'}}}, 'package-data': {'$$description': ['Mapping from package names to lists of glob patterns.', 'Usually this option is not needed when using ``include-package-data = true``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'include-package-data': {'$$description': ['Automatically include any data files inside the package directories', 'that are specified by ``MANIFEST.in``', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'boolean'}, 'exclude-package-data': {'$$description': ['Mapping from package names to lists of glob patterns that should be excluded', 'For more information on how to include data files, check ``setuptools`` `docs', '`_.'], 'type': 'object', 'additionalProperties': False, 'propertyNames': {'anyOf': [{'type': 'string', 'format': 'python-module-name'}, {'const': '*'}]}, 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'namespace-packages': {'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'https://setuptools.pypa.io/en/latest/userguide/package_discovery.html', 'description': '**DEPRECATED**: use implicit namespaces instead (:pep:`420`).'}, 'py-modules': {'description': 'Modules that setuptools will manipulate', 'type': 'array', 'items': {'type': 'string', 'format': 'python-module-name-relaxed'}, '$comment': 'TODO: clarify the relationship with ``packages``'}, 'ext-modules': {'description': 'Extension modules to be compiled by setuptools', 'type': 'array', 'items': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}}, 'data-files': {'$$description': ['``dict``-like structure where each key represents a directory and', 'the value is a list of glob patterns that should be installed in them.', '**DISCOURAGED**: please notice this might not work as expected with wheels.', 'Whenever possible, consider using data files inside the package directories', '(or create a new namespace package that only contains data files).', 'See `data files support', '`_.'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'array', 'items': {'type': 'string'}}}}, 'cmdclass': {'$$description': ['Mapping of distutils-style command names to ``setuptools.Command`` subclasses', 'which in turn should be represented by strings with a qualified class name', '(i.e., "dotted" form with module), e.g.::\n\n', '    cmdclass = {mycmd = "pkg.subpkg.module.CommandClass"}\n\n', 'The command class should be a directly defined at the top-level of the', 'containing module (no class nesting).'], 'type': 'object', 'patternProperties': {'^.*$': {'type': 'string', 'format': 'python-qualified-identifier'}}}, 'license-files': {'type': 'array', 'items': {'type': 'string'}, '$$description': ['**PROVISIONAL**: list of glob patterns for all license files being distributed.', '(likely to become standard with :pep:`639`).', "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"], '$comment': 'TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?'}, 'dynamic': {'type': 'object', 'description': 'Instructions for loading :pep:`621`-related metadata dynamically', 'additionalProperties': False, 'properties': {'version': {'$$description': ['A version dynamically loaded via either the ``attr:`` or ``file:``', 'directives. Please make sure the given file or attribute respects :pep:`440`.', 'Also ensure to set ``project.dynamic`` accordingly.'], 'oneOf': [{'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, 'classifiers': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'description': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'entry-points': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}, 'optional-dependencies': {'type': 'object', 'propertyNames': {'type': 'string', 'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'.+': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$ref': '#/definitions/file-directive'}]}}}, 'readme': {'type': 'object', 'anyOf': [{'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, {'type': 'object', 'properties': {'content-type': {'type': 'string'}, 'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'additionalProperties': False}], 'required': ['file']}}}}, 'definitions': {'package-name': {'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, 'ext-module': {'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, 'file-directive': {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, 'file-directive-for-dependencies': {'title': "'file:' directive for dependencies", 'allOf': [{'$$description': ['**BETA**: subset of the ``requirements.txt`` format', 'without ``pip`` flags and options', '(one :pep:`508`-compliant string per line,', 'lines that are blank or start with ``#`` are excluded).', 'See `dynamic metadata', '`_.']}, {'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}]}, 'attr-directive': {'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, 'find-directive': {'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}}}, rule='additionalProperties')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive_properties_file(data, custom_formats={}, name_prefix=None):
+    data_one_of_count8 = 0
+    if data_one_of_count8 < 2:
+        try:
+            if not isinstance(data, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must be string", value=data, name="" + (name_prefix or "data") + "", definition={'type': 'string'}, rule='type')
+            data_one_of_count8 += 1
+        except JsonSchemaValueException: pass
+    if data_one_of_count8 < 2:
+        try:
+            if not isinstance(data, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must be array", value=data, name="" + (name_prefix or "data") + "", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data_is_list = isinstance(data, (list, tuple))
+            if data_is_list:
+                data_len = len(data)
+                for data_x, data_item in enumerate(data):
+                    if not isinstance(data_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + "[{data_x}]".format(**locals()) + " must be string", value=data_item, name="" + (name_prefix or "data") + "[{data_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+            data_one_of_count8 += 1
+        except JsonSchemaValueException: pass
+    if data_one_of_count8 != 1:
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be valid exactly by one definition" + (" (" + str(data_one_of_count8) + " matches found)"), value=data, name="" + (name_prefix or "data") + "", definition={'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}, rule='oneOf')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive_for_dependencies(data, custom_formats={}, name_prefix=None):
+    validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data, custom_formats, (name_prefix or "data") + "")
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_file_directive(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data__missing_keys = set(['file']) - data.keys()
+        if data__missing_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, rule='required')
+        data_keys = set(data.keys())
+        if "file" in data_keys:
+            data_keys.remove("file")
+            data__file = data["file"]
+            data__file_one_of_count9 = 0
+            if data__file_one_of_count9 < 2:
+                try:
+                    if not isinstance(data__file, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".file must be string", value=data__file, name="" + (name_prefix or "data") + ".file", definition={'type': 'string'}, rule='type')
+                    data__file_one_of_count9 += 1
+                except JsonSchemaValueException: pass
+            if data__file_one_of_count9 < 2:
+                try:
+                    if not isinstance(data__file, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".file must be array", value=data__file, name="" + (name_prefix or "data") + ".file", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+                    data__file_is_list = isinstance(data__file, (list, tuple))
+                    if data__file_is_list:
+                        data__file_len = len(data__file)
+                        for data__file_x, data__file_item in enumerate(data__file):
+                            if not isinstance(data__file_item, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".file[{data__file_x}]".format(**locals()) + " must be string", value=data__file_item, name="" + (name_prefix or "data") + ".file[{data__file_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                    data__file_one_of_count9 += 1
+                except JsonSchemaValueException: pass
+            if data__file_one_of_count9 != 1:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".file must be valid exactly by one definition" + (" (" + str(data__file_one_of_count9) + " matches found)"), value=data__file, name="" + (name_prefix or "data") + ".file", definition={'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}, rule='oneOf')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/file-directive', 'title': "'file:' directive", 'description': 'Value is read from a file (or list of files and then concatenated)', 'type': 'object', 'additionalProperties': False, 'properties': {'file': {'oneOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]}}, 'required': ['file']}, rule='additionalProperties')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_attr_directive(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data__missing_keys = set(['attr']) - data.keys()
+        if data__missing_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, rule='required')
+        data_keys = set(data.keys())
+        if "attr" in data_keys:
+            data_keys.remove("attr")
+            data__attr = data["attr"]
+            if not isinstance(data__attr, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".attr must be string", value=data__attr, name="" + (name_prefix or "data") + ".attr", definition={'type': 'string', 'format': 'python-qualified-identifier'}, rule='type')
+            if isinstance(data__attr, str):
+                if not custom_formats["python-qualified-identifier"](data__attr):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".attr must be python-qualified-identifier", value=data__attr, name="" + (name_prefix or "data") + ".attr", definition={'type': 'string', 'format': 'python-qualified-identifier'}, rule='format')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'title': "'attr:' directive", '$id': '#/definitions/attr-directive', '$$description': ['Value is read from a module attribute. Supports callables and iterables;', 'unsupported types are cast via ``str()``'], 'type': 'object', 'additionalProperties': False, 'properties': {'attr': {'type': 'string', 'format': 'python-qualified-identifier'}}, 'required': ['attr']}, rule='additionalProperties')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_ext_module(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data__missing_keys = set(['name', 'sources']) - data.keys()
+        if data__missing_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, rule='required')
+        data_keys = set(data.keys())
+        if "name" in data_keys:
+            data_keys.remove("name")
+            data__name = data["name"]
+            if not isinstance(data__name, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".name must be string", value=data__name, name="" + (name_prefix or "data") + ".name", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='type')
+            if isinstance(data__name, str):
+                if not custom_formats["python-module-name-relaxed"](data__name):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".name must be python-module-name-relaxed", value=data__name, name="" + (name_prefix or "data") + ".name", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='format')
+        if "sources" in data_keys:
+            data_keys.remove("sources")
+            data__sources = data["sources"]
+            if not isinstance(data__sources, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".sources must be array", value=data__sources, name="" + (name_prefix or "data") + ".sources", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__sources_is_list = isinstance(data__sources, (list, tuple))
+            if data__sources_is_list:
+                data__sources_len = len(data__sources)
+                for data__sources_x, data__sources_item in enumerate(data__sources):
+                    if not isinstance(data__sources_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".sources[{data__sources_x}]".format(**locals()) + " must be string", value=data__sources_item, name="" + (name_prefix or "data") + ".sources[{data__sources_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "include-dirs" in data_keys:
+            data_keys.remove("include-dirs")
+            data__includedirs = data["include-dirs"]
+            if not isinstance(data__includedirs, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".include-dirs must be array", value=data__includedirs, name="" + (name_prefix or "data") + ".include-dirs", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__includedirs_is_list = isinstance(data__includedirs, (list, tuple))
+            if data__includedirs_is_list:
+                data__includedirs_len = len(data__includedirs)
+                for data__includedirs_x, data__includedirs_item in enumerate(data__includedirs):
+                    if not isinstance(data__includedirs_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".include-dirs[{data__includedirs_x}]".format(**locals()) + " must be string", value=data__includedirs_item, name="" + (name_prefix or "data") + ".include-dirs[{data__includedirs_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "define-macros" in data_keys:
+            data_keys.remove("define-macros")
+            data__definemacros = data["define-macros"]
+            if not isinstance(data__definemacros, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros must be array", value=data__definemacros, name="" + (name_prefix or "data") + ".define-macros", definition={'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, rule='type')
+            data__definemacros_is_list = isinstance(data__definemacros, (list, tuple))
+            if data__definemacros_is_list:
+                data__definemacros_len = len(data__definemacros)
+                for data__definemacros_x, data__definemacros_item in enumerate(data__definemacros):
+                    if not isinstance(data__definemacros_item, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}]".format(**locals()) + " must be array", value=data__definemacros_item, name="" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}]".format(**locals()) + "", definition={'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}, rule='type')
+                    data__definemacros_item_is_list = isinstance(data__definemacros_item, (list, tuple))
+                    if data__definemacros_item_is_list:
+                        data__definemacros_item_len = len(data__definemacros_item)
+                        if data__definemacros_item_len > 0:
+                            data__definemacros_item__0 = data__definemacros_item[0]
+                            if not isinstance(data__definemacros_item__0, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][0]".format(**locals()) + " must be string", value=data__definemacros_item__0, name="" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][0]".format(**locals()) + "", definition={'description': 'macro name', 'type': 'string'}, rule='type')
+                        if data__definemacros_item_len > 1:
+                            data__definemacros_item__1 = data__definemacros_item[1]
+                            data__definemacros_item__1_one_of_count10 = 0
+                            if data__definemacros_item__1_one_of_count10 < 2:
+                                try:
+                                    if not isinstance(data__definemacros_item__1, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][1]".format(**locals()) + " must be string", value=data__definemacros_item__1, name="" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][1]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                                    data__definemacros_item__1_one_of_count10 += 1
+                                except JsonSchemaValueException: pass
+                            if data__definemacros_item__1_one_of_count10 < 2:
+                                try:
+                                    if not isinstance(data__definemacros_item__1, (NoneType)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][1]".format(**locals()) + " must be null", value=data__definemacros_item__1, name="" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][1]".format(**locals()) + "", definition={'type': 'null'}, rule='type')
+                                    data__definemacros_item__1_one_of_count10 += 1
+                                except JsonSchemaValueException: pass
+                            if data__definemacros_item__1_one_of_count10 != 1:
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][1]".format(**locals()) + " must be valid exactly by one definition" + (" (" + str(data__definemacros_item__1_one_of_count10) + " matches found)"), value=data__definemacros_item__1, name="" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}][1]".format(**locals()) + "", definition={'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}, rule='oneOf')
+                        if data__definemacros_item_len > 2:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}]".format(**locals()) + " must contain only specified items", value=data__definemacros_item, name="" + (name_prefix or "data") + ".define-macros[{data__definemacros_x}]".format(**locals()) + "", definition={'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}, rule='items')
+        if "undef-macros" in data_keys:
+            data_keys.remove("undef-macros")
+            data__undefmacros = data["undef-macros"]
+            if not isinstance(data__undefmacros, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".undef-macros must be array", value=data__undefmacros, name="" + (name_prefix or "data") + ".undef-macros", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__undefmacros_is_list = isinstance(data__undefmacros, (list, tuple))
+            if data__undefmacros_is_list:
+                data__undefmacros_len = len(data__undefmacros)
+                for data__undefmacros_x, data__undefmacros_item in enumerate(data__undefmacros):
+                    if not isinstance(data__undefmacros_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".undef-macros[{data__undefmacros_x}]".format(**locals()) + " must be string", value=data__undefmacros_item, name="" + (name_prefix or "data") + ".undef-macros[{data__undefmacros_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "library-dirs" in data_keys:
+            data_keys.remove("library-dirs")
+            data__librarydirs = data["library-dirs"]
+            if not isinstance(data__librarydirs, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".library-dirs must be array", value=data__librarydirs, name="" + (name_prefix or "data") + ".library-dirs", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__librarydirs_is_list = isinstance(data__librarydirs, (list, tuple))
+            if data__librarydirs_is_list:
+                data__librarydirs_len = len(data__librarydirs)
+                for data__librarydirs_x, data__librarydirs_item in enumerate(data__librarydirs):
+                    if not isinstance(data__librarydirs_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".library-dirs[{data__librarydirs_x}]".format(**locals()) + " must be string", value=data__librarydirs_item, name="" + (name_prefix or "data") + ".library-dirs[{data__librarydirs_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "libraries" in data_keys:
+            data_keys.remove("libraries")
+            data__libraries = data["libraries"]
+            if not isinstance(data__libraries, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".libraries must be array", value=data__libraries, name="" + (name_prefix or "data") + ".libraries", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__libraries_is_list = isinstance(data__libraries, (list, tuple))
+            if data__libraries_is_list:
+                data__libraries_len = len(data__libraries)
+                for data__libraries_x, data__libraries_item in enumerate(data__libraries):
+                    if not isinstance(data__libraries_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".libraries[{data__libraries_x}]".format(**locals()) + " must be string", value=data__libraries_item, name="" + (name_prefix or "data") + ".libraries[{data__libraries_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "runtime-library-dirs" in data_keys:
+            data_keys.remove("runtime-library-dirs")
+            data__runtimelibrarydirs = data["runtime-library-dirs"]
+            if not isinstance(data__runtimelibrarydirs, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".runtime-library-dirs must be array", value=data__runtimelibrarydirs, name="" + (name_prefix or "data") + ".runtime-library-dirs", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__runtimelibrarydirs_is_list = isinstance(data__runtimelibrarydirs, (list, tuple))
+            if data__runtimelibrarydirs_is_list:
+                data__runtimelibrarydirs_len = len(data__runtimelibrarydirs)
+                for data__runtimelibrarydirs_x, data__runtimelibrarydirs_item in enumerate(data__runtimelibrarydirs):
+                    if not isinstance(data__runtimelibrarydirs_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".runtime-library-dirs[{data__runtimelibrarydirs_x}]".format(**locals()) + " must be string", value=data__runtimelibrarydirs_item, name="" + (name_prefix or "data") + ".runtime-library-dirs[{data__runtimelibrarydirs_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "extra-objects" in data_keys:
+            data_keys.remove("extra-objects")
+            data__extraobjects = data["extra-objects"]
+            if not isinstance(data__extraobjects, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".extra-objects must be array", value=data__extraobjects, name="" + (name_prefix or "data") + ".extra-objects", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__extraobjects_is_list = isinstance(data__extraobjects, (list, tuple))
+            if data__extraobjects_is_list:
+                data__extraobjects_len = len(data__extraobjects)
+                for data__extraobjects_x, data__extraobjects_item in enumerate(data__extraobjects):
+                    if not isinstance(data__extraobjects_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".extra-objects[{data__extraobjects_x}]".format(**locals()) + " must be string", value=data__extraobjects_item, name="" + (name_prefix or "data") + ".extra-objects[{data__extraobjects_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "extra-compile-args" in data_keys:
+            data_keys.remove("extra-compile-args")
+            data__extracompileargs = data["extra-compile-args"]
+            if not isinstance(data__extracompileargs, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".extra-compile-args must be array", value=data__extracompileargs, name="" + (name_prefix or "data") + ".extra-compile-args", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__extracompileargs_is_list = isinstance(data__extracompileargs, (list, tuple))
+            if data__extracompileargs_is_list:
+                data__extracompileargs_len = len(data__extracompileargs)
+                for data__extracompileargs_x, data__extracompileargs_item in enumerate(data__extracompileargs):
+                    if not isinstance(data__extracompileargs_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".extra-compile-args[{data__extracompileargs_x}]".format(**locals()) + " must be string", value=data__extracompileargs_item, name="" + (name_prefix or "data") + ".extra-compile-args[{data__extracompileargs_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "extra-link-args" in data_keys:
+            data_keys.remove("extra-link-args")
+            data__extralinkargs = data["extra-link-args"]
+            if not isinstance(data__extralinkargs, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".extra-link-args must be array", value=data__extralinkargs, name="" + (name_prefix or "data") + ".extra-link-args", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__extralinkargs_is_list = isinstance(data__extralinkargs, (list, tuple))
+            if data__extralinkargs_is_list:
+                data__extralinkargs_len = len(data__extralinkargs)
+                for data__extralinkargs_x, data__extralinkargs_item in enumerate(data__extralinkargs):
+                    if not isinstance(data__extralinkargs_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".extra-link-args[{data__extralinkargs_x}]".format(**locals()) + " must be string", value=data__extralinkargs_item, name="" + (name_prefix or "data") + ".extra-link-args[{data__extralinkargs_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "export-symbols" in data_keys:
+            data_keys.remove("export-symbols")
+            data__exportsymbols = data["export-symbols"]
+            if not isinstance(data__exportsymbols, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".export-symbols must be array", value=data__exportsymbols, name="" + (name_prefix or "data") + ".export-symbols", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__exportsymbols_is_list = isinstance(data__exportsymbols, (list, tuple))
+            if data__exportsymbols_is_list:
+                data__exportsymbols_len = len(data__exportsymbols)
+                for data__exportsymbols_x, data__exportsymbols_item in enumerate(data__exportsymbols):
+                    if not isinstance(data__exportsymbols_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".export-symbols[{data__exportsymbols_x}]".format(**locals()) + " must be string", value=data__exportsymbols_item, name="" + (name_prefix or "data") + ".export-symbols[{data__exportsymbols_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "swig-opts" in data_keys:
+            data_keys.remove("swig-opts")
+            data__swigopts = data["swig-opts"]
+            if not isinstance(data__swigopts, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".swig-opts must be array", value=data__swigopts, name="" + (name_prefix or "data") + ".swig-opts", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__swigopts_is_list = isinstance(data__swigopts, (list, tuple))
+            if data__swigopts_is_list:
+                data__swigopts_len = len(data__swigopts)
+                for data__swigopts_x, data__swigopts_item in enumerate(data__swigopts):
+                    if not isinstance(data__swigopts_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".swig-opts[{data__swigopts_x}]".format(**locals()) + " must be string", value=data__swigopts_item, name="" + (name_prefix or "data") + ".swig-opts[{data__swigopts_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "depends" in data_keys:
+            data_keys.remove("depends")
+            data__depends = data["depends"]
+            if not isinstance(data__depends, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".depends must be array", value=data__depends, name="" + (name_prefix or "data") + ".depends", definition={'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__depends_is_list = isinstance(data__depends, (list, tuple))
+            if data__depends_is_list:
+                data__depends_len = len(data__depends)
+                for data__depends_x, data__depends_item in enumerate(data__depends):
+                    if not isinstance(data__depends_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".depends[{data__depends_x}]".format(**locals()) + " must be string", value=data__depends_item, name="" + (name_prefix or "data") + ".depends[{data__depends_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "language" in data_keys:
+            data_keys.remove("language")
+            data__language = data["language"]
+            if not isinstance(data__language, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".language must be string", value=data__language, name="" + (name_prefix or "data") + ".language", definition={'type': 'string'}, rule='type')
+        if "optional" in data_keys:
+            data_keys.remove("optional")
+            data__optional = data["optional"]
+            if not isinstance(data__optional, (bool)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".optional must be boolean", value=data__optional, name="" + (name_prefix or "data") + ".optional", definition={'type': 'boolean'}, rule='type')
+        if "py-limited-api" in data_keys:
+            data_keys.remove("py-limited-api")
+            data__pylimitedapi = data["py-limited-api"]
+            if not isinstance(data__pylimitedapi, (bool)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".py-limited-api must be boolean", value=data__pylimitedapi, name="" + (name_prefix or "data") + ".py-limited-api", definition={'type': 'boolean'}, rule='type')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/ext-module', 'title': 'Extension module', 'description': 'Parameters to construct a :class:`setuptools.Extension` object', 'type': 'object', 'required': ['name', 'sources'], 'additionalProperties': False, 'properties': {'name': {'type': 'string', 'format': 'python-module-name-relaxed'}, 'sources': {'type': 'array', 'items': {'type': 'string'}}, 'include-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'define-macros': {'type': 'array', 'items': {'type': 'array', 'items': [{'description': 'macro name', 'type': 'string'}, {'description': 'macro value', 'oneOf': [{'type': 'string'}, {'type': 'null'}]}], 'additionalItems': False}}, 'undef-macros': {'type': 'array', 'items': {'type': 'string'}}, 'library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'libraries': {'type': 'array', 'items': {'type': 'string'}}, 'runtime-library-dirs': {'type': 'array', 'items': {'type': 'string'}}, 'extra-objects': {'type': 'array', 'items': {'type': 'string'}}, 'extra-compile-args': {'type': 'array', 'items': {'type': 'string'}}, 'extra-link-args': {'type': 'array', 'items': {'type': 'string'}}, 'export-symbols': {'type': 'array', 'items': {'type': 'string'}}, 'swig-opts': {'type': 'array', 'items': {'type': 'string'}}, 'depends': {'type': 'array', 'items': {'type': 'string'}}, 'language': {'type': 'string'}, 'optional': {'type': 'boolean'}, 'py-limited-api': {'type': 'boolean'}}}, rule='additionalProperties')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_find_directive(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data_keys = set(data.keys())
+        if "find" in data_keys:
+            data_keys.remove("find")
+            data__find = data["find"]
+            if not isinstance(data__find, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".find must be object", value=data__find, name="" + (name_prefix or "data") + ".find", definition={'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}, rule='type')
+            data__find_is_dict = isinstance(data__find, dict)
+            if data__find_is_dict:
+                data__find_keys = set(data__find.keys())
+                if "where" in data__find_keys:
+                    data__find_keys.remove("where")
+                    data__find__where = data__find["where"]
+                    if not isinstance(data__find__where, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.where must be array", value=data__find__where, name="" + (name_prefix or "data") + ".find.where", definition={'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, rule='type')
+                    data__find__where_is_list = isinstance(data__find__where, (list, tuple))
+                    if data__find__where_is_list:
+                        data__find__where_len = len(data__find__where)
+                        for data__find__where_x, data__find__where_item in enumerate(data__find__where):
+                            if not isinstance(data__find__where_item, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.where[{data__find__where_x}]".format(**locals()) + " must be string", value=data__find__where_item, name="" + (name_prefix or "data") + ".find.where[{data__find__where_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if "exclude" in data__find_keys:
+                    data__find_keys.remove("exclude")
+                    data__find__exclude = data__find["exclude"]
+                    if not isinstance(data__find__exclude, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.exclude must be array", value=data__find__exclude, name="" + (name_prefix or "data") + ".find.exclude", definition={'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, rule='type')
+                    data__find__exclude_is_list = isinstance(data__find__exclude, (list, tuple))
+                    if data__find__exclude_is_list:
+                        data__find__exclude_len = len(data__find__exclude)
+                        for data__find__exclude_x, data__find__exclude_item in enumerate(data__find__exclude):
+                            if not isinstance(data__find__exclude_item, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.exclude[{data__find__exclude_x}]".format(**locals()) + " must be string", value=data__find__exclude_item, name="" + (name_prefix or "data") + ".find.exclude[{data__find__exclude_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if "include" in data__find_keys:
+                    data__find_keys.remove("include")
+                    data__find__include = data__find["include"]
+                    if not isinstance(data__find__include, (list, tuple)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.include must be array", value=data__find__include, name="" + (name_prefix or "data") + ".find.include", definition={'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, rule='type')
+                    data__find__include_is_list = isinstance(data__find__include, (list, tuple))
+                    if data__find__include_is_list:
+                        data__find__include_len = len(data__find__include)
+                        for data__find__include_x, data__find__include_item in enumerate(data__find__include):
+                            if not isinstance(data__find__include_item, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.include[{data__find__include_x}]".format(**locals()) + " must be string", value=data__find__include_item, name="" + (name_prefix or "data") + ".find.include[{data__find__include_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+                if "namespaces" in data__find_keys:
+                    data__find_keys.remove("namespaces")
+                    data__find__namespaces = data__find["namespaces"]
+                    if not isinstance(data__find__namespaces, (bool)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".find.namespaces must be boolean", value=data__find__namespaces, name="" + (name_prefix or "data") + ".find.namespaces", definition={'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}, rule='type')
+                if data__find_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".find must not contain "+str(data__find_keys)+" properties", value=data__find, name="" + (name_prefix or "data") + ".find", definition={'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}, rule='additionalProperties')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/find-directive', 'title': "'find:' directive", 'type': 'object', 'additionalProperties': False, 'properties': {'find': {'type': 'object', '$$description': ['Dynamic `package discovery', '`_.'], 'additionalProperties': False, 'properties': {'where': {'description': 'Directories to be searched for packages (Unix-style relative path)', 'type': 'array', 'items': {'type': 'string'}}, 'exclude': {'type': 'array', '$$description': ['Exclude packages that match the values listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'include': {'type': 'array', '$$description': ['Restrict the found packages to just the ones listed in this field.', "Can container shell-style wildcards (e.g. ``'pkg.*'``)"], 'items': {'type': 'string'}}, 'namespaces': {'type': 'boolean', '$$description': ['When ``True``, directories without a ``__init__.py`` file will also', 'be scanned for :pep:`420`-style implicit namespaces']}}}}}, rule='additionalProperties')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_userguide_pyproject_config_html__definitions_package_name(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (str)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be string", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, rule='type')
+    data_any_of_count11 = 0
+    if not data_any_of_count11:
+        try:
+            if not isinstance(data, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must be string", value=data, name="" + (name_prefix or "data") + "", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='type')
+            if isinstance(data, str):
+                if not custom_formats["python-module-name-relaxed"](data):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + " must be python-module-name-relaxed", value=data, name="" + (name_prefix or "data") + "", definition={'type': 'string', 'format': 'python-module-name-relaxed'}, rule='format')
+            data_any_of_count11 += 1
+        except JsonSchemaValueException: pass
+    if not data_any_of_count11:
+        try:
+            if not isinstance(data, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must be string", value=data, name="" + (name_prefix or "data") + "", definition={'type': 'string', 'format': 'pep561-stub-name'}, rule='type')
+            if isinstance(data, str):
+                if not custom_formats["pep561-stub-name"](data):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + " must be pep561-stub-name", value=data, name="" + (name_prefix or "data") + "", definition={'type': 'string', 'format': 'pep561-stub-name'}, rule='format')
+            data_any_of_count11 += 1
+        except JsonSchemaValueException: pass
+    if not data_any_of_count11:
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " cannot be validated by any definition", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/package-name', 'title': 'Valid package name', 'description': 'Valid package name (importable or :pep:`561`).', 'type': 'string', 'anyOf': [{'type': 'string', 'format': 'python-module-name-relaxed'}, {'type': 'string', 'format': 'pep561-stub-name'}]}, rule='anyOf')
+    return data
+
+def validate_https___setuptools_pypa_io_en_latest_deprecated_distutils_configfile_html(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://setuptools.pypa.io/en/latest/deprecated/distutils/configfile.html', 'title': '``tool.distutils`` table', '$$description': ['**EXPERIMENTAL** (NOT OFFICIALLY SUPPORTED): Use ``tool.distutils``', 'subtables to configure arguments for ``distutils`` commands.', 'Originally, ``distutils`` allowed developers to configure arguments for', '``setup.py`` commands via `distutils configuration files', '`_.', 'See also `the old Python docs _`.'], 'type': 'object', 'properties': {'global': {'type': 'object', 'description': 'Global options applied to all ``distutils`` commands'}}, 'patternProperties': {'.+': {'type': 'object'}}, '$comment': 'TODO: Is there a practical way of making this schema more specific?'}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data_keys = set(data.keys())
+        if "global" in data_keys:
+            data_keys.remove("global")
+            data__global = data["global"]
+            if not isinstance(data__global, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".global must be object", value=data__global, name="" + (name_prefix or "data") + ".global", definition={'type': 'object', 'description': 'Global options applied to all ``distutils`` commands'}, rule='type')
+        for data_key, data_val in data.items():
+            if REGEX_PATTERNS['.+'].search(data_key):
+                if data_key in data_keys:
+                    data_keys.remove(data_key)
+                if not isinstance(data_val, (dict)):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".{data_key}".format(**locals()) + " must be object", value=data_val, name="" + (name_prefix or "data") + ".{data_key}".format(**locals()) + "", definition={'type': 'object'}, rule='type')
+    return data
+
+def validate_https___packaging_python_org_en_latest_specifications_pyproject_toml(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'gui-scripts': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}, rule='type')
+    try:
+        try:
+            data_is_dict = isinstance(data, dict)
+            if data_is_dict:
+                data__missing_keys = set(['dynamic']) - data.keys()
+                if data__missing_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, rule='required')
+                data_keys = set(data.keys())
+                if "dynamic" in data_keys:
+                    data_keys.remove("dynamic")
+                    data__dynamic = data["dynamic"]
+                    data__dynamic_is_list = isinstance(data__dynamic, (list, tuple))
+                    if data__dynamic_is_list:
+                        data__dynamic_contains = False
+                        for data__dynamic_key in data__dynamic:
+                            try:
+                                if data__dynamic_key != "version":
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic must be same as const definition: version", value=data__dynamic_key, name="" + (name_prefix or "data") + ".dynamic", definition={'const': 'version'}, rule='const')
+                                data__dynamic_contains = True
+                                break
+                            except JsonSchemaValueException: pass
+                        if not data__dynamic_contains:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic must contain one of contains definition", value=data__dynamic, name="" + (name_prefix or "data") + ".dynamic", definition={'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}, rule='contains')
+        except JsonSchemaValueException: pass
+        else:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must NOT match a disallowed definition", value=data, name="" + (name_prefix or "data") + "", definition={'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, rule='not')
+    except JsonSchemaValueException:
+        pass
+    else:
+        data_is_dict = isinstance(data, dict)
+        if data_is_dict:
+            data__missing_keys = set(['version']) - data.keys()
+            if data__missing_keys:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}, rule='required')
+    try:
+        data_is_dict = isinstance(data, dict)
+        if data_is_dict:
+            data__missing_keys = set(['license-files']) - data.keys()
+            if data__missing_keys:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'required': ['license-files']}, rule='required')
+    except JsonSchemaValueException:
+        pass
+    else:
+        data_is_dict = isinstance(data, dict)
+        if data_is_dict:
+            data_keys = set(data.keys())
+            if "license" in data_keys:
+                data_keys.remove("license")
+                data__license = data["license"]
+                if not isinstance(data__license, (str)):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must be string", value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'string'}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data__missing_keys = set(['name']) - data.keys()
+        if data__missing_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must contain " + (str(sorted(data__missing_keys)) + " properties"), value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'gui-scripts': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}, rule='required')
+        data_keys = set(data.keys())
+        if "name" in data_keys:
+            data_keys.remove("name")
+            data__name = data["name"]
+            if not isinstance(data__name, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".name must be string", value=data__name, name="" + (name_prefix or "data") + ".name", definition={'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, rule='type')
+            if isinstance(data__name, str):
+                if not custom_formats["pep508-identifier"](data__name):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".name must be pep508-identifier", value=data__name, name="" + (name_prefix or "data") + ".name", definition={'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, rule='format')
+        if "version" in data_keys:
+            data_keys.remove("version")
+            data__version = data["version"]
+            if not isinstance(data__version, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".version must be string", value=data__version, name="" + (name_prefix or "data") + ".version", definition={'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, rule='type')
+            if isinstance(data__version, str):
+                if not custom_formats["pep440"](data__version):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".version must be pep440", value=data__version, name="" + (name_prefix or "data") + ".version", definition={'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, rule='format')
+        if "description" in data_keys:
+            data_keys.remove("description")
+            data__description = data["description"]
+            if not isinstance(data__description, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".description must be string", value=data__description, name="" + (name_prefix or "data") + ".description", definition={'type': 'string', '$$description': ['The `summary description of the project', '`_']}, rule='type')
+        if "readme" in data_keys:
+            data_keys.remove("readme")
+            data__readme = data["readme"]
+            data__readme_one_of_count12 = 0
+            if data__readme_one_of_count12 < 2:
+                try:
+                    if not isinstance(data__readme, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme must be string", value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, rule='type')
+                    data__readme_one_of_count12 += 1
+                except JsonSchemaValueException: pass
+            if data__readme_one_of_count12 < 2:
+                try:
+                    if not isinstance(data__readme, (dict)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme must be object", value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}, rule='type')
+                    data__readme_any_of_count13 = 0
+                    if not data__readme_any_of_count13:
+                        try:
+                            data__readme_is_dict = isinstance(data__readme, dict)
+                            if data__readme_is_dict:
+                                data__readme__missing_keys = set(['file']) - data__readme.keys()
+                                if data__readme__missing_keys:
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme must contain " + (str(sorted(data__readme__missing_keys)) + " properties"), value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, rule='required')
+                                data__readme_keys = set(data__readme.keys())
+                                if "file" in data__readme_keys:
+                                    data__readme_keys.remove("file")
+                                    data__readme__file = data__readme["file"]
+                                    if not isinstance(data__readme__file, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme.file must be string", value=data__readme__file, name="" + (name_prefix or "data") + ".readme.file", definition={'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}, rule='type')
+                            data__readme_any_of_count13 += 1
+                        except JsonSchemaValueException: pass
+                    if not data__readme_any_of_count13:
+                        try:
+                            data__readme_is_dict = isinstance(data__readme, dict)
+                            if data__readme_is_dict:
+                                data__readme__missing_keys = set(['text']) - data__readme.keys()
+                                if data__readme__missing_keys:
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme must contain " + (str(sorted(data__readme__missing_keys)) + " properties"), value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}, rule='required')
+                                data__readme_keys = set(data__readme.keys())
+                                if "text" in data__readme_keys:
+                                    data__readme_keys.remove("text")
+                                    data__readme__text = data__readme["text"]
+                                    if not isinstance(data__readme__text, (str)):
+                                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme.text must be string", value=data__readme__text, name="" + (name_prefix or "data") + ".readme.text", definition={'type': 'string', 'description': 'Full text describing the project.'}, rule='type')
+                            data__readme_any_of_count13 += 1
+                        except JsonSchemaValueException: pass
+                    if not data__readme_any_of_count13:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme cannot be validated by any definition", value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, rule='anyOf')
+                    data__readme_is_dict = isinstance(data__readme, dict)
+                    if data__readme_is_dict:
+                        data__readme__missing_keys = set(['content-type']) - data__readme.keys()
+                        if data__readme__missing_keys:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme must contain " + (str(sorted(data__readme__missing_keys)) + " properties"), value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}, rule='required')
+                        data__readme_keys = set(data__readme.keys())
+                        if "content-type" in data__readme_keys:
+                            data__readme_keys.remove("content-type")
+                            data__readme__contenttype = data__readme["content-type"]
+                            if not isinstance(data__readme__contenttype, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme.content-type must be string", value=data__readme__contenttype, name="" + (name_prefix or "data") + ".readme.content-type", definition={'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}, rule='type')
+                    data__readme_one_of_count12 += 1
+                except JsonSchemaValueException: pass
+            if data__readme_one_of_count12 != 1:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".readme must be valid exactly by one definition" + (" (" + str(data__readme_one_of_count12) + " matches found)"), value=data__readme, name="" + (name_prefix or "data") + ".readme", definition={'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, rule='oneOf')
+        if "requires-python" in data_keys:
+            data_keys.remove("requires-python")
+            data__requirespython = data["requires-python"]
+            if not isinstance(data__requirespython, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".requires-python must be string", value=data__requirespython, name="" + (name_prefix or "data") + ".requires-python", definition={'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, rule='type')
+            if isinstance(data__requirespython, str):
+                if not custom_formats["pep508-versionspec"](data__requirespython):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".requires-python must be pep508-versionspec", value=data__requirespython, name="" + (name_prefix or "data") + ".requires-python", definition={'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, rule='format')
+        if "license" in data_keys:
+            data_keys.remove("license")
+            data__license = data["license"]
+            data__license_one_of_count14 = 0
+            if data__license_one_of_count14 < 2:
+                try:
+                    if not isinstance(data__license, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must be string", value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, rule='type')
+                    if isinstance(data__license, str):
+                        if not custom_formats["SPDX"](data__license):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must be SPDX", value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, rule='format')
+                    data__license_one_of_count14 += 1
+                except JsonSchemaValueException: pass
+            if data__license_one_of_count14 < 2:
+                try:
+                    if not isinstance(data__license, (dict)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must be object", value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, rule='type')
+                    data__license_is_dict = isinstance(data__license, dict)
+                    if data__license_is_dict:
+                        data__license__missing_keys = set(['file']) - data__license.keys()
+                        if data__license__missing_keys:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must contain " + (str(sorted(data__license__missing_keys)) + " properties"), value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, rule='required')
+                        data__license_keys = set(data__license.keys())
+                        if "file" in data__license_keys:
+                            data__license_keys.remove("file")
+                            data__license__file = data__license["file"]
+                            if not isinstance(data__license__file, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".license.file must be string", value=data__license__file, name="" + (name_prefix or "data") + ".license.file", definition={'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}, rule='type')
+                    data__license_one_of_count14 += 1
+                except JsonSchemaValueException: pass
+            if data__license_one_of_count14 < 2:
+                try:
+                    if not isinstance(data__license, (dict)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must be object", value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}, rule='type')
+                    data__license_is_dict = isinstance(data__license, dict)
+                    if data__license_is_dict:
+                        data__license__missing_keys = set(['text']) - data__license.keys()
+                        if data__license__missing_keys:
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must contain " + (str(sorted(data__license__missing_keys)) + " properties"), value=data__license, name="" + (name_prefix or "data") + ".license", definition={'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}, rule='required')
+                        data__license_keys = set(data__license.keys())
+                        if "text" in data__license_keys:
+                            data__license_keys.remove("text")
+                            data__license__text = data__license["text"]
+                            if not isinstance(data__license__text, (str)):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".license.text must be string", value=data__license__text, name="" + (name_prefix or "data") + ".license.text", definition={'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}, rule='type')
+                    data__license_one_of_count14 += 1
+                except JsonSchemaValueException: pass
+            if data__license_one_of_count14 != 1:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".license must be valid exactly by one definition" + (" (" + str(data__license_one_of_count14) + " matches found)"), value=data__license, name="" + (name_prefix or "data") + ".license", definition={'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, rule='oneOf')
+        if "license-files" in data_keys:
+            data_keys.remove("license-files")
+            data__licensefiles = data["license-files"]
+            if not isinstance(data__licensefiles, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".license-files must be array", value=data__licensefiles, name="" + (name_prefix or "data") + ".license-files", definition={'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, rule='type')
+            data__licensefiles_is_list = isinstance(data__licensefiles, (list, tuple))
+            if data__licensefiles_is_list:
+                data__licensefiles_len = len(data__licensefiles)
+                for data__licensefiles_x, data__licensefiles_item in enumerate(data__licensefiles):
+                    if not isinstance(data__licensefiles_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".license-files[{data__licensefiles_x}]".format(**locals()) + " must be string", value=data__licensefiles_item, name="" + (name_prefix or "data") + ".license-files[{data__licensefiles_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "authors" in data_keys:
+            data_keys.remove("authors")
+            data__authors = data["authors"]
+            if not isinstance(data__authors, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".authors must be array", value=data__authors, name="" + (name_prefix or "data") + ".authors", definition={'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, rule='type')
+            data__authors_is_list = isinstance(data__authors, (list, tuple))
+            if data__authors_is_list:
+                data__authors_len = len(data__authors)
+                for data__authors_x, data__authors_item in enumerate(data__authors):
+                    validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_author(data__authors_item, custom_formats, (name_prefix or "data") + ".authors[{data__authors_x}]".format(**locals()))
+        if "maintainers" in data_keys:
+            data_keys.remove("maintainers")
+            data__maintainers = data["maintainers"]
+            if not isinstance(data__maintainers, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".maintainers must be array", value=data__maintainers, name="" + (name_prefix or "data") + ".maintainers", definition={'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, rule='type')
+            data__maintainers_is_list = isinstance(data__maintainers, (list, tuple))
+            if data__maintainers_is_list:
+                data__maintainers_len = len(data__maintainers)
+                for data__maintainers_x, data__maintainers_item in enumerate(data__maintainers):
+                    validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_author(data__maintainers_item, custom_formats, (name_prefix or "data") + ".maintainers[{data__maintainers_x}]".format(**locals()))
+        if "keywords" in data_keys:
+            data_keys.remove("keywords")
+            data__keywords = data["keywords"]
+            if not isinstance(data__keywords, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".keywords must be array", value=data__keywords, name="" + (name_prefix or "data") + ".keywords", definition={'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, rule='type')
+            data__keywords_is_list = isinstance(data__keywords, (list, tuple))
+            if data__keywords_is_list:
+                data__keywords_len = len(data__keywords)
+                for data__keywords_x, data__keywords_item in enumerate(data__keywords):
+                    if not isinstance(data__keywords_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".keywords[{data__keywords_x}]".format(**locals()) + " must be string", value=data__keywords_item, name="" + (name_prefix or "data") + ".keywords[{data__keywords_x}]".format(**locals()) + "", definition={'type': 'string'}, rule='type')
+        if "classifiers" in data_keys:
+            data_keys.remove("classifiers")
+            data__classifiers = data["classifiers"]
+            if not isinstance(data__classifiers, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".classifiers must be array", value=data__classifiers, name="" + (name_prefix or "data") + ".classifiers", definition={'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, rule='type')
+            data__classifiers_is_list = isinstance(data__classifiers, (list, tuple))
+            if data__classifiers_is_list:
+                data__classifiers_len = len(data__classifiers)
+                for data__classifiers_x, data__classifiers_item in enumerate(data__classifiers):
+                    if not isinstance(data__classifiers_item, (str)):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".classifiers[{data__classifiers_x}]".format(**locals()) + " must be string", value=data__classifiers_item, name="" + (name_prefix or "data") + ".classifiers[{data__classifiers_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, rule='type')
+                    if isinstance(data__classifiers_item, str):
+                        if not custom_formats["trove-classifier"](data__classifiers_item):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".classifiers[{data__classifiers_x}]".format(**locals()) + " must be trove-classifier", value=data__classifiers_item, name="" + (name_prefix or "data") + ".classifiers[{data__classifiers_x}]".format(**locals()) + "", definition={'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, rule='format')
+        if "urls" in data_keys:
+            data_keys.remove("urls")
+            data__urls = data["urls"]
+            if not isinstance(data__urls, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".urls must be object", value=data__urls, name="" + (name_prefix or "data") + ".urls", definition={'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, rule='type')
+            data__urls_is_dict = isinstance(data__urls, dict)
+            if data__urls_is_dict:
+                data__urls_keys = set(data__urls.keys())
+                for data__urls_key, data__urls_val in data__urls.items():
+                    if REGEX_PATTERNS['^.+$'].search(data__urls_key):
+                        if data__urls_key in data__urls_keys:
+                            data__urls_keys.remove(data__urls_key)
+                        if not isinstance(data__urls_val, (str)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".urls.{data__urls_key}".format(**locals()) + " must be string", value=data__urls_val, name="" + (name_prefix or "data") + ".urls.{data__urls_key}".format(**locals()) + "", definition={'type': 'string', 'format': 'url'}, rule='type')
+                        if isinstance(data__urls_val, str):
+                            if not custom_formats["url"](data__urls_val):
+                                raise JsonSchemaValueException("" + (name_prefix or "data") + ".urls.{data__urls_key}".format(**locals()) + " must be url", value=data__urls_val, name="" + (name_prefix or "data") + ".urls.{data__urls_key}".format(**locals()) + "", definition={'type': 'string', 'format': 'url'}, rule='format')
+                if data__urls_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".urls must not contain "+str(data__urls_keys)+" properties", value=data__urls, name="" + (name_prefix or "data") + ".urls", definition={'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, rule='additionalProperties')
+        if "scripts" in data_keys:
+            data_keys.remove("scripts")
+            data__scripts = data["scripts"]
+            validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_entry_point_group(data__scripts, custom_formats, (name_prefix or "data") + ".scripts")
+        if "gui-scripts" in data_keys:
+            data_keys.remove("gui-scripts")
+            data__guiscripts = data["gui-scripts"]
+            validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_entry_point_group(data__guiscripts, custom_formats, (name_prefix or "data") + ".gui-scripts")
+        if "entry-points" in data_keys:
+            data_keys.remove("entry-points")
+            data__entrypoints = data["entry-points"]
+            data__entrypoints_is_dict = isinstance(data__entrypoints, dict)
+            if data__entrypoints_is_dict:
+                data__entrypoints_keys = set(data__entrypoints.keys())
+                for data__entrypoints_key, data__entrypoints_val in data__entrypoints.items():
+                    if REGEX_PATTERNS['^.+$'].search(data__entrypoints_key):
+                        if data__entrypoints_key in data__entrypoints_keys:
+                            data__entrypoints_keys.remove(data__entrypoints_key)
+                        validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_entry_point_group(data__entrypoints_val, custom_formats, (name_prefix or "data") + ".entry-points.{data__entrypoints_key}".format(**locals()))
+                if data__entrypoints_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".entry-points must not contain "+str(data__entrypoints_keys)+" properties", value=data__entrypoints, name="" + (name_prefix or "data") + ".entry-points", definition={'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}}}, rule='additionalProperties')
+                data__entrypoints_len = len(data__entrypoints)
+                if data__entrypoints_len != 0:
+                    data__entrypoints_property_names = True
+                    for data__entrypoints_key in data__entrypoints:
+                        try:
+                            if isinstance(data__entrypoints_key, str):
+                                if not custom_formats["python-entrypoint-group"](data__entrypoints_key):
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".entry-points must be python-entrypoint-group", value=data__entrypoints_key, name="" + (name_prefix or "data") + ".entry-points", definition={'format': 'python-entrypoint-group'}, rule='format')
+                        except JsonSchemaValueException:
+                            data__entrypoints_property_names = False
+                    if not data__entrypoints_property_names:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".entry-points must be named by propertyName definition", value=data__entrypoints, name="" + (name_prefix or "data") + ".entry-points", definition={'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}}}, rule='propertyNames')
+        if "dependencies" in data_keys:
+            data_keys.remove("dependencies")
+            data__dependencies = data["dependencies"]
+            if not isinstance(data__dependencies, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dependencies must be array", value=data__dependencies, name="" + (name_prefix or "data") + ".dependencies", definition={'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}, rule='type')
+            data__dependencies_is_list = isinstance(data__dependencies, (list, tuple))
+            if data__dependencies_is_list:
+                data__dependencies_len = len(data__dependencies)
+                for data__dependencies_x, data__dependencies_item in enumerate(data__dependencies):
+                    validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_dependency(data__dependencies_item, custom_formats, (name_prefix or "data") + ".dependencies[{data__dependencies_x}]".format(**locals()))
+        if "optional-dependencies" in data_keys:
+            data_keys.remove("optional-dependencies")
+            data__optionaldependencies = data["optional-dependencies"]
+            if not isinstance(data__optionaldependencies, (dict)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".optional-dependencies must be object", value=data__optionaldependencies, name="" + (name_prefix or "data") + ".optional-dependencies", definition={'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, rule='type')
+            data__optionaldependencies_is_dict = isinstance(data__optionaldependencies, dict)
+            if data__optionaldependencies_is_dict:
+                data__optionaldependencies_keys = set(data__optionaldependencies.keys())
+                for data__optionaldependencies_key, data__optionaldependencies_val in data__optionaldependencies.items():
+                    if REGEX_PATTERNS['^.+$'].search(data__optionaldependencies_key):
+                        if data__optionaldependencies_key in data__optionaldependencies_keys:
+                            data__optionaldependencies_keys.remove(data__optionaldependencies_key)
+                        if not isinstance(data__optionaldependencies_val, (list, tuple)):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + ".optional-dependencies.{data__optionaldependencies_key}".format(**locals()) + " must be array", value=data__optionaldependencies_val, name="" + (name_prefix or "data") + ".optional-dependencies.{data__optionaldependencies_key}".format(**locals()) + "", definition={'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}, rule='type')
+                        data__optionaldependencies_val_is_list = isinstance(data__optionaldependencies_val, (list, tuple))
+                        if data__optionaldependencies_val_is_list:
+                            data__optionaldependencies_val_len = len(data__optionaldependencies_val)
+                            for data__optionaldependencies_val_x, data__optionaldependencies_val_item in enumerate(data__optionaldependencies_val):
+                                validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_dependency(data__optionaldependencies_val_item, custom_formats, (name_prefix or "data") + ".optional-dependencies.{data__optionaldependencies_key}[{data__optionaldependencies_val_x}]".format(**locals()))
+                if data__optionaldependencies_keys:
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".optional-dependencies must not contain "+str(data__optionaldependencies_keys)+" properties", value=data__optionaldependencies, name="" + (name_prefix or "data") + ".optional-dependencies", definition={'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, rule='additionalProperties')
+                data__optionaldependencies_len = len(data__optionaldependencies)
+                if data__optionaldependencies_len != 0:
+                    data__optionaldependencies_property_names = True
+                    for data__optionaldependencies_key in data__optionaldependencies:
+                        try:
+                            if isinstance(data__optionaldependencies_key, str):
+                                if not custom_formats["pep508-identifier"](data__optionaldependencies_key):
+                                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".optional-dependencies must be pep508-identifier", value=data__optionaldependencies_key, name="" + (name_prefix or "data") + ".optional-dependencies", definition={'format': 'pep508-identifier'}, rule='format')
+                        except JsonSchemaValueException:
+                            data__optionaldependencies_property_names = False
+                    if not data__optionaldependencies_property_names:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".optional-dependencies must be named by propertyName definition", value=data__optionaldependencies, name="" + (name_prefix or "data") + ".optional-dependencies", definition={'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, rule='propertyNames')
+        if "dynamic" in data_keys:
+            data_keys.remove("dynamic")
+            data__dynamic = data["dynamic"]
+            if not isinstance(data__dynamic, (list, tuple)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic must be array", value=data__dynamic, name="" + (name_prefix or "data") + ".dynamic", definition={'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}, rule='type')
+            data__dynamic_is_list = isinstance(data__dynamic, (list, tuple))
+            if data__dynamic_is_list:
+                data__dynamic_len = len(data__dynamic)
+                for data__dynamic_x, data__dynamic_item in enumerate(data__dynamic):
+                    if data__dynamic_item not in ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']:
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".dynamic[{data__dynamic_x}]".format(**locals()) + " must be one of ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']", value=data__dynamic_item, name="" + (name_prefix or "data") + ".dynamic[{data__dynamic_x}]".format(**locals()) + "", definition={'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}, rule='enum')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$schema': 'http://json-schema.org/draft-07/schema#', '$id': 'https://packaging.python.org/en/latest/specifications/pyproject-toml/', 'title': 'Package metadata stored in the ``project`` table', '$$description': ['Data structure for the **project** table inside ``pyproject.toml``', '(as initially defined in :pep:`621`)'], 'type': 'object', 'properties': {'name': {'type': 'string', 'description': 'The name (primary identifier) of the project. MUST be statically defined.', 'format': 'pep508-identifier'}, 'version': {'type': 'string', 'description': 'The version of the project as supported by :pep:`440`.', 'format': 'pep440'}, 'description': {'type': 'string', '$$description': ['The `summary description of the project', '`_']}, 'readme': {'$$description': ['`Full/detailed description of the project in the form of a README', '`_', "with meaning similar to the one defined in `core metadata's Description", '`_'], 'oneOf': [{'type': 'string', '$$description': ['Relative path to a text file (UTF-8) containing the full description', 'of the project. If the file path ends in case-insensitive ``.md`` or', '``.rst`` suffixes, then the content-type is respectively', '``text/markdown`` or ``text/x-rst``']}, {'type': 'object', 'allOf': [{'anyOf': [{'properties': {'file': {'type': 'string', '$$description': ['Relative path to a text file containing the full description', 'of the project.']}}, 'required': ['file']}, {'properties': {'text': {'type': 'string', 'description': 'Full text describing the project.'}}, 'required': ['text']}]}, {'properties': {'content-type': {'type': 'string', '$$description': ['Content-type (:rfc:`1341`) of the full description', '(e.g. ``text/markdown``). The ``charset`` parameter is assumed', 'UTF-8 when not present.'], '$comment': 'TODO: add regex pattern or format?'}}, 'required': ['content-type']}]}]}, 'requires-python': {'type': 'string', 'format': 'pep508-versionspec', '$$description': ['`The Python version requirements of the project', '`_.']}, 'license': {'description': '`Project license `_.', 'oneOf': [{'type': 'string', 'description': 'An SPDX license identifier', 'format': 'SPDX'}, {'type': 'object', 'properties': {'file': {'type': 'string', '$$description': ['Relative path to the file (UTF-8) which contains the license for the', 'project.']}}, 'required': ['file']}, {'type': 'object', 'properties': {'text': {'type': 'string', '$$description': ['The license of the project whose meaning is that of the', '`License field from the core metadata', '`_.']}}, 'required': ['text']}]}, 'license-files': {'description': 'Paths or globs to paths of license files', 'type': 'array', 'items': {'type': 'string'}}, 'authors': {'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'authors' of the project.", 'The exact meaning is open to interpretation (e.g. original or primary authors,', 'current maintainers, or owners of the package).']}, 'maintainers': {'type': 'array', 'items': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, '$$description': ["The people or organizations considered to be the 'maintainers' of the project.", 'Similarly to ``authors``, the exact meaning is open to interpretation.']}, 'keywords': {'type': 'array', 'items': {'type': 'string'}, 'description': 'List of keywords to assist searching for the distribution in a larger catalog.'}, 'classifiers': {'type': 'array', 'items': {'type': 'string', 'format': 'trove-classifier', 'description': '`PyPI classifier `_.'}, '$$description': ['`Trove classifiers `_', 'which apply to the project.']}, 'urls': {'type': 'object', 'description': 'URLs associated with the project in the form ``label => value``.', 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', 'format': 'url'}}}, 'scripts': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'gui-scripts': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'entry-points': {'$$description': ['Instruct the installer to expose the given modules/functions via', '``entry-point`` discovery mechanism (useful for plugins).', 'More information available in the `Python packaging guide', '`_.'], 'propertyNames': {'format': 'python-entrypoint-group'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}}}, 'dependencies': {'type': 'array', 'description': 'Project (mandatory) dependencies.', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}, 'optional-dependencies': {'type': 'object', 'description': 'Optional dependency for the project', 'propertyNames': {'format': 'pep508-identifier'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'array', 'items': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}}, 'dynamic': {'type': 'array', '$$description': ['Specifies which fields are intentionally unspecified and expected to be', 'dynamically provided by build tools'], 'items': {'enum': ['version', 'description', 'readme', 'requires-python', 'license', 'license-files', 'authors', 'maintainers', 'keywords', 'classifiers', 'urls', 'scripts', 'gui-scripts', 'entry-points', 'dependencies', 'optional-dependencies']}}}, 'required': ['name'], 'additionalProperties': False, 'allOf': [{'if': {'not': {'required': ['dynamic'], 'properties': {'dynamic': {'contains': {'const': 'version'}, '$$description': ['version is listed in ``dynamic``']}}}, '$$comment': ['According to :pep:`621`:', '    If the core metadata specification lists a field as "Required", then', '    the metadata MUST specify the field statically or list it in dynamic', 'In turn, `core metadata`_ defines:', '    The required fields are: Metadata-Version, Name, Version.', '    All the other fields are optional.', 'Since ``Metadata-Version`` is defined by the build back-end, ``name`` and', '``version`` are the only mandatory information in ``pyproject.toml``.', '.. _core metadata: https://packaging.python.org/specifications/core-metadata/']}, 'then': {'required': ['version'], '$$description': ['version should be statically defined in the ``version`` field']}}, {'if': {'required': ['license-files']}, 'then': {'properties': {'license': {'type': 'string'}}}}], 'definitions': {'author': {'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, 'entry-point-group': {'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, 'dependency': {'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}}}, rule='additionalProperties')
+    return data
+
+def validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_dependency(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (str)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be string", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}, rule='type')
+    if isinstance(data, str):
+        if not custom_formats["pep508"](data):
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must be pep508", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/dependency', 'title': 'Dependency', 'type': 'string', 'description': 'Project dependency specification according to PEP 508', 'format': 'pep508'}, rule='format')
+    return data
+
+def validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_entry_point_group(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data_keys = set(data.keys())
+        for data_key, data_val in data.items():
+            if REGEX_PATTERNS['^.+$'].search(data_key):
+                if data_key in data_keys:
+                    data_keys.remove(data_key)
+                if not isinstance(data_val, (str)):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".{data_key}".format(**locals()) + " must be string", value=data_val, name="" + (name_prefix or "data") + ".{data_key}".format(**locals()) + "", definition={'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}, rule='type')
+                if isinstance(data_val, str):
+                    if not custom_formats["python-entrypoint-reference"](data_val):
+                        raise JsonSchemaValueException("" + (name_prefix or "data") + ".{data_key}".format(**locals()) + " must be python-entrypoint-reference", value=data_val, name="" + (name_prefix or "data") + ".{data_key}".format(**locals()) + "", definition={'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}, rule='format')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, rule='additionalProperties')
+        data_len = len(data)
+        if data_len != 0:
+            data_property_names = True
+            for data_key in data:
+                try:
+                    if isinstance(data_key, str):
+                        if not custom_formats["python-entrypoint-name"](data_key):
+                            raise JsonSchemaValueException("" + (name_prefix or "data") + " must be python-entrypoint-name", value=data_key, name="" + (name_prefix or "data") + "", definition={'format': 'python-entrypoint-name'}, rule='format')
+                except JsonSchemaValueException:
+                    data_property_names = False
+            if not data_property_names:
+                raise JsonSchemaValueException("" + (name_prefix or "data") + " must be named by propertyName definition", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/entry-point-group', 'title': 'Entry-points', 'type': 'object', '$$description': ['Entry-points are grouped together to indicate what sort of capabilities they', 'provide.', 'See the `packaging guides', '`_', 'and `setuptools docs', '`_', 'for more information.'], 'propertyNames': {'format': 'python-entrypoint-name'}, 'additionalProperties': False, 'patternProperties': {'^.+$': {'type': 'string', '$$description': ['Reference to a Python object. It is either in the form', '``importable.module``, or ``importable.module:object.attr``.'], 'format': 'python-entrypoint-reference', '$comment': 'https://packaging.python.org/specifications/entry-points/'}}}, rule='propertyNames')
+    return data
+
+def validate_https___packaging_python_org_en_latest_specifications_pyproject_toml___definitions_author(data, custom_formats={}, name_prefix=None):
+    if not isinstance(data, (dict)):
+        raise JsonSchemaValueException("" + (name_prefix or "data") + " must be object", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, rule='type')
+    data_is_dict = isinstance(data, dict)
+    if data_is_dict:
+        data_keys = set(data.keys())
+        if "name" in data_keys:
+            data_keys.remove("name")
+            data__name = data["name"]
+            if not isinstance(data__name, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".name must be string", value=data__name, name="" + (name_prefix or "data") + ".name", definition={'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, rule='type')
+        if "email" in data_keys:
+            data_keys.remove("email")
+            data__email = data["email"]
+            if not isinstance(data__email, (str)):
+                raise JsonSchemaValueException("" + (name_prefix or "data") + ".email must be string", value=data__email, name="" + (name_prefix or "data") + ".email", definition={'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}, rule='type')
+            if isinstance(data__email, str):
+                if not REGEX_PATTERNS["idn-email_re_pattern"].match(data__email):
+                    raise JsonSchemaValueException("" + (name_prefix or "data") + ".email must be idn-email", value=data__email, name="" + (name_prefix or "data") + ".email", definition={'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}, rule='format')
+        if data_keys:
+            raise JsonSchemaValueException("" + (name_prefix or "data") + " must not contain "+str(data_keys)+" properties", value=data, name="" + (name_prefix or "data") + "", definition={'$id': '#/definitions/author', 'title': 'Author or Maintainer', '$comment': 'https://peps.python.org/pep-0621/#authors-maintainers', 'type': 'object', 'additionalProperties': False, 'properties': {'name': {'type': 'string', '$$description': ['MUST be a valid email name, i.e. whatever can be put as a name, before an', 'email, in :rfc:`822`.']}, 'email': {'type': 'string', 'format': 'idn-email', 'description': 'MUST be a valid email address'}}}, rule='additionalProperties')
+    return data
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/formats.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/formats.py
new file mode 100644
index 0000000000000000000000000000000000000000..1cf4a465ef0156deef5bd4d1fc02350e40ff2fe5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/_validate_pyproject/formats.py
@@ -0,0 +1,402 @@
+"""
+The functions in this module are used to validate schemas with the
+`format JSON Schema keyword
+`_.
+
+The correspondence is given by replacing the ``_`` character in the name of the
+function with a ``-`` to obtain the format name and vice versa.
+"""
+
+import builtins
+import logging
+import os
+import re
+import string
+import typing
+from itertools import chain as _chain
+
+if typing.TYPE_CHECKING:
+    from typing_extensions import Literal
+
+_logger = logging.getLogger(__name__)
+
+# -------------------------------------------------------------------------------------
+# PEP 440
+
+VERSION_PATTERN = r"""
+    v?
+    (?:
+        (?:(?P[0-9]+)!)?                           # epoch
+        (?P[0-9]+(?:\.[0-9]+)*)                  # release segment
+        (?P
                                          # pre-release
+            [-_\.]?
+            (?Palpha|a|beta|b|preview|pre|c|rc)
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+        (?P                                         # post release
+            (?:-(?P[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?Ppost|rev|r)
+                [-_\.]?
+                (?P[0-9]+)?
+            )
+        )?
+        (?P                                          # dev release
+            [-_\.]?
+            (?Pdev)
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+    )
+    (?:\+(?P[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+VERSION_REGEX = re.compile(r"^\s*" + VERSION_PATTERN + r"\s*$", re.X | re.I)
+
+
+def pep440(version: str) -> bool:
+    """See :ref:`PyPA's version specification `
+    (initially introduced in :pep:`440`).
+    """
+    return VERSION_REGEX.match(version) is not None
+
+
+# -------------------------------------------------------------------------------------
+# PEP 508
+
+PEP508_IDENTIFIER_PATTERN = r"([A-Z0-9]|[A-Z0-9][A-Z0-9._-]*[A-Z0-9])"
+PEP508_IDENTIFIER_REGEX = re.compile(f"^{PEP508_IDENTIFIER_PATTERN}$", re.I)
+
+
+def pep508_identifier(name: str) -> bool:
+    """See :ref:`PyPA's name specification `
+    (initially introduced in :pep:`508#names`).
+    """
+    return PEP508_IDENTIFIER_REGEX.match(name) is not None
+
+
+try:
+    try:
+        from packaging import requirements as _req
+    except ImportError:  # pragma: no cover
+        # let's try setuptools vendored version
+        from setuptools._vendor.packaging import (  # type: ignore[no-redef]
+            requirements as _req,
+        )
+
+    def pep508(value: str) -> bool:
+        """See :ref:`PyPA's dependency specifiers `
+        (initially introduced in :pep:`508`).
+        """
+        try:
+            _req.Requirement(value)
+            return True
+        except _req.InvalidRequirement:
+            return False
+
+except ImportError:  # pragma: no cover
+    _logger.warning(
+        "Could not find an installation of `packaging`. Requirements, dependencies and "
+        "versions might not be validated. "
+        "To enforce validation, please install `packaging`."
+    )
+
+    def pep508(value: str) -> bool:
+        return True
+
+
+def pep508_versionspec(value: str) -> bool:
+    """Expression that can be used to specify/lock versions (including ranges)
+    See ``versionspec`` in :ref:`PyPA's dependency specifiers
+    ` (initially introduced in :pep:`508`).
+    """
+    if any(c in value for c in (";", "]", "@")):
+        # In PEP 508:
+        # conditional markers, extras and URL specs are not included in the
+        # versionspec
+        return False
+    # Let's pretend we have a dependency called `requirement` with the given
+    # version spec, then we can reuse the pep508 function for validation:
+    return pep508(f"requirement{value}")
+
+
+# -------------------------------------------------------------------------------------
+# PEP 517
+
+
+def pep517_backend_reference(value: str) -> bool:
+    """See PyPA's specification for defining build-backend references
+    introduced in :pep:`517#source-trees`.
+
+    This is similar to an entry-point reference (e.g., ``package.module:object``).
+    """
+    module, _, obj = value.partition(":")
+    identifiers = (i.strip() for i in _chain(module.split("."), obj.split(".")))
+    return all(python_identifier(i) for i in identifiers if i)
+
+
+# -------------------------------------------------------------------------------------
+# Classifiers - PEP 301
+
+
+def _download_classifiers() -> str:
+    import ssl
+    from email.message import Message
+    from urllib.request import urlopen
+
+    url = "https://pypi.org/pypi?:action=list_classifiers"
+    context = ssl.create_default_context()
+    with urlopen(url, context=context) as response:  # noqa: S310 (audit URLs)
+        headers = Message()
+        headers["content_type"] = response.getheader("content-type", "text/plain")
+        return response.read().decode(headers.get_param("charset", "utf-8"))  # type: ignore[no-any-return]
+
+
+class _TroveClassifier:
+    """The ``trove_classifiers`` package is the official way of validating classifiers,
+    however this package might not be always available.
+    As a workaround we can still download a list from PyPI.
+    We also don't want to be over strict about it, so simply skipping silently is an
+    option (classifiers will be validated anyway during the upload to PyPI).
+    """
+
+    downloaded: typing.Union[None, "Literal[False]", typing.Set[str]]
+    """
+    None => not cached yet
+    False => unavailable
+    set => cached values
+    """
+
+    def __init__(self) -> None:
+        self.downloaded = None
+        self._skip_download = False
+        self.__name__ = "trove_classifier"  # Emulate a public function
+
+    def _disable_download(self) -> None:
+        # This is a private API. Only setuptools has the consent of using it.
+        self._skip_download = True
+
+    def __call__(self, value: str) -> bool:
+        if self.downloaded is False or self._skip_download is True:
+            return True
+
+        if os.getenv("NO_NETWORK") or os.getenv("VALIDATE_PYPROJECT_NO_NETWORK"):
+            self.downloaded = False
+            msg = (
+                "Install ``trove-classifiers`` to ensure proper validation. "
+                "Skipping download of classifiers list from PyPI (NO_NETWORK)."
+            )
+            _logger.debug(msg)
+            return True
+
+        if self.downloaded is None:
+            msg = (
+                "Install ``trove-classifiers`` to ensure proper validation. "
+                "Meanwhile a list of classifiers will be downloaded from PyPI."
+            )
+            _logger.debug(msg)
+            try:
+                self.downloaded = set(_download_classifiers().splitlines())
+            except Exception:
+                self.downloaded = False
+                _logger.debug("Problem with download, skipping validation")
+                return True
+
+        return value in self.downloaded or value.lower().startswith("private ::")
+
+
+try:
+    from trove_classifiers import classifiers as _trove_classifiers
+
+    def trove_classifier(value: str) -> bool:
+        """See https://pypi.org/classifiers/"""
+        return value in _trove_classifiers or value.lower().startswith("private ::")
+
+except ImportError:  # pragma: no cover
+    trove_classifier = _TroveClassifier()
+
+
+# -------------------------------------------------------------------------------------
+# Stub packages - PEP 561
+
+
+def pep561_stub_name(value: str) -> bool:
+    """Name of a directory containing type stubs.
+    It must follow the name scheme ``-stubs`` as defined in
+    :pep:`561#stub-only-packages`.
+    """
+    top, *children = value.split(".")
+    if not top.endswith("-stubs"):
+        return False
+    return python_module_name(".".join([top[: -len("-stubs")], *children]))
+
+
+# -------------------------------------------------------------------------------------
+# Non-PEP related
+
+
+def url(value: str) -> bool:
+    """Valid URL (validation uses :obj:`urllib.parse`).
+    For maximum compatibility please make sure to include a ``scheme`` prefix
+    in your URL (e.g. ``http://``).
+    """
+    from urllib.parse import urlparse
+
+    try:
+        parts = urlparse(value)
+        if not parts.scheme:
+            _logger.warning(
+                "For maximum compatibility please make sure to include a "
+                "`scheme` prefix in your URL (e.g. 'http://'). "
+                f"Given value: {value}"
+            )
+            if not (value.startswith("/") or value.startswith("\\") or "@" in value):
+                parts = urlparse(f"http://{value}")
+
+        return bool(parts.scheme and parts.netloc)
+    except Exception:
+        return False
+
+
+# https://packaging.python.org/specifications/entry-points/
+ENTRYPOINT_PATTERN = r"[^\[\s=]([^=]*[^\s=])?"
+ENTRYPOINT_REGEX = re.compile(f"^{ENTRYPOINT_PATTERN}$", re.I)
+RECOMMEDED_ENTRYPOINT_PATTERN = r"[\w.-]+"
+RECOMMEDED_ENTRYPOINT_REGEX = re.compile(f"^{RECOMMEDED_ENTRYPOINT_PATTERN}$", re.I)
+ENTRYPOINT_GROUP_PATTERN = r"\w+(\.\w+)*"
+ENTRYPOINT_GROUP_REGEX = re.compile(f"^{ENTRYPOINT_GROUP_PATTERN}$", re.I)
+
+
+def python_identifier(value: str) -> bool:
+    """Can be used as identifier in Python.
+    (Validation uses :obj:`str.isidentifier`).
+    """
+    return value.isidentifier()
+
+
+def python_qualified_identifier(value: str) -> bool:
+    """
+    Python "dotted identifier", i.e. a sequence of :obj:`python_identifier`
+    concatenated with ``"."`` (e.g.: ``package.module.submodule``).
+    """
+    if value.startswith(".") or value.endswith("."):
+        return False
+    return all(python_identifier(m) for m in value.split("."))
+
+
+def python_module_name(value: str) -> bool:
+    """Module name that can be used in an ``import``-statement in Python.
+    See :obj:`python_qualified_identifier`.
+    """
+    return python_qualified_identifier(value)
+
+
+def python_module_name_relaxed(value: str) -> bool:
+    """Similar to :obj:`python_module_name`, but relaxed to also accept
+    dash characters (``-``) and cover special cases like ``pip-run``.
+
+    It is recommended, however, that beginners avoid dash characters,
+    as they require advanced knowledge about Python internals.
+
+    The following are disallowed:
+
+    * names starting/ending in dashes,
+    * names ending in ``-stubs`` (potentially collide with :obj:`pep561_stub_name`).
+    """
+    if value.startswith("-") or value.endswith("-"):
+        return False
+    if value.endswith("-stubs"):
+        return False  # Avoid collision with PEP 561
+    return python_module_name(value.replace("-", "_"))
+
+
+def python_entrypoint_group(value: str) -> bool:
+    """See ``Data model > group`` in the :ref:`PyPA's entry-points specification
+    `.
+    """
+    return ENTRYPOINT_GROUP_REGEX.match(value) is not None
+
+
+def python_entrypoint_name(value: str) -> bool:
+    """See ``Data model > name`` in the :ref:`PyPA's entry-points specification
+    `.
+    """
+    if not ENTRYPOINT_REGEX.match(value):
+        return False
+    if not RECOMMEDED_ENTRYPOINT_REGEX.match(value):
+        msg = f"Entry point `{value}` does not follow recommended pattern: "
+        msg += RECOMMEDED_ENTRYPOINT_PATTERN
+        _logger.warning(msg)
+    return True
+
+
+def python_entrypoint_reference(value: str) -> bool:
+    """Reference to a Python object using in the format::
+
+        importable.module:object.attr
+
+    See ``Data model >object reference`` in the :ref:`PyPA's entry-points specification
+    `.
+    """
+    module, _, rest = value.partition(":")
+    if "[" in rest:
+        obj, _, extras_ = rest.partition("[")
+        if extras_.strip()[-1] != "]":
+            return False
+        extras = (x.strip() for x in extras_.strip(string.whitespace + "[]").split(","))
+        if not all(pep508_identifier(e) for e in extras):
+            return False
+        _logger.warning(f"`{value}` - using extras for entry points is not recommended")
+    else:
+        obj = rest
+
+    module_parts = module.split(".")
+    identifiers = _chain(module_parts, obj.split(".")) if rest else iter(module_parts)
+    return all(python_identifier(i.strip()) for i in identifiers)
+
+
+def uint8(value: builtins.int) -> bool:
+    r"""Unsigned 8-bit integer (:math:`0 \leq x < 2^8`)"""
+    return 0 <= value < 2**8
+
+
+def uint16(value: builtins.int) -> bool:
+    r"""Unsigned 16-bit integer (:math:`0 \leq x < 2^{16}`)"""
+    return 0 <= value < 2**16
+
+
+def uint(value: builtins.int) -> bool:
+    r"""Unsigned 64-bit integer (:math:`0 \leq x < 2^{64}`)"""
+    return 0 <= value < 2**64
+
+
+def int(value: builtins.int) -> bool:
+    r"""Signed 64-bit integer (:math:`-2^{63} \leq x < 2^{63}`)"""
+    return -(2**63) <= value < 2**63
+
+
+try:
+    from packaging import licenses as _licenses
+
+    def SPDX(value: str) -> bool:
+        """See :ref:`PyPA's License-Expression specification
+        ` (added in :pep:`639`).
+        """
+        try:
+            _licenses.canonicalize_license_expression(value)
+            return True
+        except _licenses.InvalidLicenseExpression:
+            return False
+
+except ImportError:  # pragma: no cover
+    _logger.warning(
+        "Could not find an up-to-date installation of `packaging`. "
+        "License expressions might not be validated. "
+        "To enforce validation, please install `packaging>=24.2`."
+    )
+
+    def SPDX(value: str) -> bool:
+        return True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/distutils.schema.json b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/distutils.schema.json
new file mode 100644
index 0000000000000000000000000000000000000000..93cd2e868acdaf41bf8b1f77026e84c02a5af3f8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/distutils.schema.json
@@ -0,0 +1,26 @@
+{
+  "$schema": "http://json-schema.org/draft-07/schema#",
+
+  "$id": "https://setuptools.pypa.io/en/latest/deprecated/distutils/configfile.html",
+  "title": "``tool.distutils`` table",
+  "$$description": [
+    "**EXPERIMENTAL** (NOT OFFICIALLY SUPPORTED): Use ``tool.distutils``",
+    "subtables to configure arguments for ``distutils`` commands.",
+    "Originally, ``distutils`` allowed developers to configure arguments for",
+    "``setup.py`` commands via `distutils configuration files",
+    "`_.",
+    "See also `the old Python docs _`."
+  ],
+
+  "type": "object",
+  "properties": {
+    "global": {
+      "type": "object",
+      "description": "Global options applied to all ``distutils`` commands"
+    }
+  },
+  "patternProperties": {
+    ".+": {"type": "object"}
+  },
+  "$comment": "TODO: Is there a practical way of making this schema more specific?"
+}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/expand.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/expand.py
new file mode 100644
index 0000000000000000000000000000000000000000..531f965013031a8c5159c8b8505c38cfb0a4302f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/expand.py
@@ -0,0 +1,452 @@
+"""Utility functions to expand configuration directives or special values
+(such glob patterns).
+
+We can split the process of interpreting configuration files into 2 steps:
+
+1. The parsing the file contents from strings to value objects
+   that can be understand by Python (for example a string with a comma
+   separated list of keywords into an actual Python list of strings).
+
+2. The expansion (or post-processing) of these values according to the
+   semantics ``setuptools`` assign to them (for example a configuration field
+   with the ``file:`` directive should be expanded from a list of file paths to
+   a single string with the contents of those files concatenated)
+
+This module focus on the second step, and therefore allow sharing the expansion
+functions among several configuration file formats.
+
+**PRIVATE MODULE**: API reserved for setuptools internal usage only.
+"""
+
+from __future__ import annotations
+
+import ast
+import importlib
+import os
+import pathlib
+import sys
+from collections.abc import Iterable, Iterator, Mapping
+from configparser import ConfigParser
+from glob import iglob
+from importlib.machinery import ModuleSpec, all_suffixes
+from itertools import chain
+from pathlib import Path
+from types import ModuleType, TracebackType
+from typing import TYPE_CHECKING, Any, Callable, TypeVar
+
+from .. import _static
+from .._path import StrPath, same_path as _same_path
+from ..discovery import find_package_path
+from ..warnings import SetuptoolsWarning
+
+from distutils.errors import DistutilsOptionError
+
+if TYPE_CHECKING:
+    from typing_extensions import Self
+
+    from setuptools.dist import Distribution
+
+_K = TypeVar("_K")
+_V_co = TypeVar("_V_co", covariant=True)
+
+
+class StaticModule:
+    """Proxy to a module object that avoids executing arbitrary code."""
+
+    def __init__(self, name: str, spec: ModuleSpec) -> None:
+        module = ast.parse(pathlib.Path(spec.origin).read_bytes())  # type: ignore[arg-type] # Let it raise an error on None
+        vars(self).update(locals())
+        del self.self
+
+    def _find_assignments(self) -> Iterator[tuple[ast.AST, ast.AST]]:
+        for statement in self.module.body:
+            if isinstance(statement, ast.Assign):
+                yield from ((target, statement.value) for target in statement.targets)
+            elif isinstance(statement, ast.AnnAssign) and statement.value:
+                yield (statement.target, statement.value)
+
+    def __getattr__(self, attr: str):
+        """Attempt to load an attribute "statically", via :func:`ast.literal_eval`."""
+        try:
+            return next(
+                ast.literal_eval(value)
+                for target, value in self._find_assignments()
+                if isinstance(target, ast.Name) and target.id == attr
+            )
+        except Exception as e:
+            raise AttributeError(f"{self.name} has no attribute {attr}") from e
+
+
+def glob_relative(
+    patterns: Iterable[str], root_dir: StrPath | None = None
+) -> list[str]:
+    """Expand the list of glob patterns, but preserving relative paths.
+
+    :param list[str] patterns: List of glob patterns
+    :param str root_dir: Path to which globs should be relative
+                         (current directory by default)
+    :rtype: list
+    """
+    glob_characters = {'*', '?', '[', ']', '{', '}'}
+    expanded_values = []
+    root_dir = root_dir or os.getcwd()
+    for value in patterns:
+        # Has globby characters?
+        if any(char in value for char in glob_characters):
+            # then expand the glob pattern while keeping paths *relative*:
+            glob_path = os.path.abspath(os.path.join(root_dir, value))
+            expanded_values.extend(
+                sorted(
+                    os.path.relpath(path, root_dir).replace(os.sep, "/")
+                    for path in iglob(glob_path, recursive=True)
+                )
+            )
+
+        else:
+            # take the value as-is
+            path = os.path.relpath(value, root_dir).replace(os.sep, "/")
+            expanded_values.append(path)
+
+    return expanded_values
+
+
+def read_files(
+    filepaths: StrPath | Iterable[StrPath], root_dir: StrPath | None = None
+) -> str:
+    """Return the content of the files concatenated using ``\n`` as str
+
+    This function is sandboxed and won't reach anything outside ``root_dir``
+
+    (By default ``root_dir`` is the current directory).
+    """
+    from more_itertools import always_iterable
+
+    root_dir = os.path.abspath(root_dir or os.getcwd())
+    _filepaths = (os.path.join(root_dir, path) for path in always_iterable(filepaths))
+    return '\n'.join(
+        _read_file(path)
+        for path in _filter_existing_files(_filepaths)
+        if _assert_local(path, root_dir)
+    )
+
+
+def _filter_existing_files(filepaths: Iterable[StrPath]) -> Iterator[StrPath]:
+    for path in filepaths:
+        if os.path.isfile(path):
+            yield path
+        else:
+            SetuptoolsWarning.emit(f"File {path!r} cannot be found")
+
+
+def _read_file(filepath: bytes | StrPath) -> str:
+    with open(filepath, encoding='utf-8') as f:
+        return f.read()
+
+
+def _assert_local(filepath: StrPath, root_dir: str):
+    if Path(os.path.abspath(root_dir)) not in Path(os.path.abspath(filepath)).parents:
+        msg = f"Cannot access {filepath!r} (or anything outside {root_dir!r})"
+        raise DistutilsOptionError(msg)
+
+    return True
+
+
+def read_attr(
+    attr_desc: str,
+    package_dir: Mapping[str, str] | None = None,
+    root_dir: StrPath | None = None,
+) -> Any:
+    """Reads the value of an attribute from a module.
+
+    This function will try to read the attributed statically first
+    (via :func:`ast.literal_eval`), and only evaluate the module if it fails.
+
+    Examples:
+        read_attr("package.attr")
+        read_attr("package.module.attr")
+
+    :param str attr_desc: Dot-separated string describing how to reach the
+        attribute (see examples above)
+    :param dict[str, str] package_dir: Mapping of package names to their
+        location in disk (represented by paths relative to ``root_dir``).
+    :param str root_dir: Path to directory containing all the packages in
+        ``package_dir`` (current directory by default).
+    :rtype: str
+    """
+    root_dir = root_dir or os.getcwd()
+    attrs_path = attr_desc.strip().split('.')
+    attr_name = attrs_path.pop()
+    module_name = '.'.join(attrs_path)
+    module_name = module_name or '__init__'
+    path = _find_module(module_name, package_dir, root_dir)
+    spec = _find_spec(module_name, path)
+
+    try:
+        value = getattr(StaticModule(module_name, spec), attr_name)
+        # XXX: Is marking as static contents coming from modules too optimistic?
+        return _static.attempt_conversion(value)
+    except Exception:
+        # fallback to evaluate module
+        module = _load_spec(spec, module_name)
+        return getattr(module, attr_name)
+
+
+def _find_spec(module_name: str, module_path: StrPath | None) -> ModuleSpec:
+    spec = importlib.util.spec_from_file_location(module_name, module_path)
+    spec = spec or importlib.util.find_spec(module_name)
+
+    if spec is None:
+        raise ModuleNotFoundError(module_name)
+
+    return spec
+
+
+def _load_spec(spec: ModuleSpec, module_name: str) -> ModuleType:
+    name = getattr(spec, "__name__", module_name)
+    if name in sys.modules:
+        return sys.modules[name]
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module  # cache (it also ensures `==` works on loaded items)
+    assert spec.loader is not None
+    spec.loader.exec_module(module)
+    return module
+
+
+def _find_module(
+    module_name: str, package_dir: Mapping[str, str] | None, root_dir: StrPath
+) -> str | None:
+    """Find the path to the module named ``module_name``,
+    considering the ``package_dir`` in the build configuration and ``root_dir``.
+
+    >>> tmp = getfixture('tmpdir')
+    >>> _ = tmp.ensure("a/b/c.py")
+    >>> _ = tmp.ensure("a/b/d/__init__.py")
+    >>> r = lambda x: x.replace(str(tmp), "tmp").replace(os.sep, "/")
+    >>> r(_find_module("a.b.c", None, tmp))
+    'tmp/a/b/c.py'
+    >>> r(_find_module("f.g.h", {"": "1", "f": "2", "f.g": "3", "f.g.h": "a/b/d"}, tmp))
+    'tmp/a/b/d/__init__.py'
+    """
+    path_start = find_package_path(module_name, package_dir or {}, root_dir)
+    candidates = chain.from_iterable(
+        (f"{path_start}{ext}", os.path.join(path_start, f"__init__{ext}"))
+        for ext in all_suffixes()
+    )
+    return next((x for x in candidates if os.path.isfile(x)), None)
+
+
+def resolve_class(
+    qualified_class_name: str,
+    package_dir: Mapping[str, str] | None = None,
+    root_dir: StrPath | None = None,
+) -> Callable:
+    """Given a qualified class name, return the associated class object"""
+    root_dir = root_dir or os.getcwd()
+    idx = qualified_class_name.rfind('.')
+    class_name = qualified_class_name[idx + 1 :]
+    pkg_name = qualified_class_name[:idx]
+
+    path = _find_module(pkg_name, package_dir, root_dir)
+    module = _load_spec(_find_spec(pkg_name, path), pkg_name)
+    return getattr(module, class_name)
+
+
+def cmdclass(
+    values: dict[str, str],
+    package_dir: Mapping[str, str] | None = None,
+    root_dir: StrPath | None = None,
+) -> dict[str, Callable]:
+    """Given a dictionary mapping command names to strings for qualified class
+    names, apply :func:`resolve_class` to the dict values.
+    """
+    return {k: resolve_class(v, package_dir, root_dir) for k, v in values.items()}
+
+
+def find_packages(
+    *,
+    namespaces=True,
+    fill_package_dir: dict[str, str] | None = None,
+    root_dir: StrPath | None = None,
+    **kwargs,
+) -> list[str]:
+    """Works similarly to :func:`setuptools.find_packages`, but with all
+    arguments given as keyword arguments. Moreover, ``where`` can be given
+    as a list (the results will be simply concatenated).
+
+    When the additional keyword argument ``namespaces`` is ``True``, it will
+    behave like :func:`setuptools.find_namespace_packages`` (i.e. include
+    implicit namespaces as per :pep:`420`).
+
+    The ``where`` argument will be considered relative to ``root_dir`` (or the current
+    working directory when ``root_dir`` is not given).
+
+    If the ``fill_package_dir`` argument is passed, this function will consider it as a
+    similar data structure to the ``package_dir`` configuration parameter add fill-in
+    any missing package location.
+
+    :rtype: list
+    """
+    from more_itertools import always_iterable, unique_everseen
+
+    from setuptools.discovery import construct_package_dir
+
+    # check "not namespaces" first due to python/mypy#6232
+    if not namespaces:
+        from setuptools.discovery import PackageFinder
+    else:
+        from setuptools.discovery import PEP420PackageFinder as PackageFinder
+
+    root_dir = root_dir or os.curdir
+    where = kwargs.pop('where', ['.'])
+    packages: list[str] = []
+    fill_package_dir = {} if fill_package_dir is None else fill_package_dir
+    search = list(unique_everseen(always_iterable(where)))
+
+    if len(search) == 1 and all(not _same_path(search[0], x) for x in (".", root_dir)):
+        fill_package_dir.setdefault("", search[0])
+
+    for path in search:
+        package_path = _nest_path(root_dir, path)
+        pkgs = PackageFinder.find(package_path, **kwargs)
+        packages.extend(pkgs)
+        if pkgs and not (
+            fill_package_dir.get("") == path or os.path.samefile(package_path, root_dir)
+        ):
+            fill_package_dir.update(construct_package_dir(pkgs, path))
+
+    return packages
+
+
+def _nest_path(parent: StrPath, path: StrPath) -> str:
+    path = parent if path in {".", ""} else os.path.join(parent, path)
+    return os.path.normpath(path)
+
+
+def version(value: Callable | Iterable[str | int] | str) -> str:
+    """When getting the version directly from an attribute,
+    it should be normalised to string.
+    """
+    _value = value() if callable(value) else value
+
+    if isinstance(_value, str):
+        return _value
+    if hasattr(_value, '__iter__'):
+        return '.'.join(map(str, _value))
+    return f'{_value}'
+
+
+def canonic_package_data(package_data: dict) -> dict:
+    if "*" in package_data:
+        package_data[""] = package_data.pop("*")
+    return package_data
+
+
+def canonic_data_files(
+    data_files: list | dict, root_dir: StrPath | None = None
+) -> list[tuple[str, list[str]]]:
+    """For compatibility with ``setup.py``, ``data_files`` should be a list
+    of pairs instead of a dict.
+
+    This function also expands glob patterns.
+    """
+    if isinstance(data_files, list):
+        return data_files
+
+    return [
+        (dest, glob_relative(patterns, root_dir))
+        for dest, patterns in data_files.items()
+    ]
+
+
+def entry_points(
+    text: str, text_source: str = "entry-points"
+) -> dict[str, dict[str, str]]:
+    """Given the contents of entry-points file,
+    process it into a 2-level dictionary (``dict[str, dict[str, str]]``).
+    The first level keys are entry-point groups, the second level keys are
+    entry-point names, and the second level values are references to objects
+    (that correspond to the entry-point value).
+    """
+    # Using undocumented behaviour, see python/typeshed#12700
+    parser = ConfigParser(default_section=None, delimiters=("=",))  # type: ignore[call-overload]
+    parser.optionxform = str  # case sensitive
+    parser.read_string(text, text_source)
+    groups = {k: dict(v.items()) for k, v in parser.items()}
+    groups.pop(parser.default_section, None)
+    return groups
+
+
+class EnsurePackagesDiscovered:
+    """Some expand functions require all the packages to already be discovered before
+    they run, e.g. :func:`read_attr`, :func:`resolve_class`, :func:`cmdclass`.
+
+    Therefore in some cases we will need to run autodiscovery during the evaluation of
+    the configuration. However, it is better to postpone calling package discovery as
+    much as possible, because some parameters can influence it (e.g. ``package_dir``),
+    and those might not have been processed yet.
+    """
+
+    def __init__(self, distribution: Distribution) -> None:
+        self._dist = distribution
+        self._called = False
+
+    def __call__(self):
+        """Trigger the automatic package discovery, if it is still necessary."""
+        if not self._called:
+            self._called = True
+            self._dist.set_defaults(name=False)  # Skip name, we can still be parsing
+
+    def __enter__(self) -> Self:
+        return self
+
+    def __exit__(
+        self,
+        exc_type: type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
+    ):
+        if self._called:
+            self._dist.set_defaults.analyse_name()  # Now we can set a default name
+
+    def _get_package_dir(self) -> Mapping[str, str]:
+        self()
+        pkg_dir = self._dist.package_dir
+        return {} if pkg_dir is None else pkg_dir
+
+    @property
+    def package_dir(self) -> Mapping[str, str]:
+        """Proxy to ``package_dir`` that may trigger auto-discovery when used."""
+        return LazyMappingProxy(self._get_package_dir)
+
+
+class LazyMappingProxy(Mapping[_K, _V_co]):
+    """Mapping proxy that delays resolving the target object, until really needed.
+
+    >>> def obtain_mapping():
+    ...     print("Running expensive function!")
+    ...     return {"key": "value", "other key": "other value"}
+    >>> mapping = LazyMappingProxy(obtain_mapping)
+    >>> mapping["key"]
+    Running expensive function!
+    'value'
+    >>> mapping["other key"]
+    'other value'
+    """
+
+    def __init__(self, obtain_mapping_value: Callable[[], Mapping[_K, _V_co]]) -> None:
+        self._obtain = obtain_mapping_value
+        self._value: Mapping[_K, _V_co] | None = None
+
+    def _target(self) -> Mapping[_K, _V_co]:
+        if self._value is None:
+            self._value = self._obtain()
+        return self._value
+
+    def __getitem__(self, key: _K) -> _V_co:
+        return self._target()[key]
+
+    def __len__(self) -> int:
+        return len(self._target())
+
+    def __iter__(self) -> Iterator[_K]:
+        return iter(self._target())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/pyprojecttoml.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/pyprojecttoml.py
new file mode 100644
index 0000000000000000000000000000000000000000..fd6c5968c820435a0a8a82ecfacbe94abd7e8d3d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/pyprojecttoml.py
@@ -0,0 +1,468 @@
+"""
+Load setuptools configuration from ``pyproject.toml`` files.
+
+**PRIVATE MODULE**: API reserved for setuptools internal usage only.
+
+To read project metadata, consider using
+``build.util.project_wheel_metadata`` (https://pypi.org/project/build/).
+For simple scenarios, you can also try parsing the file directly
+with the help of ``tomllib`` or ``tomli``.
+"""
+
+from __future__ import annotations
+
+import logging
+import os
+from collections.abc import Mapping
+from contextlib import contextmanager
+from functools import partial
+from types import TracebackType
+from typing import TYPE_CHECKING, Any, Callable
+
+from .._path import StrPath
+from ..errors import FileError, InvalidConfigError
+from ..warnings import SetuptoolsWarning
+from . import expand as _expand
+from ._apply_pyprojecttoml import _PREVIOUSLY_DEFINED, _MissingDynamic, apply as _apply
+
+if TYPE_CHECKING:
+    from typing_extensions import Self
+
+    from setuptools.dist import Distribution
+
+_logger = logging.getLogger(__name__)
+
+
+def load_file(filepath: StrPath) -> dict:
+    from ..compat.py310 import tomllib
+
+    with open(filepath, "rb") as file:
+        return tomllib.load(file)
+
+
+def validate(config: dict, filepath: StrPath) -> bool:
+    from . import _validate_pyproject as validator
+
+    trove_classifier = validator.FORMAT_FUNCTIONS.get("trove-classifier")
+    if hasattr(trove_classifier, "_disable_download"):
+        # Improve reproducibility by default. See abravalheri/validate-pyproject#31
+        trove_classifier._disable_download()  # type: ignore[union-attr]
+
+    try:
+        return validator.validate(config)
+    except validator.ValidationError as ex:
+        summary = f"configuration error: {ex.summary}"
+        if ex.name.strip("`") != "project":
+            # Probably it is just a field missing/misnamed, not worthy the verbosity...
+            _logger.debug(summary)
+            _logger.debug(ex.details)
+
+        error = f"invalid pyproject.toml config: {ex.name}."
+        raise ValueError(f"{error}\n{summary}") from None
+
+
+def apply_configuration(
+    dist: Distribution,
+    filepath: StrPath,
+    ignore_option_errors: bool = False,
+) -> Distribution:
+    """Apply the configuration from a ``pyproject.toml`` file into an existing
+    distribution object.
+    """
+    config = read_configuration(filepath, True, ignore_option_errors, dist)
+    return _apply(dist, config, filepath)
+
+
+def read_configuration(
+    filepath: StrPath,
+    expand: bool = True,
+    ignore_option_errors: bool = False,
+    dist: Distribution | None = None,
+) -> dict[str, Any]:
+    """Read given configuration file and returns options from it as a dict.
+
+    :param str|unicode filepath: Path to configuration file in the ``pyproject.toml``
+        format.
+
+    :param bool expand: Whether to expand directives and other computed values
+        (i.e. post-process the given configuration)
+
+    :param bool ignore_option_errors: Whether to silently ignore
+        options, values of which could not be resolved (e.g. due to exceptions
+        in directives such as file:, attr:, etc.).
+        If False exceptions are propagated as expected.
+
+    :param Distribution|None: Distribution object to which the configuration refers.
+        If not given a dummy object will be created and discarded after the
+        configuration is read. This is used for auto-discovery of packages and in the
+        case a dynamic configuration (e.g. ``attr`` or ``cmdclass``) is expanded.
+        When ``expand=False`` this object is simply ignored.
+
+    :rtype: dict
+    """
+    filepath = os.path.abspath(filepath)
+
+    if not os.path.isfile(filepath):
+        raise FileError(f"Configuration file {filepath!r} does not exist.")
+
+    asdict = load_file(filepath) or {}
+    project_table = asdict.get("project", {})
+    tool_table = asdict.get("tool", {})
+    setuptools_table = tool_table.get("setuptools", {})
+    if not asdict or not (project_table or setuptools_table):
+        return {}  # User is not using pyproject to configure setuptools
+
+    if "setuptools" in asdict.get("tools", {}):
+        # let the user know they probably have a typo in their metadata
+        _ToolsTypoInMetadata.emit()
+
+    if "distutils" in tool_table:
+        _ExperimentalConfiguration.emit(subject="[tool.distutils]")
+
+    # There is an overall sense in the community that making include_package_data=True
+    # the default would be an improvement.
+    # `ini2toml` backfills include_package_data=False when nothing is explicitly given,
+    # therefore setting a default here is backwards compatible.
+    if dist and dist.include_package_data is not None:
+        setuptools_table.setdefault("include-package-data", dist.include_package_data)
+    else:
+        setuptools_table.setdefault("include-package-data", True)
+    # Persist changes:
+    asdict["tool"] = tool_table
+    tool_table["setuptools"] = setuptools_table
+
+    if "ext-modules" in setuptools_table:
+        _ExperimentalConfiguration.emit(subject="[tool.setuptools.ext-modules]")
+
+    with _ignore_errors(ignore_option_errors):
+        # Don't complain about unrelated errors (e.g. tools not using the "tool" table)
+        subset = {"project": project_table, "tool": {"setuptools": setuptools_table}}
+        validate(subset, filepath)
+
+    if expand:
+        root_dir = os.path.dirname(filepath)
+        return expand_configuration(asdict, root_dir, ignore_option_errors, dist)
+
+    return asdict
+
+
+def expand_configuration(
+    config: dict,
+    root_dir: StrPath | None = None,
+    ignore_option_errors: bool = False,
+    dist: Distribution | None = None,
+) -> dict:
+    """Given a configuration with unresolved fields (e.g. dynamic, cmdclass, ...)
+    find their final values.
+
+    :param dict config: Dict containing the configuration for the distribution
+    :param str root_dir: Top-level directory for the distribution/project
+        (the same directory where ``pyproject.toml`` is place)
+    :param bool ignore_option_errors: see :func:`read_configuration`
+    :param Distribution|None: Distribution object to which the configuration refers.
+        If not given a dummy object will be created and discarded after the
+        configuration is read. Used in the case a dynamic configuration
+        (e.g. ``attr`` or ``cmdclass``).
+
+    :rtype: dict
+    """
+    return _ConfigExpander(config, root_dir, ignore_option_errors, dist).expand()
+
+
+class _ConfigExpander:
+    def __init__(
+        self,
+        config: dict,
+        root_dir: StrPath | None = None,
+        ignore_option_errors: bool = False,
+        dist: Distribution | None = None,
+    ) -> None:
+        self.config = config
+        self.root_dir = root_dir or os.getcwd()
+        self.project_cfg = config.get("project", {})
+        self.dynamic = self.project_cfg.get("dynamic", [])
+        self.setuptools_cfg = config.get("tool", {}).get("setuptools", {})
+        self.dynamic_cfg = self.setuptools_cfg.get("dynamic", {})
+        self.ignore_option_errors = ignore_option_errors
+        self._dist = dist
+        self._referenced_files = set[str]()
+
+    def _ensure_dist(self) -> Distribution:
+        from setuptools.dist import Distribution
+
+        attrs = {"src_root": self.root_dir, "name": self.project_cfg.get("name", None)}
+        return self._dist or Distribution(attrs)
+
+    def _process_field(self, container: dict, field: str, fn: Callable):
+        if field in container:
+            with _ignore_errors(self.ignore_option_errors):
+                container[field] = fn(container[field])
+
+    def _canonic_package_data(self, field="package-data"):
+        package_data = self.setuptools_cfg.get(field, {})
+        return _expand.canonic_package_data(package_data)
+
+    def expand(self):
+        self._expand_packages()
+        self._canonic_package_data()
+        self._canonic_package_data("exclude-package-data")
+
+        # A distribution object is required for discovering the correct package_dir
+        dist = self._ensure_dist()
+        ctx = _EnsurePackagesDiscovered(dist, self.project_cfg, self.setuptools_cfg)
+        with ctx as ensure_discovered:
+            package_dir = ensure_discovered.package_dir
+            self._expand_data_files()
+            self._expand_cmdclass(package_dir)
+            self._expand_all_dynamic(dist, package_dir)
+
+        dist._referenced_files.update(self._referenced_files)
+        return self.config
+
+    def _expand_packages(self):
+        packages = self.setuptools_cfg.get("packages")
+        if packages is None or isinstance(packages, (list, tuple)):
+            return
+
+        find = packages.get("find")
+        if isinstance(find, dict):
+            find["root_dir"] = self.root_dir
+            find["fill_package_dir"] = self.setuptools_cfg.setdefault("package-dir", {})
+            with _ignore_errors(self.ignore_option_errors):
+                self.setuptools_cfg["packages"] = _expand.find_packages(**find)
+
+    def _expand_data_files(self):
+        data_files = partial(_expand.canonic_data_files, root_dir=self.root_dir)
+        self._process_field(self.setuptools_cfg, "data-files", data_files)
+
+    def _expand_cmdclass(self, package_dir: Mapping[str, str]):
+        root_dir = self.root_dir
+        cmdclass = partial(_expand.cmdclass, package_dir=package_dir, root_dir=root_dir)
+        self._process_field(self.setuptools_cfg, "cmdclass", cmdclass)
+
+    def _expand_all_dynamic(self, dist: Distribution, package_dir: Mapping[str, str]):
+        special = (  # need special handling
+            "version",
+            "readme",
+            "entry-points",
+            "scripts",
+            "gui-scripts",
+            "classifiers",
+            "dependencies",
+            "optional-dependencies",
+        )
+        # `_obtain` functions are assumed to raise appropriate exceptions/warnings.
+        obtained_dynamic = {
+            field: self._obtain(dist, field, package_dir)
+            for field in self.dynamic
+            if field not in special
+        }
+        obtained_dynamic.update(
+            self._obtain_entry_points(dist, package_dir) or {},
+            version=self._obtain_version(dist, package_dir),
+            readme=self._obtain_readme(dist),
+            classifiers=self._obtain_classifiers(dist),
+            dependencies=self._obtain_dependencies(dist),
+            optional_dependencies=self._obtain_optional_dependencies(dist),
+        )
+        # `None` indicates there is nothing in `tool.setuptools.dynamic` but the value
+        # might have already been set by setup.py/extensions, so avoid overwriting.
+        updates = {k: v for k, v in obtained_dynamic.items() if v is not None}
+        self.project_cfg.update(updates)
+
+    def _ensure_previously_set(self, dist: Distribution, field: str):
+        previous = _PREVIOUSLY_DEFINED[field](dist)
+        if previous is None and not self.ignore_option_errors:
+            msg = (
+                f"No configuration found for dynamic {field!r}.\n"
+                "Some dynamic fields need to be specified via `tool.setuptools.dynamic`"
+                "\nothers must be specified via the equivalent attribute in `setup.py`."
+            )
+            raise InvalidConfigError(msg)
+
+    def _expand_directive(
+        self, specifier: str, directive, package_dir: Mapping[str, str]
+    ):
+        from more_itertools import always_iterable
+
+        with _ignore_errors(self.ignore_option_errors):
+            root_dir = self.root_dir
+            if "file" in directive:
+                self._referenced_files.update(always_iterable(directive["file"]))
+                return _expand.read_files(directive["file"], root_dir)
+            if "attr" in directive:
+                return _expand.read_attr(directive["attr"], package_dir, root_dir)
+            raise ValueError(f"invalid `{specifier}`: {directive!r}")
+        return None
+
+    def _obtain(self, dist: Distribution, field: str, package_dir: Mapping[str, str]):
+        if field in self.dynamic_cfg:
+            return self._expand_directive(
+                f"tool.setuptools.dynamic.{field}",
+                self.dynamic_cfg[field],
+                package_dir,
+            )
+        self._ensure_previously_set(dist, field)
+        return None
+
+    def _obtain_version(self, dist: Distribution, package_dir: Mapping[str, str]):
+        # Since plugins can set version, let's silently skip if it cannot be obtained
+        if "version" in self.dynamic and "version" in self.dynamic_cfg:
+            return _expand.version(
+                # We already do an early check for the presence of "version"
+                self._obtain(dist, "version", package_dir)  # pyright: ignore[reportArgumentType]
+            )
+        return None
+
+    def _obtain_readme(self, dist: Distribution) -> dict[str, str] | None:
+        if "readme" not in self.dynamic:
+            return None
+
+        dynamic_cfg = self.dynamic_cfg
+        if "readme" in dynamic_cfg:
+            return {
+                # We already do an early check for the presence of "readme"
+                "text": self._obtain(dist, "readme", {}),
+                "content-type": dynamic_cfg["readme"].get("content-type", "text/x-rst"),
+            }  # pyright: ignore[reportReturnType]
+
+        self._ensure_previously_set(dist, "readme")
+        return None
+
+    def _obtain_entry_points(
+        self, dist: Distribution, package_dir: Mapping[str, str]
+    ) -> dict[str, dict[str, Any]] | None:
+        fields = ("entry-points", "scripts", "gui-scripts")
+        if not any(field in self.dynamic for field in fields):
+            return None
+
+        text = self._obtain(dist, "entry-points", package_dir)
+        if text is None:
+            return None
+
+        groups = _expand.entry_points(text)
+        # Any is str | dict[str, str], but causes variance issues
+        expanded: dict[str, dict[str, Any]] = {"entry-points": groups}
+
+        def _set_scripts(field: str, group: str):
+            if group in groups:
+                value = groups.pop(group)
+                if field not in self.dynamic:
+                    raise InvalidConfigError(_MissingDynamic.details(field, value))
+                expanded[field] = value
+
+        _set_scripts("scripts", "console_scripts")
+        _set_scripts("gui-scripts", "gui_scripts")
+
+        return expanded
+
+    def _obtain_classifiers(self, dist: Distribution):
+        if "classifiers" in self.dynamic:
+            value = self._obtain(dist, "classifiers", {})
+            if value:
+                return value.splitlines()
+        return None
+
+    def _obtain_dependencies(self, dist: Distribution):
+        if "dependencies" in self.dynamic:
+            value = self._obtain(dist, "dependencies", {})
+            if value:
+                return _parse_requirements_list(value)
+        return None
+
+    def _obtain_optional_dependencies(self, dist: Distribution):
+        if "optional-dependencies" not in self.dynamic:
+            return None
+        if "optional-dependencies" in self.dynamic_cfg:
+            optional_dependencies_map = self.dynamic_cfg["optional-dependencies"]
+            assert isinstance(optional_dependencies_map, dict)
+            return {
+                group: _parse_requirements_list(
+                    self._expand_directive(
+                        f"tool.setuptools.dynamic.optional-dependencies.{group}",
+                        directive,
+                        {},
+                    )
+                )
+                for group, directive in optional_dependencies_map.items()
+            }
+        self._ensure_previously_set(dist, "optional-dependencies")
+        return None
+
+
+def _parse_requirements_list(value):
+    return [
+        line
+        for line in value.splitlines()
+        if line.strip() and not line.strip().startswith("#")
+    ]
+
+
+@contextmanager
+def _ignore_errors(ignore_option_errors: bool):
+    if not ignore_option_errors:
+        yield
+        return
+
+    try:
+        yield
+    except Exception as ex:
+        _logger.debug(f"ignored error: {ex.__class__.__name__} - {ex}")
+
+
+class _EnsurePackagesDiscovered(_expand.EnsurePackagesDiscovered):
+    def __init__(
+        self, distribution: Distribution, project_cfg: dict, setuptools_cfg: dict
+    ) -> None:
+        super().__init__(distribution)
+        self._project_cfg = project_cfg
+        self._setuptools_cfg = setuptools_cfg
+
+    def __enter__(self) -> Self:
+        """When entering the context, the values of ``packages``, ``py_modules`` and
+        ``package_dir`` that are missing in ``dist`` are copied from ``setuptools_cfg``.
+        """
+        dist, cfg = self._dist, self._setuptools_cfg
+        package_dir: dict[str, str] = cfg.setdefault("package-dir", {})
+        package_dir.update(dist.package_dir or {})
+        dist.package_dir = package_dir  # needs to be the same object
+
+        dist.set_defaults._ignore_ext_modules()  # pyproject.toml-specific behaviour
+
+        # Set `name`, `py_modules` and `packages` in dist to short-circuit
+        # auto-discovery, but avoid overwriting empty lists purposefully set by users.
+        if dist.metadata.name is None:
+            dist.metadata.name = self._project_cfg.get("name")
+        if dist.py_modules is None:
+            dist.py_modules = cfg.get("py-modules")
+        if dist.packages is None:
+            dist.packages = cfg.get("packages")
+
+        return super().__enter__()
+
+    def __exit__(
+        self,
+        exc_type: type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
+    ) -> None:
+        """When exiting the context, if values of ``packages``, ``py_modules`` and
+        ``package_dir`` are missing in ``setuptools_cfg``, copy from ``dist``.
+        """
+        # If anything was discovered set them back, so they count in the final config.
+        self._setuptools_cfg.setdefault("packages", self._dist.packages)
+        self._setuptools_cfg.setdefault("py-modules", self._dist.py_modules)
+        return super().__exit__(exc_type, exc_value, traceback)
+
+
+class _ExperimentalConfiguration(SetuptoolsWarning):
+    _SUMMARY = (
+        "`{subject}` in `pyproject.toml` is still *experimental* "
+        "and likely to change in future releases."
+    )
+
+
+class _ToolsTypoInMetadata(SetuptoolsWarning):
+    _SUMMARY = (
+        "Ignoring [tools.setuptools] in pyproject.toml, did you mean [tool.setuptools]?"
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/setupcfg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/setupcfg.py
new file mode 100644
index 0000000000000000000000000000000000000000..633aa9d45d086dd0290a2c38bee632ed7f9a63a4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/setupcfg.py
@@ -0,0 +1,780 @@
+"""
+Load setuptools configuration from ``setup.cfg`` files.
+
+**API will be made private in the future**
+
+To read project metadata, consider using
+``build.util.project_wheel_metadata`` (https://pypi.org/project/build/).
+For simple scenarios, you can also try parsing the file directly
+with the help of ``configparser``.
+"""
+
+from __future__ import annotations
+
+import contextlib
+import functools
+import os
+from collections import defaultdict
+from collections.abc import Iterable, Iterator
+from functools import partial, wraps
+from typing import TYPE_CHECKING, Any, Callable, ClassVar, Generic, TypeVar, cast
+
+from packaging.markers import default_environment as marker_env
+from packaging.requirements import InvalidRequirement, Requirement
+from packaging.version import InvalidVersion, Version
+
+from .. import _static
+from .._path import StrPath
+from ..errors import FileError, OptionError
+from ..warnings import SetuptoolsDeprecationWarning
+from . import expand
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeAlias
+
+    from setuptools.dist import Distribution
+
+    from distutils.dist import DistributionMetadata
+
+SingleCommandOptions: TypeAlias = dict[str, tuple[str, Any]]
+"""Dict that associate the name of the options of a particular command to a
+tuple. The first element of the tuple indicates the origin of the option value
+(e.g. the name of the configuration file where it was read from),
+while the second element of the tuple is the option value itself
+"""
+AllCommandOptions: TypeAlias = dict[str, SingleCommandOptions]
+"""cmd name => its options"""
+Target = TypeVar("Target", "Distribution", "DistributionMetadata")
+
+
+def read_configuration(
+    filepath: StrPath, find_others: bool = False, ignore_option_errors: bool = False
+) -> dict:
+    """Read given configuration file and returns options from it as a dict.
+
+    :param str|unicode filepath: Path to configuration file
+        to get options from.
+
+    :param bool find_others: Whether to search for other configuration files
+        which could be on in various places.
+
+    :param bool ignore_option_errors: Whether to silently ignore
+        options, values of which could not be resolved (e.g. due to exceptions
+        in directives such as file:, attr:, etc.).
+        If False exceptions are propagated as expected.
+
+    :rtype: dict
+    """
+    from setuptools.dist import Distribution
+
+    dist = Distribution()
+    filenames = dist.find_config_files() if find_others else []
+    handlers = _apply(dist, filepath, filenames, ignore_option_errors)
+    return configuration_to_dict(handlers)
+
+
+def apply_configuration(dist: Distribution, filepath: StrPath) -> Distribution:
+    """Apply the configuration from a ``setup.cfg`` file into an existing
+    distribution object.
+    """
+    _apply(dist, filepath)
+    dist._finalize_requires()
+    return dist
+
+
+def _apply(
+    dist: Distribution,
+    filepath: StrPath,
+    other_files: Iterable[StrPath] = (),
+    ignore_option_errors: bool = False,
+) -> tuple[ConfigMetadataHandler, ConfigOptionsHandler]:
+    """Read configuration from ``filepath`` and applies to the ``dist`` object."""
+    from setuptools.dist import _Distribution
+
+    filepath = os.path.abspath(filepath)
+
+    if not os.path.isfile(filepath):
+        raise FileError(f'Configuration file {filepath} does not exist.')
+
+    current_directory = os.getcwd()
+    os.chdir(os.path.dirname(filepath))
+    filenames = [*other_files, filepath]
+
+    try:
+        # TODO: Temporary cast until mypy 1.12 is released with upstream fixes from typeshed
+        _Distribution.parse_config_files(dist, filenames=cast(list[str], filenames))
+        handlers = parse_configuration(
+            dist, dist.command_options, ignore_option_errors=ignore_option_errors
+        )
+        dist._finalize_license_files()
+    finally:
+        os.chdir(current_directory)
+
+    return handlers
+
+
+def _get_option(target_obj: Distribution | DistributionMetadata, key: str):
+    """
+    Given a target object and option key, get that option from
+    the target object, either through a get_{key} method or
+    from an attribute directly.
+    """
+    getter_name = f'get_{key}'
+    by_attribute = functools.partial(getattr, target_obj, key)
+    getter = getattr(target_obj, getter_name, by_attribute)
+    return getter()
+
+
+def configuration_to_dict(
+    handlers: Iterable[
+        ConfigHandler[Distribution] | ConfigHandler[DistributionMetadata]
+    ],
+) -> dict:
+    """Returns configuration data gathered by given handlers as a dict.
+
+    :param Iterable[ConfigHandler] handlers: Handlers list,
+        usually from parse_configuration()
+
+    :rtype: dict
+    """
+    config_dict: dict = defaultdict(dict)
+
+    for handler in handlers:
+        for option in handler.set_options:
+            value = _get_option(handler.target_obj, option)
+            config_dict[handler.section_prefix][option] = value
+
+    return config_dict
+
+
+def parse_configuration(
+    distribution: Distribution,
+    command_options: AllCommandOptions,
+    ignore_option_errors: bool = False,
+) -> tuple[ConfigMetadataHandler, ConfigOptionsHandler]:
+    """Performs additional parsing of configuration options
+    for a distribution.
+
+    Returns a list of used option handlers.
+
+    :param Distribution distribution:
+    :param dict command_options:
+    :param bool ignore_option_errors: Whether to silently ignore
+        options, values of which could not be resolved (e.g. due to exceptions
+        in directives such as file:, attr:, etc.).
+        If False exceptions are propagated as expected.
+    :rtype: list
+    """
+    with expand.EnsurePackagesDiscovered(distribution) as ensure_discovered:
+        options = ConfigOptionsHandler(
+            distribution,
+            command_options,
+            ignore_option_errors,
+            ensure_discovered,
+        )
+
+        options.parse()
+        if not distribution.package_dir:
+            distribution.package_dir = options.package_dir  # Filled by `find_packages`
+
+        meta = ConfigMetadataHandler(
+            distribution.metadata,
+            command_options,
+            ignore_option_errors,
+            ensure_discovered,
+            distribution.package_dir,
+            distribution.src_root,
+        )
+        meta.parse()
+        distribution._referenced_files.update(
+            options._referenced_files, meta._referenced_files
+        )
+
+    return meta, options
+
+
+def _warn_accidental_env_marker_misconfig(label: str, orig_value: str, parsed: list):
+    """Because users sometimes misinterpret this configuration:
+
+    [options.extras_require]
+    foo = bar;python_version<"4"
+
+    It looks like one requirement with an environment marker
+    but because there is no newline, it's parsed as two requirements
+    with a semicolon as separator.
+
+    Therefore, if:
+        * input string does not contain a newline AND
+        * parsed result contains two requirements AND
+        * parsing of the two parts from the result (";")
+        leads in a valid Requirement with a valid marker
+    a UserWarning is shown to inform the user about the possible problem.
+    """
+    if "\n" in orig_value or len(parsed) != 2:
+        return
+
+    markers = marker_env().keys()
+
+    try:
+        req = Requirement(parsed[1])
+        if req.name in markers:
+            _AmbiguousMarker.emit(field=label, req=parsed[1])
+    except InvalidRequirement as ex:
+        if any(parsed[1].startswith(marker) for marker in markers):
+            msg = _AmbiguousMarker.message(field=label, req=parsed[1])
+            raise InvalidRequirement(msg) from ex
+
+
+class ConfigHandler(Generic[Target]):
+    """Handles metadata supplied in configuration files."""
+
+    section_prefix: str
+    """Prefix for config sections handled by this handler.
+    Must be provided by class heirs.
+
+    """
+
+    aliases: ClassVar[dict[str, str]] = {}
+    """Options aliases.
+    For compatibility with various packages. E.g.: d2to1 and pbr.
+    Note: `-` in keys is replaced with `_` by config parser.
+
+    """
+
+    def __init__(
+        self,
+        target_obj: Target,
+        options: AllCommandOptions,
+        ignore_option_errors,
+        ensure_discovered: expand.EnsurePackagesDiscovered,
+    ) -> None:
+        self.ignore_option_errors = ignore_option_errors
+        self.target_obj: Target = target_obj
+        self.sections = dict(self._section_options(options))
+        self.set_options: list[str] = []
+        self.ensure_discovered = ensure_discovered
+        self._referenced_files = set[str]()
+        """After parsing configurations, this property will enumerate
+        all files referenced by the "file:" directive. Private API for setuptools only.
+        """
+
+    @classmethod
+    def _section_options(
+        cls, options: AllCommandOptions
+    ) -> Iterator[tuple[str, SingleCommandOptions]]:
+        for full_name, value in options.items():
+            pre, _sep, name = full_name.partition(cls.section_prefix)
+            if pre:
+                continue
+            yield name.lstrip('.'), value
+
+    @property
+    def parsers(self):
+        """Metadata item name to parser function mapping."""
+        raise NotImplementedError(
+            f'{self.__class__.__name__} must provide .parsers property'
+        )
+
+    def __setitem__(self, option_name, value) -> None:
+        target_obj = self.target_obj
+
+        # Translate alias into real name.
+        option_name = self.aliases.get(option_name, option_name)
+
+        try:
+            current_value = getattr(target_obj, option_name)
+        except AttributeError as e:
+            raise KeyError(option_name) from e
+
+        if current_value:
+            # Already inhabited. Skipping.
+            return
+
+        try:
+            parsed = self.parsers.get(option_name, lambda x: x)(value)
+        except (Exception,) * self.ignore_option_errors:
+            return
+
+        simple_setter = functools.partial(target_obj.__setattr__, option_name)
+        setter = getattr(target_obj, f"set_{option_name}", simple_setter)
+        setter(parsed)
+
+        self.set_options.append(option_name)
+
+    @classmethod
+    def _parse_list(cls, value, separator=','):
+        """Represents value as a list.
+
+        Value is split either by separator (defaults to comma) or by lines.
+
+        :param value:
+        :param separator: List items separator character.
+        :rtype: list
+        """
+        if isinstance(value, list):  # _get_parser_compound case
+            return value
+
+        if '\n' in value:
+            value = value.splitlines()
+        else:
+            value = value.split(separator)
+
+        return [chunk.strip() for chunk in value if chunk.strip()]
+
+    @classmethod
+    def _parse_dict(cls, value):
+        """Represents value as a dict.
+
+        :param value:
+        :rtype: dict
+        """
+        separator = '='
+        result = {}
+        for line in cls._parse_list(value):
+            key, sep, val = line.partition(separator)
+            if sep != separator:
+                raise OptionError(f"Unable to parse option value to dict: {value}")
+            result[key.strip()] = val.strip()
+
+        return result
+
+    @classmethod
+    def _parse_bool(cls, value):
+        """Represents value as boolean.
+
+        :param value:
+        :rtype: bool
+        """
+        value = value.lower()
+        return value in ('1', 'true', 'yes')
+
+    @classmethod
+    def _exclude_files_parser(cls, key):
+        """Returns a parser function to make sure field inputs
+        are not files.
+
+        Parses a value after getting the key so error messages are
+        more informative.
+
+        :param key:
+        :rtype: callable
+        """
+
+        def parser(value):
+            exclude_directive = 'file:'
+            if value.startswith(exclude_directive):
+                raise ValueError(
+                    f'Only strings are accepted for the {key} field, '
+                    'files are not accepted'
+                )
+            return _static.Str(value)
+
+        return parser
+
+    def _parse_file(self, value, root_dir: StrPath | None):
+        """Represents value as a string, allowing including text
+        from nearest files using `file:` directive.
+
+        Directive is sandboxed and won't reach anything outside
+        directory with setup.py.
+
+        Examples:
+            file: README.rst, CHANGELOG.md, src/file.txt
+
+        :param str value:
+        :rtype: str
+        """
+        include_directive = 'file:'
+
+        if not isinstance(value, str):
+            return value
+
+        if not value.startswith(include_directive):
+            return _static.Str(value)
+
+        spec = value[len(include_directive) :]
+        filepaths = [path.strip() for path in spec.split(',')]
+        self._referenced_files.update(filepaths)
+        # XXX: Is marking as static contents coming from files too optimistic?
+        return _static.Str(expand.read_files(filepaths, root_dir))
+
+    def _parse_attr(self, value, package_dir, root_dir: StrPath):
+        """Represents value as a module attribute.
+
+        Examples:
+            attr: package.attr
+            attr: package.module.attr
+
+        :param str value:
+        :rtype: str
+        """
+        attr_directive = 'attr:'
+        if not value.startswith(attr_directive):
+            return _static.Str(value)
+
+        attr_desc = value.replace(attr_directive, '')
+
+        # Make sure package_dir is populated correctly, so `attr:` directives can work
+        package_dir.update(self.ensure_discovered.package_dir)
+        return expand.read_attr(attr_desc, package_dir, root_dir)
+
+    @classmethod
+    def _get_parser_compound(cls, *parse_methods):
+        """Returns parser function to represents value as a list.
+
+        Parses a value applying given methods one after another.
+
+        :param parse_methods:
+        :rtype: callable
+        """
+
+        def parse(value):
+            parsed = value
+
+            for method in parse_methods:
+                parsed = method(parsed)
+
+            return parsed
+
+        return parse
+
+    @classmethod
+    def _parse_section_to_dict_with_key(cls, section_options, values_parser):
+        """Parses section options into a dictionary.
+
+        Applies a given parser to each option in a section.
+
+        :param dict section_options:
+        :param callable values_parser: function with 2 args corresponding to key, value
+        :rtype: dict
+        """
+        value = {}
+        for key, (_, val) in section_options.items():
+            value[key] = values_parser(key, val)
+        return value
+
+    @classmethod
+    def _parse_section_to_dict(cls, section_options, values_parser=None):
+        """Parses section options into a dictionary.
+
+        Optionally applies a given parser to each value.
+
+        :param dict section_options:
+        :param callable values_parser: function with 1 arg corresponding to option value
+        :rtype: dict
+        """
+        parser = (lambda _, v: values_parser(v)) if values_parser else (lambda _, v: v)
+        return cls._parse_section_to_dict_with_key(section_options, parser)
+
+    def parse_section(self, section_options) -> None:
+        """Parses configuration file section.
+
+        :param dict section_options:
+        """
+        for name, (_, value) in section_options.items():
+            with contextlib.suppress(KeyError):
+                # Keep silent for a new option may appear anytime.
+                self[name] = value
+
+    def parse(self) -> None:
+        """Parses configuration file items from one
+        or more related sections.
+
+        """
+        for section_name, section_options in self.sections.items():
+            method_postfix = ''
+            if section_name:  # [section.option] variant
+                method_postfix = f"_{section_name}"
+
+            section_parser_method: Callable | None = getattr(
+                self,
+                # Dots in section names are translated into dunderscores.
+                f'parse_section{method_postfix}'.replace('.', '__'),
+                None,
+            )
+
+            if section_parser_method is None:
+                raise OptionError(
+                    "Unsupported distribution option section: "
+                    f"[{self.section_prefix}.{section_name}]"
+                )
+
+            section_parser_method(section_options)
+
+    def _deprecated_config_handler(self, func, msg, **kw):
+        """this function will wrap around parameters that are deprecated
+
+        :param msg: deprecation message
+        :param func: function to be wrapped around
+        """
+
+        @wraps(func)
+        def config_handler(*args, **kwargs):
+            kw.setdefault("stacklevel", 2)
+            _DeprecatedConfig.emit("Deprecated config in `setup.cfg`", msg, **kw)
+            return func(*args, **kwargs)
+
+        return config_handler
+
+
+class ConfigMetadataHandler(ConfigHandler["DistributionMetadata"]):
+    section_prefix = 'metadata'
+
+    aliases = {
+        'home_page': 'url',
+        'summary': 'description',
+        'classifier': 'classifiers',
+        'platform': 'platforms',
+    }
+
+    strict_mode = False
+    """We need to keep it loose, to be partially compatible with
+    `pbr` and `d2to1` packages which also uses `metadata` section.
+
+    """
+
+    def __init__(
+        self,
+        target_obj: DistributionMetadata,
+        options: AllCommandOptions,
+        ignore_option_errors: bool,
+        ensure_discovered: expand.EnsurePackagesDiscovered,
+        package_dir: dict | None = None,
+        root_dir: StrPath | None = os.curdir,
+    ) -> None:
+        super().__init__(target_obj, options, ignore_option_errors, ensure_discovered)
+        self.package_dir = package_dir
+        self.root_dir = root_dir
+
+    @property
+    def parsers(self):
+        """Metadata item name to parser function mapping."""
+        parse_list_static = self._get_parser_compound(self._parse_list, _static.List)
+        parse_dict_static = self._get_parser_compound(self._parse_dict, _static.Dict)
+        parse_file = partial(self._parse_file, root_dir=self.root_dir)
+        exclude_files_parser = self._exclude_files_parser
+
+        return {
+            'author': _static.Str,
+            'author_email': _static.Str,
+            'maintainer': _static.Str,
+            'maintainer_email': _static.Str,
+            'platforms': parse_list_static,
+            'keywords': parse_list_static,
+            'provides': parse_list_static,
+            'obsoletes': parse_list_static,
+            'classifiers': self._get_parser_compound(parse_file, parse_list_static),
+            'license': exclude_files_parser('license'),
+            'license_files': parse_list_static,
+            'description': parse_file,
+            'long_description': parse_file,
+            'long_description_content_type': _static.Str,
+            'version': self._parse_version,  # Cannot be marked as dynamic
+            'url': _static.Str,
+            'project_urls': parse_dict_static,
+        }
+
+    def _parse_version(self, value):
+        """Parses `version` option value.
+
+        :param value:
+        :rtype: str
+
+        """
+        version = self._parse_file(value, self.root_dir)
+
+        if version != value:
+            version = version.strip()
+            # Be strict about versions loaded from file because it's easy to
+            # accidentally include newlines and other unintended content
+            try:
+                Version(version)
+            except InvalidVersion as e:
+                raise OptionError(
+                    f'Version loaded from {value} does not '
+                    f'comply with PEP 440: {version}'
+                ) from e
+
+            return version
+
+        return expand.version(self._parse_attr(value, self.package_dir, self.root_dir))
+
+
+class ConfigOptionsHandler(ConfigHandler["Distribution"]):
+    section_prefix = 'options'
+
+    def __init__(
+        self,
+        target_obj: Distribution,
+        options: AllCommandOptions,
+        ignore_option_errors: bool,
+        ensure_discovered: expand.EnsurePackagesDiscovered,
+    ) -> None:
+        super().__init__(target_obj, options, ignore_option_errors, ensure_discovered)
+        self.root_dir = target_obj.src_root
+        self.package_dir: dict[str, str] = {}  # To be filled by `find_packages`
+
+    @classmethod
+    def _parse_list_semicolon(cls, value):
+        return cls._parse_list(value, separator=';')
+
+    def _parse_file_in_root(self, value):
+        return self._parse_file(value, root_dir=self.root_dir)
+
+    def _parse_requirements_list(self, label: str, value: str):
+        # Parse a requirements list, either by reading in a `file:`, or a list.
+        parsed = self._parse_list_semicolon(self._parse_file_in_root(value))
+        _warn_accidental_env_marker_misconfig(label, value, parsed)
+        # Filter it to only include lines that are not comments. `parse_list`
+        # will have stripped each line and filtered out empties.
+        return _static.List(line for line in parsed if not line.startswith("#"))
+        # ^-- Use `_static.List` to mark a non-`Dynamic` Core Metadata
+
+    @property
+    def parsers(self):
+        """Metadata item name to parser function mapping."""
+        parse_list = self._parse_list
+        parse_bool = self._parse_bool
+        parse_cmdclass = self._parse_cmdclass
+
+        return {
+            'zip_safe': parse_bool,
+            'include_package_data': parse_bool,
+            'package_dir': self._parse_dict,
+            'scripts': parse_list,
+            'eager_resources': parse_list,
+            'dependency_links': parse_list,
+            'namespace_packages': self._deprecated_config_handler(
+                parse_list,
+                "The namespace_packages parameter is deprecated, "
+                "consider using implicit namespaces instead (PEP 420).",
+                # TODO: define due date, see setuptools.dist:check_nsp.
+            ),
+            'install_requires': partial(  # Core Metadata
+                self._parse_requirements_list, "install_requires"
+            ),
+            'setup_requires': self._parse_list_semicolon,
+            'packages': self._parse_packages,
+            'entry_points': self._parse_file_in_root,
+            'py_modules': parse_list,
+            'python_requires': _static.SpecifierSet,  # Core Metadata
+            'cmdclass': parse_cmdclass,
+        }
+
+    def _parse_cmdclass(self, value):
+        package_dir = self.ensure_discovered.package_dir
+        return expand.cmdclass(self._parse_dict(value), package_dir, self.root_dir)
+
+    def _parse_packages(self, value):
+        """Parses `packages` option value.
+
+        :param value:
+        :rtype: list
+        """
+        find_directives = ['find:', 'find_namespace:']
+        trimmed_value = value.strip()
+
+        if trimmed_value not in find_directives:
+            return self._parse_list(value)
+
+        # Read function arguments from a dedicated section.
+        find_kwargs = self.parse_section_packages__find(
+            self.sections.get('packages.find', {})
+        )
+
+        find_kwargs.update(
+            namespaces=(trimmed_value == find_directives[1]),
+            root_dir=self.root_dir,
+            fill_package_dir=self.package_dir,
+        )
+
+        return expand.find_packages(**find_kwargs)
+
+    def parse_section_packages__find(self, section_options):
+        """Parses `packages.find` configuration file section.
+
+        To be used in conjunction with _parse_packages().
+
+        :param dict section_options:
+        """
+        section_data = self._parse_section_to_dict(section_options, self._parse_list)
+
+        valid_keys = ['where', 'include', 'exclude']
+        find_kwargs = {k: v for k, v in section_data.items() if k in valid_keys and v}
+
+        where = find_kwargs.get('where')
+        if where is not None:
+            find_kwargs['where'] = where[0]  # cast list to single val
+
+        return find_kwargs
+
+    def parse_section_entry_points(self, section_options) -> None:
+        """Parses `entry_points` configuration file section.
+
+        :param dict section_options:
+        """
+        parsed = self._parse_section_to_dict(section_options, self._parse_list)
+        self['entry_points'] = parsed
+
+    def _parse_package_data(self, section_options):
+        package_data = self._parse_section_to_dict(section_options, self._parse_list)
+        return expand.canonic_package_data(package_data)
+
+    def parse_section_package_data(self, section_options) -> None:
+        """Parses `package_data` configuration file section.
+
+        :param dict section_options:
+        """
+        self['package_data'] = self._parse_package_data(section_options)
+
+    def parse_section_exclude_package_data(self, section_options) -> None:
+        """Parses `exclude_package_data` configuration file section.
+
+        :param dict section_options:
+        """
+        self['exclude_package_data'] = self._parse_package_data(section_options)
+
+    def parse_section_extras_require(self, section_options) -> None:  # Core Metadata
+        """Parses `extras_require` configuration file section.
+
+        :param dict section_options:
+        """
+        parsed = self._parse_section_to_dict_with_key(
+            section_options,
+            lambda k, v: self._parse_requirements_list(f"extras_require[{k}]", v),
+        )
+
+        self['extras_require'] = _static.Dict(parsed)
+        # ^-- Use `_static.Dict` to mark a non-`Dynamic` Core Metadata
+
+    def parse_section_data_files(self, section_options) -> None:
+        """Parses `data_files` configuration file section.
+
+        :param dict section_options:
+        """
+        parsed = self._parse_section_to_dict(section_options, self._parse_list)
+        self['data_files'] = expand.canonic_data_files(parsed, self.root_dir)
+
+
+class _AmbiguousMarker(SetuptoolsDeprecationWarning):
+    _SUMMARY = "Ambiguous requirement marker."
+    _DETAILS = """
+    One of the parsed requirements in `{field}` looks like a valid environment marker:
+
+        {req!r}
+
+    Please make sure that the configuration file is correct.
+    You can use dangling lines to avoid this problem.
+    """
+    _SEE_DOCS = "userguide/declarative_config.html#opt-2"
+    # TODO: should we include due_date here? Initially introduced in 6 Aug 2022.
+    # Does this make sense with latest version of packaging?
+
+    @classmethod
+    def message(cls, **kw):
+        docs = f"https://setuptools.pypa.io/en/latest/{cls._SEE_DOCS}"
+        return cls._format(cls._SUMMARY, cls._DETAILS, see_url=docs, format_args=kw)
+
+
+class _DeprecatedConfig(SetuptoolsDeprecationWarning):
+    _SEE_DOCS = "userguide/declarative_config.html"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/setuptools.schema.json b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/setuptools.schema.json
new file mode 100644
index 0000000000000000000000000000000000000000..ec887b35736e4ede6265e95e3a9e2520b43cc40f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/config/setuptools.schema.json
@@ -0,0 +1,433 @@
+{
+  "$schema": "http://json-schema.org/draft-07/schema#",
+
+  "$id": "https://setuptools.pypa.io/en/latest/userguide/pyproject_config.html",
+  "title": "``tool.setuptools`` table",
+  "$$description": [
+    "``setuptools``-specific configurations that can be set by users that require",
+    "customization.",
+    "These configurations are completely optional and probably can be skipped when",
+    "creating simple packages. They are equivalent to some of the `Keywords",
+    "`_",
+    "used by the ``setup.py`` file, and can be set via the ``tool.setuptools`` table.",
+    "It considers only ``setuptools`` `parameters",
+    "`_",
+    "that are not covered by :pep:`621`; and intentionally excludes ``dependency_links``",
+    "and ``setup_requires`` (incompatible with modern workflows/standards)."
+  ],
+
+  "type": "object",
+  "additionalProperties": false,
+  "properties": {
+    "platforms": {
+      "type": "array",
+      "items": {"type": "string"}
+    },
+    "provides": {
+      "$$description": [
+        "Package and virtual package names contained within this package",
+        "**(not supported by pip)**"
+      ],
+      "type": "array",
+      "items": {"type": "string", "format": "pep508-identifier"}
+    },
+    "obsoletes": {
+      "$$description": [
+        "Packages which this package renders obsolete",
+        "**(not supported by pip)**"
+      ],
+      "type": "array",
+      "items": {"type": "string", "format": "pep508-identifier"}
+    },
+    "zip-safe": {
+      "$$description": [
+        "Whether the project can be safely installed and run from a zip file.",
+        "**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and",
+        "``setup.py install`` in the context of ``eggs`` (**DEPRECATED**)."
+      ],
+      "type": "boolean"
+    },
+    "script-files": {
+      "$$description": [
+        "Legacy way of defining scripts (entry-points are preferred).",
+        "Equivalent to the ``script`` keyword in ``setup.py``",
+        "(it was renamed to avoid confusion with entry-point based ``project.scripts``",
+        "defined in :pep:`621`).",
+        "**DISCOURAGED**: generic script wrappers are tricky and may not work properly.",
+        "Whenever possible, please use ``project.scripts`` instead."
+      ],
+      "type": "array",
+      "items": {"type": "string"},
+      "$comment": "TODO: is this field deprecated/should be removed?"
+    },
+    "eager-resources": {
+      "$$description": [
+        "Resources that should be extracted together, if any of them is needed,",
+        "or if any C extensions included in the project are imported.",
+        "**OBSOLETE**: only relevant for ``pkg_resources``, ``easy_install`` and",
+        "``setup.py install`` in the context of ``eggs`` (**DEPRECATED**)."
+      ],
+      "type": "array",
+      "items": {"type": "string"}
+    },
+    "packages": {
+      "$$description": [
+        "Packages that should be included in the distribution.",
+        "It can be given either as a list of package identifiers",
+        "or as a ``dict``-like structure with a single key ``find``",
+        "which corresponds to a dynamic call to",
+        "``setuptools.config.expand.find_packages`` function.",
+        "The ``find`` key is associated with a nested ``dict``-like structure that can",
+        "contain ``where``, ``include``, ``exclude`` and ``namespaces`` keys,",
+        "mimicking the keyword arguments of the associated function."
+      ],
+      "oneOf": [
+        {
+          "title": "Array of Python package identifiers",
+          "type": "array",
+          "items": {"$ref": "#/definitions/package-name"}
+        },
+        {"$ref": "#/definitions/find-directive"}
+      ]
+    },
+    "package-dir": {
+      "$$description": [
+        ":class:`dict`-like structure mapping from package names to directories where their",
+        "code can be found.",
+        "The empty string (as key) means that all packages are contained inside",
+        "the given directory will be included in the distribution."
+      ],
+      "type": "object",
+      "additionalProperties": false,
+      "propertyNames": {
+        "anyOf": [{"const": ""}, {"$ref": "#/definitions/package-name"}]
+      },
+      "patternProperties": {
+        "^.*$": {"type": "string" }
+      }
+    },
+    "package-data": {
+      "$$description": [
+        "Mapping from package names to lists of glob patterns.",
+        "Usually this option is not needed when using ``include-package-data = true``",
+        "For more information on how to include data files, check ``setuptools`` `docs",
+        "`_."
+      ],
+      "type": "object",
+      "additionalProperties": false,
+      "propertyNames": {
+        "anyOf": [{"type": "string", "format": "python-module-name"}, {"const": "*"}]
+      },
+      "patternProperties": {
+        "^.*$": {"type": "array", "items": {"type": "string"}}
+      }
+    },
+    "include-package-data": {
+      "$$description": [
+        "Automatically include any data files inside the package directories",
+        "that are specified by ``MANIFEST.in``",
+        "For more information on how to include data files, check ``setuptools`` `docs",
+        "`_."
+      ],
+      "type": "boolean"
+    },
+    "exclude-package-data": {
+      "$$description": [
+        "Mapping from package names to lists of glob patterns that should be excluded",
+        "For more information on how to include data files, check ``setuptools`` `docs",
+        "`_."
+      ],
+      "type": "object",
+      "additionalProperties": false,
+      "propertyNames": {
+        "anyOf": [{"type": "string", "format": "python-module-name"}, {"const": "*"}]
+      },
+      "patternProperties": {
+          "^.*$": {"type": "array", "items": {"type": "string"}}
+      }
+    },
+    "namespace-packages": {
+      "type": "array",
+      "items": {"type": "string", "format": "python-module-name-relaxed"},
+      "$comment": "https://setuptools.pypa.io/en/latest/userguide/package_discovery.html",
+      "description": "**DEPRECATED**: use implicit namespaces instead (:pep:`420`)."
+    },
+    "py-modules": {
+      "description": "Modules that setuptools will manipulate",
+      "type": "array",
+      "items": {"type": "string", "format": "python-module-name-relaxed"},
+      "$comment": "TODO: clarify the relationship with ``packages``"
+    },
+    "ext-modules": {
+      "description": "Extension modules to be compiled by setuptools",
+      "type": "array",
+      "items": {"$ref": "#/definitions/ext-module"}
+    },
+    "data-files": {
+      "$$description": [
+        "``dict``-like structure where each key represents a directory and",
+        "the value is a list of glob patterns that should be installed in them.",
+        "**DISCOURAGED**: please notice this might not work as expected with wheels.",
+        "Whenever possible, consider using data files inside the package directories",
+        "(or create a new namespace package that only contains data files).",
+        "See `data files support",
+        "`_."
+      ],
+      "type": "object",
+      "patternProperties": {
+          "^.*$": {"type": "array", "items": {"type": "string"}}
+      }
+    },
+    "cmdclass": {
+      "$$description": [
+        "Mapping of distutils-style command names to ``setuptools.Command`` subclasses",
+        "which in turn should be represented by strings with a qualified class name",
+        "(i.e., \"dotted\" form with module), e.g.::\n\n",
+        "    cmdclass = {mycmd = \"pkg.subpkg.module.CommandClass\"}\n\n",
+        "The command class should be a directly defined at the top-level of the",
+        "containing module (no class nesting)."
+      ],
+      "type": "object",
+      "patternProperties": {
+          "^.*$": {"type": "string", "format": "python-qualified-identifier"}
+      }
+    },
+    "license-files": {
+      "type": "array",
+      "items": {"type": "string"},
+      "$$description": [
+        "**PROVISIONAL**: list of glob patterns for all license files being distributed.",
+        "(likely to become standard with :pep:`639`).",
+        "By default: ``['LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*']``"
+      ],
+      "$comment": "TODO: revise if PEP 639 is accepted. Probably ``project.license-files``?"
+    },
+    "dynamic": {
+      "type": "object",
+      "description": "Instructions for loading :pep:`621`-related metadata dynamically",
+      "additionalProperties": false,
+      "properties": {
+        "version": {
+          "$$description": [
+            "A version dynamically loaded via either the ``attr:`` or ``file:``",
+            "directives. Please make sure the given file or attribute respects :pep:`440`.",
+            "Also ensure to set ``project.dynamic`` accordingly."
+          ],
+          "oneOf": [
+            {"$ref": "#/definitions/attr-directive"},
+            {"$ref": "#/definitions/file-directive"}
+          ]
+        },
+        "classifiers": {"$ref": "#/definitions/file-directive"},
+        "description": {"$ref": "#/definitions/file-directive"},
+        "entry-points": {"$ref": "#/definitions/file-directive"},
+        "dependencies": {"$ref": "#/definitions/file-directive-for-dependencies"},
+        "optional-dependencies": {
+          "type": "object",
+          "propertyNames": {"type": "string", "format": "pep508-identifier"},
+          "additionalProperties": false,
+          "patternProperties": {
+            ".+": {"$ref": "#/definitions/file-directive-for-dependencies"}
+          }
+        },
+        "readme": {
+          "type": "object",
+          "anyOf": [
+            {"$ref": "#/definitions/file-directive"},
+            {
+              "type": "object",
+              "properties": {
+                "content-type": {"type": "string"},
+                "file": { "$ref": "#/definitions/file-directive/properties/file" }
+              },
+              "additionalProperties": false}
+          ],
+          "required": ["file"]
+        }
+      }
+    }
+  },
+
+  "definitions": {
+    "package-name": {
+      "$id": "#/definitions/package-name",
+      "title": "Valid package name",
+      "description": "Valid package name (importable or :pep:`561`).",
+      "type": "string",
+      "anyOf": [
+        {"type": "string", "format": "python-module-name-relaxed"},
+        {"type": "string", "format": "pep561-stub-name"}
+      ]
+    },
+    "ext-module": {
+      "$id": "#/definitions/ext-module",
+      "title": "Extension module",
+      "description": "Parameters to construct a :class:`setuptools.Extension` object",
+      "type": "object",
+      "required": ["name", "sources"],
+      "additionalProperties": false,
+      "properties": {
+        "name": {
+          "type": "string",
+          "format": "python-module-name-relaxed"
+        },
+        "sources": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "include-dirs":{
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "define-macros": {
+          "type": "array",
+          "items": {
+            "type": "array",
+            "items": [
+              {"description": "macro name", "type": "string"},
+              {"description": "macro value", "oneOf": [{"type": "string"}, {"type": "null"}]}
+            ],
+            "additionalItems": false
+          }
+        },
+        "undef-macros": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "library-dirs": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "libraries": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "runtime-library-dirs": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "extra-objects": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "extra-compile-args": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "extra-link-args": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "export-symbols": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "swig-opts": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "depends": {
+          "type": "array",
+          "items": {"type": "string"}
+        },
+        "language": {"type": "string"},
+        "optional": {"type": "boolean"},
+        "py-limited-api": {"type": "boolean"}
+      }
+    },
+    "file-directive": {
+      "$id": "#/definitions/file-directive",
+      "title": "'file:' directive",
+      "description":
+        "Value is read from a file (or list of files and then concatenated)",
+      "type": "object",
+      "additionalProperties": false,
+      "properties": {
+        "file": {
+          "oneOf": [
+            {"type": "string"},
+            {"type": "array", "items": {"type": "string"}}
+          ]
+        }
+      },
+      "required": ["file"]
+    },
+    "file-directive-for-dependencies": {
+      "title": "'file:' directive for dependencies",
+      "allOf": [
+        {
+          "$$description": [
+            "**BETA**: subset of the ``requirements.txt`` format",
+            "without ``pip`` flags and options",
+            "(one :pep:`508`-compliant string per line,",
+            "lines that are blank or start with ``#`` are excluded).",
+            "See `dynamic metadata",
+            "`_."
+          ]
+        },
+        {"$ref": "#/definitions/file-directive"}
+      ]
+    },
+    "attr-directive": {
+      "title": "'attr:' directive",
+      "$id": "#/definitions/attr-directive",
+      "$$description": [
+        "Value is read from a module attribute. Supports callables and iterables;",
+        "unsupported types are cast via ``str()``"
+      ],
+      "type": "object",
+      "additionalProperties": false,
+      "properties": {
+        "attr": {"type": "string", "format": "python-qualified-identifier"}
+      },
+      "required": ["attr"]
+    },
+    "find-directive": {
+      "$id": "#/definitions/find-directive",
+      "title": "'find:' directive",
+      "type": "object",
+      "additionalProperties": false,
+      "properties": {
+        "find": {
+          "type": "object",
+          "$$description": [
+            "Dynamic `package discovery",
+            "`_."
+          ],
+          "additionalProperties": false,
+          "properties": {
+            "where": {
+              "description":
+                "Directories to be searched for packages (Unix-style relative path)",
+              "type": "array",
+              "items": {"type": "string"}
+            },
+            "exclude": {
+              "type": "array",
+              "$$description": [
+                "Exclude packages that match the values listed in this field.",
+                "Can container shell-style wildcards (e.g. ``'pkg.*'``)"
+              ],
+              "items": {"type": "string"}
+            },
+            "include": {
+              "type": "array",
+              "$$description": [
+                "Restrict the found packages to just the ones listed in this field.",
+                "Can container shell-style wildcards (e.g. ``'pkg.*'``)"
+              ],
+              "items": {"type": "string"}
+            },
+            "namespaces": {
+              "type": "boolean",
+              "$$description": [
+                "When ``True``, directories without a ``__init__.py`` file will also",
+                "be scanned for :pep:`420`-style implicit namespaces"
+              ]
+            }
+          }
+        }
+      }
+    }
+  }
+}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..eb70bfb7115a2a94a8b942b31cafc3a550f0c005
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/__init__.py
@@ -0,0 +1,13 @@
+import locale
+import sys
+
+import pytest
+
+__all__ = ['fail_on_ascii']
+
+if sys.version_info >= (3, 11):
+    locale_encoding = locale.getencoding()
+else:
+    locale_encoding = locale.getpreferredencoding(False)
+is_ascii = locale_encoding == 'ANSI_X3.4-1968'
+fail_on_ascii = pytest.mark.xfail(is_ascii, reason="Test fails in this locale")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/compat/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/compat/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/compat/py39.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/compat/py39.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fdb9dac1fa3f121a634082515d1a305fc09793c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/compat/py39.py
@@ -0,0 +1,3 @@
+from jaraco.test.cpython import from_test_support, try_import
+
+os_helper = try_import('os_helper') or from_test_support('can_symlink')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/downloads/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/downloads/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..00a16423f448e7773f5e6dc9b365efe80f40a778
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/downloads/__init__.py
@@ -0,0 +1,59 @@
+from __future__ import annotations
+
+import re
+import time
+from pathlib import Path
+from urllib.error import HTTPError
+from urllib.request import urlopen
+
+__all__ = ["DOWNLOAD_DIR", "retrieve_file", "output_file", "urls_from_file"]
+
+
+NAME_REMOVE = ("http://", "https://", "github.com/", "/raw/")
+DOWNLOAD_DIR = Path(__file__).parent
+
+
+# ----------------------------------------------------------------------
+# Please update ./preload.py accordingly when modifying this file
+# ----------------------------------------------------------------------
+
+
+def output_file(url: str, download_dir: Path = DOWNLOAD_DIR) -> Path:
+    file_name = url.strip()
+    for part in NAME_REMOVE:
+        file_name = file_name.replace(part, '').strip().strip('/:').strip()
+    return Path(download_dir, re.sub(r"[^\-_\.\w\d]+", "_", file_name))
+
+
+def retrieve_file(url: str, download_dir: Path = DOWNLOAD_DIR, wait: float = 5) -> Path:
+    path = output_file(url, download_dir)
+    if path.exists():
+        print(f"Skipping {url} (already exists: {path})")
+    else:
+        download_dir.mkdir(exist_ok=True, parents=True)
+        print(f"Downloading {url} to {path}")
+        try:
+            download(url, path)
+        except HTTPError:
+            time.sleep(wait)  # wait a few seconds and try again.
+            download(url, path)
+    return path
+
+
+def urls_from_file(list_file: Path) -> list[str]:
+    """``list_file`` should be a text file where each line corresponds to a URL to
+    download.
+    """
+    print(f"file: {list_file}")
+    content = list_file.read_text(encoding="utf-8")
+    return [url for url in content.splitlines() if not url.startswith("#")]
+
+
+def download(url: str, dest: Path):
+    with urlopen(url) as f:
+        data = f.read()
+
+    with open(dest, "wb") as f:
+        f.write(data)
+
+    assert Path(dest).exists()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/downloads/preload.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/downloads/preload.py
new file mode 100644
index 0000000000000000000000000000000000000000..8eeb5dd75d3dcb375cee5acaf11ad385084bff5a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/downloads/preload.py
@@ -0,0 +1,18 @@
+"""This file can be used to preload files needed for testing.
+
+For example you can use::
+
+    cd setuptools/tests/config
+    python -m downloads.preload setupcfg_examples.txt
+
+to make sure the `setup.cfg` examples are downloaded before starting the tests.
+"""
+
+import sys
+from pathlib import Path
+
+from . import retrieve_file, urls_from_file
+
+if __name__ == "__main__":
+    urls = urls_from_file(Path(sys.argv[1]))
+    list(map(retrieve_file, urls))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/setupcfg_examples.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/setupcfg_examples.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6aab887ff1fe631d97f1abea90a8448040746a12
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/setupcfg_examples.txt
@@ -0,0 +1,22 @@
+# ====================================================================
+# Some popular packages that use setup.cfg (and others not so popular)
+# Reference: https://hugovk.github.io/top-pypi-packages/
+# ====================================================================
+https://github.com/pypa/setuptools/raw/52c990172fec37766b3566679724aa8bf70ae06d/setup.cfg
+https://github.com/pypa/wheel/raw/0acd203cd896afec7f715aa2ff5980a403459a3b/setup.cfg
+https://github.com/python/importlib_metadata/raw/2f05392ca980952a6960d82b2f2d2ea10aa53239/setup.cfg
+https://github.com/jaraco/skeleton/raw/d9008b5c510cd6969127a6a2ab6f832edddef296/setup.cfg
+https://github.com/jaraco/zipp/raw/700d3a96390e970b6b962823bfea78b4f7e1c537/setup.cfg
+https://github.com/pallets/jinja/raw/7d72eb7fefb7dce065193967f31f805180508448/setup.cfg
+https://github.com/tkem/cachetools/raw/2fd87a94b8d3861d80e9e4236cd480bfdd21c90d/setup.cfg
+https://github.com/aio-libs/aiohttp/raw/5e0e6b7080f2408d5f1dd544c0e1cf88378b7b10/setup.cfg
+https://github.com/pallets/flask/raw/9486b6cf57bd6a8a261f67091aca8ca78eeec1e3/setup.cfg
+https://github.com/pallets/click/raw/6411f425fae545f42795665af4162006b36c5e4a/setup.cfg
+https://github.com/sqlalchemy/sqlalchemy/raw/533f5718904b620be8d63f2474229945d6f8ba5d/setup.cfg
+https://github.com/pytest-dev/pluggy/raw/461ef63291d13589c4e21aa182cd1529257e9a0a/setup.cfg
+https://github.com/pytest-dev/pytest/raw/c7be96dae487edbd2f55b561b31b68afac1dabe6/setup.cfg
+https://github.com/platformdirs/platformdirs/raw/7b7852128dd6f07511b618d6edea35046bd0c6ff/setup.cfg
+https://github.com/pandas-dev/pandas/raw/bc17343f934a33dc231c8c74be95d8365537c376/setup.cfg
+https://github.com/django/django/raw/4e249d11a6e56ca8feb4b055b681cec457ef3a3d/setup.cfg
+https://github.com/pyscaffold/pyscaffold/raw/de7aa5dc059fbd04307419c667cc4961bc9df4b8/setup.cfg
+https://github.com/pypa/virtualenv/raw/f92eda6e3da26a4d28c2663ffb85c4960bdb990c/setup.cfg
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_apply_pyprojecttoml.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_apply_pyprojecttoml.py
new file mode 100644
index 0000000000000000000000000000000000000000..489fd98e26710e74d66204b6f51c2523586aaa04
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_apply_pyprojecttoml.py
@@ -0,0 +1,772 @@
+"""Make sure that applying the configuration from pyproject.toml is equivalent to
+applying a similar configuration from setup.cfg
+
+To run these tests offline, please have a look on ``./downloads/preload.py``
+"""
+
+from __future__ import annotations
+
+import io
+import re
+import tarfile
+from inspect import cleandoc
+from pathlib import Path
+from unittest.mock import Mock
+
+import pytest
+from ini2toml.api import LiteTranslator
+from packaging.metadata import Metadata
+
+import setuptools  # noqa: F401 # ensure monkey patch to metadata
+from setuptools._static import is_static
+from setuptools.command.egg_info import write_requirements
+from setuptools.config import expand, pyprojecttoml, setupcfg
+from setuptools.config._apply_pyprojecttoml import _MissingDynamic, _some_attrgetter
+from setuptools.dist import Distribution
+from setuptools.errors import InvalidConfigError, RemovedConfigError
+from setuptools.warnings import InformationOnly, SetuptoolsDeprecationWarning
+
+from .downloads import retrieve_file, urls_from_file
+
+HERE = Path(__file__).parent
+EXAMPLES_FILE = "setupcfg_examples.txt"
+
+
+def makedist(path, **attrs):
+    return Distribution({"src_root": path, **attrs})
+
+
+def _mock_expand_patterns(patterns, *_, **__):
+    """
+    Allow comparing the given patterns for 2 dist objects.
+    We need to strip special chars to avoid errors when validating.
+    """
+    return [re.sub("[^a-z0-9]+", "", p, flags=re.I) or "empty" for p in patterns]
+
+
+@pytest.mark.parametrize("url", urls_from_file(HERE / EXAMPLES_FILE))
+@pytest.mark.filterwarnings("ignore")
+@pytest.mark.uses_network
+def test_apply_pyproject_equivalent_to_setupcfg(url, monkeypatch, tmp_path):
+    monkeypatch.setattr(expand, "read_attr", Mock(return_value="0.0.1"))
+    monkeypatch.setattr(
+        Distribution, "_expand_patterns", Mock(side_effect=_mock_expand_patterns)
+    )
+    setupcfg_example = retrieve_file(url)
+    pyproject_example = Path(tmp_path, "pyproject.toml")
+    setupcfg_text = setupcfg_example.read_text(encoding="utf-8")
+    toml_config = LiteTranslator().translate(setupcfg_text, "setup.cfg")
+    pyproject_example.write_text(toml_config, encoding="utf-8")
+
+    dist_toml = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject_example)
+    dist_cfg = setupcfg.apply_configuration(makedist(tmp_path), setupcfg_example)
+
+    pkg_info_toml = core_metadata(dist_toml)
+    pkg_info_cfg = core_metadata(dist_cfg)
+    assert pkg_info_toml == pkg_info_cfg
+
+    if any(getattr(d, "license_files", None) for d in (dist_toml, dist_cfg)):
+        assert set(dist_toml.license_files) == set(dist_cfg.license_files)
+
+    if any(getattr(d, "entry_points", None) for d in (dist_toml, dist_cfg)):
+        print(dist_cfg.entry_points)
+        ep_toml = {
+            (k, *sorted(i.replace(" ", "") for i in v))
+            for k, v in dist_toml.entry_points.items()
+        }
+        ep_cfg = {
+            (k, *sorted(i.replace(" ", "") for i in v))
+            for k, v in dist_cfg.entry_points.items()
+        }
+        assert ep_toml == ep_cfg
+
+    if any(getattr(d, "package_data", None) for d in (dist_toml, dist_cfg)):
+        pkg_data_toml = {(k, *sorted(v)) for k, v in dist_toml.package_data.items()}
+        pkg_data_cfg = {(k, *sorted(v)) for k, v in dist_cfg.package_data.items()}
+        assert pkg_data_toml == pkg_data_cfg
+
+    if any(getattr(d, "data_files", None) for d in (dist_toml, dist_cfg)):
+        data_files_toml = {(k, *sorted(v)) for k, v in dist_toml.data_files}
+        data_files_cfg = {(k, *sorted(v)) for k, v in dist_cfg.data_files}
+        assert data_files_toml == data_files_cfg
+
+    assert set(dist_toml.install_requires) == set(dist_cfg.install_requires)
+    if any(getattr(d, "extras_require", None) for d in (dist_toml, dist_cfg)):
+        extra_req_toml = {(k, *sorted(v)) for k, v in dist_toml.extras_require.items()}
+        extra_req_cfg = {(k, *sorted(v)) for k, v in dist_cfg.extras_require.items()}
+        assert extra_req_toml == extra_req_cfg
+
+
+PEP621_EXAMPLE = """\
+[project]
+name = "spam"
+version = "2020.0.0"
+description = "Lovely Spam! Wonderful Spam!"
+readme = "README.rst"
+requires-python = ">=3.8"
+license-files = ["LICENSE.txt"]  # Updated to be PEP 639 compliant
+keywords = ["egg", "bacon", "sausage", "tomatoes", "Lobster Thermidor"]
+authors = [
+  {email = "hi@pradyunsg.me"},
+  {name = "Tzu-Ping Chung"}
+]
+maintainers = [
+  {name = "Brett Cannon", email = "brett@python.org"},
+  {name = "John X. Ãørçeč", email = "john@utf8.org"},
+  {name = "Γαμα קּ 東", email = "gama@utf8.org"},
+]
+classifiers = [
+  "Development Status :: 4 - Beta",
+  "Programming Language :: Python"
+]
+
+dependencies = [
+  "httpx",
+  "gidgethub[httpx]>4.0.0",
+  "django>2.1; os_name != 'nt'",
+  "django>2.0; os_name == 'nt'"
+]
+
+[project.optional-dependencies]
+test = [
+  "pytest < 5.0.0",
+  "pytest-cov[all]"
+]
+
+[project.urls]
+homepage = "http://example.com"
+documentation = "http://readthedocs.org"
+repository = "http://github.com"
+changelog = "http://github.com/me/spam/blob/master/CHANGELOG.md"
+
+[project.scripts]
+spam-cli = "spam:main_cli"
+
+[project.gui-scripts]
+spam-gui = "spam:main_gui"
+
+[project.entry-points."spam.magical"]
+tomatoes = "spam:main_tomatoes"
+"""
+
+PEP621_INTERNATIONAL_EMAIL_EXAMPLE = """\
+[project]
+name = "spam"
+version = "2020.0.0"
+authors = [
+  {email = "hi@pradyunsg.me"},
+  {name = "Tzu-Ping Chung"}
+]
+maintainers = [
+  {name = "Степан Бандера", email = "криївка@оун-упа.укр"},
+]
+"""
+
+PEP621_EXAMPLE_SCRIPT = """
+def main_cli(): pass
+def main_gui(): pass
+def main_tomatoes(): pass
+"""
+
+PEP639_LICENSE_TEXT = """\
+[project]
+name = "spam"
+version = "2020.0.0"
+authors = [
+  {email = "hi@pradyunsg.me"},
+  {name = "Tzu-Ping Chung"}
+]
+license = {text = "MIT"}
+"""
+
+PEP639_LICENSE_EXPRESSION = """\
+[project]
+name = "spam"
+version = "2020.0.0"
+authors = [
+  {email = "hi@pradyunsg.me"},
+  {name = "Tzu-Ping Chung"}
+]
+license = "mit or apache-2.0"  # should be normalized in metadata
+classifiers = [
+    "Development Status :: 5 - Production/Stable",
+    "Programming Language :: Python",
+]
+"""
+
+
+def _pep621_example_project(
+    tmp_path,
+    readme="README.rst",
+    pyproject_text=PEP621_EXAMPLE,
+):
+    pyproject = tmp_path / "pyproject.toml"
+    text = pyproject_text
+    replacements = {'readme = "README.rst"': f'readme = "{readme}"'}
+    for orig, subst in replacements.items():
+        text = text.replace(orig, subst)
+    pyproject.write_text(text, encoding="utf-8")
+
+    (tmp_path / readme).write_text("hello world", encoding="utf-8")
+    (tmp_path / "LICENSE.txt").write_text("--- LICENSE stub ---", encoding="utf-8")
+    (tmp_path / "spam.py").write_text(PEP621_EXAMPLE_SCRIPT, encoding="utf-8")
+    return pyproject
+
+
+def test_pep621_example(tmp_path):
+    """Make sure the example in PEP 621 works"""
+    pyproject = _pep621_example_project(tmp_path)
+    dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+    assert set(dist.metadata.license_files) == {"LICENSE.txt"}
+
+
+@pytest.mark.parametrize(
+    ("readme", "ctype"),
+    [
+        ("Readme.txt", "text/plain"),
+        ("readme.md", "text/markdown"),
+        ("text.rst", "text/x-rst"),
+    ],
+)
+def test_readme_content_type(tmp_path, readme, ctype):
+    pyproject = _pep621_example_project(tmp_path, readme)
+    dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+    assert dist.metadata.long_description_content_type == ctype
+
+
+def test_undefined_content_type(tmp_path):
+    pyproject = _pep621_example_project(tmp_path, "README.tex")
+    with pytest.raises(ValueError, match="Undefined content type for README.tex"):
+        pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+
+def test_no_explicit_content_type_for_missing_extension(tmp_path):
+    pyproject = _pep621_example_project(tmp_path, "README")
+    dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+    assert dist.metadata.long_description_content_type is None
+
+
+@pytest.mark.parametrize(
+    ("pyproject_text", "expected_maintainers_meta_value"),
+    (
+        pytest.param(
+            PEP621_EXAMPLE,
+            (
+                'Brett Cannon , "John X. Ãørçeč" , '
+                'Γαμα קּ 東 '
+            ),
+            id='non-international-emails',
+        ),
+        pytest.param(
+            PEP621_INTERNATIONAL_EMAIL_EXAMPLE,
+            'Степан Бандера <криївка@оун-упа.укр>',
+            marks=pytest.mark.xfail(
+                reason="CPython's `email.headerregistry.Address` only supports "
+                'RFC 5322, as of Nov 10, 2022 and latest Python 3.11.0',
+                strict=True,
+            ),
+            id='international-email',
+        ),
+    ),
+)
+def test_utf8_maintainer_in_metadata(  # issue-3663
+    expected_maintainers_meta_value,
+    pyproject_text,
+    tmp_path,
+):
+    pyproject = _pep621_example_project(
+        tmp_path,
+        "README",
+        pyproject_text=pyproject_text,
+    )
+    dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+    assert dist.metadata.maintainer_email == expected_maintainers_meta_value
+    pkg_file = tmp_path / "PKG-FILE"
+    with open(pkg_file, "w", encoding="utf-8") as fh:
+        dist.metadata.write_pkg_file(fh)
+    content = pkg_file.read_text(encoding="utf-8")
+    assert f"Maintainer-email: {expected_maintainers_meta_value}" in content
+
+
+@pytest.mark.parametrize(
+    (
+        'pyproject_text',
+        'license',
+        'license_expression',
+        'content_str',
+        'not_content_str',
+    ),
+    (
+        pytest.param(
+            PEP639_LICENSE_TEXT,
+            'MIT',
+            None,
+            'License: MIT',
+            'License-Expression: ',
+            id='license-text',
+            marks=[
+                pytest.mark.filterwarnings(
+                    "ignore:.project.license. as a TOML table is deprecated",
+                )
+            ],
+        ),
+        pytest.param(
+            PEP639_LICENSE_EXPRESSION,
+            None,
+            'MIT OR Apache-2.0',
+            'License-Expression: MIT OR Apache-2.0',
+            'License: ',
+            id='license-expression',
+        ),
+    ),
+)
+def test_license_in_metadata(
+    license,
+    license_expression,
+    content_str,
+    not_content_str,
+    pyproject_text,
+    tmp_path,
+):
+    pyproject = _pep621_example_project(
+        tmp_path,
+        "README",
+        pyproject_text=pyproject_text,
+    )
+    dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+    assert dist.metadata.license == license
+    assert dist.metadata.license_expression == license_expression
+    pkg_file = tmp_path / "PKG-FILE"
+    with open(pkg_file, "w", encoding="utf-8") as fh:
+        dist.metadata.write_pkg_file(fh)
+    content = pkg_file.read_text(encoding="utf-8")
+    assert "Metadata-Version: 2.4" in content
+    assert content_str in content
+    assert not_content_str not in content
+
+
+def test_license_classifier_with_license_expression(tmp_path):
+    text = PEP639_LICENSE_EXPRESSION.rsplit("\n", 2)[0]
+    pyproject = _pep621_example_project(
+        tmp_path,
+        "README",
+        f"{text}\n    \"License :: OSI Approved :: MIT License\"\n]",
+    )
+    msg = "License classifiers have been superseded by license expressions"
+    with pytest.raises(InvalidConfigError, match=msg) as exc:
+        pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+    assert "License :: OSI Approved :: MIT License" in str(exc.value)
+
+
+def test_license_classifier_without_license_expression(tmp_path):
+    text = """\
+    [project]
+    name = "spam"
+    version = "2020.0.0"
+    license = {text = "mit or apache-2.0"}
+    classifiers = ["License :: OSI Approved :: MIT License"]
+    """
+    pyproject = _pep621_example_project(tmp_path, "README", text)
+
+    msg1 = "License classifiers are deprecated(?:.|\n)*MIT License"
+    msg2 = ".project.license. as a TOML table is deprecated"
+    with (
+        pytest.warns(SetuptoolsDeprecationWarning, match=msg1),
+        pytest.warns(SetuptoolsDeprecationWarning, match=msg2),
+    ):
+        dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+    # Check license classifier is still included
+    assert dist.metadata.get_classifiers() == ["License :: OSI Approved :: MIT License"]
+
+
+class TestLicenseFiles:
+    def base_pyproject(
+        self,
+        tmp_path,
+        additional_text="",
+        license_toml='license = {file = "LICENSE.txt"}\n',
+    ):
+        text = PEP639_LICENSE_EXPRESSION
+
+        # Sanity-check
+        assert 'license = "mit or apache-2.0"' in text
+        assert 'license-files' not in text
+        assert "[tool.setuptools]" not in text
+
+        text = re.sub(
+            r"(license = .*)\n",
+            license_toml,
+            text,
+            count=1,
+        )
+        assert license_toml in text  # sanity check
+        text = f"{text}\n{additional_text}\n"
+        pyproject = _pep621_example_project(tmp_path, "README", pyproject_text=text)
+        return pyproject
+
+    def base_pyproject_license_pep639(self, tmp_path, additional_text=""):
+        return self.base_pyproject(
+            tmp_path,
+            additional_text=additional_text,
+            license_toml='license = "licenseref-Proprietary"'
+            '\nlicense-files = ["_FILE*"]\n',
+        )
+
+    def test_both_license_and_license_files_defined(self, tmp_path):
+        setuptools_config = '[tool.setuptools]\nlicense-files = ["_FILE*"]'
+        pyproject = self.base_pyproject(tmp_path, setuptools_config)
+
+        (tmp_path / "_FILE.txt").touch()
+        (tmp_path / "_FILE.rst").touch()
+
+        # Would normally match the `license_files` patterns, but we want to exclude it
+        # by being explicit. On the other hand, contents should be added to `license`
+        license = tmp_path / "LICENSE.txt"
+        license.write_text("LicenseRef-Proprietary\n", encoding="utf-8")
+
+        msg1 = "'tool.setuptools.license-files' is deprecated in favor of 'project.license-files'"
+        msg2 = ".project.license. as a TOML table is deprecated"
+        with (
+            pytest.warns(SetuptoolsDeprecationWarning, match=msg1),
+            pytest.warns(SetuptoolsDeprecationWarning, match=msg2),
+        ):
+            dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+        assert set(dist.metadata.license_files) == {"_FILE.rst", "_FILE.txt"}
+        assert dist.metadata.license == "LicenseRef-Proprietary\n"
+
+    def test_both_license_and_license_files_defined_pep639(self, tmp_path):
+        # Set license and license-files
+        pyproject = self.base_pyproject_license_pep639(tmp_path)
+
+        (tmp_path / "_FILE.txt").touch()
+        (tmp_path / "_FILE.rst").touch()
+
+        msg = "Normalizing.*LicenseRef"
+        with pytest.warns(InformationOnly, match=msg):
+            dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+        assert set(dist.metadata.license_files) == {"_FILE.rst", "_FILE.txt"}
+        assert dist.metadata.license is None
+        assert dist.metadata.license_expression == "LicenseRef-Proprietary"
+
+    def test_license_files_defined_twice(self, tmp_path):
+        # Set project.license-files and tools.setuptools.license-files
+        setuptools_config = '[tool.setuptools]\nlicense-files = ["_FILE*"]'
+        pyproject = self.base_pyproject_license_pep639(tmp_path, setuptools_config)
+
+        msg = "'project.license-files' is defined already. Remove 'tool.setuptools.license-files'"
+        with pytest.raises(InvalidConfigError, match=msg):
+            pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+    def test_default_patterns(self, tmp_path):
+        setuptools_config = '[tool.setuptools]\nzip-safe = false'
+        # ^ used just to trigger section validation
+        pyproject = self.base_pyproject(tmp_path, setuptools_config, license_toml="")
+
+        license_files = "LICENCE-a.html COPYING-abc.txt AUTHORS-xyz NOTICE,def".split()
+
+        for fname in license_files:
+            (tmp_path / fname).write_text(f"{fname}\n", encoding="utf-8")
+
+        dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+        assert (tmp_path / "LICENSE.txt").exists()  # from base example
+        assert set(dist.metadata.license_files) == {*license_files, "LICENSE.txt"}
+
+    def test_missing_patterns(self, tmp_path):
+        pyproject = self.base_pyproject_license_pep639(tmp_path)
+        assert list(tmp_path.glob("_FILE*")) == []  # sanity check
+
+        msg1 = "Cannot find any files for the given pattern.*"
+        msg2 = "Normalizing 'licenseref-Proprietary' to 'LicenseRef-Proprietary'"
+        with (
+            pytest.warns(SetuptoolsDeprecationWarning, match=msg1),
+            pytest.warns(InformationOnly, match=msg2),
+        ):
+            pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+    def test_deprecated_file_expands_to_text(self, tmp_path):
+        """Make sure the old example with ``license = {text = ...}`` works"""
+
+        assert 'license-files = ["LICENSE.txt"]' in PEP621_EXAMPLE  # sanity check
+        text = PEP621_EXAMPLE.replace(
+            'license-files = ["LICENSE.txt"]',
+            'license = {file = "LICENSE.txt"}',
+        )
+        pyproject = _pep621_example_project(tmp_path, pyproject_text=text)
+
+        msg = ".project.license. as a TOML table is deprecated"
+        with pytest.warns(SetuptoolsDeprecationWarning, match=msg):
+            dist = pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+        assert dist.metadata.license == "--- LICENSE stub ---"
+        assert set(dist.metadata.license_files) == {"LICENSE.txt"}  # auto-filled
+
+
+class TestPyModules:
+    # https://github.com/pypa/setuptools/issues/4316
+
+    def dist(self, name):
+        toml_config = f"""
+        [project]
+        name = "test"
+        version = "42.0"
+        [tool.setuptools]
+        py-modules = [{name!r}]
+        """
+        pyproject = Path("pyproject.toml")
+        pyproject.write_text(cleandoc(toml_config), encoding="utf-8")
+        return pyprojecttoml.apply_configuration(Distribution({}), pyproject)
+
+    @pytest.mark.parametrize("module", ["pip-run", "abc-d.λ-xyz-e"])
+    def test_valid_module_name(self, tmp_path, monkeypatch, module):
+        monkeypatch.chdir(tmp_path)
+        assert module in self.dist(module).py_modules
+
+    @pytest.mark.parametrize("module", ["pip run", "-pip-run", "pip-run-stubs"])
+    def test_invalid_module_name(self, tmp_path, monkeypatch, module):
+        monkeypatch.chdir(tmp_path)
+        with pytest.raises(ValueError, match="py-modules"):
+            self.dist(module).py_modules
+
+
+class TestExtModules:
+    def test_pyproject_sets_attribute(self, tmp_path, monkeypatch):
+        monkeypatch.chdir(tmp_path)
+        pyproject = Path("pyproject.toml")
+        toml_config = """
+        [project]
+        name = "test"
+        version = "42.0"
+        [tool.setuptools]
+        ext-modules = [
+          {name = "my.ext", sources = ["hello.c", "world.c"]}
+        ]
+        """
+        pyproject.write_text(cleandoc(toml_config), encoding="utf-8")
+        with pytest.warns(pyprojecttoml._ExperimentalConfiguration):
+            dist = pyprojecttoml.apply_configuration(Distribution({}), pyproject)
+        assert len(dist.ext_modules) == 1
+        assert dist.ext_modules[0].name == "my.ext"
+        assert set(dist.ext_modules[0].sources) == {"hello.c", "world.c"}
+
+
+class TestDeprecatedFields:
+    def test_namespace_packages(self, tmp_path):
+        pyproject = tmp_path / "pyproject.toml"
+        config = """
+        [project]
+        name = "myproj"
+        version = "42"
+        [tool.setuptools]
+        namespace-packages = ["myproj.pkg"]
+        """
+        pyproject.write_text(cleandoc(config), encoding="utf-8")
+        with pytest.raises(RemovedConfigError, match="namespace-packages"):
+            pyprojecttoml.apply_configuration(makedist(tmp_path), pyproject)
+
+
+class TestPresetField:
+    def pyproject(self, tmp_path, dynamic, extra_content=""):
+        content = f"[project]\nname = 'proj'\ndynamic = {dynamic!r}\n"
+        if "version" not in dynamic:
+            content += "version = '42'\n"
+        file = tmp_path / "pyproject.toml"
+        file.write_text(content + extra_content, encoding="utf-8")
+        return file
+
+    @pytest.mark.parametrize(
+        ("attr", "field", "value"),
+        [
+            ("license_expression", "license", "MIT"),
+            pytest.param(
+                *("license", "license", "Not SPDX"),
+                marks=[pytest.mark.filterwarnings("ignore:.*license. overwritten")],
+            ),
+            ("classifiers", "classifiers", ["Private :: Classifier"]),
+            ("entry_points", "scripts", {"console_scripts": ["foobar=foobar:main"]}),
+            ("entry_points", "gui-scripts", {"gui_scripts": ["bazquux=bazquux:main"]}),
+            pytest.param(
+                *("install_requires", "dependencies", ["six"]),
+                marks=[
+                    pytest.mark.filterwarnings("ignore:.*install_requires. overwritten")
+                ],
+            ),
+        ],
+    )
+    def test_not_listed_in_dynamic(self, tmp_path, attr, field, value):
+        """Setuptools cannot set a field if not listed in ``dynamic``"""
+        pyproject = self.pyproject(tmp_path, [])
+        dist = makedist(tmp_path, **{attr: value})
+        msg = re.compile(f"defined outside of `pyproject.toml`:.*{field}", re.S)
+        with pytest.warns(_MissingDynamic, match=msg):
+            dist = pyprojecttoml.apply_configuration(dist, pyproject)
+
+        dist_value = _some_attrgetter(f"metadata.{attr}", attr)(dist)
+        assert not dist_value
+
+    @pytest.mark.parametrize(
+        ("attr", "field", "value"),
+        [
+            ("license_expression", "license", "MIT"),
+            ("install_requires", "dependencies", []),
+            ("extras_require", "optional-dependencies", {}),
+            ("install_requires", "dependencies", ["six"]),
+            ("classifiers", "classifiers", ["Private :: Classifier"]),
+        ],
+    )
+    def test_listed_in_dynamic(self, tmp_path, attr, field, value):
+        pyproject = self.pyproject(tmp_path, [field])
+        dist = makedist(tmp_path, **{attr: value})
+        dist = pyprojecttoml.apply_configuration(dist, pyproject)
+        dist_value = _some_attrgetter(f"metadata.{attr}", attr)(dist)
+        assert dist_value == value
+
+    def test_license_files_exempt_from_dynamic(self, monkeypatch, tmp_path):
+        """
+        license-file is currently not considered in the context of dynamic.
+        As per 2025-02-19, https://packaging.python.org/en/latest/specifications/pyproject-toml/#license-files
+        allows setuptools to fill-in `license-files` the way it sees fit:
+
+        > If the license-files key is not defined, tools can decide how to handle license files.
+        > For example they can choose not to include any files or use their own
+        > logic to discover the appropriate files in the distribution.
+
+        Using license_files from setup.py to fill-in the value is in accordance
+        with this rule.
+        """
+        monkeypatch.chdir(tmp_path)
+        pyproject = self.pyproject(tmp_path, [])
+        dist = makedist(tmp_path, license_files=["LIC*"])
+        (tmp_path / "LIC1").write_text("42", encoding="utf-8")
+        dist = pyprojecttoml.apply_configuration(dist, pyproject)
+        assert dist.metadata.license_files == ["LIC1"]
+
+    def test_warning_overwritten_dependencies(self, tmp_path):
+        src = "[project]\nname='pkg'\nversion='0.1'\ndependencies=['click']\n"
+        pyproject = tmp_path / "pyproject.toml"
+        pyproject.write_text(src, encoding="utf-8")
+        dist = makedist(tmp_path, install_requires=["wheel"])
+        with pytest.warns(match="`install_requires` overwritten"):
+            dist = pyprojecttoml.apply_configuration(dist, pyproject)
+        assert "wheel" not in dist.install_requires
+
+    def test_optional_dependencies_dont_remove_env_markers(self, tmp_path):
+        """
+        Internally setuptools converts dependencies with markers to "extras".
+        If ``install_requires`` is given by ``setup.py``, we have to ensure that
+        applying ``optional-dependencies`` does not overwrite the mandatory
+        dependencies with markers (see #3204).
+        """
+        # If setuptools replace its internal mechanism that uses `requires.txt`
+        # this test has to be rewritten to adapt accordingly
+        extra = "\n[project.optional-dependencies]\nfoo = ['bar>1']\n"
+        pyproject = self.pyproject(tmp_path, ["dependencies"], extra)
+        install_req = ['importlib-resources (>=3.0.0) ; python_version < "3.7"']
+        dist = makedist(tmp_path, install_requires=install_req)
+        dist = pyprojecttoml.apply_configuration(dist, pyproject)
+        assert "foo" in dist.extras_require
+        egg_info = dist.get_command_obj("egg_info")
+        write_requirements(egg_info, tmp_path, tmp_path / "requires.txt")
+        reqs = (tmp_path / "requires.txt").read_text(encoding="utf-8")
+        assert "importlib-resources" in reqs
+        assert "bar" in reqs
+        assert ':python_version < "3.7"' in reqs
+
+    @pytest.mark.parametrize(
+        ("field", "group"),
+        [("scripts", "console_scripts"), ("gui-scripts", "gui_scripts")],
+    )
+    @pytest.mark.filterwarnings("error")
+    def test_scripts_dont_require_dynamic_entry_points(self, tmp_path, field, group):
+        # Issue 3862
+        pyproject = self.pyproject(tmp_path, [field])
+        dist = makedist(tmp_path, entry_points={group: ["foobar=foobar:main"]})
+        dist = pyprojecttoml.apply_configuration(dist, pyproject)
+        assert group in dist.entry_points
+
+
+class TestMeta:
+    def test_example_file_in_sdist(self, setuptools_sdist):
+        """Meta test to ensure tests can run from sdist"""
+        with tarfile.open(setuptools_sdist) as tar:
+            assert any(name.endswith(EXAMPLES_FILE) for name in tar.getnames())
+
+
+class TestInteropCommandLineParsing:
+    def test_version(self, tmp_path, monkeypatch, capsys):
+        # See pypa/setuptools#4047
+        # This test can be removed once the CLI interface of setup.py is removed
+        monkeypatch.chdir(tmp_path)
+        toml_config = """
+        [project]
+        name = "test"
+        version = "42.0"
+        """
+        pyproject = Path(tmp_path, "pyproject.toml")
+        pyproject.write_text(cleandoc(toml_config), encoding="utf-8")
+        opts = {"script_args": ["--version"]}
+        dist = pyprojecttoml.apply_configuration(Distribution(opts), pyproject)
+        dist.parse_command_line()  # <-- there should be no exception here.
+        captured = capsys.readouterr()
+        assert "42.0" in captured.out
+
+
+class TestStaticConfig:
+    def test_mark_static_fields(self, tmp_path, monkeypatch):
+        monkeypatch.chdir(tmp_path)
+        toml_config = """
+        [project]
+        name = "test"
+        version = "42.0"
+        dependencies = ["hello"]
+        keywords = ["world"]
+        classifiers = ["private :: hello world"]
+        [tool.setuptools]
+        obsoletes = ["abcd"]
+        provides = ["abcd"]
+        platforms = ["abcd"]
+        """
+        pyproject = Path(tmp_path, "pyproject.toml")
+        pyproject.write_text(cleandoc(toml_config), encoding="utf-8")
+        dist = pyprojecttoml.apply_configuration(Distribution({}), pyproject)
+        assert is_static(dist.install_requires)
+        assert is_static(dist.metadata.keywords)
+        assert is_static(dist.metadata.classifiers)
+        assert is_static(dist.metadata.obsoletes)
+        assert is_static(dist.metadata.provides)
+        assert is_static(dist.metadata.platforms)
+
+
+# --- Auxiliary Functions ---
+
+
+def core_metadata(dist) -> str:
+    with io.StringIO() as buffer:
+        dist.metadata.write_pkg_file(buffer)
+        pkg_file_txt = buffer.getvalue()
+
+    # Make sure core metadata is valid
+    Metadata.from_email(pkg_file_txt, validate=True)  # can raise exceptions
+
+    skip_prefixes: tuple[str, ...] = ()
+    skip_lines = set()
+    # ---- DIFF NORMALISATION ----
+    # PEP 621 is very particular about author/maintainer metadata conversion, so skip
+    skip_prefixes += ("Author:", "Author-email:", "Maintainer:", "Maintainer-email:")
+    # May be redundant with Home-page
+    skip_prefixes += ("Project-URL: Homepage,", "Home-page:")
+    # May be missing in original (relying on default) but backfilled in the TOML
+    skip_prefixes += ("Description-Content-Type:",)
+    # Remove empty lines
+    skip_lines.add("")
+
+    result = []
+    for line in pkg_file_txt.splitlines():
+        if line.startswith(skip_prefixes) or line in skip_lines:
+            continue
+        result.append(line + "\n")
+
+    return "".join(result)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_expand.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_expand.py
new file mode 100644
index 0000000000000000000000000000000000000000..c5710ec63d7d9d4ed7b709203bb2fc4b512f2093
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_expand.py
@@ -0,0 +1,247 @@
+import os
+import sys
+from pathlib import Path
+
+import pytest
+
+from setuptools._static import is_static
+from setuptools.config import expand
+from setuptools.discovery import find_package_path
+
+from distutils.errors import DistutilsOptionError
+
+
+def write_files(files, root_dir):
+    for file, content in files.items():
+        path = root_dir / file
+        path.parent.mkdir(exist_ok=True, parents=True)
+        path.write_text(content, encoding="utf-8")
+
+
+def test_glob_relative(tmp_path, monkeypatch):
+    files = {
+        "dir1/dir2/dir3/file1.txt",
+        "dir1/dir2/file2.txt",
+        "dir1/file3.txt",
+        "a.ini",
+        "b.ini",
+        "dir1/c.ini",
+        "dir1/dir2/a.ini",
+    }
+
+    write_files({k: "" for k in files}, tmp_path)
+    patterns = ["**/*.txt", "[ab].*", "**/[ac].ini"]
+    monkeypatch.chdir(tmp_path)
+    assert set(expand.glob_relative(patterns)) == files
+    # Make sure the same APIs work outside cwd
+    assert set(expand.glob_relative(patterns, tmp_path)) == files
+
+
+def test_read_files(tmp_path, monkeypatch):
+    dir_ = tmp_path / "dir_"
+    (tmp_path / "_dir").mkdir(exist_ok=True)
+    (tmp_path / "a.txt").touch()
+    files = {"a.txt": "a", "dir1/b.txt": "b", "dir1/dir2/c.txt": "c"}
+    write_files(files, dir_)
+
+    secrets = Path(str(dir_) + "secrets")
+    secrets.mkdir(exist_ok=True)
+    write_files({"secrets.txt": "secret keys"}, secrets)
+
+    with monkeypatch.context() as m:
+        m.chdir(dir_)
+        assert expand.read_files(list(files)) == "a\nb\nc"
+
+        cannot_access_msg = r"Cannot access '.*\.\..a\.txt'"
+        with pytest.raises(DistutilsOptionError, match=cannot_access_msg):
+            expand.read_files(["../a.txt"])
+
+        cannot_access_secrets_msg = r"Cannot access '.*secrets\.txt'"
+        with pytest.raises(DistutilsOptionError, match=cannot_access_secrets_msg):
+            expand.read_files(["../dir_secrets/secrets.txt"])
+
+    # Make sure the same APIs work outside cwd
+    assert expand.read_files(list(files), dir_) == "a\nb\nc"
+    with pytest.raises(DistutilsOptionError, match=cannot_access_msg):
+        expand.read_files(["../a.txt"], dir_)
+
+
+class TestReadAttr:
+    @pytest.mark.parametrize(
+        "example",
+        [
+            # No cookie means UTF-8:
+            b"__version__ = '\xc3\xa9'\nraise SystemExit(1)\n",
+            # If a cookie is present, honor it:
+            b"# -*- coding: utf-8 -*-\n__version__ = '\xc3\xa9'\nraise SystemExit(1)\n",
+            b"# -*- coding: latin1 -*-\n__version__ = '\xe9'\nraise SystemExit(1)\n",
+        ],
+    )
+    def test_read_attr_encoding_cookie(self, example, tmp_path):
+        (tmp_path / "mod.py").write_bytes(example)
+        assert expand.read_attr('mod.__version__', root_dir=tmp_path) == 'é'
+
+    def test_read_attr(self, tmp_path, monkeypatch):
+        files = {
+            "pkg/__init__.py": "",
+            "pkg/sub/__init__.py": "VERSION = '0.1.1'",
+            "pkg/sub/mod.py": (
+                "VALUES = {'a': 0, 'b': {42}, 'c': (0, 1, 1)}\nraise SystemExit(1)"
+            ),
+        }
+        write_files(files, tmp_path)
+
+        with monkeypatch.context() as m:
+            m.chdir(tmp_path)
+            # Make sure it can read the attr statically without evaluating the module
+            version = expand.read_attr('pkg.sub.VERSION')
+            values = expand.read_attr('lib.mod.VALUES', {'lib': 'pkg/sub'})
+
+        assert version == '0.1.1'
+        assert is_static(values)
+
+        assert values['a'] == 0
+        assert values['b'] == {42}
+        assert is_static(values)
+
+        # Make sure the same APIs work outside cwd
+        assert expand.read_attr('pkg.sub.VERSION', root_dir=tmp_path) == '0.1.1'
+        values = expand.read_attr('lib.mod.VALUES', {'lib': 'pkg/sub'}, tmp_path)
+        assert values['c'] == (0, 1, 1)
+
+    @pytest.mark.parametrize(
+        "example",
+        [
+            "VERSION: str\nVERSION = '0.1.1'\nraise SystemExit(1)\n",
+            "VERSION: str = '0.1.1'\nraise SystemExit(1)\n",
+        ],
+    )
+    def test_read_annotated_attr(self, tmp_path, example):
+        files = {
+            "pkg/__init__.py": "",
+            "pkg/sub/__init__.py": example,
+        }
+        write_files(files, tmp_path)
+        # Make sure this attribute can be read statically
+        version = expand.read_attr('pkg.sub.VERSION', root_dir=tmp_path)
+        assert version == '0.1.1'
+        assert is_static(version)
+
+    @pytest.mark.parametrize(
+        "example",
+        [
+            "VERSION = (lambda: '0.1.1')()\n",
+            "def fn(): return '0.1.1'\nVERSION = fn()\n",
+            "VERSION: str = (lambda: '0.1.1')()\n",
+        ],
+    )
+    def test_read_dynamic_attr(self, tmp_path, monkeypatch, example):
+        files = {
+            "pkg/__init__.py": "",
+            "pkg/sub/__init__.py": example,
+        }
+        write_files(files, tmp_path)
+        monkeypatch.chdir(tmp_path)
+        version = expand.read_attr('pkg.sub.VERSION')
+        assert version == '0.1.1'
+        assert not is_static(version)
+
+    def test_import_order(self, tmp_path):
+        """
+        Sometimes the import machinery will import the parent package of a nested
+        module, which triggers side-effects and might create problems (see issue #3176)
+
+        ``read_attr`` should bypass these limitations by resolving modules statically
+        (via ast.literal_eval).
+        """
+        files = {
+            "src/pkg/__init__.py": "from .main import func\nfrom .about import version",
+            "src/pkg/main.py": "import super_complicated_dep\ndef func(): return 42",
+            "src/pkg/about.py": "version = '42'",
+        }
+        write_files(files, tmp_path)
+        attr_desc = "pkg.about.version"
+        package_dir = {"": "src"}
+        # `import super_complicated_dep` should not run, otherwise the build fails
+        assert expand.read_attr(attr_desc, package_dir, tmp_path) == "42"
+
+
+@pytest.mark.parametrize(
+    ("package_dir", "file", "module", "return_value"),
+    [
+        ({"": "src"}, "src/pkg/main.py", "pkg.main", 42),
+        ({"pkg": "lib"}, "lib/main.py", "pkg.main", 13),
+        ({}, "single_module.py", "single_module", 70),
+        ({}, "flat_layout/pkg.py", "flat_layout.pkg", 836),
+    ],
+)
+def test_resolve_class(monkeypatch, tmp_path, package_dir, file, module, return_value):
+    monkeypatch.setattr(sys, "modules", {})  # reproducibility
+    files = {file: f"class Custom:\n    def testing(self): return {return_value}"}
+    write_files(files, tmp_path)
+    cls = expand.resolve_class(f"{module}.Custom", package_dir, tmp_path)
+    assert cls().testing() == return_value
+
+
+@pytest.mark.parametrize(
+    ("args", "pkgs"),
+    [
+        ({"where": ["."], "namespaces": False}, {"pkg", "other"}),
+        ({"where": [".", "dir1"], "namespaces": False}, {"pkg", "other", "dir2"}),
+        ({"namespaces": True}, {"pkg", "other", "dir1", "dir1.dir2"}),
+        ({}, {"pkg", "other", "dir1", "dir1.dir2"}),  # default value for `namespaces`
+    ],
+)
+def test_find_packages(tmp_path, args, pkgs):
+    files = {
+        "pkg/__init__.py",
+        "other/__init__.py",
+        "dir1/dir2/__init__.py",
+    }
+    write_files({k: "" for k in files}, tmp_path)
+
+    package_dir = {}
+    kwargs = {"root_dir": tmp_path, "fill_package_dir": package_dir, **args}
+    where = kwargs.get("where", ["."])
+    assert set(expand.find_packages(**kwargs)) == pkgs
+    for pkg in pkgs:
+        pkg_path = find_package_path(pkg, package_dir, tmp_path)
+        assert os.path.exists(pkg_path)
+
+    # Make sure the same APIs work outside cwd
+    where = [
+        str((tmp_path / p).resolve()).replace(os.sep, "/")  # ensure posix-style paths
+        for p in args.pop("where", ["."])
+    ]
+
+    assert set(expand.find_packages(where=where, **args)) == pkgs
+
+
+@pytest.mark.parametrize(
+    ("files", "where", "expected_package_dir"),
+    [
+        (["pkg1/__init__.py", "pkg1/other.py"], ["."], {}),
+        (["pkg1/__init__.py", "pkg2/__init__.py"], ["."], {}),
+        (["src/pkg1/__init__.py", "src/pkg1/other.py"], ["src"], {"": "src"}),
+        (["src/pkg1/__init__.py", "src/pkg2/__init__.py"], ["src"], {"": "src"}),
+        (
+            ["src1/pkg1/__init__.py", "src2/pkg2/__init__.py"],
+            ["src1", "src2"],
+            {"pkg1": "src1/pkg1", "pkg2": "src2/pkg2"},
+        ),
+        (
+            ["src/pkg1/__init__.py", "pkg2/__init__.py"],
+            ["src", "."],
+            {"pkg1": "src/pkg1"},
+        ),
+    ],
+)
+def test_fill_package_dir(tmp_path, files, where, expected_package_dir):
+    write_files({k: "" for k in files}, tmp_path)
+    pkg_dir = {}
+    kwargs = {"root_dir": tmp_path, "fill_package_dir": pkg_dir, "namespaces": False}
+    pkgs = expand.find_packages(where=where, **kwargs)
+    assert set(pkg_dir.items()) == set(expected_package_dir.items())
+    for pkg in pkgs:
+        pkg_path = find_package_path(pkg, pkg_dir, tmp_path)
+        assert os.path.exists(pkg_path)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_pyprojecttoml.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_pyprojecttoml.py
new file mode 100644
index 0000000000000000000000000000000000000000..db40fcd23da137dfb2f4ddde7ffb722193ee83e2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_pyprojecttoml.py
@@ -0,0 +1,396 @@
+import re
+from configparser import ConfigParser
+from inspect import cleandoc
+
+import jaraco.path
+import pytest
+import tomli_w
+from path import Path
+
+import setuptools  # noqa: F401 # force distutils.core to be patched
+from setuptools.config.pyprojecttoml import (
+    _ToolsTypoInMetadata,
+    apply_configuration,
+    expand_configuration,
+    read_configuration,
+    validate,
+)
+from setuptools.dist import Distribution
+from setuptools.errors import OptionError
+
+import distutils.core
+
+EXAMPLE = """
+[project]
+name = "myproj"
+keywords = ["some", "key", "words"]
+dynamic = ["version", "readme"]
+requires-python = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+dependencies = [
+    'importlib-metadata>=0.12;python_version<"3.8"',
+    'importlib-resources>=1.0;python_version<"3.7"',
+    'pathlib2>=2.3.3,<3;python_version < "3.4" and sys.platform != "win32"',
+]
+
+[project.optional-dependencies]
+docs = [
+    "sphinx>=3",
+    "sphinx-argparse>=0.2.5",
+    "sphinx-rtd-theme>=0.4.3",
+]
+testing = [
+    "pytest>=1",
+    "coverage>=3,<5",
+]
+
+[project.scripts]
+exec = "pkg.__main__:exec"
+
+[build-system]
+requires = ["setuptools", "wheel"]
+build-backend = "setuptools.build_meta"
+
+[tool.setuptools]
+package-dir = {"" = "src"}
+zip-safe = true
+platforms = ["any"]
+
+[tool.setuptools.packages.find]
+where = ["src"]
+
+[tool.setuptools.cmdclass]
+sdist = "pkg.mod.CustomSdist"
+
+[tool.setuptools.dynamic.version]
+attr = "pkg.__version__.VERSION"
+
+[tool.setuptools.dynamic.readme]
+file = ["README.md"]
+content-type = "text/markdown"
+
+[tool.setuptools.package-data]
+"*" = ["*.txt"]
+
+[tool.setuptools.data-files]
+"data" = ["_files/*.txt"]
+
+[tool.distutils.sdist]
+formats = "gztar"
+
+[tool.distutils.bdist_wheel]
+universal = true
+"""
+
+
+def create_example(path, pkg_root):
+    files = {
+        "pyproject.toml": EXAMPLE,
+        "README.md": "hello world",
+        "_files": {
+            "file.txt": "",
+        },
+    }
+    packages = {
+        "pkg": {
+            "__init__.py": "",
+            "mod.py": "class CustomSdist: pass",
+            "__version__.py": "VERSION = (3, 10)",
+            "__main__.py": "def exec(): print('hello')",
+        },
+    }
+
+    assert pkg_root  # Meta-test: cannot be empty string.
+
+    if pkg_root == ".":
+        files = {**files, **packages}
+        # skip other files: flat-layout will raise error for multi-package dist
+    else:
+        # Use this opportunity to ensure namespaces are discovered
+        files[pkg_root] = {**packages, "other": {"nested": {"__init__.py": ""}}}
+
+    jaraco.path.build(files, prefix=path)
+
+
+def verify_example(config, path, pkg_root):
+    pyproject = path / "pyproject.toml"
+    pyproject.write_text(tomli_w.dumps(config), encoding="utf-8")
+    expanded = expand_configuration(config, path)
+    expanded_project = expanded["project"]
+    assert read_configuration(pyproject, expand=True) == expanded
+    assert expanded_project["version"] == "3.10"
+    assert expanded_project["readme"]["text"] == "hello world"
+    assert "packages" in expanded["tool"]["setuptools"]
+    if pkg_root == ".":
+        # Auto-discovery will raise error for multi-package dist
+        assert set(expanded["tool"]["setuptools"]["packages"]) == {"pkg"}
+    else:
+        assert set(expanded["tool"]["setuptools"]["packages"]) == {
+            "pkg",
+            "other",
+            "other.nested",
+        }
+    assert expanded["tool"]["setuptools"]["include-package-data"] is True
+    assert "" in expanded["tool"]["setuptools"]["package-data"]
+    assert "*" not in expanded["tool"]["setuptools"]["package-data"]
+    assert expanded["tool"]["setuptools"]["data-files"] == [
+        ("data", ["_files/file.txt"])
+    ]
+
+
+def test_read_configuration(tmp_path):
+    create_example(tmp_path, "src")
+    pyproject = tmp_path / "pyproject.toml"
+
+    config = read_configuration(pyproject, expand=False)
+    assert config["project"].get("version") is None
+    assert config["project"].get("readme") is None
+
+    verify_example(config, tmp_path, "src")
+
+
+@pytest.mark.parametrize(
+    ("pkg_root", "opts"),
+    [
+        (".", {}),
+        ("src", {}),
+        ("lib", {"packages": {"find": {"where": ["lib"]}}}),
+    ],
+)
+def test_discovered_package_dir_with_attr_directive_in_config(tmp_path, pkg_root, opts):
+    create_example(tmp_path, pkg_root)
+
+    pyproject = tmp_path / "pyproject.toml"
+
+    config = read_configuration(pyproject, expand=False)
+    assert config["project"].get("version") is None
+    assert config["project"].get("readme") is None
+    config["tool"]["setuptools"].pop("packages", None)
+    config["tool"]["setuptools"].pop("package-dir", None)
+
+    config["tool"]["setuptools"].update(opts)
+    verify_example(config, tmp_path, pkg_root)
+
+
+ENTRY_POINTS = {
+    "console_scripts": {"a": "mod.a:func"},
+    "gui_scripts": {"b": "mod.b:func"},
+    "other": {"c": "mod.c:func [extra]"},
+}
+
+
+class TestEntryPoints:
+    def write_entry_points(self, tmp_path):
+        entry_points = ConfigParser()
+        entry_points.read_dict(ENTRY_POINTS)
+        with open(tmp_path / "entry-points.txt", "w", encoding="utf-8") as f:
+            entry_points.write(f)
+
+    def pyproject(self, dynamic=None):
+        project = {"dynamic": dynamic or ["scripts", "gui-scripts", "entry-points"]}
+        tool = {"dynamic": {"entry-points": {"file": "entry-points.txt"}}}
+        return {"project": project, "tool": {"setuptools": tool}}
+
+    def test_all_listed_in_dynamic(self, tmp_path):
+        self.write_entry_points(tmp_path)
+        expanded = expand_configuration(self.pyproject(), tmp_path)
+        expanded_project = expanded["project"]
+        assert len(expanded_project["scripts"]) == 1
+        assert expanded_project["scripts"]["a"] == "mod.a:func"
+        assert len(expanded_project["gui-scripts"]) == 1
+        assert expanded_project["gui-scripts"]["b"] == "mod.b:func"
+        assert len(expanded_project["entry-points"]) == 1
+        assert expanded_project["entry-points"]["other"]["c"] == "mod.c:func [extra]"
+
+    @pytest.mark.parametrize("missing_dynamic", ("scripts", "gui-scripts"))
+    def test_scripts_not_listed_in_dynamic(self, tmp_path, missing_dynamic):
+        self.write_entry_points(tmp_path)
+        dynamic = {"scripts", "gui-scripts", "entry-points"} - {missing_dynamic}
+
+        msg = f"defined outside of `pyproject.toml`:.*{missing_dynamic}"
+        with pytest.raises(OptionError, match=re.compile(msg, re.S)):
+            expand_configuration(self.pyproject(dynamic), tmp_path)
+
+
+class TestClassifiers:
+    def test_dynamic(self, tmp_path):
+        # Let's create a project example that has dynamic classifiers
+        # coming from a txt file.
+        create_example(tmp_path, "src")
+        classifiers = cleandoc(
+            """
+            Framework :: Flask
+            Programming Language :: Haskell
+            """
+        )
+        (tmp_path / "classifiers.txt").write_text(classifiers, encoding="utf-8")
+
+        pyproject = tmp_path / "pyproject.toml"
+        config = read_configuration(pyproject, expand=False)
+        dynamic = config["project"]["dynamic"]
+        config["project"]["dynamic"] = list({*dynamic, "classifiers"})
+        dynamic_config = config["tool"]["setuptools"]["dynamic"]
+        dynamic_config["classifiers"] = {"file": "classifiers.txt"}
+
+        # When the configuration is expanded,
+        # each line of the file should be an different classifier.
+        validate(config, pyproject)
+        expanded = expand_configuration(config, tmp_path)
+
+        assert set(expanded["project"]["classifiers"]) == {
+            "Framework :: Flask",
+            "Programming Language :: Haskell",
+        }
+
+    def test_dynamic_without_config(self, tmp_path):
+        config = """
+        [project]
+        name = "myproj"
+        version = '42'
+        dynamic = ["classifiers"]
+        """
+
+        pyproject = tmp_path / "pyproject.toml"
+        pyproject.write_text(cleandoc(config), encoding="utf-8")
+        with pytest.raises(OptionError, match="No configuration .* .classifiers."):
+            read_configuration(pyproject)
+
+    def test_dynamic_readme_from_setup_script_args(self, tmp_path):
+        config = """
+        [project]
+        name = "myproj"
+        version = '42'
+        dynamic = ["readme"]
+        """
+        pyproject = tmp_path / "pyproject.toml"
+        pyproject.write_text(cleandoc(config), encoding="utf-8")
+        dist = Distribution(attrs={"long_description": "42"})
+        # No error should occur because of missing `readme`
+        dist = apply_configuration(dist, pyproject)
+        assert dist.metadata.long_description == "42"
+
+    def test_dynamic_without_file(self, tmp_path):
+        config = """
+        [project]
+        name = "myproj"
+        version = '42'
+        dynamic = ["classifiers"]
+
+        [tool.setuptools.dynamic]
+        classifiers = {file = ["classifiers.txt"]}
+        """
+
+        pyproject = tmp_path / "pyproject.toml"
+        pyproject.write_text(cleandoc(config), encoding="utf-8")
+        with pytest.warns(UserWarning, match="File .*classifiers.txt. cannot be found"):
+            expanded = read_configuration(pyproject)
+        assert "classifiers" not in expanded["project"]
+
+
+@pytest.mark.parametrize(
+    "example",
+    (
+        """
+        [project]
+        name = "myproj"
+        version = "1.2"
+
+        [my-tool.that-disrespect.pep518]
+        value = 42
+        """,
+    ),
+)
+def test_ignore_unrelated_config(tmp_path, example):
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text(cleandoc(example), encoding="utf-8")
+
+    # Make sure no error is raised due to 3rd party configs in pyproject.toml
+    assert read_configuration(pyproject) is not None
+
+
+@pytest.mark.parametrize(
+    ("example", "error_msg"),
+    [
+        (
+            """
+            [project]
+            name = "myproj"
+            version = "1.2"
+            requires = ['pywin32; platform_system=="Windows"' ]
+            """,
+            "configuration error: .project. must not contain ..requires.. properties",
+        ),
+    ],
+)
+def test_invalid_example(tmp_path, example, error_msg):
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text(cleandoc(example), encoding="utf-8")
+
+    pattern = re.compile(f"invalid pyproject.toml.*{error_msg}.*", re.M | re.S)
+    with pytest.raises(ValueError, match=pattern):
+        read_configuration(pyproject)
+
+
+@pytest.mark.parametrize("config", ("", "[tool.something]\nvalue = 42"))
+def test_empty(tmp_path, config):
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text(config, encoding="utf-8")
+
+    # Make sure no error is raised
+    assert read_configuration(pyproject) == {}
+
+
+@pytest.mark.parametrize("config", ("[project]\nname = 'myproj'\nversion='42'\n",))
+def test_include_package_data_by_default(tmp_path, config):
+    """Builds with ``pyproject.toml`` should consider ``include-package-data=True`` as
+    default.
+    """
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text(config, encoding="utf-8")
+
+    config = read_configuration(pyproject)
+    assert config["tool"]["setuptools"]["include-package-data"] is True
+
+
+def test_include_package_data_in_setuppy(tmp_path):
+    """Builds with ``pyproject.toml`` should consider ``include_package_data`` set in
+    ``setup.py``.
+
+    See https://github.com/pypa/setuptools/issues/3197#issuecomment-1079023889
+    """
+    files = {
+        "pyproject.toml": "[project]\nname = 'myproj'\nversion='42'\n",
+        "setup.py": "__import__('setuptools').setup(include_package_data=False)",
+    }
+    jaraco.path.build(files, prefix=tmp_path)
+
+    with Path(tmp_path):
+        dist = distutils.core.run_setup("setup.py", {}, stop_after="config")
+
+    assert dist.get_name() == "myproj"
+    assert dist.get_version() == "42"
+    assert dist.include_package_data is False
+
+
+def test_warn_tools_typo(tmp_path):
+    """Test that the common ``tools.setuptools`` typo in ``pyproject.toml`` issues a warning
+
+    See https://github.com/pypa/setuptools/issues/4150
+    """
+    config = """
+    [build-system]
+    requires = ["setuptools"]
+    build-backend = "setuptools.build_meta"
+
+    [project]
+    name = "myproj"
+    version = '42'
+
+    [tools.setuptools]
+    packages = ["package"]
+    """
+
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text(cleandoc(config), encoding="utf-8")
+
+    with pytest.warns(_ToolsTypoInMetadata):
+        read_configuration(pyproject)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_pyprojecttoml_dynamic_deps.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_pyprojecttoml_dynamic_deps.py
new file mode 100644
index 0000000000000000000000000000000000000000..e42f28ffaaf5270a74fe9f03885b75bb91858030
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_pyprojecttoml_dynamic_deps.py
@@ -0,0 +1,109 @@
+from inspect import cleandoc
+
+import pytest
+from jaraco import path
+
+from setuptools.config.pyprojecttoml import apply_configuration
+from setuptools.dist import Distribution
+from setuptools.warnings import SetuptoolsWarning
+
+
+def test_dynamic_dependencies(tmp_path):
+    files = {
+        "requirements.txt": "six\n  # comment\n",
+        "pyproject.toml": cleandoc(
+            """
+            [project]
+            name = "myproj"
+            version = "1.0"
+            dynamic = ["dependencies"]
+
+            [build-system]
+            requires = ["setuptools", "wheel"]
+            build-backend = "setuptools.build_meta"
+
+            [tool.setuptools.dynamic.dependencies]
+            file = ["requirements.txt"]
+            """
+        ),
+    }
+    path.build(files, prefix=tmp_path)
+    dist = Distribution()
+    dist = apply_configuration(dist, tmp_path / "pyproject.toml")
+    assert dist.install_requires == ["six"]
+
+
+def test_dynamic_optional_dependencies(tmp_path):
+    files = {
+        "requirements-docs.txt": "sphinx\n  # comment\n",
+        "pyproject.toml": cleandoc(
+            """
+            [project]
+            name = "myproj"
+            version = "1.0"
+            dynamic = ["optional-dependencies"]
+
+            [tool.setuptools.dynamic.optional-dependencies.docs]
+            file = ["requirements-docs.txt"]
+
+            [build-system]
+            requires = ["setuptools", "wheel"]
+            build-backend = "setuptools.build_meta"
+            """
+        ),
+    }
+    path.build(files, prefix=tmp_path)
+    dist = Distribution()
+    dist = apply_configuration(dist, tmp_path / "pyproject.toml")
+    assert dist.extras_require == {"docs": ["sphinx"]}
+
+
+def test_mixed_dynamic_optional_dependencies(tmp_path):
+    """
+    Test that if PEP 621 was loosened to allow mixing of dynamic and static
+    configurations in the case of fields containing sub-fields (groups),
+    things would work out.
+    """
+    files = {
+        "requirements-images.txt": "pillow~=42.0\n  # comment\n",
+        "pyproject.toml": cleandoc(
+            """
+            [project]
+            name = "myproj"
+            version = "1.0"
+            dynamic = ["optional-dependencies"]
+
+            [project.optional-dependencies]
+            docs = ["sphinx"]
+
+            [tool.setuptools.dynamic.optional-dependencies.images]
+            file = ["requirements-images.txt"]
+            """
+        ),
+    }
+
+    path.build(files, prefix=tmp_path)
+    pyproject = tmp_path / "pyproject.toml"
+    with pytest.raises(ValueError, match="project.optional-dependencies"):
+        apply_configuration(Distribution(), pyproject)
+
+
+def test_mixed_extras_require_optional_dependencies(tmp_path):
+    files = {
+        "pyproject.toml": cleandoc(
+            """
+            [project]
+            name = "myproj"
+            version = "1.0"
+            optional-dependencies.docs = ["sphinx"]
+            """
+        ),
+    }
+
+    path.build(files, prefix=tmp_path)
+    pyproject = tmp_path / "pyproject.toml"
+
+    with pytest.warns(SetuptoolsWarning, match=".extras_require. overwritten"):
+        dist = Distribution({"extras_require": {"hello": ["world"]}})
+        dist = apply_configuration(dist, pyproject)
+        assert dist.extras_require == {"docs": ["sphinx"]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_setupcfg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_setupcfg.py
new file mode 100644
index 0000000000000000000000000000000000000000..61af99044742b46ec99ad1d38f34f576908f3e68
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/config/test_setupcfg.py
@@ -0,0 +1,980 @@
+import configparser
+import contextlib
+import inspect
+import re
+from pathlib import Path
+from unittest.mock import Mock, patch
+
+import pytest
+from packaging.requirements import InvalidRequirement
+
+from setuptools.config.setupcfg import ConfigHandler, Target, read_configuration
+from setuptools.dist import Distribution, _Distribution
+from setuptools.warnings import SetuptoolsDeprecationWarning
+
+from ..textwrap import DALS
+
+from distutils.errors import DistutilsFileError, DistutilsOptionError
+
+
+class ErrConfigHandler(ConfigHandler[Target]):
+    """Erroneous handler. Fails to implement required methods."""
+
+    section_prefix = "**err**"
+
+
+def make_package_dir(name, base_dir, ns=False):
+    dir_package = base_dir
+    for dir_name in name.split('/'):
+        dir_package = dir_package.mkdir(dir_name)
+    init_file = None
+    if not ns:
+        init_file = dir_package.join('__init__.py')
+        init_file.write('')
+    return dir_package, init_file
+
+
+def fake_env(
+    tmpdir, setup_cfg, setup_py=None, encoding='ascii', package_path='fake_package'
+):
+    if setup_py is None:
+        setup_py = 'from setuptools import setup\nsetup()\n'
+
+    tmpdir.join('setup.py').write(setup_py)
+    config = tmpdir.join('setup.cfg')
+    config.write(setup_cfg.encode(encoding), mode='wb')
+
+    package_dir, init_file = make_package_dir(package_path, tmpdir)
+
+    init_file.write(
+        'VERSION = (1, 2, 3)\n'
+        '\n'
+        'VERSION_MAJOR = 1'
+        '\n'
+        'def get_version():\n'
+        '    return [3, 4, 5, "dev"]\n'
+        '\n'
+    )
+
+    return package_dir, config
+
+
+@contextlib.contextmanager
+def get_dist(tmpdir, kwargs_initial=None, parse=True):
+    kwargs_initial = kwargs_initial or {}
+
+    with tmpdir.as_cwd():
+        dist = Distribution(kwargs_initial)
+        dist.script_name = 'setup.py'
+        parse and dist.parse_config_files()
+
+        yield dist
+
+
+def test_parsers_implemented():
+    with pytest.raises(NotImplementedError):
+        handler = ErrConfigHandler(None, {}, False, Mock())
+        handler.parsers
+
+
+class TestConfigurationReader:
+    def test_basic(self, tmpdir):
+        _, config = fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'version = 10.1.1\n'
+            'keywords = one, two\n'
+            '\n'
+            '[options]\n'
+            'scripts = bin/a.py, bin/b.py\n',
+        )
+        config_dict = read_configuration(str(config))
+        assert config_dict['metadata']['version'] == '10.1.1'
+        assert config_dict['metadata']['keywords'] == ['one', 'two']
+        assert config_dict['options']['scripts'] == ['bin/a.py', 'bin/b.py']
+
+    def test_no_config(self, tmpdir):
+        with pytest.raises(DistutilsFileError):
+            read_configuration(str(tmpdir.join('setup.cfg')))
+
+    def test_ignore_errors(self, tmpdir):
+        _, config = fake_env(
+            tmpdir,
+            '[metadata]\nversion = attr: none.VERSION\nkeywords = one, two\n',
+        )
+        with pytest.raises(ImportError):
+            read_configuration(str(config))
+
+        config_dict = read_configuration(str(config), ignore_option_errors=True)
+
+        assert config_dict['metadata']['keywords'] == ['one', 'two']
+        assert 'version' not in config_dict['metadata']
+
+        config.remove()
+
+
+class TestMetadata:
+    def test_basic(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'version = 10.1.1\n'
+            'description = Some description\n'
+            'long_description_content_type = text/something\n'
+            'long_description = file: README\n'
+            'name = fake_name\n'
+            'keywords = one, two\n'
+            'provides = package, package.sub\n'
+            'license = otherlic\n'
+            'download_url = http://test.test.com/test/\n'
+            'maintainer_email = test@test.com\n',
+        )
+
+        tmpdir.join('README').write('readme contents\nline2')
+
+        meta_initial = {
+            # This will be used so `otherlic` won't replace it.
+            'license': 'BSD 3-Clause License',
+        }
+
+        with get_dist(tmpdir, meta_initial) as dist:
+            metadata = dist.metadata
+
+            assert metadata.version == '10.1.1'
+            assert metadata.description == 'Some description'
+            assert metadata.long_description_content_type == 'text/something'
+            assert metadata.long_description == 'readme contents\nline2'
+            assert metadata.provides == ['package', 'package.sub']
+            assert metadata.license == 'BSD 3-Clause License'
+            assert metadata.name == 'fake_name'
+            assert metadata.keywords == ['one', 'two']
+            assert metadata.download_url == 'http://test.test.com/test/'
+            assert metadata.maintainer_email == 'test@test.com'
+
+    def test_license_cfg(self, tmpdir):
+        fake_env(
+            tmpdir,
+            DALS(
+                """
+            [metadata]
+            name=foo
+            version=0.0.1
+            license=Apache 2.0
+            """
+            ),
+        )
+
+        with get_dist(tmpdir) as dist:
+            metadata = dist.metadata
+
+            assert metadata.name == "foo"
+            assert metadata.version == "0.0.1"
+            assert metadata.license == "Apache 2.0"
+
+    def test_file_mixed(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\nlong_description = file: README.rst, CHANGES.rst\n\n',
+        )
+
+        tmpdir.join('README.rst').write('readme contents\nline2')
+        tmpdir.join('CHANGES.rst').write('changelog contents\nand stuff')
+
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.long_description == (
+                'readme contents\nline2\nchangelog contents\nand stuff'
+            )
+
+    def test_file_sandboxed(self, tmpdir):
+        tmpdir.ensure("README")
+        project = tmpdir.join('depth1', 'depth2')
+        project.ensure(dir=True)
+        fake_env(project, '[metadata]\nlong_description = file: ../../README\n')
+
+        with get_dist(project, parse=False) as dist:
+            with pytest.raises(DistutilsOptionError):
+                dist.parse_config_files()  # file: out of sandbox
+
+    def test_aliases(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'author_email = test@test.com\n'
+            'home_page = http://test.test.com/test/\n'
+            'summary = Short summary\n'
+            'platform = a, b\n'
+            'classifier =\n'
+            '  Framework :: Django\n'
+            '  Programming Language :: Python :: 3.5\n',
+        )
+
+        with get_dist(tmpdir) as dist:
+            metadata = dist.metadata
+            assert metadata.author_email == 'test@test.com'
+            assert metadata.url == 'http://test.test.com/test/'
+            assert metadata.description == 'Short summary'
+            assert metadata.platforms == ['a', 'b']
+            assert metadata.classifiers == [
+                'Framework :: Django',
+                'Programming Language :: Python :: 3.5',
+            ]
+
+    def test_multiline(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'name = fake_name\n'
+            'keywords =\n'
+            '  one\n'
+            '  two\n'
+            'classifiers =\n'
+            '  Framework :: Django\n'
+            '  Programming Language :: Python :: 3.5\n',
+        )
+        with get_dist(tmpdir) as dist:
+            metadata = dist.metadata
+            assert metadata.keywords == ['one', 'two']
+            assert metadata.classifiers == [
+                'Framework :: Django',
+                'Programming Language :: Python :: 3.5',
+            ]
+
+    def test_dict(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'project_urls =\n'
+            '  Link One = https://example.com/one/\n'
+            '  Link Two = https://example.com/two/\n',
+        )
+        with get_dist(tmpdir) as dist:
+            metadata = dist.metadata
+            assert metadata.project_urls == {
+                'Link One': 'https://example.com/one/',
+                'Link Two': 'https://example.com/two/',
+            }
+
+    def test_version(self, tmpdir):
+        package_dir, config = fake_env(
+            tmpdir, '[metadata]\nversion = attr: fake_package.VERSION\n'
+        )
+
+        sub_a = package_dir.mkdir('subpkg_a')
+        sub_a.join('__init__.py').write('')
+        sub_a.join('mod.py').write('VERSION = (2016, 11, 26)')
+
+        sub_b = package_dir.mkdir('subpkg_b')
+        sub_b.join('__init__.py').write('')
+        sub_b.join('mod.py').write(
+            'import third_party_module\nVERSION = (2016, 11, 26)'
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '1.2.3'
+
+        config.write('[metadata]\nversion = attr: fake_package.get_version\n')
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '3.4.5.dev'
+
+        config.write('[metadata]\nversion = attr: fake_package.VERSION_MAJOR\n')
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '1'
+
+        config.write('[metadata]\nversion = attr: fake_package.subpkg_a.mod.VERSION\n')
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '2016.11.26'
+
+        config.write('[metadata]\nversion = attr: fake_package.subpkg_b.mod.VERSION\n')
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '2016.11.26'
+
+    def test_version_file(self, tmpdir):
+        fake_env(tmpdir, '[metadata]\nversion = file: fake_package/version.txt\n')
+        tmpdir.join('fake_package', 'version.txt').write('1.2.3\n')
+
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '1.2.3'
+
+        tmpdir.join('fake_package', 'version.txt').write('1.2.3\n4.5.6\n')
+        with pytest.raises(DistutilsOptionError):
+            with get_dist(tmpdir) as dist:
+                dist.metadata.version
+
+    def test_version_with_package_dir_simple(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'version = attr: fake_package_simple.VERSION\n'
+            '[options]\n'
+            'package_dir =\n'
+            '    = src\n',
+            package_path='src/fake_package_simple',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '1.2.3'
+
+    def test_version_with_package_dir_rename(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'version = attr: fake_package_rename.VERSION\n'
+            '[options]\n'
+            'package_dir =\n'
+            '    fake_package_rename = fake_dir\n',
+            package_path='fake_dir',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '1.2.3'
+
+    def test_version_with_package_dir_complex(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[metadata]\n'
+            'version = attr: fake_package_complex.VERSION\n'
+            '[options]\n'
+            'package_dir =\n'
+            '    fake_package_complex = src/fake_dir\n',
+            package_path='src/fake_dir',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.version == '1.2.3'
+
+    def test_unknown_meta_item(self, tmpdir):
+        fake_env(tmpdir, '[metadata]\nname = fake_name\nunknown = some\n')
+        with get_dist(tmpdir, parse=False) as dist:
+            dist.parse_config_files()  # Skip unknown.
+
+    def test_usupported_section(self, tmpdir):
+        fake_env(tmpdir, '[metadata.some]\nkey = val\n')
+        with get_dist(tmpdir, parse=False) as dist:
+            with pytest.raises(DistutilsOptionError):
+                dist.parse_config_files()
+
+    def test_classifiers(self, tmpdir):
+        expected = set([
+            'Framework :: Django',
+            'Programming Language :: Python :: 3',
+            'Programming Language :: Python :: 3.5',
+        ])
+
+        # From file.
+        _, config = fake_env(tmpdir, '[metadata]\nclassifiers = file: classifiers\n')
+
+        tmpdir.join('classifiers').write(
+            'Framework :: Django\n'
+            'Programming Language :: Python :: 3\n'
+            'Programming Language :: Python :: 3.5\n'
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert set(dist.metadata.classifiers) == expected
+
+        # From list notation
+        config.write(
+            '[metadata]\n'
+            'classifiers =\n'
+            '    Framework :: Django\n'
+            '    Programming Language :: Python :: 3\n'
+            '    Programming Language :: Python :: 3.5\n'
+        )
+        with get_dist(tmpdir) as dist:
+            assert set(dist.metadata.classifiers) == expected
+
+    def test_interpolation(self, tmpdir):
+        fake_env(tmpdir, '[metadata]\ndescription = %(message)s\n')
+        with pytest.raises(configparser.InterpolationMissingOptionError):
+            with get_dist(tmpdir):
+                pass
+
+    def test_non_ascii_1(self, tmpdir):
+        fake_env(tmpdir, '[metadata]\ndescription = éàïôñ\n', encoding='utf-8')
+        with get_dist(tmpdir):
+            pass
+
+    def test_non_ascii_3(self, tmpdir):
+        fake_env(tmpdir, '\n# -*- coding: invalid\n')
+        with get_dist(tmpdir):
+            pass
+
+    def test_non_ascii_4(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '# -*- coding: utf-8\n[metadata]\ndescription = éàïôñ\n',
+            encoding='utf-8',
+        )
+        with get_dist(tmpdir) as dist:
+            assert dist.metadata.description == 'éàïôñ'
+
+    def test_not_utf8(self, tmpdir):
+        """
+        Config files encoded not in UTF-8 will fail
+        """
+        fake_env(
+            tmpdir,
+            '# vim: set fileencoding=iso-8859-15 :\n[metadata]\ndescription = éàïôñ\n',
+            encoding='iso-8859-15',
+        )
+        with pytest.raises(UnicodeDecodeError):
+            with get_dist(tmpdir):
+                pass
+
+    @pytest.mark.parametrize(
+        ("error_msg", "config", "invalid"),
+        [
+            (
+                "Invalid dash-separated key 'author-email' in 'metadata' (setup.cfg)",
+                DALS(
+                    """
+                    [metadata]
+                    author-email = test@test.com
+                    maintainer_email = foo@foo.com
+                    """
+                ),
+                {"author-email": "test@test.com"},
+            ),
+            (
+                "Invalid uppercase key 'Name' in 'metadata' (setup.cfg)",
+                DALS(
+                    """
+                    [metadata]
+                    Name = foo
+                    description = Some description
+                    """
+                ),
+                {"Name": "foo"},
+            ),
+        ],
+    )
+    def test_invalid_options_previously_deprecated(
+        self, tmpdir, error_msg, config, invalid
+    ):
+        # This test and related methods can be removed when no longer needed.
+        # Deprecation postponed due to push-back from the community in
+        # https://github.com/pypa/setuptools/issues/4910
+        fake_env(tmpdir, config)
+        with pytest.warns(SetuptoolsDeprecationWarning, match=re.escape(error_msg)):
+            dist = get_dist(tmpdir).__enter__()
+
+        tmpdir.join('setup.cfg').remove()
+
+        for field, value in invalid.items():
+            attr = field.replace("-", "_").lower()
+            assert getattr(dist.metadata, attr) == value
+
+
+class TestOptions:
+    def test_basic(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options]\n'
+            'zip_safe = True\n'
+            'include_package_data = yes\n'
+            'package_dir = b=c, =src\n'
+            'packages = pack_a, pack_b.subpack\n'
+            'namespace_packages = pack1, pack2\n'
+            'scripts = bin/one.py, bin/two.py\n'
+            'eager_resources = bin/one.py, bin/two.py\n'
+            'install_requires = docutils>=0.3; pack ==1.1, ==1.3; hey\n'
+            'setup_requires = docutils>=0.3; spack ==1.1, ==1.3; there\n'
+            'dependency_links = http://some.com/here/1, '
+            'http://some.com/there/2\n'
+            'python_requires = >=1.0, !=2.8\n'
+            'py_modules = module1, module2\n',
+        )
+        deprec = pytest.warns(SetuptoolsDeprecationWarning, match="namespace_packages")
+        with deprec, get_dist(tmpdir) as dist:
+            assert dist.zip_safe
+            assert dist.include_package_data
+            assert dist.package_dir == {'': 'src', 'b': 'c'}
+            assert dist.packages == ['pack_a', 'pack_b.subpack']
+            assert dist.namespace_packages == ['pack1', 'pack2']
+            assert dist.scripts == ['bin/one.py', 'bin/two.py']
+            assert dist.dependency_links == ([
+                'http://some.com/here/1',
+                'http://some.com/there/2',
+            ])
+            assert dist.install_requires == ([
+                'docutils>=0.3',
+                'pack==1.1,==1.3',
+                'hey',
+            ])
+            assert dist.setup_requires == ([
+                'docutils>=0.3',
+                'spack ==1.1, ==1.3',
+                'there',
+            ])
+            assert dist.python_requires == '>=1.0, !=2.8'
+            assert dist.py_modules == ['module1', 'module2']
+
+    def test_multiline(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options]\n'
+            'package_dir = \n'
+            '  b=c\n'
+            '  =src\n'
+            'packages = \n'
+            '  pack_a\n'
+            '  pack_b.subpack\n'
+            'namespace_packages = \n'
+            '  pack1\n'
+            '  pack2\n'
+            'scripts = \n'
+            '  bin/one.py\n'
+            '  bin/two.py\n'
+            'eager_resources = \n'
+            '  bin/one.py\n'
+            '  bin/two.py\n'
+            'install_requires = \n'
+            '  docutils>=0.3\n'
+            '  pack ==1.1, ==1.3\n'
+            '  hey\n'
+            'setup_requires = \n'
+            '  docutils>=0.3\n'
+            '  spack ==1.1, ==1.3\n'
+            '  there\n'
+            'dependency_links = \n'
+            '  http://some.com/here/1\n'
+            '  http://some.com/there/2\n',
+        )
+        deprec = pytest.warns(SetuptoolsDeprecationWarning, match="namespace_packages")
+        with deprec, get_dist(tmpdir) as dist:
+            assert dist.package_dir == {'': 'src', 'b': 'c'}
+            assert dist.packages == ['pack_a', 'pack_b.subpack']
+            assert dist.namespace_packages == ['pack1', 'pack2']
+            assert dist.scripts == ['bin/one.py', 'bin/two.py']
+            assert dist.dependency_links == ([
+                'http://some.com/here/1',
+                'http://some.com/there/2',
+            ])
+            assert dist.install_requires == ([
+                'docutils>=0.3',
+                'pack==1.1,==1.3',
+                'hey',
+            ])
+            assert dist.setup_requires == ([
+                'docutils>=0.3',
+                'spack ==1.1, ==1.3',
+                'there',
+            ])
+
+    def test_package_dir_fail(self, tmpdir):
+        fake_env(tmpdir, '[options]\npackage_dir = a b\n')
+        with get_dist(tmpdir, parse=False) as dist:
+            with pytest.raises(DistutilsOptionError):
+                dist.parse_config_files()
+
+    def test_package_data(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options.package_data]\n'
+            '* = *.txt, *.rst\n'
+            'hello = *.msg\n'
+            '\n'
+            '[options.exclude_package_data]\n'
+            '* = fake1.txt, fake2.txt\n'
+            'hello = *.dat\n',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.package_data == {
+                '': ['*.txt', '*.rst'],
+                'hello': ['*.msg'],
+            }
+            assert dist.exclude_package_data == {
+                '': ['fake1.txt', 'fake2.txt'],
+                'hello': ['*.dat'],
+            }
+
+    def test_packages(self, tmpdir):
+        fake_env(tmpdir, '[options]\npackages = find:\n')
+
+        with get_dist(tmpdir) as dist:
+            assert dist.packages == ['fake_package']
+
+    def test_find_directive(self, tmpdir):
+        dir_package, config = fake_env(tmpdir, '[options]\npackages = find:\n')
+
+        make_package_dir('sub_one', dir_package)
+        make_package_dir('sub_two', dir_package)
+
+        with get_dist(tmpdir) as dist:
+            assert set(dist.packages) == set([
+                'fake_package',
+                'fake_package.sub_two',
+                'fake_package.sub_one',
+            ])
+
+        config.write(
+            '[options]\n'
+            'packages = find:\n'
+            '\n'
+            '[options.packages.find]\n'
+            'where = .\n'
+            'include =\n'
+            '    fake_package.sub_one\n'
+            '    two\n'
+        )
+        with get_dist(tmpdir) as dist:
+            assert dist.packages == ['fake_package.sub_one']
+
+        config.write(
+            '[options]\n'
+            'packages = find:\n'
+            '\n'
+            '[options.packages.find]\n'
+            'exclude =\n'
+            '    fake_package.sub_one\n'
+        )
+        with get_dist(tmpdir) as dist:
+            assert set(dist.packages) == set(['fake_package', 'fake_package.sub_two'])
+
+    def test_find_namespace_directive(self, tmpdir):
+        dir_package, config = fake_env(
+            tmpdir, '[options]\npackages = find_namespace:\n'
+        )
+
+        make_package_dir('sub_one', dir_package)
+        make_package_dir('sub_two', dir_package, ns=True)
+
+        with get_dist(tmpdir) as dist:
+            assert set(dist.packages) == {
+                'fake_package',
+                'fake_package.sub_two',
+                'fake_package.sub_one',
+            }
+
+        config.write(
+            '[options]\n'
+            'packages = find_namespace:\n'
+            '\n'
+            '[options.packages.find]\n'
+            'where = .\n'
+            'include =\n'
+            '    fake_package.sub_one\n'
+            '    two\n'
+        )
+        with get_dist(tmpdir) as dist:
+            assert dist.packages == ['fake_package.sub_one']
+
+        config.write(
+            '[options]\n'
+            'packages = find_namespace:\n'
+            '\n'
+            '[options.packages.find]\n'
+            'exclude =\n'
+            '    fake_package.sub_one\n'
+        )
+        with get_dist(tmpdir) as dist:
+            assert set(dist.packages) == {'fake_package', 'fake_package.sub_two'}
+
+    def test_extras_require(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options.extras_require]\n'
+            'pdf = ReportLab>=1.2; RXP\n'
+            'rest = \n'
+            '  docutils>=0.3\n'
+            '  pack ==1.1, ==1.3\n',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.extras_require == {
+                'pdf': ['ReportLab>=1.2', 'RXP'],
+                'rest': ['docutils>=0.3', 'pack==1.1,==1.3'],
+            }
+            assert set(dist.metadata.provides_extras) == {'pdf', 'rest'}
+
+    @pytest.mark.parametrize(
+        "config",
+        [
+            "[options.extras_require]\nfoo = bar;python_version<'3'",
+            "[options.extras_require]\nfoo = bar;os_name=='linux'",
+            "[options.extras_require]\nfoo = bar;python_version<'3'\n",
+            "[options.extras_require]\nfoo = bar;os_name=='linux'\n",
+            "[options]\ninstall_requires = bar;python_version<'3'",
+            "[options]\ninstall_requires = bar;os_name=='linux'",
+            "[options]\ninstall_requires = bar;python_version<'3'\n",
+            "[options]\ninstall_requires = bar;os_name=='linux'\n",
+        ],
+    )
+    def test_raises_accidental_env_marker_misconfig(self, config, tmpdir):
+        fake_env(tmpdir, config)
+        match = (
+            r"One of the parsed requirements in `(install_requires|extras_require.+)` "
+            "looks like a valid environment marker.*"
+        )
+        with pytest.raises(InvalidRequirement, match=match):
+            with get_dist(tmpdir) as _:
+                pass
+
+    @pytest.mark.parametrize(
+        "config",
+        [
+            "[options.extras_require]\nfoo = bar;python_version<3",
+            "[options.extras_require]\nfoo = bar;python_version<3\n",
+            "[options]\ninstall_requires = bar;python_version<3",
+            "[options]\ninstall_requires = bar;python_version<3\n",
+        ],
+    )
+    def test_warn_accidental_env_marker_misconfig(self, config, tmpdir):
+        fake_env(tmpdir, config)
+        match = (
+            r"One of the parsed requirements in `(install_requires|extras_require.+)` "
+            "looks like a valid environment marker.*"
+        )
+        with pytest.warns(SetuptoolsDeprecationWarning, match=match):
+            with get_dist(tmpdir) as _:
+                pass
+
+    @pytest.mark.parametrize(
+        "config",
+        [
+            "[options.extras_require]\nfoo =\n    bar;python_version<'3'",
+            "[options.extras_require]\nfoo = bar;baz\nboo = xxx;yyy",
+            "[options.extras_require]\nfoo =\n    bar;python_version<'3'\n",
+            "[options.extras_require]\nfoo = bar;baz\nboo = xxx;yyy\n",
+            "[options.extras_require]\nfoo =\n    bar\n    python_version<3\n",
+            "[options]\ninstall_requires =\n    bar;python_version<'3'",
+            "[options]\ninstall_requires = bar;baz\nboo = xxx;yyy",
+            "[options]\ninstall_requires =\n    bar;python_version<'3'\n",
+            "[options]\ninstall_requires = bar;baz\nboo = xxx;yyy\n",
+            "[options]\ninstall_requires =\n    bar\n    python_version<3\n",
+        ],
+    )
+    @pytest.mark.filterwarnings("error::setuptools.SetuptoolsDeprecationWarning")
+    def test_nowarn_accidental_env_marker_misconfig(self, config, tmpdir, recwarn):
+        fake_env(tmpdir, config)
+        num_warnings = len(recwarn)
+        with get_dist(tmpdir) as _:
+            pass
+        # The examples are valid, no warnings shown
+        assert len(recwarn) == num_warnings
+
+    def test_dash_preserved_extras_require(self, tmpdir):
+        fake_env(tmpdir, '[options.extras_require]\nfoo-a = foo\nfoo_b = test\n')
+
+        with get_dist(tmpdir) as dist:
+            assert dist.extras_require == {'foo-a': ['foo'], 'foo_b': ['test']}
+
+    def test_entry_points(self, tmpdir):
+        _, config = fake_env(
+            tmpdir,
+            '[options.entry_points]\n'
+            'group1 = point1 = pack.module:func, '
+            '.point2 = pack.module2:func_rest [rest]\n'
+            'group2 = point3 = pack.module:func2\n',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.entry_points == {
+                'group1': [
+                    'point1 = pack.module:func',
+                    '.point2 = pack.module2:func_rest [rest]',
+                ],
+                'group2': ['point3 = pack.module:func2'],
+            }
+
+        expected = (
+            '[blogtool.parsers]\n'
+            '.rst = some.nested.module:SomeClass.some_classmethod[reST]\n'
+        )
+
+        tmpdir.join('entry_points').write(expected)
+
+        # From file.
+        config.write('[options]\nentry_points = file: entry_points\n')
+
+        with get_dist(tmpdir) as dist:
+            assert dist.entry_points == expected
+
+    def test_case_sensitive_entry_points(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options.entry_points]\n'
+            'GROUP1 = point1 = pack.module:func, '
+            '.point2 = pack.module2:func_rest [rest]\n'
+            'group2 = point3 = pack.module:func2\n',
+        )
+
+        with get_dist(tmpdir) as dist:
+            assert dist.entry_points == {
+                'GROUP1': [
+                    'point1 = pack.module:func',
+                    '.point2 = pack.module2:func_rest [rest]',
+                ],
+                'group2': ['point3 = pack.module:func2'],
+            }
+
+    def test_data_files(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options.data_files]\n'
+            'cfg =\n'
+            '      a/b.conf\n'
+            '      c/d.conf\n'
+            'data = e/f.dat, g/h.dat\n',
+        )
+
+        with get_dist(tmpdir) as dist:
+            expected = [
+                ('cfg', ['a/b.conf', 'c/d.conf']),
+                ('data', ['e/f.dat', 'g/h.dat']),
+            ]
+            assert sorted(dist.data_files) == sorted(expected)
+
+    def test_data_files_globby(self, tmpdir):
+        fake_env(
+            tmpdir,
+            '[options.data_files]\n'
+            'cfg =\n'
+            '      a/b.conf\n'
+            '      c/d.conf\n'
+            'data = *.dat\n'
+            'icons = \n'
+            '      *.ico\n'
+            'audio = \n'
+            '      *.wav\n'
+            '      sounds.db\n',
+        )
+
+        # Create dummy files for glob()'s sake:
+        tmpdir.join('a.dat').write('')
+        tmpdir.join('b.dat').write('')
+        tmpdir.join('c.dat').write('')
+        tmpdir.join('a.ico').write('')
+        tmpdir.join('b.ico').write('')
+        tmpdir.join('c.ico').write('')
+        tmpdir.join('beep.wav').write('')
+        tmpdir.join('boop.wav').write('')
+        tmpdir.join('sounds.db').write('')
+
+        with get_dist(tmpdir) as dist:
+            expected = [
+                ('cfg', ['a/b.conf', 'c/d.conf']),
+                ('data', ['a.dat', 'b.dat', 'c.dat']),
+                ('icons', ['a.ico', 'b.ico', 'c.ico']),
+                ('audio', ['beep.wav', 'boop.wav', 'sounds.db']),
+            ]
+            assert sorted(dist.data_files) == sorted(expected)
+
+    def test_python_requires_simple(self, tmpdir):
+        fake_env(
+            tmpdir,
+            DALS(
+                """
+            [options]
+            python_requires=>=2.7
+            """
+            ),
+        )
+        with get_dist(tmpdir) as dist:
+            dist.parse_config_files()
+
+    def test_python_requires_compound(self, tmpdir):
+        fake_env(
+            tmpdir,
+            DALS(
+                """
+            [options]
+            python_requires=>=2.7,!=3.0.*
+            """
+            ),
+        )
+        with get_dist(tmpdir) as dist:
+            dist.parse_config_files()
+
+    def test_python_requires_invalid(self, tmpdir):
+        fake_env(
+            tmpdir,
+            DALS(
+                """
+            [options]
+            python_requires=invalid
+            """
+            ),
+        )
+        with pytest.raises(Exception):
+            with get_dist(tmpdir) as dist:
+                dist.parse_config_files()
+
+    def test_cmdclass(self, tmpdir):
+        module_path = Path(tmpdir, "src/custom_build.py")  # auto discovery for src
+        module_path.parent.mkdir(parents=True, exist_ok=True)
+        module_path.write_text(
+            "from distutils.core import Command\nclass CustomCmd(Command): pass\n",
+            encoding="utf-8",
+        )
+
+        setup_cfg = """
+            [options]
+            cmdclass =
+                customcmd = custom_build.CustomCmd
+        """
+        fake_env(tmpdir, inspect.cleandoc(setup_cfg))
+
+        with get_dist(tmpdir) as dist:
+            cmdclass = dist.cmdclass['customcmd']
+            assert cmdclass.__name__ == "CustomCmd"
+            assert cmdclass.__module__ == "custom_build"
+            assert module_path.samefile(inspect.getfile(cmdclass))
+
+    def test_requirements_file(self, tmpdir):
+        fake_env(
+            tmpdir,
+            DALS(
+                """
+            [options]
+            install_requires = file:requirements.txt
+            [options.extras_require]
+            colors = file:requirements-extra.txt
+            """
+            ),
+        )
+
+        tmpdir.join('requirements.txt').write('\ndocutils>=0.3\n\n')
+        tmpdir.join('requirements-extra.txt').write('colorama')
+
+        with get_dist(tmpdir) as dist:
+            assert dist.install_requires == ['docutils>=0.3']
+            assert dist.extras_require == {'colors': ['colorama']}
+
+
+saved_dist_init = _Distribution.__init__
+
+
+class TestExternalSetters:
+    # During creation of the setuptools Distribution() object, we call
+    # the init of the parent distutils Distribution object via
+    # _Distribution.__init__ ().
+    #
+    # It's possible distutils calls out to various keyword
+    # implementations (i.e. distutils.setup_keywords entry points)
+    # that may set a range of variables.
+    #
+    # This wraps distutil's Distribution.__init__ and simulates
+    # pbr or something else setting these values.
+    def _fake_distribution_init(self, dist, attrs):
+        saved_dist_init(dist, attrs)
+        # see self._DISTUTILS_UNSUPPORTED_METADATA
+        dist.metadata.long_description_content_type = 'text/something'
+        # Test overwrite setup() args
+        dist.metadata.project_urls = {
+            'Link One': 'https://example.com/one/',
+            'Link Two': 'https://example.com/two/',
+        }
+
+    @patch.object(_Distribution, '__init__', autospec=True)
+    def test_external_setters(self, mock_parent_init, tmpdir):
+        mock_parent_init.side_effect = self._fake_distribution_init
+
+        dist = Distribution(attrs={'project_urls': {'will_be': 'ignored'}})
+
+        assert dist.metadata.long_description_content_type == 'text/something'
+        assert dist.metadata.project_urls == {
+            'Link One': 'https://example.com/one/',
+            'Link Two': 'https://example.com/two/',
+        }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/contexts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/contexts.py
new file mode 100644
index 0000000000000000000000000000000000000000..97cceea0e7060c6e3568956e1ba20893301da387
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/contexts.py
@@ -0,0 +1,145 @@
+import contextlib
+import io
+import os
+import shutil
+import site
+import sys
+import tempfile
+
+from filelock import FileLock
+
+
+@contextlib.contextmanager
+def tempdir(cd=lambda dir: None, **kwargs):
+    temp_dir = tempfile.mkdtemp(**kwargs)
+    orig_dir = os.getcwd()
+    try:
+        cd(temp_dir)
+        yield temp_dir
+    finally:
+        cd(orig_dir)
+        shutil.rmtree(temp_dir)
+
+
+@contextlib.contextmanager
+def environment(**replacements):
+    """
+    In a context, patch the environment with replacements. Pass None values
+    to clear the values.
+    """
+    saved = dict((key, os.environ[key]) for key in replacements if key in os.environ)
+
+    # remove values that are null
+    remove = (key for (key, value) in replacements.items() if value is None)
+    for key in list(remove):
+        os.environ.pop(key, None)
+        replacements.pop(key)
+
+    os.environ.update(replacements)
+
+    try:
+        yield saved
+    finally:
+        for key in replacements:
+            os.environ.pop(key, None)
+        os.environ.update(saved)
+
+
+@contextlib.contextmanager
+def quiet():
+    """
+    Redirect stdout/stderr to StringIO objects to prevent console output from
+    distutils commands.
+    """
+
+    old_stdout = sys.stdout
+    old_stderr = sys.stderr
+    new_stdout = sys.stdout = io.StringIO()
+    new_stderr = sys.stderr = io.StringIO()
+    try:
+        yield new_stdout, new_stderr
+    finally:
+        new_stdout.seek(0)
+        new_stderr.seek(0)
+        sys.stdout = old_stdout
+        sys.stderr = old_stderr
+
+
+@contextlib.contextmanager
+def save_user_site_setting():
+    saved = site.ENABLE_USER_SITE
+    try:
+        yield saved
+    finally:
+        site.ENABLE_USER_SITE = saved
+
+
+@contextlib.contextmanager
+def save_pkg_resources_state():
+    import pkg_resources
+
+    pr_state = pkg_resources.__getstate__()
+    # also save sys.path
+    sys_path = sys.path[:]
+    try:
+        yield pr_state, sys_path
+    finally:
+        sys.path[:] = sys_path
+        pkg_resources.__setstate__(pr_state)
+
+
+@contextlib.contextmanager
+def suppress_exceptions(*excs):
+    try:
+        yield
+    except excs:
+        pass
+
+
+def multiproc(request):
+    """
+    Return True if running under xdist and multiple
+    workers are used.
+    """
+    try:
+        worker_id = request.getfixturevalue('worker_id')
+    except Exception:
+        return False
+    return worker_id != 'master'
+
+
+@contextlib.contextmanager
+def session_locked_tmp_dir(request, tmp_path_factory, name):
+    """Uses a file lock to guarantee only one worker can access a temp dir"""
+    # get the temp directory shared by all workers
+    base = tmp_path_factory.getbasetemp()
+    shared_dir = base.parent if multiproc(request) else base
+
+    locked_dir = shared_dir / name
+    with FileLock(locked_dir.with_suffix(".lock")):
+        # ^-- prevent multiple workers to access the directory at once
+        locked_dir.mkdir(exist_ok=True, parents=True)
+        yield locked_dir
+
+
+@contextlib.contextmanager
+def save_paths():
+    """Make sure ``sys.path``, ``sys.meta_path`` and ``sys.path_hooks`` are preserved"""
+    prev = sys.path[:], sys.meta_path[:], sys.path_hooks[:]
+
+    try:
+        yield
+    finally:
+        sys.path, sys.meta_path, sys.path_hooks = prev
+
+
+@contextlib.contextmanager
+def save_sys_modules():
+    """Make sure initial ``sys.modules`` is preserved"""
+    prev_modules = sys.modules
+
+    try:
+        sys.modules = sys.modules.copy()
+        yield
+    finally:
+        sys.modules = prev_modules
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/environment.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/environment.py
new file mode 100644
index 0000000000000000000000000000000000000000..ed5499ef7d73762d033a4877bfe586d6c0b82235
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/environment.py
@@ -0,0 +1,95 @@
+import os
+import subprocess
+import sys
+import unicodedata
+from subprocess import PIPE as _PIPE, Popen as _Popen
+
+import jaraco.envs
+
+
+class VirtualEnv(jaraco.envs.VirtualEnv):
+    name = '.env'
+    # Some version of PyPy will import distutils on startup, implicitly
+    # importing setuptools, and thus leading to BackendInvalid errors
+    # when upgrading Setuptools. Bypass this behavior by avoiding the
+    # early availability and need to upgrade.
+    create_opts = ['--no-setuptools']
+
+    def run(self, cmd, *args, **kwargs):
+        cmd = [self.exe(cmd[0])] + cmd[1:]
+        kwargs = {"cwd": self.root, "encoding": "utf-8", **kwargs}  # Allow overriding
+        # In some environments (eg. downstream distro packaging), where:
+        # - tox isn't used to run tests and
+        # - PYTHONPATH is set to point to a specific setuptools codebase and
+        # - no custom env is explicitly set by a test
+        # PYTHONPATH will leak into the spawned processes.
+        # In that case tests look for module in the wrong place (on PYTHONPATH).
+        # Unless the test sets its own special env, pass a copy of the existing
+        # environment with removed PYTHONPATH to the subprocesses.
+        if "env" not in kwargs:
+            env = dict(os.environ)
+            if "PYTHONPATH" in env:
+                del env["PYTHONPATH"]
+            kwargs["env"] = env
+        return subprocess.check_output(cmd, *args, **kwargs)
+
+
+def _which_dirs(cmd):
+    result = set()
+    for path in os.environ.get('PATH', '').split(os.pathsep):
+        filename = os.path.join(path, cmd)
+        if os.access(filename, os.X_OK):
+            result.add(path)
+    return result
+
+
+def run_setup_py(cmd, pypath=None, path=None, data_stream=0, env=None):
+    """
+    Execution command for tests, separate from those used by the
+    code directly to prevent accidental behavior issues
+    """
+    if env is None:
+        env = dict()
+        for envname in os.environ:
+            env[envname] = os.environ[envname]
+
+    # override the python path if needed
+    if pypath is not None:
+        env["PYTHONPATH"] = pypath
+
+    # override the execution path if needed
+    if path is not None:
+        env["PATH"] = path
+    if not env.get("PATH", ""):
+        env["PATH"] = _which_dirs("tar").union(_which_dirs("gzip"))
+        env["PATH"] = os.pathsep.join(env["PATH"])
+
+    cmd = [sys.executable, "setup.py"] + list(cmd)
+
+    # https://bugs.python.org/issue8557
+    shell = sys.platform == 'win32'
+
+    try:
+        proc = _Popen(
+            cmd,
+            stdout=_PIPE,
+            stderr=_PIPE,
+            shell=shell,
+            env=env,
+            encoding="utf-8",
+        )
+
+        if isinstance(data_stream, tuple):
+            data_stream = slice(*data_stream)
+        data = proc.communicate()[data_stream]
+    except OSError:
+        return 1, ''
+
+    # decode the console string if needed
+    if hasattr(data, "decode"):
+        # use the default encoding
+        data = data.decode()
+        data = unicodedata.normalize('NFC', data)
+
+    # communicate calls wait()
+    return proc.returncode, data
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/fixtures.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/fixtures.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5472984b5690572285a84575f6c2d598f06dd11
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/fixtures.py
@@ -0,0 +1,157 @@
+import contextlib
+import os
+import subprocess
+import sys
+from pathlib import Path
+
+import path
+import pytest
+
+from . import contexts, environment
+
+
+@pytest.fixture
+def user_override(monkeypatch):
+    """
+    Override site.USER_BASE and site.USER_SITE with temporary directories in
+    a context.
+    """
+    with contexts.tempdir() as user_base:
+        monkeypatch.setattr('site.USER_BASE', user_base)
+        with contexts.tempdir() as user_site:
+            monkeypatch.setattr('site.USER_SITE', user_site)
+            with contexts.save_user_site_setting():
+                yield
+
+
+@pytest.fixture
+def tmpdir_cwd(tmpdir):
+    with tmpdir.as_cwd() as orig:
+        yield orig
+
+
+@pytest.fixture(autouse=True, scope="session")
+def workaround_xdist_376(request):
+    """
+    Workaround pytest-dev/pytest-xdist#376
+
+    ``pytest-xdist`` tends to inject '' into ``sys.path``,
+    which may break certain isolation expectations.
+    Remove the entry so the import
+    machinery behaves the same irrespective of xdist.
+    """
+    if not request.config.pluginmanager.has_plugin('xdist'):
+        return
+
+    with contextlib.suppress(ValueError):
+        sys.path.remove('')
+
+
+@pytest.fixture
+def sample_project(tmp_path):
+    """
+    Clone the 'sampleproject' and return a path to it.
+    """
+    cmd = ['git', 'clone', 'https://github.com/pypa/sampleproject']
+    try:
+        subprocess.check_call(cmd, cwd=str(tmp_path))
+    except Exception:
+        pytest.skip("Unable to clone sampleproject")
+    return tmp_path / 'sampleproject'
+
+
+# sdist and wheel artifacts should be stable across a round of tests
+# so we can build them once per session and use the files as "readonly"
+
+# In the case of setuptools, building the wheel without sdist may cause
+# it to contain the `build` directory, and therefore create situations with
+# `setuptools/build/lib/build/lib/...`. To avoid that, build both artifacts at once.
+
+
+def _build_distributions(tmp_path_factory, request):
+    with contexts.session_locked_tmp_dir(
+        request, tmp_path_factory, "dist_build"
+    ) as tmp:  # pragma: no cover
+        sdist = next(tmp.glob("*.tar.gz"), None)
+        wheel = next(tmp.glob("*.whl"), None)
+        if sdist and wheel:
+            return (sdist, wheel)
+
+        # Sanity check: should not create recursive setuptools/build/lib/build/lib/...
+        assert not Path(request.config.rootdir, "build/lib/build").exists()
+
+        subprocess.check_output([
+            sys.executable,
+            "-m",
+            "build",
+            "--outdir",
+            str(tmp),
+            str(request.config.rootdir),
+        ])
+
+        # Sanity check: should not create recursive setuptools/build/lib/build/lib/...
+        assert not Path(request.config.rootdir, "build/lib/build").exists()
+
+        return next(tmp.glob("*.tar.gz")), next(tmp.glob("*.whl"))
+
+
+@pytest.fixture(scope="session")
+def setuptools_sdist(tmp_path_factory, request):
+    prebuilt = os.getenv("PRE_BUILT_SETUPTOOLS_SDIST")
+    if prebuilt and os.path.exists(prebuilt):  # pragma: no cover
+        return Path(prebuilt).resolve()
+
+    sdist, _ = _build_distributions(tmp_path_factory, request)
+    return sdist
+
+
+@pytest.fixture(scope="session")
+def setuptools_wheel(tmp_path_factory, request):
+    prebuilt = os.getenv("PRE_BUILT_SETUPTOOLS_WHEEL")
+    if prebuilt and os.path.exists(prebuilt):  # pragma: no cover
+        return Path(prebuilt).resolve()
+
+    _, wheel = _build_distributions(tmp_path_factory, request)
+    return wheel
+
+
+@pytest.fixture
+def venv(tmp_path, setuptools_wheel):
+    """Virtual env with the version of setuptools under test installed"""
+    env = environment.VirtualEnv()
+    env.root = path.Path(tmp_path / 'venv')
+    env.create_opts = ['--no-setuptools', '--wheel=bundle']
+    # TODO: Use `--no-wheel` when setuptools implements its own bdist_wheel
+    env.req = str(setuptools_wheel)
+    # In some environments (eg. downstream distro packaging),
+    # where tox isn't used to run tests and PYTHONPATH is set to point to
+    # a specific setuptools codebase, PYTHONPATH will leak into the spawned
+    # processes.
+    # env.create() should install the just created setuptools
+    # wheel, but it doesn't if it finds another existing matching setuptools
+    # installation present on PYTHONPATH:
+    # `setuptools is already installed with the same version as the provided
+    # wheel. Use --force-reinstall to force an installation of the wheel.`
+    # This prevents leaking PYTHONPATH to the created environment.
+    with contexts.environment(PYTHONPATH=None):
+        return env.create()
+
+
+@pytest.fixture
+def venv_without_setuptools(tmp_path):
+    """Virtual env without any version of setuptools installed"""
+    env = environment.VirtualEnv()
+    env.root = path.Path(tmp_path / 'venv_without_setuptools')
+    env.create_opts = ['--no-setuptools', '--no-wheel']
+    env.ensure_env()
+    return env
+
+
+@pytest.fixture
+def bare_venv(tmp_path):
+    """Virtual env without any common packages installed"""
+    env = environment.VirtualEnv()
+    env.root = path.Path(tmp_path / 'bare_venv')
+    env.create_opts = ['--no-setuptools', '--no-pip', '--no-wheel', '--no-seed']
+    env.ensure_env()
+    return env
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/indexes/test_links_priority/external.html b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/indexes/test_links_priority/external.html
new file mode 100644
index 0000000000000000000000000000000000000000..92e4702f634dfb37a404bec3103b76f6afcaa917
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/indexes/test_links_priority/external.html
@@ -0,0 +1,3 @@
+
+bad old link
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/indexes/test_links_priority/simple/foobar/index.html b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/indexes/test_links_priority/simple/foobar/index.html
new file mode 100644
index 0000000000000000000000000000000000000000..fefb028bd3ee7d45a414d6e96a7b2a21ffd7eda7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/indexes/test_links_priority/simple/foobar/index.html
@@ -0,0 +1,4 @@
+
+foobar-0.1.tar.gz

+external homepage

+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/helpers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/helpers.py
new file mode 100644
index 0000000000000000000000000000000000000000..77b196e029b6d2eeb25f0b84a4f7630f65201189
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/helpers.py
@@ -0,0 +1,77 @@
+"""Reusable functions and classes for different types of integration tests.
+
+For example ``Archive`` can be used to check the contents of distribution built
+with setuptools, and ``run`` will always try to be as verbose as possible to
+facilitate debugging.
+"""
+
+import os
+import subprocess
+import tarfile
+from pathlib import Path
+from zipfile import ZipFile
+
+
+def run(cmd, env=None):
+    r = subprocess.run(
+        cmd,
+        capture_output=True,
+        text=True,
+        encoding="utf-8",
+        env={**os.environ, **(env or {})},
+        # ^-- allow overwriting instead of discarding the current env
+    )
+
+    out = r.stdout + "\n" + r.stderr
+    # pytest omits stdout/err by default, if the test fails they help debugging
+    print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
+    print(f"Command: {cmd}\nreturn code: {r.returncode}\n\n{out}")
+
+    if r.returncode == 0:
+        return out
+    raise subprocess.CalledProcessError(r.returncode, cmd, r.stdout, r.stderr)
+
+
+class Archive:
+    """Compatibility layer for ZipFile/Info and TarFile/Info"""
+
+    def __init__(self, filename):
+        self._filename = filename
+        if filename.endswith("tar.gz"):
+            self._obj = tarfile.open(filename, "r:gz")
+        elif filename.endswith("zip"):
+            self._obj = ZipFile(filename)
+        else:
+            raise ValueError(f"{filename} doesn't seem to be a zip or tar.gz")
+
+    def __iter__(self):
+        if hasattr(self._obj, "infolist"):
+            return iter(self._obj.infolist())
+        return iter(self._obj)
+
+    def get_name(self, zip_or_tar_info):
+        if hasattr(zip_or_tar_info, "filename"):
+            return zip_or_tar_info.filename
+        return zip_or_tar_info.name
+
+    def get_content(self, zip_or_tar_info):
+        if hasattr(self._obj, "extractfile"):
+            content = self._obj.extractfile(zip_or_tar_info)
+            if content is None:
+                msg = f"Invalid {zip_or_tar_info.name} in {self._filename}"
+                raise ValueError(msg)
+            return str(content.read(), "utf-8")
+        return str(self._obj.read(zip_or_tar_info), "utf-8")
+
+
+def get_sdist_members(sdist_path):
+    with tarfile.open(sdist_path, "r:gz") as tar:
+        files = [Path(f) for f in tar.getnames()]
+    # remove root folder
+    relative_files = ("/".join(f.parts[1:]) for f in files)
+    return {f for f in relative_files if f}
+
+
+def get_wheel_members(wheel_path):
+    with ZipFile(wheel_path) as zipfile:
+        return set(zipfile.namelist())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/test_pip_install_sdist.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/test_pip_install_sdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..4e84f218323e6ad67adfbce07cea5a16e91a311c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/integration/test_pip_install_sdist.py
@@ -0,0 +1,223 @@
+# https://github.com/python/mypy/issues/16936
+# mypy: disable-error-code="has-type"
+"""Integration tests for setuptools that focus on building packages via pip.
+
+The idea behind these tests is not to exhaustively check all the possible
+combinations of packages, operating systems, supporting libraries, etc, but
+rather check a limited number of popular packages and how they interact with
+the exposed public API. This way if any change in API is introduced, we hope to
+identify backward compatibility problems before publishing a release.
+
+The number of tested packages is purposefully kept small, to minimise duration
+and the associated maintenance cost (changes in the way these packages define
+their build process may require changes in the tests).
+"""
+
+import json
+import os
+import shutil
+import sys
+from enum import Enum
+from glob import glob
+from hashlib import md5
+from urllib.request import urlopen
+
+import pytest
+from packaging.requirements import Requirement
+
+from .helpers import Archive, run
+
+pytestmark = pytest.mark.integration
+
+
+(LATEST,) = Enum("v", "LATEST")  # type: ignore[misc] # https://github.com/python/mypy/issues/16936
+"""Default version to be checked"""
+# There are positive and negative aspects of checking the latest version of the
+# packages.
+# The main positive aspect is that the latest version might have already
+# removed the use of APIs deprecated in previous releases of setuptools.
+
+
+# Packages to be tested:
+# (Please notice the test environment cannot support EVERY library required for
+# compiling binary extensions. In Ubuntu/Debian nomenclature, we only assume
+# that `build-essential`, `gfortran` and `libopenblas-dev` are installed,
+# due to their relevance to the numerical/scientific programming ecosystem)
+EXAMPLES = [
+    ("pip", LATEST),  # just in case...
+    ("pytest", LATEST),  # uses setuptools_scm
+    ("mypy", LATEST),  # custom build_py + ext_modules
+    # --- Popular packages: https://hugovk.github.io/top-pypi-packages/ ---
+    ("botocore", LATEST),
+    ("kiwisolver", LATEST),  # build_ext
+    ("brotli", LATEST),  # not in the list but used by urllib3
+    ("pyyaml", LATEST),  # cython + custom build_ext + custom distclass
+    ("charset-normalizer", LATEST),  # uses mypyc, used by aiohttp
+    ("protobuf", LATEST),
+    # ("requests", LATEST),  # XXX: https://github.com/psf/requests/pull/6920
+    ("celery", LATEST),
+    # When adding packages to this list, make sure they expose a `__version__`
+    # attribute, or modify the tests below
+]
+
+
+# Some packages have "optional" dependencies that modify their build behaviour
+# and are not listed in pyproject.toml, others still use `setup_requires`
+EXTRA_BUILD_DEPS = {
+    "pyyaml": ("Cython<3.0",),  # constraint to avoid errors
+    "charset-normalizer": ("mypy>=1.4.1",),  # no pyproject.toml available
+}
+
+EXTRA_ENV_VARS = {
+    "pyyaml": {"PYYAML_FORCE_CYTHON": "1"},
+    "charset-normalizer": {"CHARSET_NORMALIZER_USE_MYPYC": "1"},
+}
+
+IMPORT_NAME = {
+    "pyyaml": "yaml",
+    "protobuf": "google.protobuf",
+}
+
+
+VIRTUALENV = (sys.executable, "-m", "virtualenv")
+
+
+# By default, pip will try to build packages in isolation (PEP 517), which
+# means it will download the previous stable version of setuptools.
+# `pip` flags can avoid that (the version of setuptools under test
+# should be the one to be used)
+INSTALL_OPTIONS = (
+    "--ignore-installed",
+    "--no-build-isolation",
+    # Omit "--no-binary :all:" the sdist is supplied directly.
+    # Allows dependencies as wheels.
+)
+# The downside of `--no-build-isolation` is that pip will not download build
+# dependencies. The test script will have to also handle that.
+
+
+@pytest.fixture
+def venv_python(tmp_path):
+    run([*VIRTUALENV, str(tmp_path / ".venv")])
+    possible_path = (str(p.parent) for p in tmp_path.glob(".venv/*/python*"))
+    return shutil.which("python", path=os.pathsep.join(possible_path))
+
+
+@pytest.fixture(autouse=True)
+def _prepare(tmp_path, venv_python, monkeypatch):
+    download_path = os.getenv("DOWNLOAD_PATH", str(tmp_path))
+    os.makedirs(download_path, exist_ok=True)
+
+    # Environment vars used for building some of the packages
+    monkeypatch.setenv("USE_MYPYC", "1")
+
+    yield
+
+    # Let's provide the maximum amount of information possible in the case
+    # it is necessary to debug the tests directly from the CI logs.
+    print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
+    print("Temporary directory:")
+    map(print, tmp_path.glob("*"))
+    print("Virtual environment:")
+    run([venv_python, "-m", "pip", "freeze"])
+
+
+@pytest.mark.parametrize(("package", "version"), EXAMPLES)
+@pytest.mark.uses_network
+def test_install_sdist(package, version, tmp_path, venv_python, setuptools_wheel):
+    venv_pip = (venv_python, "-m", "pip")
+    sdist = retrieve_sdist(package, version, tmp_path)
+    deps = build_deps(package, sdist)
+    if deps:
+        print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
+        print("Dependencies:", deps)
+        run([*venv_pip, "install", *deps])
+
+    # Use a virtualenv to simulate PEP 517 isolation
+    # but install fresh setuptools wheel to ensure the version under development
+    env = EXTRA_ENV_VARS.get(package, {})
+    run([*venv_pip, "install", "--force-reinstall", setuptools_wheel])
+    run([*venv_pip, "install", *INSTALL_OPTIONS, sdist], env)
+
+    # Execute a simple script to make sure the package was installed correctly
+    pkg = IMPORT_NAME.get(package, package).replace("-", "_")
+    script = f"import {pkg}; print(getattr({pkg}, '__version__', 0))"
+    run([venv_python, "-c", script])
+
+
+# ---- Helper Functions ----
+
+
+def retrieve_sdist(package, version, tmp_path):
+    """Either use cached sdist file or download it from PyPI"""
+    # `pip download` cannot be used due to
+    # https://github.com/pypa/pip/issues/1884
+    # https://discuss.python.org/t/pep-625-file-name-of-a-source-distribution/4686
+    # We have to find the correct distribution file and download it
+    download_path = os.getenv("DOWNLOAD_PATH", str(tmp_path))
+    dist = retrieve_pypi_sdist_metadata(package, version)
+
+    # Remove old files to prevent cache to grow indefinitely
+    for file in glob(os.path.join(download_path, f"{package}*")):
+        if dist["filename"] != file:
+            os.unlink(file)
+
+    dist_file = os.path.join(download_path, dist["filename"])
+    if not os.path.exists(dist_file):
+        download(dist["url"], dist_file, dist["md5_digest"])
+    return dist_file
+
+
+def retrieve_pypi_sdist_metadata(package, version):
+    # https://warehouse.pypa.io/api-reference/json.html
+    id_ = package if version is LATEST else f"{package}/{version}"
+    with urlopen(f"https://pypi.org/pypi/{id_}/json") as f:
+        metadata = json.load(f)
+
+    if metadata["info"]["yanked"]:
+        raise ValueError(f"Release for {package} {version} was yanked")
+
+    version = metadata["info"]["version"]
+    release = metadata["releases"][version] if version is LATEST else metadata["urls"]
+    (sdist,) = filter(lambda d: d["packagetype"] == "sdist", release)
+    return sdist
+
+
+def download(url, dest, md5_digest):
+    with urlopen(url) as f:
+        data = f.read()
+
+    assert md5(data).hexdigest() == md5_digest
+
+    with open(dest, "wb") as f:
+        f.write(data)
+
+    assert os.path.exists(dest)
+
+
+def build_deps(package, sdist_file):
+    """Find out what are the build dependencies for a package.
+
+    "Manually" install them, since pip will not install build
+    deps with `--no-build-isolation`.
+    """
+    # delay importing, since pytest discovery phase may hit this file from a
+    # testenv without tomli
+    from setuptools.compat.py310 import tomllib
+
+    archive = Archive(sdist_file)
+    info = tomllib.loads(_read_pyproject(archive))
+    deps = info.get("build-system", {}).get("requires", [])
+    deps += EXTRA_BUILD_DEPS.get(package, [])
+    # Remove setuptools from requirements (and deduplicate)
+    requirements = {Requirement(d).name: d for d in deps}
+    return [v for k, v in requirements.items() if k != "setuptools"]
+
+
+def _read_pyproject(archive):
+    contents = (
+        archive.get_content(member)
+        for member in archive
+        if os.path.basename(archive.get_name(member)) == "pyproject.toml"
+    )
+    return next(contents, "")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/mod_with_constant.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/mod_with_constant.py
new file mode 100644
index 0000000000000000000000000000000000000000..ef755dd1c7a8d1f116fe51f1b43315057f03379d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/mod_with_constant.py
@@ -0,0 +1 @@
+value = 'three, sir!'
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/namespaces.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/namespaces.py
new file mode 100644
index 0000000000000000000000000000000000000000..248db98f97951aeeee0222131417e73074cc72d2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/namespaces.py
@@ -0,0 +1,90 @@
+import ast
+import json
+import textwrap
+from pathlib import Path
+
+
+def iter_namespace_pkgs(namespace):
+    parts = namespace.split(".")
+    for i in range(len(parts)):
+        yield ".".join(parts[: i + 1])
+
+
+def build_namespace_package(tmpdir, name, version="1.0", impl="pkg_resources"):
+    src_dir = tmpdir / name
+    src_dir.mkdir()
+    setup_py = src_dir / 'setup.py'
+    namespace, _, rest = name.rpartition('.')
+    namespaces = list(iter_namespace_pkgs(namespace))
+    setup_args = {
+        "name": name,
+        "version": version,
+        "packages": namespaces,
+    }
+
+    if impl == "pkg_resources":
+        tmpl = '__import__("pkg_resources").declare_namespace(__name__)'
+        setup_args["namespace_packages"] = namespaces
+    elif impl == "pkgutil":
+        tmpl = '__path__ = __import__("pkgutil").extend_path(__path__, __name__)'
+    else:
+        raise ValueError(f"Cannot recognise {impl=} when creating namespaces")
+
+    args = json.dumps(setup_args, indent=4)
+    assert ast.literal_eval(args)  # ensure it is valid Python
+
+    script = textwrap.dedent(
+        """\
+        import setuptools
+        args = {args}
+        setuptools.setup(**args)
+        """
+    ).format(args=args)
+    setup_py.write_text(script, encoding='utf-8')
+
+    ns_pkg_dir = Path(src_dir, namespace.replace(".", "/"))
+    ns_pkg_dir.mkdir(parents=True)
+
+    for ns in namespaces:
+        pkg_init = src_dir / ns.replace(".", "/") / '__init__.py'
+        pkg_init.write_text(tmpl, encoding='utf-8')
+
+    pkg_mod = ns_pkg_dir / (rest + '.py')
+    some_functionality = 'name = {rest!r}'.format(**locals())
+    pkg_mod.write_text(some_functionality, encoding='utf-8')
+    return src_dir
+
+
+def build_pep420_namespace_package(tmpdir, name):
+    src_dir = tmpdir / name
+    src_dir.mkdir()
+    pyproject = src_dir / "pyproject.toml"
+    namespace, _, rest = name.rpartition(".")
+    script = f"""\
+        [build-system]
+        requires = ["setuptools"]
+        build-backend = "setuptools.build_meta"
+
+        [project]
+        name = "{name}"
+        version = "3.14159"
+        """
+    pyproject.write_text(textwrap.dedent(script), encoding='utf-8')
+    ns_pkg_dir = Path(src_dir, namespace.replace(".", "/"))
+    ns_pkg_dir.mkdir(parents=True)
+    pkg_mod = ns_pkg_dir / (rest + ".py")
+    some_functionality = f"name = {rest!r}"
+    pkg_mod.write_text(some_functionality, encoding='utf-8')
+    return src_dir
+
+
+def make_site_dir(target):
+    """
+    Add a sitecustomize.py module in target to cause
+    target to be added to site dirs such that .pth files
+    are processed there.
+    """
+    sc = target / 'sitecustomize.py'
+    target_str = str(target)
+    tmpl = '__import__("site").addsitedir({target_str!r})'
+    sc.write_text(tmpl.format(**locals()), encoding='utf-8')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/script-with-bom.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/script-with-bom.py
new file mode 100644
index 0000000000000000000000000000000000000000..c074d263c45bcaebe32fdba328d975c73d1ad5ca
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/script-with-bom.py
@@ -0,0 +1 @@
+result = 'passed'
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/server.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/server.py
new file mode 100644
index 0000000000000000000000000000000000000000..623a49a550f161f117d3af2173f91a2af260181d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/server.py
@@ -0,0 +1,86 @@
+"""Basic http server for tests to simulate PyPI or custom indexes"""
+
+import http.server
+import os
+import threading
+import time
+import urllib.parse
+import urllib.request
+
+
+class IndexServer(http.server.HTTPServer):
+    """Basic single-threaded http server simulating a package index
+
+    You can use this server in unittest like this::
+        s = IndexServer()
+        s.start()
+        index_url = s.base_url() + 'mytestindex'
+        # do some test requests to the index
+        # The index files should be located in setuptools/tests/indexes
+        s.stop()
+    """
+
+    def __init__(
+        self,
+        server_address=('', 0),
+        RequestHandlerClass=http.server.SimpleHTTPRequestHandler,
+    ):
+        http.server.HTTPServer.__init__(self, server_address, RequestHandlerClass)
+        self._run = True
+
+    def start(self):
+        self.thread = threading.Thread(target=self.serve_forever)
+        self.thread.start()
+
+    def stop(self):
+        "Stop the server"
+
+        # Let the server finish the last request and wait for a new one.
+        time.sleep(0.1)
+
+        self.shutdown()
+        self.thread.join()
+        self.socket.close()
+
+    def base_url(self):
+        port = self.server_port
+        return f'http://127.0.0.1:{port}/setuptools/tests/indexes/'
+
+
+class RequestRecorder(http.server.BaseHTTPRequestHandler):
+    def do_GET(self):
+        requests = vars(self.server).setdefault('requests', [])
+        requests.append(self)
+        self.send_response(200, 'OK')
+
+
+class MockServer(http.server.HTTPServer, threading.Thread):
+    """
+    A simple HTTP Server that records the requests made to it.
+    """
+
+    def __init__(self, server_address=('', 0), RequestHandlerClass=RequestRecorder):
+        http.server.HTTPServer.__init__(self, server_address, RequestHandlerClass)
+        threading.Thread.__init__(self)
+        self.daemon = True
+        self.requests = []
+
+    def run(self):
+        self.serve_forever()
+
+    @property
+    def netloc(self):
+        return f'localhost:{self.server_port}'
+
+    @property
+    def url(self):
+        return f'http://{self.netloc}/'
+
+
+def path_to_url(path, authority=None):
+    """Convert a path to a file: URL."""
+    path = os.path.normpath(os.path.abspath(path))
+    base = 'file:'
+    if authority is not None:
+        base += '//' + authority
+    return urllib.parse.urljoin(base, urllib.request.pathname2url(path))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_archive_util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_archive_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3efc62889994fa68bc9170e8a0e403f48a204e1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_archive_util.py
@@ -0,0 +1,36 @@
+import io
+import tarfile
+
+import pytest
+
+from setuptools import archive_util
+
+
+@pytest.fixture
+def tarfile_with_unicode(tmpdir):
+    """
+    Create a tarfile containing only a file whose name is
+    a zero byte file called testimäge.png.
+    """
+    tarobj = io.BytesIO()
+
+    with tarfile.open(fileobj=tarobj, mode="w:gz") as tgz:
+        data = b""
+
+        filename = "testimäge.png"
+
+        t = tarfile.TarInfo(filename)
+        t.size = len(data)
+
+        tgz.addfile(t, io.BytesIO(data))
+
+    target = tmpdir / 'unicode-pkg-1.0.tar.gz'
+    with open(str(target), mode='wb') as tf:
+        tf.write(tarobj.getvalue())
+    return str(target)
+
+
+@pytest.mark.xfail(reason="#710 and #712")
+def test_unicode_files(tarfile_with_unicode, tmpdir):
+    target = tmpdir / 'out'
+    archive_util.unpack_archive(tarfile_with_unicode, str(target))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_deprecations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_deprecations.py
new file mode 100644
index 0000000000000000000000000000000000000000..d9d67b06161a2b36e7b15fab09f797c5c15575c2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_deprecations.py
@@ -0,0 +1,28 @@
+"""develop tests"""
+
+import sys
+from unittest import mock
+
+import pytest
+
+from setuptools import SetuptoolsDeprecationWarning
+from setuptools.dist import Distribution
+
+
+@pytest.mark.skipif(sys.platform == 'win32', reason='non-Windows only')
+@pytest.mark.xfail(reason="bdist_rpm is long deprecated, should we remove it? #1988")
+@mock.patch('distutils.command.bdist_rpm.bdist_rpm')
+def test_bdist_rpm_warning(distutils_cmd, tmpdir_cwd):
+    dist = Distribution(
+        dict(
+            script_name='setup.py',
+            script_args=['bdist_rpm'],
+            name='foo',
+            py_modules=['hi'],
+        )
+    )
+    dist.parse_command_line()
+    with pytest.warns(SetuptoolsDeprecationWarning):
+        dist.run_commands()
+
+    distutils_cmd.run.assert_called_once()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_egg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_egg.py
new file mode 100644
index 0000000000000000000000000000000000000000..036167dd951e70ad543775529d5ce3f6d6544c71
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_egg.py
@@ -0,0 +1,73 @@
+"""develop tests"""
+
+import os
+import re
+import zipfile
+
+import pytest
+
+from setuptools.dist import Distribution
+
+from . import contexts
+
+SETUP_PY = """\
+from setuptools import setup
+
+setup(py_modules=['hi'])
+"""
+
+
+@pytest.fixture
+def setup_context(tmpdir):
+    with (tmpdir / 'setup.py').open('w') as f:
+        f.write(SETUP_PY)
+    with (tmpdir / 'hi.py').open('w') as f:
+        f.write('1\n')
+    with tmpdir.as_cwd():
+        yield tmpdir
+
+
+class Test:
+    @pytest.mark.usefixtures("user_override")
+    @pytest.mark.usefixtures("setup_context")
+    def test_bdist_egg(self):
+        dist = Distribution(
+            dict(
+                script_name='setup.py',
+                script_args=['bdist_egg'],
+                name='foo',
+                py_modules=['hi'],
+            )
+        )
+        os.makedirs(os.path.join('build', 'src'))
+        with contexts.quiet():
+            dist.parse_command_line()
+            dist.run_commands()
+
+        # let's see if we got our egg link at the right place
+        [content] = os.listdir('dist')
+        assert re.match(r'foo-0.0.0-py[23].\d+.egg$', content)
+
+    @pytest.mark.xfail(
+        os.environ.get('PYTHONDONTWRITEBYTECODE', False),
+        reason="Byte code disabled",
+    )
+    @pytest.mark.usefixtures("user_override")
+    @pytest.mark.usefixtures("setup_context")
+    def test_exclude_source_files(self):
+        dist = Distribution(
+            dict(
+                script_name='setup.py',
+                script_args=['bdist_egg', '--exclude-source-files'],
+                py_modules=['hi'],
+            )
+        )
+        with contexts.quiet():
+            dist.parse_command_line()
+            dist.run_commands()
+        [dist_name] = os.listdir('dist')
+        dist_filename = os.path.join('dist', dist_name)
+        zip = zipfile.ZipFile(dist_filename)
+        names = list(zi.filename for zi in zip.filelist)
+        assert 'hi.pyc' in names
+        assert 'hi.py' not in names
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_wheel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_wheel.py
new file mode 100644
index 0000000000000000000000000000000000000000..2ab4e9cfc6cf0d930b3ceeececcce10cfe91a687
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_bdist_wheel.py
@@ -0,0 +1,708 @@
+from __future__ import annotations
+
+import builtins
+import importlib
+import os.path
+import platform
+import shutil
+import stat
+import struct
+import sys
+import sysconfig
+from contextlib import suppress
+from inspect import cleandoc
+from zipfile import ZipFile
+
+import jaraco.path
+import pytest
+from packaging import tags
+
+import setuptools
+from setuptools.command.bdist_wheel import bdist_wheel, get_abi_tag
+from setuptools.dist import Distribution
+from setuptools.warnings import SetuptoolsDeprecationWarning
+
+from distutils.core import run_setup
+
+DEFAULT_FILES = {
+    "dummy_dist-1.0.dist-info/top_level.txt",
+    "dummy_dist-1.0.dist-info/METADATA",
+    "dummy_dist-1.0.dist-info/WHEEL",
+    "dummy_dist-1.0.dist-info/RECORD",
+}
+DEFAULT_LICENSE_FILES = {
+    "LICENSE",
+    "LICENSE.txt",
+    "LICENCE",
+    "LICENCE.txt",
+    "COPYING",
+    "COPYING.md",
+    "NOTICE",
+    "NOTICE.rst",
+    "AUTHORS",
+    "AUTHORS.txt",
+}
+OTHER_IGNORED_FILES = {
+    "LICENSE~",
+    "AUTHORS~",
+}
+SETUPPY_EXAMPLE = """\
+from setuptools import setup
+
+setup(
+    name='dummy_dist',
+    version='1.0',
+)
+"""
+
+
+EXAMPLES = {
+    "dummy-dist": {
+        "setup.py": SETUPPY_EXAMPLE,
+        "licenses_dir": {"DUMMYFILE": ""},
+        **dict.fromkeys(DEFAULT_LICENSE_FILES | OTHER_IGNORED_FILES, ""),
+    },
+    "simple-dist": {
+        "setup.py": cleandoc(
+            """
+            from setuptools import setup
+
+            setup(
+                name="simple.dist",
+                version="0.1",
+                description="A testing distribution \N{SNOWMAN}",
+                extras_require={"voting": ["beaglevote"]},
+            )
+            """
+        ),
+        "simpledist": "",
+    },
+    "complex-dist": {
+        "setup.py": cleandoc(
+            """
+            from setuptools import setup
+
+            setup(
+                name="complex-dist",
+                version="0.1",
+                description="Another testing distribution \N{SNOWMAN}",
+                long_description="Another testing distribution \N{SNOWMAN}",
+                author="Illustrious Author",
+                author_email="illustrious@example.org",
+                url="http://example.org/exemplary",
+                packages=["complexdist"],
+                setup_requires=["setuptools"],
+                install_requires=["quux", "splort"],
+                extras_require={"simple": ["simple.dist"]},
+                entry_points={
+                    "console_scripts": [
+                        "complex-dist=complexdist:main",
+                        "complex-dist2=complexdist:main",
+                    ],
+                },
+            )
+            """
+        ),
+        "complexdist": {"__init__.py": "def main(): return"},
+    },
+    "headers-dist": {
+        "setup.py": cleandoc(
+            """
+            from setuptools import setup
+
+            setup(
+                name="headers.dist",
+                version="0.1",
+                description="A distribution with headers",
+                headers=["header.h"],
+            )
+            """
+        ),
+        "headersdist.py": "",
+        "header.h": "",
+    },
+    "commasinfilenames-dist": {
+        "setup.py": cleandoc(
+            """
+            from setuptools import setup
+
+            setup(
+                name="testrepo",
+                version="0.1",
+                packages=["mypackage"],
+                description="A test package with commas in file names",
+                include_package_data=True,
+                package_data={"mypackage.data": ["*"]},
+            )
+            """
+        ),
+        "mypackage": {
+            "__init__.py": "",
+            "data": {"__init__.py": "", "1,2,3.txt": ""},
+        },
+        "testrepo-0.1.0": {
+            "mypackage": {"__init__.py": ""},
+        },
+    },
+    "unicode-dist": {
+        "setup.py": cleandoc(
+            """
+            from setuptools import setup
+
+            setup(
+                name="unicode.dist",
+                version="0.1",
+                description="A testing distribution \N{SNOWMAN}",
+                packages=["unicodedist"],
+                zip_safe=True,
+            )
+            """
+        ),
+        "unicodedist": {"__init__.py": "", "åäö_日本語.py": ""},
+    },
+    "utf8-metadata-dist": {
+        "setup.cfg": cleandoc(
+            """
+            [metadata]
+            name = utf8-metadata-dist
+            version = 42
+            author_email = "John X. Ãørçeč" , Γαμα קּ 東 
+            long_description = file: README.rst
+            """
+        ),
+        "README.rst": "UTF-8 描述 説明",
+    },
+    "licenses-dist": {
+        "setup.cfg": cleandoc(
+            """
+            [metadata]
+            name = licenses-dist
+            version = 1.0
+            license_files = **/LICENSE
+            """
+        ),
+        "LICENSE": "",
+        "src": {
+            "vendor": {"LICENSE": ""},
+        },
+    },
+}
+
+
+if sys.platform != "win32":
+    # ABI3 extensions don't really work on Windows
+    EXAMPLES["abi3extension-dist"] = {
+        "setup.py": cleandoc(
+            """
+            from setuptools import Extension, setup
+
+            setup(
+                name="extension.dist",
+                version="0.1",
+                description="A testing distribution \N{SNOWMAN}",
+                ext_modules=[
+                    Extension(
+                        name="extension", sources=["extension.c"], py_limited_api=True
+                    )
+                ],
+            )
+            """
+        ),
+        "setup.cfg": "[bdist_wheel]\npy_limited_api=cp32",
+        "extension.c": "#define Py_LIMITED_API 0x03020000\n#include ",
+    }
+
+
+def bdist_wheel_cmd(**kwargs):
+    """Run command in the same process so that it is easier to collect coverage"""
+    dist_obj = (
+        run_setup("setup.py", stop_after="init")
+        if os.path.exists("setup.py")
+        else Distribution({"script_name": "%%build_meta%%"})
+    )
+    dist_obj.parse_config_files()
+    cmd = bdist_wheel(dist_obj)
+    for attr, value in kwargs.items():
+        setattr(cmd, attr, value)
+    cmd.finalize_options()
+    return cmd
+
+
+def mkexample(tmp_path_factory, name):
+    basedir = tmp_path_factory.mktemp(name)
+    jaraco.path.build(EXAMPLES[name], prefix=str(basedir))
+    return basedir
+
+
+@pytest.fixture(scope="session")
+def wheel_paths(tmp_path_factory):
+    build_base = tmp_path_factory.mktemp("build")
+    dist_dir = tmp_path_factory.mktemp("dist")
+    for name in EXAMPLES:
+        example_dir = mkexample(tmp_path_factory, name)
+        build_dir = build_base / name
+        with jaraco.path.DirectoryStack().context(example_dir):
+            bdist_wheel_cmd(bdist_dir=str(build_dir), dist_dir=str(dist_dir)).run()
+
+    return sorted(str(fname) for fname in dist_dir.glob("*.whl"))
+
+
+@pytest.fixture
+def dummy_dist(tmp_path_factory):
+    return mkexample(tmp_path_factory, "dummy-dist")
+
+
+@pytest.fixture
+def licenses_dist(tmp_path_factory):
+    return mkexample(tmp_path_factory, "licenses-dist")
+
+
+def test_no_scripts(wheel_paths):
+    """Make sure entry point scripts are not generated."""
+    path = next(path for path in wheel_paths if "complex_dist" in path)
+    for entry in ZipFile(path).infolist():
+        assert ".data/scripts/" not in entry.filename
+
+
+def test_unicode_record(wheel_paths):
+    path = next(path for path in wheel_paths if "unicode_dist" in path)
+    with ZipFile(path) as zf:
+        record = zf.read("unicode_dist-0.1.dist-info/RECORD")
+
+    assert "åäö_日本語.py".encode() in record
+
+
+UTF8_PKG_INFO = """\
+Metadata-Version: 2.1
+Name: helloworld
+Version: 42
+Author-email: "John X. Ãørçeč" , Γαμα קּ 東 
+
+
+UTF-8 描述 説明
+"""
+
+
+def test_preserve_unicode_metadata(monkeypatch, tmp_path):
+    monkeypatch.chdir(tmp_path)
+    egginfo = tmp_path / "dummy_dist.egg-info"
+    distinfo = tmp_path / "dummy_dist.dist-info"
+
+    egginfo.mkdir()
+    (egginfo / "PKG-INFO").write_text(UTF8_PKG_INFO, encoding="utf-8")
+    (egginfo / "dependency_links.txt").touch()
+
+    class simpler_bdist_wheel(bdist_wheel):
+        """Avoid messing with setuptools/distutils internals"""
+
+        def __init__(self):
+            pass
+
+        @property
+        def license_paths(self):
+            return []
+
+    cmd_obj = simpler_bdist_wheel()
+    cmd_obj.egg2dist(egginfo, distinfo)
+
+    metadata = (distinfo / "METADATA").read_text(encoding="utf-8")
+    assert 'Author-email: "John X. Ãørçeč"' in metadata
+    assert "Γαμα קּ 東 " in metadata
+    assert "UTF-8 描述 説明" in metadata
+
+
+def test_licenses_default(dummy_dist, monkeypatch, tmp_path):
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path)).run()
+    with ZipFile("dist/dummy_dist-1.0-py3-none-any.whl") as wf:
+        license_files = {
+            "dummy_dist-1.0.dist-info/licenses/" + fname
+            for fname in DEFAULT_LICENSE_FILES
+        }
+        assert set(wf.namelist()) == DEFAULT_FILES | license_files
+
+
+def test_licenses_deprecated(dummy_dist, monkeypatch, tmp_path):
+    dummy_dist.joinpath("setup.cfg").write_text(
+        "[metadata]\nlicense_file=licenses_dir/DUMMYFILE", encoding="utf-8"
+    )
+    monkeypatch.chdir(dummy_dist)
+
+    bdist_wheel_cmd(bdist_dir=str(tmp_path)).run()
+
+    with ZipFile("dist/dummy_dist-1.0-py3-none-any.whl") as wf:
+        license_files = {"dummy_dist-1.0.dist-info/licenses/licenses_dir/DUMMYFILE"}
+        assert set(wf.namelist()) == DEFAULT_FILES | license_files
+
+
+@pytest.mark.parametrize(
+    ("config_file", "config"),
+    [
+        ("setup.cfg", "[metadata]\nlicense_files=licenses_dir/*\n  LICENSE"),
+        ("setup.cfg", "[metadata]\nlicense_files=licenses_dir/*, LICENSE"),
+        (
+            "setup.py",
+            SETUPPY_EXAMPLE.replace(
+                ")", "  license_files=['licenses_dir/DUMMYFILE', 'LICENSE'])"
+            ),
+        ),
+    ],
+)
+def test_licenses_override(dummy_dist, monkeypatch, tmp_path, config_file, config):
+    dummy_dist.joinpath(config_file).write_text(config, encoding="utf-8")
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path)).run()
+    with ZipFile("dist/dummy_dist-1.0-py3-none-any.whl") as wf:
+        license_files = {
+            "dummy_dist-1.0.dist-info/licenses/" + fname
+            for fname in {"licenses_dir/DUMMYFILE", "LICENSE"}
+        }
+        assert set(wf.namelist()) == DEFAULT_FILES | license_files
+        metadata = wf.read("dummy_dist-1.0.dist-info/METADATA").decode("utf8")
+        assert "License-File: licenses_dir/DUMMYFILE" in metadata
+        assert "License-File: LICENSE" in metadata
+
+
+def test_licenses_preserve_folder_structure(licenses_dist, monkeypatch, tmp_path):
+    monkeypatch.chdir(licenses_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path)).run()
+    print(os.listdir("dist"))
+    with ZipFile("dist/licenses_dist-1.0-py3-none-any.whl") as wf:
+        default_files = {name.replace("dummy_", "licenses_") for name in DEFAULT_FILES}
+        license_files = {
+            "licenses_dist-1.0.dist-info/licenses/LICENSE",
+            "licenses_dist-1.0.dist-info/licenses/src/vendor/LICENSE",
+        }
+        assert set(wf.namelist()) == default_files | license_files
+        metadata = wf.read("licenses_dist-1.0.dist-info/METADATA").decode("utf8")
+        assert "License-File: src/vendor/LICENSE" in metadata
+        assert "License-File: LICENSE" in metadata
+
+
+def test_licenses_disabled(dummy_dist, monkeypatch, tmp_path):
+    dummy_dist.joinpath("setup.cfg").write_text(
+        "[metadata]\nlicense_files=\n", encoding="utf-8"
+    )
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path)).run()
+    with ZipFile("dist/dummy_dist-1.0-py3-none-any.whl") as wf:
+        assert set(wf.namelist()) == DEFAULT_FILES
+
+
+def test_build_number(dummy_dist, monkeypatch, tmp_path):
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path), build_number="2").run()
+    with ZipFile("dist/dummy_dist-1.0-2-py3-none-any.whl") as wf:
+        filenames = set(wf.namelist())
+        assert "dummy_dist-1.0.dist-info/RECORD" in filenames
+        assert "dummy_dist-1.0.dist-info/METADATA" in filenames
+
+
+def test_universal_deprecated(dummy_dist, monkeypatch, tmp_path):
+    monkeypatch.chdir(dummy_dist)
+    with pytest.warns(SetuptoolsDeprecationWarning, match=".*universal is deprecated"):
+        bdist_wheel_cmd(bdist_dir=str(tmp_path), universal=True).run()
+
+    # For now we still respect the option
+    assert os.path.exists("dist/dummy_dist-1.0-py2.py3-none-any.whl")
+
+
+EXTENSION_EXAMPLE = """\
+#include 
+
+static PyMethodDef methods[] = {
+  { NULL, NULL, 0, NULL }
+};
+
+static struct PyModuleDef module_def = {
+  PyModuleDef_HEAD_INIT,
+  "extension",
+  "Dummy extension module",
+  -1,
+  methods
+};
+
+PyMODINIT_FUNC PyInit_extension(void) {
+  return PyModule_Create(&module_def);
+}
+"""
+EXTENSION_SETUPPY = """\
+from __future__ import annotations
+
+from setuptools import Extension, setup
+
+setup(
+    name="extension.dist",
+    version="0.1",
+    description="A testing distribution \N{SNOWMAN}",
+    ext_modules=[Extension(name="extension", sources=["extension.c"])],
+)
+"""
+
+
+@pytest.mark.filterwarnings(
+    "once:Config variable '.*' is unset.*, Python ABI tag may be incorrect"
+)
+def test_limited_abi(monkeypatch, tmp_path, tmp_path_factory):
+    """Test that building a binary wheel with the limited ABI works."""
+    source_dir = tmp_path_factory.mktemp("extension_dist")
+    (source_dir / "setup.py").write_text(EXTENSION_SETUPPY, encoding="utf-8")
+    (source_dir / "extension.c").write_text(EXTENSION_EXAMPLE, encoding="utf-8")
+    build_dir = tmp_path.joinpath("build")
+    dist_dir = tmp_path.joinpath("dist")
+    monkeypatch.chdir(source_dir)
+    bdist_wheel_cmd(bdist_dir=str(build_dir), dist_dir=str(dist_dir)).run()
+
+
+def test_build_from_readonly_tree(dummy_dist, monkeypatch, tmp_path):
+    basedir = str(tmp_path.joinpath("dummy"))
+    shutil.copytree(str(dummy_dist), basedir)
+    monkeypatch.chdir(basedir)
+
+    # Make the tree read-only
+    for root, _dirs, files in os.walk(basedir):
+        for fname in files:
+            os.chmod(os.path.join(root, fname), stat.S_IREAD)
+
+    bdist_wheel_cmd().run()
+
+
+@pytest.mark.parametrize(
+    ("option", "compress_type"),
+    list(bdist_wheel.supported_compressions.items()),
+    ids=list(bdist_wheel.supported_compressions),
+)
+def test_compression(dummy_dist, monkeypatch, tmp_path, option, compress_type):
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path), compression=option).run()
+    with ZipFile("dist/dummy_dist-1.0-py3-none-any.whl") as wf:
+        filenames = set(wf.namelist())
+        assert "dummy_dist-1.0.dist-info/RECORD" in filenames
+        assert "dummy_dist-1.0.dist-info/METADATA" in filenames
+        for zinfo in wf.filelist:
+            assert zinfo.compress_type == compress_type
+
+
+def test_wheelfile_line_endings(wheel_paths):
+    for path in wheel_paths:
+        with ZipFile(path) as wf:
+            wheelfile = next(fn for fn in wf.filelist if fn.filename.endswith("WHEEL"))
+            wheelfile_contents = wf.read(wheelfile)
+            assert b"\r" not in wheelfile_contents
+
+
+def test_unix_epoch_timestamps(dummy_dist, monkeypatch, tmp_path):
+    monkeypatch.setenv("SOURCE_DATE_EPOCH", "0")
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(bdist_dir=str(tmp_path), build_number="2a").run()
+    with ZipFile("dist/dummy_dist-1.0-2a-py3-none-any.whl") as wf:
+        for zinfo in wf.filelist:
+            assert zinfo.date_time >= (1980, 1, 1, 0, 0, 0)  # min epoch is used
+
+
+def test_get_abi_tag_windows(monkeypatch):
+    monkeypatch.setattr(tags, "interpreter_name", lambda: "cp")
+    monkeypatch.setattr(sysconfig, "get_config_var", lambda x: "cp313-win_amd64")
+    assert get_abi_tag() == "cp313"
+    monkeypatch.setattr(sys, "gettotalrefcount", lambda: 1, False)
+    assert get_abi_tag() == "cp313d"
+    monkeypatch.setattr(sysconfig, "get_config_var", lambda x: "cp313t-win_amd64")
+    assert get_abi_tag() == "cp313td"
+    monkeypatch.delattr(sys, "gettotalrefcount")
+    assert get_abi_tag() == "cp313t"
+
+
+def test_get_abi_tag_pypy_old(monkeypatch):
+    monkeypatch.setattr(tags, "interpreter_name", lambda: "pp")
+    monkeypatch.setattr(sysconfig, "get_config_var", lambda x: "pypy36-pp73")
+    assert get_abi_tag() == "pypy36_pp73"
+
+
+def test_get_abi_tag_pypy_new(monkeypatch):
+    monkeypatch.setattr(sysconfig, "get_config_var", lambda x: "pypy37-pp73-darwin")
+    monkeypatch.setattr(tags, "interpreter_name", lambda: "pp")
+    assert get_abi_tag() == "pypy37_pp73"
+
+
+def test_get_abi_tag_graalpy(monkeypatch):
+    monkeypatch.setattr(
+        sysconfig, "get_config_var", lambda x: "graalpy231-310-native-x86_64-linux"
+    )
+    monkeypatch.setattr(tags, "interpreter_name", lambda: "graalpy")
+    assert get_abi_tag() == "graalpy231_310_native"
+
+
+def test_get_abi_tag_fallback(monkeypatch):
+    monkeypatch.setattr(sysconfig, "get_config_var", lambda x: "unknown-python-310")
+    monkeypatch.setattr(tags, "interpreter_name", lambda: "unknown-python")
+    assert get_abi_tag() == "unknown_python_310"
+
+
+def test_platform_with_space(dummy_dist, monkeypatch):
+    """Ensure building on platforms with a space in the name succeed."""
+    monkeypatch.chdir(dummy_dist)
+    bdist_wheel_cmd(plat_name="isilon onefs").run()
+
+
+def test_data_dir_with_tag_build(monkeypatch, tmp_path):
+    """
+    Setuptools allow authors to set PEP 440's local version segments
+    using ``egg_info.tag_build``. This should be reflected not only in the
+    ``.whl`` file name, but also in the ``.dist-info`` and ``.data`` dirs.
+    See pypa/setuptools#3997.
+    """
+    monkeypatch.chdir(tmp_path)
+    files = {
+        "setup.py": """
+            from setuptools import setup
+            setup(headers=["hello.h"])
+            """,
+        "setup.cfg": """
+            [metadata]
+            name = test
+            version = 1.0
+
+            [options.data_files]
+            hello/world = file.txt
+
+            [egg_info]
+            tag_build = +what
+            tag_date = 0
+            """,
+        "file.txt": "",
+        "hello.h": "",
+    }
+    for file, content in files.items():
+        with open(file, "w", encoding="utf-8") as fh:
+            fh.write(cleandoc(content))
+
+    bdist_wheel_cmd().run()
+
+    # Ensure .whl, .dist-info and .data contain the local segment
+    wheel_path = "dist/test-1.0+what-py3-none-any.whl"
+    assert os.path.exists(wheel_path)
+    entries = set(ZipFile(wheel_path).namelist())
+    for expected in (
+        "test-1.0+what.data/headers/hello.h",
+        "test-1.0+what.data/data/hello/world/file.txt",
+        "test-1.0+what.dist-info/METADATA",
+        "test-1.0+what.dist-info/WHEEL",
+    ):
+        assert expected in entries
+
+    for not_expected in (
+        "test.data/headers/hello.h",
+        "test-1.0.data/data/hello/world/file.txt",
+        "test.dist-info/METADATA",
+        "test-1.0.dist-info/WHEEL",
+    ):
+        assert not_expected not in entries
+
+
+@pytest.mark.parametrize(
+    ("reported", "expected"),
+    [("linux-x86_64", "linux_i686"), ("linux-aarch64", "linux_armv7l")],
+)
+@pytest.mark.skipif(
+    platform.system() != "Linux", reason="Only makes sense to test on Linux"
+)
+def test_platform_linux32(reported, expected, monkeypatch):
+    monkeypatch.setattr(struct, "calcsize", lambda x: 4)
+    dist = setuptools.Distribution()
+    cmd = bdist_wheel(dist)
+    cmd.plat_name = reported
+    cmd.root_is_pure = False
+    _, _, actual = cmd.get_tag()
+    assert actual == expected
+
+
+def test_no_ctypes(monkeypatch) -> None:
+    def _fake_import(name: str, *args, **kwargs):
+        if name == "ctypes":
+            raise ModuleNotFoundError(f"No module named {name}")
+
+        return importlib.__import__(name, *args, **kwargs)
+
+    with suppress(KeyError):
+        monkeypatch.delitem(sys.modules, "wheel.macosx_libfile")
+
+    # Install an importer shim that refuses to load ctypes
+    monkeypatch.setattr(builtins, "__import__", _fake_import)
+    with pytest.raises(ModuleNotFoundError, match="No module named ctypes"):
+        import wheel.macosx_libfile  # noqa: F401
+
+    # Unload and reimport the bdist_wheel command module to make sure it won't try to
+    # import ctypes
+    monkeypatch.delitem(sys.modules, "setuptools.command.bdist_wheel")
+
+    import setuptools.command.bdist_wheel  # noqa: F401
+
+
+def test_dist_info_provided(dummy_dist, monkeypatch, tmp_path):
+    monkeypatch.chdir(dummy_dist)
+    distinfo = tmp_path / "dummy_dist.dist-info"
+
+    distinfo.mkdir()
+    (distinfo / "METADATA").write_text("name: helloworld", encoding="utf-8")
+
+    # We don't control the metadata. According to PEP-517, "The hook MAY also
+    # create other files inside this directory, and a build frontend MUST
+    # preserve".
+    (distinfo / "FOO").write_text("bar", encoding="utf-8")
+
+    bdist_wheel_cmd(bdist_dir=str(tmp_path), dist_info_dir=str(distinfo)).run()
+    expected = {
+        "dummy_dist-1.0.dist-info/FOO",
+        "dummy_dist-1.0.dist-info/RECORD",
+    }
+    with ZipFile("dist/dummy_dist-1.0-py3-none-any.whl") as wf:
+        files_found = set(wf.namelist())
+    # Check that all expected files are there.
+    assert expected - files_found == set()
+    # Make sure there is no accidental egg-info bleeding into the wheel.
+    assert not [path for path in files_found if 'egg-info' in str(path)]
+
+
+def test_allow_grace_period_parent_directory_license(monkeypatch, tmp_path):
+    # Motivation: https://github.com/pypa/setuptools/issues/4892
+    # TODO: Remove this test after deprecation period is over
+    files = {
+        "LICENSE.txt": "parent license",  # <---- the license files are outside
+        "NOTICE.txt": "parent notice",
+        "python": {
+            "pyproject.toml": cleandoc(
+                """
+                [project]
+                name = "test-proj"
+                dynamic = ["version"]      # <---- testing dynamic will not break
+                [tool.setuptools.dynamic]
+                version.file = "VERSION"
+                """
+            ),
+            "setup.cfg": cleandoc(
+                """
+                [metadata]
+                license_files =
+                  ../LICENSE.txt
+                  ../NOTICE.txt
+                """
+            ),
+            "VERSION": "42",
+        },
+    }
+    jaraco.path.build(files, prefix=str(tmp_path))
+    monkeypatch.chdir(tmp_path / "python")
+    msg = "Pattern '../.*.txt' cannot contain '..'"
+    with pytest.warns(SetuptoolsDeprecationWarning, match=msg):
+        bdist_wheel_cmd().run()
+    with ZipFile("dist/test_proj-42-py3-none-any.whl") as wf:
+        files_found = set(wf.namelist())
+        expected_files = {
+            "test_proj-42.dist-info/licenses/LICENSE.txt",
+            "test_proj-42.dist-info/licenses/NOTICE.txt",
+        }
+        assert expected_files <= files_found
+
+        metadata = wf.read("test_proj-42.dist-info/METADATA").decode("utf8")
+        assert "License-File: LICENSE.txt" in metadata
+        assert "License-File: NOTICE.txt" in metadata
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build.py
new file mode 100644
index 0000000000000000000000000000000000000000..f0f1d9dcf21bafe9dc82a76d373b366ddeecfcec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build.py
@@ -0,0 +1,33 @@
+from setuptools import Command
+from setuptools.command.build import build
+from setuptools.dist import Distribution
+
+
+def test_distribution_gives_setuptools_build_obj(tmpdir_cwd):
+    """
+    Check that the setuptools Distribution uses the
+    setuptools specific build object.
+    """
+
+    dist = Distribution(
+        dict(
+            script_name='setup.py',
+            script_args=['build'],
+            packages=[],
+            package_data={'': ['path/*']},
+        )
+    )
+    assert isinstance(dist.get_command_obj("build"), build)
+
+
+class Subcommand(Command):
+    """Dummy command to be used in tests"""
+
+    def initialize_options(self):
+        pass
+
+    def finalize_options(self):
+        pass
+
+    def run(self):
+        raise NotImplementedError("just to check if the command runs")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_clib.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_clib.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5315df4f6599cd376e628c0d74cb14129cd89b8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_clib.py
@@ -0,0 +1,84 @@
+import random
+from unittest import mock
+
+import pytest
+
+from setuptools.command.build_clib import build_clib
+from setuptools.dist import Distribution
+
+from distutils.errors import DistutilsSetupError
+
+
+class TestBuildCLib:
+    @mock.patch('setuptools.command.build_clib.newer_pairwise_group')
+    def test_build_libraries(self, mock_newer):
+        dist = Distribution()
+        cmd = build_clib(dist)
+
+        # this will be a long section, just making sure all
+        # exceptions are properly raised
+        libs = [('example', {'sources': 'broken.c'})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.build_libraries(libs)
+
+        obj_deps = 'some_string'
+        libs = [('example', {'sources': ['source.c'], 'obj_deps': obj_deps})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.build_libraries(libs)
+
+        obj_deps = {'': ''}
+        libs = [('example', {'sources': ['source.c'], 'obj_deps': obj_deps})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.build_libraries(libs)
+
+        obj_deps = {'source.c': ''}
+        libs = [('example', {'sources': ['source.c'], 'obj_deps': obj_deps})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.build_libraries(libs)
+
+        # with that out of the way, let's see if the crude dependency
+        # system works
+        cmd.compiler = mock.MagicMock(spec=cmd.compiler)
+        mock_newer.return_value = ([], [])
+
+        obj_deps = {'': ('global.h',), 'example.c': ('example.h',)}
+        libs = [('example', {'sources': ['example.c'], 'obj_deps': obj_deps})]
+
+        cmd.build_libraries(libs)
+        assert [['example.c', 'global.h', 'example.h']] in mock_newer.call_args[0]
+        assert not cmd.compiler.compile.called
+        assert cmd.compiler.create_static_lib.call_count == 1
+
+        # reset the call numbers so we can test again
+        cmd.compiler.reset_mock()
+
+        mock_newer.return_value = ''  # anything as long as it's not ([],[])
+        cmd.build_libraries(libs)
+        assert cmd.compiler.compile.call_count == 1
+        assert cmd.compiler.create_static_lib.call_count == 1
+
+    @mock.patch('setuptools.command.build_clib.newer_pairwise_group')
+    def test_build_libraries_reproducible(self, mock_newer):
+        dist = Distribution()
+        cmd = build_clib(dist)
+
+        # with that out of the way, let's see if the crude dependency
+        # system works
+        cmd.compiler = mock.MagicMock(spec=cmd.compiler)
+        mock_newer.return_value = ([], [])
+
+        original_sources = ['a-example.c', 'example.c']
+        sources = original_sources
+
+        obj_deps = {'': ('global.h',), 'example.c': ('example.h',)}
+        libs = [('example', {'sources': sources, 'obj_deps': obj_deps})]
+
+        cmd.build_libraries(libs)
+        computed_call_args = mock_newer.call_args[0]
+
+        while sources == original_sources:
+            sources = random.sample(original_sources, len(original_sources))
+        libs = [('example', {'sources': sources, 'obj_deps': obj_deps})]
+
+        cmd.build_libraries(libs)
+        assert computed_call_args == mock_newer.call_args[0]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_ext.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_ext.py
new file mode 100644
index 0000000000000000000000000000000000000000..c7b60ac32fcd6628cf96396a7e5d8fdb50f67c19
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_ext.py
@@ -0,0 +1,293 @@
+from __future__ import annotations
+
+import os
+import sys
+from importlib.util import cache_from_source as _compiled_file_name
+
+import pytest
+from jaraco import path
+
+from setuptools.command.build_ext import build_ext, get_abi3_suffix
+from setuptools.dist import Distribution
+from setuptools.errors import CompileError
+from setuptools.extension import Extension
+
+from . import environment
+from .textwrap import DALS
+
+import distutils.command.build_ext as orig
+from distutils.sysconfig import get_config_var
+
+IS_PYPY = '__pypy__' in sys.builtin_module_names
+
+
+class TestBuildExt:
+    def test_get_ext_filename(self):
+        """
+        Setuptools needs to give back the same
+        result as distutils, even if the fullname
+        is not in ext_map.
+        """
+        dist = Distribution()
+        cmd = build_ext(dist)
+        cmd.ext_map['foo/bar'] = ''
+        res = cmd.get_ext_filename('foo')
+        wanted = orig.build_ext.get_ext_filename(cmd, 'foo')
+        assert res == wanted
+
+    def test_abi3_filename(self):
+        """
+        Filename needs to be loadable by several versions
+        of Python 3 if 'is_abi3' is truthy on Extension()
+        """
+        print(get_abi3_suffix())
+
+        extension = Extension('spam.eggs', ['eggs.c'], py_limited_api=True)
+        dist = Distribution(dict(ext_modules=[extension]))
+        cmd = build_ext(dist)
+        cmd.finalize_options()
+        assert 'spam.eggs' in cmd.ext_map
+        res = cmd.get_ext_filename('spam.eggs')
+
+        if not get_abi3_suffix():
+            assert res.endswith(get_config_var('EXT_SUFFIX'))
+        elif sys.platform == 'win32':
+            assert res.endswith('eggs.pyd')
+        else:
+            assert 'abi3' in res
+
+    def test_ext_suffix_override(self):
+        """
+        SETUPTOOLS_EXT_SUFFIX variable always overrides
+        default extension options.
+        """
+        dist = Distribution()
+        cmd = build_ext(dist)
+        cmd.ext_map['for_abi3'] = ext = Extension(
+            'for_abi3',
+            ['s.c'],
+            # Override shouldn't affect abi3 modules
+            py_limited_api=True,
+        )
+        # Mock value needed to pass tests
+        ext._links_to_dynamic = False
+
+        if not IS_PYPY:
+            expect = cmd.get_ext_filename('for_abi3')
+        else:
+            # PyPy builds do not use ABI3 tag, so they will
+            # also get the overridden suffix.
+            expect = 'for_abi3.test-suffix'
+
+        try:
+            os.environ['SETUPTOOLS_EXT_SUFFIX'] = '.test-suffix'
+            res = cmd.get_ext_filename('normal')
+            assert 'normal.test-suffix' == res
+            res = cmd.get_ext_filename('for_abi3')
+            assert expect == res
+        finally:
+            del os.environ['SETUPTOOLS_EXT_SUFFIX']
+
+    def dist_with_example(self):
+        files = {
+            "src": {"mypkg": {"subpkg": {"ext2.c": ""}}},
+            "c-extensions": {"ext1": {"main.c": ""}},
+        }
+
+        ext1 = Extension("mypkg.ext1", ["c-extensions/ext1/main.c"])
+        ext2 = Extension("mypkg.subpkg.ext2", ["src/mypkg/subpkg/ext2.c"])
+        ext3 = Extension("ext3", ["c-extension/ext3.c"])
+
+        path.build(files)
+        return Distribution({
+            "script_name": "%test%",
+            "ext_modules": [ext1, ext2, ext3],
+            "package_dir": {"": "src"},
+        })
+
+    def test_get_outputs(self, tmpdir_cwd, monkeypatch):
+        monkeypatch.setenv('SETUPTOOLS_EXT_SUFFIX', '.mp3')  # make test OS-independent
+        monkeypatch.setattr('setuptools.command.build_ext.use_stubs', False)
+        dist = self.dist_with_example()
+
+        # Regular build: get_outputs not empty, but get_output_mappings is empty
+        build_ext = dist.get_command_obj("build_ext")
+        build_ext.editable_mode = False
+        build_ext.ensure_finalized()
+        build_lib = build_ext.build_lib.replace(os.sep, "/")
+        outputs = [x.replace(os.sep, "/") for x in build_ext.get_outputs()]
+        assert outputs == [
+            f"{build_lib}/ext3.mp3",
+            f"{build_lib}/mypkg/ext1.mp3",
+            f"{build_lib}/mypkg/subpkg/ext2.mp3",
+        ]
+        assert build_ext.get_output_mapping() == {}
+
+        # Editable build: get_output_mappings should contain everything in get_outputs
+        dist.reinitialize_command("build_ext")
+        build_ext.editable_mode = True
+        build_ext.ensure_finalized()
+        mapping = {
+            k.replace(os.sep, "/"): v.replace(os.sep, "/")
+            for k, v in build_ext.get_output_mapping().items()
+        }
+        assert mapping == {
+            f"{build_lib}/ext3.mp3": "src/ext3.mp3",
+            f"{build_lib}/mypkg/ext1.mp3": "src/mypkg/ext1.mp3",
+            f"{build_lib}/mypkg/subpkg/ext2.mp3": "src/mypkg/subpkg/ext2.mp3",
+        }
+
+    def test_get_output_mapping_with_stub(self, tmpdir_cwd, monkeypatch):
+        monkeypatch.setenv('SETUPTOOLS_EXT_SUFFIX', '.mp3')  # make test OS-independent
+        monkeypatch.setattr('setuptools.command.build_ext.use_stubs', True)
+        dist = self.dist_with_example()
+
+        # Editable build should create compiled stubs (.pyc files only, no .py)
+        build_ext = dist.get_command_obj("build_ext")
+        build_ext.editable_mode = True
+        build_ext.ensure_finalized()
+        for ext in build_ext.extensions:
+            monkeypatch.setattr(ext, "_needs_stub", True)
+
+        build_lib = build_ext.build_lib.replace(os.sep, "/")
+        mapping = {
+            k.replace(os.sep, "/"): v.replace(os.sep, "/")
+            for k, v in build_ext.get_output_mapping().items()
+        }
+
+        def C(file):
+            """Make it possible to do comparisons and tests in a OS-independent way"""
+            return _compiled_file_name(file).replace(os.sep, "/")
+
+        assert mapping == {
+            C(f"{build_lib}/ext3.py"): C("src/ext3.py"),
+            f"{build_lib}/ext3.mp3": "src/ext3.mp3",
+            C(f"{build_lib}/mypkg/ext1.py"): C("src/mypkg/ext1.py"),
+            f"{build_lib}/mypkg/ext1.mp3": "src/mypkg/ext1.mp3",
+            C(f"{build_lib}/mypkg/subpkg/ext2.py"): C("src/mypkg/subpkg/ext2.py"),
+            f"{build_lib}/mypkg/subpkg/ext2.mp3": "src/mypkg/subpkg/ext2.mp3",
+        }
+
+        # Ensure only the compiled stubs are present not the raw .py stub
+        assert f"{build_lib}/mypkg/ext1.py" not in mapping
+        assert f"{build_lib}/mypkg/subpkg/ext2.py" not in mapping
+
+        # Visualize what the cached stub files look like
+        example_stub = C(f"{build_lib}/mypkg/ext1.py")
+        assert example_stub in mapping
+        assert example_stub.startswith(f"{build_lib}/mypkg/__pycache__/ext1")
+        assert example_stub.endswith(".pyc")
+
+
+class TestBuildExtInplace:
+    def get_build_ext_cmd(self, optional: bool, **opts) -> build_ext:
+        files: dict[str, str | dict[str, dict[str, str]]] = {
+            "eggs.c": "#include missingheader.h\n",
+            ".build": {"lib": {}, "tmp": {}},
+        }
+        path.build(files)
+        extension = Extension('spam.eggs', ['eggs.c'], optional=optional)
+        dist = Distribution(dict(ext_modules=[extension]))
+        dist.script_name = 'setup.py'
+        cmd = build_ext(dist)
+        vars(cmd).update(build_lib=".build/lib", build_temp=".build/tmp", **opts)
+        cmd.ensure_finalized()
+        return cmd
+
+    def get_log_messages(self, caplog, capsys):
+        """
+        Historically, distutils "logged" by printing to sys.std*.
+        Later versions adopted the logging framework. Grab
+        messages regardless of how they were captured.
+        """
+        std = capsys.readouterr()
+        return std.out.splitlines() + std.err.splitlines() + caplog.messages
+
+    def test_optional(self, tmpdir_cwd, caplog, capsys):
+        """
+        If optional extensions fail to build, setuptools should show the error
+        in the logs but not fail to build
+        """
+        cmd = self.get_build_ext_cmd(optional=True, inplace=True)
+        cmd.run()
+        assert any(
+            'build_ext: building extension "spam.eggs" failed'
+            for msg in self.get_log_messages(caplog, capsys)
+        )
+        # No compile error exception should be raised
+
+    def test_non_optional(self, tmpdir_cwd):
+        # Non-optional extensions should raise an exception
+        cmd = self.get_build_ext_cmd(optional=False, inplace=True)
+        with pytest.raises(CompileError):
+            cmd.run()
+
+
+def test_build_ext_config_handling(tmpdir_cwd):
+    files = {
+        'setup.py': DALS(
+            """
+            from setuptools import Extension, setup
+            setup(
+                name='foo',
+                version='0.0.0',
+                ext_modules=[Extension('foo', ['foo.c'])],
+            )
+            """
+        ),
+        'foo.c': DALS(
+            """
+            #include "Python.h"
+
+            #if PY_MAJOR_VERSION >= 3
+
+            static struct PyModuleDef moduledef = {
+                    PyModuleDef_HEAD_INIT,
+                    "foo",
+                    NULL,
+                    0,
+                    NULL,
+                    NULL,
+                    NULL,
+                    NULL,
+                    NULL
+            };
+
+            #define INITERROR return NULL
+
+            PyMODINIT_FUNC PyInit_foo(void)
+
+            #else
+
+            #define INITERROR return
+
+            void initfoo(void)
+
+            #endif
+            {
+            #if PY_MAJOR_VERSION >= 3
+                PyObject *module = PyModule_Create(&moduledef);
+            #else
+                PyObject *module = Py_InitModule("extension", NULL);
+            #endif
+                if (module == NULL)
+                    INITERROR;
+            #if PY_MAJOR_VERSION >= 3
+                return module;
+            #endif
+            }
+            """
+        ),
+        'setup.cfg': DALS(
+            """
+            [build]
+            build_base = foo_build
+            """
+        ),
+    }
+    path.build(files)
+    code, (stdout, stderr) = environment.run_setup_py(
+        cmd=['build'],
+        data_stream=(0, 2),
+    )
+    assert code == 0, f'\nSTDOUT:\n{stdout}\nSTDERR:\n{stderr}'
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_meta.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_meta.py
new file mode 100644
index 0000000000000000000000000000000000000000..57162fd6afec0e3edd062232eec84b9bbb1fc26b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_meta.py
@@ -0,0 +1,959 @@
+import contextlib
+import importlib
+import os
+import re
+import shutil
+import signal
+import sys
+import tarfile
+import warnings
+from concurrent import futures
+from pathlib import Path
+from typing import Any, Callable
+from zipfile import ZipFile
+
+import pytest
+from jaraco import path
+from packaging.requirements import Requirement
+
+from setuptools.warnings import SetuptoolsDeprecationWarning
+
+from .textwrap import DALS
+
+SETUP_SCRIPT_STUB = "__import__('setuptools').setup()"
+
+
+TIMEOUT = int(os.getenv("TIMEOUT_BACKEND_TEST", "180"))  # in seconds
+IS_PYPY = '__pypy__' in sys.builtin_module_names
+
+
+pytestmark = pytest.mark.skipif(
+    sys.platform == "win32" and IS_PYPY,
+    reason="The combination of PyPy + Windows + pytest-xdist + ProcessPoolExecutor "
+    "is flaky and problematic",
+)
+
+
+class BuildBackendBase:
+    def __init__(self, cwd='.', env=None, backend_name='setuptools.build_meta'):
+        self.cwd = cwd
+        self.env = env or {}
+        self.backend_name = backend_name
+
+
+class BuildBackend(BuildBackendBase):
+    """PEP 517 Build Backend"""
+
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+        self.pool = futures.ProcessPoolExecutor(max_workers=1)
+
+    def __getattr__(self, name: str) -> Callable[..., Any]:
+        """Handles arbitrary function invocations on the build backend."""
+
+        def method(*args, **kw):
+            root = os.path.abspath(self.cwd)
+            caller = BuildBackendCaller(root, self.env, self.backend_name)
+            pid = None
+            try:
+                pid = self.pool.submit(os.getpid).result(TIMEOUT)
+                return self.pool.submit(caller, name, *args, **kw).result(TIMEOUT)
+            except futures.TimeoutError:
+                self.pool.shutdown(wait=False)  # doesn't stop already running processes
+                self._kill(pid)
+                pytest.xfail(f"Backend did not respond before timeout ({TIMEOUT} s)")
+            except (futures.process.BrokenProcessPool, MemoryError, OSError):
+                if IS_PYPY:
+                    pytest.xfail("PyPy frequently fails tests with ProcessPoolExector")
+                raise
+
+        return method
+
+    def _kill(self, pid):
+        if pid is None:
+            return
+        with contextlib.suppress(ProcessLookupError, OSError):
+            os.kill(pid, signal.SIGTERM if os.name == "nt" else signal.SIGKILL)
+
+
+class BuildBackendCaller(BuildBackendBase):
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+
+        (self.backend_name, _, self.backend_obj) = self.backend_name.partition(':')
+
+    def __call__(self, name, *args, **kw):
+        """Handles arbitrary function invocations on the build backend."""
+        os.chdir(self.cwd)
+        os.environ.update(self.env)
+        mod = importlib.import_module(self.backend_name)
+
+        if self.backend_obj:
+            backend = getattr(mod, self.backend_obj)
+        else:
+            backend = mod
+
+        return getattr(backend, name)(*args, **kw)
+
+
+defns = [
+    {  # simple setup.py script
+        'setup.py': DALS(
+            """
+            __import__('setuptools').setup(
+                name='foo',
+                version='0.0.0',
+                py_modules=['hello'],
+                setup_requires=['six'],
+            )
+            """
+        ),
+        'hello.py': DALS(
+            """
+            def run():
+                print('hello')
+            """
+        ),
+    },
+    {  # setup.py that relies on __name__
+        'setup.py': DALS(
+            """
+            assert __name__ == '__main__'
+            __import__('setuptools').setup(
+                name='foo',
+                version='0.0.0',
+                py_modules=['hello'],
+                setup_requires=['six'],
+            )
+            """
+        ),
+        'hello.py': DALS(
+            """
+            def run():
+                print('hello')
+            """
+        ),
+    },
+    {  # setup.py script that runs arbitrary code
+        'setup.py': DALS(
+            """
+            variable = True
+            def function():
+                return variable
+            assert variable
+            __import__('setuptools').setup(
+                name='foo',
+                version='0.0.0',
+                py_modules=['hello'],
+                setup_requires=['six'],
+            )
+            """
+        ),
+        'hello.py': DALS(
+            """
+            def run():
+                print('hello')
+            """
+        ),
+    },
+    {  # setup.py script that constructs temp files to be included in the distribution
+        'setup.py': DALS(
+            """
+            # Some packages construct files on the fly, include them in the package,
+            # and immediately remove them after `setup()` (e.g. pybind11==2.9.1).
+            # Therefore, we cannot use `distutils.core.run_setup(..., stop_after=...)`
+            # to obtain a distribution object first, and then run the distutils
+            # commands later, because these files will be removed in the meantime.
+
+            with open('world.py', 'w', encoding="utf-8") as f:
+                f.write('x = 42')
+
+            try:
+                __import__('setuptools').setup(
+                    name='foo',
+                    version='0.0.0',
+                    py_modules=['world'],
+                    setup_requires=['six'],
+                )
+            finally:
+                # Some packages will clean temporary files
+                __import__('os').unlink('world.py')
+            """
+        ),
+    },
+    {  # setup.cfg only
+        'setup.cfg': DALS(
+            """
+        [metadata]
+        name = foo
+        version = 0.0.0
+
+        [options]
+        py_modules=hello
+        setup_requires=six
+        """
+        ),
+        'hello.py': DALS(
+            """
+        def run():
+            print('hello')
+        """
+        ),
+    },
+    {  # setup.cfg and setup.py
+        'setup.cfg': DALS(
+            """
+        [metadata]
+        name = foo
+        version = 0.0.0
+
+        [options]
+        py_modules=hello
+        setup_requires=six
+        """
+        ),
+        'setup.py': "__import__('setuptools').setup()",
+        'hello.py': DALS(
+            """
+        def run():
+            print('hello')
+        """
+        ),
+    },
+]
+
+
+class TestBuildMetaBackend:
+    backend_name = 'setuptools.build_meta'
+
+    def get_build_backend(self):
+        return BuildBackend(backend_name=self.backend_name)
+
+    @pytest.fixture(params=defns)
+    def build_backend(self, tmpdir, request):
+        path.build(request.param, prefix=str(tmpdir))
+        with tmpdir.as_cwd():
+            yield self.get_build_backend()
+
+    def test_get_requires_for_build_wheel(self, build_backend):
+        actual = build_backend.get_requires_for_build_wheel()
+        expected = ['six']
+        assert sorted(actual) == sorted(expected)
+
+    def test_get_requires_for_build_sdist(self, build_backend):
+        actual = build_backend.get_requires_for_build_sdist()
+        expected = ['six']
+        assert sorted(actual) == sorted(expected)
+
+    def test_build_wheel(self, build_backend):
+        dist_dir = os.path.abspath('pip-wheel')
+        os.makedirs(dist_dir)
+        wheel_name = build_backend.build_wheel(dist_dir)
+
+        wheel_file = os.path.join(dist_dir, wheel_name)
+        assert os.path.isfile(wheel_file)
+
+        # Temporary files should be removed
+        assert not os.path.isfile('world.py')
+
+        with ZipFile(wheel_file) as zipfile:
+            wheel_contents = set(zipfile.namelist())
+
+        # Each one of the examples have a single module
+        # that should be included in the distribution
+        python_scripts = (f for f in wheel_contents if f.endswith('.py'))
+        modules = [f for f in python_scripts if not f.endswith('setup.py')]
+        assert len(modules) == 1
+
+    @pytest.mark.parametrize('build_type', ('wheel', 'sdist'))
+    def test_build_with_existing_file_present(self, build_type, tmpdir_cwd):
+        # Building a sdist/wheel should still succeed if there's
+        # already a sdist/wheel in the destination directory.
+        files = {
+            'setup.py': "from setuptools import setup\nsetup()",
+            'VERSION': "0.0.1",
+            'setup.cfg': DALS(
+                """
+                [metadata]
+                name = foo
+                version = file: VERSION
+                """
+            ),
+            'pyproject.toml': DALS(
+                """
+                [build-system]
+                requires = ["setuptools", "wheel"]
+                build-backend = "setuptools.build_meta"
+                """
+            ),
+        }
+
+        path.build(files)
+
+        dist_dir = os.path.abspath('preexisting-' + build_type)
+
+        build_backend = self.get_build_backend()
+        build_method = getattr(build_backend, 'build_' + build_type)
+
+        # Build a first sdist/wheel.
+        # Note: this also check the destination directory is
+        # successfully created if it does not exist already.
+        first_result = build_method(dist_dir)
+
+        # Change version.
+        with open("VERSION", "wt", encoding="utf-8") as version_file:
+            version_file.write("0.0.2")
+
+        # Build a *second* sdist/wheel.
+        second_result = build_method(dist_dir)
+
+        assert os.path.isfile(os.path.join(dist_dir, first_result))
+        assert first_result != second_result
+
+        # And if rebuilding the exact same sdist/wheel?
+        open(os.path.join(dist_dir, second_result), 'wb').close()
+        third_result = build_method(dist_dir)
+        assert third_result == second_result
+        assert os.path.getsize(os.path.join(dist_dir, third_result)) > 0
+
+    @pytest.mark.parametrize("setup_script", [None, SETUP_SCRIPT_STUB])
+    def test_build_with_pyproject_config(self, tmpdir, setup_script):
+        files = {
+            'pyproject.toml': DALS(
+                """
+                [build-system]
+                requires = ["setuptools", "wheel"]
+                build-backend = "setuptools.build_meta"
+
+                [project]
+                name = "foo"
+                license = {text = "MIT"}
+                description = "This is a Python package"
+                dynamic = ["version", "readme"]
+                classifiers = [
+                    "Development Status :: 5 - Production/Stable",
+                    "Intended Audience :: Developers"
+                ]
+                urls = {Homepage = "http://github.com"}
+                dependencies = [
+                    "appdirs",
+                ]
+
+                [project.optional-dependencies]
+                all = [
+                    "tomli>=1",
+                    "pyscaffold>=4,<5",
+                    'importlib; python_version == "2.6"',
+                ]
+
+                [project.scripts]
+                foo = "foo.cli:main"
+
+                [tool.setuptools]
+                zip-safe = false
+                package-dir = {"" = "src"}
+                packages = {find = {where = ["src"]}}
+                license-files = ["LICENSE*"]
+
+                [tool.setuptools.dynamic]
+                version = {attr = "foo.__version__"}
+                readme = {file = "README.rst"}
+
+                [tool.distutils.sdist]
+                formats = "gztar"
+                """
+            ),
+            "MANIFEST.in": DALS(
+                """
+                global-include *.py *.txt
+                global-exclude *.py[cod]
+                """
+            ),
+            "README.rst": "This is a ``README``",
+            "LICENSE.txt": "---- placeholder MIT license ----",
+            "src": {
+                "foo": {
+                    "__init__.py": "__version__ = '0.1'",
+                    "__init__.pyi": "__version__: str",
+                    "cli.py": "def main(): print('hello world')",
+                    "data.txt": "def main(): print('hello world')",
+                    "py.typed": "",
+                }
+            },
+        }
+        if setup_script:
+            files["setup.py"] = setup_script
+
+        build_backend = self.get_build_backend()
+        with tmpdir.as_cwd():
+            path.build(files)
+            msgs = [
+                "'tool.setuptools.license-files' is deprecated in favor of 'project.license-files'",
+                "`project.license` as a TOML table is deprecated",
+            ]
+            with warnings.catch_warnings():
+                for msg in msgs:
+                    warnings.filterwarnings("ignore", msg, SetuptoolsDeprecationWarning)
+                sdist_path = build_backend.build_sdist("temp")
+                wheel_file = build_backend.build_wheel("temp")
+
+        with tarfile.open(os.path.join(tmpdir, "temp", sdist_path)) as tar:
+            sdist_contents = set(tar.getnames())
+
+        with ZipFile(os.path.join(tmpdir, "temp", wheel_file)) as zipfile:
+            wheel_contents = set(zipfile.namelist())
+            metadata = str(zipfile.read("foo-0.1.dist-info/METADATA"), "utf-8")
+            license = str(
+                zipfile.read("foo-0.1.dist-info/licenses/LICENSE.txt"), "utf-8"
+            )
+            epoints = str(zipfile.read("foo-0.1.dist-info/entry_points.txt"), "utf-8")
+
+        assert sdist_contents - {"foo-0.1/setup.py"} == {
+            'foo-0.1',
+            'foo-0.1/LICENSE.txt',
+            'foo-0.1/MANIFEST.in',
+            'foo-0.1/PKG-INFO',
+            'foo-0.1/README.rst',
+            'foo-0.1/pyproject.toml',
+            'foo-0.1/setup.cfg',
+            'foo-0.1/src',
+            'foo-0.1/src/foo',
+            'foo-0.1/src/foo/__init__.py',
+            'foo-0.1/src/foo/__init__.pyi',
+            'foo-0.1/src/foo/cli.py',
+            'foo-0.1/src/foo/data.txt',
+            'foo-0.1/src/foo/py.typed',
+            'foo-0.1/src/foo.egg-info',
+            'foo-0.1/src/foo.egg-info/PKG-INFO',
+            'foo-0.1/src/foo.egg-info/SOURCES.txt',
+            'foo-0.1/src/foo.egg-info/dependency_links.txt',
+            'foo-0.1/src/foo.egg-info/entry_points.txt',
+            'foo-0.1/src/foo.egg-info/requires.txt',
+            'foo-0.1/src/foo.egg-info/top_level.txt',
+            'foo-0.1/src/foo.egg-info/not-zip-safe',
+        }
+        assert wheel_contents == {
+            "foo/__init__.py",
+            "foo/__init__.pyi",  # include type information by default
+            "foo/cli.py",
+            "foo/data.txt",  # include_package_data defaults to True
+            "foo/py.typed",  # include type information by default
+            "foo-0.1.dist-info/licenses/LICENSE.txt",
+            "foo-0.1.dist-info/METADATA",
+            "foo-0.1.dist-info/WHEEL",
+            "foo-0.1.dist-info/entry_points.txt",
+            "foo-0.1.dist-info/top_level.txt",
+            "foo-0.1.dist-info/RECORD",
+        }
+        assert license == "---- placeholder MIT license ----"
+
+        for line in (
+            "Summary: This is a Python package",
+            "License: MIT",
+            "License-File: LICENSE.txt",
+            "Classifier: Intended Audience :: Developers",
+            "Requires-Dist: appdirs",
+            "Requires-Dist: " + str(Requirement('tomli>=1 ; extra == "all"')),
+            "Requires-Dist: "
+            + str(Requirement('importlib; python_version=="2.6" and extra =="all"')),
+        ):
+            assert line in metadata, (line, metadata)
+
+        assert metadata.strip().endswith("This is a ``README``")
+        assert epoints.strip() == "[console_scripts]\nfoo = foo.cli:main"
+
+    def test_static_metadata_in_pyproject_config(self, tmpdir):
+        # Make sure static metadata in pyproject.toml is not overwritten by setup.py
+        # as required by PEP 621
+        files = {
+            'pyproject.toml': DALS(
+                """
+                [build-system]
+                requires = ["setuptools", "wheel"]
+                build-backend = "setuptools.build_meta"
+
+                [project]
+                name = "foo"
+                description = "This is a Python package"
+                version = "42"
+                dependencies = ["six"]
+                """
+            ),
+            'hello.py': DALS(
+                """
+                def run():
+                    print('hello')
+                """
+            ),
+            'setup.py': DALS(
+                """
+                __import__('setuptools').setup(
+                    name='bar',
+                    version='13',
+                )
+                """
+            ),
+        }
+        build_backend = self.get_build_backend()
+        with tmpdir.as_cwd():
+            path.build(files)
+            sdist_path = build_backend.build_sdist("temp")
+            wheel_file = build_backend.build_wheel("temp")
+
+        assert (tmpdir / "temp/foo-42.tar.gz").exists()
+        assert (tmpdir / "temp/foo-42-py3-none-any.whl").exists()
+        assert not (tmpdir / "temp/bar-13.tar.gz").exists()
+        assert not (tmpdir / "temp/bar-42.tar.gz").exists()
+        assert not (tmpdir / "temp/foo-13.tar.gz").exists()
+        assert not (tmpdir / "temp/bar-13-py3-none-any.whl").exists()
+        assert not (tmpdir / "temp/bar-42-py3-none-any.whl").exists()
+        assert not (tmpdir / "temp/foo-13-py3-none-any.whl").exists()
+
+        with tarfile.open(os.path.join(tmpdir, "temp", sdist_path)) as tar:
+            pkg_info = str(tar.extractfile('foo-42/PKG-INFO').read(), "utf-8")
+            members = tar.getnames()
+            assert "bar-13/PKG-INFO" not in members
+
+        with ZipFile(os.path.join(tmpdir, "temp", wheel_file)) as zipfile:
+            metadata = str(zipfile.read("foo-42.dist-info/METADATA"), "utf-8")
+            members = zipfile.namelist()
+            assert "bar-13.dist-info/METADATA" not in members
+
+        for file in pkg_info, metadata:
+            for line in ("Name: foo", "Version: 42"):
+                assert line in file
+            for line in ("Name: bar", "Version: 13"):
+                assert line not in file
+
+    def test_build_sdist(self, build_backend):
+        dist_dir = os.path.abspath('pip-sdist')
+        os.makedirs(dist_dir)
+        sdist_name = build_backend.build_sdist(dist_dir)
+
+        assert os.path.isfile(os.path.join(dist_dir, sdist_name))
+
+    def test_prepare_metadata_for_build_wheel(self, build_backend):
+        dist_dir = os.path.abspath('pip-dist-info')
+        os.makedirs(dist_dir)
+
+        dist_info = build_backend.prepare_metadata_for_build_wheel(dist_dir)
+
+        assert os.path.isfile(os.path.join(dist_dir, dist_info, 'METADATA'))
+
+    def test_prepare_metadata_inplace(self, build_backend):
+        """
+        Some users might pass metadata_directory pre-populated with `.tox` or `.venv`.
+        See issue #3523.
+        """
+        for pre_existing in [
+            ".tox/python/lib/python3.10/site-packages/attrs-22.1.0.dist-info",
+            ".tox/python/lib/python3.10/site-packages/autocommand-2.2.1.dist-info",
+            ".nox/python/lib/python3.10/site-packages/build-0.8.0.dist-info",
+            ".venv/python3.10/site-packages/click-8.1.3.dist-info",
+            "venv/python3.10/site-packages/distlib-0.3.5.dist-info",
+            "env/python3.10/site-packages/docutils-0.19.dist-info",
+        ]:
+            os.makedirs(pre_existing, exist_ok=True)
+        dist_info = build_backend.prepare_metadata_for_build_wheel(".")
+        assert os.path.isfile(os.path.join(dist_info, 'METADATA'))
+
+    def test_build_sdist_explicit_dist(self, build_backend):
+        # explicitly specifying the dist folder should work
+        # the folder sdist_directory and the ``--dist-dir`` can be the same
+        dist_dir = os.path.abspath('dist')
+        sdist_name = build_backend.build_sdist(dist_dir)
+        assert os.path.isfile(os.path.join(dist_dir, sdist_name))
+
+    def test_build_sdist_version_change(self, build_backend):
+        sdist_into_directory = os.path.abspath("out_sdist")
+        os.makedirs(sdist_into_directory)
+
+        sdist_name = build_backend.build_sdist(sdist_into_directory)
+        assert os.path.isfile(os.path.join(sdist_into_directory, sdist_name))
+
+        # if the setup.py changes subsequent call of the build meta
+        # should still succeed, given the
+        # sdist_directory the frontend specifies is empty
+        setup_loc = os.path.abspath("setup.py")
+        if not os.path.exists(setup_loc):
+            setup_loc = os.path.abspath("setup.cfg")
+
+        with open(setup_loc, 'rt', encoding="utf-8") as file_handler:
+            content = file_handler.read()
+        with open(setup_loc, 'wt', encoding="utf-8") as file_handler:
+            file_handler.write(content.replace("version='0.0.0'", "version='0.0.1'"))
+
+        shutil.rmtree(sdist_into_directory)
+        os.makedirs(sdist_into_directory)
+
+        sdist_name = build_backend.build_sdist("out_sdist")
+        assert os.path.isfile(os.path.join(os.path.abspath("out_sdist"), sdist_name))
+
+    def test_build_sdist_pyproject_toml_exists(self, tmpdir_cwd):
+        files = {
+            'setup.py': DALS(
+                """
+                __import__('setuptools').setup(
+                    name='foo',
+                    version='0.0.0',
+                    py_modules=['hello']
+                )"""
+            ),
+            'hello.py': '',
+            'pyproject.toml': DALS(
+                """
+                [build-system]
+                requires = ["setuptools", "wheel"]
+                build-backend = "setuptools.build_meta"
+                """
+            ),
+        }
+        path.build(files)
+        build_backend = self.get_build_backend()
+        targz_path = build_backend.build_sdist("temp")
+        with tarfile.open(os.path.join("temp", targz_path)) as tar:
+            assert any('pyproject.toml' in name for name in tar.getnames())
+
+    def test_build_sdist_setup_py_exists(self, tmpdir_cwd):
+        # If build_sdist is called from a script other than setup.py,
+        # ensure setup.py is included
+        path.build(defns[0])
+
+        build_backend = self.get_build_backend()
+        targz_path = build_backend.build_sdist("temp")
+        with tarfile.open(os.path.join("temp", targz_path)) as tar:
+            assert any('setup.py' in name for name in tar.getnames())
+
+    def test_build_sdist_setup_py_manifest_excluded(self, tmpdir_cwd):
+        # Ensure that MANIFEST.in can exclude setup.py
+        files = {
+            'setup.py': DALS(
+                """
+        __import__('setuptools').setup(
+            name='foo',
+            version='0.0.0',
+            py_modules=['hello']
+        )"""
+            ),
+            'hello.py': '',
+            'MANIFEST.in': DALS(
+                """
+        exclude setup.py
+        """
+            ),
+        }
+
+        path.build(files)
+
+        build_backend = self.get_build_backend()
+        targz_path = build_backend.build_sdist("temp")
+        with tarfile.open(os.path.join("temp", targz_path)) as tar:
+            assert not any('setup.py' in name for name in tar.getnames())
+
+    def test_build_sdist_builds_targz_even_if_zip_indicated(self, tmpdir_cwd):
+        files = {
+            'setup.py': DALS(
+                """
+                __import__('setuptools').setup(
+                    name='foo',
+                    version='0.0.0',
+                    py_modules=['hello']
+                )"""
+            ),
+            'hello.py': '',
+            'setup.cfg': DALS(
+                """
+                [sdist]
+                formats=zip
+                """
+            ),
+        }
+
+        path.build(files)
+
+        build_backend = self.get_build_backend()
+        build_backend.build_sdist("temp")
+
+    _relative_path_import_files = {
+        'setup.py': DALS(
+            """
+            __import__('setuptools').setup(
+                name='foo',
+                version=__import__('hello').__version__,
+                py_modules=['hello']
+            )"""
+        ),
+        'hello.py': '__version__ = "0.0.0"',
+        'setup.cfg': DALS(
+            """
+            [sdist]
+            formats=zip
+            """
+        ),
+    }
+
+    def test_build_sdist_relative_path_import(self, tmpdir_cwd):
+        path.build(self._relative_path_import_files)
+        build_backend = self.get_build_backend()
+        with pytest.raises(ImportError, match="^No module named 'hello'$"):
+            build_backend.build_sdist("temp")
+
+    _simple_pyproject_example = {
+        "pyproject.toml": DALS(
+            """
+            [project]
+            name = "proj"
+            version = "42"
+            """
+        ),
+        "src": {"proj": {"__init__.py": ""}},
+    }
+
+    def _assert_link_tree(self, parent_dir):
+        """All files in the directory should be either links or hard links"""
+        files = list(Path(parent_dir).glob("**/*"))
+        assert files  # Should not be empty
+        for file in files:
+            assert file.is_symlink() or os.stat(file).st_nlink > 0
+
+    def test_editable_without_config_settings(self, tmpdir_cwd):
+        """
+        Sanity check to ensure tests with --mode=strict are different from the ones
+        without --mode.
+
+        --mode=strict should create a local directory with a package tree.
+        The directory should not get created otherwise.
+        """
+        path.build(self._simple_pyproject_example)
+        build_backend = self.get_build_backend()
+        assert not Path("build").exists()
+        build_backend.build_editable("temp")
+        assert not Path("build").exists()
+
+    def test_build_wheel_inplace(self, tmpdir_cwd):
+        config_settings = {"--build-option": ["build_ext", "--inplace"]}
+        path.build(self._simple_pyproject_example)
+        build_backend = self.get_build_backend()
+        assert not Path("build").exists()
+        Path("build").mkdir()
+        build_backend.prepare_metadata_for_build_wheel("build", config_settings)
+        build_backend.build_wheel("build", config_settings)
+        assert Path("build/proj-42-py3-none-any.whl").exists()
+
+    @pytest.mark.parametrize("config_settings", [{"editable-mode": "strict"}])
+    def test_editable_with_config_settings(self, tmpdir_cwd, config_settings):
+        path.build({**self._simple_pyproject_example, '_meta': {}})
+        assert not Path("build").exists()
+        build_backend = self.get_build_backend()
+        build_backend.prepare_metadata_for_build_editable("_meta", config_settings)
+        build_backend.build_editable("temp", config_settings, "_meta")
+        self._assert_link_tree(next(Path("build").glob("__editable__.*")))
+
+    @pytest.mark.parametrize(
+        ("setup_literal", "requirements"),
+        [
+            ("'foo'", ['foo']),
+            ("['foo']", ['foo']),
+            (r"'foo\n'", ['foo']),
+            (r"'foo\n\n'", ['foo']),
+            ("['foo', 'bar']", ['foo', 'bar']),
+            (r"'# Has a comment line\nfoo'", ['foo']),
+            (r"'foo # Has an inline comment'", ['foo']),
+            (r"'foo \\\n >=3.0'", ['foo>=3.0']),
+            (r"'foo\nbar'", ['foo', 'bar']),
+            (r"'foo\nbar\n'", ['foo', 'bar']),
+            (r"['foo\n', 'bar\n']", ['foo', 'bar']),
+        ],
+    )
+    @pytest.mark.parametrize('use_wheel', [True, False])
+    def test_setup_requires(self, setup_literal, requirements, use_wheel, tmpdir_cwd):
+        files = {
+            'setup.py': DALS(
+                """
+                from setuptools import setup
+
+                setup(
+                    name="qux",
+                    version="0.0.0",
+                    py_modules=["hello"],
+                    setup_requires={setup_literal},
+                )
+            """
+            ).format(setup_literal=setup_literal),
+            'hello.py': DALS(
+                """
+            def run():
+                print('hello')
+            """
+            ),
+        }
+
+        path.build(files)
+
+        build_backend = self.get_build_backend()
+
+        if use_wheel:
+            get_requires = build_backend.get_requires_for_build_wheel
+        else:
+            get_requires = build_backend.get_requires_for_build_sdist
+
+        # Ensure that the build requirements are properly parsed
+        expected = sorted(requirements)
+        actual = get_requires()
+
+        assert expected == sorted(actual)
+
+    def test_setup_requires_with_auto_discovery(self, tmpdir_cwd):
+        # Make sure patches introduced to retrieve setup_requires don't accidentally
+        # activate auto-discovery and cause problems due to the incomplete set of
+        # attributes passed to MinimalDistribution
+        files = {
+            'pyproject.toml': DALS(
+                """
+                [project]
+                name = "proj"
+                version = "42"
+            """
+            ),
+            "setup.py": DALS(
+                """
+                __import__('setuptools').setup(
+                    setup_requires=["foo"],
+                    py_modules = ["hello", "world"]
+                )
+            """
+            ),
+            'hello.py': "'hello'",
+            'world.py': "'world'",
+        }
+        path.build(files)
+        build_backend = self.get_build_backend()
+        setup_requires = build_backend.get_requires_for_build_wheel()
+        assert setup_requires == ["foo"]
+
+    def test_dont_install_setup_requires(self, tmpdir_cwd):
+        files = {
+            'setup.py': DALS(
+                """
+                        from setuptools import setup
+
+                        setup(
+                            name="qux",
+                            version="0.0.0",
+                            py_modules=["hello"],
+                            setup_requires=["does-not-exist >99"],
+                        )
+                    """
+            ),
+            'hello.py': DALS(
+                """
+                    def run():
+                        print('hello')
+                    """
+            ),
+        }
+
+        path.build(files)
+
+        build_backend = self.get_build_backend()
+
+        dist_dir = os.path.abspath('pip-dist-info')
+        os.makedirs(dist_dir)
+
+        # does-not-exist can't be satisfied, so if it attempts to install
+        # setup_requires, it will fail.
+        build_backend.prepare_metadata_for_build_wheel(dist_dir)
+
+    _sys_argv_0_passthrough = {
+        'setup.py': DALS(
+            """
+            import os
+            import sys
+
+            __import__('setuptools').setup(
+                name='foo',
+                version='0.0.0',
+            )
+
+            sys_argv = os.path.abspath(sys.argv[0])
+            file_path = os.path.abspath('setup.py')
+            assert sys_argv == file_path
+            """
+        )
+    }
+
+    def test_sys_argv_passthrough(self, tmpdir_cwd):
+        path.build(self._sys_argv_0_passthrough)
+        build_backend = self.get_build_backend()
+        with pytest.raises(AssertionError):
+            build_backend.build_sdist("temp")
+
+    _setup_py_file_abspath = {
+        'setup.py': DALS(
+            """
+            import os
+            assert os.path.isabs(__file__)
+            __import__('setuptools').setup(
+                name='foo',
+                version='0.0.0',
+                py_modules=['hello'],
+                setup_requires=['six'],
+            )
+            """
+        )
+    }
+
+    def test_setup_py_file_abspath(self, tmpdir_cwd):
+        path.build(self._setup_py_file_abspath)
+        build_backend = self.get_build_backend()
+        build_backend.build_sdist("temp")
+
+    @pytest.mark.parametrize('build_hook', ('build_sdist', 'build_wheel'))
+    def test_build_with_empty_setuppy(self, build_backend, build_hook):
+        files = {'setup.py': ''}
+        path.build(files)
+
+        msg = re.escape('No distribution was found.')
+        with pytest.raises(ValueError, match=msg):
+            getattr(build_backend, build_hook)("temp")
+
+
+class TestBuildMetaLegacyBackend(TestBuildMetaBackend):
+    backend_name = 'setuptools.build_meta:__legacy__'
+
+    # build_meta_legacy-specific tests
+    def test_build_sdist_relative_path_import(self, tmpdir_cwd):
+        # This must fail in build_meta, but must pass in build_meta_legacy
+        path.build(self._relative_path_import_files)
+
+        build_backend = self.get_build_backend()
+        build_backend.build_sdist("temp")
+
+    def test_sys_argv_passthrough(self, tmpdir_cwd):
+        path.build(self._sys_argv_0_passthrough)
+
+        build_backend = self.get_build_backend()
+        build_backend.build_sdist("temp")
+
+
+@pytest.mark.filterwarnings("ignore::setuptools.SetuptoolsDeprecationWarning")
+def test_sys_exit_0_in_setuppy(monkeypatch, tmp_path):
+    """Setuptools should be resilient to setup.py with ``sys.exit(0)`` (#3973)."""
+    monkeypatch.chdir(tmp_path)
+    setuppy = """
+        import sys, setuptools
+        setuptools.setup(name='foo', version='0.0.0')
+        sys.exit(0)
+        """
+    (tmp_path / "setup.py").write_text(DALS(setuppy), encoding="utf-8")
+    backend = BuildBackend(backend_name="setuptools.build_meta")
+    assert backend.get_requires_for_build_wheel() == []
+
+
+def test_system_exit_in_setuppy(monkeypatch, tmp_path):
+    monkeypatch.chdir(tmp_path)
+    setuppy = "import sys; sys.exit('some error')"
+    (tmp_path / "setup.py").write_text(setuppy, encoding="utf-8")
+    with pytest.raises(SystemExit, match="some error"):
+        backend = BuildBackend(backend_name="setuptools.build_meta")
+        backend.get_requires_for_build_wheel()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_py.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..1e3a660833933717310de66978771c4e48b5b914
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_build_py.py
@@ -0,0 +1,480 @@
+import os
+import shutil
+import stat
+import warnings
+from pathlib import Path
+from unittest.mock import Mock
+
+import jaraco.path
+import pytest
+
+from setuptools import SetuptoolsDeprecationWarning
+from setuptools.dist import Distribution
+
+from .textwrap import DALS
+
+
+def test_directories_in_package_data_glob(tmpdir_cwd):
+    """
+    Directories matching the glob in package_data should
+    not be included in the package data.
+
+    Regression test for #261.
+    """
+    dist = Distribution(
+        dict(
+            script_name='setup.py',
+            script_args=['build_py'],
+            packages=[''],
+            package_data={'': ['path/*']},
+        )
+    )
+    os.makedirs('path/subpath')
+    dist.parse_command_line()
+    dist.run_commands()
+
+
+def test_recursive_in_package_data_glob(tmpdir_cwd):
+    """
+    Files matching recursive globs (**) in package_data should
+    be included in the package data.
+
+    #1806
+    """
+    dist = Distribution(
+        dict(
+            script_name='setup.py',
+            script_args=['build_py'],
+            packages=[''],
+            package_data={'': ['path/**/data']},
+        )
+    )
+    os.makedirs('path/subpath/subsubpath')
+    open('path/subpath/subsubpath/data', 'wb').close()
+
+    dist.parse_command_line()
+    dist.run_commands()
+
+    assert stat.S_ISREG(os.stat('build/lib/path/subpath/subsubpath/data').st_mode), (
+        "File is not included"
+    )
+
+
+def test_read_only(tmpdir_cwd):
+    """
+    Ensure read-only flag is not preserved in copy
+    for package modules and package data, as that
+    causes problems with deleting read-only files on
+    Windows.
+
+    #1451
+    """
+    dist = Distribution(
+        dict(
+            script_name='setup.py',
+            script_args=['build_py'],
+            packages=['pkg'],
+            package_data={'pkg': ['data.dat']},
+        )
+    )
+    os.makedirs('pkg')
+    open('pkg/__init__.py', 'wb').close()
+    open('pkg/data.dat', 'wb').close()
+    os.chmod('pkg/__init__.py', stat.S_IREAD)
+    os.chmod('pkg/data.dat', stat.S_IREAD)
+    dist.parse_command_line()
+    dist.run_commands()
+    shutil.rmtree('build')
+
+
+@pytest.mark.xfail(
+    'platform.system() == "Windows"',
+    reason="On Windows, files do not have executable bits",
+    raises=AssertionError,
+    strict=True,
+)
+def test_executable_data(tmpdir_cwd):
+    """
+    Ensure executable bit is preserved in copy for
+    package data, as users rely on it for scripts.
+
+    #2041
+    """
+    dist = Distribution(
+        dict(
+            script_name='setup.py',
+            script_args=['build_py'],
+            packages=['pkg'],
+            package_data={'pkg': ['run-me']},
+        )
+    )
+    os.makedirs('pkg')
+    open('pkg/__init__.py', 'wb').close()
+    open('pkg/run-me', 'wb').close()
+    os.chmod('pkg/run-me', 0o700)
+
+    dist.parse_command_line()
+    dist.run_commands()
+
+    assert os.stat('build/lib/pkg/run-me').st_mode & stat.S_IEXEC, (
+        "Script is not executable"
+    )
+
+
+EXAMPLE_WITH_MANIFEST = {
+    "setup.cfg": DALS(
+        """
+        [metadata]
+        name = mypkg
+        version = 42
+
+        [options]
+        include_package_data = True
+        packages = find:
+
+        [options.packages.find]
+        exclude = *.tests*
+        """
+    ),
+    "mypkg": {
+        "__init__.py": "",
+        "resource_file.txt": "",
+        "tests": {
+            "__init__.py": "",
+            "test_mypkg.py": "",
+            "test_file.txt": "",
+        },
+    },
+    "MANIFEST.in": DALS(
+        """
+        global-include *.py *.txt
+        global-exclude *.py[cod]
+        prune dist
+        prune build
+        prune *.egg-info
+        """
+    ),
+}
+
+
+def test_excluded_subpackages(tmpdir_cwd):
+    jaraco.path.build(EXAMPLE_WITH_MANIFEST)
+    dist = Distribution({"script_name": "%PEP 517%"})
+    dist.parse_config_files()
+
+    build_py = dist.get_command_obj("build_py")
+
+    msg = r"Python recognizes 'mypkg\.tests' as an importable package"
+    with pytest.warns(SetuptoolsDeprecationWarning, match=msg):
+        # TODO: To fix #3260 we need some transition period to deprecate the
+        # existing behavior of `include_package_data`. After the transition, we
+        # should remove the warning and fix the behavior.
+
+        if os.getenv("SETUPTOOLS_USE_DISTUTILS") == "stdlib":
+            # pytest.warns reset the warning filter temporarily
+            # https://github.com/pytest-dev/pytest/issues/4011#issuecomment-423494810
+            warnings.filterwarnings(
+                "ignore",
+                "'encoding' argument not specified",
+                module="distutils.text_file",
+                # This warning is already fixed in pypa/distutils but not in stdlib
+            )
+
+        build_py.finalize_options()
+        build_py.run()
+
+    build_dir = Path(dist.get_command_obj("build_py").build_lib)
+    assert (build_dir / "mypkg/__init__.py").exists()
+    assert (build_dir / "mypkg/resource_file.txt").exists()
+
+    # Setuptools is configured to ignore `mypkg.tests`, therefore the following
+    # files/dirs should not be included in the distribution.
+    for f in [
+        "mypkg/tests/__init__.py",
+        "mypkg/tests/test_mypkg.py",
+        "mypkg/tests/test_file.txt",
+        "mypkg/tests",
+    ]:
+        with pytest.raises(AssertionError):
+            # TODO: Enforce the following assertion once #3260 is fixed
+            # (remove context manager and the following xfail).
+            assert not (build_dir / f).exists()
+
+    pytest.xfail("#3260")
+
+
+@pytest.mark.filterwarnings("ignore::setuptools.SetuptoolsDeprecationWarning")
+def test_existing_egg_info(tmpdir_cwd, monkeypatch):
+    """When provided with the ``existing_egg_info_dir`` attribute, build_py should not
+    attempt to run egg_info again.
+    """
+    # == Pre-condition ==
+    # Generate an egg-info dir
+    jaraco.path.build(EXAMPLE_WITH_MANIFEST)
+    dist = Distribution({"script_name": "%PEP 517%"})
+    dist.parse_config_files()
+    assert dist.include_package_data
+
+    egg_info = dist.get_command_obj("egg_info")
+    dist.run_command("egg_info")
+    egg_info_dir = next(Path(egg_info.egg_base).glob("*.egg-info"))
+    assert egg_info_dir.is_dir()
+
+    # == Setup ==
+    build_py = dist.get_command_obj("build_py")
+    build_py.finalize_options()
+    egg_info = dist.get_command_obj("egg_info")
+    egg_info_run = Mock(side_effect=egg_info.run)
+    monkeypatch.setattr(egg_info, "run", egg_info_run)
+
+    # == Remove caches ==
+    # egg_info is called when build_py looks for data_files, which gets cached.
+    # We need to ensure it is not cached yet, otherwise it may impact on the tests
+    build_py.__dict__.pop('data_files', None)
+    dist.reinitialize_command(egg_info)
+
+    # == Sanity check ==
+    # Ensure that if existing_egg_info is not given, build_py attempts to run egg_info
+    build_py.existing_egg_info_dir = None
+    build_py.run()
+    egg_info_run.assert_called()
+
+    # == Remove caches ==
+    egg_info_run.reset_mock()
+    build_py.__dict__.pop('data_files', None)
+    dist.reinitialize_command(egg_info)
+
+    # == Actual test ==
+    # Ensure that if existing_egg_info_dir is given, egg_info doesn't run
+    build_py.existing_egg_info_dir = egg_info_dir
+    build_py.run()
+    egg_info_run.assert_not_called()
+    assert build_py.data_files
+
+    # Make sure the list of outputs is actually OK
+    outputs = map(lambda x: x.replace(os.sep, "/"), build_py.get_outputs())
+    assert outputs
+    example = str(Path(build_py.build_lib, "mypkg/__init__.py")).replace(os.sep, "/")
+    assert example in outputs
+
+
+EXAMPLE_ARBITRARY_MAPPING = {
+    "pyproject.toml": DALS(
+        """
+        [project]
+        name = "mypkg"
+        version = "42"
+
+        [tool.setuptools]
+        packages = ["mypkg", "mypkg.sub1", "mypkg.sub2", "mypkg.sub2.nested"]
+
+        [tool.setuptools.package-dir]
+        "" = "src"
+        "mypkg.sub2" = "src/mypkg/_sub2"
+        "mypkg.sub2.nested" = "other"
+        """
+    ),
+    "src": {
+        "mypkg": {
+            "__init__.py": "",
+            "resource_file.txt": "",
+            "sub1": {
+                "__init__.py": "",
+                "mod1.py": "",
+            },
+            "_sub2": {
+                "mod2.py": "",
+            },
+        },
+    },
+    "other": {
+        "__init__.py": "",
+        "mod3.py": "",
+    },
+    "MANIFEST.in": DALS(
+        """
+        global-include *.py *.txt
+        global-exclude *.py[cod]
+        """
+    ),
+}
+
+
+def test_get_outputs(tmpdir_cwd):
+    jaraco.path.build(EXAMPLE_ARBITRARY_MAPPING)
+    dist = Distribution({"script_name": "%test%"})
+    dist.parse_config_files()
+
+    build_py = dist.get_command_obj("build_py")
+    build_py.editable_mode = True
+    build_py.ensure_finalized()
+    build_lib = build_py.build_lib.replace(os.sep, "/")
+    outputs = {x.replace(os.sep, "/") for x in build_py.get_outputs()}
+    assert outputs == {
+        f"{build_lib}/mypkg/__init__.py",
+        f"{build_lib}/mypkg/resource_file.txt",
+        f"{build_lib}/mypkg/sub1/__init__.py",
+        f"{build_lib}/mypkg/sub1/mod1.py",
+        f"{build_lib}/mypkg/sub2/mod2.py",
+        f"{build_lib}/mypkg/sub2/nested/__init__.py",
+        f"{build_lib}/mypkg/sub2/nested/mod3.py",
+    }
+    mapping = {
+        k.replace(os.sep, "/"): v.replace(os.sep, "/")
+        for k, v in build_py.get_output_mapping().items()
+    }
+    assert mapping == {
+        f"{build_lib}/mypkg/__init__.py": "src/mypkg/__init__.py",
+        f"{build_lib}/mypkg/resource_file.txt": "src/mypkg/resource_file.txt",
+        f"{build_lib}/mypkg/sub1/__init__.py": "src/mypkg/sub1/__init__.py",
+        f"{build_lib}/mypkg/sub1/mod1.py": "src/mypkg/sub1/mod1.py",
+        f"{build_lib}/mypkg/sub2/mod2.py": "src/mypkg/_sub2/mod2.py",
+        f"{build_lib}/mypkg/sub2/nested/__init__.py": "other/__init__.py",
+        f"{build_lib}/mypkg/sub2/nested/mod3.py": "other/mod3.py",
+    }
+
+
+class TestTypeInfoFiles:
+    PYPROJECTS = {
+        "default_pyproject": DALS(
+            """
+            [project]
+            name = "foo"
+            version = "1"
+            """
+        ),
+        "dont_include_package_data": DALS(
+            """
+            [project]
+            name = "foo"
+            version = "1"
+
+            [tool.setuptools]
+            include-package-data = false
+            """
+        ),
+        "exclude_type_info": DALS(
+            """
+            [project]
+            name = "foo"
+            version = "1"
+
+            [tool.setuptools]
+            include-package-data = false
+
+            [tool.setuptools.exclude-package-data]
+            "*" = ["py.typed", "*.pyi"]
+            """
+        ),
+    }
+
+    EXAMPLES = {
+        "simple_namespace": {
+            "directory_structure": {
+                "foo": {
+                    "bar.pyi": "",
+                    "py.typed": "",
+                    "__init__.py": "",
+                }
+            },
+            "expected_type_files": {"foo/bar.pyi", "foo/py.typed"},
+        },
+        "nested_inside_namespace": {
+            "directory_structure": {
+                "foo": {
+                    "bar": {
+                        "py.typed": "",
+                        "mod.pyi": "",
+                    }
+                }
+            },
+            "expected_type_files": {"foo/bar/mod.pyi", "foo/bar/py.typed"},
+        },
+        "namespace_nested_inside_regular": {
+            "directory_structure": {
+                "foo": {
+                    "namespace": {
+                        "foo.pyi": "",
+                    },
+                    "__init__.pyi": "",
+                    "py.typed": "",
+                }
+            },
+            "expected_type_files": {
+                "foo/namespace/foo.pyi",
+                "foo/__init__.pyi",
+                "foo/py.typed",
+            },
+        },
+    }
+
+    @pytest.mark.parametrize(
+        "pyproject",
+        [
+            "default_pyproject",
+            pytest.param(
+                "dont_include_package_data",
+                marks=pytest.mark.xfail(reason="pypa/setuptools#4350"),
+            ),
+        ],
+    )
+    @pytest.mark.parametrize("example", EXAMPLES.keys())
+    def test_type_files_included_by_default(self, tmpdir_cwd, pyproject, example):
+        structure = {
+            **self.EXAMPLES[example]["directory_structure"],
+            "pyproject.toml": self.PYPROJECTS[pyproject],
+        }
+        expected_type_files = self.EXAMPLES[example]["expected_type_files"]
+        jaraco.path.build(structure)
+
+        build_py = get_finalized_build_py()
+        outputs = get_outputs(build_py)
+        assert expected_type_files <= outputs
+
+    @pytest.mark.parametrize("pyproject", ["exclude_type_info"])
+    @pytest.mark.parametrize("example", EXAMPLES.keys())
+    def test_type_files_can_be_excluded(self, tmpdir_cwd, pyproject, example):
+        structure = {
+            **self.EXAMPLES[example]["directory_structure"],
+            "pyproject.toml": self.PYPROJECTS[pyproject],
+        }
+        expected_type_files = self.EXAMPLES[example]["expected_type_files"]
+        jaraco.path.build(structure)
+
+        build_py = get_finalized_build_py()
+        outputs = get_outputs(build_py)
+        assert expected_type_files.isdisjoint(outputs)
+
+    def test_stub_only_package(self, tmpdir_cwd):
+        structure = {
+            "pyproject.toml": DALS(
+                """
+                [project]
+                name = "foo-stubs"
+                version = "1"
+                """
+            ),
+            "foo-stubs": {"__init__.pyi": "", "bar.pyi": ""},
+        }
+        expected_type_files = {"foo-stubs/__init__.pyi", "foo-stubs/bar.pyi"}
+        jaraco.path.build(structure)
+
+        build_py = get_finalized_build_py()
+        outputs = get_outputs(build_py)
+        assert expected_type_files <= outputs
+
+
+def get_finalized_build_py(script_name="%build_py-test%"):
+    dist = Distribution({"script_name": script_name})
+    dist.parse_config_files()
+    build_py = dist.get_command_obj("build_py")
+    build_py.finalize_options()
+    return build_py
+
+
+def get_outputs(build_py):
+    build_dir = Path(build_py.build_lib)
+    return {
+        os.path.relpath(x, build_dir).replace(os.sep, "/")
+        for x in build_py.get_outputs()
+    }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_config_discovery.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_config_discovery.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5df8203cdb6f9129a65d0c503c4f51e21315b1f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_config_discovery.py
@@ -0,0 +1,647 @@
+import os
+import sys
+from configparser import ConfigParser
+from itertools import product
+from typing import cast
+
+import jaraco.path
+import pytest
+from path import Path
+
+import setuptools  # noqa: F401 # force distutils.core to be patched
+from setuptools.command.sdist import sdist
+from setuptools.discovery import find_package_path, find_parent_package
+from setuptools.dist import Distribution
+from setuptools.errors import PackageDiscoveryError
+
+from .contexts import quiet
+from .integration.helpers import get_sdist_members, get_wheel_members, run
+from .textwrap import DALS
+
+import distutils.core
+
+
+class TestFindParentPackage:
+    def test_single_package(self, tmp_path):
+        # find_parent_package should find a non-namespace parent package
+        (tmp_path / "src/namespace/pkg/nested").mkdir(exist_ok=True, parents=True)
+        (tmp_path / "src/namespace/pkg/nested/__init__.py").touch()
+        (tmp_path / "src/namespace/pkg/__init__.py").touch()
+        packages = ["namespace", "namespace.pkg", "namespace.pkg.nested"]
+        assert find_parent_package(packages, {"": "src"}, tmp_path) == "namespace.pkg"
+
+    def test_multiple_toplevel(self, tmp_path):
+        # find_parent_package should return null if the given list of packages does not
+        # have a single parent package
+        multiple = ["pkg", "pkg1", "pkg2"]
+        for name in multiple:
+            (tmp_path / f"src/{name}").mkdir(exist_ok=True, parents=True)
+            (tmp_path / f"src/{name}/__init__.py").touch()
+        assert find_parent_package(multiple, {"": "src"}, tmp_path) is None
+
+
+class TestDiscoverPackagesAndPyModules:
+    """Make sure discovered values for ``packages`` and ``py_modules`` work
+    similarly to explicit configuration for the simple scenarios.
+    """
+
+    OPTIONS = {
+        # Different options according to the circumstance being tested
+        "explicit-src": {"package_dir": {"": "src"}, "packages": ["pkg"]},
+        "variation-lib": {
+            "package_dir": {"": "lib"},  # variation of the source-layout
+        },
+        "explicit-flat": {"packages": ["pkg"]},
+        "explicit-single_module": {"py_modules": ["pkg"]},
+        "explicit-namespace": {"packages": ["ns", "ns.pkg"]},
+        "automatic-src": {},
+        "automatic-flat": {},
+        "automatic-single_module": {},
+        "automatic-namespace": {},
+    }
+    FILES = {
+        "src": ["src/pkg/__init__.py", "src/pkg/main.py"],
+        "lib": ["lib/pkg/__init__.py", "lib/pkg/main.py"],
+        "flat": ["pkg/__init__.py", "pkg/main.py"],
+        "single_module": ["pkg.py"],
+        "namespace": ["ns/pkg/__init__.py"],
+    }
+
+    def _get_info(self, circumstance):
+        _, _, layout = circumstance.partition("-")
+        files = self.FILES[layout]
+        options = self.OPTIONS[circumstance]
+        return files, options
+
+    @pytest.mark.parametrize("circumstance", OPTIONS.keys())
+    def test_sdist_filelist(self, tmp_path, circumstance):
+        files, options = self._get_info(circumstance)
+        _populate_project_dir(tmp_path, files, options)
+
+        _, cmd = _run_sdist_programatically(tmp_path, options)
+
+        manifest = [f.replace(os.sep, "/") for f in cmd.filelist.files]
+        for file in files:
+            assert any(f.endswith(file) for f in manifest)
+
+    @pytest.mark.parametrize("circumstance", OPTIONS.keys())
+    def test_project(self, tmp_path, circumstance):
+        files, options = self._get_info(circumstance)
+        _populate_project_dir(tmp_path, files, options)
+
+        # Simulate a pre-existing `build` directory
+        (tmp_path / "build").mkdir()
+        (tmp_path / "build/lib").mkdir()
+        (tmp_path / "build/bdist.linux-x86_64").mkdir()
+        (tmp_path / "build/bdist.linux-x86_64/file.py").touch()
+        (tmp_path / "build/lib/__init__.py").touch()
+        (tmp_path / "build/lib/file.py").touch()
+        (tmp_path / "dist").mkdir()
+        (tmp_path / "dist/file.py").touch()
+
+        _run_build(tmp_path)
+
+        sdist_files = get_sdist_members(next(tmp_path.glob("dist/*.tar.gz")))
+        print("~~~~~ sdist_members ~~~~~")
+        print('\n'.join(sdist_files))
+        assert sdist_files >= set(files)
+
+        wheel_files = get_wheel_members(next(tmp_path.glob("dist/*.whl")))
+        print("~~~~~ wheel_members ~~~~~")
+        print('\n'.join(wheel_files))
+        orig_files = {f.replace("src/", "").replace("lib/", "") for f in files}
+        assert wheel_files >= orig_files
+
+        # Make sure build files are not included by mistake
+        for file in wheel_files:
+            assert "build" not in files
+            assert "dist" not in files
+
+    PURPOSEFULLY_EMPY = {
+        "setup.cfg": DALS(
+            """
+            [metadata]
+            name = myproj
+            version = 0.0.0
+
+            [options]
+            {param} =
+            """
+        ),
+        "setup.py": DALS(
+            """
+            __import__('setuptools').setup(
+                name="myproj",
+                version="0.0.0",
+                {param}=[]
+            )
+            """
+        ),
+        "pyproject.toml": DALS(
+            """
+            [build-system]
+            requires = []
+            build-backend = 'setuptools.build_meta'
+
+            [project]
+            name = "myproj"
+            version = "0.0.0"
+
+            [tool.setuptools]
+            {param} = []
+            """
+        ),
+        "template-pyproject.toml": DALS(
+            """
+            [build-system]
+            requires = []
+            build-backend = 'setuptools.build_meta'
+            """
+        ),
+    }
+
+    @pytest.mark.parametrize(
+        ("config_file", "param", "circumstance"),
+        product(
+            ["setup.cfg", "setup.py", "pyproject.toml"],
+            ["packages", "py_modules"],
+            FILES.keys(),
+        ),
+    )
+    def test_purposefully_empty(self, tmp_path, config_file, param, circumstance):
+        files = self.FILES[circumstance] + ["mod.py", "other.py", "src/pkg/__init__.py"]
+        _populate_project_dir(tmp_path, files, {})
+
+        if config_file == "pyproject.toml":
+            template_param = param.replace("_", "-")
+        else:
+            # Make sure build works with or without setup.cfg
+            pyproject = self.PURPOSEFULLY_EMPY["template-pyproject.toml"]
+            (tmp_path / "pyproject.toml").write_text(pyproject, encoding="utf-8")
+            template_param = param
+
+        config = self.PURPOSEFULLY_EMPY[config_file].format(param=template_param)
+        (tmp_path / config_file).write_text(config, encoding="utf-8")
+
+        dist = _get_dist(tmp_path, {})
+        # When either parameter package or py_modules is an empty list,
+        # then there should be no discovery
+        assert getattr(dist, param) == []
+        other = {"py_modules": "packages", "packages": "py_modules"}[param]
+        assert getattr(dist, other) is None
+
+    @pytest.mark.parametrize(
+        ("extra_files", "pkgs"),
+        [
+            (["venv/bin/simulate_venv"], {"pkg"}),
+            (["pkg-stubs/__init__.pyi"], {"pkg", "pkg-stubs"}),
+            (["other-stubs/__init__.pyi"], {"pkg", "other-stubs"}),
+            (
+                # Type stubs can also be namespaced
+                ["namespace-stubs/pkg/__init__.pyi"],
+                {"pkg", "namespace-stubs", "namespace-stubs.pkg"},
+            ),
+            (
+                # Just the top-level package can have `-stubs`, ignore nested ones
+                ["namespace-stubs/pkg-stubs/__init__.pyi"],
+                {"pkg", "namespace-stubs"},
+            ),
+            (["_hidden/file.py"], {"pkg"}),
+            (["news/finalize.py"], {"pkg"}),
+        ],
+    )
+    def test_flat_layout_with_extra_files(self, tmp_path, extra_files, pkgs):
+        files = self.FILES["flat"] + extra_files
+        _populate_project_dir(tmp_path, files, {})
+        dist = _get_dist(tmp_path, {})
+        assert set(dist.packages) == pkgs
+
+    @pytest.mark.parametrize(
+        "extra_files",
+        [
+            ["other/__init__.py"],
+            ["other/finalize.py"],
+        ],
+    )
+    def test_flat_layout_with_dangerous_extra_files(self, tmp_path, extra_files):
+        files = self.FILES["flat"] + extra_files
+        _populate_project_dir(tmp_path, files, {})
+        with pytest.raises(PackageDiscoveryError, match="multiple (packages|modules)"):
+            _get_dist(tmp_path, {})
+
+    def test_flat_layout_with_single_module(self, tmp_path):
+        files = self.FILES["single_module"] + ["invalid-module-name.py"]
+        _populate_project_dir(tmp_path, files, {})
+        dist = _get_dist(tmp_path, {})
+        assert set(dist.py_modules) == {"pkg"}
+
+    def test_flat_layout_with_multiple_modules(self, tmp_path):
+        files = self.FILES["single_module"] + ["valid_module_name.py"]
+        _populate_project_dir(tmp_path, files, {})
+        with pytest.raises(PackageDiscoveryError, match="multiple (packages|modules)"):
+            _get_dist(tmp_path, {})
+
+    def test_py_modules_when_wheel_dir_is_cwd(self, tmp_path):
+        """Regression for issue 3692"""
+        from setuptools import build_meta
+
+        pyproject = '[project]\nname = "test"\nversion = "1"'
+        (tmp_path / "pyproject.toml").write_text(DALS(pyproject), encoding="utf-8")
+        (tmp_path / "foo.py").touch()
+        with jaraco.path.DirectoryStack().context(tmp_path):
+            build_meta.build_wheel(".")
+        # Ensure py_modules are found
+        wheel_files = get_wheel_members(next(tmp_path.glob("*.whl")))
+        assert "foo.py" in wheel_files
+
+
+class TestNoConfig:
+    DEFAULT_VERSION = "0.0.0"  # Default version given by setuptools
+
+    EXAMPLES = {
+        "pkg1": ["src/pkg1.py"],
+        "pkg2": ["src/pkg2/__init__.py"],
+        "pkg3": ["src/pkg3/__init__.py", "src/pkg3-stubs/__init__.py"],
+        "pkg4": ["pkg4/__init__.py", "pkg4-stubs/__init__.py"],
+        "ns.nested.pkg1": ["src/ns/nested/pkg1/__init__.py"],
+        "ns.nested.pkg2": ["ns/nested/pkg2/__init__.py"],
+    }
+
+    @pytest.mark.parametrize("example", EXAMPLES.keys())
+    def test_discover_name(self, tmp_path, example):
+        _populate_project_dir(tmp_path, self.EXAMPLES[example], {})
+        dist = _get_dist(tmp_path, {})
+        assert dist.get_name() == example
+
+    def test_build_with_discovered_name(self, tmp_path):
+        files = ["src/ns/nested/pkg/__init__.py"]
+        _populate_project_dir(tmp_path, files, {})
+        _run_build(tmp_path, "--sdist")
+        # Expected distribution file
+        dist_file = tmp_path / f"dist/ns_nested_pkg-{self.DEFAULT_VERSION}.tar.gz"
+        assert dist_file.is_file()
+
+
+class TestWithAttrDirective:
+    @pytest.mark.parametrize(
+        ("folder", "opts"),
+        [
+            ("src", {}),
+            ("lib", {"packages": "find:", "packages.find": {"where": "lib"}}),
+        ],
+    )
+    def test_setupcfg_metadata(self, tmp_path, folder, opts):
+        files = [f"{folder}/pkg/__init__.py", "setup.cfg"]
+        _populate_project_dir(tmp_path, files, opts)
+
+        config = (tmp_path / "setup.cfg").read_text(encoding="utf-8")
+        overwrite = {
+            folder: {"pkg": {"__init__.py": "version = 42"}},
+            "setup.cfg": "[metadata]\nversion = attr: pkg.version\n" + config,
+        }
+        jaraco.path.build(overwrite, prefix=tmp_path)
+
+        dist = _get_dist(tmp_path, {})
+        assert dist.get_name() == "pkg"
+        assert dist.get_version() == "42"
+        assert dist.package_dir
+        package_path = find_package_path("pkg", dist.package_dir, tmp_path)
+        assert os.path.exists(package_path)
+        assert folder in Path(package_path).parts()
+
+        _run_build(tmp_path, "--sdist")
+        dist_file = tmp_path / "dist/pkg-42.tar.gz"
+        assert dist_file.is_file()
+
+    def test_pyproject_metadata(self, tmp_path):
+        _populate_project_dir(tmp_path, ["src/pkg/__init__.py"], {})
+
+        overwrite = {
+            "src": {"pkg": {"__init__.py": "version = 42"}},
+            "pyproject.toml": (
+                "[project]\nname = 'pkg'\ndynamic = ['version']\n"
+                "[tool.setuptools.dynamic]\nversion = {attr = 'pkg.version'}\n"
+            ),
+        }
+        jaraco.path.build(overwrite, prefix=tmp_path)
+
+        dist = _get_dist(tmp_path, {})
+        assert dist.get_version() == "42"
+        assert dist.package_dir == {"": "src"}
+
+
+class TestWithCExtension:
+    def _simulate_package_with_extension(self, tmp_path):
+        # This example is based on: https://github.com/nucleic/kiwi/tree/1.4.0
+        files = [
+            "benchmarks/file.py",
+            "docs/Makefile",
+            "docs/requirements.txt",
+            "docs/source/conf.py",
+            "proj/header.h",
+            "proj/file.py",
+            "py/proj.cpp",
+            "py/other.cpp",
+            "py/file.py",
+            "py/py.typed",
+            "py/tests/test_proj.py",
+            "README.rst",
+        ]
+        _populate_project_dir(tmp_path, files, {})
+
+        setup_script = """
+            from setuptools import Extension, setup
+
+            ext_modules = [
+                Extension(
+                    "proj",
+                    ["py/proj.cpp", "py/other.cpp"],
+                    include_dirs=["."],
+                    language="c++",
+                ),
+            ]
+            setup(ext_modules=ext_modules)
+        """
+        (tmp_path / "setup.py").write_text(DALS(setup_script), encoding="utf-8")
+
+    def test_skip_discovery_with_setupcfg_metadata(self, tmp_path):
+        """Ensure that auto-discovery is not triggered when the project is based on
+        C-extensions only, for backward compatibility.
+        """
+        self._simulate_package_with_extension(tmp_path)
+
+        pyproject = """
+            [build-system]
+            requires = []
+            build-backend = 'setuptools.build_meta'
+        """
+        (tmp_path / "pyproject.toml").write_text(DALS(pyproject), encoding="utf-8")
+
+        setupcfg = """
+            [metadata]
+            name = proj
+            version = 42
+        """
+        (tmp_path / "setup.cfg").write_text(DALS(setupcfg), encoding="utf-8")
+
+        dist = _get_dist(tmp_path, {})
+        assert dist.get_name() == "proj"
+        assert dist.get_version() == "42"
+        assert dist.py_modules is None
+        assert dist.packages is None
+        assert len(dist.ext_modules) == 1
+        assert dist.ext_modules[0].name == "proj"
+
+    def test_dont_skip_discovery_with_pyproject_metadata(self, tmp_path):
+        """When opting-in to pyproject.toml metadata, auto-discovery will be active if
+        the package lists C-extensions, but does not configure py-modules or packages.
+
+        This way we ensure users with complex package layouts that would lead to the
+        discovery of multiple top-level modules/packages see errors and are forced to
+        explicitly set ``packages`` or ``py-modules``.
+        """
+        self._simulate_package_with_extension(tmp_path)
+
+        pyproject = """
+            [project]
+            name = 'proj'
+            version = '42'
+        """
+        (tmp_path / "pyproject.toml").write_text(DALS(pyproject), encoding="utf-8")
+        with pytest.raises(PackageDiscoveryError, match="multiple (packages|modules)"):
+            _get_dist(tmp_path, {})
+
+
+class TestWithPackageData:
+    def _simulate_package_with_data_files(self, tmp_path, src_root):
+        files = [
+            f"{src_root}/proj/__init__.py",
+            f"{src_root}/proj/file1.txt",
+            f"{src_root}/proj/nested/file2.txt",
+        ]
+        _populate_project_dir(tmp_path, files, {})
+
+        manifest = """
+            global-include *.py *.txt
+        """
+        (tmp_path / "MANIFEST.in").write_text(DALS(manifest), encoding="utf-8")
+
+    EXAMPLE_SETUPCFG = """
+    [metadata]
+    name = proj
+    version = 42
+
+    [options]
+    include_package_data = True
+    """
+    EXAMPLE_PYPROJECT = """
+    [project]
+    name = "proj"
+    version = "42"
+    """
+
+    PYPROJECT_PACKAGE_DIR = """
+    [tool.setuptools]
+    package-dir = {"" = "src"}
+    """
+
+    @pytest.mark.parametrize(
+        ("src_root", "files"),
+        [
+            (".", {"setup.cfg": DALS(EXAMPLE_SETUPCFG)}),
+            (".", {"pyproject.toml": DALS(EXAMPLE_PYPROJECT)}),
+            ("src", {"setup.cfg": DALS(EXAMPLE_SETUPCFG)}),
+            ("src", {"pyproject.toml": DALS(EXAMPLE_PYPROJECT)}),
+            (
+                "src",
+                {
+                    "setup.cfg": DALS(EXAMPLE_SETUPCFG)
+                    + DALS(
+                        """
+                        packages = find:
+                        package_dir =
+                            =src
+
+                        [options.packages.find]
+                        where = src
+                        """
+                    )
+                },
+            ),
+            (
+                "src",
+                {
+                    "pyproject.toml": DALS(EXAMPLE_PYPROJECT)
+                    + DALS(
+                        """
+                        [tool.setuptools]
+                        package-dir = {"" = "src"}
+                        """
+                    )
+                },
+            ),
+        ],
+    )
+    def test_include_package_data(self, tmp_path, src_root, files):
+        """
+        Make sure auto-discovery does not affect package include_package_data.
+        See issue #3196.
+        """
+        jaraco.path.build(files, prefix=str(tmp_path))
+        self._simulate_package_with_data_files(tmp_path, src_root)
+
+        expected = {
+            os.path.normpath(f"{src_root}/proj/file1.txt").replace(os.sep, "/"),
+            os.path.normpath(f"{src_root}/proj/nested/file2.txt").replace(os.sep, "/"),
+        }
+
+        _run_build(tmp_path)
+
+        sdist_files = get_sdist_members(next(tmp_path.glob("dist/*.tar.gz")))
+        print("~~~~~ sdist_members ~~~~~")
+        print('\n'.join(sdist_files))
+        assert sdist_files >= expected
+
+        wheel_files = get_wheel_members(next(tmp_path.glob("dist/*.whl")))
+        print("~~~~~ wheel_members ~~~~~")
+        print('\n'.join(wheel_files))
+        orig_files = {f.replace("src/", "").replace("lib/", "") for f in expected}
+        assert wheel_files >= orig_files
+
+
+def test_compatible_with_numpy_configuration(tmp_path):
+    files = [
+        "dir1/__init__.py",
+        "dir2/__init__.py",
+        "file.py",
+    ]
+    _populate_project_dir(tmp_path, files, {})
+    dist = Distribution({})
+    dist.configuration = object()
+    dist.set_defaults()
+    assert dist.py_modules is None
+    assert dist.packages is None
+
+
+def test_name_discovery_doesnt_break_cli(tmpdir_cwd):
+    jaraco.path.build({"pkg.py": ""})
+    dist = Distribution({})
+    dist.script_args = ["--name"]
+    dist.set_defaults()
+    dist.parse_command_line()  # <-- no exception should be raised here.
+    assert dist.get_name() == "pkg"
+
+
+def test_preserve_explicit_name_with_dynamic_version(tmpdir_cwd, monkeypatch):
+    """According to #3545 it seems that ``name`` discovery is running,
+    even when the project already explicitly sets it.
+    This seems to be related to parsing of dynamic versions (via ``attr`` directive),
+    which requires the auto-discovery of ``package_dir``.
+    """
+    files = {
+        "src": {
+            "pkg": {"__init__.py": "__version__ = 42\n"},
+        },
+        "pyproject.toml": DALS(
+            """
+            [project]
+            name = "myproj"  # purposefully different from package name
+            dynamic = ["version"]
+            [tool.setuptools.dynamic]
+            version = {"attr" = "pkg.__version__"}
+            """
+        ),
+    }
+    jaraco.path.build(files)
+    dist = Distribution({})
+    orig_analyse_name = dist.set_defaults.analyse_name
+
+    def spy_analyse_name():
+        # We can check if name discovery was triggered by ensuring the original
+        # name remains instead of the package name.
+        orig_analyse_name()
+        assert dist.get_name() == "myproj"
+
+    monkeypatch.setattr(dist.set_defaults, "analyse_name", spy_analyse_name)
+    dist.parse_config_files()
+    assert dist.get_version() == "42"
+    assert set(dist.packages) == {"pkg"}
+
+
+def _populate_project_dir(root, files, options):
+    # NOTE: Currently pypa/build will refuse to build the project if no
+    # `pyproject.toml` or `setup.py` is found. So it is impossible to do
+    # completely "config-less" projects.
+    basic = {
+        "setup.py": "import setuptools\nsetuptools.setup()",
+        "README.md": "# Example Package",
+        "LICENSE": "Copyright (c) 2018",
+    }
+    jaraco.path.build(basic, prefix=root)
+    _write_setupcfg(root, options)
+    paths = (root / f for f in files)
+    for path in paths:
+        path.parent.mkdir(exist_ok=True, parents=True)
+        path.touch()
+
+
+def _write_setupcfg(root, options):
+    if not options:
+        print("~~~~~ **NO** setup.cfg ~~~~~")
+        return
+    setupcfg = ConfigParser()
+    setupcfg.add_section("options")
+    for key, value in options.items():
+        if key == "packages.find":
+            setupcfg.add_section(f"options.{key}")
+            setupcfg[f"options.{key}"].update(value)
+        elif isinstance(value, list):
+            setupcfg["options"][key] = ", ".join(value)
+        elif isinstance(value, dict):
+            str_value = "\n".join(f"\t{k} = {v}" for k, v in value.items())
+            setupcfg["options"][key] = "\n" + str_value
+        else:
+            setupcfg["options"][key] = str(value)
+    with open(root / "setup.cfg", "w", encoding="utf-8") as f:
+        setupcfg.write(f)
+    print("~~~~~ setup.cfg ~~~~~")
+    print((root / "setup.cfg").read_text(encoding="utf-8"))
+
+
+def _run_build(path, *flags):
+    cmd = [sys.executable, "-m", "build", "--no-isolation", *flags, str(path)]
+    return run(cmd, env={'DISTUTILS_DEBUG': ''})
+
+
+def _get_dist(dist_path, attrs):
+    root = "/".join(os.path.split(dist_path))  # POSIX-style
+
+    script = dist_path / 'setup.py'
+    if script.exists():
+        with Path(dist_path):
+            dist = cast(
+                Distribution,
+                distutils.core.run_setup("setup.py", {}, stop_after="init"),
+            )
+    else:
+        dist = Distribution(attrs)
+
+    dist.src_root = root
+    dist.script_name = "setup.py"
+    with Path(dist_path):
+        dist.parse_config_files()
+
+    dist.set_defaults()
+    return dist
+
+
+def _run_sdist_programatically(dist_path, attrs):
+    dist = _get_dist(dist_path, attrs)
+    cmd = sdist(dist)
+    cmd.ensure_finalized()
+    assert cmd.distribution.packages or cmd.distribution.py_modules
+
+    with quiet(), Path(dist_path):
+        cmd.run()
+
+    return dist, cmd
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_core_metadata.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_core_metadata.py
new file mode 100644
index 0000000000000000000000000000000000000000..0d925111fa6e611ae919df8bb30bcda0f248c5b6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_core_metadata.py
@@ -0,0 +1,622 @@
+from __future__ import annotations
+
+import functools
+import importlib
+import io
+from email import message_from_string
+from email.generator import Generator
+from email.message import EmailMessage, Message
+from email.parser import Parser
+from email.policy import EmailPolicy
+from inspect import cleandoc
+from pathlib import Path
+from unittest.mock import Mock
+
+import jaraco.path
+import pytest
+from packaging.metadata import Metadata
+from packaging.requirements import Requirement
+
+from setuptools import _reqs, sic
+from setuptools._core_metadata import rfc822_escape, rfc822_unescape
+from setuptools.command.egg_info import egg_info, write_requirements
+from setuptools.config import expand, setupcfg
+from setuptools.dist import Distribution
+
+from .config.downloads import retrieve_file, urls_from_file
+
+EXAMPLE_BASE_INFO = dict(
+    name="package",
+    version="0.0.1",
+    author="Foo Bar",
+    author_email="foo@bar.net",
+    long_description="Long\ndescription",
+    description="Short description",
+    keywords=["one", "two"],
+)
+
+
+@pytest.mark.parametrize(
+    ("content", "result"),
+    (
+        pytest.param(
+            "Just a single line",
+            None,
+            id="single_line",
+        ),
+        pytest.param(
+            "Multiline\nText\nwithout\nextra indents\n",
+            None,
+            id="multiline",
+        ),
+        pytest.param(
+            "Multiline\n    With\n\nadditional\n  indentation",
+            None,
+            id="multiline_with_indentation",
+        ),
+        pytest.param(
+            "  Leading whitespace",
+            "Leading whitespace",
+            id="remove_leading_whitespace",
+        ),
+        pytest.param(
+            "  Leading whitespace\nIn\n    Multiline comment",
+            "Leading whitespace\nIn\n    Multiline comment",
+            id="remove_leading_whitespace_multiline",
+        ),
+    ),
+)
+def test_rfc822_unescape(content, result):
+    assert (result or content) == rfc822_unescape(rfc822_escape(content))
+
+
+def __read_test_cases():
+    base = EXAMPLE_BASE_INFO
+
+    params = functools.partial(dict, base)
+
+    return [
+        ('Metadata version 1.0', params()),
+        (
+            'Metadata Version 1.0: Short long description',
+            params(
+                long_description='Short long description',
+            ),
+        ),
+        (
+            'Metadata version 1.1: Classifiers',
+            params(
+                classifiers=[
+                    'Programming Language :: Python :: 3',
+                    'Programming Language :: Python :: 3.7',
+                    'License :: OSI Approved :: MIT License',
+                ],
+            ),
+        ),
+        (
+            'Metadata version 1.1: Download URL',
+            params(
+                download_url='https://example.com',
+            ),
+        ),
+        (
+            'Metadata Version 1.2: Requires-Python',
+            params(
+                python_requires='>=3.7',
+            ),
+        ),
+        pytest.param(
+            'Metadata Version 1.2: Project-Url',
+            params(project_urls=dict(Foo='https://example.bar')),
+            marks=pytest.mark.xfail(
+                reason="Issue #1578: project_urls not read",
+            ),
+        ),
+        (
+            'Metadata Version 2.1: Long Description Content Type',
+            params(
+                long_description_content_type='text/x-rst; charset=UTF-8',
+            ),
+        ),
+        (
+            'License',
+            params(
+                license='MIT',
+            ),
+        ),
+        (
+            'License multiline',
+            params(
+                license='This is a long license \nover multiple lines',
+            ),
+        ),
+        pytest.param(
+            'Metadata Version 2.1: Provides Extra',
+            params(provides_extras=['foo', 'bar']),
+            marks=pytest.mark.xfail(reason="provides_extras not read"),
+        ),
+        (
+            'Missing author',
+            dict(
+                name='foo',
+                version='1.0.0',
+                author_email='snorri@sturluson.name',
+            ),
+        ),
+        (
+            'Missing author e-mail',
+            dict(
+                name='foo',
+                version='1.0.0',
+                author='Snorri Sturluson',
+            ),
+        ),
+        (
+            'Missing author and e-mail',
+            dict(
+                name='foo',
+                version='1.0.0',
+            ),
+        ),
+        (
+            'Bypass normalized version',
+            dict(
+                name='foo',
+                version=sic('1.0.0a'),
+            ),
+        ),
+    ]
+
+
+@pytest.mark.parametrize(("name", "attrs"), __read_test_cases())
+def test_read_metadata(name, attrs):
+    dist = Distribution(attrs)
+    metadata_out = dist.metadata
+    dist_class = metadata_out.__class__
+
+    # Write to PKG_INFO and then load into a new metadata object
+    PKG_INFO = io.StringIO()
+
+    metadata_out.write_pkg_file(PKG_INFO)
+    PKG_INFO.seek(0)
+    pkg_info = PKG_INFO.read()
+    assert _valid_metadata(pkg_info)
+
+    PKG_INFO.seek(0)
+    metadata_in = dist_class()
+    metadata_in.read_pkg_file(PKG_INFO)
+
+    tested_attrs = [
+        ('name', dist_class.get_name),
+        ('version', dist_class.get_version),
+        ('author', dist_class.get_contact),
+        ('author_email', dist_class.get_contact_email),
+        ('metadata_version', dist_class.get_metadata_version),
+        ('provides', dist_class.get_provides),
+        ('description', dist_class.get_description),
+        ('long_description', dist_class.get_long_description),
+        ('download_url', dist_class.get_download_url),
+        ('keywords', dist_class.get_keywords),
+        ('platforms', dist_class.get_platforms),
+        ('obsoletes', dist_class.get_obsoletes),
+        ('requires', dist_class.get_requires),
+        ('classifiers', dist_class.get_classifiers),
+        ('project_urls', lambda s: getattr(s, 'project_urls', {})),
+        ('provides_extras', lambda s: getattr(s, 'provides_extras', {})),
+    ]
+
+    for attr, getter in tested_attrs:
+        assert getter(metadata_in) == getter(metadata_out)
+
+
+def __maintainer_test_cases():
+    attrs = {"name": "package", "version": "1.0", "description": "xxx"}
+
+    def merge_dicts(d1, d2):
+        d1 = d1.copy()
+        d1.update(d2)
+
+        return d1
+
+    return [
+        ('No author, no maintainer', attrs.copy()),
+        (
+            'Author (no e-mail), no maintainer',
+            merge_dicts(attrs, {'author': 'Author Name'}),
+        ),
+        (
+            'Author (e-mail), no maintainer',
+            merge_dicts(
+                attrs, {'author': 'Author Name', 'author_email': 'author@name.com'}
+            ),
+        ),
+        (
+            'No author, maintainer (no e-mail)',
+            merge_dicts(attrs, {'maintainer': 'Maintainer Name'}),
+        ),
+        (
+            'No author, maintainer (e-mail)',
+            merge_dicts(
+                attrs,
+                {
+                    'maintainer': 'Maintainer Name',
+                    'maintainer_email': 'maintainer@name.com',
+                },
+            ),
+        ),
+        (
+            'Author (no e-mail), Maintainer (no-email)',
+            merge_dicts(
+                attrs, {'author': 'Author Name', 'maintainer': 'Maintainer Name'}
+            ),
+        ),
+        (
+            'Author (e-mail), Maintainer (e-mail)',
+            merge_dicts(
+                attrs,
+                {
+                    'author': 'Author Name',
+                    'author_email': 'author@name.com',
+                    'maintainer': 'Maintainer Name',
+                    'maintainer_email': 'maintainer@name.com',
+                },
+            ),
+        ),
+        (
+            'No author (e-mail), no maintainer (e-mail)',
+            merge_dicts(
+                attrs,
+                {
+                    'author_email': 'author@name.com',
+                    'maintainer_email': 'maintainer@name.com',
+                },
+            ),
+        ),
+        ('Author unicode', merge_dicts(attrs, {'author': '鉄沢寛'})),
+        ('Maintainer unicode', merge_dicts(attrs, {'maintainer': 'Jan Łukasiewicz'})),
+    ]
+
+
+@pytest.mark.parametrize(("name", "attrs"), __maintainer_test_cases())
+def test_maintainer_author(name, attrs, tmpdir):
+    tested_keys = {
+        'author': 'Author',
+        'author_email': 'Author-email',
+        'maintainer': 'Maintainer',
+        'maintainer_email': 'Maintainer-email',
+    }
+
+    # Generate a PKG-INFO file
+    dist = Distribution(attrs)
+    fn = tmpdir.mkdir('pkg_info')
+    fn_s = str(fn)
+
+    dist.metadata.write_pkg_info(fn_s)
+
+    with open(str(fn.join('PKG-INFO')), 'r', encoding='utf-8') as f:
+        pkg_info = f.read()
+
+    assert _valid_metadata(pkg_info)
+
+    # Drop blank lines and strip lines from default description
+    raw_pkg_lines = pkg_info.splitlines()
+    pkg_lines = list(filter(None, raw_pkg_lines[:-2]))
+
+    pkg_lines_set = set(pkg_lines)
+
+    # Duplicate lines should not be generated
+    assert len(pkg_lines) == len(pkg_lines_set)
+
+    for fkey, dkey in tested_keys.items():
+        val = attrs.get(dkey, None)
+        if val is None:
+            for line in pkg_lines:
+                assert not line.startswith(fkey + ':')
+        else:
+            line = f'{fkey}: {val}'
+            assert line in pkg_lines_set
+
+
+class TestParityWithMetadataFromPyPaWheel:
+    def base_example(self):
+        attrs = dict(
+            **EXAMPLE_BASE_INFO,
+            # Example with complex requirement definition
+            python_requires=">=3.8",
+            install_requires="""
+            packaging==23.2
+            more-itertools==8.8.0; extra == "other"
+            jaraco.text==3.7.0
+            importlib-resources==5.10.2; python_version<"3.8"
+            importlib-metadata==6.0.0 ; python_version<"3.8"
+            colorama>=0.4.4; sys_platform == "win32"
+            """,
+            extras_require={
+                "testing": """
+                    pytest >= 6
+                    pytest-checkdocs >= 2.4
+                    tomli ; \\
+                            # Using stdlib when possible
+                            python_version < "3.11"
+                    ini2toml[lite]>=0.9
+                    """,
+                "other": [],
+            },
+        )
+        # Generate a PKG-INFO file using setuptools
+        return Distribution(attrs)
+
+    def test_requires_dist(self, tmp_path):
+        dist = self.base_example()
+        pkg_info = _get_pkginfo(dist)
+        assert _valid_metadata(pkg_info)
+
+        # Ensure Requires-Dist is present
+        expected = [
+            'Metadata-Version:',
+            'Requires-Python: >=3.8',
+            'Provides-Extra: other',
+            'Provides-Extra: testing',
+            'Requires-Dist: tomli; python_version < "3.11" and extra == "testing"',
+            'Requires-Dist: more-itertools==8.8.0; extra == "other"',
+            'Requires-Dist: ini2toml[lite]>=0.9; extra == "testing"',
+        ]
+        for line in expected:
+            assert line in pkg_info
+
+    HERE = Path(__file__).parent
+    EXAMPLES_FILE = HERE / "config/setupcfg_examples.txt"
+
+    @pytest.fixture(params=[None, *urls_from_file(EXAMPLES_FILE)])
+    def dist(self, request, monkeypatch, tmp_path):
+        """Example of distribution with arbitrary configuration"""
+        monkeypatch.chdir(tmp_path)
+        monkeypatch.setattr(expand, "read_attr", Mock(return_value="0.42"))
+        monkeypatch.setattr(expand, "read_files", Mock(return_value="hello world"))
+        monkeypatch.setattr(
+            Distribution, "_finalize_license_files", Mock(return_value=None)
+        )
+        if request.param is None:
+            yield self.base_example()
+        else:
+            # Real-world usage
+            config = retrieve_file(request.param)
+            yield setupcfg.apply_configuration(Distribution({}), config)
+
+    @pytest.mark.uses_network
+    def test_equivalent_output(self, tmp_path, dist):
+        """Ensure output from setuptools is equivalent to the one from `pypa/wheel`"""
+        # Generate a METADATA file using pypa/wheel for comparison
+        wheel_metadata = importlib.import_module("wheel.metadata")
+        pkginfo_to_metadata = getattr(wheel_metadata, "pkginfo_to_metadata", None)
+
+        if pkginfo_to_metadata is None:  # pragma: nocover
+            pytest.xfail(
+                "wheel.metadata.pkginfo_to_metadata is undefined, "
+                "(this is likely to be caused by API changes in pypa/wheel"
+            )
+
+        # Generate an simplified "egg-info" dir for pypa/wheel to convert
+        pkg_info = _get_pkginfo(dist)
+        egg_info_dir = tmp_path / "pkg.egg-info"
+        egg_info_dir.mkdir(parents=True)
+        (egg_info_dir / "PKG-INFO").write_text(pkg_info, encoding="utf-8")
+        write_requirements(egg_info(dist), egg_info_dir, egg_info_dir / "requires.txt")
+
+        # Get pypa/wheel generated METADATA but normalize requirements formatting
+        metadata_msg = pkginfo_to_metadata(egg_info_dir, egg_info_dir / "PKG-INFO")
+        metadata_str = _normalize_metadata(metadata_msg)
+        pkg_info_msg = message_from_string(pkg_info)
+        pkg_info_str = _normalize_metadata(pkg_info_msg)
+
+        # Compare setuptools PKG-INFO x pypa/wheel METADATA
+        assert metadata_str == pkg_info_str
+
+        # Make sure it parses/serializes well in pypa/wheel
+        _assert_roundtrip_message(pkg_info)
+
+
+class TestPEP643:
+    STATIC_CONFIG = {
+        "setup.cfg": cleandoc(
+            """
+            [metadata]
+            name = package
+            version = 0.0.1
+            author = Foo Bar
+            author_email = foo@bar.net
+            long_description = Long
+                               description
+            description = Short description
+            keywords = one, two
+            platforms = abcd
+            [options]
+            install_requires = requests
+            """
+        ),
+        "pyproject.toml": cleandoc(
+            """
+            [project]
+            name = "package"
+            version = "0.0.1"
+            authors = [
+              {name = "Foo Bar", email = "foo@bar.net"}
+            ]
+            description = "Short description"
+            readme = {text = "Long\\ndescription", content-type = "text/plain"}
+            keywords = ["one", "two"]
+            dependencies = ["requests"]
+            license = "AGPL-3.0-or-later"
+            [tool.setuptools]
+            provides = ["abcd"]
+            obsoletes = ["abcd"]
+            """
+        ),
+    }
+
+    @pytest.mark.parametrize("file", STATIC_CONFIG.keys())
+    def test_static_config_has_no_dynamic(self, file, tmpdir_cwd):
+        Path(file).write_text(self.STATIC_CONFIG[file], encoding="utf-8")
+        metadata = _get_metadata()
+        assert metadata.get_all("Dynamic") is None
+        assert metadata.get_all("dynamic") is None
+
+    @pytest.mark.parametrize("file", STATIC_CONFIG.keys())
+    @pytest.mark.parametrize(
+        "fields",
+        [
+            # Single dynamic field
+            {"requires-python": ("python_requires", ">=3.12")},
+            {"author-email": ("author_email", "snoopy@peanuts.com")},
+            {"keywords": ("keywords", ["hello", "world"])},
+            {"platform": ("platforms", ["abcd"])},
+            # Multiple dynamic fields
+            {
+                "summary": ("description", "hello world"),
+                "description": ("long_description", "bla bla bla bla"),
+                "requires-dist": ("install_requires", ["hello-world"]),
+            },
+        ],
+    )
+    def test_modified_fields_marked_as_dynamic(self, file, fields, tmpdir_cwd):
+        # We start with a static config
+        Path(file).write_text(self.STATIC_CONFIG[file], encoding="utf-8")
+        dist = _makedist()
+
+        # ... but then we simulate the effects of a plugin modifying the distribution
+        for attr, value in fields.values():
+            # `dist` and `dist.metadata` are complicated...
+            # Some attributes work when set on `dist`, others on `dist.metadata`...
+            # Here we set in both just in case (this also avoids calling `_finalize_*`)
+            setattr(dist, attr, value)
+            setattr(dist.metadata, attr, value)
+
+        # Then we should be able to list the modified fields as Dynamic
+        metadata = _get_metadata(dist)
+        assert set(metadata.get_all("Dynamic")) == set(fields)
+
+    @pytest.mark.parametrize(
+        "extra_toml",
+        [
+            "# Let setuptools autofill license-files",
+            "license-files = ['LICENSE*', 'AUTHORS*', 'NOTICE']",
+        ],
+    )
+    def test_license_files_dynamic(self, extra_toml, tmpdir_cwd):
+        # For simplicity (and for the time being) setuptools is not making
+        # any special handling to guarantee `License-File` is considered static.
+        # Instead we rely in the fact that, although suboptimal, it is OK to have
+        # it as dynamics, as per:
+        # https://github.com/pypa/setuptools/issues/4629#issuecomment-2331233677
+        files = {
+            "pyproject.toml": self.STATIC_CONFIG["pyproject.toml"].replace(
+                'license = "AGPL-3.0-or-later"',
+                f"dynamic = ['license']\n{extra_toml}",
+            ),
+            "LICENSE.md": "--- mock license ---",
+            "NOTICE": "--- mock notice ---",
+            "AUTHORS.txt": "--- me ---",
+        }
+        # Sanity checks:
+        assert extra_toml in files["pyproject.toml"]
+        assert 'license = "AGPL-3.0-or-later"' not in extra_toml
+
+        jaraco.path.build(files)
+        dist = _makedist(license_expression="AGPL-3.0-or-later")
+        metadata = _get_metadata(dist)
+        assert set(metadata.get_all("Dynamic")) == {
+            'license-file',
+            'license-expression',
+        }
+        assert metadata.get("License-Expression") == "AGPL-3.0-or-later"
+        assert set(metadata.get_all("License-File")) == {
+            "NOTICE",
+            "AUTHORS.txt",
+            "LICENSE.md",
+        }
+
+
+def _makedist(**attrs):
+    dist = Distribution(attrs)
+    dist.parse_config_files()
+    return dist
+
+
+def _assert_roundtrip_message(metadata: str) -> None:
+    """Emulate the way wheel.bdist_wheel parses and regenerates the message,
+    then ensures the metadata generated by setuptools is compatible.
+    """
+    with io.StringIO(metadata) as buffer:
+        msg = Parser(EmailMessage).parse(buffer)
+
+    serialization_policy = EmailPolicy(
+        utf8=True,
+        mangle_from_=False,
+        max_line_length=0,
+    )
+    with io.BytesIO() as buffer:
+        out = io.TextIOWrapper(buffer, encoding="utf-8")
+        Generator(out, policy=serialization_policy).flatten(msg)
+        out.flush()
+        regenerated = buffer.getvalue()
+
+    raw_metadata = bytes(metadata, "utf-8")
+    # Normalise newlines to avoid test errors on Windows:
+    raw_metadata = b"\n".join(raw_metadata.splitlines())
+    regenerated = b"\n".join(regenerated.splitlines())
+    assert regenerated == raw_metadata
+
+
+def _normalize_metadata(msg: Message) -> str:
+    """Allow equivalent metadata to be compared directly"""
+    # The main challenge regards the requirements and extras.
+    # Both setuptools and wheel already apply some level of normalization
+    # but they differ regarding which character is chosen, according to the
+    # following spec it should be "-":
+    # https://packaging.python.org/en/latest/specifications/name-normalization/
+
+    # Related issues:
+    # https://github.com/pypa/packaging/issues/845
+    # https://github.com/pypa/packaging/issues/644#issuecomment-2429813968
+
+    extras = {x.replace("_", "-"): x for x in msg.get_all("Provides-Extra", [])}
+    reqs = [
+        _normalize_req(req, extras)
+        for req in _reqs.parse(msg.get_all("Requires-Dist", []))
+    ]
+    del msg["Requires-Dist"]
+    del msg["Provides-Extra"]
+
+    # Ensure consistent ord
+    for req in sorted(reqs):
+        msg["Requires-Dist"] = req
+    for extra in sorted(extras):
+        msg["Provides-Extra"] = extra
+
+    # TODO: Handle lack of PEP 643 implementation in pypa/wheel?
+    del msg["Metadata-Version"]
+
+    return msg.as_string()
+
+
+def _normalize_req(req: Requirement, extras: dict[str, str]) -> str:
+    """Allow equivalent requirement objects to be compared directly"""
+    as_str = str(req).replace(req.name, req.name.replace("_", "-"))
+    for norm, orig in extras.items():
+        as_str = as_str.replace(orig, norm)
+    return as_str
+
+
+def _get_pkginfo(dist: Distribution):
+    with io.StringIO() as fp:
+        dist.metadata.write_pkg_file(fp)
+        return fp.getvalue()
+
+
+def _get_metadata(dist: Distribution | None = None):
+    return message_from_string(_get_pkginfo(dist or _makedist()))
+
+
+def _valid_metadata(text: str) -> bool:
+    metadata = Metadata.from_email(text, validate=True)  # can raise exceptions
+    return metadata is not None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_depends.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_depends.py
new file mode 100644
index 0000000000000000000000000000000000000000..1714c041f7a23e1ecbfc3245bf964f75c13734ca
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_depends.py
@@ -0,0 +1,15 @@
+import sys
+
+from setuptools import depends
+
+
+class TestGetModuleConstant:
+    def test_basic(self):
+        """
+        Invoke get_module_constant on a module in
+        the test package.
+        """
+        mod_name = 'setuptools.tests.mod_with_constant'
+        val = depends.get_module_constant(mod_name, 'value')
+        assert val == 'three, sir!'
+        assert 'setuptools.tests.mod_with_constant' not in sys.modules
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_develop.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_develop.py
new file mode 100644
index 0000000000000000000000000000000000000000..929fa9c285eb4d11e646dab2864be6d5fa023e2b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_develop.py
@@ -0,0 +1,175 @@
+"""develop tests"""
+
+import os
+import pathlib
+import platform
+import subprocess
+import sys
+
+import pytest
+
+from setuptools._path import paths_on_pythonpath
+from setuptools.command.develop import develop
+from setuptools.dist import Distribution
+
+from . import contexts, namespaces
+
+SETUP_PY = """\
+from setuptools import setup
+
+setup(name='foo',
+    packages=['foo'],
+)
+"""
+
+INIT_PY = """print "foo"
+"""
+
+
+@pytest.fixture
+def temp_user(monkeypatch):
+    with contexts.tempdir() as user_base:
+        with contexts.tempdir() as user_site:
+            monkeypatch.setattr('site.USER_BASE', user_base)
+            monkeypatch.setattr('site.USER_SITE', user_site)
+            yield
+
+
+@pytest.fixture
+def test_env(tmpdir, temp_user):
+    target = tmpdir
+    foo = target.mkdir('foo')
+    setup = target / 'setup.py'
+    if setup.isfile():
+        raise ValueError(dir(target))
+    with setup.open('w') as f:
+        f.write(SETUP_PY)
+    init = foo / '__init__.py'
+    with init.open('w') as f:
+        f.write(INIT_PY)
+    with target.as_cwd():
+        yield target
+
+
+class TestDevelop:
+    in_virtualenv = hasattr(sys, 'real_prefix')
+    in_venv = hasattr(sys, 'base_prefix') and sys.base_prefix != sys.prefix
+
+    def test_console_scripts(self, tmpdir):
+        """
+        Test that console scripts are installed and that they reference
+        only the project by name and not the current version.
+        """
+        pytest.skip(
+            "TODO: needs a fixture to cause 'develop' "
+            "to be invoked without mutating environment."
+        )
+        settings = dict(
+            name='foo',
+            packages=['foo'],
+            version='0.0',
+            entry_points={
+                'console_scripts': [
+                    'foocmd = foo:foo',
+                ],
+            },
+        )
+        dist = Distribution(settings)
+        dist.script_name = 'setup.py'
+        cmd = develop(dist)
+        cmd.ensure_finalized()
+        cmd.install_dir = tmpdir
+        cmd.run()
+        # assert '0.0' not in foocmd_text
+
+    @pytest.mark.xfail(reason="legacy behavior retained for compatibility #4167")
+    def test_egg_link_filename(self):
+        settings = dict(
+            name='Foo $$$ Bar_baz-bing',
+        )
+        dist = Distribution(settings)
+        cmd = develop(dist)
+        cmd.ensure_finalized()
+        link = pathlib.Path(cmd.egg_link)
+        assert link.suffix == '.egg-link'
+        assert link.stem == 'Foo_Bar_baz_bing'
+
+
+class TestResolver:
+    """
+    TODO: These tests were written with a minimal understanding
+    of what _resolve_setup_path is intending to do. Come up with
+    more meaningful cases that look like real-world scenarios.
+    """
+
+    def test_resolve_setup_path_cwd(self):
+        assert develop._resolve_setup_path('.', '.', '.') == '.'
+
+    def test_resolve_setup_path_one_dir(self):
+        assert develop._resolve_setup_path('pkgs', '.', 'pkgs') == '../'
+
+    def test_resolve_setup_path_one_dir_trailing_slash(self):
+        assert develop._resolve_setup_path('pkgs/', '.', 'pkgs') == '../'
+
+
+class TestNamespaces:
+    @staticmethod
+    def install_develop(src_dir, target):
+        develop_cmd = [
+            sys.executable,
+            'setup.py',
+            'develop',
+            '--install-dir',
+            str(target),
+        ]
+        with src_dir.as_cwd():
+            with paths_on_pythonpath([str(target)]):
+                subprocess.check_call(develop_cmd)
+
+    @pytest.mark.skipif(
+        bool(os.environ.get("APPVEYOR")),
+        reason="https://github.com/pypa/setuptools/issues/851",
+    )
+    @pytest.mark.skipif(
+        platform.python_implementation() == 'PyPy',
+        reason="https://github.com/pypa/setuptools/issues/1202",
+    )
+    def test_namespace_package_importable(self, tmpdir):
+        """
+        Installing two packages sharing the same namespace, one installed
+        naturally using pip or `--single-version-externally-managed`
+        and the other installed using `develop` should leave the namespace
+        in tact and both packages reachable by import.
+        """
+        pkg_A = namespaces.build_namespace_package(tmpdir, 'myns.pkgA')
+        pkg_B = namespaces.build_namespace_package(tmpdir, 'myns.pkgB')
+        target = tmpdir / 'packages'
+        # use pip to install to the target directory
+        install_cmd = [
+            sys.executable,
+            '-m',
+            'pip',
+            'install',
+            str(pkg_A),
+            '-t',
+            str(target),
+        ]
+        subprocess.check_call(install_cmd)
+        self.install_develop(pkg_B, target)
+        namespaces.make_site_dir(target)
+        try_import = [
+            sys.executable,
+            '-c',
+            'import myns.pkgA; import myns.pkgB',
+        ]
+        with paths_on_pythonpath([str(target)]):
+            subprocess.check_call(try_import)
+
+        # additionally ensure that pkg_resources import works
+        pkg_resources_imp = [
+            sys.executable,
+            '-c',
+            'import pkg_resources',
+        ]
+        with paths_on_pythonpath([str(target)]):
+            subprocess.check_call(pkg_resources_imp)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_dist.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_dist.py
new file mode 100644
index 0000000000000000000000000000000000000000..e65ab310e7f2ad98b591affb352c855a2f86eda1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_dist.py
@@ -0,0 +1,278 @@
+import os
+import re
+import urllib.parse
+import urllib.request
+
+import pytest
+
+from setuptools import Distribution
+from setuptools.dist import check_package_data, check_specifier
+
+from .test_easy_install import make_trivial_sdist
+from .test_find_packages import ensure_files
+from .textwrap import DALS
+
+from distutils.errors import DistutilsSetupError
+
+
+def test_dist_fetch_build_egg(tmpdir):
+    """
+    Check multiple calls to `Distribution.fetch_build_egg` work as expected.
+    """
+    index = tmpdir.mkdir('index')
+    index_url = urllib.parse.urljoin('file://', urllib.request.pathname2url(str(index)))
+
+    def sdist_with_index(distname, version):
+        dist_dir = index.mkdir(distname)
+        dist_sdist = f'{distname}-{version}.tar.gz'
+        make_trivial_sdist(str(dist_dir.join(dist_sdist)), distname, version)
+        with dist_dir.join('index.html').open('w') as fp:
+            fp.write(
+                DALS(
+                    """
+                
+                {dist_sdist}

+                
+                """
+                ).format(dist_sdist=dist_sdist)
+            )
+
+    sdist_with_index('barbazquux', '3.2.0')
+    sdist_with_index('barbazquux-runner', '2.11.1')
+    with tmpdir.join('setup.cfg').open('w') as fp:
+        fp.write(
+            DALS(
+                """
+            [easy_install]
+            index_url = {index_url}
+            """
+            ).format(index_url=index_url)
+        )
+    reqs = """
+    barbazquux-runner
+    barbazquux
+    """.split()
+    with tmpdir.as_cwd():
+        dist = Distribution()
+        dist.parse_config_files()
+        resolved_dists = [dist.fetch_build_egg(r) for r in reqs]
+    assert [dist.key for dist in resolved_dists if dist] == reqs
+
+
+EXAMPLE_BASE_INFO = dict(
+    name="package",
+    version="0.0.1",
+    author="Foo Bar",
+    author_email="foo@bar.net",
+    long_description="Long\ndescription",
+    description="Short description",
+    keywords=["one", "two"],
+)
+
+
+def test_provides_extras_deterministic_order():
+    attrs = dict(extras_require=dict(a=['foo'], b=['bar']))
+    dist = Distribution(attrs)
+    assert list(dist.metadata.provides_extras) == ['a', 'b']
+    attrs['extras_require'] = dict(reversed(attrs['extras_require'].items()))
+    dist = Distribution(attrs)
+    assert list(dist.metadata.provides_extras) == ['b', 'a']
+
+
+CHECK_PACKAGE_DATA_TESTS = (
+    # Valid.
+    (
+        {
+            '': ['*.txt', '*.rst'],
+            'hello': ['*.msg'],
+        },
+        None,
+    ),
+    # Not a dictionary.
+    (
+        (
+            ('', ['*.txt', '*.rst']),
+            ('hello', ['*.msg']),
+        ),
+        (
+            "'package_data' must be a dictionary mapping package"
+            " names to lists of string wildcard patterns"
+        ),
+    ),
+    # Invalid key type.
+    (
+        {
+            400: ['*.txt', '*.rst'],
+        },
+        ("keys of 'package_data' dict must be strings (got 400)"),
+    ),
+    # Invalid value type.
+    (
+        {
+            'hello': '*.msg',
+        },
+        (
+            "\"values of 'package_data' dict\" must be of type "
+            " (got '*.msg')"
+        ),
+    ),
+    # Invalid value type (generators are single use)
+    (
+        {
+            'hello': (x for x in "generator"),
+        },
+        (
+            "\"values of 'package_data' dict\" must be of type "
+            " (got =3.0, !=3.1'}
+    dist = Distribution(attrs)
+    check_specifier(dist, attrs, attrs['python_requires'])
+
+    attrs = {'name': 'foo', 'python_requires': ['>=3.0', '!=3.1']}
+    dist = Distribution(attrs)
+    check_specifier(dist, attrs, attrs['python_requires'])
+
+    # invalid specifier value
+    attrs = {'name': 'foo', 'python_requires': '>=invalid-version'}
+    with pytest.raises(DistutilsSetupError):
+        dist = Distribution(attrs)
+
+
+def test_metadata_name():
+    with pytest.raises(DistutilsSetupError, match='missing.*name'):
+        Distribution()._validate_metadata()
+
+
+@pytest.mark.parametrize(
+    ('dist_name', 'py_module'),
+    [
+        ("my.pkg", "my_pkg"),
+        ("my-pkg", "my_pkg"),
+        ("my_pkg", "my_pkg"),
+        ("pkg", "pkg"),
+    ],
+)
+def test_dist_default_py_modules(tmp_path, dist_name, py_module):
+    (tmp_path / f"{py_module}.py").touch()
+
+    (tmp_path / "setup.py").touch()
+    (tmp_path / "noxfile.py").touch()
+    # ^-- make sure common tool files are ignored
+
+    attrs = {**EXAMPLE_BASE_INFO, "name": dist_name, "src_root": str(tmp_path)}
+    # Find `py_modules` corresponding to dist_name if not given
+    dist = Distribution(attrs)
+    dist.set_defaults()
+    assert dist.py_modules == [py_module]
+    # When `py_modules` is given, don't do anything
+    dist = Distribution({**attrs, "py_modules": ["explicity_py_module"]})
+    dist.set_defaults()
+    assert dist.py_modules == ["explicity_py_module"]
+    # When `packages` is given, don't do anything
+    dist = Distribution({**attrs, "packages": ["explicity_package"]})
+    dist.set_defaults()
+    assert not dist.py_modules
+
+
+@pytest.mark.parametrize(
+    ('dist_name', 'package_dir', 'package_files', 'packages'),
+    [
+        ("my.pkg", None, ["my_pkg/__init__.py", "my_pkg/mod.py"], ["my_pkg"]),
+        ("my-pkg", None, ["my_pkg/__init__.py", "my_pkg/mod.py"], ["my_pkg"]),
+        ("my_pkg", None, ["my_pkg/__init__.py", "my_pkg/mod.py"], ["my_pkg"]),
+        ("my.pkg", None, ["my/pkg/__init__.py"], ["my", "my.pkg"]),
+        (
+            "my_pkg",
+            None,
+            ["src/my_pkg/__init__.py", "src/my_pkg2/__init__.py"],
+            ["my_pkg", "my_pkg2"],
+        ),
+        (
+            "my_pkg",
+            {"pkg": "lib", "pkg2": "lib2"},
+            ["lib/__init__.py", "lib/nested/__init__.pyt", "lib2/__init__.py"],
+            ["pkg", "pkg.nested", "pkg2"],
+        ),
+    ],
+)
+def test_dist_default_packages(
+    tmp_path, dist_name, package_dir, package_files, packages
+):
+    ensure_files(tmp_path, package_files)
+
+    (tmp_path / "setup.py").touch()
+    (tmp_path / "noxfile.py").touch()
+    # ^-- should not be included by default
+
+    attrs = {
+        **EXAMPLE_BASE_INFO,
+        "name": dist_name,
+        "src_root": str(tmp_path),
+        "package_dir": package_dir,
+    }
+    # Find `packages` either corresponding to dist_name or inside src
+    dist = Distribution(attrs)
+    dist.set_defaults()
+    assert not dist.py_modules
+    assert not dist.py_modules
+    assert set(dist.packages) == set(packages)
+    # When `py_modules` is given, don't do anything
+    dist = Distribution({**attrs, "py_modules": ["explicit_py_module"]})
+    dist.set_defaults()
+    assert not dist.packages
+    assert set(dist.py_modules) == {"explicit_py_module"}
+    # When `packages` is given, don't do anything
+    dist = Distribution({**attrs, "packages": ["explicit_package"]})
+    dist.set_defaults()
+    assert not dist.py_modules
+    assert set(dist.packages) == {"explicit_package"}
+
+
+@pytest.mark.parametrize(
+    ('dist_name', 'package_dir', 'package_files'),
+    [
+        ("my.pkg.nested", None, ["my/pkg/nested/__init__.py"]),
+        ("my.pkg", None, ["my/pkg/__init__.py", "my/pkg/file.py"]),
+        ("my_pkg", None, ["my_pkg.py"]),
+        ("my_pkg", None, ["my_pkg/__init__.py", "my_pkg/nested/__init__.py"]),
+        ("my_pkg", None, ["src/my_pkg/__init__.py", "src/my_pkg/nested/__init__.py"]),
+        (
+            "my_pkg",
+            {"my_pkg": "lib", "my_pkg.lib2": "lib2"},
+            ["lib/__init__.py", "lib/nested/__init__.pyt", "lib2/__init__.py"],
+        ),
+        # Should not try to guess a name from multiple py_modules/packages
+        ("UNKNOWN", None, ["src/mod1.py", "src/mod2.py"]),
+        ("UNKNOWN", None, ["src/pkg1/__ini__.py", "src/pkg2/__init__.py"]),
+    ],
+)
+def test_dist_default_name(tmp_path, dist_name, package_dir, package_files):
+    """Make sure dist.name is discovered from packages/py_modules"""
+    ensure_files(tmp_path, package_files)
+    attrs = {
+        **EXAMPLE_BASE_INFO,
+        "src_root": "/".join(os.path.split(tmp_path)),  # POSIX-style
+        "package_dir": package_dir,
+    }
+    del attrs["name"]
+
+    dist = Distribution(attrs)
+    dist.set_defaults()
+    assert dist.py_modules or dist.packages
+    assert dist.get_name() == dist_name
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_dist_info.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_dist_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..426694e0198fdbe6ee7466822bc7c15634e2b648
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_dist_info.py
@@ -0,0 +1,210 @@
+"""Test .dist-info style distributions."""
+
+import pathlib
+import re
+import shutil
+import subprocess
+import sys
+from functools import partial
+
+import pytest
+
+import pkg_resources
+from setuptools.archive_util import unpack_archive
+
+from .textwrap import DALS
+
+read = partial(pathlib.Path.read_text, encoding="utf-8")
+
+
+class TestDistInfo:
+    metadata_base = DALS(
+        """
+        Metadata-Version: 1.2
+        Requires-Dist: splort (==4)
+        Provides-Extra: baz
+        Requires-Dist: quux (>=1.1); extra == 'baz'
+        """
+    )
+
+    @classmethod
+    def build_metadata(cls, **kwargs):
+        lines = ('{key}: {value}\n'.format(**locals()) for key, value in kwargs.items())
+        return cls.metadata_base + ''.join(lines)
+
+    @pytest.fixture
+    def metadata(self, tmpdir):
+        dist_info_name = 'VersionedDistribution-2.718.dist-info'
+        versioned = tmpdir / dist_info_name
+        versioned.mkdir()
+        filename = versioned / 'METADATA'
+        content = self.build_metadata(
+            Name='VersionedDistribution',
+        )
+        filename.write_text(content, encoding='utf-8')
+
+        dist_info_name = 'UnversionedDistribution.dist-info'
+        unversioned = tmpdir / dist_info_name
+        unversioned.mkdir()
+        filename = unversioned / 'METADATA'
+        content = self.build_metadata(
+            Name='UnversionedDistribution',
+            Version='0.3',
+        )
+        filename.write_text(content, encoding='utf-8')
+
+        return str(tmpdir)
+
+    def test_distinfo(self, metadata):
+        dists = dict(
+            (d.project_name, d) for d in pkg_resources.find_distributions(metadata)
+        )
+
+        assert len(dists) == 2, dists
+
+        unversioned = dists['UnversionedDistribution']
+        versioned = dists['VersionedDistribution']
+
+        assert versioned.version == '2.718'  # from filename
+        assert unversioned.version == '0.3'  # from METADATA
+
+    def test_conditional_dependencies(self, metadata):
+        specs = 'splort==4', 'quux>=1.1'
+        requires = list(map(pkg_resources.Requirement.parse, specs))
+
+        for d in pkg_resources.find_distributions(metadata):
+            assert d.requires() == requires[:1]
+            assert d.requires(extras=('baz',)) == [
+                requires[0],
+                pkg_resources.Requirement.parse('quux>=1.1;extra=="baz"'),
+            ]
+            assert d.extras == ['baz']
+
+    def test_invalid_version(self, tmp_path):
+        """
+        Supplying an invalid version crashes dist_info.
+        """
+        config = "[metadata]\nname=proj\nversion=42\n[egg_info]\ntag_build=invalid!!!\n"
+        (tmp_path / "setup.cfg").write_text(config, encoding="utf-8")
+        msg = re.compile("invalid version", re.M | re.I)
+        proc = run_command_inner("dist_info", cwd=tmp_path, check=False)
+        assert proc.returncode
+        assert msg.search(proc.stdout)
+        assert not list(tmp_path.glob("*.dist-info"))
+
+    def test_tag_arguments(self, tmp_path):
+        config = """
+        [metadata]
+        name=proj
+        version=42
+        [egg_info]
+        tag_date=1
+        tag_build=.post
+        """
+        (tmp_path / "setup.cfg").write_text(config, encoding="utf-8")
+
+        print(run_command("dist_info", "--no-date", cwd=tmp_path))
+        dist_info = next(tmp_path.glob("*.dist-info"))
+        assert dist_info.name.startswith("proj-42")
+        shutil.rmtree(dist_info)
+
+        print(run_command("dist_info", "--tag-build", ".a", cwd=tmp_path))
+        dist_info = next(tmp_path.glob("*.dist-info"))
+        assert dist_info.name.startswith("proj-42a")
+
+    @pytest.mark.parametrize("keep_egg_info", (False, True))
+    def test_output_dir(self, tmp_path, keep_egg_info):
+        config = "[metadata]\nname=proj\nversion=42\n"
+        (tmp_path / "setup.cfg").write_text(config, encoding="utf-8")
+        out = tmp_path / "__out"
+        out.mkdir()
+        opts = ["--keep-egg-info"] if keep_egg_info else []
+        run_command("dist_info", "--output-dir", out, *opts, cwd=tmp_path)
+        assert len(list(out.glob("*.dist-info"))) == 1
+        assert len(list(tmp_path.glob("*.dist-info"))) == 0
+        expected_egg_info = int(keep_egg_info)
+        assert len(list(out.glob("*.egg-info"))) == expected_egg_info
+        assert len(list(tmp_path.glob("*.egg-info"))) == 0
+        assert len(list(out.glob("*.__bkp__"))) == 0
+        assert len(list(tmp_path.glob("*.__bkp__"))) == 0
+
+
+class TestWheelCompatibility:
+    """Make sure the .dist-info directory produced with the ``dist_info`` command
+    is the same as the one produced by ``bdist_wheel``.
+    """
+
+    SETUPCFG = DALS(
+        """
+    [metadata]
+    name = {name}
+    version = {version}
+
+    [options]
+    install_requires =
+        foo>=12; sys_platform != "linux"
+
+    [options.extras_require]
+    test = pytest
+
+    [options.entry_points]
+    console_scripts =
+        executable-name = my_package.module:function
+    discover =
+        myproj = my_package.other_module:function
+    """
+    )
+
+    EGG_INFO_OPTS = [
+        # Related: #3088 #2872
+        ("", ""),
+        (".post", "[egg_info]\ntag_build = post\n"),
+        (".post", "[egg_info]\ntag_build = .post\n"),
+        (".post", "[egg_info]\ntag_build = post\ntag_date = 1\n"),
+        (".dev", "[egg_info]\ntag_build = .dev\n"),
+        (".dev", "[egg_info]\ntag_build = .dev\ntag_date = 1\n"),
+        ("a1", "[egg_info]\ntag_build = .a1\n"),
+        ("+local", "[egg_info]\ntag_build = +local\n"),
+    ]
+
+    @pytest.mark.parametrize("name", "my-proj my_proj my.proj My.Proj".split())
+    @pytest.mark.parametrize("version", ["0.42.13"])
+    @pytest.mark.parametrize(("suffix", "cfg"), EGG_INFO_OPTS)
+    def test_dist_info_is_the_same_as_in_wheel(
+        self, name, version, tmp_path, suffix, cfg
+    ):
+        config = self.SETUPCFG.format(name=name, version=version) + cfg
+
+        for i in "dir_wheel", "dir_dist":
+            (tmp_path / i).mkdir()
+            (tmp_path / i / "setup.cfg").write_text(config, encoding="utf-8")
+
+        run_command("bdist_wheel", cwd=tmp_path / "dir_wheel")
+        wheel = next(tmp_path.glob("dir_wheel/dist/*.whl"))
+        unpack_archive(wheel, tmp_path / "unpack")
+        wheel_dist_info = next(tmp_path.glob("unpack/*.dist-info"))
+
+        run_command("dist_info", cwd=tmp_path / "dir_dist")
+        dist_info = next(tmp_path.glob("dir_dist/*.dist-info"))
+
+        assert dist_info.name == wheel_dist_info.name
+        assert dist_info.name.startswith(f"my_proj-{version}{suffix}")
+        for file in "METADATA", "entry_points.txt":
+            assert read(dist_info / file) == read(wheel_dist_info / file)
+
+
+def run_command_inner(*cmd, **kwargs):
+    opts = {
+        "stderr": subprocess.STDOUT,
+        "stdout": subprocess.PIPE,
+        "text": True,
+        "encoding": "utf-8",
+        "check": True,
+        **kwargs,
+    }
+    cmd = [sys.executable, "-c", "__import__('setuptools').setup()", *map(str, cmd)]
+    return subprocess.run(cmd, **opts)
+
+
+def run_command(*args, **kwargs):
+    return run_command_inner(*args, **kwargs).stdout
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_distutils_adoption.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_distutils_adoption.py
new file mode 100644
index 0000000000000000000000000000000000000000..f99a58849950029f53322c19cde1c171fe26622c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_distutils_adoption.py
@@ -0,0 +1,198 @@
+import os
+import platform
+import sys
+import textwrap
+
+import pytest
+
+IS_PYPY = '__pypy__' in sys.builtin_module_names
+
+_TEXT_KWARGS = {"text": True, "encoding": "utf-8"}  # For subprocess.run
+
+
+def win_sr(env):
+    """
+    On Windows, SYSTEMROOT must be present to avoid
+
+    > Fatal Python error: _Py_HashRandomization_Init: failed to
+    > get random numbers to initialize Python
+    """
+    if env and platform.system() == 'Windows':
+        env['SYSTEMROOT'] = os.environ['SYSTEMROOT']
+    return env
+
+
+def find_distutils(venv, imports='distutils', env=None, **kwargs):
+    py_cmd = 'import {imports}; print(distutils.__file__)'.format(**locals())
+    cmd = ['python', '-c', py_cmd]
+    return venv.run(cmd, env=win_sr(env), **_TEXT_KWARGS, **kwargs)
+
+
+def count_meta_path(venv, env=None):
+    py_cmd = textwrap.dedent(
+        """
+        import sys
+        is_distutils = lambda finder: finder.__class__.__name__ == "DistutilsMetaFinder"
+        print(len(list(filter(is_distutils, sys.meta_path))))
+        """
+    )
+    cmd = ['python', '-c', py_cmd]
+    return int(venv.run(cmd, env=win_sr(env), **_TEXT_KWARGS))
+
+
+skip_without_stdlib_distutils = pytest.mark.skipif(
+    sys.version_info >= (3, 12),
+    reason='stdlib distutils is removed from Python 3.12+',
+)
+
+
+@skip_without_stdlib_distutils
+def test_distutils_stdlib(venv):
+    """
+    Ensure stdlib distutils is used when appropriate.
+    """
+    env = dict(SETUPTOOLS_USE_DISTUTILS='stdlib')
+    assert venv.name not in find_distutils(venv, env=env).split(os.sep)
+    assert count_meta_path(venv, env=env) == 0
+
+
+def test_distutils_local_with_setuptools(venv):
+    """
+    Ensure local distutils is used when appropriate.
+    """
+    env = dict(SETUPTOOLS_USE_DISTUTILS='local')
+    loc = find_distutils(venv, imports='setuptools, distutils', env=env)
+    assert venv.name in loc.split(os.sep)
+    assert count_meta_path(venv, env=env) <= 1
+
+
+@pytest.mark.xfail('IS_PYPY', reason='pypy imports distutils on startup')
+def test_distutils_local(venv):
+    """
+    Even without importing, the setuptools-local copy of distutils is
+    preferred.
+    """
+    env = dict(SETUPTOOLS_USE_DISTUTILS='local')
+    assert venv.name in find_distutils(venv, env=env).split(os.sep)
+    assert count_meta_path(venv, env=env) <= 1
+
+
+def test_pip_import(venv):
+    """
+    Ensure pip can be imported.
+    Regression test for #3002.
+    """
+    cmd = ['python', '-c', 'import pip']
+    venv.run(cmd, **_TEXT_KWARGS)
+
+
+def test_distutils_has_origin():
+    """
+    Distutils module spec should have an origin. #2990.
+    """
+    assert __import__('distutils').__spec__.origin
+
+
+ENSURE_IMPORTS_ARE_NOT_DUPLICATED = r"""
+# Depending on the importlib machinery and _distutils_hack, some imports are
+# duplicated resulting in different module objects being loaded, which prevents
+# patches as shown in #3042.
+# This script provides a way of verifying if this duplication is happening.
+
+from distutils import cmd
+import distutils.command.sdist as sdist
+
+# import last to prevent caching
+from distutils import {imported_module}
+
+for mod in (cmd, sdist):
+    assert mod.{imported_module} == {imported_module}, (
+        f"\n{{mod.dir_util}}\n!=\n{{{imported_module}}}"
+    )
+
+print("success")
+"""
+
+
+@pytest.mark.usefixtures("tmpdir_cwd")
+@pytest.mark.parametrize(
+    ('distutils_version', 'imported_module'),
+    [
+        pytest.param("stdlib", "dir_util", marks=skip_without_stdlib_distutils),
+        pytest.param("stdlib", "file_util", marks=skip_without_stdlib_distutils),
+        pytest.param("stdlib", "archive_util", marks=skip_without_stdlib_distutils),
+        ("local", "dir_util"),
+        ("local", "file_util"),
+        ("local", "archive_util"),
+    ],
+)
+def test_modules_are_not_duplicated_on_import(distutils_version, imported_module, venv):
+    env = dict(SETUPTOOLS_USE_DISTUTILS=distutils_version)
+    script = ENSURE_IMPORTS_ARE_NOT_DUPLICATED.format(imported_module=imported_module)
+    cmd = ['python', '-c', script]
+    output = venv.run(cmd, env=win_sr(env), **_TEXT_KWARGS).strip()
+    assert output == "success"
+
+
+ENSURE_LOG_IMPORT_IS_NOT_DUPLICATED = r"""
+import types
+import distutils.dist as dist
+from distutils import log
+if isinstance(dist.log, types.ModuleType):
+    assert dist.log == log, f"\n{dist.log}\n!=\n{log}"
+print("success")
+"""
+
+
+@pytest.mark.usefixtures("tmpdir_cwd")
+@pytest.mark.parametrize(
+    "distutils_version",
+    [
+        "local",
+        pytest.param("stdlib", marks=skip_without_stdlib_distutils),
+    ],
+)
+def test_log_module_is_not_duplicated_on_import(distutils_version, venv):
+    env = dict(SETUPTOOLS_USE_DISTUTILS=distutils_version)
+    cmd = ['python', '-c', ENSURE_LOG_IMPORT_IS_NOT_DUPLICATED]
+    output = venv.run(cmd, env=win_sr(env), **_TEXT_KWARGS).strip()
+    assert output == "success"
+
+
+ENSURE_CONSISTENT_ERROR_FROM_MODIFIED_PY = r"""
+from setuptools.modified import newer
+from {imported_module}.errors import DistutilsError
+
+# Can't use pytest.raises in this context
+try:
+    newer("", "")
+except DistutilsError:
+    print("success")
+else:
+    raise AssertionError("Expected to raise")
+"""
+
+
+@pytest.mark.usefixtures("tmpdir_cwd")
+@pytest.mark.parametrize(
+    ('distutils_version', 'imported_module'),
+    [
+        ("local", "distutils"),
+        # Unfortunately we still get ._distutils.errors.DistutilsError with SETUPTOOLS_USE_DISTUTILS=stdlib
+        # But that's a deprecated use-case we don't mind not fully supporting in newer code
+        pytest.param(
+            "stdlib", "setuptools._distutils", marks=skip_without_stdlib_distutils
+        ),
+    ],
+)
+def test_consistent_error_from_modified_py(distutils_version, imported_module, venv):
+    env = dict(SETUPTOOLS_USE_DISTUTILS=distutils_version)
+    cmd = [
+        'python',
+        '-c',
+        ENSURE_CONSISTENT_ERROR_FROM_MODIFIED_PY.format(
+            imported_module=imported_module
+        ),
+    ]
+    output = venv.run(cmd, env=win_sr(env), **_TEXT_KWARGS).strip()
+    assert output == "success"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_easy_install.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_easy_install.py
new file mode 100644
index 0000000000000000000000000000000000000000..b58b0b66663e4bfb6e26bd730e62bff8267eeff5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_easy_install.py
@@ -0,0 +1,1476 @@
+"""Easy install Tests"""
+
+import contextlib
+import io
+import itertools
+import logging
+import os
+import pathlib
+import re
+import site
+import subprocess
+import sys
+import tarfile
+import tempfile
+import time
+import warnings
+import zipfile
+from pathlib import Path
+from typing import NamedTuple
+from unittest import mock
+
+import pytest
+from jaraco import path
+
+import pkg_resources
+import setuptools.command.easy_install as ei
+from pkg_resources import Distribution as PRDistribution, normalize_path, working_set
+from setuptools import sandbox
+from setuptools._normalization import safer_name
+from setuptools.command.easy_install import PthDistributions
+from setuptools.dist import Distribution
+from setuptools.sandbox import run_setup
+from setuptools.tests import fail_on_ascii
+from setuptools.tests.server import MockServer, path_to_url
+
+from . import contexts
+from .textwrap import DALS
+
+import distutils.errors
+
+
+@pytest.fixture(autouse=True)
+def pip_disable_index(monkeypatch):
+    """
+    Important: Disable the default index for pip to avoid
+    querying packages in the index and potentially resolving
+    and installing packages there.
+    """
+    monkeypatch.setenv('PIP_NO_INDEX', 'true')
+
+
+class FakeDist:
+    def get_entry_map(self, group):
+        if group != 'console_scripts':
+            return {}
+        return {'name': 'ep'}
+
+    def as_requirement(self):
+        return 'spec'
+
+
+SETUP_PY = DALS(
+    """
+    from setuptools import setup
+
+    setup()
+    """
+)
+
+
+class TestEasyInstallTest:
+    def test_get_script_args(self):
+        header = ei.CommandSpec.best().from_environment().as_header()
+        dist = FakeDist()
+        args = next(ei.ScriptWriter.get_args(dist))
+        _name, script = itertools.islice(args, 2)
+        assert script.startswith(header)
+        assert "'spec'" in script
+        assert "'console_scripts'" in script
+        assert "'name'" in script
+        assert re.search('^# EASY-INSTALL-ENTRY-SCRIPT', script, flags=re.MULTILINE)
+
+    def test_no_find_links(self):
+        # new option '--no-find-links', that blocks find-links added at
+        # the project level
+        dist = Distribution()
+        cmd = ei.easy_install(dist)
+        cmd.check_pth_processing = lambda: True
+        cmd.no_find_links = True
+        cmd.find_links = ['link1', 'link2']
+        cmd.install_dir = os.path.join(tempfile.mkdtemp(), 'ok')
+        cmd.args = ['ok']
+        cmd.ensure_finalized()
+        assert cmd.package_index.scanned_urls == {}
+
+        # let's try without it (default behavior)
+        cmd = ei.easy_install(dist)
+        cmd.check_pth_processing = lambda: True
+        cmd.find_links = ['link1', 'link2']
+        cmd.install_dir = os.path.join(tempfile.mkdtemp(), 'ok')
+        cmd.args = ['ok']
+        cmd.ensure_finalized()
+        keys = sorted(cmd.package_index.scanned_urls.keys())
+        assert keys == ['link1', 'link2']
+
+    def test_write_exception(self):
+        """
+        Test that `cant_write_to_target` is rendered as a DistutilsError.
+        """
+        dist = Distribution()
+        cmd = ei.easy_install(dist)
+        cmd.install_dir = os.getcwd()
+        with pytest.raises(distutils.errors.DistutilsError):
+            cmd.cant_write_to_target()
+
+    def test_all_site_dirs(self, monkeypatch):
+        """
+        get_site_dirs should always return site dirs reported by
+        site.getsitepackages.
+        """
+        path = normalize_path('/setuptools/test/site-packages')
+
+        def mock_gsp():
+            return [path]
+
+        monkeypatch.setattr(site, 'getsitepackages', mock_gsp, raising=False)
+        assert path in ei.get_site_dirs()
+
+    def test_all_site_dirs_works_without_getsitepackages(self, monkeypatch):
+        monkeypatch.delattr(site, 'getsitepackages', raising=False)
+        assert ei.get_site_dirs()
+
+    @pytest.fixture
+    def sdist_unicode(self, tmpdir):
+        files = [
+            (
+                'setup.py',
+                DALS(
+                    """
+                    import setuptools
+                    setuptools.setup(
+                        name="setuptools-test-unicode",
+                        version="1.0",
+                        packages=["mypkg"],
+                        include_package_data=True,
+                    )
+                    """
+                ),
+            ),
+            (
+                'mypkg/__init__.py',
+                "",
+            ),
+            (
+                'mypkg/☃.txt',
+                "",
+            ),
+        ]
+        sdist_name = 'setuptools-test-unicode-1.0.zip'
+        sdist = tmpdir / sdist_name
+        # can't use make_sdist, because the issue only occurs
+        #  with zip sdists.
+        sdist_zip = zipfile.ZipFile(str(sdist), 'w')
+        for filename, content in files:
+            sdist_zip.writestr(filename, content)
+        sdist_zip.close()
+        return str(sdist)
+
+    @fail_on_ascii
+    def test_unicode_filename_in_sdist(self, sdist_unicode, tmpdir, monkeypatch):
+        """
+        The install command should execute correctly even if
+        the package has unicode filenames.
+        """
+        dist = Distribution({'script_args': ['easy_install']})
+        target = (tmpdir / 'target').ensure_dir()
+        cmd = ei.easy_install(
+            dist,
+            install_dir=str(target),
+            args=['x'],
+        )
+        monkeypatch.setitem(os.environ, 'PYTHONPATH', str(target))
+        cmd.ensure_finalized()
+        cmd.easy_install(sdist_unicode)
+
+    @pytest.fixture
+    def sdist_unicode_in_script(self, tmpdir):
+        files = [
+            (
+                "setup.py",
+                DALS(
+                    """
+                    import setuptools
+                    setuptools.setup(
+                        name="setuptools-test-unicode",
+                        version="1.0",
+                        packages=["mypkg"],
+                        include_package_data=True,
+                        scripts=['mypkg/unicode_in_script'],
+                    )
+                    """
+                ),
+            ),
+            ("mypkg/__init__.py", ""),
+            (
+                "mypkg/unicode_in_script",
+                DALS(
+                    """
+                    #!/bin/sh
+                    # á
+
+                    non_python_fn() {
+                    }
+                """
+                ),
+            ),
+        ]
+        sdist_name = "setuptools-test-unicode-script-1.0.zip"
+        sdist = tmpdir / sdist_name
+        # can't use make_sdist, because the issue only occurs
+        #  with zip sdists.
+        sdist_zip = zipfile.ZipFile(str(sdist), "w")
+        for filename, content in files:
+            sdist_zip.writestr(filename, content.encode('utf-8'))
+        sdist_zip.close()
+        return str(sdist)
+
+    @fail_on_ascii
+    def test_unicode_content_in_sdist(
+        self, sdist_unicode_in_script, tmpdir, monkeypatch
+    ):
+        """
+        The install command should execute correctly even if
+        the package has unicode in scripts.
+        """
+        dist = Distribution({"script_args": ["easy_install"]})
+        target = (tmpdir / "target").ensure_dir()
+        cmd = ei.easy_install(dist, install_dir=str(target), args=["x"])
+        monkeypatch.setitem(os.environ, "PYTHONPATH", str(target))
+        cmd.ensure_finalized()
+        cmd.easy_install(sdist_unicode_in_script)
+
+    @pytest.fixture
+    def sdist_script(self, tmpdir):
+        files = [
+            (
+                'setup.py',
+                DALS(
+                    """
+                    import setuptools
+                    setuptools.setup(
+                        name="setuptools-test-script",
+                        version="1.0",
+                        scripts=["mypkg_script"],
+                    )
+                    """
+                ),
+            ),
+            (
+                'mypkg_script',
+                DALS(
+                    """
+                     #/usr/bin/python
+                     print('mypkg_script')
+                     """
+                ),
+            ),
+        ]
+        sdist_name = 'setuptools-test-script-1.0.zip'
+        sdist = str(tmpdir / sdist_name)
+        make_sdist(sdist, files)
+        return sdist
+
+    @pytest.mark.skipif(
+        not sys.platform.startswith('linux'), reason="Test can only be run on Linux"
+    )
+    def test_script_install(self, sdist_script, tmpdir, monkeypatch):
+        """
+        Check scripts are installed.
+        """
+        dist = Distribution({'script_args': ['easy_install']})
+        target = (tmpdir / 'target').ensure_dir()
+        cmd = ei.easy_install(
+            dist,
+            install_dir=str(target),
+            args=['x'],
+        )
+        monkeypatch.setitem(os.environ, 'PYTHONPATH', str(target))
+        cmd.ensure_finalized()
+        cmd.easy_install(sdist_script)
+        assert (target / 'mypkg_script').exists()
+
+
+@pytest.mark.filterwarnings('ignore:Unbuilt egg')
+class TestPTHFileWriter:
+    def test_add_from_cwd_site_sets_dirty(self):
+        """a pth file manager should set dirty
+        if a distribution is in site but also the cwd
+        """
+        pth = PthDistributions('does-not_exist', [os.getcwd()])
+        assert not pth.dirty
+        pth.add(PRDistribution(os.getcwd()))
+        assert pth.dirty
+
+    def test_add_from_site_is_ignored(self):
+        location = '/test/location/does-not-have-to-exist'
+        # PthDistributions expects all locations to be normalized
+        location = pkg_resources.normalize_path(location)
+        pth = PthDistributions(
+            'does-not_exist',
+            [
+                location,
+            ],
+        )
+        assert not pth.dirty
+        pth.add(PRDistribution(location))
+        assert not pth.dirty
+
+    def test_many_pth_distributions_merge_together(self, tmpdir):
+        """
+        If the pth file is modified under the hood, then PthDistribution
+        will refresh its content before saving, merging contents when
+        necessary.
+        """
+        # putting the pth file in a dedicated sub-folder,
+        pth_subdir = tmpdir.join("pth_subdir")
+        pth_subdir.mkdir()
+        pth_path = str(pth_subdir.join("file1.pth"))
+        pth1 = PthDistributions(pth_path)
+        pth2 = PthDistributions(pth_path)
+        assert pth1.paths == pth2.paths == [], (
+            "unless there would be some default added at some point"
+        )
+        # and so putting the src_subdir in folder distinct than the pth one,
+        # so to keep it absolute by PthDistributions
+        new_src_path = tmpdir.join("src_subdir")
+        new_src_path.mkdir()  # must exist to be accounted
+        new_src_path_str = str(new_src_path)
+        pth1.paths.append(new_src_path_str)
+        pth1.save()
+        assert pth1.paths, (
+            "the new_src_path added must still be present/valid in pth1 after save"
+        )
+        # now,
+        assert new_src_path_str not in pth2.paths, (
+            "right before we save the entry should still not be present"
+        )
+        pth2.save()
+        assert new_src_path_str in pth2.paths, (
+            "the new_src_path entry should have been added by pth2 with its save() call"
+        )
+        assert pth2.paths[-1] == new_src_path, (
+            "and it should match exactly on the last entry actually "
+            "given we append to it in save()"
+        )
+        # finally,
+        assert PthDistributions(pth_path).paths == pth2.paths, (
+            "and we should have the exact same list at the end "
+            "with a fresh PthDistributions instance"
+        )
+
+
+@pytest.fixture
+def setup_context(tmpdir):
+    with (tmpdir / 'setup.py').open('w', encoding="utf-8") as f:
+        f.write(SETUP_PY)
+    with tmpdir.as_cwd():
+        yield tmpdir
+
+
+@pytest.mark.usefixtures("user_override")
+@pytest.mark.usefixtures("setup_context")
+class TestUserInstallTest:
+    # prevent check that site-packages is writable. easy_install
+    # shouldn't be writing to system site-packages during finalize
+    # options, but while it does, bypass the behavior.
+    prev_sp_write = mock.patch(
+        'setuptools.command.easy_install.easy_install.check_site_dir',
+        mock.Mock(),
+    )
+
+    # simulate setuptools installed in user site packages
+    @mock.patch('setuptools.command.easy_install.__file__', site.USER_SITE)
+    @mock.patch('site.ENABLE_USER_SITE', True)
+    @prev_sp_write
+    def test_user_install_not_implied_user_site_enabled(self):
+        self.assert_not_user_site()
+
+    @mock.patch('site.ENABLE_USER_SITE', False)
+    @prev_sp_write
+    def test_user_install_not_implied_user_site_disabled(self):
+        self.assert_not_user_site()
+
+    @staticmethod
+    def assert_not_user_site():
+        # create a finalized easy_install command
+        dist = Distribution()
+        dist.script_name = 'setup.py'
+        cmd = ei.easy_install(dist)
+        cmd.args = ['py']
+        cmd.ensure_finalized()
+        assert not cmd.user, 'user should not be implied'
+
+    def test_multiproc_atexit(self):
+        pytest.importorskip('multiprocessing')
+
+        log = logging.getLogger('test_easy_install')
+        logging.basicConfig(level=logging.INFO, stream=sys.stderr)
+        log.info('this should not break')
+
+    @pytest.fixture
+    def foo_package(self, tmpdir):
+        egg_file = tmpdir / 'foo-1.0.egg-info'
+        with egg_file.open('w') as f:
+            f.write('Name: foo\n')
+        return str(tmpdir)
+
+    @pytest.fixture
+    def install_target(self, tmpdir):
+        target = str(tmpdir)
+        with mock.patch('sys.path', sys.path + [target]):
+            python_path = os.path.pathsep.join(sys.path)
+            with mock.patch.dict(os.environ, PYTHONPATH=python_path):
+                yield target
+
+    def test_local_index(self, foo_package, install_target):
+        """
+        The local index must be used when easy_install locates installed
+        packages.
+        """
+        dist = Distribution()
+        dist.script_name = 'setup.py'
+        cmd = ei.easy_install(dist)
+        cmd.install_dir = install_target
+        cmd.args = ['foo']
+        cmd.ensure_finalized()
+        cmd.local_index.scan([foo_package])
+        res = cmd.easy_install('foo')
+        actual = os.path.normcase(os.path.realpath(res.location))
+        expected = os.path.normcase(os.path.realpath(foo_package))
+        assert actual == expected
+
+    @contextlib.contextmanager
+    def user_install_setup_context(self, *args, **kwargs):
+        """
+        Wrap sandbox.setup_context to patch easy_install in that context to
+        appear as user-installed.
+        """
+        with self.orig_context(*args, **kwargs):
+            import setuptools.command.easy_install as ei
+
+            ei.__file__ = site.USER_SITE
+            yield
+
+    def patched_setup_context(self):
+        self.orig_context = sandbox.setup_context
+
+        return mock.patch(
+            'setuptools.sandbox.setup_context',
+            self.user_install_setup_context,
+        )
+
+
+@pytest.fixture
+def distutils_package():
+    distutils_setup_py = SETUP_PY.replace(
+        'from setuptools import setup',
+        'from distutils.core import setup',
+    )
+    with contexts.tempdir(cd=os.chdir):
+        with open('setup.py', 'w', encoding="utf-8") as f:
+            f.write(distutils_setup_py)
+        yield
+
+
+@pytest.mark.usefixtures("distutils_package")
+class TestDistutilsPackage:
+    def test_bdist_egg_available_on_distutils_pkg(self):
+        run_setup('setup.py', ['bdist_egg'])
+
+
+@pytest.fixture
+def mock_index():
+    # set up a server which will simulate an alternate package index.
+    p_index = MockServer()
+    if p_index.server_port == 0:
+        # Some platforms (Jython) don't find a port to which to bind,
+        # so skip test for them.
+        pytest.skip("could not find a valid port")
+    p_index.start()
+    return p_index
+
+
+class TestInstallRequires:
+    def test_setup_install_includes_dependencies(self, tmp_path, mock_index):
+        """
+        When ``python setup.py install`` is called directly, it will use easy_install
+        to fetch dependencies.
+        """
+        # TODO: Remove these tests once `setup.py install` is completely removed
+        project_root = tmp_path / "project"
+        project_root.mkdir(exist_ok=True)
+        install_root = tmp_path / "install"
+        install_root.mkdir(exist_ok=True)
+
+        self.create_project(project_root)
+        cmd = [
+            sys.executable,
+            '-c',
+            '__import__("setuptools").setup()',
+            'install',
+            '--install-base',
+            str(install_root),
+            '--install-lib',
+            str(install_root),
+            '--install-headers',
+            str(install_root),
+            '--install-scripts',
+            str(install_root),
+            '--install-data',
+            str(install_root),
+            '--install-purelib',
+            str(install_root),
+            '--install-platlib',
+            str(install_root),
+        ]
+        env = {**os.environ, "__EASYINSTALL_INDEX": mock_index.url}
+        cp = subprocess.run(
+            cmd,
+            cwd=str(project_root),
+            env=env,
+            stdout=subprocess.PIPE,
+            stderr=subprocess.STDOUT,
+            text=True,
+            encoding="utf-8",
+        )
+        assert cp.returncode != 0
+        try:
+            assert '/does-not-exist/' in {r.path for r in mock_index.requests}
+            assert next(
+                line
+                for line in cp.stdout.splitlines()
+                if "not find suitable distribution for" in line
+                and "does-not-exist" in line
+            )
+        except Exception:
+            if "failed to get random numbers" in cp.stdout:
+                pytest.xfail(f"{sys.platform} failure - {cp.stdout}")
+            raise
+
+    def create_project(self, root):
+        config = """
+        [metadata]
+        name = project
+        version = 42
+
+        [options]
+        install_requires = does-not-exist
+        py_modules = mod
+        """
+        (root / 'setup.cfg').write_text(DALS(config), encoding="utf-8")
+        (root / 'mod.py').touch()
+
+
+class TestSetupRequires:
+    def test_setup_requires_honors_fetch_params(self, mock_index, monkeypatch):
+        """
+        When easy_install installs a source distribution which specifies
+        setup_requires, it should honor the fetch parameters (such as
+        index-url, and find-links).
+        """
+        monkeypatch.setenv('PIP_RETRIES', '0')
+        monkeypatch.setenv('PIP_TIMEOUT', '0')
+        monkeypatch.setenv('PIP_NO_INDEX', 'false')
+        with contexts.quiet():
+            # create an sdist that has a build-time dependency.
+            with TestSetupRequires.create_sdist() as dist_file:
+                with contexts.tempdir() as temp_install_dir:
+                    with contexts.environment(PYTHONPATH=temp_install_dir):
+                        cmd = [
+                            sys.executable,
+                            '-c',
+                            '__import__("setuptools").setup()',
+                            'easy_install',
+                            '--index-url',
+                            mock_index.url,
+                            '--exclude-scripts',
+                            '--install-dir',
+                            temp_install_dir,
+                            dist_file,
+                        ]
+                        subprocess.Popen(cmd).wait()
+        # there should have been one requests to the server
+        assert [r.path for r in mock_index.requests] == ['/does-not-exist/']
+
+    @staticmethod
+    @contextlib.contextmanager
+    def create_sdist():
+        """
+        Return an sdist with a setup_requires dependency (of something that
+        doesn't exist)
+        """
+        with contexts.tempdir() as dir:
+            dist_path = os.path.join(dir, 'setuptools-test-fetcher-1.0.tar.gz')
+            make_sdist(
+                dist_path,
+                [
+                    (
+                        'setup.py',
+                        DALS(
+                            """
+                    import setuptools
+                    setuptools.setup(
+                        name="setuptools-test-fetcher",
+                        version="1.0",
+                        setup_requires = ['does-not-exist'],
+                    )
+                """
+                        ),
+                    ),
+                    ('setup.cfg', ''),
+                ],
+            )
+            yield dist_path
+
+    use_setup_cfg = (
+        (),
+        ('dependency_links',),
+        ('setup_requires',),
+        ('dependency_links', 'setup_requires'),
+    )
+
+    @pytest.mark.parametrize('use_setup_cfg', use_setup_cfg)
+    def test_setup_requires_overrides_version_conflict(self, use_setup_cfg):
+        """
+        Regression test for distribution issue 323:
+        https://bitbucket.org/tarek/distribute/issues/323
+
+        Ensures that a distribution's setup_requires requirements can still be
+        installed and used locally even if a conflicting version of that
+        requirement is already on the path.
+        """
+
+        fake_dist = PRDistribution(
+            'does-not-matter', project_name='foobar', version='0.0'
+        )
+        working_set.add(fake_dist)
+
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                test_pkg = create_setup_requires_package(
+                    temp_dir, use_setup_cfg=use_setup_cfg
+                )
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                with contexts.quiet() as (stdout, _stderr):
+                    # Don't even need to install the package, just
+                    # running the setup.py at all is sufficient
+                    run_setup(test_setup_py, ['--name'])
+
+                lines = stdout.readlines()
+                assert len(lines) > 0
+                assert lines[-1].strip() == 'test_pkg'
+
+    @pytest.mark.parametrize('use_setup_cfg', use_setup_cfg)
+    def test_setup_requires_override_nspkg(self, use_setup_cfg):
+        """
+        Like ``test_setup_requires_overrides_version_conflict`` but where the
+        ``setup_requires`` package is part of a namespace package that has
+        *already* been imported.
+        """
+
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                foobar_1_archive = os.path.join(temp_dir, 'foo_bar-0.1.tar.gz')
+                make_nspkg_sdist(foobar_1_archive, 'foo.bar', '0.1')
+                # Now actually go ahead an extract to the temp dir and add the
+                # extracted path to sys.path so foo.bar v0.1 is importable
+                foobar_1_dir = os.path.join(temp_dir, 'foo_bar-0.1')
+                os.mkdir(foobar_1_dir)
+                with tarfile.open(foobar_1_archive) as tf:
+                    tf.extraction_filter = lambda member, path: member
+                    tf.extractall(foobar_1_dir)
+                sys.path.insert(1, foobar_1_dir)
+
+                dist = PRDistribution(
+                    foobar_1_dir, project_name='foo.bar', version='0.1'
+                )
+                working_set.add(dist)
+
+                template = DALS(
+                    """\
+                    import foo  # Even with foo imported first the
+                                # setup_requires package should override
+                    import setuptools
+                    setuptools.setup(**%r)
+
+                    if not (hasattr(foo, '__path__') and
+                            len(foo.__path__) == 2):
+                        print('FAIL')
+
+                    if 'foo_bar-0.2' not in foo.__path__[0]:
+                        print('FAIL')
+                """
+                )
+
+                test_pkg = create_setup_requires_package(
+                    temp_dir,
+                    'foo.bar',
+                    '0.2',
+                    make_nspkg_sdist,
+                    template,
+                    use_setup_cfg=use_setup_cfg,
+                )
+
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+
+                with contexts.quiet() as (stdout, _stderr):
+                    try:
+                        # Don't even need to install the package, just
+                        # running the setup.py at all is sufficient
+                        run_setup(test_setup_py, ['--name'])
+                    except pkg_resources.VersionConflict:  # pragma: nocover
+                        pytest.fail(
+                            'Installing setup.py requirements caused a VersionConflict'
+                        )
+
+                assert 'FAIL' not in stdout.getvalue()
+                lines = stdout.readlines()
+                assert len(lines) > 0
+                assert lines[-1].strip() == 'test_pkg'
+
+    @pytest.mark.parametrize('use_setup_cfg', use_setup_cfg)
+    def test_setup_requires_with_attr_version(self, use_setup_cfg):
+        def make_dependency_sdist(dist_path, distname, version):
+            files = [
+                (
+                    'setup.py',
+                    DALS(
+                        f"""
+                    import setuptools
+                    setuptools.setup(
+                        name={distname!r},
+                        version={version!r},
+                        py_modules=[{distname!r}],
+                    )
+                    """
+                    ),
+                ),
+                (
+                    distname + '.py',
+                    DALS(
+                        """
+                    version = 42
+                    """
+                    ),
+                ),
+            ]
+            make_sdist(dist_path, files)
+
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                test_pkg = create_setup_requires_package(
+                    temp_dir,
+                    setup_attrs=dict(version='attr: foobar.version'),
+                    make_package=make_dependency_sdist,
+                    use_setup_cfg=use_setup_cfg + ('version',),
+                )
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                with contexts.quiet() as (stdout, _stderr):
+                    run_setup(test_setup_py, ['--version'])
+                lines = stdout.readlines()
+                assert len(lines) > 0
+                assert lines[-1].strip() == '42'
+
+    def test_setup_requires_honors_pip_env(self, mock_index, monkeypatch):
+        monkeypatch.setenv('PIP_RETRIES', '0')
+        monkeypatch.setenv('PIP_TIMEOUT', '0')
+        monkeypatch.setenv('PIP_NO_INDEX', 'false')
+        monkeypatch.setenv('PIP_INDEX_URL', mock_index.url)
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                test_pkg = create_setup_requires_package(
+                    temp_dir,
+                    'python-xlib',
+                    '0.19',
+                    setup_attrs=dict(dependency_links=[]),
+                )
+                test_setup_cfg = os.path.join(test_pkg, 'setup.cfg')
+                with open(test_setup_cfg, 'w', encoding="utf-8") as fp:
+                    fp.write(
+                        DALS(
+                            """
+                        [easy_install]
+                        index_url = https://pypi.org/legacy/
+                        """
+                        )
+                    )
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                with pytest.raises(distutils.errors.DistutilsError):
+                    run_setup(test_setup_py, ['--version'])
+        assert len(mock_index.requests) == 1
+        assert mock_index.requests[0].path == '/python-xlib/'
+
+    def test_setup_requires_with_pep508_url(self, mock_index, monkeypatch):
+        monkeypatch.setenv('PIP_RETRIES', '0')
+        monkeypatch.setenv('PIP_TIMEOUT', '0')
+        monkeypatch.setenv('PIP_INDEX_URL', mock_index.url)
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                dep_sdist = os.path.join(temp_dir, 'dep.tar.gz')
+                make_trivial_sdist(dep_sdist, 'dependency', '42')
+                dep_url = path_to_url(dep_sdist, authority='localhost')
+                test_pkg = create_setup_requires_package(
+                    temp_dir,
+                    # Ignored (overridden by setup_attrs)
+                    'python-xlib',
+                    '0.19',
+                    setup_attrs=dict(setup_requires=f'dependency @ {dep_url}'),
+                )
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                run_setup(test_setup_py, ['--version'])
+        assert len(mock_index.requests) == 0
+
+    def test_setup_requires_with_allow_hosts(self, mock_index):
+        """The `allow-hosts` option in not supported anymore."""
+        files = {
+            'test_pkg': {
+                'setup.py': DALS(
+                    """
+                    from setuptools import setup
+                    setup(setup_requires='python-xlib')
+                    """
+                ),
+                'setup.cfg': DALS(
+                    """
+                    [easy_install]
+                    allow_hosts = *
+                    """
+                ),
+            }
+        }
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                path.build(files, prefix=temp_dir)
+                setup_py = str(pathlib.Path(temp_dir, 'test_pkg', 'setup.py'))
+                with pytest.raises(distutils.errors.DistutilsError):
+                    run_setup(setup_py, ['--version'])
+        assert len(mock_index.requests) == 0
+
+    def test_setup_requires_with_python_requires(self, monkeypatch, tmpdir):
+        """Check `python_requires` is honored."""
+        monkeypatch.setenv('PIP_RETRIES', '0')
+        monkeypatch.setenv('PIP_TIMEOUT', '0')
+        monkeypatch.setenv('PIP_NO_INDEX', '1')
+        monkeypatch.setenv('PIP_VERBOSE', '1')
+        dep_1_0_sdist = 'dep-1.0.tar.gz'
+        dep_1_0_url = path_to_url(str(tmpdir / dep_1_0_sdist))
+        dep_1_0_python_requires = '>=2.7'
+        make_python_requires_sdist(
+            str(tmpdir / dep_1_0_sdist), 'dep', '1.0', dep_1_0_python_requires
+        )
+        dep_2_0_sdist = 'dep-2.0.tar.gz'
+        dep_2_0_url = path_to_url(str(tmpdir / dep_2_0_sdist))
+        dep_2_0_python_requires = (
+            f'!={sys.version_info.major}.{sys.version_info.minor}.*'
+        )
+        make_python_requires_sdist(
+            str(tmpdir / dep_2_0_sdist), 'dep', '2.0', dep_2_0_python_requires
+        )
+        index = tmpdir / 'index.html'
+        index.write_text(
+            DALS(
+                """
+            
+            Links for dep
+            
+                
Links for dep

+                {dep_1_0_sdist}

+                {dep_2_0_sdist}

+            
+            
+            """
+            ).format(
+                dep_1_0_url=dep_1_0_url,
+                dep_1_0_sdist=dep_1_0_sdist,
+                dep_1_0_python_requires=dep_1_0_python_requires,
+                dep_2_0_url=dep_2_0_url,
+                dep_2_0_sdist=dep_2_0_sdist,
+                dep_2_0_python_requires=dep_2_0_python_requires,
+            ),
+            'utf-8',
+        )
+        index_url = path_to_url(str(index))
+        with contexts.save_pkg_resources_state():
+            test_pkg = create_setup_requires_package(
+                str(tmpdir),
+                'python-xlib',
+                '0.19',  # Ignored (overridden by setup_attrs).
+                setup_attrs=dict(setup_requires='dep', dependency_links=[index_url]),
+            )
+            test_setup_py = os.path.join(test_pkg, 'setup.py')
+            run_setup(test_setup_py, ['--version'])
+        eggs = list(
+            map(str, pkg_resources.find_distributions(os.path.join(test_pkg, '.eggs')))
+        )
+        assert eggs == ['dep 1.0']
+
+    @pytest.mark.parametrize('with_dependency_links_in_setup_py', (False, True))
+    def test_setup_requires_with_find_links_in_setup_cfg(
+        self, monkeypatch, with_dependency_links_in_setup_py
+    ):
+        monkeypatch.setenv('PIP_RETRIES', '0')
+        monkeypatch.setenv('PIP_TIMEOUT', '0')
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                make_trivial_sdist(
+                    os.path.join(temp_dir, 'python-xlib-42.tar.gz'), 'python-xlib', '42'
+                )
+                test_pkg = os.path.join(temp_dir, 'test_pkg')
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                test_setup_cfg = os.path.join(test_pkg, 'setup.cfg')
+                os.mkdir(test_pkg)
+                with open(test_setup_py, 'w', encoding="utf-8") as fp:
+                    if with_dependency_links_in_setup_py:
+                        dependency_links = [os.path.join(temp_dir, 'links')]
+                    else:
+                        dependency_links = []
+                    fp.write(
+                        DALS(
+                            """
+                        from setuptools import installer, setup
+                        setup(setup_requires='python-xlib==42',
+                        dependency_links={dependency_links!r})
+                        """
+                        ).format(dependency_links=dependency_links)
+                    )
+                with open(test_setup_cfg, 'w', encoding="utf-8") as fp:
+                    fp.write(
+                        DALS(
+                            """
+                        [easy_install]
+                        index_url = {index_url}
+                        find_links = {find_links}
+                        """
+                        ).format(
+                            index_url=os.path.join(temp_dir, 'index'),
+                            find_links=temp_dir,
+                        )
+                    )
+                run_setup(test_setup_py, ['--version'])
+
+    def test_setup_requires_with_transitive_extra_dependency(self, monkeypatch):
+        """
+        Use case: installing a package with a build dependency on
+        an already installed `dep[extra]`, which in turn depends
+        on `extra_dep` (whose is not already installed).
+        """
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                # Create source distribution for `extra_dep`.
+                make_trivial_sdist(
+                    os.path.join(temp_dir, 'extra_dep-1.0.tar.gz'), 'extra_dep', '1.0'
+                )
+                # Create source tree for `dep`.
+                dep_pkg = os.path.join(temp_dir, 'dep')
+                os.mkdir(dep_pkg)
+                path.build(
+                    {
+                        'setup.py': DALS(
+                            """
+                          import setuptools
+                          setuptools.setup(
+                              name='dep', version='2.0',
+                              extras_require={'extra': ['extra_dep']},
+                          )
+                         """
+                        ),
+                        'setup.cfg': '',
+                    },
+                    prefix=dep_pkg,
+                )
+                # "Install" dep.
+                run_setup(os.path.join(dep_pkg, 'setup.py'), ['dist_info'])
+                working_set.add_entry(dep_pkg)
+                # Create source tree for test package.
+                test_pkg = os.path.join(temp_dir, 'test_pkg')
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                os.mkdir(test_pkg)
+                with open(test_setup_py, 'w', encoding="utf-8") as fp:
+                    fp.write(
+                        DALS(
+                            """
+                        from setuptools import installer, setup
+                        setup(setup_requires='dep[extra]')
+                        """
+                        )
+                    )
+                # Check...
+                monkeypatch.setenv('PIP_FIND_LINKS', str(temp_dir))
+                monkeypatch.setenv('PIP_NO_INDEX', '1')
+                monkeypatch.setenv('PIP_RETRIES', '0')
+                monkeypatch.setenv('PIP_TIMEOUT', '0')
+                run_setup(test_setup_py, ['--version'])
+
+    def test_setup_requires_with_distutils_command_dep(self, monkeypatch):
+        """
+        Use case: ensure build requirements' extras
+        are properly installed and activated.
+        """
+        with contexts.save_pkg_resources_state():
+            with contexts.tempdir() as temp_dir:
+                # Create source distribution for `extra_dep`.
+                make_sdist(
+                    os.path.join(temp_dir, 'extra_dep-1.0.tar.gz'),
+                    [
+                        (
+                            'setup.py',
+                            DALS(
+                                """
+                          import setuptools
+                          setuptools.setup(
+                              name='extra_dep',
+                              version='1.0',
+                              py_modules=['extra_dep'],
+                          )
+                          """
+                            ),
+                        ),
+                        ('setup.cfg', ''),
+                        ('extra_dep.py', ''),
+                    ],
+                )
+                # Create source tree for `epdep`.
+                dep_pkg = os.path.join(temp_dir, 'epdep')
+                os.mkdir(dep_pkg)
+                path.build(
+                    {
+                        'setup.py': DALS(
+                            """
+                          import setuptools
+                          setuptools.setup(
+                              name='dep', version='2.0',
+                              py_modules=['epcmd'],
+                              extras_require={'extra': ['extra_dep']},
+                              entry_points='''
+                                           [distutils.commands]
+                                           epcmd = epcmd:epcmd [extra]
+                                           ''',
+                          )
+                         """
+                        ),
+                        'setup.cfg': '',
+                        'epcmd.py': DALS(
+                            """
+                                     from distutils.command.build_py import build_py
+
+                                     import extra_dep
+
+                                     class epcmd(build_py):
+                                         pass
+                                     """
+                        ),
+                    },
+                    prefix=dep_pkg,
+                )
+                # "Install" dep.
+                run_setup(os.path.join(dep_pkg, 'setup.py'), ['dist_info'])
+                working_set.add_entry(dep_pkg)
+                # Create source tree for test package.
+                test_pkg = os.path.join(temp_dir, 'test_pkg')
+                test_setup_py = os.path.join(test_pkg, 'setup.py')
+                os.mkdir(test_pkg)
+                with open(test_setup_py, 'w', encoding="utf-8") as fp:
+                    fp.write(
+                        DALS(
+                            """
+                        from setuptools import installer, setup
+                        setup(setup_requires='dep[extra]')
+                        """
+                        )
+                    )
+                # Check...
+                monkeypatch.setenv('PIP_FIND_LINKS', str(temp_dir))
+                monkeypatch.setenv('PIP_NO_INDEX', '1')
+                monkeypatch.setenv('PIP_RETRIES', '0')
+                monkeypatch.setenv('PIP_TIMEOUT', '0')
+                run_setup(test_setup_py, ['epcmd'])
+
+
+def make_trivial_sdist(dist_path, distname, version):
+    """
+    Create a simple sdist tarball at dist_path, containing just a simple
+    setup.py.
+    """
+
+    make_sdist(
+        dist_path,
+        [
+            (
+                'setup.py',
+                DALS(
+                    f"""\
+             import setuptools
+             setuptools.setup(
+                 name={distname!r},
+                 version={version!r}
+             )
+         """
+                ),
+            ),
+            ('setup.cfg', ''),
+        ],
+    )
+
+
+def make_nspkg_sdist(dist_path, distname, version):
+    """
+    Make an sdist tarball with distname and version which also contains one
+    package with the same name as distname.  The top-level package is
+    designated a namespace package).
+    """
+    # Assert that the distname contains at least one period
+    assert '.' in distname
+
+    parts = distname.split('.')
+    nspackage = parts[0]
+
+    packages = ['.'.join(parts[:idx]) for idx in range(1, len(parts) + 1)]
+
+    setup_py = DALS(
+        f"""\
+        import setuptools
+        setuptools.setup(
+            name={distname!r},
+            version={version!r},
+            packages={packages!r},
+            namespace_packages=[{nspackage!r}]
+        )
+    """
+    )
+
+    init = "__import__('pkg_resources').declare_namespace(__name__)"
+
+    files = [('setup.py', setup_py), (os.path.join(nspackage, '__init__.py'), init)]
+    for package in packages[1:]:
+        filename = os.path.join(*(package.split('.') + ['__init__.py']))
+        files.append((filename, ''))
+
+    make_sdist(dist_path, files)
+
+
+def make_python_requires_sdist(dist_path, distname, version, python_requires):
+    make_sdist(
+        dist_path,
+        [
+            (
+                'setup.py',
+                DALS(
+                    """\
+                import setuptools
+                setuptools.setup(
+                  name={name!r},
+                  version={version!r},
+                  python_requires={python_requires!r},
+                )
+                """
+                ).format(
+                    name=distname, version=version, python_requires=python_requires
+                ),
+            ),
+            ('setup.cfg', ''),
+        ],
+    )
+
+
+def make_sdist(dist_path, files):
+    """
+    Create a simple sdist tarball at dist_path, containing the files
+    listed in ``files`` as ``(filename, content)`` tuples.
+    """
+
+    # Distributions with only one file don't play well with pip.
+    assert len(files) > 1
+    with tarfile.open(dist_path, 'w:gz') as dist:
+        for filename, content in files:
+            file_bytes = io.BytesIO(content.encode('utf-8'))
+            file_info = tarfile.TarInfo(name=filename)
+            file_info.size = len(file_bytes.getvalue())
+            file_info.mtime = int(time.time())
+            dist.addfile(file_info, fileobj=file_bytes)
+
+
+def create_setup_requires_package(
+    path,
+    distname='foobar',
+    version='0.1',
+    make_package=make_trivial_sdist,
+    setup_py_template=None,
+    setup_attrs=None,
+    use_setup_cfg=(),
+):
+    """Creates a source tree under path for a trivial test package that has a
+    single requirement in setup_requires--a tarball for that requirement is
+    also created and added to the dependency_links argument.
+
+    ``distname`` and ``version`` refer to the name/version of the package that
+    the test package requires via ``setup_requires``.  The name of the test
+    package itself is just 'test_pkg'.
+    """
+
+    normalized_distname = safer_name(distname)
+    test_setup_attrs = {
+        'name': 'test_pkg',
+        'version': '0.0',
+        'setup_requires': [f'{normalized_distname}=={version}'],
+        'dependency_links': [os.path.abspath(path)],
+    }
+    if setup_attrs:
+        test_setup_attrs.update(setup_attrs)
+
+    test_pkg = os.path.join(path, 'test_pkg')
+    os.mkdir(test_pkg)
+
+    # setup.cfg
+    if use_setup_cfg:
+        options = []
+        metadata = []
+        for name in use_setup_cfg:
+            value = test_setup_attrs.pop(name)
+            if name in 'name version'.split():
+                section = metadata
+            else:
+                section = options
+            if isinstance(value, (tuple, list)):
+                value = ';'.join(value)
+            section.append(f'{name}: {value}')
+        test_setup_cfg_contents = DALS(
+            """
+            [metadata]
+            {metadata}
+            [options]
+            {options}
+            """
+        ).format(
+            options='\n'.join(options),
+            metadata='\n'.join(metadata),
+        )
+    else:
+        test_setup_cfg_contents = ''
+    with open(os.path.join(test_pkg, 'setup.cfg'), 'w', encoding="utf-8") as f:
+        f.write(test_setup_cfg_contents)
+
+    # setup.py
+    if setup_py_template is None:
+        setup_py_template = DALS(
+            """\
+            import setuptools
+            setuptools.setup(**%r)
+        """
+        )
+    with open(os.path.join(test_pkg, 'setup.py'), 'w', encoding="utf-8") as f:
+        f.write(setup_py_template % test_setup_attrs)
+
+    foobar_path = os.path.join(path, f'{normalized_distname}-{version}.tar.gz')
+    make_package(foobar_path, distname, version)
+
+    return test_pkg
+
+
+@pytest.mark.skipif(
+    sys.platform.startswith('java') and ei.is_sh(sys.executable),
+    reason="Test cannot run under java when executable is sh",
+)
+class TestScriptHeader:
+    non_ascii_exe = '/Users/José/bin/python'
+    exe_with_spaces = r'C:\Program Files\Python36\python.exe'
+
+    def test_get_script_header(self):
+        expected = f'#!{ei.nt_quote_arg(os.path.normpath(sys.executable))}\n'
+        actual = ei.ScriptWriter.get_header('#!/usr/local/bin/python')
+        assert actual == expected
+
+    def test_get_script_header_args(self):
+        expected = f'#!{ei.nt_quote_arg(os.path.normpath(sys.executable))} -x\n'
+        actual = ei.ScriptWriter.get_header('#!/usr/bin/python -x')
+        assert actual == expected
+
+    def test_get_script_header_non_ascii_exe(self):
+        actual = ei.ScriptWriter.get_header(
+            '#!/usr/bin/python', executable=self.non_ascii_exe
+        )
+        expected = f'#!{self.non_ascii_exe} -x\n'
+        assert actual == expected
+
+    def test_get_script_header_exe_with_spaces(self):
+        actual = ei.ScriptWriter.get_header(
+            '#!/usr/bin/python', executable='"' + self.exe_with_spaces + '"'
+        )
+        expected = f'#!"{self.exe_with_spaces}"\n'
+        assert actual == expected
+
+
+class TestCommandSpec:
+    def test_custom_launch_command(self):
+        """
+        Show how a custom CommandSpec could be used to specify a #! executable
+        which takes parameters.
+        """
+        cmd = ei.CommandSpec(['/usr/bin/env', 'python3'])
+        assert cmd.as_header() == '#!/usr/bin/env python3\n'
+
+    def test_from_param_for_CommandSpec_is_passthrough(self):
+        """
+        from_param should return an instance of a CommandSpec
+        """
+        cmd = ei.CommandSpec(['python'])
+        cmd_new = ei.CommandSpec.from_param(cmd)
+        assert cmd is cmd_new
+
+    @mock.patch('sys.executable', TestScriptHeader.exe_with_spaces)
+    @mock.patch.dict(os.environ)
+    def test_from_environment_with_spaces_in_executable(self):
+        os.environ.pop('__PYVENV_LAUNCHER__', None)
+        cmd = ei.CommandSpec.from_environment()
+        assert len(cmd) == 1
+        assert cmd.as_header().startswith('#!"')
+
+    def test_from_simple_string_uses_shlex(self):
+        """
+        In order to support `executable = /usr/bin/env my-python`, make sure
+        from_param invokes shlex on that input.
+        """
+        cmd = ei.CommandSpec.from_param('/usr/bin/env my-python')
+        assert len(cmd) == 2
+        assert '"' not in cmd.as_header()
+
+    def test_from_param_raises_expected_error(self) -> None:
+        """
+        from_param should raise its own TypeError when the argument's type is unsupported
+        """
+        with pytest.raises(TypeError) as exc_info:
+            ei.CommandSpec.from_param(object())  # type: ignore[arg-type] # We want a type error here
+        assert (
+            str(exc_info.value) == "Argument has an unsupported type "
+        ), exc_info.value
+
+
+class TestWindowsScriptWriter:
+    def test_header(self):
+        hdr = ei.WindowsScriptWriter.get_header('')
+        assert hdr.startswith('#!')
+        assert hdr.endswith('\n')
+        hdr = hdr.lstrip('#!')
+        hdr = hdr.rstrip('\n')
+        # header should not start with an escaped quote
+        assert not hdr.startswith('\\"')
+
+
+class VersionStub(NamedTuple):
+    major: int
+    minor: int
+    micro: int
+    releaselevel: str
+    serial: int
+
+
+def test_use_correct_python_version_string(tmpdir, tmpdir_cwd, monkeypatch):
+    # In issue #3001, easy_install wrongly uses the `python3.1` directory
+    # when the interpreter is `python3.10` and the `--user` option is given.
+    # See pypa/setuptools#3001.
+    dist = Distribution()
+    cmd = dist.get_command_obj('easy_install')
+    cmd.args = ['ok']
+    cmd.optimize = 0
+    cmd.user = True
+    cmd.install_userbase = str(tmpdir)
+    cmd.install_usersite = None
+    install_cmd = dist.get_command_obj('install')
+    install_cmd.install_userbase = str(tmpdir)
+    install_cmd.install_usersite = None
+
+    with monkeypatch.context() as patch, warnings.catch_warnings():
+        warnings.simplefilter("ignore")
+        version = '3.10.1 (main, Dec 21 2021, 09:17:12) [GCC 10.2.1 20210110]'
+        info = VersionStub(3, 10, 1, "final", 0)
+        patch.setattr('site.ENABLE_USER_SITE', True)
+        patch.setattr('sys.version', version)
+        patch.setattr('sys.version_info', info)
+        patch.setattr(cmd, 'create_home_path', mock.Mock())
+        cmd.finalize_options()
+
+    name = "pypy" if hasattr(sys, 'pypy_version_info') else "python"
+    install_dir = cmd.install_dir.lower()
+
+    # In some platforms (e.g. Windows), install_dir is mostly determined
+    # via `sysconfig`, which define constants eagerly at module creation.
+    # This means that monkeypatching `sys.version` to emulate 3.10 for testing
+    # may have no effect.
+    # The safest test here is to rely on the fact that 3.1 is no longer
+    # supported/tested, and make sure that if 'python3.1' ever appears in the string
+    # it is followed by another digit (e.g. 'python3.10').
+    if re.search(name + r'3\.?1', install_dir):
+        assert re.search(name + r'3\.?1\d', install_dir)
+
+    # The following "variables" are used for interpolation in distutils
+    # installation schemes, so it should be fair to treat them as "semi-public",
+    # or at least public enough so we can have a test to make sure they are correct
+    assert cmd.config_vars['py_version'] == '3.10.1'
+    assert cmd.config_vars['py_version_short'] == '3.10'
+    assert cmd.config_vars['py_version_nodot'] == '310'
+
+
+@pytest.mark.xfail(
+    sys.platform == "darwin",
+    reason="https://github.com/pypa/setuptools/pull/4716#issuecomment-2447624418",
+)
+def test_editable_user_and_build_isolation(setup_context, monkeypatch, tmp_path):
+    """`setup.py develop` should honor `--user` even under build isolation"""
+
+    # == Arrange ==
+    # Pretend that build isolation was enabled
+    # e.g pip sets the environment variable PYTHONNOUSERSITE=1
+    monkeypatch.setattr('site.ENABLE_USER_SITE', False)
+
+    # Patching $HOME for 2 reasons:
+    # 1. setuptools/command/easy_install.py:create_home_path
+    #    tries creating directories in $HOME.
+    #    Given::
+    #        self.config_vars['DESTDIRS'] = (
+    #            "/home/user/.pyenv/versions/3.9.10 "
+    #            "/home/user/.pyenv/versions/3.9.10/lib "
+    #            "/home/user/.pyenv/versions/3.9.10/lib/python3.9 "
+    #            "/home/user/.pyenv/versions/3.9.10/lib/python3.9/lib-dynload")
+    #    `create_home_path` will::
+    #        makedirs(
+    #            "/home/user/.pyenv/versions/3.9.10 "
+    #            "/home/user/.pyenv/versions/3.9.10/lib "
+    #            "/home/user/.pyenv/versions/3.9.10/lib/python3.9 "
+    #            "/home/user/.pyenv/versions/3.9.10/lib/python3.9/lib-dynload")
+    #
+    # 2. We are going to force `site` to update site.USER_BASE and site.USER_SITE
+    #    To point inside our new home
+    monkeypatch.setenv('HOME', str(tmp_path / '.home'))
+    monkeypatch.setenv('USERPROFILE', str(tmp_path / '.home'))
+    monkeypatch.setenv('APPDATA', str(tmp_path / '.home'))
+    monkeypatch.setattr('site.USER_BASE', None)
+    monkeypatch.setattr('site.USER_SITE', None)
+    user_site = Path(site.getusersitepackages())
+    user_site.mkdir(parents=True, exist_ok=True)
+
+    sys_prefix = tmp_path / '.sys_prefix'
+    sys_prefix.mkdir(parents=True, exist_ok=True)
+    monkeypatch.setattr('sys.prefix', str(sys_prefix))
+
+    setup_script = (
+        "__import__('setuptools').setup(name='aproj', version=42, packages=[])\n"
+    )
+    (tmp_path / "setup.py").write_text(setup_script, encoding="utf-8")
+
+    # == Sanity check ==
+    assert list(sys_prefix.glob("*")) == []
+    assert list(user_site.glob("*")) == []
+
+    # == Act ==
+    run_setup('setup.py', ['develop', '--user'])
+
+    # == Assert ==
+    # Should not install to sys.prefix
+    assert list(sys_prefix.glob("*")) == []
+    # Should install to user site
+    installed = {f.name for f in user_site.glob("*")}
+    # sometimes easy-install.pth is created and sometimes not
+    installed = installed - {"easy-install.pth"}
+    assert installed == {'aproj.egg-link'}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_editable_install.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_editable_install.py
new file mode 100644
index 0000000000000000000000000000000000000000..038dcadf934af20dbe11dcb13ba324ceb30bf90d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_editable_install.py
@@ -0,0 +1,1289 @@
+from __future__ import annotations
+
+import os
+import platform
+import stat
+import subprocess
+import sys
+from copy import deepcopy
+from importlib import import_module
+from importlib.machinery import EXTENSION_SUFFIXES
+from pathlib import Path
+from textwrap import dedent
+from typing import Any
+from unittest.mock import Mock
+from uuid import uuid4
+
+import jaraco.envs
+import jaraco.path
+import pytest
+from path import Path as _Path
+
+from setuptools._importlib import resources as importlib_resources
+from setuptools.command.editable_wheel import (
+    _DebuggingTips,
+    _encode_pth,
+    _find_namespaces,
+    _find_package_roots,
+    _find_virtual_namespaces,
+    _finder_template,
+    _LinkTree,
+    _TopLevelFinder,
+    editable_wheel,
+)
+from setuptools.dist import Distribution
+from setuptools.extension import Extension
+from setuptools.warnings import SetuptoolsDeprecationWarning
+
+from . import contexts, namespaces
+
+from distutils.core import run_setup
+
+
+@pytest.fixture(params=["strict", "lenient"])
+def editable_opts(request):
+    if request.param == "strict":
+        return ["--config-settings", "editable-mode=strict"]
+    return []
+
+
+EXAMPLE = {
+    'pyproject.toml': dedent(
+        """\
+        [build-system]
+        requires = ["setuptools"]
+        build-backend = "setuptools.build_meta"
+
+        [project]
+        name = "mypkg"
+        version = "3.14159"
+        license = {text = "MIT"}
+        description = "This is a Python package"
+        dynamic = ["readme"]
+        classifiers = [
+            "Development Status :: 5 - Production/Stable",
+            "Intended Audience :: Developers"
+        ]
+        urls = {Homepage = "https://github.com"}
+
+        [tool.setuptools]
+        package-dir = {"" = "src"}
+        packages = {find = {where = ["src"]}}
+        license-files = ["LICENSE*"]
+
+        [tool.setuptools.dynamic]
+        readme = {file = "README.rst"}
+
+        [tool.distutils.egg_info]
+        tag-build = ".post0"
+        """
+    ),
+    "MANIFEST.in": dedent(
+        """\
+        global-include *.py *.txt
+        global-exclude *.py[cod]
+        prune dist
+        prune build
+        """
+    ).strip(),
+    "README.rst": "This is a ``README``",
+    "LICENSE.txt": "---- placeholder MIT license ----",
+    "src": {
+        "mypkg": {
+            "__init__.py": dedent(
+                """\
+                import sys
+                from importlib.metadata import PackageNotFoundError, version
+
+                try:
+                    __version__ = version(__name__)
+                except PackageNotFoundError:
+                    __version__ = "unknown"
+                """
+            ),
+            "__main__.py": dedent(
+                """\
+                from importlib.resources import read_text
+                from . import __version__, __name__ as parent
+                from .mod import x
+
+                data = read_text(parent, "data.txt")
+                print(__version__, data, x)
+                """
+            ),
+            "mod.py": "x = ''",
+            "data.txt": "Hello World",
+        }
+    },
+}
+
+
+SETUP_SCRIPT_STUB = "__import__('setuptools').setup()"
+
+
+@pytest.mark.xfail(sys.platform == "darwin", reason="pypa/setuptools#4328")
+@pytest.mark.parametrize(
+    "files",
+    [
+        {**EXAMPLE, "setup.py": SETUP_SCRIPT_STUB},
+        EXAMPLE,  # No setup.py script
+    ],
+)
+def test_editable_with_pyproject(tmp_path, venv, files, editable_opts):
+    project = tmp_path / "mypkg"
+    project.mkdir()
+    jaraco.path.build(files, prefix=project)
+
+    cmd = [
+        "python",
+        "-m",
+        "pip",
+        "install",
+        "--no-build-isolation",  # required to force current version of setuptools
+        "-e",
+        str(project),
+        *editable_opts,
+    ]
+    print(venv.run(cmd))
+
+    cmd = ["python", "-m", "mypkg"]
+    assert venv.run(cmd).strip() == "3.14159.post0 Hello World"
+
+    (project / "src/mypkg/data.txt").write_text("foobar", encoding="utf-8")
+    (project / "src/mypkg/mod.py").write_text("x = 42", encoding="utf-8")
+    assert venv.run(cmd).strip() == "3.14159.post0 foobar 42"
+
+
+def test_editable_with_flat_layout(tmp_path, venv, editable_opts):
+    files = {
+        "mypkg": {
+            "pyproject.toml": dedent(
+                """\
+                [build-system]
+                requires = ["setuptools", "wheel"]
+                build-backend = "setuptools.build_meta"
+
+                [project]
+                name = "mypkg"
+                version = "3.14159"
+
+                [tool.setuptools]
+                packages = ["pkg"]
+                py-modules = ["mod"]
+                """
+            ),
+            "pkg": {"__init__.py": "a = 4"},
+            "mod.py": "b = 2",
+        },
+    }
+    jaraco.path.build(files, prefix=tmp_path)
+    project = tmp_path / "mypkg"
+
+    cmd = [
+        "python",
+        "-m",
+        "pip",
+        "install",
+        "--no-build-isolation",  # required to force current version of setuptools
+        "-e",
+        str(project),
+        *editable_opts,
+    ]
+    print(venv.run(cmd))
+    cmd = ["python", "-c", "import pkg, mod; print(pkg.a, mod.b)"]
+    assert venv.run(cmd).strip() == "4 2"
+
+
+def test_editable_with_single_module(tmp_path, venv, editable_opts):
+    files = {
+        "mypkg": {
+            "pyproject.toml": dedent(
+                """\
+                [build-system]
+                requires = ["setuptools", "wheel"]
+                build-backend = "setuptools.build_meta"
+
+                [project]
+                name = "mod"
+                version = "3.14159"
+
+                [tool.setuptools]
+                py-modules = ["mod"]
+                """
+            ),
+            "mod.py": "b = 2",
+        },
+    }
+    jaraco.path.build(files, prefix=tmp_path)
+    project = tmp_path / "mypkg"
+
+    cmd = [
+        "python",
+        "-m",
+        "pip",
+        "install",
+        "--no-build-isolation",  # required to force current version of setuptools
+        "-e",
+        str(project),
+        *editable_opts,
+    ]
+    print(venv.run(cmd))
+    cmd = ["python", "-c", "import mod; print(mod.b)"]
+    assert venv.run(cmd).strip() == "2"
+
+
+class TestLegacyNamespaces:
+    # legacy => pkg_resources.declare_namespace(...) + setup(namespace_packages=...)
+
+    def test_nspkg_file_is_unique(self, tmp_path, monkeypatch):
+        deprecation = pytest.warns(
+            SetuptoolsDeprecationWarning, match=".*namespace_packages parameter.*"
+        )
+        installation_dir = tmp_path / ".installation_dir"
+        installation_dir.mkdir()
+        examples = (
+            "myns.pkgA",
+            "myns.pkgB",
+            "myns.n.pkgA",
+            "myns.n.pkgB",
+        )
+
+        for name in examples:
+            pkg = namespaces.build_namespace_package(tmp_path, name, version="42")
+            with deprecation, monkeypatch.context() as ctx:
+                ctx.chdir(pkg)
+                dist = run_setup("setup.py", stop_after="config")
+                cmd = editable_wheel(dist)
+                cmd.finalize_options()
+                editable_name = cmd.get_finalized_command("dist_info").name
+                cmd._install_namespaces(installation_dir, editable_name)
+
+        files = list(installation_dir.glob("*-nspkg.pth"))
+        assert len(files) == len(examples)
+
+    @pytest.mark.parametrize(
+        "impl",
+        (
+            "pkg_resources",
+            #  "pkgutil",  => does not work
+        ),
+    )
+    @pytest.mark.parametrize("ns", ("myns.n",))
+    def test_namespace_package_importable(
+        self, venv, tmp_path, ns, impl, editable_opts
+    ):
+        """
+        Installing two packages sharing the same namespace, one installed
+        naturally using pip or `--single-version-externally-managed`
+        and the other installed in editable mode should leave the namespace
+        intact and both packages reachable by import.
+        (Ported from test_develop).
+        """
+        build_system = """\
+        [build-system]
+        requires = ["setuptools"]
+        build-backend = "setuptools.build_meta"
+        """
+        pkg_A = namespaces.build_namespace_package(tmp_path, f"{ns}.pkgA", impl=impl)
+        pkg_B = namespaces.build_namespace_package(tmp_path, f"{ns}.pkgB", impl=impl)
+        (pkg_A / "pyproject.toml").write_text(build_system, encoding="utf-8")
+        (pkg_B / "pyproject.toml").write_text(build_system, encoding="utf-8")
+        # use pip to install to the target directory
+        opts = editable_opts[:]
+        opts.append("--no-build-isolation")  # force current version of setuptools
+        venv.run(["python", "-m", "pip", "install", str(pkg_A), *opts])
+        venv.run(["python", "-m", "pip", "install", "-e", str(pkg_B), *opts])
+        venv.run(["python", "-c", f"import {ns}.pkgA; import {ns}.pkgB"])
+        # additionally ensure that pkg_resources import works
+        venv.run(["python", "-c", "import pkg_resources"])
+
+
+class TestPep420Namespaces:
+    def test_namespace_package_importable(self, venv, tmp_path, editable_opts):
+        """
+        Installing two packages sharing the same namespace, one installed
+        normally using pip and the other installed in editable mode
+        should allow importing both packages.
+        """
+        pkg_A = namespaces.build_pep420_namespace_package(tmp_path, 'myns.n.pkgA')
+        pkg_B = namespaces.build_pep420_namespace_package(tmp_path, 'myns.n.pkgB')
+        # use pip to install to the target directory
+        opts = editable_opts[:]
+        opts.append("--no-build-isolation")  # force current version of setuptools
+        venv.run(["python", "-m", "pip", "install", str(pkg_A), *opts])
+        venv.run(["python", "-m", "pip", "install", "-e", str(pkg_B), *opts])
+        venv.run(["python", "-c", "import myns.n.pkgA; import myns.n.pkgB"])
+
+    def test_namespace_created_via_package_dir(self, venv, tmp_path, editable_opts):
+        """Currently users can create a namespace by tweaking `package_dir`"""
+        files = {
+            "pkgA": {
+                "pyproject.toml": dedent(
+                    """\
+                    [build-system]
+                    requires = ["setuptools", "wheel"]
+                    build-backend = "setuptools.build_meta"
+
+                    [project]
+                    name = "pkgA"
+                    version = "3.14159"
+
+                    [tool.setuptools]
+                    package-dir = {"myns.n.pkgA" = "src"}
+                    """
+                ),
+                "src": {"__init__.py": "a = 1"},
+            },
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+        pkg_A = tmp_path / "pkgA"
+        pkg_B = namespaces.build_pep420_namespace_package(tmp_path, 'myns.n.pkgB')
+        pkg_C = namespaces.build_pep420_namespace_package(tmp_path, 'myns.n.pkgC')
+
+        # use pip to install to the target directory
+        opts = editable_opts[:]
+        opts.append("--no-build-isolation")  # force current version of setuptools
+        venv.run(["python", "-m", "pip", "install", str(pkg_A), *opts])
+        venv.run(["python", "-m", "pip", "install", "-e", str(pkg_B), *opts])
+        venv.run(["python", "-m", "pip", "install", "-e", str(pkg_C), *opts])
+        venv.run(["python", "-c", "from myns.n import pkgA, pkgB, pkgC"])
+
+    def test_namespace_accidental_config_in_lenient_mode(self, venv, tmp_path):
+        """Sometimes users might specify an ``include`` pattern that ignores parent
+        packages. In a normal installation this would ignore all modules inside the
+        parent packages, and make them namespaces (reported in issue #3504),
+        so the editable mode should preserve this behaviour.
+        """
+        files = {
+            "pkgA": {
+                "pyproject.toml": dedent(
+                    """\
+                    [build-system]
+                    requires = ["setuptools", "wheel"]
+                    build-backend = "setuptools.build_meta"
+
+                    [project]
+                    name = "pkgA"
+                    version = "3.14159"
+
+                    [tool.setuptools]
+                    packages.find.include = ["mypkg.*"]
+                    """
+                ),
+                "mypkg": {
+                    "__init__.py": "",
+                    "other.py": "b = 1",
+                    "n": {
+                        "__init__.py": "",
+                        "pkgA.py": "a = 1",
+                    },
+                },
+                "MANIFEST.in": EXAMPLE["MANIFEST.in"],
+            },
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+        pkg_A = tmp_path / "pkgA"
+
+        # use pip to install to the target directory
+        opts = ["--no-build-isolation"]  # force current version of setuptools
+        venv.run(["python", "-m", "pip", "-v", "install", "-e", str(pkg_A), *opts])
+        out = venv.run(["python", "-c", "from mypkg.n import pkgA; print(pkgA.a)"])
+        assert out.strip() == "1"
+        cmd = """\
+        try:
+            import mypkg.other
+        except ImportError:
+            print("mypkg.other not defined")
+        """
+        out = venv.run(["python", "-c", dedent(cmd)])
+        assert "mypkg.other not defined" in out
+
+
+def test_editable_with_prefix(tmp_path, sample_project, editable_opts):
+    """
+    Editable install to a prefix should be discoverable.
+    """
+    prefix = tmp_path / 'prefix'
+
+    # figure out where pip will likely install the package
+    site_packages_all = [
+        prefix / Path(path).relative_to(sys.prefix)
+        for path in sys.path
+        if 'site-packages' in path and path.startswith(sys.prefix)
+    ]
+
+    for sp in site_packages_all:
+        sp.mkdir(parents=True)
+
+    # install workaround
+    _addsitedirs(site_packages_all)
+
+    env = dict(os.environ, PYTHONPATH=os.pathsep.join(map(str, site_packages_all)))
+    cmd = [
+        sys.executable,
+        '-m',
+        'pip',
+        'install',
+        '--editable',
+        str(sample_project),
+        '--prefix',
+        str(prefix),
+        '--no-build-isolation',
+        *editable_opts,
+    ]
+    subprocess.check_call(cmd, env=env)
+
+    # now run 'sample' with the prefix on the PYTHONPATH
+    bin = 'Scripts' if platform.system() == 'Windows' else 'bin'
+    exe = prefix / bin / 'sample'
+    subprocess.check_call([exe], env=env)
+
+
+class TestFinderTemplate:
+    """This test focus in getting a particular implementation detail right.
+    If at some point in time the implementation is changed for something different,
+    this test can be modified or even excluded.
+    """
+
+    def install_finder(self, finder):
+        loc = {}
+        exec(finder, loc, loc)
+        loc["install"]()
+
+    def test_packages(self, tmp_path):
+        files = {
+            "src1": {
+                "pkg1": {
+                    "__init__.py": "",
+                    "subpkg": {"mod1.py": "a = 42"},
+                },
+            },
+            "src2": {"mod2.py": "a = 43"},
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {
+            "pkg1": str(tmp_path / "src1/pkg1"),
+            "mod2": str(tmp_path / "src2/mod2"),
+        }
+        template = _finder_template(str(uuid4()), mapping, {})
+
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in ("pkg1", "pkg1.subpkg", "pkg1.subpkg.mod1", "mod2"):
+                sys.modules.pop(mod, None)
+
+            self.install_finder(template)
+            mod1 = import_module("pkg1.subpkg.mod1")
+            mod2 = import_module("mod2")
+            subpkg = import_module("pkg1.subpkg")
+
+            assert mod1.a == 42
+            assert mod2.a == 43
+            expected = str((tmp_path / "src1/pkg1/subpkg").resolve())
+            assert_path(subpkg, expected)
+
+    def test_namespace(self, tmp_path):
+        files = {"pkg": {"__init__.py": "a = 13", "text.txt": "abc"}}
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {"ns.othername": str(tmp_path / "pkg")}
+        namespaces = {"ns": []}
+
+        template = _finder_template(str(uuid4()), mapping, namespaces)
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in ("ns", "ns.othername"):
+                sys.modules.pop(mod, None)
+
+            self.install_finder(template)
+            pkg = import_module("ns.othername")
+            text = importlib_resources.files(pkg) / "text.txt"
+
+            expected = str((tmp_path / "pkg").resolve())
+            assert_path(pkg, expected)
+            assert pkg.a == 13
+
+            # Make sure resources can also be found
+            assert text.read_text(encoding="utf-8") == "abc"
+
+    def test_combine_namespaces(self, tmp_path):
+        files = {
+            "src1": {"ns": {"pkg1": {"__init__.py": "a = 13"}}},
+            "src2": {"ns": {"mod2.py": "b = 37"}},
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {
+            "ns.pkgA": str(tmp_path / "src1/ns/pkg1"),
+            "ns": str(tmp_path / "src2/ns"),
+        }
+        namespaces_ = {"ns": [str(tmp_path / "src1"), str(tmp_path / "src2")]}
+        template = _finder_template(str(uuid4()), mapping, namespaces_)
+
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in ("ns", "ns.pkgA", "ns.mod2"):
+                sys.modules.pop(mod, None)
+
+            self.install_finder(template)
+            pkgA = import_module("ns.pkgA")
+            mod2 = import_module("ns.mod2")
+
+            expected = str((tmp_path / "src1/ns/pkg1").resolve())
+            assert_path(pkgA, expected)
+            assert pkgA.a == 13
+            assert mod2.b == 37
+
+    def test_combine_namespaces_nested(self, tmp_path):
+        """
+        Users may attempt to combine namespace packages in a nested way via
+        ``package_dir`` as shown in pypa/setuptools#4248.
+        """
+
+        files = {
+            "src": {"my_package": {"my_module.py": "a = 13"}},
+            "src2": {"my_package2": {"my_module2.py": "b = 37"}},
+        }
+
+        stack = jaraco.path.DirectoryStack()
+        with stack.context(tmp_path):
+            jaraco.path.build(files)
+            attrs = {
+                "script_name": "%PEP 517%",
+                "package_dir": {
+                    "different_name": "src/my_package",
+                    "different_name.subpkg": "src2/my_package2",
+                },
+                "packages": ["different_name", "different_name.subpkg"],
+            }
+            dist = Distribution(attrs)
+            finder = _TopLevelFinder(dist, str(uuid4()))
+            code = next(v for k, v in finder.get_implementation() if k.endswith(".py"))
+
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in attrs["packages"]:
+                sys.modules.pop(mod, None)
+
+            self.install_finder(code)
+            mod1 = import_module("different_name.my_module")
+            mod2 = import_module("different_name.subpkg.my_module2")
+
+            expected = str((tmp_path / "src/my_package/my_module.py").resolve())
+            assert str(Path(mod1.__file__).resolve()) == expected
+
+            expected = str((tmp_path / "src2/my_package2/my_module2.py").resolve())
+            assert str(Path(mod2.__file__).resolve()) == expected
+
+            assert mod1.a == 13
+            assert mod2.b == 37
+
+    def test_dynamic_path_computation(self, tmp_path):
+        # Follows the example in PEP 420
+        files = {
+            "project1": {"parent": {"child": {"one.py": "x = 1"}}},
+            "project2": {"parent": {"child": {"two.py": "x = 2"}}},
+            "project3": {"parent": {"child": {"three.py": "x = 3"}}},
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+        mapping = {}
+        namespaces_ = {"parent": [str(tmp_path / "project1/parent")]}
+        template = _finder_template(str(uuid4()), mapping, namespaces_)
+
+        mods = (f"parent.child.{name}" for name in ("one", "two", "three"))
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in ("parent", "parent.child", "parent.child", *mods):
+                sys.modules.pop(mod, None)
+
+            self.install_finder(template)
+
+            one = import_module("parent.child.one")
+            assert one.x == 1
+
+            with pytest.raises(ImportError):
+                import_module("parent.child.two")
+
+            sys.path.append(str(tmp_path / "project2"))
+            two = import_module("parent.child.two")
+            assert two.x == 2
+
+            with pytest.raises(ImportError):
+                import_module("parent.child.three")
+
+            sys.path.append(str(tmp_path / "project3"))
+            three = import_module("parent.child.three")
+            assert three.x == 3
+
+    def test_no_recursion(self, tmp_path):
+        # See issue #3550
+        files = {
+            "pkg": {
+                "__init__.py": "from . import pkg",
+            },
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {
+            "pkg": str(tmp_path / "pkg"),
+        }
+        template = _finder_template(str(uuid4()), mapping, {})
+
+        with contexts.save_paths(), contexts.save_sys_modules():
+            sys.modules.pop("pkg", None)
+
+            self.install_finder(template)
+            with pytest.raises(ImportError, match="pkg"):
+                import_module("pkg")
+
+    def test_similar_name(self, tmp_path):
+        files = {
+            "foo": {
+                "__init__.py": "",
+                "bar": {
+                    "__init__.py": "",
+                },
+            },
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {
+            "foo": str(tmp_path / "foo"),
+        }
+        template = _finder_template(str(uuid4()), mapping, {})
+
+        with contexts.save_paths(), contexts.save_sys_modules():
+            sys.modules.pop("foo", None)
+            sys.modules.pop("foo.bar", None)
+
+            self.install_finder(template)
+            with pytest.raises(ImportError, match="foobar"):
+                import_module("foobar")
+
+    def test_case_sensitivity(self, tmp_path):
+        files = {
+            "foo": {
+                "__init__.py": "",
+                "lowercase.py": "x = 1",
+                "bar": {
+                    "__init__.py": "",
+                    "lowercase.py": "x = 2",
+                },
+            },
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+        mapping = {
+            "foo": str(tmp_path / "foo"),
+        }
+        template = _finder_template(str(uuid4()), mapping, {})
+        with contexts.save_paths(), contexts.save_sys_modules():
+            sys.modules.pop("foo", None)
+
+            self.install_finder(template)
+            with pytest.raises(ImportError, match="'FOO'"):
+                import_module("FOO")
+
+            with pytest.raises(ImportError, match="'foo\\.LOWERCASE'"):
+                import_module("foo.LOWERCASE")
+
+            with pytest.raises(ImportError, match="'foo\\.bar\\.Lowercase'"):
+                import_module("foo.bar.Lowercase")
+
+            with pytest.raises(ImportError, match="'foo\\.BAR'"):
+                import_module("foo.BAR.lowercase")
+
+            with pytest.raises(ImportError, match="'FOO'"):
+                import_module("FOO.bar.lowercase")
+
+            mod = import_module("foo.lowercase")
+            assert mod.x == 1
+
+            mod = import_module("foo.bar.lowercase")
+            assert mod.x == 2
+
+    def test_namespace_case_sensitivity(self, tmp_path):
+        files = {
+            "pkg": {
+                "__init__.py": "a = 13",
+                "foo": {
+                    "__init__.py": "b = 37",
+                    "bar.py": "c = 42",
+                },
+            },
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {"ns.othername": str(tmp_path / "pkg")}
+        namespaces = {"ns": []}
+
+        template = _finder_template(str(uuid4()), mapping, namespaces)
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in ("ns", "ns.othername"):
+                sys.modules.pop(mod, None)
+
+            self.install_finder(template)
+            pkg = import_module("ns.othername")
+            expected = str((tmp_path / "pkg").resolve())
+            assert_path(pkg, expected)
+            assert pkg.a == 13
+
+            foo = import_module("ns.othername.foo")
+            assert foo.b == 37
+
+            bar = import_module("ns.othername.foo.bar")
+            assert bar.c == 42
+
+            with pytest.raises(ImportError, match="'NS'"):
+                import_module("NS.othername.foo")
+
+            with pytest.raises(ImportError, match="'ns\\.othername\\.FOO\\'"):
+                import_module("ns.othername.FOO")
+
+            with pytest.raises(ImportError, match="'ns\\.othername\\.foo\\.BAR\\'"):
+                import_module("ns.othername.foo.BAR")
+
+    def test_intermediate_packages(self, tmp_path):
+        """
+        The finder should not import ``fullname`` if the intermediate segments
+        don't exist (see pypa/setuptools#4019).
+        """
+        files = {
+            "src": {
+                "mypkg": {
+                    "__init__.py": "",
+                    "config.py": "a = 13",
+                    "helloworld.py": "b = 13",
+                    "components": {
+                        "config.py": "a = 37",
+                    },
+                },
+            }
+        }
+        jaraco.path.build(files, prefix=tmp_path)
+
+        mapping = {"mypkg": str(tmp_path / "src/mypkg")}
+        template = _finder_template(str(uuid4()), mapping, {})
+
+        with contexts.save_paths(), contexts.save_sys_modules():
+            for mod in (
+                "mypkg",
+                "mypkg.config",
+                "mypkg.helloworld",
+                "mypkg.components",
+                "mypkg.components.config",
+                "mypkg.components.helloworld",
+            ):
+                sys.modules.pop(mod, None)
+
+            self.install_finder(template)
+
+            config = import_module("mypkg.components.config")
+            assert config.a == 37
+
+            helloworld = import_module("mypkg.helloworld")
+            assert helloworld.b == 13
+
+            with pytest.raises(ImportError):
+                import_module("mypkg.components.helloworld")
+
+
+def test_pkg_roots(tmp_path):
+    """This test focus in getting a particular implementation detail right.
+    If at some point in time the implementation is changed for something different,
+    this test can be modified or even excluded.
+    """
+    files = {
+        "a": {"b": {"__init__.py": "ab = 1"}, "__init__.py": "a = 1"},
+        "d": {"__init__.py": "d = 1", "e": {"__init__.py": "de = 1"}},
+        "f": {"g": {"h": {"__init__.py": "fgh = 1"}}},
+        "other": {"__init__.py": "abc = 1"},
+        "another": {"__init__.py": "abcxyz = 1"},
+        "yet_another": {"__init__.py": "mnopq = 1"},
+    }
+    jaraco.path.build(files, prefix=tmp_path)
+    package_dir = {
+        "a.b.c": "other",
+        "a.b.c.x.y.z": "another",
+        "m.n.o.p.q": "yet_another",
+    }
+    packages = [
+        "a",
+        "a.b",
+        "a.b.c",
+        "a.b.c.x.y",
+        "a.b.c.x.y.z",
+        "d",
+        "d.e",
+        "f",
+        "f.g",
+        "f.g.h",
+        "m.n.o.p.q",
+    ]
+    roots = _find_package_roots(packages, package_dir, tmp_path)
+    assert roots == {
+        "a": str(tmp_path / "a"),
+        "a.b.c": str(tmp_path / "other"),
+        "a.b.c.x.y.z": str(tmp_path / "another"),
+        "d": str(tmp_path / "d"),
+        "f": str(tmp_path / "f"),
+        "m.n.o.p.q": str(tmp_path / "yet_another"),
+    }
+
+    ns = set(dict(_find_namespaces(packages, roots)))
+    assert ns == {"f", "f.g"}
+
+    ns = set(_find_virtual_namespaces(roots))
+    assert ns == {"a.b", "a.b.c.x", "a.b.c.x.y", "m", "m.n", "m.n.o", "m.n.o.p"}
+
+
+class TestOverallBehaviour:
+    PYPROJECT = """\
+        [build-system]
+        requires = ["setuptools"]
+        build-backend = "setuptools.build_meta"
+
+        [project]
+        name = "mypkg"
+        version = "3.14159"
+        """
+
+    # Any: Would need a TypedDict. Keep it simple for tests
+    FLAT_LAYOUT: dict[str, Any] = {
+        "pyproject.toml": dedent(PYPROJECT),
+        "MANIFEST.in": EXAMPLE["MANIFEST.in"],
+        "otherfile.py": "",
+        "mypkg": {
+            "__init__.py": "",
+            "mod1.py": "var = 42",
+            "subpackage": {
+                "__init__.py": "",
+                "mod2.py": "var = 13",
+                "resource_file.txt": "resource 39",
+            },
+        },
+    }
+
+    EXAMPLES = {
+        "flat-layout": FLAT_LAYOUT,
+        "src-layout": {
+            "pyproject.toml": dedent(PYPROJECT),
+            "MANIFEST.in": EXAMPLE["MANIFEST.in"],
+            "otherfile.py": "",
+            "src": {"mypkg": FLAT_LAYOUT["mypkg"]},
+        },
+        "custom-layout": {
+            "pyproject.toml": dedent(PYPROJECT)
+            + dedent(
+                """\
+                [tool.setuptools]
+                packages = ["mypkg", "mypkg.subpackage"]
+
+                [tool.setuptools.package-dir]
+                "mypkg.subpackage" = "other"
+                """
+            ),
+            "MANIFEST.in": EXAMPLE["MANIFEST.in"],
+            "otherfile.py": "",
+            "mypkg": {
+                "__init__.py": "",
+                "mod1.py": FLAT_LAYOUT["mypkg"]["mod1.py"],
+            },
+            "other": FLAT_LAYOUT["mypkg"]["subpackage"],
+        },
+        "namespace": {
+            "pyproject.toml": dedent(PYPROJECT),
+            "MANIFEST.in": EXAMPLE["MANIFEST.in"],
+            "otherfile.py": "",
+            "src": {
+                "mypkg": {
+                    "mod1.py": FLAT_LAYOUT["mypkg"]["mod1.py"],
+                    "subpackage": FLAT_LAYOUT["mypkg"]["subpackage"],
+                },
+            },
+        },
+    }
+
+    @pytest.mark.xfail(sys.platform == "darwin", reason="pypa/setuptools#4328")
+    @pytest.mark.parametrize("layout", EXAMPLES.keys())
+    def test_editable_install(self, tmp_path, venv, layout, editable_opts):
+        project, _ = install_project(
+            "mypkg", venv, tmp_path, self.EXAMPLES[layout], *editable_opts
+        )
+
+        # Ensure stray files are not importable
+        cmd_import_error = """\
+        try:
+            import otherfile
+        except ImportError as ex:
+            print(ex)
+        """
+        out = venv.run(["python", "-c", dedent(cmd_import_error)])
+        assert "No module named 'otherfile'" in out
+
+        # Ensure the modules are importable
+        cmd_get_vars = """\
+        import mypkg, mypkg.mod1, mypkg.subpackage.mod2
+        print(mypkg.mod1.var, mypkg.subpackage.mod2.var)
+        """
+        out = venv.run(["python", "-c", dedent(cmd_get_vars)])
+        assert "42 13" in out
+
+        # Ensure resources are reachable
+        cmd_get_resource = """\
+        import mypkg.subpackage
+        from setuptools._importlib import resources as importlib_resources
+        text = importlib_resources.files(mypkg.subpackage) / "resource_file.txt"
+        print(text.read_text(encoding="utf-8"))
+        """
+        out = venv.run(["python", "-c", dedent(cmd_get_resource)])
+        assert "resource 39" in out
+
+        # Ensure files are editable
+        mod1 = next(project.glob("**/mod1.py"))
+        mod2 = next(project.glob("**/mod2.py"))
+        resource_file = next(project.glob("**/resource_file.txt"))
+
+        mod1.write_text("var = 17", encoding="utf-8")
+        mod2.write_text("var = 781", encoding="utf-8")
+        resource_file.write_text("resource 374", encoding="utf-8")
+
+        out = venv.run(["python", "-c", dedent(cmd_get_vars)])
+        assert "42 13" not in out
+        assert "17 781" in out
+
+        out = venv.run(["python", "-c", dedent(cmd_get_resource)])
+        assert "resource 39" not in out
+        assert "resource 374" in out
+
+
+class TestLinkTree:
+    FILES = deepcopy(TestOverallBehaviour.EXAMPLES["src-layout"])
+    FILES["pyproject.toml"] += dedent(
+        """\
+        [tool.setuptools]
+        # Temporary workaround: both `include-package-data` and `package-data` configs
+        # can be removed after #3260 is fixed.
+        include-package-data = false
+        package-data = {"*" = ["*.txt"]}
+
+        [tool.setuptools.packages.find]
+        where = ["src"]
+        exclude = ["*.subpackage*"]
+        """
+    )
+    FILES["src"]["mypkg"]["resource.not_in_manifest"] = "abc"
+
+    def test_generated_tree(self, tmp_path):
+        jaraco.path.build(self.FILES, prefix=tmp_path)
+
+        with _Path(tmp_path):
+            name = "mypkg-3.14159"
+            dist = Distribution({"script_name": "%PEP 517%"})
+            dist.parse_config_files()
+
+            wheel = Mock()
+            aux = tmp_path / ".aux"
+            build = tmp_path / ".build"
+            aux.mkdir()
+            build.mkdir()
+
+            build_py = dist.get_command_obj("build_py")
+            build_py.editable_mode = True
+            build_py.build_lib = str(build)
+            build_py.ensure_finalized()
+            outputs = build_py.get_outputs()
+            output_mapping = build_py.get_output_mapping()
+
+            make_tree = _LinkTree(dist, name, aux, build)
+            make_tree(wheel, outputs, output_mapping)
+
+            mod1 = next(aux.glob("**/mod1.py"))
+            expected = tmp_path / "src/mypkg/mod1.py"
+            assert_link_to(mod1, expected)
+
+            assert next(aux.glob("**/subpackage"), None) is None
+            assert next(aux.glob("**/mod2.py"), None) is None
+            assert next(aux.glob("**/resource_file.txt"), None) is None
+
+            assert next(aux.glob("**/resource.not_in_manifest"), None) is None
+
+    def test_strict_install(self, tmp_path, venv):
+        opts = ["--config-settings", "editable-mode=strict"]
+        install_project("mypkg", venv, tmp_path, self.FILES, *opts)
+
+        out = venv.run(["python", "-c", "import mypkg.mod1; print(mypkg.mod1.var)"])
+        assert "42" in out
+
+        # Ensure packages excluded from distribution are not importable
+        cmd_import_error = """\
+        try:
+            from mypkg import subpackage
+        except ImportError as ex:
+            print(ex)
+        """
+        out = venv.run(["python", "-c", dedent(cmd_import_error)])
+        assert "cannot import name 'subpackage'" in out
+
+        # Ensure resource files excluded from distribution are not reachable
+        cmd_get_resource = """\
+        import mypkg
+        from setuptools._importlib import resources as importlib_resources
+        try:
+            text = importlib_resources.files(mypkg) / "resource.not_in_manifest"
+            print(text.read_text(encoding="utf-8"))
+        except FileNotFoundError as ex:
+            print(ex)
+        """
+        out = venv.run(["python", "-c", dedent(cmd_get_resource)])
+        assert "No such file or directory" in out
+        assert "resource.not_in_manifest" in out
+
+
+@pytest.mark.filterwarnings("ignore:.*compat.*:setuptools.SetuptoolsDeprecationWarning")
+def test_compat_install(tmp_path, venv):
+    # TODO: Remove `compat` after Dec/2022.
+    opts = ["--config-settings", "editable-mode=compat"]
+    files = TestOverallBehaviour.EXAMPLES["custom-layout"]
+    install_project("mypkg", venv, tmp_path, files, *opts)
+
+    out = venv.run(["python", "-c", "import mypkg.mod1; print(mypkg.mod1.var)"])
+    assert "42" in out
+
+    expected_path = comparable_path(str(tmp_path))
+
+    # Compatible behaviour will make spurious modules and excluded
+    # files importable directly from the original path
+    for cmd in (
+        "import otherfile; print(otherfile)",
+        "import other; print(other)",
+        "import mypkg; print(mypkg)",
+    ):
+        out = comparable_path(venv.run(["python", "-c", cmd]))
+        assert expected_path in out
+
+    # Compatible behaviour will not consider custom mappings
+    cmd = """\
+    try:
+        from mypkg import subpackage;
+    except ImportError as ex:
+        print(ex)
+    """
+    out = venv.run(["python", "-c", dedent(cmd)])
+    assert "cannot import name 'subpackage'" in out
+
+
+def test_pbr_integration(tmp_path, venv, editable_opts):
+    """Ensure editable installs work with pbr, issue #3500"""
+    files = {
+        "pyproject.toml": dedent(
+            """\
+            [build-system]
+            requires = ["setuptools"]
+            build-backend = "setuptools.build_meta"
+            """
+        ),
+        "setup.py": dedent(
+            """\
+            __import__('setuptools').setup(
+                pbr=True,
+                setup_requires=["pbr"],
+            )
+            """
+        ),
+        "setup.cfg": dedent(
+            """\
+            [metadata]
+            name = mypkg
+
+            [files]
+            packages =
+                mypkg
+            """
+        ),
+        "mypkg": {
+            "__init__.py": "",
+            "hello.py": "print('Hello world!')",
+        },
+        "other": {"test.txt": "Another file in here."},
+    }
+    venv.run(["python", "-m", "pip", "install", "pbr"])
+
+    with contexts.environment(PBR_VERSION="0.42"):
+        install_project("mypkg", venv, tmp_path, files, *editable_opts)
+
+    out = venv.run(["python", "-c", "import mypkg.hello"])
+    assert "Hello world!" in out
+
+
+class TestCustomBuildPy:
+    """
+    Issue #3501 indicates that some plugins/customizations might rely on:
+
+    1. ``build_py`` not running
+    2. ``build_py`` always copying files to ``build_lib``
+
+    During the transition period setuptools should prevent potential errors from
+    happening due to those assumptions.
+    """
+
+    # TODO: Remove tests after _run_build_steps is removed.
+
+    FILES = {
+        **TestOverallBehaviour.EXAMPLES["flat-layout"],
+        "setup.py": dedent(
+            """\
+            import pathlib
+            from setuptools import setup
+            from setuptools.command.build_py import build_py as orig
+
+            class my_build_py(orig):
+                def run(self):
+                    super().run()
+                    raise ValueError("TEST_RAISE")
+
+            setup(cmdclass={"build_py": my_build_py})
+            """
+        ),
+    }
+
+    def test_safeguarded_from_errors(self, tmp_path, venv):
+        """Ensure that errors in custom build_py are reported as warnings"""
+        # Warnings should show up
+        _, out = install_project("mypkg", venv, tmp_path, self.FILES)
+        assert "SetuptoolsDeprecationWarning" in out
+        assert "ValueError: TEST_RAISE" in out
+        # but installation should be successful
+        out = venv.run(["python", "-c", "import mypkg.mod1; print(mypkg.mod1.var)"])
+        assert "42" in out
+
+
+class TestCustomBuildWheel:
+    def install_custom_build_wheel(self, dist):
+        bdist_wheel_cls = dist.get_command_class("bdist_wheel")
+
+        class MyBdistWheel(bdist_wheel_cls):
+            def get_tag(self):
+                # In issue #3513, we can see that some extensions may try to access
+                # the `plat_name` property in bdist_wheel
+                if self.plat_name.startswith("macosx-"):
+                    _ = "macOS platform"
+                return super().get_tag()
+
+        dist.cmdclass["bdist_wheel"] = MyBdistWheel
+
+    def test_access_plat_name(self, tmpdir_cwd):
+        # Even when a custom bdist_wheel tries to access plat_name the build should
+        # be successful
+        jaraco.path.build({"module.py": "x = 42"})
+        dist = Distribution()
+        dist.script_name = "setup.py"
+        dist.set_defaults()
+        self.install_custom_build_wheel(dist)
+        cmd = editable_wheel(dist)
+        cmd.ensure_finalized()
+        cmd.run()
+        wheel_file = str(next(Path().glob('dist/*.whl')))
+        assert "editable" in wheel_file
+
+
+class TestCustomBuildExt:
+    def install_custom_build_ext_distutils(self, dist):
+        from distutils.command.build_ext import build_ext as build_ext_cls
+
+        class MyBuildExt(build_ext_cls):
+            pass
+
+        dist.cmdclass["build_ext"] = MyBuildExt
+
+    @pytest.mark.skipif(
+        sys.platform != "linux", reason="compilers may fail without correct setup"
+    )
+    def test_distutils_leave_inplace_files(self, tmpdir_cwd):
+        jaraco.path.build({"module.c": ""})
+        attrs = {
+            "ext_modules": [Extension("module", ["module.c"])],
+        }
+        dist = Distribution(attrs)
+        dist.script_name = "setup.py"
+        dist.set_defaults()
+        self.install_custom_build_ext_distutils(dist)
+        cmd = editable_wheel(dist)
+        cmd.ensure_finalized()
+        cmd.run()
+        wheel_file = str(next(Path().glob('dist/*.whl')))
+        assert "editable" in wheel_file
+        files = [p for p in Path().glob("module.*") if p.suffix != ".c"]
+        assert len(files) == 1
+        name = files[0].name
+        assert any(name.endswith(ext) for ext in EXTENSION_SUFFIXES)
+
+
+def test_debugging_tips(tmpdir_cwd, monkeypatch):
+    """Make sure to display useful debugging tips to the user."""
+    jaraco.path.build({"module.py": "x = 42"})
+    dist = Distribution()
+    dist.script_name = "setup.py"
+    dist.set_defaults()
+    cmd = editable_wheel(dist)
+    cmd.ensure_finalized()
+
+    SimulatedErr = type("SimulatedErr", (Exception,), {})
+    simulated_failure = Mock(side_effect=SimulatedErr())
+    monkeypatch.setattr(cmd, "get_finalized_command", simulated_failure)
+
+    expected_msg = "following steps are recommended to help debug"
+    with pytest.raises(SimulatedErr), pytest.warns(_DebuggingTips, match=expected_msg):
+        cmd.run()
+
+
+@pytest.mark.filterwarnings("error")
+def test_encode_pth():
+    """Ensure _encode_pth function does not produce encoding warnings"""
+    content = _encode_pth("tkmilan_ç_utf8")  # no warnings (would be turned into errors)
+    assert isinstance(content, bytes)
+
+
+def install_project(name, venv, tmp_path, files, *opts):
+    project = tmp_path / name
+    project.mkdir()
+    jaraco.path.build(files, prefix=project)
+    opts = [*opts, "--no-build-isolation"]  # force current version of setuptools
+    out = venv.run(
+        ["python", "-m", "pip", "-v", "install", "-e", str(project), *opts],
+        stderr=subprocess.STDOUT,
+    )
+    return project, out
+
+
+def _addsitedirs(new_dirs):
+    """To use this function, it is necessary to insert new_dir in front of sys.path.
+    The Python process will try to import a ``sitecustomize`` module on startup.
+    If we manipulate sys.path/PYTHONPATH, we can force it to run our code,
+    which invokes ``addsitedir`` and ensure ``.pth`` files are loaded.
+    """
+    content = '\n'.join(
+        ("import site",)
+        + tuple(f"site.addsitedir({os.fspath(new_dir)!r})" for new_dir in new_dirs)
+    )
+    (new_dirs[0] / "sitecustomize.py").write_text(content, encoding="utf-8")
+
+
+# ---- Assertion Helpers ----
+
+
+def assert_path(pkg, expected):
+    # __path__ is not guaranteed to exist, so we have to account for that
+    if pkg.__path__:
+        path = next(iter(pkg.__path__), None)
+        if path:
+            assert str(Path(path).resolve()) == expected
+
+
+def assert_link_to(file: Path, other: Path) -> None:
+    if file.is_symlink():
+        assert str(file.resolve()) == str(other.resolve())
+    else:
+        file_stat = file.stat()
+        other_stat = other.stat()
+        assert file_stat[stat.ST_INO] == other_stat[stat.ST_INO]
+        assert file_stat[stat.ST_DEV] == other_stat[stat.ST_DEV]
+
+
+def comparable_path(str_with_path: str) -> str:
+    return str_with_path.lower().replace(os.sep, "/").replace("//", "/")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_egg_info.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_egg_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..528e2c13d8513727794cf65272aa20ce33e87d9d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_egg_info.py
@@ -0,0 +1,1305 @@
+from __future__ import annotations
+
+import ast
+import glob
+import os
+import re
+import stat
+import sys
+import time
+from pathlib import Path
+from unittest import mock
+
+import pytest
+from jaraco import path
+
+from setuptools import errors
+from setuptools.command.egg_info import egg_info, manifest_maker, write_entries
+from setuptools.dist import Distribution
+
+from . import contexts, environment
+from .textwrap import DALS
+
+
+class Environment(str):
+    pass
+
+
+@pytest.fixture
+def env():
+    with contexts.tempdir(prefix='setuptools-test.') as env_dir:
+        env = Environment(env_dir)
+        os.chmod(env_dir, stat.S_IRWXU)
+        subs = 'home', 'lib', 'scripts', 'data', 'egg-base'
+        env.paths = dict((dirname, os.path.join(env_dir, dirname)) for dirname in subs)
+        list(map(os.mkdir, env.paths.values()))
+        path.build({
+            env.paths['home']: {
+                '.pydistutils.cfg': DALS(
+                    """
+                [egg_info]
+                egg-base = {egg-base}
+                """.format(**env.paths)
+                )
+            }
+        })
+        yield env
+
+
+class TestEggInfo:
+    setup_script = DALS(
+        """
+        from setuptools import setup
+
+        setup(
+            name='foo',
+            py_modules=['hello'],
+            entry_points={'console_scripts': ['hi = hello.run']},
+            zip_safe=False,
+        )
+        """
+    )
+
+    def _create_project(self):
+        path.build({
+            'setup.py': self.setup_script,
+            'hello.py': DALS(
+                """
+                def run():
+                    print('hello')
+                """
+            ),
+        })
+
+    @staticmethod
+    def _extract_mv_version(pkg_info_lines: list[str]) -> tuple[int, int]:
+        version_str = pkg_info_lines[0].split(' ')[1]
+        major, minor = map(int, version_str.split('.')[:2])
+        return major, minor
+
+    def test_egg_info_save_version_info_setup_empty(self, tmpdir_cwd, env):
+        """
+        When the egg_info section is empty or not present, running
+        save_version_info should add the settings to the setup.cfg
+        in a deterministic order.
+        """
+        setup_cfg = os.path.join(env.paths['home'], 'setup.cfg')
+        dist = Distribution()
+        ei = egg_info(dist)
+        ei.initialize_options()
+        ei.save_version_info(setup_cfg)
+
+        with open(setup_cfg, 'r', encoding="utf-8") as f:
+            content = f.read()
+
+        assert '[egg_info]' in content
+        assert 'tag_build =' in content
+        assert 'tag_date = 0' in content
+
+        expected_order = (
+            'tag_build',
+            'tag_date',
+        )
+
+        self._validate_content_order(content, expected_order)
+
+    @staticmethod
+    def _validate_content_order(content, expected):
+        """
+        Assert that the strings in expected appear in content
+        in order.
+        """
+        pattern = '.*'.join(expected)
+        flags = re.MULTILINE | re.DOTALL
+        assert re.search(pattern, content, flags)
+
+    def test_egg_info_save_version_info_setup_defaults(self, tmpdir_cwd, env):
+        """
+        When running save_version_info on an existing setup.cfg
+        with the 'default' values present from a previous run,
+        the file should remain unchanged.
+        """
+        setup_cfg = os.path.join(env.paths['home'], 'setup.cfg')
+        path.build({
+            setup_cfg: DALS(
+                """
+            [egg_info]
+            tag_build =
+            tag_date = 0
+            """
+            ),
+        })
+        dist = Distribution()
+        ei = egg_info(dist)
+        ei.initialize_options()
+        ei.save_version_info(setup_cfg)
+
+        with open(setup_cfg, 'r', encoding="utf-8") as f:
+            content = f.read()
+
+        assert '[egg_info]' in content
+        assert 'tag_build =' in content
+        assert 'tag_date = 0' in content
+
+        expected_order = (
+            'tag_build',
+            'tag_date',
+        )
+
+        self._validate_content_order(content, expected_order)
+
+    def test_expected_files_produced(self, tmpdir_cwd, env):
+        self._create_project()
+
+        self._run_egg_info_command(tmpdir_cwd, env)
+        actual = os.listdir('foo.egg-info')
+
+        expected = [
+            'PKG-INFO',
+            'SOURCES.txt',
+            'dependency_links.txt',
+            'entry_points.txt',
+            'not-zip-safe',
+            'top_level.txt',
+        ]
+        assert sorted(actual) == expected
+
+    def test_handling_utime_error(self, tmpdir_cwd, env):
+        dist = Distribution()
+        ei = egg_info(dist)
+        utime_patch = mock.patch('os.utime', side_effect=OSError("TEST"))
+        mkpath_patch = mock.patch(
+            'setuptools.command.egg_info.egg_info.mkpath', return_val=None
+        )
+
+        with utime_patch, mkpath_patch:
+            import distutils.errors
+
+            msg = r"Cannot update time stamp of directory 'None'"
+            with pytest.raises(distutils.errors.DistutilsFileError, match=msg):
+                ei.run()
+
+    def test_license_is_a_string(self, tmpdir_cwd, env):
+        setup_config = DALS(
+            """
+            [metadata]
+            name=foo
+            version=0.0.1
+            license=file:MIT
+            """
+        )
+
+        setup_script = DALS(
+            """
+            from setuptools import setup
+
+            setup()
+            """
+        )
+
+        path.build({
+            'setup.py': setup_script,
+            'setup.cfg': setup_config,
+        })
+
+        # This command should fail with a ValueError, but because it's
+        # currently configured to use a subprocess, the actual traceback
+        # object is lost and we need to parse it from stderr
+        with pytest.raises(AssertionError) as exc:
+            self._run_egg_info_command(tmpdir_cwd, env)
+
+        # The only argument to the assertion error should be a traceback
+        # containing a ValueError
+        assert 'ValueError' in exc.value.args[0]
+
+    def test_rebuilt(self, tmpdir_cwd, env):
+        """Ensure timestamps are updated when the command is re-run."""
+        self._create_project()
+
+        self._run_egg_info_command(tmpdir_cwd, env)
+        timestamp_a = os.path.getmtime('foo.egg-info')
+
+        # arbitrary sleep just to handle *really* fast systems
+        time.sleep(0.001)
+
+        self._run_egg_info_command(tmpdir_cwd, env)
+        timestamp_b = os.path.getmtime('foo.egg-info')
+
+        assert timestamp_a != timestamp_b
+
+    def test_manifest_template_is_read(self, tmpdir_cwd, env):
+        self._create_project()
+        path.build({
+            'MANIFEST.in': DALS(
+                """
+                recursive-include docs *.rst
+            """
+            ),
+            'docs': {
+                'usage.rst': "Run 'hi'",
+            },
+        })
+        self._run_egg_info_command(tmpdir_cwd, env)
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        sources_txt = os.path.join(egg_info_dir, 'SOURCES.txt')
+        with open(sources_txt, encoding="utf-8") as f:
+            assert 'docs/usage.rst' in f.read().split('\n')
+
+    def _setup_script_with_requires(self, requires, use_setup_cfg=False):
+        setup_script = DALS(
+            """
+            from setuptools import setup
+
+            setup(name='foo', zip_safe=False, %s)
+            """
+        ) % ('' if use_setup_cfg else requires)
+        setup_config = requires if use_setup_cfg else ''
+        path.build({
+            'setup.py': setup_script,
+            'setup.cfg': setup_config,
+        })
+
+    mismatch_marker = f"python_version<'{sys.version_info[0]}'"
+    # Alternate equivalent syntax.
+    mismatch_marker_alternate = f'python_version < "{sys.version_info[0]}"'
+    invalid_marker = "<=>++"
+
+    class RequiresTestHelper:
+        @staticmethod
+        def parametrize(*test_list, **format_dict):
+            idlist = []
+            argvalues = []
+            for test in test_list:
+                test_params = test.lstrip().split('\n\n', 3)
+                name_kwargs = test_params.pop(0).split('\n')
+                if len(name_kwargs) > 1:
+                    val = name_kwargs[1].strip()
+                    install_cmd_kwargs = ast.literal_eval(val)
+                else:
+                    install_cmd_kwargs = {}
+                name = name_kwargs[0].strip()
+                setup_py_requires, setup_cfg_requires, expected_requires = [
+                    DALS(a).format(**format_dict) for a in test_params
+                ]
+                for id_, requires, use_cfg in (
+                    (name, setup_py_requires, False),
+                    (name + '_in_setup_cfg', setup_cfg_requires, True),
+                ):
+                    idlist.append(id_)
+                    marks = ()
+                    if requires.startswith('@xfail\n'):
+                        requires = requires[7:]
+                        marks = pytest.mark.xfail
+                    argvalues.append(
+                        pytest.param(
+                            requires,
+                            use_cfg,
+                            expected_requires,
+                            install_cmd_kwargs,
+                            marks=marks,
+                        )
+                    )
+            return pytest.mark.parametrize(
+                (
+                    "requires",
+                    "use_setup_cfg",
+                    "expected_requires",
+                    "install_cmd_kwargs",
+                ),
+                argvalues,
+                ids=idlist,
+            )
+
+    @RequiresTestHelper.parametrize(
+        # Format of a test:
+        #
+        # id
+        # install_cmd_kwargs [optional]
+        #
+        # requires block (when used in setup.py)
+        #
+        # requires block (when used in setup.cfg)
+        #
+        # expected contents of requires.txt
+        """
+        install_requires_deterministic
+
+        install_requires=["wheel>=0.5", "pytest"]
+
+        [options]
+        install_requires =
+            wheel>=0.5
+            pytest
+
+        wheel>=0.5
+        pytest
+        """,
+        """
+        install_requires_ordered
+
+        install_requires=["pytest>=3.0.2,!=10.9999"]
+
+        [options]
+        install_requires =
+            pytest>=3.0.2,!=10.9999
+
+        pytest!=10.9999,>=3.0.2
+        """,
+        """
+        install_requires_with_marker
+
+        install_requires=["barbazquux;{mismatch_marker}"],
+
+        [options]
+        install_requires =
+            barbazquux; {mismatch_marker}
+
+        [:{mismatch_marker_alternate}]
+        barbazquux
+        """,
+        """
+        install_requires_with_extra
+        {'cmd': ['egg_info']}
+
+        install_requires=["barbazquux [test]"],
+
+        [options]
+        install_requires =
+            barbazquux [test]
+
+        barbazquux[test]
+        """,
+        """
+        install_requires_with_extra_and_marker
+
+        install_requires=["barbazquux [test]; {mismatch_marker}"],
+
+        [options]
+        install_requires =
+            barbazquux [test]; {mismatch_marker}
+
+        [:{mismatch_marker_alternate}]
+        barbazquux[test]
+        """,
+        """
+        setup_requires_with_markers
+
+        setup_requires=["barbazquux;{mismatch_marker}"],
+
+        [options]
+        setup_requires =
+            barbazquux; {mismatch_marker}
+
+        """,
+        """
+        extras_require_with_extra
+        {'cmd': ['egg_info']}
+
+        extras_require={{"extra": ["barbazquux [test]"]}},
+
+        [options.extras_require]
+        extra = barbazquux [test]
+
+        [extra]
+        barbazquux[test]
+        """,
+        """
+        extras_require_with_extra_and_marker_in_req
+
+        extras_require={{"extra": ["barbazquux [test]; {mismatch_marker}"]}},
+
+        [options.extras_require]
+        extra =
+            barbazquux [test]; {mismatch_marker}
+
+        [extra]
+
+        [extra:{mismatch_marker_alternate}]
+        barbazquux[test]
+        """,
+        # FIXME: ConfigParser does not allow : in key names!
+        """
+        extras_require_with_marker
+
+        extras_require={{":{mismatch_marker}": ["barbazquux"]}},
+
+        @xfail
+        [options.extras_require]
+        :{mismatch_marker} = barbazquux
+
+        [:{mismatch_marker}]
+        barbazquux
+        """,
+        """
+        extras_require_with_marker_in_req
+
+        extras_require={{"extra": ["barbazquux; {mismatch_marker}"]}},
+
+        [options.extras_require]
+        extra =
+            barbazquux; {mismatch_marker}
+
+        [extra]
+
+        [extra:{mismatch_marker_alternate}]
+        barbazquux
+        """,
+        """
+        extras_require_with_empty_section
+
+        extras_require={{"empty": []}},
+
+        [options.extras_require]
+        empty =
+
+        [empty]
+        """,
+        # Format arguments.
+        invalid_marker=invalid_marker,
+        mismatch_marker=mismatch_marker,
+        mismatch_marker_alternate=mismatch_marker_alternate,
+    )
+    def test_requires(
+        self,
+        tmpdir_cwd,
+        env,
+        requires,
+        use_setup_cfg,
+        expected_requires,
+        install_cmd_kwargs,
+    ):
+        self._setup_script_with_requires(requires, use_setup_cfg)
+        self._run_egg_info_command(tmpdir_cwd, env, **install_cmd_kwargs)
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        requires_txt = os.path.join(egg_info_dir, 'requires.txt')
+        if os.path.exists(requires_txt):
+            with open(requires_txt, encoding="utf-8") as fp:
+                install_requires = fp.read()
+        else:
+            install_requires = ''
+        assert install_requires.lstrip() == expected_requires
+        assert glob.glob(os.path.join(env.paths['lib'], 'barbazquux*')) == []
+
+    def test_install_requires_unordered_disallowed(self, tmpdir_cwd, env):
+        """
+        Packages that pass unordered install_requires sequences
+        should be rejected as they produce non-deterministic
+        builds. See #458.
+        """
+        req = 'install_requires={"fake-factory==0.5.2", "pytz"}'
+        self._setup_script_with_requires(req)
+        with pytest.raises(AssertionError):
+            self._run_egg_info_command(tmpdir_cwd, env)
+
+    def test_extras_require_with_invalid_marker(self, tmpdir_cwd, env):
+        tmpl = 'extras_require={{":{marker}": ["barbazquux"]}},'
+        req = tmpl.format(marker=self.invalid_marker)
+        self._setup_script_with_requires(req)
+        with pytest.raises(AssertionError):
+            self._run_egg_info_command(tmpdir_cwd, env)
+        assert glob.glob(os.path.join(env.paths['lib'], 'barbazquux*')) == []
+
+    def test_extras_require_with_invalid_marker_in_req(self, tmpdir_cwd, env):
+        tmpl = 'extras_require={{"extra": ["barbazquux; {marker}"]}},'
+        req = tmpl.format(marker=self.invalid_marker)
+        self._setup_script_with_requires(req)
+        with pytest.raises(AssertionError):
+            self._run_egg_info_command(tmpdir_cwd, env)
+        assert glob.glob(os.path.join(env.paths['lib'], 'barbazquux*')) == []
+
+    def test_provides_extra(self, tmpdir_cwd, env):
+        self._setup_script_with_requires('extras_require={"foobar": ["barbazquux"]},')
+        environ = os.environ.copy().update(
+            HOME=env.paths['home'],
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+            env=environ,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        assert 'Provides-Extra: foobar' in pkg_info_lines
+        assert 'Metadata-Version: 2.4' in pkg_info_lines
+
+    def test_doesnt_provides_extra(self, tmpdir_cwd, env):
+        self._setup_script_with_requires(
+            """install_requires=["spam ; python_version<'3.6'"]"""
+        )
+        environ = os.environ.copy().update(
+            HOME=env.paths['home'],
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+            env=environ,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_text = fp.read()
+        assert 'Provides-Extra:' not in pkg_info_text
+
+    @pytest.mark.parametrize(
+        ('files', 'license_in_sources'),
+        [
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE
+                              """
+                    ),
+                    'LICENSE': "Test license",
+                },
+                True,
+            ),  # with license
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = INVALID_LICENSE
+                              """
+                    ),
+                    'LICENSE': "Test license",
+                },
+                False,
+            ),  # with an invalid license
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              """
+                    ),
+                    'LICENSE': "Test license",
+                },
+                True,
+            ),  # no license_file attribute, LICENSE auto-included
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE
+                              """
+                    ),
+                    'MANIFEST.in': "exclude LICENSE",
+                    'LICENSE': "Test license",
+                },
+                True,
+            ),  # manifest is overwritten by license_file
+            pytest.param(
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICEN[CS]E*
+                              """
+                    ),
+                    'LICENSE': "Test license",
+                },
+                True,
+                id="glob_pattern",
+            ),
+        ],
+    )
+    def test_setup_cfg_license_file(self, tmpdir_cwd, env, files, license_in_sources):
+        self._create_project()
+        path.build(files)
+
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+
+        sources_text = Path(egg_info_dir, "SOURCES.txt").read_text(encoding="utf-8")
+
+        if license_in_sources:
+            assert 'LICENSE' in sources_text
+        else:
+            assert 'LICENSE' not in sources_text
+            # for invalid license test
+            assert 'INVALID_LICENSE' not in sources_text
+
+    @pytest.mark.parametrize(
+        ('files', 'incl_licenses', 'excl_licenses'),
+        [
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                                  LICENSE-ABC
+                                  LICENSE-XYZ
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+                [],
+            ),  # with licenses
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files = LICENSE-ABC, LICENSE-XYZ
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+                [],
+            ),  # with commas
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                                  LICENSE-ABC
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                ['LICENSE-ABC'],
+                ['LICENSE-XYZ'],
+            ),  # with one license
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                [],
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+            ),  # empty
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files = LICENSE-XYZ
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                ['LICENSE-XYZ'],
+                ['LICENSE-ABC'],
+            ),  # on same line
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                                  LICENSE-ABC
+                                  INVALID_LICENSE
+                              """
+                    ),
+                    'LICENSE-ABC': "Test license",
+                },
+                ['LICENSE-ABC'],
+                ['INVALID_LICENSE'],
+            ),  # with an invalid license
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              """
+                    ),
+                    'LICENSE': "Test license",
+                },
+                ['LICENSE'],
+                [],
+            ),  # no license_files attribute, LICENSE auto-included
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files = LICENSE
+                              """
+                    ),
+                    'MANIFEST.in': "exclude LICENSE",
+                    'LICENSE': "Test license",
+                },
+                ['LICENSE'],
+                [],
+            ),  # manifest is overwritten by license_files
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                                  LICENSE-ABC
+                                  LICENSE-XYZ
+                              """
+                    ),
+                    'MANIFEST.in': "exclude LICENSE-XYZ",
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                    # manifest is overwritten by license_files
+                },
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+                [],
+            ),
+            pytest.param(
+                {
+                    'setup.cfg': "",
+                    'LICENSE-ABC': "ABC license",
+                    'COPYING-ABC': "ABC copying",
+                    'NOTICE-ABC': "ABC notice",
+                    'AUTHORS-ABC': "ABC authors",
+                    'LICENCE-XYZ': "XYZ license",
+                    'LICENSE': "License",
+                    'INVALID-LICENSE': "Invalid license",
+                },
+                [
+                    'LICENSE-ABC',
+                    'COPYING-ABC',
+                    'NOTICE-ABC',
+                    'AUTHORS-ABC',
+                    'LICENCE-XYZ',
+                    'LICENSE',
+                ],
+                ['INVALID-LICENSE'],
+                # ('LICEN[CS]E*', 'COPYING*', 'NOTICE*', 'AUTHORS*')
+                id="default_glob_patterns",
+            ),
+            pytest.param(
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                                  LICENSE*
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'NOTICE-XYZ': "XYZ notice",
+                },
+                ['LICENSE-ABC'],
+                ['NOTICE-XYZ'],
+                id="no_default_glob_patterns",
+            ),
+            pytest.param(
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files =
+                                  LICENSE-ABC
+                                  LICENSE*
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                },
+                ['LICENSE-ABC'],
+                [],
+                id="files_only_added_once",
+            ),
+            pytest.param(
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_files = **/LICENSE
+                              """
+                    ),
+                    'LICENSE': "ABC license",
+                    'LICENSE-OTHER': "Don't include",
+                    'vendor': {'LICENSE': "Vendor license"},
+                },
+                ['LICENSE', 'vendor/LICENSE'],
+                ['LICENSE-OTHER'],
+                id="recursive_glob",
+            ),
+        ],
+    )
+    def test_setup_cfg_license_files(
+        self, tmpdir_cwd, env, files, incl_licenses, excl_licenses
+    ):
+        self._create_project()
+        path.build(files)
+
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+
+        sources_text = Path(egg_info_dir, "SOURCES.txt").read_text(encoding="utf-8")
+        sources_lines = [line.strip() for line in sources_text.splitlines()]
+
+        for lf in incl_licenses:
+            assert sources_lines.count(lf) == 1
+
+        for lf in excl_licenses:
+            assert sources_lines.count(lf) == 0
+
+    @pytest.mark.parametrize(
+        ('files', 'incl_licenses', 'excl_licenses'),
+        [
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file =
+                              license_files =
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                [],
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+            ),  # both empty
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file =
+                                  LICENSE-ABC
+                                  LICENSE-XYZ
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-XYZ': "XYZ license",
+                    # license_file is still singular
+                },
+                [],
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+            ),
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE-ABC
+                              license_files =
+                                  LICENSE-XYZ
+                                  LICENSE-PQR
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-PQR': "PQR license",
+                    'LICENSE-XYZ': "XYZ license",
+                },
+                ['LICENSE-ABC', 'LICENSE-PQR', 'LICENSE-XYZ'],
+                [],
+            ),  # combined
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE-ABC
+                              license_files =
+                                  LICENSE-ABC
+                                  LICENSE-XYZ
+                                  LICENSE-PQR
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-PQR': "PQR license",
+                    'LICENSE-XYZ': "XYZ license",
+                    # duplicate license
+                },
+                ['LICENSE-ABC', 'LICENSE-PQR', 'LICENSE-XYZ'],
+                [],
+            ),
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE-ABC
+                              license_files =
+                                  LICENSE-XYZ
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-PQR': "PQR license",
+                    'LICENSE-XYZ': "XYZ license",
+                    # combined subset
+                },
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+                ['LICENSE-PQR'],
+            ),
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE-ABC
+                              license_files =
+                                  LICENSE-XYZ
+                                  LICENSE-PQR
+                              """
+                    ),
+                    'LICENSE-PQR': "Test license",
+                    # with invalid licenses
+                },
+                ['LICENSE-PQR'],
+                ['LICENSE-ABC', 'LICENSE-XYZ'],
+            ),
+            (
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE-ABC
+                              license_files =
+                                LICENSE-PQR
+                                LICENSE-XYZ
+                              """
+                    ),
+                    'MANIFEST.in': "exclude LICENSE-ABC\nexclude LICENSE-PQR",
+                    'LICENSE-ABC': "ABC license",
+                    'LICENSE-PQR': "PQR license",
+                    'LICENSE-XYZ': "XYZ license",
+                    # manifest is overwritten
+                },
+                ['LICENSE-ABC', 'LICENSE-PQR', 'LICENSE-XYZ'],
+                [],
+            ),
+            pytest.param(
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE*
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'NOTICE-XYZ': "XYZ notice",
+                },
+                ['LICENSE-ABC'],
+                ['NOTICE-XYZ'],
+                id="no_default_glob_patterns",
+            ),
+            pytest.param(
+                {
+                    'setup.cfg': DALS(
+                        """
+                              [metadata]
+                              license_file = LICENSE*
+                              license_files =
+                                NOTICE*
+                              """
+                    ),
+                    'LICENSE-ABC': "ABC license",
+                    'NOTICE-ABC': "ABC notice",
+                    'AUTHORS-ABC': "ABC authors",
+                },
+                ['LICENSE-ABC', 'NOTICE-ABC'],
+                ['AUTHORS-ABC'],
+                id="combined_glob_patterrns",
+            ),
+        ],
+    )
+    def test_setup_cfg_license_file_license_files(
+        self, tmpdir_cwd, env, files, incl_licenses, excl_licenses
+    ):
+        self._create_project()
+        path.build(files)
+
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+
+        sources_text = Path(egg_info_dir, "SOURCES.txt").read_text(encoding="utf-8")
+        sources_lines = [line.strip() for line in sources_text.splitlines()]
+
+        for lf in incl_licenses:
+            assert sources_lines.count(lf) == 1
+
+        for lf in excl_licenses:
+            assert sources_lines.count(lf) == 0
+
+    def test_license_file_attr_pkg_info(self, tmpdir_cwd, env):
+        """All matched license files should have a corresponding License-File."""
+        self._create_project()
+        path.build({
+            "setup.cfg": DALS(
+                """
+                              [metadata]
+                              license_files =
+                                  NOTICE*
+                                  LICENSE*
+                                  **/LICENSE
+                              """
+            ),
+            "LICENSE-ABC": "ABC license",
+            "LICENSE-XYZ": "XYZ license",
+            "NOTICE": "included",
+            "IGNORE": "not include",
+            "vendor": {'LICENSE': "Vendor license"},
+        })
+
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        license_file_lines = [
+            line for line in pkg_info_lines if line.startswith('License-File:')
+        ]
+
+        # Only 'NOTICE', LICENSE-ABC', and 'LICENSE-XYZ' should have been matched
+        # Also assert that order from license_files is keeped
+        assert len(license_file_lines) == 4
+        assert "License-File: NOTICE" == license_file_lines[0]
+        assert "License-File: LICENSE-ABC" in license_file_lines[1:]
+        assert "License-File: LICENSE-XYZ" in license_file_lines[1:]
+        assert "License-File: vendor/LICENSE" in license_file_lines[3]
+
+    def test_metadata_version(self, tmpdir_cwd, env):
+        """Make sure latest metadata version is used by default."""
+        self._setup_script_with_requires("")
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        # Update metadata version if changed
+        assert self._extract_mv_version(pkg_info_lines) == (2, 4)
+
+    def test_long_description_content_type(self, tmpdir_cwd, env):
+        # Test that specifying a `long_description_content_type` keyword arg to
+        # the `setup` function results in writing a `Description-Content-Type`
+        # line to the `PKG-INFO` file in the `.egg-info`
+        # directory.
+        # `Description-Content-Type` is described at
+        # https://github.com/pypa/python-packaging-user-guide/pull/258
+
+        self._setup_script_with_requires(
+            """long_description_content_type='text/markdown',"""
+        )
+        environ = os.environ.copy().update(
+            HOME=env.paths['home'],
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+            env=environ,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        expected_line = 'Description-Content-Type: text/markdown'
+        assert expected_line in pkg_info_lines
+        assert 'Metadata-Version: 2.4' in pkg_info_lines
+
+    def test_long_description(self, tmpdir_cwd, env):
+        # Test that specifying `long_description` and `long_description_content_type`
+        # keyword args to the `setup` function results in writing
+        # the description in the message payload of the `PKG-INFO` file
+        # in the `.egg-info` directory.
+        self._setup_script_with_requires(
+            "long_description='This is a long description\\nover multiple lines',"
+            "long_description_content_type='text/markdown',"
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        assert 'Metadata-Version: 2.4' in pkg_info_lines
+        assert '' == pkg_info_lines[-1]  # last line should be empty
+        long_desc_lines = pkg_info_lines[pkg_info_lines.index('') :]
+        assert 'This is a long description' in long_desc_lines
+        assert 'over multiple lines' in long_desc_lines
+
+    def test_project_urls(self, tmpdir_cwd, env):
+        # Test that specifying a `project_urls` dict to the `setup`
+        # function results in writing multiple `Project-URL` lines to
+        # the `PKG-INFO` file in the `.egg-info`
+        # directory.
+        # `Project-URL` is described at https://packaging.python.org
+        #     /specifications/core-metadata/#project-url-multiple-use
+
+        self._setup_script_with_requires(
+            """project_urls={
+                'Link One': 'https://example.com/one/',
+                'Link Two': 'https://example.com/two/',
+                },"""
+        )
+        environ = os.environ.copy().update(
+            HOME=env.paths['home'],
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+            env=environ,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        expected_line = 'Project-URL: Link One, https://example.com/one/'
+        assert expected_line in pkg_info_lines
+        expected_line = 'Project-URL: Link Two, https://example.com/two/'
+        assert expected_line in pkg_info_lines
+        assert self._extract_mv_version(pkg_info_lines) >= (1, 2)
+
+    def test_license(self, tmpdir_cwd, env):
+        """Test single line license."""
+        self._setup_script_with_requires("license='MIT',")
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        assert 'License: MIT' in pkg_info_lines
+
+    def test_license_escape(self, tmpdir_cwd, env):
+        """Test license is escaped correctly if longer than one line."""
+        self._setup_script_with_requires(
+            "license='This is a long license text \\nover multiple lines',"
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+
+        assert 'License: This is a long license text ' in pkg_info_lines
+        assert '        over multiple lines' in pkg_info_lines
+        assert 'text \n        over multiple' in '\n'.join(pkg_info_lines)
+
+    def test_python_requires_egg_info(self, tmpdir_cwd, env):
+        self._setup_script_with_requires("""python_requires='>=2.7.12',""")
+        environ = os.environ.copy().update(
+            HOME=env.paths['home'],
+        )
+        environment.run_setup_py(
+            cmd=['egg_info'],
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+            env=environ,
+        )
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        assert 'Requires-Python: >=2.7.12' in pkg_info_lines
+        assert self._extract_mv_version(pkg_info_lines) >= (1, 2)
+
+    def test_manifest_maker_warning_suppression(self):
+        fixtures = [
+            "standard file not found: should have one of foo.py, bar.py",
+            "standard file 'setup.py' not found",
+        ]
+
+        for msg in fixtures:
+            assert manifest_maker._should_suppress_warning(msg)
+
+    def test_egg_info_includes_setup_py(self, tmpdir_cwd):
+        self._create_project()
+        dist = Distribution({"name": "foo", "version": "0.0.1"})
+        dist.script_name = "non_setup.py"
+        egg_info_instance = egg_info(dist)
+        egg_info_instance.finalize_options()
+        egg_info_instance.run()
+
+        assert 'setup.py' in egg_info_instance.filelist.files
+
+        with open(egg_info_instance.egg_info + "/SOURCES.txt", encoding="utf-8") as f:
+            sources = f.read().split('\n')
+            assert 'setup.py' in sources
+
+    def _run_egg_info_command(self, tmpdir_cwd, env, cmd=None, output=None):
+        environ = os.environ.copy().update(
+            HOME=env.paths['home'],
+        )
+        if cmd is None:
+            cmd = [
+                'egg_info',
+            ]
+        code, data = environment.run_setup_py(
+            cmd=cmd,
+            pypath=os.pathsep.join([env.paths['lib'], str(tmpdir_cwd)]),
+            data_stream=1,
+            env=environ,
+        )
+        assert not code, data
+
+        if output:
+            assert output in data
+
+    def test_egg_info_tag_only_once(self, tmpdir_cwd, env):
+        self._create_project()
+        path.build({
+            'setup.cfg': DALS(
+                """
+                              [egg_info]
+                              tag_build = dev
+                              tag_date = 0
+                              tag_svn_revision = 0
+                              """
+            ),
+        })
+        self._run_egg_info_command(tmpdir_cwd, env)
+        egg_info_dir = os.path.join('.', 'foo.egg-info')
+        with open(os.path.join(egg_info_dir, 'PKG-INFO'), encoding="utf-8") as fp:
+            pkg_info_lines = fp.read().split('\n')
+        assert 'Version: 0.0.0.dev0' in pkg_info_lines
+
+
+class TestWriteEntries:
+    def test_invalid_entry_point(self, tmpdir_cwd, env):
+        dist = Distribution({"name": "foo", "version": "0.0.1"})
+        dist.entry_points = {"foo": "foo = invalid-identifier:foo"}
+        cmd = dist.get_command_obj("egg_info")
+        expected_msg = r"Problems to parse .*invalid-identifier.*"
+        with pytest.raises(errors.OptionError, match=expected_msg) as ex:
+            write_entries(cmd, "entry_points", "entry_points.txt")
+            assert "ensure entry-point follows the spec" in ex.value.args[0]
+
+    def test_valid_entry_point(self, tmpdir_cwd, env):
+        dist = Distribution({"name": "foo", "version": "0.0.1"})
+        dist.entry_points = {
+            "abc": "foo = bar:baz",
+            "def": ["faa = bor:boz"],
+        }
+        cmd = dist.get_command_obj("egg_info")
+        write_entries(cmd, "entry_points", "entry_points.txt")
+        content = Path("entry_points.txt").read_text(encoding="utf-8")
+        assert "[abc]\nfoo = bar:baz\n" in content
+        assert "[def]\nfaa = bor:boz\n" in content
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_extern.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_extern.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7eb3c62c190dacdd4a054d2934962be2f4ee860
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_extern.py
@@ -0,0 +1,15 @@
+import importlib
+import pickle
+
+import packaging
+
+from setuptools import Distribution
+
+
+def test_reimport_extern():
+    packaging2 = importlib.import_module(packaging.__name__)
+    assert packaging is packaging2
+
+
+def test_distribution_picklable():
+    pickle.loads(pickle.dumps(Distribution()))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_find_packages.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_find_packages.py
new file mode 100644
index 0000000000000000000000000000000000000000..9fd9f8f6637d13cb898fcd446a6b090323d02014
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_find_packages.py
@@ -0,0 +1,218 @@
+"""Tests for automatic package discovery"""
+
+import os
+import shutil
+import tempfile
+
+import pytest
+
+from setuptools import find_namespace_packages, find_packages
+from setuptools.discovery import FlatLayoutPackageFinder
+
+from .compat.py39 import os_helper
+
+
+class TestFindPackages:
+    def setup_method(self, method):
+        self.dist_dir = tempfile.mkdtemp()
+        self._make_pkg_structure()
+
+    def teardown_method(self, method):
+        shutil.rmtree(self.dist_dir)
+
+    def _make_pkg_structure(self):
+        """Make basic package structure.
+
+        dist/
+            docs/
+                conf.py
+            pkg/
+                __pycache__/
+                nspkg/
+                    mod.py
+                subpkg/
+                    assets/
+                        asset
+                    __init__.py
+            setup.py
+
+        """
+        self.docs_dir = self._mkdir('docs', self.dist_dir)
+        self._touch('conf.py', self.docs_dir)
+        self.pkg_dir = self._mkdir('pkg', self.dist_dir)
+        self._mkdir('__pycache__', self.pkg_dir)
+        self.ns_pkg_dir = self._mkdir('nspkg', self.pkg_dir)
+        self._touch('mod.py', self.ns_pkg_dir)
+        self.sub_pkg_dir = self._mkdir('subpkg', self.pkg_dir)
+        self.asset_dir = self._mkdir('assets', self.sub_pkg_dir)
+        self._touch('asset', self.asset_dir)
+        self._touch('__init__.py', self.sub_pkg_dir)
+        self._touch('setup.py', self.dist_dir)
+
+    def _mkdir(self, path, parent_dir=None):
+        if parent_dir:
+            path = os.path.join(parent_dir, path)
+        os.mkdir(path)
+        return path
+
+    def _touch(self, path, dir_=None):
+        if dir_:
+            path = os.path.join(dir_, path)
+        open(path, 'wb').close()
+        return path
+
+    def test_regular_package(self):
+        self._touch('__init__.py', self.pkg_dir)
+        packages = find_packages(self.dist_dir)
+        assert packages == ['pkg', 'pkg.subpkg']
+
+    def test_exclude(self):
+        self._touch('__init__.py', self.pkg_dir)
+        packages = find_packages(self.dist_dir, exclude=('pkg.*',))
+        assert packages == ['pkg']
+
+    def test_exclude_recursive(self):
+        """
+        Excluding a parent package should not exclude child packages as well.
+        """
+        self._touch('__init__.py', self.pkg_dir)
+        self._touch('__init__.py', self.sub_pkg_dir)
+        packages = find_packages(self.dist_dir, exclude=('pkg',))
+        assert packages == ['pkg.subpkg']
+
+    def test_include_excludes_other(self):
+        """
+        If include is specified, other packages should be excluded.
+        """
+        self._touch('__init__.py', self.pkg_dir)
+        alt_dir = self._mkdir('other_pkg', self.dist_dir)
+        self._touch('__init__.py', alt_dir)
+        packages = find_packages(self.dist_dir, include=['other_pkg'])
+        assert packages == ['other_pkg']
+
+    def test_dir_with_dot_is_skipped(self):
+        shutil.rmtree(os.path.join(self.dist_dir, 'pkg/subpkg/assets'))
+        data_dir = self._mkdir('some.data', self.pkg_dir)
+        self._touch('__init__.py', data_dir)
+        self._touch('file.dat', data_dir)
+        packages = find_packages(self.dist_dir)
+        assert 'pkg.some.data' not in packages
+
+    def test_dir_with_packages_in_subdir_is_excluded(self):
+        """
+        Ensure that a package in a non-package such as build/pkg/__init__.py
+        is excluded.
+        """
+        build_dir = self._mkdir('build', self.dist_dir)
+        build_pkg_dir = self._mkdir('pkg', build_dir)
+        self._touch('__init__.py', build_pkg_dir)
+        packages = find_packages(self.dist_dir)
+        assert 'build.pkg' not in packages
+
+    @pytest.mark.skipif(not os_helper.can_symlink(), reason='Symlink support required')
+    def test_symlinked_packages_are_included(self):
+        """
+        A symbolically-linked directory should be treated like any other
+        directory when matched as a package.
+
+        Create a link from lpkg -> pkg.
+        """
+        self._touch('__init__.py', self.pkg_dir)
+        linked_pkg = os.path.join(self.dist_dir, 'lpkg')
+        os.symlink('pkg', linked_pkg)
+        assert os.path.isdir(linked_pkg)
+        packages = find_packages(self.dist_dir)
+        assert 'lpkg' in packages
+
+    def _assert_packages(self, actual, expected):
+        assert set(actual) == set(expected)
+
+    def test_pep420_ns_package(self):
+        packages = find_namespace_packages(
+            self.dist_dir, include=['pkg*'], exclude=['pkg.subpkg.assets']
+        )
+        self._assert_packages(packages, ['pkg', 'pkg.nspkg', 'pkg.subpkg'])
+
+    def test_pep420_ns_package_no_includes(self):
+        packages = find_namespace_packages(self.dist_dir, exclude=['pkg.subpkg.assets'])
+        self._assert_packages(packages, ['docs', 'pkg', 'pkg.nspkg', 'pkg.subpkg'])
+
+    def test_pep420_ns_package_no_includes_or_excludes(self):
+        packages = find_namespace_packages(self.dist_dir)
+        expected = ['docs', 'pkg', 'pkg.nspkg', 'pkg.subpkg', 'pkg.subpkg.assets']
+        self._assert_packages(packages, expected)
+
+    def test_regular_package_with_nested_pep420_ns_packages(self):
+        self._touch('__init__.py', self.pkg_dir)
+        packages = find_namespace_packages(
+            self.dist_dir, exclude=['docs', 'pkg.subpkg.assets']
+        )
+        self._assert_packages(packages, ['pkg', 'pkg.nspkg', 'pkg.subpkg'])
+
+    def test_pep420_ns_package_no_non_package_dirs(self):
+        shutil.rmtree(self.docs_dir)
+        shutil.rmtree(os.path.join(self.dist_dir, 'pkg/subpkg/assets'))
+        packages = find_namespace_packages(self.dist_dir)
+        self._assert_packages(packages, ['pkg', 'pkg.nspkg', 'pkg.subpkg'])
+
+
+class TestFlatLayoutPackageFinder:
+    EXAMPLES = {
+        "hidden-folders": (
+            [".pkg/__init__.py", "pkg/__init__.py", "pkg/nested/file.txt"],
+            ["pkg", "pkg.nested"],
+        ),
+        "private-packages": (
+            ["_pkg/__init__.py", "pkg/_private/__init__.py"],
+            ["pkg", "pkg._private"],
+        ),
+        "invalid-name": (
+            ["invalid-pkg/__init__.py", "other.pkg/__init__.py", "yet,another/file.py"],
+            [],
+        ),
+        "docs": (["pkg/__init__.py", "docs/conf.py", "docs/readme.rst"], ["pkg"]),
+        "tests": (
+            ["pkg/__init__.py", "tests/test_pkg.py", "tests/__init__.py"],
+            ["pkg"],
+        ),
+        "examples": (
+            [
+                "pkg/__init__.py",
+                "examples/__init__.py",
+                "examples/file.py",
+                "example/other_file.py",
+                # Sub-packages should always be fine
+                "pkg/example/__init__.py",
+                "pkg/examples/__init__.py",
+            ],
+            ["pkg", "pkg.examples", "pkg.example"],
+        ),
+        "tool-specific": (
+            [
+                "htmlcov/index.html",
+                "pkg/__init__.py",
+                "tasks/__init__.py",
+                "tasks/subpackage/__init__.py",
+                "fabfile/__init__.py",
+                "fabfile/subpackage/__init__.py",
+                # Sub-packages should always be fine
+                "pkg/tasks/__init__.py",
+                "pkg/fabfile/__init__.py",
+            ],
+            ["pkg", "pkg.tasks", "pkg.fabfile"],
+        ),
+    }
+
+    @pytest.mark.parametrize("example", EXAMPLES.keys())
+    def test_unwanted_directories_not_included(self, tmp_path, example):
+        files, expected_packages = self.EXAMPLES[example]
+        ensure_files(tmp_path, files)
+        found_packages = FlatLayoutPackageFinder.find(str(tmp_path))
+        assert set(found_packages) == set(expected_packages)
+
+
+def ensure_files(root_path, files):
+    for file in files:
+        path = root_path / file
+        path.parent.mkdir(parents=True, exist_ok=True)
+        path.touch()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_find_py_modules.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_find_py_modules.py
new file mode 100644
index 0000000000000000000000000000000000000000..8034b544294e5d30274bac82f24f93613120a0d4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_find_py_modules.py
@@ -0,0 +1,73 @@
+"""Tests for automatic discovery of modules"""
+
+import os
+
+import pytest
+
+from setuptools.discovery import FlatLayoutModuleFinder, ModuleFinder
+
+from .compat.py39 import os_helper
+from .test_find_packages import ensure_files
+
+
+class TestModuleFinder:
+    def find(self, path, *args, **kwargs):
+        return set(ModuleFinder.find(str(path), *args, **kwargs))
+
+    EXAMPLES = {
+        # circumstance: (files, kwargs, expected_modules)
+        "simple_folder": (
+            ["file.py", "other.py"],
+            {},  # kwargs
+            ["file", "other"],
+        ),
+        "exclude": (
+            ["file.py", "other.py"],
+            {"exclude": ["f*"]},
+            ["other"],
+        ),
+        "include": (
+            ["file.py", "fole.py", "other.py"],
+            {"include": ["f*"], "exclude": ["fo*"]},
+            ["file"],
+        ),
+        "invalid-name": (["my-file.py", "other.file.py"], {}, []),
+    }
+
+    @pytest.mark.parametrize("example", EXAMPLES.keys())
+    def test_finder(self, tmp_path, example):
+        files, kwargs, expected_modules = self.EXAMPLES[example]
+        ensure_files(tmp_path, files)
+        assert self.find(tmp_path, **kwargs) == set(expected_modules)
+
+    @pytest.mark.skipif(not os_helper.can_symlink(), reason='Symlink support required')
+    def test_symlinked_packages_are_included(self, tmp_path):
+        src = "_myfiles/file.py"
+        ensure_files(tmp_path, [src])
+        os.symlink(tmp_path / src, tmp_path / "link.py")
+        assert self.find(tmp_path) == {"link"}
+
+
+class TestFlatLayoutModuleFinder:
+    def find(self, path, *args, **kwargs):
+        return set(FlatLayoutModuleFinder.find(str(path)))
+
+    EXAMPLES = {
+        # circumstance: (files, expected_modules)
+        "hidden-files": ([".module.py"], []),
+        "private-modules": (["_module.py"], []),
+        "common-names": (
+            ["setup.py", "conftest.py", "test.py", "tests.py", "example.py", "mod.py"],
+            ["mod"],
+        ),
+        "tool-specific": (
+            ["tasks.py", "fabfile.py", "noxfile.py", "dodo.py", "manage.py", "mod.py"],
+            ["mod"],
+        ),
+    }
+
+    @pytest.mark.parametrize("example", EXAMPLES.keys())
+    def test_unwanted_files_not_included(self, tmp_path, example):
+        files, expected_modules = self.EXAMPLES[example]
+        ensure_files(tmp_path, files)
+        assert self.find(tmp_path) == set(expected_modules)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_glob.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_glob.py
new file mode 100644
index 0000000000000000000000000000000000000000..8d225a44610163c7d56d65b07c06f0f598ccfe84
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_glob.py
@@ -0,0 +1,45 @@
+import pytest
+from jaraco import path
+
+from setuptools.glob import glob
+
+
+@pytest.mark.parametrize(
+    ('tree', 'pattern', 'matches'),
+    (
+        ('', b'', []),
+        ('', '', []),
+        (
+            """
+     appveyor.yml
+     CHANGES.rst
+     LICENSE
+     MANIFEST.in
+     pyproject.toml
+     README.rst
+     setup.cfg
+     setup.py
+     """,
+            '*.rst',
+            ('CHANGES.rst', 'README.rst'),
+        ),
+        (
+            """
+     appveyor.yml
+     CHANGES.rst
+     LICENSE
+     MANIFEST.in
+     pyproject.toml
+     README.rst
+     setup.cfg
+     setup.py
+     """,
+            b'*.rst',
+            (b'CHANGES.rst', b'README.rst'),
+        ),
+    ),
+)
+def test_glob(monkeypatch, tmpdir, tree, pattern, matches):
+    monkeypatch.chdir(tmpdir)
+    path.build({name: '' for name in tree.split()})
+    assert list(sorted(glob(pattern))) == list(sorted(matches))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_install_scripts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_install_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..e62a6b7f318df2da0cf29e53c41f74e5525e78ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_install_scripts.py
@@ -0,0 +1,89 @@
+"""install_scripts tests"""
+
+import sys
+
+import pytest
+
+from setuptools.command.install_scripts import install_scripts
+from setuptools.dist import Distribution
+
+from . import contexts
+
+
+class TestInstallScripts:
+    settings = dict(
+        name='foo',
+        entry_points={'console_scripts': ['foo=foo:foo']},
+        version='0.0',
+    )
+    unix_exe = '/usr/dummy-test-path/local/bin/python'
+    unix_spaces_exe = '/usr/bin/env dummy-test-python'
+    win32_exe = 'C:\\Dummy Test Path\\Program Files\\Python 3.6\\python.exe'
+
+    def _run_install_scripts(self, install_dir, executable=None):
+        dist = Distribution(self.settings)
+        dist.script_name = 'setup.py'
+        cmd = install_scripts(dist)
+        cmd.install_dir = install_dir
+        if executable is not None:
+            bs = cmd.get_finalized_command('build_scripts')
+            bs.executable = executable
+        cmd.ensure_finalized()
+        with contexts.quiet():
+            cmd.run()
+
+    @pytest.mark.skipif(sys.platform == 'win32', reason='non-Windows only')
+    def test_sys_executable_escaping_unix(self, tmpdir, monkeypatch):
+        """
+        Ensure that shebang is not quoted on Unix when getting the Python exe
+        from sys.executable.
+        """
+        expected = f'#!{self.unix_exe}\n'
+        monkeypatch.setattr('sys.executable', self.unix_exe)
+        with tmpdir.as_cwd():
+            self._run_install_scripts(str(tmpdir))
+            with open(str(tmpdir.join('foo')), 'r', encoding="utf-8") as f:
+                actual = f.readline()
+        assert actual == expected
+
+    @pytest.mark.skipif(sys.platform != 'win32', reason='Windows only')
+    def test_sys_executable_escaping_win32(self, tmpdir, monkeypatch):
+        """
+        Ensure that shebang is quoted on Windows when getting the Python exe
+        from sys.executable and it contains a space.
+        """
+        expected = f'#!"{self.win32_exe}"\n'
+        monkeypatch.setattr('sys.executable', self.win32_exe)
+        with tmpdir.as_cwd():
+            self._run_install_scripts(str(tmpdir))
+            with open(str(tmpdir.join('foo-script.py')), 'r', encoding="utf-8") as f:
+                actual = f.readline()
+        assert actual == expected
+
+    @pytest.mark.skipif(sys.platform == 'win32', reason='non-Windows only')
+    def test_executable_with_spaces_escaping_unix(self, tmpdir):
+        """
+        Ensure that shebang on Unix is not quoted, even when
+        a value with spaces
+        is specified using --executable.
+        """
+        expected = f'#!{self.unix_spaces_exe}\n'
+        with tmpdir.as_cwd():
+            self._run_install_scripts(str(tmpdir), self.unix_spaces_exe)
+            with open(str(tmpdir.join('foo')), 'r', encoding="utf-8") as f:
+                actual = f.readline()
+        assert actual == expected
+
+    @pytest.mark.skipif(sys.platform != 'win32', reason='Windows only')
+    def test_executable_arg_escaping_win32(self, tmpdir):
+        """
+        Ensure that shebang on Windows is quoted when
+        getting a path with spaces
+        from --executable, that is itself properly quoted.
+        """
+        expected = f'#!"{self.win32_exe}"\n'
+        with tmpdir.as_cwd():
+            self._run_install_scripts(str(tmpdir), '"' + self.win32_exe + '"')
+            with open(str(tmpdir.join('foo-script.py')), 'r', encoding="utf-8") as f:
+                actual = f.readline()
+        assert actual == expected
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_logging.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_logging.py
new file mode 100644
index 0000000000000000000000000000000000000000..ea58001e93d8e4bcbd50bfd49303324d71858d16
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_logging.py
@@ -0,0 +1,76 @@
+import functools
+import inspect
+import logging
+import sys
+
+import pytest
+
+IS_PYPY = '__pypy__' in sys.builtin_module_names
+
+
+setup_py = """\
+from setuptools import setup
+
+setup(
+    name="test_logging",
+    version="0.0"
+)
+"""
+
+
+@pytest.mark.parametrize(
+    ('flag', 'expected_level'), [("--dry-run", "INFO"), ("--verbose", "DEBUG")]
+)
+def test_verbosity_level(tmp_path, monkeypatch, flag, expected_level):
+    """Make sure the correct verbosity level is set (issue #3038)"""
+    import setuptools  # noqa: F401  # import setuptools to monkeypatch distutils
+
+    import distutils  # <- load distutils after all the patches take place
+
+    logger = logging.Logger(__name__)
+    monkeypatch.setattr(logging, "root", logger)
+    unset_log_level = logger.getEffectiveLevel()
+    assert logging.getLevelName(unset_log_level) == "NOTSET"
+
+    setup_script = tmp_path / "setup.py"
+    setup_script.write_text(setup_py, encoding="utf-8")
+    dist = distutils.core.run_setup(setup_script, stop_after="init")
+    dist.script_args = [flag, "sdist"]
+    dist.parse_command_line()  # <- where the log level is set
+    log_level = logger.getEffectiveLevel()
+    log_level_name = logging.getLevelName(log_level)
+    assert log_level_name == expected_level
+
+
+def flaky_on_pypy(func):
+    @functools.wraps(func)
+    def _func():
+        try:
+            func()
+        except AssertionError:  # pragma: no cover
+            if IS_PYPY:
+                msg = "Flaky monkeypatch on PyPy (#4124)"
+                pytest.xfail(f"{msg}. Original discussion in #3707, #3709.")
+            raise
+
+    return _func
+
+
+@flaky_on_pypy
+def test_patching_does_not_cause_problems():
+    # Ensure `dist.log` is only patched if necessary
+
+    import _distutils_hack
+
+    import setuptools.logging
+
+    from distutils import dist
+
+    setuptools.logging.configure()
+
+    if _distutils_hack.enabled():
+        # Modern logging infra, no problematic patching.
+        assert dist.__file__ is None or "setuptools" in dist.__file__
+        assert isinstance(dist.log, logging.Logger)
+    else:
+        assert inspect.ismodule(dist.log)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_manifest.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_manifest.py
new file mode 100644
index 0000000000000000000000000000000000000000..903a528db0cc2bba27bbcef24aa1c59dc4156528
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_manifest.py
@@ -0,0 +1,622 @@
+"""sdist tests"""
+
+from __future__ import annotations
+
+import contextlib
+import io
+import itertools
+import logging
+import os
+import shutil
+import sys
+import tempfile
+
+import pytest
+
+from setuptools.command.egg_info import FileList, egg_info, translate_pattern
+from setuptools.dist import Distribution
+from setuptools.tests.textwrap import DALS
+
+from distutils import log
+from distutils.errors import DistutilsTemplateError
+
+IS_PYPY = '__pypy__' in sys.builtin_module_names
+
+
+def make_local_path(s):
+    """Converts '/' in a string to os.sep"""
+    return s.replace('/', os.sep)
+
+
+SETUP_ATTRS = {
+    'name': 'app',
+    'version': '0.0',
+    'packages': ['app'],
+}
+
+SETUP_PY = f"""\
+from setuptools import setup
+
+setup(**{SETUP_ATTRS!r})
+"""
+
+
+@contextlib.contextmanager
+def quiet():
+    old_stdout, old_stderr = sys.stdout, sys.stderr
+    sys.stdout, sys.stderr = io.StringIO(), io.StringIO()
+    try:
+        yield
+    finally:
+        sys.stdout, sys.stderr = old_stdout, old_stderr
+
+
+def touch(filename):
+    open(filename, 'wb').close()
+
+
+# The set of files always in the manifest, including all files in the
+# .egg-info directory
+default_files = frozenset(
+    map(
+        make_local_path,
+        [
+            'README.rst',
+            'MANIFEST.in',
+            'setup.py',
+            'app.egg-info/PKG-INFO',
+            'app.egg-info/SOURCES.txt',
+            'app.egg-info/dependency_links.txt',
+            'app.egg-info/top_level.txt',
+            'app/__init__.py',
+        ],
+    )
+)
+
+
+translate_specs: list[tuple[str, list[str], list[str]]] = [
+    ('foo', ['foo'], ['bar', 'foobar']),
+    ('foo/bar', ['foo/bar'], ['foo/bar/baz', './foo/bar', 'foo']),
+    # Glob matching
+    ('*.txt', ['foo.txt', 'bar.txt'], ['foo/foo.txt']),
+    ('dir/*.txt', ['dir/foo.txt', 'dir/bar.txt', 'dir/.txt'], ['notdir/foo.txt']),
+    ('*/*.py', ['bin/start.py'], []),
+    ('docs/page-?.txt', ['docs/page-9.txt'], ['docs/page-10.txt']),
+    # Globstars change what they mean depending upon where they are
+    (
+        'foo/**/bar',
+        ['foo/bing/bar', 'foo/bing/bang/bar', 'foo/bar'],
+        ['foo/abar'],
+    ),
+    (
+        'foo/**',
+        ['foo/bar/bing.py', 'foo/x'],
+        ['/foo/x'],
+    ),
+    (
+        '**',
+        ['x', 'abc/xyz', '@nything'],
+        [],
+    ),
+    # Character classes
+    (
+        'pre[one]post',
+        ['preopost', 'prenpost', 'preepost'],
+        ['prepost', 'preonepost'],
+    ),
+    (
+        'hello[!one]world',
+        ['helloxworld', 'helloyworld'],
+        ['hellooworld', 'helloworld', 'hellooneworld'],
+    ),
+    (
+        '[]one].txt',
+        ['o.txt', '].txt', 'e.txt'],
+        ['one].txt'],
+    ),
+    (
+        'foo[!]one]bar',
+        ['fooybar'],
+        ['foo]bar', 'fooobar', 'fooebar'],
+    ),
+]
+"""
+A spec of inputs for 'translate_pattern' and matches and mismatches
+for that input.
+"""
+
+match_params = itertools.chain.from_iterable(
+    zip(itertools.repeat(pattern), matches)
+    for pattern, matches, mismatches in translate_specs
+)
+
+
+@pytest.fixture(params=match_params)
+def pattern_match(request):
+    return map(make_local_path, request.param)
+
+
+mismatch_params = itertools.chain.from_iterable(
+    zip(itertools.repeat(pattern), mismatches)
+    for pattern, matches, mismatches in translate_specs
+)
+
+
+@pytest.fixture(params=mismatch_params)
+def pattern_mismatch(request):
+    return map(make_local_path, request.param)
+
+
+def test_translated_pattern_match(pattern_match):
+    pattern, target = pattern_match
+    assert translate_pattern(pattern).match(target)
+
+
+def test_translated_pattern_mismatch(pattern_mismatch):
+    pattern, target = pattern_mismatch
+    assert not translate_pattern(pattern).match(target)
+
+
+class TempDirTestCase:
+    def setup_method(self, method):
+        self.temp_dir = tempfile.mkdtemp()
+        self.old_cwd = os.getcwd()
+        os.chdir(self.temp_dir)
+
+    def teardown_method(self, method):
+        os.chdir(self.old_cwd)
+        shutil.rmtree(self.temp_dir)
+
+
+class TestManifestTest(TempDirTestCase):
+    def setup_method(self, method):
+        super().setup_method(method)
+
+        f = open(os.path.join(self.temp_dir, 'setup.py'), 'w', encoding="utf-8")
+        f.write(SETUP_PY)
+        f.close()
+        """
+        Create a file tree like:
+        - LICENSE
+        - README.rst
+        - testing.rst
+        - .hidden.rst
+        - app/
+            - __init__.py
+            - a.txt
+            - b.txt
+            - c.rst
+            - static/
+                - app.js
+                - app.js.map
+                - app.css
+                - app.css.map
+        """
+
+        for fname in ['README.rst', '.hidden.rst', 'testing.rst', 'LICENSE']:
+            touch(os.path.join(self.temp_dir, fname))
+
+        # Set up the rest of the test package
+        test_pkg = os.path.join(self.temp_dir, 'app')
+        os.mkdir(test_pkg)
+        for fname in ['__init__.py', 'a.txt', 'b.txt', 'c.rst']:
+            touch(os.path.join(test_pkg, fname))
+
+        # Some compiled front-end assets to include
+        static = os.path.join(test_pkg, 'static')
+        os.mkdir(static)
+        for fname in ['app.js', 'app.js.map', 'app.css', 'app.css.map']:
+            touch(os.path.join(static, fname))
+
+    def make_manifest(self, contents):
+        """Write a MANIFEST.in."""
+        manifest = os.path.join(self.temp_dir, 'MANIFEST.in')
+        with open(manifest, 'w', encoding="utf-8") as f:
+            f.write(DALS(contents))
+
+    def get_files(self):
+        """Run egg_info and get all the files to include, as a set"""
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        cmd = egg_info(dist)
+        cmd.ensure_finalized()
+
+        cmd.run()
+
+        return set(cmd.filelist.files)
+
+    def test_no_manifest(self):
+        """Check a missing MANIFEST.in includes only the standard files."""
+        assert (default_files - set(['MANIFEST.in'])) == self.get_files()
+
+    def test_empty_files(self):
+        """Check an empty MANIFEST.in includes only the standard files."""
+        self.make_manifest("")
+        assert default_files == self.get_files()
+
+    def test_include(self):
+        """Include extra rst files in the project root."""
+        self.make_manifest("include *.rst")
+        files = default_files | set(['testing.rst', '.hidden.rst'])
+        assert files == self.get_files()
+
+    def test_exclude(self):
+        """Include everything in app/ except the text files"""
+        ml = make_local_path
+        self.make_manifest(
+            """
+            include app/*
+            exclude app/*.txt
+            """
+        )
+        files = default_files | set([ml('app/c.rst')])
+        assert files == self.get_files()
+
+    def test_include_multiple(self):
+        """Include with multiple patterns."""
+        ml = make_local_path
+        self.make_manifest("include app/*.txt app/static/*")
+        files = default_files | set([
+            ml('app/a.txt'),
+            ml('app/b.txt'),
+            ml('app/static/app.js'),
+            ml('app/static/app.js.map'),
+            ml('app/static/app.css'),
+            ml('app/static/app.css.map'),
+        ])
+        assert files == self.get_files()
+
+    def test_graft(self):
+        """Include the whole app/static/ directory."""
+        ml = make_local_path
+        self.make_manifest("graft app/static")
+        files = default_files | set([
+            ml('app/static/app.js'),
+            ml('app/static/app.js.map'),
+            ml('app/static/app.css'),
+            ml('app/static/app.css.map'),
+        ])
+        assert files == self.get_files()
+
+    def test_graft_glob_syntax(self):
+        """Include the whole app/static/ directory."""
+        ml = make_local_path
+        self.make_manifest("graft */static")
+        files = default_files | set([
+            ml('app/static/app.js'),
+            ml('app/static/app.js.map'),
+            ml('app/static/app.css'),
+            ml('app/static/app.css.map'),
+        ])
+        assert files == self.get_files()
+
+    def test_graft_global_exclude(self):
+        """Exclude all *.map files in the project."""
+        ml = make_local_path
+        self.make_manifest(
+            """
+            graft app/static
+            global-exclude *.map
+            """
+        )
+        files = default_files | set([ml('app/static/app.js'), ml('app/static/app.css')])
+        assert files == self.get_files()
+
+    def test_global_include(self):
+        """Include all *.rst, *.js, and *.css files in the whole tree."""
+        ml = make_local_path
+        self.make_manifest(
+            """
+            global-include *.rst *.js *.css
+            """
+        )
+        files = default_files | set([
+            '.hidden.rst',
+            'testing.rst',
+            ml('app/c.rst'),
+            ml('app/static/app.js'),
+            ml('app/static/app.css'),
+        ])
+        assert files == self.get_files()
+
+    def test_graft_prune(self):
+        """Include all files in app/, except for the whole app/static/ dir."""
+        ml = make_local_path
+        self.make_manifest(
+            """
+            graft app
+            prune app/static
+            """
+        )
+        files = default_files | set([ml('app/a.txt'), ml('app/b.txt'), ml('app/c.rst')])
+        assert files == self.get_files()
+
+
+class TestFileListTest(TempDirTestCase):
+    """
+    A copy of the relevant bits of distutils/tests/test_filelist.py,
+    to ensure setuptools' version of FileList keeps parity with distutils.
+    """
+
+    @pytest.fixture(autouse=os.getenv("SETUPTOOLS_USE_DISTUTILS") == "stdlib")
+    def _compat_record_logs(self, monkeypatch, caplog):
+        """Account for stdlib compatibility"""
+
+        def _log(_logger, level, msg, args):
+            exc = sys.exc_info()
+            rec = logging.LogRecord("distutils", level, "", 0, msg, args, exc)
+            caplog.records.append(rec)
+
+        monkeypatch.setattr(log.Log, "_log", _log)
+
+    def get_records(self, caplog, *levels):
+        return [r for r in caplog.records if r.levelno in levels]
+
+    def assertNoWarnings(self, caplog):
+        assert self.get_records(caplog, log.WARN) == []
+        caplog.clear()
+
+    def assertWarnings(self, caplog):
+        if IS_PYPY and not caplog.records:
+            pytest.xfail("caplog checks may not work well in PyPy")
+        else:
+            assert len(self.get_records(caplog, log.WARN)) > 0
+            caplog.clear()
+
+    def make_files(self, files):
+        for file in files:
+            file = os.path.join(self.temp_dir, file)
+            dirname, _basename = os.path.split(file)
+            os.makedirs(dirname, exist_ok=True)
+            touch(file)
+
+    def test_process_template_line(self):
+        # testing  all MANIFEST.in template patterns
+        file_list = FileList()
+        ml = make_local_path
+
+        # simulated file list
+        self.make_files([
+            'foo.tmp',
+            'ok',
+            'xo',
+            'four.txt',
+            'buildout.cfg',
+            # filelist does not filter out VCS directories,
+            # it's sdist that does
+            ml('.hg/last-message.txt'),
+            ml('global/one.txt'),
+            ml('global/two.txt'),
+            ml('global/files.x'),
+            ml('global/here.tmp'),
+            ml('f/o/f.oo'),
+            ml('dir/graft-one'),
+            ml('dir/dir2/graft2'),
+            ml('dir3/ok'),
+            ml('dir3/sub/ok.txt'),
+        ])
+
+        MANIFEST_IN = DALS(
+            """\
+        include ok
+        include xo
+        exclude xo
+        include foo.tmp
+        include buildout.cfg
+        global-include *.x
+        global-include *.txt
+        global-exclude *.tmp
+        recursive-include f *.oo
+        recursive-exclude global *.x
+        graft dir
+        prune dir3
+        """
+        )
+
+        for line in MANIFEST_IN.split('\n'):
+            if not line:
+                continue
+            file_list.process_template_line(line)
+
+        wanted = [
+            'buildout.cfg',
+            'four.txt',
+            'ok',
+            ml('.hg/last-message.txt'),
+            ml('dir/graft-one'),
+            ml('dir/dir2/graft2'),
+            ml('f/o/f.oo'),
+            ml('global/one.txt'),
+            ml('global/two.txt'),
+        ]
+
+        file_list.sort()
+        assert file_list.files == wanted
+
+    def test_exclude_pattern(self):
+        # return False if no match
+        file_list = FileList()
+        assert not file_list.exclude_pattern('*.py')
+
+        # return True if files match
+        file_list = FileList()
+        file_list.files = ['a.py', 'b.py']
+        assert file_list.exclude_pattern('*.py')
+
+        # test excludes
+        file_list = FileList()
+        file_list.files = ['a.py', 'a.txt']
+        file_list.exclude_pattern('*.py')
+        file_list.sort()
+        assert file_list.files == ['a.txt']
+
+    def test_include_pattern(self):
+        # return False if no match
+        file_list = FileList()
+        self.make_files([])
+        assert not file_list.include_pattern('*.py')
+
+        # return True if files match
+        file_list = FileList()
+        self.make_files(['a.py', 'b.txt'])
+        assert file_list.include_pattern('*.py')
+
+        # test * matches all files
+        file_list = FileList()
+        self.make_files(['a.py', 'b.txt'])
+        file_list.include_pattern('*')
+        file_list.sort()
+        assert file_list.files == ['a.py', 'b.txt']
+
+    def test_process_template_line_invalid(self):
+        # invalid lines
+        file_list = FileList()
+        for action in (
+            'include',
+            'exclude',
+            'global-include',
+            'global-exclude',
+            'recursive-include',
+            'recursive-exclude',
+            'graft',
+            'prune',
+            'blarg',
+        ):
+            with pytest.raises(DistutilsTemplateError):
+                file_list.process_template_line(action)
+
+    def test_include(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # include
+        file_list = FileList()
+        self.make_files(['a.py', 'b.txt', ml('d/c.py')])
+
+        file_list.process_template_line('include *.py')
+        file_list.sort()
+        assert file_list.files == ['a.py']
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('include *.rb')
+        file_list.sort()
+        assert file_list.files == ['a.py']
+        self.assertWarnings(caplog)
+
+    def test_exclude(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # exclude
+        file_list = FileList()
+        file_list.files = ['a.py', 'b.txt', ml('d/c.py')]
+
+        file_list.process_template_line('exclude *.py')
+        file_list.sort()
+        assert file_list.files == ['b.txt', ml('d/c.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('exclude *.rb')
+        file_list.sort()
+        assert file_list.files == ['b.txt', ml('d/c.py')]
+        self.assertWarnings(caplog)
+
+    def test_global_include(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # global-include
+        file_list = FileList()
+        self.make_files(['a.py', 'b.txt', ml('d/c.py')])
+
+        file_list.process_template_line('global-include *.py')
+        file_list.sort()
+        assert file_list.files == ['a.py', ml('d/c.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('global-include *.rb')
+        file_list.sort()
+        assert file_list.files == ['a.py', ml('d/c.py')]
+        self.assertWarnings(caplog)
+
+    def test_global_exclude(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # global-exclude
+        file_list = FileList()
+        file_list.files = ['a.py', 'b.txt', ml('d/c.py')]
+
+        file_list.process_template_line('global-exclude *.py')
+        file_list.sort()
+        assert file_list.files == ['b.txt']
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('global-exclude *.rb')
+        file_list.sort()
+        assert file_list.files == ['b.txt']
+        self.assertWarnings(caplog)
+
+    def test_recursive_include(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # recursive-include
+        file_list = FileList()
+        self.make_files(['a.py', ml('d/b.py'), ml('d/c.txt'), ml('d/d/e.py')])
+
+        file_list.process_template_line('recursive-include d *.py')
+        file_list.sort()
+        assert file_list.files == [ml('d/b.py'), ml('d/d/e.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('recursive-include e *.py')
+        file_list.sort()
+        assert file_list.files == [ml('d/b.py'), ml('d/d/e.py')]
+        self.assertWarnings(caplog)
+
+    def test_recursive_exclude(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # recursive-exclude
+        file_list = FileList()
+        file_list.files = ['a.py', ml('d/b.py'), ml('d/c.txt'), ml('d/d/e.py')]
+
+        file_list.process_template_line('recursive-exclude d *.py')
+        file_list.sort()
+        assert file_list.files == ['a.py', ml('d/c.txt')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('recursive-exclude e *.py')
+        file_list.sort()
+        assert file_list.files == ['a.py', ml('d/c.txt')]
+        self.assertWarnings(caplog)
+
+    def test_graft(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # graft
+        file_list = FileList()
+        self.make_files(['a.py', ml('d/b.py'), ml('d/d/e.py'), ml('f/f.py')])
+
+        file_list.process_template_line('graft d')
+        file_list.sort()
+        assert file_list.files == [ml('d/b.py'), ml('d/d/e.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('graft e')
+        file_list.sort()
+        assert file_list.files == [ml('d/b.py'), ml('d/d/e.py')]
+        self.assertWarnings(caplog)
+
+    def test_prune(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        ml = make_local_path
+        # prune
+        file_list = FileList()
+        file_list.files = ['a.py', ml('d/b.py'), ml('d/d/e.py'), ml('f/f.py')]
+
+        file_list.process_template_line('prune d')
+        file_list.sort()
+        assert file_list.files == ['a.py', ml('f/f.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('prune e')
+        file_list.sort()
+        assert file_list.files == ['a.py', ml('f/f.py')]
+        self.assertWarnings(caplog)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_namespaces.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_namespaces.py
new file mode 100644
index 0000000000000000000000000000000000000000..a0f4120bf7900b2118cc066034e036ab7af1798b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_namespaces.py
@@ -0,0 +1,138 @@
+import subprocess
+import sys
+
+from setuptools._path import paths_on_pythonpath
+
+from . import namespaces
+
+
+class TestNamespaces:
+    def test_mixed_site_and_non_site(self, tmpdir):
+        """
+        Installing two packages sharing the same namespace, one installed
+        to a site dir and the other installed just to a path on PYTHONPATH
+        should leave the namespace in tact and both packages reachable by
+        import.
+        """
+        pkg_A = namespaces.build_namespace_package(tmpdir, 'myns.pkgA')
+        pkg_B = namespaces.build_namespace_package(tmpdir, 'myns.pkgB')
+        site_packages = tmpdir / 'site-packages'
+        path_packages = tmpdir / 'path-packages'
+        targets = site_packages, path_packages
+        # use pip to install to the target directory
+        install_cmd = [
+            sys.executable,
+            '-m',
+            'pip.__main__',
+            'install',
+            str(pkg_A),
+            '-t',
+            str(site_packages),
+        ]
+        subprocess.check_call(install_cmd)
+        namespaces.make_site_dir(site_packages)
+        install_cmd = [
+            sys.executable,
+            '-m',
+            'pip.__main__',
+            'install',
+            str(pkg_B),
+            '-t',
+            str(path_packages),
+        ]
+        subprocess.check_call(install_cmd)
+        try_import = [
+            sys.executable,
+            '-c',
+            'import myns.pkgA; import myns.pkgB',
+        ]
+        with paths_on_pythonpath(map(str, targets)):
+            subprocess.check_call(try_import)
+
+    def test_pkg_resources_import(self, tmpdir):
+        """
+        Ensure that a namespace package doesn't break on import
+        of pkg_resources.
+        """
+        pkg = namespaces.build_namespace_package(tmpdir, 'myns.pkgA')
+        target = tmpdir / 'packages'
+        target.mkdir()
+        install_cmd = [
+            sys.executable,
+            '-m',
+            'pip',
+            'install',
+            '-t',
+            str(target),
+            str(pkg),
+        ]
+        with paths_on_pythonpath([str(target)]):
+            subprocess.check_call(install_cmd)
+        namespaces.make_site_dir(target)
+        try_import = [
+            sys.executable,
+            '-c',
+            'import pkg_resources',
+        ]
+        with paths_on_pythonpath([str(target)]):
+            subprocess.check_call(try_import)
+
+    def test_namespace_package_installed_and_cwd(self, tmpdir):
+        """
+        Installing a namespace packages but also having it in the current
+        working directory, only one version should take precedence.
+        """
+        pkg_A = namespaces.build_namespace_package(tmpdir, 'myns.pkgA')
+        target = tmpdir / 'packages'
+        # use pip to install to the target directory
+        install_cmd = [
+            sys.executable,
+            '-m',
+            'pip.__main__',
+            'install',
+            str(pkg_A),
+            '-t',
+            str(target),
+        ]
+        subprocess.check_call(install_cmd)
+        namespaces.make_site_dir(target)
+
+        # ensure that package imports and pkg_resources imports
+        pkg_resources_imp = [
+            sys.executable,
+            '-c',
+            'import pkg_resources; import myns.pkgA',
+        ]
+        with paths_on_pythonpath([str(target)]):
+            subprocess.check_call(pkg_resources_imp, cwd=str(pkg_A))
+
+    def test_packages_in_the_same_namespace_installed_and_cwd(self, tmpdir):
+        """
+        Installing one namespace package and also have another in the same
+        namespace in the current working directory, both of them must be
+        importable.
+        """
+        pkg_A = namespaces.build_namespace_package(tmpdir, 'myns.pkgA')
+        pkg_B = namespaces.build_namespace_package(tmpdir, 'myns.pkgB')
+        target = tmpdir / 'packages'
+        # use pip to install to the target directory
+        install_cmd = [
+            sys.executable,
+            '-m',
+            'pip.__main__',
+            'install',
+            str(pkg_A),
+            '-t',
+            str(target),
+        ]
+        subprocess.check_call(install_cmd)
+        namespaces.make_site_dir(target)
+
+        # ensure that all packages import and pkg_resources imports
+        pkg_resources_imp = [
+            sys.executable,
+            '-c',
+            'import pkg_resources; import myns.pkgA; import myns.pkgB',
+        ]
+        with paths_on_pythonpath([str(target)]):
+            subprocess.check_call(pkg_resources_imp, cwd=str(pkg_B))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_packageindex.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_packageindex.py
new file mode 100644
index 0000000000000000000000000000000000000000..2a6e5917a8733c71a5d9b29d4bde6fc12cc1e183
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_packageindex.py
@@ -0,0 +1,267 @@
+import http.client
+import re
+import urllib.error
+import urllib.request
+from inspect import cleandoc
+
+import pytest
+
+import setuptools.package_index
+
+import distutils.errors
+
+
+class TestPackageIndex:
+    def test_regex(self):
+        hash_url = 'http://other_url?:action=show_md5&'
+        hash_url += 'digest=0123456789abcdef0123456789abcdef'
+        doc = """
+            Name
+            (md5)
+        """.lstrip().format(**locals())
+        assert setuptools.package_index.PYPI_MD5.match(doc)
+
+    def test_bad_url_bad_port(self):
+        index = setuptools.package_index.PackageIndex()
+        url = 'http://127.0.0.1:0/nonesuch/test_package_index'
+        with pytest.raises(Exception, match=re.escape(url)):
+            v = index.open_url(url)
+            assert isinstance(v, urllib.error.HTTPError)
+
+    def test_bad_url_typo(self):
+        # issue 16
+        # easy_install inquant.contentmirror.plone breaks because of a typo
+        # in its home URL
+        index = setuptools.package_index.PackageIndex(hosts=('www.example.com',))
+
+        url = 'url:%20https://svn.plone.org/svn/collective/inquant.contentmirror.plone/trunk'
+
+        with pytest.raises(Exception, match=re.escape(url)):
+            v = index.open_url(url)
+            assert isinstance(v, urllib.error.HTTPError)
+
+    def test_bad_url_bad_status_line(self):
+        index = setuptools.package_index.PackageIndex(hosts=('www.example.com',))
+
+        def _urlopen(*args):
+            raise http.client.BadStatusLine('line')
+
+        index.opener = _urlopen
+        url = 'http://example.com'
+        with pytest.raises(Exception, match=r'line'):
+            index.open_url(url)
+
+    def test_bad_url_double_scheme(self):
+        """
+        A bad URL with a double scheme should raise a DistutilsError.
+        """
+        index = setuptools.package_index.PackageIndex(hosts=('www.example.com',))
+
+        # issue 20
+        url = 'http://http://svn.pythonpaste.org/Paste/wphp/trunk'
+        try:
+            index.open_url(url)
+        except distutils.errors.DistutilsError as error:
+            msg = str(error)
+            assert (
+                'nonnumeric port' in msg
+                or 'getaddrinfo failed' in msg
+                or 'Name or service not known' in msg
+            )
+            return
+        raise RuntimeError("Did not raise")
+
+    def test_url_ok(self):
+        index = setuptools.package_index.PackageIndex(hosts=('www.example.com',))
+        url = 'file:///tmp/test_package_index'
+        assert index.url_ok(url, True)
+
+    def test_parse_bdist_wininst(self):
+        parse = setuptools.package_index.parse_bdist_wininst
+
+        actual = parse('reportlab-2.5.win32-py2.4.exe')
+        expected = 'reportlab-2.5', '2.4', 'win32'
+        assert actual == expected
+
+        actual = parse('reportlab-2.5.win32.exe')
+        expected = 'reportlab-2.5', None, 'win32'
+        assert actual == expected
+
+        actual = parse('reportlab-2.5.win-amd64-py2.7.exe')
+        expected = 'reportlab-2.5', '2.7', 'win-amd64'
+        assert actual == expected
+
+        actual = parse('reportlab-2.5.win-amd64.exe')
+        expected = 'reportlab-2.5', None, 'win-amd64'
+        assert actual == expected
+
+    def test__vcs_split_rev_from_url(self):
+        """
+        Test the basic usage of _vcs_split_rev_from_url
+        """
+        vsrfu = setuptools.package_index.PackageIndex._vcs_split_rev_from_url
+        url, rev = vsrfu('https://example.com/bar@2995')
+        assert url == 'https://example.com/bar'
+        assert rev == '2995'
+
+    def test_local_index(self, tmpdir):
+        """
+        local_open should be able to read an index from the file system.
+        """
+        index_file = tmpdir / 'index.html'
+        with index_file.open('w') as f:
+            f.write('
content
')
+        url = 'file:' + urllib.request.pathname2url(str(tmpdir)) + '/'
+        res = setuptools.package_index.local_open(url)
+        assert 'content' in res.read()
+
+    def test_egg_fragment(self):
+        """
+        EGG fragments must comply to PEP 440
+        """
+        epoch = [
+            '',
+            '1!',
+        ]
+        releases = [
+            '0',
+            '0.0',
+            '0.0.0',
+        ]
+        pre = [
+            'a0',
+            'b0',
+            'rc0',
+        ]
+        post = ['.post0']
+        dev = [
+            '.dev0',
+        ]
+        local = [
+            ('', ''),
+            ('+ubuntu.0', '+ubuntu.0'),
+            ('+ubuntu-0', '+ubuntu.0'),
+            ('+ubuntu_0', '+ubuntu.0'),
+        ]
+        versions = [
+            [''.join([e, r, p, loc]) for loc in locs]
+            for e in epoch
+            for r in releases
+            for p in sum([pre, post, dev], [''])
+            for locs in local
+        ]
+        for v, vc in versions:
+            dists = list(
+                setuptools.package_index.distros_for_url(
+                    'http://example.com/example-foo.zip#egg=example-foo-' + v
+                )
+            )
+            assert dists[0].version == ''
+            assert dists[1].version == vc
+
+    def test_download_git_with_rev(self, tmp_path, fp):
+        url = 'git+https://github.example/group/project@master#egg=foo'
+        index = setuptools.package_index.PackageIndex()
+
+        expected_dir = tmp_path / 'project@master'
+        fp.register([
+            'git',
+            'clone',
+            '--quiet',
+            'https://github.example/group/project',
+            expected_dir,
+        ])
+        fp.register(['git', '-C', expected_dir, 'checkout', '--quiet', 'master'])
+
+        result = index.download(url, tmp_path)
+
+        assert result == str(expected_dir)
+        assert len(fp.calls) == 2
+
+    def test_download_git_no_rev(self, tmp_path, fp):
+        url = 'git+https://github.example/group/project#egg=foo'
+        index = setuptools.package_index.PackageIndex()
+
+        expected_dir = tmp_path / 'project'
+        fp.register([
+            'git',
+            'clone',
+            '--quiet',
+            'https://github.example/group/project',
+            expected_dir,
+        ])
+        index.download(url, tmp_path)
+
+    def test_download_svn(self, tmp_path):
+        url = 'svn+https://svn.example/project#egg=foo'
+        index = setuptools.package_index.PackageIndex()
+
+        msg = r".*SVN download is not supported.*"
+        with pytest.raises(distutils.errors.DistutilsError, match=msg):
+            index.download(url, tmp_path)
+
+
+class TestContentCheckers:
+    def test_md5(self):
+        checker = setuptools.package_index.HashChecker.from_url(
+            'http://foo/bar#md5=f12895fdffbd45007040d2e44df98478'
+        )
+        checker.feed('You should probably not be using MD5'.encode('ascii'))
+        assert checker.hash.hexdigest() == 'f12895fdffbd45007040d2e44df98478'
+        assert checker.is_valid()
+
+    def test_other_fragment(self):
+        "Content checks should succeed silently if no hash is present"
+        checker = setuptools.package_index.HashChecker.from_url(
+            'http://foo/bar#something%20completely%20different'
+        )
+        checker.feed('anything'.encode('ascii'))
+        assert checker.is_valid()
+
+    def test_blank_md5(self):
+        "Content checks should succeed if a hash is empty"
+        checker = setuptools.package_index.HashChecker.from_url('http://foo/bar#md5=')
+        checker.feed('anything'.encode('ascii'))
+        assert checker.is_valid()
+
+    def test_get_hash_name_md5(self):
+        checker = setuptools.package_index.HashChecker.from_url(
+            'http://foo/bar#md5=f12895fdffbd45007040d2e44df98478'
+        )
+        assert checker.hash_name == 'md5'
+
+    def test_report(self):
+        checker = setuptools.package_index.HashChecker.from_url(
+            'http://foo/bar#md5=f12895fdffbd45007040d2e44df98478'
+        )
+        rep = checker.report(lambda x: x, 'My message about %s')
+        assert rep == 'My message about md5'
+
+
+class TestPyPIConfig:
+    def test_percent_in_password(self, tmp_home_dir):
+        pypirc = tmp_home_dir / '.pypirc'
+        pypirc.write_text(
+            cleandoc(
+                """
+                [pypi]
+                repository=https://pypi.org
+                username=jaraco
+                password=pity%
+                """
+            ),
+            encoding="utf-8",
+        )
+        cfg = setuptools.package_index.PyPIConfig()
+        cred = cfg.creds_by_repository['https://pypi.org']
+        assert cred.username == 'jaraco'
+        assert cred.password == 'pity%'
+
+
+@pytest.mark.timeout(1)
+def test_REL_DoS():
+    """
+    REL should not hang on a contrived attack string.
+    """
+    setuptools.package_index.REL.search('< rel=' + ' ' * 2**12)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_sandbox.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_sandbox.py
new file mode 100644
index 0000000000000000000000000000000000000000..a476b7c93d7441834f415223cb386859581724f8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_sandbox.py
@@ -0,0 +1,134 @@
+"""develop tests"""
+
+import os
+import types
+
+import pytest
+
+import pkg_resources
+import setuptools.sandbox
+
+
+class TestSandbox:
+    def test_devnull(self, tmpdir):
+        with setuptools.sandbox.DirectorySandbox(str(tmpdir)):
+            self._file_writer(os.devnull)
+
+    @staticmethod
+    def _file_writer(path):
+        def do_write():
+            with open(path, 'w', encoding="utf-8") as f:
+                f.write('xxx')
+
+        return do_write
+
+    def test_setup_py_with_BOM(self):
+        """
+        It should be possible to execute a setup.py with a Byte Order Mark
+        """
+        target = pkg_resources.resource_filename(__name__, 'script-with-bom.py')
+        namespace = types.ModuleType('namespace')
+        setuptools.sandbox._execfile(target, vars(namespace))
+        assert namespace.result == 'passed'
+
+    def test_setup_py_with_CRLF(self, tmpdir):
+        setup_py = tmpdir / 'setup.py'
+        with setup_py.open('wb') as stream:
+            stream.write(b'"degenerate script"\r\n')
+        setuptools.sandbox._execfile(str(setup_py), globals())
+
+
+class TestExceptionSaver:
+    def test_exception_trapped(self):
+        with setuptools.sandbox.ExceptionSaver():
+            raise ValueError("details")
+
+    def test_exception_resumed(self):
+        with setuptools.sandbox.ExceptionSaver() as saved_exc:
+            raise ValueError("details")
+
+        with pytest.raises(ValueError) as caught:
+            saved_exc.resume()
+
+        assert isinstance(caught.value, ValueError)
+        assert str(caught.value) == 'details'
+
+    def test_exception_reconstructed(self):
+        orig_exc = ValueError("details")
+
+        with setuptools.sandbox.ExceptionSaver() as saved_exc:
+            raise orig_exc
+
+        with pytest.raises(ValueError) as caught:
+            saved_exc.resume()
+
+        assert isinstance(caught.value, ValueError)
+        assert caught.value is not orig_exc
+
+    def test_no_exception_passes_quietly(self):
+        with setuptools.sandbox.ExceptionSaver() as saved_exc:
+            pass
+
+        saved_exc.resume()
+
+    def test_unpickleable_exception(self):
+        class CantPickleThis(Exception):
+            "This Exception is unpickleable because it's not in globals"
+
+            def __repr__(self) -> str:
+                return f'CantPickleThis{self.args!r}'
+
+        with setuptools.sandbox.ExceptionSaver() as saved_exc:
+            raise CantPickleThis('detail')
+
+        with pytest.raises(setuptools.sandbox.UnpickleableException) as caught:
+            saved_exc.resume()
+
+        assert str(caught.value) == "CantPickleThis('detail',)"
+
+    def test_unpickleable_exception_when_hiding_setuptools(self):
+        """
+        As revealed in #440, an infinite recursion can occur if an unpickleable
+        exception while setuptools is hidden. Ensure this doesn't happen.
+        """
+
+        class ExceptionUnderTest(Exception):
+            """
+            An unpickleable exception (not in globals).
+            """
+
+        with pytest.raises(setuptools.sandbox.UnpickleableException) as caught:
+            with setuptools.sandbox.save_modules():
+                setuptools.sandbox.hide_setuptools()
+                raise ExceptionUnderTest
+
+        (msg,) = caught.value.args
+        assert msg == 'ExceptionUnderTest()'
+
+    def test_sandbox_violation_raised_hiding_setuptools(self, tmpdir):
+        """
+        When in a sandbox with setuptools hidden, a SandboxViolation
+        should reflect a proper exception and not be wrapped in
+        an UnpickleableException.
+        """
+
+        def write_file():
+            "Trigger a SandboxViolation by writing outside the sandbox"
+            with open('/etc/foo', 'w', encoding="utf-8"):
+                pass
+
+        with pytest.raises(setuptools.sandbox.SandboxViolation) as caught:
+            with setuptools.sandbox.save_modules():
+                setuptools.sandbox.hide_setuptools()
+                with setuptools.sandbox.DirectorySandbox(str(tmpdir)):
+                    write_file()
+
+        cmd, args, kwargs = caught.value.args
+        assert cmd == 'open'
+        assert args == ('/etc/foo', 'w')
+        assert kwargs == {"encoding": "utf-8"}
+
+        msg = str(caught.value)
+        assert 'open' in msg
+        assert "('/etc/foo', 'w')" in msg
+        assert "{'encoding': 'utf-8'}" in msg
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_sdist.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_sdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..19d8ddf6dafb0cacc044a6021f283d3e9faaf800
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_sdist.py
@@ -0,0 +1,984 @@
+"""sdist tests"""
+
+import contextlib
+import io
+import logging
+import os
+import pathlib
+import sys
+import tarfile
+import tempfile
+import unicodedata
+from inspect import cleandoc
+from pathlib import Path
+from unittest import mock
+
+import jaraco.path
+import pytest
+
+from setuptools import Command, SetuptoolsDeprecationWarning
+from setuptools._importlib import metadata
+from setuptools.command.egg_info import manifest_maker
+from setuptools.command.sdist import sdist
+from setuptools.dist import Distribution
+from setuptools.extension import Extension
+from setuptools.tests import fail_on_ascii
+
+from .text import Filenames
+
+import distutils
+from distutils.core import run_setup
+
+SETUP_ATTRS = {
+    'name': 'sdist_test',
+    'version': '0.0',
+    'packages': ['sdist_test'],
+    'package_data': {'sdist_test': ['*.txt']},
+    'data_files': [("data", [os.path.join("d", "e.dat")])],
+}
+
+SETUP_PY = f"""\
+from setuptools import setup
+
+setup(**{SETUP_ATTRS!r})
+"""
+
+EXTENSION = Extension(
+    name="sdist_test.f",
+    sources=[os.path.join("sdist_test", "f.c")],
+    depends=[os.path.join("sdist_test", "f.h")],
+)
+EXTENSION_SOURCES = EXTENSION.sources + EXTENSION.depends
+
+
+@contextlib.contextmanager
+def quiet():
+    old_stdout, old_stderr = sys.stdout, sys.stderr
+    sys.stdout, sys.stderr = io.StringIO(), io.StringIO()
+    try:
+        yield
+    finally:
+        sys.stdout, sys.stderr = old_stdout, old_stderr
+
+
+# Convert to POSIX path
+def posix(path):
+    if not isinstance(path, str):
+        return path.replace(os.sep.encode('ascii'), b'/')
+    else:
+        return path.replace(os.sep, '/')
+
+
+# HFS Plus uses decomposed UTF-8
+def decompose(path):
+    if isinstance(path, str):
+        return unicodedata.normalize('NFD', path)
+    try:
+        path = path.decode('utf-8')
+        path = unicodedata.normalize('NFD', path)
+        path = path.encode('utf-8')
+    except UnicodeError:
+        pass  # Not UTF-8
+    return path
+
+
+def read_all_bytes(filename):
+    with open(filename, 'rb') as fp:
+        return fp.read()
+
+
+def latin1_fail():
+    try:
+        desc, filename = tempfile.mkstemp(suffix=Filenames.latin_1)
+        os.close(desc)
+        os.remove(filename)
+    except Exception:
+        return True
+
+
+fail_on_latin1_encoded_filenames = pytest.mark.xfail(
+    latin1_fail(),
+    reason="System does not support latin-1 filenames",
+)
+
+
+skip_under_xdist = pytest.mark.skipif(
+    "os.environ.get('PYTEST_XDIST_WORKER')",
+    reason="pytest-dev/pytest-xdist#843",
+)
+skip_under_stdlib_distutils = pytest.mark.skipif(
+    not distutils.__package__.startswith('setuptools'),
+    reason="the test is not supported with stdlib distutils",
+)
+
+
+def touch(path):
+    open(path, 'wb').close()
+    return path
+
+
+def symlink_or_skip_test(src, dst):
+    try:
+        os.symlink(src, dst)
+    except (OSError, NotImplementedError):
+        pytest.skip("symlink not supported in OS")
+        return None
+    return dst
+
+
+class TestSdistTest:
+    @pytest.fixture(autouse=True)
+    def source_dir(self, tmpdir):
+        tmpdir = tmpdir / "project_root"
+        tmpdir.mkdir()
+
+        (tmpdir / 'setup.py').write_text(SETUP_PY, encoding='utf-8')
+
+        # Set up the rest of the test package
+        test_pkg = tmpdir / 'sdist_test'
+        test_pkg.mkdir()
+        data_folder = tmpdir / 'd'
+        data_folder.mkdir()
+        # *.rst was not included in package_data, so c.rst should not be
+        # automatically added to the manifest when not under version control
+        for fname in ['__init__.py', 'a.txt', 'b.txt', 'c.rst']:
+            touch(test_pkg / fname)
+        touch(data_folder / 'e.dat')
+        # C sources are not included by default, but they will be,
+        # if an extension module uses them as sources or depends
+        for fname in EXTENSION_SOURCES:
+            touch(tmpdir / fname)
+
+        with tmpdir.as_cwd():
+            yield tmpdir
+
+    def assert_package_data_in_manifest(self, cmd):
+        manifest = cmd.filelist.files
+        assert os.path.join('sdist_test', 'a.txt') in manifest
+        assert os.path.join('sdist_test', 'b.txt') in manifest
+        assert os.path.join('sdist_test', 'c.rst') not in manifest
+        assert os.path.join('d', 'e.dat') in manifest
+
+    def setup_with_extension(self):
+        setup_attrs = {**SETUP_ATTRS, 'ext_modules': [EXTENSION]}
+
+        dist = Distribution(setup_attrs)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet():
+            cmd.run()
+
+        return cmd
+
+    def test_package_data_in_sdist(self):
+        """Regression test for pull request #4: ensures that files listed in
+        package_data are included in the manifest even if they're not added to
+        version control.
+        """
+
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet():
+            cmd.run()
+
+        self.assert_package_data_in_manifest(cmd)
+
+    def test_package_data_and_include_package_data_in_sdist(self):
+        """
+        Ensure package_data and include_package_data work
+        together.
+        """
+        setup_attrs = {**SETUP_ATTRS, 'include_package_data': True}
+        assert setup_attrs['package_data']
+
+        dist = Distribution(setup_attrs)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet():
+            cmd.run()
+
+        self.assert_package_data_in_manifest(cmd)
+
+    def test_extension_sources_in_sdist(self):
+        """
+        Ensure that the files listed in Extension.sources and Extension.depends
+        are automatically included in the manifest.
+        """
+        cmd = self.setup_with_extension()
+        self.assert_package_data_in_manifest(cmd)
+        manifest = cmd.filelist.files
+        for path in EXTENSION_SOURCES:
+            assert path in manifest
+
+    def test_missing_extension_sources(self):
+        """
+        Similar to test_extension_sources_in_sdist but the referenced files don't exist.
+        Missing files should not be included in distribution (with no error raised).
+        """
+        for path in EXTENSION_SOURCES:
+            os.remove(path)
+
+        cmd = self.setup_with_extension()
+        self.assert_package_data_in_manifest(cmd)
+        manifest = cmd.filelist.files
+        for path in EXTENSION_SOURCES:
+            assert path not in manifest
+
+    def test_symlinked_extension_sources(self):
+        """
+        Similar to test_extension_sources_in_sdist but the referenced files are
+        instead symbolic links to project-local files. Referenced file paths
+        should be included. Symlink targets themselves should NOT be included.
+        """
+        symlinked = []
+        for path in EXTENSION_SOURCES:
+            base, ext = os.path.splitext(path)
+            target = base + "_target." + ext
+
+            os.rename(path, target)
+            symlink_or_skip_test(os.path.basename(target), path)
+            symlinked.append(target)
+
+        cmd = self.setup_with_extension()
+        self.assert_package_data_in_manifest(cmd)
+        manifest = cmd.filelist.files
+        for path in EXTENSION_SOURCES:
+            assert path in manifest
+        for path in symlinked:
+            assert path not in manifest
+
+    _INVALID_PATHS = {
+        "must be relative": lambda: (
+            os.path.abspath(os.path.join("sdist_test", "f.h"))
+        ),
+        "can't have `..` segments": lambda: (
+            os.path.join("sdist_test", "..", "sdist_test", "f.h")
+        ),
+        "doesn't exist": lambda: (
+            os.path.join("sdist_test", "this_file_does_not_exist.h")
+        ),
+        "must be inside the project root": lambda: (
+            symlink_or_skip_test(
+                touch(os.path.join("..", "outside_of_project_root.h")),
+                "symlink.h",
+            )
+        ),
+    }
+
+    @skip_under_stdlib_distutils
+    @pytest.mark.parametrize("reason", _INVALID_PATHS.keys())
+    def test_invalid_extension_depends(self, reason, caplog):
+        """
+        Due to backwards compatibility reasons, `Extension.depends` should accept
+        invalid/weird paths, but then ignore them when building a sdist.
+
+        This test verifies that the source distribution is still built
+        successfully with such paths, but that instead of adding these paths to
+        the manifest, we emit an informational message, notifying the user that
+        the invalid path won't be automatically included.
+        """
+        invalid_path = self._INVALID_PATHS[reason]()
+        extension = Extension(
+            name="sdist_test.f",
+            sources=[],
+            depends=[invalid_path],
+        )
+        setup_attrs = {**SETUP_ATTRS, 'ext_modules': [extension]}
+
+        dist = Distribution(setup_attrs)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet(), caplog.at_level(logging.INFO):
+            cmd.run()
+
+        self.assert_package_data_in_manifest(cmd)
+        manifest = cmd.filelist.files
+        assert invalid_path not in manifest
+
+        expected_message = [
+            message
+            for (logger, level, message) in caplog.record_tuples
+            if (
+                logger == "root"  #
+                and level == logging.INFO  #
+                and invalid_path in message  #
+            )
+        ]
+        assert len(expected_message) == 1
+        (expected_message,) = expected_message
+        assert reason in expected_message
+
+    def test_custom_build_py(self):
+        """
+        Ensure projects defining custom build_py don't break
+        when creating sdists (issue #2849)
+        """
+        from distutils.command.build_py import build_py as OrigBuildPy
+
+        using_custom_command_guard = mock.Mock()
+
+        class CustomBuildPy(OrigBuildPy):
+            """
+            Some projects have custom commands inheriting from `distutils`
+            """
+
+            def get_data_files(self):
+                using_custom_command_guard()
+                return super().get_data_files()
+
+        setup_attrs = {**SETUP_ATTRS, 'include_package_data': True}
+        assert setup_attrs['package_data']
+
+        dist = Distribution(setup_attrs)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        # Make sure we use the custom command
+        cmd.cmdclass = {'build_py': CustomBuildPy}
+        cmd.distribution.cmdclass = {'build_py': CustomBuildPy}
+        assert cmd.distribution.get_command_class('build_py') == CustomBuildPy
+
+        msg = "setuptools instead of distutils"
+        with quiet(), pytest.warns(SetuptoolsDeprecationWarning, match=msg):
+            cmd.run()
+
+        using_custom_command_guard.assert_called()
+        self.assert_package_data_in_manifest(cmd)
+
+    def test_setup_py_exists(self):
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'foo.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet():
+            cmd.run()
+
+        manifest = cmd.filelist.files
+        assert 'setup.py' in manifest
+
+    def test_setup_py_missing(self):
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'foo.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        if os.path.exists("setup.py"):
+            os.remove("setup.py")
+        with quiet():
+            cmd.run()
+
+        manifest = cmd.filelist.files
+        assert 'setup.py' not in manifest
+
+    def test_setup_py_excluded(self):
+        with open("MANIFEST.in", "w", encoding="utf-8") as manifest_file:
+            manifest_file.write("exclude setup.py")
+
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'foo.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet():
+            cmd.run()
+
+        manifest = cmd.filelist.files
+        assert 'setup.py' not in manifest
+
+    def test_defaults_case_sensitivity(self, source_dir):
+        """
+        Make sure default files (README.*, etc.) are added in a case-sensitive
+        way to avoid problems with packages built on Windows.
+        """
+
+        touch(source_dir / 'readme.rst')
+        touch(source_dir / 'SETUP.cfg')
+
+        dist = Distribution(SETUP_ATTRS)
+        # the extension deliberately capitalized for this test
+        # to make sure the actual filename (not capitalized) gets added
+        # to the manifest
+        dist.script_name = 'setup.PY'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        with quiet():
+            cmd.run()
+
+        # lowercase all names so we can test in a
+        # case-insensitive way to make sure the files
+        # are not included.
+        manifest = map(lambda x: x.lower(), cmd.filelist.files)
+        assert 'readme.rst' not in manifest, manifest
+        assert 'setup.py' not in manifest, manifest
+        assert 'setup.cfg' not in manifest, manifest
+
+    def test_exclude_dev_only_cache_folders(self, source_dir):
+        included = {
+            # Emulate problem in https://github.com/pypa/setuptools/issues/4601
+            "MANIFEST.in": (
+                "global-include LICEN[CS]E* COPYING* NOTICE* AUTHORS*\n"
+                "global-include *.txt\n"
+            ),
+            # For the sake of being conservative and limiting unforeseen side-effects
+            # we just exclude dev-only cache folders at the root of the repository:
+            "test/.venv/lib/python3.9/site-packages/bar-2.dist-info/AUTHORS.rst": "",
+            "src/.nox/py/lib/python3.12/site-packages/bar-2.dist-info/COPYING.txt": "",
+            "doc/.tox/default/lib/python3.11/site-packages/foo-4.dist-info/LICENSE": "",
+            # Let's test against false positives with similarly named files:
+            ".venv-requirements.txt": "",
+            ".tox-coveragerc.txt": "",
+            ".noxy/coveragerc.txt": "",
+        }
+
+        excluded = {
+            # .tox/.nox/.venv are well-know folders present at the root of Python repos
+            # and therefore should be excluded
+            ".tox/release/lib/python3.11/site-packages/foo-4.dist-info/LICENSE": "",
+            ".nox/py/lib/python3.12/site-packages/bar-2.dist-info/COPYING.txt": "",
+            ".venv/lib/python3.9/site-packages/bar-2.dist-info/AUTHORS.rst": "",
+        }
+
+        for file, content in {**excluded, **included}.items():
+            Path(source_dir, file).parent.mkdir(parents=True, exist_ok=True)
+            Path(source_dir, file).write_text(content, encoding="utf-8")
+
+        cmd = self.setup_with_extension()
+        self.assert_package_data_in_manifest(cmd)
+        manifest = {f.replace(os.sep, '/') for f in cmd.filelist.files}
+        for path in excluded:
+            assert os.path.exists(path)
+            assert path not in manifest, (path, manifest)
+        for path in included:
+            assert os.path.exists(path)
+            assert path in manifest, (path, manifest)
+
+    @fail_on_ascii
+    def test_manifest_is_written_with_utf8_encoding(self):
+        # Test for #303.
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        mm = manifest_maker(dist)
+        mm.manifest = os.path.join('sdist_test.egg-info', 'SOURCES.txt')
+        os.mkdir('sdist_test.egg-info')
+
+        # UTF-8 filename
+        filename = os.path.join('sdist_test', 'smörbröd.py')
+
+        # Must create the file or it will get stripped.
+        touch(filename)
+
+        # Add UTF-8 filename and write manifest
+        with quiet():
+            mm.run()
+            mm.filelist.append(filename)
+            mm.write_manifest()
+
+        contents = read_all_bytes(mm.manifest)
+
+        # The manifest should be UTF-8 encoded
+        u_contents = contents.decode('UTF-8')
+
+        # The manifest should contain the UTF-8 filename
+        assert posix(filename) in u_contents
+
+    @fail_on_ascii
+    def test_write_manifest_allows_utf8_filenames(self):
+        # Test for #303.
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        mm = manifest_maker(dist)
+        mm.manifest = os.path.join('sdist_test.egg-info', 'SOURCES.txt')
+        os.mkdir('sdist_test.egg-info')
+
+        filename = os.path.join(b'sdist_test', Filenames.utf_8)
+
+        # Must touch the file or risk removal
+        touch(filename)
+
+        # Add filename and write manifest
+        with quiet():
+            mm.run()
+            u_filename = filename.decode('utf-8')
+            mm.filelist.files.append(u_filename)
+            # Re-write manifest
+            mm.write_manifest()
+
+        contents = read_all_bytes(mm.manifest)
+
+        # The manifest should be UTF-8 encoded
+        contents.decode('UTF-8')
+
+        # The manifest should contain the UTF-8 filename
+        assert posix(filename) in contents
+
+        # The filelist should have been updated as well
+        assert u_filename in mm.filelist.files
+
+    @skip_under_xdist
+    def test_write_manifest_skips_non_utf8_filenames(self):
+        """
+        Files that cannot be encoded to UTF-8 (specifically, those that
+        weren't originally successfully decoded and have surrogate
+        escapes) should be omitted from the manifest.
+        See https://bitbucket.org/tarek/distribute/issue/303 for history.
+        """
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        mm = manifest_maker(dist)
+        mm.manifest = os.path.join('sdist_test.egg-info', 'SOURCES.txt')
+        os.mkdir('sdist_test.egg-info')
+
+        # Latin-1 filename
+        filename = os.path.join(b'sdist_test', Filenames.latin_1)
+
+        # Add filename with surrogates and write manifest
+        with quiet():
+            mm.run()
+            u_filename = filename.decode('utf-8', 'surrogateescape')
+            mm.filelist.append(u_filename)
+            # Re-write manifest
+            mm.write_manifest()
+
+        contents = read_all_bytes(mm.manifest)
+
+        # The manifest should be UTF-8 encoded
+        contents.decode('UTF-8')
+
+        # The Latin-1 filename should have been skipped
+        assert posix(filename) not in contents
+
+        # The filelist should have been updated as well
+        assert u_filename not in mm.filelist.files
+
+    @fail_on_ascii
+    def test_manifest_is_read_with_utf8_encoding(self):
+        # Test for #303.
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        # Create manifest
+        with quiet():
+            cmd.run()
+
+        # Add UTF-8 filename to manifest
+        filename = os.path.join(b'sdist_test', Filenames.utf_8)
+        cmd.manifest = os.path.join('sdist_test.egg-info', 'SOURCES.txt')
+        manifest = open(cmd.manifest, 'ab')
+        manifest.write(b'\n' + filename)
+        manifest.close()
+
+        # The file must exist to be included in the filelist
+        touch(filename)
+
+        # Re-read manifest
+        cmd.filelist.files = []
+        with quiet():
+            cmd.read_manifest()
+
+        # The filelist should contain the UTF-8 filename
+        filename = filename.decode('utf-8')
+        assert filename in cmd.filelist.files
+
+    @fail_on_latin1_encoded_filenames
+    def test_read_manifest_skips_non_utf8_filenames(self):
+        # Test for #303.
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        # Create manifest
+        with quiet():
+            cmd.run()
+
+        # Add Latin-1 filename to manifest
+        filename = os.path.join(b'sdist_test', Filenames.latin_1)
+        cmd.manifest = os.path.join('sdist_test.egg-info', 'SOURCES.txt')
+        manifest = open(cmd.manifest, 'ab')
+        manifest.write(b'\n' + filename)
+        manifest.close()
+
+        # The file must exist to be included in the filelist
+        touch(filename)
+
+        # Re-read manifest
+        cmd.filelist.files = []
+        with quiet():
+            cmd.read_manifest()
+
+        # The Latin-1 filename should have been skipped
+        filename = filename.decode('latin-1')
+        assert filename not in cmd.filelist.files
+
+    @fail_on_ascii
+    @fail_on_latin1_encoded_filenames
+    def test_sdist_with_utf8_encoded_filename(self):
+        # Test for #303.
+        dist = Distribution(self.make_strings(SETUP_ATTRS))
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        filename = os.path.join(b'sdist_test', Filenames.utf_8)
+        touch(filename)
+
+        with quiet():
+            cmd.run()
+
+        if sys.platform == 'darwin':
+            filename = decompose(filename)
+
+        fs_enc = sys.getfilesystemencoding()
+
+        if sys.platform == 'win32':
+            if fs_enc == 'cp1252':
+                # Python mangles the UTF-8 filename
+                filename = filename.decode('cp1252')
+                assert filename in cmd.filelist.files
+            else:
+                filename = filename.decode('mbcs')
+                assert filename in cmd.filelist.files
+        else:
+            filename = filename.decode('utf-8')
+            assert filename in cmd.filelist.files
+
+    @classmethod
+    def make_strings(cls, item):
+        if isinstance(item, dict):
+            return {key: cls.make_strings(value) for key, value in item.items()}
+        if isinstance(item, list):
+            return list(map(cls.make_strings, item))
+        return str(item)
+
+    @fail_on_latin1_encoded_filenames
+    @skip_under_xdist
+    def test_sdist_with_latin1_encoded_filename(self):
+        # Test for #303.
+        dist = Distribution(self.make_strings(SETUP_ATTRS))
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+
+        # Latin-1 filename
+        filename = os.path.join(b'sdist_test', Filenames.latin_1)
+        touch(filename)
+        assert os.path.isfile(filename)
+
+        with quiet():
+            cmd.run()
+
+        # not all windows systems have a default FS encoding of cp1252
+        if sys.platform == 'win32':
+            # Latin-1 is similar to Windows-1252 however
+            # on mbcs filesys it is not in latin-1 encoding
+            fs_enc = sys.getfilesystemencoding()
+            if fs_enc != 'mbcs':
+                fs_enc = 'latin-1'
+            filename = filename.decode(fs_enc)
+
+            assert filename in cmd.filelist.files
+        else:
+            # The Latin-1 filename should have been skipped
+            filename = filename.decode('latin-1')
+            assert filename not in cmd.filelist.files
+
+    _EXAMPLE_DIRECTIVES = {
+        "setup.cfg - long_description and version": """
+            [metadata]
+            name = testing
+            version = file: src/VERSION.txt
+            license_files = DOWHATYOUWANT
+            long_description = file: README.rst, USAGE.rst
+            """,
+        "pyproject.toml - static readme/license files and dynamic version": """
+            [project]
+            name = "testing"
+            readme = "USAGE.rst"
+            license-files = ["DOWHATYOUWANT"]
+            dynamic = ["version"]
+            [tool.setuptools.dynamic]
+            version = {file = ["src/VERSION.txt"]}
+            """,
+        "pyproject.toml - directive with str instead of list": """
+            [project]
+            name = "testing"
+            readme = "USAGE.rst"
+            license-files = ["DOWHATYOUWANT"]
+            dynamic = ["version"]
+            [tool.setuptools.dynamic]
+            version = {file = "src/VERSION.txt"}
+            """,
+        "pyproject.toml - deprecated license table with file entry": """
+            [project]
+            name = "testing"
+            readme = "USAGE.rst"
+            license = {file = "DOWHATYOUWANT"}
+            dynamic = ["version"]
+            [tool.setuptools.dynamic]
+            version = {file = "src/VERSION.txt"}
+            """,
+    }
+
+    @pytest.mark.parametrize("config", _EXAMPLE_DIRECTIVES.keys())
+    @pytest.mark.filterwarnings(
+        "ignore:.project.license. as a TOML table is deprecated"
+    )
+    def test_add_files_referenced_by_config_directives(self, source_dir, config):
+        config_file, _, _ = config.partition(" - ")
+        config_text = self._EXAMPLE_DIRECTIVES[config]
+        (source_dir / 'src').mkdir()
+        (source_dir / 'src/VERSION.txt').write_text("0.42", encoding="utf-8")
+        (source_dir / 'README.rst').write_text("hello world!", encoding="utf-8")
+        (source_dir / 'USAGE.rst').write_text("hello world!", encoding="utf-8")
+        (source_dir / 'DOWHATYOUWANT').write_text("hello world!", encoding="utf-8")
+        (source_dir / config_file).write_text(config_text, encoding="utf-8")
+
+        dist = Distribution({"packages": []})
+        dist.script_name = 'setup.py'
+        dist.parse_config_files()
+
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+        with quiet():
+            cmd.run()
+
+        assert (
+            'src/VERSION.txt' in cmd.filelist.files
+            or 'src\\VERSION.txt' in cmd.filelist.files
+        )
+        assert 'USAGE.rst' in cmd.filelist.files
+        assert 'DOWHATYOUWANT' in cmd.filelist.files
+        assert '/' not in cmd.filelist.files
+        assert '\\' not in cmd.filelist.files
+
+    def test_pyproject_toml_in_sdist(self, source_dir):
+        """
+        Check if pyproject.toml is included in source distribution if present
+        """
+        touch(source_dir / 'pyproject.toml')
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+        with quiet():
+            cmd.run()
+        manifest = cmd.filelist.files
+        assert 'pyproject.toml' in manifest
+
+    def test_pyproject_toml_excluded(self, source_dir):
+        """
+        Check that pyproject.toml can excluded even if present
+        """
+        touch(source_dir / 'pyproject.toml')
+        with open('MANIFEST.in', 'w', encoding="utf-8") as mts:
+            print('exclude pyproject.toml', file=mts)
+        dist = Distribution(SETUP_ATTRS)
+        dist.script_name = 'setup.py'
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+        with quiet():
+            cmd.run()
+        manifest = cmd.filelist.files
+        assert 'pyproject.toml' not in manifest
+
+    def test_build_subcommand_source_files(self, source_dir):
+        touch(source_dir / '.myfile~')
+
+        # Sanity check: without custom commands file list should not be affected
+        dist = Distribution({**SETUP_ATTRS, "script_name": "setup.py"})
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+        with quiet():
+            cmd.run()
+        manifest = cmd.filelist.files
+        assert '.myfile~' not in manifest
+
+        # Test: custom command should be able to augment file list
+        dist = Distribution({**SETUP_ATTRS, "script_name": "setup.py"})
+        build = dist.get_command_obj("build")
+        build.sub_commands = [*build.sub_commands, ("build_custom", None)]
+
+        class build_custom(Command):
+            def initialize_options(self): ...
+
+            def finalize_options(self): ...
+
+            def run(self): ...
+
+            def get_source_files(self):
+                return ['.myfile~']
+
+        dist.cmdclass.update(build_custom=build_custom)
+
+        cmd = sdist(dist)
+        cmd.use_defaults = True
+        cmd.ensure_finalized()
+        with quiet():
+            cmd.run()
+        manifest = cmd.filelist.files
+        assert '.myfile~' in manifest
+
+    @pytest.mark.skipif("os.environ.get('SETUPTOOLS_USE_DISTUTILS') == 'stdlib'")
+    def test_build_base_pathlib(self, source_dir):
+        """
+        Ensure if build_base is a pathlib.Path, the build still succeeds.
+        """
+        dist = Distribution({
+            **SETUP_ATTRS,
+            "script_name": "setup.py",
+            "options": {"build": {"build_base": pathlib.Path('build')}},
+        })
+        cmd = sdist(dist)
+        cmd.ensure_finalized()
+        with quiet():
+            cmd.run()
+
+
+def test_default_revctrl():
+    """
+    When _default_revctrl was removed from the `setuptools.command.sdist`
+    module in 10.0, it broke some systems which keep an old install of
+    setuptools (Distribute) around. Those old versions require that the
+    setuptools package continue to implement that interface, so this
+    function provides that interface, stubbed. See #320 for details.
+
+    This interface must be maintained until Ubuntu 12.04 is no longer
+    supported (by Setuptools).
+    """
+    (ep,) = metadata.EntryPoints._from_text(
+        """
+        [setuptools.file_finders]
+        svn_cvs = setuptools.command.sdist:_default_revctrl
+        """
+    )
+    res = ep.load()
+    assert hasattr(res, '__iter__')
+
+
+class TestRegressions:
+    """
+    Can be removed/changed if the project decides to change how it handles symlinks
+    or external files.
+    """
+
+    @staticmethod
+    def files_for_symlink_in_extension_depends(tmp_path, dep_path):
+        return {
+            "external": {
+                "dir": {"file.h": ""},
+            },
+            "project": {
+                "setup.py": cleandoc(
+                    f"""
+                    from setuptools import Extension, setup
+                    setup(
+                        name="myproj",
+                        version="42",
+                        ext_modules=[
+                            Extension(
+                                "hello", sources=["hello.pyx"],
+                                depends=[{dep_path!r}]
+                            )
+                        ],
+                    )
+                    """
+                ),
+                "hello.pyx": "",
+                "MANIFEST.in": "global-include *.h",
+            },
+        }
+
+    @pytest.mark.parametrize(
+        "dep_path", ("myheaders/dir/file.h", "myheaders/dir/../dir/file.h")
+    )
+    def test_symlink_in_extension_depends(self, monkeypatch, tmp_path, dep_path):
+        # Given a project with a symlinked dir and a "depends" targeting that dir
+        files = self.files_for_symlink_in_extension_depends(tmp_path, dep_path)
+        jaraco.path.build(files, prefix=str(tmp_path))
+        symlink_or_skip_test(tmp_path / "external", tmp_path / "project/myheaders")
+
+        # When `sdist` runs, there should be no error
+        members = run_sdist(monkeypatch, tmp_path / "project")
+        # and the sdist should contain the symlinked files
+        for expected in (
+            "myproj-42/hello.pyx",
+            "myproj-42/myheaders/dir/file.h",
+        ):
+            assert expected in members
+
+    @staticmethod
+    def files_for_external_path_in_extension_depends(tmp_path, dep_path):
+        head, _, tail = dep_path.partition("$tmp_path$/")
+        dep_path = tmp_path / tail if tail else head
+
+        return {
+            "external": {
+                "dir": {"file.h": ""},
+            },
+            "project": {
+                "setup.py": cleandoc(
+                    f"""
+                    from setuptools import Extension, setup
+                    setup(
+                        name="myproj",
+                        version="42",
+                        ext_modules=[
+                            Extension(
+                                "hello", sources=["hello.pyx"],
+                                depends=[{str(dep_path)!r}]
+                            )
+                        ],
+                    )
+                    """
+                ),
+                "hello.pyx": "",
+                "MANIFEST.in": "global-include *.h",
+            },
+        }
+
+    @pytest.mark.parametrize(
+        "dep_path", ("$tmp_path$/external/dir/file.h", "../external/dir/file.h")
+    )
+    def test_external_path_in_extension_depends(self, monkeypatch, tmp_path, dep_path):
+        # Given a project with a "depends" targeting an external dir
+        files = self.files_for_external_path_in_extension_depends(tmp_path, dep_path)
+        jaraco.path.build(files, prefix=str(tmp_path))
+        # When `sdist` runs, there should be no error
+        members = run_sdist(monkeypatch, tmp_path / "project")
+        # and the sdist should not contain the external file
+        for name in members:
+            assert "file.h" not in name
+
+
+def run_sdist(monkeypatch, project):
+    """Given a project directory, run the sdist and return its contents"""
+    monkeypatch.chdir(project)
+    with quiet():
+        run_setup("setup.py", ["sdist"])
+
+    archive = next((project / "dist").glob("*.tar.gz"))
+    with tarfile.open(str(archive)) as tar:
+        return set(tar.getnames())
+
+
+def test_sanity_check_setuptools_own_sdist(setuptools_sdist):
+    with tarfile.open(setuptools_sdist) as tar:
+        files = tar.getnames()
+
+    # setuptools sdist should not include the .tox folder
+    tox_files = [name for name in files if ".tox" in name]
+    assert len(tox_files) == 0, f"not empty {tox_files}"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_setopt.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_setopt.py
new file mode 100644
index 0000000000000000000000000000000000000000..ccf25618a5d6e255ad0be0fbed51fc29c179dcfe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_setopt.py
@@ -0,0 +1,40 @@
+import configparser
+
+from setuptools.command import setopt
+
+
+class TestEdit:
+    @staticmethod
+    def parse_config(filename):
+        parser = configparser.ConfigParser()
+        with open(filename, encoding='utf-8') as reader:
+            parser.read_file(reader)
+        return parser
+
+    @staticmethod
+    def write_text(file, content):
+        with open(file, 'wb') as strm:
+            strm.write(content.encode('utf-8'))
+
+    def test_utf8_encoding_retained(self, tmpdir):
+        """
+        When editing a file, non-ASCII characters encoded in
+        UTF-8 should be retained.
+        """
+        config = tmpdir.join('setup.cfg')
+        self.write_text(str(config), '[names]\njaraco=джарако')
+        setopt.edit_config(str(config), dict(names=dict(other='yes')))
+        parser = self.parse_config(str(config))
+        assert parser.get('names', 'jaraco') == 'джарако'
+        assert parser.get('names', 'other') == 'yes'
+
+    def test_case_retained(self, tmpdir):
+        """
+        When editing a file, case of keys should be retained.
+        """
+        config = tmpdir.join('setup.cfg')
+        self.write_text(str(config), '[names]\nFoO=bAr')
+        setopt.edit_config(str(config), dict(names=dict(oTher='yes')))
+        actual = config.read_text(encoding='ascii')
+        assert 'FoO' in actual
+        assert 'oTher' in actual
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_setuptools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_setuptools.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d56e1a8a4ebc5c7aaeb9902ef9972f7de97ecbf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_setuptools.py
@@ -0,0 +1,290 @@
+"""Tests for the 'setuptools' package"""
+
+import os
+import re
+import sys
+from zipfile import ZipFile
+
+import pytest
+from packaging.version import Version
+
+import setuptools
+import setuptools.depends as dep
+import setuptools.dist
+from setuptools.depends import Require
+
+import distutils.cmd
+import distutils.core
+from distutils.core import Extension
+from distutils.errors import DistutilsSetupError
+
+
+@pytest.fixture(autouse=True)
+def isolated_dir(tmpdir_cwd):
+    return
+
+
+def makeSetup(**args):
+    """Return distribution from 'setup(**args)', without executing commands"""
+
+    distutils.core._setup_stop_after = "commandline"
+
+    # Don't let system command line leak into tests!
+    args.setdefault('script_args', ['install'])
+
+    try:
+        return setuptools.setup(**args)
+    finally:
+        distutils.core._setup_stop_after = None
+
+
+needs_bytecode = pytest.mark.skipif(
+    not hasattr(dep, 'get_module_constant'),
+    reason="bytecode support not available",
+)
+
+
+class TestDepends:
+    def testExtractConst(self):
+        if not hasattr(dep, 'extract_constant'):
+            # skip on non-bytecode platforms
+            return
+
+        def f1():
+            global x, y, z
+            x = "test"
+            y = z  # pyright: ignore[reportUnboundVariable] # Explicitly testing for this runtime issue
+
+        fc = f1.__code__
+
+        # unrecognized name
+        assert dep.extract_constant(fc, 'q', -1) is None
+
+        # constant assigned
+        assert dep.extract_constant(fc, 'x', -1) == "test"
+
+        # expression assigned
+        assert dep.extract_constant(fc, 'y', -1) == -1
+
+        # recognized name, not assigned
+        assert dep.extract_constant(fc, 'z', -1) is None
+
+    def testFindModule(self):
+        with pytest.raises(ImportError):
+            dep.find_module('no-such.-thing')
+        with pytest.raises(ImportError):
+            dep.find_module('setuptools.non-existent')
+        f, _p, _i = dep.find_module('setuptools.tests')
+        f.close()
+
+    @needs_bytecode
+    def testModuleExtract(self):
+        from json import __version__
+
+        assert dep.get_module_constant('json', '__version__') == __version__
+        assert dep.get_module_constant('sys', 'version') == sys.version
+        assert (
+            dep.get_module_constant('setuptools.tests.test_setuptools', '__doc__')
+            == __doc__
+        )
+
+    @needs_bytecode
+    def testRequire(self):
+        req = Require('Json', '1.0.3', 'json')
+
+        assert req.name == 'Json'
+        assert req.module == 'json'
+        assert req.requested_version == Version('1.0.3')
+        assert req.attribute == '__version__'
+        assert req.full_name() == 'Json-1.0.3'
+
+        from json import __version__
+
+        assert str(req.get_version()) == __version__
+        assert req.version_ok('1.0.9')
+        assert not req.version_ok('0.9.1')
+        assert not req.version_ok('unknown')
+
+        assert req.is_present()
+        assert req.is_current()
+
+        req = Require('Do-what-I-mean', '1.0', 'd-w-i-m')
+        assert not req.is_present()
+        assert not req.is_current()
+
+    @needs_bytecode
+    def test_require_present(self):
+        # In #1896, this test was failing for months with the only
+        # complaint coming from test runners (not end users).
+        # TODO: Evaluate if this code is needed at all.
+        req = Require('Tests', None, 'tests', homepage="http://example.com")
+        assert req.format is None
+        assert req.attribute is None
+        assert req.requested_version is None
+        assert req.full_name() == 'Tests'
+        assert req.homepage == 'http://example.com'
+
+        from setuptools.tests import __path__
+
+        paths = [os.path.dirname(p) for p in __path__]
+        assert req.is_present(paths)
+        assert req.is_current(paths)
+
+
+class TestDistro:
+    def setup_method(self, method):
+        self.e1 = Extension('bar.ext', ['bar.c'])
+        self.e2 = Extension('c.y', ['y.c'])
+
+        self.dist = makeSetup(
+            packages=['a', 'a.b', 'a.b.c', 'b', 'c'],
+            py_modules=['b.d', 'x'],
+            ext_modules=(self.e1, self.e2),
+            package_dir={},
+        )
+
+    def testDistroType(self):
+        assert isinstance(self.dist, setuptools.dist.Distribution)
+
+    def testExcludePackage(self):
+        self.dist.exclude_package('a')
+        assert self.dist.packages == ['b', 'c']
+
+        self.dist.exclude_package('b')
+        assert self.dist.packages == ['c']
+        assert self.dist.py_modules == ['x']
+        assert self.dist.ext_modules == [self.e1, self.e2]
+
+        self.dist.exclude_package('c')
+        assert self.dist.packages == []
+        assert self.dist.py_modules == ['x']
+        assert self.dist.ext_modules == [self.e1]
+
+        # test removals from unspecified options
+        makeSetup().exclude_package('x')
+
+    def testIncludeExclude(self):
+        # remove an extension
+        self.dist.exclude(ext_modules=[self.e1])
+        assert self.dist.ext_modules == [self.e2]
+
+        # add it back in
+        self.dist.include(ext_modules=[self.e1])
+        assert self.dist.ext_modules == [self.e2, self.e1]
+
+        # should not add duplicate
+        self.dist.include(ext_modules=[self.e1])
+        assert self.dist.ext_modules == [self.e2, self.e1]
+
+    def testExcludePackages(self):
+        self.dist.exclude(packages=['c', 'b', 'a'])
+        assert self.dist.packages == []
+        assert self.dist.py_modules == ['x']
+        assert self.dist.ext_modules == [self.e1]
+
+    def testEmpty(self):
+        dist = makeSetup()
+        dist.include(packages=['a'], py_modules=['b'], ext_modules=[self.e2])
+        dist = makeSetup()
+        dist.exclude(packages=['a'], py_modules=['b'], ext_modules=[self.e2])
+
+    def testContents(self):
+        assert self.dist.has_contents_for('a')
+        self.dist.exclude_package('a')
+        assert not self.dist.has_contents_for('a')
+
+        assert self.dist.has_contents_for('b')
+        self.dist.exclude_package('b')
+        assert not self.dist.has_contents_for('b')
+
+        assert self.dist.has_contents_for('c')
+        self.dist.exclude_package('c')
+        assert not self.dist.has_contents_for('c')
+
+    def testInvalidIncludeExclude(self):
+        with pytest.raises(DistutilsSetupError):
+            self.dist.include(nonexistent_option='x')
+        with pytest.raises(DistutilsSetupError):
+            self.dist.exclude(nonexistent_option='x')
+        with pytest.raises(DistutilsSetupError):
+            self.dist.include(packages={'x': 'y'})
+        with pytest.raises(DistutilsSetupError):
+            self.dist.exclude(packages={'x': 'y'})
+        with pytest.raises(DistutilsSetupError):
+            self.dist.include(ext_modules={'x': 'y'})
+        with pytest.raises(DistutilsSetupError):
+            self.dist.exclude(ext_modules={'x': 'y'})
+
+        with pytest.raises(DistutilsSetupError):
+            self.dist.include(package_dir=['q'])
+        with pytest.raises(DistutilsSetupError):
+            self.dist.exclude(package_dir=['q'])
+
+
+@pytest.fixture
+def example_source(tmpdir):
+    tmpdir.mkdir('foo')
+    (tmpdir / 'foo/bar.py').write('')
+    (tmpdir / 'readme.txt').write('')
+    return tmpdir
+
+
+def test_findall(example_source):
+    found = list(setuptools.findall(str(example_source)))
+    expected = ['readme.txt', 'foo/bar.py']
+    expected = [example_source.join(fn) for fn in expected]
+    assert found == expected
+
+
+def test_findall_curdir(example_source):
+    with example_source.as_cwd():
+        found = list(setuptools.findall())
+    expected = ['readme.txt', os.path.join('foo', 'bar.py')]
+    assert found == expected
+
+
+@pytest.fixture
+def can_symlink(tmpdir):
+    """
+    Skip if cannot create a symbolic link
+    """
+    link_fn = 'link'
+    target_fn = 'target'
+    try:
+        os.symlink(target_fn, link_fn)
+    except (OSError, NotImplementedError, AttributeError):
+        pytest.skip("Cannot create symbolic links")
+    os.remove(link_fn)
+
+
+@pytest.mark.usefixtures("can_symlink")
+def test_findall_missing_symlink(tmpdir):
+    with tmpdir.as_cwd():
+        os.symlink('foo', 'bar')
+        found = list(setuptools.findall())
+        assert found == []
+
+
+@pytest.mark.xfail(reason="unable to exclude tests; #4475 #3260")
+def test_its_own_wheel_does_not_contain_tests(setuptools_wheel):
+    with ZipFile(setuptools_wheel) as zipfile:
+        contents = [f.replace(os.sep, '/') for f in zipfile.namelist()]
+
+    for member in contents:
+        assert '/tests/' not in member
+
+
+def test_wheel_includes_cli_scripts(setuptools_wheel):
+    with ZipFile(setuptools_wheel) as zipfile:
+        contents = [f.replace(os.sep, '/') for f in zipfile.namelist()]
+
+    assert any('cli-64.exe' in member for member in contents)
+
+
+def test_wheel_includes_vendored_metadata(setuptools_wheel):
+    with ZipFile(setuptools_wheel) as zipfile:
+        contents = [f.replace(os.sep, '/') for f in zipfile.namelist()]
+
+    assert any(
+        re.search(r'_vendor/.*\.dist-info/METADATA', member) for member in contents
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_shutil_wrapper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_shutil_wrapper.py
new file mode 100644
index 0000000000000000000000000000000000000000..74ff7e9a896328a3d57ca3639658e3b9d538585f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_shutil_wrapper.py
@@ -0,0 +1,23 @@
+import stat
+import sys
+from unittest.mock import Mock
+
+from setuptools import _shutil
+
+
+def test_rmtree_readonly(monkeypatch, tmp_path):
+    """Verify onerr works as expected"""
+
+    tmp_dir = tmp_path / "with_readonly"
+    tmp_dir.mkdir()
+    some_file = tmp_dir.joinpath("file.txt")
+    some_file.touch()
+    some_file.chmod(stat.S_IREAD)
+
+    expected_count = 1 if sys.platform.startswith("win") else 0
+    chmod_fn = Mock(wraps=_shutil.attempt_chmod_verbose)
+    monkeypatch.setattr(_shutil, "attempt_chmod_verbose", chmod_fn)
+
+    _shutil.rmtree(tmp_dir)
+    assert chmod_fn.call_count == expected_count
+    assert not tmp_dir.is_dir()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_unicode_utils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_unicode_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..a24a9bd5305d1de7c1c925466bb7d222c85864a7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_unicode_utils.py
@@ -0,0 +1,10 @@
+from setuptools import unicode_utils
+
+
+def test_filesys_decode_fs_encoding_is_None(monkeypatch):
+    """
+    Test filesys_decode does not raise TypeError when
+    getfilesystemencoding returns None.
+    """
+    monkeypatch.setattr('sys.getfilesystemencoding', lambda: None)
+    unicode_utils.filesys_decode(b'test')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_virtualenv.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_virtualenv.py
new file mode 100644
index 0000000000000000000000000000000000000000..b02949baf9cef8eb4df9c697add28f79a93b64d4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_virtualenv.py
@@ -0,0 +1,113 @@
+import os
+import subprocess
+import sys
+from urllib.error import URLError
+from urllib.request import urlopen
+
+import pytest
+
+
+@pytest.fixture(autouse=True)
+def pytest_virtualenv_works(venv):
+    """
+    pytest_virtualenv may not work. if it doesn't, skip these
+    tests. See #1284.
+    """
+    venv_prefix = venv.run(["python", "-c", "import sys; print(sys.prefix)"]).strip()
+    if venv_prefix == sys.prefix:
+        pytest.skip("virtualenv is broken (see pypa/setuptools#1284)")
+
+
+def test_clean_env_install(venv_without_setuptools, setuptools_wheel):
+    """
+    Check setuptools can be installed in a clean environment.
+    """
+    cmd = ["python", "-m", "pip", "install", str(setuptools_wheel)]
+    venv_without_setuptools.run(cmd)
+
+
+def access_pypi():
+    # Detect if tests are being run without connectivity
+    if not os.environ.get('NETWORK_REQUIRED', False):  # pragma: nocover
+        try:
+            urlopen('https://pypi.org', timeout=1)
+        except URLError:
+            # No network, disable most of these tests
+            return False
+
+    return True
+
+
+@pytest.mark.skipif(
+    'platform.python_implementation() == "PyPy"',
+    reason="https://github.com/pypa/setuptools/pull/2865#issuecomment-965834995",
+)
+@pytest.mark.skipif(not access_pypi(), reason="no network")
+# ^-- Even when it is not necessary to install a different version of `pip`
+#     the build process will still try to download `wheel`, see #3147 and #2986.
+@pytest.mark.parametrize(
+    'pip_version',
+    [
+        None,
+        pytest.param(
+            'pip<20.1',
+            marks=pytest.mark.xfail(
+                'sys.version_info >= (3, 12)',
+                reason="pip 23.1.2 required for Python 3.12 and later",
+            ),
+        ),
+        pytest.param(
+            'pip<21',
+            marks=pytest.mark.xfail(
+                'sys.version_info >= (3, 12)',
+                reason="pip 23.1.2 required for Python 3.12 and later",
+            ),
+        ),
+        pytest.param(
+            'pip<22',
+            marks=pytest.mark.xfail(
+                'sys.version_info >= (3, 12)',
+                reason="pip 23.1.2 required for Python 3.12 and later",
+            ),
+        ),
+        pytest.param(
+            'pip<23',
+            marks=pytest.mark.xfail(
+                'sys.version_info >= (3, 12)',
+                reason="pip 23.1.2 required for Python 3.12 and later",
+            ),
+        ),
+        pytest.param(
+            'https://github.com/pypa/pip/archive/main.zip',
+            marks=pytest.mark.xfail(reason='#2975'),
+        ),
+    ],
+)
+def test_pip_upgrade_from_source(
+    pip_version, venv_without_setuptools, setuptools_wheel, setuptools_sdist
+):
+    """
+    Check pip can upgrade setuptools from source.
+    """
+    # Install pip/wheel, in a venv without setuptools (as it
+    # should not be needed for bootstrapping from source)
+    venv = venv_without_setuptools
+    venv.run(["pip", "install", "-U", "wheel"])
+    if pip_version is not None:
+        venv.run(["python", "-m", "pip", "install", "-U", pip_version, "--retries=1"])
+    with pytest.raises(subprocess.CalledProcessError):
+        # Meta-test to make sure setuptools is not installed
+        venv.run(["python", "-c", "import setuptools"])
+
+    # Then install from wheel.
+    venv.run(["pip", "install", str(setuptools_wheel)])
+    # And finally try to upgrade from source.
+    venv.run(["pip", "install", "--no-cache-dir", "--upgrade", str(setuptools_sdist)])
+
+
+def test_no_missing_dependencies(bare_venv, request):
+    """
+    Quick and dirty test to ensure all external dependencies are vendored.
+    """
+    setuptools_dir = request.config.rootdir
+    bare_venv.run(['python', 'setup.py', '--help'], cwd=setuptools_dir)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_warnings.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_warnings.py
new file mode 100644
index 0000000000000000000000000000000000000000..41193d4f717344546f8c70ad18b268a04740129b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_warnings.py
@@ -0,0 +1,106 @@
+from inspect import cleandoc
+
+import pytest
+
+from setuptools.warnings import SetuptoolsDeprecationWarning, SetuptoolsWarning
+
+_EXAMPLES = {
+    "default": dict(
+        args=("Hello {x}", "\n\t{target} {v:.1f}"),
+        kwargs={"x": 5, "v": 3, "target": "World"},
+        expected="""
+    Hello 5
+    !!
+
+            ********************************************************************************
+            World 3.0
+            ********************************************************************************
+
+    !!
+    """,
+    ),
+    "futue_due_date": dict(
+        args=("Summary", "Lorem ipsum"),
+        kwargs={"due_date": (9999, 11, 22)},
+        expected="""
+    Summary
+    !!
+
+            ********************************************************************************
+            Lorem ipsum
+
+            By 9999-Nov-22, you need to update your project and remove deprecated calls
+            or your builds will no longer be supported.
+            ********************************************************************************
+
+    !!
+    """,
+    ),
+    "past_due_date_with_docs": dict(
+        args=("Summary", "Lorem ipsum"),
+        kwargs={"due_date": (2000, 11, 22), "see_docs": "some_page.html"},
+        expected="""
+    Summary
+    !!
+
+            ********************************************************************************
+            Lorem ipsum
+
+            This deprecation is overdue, please update your project and remove deprecated
+            calls to avoid build errors in the future.
+
+            See https://setuptools.pypa.io/en/latest/some_page.html for details.
+            ********************************************************************************
+
+    !!
+    """,
+    ),
+}
+
+
+@pytest.mark.parametrize("example_name", _EXAMPLES.keys())
+def test_formatting(monkeypatch, example_name):
+    """
+    It should automatically handle indentation, interpolation and things like due date.
+    """
+    args = _EXAMPLES[example_name]["args"]
+    kwargs = _EXAMPLES[example_name]["kwargs"]
+    expected = _EXAMPLES[example_name]["expected"]
+
+    monkeypatch.setenv("SETUPTOOLS_ENFORCE_DEPRECATION", "false")
+    with pytest.warns(SetuptoolsWarning) as warn_info:
+        SetuptoolsWarning.emit(*args, **kwargs)
+    assert _get_message(warn_info) == cleandoc(expected)
+
+
+def test_due_date_enforcement(monkeypatch):
+    class _MyDeprecation(SetuptoolsDeprecationWarning):
+        _SUMMARY = "Summary"
+        _DETAILS = "Lorem ipsum"
+        _DUE_DATE = (2000, 11, 22)
+        _SEE_DOCS = "some_page.html"
+
+    monkeypatch.setenv("SETUPTOOLS_ENFORCE_DEPRECATION", "true")
+    with pytest.raises(SetuptoolsDeprecationWarning) as exc_info:
+        _MyDeprecation.emit()
+
+    expected = """
+    Summary
+    !!
+
+            ********************************************************************************
+            Lorem ipsum
+
+            This deprecation is overdue, please update your project and remove deprecated
+            calls to avoid build errors in the future.
+
+            See https://setuptools.pypa.io/en/latest/some_page.html for details.
+            ********************************************************************************
+
+    !!
+    """
+    assert str(exc_info.value) == cleandoc(expected)
+
+
+def _get_message(warn_info):
+    return next(warn.message.args[0] for warn in warn_info)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_wheel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_wheel.py
new file mode 100644
index 0000000000000000000000000000000000000000..70165c608b60bc70a908a8b56e1f1105feeb4712
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_wheel.py
@@ -0,0 +1,714 @@
+"""wheel tests"""
+
+from __future__ import annotations
+
+import contextlib
+import glob
+import inspect
+import os
+import pathlib
+import shutil
+import stat
+import subprocess
+import sys
+import zipfile
+from typing import Any
+
+import pytest
+from jaraco import path
+from packaging.tags import parse_tag
+from packaging.utils import canonicalize_name
+
+from pkg_resources import PY_MAJOR, Distribution, PathMetadata
+from setuptools.wheel import Wheel
+
+from .contexts import tempdir
+from .textwrap import DALS
+
+from distutils.sysconfig import get_config_var
+from distutils.util import get_platform
+
+WHEEL_INFO_TESTS = (
+    ('invalid.whl', ValueError),
+    (
+        'simplewheel-2.0-1-py2.py3-none-any.whl',
+        {
+            'project_name': 'simplewheel',
+            'version': '2.0',
+            'build': '1',
+            'py_version': 'py2.py3',
+            'abi': 'none',
+            'platform': 'any',
+        },
+    ),
+    (
+        'simple.dist-0.1-py2.py3-none-any.whl',
+        {
+            'project_name': 'simple.dist',
+            'version': '0.1',
+            'build': None,
+            'py_version': 'py2.py3',
+            'abi': 'none',
+            'platform': 'any',
+        },
+    ),
+    (
+        'example_pkg_a-1-py3-none-any.whl',
+        {
+            'project_name': 'example_pkg_a',
+            'version': '1',
+            'build': None,
+            'py_version': 'py3',
+            'abi': 'none',
+            'platform': 'any',
+        },
+    ),
+    (
+        'PyQt5-5.9-5.9.1-cp35.cp36.cp37-abi3-manylinux1_x86_64.whl',
+        {
+            'project_name': 'PyQt5',
+            'version': '5.9',
+            'build': '5.9.1',
+            'py_version': 'cp35.cp36.cp37',
+            'abi': 'abi3',
+            'platform': 'manylinux1_x86_64',
+        },
+    ),
+)
+
+
+@pytest.mark.parametrize(
+    ('filename', 'info'), WHEEL_INFO_TESTS, ids=[t[0] for t in WHEEL_INFO_TESTS]
+)
+def test_wheel_info(filename, info):
+    if inspect.isclass(info):
+        with pytest.raises(info):
+            Wheel(filename)
+        return
+    w = Wheel(filename)
+    assert {k: getattr(w, k) for k in info.keys()} == info
+
+
+@contextlib.contextmanager
+def build_wheel(extra_file_defs=None, **kwargs):
+    file_defs = {
+        'setup.py': (
+            DALS(
+                """
+            # -*- coding: utf-8 -*-
+            from setuptools import setup
+            import setuptools
+            setup(**%r)
+            """
+            )
+            % kwargs
+        ).encode('utf-8'),
+    }
+    if extra_file_defs:
+        file_defs.update(extra_file_defs)
+    with tempdir() as source_dir:
+        path.build(file_defs, source_dir)
+        subprocess.check_call(
+            (sys.executable, 'setup.py', '-q', 'bdist_wheel'), cwd=source_dir
+        )
+        yield glob.glob(os.path.join(source_dir, 'dist', '*.whl'))[0]
+
+
+def tree_set(root):
+    contents = set()
+    for dirpath, dirnames, filenames in os.walk(root):
+        for filename in filenames:
+            contents.add(os.path.join(os.path.relpath(dirpath, root), filename))
+    return contents
+
+
+def flatten_tree(tree):
+    """Flatten nested dicts and lists into a full list of paths"""
+    output = set()
+    for node, contents in tree.items():
+        if isinstance(contents, dict):
+            contents = flatten_tree(contents)
+
+        for elem in contents:
+            if isinstance(elem, dict):
+                output |= {os.path.join(node, val) for val in flatten_tree(elem)}
+            else:
+                output.add(os.path.join(node, elem))
+    return output
+
+
+def format_install_tree(tree):
+    return {
+        x.format(
+            py_version=PY_MAJOR,
+            platform=get_platform(),
+            shlib_ext=get_config_var('EXT_SUFFIX') or get_config_var('SO'),
+        )
+        for x in tree
+    }
+
+
+def _check_wheel_install(
+    filename, install_dir, install_tree_includes, project_name, version, requires_txt
+):
+    w = Wheel(filename)
+    egg_path = os.path.join(install_dir, w.egg_name())
+    w.install_as_egg(egg_path)
+    if install_tree_includes is not None:
+        install_tree = format_install_tree(install_tree_includes)
+        exp = tree_set(install_dir)
+        assert install_tree.issubset(exp), install_tree - exp
+
+    metadata = PathMetadata(egg_path, os.path.join(egg_path, 'EGG-INFO'))
+    dist = Distribution.from_filename(egg_path, metadata=metadata)
+    assert dist.project_name == project_name
+    assert dist.version == version
+    if requires_txt is None:
+        assert not dist.has_metadata('requires.txt')
+    else:
+        # Order must match to ensure reproducibility.
+        assert requires_txt == dist.get_metadata('requires.txt').lstrip()
+
+
+class Record:
+    def __init__(self, id, **kwargs):
+        self._id = id
+        self._fields = kwargs
+
+    def __repr__(self) -> str:
+        return f'{self._id}(**{self._fields!r})'
+
+
+# Using Any to avoid possible type union issues later in test
+# making a TypedDict is not worth in a test and anonymous/inline TypedDict are experimental
+# https://github.com/python/mypy/issues/9884
+WHEEL_INSTALL_TESTS: tuple[dict[str, Any], ...] = (
+    dict(
+        id='basic',
+        file_defs={'foo': {'__init__.py': ''}},
+        setup_kwargs=dict(
+            packages=['foo'],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': {
+                'EGG-INFO': ['PKG-INFO', 'RECORD', 'WHEEL', 'top_level.txt'],
+                'foo': ['__init__.py'],
+            }
+        }),
+    ),
+    dict(
+        id='utf-8',
+        setup_kwargs=dict(
+            description='Description accentuée',
+        ),
+    ),
+    dict(
+        id='data',
+        file_defs={
+            'data.txt': DALS(
+                """
+                Some data...
+                """
+            ),
+        },
+        setup_kwargs=dict(
+            data_files=[('data_dir', ['data.txt'])],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': {
+                'EGG-INFO': ['PKG-INFO', 'RECORD', 'WHEEL', 'top_level.txt'],
+                'data_dir': ['data.txt'],
+            }
+        }),
+    ),
+    dict(
+        id='extension',
+        file_defs={
+            'extension.c': DALS(
+                """
+                #include "Python.h"
+
+                #if PY_MAJOR_VERSION >= 3
+
+                static struct PyModuleDef moduledef = {
+                        PyModuleDef_HEAD_INIT,
+                        "extension",
+                        NULL,
+                        0,
+                        NULL,
+                        NULL,
+                        NULL,
+                        NULL,
+                        NULL
+                };
+
+                #define INITERROR return NULL
+
+                PyMODINIT_FUNC PyInit_extension(void)
+
+                #else
+
+                #define INITERROR return
+
+                void initextension(void)
+
+                #endif
+                {
+                #if PY_MAJOR_VERSION >= 3
+                    PyObject *module = PyModule_Create(&moduledef);
+                #else
+                    PyObject *module = Py_InitModule("extension", NULL);
+                #endif
+                    if (module == NULL)
+                        INITERROR;
+                #if PY_MAJOR_VERSION >= 3
+                    return module;
+                #endif
+                }
+                """
+            ),
+        },
+        setup_kwargs=dict(
+            ext_modules=[
+                Record(
+                    'setuptools.Extension', name='extension', sources=['extension.c']
+                )
+            ],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}-{platform}.egg': [
+                'extension{shlib_ext}',
+                {
+                    'EGG-INFO': [
+                        'PKG-INFO',
+                        'RECORD',
+                        'WHEEL',
+                        'top_level.txt',
+                    ]
+                },
+            ]
+        }),
+    ),
+    dict(
+        id='header',
+        file_defs={
+            'header.h': DALS(
+                """
+                """
+            ),
+        },
+        setup_kwargs=dict(
+            headers=['header.h'],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': [
+                'header.h',
+                {
+                    'EGG-INFO': [
+                        'PKG-INFO',
+                        'RECORD',
+                        'WHEEL',
+                        'top_level.txt',
+                    ]
+                },
+            ]
+        }),
+    ),
+    dict(
+        id='script',
+        file_defs={
+            'script.py': DALS(
+                """
+                #/usr/bin/python
+                print('hello world!')
+                """
+            ),
+            'script.sh': DALS(
+                """
+                #/bin/sh
+                echo 'hello world!'
+                """
+            ),
+        },
+        setup_kwargs=dict(
+            scripts=['script.py', 'script.sh'],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': {
+                'EGG-INFO': [
+                    'PKG-INFO',
+                    'RECORD',
+                    'WHEEL',
+                    'top_level.txt',
+                    {'scripts': ['script.py', 'script.sh']},
+                ]
+            }
+        }),
+    ),
+    dict(
+        id='requires1',
+        install_requires='foobar==2.0',
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': {
+                'EGG-INFO': [
+                    'PKG-INFO',
+                    'RECORD',
+                    'WHEEL',
+                    'requires.txt',
+                    'top_level.txt',
+                ]
+            }
+        }),
+        requires_txt=DALS(
+            """
+            foobar==2.0
+            """
+        ),
+    ),
+    dict(
+        id='requires2',
+        install_requires=f"""
+        bar
+        foo<=2.0; {sys.platform!r} in sys_platform
+        """,
+        requires_txt=DALS(
+            """
+            bar
+            foo<=2.0
+            """
+        ),
+    ),
+    dict(
+        id='requires3',
+        install_requires=f"""
+        bar; {sys.platform!r} != sys_platform
+        """,
+    ),
+    dict(
+        id='requires4',
+        install_requires="""
+        foo
+        """,
+        extras_require={
+            'extra': 'foobar>3',
+        },
+        requires_txt=DALS(
+            """
+            foo
+
+            [extra]
+            foobar>3
+            """
+        ),
+    ),
+    dict(
+        id='requires5',
+        extras_require={
+            'extra': f'foobar; {sys.platform!r} != sys_platform',
+        },
+        requires_txt=DALS(
+            """
+            [extra]
+            """
+        ),
+    ),
+    dict(
+        id='requires_ensure_order',
+        install_requires="""
+        foo
+        bar
+        baz
+        qux
+        """,
+        extras_require={
+            'extra': """
+            foobar>3
+            barbaz>4
+            bazqux>5
+            quxzap>6
+            """,
+        },
+        requires_txt=DALS(
+            """
+            foo
+            bar
+            baz
+            qux
+
+            [extra]
+            foobar>3
+            barbaz>4
+            bazqux>5
+            quxzap>6
+            """
+        ),
+    ),
+    dict(
+        id='namespace_package',
+        file_defs={
+            'foo': {
+                'bar': {'__init__.py': ''},
+            },
+        },
+        setup_kwargs=dict(
+            namespace_packages=['foo'],
+            packages=['foo.bar'],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': [
+                'foo-1.0-py{py_version}-nspkg.pth',
+                {
+                    'EGG-INFO': [
+                        'PKG-INFO',
+                        'RECORD',
+                        'WHEEL',
+                        'namespace_packages.txt',
+                        'top_level.txt',
+                    ]
+                },
+                {
+                    'foo': [
+                        '__init__.py',
+                        {'bar': ['__init__.py']},
+                    ]
+                },
+            ]
+        }),
+    ),
+    dict(
+        id='empty_namespace_package',
+        file_defs={
+            'foobar': {
+                '__init__.py': (
+                    "__import__('pkg_resources').declare_namespace(__name__)"
+                )
+            },
+        },
+        setup_kwargs=dict(
+            namespace_packages=['foobar'],
+            packages=['foobar'],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': [
+                'foo-1.0-py{py_version}-nspkg.pth',
+                {
+                    'EGG-INFO': [
+                        'PKG-INFO',
+                        'RECORD',
+                        'WHEEL',
+                        'namespace_packages.txt',
+                        'top_level.txt',
+                    ]
+                },
+                {
+                    'foobar': [
+                        '__init__.py',
+                    ]
+                },
+            ]
+        }),
+    ),
+    dict(
+        id='data_in_package',
+        file_defs={
+            'foo': {
+                '__init__.py': '',
+                'data_dir': {
+                    'data.txt': DALS(
+                        """
+                        Some data...
+                        """
+                    ),
+                },
+            }
+        },
+        setup_kwargs=dict(
+            packages=['foo'],
+            data_files=[('foo/data_dir', ['foo/data_dir/data.txt'])],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': {
+                'EGG-INFO': [
+                    'PKG-INFO',
+                    'RECORD',
+                    'WHEEL',
+                    'top_level.txt',
+                ],
+                'foo': [
+                    '__init__.py',
+                    {
+                        'data_dir': [
+                            'data.txt',
+                        ]
+                    },
+                ],
+            }
+        }),
+    ),
+)
+
+
+@pytest.mark.parametrize(
+    'params',
+    WHEEL_INSTALL_TESTS,
+    ids=[params['id'] for params in WHEEL_INSTALL_TESTS],
+)
+def test_wheel_install(params):
+    project_name = params.get('name', 'foo')
+    version = params.get('version', '1.0')
+    install_requires = params.get('install_requires', [])
+    extras_require = params.get('extras_require', {})
+    requires_txt = params.get('requires_txt', None)
+    install_tree = params.get('install_tree')
+    file_defs = params.get('file_defs', {})
+    setup_kwargs = params.get('setup_kwargs', {})
+    with (
+        build_wheel(
+            name=project_name,
+            version=version,
+            install_requires=install_requires,
+            extras_require=extras_require,
+            extra_file_defs=file_defs,
+            **setup_kwargs,
+        ) as filename,
+        tempdir() as install_dir,
+    ):
+        _check_wheel_install(
+            filename, install_dir, install_tree, project_name, version, requires_txt
+        )
+
+
+def test_wheel_install_pep_503():
+    project_name = 'Foo_Bar'  # PEP 503 canonicalized name is "foo-bar"
+    version = '1.0'
+    with (
+        build_wheel(
+            name=project_name,
+            version=version,
+        ) as filename,
+        tempdir() as install_dir,
+    ):
+        new_filename = filename.replace(project_name, canonicalize_name(project_name))
+        shutil.move(filename, new_filename)
+        _check_wheel_install(
+            new_filename,
+            install_dir,
+            None,
+            canonicalize_name(project_name),
+            version,
+            None,
+        )
+
+
+def test_wheel_no_dist_dir():
+    project_name = 'nodistinfo'
+    version = '1.0'
+    wheel_name = f'{project_name}-{version}-py2.py3-none-any.whl'
+    with tempdir() as source_dir:
+        wheel_path = os.path.join(source_dir, wheel_name)
+        # create an empty zip file
+        zipfile.ZipFile(wheel_path, 'w').close()
+        with tempdir() as install_dir:
+            with pytest.raises(ValueError):
+                _check_wheel_install(
+                    wheel_path, install_dir, None, project_name, version, None
+                )
+
+
+def test_wheel_is_compatible(monkeypatch):
+    def sys_tags():
+        return {
+            (t.interpreter, t.abi, t.platform)
+            for t in parse_tag('cp36-cp36m-manylinux1_x86_64')
+        }
+
+    monkeypatch.setattr('setuptools.wheel._get_supported_tags', sys_tags)
+    assert Wheel('onnxruntime-0.1.2-cp36-cp36m-manylinux1_x86_64.whl').is_compatible()
+
+
+def test_wheel_mode():
+    @contextlib.contextmanager
+    def build_wheel(extra_file_defs=None, **kwargs):
+        file_defs = {
+            'setup.py': (
+                DALS(
+                    """
+                # -*- coding: utf-8 -*-
+                from setuptools import setup
+                import setuptools
+                setup(**%r)
+                """
+                )
+                % kwargs
+            ).encode('utf-8'),
+        }
+        if extra_file_defs:
+            file_defs.update(extra_file_defs)
+        with tempdir() as source_dir:
+            path.build(file_defs, source_dir)
+            runsh = pathlib.Path(source_dir) / "script.sh"
+            os.chmod(runsh, 0o777)
+            subprocess.check_call(
+                (sys.executable, 'setup.py', '-q', 'bdist_wheel'), cwd=source_dir
+            )
+            yield glob.glob(os.path.join(source_dir, 'dist', '*.whl'))[0]
+
+    params = dict(
+        id='script',
+        file_defs={
+            'script.py': DALS(
+                """
+                #/usr/bin/python
+                print('hello world!')
+                """
+            ),
+            'script.sh': DALS(
+                """
+                #/bin/sh
+                echo 'hello world!'
+                """
+            ),
+        },
+        setup_kwargs=dict(
+            scripts=['script.py', 'script.sh'],
+        ),
+        install_tree=flatten_tree({
+            'foo-1.0-py{py_version}.egg': {
+                'EGG-INFO': [
+                    'PKG-INFO',
+                    'RECORD',
+                    'WHEEL',
+                    'top_level.txt',
+                    {'scripts': ['script.py', 'script.sh']},
+                ]
+            }
+        }),
+    )
+
+    project_name = params.get('name', 'foo')
+    version = params.get('version', '1.0')
+    install_tree = params.get('install_tree')
+    file_defs = params.get('file_defs', {})
+    setup_kwargs = params.get('setup_kwargs', {})
+
+    with (
+        build_wheel(
+            name=project_name,
+            version=version,
+            install_requires=[],
+            extras_require={},
+            extra_file_defs=file_defs,
+            **setup_kwargs,
+        ) as filename,
+        tempdir() as install_dir,
+    ):
+        _check_wheel_install(
+            filename, install_dir, install_tree, project_name, version, None
+        )
+        w = Wheel(filename)
+        base = pathlib.Path(install_dir) / w.egg_name()
+        script_sh = base / "EGG-INFO" / "scripts" / "script.sh"
+        assert script_sh.exists()
+        if sys.platform != 'win32':
+            # Editable file mode has no effect on Windows
+            assert oct(stat.S_IMODE(script_sh.stat().st_mode)) == "0o777"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_windows_wrappers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_windows_wrappers.py
new file mode 100644
index 0000000000000000000000000000000000000000..f895485387f2f9f673f96f7114629297a381e66c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/test_windows_wrappers.py
@@ -0,0 +1,259 @@
+"""
+Python Script Wrapper for Windows
+=================================
+
+setuptools includes wrappers for Python scripts that allows them to be
+executed like regular windows programs.  There are 2 wrappers, one
+for command-line programs, cli.exe, and one for graphical programs,
+gui.exe.  These programs are almost identical, function pretty much
+the same way, and are generated from the same source file.  The
+wrapper programs are used by copying them to the directory containing
+the script they are to wrap and with the same name as the script they
+are to wrap.
+"""
+
+import pathlib
+import platform
+import subprocess
+import sys
+import textwrap
+
+import pytest
+
+import pkg_resources
+from setuptools.command.easy_install import nt_quote_arg
+
+pytestmark = pytest.mark.skipif(sys.platform != 'win32', reason="Windows only")
+
+
+class WrapperTester:
+    @classmethod
+    def prep_script(cls, template):
+        python_exe = nt_quote_arg(sys.executable)
+        return template % locals()
+
+    @classmethod
+    def create_script(cls, tmpdir):
+        """
+        Create a simple script, foo-script.py
+
+        Note that the script starts with a Unix-style '#!' line saying which
+        Python executable to run.  The wrapper will use this line to find the
+        correct Python executable.
+        """
+
+        script = cls.prep_script(cls.script_tmpl)
+
+        with (tmpdir / cls.script_name).open('w') as f:
+            f.write(script)
+
+        # also copy cli.exe to the sample directory
+        with (tmpdir / cls.wrapper_name).open('wb') as f:
+            w = pkg_resources.resource_string('setuptools', cls.wrapper_source)
+            f.write(w)
+
+
+def win_launcher_exe(prefix):
+    """A simple routine to select launcher script based on platform."""
+    assert prefix in ('cli', 'gui')
+    if platform.machine() == "ARM64":
+        return f"{prefix}-arm64.exe"
+    else:
+        return f"{prefix}-32.exe"
+
+
+class TestCLI(WrapperTester):
+    script_name = 'foo-script.py'
+    wrapper_name = 'foo.exe'
+    wrapper_source = win_launcher_exe('cli')
+
+    script_tmpl = textwrap.dedent(
+        """
+        #!%(python_exe)s
+        import sys
+        input = repr(sys.stdin.read())
+        print(sys.argv[0][-14:])
+        print(sys.argv[1:])
+        print(input)
+        if __debug__:
+            print('non-optimized')
+        """
+    ).lstrip()
+
+    def test_basic(self, tmpdir):
+        """
+        When the copy of cli.exe, foo.exe in this example, runs, it examines
+        the path name it was run with and computes a Python script path name
+        by removing the '.exe' suffix and adding the '-script.py' suffix. (For
+        GUI programs, the suffix '-script.pyw' is added.)  This is why we
+        named out script the way we did.  Now we can run out script by running
+        the wrapper:
+
+        This example was a little pathological in that it exercised windows
+        (MS C runtime) quoting rules:
+
+        - Strings containing spaces are surrounded by double quotes.
+
+        - Double quotes in strings need to be escaped by preceding them with
+          back slashes.
+
+        - One or more backslashes preceding double quotes need to be escaped
+          by preceding each of them with back slashes.
+        """
+        self.create_script(tmpdir)
+        cmd = [
+            str(tmpdir / 'foo.exe'),
+            'arg1',
+            'arg 2',
+            'arg "2\\"',
+            'arg 4\\',
+            'arg5 a\\\\b',
+        ]
+        proc = subprocess.Popen(
+            cmd,
+            stdout=subprocess.PIPE,
+            stdin=subprocess.PIPE,
+            text=True,
+            encoding="utf-8",
+        )
+        stdout, _stderr = proc.communicate('hello\nworld\n')
+        actual = stdout.replace('\r\n', '\n')
+        expected = textwrap.dedent(
+            r"""
+            \foo-script.py
+            ['arg1', 'arg 2', 'arg "2\\"', 'arg 4\\', 'arg5 a\\\\b']
+            'hello\nworld\n'
+            non-optimized
+            """
+        ).lstrip()
+        assert actual == expected
+
+    def test_symlink(self, tmpdir):
+        """
+        Ensure that symlink for the foo.exe is working correctly.
+        """
+        script_dir = tmpdir / "script_dir"
+        script_dir.mkdir()
+        self.create_script(script_dir)
+        symlink = pathlib.Path(tmpdir / "foo.exe")
+        symlink.symlink_to(script_dir / "foo.exe")
+
+        cmd = [
+            str(tmpdir / 'foo.exe'),
+            'arg1',
+            'arg 2',
+            'arg "2\\"',
+            'arg 4\\',
+            'arg5 a\\\\b',
+        ]
+        proc = subprocess.Popen(
+            cmd,
+            stdout=subprocess.PIPE,
+            stdin=subprocess.PIPE,
+            text=True,
+            encoding="utf-8",
+        )
+        stdout, _stderr = proc.communicate('hello\nworld\n')
+        actual = stdout.replace('\r\n', '\n')
+        expected = textwrap.dedent(
+            r"""
+            \foo-script.py
+            ['arg1', 'arg 2', 'arg "2\\"', 'arg 4\\', 'arg5 a\\\\b']
+            'hello\nworld\n'
+            non-optimized
+            """
+        ).lstrip()
+        assert actual == expected
+
+    def test_with_options(self, tmpdir):
+        """
+        Specifying Python Command-line Options
+        --------------------------------------
+
+        You can specify a single argument on the '#!' line.  This can be used
+        to specify Python options like -O, to run in optimized mode or -i
+        to start the interactive interpreter.  You can combine multiple
+        options as usual. For example, to run in optimized mode and
+        enter the interpreter after running the script, you could use -Oi:
+        """
+        self.create_script(tmpdir)
+        tmpl = textwrap.dedent(
+            """
+            #!%(python_exe)s  -Oi
+            import sys
+            input = repr(sys.stdin.read())
+            print(sys.argv[0][-14:])
+            print(sys.argv[1:])
+            print(input)
+            if __debug__:
+                print('non-optimized')
+            sys.ps1 = '---'
+            """
+        ).lstrip()
+        with (tmpdir / 'foo-script.py').open('w') as f:
+            f.write(self.prep_script(tmpl))
+        cmd = [str(tmpdir / 'foo.exe')]
+        proc = subprocess.Popen(
+            cmd,
+            stdout=subprocess.PIPE,
+            stdin=subprocess.PIPE,
+            stderr=subprocess.STDOUT,
+            text=True,
+            encoding="utf-8",
+        )
+        stdout, _stderr = proc.communicate()
+        actual = stdout.replace('\r\n', '\n')
+        expected = textwrap.dedent(
+            r"""
+            \foo-script.py
+            []
+            ''
+            ---
+            """
+        ).lstrip()
+        assert actual == expected
+
+
+class TestGUI(WrapperTester):
+    """
+    Testing the GUI Version
+    -----------------------
+    """
+
+    script_name = 'bar-script.pyw'
+    wrapper_source = win_launcher_exe('gui')
+    wrapper_name = 'bar.exe'
+
+    script_tmpl = textwrap.dedent(
+        """
+        #!%(python_exe)s
+        import sys
+        f = open(sys.argv[1], 'wb')
+        bytes_written = f.write(repr(sys.argv[2]).encode('utf-8'))
+        f.close()
+        """
+    ).strip()
+
+    def test_basic(self, tmpdir):
+        """Test the GUI version with the simple script, bar-script.py"""
+        self.create_script(tmpdir)
+
+        cmd = [
+            str(tmpdir / 'bar.exe'),
+            str(tmpdir / 'test_output.txt'),
+            'Test Argument',
+        ]
+        proc = subprocess.Popen(
+            cmd,
+            stdout=subprocess.PIPE,
+            stdin=subprocess.PIPE,
+            stderr=subprocess.STDOUT,
+            text=True,
+            encoding="utf-8",
+        )
+        stdout, stderr = proc.communicate()
+        assert not stdout
+        assert not stderr
+        with (tmpdir / 'test_output.txt').open('rb') as f_out:
+            actual = f_out.read().decode('ascii')
+        assert actual == repr('Test Argument')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/text.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/text.py
new file mode 100644
index 0000000000000000000000000000000000000000..e05cc633ede9e5ce4f74b66a7bf76327c2000caa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/text.py
@@ -0,0 +1,4 @@
+class Filenames:
+    unicode = 'smörbröd.py'
+    latin_1 = unicode.encode('latin-1')
+    utf_8 = unicode.encode('utf-8')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/textwrap.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/textwrap.py
new file mode 100644
index 0000000000000000000000000000000000000000..5e39618dca4ad6c3f0d4c8cb20af59ab85fb0eba
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/setuptools/tests/textwrap.py
@@ -0,0 +1,6 @@
+import textwrap
+
+
+def DALS(s):
+    "dedent and left-strip"
+    return textwrap.dedent(s).lstrip()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/INSTALLER b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/LICENSE b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..1cc22a5aa7679ebaa10934212f356823931bdc3e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/LICENSE
@@ -0,0 +1,18 @@
+Copyright (c) 2010-2024 Benjamin Peterson
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of
+this software and associated documentation files (the "Software"), to deal in
+the Software without restriction, including without limitation the rights to
+use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+the Software, and to permit persons to whom the Software is furnished to do so,
+subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
+FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
+IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/METADATA b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..cfde03c2631c5c1d5cdc0949d0ee3379e7110f0e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/METADATA
@@ -0,0 +1,43 @@
+Metadata-Version: 2.1
+Name: six
+Version: 1.17.0
+Summary: Python 2 and 3 compatibility utilities
+Home-page: https://github.com/benjaminp/six
+Author: Benjamin Peterson
+Author-email: benjamin@python.org
+License: MIT
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Programming Language :: Python :: 2
+Classifier: Programming Language :: Python :: 3
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: MIT License
+Classifier: Topic :: Software Development :: Libraries
+Classifier: Topic :: Utilities
+Requires-Python: >=2.7, !=3.0.*, !=3.1.*, !=3.2.*
+License-File: LICENSE
+
+.. image:: https://img.shields.io/pypi/v/six.svg
+   :target: https://pypi.org/project/six/
+   :alt: six on PyPI
+
+.. image:: https://readthedocs.org/projects/six/badge/?version=latest
+   :target: https://six.readthedocs.io/
+   :alt: six's documentation on Read the Docs
+
+.. image:: https://img.shields.io/badge/license-MIT-green.svg
+   :target: https://github.com/benjaminp/six/blob/master/LICENSE
+   :alt: MIT License badge
+
+Six is a Python 2 and 3 compatibility library.  It provides utility functions
+for smoothing over the differences between the Python versions with the goal of
+writing Python code that is compatible on both Python versions.  See the
+documentation for more information on what is provided.
+
+Six supports Python 2.7 and 3.3+.  It is contained in only one Python
+file, so it can be easily copied into your project. (The copyright and license
+notice must be retained.)
+
+Online documentation is at https://six.readthedocs.io/.
+
+Bugs can be reported to https://github.com/benjaminp/six.  The code can also
+be found there.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/RECORD b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..888d9850e5c78ed5c5e19c3974b6311297fb3bae
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/RECORD
@@ -0,0 +1,8 @@
+__pycache__/six.cpython-310.pyc,,
+six-1.17.0.dist-info/INSTALLER,sha256=zuuue4knoyJ-UwPPXg8fezS7VCrXJQrAP7zeNuwvFQg,4
+six-1.17.0.dist-info/LICENSE,sha256=Q3W6IOK5xsTnytKUCmKP2Q6VzD1Q7pKq51VxXYuh-9A,1066
+six-1.17.0.dist-info/METADATA,sha256=ViBCB4wnUlSfbYp8htvF3XCAiKe-bYBnLsewcQC3JGg,1658
+six-1.17.0.dist-info/RECORD,,
+six-1.17.0.dist-info/WHEEL,sha256=pxeNX5JdtCe58PUSYP9upmc7jdRPgvT0Gm9kb1SHlVw,109
+six-1.17.0.dist-info/top_level.txt,sha256=_iVH_iYEtEXnD8nYGQYpYFUvkUW9sEO1GYbkeKSAais,4
+six.py,sha256=xRyR9wPT1LNpbJI8tf7CE-BeddkhU5O--sfy-mo5BN8,34703
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/WHEEL b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..104f3874635f24f0d2918dfeaf6a59652274460c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/WHEEL
@@ -0,0 +1,6 @@
+Wheel-Version: 1.0
+Generator: setuptools (75.6.0)
+Root-Is-Purelib: true
+Tag: py2-none-any
+Tag: py3-none-any
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/top_level.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/top_level.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ffe2fce498955b628014618b28c6bcf152466a4a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/six-1.17.0.dist-info/top_level.txt
@@ -0,0 +1 @@
+six
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/INSTALLER b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/LICENSE b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..710010f1fe0311afd9823e319ff958827a419964
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/LICENSE
@@ -0,0 +1,30 @@
+Copyright (C) 2010, 2011 Sebastian Thiel and contributors
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without 
+modification, are permitted provided that the following conditions 
+are met:
+
+* Redistributions of source code must retain the above copyright 
+notice, this list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright 
+notice, this list of conditions and the following disclaimer in the 
+documentation and/or other materials provided with the distribution.
+
+* Neither the name of the async project nor the names of 
+its contributors may be used to endorse or promote products derived 
+from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED 
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/METADATA b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..ce0537bde0f6d4cfee9549b001156bd5cabc107a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/METADATA
@@ -0,0 +1,113 @@
+Metadata-Version: 2.1
+Name: smmap
+Version: 5.0.2
+Summary: A pure Python implementation of a sliding window memory map manager
+Home-page: https://github.com/gitpython-developers/smmap
+Author: Sebastian Thiel
+Author-email: byronimo@gmail.com
+License: BSD-3-Clause
+Platform: any
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Environment :: Console
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: BSD License
+Classifier: Operating System :: OS Independent
+Classifier: Operating System :: POSIX
+Classifier: Operating System :: Microsoft :: Windows
+Classifier: Operating System :: MacOS :: MacOS X
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3.7
+Classifier: Programming Language :: Python :: 3.8
+Classifier: Programming Language :: Python :: 3.9
+Classifier: Programming Language :: Python :: 3.10
+Classifier: Programming Language :: Python :: 3.11
+Classifier: Programming Language :: Python :: 3.12
+Classifier: Programming Language :: Python :: 3 :: Only
+Requires-Python: >=3.7
+Description-Content-Type: text/markdown
+License-File: LICENSE
+
+## Motivation
+
+When reading from many possibly large files in a fashion similar to random access, it is usually the fastest and most efficient to use memory maps.
+
+Although memory maps have many advantages, they represent a very limited system resource as every map uses one file descriptor, whose amount is limited per process. On 32 bit systems, the amount of memory you can have mapped at a time is naturally limited to theoretical 4GB of memory, which may not be enough for some applications.
+
+
+## Limitations
+
+* **System resources (file-handles) are likely to be leaked!** This is due to the library authors reliance on a deterministic `__del__()` destructor.
+* The memory access is read-only by design.
+
+
+## Overview
+
+![Python package](https://github.com/gitpython-developers/smmap/workflows/Python%20package/badge.svg)
+
+Smmap wraps an interface around mmap and tracks the mapped files as well as the amount of clients who use it. If the system runs out of resources, or if a memory limit is reached, it will automatically unload unused maps to allow continued operation.
+
+To allow processing large files even on 32 bit systems, it allows only portions of the file to be mapped. Once the user reads beyond the mapped region, smmap will automatically map the next required region, unloading unused regions using a LRU algorithm.
+
+Although the library can be used most efficiently with its native interface, a Buffer implementation is provided to hide these details behind a simple string-like interface.
+
+For performance critical 64 bit applications, a simplified version of memory mapping is provided which always maps the whole file, but still provides the benefit of unloading unused mappings on demand.
+
+
+
+## Prerequisites
+
+* Python 3.7+
+* OSX, Windows or Linux
+
+The package was tested on all of the previously mentioned configurations.
+
+## Installing smmap
+
+[![Documentation Status](https://readthedocs.org/projects/smmap/badge/?version=latest)](https://readthedocs.org/projects/smmap/?badge=latest)
+
+Its easiest to install smmap using the [pip](http://www.pip-installer.org/en/latest) program:
+
+```bash
+$ pip install smmap
+```
+
+As the command will install smmap in your respective python distribution, you will most likely need root permissions to authorize the required changes.
+
+If you have downloaded the source archive, the package can be installed by running the `setup.py` script:
+
+```bash
+$ python setup.py install
+```
+
+It is advised to have a look at the **Usage Guide** for a brief introduction on the different database implementations.
+
+
+
+## Homepage and Links
+
+The project is home on github at https://github.com/gitpython-developers/smmap .
+
+The latest source can be cloned from github as well:
+
+* git://github.com/gitpython-developers/smmap.git
+
+
+For support, please use the git-python mailing list:
+
+* http://groups.google.com/group/git-python
+
+
+Issues can be filed on github:
+
+* https://github.com/gitpython-developers/smmap/issues
+
+A link to the pypi page related to this repository:
+
+* https://pypi.org/project/smmap/
+
+
+## License Information
+
+*smmap* is licensed under the New BSD License.
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/RECORD b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..5e5685f8fff0c6cfa171ef4f5e11b8e269bae405
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/RECORD
@@ -0,0 +1,27 @@
+smmap-5.0.2.dist-info/INSTALLER,sha256=zuuue4knoyJ-UwPPXg8fezS7VCrXJQrAP7zeNuwvFQg,4
+smmap-5.0.2.dist-info/LICENSE,sha256=iOnZP3CNEQsyioNDAt0dXGr72lMOdyHRXYCzUR2G8jU,1519
+smmap-5.0.2.dist-info/METADATA,sha256=3BUpM_oN3bljLC5WDH9bxeo5JqXV-AGVQ4Epw1C5h2Y,4306
+smmap-5.0.2.dist-info/RECORD,,
+smmap-5.0.2.dist-info/WHEEL,sha256=PZUExdf71Ui_so67QXpySuHtCi3-J3wvF4ORK6k_S8U,91
+smmap-5.0.2.dist-info/top_level.txt,sha256=h0Tp1UdaROCy2bjWNha1MFpwgVghxEUQsaLHbZs96Gw,6
+smmap-5.0.2.dist-info/zip-safe,sha256=AbpHGcgLb-kRsJGnwFEktk7uzpZOCcBY74-YBdrKVGs,1
+smmap/__init__.py,sha256=Bf9KWm-zr5__SoSEEXI20pqKOJFpUApidvardLulRLY,343
+smmap/__pycache__/__init__.cpython-310.pyc,,
+smmap/__pycache__/buf.cpython-310.pyc,,
+smmap/__pycache__/mman.cpython-310.pyc,,
+smmap/__pycache__/util.cpython-310.pyc,,
+smmap/buf.py,sha256=wElndUNa4Njhnes6JYmI_Xp4zwaohirLdr7eVR9XYNU,5762
+smmap/mman.py,sha256=HYxohllZqpPY4KgRF_D_lNp4fx0akZ-NQosutLDrQ60,24022
+smmap/test/__init__.py,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+smmap/test/__pycache__/__init__.cpython-310.pyc,,
+smmap/test/__pycache__/lib.cpython-310.pyc,,
+smmap/test/__pycache__/test_buf.cpython-310.pyc,,
+smmap/test/__pycache__/test_mman.cpython-310.pyc,,
+smmap/test/__pycache__/test_tutorial.cpython-310.pyc,,
+smmap/test/__pycache__/test_util.cpython-310.pyc,,
+smmap/test/lib.py,sha256=jYIT4rKckHw2s7-l5lwysft1jqrwDFkjtyNLKNpu_j0,1489
+smmap/test/test_buf.py,sha256=BCg9FbusakiYNs5MUNoJSiyuTP5HcMYl65HzvpY9SNo,5439
+smmap/test/test_mman.py,sha256=o3cPg5idyYJpq32zXgDy1qtD10RA_e88-1zPYBWi4Ms,10822
+smmap/test/test_tutorial.py,sha256=ZwCphCbKAGYt_fn_CiOJ9lWwpWwpqE4-zBUp-v-t9eM,3174
+smmap/test/test_util.py,sha256=3hJyW9Km7k7XSgxxtDOkG8eVagk3lIzP4H2pR0S2ewg,3468
+smmap/util.py,sha256=_Sl3Sd2KWdd-5nmhUegFMfT6L1j5BGchRT4z53Sobug,7476
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/WHEEL b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..ae527e7d64811439e61b93aa375defb30e06edfe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/WHEEL
@@ -0,0 +1,5 @@
+Wheel-Version: 1.0
+Generator: setuptools (75.6.0)
+Root-Is-Purelib: true
+Tag: py3-none-any
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/top_level.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/top_level.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2765cefa1c4976ec31a903f3ffb7b2f9f92531f3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/top_level.txt
@@ -0,0 +1 @@
+smmap
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/zip-safe b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/zip-safe
new file mode 100644
index 0000000000000000000000000000000000000000..8b137891791fe96927ad78e64b0aad7bded08bdc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap-5.0.2.dist-info/zip-safe
@@ -0,0 +1 @@
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..657c8c5af20f538203ef618e0b38c12bf6c998bc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/__init__.py
@@ -0,0 +1,11 @@
+"""Initialize the smmap package"""
+
+__author__ = "Sebastian Thiel"
+__contact__ = "byronimo@gmail.com"
+__homepage__ = "https://github.com/gitpython-developers/smmap"
+version_info = (5, 0, 2)
+__version__ = '.'.join(str(i) for i in version_info)
+
+# make everything available in root package for convenience
+from .mman import *
+from .buf import *
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/buf.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/buf.py
new file mode 100644
index 0000000000000000000000000000000000000000..731b0644b5a269b1f941dc7cd49163e6754878a6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/buf.py
@@ -0,0 +1,143 @@
+"""Module with a simple buffer implementation using the memory manager"""
+import sys
+
+__all__ = ["SlidingWindowMapBuffer"]
+
+
+class SlidingWindowMapBuffer:
+
+    """A buffer like object which allows direct byte-wise object and slicing into
+    memory of a mapped file. The mapping is controlled by the provided cursor.
+
+    The buffer is relative, that is if you map an offset, index 0 will map to the
+    first byte at the offset you used during initialization or begin_access
+
+    **Note:** Although this type effectively hides the fact that there are mapped windows
+    underneath, it can unfortunately not be used in any non-pure python method which
+    needs a buffer or string"""
+    __slots__ = (
+        '_c',           # our cursor
+        '_size',        # our supposed size
+    )
+
+    def __init__(self, cursor=None, offset=0, size=sys.maxsize, flags=0):
+        """Initialize the instance to operate on the given cursor.
+        :param cursor: if not None, the associated cursor to the file you want to access
+            If None, you have call begin_access before using the buffer and provide a cursor
+        :param offset: absolute offset in bytes
+        :param size: the total size of the mapping. Defaults to the maximum possible size
+            From that point on, the __len__ of the buffer will be the given size or the file size.
+            If the size is larger than the mappable area, you can only access the actually available
+            area, although the length of the buffer is reported to be your given size.
+            Hence it is in your own interest to provide a proper size !
+        :param flags: Additional flags to be passed to os.open
+        :raise ValueError: if the buffer could not achieve a valid state"""
+        self._c = cursor
+        if cursor and not self.begin_access(cursor, offset, size, flags):
+            raise ValueError("Failed to allocate the buffer - probably the given offset is out of bounds")
+        # END handle offset
+
+    def __del__(self):
+        self.end_access()
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        self.end_access()
+
+    def __len__(self):
+        return self._size
+
+    def __getitem__(self, i):
+        if isinstance(i, slice):
+            return self.__getslice__(i.start or 0, i.stop or self._size)
+        c = self._c
+        assert c.is_valid()
+        if i < 0:
+            i = self._size + i
+        if not c.includes_ofs(i):
+            c.use_region(i, 1)
+        # END handle region usage
+        return c.buffer()[i - c.ofs_begin()]
+
+    def __getslice__(self, i, j):
+        c = self._c
+        # fast path, slice fully included - safes a concatenate operation and
+        # should be the default
+        assert c.is_valid()
+        if i < 0:
+            i = self._size + i
+        if j == sys.maxsize:
+            j = self._size
+        if j < 0:
+            j = self._size + j
+        if (c.ofs_begin() <= i) and (j < c.ofs_end()):
+            b = c.ofs_begin()
+            return c.buffer()[i - b:j - b]
+        else:
+            l = j - i                 # total length
+            ofs = i
+            # It's fastest to keep tokens and join later, especially in py3, which was 7 times slower
+            # in the previous iteration of this code
+            md = list()
+            while l:
+                c.use_region(ofs, l)
+                assert c.is_valid()
+                d = c.buffer()[:l]
+                ofs += len(d)
+                l -= len(d)
+                # Make sure we don't keep references, as c.use_region() might attempt to free resources, but
+                # can't unless we use pure bytes
+                if hasattr(d, 'tobytes'):
+                    d = d.tobytes()
+                md.append(d)
+            # END while there are bytes to read
+            return b''.join(md)
+        # END fast or slow path
+    #{ Interface
+
+    def begin_access(self, cursor=None, offset=0, size=sys.maxsize, flags=0):
+        """Call this before the first use of this instance. The method was already
+        called by the constructor in case sufficient information was provided.
+
+        For more information no the parameters, see the __init__ method
+        :param path: if cursor is None the existing one will be used.
+        :return: True if the buffer can be used"""
+        if cursor:
+            self._c = cursor
+        # END update our cursor
+
+        # reuse existing cursors if possible
+        if self._c is not None and self._c.is_associated():
+            res = self._c.use_region(offset, size, flags).is_valid()
+            if res:
+                # if given size is too large or default, we computer a proper size
+                # If its smaller, we assume the combination between offset and size
+                # as chosen by the user is correct and use it !
+                # If not, the user is in trouble.
+                if size > self._c.file_size():
+                    size = self._c.file_size() - offset
+                # END handle size
+                self._size = size
+            # END set size
+            return res
+        # END use our cursor
+        return False
+
+    def end_access(self):
+        """Call this method once you are done using the instance. It is automatically
+        called on destruction, and should be called just in time to allow system
+        resources to be freed.
+
+        Once you called end_access, you must call begin access before reusing this instance!"""
+        self._size = 0
+        if self._c is not None:
+            self._c.unuse_region()
+        # END unuse region
+
+    def cursor(self):
+        """:return: the currently set cursor which provides access to the data"""
+        return self._c
+
+    #}END interface
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/mman.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/mman.py
new file mode 100644
index 0000000000000000000000000000000000000000..873f687fdc6f0d78ee24a6d25f7720708d48b6e5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/mman.py
@@ -0,0 +1,588 @@
+"""Module containing a memory memory manager which provides a sliding window on a number of memory mapped files"""
+from .util import (
+    MapWindow,
+    MapRegion,
+    MapRegionList,
+    is_64_bit,
+)
+
+import sys
+from functools import reduce
+
+__all__ = ["StaticWindowMapManager", "SlidingWindowMapManager", "WindowCursor"]
+#{ Utilities
+
+#}END utilities
+
+
+class WindowCursor:
+
+    """
+    Pointer into the mapped region of the memory manager, keeping the map
+    alive until it is destroyed and no other client uses it.
+
+    Cursors should not be created manually, but are instead returned by the SlidingWindowMapManager
+
+    **Note:**: The current implementation is suited for static and sliding window managers, but it also means
+    that it must be suited for the somewhat quite different sliding manager. It could be improved, but
+    I see no real need to do so."""
+    __slots__ = (
+        '_manager',  # the manager keeping all file regions
+        '_rlist',   # a regions list with regions for our file
+        '_region',  # our current class:`MapRegion` or None
+        '_ofs',     # relative offset from the actually mapped area to our start area
+        '_size'     # maximum size we should provide
+    )
+
+    def __init__(self, manager=None, regions=None):
+        self._manager = manager
+        self._rlist = regions
+        self._region = None
+        self._ofs = 0
+        self._size = 0
+
+    def __del__(self):
+        self._destroy()
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        self._destroy()
+
+    def _destroy(self):
+        """Destruction code to decrement counters"""
+        self.unuse_region()
+
+        if self._rlist is not None:
+            # Actual client count, which doesn't include the reference kept by the manager, nor ours
+            # as we are about to be deleted
+            try:
+                if len(self._rlist) == 0:
+                    # Free all resources associated with the mapped file
+                    self._manager._fdict.pop(self._rlist.path_or_fd())
+                # END remove regions list from manager
+            except (TypeError, KeyError):
+                # sometimes, during shutdown, getrefcount is None. Its possible
+                # to re-import it, however, its probably better to just ignore
+                # this python problem (for now).
+                # The next step is to get rid of the error prone getrefcount altogether.
+                pass
+            # END exception handling
+        # END handle regions
+
+    def _copy_from(self, rhs):
+        """Copy all data from rhs into this instance, handles usage count"""
+        self._manager = rhs._manager
+        self._rlist = type(rhs._rlist)(rhs._rlist)
+        self._region = rhs._region
+        self._ofs = rhs._ofs
+        self._size = rhs._size
+
+        for region in self._rlist:
+            region.increment_client_count()
+
+        if self._region is not None:
+            self._region.increment_client_count()
+        # END handle regions
+
+    def __copy__(self):
+        """copy module interface"""
+        cpy = type(self)()
+        cpy._copy_from(self)
+        return cpy
+
+    #{ Interface
+    def assign(self, rhs):
+        """Assign rhs to this instance. This is required in order to get a real copy.
+        Alternatively, you can copy an existing instance using the copy module"""
+        self._destroy()
+        self._copy_from(rhs)
+
+    def use_region(self, offset=0, size=0, flags=0):
+        """Assure we point to a window which allows access to the given offset into the file
+
+        :param offset: absolute offset in bytes into the file
+        :param size: amount of bytes to map. If 0, all available bytes will be mapped
+        :param flags: additional flags to be given to os.open in case a file handle is initially opened
+            for mapping. Has no effect if a region can actually be reused.
+        :return: this instance - it should be queried for whether it points to a valid memory region.
+            This is not the case if the mapping failed because we reached the end of the file
+
+        **Note:**: The size actually mapped may be smaller than the given size. If that is the case,
+        either the file has reached its end, or the map was created between two existing regions"""
+        need_region = True
+        man = self._manager
+        fsize = self._rlist.file_size()
+        size = min(size or fsize, man.window_size() or fsize)   # clamp size to window size
+
+        if self._region is not None:
+            if self._region.includes_ofs(offset):
+                need_region = False
+            else:
+                self.unuse_region()
+            # END handle existing region
+        # END check existing region
+
+        # offset too large ?
+        if offset >= fsize:
+            return self
+        # END handle offset
+
+        if need_region:
+            self._region = man._obtain_region(self._rlist, offset, size, flags, False)
+            self._region.increment_client_count()
+        # END need region handling
+
+        self._ofs = offset - self._region._b
+        self._size = min(size, self._region.ofs_end() - offset)
+
+        return self
+
+    def unuse_region(self):
+        """Unuse the current region. Does nothing if we have no current region
+
+        **Note:** the cursor unuses the region automatically upon destruction. It is recommended
+        to un-use the region once you are done reading from it in persistent cursors as it
+        helps to free up resource more quickly"""
+        if self._region is not None:
+            self._region.increment_client_count(-1)
+        self._region = None
+        # note: should reset ofs and size, but we spare that for performance. Its not
+        # allowed to query information if we are not valid !
+
+    def buffer(self):
+        """Return a buffer object which allows access to our memory region from our offset
+        to the window size. Please note that it might be smaller than you requested when calling use_region()
+
+        **Note:** You can only obtain a buffer if this instance is_valid() !
+
+        **Note:** buffers should not be cached passed the duration of your access as it will
+        prevent resources from being freed even though they might not be accounted for anymore !"""
+        return memoryview(self._region.buffer())[self._ofs:self._ofs+self._size]
+
+    def map(self):
+        """
+        :return: the underlying raw memory map. Please not that the offset and size is likely to be different
+            to what you set as offset and size. Use it only if you are sure about the region it maps, which is the whole
+            file in case of StaticWindowMapManager"""
+        return self._region.map()
+
+    def is_valid(self):
+        """:return: True if we have a valid and usable region"""
+        return self._region is not None
+
+    def is_associated(self):
+        """:return: True if we are associated with a specific file already"""
+        return self._rlist is not None
+
+    def ofs_begin(self):
+        """:return: offset to the first byte pointed to by our cursor
+
+        **Note:** only if is_valid() is True"""
+        return self._region._b + self._ofs
+
+    def ofs_end(self):
+        """:return: offset to one past the last available byte"""
+        # unroll method calls for performance !
+        return self._region._b + self._ofs + self._size
+
+    def size(self):
+        """:return: amount of bytes we point to"""
+        return self._size
+
+    def region(self):
+        """:return: our mapped region, or None if nothing is mapped yet
+        :raise AssertionError: if we have no current region. This is only useful for debugging"""
+        return self._region
+
+    def includes_ofs(self, ofs):
+        """:return: True if the given absolute offset is contained in the cursors
+            current region
+
+        **Note:** cursor must be valid for this to work"""
+        # unroll methods
+        return (self._region._b + self._ofs) <= ofs < (self._region._b + self._ofs + self._size)
+
+    def file_size(self):
+        """:return: size of the underlying file"""
+        return self._rlist.file_size()
+
+    def path_or_fd(self):
+        """:return: path or file descriptor of the underlying mapped file"""
+        return self._rlist.path_or_fd()
+
+    def path(self):
+        """:return: path of the underlying mapped file
+        :raise ValueError: if attached path is not a path"""
+        if isinstance(self._rlist.path_or_fd(), int):
+            raise ValueError("Path queried although mapping was applied to a file descriptor")
+        # END handle type
+        return self._rlist.path_or_fd()
+
+    def fd(self):
+        """:return: file descriptor used to create the underlying mapping.
+
+        **Note:** it is not required to be valid anymore
+        :raise ValueError: if the mapping was not created by a file descriptor"""
+        if isinstance(self._rlist.path_or_fd(), str):
+            raise ValueError("File descriptor queried although mapping was generated from path")
+        # END handle type
+        return self._rlist.path_or_fd()
+
+    #} END interface
+
+
+class StaticWindowMapManager:
+
+    """Provides a manager which will produce single size cursors that are allowed
+    to always map the whole file.
+
+    Clients must be written to specifically know that they are accessing their data
+    through a StaticWindowMapManager, as they otherwise have to deal with their window size.
+
+    These clients would have to use a SlidingWindowMapBuffer to hide this fact.
+
+    This type will always use a maximum window size, and optimize certain methods to
+    accommodate this fact"""
+
+    __slots__ = [
+        '_fdict',           # mapping of path -> StorageHelper (of some kind
+        '_window_size',     # maximum size of a window
+        '_max_memory_size',  # maximum amount of memory we may allocate
+        '_max_handle_count',        # maximum amount of handles to keep open
+        '_memory_size',     # currently allocated memory size
+        '_handle_count',        # amount of currently allocated file handles
+    ]
+
+    #{ Configuration
+    MapRegionListCls = MapRegionList
+    MapWindowCls = MapWindow
+    MapRegionCls = MapRegion
+    WindowCursorCls = WindowCursor
+    #} END configuration
+
+    _MB_in_bytes = 1024 * 1024
+
+    def __init__(self, window_size=0, max_memory_size=0, max_open_handles=sys.maxsize):
+        """initialize the manager with the given parameters.
+        :param window_size: if -1, a default window size will be chosen depending on
+            the operating system's architecture. It will internally be quantified to a multiple of the page size
+            If 0, the window may have any size, which basically results in mapping the whole file at one
+        :param max_memory_size: maximum amount of memory we may map at once before releasing mapped regions.
+            If 0, a viable default will be set depending on the system's architecture.
+            It is a soft limit that is tried to be kept, but nothing bad happens if we have to over-allocate
+        :param max_open_handles: if not maxint, limit the amount of open file handles to the given number.
+            Otherwise the amount is only limited by the system itself. If a system or soft limit is hit,
+            the manager will free as many handles as possible"""
+        self._fdict = dict()
+        self._window_size = window_size
+        self._max_memory_size = max_memory_size
+        self._max_handle_count = max_open_handles
+        self._memory_size = 0
+        self._handle_count = 0
+
+        if window_size < 0:
+            coeff = 64
+            if is_64_bit():
+                coeff = 1024
+            # END handle arch
+            self._window_size = coeff * self._MB_in_bytes
+        # END handle max window size
+
+        if max_memory_size == 0:
+            coeff = 1024
+            if is_64_bit():
+                coeff = 8192
+            # END handle arch
+            self._max_memory_size = coeff * self._MB_in_bytes
+        # END handle max memory size
+
+    #{ Internal Methods
+
+    def _collect_lru_region(self, size):
+        """Unmap the region which was least-recently used and has no client
+        :param size: size of the region we want to map next (assuming its not already mapped partially or full
+            if 0, we try to free any available region
+        :return: Amount of freed regions
+
+        .. Note::
+            We don't raise exceptions anymore, in order to keep the system working, allowing temporary overallocation.
+            If the system runs out of memory, it will tell.
+
+        .. TODO::
+            implement a case where all unusued regions are discarded efficiently.
+            Currently its only brute force
+        """
+        num_found = 0
+        while (size == 0) or (self._memory_size + size > self._max_memory_size):
+            lru_region = None
+            lru_list = None
+            for regions in self._fdict.values():
+                for region in regions:
+                    # check client count - if it's 1, it's just us
+                    if (region.client_count() == 1 and
+                            (lru_region is None or region._uc < lru_region._uc)):
+                        lru_region = region
+                        lru_list = regions
+                    # END update lru_region
+                # END for each region
+            # END for each regions list
+
+            if lru_region is None:
+                break
+            # END handle region not found
+
+            num_found += 1
+            del(lru_list[lru_list.index(lru_region)])
+            lru_region.increment_client_count(-1)
+            self._memory_size -= lru_region.size()
+            self._handle_count -= 1
+        # END while there is more memory to free
+        return num_found
+
+    def _obtain_region(self, a, offset, size, flags, is_recursive):
+        """Utility to create a new region - for more information on the parameters,
+        see MapCursor.use_region.
+        :param a: A regions (a)rray
+        :return: The newly created region"""
+        if self._memory_size + size > self._max_memory_size:
+            self._collect_lru_region(size)
+        # END handle collection
+
+        r = None
+        if a:
+            assert len(a) == 1
+            r = a[0]
+        else:
+            try:
+                r = self.MapRegionCls(a.path_or_fd(), 0, sys.maxsize, flags)
+            except Exception:
+                # apparently we are out of system resources or hit a limit
+                # As many more operations are likely to fail in that condition (
+                # like reading a file from disk, etc) we free up as much as possible
+                # As this invalidates our insert position, we have to recurse here
+                if is_recursive:
+                    # we already tried this, and still have no success in obtaining
+                    # a mapping. This is an exception, so we propagate it
+                    raise
+                # END handle existing recursion
+                self._collect_lru_region(0)
+                return self._obtain_region(a, offset, size, flags, True)
+            # END handle exceptions
+
+            self._handle_count += 1
+            self._memory_size += r.size()
+            a.append(r)
+        # END handle array
+
+        assert r.includes_ofs(offset)
+        return r
+
+    #}END internal methods
+
+    #{ Interface
+    def make_cursor(self, path_or_fd):
+        """
+        :return: a cursor pointing to the given path or file descriptor.
+            It can be used to map new regions of the file into memory
+
+        **Note:** if a file descriptor is given, it is assumed to be open and valid,
+        but may be closed afterwards. To refer to the same file, you may reuse
+        your existing file descriptor, but keep in mind that new windows can only
+        be mapped as long as it stays valid. This is why the using actual file paths
+        are preferred unless you plan to keep the file descriptor open.
+
+        **Note:** file descriptors are problematic as they are not necessarily unique, as two
+        different files opened and closed in succession might have the same file descriptor id.
+
+        **Note:** Using file descriptors directly is faster once new windows are mapped as it
+        prevents the file to be opened again just for the purpose of mapping it."""
+        regions = self._fdict.get(path_or_fd)
+        if regions is None:
+            regions = self.MapRegionListCls(path_or_fd)
+            self._fdict[path_or_fd] = regions
+        # END obtain region for path
+        return self.WindowCursorCls(self, regions)
+
+    def collect(self):
+        """Collect all available free-to-collect mapped regions
+        :return: Amount of freed handles"""
+        return self._collect_lru_region(0)
+
+    def num_file_handles(self):
+        """:return: amount of file handles in use. Each mapped region uses one file handle"""
+        return self._handle_count
+
+    def num_open_files(self):
+        """Amount of opened files in the system"""
+        return reduce(lambda x, y: x + y, (1 for rlist in self._fdict.values() if len(rlist) > 0), 0)
+
+    def window_size(self):
+        """:return: size of each window when allocating new regions"""
+        return self._window_size
+
+    def mapped_memory_size(self):
+        """:return: amount of bytes currently mapped in total"""
+        return self._memory_size
+
+    def max_file_handles(self):
+        """:return: maximum amount of handles we may have opened"""
+        return self._max_handle_count
+
+    def max_mapped_memory_size(self):
+        """:return: maximum amount of memory we may allocate"""
+        return self._max_memory_size
+
+    #} END interface
+
+    #{ Special Purpose Interface
+
+    def force_map_handle_removal_win(self, base_path):
+        """ONLY AVAILABLE ON WINDOWS
+        On windows removing files is not allowed if anybody still has it opened.
+        If this process is ourselves, and if the whole process uses this memory
+        manager (as far as the parent framework is concerned) we can enforce
+        closing all memory maps whose path matches the given base path to
+        allow the respective operation after all.
+        The respective system must NOT access the closed memory regions anymore !
+        This really may only be used if you know that the items which keep
+        the cursors alive will not be using it anymore. They need to be recreated !
+        :return: Amount of closed handles
+
+        **Note:** does nothing on non-windows platforms"""
+        if sys.platform != 'win32':
+            return
+        # END early bailout
+
+        num_closed = 0
+        for path, rlist in self._fdict.items():
+            if path.startswith(base_path):
+                for region in rlist:
+                    region.release()
+                    num_closed += 1
+            # END path matches
+        # END for each path
+        return num_closed
+    #} END special purpose interface
+
+
+class SlidingWindowMapManager(StaticWindowMapManager):
+
+    """Maintains a list of ranges of mapped memory regions in one or more files and allows to easily
+    obtain additional regions assuring there is no overlap.
+    Once a certain memory limit is reached globally, or if there cannot be more open file handles
+    which result from each mmap call, the least recently used, and currently unused mapped regions
+    are unloaded automatically.
+
+    **Note:** currently not thread-safe !
+
+    **Note:** in the current implementation, we will automatically unload windows if we either cannot
+        create more memory maps (as the open file handles limit is hit) or if we have allocated more than
+        a safe amount of memory already, which would possibly cause memory allocations to fail as our address
+        space is full."""
+
+    __slots__ = tuple()
+
+    def __init__(self, window_size=-1, max_memory_size=0, max_open_handles=sys.maxsize):
+        """Adjusts the default window size to -1"""
+        super().__init__(window_size, max_memory_size, max_open_handles)
+
+    def _obtain_region(self, a, offset, size, flags, is_recursive):
+        # bisect to find an existing region. The c++ implementation cannot
+        # do that as it uses a linked list for regions.
+        r = None
+        lo = 0
+        hi = len(a)
+        while lo < hi:
+            mid = (lo + hi) // 2
+            ofs = a[mid]._b
+            if ofs <= offset:
+                if a[mid].includes_ofs(offset):
+                    r = a[mid]
+                    break
+                # END have region
+                lo = mid + 1
+            else:
+                hi = mid
+            # END handle position
+        # END while bisecting
+
+        if r is None:
+            window_size = self._window_size
+            left = self.MapWindowCls(0, 0)
+            mid = self.MapWindowCls(offset, size)
+            right = self.MapWindowCls(a.file_size(), 0)
+
+            # we want to honor the max memory size, and assure we have anough
+            # memory available
+            # Save calls !
+            if self._memory_size + window_size > self._max_memory_size:
+                self._collect_lru_region(window_size)
+            # END handle collection
+
+            # we assume the list remains sorted by offset
+            insert_pos = 0
+            len_regions = len(a)
+            if len_regions == 1:
+                if a[0]._b <= offset:
+                    insert_pos = 1
+                # END maintain sort
+            else:
+                # find insert position
+                insert_pos = len_regions
+                for i, region in enumerate(a):
+                    if region._b > offset:
+                        insert_pos = i
+                        break
+                    # END if insert position is correct
+                # END for each region
+            # END obtain insert pos
+
+            # adjust the actual offset and size values to create the largest
+            # possible mapping
+            if insert_pos == 0:
+                if len_regions:
+                    right = self.MapWindowCls.from_region(a[insert_pos])
+                # END adjust right side
+            else:
+                if insert_pos != len_regions:
+                    right = self.MapWindowCls.from_region(a[insert_pos])
+                # END adjust right window
+                left = self.MapWindowCls.from_region(a[insert_pos - 1])
+            # END adjust surrounding windows
+
+            mid.extend_left_to(left, window_size)
+            mid.extend_right_to(right, window_size)
+            mid.align()
+
+            # it can happen that we align beyond the end of the file
+            if mid.ofs_end() > right.ofs:
+                mid.size = right.ofs - mid.ofs
+            # END readjust size
+
+            # insert new region at the right offset to keep the order
+            try:
+                if self._handle_count >= self._max_handle_count:
+                    raise Exception
+                # END assert own imposed max file handles
+                r = self.MapRegionCls(a.path_or_fd(), mid.ofs, mid.size, flags)
+            except Exception:
+                # apparently we are out of system resources or hit a limit
+                # As many more operations are likely to fail in that condition (
+                # like reading a file from disk, etc) we free up as much as possible
+                # As this invalidates our insert position, we have to recurse here
+                if is_recursive:
+                    # we already tried this, and still have no success in obtaining
+                    # a mapping. This is an exception, so we propagate it
+                    raise
+                # END handle existing recursion
+                self._collect_lru_region(0)
+                return self._obtain_region(a, offset, size, flags, True)
+            # END handle exceptions
+
+            self._handle_count += 1
+            self._memory_size += r.size()
+            a.insert(insert_pos, r)
+        # END create new region
+        return r
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/lib.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/lib.py
new file mode 100644
index 0000000000000000000000000000000000000000..b15b0ec6a8eca03b9b01f0f469f8687300039df6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/lib.py
@@ -0,0 +1,72 @@
+"""Provide base classes for the test system"""
+from unittest import TestCase
+import os
+import tempfile
+
+__all__ = ['TestBase', 'FileCreator']
+
+
+#{ Utilities
+
+class FileCreator:
+
+    """A instance which creates a temporary file with a prefix and a given size
+    and provides this info to the user.
+    Once it gets deleted, it will remove the temporary file as well."""
+    __slots__ = ("_size", "_path")
+
+    def __init__(self, size, prefix=''):
+        assert size, "Require size to be larger 0"
+
+        self._size = size
+
+        with tempfile.NamedTemporaryFile("wb", prefix=prefix, delete=False) as file:
+            self._path = file.name
+            file.seek(size - 1)
+            file.write(b'1')
+
+        assert os.path.getsize(self.path) == size
+
+    def __del__(self):
+        try:
+            os.remove(self.path)
+        except OSError:
+            pass
+        # END exception handling
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        self.__del__()
+
+    @property
+    def path(self):
+        return self._path
+
+    @property
+    def size(self):
+        return self._size
+
+#} END utilities
+
+
+class TestBase(TestCase):
+
+    """Foundation used by all tests"""
+
+    #{ Configuration
+    k_window_test_size = 1000 * 1000 * 8 + 5195
+    #} END configuration
+
+    #{ Overrides
+    @classmethod
+    def setUpAll(cls):
+        # nothing for now
+        pass
+
+    # END overrides
+
+    #{ Interface
+
+    #} END interface
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_buf.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_buf.py
new file mode 100644
index 0000000000000000000000000000000000000000..f0a86fb643b512454c60451de56b63e171e60960
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_buf.py
@@ -0,0 +1,126 @@
+from .lib import TestBase, FileCreator
+
+from smmap.mman import (
+    SlidingWindowMapManager,
+    StaticWindowMapManager
+)
+from smmap.buf import SlidingWindowMapBuffer
+
+from random import randint
+from time import time
+import sys
+import os
+
+
+man_optimal = SlidingWindowMapManager()
+man_worst_case = SlidingWindowMapManager(
+    window_size=TestBase.k_window_test_size // 100,
+    max_memory_size=TestBase.k_window_test_size // 3,
+    max_open_handles=15)
+static_man = StaticWindowMapManager()
+
+
+class TestBuf(TestBase):
+
+    def test_basics(self):
+        with FileCreator(self.k_window_test_size, "buffer_test") as fc:
+
+            # invalid paths fail upon construction
+            c = man_optimal.make_cursor(fc.path)
+            self.assertRaises(ValueError, SlidingWindowMapBuffer, type(c)())            # invalid cursor
+            self.assertRaises(ValueError, SlidingWindowMapBuffer, c, fc.size)       # offset too large
+
+            buf = SlidingWindowMapBuffer()                                              # can create uninitialized buffers
+            assert buf.cursor() is None
+
+            # can call end access any time
+            buf.end_access()
+            buf.end_access()
+            assert len(buf) == 0
+
+            # begin access can revive it, if the offset is suitable
+            offset = 100
+            assert buf.begin_access(c, fc.size) == False
+            assert buf.begin_access(c, offset) == True
+            assert len(buf) == fc.size - offset
+            assert buf.cursor().is_valid()
+
+            # empty begin access keeps it valid on the same path, but alters the offset
+            assert buf.begin_access() == True
+            assert len(buf) == fc.size
+            assert buf.cursor().is_valid()
+
+            # simple access
+            with open(fc.path, 'rb') as fp:
+                data = fp.read()
+            assert data[offset] == buf[0]
+            assert data[offset:offset * 2] == buf[0:offset]
+
+            # negative indices, partial slices
+            assert buf[-1] == buf[len(buf) - 1]
+            assert buf[-10:] == buf[len(buf) - 10:len(buf)]
+
+            # end access makes its cursor invalid
+            buf.end_access()
+            assert not buf.cursor().is_valid()
+            assert buf.cursor().is_associated()         # but it remains associated
+
+            # an empty begin access fixes it up again
+            assert buf.begin_access() == True and buf.cursor().is_valid()
+            del(buf)        # ends access automatically
+            del(c)
+
+            assert man_optimal.num_file_handles() == 1
+
+            # PERFORMANCE
+            # blast away with random access and a full mapping - we don't want to
+            # exaggerate the manager's overhead, but measure the buffer overhead
+            # We do it once with an optimal setting, and with a worse manager which
+            # will produce small mappings only !
+            max_num_accesses = 100
+            fd = os.open(fc.path, os.O_RDONLY)
+            for item in (fc.path, fd):
+                for manager, man_id in ((man_optimal, 'optimal'),
+                                        (man_worst_case, 'worst case'),
+                                        (static_man, 'static optimal')):
+                    buf = SlidingWindowMapBuffer(manager.make_cursor(item))
+                    assert manager.num_file_handles() == 1
+                    for access_mode in range(2):    # single, multi
+                        num_accesses_left = max_num_accesses
+                        num_bytes = 0
+                        fsize = fc.size
+
+                        st = time()
+                        buf.begin_access()
+                        while num_accesses_left:
+                            num_accesses_left -= 1
+                            if access_mode:  # multi
+                                ofs_start = randint(0, fsize)
+                                ofs_end = randint(ofs_start, fsize)
+                                d = buf[ofs_start:ofs_end]
+                                assert len(d) == ofs_end - ofs_start
+                                assert d == data[ofs_start:ofs_end]
+                                num_bytes += len(d)
+                                del d
+                            else:
+                                pos = randint(0, fsize)
+                                assert buf[pos] == data[pos]
+                                num_bytes += 1
+                            # END handle mode
+                        # END handle num accesses
+
+                        buf.end_access()
+                        assert manager.num_file_handles()
+                        assert manager.collect()
+                        assert manager.num_file_handles() == 0
+                        elapsed = max(time() - st, 0.001)  # prevent zero division errors on windows
+                        mb = float(1000 * 1000)
+                        mode_str = (access_mode and "slice") or "single byte"
+                        print("%s: Made %i random %s accesses to buffer created from %s reading a total of %f mb in %f s (%f mb/s)"
+                              % (man_id, max_num_accesses, mode_str, type(item), num_bytes / mb, elapsed, (num_bytes / mb) / elapsed),
+                              file=sys.stderr)
+                    # END handle access mode
+                    del buf
+                # END for each manager
+            # END for each input
+            os.close(fd)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_mman.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_mman.py
new file mode 100644
index 0000000000000000000000000000000000000000..7a5f4092c11e7abb6a086a87a481a9ffa0f818aa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_mman.py
@@ -0,0 +1,224 @@
+from .lib import TestBase, FileCreator
+
+from smmap.mman import (
+    WindowCursor,
+    SlidingWindowMapManager,
+    StaticWindowMapManager
+)
+from smmap.util import align_to_mmap
+
+from random import randint
+from time import time
+import os
+import sys
+from copy import copy
+
+
+class TestMMan(TestBase):
+
+    def test_cursor(self):
+        with FileCreator(self.k_window_test_size, "cursor_test") as fc:
+            man = SlidingWindowMapManager()
+            ci = WindowCursor(man)  # invalid cursor
+            assert not ci.is_valid()
+            assert not ci.is_associated()
+            assert ci.size() == 0       # this is cached, so we can query it in invalid state
+
+            cv = man.make_cursor(fc.path)
+            assert not cv.is_valid()    # no region mapped yet
+            assert cv.is_associated()  # but it know where to map it from
+            assert cv.file_size() == fc.size
+            assert cv.path() == fc.path
+
+        # copy module
+        cio = copy(cv)
+        assert not cio.is_valid() and cio.is_associated()
+
+        # assign method
+        assert not ci.is_associated()
+        ci.assign(cv)
+        assert not ci.is_valid() and ci.is_associated()
+
+        # unuse non-existing region is fine
+        cv.unuse_region()
+        cv.unuse_region()
+
+        # destruction is fine (even multiple times)
+        cv._destroy()
+        WindowCursor(man)._destroy()
+
+    def test_memory_manager(self):
+        slide_man = SlidingWindowMapManager()
+        static_man = StaticWindowMapManager()
+
+        for man in (static_man, slide_man):
+            assert man.num_file_handles() == 0
+            assert man.num_open_files() == 0
+            winsize_cmp_val = 0
+            if isinstance(man, StaticWindowMapManager):
+                winsize_cmp_val = -1
+            # END handle window size
+            assert man.window_size() > winsize_cmp_val
+            assert man.mapped_memory_size() == 0
+            assert man.max_mapped_memory_size() > 0
+
+            # collection doesn't raise in 'any' mode
+            man._collect_lru_region(0)
+            # doesn't raise if we are within the limit
+            man._collect_lru_region(10)
+
+            # doesn't fail if we over-allocate
+            assert man._collect_lru_region(sys.maxsize) == 0
+
+            # use a region, verify most basic functionality
+            with FileCreator(self.k_window_test_size, "manager_test") as fc:
+                fd = os.open(fc.path, os.O_RDONLY)
+                try:
+                    for item in (fc.path, fd):
+                        c = man.make_cursor(item)
+                        assert c.path_or_fd() is item
+                        assert c.use_region(10, 10).is_valid()
+                        assert c.ofs_begin() == 10
+                        assert c.size() == 10
+                        with open(fc.path, 'rb') as fp:
+                            assert c.buffer()[:] == fp.read(20)[10:]
+
+                    if isinstance(item, int):
+                        self.assertRaises(ValueError, c.path)
+                    else:
+                        self.assertRaises(ValueError, c.fd)
+                    # END handle value error
+                # END for each input
+                finally:
+                    os.close(fd)
+        # END for each manasger type
+
+    def test_memman_operation(self):
+        # test more access, force it to actually unmap regions
+        with FileCreator(self.k_window_test_size, "manager_operation_test") as fc:
+            with open(fc.path, 'rb') as fp:
+                data = fp.read()
+            fd = os.open(fc.path, os.O_RDONLY)
+            try:
+                max_num_handles = 15
+                # small_size =
+                for mtype, args in ((StaticWindowMapManager, (0, fc.size // 3, max_num_handles)),
+                                    (SlidingWindowMapManager, (fc.size // 100, fc.size // 3, max_num_handles)),):
+                    for item in (fc.path, fd):
+                        assert len(data) == fc.size
+
+                        # small windows, a reasonable max memory. Not too many regions at once
+                        man = mtype(window_size=args[0], max_memory_size=args[1], max_open_handles=args[2])
+                        c = man.make_cursor(item)
+
+                        # still empty (more about that is tested in test_memory_manager()
+                        assert man.num_open_files() == 0
+                        assert man.mapped_memory_size() == 0
+
+                        base_offset = 5000
+                        # window size is 0 for static managers, hence size will be 0. We take that into consideration
+                        size = man.window_size() // 2
+                        assert c.use_region(base_offset, size).is_valid()
+                        rr = c.region()
+                        assert rr.client_count() == 2  # the manager and the cursor and us
+
+                        assert man.num_open_files() == 1
+                        assert man.num_file_handles() == 1
+                        assert man.mapped_memory_size() == rr.size()
+
+                        # assert c.size() == size        # the cursor may overallocate in its static version
+                        assert c.ofs_begin() == base_offset
+                        assert rr.ofs_begin() == 0        # it was aligned and expanded
+                        if man.window_size():
+                            # but isn't larger than the max window (aligned)
+                            assert rr.size() == align_to_mmap(man.window_size(), True)
+                        else:
+                            assert rr.size() == fc.size
+                        # END ignore static managers which dont use windows and are aligned to file boundaries
+
+                        assert c.buffer()[:] == data[base_offset:base_offset + (size or c.size())]
+
+                        # obtain second window, which spans the first part of the file - it is a still the same window
+                        nsize = (size or fc.size) - 10
+                        assert c.use_region(0, nsize).is_valid()
+                        assert c.region() == rr
+                        assert man.num_file_handles() == 1
+                        assert c.size() == nsize
+                        assert c.ofs_begin() == 0
+                        assert c.buffer()[:] == data[:nsize]
+
+                        # map some part at the end, our requested size cannot be kept
+                        overshoot = 4000
+                        base_offset = fc.size - (size or c.size()) + overshoot
+                        assert c.use_region(base_offset, size).is_valid()
+                        if man.window_size():
+                            assert man.num_file_handles() == 2
+                            assert c.size() < size
+                            assert c.region() is not rr  # old region is still available, but has not cursor ref anymore
+                            assert rr.client_count() == 1  # only held by manager
+                        else:
+                            assert c.size() < fc.size
+                        # END ignore static managers which only have one handle per file
+                        rr = c.region()
+                        assert rr.client_count() == 2  # manager + cursor
+                        assert rr.ofs_begin() < c.ofs_begin()  # it should have extended itself to the left
+                        assert rr.ofs_end() <= fc.size  # it cannot be larger than the file
+                        assert c.buffer()[:] == data[base_offset:base_offset + (size or c.size())]
+
+                        # unising a region makes the cursor invalid
+                        c.unuse_region()
+                        assert not c.is_valid()
+                        if man.window_size():
+                            # but doesn't change anything regarding the handle count - we cache it and only
+                            # remove mapped regions if we have to
+                            assert man.num_file_handles() == 2
+                        # END ignore this for static managers
+
+                        # iterate through the windows, verify data contents
+                        # this will trigger map collection after a while
+                        max_random_accesses = 5000
+                        num_random_accesses = max_random_accesses
+                        memory_read = 0
+                        st = time()
+
+                        # cache everything to get some more performance
+                        includes_ofs = c.includes_ofs
+                        max_mapped_memory_size = man.max_mapped_memory_size()
+                        max_file_handles = man.max_file_handles()
+                        mapped_memory_size = man.mapped_memory_size
+                        num_file_handles = man.num_file_handles
+                        while num_random_accesses:
+                            num_random_accesses -= 1
+                            base_offset = randint(0, fc.size - 1)
+
+                            # precondition
+                            if man.window_size():
+                                assert max_mapped_memory_size >= mapped_memory_size()
+                            # END statistics will overshoot, which is fine
+                            assert max_file_handles >= num_file_handles()
+                            assert c.use_region(base_offset, (size or c.size())).is_valid()
+                            csize = c.size()
+                            assert c.buffer()[:] == data[base_offset:base_offset + csize]
+                            memory_read += csize
+
+                            assert includes_ofs(base_offset)
+                            assert includes_ofs(base_offset + csize - 1)
+                            assert not includes_ofs(base_offset + csize)
+                        # END while we should do an access
+                        elapsed = max(time() - st, 0.001)  # prevent zero division errors on windows
+                        mb = float(1000 * 1000)
+                        print("%s: Read %i mb of memory with %i random on cursor initialized with %s accesses in %fs (%f mb/s)\n"
+                              % (mtype, memory_read / mb, max_random_accesses, type(item), elapsed, (memory_read / mb) / elapsed),
+                              file=sys.stderr)
+
+                        # an offset as large as the size doesn't work !
+                        assert not c.use_region(fc.size, size).is_valid()
+
+                        # collection - it should be able to collect all
+                        assert man.num_file_handles()
+                        assert man.collect()
+                        assert man.num_file_handles() == 0
+                    # END for each item
+                # END for each manager type
+            finally:
+                os.close(fd)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_tutorial.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_tutorial.py
new file mode 100644
index 0000000000000000000000000000000000000000..31c272abbf09361b6c5dc2077e853a8d47958458
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_tutorial.py
@@ -0,0 +1,75 @@
+from .lib import TestBase
+
+
+class TestTutorial(TestBase):
+
+    def test_example(self):
+        # Memory Managers
+        ##################
+        import smmap
+        # This instance should be globally available in your application
+        # It is configured to be well suitable for 32-bit or 64 bit applications.
+        mman = smmap.SlidingWindowMapManager()
+
+        # the manager provides much useful information about its current state
+        # like the amount of open file handles or the amount of mapped memory
+        assert mman.num_file_handles() == 0
+        assert mman.mapped_memory_size() == 0
+        # and many more ...
+
+        # Cursors
+        ##########
+        import smmap.test.lib
+        with smmap.test.lib.FileCreator(1024 * 1024 * 8, "test_file") as fc:
+            # obtain a cursor to access some file.
+            c = mman.make_cursor(fc.path)
+
+            # the cursor is now associated with the file, but not yet usable
+            assert c.is_associated()
+            assert not c.is_valid()
+
+            # before you can use the cursor, you have to specify a window you want to
+            # access. The following just says you want as much data as possible starting
+            # from offset 0.
+            # To be sure your region could be mapped, query for validity
+            assert c.use_region().is_valid()        # use_region returns self
+
+            # once a region was mapped, you must query its dimension regularly
+            # to assure you don't try to access its buffer out of its bounds
+            assert c.size()
+            c.buffer()[0]           # first byte
+            c.buffer()[1:10]            # first 9 bytes
+            c.buffer()[c.size() - 1]  # last byte
+
+            # you can query absolute offsets, and check whether an offset is included
+            # in the cursor's data.
+            assert c.ofs_begin() < c.ofs_end()
+            assert c.includes_ofs(100)
+
+            # If you are over out of bounds with one of your region requests, the
+            # cursor will be come invalid. It cannot be used in that state
+            assert not c.use_region(fc.size, 100).is_valid()
+            # map as much as possible after skipping the first 100 bytes
+            assert c.use_region(100).is_valid()
+
+            # You can explicitly free cursor resources by unusing the cursor's region
+            c.unuse_region()
+            assert not c.is_valid()
+
+            # Buffers
+            #########
+            # Create a default buffer which can operate on the whole file
+            buf = smmap.SlidingWindowMapBuffer(mman.make_cursor(fc.path))
+
+            # you can use it right away
+            assert buf.cursor().is_valid()
+
+            buf[0]  # access the first byte
+            buf[-1]  # access the last ten bytes on the file
+            buf[-10:]  # access the last ten bytes
+
+            # If you want to keep the instance between different accesses, use the
+            # dedicated methods
+            buf.end_access()
+            assert not buf.cursor().is_valid()  # you cannot use the buffer anymore
+            assert buf.begin_access(offset=10)  # start using the buffer at an offset
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..e6ac10f35cb0841947b17f08a49ce52176ded51b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/test/test_util.py
@@ -0,0 +1,105 @@
+from .lib import TestBase, FileCreator
+
+from smmap.util import (
+    MapWindow,
+    MapRegion,
+    MapRegionList,
+    ALLOCATIONGRANULARITY,
+    is_64_bit,
+    align_to_mmap
+)
+
+import os
+import sys
+
+
+class TestMMan(TestBase):
+
+    def test_window(self):
+        wl = MapWindow(0, 1)        # left
+        wc = MapWindow(1, 1)        # center
+        wc2 = MapWindow(10, 5)      # another center
+        wr = MapWindow(8000, 50)    # right
+
+        assert wl.ofs_end() == 1
+        assert wc.ofs_end() == 2
+        assert wr.ofs_end() == 8050
+
+        # extension does nothing if already in place
+        maxsize = 100
+        wc.extend_left_to(wl, maxsize)
+        assert wc.ofs == 1 and wc.size == 1
+        wl.extend_right_to(wc, maxsize)
+        wl.extend_right_to(wc, maxsize)
+        assert wl.ofs == 0 and wl.size == 1
+
+        # an actual left extension
+        pofs_end = wc2.ofs_end()
+        wc2.extend_left_to(wc, maxsize)
+        assert wc2.ofs == wc.ofs_end() and pofs_end == wc2.ofs_end()
+
+        # respects maxsize
+        wc.extend_right_to(wr, maxsize)
+        assert wc.ofs == 1 and wc.size == maxsize
+        wc.extend_right_to(wr, maxsize)
+        assert wc.ofs == 1 and wc.size == maxsize
+
+        # without maxsize
+        wc.extend_right_to(wr, sys.maxsize)
+        assert wc.ofs_end() == wr.ofs and wc.ofs == 1
+
+        # extend left
+        wr.extend_left_to(wc2, maxsize)
+        wr.extend_left_to(wc2, maxsize)
+        assert wr.size == maxsize
+
+        wr.extend_left_to(wc2, sys.maxsize)
+        assert wr.ofs == wc2.ofs_end()
+
+        wc.align()
+        assert wc.ofs == 0 and wc.size == align_to_mmap(wc.size, True)
+
+    def test_region(self):
+        with FileCreator(self.k_window_test_size, "window_test") as fc:
+            half_size = fc.size // 2
+            rofs = align_to_mmap(4200, False)
+            rfull = MapRegion(fc.path, 0, fc.size)
+            rhalfofs = MapRegion(fc.path, rofs, fc.size)
+            rhalfsize = MapRegion(fc.path, 0, half_size)
+
+            # offsets
+            assert rfull.ofs_begin() == 0 and rfull.size() == fc.size
+            assert rfull.ofs_end() == fc.size   # if this method works, it works always
+
+            assert rhalfofs.ofs_begin() == rofs and rhalfofs.size() == fc.size - rofs
+            assert rhalfsize.ofs_begin() == 0 and rhalfsize.size() == half_size
+
+            assert rfull.includes_ofs(0) and rfull.includes_ofs(fc.size - 1) and rfull.includes_ofs(half_size)
+            assert not rfull.includes_ofs(-1) and not rfull.includes_ofs(sys.maxsize)
+
+        # auto-refcount
+        assert rfull.client_count() == 1
+        rfull2 = rfull
+        assert rfull.client_count() == 1, "no auto-counting"
+
+        # window constructor
+        w = MapWindow.from_region(rfull)
+        assert w.ofs == rfull.ofs_begin() and w.ofs_end() == rfull.ofs_end()
+
+    def test_region_list(self):
+        with FileCreator(100, "sample_file") as fc:
+            fd = os.open(fc.path, os.O_RDONLY)
+            try:
+                for item in (fc.path, fd):
+                    ml = MapRegionList(item)
+
+                    assert len(ml) == 0
+                    assert ml.path_or_fd() == item
+                    assert ml.file_size() == fc.size
+            finally:
+                os.close(fd)
+
+    def test_util(self):
+        assert isinstance(is_64_bit(), bool)    # just call it
+        assert align_to_mmap(1, False) == 0
+        assert align_to_mmap(1, True) == ALLOCATIONGRANULARITY
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/util.py
new file mode 100644
index 0000000000000000000000000000000000000000..fbb3872118e644ee0a920914fa5835cf2bfab44d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/smmap/util.py
@@ -0,0 +1,222 @@
+"""Module containing a memory memory manager which provides a sliding window on a number of memory mapped files"""
+import os
+import sys
+
+from mmap import mmap, ACCESS_READ
+from mmap import ALLOCATIONGRANULARITY
+
+__all__ = ["align_to_mmap", "is_64_bit",
+           "MapWindow", "MapRegion", "MapRegionList", "ALLOCATIONGRANULARITY"]
+
+#{ Utilities
+
+
+def align_to_mmap(num, round_up):
+    """
+    Align the given integer number to the closest page offset, which usually is 4096 bytes.
+
+    :param round_up: if True, the next higher multiple of page size is used, otherwise
+        the lower page_size will be used (i.e. if True, 1 becomes 4096, otherwise it becomes 0)
+    :return: num rounded to closest page"""
+    res = (num // ALLOCATIONGRANULARITY) * ALLOCATIONGRANULARITY
+    if round_up and (res != num):
+        res += ALLOCATIONGRANULARITY
+    # END handle size
+    return res
+
+
+def is_64_bit():
+    """:return: True if the system is 64 bit. Otherwise it can be assumed to be 32 bit"""
+    return sys.maxsize > (1 << 32) - 1
+
+#}END utilities
+
+
+#{ Utility Classes
+
+class MapWindow:
+
+    """Utility type which is used to snap windows towards each other, and to adjust their size"""
+    __slots__ = (
+        'ofs',      # offset into the file in bytes
+        'size'              # size of the window in bytes
+    )
+
+    def __init__(self, offset, size):
+        self.ofs = offset
+        self.size = size
+
+    def __repr__(self):
+        return "MapWindow(%i, %i)" % (self.ofs, self.size)
+
+    @classmethod
+    def from_region(cls, region):
+        """:return: new window from a region"""
+        return cls(region._b, region.size())
+
+    def ofs_end(self):
+        return self.ofs + self.size
+
+    def align(self):
+        """Assures the previous window area is contained in the new one"""
+        nofs = align_to_mmap(self.ofs, 0)
+        self.size += self.ofs - nofs    # keep size constant
+        self.ofs = nofs
+        self.size = align_to_mmap(self.size, 1)
+
+    def extend_left_to(self, window, max_size):
+        """Adjust the offset to start where the given window on our left ends if possible,
+        but don't make yourself larger than max_size.
+        The resize will assure that the new window still contains the old window area"""
+        rofs = self.ofs - window.ofs_end()
+        nsize = rofs + self.size
+        rofs -= nsize - min(nsize, max_size)
+        self.ofs -= rofs
+        self.size += rofs
+
+    def extend_right_to(self, window, max_size):
+        """Adjust the size to make our window end where the right window begins, but don't
+        get larger than max_size"""
+        self.size = min(self.size + (window.ofs - self.ofs_end()), max_size)
+
+
+class MapRegion:
+
+    """Defines a mapped region of memory, aligned to pagesizes
+
+    **Note:** deallocates used region automatically on destruction"""
+    __slots__ = [
+        '_b',   # beginning of mapping
+        '_mf',  # mapped memory chunk (as returned by mmap)
+        '_uc',  # total amount of usages
+        '_size',  # cached size of our memory map
+        '__weakref__'
+    ]
+
+    #{ Configuration
+    #} END configuration
+
+    def __init__(self, path_or_fd, ofs, size, flags=0):
+        """Initialize a region, allocate the memory map
+        :param path_or_fd: path to the file to map, or the opened file descriptor
+        :param ofs: **aligned** offset into the file to be mapped
+        :param size: if size is larger then the file on disk, the whole file will be
+            allocated the the size automatically adjusted
+        :param flags: additional flags to be given when opening the file.
+        :raise Exception: if no memory can be allocated"""
+        self._b = ofs
+        self._size = 0
+        self._uc = 0
+
+        if isinstance(path_or_fd, int):
+            fd = path_or_fd
+        else:
+            fd = os.open(path_or_fd, os.O_RDONLY | getattr(os, 'O_BINARY', 0) | flags)
+        # END handle fd
+
+        try:
+            kwargs = dict(access=ACCESS_READ, offset=ofs)
+            corrected_size = size
+            sizeofs = ofs
+
+            # have to correct size, otherwise (instead of the c version) it will
+            # bark that the size is too large ... many extra file accesses because
+            # if this ... argh !
+            actual_size = min(os.fstat(fd).st_size - sizeofs, corrected_size)
+            self._mf = mmap(fd, actual_size, **kwargs)
+            # END handle memory mode
+
+            self._size = len(self._mf)
+        finally:
+            if isinstance(path_or_fd, str):
+                os.close(fd)
+            # END only close it if we opened it
+        # END close file handle
+        # We assume the first one to use us keeps us around
+        self.increment_client_count()
+
+    def __repr__(self):
+        return "MapRegion<%i, %i>" % (self._b, self.size())
+
+    #{ Interface
+
+    def buffer(self):
+        """:return: a buffer containing the memory"""
+        return self._mf
+
+    def map(self):
+        """:return: a memory map containing the memory"""
+        return self._mf
+
+    def ofs_begin(self):
+        """:return: absolute byte offset to the first byte of the mapping"""
+        return self._b
+
+    def size(self):
+        """:return: total size of the mapped region in bytes"""
+        return self._size
+
+    def ofs_end(self):
+        """:return: Absolute offset to one byte beyond the mapping into the file"""
+        return self._b + self._size
+
+    def includes_ofs(self, ofs):
+        """:return: True if the given offset can be read in our mapped region"""
+        return self._b <= ofs < self._b + self._size
+
+    def client_count(self):
+        """:return: number of clients currently using this region"""
+        return self._uc
+
+    def increment_client_count(self, ofs = 1):
+        """Adjust the usage count by the given positive or negative offset.
+        If usage count equals 0, we will auto-release our resources
+        :return: True if we released resources, False otherwise. In the latter case, we can still be used"""
+        self._uc += ofs
+        assert self._uc > -1, "Increments must match decrements, usage counter negative: %i" % self._uc
+
+        if self.client_count() == 0:
+            self.release()
+            return True
+        else:
+            return False
+        # end handle release
+
+    def release(self):
+        """Release all resources this instance might hold. Must only be called if there usage_count() is zero"""
+        self._mf.close()
+
+    #} END interface
+
+
+class MapRegionList(list):
+
+    """List of MapRegion instances associating a path with a list of regions."""
+    __slots__ = (
+        '_path_or_fd',  # path or file descriptor which is mapped by all our regions
+        '_file_size'    # total size of the file we map
+    )
+
+    def __new__(cls, path):
+        return super().__new__(cls)
+
+    def __init__(self, path_or_fd):
+        self._path_or_fd = path_or_fd
+        self._file_size = None
+
+    def path_or_fd(self):
+        """:return: path or file descriptor we are attached to"""
+        return self._path_or_fd
+
+    def file_size(self):
+        """:return: size of file we manager"""
+        if self._file_size is None:
+            if isinstance(self._path_or_fd, str):
+                self._file_size = os.stat(self._path_or_fd).st_size
+            else:
+                self._file_size = os.fstat(self._path_or_fd).st_size
+            # END handle path type
+        # END update file size
+        return self._file_size
+
+#} END utility classes
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..c67ba49409169c49ac5d34f2be365def3c30369b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/__init__.py
@@ -0,0 +1,545 @@
+"""
+SymPy is a Python library for symbolic mathematics. It aims to become a
+full-featured computer algebra system (CAS) while keeping the code as simple
+as possible in order to be comprehensible and easily extensible.  SymPy is
+written entirely in Python. It depends on mpmath, and other external libraries
+may be optionally for things like plotting support.
+
+See the webpage for more information and documentation:
+
+    https://sympy.org
+
+"""
+
+
+# Keep this in sync with setup.py/pyproject.toml
+import sys
+if sys.version_info < (3, 9):
+    raise ImportError("Python version 3.9 or above is required for SymPy.")
+del sys
+
+
+try:
+    import mpmath
+except ImportError:
+    raise ImportError("SymPy now depends on mpmath as an external library. "
+    "See https://docs.sympy.org/latest/install.html#mpmath for more information.")
+
+del mpmath
+
+from sympy.release import __version__
+from sympy.core.cache import lazy_function
+
+if 'dev' in __version__:
+    def enable_warnings():
+        import warnings
+        warnings.filterwarnings('default',   '.*',   DeprecationWarning, module='sympy.*')
+        del warnings
+    enable_warnings()
+    del enable_warnings
+
+
+def __sympy_debug():
+    # helper function so we don't import os globally
+    import os
+    debug_str = os.getenv('SYMPY_DEBUG', 'False')
+    if debug_str in ('True', 'False'):
+        return eval(debug_str)
+    else:
+        raise RuntimeError("unrecognized value for SYMPY_DEBUG: %s" %
+                           debug_str)
+# Fails py2 test if using type hinting
+SYMPY_DEBUG = __sympy_debug()  # type: bool
+
+
+from .core import (sympify, SympifyError, cacheit, Basic, Atom,
+        preorder_traversal, S, Expr, AtomicExpr, UnevaluatedExpr, Symbol,
+        Wild, Dummy, symbols, var, Number, Float, Rational, Integer,
+        NumberSymbol, RealNumber, igcd, ilcm, seterr, E, I, nan, oo, pi, zoo,
+        AlgebraicNumber, comp, mod_inverse, Pow, integer_nthroot, integer_log,
+        trailing, Mul, prod, Add, Mod, Rel, Eq, Ne, Lt, Le, Gt, Ge, Equality,
+        GreaterThan, LessThan, Unequality, StrictGreaterThan, StrictLessThan,
+        vectorize, Lambda, WildFunction, Derivative, diff, FunctionClass,
+        Function, Subs, expand, PoleError, count_ops, expand_mul, expand_log,
+        expand_func, expand_trig, expand_complex, expand_multinomial, nfloat,
+        expand_power_base, expand_power_exp, arity, PrecisionExhausted, N,
+        evalf, Tuple, Dict, gcd_terms, factor_terms, factor_nc, evaluate,
+        Catalan, EulerGamma, GoldenRatio, TribonacciConstant, bottom_up, use,
+        postorder_traversal, default_sort_key, ordered, num_digits)
+
+from .logic import (to_cnf, to_dnf, to_nnf, And, Or, Not, Xor, Nand, Nor,
+        Implies, Equivalent, ITE, POSform, SOPform, simplify_logic, bool_map,
+        true, false, satisfiable)
+
+from .assumptions import (AppliedPredicate, Predicate, AssumptionsContext,
+        assuming, Q, ask, register_handler, remove_handler, refine)
+
+from .polys import (Poly, PurePoly, poly_from_expr, parallel_poly_from_expr,
+        degree, total_degree, degree_list, LC, LM, LT, pdiv, prem, pquo,
+        pexquo, div, rem, quo, exquo, half_gcdex, gcdex, invert,
+        subresultants, resultant, discriminant, cofactors, gcd_list, gcd,
+        lcm_list, lcm, terms_gcd, trunc, monic, content, primitive, compose,
+        decompose, sturm, gff_list, gff, sqf_norm, sqf_part, sqf_list, sqf,
+        factor_list, factor, intervals, refine_root, count_roots, all_roots,
+        real_roots, nroots, ground_roots, nth_power_roots_poly, cancel,
+        reduced, groebner, is_zero_dimensional, GroebnerBasis, poly,
+        symmetrize, horner, interpolate, rational_interpolate, viete, together,
+        BasePolynomialError, ExactQuotientFailed, PolynomialDivisionFailed,
+        OperationNotSupported, HeuristicGCDFailed, HomomorphismFailed,
+        IsomorphismFailed, ExtraneousFactors, EvaluationFailed,
+        RefinementFailed, CoercionFailed, NotInvertible, NotReversible,
+        NotAlgebraic, DomainError, PolynomialError, UnificationFailed,
+        GeneratorsError, GeneratorsNeeded, ComputationFailed,
+        UnivariatePolynomialError, MultivariatePolynomialError,
+        PolificationFailed, OptionError, FlagError, minpoly,
+        minimal_polynomial, primitive_element, field_isomorphism,
+        to_number_field, isolate, round_two, prime_decomp, prime_valuation,
+        galois_group, itermonomials, Monomial, lex, grlex,
+        grevlex, ilex, igrlex, igrevlex, CRootOf, rootof, RootOf,
+        ComplexRootOf, RootSum, roots, Domain, FiniteField, IntegerRing,
+        RationalField, RealField, ComplexField, PythonFiniteField,
+        GMPYFiniteField, PythonIntegerRing, GMPYIntegerRing, PythonRational,
+        GMPYRationalField, AlgebraicField, PolynomialRing, FractionField,
+        ExpressionDomain, FF_python, FF_gmpy, ZZ_python, ZZ_gmpy, QQ_python,
+        QQ_gmpy, GF, FF, ZZ, QQ, ZZ_I, QQ_I, RR, CC, EX, EXRAW,
+        construct_domain, swinnerton_dyer_poly, cyclotomic_poly,
+        symmetric_poly, random_poly, interpolating_poly, jacobi_poly,
+        chebyshevt_poly, chebyshevu_poly, hermite_poly, hermite_prob_poly,
+        legendre_poly, laguerre_poly, apart, apart_list, assemble_partfrac_list,
+        Options, ring, xring, vring, sring, field, xfield, vfield, sfield)
+
+from .series import (Order, O, limit, Limit, gruntz, series, approximants,
+        residue, EmptySequence, SeqPer, SeqFormula, sequence, SeqAdd, SeqMul,
+        fourier_series, fps, difference_delta, limit_seq)
+
+from .functions import (factorial, factorial2, rf, ff, binomial,
+        RisingFactorial, FallingFactorial, subfactorial, carmichael,
+        fibonacci, lucas, motzkin, tribonacci, harmonic, bernoulli, bell, euler,
+        catalan, genocchi, andre, partition, divisor_sigma, legendre_symbol,
+        jacobi_symbol, kronecker_symbol, mobius, primenu, primeomega,
+        totient, reduced_totient, primepi, sqrt, root, Min, Max, Id,
+        real_root, Rem, cbrt, re, im, sign, Abs, conjugate, arg, polar_lift,
+        periodic_argument, unbranched_argument, principal_branch, transpose,
+        adjoint, polarify, unpolarify, sin, cos, tan, sec, csc, cot, sinc,
+        asin, acos, atan, asec, acsc, acot, atan2, exp_polar, exp, ln, log,
+        LambertW, sinh, cosh, tanh, coth, sech, csch, asinh, acosh, atanh,
+        acoth, asech, acsch, floor, ceiling, frac, Piecewise, piecewise_fold,
+        piecewise_exclusive, erf, erfc, erfi, erf2, erfinv, erfcinv, erf2inv,
+        Ei, expint, E1, li, Li, Si, Ci, Shi, Chi, fresnels, fresnelc, gamma,
+        lowergamma, uppergamma, polygamma, loggamma, digamma, trigamma,
+        multigamma, dirichlet_eta, zeta, lerchphi, polylog, stieltjes, Eijk,
+        LeviCivita, KroneckerDelta, SingularityFunction, DiracDelta, Heaviside,
+        bspline_basis, bspline_basis_set, interpolating_spline, besselj,
+        bessely, besseli, besselk, hankel1, hankel2, jn, yn, jn_zeros, hn1,
+        hn2, airyai, airybi, airyaiprime, airybiprime, marcumq, hyper,
+        meijerg, appellf1, legendre, assoc_legendre, hermite, hermite_prob,
+        chebyshevt, chebyshevu, chebyshevu_root, chebyshevt_root, laguerre,
+        assoc_laguerre, gegenbauer, jacobi, jacobi_normalized, Ynm, Ynm_c,
+        Znm, elliptic_k, elliptic_f, elliptic_e, elliptic_pi, beta, mathieus,
+        mathieuc, mathieusprime, mathieucprime, riemann_xi, betainc, betainc_regularized)
+
+from .ntheory import (nextprime, prevprime, prime, primerange,
+        randprime, Sieve, sieve, primorial, cycle_length, composite,
+        compositepi, isprime, divisors, proper_divisors, factorint,
+        multiplicity, perfect_power, factor_cache, pollard_pm1, pollard_rho, primefactors,
+        divisor_count, proper_divisor_count,
+        factorrat,
+        mersenne_prime_exponent, is_perfect, is_mersenne_prime, is_abundant,
+        is_deficient, is_amicable, is_carmichael, abundance, npartitions, is_primitive_root,
+        is_quad_residue, n_order, sqrt_mod,
+        quadratic_residues, primitive_root, nthroot_mod, is_nthpow_residue,
+        sqrt_mod_iter, discrete_log, quadratic_congruence,
+        binomial_coefficients, binomial_coefficients_list,
+        multinomial_coefficients, continued_fraction_periodic,
+        continued_fraction_iterator, continued_fraction_reduce,
+        continued_fraction_convergents, continued_fraction, egyptian_fraction)
+
+from .concrete import product, Product, summation, Sum
+
+from .discrete import (fft, ifft, ntt, intt, fwht, ifwht, mobius_transform,
+        inverse_mobius_transform, convolution, covering_product,
+        intersecting_product)
+
+from .simplify import (simplify, hypersimp, hypersimilar, logcombine,
+        separatevars, posify, besselsimp, kroneckersimp, signsimp,
+        nsimplify, FU, fu, sqrtdenest, cse, epath, EPath, hyperexpand,
+        collect, rcollect, radsimp, collect_const, fraction, numer, denom,
+        trigsimp, exptrigsimp, powsimp, powdenest, combsimp, gammasimp,
+        ratsimp, ratsimpmodprime)
+
+from .sets import (Set, Interval, Union, EmptySet, FiniteSet, ProductSet,
+        Intersection, DisjointUnion, imageset, Complement, SymmetricDifference, ImageSet,
+        Range, ComplexRegion, Complexes, Reals, Contains, ConditionSet, Ordinal,
+        OmegaPower, ord0, PowerSet, Naturals, Naturals0, UniversalSet,
+        Integers, Rationals)
+
+from .solvers import (solve, solve_linear_system, solve_linear_system_LU,
+        solve_undetermined_coeffs, nsolve, solve_linear, checksol, det_quick,
+        inv_quick, check_assumptions, failing_assumptions, diophantine,
+        rsolve, rsolve_poly, rsolve_ratio, rsolve_hyper, checkodesol,
+        classify_ode, dsolve, homogeneous_order, solve_poly_system, factor_system,
+        solve_triangulated, pde_separate, pde_separate_add, pde_separate_mul,
+        pdsolve, classify_pde, checkpdesol, ode_order, reduce_inequalities,
+        reduce_abs_inequality, reduce_abs_inequalities, solve_poly_inequality,
+        solve_rational_inequalities, solve_univariate_inequality, decompogen,
+        solveset, linsolve, linear_eq_to_matrix, nonlinsolve, substitution)
+
+from .matrices import (ShapeError, NonSquareMatrixError, GramSchmidt,
+        casoratian, diag, eye, hessian, jordan_cell, list2numpy, matrix2numpy,
+        matrix_multiply_elementwise, ones, randMatrix, rot_axis1, rot_axis2,
+        rot_axis3, symarray, wronskian, zeros, MutableDenseMatrix,
+        DeferredVector, MatrixBase, Matrix, MutableMatrix,
+        MutableSparseMatrix, banded, ImmutableDenseMatrix,
+        ImmutableSparseMatrix, ImmutableMatrix, SparseMatrix, MatrixSlice,
+        BlockDiagMatrix, BlockMatrix, FunctionMatrix, Identity, Inverse,
+        MatAdd, MatMul, MatPow, MatrixExpr, MatrixSymbol, Trace, Transpose,
+        ZeroMatrix, OneMatrix, blockcut, block_collapse, matrix_symbols,
+        Adjoint, hadamard_product, HadamardProduct, HadamardPower,
+        Determinant, det, diagonalize_vector, DiagMatrix, DiagonalMatrix,
+        DiagonalOf, trace, DotProduct, kronecker_product, KroneckerProduct,
+        PermutationMatrix, MatrixPermute, Permanent, per, rot_ccw_axis1,
+        rot_ccw_axis2, rot_ccw_axis3, rot_givens)
+
+from .geometry import (Point, Point2D, Point3D, Line, Ray, Segment, Line2D,
+        Segment2D, Ray2D, Line3D, Segment3D, Ray3D, Plane, Ellipse, Circle,
+        Polygon, RegularPolygon, Triangle, rad, deg, are_similar, centroid,
+        convex_hull, idiff, intersection, closest_points, farthest_points,
+        GeometryError, Curve, Parabola)
+
+from .utilities import (flatten, group, take, subsets, variations,
+        numbered_symbols, cartes, capture, dict_merge, prefixes, postfixes,
+        sift, topological_sort, unflatten, has_dups, has_variety, reshape,
+        rotations, filldedent, lambdify,
+        threaded, xthreaded, public, memoize_property, timed)
+
+from .integrals import (integrate, Integral, line_integrate, mellin_transform,
+        inverse_mellin_transform, MellinTransform, InverseMellinTransform,
+        laplace_transform, laplace_correspondence, laplace_initial_conds,
+        inverse_laplace_transform, LaplaceTransform,
+        InverseLaplaceTransform, fourier_transform, inverse_fourier_transform,
+        FourierTransform, InverseFourierTransform, sine_transform,
+        inverse_sine_transform, SineTransform, InverseSineTransform,
+        cosine_transform, inverse_cosine_transform, CosineTransform,
+        InverseCosineTransform, hankel_transform, inverse_hankel_transform,
+        HankelTransform, InverseHankelTransform, singularityintegrate)
+
+from .tensor import (IndexedBase, Idx, Indexed, get_contraction_structure,
+        get_indices, shape, MutableDenseNDimArray, ImmutableDenseNDimArray,
+        MutableSparseNDimArray, ImmutableSparseNDimArray, NDimArray,
+        tensorproduct, tensorcontraction, tensordiagonal, derive_by_array,
+        permutedims, Array, DenseNDimArray, SparseNDimArray)
+
+from .parsing import parse_expr
+
+from .calculus import (euler_equations, singularities, is_increasing,
+        is_strictly_increasing, is_decreasing, is_strictly_decreasing,
+        is_monotonic, finite_diff_weights, apply_finite_diff,
+        differentiate_finite, periodicity, not_empty_in, AccumBounds,
+        is_convex, stationary_points, minimum, maximum)
+
+from .algebras import Quaternion
+
+from .printing import (pager_print, pretty, pretty_print, pprint,
+        pprint_use_unicode, pprint_try_use_unicode, latex, print_latex,
+        multiline_latex, mathml, print_mathml, python, print_python, pycode,
+        ccode, print_ccode, smtlib_code, glsl_code, print_glsl, cxxcode, fcode,
+        print_fcode, rcode, print_rcode, jscode, print_jscode, julia_code,
+        mathematica_code, octave_code, rust_code, print_gtk, preview, srepr,
+        print_tree, StrPrinter, sstr, sstrrepr, TableForm, dotprint,
+        maple_code, print_maple_code)
+
+test = lazy_function('sympy.testing.runtests_pytest', 'test')
+doctest = lazy_function('sympy.testing.runtests', 'doctest')
+
+# This module causes conflicts with other modules:
+# from .stats import *
+# Adds about .04-.05 seconds of import time
+# from combinatorics import *
+# This module is slow to import:
+#from physics import units
+from .plotting import plot, textplot, plot_backends, plot_implicit, plot_parametric
+from .interactive import init_session, init_printing, interactive_traversal
+
+evalf._create_evalf_table()
+
+__all__ = [
+    '__version__',
+
+    # sympy.core
+    'sympify', 'SympifyError', 'cacheit', 'Basic', 'Atom',
+    'preorder_traversal', 'S', 'Expr', 'AtomicExpr', 'UnevaluatedExpr',
+    'Symbol', 'Wild', 'Dummy', 'symbols', 'var', 'Number', 'Float',
+    'Rational', 'Integer', 'NumberSymbol', 'RealNumber', 'igcd', 'ilcm',
+    'seterr', 'E', 'I', 'nan', 'oo', 'pi', 'zoo', 'AlgebraicNumber', 'comp',
+    'mod_inverse', 'Pow', 'integer_nthroot', 'integer_log', 'trailing', 'Mul', 'prod',
+    'Add', 'Mod', 'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', 'Equality',
+    'GreaterThan', 'LessThan', 'Unequality', 'StrictGreaterThan',
+    'StrictLessThan', 'vectorize', 'Lambda', 'WildFunction', 'Derivative',
+    'diff', 'FunctionClass', 'Function', 'Subs', 'expand', 'PoleError',
+    'count_ops', 'expand_mul', 'expand_log', 'expand_func', 'expand_trig',
+    'expand_complex', 'expand_multinomial', 'nfloat', 'expand_power_base',
+    'expand_power_exp', 'arity', 'PrecisionExhausted', 'N', 'evalf', 'Tuple',
+    'Dict', 'gcd_terms', 'factor_terms', 'factor_nc', 'evaluate', 'Catalan',
+    'EulerGamma', 'GoldenRatio', 'TribonacciConstant', 'bottom_up', 'use',
+    'postorder_traversal', 'default_sort_key', 'ordered', 'num_digits',
+
+    # sympy.logic
+    'to_cnf', 'to_dnf', 'to_nnf', 'And', 'Or', 'Not', 'Xor', 'Nand', 'Nor',
+    'Implies', 'Equivalent', 'ITE', 'POSform', 'SOPform', 'simplify_logic',
+    'bool_map', 'true', 'false', 'satisfiable',
+
+    # sympy.assumptions
+    'AppliedPredicate', 'Predicate', 'AssumptionsContext', 'assuming', 'Q',
+    'ask', 'register_handler', 'remove_handler', 'refine',
+
+    # sympy.polys
+    'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree',
+    'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo',
+    'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert',
+    'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list',
+    'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content',
+    'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff',
+    'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor',
+    'intervals', 'refine_root', 'count_roots', 'all_roots', 'real_roots',
+    'nroots', 'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced',
+    'groebner', 'is_zero_dimensional', 'GroebnerBasis', 'poly', 'symmetrize',
+    'horner', 'interpolate', 'rational_interpolate', 'viete', 'together',
+    'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed',
+    'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed',
+    'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed',
+    'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible',
+    'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed',
+    'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed',
+    'UnivariatePolynomialError', 'MultivariatePolynomialError',
+    'PolificationFailed', 'OptionError', 'FlagError', 'minpoly',
+    'minimal_polynomial', 'primitive_element', 'field_isomorphism',
+    'to_number_field', 'isolate', 'round_two', 'prime_decomp',
+    'prime_valuation', 'galois_group', 'itermonomials', 'Monomial', 'lex', 'grlex',
+    'grevlex', 'ilex', 'igrlex', 'igrevlex', 'CRootOf', 'rootof', 'RootOf',
+    'ComplexRootOf', 'RootSum', 'roots', 'Domain', 'FiniteField',
+    'IntegerRing', 'RationalField', 'RealField', 'ComplexField',
+    'PythonFiniteField', 'GMPYFiniteField', 'PythonIntegerRing',
+    'GMPYIntegerRing', 'PythonRational', 'GMPYRationalField',
+    'AlgebraicField', 'PolynomialRing', 'FractionField', 'ExpressionDomain',
+    'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy', 'QQ_python', 'QQ_gmpy',
+    'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR', 'CC', 'EX', 'EXRAW',
+    'construct_domain', 'swinnerton_dyer_poly', 'cyclotomic_poly',
+    'symmetric_poly', 'random_poly', 'interpolating_poly', 'jacobi_poly',
+    'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly', 'hermite_prob_poly',
+    'legendre_poly', 'laguerre_poly', 'apart', 'apart_list', 'assemble_partfrac_list',
+    'Options', 'ring', 'xring', 'vring', 'sring', 'field', 'xfield', 'vfield',
+    'sfield',
+
+    # sympy.series
+    'Order', 'O', 'limit', 'Limit', 'gruntz', 'series', 'approximants',
+    'residue', 'EmptySequence', 'SeqPer', 'SeqFormula', 'sequence', 'SeqAdd',
+    'SeqMul', 'fourier_series', 'fps', 'difference_delta', 'limit_seq',
+
+    # sympy.functions
+    'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial',
+    'FallingFactorial', 'subfactorial', 'carmichael', 'fibonacci', 'lucas',
+    'motzkin', 'tribonacci', 'harmonic', 'bernoulli', 'bell', 'euler', 'catalan',
+    'genocchi', 'andre', 'partition',  'divisor_sigma', 'legendre_symbol', 'jacobi_symbol',
+    'kronecker_symbol', 'mobius', 'primenu', 'primeomega', 'totient', 'primepi',
+    'reduced_totient', 'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root',
+    'Rem', 'cbrt', 're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift',
+    'periodic_argument', 'unbranched_argument', 'principal_branch',
+    'transpose', 'adjoint', 'polarify', 'unpolarify', 'sin', 'cos', 'tan',
+    'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan', 'asec', 'acsc',
+    'acot', 'atan2', 'exp_polar', 'exp', 'ln', 'log', 'LambertW', 'sinh',
+    'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh',
+    'acoth', 'asech', 'acsch', 'floor', 'ceiling', 'frac', 'Piecewise',
+    'piecewise_fold', 'piecewise_exclusive', 'erf', 'erfc', 'erfi', 'erf2',
+    'erfinv', 'erfcinv', 'erf2inv', 'Ei', 'expint', 'E1', 'li', 'Li', 'Si',
+    'Ci', 'Shi', 'Chi', 'fresnels', 'fresnelc', 'gamma', 'lowergamma',
+    'uppergamma', 'polygamma', 'loggamma', 'digamma', 'trigamma', 'multigamma',
+    'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'Eijk', 'LeviCivita',
+    'KroneckerDelta', 'SingularityFunction', 'DiracDelta', 'Heaviside',
+    'bspline_basis', 'bspline_basis_set', 'interpolating_spline', 'besselj',
+    'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn', 'yn',
+    'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime',
+    'airybiprime', 'marcumq', 'hyper', 'meijerg', 'appellf1', 'legendre',
+    'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt', 'chebyshevu',
+    'chebyshevu_root', 'chebyshevt_root', 'laguerre', 'assoc_laguerre',
+    'gegenbauer', 'jacobi', 'jacobi_normalized', 'Ynm', 'Ynm_c', 'Znm',
+    'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi', 'beta',
+    'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime', 'riemann_xi','betainc',
+    'betainc_regularized',
+
+    # sympy.ntheory
+    'nextprime', 'prevprime', 'prime', 'primerange', 'randprime',
+    'Sieve', 'sieve', 'primorial', 'cycle_length', 'composite', 'compositepi',
+    'isprime', 'divisors', 'proper_divisors', 'factorint', 'multiplicity',
+    'perfect_power', 'pollard_pm1', 'factor_cache', 'pollard_rho', 'primefactors',
+    'divisor_count', 'proper_divisor_count',
+    'factorrat',
+    'mersenne_prime_exponent', 'is_perfect', 'is_mersenne_prime',
+    'is_abundant', 'is_deficient', 'is_amicable', 'is_carmichael', 'abundance',
+    'npartitions',
+    'is_primitive_root', 'is_quad_residue',
+    'n_order', 'sqrt_mod', 'quadratic_residues',
+    'primitive_root', 'nthroot_mod', 'is_nthpow_residue', 'sqrt_mod_iter',
+    'discrete_log', 'quadratic_congruence', 'binomial_coefficients',
+    'binomial_coefficients_list', 'multinomial_coefficients',
+    'continued_fraction_periodic', 'continued_fraction_iterator',
+    'continued_fraction_reduce', 'continued_fraction_convergents',
+    'continued_fraction', 'egyptian_fraction',
+
+    # sympy.concrete
+    'product', 'Product', 'summation', 'Sum',
+
+    # sympy.discrete
+    'fft', 'ifft', 'ntt', 'intt', 'fwht', 'ifwht', 'mobius_transform',
+    'inverse_mobius_transform', 'convolution', 'covering_product',
+    'intersecting_product',
+
+    # sympy.simplify
+    'simplify', 'hypersimp', 'hypersimilar', 'logcombine', 'separatevars',
+    'posify', 'besselsimp', 'kroneckersimp', 'signsimp',
+    'nsimplify', 'FU', 'fu', 'sqrtdenest', 'cse', 'epath', 'EPath',
+    'hyperexpand', 'collect', 'rcollect', 'radsimp', 'collect_const',
+    'fraction', 'numer', 'denom', 'trigsimp', 'exptrigsimp', 'powsimp',
+    'powdenest', 'combsimp', 'gammasimp', 'ratsimp', 'ratsimpmodprime',
+
+    # sympy.sets
+    'Set', 'Interval', 'Union', 'EmptySet', 'FiniteSet', 'ProductSet',
+    'Intersection', 'imageset', 'DisjointUnion', 'Complement', 'SymmetricDifference',
+    'ImageSet', 'Range', 'ComplexRegion', 'Reals', 'Contains', 'ConditionSet',
+    'Ordinal', 'OmegaPower', 'ord0', 'PowerSet', 'Naturals',
+    'Naturals0', 'UniversalSet', 'Integers', 'Rationals', 'Complexes',
+
+    # sympy.solvers
+    'solve', 'solve_linear_system', 'solve_linear_system_LU',
+    'solve_undetermined_coeffs', 'nsolve', 'solve_linear', 'checksol',
+    'det_quick', 'inv_quick', 'check_assumptions', 'failing_assumptions',
+    'diophantine', 'rsolve', 'rsolve_poly', 'rsolve_ratio', 'rsolve_hyper',
+    'checkodesol', 'classify_ode', 'dsolve', 'homogeneous_order',
+    'solve_poly_system', 'factor_system', 'solve_triangulated', 'pde_separate',
+    'pde_separate_add', 'pde_separate_mul', 'pdsolve', 'classify_pde',
+    'checkpdesol', 'ode_order', 'reduce_inequalities',
+    'reduce_abs_inequality', 'reduce_abs_inequalities',
+    'solve_poly_inequality', 'solve_rational_inequalities',
+    'solve_univariate_inequality', 'decompogen', 'solveset', 'linsolve',
+    'linear_eq_to_matrix', 'nonlinsolve', 'substitution',
+
+    # sympy.matrices
+    'ShapeError', 'NonSquareMatrixError', 'GramSchmidt', 'casoratian', 'diag',
+    'eye', 'hessian', 'jordan_cell', 'list2numpy', 'matrix2numpy',
+    'matrix_multiply_elementwise', 'ones', 'randMatrix', 'rot_axis1',
+    'rot_axis2', 'rot_axis3', 'symarray', 'wronskian', 'zeros',
+    'MutableDenseMatrix', 'DeferredVector', 'MatrixBase', 'Matrix',
+    'MutableMatrix', 'MutableSparseMatrix', 'banded', 'ImmutableDenseMatrix',
+    'ImmutableSparseMatrix', 'ImmutableMatrix', 'SparseMatrix', 'MatrixSlice',
+    'BlockDiagMatrix', 'BlockMatrix', 'FunctionMatrix', 'Identity', 'Inverse',
+    'MatAdd', 'MatMul', 'MatPow', 'MatrixExpr', 'MatrixSymbol', 'Trace',
+    'Transpose', 'ZeroMatrix', 'OneMatrix', 'blockcut', 'block_collapse',
+    'matrix_symbols', 'Adjoint', 'hadamard_product', 'HadamardProduct',
+    'HadamardPower', 'Determinant', 'det', 'diagonalize_vector', 'DiagMatrix',
+    'DiagonalMatrix', 'DiagonalOf', 'trace', 'DotProduct',
+    'kronecker_product', 'KroneckerProduct', 'PermutationMatrix',
+    'MatrixPermute', 'Permanent', 'per', 'rot_ccw_axis1', 'rot_ccw_axis2',
+    'rot_ccw_axis3', 'rot_givens',
+
+    # sympy.geometry
+    'Point', 'Point2D', 'Point3D', 'Line', 'Ray', 'Segment', 'Line2D',
+    'Segment2D', 'Ray2D', 'Line3D', 'Segment3D', 'Ray3D', 'Plane', 'Ellipse',
+    'Circle', 'Polygon', 'RegularPolygon', 'Triangle', 'rad', 'deg',
+    'are_similar', 'centroid', 'convex_hull', 'idiff', 'intersection',
+    'closest_points', 'farthest_points', 'GeometryError', 'Curve', 'Parabola',
+
+    # sympy.utilities
+    'flatten', 'group', 'take', 'subsets', 'variations', 'numbered_symbols',
+    'cartes', 'capture', 'dict_merge', 'prefixes', 'postfixes', 'sift',
+    'topological_sort', 'unflatten', 'has_dups', 'has_variety', 'reshape',
+    'rotations', 'filldedent', 'lambdify', 'threaded', 'xthreaded',
+    'public', 'memoize_property', 'timed',
+
+    # sympy.integrals
+    'integrate', 'Integral', 'line_integrate', 'mellin_transform',
+    'inverse_mellin_transform', 'MellinTransform', 'InverseMellinTransform',
+    'laplace_transform', 'inverse_laplace_transform', 'LaplaceTransform',
+    'laplace_correspondence', 'laplace_initial_conds',
+    'InverseLaplaceTransform', 'fourier_transform',
+    'inverse_fourier_transform', 'FourierTransform',
+    'InverseFourierTransform', 'sine_transform', 'inverse_sine_transform',
+    'SineTransform', 'InverseSineTransform', 'cosine_transform',
+    'inverse_cosine_transform', 'CosineTransform', 'InverseCosineTransform',
+    'hankel_transform', 'inverse_hankel_transform', 'HankelTransform',
+    'InverseHankelTransform', 'singularityintegrate',
+
+    # sympy.tensor
+    'IndexedBase', 'Idx', 'Indexed', 'get_contraction_structure',
+    'get_indices', 'shape', 'MutableDenseNDimArray', 'ImmutableDenseNDimArray',
+    'MutableSparseNDimArray', 'ImmutableSparseNDimArray', 'NDimArray',
+    'tensorproduct', 'tensorcontraction', 'tensordiagonal', 'derive_by_array',
+    'permutedims', 'Array', 'DenseNDimArray', 'SparseNDimArray',
+
+    # sympy.parsing
+    'parse_expr',
+
+    # sympy.calculus
+    'euler_equations', 'singularities', 'is_increasing',
+    'is_strictly_increasing', 'is_decreasing', 'is_strictly_decreasing',
+    'is_monotonic', 'finite_diff_weights', 'apply_finite_diff',
+    'differentiate_finite', 'periodicity', 'not_empty_in',
+    'AccumBounds', 'is_convex', 'stationary_points', 'minimum', 'maximum',
+
+    # sympy.algebras
+    'Quaternion',
+
+    # sympy.printing
+    'pager_print', 'pretty', 'pretty_print', 'pprint', 'pprint_use_unicode',
+    'pprint_try_use_unicode', 'latex', 'print_latex', 'multiline_latex',
+    'mathml', 'print_mathml', 'python', 'print_python', 'pycode', 'ccode',
+    'print_ccode', 'smtlib_code', 'glsl_code', 'print_glsl', 'cxxcode', 'fcode',
+    'print_fcode', 'rcode', 'print_rcode', 'jscode', 'print_jscode',
+    'julia_code', 'mathematica_code', 'octave_code', 'rust_code', 'print_gtk',
+    'preview', 'srepr', 'print_tree', 'StrPrinter', 'sstr', 'sstrrepr',
+    'TableForm', 'dotprint', 'maple_code', 'print_maple_code',
+
+    # sympy.plotting
+    'plot', 'textplot', 'plot_backends', 'plot_implicit', 'plot_parametric',
+
+    # sympy.interactive
+    'init_session', 'init_printing', 'interactive_traversal',
+
+    # sympy.testing
+    'test', 'doctest',
+]
+
+
+#===========================================================================#
+#                                                                           #
+# XXX: The names below were importable before SymPy 1.6 using               #
+#                                                                           #
+#          from sympy import *                                              #
+#                                                                           #
+# This happened implicitly because there was no __all__ defined in this     #
+# __init__.py file. Not every package is imported. The list matches what    #
+# would have been imported before. It is possible that these packages will  #
+# not be imported by a star-import from sympy in future.                    #
+#                                                                           #
+#===========================================================================#
+
+
+__all__.extend((
+    'algebras',
+    'assumptions',
+    'calculus',
+    'concrete',
+    'discrete',
+    'external',
+    'functions',
+    'geometry',
+    'interactive',
+    'multipledispatch',
+    'ntheory',
+    'parsing',
+    'plotting',
+    'polys',
+    'printing',
+    'release',
+    'strategies',
+    'tensor',
+    'utilities',
+))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/abc.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/abc.py
new file mode 100644
index 0000000000000000000000000000000000000000..a6f7a4056e60b0d651becc0b9909bd0ab3c1723f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/abc.py
@@ -0,0 +1,111 @@
+"""
+This module exports all latin and greek letters as Symbols, so you can
+conveniently do
+
+    >>> from sympy.abc import x, y
+
+instead of the slightly more clunky-looking
+
+    >>> from sympy import symbols
+    >>> x, y = symbols('x y')
+
+Caveats
+=======
+
+1. As of the time of writing this, the names ``O``, ``S``, ``I``, ``N``,
+``E``, and ``Q`` are colliding with names defined in SymPy. If you import them
+from both ``sympy.abc`` and ``sympy``, the second import will "win".
+This is an issue only for * imports, which should only be used for short-lived
+code such as interactive sessions and throwaway scripts that do not survive
+until the next SymPy upgrade, where ``sympy`` may contain a different set of
+names.
+
+2. This module does not define symbol names on demand, i.e.
+``from sympy.abc import foo`` will be reported as an error because
+``sympy.abc`` does not contain the name ``foo``. To get a symbol named ``foo``,
+you still need to use ``Symbol('foo')`` or ``symbols('foo')``.
+You can freely mix usage of ``sympy.abc`` and ``Symbol``/``symbols``, though
+sticking with one and only one way to get the symbols does tend to make the code
+more readable.
+
+The module also defines some special names to help detect which names clash
+with the default SymPy namespace.
+
+``_clash1`` defines all the single letter variables that clash with
+SymPy objects; ``_clash2`` defines the multi-letter clashing symbols;
+and ``_clash`` is the union of both. These can be passed for ``locals``
+during sympification if one desires Symbols rather than the non-Symbol
+objects for those names.
+
+Examples
+========
+
+>>> from sympy import S
+>>> from sympy.abc import _clash1, _clash2, _clash
+>>> S("Q & C", locals=_clash1)
+C & Q
+>>> S('pi(x)', locals=_clash2)
+pi(x)
+>>> S('pi(C, Q)', locals=_clash)
+pi(C, Q)
+
+"""
+from __future__ import annotations
+from typing import Any
+
+import string
+
+from .core import Symbol, symbols
+from .core.alphabets import greeks
+from sympy.parsing.sympy_parser import null
+
+##### Symbol definitions #####
+
+# Implementation note: The easiest way to avoid typos in the symbols()
+# parameter is to copy it from the left-hand side of the assignment.
+
+a, b, c, d, e, f, g, h, i, j = symbols('a, b, c, d, e, f, g, h, i, j')
+k, l, m, n, o, p, q, r, s, t = symbols('k, l, m, n, o, p, q, r, s, t')
+u, v, w, x, y, z = symbols('u, v, w, x, y, z')
+
+A, B, C, D, E, F, G, H, I, J = symbols('A, B, C, D, E, F, G, H, I, J')
+K, L, M, N, O, P, Q, R, S, T = symbols('K, L, M, N, O, P, Q, R, S, T')
+U, V, W, X, Y, Z = symbols('U, V, W, X, Y, Z')
+
+alpha, beta, gamma, delta = symbols('alpha, beta, gamma, delta')
+epsilon, zeta, eta, theta = symbols('epsilon, zeta, eta, theta')
+iota, kappa, lamda, mu = symbols('iota, kappa, lamda, mu')
+nu, xi, omicron, pi = symbols('nu, xi, omicron, pi')
+rho, sigma, tau, upsilon = symbols('rho, sigma, tau, upsilon')
+phi, chi, psi, omega = symbols('phi, chi, psi, omega')
+
+
+##### Clashing-symbols diagnostics #####
+
+# We want to know which names in SymPy collide with those in here.
+# This is mostly for diagnosing SymPy's namespace during SymPy development.
+
+_latin = list(string.ascii_letters)
+# QOSINE should not be imported as they clash; gamma, pi and zeta clash, too
+_greek = list(greeks) # make a copy, so we can mutate it
+# Note: We import lamda since lambda is a reserved keyword in Python
+_greek.remove("lambda")
+_greek.append("lamda")
+
+ns: dict[str, Any] = {}
+exec('from sympy import *', ns)
+_clash1: dict[str, Any] = {}
+_clash2: dict[str, Any] = {}
+while ns:
+    _k, _ = ns.popitem()
+    if _k in _greek:
+        _clash2[_k] = null
+        _greek.remove(_k)
+    elif _k in _latin:
+        _clash1[_k] = null
+        _latin.remove(_k)
+_clash = {}
+_clash.update(_clash1)
+_clash.update(_clash2)
+
+del _latin, _greek, Symbol, _k, null
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..58013d2e0377a016d1a21fbf21c344ee76765189
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/__init__.py
@@ -0,0 +1,3 @@
+from .quaternion import Quaternion
+
+__all__ = ["Quaternion",]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/quaternion.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/quaternion.py
new file mode 100644
index 0000000000000000000000000000000000000000..1bf4b363545128e50294e825461106ef9b41990d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/quaternion.py
@@ -0,0 +1,1666 @@
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.relational import is_eq
+from sympy.functions.elementary.complexes import (conjugate, im, re, sign)
+from sympy.functions.elementary.exponential import (exp, log as ln)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, asin, atan2)
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.simplify.trigsimp import trigsimp
+from sympy.integrals.integrals import integrate
+from sympy.matrices.dense import MutableDenseMatrix as Matrix
+from sympy.core.sympify import sympify, _sympify
+from sympy.core.expr import Expr
+from sympy.core.logic import fuzzy_not, fuzzy_or
+from sympy.utilities.misc import as_int
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+
+def _check_norm(elements, norm):
+    """validate if input norm is consistent"""
+    if norm is not None and norm.is_number:
+        if norm.is_positive is False:
+            raise ValueError("Input norm must be positive.")
+
+        numerical = all(i.is_number and i.is_real is True for i in elements)
+        if numerical and is_eq(norm**2, sum(i**2 for i in elements)) is False:
+            raise ValueError("Incompatible value for norm.")
+
+
+def _is_extrinsic(seq):
+    """validate seq and return True if seq is lowercase and False if uppercase"""
+    if type(seq) != str:
+        raise ValueError('Expected seq to be a string.')
+    if len(seq) != 3:
+        raise ValueError("Expected 3 axes, got `{}`.".format(seq))
+
+    intrinsic = seq.isupper()
+    extrinsic = seq.islower()
+    if not (intrinsic or extrinsic):
+        raise ValueError("seq must either be fully uppercase (for extrinsic "
+                         "rotations), or fully lowercase, for intrinsic "
+                         "rotations).")
+
+    i, j, k = seq.lower()
+    if (i == j) or (j == k):
+        raise ValueError("Consecutive axes must be different")
+
+    bad = set(seq) - set('xyzXYZ')
+    if bad:
+        raise ValueError("Expected axes from `seq` to be from "
+                         "['x', 'y', 'z'] or ['X', 'Y', 'Z'], "
+                         "got {}".format(''.join(bad)))
+
+    return extrinsic
+
+
+class Quaternion(Expr):
+    """Provides basic quaternion operations.
+    Quaternion objects can be instantiated as ``Quaternion(a, b, c, d)``
+    as in $q = a + bi + cj + dk$.
+
+    Parameters
+    ==========
+
+    norm : None or number
+        Pre-defined quaternion norm. If a value is given, Quaternion.norm
+        returns this pre-defined value instead of calculating the norm
+
+    Examples
+    ========
+
+    >>> from sympy import Quaternion
+    >>> q = Quaternion(1, 2, 3, 4)
+    >>> q
+    1 + 2*i + 3*j + 4*k
+
+    Quaternions over complex fields can be defined as:
+
+    >>> from sympy import Quaternion
+    >>> from sympy import symbols, I
+    >>> x = symbols('x')
+    >>> q1 = Quaternion(x, x**3, x, x**2, real_field = False)
+    >>> q2 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False)
+    >>> q1
+    x + x**3*i + x*j + x**2*k
+    >>> q2
+    (3 + 4*I) + (2 + 5*I)*i + 0*j + (7 + 8*I)*k
+
+    Defining symbolic unit quaternions:
+
+    >>> from sympy import Quaternion
+    >>> from sympy.abc import w, x, y, z
+    >>> q = Quaternion(w, x, y, z, norm=1)
+    >>> q
+    w + x*i + y*j + z*k
+    >>> q.norm()
+    1
+
+    References
+    ==========
+
+    .. [1] https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/
+    .. [2] https://en.wikipedia.org/wiki/Quaternion
+
+    """
+    _op_priority = 11.0
+
+    is_commutative = False
+
+    def __new__(cls, a=0, b=0, c=0, d=0, real_field=True, norm=None):
+        a, b, c, d = map(sympify, (a, b, c, d))
+
+        if any(i.is_commutative is False for i in [a, b, c, d]):
+            raise ValueError("arguments have to be commutative")
+        obj = super().__new__(cls, a, b, c, d)
+        obj._real_field = real_field
+        obj.set_norm(norm)
+        return obj
+
+    def set_norm(self, norm):
+        """Sets norm of an already instantiated quaternion.
+
+        Parameters
+        ==========
+
+        norm : None or number
+            Pre-defined quaternion norm. If a value is given, Quaternion.norm
+            returns this pre-defined value instead of calculating the norm
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import a, b, c, d
+        >>> q = Quaternion(a, b, c, d)
+        >>> q.norm()
+        sqrt(a**2 + b**2 + c**2 + d**2)
+
+        Setting the norm:
+
+        >>> q.set_norm(1)
+        >>> q.norm()
+        1
+
+        Removing set norm:
+
+        >>> q.set_norm(None)
+        >>> q.norm()
+        sqrt(a**2 + b**2 + c**2 + d**2)
+
+        """
+        norm = sympify(norm)
+        _check_norm(self.args, norm)
+        self._norm = norm
+
+    @property
+    def a(self):
+        return self.args[0]
+
+    @property
+    def b(self):
+        return self.args[1]
+
+    @property
+    def c(self):
+        return self.args[2]
+
+    @property
+    def d(self):
+        return self.args[3]
+
+    @property
+    def real_field(self):
+        return self._real_field
+
+    @property
+    def product_matrix_left(self):
+        r"""Returns 4 x 4 Matrix equivalent to a Hamilton product from the
+        left. This can be useful when treating quaternion elements as column
+        vectors. Given a quaternion $q = a + bi + cj + dk$ where a, b, c and d
+        are real numbers, the product matrix from the left is:
+
+        .. math::
+
+            M  =  \begin{bmatrix} a  &-b  &-c  &-d \\
+                                  b  & a  &-d  & c \\
+                                  c  & d  & a  &-b \\
+                                  d  &-c  & b  & a \end{bmatrix}
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import a, b, c, d
+        >>> q1 = Quaternion(1, 0, 0, 1)
+        >>> q2 = Quaternion(a, b, c, d)
+        >>> q1.product_matrix_left
+        Matrix([
+        [1, 0,  0, -1],
+        [0, 1, -1,  0],
+        [0, 1,  1,  0],
+        [1, 0,  0,  1]])
+
+        >>> q1.product_matrix_left * q2.to_Matrix()
+        Matrix([
+        [a - d],
+        [b - c],
+        [b + c],
+        [a + d]])
+
+        This is equivalent to:
+
+        >>> (q1 * q2).to_Matrix()
+        Matrix([
+        [a - d],
+        [b - c],
+        [b + c],
+        [a + d]])
+        """
+        return Matrix([
+                [self.a, -self.b, -self.c, -self.d],
+                [self.b, self.a, -self.d, self.c],
+                [self.c, self.d, self.a, -self.b],
+                [self.d, -self.c, self.b, self.a]])
+
+    @property
+    def product_matrix_right(self):
+        r"""Returns 4 x 4 Matrix equivalent to a Hamilton product from the
+        right. This can be useful when treating quaternion elements as column
+        vectors. Given a quaternion $q = a + bi + cj + dk$ where a, b, c and d
+        are real numbers, the product matrix from the left is:
+
+        .. math::
+
+            M  =  \begin{bmatrix} a  &-b  &-c  &-d \\
+                                  b  & a  & d  &-c \\
+                                  c  &-d  & a  & b \\
+                                  d  & c  &-b  & a \end{bmatrix}
+
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import a, b, c, d
+        >>> q1 = Quaternion(a, b, c, d)
+        >>> q2 = Quaternion(1, 0, 0, 1)
+        >>> q2.product_matrix_right
+        Matrix([
+        [1, 0, 0, -1],
+        [0, 1, 1, 0],
+        [0, -1, 1, 0],
+        [1, 0, 0, 1]])
+
+        Note the switched arguments: the matrix represents the quaternion on
+        the right, but is still considered as a matrix multiplication from the
+        left.
+
+        >>> q2.product_matrix_right * q1.to_Matrix()
+        Matrix([
+        [ a - d],
+        [ b + c],
+        [-b + c],
+        [ a + d]])
+
+        This is equivalent to:
+
+        >>> (q1 * q2).to_Matrix()
+        Matrix([
+        [ a - d],
+        [ b + c],
+        [-b + c],
+        [ a + d]])
+        """
+        return Matrix([
+                [self.a, -self.b, -self.c, -self.d],
+                [self.b, self.a, self.d, -self.c],
+                [self.c, -self.d, self.a, self.b],
+                [self.d, self.c, -self.b, self.a]])
+
+    def to_Matrix(self, vector_only=False):
+        """Returns elements of quaternion as a column vector.
+        By default, a ``Matrix`` of length 4 is returned, with the real part as the
+        first element.
+        If ``vector_only`` is ``True``, returns only imaginary part as a Matrix of
+        length 3.
+
+        Parameters
+        ==========
+
+        vector_only : bool
+            If True, only imaginary part is returned.
+            Default value: False
+
+        Returns
+        =======
+
+        Matrix
+            A column vector constructed by the elements of the quaternion.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import a, b, c, d
+        >>> q = Quaternion(a, b, c, d)
+        >>> q
+        a + b*i + c*j + d*k
+
+        >>> q.to_Matrix()
+        Matrix([
+        [a],
+        [b],
+        [c],
+        [d]])
+
+
+        >>> q.to_Matrix(vector_only=True)
+        Matrix([
+        [b],
+        [c],
+        [d]])
+
+        """
+        if vector_only:
+            return Matrix(self.args[1:])
+        else:
+            return Matrix(self.args)
+
+    @classmethod
+    def from_Matrix(cls, elements):
+        """Returns quaternion from elements of a column vector`.
+        If vector_only is True, returns only imaginary part as a Matrix of
+        length 3.
+
+        Parameters
+        ==========
+
+        elements : Matrix, list or tuple of length 3 or 4. If length is 3,
+            assume real part is zero.
+            Default value: False
+
+        Returns
+        =======
+
+        Quaternion
+            A quaternion created from the input elements.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import a, b, c, d
+        >>> q = Quaternion.from_Matrix([a, b, c, d])
+        >>> q
+        a + b*i + c*j + d*k
+
+        >>> q = Quaternion.from_Matrix([b, c, d])
+        >>> q
+        0 + b*i + c*j + d*k
+
+        """
+        length = len(elements)
+        if length != 3 and length != 4:
+            raise ValueError("Input elements must have length 3 or 4, got {} "
+                             "elements".format(length))
+
+        if length == 3:
+            return Quaternion(0, *elements)
+        else:
+            return Quaternion(*elements)
+
+    @classmethod
+    def from_euler(cls, angles, seq):
+        """Returns quaternion equivalent to rotation represented by the Euler
+        angles, in the sequence defined by ``seq``.
+
+        Parameters
+        ==========
+
+        angles : list, tuple or Matrix of 3 numbers
+            The Euler angles (in radians).
+        seq : string of length 3
+            Represents the sequence of rotations.
+            For extrinsic rotations, seq must be all lowercase and its elements
+            must be from the set ``{'x', 'y', 'z'}``
+            For intrinsic rotations, seq must be all uppercase and its elements
+            must be from the set ``{'X', 'Y', 'Z'}``
+
+        Returns
+        =======
+
+        Quaternion
+            The normalized rotation quaternion calculated from the Euler angles
+            in the given sequence.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import pi
+        >>> q = Quaternion.from_euler([pi/2, 0, 0], 'xyz')
+        >>> q
+        sqrt(2)/2 + sqrt(2)/2*i + 0*j + 0*k
+
+        >>> q = Quaternion.from_euler([0, pi/2, pi] , 'zyz')
+        >>> q
+        0 + (-sqrt(2)/2)*i + 0*j + sqrt(2)/2*k
+
+        >>> q = Quaternion.from_euler([0, pi/2, pi] , 'ZYZ')
+        >>> q
+        0 + sqrt(2)/2*i + 0*j + sqrt(2)/2*k
+
+        """
+
+        if len(angles) != 3:
+            raise ValueError("3 angles must be given.")
+
+        extrinsic = _is_extrinsic(seq)
+        i, j, k = seq.lower()
+
+        # get elementary basis vectors
+        ei = [1 if n == i else 0 for n in 'xyz']
+        ej = [1 if n == j else 0 for n in 'xyz']
+        ek = [1 if n == k else 0 for n in 'xyz']
+
+        # calculate distinct quaternions
+        qi = cls.from_axis_angle(ei, angles[0])
+        qj = cls.from_axis_angle(ej, angles[1])
+        qk = cls.from_axis_angle(ek, angles[2])
+
+        if extrinsic:
+            return trigsimp(qk * qj * qi)
+        else:
+            return trigsimp(qi * qj * qk)
+
+    def to_euler(self, seq, angle_addition=True, avoid_square_root=False):
+        r"""Returns Euler angles representing same rotation as the quaternion,
+        in the sequence given by ``seq``. This implements the method described
+        in [1]_.
+
+        For degenerate cases (gymbal lock cases), the third angle is
+        set to zero.
+
+        Parameters
+        ==========
+
+        seq : string of length 3
+            Represents the sequence of rotations.
+            For extrinsic rotations, seq must be all lowercase and its elements
+            must be from the set ``{'x', 'y', 'z'}``
+            For intrinsic rotations, seq must be all uppercase and its elements
+            must be from the set ``{'X', 'Y', 'Z'}``
+
+        angle_addition : bool
+            When True, first and third angles are given as an addition and
+            subtraction of two simpler ``atan2`` expressions. When False, the
+            first and third angles are each given by a single more complicated
+            ``atan2`` expression. This equivalent expression is given by:
+
+            .. math::
+
+                \operatorname{atan_2} (b,a) \pm \operatorname{atan_2} (d,c) =
+                \operatorname{atan_2} (bc\pm ad, ac\mp bd)
+
+            Default value: True
+
+        avoid_square_root : bool
+            When True, the second angle is calculated with an expression based
+            on ``acos``, which is slightly more complicated but avoids a square
+            root. When False, second angle is calculated with ``atan2``, which
+            is simpler and can be better for numerical reasons (some
+            numerical implementations of ``acos`` have problems near zero).
+            Default value: False
+
+
+        Returns
+        =======
+
+        Tuple
+            The Euler angles calculated from the quaternion
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import a, b, c, d
+        >>> euler = Quaternion(a, b, c, d).to_euler('zyz')
+        >>> euler
+        (-atan2(-b, c) + atan2(d, a),
+         2*atan2(sqrt(b**2 + c**2), sqrt(a**2 + d**2)),
+         atan2(-b, c) + atan2(d, a))
+
+
+        References
+        ==========
+
+        .. [1] https://doi.org/10.1371/journal.pone.0276302
+
+        """
+        if self.is_zero_quaternion():
+            raise ValueError('Cannot convert a quaternion with norm 0.')
+
+        angles = [0, 0, 0]
+
+        extrinsic = _is_extrinsic(seq)
+        i, j, k = seq.lower()
+
+        # get index corresponding to elementary basis vectors
+        i = 'xyz'.index(i) + 1
+        j = 'xyz'.index(j) + 1
+        k = 'xyz'.index(k) + 1
+
+        if not extrinsic:
+            i, k = k, i
+
+        # check if sequence is symmetric
+        symmetric = i == k
+        if symmetric:
+            k = 6 - i - j
+
+        # parity of the permutation
+        sign = (i - j) * (j - k) * (k - i) // 2
+
+        # permutate elements
+        elements = [self.a, self.b, self.c, self.d]
+        a = elements[0]
+        b = elements[i]
+        c = elements[j]
+        d = elements[k] * sign
+
+        if not symmetric:
+            a, b, c, d = a - c, b + d, c + a, d - b
+
+        if avoid_square_root:
+            if symmetric:
+                n2 = self.norm()**2
+                angles[1] = acos((a * a + b * b - c * c - d * d) / n2)
+            else:
+                n2 = 2 * self.norm()**2
+                angles[1] = asin((c * c + d * d - a * a - b * b) / n2)
+        else:
+            angles[1] = 2 * atan2(sqrt(c * c + d * d), sqrt(a * a + b * b))
+            if not symmetric:
+                angles[1] -= S.Pi / 2
+
+        # Check for singularities in numerical cases
+        case = 0
+        if is_eq(c, S.Zero) and is_eq(d, S.Zero):
+            case = 1
+        if is_eq(a, S.Zero) and is_eq(b, S.Zero):
+            case = 2
+
+        if case == 0:
+            if angle_addition:
+                angles[0] = atan2(b, a) + atan2(d, c)
+                angles[2] = atan2(b, a) - atan2(d, c)
+            else:
+                angles[0] = atan2(b*c + a*d, a*c - b*d)
+                angles[2] = atan2(b*c - a*d, a*c + b*d)
+
+        else:  # any degenerate case
+            angles[2 * (not extrinsic)] = S.Zero
+            if case == 1:
+                angles[2 * extrinsic] = 2 * atan2(b, a)
+            else:
+                angles[2 * extrinsic] = 2 * atan2(d, c)
+                angles[2 * extrinsic] *= (-1 if extrinsic else 1)
+
+        # for Tait-Bryan angles
+        if not symmetric:
+            angles[0] *= sign
+
+        if extrinsic:
+            return tuple(angles[::-1])
+        else:
+            return tuple(angles)
+
+    @classmethod
+    def from_axis_angle(cls, vector, angle):
+        """Returns a rotation quaternion given the axis and the angle of rotation.
+
+        Parameters
+        ==========
+
+        vector : tuple of three numbers
+            The vector representation of the given axis.
+        angle : number
+            The angle by which axis is rotated (in radians).
+
+        Returns
+        =======
+
+        Quaternion
+            The normalized rotation quaternion calculated from the given axis and the angle of rotation.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import pi, sqrt
+        >>> q = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), 2*pi/3)
+        >>> q
+        1/2 + 1/2*i + 1/2*j + 1/2*k
+
+        """
+        (x, y, z) = vector
+        norm = sqrt(x**2 + y**2 + z**2)
+        (x, y, z) = (x / norm, y / norm, z / norm)
+        s = sin(angle * S.Half)
+        a = cos(angle * S.Half)
+        b = x * s
+        c = y * s
+        d = z * s
+
+        # note that this quaternion is already normalized by construction:
+        # c^2 + (s*x)^2 + (s*y)^2 + (s*z)^2 = c^2 + s^2*(x^2 + y^2 + z^2) = c^2 + s^2 * 1 = c^2 + s^2 = 1
+        # so, what we return is a normalized quaternion
+
+        return cls(a, b, c, d)
+
+    @classmethod
+    def from_rotation_matrix(cls, M):
+        """Returns the equivalent quaternion of a matrix. The quaternion will be normalized
+        only if the matrix is special orthogonal (orthogonal and det(M) = 1).
+
+        Parameters
+        ==========
+
+        M : Matrix
+            Input matrix to be converted to equivalent quaternion. M must be special
+            orthogonal (orthogonal and det(M) = 1) for the quaternion to be normalized.
+
+        Returns
+        =======
+
+        Quaternion
+            The quaternion equivalent to given matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import Matrix, symbols, cos, sin, trigsimp
+        >>> x = symbols('x')
+        >>> M = Matrix([[cos(x), -sin(x), 0], [sin(x), cos(x), 0], [0, 0, 1]])
+        >>> q = trigsimp(Quaternion.from_rotation_matrix(M))
+        >>> q
+        sqrt(2)*sqrt(cos(x) + 1)/2 + 0*i + 0*j + sqrt(2 - 2*cos(x))*sign(sin(x))/2*k
+
+        """
+
+        absQ = M.det()**Rational(1, 3)
+
+        a = sqrt(absQ + M[0, 0] + M[1, 1] + M[2, 2]) / 2
+        b = sqrt(absQ + M[0, 0] - M[1, 1] - M[2, 2]) / 2
+        c = sqrt(absQ - M[0, 0] + M[1, 1] - M[2, 2]) / 2
+        d = sqrt(absQ - M[0, 0] - M[1, 1] + M[2, 2]) / 2
+
+        b = b * sign(M[2, 1] - M[1, 2])
+        c = c * sign(M[0, 2] - M[2, 0])
+        d = d * sign(M[1, 0] - M[0, 1])
+
+        return Quaternion(a, b, c, d)
+
+    def __add__(self, other):
+        return self.add(other)
+
+    def __radd__(self, other):
+        return self.add(other)
+
+    def __sub__(self, other):
+        return self.add(other*-1)
+
+    def __mul__(self, other):
+        return self._generic_mul(self, _sympify(other))
+
+    def __rmul__(self, other):
+        return self._generic_mul(_sympify(other), self)
+
+    def __pow__(self, p):
+        return self.pow(p)
+
+    def __neg__(self):
+        return Quaternion(-self.a, -self.b, -self.c, -self.d)
+
+    def __truediv__(self, other):
+        return self * sympify(other)**-1
+
+    def __rtruediv__(self, other):
+        return sympify(other) * self**-1
+
+    def _eval_Integral(self, *args):
+        return self.integrate(*args)
+
+    def diff(self, *symbols, **kwargs):
+        kwargs.setdefault('evaluate', True)
+        return self.func(*[a.diff(*symbols, **kwargs) for a  in self.args])
+
+    def add(self, other):
+        """Adds quaternions.
+
+        Parameters
+        ==========
+
+        other : Quaternion
+            The quaternion to add to current (self) quaternion.
+
+        Returns
+        =======
+
+        Quaternion
+            The resultant quaternion after adding self to other
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import symbols
+        >>> q1 = Quaternion(1, 2, 3, 4)
+        >>> q2 = Quaternion(5, 6, 7, 8)
+        >>> q1.add(q2)
+        6 + 8*i + 10*j + 12*k
+        >>> q1 + 5
+        6 + 2*i + 3*j + 4*k
+        >>> x = symbols('x', real = True)
+        >>> q1.add(x)
+        (x + 1) + 2*i + 3*j + 4*k
+
+        Quaternions over complex fields :
+
+        >>> from sympy import Quaternion
+        >>> from sympy import I
+        >>> q3 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False)
+        >>> q3.add(2 + 3*I)
+        (5 + 7*I) + (2 + 5*I)*i + 0*j + (7 + 8*I)*k
+
+        """
+        q1 = self
+        q2 = sympify(other)
+
+        # If q2 is a number or a SymPy expression instead of a quaternion
+        if not isinstance(q2, Quaternion):
+            if q1.real_field and q2.is_complex:
+                return Quaternion(re(q2) + q1.a, im(q2) + q1.b, q1.c, q1.d)
+            elif q2.is_commutative:
+                return Quaternion(q1.a + q2, q1.b, q1.c, q1.d)
+            else:
+                raise ValueError("Only commutative expressions can be added with a Quaternion.")
+
+        return Quaternion(q1.a + q2.a, q1.b + q2.b, q1.c + q2.c, q1.d
+                          + q2.d)
+
+    def mul(self, other):
+        """Multiplies quaternions.
+
+        Parameters
+        ==========
+
+        other : Quaternion or symbol
+            The quaternion to multiply to current (self) quaternion.
+
+        Returns
+        =======
+
+        Quaternion
+            The resultant quaternion after multiplying self with other
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import symbols
+        >>> q1 = Quaternion(1, 2, 3, 4)
+        >>> q2 = Quaternion(5, 6, 7, 8)
+        >>> q1.mul(q2)
+        (-60) + 12*i + 30*j + 24*k
+        >>> q1.mul(2)
+        2 + 4*i + 6*j + 8*k
+        >>> x = symbols('x', real = True)
+        >>> q1.mul(x)
+        x + 2*x*i + 3*x*j + 4*x*k
+
+        Quaternions over complex fields :
+
+        >>> from sympy import Quaternion
+        >>> from sympy import I
+        >>> q3 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False)
+        >>> q3.mul(2 + 3*I)
+        (2 + 3*I)*(3 + 4*I) + (2 + 3*I)*(2 + 5*I)*i + 0*j + (2 + 3*I)*(7 + 8*I)*k
+
+        """
+        return self._generic_mul(self, _sympify(other))
+
+    @staticmethod
+    def _generic_mul(q1, q2):
+        """Generic multiplication.
+
+        Parameters
+        ==========
+
+        q1 : Quaternion or symbol
+        q2 : Quaternion or symbol
+
+        It is important to note that if neither q1 nor q2 is a Quaternion,
+        this function simply returns q1 * q2.
+
+        Returns
+        =======
+
+        Quaternion
+            The resultant quaternion after multiplying q1 and q2
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import Symbol, S
+        >>> q1 = Quaternion(1, 2, 3, 4)
+        >>> q2 = Quaternion(5, 6, 7, 8)
+        >>> Quaternion._generic_mul(q1, q2)
+        (-60) + 12*i + 30*j + 24*k
+        >>> Quaternion._generic_mul(q1, S(2))
+        2 + 4*i + 6*j + 8*k
+        >>> x = Symbol('x', real = True)
+        >>> Quaternion._generic_mul(q1, x)
+        x + 2*x*i + 3*x*j + 4*x*k
+
+        Quaternions over complex fields :
+
+        >>> from sympy import I
+        >>> q3 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False)
+        >>> Quaternion._generic_mul(q3, 2 + 3*I)
+        (2 + 3*I)*(3 + 4*I) + (2 + 3*I)*(2 + 5*I)*i + 0*j + (2 + 3*I)*(7 + 8*I)*k
+
+        """
+        # None is a Quaternion:
+        if not isinstance(q1, Quaternion) and not isinstance(q2, Quaternion):
+            return q1 * q2
+
+        # If q1 is a number or a SymPy expression instead of a quaternion
+        if not isinstance(q1, Quaternion):
+            if q2.real_field and q1.is_complex:
+                return Quaternion(re(q1), im(q1), 0, 0) * q2
+            elif q1.is_commutative:
+                return Quaternion(q1 * q2.a, q1 * q2.b, q1 * q2.c, q1 * q2.d)
+            else:
+                raise ValueError("Only commutative expressions can be multiplied with a Quaternion.")
+
+        # If q2 is a number or a SymPy expression instead of a quaternion
+        if not isinstance(q2, Quaternion):
+            if q1.real_field and q2.is_complex:
+                return q1 * Quaternion(re(q2), im(q2), 0, 0)
+            elif q2.is_commutative:
+                return Quaternion(q2 * q1.a, q2 * q1.b, q2 * q1.c, q2 * q1.d)
+            else:
+                raise ValueError("Only commutative expressions can be multiplied with a Quaternion.")
+
+        # If any of the quaternions has a fixed norm, pre-compute norm
+        if q1._norm is None and q2._norm is None:
+            norm = None
+        else:
+            norm = q1.norm() * q2.norm()
+
+        return Quaternion(-q1.b*q2.b - q1.c*q2.c - q1.d*q2.d + q1.a*q2.a,
+                          q1.b*q2.a + q1.c*q2.d - q1.d*q2.c + q1.a*q2.b,
+                          -q1.b*q2.d + q1.c*q2.a + q1.d*q2.b + q1.a*q2.c,
+                          q1.b*q2.c - q1.c*q2.b + q1.d*q2.a + q1.a * q2.d,
+                          norm=norm)
+
+    def _eval_conjugate(self):
+        """Returns the conjugate of the quaternion."""
+        q = self
+        return Quaternion(q.a, -q.b, -q.c, -q.d, norm=q._norm)
+
+    def norm(self):
+        """Returns the norm of the quaternion."""
+        if self._norm is None:  # check if norm is pre-defined
+            q = self
+            # trigsimp is used to simplify sin(x)^2 + cos(x)^2 (these terms
+            # arise when from_axis_angle is used).
+            return sqrt(trigsimp(q.a**2 + q.b**2 + q.c**2 + q.d**2))
+
+        return self._norm
+
+    def normalize(self):
+        """Returns the normalized form of the quaternion."""
+        q = self
+        return q * (1/q.norm())
+
+    def inverse(self):
+        """Returns the inverse of the quaternion."""
+        q = self
+        if not q.norm():
+            raise ValueError("Cannot compute inverse for a quaternion with zero norm")
+        return conjugate(q) * (1/q.norm()**2)
+
+    def pow(self, p):
+        """Finds the pth power of the quaternion.
+
+        Parameters
+        ==========
+
+        p : int
+            Power to be applied on quaternion.
+
+        Returns
+        =======
+
+        Quaternion
+            Returns the p-th power of the current quaternion.
+            Returns the inverse if p = -1.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> q = Quaternion(1, 2, 3, 4)
+        >>> q.pow(4)
+        668 + (-224)*i + (-336)*j + (-448)*k
+
+        """
+        try:
+            q, p = self, as_int(p)
+        except ValueError:
+            return NotImplemented
+
+        if p < 0:
+            q, p = q.inverse(), -p
+
+        if p == 1:
+            return q
+
+        res = Quaternion(1, 0, 0, 0)
+        while p > 0:
+            if p & 1:
+                res *= q
+            q *= q
+            p >>= 1
+
+        return res
+
+    def exp(self):
+        """Returns the exponential of $q$, given by $e^q$.
+
+        Returns
+        =======
+
+        Quaternion
+            The exponential of the quaternion.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> q = Quaternion(1, 2, 3, 4)
+        >>> q.exp()
+        E*cos(sqrt(29))
+        + 2*sqrt(29)*E*sin(sqrt(29))/29*i
+        + 3*sqrt(29)*E*sin(sqrt(29))/29*j
+        + 4*sqrt(29)*E*sin(sqrt(29))/29*k
+
+        """
+        # exp(q) = e^a(cos||v|| + v/||v||*sin||v||)
+        q = self
+        vector_norm = sqrt(q.b**2 + q.c**2 + q.d**2)
+        a = exp(q.a) * cos(vector_norm)
+        b = exp(q.a) * sin(vector_norm) * q.b / vector_norm
+        c = exp(q.a) * sin(vector_norm) * q.c / vector_norm
+        d = exp(q.a) * sin(vector_norm) * q.d / vector_norm
+
+        return Quaternion(a, b, c, d)
+
+    def log(self):
+        r"""Returns the logarithm of the quaternion, given by $\log q$.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> q = Quaternion(1, 2, 3, 4)
+        >>> q.log()
+        log(sqrt(30))
+        + 2*sqrt(29)*acos(sqrt(30)/30)/29*i
+        + 3*sqrt(29)*acos(sqrt(30)/30)/29*j
+        + 4*sqrt(29)*acos(sqrt(30)/30)/29*k
+
+        """
+        # log(q) = log||q|| + v/||v||*arccos(a/||q||)
+        q = self
+        vector_norm = sqrt(q.b**2 + q.c**2 + q.d**2)
+        q_norm = q.norm()
+        a = ln(q_norm)
+        b = q.b * acos(q.a / q_norm) / vector_norm
+        c = q.c * acos(q.a / q_norm) / vector_norm
+        d = q.d * acos(q.a / q_norm) / vector_norm
+
+        return Quaternion(a, b, c, d)
+
+    def _eval_subs(self, *args):
+        elements = [i.subs(*args) for i in self.args]
+        norm = self._norm
+        if norm is not None:
+            norm = norm.subs(*args)
+        _check_norm(elements, norm)
+        return Quaternion(*elements, norm=norm)
+
+    def _eval_evalf(self, prec):
+        """Returns the floating point approximations (decimal numbers) of the quaternion.
+
+        Returns
+        =======
+
+        Quaternion
+            Floating point approximations of quaternion(self)
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import sqrt
+        >>> q = Quaternion(1/sqrt(1), 1/sqrt(2), 1/sqrt(3), 1/sqrt(4))
+        >>> q.evalf()
+        1.00000000000000
+        + 0.707106781186547*i
+        + 0.577350269189626*j
+        + 0.500000000000000*k
+
+        """
+        nprec = prec_to_dps(prec)
+        return Quaternion(*[arg.evalf(n=nprec) for arg in self.args])
+
+    def pow_cos_sin(self, p):
+        """Computes the pth power in the cos-sin form.
+
+        Parameters
+        ==========
+
+        p : int
+            Power to be applied on quaternion.
+
+        Returns
+        =======
+
+        Quaternion
+            The p-th power in the cos-sin form.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> q = Quaternion(1, 2, 3, 4)
+        >>> q.pow_cos_sin(4)
+        900*cos(4*acos(sqrt(30)/30))
+        + 1800*sqrt(29)*sin(4*acos(sqrt(30)/30))/29*i
+        + 2700*sqrt(29)*sin(4*acos(sqrt(30)/30))/29*j
+        + 3600*sqrt(29)*sin(4*acos(sqrt(30)/30))/29*k
+
+        """
+        # q = ||q||*(cos(a) + u*sin(a))
+        # q^p = ||q||^p * (cos(p*a) + u*sin(p*a))
+
+        q = self
+        (v, angle) = q.to_axis_angle()
+        q2 = Quaternion.from_axis_angle(v, p * angle)
+        return q2 * (q.norm()**p)
+
+    def integrate(self, *args):
+        """Computes integration of quaternion.
+
+        Returns
+        =======
+
+        Quaternion
+            Integration of the quaternion(self) with the given variable.
+
+        Examples
+        ========
+
+        Indefinite Integral of quaternion :
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import x
+        >>> q = Quaternion(1, 2, 3, 4)
+        >>> q.integrate(x)
+        x + 2*x*i + 3*x*j + 4*x*k
+
+        Definite integral of quaternion :
+
+        >>> from sympy import Quaternion
+        >>> from sympy.abc import x
+        >>> q = Quaternion(1, 2, 3, 4)
+        >>> q.integrate((x, 1, 5))
+        4 + 8*i + 12*j + 16*k
+
+        """
+        return Quaternion(integrate(self.a, *args), integrate(self.b, *args),
+                          integrate(self.c, *args), integrate(self.d, *args))
+
+    @staticmethod
+    def rotate_point(pin, r):
+        """Returns the coordinates of the point pin (a 3 tuple) after rotation.
+
+        Parameters
+        ==========
+
+        pin : tuple
+            A 3-element tuple of coordinates of a point which needs to be
+            rotated.
+        r : Quaternion or tuple
+            Axis and angle of rotation.
+
+            It's important to note that when r is a tuple, it must be of the form
+            (axis, angle)
+
+        Returns
+        =======
+
+        tuple
+            The coordinates of the point after rotation.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import symbols, trigsimp, cos, sin
+        >>> x = symbols('x')
+        >>> q = Quaternion(cos(x/2), 0, 0, sin(x/2))
+        >>> trigsimp(Quaternion.rotate_point((1, 1, 1), q))
+        (sqrt(2)*cos(x + pi/4), sqrt(2)*sin(x + pi/4), 1)
+        >>> (axis, angle) = q.to_axis_angle()
+        >>> trigsimp(Quaternion.rotate_point((1, 1, 1), (axis, angle)))
+        (sqrt(2)*cos(x + pi/4), sqrt(2)*sin(x + pi/4), 1)
+
+        """
+        if isinstance(r, tuple):
+            # if r is of the form (vector, angle)
+            q = Quaternion.from_axis_angle(r[0], r[1])
+        else:
+            # if r is a quaternion
+            q = r.normalize()
+        pout = q * Quaternion(0, pin[0], pin[1], pin[2]) * conjugate(q)
+        return (pout.b, pout.c, pout.d)
+
+    def to_axis_angle(self):
+        """Returns the axis and angle of rotation of a quaternion.
+
+        Returns
+        =======
+
+        tuple
+            Tuple of (axis, angle)
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> q = Quaternion(1, 1, 1, 1)
+        >>> (axis, angle) = q.to_axis_angle()
+        >>> axis
+        (sqrt(3)/3, sqrt(3)/3, sqrt(3)/3)
+        >>> angle
+        2*pi/3
+
+        """
+        q = self
+        if q.a.is_negative:
+            q = q * -1
+
+        q = q.normalize()
+        angle = trigsimp(2 * acos(q.a))
+
+        # Since quaternion is normalised, q.a is less than 1.
+        s = sqrt(1 - q.a*q.a)
+
+        x = trigsimp(q.b / s)
+        y = trigsimp(q.c / s)
+        z = trigsimp(q.d / s)
+
+        v = (x, y, z)
+        t = (v, angle)
+
+        return t
+
+    def to_rotation_matrix(self, v=None, homogeneous=True):
+        """Returns the equivalent rotation transformation matrix of the quaternion
+        which represents rotation about the origin if ``v`` is not passed.
+
+        Parameters
+        ==========
+
+        v : tuple or None
+            Default value: None
+        homogeneous : bool
+            When True, gives an expression that may be more efficient for
+            symbolic calculations but less so for direct evaluation. Both
+            formulas are mathematically equivalent.
+            Default value: True
+
+        Returns
+        =======
+
+        tuple
+            Returns the equivalent rotation transformation matrix of the quaternion
+            which represents rotation about the origin if v is not passed.
+
+        Examples
+        ========
+
+        >>> from sympy import Quaternion
+        >>> from sympy import symbols, trigsimp, cos, sin
+        >>> x = symbols('x')
+        >>> q = Quaternion(cos(x/2), 0, 0, sin(x/2))
+        >>> trigsimp(q.to_rotation_matrix())
+        Matrix([
+        [cos(x), -sin(x), 0],
+        [sin(x),  cos(x), 0],
+        [     0,       0, 1]])
+
+        Generates a 4x4 transformation matrix (used for rotation about a point
+        other than the origin) if the point(v) is passed as an argument.
+        """
+
+        q = self
+        s = q.norm()**-2
+
+        # diagonal elements are different according to parameter normal
+        if homogeneous:
+            m00 = s*(q.a**2 + q.b**2 - q.c**2 - q.d**2)
+            m11 = s*(q.a**2 - q.b**2 + q.c**2 - q.d**2)
+            m22 = s*(q.a**2 - q.b**2 - q.c**2 + q.d**2)
+        else:
+            m00 = 1 - 2*s*(q.c**2 + q.d**2)
+            m11 = 1 - 2*s*(q.b**2 + q.d**2)
+            m22 = 1 - 2*s*(q.b**2 + q.c**2)
+
+        m01 = 2*s*(q.b*q.c - q.d*q.a)
+        m02 = 2*s*(q.b*q.d + q.c*q.a)
+
+        m10 = 2*s*(q.b*q.c + q.d*q.a)
+        m12 = 2*s*(q.c*q.d - q.b*q.a)
+
+        m20 = 2*s*(q.b*q.d - q.c*q.a)
+        m21 = 2*s*(q.c*q.d + q.b*q.a)
+
+        if not v:
+            return Matrix([[m00, m01, m02], [m10, m11, m12], [m20, m21, m22]])
+
+        else:
+            (x, y, z) = v
+
+            m03 = x - x*m00 - y*m01 - z*m02
+            m13 = y - x*m10 - y*m11 - z*m12
+            m23 = z - x*m20 - y*m21 - z*m22
+            m30 = m31 = m32 = 0
+            m33 = 1
+
+            return Matrix([[m00, m01, m02, m03], [m10, m11, m12, m13],
+                          [m20, m21, m22, m23], [m30, m31, m32, m33]])
+
+    def scalar_part(self):
+        r"""Returns scalar part($\mathbf{S}(q)$) of the quaternion q.
+
+        Explanation
+        ===========
+
+        Given a quaternion $q = a + bi + cj + dk$, returns $\mathbf{S}(q) = a$.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(4, 8, 13, 12)
+        >>> q.scalar_part()
+        4
+
+        """
+
+        return self.a
+
+    def vector_part(self):
+        r"""
+        Returns $\mathbf{V}(q)$, the vector part of the quaternion $q$.
+
+        Explanation
+        ===========
+
+        Given a quaternion $q = a + bi + cj + dk$, returns $\mathbf{V}(q) = bi + cj + dk$.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(1, 1, 1, 1)
+        >>> q.vector_part()
+        0 + 1*i + 1*j + 1*k
+
+        >>> q = Quaternion(4, 8, 13, 12)
+        >>> q.vector_part()
+        0 + 8*i + 13*j + 12*k
+
+        """
+
+        return Quaternion(0, self.b, self.c, self.d)
+
+    def axis(self):
+        r"""
+        Returns $\mathbf{Ax}(q)$, the axis of the quaternion $q$.
+
+        Explanation
+        ===========
+
+        Given a quaternion $q = a + bi + cj + dk$, returns $\mathbf{Ax}(q)$  i.e., the versor of the vector part of that quaternion
+        equal to $\mathbf{U}[\mathbf{V}(q)]$.
+        The axis is always an imaginary unit with square equal to $-1 + 0i + 0j + 0k$.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(1, 1, 1, 1)
+        >>> q.axis()
+        0 + sqrt(3)/3*i + sqrt(3)/3*j + sqrt(3)/3*k
+
+        See Also
+        ========
+
+        vector_part
+
+        """
+        axis = self.vector_part().normalize()
+
+        return Quaternion(0, axis.b, axis.c, axis.d)
+
+    def is_pure(self):
+        """
+        Returns true if the quaternion is pure, false if the quaternion is not pure
+        or returns none if it is unknown.
+
+        Explanation
+        ===========
+
+        A pure quaternion (also a vector quaternion) is a quaternion with scalar
+        part equal to 0.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(0, 8, 13, 12)
+        >>> q.is_pure()
+        True
+
+        See Also
+        ========
+        scalar_part
+
+        """
+
+        return self.a.is_zero
+
+    def is_zero_quaternion(self):
+        """
+        Returns true if the quaternion is a zero quaternion or false if it is not a zero quaternion
+        and None if the value is unknown.
+
+        Explanation
+        ===========
+
+        A zero quaternion is a quaternion with both scalar part and
+        vector part equal to 0.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(1, 0, 0, 0)
+        >>> q.is_zero_quaternion()
+        False
+
+        >>> q = Quaternion(0, 0, 0, 0)
+        >>> q.is_zero_quaternion()
+        True
+
+        See Also
+        ========
+        scalar_part
+        vector_part
+
+        """
+
+        return self.norm().is_zero
+
+    def angle(self):
+        r"""
+        Returns the angle of the quaternion measured in the real-axis plane.
+
+        Explanation
+        ===========
+
+        Given a quaternion $q = a + bi + cj + dk$ where $a$, $b$, $c$ and $d$
+        are real numbers, returns the angle of the quaternion given by
+
+        .. math::
+            \theta := 2 \operatorname{atan_2}\left(\sqrt{b^2 + c^2 + d^2}, {a}\right)
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(1, 4, 4, 4)
+        >>> q.angle()
+        2*atan(4*sqrt(3))
+
+        """
+
+        return 2 * atan2(self.vector_part().norm(), self.scalar_part())
+
+
+    def arc_coplanar(self, other):
+        """
+        Returns True if the transformation arcs represented by the input quaternions happen in the same plane.
+
+        Explanation
+        ===========
+
+        Two quaternions are said to be coplanar (in this arc sense) when their axes are parallel.
+        The plane of a quaternion is the one normal to its axis.
+
+        Parameters
+        ==========
+
+        other : a Quaternion
+
+        Returns
+        =======
+
+        True : if the planes of the two quaternions are the same, apart from its orientation/sign.
+        False : if the planes of the two quaternions are not the same, apart from its orientation/sign.
+        None : if plane of either of the quaternion is unknown.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q1 = Quaternion(1, 4, 4, 4)
+        >>> q2 = Quaternion(3, 8, 8, 8)
+        >>> Quaternion.arc_coplanar(q1, q2)
+        True
+
+        >>> q1 = Quaternion(2, 8, 13, 12)
+        >>> Quaternion.arc_coplanar(q1, q2)
+        False
+
+        See Also
+        ========
+
+        vector_coplanar
+        is_pure
+
+        """
+        if (self.is_zero_quaternion()) or (other.is_zero_quaternion()):
+            raise ValueError('Neither of the given quaternions can be 0')
+
+        return fuzzy_or([(self.axis() - other.axis()).is_zero_quaternion(), (self.axis() + other.axis()).is_zero_quaternion()])
+
+    @classmethod
+    def vector_coplanar(cls, q1, q2, q3):
+        r"""
+        Returns True if the axis of the pure quaternions seen as 3D vectors
+        ``q1``, ``q2``, and ``q3`` are coplanar.
+
+        Explanation
+        ===========
+
+        Three pure quaternions are vector coplanar if the quaternions seen as 3D vectors are coplanar.
+
+        Parameters
+        ==========
+
+        q1
+            A pure Quaternion.
+        q2
+            A pure Quaternion.
+        q3
+            A pure Quaternion.
+
+        Returns
+        =======
+
+        True : if the axis of the pure quaternions seen as 3D vectors
+        q1, q2, and q3 are coplanar.
+        False : if the axis of the pure quaternions seen as 3D vectors
+        q1, q2, and q3 are not coplanar.
+        None : if the axis of the pure quaternions seen as 3D vectors
+        q1, q2, and q3 are coplanar is unknown.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q1 = Quaternion(0, 4, 4, 4)
+        >>> q2 = Quaternion(0, 8, 8, 8)
+        >>> q3 = Quaternion(0, 24, 24, 24)
+        >>> Quaternion.vector_coplanar(q1, q2, q3)
+        True
+
+        >>> q1 = Quaternion(0, 8, 16, 8)
+        >>> q2 = Quaternion(0, 8, 3, 12)
+        >>> Quaternion.vector_coplanar(q1, q2, q3)
+        False
+
+        See Also
+        ========
+
+        axis
+        is_pure
+
+        """
+
+        if fuzzy_not(q1.is_pure()) or fuzzy_not(q2.is_pure()) or fuzzy_not(q3.is_pure()):
+            raise ValueError('The given quaternions must be pure')
+
+        M = Matrix([[q1.b, q1.c, q1.d], [q2.b, q2.c, q2.d], [q3.b, q3.c, q3.d]]).det()
+        return M.is_zero
+
+    def parallel(self, other):
+        """
+        Returns True if the two pure quaternions seen as 3D vectors are parallel.
+
+        Explanation
+        ===========
+
+        Two pure quaternions are called parallel when their vector product is commutative which
+        implies that the quaternions seen as 3D vectors have same direction.
+
+        Parameters
+        ==========
+
+        other : a Quaternion
+
+        Returns
+        =======
+
+        True : if the two pure quaternions seen as 3D vectors are parallel.
+        False : if the two pure quaternions seen as 3D vectors are not parallel.
+        None : if the two pure quaternions seen as 3D vectors are parallel is unknown.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(0, 4, 4, 4)
+        >>> q1 = Quaternion(0, 8, 8, 8)
+        >>> q.parallel(q1)
+        True
+
+        >>> q1 = Quaternion(0, 8, 13, 12)
+        >>> q.parallel(q1)
+        False
+
+        """
+
+        if fuzzy_not(self.is_pure()) or fuzzy_not(other.is_pure()):
+            raise ValueError('The provided quaternions must be pure')
+
+        return (self*other - other*self).is_zero_quaternion()
+
+    def orthogonal(self, other):
+        """
+        Returns the orthogonality of two quaternions.
+
+        Explanation
+        ===========
+
+        Two pure quaternions are called orthogonal when their product is anti-commutative.
+
+        Parameters
+        ==========
+
+        other : a Quaternion
+
+        Returns
+        =======
+
+        True : if the two pure quaternions seen as 3D vectors are orthogonal.
+        False : if the two pure quaternions seen as 3D vectors are not orthogonal.
+        None : if the two pure quaternions seen as 3D vectors are orthogonal is unknown.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(0, 4, 4, 4)
+        >>> q1 = Quaternion(0, 8, 8, 8)
+        >>> q.orthogonal(q1)
+        False
+
+        >>> q1 = Quaternion(0, 2, 2, 0)
+        >>> q = Quaternion(0, 2, -2, 0)
+        >>> q.orthogonal(q1)
+        True
+
+        """
+
+        if fuzzy_not(self.is_pure()) or fuzzy_not(other.is_pure()):
+            raise ValueError('The given quaternions must be pure')
+
+        return (self*other + other*self).is_zero_quaternion()
+
+    def index_vector(self):
+        r"""
+        Returns the index vector of the quaternion.
+
+        Explanation
+        ===========
+
+        The index vector is given by $\mathbf{T}(q)$, the norm (or magnitude) of
+        the quaternion $q$, multiplied by $\mathbf{Ax}(q)$, the axis of $q$.
+
+        Returns
+        =======
+
+        Quaternion: representing index vector of the provided quaternion.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(2, 4, 2, 4)
+        >>> q.index_vector()
+        0 + 4*sqrt(10)/3*i + 2*sqrt(10)/3*j + 4*sqrt(10)/3*k
+
+        See Also
+        ========
+
+        axis
+        norm
+
+        """
+
+        return self.norm() * self.axis()
+
+    def mensor(self):
+        """
+        Returns the natural logarithm of the norm(magnitude) of the quaternion.
+
+        Examples
+        ========
+
+        >>> from sympy.algebras.quaternion import Quaternion
+        >>> q = Quaternion(2, 4, 2, 4)
+        >>> q.mensor()
+        log(2*sqrt(10))
+        >>> q.norm()
+        2*sqrt(10)
+
+        See Also
+        ========
+
+        norm
+
+        """
+
+        return ln(self.norm())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/tests/test_quaternion.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/tests/test_quaternion.py
new file mode 100644
index 0000000000000000000000000000000000000000..a4331cd6afa05c96e8e11d59df4b7520e4810930
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/algebras/tests/test_quaternion.py
@@ -0,0 +1,437 @@
+from sympy.testing.pytest import slow
+from sympy.core.function import diff
+from sympy.core.function import expand
+from sympy.core.numbers import (E, I, Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (Abs, conjugate, im, re, sign)
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, asin, cos, sin, atan2, atan)
+from sympy.integrals.integrals import integrate
+from sympy.matrices.dense import Matrix
+from sympy.simplify import simplify
+from sympy.simplify.trigsimp import trigsimp
+from sympy.algebras.quaternion import Quaternion
+from sympy.testing.pytest import raises
+import math
+from itertools import permutations, product
+
+w, x, y, z = symbols('w:z')
+phi = symbols('phi')
+
+def test_quaternion_construction():
+    q = Quaternion(w, x, y, z)
+    assert q + q == Quaternion(2*w, 2*x, 2*y, 2*z)
+
+    q2 = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3),
+                                    pi*Rational(2, 3))
+    assert q2 == Quaternion(S.Half, S.Half,
+                            S.Half, S.Half)
+
+    M = Matrix([[cos(phi), -sin(phi), 0], [sin(phi), cos(phi), 0], [0, 0, 1]])
+    q3 = trigsimp(Quaternion.from_rotation_matrix(M))
+    assert q3 == Quaternion(
+        sqrt(2)*sqrt(cos(phi) + 1)/2, 0, 0, sqrt(2 - 2*cos(phi))*sign(sin(phi))/2)
+
+    nc = Symbol('nc', commutative=False)
+    raises(ValueError, lambda: Quaternion(w, x, nc, z))
+
+
+def test_quaternion_construction_norm():
+    q1 = Quaternion(*symbols('a:d'))
+
+    q2 = Quaternion(w, x, y, z)
+    assert expand((q1*q2).norm()**2 - (q1.norm()**2 * q2.norm()**2)) == 0
+
+    q3 = Quaternion(w, x, y, z, norm=1)
+    assert (q1 * q3).norm() == q1.norm()
+
+
+def test_issue_25254():
+    # calculating the inverse cached the norm which caused problems
+    # when multiplying
+    p = Quaternion(1, 0, 0, 0)
+    q = Quaternion.from_axis_angle((1, 1, 1), 3 * math.pi/4)
+    qi = q.inverse()  # this operation cached the norm
+    test = q * p * qi
+    assert ((test - p).norm() < 1E-10)
+
+
+def test_to_and_from_Matrix():
+    q = Quaternion(w, x, y, z)
+    q_full = Quaternion.from_Matrix(q.to_Matrix())
+    q_vect = Quaternion.from_Matrix(q.to_Matrix(True))
+    assert (q - q_full).is_zero_quaternion()
+    assert (q.vector_part() - q_vect).is_zero_quaternion()
+
+
+def test_product_matrices():
+    q1 = Quaternion(w, x, y, z)
+    q2 = Quaternion(*(symbols("a:d")))
+    assert (q1 * q2).to_Matrix() == q1.product_matrix_left * q2.to_Matrix()
+    assert (q1 * q2).to_Matrix() == q2.product_matrix_right * q1.to_Matrix()
+
+    R1 = (q1.product_matrix_left * q1.product_matrix_right.T)[1:, 1:]
+    R2 = simplify(q1.to_rotation_matrix()*q1.norm()**2)
+    assert R1 == R2
+
+
+def test_quaternion_axis_angle():
+
+    test_data = [ # axis, angle, expected_quaternion
+        ((1, 0, 0), 0, (1, 0, 0, 0)),
+        ((1, 0, 0), pi/2, (sqrt(2)/2, sqrt(2)/2, 0, 0)),
+        ((0, 1, 0), pi/2, (sqrt(2)/2, 0, sqrt(2)/2, 0)),
+        ((0, 0, 1), pi/2, (sqrt(2)/2, 0, 0, sqrt(2)/2)),
+        ((1, 0, 0), pi, (0, 1, 0, 0)),
+        ((0, 1, 0), pi, (0, 0, 1, 0)),
+        ((0, 0, 1), pi, (0, 0, 0, 1)),
+        ((1, 1, 1), pi, (0, 1/sqrt(3),1/sqrt(3),1/sqrt(3))),
+        ((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), pi*2/3, (S.Half, S.Half, S.Half, S.Half))
+    ]
+
+    for axis, angle, expected in test_data:
+        assert Quaternion.from_axis_angle(axis, angle) == Quaternion(*expected)
+
+
+def test_quaternion_axis_angle_simplification():
+    result = Quaternion.from_axis_angle((1, 2, 3), asin(4))
+    assert result.a == cos(asin(4)/2)
+    assert result.b == sqrt(14)*sin(asin(4)/2)/14
+    assert result.c == sqrt(14)*sin(asin(4)/2)/7
+    assert result.d == 3*sqrt(14)*sin(asin(4)/2)/14
+
+def test_quaternion_complex_real_addition():
+    a = symbols("a", complex=True)
+    b = symbols("b", real=True)
+    # This symbol is not complex:
+    c = symbols("c", commutative=False)
+
+    q = Quaternion(w, x, y, z)
+    assert a + q == Quaternion(w + re(a), x + im(a), y, z)
+    assert 1 + q == Quaternion(1 + w, x, y, z)
+    assert I + q == Quaternion(w, 1 + x, y, z)
+    assert b + q == Quaternion(w + b, x, y, z)
+    raises(ValueError, lambda: c + q)
+    raises(ValueError, lambda: q * c)
+    raises(ValueError, lambda: c * q)
+
+    assert -q == Quaternion(-w, -x, -y, -z)
+
+    q1 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False)
+    q2 = Quaternion(1, 4, 7, 8)
+
+    assert q1 + (2 + 3*I) == Quaternion(5 + 7*I, 2 + 5*I, 0, 7 + 8*I)
+    assert q2 + (2 + 3*I) == Quaternion(3, 7, 7, 8)
+    assert q1 * (2 + 3*I) == \
+    Quaternion((2 + 3*I)*(3 + 4*I), (2 + 3*I)*(2 + 5*I), 0, (2 + 3*I)*(7 + 8*I))
+    assert q2 * (2 + 3*I) == Quaternion(-10, 11, 38, -5)
+
+    q1 = Quaternion(1, 2, 3, 4)
+    q0 = Quaternion(0, 0, 0, 0)
+    assert q1 + q0 == q1
+    assert q1 - q0 == q1
+    assert q1 - q1 == q0
+
+
+def test_quaternion_subs():
+    q = Quaternion.from_axis_angle((0, 0, 1), phi)
+    assert q.subs(phi, 0) == Quaternion(1, 0, 0, 0)
+
+
+def test_quaternion_evalf():
+    assert (Quaternion(sqrt(2), 0, 0, sqrt(3)).evalf() ==
+            Quaternion(sqrt(2).evalf(), 0, 0, sqrt(3).evalf()))
+    assert (Quaternion(1/sqrt(2), 0, 0, 1/sqrt(2)).evalf() ==
+            Quaternion((1/sqrt(2)).evalf(), 0, 0, (1/sqrt(2)).evalf()))
+
+
+def test_quaternion_functions():
+    q = Quaternion(w, x, y, z)
+    q1 = Quaternion(1, 2, 3, 4)
+    q0 = Quaternion(0, 0, 0, 0)
+
+    assert conjugate(q) == Quaternion(w, -x, -y, -z)
+    assert q.norm() == sqrt(w**2 + x**2 + y**2 + z**2)
+    assert q.normalize() == Quaternion(w, x, y, z) / sqrt(w**2 + x**2 + y**2 + z**2)
+    assert q.inverse() == Quaternion(w, -x, -y, -z) / (w**2 + x**2 + y**2 + z**2)
+    assert q.inverse() == q.pow(-1)
+    raises(ValueError, lambda: q0.inverse())
+    assert q.pow(2) == Quaternion(w**2 - x**2 - y**2 - z**2, 2*w*x, 2*w*y, 2*w*z)
+    assert q**(2) == Quaternion(w**2 - x**2 - y**2 - z**2, 2*w*x, 2*w*y, 2*w*z)
+    assert q1.pow(-2) == Quaternion(
+        Rational(-7, 225), Rational(-1, 225), Rational(-1, 150), Rational(-2, 225))
+    assert q1**(-2) == Quaternion(
+        Rational(-7, 225), Rational(-1, 225), Rational(-1, 150), Rational(-2, 225))
+    assert q1.pow(-0.5) == NotImplemented
+    raises(TypeError, lambda: q1**(-0.5))
+
+    assert q1.exp() == \
+    Quaternion(E * cos(sqrt(29)),
+               2 * sqrt(29) * E * sin(sqrt(29)) / 29,
+               3 * sqrt(29) * E * sin(sqrt(29)) / 29,
+               4 * sqrt(29) * E * sin(sqrt(29)) / 29)
+    assert q1.log() == \
+    Quaternion(log(sqrt(30)),
+               2 * sqrt(29) * acos(sqrt(30)/30) / 29,
+               3 * sqrt(29) * acos(sqrt(30)/30) / 29,
+               4 * sqrt(29) * acos(sqrt(30)/30) / 29)
+
+    assert q1.pow_cos_sin(2) == \
+    Quaternion(30 * cos(2 * acos(sqrt(30)/30)),
+               60 * sqrt(29) * sin(2 * acos(sqrt(30)/30)) / 29,
+               90 * sqrt(29) * sin(2 * acos(sqrt(30)/30)) / 29,
+               120 * sqrt(29) * sin(2 * acos(sqrt(30)/30)) / 29)
+
+    assert diff(Quaternion(x, x, x, x), x) == Quaternion(1, 1, 1, 1)
+
+    assert integrate(Quaternion(x, x, x, x), x) == \
+    Quaternion(x**2 / 2, x**2 / 2, x**2 / 2, x**2 / 2)
+
+    assert Quaternion(1, x, x**2, x**3).integrate(x) == \
+    Quaternion(x, x**2/2, x**3/3, x**4/4)
+
+    assert Quaternion(sin(x), cos(x), sin(2*x), cos(2*x)).integrate(x) == \
+    Quaternion(-cos(x), sin(x), -cos(2*x)/2, sin(2*x)/2)
+
+    assert Quaternion(x**2, y**2, z**2, x*y*z).integrate(x, y) == \
+    Quaternion(x**3*y/3, x*y**3/3, x*y*z**2, x**2*y**2*z/4)
+
+    assert Quaternion.rotate_point((1, 1, 1), q1) == (S.One / 5, 1, S(7) / 5)
+    n = Symbol('n')
+    raises(TypeError, lambda: q1**n)
+    n = Symbol('n', integer=True)
+    raises(TypeError, lambda: q1**n)
+
+    assert Quaternion(22, 23, 55, 8).scalar_part() == 22
+    assert Quaternion(w, x, y, z).scalar_part() == w
+
+    assert Quaternion(22, 23, 55, 8).vector_part() == Quaternion(0, 23, 55, 8)
+    assert Quaternion(w, x, y, z).vector_part() == Quaternion(0, x, y, z)
+
+    assert q1.axis() == Quaternion(0, 2*sqrt(29)/29, 3*sqrt(29)/29, 4*sqrt(29)/29)
+    assert q1.axis().pow(2) == Quaternion(-1, 0, 0, 0)
+    assert q0.axis().scalar_part() == 0
+    assert (q.axis() == Quaternion(0,
+                                   x/sqrt(x**2 + y**2 + z**2),
+                                   y/sqrt(x**2 + y**2 + z**2),
+                                   z/sqrt(x**2 + y**2 + z**2)))
+
+    assert q0.is_pure() is True
+    assert q1.is_pure() is False
+    assert Quaternion(0, 0, 0, 3).is_pure() is True
+    assert Quaternion(0, 2, 10, 3).is_pure() is True
+    assert Quaternion(w, 2, 10, 3).is_pure() is None
+
+    assert q1.angle() == 2*atan(sqrt(29))
+    assert q.angle() == 2*atan2(sqrt(x**2 + y**2 + z**2), w)
+
+    assert Quaternion.arc_coplanar(q1, Quaternion(2, 4, 6, 8)) is True
+    assert Quaternion.arc_coplanar(q1, Quaternion(1, -2, -3, -4)) is True
+    assert Quaternion.arc_coplanar(q1, Quaternion(1, 8, 12, 16)) is True
+    assert Quaternion.arc_coplanar(q1, Quaternion(1, 2, 3, 4)) is True
+    assert Quaternion.arc_coplanar(q1, Quaternion(w, 4, 6, 8)) is True
+    assert Quaternion.arc_coplanar(q1, Quaternion(2, 7, 4, 1)) is False
+    assert Quaternion.arc_coplanar(q1, Quaternion(w, x, y, z)) is None
+    raises(ValueError, lambda: Quaternion.arc_coplanar(q1, q0))
+
+    assert Quaternion.vector_coplanar(
+        Quaternion(0, 8, 12, 16),
+        Quaternion(0, 4, 6, 8),
+        Quaternion(0, 2, 3, 4)) is True
+    assert Quaternion.vector_coplanar(
+        Quaternion(0, 0, 0, 0), Quaternion(0, 4, 6, 8), Quaternion(0, 2, 3, 4)) is True
+    assert Quaternion.vector_coplanar(
+        Quaternion(0, 8, 2, 6), Quaternion(0, 1, 6, 6), Quaternion(0, 0, 3, 4)) is False
+    assert Quaternion.vector_coplanar(
+        Quaternion(0, 1, 3, 4),
+        Quaternion(0, 4, w, 6),
+        Quaternion(0, 6, 8, 1)) is None
+    raises(ValueError, lambda:
+        Quaternion.vector_coplanar(q0, Quaternion(0, 4, 6, 8), q1))
+
+    assert Quaternion(0, 1, 2, 3).parallel(Quaternion(0, 2, 4, 6)) is True
+    assert Quaternion(0, 1, 2, 3).parallel(Quaternion(0, 2, 2, 6)) is False
+    assert Quaternion(0, 1, 2, 3).parallel(Quaternion(w, x, y, 6)) is None
+    raises(ValueError, lambda: q0.parallel(q1))
+
+    assert Quaternion(0, 1, 2, 3).orthogonal(Quaternion(0, -2, 1, 0)) is True
+    assert Quaternion(0, 2, 4, 7).orthogonal(Quaternion(0, 2, 2, 6)) is False
+    assert Quaternion(0, 2, 4, 7).orthogonal(Quaternion(w, x, y, 6)) is None
+    raises(ValueError, lambda: q0.orthogonal(q1))
+
+    assert q1.index_vector() == Quaternion(
+        0, 2*sqrt(870)/29,
+        3*sqrt(870)/29,
+        4*sqrt(870)/29)
+    assert Quaternion(0, 3, 9, 4).index_vector() == Quaternion(0, 3, 9, 4)
+
+    assert Quaternion(4, 3, 9, 4).mensor() == log(sqrt(122))
+    assert Quaternion(3, 3, 0, 2).mensor() == log(sqrt(22))
+
+    assert q0.is_zero_quaternion() is True
+    assert q1.is_zero_quaternion() is False
+    assert Quaternion(w, 0, 0, 0).is_zero_quaternion() is None
+
+def test_quaternion_conversions():
+    q1 = Quaternion(1, 2, 3, 4)
+
+    assert q1.to_axis_angle() == ((2 * sqrt(29)/29,
+                                   3 * sqrt(29)/29,
+                                   4 * sqrt(29)/29),
+                                   2 * acos(sqrt(30)/30))
+
+    assert (q1.to_rotation_matrix() ==
+            Matrix([[Rational(-2, 3), Rational(2, 15), Rational(11, 15)],
+                    [Rational(2, 3), Rational(-1, 3), Rational(2, 3)],
+                    [Rational(1, 3), Rational(14, 15), Rational(2, 15)]]))
+
+    assert (q1.to_rotation_matrix((1, 1, 1)) ==
+            Matrix([
+                [Rational(-2, 3), Rational(2, 15), Rational(11, 15), Rational(4, 5)],
+                [Rational(2, 3), Rational(-1, 3), Rational(2, 3), S.Zero],
+                [Rational(1, 3), Rational(14, 15), Rational(2, 15), Rational(-2, 5)],
+                [S.Zero, S.Zero, S.Zero, S.One]]))
+
+    theta = symbols("theta", real=True)
+    q2 = Quaternion(cos(theta/2), 0, 0, sin(theta/2))
+
+    assert trigsimp(q2.to_rotation_matrix()) == Matrix([
+                                               [cos(theta), -sin(theta), 0],
+                                               [sin(theta),  cos(theta), 0],
+                                               [0,           0,          1]])
+
+    assert q2.to_axis_angle() == ((0, 0, sin(theta/2)/Abs(sin(theta/2))),
+                                   2*acos(cos(theta/2)))
+
+    assert trigsimp(q2.to_rotation_matrix((1, 1, 1))) == Matrix([
+               [cos(theta), -sin(theta), 0, sin(theta) - cos(theta) + 1],
+               [sin(theta),  cos(theta), 0, -sin(theta) - cos(theta) + 1],
+               [0,           0,          1,  0],
+               [0,           0,          0,  1]])
+
+
+def test_rotation_matrix_homogeneous():
+    q = Quaternion(w, x, y, z)
+    R1 = q.to_rotation_matrix(homogeneous=True) * q.norm()**2
+    R2 = simplify(q.to_rotation_matrix(homogeneous=False) * q.norm()**2)
+    assert R1 == R2
+
+
+def test_quaternion_rotation_iss1593():
+    """
+    There was a sign mistake in the definition,
+    of the rotation matrix. This tests that particular sign mistake.
+    See issue 1593 for reference.
+    See wikipedia
+    https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix
+    for the correct definition
+    """
+    q = Quaternion(cos(phi/2), sin(phi/2), 0, 0)
+    assert(trigsimp(q.to_rotation_matrix()) == Matrix([
+                [1,        0,         0],
+                [0, cos(phi), -sin(phi)],
+                [0, sin(phi),  cos(phi)]]))
+
+
+def test_quaternion_multiplication():
+    q1 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False)
+    q2 = Quaternion(1, 2, 3, 5)
+    q3 = Quaternion(1, 1, 1, y)
+
+    assert Quaternion._generic_mul(S(4), S.One) == 4
+    assert (Quaternion._generic_mul(S(4), q1) ==
+            Quaternion(12 + 16*I, 8 + 20*I, 0, 28 + 32*I))
+    assert q2.mul(2) == Quaternion(2, 4, 6, 10)
+    assert q2.mul(q3) == Quaternion(-5*y - 4, 3*y - 2, 9 - 2*y, y + 4)
+    assert q2.mul(q3) == q2*q3
+
+    z = symbols('z', complex=True)
+    z_quat = Quaternion(re(z), im(z), 0, 0)
+    q = Quaternion(*symbols('q:4', real=True))
+
+    assert z * q == z_quat * q
+    assert q * z == q * z_quat
+
+
+def test_issue_16318():
+    #for rtruediv
+    q0 = Quaternion(0, 0, 0, 0)
+    raises(ValueError, lambda: 1/q0)
+    #for rotate_point
+    q = Quaternion(1, 2, 3, 4)
+    (axis, angle) = q.to_axis_angle()
+    assert Quaternion.rotate_point((1, 1, 1), (axis, angle)) == (S.One / 5, 1, S(7) / 5)
+    #test for to_axis_angle
+    q = Quaternion(-1, 1, 1, 1)
+    axis = (-sqrt(3)/3, -sqrt(3)/3, -sqrt(3)/3)
+    angle = 2*pi/3
+    assert (axis, angle) == q.to_axis_angle()
+
+
+@slow
+def test_to_euler():
+    q = Quaternion(w, x, y, z)
+    q_normalized = q.normalize()
+
+    seqs = ['zxy', 'zyx', 'zyz', 'zxz']
+    seqs += [seq.upper() for seq in seqs]
+
+    for seq in seqs:
+        euler_from_q = q.to_euler(seq)
+        q_back = simplify(Quaternion.from_euler(euler_from_q, seq))
+        assert q_back == q_normalized
+
+
+def test_to_euler_iss24504():
+    """
+    There was a mistake in the degenerate case testing
+    See issue 24504 for reference.
+    """
+    q = Quaternion.from_euler((phi, 0, 0), 'zyz')
+    assert trigsimp(q.to_euler('zyz'), inverse=True) == (phi, 0, 0)
+
+
+def test_to_euler_numerical_singilarities():
+
+    def test_one_case(angles, seq):
+        q = Quaternion.from_euler(angles, seq)
+        assert q.to_euler(seq) == angles
+
+    # symmetric
+    test_one_case((pi/2,  0, 0), 'zyz')
+    test_one_case((pi/2,  0, 0), 'ZYZ')
+    test_one_case((pi/2,  pi, 0), 'zyz')
+    test_one_case((pi/2,  pi, 0), 'ZYZ')
+
+    # asymmetric
+    test_one_case((pi/2,  pi/2, 0), 'zyx')
+    test_one_case((pi/2,  -pi/2, 0), 'zyx')
+    test_one_case((pi/2,  pi/2, 0), 'ZYX')
+    test_one_case((pi/2,  -pi/2, 0), 'ZYX')
+
+
+@slow
+def test_to_euler_options():
+    def test_one_case(q):
+        angles1 = Matrix(q.to_euler(seq, True, True))
+        angles2 = Matrix(q.to_euler(seq, False, False))
+        angle_errors = simplify(angles1-angles2).evalf()
+        for angle_error in angle_errors:
+            # forcing angles to set {-pi, pi}
+            angle_error = (angle_error + pi) % (2 * pi) - pi
+            assert angle_error < 10e-7
+
+    for xyz in ('xyz', 'XYZ'):
+        for seq_tuple in permutations(xyz):
+            for symmetric in (True, False):
+                if symmetric:
+                    seq = ''.join([seq_tuple[0], seq_tuple[1], seq_tuple[0]])
+                else:
+                    seq = ''.join(seq_tuple)
+
+                for elements in product([-1, 0, 1], repeat=4):
+                    q = Quaternion(*elements)
+                    if not q.is_zero_quaternion():
+                        test_one_case(q)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..af862653f3ce0eeb67f7764e16c32f3466e87024
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/__init__.py
@@ -0,0 +1,18 @@
+"""
+A module to implement logical predicates and assumption system.
+"""
+
+from .assume import (
+    AppliedPredicate, Predicate, AssumptionsContext, assuming,
+    global_assumptions
+)
+from .ask import Q, ask, register_handler, remove_handler
+from .refine import refine
+from .relation import BinaryRelation, AppliedBinaryRelation
+
+__all__ = [
+    'AppliedPredicate', 'Predicate', 'AssumptionsContext', 'assuming',
+    'global_assumptions', 'Q', 'ask', 'register_handler', 'remove_handler',
+    'refine',
+    'BinaryRelation', 'AppliedBinaryRelation'
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/ask.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/ask.py
new file mode 100644
index 0000000000000000000000000000000000000000..ec81ec8ecce245c2a798cf9e71af1e9373292bc1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/ask.py
@@ -0,0 +1,651 @@
+"""Module for querying SymPy objects about assumptions."""
+
+from sympy.assumptions.assume import (global_assumptions, Predicate,
+        AppliedPredicate)
+from sympy.assumptions.cnf import CNF, EncodedCNF, Literal
+from sympy.core import sympify
+from sympy.core.kind import BooleanKind
+from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le
+from sympy.logic.inference import satisfiable
+from sympy.utilities.decorator import memoize_property
+from sympy.utilities.exceptions import (sympy_deprecation_warning,
+                                        SymPyDeprecationWarning,
+                                        ignore_warnings)
+
+
+# Memoization is necessary for the properties of AssumptionKeys to
+# ensure that only one object of Predicate objects are created.
+# This is because assumption handlers are registered on those objects.
+
+
+class AssumptionKeys:
+    """
+    This class contains all the supported keys by ``ask``.
+    It should be accessed via the instance ``sympy.Q``.
+
+    """
+
+    # DO NOT add methods or properties other than predicate keys.
+    # SAT solver checks the properties of Q and use them to compute the
+    # fact system. Non-predicate attributes will break this.
+
+    @memoize_property
+    def hermitian(self):
+        from .handlers.sets import HermitianPredicate
+        return HermitianPredicate()
+
+    @memoize_property
+    def antihermitian(self):
+        from .handlers.sets import AntihermitianPredicate
+        return AntihermitianPredicate()
+
+    @memoize_property
+    def real(self):
+        from .handlers.sets import RealPredicate
+        return RealPredicate()
+
+    @memoize_property
+    def extended_real(self):
+        from .handlers.sets import ExtendedRealPredicate
+        return ExtendedRealPredicate()
+
+    @memoize_property
+    def imaginary(self):
+        from .handlers.sets import ImaginaryPredicate
+        return ImaginaryPredicate()
+
+    @memoize_property
+    def complex(self):
+        from .handlers.sets import ComplexPredicate
+        return ComplexPredicate()
+
+    @memoize_property
+    def algebraic(self):
+        from .handlers.sets import AlgebraicPredicate
+        return AlgebraicPredicate()
+
+    @memoize_property
+    def transcendental(self):
+        from .predicates.sets import TranscendentalPredicate
+        return TranscendentalPredicate()
+
+    @memoize_property
+    def integer(self):
+        from .handlers.sets import IntegerPredicate
+        return IntegerPredicate()
+
+    @memoize_property
+    def noninteger(self):
+        from .predicates.sets import NonIntegerPredicate
+        return NonIntegerPredicate()
+
+    @memoize_property
+    def rational(self):
+        from .handlers.sets import RationalPredicate
+        return RationalPredicate()
+
+    @memoize_property
+    def irrational(self):
+        from .handlers.sets import IrrationalPredicate
+        return IrrationalPredicate()
+
+    @memoize_property
+    def finite(self):
+        from .handlers.calculus import FinitePredicate
+        return FinitePredicate()
+
+    @memoize_property
+    def infinite(self):
+        from .handlers.calculus import InfinitePredicate
+        return InfinitePredicate()
+
+    @memoize_property
+    def positive_infinite(self):
+        from .handlers.calculus import PositiveInfinitePredicate
+        return PositiveInfinitePredicate()
+
+    @memoize_property
+    def negative_infinite(self):
+        from .handlers.calculus import NegativeInfinitePredicate
+        return NegativeInfinitePredicate()
+
+    @memoize_property
+    def positive(self):
+        from .handlers.order import PositivePredicate
+        return PositivePredicate()
+
+    @memoize_property
+    def negative(self):
+        from .handlers.order import NegativePredicate
+        return NegativePredicate()
+
+    @memoize_property
+    def zero(self):
+        from .handlers.order import ZeroPredicate
+        return ZeroPredicate()
+
+    @memoize_property
+    def extended_positive(self):
+        from .handlers.order import ExtendedPositivePredicate
+        return ExtendedPositivePredicate()
+
+    @memoize_property
+    def extended_negative(self):
+        from .handlers.order import ExtendedNegativePredicate
+        return ExtendedNegativePredicate()
+
+    @memoize_property
+    def nonzero(self):
+        from .handlers.order import NonZeroPredicate
+        return NonZeroPredicate()
+
+    @memoize_property
+    def nonpositive(self):
+        from .handlers.order import NonPositivePredicate
+        return NonPositivePredicate()
+
+    @memoize_property
+    def nonnegative(self):
+        from .handlers.order import NonNegativePredicate
+        return NonNegativePredicate()
+
+    @memoize_property
+    def extended_nonzero(self):
+        from .handlers.order import ExtendedNonZeroPredicate
+        return ExtendedNonZeroPredicate()
+
+    @memoize_property
+    def extended_nonpositive(self):
+        from .handlers.order import ExtendedNonPositivePredicate
+        return ExtendedNonPositivePredicate()
+
+    @memoize_property
+    def extended_nonnegative(self):
+        from .handlers.order import ExtendedNonNegativePredicate
+        return ExtendedNonNegativePredicate()
+
+    @memoize_property
+    def even(self):
+        from .handlers.ntheory import EvenPredicate
+        return EvenPredicate()
+
+    @memoize_property
+    def odd(self):
+        from .handlers.ntheory import OddPredicate
+        return OddPredicate()
+
+    @memoize_property
+    def prime(self):
+        from .handlers.ntheory import PrimePredicate
+        return PrimePredicate()
+
+    @memoize_property
+    def composite(self):
+        from .handlers.ntheory import CompositePredicate
+        return CompositePredicate()
+
+    @memoize_property
+    def commutative(self):
+        from .handlers.common import CommutativePredicate
+        return CommutativePredicate()
+
+    @memoize_property
+    def is_true(self):
+        from .handlers.common import IsTruePredicate
+        return IsTruePredicate()
+
+    @memoize_property
+    def symmetric(self):
+        from .handlers.matrices import SymmetricPredicate
+        return SymmetricPredicate()
+
+    @memoize_property
+    def invertible(self):
+        from .handlers.matrices import InvertiblePredicate
+        return InvertiblePredicate()
+
+    @memoize_property
+    def orthogonal(self):
+        from .handlers.matrices import OrthogonalPredicate
+        return OrthogonalPredicate()
+
+    @memoize_property
+    def unitary(self):
+        from .handlers.matrices import UnitaryPredicate
+        return UnitaryPredicate()
+
+    @memoize_property
+    def positive_definite(self):
+        from .handlers.matrices import PositiveDefinitePredicate
+        return PositiveDefinitePredicate()
+
+    @memoize_property
+    def upper_triangular(self):
+        from .handlers.matrices import UpperTriangularPredicate
+        return UpperTriangularPredicate()
+
+    @memoize_property
+    def lower_triangular(self):
+        from .handlers.matrices import LowerTriangularPredicate
+        return LowerTriangularPredicate()
+
+    @memoize_property
+    def diagonal(self):
+        from .handlers.matrices import DiagonalPredicate
+        return DiagonalPredicate()
+
+    @memoize_property
+    def fullrank(self):
+        from .handlers.matrices import FullRankPredicate
+        return FullRankPredicate()
+
+    @memoize_property
+    def square(self):
+        from .handlers.matrices import SquarePredicate
+        return SquarePredicate()
+
+    @memoize_property
+    def integer_elements(self):
+        from .handlers.matrices import IntegerElementsPredicate
+        return IntegerElementsPredicate()
+
+    @memoize_property
+    def real_elements(self):
+        from .handlers.matrices import RealElementsPredicate
+        return RealElementsPredicate()
+
+    @memoize_property
+    def complex_elements(self):
+        from .handlers.matrices import ComplexElementsPredicate
+        return ComplexElementsPredicate()
+
+    @memoize_property
+    def singular(self):
+        from .predicates.matrices import SingularPredicate
+        return SingularPredicate()
+
+    @memoize_property
+    def normal(self):
+        from .predicates.matrices import NormalPredicate
+        return NormalPredicate()
+
+    @memoize_property
+    def triangular(self):
+        from .predicates.matrices import TriangularPredicate
+        return TriangularPredicate()
+
+    @memoize_property
+    def unit_triangular(self):
+        from .predicates.matrices import UnitTriangularPredicate
+        return UnitTriangularPredicate()
+
+    @memoize_property
+    def eq(self):
+        from .relation.equality import EqualityPredicate
+        return EqualityPredicate()
+
+    @memoize_property
+    def ne(self):
+        from .relation.equality import UnequalityPredicate
+        return UnequalityPredicate()
+
+    @memoize_property
+    def gt(self):
+        from .relation.equality import StrictGreaterThanPredicate
+        return StrictGreaterThanPredicate()
+
+    @memoize_property
+    def ge(self):
+        from .relation.equality import GreaterThanPredicate
+        return GreaterThanPredicate()
+
+    @memoize_property
+    def lt(self):
+        from .relation.equality import StrictLessThanPredicate
+        return StrictLessThanPredicate()
+
+    @memoize_property
+    def le(self):
+        from .relation.equality import LessThanPredicate
+        return LessThanPredicate()
+
+
+Q = AssumptionKeys()
+
+def _extract_all_facts(assump, exprs):
+    """
+    Extract all relevant assumptions from *assump* with respect to given *exprs*.
+
+    Parameters
+    ==========
+
+    assump : sympy.assumptions.cnf.CNF
+
+    exprs : tuple of expressions
+
+    Returns
+    =======
+
+    sympy.assumptions.cnf.CNF
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.cnf import CNF
+    >>> from sympy.assumptions.ask import _extract_all_facts
+    >>> from sympy.abc import x, y
+    >>> assump = CNF.from_prop(Q.positive(x) & Q.integer(y))
+    >>> exprs = (x,)
+    >>> cnf = _extract_all_facts(assump, exprs)
+    >>> cnf.clauses
+    {frozenset({Literal(Q.positive, False)})}
+
+    """
+    facts = set()
+
+    for clause in assump.clauses:
+        args = []
+        for literal in clause:
+            if isinstance(literal.lit, AppliedPredicate) and len(literal.lit.arguments) == 1:
+                if literal.lit.arg in exprs:
+                    # Add literal if it has matching in it
+                    args.append(Literal(literal.lit.function, literal.is_Not))
+                else:
+                    # If any of the literals doesn't have matching expr don't add the whole clause.
+                    break
+            else:
+                # If any of the literals aren't unary predicate don't add the whole clause.
+                break
+
+        else:
+            if args:
+                facts.add(frozenset(args))
+    return CNF(facts)
+
+
+def ask(proposition, assumptions=True, context=global_assumptions):
+    """
+    Function to evaluate the proposition with assumptions.
+
+    Explanation
+    ===========
+
+    This function evaluates the proposition to ``True`` or ``False`` if
+    the truth value can be determined. If not, it returns ``None``.
+
+    It should be discerned from :func:`~.refine` which, when applied to a
+    proposition, simplifies the argument to symbolic ``Boolean`` instead of
+    Python built-in ``True``, ``False`` or ``None``.
+
+    **Syntax**
+
+        * ask(proposition)
+            Evaluate the *proposition* in global assumption context.
+
+        * ask(proposition, assumptions)
+            Evaluate the *proposition* with respect to *assumptions* in
+            global assumption context.
+
+    Parameters
+    ==========
+
+    proposition : Boolean
+        Proposition which will be evaluated to boolean value. If this is
+        not ``AppliedPredicate``, it will be wrapped by ``Q.is_true``.
+
+    assumptions : Boolean, optional
+        Local assumptions to evaluate the *proposition*.
+
+    context : AssumptionsContext, optional
+        Default assumptions to evaluate the *proposition*. By default,
+        this is ``sympy.assumptions.global_assumptions`` variable.
+
+    Returns
+    =======
+
+    ``True``, ``False``, or ``None``
+
+    Raises
+    ======
+
+    TypeError : *proposition* or *assumptions* is not valid logical expression.
+
+    ValueError : assumptions are inconsistent.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, pi
+    >>> from sympy.abc import x, y
+    >>> ask(Q.rational(pi))
+    False
+    >>> ask(Q.even(x*y), Q.even(x) & Q.integer(y))
+    True
+    >>> ask(Q.prime(4*x), Q.integer(x))
+    False
+
+    If the truth value cannot be determined, ``None`` will be returned.
+
+    >>> print(ask(Q.odd(3*x))) # cannot determine unless we know x
+    None
+
+    ``ValueError`` is raised if assumptions are inconsistent.
+
+    >>> ask(Q.integer(x), Q.even(x) & Q.odd(x))
+    Traceback (most recent call last):
+      ...
+    ValueError: inconsistent assumptions Q.even(x) & Q.odd(x)
+
+    Notes
+    =====
+
+    Relations in assumptions are not implemented (yet), so the following
+    will not give a meaningful result.
+
+    >>> ask(Q.positive(x), x > 0)
+
+    It is however a work in progress.
+
+    See Also
+    ========
+
+    sympy.assumptions.refine.refine : Simplification using assumptions.
+        Proposition is not reduced to ``None`` if the truth value cannot
+        be determined.
+    """
+    from sympy.assumptions.satask import satask
+    from sympy.assumptions.lra_satask import lra_satask
+    from sympy.logic.algorithms.lra_theory import UnhandledInput
+
+    proposition = sympify(proposition)
+    assumptions = sympify(assumptions)
+
+    if isinstance(proposition, Predicate) or proposition.kind is not BooleanKind:
+        raise TypeError("proposition must be a valid logical expression")
+
+    if isinstance(assumptions, Predicate) or assumptions.kind is not BooleanKind:
+        raise TypeError("assumptions must be a valid logical expression")
+
+    binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le}
+    if isinstance(proposition, AppliedPredicate):
+        key, args = proposition.function, proposition.arguments
+    elif proposition.func in binrelpreds:
+        key, args = binrelpreds[type(proposition)], proposition.args
+    else:
+        key, args = Q.is_true, (proposition,)
+
+    # convert local and global assumptions to CNF
+    assump_cnf = CNF.from_prop(assumptions)
+    assump_cnf.extend(context)
+
+    # extract the relevant facts from assumptions with respect to args
+    local_facts = _extract_all_facts(assump_cnf, args)
+
+    # convert default facts and assumed facts to encoded CNF
+    known_facts_cnf = get_all_known_facts()
+    enc_cnf = EncodedCNF()
+    enc_cnf.from_cnf(CNF(known_facts_cnf))
+    enc_cnf.add_from_cnf(local_facts)
+
+    # check the satisfiability of given assumptions
+    if local_facts.clauses and satisfiable(enc_cnf) is False:
+        raise ValueError("inconsistent assumptions %s" % assumptions)
+
+    # quick computation for single fact
+    res = _ask_single_fact(key, local_facts)
+    if res is not None:
+        return res
+
+    # direct resolution method, no logic
+    res = key(*args)._eval_ask(assumptions)
+    if res is not None:
+        return bool(res)
+
+    # using satask (still costly)
+    res = satask(proposition, assumptions=assumptions, context=context)
+    if res is not None:
+        return res
+
+    try:
+        res = lra_satask(proposition, assumptions=assumptions, context=context)
+    except UnhandledInput:
+        return None
+
+    return res
+
+
+def _ask_single_fact(key, local_facts):
+    """
+    Compute the truth value of single predicate using assumptions.
+
+    Parameters
+    ==========
+
+    key : sympy.assumptions.assume.Predicate
+        Proposition predicate.
+
+    local_facts : sympy.assumptions.cnf.CNF
+        Local assumption in CNF form.
+
+    Returns
+    =======
+
+    ``True``, ``False`` or ``None``
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.cnf import CNF
+    >>> from sympy.assumptions.ask import _ask_single_fact
+
+    If prerequisite of proposition is rejected by the assumption,
+    return ``False``.
+
+    >>> key, assump = Q.zero, ~Q.zero
+    >>> local_facts = CNF.from_prop(assump)
+    >>> _ask_single_fact(key, local_facts)
+    False
+    >>> key, assump = Q.zero, ~Q.even
+    >>> local_facts = CNF.from_prop(assump)
+    >>> _ask_single_fact(key, local_facts)
+    False
+
+    If assumption implies the proposition, return ``True``.
+
+    >>> key, assump = Q.even, Q.zero
+    >>> local_facts = CNF.from_prop(assump)
+    >>> _ask_single_fact(key, local_facts)
+    True
+
+    If proposition rejects the assumption, return ``False``.
+
+    >>> key, assump = Q.even, Q.odd
+    >>> local_facts = CNF.from_prop(assump)
+    >>> _ask_single_fact(key, local_facts)
+    False
+    """
+    if local_facts.clauses:
+
+        known_facts_dict = get_known_facts_dict()
+
+        if len(local_facts.clauses) == 1:
+            cl, = local_facts.clauses
+            if len(cl) == 1:
+                f, = cl
+                prop_facts = known_facts_dict.get(key, None)
+                prop_req = prop_facts[0] if prop_facts is not None else set()
+                if f.is_Not and f.arg in prop_req:
+                    # the prerequisite of proposition is rejected
+                    return False
+
+        for clause in local_facts.clauses:
+            if len(clause) == 1:
+                f, = clause
+                prop_facts = known_facts_dict.get(f.arg, None) if not f.is_Not else None
+                if prop_facts is None:
+                    continue
+
+                prop_req, prop_rej = prop_facts
+                if key in prop_req:
+                    # assumption implies the proposition
+                    return True
+                elif key in prop_rej:
+                    # proposition rejects the assumption
+                    return False
+
+    return None
+
+
+def register_handler(key, handler):
+    """
+    Register a handler in the ask system. key must be a string and handler a
+    class inheriting from AskHandler.
+
+    .. deprecated:: 1.8.
+        Use multipledispatch handler instead. See :obj:`~.Predicate`.
+
+    """
+    sympy_deprecation_warning(
+        """
+        The AskHandler system is deprecated. The register_handler() function
+        should be replaced with the multipledispatch handler of Predicate.
+        """,
+        deprecated_since_version="1.8",
+        active_deprecations_target='deprecated-askhandler',
+    )
+    if isinstance(key, Predicate):
+        key = key.name.name
+    Qkey = getattr(Q, key, None)
+    if Qkey is not None:
+        Qkey.add_handler(handler)
+    else:
+        setattr(Q, key, Predicate(key, handlers=[handler]))
+
+
+def remove_handler(key, handler):
+    """
+    Removes a handler from the ask system.
+
+    .. deprecated:: 1.8.
+        Use multipledispatch handler instead. See :obj:`~.Predicate`.
+
+    """
+    sympy_deprecation_warning(
+        """
+        The AskHandler system is deprecated. The remove_handler() function
+        should be replaced with the multipledispatch handler of Predicate.
+        """,
+        deprecated_since_version="1.8",
+        active_deprecations_target='deprecated-askhandler',
+    )
+    if isinstance(key, Predicate):
+        key = key.name.name
+    # Don't show the same warning again recursively
+    with ignore_warnings(SymPyDeprecationWarning):
+        getattr(Q, key).remove_handler(handler)
+
+
+from sympy.assumptions.ask_generated import (get_all_known_facts,
+    get_known_facts_dict)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/ask_generated.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/ask_generated.py
new file mode 100644
index 0000000000000000000000000000000000000000..d90cdffc1e127d78e18f70cda13d8d5e0530d41b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/ask_generated.py
@@ -0,0 +1,352 @@
+"""
+Do NOT manually edit this file.
+Instead, run ./bin/ask_update.py.
+"""
+
+from sympy.assumptions.ask import Q
+from sympy.assumptions.cnf import Literal
+from sympy.core.cache import cacheit
+
+@cacheit
+def get_all_known_facts():
+    """
+    Known facts between unary predicates as CNF clauses.
+    """
+    return {
+        frozenset((Literal(Q.algebraic, False), Literal(Q.imaginary, True), Literal(Q.transcendental, False))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.negative, True), Literal(Q.transcendental, False))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.positive, True), Literal(Q.transcendental, False))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.rational, True))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.transcendental, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.algebraic, True), Literal(Q.finite, False))),
+        frozenset((Literal(Q.algebraic, True), Literal(Q.transcendental, True))),
+        frozenset((Literal(Q.antihermitian, False), Literal(Q.hermitian, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.antihermitian, False), Literal(Q.imaginary, True))),
+        frozenset((Literal(Q.commutative, False), Literal(Q.finite, True))),
+        frozenset((Literal(Q.commutative, False), Literal(Q.infinite, True))),
+        frozenset((Literal(Q.complex_elements, False), Literal(Q.real_elements, True))),
+        frozenset((Literal(Q.composite, False), Literal(Q.even, True), Literal(Q.positive, True), Literal(Q.prime, False))),
+        frozenset((Literal(Q.composite, True), Literal(Q.even, False), Literal(Q.odd, False))),
+        frozenset((Literal(Q.composite, True), Literal(Q.positive, False))),
+        frozenset((Literal(Q.composite, True), Literal(Q.prime, True))),
+        frozenset((Literal(Q.diagonal, False), Literal(Q.lower_triangular, True), Literal(Q.upper_triangular, True))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.lower_triangular, False))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.normal, False))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.symmetric, False))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.upper_triangular, False))),
+        frozenset((Literal(Q.even, False), Literal(Q.odd, False), Literal(Q.prime, True))),
+        frozenset((Literal(Q.even, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.even, True), Literal(Q.odd, True))),
+        frozenset((Literal(Q.even, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.finite, False), Literal(Q.transcendental, True))),
+        frozenset((Literal(Q.finite, True), Literal(Q.infinite, True))),
+        frozenset((Literal(Q.fullrank, False), Literal(Q.invertible, True))),
+        frozenset((Literal(Q.fullrank, True), Literal(Q.invertible, False), Literal(Q.square, True))),
+        frozenset((Literal(Q.hermitian, False), Literal(Q.negative, True))),
+        frozenset((Literal(Q.hermitian, False), Literal(Q.positive, True))),
+        frozenset((Literal(Q.hermitian, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.imaginary, True), Literal(Q.negative, True))),
+        frozenset((Literal(Q.imaginary, True), Literal(Q.positive, True))),
+        frozenset((Literal(Q.imaginary, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.infinite, False), Literal(Q.negative_infinite, True))),
+        frozenset((Literal(Q.infinite, False), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.integer_elements, True), Literal(Q.real_elements, False))),
+        frozenset((Literal(Q.invertible, False), Literal(Q.positive_definite, True))),
+        frozenset((Literal(Q.invertible, False), Literal(Q.singular, False))),
+        frozenset((Literal(Q.invertible, False), Literal(Q.unitary, True))),
+        frozenset((Literal(Q.invertible, True), Literal(Q.singular, True))),
+        frozenset((Literal(Q.invertible, True), Literal(Q.square, False))),
+        frozenset((Literal(Q.irrational, False), Literal(Q.negative, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.irrational, False), Literal(Q.positive, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.irrational, False), Literal(Q.rational, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.irrational, True), Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.zero, False))),
+        frozenset((Literal(Q.irrational, True), Literal(Q.rational, True))),
+        frozenset((Literal(Q.lower_triangular, False), Literal(Q.triangular, True), Literal(Q.upper_triangular, False))),
+        frozenset((Literal(Q.lower_triangular, True), Literal(Q.triangular, False))),
+        frozenset((Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.rational, True), Literal(Q.zero, False))),
+        frozenset((Literal(Q.negative, True), Literal(Q.negative_infinite, True))),
+        frozenset((Literal(Q.negative, True), Literal(Q.positive, True))),
+        frozenset((Literal(Q.negative, True), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.negative, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive, True))),
+        frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.negative_infinite, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.normal, False), Literal(Q.unitary, True))),
+        frozenset((Literal(Q.normal, True), Literal(Q.square, False))),
+        frozenset((Literal(Q.odd, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.orthogonal, False), Literal(Q.real_elements, True), Literal(Q.unitary, True))),
+        frozenset((Literal(Q.orthogonal, True), Literal(Q.positive_definite, False))),
+        frozenset((Literal(Q.orthogonal, True), Literal(Q.unitary, False))),
+        frozenset((Literal(Q.positive, False), Literal(Q.prime, True))),
+        frozenset((Literal(Q.positive, True), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.positive, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.positive_infinite, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.square, False), Literal(Q.symmetric, True))),
+        frozenset((Literal(Q.triangular, False), Literal(Q.unit_triangular, True))),
+        frozenset((Literal(Q.triangular, False), Literal(Q.upper_triangular, True)))
+    }
+
+@cacheit
+def get_all_known_matrix_facts():
+    """
+    Known facts between unary predicates for matrices as CNF clauses.
+    """
+    return {
+        frozenset((Literal(Q.complex_elements, False), Literal(Q.real_elements, True))),
+        frozenset((Literal(Q.diagonal, False), Literal(Q.lower_triangular, True), Literal(Q.upper_triangular, True))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.lower_triangular, False))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.normal, False))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.symmetric, False))),
+        frozenset((Literal(Q.diagonal, True), Literal(Q.upper_triangular, False))),
+        frozenset((Literal(Q.fullrank, False), Literal(Q.invertible, True))),
+        frozenset((Literal(Q.fullrank, True), Literal(Q.invertible, False), Literal(Q.square, True))),
+        frozenset((Literal(Q.integer_elements, True), Literal(Q.real_elements, False))),
+        frozenset((Literal(Q.invertible, False), Literal(Q.positive_definite, True))),
+        frozenset((Literal(Q.invertible, False), Literal(Q.singular, False))),
+        frozenset((Literal(Q.invertible, False), Literal(Q.unitary, True))),
+        frozenset((Literal(Q.invertible, True), Literal(Q.singular, True))),
+        frozenset((Literal(Q.invertible, True), Literal(Q.square, False))),
+        frozenset((Literal(Q.lower_triangular, False), Literal(Q.triangular, True), Literal(Q.upper_triangular, False))),
+        frozenset((Literal(Q.lower_triangular, True), Literal(Q.triangular, False))),
+        frozenset((Literal(Q.normal, False), Literal(Q.unitary, True))),
+        frozenset((Literal(Q.normal, True), Literal(Q.square, False))),
+        frozenset((Literal(Q.orthogonal, False), Literal(Q.real_elements, True), Literal(Q.unitary, True))),
+        frozenset((Literal(Q.orthogonal, True), Literal(Q.positive_definite, False))),
+        frozenset((Literal(Q.orthogonal, True), Literal(Q.unitary, False))),
+        frozenset((Literal(Q.square, False), Literal(Q.symmetric, True))),
+        frozenset((Literal(Q.triangular, False), Literal(Q.unit_triangular, True))),
+        frozenset((Literal(Q.triangular, False), Literal(Q.upper_triangular, True)))
+    }
+
+@cacheit
+def get_all_known_number_facts():
+    """
+    Known facts between unary predicates for numbers as CNF clauses.
+    """
+    return {
+        frozenset((Literal(Q.algebraic, False), Literal(Q.imaginary, True), Literal(Q.transcendental, False))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.negative, True), Literal(Q.transcendental, False))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.positive, True), Literal(Q.transcendental, False))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.rational, True))),
+        frozenset((Literal(Q.algebraic, False), Literal(Q.transcendental, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.algebraic, True), Literal(Q.finite, False))),
+        frozenset((Literal(Q.algebraic, True), Literal(Q.transcendental, True))),
+        frozenset((Literal(Q.antihermitian, False), Literal(Q.hermitian, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.antihermitian, False), Literal(Q.imaginary, True))),
+        frozenset((Literal(Q.commutative, False), Literal(Q.finite, True))),
+        frozenset((Literal(Q.commutative, False), Literal(Q.infinite, True))),
+        frozenset((Literal(Q.composite, False), Literal(Q.even, True), Literal(Q.positive, True), Literal(Q.prime, False))),
+        frozenset((Literal(Q.composite, True), Literal(Q.even, False), Literal(Q.odd, False))),
+        frozenset((Literal(Q.composite, True), Literal(Q.positive, False))),
+        frozenset((Literal(Q.composite, True), Literal(Q.prime, True))),
+        frozenset((Literal(Q.even, False), Literal(Q.odd, False), Literal(Q.prime, True))),
+        frozenset((Literal(Q.even, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.even, True), Literal(Q.odd, True))),
+        frozenset((Literal(Q.even, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.finite, False), Literal(Q.transcendental, True))),
+        frozenset((Literal(Q.finite, True), Literal(Q.infinite, True))),
+        frozenset((Literal(Q.hermitian, False), Literal(Q.negative, True))),
+        frozenset((Literal(Q.hermitian, False), Literal(Q.positive, True))),
+        frozenset((Literal(Q.hermitian, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.imaginary, True), Literal(Q.negative, True))),
+        frozenset((Literal(Q.imaginary, True), Literal(Q.positive, True))),
+        frozenset((Literal(Q.imaginary, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.infinite, False), Literal(Q.negative_infinite, True))),
+        frozenset((Literal(Q.infinite, False), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.irrational, False), Literal(Q.negative, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.irrational, False), Literal(Q.positive, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.irrational, False), Literal(Q.rational, False), Literal(Q.zero, True))),
+        frozenset((Literal(Q.irrational, True), Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.zero, False))),
+        frozenset((Literal(Q.irrational, True), Literal(Q.rational, True))),
+        frozenset((Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.rational, True), Literal(Q.zero, False))),
+        frozenset((Literal(Q.negative, True), Literal(Q.negative_infinite, True))),
+        frozenset((Literal(Q.negative, True), Literal(Q.positive, True))),
+        frozenset((Literal(Q.negative, True), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.negative, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive, True))),
+        frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.negative_infinite, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.odd, True), Literal(Q.rational, False))),
+        frozenset((Literal(Q.positive, False), Literal(Q.prime, True))),
+        frozenset((Literal(Q.positive, True), Literal(Q.positive_infinite, True))),
+        frozenset((Literal(Q.positive, True), Literal(Q.zero, True))),
+        frozenset((Literal(Q.positive_infinite, True), Literal(Q.zero, True)))
+    }
+
+@cacheit
+def get_known_facts_dict():
+    """
+    Logical relations between unary predicates as dictionary.
+
+    Each key is a predicate, and item is two groups of predicates.
+    First group contains the predicates which are implied by the key, and
+    second group contains the predicates which are rejected by the key.
+
+    """
+    return {
+        Q.algebraic: (set([Q.algebraic, Q.commutative, Q.complex, Q.finite]),
+        set([Q.infinite, Q.negative_infinite, Q.positive_infinite,
+        Q.transcendental])),
+        Q.antihermitian: (set([Q.antihermitian]), set([])),
+        Q.commutative: (set([Q.commutative]), set([])),
+        Q.complex: (set([Q.commutative, Q.complex, Q.finite]),
+        set([Q.infinite, Q.negative_infinite, Q.positive_infinite])),
+        Q.complex_elements: (set([Q.complex_elements]), set([])),
+        Q.composite: (set([Q.algebraic, Q.commutative, Q.complex, Q.composite,
+        Q.extended_nonnegative, Q.extended_nonzero,
+        Q.extended_positive, Q.extended_real, Q.finite, Q.hermitian,
+        Q.integer, Q.nonnegative, Q.nonzero, Q.positive, Q.rational,
+        Q.real]), set([Q.extended_negative, Q.extended_nonpositive,
+        Q.imaginary, Q.infinite, Q.irrational, Q.negative,
+        Q.negative_infinite, Q.nonpositive, Q.positive_infinite,
+        Q.prime, Q.transcendental, Q.zero])),
+        Q.diagonal: (set([Q.diagonal, Q.lower_triangular, Q.normal, Q.square,
+        Q.symmetric, Q.triangular, Q.upper_triangular]), set([])),
+        Q.even: (set([Q.algebraic, Q.commutative, Q.complex, Q.even,
+        Q.extended_real, Q.finite, Q.hermitian, Q.integer, Q.rational,
+        Q.real]), set([Q.imaginary, Q.infinite, Q.irrational,
+        Q.negative_infinite, Q.odd, Q.positive_infinite,
+        Q.transcendental])),
+        Q.extended_negative: (set([Q.commutative, Q.extended_negative,
+        Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real]),
+        set([Q.composite, Q.extended_nonnegative, Q.extended_positive,
+        Q.imaginary, Q.nonnegative, Q.positive, Q.positive_infinite,
+        Q.prime, Q.zero])),
+        Q.extended_nonnegative: (set([Q.commutative, Q.extended_nonnegative,
+        Q.extended_real]), set([Q.extended_negative, Q.imaginary,
+        Q.negative, Q.negative_infinite])),
+        Q.extended_nonpositive: (set([Q.commutative, Q.extended_nonpositive,
+        Q.extended_real]), set([Q.composite, Q.extended_positive,
+        Q.imaginary, Q.positive, Q.positive_infinite, Q.prime])),
+        Q.extended_nonzero: (set([Q.commutative, Q.extended_nonzero,
+        Q.extended_real]), set([Q.imaginary, Q.zero])),
+        Q.extended_positive: (set([Q.commutative, Q.extended_nonnegative,
+        Q.extended_nonzero, Q.extended_positive, Q.extended_real]),
+        set([Q.extended_negative, Q.extended_nonpositive, Q.imaginary,
+        Q.negative, Q.negative_infinite, Q.nonpositive, Q.zero])),
+        Q.extended_real: (set([Q.commutative, Q.extended_real]),
+        set([Q.imaginary])),
+        Q.finite: (set([Q.commutative, Q.finite]), set([Q.infinite,
+        Q.negative_infinite, Q.positive_infinite])),
+        Q.fullrank: (set([Q.fullrank]), set([])),
+        Q.hermitian: (set([Q.hermitian]), set([])),
+        Q.imaginary: (set([Q.antihermitian, Q.commutative, Q.complex,
+        Q.finite, Q.imaginary]), set([Q.composite, Q.even,
+        Q.extended_negative, Q.extended_nonnegative,
+        Q.extended_nonpositive, Q.extended_nonzero,
+        Q.extended_positive, Q.extended_real, Q.infinite, Q.integer,
+        Q.irrational, Q.negative, Q.negative_infinite, Q.nonnegative,
+        Q.nonpositive, Q.nonzero, Q.odd, Q.positive,
+        Q.positive_infinite, Q.prime, Q.rational, Q.real, Q.zero])),
+        Q.infinite: (set([Q.commutative, Q.infinite]), set([Q.algebraic,
+        Q.complex, Q.composite, Q.even, Q.finite, Q.imaginary,
+        Q.integer, Q.irrational, Q.negative, Q.nonnegative,
+        Q.nonpositive, Q.nonzero, Q.odd, Q.positive, Q.prime,
+        Q.rational, Q.real, Q.transcendental, Q.zero])),
+        Q.integer: (set([Q.algebraic, Q.commutative, Q.complex,
+        Q.extended_real, Q.finite, Q.hermitian, Q.integer, Q.rational,
+        Q.real]), set([Q.imaginary, Q.infinite, Q.irrational,
+        Q.negative_infinite, Q.positive_infinite, Q.transcendental])),
+        Q.integer_elements: (set([Q.complex_elements, Q.integer_elements,
+        Q.real_elements]), set([])),
+        Q.invertible: (set([Q.fullrank, Q.invertible, Q.square]),
+        set([Q.singular])),
+        Q.irrational: (set([Q.commutative, Q.complex, Q.extended_nonzero,
+        Q.extended_real, Q.finite, Q.hermitian, Q.irrational,
+        Q.nonzero, Q.real]), set([Q.composite, Q.even, Q.imaginary,
+        Q.infinite, Q.integer, Q.negative_infinite, Q.odd,
+        Q.positive_infinite, Q.prime, Q.rational, Q.zero])),
+        Q.is_true: (set([Q.is_true]), set([])),
+        Q.lower_triangular: (set([Q.lower_triangular, Q.triangular]), set([])),
+        Q.negative: (set([Q.commutative, Q.complex, Q.extended_negative,
+        Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real,
+        Q.finite, Q.hermitian, Q.negative, Q.nonpositive, Q.nonzero,
+        Q.real]), set([Q.composite, Q.extended_nonnegative,
+        Q.extended_positive, Q.imaginary, Q.infinite,
+        Q.negative_infinite, Q.nonnegative, Q.positive,
+        Q.positive_infinite, Q.prime, Q.zero])),
+        Q.negative_infinite: (set([Q.commutative, Q.extended_negative,
+        Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real,
+        Q.infinite, Q.negative_infinite]), set([Q.algebraic,
+        Q.complex, Q.composite, Q.even, Q.extended_nonnegative,
+        Q.extended_positive, Q.finite, Q.imaginary, Q.integer,
+        Q.irrational, Q.negative, Q.nonnegative, Q.nonpositive,
+        Q.nonzero, Q.odd, Q.positive, Q.positive_infinite, Q.prime,
+        Q.rational, Q.real, Q.transcendental, Q.zero])),
+        Q.noninteger: (set([Q.noninteger]), set([])),
+        Q.nonnegative: (set([Q.commutative, Q.complex, Q.extended_nonnegative,
+        Q.extended_real, Q.finite, Q.hermitian, Q.nonnegative,
+        Q.real]), set([Q.extended_negative, Q.imaginary, Q.infinite,
+        Q.negative, Q.negative_infinite, Q.positive_infinite])),
+        Q.nonpositive: (set([Q.commutative, Q.complex, Q.extended_nonpositive,
+        Q.extended_real, Q.finite, Q.hermitian, Q.nonpositive,
+        Q.real]), set([Q.composite, Q.extended_positive, Q.imaginary,
+        Q.infinite, Q.negative_infinite, Q.positive,
+        Q.positive_infinite, Q.prime])),
+        Q.nonzero: (set([Q.commutative, Q.complex, Q.extended_nonzero,
+        Q.extended_real, Q.finite, Q.hermitian, Q.nonzero, Q.real]),
+        set([Q.imaginary, Q.infinite, Q.negative_infinite,
+        Q.positive_infinite, Q.zero])),
+        Q.normal: (set([Q.normal, Q.square]), set([])),
+        Q.odd: (set([Q.algebraic, Q.commutative, Q.complex,
+        Q.extended_nonzero, Q.extended_real, Q.finite, Q.hermitian,
+        Q.integer, Q.nonzero, Q.odd, Q.rational, Q.real]),
+        set([Q.even, Q.imaginary, Q.infinite, Q.irrational,
+        Q.negative_infinite, Q.positive_infinite, Q.transcendental,
+        Q.zero])),
+        Q.orthogonal: (set([Q.fullrank, Q.invertible, Q.normal, Q.orthogonal,
+        Q.positive_definite, Q.square, Q.unitary]), set([Q.singular])),
+        Q.positive: (set([Q.commutative, Q.complex, Q.extended_nonnegative,
+        Q.extended_nonzero, Q.extended_positive, Q.extended_real,
+        Q.finite, Q.hermitian, Q.nonnegative, Q.nonzero, Q.positive,
+        Q.real]), set([Q.extended_negative, Q.extended_nonpositive,
+        Q.imaginary, Q.infinite, Q.negative, Q.negative_infinite,
+        Q.nonpositive, Q.positive_infinite, Q.zero])),
+        Q.positive_definite: (set([Q.fullrank, Q.invertible,
+        Q.positive_definite, Q.square]), set([Q.singular])),
+        Q.positive_infinite: (set([Q.commutative, Q.extended_nonnegative,
+        Q.extended_nonzero, Q.extended_positive, Q.extended_real,
+        Q.infinite, Q.positive_infinite]), set([Q.algebraic,
+        Q.complex, Q.composite, Q.even, Q.extended_negative,
+        Q.extended_nonpositive, Q.finite, Q.imaginary, Q.integer,
+        Q.irrational, Q.negative, Q.negative_infinite, Q.nonnegative,
+        Q.nonpositive, Q.nonzero, Q.odd, Q.positive, Q.prime,
+        Q.rational, Q.real, Q.transcendental, Q.zero])),
+        Q.prime: (set([Q.algebraic, Q.commutative, Q.complex,
+        Q.extended_nonnegative, Q.extended_nonzero,
+        Q.extended_positive, Q.extended_real, Q.finite, Q.hermitian,
+        Q.integer, Q.nonnegative, Q.nonzero, Q.positive, Q.prime,
+        Q.rational, Q.real]), set([Q.composite, Q.extended_negative,
+        Q.extended_nonpositive, Q.imaginary, Q.infinite, Q.irrational,
+        Q.negative, Q.negative_infinite, Q.nonpositive,
+        Q.positive_infinite, Q.transcendental, Q.zero])),
+        Q.rational: (set([Q.algebraic, Q.commutative, Q.complex,
+        Q.extended_real, Q.finite, Q.hermitian, Q.rational, Q.real]),
+        set([Q.imaginary, Q.infinite, Q.irrational,
+        Q.negative_infinite, Q.positive_infinite, Q.transcendental])),
+        Q.real: (set([Q.commutative, Q.complex, Q.extended_real, Q.finite,
+        Q.hermitian, Q.real]), set([Q.imaginary, Q.infinite,
+        Q.negative_infinite, Q.positive_infinite])),
+        Q.real_elements: (set([Q.complex_elements, Q.real_elements]), set([])),
+        Q.singular: (set([Q.singular]), set([Q.invertible, Q.orthogonal,
+        Q.positive_definite, Q.unitary])),
+        Q.square: (set([Q.square]), set([])),
+        Q.symmetric: (set([Q.square, Q.symmetric]), set([])),
+        Q.transcendental: (set([Q.commutative, Q.complex, Q.finite,
+        Q.transcendental]), set([Q.algebraic, Q.composite, Q.even,
+        Q.infinite, Q.integer, Q.negative_infinite, Q.odd,
+        Q.positive_infinite, Q.prime, Q.rational, Q.zero])),
+        Q.triangular: (set([Q.triangular]), set([])),
+        Q.unit_triangular: (set([Q.triangular, Q.unit_triangular]), set([])),
+        Q.unitary: (set([Q.fullrank, Q.invertible, Q.normal, Q.square,
+        Q.unitary]), set([Q.singular])),
+        Q.upper_triangular: (set([Q.triangular, Q.upper_triangular]), set([])),
+        Q.zero: (set([Q.algebraic, Q.commutative, Q.complex, Q.even,
+        Q.extended_nonnegative, Q.extended_nonpositive,
+        Q.extended_real, Q.finite, Q.hermitian, Q.integer,
+        Q.nonnegative, Q.nonpositive, Q.rational, Q.real, Q.zero]),
+        set([Q.composite, Q.extended_negative, Q.extended_nonzero,
+        Q.extended_positive, Q.imaginary, Q.infinite, Q.irrational,
+        Q.negative, Q.negative_infinite, Q.nonzero, Q.odd, Q.positive,
+        Q.positive_infinite, Q.prime, Q.transcendental])),
+    }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/assume.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/assume.py
new file mode 100644
index 0000000000000000000000000000000000000000..743195a865a1d39389d471b95728ca79834ed019
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/assume.py
@@ -0,0 +1,485 @@
+"""A module which implements predicates and assumption context."""
+
+from contextlib import contextmanager
+import inspect
+from sympy.core.symbol import Str
+from sympy.core.sympify import _sympify
+from sympy.logic.boolalg import Boolean, false, true
+from sympy.multipledispatch.dispatcher import Dispatcher, str_signature
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.source import get_class
+
+
+class AssumptionsContext(set):
+    """
+    Set containing default assumptions which are applied to the ``ask()``
+    function.
+
+    Explanation
+    ===========
+
+    This is used to represent global assumptions, but you can also use this
+    class to create your own local assumptions contexts. It is basically a thin
+    wrapper to Python's set, so see its documentation for advanced usage.
+
+    Examples
+    ========
+
+    The default assumption context is ``global_assumptions``, which is initially empty:
+
+    >>> from sympy import ask, Q
+    >>> from sympy.assumptions import global_assumptions
+    >>> global_assumptions
+    AssumptionsContext()
+
+    You can add default assumptions:
+
+    >>> from sympy.abc import x
+    >>> global_assumptions.add(Q.real(x))
+    >>> global_assumptions
+    AssumptionsContext({Q.real(x)})
+    >>> ask(Q.real(x))
+    True
+
+    And remove them:
+
+    >>> global_assumptions.remove(Q.real(x))
+    >>> print(ask(Q.real(x)))
+    None
+
+    The ``clear()`` method removes every assumption:
+
+    >>> global_assumptions.add(Q.positive(x))
+    >>> global_assumptions
+    AssumptionsContext({Q.positive(x)})
+    >>> global_assumptions.clear()
+    >>> global_assumptions
+    AssumptionsContext()
+
+    See Also
+    ========
+
+    assuming
+
+    """
+
+    def add(self, *assumptions):
+        """Add assumptions."""
+        for a in assumptions:
+            super().add(a)
+
+    def _sympystr(self, printer):
+        if not self:
+            return "%s()" % self.__class__.__name__
+        return "{}({})".format(self.__class__.__name__, printer._print_set(self))
+
+global_assumptions = AssumptionsContext()
+
+
+class AppliedPredicate(Boolean):
+    """
+    The class of expressions resulting from applying ``Predicate`` to
+    the arguments. ``AppliedPredicate`` merely wraps its argument and
+    remain unevaluated. To evaluate it, use the ``ask()`` function.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask
+    >>> Q.integer(1)
+    Q.integer(1)
+
+    The ``function`` attribute returns the predicate, and the ``arguments``
+    attribute returns the tuple of arguments.
+
+    >>> type(Q.integer(1))
+    
+    >>> Q.integer(1).function
+    Q.integer
+    >>> Q.integer(1).arguments
+    (1,)
+
+    Applied predicates can be evaluated to a boolean value with ``ask``:
+
+    >>> ask(Q.integer(1))
+    True
+
+    """
+    __slots__ = ()
+
+    def __new__(cls, predicate, *args):
+        if not isinstance(predicate, Predicate):
+            raise TypeError("%s is not a Predicate." % predicate)
+        args = map(_sympify, args)
+        return super().__new__(cls, predicate, *args)
+
+    @property
+    def arg(self):
+        """
+        Return the expression used by this assumption.
+
+        Examples
+        ========
+
+        >>> from sympy import Q, Symbol
+        >>> x = Symbol('x')
+        >>> a = Q.integer(x + 1)
+        >>> a.arg
+        x + 1
+
+        """
+        # Will be deprecated
+        args = self._args
+        if len(args) == 2:
+            # backwards compatibility
+            return args[1]
+        raise TypeError("'arg' property is allowed only for unary predicates.")
+
+    @property
+    def function(self):
+        """
+        Return the predicate.
+        """
+        # Will be changed to self.args[0] after args overriding is removed
+        return self._args[0]
+
+    @property
+    def arguments(self):
+        """
+        Return the arguments which are applied to the predicate.
+        """
+        # Will be changed to self.args[1:] after args overriding is removed
+        return self._args[1:]
+
+    def _eval_ask(self, assumptions):
+        return self.function.eval(self.arguments, assumptions)
+
+    @property
+    def binary_symbols(self):
+        from .ask import Q
+        if self.function == Q.is_true:
+            i = self.arguments[0]
+            if i.is_Boolean or i.is_Symbol:
+                return i.binary_symbols
+        if self.function in (Q.eq, Q.ne):
+            if true in self.arguments or false in self.arguments:
+                if self.arguments[0].is_Symbol:
+                    return {self.arguments[0]}
+                elif self.arguments[1].is_Symbol:
+                    return {self.arguments[1]}
+        return set()
+
+
+class PredicateMeta(type):
+    def __new__(cls, clsname, bases, dct):
+        # If handler is not defined, assign empty dispatcher.
+        if "handler" not in dct:
+            name = f"Ask{clsname.capitalize()}Handler"
+            handler = Dispatcher(name, doc="Handler for key %s" % name)
+            dct["handler"] = handler
+
+        dct["_orig_doc"] = dct.get("__doc__", "")
+
+        return super().__new__(cls, clsname, bases, dct)
+
+    @property
+    def __doc__(cls):
+        handler = cls.handler
+        doc = cls._orig_doc
+        if cls is not Predicate and handler is not None:
+            doc += "Handler\n"
+            doc += "    =======\n\n"
+
+            # Append the handler's doc without breaking sphinx documentation.
+            docs = ["    Multiply dispatched method: %s" % handler.name]
+            if handler.doc:
+                for line in handler.doc.splitlines():
+                    if not line:
+                        continue
+                    docs.append("    %s" % line)
+            other = []
+            for sig in handler.ordering[::-1]:
+                func = handler.funcs[sig]
+                if func.__doc__:
+                    s = '    Inputs: <%s>' % str_signature(sig)
+                    lines = []
+                    for line in func.__doc__.splitlines():
+                        lines.append("    %s" % line)
+                    s += "\n".join(lines)
+                    docs.append(s)
+                else:
+                    other.append(str_signature(sig))
+            if other:
+                othersig = "    Other signatures:"
+                for line in other:
+                    othersig += "\n        * %s" % line
+                docs.append(othersig)
+
+            doc += '\n\n'.join(docs)
+
+        return doc
+
+
+class Predicate(Boolean, metaclass=PredicateMeta):
+    """
+    Base class for mathematical predicates. It also serves as a
+    constructor for undefined predicate objects.
+
+    Explanation
+    ===========
+
+    Predicate is a function that returns a boolean value [1].
+
+    Predicate function is object, and it is instance of predicate class.
+    When a predicate is applied to arguments, ``AppliedPredicate``
+    instance is returned. This merely wraps the argument and remain
+    unevaluated. To obtain the truth value of applied predicate, use the
+    function ``ask``.
+
+    Evaluation of predicate is done by multiple dispatching. You can
+    register new handler to the predicate to support new types.
+
+    Every predicate in SymPy can be accessed via the property of ``Q``.
+    For example, ``Q.even`` returns the predicate which checks if the
+    argument is even number.
+
+    To define a predicate which can be evaluated, you must subclass this
+    class, make an instance of it, and register it to ``Q``. After then,
+    dispatch the handler by argument types.
+
+    If you directly construct predicate using this class, you will get
+    ``UndefinedPredicate`` which cannot be dispatched. This is useful
+    when you are building boolean expressions which do not need to be
+    evaluated.
+
+    Examples
+    ========
+
+    Applying and evaluating to boolean value:
+
+    >>> from sympy import Q, ask
+    >>> ask(Q.prime(7))
+    True
+
+    You can define a new predicate by subclassing and dispatching. Here,
+    we define a predicate for sexy primes [2] as an example.
+
+    >>> from sympy import Predicate, Integer
+    >>> class SexyPrimePredicate(Predicate):
+    ...     name = "sexyprime"
+    >>> Q.sexyprime = SexyPrimePredicate()
+    >>> @Q.sexyprime.register(Integer, Integer)
+    ... def _(int1, int2, assumptions):
+    ...     args = sorted([int1, int2])
+    ...     if not all(ask(Q.prime(a), assumptions) for a in args):
+    ...         return False
+    ...     return args[1] - args[0] == 6
+    >>> ask(Q.sexyprime(5, 11))
+    True
+
+    Direct constructing returns ``UndefinedPredicate``, which can be
+    applied but cannot be dispatched.
+
+    >>> from sympy import Predicate, Integer
+    >>> Q.P = Predicate("P")
+    >>> type(Q.P)
+    
+    >>> Q.P(1)
+    Q.P(1)
+    >>> Q.P.register(Integer)(lambda expr, assump: True)
+    Traceback (most recent call last):
+      ...
+    TypeError:  cannot be dispatched.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Predicate_%28mathematical_logic%29
+    .. [2] https://en.wikipedia.org/wiki/Sexy_prime
+
+    """
+
+    is_Atom = True
+
+    def __new__(cls, *args, **kwargs):
+        if cls is Predicate:
+            return UndefinedPredicate(*args, **kwargs)
+        obj = super().__new__(cls, *args)
+        return obj
+
+    @property
+    def name(self):
+        # May be overridden
+        return type(self).__name__
+
+    @classmethod
+    def register(cls, *types, **kwargs):
+        """
+        Register the signature to the handler.
+        """
+        if cls.handler is None:
+            raise TypeError("%s cannot be dispatched." % type(cls))
+        return cls.handler.register(*types, **kwargs)
+
+    @classmethod
+    def register_many(cls, *types, **kwargs):
+        """
+        Register multiple signatures to same handler.
+        """
+        def _(func):
+            for t in types:
+                if not is_sequence(t):
+                    t = (t,)  # for convenience, allow passing `type` to mean `(type,)`
+                cls.register(*t, **kwargs)(func)
+        return _
+
+    def __call__(self, *args):
+        return AppliedPredicate(self, *args)
+
+    def eval(self, args, assumptions=True):
+        """
+        Evaluate ``self(*args)`` under the given assumptions.
+
+        This uses only direct resolution methods, not logical inference.
+        """
+        result = None
+        try:
+            result = self.handler(*args, assumptions=assumptions)
+        except NotImplementedError:
+            pass
+        return result
+
+    def _eval_refine(self, assumptions):
+        # When Predicate is no longer Boolean, delete this method
+        return self
+
+
+class UndefinedPredicate(Predicate):
+    """
+    Predicate without handler.
+
+    Explanation
+    ===========
+
+    This predicate is generated by using ``Predicate`` directly for
+    construction. It does not have a handler, and evaluating this with
+    arguments is done by SAT solver.
+
+    Examples
+    ========
+
+    >>> from sympy import Predicate, Q
+    >>> Q.P = Predicate('P')
+    >>> Q.P.func
+    
+    >>> Q.P.name
+    Str('P')
+
+    """
+
+    handler = None
+
+    def __new__(cls, name, handlers=None):
+        # "handlers" parameter supports old design
+        if not isinstance(name, Str):
+            name = Str(name)
+        obj = super(Boolean, cls).__new__(cls, name)
+        obj.handlers = handlers or []
+        return obj
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    def _hashable_content(self):
+        return (self.name,)
+
+    def __getnewargs__(self):
+        return (self.name,)
+
+    def __call__(self, expr):
+        return AppliedPredicate(self, expr)
+
+    def add_handler(self, handler):
+        sympy_deprecation_warning(
+            """
+            The AskHandler system is deprecated. Predicate.add_handler()
+            should be replaced with the multipledispatch handler of Predicate.
+            """,
+            deprecated_since_version="1.8",
+            active_deprecations_target='deprecated-askhandler',
+        )
+        self.handlers.append(handler)
+
+    def remove_handler(self, handler):
+        sympy_deprecation_warning(
+            """
+            The AskHandler system is deprecated. Predicate.remove_handler()
+            should be replaced with the multipledispatch handler of Predicate.
+            """,
+            deprecated_since_version="1.8",
+            active_deprecations_target='deprecated-askhandler',
+        )
+        self.handlers.remove(handler)
+
+    def eval(self, args, assumptions=True):
+        # Support for deprecated design
+        # When old design is removed, this will always return None
+        sympy_deprecation_warning(
+            """
+            The AskHandler system is deprecated. Evaluating UndefinedPredicate
+            objects should be replaced with the multipledispatch handler of
+            Predicate.
+            """,
+            deprecated_since_version="1.8",
+            active_deprecations_target='deprecated-askhandler',
+            stacklevel=5,
+        )
+        expr, = args
+        res, _res = None, None
+        mro = inspect.getmro(type(expr))
+        for handler in self.handlers:
+            cls = get_class(handler)
+            for subclass in mro:
+                eval_ = getattr(cls, subclass.__name__, None)
+                if eval_ is None:
+                    continue
+                res = eval_(expr, assumptions)
+                # Do not stop if value returned is None
+                # Try to check for higher classes
+                if res is None:
+                    continue
+                if _res is None:
+                    _res = res
+                else:
+                    # only check consistency if both resolutors have concluded
+                    if _res != res:
+                        raise ValueError('incompatible resolutors')
+                break
+        return res
+
+
+@contextmanager
+def assuming(*assumptions):
+    """
+    Context manager for assumptions.
+
+    Examples
+    ========
+
+    >>> from sympy import assuming, Q, ask
+    >>> from sympy.abc import x, y
+    >>> print(ask(Q.integer(x + y)))
+    None
+    >>> with assuming(Q.integer(x), Q.integer(y)):
+    ...     print(ask(Q.integer(x + y)))
+    True
+    """
+    old_global_assumptions = global_assumptions.copy()
+    global_assumptions.update(assumptions)
+    try:
+        yield
+    finally:
+        global_assumptions.clear()
+        global_assumptions.update(old_global_assumptions)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/cnf.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/cnf.py
new file mode 100644
index 0000000000000000000000000000000000000000..a95d27bed6eeb64c42f4edd9d49bd8e5753069e5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/cnf.py
@@ -0,0 +1,445 @@
+"""
+The classes used here are for the internal use of assumptions system
+only and should not be used anywhere else as these do not possess the
+signatures common to SymPy objects. For general use of logic constructs
+please refer to sympy.logic classes And, Or, Not, etc.
+"""
+from itertools import combinations, product, zip_longest
+from sympy.assumptions.assume import AppliedPredicate, Predicate
+from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le
+from sympy.core.singleton import S
+from sympy.logic.boolalg import Or, And, Not, Xnor
+from sympy.logic.boolalg import (Equivalent, ITE, Implies, Nand, Nor, Xor)
+
+
+class Literal:
+    """
+    The smallest element of a CNF object.
+
+    Parameters
+    ==========
+
+    lit : Boolean expression
+
+    is_Not : bool
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.cnf import Literal
+    >>> from sympy.abc import x
+    >>> Literal(Q.even(x))
+    Literal(Q.even(x), False)
+    >>> Literal(~Q.even(x))
+    Literal(Q.even(x), True)
+    """
+
+    def __new__(cls, lit, is_Not=False):
+        if isinstance(lit, Not):
+            lit = lit.args[0]
+            is_Not = True
+        elif isinstance(lit, (AND, OR, Literal)):
+            return ~lit if is_Not else lit
+        obj = super().__new__(cls)
+        obj.lit = lit
+        obj.is_Not = is_Not
+        return obj
+
+    @property
+    def arg(self):
+        return self.lit
+
+    def rcall(self, expr):
+        if callable(self.lit):
+            lit = self.lit(expr)
+        else:
+            lit = self.lit.apply(expr)
+        return type(self)(lit, self.is_Not)
+
+    def __invert__(self):
+        is_Not = not self.is_Not
+        return Literal(self.lit, is_Not)
+
+    def __str__(self):
+        return '{}({}, {})'.format(type(self).__name__, self.lit, self.is_Not)
+
+    __repr__ = __str__
+
+    def __eq__(self, other):
+        return self.arg == other.arg and self.is_Not == other.is_Not
+
+    def __hash__(self):
+        h = hash((type(self).__name__, self.arg, self.is_Not))
+        return h
+
+
+class OR:
+    """
+    A low-level implementation for Or
+    """
+    def __init__(self, *args):
+        self._args = args
+
+    @property
+    def args(self):
+        return sorted(self._args, key=str)
+
+    def rcall(self, expr):
+        return type(self)(*[arg.rcall(expr)
+                            for arg in self._args
+                            ])
+
+    def __invert__(self):
+        return AND(*[~arg for arg in self._args])
+
+    def __hash__(self):
+        return hash((type(self).__name__,) + tuple(self.args))
+
+    def __eq__(self, other):
+        return self.args == other.args
+
+    def __str__(self):
+        s = '(' + ' | '.join([str(arg) for arg in self.args]) + ')'
+        return s
+
+    __repr__ = __str__
+
+
+class AND:
+    """
+    A low-level implementation for And
+    """
+    def __init__(self, *args):
+        self._args = args
+
+    def __invert__(self):
+        return OR(*[~arg for arg in self._args])
+
+    @property
+    def args(self):
+        return sorted(self._args, key=str)
+
+    def rcall(self, expr):
+        return type(self)(*[arg.rcall(expr)
+                            for arg in self._args
+                            ])
+
+    def __hash__(self):
+        return hash((type(self).__name__,) + tuple(self.args))
+
+    def __eq__(self, other):
+        return self.args == other.args
+
+    def __str__(self):
+        s = '('+' & '.join([str(arg) for arg in self.args])+')'
+        return s
+
+    __repr__ = __str__
+
+
+def to_NNF(expr, composite_map=None):
+    """
+    Generates the Negation Normal Form of any boolean expression in terms
+    of AND, OR, and Literal objects.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, Eq
+    >>> from sympy.assumptions.cnf import to_NNF
+    >>> from sympy.abc import x, y
+    >>> expr = Q.even(x) & ~Q.positive(x)
+    >>> to_NNF(expr)
+    (Literal(Q.even(x), False) & Literal(Q.positive(x), True))
+
+    Supported boolean objects are converted to corresponding predicates.
+
+    >>> to_NNF(Eq(x, y))
+    Literal(Q.eq(x, y), False)
+
+    If ``composite_map`` argument is given, ``to_NNF`` decomposes the
+    specified predicate into a combination of primitive predicates.
+
+    >>> cmap = {Q.nonpositive: Q.negative | Q.zero}
+    >>> to_NNF(Q.nonpositive, cmap)
+    (Literal(Q.negative, False) | Literal(Q.zero, False))
+    >>> to_NNF(Q.nonpositive(x), cmap)
+    (Literal(Q.negative(x), False) | Literal(Q.zero(x), False))
+    """
+    from sympy.assumptions.ask import Q
+
+    if composite_map is None:
+        composite_map = {}
+
+
+    binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le}
+    if type(expr) in binrelpreds:
+        pred = binrelpreds[type(expr)]
+        expr = pred(*expr.args)
+
+    if isinstance(expr, Not):
+        arg = expr.args[0]
+        tmp = to_NNF(arg, composite_map)  # Strategy: negate the NNF of expr
+        return ~tmp
+
+    if isinstance(expr, Or):
+        return OR(*[to_NNF(x, composite_map) for x in Or.make_args(expr)])
+
+    if isinstance(expr, And):
+        return AND(*[to_NNF(x, composite_map) for x in And.make_args(expr)])
+
+    if isinstance(expr, Nand):
+        tmp = AND(*[to_NNF(x, composite_map) for x in expr.args])
+        return ~tmp
+
+    if isinstance(expr, Nor):
+        tmp = OR(*[to_NNF(x, composite_map) for x in expr.args])
+        return ~tmp
+
+    if isinstance(expr, Xor):
+        cnfs = []
+        for i in range(0, len(expr.args) + 1, 2):
+            for neg in combinations(expr.args, i):
+                clause = [~to_NNF(s, composite_map) if s in neg else to_NNF(s, composite_map)
+                          for s in expr.args]
+                cnfs.append(OR(*clause))
+        return AND(*cnfs)
+
+    if isinstance(expr, Xnor):
+        cnfs = []
+        for i in range(0, len(expr.args) + 1, 2):
+            for neg in combinations(expr.args, i):
+                clause = [~to_NNF(s, composite_map) if s in neg else to_NNF(s, composite_map)
+                          for s in expr.args]
+                cnfs.append(OR(*clause))
+        return ~AND(*cnfs)
+
+    if isinstance(expr, Implies):
+        L, R = to_NNF(expr.args[0], composite_map), to_NNF(expr.args[1], composite_map)
+        return OR(~L, R)
+
+    if isinstance(expr, Equivalent):
+        cnfs = []
+        for a, b in zip_longest(expr.args, expr.args[1:], fillvalue=expr.args[0]):
+            a = to_NNF(a, composite_map)
+            b = to_NNF(b, composite_map)
+            cnfs.append(OR(~a, b))
+        return AND(*cnfs)
+
+    if isinstance(expr, ITE):
+        L = to_NNF(expr.args[0], composite_map)
+        M = to_NNF(expr.args[1], composite_map)
+        R = to_NNF(expr.args[2], composite_map)
+        return AND(OR(~L, M), OR(L, R))
+
+    if isinstance(expr, AppliedPredicate):
+        pred, args = expr.function, expr.arguments
+        newpred = composite_map.get(pred, None)
+        if newpred is not None:
+            return to_NNF(newpred.rcall(*args), composite_map)
+
+    if isinstance(expr, Predicate):
+        newpred = composite_map.get(expr, None)
+        if newpred is not None:
+            return to_NNF(newpred, composite_map)
+
+    return Literal(expr)
+
+
+def distribute_AND_over_OR(expr):
+    """
+    Distributes AND over OR in the NNF expression.
+    Returns the result( Conjunctive Normal Form of expression)
+    as a CNF object.
+    """
+    if not isinstance(expr, (AND, OR)):
+        tmp = set()
+        tmp.add(frozenset((expr,)))
+        return CNF(tmp)
+
+    if isinstance(expr, OR):
+        return CNF.all_or(*[distribute_AND_over_OR(arg)
+                            for arg in expr._args])
+
+    if isinstance(expr, AND):
+        return CNF.all_and(*[distribute_AND_over_OR(arg)
+                             for arg in expr._args])
+
+
+class CNF:
+    """
+    Class to represent CNF of a Boolean expression.
+    Consists of set of clauses, which themselves are stored as
+    frozenset of Literal objects.
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.cnf import CNF
+    >>> from sympy.abc import x
+    >>> cnf = CNF.from_prop(Q.real(x) & ~Q.zero(x))
+    >>> cnf.clauses
+    {frozenset({Literal(Q.zero(x), True)}),
+    frozenset({Literal(Q.negative(x), False),
+    Literal(Q.positive(x), False), Literal(Q.zero(x), False)})}
+    """
+    def __init__(self, clauses=None):
+        if not clauses:
+            clauses = set()
+        self.clauses = clauses
+
+    def add(self, prop):
+        clauses = CNF.to_CNF(prop).clauses
+        self.add_clauses(clauses)
+
+    def __str__(self):
+        s = ' & '.join(
+            ['(' + ' | '.join([str(lit) for lit in clause]) +')'
+            for clause in self.clauses]
+        )
+        return s
+
+    def extend(self, props):
+        for p in props:
+            self.add(p)
+        return self
+
+    def copy(self):
+        return CNF(set(self.clauses))
+
+    def add_clauses(self, clauses):
+        self.clauses |= clauses
+
+    @classmethod
+    def from_prop(cls, prop):
+        res = cls()
+        res.add(prop)
+        return res
+
+    def __iand__(self, other):
+        self.add_clauses(other.clauses)
+        return self
+
+    def all_predicates(self):
+        predicates = set()
+        for c in self.clauses:
+            predicates |= {arg.lit for arg in c}
+        return predicates
+
+    def _or(self, cnf):
+        clauses = set()
+        for a, b in product(self.clauses, cnf.clauses):
+            tmp = set(a)
+            tmp.update(b)
+            clauses.add(frozenset(tmp))
+        return CNF(clauses)
+
+    def _and(self, cnf):
+        clauses = self.clauses.union(cnf.clauses)
+        return CNF(clauses)
+
+    def _not(self):
+        clss = list(self.clauses)
+        ll = {frozenset((~x,)) for x in clss[-1]}
+        ll = CNF(ll)
+
+        for rest in clss[:-1]:
+            p = {frozenset((~x,)) for x in rest}
+            ll = ll._or(CNF(p))
+        return ll
+
+    def rcall(self, expr):
+        clause_list = []
+        for clause in self.clauses:
+            lits = [arg.rcall(expr) for arg in clause]
+            clause_list.append(OR(*lits))
+        expr = AND(*clause_list)
+        return distribute_AND_over_OR(expr)
+
+    @classmethod
+    def all_or(cls, *cnfs):
+        b = cnfs[0].copy()
+        for rest in cnfs[1:]:
+            b = b._or(rest)
+        return b
+
+    @classmethod
+    def all_and(cls, *cnfs):
+        b = cnfs[0].copy()
+        for rest in cnfs[1:]:
+            b = b._and(rest)
+        return b
+
+    @classmethod
+    def to_CNF(cls, expr):
+        from sympy.assumptions.facts import get_composite_predicates
+        expr = to_NNF(expr, get_composite_predicates())
+        expr = distribute_AND_over_OR(expr)
+        return expr
+
+    @classmethod
+    def CNF_to_cnf(cls, cnf):
+        """
+        Converts CNF object to SymPy's boolean expression
+        retaining the form of expression.
+        """
+        def remove_literal(arg):
+            return Not(arg.lit) if arg.is_Not else arg.lit
+
+        return And(*(Or(*(remove_literal(arg) for arg in clause)) for clause in cnf.clauses))
+
+
+class EncodedCNF:
+    """
+    Class for encoding the CNF expression.
+    """
+    def __init__(self, data=None, encoding=None):
+        if not data and not encoding:
+            data = []
+            encoding = {}
+        self.data = data
+        self.encoding = encoding
+        self._symbols = list(encoding.keys())
+
+    def from_cnf(self, cnf):
+        self._symbols = list(cnf.all_predicates())
+        n = len(self._symbols)
+        self.encoding = dict(zip(self._symbols, range(1, n + 1)))
+        self.data = [self.encode(clause) for clause in cnf.clauses]
+
+    @property
+    def symbols(self):
+        return self._symbols
+
+    @property
+    def variables(self):
+        return range(1, len(self._symbols) + 1)
+
+    def copy(self):
+        new_data = [set(clause) for clause in self.data]
+        return EncodedCNF(new_data, dict(self.encoding))
+
+    def add_prop(self, prop):
+        cnf = CNF.from_prop(prop)
+        self.add_from_cnf(cnf)
+
+    def add_from_cnf(self, cnf):
+        clauses = [self.encode(clause) for clause in cnf.clauses]
+        self.data += clauses
+
+    def encode_arg(self, arg):
+        literal = arg.lit
+        value = self.encoding.get(literal, None)
+        if value is None:
+            n = len(self._symbols)
+            self._symbols.append(literal)
+            value = self.encoding[literal] = n + 1
+        if arg.is_Not:
+            return -value
+        else:
+            return value
+
+    def encode(self, clause):
+        return {self.encode_arg(arg) if not arg.lit == S.false else 0 for arg in clause}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/facts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/facts.py
new file mode 100644
index 0000000000000000000000000000000000000000..2ff268677cf74e252ac6c3bc3eecbea08b9414d0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/facts.py
@@ -0,0 +1,270 @@
+"""
+Known facts in assumptions module.
+
+This module defines the facts between unary predicates in ``get_known_facts()``,
+and supports functions to generate the contents in
+``sympy.assumptions.ask_generated`` file.
+"""
+
+from sympy.assumptions.ask import Q
+from sympy.assumptions.assume import AppliedPredicate
+from sympy.core.cache import cacheit
+from sympy.core.symbol import Symbol
+from sympy.logic.boolalg import (to_cnf, And, Not, Implies, Equivalent,
+    Exclusive,)
+from sympy.logic.inference import satisfiable
+
+
+@cacheit
+def get_composite_predicates():
+    # To reduce the complexity of sat solver, these predicates are
+    # transformed into the combination of primitive predicates.
+    return {
+        Q.real : Q.negative | Q.zero | Q.positive,
+        Q.integer : Q.even | Q.odd,
+        Q.nonpositive : Q.negative | Q.zero,
+        Q.nonzero : Q.negative | Q.positive,
+        Q.nonnegative : Q.zero | Q.positive,
+        Q.extended_real : Q.negative_infinite | Q.negative | Q.zero | Q.positive | Q.positive_infinite,
+        Q.extended_positive: Q.positive | Q.positive_infinite,
+        Q.extended_negative: Q.negative | Q.negative_infinite,
+        Q.extended_nonzero: Q.negative_infinite | Q.negative | Q.positive | Q.positive_infinite,
+        Q.extended_nonpositive: Q.negative_infinite | Q.negative | Q.zero,
+        Q.extended_nonnegative: Q.zero | Q.positive | Q.positive_infinite,
+        Q.complex : Q.algebraic | Q.transcendental
+    }
+
+
+@cacheit
+def get_known_facts(x=None):
+    """
+    Facts between unary predicates.
+
+    Parameters
+    ==========
+
+    x : Symbol, optional
+        Placeholder symbol for unary facts. Default is ``Symbol('x')``.
+
+    Returns
+    =======
+
+    fact : Known facts in conjugated normal form.
+
+    """
+    if x is None:
+        x = Symbol('x')
+
+    fact = And(
+        get_number_facts(x),
+        get_matrix_facts(x)
+    )
+    return fact
+
+
+@cacheit
+def get_number_facts(x = None):
+    """
+    Facts between unary number predicates.
+
+    Parameters
+    ==========
+
+    x : Symbol, optional
+        Placeholder symbol for unary facts. Default is ``Symbol('x')``.
+
+    Returns
+    =======
+
+    fact : Known facts in conjugated normal form.
+
+    """
+    if x is None:
+        x = Symbol('x')
+
+    fact = And(
+        # primitive predicates for extended real exclude each other.
+        Exclusive(Q.negative_infinite(x), Q.negative(x), Q.zero(x),
+            Q.positive(x), Q.positive_infinite(x)),
+
+        # build complex plane
+        Exclusive(Q.real(x), Q.imaginary(x)),
+        Implies(Q.real(x) | Q.imaginary(x), Q.complex(x)),
+
+        # other subsets of complex
+        Exclusive(Q.transcendental(x), Q.algebraic(x)),
+        Equivalent(Q.real(x), Q.rational(x) | Q.irrational(x)),
+        Exclusive(Q.irrational(x), Q.rational(x)),
+        Implies(Q.rational(x), Q.algebraic(x)),
+
+        # integers
+        Exclusive(Q.even(x), Q.odd(x)),
+        Implies(Q.integer(x), Q.rational(x)),
+        Implies(Q.zero(x), Q.even(x)),
+        Exclusive(Q.composite(x), Q.prime(x)),
+        Implies(Q.composite(x) | Q.prime(x), Q.integer(x) & Q.positive(x)),
+        Implies(Q.even(x) & Q.positive(x) & ~Q.prime(x), Q.composite(x)),
+
+        # hermitian and antihermitian
+        Implies(Q.real(x), Q.hermitian(x)),
+        Implies(Q.imaginary(x), Q.antihermitian(x)),
+        Implies(Q.zero(x), Q.hermitian(x) | Q.antihermitian(x)),
+
+        # define finity and infinity, and build extended real line
+        Exclusive(Q.infinite(x), Q.finite(x)),
+        Implies(Q.complex(x), Q.finite(x)),
+        Implies(Q.negative_infinite(x) | Q.positive_infinite(x), Q.infinite(x)),
+
+        # commutativity
+        Implies(Q.finite(x) | Q.infinite(x), Q.commutative(x)),
+    )
+    return fact
+
+
+@cacheit
+def get_matrix_facts(x = None):
+    """
+    Facts between unary matrix predicates.
+
+    Parameters
+    ==========
+
+    x : Symbol, optional
+        Placeholder symbol for unary facts. Default is ``Symbol('x')``.
+
+    Returns
+    =======
+
+    fact : Known facts in conjugated normal form.
+
+    """
+    if x is None:
+        x = Symbol('x')
+
+    fact = And(
+        # matrices
+        Implies(Q.orthogonal(x), Q.positive_definite(x)),
+        Implies(Q.orthogonal(x), Q.unitary(x)),
+        Implies(Q.unitary(x) & Q.real_elements(x), Q.orthogonal(x)),
+        Implies(Q.unitary(x), Q.normal(x)),
+        Implies(Q.unitary(x), Q.invertible(x)),
+        Implies(Q.normal(x), Q.square(x)),
+        Implies(Q.diagonal(x), Q.normal(x)),
+        Implies(Q.positive_definite(x), Q.invertible(x)),
+        Implies(Q.diagonal(x), Q.upper_triangular(x)),
+        Implies(Q.diagonal(x), Q.lower_triangular(x)),
+        Implies(Q.lower_triangular(x), Q.triangular(x)),
+        Implies(Q.upper_triangular(x), Q.triangular(x)),
+        Implies(Q.triangular(x), Q.upper_triangular(x) | Q.lower_triangular(x)),
+        Implies(Q.upper_triangular(x) & Q.lower_triangular(x), Q.diagonal(x)),
+        Implies(Q.diagonal(x), Q.symmetric(x)),
+        Implies(Q.unit_triangular(x), Q.triangular(x)),
+        Implies(Q.invertible(x), Q.fullrank(x)),
+        Implies(Q.invertible(x), Q.square(x)),
+        Implies(Q.symmetric(x), Q.square(x)),
+        Implies(Q.fullrank(x) & Q.square(x), Q.invertible(x)),
+        Equivalent(Q.invertible(x), ~Q.singular(x)),
+        Implies(Q.integer_elements(x), Q.real_elements(x)),
+        Implies(Q.real_elements(x), Q.complex_elements(x)),
+    )
+    return fact
+
+
+
+def generate_known_facts_dict(keys, fact):
+    """
+    Computes and returns a dictionary which contains the relations between
+    unary predicates.
+
+    Each key is a predicate, and item is two groups of predicates.
+    First group contains the predicates which are implied by the key, and
+    second group contains the predicates which are rejected by the key.
+
+    All predicates in *keys* and *fact* must be unary and have same placeholder
+    symbol.
+
+    Parameters
+    ==========
+
+    keys : list of AppliedPredicate instances.
+
+    fact : Fact between predicates in conjugated normal form.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, And, Implies
+    >>> from sympy.assumptions.facts import generate_known_facts_dict
+    >>> from sympy.abc import x
+    >>> keys = [Q.even(x), Q.odd(x), Q.zero(x)]
+    >>> fact = And(Implies(Q.even(x), ~Q.odd(x)),
+    ...     Implies(Q.zero(x), Q.even(x)))
+    >>> generate_known_facts_dict(keys, fact)
+    {Q.even: ({Q.even}, {Q.odd}),
+     Q.odd: ({Q.odd}, {Q.even, Q.zero}),
+     Q.zero: ({Q.even, Q.zero}, {Q.odd})}
+    """
+    fact_cnf = to_cnf(fact)
+    mapping = single_fact_lookup(keys, fact_cnf)
+
+    ret = {}
+    for key, value in mapping.items():
+        implied = set()
+        rejected = set()
+        for expr in value:
+            if isinstance(expr, AppliedPredicate):
+                implied.add(expr.function)
+            elif isinstance(expr, Not):
+                pred = expr.args[0]
+                rejected.add(pred.function)
+        ret[key.function] = (implied, rejected)
+    return ret
+
+
+@cacheit
+def get_known_facts_keys():
+    """
+    Return every unary predicates registered to ``Q``.
+
+    This function is used to generate the keys for
+    ``generate_known_facts_dict``.
+
+    """
+    # exclude polyadic predicates
+    exclude = {Q.eq, Q.ne, Q.gt, Q.lt, Q.ge, Q.le}
+
+    result = []
+    for attr in Q.__class__.__dict__:
+        if attr.startswith('__'):
+            continue
+        pred = getattr(Q, attr)
+        if pred in exclude:
+            continue
+        result.append(pred)
+    return result
+
+
+def single_fact_lookup(known_facts_keys, known_facts_cnf):
+    # Return the dictionary for quick lookup of single fact
+    mapping = {}
+    for key in known_facts_keys:
+        mapping[key] = {key}
+        for other_key in known_facts_keys:
+            if other_key != key:
+                if ask_full_inference(other_key, key, known_facts_cnf):
+                    mapping[key].add(other_key)
+                if ask_full_inference(~other_key, key, known_facts_cnf):
+                    mapping[key].add(~other_key)
+    return mapping
+
+
+def ask_full_inference(proposition, assumptions, known_facts_cnf):
+    """
+    Method for inferring properties about objects.
+
+    """
+    if not satisfiable(And(known_facts_cnf, assumptions, proposition)):
+        return False
+    if not satisfiable(And(known_facts_cnf, assumptions, Not(proposition))):
+        return True
+    return None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..0fbe618eb8b43e252ac8fb0baf1eeee22bf347cc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/__init__.py
@@ -0,0 +1,13 @@
+"""
+Multipledispatch handlers for ``Predicate`` are implemented here.
+Handlers in this module are not directly imported to other modules in
+order to avoid circular import problem.
+"""
+
+from .common import (AskHandler, CommonHandler,
+    test_closed_group)
+
+__all__ = [
+    'AskHandler', 'CommonHandler',
+    'test_closed_group'
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/calculus.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/calculus.py
new file mode 100644
index 0000000000000000000000000000000000000000..e2b9c43ccea216988a25aa671ea23bc81d2209ff
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/calculus.py
@@ -0,0 +1,273 @@
+"""
+This module contains query handlers responsible for calculus queries:
+infinitesimal, finite, etc.
+"""
+
+from sympy.assumptions import Q, ask
+from sympy.core import Expr, Add, Mul, Pow, Symbol
+from sympy.core.numbers import (NegativeInfinity, GoldenRatio,
+    Infinity, Exp1, ComplexInfinity, ImaginaryUnit, NaN, Number, Pi, E,
+    TribonacciConstant)
+from sympy.functions import cos, exp, log, sign, sin
+from sympy.logic.boolalg import conjuncts
+
+from ..predicates.calculus import (FinitePredicate, InfinitePredicate,
+    PositiveInfinitePredicate, NegativeInfinitePredicate)
+
+
+# FinitePredicate
+
+
+@FinitePredicate.register(Symbol)
+def _(expr, assumptions):
+    """
+    Handles Symbol.
+    """
+    if expr.is_finite is not None:
+        return expr.is_finite
+    if Q.finite(expr) in conjuncts(assumptions):
+        return True
+    return None
+
+@FinitePredicate.register(Add)
+def _(expr, assumptions):
+    """
+    Return True if expr is bounded, False if not and None if unknown.
+
+    Truth Table:
+
+    +-------+-----+-----------+-----------+
+    |       |     |           |           |
+    |       |  B  |     U     |     ?     |
+    |       |     |           |           |
+    +-------+-----+---+---+---+---+---+---+
+    |       |     |   |   |   |   |   |   |
+    |       |     |'+'|'-'|'x'|'+'|'-'|'x'|
+    |       |     |   |   |   |   |   |   |
+    +-------+-----+---+---+---+---+---+---+
+    |       |     |           |           |
+    |   B   |  B  |     U     |     ?     |
+    |       |     |           |           |
+    +---+---+-----+---+---+---+---+---+---+
+    |   |   |     |   |   |   |   |   |   |
+    |   |'+'|     | U | ? | ? | U | ? | ? |
+    |   |   |     |   |   |   |   |   |   |
+    |   +---+-----+---+---+---+---+---+---+
+    |   |   |     |   |   |   |   |   |   |
+    | U |'-'|     | ? | U | ? | ? | U | ? |
+    |   |   |     |   |   |   |   |   |   |
+    |   +---+-----+---+---+---+---+---+---+
+    |   |   |     |           |           |
+    |   |'x'|     |     ?     |     ?     |
+    |   |   |     |           |           |
+    +---+---+-----+---+---+---+---+---+---+
+    |       |     |           |           |
+    |   ?   |     |           |     ?     |
+    |       |     |           |           |
+    +-------+-----+-----------+---+---+---+
+
+        * 'B' = Bounded
+
+        * 'U' = Unbounded
+
+        * '?' = unknown boundedness
+
+        * '+' = positive sign
+
+        * '-' = negative sign
+
+        * 'x' = sign unknown
+
+        * All Bounded -> True
+
+        * 1 Unbounded and the rest Bounded -> False
+
+        * >1 Unbounded, all with same known sign -> False
+
+        * Any Unknown and unknown sign -> None
+
+        * Else -> None
+
+    When the signs are not the same you can have an undefined
+    result as in oo - oo, hence 'bounded' is also undefined.
+    """
+    sign = -1  # sign of unknown or infinite
+    result = True
+    for arg in expr.args:
+        _bounded = ask(Q.finite(arg), assumptions)
+        if _bounded:
+            continue
+        s = ask(Q.extended_positive(arg), assumptions)
+        # if there has been more than one sign or if the sign of this arg
+        # is None and Bounded is None or there was already
+        # an unknown sign, return None
+        if sign != -1 and s != sign or \
+                s is None and None in (_bounded, sign):
+            return None
+        else:
+            sign = s
+        # once False, do not change
+        if result is not False:
+            result = _bounded
+    return result
+
+@FinitePredicate.register(Mul)
+def _(expr, assumptions):
+    """
+    Return True if expr is bounded, False if not and None if unknown.
+
+    Truth Table:
+
+    +---+---+---+--------+
+    |   |   |   |        |
+    |   | B | U |   ?    |
+    |   |   |   |        |
+    +---+---+---+---+----+
+    |   |   |   |   |    |
+    |   |   |   | s | /s |
+    |   |   |   |   |    |
+    +---+---+---+---+----+
+    |   |   |   |        |
+    | B | B | U |   ?    |
+    |   |   |   |        |
+    +---+---+---+---+----+
+    |   |   |   |   |    |
+    | U |   | U | U | ?  |
+    |   |   |   |   |    |
+    +---+---+---+---+----+
+    |   |   |   |        |
+    | ? |   |   |   ?    |
+    |   |   |   |        |
+    +---+---+---+---+----+
+
+        * B = Bounded
+
+        * U = Unbounded
+
+        * ? = unknown boundedness
+
+        * s = signed (hence nonzero)
+
+        * /s = not signed
+    """
+    result = True
+    possible_zero = False
+    for arg in expr.args:
+        _bounded = ask(Q.finite(arg), assumptions)
+        if _bounded:
+            if ask(Q.zero(arg), assumptions) is not False:
+                if result is False:
+                    return None
+                possible_zero = True
+        elif _bounded is None:
+            if result is None:
+                return None
+            if ask(Q.extended_nonzero(arg), assumptions) is None:
+                return None
+            if result is not False:
+                result = None
+        else:
+            if possible_zero:
+                return None
+            result = False
+    return result
+
+@FinitePredicate.register(Pow)
+def _(expr, assumptions):
+    """
+    * Unbounded ** NonZero -> Unbounded
+
+    * Bounded ** Bounded -> Bounded
+
+    * Abs()<=1 ** Positive -> Bounded
+
+    * Abs()>=1 ** Negative -> Bounded
+
+    * Otherwise unknown
+    """
+    if expr.base == E:
+        return ask(Q.finite(expr.exp), assumptions)
+
+    base_bounded = ask(Q.finite(expr.base), assumptions)
+    exp_bounded = ask(Q.finite(expr.exp), assumptions)
+    if base_bounded is None and exp_bounded is None:  # Common Case
+        return None
+    if base_bounded is False and ask(Q.extended_nonzero(expr.exp), assumptions):
+        return False
+    if base_bounded and exp_bounded:
+        is_base_zero = ask(Q.zero(expr.base),assumptions)
+        is_exp_negative = ask(Q.negative(expr.exp),assumptions)
+        if is_base_zero is True and is_exp_negative is True:
+            return False
+        if is_base_zero is not False and is_exp_negative is not False:
+            return None
+        return True
+    if (abs(expr.base) <= 1) == True and ask(Q.extended_positive(expr.exp), assumptions):
+        return True
+    if (abs(expr.base) >= 1) == True and ask(Q.extended_negative(expr.exp), assumptions):
+        return True
+    if (abs(expr.base) >= 1) == True and exp_bounded is False:
+        return False
+    return None
+
+@FinitePredicate.register(exp)
+def _(expr, assumptions):
+    return ask(Q.finite(expr.exp), assumptions)
+
+@FinitePredicate.register(log)
+def _(expr, assumptions):
+    # After complex -> finite fact is registered to new assumption system,
+    # querying Q.infinite may be removed.
+    if ask(Q.infinite(expr.args[0]), assumptions):
+        return False
+    return ask(~Q.zero(expr.args[0]), assumptions)
+
+@FinitePredicate.register_many(cos, sin, Number, Pi, Exp1, GoldenRatio,
+    TribonacciConstant, ImaginaryUnit, sign)
+def _(expr, assumptions):
+    return True
+
+@FinitePredicate.register_many(ComplexInfinity, Infinity, NegativeInfinity)
+def _(expr, assumptions):
+    return False
+
+@FinitePredicate.register(NaN)
+def _(expr, assumptions):
+    return None
+
+
+# InfinitePredicate
+
+
+@InfinitePredicate.register(Expr)
+def _(expr, assumptions):
+    is_finite = Q.finite(expr)._eval_ask(assumptions)
+    if is_finite is None:
+        return None
+    return not is_finite
+
+
+# PositiveInfinitePredicate
+
+
+@PositiveInfinitePredicate.register(Infinity)
+def _(expr, assumptions):
+    return True
+
+
+@PositiveInfinitePredicate.register_many(NegativeInfinity, ComplexInfinity)
+def _(expr, assumptions):
+    return False
+
+
+# NegativeInfinitePredicate
+
+
+@NegativeInfinitePredicate.register(NegativeInfinity)
+def _(expr, assumptions):
+    return True
+
+
+@NegativeInfinitePredicate.register_many(Infinity, ComplexInfinity)
+def _(expr, assumptions):
+    return False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/common.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/common.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6e9f6f321be461c09b16c03b9cec5708404d21a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/common.py
@@ -0,0 +1,164 @@
+"""
+This module defines base class for handlers and some core handlers:
+``Q.commutative`` and ``Q.is_true``.
+"""
+
+from sympy.assumptions import Q, ask, AppliedPredicate
+from sympy.core import Basic, Symbol
+from sympy.core.logic import _fuzzy_group, fuzzy_and, fuzzy_or
+from sympy.core.numbers import NaN, Number
+from sympy.logic.boolalg import (And, BooleanTrue, BooleanFalse, conjuncts,
+    Equivalent, Implies, Not, Or)
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+from ..predicates.common import CommutativePredicate, IsTruePredicate
+
+
+class AskHandler:
+    """Base class that all Ask Handlers must inherit."""
+    def __new__(cls, *args, **kwargs):
+        sympy_deprecation_warning(
+            """
+            The AskHandler system is deprecated. The AskHandler class should
+            be replaced with the multipledispatch handler of Predicate
+            """,
+            deprecated_since_version="1.8",
+            active_deprecations_target='deprecated-askhandler',
+        )
+        return super().__new__(cls, *args, **kwargs)
+
+
+class CommonHandler(AskHandler):
+    # Deprecated
+    """Defines some useful methods common to most Handlers. """
+
+    @staticmethod
+    def AlwaysTrue(expr, assumptions):
+        return True
+
+    @staticmethod
+    def AlwaysFalse(expr, assumptions):
+        return False
+
+    @staticmethod
+    def AlwaysNone(expr, assumptions):
+        return None
+
+    NaN = AlwaysFalse
+
+
+# CommutativePredicate
+
+@CommutativePredicate.register(Symbol)
+def _(expr, assumptions):
+    """Objects are expected to be commutative unless otherwise stated"""
+    assumps = conjuncts(assumptions)
+    if expr.is_commutative is not None:
+        return expr.is_commutative and not ~Q.commutative(expr) in assumps
+    if Q.commutative(expr) in assumps:
+        return True
+    elif ~Q.commutative(expr) in assumps:
+        return False
+    return True
+
+@CommutativePredicate.register(Basic)
+def _(expr, assumptions):
+    for arg in expr.args:
+        if not ask(Q.commutative(arg), assumptions):
+            return False
+    return True
+
+@CommutativePredicate.register(Number)
+def _(expr, assumptions):
+    return True
+
+@CommutativePredicate.register(NaN)
+def _(expr, assumptions):
+    return True
+
+
+# IsTruePredicate
+
+@IsTruePredicate.register(bool)
+def _(expr, assumptions):
+    return expr
+
+@IsTruePredicate.register(BooleanTrue)
+def _(expr, assumptions):
+    return True
+
+@IsTruePredicate.register(BooleanFalse)
+def _(expr, assumptions):
+    return False
+
+@IsTruePredicate.register(AppliedPredicate)
+def _(expr, assumptions):
+    return ask(expr, assumptions)
+
+@IsTruePredicate.register(Not)
+def _(expr, assumptions):
+    arg = expr.args[0]
+    if arg.is_Symbol:
+        # symbol used as abstract boolean object
+        return None
+    value = ask(arg, assumptions=assumptions)
+    if value in (True, False):
+        return not value
+    else:
+        return None
+
+@IsTruePredicate.register(Or)
+def _(expr, assumptions):
+    result = False
+    for arg in expr.args:
+        p = ask(arg, assumptions=assumptions)
+        if p is True:
+            return True
+        if p is None:
+            result = None
+    return result
+
+@IsTruePredicate.register(And)
+def _(expr, assumptions):
+    result = True
+    for arg in expr.args:
+        p = ask(arg, assumptions=assumptions)
+        if p is False:
+            return False
+        if p is None:
+            result = None
+    return result
+
+@IsTruePredicate.register(Implies)
+def _(expr, assumptions):
+    p, q = expr.args
+    return ask(~p | q, assumptions=assumptions)
+
+@IsTruePredicate.register(Equivalent)
+def _(expr, assumptions):
+    p, q = expr.args
+    pt = ask(p, assumptions=assumptions)
+    if pt is None:
+        return None
+    qt = ask(q, assumptions=assumptions)
+    if qt is None:
+        return None
+    return pt == qt
+
+
+#### Helper methods
+def test_closed_group(expr, assumptions, key):
+    """
+    Test for membership in a group with respect
+    to the current operation.
+    """
+    return _fuzzy_group(
+        (ask(key(a), assumptions) for a in expr.args), quick_exit=True)
+
+def ask_all(*queries, assumptions):
+    return fuzzy_and(
+        (ask(query, assumptions) for query in queries))
+
+def ask_any(*queries, assumptions):
+    return fuzzy_or(
+        (ask(query, assumptions) for query in queries))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..3b20385360136629ea037eb7238c45b70ba57fd2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/matrices.py
@@ -0,0 +1,716 @@
+"""
+This module contains query handlers responsible for Matrices queries:
+Square, Symmetric, Invertible etc.
+"""
+
+from sympy.logic.boolalg import conjuncts
+from sympy.assumptions import Q, ask
+from sympy.assumptions.handlers import test_closed_group
+from sympy.matrices import MatrixBase
+from sympy.matrices.expressions import (BlockMatrix, BlockDiagMatrix, Determinant,
+    DiagMatrix, DiagonalMatrix, HadamardProduct, Identity, Inverse, MatAdd, MatMul,
+    MatPow, MatrixExpr, MatrixSlice, MatrixSymbol, OneMatrix, Trace, Transpose,
+    ZeroMatrix)
+from sympy.matrices.expressions.blockmatrix import reblock_2x2
+from sympy.matrices.expressions.factorizations import Factorization
+from sympy.matrices.expressions.fourier import DFT
+from sympy.core.logic import fuzzy_and
+from sympy.utilities.iterables import sift
+from sympy.core import Basic
+
+from ..predicates.matrices import (SquarePredicate, SymmetricPredicate,
+    InvertiblePredicate, OrthogonalPredicate, UnitaryPredicate,
+    FullRankPredicate, PositiveDefinitePredicate, UpperTriangularPredicate,
+    LowerTriangularPredicate, DiagonalPredicate, IntegerElementsPredicate,
+    RealElementsPredicate, ComplexElementsPredicate)
+
+
+def _Factorization(predicate, expr, assumptions):
+    if predicate in expr.predicates:
+        return True
+
+
+# SquarePredicate
+
+@SquarePredicate.register(MatrixExpr)
+def _(expr, assumptions):
+    return expr.shape[0] == expr.shape[1]
+
+
+# SymmetricPredicate
+
+@SymmetricPredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, mmul = expr.as_coeff_mmul()
+    if all(ask(Q.symmetric(arg), assumptions) for arg in mmul.args):
+        return True
+    # TODO: implement sathandlers system for the matrices.
+    # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric).
+    if ask(Q.diagonal(expr), assumptions):
+        return True
+    if len(mmul.args) >= 2 and mmul.args[0] == mmul.args[-1].T:
+        if len(mmul.args) == 2:
+            return True
+        return ask(Q.symmetric(MatMul(*mmul.args[1:-1])), assumptions)
+
+@SymmetricPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    non_negative = ask(~Q.negative(exp), assumptions)
+    if (non_negative or non_negative == False
+                        and ask(Q.invertible(base), assumptions)):
+        return ask(Q.symmetric(base), assumptions)
+    return None
+
+@SymmetricPredicate.register(MatAdd)
+def _(expr, assumptions):
+    return all(ask(Q.symmetric(arg), assumptions) for arg in expr.args)
+
+@SymmetricPredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if not expr.is_square:
+        return False
+    # TODO: implement sathandlers system for the matrices.
+    # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric).
+    if ask(Q.diagonal(expr), assumptions):
+        return True
+    if Q.symmetric(expr) in conjuncts(assumptions):
+        return True
+
+@SymmetricPredicate.register_many(OneMatrix, ZeroMatrix)
+def _(expr, assumptions):
+    return ask(Q.square(expr), assumptions)
+
+@SymmetricPredicate.register_many(Inverse, Transpose)
+def _(expr, assumptions):
+    return ask(Q.symmetric(expr.arg), assumptions)
+
+@SymmetricPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    # TODO: implement sathandlers system for the matrices.
+    # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric).
+    if ask(Q.diagonal(expr), assumptions):
+        return True
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.symmetric(expr.parent), assumptions)
+
+@SymmetricPredicate.register(Identity)
+def _(expr, assumptions):
+    return True
+
+
+# InvertiblePredicate
+
+@InvertiblePredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, mmul = expr.as_coeff_mmul()
+    if all(ask(Q.invertible(arg), assumptions) for arg in mmul.args):
+        return True
+    if any(ask(Q.invertible(arg), assumptions) is False
+            for arg in mmul.args):
+        return False
+
+@InvertiblePredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    if exp.is_negative == False:
+        return ask(Q.invertible(base), assumptions)
+    return None
+
+@InvertiblePredicate.register(MatAdd)
+def _(expr, assumptions):
+    return None
+
+@InvertiblePredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if not expr.is_square:
+        return False
+    if Q.invertible(expr) in conjuncts(assumptions):
+        return True
+
+@InvertiblePredicate.register_many(Identity, Inverse)
+def _(expr, assumptions):
+    return True
+
+@InvertiblePredicate.register(ZeroMatrix)
+def _(expr, assumptions):
+    return False
+
+@InvertiblePredicate.register(OneMatrix)
+def _(expr, assumptions):
+    return expr.shape[0] == 1 and expr.shape[1] == 1
+
+@InvertiblePredicate.register(Transpose)
+def _(expr, assumptions):
+    return ask(Q.invertible(expr.arg), assumptions)
+
+@InvertiblePredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.invertible(expr.parent), assumptions)
+
+@InvertiblePredicate.register(MatrixBase)
+def _(expr, assumptions):
+    if not expr.is_square:
+        return False
+    return expr.rank() == expr.rows
+
+@InvertiblePredicate.register(MatrixExpr)
+def _(expr, assumptions):
+    if not expr.is_square:
+        return False
+    return None
+
+@InvertiblePredicate.register(BlockMatrix)
+def _(expr, assumptions):
+    if not expr.is_square:
+        return False
+    if expr.blockshape == (1, 1):
+        return ask(Q.invertible(expr.blocks[0, 0]), assumptions)
+    expr = reblock_2x2(expr)
+    if expr.blockshape == (2, 2):
+        [[A, B], [C, D]] = expr.blocks.tolist()
+        if ask(Q.invertible(A), assumptions) == True:
+            invertible = ask(Q.invertible(D - C * A.I * B), assumptions)
+            if invertible is not None:
+                return invertible
+        if ask(Q.invertible(B), assumptions) == True:
+            invertible = ask(Q.invertible(C - D * B.I * A), assumptions)
+            if invertible is not None:
+                return invertible
+        if ask(Q.invertible(C), assumptions) == True:
+            invertible = ask(Q.invertible(B - A * C.I * D), assumptions)
+            if invertible is not None:
+                return invertible
+        if ask(Q.invertible(D), assumptions) == True:
+            invertible = ask(Q.invertible(A - B * D.I * C), assumptions)
+            if invertible is not None:
+                return invertible
+    return None
+
+@InvertiblePredicate.register(BlockDiagMatrix)
+def _(expr, assumptions):
+    if expr.rowblocksizes != expr.colblocksizes:
+        return None
+    return fuzzy_and([ask(Q.invertible(a), assumptions) for a in expr.diag])
+
+
+# OrthogonalPredicate
+
+@OrthogonalPredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, mmul = expr.as_coeff_mmul()
+    if (all(ask(Q.orthogonal(arg), assumptions) for arg in mmul.args) and
+            factor == 1):
+        return True
+    if any(ask(Q.invertible(arg), assumptions) is False
+            for arg in mmul.args):
+        return False
+
+@OrthogonalPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if int_exp:
+        return ask(Q.orthogonal(base), assumptions)
+    return None
+
+@OrthogonalPredicate.register(MatAdd)
+def _(expr, assumptions):
+    if (len(expr.args) == 1 and
+            ask(Q.orthogonal(expr.args[0]), assumptions)):
+        return True
+
+@OrthogonalPredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if (not expr.is_square or
+                    ask(Q.invertible(expr), assumptions) is False):
+        return False
+    if Q.orthogonal(expr) in conjuncts(assumptions):
+        return True
+
+@OrthogonalPredicate.register(Identity)
+def _(expr, assumptions):
+    return True
+
+@OrthogonalPredicate.register(ZeroMatrix)
+def _(expr, assumptions):
+    return False
+
+@OrthogonalPredicate.register_many(Inverse, Transpose)
+def _(expr, assumptions):
+    return ask(Q.orthogonal(expr.arg), assumptions)
+
+@OrthogonalPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.orthogonal(expr.parent), assumptions)
+
+@OrthogonalPredicate.register(Factorization)
+def _(expr, assumptions):
+    return _Factorization(Q.orthogonal, expr, assumptions)
+
+
+# UnitaryPredicate
+
+@UnitaryPredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, mmul = expr.as_coeff_mmul()
+    if (all(ask(Q.unitary(arg), assumptions) for arg in mmul.args) and
+            abs(factor) == 1):
+        return True
+    if any(ask(Q.invertible(arg), assumptions) is False
+            for arg in mmul.args):
+        return False
+
+@UnitaryPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if int_exp:
+        return ask(Q.unitary(base), assumptions)
+    return None
+
+@UnitaryPredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if (not expr.is_square or
+                    ask(Q.invertible(expr), assumptions) is False):
+        return False
+    if Q.unitary(expr) in conjuncts(assumptions):
+        return True
+
+@UnitaryPredicate.register_many(Inverse, Transpose)
+def _(expr, assumptions):
+    return ask(Q.unitary(expr.arg), assumptions)
+
+@UnitaryPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.unitary(expr.parent), assumptions)
+
+@UnitaryPredicate.register_many(DFT, Identity)
+def _(expr, assumptions):
+    return True
+
+@UnitaryPredicate.register(ZeroMatrix)
+def _(expr, assumptions):
+    return False
+
+@UnitaryPredicate.register(Factorization)
+def _(expr, assumptions):
+    return _Factorization(Q.unitary, expr, assumptions)
+
+
+# FullRankPredicate
+
+@FullRankPredicate.register(MatMul)
+def _(expr, assumptions):
+    if all(ask(Q.fullrank(arg), assumptions) for arg in expr.args):
+        return True
+
+@FullRankPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if int_exp and ask(~Q.negative(exp), assumptions):
+        return ask(Q.fullrank(base), assumptions)
+    return None
+
+@FullRankPredicate.register(Identity)
+def _(expr, assumptions):
+    return True
+
+@FullRankPredicate.register(ZeroMatrix)
+def _(expr, assumptions):
+    return False
+
+@FullRankPredicate.register(OneMatrix)
+def _(expr, assumptions):
+    return expr.shape[0] == 1 and expr.shape[1] == 1
+
+@FullRankPredicate.register_many(Inverse, Transpose)
+def _(expr, assumptions):
+    return ask(Q.fullrank(expr.arg), assumptions)
+
+@FullRankPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if ask(Q.orthogonal(expr.parent), assumptions):
+        return True
+
+
+# PositiveDefinitePredicate
+
+@PositiveDefinitePredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, mmul = expr.as_coeff_mmul()
+    if (all(ask(Q.positive_definite(arg), assumptions)
+            for arg in mmul.args) and factor > 0):
+        return True
+    if (len(mmul.args) >= 2
+            and mmul.args[0] == mmul.args[-1].T
+            and ask(Q.fullrank(mmul.args[0]), assumptions)):
+        return ask(Q.positive_definite(
+            MatMul(*mmul.args[1:-1])), assumptions)
+
+@PositiveDefinitePredicate.register(MatPow)
+def _(expr, assumptions):
+    # a power of a positive definite matrix is positive definite
+    if ask(Q.positive_definite(expr.args[0]), assumptions):
+        return True
+
+@PositiveDefinitePredicate.register(MatAdd)
+def _(expr, assumptions):
+    if all(ask(Q.positive_definite(arg), assumptions)
+            for arg in expr.args):
+        return True
+
+@PositiveDefinitePredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if not expr.is_square:
+        return False
+    if Q.positive_definite(expr) in conjuncts(assumptions):
+        return True
+
+@PositiveDefinitePredicate.register(Identity)
+def _(expr, assumptions):
+    return True
+
+@PositiveDefinitePredicate.register(ZeroMatrix)
+def _(expr, assumptions):
+    return False
+
+@PositiveDefinitePredicate.register(OneMatrix)
+def _(expr, assumptions):
+    return expr.shape[0] == 1 and expr.shape[1] == 1
+
+@PositiveDefinitePredicate.register_many(Inverse, Transpose)
+def _(expr, assumptions):
+    return ask(Q.positive_definite(expr.arg), assumptions)
+
+@PositiveDefinitePredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.positive_definite(expr.parent), assumptions)
+
+
+# UpperTriangularPredicate
+
+@UpperTriangularPredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, matrices = expr.as_coeff_matrices()
+    if all(ask(Q.upper_triangular(m), assumptions) for m in matrices):
+        return True
+
+@UpperTriangularPredicate.register(MatAdd)
+def _(expr, assumptions):
+    if all(ask(Q.upper_triangular(arg), assumptions) for arg in expr.args):
+        return True
+
+@UpperTriangularPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    non_negative = ask(~Q.negative(exp), assumptions)
+    if (non_negative or non_negative == False
+                        and ask(Q.invertible(base), assumptions)):
+        return ask(Q.upper_triangular(base), assumptions)
+    return None
+
+@UpperTriangularPredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if Q.upper_triangular(expr) in conjuncts(assumptions):
+        return True
+
+@UpperTriangularPredicate.register_many(Identity, ZeroMatrix)
+def _(expr, assumptions):
+    return True
+
+@UpperTriangularPredicate.register(OneMatrix)
+def _(expr, assumptions):
+    return expr.shape[0] == 1 and expr.shape[1] == 1
+
+@UpperTriangularPredicate.register(Transpose)
+def _(expr, assumptions):
+    return ask(Q.lower_triangular(expr.arg), assumptions)
+
+@UpperTriangularPredicate.register(Inverse)
+def _(expr, assumptions):
+    return ask(Q.upper_triangular(expr.arg), assumptions)
+
+@UpperTriangularPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.upper_triangular(expr.parent), assumptions)
+
+@UpperTriangularPredicate.register(Factorization)
+def _(expr, assumptions):
+    return _Factorization(Q.upper_triangular, expr, assumptions)
+
+# LowerTriangularPredicate
+
+@LowerTriangularPredicate.register(MatMul)
+def _(expr, assumptions):
+    factor, matrices = expr.as_coeff_matrices()
+    if all(ask(Q.lower_triangular(m), assumptions) for m in matrices):
+        return True
+
+@LowerTriangularPredicate.register(MatAdd)
+def _(expr, assumptions):
+    if all(ask(Q.lower_triangular(arg), assumptions) for arg in expr.args):
+        return True
+
+@LowerTriangularPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    non_negative = ask(~Q.negative(exp), assumptions)
+    if (non_negative or non_negative == False
+                        and ask(Q.invertible(base), assumptions)):
+        return ask(Q.lower_triangular(base), assumptions)
+    return None
+
+@LowerTriangularPredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if Q.lower_triangular(expr) in conjuncts(assumptions):
+        return True
+
+@LowerTriangularPredicate.register_many(Identity, ZeroMatrix)
+def _(expr, assumptions):
+    return True
+
+@LowerTriangularPredicate.register(OneMatrix)
+def _(expr, assumptions):
+    return expr.shape[0] == 1 and expr.shape[1] == 1
+
+@LowerTriangularPredicate.register(Transpose)
+def _(expr, assumptions):
+    return ask(Q.upper_triangular(expr.arg), assumptions)
+
+@LowerTriangularPredicate.register(Inverse)
+def _(expr, assumptions):
+    return ask(Q.lower_triangular(expr.arg), assumptions)
+
+@LowerTriangularPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.lower_triangular(expr.parent), assumptions)
+
+@LowerTriangularPredicate.register(Factorization)
+def _(expr, assumptions):
+    return _Factorization(Q.lower_triangular, expr, assumptions)
+
+
+# DiagonalPredicate
+
+def _is_empty_or_1x1(expr):
+    return expr.shape in ((0, 0), (1, 1))
+
+@DiagonalPredicate.register(MatMul)
+def _(expr, assumptions):
+    if _is_empty_or_1x1(expr):
+        return True
+    factor, matrices = expr.as_coeff_matrices()
+    if all(ask(Q.diagonal(m), assumptions) for m in matrices):
+        return True
+
+@DiagonalPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    non_negative = ask(~Q.negative(exp), assumptions)
+    if (non_negative or non_negative == False
+                        and ask(Q.invertible(base), assumptions)):
+        return ask(Q.diagonal(base), assumptions)
+    return None
+
+@DiagonalPredicate.register(MatAdd)
+def _(expr, assumptions):
+    if all(ask(Q.diagonal(arg), assumptions) for arg in expr.args):
+        return True
+
+@DiagonalPredicate.register(MatrixSymbol)
+def _(expr, assumptions):
+    if _is_empty_or_1x1(expr):
+        return True
+    if Q.diagonal(expr) in conjuncts(assumptions):
+        return True
+
+@DiagonalPredicate.register(OneMatrix)
+def _(expr, assumptions):
+    return expr.shape[0] == 1 and expr.shape[1] == 1
+
+@DiagonalPredicate.register_many(Inverse, Transpose)
+def _(expr, assumptions):
+    return ask(Q.diagonal(expr.arg), assumptions)
+
+@DiagonalPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    if _is_empty_or_1x1(expr):
+        return True
+    if not expr.on_diag:
+        return None
+    else:
+        return ask(Q.diagonal(expr.parent), assumptions)
+
+@DiagonalPredicate.register_many(DiagonalMatrix, DiagMatrix, Identity, ZeroMatrix)
+def _(expr, assumptions):
+    return True
+
+@DiagonalPredicate.register(Factorization)
+def _(expr, assumptions):
+    return _Factorization(Q.diagonal, expr, assumptions)
+
+
+# IntegerElementsPredicate
+
+def BM_elements(predicate, expr, assumptions):
+    """ Block Matrix elements. """
+    return all(ask(predicate(b), assumptions) for b in expr.blocks)
+
+def MS_elements(predicate, expr, assumptions):
+    """ Matrix Slice elements. """
+    return ask(predicate(expr.parent), assumptions)
+
+def MatMul_elements(matrix_predicate, scalar_predicate, expr, assumptions):
+    d = sift(expr.args, lambda x: isinstance(x, MatrixExpr))
+    factors, matrices = d[False], d[True]
+    return fuzzy_and([
+        test_closed_group(Basic(*factors), assumptions, scalar_predicate),
+        test_closed_group(Basic(*matrices), assumptions, matrix_predicate)])
+
+
+@IntegerElementsPredicate.register_many(Determinant, HadamardProduct, MatAdd,
+    Trace, Transpose)
+def _(expr, assumptions):
+    return test_closed_group(expr, assumptions, Q.integer_elements)
+
+@IntegerElementsPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    if exp.is_negative == False:
+        return ask(Q.integer_elements(base), assumptions)
+    return None
+
+@IntegerElementsPredicate.register_many(Identity, OneMatrix, ZeroMatrix)
+def _(expr, assumptions):
+    return True
+
+@IntegerElementsPredicate.register(MatMul)
+def _(expr, assumptions):
+    return MatMul_elements(Q.integer_elements, Q.integer, expr, assumptions)
+
+@IntegerElementsPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    return MS_elements(Q.integer_elements, expr, assumptions)
+
+@IntegerElementsPredicate.register(BlockMatrix)
+def _(expr, assumptions):
+    return BM_elements(Q.integer_elements, expr, assumptions)
+
+
+# RealElementsPredicate
+
+@RealElementsPredicate.register_many(Determinant, Factorization, HadamardProduct,
+    MatAdd, Trace, Transpose)
+def _(expr, assumptions):
+    return test_closed_group(expr, assumptions, Q.real_elements)
+
+@RealElementsPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    non_negative = ask(~Q.negative(exp), assumptions)
+    if (non_negative or non_negative == False
+                        and ask(Q.invertible(base), assumptions)):
+        return ask(Q.real_elements(base), assumptions)
+    return None
+
+@RealElementsPredicate.register(MatMul)
+def _(expr, assumptions):
+    return MatMul_elements(Q.real_elements, Q.real, expr, assumptions)
+
+@RealElementsPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    return MS_elements(Q.real_elements, expr, assumptions)
+
+@RealElementsPredicate.register(BlockMatrix)
+def _(expr, assumptions):
+    return BM_elements(Q.real_elements, expr, assumptions)
+
+
+# ComplexElementsPredicate
+
+@ComplexElementsPredicate.register_many(Determinant, Factorization, HadamardProduct,
+    Inverse, MatAdd, Trace, Transpose)
+def _(expr, assumptions):
+    return test_closed_group(expr, assumptions, Q.complex_elements)
+
+@ComplexElementsPredicate.register(MatPow)
+def _(expr, assumptions):
+    # only for integer powers
+    base, exp = expr.args
+    int_exp = ask(Q.integer(exp), assumptions)
+    if not int_exp:
+        return None
+    non_negative = ask(~Q.negative(exp), assumptions)
+    if (non_negative or non_negative == False
+                        and ask(Q.invertible(base), assumptions)):
+        return ask(Q.complex_elements(base), assumptions)
+    return None
+
+@ComplexElementsPredicate.register(MatMul)
+def _(expr, assumptions):
+    return MatMul_elements(Q.complex_elements, Q.complex, expr, assumptions)
+
+@ComplexElementsPredicate.register(MatrixSlice)
+def _(expr, assumptions):
+    return MS_elements(Q.complex_elements, expr, assumptions)
+
+@ComplexElementsPredicate.register(BlockMatrix)
+def _(expr, assumptions):
+    return BM_elements(Q.complex_elements, expr, assumptions)
+
+@ComplexElementsPredicate.register(DFT)
+def _(expr, assumptions):
+    return True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/ntheory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/ntheory.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfe63ba6467ea6863c6112c5e35bb3a78191a23e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/ntheory.py
@@ -0,0 +1,279 @@
+"""
+Handlers for keys related to number theory: prime, even, odd, etc.
+"""
+
+from sympy.assumptions import Q, ask
+from sympy.core import Add, Basic, Expr, Float, Mul, Pow, S
+from sympy.core.numbers import (ImaginaryUnit, Infinity, Integer, NaN,
+    NegativeInfinity, NumberSymbol, Rational, int_valued)
+from sympy.functions import Abs, im, re
+from sympy.ntheory import isprime
+
+from sympy.multipledispatch import MDNotImplementedError
+
+from ..predicates.ntheory import (PrimePredicate, CompositePredicate,
+    EvenPredicate, OddPredicate)
+
+
+# PrimePredicate
+
+def _PrimePredicate_number(expr, assumptions):
+    # helper method
+    exact = not expr.atoms(Float)
+    try:
+        i = int(expr.round())
+        if (expr - i).equals(0) is False:
+            raise TypeError
+    except TypeError:
+        return False
+    if exact:
+        return isprime(i)
+    # when not exact, we won't give a True or False
+    # since the number represents an approximate value
+
+@PrimePredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_prime
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@PrimePredicate.register(Basic)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _PrimePredicate_number(expr, assumptions)
+
+@PrimePredicate.register(Mul)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _PrimePredicate_number(expr, assumptions)
+    for arg in expr.args:
+        if not ask(Q.integer(arg), assumptions):
+            return None
+    for arg in expr.args:
+        if arg.is_number and arg.is_composite:
+            return False
+
+@PrimePredicate.register(Pow)
+def _(expr, assumptions):
+    """
+    Integer**Integer     -> !Prime
+    """
+    if expr.is_number:
+        return _PrimePredicate_number(expr, assumptions)
+    if ask(Q.integer(expr.exp), assumptions) and \
+            ask(Q.integer(expr.base), assumptions):
+        prime_base = ask(Q.prime(expr.base), assumptions)
+        if prime_base is False:
+            return False
+        is_exp_one = ask(Q.eq(expr.exp, 1), assumptions)
+        if is_exp_one is False:
+            return False
+        if prime_base is True and is_exp_one is True:
+            return True
+
+@PrimePredicate.register(Integer)
+def _(expr, assumptions):
+    return isprime(expr)
+
+@PrimePredicate.register_many(Rational, Infinity, NegativeInfinity, ImaginaryUnit)
+def _(expr, assumptions):
+    return False
+
+@PrimePredicate.register(Float)
+def _(expr, assumptions):
+    return _PrimePredicate_number(expr, assumptions)
+
+@PrimePredicate.register(NumberSymbol)
+def _(expr, assumptions):
+    return _PrimePredicate_number(expr, assumptions)
+
+@PrimePredicate.register(NaN)
+def _(expr, assumptions):
+    return None
+
+
+# CompositePredicate
+
+@CompositePredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_composite
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@CompositePredicate.register(Basic)
+def _(expr, assumptions):
+    _positive = ask(Q.positive(expr), assumptions)
+    if _positive:
+        _integer = ask(Q.integer(expr), assumptions)
+        if _integer:
+            _prime = ask(Q.prime(expr), assumptions)
+            if _prime is None:
+                return
+            # Positive integer which is not prime is not
+            # necessarily composite
+            _is_one = ask(Q.eq(expr, 1), assumptions)
+            if _is_one:
+                return False
+            if _is_one is None:
+                return None
+            return not _prime
+        else:
+            return _integer
+    else:
+        return _positive
+
+
+# EvenPredicate
+
+def _EvenPredicate_number(expr, assumptions):
+    # helper method
+    if isinstance(expr, (float, Float)):
+        if int_valued(expr):
+            return None
+        return False
+    try:
+        i = int(expr.round())
+    except TypeError:
+        return False
+    if not (expr - i).equals(0):
+        return False
+    return i % 2 == 0
+
+@EvenPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_even
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@EvenPredicate.register(Basic)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _EvenPredicate_number(expr, assumptions)
+
+@EvenPredicate.register(Mul)
+def _(expr, assumptions):
+    """
+    Even * Integer    -> Even
+    Even * Odd        -> Even
+    Integer * Odd     -> ?
+    Odd * Odd         -> Odd
+    Even * Even       -> Even
+    Integer * Integer -> Even if Integer + Integer = Odd
+    otherwise         -> ?
+    """
+    if expr.is_number:
+        return _EvenPredicate_number(expr, assumptions)
+    even, odd, irrational, acc = False, 0, False, 1
+    for arg in expr.args:
+        # check for all integers and at least one even
+        if ask(Q.integer(arg), assumptions):
+            if ask(Q.even(arg), assumptions):
+                even = True
+            elif ask(Q.odd(arg), assumptions):
+                odd += 1
+            elif not even and acc != 1:
+                if ask(Q.odd(acc + arg), assumptions):
+                    even = True
+        elif ask(Q.irrational(arg), assumptions):
+            # one irrational makes the result False
+            # two makes it undefined
+            if irrational:
+                break
+            irrational = True
+        else:
+            break
+        acc = arg
+    else:
+        if irrational:
+            return False
+        if even:
+            return True
+        if odd == len(expr.args):
+            return False
+
+@EvenPredicate.register(Add)
+def _(expr, assumptions):
+    """
+    Even + Odd  -> Odd
+    Even + Even -> Even
+    Odd  + Odd  -> Even
+
+    """
+    if expr.is_number:
+        return _EvenPredicate_number(expr, assumptions)
+    _result = True
+    for arg in expr.args:
+        if ask(Q.even(arg), assumptions):
+            pass
+        elif ask(Q.odd(arg), assumptions):
+            _result = not _result
+        else:
+            break
+    else:
+        return _result
+
+@EvenPredicate.register(Pow)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _EvenPredicate_number(expr, assumptions)
+    if ask(Q.integer(expr.exp), assumptions):
+        if ask(Q.positive(expr.exp), assumptions):
+            return ask(Q.even(expr.base), assumptions)
+        elif ask(~Q.negative(expr.exp) & Q.odd(expr.base), assumptions):
+            return False
+        elif expr.base is S.NegativeOne:
+            return False
+
+@EvenPredicate.register(Integer)
+def _(expr, assumptions):
+    return not bool(expr.p & 1)
+
+@EvenPredicate.register_many(Rational, Infinity, NegativeInfinity, ImaginaryUnit)
+def _(expr, assumptions):
+    return False
+
+@EvenPredicate.register(NumberSymbol)
+def _(expr, assumptions):
+    return _EvenPredicate_number(expr, assumptions)
+
+@EvenPredicate.register(Abs)
+def _(expr, assumptions):
+    if ask(Q.real(expr.args[0]), assumptions):
+        return ask(Q.even(expr.args[0]), assumptions)
+
+@EvenPredicate.register(re)
+def _(expr, assumptions):
+    if ask(Q.real(expr.args[0]), assumptions):
+        return ask(Q.even(expr.args[0]), assumptions)
+
+@EvenPredicate.register(im)
+def _(expr, assumptions):
+    if ask(Q.real(expr.args[0]), assumptions):
+        return True
+
+@EvenPredicate.register(NaN)
+def _(expr, assumptions):
+    return None
+
+
+# OddPredicate
+
+@OddPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_odd
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@OddPredicate.register(Basic)
+def _(expr, assumptions):
+    _integer = ask(Q.integer(expr), assumptions)
+    if _integer:
+        _even = ask(Q.even(expr), assumptions)
+        if _even is None:
+            return None
+        return not _even
+    return _integer
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/order.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/order.py
new file mode 100644
index 0000000000000000000000000000000000000000..24a8bae7f30777f62a1bec0579d58b9875143679
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/order.py
@@ -0,0 +1,440 @@
+"""
+Handlers related to order relations: positive, negative, etc.
+"""
+
+from sympy.assumptions import Q, ask
+from sympy.core import Add, Basic, Expr, Mul, Pow, S
+from sympy.core.logic import fuzzy_not, fuzzy_and, fuzzy_or
+from sympy.core.numbers import E, ImaginaryUnit, NaN, I, pi
+from sympy.functions import Abs, acos, acot, asin, atan, exp, factorial, log
+from sympy.matrices import Determinant, Trace
+from sympy.matrices.expressions.matexpr import MatrixElement
+
+from sympy.multipledispatch import MDNotImplementedError
+
+from ..predicates.order import (NegativePredicate, NonNegativePredicate,
+    NonZeroPredicate, ZeroPredicate, NonPositivePredicate, PositivePredicate,
+    ExtendedNegativePredicate, ExtendedNonNegativePredicate,
+    ExtendedNonPositivePredicate, ExtendedNonZeroPredicate,
+    ExtendedPositivePredicate,)
+
+
+# NegativePredicate
+
+def _NegativePredicate_number(expr, assumptions):
+    r, i = expr.as_real_imag()
+
+    if r == S.NaN or i == S.NaN:
+        return None
+
+    # If the imaginary part can symbolically be shown to be zero then
+    # we just evaluate the real part; otherwise we evaluate the imaginary
+    # part to see if it actually evaluates to zero and if it does then
+    # we make the comparison between the real part and zero.
+    if not i:
+        r = r.evalf(2)
+        if r._prec != 1:
+            return r < 0
+    else:
+        i = i.evalf(2)
+        if i._prec != 1:
+            if i != 0:
+                return False
+            r = r.evalf(2)
+            if r._prec != 1:
+                return r < 0
+
+@NegativePredicate.register(Basic)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _NegativePredicate_number(expr, assumptions)
+
+@NegativePredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_negative
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@NegativePredicate.register(Add)
+def _(expr, assumptions):
+    """
+    Positive + Positive -> Positive,
+    Negative + Negative -> Negative
+    """
+    if expr.is_number:
+        return _NegativePredicate_number(expr, assumptions)
+
+    r = ask(Q.real(expr), assumptions)
+    if r is not True:
+        return r
+
+    nonpos = 0
+    for arg in expr.args:
+        if ask(Q.negative(arg), assumptions) is not True:
+            if ask(Q.positive(arg), assumptions) is False:
+                nonpos += 1
+            else:
+                break
+    else:
+        if nonpos < len(expr.args):
+            return True
+
+@NegativePredicate.register(Mul)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _NegativePredicate_number(expr, assumptions)
+    result = None
+    for arg in expr.args:
+        if result is None:
+            result = False
+        if ask(Q.negative(arg), assumptions):
+            result = not result
+        elif ask(Q.positive(arg), assumptions):
+            pass
+        else:
+            return
+    return result
+
+@NegativePredicate.register(Pow)
+def _(expr, assumptions):
+    """
+    Real ** Even -> NonNegative
+    Real ** Odd  -> same_as_base
+    NonNegative ** Positive -> NonNegative
+    """
+    if expr.base == E:
+        # Exponential is always positive:
+        if ask(Q.real(expr.exp), assumptions):
+            return False
+        return
+
+    if expr.is_number:
+        return _NegativePredicate_number(expr, assumptions)
+    if ask(Q.real(expr.base), assumptions):
+        if ask(Q.positive(expr.base), assumptions):
+            if ask(Q.real(expr.exp), assumptions):
+                return False
+        if ask(Q.even(expr.exp), assumptions):
+            return False
+        if ask(Q.odd(expr.exp), assumptions):
+            return ask(Q.negative(expr.base), assumptions)
+
+@NegativePredicate.register_many(Abs, ImaginaryUnit)
+def _(expr, assumptions):
+    return False
+
+@NegativePredicate.register(exp)
+def _(expr, assumptions):
+    if ask(Q.real(expr.exp), assumptions):
+        return False
+    raise MDNotImplementedError
+
+
+# NonNegativePredicate
+
+@NonNegativePredicate.register(Basic)
+def _(expr, assumptions):
+    if expr.is_number:
+        notnegative = fuzzy_not(_NegativePredicate_number(expr, assumptions))
+        if notnegative:
+            return ask(Q.real(expr), assumptions)
+        else:
+            return notnegative
+
+@NonNegativePredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_nonnegative
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+
+# NonZeroPredicate
+
+@NonZeroPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_nonzero
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@NonZeroPredicate.register(Basic)
+def _(expr, assumptions):
+    if ask(Q.real(expr)) is False:
+        return False
+    if expr.is_number:
+        # if there are no symbols just evalf
+        i = expr.evalf(2)
+        def nonz(i):
+            if i._prec != 1:
+                return i != 0
+        return fuzzy_or(nonz(i) for i in i.as_real_imag())
+
+@NonZeroPredicate.register(Add)
+def _(expr, assumptions):
+    if all(ask(Q.positive(x), assumptions) for x in expr.args) \
+            or all(ask(Q.negative(x), assumptions) for x in expr.args):
+        return True
+
+@NonZeroPredicate.register(Mul)
+def _(expr, assumptions):
+    for arg in expr.args:
+        result = ask(Q.nonzero(arg), assumptions)
+        if result:
+            continue
+        return result
+    return True
+
+@NonZeroPredicate.register(Pow)
+def _(expr, assumptions):
+    return ask(Q.nonzero(expr.base), assumptions)
+
+@NonZeroPredicate.register(Abs)
+def _(expr, assumptions):
+    return ask(Q.nonzero(expr.args[0]), assumptions)
+
+@NonZeroPredicate.register(NaN)
+def _(expr, assumptions):
+    return None
+
+
+# ZeroPredicate
+
+@ZeroPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_zero
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@ZeroPredicate.register(Basic)
+def _(expr, assumptions):
+    return fuzzy_and([fuzzy_not(ask(Q.nonzero(expr), assumptions)),
+        ask(Q.real(expr), assumptions)])
+
+@ZeroPredicate.register(Mul)
+def _(expr, assumptions):
+    # TODO: This should be deducible from the nonzero handler
+    return fuzzy_or(ask(Q.zero(arg), assumptions) for arg in expr.args)
+
+
+# NonPositivePredicate
+
+@NonPositivePredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_nonpositive
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@NonPositivePredicate.register(Basic)
+def _(expr, assumptions):
+    if expr.is_number:
+        notpositive = fuzzy_not(_PositivePredicate_number(expr, assumptions))
+        if notpositive:
+            return ask(Q.real(expr), assumptions)
+        else:
+            return notpositive
+
+
+# PositivePredicate
+
+def _PositivePredicate_number(expr, assumptions):
+    r, i = expr.as_real_imag()
+    # If the imaginary part can symbolically be shown to be zero then
+    # we just evaluate the real part; otherwise we evaluate the imaginary
+    # part to see if it actually evaluates to zero and if it does then
+    # we make the comparison between the real part and zero.
+    if not i:
+        r = r.evalf(2)
+        if r._prec != 1:
+            return r > 0
+    else:
+        i = i.evalf(2)
+        if i._prec != 1:
+            if i != 0:
+                return False
+            r = r.evalf(2)
+            if r._prec != 1:
+                return r > 0
+
+@PositivePredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_positive
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@PositivePredicate.register(Basic)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _PositivePredicate_number(expr, assumptions)
+
+@PositivePredicate.register(Mul)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _PositivePredicate_number(expr, assumptions)
+    result = True
+    for arg in expr.args:
+        if ask(Q.positive(arg), assumptions):
+            continue
+        elif ask(Q.negative(arg), assumptions):
+            result = result ^ True
+        else:
+            return
+    return result
+
+@PositivePredicate.register(Add)
+def _(expr, assumptions):
+    if expr.is_number:
+        return _PositivePredicate_number(expr, assumptions)
+
+    r = ask(Q.real(expr), assumptions)
+    if r is not True:
+        return r
+
+    nonneg = 0
+    for arg in expr.args:
+        if ask(Q.positive(arg), assumptions) is not True:
+            if ask(Q.negative(arg), assumptions) is False:
+                nonneg += 1
+            else:
+                break
+    else:
+        if nonneg < len(expr.args):
+            return True
+
+@PositivePredicate.register(Pow)
+def _(expr, assumptions):
+    if expr.base == E:
+        if ask(Q.real(expr.exp), assumptions):
+            return True
+        if ask(Q.imaginary(expr.exp), assumptions):
+            return ask(Q.even(expr.exp/(I*pi)), assumptions)
+        return
+
+    if expr.is_number:
+        return _PositivePredicate_number(expr, assumptions)
+    if ask(Q.positive(expr.base), assumptions):
+        if ask(Q.real(expr.exp), assumptions):
+            return True
+    if ask(Q.negative(expr.base), assumptions):
+        if ask(Q.even(expr.exp), assumptions):
+            return True
+        if ask(Q.odd(expr.exp), assumptions):
+            return False
+
+@PositivePredicate.register(exp)
+def _(expr, assumptions):
+    if ask(Q.real(expr.exp), assumptions):
+        return True
+    if ask(Q.imaginary(expr.exp), assumptions):
+        return ask(Q.even(expr.exp/(I*pi)), assumptions)
+
+@PositivePredicate.register(log)
+def _(expr, assumptions):
+    r = ask(Q.real(expr.args[0]), assumptions)
+    if r is not True:
+        return r
+    if ask(Q.positive(expr.args[0] - 1), assumptions):
+        return True
+    if ask(Q.negative(expr.args[0] - 1), assumptions):
+        return False
+
+@PositivePredicate.register(factorial)
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.integer(x) & Q.positive(x), assumptions):
+            return True
+
+@PositivePredicate.register(ImaginaryUnit)
+def _(expr, assumptions):
+    return False
+
+@PositivePredicate.register(Abs)
+def _(expr, assumptions):
+    return ask(Q.nonzero(expr), assumptions)
+
+@PositivePredicate.register(Trace)
+def _(expr, assumptions):
+    if ask(Q.positive_definite(expr.arg), assumptions):
+        return True
+
+@PositivePredicate.register(Determinant)
+def _(expr, assumptions):
+    if ask(Q.positive_definite(expr.arg), assumptions):
+        return True
+
+@PositivePredicate.register(MatrixElement)
+def _(expr, assumptions):
+    if (expr.i == expr.j
+            and ask(Q.positive_definite(expr.parent), assumptions)):
+        return True
+
+@PositivePredicate.register(atan)
+def _(expr, assumptions):
+    return ask(Q.positive(expr.args[0]), assumptions)
+
+@PositivePredicate.register(asin)
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.positive(x) & Q.nonpositive(x - 1), assumptions):
+        return True
+    if ask(Q.negative(x) & Q.nonnegative(x + 1), assumptions):
+        return False
+
+@PositivePredicate.register(acos)
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.nonpositive(x - 1) & Q.nonnegative(x + 1), assumptions):
+        return True
+
+@PositivePredicate.register(acot)
+def _(expr, assumptions):
+    return ask(Q.real(expr.args[0]), assumptions)
+
+@PositivePredicate.register(NaN)
+def _(expr, assumptions):
+    return None
+
+
+# ExtendedNegativePredicate
+
+@ExtendedNegativePredicate.register(object)
+def _(expr, assumptions):
+    return ask(Q.negative(expr) | Q.negative_infinite(expr), assumptions)
+
+
+# ExtendedPositivePredicate
+
+@ExtendedPositivePredicate.register(object)
+def _(expr, assumptions):
+    return ask(Q.positive(expr) | Q.positive_infinite(expr), assumptions)
+
+
+# ExtendedNonZeroPredicate
+
+@ExtendedNonZeroPredicate.register(object)
+def _(expr, assumptions):
+    return ask(
+        Q.negative_infinite(expr) | Q.negative(expr) | Q.positive(expr) | Q.positive_infinite(expr),
+        assumptions)
+
+
+# ExtendedNonPositivePredicate
+
+@ExtendedNonPositivePredicate.register(object)
+def _(expr, assumptions):
+    return ask(
+        Q.negative_infinite(expr) | Q.negative(expr) | Q.zero(expr),
+        assumptions)
+
+
+# ExtendedNonNegativePredicate
+
+@ExtendedNonNegativePredicate.register(object)
+def _(expr, assumptions):
+    return ask(
+        Q.zero(expr) | Q.positive(expr) | Q.positive_infinite(expr),
+        assumptions)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/sets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/sets.py
new file mode 100644
index 0000000000000000000000000000000000000000..7a13ed9bf99c5b0ffc4f32fd55cb60c2c15ab836
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/handlers/sets.py
@@ -0,0 +1,816 @@
+"""
+Handlers for predicates related to set membership: integer, rational, etc.
+"""
+
+from sympy.assumptions import Q, ask
+from sympy.core import Add, Basic, Expr, Mul, Pow, S
+from sympy.core.numbers import (AlgebraicNumber, ComplexInfinity, Exp1, Float,
+    GoldenRatio, ImaginaryUnit, Infinity, Integer, NaN, NegativeInfinity,
+    Number, NumberSymbol, Pi, pi, Rational, TribonacciConstant, E)
+from sympy.core.logic import fuzzy_bool
+from sympy.functions import (Abs, acos, acot, asin, atan, cos, cot, exp, im,
+    log, re, sin, tan)
+from sympy.core.numbers import I
+from sympy.core.relational import Eq
+from sympy.functions.elementary.complexes import conjugate
+from sympy.matrices import Determinant, MatrixBase, Trace
+from sympy.matrices.expressions.matexpr import MatrixElement
+
+from sympy.multipledispatch import MDNotImplementedError
+
+from .common import test_closed_group, ask_all, ask_any
+from ..predicates.sets import (IntegerPredicate, RationalPredicate,
+    IrrationalPredicate, RealPredicate, ExtendedRealPredicate,
+    HermitianPredicate, ComplexPredicate, ImaginaryPredicate,
+    AntihermitianPredicate, AlgebraicPredicate)
+
+
+# IntegerPredicate
+
+def _IntegerPredicate_number(expr, assumptions):
+    # helper function
+        try:
+            i = int(expr.round())
+            if not (expr - i).equals(0):
+                raise TypeError
+            return True
+        except TypeError:
+            return False
+
+@IntegerPredicate.register_many(int, Integer) # type:ignore
+def _(expr, assumptions):
+    return True
+
+@IntegerPredicate.register_many(Exp1, GoldenRatio, ImaginaryUnit, Infinity,
+        NegativeInfinity, Pi, Rational, TribonacciConstant)
+def _(expr, assumptions):
+    return False
+
+@IntegerPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_integer
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@IntegerPredicate.register(Add)
+def _(expr, assumptions):
+    """
+    * Integer + Integer       -> Integer
+    * Integer + !Integer      -> !Integer
+    * !Integer + !Integer -> ?
+    """
+    if expr.is_number:
+        return _IntegerPredicate_number(expr, assumptions)
+    return test_closed_group(expr, assumptions, Q.integer)
+
+@IntegerPredicate.register(Pow)
+def _(expr,assumptions):
+    if expr.is_number:
+        return _IntegerPredicate_number(expr, assumptions)
+    if ask_all(~Q.zero(expr.base), Q.finite(expr.base), Q.zero(expr.exp), assumptions=assumptions):
+        return True
+    if ask_all(Q.integer(expr.base), Q.integer(expr.exp), assumptions=assumptions):
+        if ask_any(Q.positive(expr.exp), Q.nonnegative(expr.exp) & ~Q.zero(expr.base), Q.zero(expr.base-1), Q.zero(expr.base+1), assumptions=assumptions):
+            return True
+
+@IntegerPredicate.register(Mul)
+def _(expr, assumptions):
+    """
+    * Integer*Integer      -> Integer
+    * Integer*Irrational   -> !Integer
+    * Odd/Even             -> !Integer
+    * Integer*Rational     -> ?
+    """
+    if expr.is_number:
+        return _IntegerPredicate_number(expr, assumptions)
+    _output = True
+    for arg in expr.args:
+        if not ask(Q.integer(arg), assumptions):
+            if arg.is_Rational:
+                if arg.q == 2:
+                    return ask(Q.even(2*expr), assumptions)
+                if ~(arg.q & 1):
+                    return None
+            elif ask(Q.irrational(arg), assumptions):
+                if _output:
+                    _output = False
+                else:
+                    return
+            else:
+                return
+
+    return _output
+
+@IntegerPredicate.register(Abs)
+def _(expr, assumptions):
+    if ask(Q.integer(expr.args[0]), assumptions):
+        return True
+
+@IntegerPredicate.register_many(Determinant, MatrixElement, Trace)
+def _(expr, assumptions):
+    return ask(Q.integer_elements(expr.args[0]), assumptions)
+
+
+# RationalPredicate
+
+@RationalPredicate.register(Rational)
+def _(expr, assumptions):
+    return True
+
+@RationalPredicate.register(Float)
+def _(expr, assumptions):
+    return None
+
+@RationalPredicate.register_many(Exp1, GoldenRatio, ImaginaryUnit, Infinity,
+    NegativeInfinity, Pi, TribonacciConstant)
+def _(expr, assumptions):
+    return False
+
+@RationalPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_rational
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@RationalPredicate.register_many(Add, Mul)
+def _(expr, assumptions):
+    """
+    * Rational + Rational     -> Rational
+    * Rational + !Rational    -> !Rational
+    * !Rational + !Rational   -> ?
+    """
+    if expr.is_number:
+        if expr.as_real_imag()[1]:
+            return False
+    return test_closed_group(expr, assumptions, Q.rational)
+
+@RationalPredicate.register(Pow)
+def _(expr, assumptions):
+    """
+    * Rational ** Integer      -> Rational
+    * Irrational ** Rational   -> Irrational
+    * Rational ** Irrational   -> ?
+    """
+    if expr.base == E:
+        x = expr.exp
+        if ask(Q.rational(x), assumptions):
+            return ask(Q.zero(x), assumptions)
+        return
+
+    is_exp_integer = ask(Q.integer(expr.exp), assumptions)
+    if is_exp_integer:
+        is_base_rational = ask(Q.rational(expr.base),assumptions)
+        if is_base_rational:
+            is_base_zero = ask(Q.zero(expr.base),assumptions)
+            if is_base_zero is False:
+                return True
+            if is_base_zero and ask(Q.positive(expr.exp)):
+                return True
+        if ask(Q.algebraic(expr.base),assumptions) is False:
+            return ask(Q.zero(expr.exp), assumptions)
+        if ask(Q.irrational(expr.base),assumptions) and ask(Q.eq(expr.exp,-1)):
+            return False
+        return
+    elif ask(Q.rational(expr.exp), assumptions):
+        if ask(Q.prime(expr.base), assumptions) and is_exp_integer is False:
+            return False
+        if ask(Q.zero(expr.base)) and ask(Q.positive(expr.exp)):
+            return True
+        if ask(Q.eq(expr.base,1)):
+            return True
+
+@RationalPredicate.register_many(asin, atan, cos, sin, tan)
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.rational(x), assumptions):
+        return ask(~Q.nonzero(x), assumptions)
+
+@RationalPredicate.register(exp)
+def _(expr, assumptions):
+    x = expr.exp
+    if ask(Q.rational(x), assumptions):
+        return ask(~Q.nonzero(x), assumptions)
+
+@RationalPredicate.register_many(acot, cot)
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.rational(x), assumptions):
+        return False
+
+@RationalPredicate.register_many(acos, log)
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.rational(x), assumptions):
+        return ask(~Q.nonzero(x - 1), assumptions)
+
+
+# IrrationalPredicate
+
+@IrrationalPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_irrational
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@IrrationalPredicate.register(Basic)
+def _(expr, assumptions):
+    _real = ask(Q.real(expr), assumptions)
+    if _real:
+        _rational = ask(Q.rational(expr), assumptions)
+        if _rational is None:
+            return None
+        return not _rational
+    else:
+        return _real
+
+
+# RealPredicate
+
+def _RealPredicate_number(expr, assumptions):
+    # let as_real_imag() work first since the expression may
+    # be simpler to evaluate
+    i = expr.as_real_imag()[1].evalf(2)
+    if i._prec != 1:
+        return not i
+    # allow None to be returned if we couldn't show for sure
+    # that i was 0
+
+@RealPredicate.register_many(Abs, Exp1, Float, GoldenRatio, im, Pi, Rational,
+    re, TribonacciConstant)
+def _(expr, assumptions):
+    return True
+
+@RealPredicate.register_many(ImaginaryUnit, Infinity, NegativeInfinity)
+def _(expr, assumptions):
+    return False
+
+@RealPredicate.register(Expr)
+def _(expr, assumptions):
+    ret = expr.is_real
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@RealPredicate.register(Add)
+def _(expr, assumptions):
+    """
+    * Real + Real              -> Real
+    * Real + (Complex & !Real) -> !Real
+    """
+    if expr.is_number:
+        return _RealPredicate_number(expr, assumptions)
+    return test_closed_group(expr, assumptions, Q.real)
+
+@RealPredicate.register(Mul)
+def _(expr, assumptions):
+    """
+    * Real*Real               -> Real
+    * Real*Imaginary          -> !Real
+    * Imaginary*Imaginary     -> Real
+    """
+    if expr.is_number:
+        return _RealPredicate_number(expr, assumptions)
+    result = True
+    for arg in expr.args:
+        if ask(Q.real(arg), assumptions):
+            pass
+        elif ask(Q.imaginary(arg), assumptions):
+            result = result ^ True
+        else:
+            break
+    else:
+        return result
+
+@RealPredicate.register(Pow)
+def _(expr, assumptions):
+    """
+    * Real**Integer              -> Real
+    * Positive**Real             -> Real
+    * Negative**Real             -> ?
+    * Real**(Integer/Even)       -> Real if base is nonnegative
+    * Real**(Integer/Odd)        -> Real
+    * Imaginary**(Integer/Even)  -> Real
+    * Imaginary**(Integer/Odd)   -> not Real
+    * Imaginary**Real            -> ? since Real could be 0 (giving real)
+                                    or 1 (giving imaginary)
+    * b**Imaginary               -> Real if log(b) is imaginary and b != 0
+                                    and exponent != integer multiple of
+                                    I*pi/log(b)
+    * Real**Real                 -> ? e.g. sqrt(-1) is imaginary and
+                                    sqrt(2) is not
+    """
+    if expr.is_number:
+        return _RealPredicate_number(expr, assumptions)
+
+    if expr.base == E:
+        return ask(
+            Q.integer(expr.exp/I/pi) | Q.real(expr.exp), assumptions
+        )
+
+    if expr.base.func == exp or (expr.base.is_Pow and expr.base.base == E):
+        if ask(Q.imaginary(expr.base.exp), assumptions):
+            if ask(Q.imaginary(expr.exp), assumptions):
+                return True
+        # If the i = (exp's arg)/(I*pi) is an integer or half-integer
+        # multiple of I*pi then 2*i will be an integer. In addition,
+        # exp(i*I*pi) = (-1)**i so the overall realness of the expr
+        # can be determined by replacing exp(i*I*pi) with (-1)**i.
+        i = expr.base.exp/I/pi
+        if ask(Q.integer(2*i), assumptions):
+            return ask(Q.real((S.NegativeOne**i)**expr.exp), assumptions)
+        return
+
+    if ask(Q.imaginary(expr.base), assumptions):
+        if ask(Q.integer(expr.exp), assumptions):
+            odd = ask(Q.odd(expr.exp), assumptions)
+            if odd is not None:
+                return not odd
+            return
+
+    if ask(Q.imaginary(expr.exp), assumptions):
+        imlog = ask(Q.imaginary(log(expr.base)), assumptions)
+        if imlog is not None:
+            # I**i -> real, log(I) is imag;
+            # (2*I)**i -> complex, log(2*I) is not imag
+            return imlog
+
+    if ask(Q.real(expr.base), assumptions):
+        if ask(Q.real(expr.exp), assumptions):
+            if ask(Q.zero(expr.base), assumptions) is not False:
+                if ask(Q.positive(expr.exp), assumptions):
+                    return True
+                return
+            if expr.exp.is_Rational and \
+                    ask(Q.even(expr.exp.q), assumptions):
+                return ask(Q.positive(expr.base), assumptions)
+            elif ask(Q.integer(expr.exp), assumptions):
+                return True
+            elif ask(Q.positive(expr.base), assumptions):
+                return True
+
+@RealPredicate.register_many(cos, sin)
+def _(expr, assumptions):
+    if ask(Q.real(expr.args[0]), assumptions):
+            return True
+
+@RealPredicate.register(exp)
+def _(expr, assumptions):
+    return ask(
+        Q.integer(expr.exp/I/pi) | Q.real(expr.exp), assumptions
+    )
+
+@RealPredicate.register(log)
+def _(expr, assumptions):
+    return ask(Q.positive(expr.args[0]), assumptions)
+
+@RealPredicate.register_many(Determinant, MatrixElement, Trace)
+def _(expr, assumptions):
+    return ask(Q.real_elements(expr.args[0]), assumptions)
+
+
+# ExtendedRealPredicate
+
+@ExtendedRealPredicate.register(object)
+def _(expr, assumptions):
+    return ask(Q.negative_infinite(expr)
+               | Q.negative(expr)
+               | Q.zero(expr)
+               | Q.positive(expr)
+               | Q.positive_infinite(expr),
+            assumptions)
+
+@ExtendedRealPredicate.register_many(Infinity, NegativeInfinity)
+def _(expr, assumptions):
+    return True
+
+@ExtendedRealPredicate.register_many(Add, Mul, Pow) # type:ignore
+def _(expr, assumptions):
+    return test_closed_group(expr, assumptions, Q.extended_real)
+
+
+# HermitianPredicate
+
+@HermitianPredicate.register(object) # type:ignore
+def _(expr, assumptions):
+    if isinstance(expr, MatrixBase):
+        return None
+    return ask(Q.real(expr), assumptions)
+
+@HermitianPredicate.register(Add) # type:ignore
+def _(expr, assumptions):
+    """
+    * Hermitian + Hermitian  -> Hermitian
+    * Hermitian + !Hermitian -> !Hermitian
+    """
+    if expr.is_number:
+        raise MDNotImplementedError
+    return test_closed_group(expr, assumptions, Q.hermitian)
+
+@HermitianPredicate.register(Mul) # type:ignore
+def _(expr, assumptions):
+    """
+    As long as there is at most only one noncommutative term:
+
+    * Hermitian*Hermitian         -> Hermitian
+    * Hermitian*Antihermitian     -> !Hermitian
+    * Antihermitian*Antihermitian -> Hermitian
+    """
+    if expr.is_number:
+        raise MDNotImplementedError
+    nccount = 0
+    result = True
+    for arg in expr.args:
+        if ask(Q.antihermitian(arg), assumptions):
+            result = result ^ True
+        elif not ask(Q.hermitian(arg), assumptions):
+            break
+        if ask(~Q.commutative(arg), assumptions):
+            nccount += 1
+            if nccount > 1:
+                break
+    else:
+        return result
+
+@HermitianPredicate.register(Pow) # type:ignore
+def _(expr, assumptions):
+    """
+    * Hermitian**Integer -> Hermitian
+    """
+    if expr.is_number:
+        raise MDNotImplementedError
+    if expr.base == E:
+        if ask(Q.hermitian(expr.exp), assumptions):
+            return True
+        raise MDNotImplementedError
+    if ask(Q.hermitian(expr.base), assumptions):
+        if ask(Q.integer(expr.exp), assumptions):
+            return True
+    raise MDNotImplementedError
+
+@HermitianPredicate.register_many(cos, sin) # type:ignore
+def _(expr, assumptions):
+    if ask(Q.hermitian(expr.args[0]), assumptions):
+        return True
+    raise MDNotImplementedError
+
+@HermitianPredicate.register(exp) # type:ignore
+def _(expr, assumptions):
+    if ask(Q.hermitian(expr.exp), assumptions):
+        return True
+    raise MDNotImplementedError
+
+@HermitianPredicate.register(MatrixBase) # type:ignore
+def _(mat, assumptions):
+    rows, cols = mat.shape
+    ret_val = True
+    for i in range(rows):
+        for j in range(i, cols):
+            cond = fuzzy_bool(Eq(mat[i, j], conjugate(mat[j, i])))
+            if cond is None:
+                ret_val = None
+            if cond == False:
+                return False
+    if ret_val is None:
+        raise MDNotImplementedError
+    return ret_val
+
+
+# ComplexPredicate
+
+@ComplexPredicate.register_many(Abs, cos, exp, im, ImaginaryUnit, log, Number, # type:ignore
+    NumberSymbol, re, sin)
+def _(expr, assumptions):
+    return True
+
+@ComplexPredicate.register_many(Infinity, NegativeInfinity) # type:ignore
+def _(expr, assumptions):
+    return False
+
+@ComplexPredicate.register(Expr) # type:ignore
+def _(expr, assumptions):
+    ret = expr.is_complex
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@ComplexPredicate.register_many(Add, Mul) # type:ignore
+def _(expr, assumptions):
+    return test_closed_group(expr, assumptions, Q.complex)
+
+@ComplexPredicate.register(Pow) # type:ignore
+def _(expr, assumptions):
+    if expr.base == E:
+        return True
+    return test_closed_group(expr, assumptions, Q.complex)
+
+@ComplexPredicate.register_many(Determinant, MatrixElement, Trace) # type:ignore
+def _(expr, assumptions):
+    return ask(Q.complex_elements(expr.args[0]), assumptions)
+
+@ComplexPredicate.register(NaN) # type:ignore
+def _(expr, assumptions):
+    return None
+
+
+# ImaginaryPredicate
+
+def _Imaginary_number(expr, assumptions):
+    # let as_real_imag() work first since the expression may
+    # be simpler to evaluate
+    r = expr.as_real_imag()[0].evalf(2)
+    if r._prec != 1:
+        return not r
+    # allow None to be returned if we couldn't show for sure
+    # that r was 0
+
+@ImaginaryPredicate.register(ImaginaryUnit) # type:ignore
+def _(expr, assumptions):
+    return True
+
+@ImaginaryPredicate.register(Expr) # type:ignore
+def _(expr, assumptions):
+    ret = expr.is_imaginary
+    if ret is None:
+        raise MDNotImplementedError
+    return ret
+
+@ImaginaryPredicate.register(Add) # type:ignore
+def _(expr, assumptions):
+    """
+    * Imaginary + Imaginary -> Imaginary
+    * Imaginary + Complex   -> ?
+    * Imaginary + Real      -> !Imaginary
+    """
+    if expr.is_number:
+        return _Imaginary_number(expr, assumptions)
+
+    reals = 0
+    for arg in expr.args:
+        if ask(Q.imaginary(arg), assumptions):
+            pass
+        elif ask(Q.real(arg), assumptions):
+            reals += 1
+        else:
+            break
+    else:
+        if reals == 0:
+            return True
+        if reals in (1, len(expr.args)):
+            # two reals could sum 0 thus giving an imaginary
+            return False
+
+@ImaginaryPredicate.register(Mul) # type:ignore
+def _(expr, assumptions):
+    """
+    * Real*Imaginary      -> Imaginary
+    * Imaginary*Imaginary -> Real
+    """
+    if expr.is_number:
+        return _Imaginary_number(expr, assumptions)
+    result = False
+    reals = 0
+    for arg in expr.args:
+        if ask(Q.imaginary(arg), assumptions):
+            result = result ^ True
+        elif not ask(Q.real(arg), assumptions):
+            break
+    else:
+        if reals == len(expr.args):
+            return False
+        return result
+
+@ImaginaryPredicate.register(Pow) # type:ignore
+def _(expr, assumptions):
+    """
+    * Imaginary**Odd        -> Imaginary
+    * Imaginary**Even       -> Real
+    * b**Imaginary          -> !Imaginary if exponent is an integer
+                               multiple of I*pi/log(b)
+    * Imaginary**Real       -> ?
+    * Positive**Real        -> Real
+    * Negative**Integer     -> Real
+    * Negative**(Integer/2) -> Imaginary
+    * Negative**Real        -> not Imaginary if exponent is not Rational
+    """
+    if expr.is_number:
+        return _Imaginary_number(expr, assumptions)
+
+    if expr.base == E:
+        a = expr.exp/I/pi
+        return ask(Q.integer(2*a) & ~Q.integer(a), assumptions)
+
+    if expr.base.func == exp or (expr.base.is_Pow and expr.base.base == E):
+        if ask(Q.imaginary(expr.base.exp), assumptions):
+            if ask(Q.imaginary(expr.exp), assumptions):
+                return False
+            i = expr.base.exp/I/pi
+            if ask(Q.integer(2*i), assumptions):
+                return ask(Q.imaginary((S.NegativeOne**i)**expr.exp), assumptions)
+
+    if ask(Q.imaginary(expr.base), assumptions):
+        if ask(Q.integer(expr.exp), assumptions):
+            odd = ask(Q.odd(expr.exp), assumptions)
+            if odd is not None:
+                return odd
+            return
+
+    if ask(Q.imaginary(expr.exp), assumptions):
+        imlog = ask(Q.imaginary(log(expr.base)), assumptions)
+        if imlog is not None:
+            # I**i -> real; (2*I)**i -> complex ==> not imaginary
+            return False
+
+    if ask(Q.real(expr.base) & Q.real(expr.exp), assumptions):
+        if ask(Q.positive(expr.base), assumptions):
+            return False
+        else:
+            rat = ask(Q.rational(expr.exp), assumptions)
+            if not rat:
+                return rat
+            if ask(Q.integer(expr.exp), assumptions):
+                return False
+            else:
+                half = ask(Q.integer(2*expr.exp), assumptions)
+                if half:
+                    return ask(Q.negative(expr.base), assumptions)
+                return half
+
+@ImaginaryPredicate.register(log) # type:ignore
+def _(expr, assumptions):
+    if ask(Q.real(expr.args[0]), assumptions):
+        if ask(Q.positive(expr.args[0]), assumptions):
+            return False
+        return
+    # XXX it should be enough to do
+    # return ask(Q.nonpositive(expr.args[0]), assumptions)
+    # but ask(Q.nonpositive(exp(x)), Q.imaginary(x)) -> None;
+    # it should return True since exp(x) will be either 0 or complex
+    if expr.args[0].func == exp or (expr.args[0].is_Pow and expr.args[0].base == E):
+        if expr.args[0].exp in [I, -I]:
+            return True
+    im = ask(Q.imaginary(expr.args[0]), assumptions)
+    if im is False:
+        return False
+
+@ImaginaryPredicate.register(exp) # type:ignore
+def _(expr, assumptions):
+    a = expr.exp/I/pi
+    return ask(Q.integer(2*a) & ~Q.integer(a), assumptions)
+
+@ImaginaryPredicate.register_many(Number, NumberSymbol) # type:ignore
+def _(expr, assumptions):
+    return not (expr.as_real_imag()[1] == 0)
+
+@ImaginaryPredicate.register(NaN) # type:ignore
+def _(expr, assumptions):
+    return None
+
+
+# AntihermitianPredicate
+
+@AntihermitianPredicate.register(object) # type:ignore
+def _(expr, assumptions):
+    if isinstance(expr, MatrixBase):
+        return None
+    if ask(Q.zero(expr), assumptions):
+        return True
+    return ask(Q.imaginary(expr), assumptions)
+
+@AntihermitianPredicate.register(Add) # type:ignore
+def _(expr, assumptions):
+    """
+    * Antihermitian + Antihermitian  -> Antihermitian
+    * Antihermitian + !Antihermitian -> !Antihermitian
+    """
+    if expr.is_number:
+        raise MDNotImplementedError
+    return test_closed_group(expr, assumptions, Q.antihermitian)
+
+@AntihermitianPredicate.register(Mul) # type:ignore
+def _(expr, assumptions):
+    """
+    As long as there is at most only one noncommutative term:
+
+    * Hermitian*Hermitian         -> !Antihermitian
+    * Hermitian*Antihermitian     -> Antihermitian
+    * Antihermitian*Antihermitian -> !Antihermitian
+    """
+    if expr.is_number:
+        raise MDNotImplementedError
+    nccount = 0
+    result = False
+    for arg in expr.args:
+        if ask(Q.antihermitian(arg), assumptions):
+            result = result ^ True
+        elif not ask(Q.hermitian(arg), assumptions):
+            break
+        if ask(~Q.commutative(arg), assumptions):
+            nccount += 1
+            if nccount > 1:
+                break
+    else:
+        return result
+
+@AntihermitianPredicate.register(Pow) # type:ignore
+def _(expr, assumptions):
+    """
+    * Hermitian**Integer  -> !Antihermitian
+    * Antihermitian**Even -> !Antihermitian
+    * Antihermitian**Odd  -> Antihermitian
+    """
+    if expr.is_number:
+        raise MDNotImplementedError
+    if ask(Q.hermitian(expr.base), assumptions):
+        if ask(Q.integer(expr.exp), assumptions):
+            return False
+    elif ask(Q.antihermitian(expr.base), assumptions):
+        if ask(Q.even(expr.exp), assumptions):
+            return False
+        elif ask(Q.odd(expr.exp), assumptions):
+            return True
+    raise MDNotImplementedError
+
+@AntihermitianPredicate.register(MatrixBase) # type:ignore
+def _(mat, assumptions):
+    rows, cols = mat.shape
+    ret_val = True
+    for i in range(rows):
+        for j in range(i, cols):
+            cond = fuzzy_bool(Eq(mat[i, j], -conjugate(mat[j, i])))
+            if cond is None:
+                ret_val = None
+            if cond == False:
+                return False
+    if ret_val is None:
+        raise MDNotImplementedError
+    return ret_val
+
+
+# AlgebraicPredicate
+
+@AlgebraicPredicate.register_many(AlgebraicNumber, Float, GoldenRatio, # type:ignore
+    ImaginaryUnit, TribonacciConstant)
+def _(expr, assumptions):
+    return True
+
+@AlgebraicPredicate.register_many(ComplexInfinity, Exp1, Infinity, # type:ignore
+    NegativeInfinity, Pi)
+def _(expr, assumptions):
+    return False
+
+@AlgebraicPredicate.register_many(Add, Mul) # type:ignore
+def _(expr, assumptions):
+    return test_closed_group(expr, assumptions, Q.algebraic)
+
+@AlgebraicPredicate.register(Pow) # type:ignore
+def _(expr, assumptions):
+    if expr.base == E:
+        if ask(Q.algebraic(expr.exp), assumptions):
+            return ask(~Q.nonzero(expr.exp), assumptions)
+        return
+    if expr.base == pi:
+        if ask(Q.integer(expr.exp), assumptions) and ask(Q.positive(expr.exp), assumptions):
+            return False
+        return
+    exp_rational = ask(Q.rational(expr.exp), assumptions)
+    base_algebraic = ask(Q.algebraic(expr.base), assumptions)
+    exp_algebraic = ask(Q.algebraic(expr.exp),assumptions)
+    if base_algebraic and exp_algebraic:
+        if exp_rational:
+            return True
+        # Check based on the Gelfond-Schneider theorem:
+        # If the base is algebraic and not equal to 0 or 1, and the exponent
+        # is irrational,then the result is transcendental.
+        if ask(Q.ne(expr.base,0) & Q.ne(expr.base,1)) and exp_rational is False:
+            return False
+
+@AlgebraicPredicate.register(Rational) # type:ignore
+def _(expr, assumptions):
+    return expr.q != 0
+
+@AlgebraicPredicate.register_many(asin, atan, cos, sin, tan) # type:ignore
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.algebraic(x), assumptions):
+        return ask(~Q.nonzero(x), assumptions)
+
+@AlgebraicPredicate.register(exp) # type:ignore
+def _(expr, assumptions):
+    x = expr.exp
+    if ask(Q.algebraic(x), assumptions):
+        return ask(~Q.nonzero(x), assumptions)
+
+@AlgebraicPredicate.register_many(acot, cot) # type:ignore
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.algebraic(x), assumptions):
+        return False
+
+@AlgebraicPredicate.register_many(acos, log) # type:ignore
+def _(expr, assumptions):
+    x = expr.args[0]
+    if ask(Q.algebraic(x), assumptions):
+        return ask(~Q.nonzero(x - 1), assumptions)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/lra_satask.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/lra_satask.py
new file mode 100644
index 0000000000000000000000000000000000000000..53afe3e5abe99109ec01a47f19f1a8a4c99c5628
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/lra_satask.py
@@ -0,0 +1,286 @@
+from sympy.assumptions.assume import global_assumptions
+from sympy.assumptions.cnf import CNF, EncodedCNF
+from sympy.assumptions.ask import Q
+from sympy.logic.inference import satisfiable
+from sympy.logic.algorithms.lra_theory import UnhandledInput, ALLOWED_PRED
+from sympy.matrices.kind import MatrixKind
+from sympy.core.kind import NumberKind
+from sympy.assumptions.assume import AppliedPredicate
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+
+
+def lra_satask(proposition, assumptions=True, context=global_assumptions):
+    """
+    Function to evaluate the proposition with assumptions using SAT algorithm
+    in conjunction with an Linear Real Arithmetic theory solver.
+
+    Used to handle inequalities. Should eventually be depreciated and combined
+    into satask, but infinity handling and other things need to be implemented
+    before that can happen.
+    """
+    props = CNF.from_prop(proposition)
+    _props = CNF.from_prop(~proposition)
+
+    cnf = CNF.from_prop(assumptions)
+    assumptions = EncodedCNF()
+    assumptions.from_cnf(cnf)
+
+    context_cnf = CNF()
+    if context:
+        context_cnf = context_cnf.extend(context)
+
+    assumptions.add_from_cnf(context_cnf)
+
+    return check_satisfiability(props, _props, assumptions)
+
+# Some predicates such as Q.prime can't be handled by lra_satask.
+# For example, (x > 0) & (x < 1) & Q.prime(x) is unsat but lra_satask would think it was sat.
+# WHITE_LIST is a list of predicates that can always be handled.
+WHITE_LIST = ALLOWED_PRED | {Q.positive, Q.negative, Q.zero, Q.nonzero, Q.nonpositive, Q.nonnegative,
+                                            Q.extended_positive, Q.extended_negative, Q.extended_nonpositive,
+                                            Q.extended_negative, Q.extended_nonzero, Q.negative_infinite,
+                                            Q.positive_infinite}
+
+
+def check_satisfiability(prop, _prop, factbase):
+    sat_true = factbase.copy()
+    sat_false = factbase.copy()
+    sat_true.add_from_cnf(prop)
+    sat_false.add_from_cnf(_prop)
+
+    all_pred, all_exprs = get_all_pred_and_expr_from_enc_cnf(sat_true)
+
+    for pred in all_pred:
+        if pred.function not in WHITE_LIST and pred.function != Q.ne:
+            raise UnhandledInput(f"LRASolver: {pred} is an unhandled predicate")
+    for expr in all_exprs:
+        if expr.kind == MatrixKind(NumberKind):
+            raise UnhandledInput(f"LRASolver: {expr} is of MatrixKind")
+        if expr == S.NaN:
+            raise UnhandledInput("LRASolver: nan")
+
+    # convert old assumptions into predicates and add them to sat_true and sat_false
+    # also check for unhandled predicates
+    for assm in extract_pred_from_old_assum(all_exprs):
+        n = len(sat_true.encoding)
+        if assm not in sat_true.encoding:
+            sat_true.encoding[assm] = n+1
+        sat_true.data.append([sat_true.encoding[assm]])
+
+        n = len(sat_false.encoding)
+        if assm not in sat_false.encoding:
+            sat_false.encoding[assm] = n+1
+        sat_false.data.append([sat_false.encoding[assm]])
+
+
+    sat_true = _preprocess(sat_true)
+    sat_false = _preprocess(sat_false)
+
+    can_be_true = satisfiable(sat_true, use_lra_theory=True) is not False
+    can_be_false = satisfiable(sat_false, use_lra_theory=True) is not False
+
+    if can_be_true and can_be_false:
+        return None
+
+    if can_be_true and not can_be_false:
+        return True
+
+    if not can_be_true and can_be_false:
+        return False
+
+    if not can_be_true and not can_be_false:
+        raise ValueError("Inconsistent assumptions")
+
+
+def _preprocess(enc_cnf):
+    """
+    Returns an encoded cnf with only Q.eq, Q.gt, Q.lt,
+    Q.ge, and Q.le predicate.
+
+    Converts every unequality into a disjunction of strict
+    inequalities. For example, x != 3 would become
+    x < 3 OR x > 3.
+
+    Also converts all negated Q.ne predicates into
+    equalities.
+    """
+
+    # loops through each literal in each clause
+    # to construct a new, preprocessed encodedCNF
+
+    enc_cnf = enc_cnf.copy()
+    cur_enc = 1
+    rev_encoding = {value: key for key, value in enc_cnf.encoding.items()}
+
+    new_encoding = {}
+    new_data = []
+    for clause in enc_cnf.data:
+        new_clause = []
+        for lit in clause:
+            if lit == 0:
+                new_clause.append(lit)
+                new_encoding[lit] = False
+                continue
+            prop = rev_encoding[abs(lit)]
+            negated = lit < 0
+            sign = (lit > 0) - (lit < 0)
+
+            prop = _pred_to_binrel(prop)
+
+            if not isinstance(prop, AppliedPredicate):
+                if prop not in new_encoding:
+                    new_encoding[prop] = cur_enc
+                    cur_enc += 1
+                lit = new_encoding[prop]
+                new_clause.append(sign*lit)
+                continue
+
+
+            if negated and prop.function == Q.eq:
+                negated = False
+                prop = Q.ne(*prop.arguments)
+
+            if prop.function == Q.ne:
+                arg1, arg2 = prop.arguments
+                if negated:
+                    new_prop = Q.eq(arg1, arg2)
+                    if new_prop not in new_encoding:
+                        new_encoding[new_prop] = cur_enc
+                        cur_enc += 1
+
+                    new_enc = new_encoding[new_prop]
+                    new_clause.append(new_enc)
+                    continue
+                else:
+                    new_props = (Q.gt(arg1, arg2), Q.lt(arg1, arg2))
+                    for new_prop in new_props:
+                        if new_prop not in new_encoding:
+                            new_encoding[new_prop] = cur_enc
+                            cur_enc += 1
+
+                        new_enc = new_encoding[new_prop]
+                        new_clause.append(new_enc)
+                    continue
+
+            if prop.function == Q.eq and negated:
+                assert False
+
+            if prop not in new_encoding:
+                new_encoding[prop] = cur_enc
+                cur_enc += 1
+            new_clause.append(new_encoding[prop]*sign)
+        new_data.append(new_clause)
+
+    assert len(new_encoding) >= cur_enc - 1
+
+    enc_cnf = EncodedCNF(new_data, new_encoding)
+    return enc_cnf
+
+
+def _pred_to_binrel(pred):
+    if not isinstance(pred, AppliedPredicate):
+        return pred
+
+    if pred.function in pred_to_pos_neg_zero:
+        f = pred_to_pos_neg_zero[pred.function]
+        if f is False:
+            return False
+        pred = f(pred.arguments[0])
+
+    if pred.function == Q.positive:
+        pred = Q.gt(pred.arguments[0], 0)
+    elif pred.function == Q.negative:
+        pred = Q.lt(pred.arguments[0], 0)
+    elif pred.function == Q.zero:
+        pred = Q.eq(pred.arguments[0], 0)
+    elif pred.function == Q.nonpositive:
+        pred = Q.le(pred.arguments[0], 0)
+    elif pred.function == Q.nonnegative:
+        pred = Q.ge(pred.arguments[0], 0)
+    elif pred.function == Q.nonzero:
+        pred = Q.ne(pred.arguments[0], 0)
+
+    return pred
+
+pred_to_pos_neg_zero = {
+    Q.extended_positive: Q.positive,
+    Q.extended_negative: Q.negative,
+    Q.extended_nonpositive: Q.nonpositive,
+    Q.extended_negative: Q.negative,
+    Q.extended_nonzero: Q.nonzero,
+    Q.negative_infinite: False,
+    Q.positive_infinite: False
+}
+
+def get_all_pred_and_expr_from_enc_cnf(enc_cnf):
+    all_exprs = set()
+    all_pred = set()
+    for pred in enc_cnf.encoding.keys():
+        if isinstance(pred, AppliedPredicate):
+            all_pred.add(pred)
+            all_exprs.update(pred.arguments)
+
+    return all_pred, all_exprs
+
+def extract_pred_from_old_assum(all_exprs):
+    """
+    Returns a list of relevant new assumption predicate
+    based on any old assumptions.
+
+    Raises an UnhandledInput exception if any of the assumptions are
+    unhandled.
+
+    Ignored predicate:
+    - commutative
+    - complex
+    - algebraic
+    - transcendental
+    - extended_real
+    - real
+    - all matrix predicate
+    - rational
+    - irrational
+
+    Example
+    =======
+    >>> from sympy.assumptions.lra_satask import extract_pred_from_old_assum
+    >>> from sympy import symbols
+    >>> x, y = symbols("x y", positive=True)
+    >>> extract_pred_from_old_assum([x, y, 2])
+    [Q.positive(x), Q.positive(y)]
+    """
+    ret = []
+    for expr in all_exprs:
+        if not hasattr(expr, "free_symbols"):
+            continue
+        if len(expr.free_symbols) == 0:
+            continue
+
+        if expr.is_real is not True:
+            raise UnhandledInput(f"LRASolver: {expr} must be real")
+        # test for I times imaginary variable; such expressions are considered real
+        if isinstance(expr, Mul) and any(arg.is_real is not True for arg in expr.args):
+            raise UnhandledInput(f"LRASolver: {expr} must be real")
+
+        if expr.is_integer == True and expr.is_zero != True:
+            raise UnhandledInput(f"LRASolver: {expr} is an integer")
+        if expr.is_integer == False:
+            raise UnhandledInput(f"LRASolver: {expr} can't be an integer")
+        if expr.is_rational == False:
+            raise UnhandledInput(f"LRASolver: {expr} is irational")
+
+        if expr.is_zero:
+            ret.append(Q.zero(expr))
+        elif expr.is_positive:
+            ret.append(Q.positive(expr))
+        elif expr.is_negative:
+            ret.append(Q.negative(expr))
+        elif expr.is_nonzero:
+            ret.append(Q.nonzero(expr))
+        elif expr.is_nonpositive:
+            ret.append(Q.nonpositive(expr))
+        elif expr.is_nonnegative:
+            ret.append(Q.nonnegative(expr))
+
+    return ret
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e294544bfdce13633ecff762ff42861aa12719f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/__init__.py
@@ -0,0 +1,5 @@
+"""
+Module to implement predicate classes.
+
+Class of every predicate registered to ``Q`` is defined here.
+"""
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/calculus.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/calculus.py
new file mode 100644
index 0000000000000000000000000000000000000000..f300703788683c07649ee3a0afd6e9d4eabd4567
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/calculus.py
@@ -0,0 +1,82 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+class FinitePredicate(Predicate):
+    """
+    Finite number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.finite(x)`` is true if ``x`` is a number but neither an infinity
+    nor a ``NaN``. In other words, ``ask(Q.finite(x))`` is true for all
+    numerical ``x`` having a bounded absolute value.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, S, oo, I, zoo
+    >>> from sympy.abc import x
+    >>> ask(Q.finite(oo))
+    False
+    >>> ask(Q.finite(-oo))
+    False
+    >>> ask(Q.finite(zoo))
+    False
+    >>> ask(Q.finite(1))
+    True
+    >>> ask(Q.finite(2 + 3*I))
+    True
+    >>> ask(Q.finite(x), Q.positive(x))
+    True
+    >>> print(ask(Q.finite(S.NaN)))
+    None
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Finite
+
+    """
+    name = 'finite'
+    handler = Dispatcher(
+        "FiniteHandler",
+        doc=("Handler for Q.finite. Test that an expression is bounded respect"
+        " to all its variables.")
+    )
+
+
+class InfinitePredicate(Predicate):
+    """
+    Infinite number predicate.
+
+    ``Q.infinite(x)`` is true iff the absolute value of ``x`` is
+    infinity.
+
+    """
+    # TODO: Add examples
+    name = 'infinite'
+    handler = Dispatcher(
+        "InfiniteHandler",
+        doc="""Handler for Q.infinite key."""
+    )
+
+
+class PositiveInfinitePredicate(Predicate):
+    """
+    Positive infinity predicate.
+
+    ``Q.positive_infinite(x)`` is true iff ``x`` is positive infinity ``oo``.
+    """
+    name = 'positive_infinite'
+    handler = Dispatcher("PositiveInfiniteHandler")
+
+
+class NegativeInfinitePredicate(Predicate):
+    """
+    Negative infinity predicate.
+
+    ``Q.negative_infinite(x)`` is true iff ``x`` is negative infinity ``-oo``.
+    """
+    name = 'negative_infinite'
+    handler = Dispatcher("NegativeInfiniteHandler")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/common.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/common.py
new file mode 100644
index 0000000000000000000000000000000000000000..a53892747131b03636abeb8f563c4f76cf3e281e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/common.py
@@ -0,0 +1,81 @@
+from sympy.assumptions import Predicate, AppliedPredicate, Q
+from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le
+from sympy.multipledispatch import Dispatcher
+
+
+class CommutativePredicate(Predicate):
+    """
+    Commutative predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.commutative(x))`` is true iff ``x`` commutes with any other
+    object with respect to multiplication operation.
+
+    """
+    # TODO: Add examples
+    name = 'commutative'
+    handler = Dispatcher("CommutativeHandler", doc="Handler for key 'commutative'.")
+
+
+binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le}
+
+class IsTruePredicate(Predicate):
+    """
+    Generic predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.is_true(x))`` is true iff ``x`` is true. This only makes
+    sense if ``x`` is a boolean object.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> from sympy.abc import x, y
+    >>> ask(Q.is_true(True))
+    True
+
+    Wrapping another applied predicate just returns the applied predicate.
+
+    >>> Q.is_true(Q.even(x))
+    Q.even(x)
+
+    Wrapping binary relation classes in SymPy core returns applied binary
+    relational predicates.
+
+    >>> from sympy import Eq, Gt
+    >>> Q.is_true(Eq(x, y))
+    Q.eq(x, y)
+    >>> Q.is_true(Gt(x, y))
+    Q.gt(x, y)
+
+    Notes
+    =====
+
+    This class is designed to wrap the boolean objects so that they can
+    behave as if they are applied predicates. Consequently, wrapping another
+    applied predicate is unnecessary and thus it just returns the argument.
+    Also, binary relation classes in SymPy core have binary predicates to
+    represent themselves and thus wrapping them with ``Q.is_true`` converts them
+    to these applied predicates.
+
+    """
+    name = 'is_true'
+    handler = Dispatcher(
+        "IsTrueHandler",
+        doc="Wrapper allowing to query the truth value of a boolean expression."
+    )
+
+    def __call__(self, arg):
+        # No need to wrap another predicate
+        if isinstance(arg, AppliedPredicate):
+            return arg
+        # Convert relational predicates instead of wrapping them
+        if getattr(arg, "is_Relational", False):
+            pred = binrelpreds[type(arg)]
+            return pred(*arg.args)
+        return super().__call__(arg)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..151e78c4ff345800e1d2f17973fb0591b8d379d2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/matrices.py
@@ -0,0 +1,511 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+class SquarePredicate(Predicate):
+    """
+    Square matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.square(x)`` is true iff ``x`` is a square matrix. A square matrix
+    is a matrix with the same number of rows and columns.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('X', 2, 3)
+    >>> ask(Q.square(X))
+    True
+    >>> ask(Q.square(Y))
+    False
+    >>> ask(Q.square(ZeroMatrix(3, 3)))
+    True
+    >>> ask(Q.square(Identity(3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Square_matrix
+
+    """
+    name = 'square'
+    handler = Dispatcher("SquareHandler", doc="Handler for Q.square.")
+
+
+class SymmetricPredicate(Predicate):
+    """
+    Symmetric matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.symmetric(x)`` is true iff ``x`` is a square matrix and is equal to
+    its transpose. Every square diagonal matrix is a symmetric matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.symmetric(X*Z), Q.symmetric(X) & Q.symmetric(Z))
+    True
+    >>> ask(Q.symmetric(X + Z), Q.symmetric(X) & Q.symmetric(Z))
+    True
+    >>> ask(Q.symmetric(Y))
+    False
+
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Symmetric_matrix
+
+    """
+    # TODO: Add handlers to make these keys work with
+    # actual matrices and add more examples in the docstring.
+    name = 'symmetric'
+    handler = Dispatcher("SymmetricHandler", doc="Handler for Q.symmetric.")
+
+
+class InvertiblePredicate(Predicate):
+    """
+    Invertible matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.invertible(x)`` is true iff ``x`` is an invertible matrix.
+    A square matrix is called invertible only if its determinant is 0.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.invertible(X*Y), Q.invertible(X))
+    False
+    >>> ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z))
+    True
+    >>> ask(Q.invertible(X), Q.fullrank(X) & Q.square(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Invertible_matrix
+
+    """
+    name = 'invertible'
+    handler = Dispatcher("InvertibleHandler", doc="Handler for Q.invertible.")
+
+
+class OrthogonalPredicate(Predicate):
+    """
+    Orthogonal matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.orthogonal(x)`` is true iff ``x`` is an orthogonal matrix.
+    A square matrix ``M`` is an orthogonal matrix if it satisfies
+    ``M^TM = MM^T = I`` where ``M^T`` is the transpose matrix of
+    ``M`` and ``I`` is an identity matrix. Note that an orthogonal
+    matrix is necessarily invertible.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.orthogonal(Y))
+    False
+    >>> ask(Q.orthogonal(X*Z*X), Q.orthogonal(X) & Q.orthogonal(Z))
+    True
+    >>> ask(Q.orthogonal(Identity(3)))
+    True
+    >>> ask(Q.invertible(X), Q.orthogonal(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Orthogonal_matrix
+
+    """
+    name = 'orthogonal'
+    handler = Dispatcher("OrthogonalHandler", doc="Handler for key 'orthogonal'.")
+
+
+class UnitaryPredicate(Predicate):
+    """
+    Unitary matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.unitary(x)`` is true iff ``x`` is a unitary matrix.
+    Unitary matrix is an analogue to orthogonal matrix. A square
+    matrix ``M`` with complex elements is unitary if :math:``M^TM = MM^T= I``
+    where :math:``M^T`` is the conjugate transpose matrix of ``M``.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.unitary(Y))
+    False
+    >>> ask(Q.unitary(X*Z*X), Q.unitary(X) & Q.unitary(Z))
+    True
+    >>> ask(Q.unitary(Identity(3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Unitary_matrix
+
+    """
+    name = 'unitary'
+    handler = Dispatcher("UnitaryHandler", doc="Handler for key 'unitary'.")
+
+
+class FullRankPredicate(Predicate):
+    """
+    Fullrank matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.fullrank(x)`` is true iff ``x`` is a full rank matrix.
+    A matrix is full rank if all rows and columns of the matrix
+    are linearly independent. A square matrix is full rank iff
+    its determinant is nonzero.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> ask(Q.fullrank(X.T), Q.fullrank(X))
+    True
+    >>> ask(Q.fullrank(ZeroMatrix(3, 3)))
+    False
+    >>> ask(Q.fullrank(Identity(3)))
+    True
+
+    """
+    name = 'fullrank'
+    handler = Dispatcher("FullRankHandler", doc="Handler for key 'fullrank'.")
+
+
+class PositiveDefinitePredicate(Predicate):
+    r"""
+    Positive definite matrix predicate.
+
+    Explanation
+    ===========
+
+    If $M$ is a :math:`n \times n` symmetric real matrix, it is said
+    to be positive definite if :math:`Z^TMZ` is positive for
+    every non-zero column vector $Z$ of $n$ real numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.positive_definite(Y))
+    False
+    >>> ask(Q.positive_definite(Identity(3)))
+    True
+    >>> ask(Q.positive_definite(X + Z), Q.positive_definite(X) &
+    ...     Q.positive_definite(Z))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Positive-definite_matrix
+
+    """
+    name = "positive_definite"
+    handler = Dispatcher("PositiveDefiniteHandler", doc="Handler for key 'positive_definite'.")
+
+
+class UpperTriangularPredicate(Predicate):
+    """
+    Upper triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    A matrix $M$ is called upper triangular matrix if :math:`M_{ij}=0`
+    for :math:`i>> from sympy import Q, ask, ZeroMatrix, Identity
+    >>> ask(Q.upper_triangular(Identity(3)))
+    True
+    >>> ask(Q.upper_triangular(ZeroMatrix(3, 3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/UpperTriangularMatrix.html
+
+    """
+    name = "upper_triangular"
+    handler = Dispatcher("UpperTriangularHandler", doc="Handler for key 'upper_triangular'.")
+
+
+class LowerTriangularPredicate(Predicate):
+    """
+    Lower triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    A matrix $M$ is called lower triangular matrix if :math:`M_{ij}=0`
+    for :math:`i>j`.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, ZeroMatrix, Identity
+    >>> ask(Q.lower_triangular(Identity(3)))
+    True
+    >>> ask(Q.lower_triangular(ZeroMatrix(3, 3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/LowerTriangularMatrix.html
+
+    """
+    name = "lower_triangular"
+    handler = Dispatcher("LowerTriangularHandler", doc="Handler for key 'lower_triangular'.")
+
+
+class DiagonalPredicate(Predicate):
+    """
+    Diagonal matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.diagonal(x)`` is true iff ``x`` is a diagonal matrix. A diagonal
+    matrix is a matrix in which the entries outside the main diagonal
+    are all zero.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> ask(Q.diagonal(ZeroMatrix(3, 3)))
+    True
+    >>> ask(Q.diagonal(X), Q.lower_triangular(X) &
+    ...     Q.upper_triangular(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Diagonal_matrix
+
+    """
+    name = "diagonal"
+    handler = Dispatcher("DiagonalHandler", doc="Handler for key 'diagonal'.")
+
+
+class IntegerElementsPredicate(Predicate):
+    """
+    Integer elements matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.integer_elements(x)`` is true iff all the elements of ``x``
+    are integers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.integer(X[1, 2]), Q.integer_elements(X))
+    True
+
+    """
+    name = "integer_elements"
+    handler = Dispatcher("IntegerElementsHandler", doc="Handler for key 'integer_elements'.")
+
+
+class RealElementsPredicate(Predicate):
+    """
+    Real elements matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.real_elements(x)`` is true iff all the elements of ``x``
+    are real numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.real(X[1, 2]), Q.real_elements(X))
+    True
+
+    """
+    name = "real_elements"
+    handler = Dispatcher("RealElementsHandler", doc="Handler for key 'real_elements'.")
+
+
+class ComplexElementsPredicate(Predicate):
+    """
+    Complex elements matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.complex_elements(x)`` is true iff all the elements of ``x``
+    are complex numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.complex(X[1, 2]), Q.complex_elements(X))
+    True
+    >>> ask(Q.complex_elements(X), Q.integer_elements(X))
+    True
+
+    """
+    name = "complex_elements"
+    handler = Dispatcher("ComplexElementsHandler", doc="Handler for key 'complex_elements'.")
+
+
+class SingularPredicate(Predicate):
+    """
+    Singular matrix predicate.
+
+    A matrix is singular iff the value of its determinant is 0.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.singular(X), Q.invertible(X))
+    False
+    >>> ask(Q.singular(X), ~Q.invertible(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/SingularMatrix.html
+
+    """
+    name = "singular"
+    handler = Dispatcher("SingularHandler", doc="Predicate fore key 'singular'.")
+
+
+class NormalPredicate(Predicate):
+    """
+    Normal matrix predicate.
+
+    A matrix is normal if it commutes with its conjugate transpose.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.normal(X), Q.unitary(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Normal_matrix
+
+    """
+    name = "normal"
+    handler = Dispatcher("NormalHandler", doc="Predicate fore key 'normal'.")
+
+
+class TriangularPredicate(Predicate):
+    """
+    Triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.triangular(X)`` is true if ``X`` is one that is either lower
+    triangular or upper triangular.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.triangular(X), Q.upper_triangular(X))
+    True
+    >>> ask(Q.triangular(X), Q.lower_triangular(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Triangular_matrix
+
+    """
+    name = "triangular"
+    handler = Dispatcher("TriangularHandler", doc="Predicate fore key 'triangular'.")
+
+
+class UnitTriangularPredicate(Predicate):
+    """
+    Unit triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    A unit triangular matrix is a triangular matrix with 1s
+    on the diagonal.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.triangular(X), Q.unit_triangular(X))
+    True
+
+    """
+    name = "unit_triangular"
+    handler = Dispatcher("UnitTriangularHandler", doc="Predicate fore key 'unit_triangular'.")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/ntheory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/ntheory.py
new file mode 100644
index 0000000000000000000000000000000000000000..6c598e0ed1bd4a1170aa28044f9ae6de2fa1a1e0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/ntheory.py
@@ -0,0 +1,126 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+
+class PrimePredicate(Predicate):
+    """
+    Prime number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.prime(x))`` is true iff ``x`` is a natural number greater
+    than 1 that has no positive divisors other than ``1`` and the
+    number itself.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask
+    >>> ask(Q.prime(0))
+    False
+    >>> ask(Q.prime(1))
+    False
+    >>> ask(Q.prime(2))
+    True
+    >>> ask(Q.prime(20))
+    False
+    >>> ask(Q.prime(-3))
+    False
+
+    """
+    name = 'prime'
+    handler = Dispatcher(
+        "PrimeHandler",
+        doc=("Handler for key 'prime'. Test that an expression represents a prime"
+        " number. When the expression is an exact number, the result (when True)"
+        " is subject to the limitations of isprime() which is used to return the "
+        "result.")
+    )
+
+
+class CompositePredicate(Predicate):
+    """
+    Composite number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.composite(x))`` is true iff ``x`` is a positive integer and has
+    at least one positive divisor other than ``1`` and the number itself.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask
+    >>> ask(Q.composite(0))
+    False
+    >>> ask(Q.composite(1))
+    False
+    >>> ask(Q.composite(2))
+    False
+    >>> ask(Q.composite(20))
+    True
+
+    """
+    name = 'composite'
+    handler = Dispatcher("CompositeHandler", doc="Handler for key 'composite'.")
+
+
+class EvenPredicate(Predicate):
+    """
+    Even number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.even(x))`` is true iff ``x`` belongs to the set of even
+    integers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, pi
+    >>> ask(Q.even(0))
+    True
+    >>> ask(Q.even(2))
+    True
+    >>> ask(Q.even(3))
+    False
+    >>> ask(Q.even(pi))
+    False
+
+    """
+    name = 'even'
+    handler = Dispatcher("EvenHandler", doc="Handler for key 'even'.")
+
+
+class OddPredicate(Predicate):
+    """
+    Odd number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.odd(x))`` is true iff ``x`` belongs to the set of odd numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, pi
+    >>> ask(Q.odd(0))
+    False
+    >>> ask(Q.odd(2))
+    False
+    >>> ask(Q.odd(3))
+    True
+    >>> ask(Q.odd(pi))
+    False
+
+    """
+    name = 'odd'
+    handler = Dispatcher(
+        "OddHandler",
+        doc=("Handler for key 'odd'. Test that an expression represents an odd"
+        " number.")
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/order.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/order.py
new file mode 100644
index 0000000000000000000000000000000000000000..86bfb2ae49789efd5b0df99e2cfc63984e956dd0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/order.py
@@ -0,0 +1,390 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+
+class NegativePredicate(Predicate):
+    r"""
+    Negative number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.negative(x)`` is true iff ``x`` is a real number and :math:`x < 0`, that is,
+    it is in the interval :math:`(-\infty, 0)`.  Note in particular that negative
+    infinity is not negative.
+
+    A few important facts about negative numbers:
+
+    - Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same
+        thing. ``~Q.negative(x)`` simply means that ``x`` is not negative,
+        whereas ``Q.nonnegative(x)`` means that ``x`` is real and not
+        negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to
+        ``Q.zero(x) | Q.positive(x)``.  So for example, ``~Q.negative(I)`` is
+        true, whereas ``Q.nonnegative(I)`` is false.
+
+    - See the documentation of ``Q.real`` for more information about
+        related facts.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols, I
+    >>> x = symbols('x')
+    >>> ask(Q.negative(x), Q.real(x) & ~Q.positive(x) & ~Q.zero(x))
+    True
+    >>> ask(Q.negative(-1))
+    True
+    >>> ask(Q.nonnegative(I))
+    False
+    >>> ask(~Q.negative(I))
+    True
+
+    """
+    name = 'negative'
+    handler = Dispatcher(
+        "NegativeHandler",
+        doc=("Handler for Q.negative. Test that an expression is strictly less"
+        " than zero.")
+    )
+
+
+class NonNegativePredicate(Predicate):
+    """
+    Nonnegative real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.nonnegative(x))`` is true iff ``x`` belongs to the set of
+    positive numbers including zero.
+
+    - Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same
+        thing. ``~Q.negative(x)`` simply means that ``x`` is not negative,
+        whereas ``Q.nonnegative(x)`` means that ``x`` is real and not
+        negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to
+        ``Q.zero(x) | Q.positive(x)``.  So for example, ``~Q.negative(I)`` is
+        true, whereas ``Q.nonnegative(I)`` is false.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, I
+    >>> ask(Q.nonnegative(1))
+    True
+    >>> ask(Q.nonnegative(0))
+    True
+    >>> ask(Q.nonnegative(-1))
+    False
+    >>> ask(Q.nonnegative(I))
+    False
+    >>> ask(Q.nonnegative(-I))
+    False
+
+    """
+    name = 'nonnegative'
+    handler = Dispatcher(
+        "NonNegativeHandler",
+        doc=("Handler for Q.nonnegative.")
+    )
+
+
+class NonZeroPredicate(Predicate):
+    """
+    Nonzero real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.nonzero(x))`` is true iff ``x`` is real and ``x`` is not zero.  Note in
+    particular that ``Q.nonzero(x)`` is false if ``x`` is not real.  Use
+    ``~Q.zero(x)`` if you want the negation of being zero without any real
+    assumptions.
+
+    A few important facts about nonzero numbers:
+
+    - ``Q.nonzero`` is logically equivalent to ``Q.positive | Q.negative``.
+
+    - See the documentation of ``Q.real`` for more information about
+        related facts.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols, I, oo
+    >>> x = symbols('x')
+    >>> print(ask(Q.nonzero(x), ~Q.zero(x)))
+    None
+    >>> ask(Q.nonzero(x), Q.positive(x))
+    True
+    >>> ask(Q.nonzero(x), Q.zero(x))
+    False
+    >>> ask(Q.nonzero(0))
+    False
+    >>> ask(Q.nonzero(I))
+    False
+    >>> ask(~Q.zero(I))
+    True
+    >>> ask(Q.nonzero(oo))
+    False
+
+    """
+    name = 'nonzero'
+    handler = Dispatcher(
+        "NonZeroHandler",
+        doc=("Handler for key 'nonzero'. Test that an expression is not identically"
+        " zero.")
+    )
+
+
+class ZeroPredicate(Predicate):
+    """
+    Zero number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.zero(x))`` is true iff the value of ``x`` is zero.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, oo, symbols
+    >>> x, y = symbols('x, y')
+    >>> ask(Q.zero(0))
+    True
+    >>> ask(Q.zero(1/oo))
+    True
+    >>> print(ask(Q.zero(0*oo)))
+    None
+    >>> ask(Q.zero(1))
+    False
+    >>> ask(Q.zero(x*y), Q.zero(x) | Q.zero(y))
+    True
+
+    """
+    name = 'zero'
+    handler = Dispatcher(
+        "ZeroHandler",
+        doc="Handler for key 'zero'."
+    )
+
+
+class NonPositivePredicate(Predicate):
+    """
+    Nonpositive real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.nonpositive(x))`` is true iff ``x`` belongs to the set of
+    negative numbers including zero.
+
+    - Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same
+        thing. ``~Q.positive(x)`` simply means that ``x`` is not positive,
+        whereas ``Q.nonpositive(x)`` means that ``x`` is real and not
+        positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to
+        `Q.negative(x) | Q.zero(x)``.  So for example, ``~Q.positive(I)`` is
+        true, whereas ``Q.nonpositive(I)`` is false.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, I
+
+    >>> ask(Q.nonpositive(-1))
+    True
+    >>> ask(Q.nonpositive(0))
+    True
+    >>> ask(Q.nonpositive(1))
+    False
+    >>> ask(Q.nonpositive(I))
+    False
+    >>> ask(Q.nonpositive(-I))
+    False
+
+    """
+    name = 'nonpositive'
+    handler = Dispatcher(
+        "NonPositiveHandler",
+        doc="Handler for key 'nonpositive'."
+    )
+
+
+class PositivePredicate(Predicate):
+    r"""
+    Positive real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.positive(x)`` is true iff ``x`` is real and `x > 0`, that is if ``x``
+    is in the interval `(0, \infty)`.  In particular, infinity is not
+    positive.
+
+    A few important facts about positive numbers:
+
+    - Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same
+        thing. ``~Q.positive(x)`` simply means that ``x`` is not positive,
+        whereas ``Q.nonpositive(x)`` means that ``x`` is real and not
+        positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to
+        `Q.negative(x) | Q.zero(x)``.  So for example, ``~Q.positive(I)`` is
+        true, whereas ``Q.nonpositive(I)`` is false.
+
+    - See the documentation of ``Q.real`` for more information about
+        related facts.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols, I
+    >>> x = symbols('x')
+    >>> ask(Q.positive(x), Q.real(x) & ~Q.negative(x) & ~Q.zero(x))
+    True
+    >>> ask(Q.positive(1))
+    True
+    >>> ask(Q.nonpositive(I))
+    False
+    >>> ask(~Q.positive(I))
+    True
+
+    """
+    name = 'positive'
+    handler = Dispatcher(
+        "PositiveHandler",
+        doc=("Handler for key 'positive'. Test that an expression is strictly"
+        " greater than zero.")
+    )
+
+
+class ExtendedPositivePredicate(Predicate):
+    r"""
+    Positive extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.extended_positive(x)`` is true iff ``x`` is extended real and
+    `x > 0`, that is if ``x`` is in the interval `(0, \infty]`.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_positive(1))
+    True
+    >>> ask(Q.extended_positive(oo))
+    True
+    >>> ask(Q.extended_positive(I))
+    False
+
+    """
+    name = 'extended_positive'
+    handler = Dispatcher("ExtendedPositiveHandler")
+
+
+class ExtendedNegativePredicate(Predicate):
+    r"""
+    Negative extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.extended_negative(x)`` is true iff ``x`` is extended real and
+    `x < 0`, that is if ``x`` is in the interval `[-\infty, 0)`.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_negative(-1))
+    True
+    >>> ask(Q.extended_negative(-oo))
+    True
+    >>> ask(Q.extended_negative(-I))
+    False
+
+    """
+    name = 'extended_negative'
+    handler = Dispatcher("ExtendedNegativeHandler")
+
+
+class ExtendedNonZeroPredicate(Predicate):
+    """
+    Nonzero extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.extended_nonzero(x))`` is true iff ``x`` is extended real and
+    ``x`` is not zero.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_nonzero(-1))
+    True
+    >>> ask(Q.extended_nonzero(oo))
+    True
+    >>> ask(Q.extended_nonzero(I))
+    False
+
+    """
+    name = 'extended_nonzero'
+    handler = Dispatcher("ExtendedNonZeroHandler")
+
+
+class ExtendedNonPositivePredicate(Predicate):
+    """
+    Nonpositive extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.extended_nonpositive(x))`` is true iff ``x`` is extended real and
+    ``x`` is not positive.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_nonpositive(-1))
+    True
+    >>> ask(Q.extended_nonpositive(oo))
+    False
+    >>> ask(Q.extended_nonpositive(0))
+    True
+    >>> ask(Q.extended_nonpositive(I))
+    False
+
+    """
+    name = 'extended_nonpositive'
+    handler = Dispatcher("ExtendedNonPositiveHandler")
+
+
+class ExtendedNonNegativePredicate(Predicate):
+    """
+    Nonnegative extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.extended_nonnegative(x))`` is true iff ``x`` is extended real and
+    ``x`` is not negative.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_nonnegative(-1))
+    False
+    >>> ask(Q.extended_nonnegative(oo))
+    True
+    >>> ask(Q.extended_nonnegative(0))
+    True
+    >>> ask(Q.extended_nonnegative(I))
+    False
+
+    """
+    name = 'extended_nonnegative'
+    handler = Dispatcher("ExtendedNonNegativeHandler")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/sets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/sets.py
new file mode 100644
index 0000000000000000000000000000000000000000..18261cee2d9de65df14a31a56b2cd22328328ed0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/predicates/sets.py
@@ -0,0 +1,399 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+
+class IntegerPredicate(Predicate):
+    """
+    Integer predicate.
+
+    Explanation
+    ===========
+
+    ``Q.integer(x)`` is true iff ``x`` belongs to the set of integer
+    numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, S
+    >>> ask(Q.integer(5))
+    True
+    >>> ask(Q.integer(S(1)/2))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Integer
+
+    """
+    name = 'integer'
+    handler = Dispatcher(
+        "IntegerHandler",
+        doc=("Handler for Q.integer.\n\n"
+        "Test that an expression belongs to the field of integer numbers.")
+    )
+
+
+class NonIntegerPredicate(Predicate):
+    """
+    Non-integer extended real predicate.
+    """
+    name = 'noninteger'
+    handler = Dispatcher(
+        "NonIntegerHandler",
+        doc=("Handler for Q.noninteger.\n\n"
+        "Test that an expression is a non-integer extended real number.")
+    )
+
+
+class RationalPredicate(Predicate):
+    """
+    Rational number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.rational(x)`` is true iff ``x`` belongs to the set of
+    rational numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, pi, S
+    >>> ask(Q.rational(0))
+    True
+    >>> ask(Q.rational(S(1)/2))
+    True
+    >>> ask(Q.rational(pi))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Rational_number
+
+    """
+    name = 'rational'
+    handler = Dispatcher(
+        "RationalHandler",
+        doc=("Handler for Q.rational.\n\n"
+        "Test that an expression belongs to the field of rational numbers.")
+    )
+
+
+class IrrationalPredicate(Predicate):
+    """
+    Irrational number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.irrational(x)`` is true iff ``x``  is any real number that
+    cannot be expressed as a ratio of integers.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, pi, S, I
+    >>> ask(Q.irrational(0))
+    False
+    >>> ask(Q.irrational(S(1)/2))
+    False
+    >>> ask(Q.irrational(pi))
+    True
+    >>> ask(Q.irrational(I))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Irrational_number
+
+    """
+    name = 'irrational'
+    handler = Dispatcher(
+        "IrrationalHandler",
+        doc=("Handler for Q.irrational.\n\n"
+        "Test that an expression is irrational numbers.")
+    )
+
+
+class RealPredicate(Predicate):
+    r"""
+    Real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.real(x)`` is true iff ``x`` is a real number, i.e., it is in the
+    interval `(-\infty, \infty)`.  Note that, in particular the
+    infinities are not real. Use ``Q.extended_real`` if you want to
+    consider those as well.
+
+    A few important facts about reals:
+
+    - Every real number is positive, negative, or zero.  Furthermore,
+        because these sets are pairwise disjoint, each real number is
+        exactly one of those three.
+
+    - Every real number is also complex.
+
+    - Every real number is finite.
+
+    - Every real number is either rational or irrational.
+
+    - Every real number is either algebraic or transcendental.
+
+    - The facts ``Q.negative``, ``Q.zero``, ``Q.positive``,
+        ``Q.nonnegative``, ``Q.nonpositive``, ``Q.nonzero``,
+        ``Q.integer``, ``Q.rational``, and ``Q.irrational`` all imply
+        ``Q.real``, as do all facts that imply those facts.
+
+    - The facts ``Q.algebraic``, and ``Q.transcendental`` do not imply
+        ``Q.real``; they imply ``Q.complex``. An algebraic or
+        transcendental number may or may not be real.
+
+    - The "non" facts (i.e., ``Q.nonnegative``, ``Q.nonzero``,
+        ``Q.nonpositive`` and ``Q.noninteger``) are not equivalent to
+        not the fact, but rather, not the fact *and* ``Q.real``.
+        For example, ``Q.nonnegative`` means ``~Q.negative & Q.real``.
+        So for example, ``I`` is not nonnegative, nonzero, or
+        nonpositive.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols
+    >>> x = symbols('x')
+    >>> ask(Q.real(x), Q.positive(x))
+    True
+    >>> ask(Q.real(0))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Real_number
+
+    """
+    name = 'real'
+    handler = Dispatcher(
+        "RealHandler",
+        doc=("Handler for Q.real.\n\n"
+        "Test that an expression belongs to the field of real numbers.")
+    )
+
+
+class ExtendedRealPredicate(Predicate):
+    r"""
+    Extended real predicate.
+
+    Explanation
+    ===========
+
+    ``Q.extended_real(x)`` is true iff ``x`` is a real number or
+    `\{-\infty, \infty\}`.
+
+    See documentation of ``Q.real`` for more information about related
+    facts.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, oo, I
+    >>> ask(Q.extended_real(1))
+    True
+    >>> ask(Q.extended_real(I))
+    False
+    >>> ask(Q.extended_real(oo))
+    True
+
+    """
+    name = 'extended_real'
+    handler = Dispatcher(
+        "ExtendedRealHandler",
+        doc=("Handler for Q.extended_real.\n\n"
+        "Test that an expression belongs to the field of extended real\n"
+        "numbers, that is real numbers union {Infinity, -Infinity}.")
+    )
+
+
+class HermitianPredicate(Predicate):
+    """
+    Hermitian predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.hermitian(x))`` is true iff ``x`` belongs to the set of
+    Hermitian operators.
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/HermitianOperator.html
+
+    """
+    # TODO: Add examples
+    name = 'hermitian'
+    handler = Dispatcher(
+        "HermitianHandler",
+        doc=("Handler for Q.hermitian.\n\n"
+        "Test that an expression belongs to the field of Hermitian operators.")
+    )
+
+
+class ComplexPredicate(Predicate):
+    """
+    Complex number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.complex(x)`` is true iff ``x`` belongs to the set of complex
+    numbers. Note that every complex number is finite.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, Symbol, ask, I, oo
+    >>> x = Symbol('x')
+    >>> ask(Q.complex(0))
+    True
+    >>> ask(Q.complex(2 + 3*I))
+    True
+    >>> ask(Q.complex(oo))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Complex_number
+
+    """
+    name = 'complex'
+    handler = Dispatcher(
+        "ComplexHandler",
+        doc=("Handler for Q.complex.\n\n"
+        "Test that an expression belongs to the field of complex numbers.")
+    )
+
+
+class ImaginaryPredicate(Predicate):
+    """
+    Imaginary number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.imaginary(x)`` is true iff ``x`` can be written as a real
+    number multiplied by the imaginary unit ``I``. Please note that ``0``
+    is not considered to be an imaginary number.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, I
+    >>> ask(Q.imaginary(3*I))
+    True
+    >>> ask(Q.imaginary(2 + 3*I))
+    False
+    >>> ask(Q.imaginary(0))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Imaginary_number
+
+    """
+    name = 'imaginary'
+    handler = Dispatcher(
+        "ImaginaryHandler",
+        doc=("Handler for Q.imaginary.\n\n"
+        "Test that an expression belongs to the field of imaginary numbers,\n"
+        "that is, numbers in the form x*I, where x is real.")
+    )
+
+
+class AntihermitianPredicate(Predicate):
+    """
+    Antihermitian predicate.
+
+    Explanation
+    ===========
+
+    ``Q.antihermitian(x)`` is true iff ``x`` belongs to the field of
+    antihermitian operators, i.e., operators in the form ``x*I``, where
+    ``x`` is Hermitian.
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/HermitianOperator.html
+
+    """
+    # TODO: Add examples
+    name = 'antihermitian'
+    handler = Dispatcher(
+        "AntiHermitianHandler",
+        doc=("Handler for Q.antihermitian.\n\n"
+        "Test that an expression belongs to the field of anti-Hermitian\n"
+        "operators, that is, operators in the form x*I, where x is Hermitian.")
+    )
+
+
+class AlgebraicPredicate(Predicate):
+    r"""
+    Algebraic number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.algebraic(x)`` is true iff ``x`` belongs to the set of
+    algebraic numbers. ``x`` is algebraic if there is some polynomial
+    in ``p(x)\in \mathbb\{Q\}[x]`` such that ``p(x) = 0``.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, sqrt, I, pi
+    >>> ask(Q.algebraic(sqrt(2)))
+    True
+    >>> ask(Q.algebraic(I))
+    True
+    >>> ask(Q.algebraic(pi))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Algebraic_number
+
+    """
+    name = 'algebraic'
+    AlgebraicHandler = Dispatcher(
+        "AlgebraicHandler",
+        doc="""Handler for Q.algebraic key."""
+    )
+
+
+class TranscendentalPredicate(Predicate):
+    """
+    Transcedental number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.transcendental(x)`` is true iff ``x`` belongs to the set of
+    transcendental numbers. A transcendental number is a real
+    or complex number that is not algebraic.
+
+    """
+    # TODO: Add examples
+    name = 'transcendental'
+    handler = Dispatcher(
+        "Transcendental",
+        doc="""Handler for Q.transcendental key."""
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/refine.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/refine.py
new file mode 100644
index 0000000000000000000000000000000000000000..c36a4e1cdb40f1b59a96f60a3b36182b587920fa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/refine.py
@@ -0,0 +1,405 @@
+from __future__ import annotations
+from typing import Callable
+
+from sympy.core import S, Add, Expr, Basic, Mul, Pow, Rational
+from sympy.core.logic import fuzzy_not
+from sympy.logic.boolalg import Boolean
+
+from sympy.assumptions import ask, Q  # type: ignore
+
+
+def refine(expr, assumptions=True):
+    """
+    Simplify an expression using assumptions.
+
+    Explanation
+    ===========
+
+    Unlike :func:`~.simplify` which performs structural simplification
+    without any assumption, this function transforms the expression into
+    the form which is only valid under certain assumptions. Note that
+    ``simplify()`` is generally not done in refining process.
+
+    Refining boolean expression involves reducing it to ``S.true`` or
+    ``S.false``. Unlike :func:`~.ask`, the expression will not be reduced
+    if the truth value cannot be determined.
+
+    Examples
+    ========
+
+    >>> from sympy import refine, sqrt, Q
+    >>> from sympy.abc import x
+    >>> refine(sqrt(x**2), Q.real(x))
+    Abs(x)
+    >>> refine(sqrt(x**2), Q.positive(x))
+    x
+
+    >>> refine(Q.real(x), Q.positive(x))
+    True
+    >>> refine(Q.positive(x), Q.real(x))
+    Q.positive(x)
+
+    See Also
+    ========
+
+    sympy.simplify.simplify.simplify : Structural simplification without assumptions.
+    sympy.assumptions.ask.ask : Query for boolean expressions using assumptions.
+    """
+    if not isinstance(expr, Basic):
+        return expr
+
+    if not expr.is_Atom:
+        args = [refine(arg, assumptions) for arg in expr.args]
+        # TODO: this will probably not work with Integral or Polynomial
+        expr = expr.func(*args)
+    if hasattr(expr, '_eval_refine'):
+        ref_expr = expr._eval_refine(assumptions)
+        if ref_expr is not None:
+            return ref_expr
+    name = expr.__class__.__name__
+    handler = handlers_dict.get(name, None)
+    if handler is None:
+        return expr
+    new_expr = handler(expr, assumptions)
+    if (new_expr is None) or (expr == new_expr):
+        return expr
+    if not isinstance(new_expr, Expr):
+        return new_expr
+    return refine(new_expr, assumptions)
+
+
+def refine_abs(expr, assumptions):
+    """
+    Handler for the absolute value.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, Abs
+    >>> from sympy.assumptions.refine import refine_abs
+    >>> from sympy.abc import x
+    >>> refine_abs(Abs(x), Q.real(x))
+    >>> refine_abs(Abs(x), Q.positive(x))
+    x
+    >>> refine_abs(Abs(x), Q.negative(x))
+    -x
+
+    """
+    from sympy.functions.elementary.complexes import Abs
+    arg = expr.args[0]
+    if ask(Q.real(arg), assumptions) and \
+            fuzzy_not(ask(Q.negative(arg), assumptions)):
+        # if it's nonnegative
+        return arg
+    if ask(Q.negative(arg), assumptions):
+        return -arg
+    # arg is Mul
+    if isinstance(arg, Mul):
+        r = [refine(abs(a), assumptions) for a in arg.args]
+        non_abs = []
+        in_abs = []
+        for i in r:
+            if isinstance(i, Abs):
+                in_abs.append(i.args[0])
+            else:
+                non_abs.append(i)
+        return Mul(*non_abs) * Abs(Mul(*in_abs))
+
+
+def refine_Pow(expr, assumptions):
+    """
+    Handler for instances of Pow.
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.refine import refine_Pow
+    >>> from sympy.abc import x,y,z
+    >>> refine_Pow((-1)**x, Q.real(x))
+    >>> refine_Pow((-1)**x, Q.even(x))
+    1
+    >>> refine_Pow((-1)**x, Q.odd(x))
+    -1
+
+    For powers of -1, even parts of the exponent can be simplified:
+
+    >>> refine_Pow((-1)**(x+y), Q.even(x))
+    (-1)**y
+    >>> refine_Pow((-1)**(x+y+z), Q.odd(x) & Q.odd(z))
+    (-1)**y
+    >>> refine_Pow((-1)**(x+y+2), Q.odd(x))
+    (-1)**(y + 1)
+    >>> refine_Pow((-1)**(x+3), True)
+    (-1)**(x + 1)
+
+    """
+    from sympy.functions.elementary.complexes import Abs
+    from sympy.functions import sign
+    if isinstance(expr.base, Abs):
+        if ask(Q.real(expr.base.args[0]), assumptions) and \
+                ask(Q.even(expr.exp), assumptions):
+            return expr.base.args[0] ** expr.exp
+    if ask(Q.real(expr.base), assumptions):
+        if expr.base.is_number:
+            if ask(Q.even(expr.exp), assumptions):
+                return abs(expr.base) ** expr.exp
+            if ask(Q.odd(expr.exp), assumptions):
+                return sign(expr.base) * abs(expr.base) ** expr.exp
+        if isinstance(expr.exp, Rational):
+            if isinstance(expr.base, Pow):
+                return abs(expr.base.base) ** (expr.base.exp * expr.exp)
+
+        if expr.base is S.NegativeOne:
+            if expr.exp.is_Add:
+
+                old = expr
+
+                # For powers of (-1) we can remove
+                #  - even terms
+                #  - pairs of odd terms
+                #  - a single odd term + 1
+                #  - A numerical constant N can be replaced with mod(N,2)
+
+                coeff, terms = expr.exp.as_coeff_add()
+                terms = set(terms)
+                even_terms = set()
+                odd_terms = set()
+                initial_number_of_terms = len(terms)
+
+                for t in terms:
+                    if ask(Q.even(t), assumptions):
+                        even_terms.add(t)
+                    elif ask(Q.odd(t), assumptions):
+                        odd_terms.add(t)
+
+                terms -= even_terms
+                if len(odd_terms) % 2:
+                    terms -= odd_terms
+                    new_coeff = (coeff + S.One) % 2
+                else:
+                    terms -= odd_terms
+                    new_coeff = coeff % 2
+
+                if new_coeff != coeff or len(terms) < initial_number_of_terms:
+                    terms.add(new_coeff)
+                    expr = expr.base**(Add(*terms))
+
+                # Handle (-1)**((-1)**n/2 + m/2)
+                e2 = 2*expr.exp
+                if ask(Q.even(e2), assumptions):
+                    if e2.could_extract_minus_sign():
+                        e2 *= expr.base
+                if e2.is_Add:
+                    i, p = e2.as_two_terms()
+                    if p.is_Pow and p.base is S.NegativeOne:
+                        if ask(Q.integer(p.exp), assumptions):
+                            i = (i + 1)/2
+                            if ask(Q.even(i), assumptions):
+                                return expr.base**p.exp
+                            elif ask(Q.odd(i), assumptions):
+                                return expr.base**(p.exp + 1)
+                            else:
+                                return expr.base**(p.exp + i)
+
+                if old != expr:
+                    return expr
+
+
+def refine_atan2(expr, assumptions):
+    """
+    Handler for the atan2 function.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, atan2
+    >>> from sympy.assumptions.refine import refine_atan2
+    >>> from sympy.abc import x, y
+    >>> refine_atan2(atan2(y,x), Q.real(y) & Q.positive(x))
+    atan(y/x)
+    >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.negative(x))
+    atan(y/x) - pi
+    >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.negative(x))
+    atan(y/x) + pi
+    >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.negative(x))
+    pi
+    >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.zero(x))
+    pi/2
+    >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.zero(x))
+    -pi/2
+    >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.zero(x))
+    nan
+    """
+    from sympy.functions.elementary.trigonometric import atan
+    y, x = expr.args
+    if ask(Q.real(y) & Q.positive(x), assumptions):
+        return atan(y / x)
+    elif ask(Q.negative(y) & Q.negative(x), assumptions):
+        return atan(y / x) - S.Pi
+    elif ask(Q.positive(y) & Q.negative(x), assumptions):
+        return atan(y / x) + S.Pi
+    elif ask(Q.zero(y) & Q.negative(x), assumptions):
+        return S.Pi
+    elif ask(Q.positive(y) & Q.zero(x), assumptions):
+        return S.Pi/2
+    elif ask(Q.negative(y) & Q.zero(x), assumptions):
+        return -S.Pi/2
+    elif ask(Q.zero(y) & Q.zero(x), assumptions):
+        return S.NaN
+    else:
+        return expr
+
+
+def refine_re(expr, assumptions):
+    """
+    Handler for real part.
+
+    Examples
+    ========
+
+    >>> from sympy.assumptions.refine import refine_re
+    >>> from sympy import Q, re
+    >>> from sympy.abc import x
+    >>> refine_re(re(x), Q.real(x))
+    x
+    >>> refine_re(re(x), Q.imaginary(x))
+    0
+    """
+    arg = expr.args[0]
+    if ask(Q.real(arg), assumptions):
+        return arg
+    if ask(Q.imaginary(arg), assumptions):
+        return S.Zero
+    return _refine_reim(expr, assumptions)
+
+
+def refine_im(expr, assumptions):
+    """
+    Handler for imaginary part.
+
+    Explanation
+    ===========
+
+    >>> from sympy.assumptions.refine import refine_im
+    >>> from sympy import Q, im
+    >>> from sympy.abc import x
+    >>> refine_im(im(x), Q.real(x))
+    0
+    >>> refine_im(im(x), Q.imaginary(x))
+    -I*x
+    """
+    arg = expr.args[0]
+    if ask(Q.real(arg), assumptions):
+        return S.Zero
+    if ask(Q.imaginary(arg), assumptions):
+        return - S.ImaginaryUnit * arg
+    return _refine_reim(expr, assumptions)
+
+def refine_arg(expr, assumptions):
+    """
+    Handler for complex argument
+
+    Explanation
+    ===========
+
+    >>> from sympy.assumptions.refine import refine_arg
+    >>> from sympy import Q, arg
+    >>> from sympy.abc import x
+    >>> refine_arg(arg(x), Q.positive(x))
+    0
+    >>> refine_arg(arg(x), Q.negative(x))
+    pi
+    """
+    rg = expr.args[0]
+    if ask(Q.positive(rg), assumptions):
+        return S.Zero
+    if ask(Q.negative(rg), assumptions):
+        return S.Pi
+    return None
+
+
+def _refine_reim(expr, assumptions):
+    # Helper function for refine_re & refine_im
+    expanded = expr.expand(complex = True)
+    if expanded != expr:
+        refined = refine(expanded, assumptions)
+        if refined != expanded:
+            return refined
+    # Best to leave the expression as is
+    return None
+
+
+def refine_sign(expr, assumptions):
+    """
+    Handler for sign.
+
+    Examples
+    ========
+
+    >>> from sympy.assumptions.refine import refine_sign
+    >>> from sympy import Symbol, Q, sign, im
+    >>> x = Symbol('x', real = True)
+    >>> expr = sign(x)
+    >>> refine_sign(expr, Q.positive(x) & Q.nonzero(x))
+    1
+    >>> refine_sign(expr, Q.negative(x) & Q.nonzero(x))
+    -1
+    >>> refine_sign(expr, Q.zero(x))
+    0
+    >>> y = Symbol('y', imaginary = True)
+    >>> expr = sign(y)
+    >>> refine_sign(expr, Q.positive(im(y)))
+    I
+    >>> refine_sign(expr, Q.negative(im(y)))
+    -I
+    """
+    arg = expr.args[0]
+    if ask(Q.zero(arg), assumptions):
+        return S.Zero
+    if ask(Q.real(arg)):
+        if ask(Q.positive(arg), assumptions):
+            return S.One
+        if ask(Q.negative(arg), assumptions):
+            return S.NegativeOne
+    if ask(Q.imaginary(arg)):
+        arg_re, arg_im = arg.as_real_imag()
+        if ask(Q.positive(arg_im), assumptions):
+            return S.ImaginaryUnit
+        if ask(Q.negative(arg_im), assumptions):
+            return -S.ImaginaryUnit
+    return expr
+
+
+def refine_matrixelement(expr, assumptions):
+    """
+    Handler for symmetric part.
+
+    Examples
+    ========
+
+    >>> from sympy.assumptions.refine import refine_matrixelement
+    >>> from sympy import MatrixSymbol, Q
+    >>> X = MatrixSymbol('X', 3, 3)
+    >>> refine_matrixelement(X[0, 1], Q.symmetric(X))
+    X[0, 1]
+    >>> refine_matrixelement(X[1, 0], Q.symmetric(X))
+    X[0, 1]
+    """
+    from sympy.matrices.expressions.matexpr import MatrixElement
+    matrix, i, j = expr.args
+    if ask(Q.symmetric(matrix), assumptions):
+        if (i - j).could_extract_minus_sign():
+            return expr
+        return MatrixElement(matrix, j, i)
+
+handlers_dict: dict[str, Callable[[Expr, Boolean], Expr]] = {
+    'Abs': refine_abs,
+    'Pow': refine_Pow,
+    'atan2': refine_atan2,
+    're': refine_re,
+    'im': refine_im,
+    'arg': refine_arg,
+    'sign': refine_sign,
+    'MatrixElement': refine_matrixelement
+}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..04f5ed37893766feec941614691a9177f14e4027
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/__init__.py
@@ -0,0 +1,13 @@
+"""
+A module to implement finitary relations [1] as predicate.
+
+References
+==========
+
+.. [1] https://en.wikipedia.org/wiki/Finitary_relation
+
+"""
+
+__all__ = ['BinaryRelation', 'AppliedBinaryRelation']
+
+from .binrel import BinaryRelation, AppliedBinaryRelation
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/binrel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/binrel.py
new file mode 100644
index 0000000000000000000000000000000000000000..4b4eba05bcce40f1a05483a30136b6ccd891c42f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/binrel.py
@@ -0,0 +1,212 @@
+"""
+General binary relations.
+"""
+from typing import Optional
+
+from sympy.core.singleton import S
+from sympy.assumptions import AppliedPredicate, ask, Predicate, Q  # type: ignore
+from sympy.core.kind import BooleanKind
+from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le
+from sympy.logic.boolalg import conjuncts, Not
+
+__all__ = ["BinaryRelation", "AppliedBinaryRelation"]
+
+
+class BinaryRelation(Predicate):
+    """
+    Base class for all binary relational predicates.
+
+    Explanation
+    ===========
+
+    Binary relation takes two arguments and returns ``AppliedBinaryRelation``
+    instance. To evaluate it to boolean value, use :obj:`~.ask()` or
+    :obj:`~.refine()` function.
+
+    You can add support for new types by registering the handler to dispatcher.
+    See :obj:`~.Predicate()` for more information about predicate dispatching.
+
+    Examples
+    ========
+
+    Applying and evaluating to boolean value:
+
+    >>> from sympy import Q, ask, sin, cos
+    >>> from sympy.abc import x
+    >>> Q.eq(sin(x)**2+cos(x)**2, 1)
+    Q.eq(sin(x)**2 + cos(x)**2, 1)
+    >>> ask(_)
+    True
+
+    You can define a new binary relation by subclassing and dispatching.
+    Here, we define a relation $R$ such that $x R y$ returns true if
+    $x = y + 1$.
+
+    >>> from sympy import ask, Number, Q
+    >>> from sympy.assumptions import BinaryRelation
+    >>> class MyRel(BinaryRelation):
+    ...     name = "R"
+    ...     is_reflexive = False
+    >>> Q.R = MyRel()
+    >>> @Q.R.register(Number, Number)
+    ... def _(n1, n2, assumptions):
+    ...     return ask(Q.zero(n1 - n2 - 1), assumptions)
+    >>> Q.R(2, 1)
+    Q.R(2, 1)
+
+    Now, we can use ``ask()`` to evaluate it to boolean value.
+
+    >>> ask(Q.R(2, 1))
+    True
+    >>> ask(Q.R(1, 2))
+    False
+
+    ``Q.R`` returns ``False`` with minimum cost if two arguments have same
+    structure because it is antireflexive relation [1] by
+    ``is_reflexive = False``.
+
+    >>> ask(Q.R(x, x))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Reflexive_relation
+    """
+
+    is_reflexive: Optional[bool] = None
+    is_symmetric: Optional[bool] = None
+
+    def __call__(self, *args):
+        if not len(args) == 2:
+            raise ValueError("Binary relation takes two arguments, but got %s." % len(args))
+        return AppliedBinaryRelation(self, *args)
+
+    @property
+    def reversed(self):
+        if self.is_symmetric:
+            return self
+        return None
+
+    @property
+    def negated(self):
+        return None
+
+    def _compare_reflexive(self, lhs, rhs):
+        # quick exit for structurally same arguments
+        # do not check != here because it cannot catch the
+        # equivalent arguments with different structures.
+
+        # reflexivity does not hold to NaN
+        if lhs is S.NaN or rhs is S.NaN:
+            return None
+
+        reflexive = self.is_reflexive
+        if reflexive is None:
+            pass
+        elif reflexive and (lhs == rhs):
+            return True
+        elif not reflexive and (lhs == rhs):
+            return False
+        return None
+
+    def eval(self, args, assumptions=True):
+        # quick exit for structurally same arguments
+        ret = self._compare_reflexive(*args)
+        if ret is not None:
+            return ret
+
+        # don't perform simplify on args here. (done by AppliedBinaryRelation._eval_ask)
+        # evaluate by multipledispatch
+        lhs, rhs = args
+        ret = self.handler(lhs, rhs, assumptions=assumptions)
+        if ret is not None:
+            return ret
+
+        # check reversed order if the relation is reflexive
+        if self.is_reflexive:
+            types = (type(lhs), type(rhs))
+            if self.handler.dispatch(*types) is not self.handler.dispatch(*reversed(types)):
+                ret = self.handler(rhs, lhs, assumptions=assumptions)
+
+        return ret
+
+
+class AppliedBinaryRelation(AppliedPredicate):
+    """
+    The class of expressions resulting from applying ``BinaryRelation``
+    to the arguments.
+
+    """
+
+    @property
+    def lhs(self):
+        """The left-hand side of the relation."""
+        return self.arguments[0]
+
+    @property
+    def rhs(self):
+        """The right-hand side of the relation."""
+        return self.arguments[1]
+
+    @property
+    def reversed(self):
+        """
+        Try to return the relationship with sides reversed.
+        """
+        revfunc = self.function.reversed
+        if revfunc is None:
+            return self
+        return revfunc(self.rhs, self.lhs)
+
+    @property
+    def reversedsign(self):
+        """
+        Try to return the relationship with signs reversed.
+        """
+        revfunc = self.function.reversed
+        if revfunc is None:
+            return self
+        if not any(side.kind is BooleanKind for side in self.arguments):
+            return revfunc(-self.lhs, -self.rhs)
+        return self
+
+    @property
+    def negated(self):
+        neg_rel = self.function.negated
+        if neg_rel is None:
+            return Not(self, evaluate=False)
+        return neg_rel(*self.arguments)
+
+    def _eval_ask(self, assumptions):
+        conj_assumps = set()
+        binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le}
+        for a in conjuncts(assumptions):
+            if a.func in binrelpreds:
+                conj_assumps.add(binrelpreds[type(a)](*a.args))
+            else:
+                conj_assumps.add(a)
+
+        # After CNF in assumptions module is modified to take polyadic
+        # predicate, this will be removed
+        if any(rel in conj_assumps for rel in (self, self.reversed)):
+            return True
+        neg_rels = (self.negated, self.reversed.negated, Not(self, evaluate=False),
+            Not(self.reversed, evaluate=False))
+        if any(rel in conj_assumps for rel in neg_rels):
+            return False
+
+        # evaluation using multipledispatching
+        ret = self.function.eval(self.arguments, assumptions)
+        if ret is not None:
+            return ret
+
+        # simplify the args and try again
+        args = tuple(a.simplify() for a in self.arguments)
+        return self.function.eval(args, assumptions)
+
+    def __bool__(self):
+        ret = ask(self)
+        if ret is None:
+            raise TypeError("Cannot determine truth value of %s" % self)
+        return ret
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/equality.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/equality.py
new file mode 100644
index 0000000000000000000000000000000000000000..d467cea2da706de2cbbc9875f93c7f8e324a9088
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/relation/equality.py
@@ -0,0 +1,302 @@
+"""
+Module for mathematical equality [1] and inequalities [2].
+
+The purpose of this module is to provide the instances which represent the
+binary predicates in order to combine the relationals into logical inference
+system. Objects such as ``Q.eq``, ``Q.lt`` should remain internal to
+assumptions module, and user must use the classes such as :obj:`~.Eq()`,
+:obj:`~.Lt()` instead to construct the relational expressions.
+
+References
+==========
+
+.. [1] https://en.wikipedia.org/wiki/Equality_(mathematics)
+.. [2] https://en.wikipedia.org/wiki/Inequality_(mathematics)
+"""
+from sympy.assumptions import Q
+from sympy.core.relational import is_eq, is_neq, is_gt, is_ge, is_lt, is_le
+
+from .binrel import BinaryRelation
+
+__all__ = ['EqualityPredicate', 'UnequalityPredicate', 'StrictGreaterThanPredicate',
+    'GreaterThanPredicate', 'StrictLessThanPredicate', 'LessThanPredicate']
+
+
+class EqualityPredicate(BinaryRelation):
+    """
+    Binary predicate for $=$.
+
+    The purpose of this class is to provide the instance which represent
+    the equality predicate in order to allow the logical inference.
+    This class must remain internal to assumptions module and user must
+    use :obj:`~.Eq()` instead to construct the equality expression.
+
+    Evaluating this predicate to ``True`` or ``False`` is done by
+    :func:`~.core.relational.is_eq`
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> Q.eq(0, 0)
+    Q.eq(0, 0)
+    >>> ask(_)
+    True
+
+    See Also
+    ========
+
+    sympy.core.relational.Eq
+
+    """
+    is_reflexive = True
+    is_symmetric = True
+
+    name = 'eq'
+    handler = None  # Do not allow dispatching by this predicate
+
+    @property
+    def negated(self):
+        return Q.ne
+
+    def eval(self, args, assumptions=True):
+        if assumptions == True:
+            # default assumptions for is_eq is None
+            assumptions = None
+        return is_eq(*args, assumptions)
+
+
+class UnequalityPredicate(BinaryRelation):
+    r"""
+    Binary predicate for $\neq$.
+
+    The purpose of this class is to provide the instance which represent
+    the inequation predicate in order to allow the logical inference.
+    This class must remain internal to assumptions module and user must
+    use :obj:`~.Ne()` instead to construct the inequation expression.
+
+    Evaluating this predicate to ``True`` or ``False`` is done by
+    :func:`~.core.relational.is_neq`
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> Q.ne(0, 0)
+    Q.ne(0, 0)
+    >>> ask(_)
+    False
+
+    See Also
+    ========
+
+    sympy.core.relational.Ne
+
+    """
+    is_reflexive = False
+    is_symmetric = True
+
+    name = 'ne'
+    handler = None
+
+    @property
+    def negated(self):
+        return Q.eq
+
+    def eval(self, args, assumptions=True):
+        if assumptions == True:
+            # default assumptions for is_neq is None
+            assumptions = None
+        return is_neq(*args, assumptions)
+
+
+class StrictGreaterThanPredicate(BinaryRelation):
+    """
+    Binary predicate for $>$.
+
+    The purpose of this class is to provide the instance which represent
+    the ">" predicate in order to allow the logical inference.
+    This class must remain internal to assumptions module and user must
+    use :obj:`~.Gt()` instead to construct the equality expression.
+
+    Evaluating this predicate to ``True`` or ``False`` is done by
+    :func:`~.core.relational.is_gt`
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> Q.gt(0, 0)
+    Q.gt(0, 0)
+    >>> ask(_)
+    False
+
+    See Also
+    ========
+
+    sympy.core.relational.Gt
+
+    """
+    is_reflexive = False
+    is_symmetric = False
+
+    name = 'gt'
+    handler = None
+
+    @property
+    def reversed(self):
+        return Q.lt
+
+    @property
+    def negated(self):
+        return Q.le
+
+    def eval(self, args, assumptions=True):
+        if assumptions == True:
+            # default assumptions for is_gt is None
+            assumptions = None
+        return is_gt(*args, assumptions)
+
+
+class GreaterThanPredicate(BinaryRelation):
+    """
+    Binary predicate for $>=$.
+
+    The purpose of this class is to provide the instance which represent
+    the ">=" predicate in order to allow the logical inference.
+    This class must remain internal to assumptions module and user must
+    use :obj:`~.Ge()` instead to construct the equality expression.
+
+    Evaluating this predicate to ``True`` or ``False`` is done by
+    :func:`~.core.relational.is_ge`
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> Q.ge(0, 0)
+    Q.ge(0, 0)
+    >>> ask(_)
+    True
+
+    See Also
+    ========
+
+    sympy.core.relational.Ge
+
+    """
+    is_reflexive = True
+    is_symmetric = False
+
+    name = 'ge'
+    handler = None
+
+    @property
+    def reversed(self):
+        return Q.le
+
+    @property
+    def negated(self):
+        return Q.lt
+
+    def eval(self, args, assumptions=True):
+        if assumptions == True:
+            # default assumptions for is_ge is None
+            assumptions = None
+        return is_ge(*args, assumptions)
+
+
+class StrictLessThanPredicate(BinaryRelation):
+    """
+    Binary predicate for $<$.
+
+    The purpose of this class is to provide the instance which represent
+    the "<" predicate in order to allow the logical inference.
+    This class must remain internal to assumptions module and user must
+    use :obj:`~.Lt()` instead to construct the equality expression.
+
+    Evaluating this predicate to ``True`` or ``False`` is done by
+    :func:`~.core.relational.is_lt`
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> Q.lt(0, 0)
+    Q.lt(0, 0)
+    >>> ask(_)
+    False
+
+    See Also
+    ========
+
+    sympy.core.relational.Lt
+
+    """
+    is_reflexive = False
+    is_symmetric = False
+
+    name = 'lt'
+    handler = None
+
+    @property
+    def reversed(self):
+        return Q.gt
+
+    @property
+    def negated(self):
+        return Q.ge
+
+    def eval(self, args, assumptions=True):
+        if assumptions == True:
+            # default assumptions for is_lt is None
+            assumptions = None
+        return is_lt(*args, assumptions)
+
+
+class LessThanPredicate(BinaryRelation):
+    """
+    Binary predicate for $<=$.
+
+    The purpose of this class is to provide the instance which represent
+    the "<=" predicate in order to allow the logical inference.
+    This class must remain internal to assumptions module and user must
+    use :obj:`~.Le()` instead to construct the equality expression.
+
+    Evaluating this predicate to ``True`` or ``False`` is done by
+    :func:`~.core.relational.is_le`
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> Q.le(0, 0)
+    Q.le(0, 0)
+    >>> ask(_)
+    True
+
+    See Also
+    ========
+
+    sympy.core.relational.Le
+
+    """
+    is_reflexive = True
+    is_symmetric = False
+
+    name = 'le'
+    handler = None
+
+    @property
+    def reversed(self):
+        return Q.ge
+
+    @property
+    def negated(self):
+        return Q.gt
+
+    def eval(self, args, assumptions=True):
+        if assumptions == True:
+            # default assumptions for is_le is None
+            assumptions = None
+        return is_le(*args, assumptions)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/satask.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/satask.py
new file mode 100644
index 0000000000000000000000000000000000000000..ffc13f6d3bc3fb7f573c8d5d0564b780440c1a8c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/satask.py
@@ -0,0 +1,369 @@
+"""
+Module to evaluate the proposition with assumptions using SAT algorithm.
+"""
+
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.kind import NumberKind, UndefinedKind
+from sympy.assumptions.ask_generated import get_all_known_matrix_facts, get_all_known_number_facts
+from sympy.assumptions.assume import global_assumptions, AppliedPredicate
+from sympy.assumptions.sathandlers import class_fact_registry
+from sympy.core import oo
+from sympy.logic.inference import satisfiable
+from sympy.assumptions.cnf import CNF, EncodedCNF
+from sympy.matrices.kind import MatrixKind
+
+
+def satask(proposition, assumptions=True, context=global_assumptions,
+        use_known_facts=True, iterations=oo):
+    """
+    Function to evaluate the proposition with assumptions using SAT algorithm.
+
+    This function extracts every fact relevant to the expressions composing
+    proposition and assumptions. For example, if a predicate containing
+    ``Abs(x)`` is proposed, then ``Q.zero(Abs(x)) | Q.positive(Abs(x))``
+    will be found and passed to SAT solver because ``Q.nonnegative`` is
+    registered as a fact for ``Abs``.
+
+    Proposition is evaluated to ``True`` or ``False`` if the truth value can be
+    determined. If not, ``None`` is returned.
+
+    Parameters
+    ==========
+
+    proposition : Any boolean expression.
+        Proposition which will be evaluated to boolean value.
+
+    assumptions : Any boolean expression, optional.
+        Local assumptions to evaluate the *proposition*.
+
+    context : AssumptionsContext, optional.
+        Default assumptions to evaluate the *proposition*. By default,
+        this is ``sympy.assumptions.global_assumptions`` variable.
+
+    use_known_facts : bool, optional.
+        If ``True``, facts from ``sympy.assumptions.ask_generated``
+        module are passed to SAT solver as well.
+
+    iterations : int, optional.
+        Number of times that relevant facts are recursively extracted.
+        Default is infinite times until no new fact is found.
+
+    Returns
+    =======
+
+    ``True``, ``False``, or ``None``
+
+    Examples
+    ========
+
+    >>> from sympy import Abs, Q
+    >>> from sympy.assumptions.satask import satask
+    >>> from sympy.abc import x
+    >>> satask(Q.zero(Abs(x)), Q.zero(x))
+    True
+
+    """
+    props = CNF.from_prop(proposition)
+    _props = CNF.from_prop(~proposition)
+
+    assumptions = CNF.from_prop(assumptions)
+
+    context_cnf = CNF()
+    if context:
+        context_cnf = context_cnf.extend(context)
+
+    sat = get_all_relevant_facts(props, assumptions, context_cnf,
+        use_known_facts=use_known_facts, iterations=iterations)
+    sat.add_from_cnf(assumptions)
+    if context:
+        sat.add_from_cnf(context_cnf)
+
+    return check_satisfiability(props, _props, sat)
+
+
+def check_satisfiability(prop, _prop, factbase):
+    sat_true = factbase.copy()
+    sat_false = factbase.copy()
+    sat_true.add_from_cnf(prop)
+    sat_false.add_from_cnf(_prop)
+    can_be_true = satisfiable(sat_true)
+    can_be_false = satisfiable(sat_false)
+
+    if can_be_true and can_be_false:
+        return None
+
+    if can_be_true and not can_be_false:
+        return True
+
+    if not can_be_true and can_be_false:
+        return False
+
+    if not can_be_true and not can_be_false:
+        # TODO: Run additional checks to see which combination of the
+        # assumptions, global_assumptions, and relevant_facts are
+        # inconsistent.
+        raise ValueError("Inconsistent assumptions")
+
+
+def extract_predargs(proposition, assumptions=None, context=None):
+    """
+    Extract every expression in the argument of predicates from *proposition*,
+    *assumptions* and *context*.
+
+    Parameters
+    ==========
+
+    proposition : sympy.assumptions.cnf.CNF
+
+    assumptions : sympy.assumptions.cnf.CNF, optional.
+
+    context : sympy.assumptions.cnf.CNF, optional.
+        CNF generated from assumptions context.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, Abs
+    >>> from sympy.assumptions.cnf import CNF
+    >>> from sympy.assumptions.satask import extract_predargs
+    >>> from sympy.abc import x, y
+    >>> props = CNF.from_prop(Q.zero(Abs(x*y)))
+    >>> assump = CNF.from_prop(Q.zero(x) & Q.zero(y))
+    >>> extract_predargs(props, assump)
+    {x, y, Abs(x*y)}
+
+    """
+    req_keys = find_symbols(proposition)
+    keys = proposition.all_predicates()
+    # XXX: We need this since True/False are not Basic
+    lkeys = set()
+    if assumptions:
+        lkeys |= assumptions.all_predicates()
+    if context:
+        lkeys |= context.all_predicates()
+
+    lkeys = lkeys - {S.true, S.false}
+    tmp_keys = None
+    while tmp_keys != set():
+        tmp = set()
+        for l in lkeys:
+            syms = find_symbols(l)
+            if (syms & req_keys) != set():
+                tmp |= syms
+        tmp_keys = tmp - req_keys
+        req_keys |= tmp_keys
+    keys |= {l for l in lkeys if find_symbols(l) & req_keys != set()}
+
+    exprs = set()
+    for key in keys:
+        if isinstance(key, AppliedPredicate):
+            exprs |= set(key.arguments)
+        else:
+            exprs.add(key)
+    return exprs
+
+def find_symbols(pred):
+    """
+    Find every :obj:`~.Symbol` in *pred*.
+
+    Parameters
+    ==========
+
+    pred : sympy.assumptions.cnf.CNF, or any Expr.
+
+    """
+    if isinstance(pred, CNF):
+        symbols = set()
+        for a in pred.all_predicates():
+            symbols |= find_symbols(a)
+        return symbols
+    return pred.atoms(Symbol)
+
+
+def get_relevant_clsfacts(exprs, relevant_facts=None):
+    """
+    Extract relevant facts from the items in *exprs*. Facts are defined in
+    ``assumptions.sathandlers`` module.
+
+    This function is recursively called by ``get_all_relevant_facts()``.
+
+    Parameters
+    ==========
+
+    exprs : set
+        Expressions whose relevant facts are searched.
+
+    relevant_facts : sympy.assumptions.cnf.CNF, optional.
+        Pre-discovered relevant facts.
+
+    Returns
+    =======
+
+    exprs : set
+        Candidates for next relevant fact searching.
+
+    relevant_facts : sympy.assumptions.cnf.CNF
+        Updated relevant facts.
+
+    Examples
+    ========
+
+    Here, we will see how facts relevant to ``Abs(x*y)`` are recursively
+    extracted. On the first run, set containing the expression is passed
+    without pre-discovered relevant facts. The result is a set containing
+    candidates for next run, and ``CNF()`` instance containing facts
+    which are relevant to ``Abs`` and its argument.
+
+    >>> from sympy import Abs
+    >>> from sympy.assumptions.satask import get_relevant_clsfacts
+    >>> from sympy.abc import x, y
+    >>> exprs = {Abs(x*y)}
+    >>> exprs, facts = get_relevant_clsfacts(exprs)
+    >>> exprs
+    {x*y}
+    >>> facts.clauses #doctest: +SKIP
+    {frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}),
+    frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}),
+    frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}),
+    frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}),
+    frozenset({Literal(Q.even(Abs(x*y)), False),
+                Literal(Q.odd(Abs(x*y)), False),
+                Literal(Q.odd(x*y), True)}),
+    frozenset({Literal(Q.even(Abs(x*y)), False),
+                Literal(Q.even(x*y), True),
+                Literal(Q.odd(Abs(x*y)), False)}),
+    frozenset({Literal(Q.positive(Abs(x*y)), False),
+                Literal(Q.zero(Abs(x*y)), False)})}
+
+    We pass the first run's results to the second run, and get the expressions
+    for next run and updated facts.
+
+    >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts)
+    >>> exprs
+    {x, y}
+
+    On final run, no more candidate is returned thus we know that all
+    relevant facts are successfully retrieved.
+
+    >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts)
+    >>> exprs
+    set()
+
+    """
+    if not relevant_facts:
+        relevant_facts = CNF()
+
+    newexprs = set()
+    for expr in exprs:
+        for fact in class_fact_registry(expr):
+            newfact = CNF.to_CNF(fact)
+            relevant_facts = relevant_facts._and(newfact)
+            for key in newfact.all_predicates():
+                if isinstance(key, AppliedPredicate):
+                    newexprs |= set(key.arguments)
+
+    return newexprs - exprs, relevant_facts
+
+
+def get_all_relevant_facts(proposition, assumptions, context,
+        use_known_facts=True, iterations=oo):
+    """
+    Extract all relevant facts from *proposition* and *assumptions*.
+
+    This function extracts the facts by recursively calling
+    ``get_relevant_clsfacts()``. Extracted facts are converted to
+    ``EncodedCNF`` and returned.
+
+    Parameters
+    ==========
+
+    proposition : sympy.assumptions.cnf.CNF
+        CNF generated from proposition expression.
+
+    assumptions : sympy.assumptions.cnf.CNF
+        CNF generated from assumption expression.
+
+    context : sympy.assumptions.cnf.CNF
+        CNF generated from assumptions context.
+
+    use_known_facts : bool, optional.
+        If ``True``, facts from ``sympy.assumptions.ask_generated``
+        module are encoded as well.
+
+    iterations : int, optional.
+        Number of times that relevant facts are recursively extracted.
+        Default is infinite times until no new fact is found.
+
+    Returns
+    =======
+
+    sympy.assumptions.cnf.EncodedCNF
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.cnf import CNF
+    >>> from sympy.assumptions.satask import get_all_relevant_facts
+    >>> from sympy.abc import x, y
+    >>> props = CNF.from_prop(Q.nonzero(x*y))
+    >>> assump = CNF.from_prop(Q.nonzero(x))
+    >>> context = CNF.from_prop(Q.nonzero(y))
+    >>> get_all_relevant_facts(props, assump, context) #doctest: +SKIP
+    
+
+    """
+    # The relevant facts might introduce new keys, e.g., Q.zero(x*y) will
+    # introduce the keys Q.zero(x) and Q.zero(y), so we need to run it until
+    # we stop getting new things. Hopefully this strategy won't lead to an
+    # infinite loop in the future.
+    i = 0
+    relevant_facts = CNF()
+    all_exprs = set()
+    while True:
+        if i == 0:
+            exprs = extract_predargs(proposition, assumptions, context)
+        all_exprs |= exprs
+        exprs, relevant_facts = get_relevant_clsfacts(exprs, relevant_facts)
+        i += 1
+        if i >= iterations:
+            break
+        if not exprs:
+            break
+
+    if use_known_facts:
+        known_facts_CNF = CNF()
+
+        if any(expr.kind == MatrixKind(NumberKind) for expr in all_exprs):
+            known_facts_CNF.add_clauses(get_all_known_matrix_facts())
+        # check for undefinedKind since kind system isn't fully implemented
+        if any(((expr.kind == NumberKind) or (expr.kind == UndefinedKind)) for expr in all_exprs):
+            known_facts_CNF.add_clauses(get_all_known_number_facts())
+
+        kf_encoded = EncodedCNF()
+        kf_encoded.from_cnf(known_facts_CNF)
+
+        def translate_literal(lit, delta):
+            if lit > 0:
+                return lit + delta
+            else:
+                return lit - delta
+
+        def translate_data(data, delta):
+            return [{translate_literal(i, delta) for i in clause} for clause in data]
+        data = []
+        symbols = []
+        n_lit = len(kf_encoded.symbols)
+        for i, expr in enumerate(all_exprs):
+            symbols += [pred(expr) for pred in kf_encoded.symbols]
+            data += translate_data(kf_encoded.data, i * n_lit)
+
+        encoding = dict(list(zip(symbols, range(1, len(symbols)+1))))
+        ctx = EncodedCNF(data, encoding)
+    else:
+        ctx = EncodedCNF()
+
+    ctx.add_from_cnf(relevant_facts)
+
+    return ctx
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/sathandlers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/sathandlers.py
new file mode 100644
index 0000000000000000000000000000000000000000..a11199eb0e547187ab280c18196c0259c178e004
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/sathandlers.py
@@ -0,0 +1,322 @@
+from collections import defaultdict
+
+from sympy.assumptions.ask import Q
+from sympy.core import (Add, Mul, Pow, Number, NumberSymbol, Symbol)
+from sympy.core.numbers import ImaginaryUnit
+from sympy.functions.elementary.complexes import Abs
+from sympy.logic.boolalg import (Equivalent, And, Or, Implies)
+from sympy.matrices.expressions import MatMul
+
+# APIs here may be subject to change
+
+
+### Helper functions ###
+
+def allargs(symbol, fact, expr):
+    """
+    Apply all arguments of the expression to the fact structure.
+
+    Parameters
+    ==========
+
+    symbol : Symbol
+        A placeholder symbol.
+
+    fact : Boolean
+        Resulting ``Boolean`` expression.
+
+    expr : Expr
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.sathandlers import allargs
+    >>> from sympy.abc import x, y
+    >>> allargs(x, Q.negative(x) | Q.positive(x), x*y)
+    (Q.negative(x) | Q.positive(x)) & (Q.negative(y) | Q.positive(y))
+
+    """
+    return And(*[fact.subs(symbol, arg) for arg in expr.args])
+
+
+def anyarg(symbol, fact, expr):
+    """
+    Apply any argument of the expression to the fact structure.
+
+    Parameters
+    ==========
+
+    symbol : Symbol
+        A placeholder symbol.
+
+    fact : Boolean
+        Resulting ``Boolean`` expression.
+
+    expr : Expr
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.sathandlers import anyarg
+    >>> from sympy.abc import x, y
+    >>> anyarg(x, Q.negative(x) & Q.positive(x), x*y)
+    (Q.negative(x) & Q.positive(x)) | (Q.negative(y) & Q.positive(y))
+
+    """
+    return Or(*[fact.subs(symbol, arg) for arg in expr.args])
+
+
+def exactlyonearg(symbol, fact, expr):
+    """
+    Apply exactly one argument of the expression to the fact structure.
+
+    Parameters
+    ==========
+
+    symbol : Symbol
+        A placeholder symbol.
+
+    fact : Boolean
+        Resulting ``Boolean`` expression.
+
+    expr : Expr
+
+    Examples
+    ========
+
+    >>> from sympy import Q
+    >>> from sympy.assumptions.sathandlers import exactlyonearg
+    >>> from sympy.abc import x, y
+    >>> exactlyonearg(x, Q.positive(x), x*y)
+    (Q.positive(x) & ~Q.positive(y)) | (Q.positive(y) & ~Q.positive(x))
+
+    """
+    pred_args = [fact.subs(symbol, arg) for arg in expr.args]
+    res = Or(*[And(pred_args[i], *[~lit for lit in pred_args[:i] +
+        pred_args[i+1:]]) for i in range(len(pred_args))])
+    return res
+
+
+### Fact registry ###
+
+class ClassFactRegistry:
+    """
+    Register handlers against classes.
+
+    Explanation
+    ===========
+
+    ``register`` method registers the handler function for a class. Here,
+    handler function should return a single fact. ``multiregister`` method
+    registers the handler function for multiple classes. Here, handler function
+    should return a container of multiple facts.
+
+    ``registry(expr)`` returns a set of facts for *expr*.
+
+    Examples
+    ========
+
+    Here, we register the facts for ``Abs``.
+
+    >>> from sympy import Abs, Equivalent, Q
+    >>> from sympy.assumptions.sathandlers import ClassFactRegistry
+    >>> reg = ClassFactRegistry()
+    >>> @reg.register(Abs)
+    ... def f1(expr):
+    ...     return Q.nonnegative(expr)
+    >>> @reg.register(Abs)
+    ... def f2(expr):
+    ...     arg = expr.args[0]
+    ...     return Equivalent(~Q.zero(arg), ~Q.zero(expr))
+
+    Calling the registry with expression returns the defined facts for the
+    expression.
+
+    >>> from sympy.abc import x
+    >>> reg(Abs(x))
+    {Q.nonnegative(Abs(x)), Equivalent(~Q.zero(x), ~Q.zero(Abs(x)))}
+
+    Multiple facts can be registered at once by ``multiregister`` method.
+
+    >>> reg2 = ClassFactRegistry()
+    >>> @reg2.multiregister(Abs)
+    ... def _(expr):
+    ...     arg = expr.args[0]
+    ...     return [Q.even(arg) >> Q.even(expr), Q.odd(arg) >> Q.odd(expr)]
+    >>> reg2(Abs(x))
+    {Implies(Q.even(x), Q.even(Abs(x))), Implies(Q.odd(x), Q.odd(Abs(x)))}
+
+    """
+    def __init__(self):
+        self.singlefacts = defaultdict(frozenset)
+        self.multifacts = defaultdict(frozenset)
+
+    def register(self, cls):
+        def _(func):
+            self.singlefacts[cls] |= {func}
+            return func
+        return _
+
+    def multiregister(self, *classes):
+        def _(func):
+            for cls in classes:
+                self.multifacts[cls] |= {func}
+            return func
+        return _
+
+    def __getitem__(self, key):
+        ret1 = self.singlefacts[key]
+        for k in self.singlefacts:
+            if issubclass(key, k):
+                ret1 |= self.singlefacts[k]
+
+        ret2 = self.multifacts[key]
+        for k in self.multifacts:
+            if issubclass(key, k):
+                ret2 |= self.multifacts[k]
+
+        return ret1, ret2
+
+    def __call__(self, expr):
+        ret = set()
+
+        handlers1, handlers2 = self[type(expr)]
+
+        ret.update(h(expr) for h in handlers1)
+        for h in handlers2:
+            ret.update(h(expr))
+        return ret
+
+class_fact_registry = ClassFactRegistry()
+
+
+
+### Class fact registration ###
+
+x = Symbol('x')
+
+## Abs ##
+
+@class_fact_registry.multiregister(Abs)
+def _(expr):
+    arg = expr.args[0]
+    return [Q.nonnegative(expr),
+            Equivalent(~Q.zero(arg), ~Q.zero(expr)),
+            Q.even(arg) >> Q.even(expr),
+            Q.odd(arg) >> Q.odd(expr),
+            Q.integer(arg) >> Q.integer(expr),
+            ]
+
+
+### Add ##
+
+@class_fact_registry.multiregister(Add)
+def _(expr):
+    return [allargs(x, Q.positive(x), expr) >> Q.positive(expr),
+            allargs(x, Q.negative(x), expr) >> Q.negative(expr),
+            allargs(x, Q.real(x), expr) >> Q.real(expr),
+            allargs(x, Q.rational(x), expr) >> Q.rational(expr),
+            allargs(x, Q.integer(x), expr) >> Q.integer(expr),
+            exactlyonearg(x, ~Q.integer(x), expr) >> ~Q.integer(expr),
+            ]
+
+@class_fact_registry.register(Add)
+def _(expr):
+    allargs_real = allargs(x, Q.real(x), expr)
+    onearg_irrational = exactlyonearg(x, Q.irrational(x), expr)
+    return Implies(allargs_real, Implies(onearg_irrational, Q.irrational(expr)))
+
+
+### Mul ###
+
+@class_fact_registry.multiregister(Mul)
+def _(expr):
+    return [Equivalent(Q.zero(expr), anyarg(x, Q.zero(x), expr)),
+            allargs(x, Q.positive(x), expr) >> Q.positive(expr),
+            allargs(x, Q.real(x), expr) >> Q.real(expr),
+            allargs(x, Q.rational(x), expr) >> Q.rational(expr),
+            allargs(x, Q.integer(x), expr) >> Q.integer(expr),
+            exactlyonearg(x, ~Q.rational(x), expr) >> ~Q.integer(expr),
+            allargs(x, Q.commutative(x), expr) >> Q.commutative(expr),
+            ]
+
+@class_fact_registry.register(Mul)
+def _(expr):
+    # Implicitly assumes Mul has more than one arg
+    # Would be allargs(x, Q.prime(x) | Q.composite(x)) except 1 is composite
+    # More advanced prime assumptions will require inequalities, as 1 provides
+    # a corner case.
+    allargs_prime = allargs(x, Q.prime(x), expr)
+    return Implies(allargs_prime, ~Q.prime(expr))
+
+@class_fact_registry.register(Mul)
+def _(expr):
+    # General Case: Odd number of imaginary args implies mul is imaginary(To be implemented)
+    allargs_imag_or_real = allargs(x, Q.imaginary(x) | Q.real(x), expr)
+    onearg_imaginary = exactlyonearg(x, Q.imaginary(x), expr)
+    return Implies(allargs_imag_or_real, Implies(onearg_imaginary, Q.imaginary(expr)))
+
+@class_fact_registry.register(Mul)
+def _(expr):
+    allargs_real = allargs(x, Q.real(x), expr)
+    onearg_irrational = exactlyonearg(x, Q.irrational(x), expr)
+    return Implies(allargs_real, Implies(onearg_irrational, Q.irrational(expr)))
+
+@class_fact_registry.register(Mul)
+def _(expr):
+    # Including the integer qualification means we don't need to add any facts
+    # for odd, since the assumptions already know that every integer is
+    # exactly one of even or odd.
+    allargs_integer = allargs(x, Q.integer(x), expr)
+    anyarg_even = anyarg(x, Q.even(x), expr)
+    return Implies(allargs_integer, Equivalent(anyarg_even, Q.even(expr)))
+
+
+### MatMul ###
+
+@class_fact_registry.register(MatMul)
+def _(expr):
+    allargs_square = allargs(x, Q.square(x), expr)
+    allargs_invertible = allargs(x, Q.invertible(x), expr)
+    return Implies(allargs_square, Equivalent(Q.invertible(expr), allargs_invertible))
+
+
+### Pow ###
+
+@class_fact_registry.multiregister(Pow)
+def _(expr):
+    base, exp = expr.base, expr.exp
+    return [
+        (Q.real(base) & Q.even(exp) & Q.nonnegative(exp)) >> Q.nonnegative(expr),
+        (Q.nonnegative(base) & Q.odd(exp) & Q.nonnegative(exp)) >> Q.nonnegative(expr),
+        (Q.nonpositive(base) & Q.odd(exp) & Q.nonnegative(exp)) >> Q.nonpositive(expr),
+        Equivalent(Q.zero(expr), Q.zero(base) & Q.positive(exp))
+    ]
+
+
+### Numbers ###
+
+_old_assump_getters = {
+    Q.positive: lambda o: o.is_positive,
+    Q.zero: lambda o: o.is_zero,
+    Q.negative: lambda o: o.is_negative,
+    Q.rational: lambda o: o.is_rational,
+    Q.irrational: lambda o: o.is_irrational,
+    Q.even: lambda o: o.is_even,
+    Q.odd: lambda o: o.is_odd,
+    Q.imaginary: lambda o: o.is_imaginary,
+    Q.prime: lambda o: o.is_prime,
+    Q.composite: lambda o: o.is_composite,
+}
+
+@class_fact_registry.multiregister(Number, NumberSymbol, ImaginaryUnit)
+def _(expr):
+    ret = []
+    for p, getter in _old_assump_getters.items():
+        pred = p(expr)
+        prop = getter(expr)
+        if prop is not None:
+            ret.append(Equivalent(pred, prop))
+    return ret
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_assumptions_2.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_assumptions_2.py
new file mode 100644
index 0000000000000000000000000000000000000000..493fe4a7ed70301754ad2cfe181c5acf30433768
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_assumptions_2.py
@@ -0,0 +1,35 @@
+"""
+rename this to test_assumptions.py when the old assumptions system is deleted
+"""
+from sympy.abc import x, y
+from sympy.assumptions.assume import global_assumptions
+from sympy.assumptions.ask import Q
+from sympy.printing import pretty
+
+
+def test_equal():
+    """Test for equality"""
+    assert Q.positive(x) == Q.positive(x)
+    assert Q.positive(x) != ~Q.positive(x)
+    assert ~Q.positive(x) == ~Q.positive(x)
+
+
+def test_pretty():
+    assert pretty(Q.positive(x)) == "Q.positive(x)"
+    assert pretty(
+        {Q.positive, Q.integer}) == "{Q.integer, Q.positive}"
+
+
+def test_global():
+    """Test for global assumptions"""
+    global_assumptions.add(x > 0)
+    assert (x > 0) in global_assumptions
+    global_assumptions.remove(x > 0)
+    assert not (x > 0) in global_assumptions
+    # same with multiple of assumptions
+    global_assumptions.add(x > 0, y > 0)
+    assert (x > 0) in global_assumptions
+    assert (y > 0) in global_assumptions
+    global_assumptions.clear()
+    assert not (x > 0) in global_assumptions
+    assert not (y > 0) in global_assumptions
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_context.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_context.py
new file mode 100644
index 0000000000000000000000000000000000000000..be162f1c69492218ff90ea69492925d7779567a4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_context.py
@@ -0,0 +1,39 @@
+from sympy.assumptions import ask, Q
+from sympy.assumptions.assume import assuming, global_assumptions
+from sympy.abc import x, y
+
+def test_assuming():
+    with assuming(Q.integer(x)):
+        assert ask(Q.integer(x))
+    assert not ask(Q.integer(x))
+
+def test_assuming_nested():
+    assert not ask(Q.integer(x))
+    assert not ask(Q.integer(y))
+    with assuming(Q.integer(x)):
+        assert ask(Q.integer(x))
+        assert not ask(Q.integer(y))
+        with assuming(Q.integer(y)):
+            assert ask(Q.integer(x))
+            assert ask(Q.integer(y))
+        assert ask(Q.integer(x))
+        assert not ask(Q.integer(y))
+    assert not ask(Q.integer(x))
+    assert not ask(Q.integer(y))
+
+def test_finally():
+    try:
+        with assuming(Q.integer(x)):
+            1/0
+    except ZeroDivisionError:
+        pass
+    assert not ask(Q.integer(x))
+
+def test_remove_safe():
+    global_assumptions.add(Q.integer(x))
+    with assuming():
+        assert ask(Q.integer(x))
+        global_assumptions.remove(Q.integer(x))
+        assert not ask(Q.integer(x))
+    assert ask(Q.integer(x))
+    global_assumptions.clear() # for the benefit of other tests
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bfa990f080eebe4d6dd5bfdd733ce1a19adf329
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_matrices.py
@@ -0,0 +1,283 @@
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core.symbol import Symbol
+from sympy.matrices.expressions.diagonal import (DiagMatrix, DiagonalMatrix)
+from sympy.matrices.dense import Matrix
+from sympy.matrices.expressions import (MatrixSymbol, Identity, ZeroMatrix,
+        OneMatrix, Trace, MatrixSlice, Determinant, BlockMatrix, BlockDiagMatrix)
+from sympy.matrices.expressions.factorizations import LofLU
+from sympy.testing.pytest import XFAIL
+
+X = MatrixSymbol('X', 2, 2)
+Y = MatrixSymbol('Y', 2, 3)
+Z = MatrixSymbol('Z', 2, 2)
+A1x1 = MatrixSymbol('A1x1', 1, 1)
+B1x1 = MatrixSymbol('B1x1', 1, 1)
+C0x0 = MatrixSymbol('C0x0', 0, 0)
+V1 = MatrixSymbol('V1', 2, 1)
+V2 = MatrixSymbol('V2', 2, 1)
+
+def test_square():
+    assert ask(Q.square(X))
+    assert not ask(Q.square(Y))
+    assert ask(Q.square(Y*Y.T))
+
+def test_invertible():
+    assert ask(Q.invertible(X), Q.invertible(X))
+    assert ask(Q.invertible(Y)) is False
+    assert ask(Q.invertible(X*Y), Q.invertible(X)) is False
+    assert ask(Q.invertible(X*Z), Q.invertible(X)) is None
+    assert ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z)) is True
+    assert ask(Q.invertible(X.T)) is None
+    assert ask(Q.invertible(X.T), Q.invertible(X)) is True
+    assert ask(Q.invertible(X.I)) is True
+    assert ask(Q.invertible(Identity(3))) is True
+    assert ask(Q.invertible(ZeroMatrix(3, 3))) is False
+    assert ask(Q.invertible(OneMatrix(1, 1))) is True
+    assert ask(Q.invertible(OneMatrix(3, 3))) is False
+    assert ask(Q.invertible(X), Q.fullrank(X) & Q.square(X))
+
+def test_singular():
+    assert ask(Q.singular(X)) is None
+    assert ask(Q.singular(X), Q.invertible(X)) is False
+    assert ask(Q.singular(X), ~Q.invertible(X)) is True
+
+@XFAIL
+def test_invertible_fullrank():
+    assert ask(Q.invertible(X), Q.fullrank(X)) is True
+
+
+def test_invertible_BlockMatrix():
+    assert ask(Q.invertible(BlockMatrix([Identity(3)]))) == True
+    assert ask(Q.invertible(BlockMatrix([ZeroMatrix(3, 3)]))) == False
+
+    X = Matrix([[1, 2, 3], [3, 5, 4]])
+    Y = Matrix([[4, 2, 7], [2, 3, 5]])
+    # non-invertible A block
+    assert ask(Q.invertible(BlockMatrix([
+        [Matrix.ones(3, 3), Y.T],
+        [X, Matrix.eye(2)],
+    ]))) == True
+    # non-invertible B block
+    assert ask(Q.invertible(BlockMatrix([
+        [Y.T, Matrix.ones(3, 3)],
+        [Matrix.eye(2), X],
+    ]))) == True
+    # non-invertible C block
+    assert ask(Q.invertible(BlockMatrix([
+        [X, Matrix.eye(2)],
+        [Matrix.ones(3, 3), Y.T],
+    ]))) == True
+    # non-invertible D block
+    assert ask(Q.invertible(BlockMatrix([
+        [Matrix.eye(2), X],
+        [Y.T, Matrix.ones(3, 3)],
+    ]))) == True
+
+
+def test_invertible_BlockDiagMatrix():
+    assert ask(Q.invertible(BlockDiagMatrix(Identity(3), Identity(5)))) == True
+    assert ask(Q.invertible(BlockDiagMatrix(ZeroMatrix(3, 3), Identity(5)))) == False
+    assert ask(Q.invertible(BlockDiagMatrix(Identity(3), OneMatrix(5, 5)))) == False
+
+
+def test_symmetric():
+    assert ask(Q.symmetric(X), Q.symmetric(X))
+    assert ask(Q.symmetric(X*Z), Q.symmetric(X)) is None
+    assert ask(Q.symmetric(X*Z), Q.symmetric(X) & Q.symmetric(Z)) is True
+    assert ask(Q.symmetric(X + Z), Q.symmetric(X) & Q.symmetric(Z)) is True
+    assert ask(Q.symmetric(Y)) is False
+    assert ask(Q.symmetric(Y*Y.T)) is True
+    assert ask(Q.symmetric(Y.T*X*Y)) is None
+    assert ask(Q.symmetric(Y.T*X*Y), Q.symmetric(X)) is True
+    assert ask(Q.symmetric(X**10), Q.symmetric(X)) is True
+    assert ask(Q.symmetric(A1x1)) is True
+    assert ask(Q.symmetric(A1x1 + B1x1)) is True
+    assert ask(Q.symmetric(A1x1 * B1x1)) is True
+    assert ask(Q.symmetric(V1.T*V1)) is True
+    assert ask(Q.symmetric(V1.T*(V1 + V2))) is True
+    assert ask(Q.symmetric(V1.T*(V1 + V2) + A1x1)) is True
+    assert ask(Q.symmetric(MatrixSlice(Y, (0, 1), (1, 2)))) is True
+    assert ask(Q.symmetric(Identity(3))) is True
+    assert ask(Q.symmetric(ZeroMatrix(3, 3))) is True
+    assert ask(Q.symmetric(OneMatrix(3, 3))) is True
+
+def _test_orthogonal_unitary(predicate):
+    assert ask(predicate(X), predicate(X))
+    assert ask(predicate(X.T), predicate(X)) is True
+    assert ask(predicate(X.I), predicate(X)) is True
+    assert ask(predicate(X**2), predicate(X))
+    assert ask(predicate(Y)) is False
+    assert ask(predicate(X)) is None
+    assert ask(predicate(X), ~Q.invertible(X)) is False
+    assert ask(predicate(X*Z*X), predicate(X) & predicate(Z)) is True
+    assert ask(predicate(Identity(3))) is True
+    assert ask(predicate(ZeroMatrix(3, 3))) is False
+    assert ask(Q.invertible(X), predicate(X))
+    assert not ask(predicate(X + Z), predicate(X) & predicate(Z))
+
+def test_orthogonal():
+    _test_orthogonal_unitary(Q.orthogonal)
+
+def test_unitary():
+    _test_orthogonal_unitary(Q.unitary)
+    assert ask(Q.unitary(X), Q.orthogonal(X))
+
+def test_fullrank():
+    assert ask(Q.fullrank(X), Q.fullrank(X))
+    assert ask(Q.fullrank(X**2), Q.fullrank(X))
+    assert ask(Q.fullrank(X.T), Q.fullrank(X)) is True
+    assert ask(Q.fullrank(X)) is None
+    assert ask(Q.fullrank(Y)) is None
+    assert ask(Q.fullrank(X*Z), Q.fullrank(X) & Q.fullrank(Z)) is True
+    assert ask(Q.fullrank(Identity(3))) is True
+    assert ask(Q.fullrank(ZeroMatrix(3, 3))) is False
+    assert ask(Q.fullrank(OneMatrix(1, 1))) is True
+    assert ask(Q.fullrank(OneMatrix(3, 3))) is False
+    assert ask(Q.invertible(X), ~Q.fullrank(X)) == False
+
+
+def test_positive_definite():
+    assert ask(Q.positive_definite(X), Q.positive_definite(X))
+    assert ask(Q.positive_definite(X.T), Q.positive_definite(X)) is True
+    assert ask(Q.positive_definite(X.I), Q.positive_definite(X)) is True
+    assert ask(Q.positive_definite(Y)) is False
+    assert ask(Q.positive_definite(X)) is None
+    assert ask(Q.positive_definite(X**3), Q.positive_definite(X))
+    assert ask(Q.positive_definite(X*Z*X),
+            Q.positive_definite(X) & Q.positive_definite(Z)) is True
+    assert ask(Q.positive_definite(X), Q.orthogonal(X))
+    assert ask(Q.positive_definite(Y.T*X*Y),
+            Q.positive_definite(X) & Q.fullrank(Y)) is True
+    assert not ask(Q.positive_definite(Y.T*X*Y), Q.positive_definite(X))
+    assert ask(Q.positive_definite(Identity(3))) is True
+    assert ask(Q.positive_definite(ZeroMatrix(3, 3))) is False
+    assert ask(Q.positive_definite(OneMatrix(1, 1))) is True
+    assert ask(Q.positive_definite(OneMatrix(3, 3))) is False
+    assert ask(Q.positive_definite(X + Z), Q.positive_definite(X) &
+            Q.positive_definite(Z)) is True
+    assert not ask(Q.positive_definite(-X), Q.positive_definite(X))
+    assert ask(Q.positive(X[1, 1]), Q.positive_definite(X))
+
+def test_triangular():
+    assert ask(Q.upper_triangular(X + Z.T + Identity(2)), Q.upper_triangular(X) &
+            Q.lower_triangular(Z)) is True
+    assert ask(Q.upper_triangular(X*Z.T), Q.upper_triangular(X) &
+            Q.lower_triangular(Z)) is True
+    assert ask(Q.lower_triangular(Identity(3))) is True
+    assert ask(Q.lower_triangular(ZeroMatrix(3, 3))) is True
+    assert ask(Q.upper_triangular(ZeroMatrix(3, 3))) is True
+    assert ask(Q.lower_triangular(OneMatrix(1, 1))) is True
+    assert ask(Q.upper_triangular(OneMatrix(1, 1))) is True
+    assert ask(Q.lower_triangular(OneMatrix(3, 3))) is False
+    assert ask(Q.upper_triangular(OneMatrix(3, 3))) is False
+    assert ask(Q.triangular(X), Q.unit_triangular(X))
+    assert ask(Q.upper_triangular(X**3), Q.upper_triangular(X))
+    assert ask(Q.lower_triangular(X**3), Q.lower_triangular(X))
+
+
+def test_diagonal():
+    assert ask(Q.diagonal(X + Z.T + Identity(2)), Q.diagonal(X) &
+               Q.diagonal(Z)) is True
+    assert ask(Q.diagonal(ZeroMatrix(3, 3)))
+    assert ask(Q.diagonal(OneMatrix(1, 1))) is True
+    assert ask(Q.diagonal(OneMatrix(3, 3))) is False
+    assert ask(Q.lower_triangular(X) & Q.upper_triangular(X), Q.diagonal(X))
+    assert ask(Q.diagonal(X), Q.lower_triangular(X) & Q.upper_triangular(X))
+    assert ask(Q.symmetric(X), Q.diagonal(X))
+    assert ask(Q.triangular(X), Q.diagonal(X))
+    assert ask(Q.diagonal(C0x0))
+    assert ask(Q.diagonal(A1x1))
+    assert ask(Q.diagonal(A1x1 + B1x1))
+    assert ask(Q.diagonal(A1x1*B1x1))
+    assert ask(Q.diagonal(V1.T*V2))
+    assert ask(Q.diagonal(V1.T*(X + Z)*V1))
+    assert ask(Q.diagonal(MatrixSlice(Y, (0, 1), (1, 2)))) is True
+    assert ask(Q.diagonal(V1.T*(V1 + V2))) is True
+    assert ask(Q.diagonal(X**3), Q.diagonal(X))
+    assert ask(Q.diagonal(Identity(3)))
+    assert ask(Q.diagonal(DiagMatrix(V1)))
+    assert ask(Q.diagonal(DiagonalMatrix(X)))
+
+
+def test_non_atoms():
+    assert ask(Q.real(Trace(X)), Q.positive(Trace(X)))
+
+@XFAIL
+def test_non_trivial_implies():
+    X = MatrixSymbol('X', 3, 3)
+    Y = MatrixSymbol('Y', 3, 3)
+    assert ask(Q.lower_triangular(X+Y), Q.lower_triangular(X) &
+               Q.lower_triangular(Y)) is True
+    assert ask(Q.triangular(X), Q.lower_triangular(X)) is True
+    assert ask(Q.triangular(X+Y), Q.lower_triangular(X) &
+               Q.lower_triangular(Y)) is True
+
+def test_MatrixSlice():
+    X = MatrixSymbol('X', 4, 4)
+    B = MatrixSlice(X, (1, 3), (1, 3))
+    C = MatrixSlice(X, (0, 3), (1, 3))
+    assert ask(Q.symmetric(B), Q.symmetric(X))
+    assert ask(Q.invertible(B), Q.invertible(X))
+    assert ask(Q.diagonal(B), Q.diagonal(X))
+    assert ask(Q.orthogonal(B), Q.orthogonal(X))
+    assert ask(Q.upper_triangular(B), Q.upper_triangular(X))
+
+    assert not ask(Q.symmetric(C), Q.symmetric(X))
+    assert not ask(Q.invertible(C), Q.invertible(X))
+    assert not ask(Q.diagonal(C), Q.diagonal(X))
+    assert not ask(Q.orthogonal(C), Q.orthogonal(X))
+    assert not ask(Q.upper_triangular(C), Q.upper_triangular(X))
+
+def test_det_trace_positive():
+    X = MatrixSymbol('X', 4, 4)
+    assert ask(Q.positive(Trace(X)), Q.positive_definite(X))
+    assert ask(Q.positive(Determinant(X)), Q.positive_definite(X))
+
+def test_field_assumptions():
+    X = MatrixSymbol('X', 4, 4)
+    Y = MatrixSymbol('Y', 4, 4)
+    assert ask(Q.real_elements(X), Q.real_elements(X))
+    assert not ask(Q.integer_elements(X), Q.real_elements(X))
+    assert ask(Q.complex_elements(X), Q.real_elements(X))
+    assert ask(Q.complex_elements(X**2), Q.real_elements(X))
+    assert ask(Q.real_elements(X**2), Q.integer_elements(X))
+    assert ask(Q.real_elements(X+Y), Q.real_elements(X)) is None
+    assert ask(Q.real_elements(X+Y), Q.real_elements(X) & Q.real_elements(Y))
+    from sympy.matrices.expressions.hadamard import HadamardProduct
+    assert ask(Q.real_elements(HadamardProduct(X, Y)),
+                    Q.real_elements(X) & Q.real_elements(Y))
+    assert ask(Q.complex_elements(X+Y), Q.real_elements(X) & Q.complex_elements(Y))
+
+    assert ask(Q.real_elements(X.T), Q.real_elements(X))
+    assert ask(Q.real_elements(X.I), Q.real_elements(X) & Q.invertible(X))
+    assert ask(Q.real_elements(Trace(X)), Q.real_elements(X))
+    assert ask(Q.integer_elements(Determinant(X)), Q.integer_elements(X))
+    assert not ask(Q.integer_elements(X.I), Q.integer_elements(X))
+    alpha = Symbol('alpha')
+    assert ask(Q.real_elements(alpha*X), Q.real_elements(X) & Q.real(alpha))
+    assert ask(Q.real_elements(LofLU(X)), Q.real_elements(X))
+    e = Symbol('e', integer=True, negative=True)
+    assert ask(Q.real_elements(X**e), Q.real_elements(X) & Q.invertible(X))
+    assert ask(Q.real_elements(X**e), Q.real_elements(X)) is None
+
+def test_matrix_element_sets():
+    X = MatrixSymbol('X', 4, 4)
+    assert ask(Q.real(X[1, 2]), Q.real_elements(X))
+    assert ask(Q.integer(X[1, 2]), Q.integer_elements(X))
+    assert ask(Q.complex(X[1, 2]), Q.complex_elements(X))
+    assert ask(Q.integer_elements(Identity(3)))
+    assert ask(Q.integer_elements(ZeroMatrix(3, 3)))
+    assert ask(Q.integer_elements(OneMatrix(3, 3)))
+    from sympy.matrices.expressions.fourier import DFT
+    assert ask(Q.complex_elements(DFT(3)))
+
+
+def test_matrix_element_sets_slices_blocks():
+    X = MatrixSymbol('X', 4, 4)
+    assert ask(Q.integer_elements(X[:, 3]), Q.integer_elements(X))
+    assert ask(Q.integer_elements(BlockMatrix([[X], [X]])),
+                        Q.integer_elements(X))
+
+def test_matrix_element_sets_determinant_trace():
+    assert ask(Q.integer(Determinant(X)), Q.integer_elements(X))
+    assert ask(Q.integer(Trace(X)), Q.integer_elements(X))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_query.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_query.py
new file mode 100644
index 0000000000000000000000000000000000000000..e1ae1f1e482e5c9d19e3dcce3f37ad46b6821817
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_query.py
@@ -0,0 +1,2541 @@
+from sympy.abc import t, w, x, y, z, n, k, m, p, i
+from sympy.assumptions import (ask, AssumptionsContext, Q, register_handler,
+        remove_handler)
+from sympy.assumptions.assume import assuming, global_assumptions, Predicate
+from sympy.assumptions.cnf import CNF, Literal
+from sympy.assumptions.facts import (single_fact_lookup,
+    get_known_facts, generate_known_facts_dict, get_known_facts_keys)
+from sympy.assumptions.handlers import AskHandler
+from sympy.assumptions.ask_generated import (get_all_known_facts,
+    get_known_facts_dict)
+from sympy.core.add import Add
+from sympy.core.numbers import (I, Integer, Rational, oo, zoo, pi)
+from sympy.core.singleton import S
+from sympy.core.power import Pow
+from sympy.core.symbol import Str, symbols, Symbol
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import (Abs, im, re, sign)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (
+    acos, acot, asin, atan, cos, cot, sin, tan)
+from sympy.logic.boolalg import Equivalent, Implies, Xor, And, to_cnf
+from sympy.matrices import Matrix, SparseMatrix
+from sympy.testing.pytest import (XFAIL, slow, raises, warns_deprecated_sympy,
+    _both_exp_pow)
+import math
+
+
+def test_int_1():
+    z = 1
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is True
+    assert ask(Q.rational(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is True
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_int_11():
+    z = 11
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is True
+    assert ask(Q.rational(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is True
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is True
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_int_12():
+    z = 12
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is True
+    assert ask(Q.rational(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is True
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is True
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_float_1():
+    z = 1.0
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is None
+    assert ask(Q.rational(z)) is None
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is None
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is None
+    assert ask(Q.odd(z)) is None
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is None
+    assert ask(Q.composite(z)) is None
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+    z = 7.2123
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is None
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is None
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+    # test for issue #12168
+    assert ask(Q.rational(math.pi)) is None
+
+
+def test_zero_0():
+    z = Integer(0)
+    assert ask(Q.nonzero(z)) is False
+    assert ask(Q.zero(z)) is True
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is True
+    assert ask(Q.rational(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is False
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is True
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is True
+
+
+def test_negativeone():
+    z = Integer(-1)
+    assert ask(Q.nonzero(z)) is True
+    assert ask(Q.zero(z)) is False
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is True
+    assert ask(Q.rational(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is False
+    assert ask(Q.negative(z)) is True
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is True
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_infinity():
+    assert ask(Q.commutative(oo)) is True
+    assert ask(Q.integer(oo)) is False
+    assert ask(Q.rational(oo)) is False
+    assert ask(Q.algebraic(oo)) is False
+    assert ask(Q.real(oo)) is False
+    assert ask(Q.extended_real(oo)) is True
+    assert ask(Q.complex(oo)) is False
+    assert ask(Q.irrational(oo)) is False
+    assert ask(Q.imaginary(oo)) is False
+    assert ask(Q.positive(oo)) is False
+    assert ask(Q.extended_positive(oo)) is True
+    assert ask(Q.negative(oo)) is False
+    assert ask(Q.even(oo)) is False
+    assert ask(Q.odd(oo)) is False
+    assert ask(Q.finite(oo)) is False
+    assert ask(Q.infinite(oo)) is True
+    assert ask(Q.prime(oo)) is False
+    assert ask(Q.composite(oo)) is False
+    assert ask(Q.hermitian(oo)) is False
+    assert ask(Q.antihermitian(oo)) is False
+    assert ask(Q.positive_infinite(oo)) is True
+    assert ask(Q.negative_infinite(oo)) is False
+
+
+def test_neg_infinity():
+    mm = S.NegativeInfinity
+    assert ask(Q.commutative(mm)) is True
+    assert ask(Q.integer(mm)) is False
+    assert ask(Q.rational(mm)) is False
+    assert ask(Q.algebraic(mm)) is False
+    assert ask(Q.real(mm)) is False
+    assert ask(Q.extended_real(mm)) is True
+    assert ask(Q.complex(mm)) is False
+    assert ask(Q.irrational(mm)) is False
+    assert ask(Q.imaginary(mm)) is False
+    assert ask(Q.positive(mm)) is False
+    assert ask(Q.negative(mm)) is False
+    assert ask(Q.extended_negative(mm)) is True
+    assert ask(Q.even(mm)) is False
+    assert ask(Q.odd(mm)) is False
+    assert ask(Q.finite(mm)) is False
+    assert ask(Q.infinite(oo)) is True
+    assert ask(Q.prime(mm)) is False
+    assert ask(Q.composite(mm)) is False
+    assert ask(Q.hermitian(mm)) is False
+    assert ask(Q.antihermitian(mm)) is False
+    assert ask(Q.positive_infinite(-oo)) is False
+    assert ask(Q.negative_infinite(-oo)) is True
+
+
+def test_complex_infinity():
+    assert ask(Q.commutative(zoo)) is True
+    assert ask(Q.integer(zoo)) is False
+    assert ask(Q.rational(zoo)) is False
+    assert ask(Q.algebraic(zoo)) is False
+    assert ask(Q.real(zoo)) is False
+    assert ask(Q.extended_real(zoo)) is False
+    assert ask(Q.complex(zoo)) is False
+    assert ask(Q.irrational(zoo)) is False
+    assert ask(Q.imaginary(zoo)) is False
+    assert ask(Q.positive(zoo)) is False
+    assert ask(Q.negative(zoo)) is False
+    assert ask(Q.zero(zoo)) is False
+    assert ask(Q.nonzero(zoo)) is False
+    assert ask(Q.even(zoo)) is False
+    assert ask(Q.odd(zoo)) is False
+    assert ask(Q.finite(zoo)) is False
+    assert ask(Q.infinite(zoo)) is True
+    assert ask(Q.prime(zoo)) is False
+    assert ask(Q.composite(zoo)) is False
+    assert ask(Q.hermitian(zoo)) is False
+    assert ask(Q.antihermitian(zoo)) is False
+    assert ask(Q.positive_infinite(zoo)) is False
+    assert ask(Q.negative_infinite(zoo)) is False
+
+
+def test_nan():
+    nan = S.NaN
+    assert ask(Q.commutative(nan)) is True
+    assert ask(Q.integer(nan)) is None
+    assert ask(Q.rational(nan)) is None
+    assert ask(Q.algebraic(nan)) is None
+    assert ask(Q.real(nan)) is None
+    assert ask(Q.extended_real(nan)) is None
+    assert ask(Q.complex(nan)) is None
+    assert ask(Q.irrational(nan)) is None
+    assert ask(Q.imaginary(nan)) is None
+    assert ask(Q.positive(nan)) is None
+    assert ask(Q.nonzero(nan)) is None
+    assert ask(Q.zero(nan)) is None
+    assert ask(Q.even(nan)) is None
+    assert ask(Q.odd(nan)) is None
+    assert ask(Q.finite(nan)) is None
+    assert ask(Q.infinite(nan)) is None
+    assert ask(Q.prime(nan)) is None
+    assert ask(Q.composite(nan)) is None
+    assert ask(Q.hermitian(nan)) is None
+    assert ask(Q.antihermitian(nan)) is None
+
+
+def test_Rational_number():
+    r = Rational(3, 4)
+    assert ask(Q.commutative(r)) is True
+    assert ask(Q.integer(r)) is False
+    assert ask(Q.rational(r)) is True
+    assert ask(Q.real(r)) is True
+    assert ask(Q.complex(r)) is True
+    assert ask(Q.irrational(r)) is False
+    assert ask(Q.imaginary(r)) is False
+    assert ask(Q.positive(r)) is True
+    assert ask(Q.negative(r)) is False
+    assert ask(Q.even(r)) is False
+    assert ask(Q.odd(r)) is False
+    assert ask(Q.finite(r)) is True
+    assert ask(Q.prime(r)) is False
+    assert ask(Q.composite(r)) is False
+    assert ask(Q.hermitian(r)) is True
+    assert ask(Q.antihermitian(r)) is False
+
+    r = Rational(1, 4)
+    assert ask(Q.positive(r)) is True
+    assert ask(Q.negative(r)) is False
+
+    r = Rational(5, 4)
+    assert ask(Q.negative(r)) is False
+    assert ask(Q.positive(r)) is True
+
+    r = Rational(5, 3)
+    assert ask(Q.positive(r)) is True
+    assert ask(Q.negative(r)) is False
+
+    r = Rational(-3, 4)
+    assert ask(Q.positive(r)) is False
+    assert ask(Q.negative(r)) is True
+
+    r = Rational(-1, 4)
+    assert ask(Q.positive(r)) is False
+    assert ask(Q.negative(r)) is True
+
+    r = Rational(-5, 4)
+    assert ask(Q.negative(r)) is True
+    assert ask(Q.positive(r)) is False
+
+    r = Rational(-5, 3)
+    assert ask(Q.positive(r)) is False
+    assert ask(Q.negative(r)) is True
+
+
+def test_sqrt_2():
+    z = sqrt(2)
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_pi():
+    z = S.Pi
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is False
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+    z = S.Pi + 1
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is False
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+    z = 2*S.Pi
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is False
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+    z = S.Pi ** 2
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is False
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+    z = (1 + S.Pi) ** 2
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is None
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_E():
+    z = S.Exp1
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is False
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_GoldenRatio():
+    z = S.GoldenRatio
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_TribonacciConstant():
+    z = S.TribonacciConstant
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is True
+    assert ask(Q.real(z)) is True
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is True
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is True
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is True
+    assert ask(Q.antihermitian(z)) is False
+
+
+def test_I():
+    z = I
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is True
+    assert ask(Q.real(z)) is False
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is True
+    assert ask(Q.positive(z)) is False
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is False
+    assert ask(Q.antihermitian(z)) is True
+
+    z = 1 + I
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is True
+    assert ask(Q.real(z)) is False
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is False
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is False
+    assert ask(Q.antihermitian(z)) is False
+
+    z = I*(1 + I)
+    assert ask(Q.commutative(z)) is True
+    assert ask(Q.integer(z)) is False
+    assert ask(Q.rational(z)) is False
+    assert ask(Q.algebraic(z)) is True
+    assert ask(Q.real(z)) is False
+    assert ask(Q.complex(z)) is True
+    assert ask(Q.irrational(z)) is False
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.positive(z)) is False
+    assert ask(Q.negative(z)) is False
+    assert ask(Q.even(z)) is False
+    assert ask(Q.odd(z)) is False
+    assert ask(Q.finite(z)) is True
+    assert ask(Q.prime(z)) is False
+    assert ask(Q.composite(z)) is False
+    assert ask(Q.hermitian(z)) is False
+    assert ask(Q.antihermitian(z)) is False
+
+    z = I**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+    z = (-I)**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+    z = (3*I)**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is False
+
+    z = (1)**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+    z = (-1)**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+    z = (1+I)**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is False
+
+    z = (I)**(I+3)
+    assert ask(Q.imaginary(z)) is True
+    assert ask(Q.real(z)) is False
+
+    z = (I)**(I+2)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+    z = (I)**(2)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+    z = (I)**(3)
+    assert ask(Q.imaginary(z)) is True
+    assert ask(Q.real(z)) is False
+
+    z = (3)**(I)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is False
+
+    z = (I)**(0)
+    assert ask(Q.imaginary(z)) is False
+    assert ask(Q.real(z)) is True
+
+def test_bounded():
+    x, y, z = symbols('x,y,z')
+    a = x + y
+    x, y = a.args
+    assert ask(Q.finite(a), Q.positive_infinite(y)) is None
+    assert ask(Q.finite(x)) is None
+    assert ask(Q.finite(x), Q.finite(x)) is True
+    assert ask(Q.finite(x), Q.finite(y)) is None
+    assert ask(Q.finite(x), Q.complex(x)) is True
+    assert ask(Q.finite(x), Q.extended_real(x)) is None
+
+    assert ask(Q.finite(x + 1)) is None
+    assert ask(Q.finite(x + 1), Q.finite(x)) is True
+    a = x + y
+    x, y = a.args
+    # B + B
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is True
+    assert ask(Q.finite(a), Q.positive(x) & Q.finite(y)) is True
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)) is True
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)) is True
+    assert ask(Q.finite(a), Q.positive(x) & Q.finite(y)
+        & ~Q.positive(y)) is True
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
+        & Q.positive(y)) is True
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) & ~Q.positive(x)
+        & ~Q.positive(y)) is True
+    # B + U
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is False
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)) is False
+    assert ask(Q.finite(a), Q.finite(x)
+        & Q.positive_infinite(y)) is False
+    assert ask(Q.finite(a), Q.positive(x)
+        & Q.positive_infinite(y)) is False
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
+        & ~Q.positive(y)) is False
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
+        & Q.positive_infinite(y)) is False
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) & ~Q.finite(y)
+        & ~Q.positive(y)) is False
+    # B + ?
+    assert ask(Q.finite(a), Q.finite(x)) is None
+    assert ask(Q.finite(a), Q.positive(x)) is None
+    assert ask(Q.finite(a), Q.finite(x)
+        & Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), Q.positive(x)
+        & Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.positive(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
+        & Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
+        & ~Q.positive(y)) is None
+    # U + U
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.positive_infinite(y)) is False
+    assert ask(Q.finite(a), Q.positive_infinite(x) & ~Q.finite(y)
+        & ~Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.extended_positive(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & ~Q.extended_positive(x) & ~Q.extended_positive(y)) is False
+    # U + ?
+    assert ask(Q.finite(a), ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.extended_positive(x)
+        & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.extended_positive(x)
+        & Q.positive_infinite(y)) is False
+    assert ask(Q.finite(a), Q.extended_positive(x)
+        & ~Q.finite(y) & ~Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), ~Q.extended_positive(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), ~Q.extended_positive(x) & ~Q.finite(y)
+        & ~Q.extended_positive(y)) is False
+    # ? + ?
+    assert ask(Q.finite(a)) is None
+    assert ask(Q.finite(a), Q.extended_positive(x)) is None
+    assert ask(Q.finite(a), Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), Q.extended_positive(x)
+        & Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), Q.extended_positive(x)
+        & ~Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), ~Q.extended_positive(x)
+        & Q.extended_positive(y)) is None
+    assert ask(Q.finite(a), ~Q.extended_positive(x)
+        & ~Q.extended_positive(y)) is None
+
+    x, y, z = symbols('x,y,z')
+    a = x + y + z
+    x, y, z = a.args
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.negative(z)) is True
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.finite(z)) is True
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.positive(z)) is True
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & Q.finite(z)) is True
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & Q.positive(z)) is True
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
+        & Q.positive(z)) is True
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.extended_positive(y)
+        & Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
+        & Q.extended_negative(z)) is False
+    assert ask(Q.finite(a), Q.negative(x)
+        & Q.negative_infinite(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y)
+        & Q.negative_infinite(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) &
+         Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y)
+        & Q.extended_positive(z)) is False
+    assert ask(Q.finite(a), Q.negative(x) & Q.extended_negative(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.extended_negative(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x)) is None
+    assert ask(Q.finite(a), Q.negative(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative(x) & Q.extended_positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.finite(z)) is True
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.positive(z)) is True
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
+        & Q.positive(z)) is True
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
+        & Q.extended_negative(z)) is False
+    assert ask(Q.finite(a), Q.finite(x)
+        & Q.negative_infinite(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.finite(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y)
+        & Q.extended_positive(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.extended_negative(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.finite(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.extended_negative(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x)) is None
+    assert ask(Q.finite(a), Q.finite(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.extended_positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
+        & Q.positive(z)) is True
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
+        & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
+        & Q.extended_negative(z)) is False
+    assert ask(Q.finite(a), Q.positive(x)
+        & Q.negative_infinite(y)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y)
+        & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.positive(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y)
+        & Q.extended_positive(z)) is False
+    assert ask(Q.finite(a), Q.positive(x) & Q.extended_negative(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.positive(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.extended_negative(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive(x)) is None
+    assert ask(Q.finite(a), Q.positive(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive(x) & Q.extended_positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.negative_infinite(y) & Q.negative_infinite(z)) is False
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.negative_infinite(y) & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.negative_infinite(y)& Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.negative_infinite(y) & Q.extended_negative(z)) is False
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.negative_infinite(y)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.negative_infinite(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & ~Q.finite(y) & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & ~Q.finite(y) & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & ~Q.finite(y) & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & ~Q.finite(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.positive_infinite(y) & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.positive_infinite(y) & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.positive_infinite(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.extended_negative(y) & Q.extended_negative(z)) is False
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.extended_negative(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.negative_infinite(x)
+        & Q.extended_positive(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(z)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y)
+        & Q.positive_infinite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_negative(y)
+        & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_negative(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.positive_infinite(y) & Q.positive_infinite(z)) is False
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.positive_infinite(y) & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.positive_infinite(y)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.positive_infinite(y) & Q.extended_positive(z)) is False
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.extended_negative(y) & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.extended_negative(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.positive_infinite(x)
+        & Q.extended_positive(y) & Q.extended_positive(z)) is False
+    assert ask(Q.finite(a), Q.extended_negative(x)
+        & Q.extended_negative(y) & Q.extended_negative(z)) is None
+    assert ask(Q.finite(a), Q.extended_negative(x)
+        & Q.extended_negative(y)) is None
+    assert ask(Q.finite(a), Q.extended_negative(x)
+        & Q.extended_negative(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.extended_negative(x)) is None
+    assert ask(Q.finite(a), Q.extended_negative(x)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.extended_negative(x)
+        & Q.extended_positive(y) & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a)) is None
+    assert ask(Q.finite(a), Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.extended_positive(y)
+        & Q.extended_positive(z)) is None
+    assert ask(Q.finite(a), Q.extended_positive(x)
+        & Q.extended_positive(y) & Q.extended_positive(z)) is None
+
+    assert ask(Q.finite(2*x)) is None
+    assert ask(Q.finite(2*x), Q.finite(x)) is True
+
+    x, y, z = symbols('x,y,z')
+    a = x*y
+    x, y = a.args
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is True
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.zero(x) & ~Q.finite(y)) is False
+    assert ask(Q.finite(a), Q.finite(x)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y) &~Q.zero(y)) is False
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is False
+    assert ask(Q.finite(a), ~Q.finite(x)) is None
+    assert ask(Q.finite(a), Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(y)) is None
+    assert ask(Q.finite(a)) is None
+    a = x*y*z
+    x, y, z = a.args
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & Q.finite(z)) is True
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.zero(x) & Q.finite(y)
+        & ~Q.zero(y) & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.zero(x) & ~Q.finite(y)
+        & Q.finite(z) & ~Q.zero(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.zero(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y) & ~Q.zero(y)
+        & Q.finite(z) & ~Q.zero(z)) is False
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.zero(x) & Q.finite(y)
+        & ~Q.zero(y) & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & Q.finite(z) & ~Q.zero(z)) is False
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is False
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)) is None
+    assert ask(Q.finite(a), Q.finite(y) & Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(y) & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(y) & Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(y) & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(y)) is None
+    assert ask(Q.finite(a), Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(z) & Q.extended_nonzero(x)
+        & Q.extended_nonzero(y) & Q.extended_nonzero(z)) is None
+    assert ask(Q.finite(a), Q.extended_nonzero(x) & ~Q.finite(y)
+        & Q.extended_nonzero(y) & ~Q.finite(z)
+        & Q.extended_nonzero(z)) is False
+
+    x, y, z = symbols('x,y,z')
+    assert ask(Q.finite(x**2)) is None
+    assert ask(Q.finite(2**x)) is None
+    assert ask(Q.finite(2**x), Q.finite(x)) is True
+    assert ask(Q.finite(x**x)) is None
+    assert ask(Q.finite(S.Half ** x)) is None
+    assert ask(Q.finite(S.Half ** x), Q.extended_positive(x)) is True
+    assert ask(Q.finite(S.Half ** x), Q.extended_negative(x)) is None
+    assert ask(Q.finite(2**x), Q.extended_negative(x)) is True
+    assert ask(Q.finite(sqrt(x))) is None
+    assert ask(Q.finite(2**x), ~Q.finite(x)) is False
+    assert ask(Q.finite(x**2), ~Q.finite(x)) is False
+
+    # https://github.com/sympy/sympy/issues/27707
+    assert ask(Q.finite(x**y), Q.real(x) & Q.real(y)) is None
+    assert ask(Q.finite(x**y), Q.real(x) & Q.negative(y)) is None
+    assert ask(Q.finite(x**y), Q.zero(x) & Q.negative(y)) is False
+    assert ask(Q.finite(x**y), Q.real(x) & Q.positive(y)) is True
+    assert ask(Q.finite(x**y), Q.nonzero(x) & Q.real(y)) is True
+    assert ask(Q.finite(x**y), Q.nonzero(x) & Q.negative(y)) is True
+    assert ask(Q.finite(x**y), Q.zero(x) & Q.positive(y)) is True
+
+    # sign function
+    assert ask(Q.finite(sign(x))) is True
+    assert ask(Q.finite(sign(x)), ~Q.finite(x)) is True
+
+    # exponential functions
+    assert ask(Q.finite(log(x))) is None
+    assert ask(Q.finite(log(x)), Q.finite(x)) is None
+    assert ask(Q.finite(log(x)), ~Q.zero(x)) is True
+    assert ask(Q.finite(log(x)), Q.infinite(x)) is False
+    assert ask(Q.finite(log(x)), Q.zero(x)) is False
+    assert ask(Q.finite(exp(x))) is None
+    assert ask(Q.finite(exp(x)), Q.finite(x)) is True
+    assert ask(Q.finite(exp(2))) is True
+
+    # trigonometric functions
+    assert ask(Q.finite(sin(x))) is True
+    assert ask(Q.finite(sin(x)), ~Q.finite(x)) is True
+    assert ask(Q.finite(cos(x))) is True
+    assert ask(Q.finite(cos(x)), ~Q.finite(x)) is True
+    assert ask(Q.finite(2*sin(x))) is True
+    assert ask(Q.finite(sin(x)**2)) is True
+    assert ask(Q.finite(cos(x)**2)) is True
+    assert ask(Q.finite(cos(x) + sin(x))) is True
+
+
+def test_unbounded():
+    assert ask(Q.infinite(I * oo)) is True
+    assert ask(Q.infinite(1 + I*oo)) is True
+    assert ask(Q.infinite(3 * (I * oo))) is True
+    assert ask(Q.infinite(-I * oo)) is True
+    assert ask(Q.infinite(1 + zoo)) is True
+    assert ask(Q.infinite(I * zoo)) is True
+    assert ask(Q.infinite(x / y), Q.infinite(x) & Q.finite(y) & ~Q.zero(y)) is True
+    assert ask(Q.infinite(I * oo - I * oo)) is None
+    assert ask(Q.infinite(x * I * oo)) is None
+    assert ask(Q.infinite(1 / x), Q.finite(x) & ~Q.zero(x)) is False
+    assert ask(Q.infinite(1 / (I * oo))) is False
+
+
+def test_issue_27441():
+    # https://github.com/sympy/sympy/issues/27441
+    assert ask(Q.composite(y), Q.integer(y) & Q.positive(y) & ~Q.prime(y)) is None
+
+
+def test_issue_27447():
+    x,y,z = symbols('x y z')
+    a = x*y
+    assert ask(Q.finite(a), Q.finite(x)  & ~Q.finite(y)) is None
+    assert ask(Q.finite(a), ~Q.finite(x)  & Q.finite(y)) is None
+
+    a = x*y*z
+    assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
+        & Q.finite(z) ) is None
+    assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)
+        & Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)
+        & ~Q.finite(z)) is None
+    assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
+        & Q.finite(z)) is None
+
+
+@XFAIL
+def test_issue_27662_xfail():
+    assert ask(Q.finite(x*y), ~Q.finite(x)
+        & Q.zero(y)) is None
+
+
+@XFAIL
+def test_bounded_xfail():
+    """We need to support relations in ask for this to work"""
+    assert ask(Q.finite(sin(x)**x)) is True
+    assert ask(Q.finite(cos(x)**x)) is True
+
+
+def test_commutative():
+    """By default objects are Q.commutative that is why it returns True
+    for both key=True and key=False"""
+    assert ask(Q.commutative(x)) is True
+    assert ask(Q.commutative(x), ~Q.commutative(x)) is False
+    assert ask(Q.commutative(x), Q.complex(x)) is True
+    assert ask(Q.commutative(x), Q.imaginary(x)) is True
+    assert ask(Q.commutative(x), Q.real(x)) is True
+    assert ask(Q.commutative(x), Q.positive(x)) is True
+    assert ask(Q.commutative(x), ~Q.commutative(y)) is True
+
+    assert ask(Q.commutative(2*x)) is True
+    assert ask(Q.commutative(2*x), ~Q.commutative(x)) is False
+
+    assert ask(Q.commutative(x + 1)) is True
+    assert ask(Q.commutative(x + 1), ~Q.commutative(x)) is False
+
+    assert ask(Q.commutative(x**2)) is True
+    assert ask(Q.commutative(x**2), ~Q.commutative(x)) is False
+
+    assert ask(Q.commutative(log(x))) is True
+
+
+@_both_exp_pow
+def test_complex():
+    assert ask(Q.complex(x)) is None
+    assert ask(Q.complex(x), Q.complex(x)) is True
+    assert ask(Q.complex(x), Q.complex(y)) is None
+    assert ask(Q.complex(x), ~Q.complex(x)) is False
+    assert ask(Q.complex(x), Q.real(x)) is True
+    assert ask(Q.complex(x), ~Q.real(x)) is None
+    assert ask(Q.complex(x), Q.rational(x)) is True
+    assert ask(Q.complex(x), Q.irrational(x)) is True
+    assert ask(Q.complex(x), Q.positive(x)) is True
+    assert ask(Q.complex(x), Q.imaginary(x)) is True
+    assert ask(Q.complex(x), Q.algebraic(x)) is True
+
+    # a+b
+    assert ask(Q.complex(x + 1), Q.complex(x)) is True
+    assert ask(Q.complex(x + 1), Q.real(x)) is True
+    assert ask(Q.complex(x + 1), Q.rational(x)) is True
+    assert ask(Q.complex(x + 1), Q.irrational(x)) is True
+    assert ask(Q.complex(x + 1), Q.imaginary(x)) is True
+    assert ask(Q.complex(x + 1), Q.integer(x)) is True
+    assert ask(Q.complex(x + 1), Q.even(x)) is True
+    assert ask(Q.complex(x + 1), Q.odd(x)) is True
+    assert ask(Q.complex(x + y), Q.complex(x) & Q.complex(y)) is True
+    assert ask(Q.complex(x + y), Q.real(x) & Q.imaginary(y)) is True
+
+    # a*x +b
+    assert ask(Q.complex(2*x + 1), Q.complex(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.real(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.positive(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.rational(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.irrational(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.imaginary(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.integer(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.even(x)) is True
+    assert ask(Q.complex(2*x + 1), Q.odd(x)) is True
+
+    # x**2
+    assert ask(Q.complex(x**2), Q.complex(x)) is True
+    assert ask(Q.complex(x**2), Q.real(x)) is True
+    assert ask(Q.complex(x**2), Q.positive(x)) is True
+    assert ask(Q.complex(x**2), Q.rational(x)) is True
+    assert ask(Q.complex(x**2), Q.irrational(x)) is True
+    assert ask(Q.complex(x**2), Q.imaginary(x)) is True
+    assert ask(Q.complex(x**2), Q.integer(x)) is True
+    assert ask(Q.complex(x**2), Q.even(x)) is True
+    assert ask(Q.complex(x**2), Q.odd(x)) is True
+
+    # 2**x
+    assert ask(Q.complex(2**x), Q.complex(x)) is True
+    assert ask(Q.complex(2**x), Q.real(x)) is True
+    assert ask(Q.complex(2**x), Q.positive(x)) is True
+    assert ask(Q.complex(2**x), Q.rational(x)) is True
+    assert ask(Q.complex(2**x), Q.irrational(x)) is True
+    assert ask(Q.complex(2**x), Q.imaginary(x)) is True
+    assert ask(Q.complex(2**x), Q.integer(x)) is True
+    assert ask(Q.complex(2**x), Q.even(x)) is True
+    assert ask(Q.complex(2**x), Q.odd(x)) is True
+    assert ask(Q.complex(x**y), Q.complex(x) & Q.complex(y)) is True
+
+    # trigonometric expressions
+    assert ask(Q.complex(sin(x))) is True
+    assert ask(Q.complex(sin(2*x + 1))) is True
+    assert ask(Q.complex(cos(x))) is True
+    assert ask(Q.complex(cos(2*x + 1))) is True
+
+    # exponential
+    assert ask(Q.complex(exp(x))) is True
+    assert ask(Q.complex(exp(x))) is True
+
+    # Q.complexes
+    assert ask(Q.complex(Abs(x))) is True
+    assert ask(Q.complex(re(x))) is True
+    assert ask(Q.complex(im(x))) is True
+
+
+def test_even_query():
+    assert ask(Q.even(x)) is None
+    assert ask(Q.even(x), Q.integer(x)) is None
+    assert ask(Q.even(x), ~Q.integer(x)) is False
+    assert ask(Q.even(x), Q.rational(x)) is None
+    assert ask(Q.even(x), Q.positive(x)) is None
+
+    assert ask(Q.even(2*x)) is None
+    assert ask(Q.even(2*x), Q.integer(x)) is True
+    assert ask(Q.even(2*x), Q.even(x)) is True
+    assert ask(Q.even(2*x), Q.irrational(x)) is False
+    assert ask(Q.even(2*x), Q.odd(x)) is True
+    assert ask(Q.even(2*x), ~Q.integer(x)) is None
+    assert ask(Q.even(3*x), Q.integer(x)) is None
+    assert ask(Q.even(3*x), Q.even(x)) is True
+    assert ask(Q.even(3*x), Q.odd(x)) is False
+
+    assert ask(Q.even(x + 1), Q.odd(x)) is True
+    assert ask(Q.even(x + 1), Q.even(x)) is False
+    assert ask(Q.even(x + 2), Q.odd(x)) is False
+    assert ask(Q.even(x + 2), Q.even(x)) is True
+    assert ask(Q.even(7 - x), Q.odd(x)) is True
+    assert ask(Q.even(7 + x), Q.odd(x)) is True
+    assert ask(Q.even(x + y), Q.odd(x) & Q.odd(y)) is True
+    assert ask(Q.even(x + y), Q.odd(x) & Q.even(y)) is False
+    assert ask(Q.even(x + y), Q.even(x) & Q.even(y)) is True
+
+    assert ask(Q.even(2*x + 1), Q.integer(x)) is False
+    assert ask(Q.even(2*x*y), Q.rational(x) & Q.rational(x)) is None
+    assert ask(Q.even(2*x*y), Q.irrational(x) & Q.irrational(x)) is None
+
+    assert ask(Q.even(x + y + z), Q.odd(x) & Q.odd(y) & Q.even(z)) is True
+    assert ask(Q.even(x + y + z + t),
+        Q.odd(x) & Q.odd(y) & Q.even(z) & Q.integer(t)) is None
+
+    assert ask(Q.even(Abs(x)), Q.even(x)) is True
+    assert ask(Q.even(Abs(x)), ~Q.even(x)) is None
+    assert ask(Q.even(re(x)), Q.even(x)) is True
+    assert ask(Q.even(re(x)), ~Q.even(x)) is None
+    assert ask(Q.even(im(x)), Q.even(x)) is True
+    assert ask(Q.even(im(x)), Q.real(x)) is True
+
+    assert ask(Q.even((-1)**n), Q.integer(n)) is False
+
+    assert ask(Q.even(k**2), Q.even(k)) is True
+    assert ask(Q.even(n**2), Q.odd(n)) is False
+    assert ask(Q.even(2**k), Q.even(k)) is None
+    assert ask(Q.even(x**2)) is None
+
+    assert ask(Q.even(k**m), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
+    assert ask(Q.even(n**m), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is False
+
+    assert ask(Q.even(k**p), Q.even(k) & Q.integer(p) & Q.positive(p)) is True
+    assert ask(Q.even(n**p), Q.odd(n) & Q.integer(p) & Q.positive(p)) is False
+
+    assert ask(Q.even(m**k), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
+    assert ask(Q.even(p**k), Q.even(k) & Q.integer(p) & Q.positive(p)) is None
+
+    assert ask(Q.even(m**n), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is None
+    assert ask(Q.even(p**n), Q.odd(n) & Q.integer(p) & Q.positive(p)) is None
+
+    assert ask(Q.even(k**x), Q.even(k)) is None
+    assert ask(Q.even(n**x), Q.odd(n)) is None
+
+    assert ask(Q.even(x*y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.even(x*x), Q.integer(x)) is None
+    assert ask(Q.even(x*(x + y)), Q.integer(x) & Q.odd(y)) is True
+    assert ask(Q.even(x*(x + y)), Q.integer(x) & Q.even(y)) is None
+
+
+@XFAIL
+def test_evenness_in_ternary_integer_product_with_odd():
+    # Tests that oddness inference is independent of term ordering.
+    # Term ordering at the point of testing depends on SymPy's symbol order, so
+    # we try to force a different order by modifying symbol names.
+    assert ask(Q.even(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is True
+    assert ask(Q.even(y*x*(x + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is True
+
+
+def test_evenness_in_ternary_integer_product_with_even():
+    assert ask(Q.even(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.even(z)) is None
+
+
+def test_extended_real():
+    assert ask(Q.extended_real(x), Q.positive_infinite(x)) is True
+    assert ask(Q.extended_real(x), Q.positive(x)) is True
+    assert ask(Q.extended_real(x), Q.zero(x)) is True
+    assert ask(Q.extended_real(x), Q.negative(x)) is True
+    assert ask(Q.extended_real(x), Q.negative_infinite(x)) is True
+
+    assert ask(Q.extended_real(-x), Q.positive(x)) is True
+    assert ask(Q.extended_real(-x), Q.negative(x)) is True
+
+    assert ask(Q.extended_real(x + S.Infinity), Q.real(x)) is True
+
+    assert ask(Q.extended_real(x), Q.infinite(x)) is None
+
+
+@_both_exp_pow
+def test_rational():
+    assert ask(Q.rational(x), Q.integer(x)) is True
+    assert ask(Q.rational(x), Q.irrational(x)) is False
+    assert ask(Q.rational(x), Q.real(x)) is None
+    assert ask(Q.rational(x), Q.positive(x)) is None
+    assert ask(Q.rational(x), Q.negative(x)) is None
+    assert ask(Q.rational(x), Q.nonzero(x)) is None
+    assert ask(Q.rational(x), ~Q.algebraic(x)) is False
+
+    assert ask(Q.rational(2*x), Q.rational(x)) is True
+    assert ask(Q.rational(2*x), Q.integer(x)) is True
+    assert ask(Q.rational(2*x), Q.even(x)) is True
+    assert ask(Q.rational(2*x), Q.odd(x)) is True
+    assert ask(Q.rational(2*x), Q.irrational(x)) is False
+
+    assert ask(Q.rational(x/2), Q.rational(x)) is True
+    assert ask(Q.rational(x/2), Q.integer(x)) is True
+    assert ask(Q.rational(x/2), Q.even(x)) is True
+    assert ask(Q.rational(x/2), Q.odd(x)) is True
+    assert ask(Q.rational(x/2), Q.irrational(x)) is False
+
+    assert ask(Q.rational(1/x), Q.rational(x) & Q.nonzero(x)) is True
+    assert ask(Q.rational(1/x), Q.integer(x) & Q.nonzero(x)) is True
+    assert ask(Q.rational(1/x), Q.even(x) & Q.nonzero(x)) is True
+    assert ask(Q.rational(1/x), Q.odd(x)) is True
+    assert ask(Q.rational(1/x), Q.irrational(x)) is False
+
+    assert ask(Q.rational(2/x), Q.rational(x) & Q.nonzero(x)) is True
+    assert ask(Q.rational(2/x), Q.integer(x) & Q.nonzero(x)) is True
+    assert ask(Q.rational(2/x), Q.even(x) & Q.nonzero(x)) is True
+    assert ask(Q.rational(2/x), Q.odd(x)) is True
+    assert ask(Q.rational(2/x), Q.irrational(x)) is False
+
+    assert ask(Q.rational(x), ~Q.algebraic(x)) is False
+
+    # with multiple symbols
+    assert ask(Q.rational(x*y), Q.irrational(x) & Q.irrational(y)) is None
+    assert ask(Q.rational(y/x), Q.rational(x) & Q.rational(y) & Q.nonzero(x)) is True
+    assert ask(Q.rational(y/x), Q.integer(x) & Q.rational(y) & Q.nonzero(x)) is True
+    assert ask(Q.rational(y/x), Q.even(x) & Q.rational(y) & Q.nonzero(x)) is True
+    assert ask(Q.rational(y/x), Q.odd(x) & Q.rational(y)) is True
+    assert ask(Q.rational(y/x), Q.irrational(x) & Q.rational(y) & Q.nonzero(y)) is False
+
+    for f in [exp, sin, tan, asin, atan, cos]:
+        assert ask(Q.rational(f(7))) is False
+        assert ask(Q.rational(f(7, evaluate=False))) is False
+        assert ask(Q.rational(f(0, evaluate=False))) is True
+        assert ask(Q.rational(f(x)), Q.rational(x)) is None
+        assert ask(Q.rational(f(x)), Q.rational(x) & Q.nonzero(x)) is False
+
+    for g in [log, acos]:
+        assert ask(Q.rational(g(7))) is False
+        assert ask(Q.rational(g(7, evaluate=False))) is False
+        assert ask(Q.rational(g(1, evaluate=False))) is True
+        assert ask(Q.rational(g(x)), Q.rational(x)) is None
+        assert ask(Q.rational(g(x)), Q.rational(x) & Q.nonzero(x - 1)) is False
+
+    for h in [cot, acot]:
+        assert ask(Q.rational(h(7))) is False
+        assert ask(Q.rational(h(7, evaluate=False))) is False
+        assert ask(Q.rational(h(x)), Q.rational(x)) is False
+
+    # https://github.com/sympy/sympy/issues/27442
+    assert ask(Q.rational(x**y),Q.irrational(x) & Q.rational(y)) is None
+    assert ask(Q.rational(x**y),Q.integer(x) & Q.prime(x) & Q.rational(y)) is None
+    assert ask(Q.rational(x**y),Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.rational(x**y),Q.integer(x) & Q.eq(x,0) & Q.integer(y)) is None
+    assert ask(Q.rational(x**y),Q.eq(x,1) & Q.rational(y)) is None
+    assert ask(Q.rational(x**y),Q.eq(x,-1) & Q.rational(y)) is None
+    assert ask(Q.rational(x**y), Q.prime(x) & Q.rational(y)) is None
+    assert ask(Q.rational(x**y), ~Q.rational(x) & Q.integer(y) ) is None
+    assert ask(Q.rational(Pow(-1, x, evaluate=False), Q.rational(x))) is None
+    assert ask(Q.rational(x**y), Q.integer(y) & ~Q. algebraic(x)) is None
+    assert ask(Q.rational(x**y), Q.integer(y) & ~Q. algebraic(x) & ~Q.zero(x)) is None
+    assert ask(Q.rational(x**y), Q.integer(y) & ~Q.algebraic(x) & Q.complex(x) & ~Q.real(x)) is None
+    assert ask(Q.rational(x**y), Q.integer(y) & ~Q.algebraic(x) & Q.complex(x)) is None
+
+
+def test_hermitian():
+    assert ask(Q.hermitian(x)) is None
+    assert ask(Q.hermitian(x), Q.antihermitian(x)) is None
+    assert ask(Q.hermitian(x), Q.imaginary(x)) is False
+    assert ask(Q.hermitian(x), Q.prime(x)) is True
+    assert ask(Q.hermitian(x), Q.real(x)) is True
+    assert ask(Q.hermitian(x), Q.zero(x)) is True
+
+    assert ask(Q.hermitian(x + 1), Q.antihermitian(x)) is None
+    assert ask(Q.hermitian(x + 1), Q.complex(x)) is None
+    assert ask(Q.hermitian(x + 1), Q.hermitian(x)) is True
+    assert ask(Q.hermitian(x + 1), Q.imaginary(x)) is False
+    assert ask(Q.hermitian(x + 1), Q.real(x)) is True
+    assert ask(Q.hermitian(x + I), Q.antihermitian(x)) is None
+    assert ask(Q.hermitian(x + I), Q.complex(x)) is None
+    assert ask(Q.hermitian(x + I), Q.hermitian(x)) is False
+    assert ask(Q.hermitian(x + I), Q.imaginary(x)) is None
+    assert ask(Q.hermitian(x + I), Q.real(x)) is False
+    assert ask(
+        Q.hermitian(x + y), Q.antihermitian(x) & Q.antihermitian(y)) is None
+    assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.complex(y)) is None
+    assert ask(
+        Q.hermitian(x + y), Q.antihermitian(x) & Q.hermitian(y)) is None
+    assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.imaginary(y)) is None
+    assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.real(y)) is None
+    assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.complex(y)) is None
+    assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.hermitian(y)) is True
+    assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.imaginary(y)) is False
+    assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.real(y)) is True
+    assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.complex(y)) is None
+    assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.imaginary(y)) is None
+    assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.real(y)) is False
+    assert ask(Q.hermitian(x + y), Q.real(x) & Q.complex(y)) is None
+    assert ask(Q.hermitian(x + y), Q.real(x) & Q.real(y)) is True
+
+    assert ask(Q.hermitian(I*x), Q.antihermitian(x)) is True
+    assert ask(Q.hermitian(I*x), Q.complex(x)) is None
+    assert ask(Q.hermitian(I*x), Q.hermitian(x)) is False
+    assert ask(Q.hermitian(I*x), Q.imaginary(x)) is True
+    assert ask(Q.hermitian(I*x), Q.real(x)) is False
+    assert ask(Q.hermitian(x*y), Q.hermitian(x) & Q.real(y)) is True
+
+    assert ask(
+        Q.hermitian(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True
+    assert ask(Q.hermitian(x + y + z),
+        Q.real(x) & Q.real(y) & Q.imaginary(z)) is False
+    assert ask(Q.hermitian(x + y + z),
+        Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is None
+    assert ask(Q.hermitian(x + y + z),
+        Q.imaginary(x) & Q.imaginary(y) & Q.imaginary(z)) is None
+
+    assert ask(Q.antihermitian(x)) is None
+    assert ask(Q.antihermitian(x), Q.real(x)) is False
+    assert ask(Q.antihermitian(x), Q.prime(x)) is False
+
+    assert ask(Q.antihermitian(x + 1), Q.antihermitian(x)) is False
+    assert ask(Q.antihermitian(x + 1), Q.complex(x)) is None
+    assert ask(Q.antihermitian(x + 1), Q.hermitian(x)) is None
+    assert ask(Q.antihermitian(x + 1), Q.imaginary(x)) is False
+    assert ask(Q.antihermitian(x + 1), Q.real(x)) is None
+    assert ask(Q.antihermitian(x + I), Q.antihermitian(x)) is True
+    assert ask(Q.antihermitian(x + I), Q.complex(x)) is None
+    assert ask(Q.antihermitian(x + I), Q.hermitian(x)) is None
+    assert ask(Q.antihermitian(x + I), Q.imaginary(x)) is True
+    assert ask(Q.antihermitian(x + I), Q.real(x)) is False
+    assert ask(Q.antihermitian(x), Q.zero(x)) is True
+
+    assert ask(
+        Q.antihermitian(x + y), Q.antihermitian(x) & Q.antihermitian(y)
+    ) is True
+    assert ask(
+        Q.antihermitian(x + y), Q.antihermitian(x) & Q.complex(y)) is None
+    assert ask(
+        Q.antihermitian(x + y), Q.antihermitian(x) & Q.hermitian(y)) is None
+    assert ask(
+        Q.antihermitian(x + y), Q.antihermitian(x) & Q.imaginary(y)) is True
+    assert ask(Q.antihermitian(x + y), Q.antihermitian(x) & Q.real(y)
+        ) is False
+    assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.complex(y)) is None
+    assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.hermitian(y)
+        ) is None
+    assert ask(
+        Q.antihermitian(x + y), Q.hermitian(x) & Q.imaginary(y)) is None
+    assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.real(y)) is None
+    assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.complex(y)) is None
+    assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.imaginary(y)) is True
+    assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.real(y)) is False
+    assert ask(Q.antihermitian(x + y), Q.real(x) & Q.complex(y)) is None
+    assert ask(Q.antihermitian(x + y), Q.real(x) & Q.real(y)) is None
+
+    assert ask(Q.antihermitian(I*x), Q.real(x)) is True
+    assert ask(Q.antihermitian(I*x), Q.antihermitian(x)) is False
+    assert ask(Q.antihermitian(I*x), Q.complex(x)) is None
+    assert ask(Q.antihermitian(x*y), Q.antihermitian(x) & Q.real(y)) is True
+
+    assert ask(Q.antihermitian(x + y + z),
+        Q.real(x) & Q.real(y) & Q.real(z)) is None
+    assert ask(Q.antihermitian(x + y + z),
+        Q.real(x) & Q.real(y) & Q.imaginary(z)) is None
+    assert ask(Q.antihermitian(x + y + z),
+        Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is False
+    assert ask(Q.antihermitian(x + y + z),
+        Q.imaginary(x) & Q.imaginary(y) & Q.imaginary(z)) is True
+
+
+@_both_exp_pow
+def test_imaginary():
+    assert ask(Q.imaginary(x)) is None
+    assert ask(Q.imaginary(x), Q.real(x)) is False
+    assert ask(Q.imaginary(x), Q.prime(x)) is False
+
+    assert ask(Q.imaginary(x + 1), Q.real(x)) is False
+    assert ask(Q.imaginary(x + 1), Q.imaginary(x)) is False
+    assert ask(Q.imaginary(x + I), Q.real(x)) is False
+    assert ask(Q.imaginary(x + I), Q.imaginary(x)) is True
+    assert ask(Q.imaginary(x + y), Q.imaginary(x) & Q.imaginary(y)) is True
+    assert ask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False
+    assert ask(Q.imaginary(x + y), Q.imaginary(x) & Q.real(y)) is False
+    assert ask(Q.imaginary(x + y), Q.complex(x) & Q.real(y)) is None
+    assert ask(
+        Q.imaginary(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is False
+    assert ask(Q.imaginary(x + y + z),
+        Q.real(x) & Q.real(y) & Q.imaginary(z)) is None
+    assert ask(Q.imaginary(x + y + z),
+        Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is False
+
+    assert ask(Q.imaginary(I*x), Q.real(x)) is True
+    assert ask(Q.imaginary(I*x), Q.imaginary(x)) is False
+    assert ask(Q.imaginary(I*x), Q.complex(x)) is None
+    assert ask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True
+    assert ask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False
+
+    assert ask(Q.imaginary(I**x), Q.negative(x)) is None
+    assert ask(Q.imaginary(I**x), Q.positive(x)) is None
+    assert ask(Q.imaginary(I**x), Q.even(x)) is False
+    assert ask(Q.imaginary(I**x), Q.odd(x)) is True
+    assert ask(Q.imaginary(I**x), Q.imaginary(x)) is False
+    assert ask(Q.imaginary((2*I)**x), Q.imaginary(x)) is False
+    assert ask(Q.imaginary(x**0), Q.imaginary(x)) is False
+    assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.imaginary(y)) is None
+    assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.real(y)) is None
+    assert ask(Q.imaginary(x**y), Q.real(x) & Q.imaginary(y)) is None
+    assert ask(Q.imaginary(x**y), Q.real(x) & Q.real(y)) is None
+    assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.integer(y)) is None
+    assert ask(Q.imaginary(x**y), Q.imaginary(y) & Q.integer(x)) is None
+    assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.odd(y)) is True
+    assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.rational(y)) is None
+    assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.even(y)) is False
+
+    assert ask(Q.imaginary(x**y), Q.real(x) & Q.integer(y)) is False
+    assert ask(Q.imaginary(x**y), Q.positive(x) & Q.real(y)) is False
+    assert ask(Q.imaginary(x**y), Q.negative(x) & Q.real(y)) is None
+    assert ask(Q.imaginary(x**y), Q.negative(x) & Q.real(y) & ~Q.rational(y)) is False
+    assert ask(Q.imaginary(x**y), Q.integer(x) & Q.imaginary(y)) is None
+    assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y) & Q.integer(2*y)) is True
+    assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y) & ~Q.integer(2*y)) is False
+    assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y)) is None
+    assert ask(Q.imaginary(x**y), Q.real(x) & Q.rational(y) & ~Q.integer(2*y)) is False
+    assert ask(Q.imaginary(x**y), Q.real(x) & Q.rational(y) & Q.integer(2*y)) is None
+
+    # logarithm
+    assert ask(Q.imaginary(log(I))) is True
+    assert ask(Q.imaginary(log(2*I))) is False
+    assert ask(Q.imaginary(log(I + 1))) is False
+    assert ask(Q.imaginary(log(x)), Q.complex(x)) is None
+    assert ask(Q.imaginary(log(x)), Q.imaginary(x)) is None
+    assert ask(Q.imaginary(log(x)), Q.positive(x)) is False
+    assert ask(Q.imaginary(log(exp(x))), Q.complex(x)) is None
+    assert ask(Q.imaginary(log(exp(x))), Q.imaginary(x)) is None  # zoo/I/a+I*b
+    assert ask(Q.imaginary(log(exp(I)))) is True
+
+    # exponential
+    assert ask(Q.imaginary(exp(x)**x), Q.imaginary(x)) is False
+    eq = Pow(exp(pi*I*x, evaluate=False), x, evaluate=False)
+    assert ask(Q.imaginary(eq), Q.even(x)) is False
+    eq = Pow(exp(pi*I*x/2, evaluate=False), x, evaluate=False)
+    assert ask(Q.imaginary(eq), Q.odd(x)) is True
+    assert ask(Q.imaginary(exp(3*I*pi*x)**x), Q.integer(x)) is False
+    assert ask(Q.imaginary(exp(2*pi*I, evaluate=False))) is False
+    assert ask(Q.imaginary(exp(pi*I/2, evaluate=False))) is True
+
+    # issue 7886
+    assert ask(Q.imaginary(Pow(x, Rational(1, 4))), Q.real(x) & Q.negative(x)) is False
+
+
+def test_integer():
+    assert ask(Q.integer(x)) is None
+    assert ask(Q.integer(x), Q.integer(x)) is True
+    assert ask(Q.integer(x), ~Q.integer(x)) is False
+    assert ask(Q.integer(x), ~Q.real(x)) is False
+    assert ask(Q.integer(x), ~Q.positive(x)) is None
+    assert ask(Q.integer(x), Q.even(x) | Q.odd(x)) is True
+
+    assert ask(Q.integer(2*x), Q.integer(x)) is True
+    assert ask(Q.integer(2*x), Q.even(x)) is True
+    assert ask(Q.integer(2*x), Q.prime(x)) is True
+    assert ask(Q.integer(2*x), Q.rational(x)) is None
+    assert ask(Q.integer(2*x), Q.real(x)) is None
+    assert ask(Q.integer(sqrt(2)*x), Q.integer(x)) is False
+    assert ask(Q.integer(sqrt(2)*x), Q.irrational(x)) is None
+
+    assert ask(Q.integer(x/2), Q.odd(x)) is False
+    assert ask(Q.integer(x/2), Q.even(x)) is True
+    assert ask(Q.integer(x/3), Q.odd(x)) is None
+    assert ask(Q.integer(x/3), Q.even(x)) is None
+
+    # https://github.com/sympy/sympy/issues/7286
+    assert ask(Q.integer(Abs(x)),Q.integer(x)) is True
+    assert ask(Q.integer(Abs(-x)),Q.integer(x)) is True
+    assert ask(Q.integer(Abs(x)), ~Q.integer(x)) is None
+    assert ask(Q.integer(Abs(x)),Q.complex(x)) is None
+    assert ask(Q.integer(Abs(x+I*y)),Q.real(x) & Q.real(y)) is None
+
+    # https://github.com/sympy/sympy/issues/27739
+    assert ask(Q.integer(x/y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.integer(1/x), Q.integer(x)) is None
+    assert ask(Q.integer(x**y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.integer(sqrt(5))) is False
+    assert ask(Q.integer(x**y), Q.nonzero(x) & Q.zero(y)) is True
+    assert ask(Q.integer(x**y), Q.integer(x) & Q.integer(y) & Q.positive(y)) is True
+    assert ask(Q.integer(-1**x), Q.integer(x)) is True
+    assert ask(Q.integer(x**y), Q.integer(x) & Q.integer(y) & Q.positive(y)) is True
+    assert ask(Q.integer(x**y), Q.zero(x) & Q.integer(y) & Q.positive(y)) is True
+    assert ask(Q.integer(pi**x), Q.zero(x)) is True
+    assert ask(Q.integer(x**y), Q.imaginary(x) & Q.zero(y)) is True
+
+
+def test_negative():
+    assert ask(Q.negative(x), Q.negative(x)) is True
+    assert ask(Q.negative(x), Q.positive(x)) is False
+    assert ask(Q.negative(x), ~Q.real(x)) is False
+    assert ask(Q.negative(x), Q.prime(x)) is False
+    assert ask(Q.negative(x), ~Q.prime(x)) is None
+
+    assert ask(Q.negative(-x), Q.positive(x)) is True
+    assert ask(Q.negative(-x), ~Q.positive(x)) is None
+    assert ask(Q.negative(-x), Q.negative(x)) is False
+    assert ask(Q.negative(-x), Q.positive(x)) is True
+
+    assert ask(Q.negative(x - 1), Q.negative(x)) is True
+    assert ask(Q.negative(x + y)) is None
+    assert ask(Q.negative(x + y), Q.negative(x)) is None
+    assert ask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True
+    assert ask(Q.negative(x + y), Q.negative(x) & Q.nonpositive(y)) is True
+    assert ask(Q.negative(2 + I)) is False
+    # although this could be False, it is representative of expressions
+    # that don't evaluate to a zero with precision
+    assert ask(Q.negative(cos(I)**2 + sin(I)**2 - 1)) is None
+    assert ask(Q.negative(-I + I*(cos(2)**2 + sin(2)**2))) is None
+
+    assert ask(Q.negative(x**2)) is None
+    assert ask(Q.negative(x**2), Q.real(x)) is False
+    assert ask(Q.negative(x**1.4), Q.real(x)) is None
+
+    assert ask(Q.negative(x**I), Q.positive(x)) is None
+
+    assert ask(Q.negative(x*y)) is None
+    assert ask(Q.negative(x*y), Q.positive(x) & Q.positive(y)) is False
+    assert ask(Q.negative(x*y), Q.positive(x) & Q.negative(y)) is True
+    assert ask(Q.negative(x*y), Q.complex(x) & Q.complex(y)) is None
+
+    assert ask(Q.negative(x**y)) is None
+    assert ask(Q.negative(x**y), Q.negative(x) & Q.even(y)) is False
+    assert ask(Q.negative(x**y), Q.negative(x) & Q.odd(y)) is True
+    assert ask(Q.negative(x**y), Q.positive(x) & Q.integer(y)) is False
+
+    assert ask(Q.negative(Abs(x))) is False
+
+
+def test_nonzero():
+    assert ask(Q.nonzero(x)) is None
+    assert ask(Q.nonzero(x), Q.real(x)) is None
+    assert ask(Q.nonzero(x), Q.positive(x)) is True
+    assert ask(Q.nonzero(x), Q.negative(x)) is True
+    assert ask(Q.nonzero(x), Q.negative(x) | Q.positive(x)) is True
+
+    assert ask(Q.nonzero(x + y)) is None
+    assert ask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True
+    assert ask(Q.nonzero(x + y), Q.positive(x) & Q.negative(y)) is None
+    assert ask(Q.nonzero(x + y), Q.negative(x) & Q.negative(y)) is True
+
+    assert ask(Q.nonzero(2*x)) is None
+    assert ask(Q.nonzero(2*x), Q.positive(x)) is True
+    assert ask(Q.nonzero(2*x), Q.negative(x)) is True
+    assert ask(Q.nonzero(x*y), Q.nonzero(x)) is None
+    assert ask(Q.nonzero(x*y), Q.nonzero(x) & Q.nonzero(y)) is True
+
+    assert ask(Q.nonzero(x**y), Q.nonzero(x)) is True
+
+    assert ask(Q.nonzero(Abs(x))) is None
+    assert ask(Q.nonzero(Abs(x)), Q.nonzero(x)) is True
+
+    assert ask(Q.nonzero(log(exp(2*I)))) is False
+    # although this could be False, it is representative of expressions
+    # that don't evaluate to a zero with precision
+    assert ask(Q.nonzero(cos(1)**2 + sin(1)**2 - 1)) is None
+
+
+def test_zero():
+    assert ask(Q.zero(x)) is None
+    assert ask(Q.zero(x), Q.real(x)) is None
+    assert ask(Q.zero(x), Q.positive(x)) is False
+    assert ask(Q.zero(x), Q.negative(x)) is False
+    assert ask(Q.zero(x), Q.negative(x) | Q.positive(x)) is False
+
+    assert ask(Q.zero(x), Q.nonnegative(x) & Q.nonpositive(x)) is True
+
+    assert ask(Q.zero(x + y)) is None
+    assert ask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False
+    assert ask(Q.zero(x + y), Q.positive(x) & Q.negative(y)) is None
+    assert ask(Q.zero(x + y), Q.negative(x) & Q.negative(y)) is False
+
+    assert ask(Q.zero(2*x)) is None
+    assert ask(Q.zero(2*x), Q.positive(x)) is False
+    assert ask(Q.zero(2*x), Q.negative(x)) is False
+    assert ask(Q.zero(x*y), Q.nonzero(x)) is None
+
+    assert ask(Q.zero(Abs(x))) is None
+    assert ask(Q.zero(Abs(x)), Q.zero(x)) is True
+
+    assert ask(Q.integer(x), Q.zero(x)) is True
+    assert ask(Q.even(x), Q.zero(x)) is True
+    assert ask(Q.odd(x), Q.zero(x)) is False
+    assert ask(Q.zero(x), Q.even(x)) is None
+    assert ask(Q.zero(x), Q.odd(x)) is False
+    assert ask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True
+
+
+def test_odd_query():
+    assert ask(Q.odd(x)) is None
+    assert ask(Q.odd(x), Q.odd(x)) is True
+    assert ask(Q.odd(x), Q.integer(x)) is None
+    assert ask(Q.odd(x), ~Q.integer(x)) is False
+    assert ask(Q.odd(x), Q.rational(x)) is None
+    assert ask(Q.odd(x), Q.positive(x)) is None
+
+    assert ask(Q.odd(-x), Q.odd(x)) is True
+
+    assert ask(Q.odd(2*x)) is None
+    assert ask(Q.odd(2*x), Q.integer(x)) is False
+    assert ask(Q.odd(2*x), Q.odd(x)) is False
+    assert ask(Q.odd(2*x), Q.irrational(x)) is False
+    assert ask(Q.odd(2*x), ~Q.integer(x)) is None
+    assert ask(Q.odd(3*x), Q.integer(x)) is None
+
+    assert ask(Q.odd(x/3), Q.odd(x)) is None
+    assert ask(Q.odd(x/3), Q.even(x)) is None
+
+    assert ask(Q.odd(x + 1), Q.even(x)) is True
+    assert ask(Q.odd(x + 2), Q.even(x)) is False
+    assert ask(Q.odd(x + 2), Q.odd(x)) is True
+    assert ask(Q.odd(3 - x), Q.odd(x)) is False
+    assert ask(Q.odd(3 - x), Q.even(x)) is True
+    assert ask(Q.odd(3 + x), Q.odd(x)) is False
+    assert ask(Q.odd(3 + x), Q.even(x)) is True
+    assert ask(Q.odd(x + y), Q.odd(x) & Q.odd(y)) is False
+    assert ask(Q.odd(x + y), Q.odd(x) & Q.even(y)) is True
+    assert ask(Q.odd(x - y), Q.even(x) & Q.odd(y)) is True
+    assert ask(Q.odd(x - y), Q.odd(x) & Q.odd(y)) is False
+
+    assert ask(Q.odd(x + y + z), Q.odd(x) & Q.odd(y) & Q.even(z)) is False
+    assert ask(Q.odd(x + y + z + t),
+        Q.odd(x) & Q.odd(y) & Q.even(z) & Q.integer(t)) is None
+
+    assert ask(Q.odd(2*x + 1), Q.integer(x)) is True
+    assert ask(Q.odd(2*x + y), Q.integer(x) & Q.odd(y)) is True
+    assert ask(Q.odd(2*x + y), Q.integer(x) & Q.even(y)) is False
+    assert ask(Q.odd(2*x + y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.odd(x*y), Q.odd(x) & Q.even(y)) is False
+    assert ask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True
+    assert ask(Q.odd(2*x*y), Q.rational(x) & Q.rational(x)) is None
+    assert ask(Q.odd(2*x*y), Q.irrational(x) & Q.irrational(x)) is None
+
+    assert ask(Q.odd(Abs(x)), Q.odd(x)) is True
+
+    assert ask(Q.odd((-1)**n), Q.integer(n)) is True
+
+    assert ask(Q.odd(k**2), Q.even(k)) is False
+    assert ask(Q.odd(n**2), Q.odd(n)) is True
+    assert ask(Q.odd(3**k), Q.even(k)) is None
+
+    assert ask(Q.odd(k**m), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
+    assert ask(Q.odd(n**m), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is True
+
+    assert ask(Q.odd(k**p), Q.even(k) & Q.integer(p) & Q.positive(p)) is False
+    assert ask(Q.odd(n**p), Q.odd(n) & Q.integer(p) & Q.positive(p)) is True
+
+    assert ask(Q.odd(m**k), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
+    assert ask(Q.odd(p**k), Q.even(k) & Q.integer(p) & Q.positive(p)) is None
+
+    assert ask(Q.odd(m**n), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is None
+    assert ask(Q.odd(p**n), Q.odd(n) & Q.integer(p) & Q.positive(p)) is None
+
+    assert ask(Q.odd(k**x), Q.even(k)) is None
+    assert ask(Q.odd(n**x), Q.odd(n)) is None
+
+    assert ask(Q.odd(x*y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.odd(x*x), Q.integer(x)) is None
+    assert ask(Q.odd(x*(x + y)), Q.integer(x) & Q.odd(y)) is False
+    assert ask(Q.odd(x*(x + y)), Q.integer(x) & Q.even(y)) is None
+
+
+@XFAIL
+def test_oddness_in_ternary_integer_product_with_odd():
+    # Tests that oddness inference is independent of term ordering.
+    # Term ordering at the point of testing depends on SymPy's symbol order, so
+    # we try to force a different order by modifying symbol names.
+    assert ask(Q.odd(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is False
+    assert ask(Q.odd(y*x*(x + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is False
+
+
+def test_oddness_in_ternary_integer_product_with_even():
+    assert ask(Q.odd(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.even(z)) is None
+
+
+def test_prime():
+    assert ask(Q.prime(x), Q.prime(x)) is True
+    assert ask(Q.prime(x), ~Q.prime(x)) is False
+    assert ask(Q.prime(x), Q.integer(x)) is None
+    assert ask(Q.prime(x), ~Q.integer(x)) is False
+
+    assert ask(Q.prime(2*x), Q.integer(x)) is None
+    assert ask(Q.prime(x*y)) is None
+    assert ask(Q.prime(x*y), Q.prime(x)) is None
+    assert ask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.prime(4*x), Q.integer(x)) is False
+    assert ask(Q.prime(4*x)) is None
+
+    assert ask(Q.prime(x**2), Q.integer(x)) is False
+    assert ask(Q.prime(x**2), Q.prime(x)) is False
+
+    # https://github.com/sympy/sympy/issues/27446
+    assert ask(Q.prime(4**x), Q.integer(x)) is False
+    assert ask(Q.prime(p**x), Q.prime(p) & Q.integer(x) & Q.ne(x, 1)) is False
+    assert ask(Q.prime(n**x), Q.integer(x) & Q.composite(n)) is False
+    assert ask(Q.prime(x**y), Q.integer(x) & Q.integer(y)) is None
+    assert ask(Q.prime(2**x), Q.integer(x)) is None
+    assert ask(Q.prime(p**x), Q.prime(p) & Q.integer(x)) is None
+
+    # Ideally, these should return True since the base is prime and the exponent is one,
+    # but currently, they return None.
+    assert ask(Q.prime(x**y), Q.prime(x) & Q.eq(y,1)) is None
+    assert ask(Q.prime(x**y), Q.prime(x) & Q.integer(y) & Q.gt(y,0) & Q.lt(y,2)) is None
+
+    assert ask(Q.prime(Pow(x,1, evaluate=False)), Q.prime(x)) is True
+
+
+@_both_exp_pow
+def test_positive():
+    assert ask(Q.positive(cos(I) ** 2 + sin(I) ** 2 - 1)) is None
+    assert ask(Q.positive(x), Q.positive(x)) is True
+    assert ask(Q.positive(x), Q.negative(x)) is False
+    assert ask(Q.positive(x), Q.nonzero(x)) is None
+
+    assert ask(Q.positive(-x), Q.positive(x)) is False
+    assert ask(Q.positive(-x), Q.negative(x)) is True
+
+    assert ask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True
+    assert ask(Q.positive(x + y), Q.positive(x) & Q.nonnegative(y)) is True
+    assert ask(Q.positive(x + y), Q.positive(x) & Q.negative(y)) is None
+    assert ask(Q.positive(x + y), Q.positive(x) & Q.imaginary(y)) is False
+
+    assert ask(Q.positive(2*x), Q.positive(x)) is True
+    assumptions = Q.positive(x) & Q.negative(y) & Q.negative(z) & Q.positive(w)
+    assert ask(Q.positive(x*y*z)) is None
+    assert ask(Q.positive(x*y*z), assumptions) is True
+    assert ask(Q.positive(-x*y*z), assumptions) is False
+
+    assert ask(Q.positive(x**I), Q.positive(x)) is None
+
+    assert ask(Q.positive(x**2), Q.positive(x)) is True
+    assert ask(Q.positive(x**2), Q.negative(x)) is True
+    assert ask(Q.positive(x**3), Q.negative(x)) is False
+    assert ask(Q.positive(1/(1 + x**2)), Q.real(x)) is True
+    assert ask(Q.positive(2**I)) is False
+    assert ask(Q.positive(2 + I)) is False
+    # although this could be False, it is representative of expressions
+    # that don't evaluate to a zero with precision
+    assert ask(Q.positive(cos(I)**2 + sin(I)**2 - 1)) is None
+    assert ask(Q.positive(-I + I*(cos(2)**2 + sin(2)**2))) is None
+
+    #exponential
+    assert ask(Q.positive(exp(x)), Q.real(x)) is True
+    assert ask(~Q.negative(exp(x)), Q.real(x)) is True
+    assert ask(Q.positive(x + exp(x)), Q.real(x)) is None
+    assert ask(Q.positive(exp(x)), Q.imaginary(x)) is None
+    assert ask(Q.positive(exp(2*pi*I, evaluate=False)), Q.imaginary(x)) is True
+    assert ask(Q.negative(exp(pi*I, evaluate=False)), Q.imaginary(x)) is True
+    assert ask(Q.positive(exp(x*pi*I)), Q.even(x)) is True
+    assert ask(Q.positive(exp(x*pi*I)), Q.odd(x)) is False
+    assert ask(Q.positive(exp(x*pi*I)), Q.real(x)) is None
+
+    # logarithm
+    assert ask(Q.positive(log(x)), Q.imaginary(x)) is False
+    assert ask(Q.positive(log(x)), Q.negative(x)) is False
+    assert ask(Q.positive(log(x)), Q.positive(x)) is None
+    assert ask(Q.positive(log(x + 2)), Q.positive(x)) is True
+
+    # factorial
+    assert ask(Q.positive(factorial(x)), Q.integer(x) & Q.positive(x))
+    assert ask(Q.positive(factorial(x)), Q.integer(x)) is None
+
+    #absolute value
+    assert ask(Q.positive(Abs(x))) is None  # Abs(0) = 0
+    assert ask(Q.positive(Abs(x)), Q.positive(x)) is True
+
+
+def test_nonpositive():
+    assert ask(Q.nonpositive(-1))
+    assert ask(Q.nonpositive(0))
+    assert ask(Q.nonpositive(1)) is False
+    assert ask(~Q.positive(x), Q.nonpositive(x))
+    assert ask(Q.nonpositive(x), Q.positive(x)) is False
+    assert ask(Q.nonpositive(sqrt(-1))) is False
+    assert ask(Q.nonpositive(x), Q.imaginary(x)) is False
+
+
+def test_nonnegative():
+    assert ask(Q.nonnegative(-1)) is False
+    assert ask(Q.nonnegative(0))
+    assert ask(Q.nonnegative(1))
+    assert ask(~Q.negative(x), Q.nonnegative(x))
+    assert ask(Q.nonnegative(x), Q.negative(x)) is False
+    assert ask(Q.nonnegative(sqrt(-1))) is False
+    assert ask(Q.nonnegative(x), Q.imaginary(x)) is False
+
+def test_real_basic():
+    assert ask(Q.real(x)) is None
+    assert ask(Q.real(x), Q.real(x)) is True
+    assert ask(Q.real(x), Q.nonzero(x)) is True
+    assert ask(Q.real(x), Q.positive(x)) is True
+    assert ask(Q.real(x), Q.negative(x)) is True
+    assert ask(Q.real(x), Q.integer(x)) is True
+    assert ask(Q.real(x), Q.even(x)) is True
+    assert ask(Q.real(x), Q.prime(x)) is True
+
+    assert ask(Q.real(x/sqrt(2)), Q.real(x)) is True
+    assert ask(Q.real(x/sqrt(-2)), Q.real(x)) is False
+
+    assert ask(Q.real(x + 1), Q.real(x)) is True
+    assert ask(Q.real(x + I), Q.real(x)) is False
+    assert ask(Q.real(x + I), Q.complex(x)) is None
+
+    assert ask(Q.real(2*x), Q.real(x)) is True
+    assert ask(Q.real(I*x), Q.real(x)) is False
+    assert ask(Q.real(I*x), Q.imaginary(x)) is True
+    assert ask(Q.real(I*x), Q.complex(x)) is None
+
+
+def test_real_pow():
+    assert ask(Q.real(x**2), Q.real(x)) is True
+    assert ask(Q.real(sqrt(x)), Q.negative(x)) is False
+    assert ask(Q.real(x**y), Q.real(x) & Q.integer(y)) is None
+    assert ask(Q.real(x**y), Q.real(x) & Q.real(y)) is None
+    assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) is True
+    assert ask(Q.real(x**y), Q.imaginary(x) & Q.imaginary(y)) is None  # I**I or (2*I)**I
+    assert ask(Q.real(x**y), Q.imaginary(x) & Q.real(y)) is None  # I**1 or I**0
+    assert ask(Q.real(x**y), Q.real(x) & Q.imaginary(y)) is None  # could be exp(2*pi*I) or 2**I
+    assert ask(Q.real(x**0), Q.imaginary(x)) is True
+    assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) is True
+    assert ask(Q.real(x**y), Q.real(x) & Q.rational(y)) is None
+    assert ask(Q.real(x**y), Q.imaginary(x) & Q.integer(y)) is None
+    assert ask(Q.real(x**y), Q.imaginary(x) & Q.odd(y)) is False
+    assert ask(Q.real(x**y), Q.imaginary(x) & Q.even(y)) is True
+    assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.rational(y/z) & Q.even(z) & Q.positive(x)) is True
+    assert ask(Q.real(x**(y/z)), Q.real(x) & Q.rational(y/z) & Q.even(z) & Q.negative(x)) is None
+    assert ask(Q.real(x**(y/z)), Q.real(x) & Q.integer(y/z)) is None
+    assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.positive(x)) is True
+    assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.negative(x)) is None
+    assert ask(Q.real((-I)**i), Q.imaginary(i)) is True
+    assert ask(Q.real(I**i), Q.imaginary(i)) is True
+    assert ask(Q.real(i**i), Q.imaginary(i)) is None  # i might be 2*I
+    assert ask(Q.real(x**i), Q.imaginary(i)) is None  # x could be 0
+    assert ask(Q.real(x**(I*pi/log(x))), Q.real(x)) is True
+
+    # https://github.com/sympy/sympy/issues/27485
+    assert ask(Q.real(n**p), Q.negative(n) & Q.positive(p)) is None
+
+    # https://github.com/sympy/sympy/issues/16530
+    assert ask(Q.real(1/Abs(x))) is None
+    assert ask(Q.real(x**y), Q.zero(x) & Q.real(y)) is None
+    assert ask(Q.real(x**y), Q.zero(x) & Q.positive(y)) is True
+
+
+@_both_exp_pow
+def test_real_functions():
+    # trigonometric functions
+    assert ask(Q.real(sin(x))) is None
+    assert ask(Q.real(cos(x))) is None
+    assert ask(Q.real(sin(x)), Q.real(x)) is True
+    assert ask(Q.real(cos(x)), Q.real(x)) is True
+
+    # exponential function
+    assert ask(Q.real(exp(x))) is None
+    assert ask(Q.real(exp(x)), Q.real(x)) is True
+    assert ask(Q.real(x + exp(x)), Q.real(x)) is True
+    assert ask(Q.real(exp(2*pi*I, evaluate=False))) is True
+    assert ask(Q.real(exp(pi*I, evaluate=False))) is True
+    assert ask(Q.real(exp(pi*I/2, evaluate=False))) is False
+
+    # logarithm
+    assert ask(Q.real(log(I))) is False
+    assert ask(Q.real(log(2*I))) is False
+    assert ask(Q.real(log(I + 1))) is False
+    assert ask(Q.real(log(x)), Q.complex(x)) is None
+    assert ask(Q.real(log(x)), Q.imaginary(x)) is False
+    assert ask(Q.real(log(exp(x))), Q.imaginary(x)) is None  # exp(2*pi*I) is 1, log(exp(pi*I)) is pi*I (disregarding periodicity)
+    assert ask(Q.real(log(exp(x))), Q.complex(x)) is None
+    eq = Pow(exp(2*pi*I*x, evaluate=False), x, evaluate=False)
+    assert ask(Q.real(eq), Q.integer(x)) is True
+    assert ask(Q.real(exp(x)**x), Q.imaginary(x)) is True
+    assert ask(Q.real(exp(x)**x), Q.complex(x)) is None
+
+    # Q.complexes
+    assert ask(Q.real(re(x))) is True
+    assert ask(Q.real(im(x))) is True
+
+
+def test_matrix():
+
+    # hermitian
+    assert ask(Q.hermitian(Matrix([[2, 2 + I, 4], [2 - I, 3, I], [4, -I, 1]]))) == True
+    assert ask(Q.hermitian(Matrix([[2, 2 + I, 4], [2 + I, 3, I], [4, -I, 1]]))) == False
+    z = symbols('z', complex=True)
+    assert ask(Q.hermitian(Matrix([[2, 2 + I, z], [2 - I, 3, I], [4, -I, 1]]))) == None
+    assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))))) == True
+    assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, I, 0), (-5, 0, 11))))) == False
+    assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, z, 0), (-5, 0, 11))))) == None
+
+    # antihermitian
+    A = Matrix([[0, -2 - I, 0], [2 - I, 0, -I], [0, -I, 0]])
+    B = Matrix([[-I, 2 + I, 0], [-2 + I, 0, 2 + I], [0, -2 + I, -I]])
+    assert ask(Q.antihermitian(A)) is True
+    assert ask(Q.antihermitian(B)) is True
+    assert ask(Q.antihermitian(A**2)) is False
+    C = (B**3)
+    C.simplify()
+    assert ask(Q.antihermitian(C)) is True
+    _A = Matrix([[0, -2 - I, 0], [z, 0, -I], [0, -I, 0]])
+    assert ask(Q.antihermitian(_A)) is None
+
+
+@_both_exp_pow
+def test_algebraic():
+    assert ask(Q.algebraic(x)) is None
+
+    assert ask(Q.algebraic(I)) is True
+    assert ask(Q.algebraic(2*I)) is True
+    assert ask(Q.algebraic(I/3)) is True
+
+    assert ask(Q.algebraic(sqrt(7))) is True
+    assert ask(Q.algebraic(2*sqrt(7))) is True
+    assert ask(Q.algebraic(sqrt(7)/3)) is True
+
+    assert ask(Q.algebraic(I*sqrt(3))) is True
+    assert ask(Q.algebraic(sqrt(1 + I*sqrt(3)))) is True
+
+    assert ask(Q.algebraic(1 + I*sqrt(3)**Rational(17, 31))) is True
+    assert ask(Q.algebraic(1 + I*sqrt(3)**(17/pi))) is None
+
+    for f in [exp, sin, tan, asin, atan, cos]:
+        assert ask(Q.algebraic(f(7))) is False
+        assert ask(Q.algebraic(f(7, evaluate=False))) is False
+        assert ask(Q.algebraic(f(0, evaluate=False))) is True
+        assert ask(Q.algebraic(f(x)), Q.algebraic(x)) is None
+        assert ask(Q.algebraic(f(x)), Q.algebraic(x) & Q.nonzero(x)) is False
+
+    for g in [log, acos]:
+        assert ask(Q.algebraic(g(7))) is False
+        assert ask(Q.algebraic(g(7, evaluate=False))) is False
+        assert ask(Q.algebraic(g(1, evaluate=False))) is True
+        assert ask(Q.algebraic(g(x)), Q.algebraic(x)) is None
+        assert ask(Q.algebraic(g(x)), Q.algebraic(x) & Q.nonzero(x - 1)) is False
+
+    for h in [cot, acot]:
+        assert ask(Q.algebraic(h(7))) is False
+        assert ask(Q.algebraic(h(7, evaluate=False))) is False
+        assert ask(Q.algebraic(h(x)), Q.algebraic(x)) is False
+
+    assert ask(Q.algebraic(sqrt(sin(7)))) is None
+    assert ask(Q.algebraic(sqrt(y + I*sqrt(7)))) is None
+
+    assert ask(Q.algebraic(2.47)) is True
+
+    assert ask(Q.algebraic(x), Q.transcendental(x)) is False
+    assert ask(Q.transcendental(x), Q.algebraic(x)) is False
+
+    #https://github.com/sympy/sympy/issues/27445
+    assert ask(Q.algebraic(Pow(1, x, evaluate=False)), Q.algebraic(x)) is None
+    assert ask(Q.algebraic(Pow(x, y))) is None
+    assert ask(Q.algebraic(Pow(1, x, evaluate=False))) is None
+    assert ask(Q.algebraic(x**(pi*I))) is None
+    assert ask(Q.algebraic(pi**n),Q.integer(n) & Q.positive(n)) is False
+    assert ask(Q.algebraic(x**y),Q.algebraic(x) & Q.rational(y)) is True
+
+
+def test_global():
+    """Test ask with global assumptions"""
+    assert ask(Q.integer(x)) is None
+    global_assumptions.add(Q.integer(x))
+    assert ask(Q.integer(x)) is True
+    global_assumptions.clear()
+    assert ask(Q.integer(x)) is None
+
+
+def test_custom_context():
+    """Test ask with custom assumptions context"""
+    assert ask(Q.integer(x)) is None
+    local_context = AssumptionsContext()
+    local_context.add(Q.integer(x))
+    assert ask(Q.integer(x), context=local_context) is True
+    assert ask(Q.integer(x)) is None
+
+
+def test_functions_in_assumptions():
+    assert ask(Q.negative(x), Q.real(x) >> Q.positive(x)) is False
+    assert ask(Q.negative(x), Equivalent(Q.real(x), Q.positive(x))) is False
+    assert ask(Q.negative(x), Xor(Q.real(x), Q.negative(x))) is False
+
+
+def test_composite_ask():
+    assert ask(Q.negative(x) & Q.integer(x),
+        assumptions=Q.real(x) >> Q.positive(x)) is False
+
+
+def test_composite_proposition():
+    assert ask(True) is True
+    assert ask(False) is False
+    assert ask(~Q.negative(x), Q.positive(x)) is True
+    assert ask(~Q.real(x), Q.commutative(x)) is None
+    assert ask(Q.negative(x) & Q.integer(x), Q.positive(x)) is False
+    assert ask(Q.negative(x) & Q.integer(x)) is None
+    assert ask(Q.real(x) | Q.integer(x), Q.positive(x)) is True
+    assert ask(Q.real(x) | Q.integer(x)) is None
+    assert ask(Q.real(x) >> Q.positive(x), Q.negative(x)) is False
+    assert ask(Implies(
+        Q.real(x), Q.positive(x), evaluate=False), Q.negative(x)) is False
+    assert ask(Implies(Q.real(x), Q.positive(x), evaluate=False)) is None
+    assert ask(Equivalent(Q.integer(x), Q.even(x)), Q.even(x)) is True
+    assert ask(Equivalent(Q.integer(x), Q.even(x))) is None
+    assert ask(Equivalent(Q.positive(x), Q.integer(x)), Q.integer(x)) is None
+    assert ask(Q.real(x) | Q.integer(x), Q.real(x) | Q.integer(x)) is True
+
+def test_tautology():
+    assert ask(Q.real(x) | ~Q.real(x)) is True
+    assert ask(Q.real(x) & ~Q.real(x)) is False
+
+def test_composite_assumptions():
+    assert ask(Q.real(x), Q.real(x) & Q.real(y)) is True
+    assert ask(Q.positive(x), Q.positive(x) | Q.positive(y)) is None
+    assert ask(Q.positive(x), Q.real(x) >> Q.positive(y)) is None
+    assert ask(Q.real(x), ~(Q.real(x) >> Q.real(y))) is True
+
+def test_key_extensibility():
+    """test that you can add keys to the ask system at runtime"""
+    # make sure the key is not defined
+    raises(AttributeError, lambda: ask(Q.my_key(x)))
+
+    # Old handler system
+    class MyAskHandler(AskHandler):
+        @staticmethod
+        def Symbol(expr, assumptions):
+            return True
+    try:
+        with warns_deprecated_sympy():
+            register_handler('my_key', MyAskHandler)
+        with warns_deprecated_sympy():
+            assert ask(Q.my_key(x)) is True
+        with warns_deprecated_sympy():
+            assert ask(Q.my_key(x + 1)) is None
+    finally:
+        # We have to disable the stacklevel testing here because this raises
+        # the warning twice from two different places
+        with warns_deprecated_sympy():
+            remove_handler('my_key', MyAskHandler)
+        del Q.my_key
+    raises(AttributeError, lambda: ask(Q.my_key(x)))
+
+    # New handler system
+    class MyPredicate(Predicate):
+        pass
+    try:
+        Q.my_key = MyPredicate()
+        @Q.my_key.register(Symbol)
+        def _(expr, assumptions):
+            return True
+        assert ask(Q.my_key(x)) is True
+        assert ask(Q.my_key(x+1)) is None
+    finally:
+        del Q.my_key
+    raises(AttributeError, lambda: ask(Q.my_key(x)))
+
+
+def test_type_extensibility():
+    """test that new types can be added to the ask system at runtime
+    """
+    from sympy.core import Basic
+
+    class MyType(Basic):
+        pass
+
+    @Q.prime.register(MyType)
+    def _(expr, assumptions):
+        return True
+
+    assert ask(Q.prime(MyType())) is True
+
+
+def test_single_fact_lookup():
+    known_facts = And(Implies(Q.integer, Q.rational),
+                      Implies(Q.rational, Q.real),
+                      Implies(Q.real, Q.complex))
+    known_facts_keys = {Q.integer, Q.rational, Q.real, Q.complex}
+
+    known_facts_cnf = to_cnf(known_facts)
+    mapping = single_fact_lookup(known_facts_keys, known_facts_cnf)
+
+    assert mapping[Q.rational] == {Q.real, Q.rational, Q.complex}
+
+
+def test_generate_known_facts_dict():
+    known_facts = And(Implies(Q.integer(x), Q.rational(x)),
+                      Implies(Q.rational(x), Q.real(x)),
+                      Implies(Q.real(x), Q.complex(x)))
+    known_facts_keys = {Q.integer(x), Q.rational(x), Q.real(x), Q.complex(x)}
+
+    assert generate_known_facts_dict(known_facts_keys, known_facts) == \
+        {Q.complex: ({Q.complex}, set()),
+         Q.integer: ({Q.complex, Q.integer, Q.rational, Q.real}, set()),
+         Q.rational: ({Q.complex, Q.rational, Q.real}, set()),
+         Q.real: ({Q.complex, Q.real}, set())}
+
+
+@slow
+def test_known_facts_consistent():
+    """"Test that ask_generated.py is up-to-date"""
+    x = Symbol('x')
+    fact = get_known_facts(x)
+    # test cnf clauses of fact between unary predicates
+    cnf = CNF.to_CNF(fact)
+    clauses = set()
+    clauses.update(frozenset(Literal(lit.arg.function, lit.is_Not) for lit in sorted(cl, key=str)) for cl in cnf.clauses)
+    assert get_all_known_facts() == clauses
+    # test dictionary of fact between unary predicates
+    keys = [pred(x) for pred in get_known_facts_keys()]
+    mapping = generate_known_facts_dict(keys, fact)
+    assert get_known_facts_dict() == mapping
+
+
+def test_Add_queries():
+    assert ask(Q.prime(12345678901234567890 + (cos(1)**2 + sin(1)**2))) is True
+    assert ask(Q.even(Add(S(2), S(2), evaluate=False))) is True
+    assert ask(Q.prime(Add(S(2), S(2), evaluate=False))) is False
+    assert ask(Q.integer(Add(S(2), S(2), evaluate=False))) is True
+
+
+def test_positive_assuming():
+    with assuming(Q.positive(x + 1)):
+        assert not ask(Q.positive(x))
+
+
+def test_issue_5421():
+    raises(TypeError, lambda: ask(pi/log(x), Q.real))
+
+
+def test_issue_3906():
+    raises(TypeError, lambda: ask(Q.positive))
+
+
+def test_issue_5833():
+    assert ask(Q.positive(log(x)**2), Q.positive(x)) is None
+    assert ask(~Q.negative(log(x)**2), Q.positive(x)) is True
+
+
+def test_issue_6732():
+    raises(ValueError, lambda: ask(Q.positive(x), Q.positive(x) & Q.negative(x)))
+    raises(ValueError, lambda: ask(Q.negative(x), Q.positive(x) & Q.negative(x)))
+
+
+def test_issue_7246():
+    assert ask(Q.positive(atan(p)), Q.positive(p)) is True
+    assert ask(Q.positive(atan(p)), Q.negative(p)) is False
+    assert ask(Q.positive(atan(p)), Q.zero(p)) is False
+    assert ask(Q.positive(atan(x))) is None
+
+    assert ask(Q.positive(asin(p)), Q.positive(p)) is None
+    assert ask(Q.positive(asin(p)), Q.zero(p)) is None
+    assert ask(Q.positive(asin(Rational(1, 7)))) is True
+    assert ask(Q.positive(asin(x)), Q.positive(x) & Q.nonpositive(x - 1)) is True
+    assert ask(Q.positive(asin(x)), Q.negative(x) & Q.nonnegative(x + 1)) is False
+
+    assert ask(Q.positive(acos(p)), Q.positive(p)) is None
+    assert ask(Q.positive(acos(Rational(1, 7)))) is True
+    assert ask(Q.positive(acos(x)), Q.nonnegative(x + 1) & Q.nonpositive(x - 1)) is True
+    assert ask(Q.positive(acos(x)), Q.nonnegative(x - 1)) is None
+
+    assert ask(Q.positive(acot(x)), Q.positive(x)) is True
+    assert ask(Q.positive(acot(x)), Q.real(x)) is True
+    assert ask(Q.positive(acot(x)), Q.imaginary(x)) is False
+    assert ask(Q.positive(acot(x))) is None
+
+
+@XFAIL
+def test_issue_7246_failing():
+    #Move this test to test_issue_7246 once
+    #the new assumptions module is improved.
+    assert ask(Q.positive(acos(x)), Q.zero(x)) is True
+
+
+def test_check_old_assumption():
+    x = symbols('x', real=True)
+    assert ask(Q.real(x)) is True
+    assert ask(Q.imaginary(x)) is False
+    assert ask(Q.complex(x)) is True
+
+    x = symbols('x', imaginary=True)
+    assert ask(Q.real(x)) is False
+    assert ask(Q.imaginary(x)) is True
+    assert ask(Q.complex(x)) is True
+
+    x = symbols('x', complex=True)
+    assert ask(Q.real(x)) is None
+    assert ask(Q.complex(x)) is True
+
+    x = symbols('x', positive=True)
+    assert ask(Q.positive(x)) is True
+    assert ask(Q.negative(x)) is False
+    assert ask(Q.real(x)) is True
+
+    x = symbols('x', commutative=False)
+    assert ask(Q.commutative(x)) is False
+
+    x = symbols('x', negative=True)
+    assert ask(Q.positive(x)) is False
+    assert ask(Q.negative(x)) is True
+
+    x = symbols('x', nonnegative=True)
+    assert ask(Q.negative(x)) is False
+    assert ask(Q.positive(x)) is None
+    assert ask(Q.zero(x)) is None
+
+    x = symbols('x', finite=True)
+    assert ask(Q.finite(x)) is True
+
+    x = symbols('x', prime=True)
+    assert ask(Q.prime(x)) is True
+    assert ask(Q.composite(x)) is False
+
+    x = symbols('x', composite=True)
+    assert ask(Q.prime(x)) is False
+    assert ask(Q.composite(x)) is True
+
+    x = symbols('x', even=True)
+    assert ask(Q.even(x)) is True
+    assert ask(Q.odd(x)) is False
+
+    x = symbols('x', odd=True)
+    assert ask(Q.even(x)) is False
+    assert ask(Q.odd(x)) is True
+
+    x = symbols('x', nonzero=True)
+    assert ask(Q.nonzero(x)) is True
+    assert ask(Q.zero(x)) is False
+
+    x = symbols('x', zero=True)
+    assert ask(Q.zero(x)) is True
+
+    x = symbols('x', integer=True)
+    assert ask(Q.integer(x)) is True
+
+    x = symbols('x', rational=True)
+    assert ask(Q.rational(x)) is True
+    assert ask(Q.irrational(x)) is False
+
+    x = symbols('x', irrational=True)
+    assert ask(Q.irrational(x)) is True
+    assert ask(Q.rational(x)) is False
+
+
+def test_issue_9636():
+    assert ask(Q.integer(1.0)) is None
+    assert ask(Q.prime(3.0)) is None
+    assert ask(Q.composite(4.0)) is None
+    assert ask(Q.even(2.0)) is None
+    assert ask(Q.odd(3.0)) is None
+
+
+def test_autosimp_used_to_fail():
+    # See issue #9807
+    assert ask(Q.imaginary(0**I)) is None
+    assert ask(Q.imaginary(0**(-I))) is None
+    assert ask(Q.real(0**I)) is None
+    assert ask(Q.real(0**(-I))) is None
+
+
+def test_custom_AskHandler():
+    from sympy.logic.boolalg import conjuncts
+
+    # Old handler system
+    class MersenneHandler(AskHandler):
+        @staticmethod
+        def Integer(expr, assumptions):
+            if ask(Q.integer(log(expr + 1, 2))):
+                return True
+        @staticmethod
+        def Symbol(expr, assumptions):
+            if expr in conjuncts(assumptions):
+                return True
+    try:
+        with warns_deprecated_sympy():
+            register_handler('mersenne', MersenneHandler)
+        n = Symbol('n', integer=True)
+        with warns_deprecated_sympy():
+            assert ask(Q.mersenne(7))
+        with warns_deprecated_sympy():
+            assert ask(Q.mersenne(n), Q.mersenne(n))
+    finally:
+        del Q.mersenne
+
+    # New handler system
+    class MersennePredicate(Predicate):
+        pass
+    try:
+        Q.mersenne = MersennePredicate()
+        @Q.mersenne.register(Integer)
+        def _(expr, assumptions):
+            if ask(Q.integer(log(expr + 1, 2))):
+                return True
+        @Q.mersenne.register(Symbol)
+        def _(expr, assumptions):
+            if expr in conjuncts(assumptions):
+                return True
+        assert ask(Q.mersenne(7))
+        assert ask(Q.mersenne(n), Q.mersenne(n))
+    finally:
+        del Q.mersenne
+
+
+def test_polyadic_predicate():
+
+    class SexyPredicate(Predicate):
+        pass
+    try:
+        Q.sexyprime = SexyPredicate()
+
+        @Q.sexyprime.register(Integer, Integer)
+        def _(int1, int2, assumptions):
+            args = sorted([int1, int2])
+            if not all(ask(Q.prime(a), assumptions) for a in args):
+                return False
+            return args[1] - args[0] == 6
+
+        @Q.sexyprime.register(Integer, Integer, Integer)
+        def _(int1, int2, int3, assumptions):
+            args = sorted([int1, int2, int3])
+            if not all(ask(Q.prime(a), assumptions) for a in args):
+                return False
+            return args[2] - args[1] == 6 and args[1] - args[0] == 6
+
+        assert ask(Q.sexyprime(5, 11))
+        assert ask(Q.sexyprime(7, 13, 19))
+    finally:
+        del Q.sexyprime
+
+
+def test_Predicate_handler_is_unique():
+
+    # Undefined predicate does not have a handler
+    assert Predicate('mypredicate').handler is None
+
+    # Handler of defined predicate is unique to the class
+    class MyPredicate(Predicate):
+        pass
+    mp1 = MyPredicate(Str('mp1'))
+    mp2 = MyPredicate(Str('mp2'))
+    assert mp1.handler is mp2.handler
+
+
+def test_relational():
+    assert ask(Q.eq(x, 0), Q.zero(x))
+    assert not ask(Q.eq(x, 0), Q.nonzero(x))
+    assert not ask(Q.ne(x, 0), Q.zero(x))
+    assert ask(Q.ne(x, 0), Q.nonzero(x))
+
+
+def test_issue_25221():
+    assert ask(Q.transcendental(x), Q.algebraic(x) | Q.positive(y,y)) is None
+    assert ask(Q.transcendental(x), Q.algebraic(x) | (0 > y)) is None
+    assert ask(Q.transcendental(x), Q.algebraic(x) | Q.gt(0,y)) is None
+
+
+def test_issue_27440():
+    nan = S.NaN
+    assert ask(Q.negative(nan)) is None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_refine.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_refine.py
new file mode 100644
index 0000000000000000000000000000000000000000..81533a88b232cd5c3cfb9be17d09dad404d679dc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_refine.py
@@ -0,0 +1,227 @@
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+from sympy.core.expr import Expr
+from sympy.core.numbers import (I, Rational, nan, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import (Abs, arg, im, re, sign)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (atan, atan2)
+from sympy.abc import w, x, y, z
+from sympy.core.relational import Eq, Ne
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+
+
+def test_Abs():
+    assert refine(Abs(x), Q.positive(x)) == x
+    assert refine(1 + Abs(x), Q.positive(x)) == 1 + x
+    assert refine(Abs(x), Q.negative(x)) == -x
+    assert refine(1 + Abs(x), Q.negative(x)) == 1 - x
+
+    assert refine(Abs(x**2)) != x**2
+    assert refine(Abs(x**2), Q.real(x)) == x**2
+
+
+def test_pow1():
+    assert refine((-1)**x, Q.even(x)) == 1
+    assert refine((-1)**x, Q.odd(x)) == -1
+    assert refine((-2)**x, Q.even(x)) == 2**x
+
+    # nested powers
+    assert refine(sqrt(x**2)) != Abs(x)
+    assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
+    assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
+    assert refine(sqrt(x**2), Q.positive(x)) == x
+    assert refine((x**3)**Rational(1, 3)) != x
+
+    assert refine((x**3)**Rational(1, 3), Q.real(x)) != x
+    assert refine((x**3)**Rational(1, 3), Q.positive(x)) == x
+
+    assert refine(sqrt(1/x), Q.real(x)) != 1/sqrt(x)
+    assert refine(sqrt(1/x), Q.positive(x)) == 1/sqrt(x)
+
+    # powers of (-1)
+    assert refine((-1)**(x + y), Q.even(x)) == (-1)**y
+    assert refine((-1)**(x + y + z), Q.odd(x) & Q.odd(z)) == (-1)**y
+    assert refine((-1)**(x + y + 1), Q.odd(x)) == (-1)**y
+    assert refine((-1)**(x + y + 2), Q.odd(x)) == (-1)**(y + 1)
+    assert refine((-1)**(x + 3)) == (-1)**(x + 1)
+
+    # continuation
+    assert refine((-1)**((-1)**x/2 - S.Half), Q.integer(x)) == (-1)**x
+    assert refine((-1)**((-1)**x/2 + S.Half), Q.integer(x)) == (-1)**(x + 1)
+    assert refine((-1)**((-1)**x/2 + 5*S.Half), Q.integer(x)) == (-1)**(x + 1)
+
+
+def test_pow2():
+    assert refine((-1)**((-1)**x/2 - 7*S.Half), Q.integer(x)) == (-1)**(x + 1)
+    assert refine((-1)**((-1)**x/2 - 9*S.Half), Q.integer(x)) == (-1)**x
+
+    # powers of Abs
+    assert refine(Abs(x)**2, Q.real(x)) == x**2
+    assert refine(Abs(x)**3, Q.real(x)) == Abs(x)**3
+    assert refine(Abs(x)**2) == Abs(x)**2
+
+
+def test_exp():
+    x = Symbol('x', integer=True)
+    assert refine(exp(pi*I*2*x)) == 1
+    assert refine(exp(pi*I*2*(x + S.Half))) == -1
+    assert refine(exp(pi*I*2*(x + Rational(1, 4)))) == I
+    assert refine(exp(pi*I*2*(x + Rational(3, 4)))) == -I
+
+
+def test_Piecewise():
+    assert refine(Piecewise((1, x < 0), (3, True)), (x < 0)) == 1
+    assert refine(Piecewise((1, x < 0), (3, True)), ~(x < 0)) == 3
+    assert refine(Piecewise((1, x < 0), (3, True)), (y < 0)) == \
+        Piecewise((1, x < 0), (3, True))
+    assert refine(Piecewise((1, x > 0), (3, True)), (x > 0)) == 1
+    assert refine(Piecewise((1, x > 0), (3, True)), ~(x > 0)) == 3
+    assert refine(Piecewise((1, x > 0), (3, True)), (y > 0)) == \
+        Piecewise((1, x > 0), (3, True))
+    assert refine(Piecewise((1, x <= 0), (3, True)), (x <= 0)) == 1
+    assert refine(Piecewise((1, x <= 0), (3, True)), ~(x <= 0)) == 3
+    assert refine(Piecewise((1, x <= 0), (3, True)), (y <= 0)) == \
+        Piecewise((1, x <= 0), (3, True))
+    assert refine(Piecewise((1, x >= 0), (3, True)), (x >= 0)) == 1
+    assert refine(Piecewise((1, x >= 0), (3, True)), ~(x >= 0)) == 3
+    assert refine(Piecewise((1, x >= 0), (3, True)), (y >= 0)) == \
+        Piecewise((1, x >= 0), (3, True))
+    assert refine(Piecewise((1, Eq(x, 0)), (3, True)), (Eq(x, 0)))\
+        == 1
+    assert refine(Piecewise((1, Eq(x, 0)), (3, True)), (Eq(0, x)))\
+        == 1
+    assert refine(Piecewise((1, Eq(x, 0)), (3, True)), ~(Eq(x, 0)))\
+        == 3
+    assert refine(Piecewise((1, Eq(x, 0)), (3, True)), ~(Eq(0, x)))\
+        == 3
+    assert refine(Piecewise((1, Eq(x, 0)), (3, True)), (Eq(y, 0)))\
+        == Piecewise((1, Eq(x, 0)), (3, True))
+    assert refine(Piecewise((1, Ne(x, 0)), (3, True)), (Ne(x, 0)))\
+        == 1
+    assert refine(Piecewise((1, Ne(x, 0)), (3, True)), ~(Ne(x, 0)))\
+        == 3
+    assert refine(Piecewise((1, Ne(x, 0)), (3, True)), (Ne(y, 0)))\
+        == Piecewise((1, Ne(x, 0)), (3, True))
+
+
+def test_atan2():
+    assert refine(atan2(y, x), Q.real(y) & Q.positive(x)) == atan(y/x)
+    assert refine(atan2(y, x), Q.negative(y) & Q.positive(x)) == atan(y/x)
+    assert refine(atan2(y, x), Q.negative(y) & Q.negative(x)) == atan(y/x) - pi
+    assert refine(atan2(y, x), Q.positive(y) & Q.negative(x)) == atan(y/x) + pi
+    assert refine(atan2(y, x), Q.zero(y) & Q.negative(x)) == pi
+    assert refine(atan2(y, x), Q.positive(y) & Q.zero(x)) == pi/2
+    assert refine(atan2(y, x), Q.negative(y) & Q.zero(x)) == -pi/2
+    assert refine(atan2(y, x), Q.zero(y) & Q.zero(x)) is nan
+
+
+def test_re():
+    assert refine(re(x), Q.real(x)) == x
+    assert refine(re(x), Q.imaginary(x)) is S.Zero
+    assert refine(re(x+y), Q.real(x) & Q.real(y)) == x + y
+    assert refine(re(x+y), Q.real(x) & Q.imaginary(y)) == x
+    assert refine(re(x*y), Q.real(x) & Q.real(y)) == x * y
+    assert refine(re(x*y), Q.real(x) & Q.imaginary(y)) == 0
+    assert refine(re(x*y*z), Q.real(x) & Q.real(y) & Q.real(z)) == x * y * z
+
+
+def test_im():
+    assert refine(im(x), Q.imaginary(x)) == -I*x
+    assert refine(im(x), Q.real(x)) is S.Zero
+    assert refine(im(x+y), Q.imaginary(x) & Q.imaginary(y)) == -I*x - I*y
+    assert refine(im(x+y), Q.real(x) & Q.imaginary(y)) == -I*y
+    assert refine(im(x*y), Q.imaginary(x) & Q.real(y)) == -I*x*y
+    assert refine(im(x*y), Q.imaginary(x) & Q.imaginary(y)) == 0
+    assert refine(im(1/x), Q.imaginary(x)) == -I/x
+    assert refine(im(x*y*z), Q.imaginary(x) & Q.imaginary(y)
+        & Q.imaginary(z)) == -I*x*y*z
+
+
+def test_complex():
+    assert refine(re(1/(x + I*y)), Q.real(x) & Q.real(y)) == \
+        x/(x**2 + y**2)
+    assert refine(im(1/(x + I*y)), Q.real(x) & Q.real(y)) == \
+        -y/(x**2 + y**2)
+    assert refine(re((w + I*x) * (y + I*z)), Q.real(w) & Q.real(x) & Q.real(y)
+        & Q.real(z)) == w*y - x*z
+    assert refine(im((w + I*x) * (y + I*z)), Q.real(w) & Q.real(x) & Q.real(y)
+        & Q.real(z)) == w*z + x*y
+
+
+def test_sign():
+    x = Symbol('x', real = True)
+    assert refine(sign(x), Q.positive(x)) == 1
+    assert refine(sign(x), Q.negative(x)) == -1
+    assert refine(sign(x), Q.zero(x)) == 0
+    assert refine(sign(x), True) == sign(x)
+    assert refine(sign(Abs(x)), Q.nonzero(x)) == 1
+
+    x = Symbol('x', imaginary=True)
+    assert refine(sign(x), Q.positive(im(x))) == S.ImaginaryUnit
+    assert refine(sign(x), Q.negative(im(x))) == -S.ImaginaryUnit
+    assert refine(sign(x), True) == sign(x)
+
+    x = Symbol('x', complex=True)
+    assert refine(sign(x), Q.zero(x)) == 0
+
+def test_arg():
+    x = Symbol('x', complex = True)
+    assert refine(arg(x), Q.positive(x)) == 0
+    assert refine(arg(x), Q.negative(x)) == pi
+
+def test_func_args():
+    class MyClass(Expr):
+        # A class with nontrivial .func
+
+        def __init__(self, *args):
+            self.my_member = ""
+
+        @property
+        def func(self):
+            def my_func(*args):
+                obj = MyClass(*args)
+                obj.my_member = self.my_member
+                return obj
+            return my_func
+
+    x = MyClass()
+    x.my_member = "A very important value"
+    assert x.my_member == refine(x).my_member
+
+def test_issue_refine_9384():
+    assert refine(Piecewise((1, x < 0), (0, True)), Q.positive(x)) == 0
+    assert refine(Piecewise((1, x < 0), (0, True)), Q.negative(x)) == 1
+    assert refine(Piecewise((1, x > 0), (0, True)), Q.positive(x)) == 1
+    assert refine(Piecewise((1, x > 0), (0, True)), Q.negative(x)) == 0
+
+
+def test_eval_refine():
+    class MockExpr(Expr):
+        def _eval_refine(self, assumptions):
+            return True
+
+    mock_obj = MockExpr()
+    assert refine(mock_obj)
+
+def test_refine_issue_12724():
+    expr1 = refine(Abs(x * y), Q.positive(x))
+    expr2 = refine(Abs(x * y * z), Q.positive(x))
+    assert expr1 == x * Abs(y)
+    assert expr2 == x * Abs(y * z)
+    y1 = Symbol('y1', real = True)
+    expr3 = refine(Abs(x * y1**2 * z), Q.positive(x))
+    assert expr3 == x * y1**2 * Abs(z)
+
+
+def test_matrixelement():
+    x = MatrixSymbol('x', 3, 3)
+    i = Symbol('i', positive = True)
+    j = Symbol('j', positive = True)
+    assert refine(x[0, 1], Q.symmetric(x)) == x[0, 1]
+    assert refine(x[1, 0], Q.symmetric(x)) == x[0, 1]
+    assert refine(x[i, j], Q.symmetric(x)) == x[j, i]
+    assert refine(x[j, i], Q.symmetric(x)) == x[j, i]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_rel_queries.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_rel_queries.py
new file mode 100644
index 0000000000000000000000000000000000000000..46fe3a35dc1adb23668e88d5794fe1c0ab22f33a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_rel_queries.py
@@ -0,0 +1,172 @@
+from sympy.assumptions.lra_satask import lra_satask
+from sympy.logic.algorithms.lra_theory import UnhandledInput
+from sympy.assumptions.ask import Q, ask
+
+from sympy.core import symbols, Symbol
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.core.numbers import I
+
+from sympy.testing.pytest import raises, XFAIL
+x, y, z = symbols("x y z", real=True)
+
+def test_lra_satask():
+    im = Symbol('im', imaginary=True)
+
+    # test preprocessing of unequalities is working correctly
+    assert lra_satask(Q.eq(x, 1), ~Q.ne(x, 0)) is False
+    assert lra_satask(Q.eq(x, 0), ~Q.ne(x, 0)) is True
+    assert lra_satask(~Q.ne(x, 0), Q.eq(x, 0)) is True
+    assert lra_satask(~Q.eq(x, 0), Q.eq(x, 0)) is False
+    assert lra_satask(Q.ne(x, 0), Q.eq(x, 0)) is False
+
+    # basic tests
+    assert lra_satask(Q.ne(x, x)) is False
+    assert lra_satask(Q.eq(x, x)) is True
+    assert lra_satask(Q.gt(x, 0), Q.gt(x, 1)) is True
+
+    # check that True/False are handled
+    assert lra_satask(Q.gt(x, 0), True) is None
+    assert raises(ValueError, lambda: lra_satask(Q.gt(x, 0), False))
+
+    # check imaginary numbers are correctly handled
+    # (im * I).is_real returns True so this is an edge case
+    raises(UnhandledInput, lambda: lra_satask(Q.gt(im * I, 0), Q.gt(im * I, 0)))
+
+    # check matrix inputs
+    X = MatrixSymbol("X", 2, 2)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(X, 2) & Q.gt(X, 3)))
+
+
+def test_old_assumptions():
+    # test unhandled old assumptions
+    w = symbols("w")
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", rational=False, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", odd=True, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", even=True, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", prime=True, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", composite=True, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", integer=True, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+    w = symbols("w", integer=False, real=True)
+    raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3)))
+
+    # test handled
+    w = symbols("w", positive=True, real=True)
+    assert lra_satask(Q.le(w, 0)) is False
+    assert lra_satask(Q.gt(w, 0)) is True
+    w = symbols("w", negative=True, real=True)
+    assert lra_satask(Q.lt(w, 0)) is True
+    assert lra_satask(Q.ge(w, 0)) is False
+    w = symbols("w", zero=True, real=True)
+    assert lra_satask(Q.eq(w, 0)) is True
+    assert lra_satask(Q.ne(w, 0)) is False
+    w = symbols("w", nonzero=True, real=True)
+    assert lra_satask(Q.ne(w, 0)) is True
+    assert lra_satask(Q.eq(w, 1)) is None
+    w = symbols("w", nonpositive=True, real=True)
+    assert lra_satask(Q.le(w, 0)) is True
+    assert lra_satask(Q.gt(w, 0)) is False
+    w = symbols("w", nonnegative=True, real=True)
+    assert lra_satask(Q.ge(w, 0)) is True
+    assert lra_satask(Q.lt(w, 0)) is False
+
+
+def test_rel_queries():
+    assert ask(Q.lt(x, 2) & Q.gt(x, 3)) is False
+    assert ask(Q.positive(x - z), (x > y) & (y > z)) is True
+    assert ask(x + y > 2, (x < 0) & (y <0)) is False
+    assert ask(x > z, (x > y) & (y > z)) is True
+
+
+def test_unhandled_queries():
+    X = MatrixSymbol("X", 2, 2)
+    assert ask(Q.lt(X, 2) & Q.gt(X, 3)) is None
+
+
+def test_all_pred():
+    # test usable pred
+    assert lra_satask(Q.extended_positive(x), (x > 2)) is True
+    assert lra_satask(Q.positive_infinite(x)) is False
+    assert lra_satask(Q.negative_infinite(x)) is False
+
+    # test disallowed pred
+    raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.prime(x)))
+    raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.composite(x)))
+    raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.odd(x)))
+    raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.even(x)))
+    raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.integer(x)))
+
+
+def test_number_line_properties():
+    # From:
+    # https://en.wikipedia.org/wiki/Inequality_(mathematics)#Properties_on_the_number_line
+
+    a, b, c = symbols("a b c", real=True)
+
+    # Transitivity
+    # If a <= b and b <= c, then a <= c.
+    assert ask(a <= c, (a <= b) & (b <= c)) is True
+    # If a <= b and b < c, then a < c.
+    assert ask(a < c, (a <= b) & (b < c)) is True
+    # If a < b and b <= c, then a < c.
+    assert ask(a < c, (a < b) & (b <= c)) is True
+
+    # Addition and subtraction
+    # If a <= b, then a + c <= b + c and a - c <= b - c.
+    assert ask(a + c <= b + c, a <= b) is True
+    assert ask(a - c <= b - c, a <= b) is True
+
+
+@XFAIL
+def test_failing_number_line_properties():
+    # From:
+    # https://en.wikipedia.org/wiki/Inequality_(mathematics)#Properties_on_the_number_line
+
+    a, b, c = symbols("a b c", real=True)
+
+    # Multiplication and division
+    # If a <= b and c > 0, then ac <= bc and a/c <= b/c. (True for non-zero c)
+    assert ask(a*c <= b*c, (a <= b) & (c > 0) & ~ Q.zero(c)) is True
+    assert ask(a/c <= b/c, (a <= b) & (c > 0) & ~ Q.zero(c)) is True
+    # If a <= b and c < 0, then ac >= bc and a/c >= b/c. (True for non-zero c)
+    assert ask(a*c >= b*c, (a <= b) & (c < 0) & ~ Q.zero(c)) is True
+    assert ask(a/c >= b/c, (a <= b) & (c < 0) & ~ Q.zero(c)) is True
+
+    # Additive inverse
+    # If a <= b, then -a >= -b.
+    assert ask(-a >= -b, a <= b) is True
+
+    # Multiplicative inverse
+    # For a, b that are both negative or both positive:
+    # If a <= b, then 1/a >= 1/b .
+    assert ask(1/a >= 1/b, (a <= b) & Q.positive(x) & Q.positive(b)) is True
+    assert ask(1/a >= 1/b, (a <= b) & Q.negative(x) & Q.negative(b)) is True
+
+
+def test_equality():
+    # test symmetry and reflexivity
+    assert ask(Q.eq(x, x)) is True
+    assert ask(Q.eq(y, x), Q.eq(x, y)) is True
+    assert ask(Q.eq(y, x), ~Q.eq(z, z) | Q.eq(x, y)) is True
+
+    # test transitivity
+    assert ask(Q.eq(x,z), Q.eq(x,y) & Q.eq(y,z)) is True
+
+
+@XFAIL
+def test_equality_failing():
+    # Note that implementing the substitution property of equality
+    # most likely requires a redesign of the new assumptions.
+    # See issue #25485 for why this is the case and general ideas
+    # about how things could be redesigned.
+
+    # test substitution property
+    assert ask(Q.prime(x), Q.eq(x, y) & Q.prime(y)) is True
+    assert ask(Q.real(x), Q.eq(x, y) & Q.real(y)) is True
+    assert ask(Q.imaginary(x), Q.eq(x, y) & Q.imaginary(y)) is True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_satask.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_satask.py
new file mode 100644
index 0000000000000000000000000000000000000000..5831b69e3e6bf2b1a906d1140967510c2ea8b630
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_satask.py
@@ -0,0 +1,378 @@
+from sympy.assumptions.ask import Q
+from sympy.assumptions.assume import assuming
+from sympy.core.numbers import (I, pi)
+from sympy.core.relational import (Eq, Gt)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.complexes import Abs
+from sympy.logic.boolalg import Implies
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.assumptions.cnf import CNF, Literal
+from sympy.assumptions.satask import (satask, extract_predargs,
+    get_relevant_clsfacts)
+
+from sympy.testing.pytest import raises, XFAIL
+
+
+x, y, z = symbols('x y z')
+
+
+def test_satask():
+    # No relevant facts
+    assert satask(Q.real(x), Q.real(x)) is True
+    assert satask(Q.real(x), ~Q.real(x)) is False
+    assert satask(Q.real(x)) is None
+
+    assert satask(Q.real(x), Q.positive(x)) is True
+    assert satask(Q.positive(x), Q.real(x)) is None
+    assert satask(Q.real(x), ~Q.positive(x)) is None
+    assert satask(Q.positive(x), ~Q.real(x)) is False
+
+    raises(ValueError, lambda: satask(Q.real(x), Q.real(x) & ~Q.real(x)))
+
+    with assuming(Q.positive(x)):
+        assert satask(Q.real(x)) is True
+        assert satask(~Q.positive(x)) is False
+        raises(ValueError, lambda: satask(Q.real(x), ~Q.positive(x)))
+
+    assert satask(Q.zero(x), Q.nonzero(x)) is False
+    assert satask(Q.positive(x), Q.zero(x)) is False
+    assert satask(Q.real(x), Q.zero(x)) is True
+    assert satask(Q.zero(x), Q.zero(x*y)) is None
+    assert satask(Q.zero(x*y), Q.zero(x))
+
+
+def test_zero():
+    """
+    Everything in this test doesn't work with the ask handlers, and most
+    things would be very difficult or impossible to make work under that
+    model.
+
+    """
+    assert satask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True
+    assert satask(Q.zero(x*y), Q.zero(x) | Q.zero(y)) is True
+
+    assert satask(Implies(Q.zero(x), Q.zero(x*y))) is True
+
+    # This one in particular requires computing the fixed-point of the
+    # relevant facts, because going from Q.nonzero(x*y) -> ~Q.zero(x*y) and
+    # Q.zero(x*y) -> Equivalent(Q.zero(x*y), Q.zero(x) | Q.zero(y)) takes two
+    # steps.
+    assert satask(Q.zero(x) | Q.zero(y), Q.nonzero(x*y)) is False
+
+    assert satask(Q.zero(x), Q.zero(x**2)) is True
+
+
+def test_zero_positive():
+    assert satask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False
+    assert satask(Q.positive(x) & Q.positive(y), Q.zero(x + y)) is False
+    assert satask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True
+    assert satask(Q.positive(x) & Q.positive(y), Q.nonzero(x + y)) is None
+
+    # This one requires several levels of forward chaining
+    assert satask(Q.zero(x*(x + y)), Q.positive(x) & Q.positive(y)) is False
+
+    assert satask(Q.positive(pi*x*y + 1), Q.positive(x) & Q.positive(y)) is True
+    assert satask(Q.positive(pi*x*y - 5), Q.positive(x) & Q.positive(y)) is None
+
+
+def test_zero_pow():
+    assert satask(Q.zero(x**y), Q.zero(x) & Q.positive(y)) is True
+    assert satask(Q.zero(x**y), Q.nonzero(x) & Q.zero(y)) is False
+
+    assert satask(Q.zero(x), Q.zero(x**y)) is True
+
+    assert satask(Q.zero(x**y), Q.zero(x)) is None
+
+
+@XFAIL
+# Requires correct Q.square calculation first
+def test_invertible():
+    A = MatrixSymbol('A', 5, 5)
+    B = MatrixSymbol('B', 5, 5)
+    assert satask(Q.invertible(A*B), Q.invertible(A) & Q.invertible(B)) is True
+    assert satask(Q.invertible(A), Q.invertible(A*B)) is True
+    assert satask(Q.invertible(A) & Q.invertible(B), Q.invertible(A*B)) is True
+
+
+def test_prime():
+    assert satask(Q.prime(5)) is True
+    assert satask(Q.prime(6)) is False
+    assert satask(Q.prime(-5)) is False
+
+    assert satask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None
+    assert satask(Q.prime(x*y), Q.prime(x) & Q.prime(y)) is False
+
+
+def test_old_assump():
+    assert satask(Q.positive(1)) is True
+    assert satask(Q.positive(-1)) is False
+    assert satask(Q.positive(0)) is False
+    assert satask(Q.positive(I)) is False
+    assert satask(Q.positive(pi)) is True
+
+    assert satask(Q.negative(1)) is False
+    assert satask(Q.negative(-1)) is True
+    assert satask(Q.negative(0)) is False
+    assert satask(Q.negative(I)) is False
+    assert satask(Q.negative(pi)) is False
+
+    assert satask(Q.zero(1)) is False
+    assert satask(Q.zero(-1)) is False
+    assert satask(Q.zero(0)) is True
+    assert satask(Q.zero(I)) is False
+    assert satask(Q.zero(pi)) is False
+
+    assert satask(Q.nonzero(1)) is True
+    assert satask(Q.nonzero(-1)) is True
+    assert satask(Q.nonzero(0)) is False
+    assert satask(Q.nonzero(I)) is False
+    assert satask(Q.nonzero(pi)) is True
+
+    assert satask(Q.nonpositive(1)) is False
+    assert satask(Q.nonpositive(-1)) is True
+    assert satask(Q.nonpositive(0)) is True
+    assert satask(Q.nonpositive(I)) is False
+    assert satask(Q.nonpositive(pi)) is False
+
+    assert satask(Q.nonnegative(1)) is True
+    assert satask(Q.nonnegative(-1)) is False
+    assert satask(Q.nonnegative(0)) is True
+    assert satask(Q.nonnegative(I)) is False
+    assert satask(Q.nonnegative(pi)) is True
+
+
+def test_rational_irrational():
+    assert satask(Q.irrational(2)) is False
+    assert satask(Q.rational(2)) is True
+    assert satask(Q.irrational(pi)) is True
+    assert satask(Q.rational(pi)) is False
+    assert satask(Q.irrational(I)) is False
+    assert satask(Q.rational(I)) is False
+
+    assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.irrational(y) &
+        Q.rational(z)) is None
+    assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.rational(y) &
+        Q.rational(z)) is True
+    assert satask(Q.irrational(pi*x*y), Q.rational(x) & Q.rational(y)) is True
+
+    assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.irrational(y) &
+        Q.rational(z)) is None
+    assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.rational(y) &
+        Q.rational(z)) is True
+    assert satask(Q.irrational(pi + x + y), Q.rational(x) & Q.rational(y)) is True
+
+    assert satask(Q.irrational(x*y*z), Q.rational(x) & Q.rational(y) &
+        Q.rational(z)) is False
+    assert satask(Q.rational(x*y*z), Q.rational(x) & Q.rational(y) &
+        Q.rational(z)) is True
+
+    assert satask(Q.irrational(x + y + z), Q.rational(x) & Q.rational(y) &
+        Q.rational(z)) is False
+    assert satask(Q.rational(x + y + z), Q.rational(x) & Q.rational(y) &
+        Q.rational(z)) is True
+
+
+def test_even_satask():
+    assert satask(Q.even(2)) is True
+    assert satask(Q.even(3)) is False
+
+    assert satask(Q.even(x*y), Q.even(x) & Q.odd(y)) is True
+    assert satask(Q.even(x*y), Q.even(x) & Q.integer(y)) is True
+    assert satask(Q.even(x*y), Q.even(x) & Q.even(y)) is True
+    assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False
+    assert satask(Q.even(x*y), Q.even(x)) is None
+    assert satask(Q.even(x*y), Q.odd(x) & Q.integer(y)) is None
+    assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False
+
+    assert satask(Q.even(abs(x)), Q.even(x)) is True
+    assert satask(Q.even(abs(x)), Q.odd(x)) is False
+    assert satask(Q.even(x), Q.even(abs(x))) is None # x could be complex
+
+
+def test_odd_satask():
+    assert satask(Q.odd(2)) is False
+    assert satask(Q.odd(3)) is True
+
+    assert satask(Q.odd(x*y), Q.even(x) & Q.odd(y)) is False
+    assert satask(Q.odd(x*y), Q.even(x) & Q.integer(y)) is False
+    assert satask(Q.odd(x*y), Q.even(x) & Q.even(y)) is False
+    assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True
+    assert satask(Q.odd(x*y), Q.even(x)) is None
+    assert satask(Q.odd(x*y), Q.odd(x) & Q.integer(y)) is None
+    assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True
+
+    assert satask(Q.odd(abs(x)), Q.even(x)) is False
+    assert satask(Q.odd(abs(x)), Q.odd(x)) is True
+    assert satask(Q.odd(x), Q.odd(abs(x))) is None # x could be complex
+
+
+def test_integer():
+    assert satask(Q.integer(1)) is True
+    assert satask(Q.integer(S.Half)) is False
+
+    assert satask(Q.integer(x + y), Q.integer(x) & Q.integer(y)) is True
+    assert satask(Q.integer(x + y), Q.integer(x)) is None
+
+    assert satask(Q.integer(x + y), Q.integer(x) & ~Q.integer(y)) is False
+    assert satask(Q.integer(x + y + z), Q.integer(x) & Q.integer(y) &
+        ~Q.integer(z)) is False
+    assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y) &
+        ~Q.integer(z)) is None
+    assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y)) is None
+    assert satask(Q.integer(x + y), Q.integer(x) & Q.irrational(y)) is False
+
+    assert satask(Q.integer(x*y), Q.integer(x) & Q.integer(y)) is True
+    assert satask(Q.integer(x*y), Q.integer(x)) is None
+
+    assert satask(Q.integer(x*y), Q.integer(x) & ~Q.integer(y)) is None
+    assert satask(Q.integer(x*y), Q.integer(x) & ~Q.rational(y)) is False
+    assert satask(Q.integer(x*y*z), Q.integer(x) & Q.integer(y) &
+        ~Q.rational(z)) is False
+    assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y) &
+        ~Q.rational(z)) is None
+    assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y)) is None
+    assert satask(Q.integer(x*y), Q.integer(x) & Q.irrational(y)) is False
+
+
+def test_abs():
+    assert satask(Q.nonnegative(abs(x))) is True
+    assert satask(Q.positive(abs(x)), ~Q.zero(x)) is True
+    assert satask(Q.zero(x), ~Q.zero(abs(x))) is False
+    assert satask(Q.zero(x), Q.zero(abs(x))) is True
+    assert satask(Q.nonzero(x), ~Q.zero(abs(x))) is None # x could be complex
+    assert satask(Q.zero(abs(x)), Q.zero(x)) is True
+
+
+def test_imaginary():
+    assert satask(Q.imaginary(2*I)) is True
+    assert satask(Q.imaginary(x*y), Q.imaginary(x)) is None
+    assert satask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True
+    assert satask(Q.imaginary(x), Q.real(x)) is False
+    assert satask(Q.imaginary(1)) is False
+    assert satask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False
+    assert satask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False
+
+
+def test_real():
+    assert satask(Q.real(x*y), Q.real(x) & Q.real(y)) is True
+    assert satask(Q.real(x + y), Q.real(x) & Q.real(y)) is True
+    assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.real(z)) is True
+    assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y)) is None
+    assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.imaginary(z)) is False
+    assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True
+    assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y)) is None
+
+
+def test_pos_neg():
+    assert satask(~Q.positive(x), Q.negative(x)) is True
+    assert satask(~Q.negative(x), Q.positive(x)) is True
+    assert satask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True
+    assert satask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True
+    assert satask(Q.positive(x + y), Q.negative(x) & Q.negative(y)) is False
+    assert satask(Q.negative(x + y), Q.positive(x) & Q.positive(y)) is False
+
+
+def test_pow_pos_neg():
+    assert satask(Q.nonnegative(x**2), Q.positive(x)) is True
+    assert satask(Q.nonpositive(x**2), Q.positive(x)) is False
+    assert satask(Q.positive(x**2), Q.positive(x)) is True
+    assert satask(Q.negative(x**2), Q.positive(x)) is False
+    assert satask(Q.real(x**2), Q.positive(x)) is True
+
+    assert satask(Q.nonnegative(x**2), Q.negative(x)) is True
+    assert satask(Q.nonpositive(x**2), Q.negative(x)) is False
+    assert satask(Q.positive(x**2), Q.negative(x)) is True
+    assert satask(Q.negative(x**2), Q.negative(x)) is False
+    assert satask(Q.real(x**2), Q.negative(x)) is True
+
+    assert satask(Q.nonnegative(x**2), Q.nonnegative(x)) is True
+    assert satask(Q.nonpositive(x**2), Q.nonnegative(x)) is None
+    assert satask(Q.positive(x**2), Q.nonnegative(x)) is None
+    assert satask(Q.negative(x**2), Q.nonnegative(x)) is False
+    assert satask(Q.real(x**2), Q.nonnegative(x)) is True
+
+    assert satask(Q.nonnegative(x**2), Q.nonpositive(x)) is True
+    assert satask(Q.nonpositive(x**2), Q.nonpositive(x)) is None
+    assert satask(Q.positive(x**2), Q.nonpositive(x)) is None
+    assert satask(Q.negative(x**2), Q.nonpositive(x)) is False
+    assert satask(Q.real(x**2), Q.nonpositive(x)) is True
+
+    assert satask(Q.nonnegative(x**3), Q.positive(x)) is True
+    assert satask(Q.nonpositive(x**3), Q.positive(x)) is False
+    assert satask(Q.positive(x**3), Q.positive(x)) is True
+    assert satask(Q.negative(x**3), Q.positive(x)) is False
+    assert satask(Q.real(x**3), Q.positive(x)) is True
+
+    assert satask(Q.nonnegative(x**3), Q.negative(x)) is False
+    assert satask(Q.nonpositive(x**3), Q.negative(x)) is True
+    assert satask(Q.positive(x**3), Q.negative(x)) is False
+    assert satask(Q.negative(x**3), Q.negative(x)) is True
+    assert satask(Q.real(x**3), Q.negative(x)) is True
+
+    assert satask(Q.nonnegative(x**3), Q.nonnegative(x)) is True
+    assert satask(Q.nonpositive(x**3), Q.nonnegative(x)) is None
+    assert satask(Q.positive(x**3), Q.nonnegative(x)) is None
+    assert satask(Q.negative(x**3), Q.nonnegative(x)) is False
+    assert satask(Q.real(x**3), Q.nonnegative(x)) is True
+
+    assert satask(Q.nonnegative(x**3), Q.nonpositive(x)) is None
+    assert satask(Q.nonpositive(x**3), Q.nonpositive(x)) is True
+    assert satask(Q.positive(x**3), Q.nonpositive(x)) is False
+    assert satask(Q.negative(x**3), Q.nonpositive(x)) is None
+    assert satask(Q.real(x**3), Q.nonpositive(x)) is True
+
+    # If x is zero, x**negative is not real.
+    assert satask(Q.nonnegative(x**-2), Q.nonpositive(x)) is None
+    assert satask(Q.nonpositive(x**-2), Q.nonpositive(x)) is None
+    assert satask(Q.positive(x**-2), Q.nonpositive(x)) is None
+    assert satask(Q.negative(x**-2), Q.nonpositive(x)) is None
+    assert satask(Q.real(x**-2), Q.nonpositive(x)) is None
+
+    # We could deduce things for negative powers if x is nonzero, but it
+    # isn't implemented yet.
+
+
+def test_prime_composite():
+    assert satask(Q.prime(x), Q.composite(x)) is False
+    assert satask(Q.composite(x), Q.prime(x)) is False
+    assert satask(Q.composite(x), ~Q.prime(x)) is None
+    assert satask(Q.prime(x), ~Q.composite(x)) is None
+    # since 1 is neither prime nor composite the following should hold
+    assert satask(Q.prime(x), Q.integer(x) & Q.positive(x) & ~Q.composite(x)) is None
+    assert satask(Q.prime(2)) is True
+    assert satask(Q.prime(4)) is False
+    assert satask(Q.prime(1)) is False
+    assert satask(Q.composite(1)) is False
+
+
+def test_extract_predargs():
+    props = CNF.from_prop(Q.zero(Abs(x*y)) & Q.zero(x*y))
+    assump = CNF.from_prop(Q.zero(x))
+    context = CNF.from_prop(Q.zero(y))
+    assert extract_predargs(props) == {Abs(x*y), x*y}
+    assert extract_predargs(props, assump) == {Abs(x*y), x*y, x}
+    assert extract_predargs(props, assump, context) == {Abs(x*y), x*y, x, y}
+
+    props = CNF.from_prop(Eq(x, y))
+    assump = CNF.from_prop(Gt(y, z))
+    assert extract_predargs(props, assump) == {x, y, z}
+
+
+def test_get_relevant_clsfacts():
+    exprs = {Abs(x*y)}
+    exprs, facts = get_relevant_clsfacts(exprs)
+    assert exprs == {x*y}
+    assert facts.clauses == \
+        {frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}),
+        frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}),
+        frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}),
+        frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}),
+        frozenset({Literal(Q.even(Abs(x*y)), False),
+                    Literal(Q.odd(Abs(x*y)), False),
+                    Literal(Q.odd(x*y), True)}),
+        frozenset({Literal(Q.even(Abs(x*y)), False),
+                    Literal(Q.even(x*y), True),
+                    Literal(Q.odd(Abs(x*y)), False)}),
+        frozenset({Literal(Q.positive(Abs(x*y)), False),
+                    Literal(Q.zero(Abs(x*y)), False)})}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_sathandlers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_sathandlers.py
new file mode 100644
index 0000000000000000000000000000000000000000..9d568ad8efe6ba7cf7f5eb03879ad6764c16e729
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_sathandlers.py
@@ -0,0 +1,50 @@
+from sympy.assumptions.ask import Q
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.symbol import symbols
+from sympy.logic.boolalg import (And, Or)
+
+from sympy.assumptions.sathandlers import (ClassFactRegistry, allargs,
+    anyarg, exactlyonearg,)
+
+x, y, z = symbols('x y z')
+
+
+def test_class_handler_registry():
+    my_handler_registry = ClassFactRegistry()
+
+    # The predicate doesn't matter here, so just pass
+    @my_handler_registry.register(Mul)
+    def fact1(expr):
+        pass
+    @my_handler_registry.multiregister(Expr)
+    def fact2(expr):
+        pass
+
+    assert my_handler_registry[Basic] == (frozenset(), frozenset())
+    assert my_handler_registry[Expr] == (frozenset(), frozenset({fact2}))
+    assert my_handler_registry[Mul] == (frozenset({fact1}), frozenset({fact2}))
+
+
+def test_allargs():
+    assert allargs(x, Q.zero(x), x*y) == And(Q.zero(x), Q.zero(y))
+    assert allargs(x, Q.positive(x) | Q.negative(x), x*y) == And(Q.positive(x) | Q.negative(x), Q.positive(y) | Q.negative(y))
+
+
+def test_anyarg():
+    assert anyarg(x, Q.zero(x), x*y) == Or(Q.zero(x), Q.zero(y))
+    assert anyarg(x, Q.positive(x) & Q.negative(x), x*y) == \
+        Or(Q.positive(x) & Q.negative(x), Q.positive(y) & Q.negative(y))
+
+
+def test_exactlyonearg():
+    assert exactlyonearg(x, Q.zero(x), x*y) == \
+        Or(Q.zero(x) & ~Q.zero(y), Q.zero(y) & ~Q.zero(x))
+    assert exactlyonearg(x, Q.zero(x), x*y*z) == \
+        Or(Q.zero(x) & ~Q.zero(y) & ~Q.zero(z), Q.zero(y)
+        & ~Q.zero(x) & ~Q.zero(z), Q.zero(z) & ~Q.zero(x) & ~Q.zero(y))
+    assert exactlyonearg(x, Q.positive(x) | Q.negative(x), x*y) == \
+        Or((Q.positive(x) | Q.negative(x)) &
+        ~(Q.positive(y) | Q.negative(y)), (Q.positive(y) | Q.negative(y)) &
+        ~(Q.positive(x) | Q.negative(x)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_wrapper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_wrapper.py
new file mode 100644
index 0000000000000000000000000000000000000000..af9afd5d51fb1341e0b08149dc842b78a39c329b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/tests/test_wrapper.py
@@ -0,0 +1,39 @@
+from sympy.assumptions.ask import Q
+from sympy.assumptions.wrapper import (AssumptionsWrapper, is_infinite,
+    is_extended_real)
+from sympy.core.symbol import Symbol
+from sympy.core.assumptions import _assume_defined
+
+
+def test_all_predicates():
+    for fact in _assume_defined:
+        method_name = f'_eval_is_{fact}'
+        assert hasattr(AssumptionsWrapper, method_name)
+
+
+def test_AssumptionsWrapper():
+    x = Symbol('x', positive=True)
+    y = Symbol('y')
+    assert AssumptionsWrapper(x).is_positive
+    assert AssumptionsWrapper(y).is_positive is None
+    assert AssumptionsWrapper(y, Q.positive(y)).is_positive
+
+
+def test_is_infinite():
+    x = Symbol('x', infinite=True)
+    y = Symbol('y', infinite=False)
+    z = Symbol('z')
+    assert is_infinite(x)
+    assert not is_infinite(y)
+    assert is_infinite(z) is None
+    assert is_infinite(z, Q.infinite(z))
+
+
+def test_is_extended_real():
+    x = Symbol('x', extended_real=True)
+    y = Symbol('y', extended_real=False)
+    z = Symbol('z')
+    assert is_extended_real(x)
+    assert not is_extended_real(y)
+    assert is_extended_real(z) is None
+    assert is_extended_real(z, Q.extended_real(z))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/wrapper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/wrapper.py
new file mode 100644
index 0000000000000000000000000000000000000000..cb06e9de770ed41a2b3d6fe63381ad1cb59acacc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/assumptions/wrapper.py
@@ -0,0 +1,164 @@
+"""
+Functions and wrapper object to call assumption property and predicate
+query with same syntax.
+
+In SymPy, there are two assumption systems. Old assumption system is
+defined in sympy/core/assumptions, and it can be accessed by attribute
+such as ``x.is_even``. New assumption system is defined in
+sympy/assumptions, and it can be accessed by predicates such as
+``Q.even(x)``.
+
+Old assumption is fast, while new assumptions can freely take local facts.
+In general, old assumption is used in evaluation method and new assumption
+is used in refinement method.
+
+In most cases, both evaluation and refinement follow the same process, and
+the only difference is which assumption system is used. This module provides
+``is_[...]()`` functions and ``AssumptionsWrapper()`` class which allows
+using two systems with same syntax so that parallel code implementation can be
+avoided.
+
+Examples
+========
+
+For multiple use, use ``AssumptionsWrapper()``.
+
+>>> from sympy import Q, Symbol
+>>> from sympy.assumptions.wrapper import AssumptionsWrapper
+>>> x = Symbol('x')
+>>> _x = AssumptionsWrapper(x, Q.even(x))
+>>> _x.is_integer
+True
+>>> _x.is_odd
+False
+
+For single use, use ``is_[...]()`` functions.
+
+>>> from sympy.assumptions.wrapper import is_infinite
+>>> a = Symbol('a')
+>>> print(is_infinite(a))
+None
+>>> is_infinite(a, Q.finite(a))
+False
+
+"""
+
+from sympy.assumptions import ask, Q
+from sympy.core.basic import Basic
+from sympy.core.sympify import _sympify
+
+
+def make_eval_method(fact):
+    def getit(self):
+        pred = getattr(Q, fact)
+        ret = ask(pred(self.expr), self.assumptions)
+        return ret
+    return getit
+
+
+# we subclass Basic to use the fact deduction and caching
+class AssumptionsWrapper(Basic):
+    """
+    Wrapper over ``Basic`` instances to call predicate query by
+    ``.is_[...]`` property
+
+    Parameters
+    ==========
+
+    expr : Basic
+
+    assumptions : Boolean, optional
+
+    Examples
+    ========
+
+    >>> from sympy import Q, Symbol
+    >>> from sympy.assumptions.wrapper import AssumptionsWrapper
+    >>> x = Symbol('x', even=True)
+    >>> AssumptionsWrapper(x).is_integer
+    True
+    >>> y = Symbol('y')
+    >>> AssumptionsWrapper(y, Q.even(y)).is_integer
+    True
+
+    With ``AssumptionsWrapper``, both evaluation and refinement can be supported
+    by single implementation.
+
+    >>> from sympy import Function
+    >>> class MyAbs(Function):
+    ...     @classmethod
+    ...     def eval(cls, x, assumptions=True):
+    ...         _x = AssumptionsWrapper(x, assumptions)
+    ...         if _x.is_nonnegative:
+    ...             return x
+    ...         if _x.is_negative:
+    ...             return -x
+    ...     def _eval_refine(self, assumptions):
+    ...         return MyAbs.eval(self.args[0], assumptions)
+    >>> MyAbs(x)
+    MyAbs(x)
+    >>> MyAbs(x).refine(Q.positive(x))
+    x
+    >>> MyAbs(Symbol('y', negative=True))
+    -y
+
+    """
+    def __new__(cls, expr, assumptions=None):
+        if assumptions is None:
+            return expr
+        obj = super().__new__(cls, expr, _sympify(assumptions))
+        obj.expr = expr
+        obj.assumptions = assumptions
+        return obj
+
+    _eval_is_algebraic = make_eval_method("algebraic")
+    _eval_is_antihermitian = make_eval_method("antihermitian")
+    _eval_is_commutative = make_eval_method("commutative")
+    _eval_is_complex = make_eval_method("complex")
+    _eval_is_composite = make_eval_method("composite")
+    _eval_is_even = make_eval_method("even")
+    _eval_is_extended_negative = make_eval_method("extended_negative")
+    _eval_is_extended_nonnegative = make_eval_method("extended_nonnegative")
+    _eval_is_extended_nonpositive = make_eval_method("extended_nonpositive")
+    _eval_is_extended_nonzero = make_eval_method("extended_nonzero")
+    _eval_is_extended_positive = make_eval_method("extended_positive")
+    _eval_is_extended_real = make_eval_method("extended_real")
+    _eval_is_finite = make_eval_method("finite")
+    _eval_is_hermitian = make_eval_method("hermitian")
+    _eval_is_imaginary = make_eval_method("imaginary")
+    _eval_is_infinite = make_eval_method("infinite")
+    _eval_is_integer = make_eval_method("integer")
+    _eval_is_irrational = make_eval_method("irrational")
+    _eval_is_negative = make_eval_method("negative")
+    _eval_is_noninteger = make_eval_method("noninteger")
+    _eval_is_nonnegative = make_eval_method("nonnegative")
+    _eval_is_nonpositive = make_eval_method("nonpositive")
+    _eval_is_nonzero = make_eval_method("nonzero")
+    _eval_is_odd = make_eval_method("odd")
+    _eval_is_polar = make_eval_method("polar")
+    _eval_is_positive = make_eval_method("positive")
+    _eval_is_prime = make_eval_method("prime")
+    _eval_is_rational = make_eval_method("rational")
+    _eval_is_real = make_eval_method("real")
+    _eval_is_transcendental = make_eval_method("transcendental")
+    _eval_is_zero = make_eval_method("zero")
+
+
+# one shot functions which are faster than AssumptionsWrapper
+
+def is_infinite(obj, assumptions=None):
+    if assumptions is None:
+        return obj.is_infinite
+    return ask(Q.infinite(obj), assumptions)
+
+
+def is_extended_real(obj, assumptions=None):
+    if assumptions is None:
+        return obj.is_extended_real
+    return ask(Q.extended_real(obj), assumptions)
+
+
+def is_extended_nonnegative(obj, assumptions=None):
+    if assumptions is None:
+        return obj.is_extended_nonnegative
+    return ask(Q.extended_nonnegative(obj), assumptions)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_discrete_log.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_discrete_log.py
new file mode 100644
index 0000000000000000000000000000000000000000..76b273909e415318a7d3bace00ffff2a0bc53762
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_discrete_log.py
@@ -0,0 +1,83 @@
+import sys
+from time import time
+from sympy.ntheory.residue_ntheory import (discrete_log,
+        _discrete_log_trial_mul, _discrete_log_shanks_steps,
+        _discrete_log_pollard_rho, _discrete_log_pohlig_hellman)
+
+
+# Cyclic group (Z/pZ)* with p prime, order p - 1 and generator g
+data_set_1 = [
+        # p, p - 1, g
+        [191, 190, 19],
+        [46639, 46638, 6],
+        [14789363, 14789362, 2],
+        [4254225211, 4254225210, 2],
+        [432751500361, 432751500360, 7],
+        [158505390797053, 158505390797052, 2],
+        [6575202655312007, 6575202655312006, 5],
+        [8430573471995353769, 8430573471995353768, 3],
+        [3938471339744997827267, 3938471339744997827266, 2],
+        [875260951364705563393093, 875260951364705563393092, 5],
+    ]
+
+
+# Cyclic sub-groups of (Z/nZ)* with prime order p and generator g
+# (n, p are primes and n = 2 * p + 1)
+data_set_2 = [
+        # n, p, g
+        [227, 113, 3],
+        [2447, 1223, 2],
+        [24527, 12263, 2],
+        [245639, 122819, 2],
+        [2456747, 1228373, 3],
+        [24567899, 12283949, 3],
+        [245679023, 122839511, 2],
+        [2456791307, 1228395653, 3],
+        [24567913439, 12283956719, 2],
+        [245679135407, 122839567703, 2],
+        [2456791354763, 1228395677381, 3],
+        [24567913550903, 12283956775451, 2],
+        [245679135509519, 122839567754759, 2],
+    ]
+
+
+# Cyclic sub-groups of (Z/nZ)* with smooth order o and generator g
+data_set_3 = [
+        # n, o, g
+        [2**118, 2**116, 3],
+    ]
+
+
+def bench_discrete_log(data_set, algo=None):
+    if algo is None:
+        f = discrete_log
+    elif algo == 'trial':
+        f = _discrete_log_trial_mul
+    elif algo == 'shanks':
+        f = _discrete_log_shanks_steps
+    elif algo == 'rho':
+        f = _discrete_log_pollard_rho
+    elif algo == 'ph':
+        f = _discrete_log_pohlig_hellman
+    else:
+        raise ValueError("Argument 'algo' should be one"
+                " of ('trial', 'shanks', 'rho' or 'ph')")
+
+    for i, data in enumerate(data_set):
+        for j, (n, p, g) in enumerate(data):
+            t = time()
+            l = f(n, pow(g, p - 1, n), g, p)
+            t = time() - t
+            print('[%02d-%03d] %15.10f' % (i, j, t))
+            assert l == p - 1
+
+
+if __name__ == '__main__':
+    algo = sys.argv[1] \
+            if len(sys.argv) > 1 else None
+    data_set = [
+            data_set_1,
+            data_set_2,
+            data_set_3,
+        ]
+    bench_discrete_log(data_set, algo)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_meijerint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_meijerint.py
new file mode 100644
index 0000000000000000000000000000000000000000..d648c3e02463d5a7ee1dcbe3b22af5cc22fef43d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_meijerint.py
@@ -0,0 +1,261 @@
+# conceal the implicit import from the code quality tester
+from sympy.core.numbers import (oo, pi)
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.bessel import besseli
+from sympy.functions.special.gamma_functions import gamma
+from sympy.integrals.integrals import integrate
+from sympy.integrals.transforms import (mellin_transform,
+    inverse_fourier_transform, inverse_mellin_transform,
+    laplace_transform, inverse_laplace_transform, fourier_transform)
+
+LT = laplace_transform
+FT = fourier_transform
+MT = mellin_transform
+IFT = inverse_fourier_transform
+ILT = inverse_laplace_transform
+IMT = inverse_mellin_transform
+
+from sympy.abc import x, y
+nu, beta, rho = symbols('nu beta rho')
+
+apos, bpos, cpos, dpos, posk, p = symbols('a b c d k p', positive=True)
+k = Symbol('k', real=True)
+negk = Symbol('k', negative=True)
+
+mu1, mu2 = symbols('mu1 mu2', real=True, nonzero=True, finite=True)
+sigma1, sigma2 = symbols('sigma1 sigma2', real=True, nonzero=True,
+                         finite=True, positive=True)
+rate = Symbol('lambda', positive=True)
+
+
+def normal(x, mu, sigma):
+    return 1/sqrt(2*pi*sigma**2)*exp(-(x - mu)**2/2/sigma**2)
+
+
+def exponential(x, rate):
+    return rate*exp(-rate*x)
+alpha, beta = symbols('alpha beta', positive=True)
+betadist = x**(alpha - 1)*(1 + x)**(-alpha - beta)*gamma(alpha + beta) \
+    /gamma(alpha)/gamma(beta)
+kint = Symbol('k', integer=True, positive=True)
+chi = 2**(1 - kint/2)*x**(kint - 1)*exp(-x**2/2)/gamma(kint/2)
+chisquared = 2**(-k/2)/gamma(k/2)*x**(k/2 - 1)*exp(-x/2)
+dagum = apos*p/x*(x/bpos)**(apos*p)/(1 + x**apos/bpos**apos)**(p + 1)
+d1, d2 = symbols('d1 d2', positive=True)
+f = sqrt(((d1*x)**d1 * d2**d2)/(d1*x + d2)**(d1 + d2))/x \
+    /gamma(d1/2)/gamma(d2/2)*gamma((d1 + d2)/2)
+nupos, sigmapos = symbols('nu sigma', positive=True)
+rice = x/sigmapos**2*exp(-(x**2 + nupos**2)/2/sigmapos**2)*besseli(0, x*
+                         nupos/sigmapos**2)
+mu = Symbol('mu', real=True)
+laplace = exp(-abs(x - mu)/bpos)/2/bpos
+
+u = Symbol('u', polar=True)
+tpos = Symbol('t', positive=True)
+
+
+def E(expr):
+    integrate(expr*exponential(x, rate)*normal(y, mu1, sigma1),
+                     (x, 0, oo), (y, -oo, oo), meijerg=True)
+    integrate(expr*exponential(x, rate)*normal(y, mu1, sigma1),
+                     (y, -oo, oo), (x, 0, oo), meijerg=True)
+
+bench = [
+    'MT(x**nu*Heaviside(x - 1), x, s)',
+    'MT(x**nu*Heaviside(1 - x), x, s)',
+    'MT((1-x)**(beta - 1)*Heaviside(1-x), x, s)',
+    'MT((x-1)**(beta - 1)*Heaviside(x-1), x, s)',
+    'MT((1+x)**(-rho), x, s)',
+    'MT(abs(1-x)**(-rho), x, s)',
+    'MT((1-x)**(beta-1)*Heaviside(1-x) + a*(x-1)**(beta-1)*Heaviside(x-1), x, s)',
+    'MT((x**a-b**a)/(x-b), x, s)',
+    'MT((x**a-bpos**a)/(x-bpos), x, s)',
+    'MT(exp(-x), x, s)',
+    'MT(exp(-1/x), x, s)',
+    'MT(log(x)**4*Heaviside(1-x), x, s)',
+    'MT(log(x)**3*Heaviside(x-1), x, s)',
+    'MT(log(x + 1), x, s)',
+    'MT(log(1/x + 1), x, s)',
+    'MT(log(abs(1 - x)), x, s)',
+    'MT(log(abs(1 - 1/x)), x, s)',
+    'MT(log(x)/(x+1), x, s)',
+    'MT(log(x)**2/(x+1), x, s)',
+    'MT(log(x)/(x+1)**2, x, s)',
+    'MT(erf(sqrt(x)), x, s)',
+
+    'MT(besselj(a, 2*sqrt(x)), x, s)',
+    'MT(sin(sqrt(x))*besselj(a, sqrt(x)), x, s)',
+    'MT(cos(sqrt(x))*besselj(a, sqrt(x)), x, s)',
+    'MT(besselj(a, sqrt(x))**2, x, s)',
+    'MT(besselj(a, sqrt(x))*besselj(-a, sqrt(x)), x, s)',
+    'MT(besselj(a - 1, sqrt(x))*besselj(a, sqrt(x)), x, s)',
+    'MT(besselj(a, sqrt(x))*besselj(b, sqrt(x)), x, s)',
+    'MT(besselj(a, sqrt(x))**2 + besselj(-a, sqrt(x))**2, x, s)',
+    'MT(bessely(a, 2*sqrt(x)), x, s)',
+    'MT(sin(sqrt(x))*bessely(a, sqrt(x)), x, s)',
+    'MT(cos(sqrt(x))*bessely(a, sqrt(x)), x, s)',
+    'MT(besselj(a, sqrt(x))*bessely(a, sqrt(x)), x, s)',
+    'MT(besselj(a, sqrt(x))*bessely(b, sqrt(x)), x, s)',
+    'MT(bessely(a, sqrt(x))**2, x, s)',
+
+    'MT(besselk(a, 2*sqrt(x)), x, s)',
+    'MT(besselj(a, 2*sqrt(2*sqrt(x)))*besselk(a, 2*sqrt(2*sqrt(x))), x, s)',
+    'MT(besseli(a, sqrt(x))*besselk(a, sqrt(x)), x, s)',
+    'MT(besseli(b, sqrt(x))*besselk(a, sqrt(x)), x, s)',
+    'MT(exp(-x/2)*besselk(a, x/2), x, s)',
+
+    # later: ILT, IMT
+
+    'LT((t-apos)**bpos*exp(-cpos*(t-apos))*Heaviside(t-apos), t, s)',
+    'LT(t**apos, t, s)',
+    'LT(Heaviside(t), t, s)',
+    'LT(Heaviside(t - apos), t, s)',
+    'LT(1 - exp(-apos*t), t, s)',
+    'LT((exp(2*t)-1)*exp(-bpos - t)*Heaviside(t)/2, t, s, noconds=True)',
+    'LT(exp(t), t, s)',
+    'LT(exp(2*t), t, s)',
+    'LT(exp(apos*t), t, s)',
+    'LT(log(t/apos), t, s)',
+    'LT(erf(t), t, s)',
+    'LT(sin(apos*t), t, s)',
+    'LT(cos(apos*t), t, s)',
+    'LT(exp(-apos*t)*sin(bpos*t), t, s)',
+    'LT(exp(-apos*t)*cos(bpos*t), t, s)',
+    'LT(besselj(0, t), t, s, noconds=True)',
+    'LT(besselj(1, t), t, s, noconds=True)',
+
+    'FT(Heaviside(1 - abs(2*apos*x)), x, k)',
+    'FT(Heaviside(1-abs(apos*x))*(1-abs(apos*x)), x, k)',
+    'FT(exp(-apos*x)*Heaviside(x), x, k)',
+    'IFT(1/(apos + 2*pi*I*x), x, posk, noconds=False)',
+    'IFT(1/(apos + 2*pi*I*x), x, -posk, noconds=False)',
+    'IFT(1/(apos + 2*pi*I*x), x, negk)',
+    'FT(x*exp(-apos*x)*Heaviside(x), x, k)',
+    'FT(exp(-apos*x)*sin(bpos*x)*Heaviside(x), x, k)',
+    'FT(exp(-apos*x**2), x, k)',
+    'IFT(sqrt(pi/apos)*exp(-(pi*k)**2/apos), k, x)',
+    'FT(exp(-apos*abs(x)), x, k)',
+
+    'integrate(normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)',
+    'integrate(x*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)',
+    'integrate(x**2*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)',
+    'integrate(x**3*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)',
+    'integrate(normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '          (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate(x*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '          (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate(y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '          (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate(x*y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '          (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate((x+y+1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '          (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate((x+y-1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '                   (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate(x**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '                (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate(y**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),'
+    '          (x, -oo, oo), (y, -oo, oo), meijerg=True)',
+    'integrate(exponential(x, rate), (x, 0, oo), meijerg=True)',
+    'integrate(x*exponential(x, rate), (x, 0, oo), meijerg=True)',
+    'integrate(x**2*exponential(x, rate), (x, 0, oo), meijerg=True)',
+    'E(1)',
+    'E(x*y)',
+    'E(x*y**2)',
+    'E((x+y+1)**2)',
+    'E(x+y+1)',
+    'E((x+y-1)**2)',
+    'integrate(betadist, (x, 0, oo), meijerg=True)',
+    'integrate(x*betadist, (x, 0, oo), meijerg=True)',
+    'integrate(x**2*betadist, (x, 0, oo), meijerg=True)',
+    'integrate(chi, (x, 0, oo), meijerg=True)',
+    'integrate(x*chi, (x, 0, oo), meijerg=True)',
+    'integrate(x**2*chi, (x, 0, oo), meijerg=True)',
+    'integrate(chisquared, (x, 0, oo), meijerg=True)',
+    'integrate(x*chisquared, (x, 0, oo), meijerg=True)',
+    'integrate(x**2*chisquared, (x, 0, oo), meijerg=True)',
+    'integrate(((x-k)/sqrt(2*k))**3*chisquared, (x, 0, oo), meijerg=True)',
+    'integrate(dagum, (x, 0, oo), meijerg=True)',
+    'integrate(x*dagum, (x, 0, oo), meijerg=True)',
+    'integrate(x**2*dagum, (x, 0, oo), meijerg=True)',
+    'integrate(f, (x, 0, oo), meijerg=True)',
+    'integrate(x*f, (x, 0, oo), meijerg=True)',
+    'integrate(x**2*f, (x, 0, oo), meijerg=True)',
+    'integrate(rice, (x, 0, oo), meijerg=True)',
+    'integrate(laplace, (x, -oo, oo), meijerg=True)',
+    'integrate(x*laplace, (x, -oo, oo), meijerg=True)',
+    'integrate(x**2*laplace, (x, -oo, oo), meijerg=True)',
+    'integrate(log(x) * x**(k-1) * exp(-x) / gamma(k), (x, 0, oo))',
+
+    'integrate(sin(z*x)*(x**2-1)**(-(y+S(1)/2)), (x, 1, oo), meijerg=True)',
+    'integrate(besselj(0,x)*besselj(1,x)*exp(-x**2), (x, 0, oo), meijerg=True)',
+    'integrate(besselj(0,x)*besselj(1,x)*besselk(0,x), (x, 0, oo), meijerg=True)',
+    'integrate(besselj(0,x)*besselj(1,x)*exp(-x**2), (x, 0, oo), meijerg=True)',
+    'integrate(besselj(a,x)*besselj(b,x)/x, (x,0,oo), meijerg=True)',
+
+    'hyperexpand(meijerg((-s - a/2 + 1, -s + a/2 + 1), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), (a/2, -a/2), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), 1))',
+    "gammasimp(S('2**(2*s)*(-pi*gamma(-a + 1)*gamma(a + 1)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 3/2)*gamma(a + s + 1)/(a*(a + s)) - gamma(-a - 1/2)*gamma(-a + 1)*gamma(a + 1)*gamma(a + 3/2)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a + s + 1)*gamma(a - s + 1)/(a*(-a + s)))*gamma(-2*s + 1)*gamma(s + 1)/(pi*s*gamma(-a - 1/2)*gamma(a + 3/2)*gamma(-s + 1)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 1)*gamma(a - s + 3/2))'))",
+
+    'mellin_transform(E1(x), x, s)',
+    'inverse_mellin_transform(gamma(s)/s, s, x, (0, oo))',
+    'mellin_transform(expint(a, x), x, s)',
+    'mellin_transform(Si(x), x, s)',
+    'inverse_mellin_transform(-2**s*sqrt(pi)*gamma((s + 1)/2)/(2*s*gamma(-s/2 + 1)), s, x, (-1, 0))',
+    'mellin_transform(Ci(sqrt(x)), x, s)',
+    'inverse_mellin_transform(-4**s*sqrt(pi)*gamma(s)/(2*s*gamma(-s + S(1)/2)),s, u, (0, 1))',
+    'laplace_transform(Ci(x), x, s)',
+    'laplace_transform(expint(a, x), x, s)',
+    'laplace_transform(expint(1, x), x, s)',
+    'laplace_transform(expint(2, x), x, s)',
+    'inverse_laplace_transform(-log(1 + s**2)/2/s, s, u)',
+    'inverse_laplace_transform(log(s + 1)/s, s, x)',
+    'inverse_laplace_transform((s - log(s + 1))/s**2, s, x)',
+    'laplace_transform(Chi(x), x, s)',
+    'laplace_transform(Shi(x), x, s)',
+
+    'integrate(exp(-z*x)/x, (x, 1, oo), meijerg=True, conds="none")',
+    'integrate(exp(-z*x)/x**2, (x, 1, oo), meijerg=True, conds="none")',
+    'integrate(exp(-z*x)/x**3, (x, 1, oo), meijerg=True,conds="none")',
+    'integrate(-cos(x)/x, (x, tpos, oo), meijerg=True)',
+    'integrate(-sin(x)/x, (x, tpos, oo), meijerg=True)',
+    'integrate(sin(x)/x, (x, 0, z), meijerg=True)',
+    'integrate(sinh(x)/x, (x, 0, z), meijerg=True)',
+    'integrate(exp(-x)/x, x, meijerg=True)',
+    'integrate(exp(-x)/x**2, x, meijerg=True)',
+    'integrate(cos(u)/u, u, meijerg=True)',
+    'integrate(cosh(u)/u, u, meijerg=True)',
+    'integrate(expint(1, x), x, meijerg=True)',
+    'integrate(expint(2, x), x, meijerg=True)',
+    'integrate(Si(x), x, meijerg=True)',
+    'integrate(Ci(u), u, meijerg=True)',
+    'integrate(Shi(x), x, meijerg=True)',
+    'integrate(Chi(u), u, meijerg=True)',
+    'integrate(Si(x)*exp(-x), (x, 0, oo), meijerg=True)',
+    'integrate(expint(1, x)*sin(x), (x, 0, oo), meijerg=True)'
+]
+
+from time import time
+from sympy.core.cache import clear_cache
+import sys
+
+timings = []
+
+if __name__ == '__main__':
+    for n, string in enumerate(bench):
+        clear_cache()
+        _t = time()
+        exec(string)
+        _t = time() - _t
+        timings += [(_t, string)]
+        sys.stdout.write('.')
+        sys.stdout.flush()
+        if n % (len(bench) // 10) == 0:
+            sys.stdout.write('%s' % (10*n // len(bench)))
+    print()
+
+    timings.sort(key=lambda x: -x[0])
+
+    for ti, string in timings:
+        print('%.2fs %s' % (ti, string))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_symbench.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_symbench.py
new file mode 100644
index 0000000000000000000000000000000000000000..8ea700b44b677107f5345196a8895e8ed5a9d56d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/benchmarks/bench_symbench.py
@@ -0,0 +1,134 @@
+#!/usr/bin/env python
+from sympy.core.random import random
+from sympy.core.numbers import (I, Integer, pi)
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+from sympy.polys.polytools import factor
+from sympy.simplify.simplify import simplify
+from sympy.abc import x, y, z
+from timeit import default_timer as clock
+
+
+def bench_R1():
+    "real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))"
+    def f(z):
+        return sqrt(Integer(1)/3)*z**2 + I/3
+    f(f(f(f(f(f(f(f(f(f(I/2)))))))))).as_real_imag()[0]
+
+
+def bench_R2():
+    "Hermite polynomial hermite(15, y)"
+    def hermite(n, y):
+        if n == 1:
+            return 2*y
+        if n == 0:
+            return 1
+        return (2*y*hermite(n - 1, y) - 2*(n - 1)*hermite(n - 2, y)).expand()
+
+    hermite(15, y)
+
+
+def bench_R3():
+    "a = [bool(f==f) for _ in range(10)]"
+    f = x + y + z
+    [bool(f == f) for _ in range(10)]
+
+
+def bench_R4():
+    # we don't have Tuples
+    pass
+
+
+def bench_R5():
+    "blowup(L, 8); L=uniq(L)"
+    def blowup(L, n):
+        for i in range(n):
+            L.append( (L[i] + L[i + 1]) * L[i + 2] )
+
+    def uniq(x):
+        v = set(x)
+        return v
+    L = [x, y, z]
+    blowup(L, 8)
+    L = uniq(L)
+
+
+def bench_R6():
+    "sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))"
+    sum(simplify((x + sin(i))/x + (x - sin(i))/x) for i in range(100))
+
+
+def bench_R7():
+    "[f.subs(x, random()) for _ in range(10**4)]"
+    f = x**24 + 34*x**12 + 45*x**3 + 9*x**18 + 34*x**10 + 32*x**21
+    [f.subs(x, random()) for _ in range(10**4)]
+
+
+def bench_R8():
+    "right(x^2,0,5,10^4)"
+    def right(f, a, b, n):
+        a = sympify(a)
+        b = sympify(b)
+        n = sympify(n)
+        x = f.atoms(Symbol).pop()
+        Deltax = (b - a)/n
+        c = a
+        est = 0
+        for i in range(n):
+            c += Deltax
+            est += f.subs(x, c)
+        return est*Deltax
+
+    right(x**2, 0, 5, 10**4)
+
+
+def _bench_R9():
+    "factor(x^20 - pi^5*y^20)"
+    factor(x**20 - pi**5*y**20)
+
+
+def bench_R10():
+    "v = [-pi,-pi+1/10..,pi]"
+    def srange(min, max, step):
+        v = [min]
+        while (max - v[-1]).evalf() > 0:
+            v.append(v[-1] + step)
+        return v[:-1]
+    srange(-pi, pi, sympify(1)/10)
+
+
+def bench_R11():
+    "a = [random() + random()*I for w in [0..1000]]"
+    [random() + random()*I for w in range(1000)]
+
+
+def bench_S1():
+    "e=(x+y+z+1)**7;f=e*(e+1);f.expand()"
+    e = (x + y + z + 1)**7
+    f = e*(e + 1)
+    f.expand()
+
+
+if __name__ == '__main__':
+    benchmarks = [
+        bench_R1,
+        bench_R2,
+        bench_R3,
+        bench_R5,
+        bench_R6,
+        bench_R7,
+        bench_R8,
+        #_bench_R9,
+        bench_R10,
+        bench_R11,
+        #bench_S1,
+    ]
+
+    report = []
+    for b in benchmarks:
+        t = clock()
+        b()
+        t = clock() - t
+        print("%s%65s: %f" % (b.__name__, b.__doc__, t))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..865c0556769e35ca7e8a09a4c208a1cfbd17369c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/__init__.py
@@ -0,0 +1,25 @@
+"""Calculus-related methods."""
+
+from .euler import euler_equations
+from .singularities import (singularities, is_increasing,
+                            is_strictly_increasing, is_decreasing,
+                            is_strictly_decreasing, is_monotonic)
+from .finite_diff import finite_diff_weights, apply_finite_diff, differentiate_finite
+from .util import (periodicity, not_empty_in, is_convex,
+                   stationary_points, minimum, maximum)
+from .accumulationbounds import AccumBounds
+
+__all__ = [
+'euler_equations',
+
+'singularities', 'is_increasing',
+'is_strictly_increasing', 'is_decreasing',
+'is_strictly_decreasing', 'is_monotonic',
+
+'finite_diff_weights', 'apply_finite_diff', 'differentiate_finite',
+
+'periodicity', 'not_empty_in', 'is_convex', 'stationary_points',
+'minimum', 'maximum',
+
+'AccumBounds'
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/accumulationbounds.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/accumulationbounds.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a2b0e634da1028c25399c8b03884865d981a56e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/accumulationbounds.py
@@ -0,0 +1,804 @@
+from sympy.core import Add, Mul, Pow, S
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.numbers import _sympifyit, oo, zoo
+from sympy.core.relational import is_le, is_lt, is_ge, is_gt
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.miscellaneous import Min, Max
+from sympy.logic.boolalg import And
+from sympy.multipledispatch import dispatch
+from sympy.series.order import Order
+from sympy.sets.sets import FiniteSet
+
+
+class AccumulationBounds(Expr):
+    r"""An accumulation bounds.
+
+    # Note AccumulationBounds has an alias: AccumBounds
+
+    AccumulationBounds represent an interval `[a, b]`, which is always closed
+    at the ends. Here `a` and `b` can be any value from extended real numbers.
+
+    The intended meaning of AccummulationBounds is to give an approximate
+    location of the accumulation points of a real function at a limit point.
+
+    Let `a` and `b` be reals such that `a \le b`.
+
+    `\left\langle a, b\right\rangle = \{x \in \mathbb{R} \mid a \le x \le b\}`
+
+    `\left\langle -\infty, b\right\rangle = \{x \in \mathbb{R} \mid x \le b\} \cup \{-\infty, \infty\}`
+
+    `\left\langle a, \infty \right\rangle = \{x \in \mathbb{R} \mid a \le x\} \cup \{-\infty, \infty\}`
+
+    `\left\langle -\infty, \infty \right\rangle = \mathbb{R} \cup \{-\infty, \infty\}`
+
+    ``oo`` and ``-oo`` are added to the second and third definition respectively,
+    since if either ``-oo`` or ``oo`` is an argument, then the other one should
+    be included (though not as an end point). This is forced, since we have,
+    for example, ``1/AccumBounds(0, 1) = AccumBounds(1, oo)``, and the limit at
+    `0` is not one-sided. As `x` tends to `0-`, then `1/x \rightarrow -\infty`, so `-\infty`
+    should be interpreted as belonging to ``AccumBounds(1, oo)`` though it need
+    not appear explicitly.
+
+    In many cases it suffices to know that the limit set is bounded.
+    However, in some other cases more exact information could be useful.
+    For example, all accumulation values of `\cos(x) + 1` are non-negative.
+    (``AccumBounds(-1, 1) + 1 = AccumBounds(0, 2)``)
+
+    A AccumulationBounds object is defined to be real AccumulationBounds,
+    if its end points are finite reals.
+
+    Let `X`, `Y` be real AccumulationBounds, then their sum, difference,
+    product are defined to be the following sets:
+
+    `X + Y = \{ x+y \mid x \in X \cap y \in Y\}`
+
+    `X - Y = \{ x-y \mid x \in X \cap y \in Y\}`
+
+    `X \times Y = \{ x \times y \mid x \in X \cap y \in Y\}`
+
+    When an AccumBounds is raised to a negative power, if 0 is contained
+    between the bounds then an infinite range is returned, otherwise if an
+    endpoint is 0 then a semi-infinite range with consistent sign will be returned.
+
+    AccumBounds in expressions behave a lot like Intervals but the
+    semantics are not necessarily the same. Division (or exponentiation
+    to a negative integer power) could be handled with *intervals* by
+    returning a union of the results obtained after splitting the
+    bounds between negatives and positives, but that is not done with
+    AccumBounds. In addition, bounds are assumed to be independent of
+    each other; if the same bound is used in more than one place in an
+    expression, the result may not be the supremum or infimum of the
+    expression (see below). Finally, when a boundary is ``1``,
+    exponentiation to the power of ``oo`` yields ``oo``, neither
+    ``1`` nor ``nan``.
+
+    Examples
+    ========
+
+    >>> from sympy import AccumBounds, sin, exp, log, pi, E, S, oo
+    >>> from sympy.abc import x
+
+    >>> AccumBounds(0, 1) + AccumBounds(1, 2)
+    AccumBounds(1, 3)
+
+    >>> AccumBounds(0, 1) - AccumBounds(0, 2)
+    AccumBounds(-2, 1)
+
+    >>> AccumBounds(-2, 3)*AccumBounds(-1, 1)
+    AccumBounds(-3, 3)
+
+    >>> AccumBounds(1, 2)*AccumBounds(3, 5)
+    AccumBounds(3, 10)
+
+    The exponentiation of AccumulationBounds is defined
+    as follows:
+
+    If 0 does not belong to `X` or `n > 0` then
+
+    `X^n = \{ x^n \mid x \in X\}`
+
+    >>> AccumBounds(1, 4)**(S(1)/2)
+    AccumBounds(1, 2)
+
+    otherwise, an infinite or semi-infinite result is obtained:
+
+    >>> 1/AccumBounds(-1, 1)
+    AccumBounds(-oo, oo)
+    >>> 1/AccumBounds(0, 2)
+    AccumBounds(1/2, oo)
+    >>> 1/AccumBounds(-oo, 0)
+    AccumBounds(-oo, 0)
+
+    A boundary of 1 will always generate all nonnegatives:
+
+    >>> AccumBounds(1, 2)**oo
+    AccumBounds(0, oo)
+    >>> AccumBounds(0, 1)**oo
+    AccumBounds(0, oo)
+
+    If the exponent is itself an AccumulationBounds or is not an
+    integer then unevaluated results will be returned unless the base
+    values are positive:
+
+    >>> AccumBounds(2, 3)**AccumBounds(-1, 2)
+    AccumBounds(1/3, 9)
+    >>> AccumBounds(-2, 3)**AccumBounds(-1, 2)
+    AccumBounds(-2, 3)**AccumBounds(-1, 2)
+
+    >>> AccumBounds(-2, -1)**(S(1)/2)
+    sqrt(AccumBounds(-2, -1))
+
+    Note: `\left\langle a, b\right\rangle^2` is not same as `\left\langle a, b\right\rangle \times \left\langle a, b\right\rangle`
+
+    >>> AccumBounds(-1, 1)**2
+    AccumBounds(0, 1)
+
+    >>> AccumBounds(1, 3) < 4
+    True
+
+    >>> AccumBounds(1, 3) < -1
+    False
+
+    Some elementary functions can also take AccumulationBounds as input.
+    A function `f` evaluated for some real AccumulationBounds `\left\langle a, b \right\rangle`
+    is defined as `f(\left\langle a, b\right\rangle) = \{ f(x) \mid a \le x \le b \}`
+
+    >>> sin(AccumBounds(pi/6, pi/3))
+    AccumBounds(1/2, sqrt(3)/2)
+
+    >>> exp(AccumBounds(0, 1))
+    AccumBounds(1, E)
+
+    >>> log(AccumBounds(1, E))
+    AccumBounds(0, 1)
+
+    Some symbol in an expression can be substituted for a AccumulationBounds
+    object. But it does not necessarily evaluate the AccumulationBounds for
+    that expression.
+
+    The same expression can be evaluated to different values depending upon
+    the form it is used for substitution since each instance of an
+    AccumulationBounds is considered independent. For example:
+
+    >>> (x**2 + 2*x + 1).subs(x, AccumBounds(-1, 1))
+    AccumBounds(-1, 4)
+
+    >>> ((x + 1)**2).subs(x, AccumBounds(-1, 1))
+    AccumBounds(0, 4)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Interval_arithmetic
+
+    .. [2] https://fab.cba.mit.edu/classes/S62.12/docs/Hickey_interval.pdf
+
+    Notes
+    =====
+
+    Do not use ``AccumulationBounds`` for floating point interval arithmetic
+    calculations, use ``mpmath.iv`` instead.
+    """
+
+    is_extended_real = True
+    is_number = False
+
+    def __new__(cls, min, max) -> Expr: # type: ignore
+
+        min = _sympify(min)
+        max = _sympify(max)
+
+        # Only allow real intervals (use symbols with 'is_extended_real=True').
+        if not min.is_extended_real or not max.is_extended_real:
+            raise ValueError("Only real AccumulationBounds are supported")
+
+        if max == min:
+            return max
+
+        # Make sure that the created AccumBounds object will be valid.
+        if max.is_number and min.is_number:
+            bad = max.is_comparable and min.is_comparable and max < min
+        else:
+            bad = (max - min).is_extended_negative
+        if bad:
+            raise ValueError(
+                "Lower limit should be smaller than upper limit")
+
+        return Basic.__new__(cls, min, max)
+
+    # setting the operation priority
+    _op_priority = 11.0
+
+    def _eval_is_real(self):
+        if self.min.is_real and self.max.is_real:
+            return True
+
+    @property
+    def min(self):
+        """
+        Returns the minimum possible value attained by AccumulationBounds
+        object.
+
+        Examples
+        ========
+
+        >>> from sympy import AccumBounds
+        >>> AccumBounds(1, 3).min
+        1
+
+        """
+        return self.args[0]
+
+    @property
+    def max(self):
+        """
+        Returns the maximum possible value attained by AccumulationBounds
+        object.
+
+        Examples
+        ========
+
+        >>> from sympy import AccumBounds
+        >>> AccumBounds(1, 3).max
+        3
+
+        """
+        return self.args[1]
+
+    @property
+    def delta(self):
+        """
+        Returns the difference of maximum possible value attained by
+        AccumulationBounds object and minimum possible value attained
+        by AccumulationBounds object.
+
+        Examples
+        ========
+
+        >>> from sympy import AccumBounds
+        >>> AccumBounds(1, 3).delta
+        2
+
+        """
+        return self.max - self.min
+
+    @property
+    def mid(self):
+        """
+        Returns the mean of maximum possible value attained by
+        AccumulationBounds object and minimum possible value
+        attained by AccumulationBounds object.
+
+        Examples
+        ========
+
+        >>> from sympy import AccumBounds
+        >>> AccumBounds(1, 3).mid
+        2
+
+        """
+        return (self.min + self.max) / 2
+
+    @_sympifyit('other', NotImplemented)
+    def _eval_power(self, other):
+        return self.__pow__(other)
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other):
+        if isinstance(other, Expr):
+            if isinstance(other, AccumBounds):
+                return AccumBounds(
+                    Add(self.min, other.min),
+                    Add(self.max, other.max))
+            if other is S.Infinity and self.min is S.NegativeInfinity or \
+                    other is S.NegativeInfinity and self.max is S.Infinity:
+                return AccumBounds(-oo, oo)
+            elif other.is_extended_real:
+                if self.min is S.NegativeInfinity and self.max is S.Infinity:
+                    return AccumBounds(-oo, oo)
+                elif self.min is S.NegativeInfinity:
+                    return AccumBounds(-oo, self.max + other)
+                elif self.max is S.Infinity:
+                    return AccumBounds(self.min + other, oo)
+                else:
+                    return AccumBounds(Add(self.min, other), Add(self.max, other))
+            return Add(self, other, evaluate=False)
+        return NotImplemented
+
+    __radd__ = __add__
+
+    def __neg__(self):
+        return AccumBounds(-self.max, -self.min)
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        if isinstance(other, Expr):
+            if isinstance(other, AccumBounds):
+                return AccumBounds(
+                    Add(self.min, -other.max),
+                    Add(self.max, -other.min))
+            if other is S.NegativeInfinity and self.min is S.NegativeInfinity or \
+                    other is S.Infinity and self.max is S.Infinity:
+                return AccumBounds(-oo, oo)
+            elif other.is_extended_real:
+                if self.min is S.NegativeInfinity and self.max is S.Infinity:
+                    return AccumBounds(-oo, oo)
+                elif self.min is S.NegativeInfinity:
+                    return AccumBounds(-oo, self.max - other)
+                elif self.max is S.Infinity:
+                    return AccumBounds(self.min - other, oo)
+                else:
+                    return AccumBounds(
+                        Add(self.min, -other),
+                        Add(self.max, -other))
+            return Add(self, -other, evaluate=False)
+        return NotImplemented
+
+    @_sympifyit('other', NotImplemented)
+    def __rsub__(self, other):
+        return self.__neg__() + other
+
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        if self.args == (-oo, oo):
+            return self
+        if isinstance(other, Expr):
+            if isinstance(other, AccumBounds):
+                if other.args == (-oo, oo):
+                    return other
+                v = set()
+                for a in self.args:
+                    vi = other*a
+                    v.update(vi.args or (vi,))
+                return AccumBounds(Min(*v), Max(*v))
+            if other is S.Infinity:
+                if self.min.is_zero:
+                    return AccumBounds(0, oo)
+                if self.max.is_zero:
+                    return AccumBounds(-oo, 0)
+            if other is S.NegativeInfinity:
+                if self.min.is_zero:
+                    return AccumBounds(-oo, 0)
+                if self.max.is_zero:
+                    return AccumBounds(0, oo)
+            if other.is_extended_real:
+                if other.is_zero:
+                    if self.max is S.Infinity:
+                        return AccumBounds(0, oo)
+                    if self.min is S.NegativeInfinity:
+                        return AccumBounds(-oo, 0)
+                    return S.Zero
+                if other.is_extended_positive:
+                    return AccumBounds(
+                        Mul(self.min, other),
+                        Mul(self.max, other))
+                elif other.is_extended_negative:
+                    return AccumBounds(
+                        Mul(self.max, other),
+                        Mul(self.min, other))
+            if isinstance(other, Order):
+                return other
+            return Mul(self, other, evaluate=False)
+        return NotImplemented
+
+    __rmul__ = __mul__
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        if isinstance(other, Expr):
+            if isinstance(other, AccumBounds):
+                if other.min.is_positive or other.max.is_negative:
+                    return self * AccumBounds(1/other.max, 1/other.min)
+
+                if (self.min.is_extended_nonpositive and self.max.is_extended_nonnegative and
+                    other.min.is_extended_nonpositive and other.max.is_extended_nonnegative):
+                    if self.min.is_zero and other.min.is_zero:
+                        return AccumBounds(0, oo)
+                    if self.max.is_zero and other.min.is_zero:
+                        return AccumBounds(-oo, 0)
+                    return AccumBounds(-oo, oo)
+
+                if self.max.is_extended_negative:
+                    if other.min.is_extended_negative:
+                        if other.max.is_zero:
+                            return AccumBounds(self.max / other.min, oo)
+                        if other.max.is_extended_positive:
+                            # if we were dealing with intervals we would return
+                            # Union(Interval(-oo, self.max/other.max),
+                            #       Interval(self.max/other.min, oo))
+                            return AccumBounds(-oo, oo)
+
+                    if other.min.is_zero and other.max.is_extended_positive:
+                        return AccumBounds(-oo, self.max / other.max)
+
+                if self.min.is_extended_positive:
+                    if other.min.is_extended_negative:
+                        if other.max.is_zero:
+                            return AccumBounds(-oo, self.min / other.min)
+                        if other.max.is_extended_positive:
+                            # if we were dealing with intervals we would return
+                            # Union(Interval(-oo, self.min/other.min),
+                            #       Interval(self.min/other.max, oo))
+                            return AccumBounds(-oo, oo)
+
+                    if other.min.is_zero and other.max.is_extended_positive:
+                        return AccumBounds(self.min / other.max, oo)
+
+            elif other.is_extended_real:
+                if other in (S.Infinity, S.NegativeInfinity):
+                    if self == AccumBounds(-oo, oo):
+                        return AccumBounds(-oo, oo)
+                    if self.max is S.Infinity:
+                        return AccumBounds(Min(0, other), Max(0, other))
+                    if self.min is S.NegativeInfinity:
+                        return AccumBounds(Min(0, -other), Max(0, -other))
+                if other.is_extended_positive:
+                    return AccumBounds(self.min / other, self.max / other)
+                elif other.is_extended_negative:
+                    return AccumBounds(self.max / other, self.min / other)
+            if (1 / other) is S.ComplexInfinity:
+                return Mul(self, 1 / other, evaluate=False)
+            else:
+                return Mul(self, 1 / other)
+
+        return NotImplemented
+
+    @_sympifyit('other', NotImplemented)
+    def __rtruediv__(self, other):
+        if isinstance(other, Expr):
+            if other.is_extended_real:
+                if other.is_zero:
+                    return S.Zero
+                if (self.min.is_extended_nonpositive and self.max.is_extended_nonnegative):
+                    if self.min.is_zero:
+                        if other.is_extended_positive:
+                            return AccumBounds(Mul(other, 1 / self.max), oo)
+                        if other.is_extended_negative:
+                            return AccumBounds(-oo, Mul(other, 1 / self.max))
+                    if self.max.is_zero:
+                        if other.is_extended_positive:
+                            return AccumBounds(-oo, Mul(other, 1 / self.min))
+                        if other.is_extended_negative:
+                            return AccumBounds(Mul(other, 1 / self.min), oo)
+                    return AccumBounds(-oo, oo)
+                else:
+                    return AccumBounds(Min(other / self.min, other / self.max),
+                                       Max(other / self.min, other / self.max))
+            return Mul(other, 1 / self, evaluate=False)
+        else:
+            return NotImplemented
+
+    @_sympifyit('other', NotImplemented)
+    def __pow__(self, other):
+        if isinstance(other, Expr):
+            if other is S.Infinity:
+                if self.min.is_extended_nonnegative:
+                    if self.max < 1:
+                        return S.Zero
+                    if self.min > 1:
+                        return S.Infinity
+                    return AccumBounds(0, oo)
+                elif self.max.is_extended_negative:
+                    if self.min > -1:
+                        return S.Zero
+                    if self.max < -1:
+                        return zoo
+                    return S.NaN
+                else:
+                    if self.min > -1:
+                        if self.max < 1:
+                            return S.Zero
+                        return AccumBounds(0, oo)
+                    return AccumBounds(-oo, oo)
+
+            if other is S.NegativeInfinity:
+                return (1/self)**oo
+
+            # generically true
+            if (self.max - self.min).is_nonnegative:
+                # well defined
+                if self.min.is_nonnegative:
+                    # no 0 to worry about
+                    if other.is_nonnegative:
+                        # no infinity to worry about
+                        return self.func(self.min**other, self.max**other)
+
+            if other.is_zero:
+                return S.One  # x**0 = 1
+
+            if other.is_Integer or other.is_integer:
+                if self.min.is_extended_positive:
+                    return AccumBounds(
+                        Min(self.min**other, self.max**other),
+                        Max(self.min**other, self.max**other))
+                elif self.max.is_extended_negative:
+                    return AccumBounds(
+                        Min(self.max**other, self.min**other),
+                        Max(self.max**other, self.min**other))
+
+                if other % 2 == 0:
+                    if other.is_extended_negative:
+                        if self.min.is_zero:
+                            return AccumBounds(self.max**other, oo)
+                        if self.max.is_zero:
+                            return AccumBounds(self.min**other, oo)
+                        return (1/self)**(-other)
+                    return AccumBounds(
+                        S.Zero, Max(self.min**other, self.max**other))
+                elif other % 2 == 1:
+                    if other.is_extended_negative:
+                        if self.min.is_zero:
+                            return AccumBounds(self.max**other, oo)
+                        if self.max.is_zero:
+                            return AccumBounds(-oo, self.min**other)
+                        return (1/self)**(-other)
+                    return AccumBounds(self.min**other, self.max**other)
+
+            # non-integer exponent
+            # 0**neg or neg**frac yields complex
+            if (other.is_number or other.is_rational) and (
+                    self.min.is_extended_nonnegative or (
+                    other.is_extended_nonnegative and
+                    self.min.is_extended_nonnegative)):
+                num, den = other.as_numer_denom()
+                if num is S.One:
+                    return AccumBounds(*[i**(1/den) for i in self.args])
+
+                elif den is not S.One:  # e.g. if other is not Float
+                    return (self**num)**(1/den)  # ok for non-negative base
+
+            if isinstance(other, AccumBounds):
+                if (self.min.is_extended_positive or
+                        self.min.is_extended_nonnegative and
+                        other.min.is_extended_nonnegative):
+                    p = [self**i for i in other.args]
+                    if not any(i.is_Pow for i in p):
+                        a = [j for i in p for j in i.args or (i,)]
+                        try:
+                            return self.func(min(a), max(a))
+                        except TypeError:  # can't sort
+                            pass
+
+            return Pow(self, other, evaluate=False)
+
+        return NotImplemented
+
+    @_sympifyit('other', NotImplemented)
+    def __rpow__(self, other):
+        if other.is_real and other.is_extended_nonnegative and (
+                self.max - self.min).is_extended_positive:
+            if other is S.One:
+                return S.One
+            if other.is_extended_positive:
+                a, b = [other**i for i in self.args]
+                if min(a, b) != a:
+                    a, b = b, a
+                return self.func(a, b)
+            if other.is_zero:
+                if self.min.is_zero:
+                    return self.func(0, 1)
+                if self.min.is_extended_positive:
+                    return S.Zero
+
+        return Pow(other, self, evaluate=False)
+
+    def __abs__(self):
+        if self.max.is_extended_negative:
+            return self.__neg__()
+        elif self.min.is_extended_negative:
+            return AccumBounds(S.Zero, Max(abs(self.min), self.max))
+        else:
+            return self
+
+
+    def __contains__(self, other):
+        """
+        Returns ``True`` if other is contained in self, where other
+        belongs to extended real numbers, ``False`` if not contained,
+        otherwise TypeError is raised.
+
+        Examples
+        ========
+
+        >>> from sympy import AccumBounds, oo
+        >>> 1 in AccumBounds(-1, 3)
+        True
+
+        -oo and oo go together as limits (in AccumulationBounds).
+
+        >>> -oo in AccumBounds(1, oo)
+        True
+
+        >>> oo in AccumBounds(-oo, 0)
+        True
+
+        """
+        other = _sympify(other)
+
+        if other in (S.Infinity, S.NegativeInfinity):
+            if self.min is S.NegativeInfinity or self.max is S.Infinity:
+                return True
+            return False
+
+        rv = And(self.min <= other, self.max >= other)
+        if rv not in (True, False):
+            raise TypeError("input failed to evaluate")
+        return rv
+
+    def intersection(self, other):
+        """
+        Returns the intersection of 'self' and 'other'.
+        Here other can be an instance of :py:class:`~.FiniteSet` or AccumulationBounds.
+
+        Parameters
+        ==========
+
+        other : AccumulationBounds
+            Another AccumulationBounds object with which the intersection
+            has to be computed.
+
+        Returns
+        =======
+
+        AccumulationBounds
+            Intersection of ``self`` and ``other``.
+
+        Examples
+        ========
+
+        >>> from sympy import AccumBounds, FiniteSet
+        >>> AccumBounds(1, 3).intersection(AccumBounds(2, 4))
+        AccumBounds(2, 3)
+
+        >>> AccumBounds(1, 3).intersection(AccumBounds(4, 6))
+        EmptySet
+
+        >>> AccumBounds(1, 4).intersection(FiniteSet(1, 2, 5))
+        {1, 2}
+
+        """
+        if not isinstance(other, (AccumBounds, FiniteSet)):
+            raise TypeError(
+                "Input must be AccumulationBounds or FiniteSet object")
+
+        if isinstance(other, FiniteSet):
+            fin_set = S.EmptySet
+            for i in other:
+                if i in self:
+                    fin_set = fin_set + FiniteSet(i)
+            return fin_set
+
+        if self.max < other.min or self.min > other.max:
+            return S.EmptySet
+
+        if self.min <= other.min:
+            if self.max <= other.max:
+                return AccumBounds(other.min, self.max)
+            if self.max > other.max:
+                return other
+
+        if other.min <= self.min:
+            if other.max < self.max:
+                return AccumBounds(self.min, other.max)
+            if other.max > self.max:
+                return self
+
+    def union(self, other):
+        # TODO : Devise a better method for Union of AccumBounds
+        # this method is not actually correct and
+        # can be made better
+        if not isinstance(other, AccumBounds):
+            raise TypeError(
+                "Input must be AccumulationBounds or FiniteSet object")
+
+        if self.min <= other.min and self.max >= other.min:
+            return AccumBounds(self.min, Max(self.max, other.max))
+
+        if other.min <= self.min and other.max >= self.min:
+            return AccumBounds(other.min, Max(self.max, other.max))
+
+
+@dispatch(AccumulationBounds, AccumulationBounds) # type: ignore # noqa:F811
+def _eval_is_le(lhs, rhs): # noqa:F811
+    if is_le(lhs.max, rhs.min):
+        return True
+    if is_gt(lhs.min, rhs.max):
+        return False
+
+
+@dispatch(AccumulationBounds, Basic) # type: ignore # noqa:F811
+def _eval_is_le(lhs, rhs): # noqa: F811
+
+    """
+    Returns ``True `` if range of values attained by ``lhs`` AccumulationBounds
+    object is greater than the range of values attained by ``rhs``,
+    where ``rhs`` may be any value of type AccumulationBounds object or
+    extended real number value, ``False`` if ``rhs`` satisfies
+    the same property, else an unevaluated :py:class:`~.Relational`.
+
+    Examples
+    ========
+
+    >>> from sympy import AccumBounds, oo
+    >>> AccumBounds(1, 3) > AccumBounds(4, oo)
+    False
+    >>> AccumBounds(1, 4) > AccumBounds(3, 4)
+    AccumBounds(1, 4) > AccumBounds(3, 4)
+    >>> AccumBounds(1, oo) > -1
+    True
+
+    """
+    if not rhs.is_extended_real:
+            raise TypeError(
+                "Invalid comparison of %s %s" %
+                (type(rhs), rhs))
+    elif rhs.is_comparable:
+        if is_le(lhs.max, rhs):
+            return True
+        if is_gt(lhs.min, rhs):
+            return False
+
+
+@dispatch(AccumulationBounds, AccumulationBounds)
+def _eval_is_ge(lhs, rhs): # noqa:F811
+    if is_ge(lhs.min, rhs.max):
+        return True
+    if is_lt(lhs.max, rhs.min):
+        return False
+
+
+@dispatch(AccumulationBounds, Expr)  # type:ignore
+def _eval_is_ge(lhs, rhs): # noqa: F811
+    """
+    Returns ``True`` if range of values attained by ``lhs`` AccumulationBounds
+    object is less that the range of values attained by ``rhs``, where
+    other may be any value of type AccumulationBounds object or extended
+    real number value, ``False`` if ``rhs`` satisfies the same
+    property, else an unevaluated :py:class:`~.Relational`.
+
+    Examples
+    ========
+
+    >>> from sympy import AccumBounds, oo
+    >>> AccumBounds(1, 3) >= AccumBounds(4, oo)
+    False
+    >>> AccumBounds(1, 4) >= AccumBounds(3, 4)
+    AccumBounds(1, 4) >= AccumBounds(3, 4)
+    >>> AccumBounds(1, oo) >= 1
+    True
+    """
+
+    if not rhs.is_extended_real:
+        raise TypeError(
+            "Invalid comparison of %s %s" %
+            (type(rhs), rhs))
+    elif rhs.is_comparable:
+        if is_ge(lhs.min, rhs):
+            return True
+        if is_lt(lhs.max, rhs):
+            return False
+
+
+@dispatch(Expr, AccumulationBounds)  # type:ignore
+def _eval_is_ge(lhs, rhs): # noqa:F811
+    if not lhs.is_extended_real:
+        raise TypeError(
+            "Invalid comparison of %s %s" %
+            (type(lhs), lhs))
+    elif lhs.is_comparable:
+        if is_le(rhs.max, lhs):
+            return True
+        if is_gt(rhs.min, lhs):
+            return False
+
+
+@dispatch(AccumulationBounds, AccumulationBounds)  # type:ignore
+def _eval_is_ge(lhs, rhs): # noqa:F811
+    if is_ge(lhs.min, rhs.max):
+        return True
+    if is_lt(lhs.max, rhs.min):
+        return False
+
+# setting an alias for AccumulationBounds
+AccumBounds = AccumulationBounds
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/euler.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/euler.py
new file mode 100644
index 0000000000000000000000000000000000000000..817acf76091dfba2dba40487ca7735e307c0fc15
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/euler.py
@@ -0,0 +1,108 @@
+"""
+This module implements a method to find
+Euler-Lagrange Equations for given Lagrangian.
+"""
+from itertools import combinations_with_replacement
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.utilities.iterables import iterable
+
+
+def euler_equations(L, funcs=(), vars=()):
+    r"""
+    Find the Euler-Lagrange equations [1]_ for a given Lagrangian.
+
+    Parameters
+    ==========
+
+    L : Expr
+        The Lagrangian that should be a function of the functions listed
+        in the second argument and their derivatives.
+
+        For example, in the case of two functions $f(x,y)$, $g(x,y)$ and
+        two independent variables $x$, $y$ the Lagrangian has the form:
+
+            .. math:: L\left(f(x,y),g(x,y),\frac{\partial f(x,y)}{\partial x},
+                      \frac{\partial f(x,y)}{\partial y},
+                      \frac{\partial g(x,y)}{\partial x},
+                      \frac{\partial g(x,y)}{\partial y},x,y\right)
+
+        In many cases it is not necessary to provide anything, except the
+        Lagrangian, it will be auto-detected (and an error raised if this
+        cannot be done).
+
+    funcs : Function or an iterable of Functions
+        The functions that the Lagrangian depends on. The Euler equations
+        are differential equations for each of these functions.
+
+    vars : Symbol or an iterable of Symbols
+        The Symbols that are the independent variables of the functions.
+
+    Returns
+    =======
+
+    eqns : list of Eq
+        The list of differential equations, one for each function.
+
+    Examples
+    ========
+
+    >>> from sympy import euler_equations, Symbol, Function
+    >>> x = Function('x')
+    >>> t = Symbol('t')
+    >>> L = (x(t).diff(t))**2/2 - x(t)**2/2
+    >>> euler_equations(L, x(t), t)
+    [Eq(-x(t) - Derivative(x(t), (t, 2)), 0)]
+    >>> u = Function('u')
+    >>> x = Symbol('x')
+    >>> L = (u(t, x).diff(t))**2/2 - (u(t, x).diff(x))**2/2
+    >>> euler_equations(L, u(t, x), [t, x])
+    [Eq(-Derivative(u(t, x), (t, 2)) + Derivative(u(t, x), (x, 2)), 0)]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation
+
+    """
+
+    funcs = tuple(funcs) if iterable(funcs) else (funcs,)
+
+    if not funcs:
+        funcs = tuple(L.atoms(Function))
+    else:
+        for f in funcs:
+            if not isinstance(f, Function):
+                raise TypeError('Function expected, got: %s' % f)
+
+    vars = tuple(vars) if iterable(vars) else (vars,)
+
+    if not vars:
+        vars = funcs[0].args
+    else:
+        vars = tuple(sympify(var) for var in vars)
+
+    if not all(isinstance(v, Symbol) for v in vars):
+        raise TypeError('Variables are not symbols, got %s' % vars)
+
+    for f in funcs:
+        if not vars == f.args:
+            raise ValueError("Variables %s do not match args: %s" % (vars, f))
+
+    order = max([len(d.variables) for d in L.atoms(Derivative)
+                        if d.expr in funcs] + [0])
+
+    eqns = []
+    for f in funcs:
+        eq = diff(L, f)
+        for i in range(1, order + 1):
+            for p in combinations_with_replacement(vars, i):
+                eq = eq + S.NegativeOne**i*diff(L, diff(f, *p), *p)
+        new_eq = Eq(eq, 0)
+        if isinstance(new_eq, Eq):
+            eqns.append(new_eq)
+
+    return eqns
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/finite_diff.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/finite_diff.py
new file mode 100644
index 0000000000000000000000000000000000000000..17eece149aadad236cefeb350e1ef4a383c84f01
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/finite_diff.py
@@ -0,0 +1,476 @@
+"""
+Finite difference weights
+=========================
+
+This module implements an algorithm for efficient generation of finite
+difference weights for ordinary differentials of functions for
+derivatives from 0 (interpolation) up to arbitrary order.
+
+The core algorithm is provided in the finite difference weight generating
+function (``finite_diff_weights``), and two convenience functions are provided
+for:
+
+- estimating a derivative (or interpolate) directly from a series of points
+    is also provided (``apply_finite_diff``).
+- differentiating by using finite difference approximations
+    (``differentiate_finite``).
+
+"""
+
+from sympy.core.function import Derivative
+from sympy.core.singleton import S
+from sympy.core.function import Subs
+from sympy.core.traversal import preorder_traversal
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import iterable
+
+
+
+def finite_diff_weights(order, x_list, x0=S.One):
+    """
+    Calculates the finite difference weights for an arbitrarily spaced
+    one-dimensional grid (``x_list``) for derivatives at ``x0`` of order
+    0, 1, ..., up to ``order`` using a recursive formula. Order of accuracy
+    is at least ``len(x_list) - order``, if ``x_list`` is defined correctly.
+
+    Parameters
+    ==========
+
+    order: int
+        Up to what derivative order weights should be calculated.
+        0 corresponds to interpolation.
+    x_list: sequence
+        Sequence of (unique) values for the independent variable.
+        It is useful (but not necessary) to order ``x_list`` from
+        nearest to furthest from ``x0``; see examples below.
+    x0: Number or Symbol
+        Root or value of the independent variable for which the finite
+        difference weights should be generated. Default is ``S.One``.
+
+    Returns
+    =======
+
+    list
+        A list of sublists, each corresponding to coefficients for
+        increasing derivative order, and each containing lists of
+        coefficients for increasing subsets of x_list.
+
+    Examples
+    ========
+
+    >>> from sympy import finite_diff_weights, S
+    >>> res = finite_diff_weights(1, [-S(1)/2, S(1)/2, S(3)/2, S(5)/2], 0)
+    >>> res
+    [[[1, 0, 0, 0],
+      [1/2, 1/2, 0, 0],
+      [3/8, 3/4, -1/8, 0],
+      [5/16, 15/16, -5/16, 1/16]],
+     [[0, 0, 0, 0],
+      [-1, 1, 0, 0],
+      [-1, 1, 0, 0],
+      [-23/24, 7/8, 1/8, -1/24]]]
+    >>> res[0][-1]  # FD weights for 0th derivative, using full x_list
+    [5/16, 15/16, -5/16, 1/16]
+    >>> res[1][-1]  # FD weights for 1st derivative
+    [-23/24, 7/8, 1/8, -1/24]
+    >>> res[1][-2]  # FD weights for 1st derivative, using x_list[:-1]
+    [-1, 1, 0, 0]
+    >>> res[1][-1][0]  # FD weight for 1st deriv. for x_list[0]
+    -23/24
+    >>> res[1][-1][1]  # FD weight for 1st deriv. for x_list[1], etc.
+    7/8
+
+    Each sublist contains the most accurate formula at the end.
+    Note, that in the above example ``res[1][1]`` is the same as ``res[1][2]``.
+    Since res[1][2] has an order of accuracy of
+    ``len(x_list[:3]) - order = 3 - 1 = 2``, the same is true for ``res[1][1]``!
+
+    >>> res = finite_diff_weights(1, [S(0), S(1), -S(1), S(2), -S(2)], 0)[1]
+    >>> res
+    [[0, 0, 0, 0, 0],
+     [-1, 1, 0, 0, 0],
+     [0, 1/2, -1/2, 0, 0],
+     [-1/2, 1, -1/3, -1/6, 0],
+     [0, 2/3, -2/3, -1/12, 1/12]]
+    >>> res[0]  # no approximation possible, using x_list[0] only
+    [0, 0, 0, 0, 0]
+    >>> res[1]  # classic forward step approximation
+    [-1, 1, 0, 0, 0]
+    >>> res[2]  # classic centered approximation
+    [0, 1/2, -1/2, 0, 0]
+    >>> res[3:]  # higher order approximations
+    [[-1/2, 1, -1/3, -1/6, 0], [0, 2/3, -2/3, -1/12, 1/12]]
+
+    Let us compare this to a differently defined ``x_list``. Pay attention to
+    ``foo[i][k]`` corresponding to the gridpoint defined by ``x_list[k]``.
+
+    >>> foo = finite_diff_weights(1, [-S(2), -S(1), S(0), S(1), S(2)], 0)[1]
+    >>> foo
+    [[0, 0, 0, 0, 0],
+     [-1, 1, 0, 0, 0],
+     [1/2, -2, 3/2, 0, 0],
+     [1/6, -1, 1/2, 1/3, 0],
+     [1/12, -2/3, 0, 2/3, -1/12]]
+    >>> foo[1]  # not the same and of lower accuracy as res[1]!
+    [-1, 1, 0, 0, 0]
+    >>> foo[2]  # classic double backward step approximation
+    [1/2, -2, 3/2, 0, 0]
+    >>> foo[4]  # the same as res[4]
+    [1/12, -2/3, 0, 2/3, -1/12]
+
+    Note that, unless you plan on using approximations based on subsets of
+    ``x_list``, the order of gridpoints does not matter.
+
+    The capability to generate weights at arbitrary points can be
+    used e.g. to minimize Runge's phenomenon by using Chebyshev nodes:
+
+    >>> from sympy import cos, symbols, pi, simplify
+    >>> N, (h, x) = 4, symbols('h x')
+    >>> x_list = [x+h*cos(i*pi/(N)) for i in range(N,-1,-1)] # chebyshev nodes
+    >>> print(x_list)
+    [-h + x, -sqrt(2)*h/2 + x, x, sqrt(2)*h/2 + x, h + x]
+    >>> mycoeffs = finite_diff_weights(1, x_list, 0)[1][4]
+    >>> [simplify(c) for c in  mycoeffs] #doctest: +NORMALIZE_WHITESPACE
+    [(h**3/2 + h**2*x - 3*h*x**2 - 4*x**3)/h**4,
+    (-sqrt(2)*h**3 - 4*h**2*x + 3*sqrt(2)*h*x**2 + 8*x**3)/h**4,
+    (6*h**2*x - 8*x**3)/h**4,
+    (sqrt(2)*h**3 - 4*h**2*x - 3*sqrt(2)*h*x**2 + 8*x**3)/h**4,
+    (-h**3/2 + h**2*x + 3*h*x**2 - 4*x**3)/h**4]
+
+    Notes
+    =====
+
+    If weights for a finite difference approximation of 3rd order
+    derivative is wanted, weights for 0th, 1st and 2nd order are
+    calculated "for free", so are formulae using subsets of ``x_list``.
+    This is something one can take advantage of to save computational cost.
+    Be aware that one should define ``x_list`` from nearest to furthest from
+    ``x0``. If not, subsets of ``x_list`` will yield poorer approximations,
+    which might not grand an order of accuracy of ``len(x_list) - order``.
+
+    See also
+    ========
+
+    sympy.calculus.finite_diff.apply_finite_diff
+
+    References
+    ==========
+
+    .. [1] Generation of Finite Difference Formulas on Arbitrarily Spaced
+            Grids, Bengt Fornberg; Mathematics of computation; 51; 184;
+            (1988); 699-706; doi:10.1090/S0025-5718-1988-0935077-0
+
+    """
+    # The notation below closely corresponds to the one used in the paper.
+    order = S(order)
+    if not order.is_number:
+        raise ValueError("Cannot handle symbolic order.")
+    if order < 0:
+        raise ValueError("Negative derivative order illegal.")
+    if int(order) != order:
+        raise ValueError("Non-integer order illegal")
+    M = order
+    N = len(x_list) - 1
+    delta = [[[0 for nu in range(N+1)] for n in range(N+1)] for
+             m in range(M+1)]
+    delta[0][0][0] = S.One
+    c1 = S.One
+    for n in range(1, N+1):
+        c2 = S.One
+        for nu in range(n):
+            c3 = x_list[n] - x_list[nu]
+            c2 = c2 * c3
+            if n <= M:
+                delta[n][n-1][nu] = 0
+            for m in range(min(n, M)+1):
+                delta[m][n][nu] = (x_list[n]-x0)*delta[m][n-1][nu] -\
+                    m*delta[m-1][n-1][nu]
+                delta[m][n][nu] /= c3
+        for m in range(min(n, M)+1):
+            delta[m][n][n] = c1/c2*(m*delta[m-1][n-1][n-1] -
+                                    (x_list[n-1]-x0)*delta[m][n-1][n-1])
+        c1 = c2
+    return delta
+
+
+def apply_finite_diff(order, x_list, y_list, x0=S.Zero):
+    """
+    Calculates the finite difference approximation of
+    the derivative of requested order at ``x0`` from points
+    provided in ``x_list`` and ``y_list``.
+
+    Parameters
+    ==========
+
+    order: int
+        order of derivative to approximate. 0 corresponds to interpolation.
+    x_list: sequence
+        Sequence of (unique) values for the independent variable.
+    y_list: sequence
+        The function value at corresponding values for the independent
+        variable in x_list.
+    x0: Number or Symbol
+        At what value of the independent variable the derivative should be
+        evaluated. Defaults to 0.
+
+    Returns
+    =======
+
+    sympy.core.add.Add or sympy.core.numbers.Number
+        The finite difference expression approximating the requested
+        derivative order at ``x0``.
+
+    Examples
+    ========
+
+    >>> from sympy import apply_finite_diff
+    >>> cube = lambda arg: (1.0*arg)**3
+    >>> xlist = range(-3,3+1)
+    >>> apply_finite_diff(2, xlist, map(cube, xlist), 2) - 12 # doctest: +SKIP
+    -3.55271367880050e-15
+
+    we see that the example above only contain rounding errors.
+    apply_finite_diff can also be used on more abstract objects:
+
+    >>> from sympy import IndexedBase, Idx
+    >>> x, y = map(IndexedBase, 'xy')
+    >>> i = Idx('i')
+    >>> x_list, y_list = zip(*[(x[i+j], y[i+j]) for j in range(-1,2)])
+    >>> apply_finite_diff(1, x_list, y_list, x[i])
+    ((x[i + 1] - x[i])/(-x[i - 1] + x[i]) - 1)*y[i]/(x[i + 1] - x[i]) -
+    (x[i + 1] - x[i])*y[i - 1]/((x[i + 1] - x[i - 1])*(-x[i - 1] + x[i])) +
+    (-x[i - 1] + x[i])*y[i + 1]/((x[i + 1] - x[i - 1])*(x[i + 1] - x[i]))
+
+    Notes
+    =====
+
+    Order = 0 corresponds to interpolation.
+    Only supply so many points you think makes sense
+    to around x0 when extracting the derivative (the function
+    need to be well behaved within that region). Also beware
+    of Runge's phenomenon.
+
+    See also
+    ========
+
+    sympy.calculus.finite_diff.finite_diff_weights
+
+    References
+    ==========
+
+    Fortran 90 implementation with Python interface for numerics: finitediff_
+
+    .. _finitediff: https://github.com/bjodah/finitediff
+
+    """
+
+    # In the original paper the following holds for the notation:
+    # M = order
+    # N = len(x_list) - 1
+
+    N = len(x_list) - 1
+    if len(x_list) != len(y_list):
+        raise ValueError("x_list and y_list not equal in length.")
+
+    delta = finite_diff_weights(order, x_list, x0)
+
+    derivative = 0
+    for nu in range(len(x_list)):
+        derivative += delta[order][N][nu]*y_list[nu]
+    return derivative
+
+
+def _as_finite_diff(derivative, points=1, x0=None, wrt=None):
+    """
+    Returns an approximation of a derivative of a function in
+    the form of a finite difference formula. The expression is a
+    weighted sum of the function at a number of discrete values of
+    (one of) the independent variable(s).
+
+    Parameters
+    ==========
+
+    derivative: a Derivative instance
+
+    points: sequence or coefficient, optional
+        If sequence: discrete values (length >= order+1) of the
+        independent variable used for generating the finite
+        difference weights.
+        If it is a coefficient, it will be used as the step-size
+        for generating an equidistant sequence of length order+1
+        centered around ``x0``. default: 1 (step-size 1)
+
+    x0: number or Symbol, optional
+        the value of the independent variable (``wrt``) at which the
+        derivative is to be approximated. Default: same as ``wrt``.
+
+    wrt: Symbol, optional
+        "with respect to" the variable for which the (partial)
+        derivative is to be approximated for. If not provided it
+        is required that the Derivative is ordinary. Default: ``None``.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Function, exp, sqrt, Symbol
+    >>> from sympy.calculus.finite_diff import _as_finite_diff
+    >>> x, h = symbols('x h')
+    >>> f = Function('f')
+    >>> _as_finite_diff(f(x).diff(x))
+    -f(x - 1/2) + f(x + 1/2)
+
+    The default step size and number of points are 1 and ``order + 1``
+    respectively. We can change the step size by passing a symbol
+    as a parameter:
+
+    >>> _as_finite_diff(f(x).diff(x), h)
+    -f(-h/2 + x)/h + f(h/2 + x)/h
+
+    We can also specify the discretized values to be used in a sequence:
+
+    >>> _as_finite_diff(f(x).diff(x), [x, x+h, x+2*h])
+    -3*f(x)/(2*h) + 2*f(h + x)/h - f(2*h + x)/(2*h)
+
+    The algorithm is not restricted to use equidistant spacing, nor
+    do we need to make the approximation around ``x0``, but we can get
+    an expression estimating the derivative at an offset:
+
+    >>> e, sq2 = exp(1), sqrt(2)
+    >>> xl = [x-h, x+h, x+e*h]
+    >>> _as_finite_diff(f(x).diff(x, 1), xl, x+h*sq2)
+    2*h*((h + sqrt(2)*h)/(2*h) - (-sqrt(2)*h + h)/(2*h))*f(E*h + x)/((-h + E*h)*(h + E*h)) +
+    (-(-sqrt(2)*h + h)/(2*h) - (-sqrt(2)*h + E*h)/(2*h))*f(-h + x)/(h + E*h) +
+    (-(h + sqrt(2)*h)/(2*h) + (-sqrt(2)*h + E*h)/(2*h))*f(h + x)/(-h + E*h)
+
+    Partial derivatives are also supported:
+
+    >>> y = Symbol('y')
+    >>> d2fdxdy=f(x,y).diff(x,y)
+    >>> _as_finite_diff(d2fdxdy, wrt=x)
+    -Derivative(f(x - 1/2, y), y) + Derivative(f(x + 1/2, y), y)
+
+    See also
+    ========
+
+    sympy.calculus.finite_diff.apply_finite_diff
+    sympy.calculus.finite_diff.finite_diff_weights
+
+    """
+    if derivative.is_Derivative:
+        pass
+    elif derivative.is_Atom:
+        return derivative
+    else:
+        return derivative.fromiter(
+            [_as_finite_diff(ar, points, x0, wrt) for ar
+             in derivative.args], **derivative.assumptions0)
+
+    if wrt is None:
+        old = None
+        for v in derivative.variables:
+            if old is v:
+                continue
+            derivative = _as_finite_diff(derivative, points, x0, v)
+            old = v
+        return derivative
+
+    order = derivative.variables.count(wrt)
+
+    if x0 is None:
+        x0 = wrt
+
+    if not iterable(points):
+        if getattr(points, 'is_Function', False) and wrt in points.args:
+            points = points.subs(wrt, x0)
+        # points is simply the step-size, let's make it a
+        # equidistant sequence centered around x0
+        if order % 2 == 0:
+            # even order => odd number of points, grid point included
+            points = [x0 + points*i for i
+                      in range(-order//2, order//2 + 1)]
+        else:
+            # odd order => even number of points, half-way wrt grid point
+            points = [x0 + points*S(i)/2 for i
+                      in range(-order, order + 1, 2)]
+    others = [wrt, 0]
+    for v in set(derivative.variables):
+        if v == wrt:
+            continue
+        others += [v, derivative.variables.count(v)]
+    if len(points) < order+1:
+        raise ValueError("Too few points for order %d" % order)
+    return apply_finite_diff(order, points, [
+        Derivative(derivative.expr.subs({wrt: x}), *others) for
+        x in points], x0)
+
+
+def differentiate_finite(expr, *symbols,
+                         points=1, x0=None, wrt=None, evaluate=False):
+    r""" Differentiate expr and replace Derivatives with finite differences.
+
+    Parameters
+    ==========
+
+    expr : expression
+    \*symbols : differentiate with respect to symbols
+    points: sequence, coefficient or undefined function, optional
+        see ``Derivative.as_finite_difference``
+    x0: number or Symbol, optional
+        see ``Derivative.as_finite_difference``
+    wrt: Symbol, optional
+        see ``Derivative.as_finite_difference``
+
+    Examples
+    ========
+
+    >>> from sympy import sin, Function, differentiate_finite
+    >>> from sympy.abc import x, y, h
+    >>> f, g = Function('f'), Function('g')
+    >>> differentiate_finite(f(x)*g(x), x, points=[x-h, x+h])
+    -f(-h + x)*g(-h + x)/(2*h) + f(h + x)*g(h + x)/(2*h)
+
+    ``differentiate_finite`` works on any expression, including the expressions
+    with embedded derivatives:
+
+    >>> differentiate_finite(f(x) + sin(x), x, 2)
+    -2*f(x) + f(x - 1) + f(x + 1) - 2*sin(x) + sin(x - 1) + sin(x + 1)
+    >>> differentiate_finite(f(x, y), x, y)
+    f(x - 1/2, y - 1/2) - f(x - 1/2, y + 1/2) - f(x + 1/2, y - 1/2) + f(x + 1/2, y + 1/2)
+    >>> differentiate_finite(f(x)*g(x).diff(x), x)
+    (-g(x) + g(x + 1))*f(x + 1/2) - (g(x) - g(x - 1))*f(x - 1/2)
+
+    To make finite difference with non-constant discretization step use
+    undefined functions:
+
+    >>> dx = Function('dx')
+    >>> differentiate_finite(f(x)*g(x).diff(x), points=dx(x))
+    -(-g(x - dx(x)/2 - dx(x - dx(x)/2)/2)/dx(x - dx(x)/2) +
+    g(x - dx(x)/2 + dx(x - dx(x)/2)/2)/dx(x - dx(x)/2))*f(x - dx(x)/2)/dx(x) +
+    (-g(x + dx(x)/2 - dx(x + dx(x)/2)/2)/dx(x + dx(x)/2) +
+    g(x + dx(x)/2 + dx(x + dx(x)/2)/2)/dx(x + dx(x)/2))*f(x + dx(x)/2)/dx(x)
+
+    """
+    if any(term.is_Derivative for term in list(preorder_traversal(expr))):
+        evaluate = False
+
+    Dexpr = expr.diff(*symbols, evaluate=evaluate)
+    if evaluate:
+        sympy_deprecation_warning("""
+        The evaluate flag to differentiate_finite() is deprecated.
+
+        evaluate=True expands the intermediate derivatives before computing
+        differences, but this usually not what you want, as it does not
+        satisfy the product rule.
+        """,
+            deprecated_since_version="1.5",
+             active_deprecations_target="deprecated-differentiate_finite-evaluate",
+        )
+        return Dexpr.replace(
+            lambda arg: arg.is_Derivative,
+            lambda arg: arg.as_finite_difference(points=points, x0=x0, wrt=wrt))
+    else:
+        DFexpr = Dexpr.as_finite_difference(points=points, x0=x0, wrt=wrt)
+        return DFexpr.replace(
+            lambda arg: isinstance(arg, Subs),
+            lambda arg: arg.expr.as_finite_difference(
+                    points=points, x0=arg.point[0], wrt=arg.variables[0]))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/singularities.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/singularities.py
new file mode 100644
index 0000000000000000000000000000000000000000..5adafc59efaf0bff44707f6b5e3f074be6bc1f32
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/singularities.py
@@ -0,0 +1,406 @@
+"""
+Singularities
+=============
+
+This module implements algorithms for finding singularities for a function
+and identifying types of functions.
+
+The differential calculus methods in this module include methods to identify
+the following function types in the given ``Interval``:
+- Increasing
+- Strictly Increasing
+- Decreasing
+- Strictly Decreasing
+- Monotonic
+
+"""
+
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.trigonometric import sec, csc, cot, tan, cos
+from sympy.functions.elementary.hyperbolic import (
+    sech, csch, coth, tanh, cosh, asech, acsch, atanh, acoth)
+from sympy.utilities.misc import filldedent
+
+
+def singularities(expression, symbol, domain=None):
+    """
+    Find singularities of a given function.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function in which singularities need to be found.
+    symbol : Symbol
+        The symbol over the values of which the singularity in
+        expression in being searched for.
+
+    Returns
+    =======
+
+    Set
+        A set of values for ``symbol`` for which ``expression`` has a
+        singularity. An ``EmptySet`` is returned if ``expression`` has no
+        singularities for any given value of ``Symbol``.
+
+    Raises
+    ======
+
+    NotImplementedError
+        Methods for determining the singularities of this function have
+        not been developed.
+
+    Notes
+    =====
+
+    This function does not find non-isolated singularities
+    nor does it find branch points of the expression.
+
+    Currently supported functions are:
+        - univariate continuous (real or complex) functions
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Mathematical_singularity
+
+    Examples
+    ========
+
+    >>> from sympy import singularities, Symbol, log
+    >>> x = Symbol('x', real=True)
+    >>> y = Symbol('y', real=False)
+    >>> singularities(x**2 + x + 1, x)
+    EmptySet
+    >>> singularities(1/(x + 1), x)
+    {-1}
+    >>> singularities(1/(y**2 + 1), y)
+    {-I, I}
+    >>> singularities(1/(y**3 + 1), y)
+    {-1, 1/2 - sqrt(3)*I/2, 1/2 + sqrt(3)*I/2}
+    >>> singularities(log(x), x)
+    {0}
+
+    """
+    from sympy.solvers.solveset import solveset
+
+    if domain is None:
+        domain = S.Reals if symbol.is_real else S.Complexes
+    try:
+        sings = S.EmptySet
+        e = expression.rewrite([sec, csc, cot, tan], cos)
+        e = e.rewrite([sech, csch, coth, tanh], cosh)
+        for i in e.atoms(Pow):
+            if i.exp.is_infinite:
+                raise NotImplementedError
+            if i.exp.is_negative:
+                # XXX: exponent of varying sign not handled
+                sings += solveset(i.base, symbol, domain)
+        for i in expression.atoms(log, asech, acsch):
+            sings += solveset(i.args[0], symbol, domain)
+        for i in expression.atoms(atanh, acoth):
+            sings += solveset(i.args[0] - 1, symbol, domain)
+            sings += solveset(i.args[0] + 1, symbol, domain)
+        return sings
+    except NotImplementedError:
+        raise NotImplementedError(filldedent('''
+            Methods for determining the singularities
+            of this function have not been developed.'''))
+
+
+###########################################################################
+#                      DIFFERENTIAL CALCULUS METHODS                      #
+###########################################################################
+
+
+def monotonicity_helper(expression, predicate, interval=S.Reals, symbol=None):
+    """
+    Helper function for functions checking function monotonicity.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function which is being checked
+    predicate : function
+        The property being tested for. The function takes in an integer
+        and returns a boolean. The integer input is the derivative and
+        the boolean result should be true if the property is being held,
+        and false otherwise.
+    interval : Set, optional
+        The range of values in which we are testing, defaults to all reals.
+    symbol : Symbol, optional
+        The symbol present in expression which gets varied over the given range.
+
+    It returns a boolean indicating whether the interval in which
+    the function's derivative satisfies given predicate is a superset
+    of the given interval.
+
+    Returns
+    =======
+
+    Boolean
+        True if ``predicate`` is true for all the derivatives when ``symbol``
+        is varied in ``range``, False otherwise.
+
+    """
+    from sympy.solvers.solveset import solveset
+
+    expression = sympify(expression)
+    free = expression.free_symbols
+
+    if symbol is None:
+        if len(free) > 1:
+            raise NotImplementedError(
+                'The function has not yet been implemented'
+                ' for all multivariate expressions.'
+            )
+
+    variable = symbol or (free.pop() if free else Symbol('x'))
+    derivative = expression.diff(variable)
+    predicate_interval = solveset(predicate(derivative), variable, S.Reals)
+    return interval.is_subset(predicate_interval)
+
+
+def is_increasing(expression, interval=S.Reals, symbol=None):
+    """
+    Return whether the function is increasing in the given interval.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function which is being checked.
+    interval : Set, optional
+        The range of values in which we are testing (defaults to set of
+        all real numbers).
+    symbol : Symbol, optional
+        The symbol present in expression which gets varied over the given range.
+
+    Returns
+    =======
+
+    Boolean
+        True if ``expression`` is increasing (either strictly increasing or
+        constant) in the given ``interval``, False otherwise.
+
+    Examples
+    ========
+
+    >>> from sympy import is_increasing
+    >>> from sympy.abc import x, y
+    >>> from sympy import S, Interval, oo
+    >>> is_increasing(x**3 - 3*x**2 + 4*x, S.Reals)
+    True
+    >>> is_increasing(-x**2, Interval(-oo, 0))
+    True
+    >>> is_increasing(-x**2, Interval(0, oo))
+    False
+    >>> is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3))
+    False
+    >>> is_increasing(x**2 + y, Interval(1, 2), x)
+    True
+
+    """
+    return monotonicity_helper(expression, lambda x: x >= 0, interval, symbol)
+
+
+def is_strictly_increasing(expression, interval=S.Reals, symbol=None):
+    """
+    Return whether the function is strictly increasing in the given interval.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function which is being checked.
+    interval : Set, optional
+        The range of values in which we are testing (defaults to set of
+        all real numbers).
+    symbol : Symbol, optional
+        The symbol present in expression which gets varied over the given range.
+
+    Returns
+    =======
+
+    Boolean
+        True if ``expression`` is strictly increasing in the given ``interval``,
+        False otherwise.
+
+    Examples
+    ========
+
+    >>> from sympy import is_strictly_increasing
+    >>> from sympy.abc import x, y
+    >>> from sympy import Interval, oo
+    >>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2))
+    True
+    >>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo))
+    True
+    >>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3))
+    False
+    >>> is_strictly_increasing(-x**2, Interval(0, oo))
+    False
+    >>> is_strictly_increasing(-x**2 + y, Interval(-oo, 0), x)
+    False
+
+    """
+    return monotonicity_helper(expression, lambda x: x > 0, interval, symbol)
+
+
+def is_decreasing(expression, interval=S.Reals, symbol=None):
+    """
+    Return whether the function is decreasing in the given interval.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function which is being checked.
+    interval : Set, optional
+        The range of values in which we are testing (defaults to set of
+        all real numbers).
+    symbol : Symbol, optional
+        The symbol present in expression which gets varied over the given range.
+
+    Returns
+    =======
+
+    Boolean
+        True if ``expression`` is decreasing (either strictly decreasing or
+        constant) in the given ``interval``, False otherwise.
+
+    Examples
+    ========
+
+    >>> from sympy import is_decreasing
+    >>> from sympy.abc import x, y
+    >>> from sympy import S, Interval, oo
+    >>> is_decreasing(1/(x**2 - 3*x), Interval.open(S(3)/2, 3))
+    True
+    >>> is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
+    True
+    >>> is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
+    True
+    >>> is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2))
+    False
+    >>> is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, 1.5))
+    False
+    >>> is_decreasing(-x**2, Interval(-oo, 0))
+    False
+    >>> is_decreasing(-x**2 + y, Interval(-oo, 0), x)
+    False
+
+    """
+    return monotonicity_helper(expression, lambda x: x <= 0, interval, symbol)
+
+
+def is_strictly_decreasing(expression, interval=S.Reals, symbol=None):
+    """
+    Return whether the function is strictly decreasing in the given interval.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function which is being checked.
+    interval : Set, optional
+        The range of values in which we are testing (defaults to set of
+        all real numbers).
+    symbol : Symbol, optional
+        The symbol present in expression which gets varied over the given range.
+
+    Returns
+    =======
+
+    Boolean
+        True if ``expression`` is strictly decreasing in the given ``interval``,
+        False otherwise.
+
+    Examples
+    ========
+
+    >>> from sympy import is_strictly_decreasing
+    >>> from sympy.abc import x, y
+    >>> from sympy import S, Interval, oo
+    >>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
+    True
+    >>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2))
+    False
+    >>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, 1.5))
+    False
+    >>> is_strictly_decreasing(-x**2, Interval(-oo, 0))
+    False
+    >>> is_strictly_decreasing(-x**2 + y, Interval(-oo, 0), x)
+    False
+
+    """
+    return monotonicity_helper(expression, lambda x: x < 0, interval, symbol)
+
+
+def is_monotonic(expression, interval=S.Reals, symbol=None):
+    """
+    Return whether the function is monotonic in the given interval.
+
+    Parameters
+    ==========
+
+    expression : Expr
+        The target function which is being checked.
+    interval : Set, optional
+        The range of values in which we are testing (defaults to set of
+        all real numbers).
+    symbol : Symbol, optional
+        The symbol present in expression which gets varied over the given range.
+
+    Returns
+    =======
+
+    Boolean
+        True if ``expression`` is monotonic in the given ``interval``,
+        False otherwise.
+
+    Raises
+    ======
+
+    NotImplementedError
+        Monotonicity check has not been implemented for the queried function.
+
+    Examples
+    ========
+
+    >>> from sympy import is_monotonic
+    >>> from sympy.abc import x, y
+    >>> from sympy import S, Interval, oo
+    >>> is_monotonic(1/(x**2 - 3*x), Interval.open(S(3)/2, 3))
+    True
+    >>> is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3))
+    True
+    >>> is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo))
+    True
+    >>> is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals)
+    True
+    >>> is_monotonic(-x**2, S.Reals)
+    False
+    >>> is_monotonic(x**2 + y + 1, Interval(1, 2), x)
+    True
+
+    """
+    from sympy.solvers.solveset import solveset
+
+    expression = sympify(expression)
+
+    free = expression.free_symbols
+    if symbol is None and len(free) > 1:
+        raise NotImplementedError(
+            'is_monotonic has not yet been implemented'
+            ' for all multivariate expressions.'
+        )
+
+    variable = symbol or (free.pop() if free else Symbol('x'))
+    turning_points = solveset(expression.diff(variable), variable, interval)
+    return interval.intersection(turning_points) is S.EmptySet
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_accumulationbounds.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_accumulationbounds.py
new file mode 100644
index 0000000000000000000000000000000000000000..bcc47c66327fe21ddca3a6b73ca5914e0441b38e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_accumulationbounds.py
@@ -0,0 +1,336 @@
+from sympy.core.numbers import (E, Rational, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt)
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.calculus.accumulationbounds import AccumBounds
+from sympy.core import Add, Mul, Pow
+from sympy.core.expr import unchanged
+from sympy.testing.pytest import raises, XFAIL
+from sympy.abc import x
+
+a = Symbol('a', real=True)
+B = AccumBounds
+
+
+def test_AccumBounds():
+    assert B(1, 2).args == (1, 2)
+    assert B(1, 2).delta is S.One
+    assert B(1, 2).mid == Rational(3, 2)
+    assert B(1, 3).is_real == True
+
+    assert B(1, 1) is S.One
+
+    assert B(1, 2) + 1 == B(2, 3)
+    assert 1 + B(1, 2) == B(2, 3)
+    assert B(1, 2) + B(2, 3) == B(3, 5)
+
+    assert -B(1, 2) == B(-2, -1)
+
+    assert B(1, 2) - 1 == B(0, 1)
+    assert 1 - B(1, 2) == B(-1, 0)
+    assert B(2, 3) - B(1, 2) == B(0, 2)
+
+    assert x + B(1, 2) == Add(B(1, 2), x)
+    assert a + B(1, 2) == B(1 + a, 2 + a)
+    assert B(1, 2) - x == Add(B(1, 2), -x)
+
+    assert B(-oo, 1) + oo == B(-oo, oo)
+    assert B(1, oo) + oo is oo
+    assert B(1, oo) - oo == B(-oo, oo)
+    assert (-oo - B(-1, oo)) is -oo
+    assert B(-oo, 1) - oo is -oo
+
+    assert B(1, oo) - oo == B(-oo, oo)
+    assert B(-oo, 1) - (-oo) == B(-oo, oo)
+    assert (oo - B(1, oo)) == B(-oo, oo)
+    assert (-oo - B(1, oo)) is -oo
+
+    assert B(1, 2)/2 == B(S.Half, 1)
+    assert 2/B(2, 3) == B(Rational(2, 3), 1)
+    assert 1/B(-1, 1) == B(-oo, oo)
+
+    assert abs(B(1, 2)) == B(1, 2)
+    assert abs(B(-2, -1)) == B(1, 2)
+    assert abs(B(-2, 1)) == B(0, 2)
+    assert abs(B(-1, 2)) == B(0, 2)
+    c = Symbol('c')
+    raises(ValueError, lambda: B(0, c))
+    raises(ValueError, lambda: B(1, -1))
+    r = Symbol('r', real=True)
+    raises(ValueError, lambda: B(r, r - 1))
+
+
+def test_AccumBounds_mul():
+    assert B(1, 2)*2 == B(2, 4)
+    assert 2*B(1, 2) == B(2, 4)
+    assert B(1, 2)*B(2, 3) == B(2, 6)
+    assert B(0, 2)*B(2, oo) == B(0, oo)
+    l, r = B(-oo, oo), B(-a, a)
+    assert l*r == B(-oo, oo)
+    assert r*l == B(-oo, oo)
+    l, r = B(1, oo), B(-3, -2)
+    assert l*r == B(-oo, -2)
+    assert r*l == B(-oo, -2)
+    assert B(1, 2)*0 == 0
+    assert B(1, oo)*0 == B(0, oo)
+    assert B(-oo, 1)*0 == B(-oo, 0)
+    assert B(-oo, oo)*0 == B(-oo, oo)
+
+    assert B(1, 2)*x == Mul(B(1, 2), x, evaluate=False)
+
+    assert B(0, 2)*oo == B(0, oo)
+    assert B(-2, 0)*oo == B(-oo, 0)
+    assert B(0, 2)*(-oo) == B(-oo, 0)
+    assert B(-2, 0)*(-oo) == B(0, oo)
+    assert B(-1, 1)*oo == B(-oo, oo)
+    assert B(-1, 1)*(-oo) == B(-oo, oo)
+    assert B(-oo, oo)*oo == B(-oo, oo)
+
+
+def test_AccumBounds_div():
+    assert B(-1, 3)/B(3, 4) == B(Rational(-1, 3), 1)
+    assert B(-2, 4)/B(-3, 4) == B(-oo, oo)
+    assert B(-3, -2)/B(-4, 0) == B(S.Half, oo)
+
+    # these two tests can have a better answer
+    # after Union of B is improved
+    assert B(-3, -2)/B(-2, 1) == B(-oo, oo)
+    assert B(2, 3)/B(-2, 2) == B(-oo, oo)
+
+    assert B(-3, -2)/B(0, 4) == B(-oo, Rational(-1, 2))
+    assert B(2, 4)/B(-3, 0) == B(-oo, Rational(-2, 3))
+    assert B(2, 4)/B(0, 3) == B(Rational(2, 3), oo)
+
+    assert B(0, 1)/B(0, 1) == B(0, oo)
+    assert B(-1, 0)/B(0, 1) == B(-oo, 0)
+    assert B(-1, 2)/B(-2, 2) == B(-oo, oo)
+
+    assert 1/B(-1, 2) == B(-oo, oo)
+    assert 1/B(0, 2) == B(S.Half, oo)
+    assert (-1)/B(0, 2) == B(-oo, Rational(-1, 2))
+    assert 1/B(-oo, 0) == B(-oo, 0)
+    assert 1/B(-1, 0) == B(-oo, -1)
+    assert (-2)/B(-oo, 0) == B(0, oo)
+    assert 1/B(-oo, -1) == B(-1, 0)
+
+    assert B(1, 2)/a == Mul(B(1, 2), 1/a, evaluate=False)
+
+    assert B(1, 2)/0 == B(1, 2)*zoo
+    assert B(1, oo)/oo == B(0, oo)
+    assert B(1, oo)/(-oo) == B(-oo, 0)
+    assert B(-oo, -1)/oo == B(-oo, 0)
+    assert B(-oo, -1)/(-oo) == B(0, oo)
+    assert B(-oo, oo)/oo == B(-oo, oo)
+    assert B(-oo, oo)/(-oo) == B(-oo, oo)
+    assert B(-1, oo)/oo == B(0, oo)
+    assert B(-1, oo)/(-oo) == B(-oo, 0)
+    assert B(-oo, 1)/oo == B(-oo, 0)
+    assert B(-oo, 1)/(-oo) == B(0, oo)
+
+
+def test_issue_18795():
+    r = Symbol('r', real=True)
+    a = B(-1,1)
+    c = B(7, oo)
+    b = B(-oo, oo)
+    assert c - tan(r) == B(7-tan(r), oo)
+    assert b + tan(r) == B(-oo, oo)
+    assert (a + r)/a == B(-oo, oo)*B(r - 1, r + 1)
+    assert (b + a)/a == B(-oo, oo)
+
+
+def test_AccumBounds_func():
+    assert (x**2 + 2*x + 1).subs(x, B(-1, 1)) == B(-1, 4)
+    assert exp(B(0, 1)) == B(1, E)
+    assert exp(B(-oo, oo)) == B(0, oo)
+    assert log(B(3, 6)) == B(log(3), log(6))
+
+
+@XFAIL
+def test_AccumBounds_powf():
+    nn = Symbol('nn', nonnegative=True)
+    assert B(1 + nn, 2 + nn)**B(1, 2) == B(1 + nn, (2 + nn)**2)
+    i = Symbol('i', integer=True, negative=True)
+    assert B(1, 2)**i == B(2**i, 1)
+
+
+def test_AccumBounds_pow():
+    assert B(0, 2)**2 == B(0, 4)
+    assert B(-1, 1)**2 == B(0, 1)
+    assert B(1, 2)**2 == B(1, 4)
+    assert B(-1, 2)**3 == B(-1, 8)
+    assert B(-1, 1)**0 == 1
+
+    assert B(1, 2)**Rational(5, 2) == B(1, 4*sqrt(2))
+    assert B(0, 2)**S.Half == B(0, sqrt(2))
+
+    neg = Symbol('neg', negative=True)
+    assert unchanged(Pow, B(neg, 1), S.Half)
+    nn = Symbol('nn', nonnegative=True)
+    assert B(nn, nn + 1)**S.Half == B(sqrt(nn), sqrt(nn + 1))
+    assert B(nn, nn + 1)**nn == B(nn**nn, (nn + 1)**nn)
+    assert unchanged(Pow, B(nn, nn + 1), x)
+    i = Symbol('i', integer=True)
+    assert B(1, 2)**i == B(Min(1, 2**i), Max(1, 2**i))
+    i = Symbol('i', integer=True, nonnegative=True)
+    assert B(1, 2)**i == B(1, 2**i)
+    assert B(0, 1)**i == B(0**i, 1)
+
+    assert B(1, 5)**(-2) == B(Rational(1, 25), 1)
+    assert B(-1, 3)**(-2) == B(0, oo)
+    assert B(0, 2)**(-3) == B(Rational(1, 8), oo)
+    assert B(-2, 0)**(-3) == B(-oo, -Rational(1, 8))
+    assert B(0, 2)**(-2) == B(Rational(1, 4), oo)
+    assert B(-1, 2)**(-3) == B(-oo, oo)
+    assert B(-3, -2)**(-3) == B(Rational(-1, 8), Rational(-1, 27))
+    assert B(-3, -2)**(-2) == B(Rational(1, 9), Rational(1, 4))
+    assert B(0, oo)**S.Half == B(0, oo)
+    assert B(-oo, 0)**(-2) == B(0, oo)
+    assert B(-2, 0)**(-2) == B(Rational(1, 4), oo)
+
+    assert B(Rational(1, 3), S.Half)**oo is S.Zero
+    assert B(0, S.Half)**oo is S.Zero
+    assert B(S.Half, 1)**oo == B(0, oo)
+    assert B(0, 1)**oo == B(0, oo)
+    assert B(2, 3)**oo is oo
+    assert B(1, 2)**oo == B(0, oo)
+    assert B(S.Half, 3)**oo == B(0, oo)
+    assert B(Rational(-1, 3), Rational(-1, 4))**oo is S.Zero
+    assert B(-1, Rational(-1, 2))**oo is S.NaN
+    assert B(-3, -2)**oo is zoo
+    assert B(-2, -1)**oo is S.NaN
+    assert B(-2, Rational(-1, 2))**oo is S.NaN
+    assert B(Rational(-1, 2), S.Half)**oo is S.Zero
+    assert B(Rational(-1, 2), 1)**oo == B(0, oo)
+    assert B(Rational(-2, 3), 2)**oo == B(0, oo)
+    assert B(-1, 1)**oo == B(-oo, oo)
+    assert B(-1, S.Half)**oo == B(-oo, oo)
+    assert B(-1, 2)**oo == B(-oo, oo)
+    assert B(-2, S.Half)**oo == B(-oo, oo)
+
+    assert B(1, 2)**x == Pow(B(1, 2), x, evaluate=False)
+
+    assert B(2, 3)**(-oo) is S.Zero
+    assert B(0, 2)**(-oo) == B(0, oo)
+    assert B(-1, 2)**(-oo) == B(-oo, oo)
+
+    assert (tan(x)**sin(2*x)).subs(x, B(0, pi/2)) == \
+        Pow(B(-oo, oo), B(0, 1))
+
+
+def test_AccumBounds_exponent():
+    # base is 0
+    z = 0**B(a, a + S.Half)
+    assert z.subs(a, 0) == B(0, 1)
+    assert z.subs(a, 1) == 0
+    p = z.subs(a, -1)
+    assert p.is_Pow and p.args == (0, B(-1, -S.Half))
+    # base > 0
+    #   when base is 1 the type of bounds does not matter
+    assert 1**B(a, a + 1) == 1
+    #  otherwise we need to know if 0 is in the bounds
+    assert S.Half**B(-2, 2) == B(S(1)/4, 4)
+    assert 2**B(-2, 2) == B(S(1)/4, 4)
+
+    # +eps may introduce +oo
+    # if there is a negative integer exponent
+    assert B(0, 1)**B(S(1)/2, 1) == B(0, 1)
+    assert B(0, 1)**B(0, 1) == B(0, 1)
+
+    # positive bases have positive bounds
+    assert B(2, 3)**B(-3, -2) == B(S(1)/27, S(1)/4)
+    assert B(2, 3)**B(-3, 2) == B(S(1)/27, 9)
+
+    # bounds generating imaginary parts unevaluated
+    assert unchanged(Pow, B(-1, 1), B(1, 2))
+    assert B(0, S(1)/2)**B(1, oo) == B(0, S(1)/2)
+    assert B(0, 1)**B(1, oo) == B(0, oo)
+    assert B(0, 2)**B(1, oo) == B(0, oo)
+    assert B(0, oo)**B(1, oo) == B(0, oo)
+    assert B(S(1)/2, 1)**B(1, oo) == B(0, oo)
+    assert B(S(1)/2, 1)**B(-oo, -1) == B(0, oo)
+    assert B(S(1)/2, 1)**B(-oo, oo) == B(0, oo)
+    assert B(S(1)/2, 2)**B(1, oo) == B(0, oo)
+    assert B(S(1)/2, 2)**B(-oo, -1) == B(0, oo)
+    assert B(S(1)/2, 2)**B(-oo, oo) == B(0, oo)
+    assert B(S(1)/2, oo)**B(1, oo) == B(0, oo)
+    assert B(S(1)/2, oo)**B(-oo, -1) == B(0, oo)
+    assert B(S(1)/2, oo)**B(-oo, oo) == B(0, oo)
+    assert B(1, 2)**B(1, oo) == B(0, oo)
+    assert B(1, 2)**B(-oo, -1) == B(0, oo)
+    assert B(1, 2)**B(-oo, oo) == B(0, oo)
+    assert B(1, oo)**B(1, oo) == B(0, oo)
+    assert B(1, oo)**B(-oo, -1) == B(0, oo)
+    assert B(1, oo)**B(-oo, oo) == B(0, oo)
+    assert B(2, oo)**B(1, oo) == B(2, oo)
+    assert B(2, oo)**B(-oo, -1) == B(0, S(1)/2)
+    assert B(2, oo)**B(-oo, oo) == B(0, oo)
+
+
+def test_comparison_AccumBounds():
+    assert (B(1, 3) < 4) == S.true
+    assert (B(1, 3) < -1) == S.false
+    assert (B(1, 3) < 2).rel_op == '<'
+    assert (B(1, 3) <= 2).rel_op == '<='
+
+    assert (B(1, 3) > 4) == S.false
+    assert (B(1, 3) > -1) == S.true
+    assert (B(1, 3) > 2).rel_op == '>'
+    assert (B(1, 3) >= 2).rel_op == '>='
+
+    assert (B(1, 3) < B(4, 6)) == S.true
+    assert (B(1, 3) < B(2, 4)).rel_op == '<'
+    assert (B(1, 3) < B(-2, 0)) == S.false
+
+    assert (B(1, 3) <= B(4, 6)) == S.true
+    assert (B(1, 3) <= B(-2, 0)) == S.false
+
+    assert (B(1, 3) > B(4, 6)) == S.false
+    assert (B(1, 3) > B(-2, 0)) == S.true
+
+    assert (B(1, 3) >= B(4, 6)) == S.false
+    assert (B(1, 3) >= B(-2, 0)) == S.true
+
+    # issue 13499
+    assert (cos(x) > 0).subs(x, oo) == (B(-1, 1) > 0)
+
+    c = Symbol('c')
+    raises(TypeError, lambda: (B(0, 1) < c))
+    raises(TypeError, lambda: (B(0, 1) <= c))
+    raises(TypeError, lambda: (B(0, 1) > c))
+    raises(TypeError, lambda: (B(0, 1) >= c))
+
+
+def test_contains_AccumBounds():
+    assert (1 in B(1, 2)) == S.true
+    raises(TypeError, lambda: a in B(1, 2))
+    assert 0 in B(-1, 0)
+    raises(TypeError, lambda:
+        (cos(1)**2 + sin(1)**2 - 1) in B(-1, 0))
+    assert (-oo in B(1, oo)) == S.true
+    assert (oo in B(-oo, 0)) == S.true
+
+    # issue 13159
+    assert Mul(0, B(-1, 1)) == Mul(B(-1, 1), 0) == 0
+    import itertools
+    for perm in itertools.permutations([0, B(-1, 1), x]):
+        assert Mul(*perm) == 0
+
+
+def test_intersection_AccumBounds():
+    assert B(0, 3).intersection(B(1, 2)) == B(1, 2)
+    assert B(0, 3).intersection(B(1, 4)) == B(1, 3)
+    assert B(0, 3).intersection(B(-1, 2)) == B(0, 2)
+    assert B(0, 3).intersection(B(-1, 4)) == B(0, 3)
+    assert B(0, 1).intersection(B(2, 3)) == S.EmptySet
+    raises(TypeError, lambda: B(0, 3).intersection(1))
+
+
+def test_union_AccumBounds():
+    assert B(0, 3).union(B(1, 2)) == B(0, 3)
+    assert B(0, 3).union(B(1, 4)) == B(0, 4)
+    assert B(0, 3).union(B(-1, 2)) == B(-1, 3)
+    assert B(0, 3).union(B(-1, 4)) == B(-1, 4)
+    raises(TypeError, lambda: B(0, 3).union(1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_euler.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_euler.py
new file mode 100644
index 0000000000000000000000000000000000000000..56371c8c787d9459d1390e18c306fddde94d2745
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_euler.py
@@ -0,0 +1,74 @@
+from sympy.core.function import (Derivative as D, Function)
+from sympy.core.relational import Eq
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.testing.pytest import raises
+from sympy.calculus.euler import euler_equations as euler
+
+
+def test_euler_interface():
+    x = Function('x')
+    y = Symbol('y')
+    t = Symbol('t')
+    raises(TypeError, lambda: euler())
+    raises(TypeError, lambda: euler(D(x(t), t)*y(t), [x(t), y]))
+    raises(ValueError, lambda: euler(D(x(t), t)*x(y), [x(t), x(y)]))
+    raises(TypeError, lambda: euler(D(x(t), t)**2, x(0)))
+    raises(TypeError, lambda: euler(D(x(t), t)*y(t), [t]))
+    assert euler(D(x(t), t)**2/2, {x(t)}) == [Eq(-D(x(t), t, t), 0)]
+    assert euler(D(x(t), t)**2/2, x(t), {t}) == [Eq(-D(x(t), t, t), 0)]
+
+
+def test_euler_pendulum():
+    x = Function('x')
+    t = Symbol('t')
+    L = D(x(t), t)**2/2 + cos(x(t))
+    assert euler(L, x(t), t) == [Eq(-sin(x(t)) - D(x(t), t, t), 0)]
+
+
+def test_euler_henonheiles():
+    x = Function('x')
+    y = Function('y')
+    t = Symbol('t')
+    L = sum(D(z(t), t)**2/2 - z(t)**2/2 for z in [x, y])
+    L += -x(t)**2*y(t) + y(t)**3/3
+    assert euler(L, [x(t), y(t)], t) == [Eq(-2*x(t)*y(t) - x(t) -
+                                            D(x(t), t, t), 0),
+                                         Eq(-x(t)**2 + y(t)**2 -
+                                            y(t) - D(y(t), t, t), 0)]
+
+
+def test_euler_sineg():
+    psi = Function('psi')
+    t = Symbol('t')
+    x = Symbol('x')
+    L = D(psi(t, x), t)**2/2 - D(psi(t, x), x)**2/2 + cos(psi(t, x))
+    assert euler(L, psi(t, x), [t, x]) == [Eq(-sin(psi(t, x)) -
+                                              D(psi(t, x), t, t) +
+                                              D(psi(t, x), x, x), 0)]
+
+
+def test_euler_high_order():
+    # an example from hep-th/0309038
+    m = Symbol('m')
+    k = Symbol('k')
+    x = Function('x')
+    y = Function('y')
+    t = Symbol('t')
+    L = (m*D(x(t), t)**2/2 + m*D(y(t), t)**2/2 -
+         k*D(x(t), t)*D(y(t), t, t) + k*D(y(t), t)*D(x(t), t, t))
+    assert euler(L, [x(t), y(t)]) == [Eq(2*k*D(y(t), t, t, t) -
+                                         m*D(x(t), t, t), 0),
+                                      Eq(-2*k*D(x(t), t, t, t) -
+                                         m*D(y(t), t, t), 0)]
+
+    w = Symbol('w')
+    L = D(x(t, w), t, w)**2/2
+    assert euler(L) == [Eq(D(x(t, w), t, t, w, w), 0)]
+
+def test_issue_18653():
+    x, y, z = symbols("x y z")
+    f, g, h = symbols("f g h", cls=Function, args=(x, y))
+    f, g, h = f(), g(), h()
+    expr2 = f.diff(x)*h.diff(z)
+    assert euler(expr2, (f,), (x, y)) == []
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_finite_diff.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_finite_diff.py
new file mode 100644
index 0000000000000000000000000000000000000000..e9ecfbdd61b15f516c54bd6d716ba1f264ee2ca0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_finite_diff.py
@@ -0,0 +1,164 @@
+from itertools import product
+
+from sympy.core.function import (Function, diff)
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.calculus.finite_diff import (
+    apply_finite_diff, differentiate_finite, finite_diff_weights,
+    _as_finite_diff
+)
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+def test_apply_finite_diff():
+    x, h = symbols('x h')
+    f = Function('f')
+    assert (apply_finite_diff(1, [x-h, x+h], [f(x-h), f(x+h)], x) -
+            (f(x+h)-f(x-h))/(2*h)).simplify() == 0
+
+    assert (apply_finite_diff(1, [5, 6, 7], [f(5), f(6), f(7)], 5) -
+            (Rational(-3, 2)*f(5) + 2*f(6) - S.Half*f(7))).simplify() == 0
+    raises(ValueError, lambda: apply_finite_diff(1, [x, h], [f(x)]))
+
+
+def test_finite_diff_weights():
+
+    d = finite_diff_weights(1, [5, 6, 7], 5)
+    assert d[1][2] == [Rational(-3, 2), 2, Rational(-1, 2)]
+
+    # Table 1, p. 702 in doi:10.1090/S0025-5718-1988-0935077-0
+    # --------------------------------------------------------
+    xl = [0, 1, -1, 2, -2, 3, -3, 4, -4]
+
+    # d holds all coefficients
+    d = finite_diff_weights(4, xl, S.Zero)
+
+    # Zeroeth derivative
+    for i in range(5):
+        assert d[0][i] == [S.One] + [S.Zero]*8
+
+    # First derivative
+    assert d[1][0] == [S.Zero]*9
+    assert d[1][2] == [S.Zero, S.Half, Rational(-1, 2)] + [S.Zero]*6
+    assert d[1][4] == [S.Zero, Rational(2, 3), Rational(-2, 3), Rational(-1, 12), Rational(1, 12)] + [S.Zero]*4
+    assert d[1][6] == [S.Zero, Rational(3, 4), Rational(-3, 4), Rational(-3, 20), Rational(3, 20),
+                       Rational(1, 60), Rational(-1, 60)] + [S.Zero]*2
+    assert d[1][8] == [S.Zero, Rational(4, 5), Rational(-4, 5), Rational(-1, 5), Rational(1, 5),
+                       Rational(4, 105), Rational(-4, 105), Rational(-1, 280), Rational(1, 280)]
+
+    # Second derivative
+    for i in range(2):
+        assert d[2][i] == [S.Zero]*9
+    assert d[2][2] == [-S(2), S.One, S.One] + [S.Zero]*6
+    assert d[2][4] == [Rational(-5, 2), Rational(4, 3), Rational(4, 3), Rational(-1, 12), Rational(-1, 12)] + [S.Zero]*4
+    assert d[2][6] == [Rational(-49, 18), Rational(3, 2), Rational(3, 2), Rational(-3, 20), Rational(-3, 20),
+                       Rational(1, 90), Rational(1, 90)] + [S.Zero]*2
+    assert d[2][8] == [Rational(-205, 72), Rational(8, 5), Rational(8, 5), Rational(-1, 5), Rational(-1, 5),
+                       Rational(8, 315), Rational(8, 315), Rational(-1, 560), Rational(-1, 560)]
+
+    # Third derivative
+    for i in range(3):
+        assert d[3][i] == [S.Zero]*9
+    assert d[3][4] == [S.Zero, -S.One, S.One, S.Half, Rational(-1, 2)] + [S.Zero]*4
+    assert d[3][6] == [S.Zero, Rational(-13, 8), Rational(13, 8), S.One, -S.One,
+                       Rational(-1, 8), Rational(1, 8)] + [S.Zero]*2
+    assert d[3][8] == [S.Zero, Rational(-61, 30), Rational(61, 30), Rational(169, 120), Rational(-169, 120),
+                       Rational(-3, 10), Rational(3, 10), Rational(7, 240), Rational(-7, 240)]
+
+    # Fourth derivative
+    for i in range(4):
+        assert d[4][i] == [S.Zero]*9
+    assert d[4][4] == [S(6), -S(4), -S(4), S.One, S.One] + [S.Zero]*4
+    assert d[4][6] == [Rational(28, 3), Rational(-13, 2), Rational(-13, 2), S(2), S(2),
+                       Rational(-1, 6), Rational(-1, 6)] + [S.Zero]*2
+    assert d[4][8] == [Rational(91, 8), Rational(-122, 15), Rational(-122, 15), Rational(169, 60), Rational(169, 60),
+                       Rational(-2, 5), Rational(-2, 5), Rational(7, 240), Rational(7, 240)]
+
+    # Table 2, p. 703 in doi:10.1090/S0025-5718-1988-0935077-0
+    # --------------------------------------------------------
+    xl = [[j/S(2) for j in list(range(-i*2+1, 0, 2))+list(range(1, i*2+1, 2))]
+          for i in range(1, 5)]
+
+    # d holds all coefficients
+    d = [finite_diff_weights({0: 1, 1: 2, 2: 4, 3: 4}[i], xl[i], 0) for
+         i in range(4)]
+
+    # Zeroth derivative
+    assert d[0][0][1] == [S.Half, S.Half]
+    assert d[1][0][3] == [Rational(-1, 16), Rational(9, 16), Rational(9, 16), Rational(-1, 16)]
+    assert d[2][0][5] == [Rational(3, 256), Rational(-25, 256), Rational(75, 128), Rational(75, 128),
+                          Rational(-25, 256), Rational(3, 256)]
+    assert d[3][0][7] == [Rational(-5, 2048), Rational(49, 2048), Rational(-245, 2048), Rational(1225, 2048),
+                          Rational(1225, 2048), Rational(-245, 2048), Rational(49, 2048), Rational(-5, 2048)]
+
+    # First derivative
+    assert d[0][1][1] == [-S.One, S.One]
+    assert d[1][1][3] == [Rational(1, 24), Rational(-9, 8), Rational(9, 8), Rational(-1, 24)]
+    assert d[2][1][5] == [Rational(-3, 640), Rational(25, 384), Rational(-75, 64),
+                          Rational(75, 64), Rational(-25, 384), Rational(3, 640)]
+    assert d[3][1][7] == [Rational(5, 7168), Rational(-49, 5120),
+                          Rational(245, 3072), Rational(-1225, 1024),
+                          Rational(1225, 1024), Rational(-245, 3072),
+                          Rational(49, 5120), Rational(-5, 7168)]
+
+    # Reasonably the rest of the table is also correct... (testing of that
+    # deemed excessive at the moment)
+    raises(ValueError, lambda: finite_diff_weights(-1, [1, 2]))
+    raises(ValueError, lambda: finite_diff_weights(1.2, [1, 2]))
+    x = symbols('x')
+    raises(ValueError, lambda: finite_diff_weights(x, [1, 2]))
+
+
+def test_as_finite_diff():
+    x = symbols('x')
+    f = Function('f')
+    dx = Function('dx')
+
+    _as_finite_diff(f(x).diff(x), [x-2, x-1, x, x+1, x+2])
+
+    # Use of undefined functions in ``points``
+    df_true = -f(x+dx(x)/2-dx(x+dx(x)/2)/2) / dx(x+dx(x)/2) \
+              + f(x+dx(x)/2+dx(x+dx(x)/2)/2) / dx(x+dx(x)/2)
+    df_test = diff(f(x), x).as_finite_difference(points=dx(x), x0=x+dx(x)/2)
+    assert (df_test - df_true).simplify() == 0
+
+
+def test_differentiate_finite():
+    x, y, h = symbols('x y h')
+    f = Function('f')
+    with warns_deprecated_sympy():
+        res0 = differentiate_finite(f(x, y) + exp(42), x, y, evaluate=True)
+    xm, xp, ym, yp = [v + sign*S.Half for v, sign in product([x, y], [-1, 1])]
+    ref0 = f(xm, ym) + f(xp, yp) - f(xm, yp) - f(xp, ym)
+    assert (res0 - ref0).simplify() == 0
+
+    g = Function('g')
+    with warns_deprecated_sympy():
+        res1 = differentiate_finite(f(x)*g(x) + 42, x, evaluate=True)
+    ref1 = (-f(x - S.Half) + f(x + S.Half))*g(x) + \
+           (-g(x - S.Half) + g(x + S.Half))*f(x)
+    assert (res1 - ref1).simplify() == 0
+
+    res2 = differentiate_finite(f(x) + x**3 + 42, x, points=[x-1, x+1])
+    ref2 = (f(x + 1) + (x + 1)**3 - f(x - 1) - (x - 1)**3)/2
+    assert (res2 - ref2).simplify() == 0
+    raises(TypeError, lambda: differentiate_finite(f(x)*g(x), x,
+                                                   pints=[x-1, x+1]))
+
+    res3 = differentiate_finite(f(x)*g(x).diff(x), x)
+    ref3 = (-g(x) + g(x + 1))*f(x + S.Half) - (g(x) - g(x - 1))*f(x - S.Half)
+    assert res3 == ref3
+
+    res4 = differentiate_finite(f(x)*g(x).diff(x).diff(x), x)
+    ref4 = -((g(x - Rational(3, 2)) - 2*g(x - S.Half) + g(x + S.Half))*f(x - S.Half)) \
+           + (g(x - S.Half) - 2*g(x + S.Half) + g(x + Rational(3, 2)))*f(x + S.Half)
+    assert res4 == ref4
+
+    res5_expr = f(x).diff(x)*g(x).diff(x)
+    res5 = differentiate_finite(res5_expr, points=[x-h, x, x+h])
+    ref5 = (-2*f(x)/h + f(-h + x)/(2*h) + 3*f(h + x)/(2*h))*(-2*g(x)/h + g(-h + x)/(2*h) \
+           + 3*g(h + x)/(2*h))/(2*h) - (2*f(x)/h - 3*f(-h + x)/(2*h) - \
+           f(h + x)/(2*h))*(2*g(x)/h - 3*g(-h + x)/(2*h) - g(h + x)/(2*h))/(2*h)
+    assert res5 == ref5
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_singularities.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_singularities.py
new file mode 100644
index 0000000000000000000000000000000000000000..19a042332326658021ce12a38f4e058f55903869
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_singularities.py
@@ -0,0 +1,122 @@
+from sympy.core.numbers import (I, Rational, pi, oo)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol, Dummy
+from sympy.core.function import Lambda
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.trigonometric import sec, csc
+from sympy.functions.elementary.hyperbolic import (coth, sech,
+                                                   atanh, asech, acoth, acsch)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.calculus.singularities import (
+    singularities,
+    is_increasing,
+    is_strictly_increasing,
+    is_decreasing,
+    is_strictly_decreasing,
+    is_monotonic
+)
+from sympy.sets import Interval, FiniteSet, Union, ImageSet
+from sympy.testing.pytest import raises
+from sympy.abc import x, y
+
+
+def test_singularities():
+    x = Symbol('x')
+    assert singularities(x**2, x) == S.EmptySet
+    assert singularities(x/(x**2 + 3*x + 2), x) == FiniteSet(-2, -1)
+    assert singularities(1/(x**2 + 1), x) == FiniteSet(I, -I)
+    assert singularities(x/(x**3 + 1), x) == \
+        FiniteSet(-1, (1 - sqrt(3) * I) / 2, (1 + sqrt(3) * I) / 2)
+    assert singularities(1/(y**2 + 2*I*y + 1), y) == \
+        FiniteSet(-I + sqrt(2)*I, -I - sqrt(2)*I)
+    _n = Dummy('n')
+    assert singularities(sech(x), x).dummy_eq(Union(
+        ImageSet(Lambda(_n, 2*_n*I*pi + I*pi/2), S.Integers),
+        ImageSet(Lambda(_n, 2*_n*I*pi + 3*I*pi/2), S.Integers)))
+    assert singularities(coth(x), x).dummy_eq(Union(
+        ImageSet(Lambda(_n, 2*_n*I*pi + I*pi), S.Integers),
+        ImageSet(Lambda(_n, 2*_n*I*pi), S.Integers)))
+    assert singularities(atanh(x), x) == FiniteSet(-1, 1)
+    assert singularities(acoth(x), x) == FiniteSet(-1, 1)
+    assert singularities(asech(x), x) == FiniteSet(0)
+    assert singularities(acsch(x), x) == FiniteSet(0)
+
+    x = Symbol('x', real=True)
+    assert singularities(1/(x**2 + 1), x) == S.EmptySet
+    assert singularities(exp(1/x), x, S.Reals) == FiniteSet(0)
+    assert singularities(exp(1/x), x, Interval(1, 2)) == S.EmptySet
+    assert singularities(log((x - 2)**2), x, Interval(1, 3)) == FiniteSet(2)
+    raises(NotImplementedError, lambda: singularities(x**-oo, x))
+    assert singularities(sec(x), x, Interval(0, 3*pi)) == FiniteSet(
+        pi/2, 3*pi/2, 5*pi/2)
+    assert singularities(csc(x), x, Interval(0, 3*pi)) == FiniteSet(
+        0, pi, 2*pi, 3*pi)
+
+
+def test_is_increasing():
+    """Test whether is_increasing returns correct value."""
+    a = Symbol('a', negative=True)
+
+    assert is_increasing(x**3 - 3*x**2 + 4*x, S.Reals)
+    assert is_increasing(-x**2, Interval(-oo, 0))
+    assert not is_increasing(-x**2, Interval(0, oo))
+    assert not is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3))
+    assert is_increasing(x**2 + y, Interval(1, oo), x)
+    assert is_increasing(-x**2*a, Interval(1, oo), x)
+    assert is_increasing(1)
+
+    assert is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3)) is False
+
+
+def test_is_strictly_increasing():
+    """Test whether is_strictly_increasing returns correct value."""
+    assert is_strictly_increasing(
+        4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2))
+    assert is_strictly_increasing(
+        4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo))
+    assert not is_strictly_increasing(
+        4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3))
+    assert not is_strictly_increasing(-x**2, Interval(0, oo))
+    assert not is_strictly_decreasing(1)
+
+    assert is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3)) is False
+
+
+def test_is_decreasing():
+    """Test whether is_decreasing returns correct value."""
+    b = Symbol('b', positive=True)
+
+    assert is_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
+    assert is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
+    assert is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
+    assert not is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2)))
+    assert not is_decreasing(-x**2, Interval(-oo, 0))
+    assert not is_decreasing(-x**2*b, Interval(-oo, 0), x)
+
+
+def test_is_strictly_decreasing():
+    """Test whether is_strictly_decreasing returns correct value."""
+    assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
+    assert not is_strictly_decreasing(
+        1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2)))
+    assert not is_strictly_decreasing(-x**2, Interval(-oo, 0))
+    assert not is_strictly_decreasing(1)
+    assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
+    assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
+
+
+def test_is_monotonic():
+    """Test whether is_monotonic returns correct value."""
+    assert is_monotonic(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
+    assert is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3))
+    assert is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo))
+    assert is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals)
+    assert not is_monotonic(-x**2, S.Reals)
+    assert is_monotonic(x**2 + y + 1, Interval(1, 2), x)
+    raises(NotImplementedError, lambda: is_monotonic(x**2 + y + 1))
+
+
+def test_issue_23401():
+    x = Symbol('x')
+    expr = (x + 1)/(-1.0e-3*x**2 + 0.1*x + 0.1)
+    assert is_increasing(expr, Interval(1,2), x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..c18b7a79fd54fdb2638cc746d43ab26753fc72a9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/tests/test_util.py
@@ -0,0 +1,392 @@
+from sympy.core.function import Lambda
+from sympy.core.numbers import (E, I, Rational, oo, pi)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.elementary.complexes import (Abs, re)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.integers import frac
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (
+    cos, cot, csc, sec, sin, tan, asin, acos, atan, acot, asec, acsc)
+from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth,
+    sech, csch, asinh, acosh, atanh, acoth, asech, acsch)
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.error_functions import expint
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.simplify.simplify import simplify
+from sympy.calculus.util import (function_range, continuous_domain, not_empty_in,
+                                 periodicity, lcim, is_convex,
+                                 stationary_points, minimum, maximum)
+from sympy.sets.sets import (Interval, FiniteSet, Complement, Union)
+from sympy.sets.fancysets import ImageSet
+from sympy.sets.conditionset import ConditionSet
+from sympy.testing.pytest import XFAIL, raises, _both_exp_pow, slow
+from sympy.abc import x, y
+
+a = Symbol('a', real=True)
+
+def test_function_range():
+    assert function_range(sin(x), x, Interval(-pi/2, pi/2)
+        ) == Interval(-1, 1)
+    assert function_range(sin(x), x, Interval(0, pi)
+        ) == Interval(0, 1)
+    assert function_range(tan(x), x, Interval(0, pi)
+        ) == Interval(-oo, oo)
+    assert function_range(tan(x), x, Interval(pi/2, pi)
+        ) == Interval(-oo, 0)
+    assert function_range((x + 3)/(x - 2), x, Interval(-5, 5)
+        ) == Union(Interval(-oo, Rational(2, 7)), Interval(Rational(8, 3), oo))
+    assert function_range(1/(x**2), x, Interval(-1, 1)
+        ) == Interval(1, oo)
+    assert function_range(exp(x), x, Interval(-1, 1)
+        ) == Interval(exp(-1), exp(1))
+    assert function_range(log(x) - x, x, S.Reals
+        ) == Interval(-oo, -1)
+    assert function_range(sqrt(3*x - 1), x, Interval(0, 2)
+        ) == Interval(0, sqrt(5))
+    assert function_range(x*(x - 1) - (x**2 - x), x, S.Reals
+        ) == FiniteSet(0)
+    assert function_range(x*(x - 1) - (x**2 - x) + y, x, S.Reals
+        ) == FiniteSet(y)
+    assert function_range(sin(x), x, Union(Interval(-5, -3), FiniteSet(4))
+        ) == Union(Interval(-sin(3), 1), FiniteSet(sin(4)))
+    assert function_range(cos(x), x, Interval(-oo, -4)
+        ) == Interval(-1, 1)
+    assert function_range(cos(x), x, S.EmptySet) == S.EmptySet
+    assert function_range(x/sqrt(x**2+1), x, S.Reals) == Interval.open(-1,1)
+    raises(NotImplementedError, lambda : function_range(
+        exp(x)*(sin(x) - cos(x))/2 - x, x, S.Reals))
+    raises(NotImplementedError, lambda : function_range(
+        sin(x) + x, x, S.Reals)) # issue 13273
+    raises(NotImplementedError, lambda : function_range(
+        log(x), x, S.Integers))
+    raises(NotImplementedError, lambda : function_range(
+        sin(x)/2, x, S.Naturals))
+
+
+@slow
+def test_function_range1():
+    assert function_range(tan(x)**2 + tan(3*x)**2 + 1, x, S.Reals) == Interval(1,oo)
+
+
+def test_continuous_domain():
+    assert continuous_domain(sin(x), x, Interval(0, 2*pi)) == Interval(0, 2*pi)
+    assert continuous_domain(tan(x), x, Interval(0, 2*pi)) == \
+        Union(Interval(0, pi/2, False, True), Interval(pi/2, pi*Rational(3, 2), True, True),
+              Interval(pi*Rational(3, 2), 2*pi, True, False))
+    assert continuous_domain(cot(x), x, Interval(0, 2*pi)) == Union(
+        Interval.open(0, pi), Interval.open(pi, 2*pi))
+    assert continuous_domain((x - 1)/((x - 1)**2), x, S.Reals) == \
+        Union(Interval(-oo, 1, True, True), Interval(1, oo, True, True))
+    assert continuous_domain(log(x) + log(4*x - 1), x, S.Reals) == \
+        Interval(Rational(1, 4), oo, True, True)
+    assert continuous_domain(1/sqrt(x - 3), x, S.Reals) == Interval(3, oo, True, True)
+    assert continuous_domain(1/x - 2, x, S.Reals) == \
+        Union(Interval.open(-oo, 0), Interval.open(0, oo))
+    assert continuous_domain(1/(x**2 - 4) + 2, x, S.Reals) == \
+        Union(Interval.open(-oo, -2), Interval.open(-2, 2), Interval.open(2, oo))
+    assert continuous_domain((x+1)**pi, x, S.Reals) == Interval(-1, oo)
+    assert continuous_domain((x+1)**(pi/2), x, S.Reals) == Interval(-1, oo)
+    assert continuous_domain(x**x, x, S.Reals) == Interval(0, oo)
+    assert continuous_domain((x+1)**log(x**2), x, S.Reals) == Union(
+        Interval.Ropen(-1, 0), Interval.open(0, oo))
+    domain = continuous_domain(log(tan(x)**2 + 1), x, S.Reals)
+    assert not domain.contains(3*pi/2)
+    assert domain.contains(5)
+    d = Symbol('d', even=True, zero=False)
+    assert continuous_domain(x**(1/d), x, S.Reals) == Interval(0, oo)
+    n = Dummy('n')
+    assert continuous_domain(1/sin(x), x, S.Reals).dummy_eq(Complement(
+        S.Reals, Union(ImageSet(Lambda(n, 2*n*pi + pi), S.Integers),
+                       ImageSet(Lambda(n, 2*n*pi), S.Integers))))
+    assert continuous_domain(sin(x) + cos(x), x, S.Reals) == S.Reals
+    assert continuous_domain(asin(x), x, S.Reals) == Interval(-1, 1) # issue #21786
+    assert continuous_domain(1/acos(log(x)), x, S.Reals) == Interval.Ropen(exp(-1), E)
+    assert continuous_domain(sinh(x)+cosh(x), x, S.Reals) == S.Reals
+    assert continuous_domain(tanh(x)+sech(x), x, S.Reals) == S.Reals
+    assert continuous_domain(atan(x)+asinh(x), x, S.Reals) == S.Reals
+    assert continuous_domain(acosh(x), x, S.Reals) == Interval(1, oo)
+    assert continuous_domain(atanh(x), x, S.Reals) == Interval.open(-1, 1)
+    assert continuous_domain(atanh(x)+acosh(x), x, S.Reals) == S.EmptySet
+    assert continuous_domain(asech(x), x, S.Reals) == Interval.Lopen(0, 1)
+    assert continuous_domain(acoth(x), x, S.Reals) == Union(
+        Interval.open(-oo, -1), Interval.open(1, oo))
+    assert continuous_domain(asec(x), x, S.Reals) == Union(
+        Interval(-oo, -1), Interval(1, oo))
+    assert continuous_domain(acsc(x), x, S.Reals) == Union(
+        Interval(-oo, -1), Interval(1, oo))
+    for f in (coth, acsch, csch):
+        assert continuous_domain(f(x), x, S.Reals) == Union(
+            Interval.open(-oo, 0), Interval.open(0, oo))
+    assert continuous_domain(acot(x), x, S.Reals).contains(0) == False
+    assert continuous_domain(1/(exp(x) - x), x, S.Reals) == Complement(
+        S.Reals, ConditionSet(x, Eq(-x + exp(x), 0), S.Reals))
+    assert continuous_domain(frac(x**2), x, Interval(-2,-1)) == Union(
+        Interval.open(-2, -sqrt(3)), Interval.open(-sqrt(2), -1),
+        Interval.open(-sqrt(3), -sqrt(2)))
+    assert continuous_domain(frac(x), x, S.Reals) == Complement(
+        S.Reals, S.Integers)
+    raises(NotImplementedError, lambda : continuous_domain(
+        1/(x**2+1), x, S.Complexes))
+    raises(NotImplementedError, lambda : continuous_domain(
+        gamma(x), x, Interval(-5,0)))
+    assert continuous_domain(x + gamma(pi), x, S.Reals) == S.Reals
+
+
+@XFAIL
+def test_continuous_domain_acot():
+    acot_cont = Piecewise((pi+acot(x), x<0), (acot(x), True))
+    assert continuous_domain(acot_cont, x, S.Reals) == S.Reals
+
+@XFAIL
+def test_continuous_domain_gamma():
+    assert continuous_domain(gamma(x), x, S.Reals).contains(-1) == False
+
+@XFAIL
+def test_continuous_domain_neg_power():
+    assert continuous_domain((x-2)**(1-x), x, S.Reals) == Interval.open(2, oo)
+
+
+def test_not_empty_in():
+    assert not_empty_in(FiniteSet(x, 2*x).intersect(Interval(1, 2, True, False)), x) == \
+        Interval(S.Half, 2, True, False)
+    assert not_empty_in(FiniteSet(x, x**2).intersect(Interval(1, 2)), x) == \
+        Union(Interval(-sqrt(2), -1), Interval(1, 2))
+    assert not_empty_in(FiniteSet(x**2 + x, x).intersect(Interval(2, 4)), x) == \
+        Union(Interval(-sqrt(17)/2 - S.Half, -2),
+              Interval(1, Rational(-1, 2) + sqrt(17)/2), Interval(2, 4))
+    assert not_empty_in(FiniteSet(x/(x - 1)).intersect(S.Reals), x) == \
+        Complement(S.Reals, FiniteSet(1))
+    assert not_empty_in(FiniteSet(a/(a - 1)).intersect(S.Reals), a) == \
+        Complement(S.Reals, FiniteSet(1))
+    assert not_empty_in(FiniteSet((x**2 - 3*x + 2)/(x - 1)).intersect(S.Reals), x) == \
+        Complement(S.Reals, FiniteSet(1))
+    assert not_empty_in(FiniteSet(3, 4, x/(x - 1)).intersect(Interval(2, 3)), x) == \
+        Interval(-oo, oo)
+    assert not_empty_in(FiniteSet(4, x/(x - 1)).intersect(Interval(2, 3)), x) == \
+        Interval(S(3)/2, 2)
+    assert not_empty_in(FiniteSet(x/(x**2 - 1)).intersect(S.Reals), x) == \
+        Complement(S.Reals, FiniteSet(-1, 1))
+    assert not_empty_in(FiniteSet(x, x**2).intersect(Union(Interval(1, 3, True, True),
+                                                           Interval(4, 5))), x) == \
+        Union(Interval(-sqrt(5), -2), Interval(-sqrt(3), -1, True, True),
+              Interval(1, 3, True, True), Interval(4, 5))
+    assert not_empty_in(FiniteSet(1).intersect(Interval(3, 4)), x) == S.EmptySet
+    assert not_empty_in(FiniteSet(x**2/(x + 2)).intersect(Interval(1, oo)), x) == \
+        Union(Interval(-2, -1, True, False), Interval(2, oo))
+    raises(ValueError, lambda: not_empty_in(x))
+    raises(ValueError, lambda: not_empty_in(Interval(0, 1), x))
+    raises(NotImplementedError,
+           lambda: not_empty_in(FiniteSet(x).intersect(S.Reals), x, a))
+
+
+@_both_exp_pow
+def test_periodicity():
+    assert periodicity(sin(2*x), x) == pi
+    assert periodicity((-2)*tan(4*x), x) == pi/4
+    assert periodicity(sin(x)**2, x) == 2*pi
+    assert periodicity(3**tan(3*x), x) == pi/3
+    assert periodicity(tan(x)*cos(x), x) == 2*pi
+    assert periodicity(sin(x)**(tan(x)), x) == 2*pi
+    assert periodicity(tan(x)*sec(x), x) == 2*pi
+    assert periodicity(sin(2*x)*cos(2*x) - y, x) == pi/2
+    assert periodicity(tan(x) + cot(x), x) == pi
+    assert periodicity(sin(x) - cos(2*x), x) == 2*pi
+    assert periodicity(sin(x) - 1, x) == 2*pi
+    assert periodicity(sin(4*x) + sin(x)*cos(x), x) == pi
+    assert periodicity(exp(sin(x)), x) == 2*pi
+    assert periodicity(log(cot(2*x)) - sin(cos(2*x)), x) == pi
+    assert periodicity(sin(2*x)*exp(tan(x) - csc(2*x)), x) == pi
+    assert periodicity(cos(sec(x) - csc(2*x)), x) == 2*pi
+    assert periodicity(tan(sin(2*x)), x) == pi
+    assert periodicity(2*tan(x)**2, x) == pi
+    assert periodicity(sin(x%4), x) == 4
+    assert periodicity(sin(x)%4, x) == 2*pi
+    assert periodicity(tan((3*x-2)%4), x) == Rational(4, 3)
+    assert periodicity((sqrt(2)*(x+1)+x) % 3, x) == 3 / (sqrt(2)+1)
+    assert periodicity((x**2+1) % x, x) is None
+    assert periodicity(sin(re(x)), x) == 2*pi
+    assert periodicity(sin(x)**2 + cos(x)**2, x) is S.Zero
+    assert periodicity(tan(x), y) is S.Zero
+    assert periodicity(sin(x) + I*cos(x), x) == 2*pi
+    assert periodicity(x - sin(2*y), y) == pi
+
+    assert periodicity(exp(x), x) is None
+    assert periodicity(exp(I*x), x) == 2*pi
+    assert periodicity(exp(I*a), a) == 2*pi
+    assert periodicity(exp(a), a) is None
+    assert periodicity(exp(log(sin(a) + I*cos(2*a)), evaluate=False), a) == 2*pi
+    assert periodicity(exp(log(sin(2*a) + I*cos(a)), evaluate=False), a) == 2*pi
+    assert periodicity(exp(sin(a)), a) == 2*pi
+    assert periodicity(exp(2*I*a), a) == pi
+    assert periodicity(exp(a + I*sin(a)), a) is None
+    assert periodicity(exp(cos(a/2) + sin(a)), a) == 4*pi
+    assert periodicity(log(x), x) is None
+    assert periodicity(exp(x)**sin(x), x) is None
+    assert periodicity(sin(x)**y, y) is None
+
+    assert periodicity(Abs(sin(Abs(sin(x)))), x) == pi
+    assert all(periodicity(Abs(f(x)), x) == pi for f in (
+        cos, sin, sec, csc, tan, cot))
+    assert periodicity(Abs(sin(tan(x))), x) == pi
+    assert periodicity(Abs(sin(sin(x) + tan(x))), x) == 2*pi
+    assert periodicity(sin(x) > S.Half, x) == 2*pi
+
+    assert periodicity(x > 2, x) is None
+    assert periodicity(x**3 - x**2 + 1, x) is None
+    assert periodicity(Abs(x), x) is None
+    assert periodicity(Abs(x**2 - 1), x) is None
+
+    assert periodicity((x**2 + 4)%2, x) is None
+    assert periodicity((E**x)%3, x) is None
+
+    assert periodicity(sin(expint(1, x))/expint(1, x), x) is None
+    # returning `None` for any Piecewise
+    p = Piecewise((0, x < -1), (x**2, x <= 1), (log(x), True))
+    assert periodicity(p, x) is None
+
+    m = MatrixSymbol('m', 3, 3)
+    raises(NotImplementedError, lambda: periodicity(sin(m), m))
+    raises(NotImplementedError, lambda: periodicity(sin(m[0, 0]), m))
+    raises(NotImplementedError, lambda: periodicity(sin(m), m[0, 0]))
+    raises(NotImplementedError, lambda: periodicity(sin(m[0, 0]), m[0, 0]))
+
+
+def test_periodicity_check():
+    assert periodicity(tan(x), x, check=True) == pi
+    assert periodicity(sin(x) + cos(x), x, check=True) == 2*pi
+    assert periodicity(sec(x), x) == 2*pi
+    assert periodicity(sin(x*y), x) == 2*pi/abs(y)
+    assert periodicity(Abs(sec(sec(x))), x) == pi
+
+
+def test_lcim():
+    assert lcim([S.Half, S(2), S(3)]) == 6
+    assert lcim([pi/2, pi/4, pi]) == pi
+    assert lcim([2*pi, pi/2]) == 2*pi
+    assert lcim([S.One, 2*pi]) is None
+    assert lcim([S(2) + 2*E, E/3 + Rational(1, 3), S.One + E]) == S(2) + 2*E
+
+
+def test_is_convex():
+    assert is_convex(1/x, x, domain=Interval.open(0, oo)) == True
+    assert is_convex(1/x, x, domain=Interval(-oo, 0)) == False
+    assert is_convex(x**2, x, domain=Interval(0, oo)) == True
+    assert is_convex(1/x**3, x, domain=Interval.Lopen(0, oo)) == True
+    assert is_convex(-1/x**3, x, domain=Interval.Ropen(-oo, 0)) == True
+    assert is_convex(log(x) ,x) == False
+    assert is_convex(x**2+y**2, x, y) == True
+    assert is_convex(cos(x) + cos(y), x) == False
+    assert is_convex(8*x**2 - 2*y**2, x, y) == False
+
+
+def test_stationary_points():
+    assert stationary_points(sin(x), x, Interval(-pi/2, pi/2)
+        ) == {-pi/2, pi/2}
+    assert  stationary_points(sin(x), x, Interval.Ropen(0, pi/4)
+        ) is S.EmptySet
+    assert stationary_points(tan(x), x,
+        ) is S.EmptySet
+    assert stationary_points(sin(x)*cos(x), x, Interval(0, pi)
+        ) == {pi/4, pi*Rational(3, 4)}
+    assert stationary_points(sec(x), x, Interval(0, pi)
+        ) == {0, pi}
+    assert stationary_points((x+3)*(x-2), x
+        ) == FiniteSet(Rational(-1, 2))
+    assert stationary_points((x + 3)/(x - 2), x, Interval(-5, 5)
+        ) is S.EmptySet
+    assert stationary_points((x**2+3)/(x-2), x
+        ) == {2 - sqrt(7), 2 + sqrt(7)}
+    assert stationary_points((x**2+3)/(x-2), x, Interval(0, 5)
+        ) == {2 + sqrt(7)}
+    assert stationary_points(x**4 + x**3 - 5*x**2, x, S.Reals
+        ) == FiniteSet(-2, 0, Rational(5, 4))
+    assert stationary_points(exp(x), x
+        ) is S.EmptySet
+    assert stationary_points(log(x) - x, x, S.Reals
+        ) == {1}
+    assert stationary_points(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))
+        ) == {0, -pi, pi}
+    assert stationary_points(y, x, S.Reals
+        ) == S.Reals
+    assert stationary_points(y, x, S.EmptySet) == S.EmptySet
+
+
+def test_maximum():
+    assert maximum(sin(x), x) is S.One
+    assert maximum(sin(x), x, Interval(0, 1)) == sin(1)
+    assert maximum(tan(x), x) is oo
+    assert maximum(tan(x), x, Interval(-pi/4, pi/4)) is S.One
+    assert maximum(sin(x)*cos(x), x, S.Reals) == S.Half
+    assert simplify(maximum(sin(x)*cos(x), x, Interval(pi*Rational(3, 8), pi*Rational(5, 8)))
+        ) == sqrt(2)/4
+    assert maximum((x+3)*(x-2), x) is oo
+    assert maximum((x+3)*(x-2), x, Interval(-5, 0)) == S(14)
+    assert maximum((x+3)/(x-2), x, Interval(-5, 0)) == Rational(2, 7)
+    assert simplify(maximum(-x**4-x**3+x**2+10, x)
+        ) == 41*sqrt(41)/512 + Rational(5419, 512)
+    assert maximum(exp(x), x, Interval(-oo, 2)) == exp(2)
+    assert maximum(log(x) - x, x, S.Reals) is S.NegativeOne
+    assert maximum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))
+        ) is S.One
+    assert maximum(cos(x)-sin(x), x, S.Reals) == sqrt(2)
+    assert maximum(y, x, S.Reals) == y
+    assert maximum(abs(a**3 + a), a, Interval(0, 2)) == 10
+    assert maximum(abs(60*a**3 + 24*a), a, Interval(0, 2)) == 528
+    assert maximum(abs(12*a*(5*a**2 + 2)), a, Interval(0, 2)) == 528
+    assert maximum(x/sqrt(x**2+1), x, S.Reals) == 1
+
+    raises(ValueError, lambda : maximum(sin(x), x, S.EmptySet))
+    raises(ValueError, lambda : maximum(log(cos(x)), x, S.EmptySet))
+    raises(ValueError, lambda : maximum(1/(x**2 + y**2 + 1), x, S.EmptySet))
+    raises(ValueError, lambda : maximum(sin(x), sin(x)))
+    raises(ValueError, lambda : maximum(sin(x), x*y, S.EmptySet))
+    raises(ValueError, lambda : maximum(sin(x), S.One))
+
+
+def test_minimum():
+    assert minimum(sin(x), x) is S.NegativeOne
+    assert minimum(sin(x), x, Interval(1, 4)) == sin(4)
+    assert minimum(tan(x), x) is -oo
+    assert minimum(tan(x), x, Interval(-pi/4, pi/4)) is S.NegativeOne
+    assert minimum(sin(x)*cos(x), x, S.Reals) == Rational(-1, 2)
+    assert simplify(minimum(sin(x)*cos(x), x, Interval(pi*Rational(3, 8), pi*Rational(5, 8)))
+        ) == -sqrt(2)/4
+    assert minimum((x+3)*(x-2), x) == Rational(-25, 4)
+    assert minimum((x+3)/(x-2), x, Interval(-5, 0)) == Rational(-3, 2)
+    assert minimum(x**4-x**3+x**2+10, x) == S(10)
+    assert minimum(exp(x), x, Interval(-2, oo)) == exp(-2)
+    assert minimum(log(x) - x, x, S.Reals) is -oo
+    assert minimum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))
+        ) is S.NegativeOne
+    assert minimum(cos(x)-sin(x), x, S.Reals) == -sqrt(2)
+    assert minimum(y, x, S.Reals) == y
+    assert minimum(x/sqrt(x**2+1), x, S.Reals) == -1
+
+    raises(ValueError, lambda : minimum(sin(x), x, S.EmptySet))
+    raises(ValueError, lambda : minimum(log(cos(x)), x, S.EmptySet))
+    raises(ValueError, lambda : minimum(1/(x**2 + y**2 + 1), x, S.EmptySet))
+    raises(ValueError, lambda : minimum(sin(x), sin(x)))
+    raises(ValueError, lambda : minimum(sin(x), x*y, S.EmptySet))
+    raises(ValueError, lambda : minimum(sin(x), S.One))
+
+
+def test_issue_19869():
+    assert (maximum(sqrt(3)*(x - 1)/(3*sqrt(x**2 + 1)), x)
+        ) == sqrt(3)/3
+
+
+def test_issue_16469():
+    f = abs(a)
+    assert function_range(f, a, S.Reals) == Interval(0, oo, False, True)
+
+
+@_both_exp_pow
+def test_issue_18747():
+    assert periodicity(exp(pi*I*(x/4 + S.Half/2)), x) == 8
+
+
+def test_issue_25942():
+    assert (acos(x) > pi/3).as_set() == Interval.Ropen(-1, S(1)/2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/util.py
new file mode 100644
index 0000000000000000000000000000000000000000..dac316358873de2418dd8ab56445823f07a37b1b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/calculus/util.py
@@ -0,0 +1,895 @@
+from .accumulationbounds import AccumBounds, AccumulationBounds # noqa: F401
+from .singularities import singularities
+from sympy.core import Pow, S
+from sympy.core.function import diff, expand_mul, Function
+from sympy.core.kind import NumberKind
+from sympy.core.mod import Mod
+from sympy.core.numbers import equal_valued
+from sympy.core.relational import Relational
+from sympy.core.symbol import Symbol, Dummy
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.complexes import Abs, im, re
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.integers import frac
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (
+    TrigonometricFunction, sin, cos, tan, cot, csc, sec,
+    asin, acos, acot, atan, asec, acsc)
+from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth,
+    sech, csch, asinh, acosh, atanh, acoth, asech, acsch)
+from sympy.polys.polytools import degree, lcm_list
+from sympy.sets.sets import (Interval, Intersection, FiniteSet, Union,
+                             Complement)
+from sympy.sets.fancysets import ImageSet
+from sympy.sets.conditionset import ConditionSet
+from sympy.utilities import filldedent
+from sympy.utilities.iterables import iterable
+from sympy.matrices.dense import hessian
+
+
+def continuous_domain(f, symbol, domain):
+    """
+    Returns the domain on which the function expression f is continuous.
+
+    This function is limited by the ability to determine the various
+    singularities and discontinuities of the given function.
+    The result is either given as a union of intervals or constructed using
+    other set operations.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    symbol : :py:class:`~.Symbol`
+        The variable for which the intervals are to be determined.
+    domain : :py:class:`~.Interval`
+        The domain over which the continuity of the symbol has to be checked.
+
+    Examples
+    ========
+
+    >>> from sympy import Interval, Symbol, S, tan, log, pi, sqrt
+    >>> from sympy.calculus.util import continuous_domain
+    >>> x = Symbol('x')
+    >>> continuous_domain(1/x, x, S.Reals)
+    Union(Interval.open(-oo, 0), Interval.open(0, oo))
+    >>> continuous_domain(tan(x), x, Interval(0, pi))
+    Union(Interval.Ropen(0, pi/2), Interval.Lopen(pi/2, pi))
+    >>> continuous_domain(sqrt(x - 2), x, Interval(-5, 5))
+    Interval(2, 5)
+    >>> continuous_domain(log(2*x - 1), x, S.Reals)
+    Interval.open(1/2, oo)
+
+    Returns
+    =======
+
+    :py:class:`~.Interval`
+        Union of all intervals where the function is continuous.
+
+    Raises
+    ======
+
+    NotImplementedError
+        If the method to determine continuity of such a function
+        has not yet been developed.
+
+    """
+    from sympy.solvers.inequalities import solve_univariate_inequality
+
+    if not domain.is_subset(S.Reals):
+        raise NotImplementedError(filldedent('''
+            Domain must be a subset of S.Reals.
+            '''))
+    implemented = [Pow, exp, log, Abs, frac,
+                   sin, cos, tan, cot, sec, csc,
+                   asin, acos, atan, acot, asec, acsc,
+                   sinh, cosh, tanh, coth, sech, csch,
+                   asinh, acosh, atanh, acoth, asech, acsch]
+    used = [fct.func for fct in f.atoms(Function) if fct.has(symbol)]
+    if any(func not in implemented for func in used):
+        raise NotImplementedError(filldedent('''
+            Unable to determine the domain of the given function.
+            '''))
+
+    x = Symbol('x')
+    constraints = {
+        log: (x > 0,),
+        asin: (x >= -1, x <= 1),
+        acos: (x >= -1, x <= 1),
+        acosh: (x >= 1,),
+        atanh: (x > -1, x < 1),
+        asech: (x > 0, x <= 1)
+    }
+    constraints_union = {
+        asec: (x <= -1, x >= 1),
+        acsc: (x <= -1, x >= 1),
+        acoth: (x < -1, x > 1)
+    }
+
+    cont_domain = domain
+    for atom in f.atoms(Pow):
+        den = atom.exp.as_numer_denom()[1]
+        if atom.exp.is_rational and den.is_odd:
+            pass    # 0**negative handled by singularities()
+        else:
+            constraint = solve_univariate_inequality(atom.base >= 0,
+                                                        symbol).as_set()
+            cont_domain = Intersection(constraint, cont_domain)
+
+    for atom in f.atoms(Function):
+        if atom.func in constraints:
+            for c in constraints[atom.func]:
+                constraint_relational = c.subs(x, atom.args[0])
+                constraint_set = solve_univariate_inequality(
+                    constraint_relational, symbol).as_set()
+                cont_domain = Intersection(constraint_set, cont_domain)
+        elif atom.func in constraints_union:
+            constraint_set = S.EmptySet
+            for c in constraints_union[atom.func]:
+                constraint_relational = c.subs(x, atom.args[0])
+                constraint_set += solve_univariate_inequality(
+                    constraint_relational, symbol).as_set()
+            cont_domain = Intersection(constraint_set, cont_domain)
+        # XXX: the discontinuities below could be factored out in
+        # a new "discontinuities()".
+        elif atom.func == acot:
+            from sympy.solvers.solveset import solveset_real
+            # Sympy's acot() has a step discontinuity at 0. Since it's
+            # neither an essential singularity nor a pole, singularities()
+            # will not report it. But it's still relevant for determining
+            # the continuity of the function f.
+            cont_domain -= solveset_real(atom.args[0], symbol)
+            # Note that the above may introduce spurious discontinuities, e.g.
+            # for abs(acot(x)) at 0.
+        elif atom.func == frac:
+            from sympy.solvers.solveset import solveset_real
+            r = function_range(atom.args[0], symbol, domain)
+            r = Intersection(r, S.Integers)
+            if r.is_finite_set:
+                discont = S.EmptySet
+                for n in r:
+                    discont += solveset_real(atom.args[0]-n, symbol)
+            else:
+                discont = ConditionSet(
+                    symbol, S.Integers.contains(atom.args[0]), cont_domain)
+            cont_domain -= discont
+
+    return cont_domain - singularities(f, symbol, domain)
+
+
+def function_range(f, symbol, domain):
+    """
+    Finds the range of a function in a given domain.
+    This method is limited by the ability to determine the singularities and
+    determine limits.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    symbol : :py:class:`~.Symbol`
+        The variable for which the range of function is to be determined.
+    domain : :py:class:`~.Interval`
+        The domain under which the range of the function has to be found.
+
+    Examples
+    ========
+
+    >>> from sympy import Interval, Symbol, S, exp, log, pi, sqrt, sin, tan
+    >>> from sympy.calculus.util import function_range
+    >>> x = Symbol('x')
+    >>> function_range(sin(x), x, Interval(0, 2*pi))
+    Interval(-1, 1)
+    >>> function_range(tan(x), x, Interval(-pi/2, pi/2))
+    Interval(-oo, oo)
+    >>> function_range(1/x, x, S.Reals)
+    Union(Interval.open(-oo, 0), Interval.open(0, oo))
+    >>> function_range(exp(x), x, S.Reals)
+    Interval.open(0, oo)
+    >>> function_range(log(x), x, S.Reals)
+    Interval(-oo, oo)
+    >>> function_range(sqrt(x), x, Interval(-5, 9))
+    Interval(0, 3)
+
+    Returns
+    =======
+
+    :py:class:`~.Interval`
+        Union of all ranges for all intervals under domain where function is
+        continuous.
+
+    Raises
+    ======
+
+    NotImplementedError
+        If any of the intervals, in the given domain, for which function
+        is continuous are not finite or real,
+        OR if the critical points of the function on the domain cannot be found.
+    """
+
+    if domain is S.EmptySet:
+        return S.EmptySet
+
+    period = periodicity(f, symbol)
+    if period == S.Zero:
+        # the expression is constant wrt symbol
+        return FiniteSet(f.expand())
+
+    from sympy.series.limits import limit
+    from sympy.solvers.solveset import solveset
+
+    if period is not None:
+        if isinstance(domain, Interval):
+            if (domain.inf - domain.sup).is_infinite:
+                domain = Interval(0, period)
+        elif isinstance(domain, Union):
+            for sub_dom in domain.args:
+                if isinstance(sub_dom, Interval) and \
+                ((sub_dom.inf - sub_dom.sup).is_infinite):
+                    domain = Interval(0, period)
+
+    intervals = continuous_domain(f, symbol, domain)
+    range_int = S.EmptySet
+    if isinstance(intervals,(Interval, FiniteSet)):
+        interval_iter = (intervals,)
+    elif isinstance(intervals, Union):
+        interval_iter = intervals.args
+    else:
+        raise NotImplementedError("Unable to find range for the given domain.")
+
+    for interval in interval_iter:
+        if isinstance(interval, FiniteSet):
+            for singleton in interval:
+                if singleton in domain:
+                    range_int += FiniteSet(f.subs(symbol, singleton))
+        elif isinstance(interval, Interval):
+            vals = S.EmptySet
+            critical_values = S.EmptySet
+            bounds = ((interval.left_open, interval.inf, '+'),
+                   (interval.right_open, interval.sup, '-'))
+
+            for is_open, limit_point, direction in bounds:
+                if is_open:
+                    critical_values += FiniteSet(limit(f, symbol, limit_point, direction))
+                    vals += critical_values
+                else:
+                    vals += FiniteSet(f.subs(symbol, limit_point))
+
+            critical_points = solveset(f.diff(symbol), symbol, interval)
+
+            if not iterable(critical_points):
+                raise NotImplementedError(
+                        'Unable to find critical points for {}'.format(f))
+            if isinstance(critical_points, ImageSet):
+                raise NotImplementedError(
+                        'Infinite number of critical points for {}'.format(f))
+
+            for critical_point in critical_points:
+                vals += FiniteSet(f.subs(symbol, critical_point))
+
+            left_open, right_open = False, False
+
+            if critical_values is not S.EmptySet:
+                if critical_values.inf == vals.inf:
+                    left_open = True
+
+                if critical_values.sup == vals.sup:
+                    right_open = True
+
+            range_int += Interval(vals.inf, vals.sup, left_open, right_open)
+        else:
+            raise NotImplementedError("Unable to find range for the given domain.")
+
+    return range_int
+
+
+def not_empty_in(finset_intersection, *syms):
+    """
+    Finds the domain of the functions in ``finset_intersection`` in which the
+    ``finite_set`` is not-empty.
+
+    Parameters
+    ==========
+
+    finset_intersection : Intersection of FiniteSet
+        The unevaluated intersection of FiniteSet containing
+        real-valued functions with Union of Sets
+    syms : Tuple of symbols
+        Symbol for which domain is to be found
+
+    Raises
+    ======
+
+    NotImplementedError
+        The algorithms to find the non-emptiness of the given FiniteSet are
+        not yet implemented.
+    ValueError
+        The input is not valid.
+    RuntimeError
+        It is a bug, please report it to the github issue tracker
+        (https://github.com/sympy/sympy/issues).
+
+    Examples
+    ========
+
+    >>> from sympy import FiniteSet, Interval, not_empty_in, oo
+    >>> from sympy.abc import x
+    >>> not_empty_in(FiniteSet(x/2).intersect(Interval(0, 1)), x)
+    Interval(0, 2)
+    >>> not_empty_in(FiniteSet(x, x**2).intersect(Interval(1, 2)), x)
+    Union(Interval(1, 2), Interval(-sqrt(2), -1))
+    >>> not_empty_in(FiniteSet(x**2/(x + 2)).intersect(Interval(1, oo)), x)
+    Union(Interval.Lopen(-2, -1), Interval(2, oo))
+    """
+
+    # TODO: handle piecewise defined functions
+    # TODO: handle transcendental functions
+    # TODO: handle multivariate functions
+    if len(syms) == 0:
+        raise ValueError("One or more symbols must be given in syms.")
+
+    if finset_intersection is S.EmptySet:
+        return S.EmptySet
+
+    if isinstance(finset_intersection, Union):
+        elm_in_sets = finset_intersection.args[0]
+        return Union(not_empty_in(finset_intersection.args[1], *syms),
+                     elm_in_sets)
+
+    if isinstance(finset_intersection, FiniteSet):
+        finite_set = finset_intersection
+        _sets = S.Reals
+    else:
+        finite_set = finset_intersection.args[1]
+        _sets = finset_intersection.args[0]
+
+    if not isinstance(finite_set, FiniteSet):
+        raise ValueError('A FiniteSet must be given, not %s: %s' %
+                         (type(finite_set), finite_set))
+
+    if len(syms) == 1:
+        symb = syms[0]
+    else:
+        raise NotImplementedError('more than one variables %s not handled' %
+                                  (syms,))
+
+    def elm_domain(expr, intrvl):
+        """ Finds the domain of an expression in any given interval """
+        from sympy.solvers.solveset import solveset
+
+        _start = intrvl.start
+        _end = intrvl.end
+        _singularities = solveset(expr.as_numer_denom()[1], symb,
+                                  domain=S.Reals)
+
+        if intrvl.right_open:
+            if _end is S.Infinity:
+                _domain1 = S.Reals
+            else:
+                _domain1 = solveset(expr < _end, symb, domain=S.Reals)
+        else:
+            _domain1 = solveset(expr <= _end, symb, domain=S.Reals)
+
+        if intrvl.left_open:
+            if _start is S.NegativeInfinity:
+                _domain2 = S.Reals
+            else:
+                _domain2 = solveset(expr > _start, symb, domain=S.Reals)
+        else:
+            _domain2 = solveset(expr >= _start, symb, domain=S.Reals)
+
+        # domain in the interval
+        expr_with_sing = Intersection(_domain1, _domain2)
+        expr_domain = Complement(expr_with_sing, _singularities)
+        return expr_domain
+
+    if isinstance(_sets, Interval):
+        return Union(*[elm_domain(element, _sets) for element in finite_set])
+
+    if isinstance(_sets, Union):
+        _domain = S.EmptySet
+        for intrvl in _sets.args:
+            _domain_element = Union(*[elm_domain(element, intrvl)
+                                      for element in finite_set])
+            _domain = Union(_domain, _domain_element)
+        return _domain
+
+
+def periodicity(f, symbol, check=False):
+    """
+    Tests the given function for periodicity in the given symbol.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    symbol : :py:class:`~.Symbol`
+        The variable for which the period is to be determined.
+    check : bool, optional
+        The flag to verify whether the value being returned is a period or not.
+
+    Returns
+    =======
+
+    period
+        The period of the function is returned.
+        ``None`` is returned when the function is aperiodic or has a complex period.
+        The value of $0$ is returned as the period of a constant function.
+
+    Raises
+    ======
+
+    NotImplementedError
+        The value of the period computed cannot be verified.
+
+
+    Notes
+    =====
+
+    Currently, we do not support functions with a complex period.
+    The period of functions having complex periodic values such
+    as ``exp``, ``sinh`` is evaluated to ``None``.
+
+    The value returned might not be the "fundamental" period of the given
+    function i.e. it may not be the smallest periodic value of the function.
+
+    The verification of the period through the ``check`` flag is not reliable
+    due to internal simplification of the given expression. Hence, it is set
+    to ``False`` by default.
+
+    Examples
+    ========
+    >>> from sympy import periodicity, Symbol, sin, cos, tan, exp
+    >>> x = Symbol('x')
+    >>> f = sin(x) + sin(2*x) + sin(3*x)
+    >>> periodicity(f, x)
+    2*pi
+    >>> periodicity(sin(x)*cos(x), x)
+    pi
+    >>> periodicity(exp(tan(2*x) - 1), x)
+    pi/2
+    >>> periodicity(sin(4*x)**cos(2*x), x)
+    pi
+    >>> periodicity(exp(x), x)
+    """
+    if symbol.kind is not NumberKind:
+        raise NotImplementedError("Cannot use symbol of kind %s" % symbol.kind)
+    temp = Dummy('x', real=True)
+    f = f.subs(symbol, temp)
+    symbol = temp
+
+    def _check(orig_f, period):
+        '''Return the checked period or raise an error.'''
+        new_f = orig_f.subs(symbol, symbol + period)
+        if new_f.equals(orig_f):
+            return period
+        else:
+            raise NotImplementedError(filldedent('''
+                The period of the given function cannot be verified.
+                When `%s` was replaced with `%s + %s` in `%s`, the result
+                was `%s` which was not recognized as being the same as
+                the original function.
+                So either the period was wrong or the two forms were
+                not recognized as being equal.
+                Set check=False to obtain the value.''' %
+                (symbol, symbol, period, orig_f, new_f)))
+
+    orig_f = f
+    period = None
+
+    if isinstance(f, Relational):
+        f = f.lhs - f.rhs
+
+    f = f.simplify()
+
+    if symbol not in f.free_symbols:
+        return S.Zero
+
+    if isinstance(f, TrigonometricFunction):
+        try:
+            period = f.period(symbol)
+        except NotImplementedError:
+            pass
+
+    if isinstance(f, Abs):
+        arg = f.args[0]
+        if isinstance(arg, (sec, csc, cos)):
+            # all but tan and cot might have a
+            # a period that is half as large
+            # so recast as sin
+            arg = sin(arg.args[0])
+        period = periodicity(arg, symbol)
+        if period is not None and isinstance(arg, sin):
+            # the argument of Abs was a trigonometric other than
+            # cot or tan; test to see if the half-period
+            # is valid. Abs(arg) has behaviour equivalent to
+            # orig_f, so use that for test:
+            orig_f = Abs(arg)
+            try:
+                return _check(orig_f, period/2)
+            except NotImplementedError as err:
+                if check:
+                    raise NotImplementedError(err)
+            # else let new orig_f and period be
+            # checked below
+
+    if isinstance(f, exp) or (f.is_Pow and f.base == S.Exp1):
+        f = Pow(S.Exp1, expand_mul(f.exp))
+        if im(f) != 0:
+            period_real = periodicity(re(f), symbol)
+            period_imag = periodicity(im(f), symbol)
+            if period_real is not None and period_imag is not None:
+                period = lcim([period_real, period_imag])
+
+    if f.is_Pow and f.base != S.Exp1:
+        base, expo = f.args
+        base_has_sym = base.has(symbol)
+        expo_has_sym = expo.has(symbol)
+
+        if base_has_sym and not expo_has_sym:
+            period = periodicity(base, symbol)
+
+        elif expo_has_sym and not base_has_sym:
+            period = periodicity(expo, symbol)
+
+        else:
+            period = _periodicity(f.args, symbol)
+
+    elif f.is_Mul:
+        coeff, g = f.as_independent(symbol, as_Add=False)
+        if isinstance(g, TrigonometricFunction) or not equal_valued(coeff, 1):
+            period = periodicity(g, symbol)
+        else:
+            period = _periodicity(g.args, symbol)
+
+    elif f.is_Add:
+        k, g = f.as_independent(symbol)
+        if k is not S.Zero:
+            return periodicity(g, symbol)
+
+        period = _periodicity(g.args, symbol)
+
+    elif isinstance(f, Mod):
+        a, n = f.args
+
+        if a == symbol:
+            period = n
+        elif isinstance(a, TrigonometricFunction):
+            period = periodicity(a, symbol)
+        #check if 'f' is linear in 'symbol'
+        elif (a.is_polynomial(symbol) and degree(a, symbol) == 1 and
+            symbol not in n.free_symbols):
+                period = Abs(n / a.diff(symbol))
+
+    elif isinstance(f, Piecewise):
+        pass  # not handling Piecewise yet as the return type is not favorable
+
+    elif period is None:
+        from sympy.solvers.decompogen import compogen, decompogen
+        g_s = decompogen(f, symbol)
+        num_of_gs = len(g_s)
+        if num_of_gs > 1:
+            for index, g in enumerate(reversed(g_s)):
+                start_index = num_of_gs - 1 - index
+                g = compogen(g_s[start_index:], symbol)
+                if g not in (orig_f, f): # Fix for issue 12620
+                    period = periodicity(g, symbol)
+                    if period is not None:
+                        break
+
+    if period is not None:
+        if check:
+            return _check(orig_f, period)
+        return period
+
+    return None
+
+
+def _periodicity(args, symbol):
+    """
+    Helper for `periodicity` to find the period of a list of simpler
+    functions.
+    It uses the `lcim` method to find the least common period of
+    all the functions.
+
+    Parameters
+    ==========
+
+    args : Tuple of :py:class:`~.Symbol`
+        All the symbols present in a function.
+
+    symbol : :py:class:`~.Symbol`
+        The symbol over which the function is to be evaluated.
+
+    Returns
+    =======
+
+    period
+        The least common period of the function for all the symbols
+        of the function.
+        ``None`` if for at least one of the symbols the function is aperiodic.
+
+    """
+    periods = []
+    for f in args:
+        period = periodicity(f, symbol)
+        if period is None:
+            return None
+
+        if period is not S.Zero:
+            periods.append(period)
+
+    if len(periods) > 1:
+        return lcim(periods)
+
+    if periods:
+        return periods[0]
+
+
+def lcim(numbers):
+    """Returns the least common integral multiple of a list of numbers.
+
+    The numbers can be rational or irrational or a mixture of both.
+    `None` is returned for incommensurable numbers.
+
+    Parameters
+    ==========
+
+    numbers : list
+        Numbers (rational and/or irrational) for which lcim is to be found.
+
+    Returns
+    =======
+
+    number
+        lcim if it exists, otherwise ``None`` for incommensurable numbers.
+
+    Examples
+    ========
+
+    >>> from sympy.calculus.util import lcim
+    >>> from sympy import S, pi
+    >>> lcim([S(1)/2, S(3)/4, S(5)/6])
+    15/2
+    >>> lcim([2*pi, 3*pi, pi, pi/2])
+    6*pi
+    >>> lcim([S(1), 2*pi])
+    """
+    result = None
+    if all(num.is_irrational for num in numbers):
+        factorized_nums = [num.factor() for num in numbers]
+        factors_num = [num.as_coeff_Mul() for num in factorized_nums]
+        term = factors_num[0][1]
+        if all(factor == term for coeff, factor in factors_num):
+            common_term = term
+            coeffs = [coeff for coeff, factor in factors_num]
+            result = lcm_list(coeffs) * common_term
+
+    elif all(num.is_rational for num in numbers):
+        result = lcm_list(numbers)
+
+    else:
+        pass
+
+    return result
+
+def is_convex(f, *syms, domain=S.Reals):
+    r"""Determines the  convexity of the function passed in the argument.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    syms : Tuple of :py:class:`~.Symbol`
+        The variables with respect to which the convexity is to be determined.
+    domain : :py:class:`~.Interval`, optional
+        The domain over which the convexity of the function has to be checked.
+        If unspecified, S.Reals will be the default domain.
+
+    Returns
+    =======
+
+    bool
+        The method returns ``True`` if the function is convex otherwise it
+        returns ``False``.
+
+    Raises
+    ======
+
+    NotImplementedError
+        The check for the convexity of multivariate functions is not implemented yet.
+
+    Notes
+    =====
+
+    To determine concavity of a function pass `-f` as the concerned function.
+    To determine logarithmic convexity of a function pass `\log(f)` as
+    concerned function.
+    To determine logarithmic concavity of a function pass `-\log(f)` as
+    concerned function.
+
+    Currently, convexity check of multivariate functions is not handled.
+
+    Examples
+    ========
+
+    >>> from sympy import is_convex, symbols, exp, oo, Interval
+    >>> x = symbols('x')
+    >>> is_convex(exp(x), x)
+    True
+    >>> is_convex(x**3, x, domain = Interval(-1, oo))
+    False
+    >>> is_convex(1/x**2, x, domain=Interval.open(0, oo))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Convex_function
+    .. [2] http://www.ifp.illinois.edu/~angelia/L3_convfunc.pdf
+    .. [3] https://en.wikipedia.org/wiki/Logarithmically_convex_function
+    .. [4] https://en.wikipedia.org/wiki/Logarithmically_concave_function
+    .. [5] https://en.wikipedia.org/wiki/Concave_function
+
+    """
+    if len(syms) > 1 :
+        return hessian(f, syms).is_positive_semidefinite
+    from sympy.solvers.inequalities import solve_univariate_inequality
+    f = _sympify(f)
+    var = syms[0]
+    if any(s in domain for s in singularities(f, var)):
+        return False
+    condition = f.diff(var, 2) < 0
+    if solve_univariate_inequality(condition, var, False, domain):
+        return False
+    return True
+
+
+def stationary_points(f, symbol, domain=S.Reals):
+    """
+    Returns the stationary points of a function (where derivative of the
+    function is 0) in the given domain.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    symbol : :py:class:`~.Symbol`
+        The variable for which the stationary points are to be determined.
+    domain : :py:class:`~.Interval`
+        The domain over which the stationary points have to be checked.
+        If unspecified, ``S.Reals`` will be the default domain.
+
+    Returns
+    =======
+
+    Set
+        A set of stationary points for the function. If there are no
+        stationary point, an :py:class:`~.EmptySet` is returned.
+
+    Examples
+    ========
+
+    >>> from sympy import Interval, Symbol, S, sin, pi, pprint, stationary_points
+    >>> x = Symbol('x')
+
+    >>> stationary_points(1/x, x, S.Reals)
+    EmptySet
+
+    >>> pprint(stationary_points(sin(x), x), use_unicode=False)
+              pi                              3*pi
+    {2*n*pi + -- | n in Integers} U {2*n*pi + ---- | n in Integers}
+              2                                2
+
+    >>> stationary_points(sin(x),x, Interval(0, 4*pi))
+    {pi/2, 3*pi/2, 5*pi/2, 7*pi/2}
+
+    """
+    from sympy.solvers.solveset import solveset
+
+    if domain is S.EmptySet:
+        return S.EmptySet
+
+    domain = continuous_domain(f, symbol, domain)
+    set = solveset(diff(f, symbol), symbol, domain)
+
+    return set
+
+
+def maximum(f, symbol, domain=S.Reals):
+    """
+    Returns the maximum value of a function in the given domain.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    symbol : :py:class:`~.Symbol`
+        The variable for maximum value needs to be determined.
+    domain : :py:class:`~.Interval`
+        The domain over which the maximum have to be checked.
+        If unspecified, then the global maximum is returned.
+
+    Returns
+    =======
+
+    number
+        Maximum value of the function in given domain.
+
+    Examples
+    ========
+
+    >>> from sympy import Interval, Symbol, S, sin, cos, pi, maximum
+    >>> x = Symbol('x')
+
+    >>> f = -x**2 + 2*x + 5
+    >>> maximum(f, x, S.Reals)
+    6
+
+    >>> maximum(sin(x), x, Interval(-pi, pi/4))
+    sqrt(2)/2
+
+    >>> maximum(sin(x)*cos(x), x)
+    1/2
+
+    """
+    if isinstance(symbol, Symbol):
+        if domain is S.EmptySet:
+            raise ValueError("Maximum value not defined for empty domain.")
+
+        return function_range(f, symbol, domain).sup
+    else:
+        raise ValueError("%s is not a valid symbol." % symbol)
+
+
+def minimum(f, symbol, domain=S.Reals):
+    """
+    Returns the minimum value of a function in the given domain.
+
+    Parameters
+    ==========
+
+    f : :py:class:`~.Expr`
+        The concerned function.
+    symbol : :py:class:`~.Symbol`
+        The variable for minimum value needs to be determined.
+    domain : :py:class:`~.Interval`
+        The domain over which the minimum have to be checked.
+        If unspecified, then the global minimum is returned.
+
+    Returns
+    =======
+
+    number
+        Minimum value of the function in the given domain.
+
+    Examples
+    ========
+
+    >>> from sympy import Interval, Symbol, S, sin, cos, minimum
+    >>> x = Symbol('x')
+
+    >>> f = x**2 + 2*x + 5
+    >>> minimum(f, x, S.Reals)
+    4
+
+    >>> minimum(sin(x), x, Interval(2, 3))
+    sin(3)
+
+    >>> minimum(sin(x)*cos(x), x)
+    -1/2
+
+    """
+    if isinstance(symbol, Symbol):
+        if domain is S.EmptySet:
+            raise ValueError("Minimum value not defined for empty domain.")
+
+        return function_range(f, symbol, domain).inf
+    else:
+        raise ValueError("%s is not a valid symbol." % symbol)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..4c5007308a1b232e57f9ed164276862df0c5f265
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/__init__.py
@@ -0,0 +1,33 @@
+"""
+Category Theory module.
+
+Provides some of the fundamental category-theory-related classes,
+including categories, morphisms, diagrams.  Functors are not
+implemented yet.
+
+The general reference work this module tries to follow is
+
+  [JoyOfCats] J. Adamek, H. Herrlich. G. E. Strecker: Abstract and
+              Concrete Categories. The Joy of Cats.
+
+The latest version of this book should be available for free download
+from
+
+   katmat.math.uni-bremen.de/acc/acc.pdf
+
+"""
+
+from .baseclasses import (Object, Morphism, IdentityMorphism,
+                         NamedMorphism, CompositeMorphism, Category,
+                         Diagram)
+
+from .diagram_drawing import (DiagramGrid, XypicDiagramDrawer,
+                             xypic_draw_diagram, preview_diagram)
+
+__all__ = [
+    'Object', 'Morphism', 'IdentityMorphism', 'NamedMorphism',
+    'CompositeMorphism', 'Category', 'Diagram',
+
+    'DiagramGrid', 'XypicDiagramDrawer', 'xypic_draw_diagram',
+    'preview_diagram',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/baseclasses.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/baseclasses.py
new file mode 100644
index 0000000000000000000000000000000000000000..e6ab5153ae4e95f193030864c8f32a52254f2458
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/baseclasses.py
@@ -0,0 +1,978 @@
+from sympy.core import S, Basic, Dict, Symbol, Tuple, sympify
+from sympy.core.symbol import Str
+from sympy.sets import Set, FiniteSet, EmptySet
+from sympy.utilities.iterables import iterable
+
+
+class Class(Set):
+    r"""
+    The base class for any kind of class in the set-theoretic sense.
+
+    Explanation
+    ===========
+
+    In axiomatic set theories, everything is a class.  A class which
+    can be a member of another class is a set.  A class which is not a
+    member of another class is a proper class.  The class `\{1, 2\}`
+    is a set; the class of all sets is a proper class.
+
+    This class is essentially a synonym for :class:`sympy.core.Set`.
+    The goal of this class is to assure easier migration to the
+    eventual proper implementation of set theory.
+    """
+    is_proper = False
+
+
+class Object(Symbol):
+    """
+    The base class for any kind of object in an abstract category.
+
+    Explanation
+    ===========
+
+    While technically any instance of :class:`~.Basic` will do, this
+    class is the recommended way to create abstract objects in
+    abstract categories.
+    """
+
+
+class Morphism(Basic):
+    """
+    The base class for any morphism in an abstract category.
+
+    Explanation
+    ===========
+
+    In abstract categories, a morphism is an arrow between two
+    category objects.  The object where the arrow starts is called the
+    domain, while the object where the arrow ends is called the
+    codomain.
+
+    Two morphisms between the same pair of objects are considered to
+    be the same morphisms.  To distinguish between morphisms between
+    the same objects use :class:`NamedMorphism`.
+
+    It is prohibited to instantiate this class.  Use one of the
+    derived classes instead.
+
+    See Also
+    ========
+
+    IdentityMorphism, NamedMorphism, CompositeMorphism
+    """
+    def __new__(cls, domain, codomain):
+        raise(NotImplementedError(
+            "Cannot instantiate Morphism.  Use derived classes instead."))
+
+    @property
+    def domain(self):
+        """
+        Returns the domain of the morphism.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> f.domain
+        Object("A")
+
+        """
+        return self.args[0]
+
+    @property
+    def codomain(self):
+        """
+        Returns the codomain of the morphism.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> f.codomain
+        Object("B")
+
+        """
+        return self.args[1]
+
+    def compose(self, other):
+        r"""
+        Composes self with the supplied morphism.
+
+        The order of elements in the composition is the usual order,
+        i.e., to construct `g\circ f` use ``g.compose(f)``.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> g * f
+        CompositeMorphism((NamedMorphism(Object("A"), Object("B"), "f"),
+        NamedMorphism(Object("B"), Object("C"), "g")))
+        >>> (g * f).domain
+        Object("A")
+        >>> (g * f).codomain
+        Object("C")
+
+        """
+        return CompositeMorphism(other, self)
+
+    def __mul__(self, other):
+        r"""
+        Composes self with the supplied morphism.
+
+        The semantics of this operation is given by the following
+        equation: ``g * f == g.compose(f)`` for composable morphisms
+        ``g`` and ``f``.
+
+        See Also
+        ========
+
+        compose
+        """
+        return self.compose(other)
+
+
+class IdentityMorphism(Morphism):
+    """
+    Represents an identity morphism.
+
+    Explanation
+    ===========
+
+    An identity morphism is a morphism with equal domain and codomain,
+    which acts as an identity with respect to composition.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism, IdentityMorphism
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> id_A = IdentityMorphism(A)
+    >>> id_B = IdentityMorphism(B)
+    >>> f * id_A == f
+    True
+    >>> id_B * f == f
+    True
+
+    See Also
+    ========
+
+    Morphism
+    """
+    def __new__(cls, domain):
+        return Basic.__new__(cls, domain)
+
+    @property
+    def codomain(self):
+        return self.domain
+
+
+class NamedMorphism(Morphism):
+    """
+    Represents a morphism which has a name.
+
+    Explanation
+    ===========
+
+    Names are used to distinguish between morphisms which have the
+    same domain and codomain: two named morphisms are equal if they
+    have the same domains, codomains, and names.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> f
+    NamedMorphism(Object("A"), Object("B"), "f")
+    >>> f.name
+    'f'
+
+    See Also
+    ========
+
+    Morphism
+    """
+    def __new__(cls, domain, codomain, name):
+        if not name:
+            raise ValueError("Empty morphism names not allowed.")
+
+        if not isinstance(name, Str):
+            name = Str(name)
+
+        return Basic.__new__(cls, domain, codomain, name)
+
+    @property
+    def name(self):
+        """
+        Returns the name of the morphism.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> f.name
+        'f'
+
+        """
+        return self.args[2].name
+
+
+class CompositeMorphism(Morphism):
+    r"""
+    Represents a morphism which is a composition of other morphisms.
+
+    Explanation
+    ===========
+
+    Two composite morphisms are equal if the morphisms they were
+    obtained from (components) are the same and were listed in the
+    same order.
+
+    The arguments to the constructor for this class should be listed
+    in diagram order: to obtain the composition `g\circ f` from the
+    instances of :class:`Morphism` ``g`` and ``f`` use
+    ``CompositeMorphism(f, g)``.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism, CompositeMorphism
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> g * f
+    CompositeMorphism((NamedMorphism(Object("A"), Object("B"), "f"),
+    NamedMorphism(Object("B"), Object("C"), "g")))
+    >>> CompositeMorphism(f, g) == g * f
+    True
+
+    """
+    @staticmethod
+    def _add_morphism(t, morphism):
+        """
+        Intelligently adds ``morphism`` to tuple ``t``.
+
+        Explanation
+        ===========
+
+        If ``morphism`` is a composite morphism, its components are
+        added to the tuple.  If ``morphism`` is an identity, nothing
+        is added to the tuple.
+
+        No composability checks are performed.
+        """
+        if isinstance(morphism, CompositeMorphism):
+            # ``morphism`` is a composite morphism; we have to
+            # denest its components.
+            return t + morphism.components
+        elif isinstance(morphism, IdentityMorphism):
+            # ``morphism`` is an identity.  Nothing happens.
+            return t
+        else:
+            return t + Tuple(morphism)
+
+    def __new__(cls, *components):
+        if components and not isinstance(components[0], Morphism):
+            # Maybe the user has explicitly supplied a list of
+            # morphisms.
+            return CompositeMorphism.__new__(cls, *components[0])
+
+        normalised_components = Tuple()
+
+        for current, following in zip(components, components[1:]):
+            if not isinstance(current, Morphism) or \
+                    not isinstance(following, Morphism):
+                raise TypeError("All components must be morphisms.")
+
+            if current.codomain != following.domain:
+                raise ValueError("Uncomposable morphisms.")
+
+            normalised_components = CompositeMorphism._add_morphism(
+                normalised_components, current)
+
+        # We haven't added the last morphism to the list of normalised
+        # components.  Add it now.
+        normalised_components = CompositeMorphism._add_morphism(
+            normalised_components, components[-1])
+
+        if not normalised_components:
+            # If ``normalised_components`` is empty, only identities
+            # were supplied.  Since they all were composable, they are
+            # all the same identities.
+            return components[0]
+        elif len(normalised_components) == 1:
+            # No sense to construct a whole CompositeMorphism.
+            return normalised_components[0]
+
+        return Basic.__new__(cls, normalised_components)
+
+    @property
+    def components(self):
+        """
+        Returns the components of this composite morphism.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> (g * f).components
+        (NamedMorphism(Object("A"), Object("B"), "f"),
+        NamedMorphism(Object("B"), Object("C"), "g"))
+
+        """
+        return self.args[0]
+
+    @property
+    def domain(self):
+        """
+        Returns the domain of this composite morphism.
+
+        The domain of the composite morphism is the domain of its
+        first component.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> (g * f).domain
+        Object("A")
+
+        """
+        return self.components[0].domain
+
+    @property
+    def codomain(self):
+        """
+        Returns the codomain of this composite morphism.
+
+        The codomain of the composite morphism is the codomain of its
+        last component.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> (g * f).codomain
+        Object("C")
+
+        """
+        return self.components[-1].codomain
+
+    def flatten(self, new_name):
+        """
+        Forgets the composite structure of this morphism.
+
+        Explanation
+        ===========
+
+        If ``new_name`` is not empty, returns a :class:`NamedMorphism`
+        with the supplied name, otherwise returns a :class:`Morphism`.
+        In both cases the domain of the new morphism is the domain of
+        this composite morphism and the codomain of the new morphism
+        is the codomain of this composite morphism.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> (g * f).flatten("h")
+        NamedMorphism(Object("A"), Object("C"), "h")
+
+        """
+        return NamedMorphism(self.domain, self.codomain, new_name)
+
+
+class Category(Basic):
+    r"""
+    An (abstract) category.
+
+    Explanation
+    ===========
+
+    A category [JoyOfCats] is a quadruple `\mbox{K} = (O, \hom, id,
+    \circ)` consisting of
+
+    * a (set-theoretical) class `O`, whose members are called
+      `K`-objects,
+
+    * for each pair `(A, B)` of `K`-objects, a set `\hom(A, B)` whose
+      members are called `K`-morphisms from `A` to `B`,
+
+    * for a each `K`-object `A`, a morphism `id:A\rightarrow A`,
+      called the `K`-identity of `A`,
+
+    * a composition law `\circ` associating with every `K`-morphisms
+      `f:A\rightarrow B` and `g:B\rightarrow C` a `K`-morphism `g\circ
+      f:A\rightarrow C`, called the composite of `f` and `g`.
+
+    Composition is associative, `K`-identities are identities with
+    respect to composition, and the sets `\hom(A, B)` are pairwise
+    disjoint.
+
+    This class knows nothing about its objects and morphisms.
+    Concrete cases of (abstract) categories should be implemented as
+    classes derived from this one.
+
+    Certain instances of :class:`Diagram` can be asserted to be
+    commutative in a :class:`Category` by supplying the argument
+    ``commutative_diagrams`` in the constructor.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism, Diagram, Category
+    >>> from sympy import FiniteSet
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> d = Diagram([f, g])
+    >>> K = Category("K", commutative_diagrams=[d])
+    >>> K.commutative_diagrams == FiniteSet(d)
+    True
+
+    See Also
+    ========
+
+    Diagram
+    """
+    def __new__(cls, name, objects=EmptySet, commutative_diagrams=EmptySet):
+        if not name:
+            raise ValueError("A Category cannot have an empty name.")
+
+        if not isinstance(name, Str):
+            name = Str(name)
+
+        if not isinstance(objects, Class):
+            objects = Class(objects)
+
+        new_category = Basic.__new__(cls, name, objects,
+                                     FiniteSet(*commutative_diagrams))
+        return new_category
+
+    @property
+    def name(self):
+        """
+        Returns the name of this category.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Category
+        >>> K = Category("K")
+        >>> K.name
+        'K'
+
+        """
+        return self.args[0].name
+
+    @property
+    def objects(self):
+        """
+        Returns the class of objects of this category.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, Category
+        >>> from sympy import FiniteSet
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> K = Category("K", FiniteSet(A, B))
+        >>> K.objects
+        Class({Object("A"), Object("B")})
+
+        """
+        return self.args[1]
+
+    @property
+    def commutative_diagrams(self):
+        """
+        Returns the :class:`~.FiniteSet` of diagrams which are known to
+        be commutative in this category.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism, Diagram, Category
+        >>> from sympy import FiniteSet
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g])
+        >>> K = Category("K", commutative_diagrams=[d])
+        >>> K.commutative_diagrams == FiniteSet(d)
+        True
+
+        """
+        return self.args[2]
+
+    def hom(self, A, B):
+        raise NotImplementedError(
+            "hom-sets are not implemented in Category.")
+
+    def all_morphisms(self):
+        raise NotImplementedError(
+            "Obtaining the class of morphisms is not implemented in Category.")
+
+
+class Diagram(Basic):
+    r"""
+    Represents a diagram in a certain category.
+
+    Explanation
+    ===========
+
+    Informally, a diagram is a collection of objects of a category and
+    certain morphisms between them.  A diagram is still a monoid with
+    respect to morphism composition; i.e., identity morphisms, as well
+    as all composites of morphisms included in the diagram belong to
+    the diagram.  For a more formal approach to this notion see
+    [Pare1970].
+
+    The components of composite morphisms are also added to the
+    diagram.  No properties are assigned to such morphisms by default.
+
+    A commutative diagram is often accompanied by a statement of the
+    following kind: "if such morphisms with such properties exist,
+    then such morphisms which such properties exist and the diagram is
+    commutative".  To represent this, an instance of :class:`Diagram`
+    includes a collection of morphisms which are the premises and
+    another collection of conclusions.  ``premises`` and
+    ``conclusions`` associate morphisms belonging to the corresponding
+    categories with the :class:`~.FiniteSet`'s of their properties.
+
+    The set of properties of a composite morphism is the intersection
+    of the sets of properties of its components.  The domain and
+    codomain of a conclusion morphism should be among the domains and
+    codomains of the morphisms listed as the premises of a diagram.
+
+    No checks are carried out of whether the supplied object and
+    morphisms do belong to one and the same category.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism, Diagram
+    >>> from sympy import pprint, default_sort_key
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> d = Diagram([f, g])
+    >>> premises_keys = sorted(d.premises.keys(), key=default_sort_key)
+    >>> pprint(premises_keys, use_unicode=False)
+    [g*f:A-->C, id:A-->A, id:B-->B, id:C-->C, f:A-->B, g:B-->C]
+    >>> pprint(d.premises, use_unicode=False)
+    {g*f:A-->C: EmptySet, id:A-->A: EmptySet, id:B-->B: EmptySet,
+     id:C-->C: EmptySet, f:A-->B: EmptySet, g:B-->C: EmptySet}
+    >>> d = Diagram([f, g], {g * f: "unique"})
+    >>> pprint(d.conclusions,use_unicode=False)
+    {g*f:A-->C: {unique}}
+
+    References
+    ==========
+
+    [Pare1970] B. Pareigis: Categories and functors.  Academic Press, 1970.
+
+    """
+    @staticmethod
+    def _set_dict_union(dictionary, key, value):
+        """
+        If ``key`` is in ``dictionary``, set the new value of ``key``
+        to be the union between the old value and ``value``.
+        Otherwise, set the value of ``key`` to ``value.
+
+        Returns ``True`` if the key already was in the dictionary and
+        ``False`` otherwise.
+        """
+        if key in dictionary:
+            dictionary[key] = dictionary[key] | value
+            return True
+        else:
+            dictionary[key] = value
+            return False
+
+    @staticmethod
+    def _add_morphism_closure(morphisms, morphism, props, add_identities=True,
+                              recurse_composites=True):
+        """
+        Adds a morphism and its attributes to the supplied dictionary
+        ``morphisms``.  If ``add_identities`` is True, also adds the
+        identity morphisms for the domain and the codomain of
+        ``morphism``.
+        """
+        if not Diagram._set_dict_union(morphisms, morphism, props):
+            # We have just added a new morphism.
+
+            if isinstance(morphism, IdentityMorphism):
+                if props:
+                    # Properties for identity morphisms don't really
+                    # make sense, because very much is known about
+                    # identity morphisms already, so much that they
+                    # are trivial.  Having properties for identity
+                    # morphisms would only be confusing.
+                    raise ValueError(
+                        "Instances of IdentityMorphism cannot have properties.")
+                return
+
+            if add_identities:
+                empty = EmptySet
+
+                id_dom = IdentityMorphism(morphism.domain)
+                id_cod = IdentityMorphism(morphism.codomain)
+
+                Diagram._set_dict_union(morphisms, id_dom, empty)
+                Diagram._set_dict_union(morphisms, id_cod, empty)
+
+            for existing_morphism, existing_props in list(morphisms.items()):
+                new_props = existing_props & props
+                if morphism.domain == existing_morphism.codomain:
+                    left = morphism * existing_morphism
+                    Diagram._set_dict_union(morphisms, left, new_props)
+                if morphism.codomain == existing_morphism.domain:
+                    right = existing_morphism * morphism
+                    Diagram._set_dict_union(morphisms, right, new_props)
+
+            if isinstance(morphism, CompositeMorphism) and recurse_composites:
+                # This is a composite morphism, add its components as
+                # well.
+                empty = EmptySet
+                for component in morphism.components:
+                    Diagram._add_morphism_closure(morphisms, component, empty,
+                                                  add_identities)
+
+    def __new__(cls, *args):
+        """
+        Construct a new instance of Diagram.
+
+        Explanation
+        ===========
+
+        If no arguments are supplied, an empty diagram is created.
+
+        If at least an argument is supplied, ``args[0]`` is
+        interpreted as the premises of the diagram.  If ``args[0]`` is
+        a list, it is interpreted as a list of :class:`Morphism`'s, in
+        which each :class:`Morphism` has an empty set of properties.
+        If ``args[0]`` is a Python dictionary or a :class:`Dict`, it
+        is interpreted as a dictionary associating to some
+        :class:`Morphism`'s some properties.
+
+        If at least two arguments are supplied ``args[1]`` is
+        interpreted as the conclusions of the diagram.  The type of
+        ``args[1]`` is interpreted in exactly the same way as the type
+        of ``args[0]``.  If only one argument is supplied, the diagram
+        has no conclusions.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import IdentityMorphism, Diagram
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g])
+        >>> IdentityMorphism(A) in d.premises.keys()
+        True
+        >>> g * f in d.premises.keys()
+        True
+        >>> d = Diagram([f, g], {g * f: "unique"})
+        >>> d.conclusions[g * f]
+        {unique}
+
+        """
+        premises = {}
+        conclusions = {}
+
+        # Here we will keep track of the objects which appear in the
+        # premises.
+        objects = EmptySet
+
+        if len(args) >= 1:
+            # We've got some premises in the arguments.
+            premises_arg = args[0]
+
+            if isinstance(premises_arg, list):
+                # The user has supplied a list of morphisms, none of
+                # which have any attributes.
+                empty = EmptySet
+
+                for morphism in premises_arg:
+                    objects |= FiniteSet(morphism.domain, morphism.codomain)
+                    Diagram._add_morphism_closure(premises, morphism, empty)
+            elif isinstance(premises_arg, (dict, Dict)):
+                # The user has supplied a dictionary of morphisms and
+                # their properties.
+                for morphism, props in premises_arg.items():
+                    objects |= FiniteSet(morphism.domain, morphism.codomain)
+                    Diagram._add_morphism_closure(
+                        premises, morphism, FiniteSet(*props) if iterable(props) else FiniteSet(props))
+
+        if len(args) >= 2:
+            # We also have some conclusions.
+            conclusions_arg = args[1]
+
+            if isinstance(conclusions_arg, list):
+                # The user has supplied a list of morphisms, none of
+                # which have any attributes.
+                empty = EmptySet
+
+                for morphism in conclusions_arg:
+                    # Check that no new objects appear in conclusions.
+                    if ((sympify(objects.contains(morphism.domain)) is S.true) and
+                        (sympify(objects.contains(morphism.codomain)) is S.true)):
+                        # No need to add identities and recurse
+                        # composites this time.
+                        Diagram._add_morphism_closure(
+                            conclusions, morphism, empty, add_identities=False,
+                            recurse_composites=False)
+            elif isinstance(conclusions_arg, (dict, Dict)):
+                # The user has supplied a dictionary of morphisms and
+                # their properties.
+                for morphism, props in conclusions_arg.items():
+                    # Check that no new objects appear in conclusions.
+                    if (morphism.domain in objects) and \
+                       (morphism.codomain in objects):
+                        # No need to add identities and recurse
+                        # composites this time.
+                        Diagram._add_morphism_closure(
+                            conclusions, morphism, FiniteSet(*props) if iterable(props) else FiniteSet(props),
+                            add_identities=False, recurse_composites=False)
+
+        return Basic.__new__(cls, Dict(premises), Dict(conclusions), objects)
+
+    @property
+    def premises(self):
+        """
+        Returns the premises of this diagram.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import IdentityMorphism, Diagram
+        >>> from sympy import pretty
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> id_A = IdentityMorphism(A)
+        >>> id_B = IdentityMorphism(B)
+        >>> d = Diagram([f])
+        >>> print(pretty(d.premises, use_unicode=False))
+        {id:A-->A: EmptySet, id:B-->B: EmptySet, f:A-->B: EmptySet}
+
+        """
+        return self.args[0]
+
+    @property
+    def conclusions(self):
+        """
+        Returns the conclusions of this diagram.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import IdentityMorphism, Diagram
+        >>> from sympy import FiniteSet
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g])
+        >>> IdentityMorphism(A) in d.premises.keys()
+        True
+        >>> g * f in d.premises.keys()
+        True
+        >>> d = Diagram([f, g], {g * f: "unique"})
+        >>> d.conclusions[g * f] == FiniteSet("unique")
+        True
+
+        """
+        return self.args[1]
+
+    @property
+    def objects(self):
+        """
+        Returns the :class:`~.FiniteSet` of objects that appear in this
+        diagram.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism, Diagram
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g])
+        >>> d.objects
+        {Object("A"), Object("B"), Object("C")}
+
+        """
+        return self.args[2]
+
+    def hom(self, A, B):
+        """
+        Returns a 2-tuple of sets of morphisms between objects ``A`` and
+        ``B``: one set of morphisms listed as premises, and the other set
+        of morphisms listed as conclusions.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism, Diagram
+        >>> from sympy import pretty
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g], {g * f: "unique"})
+        >>> print(pretty(d.hom(A, C), use_unicode=False))
+        ({g*f:A-->C}, {g*f:A-->C})
+
+        See Also
+        ========
+        Object, Morphism
+        """
+        premises = EmptySet
+        conclusions = EmptySet
+
+        for morphism in self.premises.keys():
+            if (morphism.domain == A) and (morphism.codomain == B):
+                premises |= FiniteSet(morphism)
+        for morphism in self.conclusions.keys():
+            if (morphism.domain == A) and (morphism.codomain == B):
+                conclusions |= FiniteSet(morphism)
+
+        return (premises, conclusions)
+
+    def is_subdiagram(self, diagram):
+        """
+        Checks whether ``diagram`` is a subdiagram of ``self``.
+        Diagram `D'` is a subdiagram of `D` if all premises
+        (conclusions) of `D'` are contained in the premises
+        (conclusions) of `D`.  The morphisms contained
+        both in `D'` and `D` should have the same properties for `D'`
+        to be a subdiagram of `D`.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism, Diagram
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g], {g * f: "unique"})
+        >>> d1 = Diagram([f])
+        >>> d.is_subdiagram(d1)
+        True
+        >>> d1.is_subdiagram(d)
+        False
+        """
+        premises = all((m in self.premises) and
+                       (diagram.premises[m] == self.premises[m])
+                       for m in diagram.premises)
+        if not premises:
+            return False
+
+        conclusions = all((m in self.conclusions) and
+                          (diagram.conclusions[m] == self.conclusions[m])
+                          for m in diagram.conclusions)
+
+        # Premises is surely ``True`` here.
+        return conclusions
+
+    def subdiagram_from_objects(self, objects):
+        """
+        If ``objects`` is a subset of the objects of ``self``, returns
+        a diagram which has as premises all those premises of ``self``
+        which have a domains and codomains in ``objects``, likewise
+        for conclusions.  Properties are preserved.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism, Diagram
+        >>> from sympy import FiniteSet
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> d = Diagram([f, g], {f: "unique", g*f: "veryunique"})
+        >>> d1 = d.subdiagram_from_objects(FiniteSet(A, B))
+        >>> d1 == Diagram([f], {f: "unique"})
+        True
+        """
+        if not objects.is_subset(self.objects):
+            raise ValueError(
+                "Supplied objects should all belong to the diagram.")
+
+        new_premises = {}
+        for morphism, props in self.premises.items():
+            if ((sympify(objects.contains(morphism.domain)) is S.true) and
+                (sympify(objects.contains(morphism.codomain)) is S.true)):
+                new_premises[morphism] = props
+
+        new_conclusions = {}
+        for morphism, props in self.conclusions.items():
+            if ((sympify(objects.contains(morphism.domain)) is S.true) and
+                (sympify(objects.contains(morphism.codomain)) is S.true)):
+                new_conclusions[morphism] = props
+
+        return Diagram(new_premises, new_conclusions)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/diagram_drawing.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/diagram_drawing.py
new file mode 100644
index 0000000000000000000000000000000000000000..2a9b507cd86cf0e633b5abf7a0c9a353740af334
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/diagram_drawing.py
@@ -0,0 +1,2580 @@
+r"""
+This module contains the functionality to arrange the nodes of a
+diagram on an abstract grid, and then to produce a graphical
+representation of the grid.
+
+The currently supported back-ends are Xy-pic [Xypic].
+
+Layout Algorithm
+================
+
+This section provides an overview of the algorithms implemented in
+:class:`DiagramGrid` to lay out diagrams.
+
+The first step of the algorithm is the removal composite and identity
+morphisms which do not have properties in the supplied diagram.  The
+premises and conclusions of the diagram are then merged.
+
+The generic layout algorithm begins with the construction of the
+"skeleton" of the diagram.  The skeleton is an undirected graph which
+has the objects of the diagram as vertices and has an (undirected)
+edge between each pair of objects between which there exist morphisms.
+The direction of the morphisms does not matter at this stage.  The
+skeleton also includes an edge between each pair of vertices `A` and
+`C` such that there exists an object `B` which is connected via
+a morphism to `A`, and via a morphism to `C`.
+
+The skeleton constructed in this way has the property that every
+object is a vertex of a triangle formed by three edges of the
+skeleton.  This property lies at the base of the generic layout
+algorithm.
+
+After the skeleton has been constructed, the algorithm lists all
+triangles which can be formed.  Note that some triangles will not have
+all edges corresponding to morphisms which will actually be drawn.
+Triangles which have only one edge or less which will actually be
+drawn are immediately discarded.
+
+The list of triangles is sorted according to the number of edges which
+correspond to morphisms, then the triangle with the least number of such
+edges is selected.  One of such edges is picked and the corresponding
+objects are placed horizontally, on a grid.  This edge is recorded to
+be in the fringe.  The algorithm then finds a "welding" of a triangle
+to the fringe.  A welding is an edge in the fringe where a triangle
+could be attached.  If the algorithm succeeds in finding such a
+welding, it adds to the grid that vertex of the triangle which was not
+yet included in any edge in the fringe and records the two new edges in
+the fringe.  This process continues iteratively until all objects of
+the diagram has been placed or until no more weldings can be found.
+
+An edge is only removed from the fringe when a welding to this edge
+has been found, and there is no room around this edge to place
+another vertex.
+
+When no more weldings can be found, but there are still triangles
+left, the algorithm searches for a possibility of attaching one of the
+remaining triangles to the existing structure by a vertex.  If such a
+possibility is found, the corresponding edge of the found triangle is
+placed in the found space and the iterative process of welding
+triangles restarts.
+
+When logical groups are supplied, each of these groups is laid out
+independently.  Then a diagram is constructed in which groups are
+objects and any two logical groups between which there exist morphisms
+are connected via a morphism.  This diagram is laid out.  Finally,
+the grid which includes all objects of the initial diagram is
+constructed by replacing the cells which contain logical groups with
+the corresponding laid out grids, and by correspondingly expanding the
+rows and columns.
+
+The sequential layout algorithm begins by constructing the
+underlying undirected graph defined by the morphisms obtained after
+simplifying premises and conclusions and merging them (see above).
+The vertex with the minimal degree is then picked up and depth-first
+search is started from it.  All objects which are located at distance
+`n` from the root in the depth-first search tree, are positioned in
+the `n`-th column of the resulting grid.  The sequential layout will
+therefore attempt to lay the objects out along a line.
+
+References
+==========
+
+.. [Xypic] https://xy-pic.sourceforge.net/
+
+"""
+from sympy.categories import (CompositeMorphism, IdentityMorphism,
+                              NamedMorphism, Diagram)
+from sympy.core import Dict, Symbol, default_sort_key
+from sympy.printing.latex import latex
+from sympy.sets import FiniteSet
+from sympy.utilities.iterables import iterable
+from sympy.utilities.decorator import doctest_depends_on
+
+from itertools import chain
+
+
+__doctest_requires__ = {('preview_diagram',): 'pyglet'}
+
+
+class _GrowableGrid:
+    """
+    Holds a growable grid of objects.
+
+    Explanation
+    ===========
+
+    It is possible to append or prepend a row or a column to the grid
+    using the corresponding methods.  Prepending rows or columns has
+    the effect of changing the coordinates of the already existing
+    elements.
+
+    This class currently represents a naive implementation of the
+    functionality with little attempt at optimisation.
+    """
+    def __init__(self, width, height):
+        self._width = width
+        self._height = height
+
+        self._array = [[None for j in range(width)] for i in range(height)]
+
+    @property
+    def width(self):
+        return self._width
+
+    @property
+    def height(self):
+        return self._height
+
+    def __getitem__(self, i_j):
+        """
+        Returns the element located at in the i-th line and j-th
+        column.
+        """
+        i, j = i_j
+        return self._array[i][j]
+
+    def __setitem__(self, i_j, newvalue):
+        """
+        Sets the element located at in the i-th line and j-th
+        column.
+        """
+        i, j = i_j
+        self._array[i][j] = newvalue
+
+    def append_row(self):
+        """
+        Appends an empty row to the grid.
+        """
+        self._height += 1
+        self._array.append([None for j in range(self._width)])
+
+    def append_column(self):
+        """
+        Appends an empty column to the grid.
+        """
+        self._width += 1
+        for i in range(self._height):
+            self._array[i].append(None)
+
+    def prepend_row(self):
+        """
+        Prepends the grid with an empty row.
+        """
+        self._height += 1
+        self._array.insert(0, [None for j in range(self._width)])
+
+    def prepend_column(self):
+        """
+        Prepends the grid with an empty column.
+        """
+        self._width += 1
+        for i in range(self._height):
+            self._array[i].insert(0, None)
+
+
+class DiagramGrid:
+    r"""
+    Constructs and holds the fitting of the diagram into a grid.
+
+    Explanation
+    ===========
+
+    The mission of this class is to analyse the structure of the
+    supplied diagram and to place its objects on a grid such that,
+    when the objects and the morphisms are actually drawn, the diagram
+    would be "readable", in the sense that there will not be many
+    intersections of moprhisms.  This class does not perform any
+    actual drawing.  It does strive nevertheless to offer sufficient
+    metadata to draw a diagram.
+
+    Consider the following simple diagram.
+
+    >>> from sympy.categories import Object, NamedMorphism
+    >>> from sympy.categories import Diagram, DiagramGrid
+    >>> from sympy import pprint
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> diagram = Diagram([f, g])
+
+    The simplest way to have a diagram laid out is the following:
+
+    >>> grid = DiagramGrid(diagram)
+    >>> (grid.width, grid.height)
+    (2, 2)
+    >>> pprint(grid)
+    A  B
+    
+       C
+
+    Sometimes one sees the diagram as consisting of logical groups.
+    One can advise ``DiagramGrid`` as to such groups by employing the
+    ``groups`` keyword argument.
+
+    Consider the following diagram:
+
+    >>> D = Object("D")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> h = NamedMorphism(D, A, "h")
+    >>> k = NamedMorphism(D, B, "k")
+    >>> diagram = Diagram([f, g, h, k])
+
+    Lay it out with generic layout:
+
+    >>> grid = DiagramGrid(diagram)
+    >>> pprint(grid)
+    A  B  D
+    
+       C
+
+    Now, we can group the objects `A` and `D` to have them near one
+    another:
+
+    >>> grid = DiagramGrid(diagram, groups=[[A, D], B, C])
+    >>> pprint(grid)
+    B     C
+    
+    A  D
+
+    Note how the positioning of the other objects changes.
+
+    Further indications can be supplied to the constructor of
+    :class:`DiagramGrid` using keyword arguments.  The currently
+    supported hints are explained in the following paragraphs.
+
+    :class:`DiagramGrid` does not automatically guess which layout
+    would suit the supplied diagram better.  Consider, for example,
+    the following linear diagram:
+
+    >>> E = Object("E")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> h = NamedMorphism(C, D, "h")
+    >>> i = NamedMorphism(D, E, "i")
+    >>> diagram = Diagram([f, g, h, i])
+
+    When laid out with the generic layout, it does not get to look
+    linear:
+
+    >>> grid = DiagramGrid(diagram)
+    >>> pprint(grid)
+    A  B
+    
+       C  D
+    
+          E
+
+    To get it laid out in a line, use ``layout="sequential"``:
+
+    >>> grid = DiagramGrid(diagram, layout="sequential")
+    >>> pprint(grid)
+    A  B  C  D  E
+
+    One may sometimes need to transpose the resulting layout.  While
+    this can always be done by hand, :class:`DiagramGrid` provides a
+    hint for that purpose:
+
+    >>> grid = DiagramGrid(diagram, layout="sequential", transpose=True)
+    >>> pprint(grid)
+    A
+    
+    B
+    
+    C
+    
+    D
+    
+    E
+
+    Separate hints can also be provided for each group.  For an
+    example, refer to ``tests/test_drawing.py``, and see the different
+    ways in which the five lemma [FiveLemma] can be laid out.
+
+    See Also
+    ========
+
+    Diagram
+
+    References
+    ==========
+
+    .. [FiveLemma] https://en.wikipedia.org/wiki/Five_lemma
+    """
+    @staticmethod
+    def _simplify_morphisms(morphisms):
+        """
+        Given a dictionary mapping morphisms to their properties,
+        returns a new dictionary in which there are no morphisms which
+        do not have properties, and which are compositions of other
+        morphisms included in the dictionary.  Identities are dropped
+        as well.
+        """
+        newmorphisms = {}
+        for morphism, props in morphisms.items():
+            if isinstance(morphism, CompositeMorphism) and not props:
+                continue
+            elif isinstance(morphism, IdentityMorphism):
+                continue
+            else:
+                newmorphisms[morphism] = props
+        return newmorphisms
+
+    @staticmethod
+    def _merge_premises_conclusions(premises, conclusions):
+        """
+        Given two dictionaries of morphisms and their properties,
+        produces a single dictionary which includes elements from both
+        dictionaries.  If a morphism has some properties in premises
+        and also in conclusions, the properties in conclusions take
+        priority.
+        """
+        return dict(chain(premises.items(), conclusions.items()))
+
+    @staticmethod
+    def _juxtapose_edges(edge1, edge2):
+        """
+        If ``edge1`` and ``edge2`` have precisely one common endpoint,
+        returns an edge which would form a triangle with ``edge1`` and
+        ``edge2``.
+
+        If ``edge1`` and ``edge2`` do not have a common endpoint,
+        returns ``None``.
+
+        If ``edge1`` and ``edge`` are the same edge, returns ``None``.
+        """
+        intersection = edge1 & edge2
+        if len(intersection) != 1:
+            # The edges either have no common points or are equal.
+            return None
+
+        # The edges have a common endpoint.  Extract the different
+        # endpoints and set up the new edge.
+        return (edge1 - intersection) | (edge2 - intersection)
+
+    @staticmethod
+    def _add_edge_append(dictionary, edge, elem):
+        """
+        If ``edge`` is not in ``dictionary``, adds ``edge`` to the
+        dictionary and sets its value to ``[elem]``.  Otherwise
+        appends ``elem`` to the value of existing entry.
+
+        Note that edges are undirected, thus `(A, B) = (B, A)`.
+        """
+        if edge in dictionary:
+            dictionary[edge].append(elem)
+        else:
+            dictionary[edge] = [elem]
+
+    @staticmethod
+    def _build_skeleton(morphisms):
+        """
+        Creates a dictionary which maps edges to corresponding
+        morphisms.  Thus for a morphism `f:A\rightarrow B`, the edge
+        `(A, B)` will be associated with `f`.  This function also adds
+        to the list those edges which are formed by juxtaposition of
+        two edges already in the list.  These new edges are not
+        associated with any morphism and are only added to assure that
+        the diagram can be decomposed into triangles.
+        """
+        edges = {}
+        # Create edges for morphisms.
+        for morphism in morphisms:
+            DiagramGrid._add_edge_append(
+                edges, frozenset([morphism.domain, morphism.codomain]), morphism)
+
+        # Create new edges by juxtaposing existing edges.
+        edges1 = dict(edges)
+        for w in edges1:
+            for v in edges1:
+                wv = DiagramGrid._juxtapose_edges(w, v)
+                if wv and wv not in edges:
+                    edges[wv] = []
+
+        return edges
+
+    @staticmethod
+    def _list_triangles(edges):
+        """
+        Builds the set of triangles formed by the supplied edges.  The
+        triangles are arbitrary and need not be commutative.  A
+        triangle is a set that contains all three of its sides.
+        """
+        triangles = set()
+
+        for w in edges:
+            for v in edges:
+                wv = DiagramGrid._juxtapose_edges(w, v)
+                if wv and wv in edges:
+                    triangles.add(frozenset([w, v, wv]))
+
+        return triangles
+
+    @staticmethod
+    def _drop_redundant_triangles(triangles, skeleton):
+        """
+        Returns a list which contains only those triangles who have
+        morphisms associated with at least two edges.
+        """
+        return [tri for tri in triangles
+                if len([e for e in tri if skeleton[e]]) >= 2]
+
+    @staticmethod
+    def _morphism_length(morphism):
+        """
+        Returns the length of a morphism.  The length of a morphism is
+        the number of components it consists of.  A non-composite
+        morphism is of length 1.
+        """
+        if isinstance(morphism, CompositeMorphism):
+            return len(morphism.components)
+        else:
+            return 1
+
+    @staticmethod
+    def _compute_triangle_min_sizes(triangles, edges):
+        r"""
+        Returns a dictionary mapping triangles to their minimal sizes.
+        The minimal size of a triangle is the sum of maximal lengths
+        of morphisms associated to the sides of the triangle.  The
+        length of a morphism is the number of components it consists
+        of.  A non-composite morphism is of length 1.
+
+        Sorting triangles by this metric attempts to address two
+        aspects of layout.  For triangles with only simple morphisms
+        in the edge, this assures that triangles with all three edges
+        visible will get typeset after triangles with less visible
+        edges, which sometimes minimizes the necessity in diagonal
+        arrows.  For triangles with composite morphisms in the edges,
+        this assures that objects connected with shorter morphisms
+        will be laid out first, resulting the visual proximity of
+        those objects which are connected by shorter morphisms.
+        """
+        triangle_sizes = {}
+        for triangle in triangles:
+            size = 0
+            for e in triangle:
+                morphisms = edges[e]
+                if morphisms:
+                    size += max(DiagramGrid._morphism_length(m)
+                                for m in morphisms)
+            triangle_sizes[triangle] = size
+        return triangle_sizes
+
+    @staticmethod
+    def _triangle_objects(triangle):
+        """
+        Given a triangle, returns the objects included in it.
+        """
+        # A triangle is a frozenset of three two-element frozensets
+        # (the edges).  This chains the three edges together and
+        # creates a frozenset from the iterator, thus producing a
+        # frozenset of objects of the triangle.
+        return frozenset(chain(*tuple(triangle)))
+
+    @staticmethod
+    def _other_vertex(triangle, edge):
+        """
+        Given a triangle and an edge of it, returns the vertex which
+        opposes the edge.
+        """
+        # This gets the set of objects of the triangle and then
+        # subtracts the set of objects employed in ``edge`` to get the
+        # vertex opposite to ``edge``.
+        return list(DiagramGrid._triangle_objects(triangle) - set(edge))[0]
+
+    @staticmethod
+    def _empty_point(pt, grid):
+        """
+        Checks if the cell at coordinates ``pt`` is either empty or
+        out of the bounds of the grid.
+        """
+        if (pt[0] < 0) or (pt[1] < 0) or \
+           (pt[0] >= grid.height) or (pt[1] >= grid.width):
+            return True
+        return grid[pt] is None
+
+    @staticmethod
+    def _put_object(coords, obj, grid, fringe):
+        """
+        Places an object at the coordinate ``cords`` in ``grid``,
+        growing the grid and updating ``fringe``, if necessary.
+        Returns (0, 0) if no row or column has been prepended, (1, 0)
+        if a row was prepended, (0, 1) if a column was prepended and
+        (1, 1) if both a column and a row were prepended.
+        """
+        (i, j) = coords
+        offset = (0, 0)
+        if i == -1:
+            grid.prepend_row()
+            i = 0
+            offset = (1, 0)
+            for k in range(len(fringe)):
+                ((i1, j1), (i2, j2)) = fringe[k]
+                fringe[k] = ((i1 + 1, j1), (i2 + 1, j2))
+        elif i == grid.height:
+            grid.append_row()
+
+        if j == -1:
+            j = 0
+            offset = (offset[0], 1)
+            grid.prepend_column()
+            for k in range(len(fringe)):
+                ((i1, j1), (i2, j2)) = fringe[k]
+                fringe[k] = ((i1, j1 + 1), (i2, j2 + 1))
+        elif j == grid.width:
+            grid.append_column()
+
+        grid[i, j] = obj
+        return offset
+
+    @staticmethod
+    def _choose_target_cell(pt1, pt2, edge, obj, skeleton, grid):
+        """
+        Given two points, ``pt1`` and ``pt2``, and the welding edge
+        ``edge``, chooses one of the two points to place the opposing
+        vertex ``obj`` of the triangle.  If neither of this points
+        fits, returns ``None``.
+        """
+        pt1_empty = DiagramGrid._empty_point(pt1, grid)
+        pt2_empty = DiagramGrid._empty_point(pt2, grid)
+
+        if pt1_empty and pt2_empty:
+            # Both cells are empty.  Of these two, choose that cell
+            # which will assure that a visible edge of the triangle
+            # will be drawn perpendicularly to the current welding
+            # edge.
+
+            A = grid[edge[0]]
+
+            if skeleton.get(frozenset([A, obj])):
+                return pt1
+            else:
+                return pt2
+        if pt1_empty:
+            return pt1
+        elif pt2_empty:
+            return pt2
+        else:
+            return None
+
+    @staticmethod
+    def _find_triangle_to_weld(triangles, fringe, grid):
+        """
+        Finds, if possible, a triangle and an edge in the ``fringe`` to
+        which the triangle could be attached.  Returns the tuple
+        containing the triangle and the index of the corresponding
+        edge in the ``fringe``.
+
+        This function relies on the fact that objects are unique in
+        the diagram.
+        """
+        for triangle in triangles:
+            for (a, b) in fringe:
+                if frozenset([grid[a], grid[b]]) in triangle:
+                    return (triangle, (a, b))
+        return None
+
+    @staticmethod
+    def _weld_triangle(tri, welding_edge, fringe, grid, skeleton):
+        """
+        If possible, welds the triangle ``tri`` to ``fringe`` and
+        returns ``False``.  If this method encounters a degenerate
+        situation in the fringe and corrects it such that a restart of
+        the search is required, it returns ``True`` (which means that
+        a restart in finding triangle weldings is required).
+
+        A degenerate situation is a situation when an edge listed in
+        the fringe does not belong to the visual boundary of the
+        diagram.
+        """
+        a, b = welding_edge
+        target_cell = None
+
+        obj = DiagramGrid._other_vertex(tri, (grid[a], grid[b]))
+
+        # We now have a triangle and an edge where it can be welded to
+        # the fringe.  Decide where to place the other vertex of the
+        # triangle and check for degenerate situations en route.
+
+        if (abs(a[0] - b[0]) == 1) and (abs(a[1] - b[1]) == 1):
+            # A diagonal edge.
+            target_cell = (a[0], b[1])
+            if grid[target_cell]:
+                # That cell is already occupied.
+                target_cell = (b[0], a[1])
+
+                if grid[target_cell]:
+                    # Degenerate situation, this edge is not
+                    # on the actual fringe.  Correct the
+                    # fringe and go on.
+                    fringe.remove((a, b))
+                    return True
+        elif a[0] == b[0]:
+            # A horizontal edge.  We first attempt to build the
+            # triangle in the downward direction.
+
+            down_left = a[0] + 1, a[1]
+            down_right = a[0] + 1, b[1]
+
+            target_cell = DiagramGrid._choose_target_cell(
+                down_left, down_right, (a, b), obj, skeleton, grid)
+
+            if not target_cell:
+                # No room below this edge.  Check above.
+                up_left = a[0] - 1, a[1]
+                up_right = a[0] - 1, b[1]
+
+                target_cell = DiagramGrid._choose_target_cell(
+                    up_left, up_right, (a, b), obj, skeleton, grid)
+
+                if not target_cell:
+                    # This edge is not in the fringe, remove it
+                    # and restart.
+                    fringe.remove((a, b))
+                    return True
+        elif a[1] == b[1]:
+            # A vertical edge.  We will attempt to place the other
+            # vertex of the triangle to the right of this edge.
+            right_up = a[0], a[1] + 1
+            right_down = b[0], a[1] + 1
+
+            target_cell = DiagramGrid._choose_target_cell(
+                right_up, right_down, (a, b), obj, skeleton, grid)
+
+            if not target_cell:
+                # No room to the left.  See what's to the right.
+                left_up = a[0], a[1] - 1
+                left_down = b[0], a[1] - 1
+
+                target_cell = DiagramGrid._choose_target_cell(
+                    left_up, left_down, (a, b), obj, skeleton, grid)
+
+                if not target_cell:
+                    # This edge is not in the fringe, remove it
+                    # and restart.
+                    fringe.remove((a, b))
+                    return True
+
+        # We now know where to place the other vertex of the
+        # triangle.
+        offset = DiagramGrid._put_object(target_cell, obj, grid, fringe)
+
+        # Take care of the displacement of coordinates if a row or
+        # a column was prepended.
+        target_cell = (target_cell[0] + offset[0],
+                       target_cell[1] + offset[1])
+        a = (a[0] + offset[0], a[1] + offset[1])
+        b = (b[0] + offset[0], b[1] + offset[1])
+
+        fringe.extend([(a, target_cell), (b, target_cell)])
+
+        # No restart is required.
+        return False
+
+    @staticmethod
+    def _triangle_key(tri, triangle_sizes):
+        """
+        Returns a key for the supplied triangle.  It should be the
+        same independently of the hash randomisation.
+        """
+        objects = sorted(
+            DiagramGrid._triangle_objects(tri), key=default_sort_key)
+        return (triangle_sizes[tri], default_sort_key(objects))
+
+    @staticmethod
+    def _pick_root_edge(tri, skeleton):
+        """
+        For a given triangle always picks the same root edge.  The
+        root edge is the edge that will be placed first on the grid.
+        """
+        candidates = [sorted(e, key=default_sort_key)
+                      for e in tri if skeleton[e]]
+        sorted_candidates = sorted(candidates, key=default_sort_key)
+        # Don't forget to assure the proper ordering of the vertices
+        # in this edge.
+        return tuple(sorted(sorted_candidates[0], key=default_sort_key))
+
+    @staticmethod
+    def _drop_irrelevant_triangles(triangles, placed_objects):
+        """
+        Returns only those triangles whose set of objects is not
+        completely included in ``placed_objects``.
+        """
+        return [tri for tri in triangles if not placed_objects.issuperset(
+            DiagramGrid._triangle_objects(tri))]
+
+    @staticmethod
+    def _grow_pseudopod(triangles, fringe, grid, skeleton, placed_objects):
+        """
+        Starting from an object in the existing structure on the ``grid``,
+        adds an edge to which a triangle from ``triangles`` could be
+        welded.  If this method has found a way to do so, it returns
+        the object it has just added.
+
+        This method should be applied when ``_weld_triangle`` cannot
+        find weldings any more.
+        """
+        for i in range(grid.height):
+            for j in range(grid.width):
+                obj = grid[i, j]
+                if not obj:
+                    continue
+
+                # Here we need to choose a triangle which has only
+                # ``obj`` in common with the existing structure.  The
+                # situations when this is not possible should be
+                # handled elsewhere.
+
+                def good_triangle(tri):
+                    objs = DiagramGrid._triangle_objects(tri)
+                    return obj in objs and \
+                        placed_objects & (objs - {obj}) == set()
+
+                tris = [tri for tri in triangles if good_triangle(tri)]
+                if not tris:
+                    # This object is not interesting.
+                    continue
+
+                # Pick the "simplest" of the triangles which could be
+                # attached.  Remember that the list of triangles is
+                # sorted according to their "simplicity" (see
+                # _compute_triangle_min_sizes for the metric).
+                #
+                # Note that ``tris`` are sequentially built from
+                # ``triangles``, so we don't have to worry about hash
+                # randomisation.
+                tri = tris[0]
+
+                # We have found a triangle which could be attached to
+                # the existing structure by a vertex.
+
+                candidates = sorted([e for e in tri if skeleton[e]],
+                                    key=lambda e: FiniteSet(*e).sort_key())
+                edges = [e for e in candidates if obj in e]
+
+                # Note that a meaningful edge (i.e., and edge that is
+                # associated with a morphism) containing ``obj``
+                # always exists.  That's because all triangles are
+                # guaranteed to have at least two meaningful edges.
+                # See _drop_redundant_triangles.
+
+                # Get the object at the other end of the edge.
+                edge = edges[0]
+                other_obj = tuple(edge - frozenset([obj]))[0]
+
+                # Now check for free directions.  When checking for
+                # free directions, prefer the horizontal and vertical
+                # directions.
+                neighbours = [(i - 1, j), (i, j + 1), (i + 1, j), (i, j - 1),
+                              (i - 1, j - 1), (i - 1, j + 1), (i + 1, j - 1), (i + 1, j + 1)]
+
+                for pt in neighbours:
+                    if DiagramGrid._empty_point(pt, grid):
+                        # We have a found a place to grow the
+                        # pseudopod into.
+                        offset = DiagramGrid._put_object(
+                            pt, other_obj, grid, fringe)
+
+                        i += offset[0]
+                        j += offset[1]
+                        pt = (pt[0] + offset[0], pt[1] + offset[1])
+                        fringe.append(((i, j), pt))
+
+                        return other_obj
+
+        # This diagram is actually cooler that I can handle.  Fail cowardly.
+        return None
+
+    @staticmethod
+    def _handle_groups(diagram, groups, merged_morphisms, hints):
+        """
+        Given the slightly preprocessed morphisms of the diagram,
+        produces a grid laid out according to ``groups``.
+
+        If a group has hints, it is laid out with those hints only,
+        without any influence from ``hints``.  Otherwise, it is laid
+        out with ``hints``.
+        """
+        def lay_out_group(group, local_hints):
+            """
+            If ``group`` is a set of objects, uses a ``DiagramGrid``
+            to lay it out and returns the grid.  Otherwise returns the
+            object (i.e., ``group``).  If ``local_hints`` is not
+            empty, it is supplied to ``DiagramGrid`` as the dictionary
+            of hints.  Otherwise, the ``hints`` argument of
+            ``_handle_groups`` is used.
+            """
+            if isinstance(group, FiniteSet):
+                # Set up the corresponding object-to-group
+                # mappings.
+                for obj in group:
+                    obj_groups[obj] = group
+
+                # Lay out the current group.
+                if local_hints:
+                    groups_grids[group] = DiagramGrid(
+                        diagram.subdiagram_from_objects(group), **local_hints)
+                else:
+                    groups_grids[group] = DiagramGrid(
+                        diagram.subdiagram_from_objects(group), **hints)
+            else:
+                obj_groups[group] = group
+
+        def group_to_finiteset(group):
+            """
+            Converts ``group`` to a :class:``FiniteSet`` if it is an
+            iterable.
+            """
+            if iterable(group):
+                return FiniteSet(*group)
+            else:
+                return group
+
+        obj_groups = {}
+        groups_grids = {}
+
+        # We would like to support various containers to represent
+        # groups.  To achieve that, before laying each group out, it
+        # should be converted to a FiniteSet, because that is what the
+        # following code expects.
+
+        if isinstance(groups, (dict, Dict)):
+            finiteset_groups = {}
+            for group, local_hints in groups.items():
+                finiteset_group = group_to_finiteset(group)
+                finiteset_groups[finiteset_group] = local_hints
+                lay_out_group(group, local_hints)
+            groups = finiteset_groups
+        else:
+            finiteset_groups = []
+            for group in groups:
+                finiteset_group = group_to_finiteset(group)
+                finiteset_groups.append(finiteset_group)
+                lay_out_group(finiteset_group, None)
+            groups = finiteset_groups
+
+        new_morphisms = []
+        for morphism in merged_morphisms:
+            dom = obj_groups[morphism.domain]
+            cod = obj_groups[morphism.codomain]
+            # Note that we are not really interested in morphisms
+            # which do not employ two different groups, because
+            # these do not influence the layout.
+            if dom != cod:
+                # These are essentially unnamed morphisms; they are
+                # not going to mess in the final layout.  By giving
+                # them the same names, we avoid unnecessary
+                # duplicates.
+                new_morphisms.append(NamedMorphism(dom, cod, "dummy"))
+
+        # Lay out the new diagram.  Since these are dummy morphisms,
+        # properties and conclusions are irrelevant.
+        top_grid = DiagramGrid(Diagram(new_morphisms))
+
+        # We now have to substitute the groups with the corresponding
+        # grids, laid out at the beginning of this function.  Compute
+        # the size of each row and column in the grid, so that all
+        # nested grids fit.
+
+        def group_size(group):
+            """
+            For the supplied group (or object, eventually), returns
+            the size of the cell that will hold this group (object).
+            """
+            if group in groups_grids:
+                grid = groups_grids[group]
+                return (grid.height, grid.width)
+            else:
+                return (1, 1)
+
+        row_heights = [max(group_size(top_grid[i, j])[0]
+                           for j in range(top_grid.width))
+                       for i in range(top_grid.height)]
+
+        column_widths = [max(group_size(top_grid[i, j])[1]
+                             for i in range(top_grid.height))
+                         for j in range(top_grid.width)]
+
+        grid = _GrowableGrid(sum(column_widths), sum(row_heights))
+
+        real_row = 0
+        real_column = 0
+        for logical_row in range(top_grid.height):
+            for logical_column in range(top_grid.width):
+                obj = top_grid[logical_row, logical_column]
+
+                if obj in groups_grids:
+                    # This is a group.  Copy the corresponding grid in
+                    # place.
+                    local_grid = groups_grids[obj]
+                    for i in range(local_grid.height):
+                        for j in range(local_grid.width):
+                            grid[real_row + i,
+                                real_column + j] = local_grid[i, j]
+                else:
+                    # This is an object.  Just put it there.
+                    grid[real_row, real_column] = obj
+
+                real_column += column_widths[logical_column]
+            real_column = 0
+            real_row += row_heights[logical_row]
+
+        return grid
+
+    @staticmethod
+    def _generic_layout(diagram, merged_morphisms):
+        """
+        Produces the generic layout for the supplied diagram.
+        """
+        all_objects = set(diagram.objects)
+        if len(all_objects) == 1:
+            # There only one object in the diagram, just put in on 1x1
+            # grid.
+            grid = _GrowableGrid(1, 1)
+            grid[0, 0] = tuple(all_objects)[0]
+            return grid
+
+        skeleton = DiagramGrid._build_skeleton(merged_morphisms)
+
+        grid = _GrowableGrid(2, 1)
+
+        if len(skeleton) == 1:
+            # This diagram contains only one morphism.  Draw it
+            # horizontally.
+            objects = sorted(all_objects, key=default_sort_key)
+            grid[0, 0] = objects[0]
+            grid[0, 1] = objects[1]
+
+            return grid
+
+        triangles = DiagramGrid._list_triangles(skeleton)
+        triangles = DiagramGrid._drop_redundant_triangles(triangles, skeleton)
+        triangle_sizes = DiagramGrid._compute_triangle_min_sizes(
+            triangles, skeleton)
+
+        triangles = sorted(triangles, key=lambda tri:
+                           DiagramGrid._triangle_key(tri, triangle_sizes))
+
+        # Place the first edge on the grid.
+        root_edge = DiagramGrid._pick_root_edge(triangles[0], skeleton)
+        grid[0, 0], grid[0, 1] = root_edge
+        fringe = [((0, 0), (0, 1))]
+
+        # Record which objects we now have on the grid.
+        placed_objects = set(root_edge)
+
+        while placed_objects != all_objects:
+            welding = DiagramGrid._find_triangle_to_weld(
+                triangles, fringe, grid)
+
+            if welding:
+                (triangle, welding_edge) = welding
+
+                restart_required = DiagramGrid._weld_triangle(
+                    triangle, welding_edge, fringe, grid, skeleton)
+                if restart_required:
+                    continue
+
+                placed_objects.update(
+                    DiagramGrid._triangle_objects(triangle))
+            else:
+                # No more weldings found.  Try to attach triangles by
+                # vertices.
+                new_obj = DiagramGrid._grow_pseudopod(
+                    triangles, fringe, grid, skeleton, placed_objects)
+
+                if not new_obj:
+                    # No more triangles can be attached, not even by
+                    # the edge.  We will set up a new diagram out of
+                    # what has been left, laid it out independently,
+                    # and then attach it to this one.
+
+                    remaining_objects = all_objects - placed_objects
+
+                    remaining_diagram = diagram.subdiagram_from_objects(
+                        FiniteSet(*remaining_objects))
+                    remaining_grid = DiagramGrid(remaining_diagram)
+
+                    # Now, let's glue ``remaining_grid`` to ``grid``.
+                    final_width = grid.width + remaining_grid.width
+                    final_height = max(grid.height, remaining_grid.height)
+                    final_grid = _GrowableGrid(final_width, final_height)
+
+                    for i in range(grid.width):
+                        for j in range(grid.height):
+                            final_grid[i, j] = grid[i, j]
+
+                    start_j = grid.width
+                    for i in range(remaining_grid.height):
+                        for j in range(remaining_grid.width):
+                            final_grid[i, start_j + j] = remaining_grid[i, j]
+
+                    return final_grid
+
+                placed_objects.add(new_obj)
+
+            triangles = DiagramGrid._drop_irrelevant_triangles(
+                triangles, placed_objects)
+
+        return grid
+
+    @staticmethod
+    def _get_undirected_graph(objects, merged_morphisms):
+        """
+        Given the objects and the relevant morphisms of a diagram,
+        returns the adjacency lists of the underlying undirected
+        graph.
+        """
+        adjlists = {obj: [] for obj in objects}
+
+        for morphism in merged_morphisms:
+            adjlists[morphism.domain].append(morphism.codomain)
+            adjlists[morphism.codomain].append(morphism.domain)
+
+        # Assure that the objects in the adjacency list are always in
+        # the same order.
+        for obj in adjlists.keys():
+            adjlists[obj].sort(key=default_sort_key)
+
+        return adjlists
+
+    @staticmethod
+    def _sequential_layout(diagram, merged_morphisms):
+        r"""
+        Lays out the diagram in "sequential" layout.  This method
+        will attempt to produce a result as close to a line as
+        possible.  For linear diagrams, the result will actually be a
+        line.
+        """
+        objects = diagram.objects
+        sorted_objects = sorted(objects, key=default_sort_key)
+
+        # Set up the adjacency lists of the underlying undirected
+        # graph of ``merged_morphisms``.
+        adjlists = DiagramGrid._get_undirected_graph(objects, merged_morphisms)
+
+        root = min(sorted_objects, key=lambda x: len(adjlists[x]))
+        grid = _GrowableGrid(1, 1)
+        grid[0, 0] = root
+
+        placed_objects = {root}
+
+        def place_objects(pt, placed_objects):
+            """
+            Does depth-first search in the underlying graph of the
+            diagram and places the objects en route.
+            """
+            # We will start placing new objects from here.
+            new_pt = (pt[0], pt[1] + 1)
+
+            for adjacent_obj in adjlists[grid[pt]]:
+                if adjacent_obj in placed_objects:
+                    # This object has already been placed.
+                    continue
+
+                DiagramGrid._put_object(new_pt, adjacent_obj, grid, [])
+                placed_objects.add(adjacent_obj)
+                placed_objects.update(place_objects(new_pt, placed_objects))
+
+                new_pt = (new_pt[0] + 1, new_pt[1])
+
+            return placed_objects
+
+        place_objects((0, 0), placed_objects)
+
+        return grid
+
+    @staticmethod
+    def _drop_inessential_morphisms(merged_morphisms):
+        r"""
+        Removes those morphisms which should appear in the diagram,
+        but which have no relevance to object layout.
+
+        Currently this removes "loop" morphisms: the non-identity
+        morphisms with the same domains and codomains.
+        """
+        morphisms = [m for m in merged_morphisms if m.domain != m.codomain]
+        return morphisms
+
+    @staticmethod
+    def _get_connected_components(objects, merged_morphisms):
+        """
+        Given a container of morphisms, returns a list of connected
+        components formed by these morphisms.  A connected component
+        is represented by a diagram consisting of the corresponding
+        morphisms.
+        """
+        component_index = {}
+        for o in objects:
+            component_index[o] = None
+
+        # Get the underlying undirected graph of the diagram.
+        adjlist = DiagramGrid._get_undirected_graph(objects, merged_morphisms)
+
+        def traverse_component(object, current_index):
+            """
+            Does a depth-first search traversal of the component
+            containing ``object``.
+            """
+            component_index[object] = current_index
+            for o in adjlist[object]:
+                if component_index[o] is None:
+                    traverse_component(o, current_index)
+
+        # Traverse all components.
+        current_index = 0
+        for o in adjlist:
+            if component_index[o] is None:
+                traverse_component(o, current_index)
+                current_index += 1
+
+        # List the objects of the components.
+        component_objects = [[] for i in range(current_index)]
+        for o, idx in component_index.items():
+            component_objects[idx].append(o)
+
+        # Finally, list the morphisms belonging to each component.
+        #
+        # Note: If some objects are isolated, they will not get any
+        # morphisms at this stage, and since the layout algorithm
+        # relies, we are essentially going to lose this object.
+        # Therefore, check if there are isolated objects and, for each
+        # of them, provide the trivial identity morphism.  It will get
+        # discarded later, but the object will be there.
+
+        component_morphisms = []
+        for component in component_objects:
+            current_morphisms = {}
+            for m in merged_morphisms:
+                if (m.domain in component) and (m.codomain in component):
+                    current_morphisms[m] = merged_morphisms[m]
+
+            if len(component) == 1:
+                # Let's add an identity morphism, for the sake of
+                # surely having morphisms in this component.
+                current_morphisms[IdentityMorphism(component[0])] = FiniteSet()
+
+            component_morphisms.append(Diagram(current_morphisms))
+
+        return component_morphisms
+
+    def __init__(self, diagram, groups=None, **hints):
+        premises = DiagramGrid._simplify_morphisms(diagram.premises)
+        conclusions = DiagramGrid._simplify_morphisms(diagram.conclusions)
+        all_merged_morphisms = DiagramGrid._merge_premises_conclusions(
+            premises, conclusions)
+        merged_morphisms = DiagramGrid._drop_inessential_morphisms(
+            all_merged_morphisms)
+
+        # Store the merged morphisms for later use.
+        self._morphisms = all_merged_morphisms
+
+        components = DiagramGrid._get_connected_components(
+            diagram.objects, all_merged_morphisms)
+
+        if groups and (groups != diagram.objects):
+            # Lay out the diagram according to the groups.
+            self._grid = DiagramGrid._handle_groups(
+                diagram, groups, merged_morphisms, hints)
+        elif len(components) > 1:
+            # Note that we check for connectedness _before_ checking
+            # the layout hints because the layout strategies don't
+            # know how to deal with disconnected diagrams.
+
+            # The diagram is disconnected.  Lay out the components
+            # independently.
+            grids = []
+
+            # Sort the components to eventually get the grids arranged
+            # in a fixed, hash-independent order.
+            components = sorted(components, key=default_sort_key)
+
+            for component in components:
+                grid = DiagramGrid(component, **hints)
+                grids.append(grid)
+
+            # Throw the grids together, in a line.
+            total_width = sum(g.width for g in grids)
+            total_height = max(g.height for g in grids)
+
+            grid = _GrowableGrid(total_width, total_height)
+            start_j = 0
+            for g in grids:
+                for i in range(g.height):
+                    for j in range(g.width):
+                        grid[i, start_j + j] = g[i, j]
+
+                start_j += g.width
+
+            self._grid = grid
+        elif "layout" in hints:
+            if hints["layout"] == "sequential":
+                self._grid = DiagramGrid._sequential_layout(
+                    diagram, merged_morphisms)
+        else:
+            self._grid = DiagramGrid._generic_layout(diagram, merged_morphisms)
+
+        if hints.get("transpose"):
+            # Transpose the resulting grid.
+            grid = _GrowableGrid(self._grid.height, self._grid.width)
+            for i in range(self._grid.height):
+                for j in range(self._grid.width):
+                    grid[j, i] = self._grid[i, j]
+            self._grid = grid
+
+    @property
+    def width(self):
+        """
+        Returns the number of columns in this diagram layout.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import Diagram, DiagramGrid
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> diagram = Diagram([f, g])
+        >>> grid = DiagramGrid(diagram)
+        >>> grid.width
+        2
+
+        """
+        return self._grid.width
+
+    @property
+    def height(self):
+        """
+        Returns the number of rows in this diagram layout.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import Diagram, DiagramGrid
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> diagram = Diagram([f, g])
+        >>> grid = DiagramGrid(diagram)
+        >>> grid.height
+        2
+
+        """
+        return self._grid.height
+
+    def __getitem__(self, i_j):
+        """
+        Returns the object placed in the row ``i`` and column ``j``.
+        The indices are 0-based.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import Diagram, DiagramGrid
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> diagram = Diagram([f, g])
+        >>> grid = DiagramGrid(diagram)
+        >>> (grid[0, 0], grid[0, 1])
+        (Object("A"), Object("B"))
+        >>> (grid[1, 0], grid[1, 1])
+        (None, Object("C"))
+
+        """
+        i, j = i_j
+        return self._grid[i, j]
+
+    @property
+    def morphisms(self):
+        """
+        Returns those morphisms (and their properties) which are
+        sufficiently meaningful to be drawn.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import Diagram, DiagramGrid
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> diagram = Diagram([f, g])
+        >>> grid = DiagramGrid(diagram)
+        >>> grid.morphisms
+        {NamedMorphism(Object("A"), Object("B"), "f"): EmptySet,
+        NamedMorphism(Object("B"), Object("C"), "g"): EmptySet}
+
+        """
+        return self._morphisms
+
+    def __str__(self):
+        """
+        Produces a string representation of this class.
+
+        This method returns a string representation of the underlying
+        list of lists of objects.
+
+        Examples
+        ========
+
+        >>> from sympy.categories import Object, NamedMorphism
+        >>> from sympy.categories import Diagram, DiagramGrid
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> diagram = Diagram([f, g])
+        >>> grid = DiagramGrid(diagram)
+        >>> print(grid)
+        [[Object("A"), Object("B")],
+        [None, Object("C")]]
+
+        """
+        return repr(self._grid._array)
+
+
+class ArrowStringDescription:
+    r"""
+    Stores the information necessary for producing an Xy-pic
+    description of an arrow.
+
+    The principal goal of this class is to abstract away the string
+    representation of an arrow and to also provide the functionality
+    to produce the actual Xy-pic string.
+
+    ``unit`` sets the unit which will be used to specify the amount of
+    curving and other distances.  ``horizontal_direction`` should be a
+    string of ``"r"`` or ``"l"`` specifying the horizontal offset of the
+    target cell of the arrow relatively to the current one.
+    ``vertical_direction`` should  specify the vertical offset using a
+    series of either ``"d"`` or ``"u"``.  ``label_position`` should be
+    either ``"^"``, ``"_"``,  or ``"|"`` to specify that the label should
+    be positioned above the arrow, below the arrow or just over the arrow,
+    in a break.  Note that the notions "above" and "below" are relative
+    to arrow direction.  ``label`` stores the morphism label.
+
+    This works as follows (disregard the yet unexplained arguments):
+
+    >>> from sympy.categories.diagram_drawing import ArrowStringDescription
+    >>> astr = ArrowStringDescription(
+    ... unit="mm", curving=None, curving_amount=None,
+    ... looping_start=None, looping_end=None, horizontal_direction="d",
+    ... vertical_direction="r", label_position="_", label="f")
+    >>> print(str(astr))
+    \ar[dr]_{f}
+
+    ``curving`` should be one of ``"^"``, ``"_"`` to specify in which
+    direction the arrow is going to curve. ``curving_amount`` is a number
+    describing how many ``unit``'s the morphism is going to curve:
+
+    >>> astr = ArrowStringDescription(
+    ... unit="mm", curving="^", curving_amount=12,
+    ... looping_start=None, looping_end=None, horizontal_direction="d",
+    ... vertical_direction="r", label_position="_", label="f")
+    >>> print(str(astr))
+    \ar@/^12mm/[dr]_{f}
+
+    ``looping_start`` and ``looping_end`` are currently only used for
+    loop morphisms, those which have the same domain and codomain.
+    These two attributes should store a valid Xy-pic direction and
+    specify, correspondingly, the direction the arrow gets out into
+    and the direction the arrow gets back from:
+
+    >>> astr = ArrowStringDescription(
+    ... unit="mm", curving=None, curving_amount=None,
+    ... looping_start="u", looping_end="l", horizontal_direction="",
+    ... vertical_direction="", label_position="_", label="f")
+    >>> print(str(astr))
+    \ar@(u,l)[]_{f}
+
+    ``label_displacement`` controls how far the arrow label is from
+    the ends of the arrow.  For example, to position the arrow label
+    near the arrow head, use ">":
+
+    >>> astr = ArrowStringDescription(
+    ... unit="mm", curving="^", curving_amount=12,
+    ... looping_start=None, looping_end=None, horizontal_direction="d",
+    ... vertical_direction="r", label_position="_", label="f")
+    >>> astr.label_displacement = ">"
+    >>> print(str(astr))
+    \ar@/^12mm/[dr]_>{f}
+
+    Finally, ``arrow_style`` is used to specify the arrow style.  To
+    get a dashed arrow, for example, use "{-->}" as arrow style:
+
+    >>> astr = ArrowStringDescription(
+    ... unit="mm", curving="^", curving_amount=12,
+    ... looping_start=None, looping_end=None, horizontal_direction="d",
+    ... vertical_direction="r", label_position="_", label="f")
+    >>> astr.arrow_style = "{-->}"
+    >>> print(str(astr))
+    \ar@/^12mm/@{-->}[dr]_{f}
+
+    Notes
+    =====
+
+    Instances of :class:`ArrowStringDescription` will be constructed
+    by :class:`XypicDiagramDrawer` and provided for further use in
+    formatters.  The user is not expected to construct instances of
+    :class:`ArrowStringDescription` themselves.
+
+    To be able to properly utilise this class, the reader is encouraged
+    to checkout the Xy-pic user guide, available at [Xypic].
+
+    See Also
+    ========
+
+    XypicDiagramDrawer
+
+    References
+    ==========
+
+    .. [Xypic] https://xy-pic.sourceforge.net/
+    """
+    def __init__(self, unit, curving, curving_amount, looping_start,
+                 looping_end, horizontal_direction, vertical_direction,
+                 label_position, label):
+        self.unit = unit
+        self.curving = curving
+        self.curving_amount = curving_amount
+        self.looping_start = looping_start
+        self.looping_end = looping_end
+        self.horizontal_direction = horizontal_direction
+        self.vertical_direction = vertical_direction
+        self.label_position = label_position
+        self.label = label
+
+        self.label_displacement = ""
+        self.arrow_style = ""
+
+        # This flag shows that the position of the label of this
+        # morphism was set while typesetting a curved morphism and
+        # should not be modified later.
+        self.forced_label_position = False
+
+    def __str__(self):
+        if self.curving:
+            curving_str = "@/%s%d%s/" % (self.curving, self.curving_amount,
+                                         self.unit)
+        else:
+            curving_str = ""
+
+        if self.looping_start and self.looping_end:
+            looping_str = "@(%s,%s)" % (self.looping_start, self.looping_end)
+        else:
+            looping_str = ""
+
+        if self.arrow_style:
+
+            style_str = "@" + self.arrow_style
+        else:
+            style_str = ""
+
+        return "\\ar%s%s%s[%s%s]%s%s{%s}" % \
+               (curving_str, looping_str, style_str, self.horizontal_direction,
+                self.vertical_direction, self.label_position,
+                self.label_displacement, self.label)
+
+
+class XypicDiagramDrawer:
+    r"""
+    Given a :class:`~.Diagram` and the corresponding
+    :class:`DiagramGrid`, produces the Xy-pic representation of the
+    diagram.
+
+    The most important method in this class is ``draw``.  Consider the
+    following triangle diagram:
+
+    >>> from sympy.categories import Object, NamedMorphism, Diagram
+    >>> from sympy.categories import DiagramGrid, XypicDiagramDrawer
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> diagram = Diagram([f, g], {g * f: "unique"})
+
+    To draw this diagram, its objects need to be laid out with a
+    :class:`DiagramGrid`::
+
+    >>> grid = DiagramGrid(diagram)
+
+    Finally, the drawing:
+
+    >>> drawer = XypicDiagramDrawer()
+    >>> print(drawer.draw(diagram, grid))
+    \xymatrix{
+    A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\
+    C &
+    }
+
+    For further details see the docstring of this method.
+
+    To control the appearance of the arrows, formatters are used.  The
+    dictionary ``arrow_formatters`` maps morphisms to formatter
+    functions.  A formatter is accepts an
+    :class:`ArrowStringDescription` and is allowed to modify any of
+    the arrow properties exposed thereby.  For example, to have all
+    morphisms with the property ``unique`` appear as dashed arrows,
+    and to have their names prepended with `\exists !`, the following
+    should be done:
+
+    >>> def formatter(astr):
+    ...   astr.label = r"\exists !" + astr.label
+    ...   astr.arrow_style = "{-->}"
+    >>> drawer.arrow_formatters["unique"] = formatter
+    >>> print(drawer.draw(diagram, grid))
+    \xymatrix{
+    A \ar@{-->}[d]_{\exists !g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\
+    C &
+    }
+
+    To modify the appearance of all arrows in the diagram, set
+    ``default_arrow_formatter``.  For example, to place all morphism
+    labels a little bit farther from the arrow head so that they look
+    more centred, do as follows:
+
+    >>> def default_formatter(astr):
+    ...   astr.label_displacement = "(0.45)"
+    >>> drawer.default_arrow_formatter = default_formatter
+    >>> print(drawer.draw(diagram, grid))
+    \xymatrix{
+    A \ar@{-->}[d]_(0.45){\exists !g\circ f} \ar[r]^(0.45){f} & B \ar[ld]^(0.45){g} \\
+    C &
+    }
+
+    In some diagrams some morphisms are drawn as curved arrows.
+    Consider the following diagram:
+
+    >>> D = Object("D")
+    >>> E = Object("E")
+    >>> h = NamedMorphism(D, A, "h")
+    >>> k = NamedMorphism(D, B, "k")
+    >>> diagram = Diagram([f, g, h, k])
+    >>> grid = DiagramGrid(diagram)
+    >>> drawer = XypicDiagramDrawer()
+    >>> print(drawer.draw(diagram, grid))
+    \xymatrix{
+    A \ar[r]_{f} & B \ar[d]^{g} & D \ar[l]^{k} \ar@/_3mm/[ll]_{h} \\
+    & C &
+    }
+
+    To control how far the morphisms are curved by default, one can
+    use the ``unit`` and ``default_curving_amount`` attributes:
+
+    >>> drawer.unit = "cm"
+    >>> drawer.default_curving_amount = 1
+    >>> print(drawer.draw(diagram, grid))
+    \xymatrix{
+    A \ar[r]_{f} & B \ar[d]^{g} & D \ar[l]^{k} \ar@/_1cm/[ll]_{h} \\
+    & C &
+    }
+
+    In some diagrams, there are multiple curved morphisms between the
+    same two objects.  To control by how much the curving changes
+    between two such successive morphisms, use
+    ``default_curving_step``:
+
+    >>> drawer.default_curving_step = 1
+    >>> h1 = NamedMorphism(A, D, "h1")
+    >>> diagram = Diagram([f, g, h, k, h1])
+    >>> grid = DiagramGrid(diagram)
+    >>> print(drawer.draw(diagram, grid))
+    \xymatrix{
+    A \ar[r]_{f} \ar@/^1cm/[rr]^{h_{1}} & B \ar[d]^{g} & D \ar[l]^{k} \ar@/_2cm/[ll]_{h} \\
+    & C &
+    }
+
+    The default value of ``default_curving_step`` is 4 units.
+
+    See Also
+    ========
+
+    draw, ArrowStringDescription
+    """
+    def __init__(self):
+        self.unit = "mm"
+        self.default_curving_amount = 3
+        self.default_curving_step = 4
+
+        # This dictionary maps properties to the corresponding arrow
+        # formatters.
+        self.arrow_formatters = {}
+
+        # This is the default arrow formatter which will be applied to
+        # each arrow independently of its properties.
+        self.default_arrow_formatter = None
+
+    @staticmethod
+    def _process_loop_morphism(i, j, grid, morphisms_str_info, object_coords):
+        """
+        Produces the information required for constructing the string
+        representation of a loop morphism.  This function is invoked
+        from ``_process_morphism``.
+
+        See Also
+        ========
+
+        _process_morphism
+        """
+        curving = ""
+        label_pos = "^"
+        looping_start = ""
+        looping_end = ""
+
+        # This is a loop morphism.  Count how many morphisms stick
+        # in each of the four quadrants.  Note that straight
+        # vertical and horizontal morphisms count in two quadrants
+        # at the same time (i.e., a morphism going up counts both
+        # in the first and the second quadrants).
+
+        # The usual numbering (counterclockwise) of quadrants
+        # applies.
+        quadrant = [0, 0, 0, 0]
+
+        obj = grid[i, j]
+
+        for m, m_str_info in morphisms_str_info.items():
+            if (m.domain == obj) and (m.codomain == obj):
+                # That's another loop morphism.  Check how it
+                # loops and mark the corresponding quadrants as
+                # busy.
+                (l_s, l_e) = (m_str_info.looping_start, m_str_info.looping_end)
+
+                if (l_s, l_e) == ("r", "u"):
+                    quadrant[0] += 1
+                elif (l_s, l_e) == ("u", "l"):
+                    quadrant[1] += 1
+                elif (l_s, l_e) == ("l", "d"):
+                    quadrant[2] += 1
+                elif (l_s, l_e) == ("d", "r"):
+                    quadrant[3] += 1
+
+                continue
+            if m.domain == obj:
+                (end_i, end_j) = object_coords[m.codomain]
+                goes_out = True
+            elif m.codomain == obj:
+                (end_i, end_j) = object_coords[m.domain]
+                goes_out = False
+            else:
+                continue
+
+            d_i = end_i - i
+            d_j = end_j - j
+            m_curving = m_str_info.curving
+
+            if (d_i != 0) and (d_j != 0):
+                # This is really a diagonal morphism.  Detect the
+                # quadrant.
+                if (d_i > 0) and (d_j > 0):
+                    quadrant[0] += 1
+                elif (d_i > 0) and (d_j < 0):
+                    quadrant[1] += 1
+                elif (d_i < 0) and (d_j < 0):
+                    quadrant[2] += 1
+                elif (d_i < 0) and (d_j > 0):
+                    quadrant[3] += 1
+            elif d_i == 0:
+                # Knowing where the other end of the morphism is
+                # and which way it goes, we now have to decide
+                # which quadrant is now the upper one and which is
+                # the lower one.
+                if d_j > 0:
+                    if goes_out:
+                        upper_quadrant = 0
+                        lower_quadrant = 3
+                    else:
+                        upper_quadrant = 3
+                        lower_quadrant = 0
+                else:
+                    if goes_out:
+                        upper_quadrant = 2
+                        lower_quadrant = 1
+                    else:
+                        upper_quadrant = 1
+                        lower_quadrant = 2
+
+                if m_curving:
+                    if m_curving == "^":
+                        quadrant[upper_quadrant] += 1
+                    elif m_curving == "_":
+                        quadrant[lower_quadrant] += 1
+                else:
+                    # This morphism counts in both upper and lower
+                    # quadrants.
+                    quadrant[upper_quadrant] += 1
+                    quadrant[lower_quadrant] += 1
+            elif d_j == 0:
+                # Knowing where the other end of the morphism is
+                # and which way it goes, we now have to decide
+                # which quadrant is now the left one and which is
+                # the right one.
+                if d_i < 0:
+                    if goes_out:
+                        left_quadrant = 1
+                        right_quadrant = 0
+                    else:
+                        left_quadrant = 0
+                        right_quadrant = 1
+                else:
+                    if goes_out:
+                        left_quadrant = 3
+                        right_quadrant = 2
+                    else:
+                        left_quadrant = 2
+                        right_quadrant = 3
+
+                if m_curving:
+                    if m_curving == "^":
+                        quadrant[left_quadrant] += 1
+                    elif m_curving == "_":
+                        quadrant[right_quadrant] += 1
+                else:
+                    # This morphism counts in both upper and lower
+                    # quadrants.
+                    quadrant[left_quadrant] += 1
+                    quadrant[right_quadrant] += 1
+
+        # Pick the freest quadrant to curve our morphism into.
+        freest_quadrant = 0
+        for i in range(4):
+            if quadrant[i] < quadrant[freest_quadrant]:
+                freest_quadrant = i
+
+        # Now set up proper looping.
+        (looping_start, looping_end) = [("r", "u"), ("u", "l"), ("l", "d"),
+                                        ("d", "r")][freest_quadrant]
+
+        return (curving, label_pos, looping_start, looping_end)
+
+    @staticmethod
+    def _process_horizontal_morphism(i, j, target_j, grid, morphisms_str_info,
+                                     object_coords):
+        """
+        Produces the information required for constructing the string
+        representation of a horizontal morphism.  This function is
+        invoked from ``_process_morphism``.
+
+        See Also
+        ========
+
+        _process_morphism
+        """
+        # The arrow is horizontal.  Check if it goes from left to
+        # right (``backwards == False``) or from right to left
+        # (``backwards == True``).
+        backwards = False
+        start = j
+        end = target_j
+        if end < start:
+            (start, end) = (end, start)
+            backwards = True
+
+        # Let's see which objects are there between ``start`` and
+        # ``end``, and then count how many morphisms stick out
+        # upwards, and how many stick out downwards.
+        #
+        # For example, consider the situation:
+        #
+        #    B1 C1
+        #    |  |
+        # A--B--C--D
+        #    |
+        #    B2
+        #
+        # Between the objects `A` and `D` there are two objects:
+        # `B` and `C`.  Further, there are two morphisms which
+        # stick out upward (the ones between `B1` and `B` and
+        # between `C` and `C1`) and one morphism which sticks out
+        # downward (the one between `B and `B2`).
+        #
+        # We need this information to decide how to curve the
+        # arrow between `A` and `D`.  First of all, since there
+        # are two objects between `A` and `D``, we must curve the
+        # arrow.  Then, we will have it curve downward, because
+        # there is more space (less morphisms stick out downward
+        # than upward).
+        up = []
+        down = []
+        straight_horizontal = []
+        for k in range(start + 1, end):
+            obj = grid[i, k]
+            if not obj:
+                continue
+
+            for m in morphisms_str_info:
+                if m.domain == obj:
+                    (end_i, end_j) = object_coords[m.codomain]
+                elif m.codomain == obj:
+                    (end_i, end_j) = object_coords[m.domain]
+                else:
+                    continue
+
+                if end_i > i:
+                    down.append(m)
+                elif end_i < i:
+                    up.append(m)
+                elif not morphisms_str_info[m].curving:
+                    # This is a straight horizontal morphism,
+                    # because it has no curving.
+                    straight_horizontal.append(m)
+
+        if len(up) < len(down):
+            # More morphisms stick out downward than upward, let's
+            # curve the morphism up.
+            if backwards:
+                curving = "_"
+                label_pos = "_"
+            else:
+                curving = "^"
+                label_pos = "^"
+
+            # Assure that the straight horizontal morphisms have
+            # their labels on the lower side of the arrow.
+            for m in straight_horizontal:
+                (i1, j1) = object_coords[m.domain]
+                (i2, j2) = object_coords[m.codomain]
+
+                m_str_info = morphisms_str_info[m]
+                if j1 < j2:
+                    m_str_info.label_position = "_"
+                else:
+                    m_str_info.label_position = "^"
+
+                # Don't allow any further modifications of the
+                # position of this label.
+                m_str_info.forced_label_position = True
+        else:
+            # More morphisms stick out downward than upward, let's
+            # curve the morphism up.
+            if backwards:
+                curving = "^"
+                label_pos = "^"
+            else:
+                curving = "_"
+                label_pos = "_"
+
+            # Assure that the straight horizontal morphisms have
+            # their labels on the upper side of the arrow.
+            for m in straight_horizontal:
+                (i1, j1) = object_coords[m.domain]
+                (i2, j2) = object_coords[m.codomain]
+
+                m_str_info = morphisms_str_info[m]
+                if j1 < j2:
+                    m_str_info.label_position = "^"
+                else:
+                    m_str_info.label_position = "_"
+
+                # Don't allow any further modifications of the
+                # position of this label.
+                m_str_info.forced_label_position = True
+
+        return (curving, label_pos)
+
+    @staticmethod
+    def _process_vertical_morphism(i, j, target_i, grid, morphisms_str_info,
+                                   object_coords):
+        """
+        Produces the information required for constructing the string
+        representation of a vertical morphism.  This function is
+        invoked from ``_process_morphism``.
+
+        See Also
+        ========
+
+        _process_morphism
+        """
+        # This arrow is vertical.  Check if it goes from top to
+        # bottom (``backwards == False``) or from bottom to top
+        # (``backwards == True``).
+        backwards = False
+        start = i
+        end = target_i
+        if end < start:
+            (start, end) = (end, start)
+            backwards = True
+
+        # Let's see which objects are there between ``start`` and
+        # ``end``, and then count how many morphisms stick out to
+        # the left, and how many stick out to the right.
+        #
+        # See the corresponding comment in the previous branch of
+        # this if-statement for more details.
+        left = []
+        right = []
+        straight_vertical = []
+        for k in range(start + 1, end):
+            obj = grid[k, j]
+            if not obj:
+                continue
+
+            for m in morphisms_str_info:
+                if m.domain == obj:
+                    (end_i, end_j) = object_coords[m.codomain]
+                elif m.codomain == obj:
+                    (end_i, end_j) = object_coords[m.domain]
+                else:
+                    continue
+
+                if end_j > j:
+                    right.append(m)
+                elif end_j < j:
+                    left.append(m)
+                elif not morphisms_str_info[m].curving:
+                    # This is a straight vertical morphism,
+                    # because it has no curving.
+                    straight_vertical.append(m)
+
+        if len(left) < len(right):
+            # More morphisms stick out to the left than to the
+            # right, let's curve the morphism to the right.
+            if backwards:
+                curving = "^"
+                label_pos = "^"
+            else:
+                curving = "_"
+                label_pos = "_"
+
+            # Assure that the straight vertical morphisms have
+            # their labels on the left side of the arrow.
+            for m in straight_vertical:
+                (i1, j1) = object_coords[m.domain]
+                (i2, j2) = object_coords[m.codomain]
+
+                m_str_info = morphisms_str_info[m]
+                if i1 < i2:
+                    m_str_info.label_position = "^"
+                else:
+                    m_str_info.label_position = "_"
+
+                # Don't allow any further modifications of the
+                # position of this label.
+                m_str_info.forced_label_position = True
+        else:
+            # More morphisms stick out to the right than to the
+            # left, let's curve the morphism to the left.
+            if backwards:
+                curving = "_"
+                label_pos = "_"
+            else:
+                curving = "^"
+                label_pos = "^"
+
+            # Assure that the straight vertical morphisms have
+            # their labels on the right side of the arrow.
+            for m in straight_vertical:
+                (i1, j1) = object_coords[m.domain]
+                (i2, j2) = object_coords[m.codomain]
+
+                m_str_info = morphisms_str_info[m]
+                if i1 < i2:
+                    m_str_info.label_position = "_"
+                else:
+                    m_str_info.label_position = "^"
+
+                # Don't allow any further modifications of the
+                # position of this label.
+                m_str_info.forced_label_position = True
+
+        return (curving, label_pos)
+
+    def _process_morphism(self, diagram, grid, morphism, object_coords,
+                          morphisms, morphisms_str_info):
+        """
+        Given the required information, produces the string
+        representation of ``morphism``.
+        """
+        def repeat_string_cond(times, str_gt, str_lt):
+            """
+            If ``times > 0``, repeats ``str_gt`` ``times`` times.
+            Otherwise, repeats ``str_lt`` ``-times`` times.
+            """
+            if times > 0:
+                return str_gt * times
+            else:
+                return str_lt * (-times)
+
+        def count_morphisms_undirected(A, B):
+            """
+            Counts how many processed morphisms there are between the
+            two supplied objects.
+            """
+            return len([m for m in morphisms_str_info
+                        if {m.domain, m.codomain} == {A, B}])
+
+        def count_morphisms_filtered(dom, cod, curving):
+            """
+            Counts the processed morphisms which go out of ``dom``
+            into ``cod`` with curving ``curving``.
+            """
+            return len([m for m, m_str_info in morphisms_str_info.items()
+                        if (m.domain, m.codomain) == (dom, cod) and
+                        (m_str_info.curving == curving)])
+
+        (i, j) = object_coords[morphism.domain]
+        (target_i, target_j) = object_coords[morphism.codomain]
+
+        # We now need to determine the direction of
+        # the arrow.
+        delta_i = target_i - i
+        delta_j = target_j - j
+        vertical_direction = repeat_string_cond(delta_i,
+                                                "d", "u")
+        horizontal_direction = repeat_string_cond(delta_j,
+                                                  "r", "l")
+
+        curving = ""
+        label_pos = "^"
+        looping_start = ""
+        looping_end = ""
+
+        if (delta_i == 0) and (delta_j == 0):
+            # This is a loop morphism.
+            (curving, label_pos, looping_start,
+             looping_end) = XypicDiagramDrawer._process_loop_morphism(
+                 i, j, grid, morphisms_str_info, object_coords)
+        elif (delta_i == 0) and (abs(j - target_j) > 1):
+            # This is a horizontal morphism.
+            (curving, label_pos) = XypicDiagramDrawer._process_horizontal_morphism(
+                i, j, target_j, grid, morphisms_str_info, object_coords)
+        elif (delta_j == 0) and (abs(i - target_i) > 1):
+            # This is a vertical morphism.
+            (curving, label_pos) = XypicDiagramDrawer._process_vertical_morphism(
+                i, j, target_i, grid, morphisms_str_info, object_coords)
+
+        count = count_morphisms_undirected(morphism.domain, morphism.codomain)
+        curving_amount = ""
+        if curving:
+            # This morphisms should be curved anyway.
+            curving_amount = self.default_curving_amount + count * \
+                self.default_curving_step
+        elif count:
+            # There are no objects between the domain and codomain of
+            # the current morphism, but this is not there already are
+            # some morphisms with the same domain and codomain, so we
+            # have to curve this one.
+            curving = "^"
+            filtered_morphisms = count_morphisms_filtered(
+                morphism.domain, morphism.codomain, curving)
+            curving_amount = self.default_curving_amount + \
+                filtered_morphisms * \
+                self.default_curving_step
+
+        # Let's now get the name of the morphism.
+        morphism_name = ""
+        if isinstance(morphism, IdentityMorphism):
+            morphism_name = "id_{%s}" + latex(grid[i, j])
+        elif isinstance(morphism, CompositeMorphism):
+            component_names = [latex(Symbol(component.name)) for
+                               component in morphism.components]
+            component_names.reverse()
+            morphism_name = "\\circ ".join(component_names)
+        elif isinstance(morphism, NamedMorphism):
+            morphism_name = latex(Symbol(morphism.name))
+
+        return ArrowStringDescription(
+            self.unit, curving, curving_amount, looping_start,
+            looping_end, horizontal_direction, vertical_direction,
+            label_pos, morphism_name)
+
+    @staticmethod
+    def _check_free_space_horizontal(dom_i, dom_j, cod_j, grid):
+        """
+        For a horizontal morphism, checks whether there is free space
+        (i.e., space not occupied by any objects) above the morphism
+        or below it.
+        """
+        if dom_j < cod_j:
+            (start, end) = (dom_j, cod_j)
+            backwards = False
+        else:
+            (start, end) = (cod_j, dom_j)
+            backwards = True
+
+        # Check for free space above.
+        if dom_i == 0:
+            free_up = True
+        else:
+            free_up = all(grid[dom_i - 1, j] for j in
+                          range(start, end + 1))
+
+        # Check for free space below.
+        if dom_i == grid.height - 1:
+            free_down = True
+        else:
+            free_down = not any(grid[dom_i + 1, j] for j in
+                                range(start, end + 1))
+
+        return (free_up, free_down, backwards)
+
+    @staticmethod
+    def _check_free_space_vertical(dom_i, cod_i, dom_j, grid):
+        """
+        For a vertical morphism, checks whether there is free space
+        (i.e., space not occupied by any objects) to the left of the
+        morphism or to the right of it.
+        """
+        if dom_i < cod_i:
+            (start, end) = (dom_i, cod_i)
+            backwards = False
+        else:
+            (start, end) = (cod_i, dom_i)
+            backwards = True
+
+        # Check if there's space to the left.
+        if dom_j == 0:
+            free_left = True
+        else:
+            free_left = not any(grid[i, dom_j - 1] for i in
+                                range(start, end + 1))
+
+        if dom_j == grid.width - 1:
+            free_right = True
+        else:
+            free_right = not any(grid[i, dom_j + 1] for i in
+                                 range(start, end + 1))
+
+        return (free_left, free_right, backwards)
+
+    @staticmethod
+    def _check_free_space_diagonal(dom_i, cod_i, dom_j, cod_j, grid):
+        """
+        For a diagonal morphism, checks whether there is free space
+        (i.e., space not occupied by any objects) above the morphism
+        or below it.
+        """
+        def abs_xrange(start, end):
+            if start < end:
+                return range(start, end + 1)
+            else:
+                return range(end, start + 1)
+
+        if dom_i < cod_i and dom_j < cod_j:
+            # This morphism goes from top-left to
+            # bottom-right.
+            (start_i, start_j) = (dom_i, dom_j)
+            (end_i, end_j) = (cod_i, cod_j)
+            backwards = False
+        elif dom_i > cod_i and dom_j > cod_j:
+            # This morphism goes from bottom-right to
+            # top-left.
+            (start_i, start_j) = (cod_i, cod_j)
+            (end_i, end_j) = (dom_i, dom_j)
+            backwards = True
+        if dom_i < cod_i and dom_j > cod_j:
+            # This morphism goes from top-right to
+            # bottom-left.
+            (start_i, start_j) = (dom_i, dom_j)
+            (end_i, end_j) = (cod_i, cod_j)
+            backwards = True
+        elif dom_i > cod_i and dom_j < cod_j:
+            # This morphism goes from bottom-left to
+            # top-right.
+            (start_i, start_j) = (cod_i, cod_j)
+            (end_i, end_j) = (dom_i, dom_j)
+            backwards = False
+
+        # This is an attempt at a fast and furious strategy to
+        # decide where there is free space on the two sides of
+        # a diagonal morphism.  For a diagonal morphism
+        # starting at ``(start_i, start_j)`` and ending at
+        # ``(end_i, end_j)`` the rectangle defined by these
+        # two points is considered.  The slope of the diagonal
+        # ``alpha`` is then computed.  Then, for every cell
+        # ``(i, j)`` within the rectangle, the slope
+        # ``alpha1`` of the line through ``(start_i,
+        # start_j)`` and ``(i, j)`` is considered.  If
+        # ``alpha1`` is between 0 and ``alpha``, the point
+        # ``(i, j)`` is above the diagonal, if ``alpha1`` is
+        # between ``alpha`` and infinity, the point is below
+        # the diagonal.  Also note that, with some beforehand
+        # precautions, this trick works for both the main and
+        # the secondary diagonals of the rectangle.
+
+        # I have considered the possibility to only follow the
+        # shorter diagonals immediately above and below the
+        # main (or secondary) diagonal.  This, however,
+        # wouldn't have resulted in much performance gain or
+        # better detection of outer edges, because of
+        # relatively small sizes of diagram grids, while the
+        # code would have become harder to understand.
+
+        alpha = float(end_i - start_i)/(end_j - start_j)
+        free_up = True
+        free_down = True
+        for i in abs_xrange(start_i, end_i):
+            if not free_up and not free_down:
+                break
+
+            for j in abs_xrange(start_j, end_j):
+                if not free_up and not free_down:
+                    break
+
+                if (i, j) == (start_i, start_j):
+                    continue
+
+                if j == start_j:
+                    alpha1 = "inf"
+                else:
+                    alpha1 = float(i - start_i)/(j - start_j)
+
+                if grid[i, j]:
+                    if (alpha1 == "inf") or (abs(alpha1) > abs(alpha)):
+                        free_down = False
+                    elif abs(alpha1) < abs(alpha):
+                        free_up = False
+
+        return (free_up, free_down, backwards)
+
+    def _push_labels_out(self, morphisms_str_info, grid, object_coords):
+        """
+        For all straight morphisms which form the visual boundary of
+        the laid out diagram, puts their labels on their outer sides.
+        """
+        def set_label_position(free1, free2, pos1, pos2, backwards, m_str_info):
+            """
+            Given the information about room available to one side and
+            to the other side of a morphism (``free1`` and ``free2``),
+            sets the position of the morphism label in such a way that
+            it is on the freer side.  This latter operations involves
+            choice between ``pos1`` and ``pos2``, taking ``backwards``
+            in consideration.
+
+            Thus this function will do nothing if either both ``free1
+            == True`` and ``free2 == True`` or both ``free1 == False``
+            and ``free2 == False``.  In either case, choosing one side
+            over the other presents no advantage.
+            """
+            if backwards:
+                (pos1, pos2) = (pos2, pos1)
+
+            if free1 and not free2:
+                m_str_info.label_position = pos1
+            elif free2 and not free1:
+                m_str_info.label_position = pos2
+
+        for m, m_str_info in morphisms_str_info.items():
+            if m_str_info.curving or m_str_info.forced_label_position:
+                # This is either a curved morphism, and curved
+                # morphisms have other magic, or the position of this
+                # label has already been fixed.
+                continue
+
+            if m.domain == m.codomain:
+                # This is a loop morphism, their labels, again have a
+                # different magic.
+                continue
+
+            (dom_i, dom_j) = object_coords[m.domain]
+            (cod_i, cod_j) = object_coords[m.codomain]
+
+            if dom_i == cod_i:
+                # Horizontal morphism.
+                (free_up, free_down,
+                 backwards) = XypicDiagramDrawer._check_free_space_horizontal(
+                     dom_i, dom_j, cod_j, grid)
+
+                set_label_position(free_up, free_down, "^", "_",
+                                   backwards, m_str_info)
+            elif dom_j == cod_j:
+                # Vertical morphism.
+                (free_left, free_right,
+                 backwards) = XypicDiagramDrawer._check_free_space_vertical(
+                     dom_i, cod_i, dom_j, grid)
+
+                set_label_position(free_left, free_right, "_", "^",
+                                   backwards, m_str_info)
+            else:
+                # A diagonal morphism.
+                (free_up, free_down,
+                 backwards) = XypicDiagramDrawer._check_free_space_diagonal(
+                     dom_i, cod_i, dom_j, cod_j, grid)
+
+                set_label_position(free_up, free_down, "^", "_",
+                                   backwards, m_str_info)
+
+    @staticmethod
+    def _morphism_sort_key(morphism, object_coords):
+        """
+        Provides a morphism sorting key such that horizontal or
+        vertical morphisms between neighbouring objects come
+        first, then horizontal or vertical morphisms between more
+        far away objects, and finally, all other morphisms.
+        """
+        (i, j) = object_coords[morphism.domain]
+        (target_i, target_j) = object_coords[morphism.codomain]
+
+        if morphism.domain == morphism.codomain:
+            # Loop morphisms should get after diagonal morphisms
+            # so that the proper direction in which to curve the
+            # loop can be determined.
+            return (3, 0, default_sort_key(morphism))
+
+        if target_i == i:
+            return (1, abs(target_j - j), default_sort_key(morphism))
+
+        if target_j == j:
+            return (1, abs(target_i - i), default_sort_key(morphism))
+
+        # Diagonal morphism.
+        return (2, 0, default_sort_key(morphism))
+
+    @staticmethod
+    def _build_xypic_string(diagram, grid, morphisms,
+                            morphisms_str_info, diagram_format):
+        """
+        Given a collection of :class:`ArrowStringDescription`
+        describing the morphisms of a diagram and the object layout
+        information of a diagram, produces the final Xy-pic picture.
+        """
+        # Build the mapping between objects and morphisms which have
+        # them as domains.
+        object_morphisms = {}
+        for obj in diagram.objects:
+            object_morphisms[obj] = []
+        for morphism in morphisms:
+            object_morphisms[morphism.domain].append(morphism)
+
+        result = "\\xymatrix%s{\n" % diagram_format
+
+        for i in range(grid.height):
+            for j in range(grid.width):
+                obj = grid[i, j]
+                if obj:
+                    result += latex(obj) + " "
+
+                    morphisms_to_draw = object_morphisms[obj]
+                    for morphism in morphisms_to_draw:
+                        result += str(morphisms_str_info[morphism]) + " "
+
+                # Don't put the & after the last column.
+                if j < grid.width - 1:
+                    result += "& "
+
+            # Don't put the line break after the last row.
+            if i < grid.height - 1:
+                result += "\\\\"
+            result += "\n"
+
+        result += "}\n"
+
+        return result
+
+    def draw(self, diagram, grid, masked=None, diagram_format=""):
+        r"""
+        Returns the Xy-pic representation of ``diagram`` laid out in
+        ``grid``.
+
+        Consider the following simple triangle diagram.
+
+        >>> from sympy.categories import Object, NamedMorphism, Diagram
+        >>> from sympy.categories import DiagramGrid, XypicDiagramDrawer
+        >>> A = Object("A")
+        >>> B = Object("B")
+        >>> C = Object("C")
+        >>> f = NamedMorphism(A, B, "f")
+        >>> g = NamedMorphism(B, C, "g")
+        >>> diagram = Diagram([f, g], {g * f: "unique"})
+
+        To draw this diagram, its objects need to be laid out with a
+        :class:`DiagramGrid`::
+
+        >>> grid = DiagramGrid(diagram)
+
+        Finally, the drawing:
+
+        >>> drawer = XypicDiagramDrawer()
+        >>> print(drawer.draw(diagram, grid))
+        \xymatrix{
+        A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\
+        C &
+        }
+
+        The argument ``masked`` can be used to skip morphisms in the
+        presentation of the diagram:
+
+        >>> print(drawer.draw(diagram, grid, masked=[g * f]))
+        \xymatrix{
+        A \ar[r]^{f} & B \ar[ld]^{g} \\
+        C &
+        }
+
+        Finally, the ``diagram_format`` argument can be used to
+        specify the format string of the diagram.  For example, to
+        increase the spacing by 1 cm, proceeding as follows:
+
+        >>> print(drawer.draw(diagram, grid, diagram_format="@+1cm"))
+        \xymatrix@+1cm{
+        A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\
+        C &
+        }
+
+        """
+        # This method works in several steps.  It starts by removing
+        # the masked morphisms, if necessary, and then maps objects to
+        # their positions in the grid (coordinate tuples).  Remember
+        # that objects are unique in ``Diagram`` and in the layout
+        # produced by ``DiagramGrid``, so every object is mapped to a
+        # single coordinate pair.
+        #
+        # The next step is the central step and is concerned with
+        # analysing the morphisms of the diagram and deciding how to
+        # draw them.  For example, how to curve the arrows is decided
+        # at this step.  The bulk of the analysis is implemented in
+        # ``_process_morphism``, to the result of which the
+        # appropriate formatters are applied.
+        #
+        # The result of the previous step is a list of
+        # ``ArrowStringDescription``.  After the analysis and
+        # application of formatters, some extra logic tries to assure
+        # better positioning of morphism labels (for example, an
+        # attempt is made to avoid the situations when arrows cross
+        # labels).  This functionality constitutes the next step and
+        # is implemented in ``_push_labels_out``.  Note that label
+        # positions which have been set via a formatter are not
+        # affected in this step.
+        #
+        # Finally, at the closing step, the array of
+        # ``ArrowStringDescription`` and the layout information
+        # incorporated in ``DiagramGrid`` are combined to produce the
+        # resulting Xy-pic picture.  This part of code lies in
+        # ``_build_xypic_string``.
+
+        if not masked:
+            morphisms_props = grid.morphisms
+        else:
+            morphisms_props = {}
+            for m, props in grid.morphisms.items():
+                if m in masked:
+                    continue
+                morphisms_props[m] = props
+
+        # Build the mapping between objects and their position in the
+        # grid.
+        object_coords = {}
+        for i in range(grid.height):
+            for j in range(grid.width):
+                if grid[i, j]:
+                    object_coords[grid[i, j]] = (i, j)
+
+        morphisms = sorted(morphisms_props,
+                           key=lambda m: XypicDiagramDrawer._morphism_sort_key(
+                               m, object_coords))
+
+        # Build the tuples defining the string representations of
+        # morphisms.
+        morphisms_str_info = {}
+        for morphism in morphisms:
+            string_description = self._process_morphism(
+                diagram, grid, morphism, object_coords, morphisms,
+                morphisms_str_info)
+
+            if self.default_arrow_formatter:
+                self.default_arrow_formatter(string_description)
+
+            for prop in morphisms_props[morphism]:
+                # prop is a Symbol.  TODO: Find out why.
+                if prop.name in self.arrow_formatters:
+                    formatter = self.arrow_formatters[prop.name]
+                    formatter(string_description)
+
+            morphisms_str_info[morphism] = string_description
+
+        # Reposition the labels a bit.
+        self._push_labels_out(morphisms_str_info, grid, object_coords)
+
+        return XypicDiagramDrawer._build_xypic_string(
+            diagram, grid, morphisms, morphisms_str_info, diagram_format)
+
+
+def xypic_draw_diagram(diagram, masked=None, diagram_format="",
+                       groups=None, **hints):
+    r"""
+    Provides a shortcut combining :class:`DiagramGrid` and
+    :class:`XypicDiagramDrawer`.  Returns an Xy-pic presentation of
+    ``diagram``.  The argument ``masked`` is a list of morphisms which
+    will be not be drawn.  The argument ``diagram_format`` is the
+    format string inserted after "\xymatrix".  ``groups`` should be a
+    set of logical groups.  The ``hints`` will be passed directly to
+    the constructor of :class:`DiagramGrid`.
+
+    For more information about the arguments, see the docstrings of
+    :class:`DiagramGrid` and ``XypicDiagramDrawer.draw``.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism, Diagram
+    >>> from sympy.categories import xypic_draw_diagram
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> diagram = Diagram([f, g], {g * f: "unique"})
+    >>> print(xypic_draw_diagram(diagram))
+    \xymatrix{
+    A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\
+    C &
+    }
+
+    See Also
+    ========
+
+    XypicDiagramDrawer, DiagramGrid
+    """
+    grid = DiagramGrid(diagram, groups, **hints)
+    drawer = XypicDiagramDrawer()
+    return drawer.draw(diagram, grid, masked, diagram_format)
+
+
+@doctest_depends_on(exe=('latex', 'dvipng'), modules=('pyglet',))
+def preview_diagram(diagram, masked=None, diagram_format="", groups=None,
+                    output='png', viewer=None, euler=True, **hints):
+    """
+    Combines the functionality of ``xypic_draw_diagram`` and
+    ``sympy.printing.preview``.  The arguments ``masked``,
+    ``diagram_format``, ``groups``, and ``hints`` are passed to
+    ``xypic_draw_diagram``, while ``output``, ``viewer, and ``euler``
+    are passed to ``preview``.
+
+    Examples
+    ========
+
+    >>> from sympy.categories import Object, NamedMorphism, Diagram
+    >>> from sympy.categories import preview_diagram
+    >>> A = Object("A")
+    >>> B = Object("B")
+    >>> C = Object("C")
+    >>> f = NamedMorphism(A, B, "f")
+    >>> g = NamedMorphism(B, C, "g")
+    >>> d = Diagram([f, g], {g * f: "unique"})
+    >>> preview_diagram(d)
+
+    See Also
+    ========
+
+    XypicDiagramDrawer
+    """
+    from sympy.printing import preview
+    latex_output = xypic_draw_diagram(diagram, masked, diagram_format,
+                                      groups, **hints)
+    preview(latex_output, output, viewer, euler, ("xypic",))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/test_baseclasses.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/test_baseclasses.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfac32229768fb5903b23b11ffb236912c0b931e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/test_baseclasses.py
@@ -0,0 +1,209 @@
+from sympy.categories import (Object, Morphism, IdentityMorphism,
+                              NamedMorphism, CompositeMorphism,
+                              Diagram, Category)
+from sympy.categories.baseclasses import Class
+from sympy.testing.pytest import raises
+from sympy.core.containers import (Dict, Tuple)
+from sympy.sets import EmptySet
+from sympy.sets.sets import FiniteSet
+
+
+def test_morphisms():
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+
+    # Test the base morphism.
+    f = NamedMorphism(A, B, "f")
+    assert f.domain == A
+    assert f.codomain == B
+    assert f == NamedMorphism(A, B, "f")
+
+    # Test identities.
+    id_A = IdentityMorphism(A)
+    id_B = IdentityMorphism(B)
+    assert id_A.domain == A
+    assert id_A.codomain == A
+    assert id_A == IdentityMorphism(A)
+    assert id_A != id_B
+
+    # Test named morphisms.
+    g = NamedMorphism(B, C, "g")
+    assert g.name == "g"
+    assert g != f
+    assert g == NamedMorphism(B, C, "g")
+    assert g != NamedMorphism(B, C, "f")
+
+    # Test composite morphisms.
+    assert f == CompositeMorphism(f)
+
+    k = g.compose(f)
+    assert k.domain == A
+    assert k.codomain == C
+    assert k.components == Tuple(f, g)
+    assert g * f == k
+    assert CompositeMorphism(f, g) == k
+
+    assert CompositeMorphism(g * f) == g * f
+
+    # Test the associativity of composition.
+    h = NamedMorphism(C, D, "h")
+
+    p = h * g
+    u = h * g * f
+
+    assert h * k == u
+    assert p * f == u
+    assert CompositeMorphism(f, g, h) == u
+
+    # Test flattening.
+    u2 = u.flatten("u")
+    assert isinstance(u2, NamedMorphism)
+    assert u2.name == "u"
+    assert u2.domain == A
+    assert u2.codomain == D
+
+    # Test identities.
+    assert f * id_A == f
+    assert id_B * f == f
+    assert id_A * id_A == id_A
+    assert CompositeMorphism(id_A) == id_A
+
+    # Test bad compositions.
+    raises(ValueError, lambda: f * g)
+
+    raises(TypeError, lambda: f.compose(None))
+    raises(TypeError, lambda: id_A.compose(None))
+    raises(TypeError, lambda: f * None)
+    raises(TypeError, lambda: id_A * None)
+
+    raises(TypeError, lambda: CompositeMorphism(f, None, 1))
+
+    raises(ValueError, lambda: NamedMorphism(A, B, ""))
+    raises(NotImplementedError, lambda: Morphism(A, B))
+
+
+def test_diagram():
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    id_A = IdentityMorphism(A)
+    id_B = IdentityMorphism(B)
+
+    empty = EmptySet
+
+    # Test the addition of identities.
+    d1 = Diagram([f])
+
+    assert d1.objects == FiniteSet(A, B)
+    assert d1.hom(A, B) == (FiniteSet(f), empty)
+    assert d1.hom(A, A) == (FiniteSet(id_A), empty)
+    assert d1.hom(B, B) == (FiniteSet(id_B), empty)
+
+    assert d1 == Diagram([id_A, f])
+    assert d1 == Diagram([f, f])
+
+    # Test the addition of composites.
+    d2 = Diagram([f, g])
+    homAC = d2.hom(A, C)[0]
+
+    assert d2.objects == FiniteSet(A, B, C)
+    assert g * f in d2.premises.keys()
+    assert homAC == FiniteSet(g * f)
+
+    # Test equality, inequality and hash.
+    d11 = Diagram([f])
+
+    assert d1 == d11
+    assert d1 != d2
+    assert hash(d1) == hash(d11)
+
+    d11 = Diagram({f: "unique"})
+    assert d1 != d11
+
+    # Make sure that (re-)adding composites (with new properties)
+    # works as expected.
+    d = Diagram([f, g], {g * f: "unique"})
+    assert d.conclusions == Dict({g * f: FiniteSet("unique")})
+
+    # Check the hom-sets when there are premises and conclusions.
+    assert d.hom(A, C) == (FiniteSet(g * f), FiniteSet(g * f))
+    d = Diagram([f, g], [g * f])
+    assert d.hom(A, C) == (FiniteSet(g * f), FiniteSet(g * f))
+
+    # Check how the properties of composite morphisms are computed.
+    d = Diagram({f: ["unique", "isomorphism"], g: "unique"})
+    assert d.premises[g * f] == FiniteSet("unique")
+
+    # Check that conclusion morphisms with new objects are not allowed.
+    d = Diagram([f], [g])
+    assert d.conclusions == Dict({})
+
+    # Test an empty diagram.
+    d = Diagram()
+    assert d.premises == Dict({})
+    assert d.conclusions == Dict({})
+    assert d.objects == empty
+
+    # Check a SymPy Dict object.
+    d = Diagram(Dict({f: FiniteSet("unique", "isomorphism"), g: "unique"}))
+    assert d.premises[g * f] == FiniteSet("unique")
+
+    # Check the addition of components of composite morphisms.
+    d = Diagram([g * f])
+    assert f in d.premises
+    assert g in d.premises
+
+    # Check subdiagrams.
+    d = Diagram([f, g], {g * f: "unique"})
+
+    d1 = Diagram([f])
+    assert d.is_subdiagram(d1)
+    assert not d1.is_subdiagram(d)
+
+    d = Diagram([NamedMorphism(B, A, "f'")])
+    assert not d.is_subdiagram(d1)
+    assert not d1.is_subdiagram(d)
+
+    d1 = Diagram([f, g], {g * f: ["unique", "something"]})
+    assert not d.is_subdiagram(d1)
+    assert not d1.is_subdiagram(d)
+
+    d = Diagram({f: "blooh"})
+    d1 = Diagram({f: "bleeh"})
+    assert not d.is_subdiagram(d1)
+    assert not d1.is_subdiagram(d)
+
+    d = Diagram([f, g], {f: "unique", g * f: "veryunique"})
+    d1 = d.subdiagram_from_objects(FiniteSet(A, B))
+    assert d1 == Diagram([f], {f: "unique"})
+    raises(ValueError, lambda: d.subdiagram_from_objects(FiniteSet(A,
+           Object("D"))))
+
+    raises(ValueError, lambda: Diagram({IdentityMorphism(A): "unique"}))
+
+
+def test_category():
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+
+    d1 = Diagram([f, g])
+    d2 = Diagram([f])
+
+    objects = d1.objects | d2.objects
+
+    K = Category("K", objects, commutative_diagrams=[d1, d2])
+
+    assert K.name == "K"
+    assert K.objects == Class(objects)
+    assert K.commutative_diagrams == FiniteSet(d1, d2)
+
+    raises(ValueError, lambda: Category(""))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/test_drawing.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/test_drawing.py
new file mode 100644
index 0000000000000000000000000000000000000000..63a13266cd6b58f6a85aad4af0813b395acbb5e1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/categories/tests/test_drawing.py
@@ -0,0 +1,919 @@
+from sympy.categories.diagram_drawing import _GrowableGrid, ArrowStringDescription
+from sympy.categories import (DiagramGrid, Object, NamedMorphism,
+                              Diagram, XypicDiagramDrawer, xypic_draw_diagram)
+from sympy.sets.sets import FiniteSet
+
+
+def test_GrowableGrid():
+    grid = _GrowableGrid(1, 2)
+
+    # Check dimensions.
+    assert grid.width == 1
+    assert grid.height == 2
+
+    # Check initialization of elements.
+    assert grid[0, 0] is None
+    assert grid[1, 0] is None
+
+    # Check assignment to elements.
+    grid[0, 0] = 1
+    grid[1, 0] = "two"
+
+    assert grid[0, 0] == 1
+    assert grid[1, 0] == "two"
+
+    # Check appending a row.
+    grid.append_row()
+
+    assert grid.width == 1
+    assert grid.height == 3
+
+    assert grid[0, 0] == 1
+    assert grid[1, 0] == "two"
+    assert grid[2, 0] is None
+
+    # Check appending a column.
+    grid.append_column()
+    assert grid.width == 2
+    assert grid.height == 3
+
+    assert grid[0, 0] == 1
+    assert grid[1, 0] == "two"
+    assert grid[2, 0] is None
+
+    assert grid[0, 1] is None
+    assert grid[1, 1] is None
+    assert grid[2, 1] is None
+
+    grid = _GrowableGrid(1, 2)
+    grid[0, 0] = 1
+    grid[1, 0] = "two"
+
+    # Check prepending a row.
+    grid.prepend_row()
+    assert grid.width == 1
+    assert grid.height == 3
+
+    assert grid[0, 0] is None
+    assert grid[1, 0] == 1
+    assert grid[2, 0] == "two"
+
+    # Check prepending a column.
+    grid.prepend_column()
+    assert grid.width == 2
+    assert grid.height == 3
+
+    assert grid[0, 0] is None
+    assert grid[1, 0] is None
+    assert grid[2, 0] is None
+
+    assert grid[0, 1] is None
+    assert grid[1, 1] == 1
+    assert grid[2, 1] == "two"
+
+
+def test_DiagramGrid():
+    # Set up some objects and morphisms.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(D, A, "h")
+    k = NamedMorphism(D, B, "k")
+
+    # A one-morphism diagram.
+    d = Diagram([f])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid.morphisms == {f: FiniteSet()}
+
+    # A triangle.
+    d = Diagram([f, g], {g * f: "unique"})
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[1, 0] == C
+    assert grid[1, 1] is None
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(),
+                              g * f: FiniteSet("unique")}
+
+    # A triangle with a "loop" morphism.
+    l_A = NamedMorphism(A, A, "l_A")
+    d = Diagram([f, g, l_A])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), l_A: FiniteSet()}
+
+    # A simple diagram.
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == D
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] is None
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              k: FiniteSet()}
+
+    assert str(grid) == '[[Object("A"), Object("B"), Object("D")], ' \
+        '[None, Object("C"), None]]'
+
+    # A chain of morphisms.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    k = NamedMorphism(D, E, "k")
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 3
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid[2, 0] is None
+    assert grid[2, 1] is None
+    assert grid[2, 2] == E
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              k: FiniteSet()}
+
+    # A square.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, D, "g")
+    h = NamedMorphism(A, C, "h")
+    k = NamedMorphism(C, D, "k")
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[1, 0] == C
+    assert grid[1, 1] == D
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              k: FiniteSet()}
+
+    # A strange diagram which resulted from a typo when creating a
+    # test for five lemma, but which allowed to stop one extra problem
+    # in the algorithm.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+    A_ = Object("A'")
+    B_ = Object("B'")
+    C_ = Object("C'")
+    D_ = Object("D'")
+    E_ = Object("E'")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+
+    # These 4 morphisms should be between primed objects.
+    j = NamedMorphism(A, B, "j")
+    k = NamedMorphism(B, C, "k")
+    l = NamedMorphism(C, D, "l")
+    m = NamedMorphism(D, E, "m")
+
+    o = NamedMorphism(A, A_, "o")
+    p = NamedMorphism(B, B_, "p")
+    q = NamedMorphism(C, C_, "q")
+    r = NamedMorphism(D, D_, "r")
+    s = NamedMorphism(E, E_, "s")
+
+    d = Diagram([f, g, h, i, j, k, l, m, o, p, q, r, s])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 4
+    assert grid[0, 0] is None
+    assert grid[0, 1] == A
+    assert grid[0, 2] == A_
+    assert grid[1, 0] == C
+    assert grid[1, 1] == B
+    assert grid[1, 2] == B_
+    assert grid[2, 0] == C_
+    assert grid[2, 1] == D
+    assert grid[2, 2] == D_
+    assert grid[3, 0] is None
+    assert grid[3, 1] == E
+    assert grid[3, 2] == E_
+
+    morphisms = {}
+    for m in [f, g, h, i, j, k, l, m, o, p, q, r, s]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # A cube.
+    A1 = Object("A1")
+    A2 = Object("A2")
+    A3 = Object("A3")
+    A4 = Object("A4")
+    A5 = Object("A5")
+    A6 = Object("A6")
+    A7 = Object("A7")
+    A8 = Object("A8")
+
+    # The top face of the cube.
+    f1 = NamedMorphism(A1, A2, "f1")
+    f2 = NamedMorphism(A1, A3, "f2")
+    f3 = NamedMorphism(A2, A4, "f3")
+    f4 = NamedMorphism(A3, A4, "f3")
+
+    # The bottom face of the cube.
+    f5 = NamedMorphism(A5, A6, "f5")
+    f6 = NamedMorphism(A5, A7, "f6")
+    f7 = NamedMorphism(A6, A8, "f7")
+    f8 = NamedMorphism(A7, A8, "f8")
+
+    # The remaining morphisms.
+    f9 = NamedMorphism(A1, A5, "f9")
+    f10 = NamedMorphism(A2, A6, "f10")
+    f11 = NamedMorphism(A3, A7, "f11")
+    f12 = NamedMorphism(A4, A8, "f11")
+
+    d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 4
+    assert grid.height == 3
+    assert grid[0, 0] is None
+    assert grid[0, 1] == A5
+    assert grid[0, 2] == A6
+    assert grid[0, 3] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == A1
+    assert grid[1, 2] == A2
+    assert grid[1, 3] is None
+    assert grid[2, 0] == A7
+    assert grid[2, 1] == A3
+    assert grid[2, 2] == A4
+    assert grid[2, 3] == A8
+
+    morphisms = {}
+    for m in [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # A line diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+    d = Diagram([f, g, h, i])
+    grid = DiagramGrid(d, layout="sequential")
+
+    assert grid.width == 5
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == C
+    assert grid[0, 3] == D
+    assert grid[0, 4] == E
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              i: FiniteSet()}
+
+    # Test the transposed version.
+    grid = DiagramGrid(d, layout="sequential", transpose=True)
+
+    assert grid.width == 1
+    assert grid.height == 5
+    assert grid[0, 0] == A
+    assert grid[1, 0] == B
+    assert grid[2, 0] == C
+    assert grid[3, 0] == D
+    assert grid[4, 0] == E
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              i: FiniteSet()}
+
+    # A pullback.
+    m1 = NamedMorphism(A, B, "m1")
+    m2 = NamedMorphism(A, C, "m2")
+    s1 = NamedMorphism(B, D, "s1")
+    s2 = NamedMorphism(C, D, "s2")
+    f1 = NamedMorphism(E, B, "f1")
+    f2 = NamedMorphism(E, C, "f2")
+    g = NamedMorphism(E, A, "g")
+
+    d = Diagram([m1, m2, s1, s2, f1, f2], {g: "unique"})
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == E
+    assert grid[1, 0] == C
+    assert grid[1, 1] == D
+    assert grid[1, 2] is None
+
+    morphisms = {g: FiniteSet("unique")}
+    for m in [m1, m2, s1, s2, f1, f2]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # Test the pullback with sequential layout, just for stress
+    # testing.
+    grid = DiagramGrid(d, layout="sequential")
+
+    assert grid.width == 5
+    assert grid.height == 1
+    assert grid[0, 0] == D
+    assert grid[0, 1] == B
+    assert grid[0, 2] == A
+    assert grid[0, 3] == C
+    assert grid[0, 4] == E
+    assert grid.morphisms == morphisms
+
+    # Test a pullback with object grouping.
+    grid = DiagramGrid(d, groups=FiniteSet(E, FiniteSet(A, B, C, D)))
+
+    assert grid.width == 3
+    assert grid.height == 2
+    assert grid[0, 0] == E
+    assert grid[0, 1] == A
+    assert grid[0, 2] == B
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid.morphisms == morphisms
+
+    # Five lemma, actually.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+    A_ = Object("A'")
+    B_ = Object("B'")
+    C_ = Object("C'")
+    D_ = Object("D'")
+    E_ = Object("E'")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+
+    j = NamedMorphism(A_, B_, "j")
+    k = NamedMorphism(B_, C_, "k")
+    l = NamedMorphism(C_, D_, "l")
+    m = NamedMorphism(D_, E_, "m")
+
+    o = NamedMorphism(A, A_, "o")
+    p = NamedMorphism(B, B_, "p")
+    q = NamedMorphism(C, C_, "q")
+    r = NamedMorphism(D, D_, "r")
+    s = NamedMorphism(E, E_, "s")
+
+    d = Diagram([f, g, h, i, j, k, l, m, o, p, q, r, s])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 5
+    assert grid.height == 3
+    assert grid[0, 0] is None
+    assert grid[0, 1] == A
+    assert grid[0, 2] == A_
+    assert grid[0, 3] is None
+    assert grid[0, 4] is None
+    assert grid[1, 0] == C
+    assert grid[1, 1] == B
+    assert grid[1, 2] == B_
+    assert grid[1, 3] == C_
+    assert grid[1, 4] is None
+    assert grid[2, 0] == D
+    assert grid[2, 1] == E
+    assert grid[2, 2] is None
+    assert grid[2, 3] == D_
+    assert grid[2, 4] == E_
+
+    morphisms = {}
+    for m in [f, g, h, i, j, k, l, m, o, p, q, r, s]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # Test the five lemma with object grouping.
+    grid = DiagramGrid(d, FiniteSet(
+        FiniteSet(A, B, C, D, E), FiniteSet(A_, B_, C_, D_, E_)))
+
+    assert grid.width == 6
+    assert grid.height == 3
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] is None
+    assert grid[0, 3] == A_
+    assert grid[0, 4] == B_
+    assert grid[0, 5] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid[1, 3] is None
+    assert grid[1, 4] == C_
+    assert grid[1, 5] == D_
+    assert grid[2, 0] is None
+    assert grid[2, 1] is None
+    assert grid[2, 2] == E
+    assert grid[2, 3] is None
+    assert grid[2, 4] is None
+    assert grid[2, 5] == E_
+    assert grid.morphisms == morphisms
+
+    # Test the five lemma with object grouping, but mixing containers
+    # to represent groups.
+    grid = DiagramGrid(d, [(A, B, C, D, E), {A_, B_, C_, D_, E_}])
+
+    assert grid.width == 6
+    assert grid.height == 3
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] is None
+    assert grid[0, 3] == A_
+    assert grid[0, 4] == B_
+    assert grid[0, 5] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid[1, 3] is None
+    assert grid[1, 4] == C_
+    assert grid[1, 5] == D_
+    assert grid[2, 0] is None
+    assert grid[2, 1] is None
+    assert grid[2, 2] == E
+    assert grid[2, 3] is None
+    assert grid[2, 4] is None
+    assert grid[2, 5] == E_
+    assert grid.morphisms == morphisms
+
+    # Test the five lemma with object grouping and hints.
+    grid = DiagramGrid(d, {
+        FiniteSet(A, B, C, D, E): {"layout": "sequential",
+                                   "transpose": True},
+        FiniteSet(A_, B_, C_, D_, E_): {"layout": "sequential",
+                                        "transpose": True}},
+        transpose=True)
+
+    assert grid.width == 5
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == C
+    assert grid[0, 3] == D
+    assert grid[0, 4] == E
+    assert grid[1, 0] == A_
+    assert grid[1, 1] == B_
+    assert grid[1, 2] == C_
+    assert grid[1, 3] == D_
+    assert grid[1, 4] == E_
+    assert grid.morphisms == morphisms
+
+    # A two-triangle disconnected diagram.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    f_ = NamedMorphism(A_, B_, "f")
+    g_ = NamedMorphism(B_, C_, "g")
+    d = Diagram([f, g, f_, g_], {g * f: "unique", g_ * f_: "unique"})
+    grid = DiagramGrid(d)
+
+    assert grid.width == 4
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == A_
+    assert grid[0, 3] == B_
+    assert grid[1, 0] == C
+    assert grid[1, 1] is None
+    assert grid[1, 2] == C_
+    assert grid[1, 3] is None
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), f_: FiniteSet(),
+                              g_: FiniteSet(), g * f: FiniteSet("unique"),
+                              g_ * f_: FiniteSet("unique")}
+
+    # A two-morphism disconnected diagram.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(C, D, "g")
+    d = Diagram([f, g])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 4
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == C
+    assert grid[0, 3] == D
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet()}
+
+    # Test a one-object diagram.
+    f = NamedMorphism(A, A, "f")
+    d = Diagram([f])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 1
+    assert grid.height == 1
+    assert grid[0, 0] == A
+
+    # Test a two-object disconnected diagram.
+    g = NamedMorphism(B, B, "g")
+    d = Diagram([f, g])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+
+
+def test_DiagramGrid_pseudopod():
+    # Test a diagram in which even growing a pseudopod does not
+    # eventually help.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+    F = Object("F")
+    A_ = Object("A'")
+    B_ = Object("B'")
+    C_ = Object("C'")
+    D_ = Object("D'")
+    E_ = Object("E'")
+
+    f1 = NamedMorphism(A, B, "f1")
+    f2 = NamedMorphism(A, C, "f2")
+    f3 = NamedMorphism(A, D, "f3")
+    f4 = NamedMorphism(A, E, "f4")
+    f5 = NamedMorphism(A, A_, "f5")
+    f6 = NamedMorphism(A, B_, "f6")
+    f7 = NamedMorphism(A, C_, "f7")
+    f8 = NamedMorphism(A, D_, "f8")
+    f9 = NamedMorphism(A, E_, "f9")
+    f10 = NamedMorphism(A, F, "f10")
+    d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 5
+    assert grid.height == 3
+    assert grid[0, 0] == E
+    assert grid[0, 1] == C
+    assert grid[0, 2] == C_
+    assert grid[0, 3] == E_
+    assert grid[0, 4] == F
+    assert grid[1, 0] == D
+    assert grid[1, 1] == A
+    assert grid[1, 2] == A_
+    assert grid[1, 3] is None
+    assert grid[1, 4] is None
+    assert grid[2, 0] == D_
+    assert grid[2, 1] == B
+    assert grid[2, 2] == B_
+    assert grid[2, 3] is None
+    assert grid[2, 4] is None
+
+    morphisms = {}
+    for f in [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10]:
+        morphisms[f] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+
+def test_ArrowStringDescription():
+    astr = ArrowStringDescription("cm", "", None, "", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "^", 12, "", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar@/^12cm/[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f")
+    assert str(astr) == "\\ar@(r,u)[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f")
+    assert str(astr) == "\\ar@(r,u)[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f")
+    astr.arrow_style = "{-->}"
+    assert str(astr) == "\\ar@(r,u)@{-->}[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "_", 12, "", "", "d", "r", "_", "f")
+    astr.arrow_style = "{-->}"
+    assert str(astr) == "\\ar@/_12cm/@{-->}[dr]_{f}"
+
+
+def test_XypicDiagramDrawer_line():
+    # A linear diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+    d = Diagram([f, g, h, i])
+    grid = DiagramGrid(d, layout="sequential")
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]^{f} & B \\ar[r]^{g} & C \\ar[r]^{h} & D \\ar[r]^{i} & E \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, layout="sequential", transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\\\\n" \
+        "B \\ar[d]^{g} \\\\\n" \
+        "C \\ar[d]^{h} \\\\\n" \
+        "D \\ar[d]^{i} \\\\\n" \
+        "E \n" \
+        "}\n"
+
+
+def test_XypicDiagramDrawer_triangle():
+    # A triangle diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+
+    d = Diagram([f, g], {g * f: "unique"})
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]_{g\\circ f} \\ar[r]^{f} & B \\ar[ld]^{g} \\\\\n" \
+        "C & \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]^{g\\circ f} \\ar[d]_{f} & C \\\\\n" \
+        "B \\ar[ru]_{g} & \n" \
+        "}\n"
+
+    # The same diagram, with a masked morphism.
+    assert drawer.draw(d, grid, masked=[g]) == "\\xymatrix{\n" \
+        "A \\ar[r]^{g\\circ f} \\ar[d]_{f} & C \\\\\n" \
+        "B & \n" \
+        "}\n"
+
+    # The same diagram with a formatter for "unique".
+    def formatter(astr):
+        astr.label = "\\exists !" + astr.label
+        astr.arrow_style = "{-->}"
+
+    drawer.arrow_formatters["unique"] = formatter
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar@{-->}[r]^{\\exists !g\\circ f} \\ar[d]_{f} & C \\\\\n" \
+        "B \\ar[ru]_{g} & \n" \
+        "}\n"
+
+    # The same diagram with a default formatter.
+    def default_formatter(astr):
+        astr.label_displacement = "(0.45)"
+
+    drawer.default_arrow_formatter = default_formatter
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar@{-->}[r]^(0.45){\\exists !g\\circ f} \\ar[d]_(0.45){f} & C \\\\\n" \
+        "B \\ar[ru]_(0.45){g} & \n" \
+        "}\n"
+
+    # A triangle diagram with a lot of morphisms between the same
+    # objects.
+    f1 = NamedMorphism(B, A, "f1")
+    f2 = NamedMorphism(A, B, "f2")
+    g1 = NamedMorphism(C, B, "g1")
+    g2 = NamedMorphism(B, C, "g2")
+    d = Diagram([f, f1, f2, g, g1, g2], {f1 * g1: "unique", g2 * f2: "unique"})
+
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid, masked=[f1*g1*g2*f2, g2*f2*f1*g1]) == \
+        "\\xymatrix{\n" \
+        "A \\ar[r]^{g_{2}\\circ f_{2}} \\ar[d]_{f} \\ar@/^3mm/[d]^{f_{2}} " \
+        "& C \\ar@/^3mm/[l]^{f_{1}\\circ g_{1}} \\ar@/^3mm/[ld]^{g_{1}} \\\\\n" \
+        "B \\ar@/^3mm/[u]^{f_{1}} \\ar[ru]_{g} \\ar@/^3mm/[ru]^{g_{2}} & \n" \
+        "}\n"
+
+
+def test_XypicDiagramDrawer_cube():
+    # A cube diagram.
+    A1 = Object("A1")
+    A2 = Object("A2")
+    A3 = Object("A3")
+    A4 = Object("A4")
+    A5 = Object("A5")
+    A6 = Object("A6")
+    A7 = Object("A7")
+    A8 = Object("A8")
+
+    # The top face of the cube.
+    f1 = NamedMorphism(A1, A2, "f1")
+    f2 = NamedMorphism(A1, A3, "f2")
+    f3 = NamedMorphism(A2, A4, "f3")
+    f4 = NamedMorphism(A3, A4, "f3")
+
+    # The bottom face of the cube.
+    f5 = NamedMorphism(A5, A6, "f5")
+    f6 = NamedMorphism(A5, A7, "f6")
+    f7 = NamedMorphism(A6, A8, "f7")
+    f8 = NamedMorphism(A7, A8, "f8")
+
+    # The remaining morphisms.
+    f9 = NamedMorphism(A1, A5, "f9")
+    f10 = NamedMorphism(A2, A6, "f10")
+    f11 = NamedMorphism(A3, A7, "f11")
+    f12 = NamedMorphism(A4, A8, "f11")
+
+    d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "& A_{5} \\ar[r]^{f_{5}} \\ar[ldd]_{f_{6}} & A_{6} \\ar[rdd]^{f_{7}} " \
+        "& \\\\\n" \
+        "& A_{1} \\ar[r]^{f_{1}} \\ar[d]^{f_{2}} \\ar[u]^{f_{9}} & A_{2} " \
+        "\\ar[d]^{f_{3}} \\ar[u]_{f_{10}} & \\\\\n" \
+        "A_{7} \\ar@/_3mm/[rrr]_{f_{8}} & A_{3} \\ar[r]^{f_{3}} \\ar[l]_{f_{11}} " \
+        "& A_{4} \\ar[r]^{f_{11}} & A_{8} \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "& & A_{7} \\ar@/^3mm/[ddd]^{f_{8}} \\\\\n" \
+        "A_{5} \\ar[d]_{f_{5}} \\ar[rru]^{f_{6}} & A_{1} \\ar[d]^{f_{1}} " \
+        "\\ar[r]^{f_{2}} \\ar[l]^{f_{9}} & A_{3} \\ar[d]_{f_{3}} " \
+        "\\ar[u]^{f_{11}} \\\\\n" \
+        "A_{6} \\ar[rrd]_{f_{7}} & A_{2} \\ar[r]^{f_{3}} \\ar[l]^{f_{10}} " \
+        "& A_{4} \\ar[d]_{f_{11}} \\\\\n" \
+        "& & A_{8} \n" \
+        "}\n"
+
+
+def test_XypicDiagramDrawer_curved_and_loops():
+    # A simple diagram, with a curved arrow.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(D, A, "h")
+    k = NamedMorphism(D, B, "k")
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} & B \\ar[d]^{g} & D \\ar[l]^{k} \\ar@/_3mm/[ll]_{h} \\\\\n" \
+        "& C & \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^3mm/[uu]^{h} & \n" \
+        "}\n"
+
+    # The same diagram, larger and rotated.
+    assert drawer.draw(d, grid, diagram_format="@+1cm@dr") == \
+        "\\xymatrix@+1cm@dr{\n" \
+        "A \\ar[d]^{f} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^3mm/[uu]^{h} & \n" \
+        "}\n"
+
+    # A simple diagram with three curved arrows.
+    h1 = NamedMorphism(D, A, "h1")
+    h2 = NamedMorphism(A, D, "h2")
+    k = NamedMorphism(D, B, "k")
+    d = Diagram([f, g, h, k, h1, h2])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} & B \\ar[d]^{g} & D \\ar[l]^{k} " \
+        "\\ar@/_7mm/[ll]_{h} \\ar@/_11mm/[ll]_{h_{1}} \\\\\n" \
+        "& C & \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} & \n" \
+        "}\n"
+
+    # The same diagram, with "loop" morphisms.
+    l_A = NamedMorphism(A, A, "l_A")
+    l_D = NamedMorphism(D, D, "l_D")
+    l_C = NamedMorphism(C, C, "l_C")
+    d = Diagram([f, g, h, k, h1, h2, l_A, l_D, l_C])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} \\ar@(u,l)[]^{l_{A}} " \
+        "& B \\ar[d]^{g} & D \\ar[l]^{k} \\ar@/_7mm/[ll]_{h} " \
+        "\\ar@/_11mm/[ll]_{h_{1}} \\ar@(r,u)[]^{l_{D}} \\\\\n" \
+        "& C \\ar@(l,d)[]^{l_{C}} & \n" \
+        "}\n"
+
+    # The same diagram with "loop" morphisms, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} \\ar@(r,u)[]^{l_{A}} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\ar@(r,u)[]^{l_{C}} \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} " \
+        "\\ar@(l,d)[]^{l_{D}} & \n" \
+        "}\n"
+
+    # The same diagram with two "loop" morphisms per object.
+    l_A_ = NamedMorphism(A, A, "n_A")
+    l_D_ = NamedMorphism(D, D, "n_D")
+    l_C_ = NamedMorphism(C, C, "n_C")
+    d = Diagram([f, g, h, k, h1, h2, l_A, l_D, l_C, l_A_, l_D_, l_C_])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} \\ar@(u,l)[]^{l_{A}} " \
+        "\\ar@/^3mm/@(l,d)[]^{n_{A}} & B \\ar[d]^{g} & D \\ar[l]^{k} " \
+        "\\ar@/_7mm/[ll]_{h} \\ar@/_11mm/[ll]_{h_{1}} \\ar@(r,u)[]^{l_{D}} " \
+        "\\ar@/^3mm/@(d,r)[]^{n_{D}} \\\\\n" \
+        "& C \\ar@(l,d)[]^{l_{C}} \\ar@/^3mm/@(d,r)[]^{n_{C}} & \n" \
+        "}\n"
+
+    # The same diagram with two "loop" morphisms per object, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} \\ar@(r,u)[]^{l_{A}} " \
+        "\\ar@/^3mm/@(u,l)[]^{n_{A}} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\ar@(r,u)[]^{l_{C}} \\ar@/^3mm/@(d,r)[]^{n_{C}} \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} " \
+        "\\ar@(l,d)[]^{l_{D}} \\ar@/^3mm/@(d,r)[]^{n_{D}} & \n" \
+        "}\n"
+
+
+def test_xypic_draw_diagram():
+    # A linear diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+    d = Diagram([f, g, h, i])
+
+    grid = DiagramGrid(d, layout="sequential")
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == xypic_draw_diagram(d, layout="sequential")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..62b195633bae28371bdf9e79317050d7fa7125ae
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/__init__.py
@@ -0,0 +1,24 @@
+""" The ``sympy.codegen`` module contains classes and functions for building
+abstract syntax trees of algorithms. These trees may then be printed by the
+code-printers in ``sympy.printing``.
+
+There are several submodules available:
+- ``sympy.codegen.ast``: AST nodes useful across multiple languages.
+- ``sympy.codegen.cnodes``: AST nodes useful for the C family of languages.
+- ``sympy.codegen.fnodes``: AST nodes useful for Fortran.
+- ``sympy.codegen.cfunctions``: functions specific to C (C99 math functions)
+- ``sympy.codegen.ffunctions``: functions specific to Fortran (e.g. ``kind``).
+
+
+
+"""
+from .ast import (
+    Assignment, aug_assign, CodeBlock, For, Attribute, Variable, Declaration,
+    While, Scope, Print, FunctionPrototype, FunctionDefinition, FunctionCall
+)
+
+__all__ = [
+    'Assignment', 'aug_assign', 'CodeBlock', 'For', 'Attribute', 'Variable',
+    'Declaration', 'While', 'Scope', 'Print', 'FunctionPrototype',
+    'FunctionDefinition', 'FunctionCall',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/abstract_nodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/abstract_nodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae0a8b3e996a7112edf2568c00138e11c3f3327d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/abstract_nodes.py
@@ -0,0 +1,18 @@
+"""This module provides containers for python objects that are valid
+printing targets but are not a subclass of SymPy's Printable.
+"""
+
+
+from sympy.core.containers import Tuple
+
+
+class List(Tuple):
+    """Represents a (frozen) (Python) list (for code printing purposes)."""
+    def __eq__(self, other):
+        if isinstance(other, list):
+            return self == List(*other)
+        else:
+            return self.args == other
+
+    def __hash__(self):
+        return super().__hash__()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/algorithms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/algorithms.py
new file mode 100644
index 0000000000000000000000000000000000000000..f4890eb8c25e565095600e2713c0de270aa0cf97
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/algorithms.py
@@ -0,0 +1,180 @@
+from sympy.core.containers import Tuple
+from sympy.core.numbers import oo
+from sympy.core.relational import (Gt, Lt)
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.miscellaneous import Min, Max
+from sympy.logic.boolalg import And
+from sympy.codegen.ast import (
+    Assignment, AddAugmentedAssignment, break_, CodeBlock, Declaration, FunctionDefinition,
+    Print, Return, Scope, While, Variable, Pointer, real
+)
+from sympy.codegen.cfunctions import isnan
+
+""" This module collects functions for constructing ASTs representing algorithms. """
+
+def newtons_method(expr, wrt, atol=1e-12, delta=None, *, rtol=4e-16, debug=False,
+                   itermax=None, counter=None, delta_fn=lambda e, x: -e/e.diff(x),
+                   cse=False, handle_nan=None,
+                   bounds=None):
+    """ Generates an AST for Newton-Raphson method (a root-finding algorithm).
+
+    Explanation
+    ===========
+
+    Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's
+    method of root-finding.
+
+    Parameters
+    ==========
+
+    expr : expression
+    wrt : Symbol
+        With respect to, i.e. what is the variable.
+    atol : number or expression
+        Absolute tolerance (stopping criterion)
+    rtol : number or expression
+        Relative tolerance (stopping criterion)
+    delta : Symbol
+        Will be a ``Dummy`` if ``None``.
+    debug : bool
+        Whether to print convergence information during iterations
+    itermax : number or expr
+        Maximum number of iterations.
+    counter : Symbol
+        Will be a ``Dummy`` if ``None``.
+    delta_fn: Callable[[Expr, Symbol], Expr]
+        computes the step, default is newtons method. For e.g. Halley's method
+        use delta_fn=lambda e, x: -2*e*e.diff(x)/(2*e.diff(x)**2 - e*e.diff(x, 2))
+    cse: bool
+        Perform common sub-expression elimination on delta expression
+    handle_nan: Token
+        How to handle occurrence of not-a-number (NaN).
+    bounds: Optional[tuple[Expr, Expr]]
+        Perform optimization within bounds
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, cos
+    >>> from sympy.codegen.ast import Assignment
+    >>> from sympy.codegen.algorithms import newtons_method
+    >>> x, dx, atol = symbols('x dx atol')
+    >>> expr = cos(x) - x**3
+    >>> algo = newtons_method(expr, x, atol=atol, delta=dx)
+    >>> algo.has(Assignment(dx, -expr/expr.diff(x)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Newton%27s_method
+
+    """
+
+    if delta is None:
+        delta = Dummy()
+        Wrapper = Scope
+        name_d = 'delta'
+    else:
+        Wrapper = lambda x: x
+        name_d = delta.name
+
+    delta_expr = delta_fn(expr, wrt)
+    if cse:
+        from sympy.simplify.cse_main import cse
+        cses, (red,) = cse([delta_expr.factor()])
+        whl_bdy = [Assignment(dum, sub_e) for dum, sub_e in cses]
+        whl_bdy += [Assignment(delta, red)]
+    else:
+        whl_bdy = [Assignment(delta, delta_expr)]
+    if handle_nan is not None:
+        whl_bdy += [While(isnan(delta), CodeBlock(handle_nan, break_))]
+    whl_bdy += [AddAugmentedAssignment(wrt, delta)]
+    if bounds is not None:
+        whl_bdy += [Assignment(wrt, Min(Max(wrt, bounds[0]), bounds[1]))]
+    if debug:
+        prnt = Print([wrt, delta], r"{}=%12.5g {}=%12.5g\n".format(wrt.name, name_d))
+        whl_bdy += [prnt]
+    req = Gt(Abs(delta), atol + rtol*Abs(wrt))
+    declars = [Declaration(Variable(delta, type=real, value=oo))]
+    if itermax is not None:
+        counter = counter or Dummy(integer=True)
+        v_counter = Variable.deduced(counter, 0)
+        declars.append(Declaration(v_counter))
+        whl_bdy.append(AddAugmentedAssignment(counter, 1))
+        req = And(req, Lt(counter, itermax))
+    whl = While(req, CodeBlock(*whl_bdy))
+    blck = declars
+    if debug:
+        blck.append(Print([wrt], r"{}=%12.5g\n".format(wrt.name)))
+    blck += [whl]
+    return Wrapper(CodeBlock(*blck))
+
+
+def _symbol_of(arg):
+    if isinstance(arg, Declaration):
+        arg = arg.variable.symbol
+    elif isinstance(arg, Variable):
+        arg = arg.symbol
+    return arg
+
+
+def newtons_method_function(expr, wrt, params=None, func_name="newton", attrs=Tuple(), *, delta=None, **kwargs):
+    """ Generates an AST for a function implementing the Newton-Raphson method.
+
+    Parameters
+    ==========
+
+    expr : expression
+    wrt : Symbol
+        With respect to, i.e. what is the variable
+    params : iterable of symbols
+        Symbols appearing in expr that are taken as constants during the iterations
+        (these will be accepted as parameters to the generated function).
+    func_name : str
+        Name of the generated function.
+    attrs : Tuple
+        Attribute instances passed as ``attrs`` to ``FunctionDefinition``.
+    \\*\\*kwargs :
+        Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, cos
+    >>> from sympy.codegen.algorithms import newtons_method_function
+    >>> from sympy.codegen.pyutils import render_as_module
+    >>> x = symbols('x')
+    >>> expr = cos(x) - x**3
+    >>> func = newtons_method_function(expr, x)
+    >>> py_mod = render_as_module(func)  # source code as string
+    >>> namespace = {}
+    >>> exec(py_mod, namespace, namespace)
+    >>> res = eval('newton(0.5)', namespace)
+    >>> abs(res - 0.865474033102) < 1e-12
+    True
+
+    See Also
+    ========
+
+    sympy.codegen.algorithms.newtons_method
+
+    """
+    if params is None:
+        params = (wrt,)
+    pointer_subs = {p.symbol: Symbol('(*%s)' % p.symbol.name)
+                    for p in params if isinstance(p, Pointer)}
+    if delta is None:
+        delta = Symbol('d_' + wrt.name)
+        if expr.has(delta):
+            delta = None  # will use Dummy
+    algo = newtons_method(expr, wrt, delta=delta, **kwargs).xreplace(pointer_subs)
+    if isinstance(algo, Scope):
+        algo = algo.body
+    not_in_params = expr.free_symbols.difference({_symbol_of(p) for p in params})
+    if not_in_params:
+        raise ValueError("Missing symbols in params: %s" % ', '.join(map(str, not_in_params)))
+    declars = tuple(Variable(p, real) for p in params)
+    body = CodeBlock(algo, Return(wrt))
+    return FunctionDefinition(real, func_name, declars, body, attrs=attrs)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/approximations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/approximations.py
new file mode 100644
index 0000000000000000000000000000000000000000..c6486926938224c5052dc5adfac29807e82eb4d8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/approximations.py
@@ -0,0 +1,187 @@
+import math
+from sympy.sets.sets import Interval
+from sympy.calculus.singularities import is_increasing, is_decreasing
+from sympy.codegen.rewriting import Optimization
+from sympy.core.function import UndefinedFunction
+
+"""
+This module collects classes useful for approximate rewriting of expressions.
+This can be beneficial when generating numeric code for which performance is
+of greater importance than precision (e.g. for preconditioners used in iterative
+methods).
+"""
+
+class SumApprox(Optimization):
+    """
+    Approximates sum by neglecting small terms.
+
+    Explanation
+    ===========
+
+    If terms are expressions which can be determined to be monotonic, then
+    bounds for those expressions are added.
+
+    Parameters
+    ==========
+
+    bounds : dict
+        Mapping expressions to length 2 tuple of bounds (low, high).
+    reltol : number
+        Threshold for when to ignore a term. Taken relative to the largest
+        lower bound among bounds.
+
+    Examples
+    ========
+
+    >>> from sympy import exp
+    >>> from sympy.abc import x, y, z
+    >>> from sympy.codegen.rewriting import optimize
+    >>> from sympy.codegen.approximations import SumApprox
+    >>> bounds = {x: (-1, 1), y: (1000, 2000), z: (-10, 3)}
+    >>> sum_approx3 = SumApprox(bounds, reltol=1e-3)
+    >>> sum_approx2 = SumApprox(bounds, reltol=1e-2)
+    >>> sum_approx1 = SumApprox(bounds, reltol=1e-1)
+    >>> expr = 3*(x + y + exp(z))
+    >>> optimize(expr, [sum_approx3])
+    3*(x + y + exp(z))
+    >>> optimize(expr, [sum_approx2])
+    3*y + 3*exp(z)
+    >>> optimize(expr, [sum_approx1])
+    3*y
+
+    """
+
+    def __init__(self, bounds, reltol, **kwargs):
+        super().__init__(**kwargs)
+        self.bounds = bounds
+        self.reltol = reltol
+
+    def __call__(self, expr):
+        return expr.factor().replace(self.query, lambda arg: self.value(arg))
+
+    def query(self, expr):
+        return expr.is_Add
+
+    def value(self, add):
+        for term in add.args:
+            if term.is_number or term in self.bounds or len(term.free_symbols) != 1:
+                continue
+            fs, = term.free_symbols
+            if fs not in self.bounds:
+                continue
+            intrvl = Interval(*self.bounds[fs])
+            if is_increasing(term, intrvl, fs):
+                self.bounds[term] = (
+                    term.subs({fs: self.bounds[fs][0]}),
+                    term.subs({fs: self.bounds[fs][1]})
+                )
+            elif is_decreasing(term, intrvl, fs):
+                self.bounds[term] = (
+                    term.subs({fs: self.bounds[fs][1]}),
+                    term.subs({fs: self.bounds[fs][0]})
+                )
+            else:
+                return add
+
+        if all(term.is_number or term in self.bounds for term in add.args):
+            bounds = [(term, term) if term.is_number else self.bounds[term] for term in add.args]
+            largest_abs_guarantee = 0
+            for lo, hi in bounds:
+                if lo <= 0 <= hi:
+                    continue
+                largest_abs_guarantee = max(largest_abs_guarantee,
+                                            min(abs(lo), abs(hi)))
+            new_terms = []
+            for term, (lo, hi) in zip(add.args, bounds):
+                if max(abs(lo), abs(hi)) >= largest_abs_guarantee*self.reltol:
+                    new_terms.append(term)
+            return add.func(*new_terms)
+        else:
+            return add
+
+
+class SeriesApprox(Optimization):
+    """ Approximates functions by expanding them as a series.
+
+    Parameters
+    ==========
+
+    bounds : dict
+        Mapping expressions to length 2 tuple of bounds (low, high).
+    reltol : number
+        Threshold for when to ignore a term. Taken relative to the largest
+        lower bound among bounds.
+    max_order : int
+        Largest order to include in series expansion
+    n_point_checks : int (even)
+        The validity of an expansion (with respect to reltol) is checked at
+        discrete points (linearly spaced over the bounds of the variable). The
+        number of points used in this numerical check is given by this number.
+
+    Examples
+    ========
+
+    >>> from sympy import sin, pi
+    >>> from sympy.abc import x, y
+    >>> from sympy.codegen.rewriting import optimize
+    >>> from sympy.codegen.approximations import SeriesApprox
+    >>> bounds = {x: (-.1, .1), y: (pi-1, pi+1)}
+    >>> series_approx2 = SeriesApprox(bounds, reltol=1e-2)
+    >>> series_approx3 = SeriesApprox(bounds, reltol=1e-3)
+    >>> series_approx8 = SeriesApprox(bounds, reltol=1e-8)
+    >>> expr = sin(x)*sin(y)
+    >>> optimize(expr, [series_approx2])
+    x*(-y + (y - pi)**3/6 + pi)
+    >>> optimize(expr, [series_approx3])
+    (-x**3/6 + x)*sin(y)
+    >>> optimize(expr, [series_approx8])
+    sin(x)*sin(y)
+
+    """
+    def __init__(self, bounds, reltol, max_order=4, n_point_checks=4, **kwargs):
+        super().__init__(**kwargs)
+        self.bounds = bounds
+        self.reltol = reltol
+        self.max_order = max_order
+        if n_point_checks % 2 == 1:
+            raise ValueError("Checking the solution at expansion point is not helpful")
+        self.n_point_checks = n_point_checks
+        self._prec = math.ceil(-math.log10(self.reltol))
+
+    def __call__(self, expr):
+        return expr.factor().replace(self.query, lambda arg: self.value(arg))
+
+    def query(self, expr):
+        return (expr.is_Function and not isinstance(expr, UndefinedFunction)
+                and len(expr.args) == 1)
+
+    def value(self, fexpr):
+        free_symbols = fexpr.free_symbols
+        if len(free_symbols) != 1:
+            return fexpr
+        symb, = free_symbols
+        if symb not in self.bounds:
+            return fexpr
+        lo, hi = self.bounds[symb]
+        x0 = (lo + hi)/2
+        cheapest = None
+        for n in range(self.max_order+1, 0, -1):
+            fseri = fexpr.series(symb, x0=x0, n=n).removeO()
+            n_ok = True
+            for idx in range(self.n_point_checks):
+                x = lo + idx*(hi - lo)/(self.n_point_checks - 1)
+                val = fseri.xreplace({symb: x})
+                ref = fexpr.xreplace({symb: x})
+                if abs((1 - val/ref).evalf(self._prec)) > self.reltol:
+                    n_ok = False
+                    break
+
+            if n_ok:
+                cheapest = fseri
+            else:
+                break
+
+        if cheapest is None:
+            return fexpr
+        else:
+            return cheapest
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/ast.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/ast.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd774ca87c5c9d4b55c8ea7a3b68837035b0d06d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/ast.py
@@ -0,0 +1,1906 @@
+"""
+Types used to represent a full function/module as an Abstract Syntax Tree.
+
+Most types are small, and are merely used as tokens in the AST. A tree diagram
+has been included below to illustrate the relationships between the AST types.
+
+
+AST Type Tree
+-------------
+::
+
+  *Basic*
+       |
+       |
+   CodegenAST
+       |
+       |--->AssignmentBase
+       |             |--->Assignment
+       |             |--->AugmentedAssignment
+       |                                    |--->AddAugmentedAssignment
+       |                                    |--->SubAugmentedAssignment
+       |                                    |--->MulAugmentedAssignment
+       |                                    |--->DivAugmentedAssignment
+       |                                    |--->ModAugmentedAssignment
+       |
+       |--->CodeBlock
+       |
+       |
+       |--->Token
+                |--->Attribute
+                |--->For
+                |--->String
+                |       |--->QuotedString
+                |       |--->Comment
+                |--->Type
+                |       |--->IntBaseType
+                |       |              |--->_SizedIntType
+                |       |                               |--->SignedIntType
+                |       |                               |--->UnsignedIntType
+                |       |--->FloatBaseType
+                |                        |--->FloatType
+                |                        |--->ComplexBaseType
+                |                                           |--->ComplexType
+                |--->Node
+                |       |--->Variable
+                |       |           |---> Pointer
+                |       |--->FunctionPrototype
+                |                            |--->FunctionDefinition
+                |--->Element
+                |--->Declaration
+                |--->While
+                |--->Scope
+                |--->Stream
+                |--->Print
+                |--->FunctionCall
+                |--->BreakToken
+                |--->ContinueToken
+                |--->NoneToken
+                |--->Return
+
+
+Predefined types
+----------------
+
+A number of ``Type`` instances are provided in the ``sympy.codegen.ast`` module
+for convenience. Perhaps the two most common ones for code-generation (of numeric
+codes) are ``float32`` and ``float64`` (known as single and double precision respectively).
+There are also precision generic versions of Types (for which the codeprinters selects the
+underlying data type at time of printing): ``real``, ``integer``, ``complex_``, ``bool_``.
+
+The other ``Type`` instances defined are:
+
+- ``intc``: Integer type used by C's "int".
+- ``intp``: Integer type used by C's "unsigned".
+- ``int8``, ``int16``, ``int32``, ``int64``: n-bit integers.
+- ``uint8``, ``uint16``, ``uint32``, ``uint64``: n-bit unsigned integers.
+- ``float80``: known as "extended precision" on modern x86/amd64 hardware.
+- ``complex64``: Complex number represented by two ``float32`` numbers
+- ``complex128``: Complex number represented by two ``float64`` numbers
+
+Using the nodes
+---------------
+
+It is possible to construct simple algorithms using the AST nodes. Let's construct a loop applying
+Newton's method::
+
+    >>> from sympy import symbols, cos
+    >>> from sympy.codegen.ast import While, Assignment, aug_assign, Print, QuotedString
+    >>> t, dx, x = symbols('tol delta val')
+    >>> expr = cos(x) - x**3
+    >>> whl = While(abs(dx) > t, [
+    ...     Assignment(dx, -expr/expr.diff(x)),
+    ...     aug_assign(x, '+', dx),
+    ...     Print([x])
+    ... ])
+    >>> from sympy import pycode
+    >>> py_str = pycode(whl)
+    >>> print(py_str)
+    while (abs(delta) > tol):
+        delta = (val**3 - math.cos(val))/(-3*val**2 - math.sin(val))
+        val += delta
+        print(val)
+    >>> import math
+    >>> tol, val, delta = 1e-5, 0.5, float('inf')
+    >>> exec(py_str)
+    1.1121416371
+    0.909672693737
+    0.867263818209
+    0.865477135298
+    0.865474033111
+    >>> print('%3.1g' % (math.cos(val) - val**3))
+    -3e-11
+
+If we want to generate Fortran code for the same while loop we simple call ``fcode``::
+
+    >>> from sympy import fcode
+    >>> print(fcode(whl, standard=2003, source_format='free'))
+    do while (abs(delta) > tol)
+       delta = (val**3 - cos(val))/(-3*val**2 - sin(val))
+       val = val + delta
+       print *, val
+    end do
+
+There is a function constructing a loop (or a complete function) like this in
+:mod:`sympy.codegen.algorithms`.
+
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from collections import defaultdict
+
+from sympy.core.relational import (Ge, Gt, Le, Lt)
+from sympy.core import Symbol, Tuple, Dummy
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr, Atom
+from sympy.core.numbers import Float, Integer, oo
+from sympy.core.sympify import _sympify, sympify, SympifyError
+from sympy.utilities.iterables import (iterable, topological_sort,
+                                       numbered_symbols, filter_symbols)
+
+
+def _mk_Tuple(args):
+    """
+    Create a SymPy Tuple object from an iterable, converting Python strings to
+    AST strings.
+
+    Parameters
+    ==========
+
+    args: iterable
+        Arguments to :class:`sympy.Tuple`.
+
+    Returns
+    =======
+
+    sympy.Tuple
+    """
+    args = [String(arg) if isinstance(arg, str) else arg for arg in args]
+    return Tuple(*args)
+
+
+class CodegenAST(Basic):
+    __slots__ = ()
+
+
+class Token(CodegenAST):
+    """ Base class for the AST types.
+
+    Explanation
+    ===========
+
+    Defining fields are set in ``_fields``. Attributes (defined in _fields)
+    are only allowed to contain instances of Basic (unless atomic, see
+    ``String``). The arguments to ``__new__()`` correspond to the attributes in
+    the order defined in ``_fields`. The ``defaults`` class attribute is a
+    dictionary mapping attribute names to their default values.
+
+    Subclasses should not need to override the ``__new__()`` method. They may
+    define a class or static method named ``_construct_`` for each
+    attribute to process the value passed to ``__new__()``. Attributes listed
+    in the class attribute ``not_in_args`` are not passed to :class:`~.Basic`.
+    """
+
+    __slots__: tuple[str, ...] = ()
+    _fields = __slots__
+    defaults: dict[str, Any] = {}
+    not_in_args: list[str] = []
+    indented_args = ['body']
+
+    @property
+    def is_Atom(self):
+        return len(self._fields) == 0
+
+    @classmethod
+    def _get_constructor(cls, attr):
+        """ Get the constructor function for an attribute by name. """
+        return getattr(cls, '_construct_%s' % attr, lambda x: x)
+
+    @classmethod
+    def _construct(cls, attr, arg):
+        """ Construct an attribute value from argument passed to ``__new__()``. """
+        # arg may be ``NoneToken()``, so comparison is done using == instead of ``is`` operator
+        if arg == None:
+            return cls.defaults.get(attr, none)
+        else:
+            if isinstance(arg, Dummy):  # SymPy's replace uses Dummy instances
+                return arg
+            else:
+                return cls._get_constructor(attr)(arg)
+
+    def __new__(cls, *args, **kwargs):
+        # Pass through existing instances when given as sole argument
+        if len(args) == 1 and not kwargs and isinstance(args[0], cls):
+            return args[0]
+
+        if len(args) > len(cls._fields):
+            raise ValueError("Too many arguments (%d), expected at most %d" % (len(args), len(cls._fields)))
+
+        attrvals = []
+
+        # Process positional arguments
+        for attrname, argval in zip(cls._fields, args):
+            if attrname in kwargs:
+                raise TypeError('Got multiple values for attribute %r' % attrname)
+
+            attrvals.append(cls._construct(attrname, argval))
+
+        # Process keyword arguments
+        for attrname in cls._fields[len(args):]:
+            if attrname in kwargs:
+                argval = kwargs.pop(attrname)
+
+            elif attrname in cls.defaults:
+                argval = cls.defaults[attrname]
+
+            else:
+                raise TypeError('No value for %r given and attribute has no default' % attrname)
+
+            attrvals.append(cls._construct(attrname, argval))
+
+        if kwargs:
+            raise ValueError("Unknown keyword arguments: %s" % ' '.join(kwargs))
+
+        # Parent constructor
+        basic_args = [
+            val for attr, val in zip(cls._fields, attrvals)
+            if attr not in cls.not_in_args
+        ]
+        obj = CodegenAST.__new__(cls, *basic_args)
+
+        # Set attributes
+        for attr, arg in zip(cls._fields, attrvals):
+            setattr(obj, attr, arg)
+
+        return obj
+
+    def __eq__(self, other):
+        if not isinstance(other, self.__class__):
+            return False
+        for attr in self._fields:
+            if getattr(self, attr) != getattr(other, attr):
+                return False
+        return True
+
+    def _hashable_content(self):
+        return tuple([getattr(self, attr) for attr in self._fields])
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def _joiner(self, k, indent_level):
+        return (',\n' + ' '*indent_level) if k in self.indented_args else ', '
+
+    def _indented(self, printer, k, v, *args, **kwargs):
+        il = printer._context['indent_level']
+        def _print(arg):
+            if isinstance(arg, Token):
+                return printer._print(arg, *args, joiner=self._joiner(k, il), **kwargs)
+            else:
+                return printer._print(arg, *args, **kwargs)
+
+        if isinstance(v, Tuple):
+            joined = self._joiner(k, il).join([_print(arg) for arg in v.args])
+            if k in self.indented_args:
+                return '(\n' + ' '*il + joined + ',\n' + ' '*(il - 4) + ')'
+            else:
+                return ('({0},)' if len(v.args) == 1 else '({0})').format(joined)
+        else:
+            return _print(v)
+
+    def _sympyrepr(self, printer, *args, joiner=', ', **kwargs):
+        from sympy.printing.printer import printer_context
+        exclude = kwargs.get('exclude', ())
+        values = [getattr(self, k) for k in self._fields]
+        indent_level = printer._context.get('indent_level', 0)
+
+        arg_reprs = []
+
+        for i, (attr, value) in enumerate(zip(self._fields, values)):
+            if attr in exclude:
+                continue
+
+            # Skip attributes which have the default value
+            if attr in self.defaults and value == self.defaults[attr]:
+                continue
+
+            ilvl = indent_level + 4 if attr in self.indented_args else 0
+            with printer_context(printer, indent_level=ilvl):
+                indented = self._indented(printer, attr, value, *args, **kwargs)
+            arg_reprs.append(('{1}' if i == 0 else '{0}={1}').format(attr, indented.lstrip()))
+
+        return "{}({})".format(self.__class__.__name__, joiner.join(arg_reprs))
+
+    _sympystr = _sympyrepr
+
+    def __repr__(self):  # sympy.core.Basic.__repr__ uses sstr
+        from sympy.printing import srepr
+        return srepr(self)
+
+    def kwargs(self, exclude=(), apply=None):
+        """ Get instance's attributes as dict of keyword arguments.
+
+        Parameters
+        ==========
+
+        exclude : collection of str
+            Collection of keywords to exclude.
+
+        apply : callable, optional
+            Function to apply to all values.
+        """
+        kwargs = {k: getattr(self, k) for k in self._fields if k not in exclude}
+        if apply is not None:
+            return {k: apply(v) for k, v in kwargs.items()}
+        else:
+            return kwargs
+
+class BreakToken(Token):
+    """ Represents 'break' in C/Python ('exit' in Fortran).
+
+    Use the premade instance ``break_`` or instantiate manually.
+
+    Examples
+    ========
+
+    >>> from sympy import ccode, fcode
+    >>> from sympy.codegen.ast import break_
+    >>> ccode(break_)
+    'break'
+    >>> fcode(break_, source_format='free')
+    'exit'
+    """
+
+break_ = BreakToken()
+
+
+class ContinueToken(Token):
+    """ Represents 'continue' in C/Python ('cycle' in Fortran)
+
+    Use the premade instance ``continue_`` or instantiate manually.
+
+    Examples
+    ========
+
+    >>> from sympy import ccode, fcode
+    >>> from sympy.codegen.ast import continue_
+    >>> ccode(continue_)
+    'continue'
+    >>> fcode(continue_, source_format='free')
+    'cycle'
+    """
+
+continue_ = ContinueToken()
+
+class NoneToken(Token):
+    """ The AST equivalence of Python's NoneType
+
+    The corresponding instance of Python's ``None`` is ``none``.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import none, Variable
+    >>> from sympy import pycode
+    >>> print(pycode(Variable('x').as_Declaration(value=none)))
+    x = None
+
+    """
+    def __eq__(self, other):
+        return other is None or isinstance(other, NoneToken)
+
+    def _hashable_content(self):
+        return ()
+
+    def __hash__(self):
+        return super().__hash__()
+
+
+none = NoneToken()
+
+
+class AssignmentBase(CodegenAST):
+    """ Abstract base class for Assignment and AugmentedAssignment.
+
+    Attributes:
+    ===========
+
+    op : str
+        Symbol for assignment operator, e.g. "=", "+=", etc.
+    """
+
+    def __new__(cls, lhs, rhs):
+        lhs = _sympify(lhs)
+        rhs = _sympify(rhs)
+
+        cls._check_args(lhs, rhs)
+
+        return super().__new__(cls, lhs, rhs)
+
+    @property
+    def lhs(self):
+        return self.args[0]
+
+    @property
+    def rhs(self):
+        return self.args[1]
+
+    @classmethod
+    def _check_args(cls, lhs, rhs):
+        """ Check arguments to __new__ and raise exception if any problems found.
+
+        Derived classes may wish to override this.
+        """
+        from sympy.matrices.expressions.matexpr import (
+            MatrixElement, MatrixSymbol)
+        from sympy.tensor.indexed import Indexed
+        from sympy.tensor.array.expressions import ArrayElement
+
+        # Tuple of things that can be on the lhs of an assignment
+        assignable = (Symbol, MatrixSymbol, MatrixElement, Indexed, Element, Variable,
+                ArrayElement)
+        if not isinstance(lhs, assignable):
+            raise TypeError("Cannot assign to lhs of type %s." % type(lhs))
+
+        # Indexed types implement shape, but don't define it until later. This
+        # causes issues in assignment validation. For now, matrices are defined
+        # as anything with a shape that is not an Indexed
+        lhs_is_mat = hasattr(lhs, 'shape') and not isinstance(lhs, Indexed)
+        rhs_is_mat = hasattr(rhs, 'shape') and not isinstance(rhs, Indexed)
+
+        # If lhs and rhs have same structure, then this assignment is ok
+        if lhs_is_mat:
+            if not rhs_is_mat:
+                raise ValueError("Cannot assign a scalar to a matrix.")
+            elif lhs.shape != rhs.shape:
+                raise ValueError("Dimensions of lhs and rhs do not align.")
+        elif rhs_is_mat and not lhs_is_mat:
+            raise ValueError("Cannot assign a matrix to a scalar.")
+
+
+class Assignment(AssignmentBase):
+    """
+    Represents variable assignment for code generation.
+
+    Parameters
+    ==========
+
+    lhs : Expr
+        SymPy object representing the lhs of the expression. These should be
+        singular objects, such as one would use in writing code. Notable types
+        include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that
+        subclass these types are also supported.
+
+    rhs : Expr
+        SymPy object representing the rhs of the expression. This can be any
+        type, provided its shape corresponds to that of the lhs. For example,
+        a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as
+        the dimensions will not align.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, MatrixSymbol, Matrix
+    >>> from sympy.codegen.ast import Assignment
+    >>> x, y, z = symbols('x, y, z')
+    >>> Assignment(x, y)
+    Assignment(x, y)
+    >>> Assignment(x, 0)
+    Assignment(x, 0)
+    >>> A = MatrixSymbol('A', 1, 3)
+    >>> mat = Matrix([x, y, z]).T
+    >>> Assignment(A, mat)
+    Assignment(A, Matrix([[x, y, z]]))
+    >>> Assignment(A[0, 1], x)
+    Assignment(A[0, 1], x)
+    """
+
+    op = ':='
+
+
+class AugmentedAssignment(AssignmentBase):
+    """
+    Base class for augmented assignments.
+
+    Attributes:
+    ===========
+
+    binop : str
+       Symbol for binary operation being applied in the assignment, such as "+",
+       "*", etc.
+    """
+    binop: str | None
+
+    @property
+    def op(self):
+        return self.binop + '='
+
+
+class AddAugmentedAssignment(AugmentedAssignment):
+    binop = '+'
+
+
+class SubAugmentedAssignment(AugmentedAssignment):
+    binop = '-'
+
+
+class MulAugmentedAssignment(AugmentedAssignment):
+    binop = '*'
+
+
+class DivAugmentedAssignment(AugmentedAssignment):
+    binop = '/'
+
+
+class ModAugmentedAssignment(AugmentedAssignment):
+    binop = '%'
+
+
+# Mapping from binary op strings to AugmentedAssignment subclasses
+augassign_classes = {
+    cls.binop: cls for cls in [
+        AddAugmentedAssignment, SubAugmentedAssignment, MulAugmentedAssignment,
+        DivAugmentedAssignment, ModAugmentedAssignment
+    ]
+}
+
+
+def aug_assign(lhs, op, rhs):
+    """
+    Create 'lhs op= rhs'.
+
+    Explanation
+    ===========
+
+    Represents augmented variable assignment for code generation. This is a
+    convenience function. You can also use the AugmentedAssignment classes
+    directly, like AddAugmentedAssignment(x, y).
+
+    Parameters
+    ==========
+
+    lhs : Expr
+        SymPy object representing the lhs of the expression. These should be
+        singular objects, such as one would use in writing code. Notable types
+        include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that
+        subclass these types are also supported.
+
+    op : str
+        Operator (+, -, /, \\*, %).
+
+    rhs : Expr
+        SymPy object representing the rhs of the expression. This can be any
+        type, provided its shape corresponds to that of the lhs. For example,
+        a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as
+        the dimensions will not align.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.codegen.ast import aug_assign
+    >>> x, y = symbols('x, y')
+    >>> aug_assign(x, '+', y)
+    AddAugmentedAssignment(x, y)
+    """
+    if op not in augassign_classes:
+        raise ValueError("Unrecognized operator %s" % op)
+    return augassign_classes[op](lhs, rhs)
+
+
+class CodeBlock(CodegenAST):
+    """
+    Represents a block of code.
+
+    Explanation
+    ===========
+
+    For now only assignments are supported. This restriction will be lifted in
+    the future.
+
+    Useful attributes on this object are:
+
+    ``left_hand_sides``:
+        Tuple of left-hand sides of assignments, in order.
+    ``left_hand_sides``:
+        Tuple of right-hand sides of assignments, in order.
+    ``free_symbols``: Free symbols of the expressions in the right-hand sides
+        which do not appear in the left-hand side of an assignment.
+
+    Useful methods on this object are:
+
+    ``topological_sort``:
+        Class method. Return a CodeBlock with assignments
+        sorted so that variables are assigned before they
+        are used.
+    ``cse``:
+        Return a new CodeBlock with common subexpressions eliminated and
+        pulled out as assignments.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, ccode
+    >>> from sympy.codegen.ast import CodeBlock, Assignment
+    >>> x, y = symbols('x y')
+    >>> c = CodeBlock(Assignment(x, 1), Assignment(y, x + 1))
+    >>> print(ccode(c))
+    x = 1;
+    y = x + 1;
+
+    """
+    def __new__(cls, *args):
+        left_hand_sides = []
+        right_hand_sides = []
+        for i in args:
+            if isinstance(i, Assignment):
+                lhs, rhs = i.args
+                left_hand_sides.append(lhs)
+                right_hand_sides.append(rhs)
+
+        obj = CodegenAST.__new__(cls, *args)
+
+        obj.left_hand_sides = Tuple(*left_hand_sides)
+        obj.right_hand_sides = Tuple(*right_hand_sides)
+        return obj
+
+    def __iter__(self):
+        return iter(self.args)
+
+    def _sympyrepr(self, printer, *args, **kwargs):
+        il = printer._context.get('indent_level', 0)
+        joiner = ',\n' + ' '*il
+        joined = joiner.join(map(printer._print, self.args))
+        return ('{}(\n'.format(' '*(il-4) + self.__class__.__name__,) +
+                ' '*il + joined + '\n' + ' '*(il - 4) + ')')
+
+    _sympystr = _sympyrepr
+
+    @property
+    def free_symbols(self):
+        return super().free_symbols - set(self.left_hand_sides)
+
+    @classmethod
+    def topological_sort(cls, assignments):
+        """
+        Return a CodeBlock with topologically sorted assignments so that
+        variables are assigned before they are used.
+
+        Examples
+        ========
+
+        The existing order of assignments is preserved as much as possible.
+
+        This function assumes that variables are assigned to only once.
+
+        This is a class constructor so that the default constructor for
+        CodeBlock can error when variables are used before they are assigned.
+
+        >>> from sympy import symbols
+        >>> from sympy.codegen.ast import CodeBlock, Assignment
+        >>> x, y, z = symbols('x y z')
+
+        >>> assignments = [
+        ...     Assignment(x, y + z),
+        ...     Assignment(y, z + 1),
+        ...     Assignment(z, 2),
+        ... ]
+        >>> CodeBlock.topological_sort(assignments)
+        CodeBlock(
+            Assignment(z, 2),
+            Assignment(y, z + 1),
+            Assignment(x, y + z)
+        )
+
+        """
+
+        if not all(isinstance(i, Assignment) for i in assignments):
+            # Will support more things later
+            raise NotImplementedError("CodeBlock.topological_sort only supports Assignments")
+
+        if any(isinstance(i, AugmentedAssignment) for i in assignments):
+            raise NotImplementedError("CodeBlock.topological_sort does not yet work with AugmentedAssignments")
+
+        # Create a graph where the nodes are assignments and there is a directed edge
+        # between nodes that use a variable and nodes that assign that
+        # variable, like
+
+        # [(x := 1, y := x + 1), (x := 1, z := y + z), (y := x + 1, z := y + z)]
+
+        # If we then topologically sort these nodes, they will be in
+        # assignment order, like
+
+        # x := 1
+        # y := x + 1
+        # z := y + z
+
+        # A = The nodes
+        #
+        # enumerate keeps nodes in the same order they are already in if
+        # possible. It will also allow us to handle duplicate assignments to
+        # the same variable when those are implemented.
+        A = list(enumerate(assignments))
+
+        # var_map = {variable: [nodes for which this variable is assigned to]}
+        # like {x: [(1, x := y + z), (4, x := 2 * w)], ...}
+        var_map = defaultdict(list)
+        for node in A:
+            i, a = node
+            var_map[a.lhs].append(node)
+
+        # E = Edges in the graph
+        E = []
+        for dst_node in A:
+            i, a = dst_node
+            for s in a.rhs.free_symbols:
+                for src_node in var_map[s]:
+                    E.append((src_node, dst_node))
+
+        ordered_assignments = topological_sort([A, E])
+
+        # De-enumerate the result
+        return cls(*[a for i, a in ordered_assignments])
+
+    def cse(self, symbols=None, optimizations=None, postprocess=None,
+        order='canonical'):
+        """
+        Return a new code block with common subexpressions eliminated.
+
+        Explanation
+        ===========
+
+        See the docstring of :func:`sympy.simplify.cse_main.cse` for more
+        information.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, sin
+        >>> from sympy.codegen.ast import CodeBlock, Assignment
+        >>> x, y, z = symbols('x y z')
+
+        >>> c = CodeBlock(
+        ...     Assignment(x, 1),
+        ...     Assignment(y, sin(x) + 1),
+        ...     Assignment(z, sin(x) - 1),
+        ... )
+        ...
+        >>> c.cse()
+        CodeBlock(
+            Assignment(x, 1),
+            Assignment(x0, sin(x)),
+            Assignment(y, x0 + 1),
+            Assignment(z, x0 - 1)
+        )
+
+        """
+        from sympy.simplify.cse_main import cse
+
+        # Check that the CodeBlock only contains assignments to unique variables
+        if not all(isinstance(i, Assignment) for i in self.args):
+            # Will support more things later
+            raise NotImplementedError("CodeBlock.cse only supports Assignments")
+
+        if any(isinstance(i, AugmentedAssignment) for i in self.args):
+            raise NotImplementedError("CodeBlock.cse does not yet work with AugmentedAssignments")
+
+        for i, lhs in enumerate(self.left_hand_sides):
+            if lhs in self.left_hand_sides[:i]:
+                raise NotImplementedError("Duplicate assignments to the same "
+                    "variable are not yet supported (%s)" % lhs)
+
+        # Ensure new symbols for subexpressions do not conflict with existing
+        existing_symbols = self.atoms(Symbol)
+        if symbols is None:
+            symbols = numbered_symbols()
+        symbols = filter_symbols(symbols, existing_symbols)
+
+        replacements, reduced_exprs = cse(list(self.right_hand_sides),
+            symbols=symbols, optimizations=optimizations, postprocess=postprocess,
+            order=order)
+
+        new_block = [Assignment(var, expr) for var, expr in
+            zip(self.left_hand_sides, reduced_exprs)]
+        new_assignments = [Assignment(var, expr) for var, expr in replacements]
+        return self.topological_sort(new_assignments + new_block)
+
+
+class For(Token):
+    """Represents a 'for-loop' in the code.
+
+    Expressions are of the form:
+        "for target in iter:
+            body..."
+
+    Parameters
+    ==========
+
+    target : symbol
+    iter : iterable
+    body : CodeBlock or iterable
+!        When passed an iterable it is used to instantiate a CodeBlock.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Range
+    >>> from sympy.codegen.ast import aug_assign, For
+    >>> x, i, j, k = symbols('x i j k')
+    >>> for_i = For(i, Range(10), [aug_assign(x, '+', i*j*k)])
+    >>> for_i  # doctest: -NORMALIZE_WHITESPACE
+    For(i, iterable=Range(0, 10, 1), body=CodeBlock(
+        AddAugmentedAssignment(x, i*j*k)
+    ))
+    >>> for_ji = For(j, Range(7), [for_i])
+    >>> for_ji  # doctest: -NORMALIZE_WHITESPACE
+    For(j, iterable=Range(0, 7, 1), body=CodeBlock(
+        For(i, iterable=Range(0, 10, 1), body=CodeBlock(
+            AddAugmentedAssignment(x, i*j*k)
+        ))
+    ))
+    >>> for_kji =For(k, Range(5), [for_ji])
+    >>> for_kji  # doctest: -NORMALIZE_WHITESPACE
+    For(k, iterable=Range(0, 5, 1), body=CodeBlock(
+        For(j, iterable=Range(0, 7, 1), body=CodeBlock(
+            For(i, iterable=Range(0, 10, 1), body=CodeBlock(
+                AddAugmentedAssignment(x, i*j*k)
+            ))
+        ))
+    ))
+    """
+    __slots__ = _fields = ('target', 'iterable', 'body')
+    _construct_target = staticmethod(_sympify)
+
+    @classmethod
+    def _construct_body(cls, itr):
+        if isinstance(itr, CodeBlock):
+            return itr
+        else:
+            return CodeBlock(*itr)
+
+    @classmethod
+    def _construct_iterable(cls, itr):
+        if not iterable(itr):
+            raise TypeError("iterable must be an iterable")
+        if isinstance(itr, list):  # _sympify errors on lists because they are mutable
+            itr = tuple(itr)
+        return _sympify(itr)
+
+
+class String(Atom, Token):
+    """ SymPy object representing a string.
+
+    Atomic object which is not an expression (as opposed to Symbol).
+
+    Parameters
+    ==========
+
+    text : str
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import String
+    >>> f = String('foo')
+    >>> f
+    foo
+    >>> str(f)
+    'foo'
+    >>> f.text
+    'foo'
+    >>> print(repr(f))
+    String('foo')
+
+    """
+    __slots__ = _fields = ('text',)
+    not_in_args = ['text']
+    is_Atom = True
+
+    @classmethod
+    def _construct_text(cls, text):
+        if not isinstance(text, str):
+            raise TypeError("Argument text is not a string type.")
+        return text
+
+    def _sympystr(self, printer, *args, **kwargs):
+        return self.text
+
+    def kwargs(self, exclude = (), apply = None):
+        return {}
+
+    #to be removed when Atom is given a suitable func
+    @property
+    def func(self):
+        return lambda: self
+
+    def _latex(self, printer):
+        from sympy.printing.latex import latex_escape
+        return r'\texttt{{"{}"}}'.format(latex_escape(self.text))
+
+class QuotedString(String):
+    """ Represents a string which should be printed with quotes. """
+
+class Comment(String):
+    """ Represents a comment. """
+
+class Node(Token):
+    """ Subclass of Token, carrying the attribute 'attrs' (Tuple)
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Node, value_const, pointer_const
+    >>> n1 = Node([value_const])
+    >>> n1.attr_params('value_const')  # get the parameters of attribute (by name)
+    ()
+    >>> from sympy.codegen.fnodes import dimension
+    >>> n2 = Node([value_const, dimension(5, 3)])
+    >>> n2.attr_params(value_const)  # get the parameters of attribute (by Attribute instance)
+    ()
+    >>> n2.attr_params('dimension')  # get the parameters of attribute (by name)
+    (5, 3)
+    >>> n2.attr_params(pointer_const) is None
+    True
+
+    """
+
+    __slots__: tuple[str, ...] = ('attrs',)
+    _fields = __slots__
+
+    defaults: dict[str, Any] = {'attrs': Tuple()}
+
+    _construct_attrs = staticmethod(_mk_Tuple)
+
+    def attr_params(self, looking_for):
+        """ Returns the parameters of the Attribute with name ``looking_for`` in self.attrs """
+        for attr in self.attrs:
+            if str(attr.name) == str(looking_for):
+                return attr.parameters
+
+
+class Type(Token):
+    """ Represents a type.
+
+    Explanation
+    ===========
+
+    The naming is a super-set of NumPy naming. Type has a classmethod
+    ``from_expr`` which offer type deduction. It also has a method
+    ``cast_check`` which casts the argument to its type, possibly raising an
+    exception if rounding error is not within tolerances, or if the value is not
+    representable by the underlying data type (e.g. unsigned integers).
+
+    Parameters
+    ==========
+
+    name : str
+        Name of the type, e.g. ``object``, ``int16``, ``float16`` (where the latter two
+        would use the ``Type`` sub-classes ``IntType`` and ``FloatType`` respectively).
+        If a ``Type`` instance is given, the said instance is returned.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Type
+    >>> t = Type.from_expr(42)
+    >>> t
+    integer
+    >>> print(repr(t))
+    IntBaseType(String('integer'))
+    >>> from sympy.codegen.ast import uint8
+    >>> uint8.cast_check(-1)   # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    ValueError: Minimum value for data type bigger than new value.
+    >>> from sympy.codegen.ast import float32
+    >>> v6 = 0.123456
+    >>> float32.cast_check(v6)
+    0.123456
+    >>> v10 = 12345.67894
+    >>> float32.cast_check(v10)  # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    ValueError: Casting gives a significantly different value.
+    >>> boost_mp50 = Type('boost::multiprecision::cpp_dec_float_50')
+    >>> from sympy import cxxcode
+    >>> from sympy.codegen.ast import Declaration, Variable
+    >>> cxxcode(Declaration(Variable('x', type=boost_mp50)))
+    'boost::multiprecision::cpp_dec_float_50 x'
+
+    References
+    ==========
+
+    .. [1] https://numpy.org/doc/stable/user/basics.types.html
+
+    """
+    __slots__: tuple[str, ...] = ('name',)
+    _fields = __slots__
+
+    _construct_name = String
+
+    def _sympystr(self, printer, *args, **kwargs):
+        return str(self.name)
+
+    @classmethod
+    def from_expr(cls, expr):
+        """ Deduces type from an expression or a ``Symbol``.
+
+        Parameters
+        ==========
+
+        expr : number or SymPy object
+            The type will be deduced from type or properties.
+
+        Examples
+        ========
+
+        >>> from sympy.codegen.ast import Type, integer, complex_
+        >>> Type.from_expr(2) == integer
+        True
+        >>> from sympy import Symbol
+        >>> Type.from_expr(Symbol('z', complex=True)) == complex_
+        True
+        >>> Type.from_expr(sum)  # doctest: +ELLIPSIS
+        Traceback (most recent call last):
+          ...
+        ValueError: Could not deduce type from expr.
+
+        Raises
+        ======
+
+        ValueError when type deduction fails.
+
+        """
+        if isinstance(expr, (float, Float)):
+            return real
+        if isinstance(expr, (int, Integer)) or getattr(expr, 'is_integer', False):
+            return integer
+        if getattr(expr, 'is_real', False):
+            return real
+        if isinstance(expr, complex) or getattr(expr, 'is_complex', False):
+            return complex_
+        if isinstance(expr, bool) or getattr(expr, 'is_Relational', False):
+            return bool_
+        else:
+            raise ValueError("Could not deduce type from expr.")
+
+    def _check(self, value):
+        pass
+
+    def cast_check(self, value, rtol=None, atol=0, precision_targets=None):
+        """ Casts a value to the data type of the instance.
+
+        Parameters
+        ==========
+
+        value : number
+        rtol : floating point number
+            Relative tolerance. (will be deduced if not given).
+        atol : floating point number
+            Absolute tolerance (in addition to ``rtol``).
+        type_aliases : dict
+            Maps substitutions for Type, e.g. {integer: int64, real: float32}
+
+        Examples
+        ========
+
+        >>> from sympy.codegen.ast import integer, float32, int8
+        >>> integer.cast_check(3.0) == 3
+        True
+        >>> float32.cast_check(1e-40)  # doctest: +ELLIPSIS
+        Traceback (most recent call last):
+          ...
+        ValueError: Minimum value for data type bigger than new value.
+        >>> int8.cast_check(256)  # doctest: +ELLIPSIS
+        Traceback (most recent call last):
+          ...
+        ValueError: Maximum value for data type smaller than new value.
+        >>> v10 = 12345.67894
+        >>> float32.cast_check(v10)  # doctest: +ELLIPSIS
+        Traceback (most recent call last):
+          ...
+        ValueError: Casting gives a significantly different value.
+        >>> from sympy.codegen.ast import float64
+        >>> float64.cast_check(v10)
+        12345.67894
+        >>> from sympy import Float
+        >>> v18 = Float('0.123456789012345646')
+        >>> float64.cast_check(v18)
+        Traceback (most recent call last):
+          ...
+        ValueError: Casting gives a significantly different value.
+        >>> from sympy.codegen.ast import float80
+        >>> float80.cast_check(v18)
+        0.123456789012345649
+
+        """
+        val = sympify(value)
+
+        ten = Integer(10)
+        exp10 = getattr(self, 'decimal_dig', None)
+
+        if rtol is None:
+            rtol = 1e-15 if exp10 is None else 2.0*ten**(-exp10)
+
+        def tol(num):
+            return atol + rtol*abs(num)
+
+        new_val = self.cast_nocheck(value)
+        self._check(new_val)
+
+        delta = new_val - val
+        if abs(delta) > tol(val):  # rounding, e.g. int(3.5) != 3.5
+            raise ValueError("Casting gives a significantly different value.")
+
+        return new_val
+
+    def _latex(self, printer):
+        from sympy.printing.latex import latex_escape
+        type_name = latex_escape(self.__class__.__name__)
+        name = latex_escape(self.name.text)
+        return r"\text{{{}}}\left(\texttt{{{}}}\right)".format(type_name, name)
+
+
+class IntBaseType(Type):
+    """ Integer base type, contains no size information. """
+    __slots__ = ()
+    cast_nocheck = lambda self, i: Integer(int(i))
+
+
+class _SizedIntType(IntBaseType):
+    __slots__ = ('nbits',)
+    _fields = Type._fields + __slots__
+
+    _construct_nbits = Integer
+
+    def _check(self, value):
+        if value < self.min:
+            raise ValueError("Value is too small: %d < %d" % (value, self.min))
+        if value > self.max:
+            raise ValueError("Value is too big: %d > %d" % (value, self.max))
+
+
+class SignedIntType(_SizedIntType):
+    """ Represents a signed integer type. """
+    __slots__ = ()
+    @property
+    def min(self):
+        return -2**(self.nbits-1)
+
+    @property
+    def max(self):
+        return 2**(self.nbits-1) - 1
+
+
+class UnsignedIntType(_SizedIntType):
+    """ Represents an unsigned integer type. """
+    __slots__ = ()
+    @property
+    def min(self):
+        return 0
+
+    @property
+    def max(self):
+        return 2**self.nbits - 1
+
+two = Integer(2)
+
+class FloatBaseType(Type):
+    """ Represents a floating point number type. """
+    __slots__ = ()
+    cast_nocheck = Float
+
+class FloatType(FloatBaseType):
+    """ Represents a floating point type with fixed bit width.
+
+    Base 2 & one sign bit is assumed.
+
+    Parameters
+    ==========
+
+    name : str
+        Name of the type.
+    nbits : integer
+        Number of bits used (storage).
+    nmant : integer
+        Number of bits used to represent the mantissa.
+    nexp : integer
+        Number of bits used to represent the mantissa.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> from sympy.codegen.ast import FloatType
+    >>> half_precision = FloatType('f16', nbits=16, nmant=10, nexp=5)
+    >>> half_precision.max
+    65504
+    >>> half_precision.tiny == S(2)**-14
+    True
+    >>> half_precision.eps == S(2)**-10
+    True
+    >>> half_precision.dig == 3
+    True
+    >>> half_precision.decimal_dig == 5
+    True
+    >>> half_precision.cast_check(1.0)
+    1.0
+    >>> half_precision.cast_check(1e5)  # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    ValueError: Maximum value for data type smaller than new value.
+    """
+
+    __slots__ = ('nbits', 'nmant', 'nexp',)
+    _fields = Type._fields + __slots__
+
+    _construct_nbits = _construct_nmant = _construct_nexp = Integer
+
+
+    @property
+    def max_exponent(self):
+        """ The largest positive number n, such that 2**(n - 1) is a representable finite value. """
+        # cf. C++'s ``std::numeric_limits::max_exponent``
+        return two**(self.nexp - 1)
+
+    @property
+    def min_exponent(self):
+        """ The lowest negative number n, such that 2**(n - 1) is a valid normalized number. """
+        # cf. C++'s ``std::numeric_limits::min_exponent``
+        return 3 - self.max_exponent
+
+    @property
+    def max(self):
+        """ Maximum value representable. """
+        return (1 - two**-(self.nmant+1))*two**self.max_exponent
+
+    @property
+    def tiny(self):
+        """ The minimum positive normalized value. """
+        # See C macros: FLT_MIN, DBL_MIN, LDBL_MIN
+        # or C++'s ``std::numeric_limits::min``
+        # or numpy.finfo(dtype).tiny
+        return two**(self.min_exponent - 1)
+
+
+    @property
+    def eps(self):
+        """ Difference between 1.0 and the next representable value. """
+        return two**(-self.nmant)
+
+    @property
+    def dig(self):
+        """ Number of decimal digits that are guaranteed to be preserved in text.
+
+        When converting text -> float -> text, you are guaranteed that at least ``dig``
+        number of digits are preserved with respect to rounding or overflow.
+        """
+        from sympy.functions import floor, log
+        return floor(self.nmant * log(2)/log(10))
+
+    @property
+    def decimal_dig(self):
+        """ Number of digits needed to store & load without loss.
+
+        Explanation
+        ===========
+
+        Number of decimal digits needed to guarantee that two consecutive conversions
+        (float -> text -> float) to be idempotent. This is useful when one do not want
+        to loose precision due to rounding errors when storing a floating point value
+        as text.
+        """
+        from sympy.functions import ceiling, log
+        return ceiling((self.nmant + 1) * log(2)/log(10) + 1)
+
+    def cast_nocheck(self, value):
+        """ Casts without checking if out of bounds or subnormal. """
+        if value == oo:  # float(oo) or oo
+            return float(oo)
+        elif value == -oo:  # float(-oo) or -oo
+            return float(-oo)
+        return Float(str(sympify(value).evalf(self.decimal_dig)), self.decimal_dig)
+
+    def _check(self, value):
+        if value < -self.max:
+            raise ValueError("Value is too small: %d < %d" % (value, -self.max))
+        if value > self.max:
+            raise ValueError("Value is too big: %d > %d" % (value, self.max))
+        if abs(value) < self.tiny:
+            raise ValueError("Smallest (absolute) value for data type bigger than new value.")
+
+class ComplexBaseType(FloatBaseType):
+
+    __slots__ = ()
+
+    def cast_nocheck(self, value):
+        """ Casts without checking if out of bounds or subnormal. """
+        from sympy.functions import re, im
+        return (
+            super().cast_nocheck(re(value)) +
+            super().cast_nocheck(im(value))*1j
+        )
+
+    def _check(self, value):
+        from sympy.functions import re, im
+        super()._check(re(value))
+        super()._check(im(value))
+
+
+class ComplexType(ComplexBaseType, FloatType):
+    """ Represents a complex floating point number. """
+    __slots__ = ()
+
+
+# NumPy types:
+intc = IntBaseType('intc')
+intp = IntBaseType('intp')
+int8 = SignedIntType('int8', 8)
+int16 = SignedIntType('int16', 16)
+int32 = SignedIntType('int32', 32)
+int64 = SignedIntType('int64', 64)
+uint8 = UnsignedIntType('uint8', 8)
+uint16 = UnsignedIntType('uint16', 16)
+uint32 = UnsignedIntType('uint32', 32)
+uint64 = UnsignedIntType('uint64', 64)
+float16 = FloatType('float16', 16, nexp=5, nmant=10)  # IEEE 754 binary16, Half precision
+float32 = FloatType('float32', 32, nexp=8, nmant=23)  # IEEE 754 binary32, Single precision
+float64 = FloatType('float64', 64, nexp=11, nmant=52)  # IEEE 754 binary64, Double precision
+float80 = FloatType('float80', 80, nexp=15, nmant=63)  # x86 extended precision (1 integer part bit), "long double"
+float128 = FloatType('float128', 128, nexp=15, nmant=112)  # IEEE 754 binary128, Quadruple precision
+float256 = FloatType('float256', 256, nexp=19, nmant=236)  # IEEE 754 binary256, Octuple precision
+
+complex64 = ComplexType('complex64', nbits=64, **float32.kwargs(exclude=('name', 'nbits')))
+complex128 = ComplexType('complex128', nbits=128, **float64.kwargs(exclude=('name', 'nbits')))
+
+# Generic types (precision may be chosen by code printers):
+untyped = Type('untyped')
+real = FloatBaseType('real')
+integer = IntBaseType('integer')
+complex_ = ComplexBaseType('complex')
+bool_ = Type('bool')
+
+
+class Attribute(Token):
+    """ Attribute (possibly parametrized)
+
+    For use with :class:`sympy.codegen.ast.Node` (which takes instances of
+    ``Attribute`` as ``attrs``).
+
+    Parameters
+    ==========
+
+    name : str
+    parameters : Tuple
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Attribute
+    >>> volatile = Attribute('volatile')
+    >>> volatile
+    volatile
+    >>> print(repr(volatile))
+    Attribute(String('volatile'))
+    >>> a = Attribute('foo', [1, 2, 3])
+    >>> a
+    foo(1, 2, 3)
+    >>> a.parameters == (1, 2, 3)
+    True
+    """
+    __slots__ = _fields = ('name', 'parameters')
+    defaults = {'parameters': Tuple()}
+
+    _construct_name = String
+    _construct_parameters = staticmethod(_mk_Tuple)
+
+    def _sympystr(self, printer, *args, **kwargs):
+        result = str(self.name)
+        if self.parameters:
+            result += '(%s)' % ', '.join((printer._print(
+                arg, *args, **kwargs) for arg in self.parameters))
+        return result
+
+value_const = Attribute('value_const')
+pointer_const = Attribute('pointer_const')
+
+
+class Variable(Node):
+    """ Represents a variable.
+
+    Parameters
+    ==========
+
+    symbol : Symbol
+    type : Type (optional)
+        Type of the variable.
+    attrs : iterable of Attribute instances
+        Will be stored as a Tuple.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol
+    >>> from sympy.codegen.ast import Variable, float32, integer
+    >>> x = Symbol('x')
+    >>> v = Variable(x, type=float32)
+    >>> v.attrs
+    ()
+    >>> v == Variable('x')
+    False
+    >>> v == Variable('x', type=float32)
+    True
+    >>> v
+    Variable(x, type=float32)
+
+    One may also construct a ``Variable`` instance with the type deduced from
+    assumptions about the symbol using the ``deduced`` classmethod:
+
+    >>> i = Symbol('i', integer=True)
+    >>> v = Variable.deduced(i)
+    >>> v.type == integer
+    True
+    >>> v == Variable('i')
+    False
+    >>> from sympy.codegen.ast import value_const
+    >>> value_const in v.attrs
+    False
+    >>> w = Variable('w', attrs=[value_const])
+    >>> w
+    Variable(w, attrs=(value_const,))
+    >>> value_const in w.attrs
+    True
+    >>> w.as_Declaration(value=42)
+    Declaration(Variable(w, value=42, attrs=(value_const,)))
+
+    """
+
+    __slots__ = ('symbol', 'type', 'value')
+    _fields = __slots__ + Node._fields
+
+    defaults = Node.defaults.copy()
+    defaults.update({'type': untyped, 'value': none})
+
+    _construct_symbol = staticmethod(sympify)
+    _construct_value = staticmethod(sympify)
+
+    @classmethod
+    def deduced(cls, symbol, value=None, attrs=Tuple(), cast_check=True):
+        """ Alt. constructor with type deduction from ``Type.from_expr``.
+
+        Deduces type primarily from ``symbol``, secondarily from ``value``.
+
+        Parameters
+        ==========
+
+        symbol : Symbol
+        value : expr
+            (optional) value of the variable.
+        attrs : iterable of Attribute instances
+        cast_check : bool
+            Whether to apply ``Type.cast_check`` on ``value``.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.codegen.ast import Variable, complex_
+        >>> n = Symbol('n', integer=True)
+        >>> str(Variable.deduced(n).type)
+        'integer'
+        >>> x = Symbol('x', real=True)
+        >>> v = Variable.deduced(x)
+        >>> v.type
+        real
+        >>> z = Symbol('z', complex=True)
+        >>> Variable.deduced(z).type == complex_
+        True
+
+        """
+        if isinstance(symbol, Variable):
+            return symbol
+
+        try:
+            type_ = Type.from_expr(symbol)
+        except ValueError:
+            type_ = Type.from_expr(value)
+
+        if value is not None and cast_check:
+            value = type_.cast_check(value)
+        return cls(symbol, type=type_, value=value, attrs=attrs)
+
+    def as_Declaration(self, **kwargs):
+        """ Convenience method for creating a Declaration instance.
+
+        Explanation
+        ===========
+
+        If the variable of the Declaration need to wrap a modified
+        variable keyword arguments may be passed (overriding e.g.
+        the ``value`` of the Variable instance).
+
+        Examples
+        ========
+
+        >>> from sympy.codegen.ast import Variable, NoneToken
+        >>> x = Variable('x')
+        >>> decl1 = x.as_Declaration()
+        >>> # value is special NoneToken() which must be tested with == operator
+        >>> decl1.variable.value is None  # won't work
+        False
+        >>> decl1.variable.value == None  # not PEP-8 compliant
+        True
+        >>> decl1.variable.value == NoneToken()  # OK
+        True
+        >>> decl2 = x.as_Declaration(value=42.0)
+        >>> decl2.variable.value == 42.0
+        True
+
+        """
+        kw = self.kwargs()
+        kw.update(kwargs)
+        return Declaration(self.func(**kw))
+
+    def _relation(self, rhs, op):
+        try:
+            rhs = _sympify(rhs)
+        except SympifyError:
+            raise TypeError("Invalid comparison %s < %s" % (self, rhs))
+        return op(self, rhs, evaluate=False)
+
+    __lt__ = lambda self, other: self._relation(other, Lt)
+    __le__ = lambda self, other: self._relation(other, Le)
+    __ge__ = lambda self, other: self._relation(other, Ge)
+    __gt__ = lambda self, other: self._relation(other, Gt)
+
+class Pointer(Variable):
+    """ Represents a pointer. See ``Variable``.
+
+    Examples
+    ========
+
+    Can create instances of ``Element``:
+
+    >>> from sympy import Symbol
+    >>> from sympy.codegen.ast import Pointer
+    >>> i = Symbol('i', integer=True)
+    >>> p = Pointer('x')
+    >>> p[i+1]
+    Element(x, indices=(i + 1,))
+
+    """
+    __slots__ = ()
+
+    def __getitem__(self, key):
+        try:
+            return Element(self.symbol, key)
+        except TypeError:
+            return Element(self.symbol, (key,))
+
+
+class Element(Token):
+    """ Element in (a possibly N-dimensional) array.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Element
+    >>> elem = Element('x', 'ijk')
+    >>> elem.symbol.name == 'x'
+    True
+    >>> elem.indices
+    (i, j, k)
+    >>> from sympy import ccode
+    >>> ccode(elem)
+    'x[i][j][k]'
+    >>> ccode(Element('x', 'ijk', strides='lmn', offset='o'))
+    'x[i*l + j*m + k*n + o]'
+
+    """
+    __slots__ = _fields = ('symbol', 'indices', 'strides', 'offset')
+    defaults = {'strides': none, 'offset': none}
+    _construct_symbol = staticmethod(sympify)
+    _construct_indices = staticmethod(lambda arg: Tuple(*arg))
+    _construct_strides = staticmethod(lambda arg: Tuple(*arg))
+    _construct_offset = staticmethod(sympify)
+
+
+class Declaration(Token):
+    """ Represents a variable declaration
+
+    Parameters
+    ==========
+
+    variable : Variable
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Declaration, NoneToken, untyped
+    >>> z = Declaration('z')
+    >>> z.variable.type == untyped
+    True
+    >>> # value is special NoneToken() which must be tested with == operator
+    >>> z.variable.value is None  # won't work
+    False
+    >>> z.variable.value == None  # not PEP-8 compliant
+    True
+    >>> z.variable.value == NoneToken()  # OK
+    True
+    """
+    __slots__ = _fields = ('variable',)
+    _construct_variable = Variable
+
+
+class While(Token):
+    """ Represents a 'for-loop' in the code.
+
+    Expressions are of the form:
+        "while condition:
+             body..."
+
+    Parameters
+    ==========
+
+    condition : expression convertible to Boolean
+    body : CodeBlock or iterable
+        When passed an iterable it is used to instantiate a CodeBlock.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Gt, Abs
+    >>> from sympy.codegen import aug_assign, Assignment, While
+    >>> x, dx = symbols('x dx')
+    >>> expr = 1 - x**2
+    >>> whl = While(Gt(Abs(dx), 1e-9), [
+    ...     Assignment(dx, -expr/expr.diff(x)),
+    ...     aug_assign(x, '+', dx)
+    ... ])
+
+    """
+    __slots__ = _fields = ('condition', 'body')
+    _construct_condition = staticmethod(lambda cond: _sympify(cond))
+
+    @classmethod
+    def _construct_body(cls, itr):
+        if isinstance(itr, CodeBlock):
+            return itr
+        else:
+            return CodeBlock(*itr)
+
+
+class Scope(Token):
+    """ Represents a scope in the code.
+
+    Parameters
+    ==========
+
+    body : CodeBlock or iterable
+        When passed an iterable it is used to instantiate a CodeBlock.
+
+    """
+    __slots__ = _fields = ('body',)
+
+    @classmethod
+    def _construct_body(cls, itr):
+        if isinstance(itr, CodeBlock):
+            return itr
+        else:
+            return CodeBlock(*itr)
+
+
+class Stream(Token):
+    """ Represents a stream.
+
+    There are two predefined Stream instances ``stdout`` & ``stderr``.
+
+    Parameters
+    ==========
+
+    name : str
+
+    Examples
+    ========
+
+    >>> from sympy import pycode, Symbol
+    >>> from sympy.codegen.ast import Print, stderr, QuotedString
+    >>> print(pycode(Print(['x'], file=stderr)))
+    print(x, file=sys.stderr)
+    >>> x = Symbol('x')
+    >>> print(pycode(Print([QuotedString('x')], file=stderr)))  # print literally "x"
+    print("x", file=sys.stderr)
+
+    """
+    __slots__ = _fields = ('name',)
+    _construct_name = String
+
+stdout = Stream('stdout')
+stderr = Stream('stderr')
+
+
+class Print(Token):
+    r""" Represents print command in the code.
+
+    Parameters
+    ==========
+
+    formatstring : str
+    *args : Basic instances (or convertible to such through sympify)
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Print
+    >>> from sympy import pycode
+    >>> print(pycode(Print('x y'.split(), "coordinate: %12.5g %12.5g\\n")))
+    print("coordinate: %12.5g %12.5g\n" % (x, y), end="")
+
+    """
+
+    __slots__ = _fields = ('print_args', 'format_string', 'file')
+    defaults = {'format_string': none, 'file': none}
+
+    _construct_print_args = staticmethod(_mk_Tuple)
+    _construct_format_string = QuotedString
+    _construct_file = Stream
+
+
+class FunctionPrototype(Node):
+    """ Represents a function prototype
+
+    Allows the user to generate forward declaration in e.g. C/C++.
+
+    Parameters
+    ==========
+
+    return_type : Type
+    name : str
+    parameters: iterable of Variable instances
+    attrs : iterable of Attribute instances
+
+    Examples
+    ========
+
+    >>> from sympy import ccode, symbols
+    >>> from sympy.codegen.ast import real, FunctionPrototype
+    >>> x, y = symbols('x y', real=True)
+    >>> fp = FunctionPrototype(real, 'foo', [x, y])
+    >>> ccode(fp)
+    'double foo(double x, double y)'
+
+    """
+
+    __slots__ = ('return_type', 'name', 'parameters')
+    _fields: tuple[str, ...] = __slots__ + Node._fields
+
+    _construct_return_type = Type
+    _construct_name = String
+
+    @staticmethod
+    def _construct_parameters(args):
+        def _var(arg):
+            if isinstance(arg, Declaration):
+                return arg.variable
+            elif isinstance(arg, Variable):
+                return arg
+            else:
+                return Variable.deduced(arg)
+        return Tuple(*map(_var, args))
+
+    @classmethod
+    def from_FunctionDefinition(cls, func_def):
+        if not isinstance(func_def, FunctionDefinition):
+            raise TypeError("func_def is not an instance of FunctionDefinition")
+        return cls(**func_def.kwargs(exclude=('body',)))
+
+
+class FunctionDefinition(FunctionPrototype):
+    """ Represents a function definition in the code.
+
+    Parameters
+    ==========
+
+    return_type : Type
+    name : str
+    parameters: iterable of Variable instances
+    body : CodeBlock or iterable
+    attrs : iterable of Attribute instances
+
+    Examples
+    ========
+
+    >>> from sympy import ccode, symbols
+    >>> from sympy.codegen.ast import real, FunctionPrototype
+    >>> x, y = symbols('x y', real=True)
+    >>> fp = FunctionPrototype(real, 'foo', [x, y])
+    >>> ccode(fp)
+    'double foo(double x, double y)'
+    >>> from sympy.codegen.ast import FunctionDefinition, Return
+    >>> body = [Return(x*y)]
+    >>> fd = FunctionDefinition.from_FunctionPrototype(fp, body)
+    >>> print(ccode(fd))
+    double foo(double x, double y){
+        return x*y;
+    }
+    """
+
+    __slots__ = ('body', )
+    _fields = FunctionPrototype._fields[:-1] + __slots__ + Node._fields
+
+    @classmethod
+    def _construct_body(cls, itr):
+        if isinstance(itr, CodeBlock):
+            return itr
+        else:
+            return CodeBlock(*itr)
+
+    @classmethod
+    def from_FunctionPrototype(cls, func_proto, body):
+        if not isinstance(func_proto, FunctionPrototype):
+            raise TypeError("func_proto is not an instance of FunctionPrototype")
+        return cls(body=body, **func_proto.kwargs())
+
+
+class Return(Token):
+    """ Represents a return command in the code.
+
+    Parameters
+    ==========
+
+    return : Basic
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Return
+    >>> from sympy.printing.pycode import pycode
+    >>> from sympy import Symbol
+    >>> x = Symbol('x')
+    >>> print(pycode(Return(x)))
+    return x
+
+    """
+    __slots__ = _fields = ('return',)
+    _construct_return=staticmethod(_sympify)
+
+
+class FunctionCall(Token, Expr):
+    """ Represents a call to a function in the code.
+
+    Parameters
+    ==========
+
+    name : str
+    function_args : Tuple
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import FunctionCall
+    >>> from sympy import pycode
+    >>> fcall = FunctionCall('foo', 'bar baz'.split())
+    >>> print(pycode(fcall))
+    foo(bar, baz)
+
+    """
+    __slots__ = _fields = ('name', 'function_args')
+
+    _construct_name = String
+    _construct_function_args = staticmethod(lambda args: Tuple(*args))
+
+
+class Raise(Token):
+    """ Prints as 'raise ...' in Python, 'throw ...' in C++"""
+    __slots__ = _fields = ('exception',)
+
+
+class RuntimeError_(Token):
+    """ Represents 'std::runtime_error' in C++ and 'RuntimeError' in Python.
+
+    Note that the latter is uncommon, and you might want to use e.g. ValueError.
+    """
+    __slots__ = _fields = ('message',)
+    _construct_message = String
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cfunctions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cfunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b79291f128aef1cb83b327782840508e59a9cc8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cfunctions.py
@@ -0,0 +1,558 @@
+"""
+This module contains SymPy functions mathcin corresponding to special math functions in the
+C standard library (since C99, also available in C++11).
+
+The functions defined in this module allows the user to express functions such as ``expm1``
+as a SymPy function for symbolic manipulation.
+
+"""
+from sympy.core.function import ArgumentIndexError, Function
+from sympy.core.numbers import Rational
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.logic.boolalg import BooleanFunction, true, false
+
+def _expm1(x):
+    return exp(x) - S.One
+
+
+class expm1(Function):
+    """
+    Represents the exponential function minus one.
+
+    Explanation
+    ===========
+
+    The benefit of using ``expm1(x)`` over ``exp(x) - 1``
+    is that the latter is prone to cancellation under finite precision
+    arithmetic when x is close to zero.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import expm1
+    >>> '%.0e' % expm1(1e-99).evalf()
+    '1e-99'
+    >>> from math import exp
+    >>> exp(1e-99) - 1
+    0.0
+    >>> expm1(x).diff(x)
+    exp(x)
+
+    See Also
+    ========
+
+    log1p
+    """
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return exp(*self.args)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_expand_func(self, **hints):
+        return _expm1(*self.args)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return exp(arg) - S.One
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_exp
+
+    @classmethod
+    def eval(cls, arg):
+        exp_arg = exp.eval(arg)
+        if exp_arg is not None:
+            return exp_arg - S.One
+
+    def _eval_is_real(self):
+        return self.args[0].is_real
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+
+def _log1p(x):
+    return log(x + S.One)
+
+
+class log1p(Function):
+    """
+    Represents the natural logarithm of a number plus one.
+
+    Explanation
+    ===========
+
+    The benefit of using ``log1p(x)`` over ``log(x + 1)``
+    is that the latter is prone to cancellation under finite precision
+    arithmetic when x is close to zero.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import log1p
+    >>> from sympy import expand_log
+    >>> '%.0e' % expand_log(log1p(1e-99)).evalf()
+    '1e-99'
+    >>> from math import log
+    >>> log(1 + 1e-99)
+    0.0
+    >>> log1p(x).diff(x)
+    1/(x + 1)
+
+    See Also
+    ========
+
+    expm1
+    """
+    nargs = 1
+
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return S.One/(self.args[0] + S.One)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    def _eval_expand_func(self, **hints):
+        return _log1p(*self.args)
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return _log1p(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Rational:
+            return log(arg + S.One)
+        elif not arg.is_Float:  # not safe to add 1 to Float
+            return log.eval(arg + S.One)
+        elif arg.is_number:
+            return log(Rational(arg) + S.One)
+
+    def _eval_is_real(self):
+        return (self.args[0] + S.One).is_nonnegative
+
+    def _eval_is_finite(self):
+        if (self.args[0] + S.One).is_zero:
+            return False
+        return self.args[0].is_finite
+
+    def _eval_is_positive(self):
+        return self.args[0].is_positive
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+    def _eval_is_nonnegative(self):
+        return self.args[0].is_nonnegative
+
+_Two = S(2)
+
+def _exp2(x):
+    return Pow(_Two, x)
+
+class exp2(Function):
+    """
+    Represents the exponential function with base two.
+
+    Explanation
+    ===========
+
+    The benefit of using ``exp2(x)`` over ``2**x``
+    is that the latter is not as efficient under finite precision
+    arithmetic.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import exp2
+    >>> exp2(2).evalf() == 4.0
+    True
+    >>> exp2(x).diff(x)
+    log(2)*exp2(x)
+
+    See Also
+    ========
+
+    log2
+    """
+    nargs = 1
+
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return self*log(_Two)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        return _exp2(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_Pow
+
+    def _eval_expand_func(self, **hints):
+        return _exp2(*self.args)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_number:
+            return _exp2(arg)
+
+
+def _log2(x):
+    return log(x)/log(_Two)
+
+
+class log2(Function):
+    """
+    Represents the logarithm function with base two.
+
+    Explanation
+    ===========
+
+    The benefit of using ``log2(x)`` over ``log(x)/log(2)``
+    is that the latter is not as efficient under finite precision
+    arithmetic.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import log2
+    >>> log2(4).evalf() == 2.0
+    True
+    >>> log2(x).diff(x)
+    1/(x*log(2))
+
+    See Also
+    ========
+
+    exp2
+    log10
+    """
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return S.One/(log(_Two)*self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_number:
+            result = log.eval(arg, base=_Two)
+            if result.is_Atom:
+                return result
+        elif arg.is_Pow and arg.base == _Two:
+            return arg.exp
+
+    def _eval_evalf(self, *args, **kwargs):
+        return self.rewrite(log).evalf(*args, **kwargs)
+
+    def _eval_expand_func(self, **hints):
+        return _log2(*self.args)
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return _log2(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+
+def _fma(x, y, z):
+    return x*y + z
+
+
+class fma(Function):
+    """
+    Represents "fused multiply add".
+
+    Explanation
+    ===========
+
+    The benefit of using ``fma(x, y, z)`` over ``x*y + z``
+    is that, under finite precision arithmetic, the former is
+    supported by special instructions on some CPUs.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y, z
+    >>> from sympy.codegen.cfunctions import fma
+    >>> fma(x, y, z).diff(x)
+    y
+
+    """
+    nargs = 3
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex in (1, 2):
+            return self.args[2 - argindex]
+        elif argindex == 3:
+            return S.One
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    def _eval_expand_func(self, **hints):
+        return _fma(*self.args)
+
+    def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs):
+        return _fma(arg)
+
+
+_Ten = S(10)
+
+
+def _log10(x):
+    return log(x)/log(_Ten)
+
+
+class log10(Function):
+    """
+    Represents the logarithm function with base ten.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import log10
+    >>> log10(100).evalf() == 2.0
+    True
+    >>> log10(x).diff(x)
+    1/(x*log(10))
+
+    See Also
+    ========
+
+    log2
+    """
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return S.One/(log(_Ten)*self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_number:
+            result = log.eval(arg, base=_Ten)
+            if result.is_Atom:
+                return result
+        elif arg.is_Pow and arg.base == _Ten:
+            return arg.exp
+
+    def _eval_expand_func(self, **hints):
+        return _log10(*self.args)
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return _log10(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+
+def _Sqrt(x):
+    return Pow(x, S.Half)
+
+
+class Sqrt(Function):  # 'sqrt' already defined in sympy.functions.elementary.miscellaneous
+    """
+    Represents the square root function.
+
+    Explanation
+    ===========
+
+    The reason why one would use ``Sqrt(x)`` over ``sqrt(x)``
+    is that the latter is internally represented as ``Pow(x, S.Half)`` which
+    may not be what one wants when doing code-generation.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import Sqrt
+    >>> Sqrt(x)
+    Sqrt(x)
+    >>> Sqrt(x).diff(x)
+    1/(2*sqrt(x))
+
+    See Also
+    ========
+
+    Cbrt
+    """
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return Pow(self.args[0], Rational(-1, 2))/_Two
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_expand_func(self, **hints):
+        return _Sqrt(*self.args)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        return _Sqrt(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_Pow
+
+
+def _Cbrt(x):
+    return Pow(x, Rational(1, 3))
+
+
+class Cbrt(Function):  # 'cbrt' already defined in sympy.functions.elementary.miscellaneous
+    """
+    Represents the cube root function.
+
+    Explanation
+    ===========
+
+    The reason why one would use ``Cbrt(x)`` over ``cbrt(x)``
+    is that the latter is internally represented as ``Pow(x, Rational(1, 3))`` which
+    may not be what one wants when doing code-generation.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cfunctions import Cbrt
+    >>> Cbrt(x)
+    Cbrt(x)
+    >>> Cbrt(x).diff(x)
+    1/(3*x**(2/3))
+
+    See Also
+    ========
+
+    Sqrt
+    """
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return Pow(self.args[0], Rational(-_Two/3))/3
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    def _eval_expand_func(self, **hints):
+        return _Cbrt(*self.args)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        return _Cbrt(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_Pow
+
+
+def _hypot(x, y):
+    return sqrt(Pow(x, 2) + Pow(y, 2))
+
+
+class hypot(Function):
+    """
+    Represents the hypotenuse function.
+
+    Explanation
+    ===========
+
+    The hypotenuse function is provided by e.g. the math library
+    in the C99 standard, hence one may want to represent the function
+    symbolically when doing code-generation.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy.codegen.cfunctions import hypot
+    >>> hypot(3, 4).evalf() == 5.0
+    True
+    >>> hypot(x, y)
+    hypot(x, y)
+    >>> hypot(x, y).diff(x)
+    x/hypot(x, y)
+
+    """
+    nargs = 2
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex in (1, 2):
+            return 2*self.args[argindex-1]/(_Two*self.func(*self.args))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    def _eval_expand_func(self, **hints):
+        return _hypot(*self.args)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        return _hypot(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_Pow
+
+
+class isnan(BooleanFunction):
+    nargs = 1
+
+    @classmethod
+    def eval(cls, arg):
+        if arg is S.NaN:
+            return true
+        elif arg.is_number:
+            return false
+        else:
+            return None
+
+
+class isinf(BooleanFunction):
+    nargs = 1
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_infinite:
+            return true
+        elif arg.is_finite:
+            return false
+        else:
+            return None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cnodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cnodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd2a324ee49cabcd42e99ca5d8e5379cc9262c4e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cnodes.py
@@ -0,0 +1,156 @@
+"""
+AST nodes specific to the C family of languages
+"""
+
+from sympy.codegen.ast import (
+    Attribute, Declaration, Node, String, Token, Type, none,
+    FunctionCall, CodeBlock
+    )
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.sympify import sympify
+
+void = Type('void')
+
+restrict = Attribute('restrict')  # guarantees no pointer aliasing
+volatile = Attribute('volatile')
+static = Attribute('static')
+
+
+def alignof(arg):
+    """ Generate of FunctionCall instance for calling 'alignof' """
+    return FunctionCall('alignof', [String(arg) if isinstance(arg, str) else arg])
+
+
+def sizeof(arg):
+    """ Generate of FunctionCall instance for calling 'sizeof'
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import real
+    >>> from sympy.codegen.cnodes import sizeof
+    >>> from sympy import ccode
+    >>> ccode(sizeof(real))
+    'sizeof(double)'
+    """
+    return FunctionCall('sizeof', [String(arg) if isinstance(arg, str) else arg])
+
+
+class CommaOperator(Basic):
+    """ Represents the comma operator in C """
+    def __new__(cls, *args):
+        return Basic.__new__(cls, *[sympify(arg) for arg in args])
+
+
+class Label(Node):
+    """ Label for use with e.g. goto statement.
+
+    Examples
+    ========
+
+    >>> from sympy import ccode, Symbol
+    >>> from sympy.codegen.cnodes import Label, PreIncrement
+    >>> print(ccode(Label('foo')))
+    foo:
+    >>> print(ccode(Label('bar', [PreIncrement(Symbol('a'))])))
+    bar:
+    ++(a);
+
+    """
+    __slots__ = _fields = ('name', 'body')
+    defaults = {'body': none}
+    _construct_name = String
+
+    @classmethod
+    def _construct_body(cls, itr):
+        if isinstance(itr, CodeBlock):
+            return itr
+        else:
+            return CodeBlock(*itr)
+
+
+class goto(Token):
+    """ Represents goto in C """
+    __slots__ = _fields = ('label',)
+    _construct_label = Label
+
+
+class PreDecrement(Basic):
+    """ Represents the pre-decrement operator
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cnodes import PreDecrement
+    >>> from sympy import ccode
+    >>> ccode(PreDecrement(x))
+    '--(x)'
+
+    """
+    nargs = 1
+
+
+class PostDecrement(Basic):
+    """ Represents the post-decrement operator
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cnodes import PostDecrement
+    >>> from sympy import ccode
+    >>> ccode(PostDecrement(x))
+    '(x)--'
+
+    """
+    nargs = 1
+
+
+class PreIncrement(Basic):
+    """ Represents the pre-increment operator
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cnodes import PreIncrement
+    >>> from sympy import ccode
+    >>> ccode(PreIncrement(x))
+    '++(x)'
+
+    """
+    nargs = 1
+
+
+class PostIncrement(Basic):
+    """ Represents the post-increment operator
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.codegen.cnodes import PostIncrement
+    >>> from sympy import ccode
+    >>> ccode(PostIncrement(x))
+    '(x)++'
+
+    """
+    nargs = 1
+
+
+class struct(Node):
+    """ Represents a struct in C """
+    __slots__ = _fields = ('name', 'declarations')
+    defaults = {'name': none}
+    _construct_name = String
+
+    @classmethod
+    def _construct_declarations(cls, args):
+        return Tuple(*[Declaration(arg) for arg in args])
+
+
+class union(struct):
+    """ Represents a union in C """
+    __slots__ = ()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..2182ac1f3455da490a0bb57f8d6731fe8a29a232
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cutils.py
@@ -0,0 +1,8 @@
+from sympy.printing.c import C99CodePrinter
+
+def render_as_source_file(content, Printer=C99CodePrinter, settings=None):
+    """ Renders a C source file (with required #include statements) """
+    printer = Printer(settings or {})
+    code_str = printer.doprint(content)
+    includes = '\n'.join(['#include <%s>' % h for h in printer.headers])
+    return includes + '\n\n' + code_str
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cxxnodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cxxnodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..7f7aafd01ab2de99ad0f668275889863fc73f5aa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/cxxnodes.py
@@ -0,0 +1,14 @@
+"""
+AST nodes specific to C++.
+"""
+
+from sympy.codegen.ast import Attribute, String, Token, Type, none
+
+class using(Token):
+    """ Represents a 'using' statement in C++ """
+    __slots__ = _fields = ('type', 'alias')
+    defaults = {'alias': none}
+    _construct_type = Type
+    _construct_alias = String
+
+constexpr = Attribute('constexpr')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/fnodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/fnodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..8b972fcfe4d4de4cfe74d75705f42c5e112a9b43
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/fnodes.py
@@ -0,0 +1,658 @@
+"""
+AST nodes specific to Fortran.
+
+The functions defined in this module allows the user to express functions such as ``dsign``
+as a SymPy function for symbolic manipulation.
+"""
+
+from __future__ import annotations
+from sympy.codegen.ast import (
+    Attribute, CodeBlock, FunctionCall, Node, none, String,
+    Token, _mk_Tuple, Variable
+)
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import Function
+from sympy.core.numbers import Float, Integer
+from sympy.core.symbol import Str
+from sympy.core.sympify import sympify
+from sympy.logic import true, false
+from sympy.utilities.iterables import iterable
+
+
+
+pure = Attribute('pure')
+elemental = Attribute('elemental')  # (all elemental procedures are also pure)
+
+intent_in = Attribute('intent_in')
+intent_out = Attribute('intent_out')
+intent_inout = Attribute('intent_inout')
+
+allocatable = Attribute('allocatable')
+
+class Program(Token):
+    """ Represents a 'program' block in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.ast import Print
+    >>> from sympy.codegen.fnodes import Program
+    >>> prog = Program('myprogram', [Print([42])])
+    >>> from sympy import fcode
+    >>> print(fcode(prog, source_format='free'))
+    program myprogram
+        print *, 42
+    end program
+
+    """
+    __slots__ = _fields = ('name', 'body')
+    _construct_name = String
+    _construct_body = staticmethod(lambda body: CodeBlock(*body))
+
+
+class use_rename(Token):
+    """ Represents a renaming in a use statement in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import use_rename, use
+    >>> from sympy import fcode
+    >>> ren = use_rename("thingy", "convolution2d")
+    >>> print(fcode(ren, source_format='free'))
+    thingy => convolution2d
+    >>> full = use('signallib', only=['snr', ren])
+    >>> print(fcode(full, source_format='free'))
+    use signallib, only: snr, thingy => convolution2d
+
+    """
+    __slots__ = _fields = ('local', 'original')
+    _construct_local = String
+    _construct_original = String
+
+def _name(arg):
+    if hasattr(arg, 'name'):
+        return arg.name
+    else:
+        return String(arg)
+
+class use(Token):
+    """ Represents a use statement in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import use
+    >>> from sympy import fcode
+    >>> fcode(use('signallib'), source_format='free')
+    'use signallib'
+    >>> fcode(use('signallib', [('metric', 'snr')]), source_format='free')
+    'use signallib, metric => snr'
+    >>> fcode(use('signallib', only=['snr', 'convolution2d']), source_format='free')
+    'use signallib, only: snr, convolution2d'
+
+    """
+    __slots__ = _fields = ('namespace', 'rename', 'only')
+    defaults = {'rename': none, 'only': none}
+    _construct_namespace = staticmethod(_name)
+    _construct_rename = staticmethod(lambda args: Tuple(*[arg if isinstance(arg, use_rename) else use_rename(*arg) for arg in args]))
+    _construct_only = staticmethod(lambda args: Tuple(*[arg if isinstance(arg, use_rename) else _name(arg) for arg in args]))
+
+
+class Module(Token):
+    """ Represents a module in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import Module
+    >>> from sympy import fcode
+    >>> print(fcode(Module('signallib', ['implicit none'], []), source_format='free'))
+    module signallib
+    implicit none
+    
+    contains
+    
+    
+    end module
+
+    """
+    __slots__ = _fields = ('name', 'declarations', 'definitions')
+    defaults = {'declarations': Tuple()}
+    _construct_name = String
+
+    @classmethod
+    def _construct_declarations(cls, args):
+        args = [Str(arg) if isinstance(arg, str) else arg for arg in args]
+        return CodeBlock(*args)
+
+    _construct_definitions = staticmethod(lambda arg: CodeBlock(*arg))
+
+
+class Subroutine(Node):
+    """ Represents a subroutine in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy import fcode, symbols
+    >>> from sympy.codegen.ast import Print
+    >>> from sympy.codegen.fnodes import Subroutine
+    >>> x, y = symbols('x y', real=True)
+    >>> sub = Subroutine('mysub', [x, y], [Print([x**2 + y**2, x*y])])
+    >>> print(fcode(sub, source_format='free', standard=2003))
+    subroutine mysub(x, y)
+    real*8 :: x
+    real*8 :: y
+    print *, x**2 + y**2, x*y
+    end subroutine
+
+    """
+    __slots__ = ('name', 'parameters', 'body')
+    _fields = __slots__ + Node._fields
+    _construct_name = String
+    _construct_parameters = staticmethod(lambda params: Tuple(*map(Variable.deduced, params)))
+
+    @classmethod
+    def _construct_body(cls, itr):
+        if isinstance(itr, CodeBlock):
+            return itr
+        else:
+            return CodeBlock(*itr)
+
+class SubroutineCall(Token):
+    """ Represents a call to a subroutine in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import SubroutineCall
+    >>> from sympy import fcode
+    >>> fcode(SubroutineCall('mysub', 'x y'.split()))
+    '       call mysub(x, y)'
+
+    """
+    __slots__ = _fields = ('name', 'subroutine_args')
+    _construct_name = staticmethod(_name)
+    _construct_subroutine_args = staticmethod(_mk_Tuple)
+
+
+class Do(Token):
+    """ Represents a Do loop in in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy import fcode, symbols
+    >>> from sympy.codegen.ast import aug_assign, Print
+    >>> from sympy.codegen.fnodes import Do
+    >>> i, n = symbols('i n', integer=True)
+    >>> r = symbols('r', real=True)
+    >>> body = [aug_assign(r, '+', 1/i), Print([i, r])]
+    >>> do1 = Do(body, i, 1, n)
+    >>> print(fcode(do1, source_format='free'))
+    do i = 1, n
+        r = r + 1d0/i
+        print *, i, r
+    end do
+    >>> do2 = Do(body, i, 1, n, 2)
+    >>> print(fcode(do2, source_format='free'))
+    do i = 1, n, 2
+        r = r + 1d0/i
+        print *, i, r
+    end do
+
+    """
+
+    __slots__ = _fields = ('body', 'counter', 'first', 'last', 'step', 'concurrent')
+    defaults = {'step': Integer(1), 'concurrent': false}
+    _construct_body = staticmethod(lambda body: CodeBlock(*body))
+    _construct_counter = staticmethod(sympify)
+    _construct_first = staticmethod(sympify)
+    _construct_last = staticmethod(sympify)
+    _construct_step = staticmethod(sympify)
+    _construct_concurrent = staticmethod(lambda arg: true if arg else false)
+
+
+class ArrayConstructor(Token):
+    """ Represents an array constructor.
+
+    Examples
+    ========
+
+    >>> from sympy import fcode
+    >>> from sympy.codegen.fnodes import ArrayConstructor
+    >>> ac = ArrayConstructor([1, 2, 3])
+    >>> fcode(ac, standard=95, source_format='free')
+    '(/1, 2, 3/)'
+    >>> fcode(ac, standard=2003, source_format='free')
+    '[1, 2, 3]'
+
+    """
+    __slots__ = _fields = ('elements',)
+    _construct_elements = staticmethod(_mk_Tuple)
+
+
+class ImpliedDoLoop(Token):
+    """ Represents an implied do loop in Fortran.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, fcode
+    >>> from sympy.codegen.fnodes import ImpliedDoLoop, ArrayConstructor
+    >>> i = Symbol('i', integer=True)
+    >>> idl = ImpliedDoLoop(i**3, i, -3, 3, 2)  # -27, -1, 1, 27
+    >>> ac = ArrayConstructor([-28, idl, 28]) # -28, -27, -1, 1, 27, 28
+    >>> fcode(ac, standard=2003, source_format='free')
+    '[-28, (i**3, i = -3, 3, 2), 28]'
+
+    """
+    __slots__ = _fields = ('expr', 'counter', 'first', 'last', 'step')
+    defaults = {'step': Integer(1)}
+    _construct_expr = staticmethod(sympify)
+    _construct_counter = staticmethod(sympify)
+    _construct_first = staticmethod(sympify)
+    _construct_last = staticmethod(sympify)
+    _construct_step = staticmethod(sympify)
+
+
+class Extent(Basic):
+    """ Represents a dimension extent.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import Extent
+    >>> e = Extent(-3, 3)  # -3, -2, -1, 0, 1, 2, 3
+    >>> from sympy import fcode
+    >>> fcode(e, source_format='free')
+    '-3:3'
+    >>> from sympy.codegen.ast import Variable, real
+    >>> from sympy.codegen.fnodes import dimension, intent_out
+    >>> dim = dimension(e, e)
+    >>> arr = Variable('x', real, attrs=[dim, intent_out])
+    >>> fcode(arr.as_Declaration(), source_format='free', standard=2003)
+    'real*8, dimension(-3:3, -3:3), intent(out) :: x'
+
+    """
+    def __new__(cls, *args):
+        if len(args) == 2:
+            low, high = args
+            return Basic.__new__(cls, sympify(low), sympify(high))
+        elif len(args) == 0 or (len(args) == 1 and args[0] in (':', None)):
+            return Basic.__new__(cls)  # assumed shape
+        else:
+            raise ValueError("Expected 0 or 2 args (or one argument == None or ':')")
+
+    def _sympystr(self, printer):
+        if len(self.args) == 0:
+            return ':'
+        return ":".join(str(arg) for arg in self.args)
+
+assumed_extent = Extent() # or Extent(':'), Extent(None)
+
+
+def dimension(*args):
+    """ Creates a 'dimension' Attribute with (up to 7) extents.
+
+    Examples
+    ========
+
+    >>> from sympy import fcode
+    >>> from sympy.codegen.fnodes import dimension, intent_in
+    >>> dim = dimension('2', ':')  # 2 rows, runtime determined number of columns
+    >>> from sympy.codegen.ast import Variable, integer
+    >>> arr = Variable('a', integer, attrs=[dim, intent_in])
+    >>> fcode(arr.as_Declaration(), source_format='free', standard=2003)
+    'integer*4, dimension(2, :), intent(in) :: a'
+
+    """
+    if len(args) > 7:
+        raise ValueError("Fortran only supports up to 7 dimensional arrays")
+    parameters = []
+    for arg in args:
+        if isinstance(arg, Extent):
+            parameters.append(arg)
+        elif isinstance(arg, str):
+            if arg == ':':
+                parameters.append(Extent())
+            else:
+                parameters.append(String(arg))
+        elif iterable(arg):
+            parameters.append(Extent(*arg))
+        else:
+            parameters.append(sympify(arg))
+    if len(args) == 0:
+        raise ValueError("Need at least one dimension")
+    return Attribute('dimension', parameters)
+
+
+assumed_size = dimension('*')
+
+def array(symbol, dim, intent=None, *, attrs=(), value=None, type=None):
+    """ Convenience function for creating a Variable instance for a Fortran array.
+
+    Parameters
+    ==========
+
+    symbol : symbol
+    dim : Attribute or iterable
+        If dim is an ``Attribute`` it need to have the name 'dimension'. If it is
+        not an ``Attribute``, then it is passed to :func:`dimension` as ``*dim``
+    intent : str
+        One of: 'in', 'out', 'inout' or None
+    \\*\\*kwargs:
+        Keyword arguments for ``Variable`` ('type' & 'value')
+
+    Examples
+    ========
+
+    >>> from sympy import fcode
+    >>> from sympy.codegen.ast import integer, real
+    >>> from sympy.codegen.fnodes import array
+    >>> arr = array('a', '*', 'in', type=integer)
+    >>> print(fcode(arr.as_Declaration(), source_format='free', standard=2003))
+    integer*4, dimension(*), intent(in) :: a
+    >>> x = array('x', [3, ':', ':'], intent='out', type=real)
+    >>> print(fcode(x.as_Declaration(value=1), source_format='free', standard=2003))
+    real*8, dimension(3, :, :), intent(out) :: x = 1
+
+    """
+    if isinstance(dim, Attribute):
+        if str(dim.name) != 'dimension':
+            raise ValueError("Got an unexpected Attribute argument as dim: %s" % str(dim))
+    else:
+        dim = dimension(*dim)
+
+    attrs = list(attrs) + [dim]
+    if intent is not None:
+        if intent not in (intent_in, intent_out, intent_inout):
+            intent = {'in': intent_in, 'out': intent_out, 'inout': intent_inout}[intent]
+        attrs.append(intent)
+    if type is None:
+        return Variable.deduced(symbol, value=value, attrs=attrs)
+    else:
+        return Variable(symbol, type, value=value, attrs=attrs)
+
+def _printable(arg):
+    return String(arg) if isinstance(arg, str) else sympify(arg)
+
+
+def allocated(array):
+    """ Creates an AST node for a function call to Fortran's "allocated(...)"
+
+    Examples
+    ========
+
+    >>> from sympy import fcode
+    >>> from sympy.codegen.fnodes import allocated
+    >>> alloc = allocated('x')
+    >>> fcode(alloc, source_format='free')
+    'allocated(x)'
+
+    """
+    return FunctionCall('allocated', [_printable(array)])
+
+
+def lbound(array, dim=None, kind=None):
+    """ Creates an AST node for a function call to Fortran's "lbound(...)"
+
+    Parameters
+    ==========
+
+    array : Symbol or String
+    dim : expr
+    kind : expr
+
+    Examples
+    ========
+
+    >>> from sympy import fcode
+    >>> from sympy.codegen.fnodes import lbound
+    >>> lb = lbound('arr', dim=2)
+    >>> fcode(lb, source_format='free')
+    'lbound(arr, 2)'
+
+    """
+    return FunctionCall(
+        'lbound',
+        [_printable(array)] +
+        ([_printable(dim)] if dim else []) +
+        ([_printable(kind)] if kind else [])
+    )
+
+
+def ubound(array, dim=None, kind=None):
+    return FunctionCall(
+        'ubound',
+        [_printable(array)] +
+        ([_printable(dim)] if dim else []) +
+        ([_printable(kind)] if kind else [])
+    )
+
+
+def shape(source, kind=None):
+    """ Creates an AST node for a function call to Fortran's "shape(...)"
+
+    Parameters
+    ==========
+
+    source : Symbol or String
+    kind : expr
+
+    Examples
+    ========
+
+    >>> from sympy import fcode
+    >>> from sympy.codegen.fnodes import shape
+    >>> shp = shape('x')
+    >>> fcode(shp, source_format='free')
+    'shape(x)'
+
+    """
+    return FunctionCall(
+        'shape',
+        [_printable(source)] +
+        ([_printable(kind)] if kind else [])
+    )
+
+
+def size(array, dim=None, kind=None):
+    """ Creates an AST node for a function call to Fortran's "size(...)"
+
+    Examples
+    ========
+
+    >>> from sympy import fcode, Symbol
+    >>> from sympy.codegen.ast import FunctionDefinition, real, Return
+    >>> from sympy.codegen.fnodes import array, sum_, size
+    >>> a = Symbol('a', real=True)
+    >>> body = [Return((sum_(a**2)/size(a))**.5)]
+    >>> arr = array(a, dim=[':'], intent='in')
+    >>> fd = FunctionDefinition(real, 'rms', [arr], body)
+    >>> print(fcode(fd, source_format='free', standard=2003))
+    real*8 function rms(a)
+    real*8, dimension(:), intent(in) :: a
+    rms = sqrt(sum(a**2)*1d0/size(a))
+    end function
+
+    """
+    return FunctionCall(
+        'size',
+        [_printable(array)] +
+        ([_printable(dim)] if dim else []) +
+        ([_printable(kind)] if kind else [])
+    )
+
+
+def reshape(source, shape, pad=None, order=None):
+    """ Creates an AST node for a function call to Fortran's "reshape(...)"
+
+    Parameters
+    ==========
+
+    source : Symbol or String
+    shape : ArrayExpr
+
+    """
+    return FunctionCall(
+        'reshape',
+        [_printable(source), _printable(shape)] +
+        ([_printable(pad)] if pad else []) +
+        ([_printable(order)] if pad else [])
+    )
+
+
+def bind_C(name=None):
+    """ Creates an Attribute ``bind_C`` with a name.
+
+    Parameters
+    ==========
+
+    name : str
+
+    Examples
+    ========
+
+    >>> from sympy import fcode, Symbol
+    >>> from sympy.codegen.ast import FunctionDefinition, real, Return
+    >>> from sympy.codegen.fnodes import array, sum_, bind_C
+    >>> a = Symbol('a', real=True)
+    >>> s = Symbol('s', integer=True)
+    >>> arr = array(a, dim=[s], intent='in')
+    >>> body = [Return((sum_(a**2)/s)**.5)]
+    >>> fd = FunctionDefinition(real, 'rms', [arr, s], body, attrs=[bind_C('rms')])
+    >>> print(fcode(fd, source_format='free', standard=2003))
+    real*8 function rms(a, s) bind(C, name="rms")
+    real*8, dimension(s), intent(in) :: a
+    integer*4 :: s
+    rms = sqrt(sum(a**2)/s)
+    end function
+
+    """
+    return Attribute('bind_C', [String(name)] if name else [])
+
+class GoTo(Token):
+    """ Represents a goto statement in Fortran
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import GoTo
+    >>> go = GoTo([10, 20, 30], 'i')
+    >>> from sympy import fcode
+    >>> fcode(go, source_format='free')
+    'go to (10, 20, 30), i'
+
+    """
+    __slots__ = _fields = ('labels', 'expr')
+    defaults = {'expr': none}
+    _construct_labels = staticmethod(_mk_Tuple)
+    _construct_expr = staticmethod(sympify)
+
+
+class FortranReturn(Token):
+    """ AST node explicitly mapped to a fortran "return".
+
+    Explanation
+    ===========
+
+    Because a return statement in fortran is different from C, and
+    in order to aid reuse of our codegen ASTs the ordinary
+    ``.codegen.ast.Return`` is interpreted as assignment to
+    the result variable of the function. If one for some reason needs
+    to generate a fortran RETURN statement, this node should be used.
+
+    Examples
+    ========
+
+    >>> from sympy.codegen.fnodes import FortranReturn
+    >>> from sympy import fcode
+    >>> fcode(FortranReturn('x'))
+    '       return x'
+
+    """
+    __slots__ = _fields = ('return_value',)
+    defaults = {'return_value': none}
+    _construct_return_value = staticmethod(sympify)
+
+
+class FFunction(Function):
+    _required_standard = 77
+
+    def _fcode(self, printer):
+        name = self.__class__.__name__
+        if printer._settings['standard'] < self._required_standard:
+            raise NotImplementedError("%s requires Fortran %d or newer" %
+                                      (name, self._required_standard))
+        return '{}({})'.format(name, ', '.join(map(printer._print, self.args)))
+
+
+class F95Function(FFunction):
+    _required_standard = 95
+
+
+class isign(FFunction):
+    """ Fortran sign intrinsic for integer arguments. """
+    nargs = 2
+
+
+class dsign(FFunction):
+    """ Fortran sign intrinsic for double precision arguments. """
+    nargs = 2
+
+
+class cmplx(FFunction):
+    """ Fortran complex conversion function. """
+    nargs = 2  # may be extended to (2, 3) at a later point
+
+
+class kind(FFunction):
+    """ Fortran kind function. """
+    nargs = 1
+
+
+class merge(F95Function):
+    """ Fortran merge function """
+    nargs = 3
+
+
+class _literal(Float):
+    _token: str
+    _decimals: int
+
+    def _fcode(self, printer, *args, **kwargs):
+        mantissa, sgnd_ex = ('%.{}e'.format(self._decimals) % self).split('e')
+        mantissa = mantissa.strip('0').rstrip('.')
+        ex_sgn, ex_num = sgnd_ex[0], sgnd_ex[1:].lstrip('0')
+        ex_sgn = '' if ex_sgn == '+' else ex_sgn
+        return (mantissa or '0') + self._token + ex_sgn + (ex_num or '0')
+
+
+class literal_sp(_literal):
+    """ Fortran single precision real literal """
+    _token = 'e'
+    _decimals = 9
+
+
+class literal_dp(_literal):
+    """ Fortran double precision real literal """
+    _token = 'd'
+    _decimals = 17
+
+
+class sum_(Token, Expr):
+    __slots__ = _fields = ('array', 'dim', 'mask')
+    defaults = {'dim': none, 'mask': none}
+    _construct_array = staticmethod(sympify)
+    _construct_dim = staticmethod(sympify)
+
+
+class product_(Token, Expr):
+    __slots__ = _fields = ('array', 'dim', 'mask')
+    defaults = {'dim': none, 'mask': none}
+    _construct_array = staticmethod(sympify)
+    _construct_dim = staticmethod(sympify)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/futils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/futils.py
new file mode 100644
index 0000000000000000000000000000000000000000..4a1f5751fbd4d6b44d99c69a74ad89a8496f8648
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/futils.py
@@ -0,0 +1,40 @@
+from itertools import chain
+from sympy.codegen.fnodes import Module
+from sympy.core.symbol import Dummy
+from sympy.printing.fortran import FCodePrinter
+
+""" This module collects utilities for rendering Fortran code. """
+
+
+def render_as_module(definitions, name, declarations=(), printer_settings=None):
+    """ Creates a ``Module`` instance and renders it as a string.
+
+    This generates Fortran source code for a module with the correct ``use`` statements.
+
+    Parameters
+    ==========
+
+    definitions : iterable
+        Passed to :class:`sympy.codegen.fnodes.Module`.
+    name : str
+        Passed to :class:`sympy.codegen.fnodes.Module`.
+    declarations : iterable
+        Passed to :class:`sympy.codegen.fnodes.Module`. It will be extended with
+        use statements, 'implicit none' and public list generated from ``definitions``.
+    printer_settings : dict
+        Passed to ``FCodePrinter`` (default: ``{'standard': 2003, 'source_format': 'free'}``).
+
+    """
+    printer_settings = printer_settings or {'standard': 2003, 'source_format': 'free'}
+    printer = FCodePrinter(printer_settings)
+    dummy = Dummy()
+    if isinstance(definitions, Module):
+        raise ValueError("This function expects to construct a module on its own.")
+    mod = Module(name, chain(declarations, [dummy]), definitions)
+    fstr = printer.doprint(mod)
+    module_use_str = '   %s\n' % '   \n'.join(['use %s, only: %s' % (k, ', '.join(v)) for
+                                                k, v in printer.module_uses.items()])
+    module_use_str += '   implicit none\n'
+    module_use_str += '   private\n'
+    module_use_str += '   public %s\n' % ', '.join([str(node.name) for node in definitions if getattr(node, 'name', None)])
+    return fstr.replace(printer.doprint(dummy), module_use_str)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/matrix_nodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/matrix_nodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..cf0a13a81c963e2c9e2b885dabd0ff3e2d2b3eb9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/matrix_nodes.py
@@ -0,0 +1,71 @@
+"""
+Additional AST nodes for operations on matrices. The nodes in this module
+are meant to represent optimization of matrix expressions within codegen's
+target languages that cannot be represented by SymPy expressions.
+
+As an example, we can use :meth:`sympy.codegen.rewriting.optimize` and the
+``matin_opt`` optimization provided in :mod:`sympy.codegen.rewriting` to
+transform matrix multiplication under certain assumptions:
+
+    >>> from sympy import symbols, MatrixSymbol
+    >>> n = symbols('n', integer=True)
+    >>> A = MatrixSymbol('A', n, n)
+    >>> x = MatrixSymbol('x', n, 1)
+    >>> expr = A**(-1) * x
+    >>> from sympy import assuming, Q
+    >>> from sympy.codegen.rewriting import matinv_opt, optimize
+    >>> with assuming(Q.fullrank(A)):
+    ...     optimize(expr, [matinv_opt])
+    MatrixSolve(A, vector=x)
+"""
+
+from .ast import Token
+from sympy.matrices import MatrixExpr
+from sympy.core.sympify import sympify
+
+
+class MatrixSolve(Token, MatrixExpr):
+    """Represents an operation to solve a linear matrix equation.
+
+    Parameters
+    ==========
+
+    matrix : MatrixSymbol
+
+      Matrix representing the coefficients of variables in the linear
+      equation. This matrix must be square and full-rank (i.e. all columns must
+      be linearly independent) for the solving operation to be valid.
+
+    vector : MatrixSymbol
+
+      One-column matrix representing the solutions to the equations
+      represented in ``matrix``.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, MatrixSymbol
+    >>> from sympy.codegen.matrix_nodes import MatrixSolve
+    >>> n = symbols('n', integer=True)
+    >>> A = MatrixSymbol('A', n, n)
+    >>> x = MatrixSymbol('x', n, 1)
+    >>> from sympy.printing.numpy import NumPyPrinter
+    >>> NumPyPrinter().doprint(MatrixSolve(A, x))
+    'numpy.linalg.solve(A, x)'
+    >>> from sympy import octave_code
+    >>> octave_code(MatrixSolve(A, x))
+    'A \\\\ x'
+
+    """
+    __slots__ = _fields = ('matrix', 'vector')
+
+    _construct_matrix = staticmethod(sympify)
+    _construct_vector = staticmethod(sympify)
+
+    @property
+    def shape(self):
+        return self.vector.shape
+
+    def _eval_derivative(self, x):
+        A, b = self.matrix, self.vector
+        return MatrixSolve(A, b.diff(x) - A.diff(x) * MatrixSolve(A, b))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/numpy_nodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/numpy_nodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..c47c87f0e1df74cd314bb70674ebff732fe500aa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/numpy_nodes.py
@@ -0,0 +1,177 @@
+from sympy.core.function import Add, ArgumentIndexError, Function
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.miscellaneous import Max, Min
+from .ast import Token, none
+
+
+def _logaddexp(x1, x2, *, evaluate=True):
+    return log(Add(exp(x1, evaluate=evaluate), exp(x2, evaluate=evaluate), evaluate=evaluate))
+
+
+_two = S.One*2
+_ln2 = log(_two)
+
+
+def _lb(x, *, evaluate=True):
+    return log(x, evaluate=evaluate)/_ln2
+
+
+def _exp2(x, *, evaluate=True):
+    return Pow(_two, x, evaluate=evaluate)
+
+
+def _logaddexp2(x1, x2, *, evaluate=True):
+    return _lb(Add(_exp2(x1, evaluate=evaluate),
+                   _exp2(x2, evaluate=evaluate), evaluate=evaluate))
+
+
+class logaddexp(Function):
+    """ Logarithm of the sum of exponentiations of the inputs.
+
+    Helper class for use with e.g. numpy.logaddexp
+
+    See Also
+    ========
+
+    https://numpy.org/doc/stable/reference/generated/numpy.logaddexp.html
+    """
+    nargs = 2
+
+    def __new__(cls, *args):
+        return Function.__new__(cls, *sorted(args, key=default_sort_key))
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            wrt, other = self.args
+        elif argindex == 2:
+            other, wrt = self.args
+        else:
+            raise ArgumentIndexError(self, argindex)
+        return S.One/(S.One + exp(other-wrt))
+
+    def _eval_rewrite_as_log(self, x1, x2, **kwargs):
+        return _logaddexp(x1, x2)
+
+    def _eval_evalf(self, *args, **kwargs):
+        return self.rewrite(log).evalf(*args, **kwargs)
+
+    def _eval_simplify(self, *args, **kwargs):
+        a, b = (x.simplify(**kwargs) for x in self.args)
+        candidate = _logaddexp(a, b)
+        if candidate != _logaddexp(a, b, evaluate=False):
+            return candidate
+        else:
+            return logaddexp(a, b)
+
+
+class logaddexp2(Function):
+    """ Logarithm of the sum of exponentiations of the inputs in base-2.
+
+    Helper class for use with e.g. numpy.logaddexp2
+
+    See Also
+    ========
+
+    https://numpy.org/doc/stable/reference/generated/numpy.logaddexp2.html
+    """
+    nargs = 2
+
+    def __new__(cls, *args):
+        return Function.__new__(cls, *sorted(args, key=default_sort_key))
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            wrt, other = self.args
+        elif argindex == 2:
+            other, wrt = self.args
+        else:
+            raise ArgumentIndexError(self, argindex)
+        return S.One/(S.One + _exp2(other-wrt))
+
+    def _eval_rewrite_as_log(self, x1, x2, **kwargs):
+        return _logaddexp2(x1, x2)
+
+    def _eval_evalf(self, *args, **kwargs):
+        return self.rewrite(log).evalf(*args, **kwargs)
+
+    def _eval_simplify(self, *args, **kwargs):
+        a, b = (x.simplify(**kwargs).factor() for x in self.args)
+        candidate = _logaddexp2(a, b)
+        if candidate != _logaddexp2(a, b, evaluate=False):
+            return candidate
+        else:
+            return logaddexp2(a, b)
+
+
+class amin(Token):
+    """ Minimum value along an axis.
+
+    Helper class for use with e.g. numpy.amin
+
+
+    See Also
+    ========
+
+    https://numpy.org/doc/stable/reference/generated/numpy.amin.html
+    """
+    __slots__ = _fields = ('array', 'axis')
+    defaults = {'axis': none}
+    _construct_axis = staticmethod(sympify)
+
+
+class amax(Token):
+    """ Maximum value along an axis.
+
+    Helper class for use with e.g. numpy.amax
+
+
+    See Also
+    ========
+
+    https://numpy.org/doc/stable/reference/generated/numpy.amax.html
+    """
+    __slots__ = _fields = ('array', 'axis')
+    defaults = {'axis': none}
+    _construct_axis = staticmethod(sympify)
+
+
+class maximum(Function):
+    """ Element-wise maximum of array elements.
+
+    Helper class for use with e.g. numpy.maximum
+
+
+    See Also
+    ========
+
+    https://numpy.org/doc/stable/reference/generated/numpy.maximum.html
+    """
+
+    def _eval_rewrite_as_Max(self, *args):
+        return Max(*self.args)
+
+
+class minimum(Function):
+    """ Element-wise minimum of array elements.
+
+    Helper class for use with e.g. numpy.minimum
+
+
+    See Also
+    ========
+
+    https://numpy.org/doc/stable/reference/generated/numpy.minimum.html
+    """
+
+    def _eval_rewrite_as_Min(self, *args):
+        return Min(*self.args)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/pynodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/pynodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..f0a08b4a79d32f63d345947d6be310b44504dbf5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/pynodes.py
@@ -0,0 +1,11 @@
+from .abstract_nodes import List as AbstractList
+from .ast import Token
+
+
+class List(AbstractList):
+    pass
+
+
+class NumExprEvaluate(Token):
+    """represents a call to :class:`numexpr`s :func:`evaluate`"""
+    __slots__ = _fields = ('expr',)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/pyutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/pyutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..e14eabe92ce50105a4055b71a49767aae04610b9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/pyutils.py
@@ -0,0 +1,24 @@
+from sympy.printing.pycode import PythonCodePrinter
+
+""" This module collects utilities for rendering Python code. """
+
+
+def render_as_module(content, standard='python3'):
+    """Renders Python code as a module (with the required imports).
+
+    Parameters
+    ==========
+
+    standard :
+        See the parameter ``standard`` in
+        :meth:`sympy.printing.pycode.pycode`
+    """
+
+    printer = PythonCodePrinter({'standard':standard})
+    pystr = printer.doprint(content)
+    if printer._settings['fully_qualified_modules']:
+        module_imports_str = '\n'.join('import %s' % k for k in printer.module_imports)
+    else:
+        module_imports_str = '\n'.join(['from %s import %s' % (k, ', '.join(v)) for
+                                        k, v in printer.module_imports.items()])
+    return module_imports_str + '\n\n' + pystr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/rewriting.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/rewriting.py
new file mode 100644
index 0000000000000000000000000000000000000000..274b7770b46ded6711468ab2a01db3a53d6fde87
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/rewriting.py
@@ -0,0 +1,357 @@
+"""
+Classes and functions useful for rewriting expressions for optimized code
+generation. Some languages (or standards thereof), e.g. C99, offer specialized
+math functions for better performance and/or precision.
+
+Using the ``optimize`` function in this module, together with a collection of
+rules (represented as instances of ``Optimization``), one can rewrite the
+expressions for this purpose::
+
+    >>> from sympy import Symbol, exp, log
+    >>> from sympy.codegen.rewriting import optimize, optims_c99
+    >>> x = Symbol('x')
+    >>> optimize(3*exp(2*x) - 3, optims_c99)
+    3*expm1(2*x)
+    >>> optimize(exp(2*x) - 1 - exp(-33), optims_c99)
+    expm1(2*x) - exp(-33)
+    >>> optimize(log(3*x + 3), optims_c99)
+    log1p(x) + log(3)
+    >>> optimize(log(2*x + 3), optims_c99)
+    log(2*x + 3)
+
+The ``optims_c99`` imported above is tuple containing the following instances
+(which may be imported from ``sympy.codegen.rewriting``):
+
+- ``expm1_opt``
+- ``log1p_opt``
+- ``exp2_opt``
+- ``log2_opt``
+- ``log2const_opt``
+
+
+"""
+from sympy.core.function import expand_log
+from sympy.core.singleton import S
+from sympy.core.symbol import Wild
+from sympy.functions.elementary.complexes import sign
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import (Max, Min)
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc)
+from sympy.assumptions import Q, ask
+from sympy.codegen.cfunctions import log1p, log2, exp2, expm1
+from sympy.codegen.matrix_nodes import MatrixSolve
+from sympy.core.expr import UnevaluatedExpr
+from sympy.core.power import Pow
+from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
+from sympy.codegen.scipy_nodes import cosm1, powm1
+from sympy.core.mul import Mul
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.utilities.iterables import sift
+
+
+class Optimization:
+    """ Abstract base class for rewriting optimization.
+
+    Subclasses should implement ``__call__`` taking an expression
+    as argument.
+
+    Parameters
+    ==========
+    cost_function : callable returning number
+    priority : number
+
+    """
+    def __init__(self, cost_function=None, priority=1):
+        self.cost_function = cost_function
+        self.priority=priority
+
+    def cheapest(self, *args):
+        return min(args, key=self.cost_function)
+
+
+class ReplaceOptim(Optimization):
+    """ Rewriting optimization calling replace on expressions.
+
+    Explanation
+    ===========
+
+    The instance can be used as a function on expressions for which
+    it will apply the ``replace`` method (see
+    :meth:`sympy.core.basic.Basic.replace`).
+
+    Parameters
+    ==========
+
+    query :
+        First argument passed to replace.
+    value :
+        Second argument passed to replace.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol
+    >>> from sympy.codegen.rewriting import ReplaceOptim
+    >>> from sympy.codegen.cfunctions import exp2
+    >>> x = Symbol('x')
+    >>> exp2_opt = ReplaceOptim(lambda p: p.is_Pow and p.base == 2,
+    ...     lambda p: exp2(p.exp))
+    >>> exp2_opt(2**x)
+    exp2(x)
+
+    """
+
+    def __init__(self, query, value, **kwargs):
+        super().__init__(**kwargs)
+        self.query = query
+        self.value = value
+
+    def __call__(self, expr):
+        return expr.replace(self.query, self.value)
+
+
+def optimize(expr, optimizations):
+    """ Apply optimizations to an expression.
+
+    Parameters
+    ==========
+
+    expr : expression
+    optimizations : iterable of ``Optimization`` instances
+        The optimizations will be sorted with respect to ``priority`` (highest first).
+
+    Examples
+    ========
+
+    >>> from sympy import log, Symbol
+    >>> from sympy.codegen.rewriting import optims_c99, optimize
+    >>> x = Symbol('x')
+    >>> optimize(log(x+3)/log(2) + log(x**2 + 1), optims_c99)
+    log1p(x**2) + log2(x + 3)
+
+    """
+
+    for optim in sorted(optimizations, key=lambda opt: opt.priority, reverse=True):
+        new_expr = optim(expr)
+        if optim.cost_function is None:
+            expr = new_expr
+        else:
+            expr = optim.cheapest(expr, new_expr)
+    return expr
+
+
+exp2_opt = ReplaceOptim(
+    lambda p: p.is_Pow and p.base == 2,
+    lambda p: exp2(p.exp)
+)
+
+
+_d = Wild('d', properties=[lambda x: x.is_Dummy])
+_u = Wild('u', properties=[lambda x: not x.is_number and not x.is_Add])
+_v = Wild('v')
+_w = Wild('w')
+_n = Wild('n', properties=[lambda x: x.is_number])
+
+sinc_opt1 = ReplaceOptim(
+    sin(_w)/_w, sinc(_w)
+)
+sinc_opt2 = ReplaceOptim(
+    sin(_n*_w)/_w, _n*sinc(_n*_w)
+)
+sinc_opts = (sinc_opt1, sinc_opt2)
+
+log2_opt = ReplaceOptim(_v*log(_w)/log(2), _v*log2(_w), cost_function=lambda expr: expr.count(
+    lambda e: (  # division & eval of transcendentals are expensive floating point operations...
+        e.is_Pow and e.exp.is_negative  # division
+        or (isinstance(e, (log, log2)) and not e.args[0].is_number))  # transcendental
+    )
+)
+
+log2const_opt = ReplaceOptim(log(2)*log2(_w), log(_w))
+
+logsumexp_2terms_opt = ReplaceOptim(
+    lambda l: (isinstance(l, log)
+               and l.args[0].is_Add
+               and len(l.args[0].args) == 2
+               and all(isinstance(t, exp) for t in l.args[0].args)),
+    lambda l: (
+        Max(*[e.args[0] for e in l.args[0].args]) +
+        log1p(exp(Min(*[e.args[0] for e in l.args[0].args])))
+    )
+)
+
+
+class FuncMinusOneOptim(ReplaceOptim):
+    """Specialization of ReplaceOptim for functions evaluating "f(x) - 1".
+
+    Explanation
+    ===========
+
+    Numerical functions which go toward one as x go toward zero is often best
+    implemented by a dedicated function in order to avoid catastrophic
+    cancellation. One such example is ``expm1(x)`` in the C standard library
+    which evaluates ``exp(x) - 1``. Such functions preserves many more
+    significant digits when its argument is much smaller than one, compared
+    to subtracting one afterwards.
+
+    Parameters
+    ==========
+
+    func :
+        The function which is subtracted by one.
+    func_m_1 :
+        The specialized function evaluating ``func(x) - 1``.
+    opportunistic : bool
+        When ``True``, apply the transformation as long as the magnitude of the
+        remaining number terms decreases. When ``False``, only apply the
+        transformation if it completely eliminates the number term.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, exp
+    >>> from sympy.codegen.rewriting import FuncMinusOneOptim
+    >>> from sympy.codegen.cfunctions import expm1
+    >>> x, y = symbols('x y')
+    >>> expm1_opt = FuncMinusOneOptim(exp, expm1)
+    >>> expm1_opt(exp(x) + 2*exp(5*y) - 3)
+    expm1(x) + 2*expm1(5*y)
+
+
+    """
+
+    def __init__(self, func, func_m_1, opportunistic=True):
+        weight = 10  # <-- this is an arbitrary number (heuristic)
+        super().__init__(lambda e: e.is_Add, self.replace_in_Add,
+                         cost_function=lambda expr: expr.count_ops() - weight*expr.count(func_m_1))
+        self.func = func
+        self.func_m_1 = func_m_1
+        self.opportunistic = opportunistic
+
+    def _group_Add_terms(self, add):
+        numbers, non_num = sift(add.args, lambda arg: arg.is_number, binary=True)
+        numsum = sum(numbers)
+        terms_with_func, other = sift(non_num, lambda arg: arg.has(self.func), binary=True)
+        return numsum, terms_with_func, other
+
+    def replace_in_Add(self, e):
+        """ passed as second argument to Basic.replace(...) """
+        numsum, terms_with_func, other_non_num_terms = self._group_Add_terms(e)
+        if numsum == 0:
+            return e
+        substituted, untouched = [], []
+        for with_func in terms_with_func:
+            if with_func.is_Mul:
+                func, coeff = sift(with_func.args, lambda arg: arg.func == self.func, binary=True)
+                if len(func) == 1 and len(coeff) == 1:
+                    func, coeff = func[0], coeff[0]
+                else:
+                    coeff = None
+            elif with_func.func == self.func:
+                func, coeff = with_func, S.One
+            else:
+                coeff = None
+
+            if coeff is not None and coeff.is_number and sign(coeff) == -sign(numsum):
+                if self.opportunistic:
+                    do_substitute = abs(coeff+numsum) < abs(numsum)
+                else:
+                    do_substitute = coeff+numsum == 0
+
+                if do_substitute:  # advantageous substitution
+                    numsum += coeff
+                    substituted.append(coeff*self.func_m_1(*func.args))
+                    continue
+            untouched.append(with_func)
+
+        return e.func(numsum, *substituted, *untouched, *other_non_num_terms)
+
+    def __call__(self, expr):
+        alt1 = super().__call__(expr)
+        alt2 = super().__call__(expr.factor())
+        return self.cheapest(alt1, alt2)
+
+
+expm1_opt = FuncMinusOneOptim(exp, expm1)
+cosm1_opt = FuncMinusOneOptim(cos, cosm1)
+powm1_opt = FuncMinusOneOptim(Pow, powm1)
+
+log1p_opt = ReplaceOptim(
+    lambda e: isinstance(e, log),
+    lambda l: expand_log(l.replace(
+        log, lambda arg: log(arg.factor())
+    )).replace(log(_u+1), log1p(_u))
+)
+
+def create_expand_pow_optimization(limit, *, base_req=lambda b: b.is_symbol):
+    """ Creates an instance of :class:`ReplaceOptim` for expanding ``Pow``.
+
+    Explanation
+    ===========
+
+    The requirements for expansions are that the base needs to be a symbol
+    and the exponent needs to be an Integer (and be less than or equal to
+    ``limit``).
+
+    Parameters
+    ==========
+
+    limit : int
+         The highest power which is expanded into multiplication.
+    base_req : function returning bool
+         Requirement on base for expansion to happen, default is to return
+         the ``is_symbol`` attribute of the base.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, sin
+    >>> from sympy.codegen.rewriting import create_expand_pow_optimization
+    >>> x = Symbol('x')
+    >>> expand_opt = create_expand_pow_optimization(3)
+    >>> expand_opt(x**5 + x**3)
+    x**5 + x*x*x
+    >>> expand_opt(x**5 + x**3 + sin(x)**3)
+    x**5 + sin(x)**3 + x*x*x
+    >>> opt2 = create_expand_pow_optimization(3, base_req=lambda b: not b.is_Function)
+    >>> opt2((x+1)**2 + sin(x)**2)
+    sin(x)**2 + (x + 1)*(x + 1)
+
+    """
+    return ReplaceOptim(
+        lambda e: e.is_Pow and base_req(e.base) and e.exp.is_Integer and abs(e.exp) <= limit,
+        lambda p: (
+            UnevaluatedExpr(Mul(*([p.base]*+p.exp), evaluate=False)) if p.exp > 0 else
+            1/UnevaluatedExpr(Mul(*([p.base]*-p.exp), evaluate=False))
+        ))
+
+# Optimization procedures for turning A**(-1) * x into MatrixSolve(A, x)
+def _matinv_predicate(expr):
+    # TODO: We should be able to support more than 2 elements
+    if expr.is_MatMul and len(expr.args) == 2:
+        left, right = expr.args
+        if left.is_Inverse and right.shape[1] == 1:
+            inv_arg = left.arg
+            if isinstance(inv_arg, MatrixSymbol):
+                return bool(ask(Q.fullrank(left.arg)))
+
+    return False
+
+def _matinv_transform(expr):
+    left, right = expr.args
+    inv_arg = left.arg
+    return MatrixSolve(inv_arg, right)
+
+
+matinv_opt = ReplaceOptim(_matinv_predicate, _matinv_transform)
+
+
+logaddexp_opt = ReplaceOptim(log(exp(_v)+exp(_w)), logaddexp(_v, _w))
+logaddexp2_opt = ReplaceOptim(log(Pow(2, _v)+Pow(2, _w)), logaddexp2(_v, _w)*log(2))
+
+# Collections of optimizations:
+optims_c99 = (expm1_opt, log1p_opt, exp2_opt, log2_opt, log2const_opt)
+
+optims_numpy = optims_c99 + (logaddexp_opt, logaddexp2_opt,) + sinc_opts
+
+optims_scipy = (cosm1_opt, powm1_opt)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/scipy_nodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/scipy_nodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..059a853fc8cac6e0b9a1a3c7395dd3a15384dcba
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/scipy_nodes.py
@@ -0,0 +1,79 @@
+from sympy.core.function import Add, ArgumentIndexError, Function
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.trigonometric import cos, sin
+
+
+def _cosm1(x, *, evaluate=True):
+    return Add(cos(x, evaluate=evaluate), -S.One, evaluate=evaluate)
+
+
+class cosm1(Function):
+    """ Minus one plus cosine of x, i.e. cos(x) - 1. For use when x is close to zero.
+
+    Helper class for use with e.g. scipy.special.cosm1
+    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.cosm1.html
+    """
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return -sin(*self.args)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_cos(self, x, **kwargs):
+        return _cosm1(x)
+
+    def _eval_evalf(self, *args, **kwargs):
+        return self.rewrite(cos).evalf(*args, **kwargs)
+
+    def _eval_simplify(self, **kwargs):
+        x, = self.args
+        candidate = _cosm1(x.simplify(**kwargs))
+        if candidate != _cosm1(x, evaluate=False):
+            return candidate
+        else:
+            return cosm1(x)
+
+
+def _powm1(x, y, *, evaluate=True):
+    return Add(Pow(x, y, evaluate=evaluate), -S.One, evaluate=evaluate)
+
+
+class powm1(Function):
+    """ Minus one plus x to the power of y, i.e. x**y - 1. For use when x is close to one or y is close to zero.
+
+    Helper class for use with e.g. scipy.special.powm1
+    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.powm1.html
+    """
+    nargs = 2
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return Pow(self.args[0], self.args[1])*self.args[1]/self.args[0]
+        elif argindex == 2:
+            return log(self.args[0])*Pow(*self.args)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Pow(self, x, y, **kwargs):
+        return _powm1(x, y)
+
+    def _eval_evalf(self, *args, **kwargs):
+        return self.rewrite(Pow).evalf(*args, **kwargs)
+
+    def _eval_simplify(self, **kwargs):
+        x, y = self.args
+        candidate = _powm1(x.simplify(**kwargs), y.simplify(**kwargs))
+        if candidate != _powm1(x, y, evaluate=False):
+            return candidate
+        else:
+            return powm1(x, y)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_abstract_nodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_abstract_nodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..89e1f73ff8cb24a4a865aa51304ec66e9901e3cb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_abstract_nodes.py
@@ -0,0 +1,14 @@
+from sympy.core.symbol import symbols
+from sympy.codegen.abstract_nodes import List
+
+
+def test_List():
+    l = List(2, 3, 4)
+    assert l == List(2, 3, 4)
+    assert str(l) == "[2, 3, 4]"
+    x, y, z = symbols('x y z')
+    l = List(x**2,y**3,z**4)
+    # contrary to python's built-in list, we can call e.g. "replace" on List.
+    m = l.replace(lambda arg: arg.is_Pow and arg.exp>2, lambda p: p.base-p.exp)
+    assert m == [x**2, y-3, z-4]
+    hash(m)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_algorithms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_algorithms.py
new file mode 100644
index 0000000000000000000000000000000000000000..c684229ec18a1e02a97eee6db8537b8d12af0582
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_algorithms.py
@@ -0,0 +1,180 @@
+import tempfile
+from sympy import log, Min, Max, sqrt
+from sympy.core.numbers import Float
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions.elementary.trigonometric import cos
+from sympy.codegen.ast import Assignment, Raise, RuntimeError_, QuotedString
+from sympy.codegen.algorithms import newtons_method, newtons_method_function
+from sympy.codegen.cfunctions import expm1
+from sympy.codegen.fnodes import bind_C
+from sympy.codegen.futils import render_as_module as f_module
+from sympy.codegen.pyutils import render_as_module as py_module
+from sympy.external import import_module
+from sympy.printing.codeprinter import ccode
+from sympy.utilities._compilation import compile_link_import_strings, has_c, has_fortran
+from sympy.utilities._compilation.util import may_xfail
+from sympy.testing.pytest import skip, raises, skip_under_pyodide
+
+cython = import_module('cython')
+wurlitzer = import_module('wurlitzer')
+
+def test_newtons_method():
+    x, dx, atol = symbols('x dx atol')
+    expr = cos(x) - x**3
+    algo = newtons_method(expr, x, atol, dx)
+    assert algo.has(Assignment(dx, -expr/expr.diff(x)))
+
+
+@may_xfail
+def test_newtons_method_function__ccode():
+    x = Symbol('x', real=True)
+    expr = cos(x) - x**3
+    func = newtons_method_function(expr, x)
+
+    if not cython:
+        skip("cython not installed.")
+    if not has_c():
+        skip("No C compiler found.")
+
+    compile_kw = {"std": 'c99'}
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('newton.c', ('#include \n'
+                          '#include \n') + ccode(func)),
+            ('_newton.pyx', ("#cython: language_level={}\n".format("3") +
+                             "cdef extern double newton(double)\n"
+                             "def py_newton(x):\n"
+                             "    return newton(x)\n"))
+        ], build_dir=folder, compile_kwargs=compile_kw)
+        assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
+
+
+@may_xfail
+def test_newtons_method_function__fcode():
+    x = Symbol('x', real=True)
+    expr = cos(x) - x**3
+    func = newtons_method_function(expr, x, attrs=[bind_C(name='newton')])
+
+    if not cython:
+        skip("cython not installed.")
+    if not has_fortran():
+        skip("No Fortran compiler found.")
+
+    f_mod = f_module([func], 'mod_newton')
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('newton.f90', f_mod),
+            ('_newton.pyx', ("#cython: language_level={}\n".format("3") +
+                             "cdef extern double newton(double*)\n"
+                             "def py_newton(double x):\n"
+                             "    return newton(&x)\n"))
+        ], build_dir=folder)
+        assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
+
+
+def test_newtons_method_function__pycode():
+    x = Symbol('x', real=True)
+    expr = cos(x) - x**3
+    func = newtons_method_function(expr, x)
+    py_mod = py_module(func)
+    namespace = {}
+    exec(py_mod, namespace, namespace)
+    res = eval('newton(0.5)', namespace)
+    assert abs(res - 0.865474033102) < 1e-12
+
+
+@may_xfail
+@skip_under_pyodide("Emscripten does not support process spawning")
+def test_newtons_method_function__ccode_parameters():
+    args = x, A, k, p = symbols('x A k p')
+    expr = A*cos(k*x) - p*x**3
+    raises(ValueError, lambda: newtons_method_function(expr, x))
+    use_wurlitzer = wurlitzer
+
+    func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
+
+    if not has_c():
+        skip("No C compiler found.")
+    if not cython:
+        skip("cython not installed.")
+
+    compile_kw = {"std": 'c99'}
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('newton_par.c', ('#include \n'
+                          '#include \n') + ccode(func)),
+            ('_newton_par.pyx', ("#cython: language_level={}\n".format("3") +
+                                 "cdef extern double newton(double, double, double, double)\n"
+                             "def py_newton(x, A=1, k=1, p=1):\n"
+                             "    return newton(x, A, k, p)\n"))
+        ], compile_kwargs=compile_kw, build_dir=folder)
+
+        if use_wurlitzer:
+            with wurlitzer.pipes() as (out, err):
+                result = mod.py_newton(0.5)
+        else:
+            result = mod.py_newton(0.5)
+
+        assert abs(result - 0.865474033102) < 1e-12
+
+        if not use_wurlitzer:
+            skip("C-level output only tested when package 'wurlitzer' is available.")
+
+        out, err = out.read(), err.read()
+        assert err == ''
+        assert out == """\
+x=         0.5
+x=      1.1121 d_x=     0.61214
+x=     0.90967 d_x=    -0.20247
+x=     0.86726 d_x=   -0.042409
+x=     0.86548 d_x=  -0.0017867
+x=     0.86547 d_x= -3.1022e-06
+x=     0.86547 d_x= -9.3421e-12
+x=     0.86547 d_x=  3.6902e-17
+"""  # try to run tests with LC_ALL=C if this assertion fails
+
+
+def test_newtons_method_function__rtol_cse_nan():
+    a, b, c, N_geo, N_tot = symbols('a b c N_geo N_tot', real=True, nonnegative=True)
+    i = Symbol('i', integer=True, nonnegative=True)
+    N_ari = N_tot - N_geo - 1
+    delta_ari = (c-b)/N_ari
+    ln_delta_geo = log(b) + log(-expm1((log(a)-log(b))/N_geo))
+    eqb_log = ln_delta_geo - log(delta_ari)
+
+    def _clamp(low, expr, high):
+        return Min(Max(low, expr), high)
+
+    meth_kw = {
+        'clamped_newton': {'delta_fn': lambda e, x: _clamp(
+            (sqrt(a*x)-x)*0.99,
+            -e/e.diff(x),
+            (sqrt(c*x)-x)*0.99
+        )},
+        'halley': {'delta_fn': lambda e, x: (-2*(e*e.diff(x))/(2*e.diff(x)**2 - e*e.diff(x, 2)))},
+        'halley_alt': {'delta_fn': lambda e, x: (-e/e.diff(x)/(1-e/e.diff(x)*e.diff(x,2)/2/e.diff(x)))},
+    }
+    args = eqb_log, b
+    for use_cse in [False, True]:
+        kwargs = {
+            'params': (b, a, c, N_geo, N_tot), 'itermax': 60, 'debug': True, 'cse': use_cse,
+            'counter': i, 'atol': 1e-100, 'rtol': 2e-16, 'bounds': (a,c),
+            'handle_nan': Raise(RuntimeError_(QuotedString("encountered NaN.")))
+        }
+        func = {k: newtons_method_function(*args, func_name=f"{k}_b", **dict(kwargs, **kw)) for k, kw in meth_kw.items()}
+        py_mod = {k: py_module(v) for k, v in func.items()}
+        namespace = {}
+        root_find_b = {}
+        for k, v in py_mod.items():
+            ns = namespace[k] = {}
+            exec(v, ns, ns)
+            root_find_b[k] = ns[f'{k}_b']
+        ref = Float('13.2261515064168768938151923226496')
+        reftol = {'clamped_newton': 2e-16, 'halley': 2e-16, 'halley_alt': 3e-16}
+        guess = 4.0
+        for meth, func in root_find_b.items():
+            result = func(guess, 1e-2, 1e2, 50, 100)
+            req = ref*reftol[meth]
+            if use_cse:
+                req *= 2
+            assert abs(result - ref) < req
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_applications.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_applications.py
new file mode 100644
index 0000000000000000000000000000000000000000..9519c06b96042b383314ef928d2ad0c1a2f92650
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_applications.py
@@ -0,0 +1,58 @@
+# This file contains tests that exercise multiple AST nodes
+
+import tempfile
+
+from sympy.external import import_module
+from sympy.printing.codeprinter import ccode
+from sympy.utilities._compilation import compile_link_import_strings, has_c
+from sympy.utilities._compilation.util import may_xfail
+from sympy.testing.pytest import skip, skip_under_pyodide
+from sympy.codegen.ast import (
+    FunctionDefinition, FunctionPrototype, Variable, Pointer, real, Assignment,
+    integer, CodeBlock, While
+)
+from sympy.codegen.cnodes import void, PreIncrement
+from sympy.codegen.cutils import render_as_source_file
+
+cython = import_module('cython')
+np = import_module('numpy')
+
+def _mk_func1():
+    declars = n, inp, out = Variable('n', integer), Pointer('inp', real), Pointer('out', real)
+    i = Variable('i', integer)
+    whl = While(i2, lambda p: p.base-p.exp)
+    assert m == [x**2, y-3, z-4]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_pyutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_pyutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..0a2f0ff358f333635c8d44195a5c39d63ac8f16f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_pyutils.py
@@ -0,0 +1,7 @@
+from sympy.codegen.ast import Print
+from sympy.codegen.pyutils import render_as_module
+
+def test_standard():
+    ast = Print('x y'.split(), r"coordinate: %12.5g %12.5g\n")
+    assert render_as_module(ast, standard='python3') == \
+        '\n\nprint("coordinate: %12.5g %12.5g\\n" % (x, y), end="")'
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_rewriting.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_rewriting.py
new file mode 100644
index 0000000000000000000000000000000000000000..51e0c9ecc940f60186cc04d4bf15650281d31cd8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_rewriting.py
@@ -0,0 +1,479 @@
+import tempfile
+from sympy.core.numbers import pi, Rational
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc)
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.assumptions import assuming, Q
+from sympy.external import import_module
+from sympy.printing.codeprinter import ccode
+from sympy.codegen.matrix_nodes import MatrixSolve
+from sympy.codegen.cfunctions import log2, exp2, expm1, log1p
+from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
+from sympy.codegen.scipy_nodes import cosm1, powm1
+from sympy.codegen.rewriting import (
+    optimize, cosm1_opt, log2_opt, exp2_opt, expm1_opt, log1p_opt, powm1_opt, optims_c99,
+    create_expand_pow_optimization, matinv_opt, logaddexp_opt, logaddexp2_opt,
+    optims_numpy, optims_scipy, sinc_opts, FuncMinusOneOptim
+)
+from sympy.testing.pytest import XFAIL, skip
+from sympy.utilities import lambdify
+from sympy.utilities._compilation import compile_link_import_strings, has_c
+from sympy.utilities._compilation.util import may_xfail
+
+cython = import_module('cython')
+numpy = import_module('numpy')
+scipy = import_module('scipy')
+
+
+def test_log2_opt():
+    x = Symbol('x')
+    expr1 = 7*log(3*x + 5)/(log(2))
+    opt1 = optimize(expr1, [log2_opt])
+    assert opt1 == 7*log2(3*x + 5)
+    assert opt1.rewrite(log) == expr1
+
+    expr2 = 3*log(5*x + 7)/(13*log(2))
+    opt2 = optimize(expr2, [log2_opt])
+    assert opt2 == 3*log2(5*x + 7)/13
+    assert opt2.rewrite(log) == expr2
+
+    expr3 = log(x)/log(2)
+    opt3 = optimize(expr3, [log2_opt])
+    assert opt3 == log2(x)
+    assert opt3.rewrite(log) == expr3
+
+    expr4 = log(x)/log(2) + log(x+1)
+    opt4 = optimize(expr4, [log2_opt])
+    assert opt4 == log2(x) + log(2)*log2(x+1)
+    assert opt4.rewrite(log) == expr4
+
+    expr5 = log(17)
+    opt5 = optimize(expr5, [log2_opt])
+    assert opt5 == expr5
+
+    expr6 = log(x + 3)/log(2)
+    opt6 = optimize(expr6, [log2_opt])
+    assert str(opt6) == 'log2(x + 3)'
+    assert opt6.rewrite(log) == expr6
+
+
+def test_exp2_opt():
+    x = Symbol('x')
+    expr1 = 1 + 2**x
+    opt1 = optimize(expr1, [exp2_opt])
+    assert opt1 == 1 + exp2(x)
+    assert opt1.rewrite(Pow) == expr1
+
+    expr2 = 1 + 3**x
+    assert expr2 == optimize(expr2, [exp2_opt])
+
+
+def test_expm1_opt():
+    x = Symbol('x')
+
+    expr1 = exp(x) - 1
+    opt1 = optimize(expr1, [expm1_opt])
+    assert expm1(x) - opt1 == 0
+    assert opt1.rewrite(exp) == expr1
+
+    expr2 = 3*exp(x) - 3
+    opt2 = optimize(expr2, [expm1_opt])
+    assert 3*expm1(x) == opt2
+    assert opt2.rewrite(exp) == expr2
+
+    expr3 = 3*exp(x) - 5
+    opt3 = optimize(expr3, [expm1_opt])
+    assert 3*expm1(x) - 2 == opt3
+    assert opt3.rewrite(exp) == expr3
+    expm1_opt_non_opportunistic = FuncMinusOneOptim(exp, expm1, opportunistic=False)
+    assert expr3 == optimize(expr3, [expm1_opt_non_opportunistic])
+    assert opt1 == optimize(expr1, [expm1_opt_non_opportunistic])
+    assert opt2 == optimize(expr2, [expm1_opt_non_opportunistic])
+
+    expr4 = 3*exp(x) + log(x) - 3
+    opt4 = optimize(expr4, [expm1_opt])
+    assert 3*expm1(x) + log(x) == opt4
+    assert opt4.rewrite(exp) == expr4
+
+    expr5 = 3*exp(2*x) - 3
+    opt5 = optimize(expr5, [expm1_opt])
+    assert 3*expm1(2*x) == opt5
+    assert opt5.rewrite(exp) == expr5
+
+    expr6 = (2*exp(x) + 1)/(exp(x) + 1) + 1
+    opt6 = optimize(expr6, [expm1_opt])
+    assert opt6.count_ops() <= expr6.count_ops()
+
+    def ev(e):
+        return e.subs(x, 3).evalf()
+    assert abs(ev(expr6) - ev(opt6)) < 1e-15
+
+    y = Symbol('y')
+    expr7 = (2*exp(x) - 1)/(1 - exp(y)) - 1/(1-exp(y))
+    opt7 = optimize(expr7, [expm1_opt])
+    assert -2*expm1(x)/expm1(y) == opt7
+    assert (opt7.rewrite(exp) - expr7).factor() == 0
+
+    expr8 = (1+exp(x))**2 - 4
+    opt8 = optimize(expr8, [expm1_opt])
+    tgt8a = (exp(x) + 3)*expm1(x)
+    tgt8b = 2*expm1(x) + expm1(2*x)
+    # Both tgt8a & tgt8b seem to give full precision (~16 digits for double)
+    # for x=1e-7 (compare with expr8 which only achieves ~8 significant digits).
+    # If we can show that either tgt8a or tgt8b is preferable, we can
+    # change this test to ensure the preferable version is returned.
+    assert (tgt8a - tgt8b).rewrite(exp).factor() == 0
+    assert opt8 in (tgt8a, tgt8b)
+    assert (opt8.rewrite(exp) - expr8).factor() == 0
+
+    expr9 = sin(expr8)
+    opt9 = optimize(expr9, [expm1_opt])
+    tgt9a = sin(tgt8a)
+    tgt9b = sin(tgt8b)
+    assert opt9 in (tgt9a, tgt9b)
+    assert (opt9.rewrite(exp) - expr9.rewrite(exp)).factor().is_zero
+
+
+def test_expm1_two_exp_terms():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = exp(x) + exp(y) - 2
+    opt1 = optimize(expr1, [expm1_opt])
+    assert opt1 == expm1(x) + expm1(y)
+
+
+def test_cosm1_opt():
+    x = Symbol('x')
+
+    expr1 = cos(x) - 1
+    opt1 = optimize(expr1, [cosm1_opt])
+    assert cosm1(x) - opt1 == 0
+    assert opt1.rewrite(cos) == expr1
+
+    expr2 = 3*cos(x) - 3
+    opt2 = optimize(expr2, [cosm1_opt])
+    assert 3*cosm1(x) == opt2
+    assert opt2.rewrite(cos) == expr2
+
+    expr3 = 3*cos(x) - 5
+    opt3 = optimize(expr3, [cosm1_opt])
+    assert 3*cosm1(x) - 2 == opt3
+    assert opt3.rewrite(cos) == expr3
+    cosm1_opt_non_opportunistic = FuncMinusOneOptim(cos, cosm1, opportunistic=False)
+    assert expr3 == optimize(expr3, [cosm1_opt_non_opportunistic])
+    assert opt1 == optimize(expr1, [cosm1_opt_non_opportunistic])
+    assert opt2 == optimize(expr2, [cosm1_opt_non_opportunistic])
+
+    expr4 = 3*cos(x) + log(x) - 3
+    opt4 = optimize(expr4, [cosm1_opt])
+    assert 3*cosm1(x) + log(x) == opt4
+    assert opt4.rewrite(cos) == expr4
+
+    expr5 = 3*cos(2*x) - 3
+    opt5 = optimize(expr5, [cosm1_opt])
+    assert 3*cosm1(2*x) == opt5
+    assert opt5.rewrite(cos) == expr5
+
+    expr6 = 2 - 2*cos(x)
+    opt6 = optimize(expr6, [cosm1_opt])
+    assert -2*cosm1(x) == opt6
+    assert opt6.rewrite(cos) == expr6
+
+
+def test_cosm1_two_cos_terms():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = cos(x) + cos(y) - 2
+    opt1 = optimize(expr1, [cosm1_opt])
+    assert opt1 == cosm1(x) + cosm1(y)
+
+
+def test_expm1_cosm1_mixed():
+    x = Symbol('x')
+    expr1 = exp(x) + cos(x) - 2
+    opt1 = optimize(expr1, [expm1_opt, cosm1_opt])
+    assert opt1 == cosm1(x) + expm1(x)
+
+
+def _check_num_lambdify(expr, opt, val_subs, approx_ref, lambdify_kw=None, poorness=1e10):
+    """ poorness=1e10 signifies that `expr` loses precision of at least ten decimal digits. """
+    num_ref = expr.subs(val_subs).evalf()
+    eps = numpy.finfo(numpy.float64).eps
+    assert abs(num_ref - approx_ref) < approx_ref*eps
+    f1 = lambdify(list(val_subs.keys()), opt, **(lambdify_kw or {}))
+    args_float = tuple(map(float, val_subs.values()))
+    num_err1 = abs(f1(*args_float) - approx_ref)
+    assert num_err1 < abs(num_ref*eps)
+    f2 = lambdify(list(val_subs.keys()), expr, **(lambdify_kw or {}))
+    num_err2 = abs(f2(*args_float) - approx_ref)
+    assert num_err2 > abs(num_ref*eps*poorness)   # this only ensures that the *test* works as intended
+
+
+def test_cosm1_apart():
+    x = Symbol('x')
+
+    expr1 = 1/cos(x) - 1
+    opt1 = optimize(expr1, [cosm1_opt])
+    assert opt1 == -cosm1(x)/cos(x)
+    if scipy:
+        _check_num_lambdify(expr1, opt1, {x: S(10)**-30}, 5e-61, lambdify_kw={"modules": 'scipy'})
+
+    expr2 = 2/cos(x) - 2
+    opt2 = optimize(expr2, optims_scipy)
+    assert opt2 == -2*cosm1(x)/cos(x)
+    if scipy:
+        _check_num_lambdify(expr2, opt2, {x: S(10)**-30}, 1e-60, lambdify_kw={"modules": 'scipy'})
+
+    expr3 = pi/cos(3*x) - pi
+    opt3 = optimize(expr3, [cosm1_opt])
+    assert opt3 == -pi*cosm1(3*x)/cos(3*x)
+    if scipy:
+        _check_num_lambdify(expr3, opt3, {x: S(10)**-30/3}, float(5e-61*pi), lambdify_kw={"modules": 'scipy'})
+
+
+def test_powm1():
+    args = x, y = map(Symbol, "xy")
+
+    expr1 = x**y - 1
+    opt1 = optimize(expr1, [powm1_opt])
+    assert opt1 == powm1(x, y)
+    for arg in args:
+        assert expr1.diff(arg) == opt1.diff(arg)
+    if scipy and tuple(map(int, scipy.version.version.split('.')[:3])) >= (1, 10, 0):
+        subs1_a = {x: Rational(*(1.0+1e-13).as_integer_ratio()), y: pi}
+        ref1_f64_a = 3.139081648208105e-13
+        _check_num_lambdify(expr1, opt1, subs1_a, ref1_f64_a, lambdify_kw={"modules": 'scipy'}, poorness=10**11)
+
+        subs1_b = {x: pi, y: Rational(*(1e-10).as_integer_ratio())}
+        ref1_f64_b = 1.1447298859149205e-10
+        _check_num_lambdify(expr1, opt1, subs1_b, ref1_f64_b, lambdify_kw={"modules": 'scipy'}, poorness=10**9)
+
+
+def test_log1p_opt():
+    x = Symbol('x')
+    expr1 = log(x + 1)
+    opt1 = optimize(expr1, [log1p_opt])
+    assert log1p(x) - opt1 == 0
+    assert opt1.rewrite(log) == expr1
+
+    expr2 = log(3*x + 3)
+    opt2 = optimize(expr2, [log1p_opt])
+    assert log1p(x) + log(3) == opt2
+    assert (opt2.rewrite(log) - expr2).simplify() == 0
+
+    expr3 = log(2*x + 1)
+    opt3 = optimize(expr3, [log1p_opt])
+    assert log1p(2*x) - opt3 == 0
+    assert opt3.rewrite(log) == expr3
+
+    expr4 = log(x+3)
+    opt4 = optimize(expr4, [log1p_opt])
+    assert str(opt4) == 'log(x + 3)'
+
+
+def test_optims_c99():
+    x = Symbol('x')
+
+    expr1 = 2**x + log(x)/log(2) + log(x + 1) + exp(x) - 1
+    opt1 = optimize(expr1, optims_c99).simplify()
+    assert opt1 == exp2(x) + log2(x) + log1p(x) + expm1(x)
+    assert opt1.rewrite(exp).rewrite(log).rewrite(Pow) == expr1
+
+    expr2 = log(x)/log(2) + log(x + 1)
+    opt2 = optimize(expr2, optims_c99)
+    assert opt2 == log2(x) + log1p(x)
+    assert opt2.rewrite(log) == expr2
+
+    expr3 = log(x)/log(2) + log(17*x + 17)
+    opt3 = optimize(expr3, optims_c99)
+    delta3 = opt3 - (log2(x) + log(17) + log1p(x))
+    assert delta3 == 0
+    assert (opt3.rewrite(log) - expr3).simplify() == 0
+
+    expr4 = 2**x + 3*log(5*x + 7)/(13*log(2)) + 11*exp(x) - 11 + log(17*x + 17)
+    opt4 = optimize(expr4, optims_c99).simplify()
+    delta4 = opt4 - (exp2(x) + 3*log2(5*x + 7)/13 + 11*expm1(x) + log(17) + log1p(x))
+    assert delta4 == 0
+    assert (opt4.rewrite(exp).rewrite(log).rewrite(Pow) - expr4).simplify() == 0
+
+    expr5 = 3*exp(2*x) - 3
+    opt5 = optimize(expr5, optims_c99)
+    delta5 = opt5 - 3*expm1(2*x)
+    assert delta5 == 0
+    assert opt5.rewrite(exp) == expr5
+
+    expr6 = exp(2*x) - 3
+    opt6 = optimize(expr6, optims_c99)
+    assert opt6 in (expm1(2*x) - 2, expr6)  # expm1(2*x) - 2 is not better or worse
+
+    expr7 = log(3*x + 3)
+    opt7 = optimize(expr7, optims_c99)
+    delta7 = opt7 - (log(3) + log1p(x))
+    assert delta7 == 0
+    assert (opt7.rewrite(log) - expr7).simplify() == 0
+
+    expr8 = log(2*x + 3)
+    opt8 = optimize(expr8, optims_c99)
+    assert opt8 == expr8
+
+
+def test_create_expand_pow_optimization():
+    cc = lambda x: ccode(
+        optimize(x, [create_expand_pow_optimization(4)]))
+    x = Symbol('x')
+    assert cc(x**4) == 'x*x*x*x'
+    assert cc(x**4 + x**2) == 'x*x + x*x*x*x'
+    assert cc(x**5 + x**4) == 'pow(x, 5) + x*x*x*x'
+    assert cc(sin(x)**4) == 'pow(sin(x), 4)'
+    # gh issue 15335
+    assert cc(x**(-4)) == '1.0/(x*x*x*x)'
+    assert cc(x**(-5)) == 'pow(x, -5)'
+    assert cc(-x**4) == '-(x*x*x*x)'
+    assert cc(x**4 - x**2) == '-(x*x) + x*x*x*x'
+    i = Symbol('i', integer=True)
+    assert cc(x**i - x**2) == 'pow(x, i) - (x*x)'
+    y = Symbol('y', real=True)
+    assert cc(Abs(exp(y**4))) == "exp(y*y*y*y)"
+
+    # gh issue 20753
+    cc2 = lambda x: ccode(optimize(x, [create_expand_pow_optimization(
+        4, base_req=lambda b: b.is_Function)]))
+    assert cc2(x**3 + sin(x)**3) == "pow(x, 3) + sin(x)*sin(x)*sin(x)"
+
+
+def test_matsolve():
+    n = Symbol('n', integer=True)
+    A = MatrixSymbol('A', n, n)
+    x = MatrixSymbol('x', n, 1)
+
+    with assuming(Q.fullrank(A)):
+        assert optimize(A**(-1) * x, [matinv_opt]) == MatrixSolve(A, x)
+        assert optimize(A**(-1) * x + x, [matinv_opt]) == MatrixSolve(A, x) + x
+
+
+def test_logaddexp_opt():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = log(exp(x) + exp(y))
+    opt1 = optimize(expr1, [logaddexp_opt])
+    assert logaddexp(x, y) - opt1 == 0
+    assert logaddexp(y, x) - opt1 == 0
+    assert opt1.rewrite(log) == expr1
+
+
+def test_logaddexp2_opt():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = log(2**x + 2**y)/log(2)
+    opt1 = optimize(expr1, [logaddexp2_opt])
+    assert logaddexp2(x, y) - opt1 == 0
+    assert logaddexp2(y, x) - opt1 == 0
+    assert opt1.rewrite(log) == expr1
+
+
+def test_sinc_opts():
+    def check(d):
+        for k, v in d.items():
+            assert optimize(k, sinc_opts) == v
+
+    x = Symbol('x')
+    check({
+        sin(x)/x       : sinc(x),
+        sin(2*x)/(2*x) : sinc(2*x),
+        sin(3*x)/x     : 3*sinc(3*x),
+        x*sin(x)       : x*sin(x)
+    })
+
+    y = Symbol('y')
+    check({
+        sin(x*y)/(x*y)       : sinc(x*y),
+        y*sin(x/y)/x         : sinc(x/y),
+        sin(sin(x))/sin(x)   : sinc(sin(x)),
+        sin(3*sin(x))/sin(x) : 3*sinc(3*sin(x)),
+        sin(x)/y             : sin(x)/y
+    })
+
+
+def test_optims_numpy():
+    def check(d):
+        for k, v in d.items():
+            assert optimize(k, optims_numpy) == v
+
+    x = Symbol('x')
+    check({
+        sin(2*x)/(2*x) + exp(2*x) - 1: sinc(2*x) + expm1(2*x),
+        log(x+3)/log(2) + log(x**2 + 1): log1p(x**2) + log2(x+3)
+    })
+
+
+@XFAIL  # room for improvement, ideally this test case should pass.
+def test_optims_numpy_TODO():
+    def check(d):
+        for k, v in d.items():
+            assert optimize(k, optims_numpy) == v
+
+    x, y = map(Symbol, 'x y'.split())
+    check({
+        log(x*y)*sin(x*y)*log(x*y+1)/(log(2)*x*y): log2(x*y)*sinc(x*y)*log1p(x*y),
+        exp(x*sin(y)/y) - 1: expm1(x*sinc(y))
+    })
+
+
+@may_xfail
+def test_compiled_ccode_with_rewriting():
+    if not cython:
+        skip("cython not installed.")
+    if not has_c():
+        skip("No C compiler found.")
+
+    x = Symbol('x')
+    about_two = 2**(58/S(117))*3**(97/S(117))*5**(4/S(39))*7**(92/S(117))/S(30)*pi
+    # about_two: 1.999999999999581826
+    unchanged = 2*exp(x) - about_two
+    xval = S(10)**-11
+    ref = unchanged.subs(x, xval).n(19) # 2.0418173913673213e-11
+
+    rewritten = optimize(2*exp(x) - about_two, [expm1_opt])
+
+    # Unfortunately, we need to call ``.n()`` on our expressions before we hand them
+    # to ``ccode``, and we need to request a large number of significant digits.
+    # In this test, results converged for double precision when the following number
+    # of significant digits were chosen:
+    NUMBER_OF_DIGITS = 25   # TODO: this should ideally be automatically handled.
+
+    func_c = '''
+#include 
+
+double func_unchanged(double x) {
+    return %(unchanged)s;
+}
+double func_rewritten(double x) {
+    return %(rewritten)s;
+}
+''' % {"unchanged": ccode(unchanged.n(NUMBER_OF_DIGITS)),
+           "rewritten": ccode(rewritten.n(NUMBER_OF_DIGITS))}
+
+    func_pyx = '''
+#cython: language_level=3
+cdef extern double func_unchanged(double)
+cdef extern double func_rewritten(double)
+def py_unchanged(x):
+    return func_unchanged(x)
+def py_rewritten(x):
+    return func_rewritten(x)
+'''
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings(
+            [('func.c', func_c), ('_func.pyx', func_pyx)],
+            build_dir=folder, compile_kwargs={"std": 'c99'}
+        )
+        err_rewritten = abs(mod.py_rewritten(1e-11) - ref)
+        err_unchanged = abs(mod.py_unchanged(1e-11) - ref)
+        assert 1e-27 < err_rewritten < 1e-25  # highly accurate.
+        assert 1e-19 < err_unchanged < 1e-16  # quite poor.
+
+    # Tolerances used above were determined as follows:
+    # >>> no_opt = unchanged.subs(x, xval.evalf()).evalf()
+    # >>> with_opt = rewritten.n(25).subs(x, 1e-11).evalf()
+    # >>> with_opt - ref, no_opt - ref
+    # (1.1536301877952077e-26, 1.6547074214222335e-18)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_scipy_nodes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_scipy_nodes.py
new file mode 100644
index 0000000000000000000000000000000000000000..c0d1461037eec81ade0c99b18fbbf5a4517ce0b7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/codegen/tests/test_scipy_nodes.py
@@ -0,0 +1,44 @@
+from itertools import product
+from sympy.core.power import Pow
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.trigonometric import cos
+from sympy.core.numbers import pi
+from sympy.codegen.scipy_nodes import cosm1, powm1
+
+x, y, z = symbols('x y z')
+
+
+def test_cosm1():
+    cm1_xy = cosm1(x*y)
+    ref_xy = cos(x*y) - 1
+    for wrt, deriv_order in product([x, y, z], range(3)):
+        assert (
+            cm1_xy.diff(wrt, deriv_order) -
+            ref_xy.diff(wrt, deriv_order)
+        ).rewrite(cos).simplify() == 0
+
+    expr_minus2 = cosm1(pi)
+    assert expr_minus2.rewrite(cos) == -2
+    assert cosm1(3.14).simplify() == cosm1(3.14)  # cannot simplify with 3.14
+    assert cosm1(pi/2).simplify() == -1
+    assert (1/cos(x) - 1 + cosm1(x)/cos(x)).simplify() == 0
+
+
+def test_powm1():
+    cases = {
+            powm1(x, y): x**y - 1,
+            powm1(x*y, z): (x*y)**z - 1,
+            powm1(x, y*z): x**(y*z)-1,
+            powm1(x*y*z, x*y*z): (x*y*z)**(x*y*z)-1
+    }
+    for pm1_e, ref_e in cases.items():
+        for wrt, deriv_order in product([x, y, z], range(3)):
+            der = pm1_e.diff(wrt, deriv_order)
+            ref = ref_e.diff(wrt, deriv_order)
+            delta = (der - ref).rewrite(Pow)
+            assert delta.simplify() == 0
+
+    eulers_constant_m1 = powm1(x, 1/log(x))
+    assert eulers_constant_m1.rewrite(Pow) == exp(1) - 1
+    assert eulers_constant_m1.simplify() == exp(1) - 1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..220c27a42975555f8fe7770fcef0dd18475c89e1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/__init__.py
@@ -0,0 +1,43 @@
+from sympy.combinatorics.permutations import Permutation, Cycle
+from sympy.combinatorics.prufer import Prufer
+from sympy.combinatorics.generators import cyclic, alternating, symmetric, dihedral
+from sympy.combinatorics.subsets import Subset
+from sympy.combinatorics.partitions import (Partition, IntegerPartition,
+    RGS_rank, RGS_unrank, RGS_enum)
+from sympy.combinatorics.polyhedron import (Polyhedron, tetrahedron, cube,
+    octahedron, dodecahedron, icosahedron)
+from sympy.combinatorics.perm_groups import PermutationGroup, Coset, SymmetricPermutationGroup
+from sympy.combinatorics.group_constructs import DirectProduct
+from sympy.combinatorics.graycode import GrayCode
+from sympy.combinatorics.named_groups import (SymmetricGroup, DihedralGroup,
+    CyclicGroup, AlternatingGroup, AbelianGroup, RubikGroup)
+from sympy.combinatorics.pc_groups import PolycyclicGroup, Collector
+from sympy.combinatorics.free_groups import free_group
+
+__all__ = [
+    'Permutation', 'Cycle',
+
+    'Prufer',
+
+    'cyclic', 'alternating', 'symmetric', 'dihedral',
+
+    'Subset',
+
+    'Partition', 'IntegerPartition', 'RGS_rank', 'RGS_unrank', 'RGS_enum',
+
+    'Polyhedron', 'tetrahedron', 'cube', 'octahedron', 'dodecahedron',
+    'icosahedron',
+
+    'PermutationGroup', 'Coset', 'SymmetricPermutationGroup',
+
+    'DirectProduct',
+
+    'GrayCode',
+
+    'SymmetricGroup', 'DihedralGroup', 'CyclicGroup', 'AlternatingGroup',
+    'AbelianGroup', 'RubikGroup',
+
+    'PolycyclicGroup', 'Collector',
+
+    'free_group',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/coset_table.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/coset_table.py
new file mode 100644
index 0000000000000000000000000000000000000000..0687aa34ec70e9062f65ff6413213848cf03e51b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/coset_table.py
@@ -0,0 +1,1259 @@
+from sympy.combinatorics.free_groups import free_group
+from sympy.printing.defaults import DefaultPrinting
+
+from itertools import chain, product
+from bisect import bisect_left
+
+
+###############################################################################
+#                           COSET TABLE                                       #
+###############################################################################
+
+class CosetTable(DefaultPrinting):
+    # coset_table: Mathematically a coset table
+    #               represented using a list of lists
+    # alpha: Mathematically a coset (precisely, a live coset)
+    #       represented by an integer between i with 1 <= i <= n
+    #       alpha in c
+    # x: Mathematically an element of "A" (set of generators and
+    #   their inverses), represented using "FpGroupElement"
+    # fp_grp: Finitely Presented Group with < X|R > as presentation.
+    # H: subgroup of fp_grp.
+    # NOTE: We start with H as being only a list of words in generators
+    #       of "fp_grp". Since `.subgroup` method has not been implemented.
+
+    r"""
+
+    Properties
+    ==========
+
+    [1] `0 \in \Omega` and `\tau(1) = \epsilon`
+    [2] `\alpha^x = \beta \Leftrightarrow \beta^{x^{-1}} = \alpha`
+    [3] If `\alpha^x = \beta`, then `H \tau(\alpha)x = H \tau(\beta)`
+    [4] `\forall \alpha \in \Omega, 1^{\tau(\alpha)} = \alpha`
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.
+           "Handbook of Computational Group Theory"
+
+    .. [2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson
+           Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490.
+           "Implementation and Analysis of the Todd-Coxeter Algorithm"
+
+    """
+    # default limit for the number of cosets allowed in a
+    # coset enumeration.
+    coset_table_max_limit = 4096000
+    # limit for the current instance
+    coset_table_limit = None
+    # maximum size of deduction stack above or equal to
+    # which it is emptied
+    max_stack_size = 100
+
+    def __init__(self, fp_grp, subgroup, max_cosets=None):
+        if not max_cosets:
+            max_cosets = CosetTable.coset_table_max_limit
+        self.fp_group = fp_grp
+        self.subgroup = subgroup
+        self.coset_table_limit = max_cosets
+        # "p" is setup independent of Omega and n
+        self.p = [0]
+        # a list of the form `[gen_1, gen_1^{-1}, ... , gen_k, gen_k^{-1}]`
+        self.A = list(chain.from_iterable((gen, gen**-1) \
+                for gen in self.fp_group.generators))
+        #P[alpha, x] Only defined when alpha^x is defined.
+        self.P = [[None]*len(self.A)]
+        # the mathematical coset table which is a list of lists
+        self.table = [[None]*len(self.A)]
+        self.A_dict = {x: self.A.index(x) for x in self.A}
+        self.A_dict_inv = {}
+        for x, index in self.A_dict.items():
+            if index % 2 == 0:
+                self.A_dict_inv[x] = self.A_dict[x] + 1
+            else:
+                self.A_dict_inv[x] = self.A_dict[x] - 1
+        # used in the coset-table based method of coset enumeration. Each of
+        # the element is called a "deduction" which is the form (alpha, x) whenever
+        # a value is assigned to alpha^x during a definition or "deduction process"
+        self.deduction_stack = []
+        # Attributes for modified methods.
+        H = self.subgroup
+        self._grp = free_group(', ' .join(["a_%d" % i for i in range(len(H))]))[0]
+        self.P = [[None]*len(self.A)]
+        self.p_p = {}
+
+    @property
+    def omega(self):
+        """Set of live cosets. """
+        return [coset for coset in range(len(self.p)) if self.p[coset] == coset]
+
+    def copy(self):
+        """
+        Return a shallow copy of Coset Table instance ``self``.
+
+        """
+        self_copy = self.__class__(self.fp_group, self.subgroup)
+        self_copy.table = [list(perm_rep) for perm_rep in self.table]
+        self_copy.p = list(self.p)
+        self_copy.deduction_stack = list(self.deduction_stack)
+        return self_copy
+
+    def __str__(self):
+        return "Coset Table on %s with %s as subgroup generators" \
+                % (self.fp_group, self.subgroup)
+
+    __repr__ = __str__
+
+    @property
+    def n(self):
+        """The number `n` represents the length of the sublist containing the
+        live cosets.
+
+        """
+        if not self.table:
+            return 0
+        return max(self.omega) + 1
+
+    # Pg. 152 [1]
+    def is_complete(self):
+        r"""
+        The coset table is called complete if it has no undefined entries
+        on the live cosets; that is, `\alpha^x` is defined for all
+        `\alpha \in \Omega` and `x \in A`.
+
+        """
+        return not any(None in self.table[coset] for coset in self.omega)
+
+    # Pg. 153 [1]
+    def define(self, alpha, x, modified=False):
+        r"""
+        This routine is used in the relator-based strategy of Todd-Coxeter
+        algorithm if some `\alpha^x` is undefined. We check whether there is
+        space available for defining a new coset. If there is enough space
+        then we remedy this by adjoining a new coset `\beta` to `\Omega`
+        (i.e to set of live cosets) and put that equal to `\alpha^x`, then
+        make an assignment satisfying Property[1]. If there is not enough space
+        then we halt the Coset Table creation. The maximum amount of space that
+        can be used by Coset Table can be manipulated using the class variable
+        ``CosetTable.coset_table_max_limit``.
+
+        See Also
+        ========
+
+        define_c
+
+        """
+        A = self.A
+        table = self.table
+        len_table = len(table)
+        if len_table >= self.coset_table_limit:
+            # abort the further generation of cosets
+            raise ValueError("the coset enumeration has defined more than "
+                    "%s cosets. Try with a greater value max number of cosets "
+                    % self.coset_table_limit)
+        table.append([None]*len(A))
+        self.P.append([None]*len(self.A))
+        # beta is the new coset generated
+        beta = len_table
+        self.p.append(beta)
+        table[alpha][self.A_dict[x]] = beta
+        table[beta][self.A_dict_inv[x]] = alpha
+        # P[alpha][x] = epsilon, P[beta][x**-1] = epsilon
+        if modified:
+            self.P[alpha][self.A_dict[x]] = self._grp.identity
+            self.P[beta][self.A_dict_inv[x]] = self._grp.identity
+            self.p_p[beta] = self._grp.identity
+
+    def define_c(self, alpha, x):
+        r"""
+        A variation of ``define`` routine, described on Pg. 165 [1], used in
+        the coset table-based strategy of Todd-Coxeter algorithm. It differs
+        from ``define`` routine in that for each definition it also adds the
+        tuple `(\alpha, x)` to the deduction stack.
+
+        See Also
+        ========
+
+        define
+
+        """
+        A = self.A
+        table = self.table
+        len_table = len(table)
+        if len_table >= self.coset_table_limit:
+            # abort the further generation of cosets
+            raise ValueError("the coset enumeration has defined more than "
+                    "%s cosets. Try with a greater value max number of cosets "
+                    % self.coset_table_limit)
+        table.append([None]*len(A))
+        # beta is the new coset generated
+        beta = len_table
+        self.p.append(beta)
+        table[alpha][self.A_dict[x]] = beta
+        table[beta][self.A_dict_inv[x]] = alpha
+        # append to deduction stack
+        self.deduction_stack.append((alpha, x))
+
+    def scan_c(self, alpha, word):
+        """
+        A variation of ``scan`` routine, described on pg. 165 of [1], which
+        puts at tuple, whenever a deduction occurs, to deduction stack.
+
+        See Also
+        ========
+
+        scan, scan_check, scan_and_fill, scan_and_fill_c
+
+        """
+        # alpha is an integer representing a "coset"
+        # since scanning can be in two cases
+        # 1. for alpha=0 and w in Y (i.e generating set of H)
+        # 2. alpha in Omega (set of live cosets), w in R (relators)
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        f = alpha
+        i = 0
+        r = len(word)
+        b = alpha
+        j = r - 1
+        # list of union of generators and their inverses
+        while i <= j and table[f][A_dict[word[i]]] is not None:
+            f = table[f][A_dict[word[i]]]
+            i += 1
+        if i > j:
+            if f != b:
+                self.coincidence_c(f, b)
+            return
+        while j >= i and table[b][A_dict_inv[word[j]]] is not None:
+            b = table[b][A_dict_inv[word[j]]]
+            j -= 1
+        if j < i:
+            # we have an incorrect completed scan with coincidence f ~ b
+            # run the "coincidence" routine
+            self.coincidence_c(f, b)
+        elif j == i:
+            # deduction process
+            table[f][A_dict[word[i]]] = b
+            table[b][A_dict_inv[word[i]]] = f
+            self.deduction_stack.append((f, word[i]))
+        # otherwise scan is incomplete and yields no information
+
+    # alpha, beta coincide, i.e. alpha, beta represent the pair of cosets where
+    # coincidence occurs
+    def coincidence_c(self, alpha, beta):
+        """
+        A variation of ``coincidence`` routine used in the coset-table based
+        method of coset enumeration. The only difference being on addition of
+        a new coset in coset table(i.e new coset introduction), then it is
+        appended to ``deduction_stack``.
+
+        See Also
+        ========
+
+        coincidence
+
+        """
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        # behaves as a queue
+        q = []
+        self.merge(alpha, beta, q)
+        while len(q) > 0:
+            gamma = q.pop(0)
+            for x in A_dict:
+                delta = table[gamma][A_dict[x]]
+                if delta is not None:
+                    table[delta][A_dict_inv[x]] = None
+                    # only line of difference from ``coincidence`` routine
+                    self.deduction_stack.append((delta, x**-1))
+                    mu = self.rep(gamma)
+                    nu = self.rep(delta)
+                    if table[mu][A_dict[x]] is not None:
+                        self.merge(nu, table[mu][A_dict[x]], q)
+                    elif table[nu][A_dict_inv[x]] is not None:
+                        self.merge(mu, table[nu][A_dict_inv[x]], q)
+                    else:
+                        table[mu][A_dict[x]] = nu
+                        table[nu][A_dict_inv[x]] = mu
+
+    def scan(self, alpha, word, y=None, fill=False, modified=False):
+        r"""
+        ``scan`` performs a scanning process on the input ``word``.
+        It first locates the largest prefix ``s`` of ``word`` for which
+        `\alpha^s` is defined (i.e is not ``None``), ``s`` may be empty. Let
+        ``word=sv``, let ``t`` be the longest suffix of ``v`` for which
+        `\alpha^{t^{-1}}` is defined, and let ``v=ut``. Then three
+        possibilities are there:
+
+        1. If ``t=v``, then we say that the scan completes, and if, in addition
+        `\alpha^s = \alpha^{t^{-1}}`, then we say that the scan completes
+        correctly.
+
+        2. It can also happen that scan does not complete, but `|u|=1`; that
+        is, the word ``u`` consists of a single generator `x \in A`. In that
+        case, if `\alpha^s = \beta` and `\alpha^{t^{-1}} = \gamma`, then we can
+        set `\beta^x = \gamma` and `\gamma^{x^{-1}} = \beta`. These assignments
+        are known as deductions and enable the scan to complete correctly.
+
+        3. See ``coicidence`` routine for explanation of third condition.
+
+        Notes
+        =====
+
+        The code for the procedure of scanning `\alpha \in \Omega`
+        under `w \in A*` is defined on pg. 155 [1]
+
+        See Also
+        ========
+
+        scan_c, scan_check, scan_and_fill, scan_and_fill_c
+
+        Scan and Fill
+        =============
+
+        Performed when the default argument fill=True.
+
+        Modified Scan
+        =============
+
+        Performed when the default argument modified=True
+
+        """
+        # alpha is an integer representing a "coset"
+        # since scanning can be in two cases
+        # 1. for alpha=0 and w in Y (i.e generating set of H)
+        # 2. alpha in Omega (set of live cosets), w in R (relators)
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        f = alpha
+        i = 0
+        r = len(word)
+        b = alpha
+        j = r - 1
+        b_p = y
+        if modified:
+            f_p = self._grp.identity
+        flag = 0
+        while fill or flag == 0:
+            flag = 1
+            while i <= j and table[f][A_dict[word[i]]] is not None:
+                if modified:
+                    f_p = f_p*self.P[f][A_dict[word[i]]]
+                f = table[f][A_dict[word[i]]]
+                i += 1
+            if i > j:
+                if f != b:
+                    if modified:
+                        self.modified_coincidence(f, b, f_p**-1*y)
+                    else:
+                        self.coincidence(f, b)
+                return
+            while j >= i and table[b][A_dict_inv[word[j]]] is not None:
+                if modified:
+                    b_p = b_p*self.P[b][self.A_dict_inv[word[j]]]
+                b = table[b][A_dict_inv[word[j]]]
+                j -= 1
+            if j < i:
+                # we have an incorrect completed scan with coincidence f ~ b
+                # run the "coincidence" routine
+                if modified:
+                    self.modified_coincidence(f, b, f_p**-1*b_p)
+                else:
+                    self.coincidence(f, b)
+            elif j == i:
+                # deduction process
+                table[f][A_dict[word[i]]] = b
+                table[b][A_dict_inv[word[i]]] = f
+                if modified:
+                    self.P[f][self.A_dict[word[i]]] = f_p**-1*b_p
+                    self.P[b][self.A_dict_inv[word[i]]] = b_p**-1*f_p
+                return
+            elif fill:
+                self.define(f, word[i], modified=modified)
+            # otherwise scan is incomplete and yields no information
+
+    # used in the low-index subgroups algorithm
+    def scan_check(self, alpha, word):
+        r"""
+        Another version of ``scan`` routine, described on, it checks whether
+        `\alpha` scans correctly under `word`, it is a straightforward
+        modification of ``scan``. ``scan_check`` returns ``False`` (rather than
+        calling ``coincidence``) if the scan completes incorrectly; otherwise
+        it returns ``True``.
+
+        See Also
+        ========
+
+        scan, scan_c, scan_and_fill, scan_and_fill_c
+
+        """
+        # alpha is an integer representing a "coset"
+        # since scanning can be in two cases
+        # 1. for alpha=0 and w in Y (i.e generating set of H)
+        # 2. alpha in Omega (set of live cosets), w in R (relators)
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        f = alpha
+        i = 0
+        r = len(word)
+        b = alpha
+        j = r - 1
+        while i <= j and table[f][A_dict[word[i]]] is not None:
+            f = table[f][A_dict[word[i]]]
+            i += 1
+        if i > j:
+            return f == b
+        while j >= i and table[b][A_dict_inv[word[j]]] is not None:
+            b = table[b][A_dict_inv[word[j]]]
+            j -= 1
+        if j < i:
+            # we have an incorrect completed scan with coincidence f ~ b
+            # return False, instead of calling coincidence routine
+            return False
+        elif j == i:
+            # deduction process
+            table[f][A_dict[word[i]]] = b
+            table[b][A_dict_inv[word[i]]] = f
+        return True
+
+    def merge(self, k, lamda, q, w=None, modified=False):
+        """
+        Merge two classes with representatives ``k`` and ``lamda``, described
+        on Pg. 157 [1] (for pseudocode), start by putting ``p[k] = lamda``.
+        It is more efficient to choose the new representative from the larger
+        of the two classes being merged, i.e larger among ``k`` and ``lamda``.
+        procedure ``merge`` performs the merging operation, adds the deleted
+        class representative to the queue ``q``.
+
+        Parameters
+        ==========
+
+        'k', 'lamda' being the two class representatives to be merged.
+
+        Notes
+        =====
+
+        Pg. 86-87 [1] contains a description of this method.
+
+        See Also
+        ========
+
+        coincidence, rep
+
+        """
+        p = self.p
+        rep = self.rep
+        phi = rep(k, modified=modified)
+        psi = rep(lamda, modified=modified)
+        if phi != psi:
+            mu = min(phi, psi)
+            v = max(phi, psi)
+            p[v] = mu
+            if modified:
+                if v == phi:
+                    self.p_p[phi] = self.p_p[k]**-1*w*self.p_p[lamda]
+                else:
+                    self.p_p[psi] = self.p_p[lamda]**-1*w**-1*self.p_p[k]
+            q.append(v)
+
+    def rep(self, k, modified=False):
+        r"""
+        Parameters
+        ==========
+
+        `k \in [0 \ldots n-1]`, as for ``self`` only array ``p`` is used
+
+        Returns
+        =======
+
+        Representative of the class containing ``k``.
+
+        Returns the representative of `\sim` class containing ``k``, it also
+        makes some modification to array ``p`` of ``self`` to ease further
+        computations, described on Pg. 157 [1].
+
+        The information on classes under `\sim` is stored in array `p` of
+        ``self`` argument, which will always satisfy the property:
+
+        `p[\alpha] \sim \alpha` and `p[\alpha]=\alpha \iff \alpha=rep(\alpha)`
+        `\forall \in [0 \ldots n-1]`.
+
+        So, for `\alpha \in [0 \ldots n-1]`, we find `rep(self, \alpha)` by
+        continually replacing `\alpha` by `p[\alpha]` until it becomes
+        constant (i.e satisfies `p[\alpha] = \alpha`):w
+
+        To increase the efficiency of later ``rep`` calculations, whenever we
+        find `rep(self, \alpha)=\beta`, we set
+        `p[\gamma] = \beta \forall \gamma \in p-chain` from `\alpha` to `\beta`
+
+        Notes
+        =====
+
+        ``rep`` routine is also described on Pg. 85-87 [1] in Atkinson's
+        algorithm, this results from the fact that ``coincidence`` routine
+        introduces functionality similar to that introduced by the
+        ``minimal_block`` routine on Pg. 85-87 [1].
+
+        See Also
+        ========
+
+        coincidence, merge
+
+        """
+        p = self.p
+        lamda = k
+        rho = p[lamda]
+        if modified:
+            s = p[:]
+        while rho != lamda:
+            if modified:
+                s[rho] = lamda
+            lamda = rho
+            rho = p[lamda]
+        if modified:
+            rho = s[lamda]
+            while rho != k:
+                mu = rho
+                rho = s[mu]
+                p[rho] = lamda
+                self.p_p[rho] = self.p_p[rho]*self.p_p[mu]
+        else:
+            mu = k
+            rho = p[mu]
+            while rho != lamda:
+                p[mu] = lamda
+                mu = rho
+                rho = p[mu]
+        return lamda
+
+    # alpha, beta coincide, i.e. alpha, beta represent the pair of cosets
+    # where coincidence occurs
+    def coincidence(self, alpha, beta, w=None, modified=False):
+        r"""
+        The third situation described in ``scan`` routine is handled by this
+        routine, described on Pg. 156-161 [1].
+
+        The unfortunate situation when the scan completes but not correctly,
+        then ``coincidence`` routine is run. i.e when for some `i` with
+        `1 \le i \le r+1`, we have `w=st` with `s = x_1 x_2 \dots x_{i-1}`,
+        `t = x_i x_{i+1} \dots x_r`, and `\beta = \alpha^s` and
+        `\gamma = \alpha^{t-1}` are defined but unequal. This means that
+        `\beta` and `\gamma` represent the same coset of `H` in `G`. Described
+        on Pg. 156 [1]. ``rep``
+
+        See Also
+        ========
+
+        scan
+
+        """
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        # behaves as a queue
+        q = []
+        if modified:
+            self.modified_merge(alpha, beta, w, q)
+        else:
+            self.merge(alpha, beta, q)
+        while len(q) > 0:
+            gamma = q.pop(0)
+            for x in A_dict:
+                delta = table[gamma][A_dict[x]]
+                if delta is not None:
+                    table[delta][A_dict_inv[x]] = None
+                    mu = self.rep(gamma, modified=modified)
+                    nu = self.rep(delta, modified=modified)
+                    if table[mu][A_dict[x]] is not None:
+                        if modified:
+                            v = self.p_p[delta]**-1*self.P[gamma][self.A_dict[x]]**-1
+                            v = v*self.p_p[gamma]*self.P[mu][self.A_dict[x]]
+                            self.modified_merge(nu, table[mu][self.A_dict[x]], v, q)
+                        else:
+                            self.merge(nu, table[mu][A_dict[x]], q)
+                    elif table[nu][A_dict_inv[x]] is not None:
+                        if modified:
+                            v = self.p_p[gamma]**-1*self.P[gamma][self.A_dict[x]]
+                            v = v*self.p_p[delta]*self.P[mu][self.A_dict_inv[x]]
+                            self.modified_merge(mu, table[nu][self.A_dict_inv[x]], v, q)
+                        else:
+                            self.merge(mu, table[nu][A_dict_inv[x]], q)
+                    else:
+                        table[mu][A_dict[x]] = nu
+                        table[nu][A_dict_inv[x]] = mu
+                        if modified:
+                            v = self.p_p[gamma]**-1*self.P[gamma][self.A_dict[x]]*self.p_p[delta]
+                            self.P[mu][self.A_dict[x]] = v
+                            self.P[nu][self.A_dict_inv[x]] = v**-1
+
+    # method used in the HLT strategy
+    def scan_and_fill(self, alpha, word):
+        """
+        A modified version of ``scan`` routine used in the relator-based
+        method of coset enumeration, described on pg. 162-163 [1], which
+        follows the idea that whenever the procedure is called and the scan
+        is incomplete then it makes new definitions to enable the scan to
+        complete; i.e it fills in the gaps in the scan of the relator or
+        subgroup generator.
+
+        """
+        self.scan(alpha, word, fill=True)
+
+    def scan_and_fill_c(self, alpha, word):
+        """
+        A modified version of ``scan`` routine, described on Pg. 165 second
+        para. [1], with modification similar to that of ``scan_anf_fill`` the
+        only difference being it calls the coincidence procedure used in the
+        coset-table based method i.e. the routine ``coincidence_c`` is used.
+
+        See Also
+        ========
+
+        scan, scan_and_fill
+
+        """
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        r = len(word)
+        f = alpha
+        i = 0
+        b = alpha
+        j = r - 1
+        # loop until it has filled the alpha row in the table.
+        while True:
+            # do the forward scanning
+            while i <= j and table[f][A_dict[word[i]]] is not None:
+                f = table[f][A_dict[word[i]]]
+                i += 1
+            if i > j:
+                if f != b:
+                    self.coincidence_c(f, b)
+                return
+            # forward scan was incomplete, scan backwards
+            while j >= i and table[b][A_dict_inv[word[j]]] is not None:
+                b = table[b][A_dict_inv[word[j]]]
+                j -= 1
+            if j < i:
+                self.coincidence_c(f, b)
+            elif j == i:
+                table[f][A_dict[word[i]]] = b
+                table[b][A_dict_inv[word[i]]] = f
+                self.deduction_stack.append((f, word[i]))
+            else:
+                self.define_c(f, word[i])
+
+    # method used in the HLT strategy
+    def look_ahead(self):
+        """
+        When combined with the HLT method this is known as HLT+Lookahead
+        method of coset enumeration, described on pg. 164 [1]. Whenever
+        ``define`` aborts due to lack of space available this procedure is
+        executed. This routine helps in recovering space resulting from
+        "coincidence" of cosets.
+
+        """
+        R = self.fp_group.relators
+        p = self.p
+        # complete scan all relators under all cosets(obviously live)
+        # without making new definitions
+        for beta in self.omega:
+            for w in R:
+                self.scan(beta, w)
+                if p[beta] < beta:
+                    break
+
+    # Pg. 166
+    def process_deductions(self, R_c_x, R_c_x_inv):
+        """
+        Processes the deductions that have been pushed onto ``deduction_stack``,
+        described on Pg. 166 [1] and is used in coset-table based enumeration.
+
+        See Also
+        ========
+
+        deduction_stack
+
+        """
+        p = self.p
+        table = self.table
+        while len(self.deduction_stack) > 0:
+            if len(self.deduction_stack) >= CosetTable.max_stack_size:
+                self.look_ahead()
+                del self.deduction_stack[:]
+                continue
+            else:
+                alpha, x = self.deduction_stack.pop()
+                if p[alpha] == alpha:
+                    for w in R_c_x:
+                        self.scan_c(alpha, w)
+                        if p[alpha] < alpha:
+                            break
+            beta = table[alpha][self.A_dict[x]]
+            if beta is not None and p[beta] == beta:
+                for w in R_c_x_inv:
+                    self.scan_c(beta, w)
+                    if p[beta] < beta:
+                        break
+
+    def process_deductions_check(self, R_c_x, R_c_x_inv):
+        """
+        A variation of ``process_deductions``, this calls ``scan_check``
+        wherever ``process_deductions`` calls ``scan``, described on Pg. [1].
+
+        See Also
+        ========
+
+        process_deductions
+
+        """
+        table = self.table
+        while len(self.deduction_stack) > 0:
+            alpha, x = self.deduction_stack.pop()
+            if not all(self.scan_check(alpha, w) for w in R_c_x):
+                return False
+            beta = table[alpha][self.A_dict[x]]
+            if beta is not None:
+                if not all(self.scan_check(beta, w) for w in R_c_x_inv):
+                    return False
+        return True
+
+    def switch(self, beta, gamma):
+        r"""Switch the elements `\beta, \gamma \in \Omega` of ``self``, used
+        by the ``standardize`` procedure, described on Pg. 167 [1].
+
+        See Also
+        ========
+
+        standardize
+
+        """
+        A = self.A
+        A_dict = self.A_dict
+        table = self.table
+        for x in A:
+            z = table[gamma][A_dict[x]]
+            table[gamma][A_dict[x]] = table[beta][A_dict[x]]
+            table[beta][A_dict[x]] = z
+            for alpha in range(len(self.p)):
+                if self.p[alpha] == alpha:
+                    if table[alpha][A_dict[x]] == beta:
+                        table[alpha][A_dict[x]] = gamma
+                    elif table[alpha][A_dict[x]] == gamma:
+                        table[alpha][A_dict[x]] = beta
+
+    def standardize(self):
+        r"""
+        A coset table is standardized if when running through the cosets and
+        within each coset through the generator images (ignoring generator
+        inverses), the cosets appear in order of the integers
+        `0, 1, \dots, n`. "Standardize" reorders the elements of `\Omega`
+        such that, if we scan the coset table first by elements of `\Omega`
+        and then by elements of A, then the cosets occur in ascending order.
+        ``standardize()`` is used at the end of an enumeration to permute the
+        cosets so that they occur in some sort of standard order.
+
+        Notes
+        =====
+
+        procedure is described on pg. 167-168 [1], it also makes use of the
+        ``switch`` routine to replace by smaller integer value.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r
+        >>> F, x, y = free_group("x, y")
+
+        # Example 5.3 from [1]
+        >>> f = FpGroup(F, [x**2*y**2, x**3*y**5])
+        >>> C = coset_enumeration_r(f, [])
+        >>> C.compress()
+        >>> C.table
+        [[1, 3, 1, 3], [2, 0, 2, 0], [3, 1, 3, 1], [0, 2, 0, 2]]
+        >>> C.standardize()
+        >>> C.table
+        [[1, 2, 1, 2], [3, 0, 3, 0], [0, 3, 0, 3], [2, 1, 2, 1]]
+
+        """
+        A = self.A
+        A_dict = self.A_dict
+        gamma = 1
+        for alpha, x in product(range(self.n), A):
+            beta = self.table[alpha][A_dict[x]]
+            if beta >= gamma:
+                if beta > gamma:
+                    self.switch(gamma, beta)
+                gamma += 1
+                if gamma == self.n:
+                    return
+
+    # Compression of a Coset Table
+    def compress(self):
+        """Removes the non-live cosets from the coset table, described on
+        pg. 167 [1].
+
+        """
+        gamma = -1
+        A = self.A
+        A_dict = self.A_dict
+        A_dict_inv = self.A_dict_inv
+        table = self.table
+        chi = tuple([i for i in range(len(self.p)) if self.p[i] != i])
+        for alpha in self.omega:
+            gamma += 1
+            if gamma != alpha:
+                # replace alpha by gamma in coset table
+                for x in A:
+                    beta = table[alpha][A_dict[x]]
+                    table[gamma][A_dict[x]] = beta
+                    # XXX: The line below uses == rather than = which means
+                    # that it has no effect. It is not clear though if it is
+                    # correct simply to delete the line or to change it to
+                    # use =. Changing it causes some tests to fail.
+                    #
+                    # https://github.com/sympy/sympy/issues/27633
+                    table[beta][A_dict_inv[x]] == gamma # noqa: B015
+        # all the cosets in the table are live cosets
+        self.p = list(range(gamma + 1))
+        # delete the useless columns
+        del table[len(self.p):]
+        # re-define values
+        for row in table:
+            for j in range(len(self.A)):
+                row[j] -= bisect_left(chi, row[j])
+
+    def conjugates(self, R):
+        R_c = list(chain.from_iterable((rel.cyclic_conjugates(), \
+                (rel**-1).cyclic_conjugates()) for rel in R))
+        R_set = set()
+        for conjugate in R_c:
+            R_set = R_set.union(conjugate)
+        R_c_list = []
+        for x in self.A:
+            r = {word for word in R_set if word[0] == x}
+            R_c_list.append(r)
+            R_set.difference_update(r)
+        return R_c_list
+
+    def coset_representative(self, coset):
+        '''
+        Compute the coset representative of a given coset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r
+        >>> F, x, y = free_group("x, y")
+        >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+        >>> C = coset_enumeration_r(f, [x])
+        >>> C.compress()
+        >>> C.table
+        [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]]
+        >>> C.coset_representative(0)
+        
+        >>> C.coset_representative(1)
+        y
+        >>> C.coset_representative(2)
+        y**-1
+
+        '''
+        for x in self.A:
+            gamma = self.table[coset][self.A_dict[x]]
+            if coset == 0:
+                return self.fp_group.identity
+            if gamma < coset:
+                return self.coset_representative(gamma)*x**-1
+
+    ##############################
+    #      Modified Methods      #
+    ##############################
+
+    def modified_define(self, alpha, x):
+        r"""
+        Define a function p_p from from [1..n] to A* as
+        an additional component of the modified coset table.
+
+        Parameters
+        ==========
+
+        \alpha \in \Omega
+        x \in A*
+
+        See Also
+        ========
+
+        define
+
+        """
+        self.define(alpha, x, modified=True)
+
+    def modified_scan(self, alpha, w, y, fill=False):
+        r"""
+        Parameters
+        ==========
+        \alpha \in \Omega
+        w \in A*
+        y \in (YUY^-1)
+        fill -- `modified_scan_and_fill` when set to True.
+
+        See Also
+        ========
+
+        scan
+        """
+        self.scan(alpha, w, y=y, fill=fill, modified=True)
+
+    def modified_scan_and_fill(self, alpha, w, y):
+        self.modified_scan(alpha, w, y, fill=True)
+
+    def modified_merge(self, k, lamda, w, q):
+        r"""
+        Parameters
+        ==========
+
+        'k', 'lamda' -- the two class representatives to be merged.
+        q -- queue of length l of elements to be deleted from `\Omega` *.
+        w -- Word in (YUY^-1)
+
+        See Also
+        ========
+
+        merge
+        """
+        self.merge(k, lamda, q, w=w, modified=True)
+
+    def modified_rep(self, k):
+        r"""
+        Parameters
+        ==========
+
+        `k \in [0 \ldots n-1]`
+
+        See Also
+        ========
+
+        rep
+        """
+        self.rep(k, modified=True)
+
+    def modified_coincidence(self, alpha, beta, w):
+        r"""
+        Parameters
+        ==========
+
+        A coincident pair `\alpha, \beta \in \Omega, w \in Y \cup Y^{-1}`
+
+        See Also
+        ========
+
+        coincidence
+
+        """
+        self.coincidence(alpha, beta, w=w, modified=True)
+
+###############################################################################
+#                           COSET ENUMERATION                                 #
+###############################################################################
+
+# relator-based method
+def coset_enumeration_r(fp_grp, Y, max_cosets=None, draft=None,
+                                    incomplete=False, modified=False):
+    """
+    This is easier of the two implemented methods of coset enumeration.
+    and is often called the HLT method, after Hazelgrove, Leech, Trotter
+    The idea is that we make use of ``scan_and_fill`` makes new definitions
+    whenever the scan is incomplete to enable the scan to complete; this way
+    we fill in the gaps in the scan of the relator or subgroup generator,
+    that's why the name relator-based method.
+
+    An instance of `CosetTable` for `fp_grp` can be passed as the keyword
+    argument `draft` in which case the coset enumeration will start with
+    that instance and attempt to complete it.
+
+    When `incomplete` is `True` and the function is unable to complete for
+    some reason, the partially complete table will be returned.
+
+    # TODO: complete the docstring
+
+    See Also
+    ========
+
+    scan_and_fill,
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.free_groups import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r
+    >>> F, x, y = free_group("x, y")
+
+    # Example 5.1 from [1]
+    >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+    >>> C = coset_enumeration_r(f, [x])
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         print(C.table[i])
+    [0, 0, 1, 2]
+    [1, 1, 2, 0]
+    [2, 2, 0, 1]
+    >>> C.p
+    [0, 1, 2, 1, 1]
+
+    # Example from exercises Q2 [1]
+    >>> f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3])
+    >>> C = coset_enumeration_r(f, [])
+    >>> C.compress(); C.standardize()
+    >>> C.table
+    [[1, 2, 3, 4],
+    [5, 0, 6, 7],
+    [0, 5, 7, 6],
+    [7, 6, 5, 0],
+    [6, 7, 0, 5],
+    [2, 1, 4, 3],
+    [3, 4, 2, 1],
+    [4, 3, 1, 2]]
+
+    # Example 5.2
+    >>> f = FpGroup(F, [x**2, y**3, (x*y)**3])
+    >>> Y = [x*y]
+    >>> C = coset_enumeration_r(f, Y)
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         print(C.table[i])
+    [1, 1, 2, 1]
+    [0, 0, 0, 2]
+    [3, 3, 1, 0]
+    [2, 2, 3, 3]
+
+    # Example 5.3
+    >>> f = FpGroup(F, [x**2*y**2, x**3*y**5])
+    >>> Y = []
+    >>> C = coset_enumeration_r(f, Y)
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         print(C.table[i])
+    [1, 3, 1, 3]
+    [2, 0, 2, 0]
+    [3, 1, 3, 1]
+    [0, 2, 0, 2]
+
+    # Example 5.4
+    >>> F, a, b, c, d, e = free_group("a, b, c, d, e")
+    >>> f = FpGroup(F, [a*b*c**-1, b*c*d**-1, c*d*e**-1, d*e*a**-1, e*a*b**-1])
+    >>> Y = [a]
+    >>> C = coset_enumeration_r(f, Y)
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         print(C.table[i])
+    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+
+    # example of "compress" method
+    >>> C.compress()
+    >>> C.table
+    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
+
+    # Exercises Pg. 161, Q2.
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3])
+    >>> Y = []
+    >>> C = coset_enumeration_r(f, Y)
+    >>> C.compress()
+    >>> C.standardize()
+    >>> C.table
+    [[1, 2, 3, 4],
+    [5, 0, 6, 7],
+    [0, 5, 7, 6],
+    [7, 6, 5, 0],
+    [6, 7, 0, 5],
+    [2, 1, 4, 3],
+    [3, 4, 2, 1],
+    [4, 3, 1, 2]]
+
+    # John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson
+    # Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490
+    # from 1973chwd.pdf
+    # Table 1. Ex. 1
+    >>> F, r, s, t = free_group("r, s, t")
+    >>> E1 = FpGroup(F, [t**-1*r*t*r**-2, r**-1*s*r*s**-2, s**-1*t*s*t**-2])
+    >>> C = coset_enumeration_r(E1, [r])
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         print(C.table[i])
+    [0, 0, 0, 0, 0, 0]
+
+    Ex. 2
+    >>> F, a, b = free_group("a, b")
+    >>> Cox = FpGroup(F, [a**6, b**6, (a*b)**2, (a**2*b**2)**2, (a**3*b**3)**5])
+    >>> C = coset_enumeration_r(Cox, [a])
+    >>> index = 0
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         index += 1
+    >>> index
+    500
+
+    # Ex. 3
+    >>> F, a, b = free_group("a, b")
+    >>> B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \
+            (a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4])
+    >>> C = coset_enumeration_r(B_2_4, [a])
+    >>> index = 0
+    >>> for i in range(len(C.p)):
+    ...     if C.p[i] == i:
+    ...         index += 1
+    >>> index
+    1024
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.
+           "Handbook of computational group theory"
+
+    """
+    # 1. Initialize a coset table C for < X|R >
+    C = CosetTable(fp_grp, Y, max_cosets=max_cosets)
+    # Define coset table methods.
+    if modified:
+        _scan_and_fill = C.modified_scan_and_fill
+        _define = C.modified_define
+    else:
+        _scan_and_fill = C.scan_and_fill
+        _define = C.define
+    if draft:
+        C.table = draft.table[:]
+        C.p = draft.p[:]
+    R = fp_grp.relators
+    A_dict = C.A_dict
+    p = C.p
+    for i in range(len(Y)):
+        if modified:
+            _scan_and_fill(0, Y[i], C._grp.generators[i])
+        else:
+            _scan_and_fill(0, Y[i])
+    alpha = 0
+    while alpha < C.n:
+        if p[alpha] == alpha:
+            try:
+                for w in R:
+                    if modified:
+                        _scan_and_fill(alpha, w, C._grp.identity)
+                    else:
+                        _scan_and_fill(alpha, w)
+                    # if alpha was eliminated during the scan then break
+                    if p[alpha] < alpha:
+                        break
+                if p[alpha] == alpha:
+                    for x in A_dict:
+                        if C.table[alpha][A_dict[x]] is None:
+                            _define(alpha, x)
+            except ValueError as e:
+                if incomplete:
+                    return C
+                raise e
+        alpha += 1
+    return C
+
+def modified_coset_enumeration_r(fp_grp, Y, max_cosets=None, draft=None,
+                                    incomplete=False):
+    r"""
+    Introduce a new set of symbols y \in Y that correspond to the
+    generators of the subgroup. Store the elements of Y as a
+    word P[\alpha, x] and compute the coset table similar to that of
+    the regular coset enumeration methods.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.free_groups import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup
+    >>> from sympy.combinatorics.coset_table import modified_coset_enumeration_r
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+    >>> C = modified_coset_enumeration_r(f, [x])
+    >>> C.table
+    [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1], [None, 1, None, None], [1, 3, None, None]]
+
+    See Also
+    ========
+
+    coset_enumertation_r
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.,
+           "Handbook of Computational Group Theory",
+           Section 5.3.2
+    """
+    return coset_enumeration_r(fp_grp, Y, max_cosets=max_cosets, draft=draft,
+                             incomplete=incomplete, modified=True)
+
+# Pg. 166
+# coset-table based method
+def coset_enumeration_c(fp_grp, Y, max_cosets=None, draft=None,
+                                                incomplete=False):
+    """
+    >>> from sympy.combinatorics.free_groups import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_c
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+    >>> C = coset_enumeration_c(f, [x])
+    >>> C.table
+    [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]]
+
+    """
+    # Initialize a coset table C for < X|R >
+    X = fp_grp.generators
+    R = fp_grp.relators
+    C = CosetTable(fp_grp, Y, max_cosets=max_cosets)
+    if draft:
+        C.table = draft.table[:]
+        C.p = draft.p[:]
+        C.deduction_stack = draft.deduction_stack
+        for alpha, x in product(range(len(C.table)), X):
+            if C.table[alpha][C.A_dict[x]] is not None:
+                C.deduction_stack.append((alpha, x))
+    A = C.A
+    # replace all the elements by cyclic reductions
+    R_cyc_red = [rel.identity_cyclic_reduction() for rel in R]
+    R_c = list(chain.from_iterable((rel.cyclic_conjugates(), (rel**-1).cyclic_conjugates()) \
+            for rel in R_cyc_red))
+    R_set = set()
+    for conjugate in R_c:
+        R_set = R_set.union(conjugate)
+    # a list of subsets of R_c whose words start with "x".
+    R_c_list = []
+    for x in C.A:
+        r = {word for word in R_set if word[0] == x}
+        R_c_list.append(r)
+        R_set.difference_update(r)
+    for w in Y:
+        C.scan_and_fill_c(0, w)
+    for x in A:
+        C.process_deductions(R_c_list[C.A_dict[x]], R_c_list[C.A_dict_inv[x]])
+    alpha = 0
+    while alpha < len(C.table):
+        if C.p[alpha] == alpha:
+            try:
+                for x in C.A:
+                    if C.p[alpha] != alpha:
+                        break
+                    if C.table[alpha][C.A_dict[x]] is None:
+                        C.define_c(alpha, x)
+                        C.process_deductions(R_c_list[C.A_dict[x]], R_c_list[C.A_dict_inv[x]])
+            except ValueError as e:
+                if incomplete:
+                    return C
+                raise e
+        alpha += 1
+    return C
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/fp_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/fp_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..95530ccd44f025eca5f029c6ba60d3727cbcb29d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/fp_groups.py
@@ -0,0 +1,1352 @@
+"""Finitely Presented Groups and its algorithms. """
+
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.combinatorics.free_groups import (FreeGroup, FreeGroupElement,
+                                                free_group)
+from sympy.combinatorics.rewritingsystem import RewritingSystem
+from sympy.combinatorics.coset_table import (CosetTable,
+                                             coset_enumeration_r,
+                                             coset_enumeration_c)
+from sympy.combinatorics import PermutationGroup
+from sympy.matrices.normalforms import invariant_factors
+from sympy.matrices import Matrix
+from sympy.polys.polytools import gcd
+from sympy.printing.defaults import DefaultPrinting
+from sympy.utilities import public
+from sympy.utilities.magic import pollute
+
+from itertools import product
+
+
+@public
+def fp_group(fr_grp, relators=()):
+    _fp_group = FpGroup(fr_grp, relators)
+    return (_fp_group,) + tuple(_fp_group._generators)
+
+@public
+def xfp_group(fr_grp, relators=()):
+    _fp_group = FpGroup(fr_grp, relators)
+    return (_fp_group, _fp_group._generators)
+
+# Does not work. Both symbols and pollute are undefined. Never tested.
+@public
+def vfp_group(fr_grpm, relators):
+    _fp_group = FpGroup(symbols, relators)
+    pollute([sym.name for sym in _fp_group.symbols], _fp_group.generators)
+    return _fp_group
+
+
+def _parse_relators(rels):
+    """Parse the passed relators."""
+    return rels
+
+
+###############################################################################
+#                           FINITELY PRESENTED GROUPS                         #
+###############################################################################
+
+
+class FpGroup(DefaultPrinting):
+    """
+    The FpGroup would take a FreeGroup and a list/tuple of relators, the
+    relators would be specified in such a way that each of them be equal to the
+    identity of the provided free group.
+
+    """
+    is_group = True
+    is_FpGroup = True
+    is_PermutationGroup = False
+
+    def __init__(self, fr_grp, relators):
+        relators = _parse_relators(relators)
+        self.free_group = fr_grp
+        self.relators = relators
+        self.generators = self._generators()
+        self.dtype = type("FpGroupElement", (FpGroupElement,), {"group": self})
+
+        # CosetTable instance on identity subgroup
+        self._coset_table = None
+        # returns whether coset table on identity subgroup
+        # has been standardized
+        self._is_standardized = False
+
+        self._order = None
+        self._center = None
+
+        self._rewriting_system = RewritingSystem(self)
+        self._perm_isomorphism = None
+        return
+
+    def _generators(self):
+        return self.free_group.generators
+
+    def make_confluent(self):
+        '''
+        Try to make the group's rewriting system confluent
+
+        '''
+        self._rewriting_system.make_confluent()
+        return
+
+    def reduce(self, word):
+        '''
+        Return the reduced form of `word` in `self` according to the group's
+        rewriting system. If it's confluent, the reduced form is the unique normal
+        form of the word in the group.
+
+        '''
+        return self._rewriting_system.reduce(word)
+
+    def equals(self, word1, word2):
+        '''
+        Compare `word1` and `word2` for equality in the group
+        using the group's rewriting system. If the system is
+        confluent, the returned answer is necessarily correct.
+        (If it is not, `False` could be returned in some cases
+        where in fact `word1 == word2`)
+
+        '''
+        if self.reduce(word1*word2**-1) == self.identity:
+            return True
+        elif self._rewriting_system.is_confluent:
+            return False
+        return None
+
+    @property
+    def identity(self):
+        return self.free_group.identity
+
+    def __contains__(self, g):
+        return g in self.free_group
+
+    def subgroup(self, gens, C=None, homomorphism=False):
+        '''
+        Return the subgroup generated by `gens` using the
+        Reidemeister-Schreier algorithm
+        homomorphism -- When set to True, return a dictionary containing the images
+                     of the presentation generators in the original group.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.fp_groups import FpGroup
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> f = FpGroup(F, [x**3, y**5, (x*y)**2])
+        >>> H = [x*y, x**-1*y**-1*x*y*x]
+        >>> K, T = f.subgroup(H, homomorphism=True)
+        >>> T(K.generators)
+        [x*y, x**-1*y**2*x**-1]
+
+        '''
+
+        if not all(isinstance(g, FreeGroupElement) for g in gens):
+            raise ValueError("Generators must be `FreeGroupElement`s")
+        if not all(g.group == self.free_group for g in gens):
+                raise ValueError("Given generators are not members of the group")
+        if homomorphism:
+            g, rels, _gens = reidemeister_presentation(self, gens, C=C, homomorphism=True)
+        else:
+            g, rels = reidemeister_presentation(self, gens, C=C)
+        if g:
+            g = FpGroup(g[0].group, rels)
+        else:
+            g = FpGroup(free_group('')[0], [])
+        if homomorphism:
+            from sympy.combinatorics.homomorphisms import homomorphism
+            return g, homomorphism(g, self, g.generators, _gens, check=False)
+        return g
+
+    def coset_enumeration(self, H, strategy="relator_based", max_cosets=None,
+                                                        draft=None, incomplete=False):
+        """
+        Return an instance of ``coset table``, when Todd-Coxeter algorithm is
+        run over the ``self`` with ``H`` as subgroup, using ``strategy``
+        argument as strategy. The returned coset table is compressed but not
+        standardized.
+
+        An instance of `CosetTable` for `fp_grp` can be passed as the keyword
+        argument `draft` in which case the coset enumeration will start with
+        that instance and attempt to complete it.
+
+        When `incomplete` is `True` and the function is unable to complete for
+        some reason, the partially complete table will be returned.
+
+        """
+        if not max_cosets:
+            max_cosets = CosetTable.coset_table_max_limit
+        if strategy == 'relator_based':
+            C = coset_enumeration_r(self, H, max_cosets=max_cosets,
+                                                    draft=draft, incomplete=incomplete)
+        else:
+            C = coset_enumeration_c(self, H, max_cosets=max_cosets,
+                                                    draft=draft, incomplete=incomplete)
+        if C.is_complete():
+            C.compress()
+        return C
+
+    def standardize_coset_table(self):
+        """
+        Standardized the coset table ``self`` and makes the internal variable
+        ``_is_standardized`` equal to ``True``.
+
+        """
+        self._coset_table.standardize()
+        self._is_standardized = True
+
+    def coset_table(self, H, strategy="relator_based", max_cosets=None,
+                                                 draft=None, incomplete=False):
+        """
+        Return the mathematical coset table of ``self`` in ``H``.
+
+        """
+        if not H:
+            if self._coset_table is not None:
+                if not self._is_standardized:
+                    self.standardize_coset_table()
+            else:
+                C = self.coset_enumeration([], strategy, max_cosets=max_cosets,
+                                            draft=draft, incomplete=incomplete)
+                self._coset_table = C
+                self.standardize_coset_table()
+            return self._coset_table.table
+        else:
+            C = self.coset_enumeration(H, strategy, max_cosets=max_cosets,
+                                            draft=draft, incomplete=incomplete)
+            C.standardize()
+            return C.table
+
+    def order(self, strategy="relator_based"):
+        """
+        Returns the order of the finitely presented group ``self``. It uses
+        the coset enumeration with identity group as subgroup, i.e ``H=[]``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> from sympy.combinatorics.fp_groups import FpGroup
+        >>> F, x, y = free_group("x, y")
+        >>> f = FpGroup(F, [x, y**2])
+        >>> f.order(strategy="coset_table_based")
+        2
+
+        """
+        if self._order is not None:
+            return self._order
+        if self._coset_table is not None:
+            self._order = len(self._coset_table.table)
+        elif len(self.relators) == 0:
+            self._order = self.free_group.order()
+        elif len(self.generators) == 1:
+            self._order = abs(gcd([r.array_form[0][1] for r in self.relators]))
+        elif self._is_infinite():
+            self._order = S.Infinity
+        else:
+            gens, C = self._finite_index_subgroup()
+            if C:
+                ind = len(C.table)
+                self._order = ind*self.subgroup(gens, C=C).order()
+            else:
+                self._order = self.index([])
+        return self._order
+
+    def _is_infinite(self):
+        '''
+        Test if the group is infinite. Return `True` if the test succeeds
+        and `None` otherwise
+
+        '''
+        used_gens = set()
+        for r in self.relators:
+            used_gens.update(r.contains_generators())
+        if not set(self.generators) <= used_gens:
+            return True
+        # Abelianisation test: check is the abelianisation is infinite
+        abelian_rels = []
+        for rel in self.relators:
+            abelian_rels.append([rel.exponent_sum(g) for g in self.generators])
+        m = Matrix(Matrix(abelian_rels))
+        if 0 in invariant_factors(m):
+            return True
+        else:
+            return None
+
+
+    def _finite_index_subgroup(self, s=None):
+        '''
+        Find the elements of `self` that generate a finite index subgroup
+        and, if found, return the list of elements and the coset table of `self` by
+        the subgroup, otherwise return `(None, None)`
+
+        '''
+        gen = self.most_frequent_generator()
+        rels = list(self.generators)
+        rels.extend(self.relators)
+        if not s:
+            if len(self.generators) == 2:
+                s = [gen] + [g for g in self.generators if g != gen]
+            else:
+                rand = self.free_group.identity
+                i = 0
+                while ((rand in rels or rand**-1 in rels or rand.is_identity)
+                        and i<10):
+                    rand = self.random()
+                    i += 1
+                s = [gen, rand] + [g for g in self.generators if g != gen]
+        mid = (len(s)+1)//2
+        half1 = s[:mid]
+        half2 = s[mid:]
+        draft1 = None
+        draft2 = None
+        m = 200
+        C = None
+        while not C and (m/2 < CosetTable.coset_table_max_limit):
+            m = min(m, CosetTable.coset_table_max_limit)
+            draft1 = self.coset_enumeration(half1, max_cosets=m,
+                                 draft=draft1, incomplete=True)
+            if draft1.is_complete():
+                C = draft1
+                half = half1
+            else:
+                draft2 = self.coset_enumeration(half2, max_cosets=m,
+                                 draft=draft2, incomplete=True)
+                if draft2.is_complete():
+                    C = draft2
+                    half = half2
+            if not C:
+                m *= 2
+        if not C:
+            return None, None
+        C.compress()
+        return half, C
+
+    def most_frequent_generator(self):
+        gens = self.generators
+        rels = self.relators
+        freqs = [sum(r.generator_count(g) for r in rels) for g in gens]
+        return gens[freqs.index(max(freqs))]
+
+    def random(self):
+        import random
+        r = self.free_group.identity
+        for i in range(random.randint(2,3)):
+            r = r*random.choice(self.generators)**random.choice([1,-1])
+        return r
+
+    def index(self, H, strategy="relator_based"):
+        """
+        Return the index of subgroup ``H`` in group ``self``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> from sympy.combinatorics.fp_groups import FpGroup
+        >>> F, x, y = free_group("x, y")
+        >>> f = FpGroup(F, [x**5, y**4, y*x*y**3*x**3])
+        >>> f.index([x])
+        4
+
+        """
+        # TODO: use |G:H| = |G|/|H| (currently H can't be made into a group)
+        # when we know |G| and |H|
+
+        if H == []:
+            return self.order()
+        else:
+            C = self.coset_enumeration(H, strategy)
+            return len(C.table)
+
+    def __str__(self):
+        if self.free_group.rank > 30:
+            str_form = "" % self.free_group.rank
+        else:
+            str_form = "" % str(self.generators)
+        return str_form
+
+    __repr__ = __str__
+
+#==============================================================================
+#                       PERMUTATION GROUP METHODS
+#==============================================================================
+
+    def _to_perm_group(self):
+        '''
+        Return an isomorphic permutation group and the isomorphism.
+        The implementation is dependent on coset enumeration so
+        will only terminate for finite groups.
+
+        '''
+        from sympy.combinatorics import Permutation
+        from sympy.combinatorics.homomorphisms import homomorphism
+        if self.order() is S.Infinity:
+            raise NotImplementedError("Permutation presentation of infinite "
+                                                  "groups is not implemented")
+        if self._perm_isomorphism:
+            T = self._perm_isomorphism
+            P = T.image()
+        else:
+            C = self.coset_table([])
+            gens = self.generators
+            images = [[C[i][2*gens.index(g)] for i in range(len(C))] for g in gens]
+            images = [Permutation(i) for i in images]
+            P = PermutationGroup(images)
+            T = homomorphism(self, P, gens, images, check=False)
+            self._perm_isomorphism = T
+        return P, T
+
+    def _perm_group_list(self, method_name, *args):
+        '''
+        Given the name of a `PermutationGroup` method (returning a subgroup
+        or a list of subgroups) and (optionally) additional arguments it takes,
+        return a list or a list of lists containing the generators of this (or
+        these) subgroups in terms of the generators of `self`.
+
+        '''
+        P, T = self._to_perm_group()
+        perm_result = getattr(P, method_name)(*args)
+        single = False
+        if isinstance(perm_result, PermutationGroup):
+            perm_result, single = [perm_result], True
+        result = []
+        for group in perm_result:
+            gens = group.generators
+            result.append(T.invert(gens))
+        return result[0] if single else result
+
+    def derived_series(self):
+        '''
+        Return the list of lists containing the generators
+        of the subgroups in the derived series of `self`.
+
+        '''
+        return self._perm_group_list('derived_series')
+
+    def lower_central_series(self):
+        '''
+        Return the list of lists containing the generators
+        of the subgroups in the lower central series of `self`.
+
+        '''
+        return self._perm_group_list('lower_central_series')
+
+    def center(self):
+        '''
+        Return the list of generators of the center of `self`.
+
+        '''
+        return self._perm_group_list('center')
+
+
+    def derived_subgroup(self):
+        '''
+        Return the list of generators of the derived subgroup of `self`.
+
+        '''
+        return self._perm_group_list('derived_subgroup')
+
+
+    def centralizer(self, other):
+        '''
+        Return the list of generators of the centralizer of `other`
+        (a list of elements of `self`) in `self`.
+
+        '''
+        T = self._to_perm_group()[1]
+        other = T(other)
+        return self._perm_group_list('centralizer', other)
+
+    def normal_closure(self, other):
+        '''
+        Return the list of generators of the normal closure of `other`
+        (a list of elements of `self`) in `self`.
+
+        '''
+        T = self._to_perm_group()[1]
+        other = T(other)
+        return self._perm_group_list('normal_closure', other)
+
+    def _perm_property(self, attr):
+        '''
+        Given an attribute of a `PermutationGroup`, return
+        its value for a permutation group isomorphic to `self`.
+
+        '''
+        P = self._to_perm_group()[0]
+        return getattr(P, attr)
+
+    @property
+    def is_abelian(self):
+        '''
+        Check if `self` is abelian.
+
+        '''
+        return self._perm_property("is_abelian")
+
+    @property
+    def is_nilpotent(self):
+        '''
+        Check if `self` is nilpotent.
+
+        '''
+        return self._perm_property("is_nilpotent")
+
+    @property
+    def is_solvable(self):
+        '''
+        Check if `self` is solvable.
+
+        '''
+        return self._perm_property("is_solvable")
+
+    @property
+    def elements(self):
+        '''
+        List the elements of `self`.
+
+        '''
+        P, T = self._to_perm_group()
+        return T.invert(P.elements)
+
+    @property
+    def is_cyclic(self):
+        """
+        Return ``True`` if group is Cyclic.
+
+        """
+        if len(self.generators) <= 1:
+            return True
+        try:
+            P, T = self._to_perm_group()
+        except NotImplementedError:
+            raise NotImplementedError("Check for infinite Cyclic group "
+                                      "is not implemented")
+        return P.is_cyclic
+
+    def abelian_invariants(self):
+        """
+        Return Abelian Invariants of a group.
+        """
+        try:
+            P, T = self._to_perm_group()
+        except NotImplementedError:
+            raise NotImplementedError("abelian invariants is not implemented"
+                                      "for infinite group")
+        return P.abelian_invariants()
+
+    def composition_series(self):
+        """
+        Return subnormal series of maximum length for a group.
+        """
+        try:
+            P, T = self._to_perm_group()
+        except NotImplementedError:
+            raise NotImplementedError("composition series is not implemented"
+                                      "for infinite group")
+        return P.composition_series()
+
+
+class FpSubgroup(DefaultPrinting):
+    '''
+    The class implementing a subgroup of an FpGroup or a FreeGroup
+    (only finite index subgroups are supported at this point). This
+    is to be used if one wishes to check if an element of the original
+    group belongs to the subgroup
+
+    '''
+    def __init__(self, G, gens, normal=False):
+        super().__init__()
+        self.parent = G
+        self.generators = list({g for g in gens if g != G.identity})
+        self._min_words = None #for use in __contains__
+        self.C = None
+        self.normal = normal
+
+    def __contains__(self, g):
+
+        if isinstance(self.parent, FreeGroup):
+            if self._min_words is None:
+                # make _min_words - a list of subwords such that
+                # g is in the subgroup if and only if it can be
+                # partitioned into these subwords. Infinite families of
+                # subwords are presented by tuples, e.g. (r, w)
+                # stands for the family of subwords r*w**n*r**-1
+
+                def _process(w):
+                    # this is to be used before adding new words
+                    # into _min_words; if the word w is not cyclically
+                    # reduced, it will generate an infinite family of
+                    # subwords so should be written as a tuple;
+                    # if it is, w**-1 should be added to the list
+                    # as well
+                    p, r = w.cyclic_reduction(removed=True)
+                    if not r.is_identity:
+                        return [(r, p)]
+                    else:
+                        return [w, w**-1]
+
+                # make the initial list
+                gens = []
+                for w in self.generators:
+                    if self.normal:
+                        w = w.cyclic_reduction()
+                    gens.extend(_process(w))
+
+                for w1 in gens:
+                    for w2 in gens:
+                        # if w1 and w2 are equal or are inverses, continue
+                        if w1 == w2 or (not isinstance(w1, tuple)
+                                                        and w1**-1 == w2):
+                            continue
+
+                        # if the start of one word is the inverse of the
+                        # end of the other, their multiple should be added
+                        # to _min_words because of cancellation
+                        if isinstance(w1, tuple):
+                            # start, end
+                            s1, s2 = w1[0][0], w1[0][0]**-1
+                        else:
+                            s1, s2 = w1[0], w1[len(w1)-1]
+
+                        if isinstance(w2, tuple):
+                            # start, end
+                            r1, r2 = w2[0][0], w2[0][0]**-1
+                        else:
+                            r1, r2 = w2[0], w2[len(w1)-1]
+
+                        # p1 and p2 are w1 and w2 or, in case when
+                        # w1 or w2 is an infinite family, a representative
+                        p1, p2 = w1, w2
+                        if isinstance(w1, tuple):
+                            p1 = w1[0]*w1[1]*w1[0]**-1
+                        if isinstance(w2, tuple):
+                            p2 = w2[0]*w2[1]*w2[0]**-1
+
+                        # add the product of the words to the list is necessary
+                        if r1**-1 == s2 and not (p1*p2).is_identity:
+                            new = _process(p1*p2)
+                            if new not in gens:
+                                gens.extend(new)
+
+                        if r2**-1 == s1 and not (p2*p1).is_identity:
+                            new = _process(p2*p1)
+                            if new not in gens:
+                                gens.extend(new)
+
+                self._min_words = gens
+
+            min_words = self._min_words
+
+            def _is_subword(w):
+                # check if w is a word in _min_words or one of
+                # the infinite families in it
+                w, r = w.cyclic_reduction(removed=True)
+                if r.is_identity or self.normal:
+                    return w in min_words
+                else:
+                    t = [s[1] for s in min_words if isinstance(s, tuple)
+                                                                and s[0] == r]
+                    return [s for s in t if w.power_of(s)] != []
+
+            # store the solution of words for which the result of
+            # _word_break (below) is known
+            known = {}
+
+            def _word_break(w):
+                # check if w can be written as a product of words
+                # in min_words
+                if len(w) == 0:
+                    return True
+                i = 0
+                while i < len(w):
+                    i += 1
+                    prefix = w.subword(0, i)
+                    if not _is_subword(prefix):
+                        continue
+                    rest = w.subword(i, len(w))
+                    if rest not in known:
+                        known[rest] = _word_break(rest)
+                    if known[rest]:
+                        return True
+                return False
+
+            if self.normal:
+                g = g.cyclic_reduction()
+            return _word_break(g)
+        else:
+            if self.C is None:
+                C = self.parent.coset_enumeration(self.generators)
+                self.C = C
+            i = 0
+            C = self.C
+            for j in range(len(g)):
+                i = C.table[i][C.A_dict[g[j]]]
+            return i == 0
+
+    def order(self):
+        if not self.generators:
+            return S.One
+        if isinstance(self.parent, FreeGroup):
+            return S.Infinity
+        if self.C is None:
+            C = self.parent.coset_enumeration(self.generators)
+            self.C = C
+        # This is valid because `len(self.C.table)` (the index of the subgroup)
+        # will always be finite - otherwise coset enumeration doesn't terminate
+        return self.parent.order()/len(self.C.table)
+
+    def to_FpGroup(self):
+        if isinstance(self.parent, FreeGroup):
+            gen_syms = [('x_%d'%i) for i in range(len(self.generators))]
+            return free_group(', '.join(gen_syms))[0]
+        return self.parent.subgroup(C=self.C)
+
+    def __str__(self):
+        if len(self.generators) > 30:
+            str_form = "" % len(self.generators)
+        else:
+            str_form = "" % str(self.generators)
+        return str_form
+
+    __repr__ = __str__
+
+
+###############################################################################
+#                           LOW INDEX SUBGROUPS                               #
+###############################################################################
+
+def low_index_subgroups(G, N, Y=()):
+    """
+    Implements the Low Index Subgroups algorithm, i.e find all subgroups of
+    ``G`` upto a given index ``N``. This implements the method described in
+    [Sim94]. This procedure involves a backtrack search over incomplete Coset
+    Tables, rather than over forced coincidences.
+
+    Parameters
+    ==========
+
+    G: An FpGroup < X|R >
+    N: positive integer, representing the maximum index value for subgroups
+    Y: (an optional argument) specifying a list of subgroup generators, such
+    that each of the resulting subgroup contains the subgroup generated by Y.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup, low_index_subgroups
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**2, y**3, (x*y)**4])
+    >>> L = low_index_subgroups(f, 4)
+    >>> for coset_table in L:
+    ...     print(coset_table.table)
+    [[0, 0, 0, 0]]
+    [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 3, 3]]
+    [[0, 0, 1, 2], [2, 2, 2, 0], [1, 1, 0, 1]]
+    [[1, 1, 0, 0], [0, 0, 1, 1]]
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.
+           "Handbook of Computational Group Theory"
+           Section 5.4
+
+    .. [2] Marston Conder and Peter Dobcsanyi
+           "Applications and Adaptions of the Low Index Subgroups Procedure"
+
+    """
+    C = CosetTable(G, [])
+    R = G.relators
+    # length chosen for the length of the short relators
+    len_short_rel = 5
+    # elements of R2 only checked at the last step for complete
+    # coset tables
+    R2 = {rel for rel in R if len(rel) > len_short_rel}
+    # elements of R1 are used in inner parts of the process to prune
+    # branches of the search tree,
+    R1 = {rel.identity_cyclic_reduction() for rel in set(R) - R2}
+    R1_c_list = C.conjugates(R1)
+    S = []
+    descendant_subgroups(S, C, R1_c_list, C.A[0], R2, N, Y)
+    return S
+
+
+def descendant_subgroups(S, C, R1_c_list, x, R2, N, Y):
+    A_dict = C.A_dict
+    A_dict_inv = C.A_dict_inv
+    if C.is_complete():
+        # if C is complete then it only needs to test
+        # whether the relators in R2 are satisfied
+        for w, alpha in product(R2, C.omega):
+            if not C.scan_check(alpha, w):
+                return
+        # relators in R2 are satisfied, append the table to list
+        S.append(C)
+    else:
+        # find the first undefined entry in Coset Table
+        for alpha, x in product(range(len(C.table)), C.A):
+            if C.table[alpha][A_dict[x]] is None:
+                # this is "x" in pseudo-code (using "y" makes it clear)
+                undefined_coset, undefined_gen = alpha, x
+                break
+        # for filling up the undefine entry we try all possible values
+        # of beta in Omega or beta = n where beta^(undefined_gen^-1) is undefined
+        reach = C.omega + [C.n]
+        for beta in reach:
+            if beta < N:
+                if beta == C.n or C.table[beta][A_dict_inv[undefined_gen]] is None:
+                    try_descendant(S, C, R1_c_list, R2, N, undefined_coset, \
+                            undefined_gen, beta, Y)
+
+
+def try_descendant(S, C, R1_c_list, R2, N, alpha, x, beta, Y):
+    r"""
+    Solves the problem of trying out each individual possibility
+    for `\alpha^x.
+
+    """
+    D = C.copy()
+    if beta == D.n and beta < N:
+        D.table.append([None]*len(D.A))
+        D.p.append(beta)
+    D.table[alpha][D.A_dict[x]] = beta
+    D.table[beta][D.A_dict_inv[x]] = alpha
+    D.deduction_stack.append((alpha, x))
+    if not D.process_deductions_check(R1_c_list[D.A_dict[x]], \
+            R1_c_list[D.A_dict_inv[x]]):
+        return
+    for w in Y:
+        if not D.scan_check(0, w):
+            return
+    if first_in_class(D, Y):
+        descendant_subgroups(S, D, R1_c_list, x, R2, N, Y)
+
+
+def first_in_class(C, Y=()):
+    """
+    Checks whether the subgroup ``H=G1`` corresponding to the Coset Table
+    could possibly be the canonical representative of its conjugacy class.
+
+    Parameters
+    ==========
+
+    C: CosetTable
+
+    Returns
+    =======
+
+    bool: True/False
+
+    If this returns False, then no descendant of C can have that property, and
+    so we can abandon C. If it returns True, then we need to process further
+    the node of the search tree corresponding to C, and so we call
+    ``descendant_subgroups`` recursively on C.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup, CosetTable, first_in_class
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**2, y**3, (x*y)**4])
+    >>> C = CosetTable(f, [])
+    >>> C.table = [[0, 0, None, None]]
+    >>> first_in_class(C)
+    True
+    >>> C.table = [[1, 1, 1, None], [0, 0, None, 1]]; C.p = [0, 1]
+    >>> first_in_class(C)
+    True
+    >>> C.table = [[1, 1, 2, 1], [0, 0, 0, None], [None, None, None, 0]]
+    >>> C.p = [0, 1, 2]
+    >>> first_in_class(C)
+    False
+    >>> C.table = [[1, 1, 1, 2], [0, 0, 2, 0], [2, None, 0, 1]]
+    >>> first_in_class(C)
+    False
+
+    # TODO:: Sims points out in [Sim94] that performance can be improved by
+    # remembering some of the information computed by ``first_in_class``. If
+    # the ``continue alpha`` statement is executed at line 14, then the same thing
+    # will happen for that value of alpha in any descendant of the table C, and so
+    # the values the values of alpha for which this occurs could profitably be
+    # stored and passed through to the descendants of C. Of course this would
+    # make the code more complicated.
+
+    # The code below is taken directly from the function on page 208 of [Sim94]
+    # nu[alpha]
+
+    """
+    n = C.n
+    # lamda is the largest numbered point in Omega_c_alpha which is currently defined
+    lamda = -1
+    # for alpha in Omega_c, nu[alpha] is the point in Omega_c_alpha corresponding to alpha
+    nu = [None]*n
+    # for alpha in Omega_c_alpha, mu[alpha] is the point in Omega_c corresponding to alpha
+    mu = [None]*n
+    # mutually nu and mu are the mutually-inverse equivalence maps between
+    # Omega_c_alpha and Omega_c
+    next_alpha = False
+    # For each 0!=alpha in [0 .. nc-1], we start by constructing the equivalent
+    # standardized coset table C_alpha corresponding to H_alpha
+    for alpha in range(1, n):
+        # reset nu to "None" after previous value of alpha
+        for beta in range(lamda+1):
+            nu[mu[beta]] = None
+        # we only want to reject our current table in favour of a preceding
+        # table in the ordering in which 1 is replaced by alpha, if the subgroup
+        # G_alpha corresponding to this preceding table definitely contains the
+        # given subgroup
+        for w in Y:
+            # TODO: this should support input of a list of general words
+            # not just the words which are in "A" (i.e gen and gen^-1)
+            if C.table[alpha][C.A_dict[w]] != alpha:
+                # continue with alpha
+                next_alpha = True
+                break
+        if next_alpha:
+            next_alpha = False
+            continue
+        # try alpha as the new point 0 in Omega_C_alpha
+        mu[0] = alpha
+        nu[alpha] = 0
+        # compare corresponding entries in C and C_alpha
+        lamda = 0
+        for beta in range(n):
+            for x in C.A:
+                gamma = C.table[beta][C.A_dict[x]]
+                delta = C.table[mu[beta]][C.A_dict[x]]
+                # if either of the entries is undefined,
+                # we move with next alpha
+                if gamma is None or delta is None:
+                    # continue with alpha
+                    next_alpha = True
+                    break
+                if nu[delta] is None:
+                    # delta becomes the next point in Omega_C_alpha
+                    lamda += 1
+                    nu[delta] = lamda
+                    mu[lamda] = delta
+                if nu[delta] < gamma:
+                    return False
+                if nu[delta] > gamma:
+                    # continue with alpha
+                    next_alpha = True
+                    break
+            if next_alpha:
+                next_alpha = False
+                break
+    return True
+
+#========================================================================
+#                    Simplifying Presentation
+#========================================================================
+
+def simplify_presentation(*args, change_gens=False):
+    '''
+    For an instance of `FpGroup`, return a simplified isomorphic copy of
+    the group (e.g. remove redundant generators or relators). Alternatively,
+    a list of generators and relators can be passed in which case the
+    simplified lists will be returned.
+
+    By default, the generators of the group are unchanged. If you would
+    like to remove redundant generators, set the keyword argument
+    `change_gens = True`.
+
+    '''
+    if len(args) == 1:
+        if not isinstance(args[0], FpGroup):
+            raise TypeError("The argument must be an instance of FpGroup")
+        G = args[0]
+        gens, rels = simplify_presentation(G.generators, G.relators,
+                                              change_gens=change_gens)
+        if gens:
+            return FpGroup(gens[0].group, rels)
+        return FpGroup(FreeGroup([]), [])
+    elif len(args) == 2:
+        gens, rels = args[0][:], args[1][:]
+        if not gens:
+            return gens, rels
+        identity = gens[0].group.identity
+    else:
+        if len(args) == 0:
+            m = "Not enough arguments"
+        else:
+            m = "Too many arguments"
+        raise RuntimeError(m)
+
+    prev_gens = []
+    prev_rels = []
+    while not set(prev_rels) == set(rels):
+        prev_rels = rels
+        while change_gens and not set(prev_gens) == set(gens):
+            prev_gens = gens
+            gens, rels = elimination_technique_1(gens, rels, identity)
+        rels = _simplify_relators(rels)
+
+    if change_gens:
+        syms = [g.array_form[0][0] for g in gens]
+        F = free_group(syms)[0]
+        identity = F.identity
+        gens = F.generators
+        subs = dict(zip(syms, gens))
+        for j, r in enumerate(rels):
+            a = r.array_form
+            rel = identity
+            for sym, p in a:
+                rel = rel*subs[sym]**p
+            rels[j] = rel
+    return gens, rels
+
+def _simplify_relators(rels):
+    """
+    Simplifies a set of relators. All relators are checked to see if they are
+    of the form `gen^n`. If any such relators are found then all other relators
+    are processed for strings in the `gen` known order.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import free_group
+    >>> from sympy.combinatorics.fp_groups import _simplify_relators
+    >>> F, x, y = free_group("x, y")
+    >>> w1 = [x**2*y**4, x**3]
+    >>> _simplify_relators(w1)
+    [x**3, x**-1*y**4]
+
+    >>> w2 = [x**2*y**-4*x**5, x**3, x**2*y**8, y**5]
+    >>> _simplify_relators(w2)
+    [x**-1*y**-2, x**-1*y*x**-1, x**3, y**5]
+
+    >>> w3 = [x**6*y**4, x**4]
+    >>> _simplify_relators(w3)
+    [x**4, x**2*y**4]
+
+    >>> w4 = [x**2, x**5, y**3]
+    >>> _simplify_relators(w4)
+    [x, y**3]
+
+    """
+    rels = rels[:]
+
+    if not rels:
+        return []
+
+    identity = rels[0].group.identity
+
+    # build dictionary with "gen: n" where gen^n is one of the relators
+    exps = {}
+    for i in range(len(rels)):
+        rel = rels[i]
+        if rel.number_syllables() == 1:
+            g = rel[0]
+            exp = abs(rel.array_form[0][1])
+            if rel.array_form[0][1] < 0:
+                rels[i] = rels[i]**-1
+                g = g**-1
+            if g in exps:
+                exp = gcd(exp, exps[g].array_form[0][1])
+            exps[g] = g**exp
+
+    one_syllables_words = list(exps.values())
+    # decrease some of the exponents in relators, making use of the single
+    # syllable relators
+    for i, rel in enumerate(rels):
+        if rel in one_syllables_words:
+            continue
+        rel = rel.eliminate_words(one_syllables_words, _all = True)
+        # if rels[i] contains g**n where abs(n) is greater than half of the power p
+        # of g in exps, g**n can be replaced by g**(n-p) (or g**(p-n) if n<0)
+        for g in rel.contains_generators():
+            if g in exps:
+                exp = exps[g].array_form[0][1]
+                max_exp = (exp + 1)//2
+                rel = rel.eliminate_word(g**(max_exp), g**(max_exp-exp), _all = True)
+                rel = rel.eliminate_word(g**(-max_exp), g**(-(max_exp-exp)), _all = True)
+        rels[i] = rel
+
+    rels = [r.identity_cyclic_reduction() for r in rels]
+
+    rels += one_syllables_words # include one_syllable_words in the list of relators
+    rels = list(set(rels)) # get unique values in rels
+    rels.sort()
+
+    # remove  entries in rels
+    try:
+        rels.remove(identity)
+    except ValueError:
+        pass
+    return rels
+
+# Pg 350, section 2.5.1 from [2]
+def elimination_technique_1(gens, rels, identity):
+    rels = rels[:]
+    # the shorter relators are examined first so that generators selected for
+    # elimination will have shorter strings as equivalent
+    rels.sort()
+    gens = gens[:]
+    redundant_gens = {}
+    redundant_rels = []
+    used_gens = set()
+    # examine each relator in relator list for any generator occurring exactly
+    # once
+    for rel in rels:
+        # don't look for a redundant generator in a relator which
+        # depends on previously found ones
+        contained_gens = rel.contains_generators()
+        if any(g in contained_gens for g in redundant_gens):
+            continue
+        contained_gens = list(contained_gens)
+        contained_gens.sort(reverse = True)
+        for gen in contained_gens:
+            if rel.generator_count(gen) == 1 and gen not in used_gens:
+                k = rel.exponent_sum(gen)
+                gen_index = rel.index(gen**k)
+                bk = rel.subword(gen_index + 1, len(rel))
+                fw = rel.subword(0, gen_index)
+                chi = bk*fw
+                redundant_gens[gen] = chi**(-1*k)
+                used_gens.update(chi.contains_generators())
+                redundant_rels.append(rel)
+                break
+    rels = [r for r in rels if r not in redundant_rels]
+    # eliminate the redundant generators from remaining relators
+    rels = [r.eliminate_words(redundant_gens, _all = True).identity_cyclic_reduction() for r in rels]
+    rels = list(set(rels))
+    try:
+        rels.remove(identity)
+    except ValueError:
+        pass
+    gens = [g for g in gens if g not in redundant_gens]
+    return gens, rels
+
+###############################################################################
+#                           SUBGROUP PRESENTATIONS                            #
+###############################################################################
+
+# Pg 175 [1]
+def define_schreier_generators(C, homomorphism=False):
+    '''
+    Parameters
+    ==========
+
+    C -- Coset table.
+    homomorphism -- When set to True, return a dictionary containing the images
+                     of the presentation generators in the original group.
+    '''
+    y = []
+    gamma = 1
+    f = C.fp_group
+    X = f.generators
+    if homomorphism:
+        # `_gens` stores the elements of the parent group to
+        # to which the schreier generators correspond to.
+        _gens = {}
+        # compute the schreier Traversal
+        tau = {}
+        tau[0] = f.identity
+    C.P = [[None]*len(C.A) for i in range(C.n)]
+    for alpha, x in product(C.omega, C.A):
+        beta = C.table[alpha][C.A_dict[x]]
+        if beta == gamma:
+            C.P[alpha][C.A_dict[x]] = ""
+            C.P[beta][C.A_dict_inv[x]] = ""
+            gamma += 1
+            if homomorphism:
+                tau[beta] = tau[alpha]*x
+        elif x in X and C.P[alpha][C.A_dict[x]] is None:
+            y_alpha_x = '%s_%s' % (x, alpha)
+            y.append(y_alpha_x)
+            C.P[alpha][C.A_dict[x]] = y_alpha_x
+            if homomorphism:
+                _gens[y_alpha_x] = tau[alpha]*x*tau[beta]**-1
+    grp_gens = list(free_group(', '.join(y)))
+    C._schreier_free_group = grp_gens.pop(0)
+    C._schreier_generators = grp_gens
+    if homomorphism:
+        C._schreier_gen_elem = _gens
+    # replace all elements of P by, free group elements
+    for i, j in product(range(len(C.P)), range(len(C.A))):
+        # if equals "", replace by identity element
+        if C.P[i][j] == "":
+            C.P[i][j] = C._schreier_free_group.identity
+        elif isinstance(C.P[i][j], str):
+            r = C._schreier_generators[y.index(C.P[i][j])]
+            C.P[i][j] = r
+            beta = C.table[i][j]
+            C.P[beta][j + 1] = r**-1
+
+def reidemeister_relators(C):
+    R = C.fp_group.relators
+    rels = [rewrite(C, coset, word) for word in R for coset in range(C.n)]
+    order_1_gens = {i for i in rels if len(i) == 1}
+
+    # remove all the order 1 generators from relators
+    rels = list(filter(lambda rel: rel not in order_1_gens, rels))
+
+    # replace order 1 generators by identity element in reidemeister relators
+    for i in range(len(rels)):
+        w = rels[i]
+        w = w.eliminate_words(order_1_gens, _all=True)
+        rels[i] = w
+
+    C._schreier_generators = [i for i in C._schreier_generators
+                    if not (i in order_1_gens or i**-1 in order_1_gens)]
+
+    # Tietze transformation 1 i.e TT_1
+    # remove cyclic conjugate elements from relators
+    i = 0
+    while i < len(rels):
+        w = rels[i]
+        j = i + 1
+        while j < len(rels):
+            if w.is_cyclic_conjugate(rels[j]):
+                del rels[j]
+            else:
+                j += 1
+        i += 1
+
+    C._reidemeister_relators = rels
+
+
+def rewrite(C, alpha, w):
+    """
+    Parameters
+    ==========
+
+    C: CosetTable
+    alpha: A live coset
+    w: A word in `A*`
+
+    Returns
+    =======
+
+    rho(tau(alpha), w)
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.fp_groups import FpGroup, CosetTable, define_schreier_generators, rewrite
+    >>> from sympy.combinatorics import free_group
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**2, y**3, (x*y)**6])
+    >>> C = CosetTable(f, [])
+    >>> C.table = [[1, 1, 2, 3], [0, 0, 4, 5], [4, 4, 3, 0], [5, 5, 0, 2], [2, 2, 5, 1], [3, 3, 1, 4]]
+    >>> C.p = [0, 1, 2, 3, 4, 5]
+    >>> define_schreier_generators(C)
+    >>> rewrite(C, 0, (x*y)**6)
+    x_4*y_2*x_3*x_1*x_2*y_4*x_5
+
+    """
+    v = C._schreier_free_group.identity
+    for i in range(len(w)):
+        x_i = w[i]
+        v = v*C.P[alpha][C.A_dict[x_i]]
+        alpha = C.table[alpha][C.A_dict[x_i]]
+    return v
+
+# Pg 350, section 2.5.2 from [2]
+def elimination_technique_2(C):
+    """
+    This technique eliminates one generator at a time. Heuristically this
+    seems superior in that we may select for elimination the generator with
+    shortest equivalent string at each stage.
+
+    >>> from sympy.combinatorics import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r, \
+            reidemeister_relators, define_schreier_generators, elimination_technique_2
+    >>> F, x, y = free_group("x, y")
+    >>> f = FpGroup(F, [x**3, y**5, (x*y)**2]); H = [x*y, x**-1*y**-1*x*y*x]
+    >>> C = coset_enumeration_r(f, H)
+    >>> C.compress(); C.standardize()
+    >>> define_schreier_generators(C)
+    >>> reidemeister_relators(C)
+    >>> elimination_technique_2(C)
+    ([y_1, y_2], [y_2**-3, y_2*y_1*y_2*y_1*y_2*y_1, y_1**2])
+
+    """
+    rels = C._reidemeister_relators
+    rels.sort(reverse=True)
+    gens = C._schreier_generators
+    for i in range(len(gens) - 1, -1, -1):
+        rel = rels[i]
+        for j in range(len(gens) - 1, -1, -1):
+            gen = gens[j]
+            if rel.generator_count(gen) == 1:
+                k = rel.exponent_sum(gen)
+                gen_index = rel.index(gen**k)
+                bk = rel.subword(gen_index + 1, len(rel))
+                fw = rel.subword(0, gen_index)
+                rep_by = (bk*fw)**(-1*k)
+                del rels[i]
+                del gens[j]
+                rels = [rel.eliminate_word(gen, rep_by) for rel in rels]
+                break
+    C._reidemeister_relators = rels
+    C._schreier_generators = gens
+    return C._schreier_generators, C._reidemeister_relators
+
+def reidemeister_presentation(fp_grp, H, C=None, homomorphism=False):
+    """
+    Parameters
+    ==========
+
+    fp_group: A finitely presented group, an instance of FpGroup
+    H: A subgroup whose presentation is to be found, given as a list
+    of words in generators of `fp_grp`
+    homomorphism: When set to True, return a homomorphism from the subgroup
+                    to the parent group
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import free_group
+    >>> from sympy.combinatorics.fp_groups import FpGroup, reidemeister_presentation
+    >>> F, x, y = free_group("x, y")
+
+    Example 5.6 Pg. 177 from [1]
+    >>> f = FpGroup(F, [x**3, y**5, (x*y)**2])
+    >>> H = [x*y, x**-1*y**-1*x*y*x]
+    >>> reidemeister_presentation(f, H)
+    ((y_1, y_2), (y_1**2, y_2**3, y_2*y_1*y_2*y_1*y_2*y_1))
+
+    Example 5.8 Pg. 183 from [1]
+    >>> f = FpGroup(F, [x**3, y**3, (x*y)**3])
+    >>> H = [x*y, x*y**-1]
+    >>> reidemeister_presentation(f, H)
+    ((x_0, y_0), (x_0**3, y_0**3, x_0*y_0*x_0*y_0*x_0*y_0))
+
+    Exercises Q2. Pg 187 from [1]
+    >>> f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3])
+    >>> H = [x]
+    >>> reidemeister_presentation(f, H)
+    ((x_0,), (x_0**4,))
+
+    Example 5.9 Pg. 183 from [1]
+    >>> f = FpGroup(F, [x**3*y**-3, (x*y)**3, (x*y**-1)**2])
+    >>> H = [x]
+    >>> reidemeister_presentation(f, H)
+    ((x_0,), (x_0**6,))
+
+    """
+    if not C:
+        C = coset_enumeration_r(fp_grp, H)
+    C.compress(); C.standardize()
+    define_schreier_generators(C, homomorphism=homomorphism)
+    reidemeister_relators(C)
+    gens, rels = C._schreier_generators, C._reidemeister_relators
+    gens, rels = simplify_presentation(gens, rels, change_gens=True)
+
+    C.schreier_generators = tuple(gens)
+    C.reidemeister_relators = tuple(rels)
+
+    if homomorphism:
+        _gens = [C._schreier_gen_elem[str(gen)] for gen in gens]
+        return C.schreier_generators, C.reidemeister_relators, _gens
+
+    return C.schreier_generators, C.reidemeister_relators
+
+
+FpGroupElement = FreeGroupElement
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/free_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/free_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..2ec85f4fac73fba95d4644a37ecb27140e45a4c5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/free_groups.py
@@ -0,0 +1,1360 @@
+from __future__ import annotations
+
+from sympy.core import S
+from sympy.core.expr import Expr
+from sympy.core.symbol import Symbol, symbols as _symbols
+from sympy.core.sympify import CantSympify
+from sympy.printing.defaults import DefaultPrinting
+from sympy.utilities import public
+from sympy.utilities.iterables import flatten, is_sequence
+from sympy.utilities.magic import pollute
+from sympy.utilities.misc import as_int
+
+
+@public
+def free_group(symbols):
+    """Construct a free group returning ``(FreeGroup, (f_0, f_1, ..., f_(n-1))``.
+
+    Parameters
+    ==========
+
+    symbols : str, Symbol/Expr or sequence of str, Symbol/Expr (may be empty)
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import free_group
+    >>> F, x, y, z = free_group("x, y, z")
+    >>> F
+    
+    >>> x**2*y**-1
+    x**2*y**-1
+    >>> type(_)
+    
+
+    """
+    _free_group = FreeGroup(symbols)
+    return (_free_group,) + tuple(_free_group.generators)
+
+@public
+def xfree_group(symbols):
+    """Construct a free group returning ``(FreeGroup, (f_0, f_1, ..., f_(n-1)))``.
+
+    Parameters
+    ==========
+
+    symbols : str, Symbol/Expr or sequence of str, Symbol/Expr (may be empty)
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.free_groups import xfree_group
+    >>> F, (x, y, z) = xfree_group("x, y, z")
+    >>> F
+    
+    >>> y**2*x**-2*z**-1
+    y**2*x**-2*z**-1
+    >>> type(_)
+    
+
+    """
+    _free_group = FreeGroup(symbols)
+    return (_free_group, _free_group.generators)
+
+@public
+def vfree_group(symbols):
+    """Construct a free group and inject ``f_0, f_1, ..., f_(n-1)`` as symbols
+    into the global namespace.
+
+    Parameters
+    ==========
+
+    symbols : str, Symbol/Expr or sequence of str, Symbol/Expr (may be empty)
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.free_groups import vfree_group
+    >>> vfree_group("x, y, z")
+    
+    >>> x**2*y**-2*z # noqa: F821
+    x**2*y**-2*z
+    >>> type(_)
+    
+
+    """
+    _free_group = FreeGroup(symbols)
+    pollute([sym.name for sym in _free_group.symbols], _free_group.generators)
+    return _free_group
+
+
+def _parse_symbols(symbols):
+    if not symbols:
+        return ()
+    if isinstance(symbols, str):
+        return _symbols(symbols, seq=True)
+    elif isinstance(symbols, (Expr, FreeGroupElement)):
+        return (symbols,)
+    elif is_sequence(symbols):
+        if all(isinstance(s, str) for s in symbols):
+            return _symbols(symbols)
+        elif all(isinstance(s, Expr) for s in symbols):
+            return symbols
+    raise ValueError("The type of `symbols` must be one of the following: "
+                     "a str, Symbol/Expr or a sequence of "
+                     "one of these types")
+
+
+##############################################################################
+#                          FREE GROUP                                        #
+##############################################################################
+
+_free_group_cache: dict[int, FreeGroup] = {}
+
+class FreeGroup(DefaultPrinting):
+    """
+    Free group with finite or infinite number of generators. Its input API
+    is that of a str, Symbol/Expr or a sequence of one of
+    these types (which may be empty)
+
+    See Also
+    ========
+
+    sympy.polys.rings.PolyRing
+
+    References
+    ==========
+
+    .. [1] https://www.gap-system.org/Manuals/doc/ref/chap37.html
+
+    .. [2] https://en.wikipedia.org/wiki/Free_group
+
+    """
+    is_associative = True
+    is_group = True
+    is_FreeGroup = True
+    is_PermutationGroup = False
+    relators: list[Expr] = []
+
+    def __new__(cls, symbols):
+        symbols = tuple(_parse_symbols(symbols))
+        rank = len(symbols)
+        _hash = hash((cls.__name__, symbols, rank))
+        obj = _free_group_cache.get(_hash)
+
+        if obj is None:
+            obj = object.__new__(cls)
+            obj._hash = _hash
+            obj._rank = rank
+            # dtype method is used to create new instances of FreeGroupElement
+            obj.dtype = type("FreeGroupElement", (FreeGroupElement,), {"group": obj})
+            obj.symbols = symbols
+            obj.generators = obj._generators()
+            obj._gens_set = set(obj.generators)
+            for symbol, generator in zip(obj.symbols, obj.generators):
+                if isinstance(symbol, Symbol):
+                    name = symbol.name
+                    if hasattr(obj, name):
+                        setattr(obj, name, generator)
+
+            _free_group_cache[_hash] = obj
+
+        return obj
+
+    def __getnewargs__(self):
+        """Return a tuple of arguments that must be passed to __new__ in order to support pickling this object."""
+        return (self.symbols,)
+
+    def __getstate__(self):
+        # Don't pickle any fields because they are regenerated within __new__
+        return None
+
+    def _generators(group):
+        """Returns the generators of the FreeGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y, z = free_group("x, y, z")
+        >>> F.generators
+        (x, y, z)
+
+        """
+        gens = []
+        for sym in group.symbols:
+            elm = ((sym, 1),)
+            gens.append(group.dtype(elm))
+        return tuple(gens)
+
+    def clone(self, symbols=None):
+        return self.__class__(symbols or self.symbols)
+
+    def __contains__(self, i):
+        """Return True if ``i`` is contained in FreeGroup."""
+        if not isinstance(i, FreeGroupElement):
+            return False
+        group = i.group
+        return self == group
+
+    def __hash__(self):
+        return self._hash
+
+    def __len__(self):
+        return self.rank
+
+    def __str__(self):
+        if self.rank > 30:
+            str_form = "" % self.rank
+        else:
+            str_form = ""
+        return str_form
+
+    __repr__ = __str__
+
+    def __getitem__(self, index):
+        symbols = self.symbols[index]
+        return self.clone(symbols=symbols)
+
+    def __eq__(self, other):
+        """No ``FreeGroup`` is equal to any "other" ``FreeGroup``.
+        """
+        return self is other
+
+    def index(self, gen):
+        """Return the index of the generator `gen` from ``(f_0, ..., f_(n-1))``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> F.index(y)
+        1
+        >>> F.index(x)
+        0
+
+        """
+        if isinstance(gen, self.dtype):
+            return self.generators.index(gen)
+        else:
+            raise ValueError("expected a generator of Free Group %s, got %s" % (self, gen))
+
+    def order(self):
+        """Return the order of the free group.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> F.order()
+        oo
+
+        >>> free_group("")[0].order()
+        1
+
+        """
+        if self.rank == 0:
+            return S.One
+        else:
+            return S.Infinity
+
+    @property
+    def elements(self):
+        """
+        Return the elements of the free group.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> (z,) = free_group("")
+        >>> z.elements
+        {}
+
+        """
+        if self.rank == 0:
+            # A set containing Identity element of `FreeGroup` self is returned
+            return {self.identity}
+        else:
+            raise ValueError("Group contains infinitely many elements"
+                            ", hence cannot be represented")
+
+    @property
+    def rank(self):
+        r"""
+        In group theory, the `rank` of a group `G`, denoted `G.rank`,
+        can refer to the smallest cardinality of a generating set
+        for G, that is
+
+        \operatorname{rank}(G)=\min\{ |X|: X\subseteq G, \left\langle X\right\rangle =G\}.
+
+        """
+        return self._rank
+
+    @property
+    def is_abelian(self):
+        """Returns if the group is Abelian.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y, z = free_group("x y z")
+        >>> f.is_abelian
+        False
+
+        """
+        return self.rank in (0, 1)
+
+    @property
+    def identity(self):
+        """Returns the identity element of free group."""
+        return self.dtype()
+
+    def contains(self, g):
+        """Tests if Free Group element ``g`` belong to self, ``G``.
+
+        In mathematical terms any linear combination of generators
+        of a Free Group is contained in it.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y, z = free_group("x y z")
+        >>> f.contains(x**3*y**2)
+        True
+
+        """
+        if not isinstance(g, FreeGroupElement):
+            return False
+        elif self != g.group:
+            return False
+        else:
+            return True
+
+    def center(self):
+        """Returns the center of the free group `self`."""
+        return {self.identity}
+
+
+############################################################################
+#                          FreeGroupElement                                #
+############################################################################
+
+
+class FreeGroupElement(CantSympify, DefaultPrinting, tuple):
+    """Used to create elements of FreeGroup. It cannot be used directly to
+    create a free group element. It is called by the `dtype` method of the
+    `FreeGroup` class.
+
+    """
+    __slots__ = ()
+    is_assoc_word = True
+
+    def new(self, init):
+        return self.__class__(init)
+
+    _hash = None
+
+    def __hash__(self):
+        _hash = self._hash
+        if _hash is None:
+            self._hash = _hash = hash((self.group, frozenset(tuple(self))))
+        return _hash
+
+    def copy(self):
+        return self.new(self)
+
+    @property
+    def is_identity(self):
+        return not self.array_form
+
+    @property
+    def array_form(self):
+        """
+        SymPy provides two different internal kinds of representation
+        of associative words. The first one is called the `array_form`
+        which is a tuple containing `tuples` as its elements, where the
+        size of each tuple is two. At the first position the tuple
+        contains the `symbol-generator`, while at the second position
+        of tuple contains the exponent of that generator at the position.
+        Since elements (i.e. words) do not commute, the indexing of tuple
+        makes that property to stay.
+
+        The structure in ``array_form`` of ``FreeGroupElement`` is of form:
+
+        ``( ( symbol_of_gen, exponent ), ( , ), ... ( , ) )``
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y, z = free_group("x y z")
+        >>> (x*z).array_form
+        ((x, 1), (z, 1))
+        >>> (x**2*z*y*x**2).array_form
+        ((x, 2), (z, 1), (y, 1), (x, 2))
+
+        See Also
+        ========
+
+        letter_repr
+
+        """
+        return tuple(self)
+
+    @property
+    def letter_form(self):
+        """
+        The letter representation of a ``FreeGroupElement`` is a tuple
+        of generator symbols, with each entry corresponding to a group
+        generator. Inverses of the generators are represented by
+        negative generator symbols.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b, c, d = free_group("a b c d")
+        >>> (a**3).letter_form
+        (a, a, a)
+        >>> (a**2*d**-2*a*b**-4).letter_form
+        (a, a, -d, -d, a, -b, -b, -b, -b)
+        >>> (a**-2*b**3*d).letter_form
+        (-a, -a, b, b, b, d)
+
+        See Also
+        ========
+
+        array_form
+
+        """
+        return tuple(flatten([(i,)*j if j > 0 else (-i,)*(-j)
+                    for i, j in self.array_form]))
+
+    def __getitem__(self, i):
+        group = self.group
+        r = self.letter_form[i]
+        if r.is_Symbol:
+            return group.dtype(((r, 1),))
+        else:
+            return group.dtype(((-r, -1),))
+
+    def index(self, gen):
+        if len(gen) != 1:
+            raise ValueError()
+        return (self.letter_form).index(gen.letter_form[0])
+
+    @property
+    def letter_form_elm(self):
+        """
+        """
+        group = self.group
+        r = self.letter_form
+        return [group.dtype(((elm,1),)) if elm.is_Symbol \
+                else group.dtype(((-elm,-1),)) for elm in r]
+
+    @property
+    def ext_rep(self):
+        """This is called the External Representation of ``FreeGroupElement``
+        """
+        return tuple(flatten(self.array_form))
+
+    def __contains__(self, gen):
+        return gen.array_form[0][0] in tuple([r[0] for r in self.array_form])
+
+    def __str__(self):
+        if self.is_identity:
+            return ""
+
+        str_form = ""
+        array_form = self.array_form
+        for i in range(len(array_form)):
+            if i == len(array_form) - 1:
+                if array_form[i][1] == 1:
+                    str_form += str(array_form[i][0])
+                else:
+                    str_form += str(array_form[i][0]) + \
+                                    "**" + str(array_form[i][1])
+            else:
+                if array_form[i][1] == 1:
+                    str_form += str(array_form[i][0]) + "*"
+                else:
+                    str_form += str(array_form[i][0]) + \
+                                    "**" + str(array_form[i][1]) + "*"
+        return str_form
+
+    __repr__ = __str__
+
+    def __pow__(self, n):
+        n = as_int(n)
+        result = self.group.identity
+        if n == 0:
+            return result
+        if n < 0:
+            n = -n
+            x = self.inverse()
+        else:
+            x = self
+        while True:
+            if n % 2:
+                result *= x
+            n >>= 1
+            if not n:
+                break
+            x *= x
+        return result
+
+    def __mul__(self, other):
+        """Returns the product of elements belonging to the same ``FreeGroup``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y, z = free_group("x y z")
+        >>> x*y**2*y**-4
+        x*y**-2
+        >>> z*y**-2
+        z*y**-2
+        >>> x**2*y*y**-1*x**-2
+        
+
+        """
+        group = self.group
+        if not isinstance(other, group.dtype):
+            raise TypeError("only FreeGroup elements of same FreeGroup can "
+                    "be multiplied")
+        if self.is_identity:
+            return other
+        if other.is_identity:
+            return self
+        r = list(self.array_form + other.array_form)
+        zero_mul_simp(r, len(self.array_form) - 1)
+        return group.dtype(tuple(r))
+
+    def __truediv__(self, other):
+        group = self.group
+        if not isinstance(other, group.dtype):
+            raise TypeError("only FreeGroup elements of same FreeGroup can "
+                    "be multiplied")
+        return self*(other.inverse())
+
+    def __rtruediv__(self, other):
+        group = self.group
+        if not isinstance(other, group.dtype):
+            raise TypeError("only FreeGroup elements of same FreeGroup can "
+                    "be multiplied")
+        return other*(self.inverse())
+
+    def __add__(self, other):
+        return NotImplemented
+
+    def inverse(self):
+        """
+        Returns the inverse of a ``FreeGroupElement`` element
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y, z = free_group("x y z")
+        >>> x.inverse()
+        x**-1
+        >>> (x*y).inverse()
+        y**-1*x**-1
+
+        """
+        group = self.group
+        r = tuple([(i, -j) for i, j in self.array_form[::-1]])
+        return group.dtype(r)
+
+    def order(self):
+        """Find the order of a ``FreeGroupElement``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y = free_group("x y")
+        >>> (x**2*y*y**-1*x**-2).order()
+        1
+
+        """
+        if self.is_identity:
+            return S.One
+        else:
+            return S.Infinity
+
+    def commutator(self, other):
+        """
+        Return the commutator of `self` and `x`: ``~x*~self*x*self``
+
+        """
+        group = self.group
+        if not isinstance(other, group.dtype):
+            raise ValueError("commutator of only FreeGroupElement of the same "
+                    "FreeGroup exists")
+        else:
+            return self.inverse()*other.inverse()*self*other
+
+    def eliminate_words(self, words, _all=False, inverse=True):
+        '''
+        Replace each subword from the dictionary `words` by words[subword].
+        If words is a list, replace the words by the identity.
+
+        '''
+        again = True
+        new = self
+        if isinstance(words, dict):
+            while again:
+                again = False
+                for sub in words:
+                    prev = new
+                    new = new.eliminate_word(sub, words[sub], _all=_all, inverse=inverse)
+                    if new != prev:
+                        again = True
+        else:
+            while again:
+                again = False
+                for sub in words:
+                    prev = new
+                    new = new.eliminate_word(sub, _all=_all, inverse=inverse)
+                    if new != prev:
+                        again = True
+        return new
+
+    def eliminate_word(self, gen, by=None, _all=False, inverse=True):
+        """
+        For an associative word `self`, a subword `gen`, and an associative
+        word `by` (identity by default), return the associative word obtained by
+        replacing each occurrence of `gen` in `self` by `by`. If `_all = True`,
+        the occurrences of `gen` that may appear after the first substitution will
+        also be replaced and so on until no occurrences are found. This might not
+        always terminate (e.g. `(x).eliminate_word(x, x**2, _all=True)`).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y = free_group("x y")
+        >>> w = x**5*y*x**2*y**-4*x
+        >>> w.eliminate_word( x, x**2 )
+        x**10*y*x**4*y**-4*x**2
+        >>> w.eliminate_word( x, y**-1 )
+        y**-11
+        >>> w.eliminate_word(x**5)
+        y*x**2*y**-4*x
+        >>> w.eliminate_word(x*y, y)
+        x**4*y*x**2*y**-4*x
+
+        See Also
+        ========
+        substituted_word
+
+        """
+        if by is None:
+            by = self.group.identity
+        if self.is_independent(gen) or gen == by:
+            return self
+        if gen == self:
+            return by
+        if gen**-1 == by:
+            _all = False
+        word = self
+        l = len(gen)
+
+        try:
+            i = word.subword_index(gen)
+            k = 1
+        except ValueError:
+            if not inverse:
+                return word
+            try:
+                i = word.subword_index(gen**-1)
+                k = -1
+            except ValueError:
+                return word
+
+        word = word.subword(0, i)*by**k*word.subword(i+l, len(word)).eliminate_word(gen, by)
+
+        if _all:
+            return word.eliminate_word(gen, by, _all=True, inverse=inverse)
+        else:
+            return word
+
+    def __len__(self):
+        """
+        For an associative word `self`, returns the number of letters in it.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a b")
+        >>> w = a**5*b*a**2*b**-4*a
+        >>> len(w)
+        13
+        >>> len(a**17)
+        17
+        >>> len(w**0)
+        0
+
+        """
+        return sum(abs(j) for (i, j) in self)
+
+    def __eq__(self, other):
+        """
+        Two  associative words are equal if they are words over the
+        same alphabet and if they are sequences of the same letters.
+        This is equivalent to saying that the external representations
+        of the words are equal.
+        There is no "universal" empty word, every alphabet has its own
+        empty word.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, swapnil0, swapnil1 = free_group("swapnil0 swapnil1")
+        >>> f
+        
+        >>> g, swap0, swap1 = free_group("swap0 swap1")
+        >>> g
+        
+
+        >>> swapnil0 == swapnil1
+        False
+        >>> swapnil0*swapnil1 == swapnil1/swapnil1*swapnil0*swapnil1
+        True
+        >>> swapnil0*swapnil1 == swapnil1*swapnil0
+        False
+        >>> swapnil1**0 == swap0**0
+        False
+
+        """
+        group = self.group
+        if not isinstance(other, group.dtype):
+            return False
+        return tuple.__eq__(self, other)
+
+    def __lt__(self, other):
+        """
+        The  ordering  of  associative  words is defined by length and
+        lexicography (this ordering is called short-lex ordering), that
+        is, shorter words are smaller than longer words, and words of the
+        same length are compared w.r.t. the lexicographical ordering induced
+        by the ordering of generators. Generators  are  sorted  according
+        to the order in which they were created. If the generators are
+        invertible then each generator `g` is larger than its inverse `g^{-1}`,
+        and `g^{-1}` is larger than every generator that is smaller than `g`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a b")
+        >>> b < a
+        False
+        >>> a < a.inverse()
+        False
+
+        """
+        group = self.group
+        if not isinstance(other, group.dtype):
+            raise TypeError("only FreeGroup elements of same FreeGroup can "
+                             "be compared")
+        l = len(self)
+        m = len(other)
+        # implement lenlex order
+        if l < m:
+            return True
+        elif l > m:
+            return False
+        for i in range(l):
+            a = self[i].array_form[0]
+            b = other[i].array_form[0]
+            p = group.symbols.index(a[0])
+            q = group.symbols.index(b[0])
+            if p < q:
+                return True
+            elif p > q:
+                return False
+            elif a[1] < b[1]:
+                return True
+            elif a[1] > b[1]:
+                return False
+        return False
+
+    def __le__(self, other):
+        return (self == other or self < other)
+
+    def __gt__(self, other):
+        """
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, x, y, z = free_group("x y z")
+        >>> y**2 > x**2
+        True
+        >>> y*z > z*y
+        False
+        >>> x > x.inverse()
+        True
+
+        """
+        group = self.group
+        if not isinstance(other, group.dtype):
+            raise TypeError("only FreeGroup elements of same FreeGroup can "
+                             "be compared")
+        return not self <= other
+
+    def __ge__(self, other):
+        return not self < other
+
+    def exponent_sum(self, gen):
+        """
+        For an associative word `self` and a generator or inverse of generator
+        `gen`, ``exponent_sum`` returns the number of times `gen` appears in
+        `self` minus the number of times its inverse appears in `self`. If
+        neither `gen` nor its inverse occur in `self` then 0 is returned.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> w = x**2*y**3
+        >>> w.exponent_sum(x)
+        2
+        >>> w.exponent_sum(x**-1)
+        -2
+        >>> w = x**2*y**4*x**-3
+        >>> w.exponent_sum(x)
+        -1
+
+        See Also
+        ========
+
+        generator_count
+
+        """
+        if len(gen) != 1:
+            raise ValueError("gen must be a generator or inverse of a generator")
+        s = gen.array_form[0]
+        return s[1]*sum(i[1] for i in self.array_form if i[0] == s[0])
+
+    def generator_count(self, gen):
+        """
+        For an associative word `self` and a generator `gen`,
+        ``generator_count`` returns the multiplicity of generator
+        `gen` in `self`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> w = x**2*y**3
+        >>> w.generator_count(x)
+        2
+        >>> w = x**2*y**4*x**-3
+        >>> w.generator_count(x)
+        5
+
+        See Also
+        ========
+
+        exponent_sum
+
+        """
+        if len(gen) != 1 or gen.array_form[0][1] < 0:
+            raise ValueError("gen must be a generator")
+        s = gen.array_form[0]
+        return s[1]*sum(abs(i[1]) for i in self.array_form if i[0] == s[0])
+
+    def subword(self, from_i, to_j, strict=True):
+        """
+        For an associative word `self` and two positive integers `from_i` and
+        `to_j`, `subword` returns the subword of `self` that begins at position
+        `from_i` and ends at `to_j - 1`, indexing is done with origin 0.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a b")
+        >>> w = a**5*b*a**2*b**-4*a
+        >>> w.subword(2, 6)
+        a**3*b
+
+        """
+        group = self.group
+        if not strict:
+            from_i = max(from_i, 0)
+            to_j = min(len(self), to_j)
+        if from_i < 0 or to_j > len(self):
+            raise ValueError("`from_i`, `to_j` must be positive and no greater than "
+                    "the length of associative word")
+        if to_j <= from_i:
+            return group.identity
+        else:
+            letter_form = self.letter_form[from_i: to_j]
+            array_form = letter_form_to_array_form(letter_form, group)
+            return group.dtype(array_form)
+
+    def subword_index(self, word, start = 0):
+        '''
+        Find the index of `word` in `self`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a b")
+        >>> w = a**2*b*a*b**3
+        >>> w.subword_index(a*b*a*b)
+        1
+
+        '''
+        l = len(word)
+        self_lf = self.letter_form
+        word_lf = word.letter_form
+        index = None
+        for i in range(start,len(self_lf)-l+1):
+            if self_lf[i:i+l] == word_lf:
+                index = i
+                break
+        if index is not None:
+            return index
+        else:
+            raise ValueError("The given word is not a subword of self")
+
+    def is_dependent(self, word):
+        """
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> (x**4*y**-3).is_dependent(x**4*y**-2)
+        True
+        >>> (x**2*y**-1).is_dependent(x*y)
+        False
+        >>> (x*y**2*x*y**2).is_dependent(x*y**2)
+        True
+        >>> (x**12).is_dependent(x**-4)
+        True
+
+        See Also
+        ========
+
+        is_independent
+
+        """
+        try:
+            return self.subword_index(word) is not None
+        except ValueError:
+            pass
+        try:
+            return self.subword_index(word**-1) is not None
+        except ValueError:
+            return False
+
+    def is_independent(self, word):
+        """
+
+        See Also
+        ========
+
+        is_dependent
+
+        """
+        return not self.is_dependent(word)
+
+    def contains_generators(self):
+        """
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y, z = free_group("x, y, z")
+        >>> (x**2*y**-1).contains_generators()
+        {x, y}
+        >>> (x**3*z).contains_generators()
+        {x, z}
+
+        """
+        group = self.group
+        gens = {group.dtype(((syllable[0], 1),)) for syllable in self.array_form}
+        return gens
+
+    def cyclic_subword(self, from_i, to_j):
+        group = self.group
+        l = len(self)
+        letter_form = self.letter_form
+        period1 = int(from_i/l)
+        if from_i >= l:
+            from_i -= l*period1
+            to_j -= l*period1
+        diff = to_j - from_i
+        word = letter_form[from_i: to_j]
+        period2 = int(to_j/l) - 1
+        word += letter_form*period2 + letter_form[:diff-l+from_i-l*period2]
+        word = letter_form_to_array_form(word, group)
+        return group.dtype(word)
+
+    def cyclic_conjugates(self):
+        """Returns a words which are cyclic to the word `self`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> w = x*y*x*y*x
+        >>> w.cyclic_conjugates()
+        {x*y*x**2*y, x**2*y*x*y, y*x*y*x**2, y*x**2*y*x, x*y*x*y*x}
+        >>> s = x*y*x**2*y*x
+        >>> s.cyclic_conjugates()
+        {x**2*y*x**2*y, y*x**2*y*x**2, x*y*x**2*y*x}
+
+        References
+        ==========
+
+        .. [1] https://planetmath.org/cyclicpermutation
+
+        """
+        return {self.cyclic_subword(i, i+len(self)) for i in range(len(self))}
+
+    def is_cyclic_conjugate(self, w):
+        """
+        Checks whether words ``self``, ``w`` are cyclic conjugates.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> w1 = x**2*y**5
+        >>> w2 = x*y**5*x
+        >>> w1.is_cyclic_conjugate(w2)
+        True
+        >>> w3 = x**-1*y**5*x**-1
+        >>> w3.is_cyclic_conjugate(w2)
+        False
+
+        """
+        l1 = len(self)
+        l2 = len(w)
+        if l1 != l2:
+            return False
+        w1 = self.identity_cyclic_reduction()
+        w2 = w.identity_cyclic_reduction()
+        letter1 = w1.letter_form
+        letter2 = w2.letter_form
+        str1 = ' '.join(map(str, letter1))
+        str2 = ' '.join(map(str, letter2))
+        if len(str1) != len(str2):
+            return False
+
+        return str1 in str2 + ' ' + str2
+
+    def number_syllables(self):
+        """Returns the number of syllables of the associative word `self`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, swapnil0, swapnil1 = free_group("swapnil0 swapnil1")
+        >>> (swapnil1**3*swapnil0*swapnil1**-1).number_syllables()
+        3
+
+        """
+        return len(self.array_form)
+
+    def exponent_syllable(self, i):
+        """
+        Returns the exponent of the `i`-th syllable of the associative word
+        `self`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a b")
+        >>> w = a**5*b*a**2*b**-4*a
+        >>> w.exponent_syllable( 2 )
+        2
+
+        """
+        return self.array_form[i][1]
+
+    def generator_syllable(self, i):
+        """
+        Returns the symbol of the generator that is involved in the
+        i-th syllable of the associative word `self`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a b")
+        >>> w = a**5*b*a**2*b**-4*a
+        >>> w.generator_syllable( 3 )
+        b
+
+        """
+        return self.array_form[i][0]
+
+    def sub_syllables(self, from_i, to_j):
+        """
+        `sub_syllables` returns the subword of the associative word `self` that
+        consists of syllables from positions `from_to` to `to_j`, where
+        `from_to` and `to_j` must be positive integers and indexing is done
+        with origin 0.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> f, a, b = free_group("a, b")
+        >>> w = a**5*b*a**2*b**-4*a
+        >>> w.sub_syllables(1, 2)
+        b
+        >>> w.sub_syllables(3, 3)
+        
+
+        """
+        if not isinstance(from_i, int) or not isinstance(to_j, int):
+            raise ValueError("both arguments should be integers")
+        group = self.group
+        if to_j <= from_i:
+            return group.identity
+        else:
+            r = tuple(self.array_form[from_i: to_j])
+            return group.dtype(r)
+
+    def substituted_word(self, from_i, to_j, by):
+        """
+        Returns the associative word obtained by replacing the subword of
+        `self` that begins at position `from_i` and ends at position `to_j - 1`
+        by the associative word `by`. `from_i` and `to_j` must be positive
+        integers, indexing is done with origin 0. In other words,
+        `w.substituted_word(w, from_i, to_j, by)` is the product of the three
+        words: `w.subword(0, from_i)`, `by`, and
+        `w.subword(to_j len(w))`.
+
+        See Also
+        ========
+
+        eliminate_word
+
+        """
+        lw = len(self)
+        if from_i >= to_j or from_i > lw or to_j > lw:
+            raise ValueError("values should be within bounds")
+
+        # otherwise there are four possibilities
+
+        # first if from=1 and to=lw then
+        if from_i == 0 and to_j == lw:
+            return by
+        elif from_i == 0:  # second if from_i=1 (and to_j < lw) then
+            return by*self.subword(to_j, lw)
+        elif to_j == lw:   # third if to_j=1 (and from_i > 1) then
+            return self.subword(0, from_i)*by
+        else:              # finally
+            return self.subword(0, from_i)*by*self.subword(to_j, lw)
+
+    def is_cyclically_reduced(self):
+        r"""Returns whether the word is cyclically reduced or not.
+        A word is cyclically reduced if by forming the cycle of the
+        word, the word is not reduced, i.e a word w = `a_1 ... a_n`
+        is called cyclically reduced if `a_1 \ne a_n^{-1}`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> (x**2*y**-1*x**-1).is_cyclically_reduced()
+        False
+        >>> (y*x**2*y**2).is_cyclically_reduced()
+        True
+
+        """
+        if not self:
+            return True
+        return self[0] != self[-1]**-1
+
+    def identity_cyclic_reduction(self):
+        """Return a unique cyclically reduced version of the word.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> (x**2*y**2*x**-1).identity_cyclic_reduction()
+        x*y**2
+        >>> (x**-3*y**-1*x**5).identity_cyclic_reduction()
+        x**2*y**-1
+
+        References
+        ==========
+
+        .. [1] https://planetmath.org/cyclicallyreduced
+
+        """
+        word = self.copy()
+        group = self.group
+        while not word.is_cyclically_reduced():
+            exp1 = word.exponent_syllable(0)
+            exp2 = word.exponent_syllable(-1)
+            r = exp1 + exp2
+            if r == 0:
+                rep = word.array_form[1: word.number_syllables() - 1]
+            else:
+                rep = ((word.generator_syllable(0), exp1 + exp2),) + \
+                        word.array_form[1: word.number_syllables() - 1]
+            word = group.dtype(rep)
+        return word
+
+    def cyclic_reduction(self, removed=False):
+        """Return a cyclically reduced version of the word. Unlike
+        `identity_cyclic_reduction`, this will not cyclically permute
+        the reduced word - just remove the "unreduced" bits on either
+        side of it. Compare the examples with those of
+        `identity_cyclic_reduction`.
+
+        When `removed` is `True`, return a tuple `(word, r)` where
+        self `r` is such that before the reduction the word was either
+        `r*word*r**-1`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> (x**2*y**2*x**-1).cyclic_reduction()
+        x*y**2
+        >>> (x**-3*y**-1*x**5).cyclic_reduction()
+        y**-1*x**2
+        >>> (x**-3*y**-1*x**5).cyclic_reduction(removed=True)
+        (y**-1*x**2, x**-3)
+
+        """
+        word = self.copy()
+        g = self.group.identity
+        while not word.is_cyclically_reduced():
+            exp1 = abs(word.exponent_syllable(0))
+            exp2 = abs(word.exponent_syllable(-1))
+            exp = min(exp1, exp2)
+            start = word[0]**abs(exp)
+            end = word[-1]**abs(exp)
+            word = start**-1*word*end**-1
+            g = g*start
+        if removed:
+            return word, g
+        return word
+
+    def power_of(self, other):
+        '''
+        Check if `self == other**n` for some integer n.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group
+        >>> F, x, y = free_group("x, y")
+        >>> ((x*y)**2).power_of(x*y)
+        True
+        >>> (x**-3*y**-2*x**3).power_of(x**-3*y*x**3)
+        True
+
+        '''
+        if self.is_identity:
+            return True
+
+        l = len(other)
+        if l == 1:
+            # self has to be a power of one generator
+            gens = self.contains_generators()
+            s = other in gens or other**-1 in gens
+            return len(gens) == 1 and s
+
+        # if self is not cyclically reduced and it is a power of other,
+        # other isn't cyclically reduced and the parts removed during
+        # their reduction must be equal
+        reduced, r1 = self.cyclic_reduction(removed=True)
+        if not r1.is_identity:
+            other, r2 = other.cyclic_reduction(removed=True)
+            if r1 == r2:
+                return reduced.power_of(other)
+            return False
+
+        if len(self) < l or len(self) % l:
+            return False
+
+        prefix = self.subword(0, l)
+        if prefix == other or prefix**-1 == other:
+            rest = self.subword(l, len(self))
+            return rest.power_of(other)
+        return False
+
+
+def letter_form_to_array_form(array_form, group):
+    """
+    This method converts a list given with possible repetitions of elements in
+    it. It returns a new list such that repetitions of consecutive elements is
+    removed and replace with a tuple element of size two such that the first
+    index contains `value` and the second index contains the number of
+    consecutive repetitions of `value`.
+
+    """
+    a = list(array_form[:])
+    new_array = []
+    n = 1
+    symbols = group.symbols
+    for i in range(len(a)):
+        if i == len(a) - 1:
+            if a[i] == a[i - 1]:
+                if (-a[i]) in symbols:
+                    new_array.append((-a[i], -n))
+                else:
+                    new_array.append((a[i], n))
+            else:
+                if (-a[i]) in symbols:
+                    new_array.append((-a[i], -1))
+                else:
+                    new_array.append((a[i], 1))
+            return new_array
+        elif a[i] == a[i + 1]:
+            n += 1
+        else:
+            if (-a[i]) in symbols:
+                new_array.append((-a[i], -n))
+            else:
+                new_array.append((a[i], n))
+            n = 1
+
+
+def zero_mul_simp(l, index):
+    """Used to combine two reduced words."""
+    while index >=0 and index < len(l) - 1 and l[index][0] == l[index + 1][0]:
+        exp = l[index][1] + l[index + 1][1]
+        base = l[index][0]
+        l[index] = (base, exp)
+        del l[index + 1]
+        if l[index][1] == 0:
+            del l[index]
+            index -= 1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/galois.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/galois.py
new file mode 100644
index 0000000000000000000000000000000000000000..f8ff89886283903e116bf40e1be6f6131386e802
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/galois.py
@@ -0,0 +1,611 @@
+r"""
+Construct transitive subgroups of symmetric groups, useful in Galois theory.
+
+Besides constructing instances of the :py:class:`~.PermutationGroup` class to
+represent the transitive subgroups of $S_n$ for small $n$, this module provides
+*names* for these groups.
+
+In some applications, it may be preferable to know the name of a group,
+rather than receive an instance of the :py:class:`~.PermutationGroup`
+class, and then have to do extra work to determine which group it is, by
+checking various properties.
+
+Names are instances of ``Enum`` classes defined in this module. With a name in
+hand, the name's ``get_perm_group`` method can then be used to retrieve a
+:py:class:`~.PermutationGroup`.
+
+The names used for groups in this module are taken from [1].
+
+References
+==========
+
+.. [1] Cohen, H. *A Course in Computational Algebraic Number Theory*.
+
+"""
+
+from collections import defaultdict
+from enum import Enum
+import itertools
+
+from sympy.combinatorics.named_groups import (
+    SymmetricGroup, AlternatingGroup, CyclicGroup, DihedralGroup,
+    set_symmetric_group_properties, set_alternating_group_properties,
+)
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.combinatorics.permutations import Permutation
+
+
+class S1TransitiveSubgroups(Enum):
+    """
+    Names for the transitive subgroups of S1.
+    """
+    S1 = "S1"
+
+    def get_perm_group(self):
+        return SymmetricGroup(1)
+
+
+class S2TransitiveSubgroups(Enum):
+    """
+    Names for the transitive subgroups of S2.
+    """
+    S2 = "S2"
+
+    def get_perm_group(self):
+        return SymmetricGroup(2)
+
+
+class S3TransitiveSubgroups(Enum):
+    """
+    Names for the transitive subgroups of S3.
+    """
+    A3 = "A3"
+    S3 = "S3"
+
+    def get_perm_group(self):
+        if self == S3TransitiveSubgroups.A3:
+            return AlternatingGroup(3)
+        elif self == S3TransitiveSubgroups.S3:
+            return SymmetricGroup(3)
+
+
+class S4TransitiveSubgroups(Enum):
+    """
+    Names for the transitive subgroups of S4.
+    """
+    C4 = "C4"
+    V = "V"
+    D4 = "D4"
+    A4 = "A4"
+    S4 = "S4"
+
+    def get_perm_group(self):
+        if self == S4TransitiveSubgroups.C4:
+            return CyclicGroup(4)
+        elif self == S4TransitiveSubgroups.V:
+            return four_group()
+        elif self == S4TransitiveSubgroups.D4:
+            return DihedralGroup(4)
+        elif self == S4TransitiveSubgroups.A4:
+            return AlternatingGroup(4)
+        elif self == S4TransitiveSubgroups.S4:
+            return SymmetricGroup(4)
+
+
+class S5TransitiveSubgroups(Enum):
+    """
+    Names for the transitive subgroups of S5.
+    """
+    C5 = "C5"
+    D5 = "D5"
+    M20 = "M20"
+    A5 = "A5"
+    S5 = "S5"
+
+    def get_perm_group(self):
+        if self == S5TransitiveSubgroups.C5:
+            return CyclicGroup(5)
+        elif self == S5TransitiveSubgroups.D5:
+            return DihedralGroup(5)
+        elif self == S5TransitiveSubgroups.M20:
+            return M20()
+        elif self == S5TransitiveSubgroups.A5:
+            return AlternatingGroup(5)
+        elif self == S5TransitiveSubgroups.S5:
+            return SymmetricGroup(5)
+
+
+class S6TransitiveSubgroups(Enum):
+    """
+    Names for the transitive subgroups of S6.
+    """
+    C6 = "C6"
+    S3 = "S3"
+    D6 = "D6"
+    A4 = "A4"
+    G18 = "G18"
+    A4xC2 = "A4 x C2"
+    S4m = "S4-"
+    S4p = "S4+"
+    G36m = "G36-"
+    G36p = "G36+"
+    S4xC2 = "S4 x C2"
+    PSL2F5 = "PSL2(F5)"
+    G72 = "G72"
+    PGL2F5 = "PGL2(F5)"
+    A6 = "A6"
+    S6 = "S6"
+
+    def get_perm_group(self):
+        if self == S6TransitiveSubgroups.C6:
+            return CyclicGroup(6)
+        elif self == S6TransitiveSubgroups.S3:
+            return S3_in_S6()
+        elif self == S6TransitiveSubgroups.D6:
+            return DihedralGroup(6)
+        elif self == S6TransitiveSubgroups.A4:
+            return A4_in_S6()
+        elif self == S6TransitiveSubgroups.G18:
+            return G18()
+        elif self == S6TransitiveSubgroups.A4xC2:
+            return A4xC2()
+        elif self == S6TransitiveSubgroups.S4m:
+            return S4m()
+        elif self == S6TransitiveSubgroups.S4p:
+            return S4p()
+        elif self == S6TransitiveSubgroups.G36m:
+            return G36m()
+        elif self == S6TransitiveSubgroups.G36p:
+            return G36p()
+        elif self == S6TransitiveSubgroups.S4xC2:
+            return S4xC2()
+        elif self == S6TransitiveSubgroups.PSL2F5:
+            return PSL2F5()
+        elif self == S6TransitiveSubgroups.G72:
+            return G72()
+        elif self == S6TransitiveSubgroups.PGL2F5:
+            return PGL2F5()
+        elif self == S6TransitiveSubgroups.A6:
+            return AlternatingGroup(6)
+        elif self == S6TransitiveSubgroups.S6:
+            return SymmetricGroup(6)
+
+
+def four_group():
+    """
+    Return a representation of the Klein four-group as a transitive subgroup
+    of S4.
+    """
+    return PermutationGroup(
+        Permutation(0, 1)(2, 3),
+        Permutation(0, 2)(1, 3)
+    )
+
+
+def M20():
+    """
+    Return a representation of the metacyclic group M20, a transitive subgroup
+    of S5 that is one of the possible Galois groups for polys of degree 5.
+
+    Notes
+    =====
+
+    See [1], Page 323.
+
+    """
+    G = PermutationGroup(Permutation(0, 1, 2, 3, 4), Permutation(1, 2, 4, 3))
+    G._degree = 5
+    G._order = 20
+    G._is_transitive = True
+    G._is_sym = False
+    G._is_alt = False
+    G._is_cyclic = False
+    G._is_dihedral = False
+    return G
+
+
+def S3_in_S6():
+    """
+    Return a representation of S3 as a transitive subgroup of S6.
+
+    Notes
+    =====
+
+    The representation is found by viewing the group as the symmetries of a
+    triangular prism.
+
+    """
+    G = PermutationGroup(Permutation(0, 1, 2)(3, 4, 5), Permutation(0, 3)(2, 4)(1, 5))
+    set_symmetric_group_properties(G, 3, 6)
+    return G
+
+
+def A4_in_S6():
+    """
+    Return a representation of A4 as a transitive subgroup of S6.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    G = PermutationGroup(Permutation(0, 4, 5)(1, 3, 2), Permutation(0, 1, 2)(3, 5, 4))
+    set_alternating_group_properties(G, 4, 6)
+    return G
+
+
+def S4m():
+    """
+    Return a representation of the S4- transitive subgroup of S6.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    G = PermutationGroup(Permutation(1, 4, 5, 3), Permutation(0, 4)(1, 5)(2, 3))
+    set_symmetric_group_properties(G, 4, 6)
+    return G
+
+
+def S4p():
+    """
+    Return a representation of the S4+ transitive subgroup of S6.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    G = PermutationGroup(Permutation(0, 2, 4, 1)(3, 5), Permutation(0, 3)(4, 5))
+    set_symmetric_group_properties(G, 4, 6)
+    return G
+
+
+def A4xC2():
+    """
+    Return a representation of the (A4 x C2) transitive subgroup of S6.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    return PermutationGroup(
+        Permutation(0, 4, 5)(1, 3, 2), Permutation(0, 1, 2)(3, 5, 4),
+        Permutation(5)(2, 4))
+
+
+def S4xC2():
+    """
+    Return a representation of the (S4 x C2) transitive subgroup of S6.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    return PermutationGroup(
+        Permutation(1, 4, 5, 3), Permutation(0, 4)(1, 5)(2, 3),
+        Permutation(1, 4)(3, 5))
+
+
+def G18():
+    """
+    Return a representation of the group G18, a transitive subgroup of S6
+    isomorphic to the semidirect product of C3^2 with C2.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    return PermutationGroup(
+        Permutation(5)(0, 1, 2), Permutation(3, 4, 5),
+        Permutation(0, 4)(1, 5)(2, 3))
+
+
+def G36m():
+    """
+    Return a representation of the group G36-, a transitive subgroup of S6
+    isomorphic to the semidirect product of C3^2 with C2^2.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    return PermutationGroup(
+        Permutation(5)(0, 1, 2), Permutation(3, 4, 5),
+        Permutation(1, 2)(3, 5), Permutation(0, 4)(1, 5)(2, 3))
+
+
+def G36p():
+    """
+    Return a representation of the group G36+, a transitive subgroup of S6
+    isomorphic to the semidirect product of C3^2 with C4.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    return PermutationGroup(
+        Permutation(5)(0, 1, 2), Permutation(3, 4, 5),
+        Permutation(0, 5, 2, 3)(1, 4))
+
+
+def G72():
+    """
+    Return a representation of the group G72, a transitive subgroup of S6
+    isomorphic to the semidirect product of C3^2 with D4.
+
+    Notes
+    =====
+
+    See [1], Page 325.
+
+    """
+    return PermutationGroup(
+        Permutation(5)(0, 1, 2),
+        Permutation(0, 4, 1, 3)(2, 5), Permutation(0, 3)(1, 4)(2, 5))
+
+
+def PSL2F5():
+    r"""
+    Return a representation of the group $PSL_2(\mathbb{F}_5)$, as a transitive
+    subgroup of S6, isomorphic to $A_5$.
+
+    Notes
+    =====
+
+    This was computed using :py:func:`~.find_transitive_subgroups_of_S6`.
+
+    """
+    G = PermutationGroup(
+        Permutation(0, 4, 5)(1, 3, 2), Permutation(0, 4, 3, 1, 5))
+    set_alternating_group_properties(G, 5, 6)
+    return G
+
+
+def PGL2F5():
+    r"""
+    Return a representation of the group $PGL_2(\mathbb{F}_5)$, as a transitive
+    subgroup of S6, isomorphic to $S_5$.
+
+    Notes
+    =====
+
+    See [1], Page 325.
+
+    """
+    G = PermutationGroup(
+        Permutation(0, 1, 2, 3, 4), Permutation(0, 5)(1, 2)(3, 4))
+    set_symmetric_group_properties(G, 5, 6)
+    return G
+
+
+def find_transitive_subgroups_of_S6(*targets, print_report=False):
+    r"""
+    Search for certain transitive subgroups of $S_6$.
+
+    The symmetric group $S_6$ has 16 different transitive subgroups, up to
+    conjugacy. Some are more easily constructed than others. For example, the
+    dihedral group $D_6$ is immediately found, but it is not at all obvious how
+    to realize $S_4$ or $S_5$ *transitively* within $S_6$.
+
+    In some cases there are well-known constructions that can be used. For
+    example, $S_5$ is isomorphic to $PGL_2(\mathbb{F}_5)$, which acts in a
+    natural way on the projective line $P^1(\mathbb{F}_5)$, a set of order 6.
+
+    In absence of such special constructions however, we can simply search for
+    generators. For example, transitive instances of $A_4$ and $S_4$ can be
+    found within $S_6$ in this way.
+
+    Once we are engaged in such searches, it may then be easier (if less
+    elegant) to find even those groups like $S_5$ that do have special
+    constructions, by mere search.
+
+    This function locates generators for transitive instances in $S_6$ of the
+    following subgroups:
+
+    * $A_4$
+    * $S_4^-$ ($S_4$ not contained within $A_6$)
+    * $S_4^+$ ($S_4$ contained within $A_6$)
+    * $A_4 \times C_2$
+    * $S_4 \times C_2$
+    * $G_{18}   = C_3^2 \rtimes C_2$
+    * $G_{36}^- = C_3^2 \rtimes C_2^2$
+    * $G_{36}^+ = C_3^2 \rtimes C_4$
+    * $G_{72}   = C_3^2 \rtimes D_4$
+    * $A_5$
+    * $S_5$
+
+    Note: Each of these groups also has a dedicated function in this module
+    that returns the group immediately, using generators that were found by
+    this search procedure.
+
+    The search procedure serves as a record of how these generators were
+    found. Also, due to randomness in the generation of the elements of
+    permutation groups, it can be called again, in order to (probably) get
+    different generators for the same groups.
+
+    Parameters
+    ==========
+
+    targets : list of :py:class:`~.S6TransitiveSubgroups` values
+        The groups you want to find.
+
+    print_report : bool (default False)
+        If True, print to stdout the generators found for each group.
+
+    Returns
+    =======
+
+    dict
+        mapping each name in *targets* to the :py:class:`~.PermutationGroup`
+        that was found
+
+    References
+    ==========
+
+    .. [2] https://en.wikipedia.org/wiki/Projective_linear_group#Exceptional_isomorphisms
+    .. [3] https://en.wikipedia.org/wiki/Automorphisms_of_the_symmetric_and_alternating_groups#PGL%282,5%29
+
+    """
+    def elts_by_order(G):
+        """Sort the elements of a group by their order. """
+        elts = defaultdict(list)
+        for g in G.elements:
+            elts[g.order()].append(g)
+        return elts
+
+    def order_profile(G, name=None):
+        """Determine how many elements a group has, of each order. """
+        elts = elts_by_order(G)
+        profile = {o:len(e) for o, e in elts.items()}
+        if name:
+            print(f'{name}: ' + ' '.join(f'{len(profile[r])}@{r}' for r in sorted(profile.keys())))
+        return profile
+
+    S6 = SymmetricGroup(6)
+    A6 = AlternatingGroup(6)
+    S6_by_order = elts_by_order(S6)
+
+    def search(existing_gens, needed_gen_orders, order, alt=None, profile=None, anti_profile=None):
+        """
+        Find a transitive subgroup of S6.
+
+        Parameters
+        ==========
+
+        existing_gens : list of Permutation
+            Optionally empty list of generators that must be in the group.
+
+        needed_gen_orders : list of positive int
+            Nonempty list of the orders of the additional generators that are
+            to be found.
+
+        order: int
+            The order of the group being sought.
+
+        alt: bool, None
+            If True, require the group to be contained in A6.
+            If False, require the group not to be contained in A6.
+
+        profile : dict
+            If given, the group's order profile must equal this.
+
+        anti_profile : dict
+            If given, the group's order profile must *not* equal this.
+
+        """
+        for gens in itertools.product(*[S6_by_order[n] for n in needed_gen_orders]):
+            if len(set(gens)) < len(gens):
+                continue
+            G = PermutationGroup(existing_gens + list(gens))
+            if G.order() == order and G.is_transitive():
+                if alt is not None and G.is_subgroup(A6) != alt:
+                    continue
+                if profile and order_profile(G) != profile:
+                    continue
+                if anti_profile and order_profile(G) == anti_profile:
+                    continue
+                return G
+
+    def match_known_group(G, alt=None):
+        needed = [g.order() for g in G.generators]
+        return search([], needed, G.order(), alt=alt, profile=order_profile(G))
+
+    found = {}
+
+    def finish_up(name, G):
+        found[name] = G
+        if print_report:
+            print("=" * 40)
+            print(f"{name}:")
+            print(G.generators)
+
+    if S6TransitiveSubgroups.A4 in targets or S6TransitiveSubgroups.A4xC2 in targets:
+        A4_in_S6 = match_known_group(AlternatingGroup(4))
+        finish_up(S6TransitiveSubgroups.A4, A4_in_S6)
+
+    if S6TransitiveSubgroups.S4m in targets or S6TransitiveSubgroups.S4xC2 in targets:
+        S4m_in_S6 = match_known_group(SymmetricGroup(4), alt=False)
+        finish_up(S6TransitiveSubgroups.S4m, S4m_in_S6)
+
+    if S6TransitiveSubgroups.S4p in targets:
+        S4p_in_S6 = match_known_group(SymmetricGroup(4), alt=True)
+        finish_up(S6TransitiveSubgroups.S4p, S4p_in_S6)
+
+    if S6TransitiveSubgroups.A4xC2 in targets:
+        A4xC2_in_S6 = search(A4_in_S6.generators, [2], 24, anti_profile=order_profile(SymmetricGroup(4)))
+        finish_up(S6TransitiveSubgroups.A4xC2, A4xC2_in_S6)
+
+    if S6TransitiveSubgroups.S4xC2 in targets:
+        S4xC2_in_S6 = search(S4m_in_S6.generators, [2], 48)
+        finish_up(S6TransitiveSubgroups.S4xC2, S4xC2_in_S6)
+
+    # For the normal factor N = C3^2 in any of the G_n subgroups, we take one
+    # obvious instance of C3^2 in S6:
+    N_gens = [Permutation(5)(0, 1, 2), Permutation(5)(3, 4, 5)]
+
+    if S6TransitiveSubgroups.G18 in targets:
+        G18_in_S6 = search(N_gens, [2], 18)
+        finish_up(S6TransitiveSubgroups.G18, G18_in_S6)
+
+    if S6TransitiveSubgroups.G36m in targets:
+        G36m_in_S6 = search(N_gens, [2, 2], 36, alt=False)
+        finish_up(S6TransitiveSubgroups.G36m, G36m_in_S6)
+
+    if S6TransitiveSubgroups.G36p in targets:
+        G36p_in_S6 = search(N_gens, [4], 36, alt=True)
+        finish_up(S6TransitiveSubgroups.G36p, G36p_in_S6)
+
+    if S6TransitiveSubgroups.G72 in targets:
+        G72_in_S6 = search(N_gens, [4, 2], 72)
+        finish_up(S6TransitiveSubgroups.G72, G72_in_S6)
+
+    # The PSL2(F5) and PGL2(F5) subgroups are isomorphic to A5 and S5, resp.
+
+    if S6TransitiveSubgroups.PSL2F5 in targets:
+        PSL2F5_in_S6 = match_known_group(AlternatingGroup(5))
+        finish_up(S6TransitiveSubgroups.PSL2F5, PSL2F5_in_S6)
+
+    if S6TransitiveSubgroups.PGL2F5 in targets:
+        PGL2F5_in_S6 = match_known_group(SymmetricGroup(5))
+        finish_up(S6TransitiveSubgroups.PGL2F5, PGL2F5_in_S6)
+
+    # There is little need to "search" for any of the groups C6, S3, D6, A6,
+    # or S6, since they all have obvious realizations within S6. However, we
+    # support them here just in case a random representation is desired.
+
+    if S6TransitiveSubgroups.C6 in targets:
+        C6 = match_known_group(CyclicGroup(6))
+        finish_up(S6TransitiveSubgroups.C6, C6)
+
+    if S6TransitiveSubgroups.S3 in targets:
+        S3 = match_known_group(SymmetricGroup(3))
+        finish_up(S6TransitiveSubgroups.S3, S3)
+
+    if S6TransitiveSubgroups.D6 in targets:
+        D6 = match_known_group(DihedralGroup(6))
+        finish_up(S6TransitiveSubgroups.D6, D6)
+
+    if S6TransitiveSubgroups.A6 in targets:
+        A6 = match_known_group(A6)
+        finish_up(S6TransitiveSubgroups.A6, A6)
+
+    if S6TransitiveSubgroups.S6 in targets:
+        S6 = match_known_group(S6)
+        finish_up(S6TransitiveSubgroups.S6, S6)
+
+    return found
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/generators.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/generators.py
new file mode 100644
index 0000000000000000000000000000000000000000..19e274a4c5b4bf0781855db6bc6bf499349fff31
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/generators.py
@@ -0,0 +1,301 @@
+from sympy.combinatorics.permutations import Permutation
+from sympy.core.symbol import symbols
+from sympy.matrices import Matrix
+from sympy.utilities.iterables import variations, rotate_left
+
+
+def symmetric(n):
+    """
+    Generates the symmetric group of order n, Sn.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.generators import symmetric
+    >>> list(symmetric(3))
+    [(2), (1 2), (2)(0 1), (0 1 2), (0 2 1), (0 2)]
+    """
+    yield from (Permutation(perm) for perm in variations(range(n), n))
+
+
+def cyclic(n):
+    """
+    Generates the cyclic group of order n, Cn.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.generators import cyclic
+    >>> list(cyclic(5))
+    [(4), (0 1 2 3 4), (0 2 4 1 3),
+     (0 3 1 4 2), (0 4 3 2 1)]
+
+    See Also
+    ========
+
+    dihedral
+    """
+    gen = list(range(n))
+    for i in range(n):
+        yield Permutation(gen)
+        gen = rotate_left(gen, 1)
+
+
+def alternating(n):
+    """
+    Generates the alternating group of order n, An.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.generators import alternating
+    >>> list(alternating(3))
+    [(2), (0 1 2), (0 2 1)]
+    """
+    for perm in variations(range(n), n):
+        p = Permutation(perm)
+        if p.is_even:
+            yield p
+
+
+def dihedral(n):
+    """
+    Generates the dihedral group of order 2n, Dn.
+
+    The result is given as a subgroup of Sn, except for the special cases n=1
+    (the group S2) and n=2 (the Klein 4-group) where that's not possible
+    and embeddings in S2 and S4 respectively are given.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.generators import dihedral
+    >>> list(dihedral(3))
+    [(2), (0 2), (0 1 2), (1 2), (0 2 1), (2)(0 1)]
+
+    See Also
+    ========
+
+    cyclic
+    """
+    if n == 1:
+        yield Permutation([0, 1])
+        yield Permutation([1, 0])
+    elif n == 2:
+        yield Permutation([0, 1, 2, 3])
+        yield Permutation([1, 0, 3, 2])
+        yield Permutation([2, 3, 0, 1])
+        yield Permutation([3, 2, 1, 0])
+    else:
+        gen = list(range(n))
+        for i in range(n):
+            yield Permutation(gen)
+            yield Permutation(gen[::-1])
+            gen = rotate_left(gen, 1)
+
+
+def rubik_cube_generators():
+    """Return the permutations of the 3x3 Rubik's cube, see
+    https://www.gap-system.org/Doc/Examples/rubik.html
+    """
+    a = [
+        [(1, 3, 8, 6), (2, 5, 7, 4), (9, 33, 25, 17), (10, 34, 26, 18),
+         (11, 35, 27, 19)],
+        [(9, 11, 16, 14), (10, 13, 15, 12), (1, 17, 41, 40), (4, 20, 44, 37),
+         (6, 22, 46, 35)],
+        [(17, 19, 24, 22), (18, 21, 23, 20), (6, 25, 43, 16), (7, 28, 42, 13),
+         (8, 30, 41, 11)],
+        [(25, 27, 32, 30), (26, 29, 31, 28), (3, 38, 43, 19), (5, 36, 45, 21),
+         (8, 33, 48, 24)],
+        [(33, 35, 40, 38), (34, 37, 39, 36), (3, 9, 46, 32), (2, 12, 47, 29),
+         (1, 14, 48, 27)],
+        [(41, 43, 48, 46), (42, 45, 47, 44), (14, 22, 30, 38),
+         (15, 23, 31, 39), (16, 24, 32, 40)]
+    ]
+    return [Permutation([[i - 1 for i in xi] for xi in x], size=48) for x in a]
+
+
+def rubik(n):
+    """Return permutations for an nxn Rubik's cube.
+
+    Permutations returned are for rotation of each of the slice
+    from the face up to the last face for each of the 3 sides (in this order):
+    front, right and bottom. Hence, the first n - 1 permutations are for the
+    slices from the front.
+    """
+
+    if n < 2:
+        raise ValueError('dimension of cube must be > 1')
+
+    # 1-based reference to rows and columns in Matrix
+    def getr(f, i):
+        return faces[f].col(n - i)
+
+    def getl(f, i):
+        return faces[f].col(i - 1)
+
+    def getu(f, i):
+        return faces[f].row(i - 1)
+
+    def getd(f, i):
+        return faces[f].row(n - i)
+
+    def setr(f, i, s):
+        faces[f][:, n - i] = Matrix(n, 1, s)
+
+    def setl(f, i, s):
+        faces[f][:, i - 1] = Matrix(n, 1, s)
+
+    def setu(f, i, s):
+        faces[f][i - 1, :] = Matrix(1, n, s)
+
+    def setd(f, i, s):
+        faces[f][n - i, :] = Matrix(1, n, s)
+
+    # motion of a single face
+    def cw(F, r=1):
+        for _ in range(r):
+            face = faces[F]
+            rv = []
+            for c in range(n):
+                for r in range(n - 1, -1, -1):
+                    rv.append(face[r, c])
+            faces[F] = Matrix(n, n, rv)
+
+    def ccw(F):
+        cw(F, 3)
+
+    # motion of plane i from the F side;
+    # fcw(0) moves the F face, fcw(1) moves the plane
+    # just behind the front face, etc...
+    def fcw(i, r=1):
+        for _ in range(r):
+            if i == 0:
+                cw(F)
+            i += 1
+            temp = getr(L, i)
+            setr(L, i, list(getu(D, i)))
+            setu(D, i, list(reversed(getl(R, i))))
+            setl(R, i, list(getd(U, i)))
+            setd(U, i, list(reversed(temp)))
+            i -= 1
+
+    def fccw(i):
+        fcw(i, 3)
+
+    # motion of the entire cube from the F side
+    def FCW(r=1):
+        for _ in range(r):
+            cw(F)
+            ccw(B)
+            cw(U)
+            t = faces[U]
+            cw(L)
+            faces[U] = faces[L]
+            cw(D)
+            faces[L] = faces[D]
+            cw(R)
+            faces[D] = faces[R]
+            faces[R] = t
+
+    def FCCW():
+        FCW(3)
+
+    # motion of the entire cube from the U side
+    def UCW(r=1):
+        for _ in range(r):
+            cw(U)
+            ccw(D)
+            t = faces[F]
+            faces[F] = faces[R]
+            faces[R] = faces[B]
+            faces[B] = faces[L]
+            faces[L] = t
+
+    def UCCW():
+        UCW(3)
+
+    # defining the permutations for the cube
+
+    U, F, R, B, L, D = names = symbols('U, F, R, B, L, D')
+
+    # the faces are represented by nxn matrices
+    faces = {}
+    count = 0
+    for fi in range(6):
+        f = []
+        for a in range(n**2):
+            f.append(count)
+            count += 1
+        faces[names[fi]] = Matrix(n, n, f)
+
+    # this will either return the value of the current permutation
+    # (show != 1) or else append the permutation to the group, g
+    def perm(show=0):
+        # add perm to the list of perms
+        p = []
+        for f in names:
+            p.extend(faces[f])
+        if show:
+            return p
+        g.append(Permutation(p))
+
+    g = []  # container for the group's permutations
+    I = list(range(6*n**2))  # the identity permutation used for checking
+
+    # define permutations corresponding to cw rotations of the planes
+    # up TO the last plane from that direction; by not including the
+    # last plane, the orientation of the cube is maintained.
+
+    # F slices
+    for i in range(n - 1):
+        fcw(i)
+        perm()
+        fccw(i)  # restore
+    assert perm(1) == I
+
+    # R slices
+    # bring R to front
+    UCW()
+    for i in range(n - 1):
+        fcw(i)
+        # put it back in place
+        UCCW()
+        # record
+        perm()
+        # restore
+        # bring face to front
+        UCW()
+        fccw(i)
+    # restore
+    UCCW()
+    assert perm(1) == I
+
+    # D slices
+    # bring up bottom
+    FCW()
+    UCCW()
+    FCCW()
+    for i in range(n - 1):
+        # turn strip
+        fcw(i)
+        # put bottom back on the bottom
+        FCW()
+        UCW()
+        FCCW()
+        # record
+        perm()
+        # restore
+        # bring up bottom
+        FCW()
+        UCCW()
+        FCCW()
+        # turn strip
+        fccw(i)
+    # put bottom back on the bottom
+    FCW()
+    UCW()
+    FCCW()
+    assert perm(1) == I
+
+    return g
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/graycode.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/graycode.py
new file mode 100644
index 0000000000000000000000000000000000000000..930fd337862a70e920a985947d74375b27741293
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/graycode.py
@@ -0,0 +1,430 @@
+from sympy.core import Basic, Integer
+
+import random
+
+
+class GrayCode(Basic):
+    """
+    A Gray code is essentially a Hamiltonian walk on
+    a n-dimensional cube with edge length of one.
+    The vertices of the cube are represented by vectors
+    whose values are binary. The Hamilton walk visits
+    each vertex exactly once. The Gray code for a 3d
+    cube is ['000','100','110','010','011','111','101',
+    '001'].
+
+    A Gray code solves the problem of sequentially
+    generating all possible subsets of n objects in such
+    a way that each subset is obtained from the previous
+    one by either deleting or adding a single object.
+    In the above example, 1 indicates that the object is
+    present, and 0 indicates that its absent.
+
+    Gray codes have applications in statistics as well when
+    we want to compute various statistics related to subsets
+    in an efficient manner.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import GrayCode
+    >>> a = GrayCode(3)
+    >>> list(a.generate_gray())
+    ['000', '001', '011', '010', '110', '111', '101', '100']
+    >>> a = GrayCode(4)
+    >>> list(a.generate_gray())
+    ['0000', '0001', '0011', '0010', '0110', '0111', '0101', '0100', \
+    '1100', '1101', '1111', '1110', '1010', '1011', '1001', '1000']
+
+    References
+    ==========
+
+    .. [1] Nijenhuis,A. and Wilf,H.S.(1978).
+           Combinatorial Algorithms. Academic Press.
+    .. [2] Knuth, D. (2011). The Art of Computer Programming, Vol 4
+           Addison Wesley
+
+
+    """
+
+    _skip = False
+    _current = 0
+    _rank = None
+
+    def __new__(cls, n, *args, **kw_args):
+        """
+        Default constructor.
+
+        It takes a single argument ``n`` which gives the dimension of the Gray
+        code. The starting Gray code string (``start``) or the starting ``rank``
+        may also be given; the default is to start at rank = 0 ('0...0').
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(3)
+        >>> a
+        GrayCode(3)
+        >>> a.n
+        3
+
+        >>> a = GrayCode(3, start='100')
+        >>> a.current
+        '100'
+
+        >>> a = GrayCode(4, rank=4)
+        >>> a.current
+        '0110'
+        >>> a.rank
+        4
+
+        """
+        if n < 1 or int(n) != n:
+            raise ValueError(
+                'Gray code dimension must be a positive integer, not %i' % n)
+        n = Integer(n)
+        args = (n,) + args
+        obj = Basic.__new__(cls, *args)
+        if 'start' in kw_args:
+            obj._current = kw_args["start"]
+            if len(obj._current) > n:
+                raise ValueError('Gray code start has length %i but '
+                'should not be greater than %i' % (len(obj._current), n))
+        elif 'rank' in kw_args:
+            if int(kw_args["rank"]) != kw_args["rank"]:
+                raise ValueError('Gray code rank must be a positive integer, '
+                'not %i' % kw_args["rank"])
+            obj._rank = int(kw_args["rank"]) % obj.selections
+            obj._current = obj.unrank(n, obj._rank)
+        return obj
+
+    def next(self, delta=1):
+        """
+        Returns the Gray code a distance ``delta`` (default = 1) from the
+        current value in canonical order.
+
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(3, start='110')
+        >>> a.next().current
+        '111'
+        >>> a.next(-1).current
+        '010'
+        """
+        return GrayCode(self.n, rank=(self.rank + delta) % self.selections)
+
+    @property
+    def selections(self):
+        """
+        Returns the number of bit vectors in the Gray code.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(3)
+        >>> a.selections
+        8
+        """
+        return 2**self.n
+
+    @property
+    def n(self):
+        """
+        Returns the dimension of the Gray code.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(5)
+        >>> a.n
+        5
+        """
+        return self.args[0]
+
+    def generate_gray(self, **hints):
+        """
+        Generates the sequence of bit vectors of a Gray Code.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(3)
+        >>> list(a.generate_gray())
+        ['000', '001', '011', '010', '110', '111', '101', '100']
+        >>> list(a.generate_gray(start='011'))
+        ['011', '010', '110', '111', '101', '100']
+        >>> list(a.generate_gray(rank=4))
+        ['110', '111', '101', '100']
+
+        See Also
+        ========
+
+        skip
+
+        References
+        ==========
+
+        .. [1] Knuth, D. (2011). The Art of Computer Programming,
+               Vol 4, Addison Wesley
+
+        """
+        bits = self.n
+        start = None
+        if "start" in hints:
+            start = hints["start"]
+        elif "rank" in hints:
+            start = GrayCode.unrank(self.n, hints["rank"])
+        if start is not None:
+            self._current = start
+        current = self.current
+        graycode_bin = gray_to_bin(current)
+        if len(graycode_bin) > self.n:
+            raise ValueError('Gray code start has length %i but should '
+            'not be greater than %i' % (len(graycode_bin), bits))
+        self._current = int(current, 2)
+        graycode_int = int(''.join(graycode_bin), 2)
+        for i in range(graycode_int, 1 << bits):
+            if self._skip:
+                self._skip = False
+            else:
+                yield self.current
+            bbtc = (i ^ (i + 1))
+            gbtc = (bbtc ^ (bbtc >> 1))
+            self._current = (self._current ^ gbtc)
+        self._current = 0
+
+    def skip(self):
+        """
+        Skips the bit generation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(3)
+        >>> for i in a.generate_gray():
+        ...     if i == '010':
+        ...         a.skip()
+        ...     print(i)
+        ...
+        000
+        001
+        011
+        010
+        111
+        101
+        100
+
+        See Also
+        ========
+
+        generate_gray
+        """
+        self._skip = True
+
+    @property
+    def rank(self):
+        """
+        Ranks the Gray code.
+
+        A ranking algorithm determines the position (or rank)
+        of a combinatorial object among all the objects w.r.t.
+        a given order. For example, the 4 bit binary reflected
+        Gray code (BRGC) '0101' has a rank of 6 as it appears in
+        the 6th position in the canonical ordering of the family
+        of 4 bit Gray codes.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> a = GrayCode(3)
+        >>> list(a.generate_gray())
+        ['000', '001', '011', '010', '110', '111', '101', '100']
+        >>> GrayCode(3, start='100').rank
+        7
+        >>> GrayCode(3, rank=7).current
+        '100'
+
+        See Also
+        ========
+
+        unrank
+
+        References
+        ==========
+
+        .. [1] https://web.archive.org/web/20200224064753/http://statweb.stanford.edu/~susan/courses/s208/node12.html
+
+        """
+        if self._rank is None:
+            self._rank = int(gray_to_bin(self.current), 2)
+        return self._rank
+
+    @property
+    def current(self):
+        """
+        Returns the currently referenced Gray code as a bit string.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> GrayCode(3, start='100').current
+        '100'
+        """
+        rv = self._current or '0'
+        if not isinstance(rv, str):
+            rv = bin(rv)[2:]
+        return rv.rjust(self.n, '0')
+
+    @classmethod
+    def unrank(self, n, rank):
+        """
+        Unranks an n-bit sized Gray code of rank k. This method exists
+        so that a derivative GrayCode class can define its own code of
+        a given rank.
+
+        The string here is generated in reverse order to allow for tail-call
+        optimization.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import GrayCode
+        >>> GrayCode(5, rank=3).current
+        '00010'
+        >>> GrayCode.unrank(5, 3)
+        '00010'
+
+        See Also
+        ========
+
+        rank
+        """
+        def _unrank(k, n):
+            if n == 1:
+                return str(k % 2)
+            m = 2**(n - 1)
+            if k < m:
+                return '0' + _unrank(k, n - 1)
+            return '1' + _unrank(m - (k % m) - 1, n - 1)
+        return _unrank(rank, n)
+
+
+def random_bitstring(n):
+    """
+    Generates a random bitlist of length n.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.graycode import random_bitstring
+    >>> random_bitstring(3) # doctest: +SKIP
+    100
+    """
+    return ''.join([random.choice('01') for i in range(n)])
+
+
+def gray_to_bin(bin_list):
+    """
+    Convert from Gray coding to binary coding.
+
+    We assume big endian encoding.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.graycode import gray_to_bin
+    >>> gray_to_bin('100')
+    '111'
+
+    See Also
+    ========
+
+    bin_to_gray
+    """
+    b = [bin_list[0]]
+    for i in range(1, len(bin_list)):
+        b += str(int(b[i - 1] != bin_list[i]))
+    return ''.join(b)
+
+
+def bin_to_gray(bin_list):
+    """
+    Convert from binary coding to gray coding.
+
+    We assume big endian encoding.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.graycode import bin_to_gray
+    >>> bin_to_gray('111')
+    '100'
+
+    See Also
+    ========
+
+    gray_to_bin
+    """
+    b = [bin_list[0]]
+    for i in range(1, len(bin_list)):
+        b += str(int(bin_list[i]) ^ int(bin_list[i - 1]))
+    return ''.join(b)
+
+
+def get_subset_from_bitstring(super_set, bitstring):
+    """
+    Gets the subset defined by the bitstring.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.graycode import get_subset_from_bitstring
+    >>> get_subset_from_bitstring(['a', 'b', 'c', 'd'], '0011')
+    ['c', 'd']
+    >>> get_subset_from_bitstring(['c', 'a', 'c', 'c'], '1100')
+    ['c', 'a']
+
+    See Also
+    ========
+
+    graycode_subsets
+    """
+    if len(super_set) != len(bitstring):
+        raise ValueError("The sizes of the lists are not equal")
+    return [super_set[i] for i, j in enumerate(bitstring)
+            if bitstring[i] == '1']
+
+
+def graycode_subsets(gray_code_set):
+    """
+    Generates the subsets as enumerated by a Gray code.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.graycode import graycode_subsets
+    >>> list(graycode_subsets(['a', 'b', 'c']))
+    [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], \
+    ['a', 'c'], ['a']]
+    >>> list(graycode_subsets(['a', 'b', 'c', 'c']))
+    [[], ['c'], ['c', 'c'], ['c'], ['b', 'c'], ['b', 'c', 'c'], \
+    ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], ['a', 'b', 'c', 'c'], \
+    ['a', 'b', 'c'], ['a', 'c'], ['a', 'c', 'c'], ['a', 'c'], ['a']]
+
+    See Also
+    ========
+
+    get_subset_from_bitstring
+    """
+    for bitstring in list(GrayCode(len(gray_code_set)).generate_gray()):
+        yield get_subset_from_bitstring(gray_code_set, bitstring)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/group_constructs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/group_constructs.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5c16ec254191646b26eee869763e2926e187da5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/group_constructs.py
@@ -0,0 +1,61 @@
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.combinatorics.permutations import Permutation
+from sympy.utilities.iterables import uniq
+
+_af_new = Permutation._af_new
+
+
+def DirectProduct(*groups):
+    """
+    Returns the direct product of several groups as a permutation group.
+
+    Explanation
+    ===========
+
+    This is implemented much like the __mul__ procedure for taking the direct
+    product of two permutation groups, but the idea of shifting the
+    generators is realized in the case of an arbitrary number of groups.
+    A call to DirectProduct(G1, G2, ..., Gn) is generally expected to be faster
+    than a call to G1*G2*...*Gn (and thus the need for this algorithm).
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.group_constructs import DirectProduct
+    >>> from sympy.combinatorics.named_groups import CyclicGroup
+    >>> C = CyclicGroup(4)
+    >>> G = DirectProduct(C, C, C)
+    >>> G.order()
+    64
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.PermutationGroup.__mul__
+
+    """
+    degrees = []
+    gens_count = []
+    total_degree = 0
+    total_gens = 0
+    for group in groups:
+        current_deg = group.degree
+        current_num_gens = len(group.generators)
+        degrees.append(current_deg)
+        total_degree += current_deg
+        gens_count.append(current_num_gens)
+        total_gens += current_num_gens
+    array_gens = []
+    for i in range(total_gens):
+        array_gens.append(list(range(total_degree)))
+    current_gen = 0
+    current_deg = 0
+    for i in range(len(gens_count)):
+        for j in range(current_gen, current_gen + gens_count[i]):
+            gen = ((groups[i].generators)[j - current_gen]).array_form
+            array_gens[j][current_deg:current_deg + degrees[i]] = \
+                [x + current_deg for x in gen]
+        current_gen += gens_count[i]
+        current_deg += degrees[i]
+    perm_gens = list(uniq([_af_new(list(a)) for a in array_gens]))
+    return PermutationGroup(perm_gens, dups=False)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/group_numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/group_numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..8099dfc2ed8a6943aa1261f9374ed84f0ad3c522
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/group_numbers.py
@@ -0,0 +1,294 @@
+from itertools import chain, combinations
+
+from sympy.external.gmpy import gcd
+from sympy.ntheory.factor_ import factorint
+from sympy.utilities.misc import as_int
+
+
+def _is_nilpotent_number(factors: dict) -> bool:
+    """ Check whether `n` is a nilpotent number.
+    Note that ``factors`` is a prime factorization of `n`.
+
+    This is a low-level helper for ``is_nilpotent_number``, for internal use.
+    """
+    for p in factors.keys():
+        for q, e in factors.items():
+            # We want to calculate
+            # any(pow(q, k, p) == 1 for k in range(1, e + 1))
+            m = 1
+            for _ in range(e):
+                m = m*q % p
+                if m == 1:
+                    return False
+    return True
+
+
+def is_nilpotent_number(n) -> bool:
+    """
+    Check whether `n` is a nilpotent number. A number `n` is said to be
+    nilpotent if and only if every finite group of order `n` is nilpotent.
+    For more information see [1]_.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.group_numbers import is_nilpotent_number
+    >>> from sympy import randprime
+    >>> is_nilpotent_number(21)
+    False
+    >>> is_nilpotent_number(randprime(1, 30)**12)
+    True
+
+    References
+    ==========
+
+    .. [1] Pakianathan, J., Shankar, K., Nilpotent Numbers,
+           The American Mathematical Monthly, 107(7), 631-634.
+    .. [2] https://oeis.org/A056867
+
+    """
+    n = as_int(n)
+    if n <= 0:
+        raise ValueError("n must be a positive integer, not %i" % n)
+    return _is_nilpotent_number(factorint(n))
+
+
+def is_abelian_number(n) -> bool:
+    """
+    Check whether `n` is an abelian number. A number `n` is said to be abelian
+    if and only if every finite group of order `n` is abelian. For more
+    information see [1]_.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.group_numbers import is_abelian_number
+    >>> from sympy import randprime
+    >>> is_abelian_number(4)
+    True
+    >>> is_abelian_number(randprime(1, 2000)**2)
+    True
+    >>> is_abelian_number(60)
+    False
+
+    References
+    ==========
+
+    .. [1] Pakianathan, J., Shankar, K., Nilpotent Numbers,
+           The American Mathematical Monthly, 107(7), 631-634.
+    .. [2] https://oeis.org/A051532
+
+    """
+    n = as_int(n)
+    if n <= 0:
+        raise ValueError("n must be a positive integer, not %i" % n)
+    factors = factorint(n)
+    return all(e < 3 for e in factors.values()) and _is_nilpotent_number(factors)
+
+
+def is_cyclic_number(n) -> bool:
+    """
+    Check whether `n` is a cyclic number. A number `n` is said to be cyclic
+    if and only if every finite group of order `n` is cyclic. For more
+    information see [1]_.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.group_numbers import is_cyclic_number
+    >>> from sympy import randprime
+    >>> is_cyclic_number(15)
+    True
+    >>> is_cyclic_number(randprime(1, 2000)**2)
+    False
+    >>> is_cyclic_number(4)
+    False
+
+    References
+    ==========
+
+    .. [1] Pakianathan, J., Shankar, K., Nilpotent Numbers,
+           The American Mathematical Monthly, 107(7), 631-634.
+    .. [2] https://oeis.org/A003277
+
+    """
+    n = as_int(n)
+    if n <= 0:
+        raise ValueError("n must be a positive integer, not %i" % n)
+    factors = factorint(n)
+    return all(e == 1 for e in factors.values()) and _is_nilpotent_number(factors)
+
+
+def _holder_formula(prime_factors):
+    r""" Number of groups of order `n`.
+    where `n` is squarefree and its prime factors are ``prime_factors``.
+    i.e., ``n == math.prod(prime_factors)``
+
+    Explanation
+    ===========
+
+    When `n` is squarefree, the number of groups of order `n` is expressed by
+
+    .. math ::
+        \sum_{d \mid n} \prod_p \frac{p^{c(p, d)} - 1}{p - 1}
+
+    where `n=de`, `p` is the prime factor of `e`,
+    and `c(p, d)` is the number of prime factors `q` of `d` such that `q \equiv 1 \pmod{p}` [2]_.
+
+    The formula is elegant, but can be improved when implemented as an algorithm.
+    Since `n` is assumed to be squarefree, the divisor `d` of `n` can be identified with the power set of prime factors.
+    We let `N` be the set of prime factors of `n`.
+    `F = \{p \in N : \forall q \in N, q \not\equiv 1 \pmod{p} \}, M = N \setminus F`, we have the following.
+
+    .. math ::
+        \sum_{d \in 2^{M}} \prod_{p \in M \setminus d} \frac{p^{c(p, F \cup d)} - 1}{p - 1}
+
+    Practically, many prime factors are expected to be members of `F`, thus reducing computation time.
+
+    Parameters
+    ==========
+
+    prime_factors : set
+        The set of prime factors of ``n``. where `n` is squarefree.
+
+    Returns
+    =======
+
+    int : Number of groups of order ``n``
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.group_numbers import _holder_formula
+    >>> _holder_formula({2}) # n = 2
+    1
+    >>> _holder_formula({2, 3}) # n = 2*3 = 6
+    2
+
+    See Also
+    ========
+
+    groups_count
+
+    References
+    ==========
+
+    .. [1] Otto Holder, Die Gruppen der Ordnungen p^3, pq^2, pqr, p^4,
+           Math. Ann. 43 pp. 301-412 (1893).
+           http://dx.doi.org/10.1007/BF01443651
+    .. [2] John H. Conway, Heiko Dietrich and E.A. O'Brien,
+           Counting groups: gnus, moas and other exotica
+           The Mathematical Intelligencer 30, 6-15 (2008)
+           https://doi.org/10.1007/BF02985731
+
+    """
+    F = {p for p in prime_factors if all(q % p != 1 for q in prime_factors)}
+    M = prime_factors - F
+
+    s = 0
+    powerset = chain.from_iterable(combinations(M, r) for r in range(len(M)+1))
+    for ps in powerset:
+        ps = set(ps)
+        prod = 1
+        for p in M - ps:
+            c = len([q for q in F | ps if q % p == 1])
+            prod *= (p**c - 1) // (p - 1)
+            if not prod:
+                break
+        s += prod
+    return s
+
+
+def groups_count(n):
+    r""" Number of groups of order `n`.
+    In [1]_, ``gnu(n)`` is given, so we follow this notation here as well.
+
+    Parameters
+    ==========
+
+    n : Integer
+        ``n`` is a positive integer
+
+    Returns
+    =======
+
+    int : ``gnu(n)``
+
+    Raises
+    ======
+
+    ValueError
+        Number of groups of order ``n`` is unknown or not implemented.
+        For example, gnu(`2^{11}`) is not yet known.
+        On the other hand, gnu(99) is known to be 2,
+        but this has not yet been implemented in this function.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.group_numbers import groups_count
+    >>> groups_count(3) # There is only one cyclic group of order 3
+    1
+    >>> # There are two groups of order 10: the cyclic group and the dihedral group
+    >>> groups_count(10)
+    2
+
+    See Also
+    ========
+
+    is_cyclic_number
+        `n` is cyclic iff gnu(n) = 1
+
+    References
+    ==========
+
+    .. [1] John H. Conway, Heiko Dietrich and E.A. O'Brien,
+           Counting groups: gnus, moas and other exotica
+           The Mathematical Intelligencer 30, 6-15 (2008)
+           https://doi.org/10.1007/BF02985731
+    .. [2] https://oeis.org/A000001
+
+    """
+    n = as_int(n)
+    if n <= 0:
+        raise ValueError("n must be a positive integer, not %i" % n)
+    factors = factorint(n)
+    if len(factors) == 1:
+        (p, e) = list(factors.items())[0]
+        if p == 2:
+            A000679 = [1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289]
+            if e < len(A000679):
+                return A000679[e]
+        if p == 3:
+            A090091 = [1, 1, 2, 5, 15, 67, 504, 9310, 1396077, 5937876645]
+            if e < len(A090091):
+                return A090091[e]
+        if e <= 2: # gnu(p) = 1, gnu(p**2) = 2
+            return e
+        if e == 3: # gnu(p**3) = 5
+            return 5
+        if e == 4: # if p is an odd prime, gnu(p**4) = 15
+            return 15
+        if e == 5: # if p >= 5, gnu(p**5) is expressed by the following equation
+            return 61 + 2*p + 2*gcd(p-1, 3) + gcd(p-1, 4)
+        if e == 6: # if p >= 6, gnu(p**6) is expressed by the following equation
+            return 3*p**2 + 39*p + 344 +\
+                  24*gcd(p-1, 3) + 11*gcd(p-1, 4) + 2*gcd(p-1, 5)
+        if e == 7: # if p >= 7, gnu(p**7) is expressed by the following equation
+            if p == 5:
+                return 34297
+            return 3*p**5 + 12*p**4 + 44*p**3 + 170*p**2 + 707*p + 2455 +\
+                  (4*p**2 + 44*p + 291)*gcd(p-1, 3) + (p**2 + 19*p + 135)*gcd(p-1, 4) + \
+                  (3*p + 31)*gcd(p-1, 5) + 4*gcd(p-1, 7) + 5*gcd(p-1, 8) + gcd(p-1, 9)
+    if any(e > 1 for e in factors.values()): # n is not squarefree
+        # some known values for small n that have more than 1 factor and are not square free (https://oeis.org/A000001)
+        small = {12: 5, 18: 5, 20: 5, 24: 15, 28: 4, 36: 14, 40: 14, 44: 4, 45: 2, 48: 52,
+                50: 5, 52: 5, 54: 15, 56: 13, 60: 13, 63: 4, 68: 5, 72: 50, 75: 3, 76: 4,
+                80: 52, 84: 15, 88: 12, 90: 10, 92: 4}
+        if n in small:
+            return small[n]
+        raise ValueError("Number of groups of order n is unknown or not implemented")
+    if len(factors) == 2: # n is squarefree semiprime
+        p, q = sorted(factors.keys())
+        return 2 if q % p == 1 else 1
+    return _holder_formula(set(factors.keys()))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/homomorphisms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/homomorphisms.py
new file mode 100644
index 0000000000000000000000000000000000000000..256f56b3aa7c5404d332f42e37d4f1117ea81db7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/homomorphisms.py
@@ -0,0 +1,549 @@
+import itertools
+from sympy.combinatorics.fp_groups import FpGroup, FpSubgroup, simplify_presentation
+from sympy.combinatorics.free_groups import FreeGroup
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.core.intfunc import igcd
+from sympy.functions.combinatorial.numbers import totient
+from sympy.core.singleton import S
+
+class GroupHomomorphism:
+    '''
+    A class representing group homomorphisms. Instantiate using `homomorphism()`.
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B. and O'Brien, E. (2005). Handbook of computational group theory.
+
+    '''
+
+    def __init__(self, domain, codomain, images):
+        self.domain = domain
+        self.codomain = codomain
+        self.images = images
+        self._inverses = None
+        self._kernel = None
+        self._image = None
+
+    def _invs(self):
+        '''
+        Return a dictionary with `{gen: inverse}` where `gen` is a rewriting
+        generator of `codomain` (e.g. strong generator for permutation groups)
+        and `inverse` is an element of its preimage
+
+        '''
+        image = self.image()
+        inverses = {}
+        for k in list(self.images.keys()):
+            v = self.images[k]
+            if not (v in inverses
+                    or v.is_identity):
+                inverses[v] = k
+        if isinstance(self.codomain, PermutationGroup):
+            gens = image.strong_gens
+        else:
+            gens = image.generators
+        for g in gens:
+            if g in inverses or g.is_identity:
+                continue
+            w = self.domain.identity
+            if isinstance(self.codomain, PermutationGroup):
+                parts = image._strong_gens_slp[g][::-1]
+            else:
+                parts = g
+            for s in parts:
+                if s in inverses:
+                    w = w*inverses[s]
+                else:
+                    w = w*inverses[s**-1]**-1
+            inverses[g] = w
+
+        return inverses
+
+    def invert(self, g):
+        '''
+        Return an element of the preimage of ``g`` or of each element
+        of ``g`` if ``g`` is a list.
+
+        Explanation
+        ===========
+
+        If the codomain is an FpGroup, the inverse for equal
+        elements might not always be the same unless the FpGroup's
+        rewriting system is confluent. However, making a system
+        confluent can be time-consuming. If it's important, try
+        `self.codomain.make_confluent()` first.
+
+        '''
+        from sympy.combinatorics import Permutation
+        from sympy.combinatorics.free_groups import FreeGroupElement
+        if isinstance(g, (Permutation, FreeGroupElement)):
+            if isinstance(self.codomain, FpGroup):
+                g = self.codomain.reduce(g)
+            if self._inverses is None:
+                self._inverses = self._invs()
+            image = self.image()
+            w = self.domain.identity
+            if isinstance(self.codomain, PermutationGroup):
+                gens = image.generator_product(g)[::-1]
+            else:
+                gens = g
+            # the following can't be "for s in gens:"
+            # because that would be equivalent to
+            # "for s in gens.array_form:" when g is
+            # a FreeGroupElement. On the other hand,
+            # when you call gens by index, the generator
+            # (or inverse) at position i is returned.
+            for i in range(len(gens)):
+                s = gens[i]
+                if s.is_identity:
+                    continue
+                if s in self._inverses:
+                    w = w*self._inverses[s]
+                else:
+                    w = w*self._inverses[s**-1]**-1
+            return w
+        elif isinstance(g, list):
+            return [self.invert(e) for e in g]
+
+    def kernel(self):
+        '''
+        Compute the kernel of `self`.
+
+        '''
+        if self._kernel is None:
+            self._kernel = self._compute_kernel()
+        return self._kernel
+
+    def _compute_kernel(self):
+        G = self.domain
+        G_order = G.order()
+        if G_order is S.Infinity:
+            raise NotImplementedError(
+                "Kernel computation is not implemented for infinite groups")
+        gens = []
+        if isinstance(G, PermutationGroup):
+            K = PermutationGroup(G.identity)
+        else:
+            K = FpSubgroup(G, gens, normal=True)
+        i = self.image().order()
+        while K.order()*i != G_order:
+            r = G.random()
+            k = r*self.invert(self(r))**-1
+            if k not in K:
+                gens.append(k)
+                if isinstance(G, PermutationGroup):
+                    K = PermutationGroup(gens)
+                else:
+                    K = FpSubgroup(G, gens, normal=True)
+        return K
+
+    def image(self):
+        '''
+        Compute the image of `self`.
+
+        '''
+        if self._image is None:
+            values = list(set(self.images.values()))
+            if isinstance(self.codomain, PermutationGroup):
+                self._image = self.codomain.subgroup(values)
+            else:
+                self._image = FpSubgroup(self.codomain, values)
+        return self._image
+
+    def _apply(self, elem):
+        '''
+        Apply `self` to `elem`.
+
+        '''
+        if elem not in self.domain:
+            if isinstance(elem, (list, tuple)):
+                return [self._apply(e) for e in elem]
+            raise ValueError("The supplied element does not belong to the domain")
+        if elem.is_identity:
+            return self.codomain.identity
+        else:
+            images = self.images
+            value = self.codomain.identity
+            if isinstance(self.domain, PermutationGroup):
+                gens = self.domain.generator_product(elem, original=True)
+                for g in gens:
+                    if g in self.images:
+                        value = images[g]*value
+                    else:
+                        value = images[g**-1]**-1*value
+            else:
+                i = 0
+                for _, p in elem.array_form:
+                    if p < 0:
+                        g = elem[i]**-1
+                    else:
+                        g = elem[i]
+                    value = value*images[g]**p
+                    i += abs(p)
+        return value
+
+    def __call__(self, elem):
+        return self._apply(elem)
+
+    def is_injective(self):
+        '''
+        Check if the homomorphism is injective
+
+        '''
+        return self.kernel().order() == 1
+
+    def is_surjective(self):
+        '''
+        Check if the homomorphism is surjective
+
+        '''
+        im = self.image().order()
+        oth = self.codomain.order()
+        if im is S.Infinity and oth is S.Infinity:
+            return None
+        else:
+            return im == oth
+
+    def is_isomorphism(self):
+        '''
+        Check if `self` is an isomorphism.
+
+        '''
+        return self.is_injective() and self.is_surjective()
+
+    def is_trivial(self):
+        '''
+        Check is `self` is a trivial homomorphism, i.e. all elements
+        are mapped to the identity.
+
+        '''
+        return self.image().order() == 1
+
+    def compose(self, other):
+        '''
+        Return the composition of `self` and `other`, i.e.
+        the homomorphism phi such that for all g in the domain
+        of `other`, phi(g) = self(other(g))
+
+        '''
+        if not other.image().is_subgroup(self.domain):
+            raise ValueError("The image of `other` must be a subgroup of "
+                    "the domain of `self`")
+        images = {g: self(other(g)) for g in other.images}
+        return GroupHomomorphism(other.domain, self.codomain, images)
+
+    def restrict_to(self, H):
+        '''
+        Return the restriction of the homomorphism to the subgroup `H`
+        of the domain.
+
+        '''
+        if not isinstance(H, PermutationGroup) or not H.is_subgroup(self.domain):
+            raise ValueError("Given H is not a subgroup of the domain")
+        domain = H
+        images = {g: self(g) for g in H.generators}
+        return GroupHomomorphism(domain, self.codomain, images)
+
+    def invert_subgroup(self, H):
+        '''
+        Return the subgroup of the domain that is the inverse image
+        of the subgroup ``H`` of the homomorphism image
+
+        '''
+        if not H.is_subgroup(self.image()):
+            raise ValueError("Given H is not a subgroup of the image")
+        gens = []
+        P = PermutationGroup(self.image().identity)
+        for h in H.generators:
+            h_i = self.invert(h)
+            if h_i not in P:
+                gens.append(h_i)
+                P = PermutationGroup(gens)
+            for k in self.kernel().generators:
+                if k*h_i not in P:
+                    gens.append(k*h_i)
+                    P = PermutationGroup(gens)
+        return P
+
+def homomorphism(domain, codomain, gens, images=(), check=True):
+    '''
+    Create (if possible) a group homomorphism from the group ``domain``
+    to the group ``codomain`` defined by the images of the domain's
+    generators ``gens``. ``gens`` and ``images`` can be either lists or tuples
+    of equal sizes. If ``gens`` is a proper subset of the group's generators,
+    the unspecified generators will be mapped to the identity. If the
+    images are not specified, a trivial homomorphism will be created.
+
+    If the given images of the generators do not define a homomorphism,
+    an exception is raised.
+
+    If ``check`` is ``False``, do not check whether the given images actually
+    define a homomorphism.
+
+    '''
+    if not isinstance(domain, (PermutationGroup, FpGroup, FreeGroup)):
+        raise TypeError("The domain must be a group")
+    if not isinstance(codomain, (PermutationGroup, FpGroup, FreeGroup)):
+        raise TypeError("The codomain must be a group")
+
+    generators = domain.generators
+    if not all(g in generators for g in gens):
+        raise ValueError("The supplied generators must be a subset of the domain's generators")
+    if not all(g in codomain for g in images):
+        raise ValueError("The images must be elements of the codomain")
+
+    if images and len(images) != len(gens):
+        raise ValueError("The number of images must be equal to the number of generators")
+
+    gens = list(gens)
+    images = list(images)
+
+    images.extend([codomain.identity]*(len(generators)-len(images)))
+    gens.extend([g for g in generators if g not in gens])
+    images = dict(zip(gens,images))
+
+    if check and not _check_homomorphism(domain, codomain, images):
+        raise ValueError("The given images do not define a homomorphism")
+    return GroupHomomorphism(domain, codomain, images)
+
+def _check_homomorphism(domain, codomain, images):
+    """
+    Check that a given mapping of generators to images defines a homomorphism.
+
+    Parameters
+    ==========
+    domain : PermutationGroup, FpGroup, FreeGroup
+    codomain : PermutationGroup, FpGroup, FreeGroup
+    images : dict
+        The set of keys must be equal to domain.generators.
+        The values must be elements of the codomain.
+
+    """
+    pres = domain if hasattr(domain, 'relators') else domain.presentation()
+    rels = pres.relators
+    gens = pres.generators
+    symbols = [g.ext_rep[0] for g in gens]
+    symbols_to_domain_generators = dict(zip(symbols, domain.generators))
+    identity = codomain.identity
+
+    def _image(r):
+        w = identity
+        for symbol, power in r.array_form:
+            g = symbols_to_domain_generators[symbol]
+            w *= images[g]**power
+        return w
+
+    for r in rels:
+        if isinstance(codomain, FpGroup):
+            s = codomain.equals(_image(r), identity)
+            if s is None:
+                # only try to make the rewriting system
+                # confluent when it can't determine the
+                # truth of equality otherwise
+                success = codomain.make_confluent()
+                s = codomain.equals(_image(r), identity)
+                if s is None and not success:
+                    raise RuntimeError("Can't determine if the images "
+                        "define a homomorphism. Try increasing "
+                        "the maximum number of rewriting rules "
+                        "(group._rewriting_system.set_max(new_value); "
+                        "the current value is stored in group._rewriting"
+                        "_system.maxeqns)")
+        else:
+            s = _image(r).is_identity
+        if not s:
+            return False
+    return True
+
+def orbit_homomorphism(group, omega):
+    '''
+    Return the homomorphism induced by the action of the permutation
+    group ``group`` on the set ``omega`` that is closed under the action.
+
+    '''
+    from sympy.combinatorics import Permutation
+    from sympy.combinatorics.named_groups import SymmetricGroup
+    codomain = SymmetricGroup(len(omega))
+    identity = codomain.identity
+    omega = list(omega)
+    images = {g: identity*Permutation([omega.index(o^g) for o in omega]) for g in group.generators}
+    group._schreier_sims(base=omega)
+    H = GroupHomomorphism(group, codomain, images)
+    if len(group.basic_stabilizers) > len(omega):
+        H._kernel = group.basic_stabilizers[len(omega)]
+    else:
+        H._kernel = PermutationGroup([group.identity])
+    return H
+
+def block_homomorphism(group, blocks):
+    '''
+    Return the homomorphism induced by the action of the permutation
+    group ``group`` on the block system ``blocks``. The latter should be
+    of the same form as returned by the ``minimal_block`` method for
+    permutation groups, namely a list of length ``group.degree`` where
+    the i-th entry is a representative of the block i belongs to.
+
+    '''
+    from sympy.combinatorics import Permutation
+    from sympy.combinatorics.named_groups import SymmetricGroup
+
+    n = len(blocks)
+
+    # number the blocks; m is the total number,
+    # b is such that b[i] is the number of the block i belongs to,
+    # p is the list of length m such that p[i] is the representative
+    # of the i-th block
+    m = 0
+    p = []
+    b = [None]*n
+    for i in range(n):
+        if blocks[i] == i:
+            p.append(i)
+            b[i] = m
+            m += 1
+    for i in range(n):
+        b[i] = b[blocks[i]]
+
+    codomain = SymmetricGroup(m)
+    # the list corresponding to the identity permutation in codomain
+    identity = range(m)
+    images = {g: Permutation([b[p[i]^g] for i in identity]) for g in group.generators}
+    H = GroupHomomorphism(group, codomain, images)
+    return H
+
+def group_isomorphism(G, H, isomorphism=True):
+    '''
+    Compute an isomorphism between 2 given groups.
+
+    Parameters
+    ==========
+
+    G : A finite ``FpGroup`` or a ``PermutationGroup``.
+        First group.
+
+    H : A finite ``FpGroup`` or a ``PermutationGroup``
+        Second group.
+
+    isomorphism : bool
+        This is used to avoid the computation of homomorphism
+        when the user only wants to check if there exists
+        an isomorphism between the groups.
+
+    Returns
+    =======
+
+    If isomorphism = False -- Returns a boolean.
+    If isomorphism = True  -- Returns a boolean and an isomorphism between `G` and `H`.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import free_group, Permutation
+    >>> from sympy.combinatorics.perm_groups import PermutationGroup
+    >>> from sympy.combinatorics.fp_groups import FpGroup
+    >>> from sympy.combinatorics.homomorphisms import group_isomorphism
+    >>> from sympy.combinatorics.named_groups import DihedralGroup, AlternatingGroup
+
+    >>> D = DihedralGroup(8)
+    >>> p = Permutation(0, 1, 2, 3, 4, 5, 6, 7)
+    >>> P = PermutationGroup(p)
+    >>> group_isomorphism(D, P)
+    (False, None)
+
+    >>> F, a, b = free_group("a, b")
+    >>> G = FpGroup(F, [a**3, b**3, (a*b)**2])
+    >>> H = AlternatingGroup(4)
+    >>> (check, T) = group_isomorphism(G, H)
+    >>> check
+    True
+    >>> T(b*a*b**-1*a**-1*b**-1)
+    (0 2 3)
+
+    Notes
+    =====
+
+    Uses the approach suggested by Robert Tarjan to compute the isomorphism between two groups.
+    First, the generators of ``G`` are mapped to the elements of ``H`` and
+    we check if the mapping induces an isomorphism.
+
+    '''
+    if not isinstance(G, (PermutationGroup, FpGroup)):
+        raise TypeError("The group must be a PermutationGroup or an FpGroup")
+    if not isinstance(H, (PermutationGroup, FpGroup)):
+        raise TypeError("The group must be a PermutationGroup or an FpGroup")
+
+    if isinstance(G, FpGroup) and isinstance(H, FpGroup):
+        G = simplify_presentation(G)
+        H = simplify_presentation(H)
+        # Two infinite FpGroups with the same generators are isomorphic
+        # when the relators are same but are ordered differently.
+        if G.generators == H.generators and (G.relators).sort() == (H.relators).sort():
+            if not isomorphism:
+                return True
+            return (True, homomorphism(G, H, G.generators, H.generators))
+
+    #  `_H` is the permutation group isomorphic to `H`.
+    _H = H
+    g_order = G.order()
+    h_order = H.order()
+
+    if g_order is S.Infinity:
+        raise NotImplementedError("Isomorphism methods are not implemented for infinite groups.")
+
+    if isinstance(H, FpGroup):
+        if h_order is S.Infinity:
+            raise NotImplementedError("Isomorphism methods are not implemented for infinite groups.")
+        _H, h_isomorphism = H._to_perm_group()
+
+    if (g_order != h_order) or (G.is_abelian != H.is_abelian):
+        if not isomorphism:
+            return False
+        return (False, None)
+
+    if not isomorphism:
+        # Two groups of the same cyclic numbered order
+        # are isomorphic to each other.
+        n = g_order
+        if (igcd(n, totient(n))) == 1:
+            return True
+
+    # Match the generators of `G` with subsets of `_H`
+    gens = list(G.generators)
+    for subset in itertools.permutations(_H, len(gens)):
+        images = list(subset)
+        images.extend([_H.identity]*(len(G.generators)-len(images)))
+        _images = dict(zip(gens,images))
+        if _check_homomorphism(G, _H, _images):
+            if isinstance(H, FpGroup):
+                images = h_isomorphism.invert(images)
+            T =  homomorphism(G, H, G.generators, images, check=False)
+            if T.is_isomorphism():
+                # It is a valid isomorphism
+                if not isomorphism:
+                    return True
+                return (True, T)
+
+    if not isomorphism:
+        return False
+    return (False, None)
+
+def is_isomorphic(G, H):
+    '''
+    Check if the groups are isomorphic to each other
+
+    Parameters
+    ==========
+
+    G : A finite ``FpGroup`` or a ``PermutationGroup``
+        First group.
+
+    H : A finite ``FpGroup`` or a ``PermutationGroup``
+        Second group.
+
+    Returns
+    =======
+
+    boolean
+    '''
+    return group_isomorphism(G, H, isomorphism=False)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/named_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/named_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..59f10c40ef716e3b644e00f936323e9f6936eb88
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/named_groups.py
@@ -0,0 +1,332 @@
+from sympy.combinatorics.group_constructs import DirectProduct
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.combinatorics.permutations import Permutation
+
+_af_new = Permutation._af_new
+
+
+def AbelianGroup(*cyclic_orders):
+    """
+    Returns the direct product of cyclic groups with the given orders.
+
+    Explanation
+    ===========
+
+    According to the structure theorem for finite abelian groups ([1]),
+    every finite abelian group can be written as the direct product of
+    finitely many cyclic groups.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import AbelianGroup
+    >>> AbelianGroup(3, 4)
+    PermutationGroup([
+            (6)(0 1 2),
+            (3 4 5 6)])
+    >>> _.is_group
+    True
+
+    See Also
+    ========
+
+    DirectProduct
+
+    References
+    ==========
+
+    .. [1] https://groupprops.subwiki.org/wiki/Structure_theorem_for_finitely_generated_abelian_groups
+
+    """
+    groups = []
+    degree = 0
+    order = 1
+    for size in cyclic_orders:
+        degree += size
+        order *= size
+        groups.append(CyclicGroup(size))
+    G = DirectProduct(*groups)
+    G._is_abelian = True
+    G._degree = degree
+    G._order = order
+
+    return G
+
+
+def AlternatingGroup(n):
+    """
+    Generates the alternating group on ``n`` elements as a permutation group.
+
+    Explanation
+    ===========
+
+    For ``n > 2``, the generators taken are ``(0 1 2), (0 1 2 ... n-1)`` for
+    ``n`` odd
+    and ``(0 1 2), (1 2 ... n-1)`` for ``n`` even (See [1], p.31, ex.6.9.).
+    After the group is generated, some of its basic properties are set.
+    The cases ``n = 1, 2`` are handled separately.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import AlternatingGroup
+    >>> G = AlternatingGroup(4)
+    >>> G.is_group
+    True
+    >>> a = list(G.generate_dimino())
+    >>> len(a)
+    12
+    >>> all(perm.is_even for perm in a)
+    True
+
+    See Also
+    ========
+
+    SymmetricGroup, CyclicGroup, DihedralGroup
+
+    References
+    ==========
+
+    .. [1] Armstrong, M. "Groups and Symmetry"
+
+    """
+    # small cases are special
+    if n in (1, 2):
+        return PermutationGroup([Permutation([0])])
+
+    a = list(range(n))
+    a[0], a[1], a[2] = a[1], a[2], a[0]
+    gen1 = a
+    if n % 2:
+        a = list(range(1, n))
+        a.append(0)
+        gen2 = a
+    else:
+        a = list(range(2, n))
+        a.append(1)
+        a.insert(0, 0)
+        gen2 = a
+    gens = [gen1, gen2]
+    if gen1 == gen2:
+        gens = gens[:1]
+    G = PermutationGroup([_af_new(a) for a in gens], dups=False)
+
+    set_alternating_group_properties(G, n, n)
+    G._is_alt = True
+    return G
+
+
+def set_alternating_group_properties(G, n, degree):
+    """Set known properties of an alternating group. """
+    if n < 4:
+        G._is_abelian = True
+        G._is_nilpotent = True
+    else:
+        G._is_abelian = False
+        G._is_nilpotent = False
+    if n < 5:
+        G._is_solvable = True
+    else:
+        G._is_solvable = False
+    G._degree = degree
+    G._is_transitive = True
+    G._is_dihedral = False
+
+
+def CyclicGroup(n):
+    """
+    Generates the cyclic group of order ``n`` as a permutation group.
+
+    Explanation
+    ===========
+
+    The generator taken is the ``n``-cycle ``(0 1 2 ... n-1)``
+    (in cycle notation). After the group is generated, some of its basic
+    properties are set.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import CyclicGroup
+    >>> G = CyclicGroup(6)
+    >>> G.is_group
+    True
+    >>> G.order()
+    6
+    >>> list(G.generate_schreier_sims(af=True))
+    [[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1],
+    [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]]
+
+    See Also
+    ========
+
+    SymmetricGroup, DihedralGroup, AlternatingGroup
+
+    """
+    a = list(range(1, n))
+    a.append(0)
+    gen = _af_new(a)
+    G = PermutationGroup([gen])
+
+    G._is_abelian = True
+    G._is_nilpotent = True
+    G._is_solvable = True
+    G._degree = n
+    G._is_transitive = True
+    G._order = n
+    G._is_dihedral = (n == 2)
+    return G
+
+
+def DihedralGroup(n):
+    r"""
+    Generates the dihedral group `D_n` as a permutation group.
+
+    Explanation
+    ===========
+
+    The dihedral group `D_n` is the group of symmetries of the regular
+    ``n``-gon. The generators taken are the ``n``-cycle ``a = (0 1 2 ... n-1)``
+    (a rotation of the ``n``-gon) and ``b = (0 n-1)(1 n-2)...``
+    (a reflection of the ``n``-gon) in cycle rotation. It is easy to see that
+    these satisfy ``a**n = b**2 = 1`` and ``bab = ~a`` so they indeed generate
+    `D_n` (See [1]). After the group is generated, some of its basic properties
+    are set.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import DihedralGroup
+    >>> G = DihedralGroup(5)
+    >>> G.is_group
+    True
+    >>> a = list(G.generate_dimino())
+    >>> [perm.cyclic_form for perm in a]
+    [[], [[0, 1, 2, 3, 4]], [[0, 2, 4, 1, 3]],
+    [[0, 3, 1, 4, 2]], [[0, 4, 3, 2, 1]], [[0, 4], [1, 3]],
+    [[1, 4], [2, 3]], [[0, 1], [2, 4]], [[0, 2], [3, 4]],
+    [[0, 3], [1, 2]]]
+
+    See Also
+    ========
+
+    SymmetricGroup, CyclicGroup, AlternatingGroup
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Dihedral_group
+
+    """
+    # small cases are special
+    if n == 1:
+        return PermutationGroup([Permutation([1, 0])])
+    if n == 2:
+        return PermutationGroup([Permutation([1, 0, 3, 2]),
+               Permutation([2, 3, 0, 1]), Permutation([3, 2, 1, 0])])
+
+    a = list(range(1, n))
+    a.append(0)
+    gen1 = _af_new(a)
+    a = list(range(n))
+    a.reverse()
+    gen2 = _af_new(a)
+    G = PermutationGroup([gen1, gen2])
+    # if n is a power of 2, group is nilpotent
+    if n & (n-1) == 0:
+        G._is_nilpotent = True
+    else:
+        G._is_nilpotent = False
+    G._is_dihedral = True
+    G._is_abelian = False
+    G._is_solvable = True
+    G._degree = n
+    G._is_transitive = True
+    G._order = 2*n
+    return G
+
+
+def SymmetricGroup(n):
+    """
+    Generates the symmetric group on ``n`` elements as a permutation group.
+
+    Explanation
+    ===========
+
+    The generators taken are the ``n``-cycle
+    ``(0 1 2 ... n-1)`` and the transposition ``(0 1)`` (in cycle notation).
+    (See [1]). After the group is generated, some of its basic properties
+    are set.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import SymmetricGroup
+    >>> G = SymmetricGroup(4)
+    >>> G.is_group
+    True
+    >>> G.order()
+    24
+    >>> list(G.generate_schreier_sims(af=True))
+    [[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 1, 2, 0], [0, 2, 3, 1],
+    [1, 3, 0, 2], [2, 0, 1, 3], [3, 2, 0, 1], [0, 3, 1, 2], [1, 0, 2, 3],
+    [2, 1, 3, 0], [3, 0, 1, 2], [0, 1, 3, 2], [1, 2, 0, 3], [2, 3, 1, 0],
+    [3, 1, 0, 2], [0, 2, 1, 3], [1, 3, 2, 0], [2, 0, 3, 1], [3, 2, 1, 0],
+    [0, 3, 2, 1], [1, 0, 3, 2], [2, 1, 0, 3], [3, 0, 2, 1]]
+
+    See Also
+    ========
+
+    CyclicGroup, DihedralGroup, AlternatingGroup
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Symmetric_group#Generators_and_relations
+
+    """
+    if n == 1:
+        G = PermutationGroup([Permutation([0])])
+    elif n == 2:
+        G = PermutationGroup([Permutation([1, 0])])
+    else:
+        a = list(range(1, n))
+        a.append(0)
+        gen1 = _af_new(a)
+        a = list(range(n))
+        a[0], a[1] = a[1], a[0]
+        gen2 = _af_new(a)
+        G = PermutationGroup([gen1, gen2])
+    set_symmetric_group_properties(G, n, n)
+    G._is_sym = True
+    return G
+
+
+def set_symmetric_group_properties(G, n, degree):
+    """Set known properties of a symmetric group. """
+    if n < 3:
+        G._is_abelian = True
+        G._is_nilpotent = True
+    else:
+        G._is_abelian = False
+        G._is_nilpotent = False
+    if n < 5:
+        G._is_solvable = True
+    else:
+        G._is_solvable = False
+    G._degree = degree
+    G._is_transitive = True
+    G._is_dihedral = (n in [2, 3])  # cf Landau's func and Stirling's approx
+
+
+def RubikGroup(n):
+    """Return a group of Rubik's cube generators
+
+    >>> from sympy.combinatorics.named_groups import RubikGroup
+    >>> RubikGroup(2).is_group
+    True
+    """
+    from sympy.combinatorics.generators import rubik
+    if n <= 1:
+        raise ValueError("Invalid cube. n has to be greater than 1")
+    return PermutationGroup(rubik(n))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/partitions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/partitions.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfe646baabbb5bf2350cba859a265ac32bbfaf53
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/partitions.py
@@ -0,0 +1,745 @@
+from sympy.core import Basic, Dict, sympify, Tuple
+from sympy.core.numbers import Integer
+from sympy.core.sorting import default_sort_key
+from sympy.core.sympify import _sympify
+from sympy.functions.combinatorial.numbers import bell
+from sympy.matrices import zeros
+from sympy.sets.sets import FiniteSet, Union
+from sympy.utilities.iterables import flatten, group
+from sympy.utilities.misc import as_int
+
+
+from collections import defaultdict
+
+
+class Partition(FiniteSet):
+    """
+    This class represents an abstract partition.
+
+    A partition is a set of disjoint sets whose union equals a given set.
+
+    See Also
+    ========
+
+    sympy.utilities.iterables.partitions,
+    sympy.utilities.iterables.multiset_partitions
+    """
+
+    _rank = None
+    _partition = None
+
+    def __new__(cls, *partition):
+        """
+        Generates a new partition object.
+
+        This method also verifies if the arguments passed are
+        valid and raises a ValueError if they are not.
+
+        Examples
+        ========
+
+        Creating Partition from Python lists:
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3])
+        >>> a
+        Partition({3}, {1, 2})
+        >>> a.partition
+        [[1, 2], [3]]
+        >>> len(a)
+        2
+        >>> a.members
+        (1, 2, 3)
+
+        Creating Partition from Python sets:
+
+        >>> Partition({1, 2, 3}, {4, 5})
+        Partition({4, 5}, {1, 2, 3})
+
+        Creating Partition from SymPy finite sets:
+
+        >>> from sympy import FiniteSet
+        >>> a = FiniteSet(1, 2, 3)
+        >>> b = FiniteSet(4, 5)
+        >>> Partition(a, b)
+        Partition({4, 5}, {1, 2, 3})
+        """
+        args = []
+        dups = False
+        for arg in partition:
+            if isinstance(arg, list):
+                as_set = set(arg)
+                if len(as_set) < len(arg):
+                    dups = True
+                    break  # error below
+                arg = as_set
+            args.append(_sympify(arg))
+
+        if not all(isinstance(part, FiniteSet) for part in args):
+            raise ValueError(
+                "Each argument to Partition should be " \
+                "a list, set, or a FiniteSet")
+
+        # sort so we have a canonical reference for RGS
+        U = Union(*args)
+        if dups or len(U) < sum(len(arg) for arg in args):
+            raise ValueError("Partition contained duplicate elements.")
+
+        obj = FiniteSet.__new__(cls, *args)
+        obj.members = tuple(U)
+        obj.size = len(U)
+        return obj
+
+    def sort_key(self, order=None):
+        """Return a canonical key that can be used for sorting.
+
+        Ordering is based on the size and sorted elements of the partition
+        and ties are broken with the rank.
+
+        Examples
+        ========
+
+        >>> from sympy import default_sort_key
+        >>> from sympy.combinatorics import Partition
+        >>> from sympy.abc import x
+        >>> a = Partition([1, 2])
+        >>> b = Partition([3, 4])
+        >>> c = Partition([1, x])
+        >>> d = Partition(list(range(4)))
+        >>> l = [d, b, a + 1, a, c]
+        >>> l.sort(key=default_sort_key); l
+        [Partition({1, 2}), Partition({1}, {2}), Partition({1, x}), Partition({3, 4}), Partition({0, 1, 2, 3})]
+        """
+        if order is None:
+            members = self.members
+        else:
+            members = tuple(sorted(self.members,
+                             key=lambda w: default_sort_key(w, order)))
+        return tuple(map(default_sort_key, (self.size, members, self.rank)))
+
+    @property
+    def partition(self):
+        """Return partition as a sorted list of lists.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> Partition([1], [2, 3]).partition
+        [[1], [2, 3]]
+        """
+        if self._partition is None:
+            self._partition = sorted([sorted(p, key=default_sort_key)
+                                      for p in self.args])
+        return self._partition
+
+    def __add__(self, other):
+        """
+        Return permutation whose rank is ``other`` greater than current rank,
+        (mod the maximum rank for the set).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3])
+        >>> a.rank
+        1
+        >>> (a + 1).rank
+        2
+        >>> (a + 100).rank
+        1
+        """
+        other = as_int(other)
+        offset = self.rank + other
+        result = RGS_unrank((offset) %
+                            RGS_enum(self.size),
+                            self.size)
+        return Partition.from_rgs(result, self.members)
+
+    def __sub__(self, other):
+        """
+        Return permutation whose rank is ``other`` less than current rank,
+        (mod the maximum rank for the set).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3])
+        >>> a.rank
+        1
+        >>> (a - 1).rank
+        0
+        >>> (a - 100).rank
+        1
+        """
+        return self.__add__(-other)
+
+    def __le__(self, other):
+        """
+        Checks if a partition is less than or equal to
+        the other based on rank.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3, 4, 5])
+        >>> b = Partition([1], [2, 3], [4], [5])
+        >>> a.rank, b.rank
+        (9, 34)
+        >>> a <= a
+        True
+        >>> a <= b
+        True
+        """
+        return self.sort_key() <= sympify(other).sort_key()
+
+    def __lt__(self, other):
+        """
+        Checks if a partition is less than the other.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3, 4, 5])
+        >>> b = Partition([1], [2, 3], [4], [5])
+        >>> a.rank, b.rank
+        (9, 34)
+        >>> a < b
+        True
+        """
+        return self.sort_key() < sympify(other).sort_key()
+
+    @property
+    def rank(self):
+        """
+        Gets the rank of a partition.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3], [4, 5])
+        >>> a.rank
+        13
+        """
+        if self._rank is not None:
+            return self._rank
+        self._rank = RGS_rank(self.RGS)
+        return self._rank
+
+    @property
+    def RGS(self):
+        """
+        Returns the "restricted growth string" of the partition.
+
+        Explanation
+        ===========
+
+        The RGS is returned as a list of indices, L, where L[i] indicates
+        the block in which element i appears. For example, in a partition
+        of 3 elements (a, b, c) into 2 blocks ([c], [a, b]) the RGS is
+        [1, 1, 0]: "a" is in block 1, "b" is in block 1 and "c" is in block 0.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> a = Partition([1, 2], [3], [4, 5])
+        >>> a.members
+        (1, 2, 3, 4, 5)
+        >>> a.RGS
+        (0, 0, 1, 2, 2)
+        >>> a + 1
+        Partition({3}, {4}, {5}, {1, 2})
+        >>> _.RGS
+        (0, 0, 1, 2, 3)
+        """
+        rgs = {}
+        partition = self.partition
+        for i, part in enumerate(partition):
+            for j in part:
+                rgs[j] = i
+        return tuple([rgs[i] for i in sorted(
+            [i for p in partition for i in p], key=default_sort_key)])
+
+    @classmethod
+    def from_rgs(self, rgs, elements):
+        """
+        Creates a set partition from a restricted growth string.
+
+        Explanation
+        ===========
+
+        The indices given in rgs are assumed to be the index
+        of the element as given in elements *as provided* (the
+        elements are not sorted by this routine). Block numbering
+        starts from 0. If any block was not referenced in ``rgs``
+        an error will be raised.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Partition
+        >>> Partition.from_rgs([0, 1, 2, 0, 1], list('abcde'))
+        Partition({c}, {a, d}, {b, e})
+        >>> Partition.from_rgs([0, 1, 2, 0, 1], list('cbead'))
+        Partition({e}, {a, c}, {b, d})
+        >>> a = Partition([1, 4], [2], [3, 5])
+        >>> Partition.from_rgs(a.RGS, a.members)
+        Partition({2}, {1, 4}, {3, 5})
+        """
+        if len(rgs) != len(elements):
+            raise ValueError('mismatch in rgs and element lengths')
+        max_elem = max(rgs) + 1
+        partition = [[] for i in range(max_elem)]
+        j = 0
+        for i in rgs:
+            partition[i].append(elements[j])
+            j += 1
+        if not all(p for p in partition):
+            raise ValueError('some blocks of the partition were empty.')
+        return Partition(*partition)
+
+
+class IntegerPartition(Basic):
+    """
+    This class represents an integer partition.
+
+    Explanation
+    ===========
+
+    In number theory and combinatorics, a partition of a positive integer,
+    ``n``, also called an integer partition, is a way of writing ``n`` as a
+    list of positive integers that sum to n. Two partitions that differ only
+    in the order of summands are considered to be the same partition; if order
+    matters then the partitions are referred to as compositions. For example,
+    4 has five partitions: [4], [3, 1], [2, 2], [2, 1, 1], and [1, 1, 1, 1];
+    the compositions [1, 2, 1] and [1, 1, 2] are the same as partition
+    [2, 1, 1].
+
+    See Also
+    ========
+
+    sympy.utilities.iterables.partitions,
+    sympy.utilities.iterables.multiset_partitions
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Partition_%28number_theory%29
+    """
+
+    _dict = None
+    _keys = None
+
+    def __new__(cls, partition, integer=None):
+        """
+        Generates a new IntegerPartition object from a list or dictionary.
+
+        Explanation
+        ===========
+
+        The partition can be given as a list of positive integers or a
+        dictionary of (integer, multiplicity) items. If the partition is
+        preceded by an integer an error will be raised if the partition
+        does not sum to that given integer.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> a = IntegerPartition([5, 4, 3, 1, 1])
+        >>> a
+        IntegerPartition(14, (5, 4, 3, 1, 1))
+        >>> print(a)
+        [5, 4, 3, 1, 1]
+        >>> IntegerPartition({1:3, 2:1})
+        IntegerPartition(5, (2, 1, 1, 1))
+
+        If the value that the partition should sum to is given first, a check
+        will be made to see n error will be raised if there is a discrepancy:
+
+        >>> IntegerPartition(10, [5, 4, 3, 1])
+        Traceback (most recent call last):
+        ...
+        ValueError: The partition is not valid
+
+        """
+        if integer is not None:
+            integer, partition = partition, integer
+        if isinstance(partition, (dict, Dict)):
+            _ = []
+            for k, v in sorted(partition.items(), reverse=True):
+                if not v:
+                    continue
+                k, v = as_int(k), as_int(v)
+                _.extend([k]*v)
+            partition = tuple(_)
+        else:
+            partition = tuple(sorted(map(as_int, partition), reverse=True))
+        sum_ok = False
+        if integer is None:
+            integer = sum(partition)
+            sum_ok = True
+        else:
+            integer = as_int(integer)
+
+        if not sum_ok and sum(partition) != integer:
+            raise ValueError("Partition did not add to %s" % integer)
+        if any(i < 1 for i in partition):
+            raise ValueError("All integer summands must be greater than one")
+
+        obj = Basic.__new__(cls, Integer(integer), Tuple(*partition))
+        obj.partition = list(partition)
+        obj.integer = integer
+        return obj
+
+    def prev_lex(self):
+        """Return the previous partition of the integer, n, in lexical order,
+        wrapping around to [1, ..., 1] if the partition is [n].
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> p = IntegerPartition([4])
+        >>> print(p.prev_lex())
+        [3, 1]
+        >>> p.partition > p.prev_lex().partition
+        True
+        """
+        d = defaultdict(int)
+        d.update(self.as_dict())
+        keys = self._keys
+        if keys == [1]:
+            return IntegerPartition({self.integer: 1})
+        if keys[-1] != 1:
+            d[keys[-1]] -= 1
+            if keys[-1] == 2:
+                d[1] = 2
+            else:
+                d[keys[-1] - 1] = d[1] = 1
+        else:
+            d[keys[-2]] -= 1
+            left = d[1] + keys[-2]
+            new = keys[-2]
+            d[1] = 0
+            while left:
+                new -= 1
+                if left - new >= 0:
+                    d[new] += left//new
+                    left -= d[new]*new
+        return IntegerPartition(self.integer, d)
+
+    def next_lex(self):
+        """Return the next partition of the integer, n, in lexical order,
+        wrapping around to [n] if the partition is [1, ..., 1].
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> p = IntegerPartition([3, 1])
+        >>> print(p.next_lex())
+        [4]
+        >>> p.partition < p.next_lex().partition
+        True
+        """
+        d = defaultdict(int)
+        d.update(self.as_dict())
+        key = self._keys
+        a = key[-1]
+        if a == self.integer:
+            d.clear()
+            d[1] = self.integer
+        elif a == 1:
+            if d[a] > 1:
+                d[a + 1] += 1
+                d[a] -= 2
+            else:
+                b = key[-2]
+                d[b + 1] += 1
+                d[1] = (d[b] - 1)*b
+                d[b] = 0
+        else:
+            if d[a] > 1:
+                if len(key) == 1:
+                    d.clear()
+                    d[a + 1] = 1
+                    d[1] = self.integer - a - 1
+                else:
+                    a1 = a + 1
+                    d[a1] += 1
+                    d[1] = d[a]*a - a1
+                    d[a] = 0
+            else:
+                b = key[-2]
+                b1 = b + 1
+                d[b1] += 1
+                need = d[b]*b + d[a]*a - b1
+                d[a] = d[b] = 0
+                d[1] = need
+        return IntegerPartition(self.integer, d)
+
+    def as_dict(self):
+        """Return the partition as a dictionary whose keys are the
+        partition integers and the values are the multiplicity of that
+        integer.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> IntegerPartition([1]*3 + [2] + [3]*4).as_dict()
+        {1: 3, 2: 1, 3: 4}
+        """
+        if self._dict is None:
+            groups = group(self.partition, multiple=False)
+            self._keys = [g[0] for g in groups]
+            self._dict = dict(groups)
+        return self._dict
+
+    @property
+    def conjugate(self):
+        """
+        Computes the conjugate partition of itself.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> a = IntegerPartition([6, 3, 3, 2, 1])
+        >>> a.conjugate
+        [5, 4, 3, 1, 1, 1]
+        """
+        j = 1
+        temp_arr = list(self.partition) + [0]
+        k = temp_arr[0]
+        b = [0]*k
+        while k > 0:
+            while k > temp_arr[j]:
+                b[k - 1] = j
+                k -= 1
+            j += 1
+        return b
+
+    def __lt__(self, other):
+        """Return True if self is less than other when the partition
+        is listed from smallest to biggest.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> a = IntegerPartition([3, 1])
+        >>> a < a
+        False
+        >>> b = a.next_lex()
+        >>> a < b
+        True
+        >>> a == b
+        False
+        """
+        return list(reversed(self.partition)) < list(reversed(other.partition))
+
+    def __le__(self, other):
+        """Return True if self is less than other when the partition
+        is listed from smallest to biggest.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> a = IntegerPartition([4])
+        >>> a <= a
+        True
+        """
+        return list(reversed(self.partition)) <= list(reversed(other.partition))
+
+    def as_ferrers(self, char='#'):
+        """
+        Prints the ferrer diagram of a partition.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.partitions import IntegerPartition
+        >>> print(IntegerPartition([1, 1, 5]).as_ferrers())
+        #####
+        #
+        #
+        """
+        return "\n".join([char*i for i in self.partition])
+
+    def __str__(self):
+        return str(list(self.partition))
+
+
+def random_integer_partition(n, seed=None):
+    """
+    Generates a random integer partition summing to ``n`` as a list
+    of reverse-sorted integers.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.partitions import random_integer_partition
+
+    For the following, a seed is given so a known value can be shown; in
+    practice, the seed would not be given.
+
+    >>> random_integer_partition(100, seed=[1, 1, 12, 1, 2, 1, 85, 1])
+    [85, 12, 2, 1]
+    >>> random_integer_partition(10, seed=[1, 2, 3, 1, 5, 1])
+    [5, 3, 1, 1]
+    >>> random_integer_partition(1)
+    [1]
+    """
+    from sympy.core.random import _randint
+
+    n = as_int(n)
+    if n < 1:
+        raise ValueError('n must be a positive integer')
+
+    randint = _randint(seed)
+
+    partition = []
+    while (n > 0):
+        k = randint(1, n)
+        mult = randint(1, n//k)
+        partition.append((k, mult))
+        n -= k*mult
+    partition.sort(reverse=True)
+    partition = flatten([[k]*m for k, m in partition])
+    return partition
+
+
+def RGS_generalized(m):
+    """
+    Computes the m + 1 generalized unrestricted growth strings
+    and returns them as rows in matrix.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.partitions import RGS_generalized
+    >>> RGS_generalized(6)
+    Matrix([
+    [  1,   1,   1,  1,  1, 1, 1],
+    [  1,   2,   3,  4,  5, 6, 0],
+    [  2,   5,  10, 17, 26, 0, 0],
+    [  5,  15,  37, 77,  0, 0, 0],
+    [ 15,  52, 151,  0,  0, 0, 0],
+    [ 52, 203,   0,  0,  0, 0, 0],
+    [203,   0,   0,  0,  0, 0, 0]])
+    """
+    d = zeros(m + 1)
+    for i in range(m + 1):
+        d[0, i] = 1
+
+    for i in range(1, m + 1):
+        for j in range(m):
+            if j <= m - i:
+                d[i, j] = j * d[i - 1, j] + d[i - 1, j + 1]
+            else:
+                d[i, j] = 0
+    return d
+
+
+def RGS_enum(m):
+    """
+    RGS_enum computes the total number of restricted growth strings
+    possible for a superset of size m.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.partitions import RGS_enum
+    >>> from sympy.combinatorics import Partition
+    >>> RGS_enum(4)
+    15
+    >>> RGS_enum(5)
+    52
+    >>> RGS_enum(6)
+    203
+
+    We can check that the enumeration is correct by actually generating
+    the partitions. Here, the 15 partitions of 4 items are generated:
+
+    >>> a = Partition(list(range(4)))
+    >>> s = set()
+    >>> for i in range(20):
+    ...     s.add(a)
+    ...     a += 1
+    ...
+    >>> assert len(s) == 15
+
+    """
+    if (m < 1):
+        return 0
+    elif (m == 1):
+        return 1
+    else:
+        return bell(m)
+
+
+def RGS_unrank(rank, m):
+    """
+    Gives the unranked restricted growth string for a given
+    superset size.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.partitions import RGS_unrank
+    >>> RGS_unrank(14, 4)
+    [0, 1, 2, 3]
+    >>> RGS_unrank(0, 4)
+    [0, 0, 0, 0]
+    """
+    if m < 1:
+        raise ValueError("The superset size must be >= 1")
+    if rank < 0 or RGS_enum(m) <= rank:
+        raise ValueError("Invalid arguments")
+
+    L = [1] * (m + 1)
+    j = 1
+    D = RGS_generalized(m)
+    for i in range(2, m + 1):
+        v = D[m - i, j]
+        cr = j*v
+        if cr <= rank:
+            L[i] = j + 1
+            rank -= cr
+            j += 1
+        else:
+            L[i] = int(rank / v + 1)
+            rank %= v
+    return [x - 1 for x in L[1:]]
+
+
+def RGS_rank(rgs):
+    """
+    Computes the rank of a restricted growth string.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.partitions import RGS_rank, RGS_unrank
+    >>> RGS_rank([0, 1, 2, 1, 3])
+    42
+    >>> RGS_rank(RGS_unrank(4, 7))
+    4
+    """
+    rgs_size = len(rgs)
+    rank = 0
+    D = RGS_generalized(rgs_size)
+    for i in range(1, rgs_size):
+        n = len(rgs[(i + 1):])
+        m = max(rgs[0:i])
+        rank += D[n, m + 1] * rgs[i]
+    return rank
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/pc_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/pc_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..abf7b82258d8bb61ba350509fcbb3110a035fc88
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/pc_groups.py
@@ -0,0 +1,710 @@
+from sympy.ntheory.primetest import isprime
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.printing.defaults import DefaultPrinting
+from sympy.combinatorics.free_groups import free_group
+
+
+class PolycyclicGroup(DefaultPrinting):
+
+    is_group = True
+    is_solvable = True
+
+    def __init__(self, pc_sequence, pc_series, relative_order, collector=None):
+        """
+
+        Parameters
+        ==========
+
+        pc_sequence : list
+            A sequence of elements whose classes generate the cyclic factor
+            groups of pc_series.
+        pc_series : list
+            A subnormal sequence of subgroups where each factor group is cyclic.
+        relative_order : list
+            The orders of factor groups of pc_series.
+        collector : Collector
+            By default, it is None. Collector class provides the
+            polycyclic presentation with various other functionalities.
+
+        """
+        self.pcgs = pc_sequence
+        self.pc_series = pc_series
+        self.relative_order = relative_order
+        self.collector = Collector(self.pcgs, pc_series, relative_order) if not collector else collector
+
+    def is_prime_order(self):
+        return all(isprime(order) for order in self.relative_order)
+
+    def length(self):
+        return len(self.pcgs)
+
+
+class Collector(DefaultPrinting):
+
+    """
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.
+           "Handbook of Computational Group Theory"
+           Section 8.1.3
+    """
+
+    def __init__(self, pcgs, pc_series, relative_order, free_group_=None, pc_presentation=None):
+        """
+
+        Most of the parameters for the Collector class are the same as for PolycyclicGroup.
+        Others are described below.
+
+        Parameters
+        ==========
+
+        free_group_ : tuple
+            free_group_ provides the mapping of polycyclic generating
+            sequence with the free group elements.
+        pc_presentation : dict
+            Provides the presentation of polycyclic groups with the
+            help of power and conjugate relators.
+
+        See Also
+        ========
+
+        PolycyclicGroup
+
+        """
+        self.pcgs = pcgs
+        self.pc_series = pc_series
+        self.relative_order = relative_order
+        self.free_group = free_group('x:{}'.format(len(pcgs)))[0] if not free_group_ else free_group_
+        self.index = {s: i for i, s in enumerate(self.free_group.symbols)}
+        self.pc_presentation = self.pc_relators()
+
+    def minimal_uncollected_subword(self, word):
+        r"""
+        Returns the minimal uncollected subwords.
+
+        Explanation
+        ===========
+
+        A word ``v`` defined on generators in ``X`` is a minimal
+        uncollected subword of the word ``w`` if ``v`` is a subword
+        of ``w`` and it has one of the following form
+
+        * `v = {x_{i+1}}^{a_j}x_i`
+
+        * `v = {x_{i+1}}^{a_j}{x_i}^{-1}`
+
+        * `v = {x_i}^{a_j}`
+
+        for `a_j` not in `\{1, \ldots, s-1\}`. Where, ``s`` is the power
+        exponent of the corresponding generator.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics import free_group
+        >>> G = SymmetricGroup(4)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> F, x1, x2 = free_group("x1, x2")
+        >>> word = x2**2*x1**7
+        >>> collector.minimal_uncollected_subword(word)
+        ((x2, 2),)
+
+        """
+        # To handle the case word = 
+        if not word:
+            return None
+
+        array = word.array_form
+        re = self.relative_order
+        index = self.index
+
+        for i in range(len(array)):
+            s1, e1 = array[i]
+
+            if re[index[s1]] and (e1 < 0 or e1 > re[index[s1]]-1):
+                return ((s1, e1), )
+
+        for i in range(len(array)-1):
+            s1, e1 = array[i]
+            s2, e2 = array[i+1]
+
+            if index[s1] > index[s2]:
+                e = 1 if e2 > 0 else -1
+                return ((s1, e1), (s2, e))
+
+        return None
+
+    def relations(self):
+        """
+        Separates the given relators of pc presentation in power and
+        conjugate relations.
+
+        Returns
+        =======
+
+        (power_rel, conj_rel)
+            Separates pc presentation into power and conjugate relations.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> G = SymmetricGroup(3)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> power_rel, conj_rel = collector.relations()
+        >>> power_rel
+        {x0**2: (), x1**3: ()}
+        >>> conj_rel
+        {x0**-1*x1*x0: x1**2}
+
+        See Also
+        ========
+
+        pc_relators
+
+        """
+        power_relators = {}
+        conjugate_relators = {}
+        for key, value in self.pc_presentation.items():
+            if len(key.array_form) == 1:
+                power_relators[key] = value
+            else:
+                conjugate_relators[key] = value
+        return power_relators, conjugate_relators
+
+    def subword_index(self, word, w):
+        """
+        Returns the start and ending index of a given
+        subword in a word.
+
+        Parameters
+        ==========
+
+        word : FreeGroupElement
+            word defined on free group elements for a
+            polycyclic group.
+        w : FreeGroupElement
+            subword of a given word, whose starting and
+            ending index to be computed.
+
+        Returns
+        =======
+
+        (i, j)
+            A tuple containing starting and ending index of ``w``
+            in the given word. If not exists, (-1,-1) is returned.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics import free_group
+        >>> G = SymmetricGroup(4)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> F, x1, x2 = free_group("x1, x2")
+        >>> word = x2**2*x1**7
+        >>> w = x2**2*x1
+        >>> collector.subword_index(word, w)
+        (0, 3)
+        >>> w = x1**7
+        >>> collector.subword_index(word, w)
+        (2, 9)
+        >>> w = x1**8
+        >>> collector.subword_index(word, w)
+        (-1, -1)
+
+        """
+        low = -1
+        high = -1
+        for i in range(len(word)-len(w)+1):
+            if word.subword(i, i+len(w)) == w:
+                low = i
+                high = i+len(w)
+                break
+        return low, high
+
+    def map_relation(self, w):
+        """
+        Return a conjugate relation.
+
+        Explanation
+        ===========
+
+        Given a word formed by two free group elements, the
+        corresponding conjugate relation with those free
+        group elements is formed and mapped with the collected
+        word in the polycyclic presentation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics import free_group
+        >>> G = SymmetricGroup(3)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> F, x0, x1 = free_group("x0, x1")
+        >>> w = x1*x0
+        >>> collector.map_relation(w)
+        x1**2
+
+        See Also
+        ========
+
+        pc_presentation
+
+        """
+        array = w.array_form
+        s1 = array[0][0]
+        s2 = array[1][0]
+        key = ((s2, -1), (s1, 1), (s2, 1))
+        key = self.free_group.dtype(key)
+        return self.pc_presentation[key]
+
+
+    def collected_word(self, word):
+        r"""
+        Return the collected form of a word.
+
+        Explanation
+        ===========
+
+        A word ``w`` is called collected, if `w = {x_{i_1}}^{a_1} * \ldots *
+        {x_{i_r}}^{a_r}` with `i_1 < i_2< \ldots < i_r` and `a_j` is in
+        `\{1, \ldots, {s_j}-1\}`.
+
+        Otherwise w is uncollected.
+
+        Parameters
+        ==========
+
+        word : FreeGroupElement
+            An uncollected word.
+
+        Returns
+        =======
+
+        word
+            A collected word of form `w = {x_{i_1}}^{a_1}, \ldots,
+            {x_{i_r}}^{a_r}` with `i_1, i_2, \ldots, i_r` and `a_j \in
+            \{1, \ldots, {s_j}-1\}`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics.perm_groups import PermutationGroup
+        >>> from sympy.combinatorics import free_group
+        >>> G = SymmetricGroup(4)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> F, x0, x1, x2, x3 = free_group("x0, x1, x2, x3")
+        >>> word = x3*x2*x1*x0
+        >>> collected_word = collector.collected_word(word)
+        >>> free_to_perm = {}
+        >>> free_group = collector.free_group
+        >>> for sym, gen in zip(free_group.symbols, collector.pcgs):
+        ...     free_to_perm[sym] = gen
+        >>> G1 = PermutationGroup()
+        >>> for w in word:
+        ...     sym = w[0]
+        ...     perm = free_to_perm[sym]
+        ...     G1 = PermutationGroup([perm] + G1.generators)
+        >>> G2 = PermutationGroup()
+        >>> for w in collected_word:
+        ...     sym = w[0]
+        ...     perm = free_to_perm[sym]
+        ...     G2 = PermutationGroup([perm] + G2.generators)
+
+        The two are not identical, but they are equivalent:
+
+        >>> G1.equals(G2), G1 == G2
+        (True, False)
+
+        See Also
+        ========
+
+        minimal_uncollected_subword
+
+        """
+        free_group = self.free_group
+        while True:
+            w = self.minimal_uncollected_subword(word)
+            if not w:
+                break
+
+            low, high = self.subword_index(word, free_group.dtype(w))
+            if low == -1:
+                continue
+
+            s1, e1 = w[0]
+            if len(w) == 1:
+                re = self.relative_order[self.index[s1]]
+                q = e1 // re
+                r = e1-q*re
+
+                key = ((w[0][0], re), )
+                key = free_group.dtype(key)
+                if self.pc_presentation[key]:
+                    presentation = self.pc_presentation[key].array_form
+                    sym, exp = presentation[0]
+                    word_ = ((w[0][0], r), (sym, q*exp))
+                    word_ = free_group.dtype(word_)
+                else:
+                    if r != 0:
+                        word_ = ((w[0][0], r), )
+                        word_ = free_group.dtype(word_)
+                    else:
+                        word_ = None
+                word = word.eliminate_word(free_group.dtype(w), word_)
+
+            if len(w) == 2 and w[1][1] > 0:
+                s2, e2 = w[1]
+                s2 = ((s2, 1), )
+                s2 = free_group.dtype(s2)
+                word_ = self.map_relation(free_group.dtype(w))
+                word_ = s2*word_**e1
+                word_ = free_group.dtype(word_)
+                word = word.substituted_word(low, high, word_)
+
+            elif len(w) == 2 and w[1][1] < 0:
+                s2, e2 = w[1]
+                s2 = ((s2, 1), )
+                s2 = free_group.dtype(s2)
+                word_ = self.map_relation(free_group.dtype(w))
+                word_ = s2**-1*word_**e1
+                word_ = free_group.dtype(word_)
+                word = word.substituted_word(low, high, word_)
+
+        return word
+
+
+    def pc_relators(self):
+        r"""
+        Return the polycyclic presentation.
+
+        Explanation
+        ===========
+
+        There are two types of relations used in polycyclic
+        presentation.
+
+        * Power relations : Power relators are of the form `x_i^{re_i}`,
+          where `i \in \{0, \ldots, \mathrm{len(pcgs)}\}`, ``x`` represents polycyclic
+          generator and ``re`` is the corresponding relative order.
+
+        * Conjugate relations : Conjugate relators are of the form `x_j^-1x_ix_j`,
+          where `j < i \in \{0, \ldots, \mathrm{len(pcgs)}\}`.
+
+        Returns
+        =======
+
+        A dictionary with power and conjugate relations as key and
+        their collected form as corresponding values.
+
+        Notes
+        =====
+
+        Identity Permutation is mapped with empty ``()``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics.permutations import Permutation
+        >>> S = SymmetricGroup(49).sylow_subgroup(7)
+        >>> der = S.derived_series()
+        >>> G = der[len(der)-2]
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> pcgs = PcGroup.pcgs
+        >>> len(pcgs)
+        6
+        >>> free_group = collector.free_group
+        >>> pc_resentation = collector.pc_presentation
+        >>> free_to_perm = {}
+        >>> for s, g in zip(free_group.symbols, pcgs):
+        ...     free_to_perm[s] = g
+
+        >>> for k, v in pc_resentation.items():
+        ...     k_array = k.array_form
+        ...     if v != ():
+        ...        v_array = v.array_form
+        ...     lhs = Permutation()
+        ...     for gen in k_array:
+        ...         s = gen[0]
+        ...         e = gen[1]
+        ...         lhs = lhs*free_to_perm[s]**e
+        ...     if v == ():
+        ...         assert lhs.is_identity
+        ...         continue
+        ...     rhs = Permutation()
+        ...     for gen in v_array:
+        ...         s = gen[0]
+        ...         e = gen[1]
+        ...         rhs = rhs*free_to_perm[s]**e
+        ...     assert lhs == rhs
+
+        """
+        free_group = self.free_group
+        rel_order = self.relative_order
+        pc_relators = {}
+        perm_to_free = {}
+        pcgs = self.pcgs
+
+        for gen, s in zip(pcgs, free_group.generators):
+            perm_to_free[gen**-1] = s**-1
+            perm_to_free[gen] = s
+
+        pcgs = pcgs[::-1]
+        series = self.pc_series[::-1]
+        rel_order = rel_order[::-1]
+        collected_gens = []
+
+        for i, gen in enumerate(pcgs):
+            re = rel_order[i]
+            relation = perm_to_free[gen]**re
+            G = series[i]
+
+            l = G.generator_product(gen**re, original = True)
+            l.reverse()
+
+            word = free_group.identity
+            for g in l:
+                word = word*perm_to_free[g]
+
+            word = self.collected_word(word)
+            pc_relators[relation] = word if word else ()
+            self.pc_presentation = pc_relators
+
+            collected_gens.append(gen)
+            if len(collected_gens) > 1:
+                conj = collected_gens[len(collected_gens)-1]
+                conjugator = perm_to_free[conj]
+
+                for j in range(len(collected_gens)-1):
+                    conjugated = perm_to_free[collected_gens[j]]
+
+                    relation = conjugator**-1*conjugated*conjugator
+                    gens = conj**-1*collected_gens[j]*conj
+
+                    l = G.generator_product(gens, original = True)
+                    l.reverse()
+                    word = free_group.identity
+                    for g in l:
+                        word = word*perm_to_free[g]
+
+                    word = self.collected_word(word)
+                    pc_relators[relation] = word if word else ()
+                    self.pc_presentation = pc_relators
+
+        return pc_relators
+
+    def exponent_vector(self, element):
+        r"""
+        Return the exponent vector of length equal to the
+        length of polycyclic generating sequence.
+
+        Explanation
+        ===========
+
+        For a given generator/element ``g`` of the polycyclic group,
+        it can be represented as `g = {x_1}^{e_1}, \ldots, {x_n}^{e_n}`,
+        where `x_i` represents polycyclic generators and ``n`` is
+        the number of generators in the free_group equal to the length
+        of pcgs.
+
+        Parameters
+        ==========
+
+        element : Permutation
+            Generator of a polycyclic group.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics.permutations import Permutation
+        >>> G = SymmetricGroup(4)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> pcgs = PcGroup.pcgs
+        >>> collector.exponent_vector(G[0])
+        [1, 0, 0, 0]
+        >>> exp = collector.exponent_vector(G[1])
+        >>> g = Permutation()
+        >>> for i in range(len(exp)):
+        ...     g = g*pcgs[i]**exp[i] if exp[i] else g
+        >>> assert g == G[1]
+
+        References
+        ==========
+
+        .. [1] Holt, D., Eick, B., O'Brien, E.
+               "Handbook of Computational Group Theory"
+               Section 8.1.1, Definition 8.4
+
+        """
+        free_group = self.free_group
+        G = PermutationGroup()
+        for g in self.pcgs:
+            G = PermutationGroup([g] + G.generators)
+        gens = G.generator_product(element, original = True)
+        gens.reverse()
+
+        perm_to_free = {}
+        for sym, g in zip(free_group.generators, self.pcgs):
+            perm_to_free[g**-1] = sym**-1
+            perm_to_free[g] = sym
+        w = free_group.identity
+        for g in gens:
+            w = w*perm_to_free[g]
+
+        word = self.collected_word(w)
+
+        index = self.index
+        exp_vector = [0]*len(free_group)
+        word = word.array_form
+        for t in word:
+            exp_vector[index[t[0]]] = t[1]
+        return exp_vector
+
+    def depth(self, element):
+        r"""
+        Return the depth of a given element.
+
+        Explanation
+        ===========
+
+        The depth of a given element ``g`` is defined by
+        `\mathrm{dep}[g] = i` if `e_1 = e_2 = \ldots = e_{i-1} = 0`
+        and `e_i != 0`, where ``e`` represents the exponent-vector.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> G = SymmetricGroup(3)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> collector.depth(G[0])
+        2
+        >>> collector.depth(G[1])
+        1
+
+        References
+        ==========
+
+        .. [1] Holt, D., Eick, B., O'Brien, E.
+               "Handbook of Computational Group Theory"
+               Section 8.1.1, Definition 8.5
+
+        """
+        exp_vector = self.exponent_vector(element)
+        return next((i+1 for i, x in enumerate(exp_vector) if x), len(self.pcgs)+1)
+
+    def leading_exponent(self, element):
+        r"""
+        Return the leading non-zero exponent.
+
+        Explanation
+        ===========
+
+        The leading exponent for a given element `g` is defined
+        by `\mathrm{leading\_exponent}[g]` `= e_i`, if `\mathrm{depth}[g] = i`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> G = SymmetricGroup(3)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> collector.leading_exponent(G[1])
+        1
+
+        """
+        exp_vector = self.exponent_vector(element)
+        depth = self.depth(element)
+        if depth != len(self.pcgs)+1:
+            return exp_vector[depth-1]
+        return None
+
+    def _sift(self, z, g):
+        h = g
+        d = self.depth(h)
+        while d < len(self.pcgs) and z[d-1] != 1:
+            k = z[d-1]
+            e = self.leading_exponent(h)*(self.leading_exponent(k))**-1
+            e = e % self.relative_order[d-1]
+            h = k**-e*h
+            d = self.depth(h)
+        return h
+
+    def induced_pcgs(self, gens):
+        """
+
+        Parameters
+        ==========
+
+        gens : list
+            A list of generators on which polycyclic subgroup
+            is to be defined.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> S = SymmetricGroup(8)
+        >>> G = S.sylow_subgroup(2)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> gens = [G[0], G[1]]
+        >>> ipcgs = collector.induced_pcgs(gens)
+        >>> [gen.order() for gen in ipcgs]
+        [2, 2, 2]
+        >>> G = S.sylow_subgroup(3)
+        >>> PcGroup = G.polycyclic_group()
+        >>> collector = PcGroup.collector
+        >>> gens = [G[0], G[1]]
+        >>> ipcgs = collector.induced_pcgs(gens)
+        >>> [gen.order() for gen in ipcgs]
+        [3]
+
+        """
+        z = [1]*len(self.pcgs)
+        G = gens
+        while G:
+            g = G.pop(0)
+            h = self._sift(z, g)
+            d = self.depth(h)
+            if d < len(self.pcgs):
+                for gen in z:
+                    if gen != 1:
+                        G.append(h**-1*gen**-1*h*gen)
+                z[d-1] = h
+        z = [gen for gen in z if gen != 1]
+        return z
+
+    def constructive_membership_test(self, ipcgs, g):
+        """
+        Return the exponent vector for induced pcgs.
+        """
+        e = [0]*len(ipcgs)
+        h = g
+        d = self.depth(h)
+        for i, gen in enumerate(ipcgs):
+            while self.depth(gen) == d:
+                f = self.leading_exponent(h)*self.leading_exponent(gen)
+                f = f % self.relative_order[d-1]
+                h = gen**(-f)*h
+                e[i] = f
+                d = self.depth(h)
+        if h == 1:
+            return e
+        return False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/perm_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/perm_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..24359cb546246d63470de92b2fb2ab0804fc9886
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/perm_groups.py
@@ -0,0 +1,5459 @@
+from math import factorial as _factorial, log, prod
+from itertools import chain, product
+
+
+from sympy.combinatorics import Permutation
+from sympy.combinatorics.permutations import (_af_commutes_with, _af_invert,
+    _af_rmul, _af_rmuln, _af_pow, Cycle)
+from sympy.combinatorics.util import (_check_cycles_alt_sym,
+    _distribute_gens_by_base, _orbits_transversals_from_bsgs,
+    _handle_precomputed_bsgs, _base_ordering, _strong_gens_from_distr,
+    _strip, _strip_af)
+from sympy.core import Basic
+from sympy.core.random import _randrange, randrange, choice
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import _sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.ntheory import primefactors, sieve
+from sympy.ntheory.factor_ import (factorint, multiplicity)
+from sympy.ntheory.primetest import isprime
+from sympy.utilities.iterables import has_variety, is_sequence, uniq
+
+rmul = Permutation.rmul_with_af
+_af_new = Permutation._af_new
+
+
+class PermutationGroup(Basic):
+    r"""The class defining a Permutation group.
+
+    Explanation
+    ===========
+
+    ``PermutationGroup([p1, p2, ..., pn])`` returns the permutation group
+    generated by the list of permutations. This group can be supplied
+    to Polyhedron if one desires to decorate the elements to which the
+    indices of the permutation refer.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation, PermutationGroup
+    >>> from sympy.combinatorics import Polyhedron
+
+    The permutations corresponding to motion of the front, right and
+    bottom face of a $2 \times 2$ Rubik's cube are defined:
+
+    >>> F = Permutation(2, 19, 21, 8)(3, 17, 20, 10)(4, 6, 7, 5)
+    >>> R = Permutation(1, 5, 21, 14)(3, 7, 23, 12)(8, 10, 11, 9)
+    >>> D = Permutation(6, 18, 14, 10)(7, 19, 15, 11)(20, 22, 23, 21)
+
+    These are passed as permutations to PermutationGroup:
+
+    >>> G = PermutationGroup(F, R, D)
+    >>> G.order()
+    3674160
+
+    The group can be supplied to a Polyhedron in order to track the
+    objects being moved. An example involving the $2 \times 2$ Rubik's cube is
+    given there, but here is a simple demonstration:
+
+    >>> a = Permutation(2, 1)
+    >>> b = Permutation(1, 0)
+    >>> G = PermutationGroup(a, b)
+    >>> P = Polyhedron(list('ABC'), pgroup=G)
+    >>> P.corners
+    (A, B, C)
+    >>> P.rotate(0) # apply permutation 0
+    >>> P.corners
+    (A, C, B)
+    >>> P.reset()
+    >>> P.corners
+    (A, B, C)
+
+    Or one can make a permutation as a product of selected permutations
+    and apply them to an iterable directly:
+
+    >>> P10 = G.make_perm([0, 1])
+    >>> P10('ABC')
+    ['C', 'A', 'B']
+
+    See Also
+    ========
+
+    sympy.combinatorics.polyhedron.Polyhedron,
+    sympy.combinatorics.permutations.Permutation
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.
+           "Handbook of Computational Group Theory"
+
+    .. [2] Seress, A.
+           "Permutation Group Algorithms"
+
+    .. [3] https://en.wikipedia.org/wiki/Schreier_vector
+
+    .. [4] https://en.wikipedia.org/wiki/Nielsen_transformation#Product_replacement_algorithm
+
+    .. [5] Frank Celler, Charles R.Leedham-Green, Scott H.Murray,
+           Alice C.Niemeyer, and E.A.O'Brien. "Generating Random
+           Elements of a Finite Group"
+
+    .. [6] https://en.wikipedia.org/wiki/Block_%28permutation_group_theory%29
+
+    .. [7] https://algorithmist.com/wiki/Union_find
+
+    .. [8] https://en.wikipedia.org/wiki/Multiply_transitive_group#Multiply_transitive_groups
+
+    .. [9] https://en.wikipedia.org/wiki/Center_%28group_theory%29
+
+    .. [10] https://en.wikipedia.org/wiki/Centralizer_and_normalizer
+
+    .. [11] https://groupprops.subwiki.org/wiki/Derived_subgroup
+
+    .. [12] https://en.wikipedia.org/wiki/Nilpotent_group
+
+    .. [13] https://www.math.colostate.edu/~hulpke/CGT/cgtnotes.pdf
+
+    .. [14] https://docs.gap-system.org/doc/ref/manual.pdf
+
+    """
+    is_group = True
+
+    def __new__(cls, *args, dups=True, **kwargs):
+        """The default constructor. Accepts Cycle and Permutation forms.
+        Removes duplicates unless ``dups`` keyword is ``False``.
+        """
+        if not args:
+            args = [Permutation()]
+        else:
+            args = list(args[0] if is_sequence(args[0]) else args)
+            if not args:
+                args = [Permutation()]
+        if any(isinstance(a, Cycle) for a in args):
+            args = [Permutation(a) for a in args]
+        if has_variety(a.size for a in args):
+            degree = kwargs.pop('degree', None)
+            if degree is None:
+                degree = max(a.size for a in args)
+            for i in range(len(args)):
+                if args[i].size != degree:
+                    args[i] = Permutation(args[i], size=degree)
+        if dups:
+            args = list(uniq([_af_new(list(a)) for a in args]))
+        if len(args) > 1:
+            args = [g for g in args if not g.is_identity]
+        return Basic.__new__(cls, *args, **kwargs)
+
+    def __init__(self, *args, **kwargs):
+        self._generators = list(self.args)
+        self._order = None
+        self._elements = []
+        self._center = None
+        self._is_abelian = None
+        self._is_transitive = None
+        self._is_sym = None
+        self._is_alt = None
+        self._is_primitive = None
+        self._is_nilpotent = None
+        self._is_solvable = None
+        self._is_trivial = None
+        self._transitivity_degree = None
+        self._max_div = None
+        self._is_perfect = None
+        self._is_cyclic = None
+        self._is_dihedral = None
+        self._r = len(self._generators)
+        self._degree = self._generators[0].size
+
+        # these attributes are assigned after running schreier_sims
+        self._base = []
+        self._strong_gens = []
+        self._strong_gens_slp = []
+        self._basic_orbits = []
+        self._transversals = []
+        self._transversal_slp = []
+
+        # these attributes are assigned after running _random_pr_init
+        self._random_gens = []
+
+        # finite presentation of the group as an instance of `FpGroup`
+        self._fp_presentation = None
+
+    def __getitem__(self, i):
+        return self._generators[i]
+
+    def __contains__(self, i):
+        """Return ``True`` if *i* is contained in PermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> p = Permutation(1, 2, 3)
+        >>> Permutation(3) in PermutationGroup(p)
+        True
+
+        """
+        if not isinstance(i, Permutation):
+            raise TypeError("A PermutationGroup contains only Permutations as "
+                            "elements, not elements of type %s" % type(i))
+        return self.contains(i)
+
+    def __len__(self):
+        return len(self._generators)
+
+    def equals(self, other):
+        """Return ``True`` if PermutationGroup generated by elements in the
+        group are same i.e they represent the same PermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> p = Permutation(0, 1, 2, 3, 4, 5)
+        >>> G = PermutationGroup([p, p**2])
+        >>> H = PermutationGroup([p**2, p])
+        >>> G.generators == H.generators
+        False
+        >>> G.equals(H)
+        True
+
+        """
+        if not isinstance(other, PermutationGroup):
+            return False
+
+        set_self_gens = set(self.generators)
+        set_other_gens = set(other.generators)
+
+        # before reaching the general case there are also certain
+        # optimisation and obvious cases requiring less or no actual
+        # computation.
+        if set_self_gens == set_other_gens:
+            return True
+
+        # in the most general case it will check that each generator of
+        # one group belongs to the other PermutationGroup and vice-versa
+        for gen1 in set_self_gens:
+            if not other.contains(gen1):
+                return False
+        for gen2 in set_other_gens:
+            if not self.contains(gen2):
+                return False
+        return True
+
+    def __mul__(self, other):
+        """
+        Return the direct product of two permutation groups as a permutation
+        group.
+
+        Explanation
+        ===========
+
+        This implementation realizes the direct product by shifting the index
+        set for the generators of the second group: so if we have ``G`` acting
+        on ``n1`` points and ``H`` acting on ``n2`` points, ``G*H`` acts on
+        ``n1 + n2`` points.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import CyclicGroup
+        >>> G = CyclicGroup(5)
+        >>> H = G*G
+        >>> H
+        PermutationGroup([
+            (9)(0 1 2 3 4),
+            (5 6 7 8 9)])
+        >>> H.order()
+        25
+
+        """
+        if isinstance(other, Permutation):
+            return Coset(other, self, dir='+')
+        gens1 = [perm._array_form for perm in self.generators]
+        gens2 = [perm._array_form for perm in other.generators]
+        n1 = self._degree
+        n2 = other._degree
+        start = list(range(n1))
+        end = list(range(n1, n1 + n2))
+        for i in range(len(gens2)):
+            gens2[i] = [x + n1 for x in gens2[i]]
+        gens2 = [start + gen for gen in gens2]
+        gens1 = [gen + end for gen in gens1]
+        together = gens1 + gens2
+        gens = [_af_new(x) for x in together]
+        return PermutationGroup(gens)
+
+    def _random_pr_init(self, r, n, _random_prec_n=None):
+        r"""Initialize random generators for the product replacement algorithm.
+
+        Explanation
+        ===========
+
+        The implementation uses a modification of the original product
+        replacement algorithm due to Leedham-Green, as described in [1],
+        pp. 69-71; also, see [2], pp. 27-29 for a detailed theoretical
+        analysis of the original product replacement algorithm, and [4].
+
+        The product replacement algorithm is used for producing random,
+        uniformly distributed elements of a group `G` with a set of generators
+        `S`. For the initialization ``_random_pr_init``, a list ``R`` of
+        `\max\{r, |S|\}` group generators is created as the attribute
+        ``G._random_gens``, repeating elements of `S` if necessary, and the
+        identity element of `G` is appended to ``R`` - we shall refer to this
+        last element as the accumulator. Then the function ``random_pr()``
+        is called ``n`` times, randomizing the list ``R`` while preserving
+        the generation of `G` by ``R``. The function ``random_pr()`` itself
+        takes two random elements ``g, h`` among all elements of ``R`` but
+        the accumulator and replaces ``g`` with a randomly chosen element
+        from `\{gh, g(~h), hg, (~h)g\}`. Then the accumulator is multiplied
+        by whatever ``g`` was replaced by. The new value of the accumulator is
+        then returned by ``random_pr()``.
+
+        The elements returned will eventually (for ``n`` large enough) become
+        uniformly distributed across `G` ([5]). For practical purposes however,
+        the values ``n = 50, r = 11`` are suggested in [1].
+
+        Notes
+        =====
+
+        THIS FUNCTION HAS SIDE EFFECTS: it changes the attribute
+        self._random_gens
+
+        See Also
+        ========
+
+        random_pr
+
+        """
+        deg = self.degree
+        random_gens = [x._array_form for x in self.generators]
+        k = len(random_gens)
+        if k < r:
+            for i in range(k, r):
+                random_gens.append(random_gens[i - k])
+        acc = list(range(deg))
+        random_gens.append(acc)
+        self._random_gens = random_gens
+
+        # handle randomized input for testing purposes
+        if _random_prec_n is None:
+            for i in range(n):
+                self.random_pr()
+        else:
+            for i in range(n):
+                self.random_pr(_random_prec=_random_prec_n[i])
+
+    def _union_find_merge(self, first, second, ranks, parents, not_rep):
+        """Merges two classes in a union-find data structure.
+
+        Explanation
+        ===========
+
+        Used in the implementation of Atkinson's algorithm as suggested in [1],
+        pp. 83-87. The class merging process uses union by rank as an
+        optimization. ([7])
+
+        Notes
+        =====
+
+        THIS FUNCTION HAS SIDE EFFECTS: the list of class representatives,
+        ``parents``, the list of class sizes, ``ranks``, and the list of
+        elements that are not representatives, ``not_rep``, are changed due to
+        class merging.
+
+        See Also
+        ========
+
+        minimal_block, _union_find_rep
+
+        References
+        ==========
+
+        .. [1] Holt, D., Eick, B., O'Brien, E.
+               "Handbook of computational group theory"
+
+        .. [7] https://algorithmist.com/wiki/Union_find
+
+        """
+        rep_first = self._union_find_rep(first, parents)
+        rep_second = self._union_find_rep(second, parents)
+        if rep_first != rep_second:
+            # union by rank
+            if ranks[rep_first] >= ranks[rep_second]:
+                new_1, new_2 = rep_first, rep_second
+            else:
+                new_1, new_2 = rep_second, rep_first
+            total_rank = ranks[new_1] + ranks[new_2]
+            if total_rank > self.max_div:
+                return -1
+            parents[new_2] = new_1
+            ranks[new_1] = total_rank
+            not_rep.append(new_2)
+            return 1
+        return 0
+
+    def _union_find_rep(self, num, parents):
+        """Find representative of a class in a union-find data structure.
+
+        Explanation
+        ===========
+
+        Used in the implementation of Atkinson's algorithm as suggested in [1],
+        pp. 83-87. After the representative of the class to which ``num``
+        belongs is found, path compression is performed as an optimization
+        ([7]).
+
+        Notes
+        =====
+
+        THIS FUNCTION HAS SIDE EFFECTS: the list of class representatives,
+        ``parents``, is altered due to path compression.
+
+        See Also
+        ========
+
+        minimal_block, _union_find_merge
+
+        References
+        ==========
+
+        .. [1] Holt, D., Eick, B., O'Brien, E.
+               "Handbook of computational group theory"
+
+        .. [7] https://algorithmist.com/wiki/Union_find
+
+        """
+        rep, parent = num, parents[num]
+        while parent != rep:
+            rep = parent
+            parent = parents[rep]
+        # path compression
+        temp, parent = num, parents[num]
+        while parent != rep:
+            parents[temp] = rep
+            temp = parent
+            parent = parents[temp]
+        return rep
+
+    @property
+    def base(self):
+        r"""Return a base from the Schreier-Sims algorithm.
+
+        Explanation
+        ===========
+
+        For a permutation group `G`, a base is a sequence of points
+        `B = (b_1, b_2, \dots, b_k)` such that no element of `G` apart
+        from the identity fixes all the points in `B`. The concepts of
+        a base and strong generating set and their applications are
+        discussed in depth in [1], pp. 87-89 and [2], pp. 55-57.
+
+        An alternative way to think of `B` is that it gives the
+        indices of the stabilizer cosets that contain more than the
+        identity permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> G = PermutationGroup([Permutation(0, 1, 3)(2, 4)])
+        >>> G.base
+        [0, 2]
+
+        See Also
+        ========
+
+        strong_gens, basic_transversals, basic_orbits, basic_stabilizers
+
+        """
+        if self._base == []:
+            self.schreier_sims()
+        return self._base
+
+    def baseswap(self, base, strong_gens, pos, randomized=False,
+                 transversals=None, basic_orbits=None, strong_gens_distr=None):
+        r"""Swap two consecutive base points in base and strong generating set.
+
+        Explanation
+        ===========
+
+        If a base for a group `G` is given by `(b_1, b_2, \dots, b_k)`, this
+        function returns a base `(b_1, b_2, \dots, b_{i+1}, b_i, \dots, b_k)`,
+        where `i` is given by ``pos``, and a strong generating set relative
+        to that base. The original base and strong generating set are not
+        modified.
+
+        The randomized version (default) is of Las Vegas type.
+
+        Parameters
+        ==========
+
+        base, strong_gens
+            The base and strong generating set.
+        pos
+            The position at which swapping is performed.
+        randomized
+            A switch between randomized and deterministic version.
+        transversals
+            The transversals for the basic orbits, if known.
+        basic_orbits
+            The basic orbits, if known.
+        strong_gens_distr
+            The strong generators distributed by basic stabilizers, if known.
+
+        Returns
+        =======
+
+        (base, strong_gens)
+            ``base`` is the new base, and ``strong_gens`` is a generating set
+            relative to it.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics.testutil import _verify_bsgs
+        >>> from sympy.combinatorics.perm_groups import PermutationGroup
+        >>> S = SymmetricGroup(4)
+        >>> S.schreier_sims()
+        >>> S.base
+        [0, 1, 2]
+        >>> base, gens = S.baseswap(S.base, S.strong_gens, 1, randomized=False)
+        >>> base, gens
+        ([0, 2, 1],
+        [(0 1 2 3), (3)(0 1), (1 3 2),
+         (2 3), (1 3)])
+
+        check that base, gens is a BSGS
+
+        >>> S1 = PermutationGroup(gens)
+        >>> _verify_bsgs(S1, base, gens)
+        True
+
+        See Also
+        ========
+
+        schreier_sims
+
+        Notes
+        =====
+
+        The deterministic version of the algorithm is discussed in
+        [1], pp. 102-103; the randomized version is discussed in [1], p.103, and
+        [2], p.98. It is of Las Vegas type.
+        Notice that [1] contains a mistake in the pseudocode and
+        discussion of BASESWAP: on line 3 of the pseudocode,
+        `|\beta_{i+1}^{\left\langle T\right\rangle}|` should be replaced by
+        `|\beta_{i}^{\left\langle T\right\rangle}|`, and the same for the
+        discussion of the algorithm.
+
+        """
+        # construct the basic orbits, generators for the stabilizer chain
+        # and transversal elements from whatever was provided
+        transversals, basic_orbits, strong_gens_distr = \
+            _handle_precomputed_bsgs(base, strong_gens, transversals,
+                                 basic_orbits, strong_gens_distr)
+        base_len = len(base)
+        degree = self.degree
+        # size of orbit of base[pos] under the stabilizer we seek to insert
+        # in the stabilizer chain at position pos + 1
+        size = len(basic_orbits[pos])*len(basic_orbits[pos + 1]) \
+            //len(_orbit(degree, strong_gens_distr[pos], base[pos + 1]))
+        # initialize the wanted stabilizer by a subgroup
+        if pos + 2 > base_len - 1:
+            T = []
+        else:
+            T = strong_gens_distr[pos + 2][:]
+        # randomized version
+        if randomized is True:
+            stab_pos = PermutationGroup(strong_gens_distr[pos])
+            schreier_vector = stab_pos.schreier_vector(base[pos + 1])
+            # add random elements of the stabilizer until they generate it
+            while len(_orbit(degree, T, base[pos])) != size:
+                new = stab_pos.random_stab(base[pos + 1],
+                                           schreier_vector=schreier_vector)
+                T.append(new)
+        # deterministic version
+        else:
+            Gamma = set(basic_orbits[pos])
+            Gamma.remove(base[pos])
+            if base[pos + 1] in Gamma:
+                Gamma.remove(base[pos + 1])
+            # add elements of the stabilizer until they generate it by
+            # ruling out member of the basic orbit of base[pos] along the way
+            while len(_orbit(degree, T, base[pos])) != size:
+                gamma = next(iter(Gamma))
+                x = transversals[pos][gamma]
+                temp = x._array_form.index(base[pos + 1]) # (~x)(base[pos + 1])
+                if temp not in basic_orbits[pos + 1]:
+                    Gamma = Gamma - _orbit(degree, T, gamma)
+                else:
+                    y = transversals[pos + 1][temp]
+                    el = rmul(x, y)
+                    if el(base[pos]) not in _orbit(degree, T, base[pos]):
+                        T.append(el)
+                        Gamma = Gamma - _orbit(degree, T, base[pos])
+        # build the new base and strong generating set
+        strong_gens_new_distr = strong_gens_distr[:]
+        strong_gens_new_distr[pos + 1] = T
+        base_new = base[:]
+        base_new[pos], base_new[pos + 1] = base_new[pos + 1], base_new[pos]
+        strong_gens_new = _strong_gens_from_distr(strong_gens_new_distr)
+        for gen in T:
+            if gen not in strong_gens_new:
+                strong_gens_new.append(gen)
+        return base_new, strong_gens_new
+
+    @property
+    def basic_orbits(self):
+        r"""
+        Return the basic orbits relative to a base and strong generating set.
+
+        Explanation
+        ===========
+
+        If `(b_1, b_2, \dots, b_k)` is a base for a group `G`, and
+        `G^{(i)} = G_{b_1, b_2, \dots, b_{i-1}}` is the ``i``-th basic stabilizer
+        (so that `G^{(1)} = G`), the ``i``-th basic orbit relative to this base
+        is the orbit of `b_i` under `G^{(i)}`. See [1], pp. 87-89 for more
+        information.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> S = SymmetricGroup(4)
+        >>> S.basic_orbits
+        [[0, 1, 2, 3], [1, 2, 3], [2, 3]]
+
+        See Also
+        ========
+
+        base, strong_gens, basic_transversals, basic_stabilizers
+
+        """
+        if self._basic_orbits == []:
+            self.schreier_sims()
+        return self._basic_orbits
+
+    @property
+    def basic_stabilizers(self):
+        r"""
+        Return a chain of stabilizers relative to a base and strong generating
+        set.
+
+        Explanation
+        ===========
+
+        The ``i``-th basic stabilizer `G^{(i)}` relative to a base
+        `(b_1, b_2, \dots, b_k)` is `G_{b_1, b_2, \dots, b_{i-1}}`. For more
+        information, see [1], pp. 87-89.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import AlternatingGroup
+        >>> A = AlternatingGroup(4)
+        >>> A.schreier_sims()
+        >>> A.base
+        [0, 1]
+        >>> for g in A.basic_stabilizers:
+        ...     print(g)
+        ...
+        PermutationGroup([
+            (3)(0 1 2),
+            (1 2 3)])
+        PermutationGroup([
+            (1 2 3)])
+
+        See Also
+        ========
+
+        base, strong_gens, basic_orbits, basic_transversals
+
+        """
+
+        if self._transversals == []:
+            self.schreier_sims()
+        strong_gens = self._strong_gens
+        base = self._base
+        if not base: # e.g. if self is trivial
+            return []
+        strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+        basic_stabilizers = []
+        for gens in strong_gens_distr:
+            basic_stabilizers.append(PermutationGroup(gens))
+        return basic_stabilizers
+
+    @property
+    def basic_transversals(self):
+        """
+        Return basic transversals relative to a base and strong generating set.
+
+        Explanation
+        ===========
+
+        The basic transversals are transversals of the basic orbits. They
+        are provided as a list of dictionaries, each dictionary having
+        keys - the elements of one of the basic orbits, and values - the
+        corresponding transversal elements. See [1], pp. 87-89 for more
+        information.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import AlternatingGroup
+        >>> A = AlternatingGroup(4)
+        >>> A.basic_transversals
+        [{0: (3), 1: (3)(0 1 2), 2: (3)(0 2 1), 3: (0 3 1)}, {1: (3), 2: (1 2 3), 3: (1 3 2)}]
+
+        See Also
+        ========
+
+        strong_gens, base, basic_orbits, basic_stabilizers
+
+        """
+
+        if self._transversals == []:
+            self.schreier_sims()
+        return self._transversals
+
+    def composition_series(self):
+        r"""
+        Return the composition series for a group as a list
+        of permutation groups.
+
+        Explanation
+        ===========
+
+        The composition series for a group `G` is defined as a
+        subnormal series `G = H_0 > H_1 > H_2 \ldots` A composition
+        series is a subnormal series such that each factor group
+        `H(i+1) / H(i)` is simple.
+        A subnormal series is a composition series only if it is of
+        maximum length.
+
+        The algorithm works as follows:
+        Starting with the derived series the idea is to fill
+        the gap between `G = der[i]` and `H = der[i+1]` for each
+        `i` independently. Since, all subgroups of the abelian group
+        `G/H` are normal so, first step is to take the generators
+        `g` of `G` and add them to generators of `H` one by one.
+
+        The factor groups formed are not simple in general. Each
+        group is obtained from the previous one by adding one
+        generator `g`, if the previous group is denoted by `H`
+        then the next group `K` is generated by `g` and `H`.
+        The factor group `K/H` is cyclic and it's order is
+        `K.order()//G.order()`. The series is then extended between
+        `K` and `H` by groups generated by powers of `g` and `H`.
+        The series formed is then prepended to the already existing
+        series.
+
+        Examples
+        ========
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics.named_groups import CyclicGroup
+        >>> S = SymmetricGroup(12)
+        >>> G = S.sylow_subgroup(2)
+        >>> C = G.composition_series()
+        >>> [H.order() for H in C]
+        [1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]
+        >>> G = S.sylow_subgroup(3)
+        >>> C = G.composition_series()
+        >>> [H.order() for H in C]
+        [243, 81, 27, 9, 3, 1]
+        >>> G = CyclicGroup(12)
+        >>> C = G.composition_series()
+        >>> [H.order() for H in C]
+        [12, 6, 3, 1]
+
+        """
+        der = self.derived_series()
+        if not all(g.is_identity for g in der[-1].generators):
+            raise NotImplementedError('Group should be solvable')
+        series = []
+
+        for i in range(len(der)-1):
+            H = der[i+1]
+            up_seg = []
+            for g in der[i].generators:
+                K = PermutationGroup([g] + H.generators)
+                order = K.order() // H.order()
+                down_seg = []
+                for p, e in factorint(order).items():
+                    for _ in range(e):
+                        down_seg.append(PermutationGroup([g] + H.generators))
+                        g = g**p
+                up_seg = down_seg + up_seg
+                H = K
+            up_seg[0] = der[i]
+            series.extend(up_seg)
+        series.append(der[-1])
+        return series
+
+    def coset_transversal(self, H):
+        """Return a transversal of the right cosets of self by its subgroup H
+        using the second method described in [1], Subsection 4.6.7
+
+        """
+
+        if not H.is_subgroup(self):
+            raise ValueError("The argument must be a subgroup")
+
+        if H.order() == 1:
+            return self.elements
+
+        self._schreier_sims(base=H.base) # make G.base an extension of H.base
+
+        base = self.base
+        base_ordering = _base_ordering(base, self.degree)
+        identity = Permutation(self.degree - 1)
+
+        transversals = self.basic_transversals[:]
+        # transversals is a list of dictionaries. Get rid of the keys
+        # so that it is a list of lists and sort each list in
+        # the increasing order of base[l]^x
+        for l, t in enumerate(transversals):
+            transversals[l] = sorted(t.values(),
+                                key = lambda x: base_ordering[base[l]^x])
+
+        orbits = H.basic_orbits
+        h_stabs = H.basic_stabilizers
+        g_stabs = self.basic_stabilizers
+
+        indices = [x.order()//y.order() for x, y in zip(g_stabs, h_stabs)]
+
+        # T^(l) should be a right transversal of H^(l) in G^(l) for
+        # 1<=l<=len(base). While H^(l) is the trivial group, T^(l)
+        # contains all the elements of G^(l) so we might just as well
+        # start with l = len(h_stabs)-1
+        if len(g_stabs) > len(h_stabs):
+            T = g_stabs[len(h_stabs)].elements
+        else:
+            T = [identity]
+        l = len(h_stabs)-1
+        t_len = len(T)
+        while l > -1:
+            T_next = []
+            for u in transversals[l]:
+                if u == identity:
+                    continue
+                b = base_ordering[base[l]^u]
+                for t in T:
+                    p = t*u
+                    if all(base_ordering[h^p] >= b for h in orbits[l]):
+                        T_next.append(p)
+                    if t_len + len(T_next) == indices[l]:
+                        break
+                if t_len + len(T_next) == indices[l]:
+                    break
+            T += T_next
+            t_len += len(T_next)
+            l -= 1
+        T.remove(identity)
+        T = [identity] + T
+        return T
+
+    def _coset_representative(self, g, H):
+        """Return the representative of Hg from the transversal that
+        would be computed by ``self.coset_transversal(H)``.
+
+        """
+        if H.order() == 1:
+            return g
+        # The base of self must be an extension of H.base.
+        if not(self.base[:len(H.base)] == H.base):
+            self._schreier_sims(base=H.base)
+        orbits = H.basic_orbits[:]
+        h_transversals = [list(_.values()) for _ in H.basic_transversals]
+        transversals = [list(_.values()) for _ in self.basic_transversals]
+        base = self.base
+        base_ordering = _base_ordering(base, self.degree)
+        def step(l, x):
+            gamma = min(orbits[l], key = lambda y: base_ordering[y^x])
+            i = [base[l]^h for h in h_transversals[l]].index(gamma)
+            x = h_transversals[l][i]*x
+            if l < len(orbits)-1:
+                for u in transversals[l]:
+                    if base[l]^u == base[l]^x:
+                        break
+                x = step(l+1, x*u**-1)*u
+            return x
+        return step(0, g)
+
+    def coset_table(self, H):
+        """Return the standardised (right) coset table of self in H as
+        a list of lists.
+        """
+        # Maybe this should be made to return an instance of CosetTable
+        # from fp_groups.py but the class would need to be changed first
+        # to be compatible with PermutationGroups
+
+        if not H.is_subgroup(self):
+            raise ValueError("The argument must be a subgroup")
+        T = self.coset_transversal(H)
+        n = len(T)
+
+        A = list(chain.from_iterable((gen, gen**-1)
+                    for gen in self.generators))
+
+        table = []
+        for i in range(n):
+            row = [self._coset_representative(T[i]*x, H) for x in A]
+            row = [T.index(r) for r in row]
+            table.append(row)
+
+        # standardize (this is the same as the algorithm used in coset_table)
+        # If CosetTable is made compatible with PermutationGroups, this
+        # should be replaced by table.standardize()
+        A = range(len(A))
+        gamma = 1
+        for alpha, a in product(range(n), A):
+            beta = table[alpha][a]
+            if beta >= gamma:
+                if beta > gamma:
+                    for x in A:
+                        z = table[gamma][x]
+                        table[gamma][x] = table[beta][x]
+                        table[beta][x] = z
+                        for i in range(n):
+                            if table[i][x] == beta:
+                                table[i][x] = gamma
+                            elif table[i][x] == gamma:
+                                table[i][x] = beta
+                gamma += 1
+            if gamma >= n-1:
+                return table
+
+    def center(self):
+        r"""
+        Return the center of a permutation group.
+
+        Explanation
+        ===========
+
+        The center for a group `G` is defined as
+        `Z(G) = \{z\in G | \forall g\in G, zg = gz \}`,
+        the set of elements of `G` that commute with all elements of `G`.
+        It is equal to the centralizer of `G` inside `G`, and is naturally a
+        subgroup of `G` ([9]).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> D = DihedralGroup(4)
+        >>> G = D.center()
+        >>> G.order()
+        2
+
+        See Also
+        ========
+
+        centralizer
+
+        Notes
+        =====
+
+        This is a naive implementation that is a straightforward application
+        of ``.centralizer()``
+
+        """
+        if not self._center:
+            self._center = self.centralizer(self)
+        return self._center
+
+    def centralizer(self, other):
+        r"""
+        Return the centralizer of a group/set/element.
+
+        Explanation
+        ===========
+
+        The centralizer of a set of permutations ``S`` inside
+        a group ``G`` is the set of elements of ``G`` that commute with all
+        elements of ``S``::
+
+            `C_G(S) = \{ g \in G | gs = sg \forall s \in S\}` ([10])
+
+        Usually, ``S`` is a subset of ``G``, but if ``G`` is a proper subgroup of
+        the full symmetric group, we allow for ``S`` to have elements outside
+        ``G``.
+
+        It is naturally a subgroup of ``G``; the centralizer of a permutation
+        group is equal to the centralizer of any set of generators for that
+        group, since any element commuting with the generators commutes with
+        any product of the  generators.
+
+        Parameters
+        ==========
+
+        other
+            a permutation group/list of permutations/single permutation
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+        ... CyclicGroup)
+        >>> S = SymmetricGroup(6)
+        >>> C = CyclicGroup(6)
+        >>> H = S.centralizer(C)
+        >>> H.is_subgroup(C)
+        True
+
+        See Also
+        ========
+
+        subgroup_search
+
+        Notes
+        =====
+
+        The implementation is an application of ``.subgroup_search()`` with
+        tests using a specific base for the group ``G``.
+
+        """
+        if hasattr(other, 'generators'):
+            if other.is_trivial or self.is_trivial:
+                return self
+            degree = self.degree
+            identity = _af_new(list(range(degree)))
+            orbits = other.orbits()
+            num_orbits = len(orbits)
+            orbits.sort(key=lambda x: -len(x))
+            long_base = []
+            orbit_reps = [None]*num_orbits
+            orbit_reps_indices = [None]*num_orbits
+            orbit_descr = [None]*degree
+            for i in range(num_orbits):
+                orbit = list(orbits[i])
+                orbit_reps[i] = orbit[0]
+                orbit_reps_indices[i] = len(long_base)
+                for point in orbit:
+                    orbit_descr[point] = i
+                long_base = long_base + orbit
+            base, strong_gens = self.schreier_sims_incremental(base=long_base)
+            strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+            i = 0
+            for i in range(len(base)):
+                if strong_gens_distr[i] == [identity]:
+                    break
+            base = base[:i]
+            base_len = i
+            for j in range(num_orbits):
+                if base[base_len - 1] in orbits[j]:
+                    break
+            rel_orbits = orbits[: j + 1]
+            num_rel_orbits = len(rel_orbits)
+            transversals = [None]*num_rel_orbits
+            for j in range(num_rel_orbits):
+                rep = orbit_reps[j]
+                transversals[j] = dict(
+                    other.orbit_transversal(rep, pairs=True))
+            trivial_test = lambda x: True
+            tests = [None]*base_len
+            for l in range(base_len):
+                if base[l] in orbit_reps:
+                    tests[l] = trivial_test
+                else:
+                    def test(computed_words, l=l):
+                        g = computed_words[l]
+                        rep_orb_index = orbit_descr[base[l]]
+                        rep = orbit_reps[rep_orb_index]
+                        im = g._array_form[base[l]]
+                        im_rep = g._array_form[rep]
+                        tr_el = transversals[rep_orb_index][base[l]]
+                        # using the definition of transversal,
+                        # base[l]^g = rep^(tr_el*g);
+                        # if g belongs to the centralizer, then
+                        # base[l]^g = (rep^g)^tr_el
+                        return im == tr_el._array_form[im_rep]
+                    tests[l] = test
+
+            def prop(g):
+                return [rmul(g, gen) for gen in other.generators] == \
+                       [rmul(gen, g) for gen in other.generators]
+            return self.subgroup_search(prop, base=base,
+                                        strong_gens=strong_gens, tests=tests)
+        elif hasattr(other, '__getitem__'):
+            gens = list(other)
+            return self.centralizer(PermutationGroup(gens))
+        elif hasattr(other, 'array_form'):
+            return self.centralizer(PermutationGroup([other]))
+
+    def commutator(self, G, H):
+        """
+        Return the commutator of two subgroups.
+
+        Explanation
+        ===========
+
+        For a permutation group ``K`` and subgroups ``G``, ``H``, the
+        commutator of ``G`` and ``H`` is defined as the group generated
+        by all the commutators `[g, h] = hgh^{-1}g^{-1}` for ``g`` in ``G`` and
+        ``h`` in ``H``. It is naturally a subgroup of ``K`` ([1], p.27).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+        ... AlternatingGroup)
+        >>> S = SymmetricGroup(5)
+        >>> A = AlternatingGroup(5)
+        >>> G = S.commutator(S, A)
+        >>> G.is_subgroup(A)
+        True
+
+        See Also
+        ========
+
+        derived_subgroup
+
+        Notes
+        =====
+
+        The commutator of two subgroups `H, G` is equal to the normal closure
+        of the commutators of all the generators, i.e. `hgh^{-1}g^{-1}` for `h`
+        a generator of `H` and `g` a generator of `G` ([1], p.28)
+
+        """
+        ggens = G.generators
+        hgens = H.generators
+        commutators = []
+        for ggen in ggens:
+            for hgen in hgens:
+                commutator = rmul(hgen, ggen, ~hgen, ~ggen)
+                if commutator not in commutators:
+                    commutators.append(commutator)
+        res = self.normal_closure(commutators)
+        return res
+
+    def coset_factor(self, g, factor_index=False):
+        """Return ``G``'s (self's) coset factorization of ``g``
+
+        Explanation
+        ===========
+
+        If ``g`` is an element of ``G`` then it can be written as the product
+        of permutations drawn from the Schreier-Sims coset decomposition,
+
+        The permutations returned in ``f`` are those for which
+        the product gives ``g``: ``g = f[n]*...f[1]*f[0]`` where ``n = len(B)``
+        and ``B = G.base``. f[i] is one of the permutations in
+        ``self._basic_orbits[i]``.
+
+        If factor_index==True,
+        returns a tuple ``[b[0],..,b[n]]``, where ``b[i]``
+        belongs to ``self._basic_orbits[i]``
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation(0, 1, 3, 7, 6, 4)(2, 5)
+        >>> b = Permutation(0, 1, 3, 2)(4, 5, 7, 6)
+        >>> G = PermutationGroup([a, b])
+
+        Define g:
+
+        >>> g = Permutation(7)(1, 2, 4)(3, 6, 5)
+
+        Confirm that it is an element of G:
+
+        >>> G.contains(g)
+        True
+
+        Thus, it can be written as a product of factors (up to
+        3) drawn from u. See below that a factor from u1 and u2
+        and the Identity permutation have been used:
+
+        >>> f = G.coset_factor(g)
+        >>> f[2]*f[1]*f[0] == g
+        True
+        >>> f1 = G.coset_factor(g, True); f1
+        [0, 4, 4]
+        >>> tr = G.basic_transversals
+        >>> f[0] == tr[0][f1[0]]
+        True
+
+        If g is not an element of G then [] is returned:
+
+        >>> c = Permutation(5, 6, 7)
+        >>> G.coset_factor(c)
+        []
+
+        See Also
+        ========
+
+        sympy.combinatorics.util._strip
+
+        """
+        if isinstance(g, (Cycle, Permutation)):
+            g = g.list()
+        if len(g) != self._degree:
+            # this could either adjust the size or return [] immediately
+            # but we don't choose between the two and just signal a possible
+            # error
+            raise ValueError('g should be the same size as permutations of G')
+        I = list(range(self._degree))
+        basic_orbits = self.basic_orbits
+        transversals = self._transversals
+        factors = []
+        base = self.base
+        h = g
+        for i in range(len(base)):
+            beta = h[base[i]]
+            if beta == base[i]:
+                factors.append(beta)
+                continue
+            if beta not in basic_orbits[i]:
+                return []
+            u = transversals[i][beta]._array_form
+            h = _af_rmul(_af_invert(u), h)
+            factors.append(beta)
+        if h != I:
+            return []
+        if factor_index:
+            return factors
+        tr = self.basic_transversals
+        factors = [tr[i][factors[i]] for i in range(len(base))]
+        return factors
+
+    def generator_product(self, g, original=False):
+        r'''
+        Return a list of strong generators `[s1, \dots, sn]`
+        s.t `g = sn \times \dots \times s1`. If ``original=True``, make the
+        list contain only the original group generators
+
+        '''
+        product = []
+        if g.is_identity:
+            return []
+        if g in self.strong_gens:
+            if not original or g in self.generators:
+                return [g]
+            else:
+                slp = self._strong_gens_slp[g]
+                for s in slp:
+                    product.extend(self.generator_product(s, original=True))
+                return product
+        elif g**-1 in self.strong_gens:
+            g = g**-1
+            if not original or g in self.generators:
+                return [g**-1]
+            else:
+                slp = self._strong_gens_slp[g]
+                for s in slp:
+                    product.extend(self.generator_product(s, original=True))
+                l = len(product)
+                product = [product[l-i-1]**-1 for i in range(l)]
+                return product
+
+        f = self.coset_factor(g, True)
+        for i, j in enumerate(f):
+            slp = self._transversal_slp[i][j]
+            for s in slp:
+                if not original:
+                    product.append(self.strong_gens[s])
+                else:
+                    s = self.strong_gens[s]
+                    product.extend(self.generator_product(s, original=True))
+        return product
+
+    def coset_rank(self, g):
+        """rank using Schreier-Sims representation.
+
+        Explanation
+        ===========
+
+        The coset rank of ``g`` is the ordering number in which
+        it appears in the lexicographic listing according to the
+        coset decomposition
+
+        The ordering is the same as in G.generate(method='coset').
+        If ``g`` does not belong to the group it returns None.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation(0, 1, 3, 7, 6, 4)(2, 5)
+        >>> b = Permutation(0, 1, 3, 2)(4, 5, 7, 6)
+        >>> G = PermutationGroup([a, b])
+        >>> c = Permutation(7)(2, 4)(3, 5)
+        >>> G.coset_rank(c)
+        16
+        >>> G.coset_unrank(16)
+        (7)(2 4)(3 5)
+
+        See Also
+        ========
+
+        coset_factor
+
+        """
+        factors = self.coset_factor(g, True)
+        if not factors:
+            return None
+        rank = 0
+        b = 1
+        transversals = self._transversals
+        base = self._base
+        basic_orbits = self._basic_orbits
+        for i in range(len(base)):
+            k = factors[i]
+            j = basic_orbits[i].index(k)
+            rank += b*j
+            b = b*len(transversals[i])
+        return rank
+
+    def coset_unrank(self, rank, af=False):
+        """unrank using Schreier-Sims representation
+
+        coset_unrank is the inverse operation of coset_rank
+        if 0 <= rank < order; otherwise it returns None.
+
+        """
+        if rank < 0 or rank >= self.order():
+            return None
+        base = self.base
+        transversals = self.basic_transversals
+        basic_orbits = self.basic_orbits
+        m = len(base)
+        v = [0]*m
+        for i in range(m):
+            rank, c = divmod(rank, len(transversals[i]))
+            v[i] = basic_orbits[i][c]
+        a = [transversals[i][v[i]]._array_form for i in range(m)]
+        h = _af_rmuln(*a)
+        if af:
+            return h
+        else:
+            return _af_new(h)
+
+    @property
+    def degree(self):
+        """Returns the size of the permutations in the group.
+
+        Explanation
+        ===========
+
+        The number of permutations comprising the group is given by
+        ``len(group)``; the number of permutations that can be generated
+        by the group is given by ``group.order()``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a])
+        >>> G.degree
+        3
+        >>> len(G)
+        1
+        >>> G.order()
+        2
+        >>> list(G.generate())
+        [(2), (2)(0 1)]
+
+        See Also
+        ========
+
+        order
+        """
+        return self._degree
+
+    @property
+    def identity(self):
+        '''
+        Return the identity element of the permutation group.
+
+        '''
+        return _af_new(list(range(self.degree)))
+
+    @property
+    def elements(self):
+        """Returns all the elements of the permutation group as a list
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> p = PermutationGroup(Permutation(1, 3), Permutation(1, 2))
+        >>> p.elements
+        [(3), (3)(1 2), (1 3), (2 3), (1 2 3), (1 3 2)]
+
+        """
+        if not self._elements:
+            self._elements = list(self.generate())
+
+        return self._elements
+
+    def derived_series(self):
+        r"""Return the derived series for the group.
+
+        Explanation
+        ===========
+
+        The derived series for a group `G` is defined as
+        `G = G_0 > G_1 > G_2 > \ldots` where `G_i = [G_{i-1}, G_{i-1}]`,
+        i.e. `G_i` is the derived subgroup of `G_{i-1}`, for
+        `i\in\mathbb{N}`. When we have `G_k = G_{k-1}` for some
+        `k\in\mathbb{N}`, the series terminates.
+
+        Returns
+        =======
+
+        A list of permutation groups containing the members of the derived
+        series in the order `G = G_0, G_1, G_2, \ldots`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+        ... AlternatingGroup, DihedralGroup)
+        >>> A = AlternatingGroup(5)
+        >>> len(A.derived_series())
+        1
+        >>> S = SymmetricGroup(4)
+        >>> len(S.derived_series())
+        4
+        >>> S.derived_series()[1].is_subgroup(AlternatingGroup(4))
+        True
+        >>> S.derived_series()[2].is_subgroup(DihedralGroup(2))
+        True
+
+        See Also
+        ========
+
+        derived_subgroup
+
+        """
+        res = [self]
+        current = self
+        nxt = self.derived_subgroup()
+        while not current.is_subgroup(nxt):
+            res.append(nxt)
+            current = nxt
+            nxt = nxt.derived_subgroup()
+        return res
+
+    def derived_subgroup(self):
+        r"""Compute the derived subgroup.
+
+        Explanation
+        ===========
+
+        The derived subgroup, or commutator subgroup is the subgroup generated
+        by all commutators `[g, h] = hgh^{-1}g^{-1}` for `g, h\in G` ; it is
+        equal to the normal closure of the set of commutators of the generators
+        ([1], p.28, [11]).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([1, 0, 2, 4, 3])
+        >>> b = Permutation([0, 1, 3, 2, 4])
+        >>> G = PermutationGroup([a, b])
+        >>> C = G.derived_subgroup()
+        >>> list(C.generate(af=True))
+        [[0, 1, 2, 3, 4], [0, 1, 3, 4, 2], [0, 1, 4, 2, 3]]
+
+        See Also
+        ========
+
+        derived_series
+
+        """
+        r = self._r
+        gens = [p._array_form for p in self.generators]
+        set_commutators = set()
+        degree = self._degree
+        rng = list(range(degree))
+        for i in range(r):
+            for j in range(r):
+                p1 = gens[i]
+                p2 = gens[j]
+                c = list(range(degree))
+                for k in rng:
+                    c[p2[p1[k]]] = p1[p2[k]]
+                ct = tuple(c)
+                if ct not in set_commutators:
+                    set_commutators.add(ct)
+        cms = [_af_new(p) for p in set_commutators]
+        G2 = self.normal_closure(cms)
+        return G2
+
+    def generate(self, method="coset", af=False):
+        """Return iterator to generate the elements of the group.
+
+        Explanation
+        ===========
+
+        Iteration is done with one of these methods::
+
+          method='coset'  using the Schreier-Sims coset representation
+          method='dimino' using the Dimino method
+
+        If ``af = True`` it yields the array form of the permutations
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import PermutationGroup
+        >>> from sympy.combinatorics.polyhedron import tetrahedron
+
+        The permutation group given in the tetrahedron object is also
+        true groups:
+
+        >>> G = tetrahedron.pgroup
+        >>> G.is_group
+        True
+
+        Also the group generated by the permutations in the tetrahedron
+        pgroup -- even the first two -- is a proper group:
+
+        >>> H = PermutationGroup(G[0], G[1])
+        >>> J = PermutationGroup(list(H.generate())); J
+        PermutationGroup([
+            (0 1)(2 3),
+            (1 2 3),
+            (1 3 2),
+            (0 3 1),
+            (0 2 3),
+            (0 3)(1 2),
+            (0 1 3),
+            (3)(0 2 1),
+            (0 3 2),
+            (3)(0 1 2),
+            (0 2)(1 3)])
+        >>> _.is_group
+        True
+        """
+        if method == "coset":
+            return self.generate_schreier_sims(af)
+        elif method == "dimino":
+            return self.generate_dimino(af)
+        else:
+            raise NotImplementedError('No generation defined for %s' % method)
+
+    def generate_dimino(self, af=False):
+        """Yield group elements using Dimino's algorithm.
+
+        If ``af == True`` it yields the array form of the permutations.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1, 3])
+        >>> b = Permutation([0, 2, 3, 1])
+        >>> g = PermutationGroup([a, b])
+        >>> list(g.generate_dimino(af=True))
+        [[0, 1, 2, 3], [0, 2, 1, 3], [0, 2, 3, 1],
+         [0, 1, 3, 2], [0, 3, 2, 1], [0, 3, 1, 2]]
+
+        References
+        ==========
+
+        .. [1] The Implementation of Various Algorithms for Permutation Groups in
+               the Computer Algebra System: AXIOM, N.J. Doye, M.Sc. Thesis
+
+        """
+        idn = list(range(self.degree))
+        order = 0
+        element_list = [idn]
+        set_element_list = {tuple(idn)}
+        if af:
+            yield idn
+        else:
+            yield _af_new(idn)
+        gens = [p._array_form for p in self.generators]
+
+        for i in range(len(gens)):
+            # D elements of the subgroup G_i generated by gens[:i]
+            D = element_list.copy()
+            N = [idn]
+            while N:
+                A = N
+                N = []
+                for a in A:
+                    for g in gens[:i + 1]:
+                        ag = _af_rmul(a, g)
+                        if tuple(ag) not in set_element_list:
+                            # produce G_i*g
+                            for d in D:
+                                order += 1
+                                ap = _af_rmul(d, ag)
+                                if af:
+                                    yield ap
+                                else:
+                                    p = _af_new(ap)
+                                    yield p
+                                element_list.append(ap)
+                                set_element_list.add(tuple(ap))
+                                N.append(ap)
+        self._order = len(element_list)
+
+    def generate_schreier_sims(self, af=False):
+        """Yield group elements using the Schreier-Sims representation
+        in coset_rank order
+
+        If ``af = True`` it yields the array form of the permutations
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1, 3])
+        >>> b = Permutation([0, 2, 3, 1])
+        >>> g = PermutationGroup([a, b])
+        >>> list(g.generate_schreier_sims(af=True))
+        [[0, 1, 2, 3], [0, 2, 1, 3], [0, 3, 2, 1],
+         [0, 1, 3, 2], [0, 2, 3, 1], [0, 3, 1, 2]]
+        """
+
+        n = self._degree
+        u = self.basic_transversals
+        basic_orbits = self._basic_orbits
+        if len(u) == 0:
+            for x in self.generators:
+                if af:
+                    yield x._array_form
+                else:
+                    yield x
+            return
+        if len(u) == 1:
+            for i in basic_orbits[0]:
+                if af:
+                    yield u[0][i]._array_form
+                else:
+                    yield u[0][i]
+            return
+
+        u = list(reversed(u))
+        basic_orbits = basic_orbits[::-1]
+        # stg stack of group elements
+        stg = [list(range(n))]
+        posmax = [len(x) for x in u]
+        n1 = len(posmax) - 1
+        pos = [0]*n1
+        h = 0
+        while 1:
+            # backtrack when finished iterating over coset
+            if pos[h] >= posmax[h]:
+                if h == 0:
+                    return
+                pos[h] = 0
+                h -= 1
+                stg.pop()
+                continue
+            p = _af_rmul(u[h][basic_orbits[h][pos[h]]]._array_form, stg[-1])
+            pos[h] += 1
+            stg.append(p)
+            h += 1
+            if h == n1:
+                if af:
+                    for i in basic_orbits[-1]:
+                        p = _af_rmul(u[-1][i]._array_form, stg[-1])
+                        yield p
+                else:
+                    for i in basic_orbits[-1]:
+                        p = _af_rmul(u[-1][i]._array_form, stg[-1])
+                        p1 = _af_new(p)
+                        yield p1
+                stg.pop()
+                h -= 1
+
+    @property
+    def generators(self):
+        """Returns the generators of the group.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.generators
+        [(1 2), (2)(0 1)]
+
+        """
+        return self._generators
+
+    def contains(self, g, strict=True):
+        """Test if permutation ``g`` belong to self, ``G``.
+
+        Explanation
+        ===========
+
+        If ``g`` is an element of ``G`` it can be written as a product
+        of factors drawn from the cosets of ``G``'s stabilizers. To see
+        if ``g`` is one of the actual generators defining the group use
+        ``G.has(g)``.
+
+        If ``strict`` is not ``True``, ``g`` will be resized, if necessary,
+        to match the size of permutations in ``self``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+
+        >>> a = Permutation(1, 2)
+        >>> b = Permutation(2, 3, 1)
+        >>> G = PermutationGroup(a, b, degree=5)
+        >>> G.contains(G[0]) # trivial check
+        True
+        >>> elem = Permutation([[2, 3]], size=5)
+        >>> G.contains(elem)
+        True
+        >>> G.contains(Permutation(4)(0, 1, 2, 3))
+        False
+
+        If strict is False, a permutation will be resized, if
+        necessary:
+
+        >>> H = PermutationGroup(Permutation(5))
+        >>> H.contains(Permutation(3))
+        False
+        >>> H.contains(Permutation(3), strict=False)
+        True
+
+        To test if a given permutation is present in the group:
+
+        >>> elem in G.generators
+        False
+        >>> G.has(elem)
+        False
+
+        See Also
+        ========
+
+        coset_factor, sympy.core.basic.Basic.has, __contains__
+
+        """
+        if not isinstance(g, Permutation):
+            return False
+        if g.size != self.degree:
+            if strict:
+                return False
+            g = Permutation(g, size=self.degree)
+        if g in self.generators:
+            return True
+        return bool(self.coset_factor(g.array_form, True))
+
+    @property
+    def is_perfect(self):
+        """Return ``True`` if the group is perfect.
+        A group is perfect if it equals to its derived subgroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation(1,2,3)(4,5)
+        >>> b = Permutation(1,2,3,4,5)
+        >>> G = PermutationGroup([a, b])
+        >>> G.is_perfect
+        False
+
+        """
+        if self._is_perfect is None:
+            self._is_perfect = self.equals(self.derived_subgroup())
+        return self._is_perfect
+
+    @property
+    def is_abelian(self):
+        """Test if the group is Abelian.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.is_abelian
+        False
+        >>> a = Permutation([0, 2, 1])
+        >>> G = PermutationGroup([a])
+        >>> G.is_abelian
+        True
+
+        """
+        if self._is_abelian is not None:
+            return self._is_abelian
+
+        self._is_abelian = True
+        gens = [p._array_form for p in self.generators]
+        for x in gens:
+            for y in gens:
+                if y <= x:
+                    continue
+                if not _af_commutes_with(x, y):
+                    self._is_abelian = False
+                    return False
+        return True
+
+    def abelian_invariants(self):
+        """
+        Returns the abelian invariants for the given group.
+        Let ``G`` be a nontrivial finite abelian group. Then G is isomorphic to
+        the direct product of finitely many nontrivial cyclic groups of
+        prime-power order.
+
+        Explanation
+        ===========
+
+        The prime-powers that occur as the orders of the factors are uniquely
+        determined by G. More precisely, the primes that occur in the orders of the
+        factors in any such decomposition of ``G`` are exactly the primes that divide
+        ``|G|`` and for any such prime ``p``, if the orders of the factors that are
+        p-groups in one such decomposition of ``G`` are ``p^{t_1} >= p^{t_2} >= ... p^{t_r}``,
+        then the orders of the factors that are p-groups in any such decomposition of ``G``
+        are ``p^{t_1} >= p^{t_2} >= ... p^{t_r}``.
+
+        The uniquely determined integers ``p^{t_1} >= p^{t_2} >= ... p^{t_r}``, taken
+        for all primes that divide ``|G|`` are called the invariants of the nontrivial
+        group ``G`` as suggested in ([14], p. 542).
+
+        Notes
+        =====
+
+        We adopt the convention that the invariants of a trivial group are [].
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.abelian_invariants()
+        [2]
+        >>> from sympy.combinatorics import CyclicGroup
+        >>> G = CyclicGroup(7)
+        >>> G.abelian_invariants()
+        [7]
+
+        """
+        if self.is_trivial:
+            return []
+        gns = self.generators
+        inv = []
+        G = self
+        H = G.derived_subgroup()
+        Hgens = H.generators
+        for p in primefactors(G.order()):
+            ranks = []
+            while True:
+                pows = []
+                for g in gns:
+                    elm = g**p
+                    if not H.contains(elm):
+                        pows.append(elm)
+                K = PermutationGroup(Hgens + pows) if pows else H
+                r = G.order()//K.order()
+                G = K
+                gns = pows
+                if r == 1:
+                    break
+                ranks.append(multiplicity(p, r))
+
+            if ranks:
+                pows = [1]*ranks[0]
+                for i in ranks:
+                    for j in range(i):
+                        pows[j] = pows[j]*p
+                inv.extend(pows)
+        inv.sort()
+        return inv
+
+    def is_elementary(self, p):
+        """Return ``True`` if the group is elementary abelian. An elementary
+        abelian group is a finite abelian group, where every nontrivial
+        element has order `p`, where `p` is a prime.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1])
+        >>> G = PermutationGroup([a])
+        >>> G.is_elementary(2)
+        True
+        >>> a = Permutation([0, 2, 1, 3])
+        >>> b = Permutation([3, 1, 2, 0])
+        >>> G = PermutationGroup([a, b])
+        >>> G.is_elementary(2)
+        True
+        >>> G.is_elementary(3)
+        False
+
+        """
+        return self.is_abelian and all(g.order() == p for g in self.generators)
+
+    def _eval_is_alt_sym_naive(self, only_sym=False, only_alt=False):
+        """A naive test using the group order."""
+        if only_sym and only_alt:
+            raise ValueError(
+                "Both {} and {} cannot be set to True"
+                .format(only_sym, only_alt))
+
+        n = self.degree
+        sym_order = _factorial(n)
+        order = self.order()
+
+        if order == sym_order:
+            self._is_sym = True
+            self._is_alt = False
+            return not only_alt
+
+        if 2*order == sym_order:
+            self._is_sym = False
+            self._is_alt = True
+            return not only_sym
+
+        return False
+
+    def _eval_is_alt_sym_monte_carlo(self, eps=0.05, perms=None):
+        """A test using monte-carlo algorithm.
+
+        Parameters
+        ==========
+
+        eps : float, optional
+            The criterion for the incorrect ``False`` return.
+
+        perms : list[Permutation], optional
+            If explicitly given, it tests over the given candidates
+            for testing.
+
+            If ``None``, it randomly computes ``N_eps`` and chooses
+            ``N_eps`` sample of the permutation from the group.
+
+        See Also
+        ========
+
+        _check_cycles_alt_sym
+        """
+        if perms is None:
+            n = self.degree
+            if n < 17:
+                c_n = 0.34
+            else:
+                c_n = 0.57
+            d_n = (c_n*log(2))/log(n)
+            N_eps = int(-log(eps)/d_n)
+
+            perms = (self.random_pr() for i in range(N_eps))
+            return self._eval_is_alt_sym_monte_carlo(perms=perms)
+
+        for perm in perms:
+            if _check_cycles_alt_sym(perm):
+                return True
+        return False
+
+    def is_alt_sym(self, eps=0.05, _random_prec=None):
+        r"""Monte Carlo test for the symmetric/alternating group for degrees
+        >= 8.
+
+        Explanation
+        ===========
+
+        More specifically, it is one-sided Monte Carlo with the
+        answer True (i.e., G is symmetric/alternating) guaranteed to be
+        correct, and the answer False being incorrect with probability eps.
+
+        For degree < 8, the order of the group is checked so the test
+        is deterministic.
+
+        Notes
+        =====
+
+        The algorithm itself uses some nontrivial results from group theory and
+        number theory:
+        1) If a transitive group ``G`` of degree ``n`` contains an element
+        with a cycle of length ``n/2 < p < n-2`` for ``p`` a prime, ``G`` is the
+        symmetric or alternating group ([1], pp. 81-82)
+        2) The proportion of elements in the symmetric/alternating group having
+        the property described in 1) is approximately `\log(2)/\log(n)`
+        ([1], p.82; [2], pp. 226-227).
+        The helper function ``_check_cycles_alt_sym`` is used to
+        go over the cycles in a permutation and look for ones satisfying 1).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> D = DihedralGroup(10)
+        >>> D.is_alt_sym()
+        False
+
+        See Also
+        ========
+
+        _check_cycles_alt_sym
+
+        """
+        if _random_prec is not None:
+            N_eps = _random_prec['N_eps']
+            perms= (_random_prec[i] for i in range(N_eps))
+            return self._eval_is_alt_sym_monte_carlo(perms=perms)
+
+        if self._is_sym or self._is_alt:
+            return True
+        if self._is_sym is False and self._is_alt is False:
+            return False
+
+        n = self.degree
+        if n < 8:
+            return self._eval_is_alt_sym_naive()
+        elif self.is_transitive():
+            return self._eval_is_alt_sym_monte_carlo(eps=eps)
+
+        self._is_sym, self._is_alt = False, False
+        return False
+
+    @property
+    def is_nilpotent(self):
+        """Test if the group is nilpotent.
+
+        Explanation
+        ===========
+
+        A group `G` is nilpotent if it has a central series of finite length.
+        Alternatively, `G` is nilpotent if its lower central series terminates
+        with the trivial group. Every nilpotent group is also solvable
+        ([1], p.29, [12]).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+        ... CyclicGroup)
+        >>> C = CyclicGroup(6)
+        >>> C.is_nilpotent
+        True
+        >>> S = SymmetricGroup(5)
+        >>> S.is_nilpotent
+        False
+
+        See Also
+        ========
+
+        lower_central_series, is_solvable
+
+        """
+        if self._is_nilpotent is None:
+            lcs = self.lower_central_series()
+            terminator = lcs[len(lcs) - 1]
+            gens = terminator.generators
+            degree = self.degree
+            identity = _af_new(list(range(degree)))
+            if all(g == identity for g in gens):
+                self._is_solvable = True
+                self._is_nilpotent = True
+                return True
+            else:
+                self._is_nilpotent = False
+                return False
+        else:
+            return self._is_nilpotent
+
+    def is_normal(self, gr, strict=True):
+        """Test if ``G=self`` is a normal subgroup of ``gr``.
+
+        Explanation
+        ===========
+
+        G is normal in gr if
+        for each g2 in G, g1 in gr, ``g = g1*g2*g1**-1`` belongs to G
+        It is sufficient to check this for each g1 in gr.generators and
+        g2 in G.generators.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([1, 2, 0])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G1 = PermutationGroup([a, Permutation([2, 0, 1])])
+        >>> G1.is_normal(G)
+        True
+
+        """
+        if not self.is_subgroup(gr, strict=strict):
+            return False
+        d_self = self.degree
+        d_gr = gr.degree
+        if self.is_trivial and (d_self == d_gr or not strict):
+            return True
+        if self._is_abelian:
+            return True
+        new_self = self.copy()
+        if not strict and d_self != d_gr:
+            if d_self < d_gr:
+                new_self = PermGroup(new_self.generators + [Permutation(d_gr - 1)])
+            else:
+                gr = PermGroup(gr.generators + [Permutation(d_self - 1)])
+        gens2 = [p._array_form for p in new_self.generators]
+        gens1 = [p._array_form for p in gr.generators]
+        for g1 in gens1:
+            for g2 in gens2:
+                p = _af_rmuln(g1, g2, _af_invert(g1))
+                if not new_self.coset_factor(p, True):
+                    return False
+        return True
+
+    def is_primitive(self, randomized=True):
+        r"""Test if a group is primitive.
+
+        Explanation
+        ===========
+
+        A permutation group ``G`` acting on a set ``S`` is called primitive if
+        ``S`` contains no nontrivial block under the action of ``G``
+        (a block is nontrivial if its cardinality is more than ``1``).
+
+        Notes
+        =====
+
+        The algorithm is described in [1], p.83, and uses the function
+        minimal_block to search for blocks of the form `\{0, k\}` for ``k``
+        ranging over representatives for the orbits of `G_0`, the stabilizer of
+        ``0``. This algorithm has complexity `O(n^2)` where ``n`` is the degree
+        of the group, and will perform badly if `G_0` is small.
+
+        There are two implementations offered: one finds `G_0`
+        deterministically using the function ``stabilizer``, and the other
+        (default) produces random elements of `G_0` using ``random_stab``,
+        hoping that they generate a subgroup of `G_0` with not too many more
+        orbits than `G_0` (this is suggested in [1], p.83). Behavior is changed
+        by the ``randomized`` flag.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> D = DihedralGroup(10)
+        >>> D.is_primitive()
+        False
+
+        See Also
+        ========
+
+        minimal_block, random_stab
+
+        """
+        if self._is_primitive is not None:
+            return self._is_primitive
+
+        if self.is_transitive() is False:
+            return False
+
+        if randomized:
+            random_stab_gens = []
+            v = self.schreier_vector(0)
+            for _ in range(len(self)):
+                random_stab_gens.append(self.random_stab(0, v))
+            stab = PermutationGroup(random_stab_gens)
+        else:
+            stab = self.stabilizer(0)
+        orbits = stab.orbits()
+        for orb in orbits:
+            x = orb.pop()
+            if x != 0 and any(e != 0 for e in self.minimal_block([0, x])):
+                self._is_primitive = False
+                return False
+        self._is_primitive = True
+        return True
+
+    def minimal_blocks(self, randomized=True):
+        '''
+        For a transitive group, return the list of all minimal
+        block systems. If a group is intransitive, return `False`.
+
+        Examples
+        ========
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> DihedralGroup(6).minimal_blocks()
+        [[0, 1, 0, 1, 0, 1], [0, 1, 2, 0, 1, 2]]
+        >>> G = PermutationGroup(Permutation(1,2,5))
+        >>> G.minimal_blocks()
+        False
+
+        See Also
+        ========
+
+        minimal_block, is_transitive, is_primitive
+
+        '''
+        def _number_blocks(blocks):
+            # number the blocks of a block system
+            # in order and return the number of
+            # blocks and the tuple with the
+            # reordering
+            n = len(blocks)
+            appeared = {}
+            m = 0
+            b = [None]*n
+            for i in range(n):
+                if blocks[i] not in appeared:
+                    appeared[blocks[i]] = m
+                    b[i] = m
+                    m += 1
+                else:
+                    b[i] = appeared[blocks[i]]
+            return tuple(b), m
+
+        if not self.is_transitive():
+            return False
+        blocks = []
+        num_blocks = []
+        rep_blocks = []
+        if randomized:
+            random_stab_gens = []
+            v = self.schreier_vector(0)
+            for i in range(len(self)):
+                random_stab_gens.append(self.random_stab(0, v))
+            stab = PermutationGroup(random_stab_gens)
+        else:
+            stab = self.stabilizer(0)
+        orbits = stab.orbits()
+        for orb in orbits:
+            x = orb.pop()
+            if x != 0:
+                block = self.minimal_block([0, x])
+                num_block, _ = _number_blocks(block)
+                # a representative block (containing 0)
+                rep = {j for j in range(self.degree) if num_block[j] == 0}
+                # check if the system is minimal with
+                # respect to the already discovere ones
+                minimal = True
+                blocks_remove_mask = [False] * len(blocks)
+                for i, r in enumerate(rep_blocks):
+                    if len(r) > len(rep) and rep.issubset(r):
+                        # i-th block system is not minimal
+                        blocks_remove_mask[i] = True
+                    elif len(r) < len(rep) and r.issubset(rep):
+                        # the system being checked is not minimal
+                        minimal = False
+                        break
+                # remove non-minimal representative blocks
+                blocks = [b for i, b in enumerate(blocks) if not blocks_remove_mask[i]]
+                num_blocks = [n for i, n in enumerate(num_blocks) if not blocks_remove_mask[i]]
+                rep_blocks = [r for i, r in enumerate(rep_blocks) if not blocks_remove_mask[i]]
+
+                if minimal and num_block not in num_blocks:
+                    blocks.append(block)
+                    num_blocks.append(num_block)
+                    rep_blocks.append(rep)
+        return blocks
+
+    @property
+    def is_solvable(self):
+        """Test if the group is solvable.
+
+        ``G`` is solvable if its derived series terminates with the trivial
+        group ([1], p.29).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> S = SymmetricGroup(3)
+        >>> S.is_solvable
+        True
+
+        See Also
+        ========
+
+        is_nilpotent, derived_series
+
+        """
+        if self._is_solvable is None:
+            if self.order() % 2 != 0:
+                return True
+            ds = self.derived_series()
+            terminator = ds[len(ds) - 1]
+            gens = terminator.generators
+            degree = self.degree
+            identity = _af_new(list(range(degree)))
+            if all(g == identity for g in gens):
+                self._is_solvable = True
+                return True
+            else:
+                self._is_solvable = False
+                return False
+        else:
+            return self._is_solvable
+
+    def is_subgroup(self, G, strict=True):
+        """Return ``True`` if all elements of ``self`` belong to ``G``.
+
+        If ``strict`` is ``False`` then if ``self``'s degree is smaller
+        than ``G``'s, the elements will be resized to have the same degree.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> from sympy.combinatorics import SymmetricGroup, CyclicGroup
+
+        Testing is strict by default: the degree of each group must be the
+        same:
+
+        >>> p = Permutation(0, 1, 2, 3, 4, 5)
+        >>> G1 = PermutationGroup([Permutation(0, 1, 2), Permutation(0, 1)])
+        >>> G2 = PermutationGroup([Permutation(0, 2), Permutation(0, 1, 2)])
+        >>> G3 = PermutationGroup([p, p**2])
+        >>> assert G1.order() == G2.order() == G3.order() == 6
+        >>> G1.is_subgroup(G2)
+        True
+        >>> G1.is_subgroup(G3)
+        False
+        >>> G3.is_subgroup(PermutationGroup(G3[1]))
+        False
+        >>> G3.is_subgroup(PermutationGroup(G3[0]))
+        True
+
+        To ignore the size, set ``strict`` to ``False``:
+
+        >>> S3 = SymmetricGroup(3)
+        >>> S5 = SymmetricGroup(5)
+        >>> S3.is_subgroup(S5, strict=False)
+        True
+        >>> C7 = CyclicGroup(7)
+        >>> G = S5*C7
+        >>> S5.is_subgroup(G, False)
+        True
+        >>> C7.is_subgroup(G, 0)
+        False
+
+        """
+        if isinstance(G, SymmetricPermutationGroup):
+            if self.degree != G.degree:
+                return False
+            return True
+        if not isinstance(G, PermutationGroup):
+            return False
+        if self == G or self.generators[0]==Permutation():
+            return True
+        if G.order() % self.order() != 0:
+            return False
+        if self.degree == G.degree or \
+                (self.degree < G.degree and not strict):
+            gens = self.generators
+        else:
+            return False
+        return all(G.contains(g, strict=strict) for g in gens)
+
+    @property
+    def is_polycyclic(self):
+        """Return ``True`` if a group is polycyclic. A group is polycyclic if
+        it has a subnormal series with cyclic factors. For finite groups,
+        this is the same as if the group is solvable.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1, 3])
+        >>> b = Permutation([2, 0, 1, 3])
+        >>> G = PermutationGroup([a, b])
+        >>> G.is_polycyclic
+        True
+
+        """
+        return self.is_solvable
+
+    def is_transitive(self, strict=True):
+        """Test if the group is transitive.
+
+        Explanation
+        ===========
+
+        A group is transitive if it has a single orbit.
+
+        If ``strict`` is ``False`` the group is transitive if it has
+        a single orbit of length different from 1.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1, 3])
+        >>> b = Permutation([2, 0, 1, 3])
+        >>> G1 = PermutationGroup([a, b])
+        >>> G1.is_transitive()
+        False
+        >>> G1.is_transitive(strict=False)
+        True
+        >>> c = Permutation([2, 3, 0, 1])
+        >>> G2 = PermutationGroup([a, c])
+        >>> G2.is_transitive()
+        True
+        >>> d = Permutation([1, 0, 2, 3])
+        >>> e = Permutation([0, 1, 3, 2])
+        >>> G3 = PermutationGroup([d, e])
+        >>> G3.is_transitive() or G3.is_transitive(strict=False)
+        False
+
+        """
+        if self._is_transitive:  # strict or not, if True then True
+            return self._is_transitive
+        if strict:
+            if self._is_transitive is not None:  # we only store strict=True
+                return self._is_transitive
+
+            ans = len(self.orbit(0)) == self.degree
+            self._is_transitive = ans
+            return ans
+
+        got_orb = False
+        for x in self.orbits():
+            if len(x) > 1:
+                if got_orb:
+                    return False
+                got_orb = True
+        return got_orb
+
+    @property
+    def is_trivial(self):
+        """Test if the group is the trivial group.
+
+        This is true if the group contains only the identity permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> G = PermutationGroup([Permutation([0, 1, 2])])
+        >>> G.is_trivial
+        True
+
+        """
+        if self._is_trivial is None:
+            self._is_trivial = len(self) == 1 and self[0].is_Identity
+        return self._is_trivial
+
+    def lower_central_series(self):
+        r"""Return the lower central series for the group.
+
+        The lower central series for a group `G` is the series
+        `G = G_0 > G_1 > G_2 > \ldots` where
+        `G_k = [G, G_{k-1}]`, i.e. every term after the first is equal to the
+        commutator of `G` and the previous term in `G1` ([1], p.29).
+
+        Returns
+        =======
+
+        A list of permutation groups in the order `G = G_0, G_1, G_2, \ldots`
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (AlternatingGroup,
+        ... DihedralGroup)
+        >>> A = AlternatingGroup(4)
+        >>> len(A.lower_central_series())
+        2
+        >>> A.lower_central_series()[1].is_subgroup(DihedralGroup(2))
+        True
+
+        See Also
+        ========
+
+        commutator, derived_series
+
+        """
+        res = [self]
+        current = self
+        nxt = self.commutator(self, current)
+        while not current.is_subgroup(nxt):
+            res.append(nxt)
+            current = nxt
+            nxt = self.commutator(self, current)
+        return res
+
+    @property
+    def max_div(self):
+        """Maximum proper divisor of the degree of a permutation group.
+
+        Explanation
+        ===========
+
+        Obviously, this is the degree divided by its minimal proper divisor
+        (larger than ``1``, if one exists). As it is guaranteed to be prime,
+        the ``sieve`` from ``sympy.ntheory`` is used.
+        This function is also used as an optimization tool for the functions
+        ``minimal_block`` and ``_union_find_merge``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> G = PermutationGroup([Permutation([0, 2, 1, 3])])
+        >>> G.max_div
+        2
+
+        See Also
+        ========
+
+        minimal_block, _union_find_merge
+
+        """
+        if self._max_div is not None:
+            return self._max_div
+        n = self.degree
+        if n == 1:
+            return 1
+        for x in sieve:
+            if n % x == 0:
+                d = n//x
+                self._max_div = d
+                return d
+
+    def minimal_block(self, points):
+        r"""For a transitive group, finds the block system generated by
+        ``points``.
+
+        Explanation
+        ===========
+
+        If a group ``G`` acts on a set ``S``, a nonempty subset ``B`` of ``S``
+        is called a block under the action of ``G`` if for all ``g`` in ``G``
+        we have ``gB = B`` (``g`` fixes ``B``) or ``gB`` and ``B`` have no
+        common points (``g`` moves ``B`` entirely). ([1], p.23; [6]).
+
+        The distinct translates ``gB`` of a block ``B`` for ``g`` in ``G``
+        partition the set ``S`` and this set of translates is known as a block
+        system. Moreover, we obviously have that all blocks in the partition
+        have the same size, hence the block size divides ``|S|`` ([1], p.23).
+        A ``G``-congruence is an equivalence relation ``~`` on the set ``S``
+        such that ``a ~ b`` implies ``g(a) ~ g(b)`` for all ``g`` in ``G``.
+        For a transitive group, the equivalence classes of a ``G``-congruence
+        and the blocks of a block system are the same thing ([1], p.23).
+
+        The algorithm below checks the group for transitivity, and then finds
+        the ``G``-congruence generated by the pairs ``(p_0, p_1), (p_0, p_2),
+        ..., (p_0,p_{k-1})`` which is the same as finding the maximal block
+        system (i.e., the one with minimum block size) such that
+        ``p_0, ..., p_{k-1}`` are in the same block ([1], p.83).
+
+        It is an implementation of Atkinson's algorithm, as suggested in [1],
+        and manipulates an equivalence relation on the set ``S`` using a
+        union-find data structure. The running time is just above
+        `O(|points||S|)`. ([1], pp. 83-87; [7]).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> D = DihedralGroup(10)
+        >>> D.minimal_block([0, 5])
+        [0, 1, 2, 3, 4, 0, 1, 2, 3, 4]
+        >>> D.minimal_block([0, 1])
+        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+
+        See Also
+        ========
+
+        _union_find_rep, _union_find_merge, is_transitive, is_primitive
+
+        """
+        if not self.is_transitive():
+            return False
+        n = self.degree
+        gens = self.generators
+        # initialize the list of equivalence class representatives
+        parents = list(range(n))
+        ranks = [1]*n
+        not_rep = []
+        k = len(points)
+        # the block size must divide the degree of the group
+        if k > self.max_div:
+            return [0]*n
+        for i in range(k - 1):
+            parents[points[i + 1]] = points[0]
+            not_rep.append(points[i + 1])
+        ranks[points[0]] = k
+        i = 0
+        len_not_rep = k - 1
+        while i < len_not_rep:
+            gamma = not_rep[i]
+            i += 1
+            for gen in gens:
+                # find has side effects: performs path compression on the list
+                # of representatives
+                delta = self._union_find_rep(gamma, parents)
+                # union has side effects: performs union by rank on the list
+                # of representatives
+                temp = self._union_find_merge(gen(gamma), gen(delta), ranks,
+                                              parents, not_rep)
+                if temp == -1:
+                    return [0]*n
+                len_not_rep += temp
+        for i in range(n):
+            # force path compression to get the final state of the equivalence
+            # relation
+            self._union_find_rep(i, parents)
+
+        # rewrite result so that block representatives are minimal
+        new_reps = {}
+        return [new_reps.setdefault(r, i) for i, r in enumerate(parents)]
+
+    def conjugacy_class(self, x):
+        r"""Return the conjugacy class of an element in the group.
+
+        Explanation
+        ===========
+
+        The conjugacy class of an element ``g`` in a group ``G`` is the set of
+        elements ``x`` in ``G`` that are conjugate with ``g``, i.e. for which
+
+            ``g = xax^{-1}``
+
+        for some ``a`` in ``G``.
+
+        Note that conjugacy is an equivalence relation, and therefore that
+        conjugacy classes are partitions of ``G``. For a list of all the
+        conjugacy classes of the group, use the conjugacy_classes() method.
+
+        In a permutation group, each conjugacy class corresponds to a particular
+        `cycle structure': for example, in ``S_3``, the conjugacy classes are:
+
+            * the identity class, ``{()}``
+            * all transpositions, ``{(1 2), (1 3), (2 3)}``
+            * all 3-cycles, ``{(1 2 3), (1 3 2)}``
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, SymmetricGroup
+        >>> S3 = SymmetricGroup(3)
+        >>> S3.conjugacy_class(Permutation(0, 1, 2))
+        {(0 1 2), (0 2 1)}
+
+        Notes
+        =====
+
+        This procedure computes the conjugacy class directly by finding the
+        orbit of the element under conjugation in G. This algorithm is only
+        feasible for permutation groups of relatively small order, but is like
+        the orbit() function itself in that respect.
+        """
+        # Ref: "Computing the conjugacy classes of finite groups"; Butler, G.
+        # Groups '93 Galway/St Andrews; edited by Campbell, C. M.
+        new_class = {x}
+        last_iteration = new_class
+
+        while len(last_iteration) > 0:
+            this_iteration = set()
+
+            for y in last_iteration:
+                for s in self.generators:
+                    conjugated = s * y * (~s)
+                    if conjugated not in new_class:
+                        this_iteration.add(conjugated)
+
+            new_class.update(last_iteration)
+            last_iteration = this_iteration
+
+        return new_class
+
+
+    def conjugacy_classes(self):
+        r"""Return the conjugacy classes of the group.
+
+        Explanation
+        ===========
+
+        As described in the documentation for the .conjugacy_class() function,
+        conjugacy is an equivalence relation on a group G which partitions the
+        set of elements. This method returns a list of all these conjugacy
+        classes of G.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import SymmetricGroup
+        >>> SymmetricGroup(3).conjugacy_classes()
+        [{(2)}, {(0 1 2), (0 2 1)}, {(0 2), (1 2), (2)(0 1)}]
+
+        """
+        identity = _af_new(list(range(self.degree)))
+        known_elements = {identity}
+        classes = [known_elements.copy()]
+
+        for x in self.generate():
+            if x not in known_elements:
+                new_class = self.conjugacy_class(x)
+                classes.append(new_class)
+                known_elements.update(new_class)
+
+        return classes
+
+    def normal_closure(self, other, k=10):
+        r"""Return the normal closure of a subgroup/set of permutations.
+
+        Explanation
+        ===========
+
+        If ``S`` is a subset of a group ``G``, the normal closure of ``A`` in ``G``
+        is defined as the intersection of all normal subgroups of ``G`` that
+        contain ``A`` ([1], p.14). Alternatively, it is the group generated by
+        the conjugates ``x^{-1}yx`` for ``x`` a generator of ``G`` and ``y`` a
+        generator of the subgroup ``\left\langle S\right\rangle`` generated by
+        ``S`` (for some chosen generating set for ``\left\langle S\right\rangle``)
+        ([1], p.73).
+
+        Parameters
+        ==========
+
+        other
+            a subgroup/list of permutations/single permutation
+        k
+            an implementation-specific parameter that determines the number
+            of conjugates that are adjoined to ``other`` at once
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+        ... CyclicGroup, AlternatingGroup)
+        >>> S = SymmetricGroup(5)
+        >>> C = CyclicGroup(5)
+        >>> G = S.normal_closure(C)
+        >>> G.order()
+        60
+        >>> G.is_subgroup(AlternatingGroup(5))
+        True
+
+        See Also
+        ========
+
+        commutator, derived_subgroup, random_pr
+
+        Notes
+        =====
+
+        The algorithm is described in [1], pp. 73-74; it makes use of the
+        generation of random elements for permutation groups by the product
+        replacement algorithm.
+
+        """
+        if hasattr(other, 'generators'):
+            degree = self.degree
+            identity = _af_new(list(range(degree)))
+
+            if all(g == identity for g in other.generators):
+                return other
+            Z = PermutationGroup(other.generators[:])
+            base, strong_gens = Z.schreier_sims_incremental()
+            strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+            basic_orbits, basic_transversals = \
+                _orbits_transversals_from_bsgs(base, strong_gens_distr)
+
+            self._random_pr_init(r=10, n=20)
+
+            _loop = True
+            while _loop:
+                Z._random_pr_init(r=10, n=10)
+                for _ in range(k):
+                    g = self.random_pr()
+                    h = Z.random_pr()
+                    conj = h^g
+                    res = _strip(conj, base, basic_orbits, basic_transversals)
+                    if res[0] != identity or res[1] != len(base) + 1:
+                        gens = Z.generators
+                        gens.append(conj)
+                        Z = PermutationGroup(gens)
+                        strong_gens.append(conj)
+                        temp_base, temp_strong_gens = \
+                            Z.schreier_sims_incremental(base, strong_gens)
+                        base, strong_gens = temp_base, temp_strong_gens
+                        strong_gens_distr = \
+                            _distribute_gens_by_base(base, strong_gens)
+                        basic_orbits, basic_transversals = \
+                            _orbits_transversals_from_bsgs(base,
+                                strong_gens_distr)
+                _loop = False
+                for g in self.generators:
+                    for h in Z.generators:
+                        conj = h^g
+                        res = _strip(conj, base, basic_orbits,
+                                     basic_transversals)
+                        if res[0] != identity or res[1] != len(base) + 1:
+                            _loop = True
+                            break
+                    if _loop:
+                        break
+            return Z
+        elif hasattr(other, '__getitem__'):
+            return self.normal_closure(PermutationGroup(other))
+        elif hasattr(other, 'array_form'):
+            return self.normal_closure(PermutationGroup([other]))
+
+    def orbit(self, alpha, action='tuples'):
+        r"""Compute the orbit of alpha `\{g(\alpha) | g \in G\}` as a set.
+
+        Explanation
+        ===========
+
+        The time complexity of the algorithm used here is `O(|Orb|*r)` where
+        `|Orb|` is the size of the orbit and ``r`` is the number of generators of
+        the group. For a more detailed analysis, see [1], p.78, [2], pp. 19-21.
+        Here alpha can be a single point, or a list of points.
+
+        If alpha is a single point, the ordinary orbit is computed.
+        if alpha is a list of points, there are three available options:
+
+        'union' - computes the union of the orbits of the points in the list
+        'tuples' - computes the orbit of the list interpreted as an ordered
+        tuple under the group action ( i.e., g((1,2,3)) = (g(1), g(2), g(3)) )
+        'sets' - computes the orbit of the list interpreted as a sets
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([1, 2, 0, 4, 5, 6, 3])
+        >>> G = PermutationGroup([a])
+        >>> G.orbit(0)
+        {0, 1, 2}
+        >>> G.orbit([0, 4], 'union')
+        {0, 1, 2, 3, 4, 5, 6}
+
+        See Also
+        ========
+
+        orbit_transversal
+
+        """
+        return _orbit(self.degree, self.generators, alpha, action)
+
+    def orbit_rep(self, alpha, beta, schreier_vector=None):
+        """Return a group element which sends ``alpha`` to ``beta``.
+
+        Explanation
+        ===========
+
+        If ``beta`` is not in the orbit of ``alpha``, the function returns
+        ``False``. This implementation makes use of the schreier vector.
+        For a proof of correctness, see [1], p.80
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import AlternatingGroup
+        >>> G = AlternatingGroup(5)
+        >>> G.orbit_rep(0, 4)
+        (0 4 1 2 3)
+
+        See Also
+        ========
+
+        schreier_vector
+
+        """
+        if schreier_vector is None:
+            schreier_vector = self.schreier_vector(alpha)
+        if schreier_vector[beta] is None:
+            return False
+        k = schreier_vector[beta]
+        gens = [x._array_form for x in self.generators]
+        a = []
+        while k != -1:
+            a.append(gens[k])
+            beta = gens[k].index(beta) # beta = (~gens[k])(beta)
+            k = schreier_vector[beta]
+        if a:
+            return _af_new(_af_rmuln(*a))
+        else:
+            return _af_new(list(range(self._degree)))
+
+    def orbit_transversal(self, alpha, pairs=False):
+        r"""Computes a transversal for the orbit of ``alpha`` as a set.
+
+        Explanation
+        ===========
+
+        For a permutation group `G`, a transversal for the orbit
+        `Orb = \{g(\alpha) | g \in G\}` is a set
+        `\{g_\beta | g_\beta(\alpha) = \beta\}` for `\beta \in Orb`.
+        Note that there may be more than one possible transversal.
+        If ``pairs`` is set to ``True``, it returns the list of pairs
+        `(\beta, g_\beta)`. For a proof of correctness, see [1], p.79
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> G = DihedralGroup(6)
+        >>> G.orbit_transversal(0)
+        [(5), (0 1 2 3 4 5), (0 5)(1 4)(2 3), (0 2 4)(1 3 5), (5)(0 4)(1 3), (0 3)(1 4)(2 5)]
+
+        See Also
+        ========
+
+        orbit
+
+        """
+        return _orbit_transversal(self._degree, self.generators, alpha, pairs)
+
+    def orbits(self, rep=False):
+        """Return the orbits of ``self``, ordered according to lowest element
+        in each orbit.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation(1, 5)(2, 3)(4, 0, 6)
+        >>> b = Permutation(1, 5)(3, 4)(2, 6, 0)
+        >>> G = PermutationGroup([a, b])
+        >>> G.orbits()
+        [{0, 2, 3, 4, 6}, {1, 5}]
+        """
+        return _orbits(self._degree, self._generators)
+
+    def order(self):
+        """Return the order of the group: the number of permutations that
+        can be generated from elements of the group.
+
+        The number of permutations comprising the group is given by
+        ``len(group)``; the length of each permutation in the group is
+        given by ``group.size``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+
+        >>> a = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a])
+        >>> G.degree
+        3
+        >>> len(G)
+        1
+        >>> G.order()
+        2
+        >>> list(G.generate())
+        [(2), (2)(0 1)]
+
+        >>> a = Permutation([0, 2, 1])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.order()
+        6
+
+        See Also
+        ========
+
+        degree
+
+        """
+        if self._order is not None:
+            return self._order
+        if self._is_sym:
+            n = self._degree
+            self._order = factorial(n)
+            return self._order
+        if self._is_alt:
+            n = self._degree
+            self._order = factorial(n)/2
+            return self._order
+
+        m = prod([len(x) for x in self.basic_transversals])
+        self._order = m
+        return m
+
+    def index(self, H):
+        """
+        Returns the index of a permutation group.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation(1,2,3)
+        >>> b =Permutation(3)
+        >>> G = PermutationGroup([a])
+        >>> H = PermutationGroup([b])
+        >>> G.index(H)
+        3
+
+        """
+        if H.is_subgroup(self):
+            return self.order()//H.order()
+
+    @property
+    def is_symmetric(self):
+        """Return ``True`` if the group is symmetric.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import SymmetricGroup
+        >>> g = SymmetricGroup(5)
+        >>> g.is_symmetric
+        True
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> g = PermutationGroup(
+        ...     Permutation(0, 1, 2, 3, 4),
+        ...     Permutation(2, 3))
+        >>> g.is_symmetric
+        True
+
+        Notes
+        =====
+
+        This uses a naive test involving the computation of the full
+        group order.
+        If you need more quicker taxonomy for large groups, you can use
+        :meth:`PermutationGroup.is_alt_sym`.
+        However, :meth:`PermutationGroup.is_alt_sym` may not be accurate
+        and is not able to distinguish between an alternating group and
+        a symmetric group.
+
+        See Also
+        ========
+
+        is_alt_sym
+        """
+        _is_sym = self._is_sym
+        if _is_sym is not None:
+            return _is_sym
+
+        n = self.degree
+        if n >= 8:
+            if self.is_transitive():
+                _is_alt_sym = self._eval_is_alt_sym_monte_carlo()
+                if _is_alt_sym:
+                    if any(g.is_odd for g in self.generators):
+                        self._is_sym, self._is_alt = True, False
+                        return True
+
+                    self._is_sym, self._is_alt = False, True
+                    return False
+
+                return self._eval_is_alt_sym_naive(only_sym=True)
+
+            self._is_sym, self._is_alt = False, False
+            return False
+
+        return self._eval_is_alt_sym_naive(only_sym=True)
+
+
+    @property
+    def is_alternating(self):
+        """Return ``True`` if the group is alternating.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import AlternatingGroup
+        >>> g = AlternatingGroup(5)
+        >>> g.is_alternating
+        True
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> g = PermutationGroup(
+        ...     Permutation(0, 1, 2, 3, 4),
+        ...     Permutation(2, 3, 4))
+        >>> g.is_alternating
+        True
+
+        Notes
+        =====
+
+        This uses a naive test involving the computation of the full
+        group order.
+        If you need more quicker taxonomy for large groups, you can use
+        :meth:`PermutationGroup.is_alt_sym`.
+        However, :meth:`PermutationGroup.is_alt_sym` may not be accurate
+        and is not able to distinguish between an alternating group and
+        a symmetric group.
+
+        See Also
+        ========
+
+        is_alt_sym
+        """
+        _is_alt = self._is_alt
+        if _is_alt is not None:
+            return _is_alt
+
+        n = self.degree
+        if n >= 8:
+            if self.is_transitive():
+                _is_alt_sym = self._eval_is_alt_sym_monte_carlo()
+                if _is_alt_sym:
+                    if all(g.is_even for g in self.generators):
+                        self._is_sym, self._is_alt = False, True
+                        return True
+
+                    self._is_sym, self._is_alt = True, False
+                    return False
+
+                return self._eval_is_alt_sym_naive(only_alt=True)
+
+            self._is_sym, self._is_alt = False, False
+            return False
+
+        return self._eval_is_alt_sym_naive(only_alt=True)
+
+    @classmethod
+    def _distinct_primes_lemma(cls, primes):
+        """Subroutine to test if there is only one cyclic group for the
+        order."""
+        primes = sorted(primes)
+        l = len(primes)
+        for i in range(l):
+            for j in range(i+1, l):
+                if primes[j] % primes[i] == 1:
+                    return None
+        return True
+
+    @property
+    def is_cyclic(self):
+        r"""
+        Return ``True`` if the group is Cyclic.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import AbelianGroup
+        >>> G = AbelianGroup(3, 4)
+        >>> G.is_cyclic
+        True
+        >>> G = AbelianGroup(4, 4)
+        >>> G.is_cyclic
+        False
+
+        Notes
+        =====
+
+        If the order of a group $n$ can be factored into the distinct
+        primes $p_1, p_2, \dots , p_s$ and if
+
+        .. math::
+            \forall i, j \in \{1, 2, \dots, s \}:
+            p_i \not \equiv 1 \pmod {p_j}
+
+        holds true, there is only one group of the order $n$ which
+        is a cyclic group [1]_. This is a generalization of the lemma
+        that the group of order $15, 35, \dots$ are cyclic.
+
+        And also, these additional lemmas can be used to test if a
+        group is cyclic if the order of the group is already found.
+
+        - If the group is abelian and the order of the group is
+          square-free, the group is cyclic.
+        - If the order of the group is less than $6$ and is not $4$, the
+          group is cyclic.
+        - If the order of the group is prime, the group is cyclic.
+
+        References
+        ==========
+
+        .. [1] 1978: John S. Rose: A Course on Group Theory,
+            Introduction to Finite Group Theory: 1.4
+        """
+        if self._is_cyclic is not None:
+            return self._is_cyclic
+
+        if len(self.generators) == 1:
+            self._is_cyclic = True
+            self._is_abelian = True
+            return True
+
+        if self._is_abelian is False:
+            self._is_cyclic = False
+            return False
+
+        order = self.order()
+
+        if order < 6:
+            self._is_abelian = True
+            if order != 4:
+                self._is_cyclic = True
+                return True
+
+        factors = factorint(order)
+        if all(v == 1 for v in factors.values()):
+            if self._is_abelian:
+                self._is_cyclic = True
+                return True
+
+            primes = list(factors.keys())
+            if PermutationGroup._distinct_primes_lemma(primes) is True:
+                self._is_cyclic = True
+                self._is_abelian = True
+                return True
+
+        if not self.is_abelian:
+            self._is_cyclic = False
+            return False
+
+        self._is_cyclic = all(
+            any(g**(order//p) != self.identity for g in self.generators)
+            for p, e in factors.items() if e > 1
+        )
+        return self._is_cyclic
+
+    @property
+    def is_dihedral(self):
+        r"""
+        Return ``True`` if the group is dihedral.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.perm_groups import PermutationGroup
+        >>> from sympy.combinatorics.permutations import Permutation
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup, CyclicGroup
+        >>> G = PermutationGroup(Permutation(1, 6)(2, 5)(3, 4), Permutation(0, 1, 2, 3, 4, 5, 6))
+        >>> G.is_dihedral
+        True
+        >>> G = SymmetricGroup(3)
+        >>> G.is_dihedral
+        True
+        >>> G = CyclicGroup(6)
+        >>> G.is_dihedral
+        False
+
+        References
+        ==========
+
+        .. [Di1] https://math.stackexchange.com/questions/827230/given-a-cayley-table-is-there-an-algorithm-to-determine-if-it-is-a-dihedral-gro/827273#827273
+        .. [Di2] https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral.pdf
+        .. [Di3] https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral2.pdf
+        .. [Di4] https://en.wikipedia.org/wiki/Dihedral_group
+        """
+        if self._is_dihedral is not None:
+            return self._is_dihedral
+
+        order = self.order()
+
+        if order % 2 == 1:
+            self._is_dihedral = False
+            return False
+        if order == 2:
+            self._is_dihedral = True
+            return True
+        if order == 4:
+            # The dihedral group of order 4 is the Klein 4-group.
+            self._is_dihedral = not self.is_cyclic
+            return self._is_dihedral
+        if self.is_abelian:
+            # The only abelian dihedral groups are the ones of orders 2 and 4.
+            self._is_dihedral = False
+            return False
+
+        # Now we know the group is of even order >= 6, and nonabelian.
+        n = order // 2
+
+        # Handle special cases where there are exactly two generators.
+        gens = self.generators
+        if len(gens) == 2:
+            x, y = gens
+            a, b = x.order(), y.order()
+            # Make a >= b
+            if a < b:
+                x, y, a, b = y, x, b, a
+            # Using Theorem 2.1 of [Di3]:
+            if a == 2 == b:
+                self._is_dihedral = True
+                return True
+            # Using Theorem 1.1 of [Di3]:
+            if a == n and b == 2 and y*x*y == ~x:
+                self._is_dihedral = True
+                return True
+
+        # Proceed with algorithm of [Di1]
+        # Find elements of orders 2 and n
+        order_2, order_n = [], []
+        for p in self.elements:
+            k = p.order()
+            if k == 2:
+                order_2.append(p)
+            elif k == n:
+                order_n.append(p)
+
+        if len(order_2) != n + 1 - (n % 2):
+            self._is_dihedral = False
+            return False
+
+        if not order_n:
+            self._is_dihedral = False
+            return False
+
+        x = order_n[0]
+        # Want an element y of order 2 that is not a power of x
+        # (i.e. that is not the 180-deg rotation, when n is even).
+        y = order_2[0]
+        if n % 2 == 0 and y == x**(n//2):
+            y = order_2[1]
+
+        self._is_dihedral = (y*x*y == ~x)
+        return self._is_dihedral
+
+    def pointwise_stabilizer(self, points, incremental=True):
+        r"""Return the pointwise stabilizer for a set of points.
+
+        Explanation
+        ===========
+
+        For a permutation group `G` and a set of points
+        `\{p_1, p_2,\ldots, p_k\}`, the pointwise stabilizer of
+        `p_1, p_2, \ldots, p_k` is defined as
+        `G_{p_1,\ldots, p_k} =
+        \{g\in G | g(p_i) = p_i \forall i\in\{1, 2,\ldots,k\}\}` ([1],p20).
+        It is a subgroup of `G`.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> S = SymmetricGroup(7)
+        >>> Stab = S.pointwise_stabilizer([2, 3, 5])
+        >>> Stab.is_subgroup(S.stabilizer(2).stabilizer(3).stabilizer(5))
+        True
+
+        See Also
+        ========
+
+        stabilizer, schreier_sims_incremental
+
+        Notes
+        =====
+
+        When incremental == True,
+        rather than the obvious implementation using successive calls to
+        ``.stabilizer()``, this uses the incremental Schreier-Sims algorithm
+        to obtain a base with starting segment - the given points.
+
+        """
+        if incremental:
+            base, strong_gens = self.schreier_sims_incremental(base=points)
+            stab_gens = []
+            degree = self.degree
+            for gen in strong_gens:
+                if [gen(point) for point in points] == points:
+                    stab_gens.append(gen)
+            if not stab_gens:
+                stab_gens = _af_new(list(range(degree)))
+            return PermutationGroup(stab_gens)
+        else:
+            gens = self._generators
+            degree = self.degree
+            for x in points:
+                gens = _stabilizer(degree, gens, x)
+        return PermutationGroup(gens)
+
+    def make_perm(self, n, seed=None):
+        """
+        Multiply ``n`` randomly selected permutations from
+        pgroup together, starting with the identity
+        permutation. If ``n`` is a list of integers, those
+        integers will be used to select the permutations and they
+        will be applied in L to R order: make_perm((A, B, C)) will
+        give CBA(I) where I is the identity permutation.
+
+        ``seed`` is used to set the seed for the random selection
+        of permutations from pgroup. If this is a list of integers,
+        the corresponding permutations from pgroup will be selected
+        in the order give. This is mainly used for testing purposes.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a, b = [Permutation([1, 0, 3, 2]), Permutation([1, 3, 0, 2])]
+        >>> G = PermutationGroup([a, b])
+        >>> G.make_perm(1, [0])
+        (0 1)(2 3)
+        >>> G.make_perm(3, [0, 1, 0])
+        (0 2 3 1)
+        >>> G.make_perm([0, 1, 0])
+        (0 2 3 1)
+
+        See Also
+        ========
+
+        random
+        """
+        if is_sequence(n):
+            if seed is not None:
+                raise ValueError('If n is a sequence, seed should be None')
+            n, seed = len(n), n
+        else:
+            try:
+                n = int(n)
+            except TypeError:
+                raise ValueError('n must be an integer or a sequence.')
+        randomrange = _randrange(seed)
+
+        # start with the identity permutation
+        result = Permutation(list(range(self.degree)))
+        m = len(self)
+        for _ in range(n):
+            p = self[randomrange(m)]
+            result = rmul(result, p)
+        return result
+
+    def random(self, af=False):
+        """Return a random group element
+        """
+        rank = randrange(self.order())
+        return self.coset_unrank(rank, af)
+
+    def random_pr(self, gen_count=11, iterations=50, _random_prec=None):
+        """Return a random group element using product replacement.
+
+        Explanation
+        ===========
+
+        For the details of the product replacement algorithm, see
+        ``_random_pr_init`` In ``random_pr`` the actual 'product replacement'
+        is performed. Notice that if the attribute ``_random_gens``
+        is empty, it needs to be initialized by ``_random_pr_init``.
+
+        See Also
+        ========
+
+        _random_pr_init
+
+        """
+        if self._random_gens == []:
+            self._random_pr_init(gen_count, iterations)
+        random_gens = self._random_gens
+        r = len(random_gens) - 1
+
+        # handle randomized input for testing purposes
+        if _random_prec is None:
+            s = randrange(r)
+            t = randrange(r - 1)
+            if t == s:
+                t = r - 1
+            x = choice([1, 2])
+            e = choice([-1, 1])
+        else:
+            s = _random_prec['s']
+            t = _random_prec['t']
+            if t == s:
+                t = r - 1
+            x = _random_prec['x']
+            e = _random_prec['e']
+
+        if x == 1:
+            random_gens[s] = _af_rmul(random_gens[s], _af_pow(random_gens[t], e))
+            random_gens[r] = _af_rmul(random_gens[r], random_gens[s])
+        else:
+            random_gens[s] = _af_rmul(_af_pow(random_gens[t], e), random_gens[s])
+            random_gens[r] = _af_rmul(random_gens[s], random_gens[r])
+        return _af_new(random_gens[r])
+
+    def random_stab(self, alpha, schreier_vector=None, _random_prec=None):
+        """Random element from the stabilizer of ``alpha``.
+
+        The schreier vector for ``alpha`` is an optional argument used
+        for speeding up repeated calls. The algorithm is described in [1], p.81
+
+        See Also
+        ========
+
+        random_pr, orbit_rep
+
+        """
+        if schreier_vector is None:
+            schreier_vector = self.schreier_vector(alpha)
+        if _random_prec is None:
+            rand = self.random_pr()
+        else:
+            rand = _random_prec['rand']
+        beta = rand(alpha)
+        h = self.orbit_rep(alpha, beta, schreier_vector)
+        return rmul(~h, rand)
+
+    def schreier_sims(self):
+        """Schreier-Sims algorithm.
+
+        Explanation
+        ===========
+
+        It computes the generators of the chain of stabilizers
+        `G > G_{b_1} > .. > G_{b1,..,b_r} > 1`
+        in which `G_{b_1,..,b_i}` stabilizes `b_1,..,b_i`,
+        and the corresponding ``s`` cosets.
+        An element of the group can be written as the product
+        `h_1*..*h_s`.
+
+        We use the incremental Schreier-Sims algorithm.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([0, 2, 1])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.schreier_sims()
+        >>> G.basic_transversals
+        [{0: (2)(0 1), 1: (2), 2: (1 2)},
+         {0: (2), 2: (0 2)}]
+        """
+        if self._transversals:
+            return
+        self._schreier_sims()
+        return
+
+    def _schreier_sims(self, base=None):
+        schreier = self.schreier_sims_incremental(base=base, slp_dict=True)
+        base, strong_gens = schreier[:2]
+        self._base = base
+        self._strong_gens = strong_gens
+        self._strong_gens_slp = schreier[2]
+        if not base:
+            self._transversals = []
+            self._basic_orbits = []
+            return
+
+        strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+        basic_orbits, transversals, slps = _orbits_transversals_from_bsgs(base,\
+                strong_gens_distr, slp=True)
+
+        # rewrite the indices stored in slps in terms of strong_gens
+        for i, slp in enumerate(slps):
+            gens = strong_gens_distr[i]
+            for k in slp:
+                slp[k] = [strong_gens.index(gens[s]) for s in slp[k]]
+
+        self._transversals = transversals
+        self._basic_orbits = [sorted(x) for x in basic_orbits]
+        self._transversal_slp = slps
+
+    def schreier_sims_incremental(self, base=None, gens=None, slp_dict=False):
+        """Extend a sequence of points and generating set to a base and strong
+        generating set.
+
+        Parameters
+        ==========
+
+        base
+            The sequence of points to be extended to a base. Optional
+            parameter with default value ``[]``.
+        gens
+            The generating set to be extended to a strong generating set
+            relative to the base obtained. Optional parameter with default
+            value ``self.generators``.
+
+        slp_dict
+            If `True`, return a dictionary `{g: gens}` for each strong
+            generator `g` where `gens` is a list of strong generators
+            coming before `g` in `strong_gens`, such that the product
+            of the elements of `gens` is equal to `g`.
+
+        Returns
+        =======
+
+        (base, strong_gens)
+            ``base`` is the base obtained, and ``strong_gens`` is the strong
+            generating set relative to it. The original parameters ``base``,
+            ``gens`` remain unchanged.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import AlternatingGroup
+        >>> from sympy.combinatorics.testutil import _verify_bsgs
+        >>> A = AlternatingGroup(7)
+        >>> base = [2, 3]
+        >>> seq = [2, 3]
+        >>> base, strong_gens = A.schreier_sims_incremental(base=seq)
+        >>> _verify_bsgs(A, base, strong_gens)
+        True
+        >>> base[:2]
+        [2, 3]
+
+        Notes
+        =====
+
+        This version of the Schreier-Sims algorithm runs in polynomial time.
+        There are certain assumptions in the implementation - if the trivial
+        group is provided, ``base`` and ``gens`` are returned immediately,
+        as any sequence of points is a base for the trivial group. If the
+        identity is present in the generators ``gens``, it is removed as
+        it is a redundant generator.
+        The implementation is described in [1], pp. 90-93.
+
+        See Also
+        ========
+
+        schreier_sims, schreier_sims_random
+
+        """
+        if base is None:
+            base = []
+        if gens is None:
+            gens = self.generators[:]
+        degree = self.degree
+        id_af = list(range(degree))
+        # handle the trivial group
+        if len(gens) == 1 and gens[0].is_Identity:
+            if slp_dict:
+                return base, gens, {gens[0]: [gens[0]]}
+            return base, gens
+        # prevent side effects
+        _base, _gens = base[:], gens[:]
+        # remove the identity as a generator
+        _gens = [x for x in _gens if not x.is_Identity]
+        # make sure no generator fixes all base points
+        for gen in _gens:
+            if all(x == gen._array_form[x] for x in _base):
+                for new in id_af:
+                    if gen._array_form[new] != new:
+                        break
+                else:
+                    assert None  # can this ever happen?
+                _base.append(new)
+        # distribute generators according to basic stabilizers
+        strong_gens_distr = _distribute_gens_by_base(_base, _gens)
+        strong_gens_slp = []
+        # initialize the basic stabilizers, basic orbits and basic transversals
+        orbs = {}
+        transversals = {}
+        slps = {}
+        base_len = len(_base)
+        for i in range(base_len):
+            transversals[i], slps[i] = _orbit_transversal(degree, strong_gens_distr[i],
+                _base[i], pairs=True, af=True, slp=True)
+            transversals[i] = dict(transversals[i])
+            orbs[i] = list(transversals[i].keys())
+        # main loop: amend the stabilizer chain until we have generators
+        # for all stabilizers
+        i = base_len - 1
+        while i >= 0:
+            # this flag is used to continue with the main loop from inside
+            # a nested loop
+            continue_i = False
+            # test the generators for being a strong generating set
+            db = {}
+            for beta, u_beta in list(transversals[i].items()):
+                for j, gen in enumerate(strong_gens_distr[i]):
+                    gb = gen._array_form[beta]
+                    u1 = transversals[i][gb]
+                    g1 = _af_rmul(gen._array_form, u_beta)
+                    slp = [(i, g) for g in slps[i][beta]]
+                    slp = [(i, j)] + slp
+                    if g1 != u1:
+                        # test if the schreier generator is in the i+1-th
+                        # would-be basic stabilizer
+                        y = True
+                        try:
+                            u1_inv = db[gb]
+                        except KeyError:
+                            u1_inv = db[gb] = _af_invert(u1)
+                        schreier_gen = _af_rmul(u1_inv, g1)
+                        u1_inv_slp = slps[i][gb][:]
+                        u1_inv_slp.reverse()
+                        u1_inv_slp = [(i, (g,)) for g in u1_inv_slp]
+                        slp = u1_inv_slp + slp
+                        h, j, slp = _strip_af(schreier_gen, _base, orbs, transversals, i, slp=slp, slps=slps)
+                        if j <= base_len:
+                            # new strong generator h at level j
+                            y = False
+                        elif h:
+                            # h fixes all base points
+                            y = False
+                            moved = 0
+                            while h[moved] == moved:
+                                moved += 1
+                            _base.append(moved)
+                            base_len += 1
+                            strong_gens_distr.append([])
+                        if y is False:
+                            # if a new strong generator is found, update the
+                            # data structures and start over
+                            h = _af_new(h)
+                            strong_gens_slp.append((h, slp))
+                            for l in range(i + 1, j):
+                                strong_gens_distr[l].append(h)
+                                transversals[l], slps[l] =\
+                                _orbit_transversal(degree, strong_gens_distr[l],
+                                    _base[l], pairs=True, af=True, slp=True)
+                                transversals[l] = dict(transversals[l])
+                                orbs[l] = list(transversals[l].keys())
+                            i = j - 1
+                            # continue main loop using the flag
+                            continue_i = True
+                    if continue_i is True:
+                        break
+                if continue_i is True:
+                    break
+            if continue_i is True:
+                continue
+            i -= 1
+
+        strong_gens = _gens[:]
+
+        if slp_dict:
+            # create the list of the strong generators strong_gens and
+            # rewrite the indices of strong_gens_slp in terms of the
+            # elements of strong_gens
+            for k, slp in strong_gens_slp:
+                strong_gens.append(k)
+                for i in range(len(slp)):
+                    s = slp[i]
+                    if isinstance(s[1], tuple):
+                        slp[i] = strong_gens_distr[s[0]][s[1][0]]**-1
+                    else:
+                        slp[i] = strong_gens_distr[s[0]][s[1]]
+            strong_gens_slp = dict(strong_gens_slp)
+            # add the original generators
+            for g in _gens:
+                strong_gens_slp[g] = [g]
+            return (_base, strong_gens, strong_gens_slp)
+
+        strong_gens.extend([k for k, _ in strong_gens_slp])
+        return _base, strong_gens
+
+    def schreier_sims_random(self, base=None, gens=None, consec_succ=10,
+                             _random_prec=None):
+        r"""Randomized Schreier-Sims algorithm.
+
+        Explanation
+        ===========
+
+        The randomized Schreier-Sims algorithm takes the sequence ``base``
+        and the generating set ``gens``, and extends ``base`` to a base, and
+        ``gens`` to a strong generating set relative to that base with
+        probability of a wrong answer at most `2^{-consec\_succ}`,
+        provided the random generators are sufficiently random.
+
+        Parameters
+        ==========
+
+        base
+            The sequence to be extended to a base.
+        gens
+            The generating set to be extended to a strong generating set.
+        consec_succ
+            The parameter defining the probability of a wrong answer.
+        _random_prec
+            An internal parameter used for testing purposes.
+
+        Returns
+        =======
+
+        (base, strong_gens)
+            ``base`` is the base and ``strong_gens`` is the strong generating
+            set relative to it.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.testutil import _verify_bsgs
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> S = SymmetricGroup(5)
+        >>> base, strong_gens = S.schreier_sims_random(consec_succ=5)
+        >>> _verify_bsgs(S, base, strong_gens) #doctest: +SKIP
+        True
+
+        Notes
+        =====
+
+        The algorithm is described in detail in [1], pp. 97-98. It extends
+        the orbits ``orbs`` and the permutation groups ``stabs`` to
+        basic orbits and basic stabilizers for the base and strong generating
+        set produced in the end.
+        The idea of the extension process
+        is to "sift" random group elements through the stabilizer chain
+        and amend the stabilizers/orbits along the way when a sift
+        is not successful.
+        The helper function ``_strip`` is used to attempt
+        to decompose a random group element according to the current
+        state of the stabilizer chain and report whether the element was
+        fully decomposed (successful sift) or not (unsuccessful sift). In
+        the latter case, the level at which the sift failed is reported and
+        used to amend ``stabs``, ``base``, ``gens`` and ``orbs`` accordingly.
+        The halting condition is for ``consec_succ`` consecutive successful
+        sifts to pass. This makes sure that the current ``base`` and ``gens``
+        form a BSGS with probability at least `1 - 1/\text{consec\_succ}`.
+
+        See Also
+        ========
+
+        schreier_sims
+
+        """
+        if base is None:
+            base = []
+        if gens is None:
+            gens = self.generators
+        base_len = len(base)
+        n = self.degree
+        # make sure no generator fixes all base points
+        for gen in gens:
+            if all(gen(x) == x for x in base):
+                new = 0
+                while gen._array_form[new] == new:
+                    new += 1
+                base.append(new)
+                base_len += 1
+        # distribute generators according to basic stabilizers
+        strong_gens_distr = _distribute_gens_by_base(base, gens)
+        # initialize the basic stabilizers, basic transversals and basic orbits
+        transversals = {}
+        orbs = {}
+        for i in range(base_len):
+            transversals[i] = dict(_orbit_transversal(n, strong_gens_distr[i],
+                base[i], pairs=True))
+            orbs[i] = list(transversals[i].keys())
+        # initialize the number of consecutive elements sifted
+        c = 0
+        # start sifting random elements while the number of consecutive sifts
+        # is less than consec_succ
+        while c < consec_succ:
+            if _random_prec is None:
+                g = self.random_pr()
+            else:
+                g = _random_prec['g'].pop()
+            h, j = _strip(g, base, orbs, transversals)
+            y = True
+            # determine whether a new base point is needed
+            if j <= base_len:
+                y = False
+            elif not h.is_Identity:
+                y = False
+                moved = 0
+                while h(moved) == moved:
+                    moved += 1
+                base.append(moved)
+                base_len += 1
+                strong_gens_distr.append([])
+            # if the element doesn't sift, amend the strong generators and
+            # associated stabilizers and orbits
+            if y is False:
+                for l in range(1, j):
+                    strong_gens_distr[l].append(h)
+                    transversals[l] = dict(_orbit_transversal(n,
+                        strong_gens_distr[l], base[l], pairs=True))
+                    orbs[l] = list(transversals[l].keys())
+                c = 0
+            else:
+                c += 1
+        # build the strong generating set
+        strong_gens = strong_gens_distr[0][:]
+        for gen in strong_gens_distr[1]:
+            if gen not in strong_gens:
+                strong_gens.append(gen)
+        return base, strong_gens
+
+    def schreier_vector(self, alpha):
+        """Computes the schreier vector for ``alpha``.
+
+        Explanation
+        ===========
+
+        The Schreier vector efficiently stores information
+        about the orbit of ``alpha``. It can later be used to quickly obtain
+        elements of the group that send ``alpha`` to a particular element
+        in the orbit. Notice that the Schreier vector depends on the order
+        in which the group generators are listed. For a definition, see [3].
+        Since list indices start from zero, we adopt the convention to use
+        "None" instead of 0 to signify that an element does not belong
+        to the orbit.
+        For the algorithm and its correctness, see [2], pp.78-80.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([2, 4, 6, 3, 1, 5, 0])
+        >>> b = Permutation([0, 1, 3, 5, 4, 6, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.schreier_vector(0)
+        [-1, None, 0, 1, None, 1, 0]
+
+        See Also
+        ========
+
+        orbit
+
+        """
+        n = self.degree
+        v = [None]*n
+        v[alpha] = -1
+        orb = [alpha]
+        used = [False]*n
+        used[alpha] = True
+        gens = self.generators
+        r = len(gens)
+        for b in orb:
+            for i in range(r):
+                temp = gens[i]._array_form[b]
+                if used[temp] is False:
+                    orb.append(temp)
+                    used[temp] = True
+                    v[temp] = i
+        return v
+
+    def stabilizer(self, alpha):
+        r"""Return the stabilizer subgroup of ``alpha``.
+
+        Explanation
+        ===========
+
+        The stabilizer of `\alpha` is the group `G_\alpha =
+        \{g \in G | g(\alpha) = \alpha\}`.
+        For a proof of correctness, see [1], p.79.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> G = DihedralGroup(6)
+        >>> G.stabilizer(5)
+        PermutationGroup([
+            (5)(0 4)(1 3)])
+
+        See Also
+        ========
+
+        orbit
+
+        """
+        return PermGroup(_stabilizer(self._degree, self._generators, alpha))
+
+    @property
+    def strong_gens(self):
+        r"""Return a strong generating set from the Schreier-Sims algorithm.
+
+        Explanation
+        ===========
+
+        A generating set `S = \{g_1, g_2, \dots, g_t\}` for a permutation group
+        `G` is a strong generating set relative to the sequence of points
+        (referred to as a "base") `(b_1, b_2, \dots, b_k)` if, for
+        `1 \leq i \leq k` we have that the intersection of the pointwise
+        stabilizer `G^{(i+1)} := G_{b_1, b_2, \dots, b_i}` with `S` generates
+        the pointwise stabilizer `G^{(i+1)}`. The concepts of a base and
+        strong generating set and their applications are discussed in depth
+        in [1], pp. 87-89 and [2], pp. 55-57.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> D = DihedralGroup(4)
+        >>> D.strong_gens
+        [(0 1 2 3), (0 3)(1 2), (1 3)]
+        >>> D.base
+        [0, 1]
+
+        See Also
+        ========
+
+        base, basic_transversals, basic_orbits, basic_stabilizers
+
+        """
+        if self._strong_gens == []:
+            self.schreier_sims()
+        return self._strong_gens
+
+    def subgroup(self, gens):
+        """
+           Return the subgroup generated by `gens` which is a list of
+           elements of the group
+        """
+
+        if not all(g in self for g in gens):
+            raise ValueError("The group does not contain the supplied generators")
+
+        G = PermutationGroup(gens)
+        return G
+
+    def subgroup_search(self, prop, base=None, strong_gens=None, tests=None,
+                        init_subgroup=None):
+        """Find the subgroup of all elements satisfying the property ``prop``.
+
+        Explanation
+        ===========
+
+        This is done by a depth-first search with respect to base images that
+        uses several tests to prune the search tree.
+
+        Parameters
+        ==========
+
+        prop
+            The property to be used. Has to be callable on group elements
+            and always return ``True`` or ``False``. It is assumed that
+            all group elements satisfying ``prop`` indeed form a subgroup.
+        base
+            A base for the supergroup.
+        strong_gens
+            A strong generating set for the supergroup.
+        tests
+            A list of callables of length equal to the length of ``base``.
+            These are used to rule out group elements by partial base images,
+            so that ``tests[l](g)`` returns False if the element ``g`` is known
+            not to satisfy prop base on where g sends the first ``l + 1`` base
+            points.
+        init_subgroup
+            if a subgroup of the sought group is
+            known in advance, it can be passed to the function as this
+            parameter.
+
+        Returns
+        =======
+
+        res
+            The subgroup of all elements satisfying ``prop``. The generating
+            set for this group is guaranteed to be a strong generating set
+            relative to the base ``base``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+        ... AlternatingGroup)
+        >>> from sympy.combinatorics.testutil import _verify_bsgs
+        >>> S = SymmetricGroup(7)
+        >>> prop_even = lambda x: x.is_even
+        >>> base, strong_gens = S.schreier_sims_incremental()
+        >>> G = S.subgroup_search(prop_even, base=base, strong_gens=strong_gens)
+        >>> G.is_subgroup(AlternatingGroup(7))
+        True
+        >>> _verify_bsgs(G, base, G.generators)
+        True
+
+        Notes
+        =====
+
+        This function is extremely lengthy and complicated and will require
+        some careful attention. The implementation is described in
+        [1], pp. 114-117, and the comments for the code here follow the lines
+        of the pseudocode in the book for clarity.
+
+        The complexity is exponential in general, since the search process by
+        itself visits all members of the supergroup. However, there are a lot
+        of tests which are used to prune the search tree, and users can define
+        their own tests via the ``tests`` parameter, so in practice, and for
+        some computations, it's not terrible.
+
+        A crucial part in the procedure is the frequent base change performed
+        (this is line 11 in the pseudocode) in order to obtain a new basic
+        stabilizer. The book mentiones that this can be done by using
+        ``.baseswap(...)``, however the current implementation uses a more
+        straightforward way to find the next basic stabilizer - calling the
+        function ``.stabilizer(...)`` on the previous basic stabilizer.
+
+        """
+        # initialize BSGS and basic group properties
+        def get_reps(orbits):
+            # get the minimal element in the base ordering
+            return [min(orbit, key = lambda x: base_ordering[x]) \
+              for orbit in orbits]
+
+        def update_nu(l):
+            temp_index = len(basic_orbits[l]) + 1 -\
+                         len(res_basic_orbits_init_base[l])
+            # this corresponds to the element larger than all points
+            if temp_index >= len(sorted_orbits[l]):
+                nu[l] = base_ordering[degree]
+            else:
+                nu[l] = sorted_orbits[l][temp_index]
+
+        if base is None:
+            base, strong_gens = self.schreier_sims_incremental()
+        base_len = len(base)
+        degree = self.degree
+        identity = _af_new(list(range(degree)))
+        base_ordering = _base_ordering(base, degree)
+        # add an element larger than all points
+        base_ordering.append(degree)
+        # add an element smaller than all points
+        base_ordering.append(-1)
+        # compute BSGS-related structures
+        strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+        basic_orbits, transversals = _orbits_transversals_from_bsgs(base,
+                                     strong_gens_distr)
+        # handle subgroup initialization and tests
+        if init_subgroup is None:
+            init_subgroup = PermutationGroup([identity])
+        if tests is None:
+            trivial_test = lambda x: True
+            tests = []
+            for i in range(base_len):
+                tests.append(trivial_test)
+        # line 1: more initializations.
+        res = init_subgroup
+        f = base_len - 1
+        l = base_len - 1
+        # line 2: set the base for K to the base for G
+        res_base = base[:]
+        # line 3: compute BSGS and related structures for K
+        res_base, res_strong_gens = res.schreier_sims_incremental(
+            base=res_base)
+        res_strong_gens_distr = _distribute_gens_by_base(res_base,
+                                res_strong_gens)
+        res_generators = res.generators
+        res_basic_orbits_init_base = \
+        [_orbit(degree, res_strong_gens_distr[i], res_base[i])\
+         for i in range(base_len)]
+        # initialize orbit representatives
+        orbit_reps = [None]*base_len
+        # line 4: orbit representatives for f-th basic stabilizer of K
+        orbits = _orbits(degree, res_strong_gens_distr[f])
+        orbit_reps[f] = get_reps(orbits)
+        # line 5: remove the base point from the representatives to avoid
+        # getting the identity element as a generator for K
+        orbit_reps[f].remove(base[f])
+        # line 6: more initializations
+        c = [0]*base_len
+        u = [identity]*base_len
+        sorted_orbits = [None]*base_len
+        for i in range(base_len):
+            sorted_orbits[i] = basic_orbits[i][:]
+            sorted_orbits[i].sort(key=lambda point: base_ordering[point])
+        # line 7: initializations
+        mu = [None]*base_len
+        nu = [None]*base_len
+        # this corresponds to the element smaller than all points
+        mu[l] = degree + 1
+        update_nu(l)
+        # initialize computed words
+        computed_words = [identity]*base_len
+        # line 8: main loop
+        while True:
+            # apply all the tests
+            while l < base_len - 1 and \
+                computed_words[l](base[l]) in orbit_reps[l] and \
+                base_ordering[mu[l]] < \
+                base_ordering[computed_words[l](base[l])] < \
+                base_ordering[nu[l]] and \
+                    tests[l](computed_words):
+                # line 11: change the (partial) base of K
+                new_point = computed_words[l](base[l])
+                res_base[l] = new_point
+                new_stab_gens = _stabilizer(degree, res_strong_gens_distr[l],
+                        new_point)
+                res_strong_gens_distr[l + 1] = new_stab_gens
+                # line 12: calculate minimal orbit representatives for the
+                # l+1-th basic stabilizer
+                orbits = _orbits(degree, new_stab_gens)
+                orbit_reps[l + 1] = get_reps(orbits)
+                # line 13: amend sorted orbits
+                l += 1
+                temp_orbit = [computed_words[l - 1](point) for point
+                             in basic_orbits[l]]
+                temp_orbit.sort(key=lambda point: base_ordering[point])
+                sorted_orbits[l] = temp_orbit
+                # lines 14 and 15: update variables used minimality tests
+                new_mu = degree + 1
+                for i in range(l):
+                    if base[l] in res_basic_orbits_init_base[i]:
+                        candidate = computed_words[i](base[i])
+                        if base_ordering[candidate] > base_ordering[new_mu]:
+                            new_mu = candidate
+                mu[l] = new_mu
+                update_nu(l)
+                # line 16: determine the new transversal element
+                c[l] = 0
+                temp_point = sorted_orbits[l][c[l]]
+                gamma = computed_words[l - 1]._array_form.index(temp_point)
+                u[l] = transversals[l][gamma]
+                # update computed words
+                computed_words[l] = rmul(computed_words[l - 1], u[l])
+            # lines 17 & 18: apply the tests to the group element found
+            g = computed_words[l]
+            temp_point = g(base[l])
+            if l == base_len - 1 and \
+                base_ordering[mu[l]] < \
+                base_ordering[temp_point] < base_ordering[nu[l]] and \
+                temp_point in orbit_reps[l] and \
+                tests[l](computed_words) and \
+                    prop(g):
+                # line 19: reset the base of K
+                res_generators.append(g)
+                res_base = base[:]
+                # line 20: recalculate basic orbits (and transversals)
+                res_strong_gens.append(g)
+                res_strong_gens_distr = _distribute_gens_by_base(res_base,
+                                                          res_strong_gens)
+                res_basic_orbits_init_base = \
+                [_orbit(degree, res_strong_gens_distr[i], res_base[i]) \
+                 for i in range(base_len)]
+                # line 21: recalculate orbit representatives
+                # line 22: reset the search depth
+                orbit_reps[f] = get_reps(orbits)
+                l = f
+            # line 23: go up the tree until in the first branch not fully
+            # searched
+            while l >= 0 and c[l] == len(basic_orbits[l]) - 1:
+                l = l - 1
+            # line 24: if the entire tree is traversed, return K
+            if l == -1:
+                return PermutationGroup(res_generators)
+            # lines 25-27: update orbit representatives
+            if l < f:
+                # line 26
+                f = l
+                c[l] = 0
+                # line 27
+                temp_orbits = _orbits(degree, res_strong_gens_distr[f])
+                orbit_reps[f] = get_reps(temp_orbits)
+                # line 28: update variables used for minimality testing
+                mu[l] = degree + 1
+                temp_index = len(basic_orbits[l]) + 1 - \
+                    len(res_basic_orbits_init_base[l])
+                if temp_index >= len(sorted_orbits[l]):
+                    nu[l] = base_ordering[degree]
+                else:
+                    nu[l] = sorted_orbits[l][temp_index]
+            # line 29: set the next element from the current branch and update
+            # accordingly
+            c[l] += 1
+            if l == 0:
+                gamma  = sorted_orbits[l][c[l]]
+            else:
+                gamma = computed_words[l - 1]._array_form.index(sorted_orbits[l][c[l]])
+
+            u[l] = transversals[l][gamma]
+            if l == 0:
+                computed_words[l] = u[l]
+            else:
+                computed_words[l] = rmul(computed_words[l - 1], u[l])
+
+    @property
+    def transitivity_degree(self):
+        r"""Compute the degree of transitivity of the group.
+
+        Explanation
+        ===========
+
+        A permutation group `G` acting on `\Omega = \{0, 1, \dots, n-1\}` is
+        ``k``-fold transitive, if, for any `k` points
+        `(a_1, a_2, \dots, a_k) \in \Omega` and any `k` points
+        `(b_1, b_2, \dots, b_k) \in \Omega` there exists `g \in  G` such that
+        `g(a_1) = b_1, g(a_2) = b_2, \dots, g(a_k) = b_k`
+        The degree of transitivity of `G` is the maximum ``k`` such that
+        `G` is ``k``-fold transitive. ([8])
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup
+        >>> a = Permutation([1, 2, 0])
+        >>> b = Permutation([1, 0, 2])
+        >>> G = PermutationGroup([a, b])
+        >>> G.transitivity_degree
+        3
+
+        See Also
+        ========
+
+        is_transitive, orbit
+
+        """
+        if self._transitivity_degree is None:
+            n = self.degree
+            G = self
+            # if G is k-transitive, a tuple (a_0,..,a_k)
+            # can be brought to (b_0,...,b_(k-1), b_k)
+            # where b_0,...,b_(k-1) are fixed points;
+            # consider the group G_k which stabilizes b_0,...,b_(k-1)
+            # if G_k is transitive on the subset excluding b_0,...,b_(k-1)
+            # then G is (k+1)-transitive
+            for i in range(n):
+                orb = G.orbit(i)
+                if len(orb) != n - i:
+                    self._transitivity_degree = i
+                    return i
+                G = G.stabilizer(i)
+            self._transitivity_degree = n
+            return n
+        else:
+            return self._transitivity_degree
+
+    def _p_elements_group(self, p):
+        '''
+        For an abelian p-group, return the subgroup consisting of
+        all elements of order p (and the identity)
+
+        '''
+        gens = self.generators[:]
+        gens = sorted(gens, key=lambda x: x.order(), reverse=True)
+        gens_p = [g**(g.order()/p) for g in gens]
+        gens_r = []
+        for i in range(len(gens)):
+            x = gens[i]
+            x_order = x.order()
+            # x_p has order p
+            x_p = x**(x_order/p)
+            if i > 0:
+                P = PermutationGroup(gens_p[:i])
+            else:
+                P = PermutationGroup(self.identity)
+            if x**(x_order/p) not in P:
+                gens_r.append(x**(x_order/p))
+            else:
+                # replace x by an element of order (x.order()/p)
+                # so that gens still generates G
+                g = P.generator_product(x_p, original=True)
+                for s in g:
+                    x = x*s**-1
+                x_order = x_order/p
+                # insert x to gens so that the sorting is preserved
+                del gens[i]
+                del gens_p[i]
+                j = i - 1
+                while j < len(gens) and gens[j].order() >= x_order:
+                    j += 1
+                gens = gens[:j] + [x] + gens[j:]
+                gens_p = gens_p[:j] + [x] + gens_p[j:]
+        return PermutationGroup(gens_r)
+
+    def _sylow_alt_sym(self, p):
+        '''
+        Return a p-Sylow subgroup of a symmetric or an
+        alternating group.
+
+        Explanation
+        ===========
+
+        The algorithm for this is hinted at in [1], Chapter 4,
+        Exercise 4.
+
+        For Sym(n) with n = p^i, the idea is as follows. Partition
+        the interval [0..n-1] into p equal parts, each of length p^(i-1):
+        [0..p^(i-1)-1], [p^(i-1)..2*p^(i-1)-1]...[(p-1)*p^(i-1)..p^i-1].
+        Find a p-Sylow subgroup of Sym(p^(i-1)) (treated as a subgroup
+        of ``self``) acting on each of the parts. Call the subgroups
+        P_1, P_2...P_p. The generators for the subgroups P_2...P_p
+        can be obtained from those of P_1 by applying a "shifting"
+        permutation to them, that is, a permutation mapping [0..p^(i-1)-1]
+        to the second part (the other parts are obtained by using the shift
+        multiple times). The union of this permutation and the generators
+        of P_1 is a p-Sylow subgroup of ``self``.
+
+        For n not equal to a power of p, partition
+        [0..n-1] in accordance with how n would be written in base p.
+        E.g. for p=2 and n=11, 11 = 2^3 + 2^2 + 1 so the partition
+        is [[0..7], [8..9], {10}]. To generate a p-Sylow subgroup,
+        take the union of the generators for each of the parts.
+        For the above example, {(0 1), (0 2)(1 3), (0 4), (1 5)(2 7)}
+        from the first part, {(8 9)} from the second part and
+        nothing from the third. This gives 4 generators in total, and
+        the subgroup they generate is p-Sylow.
+
+        Alternating groups are treated the same except when p=2. In this
+        case, (0 1)(s s+1) should be added for an appropriate s (the start
+        of a part) for each part in the partitions.
+
+        See Also
+        ========
+
+        sylow_subgroup, is_alt_sym
+
+        '''
+        n = self.degree
+        gens = []
+        identity = Permutation(n-1)
+        # the case of 2-sylow subgroups of alternating groups
+        # needs special treatment
+        alt = p == 2 and all(g.is_even for g in self.generators)
+
+        # find the presentation of n in base p
+        coeffs = []
+        m = n
+        while m > 0:
+            coeffs.append(m % p)
+            m = m // p
+
+        power = len(coeffs)-1
+        # for a symmetric group, gens[:i] is the generating
+        # set for a p-Sylow subgroup on [0..p**(i-1)-1]. For
+        # alternating groups, the same is given by gens[:2*(i-1)]
+        for i in range(1, power+1):
+            if i == 1 and alt:
+                # (0 1) shouldn't be added for alternating groups
+                continue
+            gen = Permutation([(j + p**(i-1)) % p**i for j in range(p**i)])
+            gens.append(identity*gen)
+            if alt:
+                gen = Permutation(0, 1)*gen*Permutation(0, 1)*gen
+                gens.append(gen)
+
+        # the first point in the current part (see the algorithm
+        # description in the docstring)
+        start = 0
+
+        while power > 0:
+            a = coeffs[power]
+
+            # make the permutation shifting the start of the first
+            # part ([0..p^i-1] for some i) to the current one
+            for _ in range(a):
+                shift = Permutation()
+                if start > 0:
+                    for i in range(p**power):
+                        shift = shift(i, start + i)
+
+                    if alt:
+                        gen = Permutation(0, 1)*shift*Permutation(0, 1)*shift
+                        gens.append(gen)
+                        j = 2*(power - 1)
+                    else:
+                        j = power
+
+                    for i, gen in enumerate(gens[:j]):
+                        if alt and i % 2 == 1:
+                            continue
+                        # shift the generator to the start of the
+                        # partition part
+                        gen = shift*gen*shift
+                        gens.append(gen)
+
+                start += p**power
+            power = power-1
+
+        return gens
+
+    def sylow_subgroup(self, p):
+        '''
+        Return a p-Sylow subgroup of the group.
+
+        The algorithm is described in [1], Chapter 4, Section 7
+
+        Examples
+        ========
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> from sympy.combinatorics.named_groups import SymmetricGroup
+        >>> from sympy.combinatorics.named_groups import AlternatingGroup
+
+        >>> D = DihedralGroup(6)
+        >>> S = D.sylow_subgroup(2)
+        >>> S.order()
+        4
+        >>> G = SymmetricGroup(6)
+        >>> S = G.sylow_subgroup(5)
+        >>> S.order()
+        5
+
+        >>> G1 = AlternatingGroup(3)
+        >>> G2 = AlternatingGroup(5)
+        >>> G3 = AlternatingGroup(9)
+
+        >>> S1 = G1.sylow_subgroup(3)
+        >>> S2 = G2.sylow_subgroup(3)
+        >>> S3 = G3.sylow_subgroup(3)
+
+        >>> len1 = len(S1.lower_central_series())
+        >>> len2 = len(S2.lower_central_series())
+        >>> len3 = len(S3.lower_central_series())
+
+        >>> len1 == len2
+        True
+        >>> len1 < len3
+        True
+
+        '''
+        from sympy.combinatorics.homomorphisms import (
+                orbit_homomorphism, block_homomorphism)
+
+        if not isprime(p):
+            raise ValueError("p must be a prime")
+
+        def is_p_group(G):
+            # check if the order of G is a power of p
+            # and return the power
+            m = G.order()
+            n = 0
+            while m % p == 0:
+                m = m/p
+                n += 1
+                if m == 1:
+                    return True, n
+            return False, n
+
+        def _sylow_reduce(mu, nu):
+            # reduction based on two homomorphisms
+            # mu and nu with trivially intersecting
+            # kernels
+            Q = mu.image().sylow_subgroup(p)
+            Q = mu.invert_subgroup(Q)
+            nu = nu.restrict_to(Q)
+            R = nu.image().sylow_subgroup(p)
+            return nu.invert_subgroup(R)
+
+        order = self.order()
+        if order % p != 0:
+            return PermutationGroup([self.identity])
+        p_group, n = is_p_group(self)
+        if p_group:
+            return self
+
+        if self.is_alt_sym():
+            return PermutationGroup(self._sylow_alt_sym(p))
+
+        # if there is a non-trivial orbit with size not divisible
+        # by p, the sylow subgroup is contained in its stabilizer
+        # (by orbit-stabilizer theorem)
+        orbits = self.orbits()
+        non_p_orbits = [o for o in orbits if len(o) % p != 0 and len(o) != 1]
+        if non_p_orbits:
+            G = self.stabilizer(list(non_p_orbits[0]).pop())
+            return G.sylow_subgroup(p)
+
+        if not self.is_transitive():
+            # apply _sylow_reduce to orbit actions
+            orbits = sorted(orbits, key=len)
+            omega1 = orbits.pop()
+            omega2 = orbits[0].union(*orbits)
+            mu = orbit_homomorphism(self, omega1)
+            nu = orbit_homomorphism(self, omega2)
+            return _sylow_reduce(mu, nu)
+
+        blocks = self.minimal_blocks()
+        if len(blocks) > 1:
+            # apply _sylow_reduce to block system actions
+            mu = block_homomorphism(self, blocks[0])
+            nu = block_homomorphism(self, blocks[1])
+            return _sylow_reduce(mu, nu)
+        elif len(blocks) == 1:
+            block = list(blocks)[0]
+            if any(e != 0 for e in block):
+                # self is imprimitive
+                mu = block_homomorphism(self, block)
+                if not is_p_group(mu.image())[0]:
+                    S = mu.image().sylow_subgroup(p)
+                    return mu.invert_subgroup(S).sylow_subgroup(p)
+
+        # find an element of order p
+        g = self.random()
+        g_order = g.order()
+        while g_order % p != 0 or g_order == 0:
+            g = self.random()
+            g_order = g.order()
+        g = g**(g_order // p)
+        if order % p**2 != 0:
+            return PermutationGroup(g)
+
+        C = self.centralizer(g)
+        while C.order() % p**n != 0:
+            S = C.sylow_subgroup(p)
+            s_order = S.order()
+            Z = S.center()
+            P = Z._p_elements_group(p)
+            h = P.random()
+            C_h = self.centralizer(h)
+            while C_h.order() % p*s_order != 0:
+                h = P.random()
+                C_h = self.centralizer(h)
+            C = C_h
+
+        return C.sylow_subgroup(p)
+
+    def _block_verify(self, L, alpha):
+        delta = sorted(self.orbit(alpha))
+        # p[i] will be the number of the block
+        # delta[i] belongs to
+        p = [-1]*len(delta)
+        blocks = [-1]*len(delta)
+
+        B = [[]] # future list of blocks
+        u = [0]*len(delta) # u[i] in L s.t. alpha^u[i] = B[0][i]
+
+        t = L.orbit_transversal(alpha, pairs=True)
+        for a, beta in t:
+            B[0].append(a)
+            i_a = delta.index(a)
+            p[i_a] = 0
+            blocks[i_a] = alpha
+            u[i_a] = beta
+
+        rho = 0
+        m = 0 # number of blocks - 1
+
+        while rho <= m:
+            beta = B[rho][0]
+            for g in self.generators:
+                d = beta^g
+                i_d = delta.index(d)
+                sigma = p[i_d]
+                if sigma < 0:
+                    # define a new block
+                    m += 1
+                    sigma = m
+                    u[i_d] = u[delta.index(beta)]*g
+                    p[i_d] = sigma
+                    rep = d
+                    blocks[i_d] = rep
+                    newb = [rep]
+                    for gamma in B[rho][1:]:
+                        i_gamma = delta.index(gamma)
+                        d = gamma^g
+                        i_d = delta.index(d)
+                        if p[i_d] < 0:
+                            u[i_d] = u[i_gamma]*g
+                            p[i_d] = sigma
+                            blocks[i_d] = rep
+                            newb.append(d)
+                        else:
+                            # B[rho] is not a block
+                            s = u[i_gamma]*g*u[i_d]**(-1)
+                            return False, s
+
+                    B.append(newb)
+                else:
+                    for h in B[rho][1:]:
+                        if h^g not in B[sigma]:
+                            # B[rho] is not a block
+                            s = u[delta.index(beta)]*g*u[i_d]**(-1)
+                            return False, s
+            rho += 1
+
+        return True, blocks
+
+    def _verify(H, K, phi, z, alpha):
+        '''
+        Return a list of relators ``rels`` in generators ``gens`_h` that
+        are mapped to ``H.generators`` by ``phi`` so that given a finite
+        presentation  of ``K`` on a subset of ``gens_h``
+         is a finite presentation of ``H``.
+
+        Explanation
+        ===========
+
+        ``H`` should be generated by the union of ``K.generators`` and ``z``
+        (a single generator), and ``H.stabilizer(alpha) == K``; ``phi`` is a
+        canonical injection from a free group into a permutation group
+        containing ``H``.
+
+        The algorithm is described in [1], Chapter 6.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import free_group, Permutation, PermutationGroup
+        >>> from sympy.combinatorics.homomorphisms import homomorphism
+        >>> from sympy.combinatorics.fp_groups import FpGroup
+
+        >>> H = PermutationGroup(Permutation(0, 2), Permutation (1, 5))
+        >>> K = PermutationGroup(Permutation(5)(0, 2))
+        >>> F = free_group("x_0 x_1")[0]
+        >>> gens = F.generators
+        >>> phi = homomorphism(F, H, F.generators, H.generators)
+        >>> rels_k = [gens[0]**2] # relators for presentation of K
+        >>> z= Permutation(1, 5)
+        >>> check, rels_h = H._verify(K, phi, z, 1)
+        >>> check
+        True
+        >>> rels = rels_k + rels_h
+        >>> G = FpGroup(F, rels) # presentation of H
+        >>> G.order() == H.order()
+        True
+
+        See also
+        ========
+
+        strong_presentation, presentation, stabilizer
+
+        '''
+
+        orbit = H.orbit(alpha)
+        beta = alpha^(z**-1)
+
+        K_beta = K.stabilizer(beta)
+
+        # orbit representatives of K_beta
+        gammas = [alpha, beta]
+        orbits = list({tuple(K_beta.orbit(o)) for o in orbit})
+        orbit_reps = [orb[0] for orb in orbits]
+        for rep in orbit_reps:
+            if rep not in gammas:
+                gammas.append(rep)
+
+        # orbit transversal of K
+        betas = [alpha, beta]
+        transversal = {alpha: phi.invert(H.identity), beta: phi.invert(z**-1)}
+
+        for s, g in K.orbit_transversal(beta, pairs=True):
+            if s not in transversal:
+                transversal[s] = transversal[beta]*phi.invert(g)
+
+
+        union = K.orbit(alpha).union(K.orbit(beta))
+        while (len(union) < len(orbit)):
+            for gamma in gammas:
+                if gamma in union:
+                    r = gamma^z
+                    if r not in union:
+                        betas.append(r)
+                        transversal[r] = transversal[gamma]*phi.invert(z)
+                        for s, g in K.orbit_transversal(r, pairs=True):
+                            if s not in transversal:
+                                transversal[s] = transversal[r]*phi.invert(g)
+                        union = union.union(K.orbit(r))
+                        break
+
+        # compute relators
+        rels = []
+
+        for b in betas:
+            k_gens = K.stabilizer(b).generators
+            for y in k_gens:
+                new_rel = transversal[b]
+                gens = K.generator_product(y, original=True)
+                for g in gens[::-1]:
+                    new_rel = new_rel*phi.invert(g)
+                new_rel = new_rel*transversal[b]**-1
+
+                perm = phi(new_rel)
+                try:
+                    gens = K.generator_product(perm, original=True)
+                except ValueError:
+                    return False, perm
+                for g in gens:
+                    new_rel = new_rel*phi.invert(g)**-1
+                if new_rel not in rels:
+                    rels.append(new_rel)
+
+        for gamma in gammas:
+            new_rel = transversal[gamma]*phi.invert(z)*transversal[gamma^z]**-1
+            perm = phi(new_rel)
+            try:
+                gens = K.generator_product(perm, original=True)
+            except ValueError:
+                return False, perm
+            for g in gens:
+                new_rel = new_rel*phi.invert(g)**-1
+            if new_rel not in rels:
+                rels.append(new_rel)
+
+        return True, rels
+
+    def strong_presentation(self):
+        '''
+        Return a strong finite presentation of group. The generators
+        of the returned group are in the same order as the strong
+        generators of group.
+
+        The algorithm is based on Sims' Verify algorithm described
+        in [1], Chapter 6.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.named_groups import DihedralGroup
+        >>> P = DihedralGroup(4)
+        >>> G = P.strong_presentation()
+        >>> P.order() == G.order()
+        True
+
+        See Also
+        ========
+
+        presentation, _verify
+
+        '''
+        from sympy.combinatorics.fp_groups import (FpGroup,
+                                            simplify_presentation)
+        from sympy.combinatorics.free_groups import free_group
+        from sympy.combinatorics.homomorphisms import (block_homomorphism,
+                                           homomorphism, GroupHomomorphism)
+
+        strong_gens = self.strong_gens[:]
+        stabs = self.basic_stabilizers[:]
+        base = self.base[:]
+
+        # injection from a free group on len(strong_gens)
+        # generators into G
+        gen_syms = [('x_%d'%i) for i in range(len(strong_gens))]
+        F = free_group(', '.join(gen_syms))[0]
+        phi = homomorphism(F, self, F.generators, strong_gens)
+
+        H = PermutationGroup(self.identity)
+        while stabs:
+            alpha = base.pop()
+            K = H
+            H = stabs.pop()
+            new_gens = [g for g in H.generators if g not in K]
+
+            if K.order() == 1:
+                z = new_gens.pop()
+                rels = [F.generators[-1]**z.order()]
+                intermediate_gens = [z]
+                K = PermutationGroup(intermediate_gens)
+
+            # add generators one at a time building up from K to H
+            while new_gens:
+                z = new_gens.pop()
+                intermediate_gens = [z] + intermediate_gens
+                K_s = PermutationGroup(intermediate_gens)
+                orbit = K_s.orbit(alpha)
+                orbit_k = K.orbit(alpha)
+
+                # split into cases based on the orbit of K_s
+                if orbit_k == orbit:
+                    if z in K:
+                        rel = phi.invert(z)
+                        perm = z
+                    else:
+                        t = K.orbit_rep(alpha, alpha^z)
+                        rel = phi.invert(z)*phi.invert(t)**-1
+                        perm = z*t**-1
+                    for g in K.generator_product(perm, original=True):
+                        rel = rel*phi.invert(g)**-1
+                    new_rels = [rel]
+                elif len(orbit_k) == 1:
+                    # `success` is always true because `strong_gens`
+                    # and `base` are already a verified BSGS. Later
+                    # this could be changed to start with a randomly
+                    # generated (potential) BSGS, and then new elements
+                    # would have to be appended to it when `success`
+                    # is false.
+                    success, new_rels = K_s._verify(K, phi, z, alpha)
+                else:
+                    # K.orbit(alpha) should be a block
+                    # under the action of K_s on K_s.orbit(alpha)
+                    check, block = K_s._block_verify(K, alpha)
+                    if check:
+                        # apply _verify to the action of K_s
+                        # on the block system; for convenience,
+                        # add the blocks as additional points
+                        # that K_s should act on
+                        t = block_homomorphism(K_s, block)
+                        m = t.codomain.degree # number of blocks
+                        d = K_s.degree
+
+                        # conjugating with p will shift
+                        # permutations in t.image() to
+                        # higher numbers, e.g.
+                        # p*(0 1)*p = (m m+1)
+                        p = Permutation()
+                        for i in range(m):
+                            p *= Permutation(i, i+d)
+
+                        t_img = t.images
+                        # combine generators of K_s with their
+                        # action on the block system
+                        images = {g: g*p*t_img[g]*p for g in t_img}
+                        for g in self.strong_gens[:-len(K_s.generators)]:
+                            images[g] = g
+                        K_s_act = PermutationGroup(list(images.values()))
+                        f = GroupHomomorphism(self, K_s_act, images)
+
+                        K_act = PermutationGroup([f(g) for g in K.generators])
+                        success, new_rels = K_s_act._verify(K_act, f.compose(phi), f(z), d)
+
+                for n in new_rels:
+                    if n not in rels:
+                        rels.append(n)
+                K = K_s
+
+        group = FpGroup(F, rels)
+        return simplify_presentation(group)
+
+    def presentation(self, eliminate_gens=True):
+        '''
+        Return an `FpGroup` presentation of the group.
+
+        The algorithm is described in [1], Chapter 6.1.
+
+        '''
+        from sympy.combinatorics.fp_groups import (FpGroup,
+                                            simplify_presentation)
+        from sympy.combinatorics.coset_table import CosetTable
+        from sympy.combinatorics.free_groups import free_group
+        from sympy.combinatorics.homomorphisms import homomorphism
+
+        if self._fp_presentation:
+            return self._fp_presentation
+
+        def _factor_group_by_rels(G, rels):
+            if isinstance(G, FpGroup):
+                rels.extend(G.relators)
+                return FpGroup(G.free_group, list(set(rels)))
+            return FpGroup(G, rels)
+
+        gens = self.generators
+        len_g = len(gens)
+
+        if len_g == 1:
+            order = gens[0].order()
+            # handle the trivial group
+            if order == 1:
+                return free_group([])[0]
+            F, x = free_group('x')
+            return FpGroup(F, [x**order])
+
+        if self.order() > 20:
+            half_gens = self.generators[0:(len_g+1)//2]
+        else:
+            half_gens = []
+        H = PermutationGroup(half_gens)
+        H_p = H.presentation()
+
+        len_h = len(H_p.generators)
+
+        C = self.coset_table(H)
+        n = len(C) # subgroup index
+
+        gen_syms = [('x_%d'%i) for i in range(len(gens))]
+        F = free_group(', '.join(gen_syms))[0]
+
+        # mapping generators of H_p to those of F
+        images = [F.generators[i] for i in range(len_h)]
+        R = homomorphism(H_p, F, H_p.generators, images, check=False)
+
+        # rewrite relators
+        rels = R(H_p.relators)
+        G_p = FpGroup(F, rels)
+
+        # injective homomorphism from G_p into self
+        T = homomorphism(G_p, self, G_p.generators, gens)
+
+        C_p = CosetTable(G_p, [])
+
+        C_p.table = [[None]*(2*len_g) for i in range(n)]
+
+        # initiate the coset transversal
+        transversal = [None]*n
+        transversal[0] = G_p.identity
+
+        # fill in the coset table as much as possible
+        for i in range(2*len_h):
+            C_p.table[0][i] = 0
+
+        gamma = 1
+        for alpha, x in product(range(n), range(2*len_g)):
+            beta = C[alpha][x]
+            if beta == gamma:
+                gen = G_p.generators[x//2]**((-1)**(x % 2))
+                transversal[beta] = transversal[alpha]*gen
+                C_p.table[alpha][x] = beta
+                C_p.table[beta][x + (-1)**(x % 2)] = alpha
+                gamma += 1
+                if gamma == n:
+                    break
+
+        C_p.p = list(range(n))
+        beta = x = 0
+
+        while not C_p.is_complete():
+            # find the first undefined entry
+            while C_p.table[beta][x] == C[beta][x]:
+                x = (x + 1) % (2*len_g)
+                if x == 0:
+                    beta = (beta + 1) % n
+
+            # define a new relator
+            gen = G_p.generators[x//2]**((-1)**(x % 2))
+            new_rel = transversal[beta]*gen*transversal[C[beta][x]]**-1
+            perm = T(new_rel)
+            nxt = G_p.identity
+            for s in H.generator_product(perm, original=True):
+                nxt = nxt*T.invert(s)**-1
+            new_rel = new_rel*nxt
+
+            # continue coset enumeration
+            G_p = _factor_group_by_rels(G_p, [new_rel])
+            C_p.scan_and_fill(0, new_rel)
+            C_p = G_p.coset_enumeration([], strategy="coset_table",
+                                draft=C_p, max_cosets=n, incomplete=True)
+
+        self._fp_presentation = simplify_presentation(G_p)
+        return self._fp_presentation
+
+    def polycyclic_group(self):
+        """
+        Return the PolycyclicGroup instance with below parameters:
+
+        Explanation
+        ===========
+
+        * pc_sequence : Polycyclic sequence is formed by collecting all
+          the missing generators between the adjacent groups in the
+          derived series of given permutation group.
+
+        * pc_series : Polycyclic series is formed by adding all the missing
+          generators of ``der[i+1]`` in ``der[i]``, where ``der`` represents
+          the derived series.
+
+        * relative_order : A list, computed by the ratio of adjacent groups in
+          pc_series.
+
+        """
+        from sympy.combinatorics.pc_groups import PolycyclicGroup
+        if not self.is_polycyclic:
+            raise ValueError("The group must be solvable")
+
+        der = self.derived_series()
+        pc_series = []
+        pc_sequence = []
+        relative_order = []
+        pc_series.append(der[-1])
+        der.reverse()
+
+        for i in range(len(der)-1):
+            H = der[i]
+            for g in der[i+1].generators:
+                if g not in H:
+                    H = PermutationGroup([g] + H.generators)
+                    pc_series.insert(0, H)
+                    pc_sequence.insert(0, g)
+
+                    G1 = pc_series[0].order()
+                    G2 = pc_series[1].order()
+                    relative_order.insert(0, G1 // G2)
+
+        return PolycyclicGroup(pc_sequence, pc_series, relative_order, collector=None)
+
+
+def _orbit(degree, generators, alpha, action='tuples'):
+    r"""Compute the orbit of alpha `\{g(\alpha) | g \in G\}` as a set.
+
+    Explanation
+    ===========
+
+    The time complexity of the algorithm used here is `O(|Orb|*r)` where
+    `|Orb|` is the size of the orbit and ``r`` is the number of generators of
+    the group. For a more detailed analysis, see [1], p.78, [2], pp. 19-21.
+    Here alpha can be a single point, or a list of points.
+
+    If alpha is a single point, the ordinary orbit is computed.
+    if alpha is a list of points, there are three available options:
+
+    'union' - computes the union of the orbits of the points in the list
+    'tuples' - computes the orbit of the list interpreted as an ordered
+    tuple under the group action ( i.e., g((1, 2, 3)) = (g(1), g(2), g(3)) )
+    'sets' - computes the orbit of the list interpreted as a sets
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation, PermutationGroup
+    >>> from sympy.combinatorics.perm_groups import _orbit
+    >>> a = Permutation([1, 2, 0, 4, 5, 6, 3])
+    >>> G = PermutationGroup([a])
+    >>> _orbit(G.degree, G.generators, 0)
+    {0, 1, 2}
+    >>> _orbit(G.degree, G.generators, [0, 4], 'union')
+    {0, 1, 2, 3, 4, 5, 6}
+
+    See Also
+    ========
+
+    orbit, orbit_transversal
+
+    """
+    if not hasattr(alpha, '__getitem__'):
+        alpha = [alpha]
+
+    gens = [x._array_form for x in generators]
+    if len(alpha) == 1 or action == 'union':
+        orb = alpha
+        used = [False]*degree
+        for el in alpha:
+            used[el] = True
+        for b in orb:
+            for gen in gens:
+                temp = gen[b]
+                if used[temp] == False:
+                    orb.append(temp)
+                    used[temp] = True
+        return set(orb)
+    elif action == 'tuples':
+        alpha = tuple(alpha)
+        orb = [alpha]
+        used = {alpha}
+        for b in orb:
+            for gen in gens:
+                temp = tuple([gen[x] for x in b])
+                if temp not in used:
+                    orb.append(temp)
+                    used.add(temp)
+        return set(orb)
+    elif action == 'sets':
+        alpha = frozenset(alpha)
+        orb = [alpha]
+        used = {alpha}
+        for b in orb:
+            for gen in gens:
+                temp = frozenset([gen[x] for x in b])
+                if temp not in used:
+                    orb.append(temp)
+                    used.add(temp)
+        return {tuple(x) for x in orb}
+
+
+def _orbits(degree, generators):
+    """Compute the orbits of G.
+
+    If ``rep=False`` it returns a list of sets else it returns a list of
+    representatives of the orbits
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy.combinatorics.perm_groups import _orbits
+    >>> a = Permutation([0, 2, 1])
+    >>> b = Permutation([1, 0, 2])
+    >>> _orbits(a.size, [a, b])
+    [{0, 1, 2}]
+    """
+
+    orbs = []
+    sorted_I = list(range(degree))
+    I = set(sorted_I)
+    while I:
+        i = sorted_I[0]
+        orb = _orbit(degree, generators, i)
+        orbs.append(orb)
+        # remove all indices that are in this orbit
+        I -= orb
+        sorted_I = [i for i in sorted_I if i not in orb]
+    return orbs
+
+
+def _orbit_transversal(degree, generators, alpha, pairs, af=False, slp=False):
+    r"""Computes a transversal for the orbit of ``alpha`` as a set.
+
+    Explanation
+    ===========
+
+    generators   generators of the group ``G``
+
+    For a permutation group ``G``, a transversal for the orbit
+    `Orb = \{g(\alpha) | g \in G\}` is a set
+    `\{g_\beta | g_\beta(\alpha) = \beta\}` for `\beta \in Orb`.
+    Note that there may be more than one possible transversal.
+    If ``pairs`` is set to ``True``, it returns the list of pairs
+    `(\beta, g_\beta)`. For a proof of correctness, see [1], p.79
+
+    if ``af`` is ``True``, the transversal elements are given in
+    array form.
+
+    If `slp` is `True`, a dictionary `{beta: slp_beta}` is returned
+    for `\beta \in Orb` where `slp_beta` is a list of indices of the
+    generators in `generators` s.t. if `slp_beta = [i_1 \dots i_n]`
+    `g_\beta = generators[i_n] \times \dots \times generators[i_1]`.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import DihedralGroup
+    >>> from sympy.combinatorics.perm_groups import _orbit_transversal
+    >>> G = DihedralGroup(6)
+    >>> _orbit_transversal(G.degree, G.generators, 0, False)
+    [(5), (0 1 2 3 4 5), (0 5)(1 4)(2 3), (0 2 4)(1 3 5), (5)(0 4)(1 3), (0 3)(1 4)(2 5)]
+    """
+
+    tr = [(alpha, list(range(degree)))]
+    slp_dict = {alpha: []}
+    used = [False]*degree
+    used[alpha] = True
+    gens = [x._array_form for x in generators]
+    for x, px in tr:
+        px_slp = slp_dict[x]
+        for gen in gens:
+            temp = gen[x]
+            if used[temp] == False:
+                slp_dict[temp] = [gens.index(gen)] + px_slp
+                tr.append((temp, _af_rmul(gen, px)))
+                used[temp] = True
+    if pairs:
+        if not af:
+            tr = [(x, _af_new(y)) for x, y in tr]
+        if not slp:
+            return tr
+        return tr, slp_dict
+
+    if af:
+        tr = [y for _, y in tr]
+        if not slp:
+            return tr
+        return tr, slp_dict
+
+    tr = [_af_new(y) for _, y in tr]
+    if not slp:
+        return tr
+    return tr, slp_dict
+
+
+def _stabilizer(degree, generators, alpha):
+    r"""Return the stabilizer subgroup of ``alpha``.
+
+    Explanation
+    ===========
+
+    The stabilizer of `\alpha` is the group `G_\alpha =
+    \{g \in G | g(\alpha) = \alpha\}`.
+    For a proof of correctness, see [1], p.79.
+
+    degree :       degree of G
+    generators :   generators of G
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.perm_groups import _stabilizer
+    >>> from sympy.combinatorics.named_groups import DihedralGroup
+    >>> G = DihedralGroup(6)
+    >>> _stabilizer(G.degree, G.generators, 5)
+    [(5)(0 4)(1 3), (5)]
+
+    See Also
+    ========
+
+    orbit
+
+    """
+    orb = [alpha]
+    table = {alpha: list(range(degree))}
+    table_inv = {alpha: list(range(degree))}
+    used = [False]*degree
+    used[alpha] = True
+    gens = [x._array_form for x in generators]
+    stab_gens = []
+    for b in orb:
+        for gen in gens:
+            temp = gen[b]
+            if used[temp] is False:
+                gen_temp = _af_rmul(gen, table[b])
+                orb.append(temp)
+                table[temp] = gen_temp
+                table_inv[temp] = _af_invert(gen_temp)
+                used[temp] = True
+            else:
+                schreier_gen = _af_rmuln(table_inv[temp], gen, table[b])
+                if schreier_gen not in stab_gens:
+                    stab_gens.append(schreier_gen)
+    return [_af_new(x) for x in stab_gens]
+
+
+PermGroup = PermutationGroup
+
+
+class SymmetricPermutationGroup(Basic):
+    """
+    The class defining the lazy form of SymmetricGroup.
+
+    deg : int
+
+    """
+    def __new__(cls, deg):
+        deg = _sympify(deg)
+        obj = Basic.__new__(cls, deg)
+        return obj
+
+    def __init__(self, *args, **kwargs):
+        self._deg = self.args[0]
+        self._order = None
+
+    def __contains__(self, i):
+        """Return ``True`` if *i* is contained in SymmetricPermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, SymmetricPermutationGroup
+        >>> G = SymmetricPermutationGroup(4)
+        >>> Permutation(1, 2, 3) in G
+        True
+
+        """
+        if not isinstance(i, Permutation):
+            raise TypeError("A SymmetricPermutationGroup contains only Permutations as "
+                            "elements, not elements of type %s" % type(i))
+        return i.size == self.degree
+
+    def order(self):
+        """
+        Return the order of the SymmetricPermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import SymmetricPermutationGroup
+        >>> G = SymmetricPermutationGroup(4)
+        >>> G.order()
+        24
+        """
+        if self._order is not None:
+            return self._order
+        n = self._deg
+        self._order = factorial(n)
+        return self._order
+
+    @property
+    def degree(self):
+        """
+        Return the degree of the SymmetricPermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import SymmetricPermutationGroup
+        >>> G = SymmetricPermutationGroup(4)
+        >>> G.degree
+        4
+
+        """
+        return self._deg
+
+    @property
+    def identity(self):
+        '''
+        Return the identity element of the SymmetricPermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import SymmetricPermutationGroup
+        >>> G = SymmetricPermutationGroup(4)
+        >>> G.identity()
+        (3)
+
+        '''
+        return _af_new(list(range(self._deg)))
+
+
+class Coset(Basic):
+    """A left coset of a permutation group with respect to an element.
+
+    Parameters
+    ==========
+
+    g : Permutation
+
+    H : PermutationGroup
+
+    dir : "+" or "-", If not specified by default it will be "+"
+        here ``dir`` specified the type of coset "+" represent the
+        right coset and "-" represent the left coset.
+
+    G : PermutationGroup, optional
+        The group which contains *H* as its subgroup and *g* as its
+        element.
+
+        If not specified, it would automatically become a symmetric
+        group ``SymmetricPermutationGroup(g.size)`` and
+        ``SymmetricPermutationGroup(H.degree)`` if ``g.size`` and ``H.degree``
+        are matching.``SymmetricPermutationGroup`` is a lazy form of SymmetricGroup
+        used for representation purpose.
+
+    """
+
+    def __new__(cls, g, H, G=None, dir="+"):
+        g = _sympify(g)
+        if not isinstance(g, Permutation):
+            raise NotImplementedError
+
+        H = _sympify(H)
+        if not isinstance(H, PermutationGroup):
+            raise NotImplementedError
+
+        if G is not None:
+            G = _sympify(G)
+            if not isinstance(G, (PermutationGroup, SymmetricPermutationGroup)):
+                raise NotImplementedError
+            if not H.is_subgroup(G):
+                raise ValueError("{} must be a subgroup of {}.".format(H, G))
+            if g not in G:
+                raise ValueError("{} must be an element of {}.".format(g, G))
+        else:
+            g_size = g.size
+            h_degree = H.degree
+            if g_size != h_degree:
+                raise ValueError(
+                    "The size of the permutation {} and the degree of "
+                    "the permutation group {} should be matching "
+                    .format(g, H))
+            G = SymmetricPermutationGroup(g.size)
+
+        if isinstance(dir, str):
+            dir = Symbol(dir)
+        elif not isinstance(dir, Symbol):
+            raise TypeError("dir must be of type basestring or "
+                    "Symbol, not %s" % type(dir))
+        if str(dir) not in ('+', '-'):
+            raise ValueError("dir must be one of '+' or '-' not %s" % dir)
+        obj = Basic.__new__(cls, g, H, G, dir)
+        return obj
+
+    def __init__(self, *args, **kwargs):
+        self._dir = self.args[3]
+
+    @property
+    def is_left_coset(self):
+        """
+        Check if the coset is left coset that is ``gH``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup, Coset
+        >>> a = Permutation(1, 2)
+        >>> b = Permutation(0, 1)
+        >>> G = PermutationGroup([a, b])
+        >>> cst = Coset(a, G, dir="-")
+        >>> cst.is_left_coset
+        True
+
+        """
+        return str(self._dir) == '-'
+
+    @property
+    def is_right_coset(self):
+        """
+        Check if the coset is right coset that is ``Hg``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation, PermutationGroup, Coset
+        >>> a = Permutation(1, 2)
+        >>> b = Permutation(0, 1)
+        >>> G = PermutationGroup([a, b])
+        >>> cst = Coset(a, G, dir="+")
+        >>> cst.is_right_coset
+        True
+
+        """
+        return str(self._dir) == '+'
+
+    def as_list(self):
+        """
+        Return all the elements of coset in the form of list.
+        """
+        g = self.args[0]
+        H = self.args[1]
+        cst = []
+        if str(self._dir) == '+':
+            for h in H.elements:
+                cst.append(h*g)
+        else:
+            for h in H.elements:
+                cst.append(g*h)
+        return cst
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/permutations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/permutations.py
new file mode 100644
index 0000000000000000000000000000000000000000..3718467b69cbab2b9b0dd73e8fa160cceb0324bf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/permutations.py
@@ -0,0 +1,3114 @@
+import random
+from collections import defaultdict
+from collections.abc import Iterable
+from functools import reduce
+
+from sympy.core.parameters import global_parameters
+from sympy.core.basic import Atom
+from sympy.core.expr import Expr
+from sympy.core.numbers import int_valued
+from sympy.core.numbers import Integer
+from sympy.core.sympify import _sympify
+from sympy.matrices import zeros
+from sympy.polys.polytools import lcm
+from sympy.printing.repr import srepr
+from sympy.utilities.iterables import (flatten, has_variety, minlex,
+    has_dups, runs, is_sequence)
+from sympy.utilities.misc import as_int
+from mpmath.libmp.libintmath import ifac
+from sympy.multipledispatch import dispatch
+
+def _af_rmul(a, b):
+    """
+    Return the product b*a; input and output are array forms. The ith value
+    is a[b[i]].
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import _af_rmul, Permutation
+
+    >>> a, b = [1, 0, 2], [0, 2, 1]
+    >>> _af_rmul(a, b)
+    [1, 2, 0]
+    >>> [a[b[i]] for i in range(3)]
+    [1, 2, 0]
+
+    This handles the operands in reverse order compared to the ``*`` operator:
+
+    >>> a = Permutation(a)
+    >>> b = Permutation(b)
+    >>> list(a*b)
+    [2, 0, 1]
+    >>> [b(a(i)) for i in range(3)]
+    [2, 0, 1]
+
+    See Also
+    ========
+
+    rmul, _af_rmuln
+    """
+    return [a[i] for i in b]
+
+
+def _af_rmuln(*abc):
+    """
+    Given [a, b, c, ...] return the product of ...*c*b*a using array forms.
+    The ith value is a[b[c[i]]].
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import _af_rmul, Permutation
+
+    >>> a, b = [1, 0, 2], [0, 2, 1]
+    >>> _af_rmul(a, b)
+    [1, 2, 0]
+    >>> [a[b[i]] for i in range(3)]
+    [1, 2, 0]
+
+    This handles the operands in reverse order compared to the ``*`` operator:
+
+    >>> a = Permutation(a); b = Permutation(b)
+    >>> list(a*b)
+    [2, 0, 1]
+    >>> [b(a(i)) for i in range(3)]
+    [2, 0, 1]
+
+    See Also
+    ========
+
+    rmul, _af_rmul
+    """
+    a = abc
+    m = len(a)
+    if m == 3:
+        p0, p1, p2 = a
+        return [p0[p1[i]] for i in p2]
+    if m == 4:
+        p0, p1, p2, p3 = a
+        return [p0[p1[p2[i]]] for i in p3]
+    if m == 5:
+        p0, p1, p2, p3, p4 = a
+        return [p0[p1[p2[p3[i]]]] for i in p4]
+    if m == 6:
+        p0, p1, p2, p3, p4, p5 = a
+        return [p0[p1[p2[p3[p4[i]]]]] for i in p5]
+    if m == 7:
+        p0, p1, p2, p3, p4, p5, p6 = a
+        return [p0[p1[p2[p3[p4[p5[i]]]]]] for i in p6]
+    if m == 8:
+        p0, p1, p2, p3, p4, p5, p6, p7 = a
+        return [p0[p1[p2[p3[p4[p5[p6[i]]]]]]] for i in p7]
+    if m == 1:
+        return a[0][:]
+    if m == 2:
+        a, b = a
+        return [a[i] for i in b]
+    if m == 0:
+        raise ValueError("String must not be empty")
+    p0 = _af_rmuln(*a[:m//2])
+    p1 = _af_rmuln(*a[m//2:])
+    return [p0[i] for i in p1]
+
+
+def _af_parity(pi):
+    """
+    Computes the parity of a permutation in array form.
+
+    Explanation
+    ===========
+
+    The parity of a permutation reflects the parity of the
+    number of inversions in the permutation, i.e., the
+    number of pairs of x and y such that x > y but p[x] < p[y].
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import _af_parity
+    >>> _af_parity([0, 1, 2, 3])
+    0
+    >>> _af_parity([3, 2, 0, 1])
+    1
+
+    See Also
+    ========
+
+    Permutation
+    """
+    n = len(pi)
+    a = [0] * n
+    c = 0
+    for j in range(n):
+        if a[j] == 0:
+            c += 1
+            a[j] = 1
+            i = j
+            while pi[i] != j:
+                i = pi[i]
+                a[i] = 1
+    return (n - c) % 2
+
+
+def _af_invert(a):
+    """
+    Finds the inverse, ~A, of a permutation, A, given in array form.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import _af_invert, _af_rmul
+    >>> A = [1, 2, 0, 3]
+    >>> _af_invert(A)
+    [2, 0, 1, 3]
+    >>> _af_rmul(_, A)
+    [0, 1, 2, 3]
+
+    See Also
+    ========
+
+    Permutation, __invert__
+    """
+    inv_form = [0] * len(a)
+    for i, ai in enumerate(a):
+        inv_form[ai] = i
+    return inv_form
+
+
+def _af_pow(a, n):
+    """
+    Routine for finding powers of a permutation.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy.combinatorics.permutations import _af_pow
+    >>> p = Permutation([2, 0, 3, 1])
+    >>> p.order()
+    4
+    >>> _af_pow(p._array_form, 4)
+    [0, 1, 2, 3]
+    """
+    if n == 0:
+        return list(range(len(a)))
+    if n < 0:
+        return _af_pow(_af_invert(a), -n)
+    if n == 1:
+        return a[:]
+    elif n == 2:
+        b = [a[i] for i in a]
+    elif n == 3:
+        b = [a[a[i]] for i in a]
+    elif n == 4:
+        b = [a[a[a[i]]] for i in a]
+    else:
+        # use binary multiplication
+        b = list(range(len(a)))
+        while 1:
+            if n & 1:
+                b = [b[i] for i in a]
+                n -= 1
+                if not n:
+                    break
+            if n % 4 == 0:
+                a = [a[a[a[i]]] for i in a]
+                n = n // 4
+            elif n % 2 == 0:
+                a = [a[i] for i in a]
+                n = n // 2
+    return b
+
+
+def _af_commutes_with(a, b):
+    """
+    Checks if the two permutations with array forms
+    given by ``a`` and ``b`` commute.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import _af_commutes_with
+    >>> _af_commutes_with([1, 2, 0], [0, 2, 1])
+    False
+
+    See Also
+    ========
+
+    Permutation, commutes_with
+    """
+    return not any(a[b[i]] != b[a[i]] for i in range(len(a) - 1))
+
+
+class Cycle(dict):
+    """
+    Wrapper around dict which provides the functionality of a disjoint cycle.
+
+    Explanation
+    ===========
+
+    A cycle shows the rule to use to move subsets of elements to obtain
+    a permutation. The Cycle class is more flexible than Permutation in
+    that 1) all elements need not be present in order to investigate how
+    multiple cycles act in sequence and 2) it can contain singletons:
+
+    >>> from sympy.combinatorics.permutations import Perm, Cycle
+
+    A Cycle will automatically parse a cycle given as a tuple on the rhs:
+
+    >>> Cycle(1, 2)(2, 3)
+    (1 3 2)
+
+    The identity cycle, Cycle(), can be used to start a product:
+
+    >>> Cycle()(1, 2)(2, 3)
+    (1 3 2)
+
+    The array form of a Cycle can be obtained by calling the list
+    method (or passing it to the list function) and all elements from
+    0 will be shown:
+
+    >>> a = Cycle(1, 2)
+    >>> a.list()
+    [0, 2, 1]
+    >>> list(a)
+    [0, 2, 1]
+
+    If a larger (or smaller) range is desired use the list method and
+    provide the desired size -- but the Cycle cannot be truncated to
+    a size smaller than the largest element that is out of place:
+
+    >>> b = Cycle(2, 4)(1, 2)(3, 1, 4)(1, 3)
+    >>> b.list()
+    [0, 2, 1, 3, 4]
+    >>> b.list(b.size + 1)
+    [0, 2, 1, 3, 4, 5]
+    >>> b.list(-1)
+    [0, 2, 1]
+
+    Singletons are not shown when printing with one exception: the largest
+    element is always shown -- as a singleton if necessary:
+
+    >>> Cycle(1, 4, 10)(4, 5)
+    (1 5 4 10)
+    >>> Cycle(1, 2)(4)(5)(10)
+    (1 2)(10)
+
+    The array form can be used to instantiate a Permutation so other
+    properties of the permutation can be investigated:
+
+    >>> Perm(Cycle(1, 2)(3, 4).list()).transpositions()
+    [(1, 2), (3, 4)]
+
+    Notes
+    =====
+
+    The underlying structure of the Cycle is a dictionary and although
+    the __iter__ method has been redefined to give the array form of the
+    cycle, the underlying dictionary items are still available with the
+    such methods as items():
+
+    >>> list(Cycle(1, 2).items())
+    [(1, 2), (2, 1)]
+
+    See Also
+    ========
+
+    Permutation
+    """
+    def __missing__(self, arg):
+        """Enter arg into dictionary and return arg."""
+        return as_int(arg)
+
+    def __iter__(self):
+        yield from self.list()
+
+    def __call__(self, *other):
+        """Return product of cycles processed from R to L.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Cycle
+        >>> Cycle(1, 2)(2, 3)
+        (1 3 2)
+
+        An instance of a Cycle will automatically parse list-like
+        objects and Permutations that are on the right. It is more
+        flexible than the Permutation in that all elements need not
+        be present:
+
+        >>> a = Cycle(1, 2)
+        >>> a(2, 3)
+        (1 3 2)
+        >>> a(2, 3)(4, 5)
+        (1 3 2)(4 5)
+
+        """
+        rv = Cycle(*other)
+        for k, v in zip(list(self.keys()), [rv[self[k]] for k in self.keys()]):
+            rv[k] = v
+        return rv
+
+    def list(self, size=None):
+        """Return the cycles as an explicit list starting from 0 up
+        to the greater of the largest value in the cycles and size.
+
+        Truncation of trailing unmoved items will occur when size
+        is less than the maximum element in the cycle; if this is
+        desired, setting ``size=-1`` will guarantee such trimming.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Cycle
+        >>> p = Cycle(2, 3)(4, 5)
+        >>> p.list()
+        [0, 1, 3, 2, 5, 4]
+        >>> p.list(10)
+        [0, 1, 3, 2, 5, 4, 6, 7, 8, 9]
+
+        Passing a length too small will trim trailing, unchanged elements
+        in the permutation:
+
+        >>> Cycle(2, 4)(1, 2, 4).list(-1)
+        [0, 2, 1]
+        """
+        if not self and size is None:
+            raise ValueError('must give size for empty Cycle')
+        if size is not None:
+            big = max([i for i in self.keys() if self[i] != i] + [0])
+            size = max(size, big + 1)
+        else:
+            size = self.size
+        return [self[i] for i in range(size)]
+
+    def __repr__(self):
+        """We want it to print as a Cycle, not as a dict.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Cycle
+        >>> Cycle(1, 2)
+        (1 2)
+        >>> print(_)
+        (1 2)
+        >>> list(Cycle(1, 2).items())
+        [(1, 2), (2, 1)]
+        """
+        if not self:
+            return 'Cycle()'
+        cycles = Permutation(self).cyclic_form
+        s = ''.join(str(tuple(c)) for c in cycles)
+        big = self.size - 1
+        if not any(i == big for c in cycles for i in c):
+            s += '(%s)' % big
+        return 'Cycle%s' % s
+
+    def __str__(self):
+        """We want it to be printed in a Cycle notation with no
+        comma in-between.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Cycle
+        >>> Cycle(1, 2)
+        (1 2)
+        >>> Cycle(1, 2, 4)(5, 6)
+        (1 2 4)(5 6)
+        """
+        if not self:
+            return '()'
+        cycles = Permutation(self).cyclic_form
+        s = ''.join(str(tuple(c)) for c in cycles)
+        big = self.size - 1
+        if not any(i == big for c in cycles for i in c):
+            s += '(%s)' % big
+        s = s.replace(',', '')
+        return s
+
+    def __init__(self, *args):
+        """Load up a Cycle instance with the values for the cycle.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Cycle
+        >>> Cycle(1, 2, 6)
+        (1 2 6)
+        """
+
+        if not args:
+            return
+        if len(args) == 1:
+            if isinstance(args[0], Permutation):
+                for c in args[0].cyclic_form:
+                    self.update(self(*c))
+                return
+            elif isinstance(args[0], Cycle):
+                for k, v in args[0].items():
+                    self[k] = v
+                return
+        args = [as_int(a) for a in args]
+        if any(i < 0 for i in args):
+            raise ValueError('negative integers are not allowed in a cycle.')
+        if has_dups(args):
+            raise ValueError('All elements must be unique in a cycle.')
+        for i in range(-len(args), 0):
+            self[args[i]] = args[i + 1]
+
+    @property
+    def size(self):
+        if not self:
+            return 0
+        return max(self.keys()) + 1
+
+    def copy(self):
+        return Cycle(self)
+
+
+class Permutation(Atom):
+    r"""
+    A permutation, alternatively known as an 'arrangement number' or 'ordering'
+    is an arrangement of the elements of an ordered list into a one-to-one
+    mapping with itself. The permutation of a given arrangement is given by
+    indicating the positions of the elements after re-arrangement [2]_. For
+    example, if one started with elements ``[x, y, a, b]`` (in that order) and
+    they were reordered as ``[x, y, b, a]`` then the permutation would be
+    ``[0, 1, 3, 2]``. Notice that (in SymPy) the first element is always referred
+    to as 0 and the permutation uses the indices of the elements in the
+    original ordering, not the elements ``(a, b, ...)`` themselves.
+
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy import init_printing
+    >>> init_printing(perm_cyclic=False, pretty_print=False)
+
+    Permutations Notation
+    =====================
+
+    Permutations are commonly represented in disjoint cycle or array forms.
+
+    Array Notation and 2-line Form
+    ------------------------------------
+
+    In the 2-line form, the elements and their final positions are shown
+    as a matrix with 2 rows:
+
+    [0    1    2     ... n-1]
+    [p(0) p(1) p(2)  ... p(n-1)]
+
+    Since the first line is always ``range(n)``, where n is the size of p,
+    it is sufficient to represent the permutation by the second line,
+    referred to as the "array form" of the permutation. This is entered
+    in brackets as the argument to the Permutation class:
+
+    >>> p = Permutation([0, 2, 1]); p
+    Permutation([0, 2, 1])
+
+    Given i in range(p.size), the permutation maps i to i^p
+
+    >>> [i^p for i in range(p.size)]
+    [0, 2, 1]
+
+    The composite of two permutations p*q means first apply p, then q, so
+    i^(p*q) = (i^p)^q which is i^p^q according to Python precedence rules:
+
+    >>> q = Permutation([2, 1, 0])
+    >>> [i^p^q for i in range(3)]
+    [2, 0, 1]
+    >>> [i^(p*q) for i in range(3)]
+    [2, 0, 1]
+
+    One can use also the notation p(i) = i^p, but then the composition
+    rule is (p*q)(i) = q(p(i)), not p(q(i)):
+
+    >>> [(p*q)(i) for i in range(p.size)]
+    [2, 0, 1]
+    >>> [q(p(i)) for i in range(p.size)]
+    [2, 0, 1]
+    >>> [p(q(i)) for i in range(p.size)]
+    [1, 2, 0]
+
+    Disjoint Cycle Notation
+    -----------------------
+
+    In disjoint cycle notation, only the elements that have shifted are
+    indicated.
+
+    For example, [1, 3, 2, 0] can be represented as (0, 1, 3)(2).
+    This can be understood from the 2 line format of the given permutation.
+    In the 2-line form,
+    [0    1    2   3]
+    [1    3    2   0]
+
+    The element in the 0th position is 1, so 0 -> 1. The element in the 1st
+    position is three, so 1 -> 3. And the element in the third position is again
+    0, so 3 -> 0. Thus, 0 -> 1 -> 3 -> 0, and 2 -> 2. Thus, this can be represented
+    as 2 cycles: (0, 1, 3)(2).
+    In common notation, singular cycles are not explicitly written as they can be
+    inferred implicitly.
+
+    Only the relative ordering of elements in a cycle matter:
+
+    >>> Permutation(1,2,3) == Permutation(2,3,1) == Permutation(3,1,2)
+    True
+
+    The disjoint cycle notation is convenient when representing
+    permutations that have several cycles in them:
+
+    >>> Permutation(1, 2)(3, 5) == Permutation([[1, 2], [3, 5]])
+    True
+
+    It also provides some economy in entry when computing products of
+    permutations that are written in disjoint cycle notation:
+
+    >>> Permutation(1, 2)(1, 3)(2, 3)
+    Permutation([0, 3, 2, 1])
+    >>> _ == Permutation([[1, 2]])*Permutation([[1, 3]])*Permutation([[2, 3]])
+    True
+
+        Caution: when the cycles have common elements between them then the order
+        in which the permutations are applied matters. This module applies
+        the permutations from *left to right*.
+
+        >>> Permutation(1, 2)(2, 3) == Permutation([(1, 2), (2, 3)])
+        True
+        >>> Permutation(1, 2)(2, 3).list()
+        [0, 3, 1, 2]
+
+        In the above case, (1,2) is computed before (2,3).
+        As 0 -> 0, 0 -> 0, element in position 0 is 0.
+        As 1 -> 2, 2 -> 3, element in position 1 is 3.
+        As 2 -> 1, 1 -> 1, element in position 2 is 1.
+        As 3 -> 3, 3 -> 2, element in position 3 is 2.
+
+        If the first and second elements had been
+        swapped first, followed by the swapping of the second
+        and third, the result would have been [0, 2, 3, 1].
+        If, you want to apply the cycles in the conventional
+        right to left order, call the function with arguments in reverse order
+        as demonstrated below:
+
+        >>> Permutation([(1, 2), (2, 3)][::-1]).list()
+        [0, 2, 3, 1]
+
+    Entering a singleton in a permutation is a way to indicate the size of the
+    permutation. The ``size`` keyword can also be used.
+
+    Array-form entry:
+
+    >>> Permutation([[1, 2], [9]])
+    Permutation([0, 2, 1], size=10)
+    >>> Permutation([[1, 2]], size=10)
+    Permutation([0, 2, 1], size=10)
+
+    Cyclic-form entry:
+
+    >>> Permutation(1, 2, size=10)
+    Permutation([0, 2, 1], size=10)
+    >>> Permutation(9)(1, 2)
+    Permutation([0, 2, 1], size=10)
+
+    Caution: no singleton containing an element larger than the largest
+    in any previous cycle can be entered. This is an important difference
+    in how Permutation and Cycle handle the ``__call__`` syntax. A singleton
+    argument at the start of a Permutation performs instantiation of the
+    Permutation and is permitted:
+
+    >>> Permutation(5)
+    Permutation([], size=6)
+
+    A singleton entered after instantiation is a call to the permutation
+    -- a function call -- and if the argument is out of range it will
+    trigger an error. For this reason, it is better to start the cycle
+    with the singleton:
+
+    The following fails because there is no element 3:
+
+    >>> Permutation(1, 2)(3)
+    Traceback (most recent call last):
+    ...
+    IndexError: list index out of range
+
+    This is ok: only the call to an out of range singleton is prohibited;
+    otherwise the permutation autosizes:
+
+    >>> Permutation(3)(1, 2)
+    Permutation([0, 2, 1, 3])
+    >>> Permutation(1, 2)(3, 4) == Permutation(3, 4)(1, 2)
+    True
+
+
+    Equality testing
+    ----------------
+
+    The array forms must be the same in order for permutations to be equal:
+
+    >>> Permutation([1, 0, 2, 3]) == Permutation([1, 0])
+    False
+
+
+    Identity Permutation
+    --------------------
+
+    The identity permutation is a permutation in which no element is out of
+    place. It can be entered in a variety of ways. All the following create
+    an identity permutation of size 4:
+
+    >>> I = Permutation([0, 1, 2, 3])
+    >>> all(p == I for p in [
+    ... Permutation(3),
+    ... Permutation(range(4)),
+    ... Permutation([], size=4),
+    ... Permutation(size=4)])
+    True
+
+    Watch out for entering the range *inside* a set of brackets (which is
+    cycle notation):
+
+    >>> I == Permutation([range(4)])
+    False
+
+
+    Permutation Printing
+    ====================
+
+    There are a few things to note about how Permutations are printed.
+
+    .. deprecated:: 1.6
+
+       Configuring Permutation printing by setting
+       ``Permutation.print_cyclic`` is deprecated. Users should use the
+       ``perm_cyclic`` flag to the printers, as described below.
+
+    1) If you prefer one form (array or cycle) over another, you can set
+    ``init_printing`` with the ``perm_cyclic`` flag.
+
+    >>> from sympy import init_printing
+    >>> p = Permutation(1, 2)(4, 5)(3, 4)
+    >>> p
+    Permutation([0, 2, 1, 4, 5, 3])
+
+    >>> init_printing(perm_cyclic=True, pretty_print=False)
+    >>> p
+    (1 2)(3 4 5)
+
+    2) Regardless of the setting, a list of elements in the array for cyclic
+    form can be obtained and either of those can be copied and supplied as
+    the argument to Permutation:
+
+    >>> p.array_form
+    [0, 2, 1, 4, 5, 3]
+    >>> p.cyclic_form
+    [[1, 2], [3, 4, 5]]
+    >>> Permutation(_) == p
+    True
+
+    3) Printing is economical in that as little as possible is printed while
+    retaining all information about the size of the permutation:
+
+    >>> init_printing(perm_cyclic=False, pretty_print=False)
+    >>> Permutation([1, 0, 2, 3])
+    Permutation([1, 0, 2, 3])
+    >>> Permutation([1, 0, 2, 3], size=20)
+    Permutation([1, 0], size=20)
+    >>> Permutation([1, 0, 2, 4, 3, 5, 6], size=20)
+    Permutation([1, 0, 2, 4, 3], size=20)
+
+    >>> p = Permutation([1, 0, 2, 3])
+    >>> init_printing(perm_cyclic=True, pretty_print=False)
+    >>> p
+    (3)(0 1)
+    >>> init_printing(perm_cyclic=False, pretty_print=False)
+
+    The 2 was not printed but it is still there as can be seen with the
+    array_form and size methods:
+
+    >>> p.array_form
+    [1, 0, 2, 3]
+    >>> p.size
+    4
+
+    Short introduction to other methods
+    ===================================
+
+    The permutation can act as a bijective function, telling what element is
+    located at a given position
+
+    >>> q = Permutation([5, 2, 3, 4, 1, 0])
+    >>> q.array_form[1] # the hard way
+    2
+    >>> q(1) # the easy way
+    2
+    >>> {i: q(i) for i in range(q.size)} # showing the bijection
+    {0: 5, 1: 2, 2: 3, 3: 4, 4: 1, 5: 0}
+
+    The full cyclic form (including singletons) can be obtained:
+
+    >>> p.full_cyclic_form
+    [[0, 1], [2], [3]]
+
+    Any permutation can be factored into transpositions of pairs of elements:
+
+    >>> Permutation([[1, 2], [3, 4, 5]]).transpositions()
+    [(1, 2), (3, 5), (3, 4)]
+    >>> Permutation.rmul(*[Permutation([ti], size=6) for ti in _]).cyclic_form
+    [[1, 2], [3, 4, 5]]
+
+    The number of permutations on a set of n elements is given by n! and is
+    called the cardinality.
+
+    >>> p.size
+    4
+    >>> p.cardinality
+    24
+
+    A given permutation has a rank among all the possible permutations of the
+    same elements, but what that rank is depends on how the permutations are
+    enumerated. (There are a number of different methods of doing so.) The
+    lexicographic rank is given by the rank method and this rank is used to
+    increment a permutation with addition/subtraction:
+
+    >>> p.rank()
+    6
+    >>> p + 1
+    Permutation([1, 0, 3, 2])
+    >>> p.next_lex()
+    Permutation([1, 0, 3, 2])
+    >>> _.rank()
+    7
+    >>> p.unrank_lex(p.size, rank=7)
+    Permutation([1, 0, 3, 2])
+
+    The product of two permutations p and q is defined as their composition as
+    functions, (p*q)(i) = q(p(i)) [6]_.
+
+    >>> p = Permutation([1, 0, 2, 3])
+    >>> q = Permutation([2, 3, 1, 0])
+    >>> list(q*p)
+    [2, 3, 0, 1]
+    >>> list(p*q)
+    [3, 2, 1, 0]
+    >>> [q(p(i)) for i in range(p.size)]
+    [3, 2, 1, 0]
+
+    The permutation can be 'applied' to any list-like object, not only
+    Permutations:
+
+    >>> p(['zero', 'one', 'four', 'two'])
+    ['one', 'zero', 'four', 'two']
+    >>> p('zo42')
+    ['o', 'z', '4', '2']
+
+    If you have a list of arbitrary elements, the corresponding permutation
+    can be found with the from_sequence method:
+
+    >>> Permutation.from_sequence('SymPy')
+    Permutation([1, 3, 2, 0, 4])
+
+    Checking if a Permutation is contained in a Group
+    =================================================
+
+    Generally if you have a group of permutations G on n symbols, and
+    you're checking if a permutation on less than n symbols is part
+    of that group, the check will fail.
+
+    Here is an example for n=5 and we check if the cycle
+    (1,2,3) is in G:
+
+    >>> from sympy import init_printing
+    >>> init_printing(perm_cyclic=True, pretty_print=False)
+    >>> from sympy.combinatorics import Cycle, Permutation
+    >>> from sympy.combinatorics.perm_groups import PermutationGroup
+    >>> G = PermutationGroup(Cycle(2, 3)(4, 5), Cycle(1, 2, 3, 4, 5))
+    >>> p1 = Permutation(Cycle(2, 5, 3))
+    >>> p2 = Permutation(Cycle(1, 2, 3))
+    >>> a1 = Permutation(Cycle(1, 2, 3).list(6))
+    >>> a2 = Permutation(Cycle(1, 2, 3)(5))
+    >>> a3 = Permutation(Cycle(1, 2, 3),size=6)
+    >>> for p in [p1,p2,a1,a2,a3]: p, G.contains(p)
+    ((2 5 3), True)
+    ((1 2 3), False)
+    ((5)(1 2 3), True)
+    ((5)(1 2 3), True)
+    ((5)(1 2 3), True)
+
+    The check for p2 above will fail.
+
+    Checking if p1 is in G works because SymPy knows
+    G is a group on 5 symbols, and p1 is also on 5 symbols
+    (its largest element is 5).
+
+    For ``a1``, the ``.list(6)`` call will extend the permutation to 5
+    symbols, so the test will work as well. In the case of ``a2`` the
+    permutation is being extended to 5 symbols by using a singleton,
+    and in the case of ``a3`` it's extended through the constructor
+    argument ``size=6``.
+
+    There is another way to do this, which is to tell the ``contains``
+    method that the number of symbols the group is on does not need to
+    match perfectly the number of symbols for the permutation:
+
+    >>> G.contains(p2,strict=False)
+    True
+
+    This can be via the ``strict`` argument to the ``contains`` method,
+    and SymPy will try to extend the permutation on its own and then
+    perform the containment check.
+
+    See Also
+    ========
+
+    Cycle
+
+    References
+    ==========
+
+    .. [1] Skiena, S. 'Permutations.' 1.1 in Implementing Discrete Mathematics
+           Combinatorics and Graph Theory with Mathematica.  Reading, MA:
+           Addison-Wesley, pp. 3-16, 1990.
+
+    .. [2] Knuth, D. E. The Art of Computer Programming, Vol. 4: Combinatorial
+           Algorithms, 1st ed. Reading, MA: Addison-Wesley, 2011.
+
+    .. [3] Wendy Myrvold and Frank Ruskey. 2001. Ranking and unranking
+           permutations in linear time. Inf. Process. Lett. 79, 6 (September 2001),
+           281-284. DOI=10.1016/S0020-0190(01)00141-7
+
+    .. [4] D. L. Kreher, D. R. Stinson 'Combinatorial Algorithms'
+           CRC Press, 1999
+
+    .. [5] Graham, R. L.; Knuth, D. E.; and Patashnik, O.
+           Concrete Mathematics: A Foundation for Computer Science, 2nd ed.
+           Reading, MA: Addison-Wesley, 1994.
+
+    .. [6] https://en.wikipedia.org/w/index.php?oldid=499948155#Product_and_inverse
+
+    .. [7] https://en.wikipedia.org/wiki/Lehmer_code
+
+    """
+
+    is_Permutation = True
+
+    _array_form = None
+    _cyclic_form = None
+    _cycle_structure = None
+    _size = None
+    _rank = None
+
+    def __new__(cls, *args, size=None, **kwargs):
+        """
+        Constructor for the Permutation object from a list or a
+        list of lists in which all elements of the permutation may
+        appear only once.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+
+        Permutations entered in array-form are left unaltered:
+
+        >>> Permutation([0, 2, 1])
+        Permutation([0, 2, 1])
+
+        Permutations entered in cyclic form are converted to array form;
+        singletons need not be entered, but can be entered to indicate the
+        largest element:
+
+        >>> Permutation([[4, 5, 6], [0, 1]])
+        Permutation([1, 0, 2, 3, 5, 6, 4])
+        >>> Permutation([[4, 5, 6], [0, 1], [19]])
+        Permutation([1, 0, 2, 3, 5, 6, 4], size=20)
+
+        All manipulation of permutations assumes that the smallest element
+        is 0 (in keeping with 0-based indexing in Python) so if the 0 is
+        missing when entering a permutation in array form, an error will be
+        raised:
+
+        >>> Permutation([2, 1])
+        Traceback (most recent call last):
+        ...
+        ValueError: Integers 0 through 2 must be present.
+
+        If a permutation is entered in cyclic form, it can be entered without
+        singletons and the ``size`` specified so those values can be filled
+        in, otherwise the array form will only extend to the maximum value
+        in the cycles:
+
+        >>> Permutation([[1, 4], [3, 5, 2]], size=10)
+        Permutation([0, 4, 3, 5, 1, 2], size=10)
+        >>> _.array_form
+        [0, 4, 3, 5, 1, 2, 6, 7, 8, 9]
+        """
+        if size is not None:
+            size = int(size)
+
+        #a) ()
+        #b) (1) = identity
+        #c) (1, 2) = cycle
+        #d) ([1, 2, 3]) = array form
+        #e) ([[1, 2]]) = cyclic form
+        #f) (Cycle) = conversion to permutation
+        #g) (Permutation) = adjust size or return copy
+        ok = True
+        if not args:  # a
+            return cls._af_new(list(range(size or 0)))
+        elif len(args) > 1:  # c
+            return cls._af_new(Cycle(*args).list(size))
+        if len(args) == 1:
+            a = args[0]
+            if isinstance(a, cls):  # g
+                if size is None or size == a.size:
+                    return a
+                return cls(a.array_form, size=size)
+            if isinstance(a, Cycle):  # f
+                return cls._af_new(a.list(size))
+            if not is_sequence(a):  # b
+                if size is not None and a + 1 > size:
+                    raise ValueError('size is too small when max is %s' % a)
+                return cls._af_new(list(range(a + 1)))
+            if has_variety(is_sequence(ai) for ai in a):
+                ok = False
+        else:
+            ok = False
+        if not ok:
+            raise ValueError("Permutation argument must be a list of ints, "
+                             "a list of lists, Permutation or Cycle.")
+
+        # safe to assume args are valid; this also makes a copy
+        # of the args
+        args = list(args[0])
+
+        is_cycle = args and is_sequence(args[0])
+        if is_cycle:  # e
+            args = [[int(i) for i in c] for c in args]
+        else:  # d
+            args = [int(i) for i in args]
+
+        # if there are n elements present, 0, 1, ..., n-1 should be present
+        # unless a cycle notation has been provided. A 0 will be added
+        # for convenience in case one wants to enter permutations where
+        # counting starts from 1.
+
+        temp = flatten(args)
+        if has_dups(temp) and not is_cycle:
+            raise ValueError('there were repeated elements.')
+        temp = set(temp)
+
+        if not is_cycle:
+            if temp != set(range(len(temp))):
+                raise ValueError('Integers 0 through %s must be present.' %
+                max(temp))
+            if size is not None and temp and max(temp) + 1 > size:
+                raise ValueError('max element should not exceed %s' % (size - 1))
+
+        if is_cycle:
+            # it's not necessarily canonical so we won't store
+            # it -- use the array form instead
+            c = Cycle()
+            for ci in args:
+                c = c(*ci)
+            aform = c.list()
+        else:
+            aform = list(args)
+        if size and size > len(aform):
+            # don't allow for truncation of permutation which
+            # might split a cycle and lead to an invalid aform
+            # but do allow the permutation size to be increased
+            aform.extend(list(range(len(aform), size)))
+
+        return cls._af_new(aform)
+
+    @classmethod
+    def _af_new(cls, perm):
+        """A method to produce a Permutation object from a list;
+        the list is bound to the _array_form attribute, so it must
+        not be modified; this method is meant for internal use only;
+        the list ``a`` is supposed to be generated as a temporary value
+        in a method, so p = Perm._af_new(a) is the only object
+        to hold a reference to ``a``::
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.permutations import Perm
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> a = [2, 1, 3, 0]
+        >>> p = Perm._af_new(a)
+        >>> p
+        Permutation([2, 1, 3, 0])
+
+        """
+        p = super().__new__(cls)
+        p._array_form = perm
+        p._size = len(perm)
+        return p
+
+    def copy(self):
+        return self.__class__(self.array_form)
+
+    def __getnewargs__(self):
+        return (self.array_form,)
+
+    def _hashable_content(self):
+        # the array_form (a list) is the Permutation arg, so we need to
+        # return a tuple, instead
+        return tuple(self.array_form)
+
+    @property
+    def array_form(self):
+        """
+        Return a copy of the attribute _array_form
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([[2, 0], [3, 1]])
+        >>> p.array_form
+        [2, 3, 0, 1]
+        >>> Permutation([[2, 0, 3, 1]]).array_form
+        [3, 2, 0, 1]
+        >>> Permutation([2, 0, 3, 1]).array_form
+        [2, 0, 3, 1]
+        >>> Permutation([[1, 2], [4, 5]]).array_form
+        [0, 2, 1, 3, 5, 4]
+        """
+        return self._array_form[:]
+
+    def list(self, size=None):
+        """Return the permutation as an explicit list, possibly
+        trimming unmoved elements if size is less than the maximum
+        element in the permutation; if this is desired, setting
+        ``size=-1`` will guarantee such trimming.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation(2, 3)(4, 5)
+        >>> p.list()
+        [0, 1, 3, 2, 5, 4]
+        >>> p.list(10)
+        [0, 1, 3, 2, 5, 4, 6, 7, 8, 9]
+
+        Passing a length too small will trim trailing, unchanged elements
+        in the permutation:
+
+        >>> Permutation(2, 4)(1, 2, 4).list(-1)
+        [0, 2, 1]
+        >>> Permutation(3).list(-1)
+        []
+        """
+        if not self and size is None:
+            raise ValueError('must give size for empty Cycle')
+        rv = self.array_form
+        if size is not None:
+            if size > self.size:
+                rv.extend(list(range(self.size, size)))
+            else:
+                # find first value from rhs where rv[i] != i
+                i = self.size - 1
+                while rv:
+                    if rv[-1] != i:
+                        break
+                    rv.pop()
+                    i -= 1
+        return rv
+
+    @property
+    def cyclic_form(self):
+        """
+        This is used to convert to the cyclic notation
+        from the canonical notation. Singletons are omitted.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 3, 1, 2])
+        >>> p.cyclic_form
+        [[1, 3, 2]]
+        >>> Permutation([1, 0, 2, 4, 3, 5]).cyclic_form
+        [[0, 1], [3, 4]]
+
+        See Also
+        ========
+
+        array_form, full_cyclic_form
+        """
+        if self._cyclic_form is not None:
+            return list(self._cyclic_form)
+        array_form = self.array_form
+        unchecked = [True] * len(array_form)
+        cyclic_form = []
+        for i in range(len(array_form)):
+            if unchecked[i]:
+                cycle = []
+                cycle.append(i)
+                unchecked[i] = False
+                j = i
+                while unchecked[array_form[j]]:
+                    j = array_form[j]
+                    cycle.append(j)
+                    unchecked[j] = False
+                if len(cycle) > 1:
+                    cyclic_form.append(cycle)
+                    assert cycle == list(minlex(cycle))
+        cyclic_form.sort()
+        self._cyclic_form = cyclic_form.copy()
+        return cyclic_form
+
+    @property
+    def full_cyclic_form(self):
+        """Return permutation in cyclic form including singletons.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([0, 2, 1]).full_cyclic_form
+        [[0], [1, 2]]
+        """
+        need = set(range(self.size)) - set(flatten(self.cyclic_form))
+        rv = self.cyclic_form + [[i] for i in need]
+        rv.sort()
+        return rv
+
+    @property
+    def size(self):
+        """
+        Returns the number of elements in the permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([[3, 2], [0, 1]]).size
+        4
+
+        See Also
+        ========
+
+        cardinality, length, order, rank
+        """
+        return self._size
+
+    def support(self):
+        """Return the elements in permutation, P, for which P[i] != i.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([[3, 2], [0, 1], [4]])
+        >>> p.array_form
+        [1, 0, 3, 2, 4]
+        >>> p.support()
+        [0, 1, 2, 3]
+        """
+        a = self.array_form
+        return [i for i, e in enumerate(a) if e != i]
+
+    def __add__(self, other):
+        """Return permutation that is other higher in rank than self.
+
+        The rank is the lexicographical rank, with the identity permutation
+        having rank of 0.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> I = Permutation([0, 1, 2, 3])
+        >>> a = Permutation([2, 1, 3, 0])
+        >>> I + a.rank() == a
+        True
+
+        See Also
+        ========
+
+        __sub__, inversion_vector
+
+        """
+        rank = (self.rank() + other) % self.cardinality
+        rv = self.unrank_lex(self.size, rank)
+        rv._rank = rank
+        return rv
+
+    def __sub__(self, other):
+        """Return the permutation that is other lower in rank than self.
+
+        See Also
+        ========
+
+        __add__
+        """
+        return self.__add__(-other)
+
+    @staticmethod
+    def rmul(*args):
+        """
+        Return product of Permutations [a, b, c, ...] as the Permutation whose
+        ith value is a(b(c(i))).
+
+        a, b, c, ... can be Permutation objects or tuples.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+
+        >>> a, b = [1, 0, 2], [0, 2, 1]
+        >>> a = Permutation(a); b = Permutation(b)
+        >>> list(Permutation.rmul(a, b))
+        [1, 2, 0]
+        >>> [a(b(i)) for i in range(3)]
+        [1, 2, 0]
+
+        This handles the operands in reverse order compared to the ``*`` operator:
+
+        >>> a = Permutation(a); b = Permutation(b)
+        >>> list(a*b)
+        [2, 0, 1]
+        >>> [b(a(i)) for i in range(3)]
+        [2, 0, 1]
+
+        Notes
+        =====
+
+        All items in the sequence will be parsed by Permutation as
+        necessary as long as the first item is a Permutation:
+
+        >>> Permutation.rmul(a, [0, 2, 1]) == Permutation.rmul(a, b)
+        True
+
+        The reverse order of arguments will raise a TypeError.
+
+        """
+        rv = args[0]
+        for i in range(1, len(args)):
+            rv = args[i]*rv
+        return rv
+
+    @classmethod
+    def rmul_with_af(cls, *args):
+        """
+        same as rmul, but the elements of args are Permutation objects
+        which have _array_form
+        """
+        a = [x._array_form for x in args]
+        rv = cls._af_new(_af_rmuln(*a))
+        return rv
+
+    def mul_inv(self, other):
+        """
+        other*~self, self and other have _array_form
+        """
+        a = _af_invert(self._array_form)
+        b = other._array_form
+        return self._af_new(_af_rmul(a, b))
+
+    def __rmul__(self, other):
+        """This is needed to coerce other to Permutation in rmul."""
+        cls = type(self)
+        return cls(other)*self
+
+    def __mul__(self, other):
+        """
+        Return the product a*b as a Permutation; the ith value is b(a(i)).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.permutations import _af_rmul, Permutation
+
+        >>> a, b = [1, 0, 2], [0, 2, 1]
+        >>> a = Permutation(a); b = Permutation(b)
+        >>> list(a*b)
+        [2, 0, 1]
+        >>> [b(a(i)) for i in range(3)]
+        [2, 0, 1]
+
+        This handles operands in reverse order compared to _af_rmul and rmul:
+
+        >>> al = list(a); bl = list(b)
+        >>> _af_rmul(al, bl)
+        [1, 2, 0]
+        >>> [al[bl[i]] for i in range(3)]
+        [1, 2, 0]
+
+        It is acceptable for the arrays to have different lengths; the shorter
+        one will be padded to match the longer one:
+
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> b*Permutation([1, 0])
+        Permutation([1, 2, 0])
+        >>> Permutation([1, 0])*b
+        Permutation([2, 0, 1])
+
+        It is also acceptable to allow coercion to handle conversion of a
+        single list to the left of a Permutation:
+
+        >>> [0, 1]*a # no change: 2-element identity
+        Permutation([1, 0, 2])
+        >>> [[0, 1]]*a # exchange first two elements
+        Permutation([0, 1, 2])
+
+        You cannot use more than 1 cycle notation in a product of cycles
+        since coercion can only handle one argument to the left. To handle
+        multiple cycles it is convenient to use Cycle instead of Permutation:
+
+        >>> [[1, 2]]*[[2, 3]]*Permutation([]) # doctest: +SKIP
+        >>> from sympy.combinatorics.permutations import Cycle
+        >>> Cycle(1, 2)(2, 3)
+        (1 3 2)
+
+        """
+        from sympy.combinatorics.perm_groups import PermutationGroup, Coset
+        if isinstance(other, PermutationGroup):
+            return Coset(self, other, dir='-')
+        a = self.array_form
+        # __rmul__ makes sure the other is a Permutation
+        b = other.array_form
+        if not b:
+            perm = a
+        else:
+            b.extend(list(range(len(b), len(a))))
+            perm = [b[i] for i in a] + b[len(a):]
+        return self._af_new(perm)
+
+    def commutes_with(self, other):
+        """
+        Checks if the elements are commuting.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> a = Permutation([1, 4, 3, 0, 2, 5])
+        >>> b = Permutation([0, 1, 2, 3, 4, 5])
+        >>> a.commutes_with(b)
+        True
+        >>> b = Permutation([2, 3, 5, 4, 1, 0])
+        >>> a.commutes_with(b)
+        False
+        """
+        a = self.array_form
+        b = other.array_form
+        return _af_commutes_with(a, b)
+
+    def __pow__(self, n):
+        """
+        Routine for finding powers of a permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation([2, 0, 3, 1])
+        >>> p.order()
+        4
+        >>> p**4
+        Permutation([0, 1, 2, 3])
+        """
+        if isinstance(n, Permutation):
+            raise NotImplementedError(
+                'p**p is not defined; do you mean p^p (conjugate)?')
+        n = int(n)
+        return self._af_new(_af_pow(self.array_form, n))
+
+    def __rxor__(self, i):
+        """Return self(i) when ``i`` is an int.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation(1, 2, 9)
+        >>> 2^p == p(2) == 9
+        True
+        """
+        if int_valued(i):
+            return self(i)
+        else:
+            raise NotImplementedError(
+                "i^p = p(i) when i is an integer, not %s." % i)
+
+    def __xor__(self, h):
+        """Return the conjugate permutation ``~h*self*h` `.
+
+        Explanation
+        ===========
+
+        If ``a`` and ``b`` are conjugates, ``a = h*b*~h`` and
+        ``b = ~h*a*h`` and both have the same cycle structure.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation(1, 2, 9)
+        >>> q = Permutation(6, 9, 8)
+        >>> p*q != q*p
+        True
+
+        Calculate and check properties of the conjugate:
+
+        >>> c = p^q
+        >>> c == ~q*p*q and p == q*c*~q
+        True
+
+        The expression q^p^r is equivalent to q^(p*r):
+
+        >>> r = Permutation(9)(4, 6, 8)
+        >>> q^p^r == q^(p*r)
+        True
+
+        If the term to the left of the conjugate operator, i, is an integer
+        then this is interpreted as selecting the ith element from the
+        permutation to the right:
+
+        >>> all(i^p == p(i) for i in range(p.size))
+        True
+
+        Note that the * operator as higher precedence than the ^ operator:
+
+        >>> q^r*p^r == q^(r*p)^r == Permutation(9)(1, 6, 4)
+        True
+
+        Notes
+        =====
+
+        In Python the precedence rule is p^q^r = (p^q)^r which differs
+        in general from p^(q^r)
+
+        >>> q^p^r
+        (9)(1 4 8)
+        >>> q^(p^r)
+        (9)(1 8 6)
+
+        For a given r and p, both of the following are conjugates of p:
+        ~r*p*r and r*p*~r. But these are not necessarily the same:
+
+        >>> ~r*p*r == r*p*~r
+        True
+
+        >>> p = Permutation(1, 2, 9)(5, 6)
+        >>> ~r*p*r == r*p*~r
+        False
+
+        The conjugate ~r*p*r was chosen so that ``p^q^r`` would be equivalent
+        to ``p^(q*r)`` rather than ``p^(r*q)``. To obtain r*p*~r, pass ~r to
+        this method:
+
+        >>> p^~r == r*p*~r
+        True
+        """
+
+        if self.size != h.size:
+            raise ValueError("The permutations must be of equal size.")
+        a = [None]*self.size
+        h = h._array_form
+        p = self._array_form
+        for i in range(self.size):
+            a[h[i]] = h[p[i]]
+        return self._af_new(a)
+
+    def transpositions(self):
+        """
+        Return the permutation decomposed into a list of transpositions.
+
+        Explanation
+        ===========
+
+        It is always possible to express a permutation as the product of
+        transpositions, see [1]
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([[1, 2, 3], [0, 4, 5, 6, 7]])
+        >>> t = p.transpositions()
+        >>> t
+        [(0, 7), (0, 6), (0, 5), (0, 4), (1, 3), (1, 2)]
+        >>> print(''.join(str(c) for c in t))
+        (0, 7)(0, 6)(0, 5)(0, 4)(1, 3)(1, 2)
+        >>> Permutation.rmul(*[Permutation([ti], size=p.size) for ti in t]) == p
+        True
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Transposition_%28mathematics%29#Properties
+
+        """
+        a = self.cyclic_form
+        res = []
+        for x in a:
+            nx = len(x)
+            if nx == 2:
+                res.append(tuple(x))
+            elif nx > 2:
+                first = x[0]
+                res.extend((first, y) for y in x[nx - 1:0:-1])
+        return res
+
+    @classmethod
+    def from_sequence(self, i, key=None):
+        """Return the permutation needed to obtain ``i`` from the sorted
+        elements of ``i``. If custom sorting is desired, a key can be given.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+
+        >>> Permutation.from_sequence('SymPy')
+        (4)(0 1 3)
+        >>> _(sorted("SymPy"))
+        ['S', 'y', 'm', 'P', 'y']
+        >>> Permutation.from_sequence('SymPy', key=lambda x: x.lower())
+        (4)(0 2)(1 3)
+        """
+        ic = list(zip(i, list(range(len(i)))))
+        if key:
+            ic.sort(key=lambda x: key(x[0]))
+        else:
+            ic.sort()
+        return ~Permutation([i[1] for i in ic])
+
+    def __invert__(self):
+        """
+        Return the inverse of the permutation.
+
+        A permutation multiplied by its inverse is the identity permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation([[2, 0], [3, 1]])
+        >>> ~p
+        Permutation([2, 3, 0, 1])
+        >>> _ == p**-1
+        True
+        >>> p*~p == ~p*p == Permutation([0, 1, 2, 3])
+        True
+        """
+        return self._af_new(_af_invert(self._array_form))
+
+    def __iter__(self):
+        """Yield elements from array form.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> list(Permutation(range(3)))
+        [0, 1, 2]
+        """
+        yield from self.array_form
+
+    def __repr__(self):
+        return srepr(self)
+
+    def __call__(self, *i):
+        """
+        Allows applying a permutation instance as a bijective function.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([[2, 0], [3, 1]])
+        >>> p.array_form
+        [2, 3, 0, 1]
+        >>> [p(i) for i in range(4)]
+        [2, 3, 0, 1]
+
+        If an array is given then the permutation selects the items
+        from the array (i.e. the permutation is applied to the array):
+
+        >>> from sympy.abc import x
+        >>> p([x, 1, 0, x**2])
+        [0, x**2, x, 1]
+        """
+        # list indices can be Integer or int; leave this
+        # as it is (don't test or convert it) because this
+        # gets called a lot and should be fast
+        if len(i) == 1:
+            i = i[0]
+            if not isinstance(i, Iterable):
+                i = as_int(i)
+                if i < 0 or i > self.size:
+                    raise TypeError(
+                        "{} should be an integer between 0 and {}"
+                        .format(i, self.size-1))
+                return self._array_form[i]
+            # P([a, b, c])
+            if len(i) != self.size:
+                raise TypeError(
+                    "{} should have the length {}.".format(i, self.size))
+            return [i[j] for j in self._array_form]
+        # P(1, 2, 3)
+        return self*Permutation(Cycle(*i), size=self.size)
+
+    def atoms(self):
+        """
+        Returns all the elements of a permutation
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([0, 1, 2, 3, 4, 5]).atoms()
+        {0, 1, 2, 3, 4, 5}
+        >>> Permutation([[0, 1], [2, 3], [4, 5]]).atoms()
+        {0, 1, 2, 3, 4, 5}
+        """
+        return set(self.array_form)
+
+    def apply(self, i):
+        r"""Apply the permutation to an expression.
+
+        Parameters
+        ==========
+
+        i : Expr
+            It should be an integer between $0$ and $n-1$ where $n$
+            is the size of the permutation.
+
+            If it is a symbol or a symbolic expression that can
+            have integer values, an ``AppliedPermutation`` object
+            will be returned which can represent an unevaluated
+            function.
+
+        Notes
+        =====
+
+        Any permutation can be defined as a bijective function
+        $\sigma : \{ 0, 1, \dots, n-1 \} \rightarrow \{ 0, 1, \dots, n-1 \}$
+        where $n$ denotes the size of the permutation.
+
+        The definition may even be extended for any set with distinctive
+        elements, such that the permutation can even be applied for
+        real numbers or such, however, it is not implemented for now for
+        computational reasons and the integrity with the group theory
+        module.
+
+        This function is similar to the ``__call__`` magic, however,
+        ``__call__`` magic already has some other applications like
+        permuting an array or attaching new cycles, which would
+        not always be mathematically consistent.
+
+        This also guarantees that the return type is a SymPy integer,
+        which guarantees the safety to use assumptions.
+        """
+        i = _sympify(i)
+        if i.is_integer is False:
+            raise NotImplementedError("{} should be an integer.".format(i))
+
+        n = self.size
+        if (i < 0) == True or (i >= n) == True:
+            raise NotImplementedError(
+                "{} should be an integer between 0 and {}".format(i, n-1))
+
+        if i.is_Integer:
+            return Integer(self._array_form[i])
+        return AppliedPermutation(self, i)
+
+    def next_lex(self):
+        """
+        Returns the next permutation in lexicographical order.
+        If self is the last permutation in lexicographical order
+        it returns None.
+        See [4] section 2.4.
+
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([2, 3, 1, 0])
+        >>> p = Permutation([2, 3, 1, 0]); p.rank()
+        17
+        >>> p = p.next_lex(); p.rank()
+        18
+
+        See Also
+        ========
+
+        rank, unrank_lex
+        """
+        perm = self.array_form[:]
+        n = len(perm)
+        i = n - 2
+        while perm[i + 1] < perm[i]:
+            i -= 1
+        if i == -1:
+            return None
+        else:
+            j = n - 1
+            while perm[j] < perm[i]:
+                j -= 1
+            perm[j], perm[i] = perm[i], perm[j]
+            i += 1
+            j = n - 1
+            while i < j:
+                perm[j], perm[i] = perm[i], perm[j]
+                i += 1
+                j -= 1
+        return self._af_new(perm)
+
+    @classmethod
+    def unrank_nonlex(self, n, r):
+        """
+        This is a linear time unranking algorithm that does not
+        respect lexicographic order [3].
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> Permutation.unrank_nonlex(4, 5)
+        Permutation([2, 0, 3, 1])
+        >>> Permutation.unrank_nonlex(4, -1)
+        Permutation([0, 1, 2, 3])
+
+        See Also
+        ========
+
+        next_nonlex, rank_nonlex
+        """
+        def _unrank1(n, r, a):
+            if n > 0:
+                a[n - 1], a[r % n] = a[r % n], a[n - 1]
+                _unrank1(n - 1, r//n, a)
+
+        id_perm = list(range(n))
+        n = int(n)
+        r = r % ifac(n)
+        _unrank1(n, r, id_perm)
+        return self._af_new(id_perm)
+
+    def rank_nonlex(self, inv_perm=None):
+        """
+        This is a linear time ranking algorithm that does not
+        enforce lexicographic order [3].
+
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.rank_nonlex()
+        23
+
+        See Also
+        ========
+
+        next_nonlex, unrank_nonlex
+        """
+        def _rank1(n, perm, inv_perm):
+            if n == 1:
+                return 0
+            s = perm[n - 1]
+            t = inv_perm[n - 1]
+            perm[n - 1], perm[t] = perm[t], s
+            inv_perm[n - 1], inv_perm[s] = inv_perm[s], t
+            return s + n*_rank1(n - 1, perm, inv_perm)
+
+        if inv_perm is None:
+            inv_perm = (~self).array_form
+        if not inv_perm:
+            return 0
+        perm = self.array_form[:]
+        r = _rank1(len(perm), perm, inv_perm)
+        return r
+
+    def next_nonlex(self):
+        """
+        Returns the next permutation in nonlex order [3].
+        If self is the last permutation in this order it returns None.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation([2, 0, 3, 1]); p.rank_nonlex()
+        5
+        >>> p = p.next_nonlex(); p
+        Permutation([3, 0, 1, 2])
+        >>> p.rank_nonlex()
+        6
+
+        See Also
+        ========
+
+        rank_nonlex, unrank_nonlex
+        """
+        r = self.rank_nonlex()
+        if r == ifac(self.size) - 1:
+            return None
+        return self.unrank_nonlex(self.size, r + 1)
+
+    def rank(self):
+        """
+        Returns the lexicographic rank of the permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.rank()
+        0
+        >>> p = Permutation([3, 2, 1, 0])
+        >>> p.rank()
+        23
+
+        See Also
+        ========
+
+        next_lex, unrank_lex, cardinality, length, order, size
+        """
+        if self._rank is not None:
+            return self._rank
+        rank = 0
+        rho = self.array_form[:]
+        n = self.size - 1
+        size = n + 1
+        psize = int(ifac(n))
+        for j in range(size - 1):
+            rank += rho[j]*psize
+            for i in range(j + 1, size):
+                if rho[i] > rho[j]:
+                    rho[i] -= 1
+            psize //= n
+            n -= 1
+        self._rank = rank
+        return rank
+
+    @property
+    def cardinality(self):
+        """
+        Returns the number of all possible permutations.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.cardinality
+        24
+
+        See Also
+        ========
+
+        length, order, rank, size
+        """
+        return int(ifac(self.size))
+
+    def parity(self):
+        """
+        Computes the parity of a permutation.
+
+        Explanation
+        ===========
+
+        The parity of a permutation reflects the parity of the
+        number of inversions in the permutation, i.e., the
+        number of pairs of x and y such that ``x > y`` but ``p[x] < p[y]``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.parity()
+        0
+        >>> p = Permutation([3, 2, 0, 1])
+        >>> p.parity()
+        1
+
+        See Also
+        ========
+
+        _af_parity
+        """
+        if self._cyclic_form is not None:
+            return (self.size - self.cycles) % 2
+
+        return _af_parity(self.array_form)
+
+    @property
+    def is_even(self):
+        """
+        Checks if a permutation is even.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.is_even
+        True
+        >>> p = Permutation([3, 2, 1, 0])
+        >>> p.is_even
+        True
+
+        See Also
+        ========
+
+        is_odd
+        """
+        return not self.is_odd
+
+    @property
+    def is_odd(self):
+        """
+        Checks if a permutation is odd.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.is_odd
+        False
+        >>> p = Permutation([3, 2, 0, 1])
+        >>> p.is_odd
+        True
+
+        See Also
+        ========
+
+        is_even
+        """
+        return bool(self.parity() % 2)
+
+    @property
+    def is_Singleton(self):
+        """
+        Checks to see if the permutation contains only one number and is
+        thus the only possible permutation of this set of numbers
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([0]).is_Singleton
+        True
+        >>> Permutation([0, 1]).is_Singleton
+        False
+
+        See Also
+        ========
+
+        is_Empty
+        """
+        return self.size == 1
+
+    @property
+    def is_Empty(self):
+        """
+        Checks to see if the permutation is a set with zero elements
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([]).is_Empty
+        True
+        >>> Permutation([0]).is_Empty
+        False
+
+        See Also
+        ========
+
+        is_Singleton
+        """
+        return self.size == 0
+
+    @property
+    def is_identity(self):
+        return self.is_Identity
+
+    @property
+    def is_Identity(self):
+        """
+        Returns True if the Permutation is an identity permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([])
+        >>> p.is_Identity
+        True
+        >>> p = Permutation([[0], [1], [2]])
+        >>> p.is_Identity
+        True
+        >>> p = Permutation([0, 1, 2])
+        >>> p.is_Identity
+        True
+        >>> p = Permutation([0, 2, 1])
+        >>> p.is_Identity
+        False
+
+        See Also
+        ========
+
+        order
+        """
+        af = self.array_form
+        return not af or all(i == af[i] for i in range(self.size))
+
+    def ascents(self):
+        """
+        Returns the positions of ascents in a permutation, ie, the location
+        where p[i] < p[i+1]
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([4, 0, 1, 3, 2])
+        >>> p.ascents()
+        [1, 2]
+
+        See Also
+        ========
+
+        descents, inversions, min, max
+        """
+        a = self.array_form
+        pos = [i for i in range(len(a) - 1) if a[i] < a[i + 1]]
+        return pos
+
+    def descents(self):
+        """
+        Returns the positions of descents in a permutation, ie, the location
+        where p[i] > p[i+1]
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([4, 0, 1, 3, 2])
+        >>> p.descents()
+        [0, 3]
+
+        See Also
+        ========
+
+        ascents, inversions, min, max
+        """
+        a = self.array_form
+        pos = [i for i in range(len(a) - 1) if a[i] > a[i + 1]]
+        return pos
+
+    def max(self) -> int:
+        """
+        The maximum element moved by the permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([1, 0, 2, 3, 4])
+        >>> p.max()
+        1
+
+        See Also
+        ========
+
+        min, descents, ascents, inversions
+        """
+        a = self.array_form
+        if not a:
+            return 0
+        return max(_a for i, _a in enumerate(a) if _a != i)
+
+    def min(self) -> int:
+        """
+        The minimum element moved by the permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 4, 3, 2])
+        >>> p.min()
+        2
+
+        See Also
+        ========
+
+        max, descents, ascents, inversions
+        """
+        a = self.array_form
+        if not a:
+            return 0
+        return min(_a for i, _a in enumerate(a) if _a != i)
+
+    def inversions(self):
+        """
+        Computes the number of inversions of a permutation.
+
+        Explanation
+        ===========
+
+        An inversion is where i > j but p[i] < p[j].
+
+        For small length of p, it iterates over all i and j
+        values and calculates the number of inversions.
+        For large length of p, it uses a variation of merge
+        sort to calculate the number of inversions.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3, 4, 5])
+        >>> p.inversions()
+        0
+        >>> Permutation([3, 2, 1, 0]).inversions()
+        6
+
+        See Also
+        ========
+
+        descents, ascents, min, max
+
+        References
+        ==========
+
+        .. [1] https://www.cp.eng.chula.ac.th/~prabhas//teaching/algo/algo2008/count-inv.htm
+
+        """
+        inversions = 0
+        a = self.array_form
+        n = len(a)
+        if n < 130:
+            for i in range(n - 1):
+                b = a[i]
+                for c in a[i + 1:]:
+                    if b > c:
+                        inversions += 1
+        else:
+            k = 1
+            right = 0
+            arr = a[:]
+            temp = a[:]
+            while k < n:
+                i = 0
+                while i + k < n:
+                    right = i + k * 2 - 1
+                    if right >= n:
+                        right = n - 1
+                    inversions += _merge(arr, temp, i, i + k, right)
+                    i = i + k * 2
+                k = k * 2
+        return inversions
+
+    def commutator(self, x):
+        """Return the commutator of ``self`` and ``x``: ``~x*~self*x*self``
+
+        If f and g are part of a group, G, then the commutator of f and g
+        is the group identity iff f and g commute, i.e. fg == gf.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation([0, 2, 3, 1])
+        >>> x = Permutation([2, 0, 3, 1])
+        >>> c = p.commutator(x); c
+        Permutation([2, 1, 3, 0])
+        >>> c == ~x*~p*x*p
+        True
+
+        >>> I = Permutation(3)
+        >>> p = [I + i for i in range(6)]
+        >>> for i in range(len(p)):
+        ...     for j in range(len(p)):
+        ...         c = p[i].commutator(p[j])
+        ...         if p[i]*p[j] == p[j]*p[i]:
+        ...             assert c == I
+        ...         else:
+        ...             assert c != I
+        ...
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Commutator
+        """
+
+        a = self.array_form
+        b = x.array_form
+        n = len(a)
+        if len(b) != n:
+            raise ValueError("The permutations must be of equal size.")
+        inva = [None]*n
+        for i in range(n):
+            inva[a[i]] = i
+        invb = [None]*n
+        for i in range(n):
+            invb[b[i]] = i
+        return self._af_new([a[b[inva[i]]] for i in invb])
+
+    def signature(self):
+        """
+        Gives the signature of the permutation needed to place the
+        elements of the permutation in canonical order.
+
+        The signature is calculated as (-1)^
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2])
+        >>> p.inversions()
+        0
+        >>> p.signature()
+        1
+        >>> q = Permutation([0,2,1])
+        >>> q.inversions()
+        1
+        >>> q.signature()
+        -1
+
+        See Also
+        ========
+
+        inversions
+        """
+        if self.is_even:
+            return 1
+        return -1
+
+    def order(self):
+        """
+        Computes the order of a permutation.
+
+        When the permutation is raised to the power of its
+        order it equals the identity permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation([3, 1, 5, 2, 4, 0])
+        >>> p.order()
+        4
+        >>> (p**(p.order()))
+        Permutation([], size=6)
+
+        See Also
+        ========
+
+        identity, cardinality, length, rank, size
+        """
+
+        return reduce(lcm, [len(cycle) for cycle in self.cyclic_form], 1)
+
+    def length(self):
+        """
+        Returns the number of integers moved by a permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([0, 3, 2, 1]).length()
+        2
+        >>> Permutation([[0, 1], [2, 3]]).length()
+        4
+
+        See Also
+        ========
+
+        min, max, support, cardinality, order, rank, size
+        """
+
+        return len(self.support())
+
+    @property
+    def cycle_structure(self):
+        """Return the cycle structure of the permutation as a dictionary
+        indicating the multiplicity of each cycle length.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation(3).cycle_structure
+        {1: 4}
+        >>> Permutation(0, 4, 3)(1, 2)(5, 6).cycle_structure
+        {2: 2, 3: 1}
+        """
+        if self._cycle_structure:
+            rv = self._cycle_structure
+        else:
+            rv = defaultdict(int)
+            singletons = self.size
+            for c in self.cyclic_form:
+                rv[len(c)] += 1
+                singletons -= len(c)
+            if singletons:
+                rv[1] = singletons
+            self._cycle_structure = rv
+        return dict(rv)  # make a copy
+
+    @property
+    def cycles(self):
+        """
+        Returns the number of cycles contained in the permutation
+        (including singletons).
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation([0, 1, 2]).cycles
+        3
+        >>> Permutation([0, 1, 2]).full_cyclic_form
+        [[0], [1], [2]]
+        >>> Permutation(0, 1)(2, 3).cycles
+        2
+
+        See Also
+        ========
+        sympy.functions.combinatorial.numbers.stirling
+        """
+        return len(self.full_cyclic_form)
+
+    def index(self):
+        """
+        Returns the index of a permutation.
+
+        The index of a permutation is the sum of all subscripts j such
+        that p[j] is greater than p[j+1].
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([3, 0, 2, 1, 4])
+        >>> p.index()
+        2
+        """
+        a = self.array_form
+
+        return sum(j for j in range(len(a) - 1) if a[j] > a[j + 1])
+
+    def runs(self):
+        """
+        Returns the runs of a permutation.
+
+        An ascending sequence in a permutation is called a run [5].
+
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([2, 5, 7, 3, 6, 0, 1, 4, 8])
+        >>> p.runs()
+        [[2, 5, 7], [3, 6], [0, 1, 4, 8]]
+        >>> q = Permutation([1,3,2,0])
+        >>> q.runs()
+        [[1, 3], [2], [0]]
+        """
+        return runs(self.array_form)
+
+    def inversion_vector(self):
+        """Return the inversion vector of the permutation.
+
+        The inversion vector consists of elements whose value
+        indicates the number of elements in the permutation
+        that are lesser than it and lie on its right hand side.
+
+        The inversion vector is the same as the Lehmer encoding of a
+        permutation.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([4, 8, 0, 7, 1, 5, 3, 6, 2])
+        >>> p.inversion_vector()
+        [4, 7, 0, 5, 0, 2, 1, 1]
+        >>> p = Permutation([3, 2, 1, 0])
+        >>> p.inversion_vector()
+        [3, 2, 1]
+
+        The inversion vector increases lexicographically with the rank
+        of the permutation, the -ith element cycling through 0..i.
+
+        >>> p = Permutation(2)
+        >>> while p:
+        ...     print('%s %s %s' % (p, p.inversion_vector(), p.rank()))
+        ...     p = p.next_lex()
+        (2) [0, 0] 0
+        (1 2) [0, 1] 1
+        (2)(0 1) [1, 0] 2
+        (0 1 2) [1, 1] 3
+        (0 2 1) [2, 0] 4
+        (0 2) [2, 1] 5
+
+        See Also
+        ========
+
+        from_inversion_vector
+        """
+        self_array_form = self.array_form
+        n = len(self_array_form)
+        inversion_vector = [0] * (n - 1)
+
+        for i in range(n - 1):
+            val = 0
+            for j in range(i + 1, n):
+                if self_array_form[j] < self_array_form[i]:
+                    val += 1
+            inversion_vector[i] = val
+        return inversion_vector
+
+    def rank_trotterjohnson(self):
+        """
+        Returns the Trotter Johnson rank, which we get from the minimal
+        change algorithm. See [4] section 2.4.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 1, 2, 3])
+        >>> p.rank_trotterjohnson()
+        0
+        >>> p = Permutation([0, 2, 1, 3])
+        >>> p.rank_trotterjohnson()
+        7
+
+        See Also
+        ========
+
+        unrank_trotterjohnson, next_trotterjohnson
+        """
+        if self.array_form == [] or self.is_Identity:
+            return 0
+        if self.array_form == [1, 0]:
+            return 1
+        perm = self.array_form
+        n = self.size
+        rank = 0
+        for j in range(1, n):
+            k = 1
+            i = 0
+            while perm[i] != j:
+                if perm[i] < j:
+                    k += 1
+                i += 1
+            j1 = j + 1
+            if rank % 2 == 0:
+                rank = j1*rank + j1 - k
+            else:
+                rank = j1*rank + k - 1
+        return rank
+
+    @classmethod
+    def unrank_trotterjohnson(cls, size, rank):
+        """
+        Trotter Johnson permutation unranking. See [4] section 2.4.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> Permutation.unrank_trotterjohnson(5, 10)
+        Permutation([0, 3, 1, 2, 4])
+
+        See Also
+        ========
+
+        rank_trotterjohnson, next_trotterjohnson
+        """
+        perm = [0]*size
+        r2 = 0
+        n = ifac(size)
+        pj = 1
+        for j in range(2, size + 1):
+            pj *= j
+            r1 = (rank * pj) // n
+            k = r1 - j*r2
+            if r2 % 2 == 0:
+                for i in range(j - 1, j - k - 1, -1):
+                    perm[i] = perm[i - 1]
+                perm[j - k - 1] = j - 1
+            else:
+                for i in range(j - 1, k, -1):
+                    perm[i] = perm[i - 1]
+                perm[k] = j - 1
+            r2 = r1
+        return cls._af_new(perm)
+
+    def next_trotterjohnson(self):
+        """
+        Returns the next permutation in Trotter-Johnson order.
+        If self is the last permutation it returns None.
+        See [4] section 2.4. If it is desired to generate all such
+        permutations, they can be generated in order more quickly
+        with the ``generate_bell`` function.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation([3, 0, 2, 1])
+        >>> p.rank_trotterjohnson()
+        4
+        >>> p = p.next_trotterjohnson(); p
+        Permutation([0, 3, 2, 1])
+        >>> p.rank_trotterjohnson()
+        5
+
+        See Also
+        ========
+
+        rank_trotterjohnson, unrank_trotterjohnson, sympy.utilities.iterables.generate_bell
+        """
+        pi = self.array_form[:]
+        n = len(pi)
+        st = 0
+        rho = pi[:]
+        done = False
+        m = n-1
+        while m > 0 and not done:
+            d = rho.index(m)
+            for i in range(d, m):
+                rho[i] = rho[i + 1]
+            par = _af_parity(rho[:m])
+            if par == 1:
+                if d == m:
+                    m -= 1
+                else:
+                    pi[st + d], pi[st + d + 1] = pi[st + d + 1], pi[st + d]
+                    done = True
+            else:
+                if d == 0:
+                    m -= 1
+                    st += 1
+                else:
+                    pi[st + d], pi[st + d - 1] = pi[st + d - 1], pi[st + d]
+                    done = True
+        if m == 0:
+            return None
+        return self._af_new(pi)
+
+    def get_precedence_matrix(self):
+        """
+        Gets the precedence matrix. This is used for computing the
+        distance between two permutations.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> p = Permutation.josephus(3, 6, 1)
+        >>> p
+        Permutation([2, 5, 3, 1, 4, 0])
+        >>> p.get_precedence_matrix()
+        Matrix([
+        [0, 0, 0, 0, 0, 0],
+        [1, 0, 0, 0, 1, 0],
+        [1, 1, 0, 1, 1, 1],
+        [1, 1, 0, 0, 1, 0],
+        [1, 0, 0, 0, 0, 0],
+        [1, 1, 0, 1, 1, 0]])
+
+        See Also
+        ========
+
+        get_precedence_distance, get_adjacency_matrix, get_adjacency_distance
+        """
+        m = zeros(self.size)
+        perm = self.array_form
+        for i in range(m.rows):
+            for j in range(i + 1, m.cols):
+                m[perm[i], perm[j]] = 1
+        return m
+
+    def get_precedence_distance(self, other):
+        """
+        Computes the precedence distance between two permutations.
+
+        Explanation
+        ===========
+
+        Suppose p and p' represent n jobs. The precedence metric
+        counts the number of times a job j is preceded by job i
+        in both p and p'. This metric is commutative.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([2, 0, 4, 3, 1])
+        >>> q = Permutation([3, 1, 2, 4, 0])
+        >>> p.get_precedence_distance(q)
+        7
+        >>> q.get_precedence_distance(p)
+        7
+
+        See Also
+        ========
+
+        get_precedence_matrix, get_adjacency_matrix, get_adjacency_distance
+        """
+        if self.size != other.size:
+            raise ValueError("The permutations must be of equal size.")
+        self_prec_mat = self.get_precedence_matrix()
+        other_prec_mat = other.get_precedence_matrix()
+        n_prec = 0
+        for i in range(self.size):
+            for j in range(self.size):
+                if i == j:
+                    continue
+                if self_prec_mat[i, j] * other_prec_mat[i, j] == 1:
+                    n_prec += 1
+        d = self.size * (self.size - 1)//2 - n_prec
+        return d
+
+    def get_adjacency_matrix(self):
+        """
+        Computes the adjacency matrix of a permutation.
+
+        Explanation
+        ===========
+
+        If job i is adjacent to job j in a permutation p
+        then we set m[i, j] = 1 where m is the adjacency
+        matrix of p.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation.josephus(3, 6, 1)
+        >>> p.get_adjacency_matrix()
+        Matrix([
+        [0, 0, 0, 0, 0, 0],
+        [0, 0, 0, 0, 1, 0],
+        [0, 0, 0, 0, 0, 1],
+        [0, 1, 0, 0, 0, 0],
+        [1, 0, 0, 0, 0, 0],
+        [0, 0, 0, 1, 0, 0]])
+        >>> q = Permutation([0, 1, 2, 3])
+        >>> q.get_adjacency_matrix()
+        Matrix([
+        [0, 1, 0, 0],
+        [0, 0, 1, 0],
+        [0, 0, 0, 1],
+        [0, 0, 0, 0]])
+
+        See Also
+        ========
+
+        get_precedence_matrix, get_precedence_distance, get_adjacency_distance
+        """
+        m = zeros(self.size)
+        perm = self.array_form
+        for i in range(self.size - 1):
+            m[perm[i], perm[i + 1]] = 1
+        return m
+
+    def get_adjacency_distance(self, other):
+        """
+        Computes the adjacency distance between two permutations.
+
+        Explanation
+        ===========
+
+        This metric counts the number of times a pair i,j of jobs is
+        adjacent in both p and p'. If n_adj is this quantity then
+        the adjacency distance is n - n_adj - 1 [1]
+
+        [1] Reeves, Colin R. Landscapes, Operators and Heuristic search, Annals
+        of Operational Research, 86, pp 473-490. (1999)
+
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 3, 1, 2, 4])
+        >>> q = Permutation.josephus(4, 5, 2)
+        >>> p.get_adjacency_distance(q)
+        3
+        >>> r = Permutation([0, 2, 1, 4, 3])
+        >>> p.get_adjacency_distance(r)
+        4
+
+        See Also
+        ========
+
+        get_precedence_matrix, get_precedence_distance, get_adjacency_matrix
+        """
+        if self.size != other.size:
+            raise ValueError("The permutations must be of the same size.")
+        self_adj_mat = self.get_adjacency_matrix()
+        other_adj_mat = other.get_adjacency_matrix()
+        n_adj = 0
+        for i in range(self.size):
+            for j in range(self.size):
+                if i == j:
+                    continue
+                if self_adj_mat[i, j] * other_adj_mat[i, j] == 1:
+                    n_adj += 1
+        d = self.size - n_adj - 1
+        return d
+
+    def get_positional_distance(self, other):
+        """
+        Computes the positional distance between two permutations.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> p = Permutation([0, 3, 1, 2, 4])
+        >>> q = Permutation.josephus(4, 5, 2)
+        >>> r = Permutation([3, 1, 4, 0, 2])
+        >>> p.get_positional_distance(q)
+        12
+        >>> p.get_positional_distance(r)
+        12
+
+        See Also
+        ========
+
+        get_precedence_distance, get_adjacency_distance
+        """
+        a = self.array_form
+        b = other.array_form
+        if len(a) != len(b):
+            raise ValueError("The permutations must be of the same size.")
+        return sum(abs(a[i] - b[i]) for i in range(len(a)))
+
+    @classmethod
+    def josephus(cls, m, n, s=1):
+        """Return as a permutation the shuffling of range(n) using the Josephus
+        scheme in which every m-th item is selected until all have been chosen.
+        The returned permutation has elements listed by the order in which they
+        were selected.
+
+        The parameter ``s`` stops the selection process when there are ``s``
+        items remaining and these are selected by continuing the selection,
+        counting by 1 rather than by ``m``.
+
+        Consider selecting every 3rd item from 6 until only 2 remain::
+
+            choices    chosen
+            ========   ======
+              012345
+              01 345   2
+              01 34    25
+              01  4    253
+              0   4    2531
+              0        25314
+                       253140
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation.josephus(3, 6, 2).array_form
+        [2, 5, 3, 1, 4, 0]
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Flavius_Josephus
+        .. [2] https://en.wikipedia.org/wiki/Josephus_problem
+        .. [3] https://web.archive.org/web/20171008094331/http://www.wou.edu/~burtonl/josephus.html
+
+        """
+        from collections import deque
+        m -= 1
+        Q = deque(list(range(n)))
+        perm = []
+        while len(Q) > max(s, 1):
+            for dp in range(m):
+                Q.append(Q.popleft())
+            perm.append(Q.popleft())
+        perm.extend(list(Q))
+        return cls(perm)
+
+    @classmethod
+    def from_inversion_vector(cls, inversion):
+        """
+        Calculates the permutation from the inversion vector.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> Permutation.from_inversion_vector([3, 2, 1, 0, 0])
+        Permutation([3, 2, 1, 0, 4, 5])
+
+        """
+        size = len(inversion)
+        N = list(range(size + 1))
+        perm = []
+        try:
+            for k in range(size):
+                val = N[inversion[k]]
+                perm.append(val)
+                N.remove(val)
+        except IndexError:
+            raise ValueError("The inversion vector is not valid.")
+        perm.extend(N)
+        return cls._af_new(perm)
+
+    @classmethod
+    def random(cls, n):
+        """
+        Generates a random permutation of length ``n``.
+
+        Uses the underlying Python pseudo-random number generator.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> Permutation.random(2) in (Permutation([1, 0]), Permutation([0, 1]))
+        True
+
+        """
+        perm_array = list(range(n))
+        random.shuffle(perm_array)
+        return cls._af_new(perm_array)
+
+    @classmethod
+    def unrank_lex(cls, size, rank):
+        """
+        Lexicographic permutation unranking.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+        >>> from sympy import init_printing
+        >>> init_printing(perm_cyclic=False, pretty_print=False)
+        >>> a = Permutation.unrank_lex(5, 10)
+        >>> a.rank()
+        10
+        >>> a
+        Permutation([0, 2, 4, 1, 3])
+
+        See Also
+        ========
+
+        rank, next_lex
+        """
+        perm_array = [0] * size
+        psize = 1
+        for i in range(size):
+            new_psize = psize*(i + 1)
+            d = (rank % new_psize) // psize
+            rank -= d*psize
+            perm_array[size - i - 1] = d
+            for j in range(size - i, size):
+                if perm_array[j] > d - 1:
+                    perm_array[j] += 1
+            psize = new_psize
+        return cls._af_new(perm_array)
+
+    def resize(self, n):
+        """Resize the permutation to the new size ``n``.
+
+        Parameters
+        ==========
+
+        n : int
+            The new size of the permutation.
+
+        Raises
+        ======
+
+        ValueError
+            If the permutation cannot be resized to the given size.
+            This may only happen when resized to a smaller size than
+            the original.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Permutation
+
+        Increasing the size of a permutation:
+
+        >>> p = Permutation(0, 1, 2)
+        >>> p = p.resize(5)
+        >>> p
+        (4)(0 1 2)
+
+        Decreasing the size of the permutation:
+
+        >>> p = p.resize(4)
+        >>> p
+        (3)(0 1 2)
+
+        If resizing to the specific size breaks the cycles:
+
+        >>> p.resize(2)
+        Traceback (most recent call last):
+        ...
+        ValueError: The permutation cannot be resized to 2 because the
+        cycle (0, 1, 2) may break.
+        """
+        aform = self.array_form
+        l = len(aform)
+        if n > l:
+            aform += list(range(l, n))
+            return Permutation._af_new(aform)
+
+        elif n < l:
+            cyclic_form = self.full_cyclic_form
+            new_cyclic_form = []
+            for cycle in cyclic_form:
+                cycle_min = min(cycle)
+                cycle_max = max(cycle)
+                if cycle_min <= n-1:
+                    if cycle_max > n-1:
+                        raise ValueError(
+                            "The permutation cannot be resized to {} "
+                            "because the cycle {} may break."
+                            .format(n, tuple(cycle)))
+
+                    new_cyclic_form.append(cycle)
+            return Permutation(new_cyclic_form)
+
+        return self
+
+    # XXX Deprecated flag
+    print_cyclic = None
+
+
+def _merge(arr, temp, left, mid, right):
+    """
+    Merges two sorted arrays and calculates the inversion count.
+
+    Helper function for calculating inversions. This method is
+    for internal use only.
+    """
+    i = k = left
+    j = mid
+    inv_count = 0
+    while i < mid and j <= right:
+        if arr[i] < arr[j]:
+            temp[k] = arr[i]
+            k += 1
+            i += 1
+        else:
+            temp[k] = arr[j]
+            k += 1
+            j += 1
+            inv_count += (mid -i)
+    while i < mid:
+        temp[k] = arr[i]
+        k += 1
+        i += 1
+    if j <= right:
+        k += right - j + 1
+        j += right - j + 1
+        arr[left:k + 1] = temp[left:k + 1]
+    else:
+        arr[left:right + 1] = temp[left:right + 1]
+    return inv_count
+
+Perm = Permutation
+_af_new = Perm._af_new
+
+
+class AppliedPermutation(Expr):
+    """A permutation applied to a symbolic variable.
+
+    Parameters
+    ==========
+
+    perm : Permutation
+    x : Expr
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol
+    >>> from sympy.combinatorics import Permutation
+
+    Creating a symbolic permutation function application:
+
+    >>> x = Symbol('x')
+    >>> p = Permutation(0, 1, 2)
+    >>> p.apply(x)
+    AppliedPermutation((0 1 2), x)
+    >>> _.subs(x, 1)
+    2
+    """
+    def __new__(cls, perm, x, evaluate=None):
+        if evaluate is None:
+            evaluate = global_parameters.evaluate
+
+        perm = _sympify(perm)
+        x = _sympify(x)
+
+        if not isinstance(perm, Permutation):
+            raise ValueError("{} must be a Permutation instance."
+                .format(perm))
+
+        if evaluate:
+            if x.is_Integer:
+                return perm.apply(x)
+
+        obj = super().__new__(cls, perm, x)
+        return obj
+
+
+@dispatch(Permutation, Permutation)
+def _eval_is_eq(lhs, rhs):
+    if lhs._size != rhs._size:
+        return None
+    return lhs._array_form == rhs._array_form
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/polyhedron.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/polyhedron.py
new file mode 100644
index 0000000000000000000000000000000000000000..2bc05d7d97c840649661f3290442499c841ca7c1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/polyhedron.py
@@ -0,0 +1,1019 @@
+from sympy.combinatorics import Permutation as Perm
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.core import Basic, Tuple, default_sort_key
+from sympy.sets import FiniteSet
+from sympy.utilities.iterables import (minlex, unflatten, flatten)
+from sympy.utilities.misc import as_int
+
+rmul = Perm.rmul
+
+
+class Polyhedron(Basic):
+    """
+    Represents the polyhedral symmetry group (PSG).
+
+    Explanation
+    ===========
+
+    The PSG is one of the symmetry groups of the Platonic solids.
+    There are three polyhedral groups: the tetrahedral group
+    of order 12, the octahedral group of order 24, and the
+    icosahedral group of order 60.
+
+    All doctests have been given in the docstring of the
+    constructor of the object.
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PolyhedralGroup.html
+
+    """
+    _edges = None
+
+    def __new__(cls, corners, faces=(), pgroup=()):
+        """
+        The constructor of the Polyhedron group object.
+
+        Explanation
+        ===========
+
+        It takes up to three parameters: the corners, faces, and
+        allowed transformations.
+
+        The corners/vertices are entered as a list of arbitrary
+        expressions that are used to identify each vertex.
+
+        The faces are entered as a list of tuples of indices; a tuple
+        of indices identifies the vertices which define the face. They
+        should be entered in a cw or ccw order; they will be standardized
+        by reversal and rotation to be give the lowest lexical ordering.
+        If no faces are given then no edges will be computed.
+
+            >>> from sympy.combinatorics.polyhedron import Polyhedron
+            >>> Polyhedron(list('abc'), [(1, 2, 0)]).faces
+            {(0, 1, 2)}
+            >>> Polyhedron(list('abc'), [(1, 0, 2)]).faces
+            {(0, 1, 2)}
+
+        The allowed transformations are entered as allowable permutations
+        of the vertices for the polyhedron. Instance of Permutations
+        (as with faces) should refer to the supplied vertices by index.
+        These permutation are stored as a PermutationGroup.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.permutations import Permutation
+        >>> from sympy import init_printing
+        >>> from sympy.abc import w, x, y, z
+        >>> init_printing(pretty_print=False, perm_cyclic=False)
+
+        Here we construct the Polyhedron object for a tetrahedron.
+
+        >>> corners = [w, x, y, z]
+        >>> faces = [(0, 1, 2), (0, 2, 3), (0, 3, 1), (1, 2, 3)]
+
+        Next, allowed transformations of the polyhedron must be given. This
+        is given as permutations of vertices.
+
+        Although the vertices of a tetrahedron can be numbered in 24 (4!)
+        different ways, there are only 12 different orientations for a
+        physical tetrahedron. The following permutations, applied once or
+        twice, will generate all 12 of the orientations. (The identity
+        permutation, Permutation(range(4)), is not included since it does
+        not change the orientation of the vertices.)
+
+        >>> pgroup = [Permutation([[0, 1, 2], [3]]), \
+                      Permutation([[0, 1, 3], [2]]), \
+                      Permutation([[0, 2, 3], [1]]), \
+                      Permutation([[1, 2, 3], [0]]), \
+                      Permutation([[0, 1], [2, 3]]), \
+                      Permutation([[0, 2], [1, 3]]), \
+                      Permutation([[0, 3], [1, 2]])]
+
+        The Polyhedron is now constructed and demonstrated:
+
+        >>> tetra = Polyhedron(corners, faces, pgroup)
+        >>> tetra.size
+        4
+        >>> tetra.edges
+        {(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)}
+        >>> tetra.corners
+        (w, x, y, z)
+
+        It can be rotated with an arbitrary permutation of vertices, e.g.
+        the following permutation is not in the pgroup:
+
+        >>> tetra.rotate(Permutation([0, 1, 3, 2]))
+        >>> tetra.corners
+        (w, x, z, y)
+
+        An allowed permutation of the vertices can be constructed by
+        repeatedly applying permutations from the pgroup to the vertices.
+        Here is a demonstration that applying p and p**2 for every p in
+        pgroup generates all the orientations of a tetrahedron and no others:
+
+        >>> all = ( (w, x, y, z), \
+                    (x, y, w, z), \
+                    (y, w, x, z), \
+                    (w, z, x, y), \
+                    (z, w, y, x), \
+                    (w, y, z, x), \
+                    (y, z, w, x), \
+                    (x, z, y, w), \
+                    (z, y, x, w), \
+                    (y, x, z, w), \
+                    (x, w, z, y), \
+                    (z, x, w, y) )
+
+        >>> got = []
+        >>> for p in (pgroup + [p**2 for p in pgroup]):
+        ...     h = Polyhedron(corners)
+        ...     h.rotate(p)
+        ...     got.append(h.corners)
+        ...
+        >>> set(got) == set(all)
+        True
+
+        The make_perm method of a PermutationGroup will randomly pick
+        permutations, multiply them together, and return the permutation that
+        can be applied to the polyhedron to give the orientation produced
+        by those individual permutations.
+
+        Here, 3 permutations are used:
+
+        >>> tetra.pgroup.make_perm(3) # doctest: +SKIP
+        Permutation([0, 3, 1, 2])
+
+        To select the permutations that should be used, supply a list
+        of indices to the permutations in pgroup in the order they should
+        be applied:
+
+        >>> use = [0, 0, 2]
+        >>> p002 = tetra.pgroup.make_perm(3, use)
+        >>> p002
+        Permutation([1, 0, 3, 2])
+
+
+        Apply them one at a time:
+
+        >>> tetra.reset()
+        >>> for i in use:
+        ...     tetra.rotate(pgroup[i])
+        ...
+        >>> tetra.vertices
+        (x, w, z, y)
+        >>> sequentially = tetra.vertices
+
+        Apply the composite permutation:
+
+        >>> tetra.reset()
+        >>> tetra.rotate(p002)
+        >>> tetra.corners
+        (x, w, z, y)
+        >>> tetra.corners in all and tetra.corners == sequentially
+        True
+
+        Notes
+        =====
+
+        Defining permutation groups
+        ---------------------------
+
+        It is not necessary to enter any permutations, nor is necessary to
+        enter a complete set of transformations. In fact, for a polyhedron,
+        all configurations can be constructed from just two permutations.
+        For example, the orientations of a tetrahedron can be generated from
+        an axis passing through a vertex and face and another axis passing
+        through a different vertex or from an axis passing through the
+        midpoints of two edges opposite of each other.
+
+        For simplicity of presentation, consider a square --
+        not a cube -- with vertices 1, 2, 3, and 4:
+
+        1-----2  We could think of axes of rotation being:
+        |     |  1) through the face
+        |     |  2) from midpoint 1-2 to 3-4 or 1-3 to 2-4
+        3-----4  3) lines 1-4 or 2-3
+
+
+        To determine how to write the permutations, imagine 4 cameras,
+        one at each corner, labeled A-D:
+
+        A       B          A       B
+         1-----2            1-----3             vertex index:
+         |     |            |     |                 1   0
+         |     |            |     |                 2   1
+         3-----4            2-----4                 3   2
+        C       D          C       D                4   3
+
+        original           after rotation
+                           along 1-4
+
+        A diagonal and a face axis will be chosen for the "permutation group"
+        from which any orientation can be constructed.
+
+        >>> pgroup = []
+
+        Imagine a clockwise rotation when viewing 1-4 from camera A. The new
+        orientation is (in camera-order): 1, 3, 2, 4 so the permutation is
+        given using the *indices* of the vertices as:
+
+        >>> pgroup.append(Permutation((0, 2, 1, 3)))
+
+        Now imagine rotating clockwise when looking down an axis entering the
+        center of the square as viewed. The new camera-order would be
+        3, 1, 4, 2 so the permutation is (using indices):
+
+        >>> pgroup.append(Permutation((2, 0, 3, 1)))
+
+        The square can now be constructed:
+            ** use real-world labels for the vertices, entering them in
+               camera order
+            ** for the faces we use zero-based indices of the vertices
+               in *edge-order* as the face is traversed; neither the
+               direction nor the starting point matter -- the faces are
+               only used to define edges (if so desired).
+
+        >>> square = Polyhedron((1, 2, 3, 4), [(0, 1, 3, 2)], pgroup)
+
+        To rotate the square with a single permutation we can do:
+
+        >>> square.rotate(square.pgroup[0])
+        >>> square.corners
+        (1, 3, 2, 4)
+
+        To use more than one permutation (or to use one permutation more
+        than once) it is more convenient to use the make_perm method:
+
+        >>> p011 = square.pgroup.make_perm([0, 1, 1]) # diag flip + 2 rotations
+        >>> square.reset() # return to initial orientation
+        >>> square.rotate(p011)
+        >>> square.corners
+        (4, 2, 3, 1)
+
+        Thinking outside the box
+        ------------------------
+
+        Although the Polyhedron object has a direct physical meaning, it
+        actually has broader application. In the most general sense it is
+        just a decorated PermutationGroup, allowing one to connect the
+        permutations to something physical. For example, a Rubik's cube is
+        not a proper polyhedron, but the Polyhedron class can be used to
+        represent it in a way that helps to visualize the Rubik's cube.
+
+        >>> from sympy import flatten, unflatten, symbols
+        >>> from sympy.combinatorics import RubikGroup
+        >>> facelets = flatten([symbols(s+'1:5') for s in 'UFRBLD'])
+        >>> def show():
+        ...     pairs = unflatten(r2.corners, 2)
+        ...     print(pairs[::2])
+        ...     print(pairs[1::2])
+        ...
+        >>> r2 = Polyhedron(facelets, pgroup=RubikGroup(2))
+        >>> show()
+        [(U1, U2), (F1, F2), (R1, R2), (B1, B2), (L1, L2), (D1, D2)]
+        [(U3, U4), (F3, F4), (R3, R4), (B3, B4), (L3, L4), (D3, D4)]
+        >>> r2.rotate(0) # cw rotation of F
+        >>> show()
+        [(U1, U2), (F3, F1), (U3, R2), (B1, B2), (L1, D1), (R3, R1)]
+        [(L4, L2), (F4, F2), (U4, R4), (B3, B4), (L3, D2), (D3, D4)]
+
+        Predefined Polyhedra
+        ====================
+
+        For convenience, the vertices and faces are defined for the following
+        standard solids along with a permutation group for transformations.
+        When the polyhedron is oriented as indicated below, the vertices in
+        a given horizontal plane are numbered in ccw direction, starting from
+        the vertex that will give the lowest indices in a given face. (In the
+        net of the vertices, indices preceded by "-" indicate replication of
+        the lhs index in the net.)
+
+        tetrahedron, tetrahedron_faces
+        ------------------------------
+
+            4 vertices (vertex up) net:
+
+                 0 0-0
+                1 2 3-1
+
+            4 faces:
+
+            (0, 1, 2) (0, 2, 3) (0, 3, 1) (1, 2, 3)
+
+        cube, cube_faces
+        ----------------
+
+            8 vertices (face up) net:
+
+                0 1 2 3-0
+                4 5 6 7-4
+
+            6 faces:
+
+            (0, 1, 2, 3)
+            (0, 1, 5, 4) (1, 2, 6, 5) (2, 3, 7, 6) (0, 3, 7, 4)
+            (4, 5, 6, 7)
+
+        octahedron, octahedron_faces
+        ----------------------------
+
+            6 vertices (vertex up) net:
+
+                 0 0 0-0
+                1 2 3 4-1
+                 5 5 5-5
+
+            8 faces:
+
+            (0, 1, 2) (0, 2, 3) (0, 3, 4) (0, 1, 4)
+            (1, 2, 5) (2, 3, 5) (3, 4, 5) (1, 4, 5)
+
+        dodecahedron, dodecahedron_faces
+        --------------------------------
+
+            20 vertices (vertex up) net:
+
+                  0  1  2  3  4 -0
+                  5  6  7  8  9 -5
+                14 10 11 12 13-14
+                15 16 17 18 19-15
+
+            12 faces:
+
+            (0, 1, 2, 3, 4) (0, 1, 6, 10, 5) (1, 2, 7, 11, 6)
+            (2, 3, 8, 12, 7) (3, 4, 9, 13, 8) (0, 4, 9, 14, 5)
+            (5, 10, 16, 15, 14) (6, 10, 16, 17, 11) (7, 11, 17, 18, 12)
+            (8, 12, 18, 19, 13) (9, 13, 19, 15, 14)(15, 16, 17, 18, 19)
+
+        icosahedron, icosahedron_faces
+        ------------------------------
+
+            12 vertices (face up) net:
+
+                 0  0  0  0 -0
+                1  2  3  4  5 -1
+                 6  7  8  9  10 -6
+                  11 11 11 11 -11
+
+            20 faces:
+
+            (0, 1, 2) (0, 2, 3) (0, 3, 4)
+            (0, 4, 5) (0, 1, 5) (1, 2, 6)
+            (2, 3, 7) (3, 4, 8) (4, 5, 9)
+            (1, 5, 10) (2, 6, 7) (3, 7, 8)
+            (4, 8, 9) (5, 9, 10) (1, 6, 10)
+            (6, 7, 11) (7, 8, 11) (8, 9, 11)
+            (9, 10, 11) (6, 10, 11)
+
+        >>> from sympy.combinatorics.polyhedron import cube
+        >>> cube.edges
+        {(0, 1), (0, 3), (0, 4), (1, 2), (1, 5), (2, 3), (2, 6), (3, 7), (4, 5), (4, 7), (5, 6), (6, 7)}
+
+        If you want to use letters or other names for the corners you
+        can still use the pre-calculated faces:
+
+        >>> corners = list('abcdefgh')
+        >>> Polyhedron(corners, cube.faces).corners
+        (a, b, c, d, e, f, g, h)
+
+        References
+        ==========
+
+        .. [1] www.ocf.berkeley.edu/~wwu/articles/platonicsolids.pdf
+
+        """
+        faces = [minlex(f, directed=False, key=default_sort_key) for f in faces]
+        corners, faces, pgroup = args = \
+            [Tuple(*a) for a in (corners, faces, pgroup)]
+        obj = Basic.__new__(cls, *args)
+        obj._corners = tuple(corners)  # in order given
+        obj._faces = FiniteSet(*faces)
+        if pgroup and pgroup[0].size != len(corners):
+            raise ValueError("Permutation size unequal to number of corners.")
+        # use the identity permutation if none are given
+        obj._pgroup = PermutationGroup(
+            pgroup or [Perm(range(len(corners)))] )
+        return obj
+
+    @property
+    def corners(self):
+        """
+        Get the corners of the Polyhedron.
+
+        The method ``vertices`` is an alias for ``corners``.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Polyhedron
+        >>> from sympy.abc import a, b, c, d
+        >>> p = Polyhedron(list('abcd'))
+        >>> p.corners == p.vertices == (a, b, c, d)
+        True
+
+        See Also
+        ========
+
+        array_form, cyclic_form
+        """
+        return self._corners
+    vertices = corners
+
+    @property
+    def array_form(self):
+        """Return the indices of the corners.
+
+        The indices are given relative to the original position of corners.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.polyhedron import tetrahedron
+        >>> tetrahedron = tetrahedron.copy()
+        >>> tetrahedron.array_form
+        [0, 1, 2, 3]
+
+        >>> tetrahedron.rotate(0)
+        >>> tetrahedron.array_form
+        [0, 2, 3, 1]
+        >>> tetrahedron.pgroup[0].array_form
+        [0, 2, 3, 1]
+
+        See Also
+        ========
+
+        corners, cyclic_form
+        """
+        corners = list(self.args[0])
+        return [corners.index(c) for c in self.corners]
+
+    @property
+    def cyclic_form(self):
+        """Return the indices of the corners in cyclic notation.
+
+        The indices are given relative to the original position of corners.
+
+        See Also
+        ========
+
+        corners, array_form
+        """
+        return Perm._af_new(self.array_form).cyclic_form
+
+    @property
+    def size(self):
+        """
+        Get the number of corners of the Polyhedron.
+        """
+        return len(self._corners)
+
+    @property
+    def faces(self):
+        """
+        Get the faces of the Polyhedron.
+        """
+        return self._faces
+
+    @property
+    def pgroup(self):
+        """
+        Get the permutations of the Polyhedron.
+        """
+        return self._pgroup
+
+    @property
+    def edges(self):
+        """
+        Given the faces of the polyhedra we can get the edges.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Polyhedron
+        >>> from sympy.abc import a, b, c
+        >>> corners = (a, b, c)
+        >>> faces = [(0, 1, 2)]
+        >>> Polyhedron(corners, faces).edges
+        {(0, 1), (0, 2), (1, 2)}
+
+        """
+        if self._edges is None:
+            output = set()
+            for face in self.faces:
+                for i in range(len(face)):
+                    edge = tuple(sorted([face[i], face[i - 1]]))
+                    output.add(edge)
+            self._edges = FiniteSet(*output)
+        return self._edges
+
+    def rotate(self, perm):
+        """
+        Apply a permutation to the polyhedron *in place*. The permutation
+        may be given as a Permutation instance or an integer indicating
+        which permutation from pgroup of the Polyhedron should be
+        applied.
+
+        This is an operation that is analogous to rotation about
+        an axis by a fixed increment.
+
+        Notes
+        =====
+
+        When a Permutation is applied, no check is done to see if that
+        is a valid permutation for the Polyhedron. For example, a cube
+        could be given a permutation which effectively swaps only 2
+        vertices. A valid permutation (that rotates the object in a
+        physical way) will be obtained if one only uses
+        permutations from the ``pgroup`` of the Polyhedron. On the other
+        hand, allowing arbitrary rotations (applications of permutations)
+        gives a way to follow named elements rather than indices since
+        Polyhedron allows vertices to be named while Permutation works
+        only with indices.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Polyhedron, Permutation
+        >>> from sympy.combinatorics.polyhedron import cube
+        >>> cube = cube.copy()
+        >>> cube.corners
+        (0, 1, 2, 3, 4, 5, 6, 7)
+        >>> cube.rotate(0)
+        >>> cube.corners
+        (1, 2, 3, 0, 5, 6, 7, 4)
+
+        A non-physical "rotation" that is not prohibited by this method:
+
+        >>> cube.reset()
+        >>> cube.rotate(Permutation([[1, 2]], size=8))
+        >>> cube.corners
+        (0, 2, 1, 3, 4, 5, 6, 7)
+
+        Polyhedron can be used to follow elements of set that are
+        identified by letters instead of integers:
+
+        >>> shadow = h5 = Polyhedron(list('abcde'))
+        >>> p = Permutation([3, 0, 1, 2, 4])
+        >>> h5.rotate(p)
+        >>> h5.corners
+        (d, a, b, c, e)
+        >>> _ == shadow.corners
+        True
+        >>> copy = h5.copy()
+        >>> h5.rotate(p)
+        >>> h5.corners == copy.corners
+        False
+        """
+        if not isinstance(perm, Perm):
+            perm = self.pgroup[perm]
+            # and we know it's valid
+        else:
+            if perm.size != self.size:
+                raise ValueError('Polyhedron and Permutation sizes differ.')
+        a = perm.array_form
+        corners = [self.corners[a[i]] for i in range(len(self.corners))]
+        self._corners = tuple(corners)
+
+    def reset(self):
+        """Return corners to their original positions.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.polyhedron import tetrahedron as T
+        >>> T = T.copy()
+        >>> T.corners
+        (0, 1, 2, 3)
+        >>> T.rotate(0)
+        >>> T.corners
+        (0, 2, 3, 1)
+        >>> T.reset()
+        >>> T.corners
+        (0, 1, 2, 3)
+        """
+        self._corners = self.args[0]
+
+
+def _pgroup_calcs():
+    """Return the permutation groups for each of the polyhedra and the face
+    definitions: tetrahedron, cube, octahedron, dodecahedron, icosahedron,
+    tetrahedron_faces, cube_faces, octahedron_faces, dodecahedron_faces,
+    icosahedron_faces
+
+    Explanation
+    ===========
+
+    (This author did not find and did not know of a better way to do it though
+    there likely is such a way.)
+
+    Although only 2 permutations are needed for a polyhedron in order to
+    generate all the possible orientations, a group of permutations is
+    provided instead. A set of permutations is called a "group" if::
+
+    a*b = c (for any pair of permutations in the group, a and b, their
+    product, c, is in the group)
+
+    a*(b*c) = (a*b)*c (for any 3 permutations in the group associativity holds)
+
+    there is an identity permutation, I, such that I*a = a*I for all elements
+    in the group
+
+    a*b = I (the inverse of each permutation is also in the group)
+
+    None of the polyhedron groups defined follow these definitions of a group.
+    Instead, they are selected to contain those permutations whose powers
+    alone will construct all orientations of the polyhedron, i.e. for
+    permutations ``a``, ``b``, etc... in the group, ``a, a**2, ..., a**o_a``,
+    ``b, b**2, ..., b**o_b``, etc... (where ``o_i`` is the order of
+    permutation ``i``) generate all permutations of the polyhedron instead of
+    mixed products like ``a*b``, ``a*b**2``, etc....
+
+    Note that for a polyhedron with n vertices, the valid permutations of the
+    vertices exclude those that do not maintain its faces. e.g. the
+    permutation BCDE of a square's four corners, ABCD, is a valid
+    permutation while CBDE is not (because this would twist the square).
+
+    Examples
+    ========
+
+    The is_group checks for: closure, the presence of the Identity permutation,
+    and the presence of the inverse for each of the elements in the group. This
+    confirms that none of the polyhedra are true groups:
+
+    >>> from sympy.combinatorics.polyhedron import (
+    ... tetrahedron, cube, octahedron, dodecahedron, icosahedron)
+    ...
+    >>> polyhedra = (tetrahedron, cube, octahedron, dodecahedron, icosahedron)
+    >>> [h.pgroup.is_group for h in polyhedra]
+    ...
+    [True, True, True, True, True]
+
+    Although tests in polyhedron's test suite check that powers of the
+    permutations in the groups generate all permutations of the vertices
+    of the polyhedron, here we also demonstrate the powers of the given
+    permutations create a complete group for the tetrahedron:
+
+    >>> from sympy.combinatorics import Permutation, PermutationGroup
+    >>> for h in polyhedra[:1]:
+    ...     G = h.pgroup
+    ...     perms = set()
+    ...     for g in G:
+    ...         for e in range(g.order()):
+    ...             p = tuple((g**e).array_form)
+    ...             perms.add(p)
+    ...
+    ...     perms = [Permutation(p) for p in perms]
+    ...     assert PermutationGroup(perms).is_group
+
+    In addition to doing the above, the tests in the suite confirm that the
+    faces are all present after the application of each permutation.
+
+    References
+    ==========
+
+    .. [1] https://dogschool.tripod.com/trianglegroup.html
+
+    """
+    def _pgroup_of_double(polyh, ordered_faces, pgroup):
+        n = len(ordered_faces[0])
+        # the vertices of the double which sits inside a give polyhedron
+        # can be found by tracking the faces of the outer polyhedron.
+        # A map between face and the vertex of the double is made so that
+        # after rotation the position of the vertices can be located
+        fmap = dict(zip(ordered_faces,
+                        range(len(ordered_faces))))
+        flat_faces = flatten(ordered_faces)
+        new_pgroup = []
+        for p in pgroup:
+            h = polyh.copy()
+            h.rotate(p)
+            c = h.corners
+            # reorder corners in the order they should appear when
+            # enumerating the faces
+            reorder = unflatten([c[j] for j in flat_faces], n)
+            # make them canonical
+            reorder = [tuple(map(as_int,
+                       minlex(f, directed=False)))
+                       for f in reorder]
+            # map face to vertex: the resulting list of vertices are the
+            # permutation that we seek for the double
+            new_pgroup.append(Perm([fmap[f] for f in reorder]))
+        return new_pgroup
+
+    tetrahedron_faces = [
+        (0, 1, 2), (0, 2, 3), (0, 3, 1),  # upper 3
+        (1, 2, 3),  # bottom
+    ]
+
+    # cw from top
+    #
+    _t_pgroup = [
+        Perm([[1, 2, 3], [0]]),  # cw from top
+        Perm([[0, 1, 2], [3]]),  # cw from front face
+        Perm([[0, 3, 2], [1]]),  # cw from back right face
+        Perm([[0, 3, 1], [2]]),  # cw from back left face
+        Perm([[0, 1], [2, 3]]),  # through front left edge
+        Perm([[0, 2], [1, 3]]),  # through front right edge
+        Perm([[0, 3], [1, 2]]),  # through back edge
+    ]
+
+    tetrahedron = Polyhedron(
+        range(4),
+        tetrahedron_faces,
+        _t_pgroup)
+
+    cube_faces = [
+        (0, 1, 2, 3),  # upper
+        (0, 1, 5, 4), (1, 2, 6, 5), (2, 3, 7, 6), (0, 3, 7, 4),  # middle 4
+        (4, 5, 6, 7),  # lower
+    ]
+
+    # U, D, F, B, L, R = up, down, front, back, left, right
+    _c_pgroup = [Perm(p) for p in
+        [
+        [1, 2, 3, 0, 5, 6, 7, 4],  # cw from top, U
+        [4, 0, 3, 7, 5, 1, 2, 6],  # cw from F face
+        [4, 5, 1, 0, 7, 6, 2, 3],  # cw from R face
+
+        [1, 0, 4, 5, 2, 3, 7, 6],  # cw through UF edge
+        [6, 2, 1, 5, 7, 3, 0, 4],  # cw through UR edge
+        [6, 7, 3, 2, 5, 4, 0, 1],  # cw through UB edge
+        [3, 7, 4, 0, 2, 6, 5, 1],  # cw through UL edge
+        [4, 7, 6, 5, 0, 3, 2, 1],  # cw through FL edge
+        [6, 5, 4, 7, 2, 1, 0, 3],  # cw through FR edge
+
+        [0, 3, 7, 4, 1, 2, 6, 5],  # cw through UFL vertex
+        [5, 1, 0, 4, 6, 2, 3, 7],  # cw through UFR vertex
+        [5, 6, 2, 1, 4, 7, 3, 0],  # cw through UBR vertex
+        [7, 4, 0, 3, 6, 5, 1, 2],  # cw through UBL
+        ]]
+
+    cube = Polyhedron(
+        range(8),
+        cube_faces,
+        _c_pgroup)
+
+    octahedron_faces = [
+        (0, 1, 2), (0, 2, 3), (0, 3, 4), (0, 1, 4),  # top 4
+        (1, 2, 5), (2, 3, 5), (3, 4, 5), (1, 4, 5),  # bottom 4
+    ]
+
+    octahedron = Polyhedron(
+        range(6),
+        octahedron_faces,
+        _pgroup_of_double(cube, cube_faces, _c_pgroup))
+
+    dodecahedron_faces = [
+        (0, 1, 2, 3, 4),  # top
+        (0, 1, 6, 10, 5), (1, 2, 7, 11, 6), (2, 3, 8, 12, 7),  # upper 5
+        (3, 4, 9, 13, 8), (0, 4, 9, 14, 5),
+        (5, 10, 16, 15, 14), (6, 10, 16, 17, 11), (7, 11, 17, 18,
+          12),  # lower 5
+        (8, 12, 18, 19, 13), (9, 13, 19, 15, 14),
+        (15, 16, 17, 18, 19)  # bottom
+    ]
+
+    def _string_to_perm(s):
+        rv = [Perm(range(20))]
+        p = None
+        for si in s:
+            if si not in '01':
+                count = int(si) - 1
+            else:
+                count = 1
+                if si == '0':
+                    p = _f0
+                elif si == '1':
+                    p = _f1
+            rv.extend([p]*count)
+        return Perm.rmul(*rv)
+
+    # top face cw
+    _f0 = Perm([
+        1, 2, 3, 4, 0, 6, 7, 8, 9, 5, 11,
+        12, 13, 14, 10, 16, 17, 18, 19, 15])
+    # front face cw
+    _f1 = Perm([
+        5, 0, 4, 9, 14, 10, 1, 3, 13, 15,
+        6, 2, 8, 19, 16, 17, 11, 7, 12, 18])
+    # the strings below, like 0104 are shorthand for F0*F1*F0**4 and are
+    # the remaining 4 face rotations, 15 edge permutations, and the
+    # 10 vertex rotations.
+    _dodeca_pgroup = [_f0, _f1] + [_string_to_perm(s) for s in '''
+    0104 140 014 0410
+    010 1403 03104 04103 102
+    120 1304 01303 021302 03130
+    0412041 041204103 04120410 041204104 041204102
+    10 01 1402 0140 04102 0412 1204 1302 0130 03120'''.strip().split()]
+
+    dodecahedron = Polyhedron(
+        range(20),
+        dodecahedron_faces,
+        _dodeca_pgroup)
+
+    icosahedron_faces = [
+        (0, 1, 2), (0, 2, 3), (0, 3, 4), (0, 4, 5), (0, 1, 5),
+        (1, 6, 7), (1, 2, 7), (2, 7, 8), (2, 3, 8), (3, 8, 9),
+        (3, 4, 9), (4, 9, 10), (4, 5, 10), (5, 6, 10), (1, 5, 6),
+        (6, 7, 11), (7, 8, 11), (8, 9, 11), (9, 10, 11), (6, 10, 11)]
+
+    icosahedron = Polyhedron(
+        range(12),
+        icosahedron_faces,
+        _pgroup_of_double(
+            dodecahedron, dodecahedron_faces, _dodeca_pgroup))
+
+    return (tetrahedron, cube, octahedron, dodecahedron, icosahedron,
+        tetrahedron_faces, cube_faces, octahedron_faces,
+        dodecahedron_faces, icosahedron_faces)
+
+# -----------------------------------------------------------------------
+#   Standard Polyhedron groups
+#
+#   These are generated using _pgroup_calcs() above. However to save
+#   import time we encode them explicitly here.
+# -----------------------------------------------------------------------
+
+tetrahedron = Polyhedron(
+    Tuple(0, 1, 2, 3),
+    Tuple(
+        Tuple(0, 1, 2),
+        Tuple(0, 2, 3),
+        Tuple(0, 1, 3),
+        Tuple(1, 2, 3)),
+    Tuple(
+        Perm(1, 2, 3),
+        Perm(3)(0, 1, 2),
+        Perm(0, 3, 2),
+        Perm(0, 3, 1),
+        Perm(0, 1)(2, 3),
+        Perm(0, 2)(1, 3),
+        Perm(0, 3)(1, 2)
+    ))
+
+cube = Polyhedron(
+    Tuple(0, 1, 2, 3, 4, 5, 6, 7),
+    Tuple(
+        Tuple(0, 1, 2, 3),
+        Tuple(0, 1, 5, 4),
+        Tuple(1, 2, 6, 5),
+        Tuple(2, 3, 7, 6),
+        Tuple(0, 3, 7, 4),
+        Tuple(4, 5, 6, 7)),
+    Tuple(
+        Perm(0, 1, 2, 3)(4, 5, 6, 7),
+        Perm(0, 4, 5, 1)(2, 3, 7, 6),
+        Perm(0, 4, 7, 3)(1, 5, 6, 2),
+        Perm(0, 1)(2, 4)(3, 5)(6, 7),
+        Perm(0, 6)(1, 2)(3, 5)(4, 7),
+        Perm(0, 6)(1, 7)(2, 3)(4, 5),
+        Perm(0, 3)(1, 7)(2, 4)(5, 6),
+        Perm(0, 4)(1, 7)(2, 6)(3, 5),
+        Perm(0, 6)(1, 5)(2, 4)(3, 7),
+        Perm(1, 3, 4)(2, 7, 5),
+        Perm(7)(0, 5, 2)(3, 4, 6),
+        Perm(0, 5, 7)(1, 6, 3),
+        Perm(0, 7, 2)(1, 4, 6)))
+
+octahedron = Polyhedron(
+    Tuple(0, 1, 2, 3, 4, 5),
+    Tuple(
+        Tuple(0, 1, 2),
+        Tuple(0, 2, 3),
+        Tuple(0, 3, 4),
+        Tuple(0, 1, 4),
+        Tuple(1, 2, 5),
+        Tuple(2, 3, 5),
+        Tuple(3, 4, 5),
+        Tuple(1, 4, 5)),
+    Tuple(
+        Perm(5)(1, 2, 3, 4),
+        Perm(0, 4, 5, 2),
+        Perm(0, 1, 5, 3),
+        Perm(0, 1)(2, 4)(3, 5),
+        Perm(0, 2)(1, 3)(4, 5),
+        Perm(0, 3)(1, 5)(2, 4),
+        Perm(0, 4)(1, 3)(2, 5),
+        Perm(0, 5)(1, 4)(2, 3),
+        Perm(0, 5)(1, 2)(3, 4),
+        Perm(0, 4, 1)(2, 3, 5),
+        Perm(0, 1, 2)(3, 4, 5),
+        Perm(0, 2, 3)(1, 5, 4),
+        Perm(0, 4, 3)(1, 5, 2)))
+
+dodecahedron = Polyhedron(
+    Tuple(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19),
+    Tuple(
+        Tuple(0, 1, 2, 3, 4),
+        Tuple(0, 1, 6, 10, 5),
+        Tuple(1, 2, 7, 11, 6),
+        Tuple(2, 3, 8, 12, 7),
+        Tuple(3, 4, 9, 13, 8),
+        Tuple(0, 4, 9, 14, 5),
+        Tuple(5, 10, 16, 15, 14),
+        Tuple(6, 10, 16, 17, 11),
+        Tuple(7, 11, 17, 18, 12),
+        Tuple(8, 12, 18, 19, 13),
+        Tuple(9, 13, 19, 15, 14),
+        Tuple(15, 16, 17, 18, 19)),
+    Tuple(
+        Perm(0, 1, 2, 3, 4)(5, 6, 7, 8, 9)(10, 11, 12, 13, 14)(15, 16, 17, 18, 19),
+        Perm(0, 5, 10, 6, 1)(2, 4, 14, 16, 11)(3, 9, 15, 17, 7)(8, 13, 19, 18, 12),
+        Perm(0, 10, 17, 12, 3)(1, 6, 11, 7, 2)(4, 5, 16, 18, 8)(9, 14, 15, 19, 13),
+        Perm(0, 6, 17, 19, 9)(1, 11, 18, 13, 4)(2, 7, 12, 8, 3)(5, 10, 16, 15, 14),
+        Perm(0, 2, 12, 19, 14)(1, 7, 18, 15, 5)(3, 8, 13, 9, 4)(6, 11, 17, 16, 10),
+        Perm(0, 4, 9, 14, 5)(1, 3, 13, 15, 10)(2, 8, 19, 16, 6)(7, 12, 18, 17, 11),
+        Perm(0, 1)(2, 5)(3, 10)(4, 6)(7, 14)(8, 16)(9, 11)(12, 15)(13, 17)(18, 19),
+        Perm(0, 7)(1, 2)(3, 6)(4, 11)(5, 12)(8, 10)(9, 17)(13, 16)(14, 18)(15, 19),
+        Perm(0, 12)(1, 8)(2, 3)(4, 7)(5, 18)(6, 13)(9, 11)(10, 19)(14, 17)(15, 16),
+        Perm(0, 8)(1, 13)(2, 9)(3, 4)(5, 12)(6, 19)(7, 14)(10, 18)(11, 15)(16, 17),
+        Perm(0, 4)(1, 9)(2, 14)(3, 5)(6, 13)(7, 15)(8, 10)(11, 19)(12, 16)(17, 18),
+        Perm(0, 5)(1, 14)(2, 15)(3, 16)(4, 10)(6, 9)(7, 19)(8, 17)(11, 13)(12, 18),
+        Perm(0, 11)(1, 6)(2, 10)(3, 16)(4, 17)(5, 7)(8, 15)(9, 18)(12, 14)(13, 19),
+        Perm(0, 18)(1, 12)(2, 7)(3, 11)(4, 17)(5, 19)(6, 8)(9, 16)(10, 13)(14, 15),
+        Perm(0, 18)(1, 19)(2, 13)(3, 8)(4, 12)(5, 17)(6, 15)(7, 9)(10, 16)(11, 14),
+        Perm(0, 13)(1, 19)(2, 15)(3, 14)(4, 9)(5, 8)(6, 18)(7, 16)(10, 12)(11, 17),
+        Perm(0, 16)(1, 15)(2, 19)(3, 18)(4, 17)(5, 10)(6, 14)(7, 13)(8, 12)(9, 11),
+        Perm(0, 18)(1, 17)(2, 16)(3, 15)(4, 19)(5, 12)(6, 11)(7, 10)(8, 14)(9, 13),
+        Perm(0, 15)(1, 19)(2, 18)(3, 17)(4, 16)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10),
+        Perm(0, 17)(1, 16)(2, 15)(3, 19)(4, 18)(5, 11)(6, 10)(7, 14)(8, 13)(9, 12),
+        Perm(0, 19)(1, 18)(2, 17)(3, 16)(4, 15)(5, 13)(6, 12)(7, 11)(8, 10)(9, 14),
+        Perm(1, 4, 5)(2, 9, 10)(3, 14, 6)(7, 13, 16)(8, 15, 11)(12, 19, 17),
+        Perm(19)(0, 6, 2)(3, 5, 11)(4, 10, 7)(8, 14, 17)(9, 16, 12)(13, 15, 18),
+        Perm(0, 11, 8)(1, 7, 3)(4, 6, 12)(5, 17, 13)(9, 10, 18)(14, 16, 19),
+        Perm(0, 7, 13)(1, 12, 9)(2, 8, 4)(5, 11, 19)(6, 18, 14)(10, 17, 15),
+        Perm(0, 3, 9)(1, 8, 14)(2, 13, 5)(6, 12, 15)(7, 19, 10)(11, 18, 16),
+        Perm(0, 14, 10)(1, 9, 16)(2, 13, 17)(3, 19, 11)(4, 15, 6)(7, 8, 18),
+        Perm(0, 16, 7)(1, 10, 11)(2, 5, 17)(3, 14, 18)(4, 15, 12)(8, 9, 19),
+        Perm(0, 16, 13)(1, 17, 8)(2, 11, 12)(3, 6, 18)(4, 10, 19)(5, 15, 9),
+        Perm(0, 11, 15)(1, 17, 14)(2, 18, 9)(3, 12, 13)(4, 7, 19)(5, 6, 16),
+        Perm(0, 8, 15)(1, 12, 16)(2, 18, 10)(3, 19, 5)(4, 13, 14)(6, 7, 17)))
+
+icosahedron = Polyhedron(
+    Tuple(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11),
+    Tuple(
+        Tuple(0, 1, 2),
+        Tuple(0, 2, 3),
+        Tuple(0, 3, 4),
+        Tuple(0, 4, 5),
+        Tuple(0, 1, 5),
+        Tuple(1, 6, 7),
+        Tuple(1, 2, 7),
+        Tuple(2, 7, 8),
+        Tuple(2, 3, 8),
+        Tuple(3, 8, 9),
+        Tuple(3, 4, 9),
+        Tuple(4, 9, 10),
+        Tuple(4, 5, 10),
+        Tuple(5, 6, 10),
+        Tuple(1, 5, 6),
+        Tuple(6, 7, 11),
+        Tuple(7, 8, 11),
+        Tuple(8, 9, 11),
+        Tuple(9, 10, 11),
+        Tuple(6, 10, 11)),
+    Tuple(
+        Perm(11)(1, 2, 3, 4, 5)(6, 7, 8, 9, 10),
+        Perm(0, 5, 6, 7, 2)(3, 4, 10, 11, 8),
+        Perm(0, 1, 7, 8, 3)(4, 5, 6, 11, 9),
+        Perm(0, 2, 8, 9, 4)(1, 7, 11, 10, 5),
+        Perm(0, 3, 9, 10, 5)(1, 2, 8, 11, 6),
+        Perm(0, 4, 10, 6, 1)(2, 3, 9, 11, 7),
+        Perm(0, 1)(2, 5)(3, 6)(4, 7)(8, 10)(9, 11),
+        Perm(0, 2)(1, 3)(4, 7)(5, 8)(6, 9)(10, 11),
+        Perm(0, 3)(1, 9)(2, 4)(5, 8)(6, 11)(7, 10),
+        Perm(0, 4)(1, 9)(2, 10)(3, 5)(6, 8)(7, 11),
+        Perm(0, 5)(1, 4)(2, 10)(3, 6)(7, 9)(8, 11),
+        Perm(0, 6)(1, 5)(2, 10)(3, 11)(4, 7)(8, 9),
+        Perm(0, 7)(1, 2)(3, 6)(4, 11)(5, 8)(9, 10),
+        Perm(0, 8)(1, 9)(2, 3)(4, 7)(5, 11)(6, 10),
+        Perm(0, 9)(1, 11)(2, 10)(3, 4)(5, 8)(6, 7),
+        Perm(0, 10)(1, 9)(2, 11)(3, 6)(4, 5)(7, 8),
+        Perm(0, 11)(1, 6)(2, 10)(3, 9)(4, 8)(5, 7),
+        Perm(0, 11)(1, 8)(2, 7)(3, 6)(4, 10)(5, 9),
+        Perm(0, 11)(1, 10)(2, 9)(3, 8)(4, 7)(5, 6),
+        Perm(0, 11)(1, 7)(2, 6)(3, 10)(4, 9)(5, 8),
+        Perm(0, 11)(1, 9)(2, 8)(3, 7)(4, 6)(5, 10),
+        Perm(0, 5, 1)(2, 4, 6)(3, 10, 7)(8, 9, 11),
+        Perm(0, 1, 2)(3, 5, 7)(4, 6, 8)(9, 10, 11),
+        Perm(0, 2, 3)(1, 8, 4)(5, 7, 9)(6, 11, 10),
+        Perm(0, 3, 4)(1, 8, 10)(2, 9, 5)(6, 7, 11),
+        Perm(0, 4, 5)(1, 3, 10)(2, 9, 6)(7, 8, 11),
+        Perm(0, 10, 7)(1, 5, 6)(2, 4, 11)(3, 9, 8),
+        Perm(0, 6, 8)(1, 7, 2)(3, 5, 11)(4, 10, 9),
+        Perm(0, 7, 9)(1, 11, 4)(2, 8, 3)(5, 6, 10),
+        Perm(0, 8, 10)(1, 7, 6)(2, 11, 5)(3, 9, 4),
+        Perm(0, 9, 6)(1, 3, 11)(2, 8, 7)(4, 10, 5)))
+
+tetrahedron_faces = [tuple(arg) for arg in tetrahedron.faces]
+
+cube_faces = [tuple(arg) for arg in cube.faces]
+
+octahedron_faces = [tuple(arg) for arg in octahedron.faces]
+
+dodecahedron_faces = [tuple(arg) for arg in dodecahedron.faces]
+
+icosahedron_faces = [tuple(arg) for arg in icosahedron.faces]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/prufer.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/prufer.py
new file mode 100644
index 0000000000000000000000000000000000000000..e389df87cddc0152b2376e18b9f3df2e94d3d2fb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/prufer.py
@@ -0,0 +1,435 @@
+from sympy.core import Basic
+from sympy.core.containers import Tuple
+from sympy.tensor.array import Array
+from sympy.core.sympify import _sympify
+from sympy.utilities.iterables import flatten, iterable
+from sympy.utilities.misc import as_int
+
+from collections import defaultdict
+
+
+class Prufer(Basic):
+    """
+    The Prufer correspondence is an algorithm that describes the
+    bijection between labeled trees and the Prufer code. A Prufer
+    code of a labeled tree is unique up to isomorphism and has
+    a length of n - 2.
+
+    Prufer sequences were first used by Heinz Prufer to give a
+    proof of Cayley's formula.
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/LabeledTree.html
+
+    """
+    _prufer_repr = None
+    _tree_repr = None
+    _nodes = None
+    _rank = None
+
+    @property
+    def prufer_repr(self):
+        """Returns Prufer sequence for the Prufer object.
+
+        This sequence is found by removing the highest numbered vertex,
+        recording the node it was attached to, and continuing until only
+        two vertices remain. The Prufer sequence is the list of recorded nodes.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]).prufer_repr
+        [3, 3, 3, 4]
+        >>> Prufer([1, 0, 0]).prufer_repr
+        [1, 0, 0]
+
+        See Also
+        ========
+
+        to_prufer
+
+        """
+        if self._prufer_repr is None:
+            self._prufer_repr = self.to_prufer(self._tree_repr[:], self.nodes)
+        return self._prufer_repr
+
+    @property
+    def tree_repr(self):
+        """Returns the tree representation of the Prufer object.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]).tree_repr
+        [[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]
+        >>> Prufer([1, 0, 0]).tree_repr
+        [[1, 2], [0, 1], [0, 3], [0, 4]]
+
+        See Also
+        ========
+
+        to_tree
+
+        """
+        if self._tree_repr is None:
+            self._tree_repr = self.to_tree(self._prufer_repr[:])
+        return self._tree_repr
+
+    @property
+    def nodes(self):
+        """Returns the number of nodes in the tree.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]).nodes
+        6
+        >>> Prufer([1, 0, 0]).nodes
+        5
+
+        """
+        return self._nodes
+
+    @property
+    def rank(self):
+        """Returns the rank of the Prufer sequence.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> p = Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]])
+        >>> p.rank
+        778
+        >>> p.next(1).rank
+        779
+        >>> p.prev().rank
+        777
+
+        See Also
+        ========
+
+        prufer_rank, next, prev, size
+
+        """
+        if self._rank is None:
+            self._rank = self.prufer_rank()
+        return self._rank
+
+    @property
+    def size(self):
+        """Return the number of possible trees of this Prufer object.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> Prufer([0]*4).size == Prufer([6]*4).size == 1296
+        True
+
+        See Also
+        ========
+
+        prufer_rank, rank, next, prev
+
+        """
+        return self.prev(self.rank).prev().rank + 1
+
+    @staticmethod
+    def to_prufer(tree, n):
+        """Return the Prufer sequence for a tree given as a list of edges where
+        ``n`` is the number of nodes in the tree.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> a = Prufer([[0, 1], [0, 2], [0, 3]])
+        >>> a.prufer_repr
+        [0, 0]
+        >>> Prufer.to_prufer([[0, 1], [0, 2], [0, 3]], 4)
+        [0, 0]
+
+        See Also
+        ========
+        prufer_repr: returns Prufer sequence of a Prufer object.
+
+        """
+        d = defaultdict(int)
+        L = []
+        for edge in tree:
+            # Increment the value of the corresponding
+            # node in the degree list as we encounter an
+            # edge involving it.
+            d[edge[0]] += 1
+            d[edge[1]] += 1
+        for i in range(n - 2):
+            # find the smallest leaf
+            for x in range(n):
+                if d[x] == 1:
+                    break
+            # find the node it was connected to
+            y = None
+            for edge in tree:
+                if x == edge[0]:
+                    y = edge[1]
+                elif x == edge[1]:
+                    y = edge[0]
+                if y is not None:
+                    break
+            # record and update
+            L.append(y)
+            for j in (x, y):
+                d[j] -= 1
+                if not d[j]:
+                    d.pop(j)
+            tree.remove(edge)
+        return L
+
+    @staticmethod
+    def to_tree(prufer):
+        """Return the tree (as a list of edges) of the given Prufer sequence.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> a = Prufer([0, 2], 4)
+        >>> a.tree_repr
+        [[0, 1], [0, 2], [2, 3]]
+        >>> Prufer.to_tree([0, 2])
+        [[0, 1], [0, 2], [2, 3]]
+
+        References
+        ==========
+
+        .. [1] https://hamberg.no/erlend/posts/2010-11-06-prufer-sequence-compact-tree-representation.html
+
+        See Also
+        ========
+        tree_repr: returns tree representation of a Prufer object.
+
+        """
+        tree = []
+        last = []
+        n = len(prufer) + 2
+        d = defaultdict(lambda: 1)
+        for p in prufer:
+            d[p] += 1
+        for i in prufer:
+            for j in range(n):
+            # find the smallest leaf (degree = 1)
+                if d[j] == 1:
+                    break
+            # (i, j) is the new edge that we append to the tree
+            # and remove from the degree dictionary
+            d[i] -= 1
+            d[j] -= 1
+            tree.append(sorted([i, j]))
+        last = [i for i in range(n) if d[i] == 1] or [0, 1]
+        tree.append(last)
+
+        return tree
+
+    @staticmethod
+    def edges(*runs):
+        """Return a list of edges and the number of nodes from the given runs
+        that connect nodes in an integer-labelled tree.
+
+        All node numbers will be shifted so that the minimum node is 0. It is
+        not a problem if edges are repeated in the runs; only unique edges are
+        returned. There is no assumption made about what the range of the node
+        labels should be, but all nodes from the smallest through the largest
+        must be present.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> Prufer.edges([1, 2, 3], [2, 4, 5]) # a T
+        ([[0, 1], [1, 2], [1, 3], [3, 4]], 5)
+
+        Duplicate edges are removed:
+
+        >>> Prufer.edges([0, 1, 2, 3], [1, 4, 5], [1, 4, 6]) # a K
+        ([[0, 1], [1, 2], [1, 4], [2, 3], [4, 5], [4, 6]], 7)
+
+        """
+        e = set()
+        nmin = runs[0][0]
+        for r in runs:
+            for i in range(len(r) - 1):
+                a, b = r[i: i + 2]
+                if b < a:
+                    a, b = b, a
+                e.add((a, b))
+        rv = []
+        got = set()
+        nmin = nmax = None
+        for ei in e:
+            got.update(ei)
+            nmin = min(ei[0], nmin) if nmin is not None else ei[0]
+            nmax = max(ei[1], nmax) if nmax is not None else ei[1]
+            rv.append(list(ei))
+        missing = set(range(nmin, nmax + 1)) - got
+        if missing:
+            missing = [i + nmin for i in missing]
+            if len(missing) == 1:
+                msg = 'Node %s is missing.' % missing.pop()
+            else:
+                msg = 'Nodes %s are missing.' % sorted(missing)
+            raise ValueError(msg)
+        if nmin != 0:
+            for i, ei in enumerate(rv):
+                rv[i] = [n - nmin for n in ei]
+            nmax -= nmin
+        return sorted(rv), nmax + 1
+
+    def prufer_rank(self):
+        """Computes the rank of a Prufer sequence.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> a = Prufer([[0, 1], [0, 2], [0, 3]])
+        >>> a.prufer_rank()
+        0
+
+        See Also
+        ========
+
+        rank, next, prev, size
+
+        """
+        r = 0
+        p = 1
+        for i in range(self.nodes - 3, -1, -1):
+            r += p*self.prufer_repr[i]
+            p *= self.nodes
+        return r
+
+    @classmethod
+    def unrank(self, rank, n):
+        """Finds the unranked Prufer sequence.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> Prufer.unrank(0, 4)
+        Prufer([0, 0])
+
+        """
+        n, rank = as_int(n), as_int(rank)
+        L = defaultdict(int)
+        for i in range(n - 3, -1, -1):
+            L[i] = rank % n
+            rank = (rank - L[i])//n
+        return Prufer([L[i] for i in range(len(L))])
+
+    def __new__(cls, *args, **kw_args):
+        """The constructor for the Prufer object.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+
+        A Prufer object can be constructed from a list of edges:
+
+        >>> a = Prufer([[0, 1], [0, 2], [0, 3]])
+        >>> a.prufer_repr
+        [0, 0]
+
+        If the number of nodes is given, no checking of the nodes will
+        be performed; it will be assumed that nodes 0 through n - 1 are
+        present:
+
+        >>> Prufer([[0, 1], [0, 2], [0, 3]], 4)
+        Prufer([[0, 1], [0, 2], [0, 3]], 4)
+
+        A Prufer object can be constructed from a Prufer sequence:
+
+        >>> b = Prufer([1, 3])
+        >>> b.tree_repr
+        [[0, 1], [1, 3], [2, 3]]
+
+        """
+        arg0 = Array(args[0]) if args[0] else Tuple()
+        args = (arg0,) + tuple(_sympify(arg) for arg in args[1:])
+        ret_obj = Basic.__new__(cls, *args, **kw_args)
+        args = [list(args[0])]
+        if args[0] and iterable(args[0][0]):
+            if not args[0][0]:
+                raise ValueError(
+                    'Prufer expects at least one edge in the tree.')
+            if len(args) > 1:
+                nnodes = args[1]
+            else:
+                nodes = set(flatten(args[0]))
+                nnodes = max(nodes) + 1
+                if nnodes != len(nodes):
+                    missing = set(range(nnodes)) - nodes
+                    if len(missing) == 1:
+                        msg = 'Node %s is missing.' % missing.pop()
+                    else:
+                        msg = 'Nodes %s are missing.' % sorted(missing)
+                    raise ValueError(msg)
+            ret_obj._tree_repr = [list(i) for i in args[0]]
+            ret_obj._nodes = nnodes
+        else:
+            ret_obj._prufer_repr = args[0]
+            ret_obj._nodes = len(ret_obj._prufer_repr) + 2
+        return ret_obj
+
+    def next(self, delta=1):
+        """Generates the Prufer sequence that is delta beyond the current one.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> a = Prufer([[0, 1], [0, 2], [0, 3]])
+        >>> b = a.next(1) # == a.next()
+        >>> b.tree_repr
+        [[0, 2], [0, 1], [1, 3]]
+        >>> b.rank
+        1
+
+        See Also
+        ========
+
+        prufer_rank, rank, prev, size
+
+        """
+        return Prufer.unrank(self.rank + delta, self.nodes)
+
+    def prev(self, delta=1):
+        """Generates the Prufer sequence that is -delta before the current one.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics.prufer import Prufer
+        >>> a = Prufer([[0, 1], [1, 2], [2, 3], [1, 4]])
+        >>> a.rank
+        36
+        >>> b = a.prev()
+        >>> b
+        Prufer([1, 2, 0])
+        >>> b.rank
+        35
+
+        See Also
+        ========
+
+        prufer_rank, rank, next, size
+
+        """
+        return Prufer.unrank(self.rank -delta, self.nodes)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/rewritingsystem.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/rewritingsystem.py
new file mode 100644
index 0000000000000000000000000000000000000000..b9e8dfe4c831db6490c987c85a57d0d1a939de61
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/rewritingsystem.py
@@ -0,0 +1,453 @@
+from collections import deque
+from sympy.combinatorics.rewritingsystem_fsm import StateMachine
+
+class RewritingSystem:
+    '''
+    A class implementing rewriting systems for `FpGroup`s.
+
+    References
+    ==========
+    .. [1] Epstein, D., Holt, D. and Rees, S. (1991).
+           The use of Knuth-Bendix methods to solve the word problem in automatic groups.
+           Journal of Symbolic Computation, 12(4-5), pp.397-414.
+
+    .. [2] GAP's Manual on its KBMAG package
+           https://www.gap-system.org/Manuals/pkg/kbmag-1.5.3/doc/manual.pdf
+
+    '''
+    def __init__(self, group):
+        self.group = group
+        self.alphabet = group.generators
+        self._is_confluent = None
+
+        # these values are taken from [2]
+        self.maxeqns = 32767 # max rules
+        self.tidyint = 100 # rules before tidying
+
+        # _max_exceeded is True if maxeqns is exceeded
+        # at any point
+        self._max_exceeded = False
+
+        # Reduction automaton
+        self.reduction_automaton = None
+        self._new_rules = {}
+
+        # dictionary of reductions
+        self.rules = {}
+        self.rules_cache = deque([], 50)
+        self._init_rules()
+
+
+        # All the transition symbols in the automaton
+        generators = list(self.alphabet)
+        generators += [gen**-1 for gen in generators]
+        # Create a finite state machine as an instance of the StateMachine object
+        self.reduction_automaton = StateMachine('Reduction automaton for '+ repr(self.group), generators)
+        self.construct_automaton()
+
+    def set_max(self, n):
+        '''
+        Set the maximum number of rules that can be defined
+
+        '''
+        if n > self.maxeqns:
+            self._max_exceeded = False
+        self.maxeqns = n
+        return
+
+    @property
+    def is_confluent(self):
+        '''
+        Return `True` if the system is confluent
+
+        '''
+        if self._is_confluent is None:
+            self._is_confluent = self._check_confluence()
+        return self._is_confluent
+
+    def _init_rules(self):
+        identity = self.group.free_group.identity
+        for r in self.group.relators:
+            self.add_rule(r, identity)
+        self._remove_redundancies()
+        return
+
+    def _add_rule(self, r1, r2):
+        '''
+        Add the rule r1 -> r2 with no checking or further
+        deductions
+
+        '''
+        if len(self.rules) + 1 > self.maxeqns:
+            self._is_confluent = self._check_confluence()
+            self._max_exceeded = True
+            raise RuntimeError("Too many rules were defined.")
+        self.rules[r1] = r2
+        # Add the newly added rule to the `new_rules` dictionary.
+        if self.reduction_automaton:
+            self._new_rules[r1] = r2
+
+    def add_rule(self, w1, w2, check=False):
+        new_keys = set()
+
+        if w1 == w2:
+            return new_keys
+
+        if w1 < w2:
+            w1, w2 = w2, w1
+
+        if (w1, w2) in self.rules_cache:
+            return new_keys
+        self.rules_cache.append((w1, w2))
+
+        s1, s2 = w1, w2
+
+        # The following is the equivalent of checking
+        # s1 for overlaps with the implicit reductions
+        # {g*g**-1 -> } and {g**-1*g -> }
+        # for any generator g without installing the
+        # redundant rules that would result from processing
+        # the overlaps. See [1], Section 3 for details.
+
+        if len(s1) - len(s2) < 3:
+            if s1 not in self.rules:
+                new_keys.add(s1)
+                if not check:
+                    self._add_rule(s1, s2)
+            if s2**-1 > s1**-1 and s2**-1 not in self.rules:
+                new_keys.add(s2**-1)
+                if not check:
+                    self._add_rule(s2**-1, s1**-1)
+
+        # overlaps on the right
+        while len(s1) - len(s2) > -1:
+            g = s1[len(s1)-1]
+            s1 = s1.subword(0, len(s1)-1)
+            s2 = s2*g**-1
+            if len(s1) - len(s2) < 0:
+                if s2 not in self.rules:
+                    if not check:
+                        self._add_rule(s2, s1)
+                    new_keys.add(s2)
+            elif len(s1) - len(s2) < 3:
+                new = self.add_rule(s1, s2, check)
+                new_keys.update(new)
+
+        # overlaps on the left
+        while len(w1) - len(w2) > -1:
+            g = w1[0]
+            w1 = w1.subword(1, len(w1))
+            w2 = g**-1*w2
+            if len(w1) - len(w2) < 0:
+                if w2 not in self.rules:
+                    if not check:
+                        self._add_rule(w2, w1)
+                    new_keys.add(w2)
+            elif len(w1) - len(w2) < 3:
+                new = self.add_rule(w1, w2, check)
+                new_keys.update(new)
+
+        return new_keys
+
+    def _remove_redundancies(self, changes=False):
+        '''
+        Reduce left- and right-hand sides of reduction rules
+        and remove redundant equations (i.e. those for which
+        lhs == rhs). If `changes` is `True`, return a set
+        containing the removed keys and a set containing the
+        added keys
+
+        '''
+        removed = set()
+        added = set()
+        rules = self.rules.copy()
+        for r in rules:
+            v = self.reduce(r, exclude=r)
+            w = self.reduce(rules[r])
+            if v != r:
+                del self.rules[r]
+                removed.add(r)
+                if v > w:
+                    added.add(v)
+                    self.rules[v] = w
+                elif v < w:
+                    added.add(w)
+                    self.rules[w] = v
+            else:
+                self.rules[v] = w
+        if changes:
+            return removed, added
+        return
+
+    def make_confluent(self, check=False):
+        '''
+        Try to make the system confluent using the Knuth-Bendix
+        completion algorithm
+
+        '''
+        if self._max_exceeded:
+            return self._is_confluent
+        lhs = list(self.rules.keys())
+
+        def _overlaps(r1, r2):
+            len1 = len(r1)
+            len2 = len(r2)
+            result = []
+            for j in range(1, len1 + len2):
+                if (r1.subword(len1 - j, len1 + len2 - j, strict=False)
+                       == r2.subword(j - len1, j, strict=False)):
+                    a = r1.subword(0, len1-j, strict=False)
+                    a = a*r2.subword(0, j-len1, strict=False)
+                    b = r2.subword(j-len1, j, strict=False)
+                    c = r2.subword(j, len2, strict=False)
+                    c = c*r1.subword(len1 + len2 - j, len1, strict=False)
+                    result.append(a*b*c)
+            return result
+
+        def _process_overlap(w, r1, r2, check):
+                s = w.eliminate_word(r1, self.rules[r1])
+                s = self.reduce(s)
+                t = w.eliminate_word(r2, self.rules[r2])
+                t = self.reduce(t)
+                if s != t:
+                    if check:
+                        # system not confluent
+                        return [0]
+                    try:
+                        new_keys = self.add_rule(t, s, check)
+                        return new_keys
+                    except RuntimeError:
+                        return False
+                return
+
+        added = 0
+        i = 0
+        while i < len(lhs):
+            r1 = lhs[i]
+            i += 1
+            # j could be i+1 to not
+            # check each pair twice but lhs
+            # is extended in the loop and the new
+            # elements have to be checked with the
+            # preceding ones. there is probably a better way
+            # to handle this
+            j = 0
+            while j < len(lhs):
+                r2 = lhs[j]
+                j += 1
+                if r1 == r2:
+                    continue
+                overlaps = _overlaps(r1, r2)
+                overlaps.extend(_overlaps(r1**-1, r2))
+                if not overlaps:
+                    continue
+                for w in overlaps:
+                    new_keys = _process_overlap(w, r1, r2, check)
+                    if new_keys:
+                        if check:
+                            return False
+                        lhs.extend(new_keys)
+                        added += len(new_keys)
+                    elif new_keys == False:
+                        # too many rules were added so the process
+                        # couldn't complete
+                        return self._is_confluent
+
+                if added > self.tidyint and not check:
+                    # tidy up
+                    r, a = self._remove_redundancies(changes=True)
+                    added = 0
+                    if r:
+                        # reset i since some elements were removed
+                        i = min(lhs.index(s) for s in r)
+                    lhs = [l for l in lhs if l not in r]
+                    lhs.extend(a)
+                    if r1 in r:
+                        # r1 was removed as redundant
+                        break
+
+        self._is_confluent = True
+        if not check:
+            self._remove_redundancies()
+        return True
+
+    def _check_confluence(self):
+        return self.make_confluent(check=True)
+
+    def reduce(self, word, exclude=None):
+        '''
+        Apply reduction rules to `word` excluding the reduction rule
+        for the lhs equal to `exclude`
+
+        '''
+        rules = {r: self.rules[r] for r in self.rules if r != exclude}
+        # the following is essentially `eliminate_words()` code from the
+        # `FreeGroupElement` class, the only difference being the first
+        # "if" statement
+        again = True
+        new = word
+        while again:
+            again = False
+            for r in rules:
+                prev = new
+                if rules[r]**-1 > r**-1:
+                    new = new.eliminate_word(r, rules[r], _all=True, inverse=False)
+                else:
+                    new = new.eliminate_word(r, rules[r], _all=True)
+                if new != prev:
+                    again = True
+        return new
+
+    def _compute_inverse_rules(self, rules):
+        '''
+        Compute the inverse rules for a given set of rules.
+        The inverse rules are used in the automaton for word reduction.
+
+        Arguments:
+            rules (dictionary): Rules for which the inverse rules are to computed.
+
+        Returns:
+            Dictionary of inverse_rules.
+
+        '''
+        inverse_rules = {}
+        for r in rules:
+            rule_key_inverse = r**-1
+            rule_value_inverse = (rules[r])**-1
+            if (rule_value_inverse < rule_key_inverse):
+                inverse_rules[rule_key_inverse] = rule_value_inverse
+            else:
+                inverse_rules[rule_value_inverse] = rule_key_inverse
+        return inverse_rules
+
+    def construct_automaton(self):
+        '''
+        Construct the automaton based on the set of reduction rules of the system.
+
+        Automata Design:
+        The accept states of the automaton are the proper prefixes of the left hand side of the rules.
+        The complete left hand side of the rules are the dead states of the automaton.
+
+        '''
+        self._add_to_automaton(self.rules)
+
+    def _add_to_automaton(self, rules):
+        '''
+        Add new states and transitions to the automaton.
+
+        Summary:
+        States corresponding to the new rules added to the system are computed and added to the automaton.
+        Transitions in the previously added states are also modified if necessary.
+
+        Arguments:
+            rules (dictionary) -- Dictionary of the newly added rules.
+
+        '''
+        # Automaton variables
+        automaton_alphabet = []
+        proper_prefixes = {}
+
+        # compute the inverses of all the new rules added
+        all_rules = rules
+        inverse_rules = self._compute_inverse_rules(all_rules)
+        all_rules.update(inverse_rules)
+
+        # Keep track of the accept_states.
+        accept_states = []
+
+        for rule in all_rules:
+            # The symbols present in the new rules are the symbols to be verified at each state.
+            # computes the automaton_alphabet, as the transitions solely depend upon the new states.
+            automaton_alphabet += rule.letter_form_elm
+            # Compute the proper prefixes for every rule.
+            proper_prefixes[rule] = []
+            letter_word_array = list(rule.letter_form_elm)
+            len_letter_word_array = len(letter_word_array)
+            for i in range (1, len_letter_word_array):
+                letter_word_array[i] = letter_word_array[i-1]*letter_word_array[i]
+                # Add accept states.
+                elem = letter_word_array[i-1]
+                if elem not in self.reduction_automaton.states:
+                    self.reduction_automaton.add_state(elem, state_type='a')
+                    accept_states.append(elem)
+            proper_prefixes[rule] = letter_word_array
+            # Check for overlaps between dead and accept states.
+            if rule in accept_states:
+                self.reduction_automaton.states[rule].state_type = 'd'
+                self.reduction_automaton.states[rule].rh_rule = all_rules[rule]
+                accept_states.remove(rule)
+            # Add dead states
+            if rule not in self.reduction_automaton.states:
+                self.reduction_automaton.add_state(rule, state_type='d', rh_rule=all_rules[rule])
+
+        automaton_alphabet = set(automaton_alphabet)
+
+        # Add new transitions for every state.
+        for state in self.reduction_automaton.states:
+            current_state_name = state
+            current_state_type = self.reduction_automaton.states[state].state_type
+            # Transitions will be modified only when suffixes of the current_state
+            # belongs to the proper_prefixes of the new rules.
+            # The rest are ignored if they cannot lead to a dead state after a finite number of transisitons.
+            if current_state_type == 's':
+                for letter in automaton_alphabet:
+                    if letter in self.reduction_automaton.states:
+                        self.reduction_automaton.states[state].add_transition(letter, letter)
+                    else:
+                        self.reduction_automaton.states[state].add_transition(letter, current_state_name)
+            elif current_state_type == 'a':
+                # Check if the transition to any new state in possible.
+                for letter in automaton_alphabet:
+                    _next = current_state_name*letter
+                    while len(_next) and _next not in self.reduction_automaton.states:
+                        _next = _next.subword(1, len(_next))
+                    if not len(_next):
+                        _next = 'start'
+                    self.reduction_automaton.states[state].add_transition(letter, _next)
+
+        # Add transitions for new states. All symbols used in the automaton are considered here.
+        # Ignore this if `reduction_automaton.automaton_alphabet` = `automaton_alphabet`.
+        if len(self.reduction_automaton.automaton_alphabet) != len(automaton_alphabet):
+            for state in accept_states:
+                current_state_name = state
+                for letter in self.reduction_automaton.automaton_alphabet:
+                    _next = current_state_name*letter
+                    while len(_next) and _next not in self.reduction_automaton.states:
+                        _next = _next.subword(1, len(_next))
+                    if not len(_next):
+                        _next = 'start'
+                    self.reduction_automaton.states[state].add_transition(letter, _next)
+
+    def reduce_using_automaton(self, word):
+        '''
+        Reduce a word using an automaton.
+
+        Summary:
+        All the symbols of the word are stored in an array and are given as the input to the automaton.
+        If the automaton reaches a dead state that subword is replaced and the automaton is run from the beginning.
+        The complete word has to be replaced when the word is read and the automaton reaches a dead state.
+        So, this process is repeated until the word is read completely and the automaton reaches the accept state.
+
+        Arguments:
+            word (instance of FreeGroupElement) -- Word that needs to be reduced.
+
+        '''
+        # Modify the automaton if new rules are found.
+        if self._new_rules:
+            self._add_to_automaton(self._new_rules)
+            self._new_rules = {}
+
+        flag = 1
+        while flag:
+            flag = 0
+            current_state = self.reduction_automaton.states['start']
+            for i, s in enumerate(word.letter_form_elm):
+                next_state_name = current_state.transitions[s]
+                next_state = self.reduction_automaton.states[next_state_name]
+                if next_state.state_type == 'd':
+                    subst = next_state.rh_rule
+                    word = word.substituted_word(i - len(next_state_name) + 1, i+1, subst)
+                    flag = 1
+                    break
+                current_state = next_state
+        return word
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/rewritingsystem_fsm.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/rewritingsystem_fsm.py
new file mode 100644
index 0000000000000000000000000000000000000000..21916530040ac321180692d1a0811da4ae36a056
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/rewritingsystem_fsm.py
@@ -0,0 +1,60 @@
+class State:
+    '''
+    A representation of a state managed by a ``StateMachine``.
+
+    Attributes:
+        name (instance of FreeGroupElement or string) -- State name which is also assigned to the Machine.
+        transisitons (OrderedDict) -- Represents all the transitions of the state object.
+        state_type (string) -- Denotes the type (accept/start/dead) of the state.
+        rh_rule (instance of FreeGroupElement) -- right hand rule for dead state.
+        state_machine (instance of StateMachine object) -- The finite state machine that the state belongs to.
+    '''
+
+    def __init__(self, name, state_machine, state_type=None, rh_rule=None):
+        self.name = name
+        self.transitions = {}
+        self.state_machine = state_machine
+        self.state_type = state_type[0]
+        self.rh_rule = rh_rule
+
+    def add_transition(self, letter, state):
+        '''
+        Add a transition from the current state to a new state.
+
+        Keyword Arguments:
+            letter -- The alphabet element the current state reads to make the state transition.
+            state -- This will be an instance of the State object which represents a new state after in the transition after the alphabet is read.
+
+        '''
+        self.transitions[letter] = state
+
+class StateMachine:
+    '''
+    Representation of a finite state machine the manages the states and the transitions of the automaton.
+
+    Attributes:
+        states (dictionary) -- Collection of all registered `State` objects.
+        name (str) -- Name of the state machine.
+    '''
+
+    def __init__(self, name, automaton_alphabet):
+        self.name = name
+        self.automaton_alphabet = automaton_alphabet
+        self.states = {} # Contains all the states in the machine.
+        self.add_state('start', state_type='s')
+
+    def add_state(self, state_name, state_type=None, rh_rule=None):
+        '''
+        Instantiate a state object and stores it in the 'states' dictionary.
+
+        Arguments:
+            state_name (instance of FreeGroupElement or string) -- name of the new states.
+            state_type (string) -- Denotes the type (accept/start/dead) of the state added.
+            rh_rule (instance of FreeGroupElement) -- right hand rule for dead state.
+
+        '''
+        new_state = State(state_name, self, state_type, rh_rule)
+        self.states[state_name] = new_state
+
+    def __repr__(self):
+        return "%s" % (self.name)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/schur_number.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/schur_number.py
new file mode 100644
index 0000000000000000000000000000000000000000..83aac98e543d4b54d4e6af17adca6e4f4de1b9ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/schur_number.py
@@ -0,0 +1,160 @@
+"""
+The Schur number S(k) is the largest integer n for which the interval [1,n]
+can be partitioned into k sum-free sets.(https://mathworld.wolfram.com/SchurNumber.html)
+"""
+import math
+from sympy.core import S
+from sympy.core.basic import Basic
+from sympy.core.function import Function
+from sympy.core.numbers import Integer
+
+
+class SchurNumber(Function):
+    r"""
+    This function creates a SchurNumber object
+    which is evaluated for `k \le 5` otherwise only
+    the lower bound information can be retrieved.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.schur_number import SchurNumber
+
+    Since S(3) = 13, hence the output is a number
+    >>> SchurNumber(3)
+    13
+
+    We do not know the Schur number for values greater than 5, hence
+    only the object is returned
+    >>> SchurNumber(6)
+    SchurNumber(6)
+
+    Now, the lower bound information can be retrieved using lower_bound()
+    method
+    >>> SchurNumber(6).lower_bound()
+    536
+
+    """
+
+    @classmethod
+    def eval(cls, k):
+        if k.is_Number:
+            if k is S.Infinity:
+                return S.Infinity
+            if k.is_zero:
+                return S.Zero
+            if not k.is_integer or k.is_negative:
+                raise ValueError("k should be a positive integer")
+            first_known_schur_numbers = {1: 1, 2: 4, 3: 13, 4: 44, 5: 160}
+            if k <= 5:
+                return Integer(first_known_schur_numbers[k])
+
+    def lower_bound(self):
+        f_ = self.args[0]
+        # Improved lower bounds known for S(6) and S(7)
+        if f_ == 6:
+            return Integer(536)
+        if f_ == 7:
+            return Integer(1680)
+        # For other cases, use general expression
+        if f_.is_Integer:
+            return 3*self.func(f_ - 1).lower_bound() - 1
+        return (3**f_ - 1)/2
+
+
+def _schur_subsets_number(n):
+
+    if n is S.Infinity:
+        raise ValueError("Input must be finite")
+    if n <= 0:
+        raise ValueError("n must be a non-zero positive integer.")
+    elif n <= 3:
+        min_k = 1
+    else:
+        min_k = math.ceil(math.log(2*n + 1, 3))
+
+    return Integer(min_k)
+
+
+def schur_partition(n):
+    """
+
+    This function returns the partition in the minimum number of sum-free subsets
+    according to the lower bound given by the Schur Number.
+
+    Parameters
+    ==========
+
+    n: a number
+        n is the upper limit of the range [1, n] for which we need to find and
+        return the minimum number of free subsets according to the lower bound
+        of schur number
+
+    Returns
+    =======
+
+    List of lists
+        List of the minimum number of sum-free subsets
+
+    Notes
+    =====
+
+    It is possible for some n to make the partition into less
+    subsets since the only known Schur numbers are:
+    S(1) = 1, S(2) = 4, S(3) = 13, S(4) = 44.
+    e.g for n = 44 the lower bound from the function above is 5 subsets but it has been proven
+    that can be done with 4 subsets.
+
+    Examples
+    ========
+
+    For n = 1, 2, 3 the answer is the set itself
+
+    >>> from sympy.combinatorics.schur_number import schur_partition
+    >>> schur_partition(2)
+    [[1, 2]]
+
+    For n > 3, the answer is the minimum number of sum-free subsets:
+
+    >>> schur_partition(5)
+    [[3, 2], [5], [1, 4]]
+
+    >>> schur_partition(8)
+    [[3, 2], [6, 5, 8], [1, 4, 7]]
+    """
+
+    if isinstance(n, Basic) and not n.is_Number:
+        raise ValueError("Input value must be a number")
+
+    number_of_subsets = _schur_subsets_number(n)
+    if n == 1:
+        sum_free_subsets = [[1]]
+    elif n == 2:
+        sum_free_subsets = [[1, 2]]
+    elif n == 3:
+        sum_free_subsets = [[1, 2, 3]]
+    else:
+        sum_free_subsets = [[1, 4], [2, 3]]
+
+    while len(sum_free_subsets) < number_of_subsets:
+        sum_free_subsets = _generate_next_list(sum_free_subsets, n)
+        missed_elements = [3*k + 1 for k in range(len(sum_free_subsets), (n-1)//3 + 1)]
+        sum_free_subsets[-1] += missed_elements
+
+    return sum_free_subsets
+
+
+def _generate_next_list(current_list, n):
+    new_list = []
+
+    for item in current_list:
+        temp_1 = [number*3 for number in item if number*3 <= n]
+        temp_2 = [number*3 - 1 for number in item if number*3 - 1 <= n]
+        new_item = temp_1 + temp_2
+        new_list.append(new_item)
+
+    last_list = [3*k + 1 for k in range(len(current_list)+1) if 3*k + 1 <= n]
+    new_list.append(last_list)
+    current_list = new_list
+
+    return current_list
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/subsets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/subsets.py
new file mode 100644
index 0000000000000000000000000000000000000000..e540cb2395cb27e04c9d513831cb834a05ec2abd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/subsets.py
@@ -0,0 +1,619 @@
+from itertools import combinations
+
+from sympy.combinatorics.graycode import GrayCode
+
+
+class Subset():
+    """
+    Represents a basic subset object.
+
+    Explanation
+    ===========
+
+    We generate subsets using essentially two techniques,
+    binary enumeration and lexicographic enumeration.
+    The Subset class takes two arguments, the first one
+    describes the initial subset to consider and the second
+    describes the superset.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Subset
+    >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+    >>> a.next_binary().subset
+    ['b']
+    >>> a.prev_binary().subset
+    ['c']
+    """
+
+    _rank_binary = None
+    _rank_lex = None
+    _rank_graycode = None
+    _subset = None
+    _superset = None
+
+    def __new__(cls, subset, superset):
+        """
+        Default constructor.
+
+        It takes the ``subset`` and its ``superset`` as its parameters.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.subset
+        ['c', 'd']
+        >>> a.superset
+        ['a', 'b', 'c', 'd']
+        >>> a.size
+        2
+        """
+        if len(subset) > len(superset):
+            raise ValueError('Invalid arguments have been provided. The '
+                             'superset must be larger than the subset.')
+        for elem in subset:
+            if elem not in superset:
+                raise ValueError('The superset provided is invalid as it does '
+                                 'not contain the element {}'.format(elem))
+        obj = object.__new__(cls)
+        obj._subset = subset
+        obj._superset = superset
+        return obj
+
+    def __eq__(self, other):
+        """Return a boolean indicating whether a == b on the basis of
+        whether both objects are of the class Subset and if the values
+        of the subset and superset attributes are the same.
+        """
+        if not isinstance(other, Subset):
+            return NotImplemented
+        return self.subset == other.subset and self.superset == other.superset
+
+    def iterate_binary(self, k):
+        """
+        This is a helper function. It iterates over the
+        binary subsets by ``k`` steps. This variable can be
+        both positive or negative.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.iterate_binary(-2).subset
+        ['d']
+        >>> a = Subset(['a', 'b', 'c'], ['a', 'b', 'c', 'd'])
+        >>> a.iterate_binary(2).subset
+        []
+
+        See Also
+        ========
+
+        next_binary, prev_binary
+        """
+        bin_list = Subset.bitlist_from_subset(self.subset, self.superset)
+        n = (int(''.join(bin_list), 2) + k) % 2**self.superset_size
+        bits = bin(n)[2:].rjust(self.superset_size, '0')
+        return Subset.subset_from_bitlist(self.superset, bits)
+
+    def next_binary(self):
+        """
+        Generates the next binary ordered subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.next_binary().subset
+        ['b']
+        >>> a = Subset(['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.next_binary().subset
+        []
+
+        See Also
+        ========
+
+        prev_binary, iterate_binary
+        """
+        return self.iterate_binary(1)
+
+    def prev_binary(self):
+        """
+        Generates the previous binary ordered subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset([], ['a', 'b', 'c', 'd'])
+        >>> a.prev_binary().subset
+        ['a', 'b', 'c', 'd']
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.prev_binary().subset
+        ['c']
+
+        See Also
+        ========
+
+        next_binary, iterate_binary
+        """
+        return self.iterate_binary(-1)
+
+    def next_lexicographic(self):
+        """
+        Generates the next lexicographically ordered subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.next_lexicographic().subset
+        ['d']
+        >>> a = Subset(['d'], ['a', 'b', 'c', 'd'])
+        >>> a.next_lexicographic().subset
+        []
+
+        See Also
+        ========
+
+        prev_lexicographic
+        """
+        i = self.superset_size - 1
+        indices = Subset.subset_indices(self.subset, self.superset)
+
+        if i in indices:
+            if i - 1 in indices:
+                indices.remove(i - 1)
+            else:
+                indices.remove(i)
+                i = i - 1
+                while i >= 0 and i not in indices:
+                    i = i - 1
+                if i >= 0:
+                    indices.remove(i)
+                    indices.append(i+1)
+        else:
+            while i not in indices and i >= 0:
+                i = i - 1
+            indices.append(i + 1)
+
+        ret_set = []
+        super_set = self.superset
+        for i in indices:
+            ret_set.append(super_set[i])
+        return Subset(ret_set, super_set)
+
+    def prev_lexicographic(self):
+        """
+        Generates the previous lexicographically ordered subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset([], ['a', 'b', 'c', 'd'])
+        >>> a.prev_lexicographic().subset
+        ['d']
+        >>> a = Subset(['c','d'], ['a', 'b', 'c', 'd'])
+        >>> a.prev_lexicographic().subset
+        ['c']
+
+        See Also
+        ========
+
+        next_lexicographic
+        """
+        i = self.superset_size - 1
+        indices = Subset.subset_indices(self.subset, self.superset)
+
+        while i >= 0 and i not in indices:
+            i = i - 1
+
+        if i == 0 or i - 1 in indices:
+            indices.remove(i)
+        else:
+            if i >= 0:
+                indices.remove(i)
+                indices.append(i - 1)
+            indices.append(self.superset_size - 1)
+
+        ret_set = []
+        super_set = self.superset
+        for i in indices:
+            ret_set.append(super_set[i])
+        return Subset(ret_set, super_set)
+
+    def iterate_graycode(self, k):
+        """
+        Helper function used for prev_gray and next_gray.
+        It performs ``k`` step overs to get the respective Gray codes.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset([1, 2, 3], [1, 2, 3, 4])
+        >>> a.iterate_graycode(3).subset
+        [1, 4]
+        >>> a.iterate_graycode(-2).subset
+        [1, 2, 4]
+
+        See Also
+        ========
+
+        next_gray, prev_gray
+        """
+        unranked_code = GrayCode.unrank(self.superset_size,
+                                       (self.rank_gray + k) % self.cardinality)
+        return Subset.subset_from_bitlist(self.superset,
+                                          unranked_code)
+
+    def next_gray(self):
+        """
+        Generates the next Gray code ordered subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset([1, 2, 3], [1, 2, 3, 4])
+        >>> a.next_gray().subset
+        [1, 3]
+
+        See Also
+        ========
+
+        iterate_graycode, prev_gray
+        """
+        return self.iterate_graycode(1)
+
+    def prev_gray(self):
+        """
+        Generates the previous Gray code ordered subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset([2, 3, 4], [1, 2, 3, 4, 5])
+        >>> a.prev_gray().subset
+        [2, 3, 4, 5]
+
+        See Also
+        ========
+
+        iterate_graycode, next_gray
+        """
+        return self.iterate_graycode(-1)
+
+    @property
+    def rank_binary(self):
+        """
+        Computes the binary ordered rank.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset([], ['a','b','c','d'])
+        >>> a.rank_binary
+        0
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.rank_binary
+        3
+
+        See Also
+        ========
+
+        iterate_binary, unrank_binary
+        """
+        if self._rank_binary is None:
+            self._rank_binary = int("".join(
+                Subset.bitlist_from_subset(self.subset,
+                                           self.superset)), 2)
+        return self._rank_binary
+
+    @property
+    def rank_lexicographic(self):
+        """
+        Computes the lexicographic ranking of the subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.rank_lexicographic
+        14
+        >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6])
+        >>> a.rank_lexicographic
+        43
+        """
+        if self._rank_lex is None:
+            def _ranklex(self, subset_index, i, n):
+                if subset_index == [] or i > n:
+                    return 0
+                if i in subset_index:
+                    subset_index.remove(i)
+                    return 1 + _ranklex(self, subset_index, i + 1, n)
+                return 2**(n - i - 1) + _ranklex(self, subset_index, i + 1, n)
+            indices = Subset.subset_indices(self.subset, self.superset)
+            self._rank_lex = _ranklex(self, indices, 0, self.superset_size)
+        return self._rank_lex
+
+    @property
+    def rank_gray(self):
+        """
+        Computes the Gray code ranking of the subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c','d'], ['a','b','c','d'])
+        >>> a.rank_gray
+        2
+        >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6])
+        >>> a.rank_gray
+        27
+
+        See Also
+        ========
+
+        iterate_graycode, unrank_gray
+        """
+        if self._rank_graycode is None:
+            bits = Subset.bitlist_from_subset(self.subset, self.superset)
+            self._rank_graycode = GrayCode(len(bits), start=bits).rank
+        return self._rank_graycode
+
+    @property
+    def subset(self):
+        """
+        Gets the subset represented by the current instance.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.subset
+        ['c', 'd']
+
+        See Also
+        ========
+
+        superset, size, superset_size, cardinality
+        """
+        return self._subset
+
+    @property
+    def size(self):
+        """
+        Gets the size of the subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.size
+        2
+
+        See Also
+        ========
+
+        subset, superset, superset_size, cardinality
+        """
+        return len(self.subset)
+
+    @property
+    def superset(self):
+        """
+        Gets the superset of the subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.superset
+        ['a', 'b', 'c', 'd']
+
+        See Also
+        ========
+
+        subset, size, superset_size, cardinality
+        """
+        return self._superset
+
+    @property
+    def superset_size(self):
+        """
+        Returns the size of the superset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.superset_size
+        4
+
+        See Also
+        ========
+
+        subset, superset, size, cardinality
+        """
+        return len(self.superset)
+
+    @property
+    def cardinality(self):
+        """
+        Returns the number of all possible subsets.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        >>> a.cardinality
+        16
+
+        See Also
+        ========
+
+        subset, superset, size, superset_size
+        """
+        return 2**(self.superset_size)
+
+    @classmethod
+    def subset_from_bitlist(self, super_set, bitlist):
+        """
+        Gets the subset defined by the bitlist.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> Subset.subset_from_bitlist(['a', 'b', 'c', 'd'], '0011').subset
+        ['c', 'd']
+
+        See Also
+        ========
+
+        bitlist_from_subset
+        """
+        if len(super_set) != len(bitlist):
+            raise ValueError("The sizes of the lists are not equal")
+        ret_set = []
+        for i in range(len(bitlist)):
+            if bitlist[i] == '1':
+                ret_set.append(super_set[i])
+        return Subset(ret_set, super_set)
+
+    @classmethod
+    def bitlist_from_subset(self, subset, superset):
+        """
+        Gets the bitlist corresponding to a subset.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> Subset.bitlist_from_subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+        '0011'
+
+        See Also
+        ========
+
+        subset_from_bitlist
+        """
+        bitlist = ['0'] * len(superset)
+        if isinstance(subset, Subset):
+            subset = subset.subset
+        for i in Subset.subset_indices(subset, superset):
+            bitlist[i] = '1'
+        return ''.join(bitlist)
+
+    @classmethod
+    def unrank_binary(self, rank, superset):
+        """
+        Gets the binary ordered subset of the specified rank.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> Subset.unrank_binary(4, ['a', 'b', 'c', 'd']).subset
+        ['b']
+
+        See Also
+        ========
+
+        iterate_binary, rank_binary
+        """
+        bits = bin(rank)[2:].rjust(len(superset), '0')
+        return Subset.subset_from_bitlist(superset, bits)
+
+    @classmethod
+    def unrank_gray(self, rank, superset):
+        """
+        Gets the Gray code ordered subset of the specified rank.
+
+        Examples
+        ========
+
+        >>> from sympy.combinatorics import Subset
+        >>> Subset.unrank_gray(4, ['a', 'b', 'c']).subset
+        ['a', 'b']
+        >>> Subset.unrank_gray(0, ['a', 'b', 'c']).subset
+        []
+
+        See Also
+        ========
+
+        iterate_graycode, rank_gray
+        """
+        graycode_bitlist = GrayCode.unrank(len(superset), rank)
+        return Subset.subset_from_bitlist(superset, graycode_bitlist)
+
+    @classmethod
+    def subset_indices(self, subset, superset):
+        """Return indices of subset in superset in a list; the list is empty
+        if all elements of ``subset`` are not in ``superset``.
+
+        Examples
+        ========
+
+            >>> from sympy.combinatorics import Subset
+            >>> superset = [1, 3, 2, 5, 4]
+            >>> Subset.subset_indices([3, 2, 1], superset)
+            [1, 2, 0]
+            >>> Subset.subset_indices([1, 6], superset)
+            []
+            >>> Subset.subset_indices([], superset)
+            []
+
+        """
+        a, b = superset, subset
+        sb = set(b)
+        d = {}
+        for i, ai in enumerate(a):
+            if ai in sb:
+                d[ai] = i
+                sb.remove(ai)
+                if not sb:
+                    break
+        else:
+            return []
+        return [d[bi] for bi in b]
+
+
+def ksubsets(superset, k):
+    """
+    Finds the subsets of size ``k`` in lexicographic order.
+
+    This uses the itertools generator.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.subsets import ksubsets
+    >>> list(ksubsets([1, 2, 3], 2))
+    [(1, 2), (1, 3), (2, 3)]
+    >>> list(ksubsets([1, 2, 3, 4, 5], 2))
+    [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), \
+    (2, 5), (3, 4), (3, 5), (4, 5)]
+
+    See Also
+    ========
+
+    Subset
+    """
+    return combinations(superset, k)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tensor_can.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tensor_can.py
new file mode 100644
index 0000000000000000000000000000000000000000..d43e96ed27a21f988aaaa8fd16827987541f7373
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tensor_can.py
@@ -0,0 +1,1189 @@
+from sympy.combinatorics.permutations import Permutation, _af_rmul, \
+    _af_invert, _af_new
+from sympy.combinatorics.perm_groups import PermutationGroup, _orbit, \
+    _orbit_transversal
+from sympy.combinatorics.util import _distribute_gens_by_base, \
+    _orbits_transversals_from_bsgs
+
+"""
+    References for tensor canonicalization:
+
+    [1] R. Portugal "Algorithmic simplification of tensor expressions",
+        J. Phys. A 32 (1999) 7779-7789
+
+    [2] R. Portugal, B.F. Svaiter "Group-theoretic Approach for Symbolic
+        Tensor Manipulation: I. Free Indices"
+        arXiv:math-ph/0107031v1
+
+    [3] L.R.U. Manssur, R. Portugal "Group-theoretic Approach for Symbolic
+        Tensor Manipulation: II. Dummy Indices"
+        arXiv:math-ph/0107032v1
+
+    [4] xperm.c part of XPerm written by J. M. Martin-Garcia
+        http://www.xact.es/index.html
+"""
+
+
+def dummy_sgs(dummies, sym, n):
+    """
+    Return the strong generators for dummy indices.
+
+    Parameters
+    ==========
+
+    dummies : List of dummy indices.
+        `dummies[2k], dummies[2k+1]` are paired indices.
+        In base form, the dummy indices are always in
+        consecutive positions.
+    sym : symmetry under interchange of contracted dummies::
+        * None  no symmetry
+        * 0     commuting
+        * 1     anticommuting
+
+    n : number of indices
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import dummy_sgs
+    >>> dummy_sgs(list(range(2, 8)), 0, 8)
+    [[0, 1, 3, 2, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 5, 4, 6, 7, 8, 9],
+     [0, 1, 2, 3, 4, 5, 7, 6, 8, 9], [0, 1, 4, 5, 2, 3, 6, 7, 8, 9],
+     [0, 1, 2, 3, 6, 7, 4, 5, 8, 9]]
+    """
+    if len(dummies) > n:
+        raise ValueError("List too large")
+    res = []
+    # exchange of contravariant and covariant indices
+    if sym is not None:
+        for j in dummies[::2]:
+            a = list(range(n + 2))
+            if sym == 1:
+                a[n] = n + 1
+                a[n + 1] = n
+            a[j], a[j + 1] = a[j + 1], a[j]
+            res.append(a)
+    # rename dummy indices
+    for j in dummies[:-3:2]:
+        a = list(range(n + 2))
+        a[j:j + 4] = a[j + 2], a[j + 3], a[j], a[j + 1]
+        res.append(a)
+    return res
+
+
+def _min_dummies(dummies, sym, indices):
+    """
+    Return list of minima of the orbits of indices in group of dummies.
+    See ``double_coset_can_rep`` for the description of ``dummies`` and ``sym``.
+    ``indices`` is the initial list of dummy indices.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import _min_dummies
+    >>> _min_dummies([list(range(2, 8))], [0], list(range(10)))
+    [0, 1, 2, 2, 2, 2, 2, 2, 8, 9]
+    """
+    num_types = len(sym)
+    m = [min(dx) if dx else None for dx in dummies]
+    res = indices[:]
+    for i in range(num_types):
+        for c, i in enumerate(indices):
+            for j in range(num_types):
+                if i in dummies[j]:
+                    res[c] = m[j]
+                    break
+    return res
+
+
+def _trace_S(s, j, b, S_cosets):
+    """
+    Return the representative h satisfying s[h[b]] == j
+
+    If there is not such a representative return None
+    """
+    for h in S_cosets[b]:
+        if s[h[b]] == j:
+            return h
+    return None
+
+
+def _trace_D(gj, p_i, Dxtrav):
+    """
+    Return the representative h satisfying h[gj] == p_i
+
+    If there is not such a representative return None
+    """
+    for h in Dxtrav:
+        if h[gj] == p_i:
+            return h
+    return None
+
+
+def _dumx_remove(dumx, dumx_flat, p0):
+    """
+    remove p0 from dumx
+    """
+    res = []
+    for dx in dumx:
+        if p0 not in dx:
+            res.append(dx)
+            continue
+        k = dx.index(p0)
+        if k % 2 == 0:
+            p0_paired = dx[k + 1]
+        else:
+            p0_paired = dx[k - 1]
+        dx.remove(p0)
+        dx.remove(p0_paired)
+        dumx_flat.remove(p0)
+        dumx_flat.remove(p0_paired)
+        res.append(dx)
+
+
+def transversal2coset(size, base, transversal):
+    a = []
+    j = 0
+    for i in range(size):
+        if i in base:
+            a.append(sorted(transversal[j].values()))
+            j += 1
+        else:
+            a.append([list(range(size))])
+    j = len(a) - 1
+    while a[j] == [list(range(size))]:
+        j -= 1
+    return a[:j + 1]
+
+
+def double_coset_can_rep(dummies, sym, b_S, sgens, S_transversals, g):
+    r"""
+    Butler-Portugal algorithm for tensor canonicalization with dummy indices.
+
+    Parameters
+    ==========
+
+      dummies
+        list of lists of dummy indices,
+        one list for each type of index;
+        the dummy indices are put in order contravariant, covariant
+        [d0, -d0, d1, -d1, ...].
+
+      sym
+        list of the symmetries of the index metric for each type.
+
+      possible symmetries of the metrics
+              * 0     symmetric
+              * 1     antisymmetric
+              * None  no symmetry
+
+      b_S
+        base of a minimal slot symmetry BSGS.
+
+      sgens
+        generators of the slot symmetry BSGS.
+
+      S_transversals
+        transversals for the slot BSGS.
+
+      g
+        permutation representing the tensor.
+
+    Returns
+    =======
+
+    Return 0 if the tensor is zero, else return the array form of
+    the permutation representing the canonical form of the tensor.
+
+    Notes
+    =====
+
+    A tensor with dummy indices can be represented in a number
+    of equivalent ways which typically grows exponentially with
+    the number of indices. To be able to establish if two tensors
+    with many indices are equal becomes computationally very slow
+    in absence of an efficient algorithm.
+
+    The Butler-Portugal algorithm [3] is an efficient algorithm to
+    put tensors in canonical form, solving the above problem.
+
+    Portugal observed that a tensor can be represented by a permutation,
+    and that the class of tensors equivalent to it under slot and dummy
+    symmetries is equivalent to the double coset `D*g*S`
+    (Note: in this documentation we use the conventions for multiplication
+    of permutations p, q with (p*q)(i) = p[q[i]] which is opposite
+    to the one used in the Permutation class)
+
+    Using the algorithm by Butler to find a representative of the
+    double coset one can find a canonical form for the tensor.
+
+    To see this correspondence,
+    let `g` be a permutation in array form; a tensor with indices `ind`
+    (the indices including both the contravariant and the covariant ones)
+    can be written as
+
+    `t = T(ind[g[0]], \dots, ind[g[n-1]])`,
+
+    where `n = len(ind)`;
+    `g` has size `n + 2`, the last two indices for the sign of the tensor
+    (trick introduced in [4]).
+
+    A slot symmetry transformation `s` is a permutation acting on the slots
+    `t \rightarrow T(ind[(g*s)[0]], \dots, ind[(g*s)[n-1]])`
+
+    A dummy symmetry transformation acts on `ind`
+    `t \rightarrow T(ind[(d*g)[0]], \dots, ind[(d*g)[n-1]])`
+
+    Being interested only in the transformations of the tensor under
+    these symmetries, one can represent the tensor by `g`, which transforms
+    as
+
+    `g -> d*g*s`, so it belongs to the coset `D*g*S`, or in other words
+    to the set of all permutations allowed by the slot and dummy symmetries.
+
+    Let us explain the conventions by an example.
+
+    Given a tensor `T^{d3 d2 d1}{}_{d1 d2 d3}` with the slot symmetries
+          `T^{a0 a1 a2 a3 a4 a5} = -T^{a2 a1 a0 a3 a4 a5}`
+
+          `T^{a0 a1 a2 a3 a4 a5} = -T^{a4 a1 a2 a3 a0 a5}`
+
+    and symmetric metric, find the tensor equivalent to it which
+    is the lowest under the ordering of indices:
+    lexicographic ordering `d1, d2, d3` and then contravariant
+    before covariant index; that is the canonical form of the tensor.
+
+    The canonical form is `-T^{d1 d2 d3}{}_{d1 d2 d3}`
+    obtained using `T^{a0 a1 a2 a3 a4 a5} = -T^{a2 a1 a0 a3 a4 a5}`.
+
+    To convert this problem in the input for this function,
+    use the following ordering of the index names
+    (- for covariant for short) `d1, -d1, d2, -d2, d3, -d3`
+
+    `T^{d3 d2 d1}{}_{d1 d2 d3}` corresponds to `g = [4, 2, 0, 1, 3, 5, 6, 7]`
+    where the last two indices are for the sign
+
+    `sgens = [Permutation(0, 2)(6, 7), Permutation(0, 4)(6, 7)]`
+
+    sgens[0] is the slot symmetry `-(0, 2)`
+    `T^{a0 a1 a2 a3 a4 a5} = -T^{a2 a1 a0 a3 a4 a5}`
+
+    sgens[1] is the slot symmetry `-(0, 4)`
+    `T^{a0 a1 a2 a3 a4 a5} = -T^{a4 a1 a2 a3 a0 a5}`
+
+    The dummy symmetry group D is generated by the strong base generators
+    `[(0, 1), (2, 3), (4, 5), (0, 2)(1, 3), (0, 4)(1, 5)]`
+    where the first three interchange covariant and contravariant
+    positions of the same index (d1 <-> -d1) and the last two interchange
+    the dummy indices themselves (d1 <-> d2).
+
+    The dummy symmetry acts from the left
+    `d = [1, 0, 2, 3, 4, 5, 6, 7]`  exchange `d1 \leftrightarrow -d1`
+    `T^{d3 d2 d1}{}_{d1 d2 d3} == T^{d3 d2}{}_{d1}{}^{d1}{}_{d2 d3}`
+
+    `g=[4, 2, 0, 1, 3, 5, 6, 7]  -> [4, 2, 1, 0, 3, 5, 6, 7] = _af_rmul(d, g)`
+    which differs from `_af_rmul(g, d)`.
+
+    The slot symmetry acts from the right
+    `s = [2, 1, 0, 3, 4, 5, 7, 6]`  exchanges slots 0 and 2 and changes sign
+    `T^{d3 d2 d1}{}_{d1 d2 d3} == -T^{d1 d2 d3}{}_{d1 d2 d3}`
+
+    `g=[4,2,0,1,3,5,6,7]  -> [0, 2, 4, 1, 3, 5, 7, 6] = _af_rmul(g, s)`
+
+    Example in which the tensor is zero, same slot symmetries as above:
+    `T^{d2}{}_{d1 d3}{}^{d1 d3}{}_{d2}`
+
+    `= -T^{d3}{}_{d1 d3}{}^{d1 d2}{}_{d2}`   under slot symmetry `-(0,4)`;
+
+    `= T_{d3 d1}{}^{d3}{}^{d1 d2}{}_{d2}`    under slot symmetry `-(0,2)`;
+
+    `= T^{d3}{}_{d1 d3}{}^{d1 d2}{}_{d2}`    symmetric metric;
+
+    `= 0`  since two of these lines have tensors differ only for the sign.
+
+    The double coset D*g*S consists of permutations `h = d*g*s` corresponding
+    to equivalent tensors; if there are two `h` which are the same apart
+    from the sign, return zero; otherwise
+    choose as representative the tensor with indices
+    ordered lexicographically according to `[d1, -d1, d2, -d2, d3, -d3]`
+    that is ``rep = min(D*g*S) = min([d*g*s for d in D for s in S])``
+
+    The indices are fixed one by one; first choose the lowest index
+    for slot 0, then the lowest remaining index for slot 1, etc.
+    Doing this one obtains a chain of stabilizers
+
+    `S \rightarrow S_{b0} \rightarrow S_{b0,b1} \rightarrow \dots` and
+    `D \rightarrow D_{p0} \rightarrow D_{p0,p1} \rightarrow \dots`
+
+    where ``[b0, b1, ...] = range(b)`` is a base of the symmetric group;
+    the strong base `b_S` of S is an ordered sublist of it;
+    therefore it is sufficient to compute once the
+    strong base generators of S using the Schreier-Sims algorithm;
+    the stabilizers of the strong base generators are the
+    strong base generators of the stabilizer subgroup.
+
+    ``dbase = [p0, p1, ...]`` is not in general in lexicographic order,
+    so that one must recompute the strong base generators each time;
+    however this is trivial, there is no need to use the Schreier-Sims
+    algorithm for D.
+
+    The algorithm keeps a TAB of elements `(s_i, d_i, h_i)`
+    where `h_i = d_i \times g \times s_i` satisfying `h_i[j] = p_j` for `0 \le j < i`
+    starting from `s_0 = id, d_0 = id, h_0 = g`.
+
+    The equations `h_0[0] = p_0, h_1[1] = p_1, \dots` are solved in this order,
+    choosing each time the lowest possible value of p_i
+
+    For `j < i`
+    `d_i*g*s_i*S_{b_0, \dots, b_{i-1}}*b_j = D_{p_0, \dots, p_{i-1}}*p_j`
+    so that for dx in `D_{p_0,\dots,p_{i-1}}` and sx in
+    `S_{base[0], \dots, base[i-1]}` one has `dx*d_i*g*s_i*sx*b_j = p_j`
+
+    Search for dx, sx such that this equation holds for `j = i`;
+    it can be written as `s_i*sx*b_j = J, dx*d_i*g*J = p_j`
+    `sx*b_j = s_i**-1*J; sx = trace(s_i**-1, S_{b_0,...,b_{i-1}})`
+    `dx**-1*p_j = d_i*g*J; dx = trace(d_i*g*J, D_{p_0,...,p_{i-1}})`
+
+    `s_{i+1} = s_i*trace(s_i**-1*J, S_{b_0,...,b_{i-1}})`
+    `d_{i+1} = trace(d_i*g*J, D_{p_0,...,p_{i-1}})**-1*d_i`
+    `h_{i+1}*b_i = d_{i+1}*g*s_{i+1}*b_i = p_i`
+
+    `h_n*b_j = p_j` for all j, so that `h_n` is the solution.
+
+    Add the found `(s, d, h)` to TAB1.
+
+    At the end of the iteration sort TAB1 with respect to the `h`;
+    if there are two consecutive `h` in TAB1 which differ only for the
+    sign, the tensor is zero, so return 0;
+    if there are two consecutive `h` which are equal, keep only one.
+
+    Then stabilize the slot generators under `i` and the dummy generators
+    under `p_i`.
+
+    Assign `TAB = TAB1` at the end of the iteration step.
+
+    At the end `TAB` contains a unique `(s, d, h)`, since all the slots
+    of the tensor `h` have been fixed to have the minimum value according
+    to the symmetries. The algorithm returns `h`.
+
+    It is important that the slot BSGS has lexicographic minimal base,
+    otherwise there is an `i` which does not belong to the slot base
+    for which `p_i` is fixed by the dummy symmetry only, while `i`
+    is not invariant from the slot stabilizer, so `p_i` is not in
+    general the minimal value.
+
+    This algorithm differs slightly from the original algorithm [3]:
+      the canonical form is minimal lexicographically, and
+      the BSGS has minimal base under lexicographic order.
+      Equal tensors `h` are eliminated from TAB.
+
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import Permutation
+    >>> from sympy.combinatorics.tensor_can import double_coset_can_rep, get_transversals
+    >>> gens = [Permutation(x) for x in [[2, 1, 0, 3, 4, 5, 7, 6], [4, 1, 2, 3, 0, 5, 7, 6]]]
+    >>> base = [0, 2]
+    >>> g = Permutation([4, 2, 0, 1, 3, 5, 6, 7])
+    >>> transversals = get_transversals(base, gens)
+    >>> double_coset_can_rep([list(range(6))], [0], base, gens, transversals, g)
+    [0, 1, 2, 3, 4, 5, 7, 6]
+
+    >>> g = Permutation([4, 1, 3, 0, 5, 2, 6, 7])
+    >>> double_coset_can_rep([list(range(6))], [0], base, gens, transversals, g)
+    0
+    """
+    size = g.size
+    g = g.array_form
+    num_dummies = size - 2
+    indices = list(range(num_dummies))
+    all_metrics_with_sym = not any(_ is None for _ in sym)
+    num_types = len(sym)
+    dumx = dummies[:]
+    dumx_flat = []
+    for dx in dumx:
+        dumx_flat.extend(dx)
+    b_S = b_S[:]
+    sgensx = [h._array_form for h in sgens]
+    if b_S:
+        S_transversals = transversal2coset(size, b_S, S_transversals)
+    # strong generating set for D
+    dsgsx = []
+    for i in range(num_types):
+        dsgsx.extend(dummy_sgs(dumx[i], sym[i], num_dummies))
+    idn = list(range(size))
+    # TAB = list of entries (s, d, h) where h = _af_rmuln(d,g,s)
+    # for short, in the following d*g*s means _af_rmuln(d,g,s)
+    TAB = [(idn, idn, g)]
+    for i in range(size - 2):
+        b = i
+        testb = b in b_S and sgensx
+        if testb:
+            sgensx1 = [_af_new(_) for _ in sgensx]
+            deltab = _orbit(size, sgensx1, b)
+        else:
+            deltab = {b}
+        # p1 = min(IMAGES) = min(Union D_p*h*deltab for h in TAB)
+        if all_metrics_with_sym:
+            md = _min_dummies(dumx, sym, indices)
+        else:
+            md = [min(_orbit(size, [_af_new(
+                ddx) for ddx in dsgsx], ii)) for ii in range(size - 2)]
+
+        p_i = min(min(md[h[x]] for x in deltab) for s, d, h in TAB)
+        dsgsx1 = [_af_new(_) for _ in dsgsx]
+        Dxtrav = _orbit_transversal(size, dsgsx1, p_i, False, af=True) \
+            if dsgsx else None
+        if Dxtrav:
+            Dxtrav = [_af_invert(x) for x in Dxtrav]
+        # compute the orbit of p_i
+        for ii in range(num_types):
+            if p_i in dumx[ii]:
+                # the orbit is made by all the indices in dum[ii]
+                if sym[ii] is not None:
+                    deltap = dumx[ii]
+                else:
+                    # the orbit is made by all the even indices if p_i
+                    # is even, by all the odd indices if p_i is odd
+                    p_i_index = dumx[ii].index(p_i) % 2
+                    deltap = dumx[ii][p_i_index::2]
+                break
+        else:
+            deltap = [p_i]
+        TAB1 = []
+        while TAB:
+            s, d, h = TAB.pop()
+            if min(md[h[x]] for x in deltab) != p_i:
+                continue
+            deltab1 = [x for x in deltab if md[h[x]] == p_i]
+            # NEXT = s*deltab1 intersection (d*g)**-1*deltap
+            dg = _af_rmul(d, g)
+            dginv = _af_invert(dg)
+            sdeltab = [s[x] for x in deltab1]
+            gdeltap = [dginv[x] for x in deltap]
+            NEXT = [x for x in sdeltab if x in gdeltap]
+            # d, s satisfy
+            # d*g*s*base[i-1] = p_{i-1}; using the stabilizers
+            # d*g*s*S_{base[0],...,base[i-1]}*base[i-1] =
+            # D_{p_0,...,p_{i-1}}*p_{i-1}
+            # so that to find d1, s1 satisfying d1*g*s1*b = p_i
+            # one can look for dx in D_{p_0,...,p_{i-1}} and
+            # sx in S_{base[0],...,base[i-1]}
+            # d1 = dx*d; s1 = s*sx
+            # d1*g*s1*b = dx*d*g*s*sx*b = p_i
+            for j in NEXT:
+                if testb:
+                    # solve s1*b = j with s1 = s*sx for some element sx
+                    # of the stabilizer of ..., base[i-1]
+                    # sx*b = s**-1*j; sx = _trace_S(s, j,...)
+                    # s1 = s*trace_S(s**-1*j,...)
+                    s1 = _trace_S(s, j, b, S_transversals)
+                    if not s1:
+                        continue
+                    else:
+                        s1 = [s[ix] for ix in s1]
+                else:
+                    s1 = s
+                # assert s1[b] == j  # invariant
+                # solve d1*g*j = p_i with d1 = dx*d for some element dg
+                # of the stabilizer of ..., p_{i-1}
+                # dx**-1*p_i = d*g*j; dx**-1 = trace_D(d*g*j,...)
+                # d1 = trace_D(d*g*j,...)**-1*d
+                # to save an inversion in the inner loop; notice we did
+                # Dxtrav = [perm_af_invert(x) for x in Dxtrav] out of the loop
+                if Dxtrav:
+                    d1 = _trace_D(dg[j], p_i, Dxtrav)
+                    if not d1:
+                        continue
+                else:
+                    if p_i != dg[j]:
+                        continue
+                    d1 = idn
+                assert d1[dg[j]] == p_i  # invariant
+                d1 = [d1[ix] for ix in d]
+                h1 = [d1[g[ix]] for ix in s1]
+                # assert h1[b] == p_i  # invariant
+                TAB1.append((s1, d1, h1))
+
+        # if TAB contains equal permutations, keep only one of them;
+        # if TAB contains equal permutations up to the sign, return 0
+        TAB1.sort(key=lambda x: x[-1])
+        prev = [0] * size
+        while TAB1:
+            s, d, h = TAB1.pop()
+            if h[:-2] == prev[:-2]:
+                if h[-1] != prev[-1]:
+                    return 0
+            else:
+                TAB.append((s, d, h))
+            prev = h
+
+        # stabilize the SGS
+        sgensx = [h for h in sgensx if h[b] == b]
+        if b in b_S:
+            b_S.remove(b)
+        _dumx_remove(dumx, dumx_flat, p_i)
+        dsgsx = []
+        for i in range(num_types):
+            dsgsx.extend(dummy_sgs(dumx[i], sym[i], num_dummies))
+    return TAB[0][-1]
+
+
+def canonical_free(base, gens, g, num_free):
+    """
+    Canonicalization of a tensor with respect to free indices
+    choosing the minimum with respect to lexicographical ordering
+    in the free indices.
+
+    Explanation
+    ===========
+
+    ``base``, ``gens``  BSGS for slot permutation group
+    ``g``               permutation representing the tensor
+    ``num_free``        number of free indices
+    The indices must be ordered with first the free indices
+
+    See explanation in double_coset_can_rep
+    The algorithm is a variation of the one given in [2].
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy.combinatorics.tensor_can import canonical_free
+    >>> gens = [[1, 0, 2, 3, 5, 4], [2, 3, 0, 1, 4, 5],[0, 1, 3, 2, 5, 4]]
+    >>> gens = [Permutation(h) for h in gens]
+    >>> base = [0, 2]
+    >>> g = Permutation([2, 1, 0, 3, 4, 5])
+    >>> canonical_free(base, gens, g, 4)
+    [0, 3, 1, 2, 5, 4]
+
+    Consider the product of Riemann tensors
+    ``T = R^{a}_{d0}^{d1,d2}*R_{d2,d1}^{d0,b}``
+    The order of the indices is ``[a, b, d0, -d0, d1, -d1, d2, -d2]``
+    The permutation corresponding to the tensor is
+    ``g = [0, 3, 4, 6, 7, 5, 2, 1, 8, 9]``
+
+    In particular ``a`` is position ``0``, ``b`` is in position ``9``.
+    Use the slot symmetries to get `T` is a form which is the minimal
+    in lexicographic order in the free indices ``a`` and ``b``, e.g.
+    ``-R^{a}_{d0}^{d1,d2}*R^{b,d0}_{d2,d1}`` corresponding to
+    ``[0, 3, 4, 6, 1, 2, 7, 5, 9, 8]``
+
+    >>> from sympy.combinatorics.tensor_can import riemann_bsgs, tensor_gens
+    >>> base, gens = riemann_bsgs
+    >>> size, sbase, sgens = tensor_gens(base, gens, [[], []], 0)
+    >>> g = Permutation([0, 3, 4, 6, 7, 5, 2, 1, 8, 9])
+    >>> canonical_free(sbase, [Permutation(h) for h in sgens], g, 2)
+    [0, 3, 4, 6, 1, 2, 7, 5, 9, 8]
+    """
+    g = g.array_form
+    size = len(g)
+    if not base:
+        return g[:]
+
+    transversals = get_transversals(base, gens)
+    for x in sorted(g[:-2]):
+        if x not in base:
+            base.append(x)
+    h = g
+    for transv in transversals:
+        h_i = [size]*num_free
+        # find the element s in transversals[i] such that
+        # _af_rmul(h, s) has its free elements with the lowest position in h
+        s = None
+        for sk in transv.values():
+            h1 = _af_rmul(h, sk)
+            hi = [h1.index(ix) for ix in range(num_free)]
+            if hi < h_i:
+                h_i = hi
+                s = sk
+        if s:
+            h = _af_rmul(h, s)
+    return h
+
+
+def _get_map_slots(size, fixed_slots):
+    res = list(range(size))
+    pos = 0
+    for i in range(size):
+        if i in fixed_slots:
+            continue
+        res[i] = pos
+        pos += 1
+    return res
+
+
+def _lift_sgens(size, fixed_slots, free, s):
+    a = []
+    j = k = 0
+    fd = [y for _, y in sorted(zip(fixed_slots, free))]
+    num_free = len(free)
+    for i in range(size):
+        if i in fixed_slots:
+            a.append(fd[k])
+            k += 1
+        else:
+            a.append(s[j] + num_free)
+            j += 1
+    return a
+
+
+def canonicalize(g, dummies, msym, *v):
+    """
+    canonicalize tensor formed by tensors
+
+    Parameters
+    ==========
+
+    g : permutation representing the tensor
+
+    dummies : list representing the dummy indices
+      it can be a list of dummy indices of the same type
+      or a list of lists of dummy indices, one list for each
+      type of index;
+      the dummy indices must come after the free indices,
+      and put in order contravariant, covariant
+      [d0, -d0, d1,-d1,...]
+
+    msym :  symmetry of the metric(s)
+        it can be an integer or a list;
+        in the first case it is the symmetry of the dummy index metric;
+        in the second case it is the list of the symmetries of the
+        index metric for each type
+
+    v : list, (base_i, gens_i, n_i, sym_i) for tensors of type `i`
+
+    base_i, gens_i : BSGS for tensors of this type.
+        The BSGS should have minimal base under lexicographic ordering;
+        if not, an attempt is made do get the minimal BSGS;
+        in case of failure,
+        canonicalize_naive is used, which is much slower.
+
+    n_i :    number of tensors of type `i`.
+
+    sym_i :  symmetry under exchange of component tensors of type `i`.
+
+        Both for msym and sym_i the cases are
+            * None  no symmetry
+            * 0     commuting
+            * 1     anticommuting
+
+    Returns
+    =======
+
+    0 if the tensor is zero, else return the array form of
+    the permutation representing the canonical form of the tensor.
+
+    Algorithm
+    =========
+
+    First one uses canonical_free to get the minimum tensor under
+    lexicographic order, using only the slot symmetries.
+    If the component tensors have not minimal BSGS, it is attempted
+    to find it; if the attempt fails canonicalize_naive
+    is used instead.
+
+    Compute the residual slot symmetry keeping fixed the free indices
+    using tensor_gens(base, gens, list_free_indices, sym).
+
+    Reduce the problem eliminating the free indices.
+
+    Then use double_coset_can_rep and lift back the result reintroducing
+    the free indices.
+
+    Examples
+    ========
+
+    one type of index with commuting metric;
+
+    `A_{a b}` and `B_{a b}` antisymmetric and commuting
+
+    `T = A_{d0 d1} * B^{d0}{}_{d2} * B^{d2 d1}`
+
+    `ord = [d0,-d0,d1,-d1,d2,-d2]` order of the indices
+
+    g = [1, 3, 0, 5, 4, 2, 6, 7]
+
+    `T_c = 0`
+
+    >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs, canonicalize, bsgs_direct_product
+    >>> from sympy.combinatorics import Permutation
+    >>> base2a, gens2a = get_symmetric_group_sgs(2, 1)
+    >>> t0 = (base2a, gens2a, 1, 0)
+    >>> t1 = (base2a, gens2a, 2, 0)
+    >>> g = Permutation([1, 3, 0, 5, 4, 2, 6, 7])
+    >>> canonicalize(g, range(6), 0, t0, t1)
+    0
+
+    same as above, but with `B_{a b}` anticommuting
+
+    `T_c = -A^{d0 d1} * B_{d0}{}^{d2} * B_{d1 d2}`
+
+    can = [0,2,1,4,3,5,7,6]
+
+    >>> t1 = (base2a, gens2a, 2, 1)
+    >>> canonicalize(g, range(6), 0, t0, t1)
+    [0, 2, 1, 4, 3, 5, 7, 6]
+
+    two types of indices `[a,b,c,d,e,f]` and `[m,n]`, in this order,
+    both with commuting metric
+
+    `f^{a b c}` antisymmetric, commuting
+
+    `A_{m a}` no symmetry, commuting
+
+    `T = f^c{}_{d a} * f^f{}_{e b} * A_m{}^d * A^{m b} * A_n{}^a * A^{n e}`
+
+    ord = [c,f,a,-a,b,-b,d,-d,e,-e,m,-m,n,-n]
+
+    g = [0,7,3, 1,9,5, 11,6, 10,4, 13,2, 12,8, 14,15]
+
+    The canonical tensor is
+    `T_c = -f^{c a b} * f^{f d e} * A^m{}_a * A_{m d} * A^n{}_b * A_{n e}`
+
+    can = [0,2,4, 1,6,8, 10,3, 11,7, 12,5, 13,9, 15,14]
+
+    >>> base_f, gens_f = get_symmetric_group_sgs(3, 1)
+    >>> base1, gens1 = get_symmetric_group_sgs(1)
+    >>> base_A, gens_A = bsgs_direct_product(base1, gens1, base1, gens1)
+    >>> t0 = (base_f, gens_f, 2, 0)
+    >>> t1 = (base_A, gens_A, 4, 0)
+    >>> dummies = [range(2, 10), range(10, 14)]
+    >>> g = Permutation([0, 7, 3, 1, 9, 5, 11, 6, 10, 4, 13, 2, 12, 8, 14, 15])
+    >>> canonicalize(g, dummies, [0, 0], t0, t1)
+    [0, 2, 4, 1, 6, 8, 10, 3, 11, 7, 12, 5, 13, 9, 15, 14]
+    """
+    from sympy.combinatorics.testutil import canonicalize_naive
+    if not isinstance(msym, list):
+        if msym not in (0, 1, None):
+            raise ValueError('msym must be 0, 1 or None')
+        num_types = 1
+    else:
+        num_types = len(msym)
+        if not all(msymx in (0, 1, None) for msymx in msym):
+            raise ValueError('msym entries must be 0, 1 or None')
+        if len(dummies) != num_types:
+            raise ValueError(
+                'dummies and msym must have the same number of elements')
+    size = g.size
+    num_tensors = 0
+    v1 = []
+    for base_i, gens_i, n_i, sym_i in v:
+        # check that the BSGS is minimal;
+        # this property is used in double_coset_can_rep;
+        # if it is not minimal use canonicalize_naive
+        if not _is_minimal_bsgs(base_i, gens_i):
+            mbsgs = get_minimal_bsgs(base_i, gens_i)
+            if not mbsgs:
+                can = canonicalize_naive(g, dummies, msym, *v)
+                return can
+            base_i, gens_i = mbsgs
+        v1.append((base_i, gens_i, [[]] * n_i, sym_i))
+        num_tensors += n_i
+
+    if num_types == 1 and not isinstance(msym, list):
+        dummies = [dummies]
+        msym = [msym]
+    flat_dummies = []
+    for dumx in dummies:
+        flat_dummies.extend(dumx)
+
+    if flat_dummies and flat_dummies != list(range(flat_dummies[0], flat_dummies[-1] + 1)):
+        raise ValueError('dummies is not valid')
+
+    # slot symmetry of the tensor
+    size1, sbase, sgens = gens_products(*v1)
+    if size != size1:
+        raise ValueError(
+            'g has size %d, generators have size %d' % (size, size1))
+    free = [i for i in range(size - 2) if i not in flat_dummies]
+    num_free = len(free)
+
+    # g1 minimal tensor under slot symmetry
+    g1 = canonical_free(sbase, sgens, g, num_free)
+    if not flat_dummies:
+        return g1
+    # save the sign of g1
+    sign = 0 if g1[-1] == size - 1 else 1
+
+    # the free indices are kept fixed.
+    # Determine free_i, the list of slots of tensors which are fixed
+    # since they are occupied by free indices, which are fixed.
+    start = 0
+    for i, (base_i, gens_i, n_i, sym_i) in enumerate(v):
+        free_i = []
+        len_tens = gens_i[0].size - 2
+        # for each component tensor get a list od fixed islots
+        for j in range(n_i):
+            # get the elements corresponding to the component tensor
+            h = g1[start:(start + len_tens)]
+            fr = []
+            # get the positions of the fixed elements in h
+            for k in free:
+                if k in h:
+                    fr.append(h.index(k))
+            free_i.append(fr)
+            start += len_tens
+        v1[i] = (base_i, gens_i, free_i, sym_i)
+    # BSGS of the tensor with fixed free indices
+    # if tensor_gens fails in gens_product, use canonicalize_naive
+    size, sbase, sgens = gens_products(*v1)
+
+    # reduce the permutations getting rid of the free indices
+    pos_free = [g1.index(x) for x in range(num_free)]
+    size_red = size - num_free
+    g1_red = [x - num_free for x in g1 if x in flat_dummies]
+    if sign:
+        g1_red.extend([size_red - 1, size_red - 2])
+    else:
+        g1_red.extend([size_red - 2, size_red - 1])
+    map_slots = _get_map_slots(size, pos_free)
+    sbase_red = [map_slots[i] for i in sbase if i not in pos_free]
+    sgens_red = [_af_new([map_slots[i] for i in y._array_form if i not in pos_free]) for y in sgens]
+    dummies_red = [[x - num_free for x in y] for y in dummies]
+    transv_red = get_transversals(sbase_red, sgens_red)
+    g1_red = _af_new(g1_red)
+    g2 = double_coset_can_rep(
+        dummies_red, msym, sbase_red, sgens_red, transv_red, g1_red)
+    if g2 == 0:
+        return 0
+    # lift to the case with the free indices
+    g3 = _lift_sgens(size, pos_free, free, g2)
+    return g3
+
+
+def perm_af_direct_product(gens1, gens2, signed=True):
+    """
+    Direct products of the generators gens1 and gens2.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import perm_af_direct_product
+    >>> gens1 = [[1, 0, 2, 3], [0, 1, 3, 2]]
+    >>> gens2 = [[1, 0]]
+    >>> perm_af_direct_product(gens1, gens2, False)
+    [[1, 0, 2, 3, 4, 5], [0, 1, 3, 2, 4, 5], [0, 1, 2, 3, 5, 4]]
+    >>> gens1 = [[1, 0, 2, 3, 5, 4], [0, 1, 3, 2, 4, 5]]
+    >>> gens2 = [[1, 0, 2, 3]]
+    >>> perm_af_direct_product(gens1, gens2, True)
+    [[1, 0, 2, 3, 4, 5, 7, 6], [0, 1, 3, 2, 4, 5, 6, 7], [0, 1, 2, 3, 5, 4, 6, 7]]
+    """
+    gens1 = [list(x) for x in gens1]
+    gens2 = [list(x) for x in gens2]
+    s = 2 if signed else 0
+    n1 = len(gens1[0]) - s
+    n2 = len(gens2[0]) - s
+    start = list(range(n1))
+    end = list(range(n1, n1 + n2))
+    if signed:
+        gens1 = [gen[:-2] + end + [gen[-2] + n2, gen[-1] + n2]
+                 for gen in gens1]
+        gens2 = [start + [x + n1 for x in gen] for gen in gens2]
+    else:
+        gens1 = [gen + end for gen in gens1]
+        gens2 = [start + [x + n1 for x in gen] for gen in gens2]
+
+    res = gens1 + gens2
+
+    return res
+
+
+def bsgs_direct_product(base1, gens1, base2, gens2, signed=True):
+    """
+    Direct product of two BSGS.
+
+    Parameters
+    ==========
+
+    base1 : base of the first BSGS.
+
+    gens1 : strong generating sequence of the first BSGS.
+
+    base2, gens2 : similarly for the second BSGS.
+
+    signed : flag for signed permutations.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import (get_symmetric_group_sgs, bsgs_direct_product)
+    >>> base1, gens1 = get_symmetric_group_sgs(1)
+    >>> base2, gens2 = get_symmetric_group_sgs(2)
+    >>> bsgs_direct_product(base1, gens1, base2, gens2)
+    ([1], [(4)(1 2)])
+    """
+    s = 2 if signed else 0
+    n1 = gens1[0].size - s
+    base = list(base1)
+    base += [x + n1 for x in base2]
+    gens1 = [h._array_form for h in gens1]
+    gens2 = [h._array_form for h in gens2]
+    gens = perm_af_direct_product(gens1, gens2, signed)
+    size = len(gens[0])
+    id_af = list(range(size))
+    gens = [h for h in gens if h != id_af]
+    if not gens:
+        gens = [id_af]
+    return base, [_af_new(h) for h in gens]
+
+
+def get_symmetric_group_sgs(n, antisym=False):
+    """
+    Return base, gens of the minimal BSGS for (anti)symmetric tensor
+
+    Parameters
+    ==========
+
+    n : rank of the tensor
+    antisym : bool
+        ``antisym = False`` symmetric tensor
+        ``antisym = True``  antisymmetric tensor
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs
+    >>> get_symmetric_group_sgs(3)
+    ([0, 1], [(4)(0 1), (4)(1 2)])
+    """
+    if n == 1:
+        return [], [_af_new(list(range(3)))]
+    gens = [Permutation(n - 1)(i, i + 1)._array_form for i in range(n - 1)]
+    if antisym == 0:
+        gens = [x + [n, n + 1] for x in gens]
+    else:
+        gens = [x + [n + 1, n] for x in gens]
+    base = list(range(n - 1))
+    return base, [_af_new(h) for h in gens]
+
+riemann_bsgs = [0, 2], [Permutation(0, 1)(4, 5), Permutation(2, 3)(4, 5),
+                        Permutation(5)(0, 2)(1, 3)]
+
+
+def get_transversals(base, gens):
+    """
+    Return transversals for the group with BSGS base, gens
+    """
+    if not base:
+        return []
+    stabs = _distribute_gens_by_base(base, gens)
+    orbits, transversals = _orbits_transversals_from_bsgs(base, stabs)
+    transversals = [{x: h._array_form for x, h in y.items()} for y in
+                    transversals]
+    return transversals
+
+
+def _is_minimal_bsgs(base, gens):
+    """
+    Check if the BSGS has minimal base under lexigographic order.
+
+    base, gens BSGS
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy.combinatorics.tensor_can import riemann_bsgs, _is_minimal_bsgs
+    >>> _is_minimal_bsgs(*riemann_bsgs)
+    True
+    >>> riemann_bsgs1 = ([2, 0], ([Permutation(5)(0, 1)(4, 5), Permutation(5)(0, 2)(1, 3)]))
+    >>> _is_minimal_bsgs(*riemann_bsgs1)
+    False
+    """
+    base1 = []
+    sgs1 = gens[:]
+    size = gens[0].size
+    for i in range(size):
+        if not all(h._array_form[i] == i for h in sgs1):
+            base1.append(i)
+            sgs1 = [h for h in sgs1 if h._array_form[i] == i]
+    return base1 == base
+
+
+def get_minimal_bsgs(base, gens):
+    """
+    Compute a minimal GSGS
+
+    base, gens BSGS
+
+    If base, gens is a minimal BSGS return it; else return a minimal BSGS
+    if it fails in finding one, it returns None
+
+    TODO: use baseswap in the case in which if it fails in finding a
+    minimal BSGS
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy.combinatorics.tensor_can import get_minimal_bsgs
+    >>> riemann_bsgs1 = ([2, 0], ([Permutation(5)(0, 1)(4, 5), Permutation(5)(0, 2)(1, 3)]))
+    >>> get_minimal_bsgs(*riemann_bsgs1)
+    ([0, 2], [(0 1)(4 5), (5)(0 2)(1 3), (2 3)(4 5)])
+    """
+    G = PermutationGroup(gens)
+    base, gens = G.schreier_sims_incremental()
+    if not _is_minimal_bsgs(base, gens):
+        return None
+    return base, gens
+
+
+def tensor_gens(base, gens, list_free_indices, sym=0):
+    """
+    Returns size, res_base, res_gens BSGS for n tensors of the
+    same type.
+
+    Explanation
+    ===========
+
+    base, gens BSGS for tensors of this type
+    list_free_indices  list of the slots occupied by fixed indices
+                       for each of the tensors
+
+    sym symmetry under commutation of two tensors
+    sym   None  no symmetry
+    sym   0     commuting
+    sym   1     anticommuting
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import tensor_gens, get_symmetric_group_sgs
+
+    two symmetric tensors with 3 indices without free indices
+
+    >>> base, gens = get_symmetric_group_sgs(3)
+    >>> tensor_gens(base, gens, [[], []])
+    (8, [0, 1, 3, 4], [(7)(0 1), (7)(1 2), (7)(3 4), (7)(4 5), (7)(0 3)(1 4)(2 5)])
+
+    two symmetric tensors with 3 indices with free indices in slot 1 and 0
+
+    >>> tensor_gens(base, gens, [[1], [0]])
+    (8, [0, 4], [(7)(0 2), (7)(4 5)])
+
+    four symmetric tensors with 3 indices, two of which with free indices
+
+    """
+    def _get_bsgs(G, base, gens, free_indices):
+        """
+        return the BSGS for G.pointwise_stabilizer(free_indices)
+        """
+        if not free_indices:
+            return base[:], gens[:]
+        else:
+            H = G.pointwise_stabilizer(free_indices)
+            base, sgs = H.schreier_sims_incremental()
+            return base, sgs
+
+    # if not base there is no slot symmetry for the component tensors
+    # if list_free_indices.count([]) < 2 there is no commutation symmetry
+    # so there is no resulting slot symmetry
+    if not base and list_free_indices.count([]) < 2:
+        n = len(list_free_indices)
+        size = gens[0].size
+        size = n * (size - 2) + 2
+        return size, [], [_af_new(list(range(size)))]
+
+    # if any(list_free_indices) one needs to compute the pointwise
+    # stabilizer, so G is needed
+    if any(list_free_indices):
+        G = PermutationGroup(gens)
+    else:
+        G = None
+
+    # no_free list of lists of indices for component tensors without fixed
+    # indices
+    no_free = []
+    size = gens[0].size
+    id_af = list(range(size))
+    num_indices = size - 2
+    if not list_free_indices[0]:
+        no_free.append(list(range(num_indices)))
+    res_base, res_gens = _get_bsgs(G, base, gens, list_free_indices[0])
+    for i in range(1, len(list_free_indices)):
+        base1, gens1 = _get_bsgs(G, base, gens, list_free_indices[i])
+        res_base, res_gens = bsgs_direct_product(res_base, res_gens,
+                                                 base1, gens1, 1)
+        if not list_free_indices[i]:
+            no_free.append(list(range(size - 2, size - 2 + num_indices)))
+        size += num_indices
+    nr = size - 2
+    res_gens = [h for h in res_gens if h._array_form != id_af]
+    # if sym there are no commuting tensors stop here
+    if sym is None or not no_free:
+        if not res_gens:
+            res_gens = [_af_new(id_af)]
+        return size, res_base, res_gens
+
+    # if the component tensors have moinimal BSGS, so is their direct
+    # product P; the slot symmetry group is S = P*C, where C is the group
+    # to (anti)commute the component tensors with no free indices
+    # a stabilizer has the property S_i = P_i*C_i;
+    # the BSGS of P*C has SGS_P + SGS_C and the base is
+    # the ordered union of the bases of P and C.
+    # If P has minimal BSGS, so has S with this base.
+    base_comm = []
+    for i in range(len(no_free) - 1):
+        ind1 = no_free[i]
+        ind2 = no_free[i + 1]
+        a = list(range(ind1[0]))
+        a.extend(ind2)
+        a.extend(ind1)
+        base_comm.append(ind1[0])
+        a.extend(list(range(ind2[-1] + 1, nr)))
+        if sym == 0:
+            a.extend([nr, nr + 1])
+        else:
+            a.extend([nr + 1, nr])
+        res_gens.append(_af_new(a))
+    res_base = list(res_base)
+    # each base is ordered; order the union of the two bases
+    for i in base_comm:
+        if i not in res_base:
+            res_base.append(i)
+    res_base.sort()
+    if not res_gens:
+        res_gens = [_af_new(id_af)]
+
+    return size, res_base, res_gens
+
+
+def gens_products(*v):
+    """
+    Returns size, res_base, res_gens BSGS for n tensors of different types.
+
+    Explanation
+    ===========
+
+    v is a sequence of (base_i, gens_i, free_i, sym_i)
+    where
+    base_i, gens_i  BSGS of tensor of type `i`
+    free_i          list of the fixed slots for each of the tensors
+                    of type `i`; if there are `n_i` tensors of type `i`
+                    and none of them have fixed slots, `free = [[]]*n_i`
+    sym   0 (1) if the tensors of type `i` (anti)commute among themselves
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs, gens_products
+    >>> base, gens = get_symmetric_group_sgs(2)
+    >>> gens_products((base, gens, [[], []], 0))
+    (6, [0, 2], [(5)(0 1), (5)(2 3), (5)(0 2)(1 3)])
+    >>> gens_products((base, gens, [[1], []], 0))
+    (6, [2], [(5)(2 3)])
+    """
+    res_size, res_base, res_gens = tensor_gens(*v[0])
+    for i in range(1, len(v)):
+        size, base, gens = tensor_gens(*v[i])
+        res_base, res_gens = bsgs_direct_product(res_base, res_gens, base,
+                                                 gens, 1)
+    res_size = res_gens[0].size
+    id_af = list(range(res_size))
+    res_gens = [h for h in res_gens if h != id_af]
+    if not res_gens:
+        res_gens = [id_af]
+    return res_size, res_base, res_gens
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_coset_table.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_coset_table.py
new file mode 100644
index 0000000000000000000000000000000000000000..ab3f62880445c5deb526797ee0623fe3510bcbc3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_coset_table.py
@@ -0,0 +1,825 @@
+from sympy.combinatorics.fp_groups import FpGroup
+from sympy.combinatorics.coset_table import (CosetTable,
+                    coset_enumeration_r, coset_enumeration_c)
+from sympy.combinatorics.coset_table import modified_coset_enumeration_r
+from sympy.combinatorics.free_groups import free_group
+
+from sympy.testing.pytest import slow
+
+"""
+References
+==========
+
+[1] Holt, D., Eick, B., O'Brien, E.
+"Handbook of Computational Group Theory"
+
+[2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson
+Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490.
+"Implementation and Analysis of the Todd-Coxeter Algorithm"
+
+"""
+
+def test_scan_1():
+    # Example 5.1 from [1]
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+    c = CosetTable(f, [x])
+
+    c.scan_and_fill(0, x)
+    assert c.table == [[0, 0, None, None]]
+    assert c.p == [0]
+    assert c.n == 1
+    assert c.omega == [0]
+
+    c.scan_and_fill(0, x**3)
+    assert c.table == [[0, 0, None, None]]
+    assert c.p == [0]
+    assert c.n == 1
+    assert c.omega == [0]
+
+    c.scan_and_fill(0, y**3)
+    assert c.table == [[0, 0, 1, 2], [None, None, 2, 0], [None, None, 0, 1]]
+    assert c.p == [0, 1, 2]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    c.scan_and_fill(0, x**-1*y**-1*x*y)
+    assert c.table == [[0, 0, 1, 2], [None, None, 2, 0], [2, 2, 0, 1]]
+    assert c.p == [0, 1, 2]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    c.scan_and_fill(1, x**3)
+    assert c.table == [[0, 0, 1, 2], [3, 4, 2, 0], [2, 2, 0, 1], \
+            [4, 1, None, None], [1, 3, None, None]]
+    assert c.p == [0, 1, 2, 3, 4]
+    assert c.n == 5
+    assert c.omega == [0, 1, 2, 3, 4]
+
+    c.scan_and_fill(1, y**3)
+    assert c.table == [[0, 0, 1, 2], [3, 4, 2, 0], [2, 2, 0, 1], \
+            [4, 1, None, None], [1, 3, None, None]]
+    assert c.p == [0, 1, 2, 3, 4]
+    assert c.n == 5
+    assert c.omega == [0, 1, 2, 3, 4]
+
+    c.scan_and_fill(1, x**-1*y**-1*x*y)
+    assert c.table == [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1], \
+            [None, 1, None, None], [1, 3, None, None]]
+    assert c.p == [0, 1, 2, 1, 1]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    # Example 5.2 from [1]
+    f = FpGroup(F, [x**2, y**3, (x*y)**3])
+    c = CosetTable(f, [x*y])
+
+    c.scan_and_fill(0, x*y)
+    assert c.table == [[1, None, None, 1], [None, 0, 0, None]]
+    assert c.p == [0, 1]
+    assert c.n == 2
+    assert c.omega == [0, 1]
+
+    c.scan_and_fill(0, x**2)
+    assert c.table == [[1, 1, None, 1], [0, 0, 0, None]]
+    assert c.p == [0, 1]
+    assert c.n == 2
+    assert c.omega == [0, 1]
+
+    c.scan_and_fill(0, y**3)
+    assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]]
+    assert c.p == [0, 1, 2]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    c.scan_and_fill(0, (x*y)**3)
+    assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]]
+    assert c.p == [0, 1, 2]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    c.scan_and_fill(1, x**2)
+    assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]]
+    assert c.p == [0, 1, 2]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    c.scan_and_fill(1, y**3)
+    assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]]
+    assert c.p == [0, 1, 2]
+    assert c.n == 3
+    assert c.omega == [0, 1, 2]
+
+    c.scan_and_fill(1, (x*y)**3)
+    assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [3, 4, 1, 0], [None, 2, 4, None], [2, None, None, 3]]
+    assert c.p == [0, 1, 2, 3, 4]
+    assert c.n == 5
+    assert c.omega == [0, 1, 2, 3, 4]
+
+    c.scan_and_fill(2, x**2)
+    assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [3, 3, 1, 0], [2, 2, 3, 3], [2, None, None, 3]]
+    assert c.p == [0, 1, 2, 3, 3]
+    assert c.n == 4
+    assert c.omega == [0, 1, 2, 3]
+
+
+@slow
+def test_coset_enumeration():
+    # this test function contains the combined tests for the two strategies
+    # i.e. HLT and Felsch strategies.
+
+    # Example 5.1 from [1]
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+    C_r = coset_enumeration_r(f, [x])
+    C_r.compress(); C_r.standardize()
+    C_c = coset_enumeration_c(f, [x])
+    C_c.compress(); C_c.standardize()
+    table1 = [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]]
+    assert C_r.table == table1
+    assert C_c.table == table1
+
+    # E1 from [2] Pg. 474
+    F, r, s, t = free_group("r, s, t")
+    E1 = FpGroup(F, [t**-1*r*t*r**-2, r**-1*s*r*s**-2, s**-1*t*s*t**-2])
+    C_r = coset_enumeration_r(E1, [])
+    C_r.compress()
+    C_c = coset_enumeration_c(E1, [])
+    C_c.compress()
+    table2 = [[0, 0, 0, 0, 0, 0]]
+    assert C_r.table == table2
+    # test for issue #11449
+    assert C_c.table == table2
+
+    # Cox group from [2] Pg. 474
+    F, a, b = free_group("a, b")
+    Cox = FpGroup(F, [a**6, b**6, (a*b)**2, (a**2*b**2)**2, (a**3*b**3)**5])
+    C_r = coset_enumeration_r(Cox, [a])
+    C_r.compress(); C_r.standardize()
+    C_c = coset_enumeration_c(Cox, [a])
+    C_c.compress(); C_c.standardize()
+    table3 = [[0, 0, 1, 2],
+             [2, 3, 4, 0],
+             [5, 1, 0, 6],
+             [1, 7, 8, 9],
+             [9, 10, 11, 1],
+             [12, 2, 9, 13],
+             [14, 9, 2, 11],
+             [3, 12, 15, 16],
+             [16, 17, 18, 3],
+             [6, 4, 3, 5],
+             [4, 19, 20, 21],
+             [21, 22, 6, 4],
+             [7, 5, 23, 24],
+             [25, 23, 5, 18],
+             [19, 6, 22, 26],
+             [24, 27, 28, 7],
+             [29, 8, 7, 30],
+             [8, 31, 32, 33],
+             [33, 34, 13, 8],
+             [10, 14, 35, 35],
+             [35, 36, 37, 10],
+             [30, 11, 10, 29],
+             [11, 38, 39, 14],
+             [13, 39, 38, 12],
+             [40, 15, 12, 41],
+             [42, 13, 34, 43],
+             [44, 35, 14, 45],
+             [15, 46, 47, 34],
+             [34, 48, 49, 15],
+             [50, 16, 21, 51],
+             [52, 21, 16, 49],
+             [17, 50, 53, 54],
+             [54, 55, 56, 17],
+             [41, 18, 17, 40],
+             [18, 28, 27, 25],
+             [26, 20, 19, 19],
+             [20, 57, 58, 59],
+             [59, 60, 51, 20],
+             [22, 52, 61, 23],
+             [23, 62, 63, 22],
+             [64, 24, 33, 65],
+             [48, 33, 24, 61],
+             [62, 25, 54, 66],
+             [67, 54, 25, 68],
+             [57, 26, 59, 69],
+             [70, 59, 26, 63],
+             [27, 64, 71, 72],
+             [72, 73, 68, 27],
+             [28, 41, 74, 75],
+             [75, 76, 30, 28],
+             [31, 29, 77, 78],
+             [79, 77, 29, 37],
+             [38, 30, 76, 80],
+             [78, 81, 82, 31],
+             [43, 32, 31, 42],
+             [32, 83, 84, 85],
+             [85, 86, 65, 32],
+             [36, 44, 87, 88],
+             [88, 89, 90, 36],
+             [45, 37, 36, 44],
+             [37, 82, 81, 79],
+             [80, 74, 41, 38],
+             [39, 42, 91, 92],
+             [92, 93, 45, 39],
+             [46, 40, 94, 95],
+             [96, 94, 40, 56],
+             [97, 91, 42, 82],
+             [83, 43, 98, 99],
+             [100, 98, 43, 47],
+             [101, 87, 44, 90],
+             [82, 45, 93, 97],
+             [95, 102, 103, 46],
+             [104, 47, 46, 105],
+             [47, 106, 107, 100],
+             [61, 108, 109, 48],
+             [105, 49, 48, 104],
+             [49, 110, 111, 52],
+             [51, 111, 110, 50],
+             [112, 53, 50, 113],
+             [114, 51, 60, 115],
+             [116, 61, 52, 117],
+             [53, 118, 119, 60],
+             [60, 70, 66, 53],
+             [55, 67, 120, 121],
+             [121, 122, 123, 55],
+             [113, 56, 55, 112],
+             [56, 103, 102, 96],
+             [69, 124, 125, 57],
+             [115, 58, 57, 114],
+             [58, 126, 127, 128],
+             [128, 128, 69, 58],
+             [66, 129, 130, 62],
+             [117, 63, 62, 116],
+             [63, 125, 124, 70],
+             [65, 109, 108, 64],
+             [131, 71, 64, 132],
+             [133, 65, 86, 134],
+             [135, 66, 70, 136],
+             [68, 130, 129, 67],
+             [137, 120, 67, 138],
+             [132, 68, 73, 131],
+             [139, 69, 128, 140],
+             [71, 141, 142, 86],
+             [86, 143, 144, 71],
+             [145, 72, 75, 146],
+             [147, 75, 72, 144],
+             [73, 145, 148, 120],
+             [120, 149, 150, 73],
+             [74, 151, 152, 94],
+             [94, 153, 146, 74],
+             [76, 147, 154, 77],
+             [77, 155, 156, 76],
+             [157, 78, 85, 158],
+             [143, 85, 78, 154],
+             [155, 79, 88, 159],
+             [160, 88, 79, 161],
+             [151, 80, 92, 162],
+             [163, 92, 80, 156],
+             [81, 157, 164, 165],
+             [165, 166, 161, 81],
+             [99, 107, 106, 83],
+             [134, 84, 83, 133],
+             [84, 167, 168, 169],
+             [169, 170, 158, 84],
+             [87, 171, 172, 93],
+             [93, 163, 159, 87],
+             [89, 160, 173, 174],
+             [174, 175, 176, 89],
+             [90, 90, 89, 101],
+             [91, 177, 178, 98],
+             [98, 179, 162, 91],
+             [180, 95, 100, 181],
+             [179, 100, 95, 152],
+             [153, 96, 121, 148],
+             [182, 121, 96, 183],
+             [177, 97, 165, 184],
+             [185, 165, 97, 172],
+             [186, 99, 169, 187],
+             [188, 169, 99, 178],
+             [171, 101, 174, 189],
+             [190, 174, 101, 176],
+             [102, 180, 191, 192],
+             [192, 193, 183, 102],
+             [103, 113, 194, 195],
+             [195, 196, 105, 103],
+             [106, 104, 197, 198],
+             [199, 197, 104, 109],
+             [110, 105, 196, 200],
+             [198, 201, 133, 106],
+             [107, 186, 202, 203],
+             [203, 204, 181, 107],
+             [108, 116, 205, 206],
+             [206, 207, 132, 108],
+             [109, 133, 201, 199],
+             [200, 194, 113, 110],
+             [111, 114, 208, 209],
+             [209, 210, 117, 111],
+             [118, 112, 211, 212],
+             [213, 211, 112, 123],
+             [214, 208, 114, 125],
+             [126, 115, 215, 216],
+             [217, 215, 115, 119],
+             [218, 205, 116, 130],
+             [125, 117, 210, 214],
+             [212, 219, 220, 118],
+             [136, 119, 118, 135],
+             [119, 221, 222, 217],
+             [122, 182, 223, 224],
+             [224, 225, 226, 122],
+             [138, 123, 122, 137],
+             [123, 220, 219, 213],
+             [124, 139, 227, 228],
+             [228, 229, 136, 124],
+             [216, 222, 221, 126],
+             [140, 127, 126, 139],
+             [127, 230, 231, 232],
+             [232, 233, 140, 127],
+             [129, 135, 234, 235],
+             [235, 236, 138, 129],
+             [130, 132, 207, 218],
+             [141, 131, 237, 238],
+             [239, 237, 131, 150],
+             [167, 134, 240, 241],
+             [242, 240, 134, 142],
+             [243, 234, 135, 220],
+             [221, 136, 229, 244],
+             [149, 137, 245, 246],
+             [247, 245, 137, 226],
+             [220, 138, 236, 243],
+             [244, 227, 139, 221],
+             [230, 140, 233, 248],
+             [238, 249, 250, 141],
+             [251, 142, 141, 252],
+             [142, 253, 254, 242],
+             [154, 255, 256, 143],
+             [252, 144, 143, 251],
+             [144, 257, 258, 147],
+             [146, 258, 257, 145],
+             [259, 148, 145, 260],
+             [261, 146, 153, 262],
+             [263, 154, 147, 264],
+             [148, 265, 266, 153],
+             [246, 267, 268, 149],
+             [260, 150, 149, 259],
+             [150, 250, 249, 239],
+             [162, 269, 270, 151],
+             [262, 152, 151, 261],
+             [152, 271, 272, 179],
+             [159, 273, 274, 155],
+             [264, 156, 155, 263],
+             [156, 270, 269, 163],
+             [158, 256, 255, 157],
+             [275, 164, 157, 276],
+             [277, 158, 170, 278],
+             [279, 159, 163, 280],
+             [161, 274, 273, 160],
+             [281, 173, 160, 282],
+             [276, 161, 166, 275],
+             [283, 162, 179, 284],
+             [164, 285, 286, 170],
+             [170, 188, 184, 164],
+             [166, 185, 189, 173],
+             [173, 287, 288, 166],
+             [241, 254, 253, 167],
+             [278, 168, 167, 277],
+             [168, 289, 290, 291],
+             [291, 292, 187, 168],
+             [189, 293, 294, 171],
+             [280, 172, 171, 279],
+             [172, 295, 296, 185],
+             [175, 190, 297, 297],
+             [297, 298, 299, 175],
+             [282, 176, 175, 281],
+             [176, 294, 293, 190],
+             [184, 296, 295, 177],
+             [284, 178, 177, 283],
+             [178, 300, 301, 188],
+             [181, 272, 271, 180],
+             [302, 191, 180, 303],
+             [304, 181, 204, 305],
+             [183, 266, 265, 182],
+             [306, 223, 182, 307],
+             [303, 183, 193, 302],
+             [308, 184, 188, 309],
+             [310, 189, 185, 311],
+             [187, 301, 300, 186],
+             [305, 202, 186, 304],
+             [312, 187, 292, 313],
+             [314, 297, 190, 315],
+             [191, 316, 317, 204],
+             [204, 318, 319, 191],
+             [320, 192, 195, 321],
+             [322, 195, 192, 319],
+             [193, 320, 323, 223],
+             [223, 324, 325, 193],
+             [194, 326, 327, 211],
+             [211, 328, 321, 194],
+             [196, 322, 329, 197],
+             [197, 330, 331, 196],
+             [332, 198, 203, 333],
+             [318, 203, 198, 329],
+             [330, 199, 206, 334],
+             [335, 206, 199, 336],
+             [326, 200, 209, 337],
+             [338, 209, 200, 331],
+             [201, 332, 339, 240],
+             [240, 340, 336, 201],
+             [202, 341, 342, 292],
+             [292, 343, 333, 202],
+             [205, 344, 345, 210],
+             [210, 338, 334, 205],
+             [207, 335, 346, 237],
+             [237, 347, 348, 207],
+             [208, 349, 350, 215],
+             [215, 351, 337, 208],
+             [352, 212, 217, 353],
+             [351, 217, 212, 327],
+             [328, 213, 224, 323],
+             [354, 224, 213, 355],
+             [349, 214, 228, 356],
+             [357, 228, 214, 345],
+             [358, 216, 232, 359],
+             [360, 232, 216, 350],
+             [344, 218, 235, 361],
+             [362, 235, 218, 348],
+             [219, 352, 363, 364],
+             [364, 365, 355, 219],
+             [222, 358, 366, 367],
+             [367, 368, 353, 222],
+             [225, 354, 369, 370],
+             [370, 371, 372, 225],
+             [307, 226, 225, 306],
+             [226, 268, 267, 247],
+             [227, 373, 374, 233],
+             [233, 360, 356, 227],
+             [229, 357, 361, 234],
+             [234, 375, 376, 229],
+             [248, 231, 230, 230],
+             [231, 377, 378, 379],
+             [379, 380, 359, 231],
+             [236, 362, 381, 245],
+             [245, 382, 383, 236],
+             [384, 238, 242, 385],
+             [340, 242, 238, 346],
+             [347, 239, 246, 381],
+             [386, 246, 239, 387],
+             [388, 241, 291, 389],
+             [343, 291, 241, 339],
+             [375, 243, 364, 390],
+             [391, 364, 243, 383],
+             [373, 244, 367, 392],
+             [393, 367, 244, 376],
+             [382, 247, 370, 394],
+             [395, 370, 247, 396],
+             [377, 248, 379, 397],
+             [398, 379, 248, 374],
+             [249, 384, 399, 400],
+             [400, 401, 387, 249],
+             [250, 260, 402, 403],
+             [403, 404, 252, 250],
+             [253, 251, 405, 406],
+             [407, 405, 251, 256],
+             [257, 252, 404, 408],
+             [406, 409, 277, 253],
+             [254, 388, 410, 411],
+             [411, 412, 385, 254],
+             [255, 263, 413, 414],
+             [414, 415, 276, 255],
+             [256, 277, 409, 407],
+             [408, 402, 260, 257],
+             [258, 261, 416, 417],
+             [417, 418, 264, 258],
+             [265, 259, 419, 420],
+             [421, 419, 259, 268],
+             [422, 416, 261, 270],
+             [271, 262, 423, 424],
+             [425, 423, 262, 266],
+             [426, 413, 263, 274],
+             [270, 264, 418, 422],
+             [420, 427, 307, 265],
+             [266, 303, 428, 425],
+             [267, 386, 429, 430],
+             [430, 431, 396, 267],
+             [268, 307, 427, 421],
+             [269, 283, 432, 433],
+             [433, 434, 280, 269],
+             [424, 428, 303, 271],
+             [272, 304, 435, 436],
+             [436, 437, 284, 272],
+             [273, 279, 438, 439],
+             [439, 440, 282, 273],
+             [274, 276, 415, 426],
+             [285, 275, 441, 442],
+             [443, 441, 275, 288],
+             [289, 278, 444, 445],
+             [446, 444, 278, 286],
+             [447, 438, 279, 294],
+             [295, 280, 434, 448],
+             [287, 281, 449, 450],
+             [451, 449, 281, 299],
+             [294, 282, 440, 447],
+             [448, 432, 283, 295],
+             [300, 284, 437, 452],
+             [442, 453, 454, 285],
+             [309, 286, 285, 308],
+             [286, 455, 456, 446],
+             [450, 457, 458, 287],
+             [311, 288, 287, 310],
+             [288, 454, 453, 443],
+             [445, 456, 455, 289],
+             [313, 290, 289, 312],
+             [290, 459, 460, 461],
+             [461, 462, 389, 290],
+             [293, 310, 463, 464],
+             [464, 465, 315, 293],
+             [296, 308, 466, 467],
+             [467, 468, 311, 296],
+             [298, 314, 469, 470],
+             [470, 471, 472, 298],
+             [315, 299, 298, 314],
+             [299, 458, 457, 451],
+             [452, 435, 304, 300],
+             [301, 312, 473, 474],
+             [474, 475, 309, 301],
+             [316, 302, 476, 477],
+             [478, 476, 302, 325],
+             [341, 305, 479, 480],
+             [481, 479, 305, 317],
+             [324, 306, 482, 483],
+             [484, 482, 306, 372],
+             [485, 466, 308, 454],
+             [455, 309, 475, 486],
+             [487, 463, 310, 458],
+             [454, 311, 468, 485],
+             [486, 473, 312, 455],
+             [459, 313, 488, 489],
+             [490, 488, 313, 342],
+             [491, 469, 314, 472],
+             [458, 315, 465, 487],
+             [477, 492, 485, 316],
+             [463, 317, 316, 468],
+             [317, 487, 493, 481],
+             [329, 447, 464, 318],
+             [468, 319, 318, 463],
+             [319, 467, 448, 322],
+             [321, 448, 467, 320],
+             [475, 323, 320, 466],
+             [432, 321, 328, 437],
+             [438, 329, 322, 434],
+             [323, 474, 452, 328],
+             [483, 494, 486, 324],
+             [466, 325, 324, 475],
+             [325, 485, 492, 478],
+             [337, 422, 433, 326],
+             [437, 327, 326, 432],
+             [327, 436, 424, 351],
+             [334, 426, 439, 330],
+             [434, 331, 330, 438],
+             [331, 433, 422, 338],
+             [333, 464, 447, 332],
+             [449, 339, 332, 440],
+             [465, 333, 343, 469],
+             [413, 334, 338, 418],
+             [336, 439, 426, 335],
+             [441, 346, 335, 415],
+             [440, 336, 340, 449],
+             [416, 337, 351, 423],
+             [339, 451, 470, 343],
+             [346, 443, 450, 340],
+             [480, 493, 487, 341],
+             [469, 342, 341, 465],
+             [342, 491, 495, 490],
+             [361, 407, 414, 344],
+             [418, 345, 344, 413],
+             [345, 417, 408, 357],
+             [381, 446, 442, 347],
+             [415, 348, 347, 441],
+             [348, 414, 407, 362],
+             [356, 408, 417, 349],
+             [423, 350, 349, 416],
+             [350, 425, 420, 360],
+             [353, 424, 436, 352],
+             [479, 363, 352, 435],
+             [428, 353, 368, 476],
+             [355, 452, 474, 354],
+             [488, 369, 354, 473],
+             [435, 355, 365, 479],
+             [402, 356, 360, 419],
+             [405, 361, 357, 404],
+             [359, 420, 425, 358],
+             [476, 366, 358, 428],
+             [427, 359, 380, 482],
+             [444, 381, 362, 409],
+             [363, 481, 477, 368],
+             [368, 393, 390, 363],
+             [365, 391, 394, 369],
+             [369, 490, 480, 365],
+             [366, 478, 483, 380],
+             [380, 398, 392, 366],
+             [371, 395, 496, 497],
+             [497, 498, 489, 371],
+             [473, 372, 371, 488],
+             [372, 486, 494, 484],
+             [392, 400, 403, 373],
+             [419, 374, 373, 402],
+             [374, 421, 430, 398],
+             [390, 411, 406, 375],
+             [404, 376, 375, 405],
+             [376, 403, 400, 393],
+             [397, 430, 421, 377],
+             [482, 378, 377, 427],
+             [378, 484, 497, 499],
+             [499, 499, 397, 378],
+             [394, 461, 445, 382],
+             [409, 383, 382, 444],
+             [383, 406, 411, 391],
+             [385, 450, 443, 384],
+             [492, 399, 384, 453],
+             [457, 385, 412, 493],
+             [387, 442, 446, 386],
+             [494, 429, 386, 456],
+             [453, 387, 401, 492],
+             [389, 470, 451, 388],
+             [493, 410, 388, 457],
+             [471, 389, 462, 495],
+             [412, 390, 393, 399],
+             [462, 394, 391, 410],
+             [401, 392, 398, 429],
+             [396, 445, 461, 395],
+             [498, 496, 395, 460],
+             [456, 396, 431, 494],
+             [431, 397, 499, 496],
+             [399, 477, 481, 412],
+             [429, 483, 478, 401],
+             [410, 480, 490, 462],
+             [496, 497, 484, 431],
+             [489, 495, 491, 459],
+             [495, 460, 459, 471],
+             [460, 489, 498, 498],
+             [472, 472, 471, 491]]
+
+    assert C_r.table == table3
+    assert C_c.table == table3
+
+    # Group denoted by B2,4 from [2] Pg. 474
+    F, a, b = free_group("a, b")
+    B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \
+            (a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4])
+    C_r = coset_enumeration_r(B_2_4, [a])
+    C_c = coset_enumeration_c(B_2_4, [a])
+    index_r = 0
+    for i in range(len(C_r.p)):
+        if C_r.p[i] == i:
+            index_r += 1
+    assert index_r == 1024
+
+    index_c = 0
+    for i in range(len(C_c.p)):
+        if C_c.p[i] == i:
+            index_c += 1
+    assert index_c == 1024
+
+    # trivial Macdonald group G(2,2) from [2] Pg. 480
+    M = FpGroup(F, [b**-1*a**-1*b*a*b**-1*a*b*a**-2, a**-1*b**-1*a*b*a**-1*b*a*b**-2])
+    C_r = coset_enumeration_r(M, [a])
+    C_r.compress(); C_r.standardize()
+    C_c = coset_enumeration_c(M, [a])
+    C_c.compress(); C_c.standardize()
+    table4 = [[0, 0, 0, 0]]
+    assert C_r.table == table4
+    assert C_c.table == table4
+
+
+def test_look_ahead():
+    # Section 3.2 [Test Example] Example (d) from [2]
+    F, a, b, c = free_group("a, b, c")
+    f = FpGroup(F, [a**11, b**5, c**4, (a*c)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b])
+    H = [c, b, c**2]
+    table0 = [[1, 2, 0, 0, 0, 0],
+              [3, 0, 4, 5, 6, 7],
+              [0, 8, 9, 10, 11, 12],
+              [5, 1, 10, 13, 14, 15],
+              [16, 5, 16, 1, 17, 18],
+              [4, 3, 1, 8, 19, 20],
+              [12, 21, 22, 23, 24, 1],
+              [25, 26, 27, 28, 1, 24],
+              [2, 10, 5, 16, 22, 28],
+              [10, 13, 13, 2, 29, 30]]
+    CosetTable.max_stack_size = 10
+    C_c = coset_enumeration_c(f, H)
+    C_c.compress(); C_c.standardize()
+    assert C_c.table[: 10] == table0
+
+def test_modified_methods():
+    '''
+    Tests for modified coset table methods.
+    Example 5.7 from [1] Holt, D., Eick, B., O'Brien
+    "Handbook of Computational Group Theory".
+
+    '''
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x**3, y**5, (x*y)**2])
+    H = [x*y, x**-1*y**-1*x*y*x]
+    C = CosetTable(f, H)
+    C.modified_define(0, x)
+    identity = C._grp.identity
+    a_0 = C._grp.generators[0]
+    a_1 = C._grp.generators[1]
+
+    assert C.P == [[identity, None, None, None],
+                    [None, identity, None, None]]
+    assert C.table == [[1, None, None, None],
+                        [None, 0, None, None]]
+
+    C.modified_define(1, x)
+    assert C.table == [[1, None, None, None],
+                        [2, 0, None, None],
+                        [None, 1, None, None]]
+    assert C.P == [[identity, None, None, None],
+                    [identity, identity, None, None],
+                    [None, identity, None, None]]
+
+    C.modified_scan(0, x**3, C._grp.identity, fill=False)
+    assert C.P == [[identity, identity, None, None],
+                     [identity, identity, None, None],
+                     [identity, identity, None, None]]
+    assert C.table == [[1, 2, None, None],
+                        [2, 0, None, None],
+                        [0, 1, None, None]]
+
+    C.modified_scan(0, x*y, C._grp.generators[0], fill=False)
+    assert C.P == [[identity, identity, None, a_0**-1],
+                    [identity, identity, a_0, None],
+                    [identity, identity, None, None]]
+    assert C.table == [[1, 2, None, 1],
+                        [2, 0, 0, None],
+                        [0, 1, None, None]]
+
+    C.modified_define(2, y**-1)
+    assert C.table == [[1, 2, None, 1],
+                        [2, 0, 0, None],
+                        [0, 1, None, 3],
+                        [None, None, 2, None]]
+    assert C.P == [[identity, identity, None, a_0**-1],
+                    [identity, identity, a_0, None],
+                    [identity, identity, None, identity],
+                    [None, None, identity, None]]
+
+    C.modified_scan(0, x**-1*y**-1*x*y*x, C._grp.generators[1])
+    assert C.table == [[1, 2, None, 1],
+                        [2, 0, 0, None],
+                        [0, 1, None, 3],
+                        [3, 3, 2, None]]
+    assert C.P == [[identity, identity, None, a_0**-1],
+                    [identity, identity, a_0, None],
+                    [identity, identity, None, identity],
+                    [a_1, a_1**-1, identity, None]]
+
+    C.modified_scan(2, (x*y)**2, C._grp.identity)
+    assert C.table == [[1, 2, 3, 1],
+                        [2, 0, 0, None],
+                        [0, 1, None, 3],
+                        [3, 3, 2, 0]]
+    assert C.P == [[identity, identity, a_1**-1, a_0**-1],
+                    [identity, identity, a_0, None],
+                    [identity, identity, None, identity],
+                    [a_1, a_1**-1, identity, a_1]]
+
+    C.modified_define(2, y)
+    assert C.table == [[1, 2, 3, 1],
+                        [2, 0, 0, None],
+                        [0, 1, 4, 3],
+                        [3, 3, 2, 0],
+                        [None, None, None, 2]]
+    assert C.P == [[identity, identity, a_1**-1, a_0**-1],
+                    [identity, identity, a_0, None],
+                    [identity, identity, identity, identity],
+                    [a_1, a_1**-1, identity, a_1],
+                    [None, None, None, identity]]
+
+    C.modified_scan(0, y**5, C._grp.identity)
+    assert C.table == [[1, 2, 3, 1], [2, 0, 0, 4], [0, 1, 4, 3], [3, 3, 2, 0], [None, None, 1, 2]]
+    assert C.P == [[identity, identity, a_1**-1, a_0**-1],
+                    [identity, identity, a_0, a_0*a_1**-1],
+                    [identity, identity, identity, identity],
+                    [a_1, a_1**-1, identity, a_1],
+                    [None, None, a_1*a_0**-1, identity]]
+
+    C.modified_scan(1, (x*y)**2, C._grp.identity)
+    assert C.table == [[1, 2, 3, 1],
+                        [2, 0, 0, 4],
+                        [0, 1, 4, 3],
+                        [3, 3, 2, 0],
+                        [4, 4, 1, 2]]
+    assert C.P == [[identity, identity, a_1**-1, a_0**-1],
+                    [identity, identity, a_0, a_0*a_1**-1],
+                    [identity, identity, identity, identity],
+                    [a_1, a_1**-1, identity, a_1],
+                    [a_0*a_1**-1, a_1*a_0**-1, a_1*a_0**-1, identity]]
+
+    # Modified coset enumeration test
+    f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
+    C = coset_enumeration_r(f, [x])
+    C_m = modified_coset_enumeration_r(f, [x])
+    assert C_m.table == C.table
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_fp_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_fp_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..3f57bdf8eff92a3022d8e01cd74ce98575987929
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_fp_groups.py
@@ -0,0 +1,257 @@
+from sympy.core.singleton import S
+from sympy.combinatorics.fp_groups import (FpGroup, low_index_subgroups,
+                                   reidemeister_presentation, FpSubgroup,
+                                           simplify_presentation)
+from sympy.combinatorics.free_groups import (free_group, FreeGroup)
+
+from sympy.testing.pytest import slow
+
+"""
+References
+==========
+
+[1] Holt, D., Eick, B., O'Brien, E.
+"Handbook of Computational Group Theory"
+
+[2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson
+Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490.
+"Implementation and Analysis of the Todd-Coxeter Algorithm"
+
+[3] PROC. SECOND  INTERNAT. CONF. THEORY OF GROUPS, CANBERRA 1973,
+pp. 347-356. "A Reidemeister-Schreier program" by George Havas.
+http://staff.itee.uq.edu.au/havas/1973cdhw.pdf
+
+"""
+
+def test_low_index_subgroups():
+    F, x, y = free_group("x, y")
+
+    # Example 5.10 from [1] Pg. 194
+    f = FpGroup(F, [x**2, y**3, (x*y)**4])
+    L = low_index_subgroups(f, 4)
+    t1 = [[[0, 0, 0, 0]],
+          [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 3, 3]],
+          [[0, 0, 1, 2], [2, 2, 2, 0], [1, 1, 0, 1]],
+          [[1, 1, 0, 0], [0, 0, 1, 1]]]
+    for i in range(len(t1)):
+        assert L[i].table == t1[i]
+
+    f = FpGroup(F, [x**2, y**3, (x*y)**7])
+    L = low_index_subgroups(f, 15)
+    t2 = [[[0, 0, 0, 0]],
+           [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5],
+            [4, 4, 5, 3], [6, 6, 3, 4], [5, 5, 6, 6]],
+           [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5],
+            [6, 6, 5, 3], [5, 5, 3, 4], [4, 4, 6, 6]],
+           [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5],
+            [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11],
+            [11, 11, 9, 6], [9, 9, 6, 8], [12, 12, 11, 7], [8, 8, 7, 10],
+            [10, 10, 13, 14], [14, 14, 14, 12], [13, 13, 12, 13]],
+           [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5],
+            [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11],
+            [11, 11, 9, 6], [12, 12, 6, 8], [10, 10, 11, 7], [8, 8, 7, 10],
+            [9, 9, 13, 14], [14, 14, 14, 12], [13, 13, 12, 13]],
+           [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5],
+            [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11],
+            [11, 11, 9, 6], [12, 12, 6, 8], [13, 13, 11, 7], [8, 8, 7, 10],
+            [9, 9, 12, 12], [10, 10, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 3, 3], [2, 2, 5, 6]
+            , [7, 7, 6, 4], [8, 8, 4, 5], [5, 5, 8, 9], [6, 6, 9, 7],
+            [10, 10, 7, 8], [9, 9, 11, 12], [11, 11, 12, 10], [13, 13, 10, 11],
+            [12, 12, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 3, 3], [2, 2, 5, 6]
+            , [7, 7, 6, 4], [8, 8, 4, 5], [5, 5, 8, 9], [6, 6, 9, 7],
+            [10, 10, 7, 8], [9, 9, 11, 12], [13, 13, 12, 10], [12, 12, 10, 11],
+            [11, 11, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 4, 4]
+            , [7, 7, 6, 3], [8, 8, 3, 5], [5, 5, 8, 9], [6, 6, 9, 7],
+            [10, 10, 7, 8], [9, 9, 11, 12], [13, 13, 12, 10], [12, 12, 10, 11],
+            [11, 11, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [5, 5, 6, 3], [9, 9, 3, 5], [10, 10, 8, 4], [8, 8, 4, 7],
+            [6, 6, 10, 11], [7, 7, 11, 9], [12, 12, 9, 10], [11, 11, 13, 14],
+            [14, 14, 14, 12], [13, 13, 12, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [6, 6, 6, 3], [5, 5, 3, 5], [8, 8, 8, 4], [7, 7, 4, 7]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [9, 9, 6, 3], [6, 6, 3, 5], [10, 10, 8, 4], [11, 11, 4, 7],
+            [5, 5, 10, 12], [7, 7, 12, 9], [8, 8, 11, 11], [13, 13, 9, 10],
+            [12, 12, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [9, 9, 6, 3], [6, 6, 3, 5], [10, 10, 8, 4], [11, 11, 4, 7],
+            [5, 5, 12, 11], [7, 7, 10, 10], [8, 8, 9, 12], [13, 13, 11, 9],
+            [12, 12, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [9, 9, 6, 3], [10, 10, 3, 5], [7, 7, 8, 4], [11, 11, 4, 7],
+            [5, 5, 9, 9], [6, 6, 11, 12], [8, 8, 12, 10], [13, 13, 10, 11],
+            [12, 12, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [9, 9, 6, 3], [10, 10, 3, 5], [7, 7, 8, 4], [11, 11, 4, 7],
+            [5, 5, 12, 11], [6, 6, 10, 10], [8, 8, 9, 12], [13, 13, 11, 9],
+            [12, 12, 13, 13]],
+           [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8]
+            , [9, 9, 6, 3], [10, 10, 3, 5], [11, 11, 8, 4], [12, 12, 4, 7],
+            [5, 5, 9, 9], [6, 6, 12, 13], [7, 7, 11, 11], [8, 8, 13, 10],
+            [13, 13, 10, 12]],
+           [[1, 1, 0, 0], [0, 0, 2, 3], [4, 4, 3, 1], [5, 5, 1, 2], [2, 2, 4, 4]
+            , [3, 3, 6, 7], [7, 7, 7, 5], [6, 6, 5, 6]]]
+    for i  in range(len(t2)):
+        assert L[i].table == t2[i]
+
+    f = FpGroup(F, [x**2, y**3, (x*y)**7])
+    L = low_index_subgroups(f, 10, [x])
+    t3 = [[[0, 0, 0, 0]],
+          [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], [4, 4, 5, 3],
+           [6, 6, 3, 4], [5, 5, 6, 6]],
+          [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], [6, 6, 5, 3],
+           [5, 5, 3, 4], [4, 4, 6, 6]],
+          [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8],
+           [6, 6, 6, 3], [5, 5, 3, 5], [8, 8, 8, 4], [7, 7, 4, 7]]]
+    for i in range(len(t3)):
+        assert L[i].table == t3[i]
+
+
+def test_subgroup_presentations():
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x**3, y**5, (x*y)**2])
+    H = [x*y, x**-1*y**-1*x*y*x]
+    p1 = reidemeister_presentation(f, H)
+    assert str(p1) == "((y_1, y_2), (y_1**2, y_2**3, y_2*y_1*y_2*y_1*y_2*y_1))"
+
+    H = f.subgroup(H)
+    assert (H.generators, H.relators) == p1
+
+    f = FpGroup(F, [x**3, y**3, (x*y)**3])
+    H = [x*y, x*y**-1]
+    p2 = reidemeister_presentation(f, H)
+    assert str(p2) == "((x_0, y_0), (x_0**3, y_0**3, x_0*y_0*x_0*y_0*x_0*y_0))"
+
+    f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3])
+    H = [x]
+    p3 = reidemeister_presentation(f, H)
+    assert str(p3) == "((x_0,), (x_0**4,))"
+
+    f = FpGroup(F, [x**3*y**-3, (x*y)**3, (x*y**-1)**2])
+    H = [x]
+    p4 = reidemeister_presentation(f, H)
+    assert str(p4) == "((x_0,), (x_0**6,))"
+
+    # this presentation can be improved, the most simplified form
+    # of presentation is 
+    # See [2] Pg 474 group PSL_2(11)
+    # This is the group PSL_2(11)
+    F, a, b, c = free_group("a, b, c")
+    f = FpGroup(F, [a**11, b**5, c**4, (b*c**2)**2, (a*b*c)**3, (a**4*c**2)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b])
+    H = [a, b, c**2]
+    gens, rels = reidemeister_presentation(f, H)
+    assert str(gens) == "(b_1, c_3)"
+    assert len(rels) == 18
+
+
+@slow
+def test_order():
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x**4, y**2, x*y*x**-1*y])
+    assert f.order() == 8
+
+    f = FpGroup(F, [x*y*x**-1*y**-1, y**2])
+    assert f.order() is S.Infinity
+
+    F, a, b, c = free_group("a, b, c")
+    f = FpGroup(F, [a**250, b**2, c*b*c**-1*b, c**4, c**-1*a**-1*c*a, a**-1*b**-1*a*b])
+    assert f.order() == 2000
+
+    F, x = free_group("x")
+    f = FpGroup(F, [])
+    assert f.order() is S.Infinity
+
+    f = FpGroup(free_group('')[0], [])
+    assert f.order() == 1
+
+def test_fp_subgroup():
+    def _test_subgroup(K, T, S):
+        _gens = T(K.generators)
+        assert all(elem in S for elem in _gens)
+        assert T.is_injective()
+        assert T.image().order() == S.order()
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x**4, y**2, x*y*x**-1*y])
+    S = FpSubgroup(f, [x*y])
+    assert (x*y)**-3 in S
+    K, T = f.subgroup([x*y], homomorphism=True)
+    assert T(K.generators) == [y*x**-1]
+    _test_subgroup(K, T, S)
+
+    S = FpSubgroup(f, [x**-1*y*x])
+    assert x**-1*y**4*x in S
+    assert x**-1*y**4*x**2 not in S
+    K, T = f.subgroup([x**-1*y*x], homomorphism=True)
+    assert T(K.generators[0]**3) == y**3
+    _test_subgroup(K, T, S)
+
+    f = FpGroup(F, [x**3, y**5, (x*y)**2])
+    H = [x*y, x**-1*y**-1*x*y*x]
+    K, T = f.subgroup(H, homomorphism=True)
+    S = FpSubgroup(f, H)
+    _test_subgroup(K, T, S)
+
+def test_permutation_methods():
+    F, x, y = free_group("x, y")
+    # DihedralGroup(8)
+    G = FpGroup(F, [x**2, y**8, x*y*x**-1*y])
+    T = G._to_perm_group()[1]
+    assert T.is_isomorphism()
+    assert G.center() == [y**4]
+
+    # DiheadralGroup(4)
+    G = FpGroup(F, [x**2, y**4, x*y*x**-1*y])
+    S = FpSubgroup(G, G.normal_closure([x]))
+    assert x in S
+    assert y**-1*x*y in S
+
+    # Z_5xZ_4
+    G = FpGroup(F, [x*y*x**-1*y**-1, y**5, x**4])
+    assert G.is_abelian
+    assert G.is_solvable
+
+    # AlternatingGroup(5)
+    G = FpGroup(F, [x**3, y**2, (x*y)**5])
+    assert not G.is_solvable
+
+    # AlternatingGroup(4)
+    G = FpGroup(F, [x**3, y**2, (x*y)**3])
+    assert len(G.derived_series()) == 3
+    S = FpSubgroup(G, G.derived_subgroup())
+    assert S.order() == 4
+
+
+def test_simplify_presentation():
+    # ref #16083
+    G = simplify_presentation(FpGroup(FreeGroup([]), []))
+    assert not G.generators
+    assert not G.relators
+
+    # CyclicGroup(3)
+    # The second generator in  is trivial due to relators {x^2, x^5}
+    F, x, y = free_group("x, y")
+    G = simplify_presentation(FpGroup(F, [x**2, x**5, y**3]))
+    assert x in G.relators
+
+def test_cyclic():
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x*y, x**-1*y**-1*x*y*x])
+    assert f.is_cyclic
+    f = FpGroup(F, [x*y, x*y**-1])
+    assert f.is_cyclic
+    f = FpGroup(F, [x**4, y**2, x*y*x**-1*y])
+    assert not f.is_cyclic
+
+
+def test_abelian_invariants():
+    F, x, y = free_group("x, y")
+    f = FpGroup(F, [x*y, x**-1*y**-1*x*y*x])
+    assert f.abelian_invariants() == []
+    f = FpGroup(F, [x*y, x*y**-1])
+    assert f.abelian_invariants() == [2]
+    f = FpGroup(F, [x**4, y**2, x*y*x**-1*y])
+    assert f.abelian_invariants() == [2, 4]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_free_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_free_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..439be4b7c5e8bb5ff592c9b7f07773e82952b3d5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_free_groups.py
@@ -0,0 +1,226 @@
+from sympy.combinatorics.free_groups import free_group, FreeGroup
+from sympy.core import Symbol
+from sympy.testing.pytest import raises
+from sympy.core.numbers import oo
+
+F, x, y, z = free_group("x, y, z")
+
+
+def test_FreeGroup__init__():
+    x, y, z = map(Symbol, "xyz")
+
+    assert len(FreeGroup("x, y, z").generators) == 3
+    assert len(FreeGroup(x).generators) == 1
+    assert len(FreeGroup(("x", "y", "z"))) == 3
+    assert len(FreeGroup((x, y, z)).generators) == 3
+
+
+def test_FreeGroup__getnewargs__():
+    x, y, z = map(Symbol, "xyz")
+    assert FreeGroup("x, y, z").__getnewargs__() == ((x, y, z),)
+
+
+def test_free_group():
+    G, a, b, c = free_group("a, b, c")
+    assert F.generators == (x, y, z)
+    assert x*z**2 in F
+    assert x in F
+    assert y*z**-1 in F
+    assert (y*z)**0 in F
+    assert a not in F
+    assert a**0 not in F
+    assert len(F) == 3
+    assert str(F) == ''
+    assert not F == G
+    assert F.order() is oo
+    assert F.is_abelian == False
+    assert F.center() == {F.identity}
+
+    (e,) = free_group("")
+    assert e.order() == 1
+    assert e.generators == ()
+    assert e.elements == {e.identity}
+    assert e.is_abelian == True
+
+
+def test_FreeGroup__hash__():
+    assert hash(F)
+
+
+def test_FreeGroup__eq__():
+    assert free_group("x, y, z")[0] == free_group("x, y, z")[0]
+    assert free_group("x, y, z")[0] is free_group("x, y, z")[0]
+
+    assert free_group("x, y, z")[0] != free_group("a, x, y")[0]
+    assert free_group("x, y, z")[0] is not free_group("a, x, y")[0]
+
+    assert free_group("x, y")[0] != free_group("x, y, z")[0]
+    assert free_group("x, y")[0] is not free_group("x, y, z")[0]
+
+    assert free_group("x, y, z")[0] != free_group("x, y")[0]
+    assert free_group("x, y, z")[0] is not free_group("x, y")[0]
+
+
+def test_FreeGroup__getitem__():
+    assert F[0:] == FreeGroup("x, y, z")
+    assert F[1:] == FreeGroup("y, z")
+    assert F[2:] == FreeGroup("z")
+
+
+def test_FreeGroupElm__hash__():
+    assert hash(x*y*z)
+
+
+def test_FreeGroupElm_copy():
+    f = x*y*z**3
+    g = f.copy()
+    h = x*y*z**7
+
+    assert f == g
+    assert f != h
+
+
+def test_FreeGroupElm_inverse():
+    assert x.inverse() == x**-1
+    assert (x*y).inverse() == y**-1*x**-1
+    assert (y*x*y**-1).inverse() == y*x**-1*y**-1
+    assert (y**2*x**-1).inverse() == x*y**-2
+
+
+def test_FreeGroupElm_type_error():
+    raises(TypeError, lambda: 2/x)
+    raises(TypeError, lambda: x**2 + y**2)
+    raises(TypeError, lambda: x/2)
+
+
+def test_FreeGroupElm_methods():
+    assert (x**0).order() == 1
+    assert (y**2).order() is oo
+    assert (x**-1*y).commutator(x) == y**-1*x**-1*y*x
+    assert len(x**2*y**-1) == 3
+    assert len(x**-1*y**3*z) == 5
+
+
+def test_FreeGroupElm_eliminate_word():
+    w = x**5*y*x**2*y**-4*x
+    assert w.eliminate_word( x, x**2 ) == x**10*y*x**4*y**-4*x**2
+    w3 = x**2*y**3*x**-1*y
+    assert w3.eliminate_word(x, x**2) == x**4*y**3*x**-2*y
+    assert w3.eliminate_word(x, y) == y**5
+    assert w3.eliminate_word(x, y**4) == y**8
+    assert w3.eliminate_word(y, x**-1) == x**-3
+    assert w3.eliminate_word(x, y*z) == y*z*y*z*y**3*z**-1
+    assert (y**-3).eliminate_word(y, x**-1*z**-1) == z*x*z*x*z*x
+    #assert w3.eliminate_word(x, y*x) == y*x*y*x**2*y*x*y*x*y*x*z**3
+    #assert w3.eliminate_word(x, x*y) == x*y*x**2*y*x*y*x*y*x*y*z**3
+
+
+def test_FreeGroupElm_array_form():
+    assert (x*z).array_form == ((Symbol('x'), 1), (Symbol('z'), 1))
+    assert (x**2*z*y*x**-2).array_form == \
+        ((Symbol('x'), 2), (Symbol('z'), 1), (Symbol('y'), 1), (Symbol('x'), -2))
+    assert (x**-2*y**-1).array_form == ((Symbol('x'), -2), (Symbol('y'), -1))
+
+
+def test_FreeGroupElm_letter_form():
+    assert (x**3).letter_form == (Symbol('x'), Symbol('x'), Symbol('x'))
+    assert (x**2*z**-2*x).letter_form == \
+        (Symbol('x'), Symbol('x'), -Symbol('z'), -Symbol('z'), Symbol('x'))
+
+
+def test_FreeGroupElm_ext_rep():
+    assert (x**2*z**-2*x).ext_rep == \
+        (Symbol('x'), 2, Symbol('z'), -2, Symbol('x'), 1)
+    assert (x**-2*y**-1).ext_rep == (Symbol('x'), -2, Symbol('y'), -1)
+    assert (x*z).ext_rep == (Symbol('x'), 1, Symbol('z'), 1)
+
+
+def test_FreeGroupElm__mul__pow__():
+    x1 = x.group.dtype(((Symbol('x'), 1),))
+    assert x**2 == x1*x
+
+    assert (x**2*y*x**-2)**4 == x**2*y**4*x**-2
+    assert (x**2)**2 == x**4
+    assert (x**-1)**-1 == x
+    assert (x**-1)**0 == F.identity
+    assert (y**2)**-2 == y**-4
+
+    assert x**2*x**-1 == x
+    assert x**2*y**2*y**-1 == x**2*y
+    assert x*x**-1 == F.identity
+
+    assert x/x == F.identity
+    assert x/x**2 == x**-1
+    assert (x**2*y)/(x**2*y**-1) == x**2*y**2*x**-2
+    assert (x**2*y)/(y**-1*x**2) == x**2*y*x**-2*y
+
+    assert x*(x**-1*y*z*y**-1) == y*z*y**-1
+    assert x**2*(x**-2*y**-1*z**2*y) == y**-1*z**2*y
+
+    a = F.identity
+    for n in range(10):
+        assert a == x**n
+        assert a**-1 == x**-n
+        a *= x
+
+
+def test_FreeGroupElm__len__():
+    assert len(x**5*y*x**2*y**-4*x) == 13
+    assert len(x**17) == 17
+    assert len(y**0) == 0
+
+
+def test_FreeGroupElm_comparison():
+    assert not (x*y == y*x)
+    assert x**0 == y**0
+
+    assert x**2 < y**3
+    assert not x**3 < y**2
+    assert x*y < x**2*y
+    assert x**2*y**2 < y**4
+    assert not y**4 < y**-4
+    assert not y**4 < x**-4
+    assert y**-2 < y**2
+
+    assert x**2 <= y**2
+    assert x**2 <= x**2
+
+    assert not y*z > z*y
+    assert x > x**-1
+
+    assert not x**2 >= y**2
+
+
+def test_FreeGroupElm_syllables():
+    w = x**5*y*x**2*y**-4*x
+    assert w.number_syllables() == 5
+    assert w.exponent_syllable(2) == 2
+    assert w.generator_syllable(3) == Symbol('y')
+    assert w.sub_syllables(1, 2) == y
+    assert w.sub_syllables(3, 3) == F.identity
+
+
+def test_FreeGroup_exponents():
+    w1 = x**2*y**3
+    assert w1.exponent_sum(x) == 2
+    assert w1.exponent_sum(x**-1) == -2
+    assert w1.generator_count(x) == 2
+
+    w2 = x**2*y**4*x**-3
+    assert w2.exponent_sum(x) == -1
+    assert w2.generator_count(x) == 5
+
+
+def test_FreeGroup_generators():
+    assert (x**2*y**4*z**-1).contains_generators() == {x, y, z}
+    assert (x**-1*y**3).contains_generators() == {x, y}
+
+
+def test_FreeGroupElm_words():
+    w = x**5*y*x**2*y**-4*x
+    assert w.subword(2, 6) == x**3*y
+    assert w.subword(3, 2) == F.identity
+    assert w.subword(6, 10) == x**2*y**-2
+
+    assert w.substituted_word(0, 7, y**-1) == y**-1*x*y**-4*x
+    assert w.substituted_word(0, 7, y**2*x) == y**2*x**2*y**-4*x
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_galois.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_galois.py
new file mode 100644
index 0000000000000000000000000000000000000000..0d2ac29a846db88444d275b72a85ce3debaeaf05
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_galois.py
@@ -0,0 +1,82 @@
+"""Test groups defined by the galois module. """
+
+from sympy.combinatorics.galois import (
+    S4TransitiveSubgroups, S5TransitiveSubgroups, S6TransitiveSubgroups,
+    find_transitive_subgroups_of_S6,
+)
+from sympy.combinatorics.homomorphisms import is_isomorphic
+from sympy.combinatorics.named_groups import (
+    SymmetricGroup, AlternatingGroup, CyclicGroup,
+)
+
+
+def test_four_group():
+    G = S4TransitiveSubgroups.V.get_perm_group()
+    A4 = AlternatingGroup(4)
+    assert G.is_subgroup(A4)
+    assert G.degree == 4
+    assert G.is_transitive()
+    assert G.order() == 4
+    assert not G.is_cyclic
+
+
+def test_M20():
+    G = S5TransitiveSubgroups.M20.get_perm_group()
+    S5 = SymmetricGroup(5)
+    A5 = AlternatingGroup(5)
+    assert G.is_subgroup(S5)
+    assert not G.is_subgroup(A5)
+    assert G.degree == 5
+    assert G.is_transitive()
+    assert G.order() == 20
+
+
+# Setting this True means that for each of the transitive subgroups of S6,
+# we run a test not only on the fixed representation, but also on one freshly
+# generated by the search procedure.
+INCLUDE_SEARCH_REPS = False
+S6_randomized = {}
+if INCLUDE_SEARCH_REPS:
+    S6_randomized = find_transitive_subgroups_of_S6(*list(S6TransitiveSubgroups))
+
+
+def get_versions_of_S6_subgroup(name):
+    vers = [name.get_perm_group()]
+    if INCLUDE_SEARCH_REPS:
+        vers.append(S6_randomized[name])
+    return vers
+
+
+def test_S6_transitive_subgroups():
+    """
+    Test enough characteristics to distinguish all 16 transitive subgroups.
+    """
+    ts = S6TransitiveSubgroups
+    A6 = AlternatingGroup(6)
+    for name, alt, order, is_isom, not_isom in [
+        (ts.C6,     False,    6, CyclicGroup(6), None),
+        (ts.S3,     False,    6, SymmetricGroup(3), None),
+        (ts.D6,     False,   12, None, None),
+        (ts.A4,     True,    12, None, None),
+        (ts.G18,    False,   18, None, None),
+        (ts.A4xC2,  False,   24, None, SymmetricGroup(4)),
+        (ts.S4m,    False,   24, SymmetricGroup(4), None),
+        (ts.S4p,    True,    24, None, None),
+        (ts.G36m,   False,   36, None, None),
+        (ts.G36p,   True,    36, None, None),
+        (ts.S4xC2,  False,   48, None, None),
+        (ts.PSL2F5, True,    60, None, None),
+        (ts.G72,    False,   72, None, None),
+        (ts.PGL2F5, False,  120, None, None),
+        (ts.A6,     True,   360, None, None),
+        (ts.S6,     False,  720, None, None),
+    ]:
+        for G in get_versions_of_S6_subgroup(name):
+            assert G.is_transitive()
+            assert G.degree == 6
+            assert G.is_subgroup(A6) is alt
+            assert G.order() == order
+            if is_isom:
+                assert is_isomorphic(G, is_isom)
+            if not_isom:
+                assert not is_isomorphic(G, not_isom)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_generators.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_generators.py
new file mode 100644
index 0000000000000000000000000000000000000000..795ef8f08f6ec212879f528c6a0c2f0bd73037f0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_generators.py
@@ -0,0 +1,105 @@
+from sympy.combinatorics.generators import symmetric, cyclic, alternating, \
+    dihedral, rubik
+from sympy.combinatorics.permutations import Permutation
+from sympy.testing.pytest import raises
+
+def test_generators():
+
+    assert list(cyclic(6)) == [
+        Permutation([0, 1, 2, 3, 4, 5]),
+        Permutation([1, 2, 3, 4, 5, 0]),
+        Permutation([2, 3, 4, 5, 0, 1]),
+        Permutation([3, 4, 5, 0, 1, 2]),
+        Permutation([4, 5, 0, 1, 2, 3]),
+        Permutation([5, 0, 1, 2, 3, 4])]
+
+    assert list(cyclic(10)) == [
+        Permutation([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
+        Permutation([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),
+        Permutation([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]),
+        Permutation([3, 4, 5, 6, 7, 8, 9, 0, 1, 2]),
+        Permutation([4, 5, 6, 7, 8, 9, 0, 1, 2, 3]),
+        Permutation([5, 6, 7, 8, 9, 0, 1, 2, 3, 4]),
+        Permutation([6, 7, 8, 9, 0, 1, 2, 3, 4, 5]),
+        Permutation([7, 8, 9, 0, 1, 2, 3, 4, 5, 6]),
+        Permutation([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]),
+        Permutation([9, 0, 1, 2, 3, 4, 5, 6, 7, 8])]
+
+    assert list(alternating(4)) == [
+        Permutation([0, 1, 2, 3]),
+        Permutation([0, 2, 3, 1]),
+        Permutation([0, 3, 1, 2]),
+        Permutation([1, 0, 3, 2]),
+        Permutation([1, 2, 0, 3]),
+        Permutation([1, 3, 2, 0]),
+        Permutation([2, 0, 1, 3]),
+        Permutation([2, 1, 3, 0]),
+        Permutation([2, 3, 0, 1]),
+        Permutation([3, 0, 2, 1]),
+        Permutation([3, 1, 0, 2]),
+        Permutation([3, 2, 1, 0])]
+
+    assert list(symmetric(3)) == [
+        Permutation([0, 1, 2]),
+        Permutation([0, 2, 1]),
+        Permutation([1, 0, 2]),
+        Permutation([1, 2, 0]),
+        Permutation([2, 0, 1]),
+        Permutation([2, 1, 0])]
+
+    assert list(symmetric(4)) == [
+        Permutation([0, 1, 2, 3]),
+        Permutation([0, 1, 3, 2]),
+        Permutation([0, 2, 1, 3]),
+        Permutation([0, 2, 3, 1]),
+        Permutation([0, 3, 1, 2]),
+        Permutation([0, 3, 2, 1]),
+        Permutation([1, 0, 2, 3]),
+        Permutation([1, 0, 3, 2]),
+        Permutation([1, 2, 0, 3]),
+        Permutation([1, 2, 3, 0]),
+        Permutation([1, 3, 0, 2]),
+        Permutation([1, 3, 2, 0]),
+        Permutation([2, 0, 1, 3]),
+        Permutation([2, 0, 3, 1]),
+        Permutation([2, 1, 0, 3]),
+        Permutation([2, 1, 3, 0]),
+        Permutation([2, 3, 0, 1]),
+        Permutation([2, 3, 1, 0]),
+        Permutation([3, 0, 1, 2]),
+        Permutation([3, 0, 2, 1]),
+        Permutation([3, 1, 0, 2]),
+        Permutation([3, 1, 2, 0]),
+        Permutation([3, 2, 0, 1]),
+        Permutation([3, 2, 1, 0])]
+
+    assert list(dihedral(1)) == [
+        Permutation([0, 1]), Permutation([1, 0])]
+
+    assert list(dihedral(2)) == [
+        Permutation([0, 1, 2, 3]),
+        Permutation([1, 0, 3, 2]),
+        Permutation([2, 3, 0, 1]),
+        Permutation([3, 2, 1, 0])]
+
+    assert list(dihedral(3)) == [
+        Permutation([0, 1, 2]),
+        Permutation([2, 1, 0]),
+        Permutation([1, 2, 0]),
+        Permutation([0, 2, 1]),
+        Permutation([2, 0, 1]),
+        Permutation([1, 0, 2])]
+
+    assert list(dihedral(5)) == [
+        Permutation([0, 1, 2, 3, 4]),
+        Permutation([4, 3, 2, 1, 0]),
+        Permutation([1, 2, 3, 4, 0]),
+        Permutation([0, 4, 3, 2, 1]),
+        Permutation([2, 3, 4, 0, 1]),
+        Permutation([1, 0, 4, 3, 2]),
+        Permutation([3, 4, 0, 1, 2]),
+        Permutation([2, 1, 0, 4, 3]),
+        Permutation([4, 0, 1, 2, 3]),
+        Permutation([3, 2, 1, 0, 4])]
+
+    raises(ValueError, lambda: rubik(1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_graycode.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_graycode.py
new file mode 100644
index 0000000000000000000000000000000000000000..a754a3c401b07c9c12cb9bdeeefdfc94f6cb8b5c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_graycode.py
@@ -0,0 +1,72 @@
+from sympy.combinatorics.graycode import (GrayCode, bin_to_gray,
+    random_bitstring, get_subset_from_bitstring, graycode_subsets,
+    gray_to_bin)
+from sympy.testing.pytest import raises
+
+def test_graycode():
+    g = GrayCode(2)
+    got = []
+    for i in g.generate_gray():
+        if i.startswith('0'):
+            g.skip()
+        got.append(i)
+    assert got == '00 11 10'.split()
+    a = GrayCode(6)
+    assert a.current == '0'*6
+    assert a.rank == 0
+    assert len(list(a.generate_gray())) == 64
+    codes = ['011001', '011011', '011010',
+    '011110', '011111', '011101', '011100', '010100', '010101', '010111',
+    '010110', '010010', '010011', '010001', '010000', '110000', '110001',
+    '110011', '110010', '110110', '110111', '110101', '110100', '111100',
+    '111101', '111111', '111110', '111010', '111011', '111001', '111000',
+    '101000', '101001', '101011', '101010', '101110', '101111', '101101',
+    '101100', '100100', '100101', '100111', '100110', '100010', '100011',
+    '100001', '100000']
+    assert list(a.generate_gray(start='011001')) == codes
+    assert list(
+        a.generate_gray(rank=GrayCode(6, start='011001').rank)) == codes
+    assert a.next().current == '000001'
+    assert a.next(2).current == '000011'
+    assert a.next(-1).current == '100000'
+
+    a = GrayCode(5, start='10010')
+    assert a.rank == 28
+    a = GrayCode(6, start='101000')
+    assert a.rank == 48
+
+    assert GrayCode(6, rank=4).current == '000110'
+    assert GrayCode(6, rank=4).rank == 4
+    assert [GrayCode(4, start=s).rank for s in
+            GrayCode(4).generate_gray()] == [0, 1, 2, 3, 4, 5, 6, 7, 8,
+                                             9, 10, 11, 12, 13, 14, 15]
+    a = GrayCode(15, rank=15)
+    assert a.current == '000000000001000'
+
+    assert bin_to_gray('111') == '100'
+
+    a = random_bitstring(5)
+    assert type(a) is str
+    assert len(a) == 5
+    assert all(i in ['0', '1'] for i in a)
+
+    assert get_subset_from_bitstring(
+        ['a', 'b', 'c', 'd'], '0011') == ['c', 'd']
+    assert get_subset_from_bitstring('abcd', '1001') == ['a', 'd']
+    assert list(graycode_subsets(['a', 'b', 'c'])) == \
+        [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'],
+         ['a', 'c'], ['a']]
+
+    raises(ValueError, lambda: GrayCode(0))
+    raises(ValueError, lambda: GrayCode(2.2))
+    raises(ValueError, lambda: GrayCode(2, start=[1, 1, 0]))
+    raises(ValueError, lambda: GrayCode(2, rank=2.5))
+    raises(ValueError, lambda: get_subset_from_bitstring(['c', 'a', 'c'], '1100'))
+    raises(ValueError, lambda: list(GrayCode(3).generate_gray(start="1111")))
+
+
+def test_live_issue_117():
+    assert bin_to_gray('0100') == '0110'
+    assert bin_to_gray('0101') == '0111'
+    for bits in ('0100', '0101'):
+        assert gray_to_bin(bin_to_gray(bits)) == bits
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_group_constructs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_group_constructs.py
new file mode 100644
index 0000000000000000000000000000000000000000..d0f7d6394bbc2e285650ea95d36be8e2ed5ea69e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_group_constructs.py
@@ -0,0 +1,15 @@
+from sympy.combinatorics.group_constructs import DirectProduct
+from sympy.combinatorics.named_groups import CyclicGroup, DihedralGroup
+
+
+def test_direct_product_n():
+    C = CyclicGroup(4)
+    D = DihedralGroup(4)
+    G = DirectProduct(C, C, C)
+    assert G.order() == 64
+    assert G.degree == 12
+    assert len(G.orbits()) == 3
+    assert G.is_abelian is True
+    H = DirectProduct(D, C)
+    assert H.order() == 32
+    assert H.is_abelian is False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_group_numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_group_numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..743f1dcc8b642c19706687eeeddf6c9070b59166
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_group_numbers.py
@@ -0,0 +1,110 @@
+from sympy.combinatorics.group_numbers import (is_nilpotent_number,
+    is_abelian_number, is_cyclic_number, _holder_formula, groups_count)
+from sympy.ntheory.factor_ import factorint
+from sympy.ntheory.generate import prime
+from sympy.testing.pytest import raises
+from sympy import randprime
+
+
+def test_is_nilpotent_number():
+    assert is_nilpotent_number(21) == False
+    assert is_nilpotent_number(randprime(1, 30)**12) == True
+    raises(ValueError, lambda: is_nilpotent_number(-5))
+
+    A056867	= [1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19,
+               23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45,
+               47, 49, 51, 53, 59, 61, 64, 65, 67, 69, 71, 73,
+               77, 79, 81, 83, 85, 87, 89, 91, 95, 97, 99]
+    for n in range(1, 100):
+        assert is_nilpotent_number(n) == (n in A056867)
+
+
+def test_is_abelian_number():
+    assert is_abelian_number(4) == True
+    assert is_abelian_number(randprime(1, 2000)**2) == True
+    assert is_abelian_number(randprime(1000, 100000)) == True
+    assert is_abelian_number(60) == False
+    assert is_abelian_number(24) == False
+    raises(ValueError, lambda: is_abelian_number(-5))
+
+    A051532 = [1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25,
+               29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53,
+               59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87,
+               89, 91, 95, 97, 99]
+    for n in range(1, 100):
+        assert is_abelian_number(n) == (n in A051532)
+
+
+A003277 = [1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29,
+           31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61,
+           65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89,
+           91, 95, 97]
+
+
+def test_is_cyclic_number():
+    assert is_cyclic_number(15) == True
+    assert is_cyclic_number(randprime(1, 2000)**2) == False
+    assert is_cyclic_number(randprime(1000, 100000)) == True
+    assert is_cyclic_number(4) == False
+    raises(ValueError, lambda: is_cyclic_number(-5))
+
+    for n in range(1, 100):
+        assert is_cyclic_number(n) == (n in A003277)
+
+
+def test_holder_formula():
+    # semiprime
+    assert _holder_formula({3, 5}) == 1
+    assert _holder_formula({5, 11}) == 2
+    # n in A003277 is always 1
+    for n in A003277:
+        assert _holder_formula(set(factorint(n).keys())) == 1
+    # otherwise
+    assert _holder_formula({2, 3, 5, 7}) == 12
+
+
+def test_groups_count():
+    A000001 = [0, 1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1,
+               2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2,
+               5, 4, 1, 4, 1, 51, 1, 2, 1, 14, 1, 2, 2,
+               14, 1, 6, 1, 4, 2, 2, 1, 52, 2, 5, 1, 5,
+               1, 15, 2, 13, 2, 2, 1, 13, 1, 2, 4, 267,
+               1, 4, 1, 5, 1, 4, 1, 50, 1, 2, 3, 4, 1,
+               6, 1, 52, 15, 2, 1, 15, 1, 2, 1, 12, 1,
+               10, 1, 4, 2]
+    for n in range(1, len(A000001)):
+        try:
+            assert groups_count(n) == A000001[n]
+        except ValueError:
+            pass
+
+    A000679 = [1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289]
+    for e in range(1, len(A000679)):
+        assert groups_count(2**e) == A000679[e]
+
+    A090091 = [1, 1, 2, 5, 15, 67, 504, 9310, 1396077, 5937876645]
+    for e in range(1, len(A090091)):
+        assert groups_count(3**e) == A090091[e]
+
+    A090130 = [1, 1, 2, 5, 15, 77, 684, 34297]
+    for e in range(1, len(A090130)):
+        assert groups_count(5**e) == A090130[e]
+
+    A090140 = [1, 1, 2, 5, 15, 83, 860, 113147]
+    for e in range(1, len(A090140)):
+        assert groups_count(7**e) == A090140[e]
+
+    A232105 = [51, 67, 77, 83, 87, 97, 101, 107, 111, 125, 131,
+               145, 149, 155, 159, 173, 183, 193, 203, 207, 217]
+    for i in range(len(A232105)):
+        assert groups_count(prime(i+1)**5) == A232105[i]
+
+    A232106 = [267, 504, 684, 860, 1192, 1476, 1944, 2264, 2876,
+               4068, 4540, 6012, 7064, 7664, 8852, 10908, 13136]
+    for i in range(len(A232106)):
+        assert groups_count(prime(i+1)**6) == A232106[i]
+
+    A232107 = [2328, 9310, 34297, 113147, 750735, 1600573,
+               5546909, 9380741, 23316851, 71271069, 98488755]
+    for i in range(len(A232107)):
+        assert groups_count(prime(i+1)**7) == A232107[i]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_homomorphisms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_homomorphisms.py
new file mode 100644
index 0000000000000000000000000000000000000000..0936bbddf46a16dccdfbaebda8d1c675c131f05a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_homomorphisms.py
@@ -0,0 +1,114 @@
+from sympy.combinatorics import Permutation
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.combinatorics.homomorphisms import homomorphism, group_isomorphism, is_isomorphic
+from sympy.combinatorics.free_groups import free_group
+from sympy.combinatorics.fp_groups import FpGroup
+from sympy.combinatorics.named_groups import AlternatingGroup, DihedralGroup, CyclicGroup
+from sympy.testing.pytest import raises
+
+def test_homomorphism():
+    # FpGroup -> PermutationGroup
+    F, a, b = free_group("a, b")
+    G = FpGroup(F, [a**3, b**3, (a*b)**2])
+
+    c = Permutation(3)(0, 1, 2)
+    d = Permutation(3)(1, 2, 3)
+    A = AlternatingGroup(4)
+    T = homomorphism(G, A, [a, b], [c, d])
+    assert T(a*b**2*a**-1) == c*d**2*c**-1
+    assert T.is_isomorphism()
+    assert T(T.invert(Permutation(3)(0, 2, 3))) == Permutation(3)(0, 2, 3)
+
+    T = homomorphism(G, AlternatingGroup(4), G.generators)
+    assert T.is_trivial()
+    assert T.kernel().order() == G.order()
+
+    E, e = free_group("e")
+    G = FpGroup(E, [e**8])
+    P = PermutationGroup([Permutation(0, 1, 2, 3), Permutation(0, 2)])
+    T = homomorphism(G, P, [e], [Permutation(0, 1, 2, 3)])
+    assert T.image().order() == 4
+    assert T(T.invert(Permutation(0, 2)(1, 3))) == Permutation(0, 2)(1, 3)
+
+    T = homomorphism(E, AlternatingGroup(4), E.generators, [c])
+    assert T.invert(c**2) == e**-1 #order(c) == 3 so c**2 == c**-1
+
+    # FreeGroup -> FreeGroup
+    T = homomorphism(F, E, [a], [e])
+    assert T(a**-2*b**4*a**2).is_identity
+
+    # FreeGroup -> FpGroup
+    G = FpGroup(F, [a*b*a**-1*b**-1])
+    T = homomorphism(F, G, F.generators, G.generators)
+    assert T.invert(a**-1*b**-1*a**2) == a*b**-1
+
+    # PermutationGroup -> PermutationGroup
+    D = DihedralGroup(8)
+    p = Permutation(0, 1, 2, 3, 4, 5, 6, 7)
+    P = PermutationGroup(p)
+    T = homomorphism(P, D, [p], [p])
+    assert T.is_injective()
+    assert not T.is_isomorphism()
+    assert T.invert(p**3) == p**3
+
+    T2 = homomorphism(F, P, [F.generators[0]], P.generators)
+    T = T.compose(T2)
+    assert T.domain == F
+    assert T.codomain == D
+    assert T(a*b) == p
+
+    D3 = DihedralGroup(3)
+    T = homomorphism(D3, D3, D3.generators, D3.generators)
+    assert T.is_isomorphism()
+
+
+def test_isomorphisms():
+
+    F, a, b = free_group("a, b")
+    E, c, d = free_group("c, d")
+    # Infinite groups with differently ordered relators.
+    G = FpGroup(F, [a**2, b**3])
+    H = FpGroup(F, [b**3, a**2])
+    assert is_isomorphic(G, H)
+
+    # Trivial Case
+    # FpGroup -> FpGroup
+    H = FpGroup(F, [a**3, b**3, (a*b)**2])
+    F, c, d = free_group("c, d")
+    G = FpGroup(F, [c**3, d**3, (c*d)**2])
+    check, T =  group_isomorphism(G, H)
+    assert check
+    assert T(c**3*d**2) == a**3*b**2
+
+    # FpGroup -> PermutationGroup
+    # FpGroup is converted to the equivalent isomorphic group.
+    F, a, b = free_group("a, b")
+    G = FpGroup(F, [a**3, b**3, (a*b)**2])
+    H = AlternatingGroup(4)
+    check, T = group_isomorphism(G, H)
+    assert check
+    assert T(b*a*b**-1*a**-1*b**-1) == Permutation(0, 2, 3)
+    assert T(b*a*b*a**-1*b**-1) == Permutation(0, 3, 2)
+
+    # PermutationGroup -> PermutationGroup
+    D = DihedralGroup(8)
+    p = Permutation(0, 1, 2, 3, 4, 5, 6, 7)
+    P = PermutationGroup(p)
+    assert not is_isomorphic(D, P)
+
+    A = CyclicGroup(5)
+    B = CyclicGroup(7)
+    assert not is_isomorphic(A, B)
+
+    # Two groups of the same prime order are isomorphic to each other.
+    G = FpGroup(F, [a, b**5])
+    H = CyclicGroup(5)
+    assert G.order() == H.order()
+    assert is_isomorphic(G, H)
+
+
+def test_check_homomorphism():
+    a = Permutation(1,2,3,4)
+    b = Permutation(1,3)
+    G = PermutationGroup([a, b])
+    raises(ValueError, lambda: homomorphism(G, G, [a], [a]))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_named_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_named_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..59bcb6ef3f020335de76d7a72152a0b58cbc6976
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_named_groups.py
@@ -0,0 +1,70 @@
+from sympy.combinatorics.named_groups import (SymmetricGroup, CyclicGroup,
+                                              DihedralGroup, AlternatingGroup,
+                                              AbelianGroup, RubikGroup)
+from sympy.testing.pytest import raises
+
+
+def test_SymmetricGroup():
+    G = SymmetricGroup(5)
+    elements = list(G.generate())
+    assert (G.generators[0]).size == 5
+    assert len(elements) == 120
+    assert G.is_solvable is False
+    assert G.is_abelian is False
+    assert G.is_nilpotent is False
+    assert G.is_transitive() is True
+    H = SymmetricGroup(1)
+    assert H.order() == 1
+    L = SymmetricGroup(2)
+    assert L.order() == 2
+
+
+def test_CyclicGroup():
+    G = CyclicGroup(10)
+    elements = list(G.generate())
+    assert len(elements) == 10
+    assert (G.derived_subgroup()).order() == 1
+    assert G.is_abelian is True
+    assert G.is_solvable is True
+    assert G.is_nilpotent is True
+    H = CyclicGroup(1)
+    assert H.order() == 1
+    L = CyclicGroup(2)
+    assert L.order() == 2
+
+
+def test_DihedralGroup():
+    G = DihedralGroup(6)
+    elements = list(G.generate())
+    assert len(elements) == 12
+    assert G.is_transitive() is True
+    assert G.is_abelian is False
+    assert G.is_solvable is True
+    assert G.is_nilpotent is False
+    H = DihedralGroup(1)
+    assert H.order() == 2
+    L = DihedralGroup(2)
+    assert L.order() == 4
+    assert L.is_abelian is True
+    assert L.is_nilpotent is True
+
+
+def test_AlternatingGroup():
+    G = AlternatingGroup(5)
+    elements = list(G.generate())
+    assert len(elements) == 60
+    assert [perm.is_even for perm in elements] == [True]*60
+    H = AlternatingGroup(1)
+    assert H.order() == 1
+    L = AlternatingGroup(2)
+    assert L.order() == 1
+
+
+def test_AbelianGroup():
+    A = AbelianGroup(3, 3, 3)
+    assert A.order() == 27
+    assert A.is_abelian is True
+
+
+def test_RubikGroup():
+    raises(ValueError, lambda: RubikGroup(1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_partitions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_partitions.py
new file mode 100644
index 0000000000000000000000000000000000000000..32e70e53a53aadbb17c8292bbef8f52d1144d6e0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_partitions.py
@@ -0,0 +1,118 @@
+from sympy.core.sorting import ordered, default_sort_key
+from sympy.combinatorics.partitions import (Partition, IntegerPartition,
+                                            RGS_enum, RGS_unrank, RGS_rank,
+                                            random_integer_partition)
+from sympy.testing.pytest import raises
+from sympy.utilities.iterables import partitions
+from sympy.sets.sets import Set, FiniteSet
+
+
+def test_partition_constructor():
+    raises(ValueError, lambda: Partition([1, 1, 2]))
+    raises(ValueError, lambda: Partition([1, 2, 3], [2, 3, 4]))
+    raises(ValueError, lambda: Partition(1, 2, 3))
+    raises(ValueError, lambda: Partition(*list(range(3))))
+
+    assert Partition([1, 2, 3], [4, 5]) == Partition([4, 5], [1, 2, 3])
+    assert Partition({1, 2, 3}, {4, 5}) == Partition([1, 2, 3], [4, 5])
+
+    a = FiniteSet(1, 2, 3)
+    b = FiniteSet(4, 5)
+    assert Partition(a, b) == Partition([1, 2, 3], [4, 5])
+    assert Partition({a, b}) == Partition(FiniteSet(a, b))
+    assert Partition({a, b}) != Partition(a, b)
+
+def test_partition():
+    from sympy.abc import x
+
+    a = Partition([1, 2, 3], [4])
+    b = Partition([1, 2], [3, 4])
+    c = Partition([x])
+    l = [a, b, c]
+    l.sort(key=default_sort_key)
+    assert l == [c, a, b]
+    l.sort(key=lambda w: default_sort_key(w, order='rev-lex'))
+    assert l == [c, a, b]
+
+    assert (a == b) is False
+    assert a <= b
+    assert (a > b) is False
+    assert a != b
+    assert a < b
+
+    assert (a + 2).partition == [[1, 2], [3, 4]]
+    assert (b - 1).partition == [[1, 2, 4], [3]]
+
+    assert (a - 1).partition == [[1, 2, 3, 4]]
+    assert (a + 1).partition == [[1, 2, 4], [3]]
+    assert (b + 1).partition == [[1, 2], [3], [4]]
+
+    assert a.rank == 1
+    assert b.rank == 3
+
+    assert a.RGS == (0, 0, 0, 1)
+    assert b.RGS == (0, 0, 1, 1)
+
+
+def test_integer_partition():
+    # no zeros in partition
+    raises(ValueError, lambda: IntegerPartition(list(range(3))))
+    # check fails since 1 + 2 != 100
+    raises(ValueError, lambda: IntegerPartition(100, list(range(1, 3))))
+    a = IntegerPartition(8, [1, 3, 4])
+    b = a.next_lex()
+    c = IntegerPartition([1, 3, 4])
+    d = IntegerPartition(8, {1: 3, 3: 1, 2: 1})
+    assert a == c
+    assert a.integer == d.integer
+    assert a.conjugate == [3, 2, 2, 1]
+    assert (a == b) is False
+    assert a <= b
+    assert (a > b) is False
+    assert a != b
+
+    for i in range(1, 11):
+        next = set()
+        prev = set()
+        a = IntegerPartition([i])
+        ans = {IntegerPartition(p) for p in partitions(i)}
+        n = len(ans)
+        for j in range(n):
+            next.add(a)
+            a = a.next_lex()
+            IntegerPartition(i, a.partition)  # check it by giving i
+        for j in range(n):
+            prev.add(a)
+            a = a.prev_lex()
+            IntegerPartition(i, a.partition)  # check it by giving i
+        assert next == ans
+        assert prev == ans
+
+    assert IntegerPartition([1, 2, 3]).as_ferrers() == '###\n##\n#'
+    assert IntegerPartition([1, 1, 3]).as_ferrers('o') == 'ooo\no\no'
+    assert str(IntegerPartition([1, 1, 3])) == '[3, 1, 1]'
+    assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1]
+
+    raises(ValueError, lambda: random_integer_partition(-1))
+    assert random_integer_partition(1) == [1]
+    assert random_integer_partition(10, seed=[1, 3, 2, 1, 5, 1]
+            ) == [5, 2, 1, 1, 1]
+
+
+def test_rgs():
+    raises(ValueError, lambda: RGS_unrank(-1, 3))
+    raises(ValueError, lambda: RGS_unrank(3, 0))
+    raises(ValueError, lambda: RGS_unrank(10, 1))
+
+    raises(ValueError, lambda: Partition.from_rgs(list(range(3)), list(range(2))))
+    raises(ValueError, lambda: Partition.from_rgs(list(range(1, 3)), list(range(2))))
+    assert RGS_enum(-1) == 0
+    assert RGS_enum(1) == 1
+    assert RGS_unrank(7, 5) == [0, 0, 1, 0, 2]
+    assert RGS_unrank(23, 14) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2]
+    assert RGS_rank(RGS_unrank(40, 100)) == 40
+
+def test_ordered_partition_9608():
+    a = Partition([1, 2, 3], [4])
+    b = Partition([1, 2], [3, 4])
+    assert list(ordered([a,b], Set._infimum_key))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_pc_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_pc_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..b0c146279921e1e6499534fe9e33b993348d1503
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_pc_groups.py
@@ -0,0 +1,87 @@
+from sympy.combinatorics.permutations import Permutation
+from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, DihedralGroup
+from sympy.matrices import Matrix
+
+def test_pc_presentation():
+    Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3),
+         SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2), DihedralGroup(10)]
+
+    S = SymmetricGroup(125).sylow_subgroup(5)
+    G = S.derived_series()[2]
+    Groups.append(G)
+
+    G = SymmetricGroup(25).sylow_subgroup(5)
+    Groups.append(G)
+
+    S = SymmetricGroup(11**2).sylow_subgroup(11)
+    G = S.derived_series()[2]
+    Groups.append(G)
+
+    for G in Groups:
+        PcGroup = G.polycyclic_group()
+        collector = PcGroup.collector
+        pc_presentation = collector.pc_presentation
+
+        pcgs = PcGroup.pcgs
+        free_group = collector.free_group
+        free_to_perm = {}
+        for s, g in zip(free_group.symbols, pcgs):
+            free_to_perm[s] = g
+
+        for k, v in pc_presentation.items():
+            k_array = k.array_form
+            if v != ():
+                v_array = v.array_form
+
+            lhs = Permutation()
+            for gen in k_array:
+                s = gen[0]
+                e = gen[1]
+                lhs = lhs*free_to_perm[s]**e
+
+            if v == ():
+                assert lhs.is_identity
+                continue
+
+            rhs = Permutation()
+            for gen in v_array:
+                s = gen[0]
+                e = gen[1]
+                rhs = rhs*free_to_perm[s]**e
+
+            assert lhs == rhs
+
+
+def test_exponent_vector():
+
+    Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3),
+         SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2)]
+
+    for G in Groups:
+        PcGroup = G.polycyclic_group()
+        collector = PcGroup.collector
+
+        pcgs = PcGroup.pcgs
+        # free_group = collector.free_group
+
+        for gen in G.generators:
+            exp = collector.exponent_vector(gen)
+            g = Permutation()
+            for i in range(len(exp)):
+                g = g*pcgs[i]**exp[i] if exp[i] else g
+            assert g == gen
+
+
+def test_induced_pcgs():
+    G = [SymmetricGroup(9).sylow_subgroup(3), SymmetricGroup(20).sylow_subgroup(2), AlternatingGroup(4),
+    DihedralGroup(4), DihedralGroup(10), DihedralGroup(9), SymmetricGroup(3), SymmetricGroup(4)]
+
+    for g in G:
+        PcGroup = g.polycyclic_group()
+        collector = PcGroup.collector
+        gens = list(g.generators)
+        ipcgs = collector.induced_pcgs(gens)
+        m = []
+        for i in ipcgs:
+            m.append(collector.exponent_vector(i))
+        assert Matrix(m).is_upper
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_perm_groups.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_perm_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..763b8fb0ae357500d68c29fe1c9e6b156e224949
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_perm_groups.py
@@ -0,0 +1,1243 @@
+from sympy.core.containers import Tuple
+from sympy.combinatorics.generators import rubik_cube_generators
+from sympy.combinatorics.homomorphisms import is_isomorphic
+from sympy.combinatorics.named_groups import SymmetricGroup, CyclicGroup,\
+    DihedralGroup, AlternatingGroup, AbelianGroup, RubikGroup
+from sympy.combinatorics.perm_groups import (PermutationGroup,
+    _orbit_transversal, Coset, SymmetricPermutationGroup)
+from sympy.combinatorics.permutations import Permutation
+from sympy.combinatorics.polyhedron import tetrahedron as Tetra, cube
+from sympy.combinatorics.testutil import _verify_bsgs, _verify_centralizer,\
+    _verify_normal_closure
+from sympy.testing.pytest import skip, XFAIL, slow
+
+rmul = Permutation.rmul
+
+
+def test_has():
+    a = Permutation([1, 0])
+    G = PermutationGroup([a])
+    assert G.is_abelian
+    a = Permutation([2, 0, 1])
+    b = Permutation([2, 1, 0])
+    G = PermutationGroup([a, b])
+    assert not G.is_abelian
+
+    G = PermutationGroup([a])
+    assert G.has(a)
+    assert not G.has(b)
+
+    a = Permutation([2, 0, 1, 3, 4, 5])
+    b = Permutation([0, 2, 1, 3, 4])
+    assert PermutationGroup(a, b).degree == \
+        PermutationGroup(a, b).degree == 6
+
+    g = PermutationGroup(Permutation(0, 2, 1))
+    assert Tuple(1, g).has(g)
+
+
+def test_generate():
+    a = Permutation([1, 0])
+    g = list(PermutationGroup([a]).generate())
+    assert g == [Permutation([0, 1]), Permutation([1, 0])]
+    assert len(list(PermutationGroup(Permutation((0, 1))).generate())) == 1
+    g = PermutationGroup([a]).generate(method='dimino')
+    assert list(g) == [Permutation([0, 1]), Permutation([1, 0])]
+    a = Permutation([2, 0, 1])
+    b = Permutation([2, 1, 0])
+    G = PermutationGroup([a, b])
+    g = G.generate()
+    v1 = [p.array_form for p in list(g)]
+    v1.sort()
+    assert v1 == [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0,
+        1], [2, 1, 0]]
+    v2 = list(G.generate(method='dimino', af=True))
+    assert v1 == sorted(v2)
+    a = Permutation([2, 0, 1, 3, 4, 5])
+    b = Permutation([2, 1, 3, 4, 5, 0])
+    g = PermutationGroup([a, b]).generate(af=True)
+    assert len(list(g)) == 360
+
+
+def test_order():
+    a = Permutation([2, 0, 1, 3, 4, 5, 6, 7, 8, 9])
+    b = Permutation([2, 1, 3, 4, 5, 6, 7, 8, 9, 0])
+    g = PermutationGroup([a, b])
+    assert g.order() == 1814400
+    assert PermutationGroup().order() == 1
+
+
+def test_equality():
+    p_1 = Permutation(0, 1, 3)
+    p_2 = Permutation(0, 2, 3)
+    p_3 = Permutation(0, 1, 2)
+    p_4 = Permutation(0, 1, 3)
+    g_1 = PermutationGroup(p_1, p_2)
+    g_2 = PermutationGroup(p_3, p_4)
+    g_3 = PermutationGroup(p_2, p_1)
+    g_4 = PermutationGroup(p_1, p_2)
+
+    assert g_1 != g_2
+    assert g_1.generators != g_2.generators
+    assert g_1.equals(g_2)
+    assert g_1 != g_3
+    assert g_1.equals(g_3)
+    assert g_1 == g_4
+
+
+def test_stabilizer():
+    S = SymmetricGroup(2)
+    H = S.stabilizer(0)
+    assert H.generators == [Permutation(1)]
+    a = Permutation([2, 0, 1, 3, 4, 5])
+    b = Permutation([2, 1, 3, 4, 5, 0])
+    G = PermutationGroup([a, b])
+    G0 = G.stabilizer(0)
+    assert G0.order() == 60
+
+    gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
+    gens = [Permutation(p) for p in gens_cube]
+    G = PermutationGroup(gens)
+    G2 = G.stabilizer(2)
+    assert G2.order() == 6
+    G2_1 = G2.stabilizer(1)
+    v = list(G2_1.generate(af=True))
+    assert v == [[0, 1, 2, 3, 4, 5, 6, 7], [3, 1, 2, 0, 7, 5, 6, 4]]
+
+    gens = (
+        (1, 2, 0, 4, 5, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19),
+        (0, 1, 2, 3, 4, 5, 19, 6, 8, 9, 10, 11, 12, 13, 14,
+         15, 16, 7, 17, 18),
+        (0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 16, 11, 12, 13, 14, 15, 8, 17, 10, 19))
+    gens = [Permutation(p) for p in gens]
+    G = PermutationGroup(gens)
+    G2 = G.stabilizer(2)
+    assert G2.order() == 181440
+    S = SymmetricGroup(3)
+    assert [G.order() for G in S.basic_stabilizers] == [6, 2]
+
+
+def test_center():
+    # the center of the dihedral group D_n is of order 2 for even n
+    for i in (4, 6, 10):
+        D = DihedralGroup(i)
+        assert (D.center()).order() == 2
+    # the center of the dihedral group D_n is of order 1 for odd n>2
+    for i in (3, 5, 7):
+        D = DihedralGroup(i)
+        assert (D.center()).order() == 1
+    # the center of an abelian group is the group itself
+    for i in (2, 3, 5):
+        for j in (1, 5, 7):
+            for k in (1, 1, 11):
+                G = AbelianGroup(i, j, k)
+                assert G.center().is_subgroup(G)
+    # the center of a nonabelian simple group is trivial
+    for i in(1, 5, 9):
+        A = AlternatingGroup(i)
+        assert (A.center()).order() == 1
+    # brute-force verifications
+    D = DihedralGroup(5)
+    A = AlternatingGroup(3)
+    C = CyclicGroup(4)
+    G.is_subgroup(D*A*C)
+    assert _verify_centralizer(G, G)
+
+
+def test_centralizer():
+    # the centralizer of the trivial group is the entire group
+    S = SymmetricGroup(2)
+    assert S.centralizer(Permutation(list(range(2)))).is_subgroup(S)
+    A = AlternatingGroup(5)
+    assert A.centralizer(Permutation(list(range(5)))).is_subgroup(A)
+    # a centralizer in the trivial group is the trivial group itself
+    triv = PermutationGroup([Permutation([0, 1, 2, 3])])
+    D = DihedralGroup(4)
+    assert triv.centralizer(D).is_subgroup(triv)
+    # brute-force verifications for centralizers of groups
+    for i in (4, 5, 6):
+        S = SymmetricGroup(i)
+        A = AlternatingGroup(i)
+        C = CyclicGroup(i)
+        D = DihedralGroup(i)
+        for gp in (S, A, C, D):
+            for gp2 in (S, A, C, D):
+                if not gp2.is_subgroup(gp):
+                    assert _verify_centralizer(gp, gp2)
+    # verify the centralizer for all elements of several groups
+    S = SymmetricGroup(5)
+    elements = list(S.generate_dimino())
+    for element in elements:
+        assert _verify_centralizer(S, element)
+    A = AlternatingGroup(5)
+    elements = list(A.generate_dimino())
+    for element in elements:
+        assert _verify_centralizer(A, element)
+    D = DihedralGroup(7)
+    elements = list(D.generate_dimino())
+    for element in elements:
+        assert _verify_centralizer(D, element)
+    # verify centralizers of small groups within small groups
+    small = []
+    for i in (1, 2, 3):
+        small.append(SymmetricGroup(i))
+        small.append(AlternatingGroup(i))
+        small.append(DihedralGroup(i))
+        small.append(CyclicGroup(i))
+    for gp in small:
+        for gp2 in small:
+            if gp.degree == gp2.degree:
+                assert _verify_centralizer(gp, gp2)
+
+
+def test_coset_rank():
+    gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
+    gens = [Permutation(p) for p in gens_cube]
+    G = PermutationGroup(gens)
+    i = 0
+    for h in G.generate(af=True):
+        rk = G.coset_rank(h)
+        assert rk == i
+        h1 = G.coset_unrank(rk, af=True)
+        assert h == h1
+        i += 1
+    assert G.coset_unrank(48) is None
+    assert G.coset_unrank(G.coset_rank(gens[0])) == gens[0]
+
+
+def test_coset_factor():
+    a = Permutation([0, 2, 1])
+    G = PermutationGroup([a])
+    c = Permutation([2, 1, 0])
+    assert not G.coset_factor(c)
+    assert G.coset_rank(c) is None
+
+    a = Permutation([2, 0, 1, 3, 4, 5])
+    b = Permutation([2, 1, 3, 4, 5, 0])
+    g = PermutationGroup([a, b])
+    assert g.order() == 360
+    d = Permutation([1, 0, 2, 3, 4, 5])
+    assert not g.coset_factor(d.array_form)
+    assert not g.contains(d)
+    assert Permutation(2) in G
+    c = Permutation([1, 0, 2, 3, 5, 4])
+    v = g.coset_factor(c, True)
+    tr = g.basic_transversals
+    p = Permutation.rmul(*[tr[i][v[i]] for i in range(len(g.base))])
+    assert p == c
+    v = g.coset_factor(c)
+    p = Permutation.rmul(*v)
+    assert p == c
+    assert g.contains(c)
+    G = PermutationGroup([Permutation([2, 1, 0])])
+    p = Permutation([1, 0, 2])
+    assert G.coset_factor(p) == []
+
+
+def test_orbits():
+    a = Permutation([2, 0, 1])
+    b = Permutation([2, 1, 0])
+    g = PermutationGroup([a, b])
+    assert g.orbit(0) == {0, 1, 2}
+    assert g.orbits() == [{0, 1, 2}]
+    assert g.is_transitive() and g.is_transitive(strict=False)
+    assert g.orbit_transversal(0) == \
+        [Permutation(
+            [0, 1, 2]), Permutation([2, 0, 1]), Permutation([1, 2, 0])]
+    assert g.orbit_transversal(0, True) == \
+        [(0, Permutation([0, 1, 2])), (2, Permutation([2, 0, 1])),
+        (1, Permutation([1, 2, 0]))]
+
+    G = DihedralGroup(6)
+    transversal, slps = _orbit_transversal(G.degree, G.generators, 0, True, slp=True)
+    for i, t in transversal:
+        slp = slps[i]
+        w = G.identity
+        for s in slp:
+            w = G.generators[s]*w
+        assert w == t
+
+    a = Permutation(list(range(1, 100)) + [0])
+    G = PermutationGroup([a])
+    assert [min(o) for o in G.orbits()] == [0]
+    G = PermutationGroup(rubik_cube_generators())
+    assert [min(o) for o in G.orbits()] == [0, 1]
+    assert not G.is_transitive() and not G.is_transitive(strict=False)
+    G = PermutationGroup([Permutation(0, 1, 3), Permutation(3)(0, 1)])
+    assert not G.is_transitive() and G.is_transitive(strict=False)
+    assert PermutationGroup(
+        Permutation(3)).is_transitive(strict=False) is False
+
+
+def test_is_normal():
+    gens_s5 = [Permutation(p) for p in [[1, 2, 3, 4, 0], [2, 1, 4, 0, 3]]]
+    G1 = PermutationGroup(gens_s5)
+    assert G1.order() == 120
+    gens_a5 = [Permutation(p) for p in [[1, 0, 3, 2, 4], [2, 1, 4, 3, 0]]]
+    G2 = PermutationGroup(gens_a5)
+    assert G2.order() == 60
+    assert G2.is_normal(G1)
+    gens3 = [Permutation(p) for p in [[2, 1, 3, 0, 4], [1, 2, 0, 3, 4]]]
+    G3 = PermutationGroup(gens3)
+    assert not G3.is_normal(G1)
+    assert G3.order() == 12
+    G4 = G1.normal_closure(G3.generators)
+    assert G4.order() == 60
+    gens5 = [Permutation(p) for p in [[1, 2, 3, 0, 4], [1, 2, 0, 3, 4]]]
+    G5 = PermutationGroup(gens5)
+    assert G5.order() == 24
+    G6 = G1.normal_closure(G5.generators)
+    assert G6.order() == 120
+    assert G1.is_subgroup(G6)
+    assert not G1.is_subgroup(G4)
+    assert G2.is_subgroup(G4)
+    I5 = PermutationGroup(Permutation(4))
+    assert I5.is_normal(G5)
+    assert I5.is_normal(G6, strict=False)
+    p1 = Permutation([1, 0, 2, 3, 4])
+    p2 = Permutation([0, 1, 2, 4, 3])
+    p3 = Permutation([3, 4, 2, 1, 0])
+    id_ = Permutation([0, 1, 2, 3, 4])
+    H = PermutationGroup([p1, p3])
+    H_n1 = PermutationGroup([p1, p2])
+    H_n2_1 = PermutationGroup(p1)
+    H_n2_2 = PermutationGroup(p2)
+    H_id = PermutationGroup(id_)
+    assert H_n1.is_normal(H)
+    assert H_n2_1.is_normal(H_n1)
+    assert H_n2_2.is_normal(H_n1)
+    assert H_id.is_normal(H_n2_1)
+    assert H_id.is_normal(H_n1)
+    assert H_id.is_normal(H)
+    assert not H_n2_1.is_normal(H)
+    assert not H_n2_2.is_normal(H)
+
+
+def test_eq():
+    a = [[1, 2, 0, 3, 4, 5], [1, 0, 2, 3, 4, 5], [2, 1, 0, 3, 4, 5], [
+        1, 2, 0, 3, 4, 5]]
+    a = [Permutation(p) for p in a + [[1, 2, 3, 4, 5, 0]]]
+    g = Permutation([1, 2, 3, 4, 5, 0])
+    G1, G2, G3 = [PermutationGroup(x) for x in [a[:2], a[2:4], [g, g**2]]]
+    assert G1.order() == G2.order() == G3.order() == 6
+    assert G1.is_subgroup(G2)
+    assert not G1.is_subgroup(G3)
+    G4 = PermutationGroup([Permutation([0, 1])])
+    assert not G1.is_subgroup(G4)
+    assert G4.is_subgroup(G1, 0)
+    assert PermutationGroup(g, g).is_subgroup(PermutationGroup(g))
+    assert SymmetricGroup(3).is_subgroup(SymmetricGroup(4), 0)
+    assert SymmetricGroup(3).is_subgroup(SymmetricGroup(3)*CyclicGroup(5), 0)
+    assert not CyclicGroup(5).is_subgroup(SymmetricGroup(3)*CyclicGroup(5), 0)
+    assert CyclicGroup(3).is_subgroup(SymmetricGroup(3)*CyclicGroup(5), 0)
+
+
+def test_derived_subgroup():
+    a = Permutation([1, 0, 2, 4, 3])
+    b = Permutation([0, 1, 3, 2, 4])
+    G = PermutationGroup([a, b])
+    C = G.derived_subgroup()
+    assert C.order() == 3
+    assert C.is_normal(G)
+    assert C.is_subgroup(G, 0)
+    assert not G.is_subgroup(C, 0)
+    gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
+    gens = [Permutation(p) for p in gens_cube]
+    G = PermutationGroup(gens)
+    C = G.derived_subgroup()
+    assert C.order() == 12
+
+
+def test_is_solvable():
+    a = Permutation([1, 2, 0])
+    b = Permutation([1, 0, 2])
+    G = PermutationGroup([a, b])
+    assert G.is_solvable
+    G = PermutationGroup([a])
+    assert G.is_solvable
+    a = Permutation([1, 2, 3, 4, 0])
+    b = Permutation([1, 0, 2, 3, 4])
+    G = PermutationGroup([a, b])
+    assert not G.is_solvable
+    P = SymmetricGroup(10)
+    S = P.sylow_subgroup(3)
+    assert S.is_solvable
+
+def test_rubik1():
+    gens = rubik_cube_generators()
+    gens1 = [gens[-1]] + [p**2 for p in gens[1:]]
+    G1 = PermutationGroup(gens1)
+    assert G1.order() == 19508428800
+    gens2 = [p**2 for p in gens]
+    G2 = PermutationGroup(gens2)
+    assert G2.order() == 663552
+    assert G2.is_subgroup(G1, 0)
+    C1 = G1.derived_subgroup()
+    assert C1.order() == 4877107200
+    assert C1.is_subgroup(G1, 0)
+    assert not G2.is_subgroup(C1, 0)
+
+    G = RubikGroup(2)
+    assert G.order() == 3674160
+
+
+@XFAIL
+def test_rubik():
+    skip('takes too much time')
+    G = PermutationGroup(rubik_cube_generators())
+    assert G.order() == 43252003274489856000
+    G1 = PermutationGroup(G[:3])
+    assert G1.order() == 170659735142400
+    assert not G1.is_normal(G)
+    G2 = G.normal_closure(G1.generators)
+    assert G2.is_subgroup(G)
+
+
+def test_direct_product():
+    C = CyclicGroup(4)
+    D = DihedralGroup(4)
+    G = C*C*C
+    assert G.order() == 64
+    assert G.degree == 12
+    assert len(G.orbits()) == 3
+    assert G.is_abelian is True
+    H = D*C
+    assert H.order() == 32
+    assert H.is_abelian is False
+
+
+def test_orbit_rep():
+    G = DihedralGroup(6)
+    assert G.orbit_rep(1, 3) in [Permutation([2, 3, 4, 5, 0, 1]),
+    Permutation([4, 3, 2, 1, 0, 5])]
+    H = CyclicGroup(4)*G
+    assert H.orbit_rep(1, 5) is False
+
+
+def test_schreier_vector():
+    G = CyclicGroup(50)
+    v = [0]*50
+    v[23] = -1
+    assert G.schreier_vector(23) == v
+    H = DihedralGroup(8)
+    assert H.schreier_vector(2) == [0, 1, -1, 0, 0, 1, 0, 0]
+    L = SymmetricGroup(4)
+    assert L.schreier_vector(1) == [1, -1, 0, 0]
+
+
+def test_random_pr():
+    D = DihedralGroup(6)
+    r = 11
+    n = 3
+    _random_prec_n = {}
+    _random_prec_n[0] = {'s': 7, 't': 3, 'x': 2, 'e': -1}
+    _random_prec_n[1] = {'s': 5, 't': 5, 'x': 1, 'e': -1}
+    _random_prec_n[2] = {'s': 3, 't': 4, 'x': 2, 'e': 1}
+    D._random_pr_init(r, n, _random_prec_n=_random_prec_n)
+    assert D._random_gens[11] == [0, 1, 2, 3, 4, 5]
+    _random_prec = {'s': 2, 't': 9, 'x': 1, 'e': -1}
+    assert D.random_pr(_random_prec=_random_prec) == \
+        Permutation([0, 5, 4, 3, 2, 1])
+
+
+def test_is_alt_sym():
+    G = DihedralGroup(10)
+    assert G.is_alt_sym() is False
+    assert G._eval_is_alt_sym_naive() is False
+    assert G._eval_is_alt_sym_naive(only_alt=True) is False
+    assert G._eval_is_alt_sym_naive(only_sym=True) is False
+
+    S = SymmetricGroup(10)
+    assert S._eval_is_alt_sym_naive() is True
+    assert S._eval_is_alt_sym_naive(only_alt=True) is False
+    assert S._eval_is_alt_sym_naive(only_sym=True) is True
+
+    N_eps = 10
+    _random_prec = {'N_eps': N_eps,
+        0: Permutation([[2], [1, 4], [0, 6, 7, 8, 9, 3, 5]]),
+        1: Permutation([[1, 8, 7, 6, 3, 5, 2, 9], [0, 4]]),
+        2: Permutation([[5, 8], [4, 7], [0, 1, 2, 3, 6, 9]]),
+        3: Permutation([[3], [0, 8, 2, 7, 4, 1, 6, 9, 5]]),
+        4: Permutation([[8], [4, 7, 9], [3, 6], [0, 5, 1, 2]]),
+        5: Permutation([[6], [0, 2, 4, 5, 1, 8, 3, 9, 7]]),
+        6: Permutation([[6, 9, 8], [4, 5], [1, 3, 7], [0, 2]]),
+        7: Permutation([[4], [0, 2, 9, 1, 3, 8, 6, 5, 7]]),
+        8: Permutation([[1, 5, 6, 3], [0, 2, 7, 8, 4, 9]]),
+        9: Permutation([[8], [6, 7], [2, 3, 4, 5], [0, 1, 9]])}
+    assert S.is_alt_sym(_random_prec=_random_prec) is True
+
+    A = AlternatingGroup(10)
+    assert A._eval_is_alt_sym_naive() is True
+    assert A._eval_is_alt_sym_naive(only_alt=True) is True
+    assert A._eval_is_alt_sym_naive(only_sym=True) is False
+
+    _random_prec = {'N_eps': N_eps,
+        0: Permutation([[1, 6, 4, 2, 7, 8, 5, 9, 3], [0]]),
+        1: Permutation([[1], [0, 5, 8, 4, 9, 2, 3, 6, 7]]),
+        2: Permutation([[1, 9, 8, 3, 2, 5], [0, 6, 7, 4]]),
+        3: Permutation([[6, 8, 9], [4, 5], [1, 3, 7, 2], [0]]),
+        4: Permutation([[8], [5], [4], [2, 6, 9, 3], [1], [0, 7]]),
+        5: Permutation([[3, 6], [0, 8, 1, 7, 5, 9, 4, 2]]),
+        6: Permutation([[5], [2, 9], [1, 8, 3], [0, 4, 7, 6]]),
+        7: Permutation([[1, 8, 4, 7, 2, 3], [0, 6, 9, 5]]),
+        8: Permutation([[5, 8, 7], [3], [1, 4, 2, 6], [0, 9]]),
+        9: Permutation([[4, 9, 6], [3, 8], [1, 2], [0, 5, 7]])}
+    assert A.is_alt_sym(_random_prec=_random_prec) is False
+
+    G = PermutationGroup(
+        Permutation(1, 3, size=8)(0, 2, 4, 6),
+        Permutation(5, 7, size=8)(0, 2, 4, 6))
+    assert G.is_alt_sym() is False
+
+    # Tests for monte-carlo c_n parameter setting, and which guarantees
+    # to give False.
+    G = DihedralGroup(10)
+    assert G._eval_is_alt_sym_monte_carlo() is False
+    G = DihedralGroup(20)
+    assert G._eval_is_alt_sym_monte_carlo() is False
+
+    # A dry-running test to check if it looks up for the updated cache.
+    G = DihedralGroup(6)
+    G.is_alt_sym()
+    assert G.is_alt_sym() is False
+
+
+def test_minimal_block():
+    D = DihedralGroup(6)
+    block_system = D.minimal_block([0, 3])
+    for i in range(3):
+        assert block_system[i] == block_system[i + 3]
+    S = SymmetricGroup(6)
+    assert S.minimal_block([0, 1]) == [0, 0, 0, 0, 0, 0]
+
+    assert Tetra.pgroup.minimal_block([0, 1]) == [0, 0, 0, 0]
+
+    P1 = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5))
+    P2 = PermutationGroup(Permutation(0, 1, 2, 3, 4, 5), Permutation(1, 5)(2, 4))
+    assert P1.minimal_block([0, 2]) == [0, 1, 0, 1, 0, 1]
+    assert P2.minimal_block([0, 2]) == [0, 1, 0, 1, 0, 1]
+
+
+def test_minimal_blocks():
+    P = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5))
+    assert P.minimal_blocks() == [[0, 1, 0, 1, 0, 1], [0, 1, 2, 0, 1, 2]]
+
+    P = SymmetricGroup(5)
+    assert P.minimal_blocks() == [[0]*5]
+
+    P = PermutationGroup(Permutation(0, 3))
+    assert P.minimal_blocks() is False
+
+
+def test_max_div():
+    S = SymmetricGroup(10)
+    assert S.max_div == 5
+
+
+def test_is_primitive():
+    S = SymmetricGroup(5)
+    assert S.is_primitive() is True
+    C = CyclicGroup(7)
+    assert C.is_primitive() is True
+
+    a = Permutation(0, 1, 2, size=6)
+    b = Permutation(3, 4, 5, size=6)
+    G = PermutationGroup(a, b)
+    assert G.is_primitive() is False
+
+
+def test_random_stab():
+    S = SymmetricGroup(5)
+    _random_el = Permutation([1, 3, 2, 0, 4])
+    _random_prec = {'rand': _random_el}
+    g = S.random_stab(2, _random_prec=_random_prec)
+    assert g == Permutation([1, 3, 2, 0, 4])
+    h = S.random_stab(1)
+    assert h(1) == 1
+
+
+def test_transitivity_degree():
+    perm = Permutation([1, 2, 0])
+    C = PermutationGroup([perm])
+    assert C.transitivity_degree == 1
+    gen1 = Permutation([1, 2, 0, 3, 4])
+    gen2 = Permutation([1, 2, 3, 4, 0])
+    # alternating group of degree 5
+    Alt = PermutationGroup([gen1, gen2])
+    assert Alt.transitivity_degree == 3
+
+
+def test_schreier_sims_random():
+    assert sorted(Tetra.pgroup.base) == [0, 1]
+
+    S = SymmetricGroup(3)
+    base = [0, 1]
+    strong_gens = [Permutation([1, 2, 0]), Permutation([1, 0, 2]),
+                  Permutation([0, 2, 1])]
+    assert S.schreier_sims_random(base, strong_gens, 5) == (base, strong_gens)
+    D = DihedralGroup(3)
+    _random_prec = {'g': [Permutation([2, 0, 1]), Permutation([1, 2, 0]),
+                         Permutation([1, 0, 2])]}
+    base = [0, 1]
+    strong_gens = [Permutation([1, 2, 0]), Permutation([2, 1, 0]),
+                  Permutation([0, 2, 1])]
+    assert D.schreier_sims_random([], D.generators, 2,
+           _random_prec=_random_prec) == (base, strong_gens)
+
+
+def test_baseswap():
+    S = SymmetricGroup(4)
+    S.schreier_sims()
+    base = S.base
+    strong_gens = S.strong_gens
+    assert base == [0, 1, 2]
+    deterministic = S.baseswap(base, strong_gens, 1, randomized=False)
+    randomized = S.baseswap(base, strong_gens, 1)
+    assert deterministic[0] == [0, 2, 1]
+    assert _verify_bsgs(S, deterministic[0], deterministic[1]) is True
+    assert randomized[0] == [0, 2, 1]
+    assert _verify_bsgs(S, randomized[0], randomized[1]) is True
+
+
+def test_schreier_sims_incremental():
+    identity = Permutation([0, 1, 2, 3, 4])
+    TrivialGroup = PermutationGroup([identity])
+    base, strong_gens = TrivialGroup.schreier_sims_incremental(base=[0, 1, 2])
+    assert _verify_bsgs(TrivialGroup, base, strong_gens) is True
+    S = SymmetricGroup(5)
+    base, strong_gens = S.schreier_sims_incremental(base=[0, 1, 2])
+    assert _verify_bsgs(S, base, strong_gens) is True
+    D = DihedralGroup(2)
+    base, strong_gens = D.schreier_sims_incremental(base=[1])
+    assert _verify_bsgs(D, base, strong_gens) is True
+    A = AlternatingGroup(7)
+    gens = A.generators[:]
+    gen0 = gens[0]
+    gen1 = gens[1]
+    gen1 = rmul(gen1, ~gen0)
+    gen0 = rmul(gen0, gen1)
+    gen1 = rmul(gen0, gen1)
+    base, strong_gens = A.schreier_sims_incremental(base=[0, 1], gens=gens)
+    assert _verify_bsgs(A, base, strong_gens) is True
+    C = CyclicGroup(11)
+    gen = C.generators[0]
+    base, strong_gens = C.schreier_sims_incremental(gens=[gen**3])
+    assert _verify_bsgs(C, base, strong_gens) is True
+
+
+def _subgroup_search(i, j, k):
+    prop_true = lambda x: True
+    prop_fix_points = lambda x: [x(point) for point in points] == points
+    prop_comm_g = lambda x: rmul(x, g) == rmul(g, x)
+    prop_even = lambda x: x.is_even
+    for i in range(i, j, k):
+        S = SymmetricGroup(i)
+        A = AlternatingGroup(i)
+        C = CyclicGroup(i)
+        Sym = S.subgroup_search(prop_true)
+        assert Sym.is_subgroup(S)
+        Alt = S.subgroup_search(prop_even)
+        assert Alt.is_subgroup(A)
+        Sym = S.subgroup_search(prop_true, init_subgroup=C)
+        assert Sym.is_subgroup(S)
+        points = [7]
+        assert S.stabilizer(7).is_subgroup(S.subgroup_search(prop_fix_points))
+        points = [3, 4]
+        assert S.stabilizer(3).stabilizer(4).is_subgroup(
+            S.subgroup_search(prop_fix_points))
+        points = [3, 5]
+        fix35 = A.subgroup_search(prop_fix_points)
+        points = [5]
+        fix5 = A.subgroup_search(prop_fix_points)
+        assert A.subgroup_search(prop_fix_points, init_subgroup=fix35
+            ).is_subgroup(fix5)
+        base, strong_gens = A.schreier_sims_incremental()
+        g = A.generators[0]
+        comm_g = \
+            A.subgroup_search(prop_comm_g, base=base, strong_gens=strong_gens)
+        assert _verify_bsgs(comm_g, base, comm_g.generators) is True
+        assert [prop_comm_g(gen) is True for gen in comm_g.generators]
+
+
+def test_subgroup_search():
+    _subgroup_search(10, 15, 2)
+
+
+@XFAIL
+def test_subgroup_search2():
+    skip('takes too much time')
+    _subgroup_search(16, 17, 1)
+
+
+def test_normal_closure():
+    # the normal closure of the trivial group is trivial
+    S = SymmetricGroup(3)
+    identity = Permutation([0, 1, 2])
+    closure = S.normal_closure(identity)
+    assert closure.is_trivial
+    # the normal closure of the entire group is the entire group
+    A = AlternatingGroup(4)
+    assert A.normal_closure(A).is_subgroup(A)
+    # brute-force verifications for subgroups
+    for i in (3, 4, 5):
+        S = SymmetricGroup(i)
+        A = AlternatingGroup(i)
+        D = DihedralGroup(i)
+        C = CyclicGroup(i)
+        for gp in (A, D, C):
+            assert _verify_normal_closure(S, gp)
+    # brute-force verifications for all elements of a group
+    S = SymmetricGroup(5)
+    elements = list(S.generate_dimino())
+    for element in elements:
+        assert _verify_normal_closure(S, element)
+    # small groups
+    small = []
+    for i in (1, 2, 3):
+        small.append(SymmetricGroup(i))
+        small.append(AlternatingGroup(i))
+        small.append(DihedralGroup(i))
+        small.append(CyclicGroup(i))
+    for gp in small:
+        for gp2 in small:
+            if gp2.is_subgroup(gp, 0) and gp2.degree == gp.degree:
+                assert _verify_normal_closure(gp, gp2)
+
+
+def test_derived_series():
+    # the derived series of the trivial group consists only of the trivial group
+    triv = PermutationGroup([Permutation([0, 1, 2])])
+    assert triv.derived_series()[0].is_subgroup(triv)
+    # the derived series for a simple group consists only of the group itself
+    for i in (5, 6, 7):
+        A = AlternatingGroup(i)
+        assert A.derived_series()[0].is_subgroup(A)
+    # the derived series for S_4 is S_4 > A_4 > K_4 > triv
+    S = SymmetricGroup(4)
+    series = S.derived_series()
+    assert series[1].is_subgroup(AlternatingGroup(4))
+    assert series[2].is_subgroup(DihedralGroup(2))
+    assert series[3].is_trivial
+
+
+def test_lower_central_series():
+    # the lower central series of the trivial group consists of the trivial
+    # group
+    triv = PermutationGroup([Permutation([0, 1, 2])])
+    assert triv.lower_central_series()[0].is_subgroup(triv)
+    # the lower central series of a simple group consists of the group itself
+    for i in (5, 6, 7):
+        A = AlternatingGroup(i)
+        assert A.lower_central_series()[0].is_subgroup(A)
+    # GAP-verified example
+    S = SymmetricGroup(6)
+    series = S.lower_central_series()
+    assert len(series) == 2
+    assert series[1].is_subgroup(AlternatingGroup(6))
+
+
+def test_commutator():
+    # the commutator of the trivial group and the trivial group is trivial
+    S = SymmetricGroup(3)
+    triv = PermutationGroup([Permutation([0, 1, 2])])
+    assert S.commutator(triv, triv).is_subgroup(triv)
+    # the commutator of the trivial group and any other group is again trivial
+    A = AlternatingGroup(3)
+    assert S.commutator(triv, A).is_subgroup(triv)
+    # the commutator is commutative
+    for i in (3, 4, 5):
+        S = SymmetricGroup(i)
+        A = AlternatingGroup(i)
+        D = DihedralGroup(i)
+        assert S.commutator(A, D).is_subgroup(S.commutator(D, A))
+    # the commutator of an abelian group is trivial
+    S = SymmetricGroup(7)
+    A1 = AbelianGroup(2, 5)
+    A2 = AbelianGroup(3, 4)
+    triv = PermutationGroup([Permutation([0, 1, 2, 3, 4, 5, 6])])
+    assert S.commutator(A1, A1).is_subgroup(triv)
+    assert S.commutator(A2, A2).is_subgroup(triv)
+    # examples calculated by hand
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    assert S.commutator(A, S).is_subgroup(A)
+
+
+def test_is_nilpotent():
+    # every abelian group is nilpotent
+    for i in (1, 2, 3):
+        C = CyclicGroup(i)
+        Ab = AbelianGroup(i, i + 2)
+        assert C.is_nilpotent
+        assert Ab.is_nilpotent
+    Ab = AbelianGroup(5, 7, 10)
+    assert Ab.is_nilpotent
+    # A_5 is not solvable and thus not nilpotent
+    assert AlternatingGroup(5).is_nilpotent is False
+
+
+def test_is_trivial():
+    for i in range(5):
+        triv = PermutationGroup([Permutation(list(range(i)))])
+        assert triv.is_trivial
+
+
+def test_pointwise_stabilizer():
+    S = SymmetricGroup(2)
+    stab = S.pointwise_stabilizer([0])
+    assert stab.generators == [Permutation(1)]
+    S = SymmetricGroup(5)
+    points = []
+    stab = S
+    for point in (2, 0, 3, 4, 1):
+        stab = stab.stabilizer(point)
+        points.append(point)
+        assert S.pointwise_stabilizer(points).is_subgroup(stab)
+
+
+def test_make_perm():
+    assert cube.pgroup.make_perm(5, seed=list(range(5))) == \
+        Permutation([4, 7, 6, 5, 0, 3, 2, 1])
+    assert cube.pgroup.make_perm(7, seed=list(range(7))) == \
+        Permutation([6, 7, 3, 2, 5, 4, 0, 1])
+
+
+def test_elements():
+    from sympy.sets.sets import FiniteSet
+
+    p = Permutation(2, 3)
+    assert set(PermutationGroup(p).elements) == {Permutation(3), Permutation(2, 3)}
+    assert FiniteSet(*PermutationGroup(p).elements) \
+        == FiniteSet(Permutation(2, 3), Permutation(3))
+
+
+def test_is_group():
+    assert PermutationGroup(Permutation(1,2), Permutation(2,4)).is_group is True
+    assert SymmetricGroup(4).is_group is True
+
+
+def test_PermutationGroup():
+    assert PermutationGroup() == PermutationGroup(Permutation())
+    assert (PermutationGroup() == 0) is False
+
+
+def test_coset_transvesal():
+    G = AlternatingGroup(5)
+    H = PermutationGroup(Permutation(0,1,2),Permutation(1,2)(3,4))
+    assert G.coset_transversal(H) == \
+        [Permutation(4), Permutation(2, 3, 4), Permutation(2, 4, 3),
+         Permutation(1, 2, 4), Permutation(4)(1, 2, 3), Permutation(1, 3)(2, 4),
+         Permutation(0, 1, 2, 3, 4), Permutation(0, 1, 2, 4, 3),
+         Permutation(0, 1, 3, 2, 4), Permutation(0, 2, 4, 1, 3)]
+
+
+def test_coset_table():
+    G = PermutationGroup(Permutation(0,1,2,3), Permutation(0,1,2),
+         Permutation(0,4,2,7), Permutation(5,6), Permutation(0,7))
+    H = PermutationGroup(Permutation(0,1,2,3), Permutation(0,7))
+    assert G.coset_table(H) == \
+        [[0, 0, 0, 0, 1, 2, 3, 3, 0, 0], [4, 5, 2, 5, 6, 0, 7, 7, 1, 1],
+         [5, 4, 5, 1, 0, 6, 8, 8, 6, 6], [3, 3, 3, 3, 7, 8, 0, 0, 3, 3],
+         [2, 1, 4, 4, 4, 4, 9, 9, 4, 4], [1, 2, 1, 2, 5, 5, 10, 10, 5, 5],
+         [6, 6, 6, 6, 2, 1, 11, 11, 2, 2], [9, 10, 8, 10, 11, 3, 1, 1, 7, 7],
+         [10, 9, 10, 7, 3, 11, 2, 2, 11, 11], [8, 7, 9, 9, 9, 9, 4, 4, 9, 9],
+         [7, 8, 7, 8, 10, 10, 5, 5, 10, 10], [11, 11, 11, 11, 8, 7, 6, 6, 8, 8]]
+
+
+def test_subgroup():
+    G = PermutationGroup(Permutation(0,1,2), Permutation(0,2,3))
+    H = G.subgroup([Permutation(0,1,3)])
+    assert H.is_subgroup(G)
+
+
+def test_generator_product():
+    G = SymmetricGroup(5)
+    p = Permutation(0, 2, 3)(1, 4)
+    gens = G.generator_product(p)
+    assert all(g in G.strong_gens for g in gens)
+    w = G.identity
+    for g in gens:
+        w = g*w
+    assert w == p
+
+
+def test_sylow_subgroup():
+    P = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5))
+    S = P.sylow_subgroup(2)
+    assert S.order() == 4
+
+    P = DihedralGroup(12)
+    S = P.sylow_subgroup(3)
+    assert S.order() == 3
+
+    P = PermutationGroup(
+        Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5), Permutation(0, 2))
+    S = P.sylow_subgroup(3)
+    assert S.order() == 9
+    S = P.sylow_subgroup(2)
+    assert S.order() == 8
+
+    P = SymmetricGroup(10)
+    S = P.sylow_subgroup(2)
+    assert S.order() == 256
+    S = P.sylow_subgroup(3)
+    assert S.order() == 81
+    S = P.sylow_subgroup(5)
+    assert S.order() == 25
+
+    # the length of the lower central series
+    # of a p-Sylow subgroup of Sym(n) grows with
+    # the highest exponent exp of p such
+    # that n >= p**exp
+    exp = 1
+    length = 0
+    for i in range(2, 9):
+        P = SymmetricGroup(i)
+        S = P.sylow_subgroup(2)
+        ls = S.lower_central_series()
+        if i // 2**exp > 0:
+            # length increases with exponent
+            assert len(ls) > length
+            length = len(ls)
+            exp += 1
+        else:
+            assert len(ls) == length
+
+    G = SymmetricGroup(100)
+    S = G.sylow_subgroup(3)
+    assert G.order() % S.order() == 0
+    assert G.order()/S.order() % 3 > 0
+
+    G = AlternatingGroup(100)
+    S = G.sylow_subgroup(2)
+    assert G.order() % S.order() == 0
+    assert G.order()/S.order() % 2 > 0
+
+    G = DihedralGroup(18)
+    S = G.sylow_subgroup(p=2)
+    assert S.order() == 4
+
+    G = DihedralGroup(50)
+    S = G.sylow_subgroup(p=2)
+    assert S.order() == 4
+
+
+@slow
+def test_presentation():
+    def _test(P):
+        G = P.presentation()
+        return G.order() == P.order()
+
+    def _strong_test(P):
+        G = P.strong_presentation()
+        chk = len(G.generators) == len(P.strong_gens)
+        return chk and G.order() == P.order()
+
+    P = PermutationGroup(Permutation(0,1,5,2)(3,7,4,6), Permutation(0,3,5,4)(1,6,2,7))
+    assert _test(P)
+
+    P = AlternatingGroup(5)
+    assert _test(P)
+
+    P = SymmetricGroup(5)
+    assert _test(P)
+
+    P = PermutationGroup(
+        [Permutation(0,3,1,2), Permutation(3)(0,1), Permutation(0,1)(2,3)])
+    assert _strong_test(P)
+
+    P = DihedralGroup(6)
+    assert _strong_test(P)
+
+    a = Permutation(0,1)(2,3)
+    b = Permutation(0,2)(3,1)
+    c = Permutation(4,5)
+    P = PermutationGroup(c, a, b)
+    assert _strong_test(P)
+
+
+def test_polycyclic():
+    a = Permutation([0, 1, 2])
+    b = Permutation([2, 1, 0])
+    G = PermutationGroup([a, b])
+    assert G.is_polycyclic is True
+
+    a = Permutation([1, 2, 3, 4, 0])
+    b = Permutation([1, 0, 2, 3, 4])
+    G = PermutationGroup([a, b])
+    assert G.is_polycyclic is False
+
+
+def test_elementary():
+    a = Permutation([1, 5, 2, 0, 3, 6, 4])
+    G = PermutationGroup([a])
+    assert G.is_elementary(7) is False
+
+    a = Permutation(0, 1)(2, 3)
+    b = Permutation(0, 2)(3, 1)
+    G = PermutationGroup([a, b])
+    assert G.is_elementary(2) is True
+    c = Permutation(4, 5, 6)
+    G = PermutationGroup([a, b, c])
+    assert G.is_elementary(2) is False
+
+    G = SymmetricGroup(4).sylow_subgroup(2)
+    assert G.is_elementary(2) is False
+    H = AlternatingGroup(4).sylow_subgroup(2)
+    assert H.is_elementary(2) is True
+
+
+def test_perfect():
+    G = AlternatingGroup(3)
+    assert G.is_perfect is False
+    G = AlternatingGroup(5)
+    assert G.is_perfect is True
+
+
+def test_index():
+    G = PermutationGroup(Permutation(0,1,2), Permutation(0,2,3))
+    H = G.subgroup([Permutation(0,1,3)])
+    assert G.index(H) == 4
+
+
+def test_cyclic():
+    G = SymmetricGroup(2)
+    assert G.is_cyclic
+    G = AbelianGroup(3, 7)
+    assert G.is_cyclic
+    G = AbelianGroup(7, 7)
+    assert not G.is_cyclic
+    G = AlternatingGroup(3)
+    assert G.is_cyclic
+    G = AlternatingGroup(4)
+    assert not G.is_cyclic
+
+    # Order less than 6
+    G = PermutationGroup(Permutation(0, 1, 2), Permutation(0, 2, 1))
+    assert G.is_cyclic
+    G = PermutationGroup(
+        Permutation(0, 1, 2, 3),
+        Permutation(0, 2)(1, 3)
+    )
+    assert G.is_cyclic
+    G = PermutationGroup(
+        Permutation(3),
+        Permutation(0, 1)(2, 3),
+        Permutation(0, 2)(1, 3),
+        Permutation(0, 3)(1, 2)
+    )
+    assert G.is_cyclic is False
+
+    # Order 15
+    G = PermutationGroup(
+        Permutation(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14),
+        Permutation(0, 2, 4, 6, 8, 10, 12, 14, 1, 3, 5, 7, 9, 11, 13)
+    )
+    assert G.is_cyclic
+
+    # Distinct prime orders
+    assert PermutationGroup._distinct_primes_lemma([3, 5]) is True
+    assert PermutationGroup._distinct_primes_lemma([5, 7]) is True
+    assert PermutationGroup._distinct_primes_lemma([2, 3]) is None
+    assert PermutationGroup._distinct_primes_lemma([3, 5, 7]) is None
+    assert PermutationGroup._distinct_primes_lemma([5, 7, 13]) is True
+
+    G = PermutationGroup(
+        Permutation(0, 1, 2, 3),
+        Permutation(0, 2)(1, 3))
+    assert G.is_cyclic
+    assert G._is_abelian
+
+    # Non-abelian and therefore not cyclic
+    G = PermutationGroup(*SymmetricGroup(3).generators)
+    assert G.is_cyclic is False
+
+    # Abelian and cyclic
+    G = PermutationGroup(
+        Permutation(0, 1, 2, 3),
+        Permutation(4, 5, 6)
+    )
+    assert G.is_cyclic
+
+    # Abelian but not cyclic
+    G = PermutationGroup(
+        Permutation(0, 1),
+        Permutation(2, 3),
+        Permutation(4, 5, 6)
+    )
+    assert G.is_cyclic is False
+
+
+def test_dihedral():
+    G = SymmetricGroup(2)
+    assert G.is_dihedral
+    G = SymmetricGroup(3)
+    assert G.is_dihedral
+
+    G = AbelianGroup(2, 2)
+    assert G.is_dihedral
+    G = CyclicGroup(4)
+    assert not G.is_dihedral
+
+    G = AbelianGroup(3, 5)
+    assert not G.is_dihedral
+    G = AbelianGroup(2)
+    assert G.is_dihedral
+    G = AbelianGroup(6)
+    assert not G.is_dihedral
+
+    # D6, generated by two adjacent flips
+    G = PermutationGroup(
+        Permutation(1, 5)(2, 4),
+        Permutation(0, 1)(3, 4)(2, 5))
+    assert G.is_dihedral
+
+    # D7, generated by a flip and a rotation
+    G = PermutationGroup(
+        Permutation(1, 6)(2, 5)(3, 4),
+        Permutation(0, 1, 2, 3, 4, 5, 6))
+    assert G.is_dihedral
+
+    # S4, presented by three generators, fails due to having exactly 9
+    # elements of order 2:
+    G = PermutationGroup(
+        Permutation(0, 1), Permutation(0, 2),
+        Permutation(0, 3))
+    assert not G.is_dihedral
+
+    # D7, given by three generators
+    G = PermutationGroup(
+        Permutation(1, 6)(2, 5)(3, 4),
+        Permutation(2, 0)(3, 6)(4, 5),
+        Permutation(0, 1, 2, 3, 4, 5, 6))
+    assert G.is_dihedral
+
+
+def test_abelian_invariants():
+    G = AbelianGroup(2, 3, 4)
+    assert G.abelian_invariants() == [2, 3, 4]
+    G=PermutationGroup([Permutation(1, 2, 3, 4), Permutation(1, 2), Permutation(5, 6)])
+    assert G.abelian_invariants() == [2, 2]
+    G = AlternatingGroup(7)
+    assert G.abelian_invariants() == []
+    G = AlternatingGroup(4)
+    assert G.abelian_invariants() == [3]
+    G = DihedralGroup(4)
+    assert G.abelian_invariants() == [2, 2]
+
+    G = PermutationGroup([Permutation(1, 2, 3, 4, 5, 6, 7)])
+    assert G.abelian_invariants() == [7]
+    G = DihedralGroup(12)
+    S = G.sylow_subgroup(3)
+    assert S.abelian_invariants() == [3]
+    G = PermutationGroup(Permutation(0, 1, 2), Permutation(0, 2, 3))
+    assert G.abelian_invariants() == [3]
+    G = PermutationGroup([Permutation(0, 1), Permutation(0, 2, 4, 6)(1, 3, 5, 7)])
+    assert G.abelian_invariants() == [2, 4]
+    G = SymmetricGroup(30)
+    S = G.sylow_subgroup(2)
+    assert S.abelian_invariants() == [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
+    S = G.sylow_subgroup(3)
+    assert S.abelian_invariants() == [3, 3, 3, 3]
+    S = G.sylow_subgroup(5)
+    assert S.abelian_invariants() == [5, 5, 5]
+
+
+def test_composition_series():
+    a = Permutation(1, 2, 3)
+    b = Permutation(1, 2)
+    G = PermutationGroup([a, b])
+    comp_series = G.composition_series()
+    assert comp_series == G.derived_series()
+    # The first group in the composition series is always the group itself and
+    # the last group in the series is the trivial group.
+    S = SymmetricGroup(4)
+    assert S.composition_series()[0] == S
+    assert len(S.composition_series()) == 5
+    A = AlternatingGroup(4)
+    assert A.composition_series()[0] == A
+    assert len(A.composition_series()) == 4
+
+    # the composition series for C_8 is C_8 > C_4 > C_2 > triv
+    G = CyclicGroup(8)
+    series = G.composition_series()
+    assert is_isomorphic(series[1], CyclicGroup(4))
+    assert is_isomorphic(series[2], CyclicGroup(2))
+    assert series[3].is_trivial
+
+
+def test_is_symmetric():
+    a = Permutation(0, 1, 2)
+    b = Permutation(0, 1, size=3)
+    assert PermutationGroup(a, b).is_symmetric is True
+
+    a = Permutation(0, 2, 1)
+    b = Permutation(1, 2, size=3)
+    assert PermutationGroup(a, b).is_symmetric is True
+
+    a = Permutation(0, 1, 2, 3)
+    b = Permutation(0, 3)(1, 2)
+    assert PermutationGroup(a, b).is_symmetric is False
+
+def test_conjugacy_class():
+    S = SymmetricGroup(4)
+    x = Permutation(1, 2, 3)
+    C = {Permutation(0, 1, 2, size = 4), Permutation(0, 1, 3),
+             Permutation(0, 2, 1, size = 4), Permutation(0, 2, 3),
+             Permutation(0, 3, 1), Permutation(0, 3, 2),
+             Permutation(1, 2, 3), Permutation(1, 3, 2)}
+    assert S.conjugacy_class(x) == C
+
+def test_conjugacy_classes():
+    S = SymmetricGroup(3)
+    expected = [{Permutation(size = 3)},
+         {Permutation(0, 1, size = 3), Permutation(0, 2), Permutation(1, 2)},
+         {Permutation(0, 1, 2), Permutation(0, 2, 1)}]
+    computed = S.conjugacy_classes()
+
+    assert len(expected) == len(computed)
+    assert all(e in computed for e in expected)
+
+def test_coset_class():
+    a = Permutation(1, 2)
+    b = Permutation(0, 1)
+    G = PermutationGroup([a, b])
+    #Creating right coset
+    rht_coset = G*a
+    #Checking whether it is left coset or right coset
+    assert rht_coset.is_right_coset
+    assert not rht_coset.is_left_coset
+    #Creating list representation of coset
+    list_repr = rht_coset.as_list()
+    expected = [Permutation(0, 2), Permutation(0, 2, 1), Permutation(1, 2),
+                Permutation(2), Permutation(2)(0, 1), Permutation(0, 1, 2)]
+    for ele in list_repr:
+        assert ele in expected
+    #Creating left coset
+    left_coset = a*G
+    #Checking whether it is left coset or right coset
+    assert not left_coset.is_right_coset
+    assert left_coset.is_left_coset
+    #Creating list representation of Coset
+    list_repr = left_coset.as_list()
+    expected = [Permutation(2)(0, 1), Permutation(0, 1, 2), Permutation(1, 2),
+    Permutation(2), Permutation(0, 2), Permutation(0, 2, 1)]
+    for ele in list_repr:
+        assert ele in expected
+
+    G = PermutationGroup(Permutation(1, 2, 3, 4), Permutation(2, 3, 4))
+    H = PermutationGroup(Permutation(1, 2, 3, 4))
+    g = Permutation(1, 3)(2, 4)
+    rht_coset = Coset(g, H, G, dir='+')
+    assert rht_coset.is_right_coset
+    list_repr = rht_coset.as_list()
+    expected = [Permutation(1, 2, 3, 4), Permutation(4), Permutation(1, 3)(2, 4),
+    Permutation(1, 4, 3, 2)]
+    for ele in list_repr:
+        assert ele in expected
+
+def test_symmetricpermutationgroup():
+    a = SymmetricPermutationGroup(5)
+    assert a.degree == 5
+    assert a.order() == 120
+    assert a.identity() == Permutation(4)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_permutations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_permutations.py
new file mode 100644
index 0000000000000000000000000000000000000000..b52fcfec0e2fb3be872efaa814077760e121c748
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_permutations.py
@@ -0,0 +1,564 @@
+from itertools import permutations
+from copy import copy
+
+from sympy.core.expr import unchanged
+from sympy.core.numbers import Integer
+from sympy.core.relational import Eq
+from sympy.core.symbol import Symbol
+from sympy.core.singleton import S
+from sympy.combinatorics.permutations import \
+    Permutation, _af_parity, _af_rmul, _af_rmuln, AppliedPermutation, Cycle
+from sympy.printing import sstr, srepr, pretty, latex
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+rmul = Permutation.rmul
+a = Symbol('a', integer=True)
+
+
+def test_Permutation():
+    # don't auto fill 0
+    raises(ValueError, lambda: Permutation([1]))
+    p = Permutation([0, 1, 2, 3])
+    # call as bijective
+    assert [p(i) for i in range(p.size)] == list(p)
+    # call as operator
+    assert p(list(range(p.size))) == list(p)
+    # call as function
+    assert list(p(1, 2)) == [0, 2, 1, 3]
+    raises(TypeError, lambda: p(-1))
+    raises(TypeError, lambda: p(5))
+    # conversion to list
+    assert list(p) == list(range(4))
+    assert p.copy() == p
+    assert copy(p) == p
+    assert Permutation(size=4) == Permutation(3)
+    assert Permutation(Permutation(3), size=5) == Permutation(4)
+    # cycle form with size
+    assert Permutation([[1, 2]], size=4) == Permutation([[1, 2], [0], [3]])
+    # random generation
+    assert Permutation.random(2) in (Permutation([1, 0]), Permutation([0, 1]))
+
+    p = Permutation([2, 5, 1, 6, 3, 0, 4])
+    q = Permutation([[1], [0, 3, 5, 6, 2, 4]])
+    assert len({p, p}) == 1
+    r = Permutation([1, 3, 2, 0, 4, 6, 5])
+    ans = Permutation(_af_rmuln(*[w.array_form for w in (p, q, r)])).array_form
+    assert rmul(p, q, r).array_form == ans
+    # make sure no other permutation of p, q, r could have given
+    # that answer
+    for a, b, c in permutations((p, q, r)):
+        if (a, b, c) == (p, q, r):
+            continue
+        assert rmul(a, b, c).array_form != ans
+
+    assert p.support() == list(range(7))
+    assert q.support() == [0, 2, 3, 4, 5, 6]
+    assert Permutation(p.cyclic_form).array_form == p.array_form
+    assert p.cardinality == 5040
+    assert q.cardinality == 5040
+    assert q.cycles == 2
+    assert rmul(q, p) == Permutation([4, 6, 1, 2, 5, 3, 0])
+    assert rmul(p, q) == Permutation([6, 5, 3, 0, 2, 4, 1])
+    assert _af_rmul(p.array_form, q.array_form) == \
+        [6, 5, 3, 0, 2, 4, 1]
+
+    assert rmul(Permutation([[1, 2, 3], [0, 4]]),
+                Permutation([[1, 2, 4], [0], [3]])).cyclic_form == \
+        [[0, 4, 2], [1, 3]]
+    assert q.array_form == [3, 1, 4, 5, 0, 6, 2]
+    assert q.cyclic_form == [[0, 3, 5, 6, 2, 4]]
+    assert q.full_cyclic_form == [[0, 3, 5, 6, 2, 4], [1]]
+    assert p.cyclic_form == [[0, 2, 1, 5], [3, 6, 4]]
+    t = p.transpositions()
+    assert t == [(0, 5), (0, 1), (0, 2), (3, 4), (3, 6)]
+    assert Permutation.rmul(*[Permutation(Cycle(*ti)) for ti in (t)])
+    assert Permutation([1, 0]).transpositions() == [(0, 1)]
+
+    assert p**13 == p
+    assert q**0 == Permutation(list(range(q.size)))
+    assert q**-2 == ~q**2
+    assert q**2 == Permutation([5, 1, 0, 6, 3, 2, 4])
+    assert q**3 == q**2*q
+    assert q**4 == q**2*q**2
+
+    a = Permutation(1, 3)
+    b = Permutation(2, 0, 3)
+    I = Permutation(3)
+    assert ~a == a**-1
+    assert a*~a == I
+    assert a*b**-1 == a*~b
+
+    ans = Permutation(0, 5, 3, 1, 6)(2, 4)
+    assert (p + q.rank()).rank() == ans.rank()
+    assert (p + q.rank())._rank == ans.rank()
+    assert (q + p.rank()).rank() == ans.rank()
+    raises(TypeError, lambda: p + Permutation(list(range(10))))
+
+    assert (p - q.rank()).rank() == Permutation(0, 6, 3, 1, 2, 5, 4).rank()
+    assert p.rank() - q.rank() < 0  # for coverage: make sure mod is used
+    assert (q - p.rank()).rank() == Permutation(1, 4, 6, 2)(3, 5).rank()
+
+    assert p*q == Permutation(_af_rmuln(*[list(w) for w in (q, p)]))
+    assert p*Permutation([]) == p
+    assert Permutation([])*p == p
+    assert p*Permutation([[0, 1]]) == Permutation([2, 5, 0, 6, 3, 1, 4])
+    assert Permutation([[0, 1]])*p == Permutation([5, 2, 1, 6, 3, 0, 4])
+
+    pq = p ^ q
+    assert pq == Permutation([5, 6, 0, 4, 1, 2, 3])
+    assert pq == rmul(q, p, ~q)
+    qp = q ^ p
+    assert qp == Permutation([4, 3, 6, 2, 1, 5, 0])
+    assert qp == rmul(p, q, ~p)
+    raises(ValueError, lambda: p ^ Permutation([]))
+
+    assert p.commutator(q) == Permutation(0, 1, 3, 4, 6, 5, 2)
+    assert q.commutator(p) == Permutation(0, 2, 5, 6, 4, 3, 1)
+    assert p.commutator(q) == ~q.commutator(p)
+    raises(ValueError, lambda: p.commutator(Permutation([])))
+
+    assert len(p.atoms()) == 7
+    assert q.atoms() == {0, 1, 2, 3, 4, 5, 6}
+
+    assert p.inversion_vector() == [2, 4, 1, 3, 1, 0]
+    assert q.inversion_vector() == [3, 1, 2, 2, 0, 1]
+
+    assert Permutation.from_inversion_vector(p.inversion_vector()) == p
+    assert Permutation.from_inversion_vector(q.inversion_vector()).array_form\
+        == q.array_form
+    raises(ValueError, lambda: Permutation.from_inversion_vector([0, 2]))
+    assert Permutation(list(range(500, -1, -1))).inversions() == 125250
+
+    s = Permutation([0, 4, 1, 3, 2])
+    assert s.parity() == 0
+    _ = s.cyclic_form  # needed to create a value for _cyclic_form
+    assert len(s._cyclic_form) != s.size and s.parity() == 0
+    assert not s.is_odd
+    assert s.is_even
+    assert Permutation([0, 1, 4, 3, 2]).parity() == 1
+    assert _af_parity([0, 4, 1, 3, 2]) == 0
+    assert _af_parity([0, 1, 4, 3, 2]) == 1
+
+    s = Permutation([0])
+
+    assert s.is_Singleton
+    assert Permutation([]).is_Empty
+
+    r = Permutation([3, 2, 1, 0])
+    assert (r**2).is_Identity
+
+    assert rmul(~p, p).is_Identity
+    assert (~p)**13 == Permutation([5, 2, 0, 4, 6, 1, 3])
+    assert p.max() == 6
+    assert p.min() == 0
+
+    q = Permutation([[6], [5], [0, 1, 2, 3, 4]])
+
+    assert q.max() == 4
+    assert q.min() == 0
+
+    p = Permutation([1, 5, 2, 0, 3, 6, 4])
+    q = Permutation([[1, 2, 3, 5, 6], [0, 4]])
+
+    assert p.ascents() == [0, 3, 4]
+    assert q.ascents() == [1, 2, 4]
+    assert r.ascents() == []
+
+    assert p.descents() == [1, 2, 5]
+    assert q.descents() == [0, 3, 5]
+    assert Permutation(r.descents()).is_Identity
+
+    assert p.inversions() == 7
+    # test the merge-sort with a longer permutation
+    big = list(p) + list(range(p.max() + 1, p.max() + 130))
+    assert Permutation(big).inversions() == 7
+    assert p.signature() == -1
+    assert q.inversions() == 11
+    assert q.signature() == -1
+    assert rmul(p, ~p).inversions() == 0
+    assert rmul(p, ~p).signature() == 1
+
+    assert p.order() == 6
+    assert q.order() == 10
+    assert (p**(p.order())).is_Identity
+
+    assert p.length() == 6
+    assert q.length() == 7
+    assert r.length() == 4
+
+    assert p.runs() == [[1, 5], [2], [0, 3, 6], [4]]
+    assert q.runs() == [[4], [2, 3, 5], [0, 6], [1]]
+    assert r.runs() == [[3], [2], [1], [0]]
+
+    assert p.index() == 8
+    assert q.index() == 8
+    assert r.index() == 3
+
+    assert p.get_precedence_distance(q) == q.get_precedence_distance(p)
+    assert p.get_adjacency_distance(q) == p.get_adjacency_distance(q)
+    assert p.get_positional_distance(q) == p.get_positional_distance(q)
+    p = Permutation([0, 1, 2, 3])
+    q = Permutation([3, 2, 1, 0])
+    assert p.get_precedence_distance(q) == 6
+    assert p.get_adjacency_distance(q) == 3
+    assert p.get_positional_distance(q) == 8
+    p = Permutation([0, 3, 1, 2, 4])
+    q = Permutation.josephus(4, 5, 2)
+    assert p.get_adjacency_distance(q) == 3
+    raises(ValueError, lambda: p.get_adjacency_distance(Permutation([])))
+    raises(ValueError, lambda: p.get_positional_distance(Permutation([])))
+    raises(ValueError, lambda: p.get_precedence_distance(Permutation([])))
+
+    a = [Permutation.unrank_nonlex(4, i) for i in range(5)]
+    iden = Permutation([0, 1, 2, 3])
+    for i in range(5):
+        for j in range(i + 1, 5):
+            assert a[i].commutes_with(a[j]) == \
+                (rmul(a[i], a[j]) == rmul(a[j], a[i]))
+            if a[i].commutes_with(a[j]):
+                assert a[i].commutator(a[j]) == iden
+                assert a[j].commutator(a[i]) == iden
+
+    a = Permutation(3)
+    b = Permutation(0, 6, 3)(1, 2)
+    assert a.cycle_structure == {1: 4}
+    assert b.cycle_structure == {2: 1, 3: 1, 1: 2}
+    # issue 11130
+    raises(ValueError, lambda: Permutation(3, size=3))
+    raises(ValueError, lambda: Permutation([1, 2, 0, 3], size=3))
+
+
+def test_Permutation_subclassing():
+    # Subclass that adds permutation application on iterables
+    class CustomPermutation(Permutation):
+        def __call__(self, *i):
+            try:
+                return super().__call__(*i)
+            except TypeError:
+                pass
+
+            try:
+                perm_obj = i[0]
+                return [self._array_form[j] for j in perm_obj]
+            except TypeError:
+                raise TypeError('unrecognized argument')
+
+        def __eq__(self, other):
+            if isinstance(other, Permutation):
+                return self._hashable_content() == other._hashable_content()
+            else:
+                return super().__eq__(other)
+
+        def __hash__(self):
+            return super().__hash__()
+
+    p = CustomPermutation([1, 2, 3, 0])
+    q = Permutation([1, 2, 3, 0])
+
+    assert p == q
+    raises(TypeError, lambda: q([1, 2]))
+    assert [2, 3] == p([1, 2])
+
+    assert type(p * q) == CustomPermutation
+    assert type(q * p) == Permutation  # True because q.__mul__(p) is called!
+
+    # Run all tests for the Permutation class also on the subclass
+    def wrapped_test_Permutation():
+        # Monkeypatch the class definition in the globals
+        globals()['__Perm'] = globals()['Permutation']
+        globals()['Permutation'] = CustomPermutation
+        test_Permutation()
+        globals()['Permutation'] = globals()['__Perm']  # Restore
+        del globals()['__Perm']
+
+    wrapped_test_Permutation()
+
+
+def test_josephus():
+    assert Permutation.josephus(4, 6, 1) == Permutation([3, 1, 0, 2, 5, 4])
+    assert Permutation.josephus(1, 5, 1).is_Identity
+
+
+def test_ranking():
+    assert Permutation.unrank_lex(5, 10).rank() == 10
+    p = Permutation.unrank_lex(15, 225)
+    assert p.rank() == 225
+    p1 = p.next_lex()
+    assert p1.rank() == 226
+    assert Permutation.unrank_lex(15, 225).rank() == 225
+    assert Permutation.unrank_lex(10, 0).is_Identity
+    p = Permutation.unrank_lex(4, 23)
+    assert p.rank() == 23
+    assert p.array_form == [3, 2, 1, 0]
+    assert p.next_lex() is None
+
+    p = Permutation([1, 5, 2, 0, 3, 6, 4])
+    q = Permutation([[1, 2, 3, 5, 6], [0, 4]])
+    a = [Permutation.unrank_trotterjohnson(4, i).array_form for i in range(5)]
+    assert a == [[0, 1, 2, 3], [0, 1, 3, 2], [0, 3, 1, 2], [3, 0, 1,
+        2], [3, 0, 2, 1] ]
+    assert [Permutation(pa).rank_trotterjohnson() for pa in a] == list(range(5))
+    assert Permutation([0, 1, 2, 3]).next_trotterjohnson() == \
+        Permutation([0, 1, 3, 2])
+
+    assert q.rank_trotterjohnson() == 2283
+    assert p.rank_trotterjohnson() == 3389
+    assert Permutation([1, 0]).rank_trotterjohnson() == 1
+    a = Permutation(list(range(3)))
+    b = a
+    l = []
+    tj = []
+    for i in range(6):
+        l.append(a)
+        tj.append(b)
+        a = a.next_lex()
+        b = b.next_trotterjohnson()
+    assert a == b is None
+    assert {tuple(a) for a in l} == {tuple(a) for a in tj}
+
+    p = Permutation([2, 5, 1, 6, 3, 0, 4])
+    q = Permutation([[6], [5], [0, 1, 2, 3, 4]])
+    assert p.rank() == 1964
+    assert q.rank() == 870
+    assert Permutation([]).rank_nonlex() == 0
+    prank = p.rank_nonlex()
+    assert prank == 1600
+    assert Permutation.unrank_nonlex(7, 1600) == p
+    qrank = q.rank_nonlex()
+    assert qrank == 41
+    assert Permutation.unrank_nonlex(7, 41) == Permutation(q.array_form)
+
+    a = [Permutation.unrank_nonlex(4, i).array_form for i in range(24)]
+    assert a == [
+        [1, 2, 3, 0], [3, 2, 0, 1], [1, 3, 0, 2], [1, 2, 0, 3], [2, 3, 1, 0],
+        [2, 0, 3, 1], [3, 0, 1, 2], [2, 0, 1, 3], [1, 3, 2, 0], [3, 0, 2, 1],
+        [1, 0, 3, 2], [1, 0, 2, 3], [2, 1, 3, 0], [2, 3, 0, 1], [3, 1, 0, 2],
+        [2, 1, 0, 3], [3, 2, 1, 0], [0, 2, 3, 1], [0, 3, 1, 2], [0, 2, 1, 3],
+        [3, 1, 2, 0], [0, 3, 2, 1], [0, 1, 3, 2], [0, 1, 2, 3]]
+
+    N = 10
+    p1 = Permutation(a[0])
+    for i in range(1, N+1):
+        p1 = p1*Permutation(a[i])
+    p2 = Permutation.rmul_with_af(*[Permutation(h) for h in a[N::-1]])
+    assert p1 == p2
+
+    ok = []
+    p = Permutation([1, 0])
+    for i in range(3):
+        ok.append(p.array_form)
+        p = p.next_nonlex()
+        if p is None:
+            ok.append(None)
+            break
+    assert ok == [[1, 0], [0, 1], None]
+    assert Permutation([3, 2, 0, 1]).next_nonlex() == Permutation([1, 3, 0, 2])
+    assert [Permutation(pa).rank_nonlex() for pa in a] == list(range(24))
+
+
+def test_mul():
+    a, b = [0, 2, 1, 3], [0, 1, 3, 2]
+    assert _af_rmul(a, b) == [0, 2, 3, 1]
+    assert _af_rmuln(a, b, list(range(4))) == [0, 2, 3, 1]
+    assert rmul(Permutation(a), Permutation(b)).array_form == [0, 2, 3, 1]
+
+    a = Permutation([0, 2, 1, 3])
+    b = (0, 1, 3, 2)
+    c = (3, 1, 2, 0)
+    assert Permutation.rmul(a, b, c) == Permutation([1, 2, 3, 0])
+    assert Permutation.rmul(a, c) == Permutation([3, 2, 1, 0])
+    raises(TypeError, lambda: Permutation.rmul(b, c))
+
+    n = 6
+    m = 8
+    a = [Permutation.unrank_nonlex(n, i).array_form for i in range(m)]
+    h = list(range(n))
+    for i in range(m):
+        h = _af_rmul(h, a[i])
+        h2 = _af_rmuln(*a[:i + 1])
+        assert h == h2
+
+
+def test_args():
+    p = Permutation([(0, 3, 1, 2), (4, 5)])
+    assert p._cyclic_form is None
+    assert Permutation(p) == p
+    assert p.cyclic_form == [[0, 3, 1, 2], [4, 5]]
+    assert p._array_form == [3, 2, 0, 1, 5, 4]
+    p = Permutation((0, 3, 1, 2))
+    assert p._cyclic_form is None
+    assert p._array_form == [0, 3, 1, 2]
+    assert Permutation([0]) == Permutation((0, ))
+    assert Permutation([[0], [1]]) == Permutation(((0, ), (1, ))) == \
+        Permutation(((0, ), [1]))
+    assert Permutation([[1, 2]]) == Permutation([0, 2, 1])
+    assert Permutation([[1], [4, 2]]) == Permutation([0, 1, 4, 3, 2])
+    assert Permutation([[1], [4, 2]], size=1) == Permutation([0, 1, 4, 3, 2])
+    assert Permutation(
+        [[1], [4, 2]], size=6) == Permutation([0, 1, 4, 3, 2, 5])
+    assert Permutation([[0, 1], [0, 2]]) == Permutation(0, 1, 2)
+    assert Permutation([], size=3) == Permutation([0, 1, 2])
+    assert Permutation(3).list(5) == [0, 1, 2, 3, 4]
+    assert Permutation(3).list(-1) == []
+    assert Permutation(5)(1, 2).list(-1) == [0, 2, 1]
+    assert Permutation(5)(1, 2).list() == [0, 2, 1, 3, 4, 5]
+    raises(ValueError, lambda: Permutation([1, 2], [0]))
+           # enclosing brackets needed
+    raises(ValueError, lambda: Permutation([[1, 2], 0]))
+           # enclosing brackets needed on 0
+    raises(ValueError, lambda: Permutation([1, 1, 0]))
+    raises(ValueError, lambda: Permutation([4, 5], size=10))  # where are 0-3?
+    # but this is ok because cycles imply that only those listed moved
+    assert Permutation(4, 5) == Permutation([0, 1, 2, 3, 5, 4])
+
+
+def test_Cycle():
+    assert str(Cycle()) == '()'
+    assert Cycle(Cycle(1,2)) == Cycle(1, 2)
+    assert Cycle(1,2).copy() == Cycle(1,2)
+    assert list(Cycle(1, 3, 2)) == [0, 3, 1, 2]
+    assert Cycle(1, 2)(2, 3) == Cycle(1, 3, 2)
+    assert Cycle(1, 2)(2, 3)(4, 5) == Cycle(1, 3, 2)(4, 5)
+    assert Permutation(Cycle(1, 2)(2, 1, 0, 3)).cyclic_form, Cycle(0, 2, 1)
+    raises(ValueError, lambda: Cycle().list())
+    assert Cycle(1, 2).list() == [0, 2, 1]
+    assert Cycle(1, 2).list(4) == [0, 2, 1, 3]
+    assert Cycle(3).list(2) == [0, 1]
+    assert Cycle(3).list(6) == [0, 1, 2, 3, 4, 5]
+    assert Permutation(Cycle(1, 2), size=4) == \
+        Permutation([0, 2, 1, 3])
+    assert str(Cycle(1, 2)(4, 5)) == '(1 2)(4 5)'
+    assert str(Cycle(1, 2)) == '(1 2)'
+    assert Cycle(Permutation(list(range(3)))) == Cycle()
+    assert Cycle(1, 2).list() == [0, 2, 1]
+    assert Cycle(1, 2).list(4) == [0, 2, 1, 3]
+    assert Cycle().size == 0
+    raises(ValueError, lambda: Cycle((1, 2)))
+    raises(ValueError, lambda: Cycle(1, 2, 1))
+    raises(TypeError, lambda: Cycle(1, 2)*{})
+    raises(ValueError, lambda: Cycle(4)[a])
+    raises(ValueError, lambda: Cycle(2, -4, 3))
+
+    # check round-trip
+    p = Permutation([[1, 2], [4, 3]], size=5)
+    assert Permutation(Cycle(p)) == p
+
+
+def test_from_sequence():
+    assert Permutation.from_sequence('SymPy') == Permutation(4)(0, 1, 3)
+    assert Permutation.from_sequence('SymPy', key=lambda x: x.lower()) == \
+        Permutation(4)(0, 2)(1, 3)
+
+
+def test_resize():
+    p = Permutation(0, 1, 2)
+    assert p.resize(5) == Permutation(0, 1, 2, size=5)
+    assert p.resize(4) == Permutation(0, 1, 2, size=4)
+    assert p.resize(3) == p
+    raises(ValueError, lambda: p.resize(2))
+
+    p = Permutation(0, 1, 2)(3, 4)(5, 6)
+    assert p.resize(3) == Permutation(0, 1, 2)
+    raises(ValueError, lambda: p.resize(4))
+
+
+def test_printing_cyclic():
+    p1 = Permutation([0, 2, 1])
+    assert repr(p1) == 'Permutation(1, 2)'
+    assert str(p1) == '(1 2)'
+    p2 = Permutation()
+    assert repr(p2) == 'Permutation()'
+    assert str(p2) == '()'
+    p3 = Permutation([1, 2, 0, 3])
+    assert repr(p3) == 'Permutation(3)(0, 1, 2)'
+
+
+def test_printing_non_cyclic():
+    p1 = Permutation([0, 1, 2, 3, 4, 5])
+    assert srepr(p1, perm_cyclic=False) == 'Permutation([], size=6)'
+    assert sstr(p1, perm_cyclic=False) == 'Permutation([], size=6)'
+    p2 = Permutation([0, 1, 2])
+    assert srepr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])'
+    assert sstr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])'
+
+    p3 = Permutation([0, 2, 1])
+    assert srepr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])'
+    assert sstr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])'
+    p4 = Permutation([0, 1, 3, 2, 4, 5, 6, 7])
+    assert srepr(p4, perm_cyclic=False) == 'Permutation([0, 1, 3, 2], size=8)'
+
+
+def test_deprecated_print_cyclic():
+    p = Permutation(0, 1, 2)
+    try:
+        Permutation.print_cyclic = True
+        with warns_deprecated_sympy():
+            assert sstr(p) == '(0 1 2)'
+        with warns_deprecated_sympy():
+            assert srepr(p) == 'Permutation(0, 1, 2)'
+        with warns_deprecated_sympy():
+            assert pretty(p) == '(0 1 2)'
+        with warns_deprecated_sympy():
+            assert latex(p) == r'\left( 0\; 1\; 2\right)'
+
+        Permutation.print_cyclic = False
+        with warns_deprecated_sympy():
+            assert sstr(p) == 'Permutation([1, 2, 0])'
+        with warns_deprecated_sympy():
+            assert srepr(p) == 'Permutation([1, 2, 0])'
+        with warns_deprecated_sympy():
+            assert pretty(p, use_unicode=False) == '/0 1 2\\\n\\1 2 0/'
+        with warns_deprecated_sympy():
+            assert latex(p) == \
+                r'\begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 0 \end{pmatrix}'
+    finally:
+        Permutation.print_cyclic = None
+
+
+def test_permutation_equality():
+    a = Permutation(0, 1, 2)
+    b = Permutation(0, 1, 2)
+    assert Eq(a, b) is S.true
+    c = Permutation(0, 2, 1)
+    assert Eq(a, c) is S.false
+
+    d = Permutation(0, 1, 2, size=4)
+    assert unchanged(Eq, a, d)
+    e = Permutation(0, 2, 1, size=4)
+    assert unchanged(Eq, a, e)
+
+    i = Permutation()
+    assert unchanged(Eq, i, 0)
+    assert unchanged(Eq, 0, i)
+
+
+def test_issue_17661():
+    c1 = Cycle(1,2)
+    c2 = Cycle(1,2)
+    assert c1 == c2
+    assert repr(c1) == 'Cycle(1, 2)'
+    assert c1 == c2
+
+
+def test_permutation_apply():
+    x = Symbol('x')
+    p = Permutation(0, 1, 2)
+    assert p.apply(0) == 1
+    assert isinstance(p.apply(0), Integer)
+    assert p.apply(x) == AppliedPermutation(p, x)
+    assert AppliedPermutation(p, x).subs(x, 0) == 1
+
+    x = Symbol('x', integer=False)
+    raises(NotImplementedError, lambda: p.apply(x))
+    x = Symbol('x', negative=True)
+    raises(NotImplementedError, lambda: p.apply(x))
+
+
+def test_AppliedPermutation():
+    x = Symbol('x')
+    p = Permutation(0, 1, 2)
+    raises(ValueError, lambda: AppliedPermutation((0, 1, 2), x))
+    assert AppliedPermutation(p, 1, evaluate=True) == 2
+    assert AppliedPermutation(p, 1, evaluate=False).__class__ == \
+        AppliedPermutation
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_polyhedron.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_polyhedron.py
new file mode 100644
index 0000000000000000000000000000000000000000..abf469bb560eef1f378eff4740a84b80b696035f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_polyhedron.py
@@ -0,0 +1,105 @@
+from sympy.core.symbol import symbols
+from sympy.sets.sets import FiniteSet
+from sympy.combinatorics.polyhedron import (Polyhedron,
+    tetrahedron, cube as square, octahedron, dodecahedron, icosahedron,
+    cube_faces)
+from sympy.combinatorics.permutations import Permutation
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.testing.pytest import raises
+
+rmul = Permutation.rmul
+
+
+def test_polyhedron():
+    raises(ValueError, lambda: Polyhedron(list('ab'),
+        pgroup=[Permutation([0])]))
+    pgroup = [Permutation([[0, 7, 2, 5], [6, 1, 4, 3]]),
+              Permutation([[0, 7, 1, 6], [5, 2, 4, 3]]),
+              Permutation([[3, 6, 0, 5], [4, 1, 7, 2]]),
+              Permutation([[7, 4, 5], [1, 3, 0], [2], [6]]),
+              Permutation([[1, 3, 2], [7, 6, 5], [4], [0]]),
+              Permutation([[4, 7, 6], [2, 0, 3], [1], [5]]),
+              Permutation([[1, 2, 0], [4, 5, 6], [3], [7]]),
+              Permutation([[4, 2], [0, 6], [3, 7], [1, 5]]),
+              Permutation([[3, 5], [7, 1], [2, 6], [0, 4]]),
+              Permutation([[2, 5], [1, 6], [0, 4], [3, 7]]),
+              Permutation([[4, 3], [7, 0], [5, 1], [6, 2]]),
+              Permutation([[4, 1], [0, 5], [6, 2], [7, 3]]),
+              Permutation([[7, 2], [3, 6], [0, 4], [1, 5]]),
+              Permutation([0, 1, 2, 3, 4, 5, 6, 7])]
+    corners = tuple(symbols('A:H'))
+    faces = cube_faces
+    cube = Polyhedron(corners, faces, pgroup)
+
+    assert cube.edges == FiniteSet(*(
+        (0, 1), (6, 7), (1, 2), (5, 6), (0, 3), (2, 3),
+        (4, 7), (4, 5), (3, 7), (1, 5), (0, 4), (2, 6)))
+
+    for i in range(3):  # add 180 degree face rotations
+        cube.rotate(cube.pgroup[i]**2)
+
+    assert cube.corners == corners
+
+    for i in range(3, 7):  # add 240 degree axial corner rotations
+        cube.rotate(cube.pgroup[i]**2)
+
+    assert cube.corners == corners
+    cube.rotate(1)
+    raises(ValueError, lambda: cube.rotate(Permutation([0, 1])))
+    assert cube.corners != corners
+    assert cube.array_form == [7, 6, 4, 5, 3, 2, 0, 1]
+    assert cube.cyclic_form == [[0, 7, 1, 6], [2, 4, 3, 5]]
+    cube.reset()
+    assert cube.corners == corners
+
+    def check(h, size, rpt, target):
+
+        assert len(h.faces) + len(h.vertices) - len(h.edges) == 2
+        assert h.size == size
+
+        got = set()
+        for p in h.pgroup:
+            # make sure it restores original
+            P = h.copy()
+            hit = P.corners
+            for i in range(rpt):
+                P.rotate(p)
+                if P.corners == hit:
+                    break
+            else:
+                print('error in permutation', p.array_form)
+            for i in range(rpt):
+                P.rotate(p)
+                got.add(tuple(P.corners))
+                c = P.corners
+                f = [[c[i] for i in f] for f in P.faces]
+                assert h.faces == Polyhedron(c, f).faces
+        assert len(got) == target
+        assert PermutationGroup([Permutation(g) for g in got]).is_group
+
+    for h, size, rpt, target in zip(
+        (tetrahedron, square, octahedron, dodecahedron, icosahedron),
+        (4, 8, 6, 20, 12),
+        (3, 4, 4, 5, 5),
+            (12, 24, 24, 60, 60)):
+        check(h, size, rpt, target)
+
+
+def test_pgroups():
+    from sympy.combinatorics.polyhedron import (cube, tetrahedron_faces,
+            octahedron_faces, dodecahedron_faces, icosahedron_faces)
+    from sympy.combinatorics.polyhedron import _pgroup_calcs
+    (tetrahedron2, cube2, octahedron2, dodecahedron2, icosahedron2,
+     tetrahedron_faces2, cube_faces2, octahedron_faces2,
+     dodecahedron_faces2, icosahedron_faces2) = _pgroup_calcs()
+
+    assert tetrahedron == tetrahedron2
+    assert cube == cube2
+    assert octahedron == octahedron2
+    assert dodecahedron == dodecahedron2
+    assert icosahedron == icosahedron2
+    assert sorted(map(sorted, tetrahedron_faces)) == sorted(map(sorted, tetrahedron_faces2))
+    assert sorted(cube_faces) == sorted(cube_faces2)
+    assert sorted(octahedron_faces) == sorted(octahedron_faces2)
+    assert sorted(dodecahedron_faces) == sorted(dodecahedron_faces2)
+    assert sorted(icosahedron_faces) == sorted(icosahedron_faces2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_prufer.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_prufer.py
new file mode 100644
index 0000000000000000000000000000000000000000..b077c7cf3f023a4c36d7039505e6165ab29f275a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_prufer.py
@@ -0,0 +1,74 @@
+from sympy.combinatorics.prufer import Prufer
+from sympy.testing.pytest import raises
+
+
+def test_prufer():
+    # number of nodes is optional
+    assert Prufer([[0, 1], [0, 2], [0, 3], [0, 4]], 5).nodes == 5
+    assert Prufer([[0, 1], [0, 2], [0, 3], [0, 4]]).nodes == 5
+
+    a = Prufer([[0, 1], [0, 2], [0, 3], [0, 4]])
+    assert a.rank == 0
+    assert a.nodes == 5
+    assert a.prufer_repr == [0, 0, 0]
+
+    a = Prufer([[2, 4], [1, 4], [1, 3], [0, 5], [0, 4]])
+    assert a.rank == 924
+    assert a.nodes == 6
+    assert a.tree_repr == [[2, 4], [1, 4], [1, 3], [0, 5], [0, 4]]
+    assert a.prufer_repr == [4, 1, 4, 0]
+
+    assert Prufer.edges([0, 1, 2, 3], [1, 4, 5], [1, 4, 6]) == \
+        ([[0, 1], [1, 2], [1, 4], [2, 3], [4, 5], [4, 6]], 7)
+    assert Prufer([0]*4).size == Prufer([6]*4).size == 1296
+
+    # accept iterables but convert to list of lists
+    tree = [(0, 1), (1, 5), (0, 3), (0, 2), (2, 6), (4, 7), (2, 4)]
+    tree_lists = [list(t) for t in tree]
+    assert Prufer(tree).tree_repr == tree_lists
+    assert sorted(Prufer(set(tree)).tree_repr) == sorted(tree_lists)
+
+    raises(ValueError, lambda: Prufer([[1, 2], [3, 4]]))  # 0 is missing
+    raises(ValueError, lambda: Prufer([[2, 3], [3, 4]]))  # 0, 1 are missing
+    assert Prufer(*Prufer.edges([1, 2], [3, 4])).prufer_repr == [1, 3]
+    raises(ValueError, lambda: Prufer.edges(
+        [1, 3], [3, 4]))  # a broken tree but edges doesn't care
+    raises(ValueError, lambda: Prufer.edges([1, 2], [5, 6]))
+    raises(ValueError, lambda: Prufer([[]]))
+
+    a = Prufer([[0, 1], [0, 2], [0, 3]])
+    b = a.next()
+    assert b.tree_repr == [[0, 2], [0, 1], [1, 3]]
+    assert b.rank == 1
+
+
+def test_round_trip():
+    def doit(t, b):
+        e, n = Prufer.edges(*t)
+        t = Prufer(e, n)
+        a = sorted(t.tree_repr)
+        b = [i - 1 for i in b]
+        assert t.prufer_repr == b
+        assert sorted(Prufer(b).tree_repr) == a
+        assert Prufer.unrank(t.rank, n).prufer_repr == b
+
+    doit([[1, 2]], [])
+    doit([[2, 1, 3]], [1])
+    doit([[1, 3, 2]], [3])
+    doit([[1, 2, 3]], [2])
+    doit([[2, 1, 4], [1, 3]], [1, 1])
+    doit([[3, 2, 1, 4]], [2, 1])
+    doit([[3, 2, 1], [2, 4]], [2, 2])
+    doit([[1, 3, 2, 4]], [3, 2])
+    doit([[1, 4, 2, 3]], [4, 2])
+    doit([[3, 1, 4, 2]], [4, 1])
+    doit([[4, 2, 1, 3]], [1, 2])
+    doit([[1, 2, 4, 3]], [2, 4])
+    doit([[1, 3, 4, 2]], [3, 4])
+    doit([[2, 4, 1], [4, 3]], [4, 4])
+    doit([[1, 2, 3, 4]], [2, 3])
+    doit([[2, 3, 1], [3, 4]], [3, 3])
+    doit([[1, 4, 3, 2]], [4, 3])
+    doit([[2, 1, 4, 3]], [1, 4])
+    doit([[2, 1, 3, 4]], [1, 3])
+    doit([[6, 2, 1, 4], [1, 3, 5, 8], [3, 7]], [1, 2, 1, 3, 3, 5])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_rewriting.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_rewriting.py
new file mode 100644
index 0000000000000000000000000000000000000000..97c562bd57a2cd6318fa1dcb13c6f6278c861cca
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_rewriting.py
@@ -0,0 +1,49 @@
+from sympy.combinatorics.fp_groups import FpGroup
+from sympy.combinatorics.free_groups import free_group
+from sympy.testing.pytest import raises
+
+
+def test_rewriting():
+    F, a, b = free_group("a, b")
+    G = FpGroup(F, [a*b*a**-1*b**-1])
+    a, b = G.generators
+    R = G._rewriting_system
+    assert R.is_confluent
+
+    assert G.reduce(b**-1*a) == a*b**-1
+    assert G.reduce(b**3*a**4*b**-2*a) == a**5*b
+    assert G.equals(b**2*a**-1*b, b**4*a**-1*b**-1)
+
+    assert R.reduce_using_automaton(b*a*a**2*b**-1) == a**3
+    assert R.reduce_using_automaton(b**3*a**4*b**-2*a) == a**5*b
+    assert R.reduce_using_automaton(b**-1*a) == a*b**-1
+
+    G = FpGroup(F, [a**3, b**3, (a*b)**2])
+    R = G._rewriting_system
+    R.make_confluent()
+    # R._is_confluent should be set to True after
+    # a successful run of make_confluent
+    assert R.is_confluent
+    # but also the system should actually be confluent
+    assert R._check_confluence()
+    assert G.reduce(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1
+    # check for automaton reduction
+    assert R.reduce_using_automaton(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1
+
+    G = FpGroup(F, [a**2, b**3, (a*b)**4])
+    R = G._rewriting_system
+    assert G.reduce(a**2*b**-2*a**2*b) == b**-1
+    assert R.reduce_using_automaton(a**2*b**-2*a**2*b) == b**-1
+    assert G.reduce(a**3*b**-2*a**2*b) == a**-1*b**-1
+    assert R.reduce_using_automaton(a**3*b**-2*a**2*b) == a**-1*b**-1
+    # Check after adding a rule
+    R.add_rule(a**2, b)
+    assert R.reduce_using_automaton(a**2*b**-2*a**2*b) == b**-1
+    assert R.reduce_using_automaton(a**4*b**-2*a**2*b**3) == b
+
+    R.set_max(15)
+    raises(RuntimeError, lambda:  R.add_rule(a**-3, b))
+    R.set_max(20)
+    R.add_rule(a**-3, b)
+
+    assert R.add_rule(a, a) == set()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_schur_number.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_schur_number.py
new file mode 100644
index 0000000000000000000000000000000000000000..e6beb9b11fa993a99b71d89b8485050fc3575b8e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_schur_number.py
@@ -0,0 +1,55 @@
+from sympy.core import S, Rational
+from sympy.combinatorics.schur_number import schur_partition, SchurNumber
+from sympy.core.random import _randint
+from sympy.testing.pytest import raises
+from sympy.core.symbol import symbols
+
+
+def _sum_free_test(subset):
+    """
+    Checks if subset is sum-free(There are no x,y,z in the subset such that
+    x + y = z)
+    """
+    for i in subset:
+        for j in subset:
+            assert (i + j in subset) is False
+
+
+def test_schur_partition():
+    raises(ValueError, lambda: schur_partition(S.Infinity))
+    raises(ValueError, lambda: schur_partition(-1))
+    raises(ValueError, lambda: schur_partition(0))
+    assert schur_partition(2) == [[1, 2]]
+
+    random_number_generator = _randint(1000)
+    for _ in range(5):
+        n = random_number_generator(1, 1000)
+        result = schur_partition(n)
+        t = 0
+        numbers = []
+        for item in result:
+            _sum_free_test(item)
+            """
+            Checks if the occurrence of all numbers is exactly one
+            """
+            t += len(item)
+            for l in item:
+                assert (l in numbers) is False
+                numbers.append(l)
+        assert n == t
+
+    x = symbols("x")
+    raises(ValueError, lambda: schur_partition(x))
+
+def test_schur_number():
+    first_known_schur_numbers = {1: 1, 2: 4, 3: 13, 4: 44, 5: 160}
+    for k in first_known_schur_numbers:
+        assert SchurNumber(k) == first_known_schur_numbers[k]
+
+    assert SchurNumber(S.Infinity) == S.Infinity
+    assert SchurNumber(0) == 0
+    raises(ValueError, lambda: SchurNumber(0.5))
+
+    n = symbols("n")
+    assert SchurNumber(n).lower_bound() == 3**n/2 - Rational(1, 2)
+    assert SchurNumber(8).lower_bound() == 5039
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_subsets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_subsets.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d50076da1c685294c2d2561dcc2a6af629eaf83
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_subsets.py
@@ -0,0 +1,63 @@
+from sympy.combinatorics.subsets import Subset, ksubsets
+from sympy.testing.pytest import raises
+
+
+def test_subset():
+    a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
+    assert a.next_binary() == Subset(['b'], ['a', 'b', 'c', 'd'])
+    assert a.prev_binary() == Subset(['c'], ['a', 'b', 'c', 'd'])
+    assert a.next_lexicographic() == Subset(['d'], ['a', 'b', 'c', 'd'])
+    assert a.prev_lexicographic() == Subset(['c'], ['a', 'b', 'c', 'd'])
+    assert a.next_gray() == Subset(['c'], ['a', 'b', 'c', 'd'])
+    assert a.prev_gray() == Subset(['d'], ['a', 'b', 'c', 'd'])
+    assert a.rank_binary == 3
+    assert a.rank_lexicographic == 14
+    assert a.rank_gray == 2
+    assert a.cardinality == 16
+    assert a.size == 2
+    assert Subset.bitlist_from_subset(a, ['a', 'b', 'c', 'd']) == '0011'
+
+    a = Subset([2, 5, 7], [1, 2, 3, 4, 5, 6, 7])
+    assert a.next_binary() == Subset([2, 5, 6], [1, 2, 3, 4, 5, 6, 7])
+    assert a.prev_binary() == Subset([2, 5], [1, 2, 3, 4, 5, 6, 7])
+    assert a.next_lexicographic() == Subset([2, 6], [1, 2, 3, 4, 5, 6, 7])
+    assert a.prev_lexicographic() == Subset([2, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7])
+    assert a.next_gray() == Subset([2, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7])
+    assert a.prev_gray() == Subset([2, 5], [1, 2, 3, 4, 5, 6, 7])
+    assert a.rank_binary == 37
+    assert a.rank_lexicographic == 93
+    assert a.rank_gray == 57
+    assert a.cardinality == 128
+
+    superset = ['a', 'b', 'c', 'd']
+    assert Subset.unrank_binary(4, superset).rank_binary == 4
+    assert Subset.unrank_gray(10, superset).rank_gray == 10
+
+    superset = [1, 2, 3, 4, 5, 6, 7, 8, 9]
+    assert Subset.unrank_binary(33, superset).rank_binary == 33
+    assert Subset.unrank_gray(25, superset).rank_gray == 25
+
+    a = Subset([], ['a', 'b', 'c', 'd'])
+    i = 1
+    while a.subset != Subset(['d'], ['a', 'b', 'c', 'd']).subset:
+        a = a.next_lexicographic()
+        i = i + 1
+    assert i == 16
+
+    i = 1
+    while a.subset != Subset([], ['a', 'b', 'c', 'd']).subset:
+        a = a.prev_lexicographic()
+        i = i + 1
+    assert i == 16
+
+    raises(ValueError, lambda: Subset(['a', 'b'], ['a']))
+    raises(ValueError, lambda: Subset(['a'], ['b', 'c']))
+    raises(ValueError, lambda: Subset.subset_from_bitlist(['a', 'b'], '010'))
+
+    assert Subset(['a'], ['a', 'b']) != Subset(['b'], ['a', 'b'])
+    assert Subset(['a'], ['a', 'b']) != Subset(['a'], ['a', 'c'])
+
+def test_ksubsets():
+    assert list(ksubsets([1, 2, 3], 2)) == [(1, 2), (1, 3), (2, 3)]
+    assert list(ksubsets([1, 2, 3, 4, 5], 2)) == [(1, 2), (1, 3), (1, 4),
+               (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_tensor_can.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_tensor_can.py
new file mode 100644
index 0000000000000000000000000000000000000000..3922419f20b92536426bfaae4b7e94df5db671b5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_tensor_can.py
@@ -0,0 +1,560 @@
+from sympy.combinatorics.permutations import Permutation, Perm
+from sympy.combinatorics.tensor_can import (perm_af_direct_product, dummy_sgs,
+    riemann_bsgs, get_symmetric_group_sgs, canonicalize, bsgs_direct_product)
+from sympy.combinatorics.testutil import canonicalize_naive, graph_certificate
+from sympy.testing.pytest import skip, XFAIL
+
+def test_perm_af_direct_product():
+    gens1 = [[1,0,2,3], [0,1,3,2]]
+    gens2 = [[1,0]]
+    assert perm_af_direct_product(gens1, gens2, 0) == [[1, 0, 2, 3, 4, 5], [0, 1, 3, 2, 4, 5], [0, 1, 2, 3, 5, 4]]
+    gens1 = [[1,0,2,3,5,4], [0,1,3,2,4,5]]
+    gens2 = [[1,0,2,3]]
+    assert [[1, 0, 2, 3, 4, 5, 7, 6], [0, 1, 3, 2, 4, 5, 6, 7], [0, 1, 2, 3, 5, 4, 6, 7]]
+
+def test_dummy_sgs():
+    a = dummy_sgs([1,2], 0, 4)
+    assert a == [[0,2,1,3,4,5]]
+    a = dummy_sgs([2,3,4,5], 0, 8)
+    assert a == [x._array_form for x in [Perm(9)(2,3), Perm(9)(4,5),
+        Perm(9)(2,4)(3,5)]]
+
+    a = dummy_sgs([2,3,4,5], 1, 8)
+    assert a == [x._array_form for x in [Perm(2,3)(8,9), Perm(4,5)(8,9),
+        Perm(9)(2,4)(3,5)]]
+
+def test_get_symmetric_group_sgs():
+    assert get_symmetric_group_sgs(2) == ([0], [Permutation(3)(0,1)])
+    assert get_symmetric_group_sgs(2, 1) == ([0], [Permutation(0,1)(2,3)])
+    assert get_symmetric_group_sgs(3) == ([0,1], [Permutation(4)(0,1), Permutation(4)(1,2)])
+    assert get_symmetric_group_sgs(3, 1) == ([0,1], [Permutation(0,1)(3,4), Permutation(1,2)(3,4)])
+    assert get_symmetric_group_sgs(4) == ([0,1,2], [Permutation(5)(0,1), Permutation(5)(1,2), Permutation(5)(2,3)])
+    assert get_symmetric_group_sgs(4, 1) == ([0,1,2], [Permutation(0,1)(4,5), Permutation(1,2)(4,5), Permutation(2,3)(4,5)])
+
+
+def test_canonicalize_no_slot_sym():
+    # cases in which there is no slot symmetry after fixing the
+    # free indices; here and in the following if the symmetry of the
+    # metric is not specified, it is assumed to be symmetric.
+    # If it is not specified, tensors are commuting.
+
+    # A_d0 * B^d0; g = [1,0, 2,3]; T_c = A^d0*B_d0; can = [0,1,2,3]
+    base1, gens1 = get_symmetric_group_sgs(1)
+    dummies = [0, 1]
+    g = Permutation([1,0,2,3])
+    can = canonicalize(g, dummies, 0, (base1,gens1,1,0), (base1,gens1,1,0))
+    assert can == [0,1,2,3]
+    # equivalently
+    can = canonicalize(g, dummies, 0, (base1, gens1, 2, None))
+    assert can == [0,1,2,3]
+
+    # with antisymmetric metric; T_c = -A^d0*B_d0; can = [0,1,3,2]
+    can = canonicalize(g, dummies, 1, (base1,gens1,1,0), (base1,gens1,1,0))
+    assert can == [0,1,3,2]
+
+    # A^a * B^b; ord = [a,b]; g = [0,1,2,3]; can = g
+    g = Permutation([0,1,2,3])
+    dummies = []
+    t0 = t1 = (base1, gens1, 1, 0)
+    can = canonicalize(g, dummies, 0, t0, t1)
+    assert can == [0,1,2,3]
+    # B^b * A^a
+    g = Permutation([1,0,2,3])
+    can = canonicalize(g, dummies, 0, t0, t1)
+    assert can == [1,0,2,3]
+
+    # A symmetric
+    # A^{b}_{d0}*A^{d0, a} order a,b,d0,-d0; T_c = A^{a d0}*A{b}_{d0}
+    # g = [1,3,2,0,4,5]; can = [0,2,1,3,4,5]
+    base2, gens2 = get_symmetric_group_sgs(2)
+    dummies = [2,3]
+    g = Permutation([1,3,2,0,4,5])
+    can = canonicalize(g, dummies, 0, (base2, gens2, 2, 0))
+    assert can == [0, 2, 1, 3, 4, 5]
+    # with antisymmetric metric
+    can = canonicalize(g, dummies, 1, (base2, gens2, 2, 0))
+    assert can == [0, 2, 1, 3, 4, 5]
+    # A^{a}_{d0}*A^{d0, b}
+    g = Permutation([0,3,2,1,4,5])
+    can = canonicalize(g, dummies, 1, (base2, gens2, 2, 0))
+    assert can == [0, 2, 1, 3, 5, 4]
+
+    # A, B symmetric
+    # A^b_d0*B^{d0,a}; g=[1,3,2,0,4,5]
+    # T_c = A^{b,d0}*B_{a,d0}; can = [1,2,0,3,4,5]
+    dummies = [2,3]
+    g = Permutation([1,3,2,0,4,5])
+    can = canonicalize(g, dummies, 0, (base2,gens2,1,0), (base2,gens2,1,0))
+    assert can == [1,2,0,3,4,5]
+    # same with antisymmetric metric
+    can = canonicalize(g, dummies, 1, (base2,gens2,1,0), (base2,gens2,1,0))
+    assert can == [1,2,0,3,5,4]
+
+    # A^{d1}_{d0}*B^d0*C_d1 ord=[d0,-d0,d1,-d1]; g = [2,1,0,3,4,5]
+    # T_c = A^{d0 d1}*B_d0*C_d1; can = [0,2,1,3,4,5]
+    base1, gens1 = get_symmetric_group_sgs(1)
+    base2, gens2 = get_symmetric_group_sgs(2)
+    g = Permutation([2,1,0,3,4,5])
+    dummies = [0,1,2,3]
+    t0 = (base2, gens2, 1, 0)
+    t1 = t2 = (base1, gens1, 1, 0)
+    can = canonicalize(g, dummies, 0, t0, t1, t2)
+    assert can == [0, 2, 1, 3, 4, 5]
+
+    # A without symmetry
+    # A^{d1}_{d0}*B^d0*C_d1 ord=[d0,-d0,d1,-d1]; g = [2,1,0,3,4,5]
+    # T_c = A^{d0 d1}*B_d1*C_d0; can = [0,2,3,1,4,5]
+    g = Permutation([2,1,0,3,4,5])
+    dummies = [0,1,2,3]
+    t0 = ([], [Permutation(list(range(4)))], 1, 0)
+    can = canonicalize(g, dummies, 0, t0, t1, t2)
+    assert can == [0,2,3,1,4,5]
+    # A, B without symmetry
+    # A^{d1}_{d0}*B_{d1}^{d0}; g = [2,1,3,0,4,5]
+    # T_c = A^{d0 d1}*B_{d0 d1}; can = [0,2,1,3,4,5]
+    t0 = t1 = ([], [Permutation(list(range(4)))], 1, 0)
+    dummies = [0,1,2,3]
+    g = Permutation([2,1,3,0,4,5])
+    can = canonicalize(g, dummies, 0, t0, t1)
+    assert can == [0, 2, 1, 3, 4, 5]
+    # A_{d0}^{d1}*B_{d1}^{d0}; g = [1,2,3,0,4,5]
+    # T_c = A^{d0 d1}*B_{d1 d0}; can = [0,2,3,1,4,5]
+    g = Permutation([1,2,3,0,4,5])
+    can = canonicalize(g, dummies, 0, t0, t1)
+    assert can == [0,2,3,1,4,5]
+
+    # A, B, C without symmetry
+    # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1]
+    # g=[4,2,0,3,5,1,6,7]
+    # T_c=A^{d0 d1}*B_{a d1}*C_{d0 b}; can = [2,4,0,5,3,1,6,7]
+    t0 = t1 = t2 = ([], [Permutation(list(range(4)))], 1, 0)
+    dummies = [2,3,4,5]
+    g = Permutation([4,2,0,3,5,1,6,7])
+    can = canonicalize(g, dummies, 0, t0, t1, t2)
+    assert can == [2,4,0,5,3,1,6,7]
+
+    # A symmetric, B and C without symmetry
+    # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1]
+    # g=[4,2,0,3,5,1,6,7]
+    # T_c = A^{d0 d1}*B_{a d0}*C_{d1 b}; can = [2,4,0,3,5,1,6,7]
+    t0 = (base2,gens2,1,0)
+    t1 = t2 = ([], [Permutation(list(range(4)))], 1, 0)
+    dummies = [2,3,4,5]
+    g = Permutation([4,2,0,3,5,1,6,7])
+    can = canonicalize(g, dummies, 0, t0, t1, t2)
+    assert can == [2,4,0,3,5,1,6,7]
+
+    # A and C symmetric, B without symmetry
+    # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1]
+    # g=[4,2,0,3,5,1,6,7]
+    # T_c = A^{d0 d1}*B_{a d0}*C_{b d1}; can = [2,4,0,3,1,5,6,7]
+    t0 = t2 = (base2,gens2,1,0)
+    t1 = ([], [Permutation(list(range(4)))], 1, 0)
+    dummies = [2,3,4,5]
+    g = Permutation([4,2,0,3,5,1,6,7])
+    can = canonicalize(g, dummies, 0, t0, t1, t2)
+    assert can == [2,4,0,3,1,5,6,7]
+
+    # A symmetric, B without symmetry, C antisymmetric
+    # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1]
+    # g=[4,2,0,3,5,1,6,7]
+    # T_c = -A^{d0 d1}*B_{a d0}*C_{b d1}; can = [2,4,0,3,1,5,7,6]
+    t0 = (base2,gens2, 1, 0)
+    t1 = ([], [Permutation(list(range(4)))], 1, 0)
+    base2a, gens2a = get_symmetric_group_sgs(2, 1)
+    t2 = (base2a, gens2a, 1, 0)
+    dummies = [2,3,4,5]
+    g = Permutation([4,2,0,3,5,1,6,7])
+    can = canonicalize(g, dummies, 0, t0, t1, t2)
+    assert can == [2,4,0,3,1,5,7,6]
+
+
+def test_canonicalize_no_dummies():
+    base1, gens1 = get_symmetric_group_sgs(1)
+    base2, gens2 = get_symmetric_group_sgs(2)
+    base2a, gens2a = get_symmetric_group_sgs(2, 1)
+
+    # A commuting
+    # A^c A^b A^a; ord = [a,b,c]; g = [2,1,0,3,4]
+    # T_c = A^a A^b A^c; can = list(range(5))
+    g = Permutation([2,1,0,3,4])
+    can = canonicalize(g, [], 0, (base1, gens1, 3, 0))
+    assert can == list(range(5))
+
+    # A anticommuting
+    # A^c A^b A^a; ord = [a,b,c]; g = [2,1,0,3,4]
+    # T_c = -A^a A^b A^c; can = [0,1,2,4,3]
+    g = Permutation([2,1,0,3,4])
+    can = canonicalize(g, [], 0, (base1, gens1, 3, 1))
+    assert can == [0,1,2,4,3]
+
+    # A commuting and symmetric
+    # A^{b,d}*A^{c,a}; ord = [a,b,c,d]; g = [1,3,2,0,4,5]
+    # T_c = A^{a c}*A^{b d}; can = [0,2,1,3,4,5]
+    g = Permutation([1,3,2,0,4,5])
+    can = canonicalize(g, [], 0, (base2, gens2, 2, 0))
+    assert can == [0,2,1,3,4,5]
+
+    # A anticommuting and symmetric
+    # A^{b,d}*A^{c,a}; ord = [a,b,c,d]; g = [1,3,2,0,4,5]
+    # T_c = -A^{a c}*A^{b d}; can = [0,2,1,3,5,4]
+    g = Permutation([1,3,2,0,4,5])
+    can = canonicalize(g, [], 0, (base2, gens2, 2, 1))
+    assert can == [0,2,1,3,5,4]
+    # A^{c,a}*A^{b,d} ; g = [2,0,1,3,4,5]
+    # T_c = A^{a c}*A^{b d}; can = [0,2,1,3,4,5]
+    g = Permutation([2,0,1,3,4,5])
+    can = canonicalize(g, [], 0, (base2, gens2, 2, 1))
+    assert can == [0,2,1,3,4,5]
+
+def test_no_metric_symmetry():
+    # no metric symmetry
+    # A^d1_d0 * A^d0_d1; ord = [d0,-d0,d1,-d1]; g= [2,1,0,3,4,5]
+    # T_c = A^d0_d1 * A^d1_d0; can = [0,3,2,1,4,5]
+    g = Permutation([2,1,0,3,4,5])
+    can = canonicalize(g, list(range(4)), None, [[], [Permutation(list(range(4)))], 2, 0])
+    assert can == [0,3,2,1,4,5]
+
+    # A^d1_d2 * A^d0_d3 * A^d2_d1 * A^d3_d0
+    # ord = [d0,-d0,d1,-d1,d2,-d2,d3,-d3]
+    #        0    1  2  3  4   5   6   7
+    # g = [2,5,0,7,4,3,6,1,8,9]
+    # T_c = A^d0_d1 * A^d1_d0 * A^d2_d3 * A^d3_d2
+    # can = [0,3,2,1,4,7,6,5,8,9]
+    g = Permutation([2,5,0,7,4,3,6,1,8,9])
+    #can = canonicalize(g, list(range(8)), 0, [[], [list(range(4))], 4, 0])
+    #assert can == [0, 2, 3, 1, 4, 6, 7, 5, 8, 9]
+    can = canonicalize(g, list(range(8)), None, [[], [Permutation(list(range(4)))], 4, 0])
+    assert can == [0, 3, 2, 1, 4, 7, 6, 5, 8, 9]
+
+    # A^d0_d2 * A^d1_d3 * A^d3_d0 * A^d2_d1
+    # g = [0,5,2,7,6,1,4,3,8,9]
+    # T_c = A^d0_d1 * A^d1_d2 * A^d2_d3 * A^d3_d0
+    # can = [0,3,2,5,4,7,6,1,8,9]
+    g = Permutation([0,5,2,7,6,1,4,3,8,9])
+    can = canonicalize(g, list(range(8)), None, [[], [Permutation(list(range(4)))], 4, 0])
+    assert can == [0,3,2,5,4,7,6,1,8,9]
+
+    g = Permutation([12,7,10,3,14,13,4,11,6,1,2,9,0,15,8,5,16,17])
+    can = canonicalize(g, list(range(16)), None, [[], [Permutation(list(range(4)))], 8, 0])
+    assert can == [0,3,2,5,4,7,6,1,8,11,10,13,12,15,14,9,16,17]
+
+def test_canonical_free():
+    # t = A^{d0 a1}*A_d0^a0
+    # ord = [a0,a1,d0,-d0];  g = [2,1,3,0,4,5]; dummies = [[2,3]]
+    # t_c = A_d0^a0*A^{d0 a1}
+    # can = [3,0, 2,1, 4,5]
+    g = Permutation([2,1,3,0,4,5])
+    dummies = [[2,3]]
+    can = canonicalize(g, dummies, [None], ([], [Permutation(3)], 2, 0))
+    assert can == [3,0, 2,1, 4,5]
+
+def test_canonicalize1():
+    base1, gens1 = get_symmetric_group_sgs(1)
+    base1a, gens1a = get_symmetric_group_sgs(1, 1)
+    base2, gens2 = get_symmetric_group_sgs(2)
+    base3, gens3 = get_symmetric_group_sgs(3)
+    base2a, gens2a = get_symmetric_group_sgs(2, 1)
+    base3a, gens3a = get_symmetric_group_sgs(3, 1)
+
+    # A_d0*A^d0; ord = [d0,-d0]; g = [1,0,2,3]
+    # T_c = A^d0*A_d0; can = [0,1,2,3]
+    g = Permutation([1,0,2,3])
+    can = canonicalize(g, [0, 1], 0, (base1, gens1, 2, 0))
+    assert can == list(range(4))
+
+    # A commuting
+    # A_d0*A_d1*A_d2*A^d2*A^d1*A^d0; ord=[d0,-d0,d1,-d1,d2,-d2]
+    # g = [1,3,5,4,2,0,6,7]
+    # T_c = A^d0*A_d0*A^d1*A_d1*A^d2*A_d2; can = list(range(8))
+    g = Permutation([1,3,5,4,2,0,6,7])
+    can = canonicalize(g, list(range(6)), 0, (base1, gens1, 6, 0))
+    assert can == list(range(8))
+
+    # A anticommuting
+    # A_d0*A_d1*A_d2*A^d2*A^d1*A^d0; ord=[d0,-d0,d1,-d1,d2,-d2]
+    # g = [1,3,5,4,2,0,6,7]
+    # T_c 0;  can = 0
+    g = Permutation([1,3,5,4,2,0,6,7])
+    can = canonicalize(g, list(range(6)), 0, (base1, gens1, 6, 1))
+    assert can == 0
+    can1 = canonicalize_naive(g, list(range(6)), 0, (base1, gens1, 6, 1))
+    assert can1 == 0
+
+    # A commuting symmetric
+    # A^{d0 b}*A^a_d1*A^d1_d0; ord=[a,b,d0,-d0,d1,-d1]
+    # g = [2,1,0,5,4,3,6,7]
+    # T_c = A^{a d0}*A^{b d1}*A_{d0 d1}; can = [0,2,1,4,3,5,6,7]
+    g = Permutation([2,1,0,5,4,3,6,7])
+    can = canonicalize(g, list(range(2,6)), 0, (base2, gens2, 3, 0))
+    assert can == [0,2,1,4,3,5,6,7]
+
+    # A, B commuting symmetric
+    # A^{d0 b}*A^d1_d0*B^a_d1; ord=[a,b,d0,-d0,d1,-d1]
+    # g = [2,1,4,3,0,5,6,7]
+    # T_c = A^{b d0}*A_d0^d1*B^a_d1; can = [1,2,3,4,0,5,6,7]
+    g = Permutation([2,1,4,3,0,5,6,7])
+    can = canonicalize(g, list(range(2,6)), 0, (base2,gens2,2,0), (base2,gens2,1,0))
+    assert can == [1,2,3,4,0,5,6,7]
+
+    # A commuting symmetric
+    # A^{d1 d0 b}*A^{a}_{d1 d0}; ord=[a,b, d0,-d0,d1,-d1]
+    # g = [4,2,1,0,5,3,6,7]
+    # T_c = A^{a d0 d1}*A^{b}_{d0 d1}; can = [0,2,4,1,3,5,6,7]
+    g = Permutation([4,2,1,0,5,3,6,7])
+    can = canonicalize(g, list(range(2,6)), 0, (base3, gens3, 2, 0))
+    assert can == [0,2,4,1,3,5,6,7]
+
+
+    # A^{d3 d0 d2}*A^a0_{d1 d2}*A^d1_d3^a1*A^{a2 a3}_d0
+    # ord = [a0,a1,a2,a3,d0,-d0,d1,-d1,d2,-d2,d3,-d3]
+    #        0   1  2  3  4  5  6   7  8   9  10  11
+    # g = [10,4,8, 0,7,9, 6,11,1, 2,3,5, 12,13]
+    # T_c = A^{a0 d0 d1}*A^a1_d0^d2*A^{a2 a3 d3}*A_{d1 d2 d3}
+    # can = [0,4,6, 1,5,8, 2,3,10, 7,9,11, 12,13]
+    g = Permutation([10,4,8, 0,7,9, 6,11,1, 2,3,5, 12,13])
+    can = canonicalize(g, list(range(4,12)), 0, (base3, gens3, 4, 0))
+    assert can == [0,4,6, 1,5,8, 2,3,10, 7,9,11, 12,13]
+
+    # A commuting symmetric, B antisymmetric
+    # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3
+    # ord = [d0,-d0,d1,-d1,d2,-d2,d3,-d3]
+    # g = [0,2,4,5,7,3,1,6,8,9]
+    # in this esxample and in the next three,
+    # renaming dummy indices and using symmetry of A,
+    # T = A^{d0 d1 d2} * A_{d0 d1 d3} * B_d2^d3
+    # can = 0
+    g = Permutation([0,2,4,5,7,3,1,6,8,9])
+    can = canonicalize(g, list(range(8)), 0, (base3, gens3,2,0), (base2a,gens2a,1,0))
+    assert can == 0
+    # A anticommuting symmetric, B anticommuting
+    # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3
+    # T_c = A^{d0 d1 d2} * A_{d0 d1}^d3 * B_{d2 d3}
+    # can = [0,2,4, 1,3,6, 5,7, 8,9]
+    can = canonicalize(g, list(range(8)), 0, (base3, gens3,2,1), (base2a,gens2a,1,0))
+    assert can == [0,2,4, 1,3,6, 5,7, 8,9]
+    # A anticommuting symmetric, B antisymmetric commuting, antisymmetric metric
+    # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3
+    # T_c = -A^{d0 d1 d2} * A_{d0 d1}^d3 * B_{d2 d3}
+    # can = [0,2,4, 1,3,6, 5,7, 9,8]
+    can = canonicalize(g, list(range(8)), 1, (base3, gens3,2,1), (base2a,gens2a,1,0))
+    assert can == [0,2,4, 1,3,6, 5,7, 9,8]
+
+    # A anticommuting symmetric, B anticommuting anticommuting,
+    # no metric symmetry
+    # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3
+    # T_c = A^{d0 d1 d2} * A_{d0 d1 d3} * B_d2^d3
+    # can = [0,2,4, 1,3,7, 5,6, 8,9]
+    can = canonicalize(g, list(range(8)), None, (base3, gens3,2,1), (base2a,gens2a,1,0))
+    assert can == [0,2,4,1,3,7,5,6,8,9]
+
+    # Gamma anticommuting
+    # Gamma_{mu nu} * gamma^rho * Gamma^{nu mu alpha}
+    # ord = [alpha, rho, mu,-mu,nu,-nu]
+    # g = [3,5,1,4,2,0,6,7]
+    # T_c = -Gamma^{mu nu} * gamma^rho * Gamma_{alpha mu nu}
+    # can = [2,4,1,0,3,5,7,6]]
+    g = Permutation([3,5,1,4,2,0,6,7])
+    t0 = (base2a, gens2a, 1, None)
+    t1 = (base1, gens1, 1, None)
+    t2 = (base3a, gens3a, 1, None)
+    can = canonicalize(g, list(range(2, 6)), 0, t0, t1, t2)
+    assert can == [2,4,1,0,3,5,7,6]
+
+    # Gamma_{mu nu} * Gamma^{gamma beta} * gamma_rho * Gamma^{nu mu alpha}
+    # ord = [alpha, beta, gamma, -rho, mu,-mu,nu,-nu]
+    #         0      1      2     3    4   5   6  7
+    # g = [5,7,2,1,3,6,4,0,8,9]
+    # T_c = Gamma^{mu nu} * Gamma^{beta gamma} * gamma_rho * Gamma^alpha_{mu nu}    # can = [4,6,1,2,3,0,5,7,8,9]
+    t0 = (base2a, gens2a, 2, None)
+    g = Permutation([5,7,2,1,3,6,4,0,8,9])
+    can = canonicalize(g, list(range(4, 8)), 0, t0, t1, t2)
+    assert can == [4,6,1,2,3,0,5,7,8,9]
+
+    # f^a_{b,c} antisymmetric in b,c; A_mu^a no symmetry
+    # f^c_{d a} * f_{c e b} * A_mu^d * A_nu^a * A^{nu e} * A^{mu b}
+    # ord = [mu,-mu,nu,-nu,a,-a,b,-b,c,-c,d,-d, e, -e]
+    #         0  1  2   3  4  5 6  7 8  9 10 11 12 13
+    # g = [8,11,5, 9,13,7, 1,10, 3,4, 2,12, 0,6, 14,15]
+    # T_c = -f^{a b c} * f_a^{d e} * A^mu_b * A_{mu d} * A^nu_c * A_{nu e}
+    # can = [4,6,8,       5,10,12,   0,7,     1,11,       2,9,    3,13, 15,14]
+    g = Permutation([8,11,5, 9,13,7, 1,10, 3,4, 2,12, 0,6, 14,15])
+    base_f, gens_f = bsgs_direct_product(base1, gens1, base2a, gens2a)
+    base_A, gens_A = bsgs_direct_product(base1, gens1, base1, gens1)
+    t0 = (base_f, gens_f, 2, 0)
+    t1 = (base_A, gens_A, 4, 0)
+    can = canonicalize(g, [list(range(4)), list(range(4, 14))], [0, 0], t0, t1)
+    assert can == [4,6,8, 5,10,12, 0,7, 1,11, 2,9, 3,13, 15,14]
+
+
+def test_riemann_invariants():
+    baser, gensr = riemann_bsgs
+    # R^{d0 d1}_{d1 d0}; ord = [d0,-d0,d1,-d1]; g = [0,2,3,1,4,5]
+    # T_c = -R^{d0 d1}_{d0 d1}; can = [0,2,1,3,5,4]
+    g = Permutation([0,2,3,1,4,5])
+    can = canonicalize(g, list(range(2, 4)), 0, (baser, gensr, 1, 0))
+    assert can == [0,2,1,3,5,4]
+    # use a non minimal BSGS
+    can = canonicalize(g, list(range(2, 4)), 0, ([2, 0], [Permutation([1,0,2,3,5,4]), Permutation([2,3,0,1,4,5])], 1, 0))
+    assert can == [0,2,1,3,5,4]
+
+    """
+    The following tests in test_riemann_invariants and in
+    test_riemann_invariants1 have been checked using xperm.c from XPerm in
+    in [1] and with an older version contained in [2]
+
+    [1] xperm.c part of xPerm written by J. M. Martin-Garcia
+        http://www.xact.es/index.html
+    [2] test_xperm.cc in cadabra by Kasper Peeters, http://cadabra.phi-sci.com/
+    """
+    # R_d11^d1_d0^d5 * R^{d6 d4 d0}_d5 * R_{d7 d2 d8 d9} *
+    # R_{d10 d3 d6 d4} * R^{d2 d7 d11}_d1 * R^{d8 d9 d3 d10}
+    # ord: contravariant d_k ->2*k, covariant d_k -> 2*k+1
+    # T_c = R^{d0 d1 d2 d3} * R_{d0 d1}^{d4 d5} * R_{d2 d3}^{d6 d7} *
+    # R_{d4 d5}^{d8 d9} * R_{d6 d7}^{d10 d11} * R_{d8 d9 d10 d11}
+    g = Permutation([23,2,1,10,12,8,0,11,15,5,17,19,21,7,13,9,4,14,22,3,16,18,6,20,24,25])
+    can = canonicalize(g, list(range(24)), 0, (baser, gensr, 6, 0))
+    assert can == [0,2,4,6,1,3,8,10,5,7,12,14,9,11,16,18,13,15,20,22,17,19,21,23,24,25]
+
+    # use a non minimal BSGS
+    can = canonicalize(g, list(range(24)), 0, ([2, 0], [Permutation([1,0,2,3,5,4]), Permutation([2,3,0,1,4,5])], 6, 0))
+    assert can == [0,2,4,6,1,3,8,10,5,7,12,14,9,11,16,18,13,15,20,22,17,19,21,23,24,25]
+
+    g = Permutation([0,2,5,7,4,6,9,11,8,10,13,15,12,14,17,19,16,18,21,23,20,22,25,27,24,26,29,31,28,30,33,35,32,34,37,39,36,38,1,3,40,41])
+    can = canonicalize(g, list(range(40)), 0, (baser, gensr, 10, 0))
+    assert can == [0,2,4,6,1,3,8,10,5,7,12,14,9,11,16,18,13,15,20,22,17,19,24,26,21,23,28,30,25,27,32,34,29,31,36,38,33,35,37,39,40,41]
+
+
+@XFAIL
+def test_riemann_invariants1():
+    skip('takes too much time')
+    baser, gensr = riemann_bsgs
+    g = Permutation([17, 44, 11, 3, 0, 19, 23, 15, 38, 4, 25, 27, 43, 36, 22, 14, 8, 30, 41, 20, 2, 10, 12, 28, 18, 1, 29, 13, 37, 42, 33, 7, 9, 31, 24, 26, 39, 5, 34, 47, 32, 6, 21, 40, 35, 46, 45, 16, 48, 49])
+    can = canonicalize(g, list(range(48)), 0, (baser, gensr, 12, 0))
+    assert can == [0, 2, 4, 6, 1, 3, 8, 10, 5, 7, 12, 14, 9, 11, 16, 18, 13, 15, 20, 22, 17, 19, 24, 26, 21, 23, 28, 30, 25, 27, 32, 34, 29, 31, 36, 38, 33, 35, 40, 42, 37, 39, 44, 46, 41, 43, 45, 47, 48, 49]
+
+    g = Permutation([0,2,4,6, 7,8,10,12, 14,16,18,20, 19,22,24,26, 5,21,28,30, 32,34,36,38, 40,42,44,46, 13,48,50,52, 15,49,54,56, 17,33,41,58, 9,23,60,62, 29,35,63,64, 3,45,66,68, 25,37,47,57, 11,31,69,70, 27,39,53,72, 1,59,73,74, 55,61,67,76, 43,65,75,78, 51,71,77,79, 80,81])
+    can = canonicalize(g, list(range(80)), 0, (baser, gensr, 20, 0))
+    assert can == [0,2,4,6, 1,8,10,12, 3,14,16,18, 5,20,22,24, 7,26,28,30, 9,15,32,34, 11,36,23,38, 13,40,42,44, 17,39,29,46, 19,48,43,50, 21,45,52,54, 25,56,33,58, 27,60,53,62, 31,51,64,66, 35,65,47,68, 37,70,49,72, 41,74,57,76, 55,67,59,78, 61,69,71,75, 63,79,73,77, 80,81]
+
+
+def test_riemann_products():
+    baser, gensr = riemann_bsgs
+    base1, gens1 = get_symmetric_group_sgs(1)
+    base2, gens2 = get_symmetric_group_sgs(2)
+    base2a, gens2a = get_symmetric_group_sgs(2, 1)
+
+    # R^{a b d0}_d0 = 0
+    g = Permutation([0,1,2,3,4,5])
+    can = canonicalize(g, list(range(2,4)), 0, (baser, gensr, 1, 0))
+    assert can == 0
+
+    # R^{d0 b a}_d0 ; ord = [a,b,d0,-d0}; g = [2,1,0,3,4,5]
+    # T_c = -R^{a d0 b}_d0;  can = [0,2,1,3,5,4]
+    g = Permutation([2,1,0,3,4,5])
+    can = canonicalize(g, list(range(2, 4)), 0, (baser, gensr, 1, 0))
+    assert can == [0,2,1,3,5,4]
+
+    # R^d1_d2^b_d0 * R^{d0 a}_d1^d2; ord=[a,b,d0,-d0,d1,-d1,d2,-d2]
+    # g = [4,7,1,3,2,0,5,6,8,9]
+    # T_c = -R^{a d0 d1 d2}* R^b_{d0 d1 d2}
+    # can = [0,2,4,6,1,3,5,7,9,8]
+    g = Permutation([4,7,1,3,2,0,5,6,8,9])
+    can = canonicalize(g, list(range(2,8)), 0, (baser, gensr, 2, 0))
+    assert can == [0,2,4,6,1,3,5,7,9,8]
+    can1 = canonicalize_naive(g, list(range(2,8)), 0, (baser, gensr, 2, 0))
+    assert can == can1
+
+    # A symmetric commuting
+    # R^{d6 d5}_d2^d1 * R^{d4 d0 d2 d3} * A_{d6 d0} A_{d3 d1} * A_{d4 d5}
+    # g = [12,10,5,2, 8,0,4,6, 13,1, 7,3, 9,11,14,15]
+    # T_c = -R^{d0 d1 d2 d3} * R_d0^{d4 d5 d6} * A_{d1 d4}*A_{d2 d5}*A_{d3 d6}
+
+    g = Permutation([12,10,5,2,8,0,4,6,13,1,7,3,9,11,14,15])
+    can = canonicalize(g, list(range(14)), 0, ((baser,gensr,2,0)), (base2,gens2,3,0))
+    assert can == [0, 2, 4, 6, 1, 8, 10, 12, 3, 9, 5, 11, 7, 13, 15, 14]
+
+    # R^{d2 a0 a2 d0} * R^d1_d2^{a1 a3} * R^{a4 a5}_{d0 d1}
+    # ord = [a0,a1,a2,a3,a4,a5,d0,-d0,d1,-d1,d2,-d2]
+    #         0  1  2  3 4  5  6   7  8   9  10  11
+    # can = [0, 6, 2, 8, 1, 3, 7, 10, 4, 5, 9, 11, 12, 13]
+    # T_c = R^{a0 d0 a2 d1}*R^{a1 a3}_d0^d2*R^{a4 a5}_{d1 d2}
+    g = Permutation([10,0,2,6,8,11,1,3,4,5,7,9,12,13])
+    can = canonicalize(g, list(range(6,12)), 0, (baser, gensr, 3, 0))
+    assert can == [0, 6, 2, 8, 1, 3, 7, 10, 4, 5, 9, 11, 12, 13]
+    #can1 = canonicalize_naive(g, list(range(6,12)), 0, (baser, gensr, 3, 0))
+    #assert can == can1
+
+    # A^n_{i, j} antisymmetric in i,j
+    # A_m0^d0_a1 * A_m1^a0_d0; ord = [m0,m1,a0,a1,d0,-d0]
+    # g = [0,4,3,1,2,5,6,7]
+    # T_c = -A_{m a1}^d0 * A_m1^a0_d0
+    # can = [0,3,4,1,2,5,7,6]
+    base, gens = bsgs_direct_product(base1, gens1, base2a, gens2a)
+    dummies = list(range(4, 6))
+    g = Permutation([0,4,3,1,2,5,6,7])
+    can = canonicalize(g, dummies, 0, (base, gens, 2, 0))
+    assert can == [0, 3, 4, 1, 2, 5, 7, 6]
+
+
+    # A^n_{i, j} symmetric in i,j
+    # A^m0_a0^d2 * A^n0_d2^d1 * A^n1_d1^d0 * A_{m0 d0}^a1
+    # ordering: first the free indices; then first n, then d
+    # ord=[n0,n1,a0,a1, m0,-m0,d0,-d0,d1,-d1,d2,-d2]
+    #      0  1   2  3   4  5  6   7  8   9  10  11]
+    # g = [4,2,10, 0,11,8, 1,9,6, 5,7,3, 12,13]
+    # if the dummy indices m_i and d_i were separated,
+    # one gets
+    # T_c = A^{n0 d0 d1} * A^n1_d0^d2 * A^m0^a0_d1 * A_m0^a1_d2
+    # can = [0, 6, 8, 1, 7, 10, 4, 2, 9, 5, 3, 11, 12, 13]
+    # If they are not, so can is
+    # T_c = A^{n0 m0 d0} A^n1_m0^d1 A^{d2 a0}_d0 A_d2^a1_d1
+    # can = [0, 4, 6, 1, 5, 8, 10, 2, 7, 11, 3, 9, 12, 13]
+    # case with single type of indices
+
+    base, gens = bsgs_direct_product(base1, gens1, base2, gens2)
+    dummies = list(range(4, 12))
+    g = Permutation([4,2,10, 0,11,8, 1,9,6, 5,7,3, 12,13])
+    can = canonicalize(g, dummies, 0, (base, gens, 4, 0))
+    assert can == [0, 4, 6, 1, 5, 8, 10, 2, 7, 11, 3, 9, 12, 13]
+    # case with separated indices
+    dummies = [list(range(4, 6)), list(range(6,12))]
+    sym = [0, 0]
+    can = canonicalize(g, dummies, sym, (base, gens, 4, 0))
+    assert can == [0, 6, 8, 1, 7, 10, 4, 2, 9, 5, 3, 11, 12, 13]
+    # case with separated indices with the second type of index
+    # with antisymmetric metric: there is a sign change
+    sym = [0, 1]
+    can = canonicalize(g, dummies, sym, (base, gens, 4, 0))
+    assert can == [0, 6, 8, 1, 7, 10, 4, 2, 9, 5, 3, 11, 13, 12]
+
+def test_graph_certificate():
+    # test tensor invariants constructed from random regular graphs;
+    # checked graph isomorphism with networkx
+    import random
+    def randomize_graph(size, g):
+        p = list(range(size))
+        random.shuffle(p)
+        g1a = {}
+        for k, v in g1.items():
+            g1a[p[k]] = [p[i] for i in v]
+        return g1a
+
+    g1 = {0: [2, 3, 7], 1: [4, 5, 7], 2: [0, 4, 6], 3: [0, 6, 7], 4: [1, 2, 5], 5: [1, 4, 6], 6: [2, 3, 5], 7: [0, 1, 3]}
+    g2 = {0: [2, 3, 7], 1: [2, 4, 5], 2: [0, 1, 5], 3: [0, 6, 7], 4: [1, 5, 6], 5: [1, 2, 4], 6: [3, 4, 7], 7: [0, 3, 6]}
+
+    c1 = graph_certificate(g1)
+    c2 = graph_certificate(g2)
+    assert c1 != c2
+    g1a = randomize_graph(8, g1)
+    c1a = graph_certificate(g1a)
+    assert c1 == c1a
+
+    g1 = {0: [8, 1, 9, 7], 1: [0, 9, 3, 4], 2: [3, 4, 6, 7], 3: [1, 2, 5, 6], 4: [8, 1, 2, 5], 5: [9, 3, 4, 7], 6: [8, 2, 3, 7], 7: [0, 2, 5, 6], 8: [0, 9, 4, 6], 9: [8, 0, 5, 1]}
+    g2 = {0: [1, 2, 5, 6], 1: [0, 9, 5, 7], 2: [0, 4, 6, 7], 3: [8, 9, 6, 7], 4: [8, 2, 6, 7], 5: [0, 9, 8, 1], 6: [0, 2, 3, 4], 7: [1, 2, 3, 4], 8: [9, 3, 4, 5], 9: [8, 1, 3, 5]}
+    c1 = graph_certificate(g1)
+    c2 = graph_certificate(g2)
+    assert c1 != c2
+    g1a = randomize_graph(10, g1)
+    c1a = graph_certificate(g1a)
+    assert c1 == c1a
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_testutil.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_testutil.py
new file mode 100644
index 0000000000000000000000000000000000000000..736e7a4ff86967e41dca71cf12de6c387a82d26d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_testutil.py
@@ -0,0 +1,55 @@
+from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup,\
+    CyclicGroup
+from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists,\
+    _naive_list_centralizer, _verify_centralizer,\
+    _verify_normal_closure
+from sympy.combinatorics.permutations import Permutation
+from sympy.combinatorics.perm_groups import PermutationGroup
+from sympy.core.random import shuffle
+
+
+def test_cmp_perm_lists():
+    S = SymmetricGroup(4)
+    els = list(S.generate_dimino())
+    other = els.copy()
+    shuffle(other)
+    assert _cmp_perm_lists(els, other) is True
+
+
+def test_naive_list_centralizer():
+    # verified by GAP
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    assert _naive_list_centralizer(S, S) == [Permutation([0, 1, 2])]
+    assert PermutationGroup(_naive_list_centralizer(S, A)).is_subgroup(A)
+
+
+def test_verify_bsgs():
+    S = SymmetricGroup(5)
+    S.schreier_sims()
+    base = S.base
+    strong_gens = S.strong_gens
+    assert _verify_bsgs(S, base, strong_gens) is True
+    assert _verify_bsgs(S, base[:-1], strong_gens) is False
+    assert _verify_bsgs(S, base, S.generators) is False
+
+
+def test_verify_centralizer():
+    # verified by GAP
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    triv = PermutationGroup([Permutation([0, 1, 2])])
+    assert _verify_centralizer(S, S, centr=triv)
+    assert _verify_centralizer(S, A, centr=A)
+
+
+def test_verify_normal_closure():
+    # verified by GAP
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    assert _verify_normal_closure(S, A, closure=A)
+    S = SymmetricGroup(5)
+    A = AlternatingGroup(5)
+    C = CyclicGroup(5)
+    assert _verify_normal_closure(S, A, closure=A)
+    assert _verify_normal_closure(S, C, closure=A)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..bca183e81f354e398aee9ae809fe79b20c7f2468
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/tests/test_util.py
@@ -0,0 +1,120 @@
+from sympy.combinatorics.named_groups import SymmetricGroup, DihedralGroup,\
+    AlternatingGroup
+from sympy.combinatorics.permutations import Permutation
+from sympy.combinatorics.util import _check_cycles_alt_sym, _strip,\
+    _distribute_gens_by_base, _strong_gens_from_distr,\
+    _orbits_transversals_from_bsgs, _handle_precomputed_bsgs, _base_ordering,\
+    _remove_gens
+from sympy.combinatorics.testutil import _verify_bsgs
+
+
+def test_check_cycles_alt_sym():
+    perm1 = Permutation([[0, 1, 2, 3, 4, 5, 6], [7], [8], [9]])
+    perm2 = Permutation([[0, 1, 2, 3, 4, 5], [6, 7, 8, 9]])
+    perm3 = Permutation([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]])
+    assert _check_cycles_alt_sym(perm1) is True
+    assert _check_cycles_alt_sym(perm2) is False
+    assert _check_cycles_alt_sym(perm3) is False
+
+
+def test_strip():
+    D = DihedralGroup(5)
+    D.schreier_sims()
+    member = Permutation([4, 0, 1, 2, 3])
+    not_member1 = Permutation([0, 1, 4, 3, 2])
+    not_member2 = Permutation([3, 1, 4, 2, 0])
+    identity = Permutation([0, 1, 2, 3, 4])
+    res1 = _strip(member, D.base, D.basic_orbits, D.basic_transversals)
+    res2 = _strip(not_member1, D.base, D.basic_orbits, D.basic_transversals)
+    res3 = _strip(not_member2, D.base, D.basic_orbits, D.basic_transversals)
+    assert res1[0] == identity
+    assert res1[1] == len(D.base) + 1
+    assert res2[0] == not_member1
+    assert res2[1] == len(D.base) + 1
+    assert res3[0] != identity
+    assert res3[1] == 2
+
+
+def test_distribute_gens_by_base():
+    base = [0, 1, 2]
+    gens = [Permutation([0, 1, 2, 3]), Permutation([0, 1, 3, 2]),
+           Permutation([0, 2, 3, 1]), Permutation([3, 2, 1, 0])]
+    assert _distribute_gens_by_base(base, gens) == [gens,
+                                                   [Permutation([0, 1, 2, 3]),
+                                                   Permutation([0, 1, 3, 2]),
+                                                   Permutation([0, 2, 3, 1])],
+                                                   [Permutation([0, 1, 2, 3]),
+                                                   Permutation([0, 1, 3, 2])]]
+
+
+def test_strong_gens_from_distr():
+    strong_gens_distr = [[Permutation([0, 2, 1]), Permutation([1, 2, 0]),
+                  Permutation([1, 0, 2])], [Permutation([0, 2, 1])]]
+    assert _strong_gens_from_distr(strong_gens_distr) == \
+        [Permutation([0, 2, 1]),
+         Permutation([1, 2, 0]),
+         Permutation([1, 0, 2])]
+
+
+def test_orbits_transversals_from_bsgs():
+    S = SymmetricGroup(4)
+    S.schreier_sims()
+    base = S.base
+    strong_gens = S.strong_gens
+    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+    result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
+    orbits = result[0]
+    transversals = result[1]
+    base_len = len(base)
+    for i in range(base_len):
+        for el in orbits[i]:
+            assert transversals[i][el](base[i]) == el
+            for j in range(i):
+                assert transversals[i][el](base[j]) == base[j]
+    order = 1
+    for i in range(base_len):
+        order *= len(orbits[i])
+    assert S.order() == order
+
+
+def test_handle_precomputed_bsgs():
+    A = AlternatingGroup(5)
+    A.schreier_sims()
+    base = A.base
+    strong_gens = A.strong_gens
+    result = _handle_precomputed_bsgs(base, strong_gens)
+    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+    assert strong_gens_distr == result[2]
+    transversals = result[0]
+    orbits = result[1]
+    base_len = len(base)
+    for i in range(base_len):
+        for el in orbits[i]:
+            assert transversals[i][el](base[i]) == el
+            for j in range(i):
+                assert transversals[i][el](base[j]) == base[j]
+    order = 1
+    for i in range(base_len):
+        order *= len(orbits[i])
+    assert A.order() == order
+
+
+def test_base_ordering():
+    base = [2, 4, 5]
+    degree = 7
+    assert _base_ordering(base, degree) == [3, 4, 0, 5, 1, 2, 6]
+
+
+def test_remove_gens():
+    S = SymmetricGroup(10)
+    base, strong_gens = S.schreier_sims_incremental()
+    new_gens = _remove_gens(base, strong_gens)
+    assert _verify_bsgs(S, base, new_gens) is True
+    A = AlternatingGroup(7)
+    base, strong_gens = A.schreier_sims_incremental()
+    new_gens = _remove_gens(base, strong_gens)
+    assert _verify_bsgs(A, base, new_gens) is True
+    D = DihedralGroup(2)
+    base, strong_gens = D.schreier_sims_incremental()
+    new_gens = _remove_gens(base, strong_gens)
+    assert _verify_bsgs(D, base, new_gens) is True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/testutil.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/testutil.py
new file mode 100644
index 0000000000000000000000000000000000000000..9fe664ce9e7437b97feec90f2052eb2987c57a4e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/testutil.py
@@ -0,0 +1,357 @@
+from sympy.combinatorics import Permutation
+from sympy.combinatorics.util import _distribute_gens_by_base
+
+rmul = Permutation.rmul
+
+
+def _cmp_perm_lists(first, second):
+    """
+    Compare two lists of permutations as sets.
+
+    Explanation
+    ===========
+
+    This is used for testing purposes. Since the array form of a
+    permutation is currently a list, Permutation is not hashable
+    and cannot be put into a set.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.permutations import Permutation
+    >>> from sympy.combinatorics.testutil import _cmp_perm_lists
+    >>> a = Permutation([0, 2, 3, 4, 1])
+    >>> b = Permutation([1, 2, 0, 4, 3])
+    >>> c = Permutation([3, 4, 0, 1, 2])
+    >>> ls1 = [a, b, c]
+    >>> ls2 = [b, c, a]
+    >>> _cmp_perm_lists(ls1, ls2)
+    True
+
+    """
+    return {tuple(a) for a in first} == \
+           {tuple(a) for a in second}
+
+
+def _naive_list_centralizer(self, other, af=False):
+    from sympy.combinatorics.perm_groups import PermutationGroup
+    """
+    Return a list of elements for the centralizer of a subgroup/set/element.
+
+    Explanation
+    ===========
+
+    This is a brute force implementation that goes over all elements of the
+    group and checks for membership in the centralizer. It is used to
+    test ``.centralizer()`` from ``sympy.combinatorics.perm_groups``.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.testutil import _naive_list_centralizer
+    >>> from sympy.combinatorics.named_groups import DihedralGroup
+    >>> D = DihedralGroup(4)
+    >>> _naive_list_centralizer(D, D)
+    [Permutation([0, 1, 2, 3]), Permutation([2, 3, 0, 1])]
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.centralizer
+
+    """
+    from sympy.combinatorics.permutations import _af_commutes_with
+    if hasattr(other, 'generators'):
+        elements = list(self.generate_dimino(af=True))
+        gens = [x._array_form for x in other.generators]
+        commutes_with_gens = lambda x: all(_af_commutes_with(x, gen) for gen in gens)
+        centralizer_list = []
+        if not af:
+            for element in elements:
+                if commutes_with_gens(element):
+                    centralizer_list.append(Permutation._af_new(element))
+        else:
+            for element in elements:
+                if commutes_with_gens(element):
+                    centralizer_list.append(element)
+        return centralizer_list
+    elif hasattr(other, 'getitem'):
+        return _naive_list_centralizer(self, PermutationGroup(other), af)
+    elif hasattr(other, 'array_form'):
+        return _naive_list_centralizer(self, PermutationGroup([other]), af)
+
+
+def _verify_bsgs(group, base, gens):
+    """
+    Verify the correctness of a base and strong generating set.
+
+    Explanation
+    ===========
+
+    This is a naive implementation using the definition of a base and a strong
+    generating set relative to it. There are other procedures for
+    verifying a base and strong generating set, but this one will
+    serve for more robust testing.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import AlternatingGroup
+    >>> from sympy.combinatorics.testutil import _verify_bsgs
+    >>> A = AlternatingGroup(4)
+    >>> A.schreier_sims()
+    >>> _verify_bsgs(A, A.base, A.strong_gens)
+    True
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims
+
+    """
+    from sympy.combinatorics.perm_groups import PermutationGroup
+    strong_gens_distr = _distribute_gens_by_base(base, gens)
+    current_stabilizer = group
+    for i in range(len(base)):
+        candidate = PermutationGroup(strong_gens_distr[i])
+        if current_stabilizer.order() != candidate.order():
+            return False
+        current_stabilizer = current_stabilizer.stabilizer(base[i])
+    if current_stabilizer.order() != 1:
+        return False
+    return True
+
+
+def _verify_centralizer(group, arg, centr=None):
+    """
+    Verify the centralizer of a group/set/element inside another group.
+
+    This is used for testing ``.centralizer()`` from
+    ``sympy.combinatorics.perm_groups``
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+    ... AlternatingGroup)
+    >>> from sympy.combinatorics.perm_groups import PermutationGroup
+    >>> from sympy.combinatorics.permutations import Permutation
+    >>> from sympy.combinatorics.testutil import _verify_centralizer
+    >>> S = SymmetricGroup(5)
+    >>> A = AlternatingGroup(5)
+    >>> centr = PermutationGroup([Permutation([0, 1, 2, 3, 4])])
+    >>> _verify_centralizer(S, A, centr)
+    True
+
+    See Also
+    ========
+
+    _naive_list_centralizer,
+    sympy.combinatorics.perm_groups.PermutationGroup.centralizer,
+    _cmp_perm_lists
+
+    """
+    if centr is None:
+        centr = group.centralizer(arg)
+    centr_list = list(centr.generate_dimino(af=True))
+    centr_list_naive = _naive_list_centralizer(group, arg, af=True)
+    return _cmp_perm_lists(centr_list, centr_list_naive)
+
+
+def _verify_normal_closure(group, arg, closure=None):
+    from sympy.combinatorics.perm_groups import PermutationGroup
+    """
+    Verify the normal closure of a subgroup/subset/element in a group.
+
+    This is used to test
+    sympy.combinatorics.perm_groups.PermutationGroup.normal_closure
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
+    ... AlternatingGroup)
+    >>> from sympy.combinatorics.testutil import _verify_normal_closure
+    >>> S = SymmetricGroup(3)
+    >>> A = AlternatingGroup(3)
+    >>> _verify_normal_closure(S, A, closure=A)
+    True
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.PermutationGroup.normal_closure
+
+    """
+    if closure is None:
+        closure = group.normal_closure(arg)
+    conjugates = set()
+    if hasattr(arg, 'generators'):
+        subgr_gens = arg.generators
+    elif hasattr(arg, '__getitem__'):
+        subgr_gens = arg
+    elif hasattr(arg, 'array_form'):
+        subgr_gens = [arg]
+    for el in group.generate_dimino():
+        conjugates.update(gen ^ el for gen in subgr_gens)
+    naive_closure = PermutationGroup(list(conjugates))
+    return closure.is_subgroup(naive_closure)
+
+
+def canonicalize_naive(g, dummies, sym, *v):
+    """
+    Canonicalize tensor formed by tensors of the different types.
+
+    Explanation
+    ===========
+
+    sym_i symmetry under exchange of two component tensors of type `i`
+          None  no symmetry
+          0     commuting
+          1     anticommuting
+
+    Parameters
+    ==========
+
+    g : Permutation representing the tensor.
+    dummies : List of dummy indices.
+    msym : Symmetry of the metric.
+    v : A list of (base_i, gens_i, n_i, sym_i) for tensors of type `i`.
+        base_i, gens_i BSGS for tensors of this type
+        n_i  number of tensors of type `i`
+
+    Returns
+    =======
+
+    Returns 0 if the tensor is zero, else returns the array form of
+    the permutation representing the canonical form of the tensor.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.testutil import canonicalize_naive
+    >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs
+    >>> from sympy.combinatorics import Permutation
+    >>> g = Permutation([1, 3, 2, 0, 4, 5])
+    >>> base2, gens2 = get_symmetric_group_sgs(2)
+    >>> canonicalize_naive(g, [2, 3], 0, (base2, gens2, 2, 0))
+    [0, 2, 1, 3, 4, 5]
+    """
+    from sympy.combinatorics.perm_groups import PermutationGroup
+    from sympy.combinatorics.tensor_can import gens_products, dummy_sgs
+    from sympy.combinatorics.permutations import _af_rmul
+    v1 = []
+    for i in range(len(v)):
+        base_i, gens_i, n_i, sym_i = v[i]
+        v1.append((base_i, gens_i, [[]]*n_i, sym_i))
+    size, sbase, sgens = gens_products(*v1)
+    dgens = dummy_sgs(dummies, sym, size-2)
+    if isinstance(sym, int):
+        num_types = 1
+        dummies = [dummies]
+        sym = [sym]
+    else:
+        num_types = len(sym)
+    dgens = []
+    for i in range(num_types):
+        dgens.extend(dummy_sgs(dummies[i], sym[i], size - 2))
+    S = PermutationGroup(sgens)
+    D = PermutationGroup([Permutation(x) for x in dgens])
+    dlist = list(D.generate(af=True))
+    g = g.array_form
+    st = set()
+    for s in S.generate(af=True):
+        h = _af_rmul(g, s)
+        for d in dlist:
+            q = tuple(_af_rmul(d, h))
+            st.add(q)
+    a = list(st)
+    a.sort()
+    prev = (0,)*size
+    for h in a:
+        if h[:-2] == prev[:-2]:
+            if h[-1] != prev[-1]:
+                return 0
+        prev = h
+    return list(a[0])
+
+
+def graph_certificate(gr):
+    """
+    Return a certificate for the graph
+
+    Parameters
+    ==========
+
+    gr : adjacency list
+
+    Explanation
+    ===========
+
+    The graph is assumed to be unoriented and without
+    external lines.
+
+    Associate to each vertex of the graph a symmetric tensor with
+    number of indices equal to the degree of the vertex; indices
+    are contracted when they correspond to the same line of the graph.
+    The canonical form of the tensor gives a certificate for the graph.
+
+    This is not an efficient algorithm to get the certificate of a graph.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.testutil import graph_certificate
+    >>> gr1 = {0:[1, 2, 3, 5], 1:[0, 2, 4], 2:[0, 1, 3, 4], 3:[0, 2, 4], 4:[1, 2, 3, 5], 5:[0, 4]}
+    >>> gr2 = {0:[1, 5], 1:[0, 2, 3, 4], 2:[1, 3, 5], 3:[1, 2, 4, 5], 4:[1, 3, 5], 5:[0, 2, 3, 4]}
+    >>> c1 = graph_certificate(gr1)
+    >>> c2 = graph_certificate(gr2)
+    >>> c1
+    [0, 2, 4, 6, 1, 8, 10, 12, 3, 14, 16, 18, 5, 9, 15, 7, 11, 17, 13, 19, 20, 21]
+    >>> c1 == c2
+    True
+    """
+    from sympy.combinatorics.permutations import _af_invert
+    from sympy.combinatorics.tensor_can import get_symmetric_group_sgs, canonicalize
+    items = list(gr.items())
+    items.sort(key=lambda x: len(x[1]), reverse=True)
+    pvert = [x[0] for x in items]
+    pvert = _af_invert(pvert)
+
+    # the indices of the tensor are twice the number of lines of the graph
+    num_indices = 0
+    for v, neigh in items:
+        num_indices += len(neigh)
+    # associate to each vertex its indices; for each line
+    # between two vertices assign the
+    # even index to the vertex which comes first in items,
+    # the odd index to the other vertex
+    vertices = [[] for i in items]
+    i = 0
+    for v, neigh in items:
+        for v2 in neigh:
+            if pvert[v] < pvert[v2]:
+                vertices[pvert[v]].append(i)
+                vertices[pvert[v2]].append(i+1)
+                i += 2
+    g = []
+    for v in vertices:
+        g.extend(v)
+    assert len(g) == num_indices
+    g += [num_indices, num_indices + 1]
+    size = num_indices + 2
+    assert sorted(g) == list(range(size))
+    g = Permutation(g)
+    vlen = [0]*(len(vertices[0])+1)
+    for neigh in vertices:
+        vlen[len(neigh)] += 1
+    v = []
+    for i in range(len(vlen)):
+        n = vlen[i]
+        if n:
+            base, gens = get_symmetric_group_sgs(i)
+            v.append((base, gens, n, 0))
+    v.reverse()
+    dummies = list(range(num_indices))
+    can = canonicalize(g, dummies, 0, *v)
+    return can
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/util.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc73b02f94f4aae6f1b98bb3f0c837fd5a1d1e6d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/combinatorics/util.py
@@ -0,0 +1,532 @@
+from sympy.combinatorics.permutations import Permutation, _af_invert, _af_rmul
+from sympy.ntheory import isprime
+
+rmul = Permutation.rmul
+_af_new = Permutation._af_new
+
+############################################
+#
+# Utilities for computational group theory
+#
+############################################
+
+
+def _base_ordering(base, degree):
+    r"""
+    Order `\{0, 1, \dots, n-1\}` so that base points come first and in order.
+
+    Parameters
+    ==========
+
+    base : the base
+    degree : the degree of the associated permutation group
+
+    Returns
+    =======
+
+    A list ``base_ordering`` such that ``base_ordering[point]`` is the
+    number of ``point`` in the ordering.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import SymmetricGroup
+    >>> from sympy.combinatorics.util import _base_ordering
+    >>> S = SymmetricGroup(4)
+    >>> S.schreier_sims()
+    >>> _base_ordering(S.base, S.degree)
+    [0, 1, 2, 3]
+
+    Notes
+    =====
+
+    This is used in backtrack searches, when we define a relation `\ll` on
+    the underlying set for a permutation group of degree `n`,
+    `\{0, 1, \dots, n-1\}`, so that if `(b_1, b_2, \dots, b_k)` is a base we
+    have `b_i \ll b_j` whenever `i>> from sympy.combinatorics.util import _check_cycles_alt_sym
+    >>> from sympy.combinatorics import Permutation
+    >>> a = Permutation([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12]])
+    >>> _check_cycles_alt_sym(a)
+    False
+    >>> b = Permutation([[0, 1, 2, 3, 4, 5, 6], [7, 8, 9, 10]])
+    >>> _check_cycles_alt_sym(b)
+    True
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.PermutationGroup.is_alt_sym
+
+    """
+    n = perm.size
+    af = perm.array_form
+    current_len = 0
+    total_len = 0
+    used = set()
+    for i in range(n//2):
+        if i not in used and i < n//2 - total_len:
+            current_len = 1
+            used.add(i)
+            j = i
+            while af[j] != i:
+                current_len += 1
+                j = af[j]
+                used.add(j)
+            total_len += current_len
+            if current_len > n//2 and current_len < n - 2 and isprime(current_len):
+                return True
+    return False
+
+
+def _distribute_gens_by_base(base, gens):
+    r"""
+    Distribute the group elements ``gens`` by membership in basic stabilizers.
+
+    Explanation
+    ===========
+
+    Notice that for a base `(b_1, b_2, \dots, b_k)`, the basic stabilizers
+    are defined as `G^{(i)} = G_{b_1, \dots, b_{i-1}}` for
+    `i \in\{1, 2, \dots, k\}`.
+
+    Parameters
+    ==========
+
+    base : a sequence of points in `\{0, 1, \dots, n-1\}`
+    gens : a list of elements of a permutation group of degree `n`.
+
+    Returns
+    =======
+    list
+        List of length `k`, where `k` is the length of *base*. The `i`-th entry
+        contains those elements in *gens* which fix the first `i` elements of
+        *base* (so that the `0`-th entry is equal to *gens* itself). If no
+        element fixes the first `i` elements of *base*, the `i`-th element is
+        set to a list containing the identity element.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import DihedralGroup
+    >>> from sympy.combinatorics.util import _distribute_gens_by_base
+    >>> D = DihedralGroup(3)
+    >>> D.schreier_sims()
+    >>> D.strong_gens
+    [(0 1 2), (0 2), (1 2)]
+    >>> D.base
+    [0, 1]
+    >>> _distribute_gens_by_base(D.base, D.strong_gens)
+    [[(0 1 2), (0 2), (1 2)],
+     [(1 2)]]
+
+    See Also
+    ========
+
+    _strong_gens_from_distr, _orbits_transversals_from_bsgs,
+    _handle_precomputed_bsgs
+
+    """
+    base_len = len(base)
+    degree = gens[0].size
+    stabs = [[] for _ in range(base_len)]
+    max_stab_index = 0
+    for gen in gens:
+        j = 0
+        while j < base_len - 1 and gen._array_form[base[j]] == base[j]:
+            j += 1
+        if j > max_stab_index:
+            max_stab_index = j
+        for k in range(j + 1):
+            stabs[k].append(gen)
+    for i in range(max_stab_index + 1, base_len):
+        stabs[i].append(_af_new(list(range(degree))))
+    return stabs
+
+
+def _handle_precomputed_bsgs(base, strong_gens, transversals=None,
+                             basic_orbits=None, strong_gens_distr=None):
+    """
+    Calculate BSGS-related structures from those present.
+
+    Explanation
+    ===========
+
+    The base and strong generating set must be provided; if any of the
+    transversals, basic orbits or distributed strong generators are not
+    provided, they will be calculated from the base and strong generating set.
+
+    Parameters
+    ==========
+
+    base : the base
+    strong_gens : the strong generators
+    transversals : basic transversals
+    basic_orbits : basic orbits
+    strong_gens_distr : strong generators distributed by membership in basic stabilizers
+
+    Returns
+    =======
+
+    (transversals, basic_orbits, strong_gens_distr)
+        where *transversals* are the basic transversals, *basic_orbits* are the
+        basic orbits, and *strong_gens_distr* are the strong generators distributed
+        by membership in basic stabilizers.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import DihedralGroup
+    >>> from sympy.combinatorics.util import _handle_precomputed_bsgs
+    >>> D = DihedralGroup(3)
+    >>> D.schreier_sims()
+    >>> _handle_precomputed_bsgs(D.base, D.strong_gens,
+    ... basic_orbits=D.basic_orbits)
+    ([{0: (2), 1: (0 1 2), 2: (0 2)}, {1: (2), 2: (1 2)}], [[0, 1, 2], [1, 2]], [[(0 1 2), (0 2), (1 2)], [(1 2)]])
+
+    See Also
+    ========
+
+    _orbits_transversals_from_bsgs, _distribute_gens_by_base
+
+    """
+    if strong_gens_distr is None:
+        strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+    if transversals is None:
+        if basic_orbits is None:
+            basic_orbits, transversals = \
+                _orbits_transversals_from_bsgs(base, strong_gens_distr)
+        else:
+            transversals = \
+                _orbits_transversals_from_bsgs(base, strong_gens_distr,
+                                           transversals_only=True)
+    else:
+        if basic_orbits is None:
+            base_len = len(base)
+            basic_orbits = [None]*base_len
+            for i in range(base_len):
+                basic_orbits[i] = list(transversals[i].keys())
+    return transversals, basic_orbits, strong_gens_distr
+
+
+def _orbits_transversals_from_bsgs(base, strong_gens_distr,
+                                   transversals_only=False, slp=False):
+    """
+    Compute basic orbits and transversals from a base and strong generating set.
+
+    Explanation
+    ===========
+
+    The generators are provided as distributed across the basic stabilizers.
+    If the optional argument ``transversals_only`` is set to True, only the
+    transversals are returned.
+
+    Parameters
+    ==========
+
+    base : The base.
+    strong_gens_distr : Strong generators distributed by membership in basic stabilizers.
+    transversals_only : bool, default: False
+        A flag switching between returning only the
+        transversals and both orbits and transversals.
+    slp : bool, default: False
+        If ``True``, return a list of dictionaries containing the
+        generator presentations of the elements of the transversals,
+        i.e. the list of indices of generators from ``strong_gens_distr[i]``
+        such that their product is the relevant transversal element.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import SymmetricGroup
+    >>> from sympy.combinatorics.util import _distribute_gens_by_base
+    >>> S = SymmetricGroup(3)
+    >>> S.schreier_sims()
+    >>> strong_gens_distr = _distribute_gens_by_base(S.base, S.strong_gens)
+    >>> (S.base, strong_gens_distr)
+    ([0, 1], [[(0 1 2), (2)(0 1), (1 2)], [(1 2)]])
+
+    See Also
+    ========
+
+    _distribute_gens_by_base, _handle_precomputed_bsgs
+
+    """
+    from sympy.combinatorics.perm_groups import _orbit_transversal
+    base_len = len(base)
+    degree = strong_gens_distr[0][0].size
+    transversals = [None]*base_len
+    slps = [None]*base_len
+    if transversals_only is False:
+        basic_orbits = [None]*base_len
+    for i in range(base_len):
+        transversals[i], slps[i] = _orbit_transversal(degree, strong_gens_distr[i],
+                                 base[i], pairs=True, slp=True)
+        transversals[i] = dict(transversals[i])
+        if transversals_only is False:
+            basic_orbits[i] = list(transversals[i].keys())
+    if transversals_only:
+        return transversals
+    else:
+        if not slp:
+            return basic_orbits, transversals
+        return basic_orbits, transversals, slps
+
+
+def _remove_gens(base, strong_gens, basic_orbits=None, strong_gens_distr=None):
+    """
+    Remove redundant generators from a strong generating set.
+
+    Parameters
+    ==========
+
+    base : a base
+    strong_gens : a strong generating set relative to *base*
+    basic_orbits : basic orbits
+    strong_gens_distr : strong generators distributed by membership in basic stabilizers
+
+    Returns
+    =======
+
+    A strong generating set with respect to ``base`` which is a subset of
+    ``strong_gens``.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import SymmetricGroup
+    >>> from sympy.combinatorics.util import _remove_gens
+    >>> from sympy.combinatorics.testutil import _verify_bsgs
+    >>> S = SymmetricGroup(15)
+    >>> base, strong_gens = S.schreier_sims_incremental()
+    >>> new_gens = _remove_gens(base, strong_gens)
+    >>> len(new_gens)
+    14
+    >>> _verify_bsgs(S, base, new_gens)
+    True
+
+    Notes
+    =====
+
+    This procedure is outlined in [1],p.95.
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E.
+           "Handbook of computational group theory"
+
+    """
+    from sympy.combinatorics.perm_groups import _orbit
+    base_len = len(base)
+    degree = strong_gens[0].size
+    if strong_gens_distr is None:
+        strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
+    if basic_orbits is None:
+        basic_orbits = []
+        for i in range(base_len):
+            basic_orbit = _orbit(degree, strong_gens_distr[i], base[i])
+            basic_orbits.append(basic_orbit)
+    strong_gens_distr.append([])
+    res = strong_gens[:]
+    for i in range(base_len - 1, -1, -1):
+        gens_copy = strong_gens_distr[i][:]
+        for gen in strong_gens_distr[i]:
+            if gen not in strong_gens_distr[i + 1]:
+                temp_gens = gens_copy[:]
+                temp_gens.remove(gen)
+                if temp_gens == []:
+                    continue
+                temp_orbit = _orbit(degree, temp_gens, base[i])
+                if temp_orbit == basic_orbits[i]:
+                    gens_copy.remove(gen)
+                    res.remove(gen)
+    return res
+
+
+def _strip(g, base, orbits, transversals):
+    """
+    Attempt to decompose a permutation using a (possibly partial) BSGS
+    structure.
+
+    Explanation
+    ===========
+
+    This is done by treating the sequence ``base`` as an actual base, and
+    the orbits ``orbits`` and transversals ``transversals`` as basic orbits and
+    transversals relative to it.
+
+    This process is called "sifting". A sift is unsuccessful when a certain
+    orbit element is not found or when after the sift the decomposition
+    does not end with the identity element.
+
+    The argument ``transversals`` is a list of dictionaries that provides
+    transversal elements for the orbits ``orbits``.
+
+    Parameters
+    ==========
+
+    g : permutation to be decomposed
+    base : sequence of points
+    orbits : list
+        A list in which the ``i``-th entry is an orbit of ``base[i]``
+        under some subgroup of the pointwise stabilizer of `
+        `base[0], base[1], ..., base[i - 1]``. The groups themselves are implicit
+        in this function since the only information we need is encoded in the orbits
+        and transversals
+    transversals : list
+        A list of orbit transversals associated with the orbits *orbits*.
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import Permutation, SymmetricGroup
+    >>> from sympy.combinatorics.util import _strip
+    >>> S = SymmetricGroup(5)
+    >>> S.schreier_sims()
+    >>> g = Permutation([0, 2, 3, 1, 4])
+    >>> _strip(g, S.base, S.basic_orbits, S.basic_transversals)
+    ((4), 5)
+
+    Notes
+    =====
+
+    The algorithm is described in [1],pp.89-90. The reason for returning
+    both the current state of the element being decomposed and the level
+    at which the sifting ends is that they provide important information for
+    the randomized version of the Schreier-Sims algorithm.
+
+    References
+    ==========
+
+    .. [1] Holt, D., Eick, B., O'Brien, E."Handbook of computational group theory"
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims
+    sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims_random
+
+    """
+    h = g._array_form
+    base_len = len(base)
+    for i in range(base_len):
+        beta = h[base[i]]
+        if beta == base[i]:
+            continue
+        if beta not in orbits[i]:
+            return _af_new(h), i + 1
+        u = transversals[i][beta]._array_form
+        h = _af_rmul(_af_invert(u), h)
+    return _af_new(h), base_len + 1
+
+
+def _strip_af(h, base, orbits, transversals, j, slp=[], slps={}):
+    """
+    optimized _strip, with h, transversals and result in array form
+    if the stripped elements is the identity, it returns False, base_len + 1
+
+    j    h[base[i]] == base[i] for i <= j
+
+    """
+    base_len = len(base)
+    for i in range(j+1, base_len):
+        beta = h[base[i]]
+        if beta == base[i]:
+            continue
+        if beta not in orbits[i]:
+            if not slp:
+                return h, i + 1
+            return h, i + 1, slp
+        u = transversals[i][beta]
+        if h == u:
+            if not slp:
+                return False, base_len + 1
+            return False, base_len + 1, slp
+        h = _af_rmul(_af_invert(u), h)
+        if slp:
+            u_slp = slps[i][beta][:]
+            u_slp.reverse()
+            u_slp = [(i, (g,)) for g in u_slp]
+            slp = u_slp + slp
+    if not slp:
+        return h, base_len + 1
+    return h, base_len + 1, slp
+
+
+def _strong_gens_from_distr(strong_gens_distr):
+    """
+    Retrieve strong generating set from generators of basic stabilizers.
+
+    This is just the union of the generators of the first and second basic
+    stabilizers.
+
+    Parameters
+    ==========
+
+    strong_gens_distr : strong generators distributed by membership in basic stabilizers
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics import SymmetricGroup
+    >>> from sympy.combinatorics.util import (_strong_gens_from_distr,
+    ... _distribute_gens_by_base)
+    >>> S = SymmetricGroup(3)
+    >>> S.schreier_sims()
+    >>> S.strong_gens
+    [(0 1 2), (2)(0 1), (1 2)]
+    >>> strong_gens_distr = _distribute_gens_by_base(S.base, S.strong_gens)
+    >>> _strong_gens_from_distr(strong_gens_distr)
+    [(0 1 2), (2)(0 1), (1 2)]
+
+    See Also
+    ========
+
+    _distribute_gens_by_base
+
+    """
+    if len(strong_gens_distr) == 1:
+        return strong_gens_distr[0][:]
+    else:
+        result = strong_gens_distr[0]
+        for gen in strong_gens_distr[1]:
+            if gen not in result:
+                result.append(gen)
+        return result
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..7048bd548cca04780479539339dd8cc49a21990f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/__init__.py
@@ -0,0 +1,8 @@
+from .products import product, Product
+from .summations import summation, Sum
+
+__all__ = [
+    'product', 'Product',
+
+    'summation', 'Sum',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/delta.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/delta.py
new file mode 100644
index 0000000000000000000000000000000000000000..0471d2b2891a66a1b97b7a3a37bbd31d7b173a81
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/delta.py
@@ -0,0 +1,327 @@
+"""
+This module implements sums and products containing the Kronecker Delta function.
+
+References
+==========
+
+.. [1] https://mathworld.wolfram.com/KroneckerDelta.html
+
+"""
+from .products import product
+from .summations import Sum, summation
+from sympy.core import Add, Mul, S, Dummy
+from sympy.core.cache import cacheit
+from sympy.core.sorting import default_sort_key
+from sympy.functions import KroneckerDelta, Piecewise, piecewise_fold
+from sympy.polys.polytools import factor
+from sympy.sets.sets import Interval
+from sympy.solvers.solvers import solve
+
+
+@cacheit
+def _expand_delta(expr, index):
+    """
+    Expand the first Add containing a simple KroneckerDelta.
+    """
+    if not expr.is_Mul:
+        return expr
+    delta = None
+    func = Add
+    terms = [S.One]
+    for h in expr.args:
+        if delta is None and h.is_Add and _has_simple_delta(h, index):
+            delta = True
+            func = h.func
+            terms = [terms[0]*t for t in h.args]
+        else:
+            terms = [t*h for t in terms]
+    return func(*terms)
+
+
+@cacheit
+def _extract_delta(expr, index):
+    """
+    Extract a simple KroneckerDelta from the expression.
+
+    Explanation
+    ===========
+
+    Returns the tuple ``(delta, newexpr)`` where:
+
+      - ``delta`` is a simple KroneckerDelta expression if one was found,
+        or ``None`` if no simple KroneckerDelta expression was found.
+
+      - ``newexpr`` is a Mul containing the remaining terms; ``expr`` is
+        returned unchanged if no simple KroneckerDelta expression was found.
+
+    Examples
+    ========
+
+    >>> from sympy import KroneckerDelta
+    >>> from sympy.concrete.delta import _extract_delta
+    >>> from sympy.abc import x, y, i, j, k
+    >>> _extract_delta(4*x*y*KroneckerDelta(i, j), i)
+    (KroneckerDelta(i, j), 4*x*y)
+    >>> _extract_delta(4*x*y*KroneckerDelta(i, j), k)
+    (None, 4*x*y*KroneckerDelta(i, j))
+
+    See Also
+    ========
+
+    sympy.functions.special.tensor_functions.KroneckerDelta
+    deltaproduct
+    deltasummation
+    """
+    if not _has_simple_delta(expr, index):
+        return (None, expr)
+    if isinstance(expr, KroneckerDelta):
+        return (expr, S.One)
+    if not expr.is_Mul:
+        raise ValueError("Incorrect expr")
+    delta = None
+    terms = []
+
+    for arg in expr.args:
+        if delta is None and _is_simple_delta(arg, index):
+            delta = arg
+        else:
+            terms.append(arg)
+    return (delta, expr.func(*terms))
+
+
+@cacheit
+def _has_simple_delta(expr, index):
+    """
+    Returns True if ``expr`` is an expression that contains a KroneckerDelta
+    that is simple in the index ``index``, meaning that this KroneckerDelta
+    is nonzero for a single value of the index ``index``.
+    """
+    if expr.has(KroneckerDelta):
+        if _is_simple_delta(expr, index):
+            return True
+        if expr.is_Add or expr.is_Mul:
+            return any(_has_simple_delta(arg, index) for arg in expr.args)
+    return False
+
+
+@cacheit
+def _is_simple_delta(delta, index):
+    """
+    Returns True if ``delta`` is a KroneckerDelta and is nonzero for a single
+    value of the index ``index``.
+    """
+    if isinstance(delta, KroneckerDelta) and delta.has(index):
+        p = (delta.args[0] - delta.args[1]).as_poly(index)
+        if p:
+            return p.degree() == 1
+    return False
+
+
+@cacheit
+def _remove_multiple_delta(expr):
+    """
+    Evaluate products of KroneckerDelta's.
+    """
+    if expr.is_Add:
+        return expr.func(*list(map(_remove_multiple_delta, expr.args)))
+    if not expr.is_Mul:
+        return expr
+    eqs = []
+    newargs = []
+    for arg in expr.args:
+        if isinstance(arg, KroneckerDelta):
+            eqs.append(arg.args[0] - arg.args[1])
+        else:
+            newargs.append(arg)
+    if not eqs:
+        return expr
+    solns = solve(eqs, dict=True)
+    if len(solns) == 0:
+        return S.Zero
+    elif len(solns) == 1:
+        newargs += [KroneckerDelta(k, v) for k, v in solns[0].items()]
+        expr2 = expr.func(*newargs)
+        if expr != expr2:
+            return _remove_multiple_delta(expr2)
+    return expr
+
+
+@cacheit
+def _simplify_delta(expr):
+    """
+    Rewrite a KroneckerDelta's indices in its simplest form.
+    """
+    if isinstance(expr, KroneckerDelta):
+        try:
+            slns = solve(expr.args[0] - expr.args[1], dict=True)
+            if slns and len(slns) == 1:
+                return Mul(*[KroneckerDelta(*(key, value))
+                            for key, value in slns[0].items()])
+        except NotImplementedError:
+            pass
+    return expr
+
+
+@cacheit
+def deltaproduct(f, limit):
+    """
+    Handle products containing a KroneckerDelta.
+
+    See Also
+    ========
+
+    deltasummation
+    sympy.functions.special.tensor_functions.KroneckerDelta
+    sympy.concrete.products.product
+    """
+    if ((limit[2] - limit[1]) < 0) == True:
+        return S.One
+
+    if not f.has(KroneckerDelta):
+        return product(f, limit)
+
+    if f.is_Add:
+        # Identify the term in the Add that has a simple KroneckerDelta
+        delta = None
+        terms = []
+        for arg in sorted(f.args, key=default_sort_key):
+            if delta is None and _has_simple_delta(arg, limit[0]):
+                delta = arg
+            else:
+                terms.append(arg)
+        newexpr = f.func(*terms)
+        k = Dummy("kprime", integer=True)
+        if isinstance(limit[1], int) and isinstance(limit[2], int):
+            result = deltaproduct(newexpr, limit) + sum(deltaproduct(newexpr, (limit[0], limit[1], ik - 1)) *
+                delta.subs(limit[0], ik) *
+                deltaproduct(newexpr, (limit[0], ik + 1, limit[2])) for ik in range(int(limit[1]), int(limit[2] + 1))
+            )
+        else:
+            result = deltaproduct(newexpr, limit) + deltasummation(
+                deltaproduct(newexpr, (limit[0], limit[1], k - 1)) *
+                delta.subs(limit[0], k) *
+                deltaproduct(newexpr, (limit[0], k + 1, limit[2])),
+                (k, limit[1], limit[2]),
+                no_piecewise=_has_simple_delta(newexpr, limit[0])
+            )
+        return _remove_multiple_delta(result)
+
+    delta, _ = _extract_delta(f, limit[0])
+
+    if not delta:
+        g = _expand_delta(f, limit[0])
+        if f != g:
+            try:
+                return factor(deltaproduct(g, limit))
+            except AssertionError:
+                return deltaproduct(g, limit)
+        return product(f, limit)
+
+    return _remove_multiple_delta(f.subs(limit[0], limit[1])*KroneckerDelta(limit[2], limit[1])) + \
+        S.One*_simplify_delta(KroneckerDelta(limit[2], limit[1] - 1))
+
+
+@cacheit
+def deltasummation(f, limit, no_piecewise=False):
+    """
+    Handle summations containing a KroneckerDelta.
+
+    Explanation
+    ===========
+
+    The idea for summation is the following:
+
+    - If we are dealing with a KroneckerDelta expression, i.e. KroneckerDelta(g(x), j),
+      we try to simplify it.
+
+      If we could simplify it, then we sum the resulting expression.
+      We already know we can sum a simplified expression, because only
+      simple KroneckerDelta expressions are involved.
+
+      If we could not simplify it, there are two cases:
+
+      1) The expression is a simple expression: we return the summation,
+         taking care if we are dealing with a Derivative or with a proper
+         KroneckerDelta.
+
+      2) The expression is not simple (i.e. KroneckerDelta(cos(x))): we can do
+         nothing at all.
+
+    - If the expr is a multiplication expr having a KroneckerDelta term:
+
+      First we expand it.
+
+      If the expansion did work, then we try to sum the expansion.
+
+      If not, we try to extract a simple KroneckerDelta term, then we have two
+      cases:
+
+      1) We have a simple KroneckerDelta term, so we return the summation.
+
+      2) We did not have a simple term, but we do have an expression with
+         simplified KroneckerDelta terms, so we sum this expression.
+
+    Examples
+    ========
+
+    >>> from sympy import oo, symbols
+    >>> from sympy.abc import k
+    >>> i, j = symbols('i, j', integer=True, finite=True)
+    >>> from sympy.concrete.delta import deltasummation
+    >>> from sympy import KroneckerDelta
+    >>> deltasummation(KroneckerDelta(i, k), (k, -oo, oo))
+    1
+    >>> deltasummation(KroneckerDelta(i, k), (k, 0, oo))
+    Piecewise((1, i >= 0), (0, True))
+    >>> deltasummation(KroneckerDelta(i, k), (k, 1, 3))
+    Piecewise((1, (i >= 1) & (i <= 3)), (0, True))
+    >>> deltasummation(k*KroneckerDelta(i, j)*KroneckerDelta(j, k), (k, -oo, oo))
+    j*KroneckerDelta(i, j)
+    >>> deltasummation(j*KroneckerDelta(i, j), (j, -oo, oo))
+    i
+    >>> deltasummation(i*KroneckerDelta(i, j), (i, -oo, oo))
+    j
+
+    See Also
+    ========
+
+    deltaproduct
+    sympy.functions.special.tensor_functions.KroneckerDelta
+    sympy.concrete.sums.summation
+    """
+    if ((limit[2] - limit[1]) < 0) == True:
+        return S.Zero
+
+    if not f.has(KroneckerDelta):
+        return summation(f, limit)
+
+    x = limit[0]
+
+    g = _expand_delta(f, x)
+    if g.is_Add:
+        return piecewise_fold(
+            g.func(*[deltasummation(h, limit, no_piecewise) for h in g.args]))
+
+    # try to extract a simple KroneckerDelta term
+    delta, expr = _extract_delta(g, x)
+
+    if (delta is not None) and (delta.delta_range is not None):
+        dinf, dsup = delta.delta_range
+        if (limit[1] - dinf <= 0) == True and (limit[2] - dsup >= 0) == True:
+            no_piecewise = True
+
+    if not delta:
+        return summation(f, limit)
+
+    solns = solve(delta.args[0] - delta.args[1], x)
+    if len(solns) == 0:
+        return S.Zero
+    elif len(solns) != 1:
+        return Sum(f, limit)
+    value = solns[0]
+    if no_piecewise:
+        return expr.subs(x, value)
+    return Piecewise(
+        (expr.subs(x, value), Interval(*limit[1:3]).as_relational(value)),
+        (S.Zero, True)
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/expr_with_intlimits.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/expr_with_intlimits.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e109913cdb2f3018096972b14651b990f4b985e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/expr_with_intlimits.py
@@ -0,0 +1,354 @@
+from sympy.concrete.expr_with_limits import ExprWithLimits
+from sympy.core.singleton import S
+from sympy.core.relational import Eq
+
+class ReorderError(NotImplementedError):
+    """
+    Exception raised when trying to reorder dependent limits.
+    """
+    def __init__(self, expr, msg):
+        super().__init__(
+            "%s could not be reordered: %s." % (expr, msg))
+
+class ExprWithIntLimits(ExprWithLimits):
+    """
+    Superclass for Product and Sum.
+
+    See Also
+    ========
+
+    sympy.concrete.expr_with_limits.ExprWithLimits
+    sympy.concrete.products.Product
+    sympy.concrete.summations.Sum
+    """
+    __slots__ = ()
+
+    def change_index(self, var, trafo, newvar=None):
+        r"""
+        Change index of a Sum or Product.
+
+        Perform a linear transformation `x \mapsto a x + b` on the index variable
+        `x`. For `a` the only values allowed are `\pm 1`. A new variable to be used
+        after the change of index can also be specified.
+
+        Explanation
+        ===========
+
+        ``change_index(expr, var, trafo, newvar=None)`` where ``var`` specifies the
+        index variable `x` to transform. The transformation ``trafo`` must be linear
+        and given in terms of ``var``. If the optional argument ``newvar`` is
+        provided then ``var`` gets replaced by ``newvar`` in the final expression.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, Product, simplify
+        >>> from sympy.abc import x, y, a, b, c, d, u, v, i, j, k, l
+
+        >>> S = Sum(x, (x, a, b))
+        >>> S.doit()
+        -a**2/2 + a/2 + b**2/2 + b/2
+
+        >>> Sn = S.change_index(x, x + 1, y)
+        >>> Sn
+        Sum(y - 1, (y, a + 1, b + 1))
+        >>> Sn.doit()
+        -a**2/2 + a/2 + b**2/2 + b/2
+
+        >>> Sn = S.change_index(x, -x, y)
+        >>> Sn
+        Sum(-y, (y, -b, -a))
+        >>> Sn.doit()
+        -a**2/2 + a/2 + b**2/2 + b/2
+
+        >>> Sn = S.change_index(x, x+u)
+        >>> Sn
+        Sum(-u + x, (x, a + u, b + u))
+        >>> Sn.doit()
+        -a**2/2 - a*u + a/2 + b**2/2 + b*u + b/2 - u*(-a + b + 1) + u
+        >>> simplify(Sn.doit())
+        -a**2/2 + a/2 + b**2/2 + b/2
+
+        >>> Sn = S.change_index(x, -x - u, y)
+        >>> Sn
+        Sum(-u - y, (y, -b - u, -a - u))
+        >>> Sn.doit()
+        -a**2/2 - a*u + a/2 + b**2/2 + b*u + b/2 - u*(-a + b + 1) + u
+        >>> simplify(Sn.doit())
+        -a**2/2 + a/2 + b**2/2 + b/2
+
+        >>> P = Product(i*j**2, (i, a, b), (j, c, d))
+        >>> P
+        Product(i*j**2, (i, a, b), (j, c, d))
+        >>> P2 = P.change_index(i, i+3, k)
+        >>> P2
+        Product(j**2*(k - 3), (k, a + 3, b + 3), (j, c, d))
+        >>> P3 = P2.change_index(j, -j, l)
+        >>> P3
+        Product(l**2*(k - 3), (k, a + 3, b + 3), (l, -d, -c))
+
+        When dealing with symbols only, we can make a
+        general linear transformation:
+
+        >>> Sn = S.change_index(x, u*x+v, y)
+        >>> Sn
+        Sum((-v + y)/u, (y, b*u + v, a*u + v))
+        >>> Sn.doit()
+        -v*(a*u - b*u + 1)/u + (a**2*u**2/2 + a*u*v + a*u/2 - b**2*u**2/2 - b*u*v + b*u/2 + v)/u
+        >>> simplify(Sn.doit())
+        a**2*u/2 + a/2 - b**2*u/2 + b/2
+
+        However, the last result can be inconsistent with usual
+        summation where the index increment is always 1. This is
+        obvious as we get back the original value only for ``u``
+        equal +1 or -1.
+
+        See Also
+        ========
+
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.index,
+        reorder_limit,
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.reorder,
+        sympy.concrete.summations.Sum.reverse_order,
+        sympy.concrete.products.Product.reverse_order
+        """
+        if newvar is None:
+            newvar = var
+
+        limits = []
+        for limit in self.limits:
+            if limit[0] == var:
+                p = trafo.as_poly(var)
+                if p.degree() != 1:
+                    raise ValueError("Index transformation is not linear")
+                alpha = p.coeff_monomial(var)
+                beta = p.coeff_monomial(S.One)
+                if alpha.is_number:
+                    if alpha == S.One:
+                        limits.append((newvar, alpha*limit[1] + beta, alpha*limit[2] + beta))
+                    elif alpha == S.NegativeOne:
+                        limits.append((newvar, alpha*limit[2] + beta, alpha*limit[1] + beta))
+                    else:
+                        raise ValueError("Linear transformation results in non-linear summation stepsize")
+                else:
+                    # Note that the case of alpha being symbolic can give issues if alpha < 0.
+                    limits.append((newvar, alpha*limit[2] + beta, alpha*limit[1] + beta))
+            else:
+                limits.append(limit)
+
+        function = self.function.subs(var, (var - beta)/alpha)
+        function = function.subs(var, newvar)
+
+        return self.func(function, *limits)
+
+
+    def index(expr, x):
+        """
+        Return the index of a dummy variable in the list of limits.
+
+        Explanation
+        ===========
+
+        ``index(expr, x)``  returns the index of the dummy variable ``x`` in the
+        limits of ``expr``. Note that we start counting with 0 at the inner-most
+        limits tuple.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y, a, b, c, d
+        >>> from sympy import Sum, Product
+        >>> Sum(x*y, (x, a, b), (y, c, d)).index(x)
+        0
+        >>> Sum(x*y, (x, a, b), (y, c, d)).index(y)
+        1
+        >>> Product(x*y, (x, a, b), (y, c, d)).index(x)
+        0
+        >>> Product(x*y, (x, a, b), (y, c, d)).index(y)
+        1
+
+        See Also
+        ========
+
+        reorder_limit, reorder, sympy.concrete.summations.Sum.reverse_order,
+        sympy.concrete.products.Product.reverse_order
+        """
+        variables = [limit[0] for limit in expr.limits]
+
+        if variables.count(x) != 1:
+            raise ValueError(expr, "Number of instances of variable not equal to one")
+        else:
+            return variables.index(x)
+
+    def reorder(expr, *arg):
+        """
+        Reorder limits in a expression containing a Sum or a Product.
+
+        Explanation
+        ===========
+
+        ``expr.reorder(*arg)`` reorders the limits in the expression ``expr``
+        according to the list of tuples given by ``arg``. These tuples can
+        contain numerical indices or index variable names or involve both.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, Product
+        >>> from sympy.abc import x, y, z, a, b, c, d, e, f
+
+        >>> Sum(x*y, (x, a, b), (y, c, d)).reorder((x, y))
+        Sum(x*y, (y, c, d), (x, a, b))
+
+        >>> Sum(x*y*z, (x, a, b), (y, c, d), (z, e, f)).reorder((x, y), (x, z), (y, z))
+        Sum(x*y*z, (z, e, f), (y, c, d), (x, a, b))
+
+        >>> P = Product(x*y*z, (x, a, b), (y, c, d), (z, e, f))
+        >>> P.reorder((x, y), (x, z), (y, z))
+        Product(x*y*z, (z, e, f), (y, c, d), (x, a, b))
+
+        We can also select the index variables by counting them, starting
+        with the inner-most one:
+
+        >>> Sum(x**2, (x, a, b), (x, c, d)).reorder((0, 1))
+        Sum(x**2, (x, c, d), (x, a, b))
+
+        And of course we can mix both schemes:
+
+        >>> Sum(x*y, (x, a, b), (y, c, d)).reorder((y, x))
+        Sum(x*y, (y, c, d), (x, a, b))
+        >>> Sum(x*y, (x, a, b), (y, c, d)).reorder((y, 0))
+        Sum(x*y, (y, c, d), (x, a, b))
+
+        See Also
+        ========
+
+        reorder_limit, index, sympy.concrete.summations.Sum.reverse_order,
+        sympy.concrete.products.Product.reverse_order
+        """
+        new_expr = expr
+
+        for r in arg:
+            if len(r) != 2:
+                raise ValueError(r, "Invalid number of arguments")
+
+            index1 = r[0]
+            index2 = r[1]
+
+            if not isinstance(r[0], int):
+                index1 = expr.index(r[0])
+            if not isinstance(r[1], int):
+                index2 = expr.index(r[1])
+
+            new_expr = new_expr.reorder_limit(index1, index2)
+
+        return new_expr
+
+
+    def reorder_limit(expr, x, y):
+        """
+        Interchange two limit tuples of a Sum or Product expression.
+
+        Explanation
+        ===========
+
+        ``expr.reorder_limit(x, y)`` interchanges two limit tuples. The
+        arguments ``x`` and ``y`` are integers corresponding to the index
+        variables of the two limits which are to be interchanged. The
+        expression ``expr`` has to be either a Sum or a Product.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y, z, a, b, c, d, e, f
+        >>> from sympy import Sum, Product
+
+        >>> Sum(x*y*z, (x, a, b), (y, c, d), (z, e, f)).reorder_limit(0, 2)
+        Sum(x*y*z, (z, e, f), (y, c, d), (x, a, b))
+        >>> Sum(x**2, (x, a, b), (x, c, d)).reorder_limit(1, 0)
+        Sum(x**2, (x, c, d), (x, a, b))
+
+        >>> Product(x*y*z, (x, a, b), (y, c, d), (z, e, f)).reorder_limit(0, 2)
+        Product(x*y*z, (z, e, f), (y, c, d), (x, a, b))
+
+        See Also
+        ========
+
+        index, reorder, sympy.concrete.summations.Sum.reverse_order,
+        sympy.concrete.products.Product.reverse_order
+        """
+        var = {limit[0] for limit in expr.limits}
+        limit_x = expr.limits[x]
+        limit_y = expr.limits[y]
+
+        if (len(set(limit_x[1].free_symbols).intersection(var)) == 0 and
+            len(set(limit_x[2].free_symbols).intersection(var)) == 0 and
+            len(set(limit_y[1].free_symbols).intersection(var)) == 0 and
+            len(set(limit_y[2].free_symbols).intersection(var)) == 0):
+
+            limits = []
+            for i, limit in enumerate(expr.limits):
+                if i == x:
+                    limits.append(limit_y)
+                elif i == y:
+                    limits.append(limit_x)
+                else:
+                    limits.append(limit)
+
+            return type(expr)(expr.function, *limits)
+        else:
+            raise ReorderError(expr, "could not interchange the two limits specified")
+
+    @property
+    def has_empty_sequence(self):
+        """
+        Returns True if the Sum or Product is computed for an empty sequence.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, Product, Symbol
+        >>> m = Symbol('m')
+        >>> Sum(m, (m, 1, 0)).has_empty_sequence
+        True
+
+        >>> Sum(m, (m, 1, 1)).has_empty_sequence
+        False
+
+        >>> M = Symbol('M', integer=True, positive=True)
+        >>> Product(m, (m, 1, M)).has_empty_sequence
+        False
+
+        >>> Product(m, (m, 2, M)).has_empty_sequence
+
+        >>> Product(m, (m, M + 1, M)).has_empty_sequence
+        True
+
+        >>> N = Symbol('N', integer=True, positive=True)
+        >>> Sum(m, (m, N, M)).has_empty_sequence
+
+        >>> N = Symbol('N', integer=True, negative=True)
+        >>> Sum(m, (m, N, M)).has_empty_sequence
+        False
+
+        See Also
+        ========
+
+        has_reversed_limits
+        has_finite_limits
+
+        """
+        ret_None = False
+        for lim in self.limits:
+            dif = lim[1] - lim[2]
+            eq = Eq(dif, 1)
+            if eq == True:
+                return True
+            elif eq == False:
+                continue
+            else:
+                ret_None = True
+
+        if ret_None:
+            return None
+        return False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/expr_with_limits.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/expr_with_limits.py
new file mode 100644
index 0000000000000000000000000000000000000000..034e6ab0a7663525632abe0224fbac973c505c08
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/expr_with_limits.py
@@ -0,0 +1,603 @@
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import AppliedUndef, UndefinedFunction
+from sympy.core.mul import Mul
+from sympy.core.relational import Equality, Relational
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol, Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.piecewise import (piecewise_fold,
+    Piecewise)
+from sympy.logic.boolalg import BooleanFunction
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.sets.sets import Interval, Set
+from sympy.sets.fancysets import Range
+from sympy.tensor.indexed import Idx
+from sympy.utilities import flatten
+from sympy.utilities.iterables import sift, is_sequence
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+
+def _common_new(cls, function, *symbols, discrete, **assumptions):
+    """Return either a special return value or the tuple,
+    (function, limits, orientation). This code is common to
+    both ExprWithLimits and AddWithLimits."""
+    function = sympify(function)
+
+    if isinstance(function, Equality):
+        # This transforms e.g. Integral(Eq(x, y)) to Eq(Integral(x), Integral(y))
+        # but that is only valid for definite integrals.
+        limits, orientation = _process_limits(*symbols, discrete=discrete)
+        if not (limits and all(len(limit) == 3 for limit in limits)):
+            sympy_deprecation_warning(
+                """
+                Creating a indefinite integral with an Eq() argument is
+                deprecated.
+
+                This is because indefinite integrals do not preserve equality
+                due to the arbitrary constants. If you want an equality of
+                indefinite integrals, use Eq(Integral(a, x), Integral(b, x))
+                explicitly.
+                """,
+                deprecated_since_version="1.6",
+                active_deprecations_target="deprecated-indefinite-integral-eq",
+                stacklevel=5,
+            )
+
+        lhs = function.lhs
+        rhs = function.rhs
+        return Equality(cls(lhs, *symbols, **assumptions), \
+                        cls(rhs, *symbols, **assumptions))
+
+    if function is S.NaN:
+        return S.NaN
+
+    if symbols:
+        limits, orientation = _process_limits(*symbols, discrete=discrete)
+        for i, li in enumerate(limits):
+            if len(li) == 4:
+                function = function.subs(li[0], li[-1])
+                limits[i] = Tuple(*li[:-1])
+    else:
+        # symbol not provided -- we can still try to compute a general form
+        free = function.free_symbols
+        if len(free) != 1:
+            raise ValueError(
+                "specify dummy variables for %s" % function)
+        limits, orientation = [Tuple(s) for s in free], 1
+
+    # denest any nested calls
+    while cls == type(function):
+        limits = list(function.limits) + limits
+        function = function.function
+
+    # Any embedded piecewise functions need to be brought out to the
+    # top level. We only fold Piecewise that contain the integration
+    # variable.
+    reps = {}
+    symbols_of_integration = {i[0] for i in limits}
+    for p in function.atoms(Piecewise):
+        if not p.has(*symbols_of_integration):
+            reps[p] = Dummy()
+    # mask off those that don't
+    function = function.xreplace(reps)
+    # do the fold
+    function = piecewise_fold(function)
+    # remove the masking
+    function = function.xreplace({v: k for k, v in reps.items()})
+
+    return function, limits, orientation
+
+
+def _process_limits(*symbols, discrete=None):
+    """Process the list of symbols and convert them to canonical limits,
+    storing them as Tuple(symbol, lower, upper). The orientation of
+    the function is also returned when the upper limit is missing
+    so (x, 1, None) becomes (x, None, 1) and the orientation is changed.
+    In the case that a limit is specified as (symbol, Range), a list of
+    length 4 may be returned if a change of variables is needed; the
+    expression that should replace the symbol in the expression is
+    the fourth element in the list.
+    """
+    limits = []
+    orientation = 1
+    if discrete is None:
+        err_msg = 'discrete must be True or False'
+    elif discrete:
+        err_msg = 'use Range, not Interval or Relational'
+    else:
+        err_msg = 'use Interval or Relational, not Range'
+    for V in symbols:
+        if isinstance(V, (Relational, BooleanFunction)):
+            if discrete:
+                raise TypeError(err_msg)
+            variable = V.atoms(Symbol).pop()
+            V = (variable, V.as_set())
+        elif isinstance(V, Symbol) or getattr(V, '_diff_wrt', False):
+            if isinstance(V, Idx):
+                if V.lower is None or V.upper is None:
+                    limits.append(Tuple(V))
+                else:
+                    limits.append(Tuple(V, V.lower, V.upper))
+            else:
+                limits.append(Tuple(V))
+            continue
+        if is_sequence(V) and not isinstance(V, Set):
+            if len(V) == 2 and isinstance(V[1], Set):
+                V = list(V)
+                if isinstance(V[1], Interval):  # includes Reals
+                    if discrete:
+                        raise TypeError(err_msg)
+                    V[1:] = V[1].inf, V[1].sup
+                elif isinstance(V[1], Range):
+                    if not discrete:
+                        raise TypeError(err_msg)
+                    lo = V[1].inf
+                    hi = V[1].sup
+                    dx = abs(V[1].step)  # direction doesn't matter
+                    if dx == 1:
+                        V[1:] = [lo, hi]
+                    else:
+                        if lo is not S.NegativeInfinity:
+                            V = [V[0]] + [0, (hi - lo)//dx, dx*V[0] + lo]
+                        else:
+                            V = [V[0]] + [0, S.Infinity, -dx*V[0] + hi]
+                else:
+                    # more complicated sets would require splitting, e.g.
+                    # Union(Interval(1, 3), interval(6,10))
+                    raise NotImplementedError(
+                        'expecting Range' if discrete else
+                        'Relational or single Interval' )
+            V = sympify(flatten(V))  # list of sympified elements/None
+            if isinstance(V[0], (Symbol, Idx)) or getattr(V[0], '_diff_wrt', False):
+                newsymbol = V[0]
+                if len(V) == 3:
+                    # general case
+                    if V[2] is None and V[1] is not None:
+                        orientation *= -1
+                    V = [newsymbol] + [i for i in V[1:] if i is not None]
+
+                lenV = len(V)
+                if not isinstance(newsymbol, Idx) or lenV == 3:
+                    if lenV == 4:
+                        limits.append(Tuple(*V))
+                        continue
+                    if lenV == 3:
+                        if isinstance(newsymbol, Idx):
+                            # Idx represents an integer which may have
+                            # specified values it can take on; if it is
+                            # given such a value, an error is raised here
+                            # if the summation would try to give it a larger
+                            # or smaller value than permitted. None and Symbolic
+                            # values will not raise an error.
+                            lo, hi = newsymbol.lower, newsymbol.upper
+                            try:
+                                if lo is not None and not bool(V[1] >= lo):
+                                    raise ValueError("Summation will set Idx value too low.")
+                            except TypeError:
+                                pass
+                            try:
+                                if hi is not None and not bool(V[2] <= hi):
+                                    raise ValueError("Summation will set Idx value too high.")
+                            except TypeError:
+                                pass
+                        limits.append(Tuple(*V))
+                        continue
+                    if lenV == 1 or (lenV == 2 and V[1] is None):
+                        limits.append(Tuple(newsymbol))
+                        continue
+                    elif lenV == 2:
+                        limits.append(Tuple(newsymbol, V[1]))
+                        continue
+
+        raise ValueError('Invalid limits given: %s' % str(symbols))
+
+    return limits, orientation
+
+
+class ExprWithLimits(Expr):
+    __slots__ = ('is_commutative',)
+
+    def __new__(cls, function, *symbols, **assumptions):
+        from sympy.concrete.products import Product
+        pre = _common_new(cls, function, *symbols,
+            discrete=issubclass(cls, Product), **assumptions)
+        if isinstance(pre, tuple):
+            function, limits, _ = pre
+        else:
+            return pre
+
+        # limits must have upper and lower bounds; the indefinite form
+        # is not supported. This restriction does not apply to AddWithLimits
+        if any(len(l) != 3 or None in l for l in limits):
+            raise ValueError('ExprWithLimits requires values for lower and upper bounds.')
+
+        obj = Expr.__new__(cls, **assumptions)
+        arglist = [function]
+        arglist.extend(limits)
+        obj._args = tuple(arglist)
+        obj.is_commutative = function.is_commutative  # limits already checked
+
+        return obj
+
+    @property
+    def function(self):
+        """Return the function applied across limits.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x
+        >>> Integral(x**2, (x,)).function
+        x**2
+
+        See Also
+        ========
+
+        limits, variables, free_symbols
+        """
+        return self._args[0]
+
+    @property
+    def kind(self):
+        return self.function.kind
+
+    @property
+    def limits(self):
+        """Return the limits of expression.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x, i
+        >>> Integral(x**i, (i, 1, 3)).limits
+        ((i, 1, 3),)
+
+        See Also
+        ========
+
+        function, variables, free_symbols
+        """
+        return self._args[1:]
+
+    @property
+    def variables(self):
+        """Return a list of the limit variables.
+
+        >>> from sympy import Sum
+        >>> from sympy.abc import x, i
+        >>> Sum(x**i, (i, 1, 3)).variables
+        [i]
+
+        See Also
+        ========
+
+        function, limits, free_symbols
+        as_dummy : Rename dummy variables
+        sympy.integrals.integrals.Integral.transform : Perform mapping on the dummy variable
+        """
+        return [l[0] for l in self.limits]
+
+    @property
+    def bound_symbols(self):
+        """Return only variables that are dummy variables.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x, i, j, k
+        >>> Integral(x**i, (i, 1, 3), (j, 2), k).bound_symbols
+        [i, j]
+
+        See Also
+        ========
+
+        function, limits, free_symbols
+        as_dummy : Rename dummy variables
+        sympy.integrals.integrals.Integral.transform : Perform mapping on the dummy variable
+        """
+        return [l[0] for l in self.limits if len(l) != 1]
+
+    @property
+    def free_symbols(self):
+        """
+        This method returns the symbols in the object, excluding those
+        that take on a specific value (i.e. the dummy symbols).
+
+        Examples
+        ========
+
+        >>> from sympy import Sum
+        >>> from sympy.abc import x, y
+        >>> Sum(x, (x, y, 1)).free_symbols
+        {y}
+        """
+        # don't test for any special values -- nominal free symbols
+        # should be returned, e.g. don't return set() if the
+        # function is zero -- treat it like an unevaluated expression.
+        function, limits = self.function, self.limits
+        # mask off non-symbol integration variables that have
+        # more than themself as a free symbol
+        reps = {i[0]: i[0] if i[0].free_symbols == {i[0]} else Dummy()
+            for i in self.limits}
+        function = function.xreplace(reps)
+        isyms = function.free_symbols
+        for xab in limits:
+            v = reps[xab[0]]
+            if len(xab) == 1:
+                isyms.add(v)
+                continue
+            # take out the target symbol
+            if v in isyms:
+                isyms.remove(v)
+            # add in the new symbols
+            for i in xab[1:]:
+                isyms.update(i.free_symbols)
+        reps = {v: k for k, v in reps.items()}
+        return {reps.get(_, _) for _ in isyms}
+
+    @property
+    def is_number(self):
+        """Return True if the Sum has no free symbols, else False."""
+        return not self.free_symbols
+
+    def _eval_interval(self, x, a, b):
+        limits = [(i if i[0] != x else (x, a, b)) for i in self.limits]
+        integrand = self.function
+        return self.func(integrand, *limits)
+
+    def _eval_subs(self, old, new):
+        """
+        Perform substitutions over non-dummy variables
+        of an expression with limits.  Also, can be used
+        to specify point-evaluation of an abstract antiderivative.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, oo
+        >>> from sympy.abc import s, n
+        >>> Sum(1/n**s, (n, 1, oo)).subs(s, 2)
+        Sum(n**(-2), (n, 1, oo))
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x, a
+        >>> Integral(a*x**2, x).subs(x, 4)
+        Integral(a*x**2, (x, 4))
+
+        See Also
+        ========
+
+        variables : Lists the integration variables
+        transform : Perform mapping on the dummy variable for integrals
+        change_index : Perform mapping on the sum and product dummy variables
+
+        """
+        func, limits = self.function, list(self.limits)
+
+        # If one of the expressions we are replacing is used as a func index
+        # one of two things happens.
+        #   - the old variable first appears as a free variable
+        #     so we perform all free substitutions before it becomes
+        #     a func index.
+        #   - the old variable first appears as a func index, in
+        #     which case we ignore.  See change_index.
+
+        # Reorder limits to match standard mathematical practice for scoping
+        limits.reverse()
+
+        if not isinstance(old, Symbol) or \
+                old.free_symbols.intersection(self.free_symbols):
+            sub_into_func = True
+            for i, xab in enumerate(limits):
+                if 1 == len(xab) and old == xab[0]:
+                    if new._diff_wrt:
+                        xab = (new,)
+                    else:
+                        xab = (old, old)
+                limits[i] = Tuple(xab[0], *[l._subs(old, new) for l in xab[1:]])
+                if len(xab[0].free_symbols.intersection(old.free_symbols)) != 0:
+                    sub_into_func = False
+                    break
+            if isinstance(old, (AppliedUndef, UndefinedFunction)):
+                sy2 = set(self.variables).intersection(set(new.atoms(Symbol)))
+                sy1 = set(self.variables).intersection(set(old.args))
+                if not sy2.issubset(sy1):
+                    raise ValueError(
+                        "substitution cannot create dummy dependencies")
+                sub_into_func = True
+            if sub_into_func:
+                func = func.subs(old, new)
+        else:
+            # old is a Symbol and a dummy variable of some limit
+            for i, xab in enumerate(limits):
+                if len(xab) == 3:
+                    limits[i] = Tuple(xab[0], *[l._subs(old, new) for l in xab[1:]])
+                    if old == xab[0]:
+                        break
+        # simplify redundant limits (x, x)  to (x, )
+        for i, xab in enumerate(limits):
+            if len(xab) == 2 and (xab[0] - xab[1]).is_zero:
+                limits[i] = Tuple(xab[0], )
+
+        # Reorder limits back to representation-form
+        limits.reverse()
+
+        return self.func(func, *limits)
+
+    @property
+    def has_finite_limits(self):
+        """
+        Returns True if the limits are known to be finite, either by the
+        explicit bounds, assumptions on the bounds, or assumptions on the
+        variables.  False if known to be infinite, based on the bounds.
+        None if not enough information is available to determine.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, Integral, Product, oo, Symbol
+        >>> x = Symbol('x')
+        >>> Sum(x, (x, 1, 8)).has_finite_limits
+        True
+
+        >>> Integral(x, (x, 1, oo)).has_finite_limits
+        False
+
+        >>> M = Symbol('M')
+        >>> Sum(x, (x, 1, M)).has_finite_limits
+
+        >>> N = Symbol('N', integer=True)
+        >>> Product(x, (x, 1, N)).has_finite_limits
+        True
+
+        See Also
+        ========
+
+        has_reversed_limits
+
+        """
+
+        ret_None = False
+        for lim in self.limits:
+            if len(lim) == 3:
+                if any(l.is_infinite for l in lim[1:]):
+                    # Any of the bounds are +/-oo
+                    return False
+                elif any(l.is_infinite is None for l in lim[1:]):
+                    # Maybe there are assumptions on the variable?
+                    if lim[0].is_infinite is None:
+                        ret_None = True
+            else:
+                if lim[0].is_infinite is None:
+                    ret_None = True
+
+        if ret_None:
+            return None
+        return True
+
+    @property
+    def has_reversed_limits(self):
+        """
+        Returns True if the limits are known to be in reversed order, either
+        by the explicit bounds, assumptions on the bounds, or assumptions on the
+        variables.  False if known to be in normal order, based on the bounds.
+        None if not enough information is available to determine.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, Integral, Product, oo, Symbol
+        >>> x = Symbol('x')
+        >>> Sum(x, (x, 8, 1)).has_reversed_limits
+        True
+
+        >>> Sum(x, (x, 1, oo)).has_reversed_limits
+        False
+
+        >>> M = Symbol('M')
+        >>> Integral(x, (x, 1, M)).has_reversed_limits
+
+        >>> N = Symbol('N', integer=True, positive=True)
+        >>> Sum(x, (x, 1, N)).has_reversed_limits
+        False
+
+        >>> Product(x, (x, 2, N)).has_reversed_limits
+
+        >>> Product(x, (x, 2, N)).subs(N, N + 2).has_reversed_limits
+        False
+
+        See Also
+        ========
+
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.has_empty_sequence
+
+        """
+        ret_None = False
+        for lim in self.limits:
+            if len(lim) == 3:
+                var, a, b = lim
+                dif = b - a
+                if dif.is_extended_negative:
+                    return True
+                elif dif.is_extended_nonnegative:
+                    continue
+                else:
+                    ret_None = True
+            else:
+                return None
+        if ret_None:
+            return None
+        return False
+
+
+class AddWithLimits(ExprWithLimits):
+    r"""Represents unevaluated oriented additions.
+        Parent class for Integral and Sum.
+    """
+
+    __slots__ = ()
+
+    def __new__(cls, function, *symbols, **assumptions):
+        from sympy.concrete.summations import Sum
+        pre = _common_new(cls, function, *symbols,
+            discrete=issubclass(cls, Sum), **assumptions)
+        if isinstance(pre, tuple):
+            function, limits, orientation = pre
+        else:
+            return pre
+
+        obj = Expr.__new__(cls, **assumptions)
+        arglist = [orientation*function]  # orientation not used in ExprWithLimits
+        arglist.extend(limits)
+        obj._args = tuple(arglist)
+        obj.is_commutative = function.is_commutative  # limits already checked
+
+        return obj
+
+    def _eval_adjoint(self):
+        if all(x.is_real for x in flatten(self.limits)):
+            return self.func(self.function.adjoint(), *self.limits)
+        return None
+
+    def _eval_conjugate(self):
+        if all(x.is_real for x in flatten(self.limits)):
+            return self.func(self.function.conjugate(), *self.limits)
+        return None
+
+    def _eval_transpose(self):
+        if all(x.is_real for x in flatten(self.limits)):
+            return self.func(self.function.transpose(), *self.limits)
+        return None
+
+    def _eval_factor(self, **hints):
+        if 1 == len(self.limits):
+            summand = self.function.factor(**hints)
+            if summand.is_Mul:
+                out = sift(summand.args, lambda w: w.is_commutative \
+                    and not set(self.variables) & w.free_symbols)
+                return Mul(*out[True])*self.func(Mul(*out[False]), \
+                    *self.limits)
+        else:
+            summand = self.func(self.function, *self.limits[0:-1]).factor()
+            if not summand.has(self.variables[-1]):
+                return self.func(1, [self.limits[-1]]).doit()*summand
+            elif isinstance(summand, Mul):
+                return self.func(summand, self.limits[-1]).factor()
+        return self
+
+    def _eval_expand_basic(self, **hints):
+        summand = self.function.expand(**hints)
+        force = hints.get('force', False)
+        if (summand.is_Add and (force or summand.is_commutative and
+                 self.has_finite_limits is not False)):
+            return Add(*[self.func(i, *self.limits) for i in summand.args])
+        elif isinstance(summand, MatrixBase):
+            return summand.applyfunc(lambda x: self.func(x, *self.limits))
+        elif summand != self.function:
+            return self.func(summand, *self.limits)
+        return self
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/gosper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/gosper.py
new file mode 100644
index 0000000000000000000000000000000000000000..76eb20ef4f94bc6bff6324a1dcc09f90e05274b3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/gosper.py
@@ -0,0 +1,222 @@
+"""Gosper's algorithm for hypergeometric summation. """
+
+from sympy.core import S, Dummy, symbols
+from sympy.polys import Poly, parallel_poly_from_expr, factor
+from sympy.utilities.iterables import is_sequence
+
+
+def gosper_normal(f, g, n, polys=True):
+    r"""
+    Compute the Gosper's normal form of ``f`` and ``g``.
+
+    Explanation
+    ===========
+
+    Given relatively prime univariate polynomials ``f`` and ``g``,
+    rewrite their quotient to a normal form defined as follows:
+
+    .. math::
+        \frac{f(n)}{g(n)} = Z \cdot \frac{A(n) C(n+1)}{B(n) C(n)}
+
+    where ``Z`` is an arbitrary constant and ``A``, ``B``, ``C`` are
+    monic polynomials in ``n`` with the following properties:
+
+    1. `\gcd(A(n), B(n+h)) = 1 \forall h \in \mathbb{N}`
+    2. `\gcd(B(n), C(n+1)) = 1`
+    3. `\gcd(A(n), C(n)) = 1`
+
+    This normal form, or rational factorization in other words, is a
+    crucial step in Gosper's algorithm and in solving of difference
+    equations. It can be also used to decide if two hypergeometric
+    terms are similar or not.
+
+    This procedure will return a tuple containing elements of this
+    factorization in the form ``(Z*A, B, C)``.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.gosper import gosper_normal
+    >>> from sympy.abc import n
+
+    >>> gosper_normal(4*n+5, 2*(4*n+1)*(2*n+3), n, polys=False)
+    (1/4, n + 3/2, n + 1/4)
+
+    """
+    (p, q), opt = parallel_poly_from_expr(
+        (f, g), n, field=True, extension=True)
+
+    a, A = p.LC(), p.monic()
+    b, B = q.LC(), q.monic()
+
+    C, Z = A.one, a/b
+    h = Dummy('h')
+
+    D = Poly(n + h, n, h, domain=opt.domain)
+
+    R = A.resultant(B.compose(D))
+    roots = {r for r in R.ground_roots().keys() if r.is_Integer and r >= 0}
+    for i in sorted(roots):
+        d = A.gcd(B.shift(+i))
+
+        A = A.quo(d)
+        B = B.quo(d.shift(-i))
+
+        for j in range(1, i + 1):
+            C *= d.shift(-j)
+
+    A = A.mul_ground(Z)
+
+    if not polys:
+        A = A.as_expr()
+        B = B.as_expr()
+        C = C.as_expr()
+
+    return A, B, C
+
+
+def gosper_term(f, n):
+    r"""
+    Compute Gosper's hypergeometric term for ``f``.
+
+    Explanation
+    ===========
+
+    Suppose ``f`` is a hypergeometric term such that:
+
+    .. math::
+        s_n = \sum_{k=0}^{n-1} f_k
+
+    and `f_k` does not depend on `n`. Returns a hypergeometric
+    term `g_n` such that `g_{n+1} - g_n = f_n`.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.gosper import gosper_term
+    >>> from sympy import factorial
+    >>> from sympy.abc import n
+
+    >>> gosper_term((4*n + 1)*factorial(n)/factorial(2*n + 1), n)
+    (-n - 1/2)/(n + 1/4)
+
+    """
+    from sympy.simplify import hypersimp
+    r = hypersimp(f, n)
+
+    if r is None:
+        return None    # 'f' is *not* a hypergeometric term
+
+    p, q = r.as_numer_denom()
+
+    A, B, C = gosper_normal(p, q, n)
+    B = B.shift(-1)
+
+    N = S(A.degree())
+    M = S(B.degree())
+    K = S(C.degree())
+
+    if (N != M) or (A.LC() != B.LC()):
+        D = {K - max(N, M)}
+    elif not N:
+        D = {K - N + 1, S.Zero}
+    else:
+        D = {K - N + 1, (B.nth(N - 1) - A.nth(N - 1))/A.LC()}
+
+    for d in set(D):
+        if not d.is_Integer or d < 0:
+            D.remove(d)
+
+    if not D:
+        return None    # 'f(n)' is *not* Gosper-summable
+
+    d = max(D)
+
+    coeffs = symbols('c:%s' % (d + 1), cls=Dummy)
+    domain = A.get_domain().inject(*coeffs)
+
+    x = Poly(coeffs, n, domain=domain)
+    H = A*x.shift(1) - B*x - C
+
+    from sympy.solvers.solvers import solve
+    solution = solve(H.coeffs(), coeffs)
+
+    if solution is None:
+        return None    # 'f(n)' is *not* Gosper-summable
+
+    x = x.as_expr().subs(solution)
+
+    for coeff in coeffs:
+        if coeff not in solution:
+            x = x.subs(coeff, 0)
+
+    if x.is_zero:
+        return None    # 'f(n)' is *not* Gosper-summable
+    else:
+        return B.as_expr()*x/C.as_expr()
+
+
+def gosper_sum(f, k):
+    r"""
+    Gosper's hypergeometric summation algorithm.
+
+    Explanation
+    ===========
+
+    Given a hypergeometric term ``f`` such that:
+
+    .. math ::
+        s_n = \sum_{k=0}^{n-1} f_k
+
+    and `f(n)` does not depend on `n`, returns `g_{n} - g(0)` where
+    `g_{n+1} - g_n = f_n`, or ``None`` if `s_n` cannot be expressed
+    in closed form as a sum of hypergeometric terms.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.gosper import gosper_sum
+    >>> from sympy import factorial
+    >>> from sympy.abc import n, k
+
+    >>> f = (4*k + 1)*factorial(k)/factorial(2*k + 1)
+    >>> gosper_sum(f, (k, 0, n))
+    (-factorial(n) + 2*factorial(2*n + 1))/factorial(2*n + 1)
+    >>> _.subs(n, 2) == sum(f.subs(k, i) for i in [0, 1, 2])
+    True
+    >>> gosper_sum(f, (k, 3, n))
+    (-60*factorial(n) + factorial(2*n + 1))/(60*factorial(2*n + 1))
+    >>> _.subs(n, 5) == sum(f.subs(k, i) for i in [3, 4, 5])
+    True
+
+    References
+    ==========
+
+    .. [1] Marko Petkovsek, Herbert S. Wilf, Doron Zeilberger, A = B,
+           AK Peters, Ltd., Wellesley, MA, USA, 1997, pp. 73--100
+
+    """
+    indefinite = False
+
+    if is_sequence(k):
+        k, a, b = k
+    else:
+        indefinite = True
+
+    g = gosper_term(f, k)
+
+    if g is None:
+        return None
+
+    if indefinite:
+        result = f*g
+    else:
+        result = (f*(g + 1)).subs(k, b) - (f*g).subs(k, a)
+
+        if result is S.NaN:
+            try:
+                result = (f*(g + 1)).limit(k, b) - (f*g).limit(k, a)
+            except NotImplementedError:
+                result = None
+
+    return factor(result)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/guess.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/guess.py
new file mode 100644
index 0000000000000000000000000000000000000000..90aac54b442ce67c90cbb262e10d525e5f2ba316
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/guess.py
@@ -0,0 +1,473 @@
+"""Various algorithms for helping identifying numbers and sequences."""
+
+
+from sympy.concrete.products import (Product, product)
+from sympy.core import Function, S
+from sympy.core.add import Add
+from sympy.core.numbers import Integer, Rational
+from sympy.core.symbol import Symbol, symbols
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.integers import floor
+from sympy.integrals.integrals import integrate
+from sympy.polys.polyfuncs import rational_interpolate as rinterp
+from sympy.polys.polytools import lcm
+from sympy.simplify.radsimp import denom
+from sympy.utilities import public
+
+
+@public
+def find_simple_recurrence_vector(l):
+    """
+    This function is used internally by other functions from the
+    sympy.concrete.guess module. While most users may want to rather use the
+    function find_simple_recurrence when looking for recurrence relations
+    among rational numbers, the current function may still be useful when
+    some post-processing has to be done.
+
+    Explanation
+    ===========
+
+    The function returns a vector of length n when a recurrence relation of
+    order n is detected in the sequence of rational numbers v.
+
+    If the returned vector has a length 1, then the returned value is always
+    the list [0], which means that no relation has been found.
+
+    While the functions is intended to be used with rational numbers, it should
+    work for other kinds of real numbers except for some cases involving
+    quadratic numbers; for that reason it should be used with some caution when
+    the argument is not a list of rational numbers.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.guess import find_simple_recurrence_vector
+    >>> from sympy import fibonacci
+    >>> find_simple_recurrence_vector([fibonacci(k) for k in range(12)])
+    [1, -1, -1]
+
+    See Also
+    ========
+
+    See the function sympy.concrete.guess.find_simple_recurrence which is more
+    user-friendly.
+
+    """
+    q1 = [0]
+    q2 = [1]
+    b, z = 0, len(l) >> 1
+    while len(q2) <= z:
+        while l[b]==0:
+            b += 1
+            if b == len(l):
+                c = 1
+                for x in q2:
+                    c = lcm(c, denom(x))
+                if q2[0]*c < 0: c = -c
+                for k in range(len(q2)):
+                    q2[k] = int(q2[k]*c)
+                return q2
+        a = S.One/l[b]
+        m = [a]
+        for k in range(b+1, len(l)):
+            m.append(-sum(l[j+1]*m[b-j-1] for j in range(b, k))*a)
+        l, m = m, [0] * max(len(q2), b+len(q1))
+        for k, q in enumerate(q2):
+            m[k] = a*q
+        for k, q in enumerate(q1):
+            m[k+b] += q
+        while m[-1]==0: m.pop() # because trailing zeros can occur
+        q1, q2, b = q2, m, 1
+    return [0]
+
+@public
+def find_simple_recurrence(v, A=Function('a'), N=Symbol('n')):
+    """
+    Detects and returns a recurrence relation from a sequence of several integer
+    (or rational) terms. The name of the function in the returned expression is
+    'a' by default; the main variable is 'n' by default. The smallest index in
+    the returned expression is always n (and never n-1, n-2, etc.).
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.guess import find_simple_recurrence
+    >>> from sympy import fibonacci
+    >>> find_simple_recurrence([fibonacci(k) for k in range(12)])
+    -a(n) - a(n + 1) + a(n + 2)
+
+    >>> from sympy import Function, Symbol
+    >>> a = [1, 1, 1]
+    >>> for k in range(15): a.append(5*a[-1]-3*a[-2]+8*a[-3])
+    >>> find_simple_recurrence(a, A=Function('f'), N=Symbol('i'))
+    -8*f(i) + 3*f(i + 1) - 5*f(i + 2) + f(i + 3)
+
+    """
+    p = find_simple_recurrence_vector(v)
+    n = len(p)
+    if n <= 1: return S.Zero
+
+    return Add(*[A(N+n-1-k)*p[k] for k in range(n)])
+
+
+@public
+def rationalize(x, maxcoeff=10000):
+    """
+    Helps identifying a rational number from a float (or mpmath.mpf) value by
+    using a continued fraction. The algorithm stops as soon as a large partial
+    quotient is detected (greater than 10000 by default).
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.guess import rationalize
+    >>> from mpmath import cos, pi
+    >>> rationalize(cos(pi/3))
+    1/2
+
+    >>> from mpmath import mpf
+    >>> rationalize(mpf("0.333333333333333"))
+    1/3
+
+    While the function is rather intended to help 'identifying' rational
+    values, it may be used in some cases for approximating real numbers.
+    (Though other functions may be more relevant in that case.)
+
+    >>> rationalize(pi, maxcoeff = 250)
+    355/113
+
+    See Also
+    ========
+
+    Several other methods can approximate a real number as a rational, like:
+
+      * fractions.Fraction.from_decimal
+      * fractions.Fraction.from_float
+      * mpmath.identify
+      * mpmath.pslq by using the following syntax: mpmath.pslq([x, 1])
+      * mpmath.findpoly by using the following syntax: mpmath.findpoly(x, 1)
+      * sympy.simplify.nsimplify (which is a more general function)
+
+    The main difference between the current function and all these variants is
+    that control focuses on magnitude of partial quotients here rather than on
+    global precision of the approximation. If the real is "known to be" a
+    rational number, the current function should be able to detect it correctly
+    with the default settings even when denominator is great (unless its
+    expansion contains unusually big partial quotients) which may occur
+    when studying sequences of increasing numbers. If the user cares more
+    on getting simple fractions, other methods may be more convenient.
+
+    """
+    p0, p1 = 0, 1
+    q0, q1 = 1, 0
+    a = floor(x)
+    while a < maxcoeff or q1==0:
+        p = a*p1 + p0
+        q = a*q1 + q0
+        p0, p1 = p1, p
+        q0, q1 = q1, q
+        if x==a: break
+        x = 1/(x-a)
+        a = floor(x)
+    return sympify(p) / q
+
+
+@public
+def guess_generating_function_rational(v, X=Symbol('x')):
+    """
+    Tries to "guess" a rational generating function for a sequence of rational
+    numbers v.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.guess import guess_generating_function_rational
+    >>> from sympy import fibonacci
+    >>> l = [fibonacci(k) for k in range(5,15)]
+    >>> guess_generating_function_rational(l)
+    (3*x + 5)/(-x**2 - x + 1)
+
+    See Also
+    ========
+
+    sympy.series.approximants
+    mpmath.pade
+
+    """
+    #   a) compute the denominator as q
+    q = find_simple_recurrence_vector(v)
+    n = len(q)
+    if n <= 1: return None
+    #   b) compute the numerator as p
+    p = [sum(v[i-k]*q[k] for k in range(min(i+1, n)))
+            for i in range(len(v)>>1)]
+    return (sum(p[k]*X**k for k in range(len(p)))
+            / sum(q[k]*X**k for k in range(n)))
+
+
+@public
+def guess_generating_function(v, X=Symbol('x'), types=['all'], maxsqrtn=2):
+    """
+    Tries to "guess" a generating function for a sequence of rational numbers v.
+    Only a few patterns are implemented yet.
+
+    Explanation
+    ===========
+
+    The function returns a dictionary where keys are the name of a given type of
+    generating function. Six types are currently implemented:
+
+         type  |  formal definition
+        -------+----------------------------------------------------------------
+        ogf    | f(x) = Sum(            a_k * x^k       ,  k: 0..infinity )
+        egf    | f(x) = Sum(            a_k * x^k / k!  ,  k: 0..infinity )
+        lgf    | f(x) = Sum( (-1)^(k+1) a_k * x^k / k   ,  k: 1..infinity )
+               |        (with initial index being hold as 1 rather than 0)
+        hlgf   | f(x) = Sum(            a_k * x^k / k   ,  k: 1..infinity )
+               |        (with initial index being hold as 1 rather than 0)
+        lgdogf | f(x) = derivate( log(Sum( a_k * x^k, k: 0..infinity )), x)
+        lgdegf | f(x) = derivate( log(Sum( a_k * x^k / k!, k: 0..infinity )), x)
+
+    In order to spare time, the user can select only some types of generating
+    functions (default being ['all']). While forgetting to use a list in the
+    case of a single type may seem to work most of the time as in: types='ogf'
+    this (convenient) syntax may lead to unexpected extra results in some cases.
+
+    Discarding a type when calling the function does not mean that the type will
+    not be present in the returned dictionary; it only means that no extra
+    computation will be performed for that type, but the function may still add
+    it in the result when it can be easily converted from another type.
+
+    Two generating functions (lgdogf and lgdegf) are not even computed if the
+    initial term of the sequence is 0; it may be useful in that case to try
+    again after having removed the leading zeros.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.guess import guess_generating_function as ggf
+    >>> ggf([k+1 for k in range(12)], types=['ogf', 'lgf', 'hlgf'])
+    {'hlgf': 1/(1 - x), 'lgf': 1/(x + 1), 'ogf': 1/(x**2 - 2*x + 1)}
+
+    >>> from sympy import sympify
+    >>> l = sympify("[3/2, 11/2, 0, -121/2, -363/2, 121]")
+    >>> ggf(l)
+    {'ogf': (x + 3/2)/(11*x**2 - 3*x + 1)}
+
+    >>> from sympy import fibonacci
+    >>> ggf([fibonacci(k) for k in range(5, 15)], types=['ogf'])
+    {'ogf': (3*x + 5)/(-x**2 - x + 1)}
+
+    >>> from sympy import factorial
+    >>> ggf([factorial(k) for k in range(12)], types=['ogf', 'egf', 'lgf'])
+    {'egf': 1/(1 - x)}
+
+    >>> ggf([k+1 for k in range(12)], types=['egf'])
+    {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)}
+
+    N-th root of a rational function can also be detected (below is an example
+    coming from the sequence A108626 from https://oeis.org).
+    The greatest n-th root to be tested is specified as maxsqrtn (default 2).
+
+    >>> ggf([1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf']
+    sqrt(1/(x**4 + 2*x**2 - 4*x + 1))
+
+    References
+    ==========
+
+    .. [1] "Concrete Mathematics", R.L. Graham, D.E. Knuth, O. Patashnik
+    .. [2] https://oeis.org/wiki/Generating_functions
+
+    """
+    # List of all types of all g.f. known by the algorithm
+    if 'all' in types:
+        types = ('ogf', 'egf', 'lgf', 'hlgf', 'lgdogf', 'lgdegf')
+
+    result = {}
+
+    # Ordinary Generating Function (ogf)
+    if 'ogf' in types:
+        # Perform some convolutions of the sequence with itself
+        t = [1] + [0]*(len(v) - 1)
+        for d in range(max(1, maxsqrtn)):
+            t = [sum(t[n-i]*v[i] for i in range(n+1)) for n in range(len(v))]
+            g = guess_generating_function_rational(t, X=X)
+            if g:
+                result['ogf'] = g**Rational(1, d+1)
+                break
+
+    # Exponential Generating Function (egf)
+    if 'egf' in types:
+        # Transform sequence (division by factorial)
+        w, f = [], S.One
+        for i, k in enumerate(v):
+            f *= i if i else 1
+            w.append(k/f)
+        # Perform some convolutions of the sequence with itself
+        t = [1] + [0]*(len(w) - 1)
+        for d in range(max(1, maxsqrtn)):
+            t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))]
+            g = guess_generating_function_rational(t, X=X)
+            if g:
+                result['egf'] = g**Rational(1, d+1)
+                break
+
+    # Logarithmic Generating Function (lgf)
+    if 'lgf' in types:
+        # Transform sequence (multiplication by (-1)^(n+1) / n)
+        w, f = [], S.NegativeOne
+        for i, k in enumerate(v):
+            f = -f
+            w.append(f*k/Integer(i+1))
+        # Perform some convolutions of the sequence with itself
+        t = [1] + [0]*(len(w) - 1)
+        for d in range(max(1, maxsqrtn)):
+            t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))]
+            g = guess_generating_function_rational(t, X=X)
+            if g:
+                result['lgf'] = g**Rational(1, d+1)
+                break
+
+    # Hyperbolic logarithmic Generating Function (hlgf)
+    if 'hlgf' in types:
+        # Transform sequence (division by n+1)
+        w = []
+        for i, k in enumerate(v):
+            w.append(k/Integer(i+1))
+        # Perform some convolutions of the sequence with itself
+        t = [1] + [0]*(len(w) - 1)
+        for d in range(max(1, maxsqrtn)):
+            t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))]
+            g = guess_generating_function_rational(t, X=X)
+            if g:
+                result['hlgf'] = g**Rational(1, d+1)
+                break
+
+    # Logarithmic derivative of ordinary generating Function (lgdogf)
+    if v[0] != 0 and ('lgdogf' in types
+                       or ('ogf' in types and 'ogf' not in result)):
+        # Transform sequence by computing f'(x)/f(x)
+        # because log(f(x)) = integrate( f'(x)/f(x) )
+        a, w = sympify(v[0]), []
+        for n in range(len(v)-1):
+            w.append(
+               (v[n+1]*(n+1) - sum(w[-i-1]*v[i+1] for i in range(n)))/a)
+        # Perform some convolutions of the sequence with itself
+        t = [1] + [0]*(len(w) - 1)
+        for d in range(max(1, maxsqrtn)):
+            t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))]
+            g = guess_generating_function_rational(t, X=X)
+            if g:
+                result['lgdogf'] = g**Rational(1, d+1)
+                if 'ogf' not in result:
+                    result['ogf'] = exp(integrate(result['lgdogf'], X))
+                break
+
+    # Logarithmic derivative of exponential generating Function (lgdegf)
+    if v[0] != 0 and ('lgdegf' in types
+                       or ('egf' in types and 'egf' not in result)):
+        # Transform sequence / step 1 (division by factorial)
+        z, f = [], S.One
+        for i, k in enumerate(v):
+            f *= i if i else 1
+            z.append(k/f)
+        # Transform sequence / step 2 by computing f'(x)/f(x)
+        # because log(f(x)) = integrate( f'(x)/f(x) )
+        a, w = z[0], []
+        for n in range(len(z)-1):
+            w.append(
+               (z[n+1]*(n+1) - sum(w[-i-1]*z[i+1] for i in range(n)))/a)
+        # Perform some convolutions of the sequence with itself
+        t = [1] + [0]*(len(w) - 1)
+        for d in range(max(1, maxsqrtn)):
+            t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))]
+            g = guess_generating_function_rational(t, X=X)
+            if g:
+                result['lgdegf'] = g**Rational(1, d+1)
+                if 'egf' not in result:
+                    result['egf'] = exp(integrate(result['lgdegf'], X))
+                break
+
+    return result
+
+
+@public
+def guess(l, all=False, evaluate=True, niter=2, variables=None):
+    """
+    This function is adapted from the Rate.m package for Mathematica
+    written by Christian Krattenthaler.
+    It tries to guess a formula from a given sequence of rational numbers.
+
+    Explanation
+    ===========
+
+    In order to speed up the process, the 'all' variable is set to False by
+    default, stopping the computation as some results are returned during an
+    iteration; the variable can be set to True if more iterations are needed
+    (other formulas may be found; however they may be equivalent to the first
+    ones).
+
+    Another option is the 'evaluate' variable (default is True); setting it
+    to False will leave the involved products unevaluated.
+
+    By default, the number of iterations is set to 2 but a greater value (up
+    to len(l)-1) can be specified with the optional 'niter' variable.
+    More and more convoluted results are found when the order of the
+    iteration gets higher:
+
+      * first iteration returns polynomial or rational functions;
+      * second iteration returns products of rising factorials and their
+        inverses;
+      * third iteration returns products of products of rising factorials
+        and their inverses;
+      * etc.
+
+    The returned formulas contain symbols i0, i1, i2, ... where the main
+    variables is i0 (and auxiliary variables are i1, i2, ...). A list of
+    other symbols can be provided in the 'variables' option; the length of
+    the least should be the value of 'niter' (more is acceptable but only
+    the first symbols will be used); in this case, the main variable will be
+    the first symbol in the list.
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.guess import guess
+    >>> guess([1,2,6,24,120], evaluate=False)
+    [Product(i1 + 1, (i1, 1, i0 - 1))]
+
+    >>> from sympy import symbols
+    >>> r = guess([1,2,7,42,429,7436,218348,10850216], niter=4)
+    >>> i0 = symbols("i0")
+    >>> [r[0].subs(i0,n).doit() for n in range(1,10)]
+    [1, 2, 7, 42, 429, 7436, 218348, 10850216, 911835460]
+    """
+    if any(a==0 for a in l[:-1]):
+        return []
+    N = len(l)
+    niter = min(N-1, niter)
+    myprod = product if evaluate else Product
+    g = []
+    res = []
+    if variables is None:
+        symb = symbols('i:'+str(niter))
+    else:
+        symb = variables
+    for k, s in enumerate(symb):
+        g.append(l)
+        n, r = len(l), []
+        for i in range(n-2-1, -1, -1):
+            ri = rinterp(enumerate(g[k][:-1], start=1), i, X=s)
+            if ((denom(ri).subs({s:n}) != 0)
+                    and (ri.subs({s:n}) - g[k][-1] == 0)
+                    and ri not in r):
+                r.append(ri)
+        if r:
+            for i in range(k-1, -1, -1):
+                r = [g[i][0]
+                      * myprod(v, (symb[i+1], 1, symb[i]-1)) for v in r]
+            if not all: return r
+            res += r
+        l = [Rational(l[i+1], l[i]) for i in range(N-k-1)]
+    return res
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/products.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/products.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd035551683531f80b0e4467fe1cdfbb6ebbe9ad
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/products.py
@@ -0,0 +1,605 @@
+from __future__ import annotations
+
+from .expr_with_intlimits import ExprWithIntLimits
+from .summations import Sum, summation, _dummy_with_inherited_properties_concrete
+from sympy.core.expr import Expr
+from sympy.core.exprtools import factor_terms
+from sympy.core.function import Derivative
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy, Symbol
+from sympy.functions.combinatorial.factorials import RisingFactorial
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.polys import quo, roots
+
+
+class Product(ExprWithIntLimits):
+    r"""
+    Represents unevaluated products.
+
+    Explanation
+    ===========
+
+    ``Product`` represents a finite or infinite product, with the first
+    argument being the general form of terms in the series, and the second
+    argument being ``(dummy_variable, start, end)``, with ``dummy_variable``
+    taking all integer values from ``start`` through ``end``. In accordance
+    with long-standing mathematical convention, the end term is included in
+    the product.
+
+    Finite products
+    ===============
+
+    For finite products (and products with symbolic limits assumed to be finite)
+    we follow the analogue of the summation convention described by Karr [1],
+    especially definition 3 of section 1.4. The product:
+
+    .. math::
+
+        \prod_{m \leq i < n} f(i)
+
+    has *the obvious meaning* for `m < n`, namely:
+
+    .. math::
+
+        \prod_{m \leq i < n} f(i) = f(m) f(m+1) \cdot \ldots \cdot f(n-2) f(n-1)
+
+    with the upper limit value `f(n)` excluded. The product over an empty set is
+    one if and only if `m = n`:
+
+    .. math::
+
+        \prod_{m \leq i < n} f(i) = 1  \quad \mathrm{for} \quad  m = n
+
+    Finally, for all other products over empty sets we assume the following
+    definition:
+
+    .. math::
+
+        \prod_{m \leq i < n} f(i) = \frac{1}{\prod_{n \leq i < m} f(i)}  \quad \mathrm{for} \quad  m > n
+
+    It is important to note that above we define all products with the upper
+    limit being exclusive. This is in contrast to the usual mathematical notation,
+    but does not affect the product convention. Indeed we have:
+
+    .. math::
+
+        \prod_{m \leq i < n} f(i) = \prod_{i = m}^{n - 1} f(i)
+
+    where the difference in notation is intentional to emphasize the meaning,
+    with limits typeset on the top being inclusive.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import a, b, i, k, m, n, x
+    >>> from sympy import Product, oo
+    >>> Product(k, (k, 1, m))
+    Product(k, (k, 1, m))
+    >>> Product(k, (k, 1, m)).doit()
+    factorial(m)
+    >>> Product(k**2,(k, 1, m))
+    Product(k**2, (k, 1, m))
+    >>> Product(k**2,(k, 1, m)).doit()
+    factorial(m)**2
+
+    Wallis' product for pi:
+
+    >>> W = Product(2*i/(2*i-1) * 2*i/(2*i+1), (i, 1, oo))
+    >>> W
+    Product(4*i**2/((2*i - 1)*(2*i + 1)), (i, 1, oo))
+
+    Direct computation currently fails:
+
+    >>> W.doit()
+    Product(4*i**2/((2*i - 1)*(2*i + 1)), (i, 1, oo))
+
+    But we can approach the infinite product by a limit of finite products:
+
+    >>> from sympy import limit
+    >>> W2 = Product(2*i/(2*i-1)*2*i/(2*i+1), (i, 1, n))
+    >>> W2
+    Product(4*i**2/((2*i - 1)*(2*i + 1)), (i, 1, n))
+    >>> W2e = W2.doit()
+    >>> W2e
+    4**n*factorial(n)**2/(2**(2*n)*RisingFactorial(1/2, n)*RisingFactorial(3/2, n))
+    >>> limit(W2e, n, oo)
+    pi/2
+
+    By the same formula we can compute sin(pi/2):
+
+    >>> from sympy import combsimp, pi, gamma, simplify
+    >>> P = pi * x * Product(1 - x**2/k**2, (k, 1, n))
+    >>> P = P.subs(x, pi/2)
+    >>> P
+    pi**2*Product(1 - pi**2/(4*k**2), (k, 1, n))/2
+    >>> Pe = P.doit()
+    >>> Pe
+    pi**2*RisingFactorial(1 - pi/2, n)*RisingFactorial(1 + pi/2, n)/(2*factorial(n)**2)
+    >>> limit(Pe, n, oo).gammasimp()
+    sin(pi**2/2)
+    >>> Pe.rewrite(gamma)
+    (-1)**n*pi**2*gamma(pi/2)*gamma(n + 1 + pi/2)/(2*gamma(1 + pi/2)*gamma(-n + pi/2)*gamma(n + 1)**2)
+
+    Products with the lower limit being larger than the upper one:
+
+    >>> Product(1/i, (i, 6, 1)).doit()
+    120
+    >>> Product(i, (i, 2, 5)).doit()
+    120
+
+    The empty product:
+
+    >>> Product(i, (i, n, n-1)).doit()
+    1
+
+    An example showing that the symbolic result of a product is still
+    valid for seemingly nonsensical values of the limits. Then the Karr
+    convention allows us to give a perfectly valid interpretation to
+    those products by interchanging the limits according to the above rules:
+
+    >>> P = Product(2, (i, 10, n)).doit()
+    >>> P
+    2**(n - 9)
+    >>> P.subs(n, 5)
+    1/16
+    >>> Product(2, (i, 10, 5)).doit()
+    1/16
+    >>> 1/Product(2, (i, 6, 9)).doit()
+    1/16
+
+    An explicit example of the Karr summation convention applied to products:
+
+    >>> P1 = Product(x, (i, a, b)).doit()
+    >>> P1
+    x**(-a + b + 1)
+    >>> P2 = Product(x, (i, b+1, a-1)).doit()
+    >>> P2
+    x**(a - b - 1)
+    >>> simplify(P1 * P2)
+    1
+
+    And another one:
+
+    >>> P1 = Product(i, (i, b, a)).doit()
+    >>> P1
+    RisingFactorial(b, a - b + 1)
+    >>> P2 = Product(i, (i, a+1, b-1)).doit()
+    >>> P2
+    RisingFactorial(a + 1, -a + b - 1)
+    >>> P1 * P2
+    RisingFactorial(b, a - b + 1)*RisingFactorial(a + 1, -a + b - 1)
+    >>> combsimp(P1 * P2)
+    1
+
+    See Also
+    ========
+
+    Sum, summation
+    product
+
+    References
+    ==========
+
+    .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM,
+           Volume 28 Issue 2, April 1981, Pages 305-350
+           https://dl.acm.org/doi/10.1145/322248.322255
+    .. [2] https://en.wikipedia.org/wiki/Multiplication#Capital_Pi_notation
+    .. [3] https://en.wikipedia.org/wiki/Empty_product
+    """
+
+    __slots__ = ()
+
+    limits: tuple[tuple[Symbol, Expr, Expr]]
+
+    def __new__(cls, function, *symbols, **assumptions):
+        obj = ExprWithIntLimits.__new__(cls, function, *symbols, **assumptions)
+        return obj
+
+    def _eval_rewrite_as_Sum(self, *args, **kwargs):
+        return exp(Sum(log(self.function), *self.limits))
+
+    @property
+    def term(self):
+        return self._args[0]
+    function = term
+
+    def _eval_is_zero(self):
+        if self.has_empty_sequence:
+            return False
+
+        z = self.term.is_zero
+        if z is True:
+            return True
+        if self.has_finite_limits:
+            # A Product is zero only if its term is zero assuming finite limits.
+            return z
+
+    def _eval_is_extended_real(self):
+        if self.has_empty_sequence:
+            return True
+
+        return self.function.is_extended_real
+
+    def _eval_is_positive(self):
+        if self.has_empty_sequence:
+            return True
+        if self.function.is_positive and self.has_finite_limits:
+            return True
+
+    def _eval_is_nonnegative(self):
+        if self.has_empty_sequence:
+            return True
+        if self.function.is_nonnegative and self.has_finite_limits:
+            return True
+
+    def _eval_is_extended_nonnegative(self):
+        if self.has_empty_sequence:
+            return True
+        if self.function.is_extended_nonnegative:
+            return True
+
+    def _eval_is_extended_nonpositive(self):
+        if self.has_empty_sequence:
+            return True
+
+    def _eval_is_finite(self):
+        if self.has_finite_limits and self.function.is_finite:
+            return True
+
+    def doit(self, **hints):
+        # first make sure any definite limits have product
+        # variables with matching assumptions
+        reps = {}
+        for xab in self.limits:
+            d = _dummy_with_inherited_properties_concrete(xab)
+            if d:
+                reps[xab[0]] = d
+        if reps:
+            undo = {v: k for k, v in reps.items()}
+            did = self.xreplace(reps).doit(**hints)
+            if isinstance(did, tuple):  # when separate=True
+                did = tuple([i.xreplace(undo) for i in did])
+            else:
+                did = did.xreplace(undo)
+            return did
+
+        from sympy.simplify.powsimp import powsimp
+        f = self.function
+        for index, limit in enumerate(self.limits):
+            i, a, b = limit
+            dif = b - a
+            if dif.is_integer and dif.is_negative:
+                a, b = b + 1, a - 1
+                f = 1 / f
+
+            g = self._eval_product(f, (i, a, b))
+            if g in (None, S.NaN):
+                return self.func(powsimp(f), *self.limits[index:])
+            else:
+                f = g
+
+        if hints.get('deep', True):
+            return f.doit(**hints)
+        else:
+            return powsimp(f)
+
+    def _eval_conjugate(self):
+        return self.func(self.function.conjugate(), *self.limits)
+
+    def _eval_product(self, term, limits):
+
+        (k, a, n) = limits
+
+        if k not in term.free_symbols:
+            if (term - 1).is_zero:
+                return S.One
+            return term**(n - a + 1)
+
+        if a == n:
+            return term.subs(k, a)
+
+        from .delta import deltaproduct, _has_simple_delta
+        if term.has(KroneckerDelta) and _has_simple_delta(term, limits[0]):
+            return deltaproduct(term, limits)
+
+        dif = n - a
+        definite = dif.is_Integer
+        if definite and (dif < 100):
+            return self._eval_product_direct(term, limits)
+
+        elif term.is_polynomial(k):
+            poly = term.as_poly(k)
+
+            A = B = Q = S.One
+
+            all_roots = roots(poly)
+
+            M = 0
+            for r, m in all_roots.items():
+                M += m
+                A *= RisingFactorial(a - r, n - a + 1)**m
+                Q *= (n - r)**m
+
+            if M < poly.degree():
+                arg = quo(poly, Q.as_poly(k))
+                B = self.func(arg, (k, a, n)).doit()
+
+            return poly.LC()**(n - a + 1) * A * B
+
+        elif term.is_Add:
+            factored = factor_terms(term, fraction=True)
+            if factored.is_Mul:
+                return self._eval_product(factored, (k, a, n))
+
+        elif term.is_Mul:
+            # Factor in part without the summation variable and part with
+            without_k, with_k = term.as_coeff_mul(k)
+
+            if len(with_k) >= 2:
+                # More than one term including k, so still a multiplication
+                exclude, include = [], []
+                for t in with_k:
+                    p = self._eval_product(t, (k, a, n))
+
+                    if p is not None:
+                        exclude.append(p)
+                    else:
+                        include.append(t)
+
+                if not exclude:
+                    return None
+                else:
+                    arg = term._new_rawargs(*include)
+                    A = Mul(*exclude)
+                    B = self.func(arg, (k, a, n)).doit()
+                    return without_k**(n - a + 1)*A * B
+            else:
+                # Just a single term
+                p = self._eval_product(with_k[0], (k, a, n))
+                if p is None:
+                    p = self.func(with_k[0], (k, a, n)).doit()
+                return without_k**(n - a + 1)*p
+
+
+        elif term.is_Pow:
+            if not term.base.has(k):
+                s = summation(term.exp, (k, a, n))
+
+                return term.base**s
+            elif not term.exp.has(k):
+                p = self._eval_product(term.base, (k, a, n))
+
+                if p is not None:
+                    return p**term.exp
+
+        elif isinstance(term, Product):
+            evaluated = term.doit()
+            f = self._eval_product(evaluated, limits)
+            if f is None:
+                return self.func(evaluated, limits)
+            else:
+                return f
+
+        if definite:
+            return self._eval_product_direct(term, limits)
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.simplify.simplify import product_simplify
+        rv = product_simplify(self, **kwargs)
+        return rv.doit() if kwargs['doit'] else rv
+
+    def _eval_transpose(self):
+        if self.is_commutative:
+            return self.func(self.function.transpose(), *self.limits)
+        return None
+
+    def _eval_product_direct(self, term, limits):
+        (k, a, n) = limits
+        return Mul(*[term.subs(k, a + i) for i in range(n - a + 1)])
+
+    def _eval_derivative(self, x):
+        if isinstance(x, Symbol) and x not in self.free_symbols:
+            return S.Zero
+        f, limits = self.function, list(self.limits)
+        limit = limits.pop(-1)
+        if limits:
+            f = self.func(f, *limits)
+        i, a, b = limit
+        if x in a.free_symbols or x in b.free_symbols:
+            return None
+        h = Dummy()
+        rv = Sum( Product(f, (i, a, h - 1)) * Product(f, (i, h + 1, b)) * Derivative(f, x, evaluate=True).subs(i, h), (h, a, b))
+        return rv
+
+    def is_convergent(self):
+        r"""
+        See docs of :obj:`.Sum.is_convergent()` for explanation of convergence
+        in SymPy.
+
+        Explanation
+        ===========
+
+        The infinite product:
+
+        .. math::
+
+            \prod_{1 \leq i < \infty} f(i)
+
+        is defined by the sequence of partial products:
+
+        .. math::
+
+            \prod_{i=1}^{n} f(i) = f(1) f(2) \cdots f(n)
+
+        as n increases without bound. The product converges to a non-zero
+        value if and only if the sum:
+
+        .. math::
+
+            \sum_{1 \leq i < \infty} \log{f(n)}
+
+        converges.
+
+        Examples
+        ========
+
+        >>> from sympy import Product, Symbol, cos, pi, exp, oo
+        >>> n = Symbol('n', integer=True)
+        >>> Product(n/(n + 1), (n, 1, oo)).is_convergent()
+        False
+        >>> Product(1/n**2, (n, 1, oo)).is_convergent()
+        False
+        >>> Product(cos(pi/n), (n, 1, oo)).is_convergent()
+        True
+        >>> Product(exp(-n**2), (n, 1, oo)).is_convergent()
+        False
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Infinite_product
+        """
+        sequence_term = self.function
+        log_sum = log(sequence_term)
+        lim = self.limits
+        try:
+            is_conv = Sum(log_sum, *lim).is_convergent()
+        except NotImplementedError:
+            if Sum(sequence_term - 1, *lim).is_absolutely_convergent() is S.true:
+                return S.true
+            raise NotImplementedError("The algorithm to find the product convergence of %s "
+                                        "is not yet implemented" % (sequence_term))
+        return is_conv
+
+    def reverse_order(expr, *indices):
+        """
+        Reverse the order of a limit in a Product.
+
+        Explanation
+        ===========
+
+        ``reverse_order(expr, *indices)`` reverses some limits in the expression
+        ``expr`` which can be either a ``Sum`` or a ``Product``. The selectors in
+        the argument ``indices`` specify some indices whose limits get reversed.
+        These selectors are either variable names or numerical indices counted
+        starting from the inner-most limit tuple.
+
+        Examples
+        ========
+
+        >>> from sympy import gamma, Product, simplify, Sum
+        >>> from sympy.abc import x, y, a, b, c, d
+        >>> P = Product(x, (x, a, b))
+        >>> Pr = P.reverse_order(x)
+        >>> Pr
+        Product(1/x, (x, b + 1, a - 1))
+        >>> Pr = Pr.doit()
+        >>> Pr
+        1/RisingFactorial(b + 1, a - b - 1)
+        >>> simplify(Pr.rewrite(gamma))
+        Piecewise((gamma(b + 1)/gamma(a), b > -1), ((-1)**(-a + b + 1)*gamma(1 - a)/gamma(-b), True))
+        >>> P = P.doit()
+        >>> P
+        RisingFactorial(a, -a + b + 1)
+        >>> simplify(P.rewrite(gamma))
+        Piecewise((gamma(b + 1)/gamma(a), a > 0), ((-1)**(-a + b + 1)*gamma(1 - a)/gamma(-b), True))
+
+        While one should prefer variable names when specifying which limits
+        to reverse, the index counting notation comes in handy in case there
+        are several symbols with the same name.
+
+        >>> S = Sum(x*y, (x, a, b), (y, c, d))
+        >>> S
+        Sum(x*y, (x, a, b), (y, c, d))
+        >>> S0 = S.reverse_order(0)
+        >>> S0
+        Sum(-x*y, (x, b + 1, a - 1), (y, c, d))
+        >>> S1 = S0.reverse_order(1)
+        >>> S1
+        Sum(x*y, (x, b + 1, a - 1), (y, d + 1, c - 1))
+
+        Of course we can mix both notations:
+
+        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1)
+        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
+        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x)
+        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
+
+        See Also
+        ========
+
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.index,
+        reorder_limit,
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.reorder
+
+        References
+        ==========
+
+        .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM,
+               Volume 28 Issue 2, April 1981, Pages 305-350
+               https://dl.acm.org/doi/10.1145/322248.322255
+
+        """
+        l_indices = list(indices)
+
+        for i, indx in enumerate(l_indices):
+            if not isinstance(indx, int):
+                l_indices[i] = expr.index(indx)
+
+        e = 1
+        limits = []
+        for i, limit in enumerate(expr.limits):
+            l = limit
+            if i in l_indices:
+                e = -e
+                l = (limit[0], limit[2] + 1, limit[1] - 1)
+            limits.append(l)
+
+        return Product(expr.function ** e, *limits)
+
+
+def product(*args, **kwargs):
+    r"""
+    Compute the product.
+
+    Explanation
+    ===========
+
+    The notation for symbols is similar to the notation used in Sum or
+    Integral. product(f, (i, a, b)) computes the product of f with
+    respect to i from a to b, i.e.,
+
+    ::
+
+                                     b
+                                   _____
+        product(f(n), (i, a, b)) = |   | f(n)
+                                   |   |
+                                   i = a
+
+    If it cannot compute the product, it returns an unevaluated Product object.
+    Repeated products can be computed by introducing additional symbols tuples::
+
+    Examples
+    ========
+
+    >>> from sympy import product, symbols
+    >>> i, n, m, k = symbols('i n m k', integer=True)
+
+    >>> product(i, (i, 1, k))
+    factorial(k)
+    >>> product(m, (i, 1, k))
+    m**k
+    >>> product(i, (i, 1, k), (k, 1, n))
+    Product(factorial(k), (k, 1, n))
+
+    """
+
+    prod = Product(*args, **kwargs)
+
+    if isinstance(prod, Product):
+        return prod.doit(deep=False)
+    else:
+        return prod
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/summations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/summations.py
new file mode 100644
index 0000000000000000000000000000000000000000..96bdbd69b7820798fade4bc5ec145172b95947ef
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/summations.py
@@ -0,0 +1,1659 @@
+from __future__ import annotations
+
+from sympy.calculus.singularities import is_decreasing
+from sympy.calculus.accumulationbounds import AccumulationBounds
+from .expr_with_intlimits import ExprWithIntLimits
+from .expr_with_limits import AddWithLimits
+from .gosper import gosper_sum
+from sympy.core.expr import Expr
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.function import Derivative, expand
+from sympy.core.mul import Mul
+from sympy.core.numbers import Float, _illegal
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.sorting import ordered
+from sympy.core.symbol import Dummy, Wild, Symbol, symbols
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.combinatorial.numbers import bernoulli, harmonic
+from sympy.functions.elementary.complexes import re
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import cot, csc
+from sympy.functions.special.hyper import hyper
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.functions.special.zeta_functions import zeta
+from sympy.integrals.integrals import Integral
+from sympy.logic.boolalg import And, Not
+from sympy.polys.partfrac import apart
+from sympy.polys.polyerrors import PolynomialError, PolificationFailed
+from sympy.polys.polytools import parallel_poly_from_expr, Poly, factor
+from sympy.polys.rationaltools import together
+from sympy.series.limitseq import limit_seq
+from sympy.series.order import O
+from sympy.series.residues import residue
+from sympy.sets.contains import Contains
+from sympy.sets.sets import FiniteSet, Interval
+from sympy.utilities.iterables import sift
+import itertools
+
+
+class Sum(AddWithLimits, ExprWithIntLimits):
+    r"""
+    Represents unevaluated summation.
+
+    Explanation
+    ===========
+
+    ``Sum`` represents a finite or infinite series, with the first argument
+    being the general form of terms in the series, and the second argument
+    being ``(dummy_variable, start, end)``, with ``dummy_variable`` taking
+    all integer values from ``start`` through ``end``. In accordance with
+    long-standing mathematical convention, the end term is included in the
+    summation.
+
+    Finite sums
+    ===========
+
+    For finite sums (and sums with symbolic limits assumed to be finite) we
+    follow the summation convention described by Karr [1], especially
+    definition 3 of section 1.4. The sum:
+
+    .. math::
+
+        \sum_{m \leq i < n} f(i)
+
+    has *the obvious meaning* for `m < n`, namely:
+
+    .. math::
+
+        \sum_{m \leq i < n} f(i) = f(m) + f(m+1) + \ldots + f(n-2) + f(n-1)
+
+    with the upper limit value `f(n)` excluded. The sum over an empty set is
+    zero if and only if `m = n`:
+
+    .. math::
+
+        \sum_{m \leq i < n} f(i) = 0  \quad \mathrm{for} \quad  m = n
+
+    Finally, for all other sums over empty sets we assume the following
+    definition:
+
+    .. math::
+
+        \sum_{m \leq i < n} f(i) = - \sum_{n \leq i < m} f(i)  \quad \mathrm{for} \quad  m > n
+
+    It is important to note that Karr defines all sums with the upper
+    limit being exclusive. This is in contrast to the usual mathematical notation,
+    but does not affect the summation convention. Indeed we have:
+
+    .. math::
+
+        \sum_{m \leq i < n} f(i) = \sum_{i = m}^{n - 1} f(i)
+
+    where the difference in notation is intentional to emphasize the meaning,
+    with limits typeset on the top being inclusive.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import i, k, m, n, x
+    >>> from sympy import Sum, factorial, oo, IndexedBase, Function
+    >>> Sum(k, (k, 1, m))
+    Sum(k, (k, 1, m))
+    >>> Sum(k, (k, 1, m)).doit()
+    m**2/2 + m/2
+    >>> Sum(k**2, (k, 1, m))
+    Sum(k**2, (k, 1, m))
+    >>> Sum(k**2, (k, 1, m)).doit()
+    m**3/3 + m**2/2 + m/6
+    >>> Sum(x**k, (k, 0, oo))
+    Sum(x**k, (k, 0, oo))
+    >>> Sum(x**k, (k, 0, oo)).doit()
+    Piecewise((1/(1 - x), Abs(x) < 1), (Sum(x**k, (k, 0, oo)), True))
+    >>> Sum(x**k/factorial(k), (k, 0, oo)).doit()
+    exp(x)
+
+    Here are examples to do summation with symbolic indices.  You
+    can use either Function of IndexedBase classes:
+
+    >>> f = Function('f')
+    >>> Sum(f(n), (n, 0, 3)).doit()
+    f(0) + f(1) + f(2) + f(3)
+    >>> Sum(f(n), (n, 0, oo)).doit()
+    Sum(f(n), (n, 0, oo))
+    >>> f = IndexedBase('f')
+    >>> Sum(f[n]**2, (n, 0, 3)).doit()
+    f[0]**2 + f[1]**2 + f[2]**2 + f[3]**2
+
+    An example showing that the symbolic result of a summation is still
+    valid for seemingly nonsensical values of the limits. Then the Karr
+    convention allows us to give a perfectly valid interpretation to
+    those sums by interchanging the limits according to the above rules:
+
+    >>> S = Sum(i, (i, 1, n)).doit()
+    >>> S
+    n**2/2 + n/2
+    >>> S.subs(n, -4)
+    6
+    >>> Sum(i, (i, 1, -4)).doit()
+    6
+    >>> Sum(-i, (i, -3, 0)).doit()
+    6
+
+    An explicit example of the Karr summation convention:
+
+    >>> S1 = Sum(i**2, (i, m, m+n-1)).doit()
+    >>> S1
+    m**2*n + m*n**2 - m*n + n**3/3 - n**2/2 + n/6
+    >>> S2 = Sum(i**2, (i, m+n, m-1)).doit()
+    >>> S2
+    -m**2*n - m*n**2 + m*n - n**3/3 + n**2/2 - n/6
+    >>> S1 + S2
+    0
+    >>> S3 = Sum(i, (i, m, m-1)).doit()
+    >>> S3
+    0
+
+    See Also
+    ========
+
+    summation
+    Product, sympy.concrete.products.product
+
+    References
+    ==========
+
+    .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM,
+           Volume 28 Issue 2, April 1981, Pages 305-350
+           https://dl.acm.org/doi/10.1145/322248.322255
+    .. [2] https://en.wikipedia.org/wiki/Summation#Capital-sigma_notation
+    .. [3] https://en.wikipedia.org/wiki/Empty_sum
+    """
+
+    __slots__ = ()
+
+    limits: tuple[tuple[Symbol, Expr, Expr]]
+
+    def __new__(cls, function, *symbols, **assumptions):
+        obj = AddWithLimits.__new__(cls, function, *symbols, **assumptions)
+        if not hasattr(obj, 'limits'):
+            return obj
+        if any(len(l) != 3 or None in l for l in obj.limits):
+            raise ValueError('Sum requires values for lower and upper bounds.')
+
+        return obj
+
+    def _eval_is_zero(self):
+        # a Sum is only zero if its function is zero or if all terms
+        # cancel out. This only answers whether the summand is zero; if
+        # not then None is returned since we don't analyze whether all
+        # terms cancel out.
+        if self.function.is_zero or self.has_empty_sequence:
+            return True
+
+    def _eval_is_extended_real(self):
+        if self.has_empty_sequence:
+            return True
+        return self.function.is_extended_real
+
+    def _eval_is_positive(self):
+        if self.has_finite_limits and self.has_reversed_limits is False:
+            return self.function.is_positive
+
+    def _eval_is_negative(self):
+        if self.has_finite_limits and self.has_reversed_limits is False:
+            return self.function.is_negative
+
+    def _eval_is_finite(self):
+        if self.has_finite_limits and self.function.is_finite:
+            return True
+
+    def doit(self, **hints):
+        if hints.get('deep', True):
+            f = self.function.doit(**hints)
+        else:
+            f = self.function
+
+        # first make sure any definite limits have summation
+        # variables with matching assumptions
+        reps = {}
+        for xab in self.limits:
+            d = _dummy_with_inherited_properties_concrete(xab)
+            if d:
+                reps[xab[0]] = d
+        if reps:
+            undo = {v: k for k, v in reps.items()}
+            did = self.xreplace(reps).doit(**hints)
+            if isinstance(did, tuple):  # when separate=True
+                did = tuple([i.xreplace(undo) for i in did])
+            elif did is not None:
+                did = did.xreplace(undo)
+            else:
+                did = self
+            return did
+
+
+        if self.function.is_Matrix:
+            expanded = self.expand()
+            if self != expanded:
+                return expanded.doit()
+            return _eval_matrix_sum(self)
+
+        for n, limit in enumerate(self.limits):
+            i, a, b = limit
+            dif = b - a
+            if dif == -1:
+                # Any summation over an empty set is zero
+                return S.Zero
+            if dif.is_integer and dif.is_negative:
+                a, b = b + 1, a - 1
+                f = -f
+
+            newf = eval_sum(f, (i, a, b))
+            if newf is None:
+                if f == self.function:
+                    zeta_function = self.eval_zeta_function(f, (i, a, b))
+                    if zeta_function is not None:
+                        return zeta_function
+                    return self
+                else:
+                    return self.func(f, *self.limits[n:])
+            f = newf
+
+        if hints.get('deep', True):
+            # eval_sum could return partially unevaluated
+            # result with Piecewise.  In this case we won't
+            # doit() recursively.
+            if not isinstance(f, Piecewise):
+                return f.doit(**hints)
+
+        return f
+
+    def eval_zeta_function(self, f, limits):
+        """
+        Check whether the function matches with the zeta function.
+
+        If it matches, then return a `Piecewise` expression because
+        zeta function does not converge unless `s > 1` and `q > 0`
+        """
+        i, a, b = limits
+        if a.is_comparable and b.is_comparable and a > b:
+            return self.eval_zeta_function(f, (i, b + S.One, a - S.One))
+        if b is not S.Infinity:
+            return
+        w, y, z = Wild('w', exclude=[i]), Wild('y', exclude=[i]), Wild('z', exclude=[i])
+        if result := f.match((w * i + y) ** (-z)):
+            coeff = 1 / result[w] ** result[z]
+            s = result[z]
+            q = result[y] / result[w] + a
+            return Piecewise((coeff * zeta(s, q),
+                              And(Not(Contains(-q, S.Naturals0)), re(s) > S.One)),
+                             (self, True))
+
+    def _eval_derivative(self, x):
+        """
+        Differentiate wrt x as long as x is not in the free symbols of any of
+        the upper or lower limits.
+
+        Explanation
+        ===========
+
+        Sum(a*b*x, (x, 1, a)) can be differentiated wrt x or b but not `a`
+        since the value of the sum is discontinuous in `a`. In a case
+        involving a limit variable, the unevaluated derivative is returned.
+        """
+
+        # diff already confirmed that x is in the free symbols of self, but we
+        # don't want to differentiate wrt any free symbol in the upper or lower
+        # limits
+        # XXX remove this test for free_symbols when the default _eval_derivative is in
+        if isinstance(x, Symbol) and x not in self.free_symbols:
+            return S.Zero
+
+        # get limits and the function
+        f, limits = self.function, list(self.limits)
+
+        limit = limits.pop(-1)
+
+        if limits:  # f is the argument to a Sum
+            f = self.func(f, *limits)
+
+        _, a, b = limit
+        if x in a.free_symbols or x in b.free_symbols:
+            return None
+        df = Derivative(f, x, evaluate=True)
+        rv = self.func(df, limit)
+        return rv
+
+    def _eval_difference_delta(self, n, step):
+        k, _, upper = self.args[-1]
+        new_upper = upper.subs(n, n + step)
+
+        if len(self.args) == 2:
+            f = self.args[0]
+        else:
+            f = self.func(*self.args[:-1])
+
+        return Sum(f, (k, upper + 1, new_upper)).doit()
+
+    def _eval_simplify(self, **kwargs):
+
+        function = self.function
+
+        if kwargs.get('deep', True):
+            function = function.simplify(**kwargs)
+
+        # split the function into adds
+        terms = Add.make_args(expand(function))
+        s_t = [] # Sum Terms
+        o_t = [] # Other Terms
+
+        for term in terms:
+            if term.has(Sum):
+                # if there is an embedded sum here
+                # it is of the form x * (Sum(whatever))
+                # hence we make a Mul out of it, and simplify all interior sum terms
+                subterms = Mul.make_args(expand(term))
+                out_terms = []
+                for subterm in subterms:
+                    # go through each term
+                    if isinstance(subterm, Sum):
+                        # if it's a sum, simplify it
+                        out_terms.append(subterm._eval_simplify(**kwargs))
+                    else:
+                        # otherwise, add it as is
+                        out_terms.append(subterm)
+
+                # turn it back into a Mul
+                s_t.append(Mul(*out_terms))
+            else:
+                o_t.append(term)
+
+        # next try to combine any interior sums for further simplification
+        from sympy.simplify.simplify import factor_sum, sum_combine
+        result = Add(sum_combine(s_t), *o_t)
+
+        return factor_sum(result, limits=self.limits)
+
+    def is_convergent(self):
+        r"""
+        Checks for the convergence of a Sum.
+
+        Explanation
+        ===========
+
+        We divide the study of convergence of infinite sums and products in
+        two parts.
+
+        First Part:
+        One part is the question whether all the terms are well defined, i.e.,
+        they are finite in a sum and also non-zero in a product. Zero
+        is the analogy of (minus) infinity in products as
+        :math:`e^{-\infty} = 0`.
+
+        Second Part:
+        The second part is the question of convergence after infinities,
+        and zeros in products, have been omitted assuming that their number
+        is finite. This means that we only consider the tail of the sum or
+        product, starting from some point after which all terms are well
+        defined.
+
+        For example, in a sum of the form:
+
+        .. math::
+
+            \sum_{1 \leq i < \infty} \frac{1}{n^2 + an + b}
+
+        where a and b are numbers. The routine will return true, even if there
+        are infinities in the term sequence (at most two). An analogous
+        product would be:
+
+        .. math::
+
+            \prod_{1 \leq i < \infty} e^{\frac{1}{n^2 + an + b}}
+
+        This is how convergence is interpreted. It is concerned with what
+        happens at the limit. Finding the bad terms is another independent
+        matter.
+
+        Note: It is responsibility of user to see that the sum or product
+        is well defined.
+
+        There are various tests employed to check the convergence like
+        divergence test, root test, integral test, alternating series test,
+        comparison tests, Dirichlet tests. It returns true if Sum is convergent
+        and false if divergent and NotImplementedError if it cannot be checked.
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Convergence_tests
+
+        Examples
+        ========
+
+        >>> from sympy import factorial, S, Sum, Symbol, oo
+        >>> n = Symbol('n', integer=True)
+        >>> Sum(n/(n - 1), (n, 4, 7)).is_convergent()
+        True
+        >>> Sum(n/(2*n + 1), (n, 1, oo)).is_convergent()
+        False
+        >>> Sum(factorial(n)/5**n, (n, 1, oo)).is_convergent()
+        False
+        >>> Sum(1/n**(S(6)/5), (n, 1, oo)).is_convergent()
+        True
+
+        See Also
+        ========
+
+        Sum.is_absolutely_convergent
+        sympy.concrete.products.Product.is_convergent
+        """
+        p, q, r = symbols('p q r', cls=Wild)
+
+        sym = self.limits[0][0]
+        lower_limit = self.limits[0][1]
+        upper_limit = self.limits[0][2]
+        sequence_term = self.function.simplify()
+
+        if len(sequence_term.free_symbols) > 1:
+            raise NotImplementedError("convergence checking for more than one symbol "
+                                      "containing series is not handled")
+
+        if lower_limit.is_finite and upper_limit.is_finite:
+            return S.true
+
+        # transform sym -> -sym and swap the upper_limit = S.Infinity
+        # and lower_limit = - upper_limit
+        if lower_limit is S.NegativeInfinity:
+            if upper_limit is S.Infinity:
+                return Sum(sequence_term, (sym, 0, S.Infinity)).is_convergent() and \
+                        Sum(sequence_term, (sym, S.NegativeInfinity, 0)).is_convergent()
+            from sympy.simplify.simplify import simplify
+            sequence_term = simplify(sequence_term.xreplace({sym: -sym}))
+            lower_limit = -upper_limit
+            upper_limit = S.Infinity
+
+        sym_ = Dummy(sym.name, integer=True, positive=True)
+        sequence_term = sequence_term.xreplace({sym: sym_})
+        sym = sym_
+
+        interval = Interval(lower_limit, upper_limit)
+
+        # Piecewise function handle
+        if sequence_term.is_Piecewise:
+            for func, cond in sequence_term.args:
+                # see if it represents something going to oo
+                if cond == True or cond.as_set().sup is S.Infinity:
+                    s = Sum(func, (sym, lower_limit, upper_limit))
+                    return s.is_convergent()
+            return S.true
+
+        ###  -------- Divergence test ----------- ###
+        try:
+            lim_val = limit_seq(sequence_term, sym)
+            if lim_val is not None and lim_val.is_zero is False:
+                return S.false
+        except NotImplementedError:
+            pass
+
+        try:
+            lim_val_abs = limit_seq(abs(sequence_term), sym)
+            if lim_val_abs is not None and lim_val_abs.is_zero is False:
+                return S.false
+        except NotImplementedError:
+            pass
+
+        order = O(sequence_term, (sym, S.Infinity))
+
+        ### --------- p-series test (1/n**p) ---------- ###
+        p_series_test = order.expr.match(sym**p)
+        if p_series_test is not None:
+            if p_series_test[p] < -1:
+                return S.true
+            if p_series_test[p] >= -1:
+                return S.false
+
+        ### ------------- comparison test ------------- ###
+        # 1/(n**p*log(n)**q*log(log(n))**r) comparison
+        n_log_test = (order.expr.match(1/(sym**p*log(1/sym)**q*log(-log(1/sym))**r)) or
+                      order.expr.match(1/(sym**p*(-log(1/sym))**q*log(-log(1/sym))**r)))
+        if n_log_test is not None:
+            if (n_log_test[p] > 1 or
+                (n_log_test[p] == 1 and n_log_test[q] > 1) or
+                (n_log_test[p] == n_log_test[q] == 1 and n_log_test[r] > 1)):
+                    return S.true
+            return S.false
+
+        ### ------------- Limit comparison test -----------###
+        # (1/n) comparison
+        try:
+            lim_comp = limit_seq(sym*sequence_term, sym)
+            if lim_comp is not None and lim_comp.is_number and lim_comp > 0:
+                return S.false
+        except NotImplementedError:
+            pass
+
+        ### ----------- ratio test ---------------- ###
+        next_sequence_term = sequence_term.xreplace({sym: sym + 1})
+        from sympy.simplify.combsimp import combsimp
+        from sympy.simplify.powsimp import powsimp
+        ratio = combsimp(powsimp(next_sequence_term/sequence_term))
+        try:
+            lim_ratio = limit_seq(ratio, sym)
+            if lim_ratio is not None and lim_ratio.is_number and lim_ratio is not S.NaN:
+                if abs(lim_ratio) > 1:
+                    return S.false
+                if abs(lim_ratio) < 1:
+                    return S.true
+        except NotImplementedError:
+            lim_ratio = None
+
+        ### ---------- Raabe's test -------------- ###
+        if lim_ratio == 1:  # ratio test inconclusive
+            test_val = sym*(sequence_term/
+                         sequence_term.subs(sym, sym + 1) - 1)
+            test_val = test_val.gammasimp()
+            try:
+                lim_val = limit_seq(test_val, sym)
+                if lim_val is not None and lim_val.is_number:
+                    if lim_val > 1:
+                        return S.true
+                    if lim_val < 1:
+                        return S.false
+            except NotImplementedError:
+                pass
+
+        ### ----------- root test ---------------- ###
+        # lim = Limit(abs(sequence_term)**(1/sym), sym, S.Infinity)
+        try:
+            lim_evaluated = limit_seq(abs(sequence_term)**(1/sym), sym)
+            if lim_evaluated is not None and lim_evaluated.is_number:
+                if lim_evaluated < 1:
+                    return S.true
+                if lim_evaluated > 1:
+                    return S.false
+        except NotImplementedError:
+            pass
+
+        ### ------------- alternating series test ----------- ###
+        dict_val = sequence_term.match(S.NegativeOne**(sym + p)*q)
+        if not dict_val[p].has(sym) and is_decreasing(dict_val[q], interval):
+            return S.true
+
+        ### ------------- integral test -------------- ###
+        check_interval = None
+        from sympy.solvers.solveset import solveset
+        maxima = solveset(sequence_term.diff(sym), sym, interval)
+        if not maxima:
+            check_interval = interval
+        elif isinstance(maxima, FiniteSet) and maxima.sup.is_number:
+            check_interval = Interval(maxima.sup, interval.sup)
+        if (check_interval is not None and
+            (is_decreasing(sequence_term, check_interval) or
+            is_decreasing(-sequence_term, check_interval))):
+                integral_val = Integral(
+                    sequence_term, (sym, lower_limit, upper_limit))
+                try:
+                    integral_val_evaluated = integral_val.doit()
+                    if integral_val_evaluated.is_number:
+                        return S(integral_val_evaluated.is_finite)
+                except NotImplementedError:
+                    pass
+
+        ### ----- Dirichlet and bounded times convergent tests ----- ###
+        # TODO
+        #
+        # Dirichlet_test
+        # https://en.wikipedia.org/wiki/Dirichlet%27s_test
+        #
+        # Bounded times convergent test
+        # It is based on comparison theorems for series.
+        # In particular, if the general term of a series can
+        # be written as a product of two terms a_n and b_n
+        # and if a_n is bounded and if Sum(b_n) is absolutely
+        # convergent, then the original series Sum(a_n * b_n)
+        # is absolutely convergent and so convergent.
+        #
+        # The following code can grows like 2**n where n is the
+        # number of args in order.expr
+        # Possibly combined with the potentially slow checks
+        # inside the loop, could make this test extremely slow
+        # for larger summation expressions.
+
+        if order.expr.is_Mul:
+            args = order.expr.args
+            argset = set(args)
+
+            ### -------------- Dirichlet tests -------------- ###
+            m = Dummy('m', integer=True)
+            def _dirichlet_test(g_n):
+                try:
+                    ing_val = limit_seq(Sum(g_n, (sym, interval.inf, m)).doit(), m)
+                    if ing_val is not None and ing_val.is_finite:
+                        return S.true
+                except NotImplementedError:
+                    pass
+
+            ### -------- bounded times convergent test ---------###
+            def _bounded_convergent_test(g1_n, g2_n):
+                try:
+                    lim_val = limit_seq(g1_n, sym)
+                    if lim_val is not None and (lim_val.is_finite or (
+                        isinstance(lim_val, AccumulationBounds)
+                        and (lim_val.max - lim_val.min).is_finite)):
+                            if Sum(g2_n, (sym, lower_limit, upper_limit)).is_absolutely_convergent():
+                                return S.true
+                except NotImplementedError:
+                    pass
+
+            for n in range(1, len(argset)):
+                for a_tuple in itertools.combinations(args, n):
+                    b_set = argset - set(a_tuple)
+                    a_n = Mul(*a_tuple)
+                    b_n = Mul(*b_set)
+
+                    if is_decreasing(a_n, interval):
+                        dirich = _dirichlet_test(b_n)
+                        if dirich is not None:
+                            return dirich
+
+                    bc_test = _bounded_convergent_test(a_n, b_n)
+                    if bc_test is not None:
+                        return bc_test
+
+        _sym = self.limits[0][0]
+        sequence_term = sequence_term.xreplace({sym: _sym})
+        raise NotImplementedError("The algorithm to find the Sum convergence of %s "
+                                  "is not yet implemented" % (sequence_term))
+
+    def is_absolutely_convergent(self):
+        """
+        Checks for the absolute convergence of an infinite series.
+
+        Same as checking convergence of absolute value of sequence_term of
+        an infinite series.
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Absolute_convergence
+
+        Examples
+        ========
+
+        >>> from sympy import Sum, Symbol, oo
+        >>> n = Symbol('n', integer=True)
+        >>> Sum((-1)**n, (n, 1, oo)).is_absolutely_convergent()
+        False
+        >>> Sum((-1)**n/n**2, (n, 1, oo)).is_absolutely_convergent()
+        True
+
+        See Also
+        ========
+
+        Sum.is_convergent
+        """
+        return Sum(abs(self.function), self.limits).is_convergent()
+
+    def euler_maclaurin(self, m=0, n=0, eps=0, eval_integral=True):
+        """
+        Return an Euler-Maclaurin approximation of self, where m is the
+        number of leading terms to sum directly and n is the number of
+        terms in the tail.
+
+        With m = n = 0, this is simply the corresponding integral
+        plus a first-order endpoint correction.
+
+        Returns (s, e) where s is the Euler-Maclaurin approximation
+        and e is the estimated error (taken to be the magnitude of
+        the first omitted term in the tail):
+
+            >>> from sympy.abc import k, a, b
+            >>> from sympy import Sum
+            >>> Sum(1/k, (k, 2, 5)).doit().evalf()
+            1.28333333333333
+            >>> s, e = Sum(1/k, (k, 2, 5)).euler_maclaurin()
+            >>> s
+            -log(2) + 7/20 + log(5)
+            >>> from sympy import sstr
+            >>> print(sstr((s.evalf(), e.evalf()), full_prec=True))
+            (1.26629073187415, 0.0175000000000000)
+
+        The endpoints may be symbolic:
+
+            >>> s, e = Sum(1/k, (k, a, b)).euler_maclaurin()
+            >>> s
+            -log(a) + log(b) + 1/(2*b) + 1/(2*a)
+            >>> e
+            Abs(1/(12*b**2) - 1/(12*a**2))
+
+        If the function is a polynomial of degree at most 2n+1, the
+        Euler-Maclaurin formula becomes exact (and e = 0 is returned):
+
+            >>> Sum(k, (k, 2, b)).euler_maclaurin()
+            (b**2/2 + b/2 - 1, 0)
+            >>> Sum(k, (k, 2, b)).doit()
+            b**2/2 + b/2 - 1
+
+        With a nonzero eps specified, the summation is ended
+        as soon as the remainder term is less than the epsilon.
+        """
+        m = int(m)
+        n = int(n)
+        f = self.function
+        if len(self.limits) != 1:
+            raise ValueError("More than 1 limit")
+        i, a, b = self.limits[0]
+        if (a > b) == True:
+            if a - b == 1:
+                return S.Zero, S.Zero
+            a, b = b + 1, a - 1
+            f = -f
+        s = S.Zero
+        if m:
+            if b.is_Integer and a.is_Integer:
+                m = min(m, b - a + 1)
+            if not eps or f.is_polynomial(i):
+                s = Add(*[f.subs(i, a + k) for k in range(m)])
+            else:
+                term = f.subs(i, a)
+                if term:
+                    test = abs(term.evalf(3)) < eps
+                    if test == True:
+                        return s, abs(term)
+                    elif not (test == False):
+                        # a symbolic Relational class, can't go further
+                        return term, S.Zero
+                s = term
+                for k in range(1, m):
+                    term = f.subs(i, a + k)
+                    if abs(term.evalf(3)) < eps and term != 0:
+                        return s, abs(term)
+                    s += term
+            if b - a + 1 == m:
+                return s, S.Zero
+            a += m
+        x = Dummy('x')
+        I = Integral(f.subs(i, x), (x, a, b))
+        if eval_integral:
+            I = I.doit()
+        s += I
+
+        def fpoint(expr):
+            if b is S.Infinity:
+                return expr.subs(i, a), 0
+            return expr.subs(i, a), expr.subs(i, b)
+        fa, fb = fpoint(f)
+        iterm = (fa + fb)/2
+        g = f.diff(i)
+        for k in range(1, n + 2):
+            ga, gb = fpoint(g)
+            term = bernoulli(2*k)/factorial(2*k)*(gb - ga)
+            if k > n:
+                break
+            if eps and term:
+                term_evalf = term.evalf(3)
+                if term_evalf is S.NaN:
+                    return S.NaN, S.NaN
+                if abs(term_evalf) < eps:
+                    break
+            s += term
+            g = g.diff(i, 2, simplify=False)
+        return s + iterm, abs(term)
+
+
+    def reverse_order(self, *indices):
+        """
+        Reverse the order of a limit in a Sum.
+
+        Explanation
+        ===========
+
+        ``reverse_order(self, *indices)`` reverses some limits in the expression
+        ``self`` which can be either a ``Sum`` or a ``Product``. The selectors in
+        the argument ``indices`` specify some indices whose limits get reversed.
+        These selectors are either variable names or numerical indices counted
+        starting from the inner-most limit tuple.
+
+        Examples
+        ========
+
+        >>> from sympy import Sum
+        >>> from sympy.abc import x, y, a, b, c, d
+
+        >>> Sum(x, (x, 0, 3)).reverse_order(x)
+        Sum(-x, (x, 4, -1))
+        >>> Sum(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(x, y)
+        Sum(x*y, (x, 6, 0), (y, 7, -1))
+        >>> Sum(x, (x, a, b)).reverse_order(x)
+        Sum(-x, (x, b + 1, a - 1))
+        >>> Sum(x, (x, a, b)).reverse_order(0)
+        Sum(-x, (x, b + 1, a - 1))
+
+        While one should prefer variable names when specifying which limits
+        to reverse, the index counting notation comes in handy in case there
+        are several symbols with the same name.
+
+        >>> S = Sum(x**2, (x, a, b), (x, c, d))
+        >>> S
+        Sum(x**2, (x, a, b), (x, c, d))
+        >>> S0 = S.reverse_order(0)
+        >>> S0
+        Sum(-x**2, (x, b + 1, a - 1), (x, c, d))
+        >>> S1 = S0.reverse_order(1)
+        >>> S1
+        Sum(x**2, (x, b + 1, a - 1), (x, d + 1, c - 1))
+
+        Of course we can mix both notations:
+
+        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1)
+        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
+        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x)
+        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
+
+        See Also
+        ========
+
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.index, reorder_limit,
+        sympy.concrete.expr_with_intlimits.ExprWithIntLimits.reorder
+
+        References
+        ==========
+
+        .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM,
+               Volume 28 Issue 2, April 1981, Pages 305-350
+               https://dl.acm.org/doi/10.1145/322248.322255
+        """
+        l_indices = list(indices)
+
+        for i, indx in enumerate(l_indices):
+            if not isinstance(indx, int):
+                l_indices[i] = self.index(indx)
+
+        e = 1
+        limits = []
+        for i, limit in enumerate(self.limits):
+            l = limit
+            if i in l_indices:
+                e = -e
+                l = (limit[0], limit[2] + 1, limit[1] - 1)
+            limits.append(l)
+
+        return Sum(e * self.function, *limits)
+
+    def _eval_rewrite_as_Product(self, *args, **kwargs):
+        from sympy.concrete.products import Product
+        if self.function.is_extended_real:
+            return log(Product(exp(self.function), *self.limits))
+
+
+def summation(f, *symbols, **kwargs):
+    r"""
+    Compute the summation of f with respect to symbols.
+
+    Explanation
+    ===========
+
+    The notation for symbols is similar to the notation used in Integral.
+    summation(f, (i, a, b)) computes the sum of f with respect to i from a to b,
+    i.e.,
+
+    ::
+
+                                    b
+                                  ____
+                                  \   `
+        summation(f, (i, a, b)) =  )    f
+                                  /___,
+                                  i = a
+
+    If it cannot compute the sum, it returns an unevaluated Sum object.
+    Repeated sums can be computed by introducing additional symbols tuples::
+
+    Examples
+    ========
+
+    >>> from sympy import summation, oo, symbols, log
+    >>> i, n, m = symbols('i n m', integer=True)
+
+    >>> summation(2*i - 1, (i, 1, n))
+    n**2
+    >>> summation(1/2**i, (i, 0, oo))
+    2
+    >>> summation(1/log(n)**n, (n, 2, oo))
+    Sum(log(n)**(-n), (n, 2, oo))
+    >>> summation(i, (i, 0, n), (n, 0, m))
+    m**3/6 + m**2/2 + m/3
+
+    >>> from sympy.abc import x
+    >>> from sympy import factorial
+    >>> summation(x**n/factorial(n), (n, 0, oo))
+    exp(x)
+
+    See Also
+    ========
+
+    Sum
+    Product, sympy.concrete.products.product
+
+    """
+    return Sum(f, *symbols, **kwargs).doit(deep=False)
+
+
+def telescopic_direct(L, R, n, limits):
+    """
+    Returns the direct summation of the terms of a telescopic sum
+
+    Explanation
+    ===========
+
+    L is the term with lower index
+    R is the term with higher index
+    n difference between the indexes of L and R
+
+    Examples
+    ========
+
+    >>> from sympy.concrete.summations import telescopic_direct
+    >>> from sympy.abc import k, a, b
+    >>> telescopic_direct(1/k, -1/(k+2), 2, (k, a, b))
+    -1/(b + 2) - 1/(b + 1) + 1/(a + 1) + 1/a
+
+    """
+    (i, a, b) = limits
+    return Add(*[L.subs(i, a + m) + R.subs(i, b - m) for m in range(n)])
+
+
+def telescopic(L, R, limits):
+    '''
+    Tries to perform the summation using the telescopic property.
+
+    Return None if not possible.
+    '''
+    (i, a, b) = limits
+    if L.is_Add or R.is_Add:
+        return None
+
+    # We want to solve(L.subs(i, i + m) + R, m)
+    # First we try a simple match since this does things that
+    # solve doesn't do, e.g. solve(cos(k+m)-cos(k), m) gives
+    # a more complicated solution than m == 0.
+
+    k = Wild("k")
+    sol = (-R).match(L.subs(i, i + k))
+    s = None
+    if sol and k in sol:
+        s = sol[k]
+        if not (s.is_Integer and L.subs(i, i + s) + R == 0):
+            # invalid match or match didn't work
+            s = None
+
+    # But there are things that match doesn't do that solve
+    # can do, e.g. determine that 1/(x + m) = 1/(1 - x) when m = 1
+
+    if s is None:
+        m = Dummy('m')
+        try:
+            from sympy.solvers.solvers import solve
+            sol = solve(L.subs(i, i + m) + R, m) or []
+        except NotImplementedError:
+            return None
+        sol = [si for si in sol if si.is_Integer and
+               (L.subs(i, i + si) + R).expand().is_zero]
+        if len(sol) != 1:
+            return None
+        s = sol[0]
+
+    if s < 0:
+        return telescopic_direct(R, L, abs(s), (i, a, b))
+    elif s > 0:
+        return telescopic_direct(L, R, s, (i, a, b))
+
+
+def eval_sum(f, limits):
+    (i, a, b) = limits
+    if f.is_zero:
+        return S.Zero
+    if i not in f.free_symbols:
+        return f*(b - a + 1)
+    if a == b:
+        return f.subs(i, a)
+    if a.is_comparable and b.is_comparable and a > b:
+        return eval_sum(f, (i, b + S.One, a - S.One))
+    if isinstance(f, Piecewise):
+        if not any(i in arg.args[1].free_symbols for arg in f.args):
+            # Piecewise conditions do not depend on the dummy summation variable,
+            # therefore we can fold:     Sum(Piecewise((e, c), ...), limits)
+            #                        --> Piecewise((Sum(e, limits), c), ...)
+            newargs = []
+            for arg in f.args:
+                newexpr = eval_sum(arg.expr, limits)
+                if newexpr is None:
+                    return None
+                newargs.append((newexpr, arg.cond))
+            return f.func(*newargs)
+
+    if f.has(KroneckerDelta):
+        from .delta import deltasummation, _has_simple_delta
+        f = f.replace(
+            lambda x: isinstance(x, Sum),
+            lambda x: x.factor()
+        )
+        if _has_simple_delta(f, limits[0]):
+            return deltasummation(f, limits)
+
+    dif = b - a
+    definite = dif.is_Integer
+    # Doing it directly may be faster if there are very few terms.
+    if definite and (dif < 100):
+        return eval_sum_direct(f, (i, a, b))
+    if isinstance(f, Piecewise):
+        return None
+    # Try to do it symbolically. Even when the number of terms is
+    # known, this can save time when b-a is big.
+    value = eval_sum_symbolic(f.expand(), (i, a, b))
+    if value is not None:
+        return value
+    # Do it directly
+    if definite:
+        return eval_sum_direct(f, (i, a, b))
+
+
+def eval_sum_direct(expr, limits):
+    """
+    Evaluate expression directly, but perform some simple checks first
+    to possibly result in a smaller expression and faster execution.
+    """
+    (i, a, b) = limits
+
+    dif = b - a
+    # Linearity
+    if expr.is_Mul:
+        # Try factor out everything not including i
+        without_i, with_i = expr.as_independent(i)
+        if without_i != 1:
+            s = eval_sum_direct(with_i, (i, a, b))
+            if s:
+                r = without_i*s
+                if r is not S.NaN:
+                    return r
+        else:
+            # Try term by term
+            L, R = expr.as_two_terms()
+
+            if not L.has(i):
+                sR = eval_sum_direct(R, (i, a, b))
+                if sR:
+                    return L*sR
+
+            if not R.has(i):
+                sL = eval_sum_direct(L, (i, a, b))
+                if sL:
+                    return sL*R
+
+    # do this whether its an Add or Mul
+    # e.g. apart(1/(25*i**2 + 45*i + 14)) and
+    # apart(1/((5*i + 2)*(5*i + 7))) ->
+    # -1/(5*(5*i + 7)) + 1/(5*(5*i + 2))
+    try:
+        expr = apart(expr, i)  # see if it becomes an Add
+    except PolynomialError:
+        pass
+
+    if expr.is_Add:
+        # Try factor out everything not including i
+        without_i, with_i = expr.as_independent(i)
+        if without_i != 0:
+            s = eval_sum_direct(with_i, (i, a, b))
+            if s:
+                r = without_i*(dif + 1) + s
+                if r is not S.NaN:
+                    return r
+        else:
+            # Try term by term
+            L, R = expr.as_two_terms()
+            lsum = eval_sum_direct(L, (i, a, b))
+            rsum = eval_sum_direct(R, (i, a, b))
+
+            if None not in (lsum, rsum):
+                r = lsum + rsum
+                if r is not S.NaN:
+                    return r
+
+    return Add(*[expr.subs(i, a + j) for j in range(dif + 1)])
+
+
+def eval_sum_symbolic(f, limits):
+    f_orig = f
+    (i, a, b) = limits
+    if not f.has(i):
+        return f*(b - a + 1)
+
+    # Linearity
+    if f.is_Mul:
+        # Try factor out everything not including i
+        without_i, with_i = f.as_independent(i)
+        if without_i != 1:
+            s = eval_sum_symbolic(with_i, (i, a, b))
+            if s:
+                r = without_i*s
+                if r is not S.NaN:
+                    return r
+        else:
+            # Try term by term
+            L, R = f.as_two_terms()
+
+            if not L.has(i):
+                sR = eval_sum_symbolic(R, (i, a, b))
+                if sR:
+                    return L*sR
+
+            if not R.has(i):
+                sL = eval_sum_symbolic(L, (i, a, b))
+                if sL:
+                    return sL*R
+
+    # do this whether its an Add or Mul
+    # e.g. apart(1/(25*i**2 + 45*i + 14)) and
+    # apart(1/((5*i + 2)*(5*i + 7))) ->
+    # -1/(5*(5*i + 7)) + 1/(5*(5*i + 2))
+    try:
+        f = apart(f, i)
+    except PolynomialError:
+        pass
+
+    if f.is_Add:
+        L, R = f.as_two_terms()
+        lrsum = telescopic(L, R, (i, a, b))
+
+        if lrsum:
+            return lrsum
+
+        # Try factor out everything not including i
+        without_i, with_i = f.as_independent(i)
+        if without_i != 0:
+            s = eval_sum_symbolic(with_i, (i, a, b))
+            if s:
+                r = without_i*(b - a + 1) + s
+                if r is not S.NaN:
+                    return r
+        else:
+            # Try term by term
+            lsum = eval_sum_symbolic(L, (i, a, b))
+            rsum = eval_sum_symbolic(R, (i, a, b))
+
+            if None not in (lsum, rsum):
+                r = lsum + rsum
+                if r is not S.NaN:
+                    return r
+
+
+    # Polynomial terms with Faulhaber's formula
+    n = Wild('n')
+    result = f.match(i**n)
+
+    if result is not None:
+        n = result[n]
+
+        if n.is_Integer:
+            if n >= 0:
+                if (b is S.Infinity and a is not S.NegativeInfinity) or \
+                   (a is S.NegativeInfinity and b is not S.Infinity):
+                    return S.Infinity
+                return ((bernoulli(n + 1, b + 1) - bernoulli(n + 1, a))/(n + 1)).expand()
+            elif a.is_Integer and a >= 1:
+                if n == -1:
+                    return harmonic(b) - harmonic(a - 1)
+                else:
+                    return harmonic(b, abs(n)) - harmonic(a - 1, abs(n))
+
+    if not (a.has(S.Infinity, S.NegativeInfinity) or
+            b.has(S.Infinity, S.NegativeInfinity)):
+        # Geometric terms
+        c1 = Wild('c1', exclude=[i])
+        c2 = Wild('c2', exclude=[i])
+        c3 = Wild('c3', exclude=[i])
+        wexp = Wild('wexp')
+
+        # Here we first attempt powsimp on f for easier matching with the
+        # exponential pattern, and attempt expansion on the exponent for easier
+        # matching with the linear pattern.
+        e = f.powsimp().match(c1 ** wexp)
+        if e is not None:
+            e_exp = e.pop(wexp).expand().match(c2*i + c3)
+            if e_exp is not None:
+                e.update(e_exp)
+
+                p = (c1**c3).subs(e)
+                q = (c1**c2).subs(e)
+                r = p*(q**a - q**(b + 1))/(1 - q)
+                l = p*(b - a + 1)
+                return Piecewise((l, Eq(q, S.One)), (r, True))
+
+        r = gosper_sum(f, (i, a, b))
+
+        if isinstance(r, (Mul,Add)):
+            from sympy.simplify.radsimp import denom
+            from sympy.solvers.solvers import solve
+            non_limit = r.free_symbols - Tuple(*limits[1:]).free_symbols
+            den = denom(together(r))
+            den_sym = non_limit & den.free_symbols
+            args = []
+            for v in ordered(den_sym):
+                try:
+                    s = solve(den, v)
+                    m = Eq(v, s[0]) if s else S.false
+                    if m != False:
+                        args.append((Sum(f_orig.subs(*m.args), limits).doit(), m))
+                    break
+                except NotImplementedError:
+                    continue
+
+            args.append((r, True))
+            return Piecewise(*args)
+
+        if r not in (None, S.NaN):
+            return r
+
+    h = eval_sum_hyper(f_orig, (i, a, b))
+    if h is not None:
+        return h
+
+    r = eval_sum_residue(f_orig, (i, a, b))
+    if r is not None:
+        return r
+
+    factored = f_orig.factor()
+    if factored != f_orig:
+        return eval_sum_symbolic(factored, (i, a, b))
+
+
+def _eval_sum_hyper(f, i, a):
+    """ Returns (res, cond). Sums from a to oo. """
+    if a != 0:
+        return _eval_sum_hyper(f.subs(i, i + a), i, 0)
+
+    if f.subs(i, 0) == 0:
+        from sympy.simplify.simplify import simplify
+        if simplify(f.subs(i, Dummy('i', integer=True, positive=True))) == 0:
+            return S.Zero, True
+        return _eval_sum_hyper(f.subs(i, i + 1), i, 0)
+
+    from sympy.simplify.simplify import hypersimp
+    hs = hypersimp(f, i)
+    if hs is None:
+        return None
+
+    if isinstance(hs, Float):
+        from sympy.simplify.simplify import nsimplify
+        hs = nsimplify(hs)
+
+    from sympy.simplify.combsimp import combsimp
+    from sympy.simplify.hyperexpand import hyperexpand
+    from sympy.simplify.radsimp import fraction
+    numer, denom = fraction(factor(hs))
+    top, topl = numer.as_coeff_mul(i)
+    bot, botl = denom.as_coeff_mul(i)
+    ab = [top, bot]
+    factors = [topl, botl]
+    params = [[], []]
+    for k in range(2):
+        for fac in factors[k]:
+            mul = 1
+            if fac.is_Pow:
+                mul = fac.exp
+                fac = fac.base
+                if not mul.is_Integer:
+                    return None
+            p = Poly(fac, i)
+            if p.degree() != 1:
+                return None
+            m, n = p.all_coeffs()
+            ab[k] *= m**mul
+            params[k] += [n/m]*mul
+
+    # Add "1" to numerator parameters, to account for implicit n! in
+    # hypergeometric series.
+    ap = params[0] + [1]
+    bq = params[1]
+    x = ab[0]/ab[1]
+    h = hyper(ap, bq, x)
+    f = combsimp(f)
+    return f.subs(i, 0)*hyperexpand(h), h.convergence_statement
+
+
+def eval_sum_hyper(f, i_a_b):
+    i, a, b = i_a_b
+
+    if f.is_hypergeometric(i) is False:
+        return
+
+    if (b - a).is_Integer:
+        # We are never going to do better than doing the sum in the obvious way
+        return None
+
+    old_sum = Sum(f, (i, a, b))
+
+    if b != S.Infinity:
+        if a is S.NegativeInfinity:
+            res = _eval_sum_hyper(f.subs(i, -i), i, -b)
+            if res is not None:
+                return Piecewise(res, (old_sum, True))
+        else:
+            n_illegal = lambda x: sum(x.count(_) for _ in _illegal)
+            had = n_illegal(f)
+            # check that no extra illegals are introduced
+            res1 = _eval_sum_hyper(f, i, a)
+            if res1 is None or n_illegal(res1) > had:
+                return
+            res2 = _eval_sum_hyper(f, i, b + 1)
+            if res2 is None or n_illegal(res2) > had:
+                return
+            (res1, cond1), (res2, cond2) = res1, res2
+            cond = And(cond1, cond2)
+            if cond == False:
+                return None
+            return Piecewise((res1 - res2, cond), (old_sum, True))
+
+    if a is S.NegativeInfinity:
+        res1 = _eval_sum_hyper(f.subs(i, -i), i, 1)
+        res2 = _eval_sum_hyper(f, i, 0)
+        if res1 is None or res2 is None:
+            return None
+        res1, cond1 = res1
+        res2, cond2 = res2
+        cond = And(cond1, cond2)
+        if cond == False or cond.as_set() == S.EmptySet:
+            return None
+        return Piecewise((res1 + res2, cond), (old_sum, True))
+
+    # Now b == oo, a != -oo
+    res = _eval_sum_hyper(f, i, a)
+    if res is not None:
+        r, c = res
+        if c == False:
+            if r.is_number:
+                f = f.subs(i, Dummy('i', integer=True, positive=True) + a)
+                if f.is_positive or f.is_zero:
+                    return S.Infinity
+                elif f.is_negative:
+                    return S.NegativeInfinity
+            return None
+        return Piecewise(res, (old_sum, True))
+
+
+def eval_sum_residue(f, i_a_b):
+    r"""Compute the infinite summation with residues
+
+    Notes
+    =====
+
+    If $f(n), g(n)$ are polynomials with $\deg(g(n)) - \deg(f(n)) \ge 2$,
+    some infinite summations can be computed by the following residue
+    evaluations.
+
+    .. math::
+        \sum_{n=-\infty, g(n) \ne 0}^{\infty} \frac{f(n)}{g(n)} =
+        -\pi \sum_{\alpha|g(\alpha)=0}
+        \text{Res}(\cot(\pi x) \frac{f(x)}{g(x)}, \alpha)
+
+    .. math::
+        \sum_{n=-\infty, g(n) \ne 0}^{\infty} (-1)^n \frac{f(n)}{g(n)} =
+        -\pi \sum_{\alpha|g(\alpha)=0}
+        \text{Res}(\csc(\pi x) \frac{f(x)}{g(x)}, \alpha)
+
+    Examples
+    ========
+
+    >>> from sympy import Sum, oo, Symbol
+    >>> x = Symbol('x')
+
+    Doubly infinite series of rational functions.
+
+    >>> Sum(1 / (x**2 + 1), (x, -oo, oo)).doit()
+    pi/tanh(pi)
+
+    Doubly infinite alternating series of rational functions.
+
+    >>> Sum((-1)**x / (x**2 + 1), (x, -oo, oo)).doit()
+    pi/sinh(pi)
+
+    Infinite series of even rational functions.
+
+    >>> Sum(1 / (x**2 + 1), (x, 0, oo)).doit()
+    1/2 + pi/(2*tanh(pi))
+
+    Infinite series of alternating even rational functions.
+
+    >>> Sum((-1)**x / (x**2 + 1), (x, 0, oo)).doit()
+    pi/(2*sinh(pi)) + 1/2
+
+    This also have heuristics to transform arbitrarily shifted summand or
+    arbitrarily shifted summation range to the canonical problem the
+    formula can handle.
+
+    >>> Sum(1 / (x**2 + 2*x + 2), (x, -1, oo)).doit()
+    1/2 + pi/(2*tanh(pi))
+    >>> Sum(1 / (x**2 + 4*x + 5), (x, -2, oo)).doit()
+    1/2 + pi/(2*tanh(pi))
+    >>> Sum(1 / (x**2 + 1), (x, 1, oo)).doit()
+    -1/2 + pi/(2*tanh(pi))
+    >>> Sum(1 / (x**2 + 1), (x, 2, oo)).doit()
+    -1 + pi/(2*tanh(pi))
+
+    References
+    ==========
+
+    .. [#] http://www.supermath.info/InfiniteSeriesandtheResidueTheorem.pdf
+
+    .. [#] Asmar N.H., Grafakos L. (2018) Residue Theory.
+           In: Complex Analysis with Applications.
+           Undergraduate Texts in Mathematics. Springer, Cham.
+           https://doi.org/10.1007/978-3-319-94063-2_5
+    """
+    i, a, b = i_a_b
+
+    # If lower limit > upper limit: Karr Summation Convention
+    if a.is_comparable and b.is_comparable and a > b:
+        return eval_sum_residue(f, (i, b + S.One, a - S.One))
+
+    def is_even_function(numer, denom):
+        """Test if the rational function is an even function"""
+        numer_even = all(i % 2 == 0 for (i,) in numer.monoms())
+        denom_even = all(i % 2 == 0 for (i,) in denom.monoms())
+        numer_odd = all(i % 2 == 1 for (i,) in numer.monoms())
+        denom_odd = all(i % 2 == 1 for (i,) in denom.monoms())
+        return (numer_even and denom_even) or (numer_odd and denom_odd)
+
+    def match_rational(f, i):
+        numer, denom = f.as_numer_denom()
+        try:
+            (numer, denom), opt = parallel_poly_from_expr((numer, denom), i)
+        except (PolificationFailed, PolynomialError):
+            return None
+        return numer, denom
+
+    def get_poles(denom):
+        roots = denom.sqf_part().all_roots()
+        roots = sift(roots, lambda x: x.is_integer)
+        if None in roots:
+            return None
+        int_roots, nonint_roots = roots[True], roots[False]
+        return int_roots, nonint_roots
+
+    def get_shift(denom):
+        n = denom.degree(i)
+        a = denom.coeff_monomial(i**n)
+        b = denom.coeff_monomial(i**(n-1))
+        shift = - b / a / n
+        return shift
+
+    #Need a dummy symbol with no assumptions set for get_residue_factor
+    z = Dummy('z')
+
+    def get_residue_factor(numer, denom, alternating):
+        residue_factor = (numer.as_expr() / denom.as_expr()).subs(i, z)
+        if not alternating:
+            residue_factor *= cot(S.Pi * z)
+        else:
+            residue_factor *= csc(S.Pi * z)
+        return residue_factor
+
+    # We don't know how to deal with symbolic constants in summand
+    if f.free_symbols - {i}:
+        return None
+
+    if not (a.is_Integer or a in (S.Infinity, S.NegativeInfinity)):
+        return None
+    if not (b.is_Integer or b in (S.Infinity, S.NegativeInfinity)):
+        return None
+
+    # Quick exit heuristic for the sums which doesn't have infinite range
+    if a != S.NegativeInfinity and b != S.Infinity:
+        return None
+
+    match = match_rational(f, i)
+    if match:
+        alternating = False
+        numer, denom = match
+    else:
+        match = match_rational(f / S.NegativeOne**i, i)
+        if match:
+            alternating = True
+            numer, denom = match
+        else:
+            return None
+
+    if denom.degree(i) - numer.degree(i) < 2:
+        return None
+
+    if (a, b) == (S.NegativeInfinity, S.Infinity):
+        poles = get_poles(denom)
+        if poles is None:
+            return None
+        int_roots, nonint_roots = poles
+
+        if int_roots:
+            return None
+
+        residue_factor = get_residue_factor(numer, denom, alternating)
+        residues = [residue(residue_factor, z, root) for root in nonint_roots]
+        return -S.Pi * sum(residues)
+
+    if not (a.is_finite and b is S.Infinity):
+        return None
+
+    if not is_even_function(numer, denom):
+        # Try shifting summation and check if the summand can be made
+        # and even function from the origin.
+        # Sum(f(n), (n, a, b)) => Sum(f(n + s), (n, a - s, b - s))
+        shift = get_shift(denom)
+
+        if not shift.is_Integer:
+            return None
+        if shift == 0:
+            return None
+
+        numer = numer.shift(shift)
+        denom = denom.shift(shift)
+
+        if not is_even_function(numer, denom):
+            return None
+
+        if alternating:
+            f = S.NegativeOne**i * (S.NegativeOne**shift * numer.as_expr() / denom.as_expr())
+        else:
+            f = numer.as_expr() / denom.as_expr()
+        return eval_sum_residue(f, (i, a-shift, b-shift))
+
+    poles = get_poles(denom)
+    if poles is None:
+        return None
+    int_roots, nonint_roots = poles
+
+    if int_roots:
+        int_roots = [int(root) for root in int_roots]
+        int_roots_max = max(int_roots)
+        int_roots_min = min(int_roots)
+        # Integer valued poles must be next to each other
+        # and also symmetric from origin (Because the function is even)
+        if not len(int_roots) == int_roots_max - int_roots_min + 1:
+            return None
+
+        # Check whether the summation indices contain poles
+        if a <= max(int_roots):
+            return None
+
+    residue_factor = get_residue_factor(numer, denom, alternating)
+    residues = [residue(residue_factor, z, root) for root in int_roots + nonint_roots]
+    full_sum = -S.Pi * sum(residues)
+
+    if not int_roots:
+        # Compute Sum(f, (i, 0, oo)) by adding a extraneous evaluation
+        # at the origin.
+        half_sum = (full_sum + f.xreplace({i: 0})) / 2
+
+        # Add and subtract extraneous evaluations
+        extraneous_neg = [f.xreplace({i: i0}) for i0 in range(int(a), 0)]
+        extraneous_pos = [f.xreplace({i: i0}) for i0 in range(0, int(a))]
+        result = half_sum + sum(extraneous_neg) - sum(extraneous_pos)
+
+        return result
+
+    # Compute Sum(f, (i, min(poles) + 1, oo))
+    half_sum = full_sum / 2
+
+    # Subtract extraneous evaluations
+    extraneous = [f.xreplace({i: i0}) for i0 in range(max(int_roots) + 1, int(a))]
+    result = half_sum - sum(extraneous)
+
+    return result
+
+
+def _eval_matrix_sum(expression):
+    f = expression.function
+    for limit in expression.limits:
+        i, a, b = limit
+        dif = b - a
+        if dif.is_Integer:
+            if (dif < 0) == True:
+                a, b = b + 1, a - 1
+                f = -f
+
+            newf = eval_sum_direct(f, (i, a, b))
+            if newf is not None:
+                return newf.doit()
+
+
+def _dummy_with_inherited_properties_concrete(limits):
+    """
+    Return a Dummy symbol that inherits as many assumptions as possible
+    from the provided symbol and limits.
+
+    If the symbol already has all True assumption shared by the limits
+    then return None.
+    """
+    x, a, b = limits
+    l = [a, b]
+
+    assumptions_to_consider = ['extended_nonnegative', 'nonnegative',
+                               'extended_nonpositive', 'nonpositive',
+                               'extended_positive', 'positive',
+                               'extended_negative', 'negative',
+                               'integer', 'rational', 'finite',
+                               'zero', 'real', 'extended_real']
+
+    assumptions_to_keep = {}
+    assumptions_to_add = {}
+    for assum in assumptions_to_consider:
+        assum_true = x._assumptions.get(assum, None)
+        if assum_true:
+            assumptions_to_keep[assum] = True
+        elif all(getattr(i, 'is_' + assum) for i in l):
+            assumptions_to_add[assum] = True
+    if assumptions_to_add:
+        assumptions_to_keep.update(assumptions_to_add)
+        return Dummy('d', **assumptions_to_keep)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_delta.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_delta.py
new file mode 100644
index 0000000000000000000000000000000000000000..9dc6e88d16346acc7dc775446d7de3f3696d0e03
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_delta.py
@@ -0,0 +1,499 @@
+from sympy.concrete import Sum
+from sympy.concrete.delta import deltaproduct as dp, deltasummation as ds, _extract_delta
+from sympy.core import Eq, S, symbols, oo
+from sympy.functions import KroneckerDelta as KD, Piecewise, piecewise_fold
+from sympy.logic import And
+from sympy.testing.pytest import raises
+
+i, j, k, l, m = symbols("i j k l m", integer=True, finite=True)
+x, y = symbols("x y", commutative=False)
+
+
+def test_deltaproduct_trivial():
+    assert dp(x, (j, 1, 0)) == 1
+    assert dp(x, (j, 1, 3)) == x**3
+    assert dp(x + y, (j, 1, 3)) == (x + y)**3
+    assert dp(x*y, (j, 1, 3)) == (x*y)**3
+    assert dp(KD(i, j), (k, 1, 3)) == KD(i, j)
+    assert dp(x*KD(i, j), (k, 1, 3)) == x**3*KD(i, j)
+    assert dp(x*y*KD(i, j), (k, 1, 3)) == (x*y)**3*KD(i, j)
+
+
+def test_deltaproduct_basic():
+    assert dp(KD(i, j), (j, 1, 3)) == 0
+    assert dp(KD(i, j), (j, 1, 1)) == KD(i, 1)
+    assert dp(KD(i, j), (j, 2, 2)) == KD(i, 2)
+    assert dp(KD(i, j), (j, 3, 3)) == KD(i, 3)
+    assert dp(KD(i, j), (j, 1, k)) == KD(i, 1)*KD(k, 1) + KD(k, 0)
+    assert dp(KD(i, j), (j, k, 3)) == KD(i, 3)*KD(k, 3) + KD(k, 4)
+    assert dp(KD(i, j), (j, k, l)) == KD(i, l)*KD(k, l) + KD(k, l + 1)
+
+
+def test_deltaproduct_mul_x_kd():
+    assert dp(x*KD(i, j), (j, 1, 3)) == 0
+    assert dp(x*KD(i, j), (j, 1, 1)) == x*KD(i, 1)
+    assert dp(x*KD(i, j), (j, 2, 2)) == x*KD(i, 2)
+    assert dp(x*KD(i, j), (j, 3, 3)) == x*KD(i, 3)
+    assert dp(x*KD(i, j), (j, 1, k)) == x*KD(i, 1)*KD(k, 1) + KD(k, 0)
+    assert dp(x*KD(i, j), (j, k, 3)) == x*KD(i, 3)*KD(k, 3) + KD(k, 4)
+    assert dp(x*KD(i, j), (j, k, l)) == x*KD(i, l)*KD(k, l) + KD(k, l + 1)
+
+
+def test_deltaproduct_mul_add_x_y_kd():
+    assert dp((x + y)*KD(i, j), (j, 1, 3)) == 0
+    assert dp((x + y)*KD(i, j), (j, 1, 1)) == (x + y)*KD(i, 1)
+    assert dp((x + y)*KD(i, j), (j, 2, 2)) == (x + y)*KD(i, 2)
+    assert dp((x + y)*KD(i, j), (j, 3, 3)) == (x + y)*KD(i, 3)
+    assert dp((x + y)*KD(i, j), (j, 1, k)) == \
+        (x + y)*KD(i, 1)*KD(k, 1) + KD(k, 0)
+    assert dp((x + y)*KD(i, j), (j, k, 3)) == \
+        (x + y)*KD(i, 3)*KD(k, 3) + KD(k, 4)
+    assert dp((x + y)*KD(i, j), (j, k, l)) == \
+        (x + y)*KD(i, l)*KD(k, l) + KD(k, l + 1)
+
+
+def test_deltaproduct_add_kd_kd():
+    assert dp(KD(i, k) + KD(j, k), (k, 1, 3)) == 0
+    assert dp(KD(i, k) + KD(j, k), (k, 1, 1)) == KD(i, 1) + KD(j, 1)
+    assert dp(KD(i, k) + KD(j, k), (k, 2, 2)) == KD(i, 2) + KD(j, 2)
+    assert dp(KD(i, k) + KD(j, k), (k, 3, 3)) == KD(i, 3) + KD(j, 3)
+    assert dp(KD(i, k) + KD(j, k), (k, 1, l)) == KD(l, 0) + \
+        KD(i, 1)*KD(l, 1) + KD(j, 1)*KD(l, 1) + \
+        KD(i, 1)*KD(j, 2)*KD(l, 2) + KD(j, 1)*KD(i, 2)*KD(l, 2)
+    assert dp(KD(i, k) + KD(j, k), (k, l, 3)) == KD(l, 4) + \
+        KD(i, 3)*KD(l, 3) + KD(j, 3)*KD(l, 3) + \
+        KD(i, 2)*KD(j, 3)*KD(l, 2) + KD(i, 3)*KD(j, 2)*KD(l, 2)
+    assert dp(KD(i, k) + KD(j, k), (k, l, m)) == KD(l, m + 1) + \
+        KD(i, m)*KD(l, m) + KD(j, m)*KD(l, m) + \
+        KD(i, m)*KD(j, m - 1)*KD(l, m - 1) + KD(i, m - 1)*KD(j, m)*KD(l, m - 1)
+
+
+def test_deltaproduct_mul_x_add_kd_kd():
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 3)) == 0
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 1)) == x*(KD(i, 1) + KD(j, 1))
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, 2, 2)) == x*(KD(i, 2) + KD(j, 2))
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, 3, 3)) == x*(KD(i, 3) + KD(j, 3))
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, l)) == KD(l, 0) + \
+        x*KD(i, 1)*KD(l, 1) + x*KD(j, 1)*KD(l, 1) + \
+        x**2*KD(i, 1)*KD(j, 2)*KD(l, 2) + x**2*KD(j, 1)*KD(i, 2)*KD(l, 2)
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, l, 3)) == KD(l, 4) + \
+        x*KD(i, 3)*KD(l, 3) + x*KD(j, 3)*KD(l, 3) + \
+        x**2*KD(i, 2)*KD(j, 3)*KD(l, 2) + x**2*KD(i, 3)*KD(j, 2)*KD(l, 2)
+    assert dp(x*(KD(i, k) + KD(j, k)), (k, l, m)) == KD(l, m + 1) + \
+        x*KD(i, m)*KD(l, m) + x*KD(j, m)*KD(l, m) + \
+        x**2*KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + \
+        x**2*KD(i, m)*KD(j, m - 1)*KD(l, m - 1)
+
+
+def test_deltaproduct_mul_add_x_y_add_kd_kd():
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 3)) == 0
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 1)) == \
+        (x + y)*(KD(i, 1) + KD(j, 1))
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 2, 2)) == \
+        (x + y)*(KD(i, 2) + KD(j, 2))
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 3, 3)) == \
+        (x + y)*(KD(i, 3) + KD(j, 3))
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 1, l)) == KD(l, 0) + \
+        (x + y)*KD(i, 1)*KD(l, 1) + (x + y)*KD(j, 1)*KD(l, 1) + \
+        (x + y)**2*KD(i, 1)*KD(j, 2)*KD(l, 2) + \
+        (x + y)**2*KD(j, 1)*KD(i, 2)*KD(l, 2)
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, l, 3)) == KD(l, 4) + \
+        (x + y)*KD(i, 3)*KD(l, 3) + (x + y)*KD(j, 3)*KD(l, 3) + \
+        (x + y)**2*KD(i, 2)*KD(j, 3)*KD(l, 2) + \
+        (x + y)**2*KD(i, 3)*KD(j, 2)*KD(l, 2)
+    assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, l, m)) == KD(l, m + 1) + \
+        (x + y)*KD(i, m)*KD(l, m) + (x + y)*KD(j, m)*KD(l, m) + \
+        (x + y)**2*KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + \
+        (x + y)**2*KD(i, m)*KD(j, m - 1)*KD(l, m - 1)
+
+
+def test_deltaproduct_add_mul_x_y_mul_x_kd():
+    assert dp(x*y + x*KD(i, j), (j, 1, 3)) == (x*y)**3 + \
+        x*(x*y)**2*KD(i, 1) + (x*y)*x*(x*y)*KD(i, 2) + (x*y)**2*x*KD(i, 3)
+    assert dp(x*y + x*KD(i, j), (j, 1, 1)) == x*y + x*KD(i, 1)
+    assert dp(x*y + x*KD(i, j), (j, 2, 2)) == x*y + x*KD(i, 2)
+    assert dp(x*y + x*KD(i, j), (j, 3, 3)) == x*y + x*KD(i, 3)
+    assert dp(x*y + x*KD(i, j), (j, 1, k)) == \
+        (x*y)**k + Piecewise(
+            ((x*y)**(i - 1)*x*(x*y)**(k - i), And(1 <= i, i <= k)),
+            (0, True)
+        )
+    assert dp(x*y + x*KD(i, j), (j, k, 3)) == \
+        (x*y)**(-k + 4) + Piecewise(
+            ((x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)),
+            (0, True)
+        )
+    assert dp(x*y + x*KD(i, j), (j, k, l)) == \
+        (x*y)**(-k + l + 1) + Piecewise(
+            ((x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)),
+            (0, True)
+        )
+
+
+def test_deltaproduct_mul_x_add_y_kd():
+    assert dp(x*(y + KD(i, j)), (j, 1, 3)) == (x*y)**3 + \
+        x*(x*y)**2*KD(i, 1) + (x*y)*x*(x*y)*KD(i, 2) + (x*y)**2*x*KD(i, 3)
+    assert dp(x*(y + KD(i, j)), (j, 1, 1)) == x*(y + KD(i, 1))
+    assert dp(x*(y + KD(i, j)), (j, 2, 2)) == x*(y + KD(i, 2))
+    assert dp(x*(y + KD(i, j)), (j, 3, 3)) == x*(y + KD(i, 3))
+    assert dp(x*(y + KD(i, j)), (j, 1, k)) == \
+        (x*y)**k + Piecewise(
+            ((x*y)**(i - 1)*x*(x*y)**(k - i), And(1 <= i, i <= k)),
+            (0, True)
+        ).expand()
+    assert dp(x*(y + KD(i, j)), (j, k, 3)) == \
+        ((x*y)**(-k + 4) + Piecewise(
+            ((x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)),
+            (0, True)
+        )).expand()
+    assert dp(x*(y + KD(i, j)), (j, k, l)) == \
+        ((x*y)**(-k + l + 1) + Piecewise(
+            ((x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)),
+            (0, True)
+        )).expand()
+
+
+def test_deltaproduct_mul_x_add_y_twokd():
+    assert dp(x*(y + 2*KD(i, j)), (j, 1, 3)) == (x*y)**3 + \
+        2*x*(x*y)**2*KD(i, 1) + 2*x*y*x*x*y*KD(i, 2) + 2*(x*y)**2*x*KD(i, 3)
+    assert dp(x*(y + 2*KD(i, j)), (j, 1, 1)) == x*(y + 2*KD(i, 1))
+    assert dp(x*(y + 2*KD(i, j)), (j, 2, 2)) == x*(y + 2*KD(i, 2))
+    assert dp(x*(y + 2*KD(i, j)), (j, 3, 3)) == x*(y + 2*KD(i, 3))
+    assert dp(x*(y + 2*KD(i, j)), (j, 1, k)) == \
+        (x*y)**k + Piecewise(
+            (2*(x*y)**(i - 1)*x*(x*y)**(k - i), And(1 <= i, i <= k)),
+            (0, True)
+        ).expand()
+    assert dp(x*(y + 2*KD(i, j)), (j, k, 3)) == \
+        ((x*y)**(-k + 4) + Piecewise(
+            (2*(x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)),
+            (0, True)
+        )).expand()
+    assert dp(x*(y + 2*KD(i, j)), (j, k, l)) == \
+        ((x*y)**(-k + l + 1) + Piecewise(
+            (2*(x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)),
+            (0, True)
+        )).expand()
+
+
+def test_deltaproduct_mul_add_x_y_add_y_kd():
+    assert dp((x + y)*(y + KD(i, j)), (j, 1, 3)) == ((x + y)*y)**3 + \
+        (x + y)*((x + y)*y)**2*KD(i, 1) + \
+        (x + y)*y*(x + y)**2*y*KD(i, 2) + \
+        ((x + y)*y)**2*(x + y)*KD(i, 3)
+    assert dp((x + y)*(y + KD(i, j)), (j, 1, 1)) == (x + y)*(y + KD(i, 1))
+    assert dp((x + y)*(y + KD(i, j)), (j, 2, 2)) == (x + y)*(y + KD(i, 2))
+    assert dp((x + y)*(y + KD(i, j)), (j, 3, 3)) == (x + y)*(y + KD(i, 3))
+    assert dp((x + y)*(y + KD(i, j)), (j, 1, k)) == \
+        ((x + y)*y)**k + Piecewise(
+            (((x + y)*y)**(-1)*((x + y)*y)**i*(x + y)*((x + y)*y
+            )**k*((x + y)*y)**(-i), (i >= 1) & (i <= k)), (0, True))
+    assert dp((x + y)*(y + KD(i, j)), (j, k, 3)) == (
+        (x + y)*y)**4*((x + y)*y)**(-k) + Piecewise((((x + y)*y)**i*(
+        (x + y)*y)**(-k)*(x + y)*((x + y)*y)**3*((x + y)*y)**(-i),
+        (i >= k) & (i <= 3)), (0, True))
+    assert dp((x + y)*(y + KD(i, j)), (j, k, l)) == \
+        (x + y)*y*((x + y)*y)**l*((x + y)*y)**(-k) + Piecewise(
+        (((x + y)*y)**i*((x + y)*y)**(-k)*(x + y)*((x + y)*y
+        )**l*((x + y)*y)**(-i), (i >= k) & (i <= l)), (0, True))
+
+
+def test_deltaproduct_mul_add_x_kd_add_y_kd():
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 3)) == \
+        KD(i, 1)*(KD(i, k) + x)*((KD(i, k) + x)*y)**2 + \
+        KD(i, 2)*(KD(i, k) + x)*y*(KD(i, k) + x)**2*y + \
+        KD(i, 3)*((KD(i, k) + x)*y)**2*(KD(i, k) + x) + \
+        ((KD(i, k) + x)*y)**3
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 1)) == \
+        (x + KD(i, k))*(y + KD(i, 1))
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 2, 2)) == \
+        (x + KD(i, k))*(y + KD(i, 2))
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 3, 3)) == \
+        (x + KD(i, k))*(y + KD(i, 3))
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, k)) == \
+        ((KD(i, k) + x)*y)**k + Piecewise(
+        (((KD(i, k) + x)*y)**(-1)*((KD(i, k) + x)*y)**i*(KD(i, k) + x
+        )*((KD(i, k) + x)*y)**k*((KD(i, k) + x)*y)**(-i), (i >= 1
+        ) & (i <= k)), (0, True))
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, 3)) == (
+        (KD(i, k) + x)*y)**4*((KD(i, k) + x)*y)**(-k) + Piecewise(
+        (((KD(i, k) + x)*y)**i*((KD(i, k) + x)*y)**(-k)*(KD(i, k)
+        + x)*((KD(i, k) + x)*y)**3*((KD(i, k) + x)*y)**(-i),
+        (i >= k) & (i <= 3)), (0, True))
+    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, l)) == (
+        KD(i, k) + x)*y*((KD(i, k) + x)*y)**l*((KD(i, k) + x)*y
+        )**(-k) + Piecewise((((KD(i, k) + x)*y)**i*((KD(i, k) + x
+        )*y)**(-k)*(KD(i, k) + x)*((KD(i, k) + x)*y)**l*((KD(i, k) + x
+        )*y)**(-i), (i >= k) & (i <= l)), (0, True))
+
+
+def test_deltasummation_trivial():
+    assert ds(x, (j, 1, 0)) == 0
+    assert ds(x, (j, 1, 3)) == 3*x
+    assert ds(x + y, (j, 1, 3)) == 3*(x + y)
+    assert ds(x*y, (j, 1, 3)) == 3*x*y
+    assert ds(KD(i, j), (k, 1, 3)) == 3*KD(i, j)
+    assert ds(x*KD(i, j), (k, 1, 3)) == 3*x*KD(i, j)
+    assert ds(x*y*KD(i, j), (k, 1, 3)) == 3*x*y*KD(i, j)
+
+
+def test_deltasummation_basic_numerical():
+    n = symbols('n', integer=True, nonzero=True)
+    assert ds(KD(n, 0), (n, 1, 3)) == 0
+
+    # return unevaluated, until it gets implemented
+    assert ds(KD(i**2, j**2), (j, -oo, oo)) == \
+        Sum(KD(i**2, j**2), (j, -oo, oo))
+
+    assert Piecewise((KD(i, k), And(1 <= i, i <= 3)), (0, True)) == \
+        ds(KD(i, j)*KD(j, k), (j, 1, 3)) == \
+        ds(KD(j, k)*KD(i, j), (j, 1, 3))
+
+    assert ds(KD(i, k), (k, -oo, oo)) == 1
+    assert ds(KD(i, k), (k, 0, oo)) == Piecewise((1, S.Zero <= i), (0, True))
+    assert ds(KD(i, k), (k, 1, 3)) == \
+        Piecewise((1, And(1 <= i, i <= 3)), (0, True))
+    assert ds(k*KD(i, j)*KD(j, k), (k, -oo, oo)) == j*KD(i, j)
+    assert ds(j*KD(i, j), (j, -oo, oo)) == i
+    assert ds(i*KD(i, j), (i, -oo, oo)) == j
+    assert ds(x, (i, 1, 3)) == 3*x
+    assert ds((i + j)*KD(i, j), (j, -oo, oo)) == 2*i
+
+
+def test_deltasummation_basic_symbolic():
+    assert ds(KD(i, j), (j, 1, 3)) == \
+        Piecewise((1, And(1 <= i, i <= 3)), (0, True))
+    assert ds(KD(i, j), (j, 1, 1)) == Piecewise((1, Eq(i, 1)), (0, True))
+    assert ds(KD(i, j), (j, 2, 2)) == Piecewise((1, Eq(i, 2)), (0, True))
+    assert ds(KD(i, j), (j, 3, 3)) == Piecewise((1, Eq(i, 3)), (0, True))
+    assert ds(KD(i, j), (j, 1, k)) == \
+        Piecewise((1, And(1 <= i, i <= k)), (0, True))
+    assert ds(KD(i, j), (j, k, 3)) == \
+        Piecewise((1, And(k <= i, i <= 3)), (0, True))
+    assert ds(KD(i, j), (j, k, l)) == \
+        Piecewise((1, And(k <= i, i <= l)), (0, True))
+
+
+def test_deltasummation_mul_x_kd():
+    assert ds(x*KD(i, j), (j, 1, 3)) == \
+        Piecewise((x, And(1 <= i, i <= 3)), (0, True))
+    assert ds(x*KD(i, j), (j, 1, 1)) == Piecewise((x, Eq(i, 1)), (0, True))
+    assert ds(x*KD(i, j), (j, 2, 2)) == Piecewise((x, Eq(i, 2)), (0, True))
+    assert ds(x*KD(i, j), (j, 3, 3)) == Piecewise((x, Eq(i, 3)), (0, True))
+    assert ds(x*KD(i, j), (j, 1, k)) == \
+        Piecewise((x, And(1 <= i, i <= k)), (0, True))
+    assert ds(x*KD(i, j), (j, k, 3)) == \
+        Piecewise((x, And(k <= i, i <= 3)), (0, True))
+    assert ds(x*KD(i, j), (j, k, l)) == \
+        Piecewise((x, And(k <= i, i <= l)), (0, True))
+
+
+def test_deltasummation_mul_add_x_y_kd():
+    assert ds((x + y)*KD(i, j), (j, 1, 3)) == \
+        Piecewise((x + y, And(1 <= i, i <= 3)), (0, True))
+    assert ds((x + y)*KD(i, j), (j, 1, 1)) == \
+        Piecewise((x + y, Eq(i, 1)), (0, True))
+    assert ds((x + y)*KD(i, j), (j, 2, 2)) == \
+        Piecewise((x + y, Eq(i, 2)), (0, True))
+    assert ds((x + y)*KD(i, j), (j, 3, 3)) == \
+        Piecewise((x + y, Eq(i, 3)), (0, True))
+    assert ds((x + y)*KD(i, j), (j, 1, k)) == \
+        Piecewise((x + y, And(1 <= i, i <= k)), (0, True))
+    assert ds((x + y)*KD(i, j), (j, k, 3)) == \
+        Piecewise((x + y, And(k <= i, i <= 3)), (0, True))
+    assert ds((x + y)*KD(i, j), (j, k, l)) == \
+        Piecewise((x + y, And(k <= i, i <= l)), (0, True))
+
+
+def test_deltasummation_add_kd_kd():
+    assert ds(KD(i, k) + KD(j, k), (k, 1, 3)) == piecewise_fold(
+        Piecewise((1, And(1 <= i, i <= 3)), (0, True)) +
+        Piecewise((1, And(1 <= j, j <= 3)), (0, True)))
+    assert ds(KD(i, k) + KD(j, k), (k, 1, 1)) == piecewise_fold(
+        Piecewise((1, Eq(i, 1)), (0, True)) +
+        Piecewise((1, Eq(j, 1)), (0, True)))
+    assert ds(KD(i, k) + KD(j, k), (k, 2, 2)) == piecewise_fold(
+        Piecewise((1, Eq(i, 2)), (0, True)) +
+        Piecewise((1, Eq(j, 2)), (0, True)))
+    assert ds(KD(i, k) + KD(j, k), (k, 3, 3)) == piecewise_fold(
+        Piecewise((1, Eq(i, 3)), (0, True)) +
+        Piecewise((1, Eq(j, 3)), (0, True)))
+    assert ds(KD(i, k) + KD(j, k), (k, 1, l)) == piecewise_fold(
+        Piecewise((1, And(1 <= i, i <= l)), (0, True)) +
+        Piecewise((1, And(1 <= j, j <= l)), (0, True)))
+    assert ds(KD(i, k) + KD(j, k), (k, l, 3)) == piecewise_fold(
+        Piecewise((1, And(l <= i, i <= 3)), (0, True)) +
+        Piecewise((1, And(l <= j, j <= 3)), (0, True)))
+    assert ds(KD(i, k) + KD(j, k), (k, l, m)) == piecewise_fold(
+        Piecewise((1, And(l <= i, i <= m)), (0, True)) +
+        Piecewise((1, And(l <= j, j <= m)), (0, True)))
+
+
+def test_deltasummation_add_mul_x_kd_kd():
+    assert ds(x*KD(i, k) + KD(j, k), (k, 1, 3)) == piecewise_fold(
+        Piecewise((x, And(1 <= i, i <= 3)), (0, True)) +
+        Piecewise((1, And(1 <= j, j <= 3)), (0, True)))
+    assert ds(x*KD(i, k) + KD(j, k), (k, 1, 1)) == piecewise_fold(
+        Piecewise((x, Eq(i, 1)), (0, True)) +
+        Piecewise((1, Eq(j, 1)), (0, True)))
+    assert ds(x*KD(i, k) + KD(j, k), (k, 2, 2)) == piecewise_fold(
+        Piecewise((x, Eq(i, 2)), (0, True)) +
+        Piecewise((1, Eq(j, 2)), (0, True)))
+    assert ds(x*KD(i, k) + KD(j, k), (k, 3, 3)) == piecewise_fold(
+        Piecewise((x, Eq(i, 3)), (0, True)) +
+        Piecewise((1, Eq(j, 3)), (0, True)))
+    assert ds(x*KD(i, k) + KD(j, k), (k, 1, l)) == piecewise_fold(
+        Piecewise((x, And(1 <= i, i <= l)), (0, True)) +
+        Piecewise((1, And(1 <= j, j <= l)), (0, True)))
+    assert ds(x*KD(i, k) + KD(j, k), (k, l, 3)) == piecewise_fold(
+        Piecewise((x, And(l <= i, i <= 3)), (0, True)) +
+        Piecewise((1, And(l <= j, j <= 3)), (0, True)))
+    assert ds(x*KD(i, k) + KD(j, k), (k, l, m)) == piecewise_fold(
+        Piecewise((x, And(l <= i, i <= m)), (0, True)) +
+        Piecewise((1, And(l <= j, j <= m)), (0, True)))
+
+
+def test_deltasummation_mul_x_add_kd_kd():
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, 1, 3)) == piecewise_fold(
+        Piecewise((x, And(1 <= i, i <= 3)), (0, True)) +
+        Piecewise((x, And(1 <= j, j <= 3)), (0, True)))
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, 1, 1)) == piecewise_fold(
+        Piecewise((x, Eq(i, 1)), (0, True)) +
+        Piecewise((x, Eq(j, 1)), (0, True)))
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, 2, 2)) == piecewise_fold(
+        Piecewise((x, Eq(i, 2)), (0, True)) +
+        Piecewise((x, Eq(j, 2)), (0, True)))
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, 3, 3)) == piecewise_fold(
+        Piecewise((x, Eq(i, 3)), (0, True)) +
+        Piecewise((x, Eq(j, 3)), (0, True)))
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, 1, l)) == piecewise_fold(
+        Piecewise((x, And(1 <= i, i <= l)), (0, True)) +
+        Piecewise((x, And(1 <= j, j <= l)), (0, True)))
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, l, 3)) == piecewise_fold(
+        Piecewise((x, And(l <= i, i <= 3)), (0, True)) +
+        Piecewise((x, And(l <= j, j <= 3)), (0, True)))
+    assert ds(x*(KD(i, k) + KD(j, k)), (k, l, m)) == piecewise_fold(
+        Piecewise((x, And(l <= i, i <= m)), (0, True)) +
+        Piecewise((x, And(l <= j, j <= m)), (0, True)))
+
+
+def test_deltasummation_mul_add_x_y_add_kd_kd():
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 3)) == piecewise_fold(
+        Piecewise((x + y, And(1 <= i, i <= 3)), (0, True)) +
+        Piecewise((x + y, And(1 <= j, j <= 3)), (0, True)))
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 1)) == piecewise_fold(
+        Piecewise((x + y, Eq(i, 1)), (0, True)) +
+        Piecewise((x + y, Eq(j, 1)), (0, True)))
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 2, 2)) == piecewise_fold(
+        Piecewise((x + y, Eq(i, 2)), (0, True)) +
+        Piecewise((x + y, Eq(j, 2)), (0, True)))
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 3, 3)) == piecewise_fold(
+        Piecewise((x + y, Eq(i, 3)), (0, True)) +
+        Piecewise((x + y, Eq(j, 3)), (0, True)))
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 1, l)) == piecewise_fold(
+        Piecewise((x + y, And(1 <= i, i <= l)), (0, True)) +
+        Piecewise((x + y, And(1 <= j, j <= l)), (0, True)))
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, l, 3)) == piecewise_fold(
+        Piecewise((x + y, And(l <= i, i <= 3)), (0, True)) +
+        Piecewise((x + y, And(l <= j, j <= 3)), (0, True)))
+    assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, l, m)) == piecewise_fold(
+        Piecewise((x + y, And(l <= i, i <= m)), (0, True)) +
+        Piecewise((x + y, And(l <= j, j <= m)), (0, True)))
+
+
+def test_deltasummation_add_mul_x_y_mul_x_kd():
+    assert ds(x*y + x*KD(i, j), (j, 1, 3)) == \
+        Piecewise((3*x*y + x, And(1 <= i, i <= 3)), (3*x*y, True))
+    assert ds(x*y + x*KD(i, j), (j, 1, 1)) == \
+        Piecewise((x*y + x, Eq(i, 1)), (x*y, True))
+    assert ds(x*y + x*KD(i, j), (j, 2, 2)) == \
+        Piecewise((x*y + x, Eq(i, 2)), (x*y, True))
+    assert ds(x*y + x*KD(i, j), (j, 3, 3)) == \
+        Piecewise((x*y + x, Eq(i, 3)), (x*y, True))
+    assert ds(x*y + x*KD(i, j), (j, 1, k)) == \
+        Piecewise((k*x*y + x, And(1 <= i, i <= k)), (k*x*y, True))
+    assert ds(x*y + x*KD(i, j), (j, k, 3)) == \
+        Piecewise(((4 - k)*x*y + x, And(k <= i, i <= 3)), ((4 - k)*x*y, True))
+    assert ds(x*y + x*KD(i, j), (j, k, l)) == Piecewise(
+        ((l - k + 1)*x*y + x, And(k <= i, i <= l)), ((l - k + 1)*x*y, True))
+
+
+def test_deltasummation_mul_x_add_y_kd():
+    assert ds(x*(y + KD(i, j)), (j, 1, 3)) == \
+        Piecewise((3*x*y + x, And(1 <= i, i <= 3)), (3*x*y, True))
+    assert ds(x*(y + KD(i, j)), (j, 1, 1)) == \
+        Piecewise((x*y + x, Eq(i, 1)), (x*y, True))
+    assert ds(x*(y + KD(i, j)), (j, 2, 2)) == \
+        Piecewise((x*y + x, Eq(i, 2)), (x*y, True))
+    assert ds(x*(y + KD(i, j)), (j, 3, 3)) == \
+        Piecewise((x*y + x, Eq(i, 3)), (x*y, True))
+    assert ds(x*(y + KD(i, j)), (j, 1, k)) == \
+        Piecewise((k*x*y + x, And(1 <= i, i <= k)), (k*x*y, True))
+    assert ds(x*(y + KD(i, j)), (j, k, 3)) == \
+        Piecewise(((4 - k)*x*y + x, And(k <= i, i <= 3)), ((4 - k)*x*y, True))
+    assert ds(x*(y + KD(i, j)), (j, k, l)) == Piecewise(
+        ((l - k + 1)*x*y + x, And(k <= i, i <= l)), ((l - k + 1)*x*y, True))
+
+
+def test_deltasummation_mul_x_add_y_twokd():
+    assert ds(x*(y + 2*KD(i, j)), (j, 1, 3)) == \
+        Piecewise((3*x*y + 2*x, And(1 <= i, i <= 3)), (3*x*y, True))
+    assert ds(x*(y + 2*KD(i, j)), (j, 1, 1)) == \
+        Piecewise((x*y + 2*x, Eq(i, 1)), (x*y, True))
+    assert ds(x*(y + 2*KD(i, j)), (j, 2, 2)) == \
+        Piecewise((x*y + 2*x, Eq(i, 2)), (x*y, True))
+    assert ds(x*(y + 2*KD(i, j)), (j, 3, 3)) == \
+        Piecewise((x*y + 2*x, Eq(i, 3)), (x*y, True))
+    assert ds(x*(y + 2*KD(i, j)), (j, 1, k)) == \
+        Piecewise((k*x*y + 2*x, And(1 <= i, i <= k)), (k*x*y, True))
+    assert ds(x*(y + 2*KD(i, j)), (j, k, 3)) == Piecewise(
+        ((4 - k)*x*y + 2*x, And(k <= i, i <= 3)), ((4 - k)*x*y, True))
+    assert ds(x*(y + 2*KD(i, j)), (j, k, l)) == Piecewise(
+        ((l - k + 1)*x*y + 2*x, And(k <= i, i <= l)), ((l - k + 1)*x*y, True))
+
+
+def test_deltasummation_mul_add_x_y_add_y_kd():
+    assert ds((x + y)*(y + KD(i, j)), (j, 1, 3)) == Piecewise(
+        (3*(x + y)*y + x + y, And(1 <= i, i <= 3)), (3*(x + y)*y, True))
+    assert ds((x + y)*(y + KD(i, j)), (j, 1, 1)) == \
+        Piecewise(((x + y)*y + x + y, Eq(i, 1)), ((x + y)*y, True))
+    assert ds((x + y)*(y + KD(i, j)), (j, 2, 2)) == \
+        Piecewise(((x + y)*y + x + y, Eq(i, 2)), ((x + y)*y, True))
+    assert ds((x + y)*(y + KD(i, j)), (j, 3, 3)) == \
+        Piecewise(((x + y)*y + x + y, Eq(i, 3)), ((x + y)*y, True))
+    assert ds((x + y)*(y + KD(i, j)), (j, 1, k)) == Piecewise(
+        (k*(x + y)*y + x + y, And(1 <= i, i <= k)), (k*(x + y)*y, True))
+    assert ds((x + y)*(y + KD(i, j)), (j, k, 3)) == Piecewise(
+        ((4 - k)*(x + y)*y + x + y, And(k <= i, i <= 3)),
+        ((4 - k)*(x + y)*y, True))
+    assert ds((x + y)*(y + KD(i, j)), (j, k, l)) == Piecewise(
+        ((l - k + 1)*(x + y)*y + x + y, And(k <= i, i <= l)),
+        ((l - k + 1)*(x + y)*y, True))
+
+
+def test_deltasummation_mul_add_x_kd_add_y_kd():
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 1, 3)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, And(1 <= i, i <= 3)), (0, True)) +
+        3*(KD(i, k) + x)*y)
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 1, 1)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, Eq(i, 1)), (0, True)) +
+        (KD(i, k) + x)*y)
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 2, 2)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, Eq(i, 2)), (0, True)) +
+        (KD(i, k) + x)*y)
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 3, 3)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, Eq(i, 3)), (0, True)) +
+        (KD(i, k) + x)*y)
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 1, k)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, And(1 <= i, i <= k)), (0, True)) +
+        k*(KD(i, k) + x)*y)
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, k, 3)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, And(k <= i, i <= 3)), (0, True)) +
+        (4 - k)*(KD(i, k) + x)*y)
+    assert ds((x + KD(i, k))*(y + KD(i, j)), (j, k, l)) == piecewise_fold(
+        Piecewise((KD(i, k) + x, And(k <= i, i <= l)), (0, True)) +
+        (l - k + 1)*(KD(i, k) + x)*y)
+
+
+def test_extract_delta():
+    raises(ValueError, lambda: _extract_delta(KD(i, j) + KD(k, l), i))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_gosper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_gosper.py
new file mode 100644
index 0000000000000000000000000000000000000000..77b642a9b7cd55f96840a8e20e517206b6a6f8f0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_gosper.py
@@ -0,0 +1,204 @@
+"""Tests for Gosper's algorithm for hypergeometric summation. """
+
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import (binomial, factorial)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.gamma_functions import gamma
+from sympy.polys.polytools import Poly
+from sympy.simplify.simplify import simplify
+from sympy.concrete.gosper import gosper_normal, gosper_sum, gosper_term
+from sympy.abc import a, b, j, k, m, n, r, x
+
+
+def test_gosper_normal():
+    eq = 4*n + 5, 2*(4*n + 1)*(2*n + 3), n
+    assert gosper_normal(*eq) == \
+        (Poly(Rational(1, 4), n), Poly(n + Rational(3, 2)), Poly(n + Rational(1, 4)))
+    assert gosper_normal(*eq, polys=False) == \
+        (Rational(1, 4), n + Rational(3, 2), n + Rational(1, 4))
+
+
+def test_gosper_term():
+    assert gosper_term((4*k + 1)*factorial(
+        k)/factorial(2*k + 1), k) == (-k - S.Half)/(k + Rational(1, 4))
+
+
+def test_gosper_sum():
+    assert gosper_sum(1, (k, 0, n)) == 1 + n
+    assert gosper_sum(k, (k, 0, n)) == n*(1 + n)/2
+    assert gosper_sum(k**2, (k, 0, n)) == n*(1 + n)*(1 + 2*n)/6
+    assert gosper_sum(k**3, (k, 0, n)) == n**2*(1 + n)**2/4
+
+    assert gosper_sum(2**k, (k, 0, n)) == 2*2**n - 1
+
+    assert gosper_sum(factorial(k), (k, 0, n)) is None
+    assert gosper_sum(binomial(n, k), (k, 0, n)) is None
+
+    assert gosper_sum(factorial(k)/k**2, (k, 0, n)) is None
+    assert gosper_sum((k - 3)*factorial(k), (k, 0, n)) is None
+
+    assert gosper_sum(k*factorial(k), k) == factorial(k)
+    assert gosper_sum(
+        k*factorial(k), (k, 0, n)) == n*factorial(n) + factorial(n) - 1
+
+    assert gosper_sum((-1)**k*binomial(n, k), (k, 0, n)) == 0
+    assert gosper_sum((
+        -1)**k*binomial(n, k), (k, 0, m)) == -(-1)**m*(m - n)*binomial(n, m)/n
+
+    assert gosper_sum((4*k + 1)*factorial(k)/factorial(2*k + 1), (k, 0, n)) == \
+        (2*factorial(2*n + 1) - factorial(n))/factorial(2*n + 1)
+
+    # issue 6033:
+    assert gosper_sum(
+        n*(n + a + b)*a**n*b**n/(factorial(n + a)*factorial(n + b)), \
+        (n, 0, m)).simplify() == -exp(m*log(a) + m*log(b))*gamma(a + 1) \
+        *gamma(b + 1)/(gamma(a)*gamma(b)*gamma(a + m + 1)*gamma(b + m + 1)) \
+        + 1/(gamma(a)*gamma(b))
+
+
+def test_gosper_sum_indefinite():
+    assert gosper_sum(k, k) == k*(k - 1)/2
+    assert gosper_sum(k**2, k) == k*(k - 1)*(2*k - 1)/6
+
+    assert gosper_sum(1/(k*(k + 1)), k) == -1/k
+    assert gosper_sum(-(27*k**4 + 158*k**3 + 430*k**2 + 678*k + 445)*gamma(2*k
+                      + 4)/(3*(3*k + 7)*gamma(3*k + 6)), k) == \
+        (3*k + 5)*(k**2 + 2*k + 5)*gamma(2*k + 4)/gamma(3*k + 6)
+
+
+def test_gosper_sum_parametric():
+    assert gosper_sum(binomial(S.Half, m - j + 1)*binomial(S.Half, m + j), (j, 1, n)) == \
+        n*(1 + m - n)*(-1 + 2*m + 2*n)*binomial(S.Half, 1 + m - n)* \
+        binomial(S.Half, m + n)/(m*(1 + 2*m))
+
+
+def test_gosper_sum_algebraic():
+    assert gosper_sum(
+        n**2 + sqrt(2), (n, 0, m)) == (m + 1)*(2*m**2 + m + 6*sqrt(2))/6
+
+
+def test_gosper_sum_iterated():
+    f1 = binomial(2*k, k)/4**k
+    f2 = (1 + 2*n)*binomial(2*n, n)/4**n
+    f3 = (1 + 2*n)*(3 + 2*n)*binomial(2*n, n)/(3*4**n)
+    f4 = (1 + 2*n)*(3 + 2*n)*(5 + 2*n)*binomial(2*n, n)/(15*4**n)
+    f5 = (1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*binomial(2*n, n)/(105*4**n)
+
+    assert gosper_sum(f1, (k, 0, n)) == f2
+    assert gosper_sum(f2, (n, 0, n)) == f3
+    assert gosper_sum(f3, (n, 0, n)) == f4
+    assert gosper_sum(f4, (n, 0, n)) == f5
+
+# the AeqB tests test expressions given in
+# www.math.upenn.edu/~wilf/AeqB.pdf
+
+
+def test_gosper_sum_AeqB_part1():
+    f1a = n**4
+    f1b = n**3*2**n
+    f1c = 1/(n**2 + sqrt(5)*n - 1)
+    f1d = n**4*4**n/binomial(2*n, n)
+    f1e = factorial(3*n)/(factorial(n)*factorial(n + 1)*factorial(n + 2)*27**n)
+    f1f = binomial(2*n, n)**2/((n + 1)*4**(2*n))
+    f1g = (4*n - 1)*binomial(2*n, n)**2/((2*n - 1)**2*4**(2*n))
+    f1h = n*factorial(n - S.Half)**2/factorial(n + 1)**2
+
+    g1a = m*(m + 1)*(2*m + 1)*(3*m**2 + 3*m - 1)/30
+    g1b = 26 + 2**(m + 1)*(m**3 - 3*m**2 + 9*m - 13)
+    g1c = (m + 1)*(m*(m**2 - 7*m + 3)*sqrt(5) - (
+        3*m**3 - 7*m**2 + 19*m - 6))/(2*m**3*sqrt(5) + m**4 + 5*m**2 - 1)/6
+    g1d = Rational(-2, 231) + 2*4**m*(m + 1)*(63*m**4 + 112*m**3 + 18*m**2 -
+             22*m + 3)/(693*binomial(2*m, m))
+    g1e = Rational(-9, 2) + (81*m**2 + 261*m + 200)*factorial(
+        3*m + 2)/(40*27**m*factorial(m)*factorial(m + 1)*factorial(m + 2))
+    g1f = (2*m + 1)**2*binomial(2*m, m)**2/(4**(2*m)*(m + 1))
+    g1g = -binomial(2*m, m)**2/4**(2*m)
+    g1h = 4*pi -(2*m + 1)**2*(3*m + 4)*factorial(m - S.Half)**2/factorial(m + 1)**2
+
+    g = gosper_sum(f1a, (n, 0, m))
+    assert g is not None and simplify(g - g1a) == 0
+    g = gosper_sum(f1b, (n, 0, m))
+    assert g is not None and simplify(g - g1b) == 0
+    g = gosper_sum(f1c, (n, 0, m))
+    assert g is not None and simplify(g - g1c) == 0
+    g = gosper_sum(f1d, (n, 0, m))
+    assert g is not None and simplify(g - g1d) == 0
+    g = gosper_sum(f1e, (n, 0, m))
+    assert g is not None and simplify(g - g1e) == 0
+    g = gosper_sum(f1f, (n, 0, m))
+    assert g is not None and simplify(g - g1f) == 0
+    g = gosper_sum(f1g, (n, 0, m))
+    assert g is not None and simplify(g - g1g) == 0
+    g = gosper_sum(f1h, (n, 0, m))
+    # need to call rewrite(gamma) here because we have terms involving
+    # factorial(1/2)
+    assert g is not None and simplify(g - g1h).rewrite(gamma) == 0
+
+
+def test_gosper_sum_AeqB_part2():
+    f2a = n**2*a**n
+    f2b = (n - r/2)*binomial(r, n)
+    f2c = factorial(n - 1)**2/(factorial(n - x)*factorial(n + x))
+
+    g2a = -a*(a + 1)/(a - 1)**3 + a**(
+        m + 1)*(a**2*m**2 - 2*a*m**2 + m**2 - 2*a*m + 2*m + a + 1)/(a - 1)**3
+    g2b = (m - r)*binomial(r, m)/2
+    ff = factorial(1 - x)*factorial(1 + x)
+    g2c = 1/ff*(
+        1 - 1/x**2) + factorial(m)**2/(x**2*factorial(m - x)*factorial(m + x))
+
+    g = gosper_sum(f2a, (n, 0, m))
+    assert g is not None and simplify(g - g2a) == 0
+    g = gosper_sum(f2b, (n, 0, m))
+    assert g is not None and simplify(g - g2b) == 0
+    g = gosper_sum(f2c, (n, 1, m))
+    assert g is not None and simplify(g - g2c) == 0
+
+
+def test_gosper_nan():
+    a = Symbol('a', positive=True)
+    b = Symbol('b', positive=True)
+    n = Symbol('n', integer=True)
+    m = Symbol('m', integer=True)
+    f2d = n*(n + a + b)*a**n*b**n/(factorial(n + a)*factorial(n + b))
+    g2d = 1/(factorial(a - 1)*factorial(
+        b - 1)) - a**(m + 1)*b**(m + 1)/(factorial(a + m)*factorial(b + m))
+    g = gosper_sum(f2d, (n, 0, m))
+    assert simplify(g - g2d) == 0
+
+
+def test_gosper_sum_AeqB_part3():
+    f3a = 1/n**4
+    f3b = (6*n + 3)/(4*n**4 + 8*n**3 + 8*n**2 + 4*n + 3)
+    f3c = 2**n*(n**2 - 2*n - 1)/(n**2*(n + 1)**2)
+    f3d = n**2*4**n/((n + 1)*(n + 2))
+    f3e = 2**n/(n + 1)
+    f3f = 4*(n - 1)*(n**2 - 2*n - 1)/(n**2*(n + 1)**2*(n - 2)**2*(n - 3)**2)
+    f3g = (n**4 - 14*n**2 - 24*n - 9)*2**n/(n**2*(n + 1)**2*(n + 2)**2*
+           (n + 3)**2)
+
+    # g3a -> no closed form
+    g3b = m*(m + 2)/(2*m**2 + 4*m + 3)
+    g3c = 2**m/m**2 - 2
+    g3d = Rational(2, 3) + 4**(m + 1)*(m - 1)/(m + 2)/3
+    # g3e -> no closed form
+    g3f = -(Rational(-1, 16) + 1/((m - 2)**2*(m + 1)**2))  # the AeqB key is wrong
+    g3g = Rational(-2, 9) + 2**(m + 1)/((m + 1)**2*(m + 3)**2)
+
+    g = gosper_sum(f3a, (n, 1, m))
+    assert g is None
+    g = gosper_sum(f3b, (n, 1, m))
+    assert g is not None and simplify(g - g3b) == 0
+    g = gosper_sum(f3c, (n, 1, m - 1))
+    assert g is not None and simplify(g - g3c) == 0
+    g = gosper_sum(f3d, (n, 1, m))
+    assert g is not None and simplify(g - g3d) == 0
+    g = gosper_sum(f3e, (n, 0, m - 1))
+    assert g is None
+    g = gosper_sum(f3f, (n, 4, m))
+    assert g is not None and simplify(g - g3f) == 0
+    g = gosper_sum(f3g, (n, 1, m))
+    assert g is not None and simplify(g - g3g) == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_guess.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_guess.py
new file mode 100644
index 0000000000000000000000000000000000000000..5ac5d02b89ad62a70a29bd450b71b284b6aea76d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_guess.py
@@ -0,0 +1,82 @@
+from sympy.concrete.guess import (
+            find_simple_recurrence_vector,
+            find_simple_recurrence,
+            rationalize,
+            guess_generating_function_rational,
+            guess_generating_function,
+            guess
+        )
+from sympy.concrete.products import Product
+from sympy.core.function import Function
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import (RisingFactorial, factorial)
+from sympy.functions.combinatorial.numbers import fibonacci
+from sympy.functions.elementary.exponential import exp
+
+
+def test_find_simple_recurrence_vector():
+    assert find_simple_recurrence_vector(
+            [fibonacci(k) for k in range(12)]) == [1, -1, -1]
+
+
+def test_find_simple_recurrence():
+    a = Function('a')
+    n = Symbol('n')
+    assert find_simple_recurrence([fibonacci(k) for k in range(12)]) == (
+        -a(n) - a(n + 1) + a(n + 2))
+
+    f = Function('a')
+    i = Symbol('n')
+    a = [1, 1, 1]
+    for k in range(15): a.append(5*a[-1]-3*a[-2]+8*a[-3])
+    assert find_simple_recurrence(a, A=f, N=i) == (
+        -8*f(i) + 3*f(i + 1) - 5*f(i + 2) + f(i + 3))
+    assert find_simple_recurrence([0, 2, 15, 74, 12, 3, 0,
+                                    1, 2, 85, 4, 5, 63]) == 0
+
+
+def test_rationalize():
+    from mpmath import cos, pi, mpf
+    assert rationalize(cos(pi/3)) == S.Half
+    assert rationalize(mpf("0.333333333333333")) == Rational(1, 3)
+    assert rationalize(mpf("-0.333333333333333")) == Rational(-1, 3)
+    assert rationalize(pi, maxcoeff = 250) == Rational(355, 113)
+
+
+def test_guess_generating_function_rational():
+    x = Symbol('x')
+    assert guess_generating_function_rational([fibonacci(k)
+        for k in range(5, 15)]) == ((3*x + 5)/(-x**2 - x + 1))
+
+
+def test_guess_generating_function():
+    x = Symbol('x')
+    assert guess_generating_function([fibonacci(k)
+        for k in range(5, 15)])['ogf'] == ((3*x + 5)/(-x**2 - x + 1))
+    assert guess_generating_function(
+        [1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf'] == (
+        (1/(x**4 + 2*x**2 - 4*x + 1))**S.Half)
+    assert guess_generating_function(sympify(
+       "[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]")
+       )['ogf'] == (x + Rational(3, 2))/(11*x**2 - 3*x + 1)
+    assert guess_generating_function([factorial(k) for k in range(12)],
+       types=['egf'])['egf'] == 1/(-x + 1)
+    assert guess_generating_function([k+1 for k in range(12)],
+       types=['egf']) == {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)}
+
+
+def test_guess():
+    i0, i1 = symbols('i0 i1')
+    assert guess([1, 2, 6, 24, 120], evaluate=False) == [Product(i1 + 1, (i1, 1, i0 - 1))]
+    assert guess([1, 2, 6, 24, 120]) == [RisingFactorial(2, i0 - 1)]
+    assert guess([1, 2, 7, 42, 429, 7436, 218348, 10850216], niter=4) == [
+        2**(i0 - 1)*(Rational(27, 16))**(i0**2/2 - 3*i0/2 +
+        1)*Product(RisingFactorial(Rational(5, 3), i1 - 1)*RisingFactorial(Rational(7, 3), i1
+        - 1)/(RisingFactorial(Rational(3, 2), i1 - 1)*RisingFactorial(Rational(5, 2), i1 -
+        1)), (i1, 1, i0 - 1))]
+    assert guess([1, 0, 2]) == []
+    x, y = symbols('x y')
+    assert guess([1, 2, 6, 24, 120], variables=[x, y]) == [RisingFactorial(2, x - 1)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_products.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_products.py
new file mode 100644
index 0000000000000000000000000000000000000000..9be053a7040014c6ed38c1279a609fcb2426258e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_products.py
@@ -0,0 +1,410 @@
+from sympy.concrete.products import (Product, product)
+from sympy.concrete.summations import Sum
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.numbers import (Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.combinatorial.factorials import (rf, factorial)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.simplify.combsimp import combsimp
+from sympy.simplify.simplify import simplify
+from sympy.testing.pytest import raises
+
+a, k, n, m, x = symbols('a,k,n,m,x', integer=True)
+f = Function('f')
+
+
+def test_karr_convention():
+    # Test the Karr product convention that we want to hold.
+    # See his paper "Summation in Finite Terms" for a detailed
+    # reasoning why we really want exactly this definition.
+    # The convention is described for sums on page 309 and
+    # essentially in section 1.4, definition 3. For products
+    # we can find in analogy:
+    #
+    # \prod_{m <= i < n} f(i) 'has the obvious meaning'      for m < n
+    # \prod_{m <= i < n} f(i) = 0                            for m = n
+    # \prod_{m <= i < n} f(i) = 1 / \prod_{n <= i < m} f(i)  for m > n
+    #
+    # It is important to note that he defines all products with
+    # the upper limit being *exclusive*.
+    # In contrast, SymPy and the usual mathematical notation has:
+    #
+    # prod_{i = a}^b f(i) = f(a) * f(a+1) * ... * f(b-1) * f(b)
+    #
+    # with the upper limit *inclusive*. So translating between
+    # the two we find that:
+    #
+    # \prod_{m <= i < n} f(i) = \prod_{i = m}^{n-1} f(i)
+    #
+    # where we intentionally used two different ways to typeset the
+    # products and its limits.
+
+    i = Symbol("i", integer=True)
+    k = Symbol("k", integer=True)
+    j = Symbol("j", integer=True, positive=True)
+
+    # A simple example with a concrete factors and symbolic limits.
+
+    # The normal product: m = k and n = k + j and therefore m < n:
+    m = k
+    n = k + j
+
+    a = m
+    b = n - 1
+    S1 = Product(i**2, (i, a, b)).doit()
+
+    # The reversed product: m = k + j and n = k and therefore m > n:
+    m = k + j
+    n = k
+
+    a = m
+    b = n - 1
+    S2 = Product(i**2, (i, a, b)).doit()
+
+    assert S1 * S2 == 1
+
+    # Test the empty product: m = k and n = k and therefore m = n:
+    m = k
+    n = k
+
+    a = m
+    b = n - 1
+    Sz = Product(i**2, (i, a, b)).doit()
+
+    assert Sz == 1
+
+    # Another example this time with an unspecified factor and
+    # numeric limits. (We can not do both tests in the same example.)
+    f = Function("f")
+
+    # The normal product with m < n:
+    m = 2
+    n = 11
+
+    a = m
+    b = n - 1
+    S1 = Product(f(i), (i, a, b)).doit()
+
+    # The reversed product with m > n:
+    m = 11
+    n = 2
+
+    a = m
+    b = n - 1
+    S2 = Product(f(i), (i, a, b)).doit()
+
+    assert simplify(S1 * S2) == 1
+
+    # Test the empty product with m = n:
+    m = 5
+    n = 5
+
+    a = m
+    b = n - 1
+    Sz = Product(f(i), (i, a, b)).doit()
+
+    assert Sz == 1
+
+
+def test_karr_proposition_2a():
+    # Test Karr, page 309, proposition 2, part a
+    i, u, v = symbols('i u v', integer=True)
+
+    def test_the_product(m, n):
+        # g
+        g = i**3 + 2*i**2 - 3*i
+        # f = Delta g
+        f = simplify(g.subs(i, i+1) / g)
+        # The product
+        a = m
+        b = n - 1
+        P = Product(f, (i, a, b)).doit()
+        # Test if Product_{m <= i < n} f(i) = g(n) / g(m)
+        assert combsimp(P / (g.subs(i, n) / g.subs(i, m))) == 1
+
+    # m < n
+    test_the_product(u, u + v)
+    # m = n
+    test_the_product(u, u)
+    # m > n
+    test_the_product(u + v, u)
+
+
+def test_karr_proposition_2b():
+    # Test Karr, page 309, proposition 2, part b
+    i, u, v, w = symbols('i u v w', integer=True)
+
+    def test_the_product(l, n, m):
+        # Productmand
+        s = i**3
+        # First product
+        a = l
+        b = n - 1
+        S1 = Product(s, (i, a, b)).doit()
+        # Second product
+        a = l
+        b = m - 1
+        S2 = Product(s, (i, a, b)).doit()
+        # Third product
+        a = m
+        b = n - 1
+        S3 = Product(s, (i, a, b)).doit()
+        # Test if S1 = S2 * S3 as required
+        assert combsimp(S1 / (S2 * S3)) == 1
+
+    # l < m < n
+    test_the_product(u, u + v, u + v + w)
+    # l < m = n
+    test_the_product(u, u + v, u + v)
+    # l < m > n
+    test_the_product(u, u + v + w, v)
+    # l = m < n
+    test_the_product(u, u, u + v)
+    # l = m = n
+    test_the_product(u, u, u)
+    # l = m > n
+    test_the_product(u + v, u + v, u)
+    # l > m < n
+    test_the_product(u + v, u, u + w)
+    # l > m = n
+    test_the_product(u + v, u, u)
+    # l > m > n
+    test_the_product(u + v + w, u + v, u)
+
+
+def test_simple_products():
+    assert product(2, (k, a, n)) == 2**(n - a + 1)
+    assert product(k, (k, 1, n)) == factorial(n)
+    assert product(k**3, (k, 1, n)) == factorial(n)**3
+
+    assert product(k + 1, (k, 0, n - 1)) == factorial(n)
+    assert product(k + 1, (k, a, n - 1)) == rf(1 + a, n - a)
+
+    assert product(cos(k), (k, 0, 5)) == cos(1)*cos(2)*cos(3)*cos(4)*cos(5)
+    assert product(cos(k), (k, 3, 5)) == cos(3)*cos(4)*cos(5)
+    assert product(cos(k), (k, 1, Rational(5, 2))) != cos(1)*cos(2)
+
+    assert isinstance(product(k**k, (k, 1, n)), Product)
+
+    assert Product(x**k, (k, 1, n)).variables == [k]
+
+    raises(ValueError, lambda: Product(n))
+    raises(ValueError, lambda: Product(n, k))
+    raises(ValueError, lambda: Product(n, k, 1))
+    raises(ValueError, lambda: Product(n, k, 1, 10))
+    raises(ValueError, lambda: Product(n, (k, 1)))
+
+    assert product(1, (n, 1, oo)) == 1  # issue 8301
+    assert product(2, (n, 1, oo)) is oo
+    assert product(-1, (n, 1, oo)).func is Product
+
+
+def test_multiple_products():
+    assert product(x, (n, 1, k), (k, 1, m)) == x**(m**2/2 + m/2)
+    assert product(f(n), (
+        n, 1, m), (m, 1, k)) == Product(f(n), (n, 1, m), (m, 1, k)).doit()
+    assert Product(f(n), (m, 1, k), (n, 1, k)).doit() == \
+        Product(Product(f(n), (m, 1, k)), (n, 1, k)).doit() == \
+        product(f(n), (m, 1, k), (n, 1, k)) == \
+        product(product(f(n), (m, 1, k)), (n, 1, k)) == \
+        Product(f(n)**k, (n, 1, k))
+    assert Product(
+        x, (x, 1, k), (k, 1, n)).doit() == Product(factorial(k), (k, 1, n))
+
+    assert Product(x**k, (n, 1, k), (k, 1, m)).variables == [n, k]
+
+
+def test_rational_products():
+    assert product(1 + 1/k, (k, 1, n)) == rf(2, n)/factorial(n)
+
+
+def test_special_products():
+    # Wallis product
+    assert product((4*k)**2 / (4*k**2 - 1), (k, 1, n)) == \
+        4**n*factorial(n)**2/rf(S.Half, n)/rf(Rational(3, 2), n)
+
+    # Euler's product formula for sin
+    assert product(1 + a/k**2, (k, 1, n)) == \
+        rf(1 - sqrt(-a), n)*rf(1 + sqrt(-a), n)/factorial(n)**2
+
+
+def test__eval_product():
+    from sympy.abc import i, n
+    # issue 4809
+    a = Function('a')
+    assert product(2*a(i), (i, 1, n)) == 2**n * Product(a(i), (i, 1, n))
+    # issue 4810
+    assert product(2**i, (i, 1, n)) == 2**(n*(n + 1)/2)
+    k, m = symbols('k m', integer=True)
+    assert product(2**i, (i, k, m)) == 2**(-k**2/2 + k/2 + m**2/2 + m/2)
+    n = Symbol('n', negative=True, integer=True)
+    p = Symbol('p', positive=True, integer=True)
+    assert product(2**i, (i, n, p)) == 2**(-n**2/2 + n/2 + p**2/2 + p/2)
+    assert product(2**i, (i, p, n)) == 2**(n**2/2 + n/2 - p**2/2 + p/2)
+
+
+def test_product_pow():
+    # issue 4817
+    assert product(2**f(k), (k, 1, n)) == 2**Sum(f(k), (k, 1, n))
+    assert product(2**(2*f(k)), (k, 1, n)) == 2**Sum(2*f(k), (k, 1, n))
+
+
+def test_infinite_product():
+    # issue 5737
+    assert isinstance(Product(2**(1/factorial(n)), (n, 0, oo)), Product)
+
+
+def test_conjugate_transpose():
+    p = Product(x**k, (k, 1, 3))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+    A, B = symbols("A B", commutative=False)
+    p = Product(A*B**k, (k, 1, 3))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+    p = Product(B**k*A, (k, 1, 3))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+
+def test_simplify_prod():
+    y, t, b, c, v, d = symbols('y, t, b, c, v, d', integer = True)
+
+    _simplify = lambda e: simplify(e, doit=False)
+    assert _simplify(Product(x*y, (x, n, m), (y, a, k)) * \
+        Product(y, (x, n, m), (y, a, k))) == \
+            Product(x*y**2, (x, n, m), (y, a, k))
+    assert _simplify(3 * y* Product(x, (x, n, m)) * Product(x, (x, m + 1, a))) \
+        == 3 * y * Product(x, (x, n, a))
+    assert _simplify(Product(x, (x, k + 1, a)) * Product(x, (x, n, k))) == \
+        Product(x, (x, n, a))
+    assert _simplify(Product(x, (x, k + 1, a)) * Product(x + 1, (x, n, k))) == \
+        Product(x, (x, k + 1, a)) * Product(x + 1, (x, n, k))
+    assert _simplify(Product(x, (t, a, b)) * Product(y, (t, a, b)) * \
+        Product(x, (t, b+1, c))) == Product(x*y, (t, a, b)) * \
+            Product(x, (t, b+1, c))
+    assert _simplify(Product(x, (t, a, b)) * Product(x, (t, b+1, c)) * \
+        Product(y, (t, a, b))) == Product(x*y, (t, a, b)) * \
+            Product(x, (t, b+1, c))
+    assert _simplify(Product(sin(t)**2 + cos(t)**2 + 1, (t, a, b))) == \
+        Product(2, (t, a, b))
+    assert _simplify(Product(sin(t)**2 + cos(t)**2 - 1, (t, a, b))) == \
+           Product(0, (t, a, b))
+    assert _simplify(Product(v*Product(sin(t)**2 + cos(t)**2, (t, a, b)),
+                             (v, c, d))) == Product(v*Product(1, (t, a, b)), (v, c, d))
+
+
+def test_change_index():
+    b, y, c, d, z = symbols('b, y, c, d, z', integer = True)
+
+    assert Product(x, (x, a, b)).change_index(x, x + 1, y) == \
+        Product(y - 1, (y, a + 1, b + 1))
+    assert Product(x**2, (x, a, b)).change_index(x, x - 1) == \
+        Product((x + 1)**2, (x, a - 1, b - 1))
+    assert Product(x**2, (x, a, b)).change_index(x, -x, y) == \
+        Product((-y)**2, (y, -b, -a))
+    assert Product(x, (x, a, b)).change_index(x, -x - 1) == \
+        Product(-x - 1, (x, - b - 1, -a - 1))
+    assert Product(x*y, (x, a, b), (y, c, d)).change_index(x, x - 1, z) == \
+        Product((z + 1)*y, (z, a - 1, b - 1), (y, c, d))
+
+
+def test_reorder():
+    b, y, c, d, z = symbols('b, y, c, d, z', integer = True)
+
+    assert Product(x*y, (x, a, b), (y, c, d)).reorder((0, 1)) == \
+        Product(x*y, (y, c, d), (x, a, b))
+    assert Product(x, (x, a, b), (x, c, d)).reorder((0, 1)) == \
+        Product(x, (x, c, d), (x, a, b))
+    assert Product(x*y + z, (x, a, b), (z, m, n), (y, c, d)).reorder(\
+        (2, 0), (0, 1)) == Product(x*y + z, (z, m, n), (y, c, d), (x, a, b))
+    assert Product(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\
+        (0, 1), (1, 2), (0, 2)) == \
+        Product(x*y*z, (x, a, b), (z, m, n), (y, c, d))
+    assert Product(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\
+        (x, y), (y, z), (x, z)) == \
+        Product(x*y*z, (x, a, b), (z, m, n), (y, c, d))
+    assert Product(x*y, (x, a, b), (y, c, d)).reorder((x, 1)) == \
+        Product(x*y, (y, c, d), (x, a, b))
+    assert Product(x*y, (x, a, b), (y, c, d)).reorder((y, x)) == \
+        Product(x*y, (y, c, d), (x, a, b))
+
+
+def test_Product_is_convergent():
+    assert Product(1/n**2, (n, 1, oo)).is_convergent() is S.false
+    assert Product(exp(1/n**2), (n, 1, oo)).is_convergent() is S.true
+    assert Product(1/n, (n, 1, oo)).is_convergent() is S.false
+    assert Product(1 + 1/n, (n, 1, oo)).is_convergent() is S.false
+    assert Product(1 + 1/n**2, (n, 1, oo)).is_convergent() is S.true
+
+
+def test_reverse_order():
+    x, y, a, b, c, d= symbols('x, y, a, b, c, d', integer = True)
+
+    assert Product(x, (x, 0, 3)).reverse_order(0) == Product(1/x, (x, 4, -1))
+    assert Product(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(0, 1) == \
+           Product(x*y, (x, 6, 0), (y, 7, -1))
+    assert Product(x, (x, 1, 2)).reverse_order(0) == Product(1/x, (x, 3, 0))
+    assert Product(x, (x, 1, 3)).reverse_order(0) == Product(1/x, (x, 4, 0))
+    assert Product(x, (x, 1, a)).reverse_order(0) == Product(1/x, (x, a + 1, 0))
+    assert Product(x, (x, a, 5)).reverse_order(0) == Product(1/x, (x, 6, a - 1))
+    assert Product(x, (x, a + 1, a + 5)).reverse_order(0) == \
+           Product(1/x, (x, a + 6, a))
+    assert Product(x, (x, a + 1, a + 2)).reverse_order(0) == \
+           Product(1/x, (x, a + 3, a))
+    assert Product(x, (x, a + 1, a + 1)).reverse_order(0) == \
+           Product(1/x, (x, a + 2, a))
+    assert Product(x, (x, a, b)).reverse_order(0) == Product(1/x, (x, b + 1, a - 1))
+    assert Product(x, (x, a, b)).reverse_order(x) == Product(1/x, (x, b + 1, a - 1))
+    assert Product(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1) == \
+           Product(x*y, (x, b + 1, a - 1), (y, 6, 1))
+    assert Product(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x) == \
+           Product(x*y, (x, b + 1, a - 1), (y, 6, 1))
+
+
+def test_issue_9983():
+    n = Symbol('n', integer=True, positive=True)
+    p = Product(1 + 1/n**Rational(2, 3), (n, 1, oo))
+    assert p.is_convergent() is S.false
+    assert product(1 + 1/n**Rational(2, 3), (n, 1, oo)) == p.doit()
+
+
+def test_issue_13546():
+    n = Symbol('n')
+    k = Symbol('k')
+    p = Product(n + 1 / 2**k, (k, 0, n-1)).doit()
+    assert p.subs(n, 2).doit() == Rational(15, 2)
+
+
+def test_issue_14036():
+    a, n = symbols('a n')
+    assert product(1 - a**2 / (n*pi)**2, [n, 1, oo]) != 0
+
+
+def test_rewrite_Sum():
+    assert Product(1 - S.Half**2/k**2, (k, 1, oo)).rewrite(Sum) == \
+        exp(Sum(log(1 - 1/(4*k**2)), (k, 1, oo)))
+
+
+def test_KroneckerDelta_Product():
+    y = Symbol('y')
+    assert Product(x*KroneckerDelta(x, y), (x, 0, 1)).doit() == 0
+
+
+def test_issue_20848():
+    _i = Dummy('i')
+    t, y, z = symbols('t y z')
+    assert diff(Product(x, (y, 1, z)), x).as_dummy() == Sum(Product(x, (y, 1, _i - 1))*Product(x, (y, _i + 1, z)), (_i, 1, z)).as_dummy()
+    assert diff(Product(x, (y, 1, z)), x).doit() == x**(z - 1)*z
+    assert diff(Product(x, (y, x, z)), x) == Derivative(Product(x, (y, x, z)), x)
+    assert diff(Product(t, (x, 1, z)), x) == S(0)
+    assert Product(sin(n*x), (n, -1, 1)).diff(x).doit() == S(0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_sums_products.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_sums_products.py
new file mode 100644
index 0000000000000000000000000000000000000000..b190afe0bd403819d3525453879d7d5d39e20a56
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/concrete/tests/test_sums_products.py
@@ -0,0 +1,1676 @@
+from math import prod
+
+from sympy.concrete.expr_with_intlimits import ReorderError
+from sympy.concrete.products import (Product, product)
+from sympy.concrete.summations import (Sum, summation, telescopic,
+     eval_sum_residue, _dummy_with_inherited_properties_concrete)
+from sympy.core.function import (Derivative, Function)
+from sympy.core import (Catalan, EulerGamma)
+from sympy.core.facts import InconsistentAssumptions
+from sympy.core.mod import Mod
+from sympy.core.numbers import (E, I, Rational, nan, oo, pi)
+from sympy.core.relational import Eq, Ne
+from sympy.core.numbers import Float
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import (rf, binomial, factorial)
+from sympy.functions.combinatorial.numbers import harmonic
+from sympy.functions.elementary.complexes import Abs, re
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (sinh, tanh)
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (cos, sin, atan)
+from sympy.functions.special.gamma_functions import (gamma, lowergamma)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.functions.special.zeta_functions import zeta
+from sympy.integrals.integrals import Integral
+from sympy.logic.boolalg import And, Or
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.special import Identity
+from sympy.matrices import (Matrix, SparseMatrix,
+    ImmutableDenseMatrix, ImmutableSparseMatrix, diag)
+from sympy.sets.contains import Contains
+from sympy.sets.fancysets import Range
+from sympy.sets.sets import Interval
+from sympy.simplify.combsimp import combsimp
+from sympy.simplify.simplify import simplify
+from sympy.tensor.indexed import (Idx, Indexed, IndexedBase)
+from sympy.testing.pytest import XFAIL, raises, slow
+from sympy.abc import a, b, c, d, k, m, x, y, z
+
+n = Symbol('n', integer=True)
+f, g = symbols('f g', cls=Function)
+
+def test_karr_convention():
+    # Test the Karr summation convention that we want to hold.
+    # See his paper "Summation in Finite Terms" for a detailed
+    # reasoning why we really want exactly this definition.
+    # The convention is described on page 309 and essentially
+    # in section 1.4, definition 3:
+    #
+    # \sum_{m <= i < n} f(i) 'has the obvious meaning'   for m < n
+    # \sum_{m <= i < n} f(i) = 0                         for m = n
+    # \sum_{m <= i < n} f(i) = - \sum_{n <= i < m} f(i)  for m > n
+    #
+    # It is important to note that he defines all sums with
+    # the upper limit being *exclusive*.
+    # In contrast, SymPy and the usual mathematical notation has:
+    #
+    # sum_{i = a}^b f(i) = f(a) + f(a+1) + ... + f(b-1) + f(b)
+    #
+    # with the upper limit *inclusive*. So translating between
+    # the two we find that:
+    #
+    # \sum_{m <= i < n} f(i) = \sum_{i = m}^{n-1} f(i)
+    #
+    # where we intentionally used two different ways to typeset the
+    # sum and its limits.
+
+    i = Symbol("i", integer=True)
+    k = Symbol("k", integer=True)
+    j = Symbol("j", integer=True)
+
+    # A simple example with a concrete summand and symbolic limits.
+
+    # The normal sum: m = k and n = k + j and therefore m < n:
+    m = k
+    n = k + j
+
+    a = m
+    b = n - 1
+    S1 = Sum(i**2, (i, a, b)).doit()
+
+    # The reversed sum: m = k + j and n = k and therefore m > n:
+    m = k + j
+    n = k
+
+    a = m
+    b = n - 1
+    S2 = Sum(i**2, (i, a, b)).doit()
+
+    assert simplify(S1 + S2) == 0
+
+    # Test the empty sum: m = k and n = k and therefore m = n:
+    m = k
+    n = k
+
+    a = m
+    b = n - 1
+    Sz = Sum(i**2, (i, a, b)).doit()
+
+    assert Sz == 0
+
+    # Another example this time with an unspecified summand and
+    # numeric limits. (We can not do both tests in the same example.)
+
+    # The normal sum with m < n:
+    m = 2
+    n = 11
+
+    a = m
+    b = n - 1
+    S1 = Sum(f(i), (i, a, b)).doit()
+
+    # The reversed sum with m > n:
+    m = 11
+    n = 2
+
+    a = m
+    b = n - 1
+    S2 = Sum(f(i), (i, a, b)).doit()
+
+    assert simplify(S1 + S2) == 0
+
+    # Test the empty sum with m = n:
+    m = 5
+    n = 5
+
+    a = m
+    b = n - 1
+    Sz = Sum(f(i), (i, a, b)).doit()
+
+    assert Sz == 0
+
+    e = Piecewise((exp(-i), Mod(i, 2) > 0), (0, True))
+    s = Sum(e, (i, 0, 11))
+    assert s.n(3) == s.doit().n(3)
+
+    # issue #27893
+    n = Symbol('n', integer=True)
+    assert Sum(1/(x**2 + 1), (x, oo, 0)).doit(deep=False) == Rational(-1, 2) + pi / (2 * tanh(pi))
+    assert Sum(c**x/factorial(x), (x, oo, 0)).doit(deep=False).simplify() == exp(c) - 1 # exponential series
+    assert Sum((-1)**x/x, (x, oo,0)).doit() == -log(2) # alternating harmnic series
+    assert Sum((1/2)**x,(x, oo, -1)).doit() == S(2) # geometric series
+    assert Sum(1/x, (x, oo, 0)).doit() == oo # harmonic series, divergent
+    assert Sum((-1)**x/(2*x+1), (x, oo, -1)).doit() == pi/4 # leibniz series
+    assert Sum((((-1)**x) * c**(2*x+1)) / factorial(2*x+1), (x, oo, -1)).doit() == sin(c) # sinusoidal series
+    assert Sum((((-1)**x) * c**(2*x+1)) / (2*x+1), (x, 0, oo)).doit() \
+        == Piecewise((atan(c), Ne(c**2, -1) & (Abs(c**2) <= 1)), \
+                     (Sum((-1)**x*c**(2*x + 1)/(2*x + 1), (x, 0, oo)), True)) # arctangent series
+    assert Sum(binomial(n, x) * c**x, (x, 0, oo)).doit() \
+        == Piecewise(((c + 1)**n, \
+                     ((n <= -1) & (Abs(c) < 1)) \
+                        | ((n > 0) & (Abs(c) <= 1)) \
+                        | ((n <= 0) & (n > -1) & Ne(c, -1) & (Abs(c) <= 1))), \
+                     (Sum(c**x*binomial(n, x), (x, 0, oo)), True)) # binomial series
+    assert Sum(1/x**n, (x, oo, 0)).doit() \
+        == Piecewise((zeta(n), n > 1), (Sum(x**(-n), (x, oo, 0)), True)) # Euler's zeta function
+
+def test_karr_proposition_2a():
+    # Test Karr, page 309, proposition 2, part a
+    i = Symbol("i", integer=True)
+    u = Symbol("u", integer=True)
+    v = Symbol("v", integer=True)
+
+    def test_the_sum(m, n):
+        # g
+        g = i**3 + 2*i**2 - 3*i
+        # f = Delta g
+        f = simplify(g.subs(i, i+1) - g)
+        # The sum
+        a = m
+        b = n - 1
+        S = Sum(f, (i, a, b)).doit()
+        # Test if Sum_{m <= i < n} f(i) = g(n) - g(m)
+        assert simplify(S - (g.subs(i, n) - g.subs(i, m))) == 0
+
+    # m < n
+    test_the_sum(u,   u+v)
+    # m = n
+    test_the_sum(u,   u  )
+    # m > n
+    test_the_sum(u+v, u  )
+
+
+def test_karr_proposition_2b():
+    # Test Karr, page 309, proposition 2, part b
+    i = Symbol("i", integer=True)
+    u = Symbol("u", integer=True)
+    v = Symbol("v", integer=True)
+    w = Symbol("w", integer=True)
+
+    def test_the_sum(l, n, m):
+        # Summand
+        s = i**3
+        # First sum
+        a = l
+        b = n - 1
+        S1 = Sum(s, (i, a, b)).doit()
+        # Second sum
+        a = l
+        b = m - 1
+        S2 = Sum(s, (i, a, b)).doit()
+        # Third sum
+        a = m
+        b = n - 1
+        S3 = Sum(s, (i, a, b)).doit()
+        # Test if S1 = S2 + S3 as required
+        assert S1 - (S2 + S3) == 0
+
+    # l < m < n
+    test_the_sum(u,     u+v,   u+v+w)
+    # l < m = n
+    test_the_sum(u,     u+v,   u+v  )
+    # l < m > n
+    test_the_sum(u,     u+v+w, v    )
+    # l = m < n
+    test_the_sum(u,     u,     u+v  )
+    # l = m = n
+    test_the_sum(u,     u,     u    )
+    # l = m > n
+    test_the_sum(u+v,   u+v,   u    )
+    # l > m < n
+    test_the_sum(u+v,   u,     u+w  )
+    # l > m = n
+    test_the_sum(u+v,   u,     u    )
+    # l > m > n
+    test_the_sum(u+v+w, u+v,   u    )
+
+
+def test_arithmetic_sums():
+    assert summation(1, (n, a, b)) == b - a + 1
+    assert Sum(S.NaN, (n, a, b)) is S.NaN
+    assert Sum(x, (n, a, a)).doit() == x
+    assert Sum(x, (x, a, a)).doit() == a
+    assert Sum(x, (n, 1, a)).doit() == a*x
+    assert Sum(x, (x, Range(1, 11))).doit() == 55
+    assert Sum(x, (x, Range(1, 11, 2))).doit() == 25
+    assert Sum(x, (x, Range(1, 10, 2))) == Sum(x, (x, Range(9, 0, -2)))
+    lo, hi = 1, 2
+    s1 = Sum(n, (n, lo, hi))
+    s2 = Sum(n, (n, hi, lo))
+    assert s1 != s2
+    assert s1.doit() == 3 and s2.doit() == 0
+    lo, hi = x, x + 1
+    s1 = Sum(n, (n, lo, hi))
+    s2 = Sum(n, (n, hi, lo))
+    assert s1 != s2
+    assert s1.doit() == 2*x + 1 and s2.doit() == 0
+    assert Sum(Integral(x, (x, 1, y)) + x, (x, 1, 2)).doit() == \
+        y**2 + 2
+    assert summation(1, (n, 1, 10)) == 10
+    assert summation(2*n, (n, 0, 10**10)) == 100000000010000000000
+    assert summation(4*n*m, (n, a, 1), (m, 1, d)).expand() == \
+        2*d + 2*d**2 + a*d + a*d**2 - d*a**2 - a**2*d**2
+    assert summation(cos(n), (n, -2, 1)) == cos(-2) + cos(-1) + cos(0) + cos(1)
+    assert summation(cos(n), (n, x, x + 2)) == cos(x) + cos(x + 1) + cos(x + 2)
+    assert isinstance(summation(cos(n), (n, x, x + S.Half)), Sum)
+    assert summation(k, (k, 0, oo)) is oo
+    assert summation(k, (k, Range(1, 11))) == 55
+
+
+def test_polynomial_sums():
+    assert summation(n**2, (n, 3, 8)) == 199
+    assert summation(n, (n, a, b)) == \
+        ((a + b)*(b - a + 1)/2).expand()
+    assert summation(n**2, (n, 1, b)) == \
+        ((2*b**3 + 3*b**2 + b)/6).expand()
+    assert summation(n**3, (n, 1, b)) == \
+        ((b**4 + 2*b**3 + b**2)/4).expand()
+    assert summation(n**6, (n, 1, b)) == \
+        ((6*b**7 + 21*b**6 + 21*b**5 - 7*b**3 + b)/42).expand()
+
+
+def test_geometric_sums():
+    assert summation(pi**n, (n, 0, b)) == (1 - pi**(b + 1)) / (1 - pi)
+    assert summation(2 * 3**n, (n, 0, b)) == 3**(b + 1) - 1
+    assert summation(S.Half**n, (n, 1, oo)) == 1
+    assert summation(2**n, (n, 0, b)) == 2**(b + 1) - 1
+    assert summation(2**n, (n, 1, oo)) is oo
+    assert summation(2**(-n), (n, 1, oo)) == 1
+    assert summation(3**(-n), (n, 4, oo)) == Rational(1, 54)
+    assert summation(2**(-4*n + 3), (n, 1, oo)) == Rational(8, 15)
+    assert summation(2**(n + 1), (n, 1, b)).expand() == 4*(2**b - 1)
+
+    # issue 6664:
+    assert summation(x**n, (n, 0, oo)) == \
+        Piecewise((1/(-x + 1), Abs(x) < 1), (Sum(x**n, (n, 0, oo)), True))
+
+    assert summation(-2**n, (n, 0, oo)) is -oo
+    assert summation(I**n, (n, 0, oo)) == Sum(I**n, (n, 0, oo))
+
+    # issue 6802:
+    assert summation((-1)**(2*x + 2), (x, 0, n)) == n + 1
+    assert summation((-2)**(2*x + 2), (x, 0, n)) == 4*4**(n + 1)/S(3) - Rational(4, 3)
+    assert summation((-1)**x, (x, 0, n)) == -(-1)**(n + 1)/S(2) + S.Half
+    assert summation(y**x, (x, a, b)) == \
+        Piecewise((-a + b + 1, Eq(y, 1)), ((y**a - y**(b + 1))/(-y + 1), True))
+    assert summation((-2)**(y*x + 2), (x, 0, n)) == \
+        4*Piecewise((n + 1, Eq((-2)**y, 1)),
+                    ((-(-2)**(y*(n + 1)) + 1)/(-(-2)**y + 1), True))
+
+    # issue 8251:
+    assert summation((1/(n + 1)**2)*n**2, (n, 0, oo)) is oo
+
+    #issue 9908:
+    assert Sum(1/(n**3 - 1), (n, -oo, -2)).doit() == summation(1/(n**3 - 1), (n, -oo, -2))
+
+    #issue 11642:
+    result = Sum(0.5**n, (n, 1, oo)).doit()
+    assert result == 1.0
+    assert result.is_Float
+
+    result = Sum(0.25**n, (n, 1, oo)).doit()
+    assert result == 1/3.
+    assert result.is_Float
+
+    result = Sum(0.99999**n, (n, 1, oo)).doit()
+    assert result == 99999.0
+    assert result.is_Float
+
+    result = Sum(S.Half**n, (n, 1, oo)).doit()
+    assert result == 1
+    assert not result.is_Float
+
+    result = Sum(Rational(3, 5)**n, (n, 1, oo)).doit()
+    assert result == Rational(3, 2)
+    assert not result.is_Float
+
+    assert Sum(1.0**n, (n, 1, oo)).doit() is oo
+    assert Sum(2.43**n, (n, 1, oo)).doit() is oo
+
+    # Issue 13979
+    i, k, q = symbols('i k q', integer=True)
+    result = summation(
+        exp(-2*I*pi*k*i/n) * exp(2*I*pi*q*i/n) / n, (i, 0, n - 1)
+    )
+    assert result.simplify() == Piecewise(
+            (1, Eq(exp(-2*I*pi*(k - q)/n), 1)), (0, True)
+    )
+
+    #Issue 23491
+    assert Sum(1/(n**2 + 1), (n, 1, oo)).doit() == S(-1)/2 + pi/(2*tanh(pi))
+
+def test_harmonic_sums():
+    assert summation(1/k, (k, 0, n)) == Sum(1/k, (k, 0, n))
+    assert summation(1/k, (k, 1, n)) == harmonic(n)
+    assert summation(n/k, (k, 1, n)) == n*harmonic(n)
+    assert summation(1/k, (k, 5, n)) == harmonic(n) - harmonic(4)
+
+
+def test_composite_sums():
+    f = S.Half*(7 - 6*n + Rational(1, 7)*n**3)
+    s = summation(f, (n, a, b))
+    assert not isinstance(s, Sum)
+    A = 0
+    for i in range(-3, 5):
+        A += f.subs(n, i)
+    B = s.subs(a, -3).subs(b, 4)
+    assert A == B
+
+
+def test_hypergeometric_sums():
+    assert summation(
+        binomial(2*k, k)/4**k, (k, 0, n)) == (1 + 2*n)*binomial(2*n, n)/4**n
+    assert summation(binomial(2*k, k)/5**k, (k, -oo, oo)) == sqrt(5)
+
+
+def test_other_sums():
+    f = m**2 + m*exp(m)
+    g = 3*exp(Rational(3, 2))/2 + exp(S.Half)/2 - exp(Rational(-1, 2))/2 - 3*exp(Rational(-3, 2))/2 + 5
+
+    assert summation(f, (m, Rational(-3, 2), Rational(3, 2))) == g
+    assert summation(f, (m, -1.5, 1.5)).evalf().epsilon_eq(g.evalf(), 1e-10)
+
+fac = factorial
+
+
+def NS(e, n=15, **options):
+    return str(sympify(e).evalf(n, **options))
+
+
+def test_evalf_fast_series():
+    # Euler transformed series for sqrt(1+x)
+    assert NS(Sum(
+        fac(2*n + 1)/fac(n)**2/2**(3*n + 1), (n, 0, oo)), 100) == NS(sqrt(2), 100)
+
+    # Some series for exp(1)
+    estr = NS(E, 100)
+    assert NS(Sum(1/fac(n), (n, 0, oo)), 100) == estr
+    assert NS(1/Sum((1 - 2*n)/fac(2*n), (n, 0, oo)), 100) == estr
+    assert NS(Sum((2*n + 1)/fac(2*n), (n, 0, oo)), 100) == estr
+    assert NS(Sum((4*n + 3)/2**(2*n + 1)/fac(2*n + 1), (n, 0, oo))**2, 100) == estr
+
+    pistr = NS(pi, 100)
+    # Ramanujan series for pi
+    assert NS(9801/sqrt(8)/Sum(fac(
+        4*n)*(1103 + 26390*n)/fac(n)**4/396**(4*n), (n, 0, oo)), 100) == pistr
+    assert NS(1/Sum(
+        binomial(2*n, n)**3 * (42*n + 5)/2**(12*n + 4), (n, 0, oo)), 100) == pistr
+    # Machin's formula for pi
+    assert NS(16*Sum((-1)**n/(2*n + 1)/5**(2*n + 1), (n, 0, oo)) -
+        4*Sum((-1)**n/(2*n + 1)/239**(2*n + 1), (n, 0, oo)), 100) == pistr
+
+    # Apery's constant
+    astr = NS(zeta(3), 100)
+    P = 126392*n**5 + 412708*n**4 + 531578*n**3 + 336367*n**2 + 104000* \
+        n + 12463
+    assert NS(Sum((-1)**n * P / 24 * (fac(2*n + 1)*fac(2*n)*fac(
+        n))**3 / fac(3*n + 2) / fac(4*n + 3)**3, (n, 0, oo)), 100) == astr
+    assert NS(Sum((-1)**n * (205*n**2 + 250*n + 77)/64 * fac(n)**10 /
+              fac(2*n + 1)**5, (n, 0, oo)), 100) == astr
+
+
+def test_evalf_fast_series_issue_4021():
+    # Catalan's constant
+    assert NS(Sum((-1)**(n - 1)*2**(8*n)*(40*n**2 - 24*n + 3)*fac(2*n)**3*
+        fac(n)**2/n**3/(2*n - 1)/fac(4*n)**2, (n, 1, oo))/64, 100) == \
+        NS(Catalan, 100)
+    astr = NS(zeta(3), 100)
+    assert NS(5*Sum(
+        (-1)**(n - 1)*fac(n)**2 / n**3 / fac(2*n), (n, 1, oo))/2, 100) == astr
+    assert NS(Sum((-1)**(n - 1)*(56*n**2 - 32*n + 5) / (2*n - 1)**2 * fac(n - 1)
+              **3 / fac(3*n), (n, 1, oo))/4, 100) == astr
+
+
+def test_evalf_slow_series():
+    assert NS(Sum((-1)**n / n, (n, 1, oo)), 15) == NS(-log(2), 15)
+    assert NS(Sum((-1)**n / n, (n, 1, oo)), 50) == NS(-log(2), 50)
+    assert NS(Sum(1/n**2, (n, 1, oo)), 15) == NS(pi**2/6, 15)
+    assert NS(Sum(1/n**2, (n, 1, oo)), 100) == NS(pi**2/6, 100)
+    assert NS(Sum(1/n**2, (n, 1, oo)), 500) == NS(pi**2/6, 500)
+    assert NS(Sum((-1)**n / (2*n + 1)**3, (n, 0, oo)), 15) == NS(pi**3/32, 15)
+    assert NS(Sum((-1)**n / (2*n + 1)**3, (n, 0, oo)), 50) == NS(pi**3/32, 50)
+
+
+def test_evalf_oo_to_oo():
+    # There used to be an error in certain cases
+    # Does not evaluate, but at least do not throw an error
+    # Evaluates symbolically to 0, which is not correct
+    assert Sum(1/(n**2+1), (n, -oo, oo)).evalf() == Sum(1/(n**2+1), (n, -oo, oo))
+    # This evaluates if from 1 to oo and symbolically
+    assert Sum(1/(factorial(abs(n))), (n, -oo, -1)).evalf() == Sum(1/(factorial(abs(n))), (n, -oo, -1))
+
+
+def test_euler_maclaurin():
+    # Exact polynomial sums with E-M
+    def check_exact(f, a, b, m, n):
+        A = Sum(f, (k, a, b))
+        s, e = A.euler_maclaurin(m, n)
+        assert (e == 0) and (s.expand() == A.doit())
+    check_exact(k**4, a, b, 0, 2)
+    check_exact(k**4 + 2*k, a, b, 1, 2)
+    check_exact(k**4 + k**2, a, b, 1, 5)
+    check_exact(k**5, 2, 6, 1, 2)
+    check_exact(k**5, 2, 6, 1, 3)
+    assert Sum(x-1, (x, 0, 2)).euler_maclaurin(m=30, n=30, eps=2**-15) == (0, 0)
+    # Not exact
+    assert Sum(k**6, (k, a, b)).euler_maclaurin(0, 2)[1] != 0
+    # Numerical test
+    for mi, ni in [(2, 4), (2, 20), (10, 20), (18, 20)]:
+        A = Sum(1/k**3, (k, 1, oo))
+        s, e = A.euler_maclaurin(mi, ni)
+        assert abs((s - zeta(3)).evalf()) < e.evalf()
+
+    raises(ValueError, lambda: Sum(1, (x, 0, 1), (k, 0, 1)).euler_maclaurin())
+
+
+@slow
+def test_evalf_euler_maclaurin():
+    assert NS(Sum(1/k**k, (k, 1, oo)), 15) == '1.29128599706266'
+    assert NS(Sum(1/k**k, (k, 1, oo)),
+              50) == '1.2912859970626635404072825905956005414986193682745'
+    assert NS(Sum(1/k - log(1 + 1/k), (k, 1, oo)), 15) == NS(EulerGamma, 15)
+    assert NS(Sum(1/k - log(1 + 1/k), (k, 1, oo)), 50) == NS(EulerGamma, 50)
+    assert NS(Sum(log(k)/k**2, (k, 1, oo)), 15) == '0.937548254315844'
+    assert NS(Sum(log(k)/k**2, (k, 1, oo)),
+              50) == '0.93754825431584375370257409456786497789786028861483'
+    assert NS(Sum(1/k, (k, 1000000, 2000000)), 15) == '0.693147930560008'
+    assert NS(Sum(1/k, (k, 1000000, 2000000)),
+              50) == '0.69314793056000780941723211364567656807940638436025'
+
+
+def test_evalf_symbolic():
+    # issue 6328
+    expr = Sum(f(x), (x, 1, 3)) + Sum(g(x), (x, 1, 3))
+    assert expr.evalf() == expr
+
+
+def test_evalf_issue_3273():
+    assert Sum(0, (k, 1, oo)).evalf() == 0
+
+
+def test_simple_products():
+    assert Product(S.NaN, (x, 1, 3)) is S.NaN
+    assert product(S.NaN, (x, 1, 3)) is S.NaN
+    assert Product(x, (n, a, a)).doit() == x
+    assert Product(x, (x, a, a)).doit() == a
+    assert Product(x, (y, 1, a)).doit() == x**a
+
+    lo, hi = 1, 2
+    s1 = Product(n, (n, lo, hi))
+    s2 = Product(n, (n, hi, lo))
+    assert s1 != s2
+    # This IS correct according to Karr product convention
+    assert s1.doit() == 2
+    assert s2.doit() == 1
+
+    lo, hi = x, x + 1
+    s1 = Product(n, (n, lo, hi))
+    s2 = Product(n, (n, hi, lo))
+    s3 = 1 / Product(n, (n, hi + 1, lo - 1))
+    assert s1 != s2
+    # This IS correct according to Karr product convention
+    assert s1.doit() == x*(x + 1)
+    assert s2.doit() == 1
+    assert s3.doit() == x*(x + 1)
+
+    assert Product(Integral(2*x, (x, 1, y)) + 2*x, (x, 1, 2)).doit() == \
+        (y**2 + 1)*(y**2 + 3)
+    assert product(2, (n, a, b)) == 2**(b - a + 1)
+    assert product(n, (n, 1, b)) == factorial(b)
+    assert product(n**3, (n, 1, b)) == factorial(b)**3
+    assert product(3**(2 + n), (n, a, b)) \
+        == 3**(2*(1 - a + b) + b/2 + (b**2)/2 + a/2 - (a**2)/2)
+    assert product(cos(n), (n, 3, 5)) == cos(3)*cos(4)*cos(5)
+    assert product(cos(n), (n, x, x + 2)) == cos(x)*cos(x + 1)*cos(x + 2)
+    assert isinstance(product(cos(n), (n, x, x + S.Half)), Product)
+    # If Product managed to evaluate this one, it most likely got it wrong!
+    assert isinstance(Product(n**n, (n, 1, b)), Product)
+
+
+def test_rational_products():
+    assert combsimp(product(1 + 1/n, (n, a, b))) == (1 + b)/a
+    assert combsimp(product(n + 1, (n, a, b))) == gamma(2 + b)/gamma(1 + a)
+    assert combsimp(product((n + 1)/(n - 1), (n, a, b))) == b*(1 + b)/(a*(a - 1))
+    assert combsimp(product(n/(n + 1)/(n + 2), (n, a, b))) == \
+        a*gamma(a + 2)/(b + 1)/gamma(b + 3)
+    assert combsimp(product(n*(n + 1)/(n - 1)/(n - 2), (n, a, b))) == \
+        b**2*(b - 1)*(1 + b)/(a - 1)**2/(a*(a - 2))
+
+
+def test_wallis_product():
+    # Wallis product, given in two different forms to ensure that Product
+    # can factor simple rational expressions
+    A = Product(4*n**2 / (4*n**2 - 1), (n, 1, b))
+    B = Product((2*n)*(2*n)/(2*n - 1)/(2*n + 1), (n, 1, b))
+    R = pi*gamma(b + 1)**2/(2*gamma(b + S.Half)*gamma(b + Rational(3, 2)))
+    assert simplify(A.doit()) == R
+    assert simplify(B.doit()) == R
+    # This one should eventually also be doable (Euler's product formula for sin)
+    # assert Product(1+x/n**2, (n, 1, b)) == ...
+
+
+def test_telescopic_sums():
+    #checks also input 2 of comment 1 issue 4127
+    assert Sum(1/k - 1/(k + 1), (k, 1, n)).doit() == 1 - 1/(1 + n)
+    assert Sum(
+        f(k) - f(k + 2), (k, m, n)).doit() == -f(1 + n) - f(2 + n) + f(m) + f(1 + m)
+    assert Sum(cos(k) - cos(k + 3), (k, 1, n)).doit() == -cos(1 + n) - \
+        cos(2 + n) - cos(3 + n) + cos(1) + cos(2) + cos(3)
+
+    # dummy variable shouldn't matter
+    assert telescopic(1/m, -m/(1 + m), (m, n - 1, n)) == \
+        telescopic(1/k, -k/(1 + k), (k, n - 1, n))
+
+    assert Sum(1/x/(x - 1), (x, a, b)).doit() == 1/(a - 1) - 1/b
+    eq = 1/((5*n + 2)*(5*(n + 1) + 2))
+    assert Sum(eq, (n, 0, oo)).doit() == S(1)/10
+    nz = symbols('nz', nonzero=True)
+    v = Sum(eq.subs(5, nz), (n, 0, oo)).doit()
+    assert v.subs(nz, 5).simplify() == S(1)/10
+    # check that apart is being used in non-symbolic case
+    s = Sum(eq, (n, 0, k)).doit()
+    v = Sum(eq, (n, 0, 10**100)).doit()
+    assert v == s.subs(k, 10**100)
+
+
+def test_sum_reconstruct():
+    s = Sum(n**2, (n, -1, 1))
+    assert s == Sum(*s.args)
+    raises(ValueError, lambda: Sum(x, x))
+    raises(ValueError, lambda: Sum(x, (x, 1)))
+
+
+def test_limit_subs():
+    for F in (Sum, Product, Integral):
+        assert F(a*exp(a), (a, -2, 2)) == F(a*exp(a), (a, -b, b)).subs(b, 2)
+        assert F(a, (a, F(b, (b, 1, 2)), 4)).subs(F(b, (b, 1, 2)), c) == \
+            F(a, (a, c, 4))
+        assert F(x, (x, 1, x + y)).subs(x, 1) == F(x, (x, 1, y + 1))
+
+
+def test_function_subs():
+    S = Sum(x*f(y),(x,0,oo),(y,0,oo))
+    assert S.subs(f(y),y) == Sum(x*y,(x,0,oo),(y,0,oo))
+    assert S.subs(f(x),x) == S
+    raises(ValueError, lambda: S.subs(f(y),x+y) )
+    S = Sum(x*log(y),(x,0,oo),(y,0,oo))
+    assert S.subs(log(y),y) == S
+    S = Sum(x*f(y),(x,0,oo),(y,0,oo))
+    assert S.subs(f(y),y) == Sum(x*y,(x,0,oo),(y,0,oo))
+
+
+def test_equality():
+    # if this fails remove special handling below
+    raises(ValueError, lambda: Sum(x, x))
+    r = symbols('x', real=True)
+    for F in (Sum, Product, Integral):
+        try:
+            assert F(x, x) != F(y, y)
+            assert F(x, (x, 1, 2)) != F(x, x)
+            assert F(x, (x, x)) != F(x, x)  # or else they print the same
+            assert F(1, x) != F(1, y)
+        except ValueError:
+            pass
+        assert F(a, (x, 1, 2)) != F(a, (x, 1, 3))  # diff limit
+        assert F(a, (x, 1, x)) != F(a, (y, 1, y))
+        assert F(a, (x, 1, 2)) != F(b, (x, 1, 2))  # diff expression
+        assert F(x, (x, 1, 2)) != F(r, (r, 1, 2))  # diff assumptions
+        assert F(1, (x, 1, x)) != F(1, (y, 1, x))  # only dummy is diff
+        assert F(1, (x, 1, x)).dummy_eq(F(1, (y, 1, x)))
+
+    # issue 5265
+    assert Sum(x, (x, 1, x)).subs(x, a) == Sum(x, (x, 1, a))
+
+
+def test_Sum_doit():
+    assert Sum(n*Integral(a**2), (n, 0, 2)).doit() == a**3
+    assert Sum(n*Integral(a**2), (n, 0, 2)).doit(deep=False) == \
+        3*Integral(a**2)
+    assert summation(n*Integral(a**2), (n, 0, 2)) == 3*Integral(a**2)
+
+    # test nested sum evaluation
+    s = Sum( Sum( Sum(2,(z,1,n+1)), (y,x+1,n)), (x,1,n))
+    assert 0 == (s.doit() - n*(n+1)*(n-1)).factor()
+
+    # Integer assumes finite
+    assert Sum(KroneckerDelta(x, y), (x, -oo, oo)).doit() == Piecewise((1, And(-oo < y, y < oo)), (0, True))
+    assert Sum(KroneckerDelta(m, n), (m, -oo, oo)).doit() == 1
+    assert Sum(m*KroneckerDelta(x, y), (x, -oo, oo)).doit() == Piecewise((m, And(-oo < y, y < oo)), (0, True))
+    assert Sum(x*KroneckerDelta(m, n), (m, -oo, oo)).doit() == x
+    assert Sum(Sum(KroneckerDelta(m, n), (m, 1, 3)), (n, 1, 3)).doit() == 3
+    assert Sum(Sum(KroneckerDelta(k, m), (m, 1, 3)), (n, 1, 3)).doit() == \
+           3 * Piecewise((1, And(1 <= k, k <= 3)), (0, True))
+    assert Sum(f(n) * Sum(KroneckerDelta(m, n), (m, 0, oo)), (n, 1, 3)).doit() == \
+           f(1) + f(2) + f(3)
+    assert Sum(f(n) * Sum(KroneckerDelta(m, n), (m, 0, oo)), (n, 1, oo)).doit() == \
+           Sum(f(n), (n, 1, oo))
+
+    # issue 2597
+    nmax = symbols('N', integer=True, positive=True)
+    pw = Piecewise((1, And(1 <= n, n <= nmax)), (0, True))
+    assert Sum(pw, (n, 1, nmax)).doit() == Sum(Piecewise((1, nmax >= n),
+                    (0, True)), (n, 1, nmax))
+
+    q, s = symbols('q, s')
+    assert summation(1/n**(2*s), (n, 1, oo)) == Piecewise((zeta(2*s), 2*re(s) > 1),
+        (Sum(n**(-2*s), (n, 1, oo)), True))
+    assert summation(1/(n+1)**s, (n, 0, oo)) == Piecewise((zeta(s), re(s) > 1),
+        (Sum((n + 1)**(-s), (n, 0, oo)), True))
+    assert summation(1/(n+q)**s, (n, 0, oo)) == Piecewise(
+        (zeta(s, q), And(~Contains(-q, S.Naturals0), re(s) > 1)),
+        (Sum((n + q)**(-s), (n, 0, oo)), True))
+    assert summation(1/(n+q)**s, (n, q, oo)) == Piecewise(
+        (zeta(s, 2*q), And(~Contains(-2*q, S.Naturals0), re(s) > 1)),
+        (Sum((n + q)**(-s), (n, q, oo)), True))
+    assert summation(1/n**2, (n, 1, oo)) == zeta(2)
+    assert summation(1/n**s, (n, 0, oo)) == Sum(n**(-s), (n, 0, oo))
+    assert summation(1/(n+1)**(2+I), (n, 0, oo)) == zeta(2+I)
+    t = symbols('t', real=True, positive=True)
+    assert summation(1/(n+I)**(t+1), (n, 0, oo)) == zeta(t+1, I)
+
+
+def test_Product_doit():
+    assert Product(n*Integral(a**2), (n, 1, 3)).doit() == 2 * a**9 / 9
+    assert Product(n*Integral(a**2), (n, 1, 3)).doit(deep=False) == \
+        6*Integral(a**2)**3
+    assert product(n*Integral(a**2), (n, 1, 3)) == 6*Integral(a**2)**3
+
+
+def test_Sum_interface():
+    assert isinstance(Sum(0, (n, 0, 2)), Sum)
+    assert Sum(nan, (n, 0, 2)) is nan
+    assert Sum(nan, (n, 0, oo)) is nan
+    assert Sum(0, (n, 0, 2)).doit() == 0
+    assert isinstance(Sum(0, (n, 0, oo)), Sum)
+    assert Sum(0, (n, 0, oo)).doit() == 0
+    raises(ValueError, lambda: Sum(1))
+    raises(ValueError, lambda: summation(1))
+
+
+def test_diff():
+    assert Sum(x, (x, 1, 2)).diff(x) == 0
+    assert Sum(x*y, (x, 1, 2)).diff(x) == 0
+    assert Sum(x*y, (y, 1, 2)).diff(x) == Sum(y, (y, 1, 2))
+    e = Sum(x*y, (x, 1, a))
+    assert e.diff(a) == Derivative(e, a)
+    assert Sum(x*y, (x, 1, 3), (a, 2, 5)).diff(y).doit() == \
+        Sum(x*y, (x, 1, 3), (a, 2, 5)).doit().diff(y) == 24
+    assert Sum(x, (x, 1, 2)).diff(y) == 0
+
+
+def test_hypersum():
+    assert simplify(summation(x**n/fac(n), (n, 1, oo))) == -1 + exp(x)
+    assert summation((-1)**n * x**(2*n) / fac(2*n), (n, 0, oo)) == cos(x)
+    assert simplify(summation((-1)**n*x**(2*n + 1) /
+        factorial(2*n + 1), (n, 3, oo))) == -x + sin(x) + x**3/6 - x**5/120
+
+    assert summation(1/(n + 2)**3, (n, 1, oo)) == Rational(-9, 8) + zeta(3)
+    assert summation(1/n**4, (n, 1, oo)) == pi**4/90
+
+    s = summation(x**n*n, (n, -oo, 0))
+    assert s.is_Piecewise
+    assert s.args[0].args[0] == -1/(x*(1 - 1/x)**2)
+    assert s.args[0].args[1] == (abs(1/x) < 1)
+
+    m = Symbol('n', integer=True, positive=True)
+    assert summation(binomial(m, k), (k, 0, m)) == 2**m
+
+
+def test_issue_4170():
+    assert summation(1/factorial(k), (k, 0, oo)) == E
+
+
+def test_is_commutative():
+    from sympy.physics.secondquant import NO, F, Fd
+    m = Symbol('m', commutative=False)
+    for f in (Sum, Product, Integral):
+        assert f(z, (z, 1, 1)).is_commutative is True
+        assert f(z*y, (z, 1, 6)).is_commutative is True
+        assert f(m*x, (x, 1, 2)).is_commutative is False
+
+        assert f(NO(Fd(x)*F(y))*z, (z, 1, 2)).is_commutative is False
+
+
+def test_is_zero():
+    for func in [Sum, Product]:
+        assert func(0, (x, 1, 1)).is_zero is True
+        assert func(x, (x, 1, 1)).is_zero is None
+
+    assert Sum(0, (x, 1, 0)).is_zero is True
+    assert Product(0, (x, 1, 0)).is_zero is False
+
+
+def test_is_number():
+    # is number should not rely on evaluation or assumptions,
+    # it should be equivalent to `not foo.free_symbols`
+    assert Sum(1, (x, 1, 1)).is_number is True
+    assert Sum(1, (x, 1, x)).is_number is False
+    assert Sum(0, (x, y, z)).is_number is False
+    assert Sum(x, (y, 1, 2)).is_number is False
+    assert Sum(x, (y, 1, 1)).is_number is False
+    assert Sum(x, (x, 1, 2)).is_number is True
+    assert Sum(x*y, (x, 1, 2), (y, 1, 3)).is_number is True
+
+    assert Product(2, (x, 1, 1)).is_number is True
+    assert Product(2, (x, 1, y)).is_number is False
+    assert Product(0, (x, y, z)).is_number is False
+    assert Product(1, (x, y, z)).is_number is False
+    assert Product(x, (y, 1, x)).is_number is False
+    assert Product(x, (y, 1, 2)).is_number is False
+    assert Product(x, (y, 1, 1)).is_number is False
+    assert Product(x, (x, 1, 2)).is_number is True
+
+
+def test_free_symbols():
+    for func in [Sum, Product]:
+        assert func(1, (x, 1, 2)).free_symbols == set()
+        assert func(0, (x, 1, y)).free_symbols == {y}
+        assert func(2, (x, 1, y)).free_symbols == {y}
+        assert func(x, (x, 1, 2)).free_symbols == set()
+        assert func(x, (x, 1, y)).free_symbols == {y}
+        assert func(x, (y, 1, y)).free_symbols == {x, y}
+        assert func(x, (y, 1, 2)).free_symbols == {x}
+        assert func(x, (y, 1, 1)).free_symbols == {x}
+        assert func(x, (y, 1, z)).free_symbols == {x, z}
+        assert func(x, (x, 1, y), (y, 1, 2)).free_symbols == set()
+        assert func(x, (x, 1, y), (y, 1, z)).free_symbols == {z}
+        assert func(x, (x, 1, y), (y, 1, y)).free_symbols == {y}
+        assert func(x, (y, 1, y), (y, 1, z)).free_symbols == {x, z}
+    assert Sum(1, (x, 1, y)).free_symbols == {y}
+    # free_symbols answers whether the object *as written* has free symbols,
+    # not whether the evaluated expression has free symbols
+    assert Product(1, (x, 1, y)).free_symbols == {y}
+    # don't count free symbols that are not independent of integration
+    # variable(s)
+    assert func(f(x), (f(x), 1, 2)).free_symbols == set()
+    assert func(f(x), (f(x), 1, x)).free_symbols == {x}
+    assert func(f(x), (f(x), 1, y)).free_symbols == {y}
+    assert func(f(x), (z, 1, y)).free_symbols == {x, y}
+
+
+def test_conjugate_transpose():
+    A, B = symbols("A B", commutative=False)
+    p = Sum(A*B**n, (n, 1, 3))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+    p = Sum(B**n*A, (n, 1, 3))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+
+def test_noncommutativity_honoured():
+    A, B = symbols("A B", commutative=False)
+    M = symbols('M', integer=True, positive=True)
+    p = Sum(A*B**n, (n, 1, M))
+    assert p.doit() == A*Piecewise((M, Eq(B, 1)),
+                                   ((B - B**(M + 1))*(1 - B)**(-1), True))
+
+    p = Sum(B**n*A, (n, 1, M))
+    assert p.doit() == Piecewise((M, Eq(B, 1)),
+                                 ((B - B**(M + 1))*(1 - B)**(-1), True))*A
+
+    p = Sum(B**n*A*B**n, (n, 1, M))
+    assert p.doit() == p
+
+
+def test_issue_4171():
+    assert summation(factorial(2*k + 1)/factorial(2*k), (k, 0, oo)) is oo
+    assert summation(2*k + 1, (k, 0, oo)) is oo
+
+
+def test_issue_6273():
+    assert Sum(x, (x, 1, n)).n(2, subs={n: 1}) == Float(1, 2)
+
+
+def test_issue_6274():
+    assert Sum(x, (x, 1, 0)).doit() == 0
+    assert NS(Sum(x, (x, 1, 0))) == '0'
+    assert Sum(n, (n, 10, 5)).doit() == -30
+    assert NS(Sum(n, (n, 10, 5))) == '-30.0000000000000'
+
+
+def test_simplify_sum():
+    y, t, v = symbols('y, t, v')
+
+    _simplify = lambda e: simplify(e, doit=False)
+    assert _simplify(Sum(x*y, (x, n, m), (y, a, k)) + \
+        Sum(y, (x, n, m), (y, a, k))) == Sum(y * (x + 1), (x, n, m), (y, a, k))
+    assert _simplify(Sum(x, (x, n, m)) + Sum(x, (x, m + 1, a))) == \
+        Sum(x, (x, n, a))
+    assert _simplify(Sum(x, (x, k + 1, a)) + Sum(x, (x, n, k))) == \
+        Sum(x, (x, n, a))
+    assert _simplify(Sum(x, (x, k + 1, a)) + Sum(x + 1, (x, n, k))) == \
+        Sum(x, (x, n, a)) + Sum(1, (x, n, k))
+    assert _simplify(Sum(x, (x, 0, 3)) * 3 + 3 * Sum(x, (x, 4, 6)) + \
+        4 * Sum(z, (z, 0, 1))) == 4*Sum(z, (z, 0, 1)) + 3*Sum(x, (x, 0, 6))
+    assert _simplify(3*Sum(x**2, (x, a, b)) + Sum(x, (x, a, b))) == \
+        Sum(x*(3*x + 1), (x, a, b))
+    assert _simplify(Sum(x**3, (x, n, k)) * 3 + 3 * Sum(x, (x, n, k)) + \
+        4 * y * Sum(z, (z, n, k))) + 1 == \
+            4*y*Sum(z, (z, n, k)) + 3*Sum(x**3 + x, (x, n, k)) + 1
+    assert _simplify(Sum(x, (x, a, b)) + 1 + Sum(x, (x, b + 1, c))) == \
+        1 + Sum(x, (x, a, c))
+    assert _simplify(Sum(x, (t, a, b)) + Sum(y, (t, a, b)) + \
+        Sum(x, (t, b+1, c))) == x * Sum(1, (t, a, c)) + y * Sum(1, (t, a, b))
+    assert _simplify(Sum(x, (t, a, b)) + Sum(x, (t, b+1, c)) + \
+        Sum(y, (t, a, b))) == x * Sum(1, (t, a, c)) + y * Sum(1, (t, a, b))
+    assert _simplify(Sum(x, (t, a, b)) + 2 * Sum(x, (t, b+1, c))) == \
+        _simplify(Sum(x, (t, a, b)) + Sum(x, (t, b+1, c)) + Sum(x, (t, b+1, c)))
+    assert _simplify(Sum(x, (x, a, b))*Sum(x**2, (x, a, b))) == \
+        Sum(x, (x, a, b)) * Sum(x**2, (x, a, b))
+    assert _simplify(Sum(x, (t, a, b)) + Sum(y, (t, a, b)) + Sum(z, (t, a, b))) \
+        == (x + y + z) * Sum(1, (t, a, b))          # issue 8596
+    assert _simplify(Sum(x, (t, a, b)) + Sum(y, (t, a, b)) + Sum(z, (t, a, b)) + \
+        Sum(v, (t, a, b))) == (x + y + z + v) * Sum(1, (t, a, b))  # issue 8596
+    assert _simplify(Sum(x * y, (x, a, b)) / (3 * y)) == \
+        (Sum(x, (x, a, b)) / 3)
+    assert _simplify(Sum(f(x) * y * z, (x, a, b)) / (y * z)) \
+        == Sum(f(x), (x, a, b))
+    assert _simplify(Sum(c * x, (x, a, b)) - c * Sum(x, (x, a, b))) == 0
+    assert _simplify(c * (Sum(x, (x, a, b))  + y)) == c * (y + Sum(x, (x, a, b)))
+    assert _simplify(c * (Sum(x, (x, a, b)) + y * Sum(x, (x, a, b)))) == \
+        c * (y + 1) * Sum(x, (x, a, b))
+    assert _simplify(Sum(Sum(c * x, (x, a, b)), (y, a, b))) == \
+                c * Sum(x, (x, a, b), (y, a, b))
+    assert _simplify(Sum((3 + y) * Sum(c * x, (x, a, b)), (y, a, b))) == \
+                c * Sum((3 + y), (y, a, b)) * Sum(x, (x, a, b))
+    assert _simplify(Sum((3 + t) * Sum(c * t, (x, a, b)), (y, a, b))) == \
+                c*t*(t + 3)*Sum(1, (x, a, b))*Sum(1, (y, a, b))
+    assert _simplify(Sum(Sum(d * t, (x, a, b - 1)) + \
+                Sum(d * t, (x, b, c)), (t, a, b))) == \
+                    d * Sum(1, (x, a, c)) * Sum(t, (t, a, b))
+    assert _simplify(Sum(sin(t)**2 + cos(t)**2 + 1, (t, a, b))) == \
+        2 * Sum(1, (t, a, b))
+
+
+def test_change_index():
+    b, v, w = symbols('b, v, w', integer = True)
+
+    assert Sum(x, (x, a, b)).change_index(x, x + 1, y) == \
+        Sum(y - 1, (y, a + 1, b + 1))
+    assert Sum(x**2, (x, a, b)).change_index( x, x - 1) == \
+        Sum((x+1)**2, (x, a - 1, b - 1))
+    assert Sum(x**2, (x, a, b)).change_index( x, -x, y) == \
+        Sum((-y)**2, (y, -b, -a))
+    assert Sum(x, (x, a, b)).change_index( x, -x - 1) == \
+        Sum(-x - 1, (x, -b - 1, -a - 1))
+    assert Sum(x*y, (x, a, b), (y, c, d)).change_index( x, x - 1, z) == \
+        Sum((z + 1)*y, (z, a - 1, b - 1), (y, c, d))
+    assert Sum(x, (x, a, b)).change_index( x, x + v) == \
+        Sum(-v + x, (x, a + v, b + v))
+    assert Sum(x, (x, a, b)).change_index( x, -x - v) == \
+        Sum(-v - x, (x, -b - v, -a - v))
+    assert Sum(x, (x, a, b)).change_index(x, w*x, v) == \
+        Sum(v/w, (v, b*w, a*w))
+    raises(ValueError, lambda: Sum(x, (x, a, b)).change_index(x, 2*x))
+
+
+def test_reorder():
+    b, y, c, d, z = symbols('b, y, c, d, z', integer = True)
+
+    assert Sum(x*y, (x, a, b), (y, c, d)).reorder((0, 1)) == \
+        Sum(x*y, (y, c, d), (x, a, b))
+    assert Sum(x, (x, a, b), (x, c, d)).reorder((0, 1)) == \
+        Sum(x, (x, c, d), (x, a, b))
+    assert Sum(x*y + z, (x, a, b), (z, m, n), (y, c, d)).reorder(\
+        (2, 0), (0, 1)) == Sum(x*y + z, (z, m, n), (y, c, d), (x, a, b))
+    assert Sum(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\
+        (0, 1), (1, 2), (0, 2)) == Sum(x*y*z, (x, a, b), (z, m, n), (y, c, d))
+    assert Sum(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\
+        (x, y), (y, z), (x, z)) == Sum(x*y*z, (x, a, b), (z, m, n), (y, c, d))
+    assert Sum(x*y, (x, a, b), (y, c, d)).reorder((x, 1)) == \
+        Sum(x*y, (y, c, d), (x, a, b))
+    assert Sum(x*y, (x, a, b), (y, c, d)).reorder((y, x)) == \
+        Sum(x*y, (y, c, d), (x, a, b))
+
+
+def test_reverse_order():
+    assert Sum(x, (x, 0, 3)).reverse_order(0) == Sum(-x, (x, 4, -1))
+    assert Sum(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(0, 1) == \
+           Sum(x*y, (x, 6, 0), (y, 7, -1))
+    assert Sum(x, (x, 1, 2)).reverse_order(0) == Sum(-x, (x, 3, 0))
+    assert Sum(x, (x, 1, 3)).reverse_order(0) == Sum(-x, (x, 4, 0))
+    assert Sum(x, (x, 1, a)).reverse_order(0) == Sum(-x, (x, a + 1, 0))
+    assert Sum(x, (x, a, 5)).reverse_order(0) == Sum(-x, (x, 6, a - 1))
+    assert Sum(x, (x, a + 1, a + 5)).reverse_order(0) == \
+                         Sum(-x, (x, a + 6, a))
+    assert Sum(x, (x, a + 1, a + 2)).reverse_order(0) == \
+           Sum(-x, (x, a + 3, a))
+    assert Sum(x, (x, a + 1, a + 1)).reverse_order(0) == \
+           Sum(-x, (x, a + 2, a))
+    assert Sum(x, (x, a, b)).reverse_order(0) == Sum(-x, (x, b + 1, a - 1))
+    assert Sum(x, (x, a, b)).reverse_order(x) == Sum(-x, (x, b + 1, a - 1))
+    assert Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1) == \
+        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
+    assert Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x) == \
+        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
+
+
+def test_issue_7097():
+    assert sum(x**n/n for n in range(1, 401)) == summation(x**n/n, (n, 1, 400))
+
+
+def test_factor_expand_subs():
+    # test factoring
+    assert Sum(4 * x, (x, 1, y)).factor() == 4 * Sum(x, (x, 1, y))
+    assert Sum(x * a, (x, 1, y)).factor() == a * Sum(x, (x, 1, y))
+    assert Sum(4 * x * a, (x, 1, y)).factor() == 4 * a * Sum(x, (x, 1, y))
+    assert Sum(4 * x * y, (x, 1, y)).factor() == 4 * y * Sum(x, (x, 1, y))
+
+    # test expand
+    _x = Symbol('x', zero=False)
+    assert Sum(x+1,(x,1,y)).expand() == Sum(x,(x,1,y)) + Sum(1,(x,1,y))
+    assert Sum(x+a*x**2,(x,1,y)).expand() == Sum(x,(x,1,y)) + Sum(a*x**2,(x,1,y))
+    assert Sum(_x**(n + 1)*(n + 1), (n, -1, oo)).expand() \
+        == Sum(n*_x*_x**n + _x*_x**n, (n, -1, oo))
+    assert Sum(x**(n + 1)*(n + 1), (n, -1, oo)).expand(power_exp=False) \
+        == Sum(n*x**(n + 1) + x**(n + 1), (n, -1, oo))
+    assert Sum(x**(n + 1)*(n + 1), (n, -1, oo)).expand(force=True) \
+           == Sum(x*x**n, (n, -1, oo)) + Sum(n*x*x**n, (n, -1, oo))
+    assert Sum(a*n+a*n**2,(n,0,4)).expand() \
+        == Sum(a*n,(n,0,4)) + Sum(a*n**2,(n,0,4))
+    assert Sum(_x**a*_x**n,(x,0,3)) \
+        == Sum(_x**(a+n),(x,0,3)).expand(power_exp=True)
+    _a, _n = symbols('a n', positive=True)
+    assert Sum(x**(_a+_n),(x,0,3)).expand(power_exp=True) \
+        == Sum(x**_a*x**_n, (x, 0, 3))
+    assert Sum(x**(_a-_n),(x,0,3)).expand(power_exp=True) \
+        == Sum(x**(_a-_n),(x,0,3)).expand(power_exp=False)
+
+    # test subs
+    assert Sum(1/(1+a*x**2),(x,0,3)).subs([(a,3)]) == Sum(1/(1+3*x**2),(x,0,3))
+    assert Sum(x*y,(x,0,y),(y,0,x)).subs([(x,3)]) == Sum(x*y,(x,0,y),(y,0,3))
+    assert Sum(x,(x,1,10)).subs([(x,y-2)]) == Sum(x,(x,1,10))
+    assert Sum(1/x,(x,1,10)).subs([(x,(3+n)**3)]) == Sum(1/x,(x,1,10))
+    assert Sum(1/x,(x,1,10)).subs([(x,3*x-2)]) == Sum(1/x,(x,1,10))
+
+
+def test_distribution_over_equality():
+    assert Product(Eq(x*2, f(x)), (x, 1, 3)).doit() == Eq(48, f(1)*f(2)*f(3))
+    assert Sum(Eq(f(x), x**2), (x, 0, y)) == \
+        Eq(Sum(f(x), (x, 0, y)), Sum(x**2, (x, 0, y)))
+
+
+def test_issue_2787():
+    n, k = symbols('n k', positive=True, integer=True)
+    p = symbols('p', positive=True)
+    binomial_dist = binomial(n, k)*p**k*(1 - p)**(n - k)
+    s = Sum(binomial_dist*k, (k, 0, n))
+    res = s.doit().simplify()
+    ans = Piecewise(
+        (n*p, x),
+        (Sum(k*p**k*binomial(n, k)*(1 - p)**(n - k), (k, 0, n)),
+        True)).subs(x, (Eq(n, 1) | (n > 1)) & (p/Abs(p - 1) <= 1))
+    ans2 = Piecewise(
+        (n*p, x),
+        (factorial(n)*Sum(p**k*(1 - p)**(-k + n)/
+        (factorial(-k + n)*factorial(k - 1)), (k, 0, n)),
+        True)).subs(x, (Eq(n, 1) | (n > 1)) & (p/Abs(p - 1) <= 1))
+    assert res in [ans, ans2]  # XXX system dependent
+    # Issue #17165: make sure that another simplify does not complicate
+    # the result by much. Why didn't first simplify replace
+    # Eq(n, 1) | (n > 1) with True?
+    assert res.simplify().count_ops() <= res.count_ops() + 2
+
+
+def test_issue_4668():
+    assert summation(1/n, (n, 2, oo)) is oo
+
+
+def test_matrix_sum():
+    A = Matrix([[0, 1], [n, 0]])
+
+    result = Sum(A, (n, 0, 3)).doit()
+    assert result == Matrix([[0, 4], [6, 0]])
+    assert result.__class__ == ImmutableDenseMatrix
+
+    A = SparseMatrix([[0, 1], [n, 0]])
+
+    result = Sum(A, (n, 0, 3)).doit()
+    assert result.__class__ == ImmutableSparseMatrix
+
+
+def test_failing_matrix_sum():
+    n = Symbol('n')
+    # TODO Implement matrix geometric series summation.
+    A = Matrix([[0, 1, 0], [-1, 0, 0], [0, 0, 0]])
+    assert Sum(A ** n, (n, 1, 4)).doit() == \
+        Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+    # issue sympy/sympy#16989
+    assert summation(A**n, (n, 1, 1)) == A
+
+
+def test_indexed_idx_sum():
+    i = symbols('i', cls=Idx)
+    r = Indexed('r', i)
+    assert Sum(r, (i, 0, 3)).doit() == sum(r.xreplace({i: j}) for j in range(4))
+    assert Product(r, (i, 0, 3)).doit() == prod([r.xreplace({i: j}) for j in range(4)])
+
+    j = symbols('j', integer=True)
+    assert Sum(r, (i, j, j+2)).doit() == sum(r.xreplace({i: j+k}) for k in range(3))
+    assert Product(r, (i, j, j+2)).doit() == prod([r.xreplace({i: j+k}) for k in range(3)])
+
+    k = Idx('k', range=(1, 3))
+    A = IndexedBase('A')
+    assert Sum(A[k], k).doit() == sum(A[Idx(j, (1, 3))] for j in range(1, 4))
+    assert Product(A[k], k).doit() == prod([A[Idx(j, (1, 3))] for j in range(1, 4)])
+
+    raises(ValueError, lambda: Sum(A[k], (k, 1, 4)))
+    raises(ValueError, lambda: Sum(A[k], (k, 0, 3)))
+    raises(ValueError, lambda: Sum(A[k], (k, 2, oo)))
+
+    raises(ValueError, lambda: Product(A[k], (k, 1, 4)))
+    raises(ValueError, lambda: Product(A[k], (k, 0, 3)))
+    raises(ValueError, lambda: Product(A[k], (k, 2, oo)))
+
+
+@slow
+def test_is_convergent():
+    # divergence tests --
+    assert Sum(n/(2*n + 1), (n, 1, oo)).is_convergent() is S.false
+    assert Sum(factorial(n)/5**n, (n, 1, oo)).is_convergent() is S.false
+    assert Sum(3**(-2*n - 1)*n**n, (n, 1, oo)).is_convergent() is S.false
+    assert Sum((-1)**n*n, (n, 3, oo)).is_convergent() is S.false
+    assert Sum((-1)**n, (n, 1, oo)).is_convergent() is S.false
+    assert Sum(log(1/n), (n, 2, oo)).is_convergent() is S.false
+    assert Sum(sin(n), (n, 1, oo)).is_convergent() is S.false
+
+    # Raabe's test --
+    assert Sum(Product((3*m),(m,1,n))/Product((3*m+4),(m,1,n)),(n,1,oo)).is_convergent() is S.true
+
+    # root test --
+    assert Sum((-12)**n/n, (n, 1, oo)).is_convergent() is S.false
+
+    # integral test --
+
+    # p-series test --
+    assert Sum(1/(n**2 + 1), (n, 1, oo)).is_convergent() is S.true
+    assert Sum(1/n**Rational(6, 5), (n, 1, oo)).is_convergent() is S.true
+    assert Sum(2/(n*sqrt(n - 1)), (n, 2, oo)).is_convergent() is S.true
+    assert Sum(1/(sqrt(n)*sqrt(n)), (n, 2, oo)).is_convergent() is S.false
+    assert Sum(factorial(n) / factorial(n+2), (n, 1, oo)).is_convergent() is S.true
+    assert Sum(rf(5,n)/rf(7,n),(n,1,oo)).is_convergent() is S.true
+    assert Sum((rf(1, n)*rf(2, n))/(rf(3, n)*factorial(n)),(n,1,oo)).is_convergent() is S.false
+
+    # comparison test --
+    assert Sum(1/(n + log(n)), (n, 1, oo)).is_convergent() is S.false
+    assert Sum(1/(n**2*log(n)), (n, 2, oo)).is_convergent() is S.true
+    assert Sum(1/(n*log(n)), (n, 2, oo)).is_convergent() is S.false
+    assert Sum(2/(n*log(n)*log(log(n))**2), (n, 5, oo)).is_convergent() is S.true
+    assert Sum(2/(n*log(n)**2), (n, 2, oo)).is_convergent() is S.true
+    assert Sum((n - 1)/(n**2*log(n)**3), (n, 2, oo)).is_convergent() is S.true
+    assert Sum(1/(n*log(n)*log(log(n))), (n, 5, oo)).is_convergent() is S.false
+    assert Sum((n - 1)/(n*log(n)**3), (n, 3, oo)).is_convergent() is S.false
+    assert Sum(2/(n**2*log(n)), (n, 2, oo)).is_convergent() is S.true
+    assert Sum(1/(n*sqrt(log(n))*log(log(n))), (n, 100, oo)).is_convergent() is S.false
+    assert Sum(log(log(n))/(n*log(n)**2), (n, 100, oo)).is_convergent() is S.true
+    assert Sum(log(n)/n**2, (n, 5, oo)).is_convergent() is S.true
+
+    # alternating series tests --
+    assert Sum((-1)**(n - 1)/(n**2 - 1), (n, 3, oo)).is_convergent() is S.true
+
+    # with -negativeInfinite Limits
+    assert Sum(1/(n**2 + 1), (n, -oo, 1)).is_convergent() is S.true
+    assert Sum(1/(n - 1), (n, -oo, -1)).is_convergent() is S.false
+    assert Sum(1/(n**2 - 1), (n, -oo, -5)).is_convergent() is S.true
+    assert Sum(1/(n**2 - 1), (n, -oo, 2)).is_convergent() is S.true
+    assert Sum(1/(n**2 - 1), (n, -oo, oo)).is_convergent() is S.true
+
+    # piecewise functions
+    f = Piecewise((n**(-2), n <= 1), (n**2, n > 1))
+    assert Sum(f, (n, 1, oo)).is_convergent() is S.false
+    assert Sum(f, (n, -oo, oo)).is_convergent() is S.false
+    assert Sum(f, (n, 1, 100)).is_convergent() is S.true
+    #assert Sum(f, (n, -oo, 1)).is_convergent() is S.true
+
+    # integral test
+
+    assert Sum(log(n)/n**3, (n, 1, oo)).is_convergent() is S.true
+    assert Sum(-log(n)/n**3, (n, 1, oo)).is_convergent() is S.true
+    # the following function has maxima located at (x, y) =
+    # (1.2, 0.43), (3.0, -0.25) and (6.8, 0.050)
+    eq = (x - 2)*(x**2 - 6*x + 4)*exp(-x)
+    assert Sum(eq, (x, 1, oo)).is_convergent() is S.true
+    assert Sum(eq, (x, 1, 2)).is_convergent() is S.true
+    assert Sum(1/(x**3), (x, 1, oo)).is_convergent() is S.true
+    assert Sum(1/(x**S.Half), (x, 1, oo)).is_convergent() is S.false
+
+    # issue 19545
+    assert Sum(1/n - 3/(3*n +2), (n, 1, oo)).is_convergent() is S.true
+
+    # issue 19836
+    assert Sum(4/(n + 2) - 5/(n + 1) + 1/n,(n, 7, oo)).is_convergent() is S.true
+
+
+def test_is_absolutely_convergent():
+    assert Sum((-1)**n, (n, 1, oo)).is_absolutely_convergent() is S.false
+    assert Sum((-1)**n/n**2, (n, 1, oo)).is_absolutely_convergent() is S.true
+
+
+@XFAIL
+def test_convergent_failing():
+    # dirichlet tests
+    assert Sum(sin(n)/n, (n, 1, oo)).is_convergent() is S.true
+    assert Sum(sin(2*n)/n, (n, 1, oo)).is_convergent() is S.true
+
+
+def test_issue_6966():
+    i, k, m = symbols('i k m', integer=True)
+    z_i, q_i = symbols('z_i q_i')
+    a_k = Sum(-q_i*z_i/k,(i,1,m))
+    b_k = a_k.diff(z_i)
+    assert isinstance(b_k, Sum)
+    assert b_k == Sum(-q_i/k,(i,1,m))
+
+
+def test_issue_10156():
+    cx = Sum(2*y**2*x, (x, 1,3))
+    e = 2*y*Sum(2*cx*x**2, (x, 1, 9))
+    assert e.factor() == \
+        8*y**3*Sum(x, (x, 1, 3))*Sum(x**2, (x, 1, 9))
+
+
+def test_issue_10973():
+    assert Sum((-n + (n**3 + 1)**(S(1)/3))/log(n), (n, 1, oo)).is_convergent() is S.true
+
+
+def test_issue_14103():
+    assert Sum(sin(n)**2 + cos(n)**2 - 1, (n, 1, oo)).is_convergent() is S.true
+    assert Sum(sin(pi*n), (n, 1, oo)).is_convergent() is S.true
+
+
+def test_issue_14129():
+    x = Symbol('x', zero=False)
+    assert Sum( k*x**k, (k, 0, n-1)).doit() == \
+        Piecewise((n**2/2 - n/2, Eq(x, 1)), ((n*x*x**n -
+            n*x**n - x*x**n + x)/(x - 1)**2, True))
+    assert Sum( x**k, (k, 0, n-1)).doit() == \
+        Piecewise((n, Eq(x, 1)), ((-x**n + 1)/(-x + 1), True))
+    assert Sum( k*(x/y+x)**k, (k, 0, n-1)).doit() == \
+        Piecewise((n*(n - 1)/2, Eq(x, y/(y + 1))),
+        (x*(y + 1)*(n*x*y*(x + x/y)**(n - 1) +
+        n*x*(x + x/y)**(n - 1) - n*y*(x + x/y)**(n - 1) -
+        x*y*(x + x/y)**(n - 1) - x*(x + x/y)**(n - 1) + y)/
+        (x*y + x - y)**2, True))
+
+
+def test_issue_14112():
+    assert Sum((-1)**n/sqrt(n), (n, 1, oo)).is_absolutely_convergent() is S.false
+    assert Sum((-1)**(2*n)/n, (n, 1, oo)).is_convergent() is S.false
+    assert Sum((-2)**n + (-3)**n, (n, 1, oo)).is_convergent() is S.false
+
+
+def test_issue_14219():
+    A = diag(0, 2, -3)
+    res = diag(1, 15, -20)
+    assert Sum(A**n, (n, 0, 3)).doit() == res
+
+
+def test_sin_times_absolutely_convergent():
+    assert Sum(sin(n) / n**3, (n, 1, oo)).is_convergent() is S.true
+    assert Sum(sin(n) * log(n) / n**3, (n, 1, oo)).is_convergent() is S.true
+
+
+def test_issue_14111():
+    assert Sum(1/log(log(n)), (n, 22, oo)).is_convergent() is S.false
+
+
+def test_issue_14484():
+    assert Sum(sin(n)/log(log(n)), (n, 22, oo)).is_convergent() is S.false
+
+
+def test_issue_14640():
+    i, n = symbols("i n", integer=True)
+    a, b, c = symbols("a b c", zero=False)
+
+    assert Sum(a**-i/(a - b), (i, 0, n)).doit() == Sum(
+        1/(a*a**i - a**i*b), (i, 0, n)).doit() == Piecewise(
+            (n + 1, Eq(1/a, 1)),
+            ((-a**(-n - 1) + 1)/(1 - 1/a), True))/(a - b)
+
+    assert Sum((b*a**i - c*a**i)**-2, (i, 0, n)).doit() == Piecewise(
+        (n + 1, Eq(a**(-2), 1)),
+        ((-a**(-2*n - 2) + 1)/(1 - 1/a**2), True))/(b - c)**2
+
+    s = Sum(i*(a**(n - i) - b**(n - i))/(a - b), (i, 0, n)).doit()
+    assert not s.has(Sum)
+    assert s.subs({a: 2, b: 3, n: 5}) == 122
+
+
+def test_issue_15943():
+    s = Sum(binomial(n, k)*factorial(n - k), (k, 0, n)).doit().rewrite(gamma)
+    assert s == -E*(n + 1)*gamma(n + 1)*lowergamma(n + 1, 1)/gamma(n + 2
+        ) + E*gamma(n + 1)
+    assert s.simplify() == E*(factorial(n) - lowergamma(n + 1, 1))
+
+
+def test_Sum_dummy_eq():
+    assert not Sum(x, (x, a, b)).dummy_eq(1)
+    assert not Sum(x, (x, a, b)).dummy_eq(Sum(x, (x, a, b), (a, 1, 2)))
+    assert not Sum(x, (x, a, b)).dummy_eq(Sum(x, (x, a, c)))
+    assert Sum(x, (x, a, b)).dummy_eq(Sum(x, (x, a, b)))
+    d = Dummy()
+    assert Sum(x, (x, a, d)).dummy_eq(Sum(x, (x, a, c)), c)
+    assert not Sum(x, (x, a, d)).dummy_eq(Sum(x, (x, a, c)))
+    assert Sum(x, (x, a, c)).dummy_eq(Sum(y, (y, a, c)))
+    assert Sum(x, (x, a, d)).dummy_eq(Sum(y, (y, a, c)), c)
+    assert not Sum(x, (x, a, d)).dummy_eq(Sum(y, (y, a, c)))
+
+
+def test_issue_15852():
+    assert summation(x**y*y, (y, -oo, oo)).doit() == Sum(x**y*y, (y, -oo, oo))
+
+
+def test_exceptions():
+    S = Sum(x, (x, a, b))
+    raises(ValueError, lambda: S.change_index(x, x**2, y))
+    S = Sum(x, (x, a, b), (x, 1, 4))
+    raises(ValueError, lambda: S.index(x))
+    S = Sum(x, (x, a, b), (y, 1, 4))
+    raises(ValueError, lambda: S.reorder([x]))
+    S = Sum(x, (x, y, b), (y, 1, 4))
+    raises(ReorderError, lambda: S.reorder_limit(0, 1))
+    S = Sum(x*y, (x, a, b), (y, 1, 4))
+    raises(NotImplementedError, lambda: S.is_convergent())
+
+
+def test_sumproducts_assumptions():
+    M = Symbol('M', integer=True, positive=True)
+
+    m = Symbol('m', integer=True)
+    for func in [Sum, Product]:
+        assert func(m, (m, -M, M)).is_positive is None
+        assert func(m, (m, -M, M)).is_nonpositive is None
+        assert func(m, (m, -M, M)).is_negative is None
+        assert func(m, (m, -M, M)).is_nonnegative is None
+        assert func(m, (m, -M, M)).is_finite is True
+
+    m = Symbol('m', integer=True, nonnegative=True)
+    for func in [Sum, Product]:
+        assert func(m, (m, 0, M)).is_positive is None
+        assert func(m, (m, 0, M)).is_nonpositive is None
+        assert func(m, (m, 0, M)).is_negative is False
+        assert func(m, (m, 0, M)).is_nonnegative is True
+        assert func(m, (m, 0, M)).is_finite is True
+
+    m = Symbol('m', integer=True, positive=True)
+    for func in [Sum, Product]:
+        assert func(m, (m, 1, M)).is_positive is True
+        assert func(m, (m, 1, M)).is_nonpositive is False
+        assert func(m, (m, 1, M)).is_negative is False
+        assert func(m, (m, 1, M)).is_nonnegative is True
+        assert func(m, (m, 1, M)).is_finite is True
+
+    m = Symbol('m', integer=True, negative=True)
+    assert Sum(m, (m, -M, -1)).is_positive is False
+    assert Sum(m, (m, -M, -1)).is_nonpositive is True
+    assert Sum(m, (m, -M, -1)).is_negative is True
+    assert Sum(m, (m, -M, -1)).is_nonnegative is False
+    assert Sum(m, (m, -M, -1)).is_finite is True
+    assert Product(m, (m, -M, -1)).is_positive is None
+    assert Product(m, (m, -M, -1)).is_nonpositive is None
+    assert Product(m, (m, -M, -1)).is_negative is None
+    assert Product(m, (m, -M, -1)).is_nonnegative is None
+    assert Product(m, (m, -M, -1)).is_finite is True
+
+    m = Symbol('m', integer=True, nonpositive=True)
+    assert Sum(m, (m, -M, 0)).is_positive is False
+    assert Sum(m, (m, -M, 0)).is_nonpositive is True
+    assert Sum(m, (m, -M, 0)).is_negative is None
+    assert Sum(m, (m, -M, 0)).is_nonnegative is None
+    assert Sum(m, (m, -M, 0)).is_finite is True
+    assert Product(m, (m, -M, 0)).is_positive is None
+    assert Product(m, (m, -M, 0)).is_nonpositive is None
+    assert Product(m, (m, -M, 0)).is_negative is None
+    assert Product(m, (m, -M, 0)).is_nonnegative is None
+    assert Product(m, (m, -M, 0)).is_finite is True
+
+    m = Symbol('m', integer=True)
+    assert Sum(2, (m, 0, oo)).is_positive is None
+    assert Sum(2, (m, 0, oo)).is_nonpositive is None
+    assert Sum(2, (m, 0, oo)).is_negative is None
+    assert Sum(2, (m, 0, oo)).is_nonnegative is None
+    assert Sum(2, (m, 0, oo)).is_finite is None
+
+    assert Product(2, (m, 0, oo)).is_positive is None
+    assert Product(2, (m, 0, oo)).is_nonpositive is None
+    assert Product(2, (m, 0, oo)).is_negative is False
+    assert Product(2, (m, 0, oo)).is_nonnegative is None
+    assert Product(2, (m, 0, oo)).is_finite is None
+
+    assert Product(0, (x, M, M-1)).is_positive is True
+    assert Product(0, (x, M, M-1)).is_finite is True
+
+
+def test_expand_with_assumptions():
+    M = Symbol('M', integer=True, positive=True)
+    x = Symbol('x', positive=True)
+    m = Symbol('m', nonnegative=True)
+    assert log(Product(x**m, (m, 0, M))).expand() == Sum(m*log(x), (m, 0, M))
+    assert log(Product(exp(x**m), (m, 0, M))).expand() == Sum(x**m, (m, 0, M))
+    assert log(Product(x**m, (m, 0, M))).rewrite(Sum).expand() == Sum(m*log(x), (m, 0, M))
+    assert log(Product(exp(x**m), (m, 0, M))).rewrite(Sum).expand() == Sum(x**m, (m, 0, M))
+
+    n = Symbol('n', nonnegative=True)
+    i, j = symbols('i,j', positive=True, integer=True)
+    x, y = symbols('x,y', positive=True)
+    assert log(Product(x**i*y**j, (i, 1, n), (j, 1, m))).expand() \
+        == Sum(i*log(x) + j*log(y), (i, 1, n), (j, 1, m))
+
+    m = Symbol('m', nonnegative=True, integer=True)
+    s = Sum(x**m, (m, 0, M))
+    s_as_product = s.rewrite(Product)
+    assert s_as_product.has(Product)
+    assert s_as_product == log(Product(exp(x**m), (m, 0, M)))
+    assert s_as_product.expand() == s
+    s5 = s.subs(M, 5)
+    s5_as_product = s5.rewrite(Product)
+    assert s5_as_product.has(Product)
+    assert s5_as_product.doit().expand() == s5.doit()
+
+
+def test_has_finite_limits():
+    x = Symbol('x')
+    assert Sum(1, (x, 1, 9)).has_finite_limits is True
+    assert Sum(1, (x, 1, oo)).has_finite_limits is False
+    M = Symbol('M')
+    assert Sum(1, (x, 1, M)).has_finite_limits is None
+    M = Symbol('M', positive=True)
+    assert Sum(1, (x, 1, M)).has_finite_limits is True
+    x = Symbol('x', positive=True)
+    M = Symbol('M')
+    assert Sum(1, (x, 1, M)).has_finite_limits is True
+
+    assert Sum(1, (x, 1, M), (y, -oo, oo)).has_finite_limits is False
+
+def test_has_reversed_limits():
+    assert Sum(1, (x, 1, 1)).has_reversed_limits is False
+    assert Sum(1, (x, 1, 9)).has_reversed_limits is False
+    assert Sum(1, (x, 1, -9)).has_reversed_limits is True
+    assert Sum(1, (x, 1, 0)).has_reversed_limits is True
+    assert Sum(1, (x, 1, oo)).has_reversed_limits is False
+    M = Symbol('M')
+    assert Sum(1, (x, 1, M)).has_reversed_limits is None
+    M = Symbol('M', positive=True, integer=True)
+    assert Sum(1, (x, 1, M)).has_reversed_limits is False
+    assert Sum(1, (x, 1, M), (y, -oo, oo)).has_reversed_limits is False
+    M = Symbol('M', negative=True)
+    assert Sum(1, (x, 1, M)).has_reversed_limits is True
+
+    assert Sum(1, (x, 1, M), (y, -oo, oo)).has_reversed_limits is True
+    assert Sum(1, (x, oo, oo)).has_reversed_limits is None
+
+
+def test_has_empty_sequence():
+    assert Sum(1, (x, 1, 1)).has_empty_sequence is False
+    assert Sum(1, (x, 1, 9)).has_empty_sequence is False
+    assert Sum(1, (x, 1, -9)).has_empty_sequence is False
+    assert Sum(1, (x, 1, 0)).has_empty_sequence is True
+    assert Sum(1, (x, y, y - 1)).has_empty_sequence is True
+    assert Sum(1, (x, 3, 2), (y, -oo, oo)).has_empty_sequence is True
+    assert Sum(1, (y, -oo, oo), (x, 3, 2)).has_empty_sequence is True
+    assert Sum(1, (x, oo, oo)).has_empty_sequence is False
+
+
+def test_empty_sequence():
+    assert Product(x*y, (x, -oo, oo), (y, 1, 0)).doit() == 1
+    assert Product(x*y, (y, 1, 0), (x, -oo, oo)).doit() == 1
+    assert Sum(x, (x, -oo, oo), (y, 1, 0)).doit() == 0
+    assert Sum(x, (y, 1, 0), (x, -oo, oo)).doit() == 0
+
+
+def test_issue_8016():
+    k = Symbol('k', integer=True)
+    n, m = symbols('n, m', integer=True, positive=True)
+    s = Sum(binomial(m, k)*binomial(m, n - k)*(-1)**k, (k, 0, n))
+    assert s.doit().simplify() == \
+        cos(pi*n/2)*gamma(m + 1)/gamma(n/2 + 1)/gamma(m - n/2 + 1)
+
+
+def test_issue_14313():
+    assert Sum(S.Half**floor(n/2), (n, 1, oo)).is_convergent()
+
+
+def test_issue_14563():
+    # The assertion was failing due to no assumptions methods in Sums and Product
+    assert 1 % Sum(1, (x, 0, 1)) == 1
+
+
+def test_issue_16735():
+    assert Sum(5**n/gamma(n+1), (n, 1, oo)).is_convergent() is S.true
+
+
+def test_issue_14871():
+    assert Sum((Rational(1, 10))**n*rf(0, n)/factorial(n), (n, 0, oo)).rewrite(factorial).doit() == 1
+
+
+def test_issue_17165():
+    n = symbols("n", integer=True)
+    x = symbols('x')
+    s = (x*Sum(x**n, (n, -1, oo)))
+    ssimp = s.doit().simplify()
+
+    assert ssimp == Piecewise((-1/(x - 1), (x > -1) & (x < 1)),
+                              (x*Sum(x**n, (n, -1, oo)), True)), ssimp
+    assert ssimp.simplify() == ssimp
+
+
+def test_issue_19379():
+    assert Sum(factorial(n)/factorial(n + 2), (n, 1, oo)).is_convergent() is S.true
+
+
+def test_issue_20777():
+    assert Sum(exp(x*sin(n/m)), (n, 1, m)).doit() == Sum(exp(x*sin(n/m)), (n, 1, m))
+
+
+def test__dummy_with_inherited_properties_concrete():
+    x = Symbol('x')
+
+    from sympy.core.containers import Tuple
+    d = _dummy_with_inherited_properties_concrete(Tuple(x, 0, 5))
+    assert d.is_real
+    assert d.is_integer
+    assert d.is_nonnegative
+    assert d.is_extended_nonnegative
+
+    d = _dummy_with_inherited_properties_concrete(Tuple(x, 1, 9))
+    assert d.is_real
+    assert d.is_integer
+    assert d.is_positive
+    assert d.is_odd is None
+
+    d = _dummy_with_inherited_properties_concrete(Tuple(x, -5, 5))
+    assert d.is_real
+    assert d.is_integer
+    assert d.is_positive is None
+    assert d.is_extended_nonnegative is None
+    assert d.is_odd is None
+
+    d = _dummy_with_inherited_properties_concrete(Tuple(x, -1.5, 1.5))
+    assert d.is_real
+    assert d.is_integer is None
+    assert d.is_positive is None
+    assert d.is_extended_nonnegative is None
+
+    N = Symbol('N', integer=True, positive=True)
+    d = _dummy_with_inherited_properties_concrete(Tuple(x, 2, N))
+    assert d.is_real
+    assert d.is_positive
+    assert d.is_integer
+
+    # Return None if no assumptions are added
+    N = Symbol('N', integer=True, positive=True)
+    d = _dummy_with_inherited_properties_concrete(Tuple(N, 2, 4))
+    assert d is None
+
+    x = Symbol('x', negative=True)
+    raises(InconsistentAssumptions,
+           lambda: _dummy_with_inherited_properties_concrete(Tuple(x, 1, 5)))
+
+
+def test_matrixsymbol_summation_numerical_limits():
+    A = MatrixSymbol('A', 3, 3)
+    n = Symbol('n', integer=True)
+
+    assert Sum(A**n, (n, 0, 2)).doit() == Identity(3) + A + A**2
+    assert Sum(A, (n, 0, 2)).doit() == 3*A
+    assert Sum(n*A, (n, 0, 2)).doit() == 3*A
+
+    B = Matrix([[0, n, 0], [-1, 0, 0], [0, 0, 2]])
+    ans = Matrix([[0, 6, 0], [-4, 0, 0], [0, 0, 8]]) + 4*A
+    assert Sum(A+B, (n, 0, 3)).doit() == ans
+    ans = A*Matrix([[0, 6, 0], [-4, 0, 0], [0, 0, 8]])
+    assert Sum(A*B, (n, 0, 3)).doit() == ans
+
+    ans = (A**2*Matrix([[-2, 0, 0], [0,-2, 0], [0, 0, 4]]) +
+           A**3*Matrix([[0, -9, 0], [3, 0, 0], [0, 0, 8]]) +
+           A*Matrix([[0, 1, 0], [-1, 0, 0], [0, 0, 2]]))
+    assert Sum(A**n*B**n, (n, 1, 3)).doit() == ans
+
+
+def test_issue_21651():
+    i = Symbol('i')
+    a = Sum(floor(2*2**(-i)), (i, S.One, 2))
+    assert a.doit() == S.One
+
+
+@XFAIL
+def test_matrixsymbol_summation_symbolic_limits():
+    N = Symbol('N', integer=True, positive=True)
+
+    A = MatrixSymbol('A', 3, 3)
+    n = Symbol('n', integer=True)
+    assert Sum(A, (n, 0, N)).doit() == (N+1)*A
+    assert Sum(n*A, (n, 0, N)).doit() == (N**2/2+N/2)*A
+
+
+def test_summation_by_residues():
+    x = Symbol('x')
+
+    # Examples from Nakhle H. Asmar, Loukas Grafakos,
+    # Complex Analysis with Applications
+    assert eval_sum_residue(1 / (x**2 + 1), (x, -oo, oo)) == pi/tanh(pi)
+    assert eval_sum_residue(1 / x**6, (x, S(1), oo)) == pi**6/945
+    assert eval_sum_residue(1 / (x**2 + 9), (x, -oo, oo)) == pi/(3*tanh(3*pi))
+    assert eval_sum_residue(1 / (x**2 + 1)**2, (x, -oo, oo)).cancel() == \
+        (-pi**2*tanh(pi)**2 + pi*tanh(pi) + pi**2)/(2*tanh(pi)**2)
+    assert eval_sum_residue(x**2 / (x**2 + 1)**2, (x, -oo, oo)).cancel() == \
+        (-pi**2 + pi*tanh(pi) + pi**2*tanh(pi)**2)/(2*tanh(pi)**2)
+    assert eval_sum_residue(1 / (4*x**2 - 1), (x, -oo, oo)) == 0
+    assert eval_sum_residue(x**2 / (x**2 - S(1)/4)**2, (x, -oo, oo)) == pi**2/2
+    assert eval_sum_residue(1 / (4*x**2 - 1)**2, (x, -oo, oo)) == pi**2/8
+    assert eval_sum_residue(1 / ((x - S(1)/2)**2 + 1), (x, -oo, oo)) == pi*tanh(pi)
+    assert eval_sum_residue(1 / x**2, (x, S(1), oo)) == pi**2/6
+    assert eval_sum_residue(1 / x**4, (x, S(1), oo)) == pi**4/90
+    assert eval_sum_residue(1 / x**2 / (x**2 + 4), (x, S(1), oo)) == \
+        -pi*(-pi/12 - 1/(16*pi) + 1/(8*tanh(2*pi)))/2
+
+    # Some examples made from 1 / (x**2 + 1)
+    assert eval_sum_residue(1 / (x**2 + 1), (x, S(0), oo)) == \
+        S(1)/2 + pi/(2*tanh(pi))
+    assert eval_sum_residue(1 / (x**2 + 1), (x, S(1), oo)) == \
+        -S(1)/2 + pi/(2*tanh(pi))
+    assert eval_sum_residue(1 / (x**2 + 1), (x, S(-1), oo)) == \
+        1 + pi/(2*tanh(pi))
+    assert eval_sum_residue((-1)**x / (x**2 + 1), (x, -oo, oo)) == \
+        pi/sinh(pi)
+    assert eval_sum_residue((-1)**x / (x**2 + 1), (x, S(0), oo)) == \
+        pi/(2*sinh(pi)) + S(1)/2
+    assert eval_sum_residue((-1)**x / (x**2 + 1), (x, S(1), oo)) == \
+        -S(1)/2 + pi/(2*sinh(pi))
+    assert eval_sum_residue((-1)**x / (x**2 + 1), (x, S(-1), oo)) == \
+        pi/(2*sinh(pi))
+
+    # Some examples made from shifting of 1 / (x**2 + 1)
+    assert eval_sum_residue(1 / (x**2 + 2*x + 2), (x, S(-1), oo)) == S(1)/2 + pi/(2*tanh(pi))
+    assert eval_sum_residue(1 / (x**2 + 4*x + 5), (x, S(-2), oo)) == S(1)/2 + pi/(2*tanh(pi))
+    assert eval_sum_residue(1 / (x**2 - 2*x + 2), (x, S(1), oo)) == S(1)/2 + pi/(2*tanh(pi))
+    assert eval_sum_residue(1 / (x**2 - 4*x + 5), (x, S(2), oo)) == S(1)/2 + pi/(2*tanh(pi))
+    assert eval_sum_residue((-1)**x * -1 / (x**2 + 2*x + 2), (x, S(-1), oo)) ==  S(1)/2 + pi/(2*sinh(pi))
+    assert eval_sum_residue((-1)**x * -1 / (x**2 -2*x + 2), (x, S(1), oo)) == S(1)/2 + pi/(2*sinh(pi))
+
+    # Some examples made from 1 / x**2
+    assert eval_sum_residue(1 / x**2, (x, S(2), oo)) == -1 + pi**2/6
+    assert eval_sum_residue(1 / x**2, (x, S(3), oo)) == -S(5)/4 + pi**2/6
+    assert eval_sum_residue((-1)**x / x**2, (x, S(1), oo)) == -pi**2/12
+    assert eval_sum_residue((-1)**x / x**2, (x, S(2), oo)) == 1 - pi**2/12
+
+
+@slow
+def test_summation_by_residues_failing():
+    x = Symbol('x')
+
+    # Failing because of the bug in residue computation
+    assert eval_sum_residue(x**2 / (x**4 + 1), (x, S(1), oo))
+    assert eval_sum_residue(1 / ((x - 1)*(x - 2) + 1), (x, -oo, oo)) != 0
+
+
+def test_process_limits():
+    from sympy.concrete.expr_with_limits import _process_limits
+
+    # these should be (x, Range(3)) not Range(3)
+    raises(ValueError, lambda: _process_limits(
+        Range(3), discrete=True))
+    raises(ValueError, lambda: _process_limits(
+        Range(3), discrete=False))
+    # these should be (x, union) not union
+    # (but then we would get a TypeError because we don't
+    # handle non-contiguous sets: see below use of `union`)
+    union = Or(x < 1, x > 3).as_set()
+    raises(ValueError, lambda: _process_limits(
+        union, discrete=True))
+    raises(ValueError, lambda: _process_limits(
+        union, discrete=False))
+
+    # error not triggered if not needed
+    assert _process_limits((x, 1, 2)) == ([(x, 1, 2)], 1)
+
+    # this equivalence is used to detect Reals in _process_limits
+    assert isinstance(S.Reals, Interval)
+
+    C = Integral  # continuous limits
+    assert C(x, x >= 5) == C(x, (x, 5, oo))
+    assert C(x, x < 3) == C(x, (x, -oo, 3))
+    ans = C(x, (x, 0, 3))
+    assert C(x, And(x >= 0, x < 3)) == ans
+    assert C(x, (x, Interval.Ropen(0, 3))) == ans
+    raises(TypeError, lambda: C(x, (x, Range(3))))
+
+    # discrete limits
+    for D in (Sum, Product):
+        r, ans = Range(3, 10, 2), D(2*x + 3, (x, 0, 3))
+        assert D(x, (x, r)) == ans
+        assert D(x, (x, r.reversed)) == ans
+        r, ans = Range(3, oo, 2), D(2*x + 3, (x, 0, oo))
+        assert D(x, (x, r)) == ans
+        assert D(x, (x, r.reversed)) == ans
+        r, ans = Range(-oo, 5, 2), D(3 - 2*x, (x, 0, oo))
+        assert D(x, (x, r)) == ans
+        assert D(x, (x, r.reversed)) == ans
+        raises(TypeError, lambda: D(x, x > 0))
+        raises(ValueError, lambda: D(x, Interval(1, 3)))
+        raises(NotImplementedError, lambda: D(x, (x, union)))
+
+
+def test_pr_22677():
+    b = Symbol('b', integer=True, positive=True)
+    assert Sum(1/x**2,(x, 0, b)).doit() == Sum(x**(-2), (x, 0, b))
+    assert Sum(1/(x - b)**2,(x, 0, b-1)).doit() == Sum(
+        (-b + x)**(-2), (x, 0, b - 1))
+
+
+def test_issue_23952():
+    p, q = symbols("p q", real=True, nonnegative=True)
+    k1, k2 = symbols("k1 k2", integer=True, nonnegative=True)
+    n = Symbol("n", integer=True, positive=True)
+    expr = Sum(abs(k1 - k2)*p**k1 *(1 - q)**(n - k2),
+        (k1, 0, n), (k2, 0, n))
+    assert expr.subs(p,0).subs(q,1).subs(n, 3).doit() == 3
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/conftest.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/conftest.py
new file mode 100644
index 0000000000000000000000000000000000000000..788ec7ed8a38de422b76c4ac19057513670d2d38
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/conftest.py
@@ -0,0 +1,96 @@
+import sys
+
+sys._running_pytest = True  # type: ignore
+from sympy.external.importtools import version_tuple
+
+import pytest
+from sympy.core.cache import clear_cache, USE_CACHE
+from sympy.external.gmpy import GROUND_TYPES
+from sympy.utilities.misc import ARCH
+import re
+
+try:
+    import hypothesis
+
+    hypothesis.settings.register_profile("sympy_hypothesis_profile", deadline=None)
+    hypothesis.settings.load_profile("sympy_hypothesis_profile")
+except ImportError:
+    raise ImportError(
+        "hypothesis is a required dependency to run the SymPy test suite. "
+        "Install it with 'pip install hypothesis' or 'conda install -c conda-forge hypothesis'"
+    )
+
+
+sp = re.compile(r"([0-9]+)/([1-9][0-9]*)")
+
+
+def process_split(config, items):
+    split = config.getoption("--split")
+    if not split:
+        return
+    m = sp.match(split)
+    if not m:
+        raise ValueError(
+            "split must be a string of the form a/b " "where a and b are ints."
+        )
+    i, t = map(int, m.groups())
+    start, end = (i - 1) * len(items) // t, i * len(items) // t
+
+    if i < t:
+        # remove elements from end of list first
+        del items[end:]
+    del items[:start]
+
+
+def pytest_report_header(config):
+    s = "architecture: %s\n" % ARCH
+    s += "cache:        %s\n" % USE_CACHE
+    version = ""
+    if GROUND_TYPES == "gmpy":
+        import gmpy2
+
+        version = gmpy2.version()
+    elif GROUND_TYPES == "flint":
+        try:
+            from flint import __version__
+        except ImportError:
+            version = "unknown"
+        else:
+            version = f'(python-flint=={__version__})'
+    s += "ground types: %s %s\n" % (GROUND_TYPES, version)
+    return s
+
+
+def pytest_terminal_summary(terminalreporter):
+    if terminalreporter.stats.get("error", None) or terminalreporter.stats.get(
+        "failed", None
+    ):
+        terminalreporter.write_sep(" ", "DO *NOT* COMMIT!", red=True, bold=True)
+
+
+def pytest_addoption(parser):
+    parser.addoption("--split", action="store", default="", help="split tests")
+
+
+def pytest_collection_modifyitems(config, items):
+    """pytest hook."""
+    # handle splits
+    process_split(config, items)
+
+
+@pytest.fixture(autouse=True, scope="module")
+def file_clear_cache():
+    clear_cache()
+
+
+@pytest.fixture(autouse=True, scope="module")
+def check_disabled(request):
+    if getattr(request.module, "disabled", False):
+        pytest.skip("test requirements not met.")
+    elif getattr(request.module, "ipython", False):
+        # need to check version and options for ipython tests
+        if (
+            version_tuple(pytest.__version__) < version_tuple("2.6.3")
+            and pytest.config.getvalue("-s") != "no"
+        ):
+            pytest.skip("run py.test with -s or upgrade to newer version.")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..4c03c9fc11479bb6d93a3bff3dfd0992ef994a19
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/__init__.py
@@ -0,0 +1,103 @@
+"""Core module. Provides the basic operations needed in sympy.
+"""
+
+from .sympify import sympify, SympifyError
+from .cache import cacheit
+from .assumptions import assumptions, check_assumptions, failing_assumptions, common_assumptions
+from .basic import Basic, Atom
+from .singleton import S
+from .expr import Expr, AtomicExpr, UnevaluatedExpr
+from .symbol import Symbol, Wild, Dummy, symbols, var
+from .numbers import Number, Float, Rational, Integer, NumberSymbol, \
+    RealNumber, igcd, ilcm, seterr, E, I, nan, oo, pi, zoo, \
+    AlgebraicNumber, comp, mod_inverse
+from .power import Pow
+from .intfunc import integer_nthroot, integer_log, num_digits, trailing
+from .mul import Mul, prod
+from .add import Add
+from .mod import Mod
+from .relational import ( Rel, Eq, Ne, Lt, Le, Gt, Ge,
+    Equality, GreaterThan, LessThan, Unequality, StrictGreaterThan,
+    StrictLessThan )
+from .multidimensional import vectorize
+from .function import Lambda, WildFunction, Derivative, diff, FunctionClass, \
+    Function, Subs, expand, PoleError, count_ops, \
+    expand_mul, expand_log, expand_func, \
+    expand_trig, expand_complex, expand_multinomial, nfloat, \
+    expand_power_base, expand_power_exp, arity
+from .evalf import PrecisionExhausted, N
+from .containers import Tuple, Dict
+from .exprtools import gcd_terms, factor_terms, factor_nc
+from .parameters import evaluate
+from .kind import UndefinedKind, NumberKind, BooleanKind
+from .traversal import preorder_traversal, bottom_up, use, postorder_traversal
+from .sorting import default_sort_key, ordered
+
+# expose singletons
+Catalan = S.Catalan
+EulerGamma = S.EulerGamma
+GoldenRatio = S.GoldenRatio
+TribonacciConstant = S.TribonacciConstant
+
+__all__ = [
+    'sympify', 'SympifyError',
+
+    'cacheit',
+
+    'assumptions', 'check_assumptions', 'failing_assumptions',
+    'common_assumptions',
+
+    'Basic', 'Atom',
+
+    'S',
+
+    'Expr', 'AtomicExpr', 'UnevaluatedExpr',
+
+    'Symbol', 'Wild', 'Dummy', 'symbols', 'var',
+
+    'Number', 'Float', 'Rational', 'Integer', 'NumberSymbol', 'RealNumber',
+    'igcd', 'ilcm', 'seterr', 'E', 'I', 'nan', 'oo', 'pi', 'zoo',
+    'AlgebraicNumber', 'comp', 'mod_inverse',
+
+    'Pow',
+
+    'integer_nthroot', 'integer_log', 'num_digits', 'trailing',
+
+    'Mul', 'prod',
+
+    'Add',
+
+    'Mod',
+
+    'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', 'Equality', 'GreaterThan',
+    'LessThan', 'Unequality', 'StrictGreaterThan', 'StrictLessThan',
+
+    'vectorize',
+
+    'Lambda', 'WildFunction', 'Derivative', 'diff', 'FunctionClass',
+    'Function', 'Subs', 'expand', 'PoleError', 'count_ops', 'expand_mul',
+    'expand_log', 'expand_func', 'expand_trig', 'expand_complex',
+    'expand_multinomial', 'nfloat', 'expand_power_base', 'expand_power_exp',
+    'arity',
+
+    'PrecisionExhausted', 'N',
+
+    'evalf', # The module?
+
+    'Tuple', 'Dict',
+
+    'gcd_terms', 'factor_terms', 'factor_nc',
+
+    'evaluate',
+
+    'Catalan',
+    'EulerGamma',
+    'GoldenRatio',
+    'TribonacciConstant',
+
+    'UndefinedKind', 'NumberKind', 'BooleanKind',
+
+    'preorder_traversal', 'bottom_up', 'use', 'postorder_traversal',
+
+    'default_sort_key', 'ordered',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/_print_helpers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/_print_helpers.py
new file mode 100644
index 0000000000000000000000000000000000000000..d704ed220d444e2d8510b280dca85c8ae6149d4c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/_print_helpers.py
@@ -0,0 +1,65 @@
+"""
+Base class to provide str and repr hooks that `init_printing` can overwrite.
+
+This is exposed publicly in the `printing.defaults` module,
+but cannot be defined there without causing circular imports.
+"""
+
+class Printable:
+    """
+    The default implementation of printing for SymPy classes.
+
+    This implements a hack that allows us to print elements of built-in
+    Python containers in a readable way. Natively Python uses ``repr()``
+    even if ``str()`` was explicitly requested. Mix in this trait into
+    a class to get proper default printing.
+
+    This also adds support for LaTeX printing in jupyter notebooks.
+    """
+
+    # Since this class is used as a mixin we set empty slots. That means that
+    # instances of any subclasses that use slots will not need to have a
+    # __dict__.
+    __slots__ = ()
+
+    # Note, we always use the default ordering (lex) in __str__ and __repr__,
+    # regardless of the global setting. See issue 5487.
+    def __str__(self):
+        from sympy.printing.str import sstr
+        return sstr(self, order=None)
+
+    __repr__ = __str__
+
+    def _repr_disabled(self):
+        """
+        No-op repr function used to disable jupyter display hooks.
+
+        When :func:`sympy.init_printing` is used to disable certain display
+        formats, this function is copied into the appropriate ``_repr_*_``
+        attributes.
+
+        While we could just set the attributes to `None``, doing it this way
+        allows derived classes to call `super()`.
+        """
+        return None
+
+    # We don't implement _repr_png_ here because it would add a large amount of
+    # data to any notebook containing SymPy expressions, without adding
+    # anything useful to the notebook. It can still enabled manually, e.g.,
+    # for the qtconsole, with init_printing().
+    _repr_png_ = _repr_disabled
+
+    _repr_svg_ = _repr_disabled
+
+    def _repr_latex_(self):
+        """
+        IPython/Jupyter LaTeX printing
+
+        To change the behavior of this (e.g., pass in some settings to LaTeX),
+        use init_printing(). init_printing() will also enable LaTeX printing
+        for built in numeric types like ints and container types that contain
+        SymPy objects, like lists and dictionaries of expressions.
+        """
+        from sympy.printing.latex import latex
+        s = latex(self, mode='plain')
+        return "$\\displaystyle %s$" % s
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/add.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/add.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d280f3286c34cd0dea14bf61194ed03ee6bf6ae
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/add.py
@@ -0,0 +1,1280 @@
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, ClassVar
+from collections import defaultdict
+from functools import reduce
+from operator import attrgetter
+from .basic import _args_sortkey
+from .parameters import global_parameters
+from .logic import _fuzzy_group, fuzzy_or, fuzzy_not
+from .singleton import S
+from .operations import AssocOp, AssocOpDispatcher
+from .cache import cacheit
+from .intfunc import ilcm, igcd
+from .expr import Expr
+from .kind import UndefinedKind
+from sympy.utilities.iterables import is_sequence, sift
+
+
+if TYPE_CHECKING:
+    from sympy.core.numbers import Number
+    from sympy.series.order import Order
+
+
+def _could_extract_minus_sign(expr):
+    # assume expr is Add-like
+    # We choose the one with less arguments with minus signs
+    negative_args = sum(1 for i in expr.args
+        if i.could_extract_minus_sign())
+    positive_args = len(expr.args) - negative_args
+    if positive_args > negative_args:
+        return False
+    elif positive_args < negative_args:
+        return True
+    # choose based on .sort_key() to prefer
+    # x - 1 instead of 1 - x and
+    # 3 - sqrt(2) instead of -3 + sqrt(2)
+    return bool(expr.sort_key() < (-expr).sort_key())
+
+
+def _addsort(args):
+    # in-place sorting of args
+    args.sort(key=_args_sortkey)
+
+
+def _unevaluated_Add(*args):
+    """Return a well-formed unevaluated Add: Numbers are collected and
+    put in slot 0 and args are sorted. Use this when args have changed
+    but you still want to return an unevaluated Add.
+
+    Examples
+    ========
+
+    >>> from sympy.core.add import _unevaluated_Add as uAdd
+    >>> from sympy import S, Add
+    >>> from sympy.abc import x, y
+    >>> a = uAdd(*[S(1.0), x, S(2)])
+    >>> a.args[0]
+    3.00000000000000
+    >>> a.args[1]
+    x
+
+    Beyond the Number being in slot 0, there is no other assurance of
+    order for the arguments since they are hash sorted. So, for testing
+    purposes, output produced by this in some other function can only
+    be tested against the output of this function or as one of several
+    options:
+
+    >>> opts = (Add(x, y, evaluate=False), Add(y, x, evaluate=False))
+    >>> a = uAdd(x, y)
+    >>> assert a in opts and a == uAdd(x, y)
+    >>> uAdd(x + 1, x + 2)
+    x + x + 3
+    """
+    args = list(args)
+    newargs = []
+    co = S.Zero
+    while args:
+        a = args.pop()
+        if a.is_Add:
+            # this will keep nesting from building up
+            # so that x + (x + 1) -> x + x + 1 (3 args)
+            args.extend(a.args)
+        elif a.is_Number:
+            co += a
+        else:
+            newargs.append(a)
+    _addsort(newargs)
+    if co:
+        newargs.insert(0, co)
+    return Add._from_args(newargs)
+
+
+class Add(Expr, AssocOp):
+    """
+    Expression representing addition operation for algebraic group.
+
+    .. deprecated:: 1.7
+
+       Using arguments that aren't subclasses of :class:`~.Expr` in core
+       operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is
+       deprecated. See :ref:`non-expr-args-deprecated` for details.
+
+    Every argument of ``Add()`` must be ``Expr``. Infix operator ``+``
+    on most scalar objects in SymPy calls this class.
+
+    Another use of ``Add()`` is to represent the structure of abstract
+    addition so that its arguments can be substituted to return different
+    class. Refer to examples section for this.
+
+    ``Add()`` evaluates the argument unless ``evaluate=False`` is passed.
+    The evaluation logic includes:
+
+    1. Flattening
+        ``Add(x, Add(y, z))`` -> ``Add(x, y, z)``
+
+    2. Identity removing
+        ``Add(x, 0, y)`` -> ``Add(x, y)``
+
+    3. Coefficient collecting by ``.as_coeff_Mul()``
+        ``Add(x, 2*x)`` -> ``Mul(3, x)``
+
+    4. Term sorting
+        ``Add(y, x, 2)`` -> ``Add(2, x, y)``
+
+    If no argument is passed, identity element 0 is returned. If single
+    element is passed, that element is returned.
+
+    Note that ``Add(*args)`` is more efficient than ``sum(args)`` because
+    it flattens the arguments. ``sum(a, b, c, ...)`` recursively adds the
+    arguments as ``a + (b + (c + ...))``, which has quadratic complexity.
+    On the other hand, ``Add(a, b, c, d)`` does not assume nested
+    structure, making the complexity linear.
+
+    Since addition is group operation, every argument should have the
+    same :obj:`sympy.core.kind.Kind()`.
+
+    Examples
+    ========
+
+    >>> from sympy import Add, I
+    >>> from sympy.abc import x, y
+    >>> Add(x, 1)
+    x + 1
+    >>> Add(x, x)
+    2*x
+    >>> 2*x**2 + 3*x + I*y + 2*y + 2*x/5 + 1.0*y + 1
+    2*x**2 + 17*x/5 + 3.0*y + I*y + 1
+
+    If ``evaluate=False`` is passed, result is not evaluated.
+
+    >>> Add(1, 2, evaluate=False)
+    1 + 2
+    >>> Add(x, x, evaluate=False)
+    x + x
+
+    ``Add()`` also represents the general structure of addition operation.
+
+    >>> from sympy import MatrixSymbol
+    >>> A,B = MatrixSymbol('A', 2,2), MatrixSymbol('B', 2,2)
+    >>> expr = Add(x,y).subs({x:A, y:B})
+    >>> expr
+    A + B
+    >>> type(expr)
+    
+
+    Note that the printers do not display in args order.
+
+    >>> Add(x, 1)
+    x + 1
+    >>> Add(x, 1).args
+    (1, x)
+
+    See Also
+    ========
+
+    MatAdd
+
+    """
+
+    __slots__ = ()
+
+    is_Add = True
+
+    _args_type = Expr
+
+    identity: ClassVar[Expr]
+
+    if TYPE_CHECKING:
+
+        def __new__(cls, *args: Expr | complex, evaluate: bool=True) -> Expr: # type: ignore
+            ...
+
+        @property
+        def args(self) -> tuple[Expr, ...]:
+            ...
+
+    @classmethod
+    def flatten(cls, seq: list[Expr]) -> tuple[list[Expr], list[Expr], None]:
+        """
+        Takes the sequence "seq" of nested Adds and returns a flatten list.
+
+        Returns: (commutative_part, noncommutative_part, order_symbols)
+
+        Applies associativity, all terms are commutable with respect to
+        addition.
+
+        NB: the removal of 0 is already handled by AssocOp.__new__
+
+        See Also
+        ========
+
+        sympy.core.mul.Mul.flatten
+
+        """
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.matrices.expressions import MatrixExpr
+        from sympy.tensor.tensor import TensExpr, TensAdd
+        rv = None
+        if len(seq) == 2:
+            a, b = seq
+            if b.is_Rational:
+                a, b = b, a
+            if a.is_Rational:
+                if b.is_Mul:
+                    rv = [a, b], [], None
+            if rv:
+                if all(s.is_commutative for s in rv[0]):
+                    return rv
+                return [], rv[0], None
+
+        # term -> coeff
+        # e.g. x**2 -> 5   for ... + 5*x**2 + ...
+        terms: dict[Expr, Number] = {}
+
+        # coefficient (Number or zoo) to always be in slot 0
+        # e.g. 3 + ...
+        coeff: Expr = S.Zero
+
+        order_factors: list[Order] = []
+
+        extra: list[MatrixExpr] = []
+
+        for o in seq:
+
+            # O(x)
+            if o.is_Order:
+                if o.expr.is_zero: # type: ignore
+                    continue
+                if any(o1.contains(o) for o1 in order_factors):
+                    continue
+                order_factors = [o1 for o1 in order_factors if not o.contains(o1)] # type: ignore
+                order_factors = [o] + order_factors # type: ignore
+                continue
+
+            # 3 or NaN
+            elif o.is_Number:
+                if (o is S.NaN or coeff is S.ComplexInfinity and
+                        o.is_finite is False) and not extra:
+                    # we know for sure the result will be nan
+                    return [S.NaN], [], None
+                if coeff.is_Number or isinstance(coeff, AccumBounds):
+                    coeff += o
+                    if coeff is S.NaN and not extra:
+                        # we know for sure the result will be nan
+                        return [S.NaN], [], None
+                continue
+
+            elif isinstance(o, AccumBounds):
+                coeff = o.__add__(coeff)
+                continue
+
+            elif isinstance(o, MatrixExpr):
+                # can't add 0 to Matrix so make sure coeff is not 0
+                extra.append(o)
+                continue
+
+            elif isinstance(o, TensExpr):
+                coeff = TensAdd(o, coeff).doit(deep=False)
+                continue
+
+            elif o is S.ComplexInfinity:
+                if coeff.is_finite is False and not extra:
+                    # we know for sure the result will be nan
+                    return [S.NaN], [], None
+                coeff = S.ComplexInfinity
+                continue
+
+            # Add([...])
+            elif o.is_Add:
+                # NB: here we assume Add is always commutative
+                o_args: tuple[Expr, ...] = o.args # type: ignore
+                seq.extend(o_args)  # TODO zerocopy?
+                continue
+
+            # Mul([...])
+            elif o.is_Mul:
+                c, s = o.as_coeff_Mul()
+
+            # check for unevaluated Pow, e.g. 2**3 or 2**(-1/2)
+            elif o.is_Pow:
+                b, e = o.as_base_exp()
+                if b.is_Number and (e.is_Integer or
+                                   (e.is_Rational and e.is_negative)):
+                    seq.append(b**e)
+                    continue
+                c, s = S.One, o
+
+            else:
+                # everything else
+                c = S.One
+                s = o
+
+            # now we have:
+            # o = c*s, where
+            #
+            # c is a Number
+            # s is an expression with number factor extracted
+            # let's collect terms with the same s, so e.g.
+            # 2*x**2 + 3*x**2  ->  5*x**2
+            if s in terms:
+                terms[s] += c
+                if terms[s] is S.NaN and not extra:
+                    # we know for sure the result will be nan
+                    return [S.NaN], [], None
+            else:
+                terms[s] = c
+
+        # now let's construct new args:
+        # [2*x**2, x**3, 7*x**4, pi, ...]
+        newseq = []
+        noncommutative = False
+        for s, c in terms.items():
+            # 0*s
+            if c.is_zero:
+                continue
+            # 1*s
+            elif c is S.One:
+                newseq.append(s)
+            # c*s
+            else:
+                if s.is_Mul:
+                    # Mul, already keeps its arguments in perfect order.
+                    # so we can simply put c in slot0 and go the fast way.
+                    #
+                    # XXX: This breaks VectorMul unless it overrides
+                    # _new_rawargs
+                    cs = s._new_rawargs(*((c,) + s.args)) # type: ignore
+                    newseq.append(cs)
+                elif s.is_Add:
+                    # we just re-create the unevaluated Mul
+                    newseq.append(Mul(c, s, evaluate=False))
+                else:
+                    # alternatively we have to call all Mul's machinery (slow)
+                    newseq.append(Mul(c, s))
+
+            noncommutative = noncommutative or not s.is_commutative
+
+        # oo, -oo
+        if coeff is S.Infinity:
+            newseq = [f for f in newseq if not (f.is_extended_nonnegative or f.is_real)]
+
+        elif coeff is S.NegativeInfinity:
+            newseq = [f for f in newseq if not (f.is_extended_nonpositive or f.is_real)]
+
+        if coeff is S.ComplexInfinity:
+            # zoo might be
+            #   infinite_real + finite_im
+            #   finite_real + infinite_im
+            #   infinite_real + infinite_im
+            # addition of a finite real or imaginary number won't be able to
+            # change the zoo nature; adding an infinite qualtity would result
+            # in a NaN condition if it had sign opposite of the infinite
+            # portion of zoo, e.g., infinite_real - infinite_real.
+            newseq = [c for c in newseq if not (c.is_finite and
+                                                c.is_extended_real is not None)]
+
+        # process O(x)
+        if order_factors:
+            newseq2 = []
+            for t in newseq:
+                # x + O(x) -> O(x)
+                if not any(o.contains(t) for o in order_factors):
+                    newseq2.append(t)
+            newseq = newseq2 + order_factors # type: ignore
+            # 1 + O(1) -> O(1)
+            for o in order_factors:
+                if o.contains(coeff):
+                    coeff = S.Zero
+                    break
+
+        # order args canonically
+        _addsort(newseq)
+
+        # current code expects coeff to be first
+        if coeff is not S.Zero:
+            newseq.insert(0, coeff)
+
+        if extra:
+            newseq += extra
+            noncommutative = True
+
+        # we are done
+        if noncommutative:
+            return [], newseq, None
+        else:
+            return newseq, [], None
+
+    @classmethod
+    def class_key(cls):
+        return 3, 1, cls.__name__
+
+    @property
+    def kind(self):
+        k = attrgetter('kind')
+        kinds = map(k, self.args)
+        kinds = frozenset(kinds)
+        if len(kinds) != 1:
+            # Since addition is group operator, kind must be same.
+            # We know that this is unexpected signature, so return this.
+            result = UndefinedKind
+        else:
+            result, = kinds
+        return result
+
+    def could_extract_minus_sign(self):
+        return _could_extract_minus_sign(self)
+
+    @cacheit
+    def as_coeff_add(self, *deps):
+        """
+        Returns a tuple (coeff, args) where self is treated as an Add and coeff
+        is the Number term and args is a tuple of all other terms.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> (7 + 3*x).as_coeff_add()
+        (7, (3*x,))
+        >>> (7*x).as_coeff_add()
+        (0, (7*x,))
+        """
+        if deps:
+            l1, l2 = sift(self.args, lambda x: x.has_free(*deps), binary=True)
+            return self._new_rawargs(*l2), tuple(l1)
+        coeff, notrat = self.args[0].as_coeff_add()
+        if coeff is not S.Zero:
+            return coeff, notrat + self.args[1:]
+        return S.Zero, self.args
+
+    def as_coeff_Add(self, rational=False, deps=None) -> tuple[Number, Expr]:
+        """
+        Efficiently extract the coefficient of a summation.
+        """
+        coeff, args = self.args[0], self.args[1:]
+
+        if coeff.is_Number and not rational or coeff.is_Rational:
+            return coeff, self._new_rawargs(*args) # type: ignore
+        return S.Zero, self
+
+    # Note, we intentionally do not implement Add.as_coeff_mul().  Rather, we
+    # let Expr.as_coeff_mul() just always return (S.One, self) for an Add.  See
+    # issue 5524.
+
+    def _eval_power(self, expt):
+        from .evalf import pure_complex
+        from .relational import is_eq
+        if len(self.args) == 2 and any(_.is_infinite for _ in self.args):
+            if expt.is_zero is False and is_eq(expt, S.One) is False:
+                # looking for literal a + I*b
+                a, b = self.args
+                if a.coeff(S.ImaginaryUnit):
+                    a, b = b, a
+                ico = b.coeff(S.ImaginaryUnit)
+                if ico and ico.is_extended_real and a.is_extended_real:
+                    if expt.is_extended_negative:
+                        return S.Zero
+                    if expt.is_extended_positive:
+                        return S.ComplexInfinity
+            return
+        if expt.is_Rational and self.is_number:
+            ri = pure_complex(self)
+            if ri:
+                r, i = ri
+                if expt.q == 2:
+                    from sympy.functions.elementary.miscellaneous import sqrt
+                    D = sqrt(r**2 + i**2)
+                    if D.is_Rational:
+                        from .exprtools import factor_terms
+                        from sympy.functions.elementary.complexes import sign
+                        from .function import expand_multinomial
+                        # (r, i, D) is a Pythagorean triple
+                        root = sqrt(factor_terms((D - r)/2))**expt.p
+                        return root*expand_multinomial((
+                            # principle value
+                            (D + r)/abs(i) + sign(i)*S.ImaginaryUnit)**expt.p)
+                elif expt == -1:
+                    return _unevaluated_Mul(
+                        r - i*S.ImaginaryUnit,
+                        1/(r**2 + i**2))
+
+    @cacheit
+    def _eval_derivative(self, s):
+        return self.func(*[a.diff(s) for a in self.args])
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        terms = [t.nseries(x, n=n, logx=logx, cdir=cdir) for t in self.args]
+        return self.func(*terms)
+
+    def _matches_simple(self, expr, repl_dict):
+        # handle (w+3).matches('x+5') -> {w: x+2}
+        coeff, terms = self.as_coeff_add()
+        if len(terms) == 1:
+            return terms[0].matches(expr - coeff, repl_dict)
+        return
+
+    def matches(self, expr, repl_dict=None, old=False):
+        return self._matches_commutative(expr, repl_dict, old)
+
+    @staticmethod
+    def _combine_inverse(lhs, rhs):
+        """
+        Returns lhs - rhs, but treats oo like a symbol so oo - oo
+        returns 0, instead of a nan.
+        """
+        from sympy.simplify.simplify import signsimp
+        inf = (S.Infinity, S.NegativeInfinity)
+        if lhs.has(*inf) or rhs.has(*inf):
+            from .symbol import Dummy
+            oo = Dummy('oo')
+            reps = {
+                S.Infinity: oo,
+                S.NegativeInfinity: -oo}
+            ireps = {v: k for k, v in reps.items()}
+            eq = lhs.xreplace(reps) - rhs.xreplace(reps)
+            if eq.has(oo):
+                eq = eq.replace(
+                    lambda x: x.is_Pow and x.base is oo,
+                    lambda x: x.base)
+            rv = eq.xreplace(ireps)
+        else:
+            rv = lhs - rhs
+        srv = signsimp(rv)
+        return srv if srv.is_Number else rv
+
+    @cacheit
+    def as_two_terms(self):
+        """Return head and tail of self.
+
+        This is the most efficient way to get the head and tail of an
+        expression.
+
+        - if you want only the head, use self.args[0];
+        - if you want to process the arguments of the tail then use
+          self.as_coef_add() which gives the head and a tuple containing
+          the arguments of the tail when treated as an Add.
+        - if you want the coefficient when self is treated as a Mul
+          then use self.as_coeff_mul()[0]
+
+        >>> from sympy.abc import x, y
+        >>> (3*x - 2*y + 5).as_two_terms()
+        (5, 3*x - 2*y)
+        """
+        return self.args[0], self._new_rawargs(*self.args[1:])
+
+    def as_numer_denom(self) -> tuple[Expr, Expr]:
+        """
+        Decomposes an expression to its numerator part and its
+        denominator part.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y, z
+        >>> (x*y/z).as_numer_denom()
+        (x*y, z)
+        >>> (x*(y + 1)/y**7).as_numer_denom()
+        (x*(y + 1), y**7)
+
+        See Also
+        ========
+
+        sympy.core.expr.Expr.as_numer_denom
+        """
+        # clear rational denominator
+        content, expr = self.primitive()
+        if not isinstance(expr, Add):
+            return Mul(content, expr, evaluate=False).as_numer_denom()
+        ncon, dcon = content.as_numer_denom()
+
+        # collect numerators and denominators of the terms
+        nd = defaultdict(list)
+        for f in expr.args:
+            ni, di = f.as_numer_denom()
+            nd[di].append(ni)
+
+        # check for quick exit
+        if len(nd) == 1:
+            d, n = nd.popitem()
+            return self.func(
+                *[_keep_coeff(ncon, ni) for ni in n]), _keep_coeff(dcon, d)
+
+        # sum up the terms having a common denominator
+        nd2 = {d: self.func(*n) if len(n) > 1 else n[0] for d, n in nd.items()}
+
+        # assemble single numerator and denominator
+        denoms, numers = [list(i) for i in zip(*iter(nd2.items()))]
+        n, d = self.func(*[Mul(*(denoms[:i] + [numers[i]] + denoms[i + 1:]))
+                   for i in range(len(numers))]), Mul(*denoms)
+
+        return _keep_coeff(ncon, n), _keep_coeff(dcon, d)
+
+    def _eval_is_polynomial(self, syms):
+        return all(term._eval_is_polynomial(syms) for term in self.args)
+
+    def _eval_is_rational_function(self, syms):
+        return all(term._eval_is_rational_function(syms) for term in self.args)
+
+    def _eval_is_meromorphic(self, x, a):
+        return _fuzzy_group((arg.is_meromorphic(x, a) for arg in self.args),
+                            quick_exit=True)
+
+    def _eval_is_algebraic_expr(self, syms):
+        return all(term._eval_is_algebraic_expr(syms) for term in self.args)
+
+    # assumption methods
+    _eval_is_real = lambda self: _fuzzy_group(
+        (a.is_real for a in self.args), quick_exit=True)
+    _eval_is_extended_real = lambda self: _fuzzy_group(
+        (a.is_extended_real for a in self.args), quick_exit=True)
+    _eval_is_complex = lambda self: _fuzzy_group(
+        (a.is_complex for a in self.args), quick_exit=True)
+    _eval_is_antihermitian = lambda self: _fuzzy_group(
+        (a.is_antihermitian for a in self.args), quick_exit=True)
+    _eval_is_finite = lambda self: _fuzzy_group(
+        (a.is_finite for a in self.args), quick_exit=True)
+    _eval_is_hermitian = lambda self: _fuzzy_group(
+        (a.is_hermitian for a in self.args), quick_exit=True)
+    _eval_is_integer = lambda self: _fuzzy_group(
+        (a.is_integer for a in self.args), quick_exit=True)
+    _eval_is_rational = lambda self: _fuzzy_group(
+        (a.is_rational for a in self.args), quick_exit=True)
+    _eval_is_algebraic = lambda self: _fuzzy_group(
+        (a.is_algebraic for a in self.args), quick_exit=True)
+    _eval_is_commutative = lambda self: _fuzzy_group(
+        a.is_commutative for a in self.args)
+
+    def _eval_is_infinite(self):
+        sawinf = False
+        for a in self.args:
+            ainf = a.is_infinite
+            if ainf is None:
+                return None
+            elif ainf is True:
+                # infinite+infinite might not be infinite
+                if sawinf is True:
+                    return None
+                sawinf = True
+        return sawinf
+
+    def _eval_is_imaginary(self):
+        nz = []
+        im_I = []
+        for a in self.args:
+            if a.is_extended_real:
+                if a.is_zero:
+                    pass
+                elif a.is_zero is False:
+                    nz.append(a)
+                else:
+                    return
+            elif a.is_imaginary:
+                im_I.append(a*S.ImaginaryUnit)
+            elif a.is_Mul and S.ImaginaryUnit in a.args:
+                coeff, ai = a.as_coeff_mul(S.ImaginaryUnit)
+                if ai == (S.ImaginaryUnit,) and coeff.is_extended_real:
+                    im_I.append(-coeff)
+                else:
+                    return
+            else:
+                return
+        b = self.func(*nz)
+        if b != self:
+            if b.is_zero:
+                return fuzzy_not(self.func(*im_I).is_zero)
+            elif b.is_zero is False:
+                return False
+
+    def _eval_is_zero(self):
+        if self.is_commutative is False:
+            # issue 10528: there is no way to know if a nc symbol
+            # is zero or not
+            return
+        nz = []
+        z = 0
+        im_or_z = False
+        im = 0
+        for a in self.args:
+            if a.is_extended_real:
+                if a.is_zero:
+                    z += 1
+                elif a.is_zero is False:
+                    nz.append(a)
+                else:
+                    return
+            elif a.is_imaginary:
+                im += 1
+            elif a.is_Mul and S.ImaginaryUnit in a.args:
+                coeff, ai = a.as_coeff_mul(S.ImaginaryUnit)
+                if ai == (S.ImaginaryUnit,) and coeff.is_extended_real:
+                    im_or_z = True
+                else:
+                    return
+            else:
+                return
+        if z == len(self.args):
+            return True
+        if len(nz) in [0, len(self.args)]:
+            return None
+        b = self.func(*nz)
+        if b.is_zero:
+            if not im_or_z:
+                if im == 0:
+                    return True
+                elif im == 1:
+                    return False
+        if b.is_zero is False:
+            return False
+
+    def _eval_is_odd(self):
+        l = [f for f in self.args if not (f.is_even is True)]
+        if not l:
+            return False
+        if l[0].is_odd:
+            return self._new_rawargs(*l[1:]).is_even
+
+    def _eval_is_irrational(self):
+        for t in self.args:
+            a = t.is_irrational
+            if a:
+                others = list(self.args)
+                others.remove(t)
+                if all(x.is_rational is True for x in others):
+                    return True
+                return None
+            if a is None:
+                return
+        return False
+
+    def _all_nonneg_or_nonppos(self):
+        nn = np = 0
+        for a in self.args:
+            if a.is_nonnegative:
+                if np:
+                    return False
+                nn = 1
+            elif a.is_nonpositive:
+                if nn:
+                    return False
+                np = 1
+            else:
+                break
+        else:
+            return True
+
+    def _eval_is_extended_positive(self):
+        if self.is_number:
+            return super()._eval_is_extended_positive()
+        c, a = self.as_coeff_Add()
+        if not c.is_zero:
+            from .exprtools import _monotonic_sign
+            v = _monotonic_sign(a)
+            if v is not None:
+                s = v + c
+                if s != self and s.is_extended_positive and a.is_extended_nonnegative:
+                    return True
+                if len(self.free_symbols) == 1:
+                    v = _monotonic_sign(self)
+                    if v is not None and v != self and v.is_extended_positive:
+                        return True
+        pos = nonneg = nonpos = unknown_sign = False
+        saw_INF = set()
+        args = [a for a in self.args if not a.is_zero]
+        if not args:
+            return False
+        for a in args:
+            ispos = a.is_extended_positive
+            infinite = a.is_infinite
+            if infinite:
+                saw_INF.add(fuzzy_or((ispos, a.is_extended_nonnegative)))
+                if True in saw_INF and False in saw_INF:
+                    return
+            if ispos:
+                pos = True
+                continue
+            elif a.is_extended_nonnegative:
+                nonneg = True
+                continue
+            elif a.is_extended_nonpositive:
+                nonpos = True
+                continue
+
+            if infinite is None:
+                return
+            unknown_sign = True
+
+        if saw_INF:
+            if len(saw_INF) > 1:
+                return
+            return saw_INF.pop()
+        elif unknown_sign:
+            return
+        elif not nonpos and not nonneg and pos:
+            return True
+        elif not nonpos and pos:
+            return True
+        elif not pos and not nonneg:
+            return False
+
+    def _eval_is_extended_nonnegative(self):
+        if not self.is_number:
+            c, a = self.as_coeff_Add()
+            if not c.is_zero and a.is_extended_nonnegative:
+                from .exprtools import _monotonic_sign
+                v = _monotonic_sign(a)
+                if v is not None:
+                    s = v + c
+                    if s != self and s.is_extended_nonnegative:
+                        return True
+                    if len(self.free_symbols) == 1:
+                        v = _monotonic_sign(self)
+                        if v is not None and v != self and v.is_extended_nonnegative:
+                            return True
+
+    def _eval_is_extended_nonpositive(self):
+        if not self.is_number:
+            c, a = self.as_coeff_Add()
+            if not c.is_zero and a.is_extended_nonpositive:
+                from .exprtools import _monotonic_sign
+                v = _monotonic_sign(a)
+                if v is not None:
+                    s = v + c
+                    if s != self and s.is_extended_nonpositive:
+                        return True
+                    if len(self.free_symbols) == 1:
+                        v = _monotonic_sign(self)
+                        if v is not None and v != self and v.is_extended_nonpositive:
+                            return True
+
+    def _eval_is_extended_negative(self):
+        if self.is_number:
+            return super()._eval_is_extended_negative()
+        c, a = self.as_coeff_Add()
+        if not c.is_zero:
+            from .exprtools import _monotonic_sign
+            v = _monotonic_sign(a)
+            if v is not None:
+                s = v + c
+                if s != self and s.is_extended_negative and a.is_extended_nonpositive:
+                    return True
+                if len(self.free_symbols) == 1:
+                    v = _monotonic_sign(self)
+                    if v is not None and v != self and v.is_extended_negative:
+                        return True
+        neg = nonpos = nonneg = unknown_sign = False
+        saw_INF = set()
+        args = [a for a in self.args if not a.is_zero]
+        if not args:
+            return False
+        for a in args:
+            isneg = a.is_extended_negative
+            infinite = a.is_infinite
+            if infinite:
+                saw_INF.add(fuzzy_or((isneg, a.is_extended_nonpositive)))
+                if True in saw_INF and False in saw_INF:
+                    return
+            if isneg:
+                neg = True
+                continue
+            elif a.is_extended_nonpositive:
+                nonpos = True
+                continue
+            elif a.is_extended_nonnegative:
+                nonneg = True
+                continue
+
+            if infinite is None:
+                return
+            unknown_sign = True
+
+        if saw_INF:
+            if len(saw_INF) > 1:
+                return
+            return saw_INF.pop()
+        elif unknown_sign:
+            return
+        elif not nonneg and not nonpos and neg:
+            return True
+        elif not nonneg and neg:
+            return True
+        elif not neg and not nonpos:
+            return False
+
+    def _eval_subs(self, old, new):
+        if not old.is_Add:
+            if old is S.Infinity and -old in self.args:
+                # foo - oo is foo + (-oo) internally
+                return self.xreplace({-old: -new})
+            return None
+
+        coeff_self, terms_self = self.as_coeff_Add()
+        coeff_old, terms_old = old.as_coeff_Add()
+
+        if coeff_self.is_Rational and coeff_old.is_Rational:
+            if terms_self == terms_old:   # (2 + a).subs( 3 + a, y) -> -1 + y
+                return self.func(new, coeff_self, -coeff_old)
+            if terms_self == -terms_old:  # (2 + a).subs(-3 - a, y) -> -1 - y
+                return self.func(-new, coeff_self, coeff_old)
+
+        if coeff_self.is_Rational and coeff_old.is_Rational \
+                or coeff_self == coeff_old:
+            args_old, args_self = self.func.make_args(
+                terms_old), self.func.make_args(terms_self)
+            if len(args_old) < len(args_self):  # (a+b+c).subs(b+c,x) -> a+x
+                self_set = set(args_self)
+                old_set = set(args_old)
+
+                if old_set < self_set:
+                    ret_set = self_set - old_set
+                    return self.func(new, coeff_self, -coeff_old,
+                               *[s._subs(old, new) for s in ret_set])
+
+                args_old = self.func.make_args(
+                    -terms_old)     # (a+b+c+d).subs(-b-c,x) -> a-x+d
+                old_set = set(args_old)
+                if old_set < self_set:
+                    ret_set = self_set - old_set
+                    return self.func(-new, coeff_self, coeff_old,
+                               *[s._subs(old, new) for s in ret_set])
+
+    def removeO(self):
+        args = [a for a in self.args if not a.is_Order]
+        return self._new_rawargs(*args)
+
+    def getO(self):
+        args = [a for a in self.args if a.is_Order]
+        if args:
+            return self._new_rawargs(*args)
+
+    @cacheit
+    def extract_leading_order(self, symbols, point=None):
+        """
+        Returns the leading term and its order.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> (x + 1 + 1/x**5).extract_leading_order(x)
+        ((x**(-5), O(x**(-5))),)
+        >>> (1 + x).extract_leading_order(x)
+        ((1, O(1)),)
+        >>> (x + x**2).extract_leading_order(x)
+        ((x, O(x)),)
+
+        """
+        from sympy.series.order import Order
+        lst = []
+        symbols = list(symbols if is_sequence(symbols) else [symbols])
+        if not point:
+            point = [0]*len(symbols)
+        seq = [(f, Order(f, *zip(symbols, point))) for f in self.args]
+        for ef, of in seq:
+            for e, o in lst:
+                if o.contains(of) and o != of:
+                    of = None
+                    break
+            if of is None:
+                continue
+            new_lst = [(ef, of)]
+            for e, o in lst:
+                if of.contains(o) and o != of:
+                    continue
+                new_lst.append((e, o))
+            lst = new_lst
+        return tuple(lst)
+
+    def as_real_imag(self, deep=True, **hints):
+        """
+        Return a tuple representing a complex number.
+
+        Examples
+        ========
+
+        >>> from sympy import I
+        >>> (7 + 9*I).as_real_imag()
+        (7, 9)
+        >>> ((1 + I)/(1 - I)).as_real_imag()
+        (0, 1)
+        >>> ((1 + 2*I)*(1 + 3*I)).as_real_imag()
+        (-5, 5)
+        """
+        sargs = self.args
+        re_part, im_part = [], []
+        for term in sargs:
+            re, im = term.as_real_imag(deep=deep)
+            re_part.append(re)
+            im_part.append(im)
+        return (self.func(*re_part), self.func(*im_part))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.core.symbol import Dummy, Symbol
+        from sympy.series.order import Order
+        from sympy.functions.elementary.exponential import log
+        from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold
+        from .function import expand_mul
+
+        o = self.getO()
+        if o is None:
+            o = Order(0)
+        old = self.removeO()
+
+        if old.has(Piecewise):
+            old = piecewise_fold(old)
+
+        # This expansion is the last part of expand_log. expand_log also calls
+        # expand_mul with factor=True, which would be more expensive
+        if any(isinstance(a, log) for a in self.args):
+            logflags = {"deep": True, "log": True, "mul": False, "power_exp": False,
+                "power_base": False, "multinomial": False, "basic": False, "force": False,
+                "factor": False}
+            old = old.expand(**logflags)
+        expr = expand_mul(old)
+
+        if not expr.is_Add:
+            return expr.as_leading_term(x, logx=logx, cdir=cdir)
+
+        infinite = [t for t in expr.args if t.is_infinite]
+
+        _logx = Dummy('logx') if logx is None else logx
+        leading_terms = [t.as_leading_term(x, logx=_logx, cdir=cdir) for t in expr.args]
+
+        min, new_expr = Order(0), S.Zero
+
+        try:
+            for term in leading_terms:
+                order = Order(term, x)
+                if not min or order not in min:
+                    min = order
+                    new_expr = term
+                elif min in order:
+                    new_expr += term
+
+        except TypeError:
+            return expr
+
+        if logx is None:
+            new_expr = new_expr.subs(_logx, log(x))
+
+        is_zero = new_expr.is_zero
+        if is_zero is None:
+            new_expr = new_expr.trigsimp().cancel()
+            is_zero = new_expr.is_zero
+        if is_zero is True:
+            # simple leading term analysis gave us cancelled terms but we have to send
+            # back a term, so compute the leading term (via series)
+            try:
+                n0 = min.getn()
+            except NotImplementedError:
+                n0 = S.One
+            if n0.has(Symbol):
+                n0 = S.One
+            res = Order(1)
+            incr = S.One
+            while res.is_Order:
+                res = old._eval_nseries(x, n=n0+incr, logx=logx, cdir=cdir).cancel().powsimp().trigsimp()
+                incr *= 2
+            return res.as_leading_term(x, logx=logx, cdir=cdir)
+
+        elif new_expr is S.NaN:
+            return old.func._from_args(infinite) + o
+
+        else:
+            return new_expr
+
+    def _eval_adjoint(self):
+        return self.func(*[t.adjoint() for t in self.args])
+
+    def _eval_conjugate(self):
+        return self.func(*[t.conjugate() for t in self.args])
+
+    def _eval_transpose(self):
+        return self.func(*[t.transpose() for t in self.args])
+
+    def primitive(self):
+        """
+        Return ``(R, self/R)`` where ``R``` is the Rational GCD of ``self```.
+
+        ``R`` is collected only from the leading coefficient of each term.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+
+        >>> (2*x + 4*y).primitive()
+        (2, x + 2*y)
+
+        >>> (2*x/3 + 4*y/9).primitive()
+        (2/9, 3*x + 2*y)
+
+        >>> (2*x/3 + 4.2*y).primitive()
+        (1/3, 2*x + 12.6*y)
+
+        No subprocessing of term factors is performed:
+
+        >>> ((2 + 2*x)*x + 2).primitive()
+        (1, x*(2*x + 2) + 2)
+
+        Recursive processing can be done with the ``as_content_primitive()``
+        method:
+
+        >>> ((2 + 2*x)*x + 2).as_content_primitive()
+        (2, x*(x + 1) + 1)
+
+        See also: primitive() function in polytools.py
+
+        """
+
+        terms = []
+        inf = False
+        for a in self.args:
+            c, m = a.as_coeff_Mul()
+            if not c.is_Rational:
+                c = S.One
+                m = a
+            inf = inf or m is S.ComplexInfinity
+            terms.append((c.p, c.q, m))
+
+        if not inf:
+            ngcd = reduce(igcd, [t[0] for t in terms], 0)
+            dlcm = reduce(ilcm, [t[1] for t in terms], 1)
+        else:
+            ngcd = reduce(igcd, [t[0] for t in terms if t[1]], 0)
+            dlcm = reduce(ilcm, [t[1] for t in terms if t[1]], 1)
+
+        if ngcd == dlcm == 1:
+            return S.One, self
+        if not inf:
+            for i, (p, q, term) in enumerate(terms):
+                terms[i] = _keep_coeff(Rational((p//ngcd)*(dlcm//q)), term)
+        else:
+            for i, (p, q, term) in enumerate(terms):
+                if q:
+                    terms[i] = _keep_coeff(Rational((p//ngcd)*(dlcm//q)), term)
+                else:
+                    terms[i] = _keep_coeff(Rational(p, q), term)
+
+        # we don't need a complete re-flattening since no new terms will join
+        # so we just use the same sort as is used in Add.flatten. When the
+        # coefficient changes, the ordering of terms may change, e.g.
+        #     (3*x, 6*y) -> (2*y, x)
+        #
+        # We do need to make sure that term[0] stays in position 0, however.
+        #
+        if terms[0].is_Number or terms[0] is S.ComplexInfinity:
+            c = terms.pop(0)
+        else:
+            c = None
+        _addsort(terms)
+        if c:
+            terms.insert(0, c)
+        return Rational(ngcd, dlcm), self._new_rawargs(*terms)
+
+    def as_content_primitive(self, radical=False, clear=True):
+        """Return the tuple (R, self/R) where R is the positive Rational
+        extracted from self. If radical is True (default is False) then
+        common radicals will be removed and included as a factor of the
+        primitive expression.
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt
+        >>> (3 + 3*sqrt(2)).as_content_primitive()
+        (3, 1 + sqrt(2))
+
+        Radical content can also be factored out of the primitive:
+
+        >>> (2*sqrt(2) + 4*sqrt(10)).as_content_primitive(radical=True)
+        (2, sqrt(2)*(1 + 2*sqrt(5)))
+
+        See docstring of Expr.as_content_primitive for more examples.
+        """
+        con, prim = self.func(*[_keep_coeff(*a.as_content_primitive(
+            radical=radical, clear=clear)) for a in self.args]).primitive()
+        if not clear and not con.is_Integer and prim.is_Add:
+            con, d = con.as_numer_denom()
+            _p = prim/d
+            if any(a.as_coeff_Mul()[0].is_Integer for a in _p.args):
+                prim = _p
+            else:
+                con /= d
+        if radical and prim.is_Add:
+            # look for common radicals that can be removed
+            args = prim.args
+            rads = []
+            common_q = None
+            for m in args:
+                term_rads = defaultdict(list)
+                for ai in Mul.make_args(m):
+                    if ai.is_Pow:
+                        b, e = ai.as_base_exp()
+                        if e.is_Rational and b.is_Integer:
+                            term_rads[e.q].append(abs(int(b))**e.p)
+                if not term_rads:
+                    break
+                if common_q is None:
+                    common_q = set(term_rads.keys())
+                else:
+                    common_q = common_q & set(term_rads.keys())
+                    if not common_q:
+                        break
+                rads.append(term_rads)
+            else:
+                # process rads
+                # keep only those in common_q
+                for r in rads:
+                    for q in list(r.keys()):
+                        if q not in common_q:
+                            r.pop(q)
+                    for q in r:
+                        r[q] = Mul(*r[q])
+                # find the gcd of bases for each q
+                G = []
+                for q in common_q:
+                    g = reduce(igcd, [r[q] for r in rads], 0)
+                    if g != 1:
+                        G.append(g**Rational(1, q))
+                if G:
+                    G = Mul(*G)
+                    args = [ai/G for ai in args]
+                    prim = G*prim.func(*args)
+
+        return con, prim
+
+    @property
+    def _sorted_args(self):
+        from .sorting import default_sort_key
+        return tuple(sorted(self.args, key=default_sort_key))
+
+    def _eval_difference_delta(self, n, step):
+        from sympy.series.limitseq import difference_delta as dd
+        return self.func(*[dd(a, n, step) for a in self.args])
+
+    @property
+    def _mpc_(self):
+        """
+        Convert self to an mpmath mpc if possible
+        """
+        from .numbers import Float
+        re_part, rest = self.as_coeff_Add()
+        im_part, imag_unit = rest.as_coeff_Mul()
+        if not imag_unit == S.ImaginaryUnit:
+            # ValueError may seem more reasonable but since it's a @property,
+            # we need to use AttributeError to keep from confusing things like
+            # hasattr.
+            raise AttributeError("Cannot convert Add to mpc. Must be of the form Number + Number*I")
+
+        return (Float(re_part)._mpf_, Float(im_part)._mpf_)
+
+    def __neg__(self):
+        if not global_parameters.distribute:
+            return super().__neg__()
+        return Mul(S.NegativeOne, self)
+
+add = AssocOpDispatcher('add')
+
+from .mul import Mul, _keep_coeff, _unevaluated_Mul
+from .numbers import Rational
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/alphabets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/alphabets.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ea2ae1c410ccd30e7ec9551f4cd8b19a36cdba1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/alphabets.py
@@ -0,0 +1,4 @@
+greeks = ('alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta',
+                    'eta', 'theta', 'iota', 'kappa', 'lambda', 'mu', 'nu',
+                    'xi', 'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon',
+                    'phi', 'chi', 'psi', 'omega')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/assumptions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/assumptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..677e86c5e39390b0b188a5158dd2fabfbac4c760
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/assumptions.py
@@ -0,0 +1,692 @@
+"""
+This module contains the machinery handling assumptions.
+Do also consider the guide :ref:`assumptions-guide`.
+
+All symbolic objects have assumption attributes that can be accessed via
+``.is_`` attribute.
+
+Assumptions determine certain properties of symbolic objects and can
+have 3 possible values: ``True``, ``False``, ``None``.  ``True`` is returned if the
+object has the property and ``False`` is returned if it does not or cannot
+(i.e. does not make sense):
+
+    >>> from sympy import I
+    >>> I.is_algebraic
+    True
+    >>> I.is_real
+    False
+    >>> I.is_prime
+    False
+
+When the property cannot be determined (or when a method is not
+implemented) ``None`` will be returned. For example,  a generic symbol, ``x``,
+may or may not be positive so a value of ``None`` is returned for ``x.is_positive``.
+
+By default, all symbolic values are in the largest set in the given context
+without specifying the property. For example, a symbol that has a property
+being integer, is also real, complex, etc.
+
+Here follows a list of possible assumption names:
+
+.. glossary::
+
+    commutative
+        object commutes with any other object with
+        respect to multiplication operation. See [12]_.
+
+    complex
+        object can have only values from the set
+        of complex numbers. See [13]_.
+
+    imaginary
+        object value is a number that can be written as a real
+        number multiplied by the imaginary unit ``I``.  See
+        [3]_.  Please note that ``0`` is not considered to be an
+        imaginary number, see
+        `issue #7649 `_.
+
+    real
+        object can have only values from the set
+        of real numbers.
+
+    extended_real
+        object can have only values from the set
+        of real numbers, ``oo`` and ``-oo``.
+
+    integer
+        object can have only values from the set
+        of integers.
+
+    odd
+    even
+        object can have only values from the set of
+        odd (even) integers [2]_.
+
+    prime
+        object is a natural number greater than 1 that has
+        no positive divisors other than 1 and itself.  See [6]_.
+
+    composite
+        object is a positive integer that has at least one positive
+        divisor other than 1 or the number itself.  See [4]_.
+
+    zero
+        object has the value of 0.
+
+    nonzero
+        object is a real number that is not zero.
+
+    rational
+        object can have only values from the set
+        of rationals.
+
+    algebraic
+        object can have only values from the set
+        of algebraic numbers [11]_.
+
+    transcendental
+        object can have only values from the set
+        of transcendental numbers [10]_.
+
+    irrational
+        object value cannot be represented exactly by :class:`~.Rational`, see [5]_.
+
+    finite
+    infinite
+        object absolute value is bounded (arbitrarily large).
+        See [7]_, [8]_, [9]_.
+
+    negative
+    nonnegative
+        object can have only negative (nonnegative)
+        values [1]_.
+
+    positive
+    nonpositive
+        object can have only positive (nonpositive) values.
+
+    extended_negative
+    extended_nonnegative
+    extended_positive
+    extended_nonpositive
+    extended_nonzero
+        as without the extended part, but also including infinity with
+        corresponding sign, e.g., extended_positive includes ``oo``
+
+    hermitian
+    antihermitian
+        object belongs to the field of Hermitian
+        (antihermitian) operators.
+
+Examples
+========
+
+    >>> from sympy import Symbol
+    >>> x = Symbol('x', real=True); x
+    x
+    >>> x.is_real
+    True
+    >>> x.is_complex
+    True
+
+See Also
+========
+
+.. seealso::
+
+    :py:class:`sympy.core.numbers.ImaginaryUnit`
+    :py:class:`sympy.core.numbers.Zero`
+    :py:class:`sympy.core.numbers.One`
+    :py:class:`sympy.core.numbers.Infinity`
+    :py:class:`sympy.core.numbers.NegativeInfinity`
+    :py:class:`sympy.core.numbers.ComplexInfinity`
+
+Notes
+=====
+
+The fully-resolved assumptions for any SymPy expression
+can be obtained as follows:
+
+    >>> from sympy.core.assumptions import assumptions
+    >>> x = Symbol('x',positive=True)
+    >>> assumptions(x + I)
+    {'commutative': True, 'complex': True, 'composite': False, 'even':
+    False, 'extended_negative': False, 'extended_nonnegative': False,
+    'extended_nonpositive': False, 'extended_nonzero': False,
+    'extended_positive': False, 'extended_real': False, 'finite': True,
+    'imaginary': False, 'infinite': False, 'integer': False, 'irrational':
+    False, 'negative': False, 'noninteger': False, 'nonnegative': False,
+    'nonpositive': False, 'nonzero': False, 'odd': False, 'positive':
+    False, 'prime': False, 'rational': False, 'real': False, 'zero':
+    False}
+
+Developers Notes
+================
+
+The current (and possibly incomplete) values are stored
+in the ``obj._assumptions dictionary``; queries to getter methods
+(with property decorators) or attributes of objects/classes
+will return values and update the dictionary.
+
+    >>> eq = x**2 + I
+    >>> eq._assumptions
+    {}
+    >>> eq.is_finite
+    True
+    >>> eq._assumptions
+    {'finite': True, 'infinite': False}
+
+For a :class:`~.Symbol`, there are two locations for assumptions that may
+be of interest. The ``assumptions0`` attribute gives the full set of
+assumptions derived from a given set of initial assumptions. The
+latter assumptions are stored as ``Symbol._assumptions_orig``
+
+    >>> Symbol('x', prime=True, even=True)._assumptions_orig
+    {'even': True, 'prime': True}
+
+The ``_assumptions_orig`` are not necessarily canonical nor are they filtered
+in any way: they records the assumptions used to instantiate a Symbol and (for
+storage purposes) represent a more compact representation of the assumptions
+needed to recreate the full set in ``Symbol.assumptions0``.
+
+
+References
+==========
+
+.. [1] https://en.wikipedia.org/wiki/Negative_number
+.. [2] https://en.wikipedia.org/wiki/Parity_%28mathematics%29
+.. [3] https://en.wikipedia.org/wiki/Imaginary_number
+.. [4] https://en.wikipedia.org/wiki/Composite_number
+.. [5] https://en.wikipedia.org/wiki/Irrational_number
+.. [6] https://en.wikipedia.org/wiki/Prime_number
+.. [7] https://en.wikipedia.org/wiki/Finite
+.. [8] https://docs.python.org/3/library/math.html#math.isfinite
+.. [9] https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html
+.. [10] https://en.wikipedia.org/wiki/Transcendental_number
+.. [11] https://en.wikipedia.org/wiki/Algebraic_number
+.. [12] https://en.wikipedia.org/wiki/Commutative_property
+.. [13] https://en.wikipedia.org/wiki/Complex_number
+
+"""
+
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+from .facts import FactRules, FactKB
+from .sympify import sympify
+
+from sympy.core.random import _assumptions_shuffle as shuffle
+from sympy.core.assumptions_generated import generated_assumptions as _assumptions
+
+def _load_pre_generated_assumption_rules() -> FactRules:
+    """ Load the assumption rules from pre-generated data
+
+    To update the pre-generated data, see :method::`_generate_assumption_rules`
+    """
+    _assume_rules=FactRules._from_python(_assumptions)
+    return _assume_rules
+
+def _generate_assumption_rules():
+    """ Generate the default assumption rules
+
+    This method should only be called to update the pre-generated
+    assumption rules.
+
+    To update the pre-generated assumptions run: bin/ask_update.py
+
+    """
+    _assume_rules = FactRules([
+
+    'integer        ->  rational',
+    'rational       ->  real',
+    'rational       ->  algebraic',
+    'algebraic      ->  complex',
+    'transcendental ==  complex & !algebraic',
+    'real           ->  hermitian',
+    'imaginary      ->  complex',
+    'imaginary      ->  antihermitian',
+    'extended_real  ->  commutative',
+    'complex        ->  commutative',
+    'complex        ->  finite',
+
+    'odd            ==  integer & !even',
+    'even           ==  integer & !odd',
+
+    'real           ->  complex',
+    'extended_real  ->  real | infinite',
+    'real           ==  extended_real & finite',
+
+    'extended_real        ==  extended_negative | zero | extended_positive',
+    'extended_negative    ==  extended_nonpositive & extended_nonzero',
+    'extended_positive    ==  extended_nonnegative & extended_nonzero',
+
+    'extended_nonpositive ==  extended_real & !extended_positive',
+    'extended_nonnegative ==  extended_real & !extended_negative',
+
+    'real           ==  negative | zero | positive',
+    'negative       ==  nonpositive & nonzero',
+    'positive       ==  nonnegative & nonzero',
+
+    'nonpositive    ==  real & !positive',
+    'nonnegative    ==  real & !negative',
+
+    'positive       ==  extended_positive & finite',
+    'negative       ==  extended_negative & finite',
+    'nonpositive    ==  extended_nonpositive & finite',
+    'nonnegative    ==  extended_nonnegative & finite',
+    'nonzero        ==  extended_nonzero & finite',
+
+    'zero           ->  even & finite',
+    'zero           ==  extended_nonnegative & extended_nonpositive',
+    'zero           ==  nonnegative & nonpositive',
+    'nonzero        ->  real',
+
+    'prime          ->  integer & positive',
+    'composite      ->  integer & positive & !prime',
+    '!composite     ->  !positive | !even | prime',
+
+    'irrational     ==  real & !rational',
+
+    'imaginary      ->  !extended_real',
+
+    'infinite       ==  !finite',
+    'noninteger     ==  extended_real & !integer',
+    'extended_nonzero == extended_real & !zero',
+    ])
+    return _assume_rules
+
+
+_assume_rules = _load_pre_generated_assumption_rules()
+_assume_defined = _assume_rules.defined_facts.copy()
+_assume_defined.add('polar')
+_assume_defined = frozenset(_assume_defined)
+
+
+def assumptions(expr, _check=None):
+    """return the T/F assumptions of ``expr``"""
+    n = sympify(expr)
+    if n.is_Symbol:
+        rv = n.assumptions0  # are any important ones missing?
+        if _check is not None:
+            rv = {k: rv[k] for k in set(rv) & set(_check)}
+        return rv
+    rv = {}
+    for k in _assume_defined if _check is None else _check:
+        v = getattr(n, 'is_{}'.format(k))
+        if v is not None:
+            rv[k] = v
+    return rv
+
+
+def common_assumptions(exprs, check=None):
+    """return those assumptions which have the same True or False
+    value for all the given expressions.
+
+    Examples
+    ========
+
+    >>> from sympy.core import common_assumptions
+    >>> from sympy import oo, pi, sqrt
+    >>> common_assumptions([-4, 0, sqrt(2), 2, pi, oo])
+    {'commutative': True, 'composite': False,
+    'extended_real': True, 'imaginary': False, 'odd': False}
+
+    By default, all assumptions are tested; pass an iterable of the
+    assumptions to limit those that are reported:
+
+    >>> common_assumptions([0, 1, 2], ['positive', 'integer'])
+    {'integer': True}
+    """
+    check = _assume_defined if check is None else set(check)
+    if not check or not exprs:
+        return {}
+
+    # get all assumptions for each
+    assume = [assumptions(i, _check=check) for i in sympify(exprs)]
+    # focus on those of interest that are True
+    for i, e in enumerate(assume):
+        assume[i] = {k: e[k] for k in set(e) & check}
+    # what assumptions are in common?
+    common = set.intersection(*[set(i) for i in assume])
+    # which ones hold the same value
+    a = assume[0]
+    return {k: a[k] for k in common if all(a[k] == b[k]
+        for b in assume)}
+
+
+def failing_assumptions(expr, **assumptions):
+    """
+    Return a dictionary containing assumptions with values not
+    matching those of the passed assumptions.
+
+    Examples
+    ========
+
+    >>> from sympy import failing_assumptions, Symbol
+
+    >>> x = Symbol('x', positive=True)
+    >>> y = Symbol('y')
+    >>> failing_assumptions(6*x + y, positive=True)
+    {'positive': None}
+
+    >>> failing_assumptions(x**2 - 1, positive=True)
+    {'positive': None}
+
+    If *expr* satisfies all of the assumptions, an empty dictionary is returned.
+
+    >>> failing_assumptions(x**2, positive=True)
+    {}
+
+    """
+    expr = sympify(expr)
+    failed = {}
+    for k in assumptions:
+        test = getattr(expr, 'is_%s' % k, None)
+        if test is not assumptions[k]:
+            failed[k] = test
+    return failed  # {} or {assumption: value != desired}
+
+
+def check_assumptions(expr, against=None, **assume):
+    """
+    Checks whether assumptions of ``expr`` match the T/F assumptions
+    given (or possessed by ``against``). True is returned if all
+    assumptions match; False is returned if there is a mismatch and
+    the assumption in ``expr`` is not None; else None is returned.
+
+    Explanation
+    ===========
+
+    *assume* is a dict of assumptions with True or False values
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, pi, I, exp, check_assumptions
+    >>> check_assumptions(-5, integer=True)
+    True
+    >>> check_assumptions(pi, real=True, integer=False)
+    True
+    >>> check_assumptions(pi, negative=True)
+    False
+    >>> check_assumptions(exp(I*pi/7), real=False)
+    True
+    >>> x = Symbol('x', positive=True)
+    >>> check_assumptions(2*x + 1, positive=True)
+    True
+    >>> check_assumptions(-2*x - 5, positive=True)
+    False
+
+    To check assumptions of *expr* against another variable or expression,
+    pass the expression or variable as ``against``.
+
+    >>> check_assumptions(2*x + 1, x)
+    True
+
+    To see if a number matches the assumptions of an expression, pass
+    the number as the first argument, else its specific assumptions
+    may not have a non-None value in the expression:
+
+    >>> check_assumptions(x, 3)
+    >>> check_assumptions(3, x)
+    True
+
+    ``None`` is returned if ``check_assumptions()`` could not conclude.
+
+    >>> check_assumptions(2*x - 1, x)
+
+    >>> z = Symbol('z')
+    >>> check_assumptions(z, real=True)
+
+    See Also
+    ========
+
+    failing_assumptions
+
+    """
+    expr = sympify(expr)
+    if against is not None:
+        if assume:
+            raise ValueError(
+                'Expecting `against` or `assume`, not both.')
+        assume = assumptions(against)
+    known = True
+    for k, v in assume.items():
+        if v is None:
+            continue
+        e = getattr(expr, 'is_' + k, None)
+        if e is None:
+            known = None
+        elif v != e:
+            return False
+    return known
+
+
+class StdFactKB(FactKB):
+    """A FactKB specialized for the built-in rules
+
+    This is the only kind of FactKB that Basic objects should use.
+    """
+    def __init__(self, facts=None):
+        super().__init__(_assume_rules)
+        # save a copy of the facts dict
+        if not facts:
+            self._generator = {}
+        elif not isinstance(facts, FactKB):
+            self._generator = facts.copy()
+        else:
+            self._generator = facts.generator
+        if facts:
+            self.deduce_all_facts(facts)
+
+    def copy(self):
+        return self.__class__(self)
+
+    @property
+    def generator(self):
+        return self._generator.copy()
+
+
+def as_property(fact):
+    """Convert a fact name to the name of the corresponding property"""
+    return 'is_%s' % fact
+
+
+def make_property(fact):
+    """Create the automagic property corresponding to a fact."""
+
+    def getit(self):
+        try:
+            return self._assumptions[fact]
+        except KeyError:
+            if self._assumptions is self.default_assumptions:
+                self._assumptions = self.default_assumptions.copy()
+            return _ask(fact, self)
+
+    getit.func_name = as_property(fact)
+    return property(getit)
+
+
+def _ask(fact, obj):
+    """
+    Find the truth value for a property of an object.
+
+    This function is called when a request is made to see what a fact
+    value is.
+
+    For this we use several techniques:
+
+    First, the fact-evaluation function is tried, if it exists (for
+    example _eval_is_integer). Then we try related facts. For example
+
+        rational   -->   integer
+
+    another example is joined rule:
+
+        integer & !odd  --> even
+
+    so in the latter case if we are looking at what 'even' value is,
+    'integer' and 'odd' facts will be asked.
+
+    In all cases, when we settle on some fact value, its implications are
+    deduced, and the result is cached in ._assumptions.
+    """
+    # FactKB which is dict-like and maps facts to their known values:
+    assumptions = obj._assumptions
+
+    # A dict that maps facts to their handlers:
+    handler_map = obj._prop_handler
+
+    # This is our queue of facts to check:
+    facts_to_check = [fact]
+    facts_queued = {fact}
+
+    # Loop over the queue as it extends
+    for fact_i in facts_to_check:
+
+        # If fact_i has already been determined then we don't need to rerun the
+        # handler. There is a potential race condition for multithreaded code
+        # though because it's possible that fact_i was checked in another
+        # thread. The main logic of the loop below would potentially skip
+        # checking assumptions[fact] in this case so we check it once after the
+        # loop to be sure.
+        if fact_i in assumptions:
+            continue
+
+        # Now we call the associated handler for fact_i if it exists.
+        fact_i_value = None
+        handler_i = handler_map.get(fact_i)
+        if handler_i is not None:
+            fact_i_value = handler_i(obj)
+
+        # If we get a new value for fact_i then we should update our knowledge
+        # of fact_i as well as any related facts that can be inferred using the
+        # inference rules connecting the fact_i and any other fact values that
+        # are already known.
+        if fact_i_value is not None:
+            assumptions.deduce_all_facts(((fact_i, fact_i_value),))
+
+        # Usually if assumptions[fact] is now not None then that is because of
+        # the call to deduce_all_facts above. The handler for fact_i returned
+        # True or False and knowing fact_i (which is equal to fact in the first
+        # iteration) implies knowing a value for fact. It is also possible
+        # though that independent code e.g. called indirectly by the handler or
+        # called in another thread in a multithreaded context might have
+        # resulted in assumptions[fact] being set. Either way we return it.
+        fact_value = assumptions.get(fact)
+        if fact_value is not None:
+            return fact_value
+
+        # Extend the queue with other facts that might determine fact_i. Here
+        # we randomise the order of the facts that are checked. This should not
+        # lead to any non-determinism if all handlers are logically consistent
+        # with the inference rules for the facts. Non-deterministic assumptions
+        # queries can result from bugs in the handlers that are exposed by this
+        # call to shuffle. These are pushed to the back of the queue meaning
+        # that the inference graph is traversed in breadth-first order.
+        new_facts_to_check = list(_assume_rules.prereq[fact_i] - facts_queued)
+        shuffle(new_facts_to_check)
+        facts_to_check.extend(new_facts_to_check)
+        facts_queued.update(new_facts_to_check)
+
+    # The above loop should be able to handle everything fine in a
+    # single-threaded context but in multithreaded code it is possible that
+    # this thread skipped computing a particular fact that was computed in
+    # another thread (due to the continue). In that case it is possible that
+    # fact was inferred and is now stored in the assumptions dict but it wasn't
+    # checked for in the body of the loop. This is an obscure case but to make
+    # sure we catch it we check once here at the end of the loop.
+    if fact in assumptions:
+        return assumptions[fact]
+
+    # This query can not be answered. It's possible that e.g. another thread
+    # has already stored None for fact but assumptions._tell does not mind if
+    # we call _tell twice setting the same value. If this raises
+    # InconsistentAssumptions then it probably means that another thread
+    # attempted to compute this and got a value of True or False rather than
+    # None. In that case there must be a bug in at least one of the handlers.
+    # If the handlers are all deterministic and are consistent with the
+    # inference rules then the same value should be computed for fact in all
+    # threads.
+    assumptions._tell(fact, None)
+    return None
+
+
+def _prepare_class_assumptions(cls):
+    """Precompute class level assumptions and generate handlers.
+
+    This is called by Basic.__init_subclass__ each time a Basic subclass is
+    defined.
+    """
+
+    local_defs = {}
+    for k in _assume_defined:
+        attrname = as_property(k)
+        v = cls.__dict__.get(attrname, '')
+        if isinstance(v, (bool, int, type(None))):
+            if v is not None:
+                v = bool(v)
+            local_defs[k] = v
+
+    defs = {}
+    for base in reversed(cls.__bases__):
+        assumptions = getattr(base, '_explicit_class_assumptions', None)
+        if assumptions is not None:
+            defs.update(assumptions)
+    defs.update(local_defs)
+
+    cls._explicit_class_assumptions = defs
+    cls.default_assumptions = StdFactKB(defs)
+
+    cls._prop_handler = {}
+    for k in _assume_defined:
+        eval_is_meth = getattr(cls, '_eval_is_%s' % k, None)
+        if eval_is_meth is not None:
+            cls._prop_handler[k] = eval_is_meth
+
+    # Put definite results directly into the class dict, for speed
+    for k, v in cls.default_assumptions.items():
+        setattr(cls, as_property(k), v)
+
+    # protection e.g. for Integer.is_even=F <- (Rational.is_integer=F)
+    derived_from_bases = set()
+    for base in cls.__bases__:
+        default_assumptions = getattr(base, 'default_assumptions', None)
+        # is an assumption-aware class
+        if default_assumptions is not None:
+            derived_from_bases.update(default_assumptions)
+
+    for fact in derived_from_bases - set(cls.default_assumptions):
+        pname = as_property(fact)
+        if pname not in cls.__dict__:
+            setattr(cls, pname, make_property(fact))
+
+    # Finally, add any missing automagic property (e.g. for Basic)
+    for fact in _assume_defined:
+        pname = as_property(fact)
+        if not hasattr(cls, pname):
+            setattr(cls, pname, make_property(fact))
+
+
+# XXX: ManagedProperties used to be the metaclass for Basic but now Basic does
+# not use a metaclass. We leave this here for backwards compatibility for now
+# in case someone has been using the ManagedProperties class in downstream
+# code. The reason that it might have been used is that when subclassing a
+# class and wanting to use a metaclass the metaclass must be a subclass of the
+# metaclass for the class that is being subclassed. Anyone wanting to subclass
+# Basic and use a metaclass in their subclass would have needed to subclass
+# ManagedProperties. Here ManagedProperties is not the metaclass for Basic any
+# more but it should still be usable as a metaclass for Basic subclasses since
+# it is a subclass of type which is now the metaclass for Basic.
+class ManagedProperties(type):
+    def __init__(cls, *args, **kwargs):
+        msg = ("The ManagedProperties metaclass. "
+               "Basic does not use metaclasses any more")
+        sympy_deprecation_warning(msg,
+            deprecated_since_version="1.12",
+            active_deprecations_target='managedproperties')
+
+        # Here we still call this function in case someone is using
+        # ManagedProperties for something that is not a Basic subclass. For
+        # Basic subclasses this function is now called by __init_subclass__ and
+        # so this metaclass is not needed any more.
+        _prepare_class_assumptions(cls)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/assumptions_generated.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/assumptions_generated.py
new file mode 100644
index 0000000000000000000000000000000000000000..b4b2597a72b500155370db385b58e61f0f951984
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/assumptions_generated.py
@@ -0,0 +1,1615 @@
+"""
+Do NOT manually edit this file.
+Instead, run ./bin/ask_update.py.
+"""
+
+defined_facts = [
+    'algebraic',
+    'antihermitian',
+    'commutative',
+    'complex',
+    'composite',
+    'even',
+    'extended_negative',
+    'extended_nonnegative',
+    'extended_nonpositive',
+    'extended_nonzero',
+    'extended_positive',
+    'extended_real',
+    'finite',
+    'hermitian',
+    'imaginary',
+    'infinite',
+    'integer',
+    'irrational',
+    'negative',
+    'noninteger',
+    'nonnegative',
+    'nonpositive',
+    'nonzero',
+    'odd',
+    'positive',
+    'prime',
+    'rational',
+    'real',
+    'transcendental',
+    'zero',
+] # defined_facts
+
+
+full_implications = dict( [
+    # Implications of algebraic = True:
+    (('algebraic', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('finite', True),
+        ('infinite', False),
+        ('transcendental', False),
+       ) ),
+     ),
+    # Implications of algebraic = False:
+    (('algebraic', False), set( (
+        ('composite', False),
+        ('even', False),
+        ('integer', False),
+        ('odd', False),
+        ('prime', False),
+        ('rational', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of antihermitian = True:
+    (('antihermitian', True), set( (
+       ) ),
+     ),
+    # Implications of antihermitian = False:
+    (('antihermitian', False), set( (
+        ('imaginary', False),
+       ) ),
+     ),
+    # Implications of commutative = True:
+    (('commutative', True), set( (
+       ) ),
+     ),
+    # Implications of commutative = False:
+    (('commutative', False), set( (
+        ('algebraic', False),
+        ('complex', False),
+        ('composite', False),
+        ('even', False),
+        ('extended_negative', False),
+        ('extended_nonnegative', False),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', False),
+        ('extended_positive', False),
+        ('extended_real', False),
+        ('imaginary', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('noninteger', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of complex = True:
+    (('complex', True), set( (
+        ('commutative', True),
+        ('finite', True),
+        ('infinite', False),
+       ) ),
+     ),
+    # Implications of complex = False:
+    (('complex', False), set( (
+        ('algebraic', False),
+        ('composite', False),
+        ('even', False),
+        ('imaginary', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of composite = True:
+    (('composite', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('extended_negative', False),
+        ('extended_nonnegative', True),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', True),
+        ('extended_positive', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('integer', True),
+        ('irrational', False),
+        ('negative', False),
+        ('noninteger', False),
+        ('nonnegative', True),
+        ('nonpositive', False),
+        ('nonzero', True),
+        ('positive', True),
+        ('prime', False),
+        ('rational', True),
+        ('real', True),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of composite = False:
+    (('composite', False), set( (
+       ) ),
+     ),
+    # Implications of even = True:
+    (('even', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('integer', True),
+        ('irrational', False),
+        ('noninteger', False),
+        ('odd', False),
+        ('rational', True),
+        ('real', True),
+        ('transcendental', False),
+       ) ),
+     ),
+    # Implications of even = False:
+    (('even', False), set( (
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of extended_negative = True:
+    (('extended_negative', True), set( (
+        ('commutative', True),
+        ('composite', False),
+        ('extended_nonnegative', False),
+        ('extended_nonpositive', True),
+        ('extended_nonzero', True),
+        ('extended_positive', False),
+        ('extended_real', True),
+        ('imaginary', False),
+        ('nonnegative', False),
+        ('positive', False),
+        ('prime', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of extended_negative = False:
+    (('extended_negative', False), set( (
+        ('negative', False),
+       ) ),
+     ),
+    # Implications of extended_nonnegative = True:
+    (('extended_nonnegative', True), set( (
+        ('commutative', True),
+        ('extended_negative', False),
+        ('extended_real', True),
+        ('imaginary', False),
+        ('negative', False),
+       ) ),
+     ),
+    # Implications of extended_nonnegative = False:
+    (('extended_nonnegative', False), set( (
+        ('composite', False),
+        ('extended_positive', False),
+        ('nonnegative', False),
+        ('positive', False),
+        ('prime', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of extended_nonpositive = True:
+    (('extended_nonpositive', True), set( (
+        ('commutative', True),
+        ('composite', False),
+        ('extended_positive', False),
+        ('extended_real', True),
+        ('imaginary', False),
+        ('positive', False),
+        ('prime', False),
+       ) ),
+     ),
+    # Implications of extended_nonpositive = False:
+    (('extended_nonpositive', False), set( (
+        ('extended_negative', False),
+        ('negative', False),
+        ('nonpositive', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of extended_nonzero = True:
+    (('extended_nonzero', True), set( (
+        ('commutative', True),
+        ('extended_real', True),
+        ('imaginary', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of extended_nonzero = False:
+    (('extended_nonzero', False), set( (
+        ('composite', False),
+        ('extended_negative', False),
+        ('extended_positive', False),
+        ('negative', False),
+        ('nonzero', False),
+        ('positive', False),
+        ('prime', False),
+       ) ),
+     ),
+    # Implications of extended_positive = True:
+    (('extended_positive', True), set( (
+        ('commutative', True),
+        ('extended_negative', False),
+        ('extended_nonnegative', True),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', True),
+        ('extended_real', True),
+        ('imaginary', False),
+        ('negative', False),
+        ('nonpositive', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of extended_positive = False:
+    (('extended_positive', False), set( (
+        ('composite', False),
+        ('positive', False),
+        ('prime', False),
+       ) ),
+     ),
+    # Implications of extended_real = True:
+    (('extended_real', True), set( (
+        ('commutative', True),
+        ('imaginary', False),
+       ) ),
+     ),
+    # Implications of extended_real = False:
+    (('extended_real', False), set( (
+        ('composite', False),
+        ('even', False),
+        ('extended_negative', False),
+        ('extended_nonnegative', False),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', False),
+        ('extended_positive', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('noninteger', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of finite = True:
+    (('finite', True), set( (
+        ('infinite', False),
+       ) ),
+     ),
+    # Implications of finite = False:
+    (('finite', False), set( (
+        ('algebraic', False),
+        ('complex', False),
+        ('composite', False),
+        ('even', False),
+        ('imaginary', False),
+        ('infinite', True),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of hermitian = True:
+    (('hermitian', True), set( (
+       ) ),
+     ),
+    # Implications of hermitian = False:
+    (('hermitian', False), set( (
+        ('composite', False),
+        ('even', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of imaginary = True:
+    (('imaginary', True), set( (
+        ('antihermitian', True),
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('even', False),
+        ('extended_negative', False),
+        ('extended_nonnegative', False),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', False),
+        ('extended_positive', False),
+        ('extended_real', False),
+        ('finite', True),
+        ('infinite', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('noninteger', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of imaginary = False:
+    (('imaginary', False), set( (
+       ) ),
+     ),
+    # Implications of infinite = True:
+    (('infinite', True), set( (
+        ('algebraic', False),
+        ('complex', False),
+        ('composite', False),
+        ('even', False),
+        ('finite', False),
+        ('imaginary', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', False),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of infinite = False:
+    (('infinite', False), set( (
+        ('finite', True),
+       ) ),
+     ),
+    # Implications of integer = True:
+    (('integer', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('irrational', False),
+        ('noninteger', False),
+        ('rational', True),
+        ('real', True),
+        ('transcendental', False),
+       ) ),
+     ),
+    # Implications of integer = False:
+    (('integer', False), set( (
+        ('composite', False),
+        ('even', False),
+        ('odd', False),
+        ('prime', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of irrational = True:
+    (('irrational', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('even', False),
+        ('extended_nonzero', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('integer', False),
+        ('noninteger', True),
+        ('nonzero', True),
+        ('odd', False),
+        ('prime', False),
+        ('rational', False),
+        ('real', True),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of irrational = False:
+    (('irrational', False), set( (
+       ) ),
+     ),
+    # Implications of negative = True:
+    (('negative', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('extended_negative', True),
+        ('extended_nonnegative', False),
+        ('extended_nonpositive', True),
+        ('extended_nonzero', True),
+        ('extended_positive', False),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('nonnegative', False),
+        ('nonpositive', True),
+        ('nonzero', True),
+        ('positive', False),
+        ('prime', False),
+        ('real', True),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of negative = False:
+    (('negative', False), set( (
+       ) ),
+     ),
+    # Implications of noninteger = True:
+    (('noninteger', True), set( (
+        ('commutative', True),
+        ('composite', False),
+        ('even', False),
+        ('extended_nonzero', True),
+        ('extended_real', True),
+        ('imaginary', False),
+        ('integer', False),
+        ('odd', False),
+        ('prime', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of noninteger = False:
+    (('noninteger', False), set( (
+       ) ),
+     ),
+    # Implications of nonnegative = True:
+    (('nonnegative', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('extended_negative', False),
+        ('extended_nonnegative', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('negative', False),
+        ('real', True),
+       ) ),
+     ),
+    # Implications of nonnegative = False:
+    (('nonnegative', False), set( (
+        ('composite', False),
+        ('positive', False),
+        ('prime', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of nonpositive = True:
+    (('nonpositive', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('extended_nonpositive', True),
+        ('extended_positive', False),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('positive', False),
+        ('prime', False),
+        ('real', True),
+       ) ),
+     ),
+    # Implications of nonpositive = False:
+    (('nonpositive', False), set( (
+        ('negative', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of nonzero = True:
+    (('nonzero', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('extended_nonzero', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('real', True),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of nonzero = False:
+    (('nonzero', False), set( (
+        ('composite', False),
+        ('negative', False),
+        ('positive', False),
+        ('prime', False),
+       ) ),
+     ),
+    # Implications of odd = True:
+    (('odd', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('even', False),
+        ('extended_nonzero', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('integer', True),
+        ('irrational', False),
+        ('noninteger', False),
+        ('nonzero', True),
+        ('rational', True),
+        ('real', True),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of odd = False:
+    (('odd', False), set( (
+       ) ),
+     ),
+    # Implications of positive = True:
+    (('positive', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('extended_negative', False),
+        ('extended_nonnegative', True),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', True),
+        ('extended_positive', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('negative', False),
+        ('nonnegative', True),
+        ('nonpositive', False),
+        ('nonzero', True),
+        ('real', True),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of positive = False:
+    (('positive', False), set( (
+        ('composite', False),
+        ('prime', False),
+       ) ),
+     ),
+    # Implications of prime = True:
+    (('prime', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('extended_negative', False),
+        ('extended_nonnegative', True),
+        ('extended_nonpositive', False),
+        ('extended_nonzero', True),
+        ('extended_positive', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('integer', True),
+        ('irrational', False),
+        ('negative', False),
+        ('noninteger', False),
+        ('nonnegative', True),
+        ('nonpositive', False),
+        ('nonzero', True),
+        ('positive', True),
+        ('rational', True),
+        ('real', True),
+        ('transcendental', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of prime = False:
+    (('prime', False), set( (
+       ) ),
+     ),
+    # Implications of rational = True:
+    (('rational', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('irrational', False),
+        ('real', True),
+        ('transcendental', False),
+       ) ),
+     ),
+    # Implications of rational = False:
+    (('rational', False), set( (
+        ('composite', False),
+        ('even', False),
+        ('integer', False),
+        ('odd', False),
+        ('prime', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of real = True:
+    (('real', True), set( (
+        ('commutative', True),
+        ('complex', True),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+       ) ),
+     ),
+    # Implications of real = False:
+    (('real', False), set( (
+        ('composite', False),
+        ('even', False),
+        ('integer', False),
+        ('irrational', False),
+        ('negative', False),
+        ('nonnegative', False),
+        ('nonpositive', False),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of transcendental = True:
+    (('transcendental', True), set( (
+        ('algebraic', False),
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('even', False),
+        ('finite', True),
+        ('infinite', False),
+        ('integer', False),
+        ('odd', False),
+        ('prime', False),
+        ('rational', False),
+        ('zero', False),
+       ) ),
+     ),
+    # Implications of transcendental = False:
+    (('transcendental', False), set( (
+       ) ),
+     ),
+    # Implications of zero = True:
+    (('zero', True), set( (
+        ('algebraic', True),
+        ('commutative', True),
+        ('complex', True),
+        ('composite', False),
+        ('even', True),
+        ('extended_negative', False),
+        ('extended_nonnegative', True),
+        ('extended_nonpositive', True),
+        ('extended_nonzero', False),
+        ('extended_positive', False),
+        ('extended_real', True),
+        ('finite', True),
+        ('hermitian', True),
+        ('imaginary', False),
+        ('infinite', False),
+        ('integer', True),
+        ('irrational', False),
+        ('negative', False),
+        ('noninteger', False),
+        ('nonnegative', True),
+        ('nonpositive', True),
+        ('nonzero', False),
+        ('odd', False),
+        ('positive', False),
+        ('prime', False),
+        ('rational', True),
+        ('real', True),
+        ('transcendental', False),
+       ) ),
+     ),
+    # Implications of zero = False:
+    (('zero', False), set( (
+       ) ),
+     ),
+ ] ) # full_implications
+
+
+prereq = {
+
+    # facts that could determine the value of algebraic
+    'algebraic': {
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'finite',
+        'infinite',
+        'integer',
+        'odd',
+        'prime',
+        'rational',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of antihermitian
+    'antihermitian': {
+        'imaginary',
+    },
+
+    # facts that could determine the value of commutative
+    'commutative': {
+        'algebraic',
+        'complex',
+        'composite',
+        'even',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'imaginary',
+        'integer',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of complex
+    'complex': {
+        'algebraic',
+        'commutative',
+        'composite',
+        'even',
+        'finite',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of composite
+    'composite': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of even
+    'even': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'noninteger',
+        'odd',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of extended_negative
+    'extended_negative': {
+        'commutative',
+        'composite',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'imaginary',
+        'negative',
+        'nonnegative',
+        'positive',
+        'prime',
+        'zero',
+    },
+
+    # facts that could determine the value of extended_nonnegative
+    'extended_nonnegative': {
+        'commutative',
+        'composite',
+        'extended_negative',
+        'extended_positive',
+        'extended_real',
+        'imaginary',
+        'negative',
+        'nonnegative',
+        'positive',
+        'prime',
+        'zero',
+    },
+
+    # facts that could determine the value of extended_nonpositive
+    'extended_nonpositive': {
+        'commutative',
+        'composite',
+        'extended_negative',
+        'extended_positive',
+        'extended_real',
+        'imaginary',
+        'negative',
+        'nonpositive',
+        'positive',
+        'prime',
+        'zero',
+    },
+
+    # facts that could determine the value of extended_nonzero
+    'extended_nonzero': {
+        'commutative',
+        'composite',
+        'extended_negative',
+        'extended_positive',
+        'extended_real',
+        'imaginary',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'zero',
+    },
+
+    # facts that could determine the value of extended_positive
+    'extended_positive': {
+        'commutative',
+        'composite',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_real',
+        'imaginary',
+        'negative',
+        'nonpositive',
+        'positive',
+        'prime',
+        'zero',
+    },
+
+    # facts that could determine the value of extended_real
+    'extended_real': {
+        'commutative',
+        'composite',
+        'even',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'imaginary',
+        'integer',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of finite
+    'finite': {
+        'algebraic',
+        'complex',
+        'composite',
+        'even',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of hermitian
+    'hermitian': {
+        'composite',
+        'even',
+        'integer',
+        'irrational',
+        'negative',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of imaginary
+    'imaginary': {
+        'antihermitian',
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of infinite
+    'infinite': {
+        'algebraic',
+        'complex',
+        'composite',
+        'even',
+        'finite',
+        'imaginary',
+        'integer',
+        'irrational',
+        'negative',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of integer
+    'integer': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'irrational',
+        'noninteger',
+        'odd',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of irrational
+    'irrational': {
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'odd',
+        'prime',
+        'rational',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of negative
+    'negative': {
+        'commutative',
+        'complex',
+        'composite',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'positive',
+        'prime',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of noninteger
+    'noninteger': {
+        'commutative',
+        'composite',
+        'even',
+        'extended_real',
+        'imaginary',
+        'integer',
+        'irrational',
+        'odd',
+        'prime',
+        'zero',
+    },
+
+    # facts that could determine the value of nonnegative
+    'nonnegative': {
+        'commutative',
+        'complex',
+        'composite',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'negative',
+        'positive',
+        'prime',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of nonpositive
+    'nonpositive': {
+        'commutative',
+        'complex',
+        'composite',
+        'extended_nonpositive',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'negative',
+        'positive',
+        'prime',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of nonzero
+    'nonzero': {
+        'commutative',
+        'complex',
+        'composite',
+        'extended_nonzero',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'irrational',
+        'negative',
+        'odd',
+        'positive',
+        'prime',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of odd
+    'odd': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'even',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'noninteger',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of positive
+    'positive': {
+        'commutative',
+        'complex',
+        'composite',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'negative',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'prime',
+        'real',
+        'zero',
+    },
+
+    # facts that could determine the value of prime
+    'prime': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'composite',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'positive',
+        'rational',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of rational
+    'rational': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'odd',
+        'prime',
+        'real',
+        'transcendental',
+        'zero',
+    },
+
+    # facts that could determine the value of real
+    'real': {
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'zero',
+    },
+
+    # facts that could determine the value of transcendental
+    'transcendental': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'finite',
+        'infinite',
+        'integer',
+        'odd',
+        'prime',
+        'rational',
+        'zero',
+    },
+
+    # facts that could determine the value of zero
+    'zero': {
+        'algebraic',
+        'commutative',
+        'complex',
+        'composite',
+        'even',
+        'extended_negative',
+        'extended_nonnegative',
+        'extended_nonpositive',
+        'extended_nonzero',
+        'extended_positive',
+        'extended_real',
+        'finite',
+        'hermitian',
+        'imaginary',
+        'infinite',
+        'integer',
+        'irrational',
+        'negative',
+        'noninteger',
+        'nonnegative',
+        'nonpositive',
+        'nonzero',
+        'odd',
+        'positive',
+        'prime',
+        'rational',
+        'real',
+        'transcendental',
+    },
+
+} # prereq
+
+
+# Note: the order of the beta rules is used in the beta_triggers
+beta_rules = [
+
+    # Rules implying composite = True
+    ({('even', True), ('positive', True), ('prime', False)},
+        ('composite', True)),
+
+    # Rules implying even = False
+    ({('composite', False), ('positive', True), ('prime', False)},
+        ('even', False)),
+
+    # Rules implying even = True
+    ({('integer', True), ('odd', False)},
+        ('even', True)),
+
+    # Rules implying extended_negative = True
+    ({('extended_positive', False), ('extended_real', True), ('zero', False)},
+        ('extended_negative', True)),
+    ({('extended_nonpositive', True), ('extended_nonzero', True)},
+        ('extended_negative', True)),
+
+    # Rules implying extended_nonnegative = True
+    ({('extended_negative', False), ('extended_real', True)},
+        ('extended_nonnegative', True)),
+
+    # Rules implying extended_nonpositive = True
+    ({('extended_positive', False), ('extended_real', True)},
+        ('extended_nonpositive', True)),
+
+    # Rules implying extended_nonzero = True
+    ({('extended_real', True), ('zero', False)},
+        ('extended_nonzero', True)),
+
+    # Rules implying extended_positive = True
+    ({('extended_negative', False), ('extended_real', True), ('zero', False)},
+        ('extended_positive', True)),
+    ({('extended_nonnegative', True), ('extended_nonzero', True)},
+        ('extended_positive', True)),
+
+    # Rules implying extended_real = False
+    ({('infinite', False), ('real', False)},
+        ('extended_real', False)),
+    ({('extended_negative', False), ('extended_positive', False), ('zero', False)},
+        ('extended_real', False)),
+
+    # Rules implying infinite = True
+    ({('extended_real', True), ('real', False)},
+        ('infinite', True)),
+
+    # Rules implying irrational = True
+    ({('rational', False), ('real', True)},
+        ('irrational', True)),
+
+    # Rules implying negative = True
+    ({('positive', False), ('real', True), ('zero', False)},
+        ('negative', True)),
+    ({('nonpositive', True), ('nonzero', True)},
+        ('negative', True)),
+    ({('extended_negative', True), ('finite', True)},
+        ('negative', True)),
+
+    # Rules implying noninteger = True
+    ({('extended_real', True), ('integer', False)},
+        ('noninteger', True)),
+
+    # Rules implying nonnegative = True
+    ({('negative', False), ('real', True)},
+        ('nonnegative', True)),
+    ({('extended_nonnegative', True), ('finite', True)},
+        ('nonnegative', True)),
+
+    # Rules implying nonpositive = True
+    ({('positive', False), ('real', True)},
+        ('nonpositive', True)),
+    ({('extended_nonpositive', True), ('finite', True)},
+        ('nonpositive', True)),
+
+    # Rules implying nonzero = True
+    ({('extended_nonzero', True), ('finite', True)},
+        ('nonzero', True)),
+
+    # Rules implying odd = True
+    ({('even', False), ('integer', True)},
+        ('odd', True)),
+
+    # Rules implying positive = False
+    ({('composite', False), ('even', True), ('prime', False)},
+        ('positive', False)),
+
+    # Rules implying positive = True
+    ({('negative', False), ('real', True), ('zero', False)},
+        ('positive', True)),
+    ({('nonnegative', True), ('nonzero', True)},
+        ('positive', True)),
+    ({('extended_positive', True), ('finite', True)},
+        ('positive', True)),
+
+    # Rules implying prime = True
+    ({('composite', False), ('even', True), ('positive', True)},
+        ('prime', True)),
+
+    # Rules implying real = False
+    ({('negative', False), ('positive', False), ('zero', False)},
+        ('real', False)),
+
+    # Rules implying real = True
+    ({('extended_real', True), ('infinite', False)},
+        ('real', True)),
+    ({('extended_real', True), ('finite', True)},
+        ('real', True)),
+
+    # Rules implying transcendental = True
+    ({('algebraic', False), ('complex', True)},
+        ('transcendental', True)),
+
+    # Rules implying zero = True
+    ({('extended_negative', False), ('extended_positive', False), ('extended_real', True)},
+        ('zero', True)),
+    ({('negative', False), ('positive', False), ('real', True)},
+        ('zero', True)),
+    ({('extended_nonnegative', True), ('extended_nonpositive', True)},
+        ('zero', True)),
+    ({('nonnegative', True), ('nonpositive', True)},
+        ('zero', True)),
+
+] # beta_rules
+beta_triggers = {
+    ('algebraic', False): [32, 11, 3, 8, 29, 14, 25, 13, 17, 7],
+    ('algebraic', True): [10, 30, 31, 27, 16, 21, 19, 22],
+    ('antihermitian', False): [],
+    ('commutative', False): [],
+    ('complex', False): [10, 12, 11, 3, 8, 17, 7],
+    ('complex', True): [32, 10, 30, 31, 27, 16, 21, 19, 22],
+    ('composite', False): [1, 28, 24],
+    ('composite', True): [23, 2],
+    ('even', False): [23, 11, 3, 8, 29, 14, 25, 7],
+    ('even', True): [3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 0, 28, 24, 7],
+    ('extended_negative', False): [11, 33, 8, 5, 29, 34, 25, 18],
+    ('extended_negative', True): [30, 12, 31, 29, 14, 20, 16, 21, 22, 17],
+    ('extended_nonnegative', False): [11, 3, 6, 29, 14, 20, 7],
+    ('extended_nonnegative', True): [30, 12, 31, 33, 8, 9, 6, 29, 34, 25, 18, 19, 35, 17, 7],
+    ('extended_nonpositive', False): [11, 8, 5, 29, 25, 18, 7],
+    ('extended_nonpositive', True): [30, 12, 31, 3, 33, 4, 5, 29, 14, 34, 20, 21, 35, 17, 7],
+    ('extended_nonzero', False): [11, 33, 6, 5, 29, 34, 20, 18],
+    ('extended_nonzero', True): [30, 12, 31, 3, 8, 4, 9, 6, 5, 29, 14, 25, 22, 17],
+    ('extended_positive', False): [11, 3, 33, 6, 29, 14, 34, 20],
+    ('extended_positive', True): [30, 12, 31, 29, 25, 18, 27, 19, 22, 17],
+    ('extended_real', False): [],
+    ('extended_real', True): [30, 12, 31, 3, 33, 8, 6, 5, 17, 7],
+    ('finite', False): [11, 3, 8, 17, 7],
+    ('finite', True): [10, 30, 31, 27, 16, 21, 19, 22],
+    ('hermitian', False): [10, 12, 11, 3, 8, 17, 7],
+    ('imaginary', True): [32],
+    ('infinite', False): [10, 30, 31, 27, 16, 21, 19, 22],
+    ('infinite', True): [11, 3, 8, 17, 7],
+    ('integer', False): [11, 3, 8, 29, 14, 25, 17, 7],
+    ('integer', True): [23, 2, 3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 7],
+    ('irrational', True): [32, 3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19],
+    ('negative', False): [29, 34, 25, 18],
+    ('negative', True): [32, 13, 17],
+    ('noninteger', True): [30, 12, 31, 3, 8, 4, 9, 6, 5, 29, 14, 25, 22],
+    ('nonnegative', False): [11, 3, 8, 29, 14, 20, 7],
+    ('nonnegative', True): [32, 33, 8, 9, 6, 34, 25, 26, 20, 27, 21, 22, 35, 36, 13, 17, 7],
+    ('nonpositive', False): [11, 3, 8, 29, 25, 18, 7],
+    ('nonpositive', True): [32, 3, 33, 4, 5, 14, 34, 15, 18, 16, 19, 22, 35, 36, 13, 17, 7],
+    ('nonzero', False): [29, 34, 20, 18],
+    ('nonzero', True): [32, 3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19, 13, 17],
+    ('odd', False): [2],
+    ('odd', True): [3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19],
+    ('positive', False): [29, 14, 34, 20],
+    ('positive', True): [32, 0, 1, 28, 13, 17],
+    ('prime', False): [0, 1, 24],
+    ('prime', True): [23, 2],
+    ('rational', False): [11, 3, 8, 29, 14, 25, 13, 17, 7],
+    ('rational', True): [3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 17, 7],
+    ('real', False): [10, 12, 11, 3, 8, 17, 7],
+    ('real', True): [32, 3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 13, 17, 7],
+    ('transcendental', True): [10, 30, 31, 11, 3, 8, 29, 14, 25, 27, 16, 21, 19, 22, 13, 17, 7],
+    ('zero', False): [11, 3, 8, 29, 14, 25, 7],
+    ('zero', True): [],
+} # beta_triggers
+
+
+generated_assumptions = {'defined_facts': defined_facts, 'full_implications': full_implications,
+               'prereq': prereq, 'beta_rules': beta_rules, 'beta_triggers': beta_triggers}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/backend.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..34a4e05a4a4ac50d0830960cb324871a20e9a12d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/backend.py
@@ -0,0 +1,120 @@
+import os
+USE_SYMENGINE = os.getenv('USE_SYMENGINE', '0')
+USE_SYMENGINE = USE_SYMENGINE.lower() in ('1', 't', 'true')  # type: ignore
+
+if USE_SYMENGINE:
+    from symengine import (Symbol, Integer, sympify as sympify_symengine, S,
+        SympifyError, exp, log, gamma, sqrt, I, E, pi, Matrix,
+        sin, cos, tan, cot, csc, sec, asin, acos, atan, acot, acsc, asec,
+        sinh, cosh, tanh, coth, asinh, acosh, atanh, acoth,
+        lambdify, symarray, diff, zeros, eye, diag, ones,
+        expand, Function, symbols, var, Add, Mul, Derivative,
+        ImmutableMatrix, MatrixBase, Rational, Basic)
+    from symengine.lib.symengine_wrapper import gcd as igcd
+    from symengine import AppliedUndef
+
+    def sympify(a, *, strict=False):
+        """
+        Notes
+        =====
+
+        SymEngine's ``sympify`` does not accept keyword arguments and is
+        therefore not compatible with SymPy's ``sympify`` with ``strict=True``
+        (which ensures that only the types for which an explicit conversion has
+        been defined are converted). This wrapper adds an additional parameter
+        ``strict`` (with default ``False``) that will raise a ``SympifyError``
+        if ``strict=True`` and the argument passed to the parameter ``a`` is a
+        string.
+
+        See Also
+        ========
+
+        sympify: Converts an arbitrary expression to a type that can be used
+            inside SymPy.
+
+        """
+        # The parameter ``a`` is used for this function to keep compatibility
+        # with the SymEngine docstring.
+        if strict and isinstance(a, str):
+            raise SympifyError(a)
+        return sympify_symengine(a)
+
+    # Keep the SymEngine docstring and append the additional "Notes" and "See
+    # Also" sections. Replacement of spaces is required to correctly format the
+    # indentation of the combined docstring.
+    sympify.__doc__ = (
+        sympify_symengine.__doc__
+        + sympify.__doc__.replace('        ', '    ')  # type: ignore
+    )
+else:
+    from sympy.core.add import Add
+    from sympy.core.basic import Basic
+    from sympy.core.function import (diff, Function, AppliedUndef,
+        expand, Derivative)
+    from sympy.core.mul import Mul
+    from sympy.core.intfunc import igcd
+    from sympy.core.numbers import pi, I, Integer, Rational, E
+    from sympy.core.singleton import S
+    from sympy.core.symbol import Symbol, var, symbols
+    from sympy.core.sympify import SympifyError, sympify
+    from sympy.functions.elementary.exponential import log, exp
+    from sympy.functions.elementary.hyperbolic import (coth, sinh,
+        acosh, acoth, tanh, asinh, atanh, cosh)
+    from sympy.functions.elementary.miscellaneous import sqrt
+    from sympy.functions.elementary.trigonometric import (csc,
+        asec, cos, atan, sec, acot, asin, tan, sin, cot, acsc, acos)
+    from sympy.functions.special.gamma_functions import gamma
+    from sympy.matrices.dense import (eye, zeros, diag, Matrix,
+        ones, symarray)
+    from sympy.matrices.immutable import ImmutableMatrix
+    from sympy.matrices.matrixbase import MatrixBase
+    from sympy.utilities.lambdify import lambdify
+
+
+#
+# XXX: Handling of immutable and mutable matrices in SymEngine is inconsistent
+# with SymPy's matrix classes in at least SymEngine version 0.7.0. Until that
+# is fixed the function below is needed for consistent behaviour when
+# attempting to simplify a matrix.
+#
+# Expected behaviour of a SymPy mutable/immutable matrix .simplify() method:
+#
+#   Matrix.simplify() : works in place, returns None
+#   ImmutableMatrix.simplify() : returns a simplified copy
+#
+# In SymEngine both mutable and immutable matrices simplify in place and return
+# None. This is inconsistent with the matrix being "immutable" and also the
+# returned None leads to problems in the mechanics module.
+#
+# The simplify function should not be used because simplify(M) sympifies the
+# matrix M and the SymEngine matrices all sympify to SymPy matrices. If we want
+# to work with SymEngine matrices then we need to use their .simplify() method
+# but that method does not work correctly with immutable matrices.
+#
+# The _simplify_matrix function can be removed when the SymEngine bug is fixed.
+# Since this should be a temporary problem we do not make this function part of
+# the public API.
+#
+#   SymEngine issue: https://github.com/symengine/symengine.py/issues/363
+#
+
+def _simplify_matrix(M):
+    """Return a simplified copy of the matrix M"""
+    if not isinstance(M, (Matrix, ImmutableMatrix)):
+        raise TypeError("The matrix M must be an instance of Matrix or ImmutableMatrix")
+    Mnew = M.as_mutable() # makes a copy if mutable
+    Mnew.simplify()
+    if isinstance(M, ImmutableMatrix):
+        Mnew = Mnew.as_immutable()
+    return Mnew
+
+
+__all__ = [
+    'Symbol', 'Integer', 'sympify', 'S', 'SympifyError', 'exp', 'log',
+    'gamma', 'sqrt', 'I', 'E', 'pi', 'Matrix', 'sin', 'cos', 'tan', 'cot',
+    'csc', 'sec', 'asin', 'acos', 'atan', 'acot', 'acsc', 'asec', 'sinh',
+    'cosh', 'tanh', 'coth', 'asinh', 'acosh', 'atanh', 'acoth', 'lambdify',
+    'symarray', 'diff', 'zeros', 'eye', 'diag', 'ones', 'expand', 'Function',
+    'symbols', 'var', 'Add', 'Mul', 'Derivative', 'ImmutableMatrix',
+    'MatrixBase', 'Rational', 'Basic', 'igcd', 'AppliedUndef',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/basic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..92f6e710113ce0523ad15100abb0acd00f03f741
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/basic.py
@@ -0,0 +1,2355 @@
+"""Base class for all the objects in SymPy"""
+from __future__ import annotations
+
+from collections import Counter
+from collections.abc import Mapping, Iterable
+from itertools import zip_longest
+from functools import cmp_to_key
+from typing import TYPE_CHECKING, overload
+
+from .assumptions import _prepare_class_assumptions
+from .cache import cacheit
+from .sympify import _sympify, sympify, SympifyError, _external_converter
+from .sorting import ordered
+from .kind import Kind, UndefinedKind
+from ._print_helpers import Printable
+
+from sympy.utilities.decorator import deprecated
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import iterable, numbered_symbols
+from sympy.utilities.misc import filldedent, func_name
+
+
+if TYPE_CHECKING:
+    from typing import ClassVar, TypeVar, Any
+    from typing_extensions import Self
+    from .assumptions import StdFactKB
+    from .symbol import Symbol
+
+    Tbasic = TypeVar("Tbasic", bound='Basic')
+
+
+def as_Basic(expr):
+    """Return expr as a Basic instance using strict sympify
+    or raise a TypeError; this is just a wrapper to _sympify,
+    raising a TypeError instead of a SympifyError."""
+    try:
+        return _sympify(expr)
+    except SympifyError:
+        raise TypeError(
+            'Argument must be a Basic object, not `%s`' % func_name(
+            expr))
+
+
+# Key for sorting commutative args in canonical order
+# by name. This is used for canonical ordering of the
+# args for Add and Mul *if* the names of both classes
+# being compared appear here. Some things in this list
+# are not spelled the same as their name so they do not,
+# in effect, appear here. See Basic.compare.
+ordering_of_classes = [
+    # singleton numbers
+    'Zero', 'One', 'Half', 'Infinity', 'NaN', 'NegativeOne', 'NegativeInfinity',
+    # numbers
+    'Integer', 'Rational', 'Float',
+    # singleton symbols
+    'Exp1', 'Pi', 'ImaginaryUnit',
+    # symbols
+    'Symbol', 'Wild',
+    # arithmetic operations
+    'Pow', 'Mul', 'Add',
+    # function values
+    'Derivative', 'Integral',
+    # defined singleton functions
+    'Abs', 'Sign', 'Sqrt',
+    'Floor', 'Ceiling',
+    'Re', 'Im', 'Arg',
+    'Conjugate',
+    'Exp', 'Log',
+    'Sin', 'Cos', 'Tan', 'Cot', 'ASin', 'ACos', 'ATan', 'ACot',
+    'Sinh', 'Cosh', 'Tanh', 'Coth', 'ASinh', 'ACosh', 'ATanh', 'ACoth',
+    'RisingFactorial', 'FallingFactorial',
+    'factorial', 'binomial',
+    'Gamma', 'LowerGamma', 'UpperGamma', 'PolyGamma',
+    'Erf',
+    # special polynomials
+    'Chebyshev', 'Chebyshev2',
+    # undefined functions
+    'Function', 'WildFunction',
+    # anonymous functions
+    'Lambda',
+    # Landau O symbol
+    'Order',
+    # relational operations
+    'Equality', 'Unequality', 'StrictGreaterThan', 'StrictLessThan',
+    'GreaterThan', 'LessThan',
+]
+
+def _cmp_name(x: type, y: type) -> int:
+    """return -1, 0, 1 if the name of x is before that of y.
+    A string comparison is done if either name does not appear
+    in `ordering_of_classes`. This is the helper for
+    ``Basic.compare``
+
+    Examples
+    ========
+
+    >>> from sympy import cos, tan, sin
+    >>> from sympy.core import basic
+    >>> save = basic.ordering_of_classes
+    >>> basic.ordering_of_classes = ()
+    >>> basic._cmp_name(cos, tan)
+    -1
+    >>> basic.ordering_of_classes = ["tan", "sin", "cos"]
+    >>> basic._cmp_name(cos, tan)
+    1
+    >>> basic._cmp_name(sin, cos)
+    -1
+    >>> basic.ordering_of_classes = save
+
+    """
+    n1 = x.__name__
+    n2 = y.__name__
+    if n1 == n2:
+        return 0
+
+    # If the other object is not a Basic subclass, then we are not equal to it.
+    if not issubclass(y, Basic):
+        return -1
+
+    UNKNOWN = len(ordering_of_classes) + 1
+    try:
+        i1 = ordering_of_classes.index(n1)
+    except ValueError:
+        i1 = UNKNOWN
+    try:
+        i2 = ordering_of_classes.index(n2)
+    except ValueError:
+        i2 = UNKNOWN
+    if i1 == UNKNOWN and i2 == UNKNOWN:
+        return (n1 > n2) - (n1 < n2)
+    return (i1 > i2) - (i1 < i2)
+
+
+
+@cacheit
+def _get_postprocessors(clsname, arg_type):
+    # Since only Add, Mul, Pow can be clsname, this cache
+    # is not quadratic.
+    postprocessors = set()
+    mappings = _get_postprocessors_for_type(arg_type)
+    for mapping in mappings:
+        f = mapping.get(clsname, None)
+        if f is not None:
+            postprocessors.update(f)
+    return postprocessors
+
+@cacheit
+def _get_postprocessors_for_type(arg_type):
+    return tuple(
+        Basic._constructor_postprocessor_mapping[cls]
+        for cls in arg_type.mro()
+        if cls in Basic._constructor_postprocessor_mapping
+    )
+
+
+class Basic(Printable):
+    """
+    Base class for all SymPy objects.
+
+    Notes and conventions
+    =====================
+
+    1) Always use ``.args``, when accessing parameters of some instance:
+
+    >>> from sympy import cot
+    >>> from sympy.abc import x, y
+
+    >>> cot(x).args
+    (x,)
+
+    >>> cot(x).args[0]
+    x
+
+    >>> (x*y).args
+    (x, y)
+
+    >>> (x*y).args[1]
+    y
+
+
+    2) Never use internal methods or variables (the ones prefixed with ``_``):
+
+    >>> cot(x)._args    # do not use this, use cot(x).args instead
+    (x,)
+
+
+    3)  By "SymPy object" we mean something that can be returned by
+        ``sympify``.  But not all objects one encounters using SymPy are
+        subclasses of Basic.  For example, mutable objects are not:
+
+        >>> from sympy import Basic, Matrix, sympify
+        >>> A = Matrix([[1, 2], [3, 4]]).as_mutable()
+        >>> isinstance(A, Basic)
+        False
+
+        >>> B = sympify(A)
+        >>> isinstance(B, Basic)
+        True
+    """
+    __slots__ = ('_mhash',              # hash value
+                 '_args',               # arguments
+                 '_assumptions'
+                )
+
+    _args: tuple[Basic, ...]
+    _mhash: int | None
+
+    @property
+    def __sympy__(self):
+        return True
+
+    def __init_subclass__(cls):
+        # Initialize the default_assumptions FactKB and also any assumptions
+        # property methods. This method will only be called for subclasses of
+        # Basic but not for Basic itself so we call
+        # _prepare_class_assumptions(Basic) below the class definition.
+        super().__init_subclass__()
+        _prepare_class_assumptions(cls)
+
+    # To be overridden with True in the appropriate subclasses
+    is_number = False
+    is_Atom = False
+    is_Symbol = False
+    is_symbol = False
+    is_Indexed = False
+    is_Dummy = False
+    is_Wild = False
+    is_Function = False
+    is_Add = False
+    is_Mul = False
+    is_Pow = False
+    is_Number = False
+    is_Float = False
+    is_Rational = False
+    is_Integer = False
+    is_NumberSymbol = False
+    is_Order = False
+    is_Derivative = False
+    is_Piecewise = False
+    is_Poly = False
+    is_AlgebraicNumber = False
+    is_Relational = False
+    is_Equality = False
+    is_Boolean = False
+    is_Not = False
+    is_Matrix = False
+    is_Vector = False
+    is_Point = False
+    is_MatAdd = False
+    is_MatMul = False
+
+    default_assumptions: ClassVar[StdFactKB]
+
+    is_composite: bool | None
+    is_noninteger: bool | None
+    is_extended_positive: bool | None
+    is_negative: bool | None
+    is_complex: bool | None
+    is_extended_nonpositive: bool | None
+    is_integer: bool | None
+    is_positive: bool | None
+    is_rational: bool | None
+    is_extended_nonnegative: bool | None
+    is_infinite: bool | None
+    is_antihermitian: bool | None
+    is_extended_negative: bool | None
+    is_extended_real: bool | None
+    is_finite: bool | None
+    is_polar: bool | None
+    is_imaginary: bool | None
+    is_transcendental: bool | None
+    is_extended_nonzero: bool | None
+    is_nonzero: bool | None
+    is_odd: bool | None
+    is_algebraic: bool | None
+    is_prime: bool | None
+    is_commutative: bool | None
+    is_nonnegative: bool | None
+    is_nonpositive: bool | None
+    is_hermitian: bool | None
+    is_irrational: bool | None
+    is_real: bool | None
+    is_zero: bool | None
+    is_even: bool | None
+
+    kind: Kind = UndefinedKind
+
+    def __new__(cls, *args):
+        obj = object.__new__(cls)
+        obj._assumptions = cls.default_assumptions
+        obj._mhash = None  # will be set by __hash__ method.
+
+        obj._args = args  # all items in args must be Basic objects
+        return obj
+
+    def copy(self):
+        return self.func(*self.args)
+
+    def __getnewargs__(self):
+        return self.args
+
+    def __getstate__(self):
+        return None
+
+    def __setstate__(self, state):
+        for name, value in state.items():
+            setattr(self, name, value)
+
+    def __reduce_ex__(self, protocol):
+        if protocol < 2:
+            msg = "Only pickle protocol 2 or higher is supported by SymPy"
+            raise NotImplementedError(msg)
+        return super().__reduce_ex__(protocol)
+
+    def __hash__(self) -> int:
+        # hash cannot be cached using cache_it because infinite recurrence
+        # occurs as hash is needed for setting cache dictionary keys
+        h = self._mhash
+        if h is None:
+            h = hash((type(self).__name__,) + self._hashable_content())
+            self._mhash = h
+        return h
+
+    def _hashable_content(self):
+        """Return a tuple of information about self that can be used to
+        compute the hash. If a class defines additional attributes,
+        like ``name`` in Symbol, then this method should be updated
+        accordingly to return such relevant attributes.
+
+        Defining more than _hashable_content is necessary if __eq__ has
+        been defined by a class. See note about this in Basic.__eq__."""
+        return self._args
+
+    @property
+    def assumptions0(self):
+        """
+        Return object `type` assumptions.
+
+        For example:
+
+          Symbol('x', real=True)
+          Symbol('x', integer=True)
+
+        are different objects. In other words, besides Python type (Symbol in
+        this case), the initial assumptions are also forming their typeinfo.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.abc import x
+        >>> x.assumptions0
+        {'commutative': True}
+        >>> x = Symbol("x", positive=True)
+        >>> x.assumptions0
+        {'commutative': True, 'complex': True, 'extended_negative': False,
+         'extended_nonnegative': True, 'extended_nonpositive': False,
+         'extended_nonzero': True, 'extended_positive': True, 'extended_real':
+         True, 'finite': True, 'hermitian': True, 'imaginary': False,
+         'infinite': False, 'negative': False, 'nonnegative': True,
+         'nonpositive': False, 'nonzero': True, 'positive': True, 'real':
+         True, 'zero': False}
+        """
+        return {}
+
+    def compare(self, other):
+        """
+        Return -1, 0, 1 if the object is less than, equal,
+        or greater than other in a canonical sense.
+        Non-Basic are always greater than Basic.
+        If both names of the classes being compared appear
+        in the `ordering_of_classes` then the ordering will
+        depend on the appearance of the names there.
+        If either does not appear in that list, then the
+        comparison is based on the class name.
+        If the names are the same then a comparison is made
+        on the length of the hashable content.
+        Items of the equal-lengthed contents are then
+        successively compared using the same rules. If there
+        is never a difference then 0 is returned.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> x.compare(y)
+        -1
+        >>> x.compare(x)
+        0
+        >>> y.compare(x)
+        1
+
+        """
+        # all redefinitions of __cmp__ method should start with the
+        # following lines:
+        if self is other:
+            return 0
+        n1 = self.__class__
+        n2 = other.__class__
+        c = _cmp_name(n1, n2)
+        if c:
+            return c
+        #
+        st = self._hashable_content()
+        ot = other._hashable_content()
+        len_st = len(st)
+        len_ot = len(ot)
+        c = (len_st > len_ot) - (len_st < len_ot)
+        if c:
+            return c
+        for l, r in zip(st, ot):
+            if isinstance(l, Basic):
+                c = l.compare(r)
+            elif isinstance(l, frozenset):
+                l = Basic(*l) if isinstance(l, frozenset) else l
+                r = Basic(*r) if isinstance(r, frozenset) else r
+                c = l.compare(r)
+            else:
+                c = (l > r) - (l < r)
+            if c:
+                return c
+        return 0
+
+    @classmethod
+    def fromiter(cls, args, **assumptions):
+        """
+        Create a new object from an iterable.
+
+        This is a convenience function that allows one to create objects from
+        any iterable, without having to convert to a list or tuple first.
+
+        Examples
+        ========
+
+        >>> from sympy import Tuple
+        >>> Tuple.fromiter(i for i in range(5))
+        (0, 1, 2, 3, 4)
+
+        """
+        return cls(*tuple(args), **assumptions)
+
+    @classmethod
+    def class_key(cls) -> tuple[int, int, str]:
+        """Nice order of classes."""
+        return 5, 0, cls.__name__
+
+    @cacheit
+    def sort_key(self, order=None):
+        """
+        Return a sort key.
+
+        Examples
+        ========
+
+        >>> from sympy import S, I
+
+        >>> sorted([S(1)/2, I, -I], key=lambda x: x.sort_key())
+        [1/2, -I, I]
+
+        >>> S("[x, 1/x, 1/x**2, x**2, x**(1/2), x**(1/4), x**(3/2)]")
+        [x, 1/x, x**(-2), x**2, sqrt(x), x**(1/4), x**(3/2)]
+        >>> sorted(_, key=lambda x: x.sort_key())
+        [x**(-2), 1/x, x**(1/4), sqrt(x), x, x**(3/2), x**2]
+
+        """
+
+        # XXX: remove this when issue 5169 is fixed
+        def inner_key(arg):
+            if isinstance(arg, Basic):
+                return arg.sort_key(order)
+            else:
+                return arg
+
+        args = self._sorted_args
+        args = len(args), tuple([inner_key(arg) for arg in args])
+        return self.class_key(), args, S.One.sort_key(), S.One
+
+    def _do_eq_sympify(self, other):
+        """Returns a boolean indicating whether a == b when either a
+        or b is not a Basic. This is only done for types that were either
+        added to `converter` by a 3rd party or when the object has `_sympy_`
+        defined. This essentially reuses the code in `_sympify` that is
+        specific for this use case. Non-user defined types that are meant
+        to work with SymPy should be handled directly in the __eq__ methods
+        of the `Basic` classes it could equate to and not be converted. Note
+        that after conversion, `==`  is used again since it is not
+        necessarily clear whether `self` or `other`'s __eq__ method needs
+        to be used."""
+        for superclass in type(other).__mro__:
+            conv = _external_converter.get(superclass)
+            if conv is not None:
+                return self == conv(other)
+        if hasattr(other, '_sympy_'):
+            return self == other._sympy_()
+        return NotImplemented
+
+    def __eq__(self, other):
+        """Return a boolean indicating whether a == b on the basis of
+        their symbolic trees.
+
+        This is the same as a.compare(b) == 0 but faster.
+
+        Notes
+        =====
+
+        If a class that overrides __eq__() needs to retain the
+        implementation of __hash__() from a parent class, the
+        interpreter must be told this explicitly by setting
+        __hash__ : Callable[[object], int] = .__hash__.
+        Otherwise the inheritance of __hash__() will be blocked,
+        just as if __hash__ had been explicitly set to None.
+
+        References
+        ==========
+
+        from https://docs.python.org/dev/reference/datamodel.html#object.__hash__
+        """
+        if self is other:
+            return True
+
+        if not isinstance(other, Basic):
+            return self._do_eq_sympify(other)
+
+        # check for pure number expr
+        if  not (self.is_Number and other.is_Number) and (
+                type(self) != type(other)):
+            return False
+        a, b = self._hashable_content(), other._hashable_content()
+        if a != b:
+            return False
+        # check number *in* an expression
+        for a, b in zip(a, b):
+            if not isinstance(a, Basic):
+                continue
+            if a.is_Number and type(a) != type(b):
+                return False
+        return True
+
+    def __ne__(self, other):
+        """``a != b``  -> Compare two symbolic trees and see whether they are different
+
+        this is the same as:
+
+        ``a.compare(b) != 0``
+
+        but faster
+        """
+        return not self == other
+
+    def dummy_eq(self, other, symbol=None):
+        """
+        Compare two expressions and handle dummy symbols.
+
+        Examples
+        ========
+
+        >>> from sympy import Dummy
+        >>> from sympy.abc import x, y
+
+        >>> u = Dummy('u')
+
+        >>> (u**2 + 1).dummy_eq(x**2 + 1)
+        True
+        >>> (u**2 + 1) == (x**2 + 1)
+        False
+
+        >>> (u**2 + y).dummy_eq(x**2 + y, x)
+        True
+        >>> (u**2 + y).dummy_eq(x**2 + y, y)
+        False
+
+        """
+        s = self.as_dummy()
+        o = _sympify(other)
+        o = o.as_dummy()
+
+        dummy_symbols = [i for i in s.free_symbols if i.is_Dummy]
+
+        if len(dummy_symbols) == 1:
+            dummy = dummy_symbols.pop()
+        else:
+            return s == o
+
+        if symbol is None:
+            symbols = o.free_symbols
+
+            if len(symbols) == 1:
+                symbol = symbols.pop()
+            else:
+                return s == o
+
+        tmp = dummy.__class__()
+
+        return s.xreplace({dummy: tmp}) == o.xreplace({symbol: tmp})
+
+    @overload
+    def atoms(self) -> set[Basic]: ...
+    @overload
+    def atoms(self, *types: Tbasic | type[Tbasic]) -> set[Tbasic]: ...
+
+    def atoms(self, *types: Tbasic | type[Tbasic]) -> set[Basic] | set[Tbasic]:
+        """Returns the atoms that form the current object.
+
+        By default, only objects that are truly atomic and cannot
+        be divided into smaller pieces are returned: symbols, numbers,
+        and number symbols like I and pi. It is possible to request
+        atoms of any type, however, as demonstrated below.
+
+        Examples
+        ========
+
+        >>> from sympy import I, pi, sin
+        >>> from sympy.abc import x, y
+        >>> (1 + x + 2*sin(y + I*pi)).atoms()
+        {1, 2, I, pi, x, y}
+
+        If one or more types are given, the results will contain only
+        those types of atoms.
+
+        >>> from sympy import Number, NumberSymbol, Symbol
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(Symbol)
+        {x, y}
+
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(Number)
+        {1, 2}
+
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(Number, NumberSymbol)
+        {1, 2, pi}
+
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(Number, NumberSymbol, I)
+        {1, 2, I, pi}
+
+        Note that I (imaginary unit) and zoo (complex infinity) are special
+        types of number symbols and are not part of the NumberSymbol class.
+
+        The type can be given implicitly, too:
+
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(x) # x is a Symbol
+        {x, y}
+
+        Be careful to check your assumptions when using the implicit option
+        since ``S(1).is_Integer = True`` but ``type(S(1))`` is ``One``, a special type
+        of SymPy atom, while ``type(S(2))`` is type ``Integer`` and will find all
+        integers in an expression:
+
+        >>> from sympy import S
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(S(1))
+        {1}
+
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(S(2))
+        {1, 2}
+
+        Finally, arguments to atoms() can select more than atomic atoms: any
+        SymPy type (loaded in core/__init__.py) can be listed as an argument
+        and those types of "atoms" as found in scanning the arguments of the
+        expression recursively:
+
+        >>> from sympy import Function, Mul
+        >>> from sympy.core.function import AppliedUndef
+        >>> f = Function('f')
+        >>> (1 + f(x) + 2*sin(y + I*pi)).atoms(Function)
+        {f(x), sin(y + I*pi)}
+        >>> (1 + f(x) + 2*sin(y + I*pi)).atoms(AppliedUndef)
+        {f(x)}
+
+        >>> (1 + x + 2*sin(y + I*pi)).atoms(Mul)
+        {I*pi, 2*sin(y + I*pi)}
+
+        """
+        nodes = _preorder_traversal(self)
+        if types:
+            types2 = tuple([t if isinstance(t, type) else type(t) for t in types])
+            return {node for node in nodes if isinstance(node, types2)}
+        else:
+            return {node for node in nodes if not node.args}
+
+    @property
+    def free_symbols(self) -> set[Basic]:
+        """Return from the atoms of self those which are free symbols.
+
+        Not all free symbols are ``Symbol`` (see examples)
+
+        For most expressions, all symbols are free symbols. For some classes
+        this is not true. e.g. Integrals use Symbols for the dummy variables
+        which are bound variables, so Integral has a method to return all
+        symbols except those. Derivative keeps track of symbols with respect
+        to which it will perform a derivative; those are
+        bound variables, too, so it has its own free_symbols method.
+
+        Any other method that uses bound variables should implement a
+        free_symbols method.
+
+        Examples
+        ========
+
+        >>> from sympy import Derivative, Integral, IndexedBase
+        >>> from sympy.abc import x, y, n
+        >>> (x + 1).free_symbols
+        {x}
+        >>> Integral(x, y).free_symbols
+        {x, y}
+
+        Not all free symbols are actually symbols:
+
+        >>> IndexedBase('F')[0].free_symbols
+        {F, F[0]}
+
+        The symbols of differentiation are not included unless they
+        appear in the expression being differentiated.
+
+        >>> Derivative(x + y, y).free_symbols
+        {x, y}
+        >>> Derivative(x, y).free_symbols
+        {x}
+        >>> Derivative(x, (y, n)).free_symbols
+        {n, x}
+
+        If you want to know if a symbol is in the variables of the
+        Derivative you can do so as follows:
+
+        >>> Derivative(x, y).has_free(y)
+        True
+        """
+        empty: set[Basic] = set()
+        return empty.union(*(a.free_symbols for a in self.args))
+
+    @property
+    def expr_free_symbols(self):
+        sympy_deprecation_warning("""
+        The expr_free_symbols property is deprecated. Use free_symbols to get
+        the free symbols of an expression.
+        """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-expr-free-symbols")
+        return set()
+
+    def as_dummy(self) -> "Self":
+        """Return the expression with any objects having structurally
+        bound symbols replaced with unique, canonical symbols within
+        the object in which they appear and having only the default
+        assumption for commutativity being True. When applied to a
+        symbol a new symbol having only the same commutativity will be
+        returned.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral, Symbol
+        >>> from sympy.abc import x
+        >>> r = Symbol('r', real=True)
+        >>> Integral(r, (r, x)).as_dummy()
+        Integral(_0, (_0, x))
+        >>> _.variables[0].is_real is None
+        True
+        >>> r.as_dummy()
+        _r
+
+        Notes
+        =====
+
+        Any object that has structurally bound variables should have
+        a property, ``bound_symbols`` that returns those symbols
+        appearing in the object.
+        """
+        from .symbol import Dummy, Symbol
+        def can(x):
+            # mask free that shadow bound
+            free = x.free_symbols
+            bound = set(x.bound_symbols)
+            d = {i: Dummy() for i in bound & free}
+            x = x.subs(d)
+            # replace bound with canonical names
+            x = x.xreplace(x.canonical_variables)
+            # return after undoing masking
+            return x.xreplace({v: k for k, v in d.items()})
+        if not self.has(Symbol):
+            return self
+        return self.replace(
+            lambda x: hasattr(x, 'bound_symbols'),
+            can,
+            simultaneous=False) # type:ignore
+
+    @property
+    def canonical_variables(self) -> dict[Basic, Symbol]:
+        """Return a dictionary mapping any variable defined in
+        ``self.bound_symbols`` to Symbols that do not clash
+        with any free symbols in the expression.
+
+        Examples
+        ========
+
+        >>> from sympy import Lambda
+        >>> from sympy.abc import x
+        >>> Lambda(x, 2*x).canonical_variables
+        {x: _0}
+        """
+        bound: list[Basic] | None = getattr(self, 'bound_symbols', None)
+        if bound is None:
+            return {}
+        dums = numbered_symbols('_')
+        reps = {}
+        # watch out for free symbol that are not in bound symbols;
+        # those that are in bound symbols are about to get changed
+
+        # XXX: free_symbols only returns particular kinds of expressions that
+        # generally have a .name attribute. There is not a proper class/type
+        # that represents this.
+        names = {i.name for i in self.free_symbols - set(bound)} # type: ignore
+        for b in bound:
+            d = next(dums)
+            if b.is_Symbol:
+                while d.name in names:
+                    d = next(dums)
+            reps[b] = d
+        return reps
+
+    def rcall(self, *args):
+        """Apply on the argument recursively through the expression tree.
+
+        This method is used to simulate a common abuse of notation for
+        operators. For instance, in SymPy the following will not work:
+
+        ``(x+Lambda(y, 2*y))(z) == x+2*z``,
+
+        however, you can use:
+
+        >>> from sympy import Lambda
+        >>> from sympy.abc import x, y, z
+        >>> (x + Lambda(y, 2*y)).rcall(z)
+        x + 2*z
+        """
+        if callable(self):
+            return self(*args)
+        elif self.args:
+            newargs = [sub.rcall(*args) for sub in self.args]
+            return self.func(*newargs)
+        else:
+            return self
+
+    def is_hypergeometric(self, k):
+        from sympy.simplify.simplify import hypersimp
+        from sympy.functions.elementary.piecewise import Piecewise
+        if self.has(Piecewise):
+            return None
+        return hypersimp(self, k) is not None
+
+    @property
+    def is_comparable(self):
+        """Return True if self can be computed to a real number
+        (or already is a real number) with precision, else False.
+
+        Examples
+        ========
+
+        >>> from sympy import exp_polar, pi, I
+        >>> (I*exp_polar(I*pi/2)).is_comparable
+        True
+        >>> (I*exp_polar(I*pi*2)).is_comparable
+        False
+
+        A False result does not mean that `self` cannot be rewritten
+        into a form that would be comparable. For example, the
+        difference computed below is zero but without simplification
+        it does not evaluate to a zero with precision:
+
+        >>> e = 2**pi*(1 + 2**pi)
+        >>> dif = e - e.expand()
+        >>> dif.is_comparable
+        False
+        >>> dif.n(2)._prec
+        1
+
+        """
+        return self._eval_is_comparable()
+
+    def _eval_is_comparable(self) -> bool:
+        # Expr.is_comparable overrides this
+        return False
+
+    @property
+    def func(self):
+        """
+        The top-level function in an expression.
+
+        The following should hold for all objects::
+
+            >> x == x.func(*x.args)
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> a = 2*x
+        >>> a.func
+        
+        >>> a.args
+        (2, x)
+        >>> a.func(*a.args)
+        2*x
+        >>> a == a.func(*a.args)
+        True
+
+        """
+        return self.__class__
+
+    @property
+    def args(self) -> tuple[Basic, ...]:
+        """Returns a tuple of arguments of 'self'.
+
+        Examples
+        ========
+
+        >>> from sympy import cot
+        >>> from sympy.abc import x, y
+
+        >>> cot(x).args
+        (x,)
+
+        >>> cot(x).args[0]
+        x
+
+        >>> (x*y).args
+        (x, y)
+
+        >>> (x*y).args[1]
+        y
+
+        Notes
+        =====
+
+        Never use self._args, always use self.args.
+        Only use _args in __new__ when creating a new function.
+        Do not override .args() from Basic (so that it is easy to
+        change the interface in the future if needed).
+        """
+        return self._args
+
+    @property
+    def _sorted_args(self):
+        """
+        The same as ``args``.  Derived classes which do not fix an
+        order on their arguments should override this method to
+        produce the sorted representation.
+        """
+        return self.args
+
+    def as_content_primitive(self, radical=False, clear=True):
+        """A stub to allow Basic args (like Tuple) to be skipped when computing
+        the content and primitive components of an expression.
+
+        See Also
+        ========
+
+        sympy.core.expr.Expr.as_content_primitive
+        """
+        return S.One, self
+
+    @overload
+    def subs(self, arg1: Mapping[Basic | complex, Basic | complex], arg2: None=None, **kwargs: Any) -> Basic: ...
+    @overload
+    def subs(self, arg1: Iterable[tuple[Basic | complex, Basic | complex]], arg2: None=None, **kwargs: Any) -> Basic: ...
+    @overload
+    def subs(self, arg1: Basic | complex, arg2: Basic | complex, **kwargs: Any) -> Basic: ...
+
+    def subs(self, arg1: Mapping[Basic | complex, Basic | complex]
+            | Iterable[tuple[Basic | complex, Basic | complex]] | Basic | complex,
+             arg2: Basic | complex | None = None, **kwargs: Any) -> Basic:
+        """
+        Substitutes old for new in an expression after sympifying args.
+
+        `args` is either:
+          - two arguments, e.g. foo.subs(old, new)
+          - one iterable argument, e.g. foo.subs(iterable). The iterable may be
+             o an iterable container with (old, new) pairs. In this case the
+               replacements are processed in the order given with successive
+               patterns possibly affecting replacements already made.
+             o a dict or set whose key/value items correspond to old/new pairs.
+               In this case the old/new pairs will be sorted by op count and in
+               case of a tie, by number of args and the default_sort_key. The
+               resulting sorted list is then processed as an iterable container
+               (see previous).
+
+        If the keyword ``simultaneous`` is True, the subexpressions will not be
+        evaluated until all the substitutions have been made.
+
+        Examples
+        ========
+
+        >>> from sympy import pi, exp, limit, oo
+        >>> from sympy.abc import x, y
+        >>> (1 + x*y).subs(x, pi)
+        pi*y + 1
+        >>> (1 + x*y).subs({x:pi, y:2})
+        1 + 2*pi
+        >>> (1 + x*y).subs([(x, pi), (y, 2)])
+        1 + 2*pi
+        >>> reps = [(y, x**2), (x, 2)]
+        >>> (x + y).subs(reps)
+        6
+        >>> (x + y).subs(reversed(reps))
+        x**2 + 2
+
+        >>> (x**2 + x**4).subs(x**2, y)
+        y**2 + y
+
+        To replace only the x**2 but not the x**4, use xreplace:
+
+        >>> (x**2 + x**4).xreplace({x**2: y})
+        x**4 + y
+
+        To delay evaluation until all substitutions have been made,
+        set the keyword ``simultaneous`` to True:
+
+        >>> (x/y).subs([(x, 0), (y, 0)])
+        0
+        >>> (x/y).subs([(x, 0), (y, 0)], simultaneous=True)
+        nan
+
+        This has the added feature of not allowing subsequent substitutions
+        to affect those already made:
+
+        >>> ((x + y)/y).subs({x + y: y, y: x + y})
+        1
+        >>> ((x + y)/y).subs({x + y: y, y: x + y}, simultaneous=True)
+        y/(x + y)
+
+        In order to obtain a canonical result, unordered iterables are
+        sorted by count_op length, number of arguments and by the
+        default_sort_key to break any ties. All other iterables are left
+        unsorted.
+
+        >>> from sympy import sqrt, sin, cos
+        >>> from sympy.abc import a, b, c, d, e
+
+        >>> A = (sqrt(sin(2*x)), a)
+        >>> B = (sin(2*x), b)
+        >>> C = (cos(2*x), c)
+        >>> D = (x, d)
+        >>> E = (exp(x), e)
+
+        >>> expr = sqrt(sin(2*x))*sin(exp(x)*x)*cos(2*x) + sin(2*x)
+
+        >>> expr.subs(dict([A, B, C, D, E]))
+        a*c*sin(d*e) + b
+
+        The resulting expression represents a literal replacement of the
+        old arguments with the new arguments. This may not reflect the
+        limiting behavior of the expression:
+
+        >>> (x**3 - 3*x).subs({x: oo})
+        nan
+
+        >>> limit(x**3 - 3*x, x, oo)
+        oo
+
+        If the substitution will be followed by numerical
+        evaluation, it is better to pass the substitution to
+        evalf as
+
+        >>> (1/x).evalf(subs={x: 3.0}, n=21)
+        0.333333333333333333333
+
+        rather than
+
+        >>> (1/x).subs({x: 3.0}).evalf(21)
+        0.333333333333333314830
+
+        as the former will ensure that the desired level of precision is
+        obtained.
+
+        See Also
+        ========
+        replace: replacement capable of doing wildcard-like matching,
+                 parsing of match, and conditional replacements
+        xreplace: exact node replacement in expr tree; also capable of
+                  using matching rules
+        sympy.core.evalf.EvalfMixin.evalf: calculates the given formula to a desired level of precision
+
+        """
+        from .containers import Dict
+        from .symbol import Dummy, Symbol
+        from .numbers import _illegal
+
+        items: Iterable[tuple[Basic | complex, Basic | complex]]
+
+        unordered = False
+        if arg2 is None:
+
+            if isinstance(arg1, set):
+                items = arg1
+                unordered = True
+            elif isinstance(arg1, (Dict, Mapping)):
+                unordered = True
+                items = arg1.items() # type: ignore
+            elif not iterable(arg1):
+                raise ValueError(filldedent("""
+                   When a single argument is passed to subs
+                   it should be a dictionary of old: new pairs or an iterable
+                   of (old, new) tuples."""))
+            else:
+                items = arg1 # type: ignore
+        else:
+            items = [(arg1, arg2)] # type: ignore
+
+        def sympify_old(old) -> Basic:
+            if isinstance(old, str):
+                # Use Symbol rather than parse_expr for old
+                return Symbol(old)
+            elif isinstance(old, type):
+                # Allow a type e.g. Function('f') or sin
+                return sympify(old, strict=False)
+            else:
+                return sympify(old, strict=True)
+
+        def sympify_new(new) -> Basic:
+            if isinstance(new, (str, type)):
+                # Allow a type or parse a string input
+                return sympify(new, strict=False)
+            else:
+                return sympify(new, strict=True)
+
+        sequence = [(sympify_old(s1), sympify_new(s2)) for s1, s2 in items]
+
+        # skip if there is no change
+        sequence = [(s1, s2) for s1, s2 in sequence if not _aresame(s1, s2)]
+
+        simultaneous = kwargs.pop('simultaneous', False)
+
+        if unordered:
+            from .sorting import _nodes, default_sort_key
+            sequence_dict = dict(sequence)
+            # order so more complex items are first and items
+            # of identical complexity are ordered so
+            # f(x) < f(y) < x < y
+            # \___ 2 __/    \_1_/  <- number of nodes
+            #
+            # For more complex ordering use an unordered sequence.
+            k = list(ordered(sequence_dict, default=False, keys=(
+                lambda x: -_nodes(x),
+                default_sort_key,
+                )))
+            sequence = [(k, sequence_dict[k]) for k in k]
+            # do infinities first
+            if not simultaneous:
+                redo = [i for i, seq in enumerate(sequence) if seq[1] in _illegal]
+                for i in reversed(redo):
+                    sequence.insert(0, sequence.pop(i))
+
+        if simultaneous:  # XXX should this be the default for dict subs?
+            reps = {}
+            rv = self
+            kwargs['hack2'] = True
+            m = Dummy('subs_m')
+            for old, new in sequence:
+                com = new.is_commutative
+                if com is None:
+                    com = True
+                d = Dummy('subs_d', commutative=com)
+                # using d*m so Subs will be used on dummy variables
+                # in things like Derivative(f(x, y), x) in which x
+                # is both free and bound
+                rv = rv._subs(old, d*m, **kwargs)
+                if not isinstance(rv, Basic):
+                    break
+                reps[d] = new
+            reps[m] = S.One  # get rid of m
+            return rv.xreplace(reps)
+        else:
+            rv = self
+            for old, new in sequence:
+                rv = rv._subs(old, new, **kwargs)
+                if not isinstance(rv, Basic):
+                    break
+            return rv
+
+    @cacheit
+    def _subs(self, old, new, **hints):
+        """Substitutes an expression old -> new.
+
+        If self is not equal to old then _eval_subs is called.
+        If _eval_subs does not want to make any special replacement
+        then a None is received which indicates that the fallback
+        should be applied wherein a search for replacements is made
+        amongst the arguments of self.
+
+        >>> from sympy import Add
+        >>> from sympy.abc import x, y, z
+
+        Examples
+        ========
+
+        Add's _eval_subs knows how to target x + y in the following
+        so it makes the change:
+
+        >>> (x + y + z).subs(x + y, 1)
+        z + 1
+
+        Add's _eval_subs does not need to know how to find x + y in
+        the following:
+
+        >>> Add._eval_subs(z*(x + y) + 3, x + y, 1) is None
+        True
+
+        The returned None will cause the fallback routine to traverse the args and
+        pass the z*(x + y) arg to Mul where the change will take place and the
+        substitution will succeed:
+
+        >>> (z*(x + y) + 3).subs(x + y, 1)
+        z + 3
+
+        ** Developers Notes **
+
+        An _eval_subs routine for a class should be written if:
+
+            1) any arguments are not instances of Basic (e.g. bool, tuple);
+
+            2) some arguments should not be targeted (as in integration
+               variables);
+
+            3) if there is something other than a literal replacement
+               that should be attempted (as in Piecewise where the condition
+               may be updated without doing a replacement).
+
+        If it is overridden, here are some special cases that might arise:
+
+            1) If it turns out that no special change was made and all
+               the original sub-arguments should be checked for
+               replacements then None should be returned.
+
+            2) If it is necessary to do substitutions on a portion of
+               the expression then _subs should be called. _subs will
+               handle the case of any sub-expression being equal to old
+               (which usually would not be the case) while its fallback
+               will handle the recursion into the sub-arguments. For
+               example, after Add's _eval_subs removes some matching terms
+               it must process the remaining terms so it calls _subs
+               on each of the un-matched terms and then adds them
+               onto the terms previously obtained.
+
+           3) If the initial expression should remain unchanged then
+              the original expression should be returned. (Whenever an
+              expression is returned, modified or not, no further
+              substitution of old -> new is attempted.) Sum's _eval_subs
+              routine uses this strategy when a substitution is attempted
+              on any of its summation variables.
+        """
+
+        def fallback(self, old, new):
+            """
+            Try to replace old with new in any of self's arguments.
+            """
+            hit = False
+            args = list(self.args)
+            for i, arg in enumerate(args):
+                if not hasattr(arg, '_eval_subs'):
+                    continue
+                arg = arg._subs(old, new, **hints)
+                if not _aresame(arg, args[i]):
+                    hit = True
+                    args[i] = arg
+            if hit:
+                rv = self.func(*args)
+                hack2 = hints.get('hack2', False)
+                if hack2 and self.is_Mul and not rv.is_Mul:  # 2-arg hack
+                    coeff = S.One
+                    nonnumber = []
+                    for i in args:
+                        if i.is_Number:
+                            coeff *= i
+                        else:
+                            nonnumber.append(i)
+                    nonnumber = self.func(*nonnumber)
+                    if coeff is S.One:
+                        return nonnumber
+                    else:
+                        return self.func(coeff, nonnumber, evaluate=False)
+                return rv
+            return self
+
+        if _aresame(self, old):
+            return new
+
+        rv = self._eval_subs(old, new)
+        if rv is None:
+            rv = fallback(self, old, new)
+        return rv
+
+    def _eval_subs(self, old, new) -> Basic | None:
+        """Override this stub if you want to do anything more than
+        attempt a replacement of old with new in the arguments of self.
+
+        See also
+        ========
+
+        _subs
+        """
+        return None
+
+    def xreplace(self, rule):
+        """
+        Replace occurrences of objects within the expression.
+
+        Parameters
+        ==========
+
+        rule : dict-like
+            Expresses a replacement rule
+
+        Returns
+        =======
+
+        xreplace : the result of the replacement
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, pi, exp
+        >>> x, y, z = symbols('x y z')
+        >>> (1 + x*y).xreplace({x: pi})
+        pi*y + 1
+        >>> (1 + x*y).xreplace({x: pi, y: 2})
+        1 + 2*pi
+
+        Replacements occur only if an entire node in the expression tree is
+        matched:
+
+        >>> (x*y + z).xreplace({x*y: pi})
+        z + pi
+        >>> (x*y*z).xreplace({x*y: pi})
+        x*y*z
+        >>> (2*x).xreplace({2*x: y, x: z})
+        y
+        >>> (2*2*x).xreplace({2*x: y, x: z})
+        4*z
+        >>> (x + y + 2).xreplace({x + y: 2})
+        x + y + 2
+        >>> (x + 2 + exp(x + 2)).xreplace({x + 2: y})
+        x + exp(y) + 2
+
+        xreplace does not differentiate between free and bound symbols. In the
+        following, subs(x, y) would not change x since it is a bound symbol,
+        but xreplace does:
+
+        >>> from sympy import Integral
+        >>> Integral(x, (x, 1, 2*x)).xreplace({x: y})
+        Integral(y, (y, 1, 2*y))
+
+        Trying to replace x with an expression raises an error:
+
+        >>> Integral(x, (x, 1, 2*x)).xreplace({x: 2*y}) # doctest: +SKIP
+        ValueError: Invalid limits given: ((2*y, 1, 4*y),)
+
+        See Also
+        ========
+        replace: replacement capable of doing wildcard-like matching,
+                 parsing of match, and conditional replacements
+        subs: substitution of subexpressions as defined by the objects
+              themselves.
+
+        """
+        value, _ = self._xreplace(rule)
+        return value
+
+    def _xreplace(self, rule):
+        """
+        Helper for xreplace. Tracks whether a replacement actually occurred.
+        """
+        if self in rule:
+            return rule[self], True
+        elif rule:
+            args = []
+            changed = False
+            for a in self.args:
+                _xreplace = getattr(a, '_xreplace', None)
+                if _xreplace is not None:
+                    a_xr = _xreplace(rule)
+                    args.append(a_xr[0])
+                    changed |= a_xr[1]
+                else:
+                    args.append(a)
+            args = tuple(args)
+            if changed:
+                return self.func(*args), True
+        return self, False
+
+    @cacheit
+    def has(self, *patterns):
+        """
+        Test whether any subexpression matches any of the patterns.
+
+        Examples
+        ========
+
+        >>> from sympy import sin
+        >>> from sympy.abc import x, y, z
+        >>> (x**2 + sin(x*y)).has(z)
+        False
+        >>> (x**2 + sin(x*y)).has(x, y, z)
+        True
+        >>> x.has(x)
+        True
+
+        Note ``has`` is a structural algorithm with no knowledge of
+        mathematics. Consider the following half-open interval:
+
+        >>> from sympy import Interval
+        >>> i = Interval.Lopen(0, 5); i
+        Interval.Lopen(0, 5)
+        >>> i.args
+        (0, 5, True, False)
+        >>> i.has(4)  # there is no "4" in the arguments
+        False
+        >>> i.has(0)  # there *is* a "0" in the arguments
+        True
+
+        Instead, use ``contains`` to determine whether a number is in the
+        interval or not:
+
+        >>> i.contains(4)
+        True
+        >>> i.contains(0)
+        False
+
+
+        Note that ``expr.has(*patterns)`` is exactly equivalent to
+        ``any(expr.has(p) for p in patterns)``. In particular, ``False`` is
+        returned when the list of patterns is empty.
+
+        >>> x.has()
+        False
+
+        """
+        return self._has(iterargs, *patterns)
+
+    def has_xfree(self, s: set[Basic]):
+        """Return True if self has any of the patterns in s as a
+        free argument, else False. This is like `Basic.has_free`
+        but this will only report exact argument matches.
+
+        Examples
+        ========
+
+        >>> from sympy import Function
+        >>> from sympy.abc import x, y
+        >>> f = Function('f')
+        >>> f(x).has_xfree({f})
+        False
+        >>> f(x).has_xfree({f(x)})
+        True
+        >>> f(x + 1).has_xfree({x})
+        True
+        >>> f(x + 1).has_xfree({x + 1})
+        True
+        >>> f(x + y + 1).has_xfree({x + 1})
+        False
+        """
+        # protect O(1) containment check by requiring:
+        if type(s) is not set:
+            raise TypeError('expecting set argument')
+        return any(a in s for a in iterfreeargs(self))
+
+    @cacheit
+    def has_free(self, *patterns):
+        """Return True if self has object(s) ``x`` as a free expression
+        else False.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral, Function
+        >>> from sympy.abc import x, y
+        >>> f = Function('f')
+        >>> g = Function('g')
+        >>> expr = Integral(f(x), (f(x), 1, g(y)))
+        >>> expr.free_symbols
+        {y}
+        >>> expr.has_free(g(y))
+        True
+        >>> expr.has_free(*(x, f(x)))
+        False
+
+        This works for subexpressions and types, too:
+
+        >>> expr.has_free(g)
+        True
+        >>> (x + y + 1).has_free(y + 1)
+        True
+        """
+        if not patterns:
+            return False
+        p0 = patterns[0]
+        if len(patterns) == 1 and iterable(p0) and not isinstance(p0, Basic):
+            # Basic can contain iterables (though not non-Basic, ideally)
+            # but don't encourage mixed passing patterns
+            raise TypeError(filldedent('''
+                Expecting 1 or more Basic args, not a single
+                non-Basic iterable. Don't forget to unpack
+                iterables: `eq.has_free(*patterns)`'''))
+        # try quick test first
+        s = set(patterns)
+        rv = self.has_xfree(s)
+        if rv:
+            return rv
+        # now try matching through slower _has
+        return self._has(iterfreeargs, *patterns)
+
+    def _has(self, iterargs, *patterns):
+        # separate out types and unhashable objects
+        type_set = set()  # only types
+        p_set = set()  # hashable non-types
+        for p in patterns:
+            if isinstance(p, type) and issubclass(p, Basic):
+                type_set.add(p)
+                continue
+            if not isinstance(p, Basic):
+                try:
+                    p = _sympify(p)
+                except SympifyError:
+                    continue  # Basic won't have this in it
+            p_set.add(p)  # fails if object defines __eq__ but
+                          # doesn't define __hash__
+        types = tuple(type_set)   #
+        for i in iterargs(self):  #
+            if i in p_set:        # <--- here, too
+                return True
+            if isinstance(i, types):
+                return True
+
+        # use matcher if defined, e.g. operations defines
+        # matcher that checks for exact subset containment,
+        # (x + y + 1).has(x + 1) -> True
+        for i in p_set - type_set:  # types don't have matchers
+            if not hasattr(i, '_has_matcher'):
+                continue
+            match = i._has_matcher()
+            if any(match(arg) for arg in iterargs(self)):
+                return True
+
+        # no success
+        return False
+
+    def replace(self, query, value, map=False, simultaneous=True, exact=None) -> Basic:
+        """
+        Replace matching subexpressions of ``self`` with ``value``.
+
+        If ``map = True`` then also return the mapping {old: new} where ``old``
+        was a sub-expression found with query and ``new`` is the replacement
+        value for it. If the expression itself does not match the query, then
+        the returned value will be ``self.xreplace(map)`` otherwise it should
+        be ``self.subs(ordered(map.items()))``.
+
+        Traverses an expression tree and performs replacement of matching
+        subexpressions from the bottom to the top of the tree. The default
+        approach is to do the replacement in a simultaneous fashion so
+        changes made are targeted only once. If this is not desired or causes
+        problems, ``simultaneous`` can be set to False.
+
+        In addition, if an expression containing more than one Wild symbol
+        is being used to match subexpressions and the ``exact`` flag is None
+        it will be set to True so the match will only succeed if all non-zero
+        values are received for each Wild that appears in the match pattern.
+        Setting this to False accepts a match of 0; while setting it True
+        accepts all matches that have a 0 in them. See example below for
+        cautions.
+
+        The list of possible combinations of queries and replacement values
+        is listed below:
+
+        Examples
+        ========
+
+        Initial setup
+
+        >>> from sympy import log, sin, cos, tan, Wild, Mul, Add
+        >>> from sympy.abc import x, y
+        >>> f = log(sin(x)) + tan(sin(x**2))
+
+        1.1. type -> type
+            obj.replace(type, newtype)
+
+            When object of type ``type`` is found, replace it with the
+            result of passing its argument(s) to ``newtype``.
+
+            >>> f.replace(sin, cos)
+            log(cos(x)) + tan(cos(x**2))
+            >>> sin(x).replace(sin, cos, map=True)
+            (cos(x), {sin(x): cos(x)})
+            >>> (x*y).replace(Mul, Add)
+            x + y
+
+        1.2. type -> func
+            obj.replace(type, func)
+
+            When object of type ``type`` is found, apply ``func`` to its
+            argument(s). ``func`` must be written to handle the number
+            of arguments of ``type``.
+
+            >>> f.replace(sin, lambda arg: sin(2*arg))
+            log(sin(2*x)) + tan(sin(2*x**2))
+            >>> (x*y).replace(Mul, lambda *args: sin(2*Mul(*args)))
+            sin(2*x*y)
+
+        2.1. pattern -> expr
+            obj.replace(pattern(wild), expr(wild))
+
+            Replace subexpressions matching ``pattern`` with the expression
+            written in terms of the Wild symbols in ``pattern``.
+
+            >>> a, b = map(Wild, 'ab')
+            >>> f.replace(sin(a), tan(a))
+            log(tan(x)) + tan(tan(x**2))
+            >>> f.replace(sin(a), tan(a/2))
+            log(tan(x/2)) + tan(tan(x**2/2))
+            >>> f.replace(sin(a), a)
+            log(x) + tan(x**2)
+            >>> (x*y).replace(a*x, a)
+            y
+
+            Matching is exact by default when more than one Wild symbol
+            is used: matching fails unless the match gives non-zero
+            values for all Wild symbols:
+
+            >>> (2*x + y).replace(a*x + b, b - a)
+            y - 2
+            >>> (2*x).replace(a*x + b, b - a)
+            2*x
+
+            When set to False, the results may be non-intuitive:
+
+            >>> (2*x).replace(a*x + b, b - a, exact=False)
+            2/x
+
+        2.2. pattern -> func
+            obj.replace(pattern(wild), lambda wild: expr(wild))
+
+            All behavior is the same as in 2.1 but now a function in terms of
+            pattern variables is used rather than an expression:
+
+            >>> f.replace(sin(a), lambda a: sin(2*a))
+            log(sin(2*x)) + tan(sin(2*x**2))
+
+        3.1. func -> func
+            obj.replace(filter, func)
+
+            Replace subexpression ``e`` with ``func(e)`` if ``filter(e)``
+            is True.
+
+            >>> g = 2*sin(x**3)
+            >>> g.replace(lambda expr: expr.is_Number, lambda expr: expr**2)
+            4*sin(x**9)
+
+        The expression itself is also targeted by the query but is done in
+        such a fashion that changes are not made twice.
+
+            >>> e = x*(x*y + 1)
+            >>> e.replace(lambda x: x.is_Mul, lambda x: 2*x)
+            2*x*(2*x*y + 1)
+
+        When matching a single symbol, `exact` will default to True, but
+        this may or may not be the behavior that is desired:
+
+        Here, we want `exact=False`:
+
+        >>> from sympy import Function
+        >>> f = Function('f')
+        >>> e = f(1) + f(0)
+        >>> q = f(a), lambda a: f(a + 1)
+        >>> e.replace(*q, exact=False)
+        f(1) + f(2)
+        >>> e.replace(*q, exact=True)
+        f(0) + f(2)
+
+        But here, the nature of matching makes selecting
+        the right setting tricky:
+
+        >>> e = x**(1 + y)
+        >>> (x**(1 + y)).replace(x**(1 + a), lambda a: x**-a, exact=False)
+        x
+        >>> (x**(1 + y)).replace(x**(1 + a), lambda a: x**-a, exact=True)
+        x**(-x - y + 1)
+        >>> (x**y).replace(x**(1 + a), lambda a: x**-a, exact=False)
+        x
+        >>> (x**y).replace(x**(1 + a), lambda a: x**-a, exact=True)
+        x**(1 - y)
+
+        It is probably better to use a different form of the query
+        that describes the target expression more precisely:
+
+        >>> (1 + x**(1 + y)).replace(
+        ... lambda x: x.is_Pow and x.exp.is_Add and x.exp.args[0] == 1,
+        ... lambda x: x.base**(1 - (x.exp - 1)))
+        ...
+        x**(1 - y) + 1
+
+        See Also
+        ========
+
+        subs: substitution of subexpressions as defined by the objects
+              themselves.
+        xreplace: exact node replacement in expr tree; also capable of
+                  using matching rules
+
+        """
+
+        try:
+            query = _sympify(query)
+        except SympifyError:
+            pass
+        try:
+            value = _sympify(value)
+        except SympifyError:
+            pass
+        if isinstance(query, type):
+            _query = lambda expr: isinstance(expr, query)
+
+            if isinstance(value, type):
+                _value = lambda expr, result: value(*expr.args)
+            elif callable(value):
+                _value = lambda expr, result: value(*expr.args)
+            else:
+                raise TypeError(
+                    "given a type, replace() expects another "
+                    "type or a callable")
+        elif isinstance(query, Basic):
+            _query = lambda expr: expr.match(query)
+            if exact is None:
+                from .symbol import Wild
+                exact = (len(query.atoms(Wild)) > 1)
+
+            if isinstance(value, Basic):
+                if exact:
+                    _value = lambda expr, result: (value.subs(result)
+                        if all(result.values()) else expr)
+                else:
+                    _value = lambda expr, result: value.subs(result)
+            elif callable(value):
+                # match dictionary keys get the trailing underscore stripped
+                # from them and are then passed as keywords to the callable;
+                # if ``exact`` is True, only accept match if there are no null
+                # values amongst those matched.
+                if exact:
+                    _value = lambda expr, result: (value(**
+                        {str(k)[:-1]: v for k, v in result.items()})
+                        if all(val for val in result.values()) else expr)
+                else:
+                    _value = lambda expr, result: value(**
+                        {str(k)[:-1]: v for k, v in result.items()})
+            else:
+                raise TypeError(
+                    "given an expression, replace() expects "
+                    "another expression or a callable")
+        elif callable(query):
+            _query = query
+
+            if callable(value):
+                _value = lambda expr, result: value(expr)
+            else:
+                raise TypeError(
+                    "given a callable, replace() expects "
+                    "another callable")
+        else:
+            raise TypeError(
+                "first argument to replace() must be a "
+                "type, an expression or a callable")
+
+        def walk(rv, F):
+            """Apply ``F`` to args and then to result.
+            """
+            args = getattr(rv, 'args', None)
+            if args is not None:
+                if args:
+                    newargs = tuple([walk(a, F) for a in args])
+                    if args != newargs:
+                        rv = rv.func(*newargs)
+                        if simultaneous:
+                            # if rv is something that was already
+                            # matched (that was changed) then skip
+                            # applying F again
+                            for i, e in enumerate(args):
+                                if rv == e and e != newargs[i]:
+                                    return rv
+                rv = F(rv)
+            return rv
+
+        mapping = {}  # changes that took place
+
+        def rec_replace(expr):
+            result = _query(expr)
+            if result or result == {}:
+                v = _value(expr, result)
+                if v is not None and v != expr:
+                    if map:
+                        mapping[expr] = v
+                    expr = v
+            return expr
+
+        rv = walk(self, rec_replace)
+        return (rv, mapping) if map else rv # type: ignore
+
+    def find(self, query, group=False):
+        """Find all subexpressions matching a query."""
+        query = _make_find_query(query)
+        results = list(filter(query, _preorder_traversal(self)))
+
+        if not group:
+            return set(results)
+        return dict(Counter(results))
+
+    def count(self, query):
+        """Count the number of matching subexpressions."""
+        query = _make_find_query(query)
+        return sum(bool(query(sub)) for sub in _preorder_traversal(self))
+
+    def matches(self, expr, repl_dict=None, old=False):
+        """
+        Helper method for match() that looks for a match between Wild symbols
+        in self and expressions in expr.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Wild, Basic
+        >>> a, b, c = symbols('a b c')
+        >>> x = Wild('x')
+        >>> Basic(a + x, x).matches(Basic(a + b, c)) is None
+        True
+        >>> Basic(a + x, x).matches(Basic(a + b + c, b + c))
+        {x_: b + c}
+        """
+        expr = sympify(expr)
+        if not isinstance(expr, self.__class__):
+            return None
+
+        if repl_dict is None:
+            repl_dict = {}
+        else:
+            repl_dict = repl_dict.copy()
+
+        if self == expr:
+            return repl_dict
+
+        if len(self.args) != len(expr.args):
+            return None
+
+        d = repl_dict  # already a copy
+        for arg, other_arg in zip(self.args, expr.args):
+            if arg == other_arg:
+                continue
+            if arg.is_Relational:
+                try:
+                    d = arg.xreplace(d).matches(other_arg, d, old=old)
+                except TypeError: # Should be InvalidComparisonError when introduced
+                    d = None
+            else:
+                    d = arg.xreplace(d).matches(other_arg, d, old=old)
+            if d is None:
+                return None
+        return d
+
+    def match(self, pattern, old=False):
+        """
+        Pattern matching.
+
+        Wild symbols match all.
+
+        Return ``None`` when expression (self) does not match with pattern.
+        Otherwise return a dictionary such that::
+
+          pattern.xreplace(self.match(pattern)) == self
+
+        Examples
+        ========
+
+        >>> from sympy import Wild, Sum
+        >>> from sympy.abc import x, y
+        >>> p = Wild("p")
+        >>> q = Wild("q")
+        >>> r = Wild("r")
+        >>> e = (x+y)**(x+y)
+        >>> e.match(p**p)
+        {p_: x + y}
+        >>> e.match(p**q)
+        {p_: x + y, q_: x + y}
+        >>> e = (2*x)**2
+        >>> e.match(p*q**r)
+        {p_: 4, q_: x, r_: 2}
+        >>> (p*q**r).xreplace(e.match(p*q**r))
+        4*x**2
+
+        Since match is purely structural expressions that are equivalent up to
+        bound symbols will not match:
+
+        >>> print(Sum(x, (x, 1, 2)).match(Sum(y, (y, 1, p))))
+        None
+
+        An expression with bound symbols can be matched if the pattern uses
+        a distinct ``Wild`` for each bound symbol:
+
+        >>> Sum(x, (x, 1, 2)).match(Sum(q, (q, 1, p)))
+        {p_: 2, q_: x}
+
+        The ``old`` flag will give the old-style pattern matching where
+        expressions and patterns are essentially solved to give the match. Both
+        of the following give None unless ``old=True``:
+
+        >>> (x - 2).match(p - x, old=True)
+        {p_: 2*x - 2}
+        >>> (2/x).match(p*x, old=True)
+        {p_: 2/x**2}
+
+        See Also
+        ========
+
+        matches: pattern.matches(expr) is the same as expr.match(pattern)
+        xreplace: exact structural replacement
+        replace: structural replacement with pattern matching
+        Wild: symbolic placeholders for expressions in pattern matching
+        """
+        pattern = sympify(pattern)
+        return pattern.matches(self, old=old)
+
+    def count_ops(self, visual=False):
+        """Wrapper for count_ops that returns the operation count."""
+        from .function import count_ops
+        return count_ops(self, visual)
+
+    def doit(self, **hints):
+        """Evaluate objects that are not evaluated by default like limits,
+        integrals, sums and products. All objects of this kind will be
+        evaluated recursively, unless some species were excluded via 'hints'
+        or unless the 'deep' hint was set to 'False'.
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x
+
+        >>> 2*Integral(x, x)
+        2*Integral(x, x)
+
+        >>> (2*Integral(x, x)).doit()
+        x**2
+
+        >>> (2*Integral(x, x)).doit(deep=False)
+        2*Integral(x, x)
+
+        """
+        if hints.get('deep', True):
+            terms = [term.doit(**hints) if isinstance(term, Basic) else term
+                                         for term in self.args]
+            return self.func(*terms)
+        else:
+            return self
+
+    def simplify(self, **kwargs) -> Basic:
+        """See the simplify function in sympy.simplify"""
+        from sympy.simplify.simplify import simplify
+        return simplify(self, **kwargs)
+
+    def refine(self, assumption=True):
+        """See the refine function in sympy.assumptions"""
+        from sympy.assumptions.refine import refine
+        return refine(self, assumption)
+
+    def _eval_derivative_n_times(self, s, n):
+        # This is the default evaluator for derivatives (as called by `diff`
+        # and `Derivative`), it will attempt a loop to derive the expression
+        # `n` times by calling the corresponding `_eval_derivative` method,
+        # while leaving the derivative unevaluated if `n` is symbolic.  This
+        # method should be overridden if the object has a closed form for its
+        # symbolic n-th derivative.
+        from .numbers import Integer
+        if isinstance(n, (int, Integer)):
+            obj = self
+            for i in range(n):
+                prev = obj
+                obj = obj._eval_derivative(s)
+                if obj is None:
+                    return None
+                elif obj == prev:
+                    break
+            return obj
+        else:
+            return None
+
+    def rewrite(self, *args, deep=True, **hints):
+        """
+        Rewrite *self* using a defined rule.
+
+        Rewriting transforms an expression to another, which is mathematically
+        equivalent but structurally different. For example you can rewrite
+        trigonometric functions as complex exponentials or combinatorial
+        functions as gamma function.
+
+        This method takes a *pattern* and a *rule* as positional arguments.
+        *pattern* is optional parameter which defines the types of expressions
+        that will be transformed. If it is not passed, all possible expressions
+        will be rewritten. *rule* defines how the expression will be rewritten.
+
+        Parameters
+        ==========
+
+        args : Expr
+            A *rule*, or *pattern* and *rule*.
+            - *pattern* is a type or an iterable of types.
+            - *rule* can be any object.
+
+        deep : bool, optional
+            If ``True``, subexpressions are recursively transformed. Default is
+            ``True``.
+
+        Examples
+        ========
+
+        If *pattern* is unspecified, all possible expressions are transformed.
+
+        >>> from sympy import cos, sin, exp, I
+        >>> from sympy.abc import x
+        >>> expr = cos(x) + I*sin(x)
+        >>> expr.rewrite(exp)
+        exp(I*x)
+
+        Pattern can be a type or an iterable of types.
+
+        >>> expr.rewrite(sin, exp)
+        exp(I*x)/2 + cos(x) - exp(-I*x)/2
+        >>> expr.rewrite([cos,], exp)
+        exp(I*x)/2 + I*sin(x) + exp(-I*x)/2
+        >>> expr.rewrite([cos, sin], exp)
+        exp(I*x)
+
+        Rewriting behavior can be implemented by defining ``_eval_rewrite()``
+        method.
+
+        >>> from sympy import Expr, sqrt, pi
+        >>> class MySin(Expr):
+        ...     def _eval_rewrite(self, rule, args, **hints):
+        ...         x, = args
+        ...         if rule == cos:
+        ...             return cos(pi/2 - x, evaluate=False)
+        ...         if rule == sqrt:
+        ...             return sqrt(1 - cos(x)**2)
+        >>> MySin(MySin(x)).rewrite(cos)
+        cos(-cos(-x + pi/2) + pi/2)
+        >>> MySin(x).rewrite(sqrt)
+        sqrt(1 - cos(x)**2)
+
+        Defining ``_eval_rewrite_as_[...]()`` method is supported for backwards
+        compatibility reason. This may be removed in the future and using it is
+        discouraged.
+
+        >>> class MySin(Expr):
+        ...     def _eval_rewrite_as_cos(self, *args, **hints):
+        ...         x, = args
+        ...         return cos(pi/2 - x, evaluate=False)
+        >>> MySin(x).rewrite(cos)
+        cos(-x + pi/2)
+
+        """
+        if not args:
+            return self
+
+        hints.update(deep=deep)
+
+        pattern = args[:-1]
+        rule = args[-1]
+
+        # Special case: map `abs` to `Abs`
+        if rule is abs:
+            from sympy.functions.elementary.complexes import Abs
+            rule = Abs
+
+        # support old design by _eval_rewrite_as_[...] method
+        if isinstance(rule, str):
+            method = "_eval_rewrite_as_%s" % rule
+        elif hasattr(rule, "__name__"):
+            # rule is class or function
+            clsname = rule.__name__
+            method = "_eval_rewrite_as_%s" % clsname
+        else:
+            # rule is instance
+            clsname = rule.__class__.__name__
+            method = "_eval_rewrite_as_%s" % clsname
+
+        if pattern:
+            if iterable(pattern[0]):
+                pattern = pattern[0]
+            pattern = tuple(p for p in pattern if self.has(p))
+            if not pattern:
+                return self
+        # hereafter, empty pattern is interpreted as all pattern.
+
+        return self._rewrite(pattern, rule, method, **hints)
+
+    def _rewrite(self, pattern, rule, method, **hints):
+        deep = hints.pop('deep', True)
+        if deep:
+            args = [a._rewrite(pattern, rule, method, **hints)
+                    for a in self.args]
+        else:
+            args = self.args
+        if not pattern or any(isinstance(self, p) for p in pattern):
+            meth = getattr(self, method, None)
+            if meth is not None:
+                rewritten = meth(*args, **hints)
+            else:
+                rewritten = self._eval_rewrite(rule, args, **hints)
+            if rewritten is not None:
+                return rewritten
+        if not args:
+            return self
+        return self.func(*args)
+
+    def _eval_rewrite(self, rule, args, **hints):
+        return None
+
+    _constructor_postprocessor_mapping = {}  # type: ignore
+
+    @classmethod
+    def _exec_constructor_postprocessors(cls, obj):
+        # WARNING: This API is experimental.
+
+        # This is an experimental API that introduces constructor
+        # postprosessors for SymPy Core elements. If an argument of a SymPy
+        # expression has a `_constructor_postprocessor_mapping` attribute, it will
+        # be interpreted as a dictionary containing lists of postprocessing
+        # functions for matching expression node names.
+
+        clsname = obj.__class__.__name__
+        postprocessors = {f for i in obj.args
+                            for f in _get_postprocessors(clsname, type(i))}
+        for f in postprocessors:
+            obj = f(obj)
+
+        return obj
+
+    def _sage_(self):
+        """
+        Convert *self* to a symbolic expression of SageMath.
+
+        This version of the method is merely a placeholder.
+        """
+        old_method = self._sage_
+        from sage.interfaces.sympy import sympy_init # type: ignore
+        sympy_init()  # may monkey-patch _sage_ method into self's class or superclasses
+        if old_method == self._sage_:
+            raise NotImplementedError('conversion to SageMath is not implemented')
+        else:
+            # call the freshly monkey-patched method
+            return self._sage_()
+
+    def could_extract_minus_sign(self) -> bool:
+        return False  # see Expr.could_extract_minus_sign
+
+    def is_same(a, b, approx=None):
+        """Return True if a and b are structurally the same, else False.
+        If `approx` is supplied, it will be used to test whether two
+        numbers are the same or not. By default, only numbers of the
+        same type will compare equal, so S.Half != Float(0.5).
+
+        Examples
+        ========
+
+        In SymPy (unlike Python) two numbers do not compare the same if they are
+        not of the same type:
+
+        >>> from sympy import S
+        >>> 2.0 == S(2)
+        False
+        >>> 0.5 == S.Half
+        False
+
+        By supplying a function with which to compare two numbers, such
+        differences can be ignored. e.g. `equal_valued` will return True
+        for decimal numbers having a denominator that is a power of 2,
+        regardless of precision.
+
+        >>> from sympy import Float
+        >>> from sympy.core.numbers import equal_valued
+        >>> (S.Half/4).is_same(Float(0.125, 1), equal_valued)
+        True
+        >>> Float(1, 2).is_same(Float(1, 10), equal_valued)
+        True
+
+        But decimals without a power of 2 denominator will compare
+        as not being the same.
+
+        >>> Float(0.1, 9).is_same(Float(0.1, 10), equal_valued)
+        False
+
+        But arbitrary differences can be ignored by supplying a function
+        to test the equivalence of two numbers:
+
+        >>> import math
+        >>> Float(0.1, 9).is_same(Float(0.1, 10), math.isclose)
+        True
+
+        Other objects might compare the same even though types are not the
+        same. This routine will only return True if two expressions are
+        identical in terms of class types.
+
+        >>> from sympy import eye, Basic
+        >>> eye(1) == S(eye(1))  # mutable vs immutable
+        True
+        >>> Basic.is_same(eye(1), S(eye(1)))
+        False
+
+        """
+        from .numbers import Number
+        from .traversal import postorder_traversal as pot
+        for t in zip_longest(pot(a), pot(b)):
+            if None in t:
+                return False
+            a, b = t
+            if isinstance(a, Number):
+                if not isinstance(b, Number):
+                    return False
+                if approx:
+                    return approx(a, b)
+            if not (a == b and a.__class__ == b.__class__):
+                return False
+        return True
+
+_aresame = Basic.is_same  # for sake of others importing this
+
+# key used by Mul and Add to make canonical args
+_args_sortkey = cmp_to_key(Basic.compare)
+
+# For all Basic subclasses _prepare_class_assumptions is called by
+# Basic.__init_subclass__ but that method is not called for Basic itself so we
+# call the function here instead.
+_prepare_class_assumptions(Basic)
+
+
+class Atom(Basic):
+    """
+    A parent class for atomic things. An atom is an expression with no subexpressions.
+
+    Examples
+    ========
+
+    Symbol, Number, Rational, Integer, ...
+    But not: Add, Mul, Pow, ...
+    """
+
+    is_Atom = True
+
+    __slots__ = ()
+
+    def matches(self, expr, repl_dict=None, old=False):
+        if self == expr:
+            if repl_dict is None:
+                return {}
+            return repl_dict.copy()
+
+    def xreplace(self, rule, hack2=False):
+        return rule.get(self, self)
+
+    def doit(self, **hints):
+        return self
+
+    @classmethod
+    def class_key(cls):
+        return 2, 0, cls.__name__
+
+    @cacheit
+    def sort_key(self, order=None):
+        return self.class_key(), (1, (str(self),)), S.One.sort_key(), S.One
+
+    def _eval_simplify(self, **kwargs):
+        return self
+
+    @property
+    def _sorted_args(self):
+        # this is here as a safeguard against accidentally using _sorted_args
+        # on Atoms -- they cannot be rebuilt as atom.func(*atom._sorted_args)
+        # since there are no args. So the calling routine should be checking
+        # to see that this property is not called for Atoms.
+        raise AttributeError('Atoms have no args. It might be necessary'
+        ' to make a check for Atoms in the calling code.')
+
+
+def _atomic(e, recursive=False):
+    """Return atom-like quantities as far as substitution is
+    concerned: Derivatives, Functions and Symbols. Do not
+    return any 'atoms' that are inside such quantities unless
+    they also appear outside, too, unless `recursive` is True.
+
+    Examples
+    ========
+
+    >>> from sympy import Derivative, Function, cos
+    >>> from sympy.abc import x, y
+    >>> from sympy.core.basic import _atomic
+    >>> f = Function('f')
+    >>> _atomic(x + y)
+    {x, y}
+    >>> _atomic(x + f(y))
+    {x, f(y)}
+    >>> _atomic(Derivative(f(x), x) + cos(x) + y)
+    {y, cos(x), Derivative(f(x), x)}
+
+    """
+    pot = _preorder_traversal(e)
+    seen = set()
+    if isinstance(e, Basic):
+        free = getattr(e, "free_symbols", None)
+        if free is None:
+            return {e}
+    else:
+        return set()
+    from .symbol import Symbol
+    from .function import Derivative, Function
+    atoms = set()
+    for p in pot:
+        if p in seen:
+            pot.skip()
+            continue
+        seen.add(p)
+        if isinstance(p, Symbol) and p in free:
+            atoms.add(p)
+        elif isinstance(p, (Derivative, Function)):
+            if not recursive:
+                pot.skip()
+            atoms.add(p)
+    return atoms
+
+
+def _make_find_query(query):
+    """Convert the argument of Basic.find() into a callable"""
+    try:
+        query = _sympify(query)
+    except SympifyError:
+        pass
+    if isinstance(query, type):
+        return lambda expr: isinstance(expr, query)
+    elif isinstance(query, Basic):
+        return lambda expr: expr.match(query) is not None
+    return query
+
+# Delayed to avoid cyclic import
+from .singleton import S
+from .traversal import (preorder_traversal as _preorder_traversal,
+   iterargs, iterfreeargs)
+
+preorder_traversal = deprecated(
+    """
+    Using preorder_traversal from the sympy.core.basic submodule is
+    deprecated.
+
+    Instead, use preorder_traversal from the top-level sympy namespace, like
+
+        sympy.preorder_traversal
+    """,
+    deprecated_since_version="1.10",
+    active_deprecations_target="deprecated-traversal-functions-moved",
+)(_preorder_traversal)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_arit.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_arit.py
new file mode 100644
index 0000000000000000000000000000000000000000..39860943b763a30cf4f91578dbac37dc7e6e444e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_arit.py
@@ -0,0 +1,43 @@
+from sympy.core import Add, Mul, symbols
+
+x, y, z = symbols('x,y,z')
+
+
+def timeit_neg():
+    -x
+
+
+def timeit_Add_x1():
+    x + 1
+
+
+def timeit_Add_1x():
+    1 + x
+
+
+def timeit_Add_x05():
+    x + 0.5
+
+
+def timeit_Add_xy():
+    x + y
+
+
+def timeit_Add_xyz():
+    Add(*[x, y, z])
+
+
+def timeit_Mul_xy():
+    x*y
+
+
+def timeit_Mul_xyz():
+    Mul(*[x, y, z])
+
+
+def timeit_Div_xy():
+    x/y
+
+
+def timeit_Div_2y():
+    2/y
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_assumptions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_assumptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a8e47928b76034dd1d7ba8b8f87bd527bb1cdeb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_assumptions.py
@@ -0,0 +1,12 @@
+from sympy.core import Symbol, Integer
+
+x = Symbol('x')
+i3 = Integer(3)
+
+
+def timeit_x_is_integer():
+    x.is_integer
+
+
+def timeit_Integer_is_irrational():
+    i3.is_irrational
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_basic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..df2a382ecbd3cf6eb1f8555577dabb5e07c6643b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_basic.py
@@ -0,0 +1,15 @@
+from sympy.core import symbols, S
+
+x, y = symbols('x,y')
+
+
+def timeit_Symbol_meth_lookup():
+    x.diff  # no call, just method lookup
+
+
+def timeit_S_lookup():
+    S.Exp1
+
+
+def timeit_Symbol_eq_xy():
+    x == y
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_expand.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_expand.py
new file mode 100644
index 0000000000000000000000000000000000000000..4f5ac513e368cb7e9b542926bc25a5695de6d914
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_expand.py
@@ -0,0 +1,23 @@
+from sympy.core import symbols, I
+
+x, y, z = symbols('x,y,z')
+
+p = 3*x**2*y*z**7 + 7*x*y*z**2 + 4*x + x*y**4
+e = (x + y + z + 1)**32
+
+
+def timeit_expand_nothing_todo():
+    p.expand()
+
+
+def bench_expand_32():
+    """(x+y+z+1)**32  -> expand"""
+    e.expand()
+
+
+def timeit_expand_complex_number_1():
+    ((2 + 3*I)**1000).expand(complex=True)
+
+
+def timeit_expand_complex_number_2():
+    ((2 + 3*I/4)**1000).expand(complex=True)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..5c7484c389232b3622fb4b6724e4ab8534dde382
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_numbers.py
@@ -0,0 +1,92 @@
+from sympy.core.numbers import Integer, Rational, pi, oo
+from sympy.core.intfunc import integer_nthroot, igcd
+from sympy.core.singleton import S
+
+i3 = Integer(3)
+i4 = Integer(4)
+r34 = Rational(3, 4)
+q45 = Rational(4, 5)
+
+
+def timeit_Integer_create():
+    Integer(2)
+
+
+def timeit_Integer_int():
+    int(i3)
+
+
+def timeit_neg_one():
+    -S.One
+
+
+def timeit_Integer_neg():
+    -i3
+
+
+def timeit_Integer_abs():
+    abs(i3)
+
+
+def timeit_Integer_sub():
+    i3 - i3
+
+
+def timeit_abs_pi():
+    abs(pi)
+
+
+def timeit_neg_oo():
+    -oo
+
+
+def timeit_Integer_add_i1():
+    i3 + 1
+
+
+def timeit_Integer_add_ij():
+    i3 + i4
+
+
+def timeit_Integer_add_Rational():
+    i3 + r34
+
+
+def timeit_Integer_mul_i4():
+    i3*4
+
+
+def timeit_Integer_mul_ij():
+    i3*i4
+
+
+def timeit_Integer_mul_Rational():
+    i3*r34
+
+
+def timeit_Integer_eq_i3():
+    i3 == 3
+
+
+def timeit_Integer_ed_Rational():
+    i3 == r34
+
+
+def timeit_integer_nthroot():
+    integer_nthroot(100, 2)
+
+
+def timeit_number_igcd_23_17():
+    igcd(23, 17)
+
+
+def timeit_number_igcd_60_3600():
+    igcd(60, 3600)
+
+
+def timeit_Rational_add_r1():
+    r34 + 1
+
+
+def timeit_Rational_add_rq():
+    r34 + q45
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_sympify.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_sympify.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8cc0abc1e35439a1a495454abf87769d5b40d04
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/benchmarks/bench_sympify.py
@@ -0,0 +1,11 @@
+from sympy.core import sympify, Symbol
+
+x = Symbol('x')
+
+
+def timeit_sympify_1():
+    sympify(1)
+
+
+def timeit_sympify_x():
+    sympify(x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/cache.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/cache.py
new file mode 100644
index 0000000000000000000000000000000000000000..ec11600a5e40ad446a6e5dde8820d46ea915b06a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/cache.py
@@ -0,0 +1,210 @@
+""" Caching facility for SymPy """
+from importlib import import_module
+from typing import Callable
+
+class _cache(list):
+    """ List of cached functions """
+
+    def print_cache(self):
+        """print cache info"""
+
+        for item in self:
+            name = item.__name__
+            myfunc = item
+            while hasattr(myfunc, '__wrapped__'):
+                if hasattr(myfunc, 'cache_info'):
+                    info = myfunc.cache_info()
+                    break
+                else:
+                    myfunc = myfunc.__wrapped__
+            else:
+                info = None
+
+            print(name, info)
+
+    def clear_cache(self):
+        """clear cache content"""
+        for item in self:
+            myfunc = item
+            while hasattr(myfunc, '__wrapped__'):
+                if hasattr(myfunc, 'cache_clear'):
+                    myfunc.cache_clear()
+                    break
+                else:
+                    myfunc = myfunc.__wrapped__
+
+
+# global cache registry:
+CACHE = _cache()
+# make clear and print methods available
+print_cache = CACHE.print_cache
+clear_cache = CACHE.clear_cache
+
+from functools import lru_cache, wraps
+
+def __cacheit(maxsize):
+    """caching decorator.
+
+        important: the result of cached function must be *immutable*
+
+
+        Examples
+        ========
+
+        >>> from sympy import cacheit
+        >>> @cacheit
+        ... def f(a, b):
+        ...    return a+b
+
+        >>> @cacheit
+        ... def f(a, b): # noqa: F811
+        ...    return [a, b] # <-- WRONG, returns mutable object
+
+        to force cacheit to check returned results mutability and consistency,
+        set environment variable SYMPY_USE_CACHE to 'debug'
+    """
+    def func_wrapper(func):
+        cfunc = lru_cache(maxsize, typed=True)(func)
+
+        @wraps(func)
+        def wrapper(*args, **kwargs):
+            try:
+                retval = cfunc(*args, **kwargs)
+            except TypeError as e:
+                if not e.args or not e.args[0].startswith('unhashable type:'):
+                    raise
+                retval = func(*args, **kwargs)
+            return retval
+
+        wrapper.cache_info = cfunc.cache_info
+        wrapper.cache_clear = cfunc.cache_clear
+
+        CACHE.append(wrapper)
+        return wrapper
+
+    return func_wrapper
+########################################
+
+
+def __cacheit_nocache(func):
+    return func
+
+
+def __cacheit_debug(maxsize):
+    """cacheit + code to check cache consistency"""
+    def func_wrapper(func):
+        cfunc = __cacheit(maxsize)(func)
+
+        @wraps(func)
+        def wrapper(*args, **kw_args):
+            # always call function itself and compare it with cached version
+            r1 = func(*args, **kw_args)
+            r2 = cfunc(*args, **kw_args)
+
+            # try to see if the result is immutable
+            #
+            # this works because:
+            #
+            # hash([1,2,3])         -> raise TypeError
+            # hash({'a':1, 'b':2})  -> raise TypeError
+            # hash((1,[2,3]))       -> raise TypeError
+            #
+            # hash((1,2,3))         -> just computes the hash
+            hash(r1), hash(r2)
+
+            # also see if returned values are the same
+            if r1 != r2:
+                raise RuntimeError("Returned values are not the same")
+            return r1
+        return wrapper
+    return func_wrapper
+
+
+def _getenv(key, default=None):
+    from os import getenv
+    return getenv(key, default)
+
+# SYMPY_USE_CACHE=yes/no/debug
+USE_CACHE = _getenv('SYMPY_USE_CACHE', 'yes').lower()
+# SYMPY_CACHE_SIZE=some_integer/None
+# special cases :
+#  SYMPY_CACHE_SIZE=0    -> No caching
+#  SYMPY_CACHE_SIZE=None -> Unbounded caching
+scs = _getenv('SYMPY_CACHE_SIZE', '1000')
+if scs.lower() == 'none':
+    SYMPY_CACHE_SIZE = None
+else:
+    try:
+        SYMPY_CACHE_SIZE = int(scs)
+    except ValueError:
+        raise RuntimeError(
+            'SYMPY_CACHE_SIZE must be a valid integer or None. ' + \
+            'Got: %s' % SYMPY_CACHE_SIZE)
+
+if USE_CACHE == 'no':
+    cacheit = __cacheit_nocache
+elif USE_CACHE == 'yes':
+    cacheit = __cacheit(SYMPY_CACHE_SIZE)
+elif USE_CACHE == 'debug':
+    cacheit = __cacheit_debug(SYMPY_CACHE_SIZE)   # a lot slower
+else:
+    raise RuntimeError(
+        'unrecognized value for SYMPY_USE_CACHE: %s' % USE_CACHE)
+
+
+def cached_property(func):
+    '''Decorator to cache property method'''
+    attrname = '__' + func.__name__
+    _cached_property_sentinel = object()
+    def propfunc(self):
+        val = getattr(self, attrname, _cached_property_sentinel)
+        if val is _cached_property_sentinel:
+            val = func(self)
+            setattr(self, attrname, val)
+        return val
+    return property(propfunc)
+
+
+def lazy_function(module : str, name : str) -> Callable:
+    """Create a lazy proxy for a function in a module.
+
+    The module containing the function is not imported until the function is used.
+
+    """
+    func = None
+
+    def _get_function():
+        nonlocal func
+        if func is None:
+            func = getattr(import_module(module), name)
+        return func
+
+    # The metaclass is needed so that help() shows the docstring
+    class LazyFunctionMeta(type):
+        @property
+        def __doc__(self):
+            docstring = _get_function().__doc__
+            docstring += f"\n\nNote: this is a {self.__class__.__name__} wrapper of '{module}.{name}'"
+            return docstring
+
+    class LazyFunction(metaclass=LazyFunctionMeta):
+        def __call__(self, *args, **kwargs):
+            # inline get of function for performance gh-23832
+            nonlocal func
+            if func is None:
+                func = getattr(import_module(module), name)
+            return func(*args, **kwargs)
+
+        @property
+        def __doc__(self):
+            docstring = _get_function().__doc__
+            docstring += f"\n\nNote: this is a {self.__class__.__name__} wrapper of '{module}.{name}'"
+            return docstring
+
+        def __str__(self):
+            return _get_function().__str__()
+
+        def __repr__(self):
+            return f"<{__class__.__name__} object at 0x{id(self):x}>: wrapping '{module}.{name}'"
+
+    return LazyFunction()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/compatibility.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/compatibility.py
new file mode 100644
index 0000000000000000000000000000000000000000..637a2698dbb39a042d3d664404bb0a4cba7fd004
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/compatibility.py
@@ -0,0 +1,35 @@
+"""
+.. deprecated:: 1.10
+
+   ``sympy.core.compatibility`` is deprecated. See
+   :ref:`sympy-core-compatibility`.
+
+Reimplementations of constructs introduced in later versions of Python than
+we support. Also some functions that are needed SymPy-wide and are located
+here for easy import.
+
+"""
+
+
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+sympy_deprecation_warning("""
+The sympy.core.compatibility submodule is deprecated.
+
+This module was only ever intended for internal use. Some of the functions
+that were in this module are available from the top-level SymPy namespace,
+i.e.,
+
+    from sympy import ordered, default_sort_key
+
+The remaining were only intended for internal SymPy use and should not be used
+by user code.
+""",
+                          deprecated_since_version="1.10",
+                          active_deprecations_target="deprecated-sympy-core-compatibility",
+                          )
+
+
+from .sorting import ordered, _nodes, default_sort_key # noqa:F401
+from sympy.utilities.misc import as_int as _as_int # noqa:F401
+from sympy.utilities.iterables import iterable, is_sequence, NotIterable # noqa:F401
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/containers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/containers.py
new file mode 100644
index 0000000000000000000000000000000000000000..35352009e87f3a7809a53031080cefdadb6528be
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/containers.py
@@ -0,0 +1,415 @@
+"""Module for SymPy containers
+
+    (SymPy objects that store other SymPy objects)
+
+    The containers implemented in this module are subclassed to Basic.
+    They are supposed to work seamlessly within the SymPy framework.
+"""
+
+from __future__ import annotations
+
+from collections import OrderedDict
+from collections.abc import MutableSet
+from typing import Any, Callable
+
+from .basic import Basic
+from .sorting import default_sort_key, ordered
+from .sympify import _sympify, sympify, _sympy_converter, SympifyError
+from sympy.core.kind import Kind
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import as_int
+
+
+class Tuple(Basic):
+    """
+    Wrapper around the builtin tuple object.
+
+    Explanation
+    ===========
+
+    The Tuple is a subclass of Basic, so that it works well in the
+    SymPy framework.  The wrapped tuple is available as self.args, but
+    you can also access elements or slices with [:] syntax.
+
+    Parameters
+    ==========
+
+    sympify : bool
+        If ``False``, ``sympify`` is not called on ``args``. This
+        can be used for speedups for very large tuples where the
+        elements are known to already be SymPy objects.
+
+    Examples
+    ========
+
+    >>> from sympy import Tuple, symbols
+    >>> a, b, c, d = symbols('a b c d')
+    >>> Tuple(a, b, c)[1:]
+    (b, c)
+    >>> Tuple(a, b, c).subs(a, d)
+    (d, b, c)
+
+    """
+
+    def __new__(cls, *args, **kwargs):
+        if kwargs.get('sympify', True):
+            args = (sympify(arg) for arg in args)
+        obj = Basic.__new__(cls, *args)
+        return obj
+
+    def __getitem__(self, i):
+        if isinstance(i, slice):
+            indices = i.indices(len(self))
+            return Tuple(*(self.args[j] for j in range(*indices)))
+        return self.args[i]
+
+    def __len__(self):
+        return len(self.args)
+
+    def __contains__(self, item):
+        return item in self.args
+
+    def __iter__(self):
+        return iter(self.args)
+
+    def __add__(self, other):
+        if isinstance(other, Tuple):
+            return Tuple(*(self.args + other.args))
+        elif isinstance(other, tuple):
+            return Tuple(*(self.args + other))
+        else:
+            return NotImplemented
+
+    def __radd__(self, other):
+        if isinstance(other, Tuple):
+            return Tuple(*(other.args + self.args))
+        elif isinstance(other, tuple):
+            return Tuple(*(other + self.args))
+        else:
+            return NotImplemented
+
+    def __mul__(self, other):
+        try:
+            n = as_int(other)
+        except ValueError:
+            raise TypeError("Can't multiply sequence by non-integer of type '%s'" % type(other))
+        return self.func(*(self.args*n))
+
+    __rmul__ = __mul__
+
+    def __eq__(self, other):
+        if isinstance(other, Basic):
+            return super().__eq__(other)
+        return self.args == other
+
+    def __ne__(self, other):
+        if isinstance(other, Basic):
+            return super().__ne__(other)
+        return self.args != other
+
+    def __hash__(self):
+        return hash(self.args)
+
+    def _to_mpmath(self, prec):
+        return tuple(a._to_mpmath(prec) for a in self.args)
+
+    def __lt__(self, other):
+        return _sympify(self.args < other.args)
+
+    def __le__(self, other):
+        return _sympify(self.args <= other.args)
+
+    # XXX: Basic defines count() as something different, so we can't
+    # redefine it here. Originally this lead to cse() test failure.
+    def tuple_count(self, value) -> int:
+        """Return number of occurrences of value."""
+        return self.args.count(value)
+
+    def index(self, value, start=None, stop=None):
+        """Searches and returns the first index of the value."""
+        # XXX: One would expect:
+        #
+        # return self.args.index(value, start, stop)
+        #
+        # here. Any trouble with that? Yes:
+        #
+        # >>> (1,).index(1, None, None)
+        # Traceback (most recent call last):
+        #   File "", line 1, in 
+        # TypeError: slice indices must be integers or None or have an __index__ method
+        #
+        # See: http://bugs.python.org/issue13340
+
+        if start is None and stop is None:
+            return self.args.index(value)
+        elif stop is None:
+            return self.args.index(value, start)
+        else:
+            return self.args.index(value, start, stop)
+
+    @property
+    def kind(self):
+        """
+        The kind of a Tuple instance.
+
+        The kind of a Tuple is always of :class:`TupleKind` but
+        parametrised by the number of elements and the kind of each element.
+
+        Examples
+        ========
+
+        >>> from sympy import Tuple, Matrix
+        >>> Tuple(1, 2).kind
+        TupleKind(NumberKind, NumberKind)
+        >>> Tuple(Matrix([1, 2]), 1).kind
+        TupleKind(MatrixKind(NumberKind), NumberKind)
+        >>> Tuple(1, 2).kind.element_kind
+        (NumberKind, NumberKind)
+
+        See Also
+        ========
+
+        sympy.matrices.kind.MatrixKind
+        sympy.core.kind.NumberKind
+        """
+        return TupleKind(*(i.kind for i in self.args))
+
+_sympy_converter[tuple] = lambda tup: Tuple(*tup)
+
+
+
+
+
+def tuple_wrapper(method):
+    """
+    Decorator that converts any tuple in the function arguments into a Tuple.
+
+    Explanation
+    ===========
+
+    The motivation for this is to provide simple user interfaces.  The user can
+    call a function with regular tuples in the argument, and the wrapper will
+    convert them to Tuples before handing them to the function.
+
+    Explanation
+    ===========
+
+    >>> from sympy.core.containers import tuple_wrapper
+    >>> def f(*args):
+    ...    return args
+    >>> g = tuple_wrapper(f)
+
+    The decorated function g sees only the Tuple argument:
+
+    >>> g(0, (1, 2), 3)
+    (0, (1, 2), 3)
+
+    """
+    def wrap_tuples(*args, **kw_args):
+        newargs = []
+        for arg in args:
+            if isinstance(arg, tuple):
+                newargs.append(Tuple(*arg))
+            else:
+                newargs.append(arg)
+        return method(*newargs, **kw_args)
+    return wrap_tuples
+
+
+class Dict(Basic):
+    """
+    Wrapper around the builtin dict object.
+
+    Explanation
+    ===========
+
+    The Dict is a subclass of Basic, so that it works well in the
+    SymPy framework.  Because it is immutable, it may be included
+    in sets, but its values must all be given at instantiation and
+    cannot be changed afterwards.  Otherwise it behaves identically
+    to the Python dict.
+
+    Examples
+    ========
+
+    >>> from sympy import Dict, Symbol
+
+    >>> D = Dict({1: 'one', 2: 'two'})
+    >>> for key in D:
+    ...    if key == 1:
+    ...        print('%s %s' % (key, D[key]))
+    1 one
+
+    The args are sympified so the 1 and 2 are Integers and the values
+    are Symbols. Queries automatically sympify args so the following work:
+
+    >>> 1 in D
+    True
+    >>> D.has(Symbol('one')) # searches keys and values
+    True
+    >>> 'one' in D # not in the keys
+    False
+    >>> D[1]
+    one
+
+    """
+
+    elements: frozenset[Tuple]
+    _dict: dict[Basic, Basic]
+
+    def __new__(cls, *args):
+        if len(args) == 1 and isinstance(args[0], (dict, Dict)):
+            items = [Tuple(k, v) for k, v in args[0].items()]
+        elif iterable(args) and all(len(arg) == 2 for arg in args):
+            items = [Tuple(k, v) for k, v in args]
+        else:
+            raise TypeError('Pass Dict args as Dict((k1, v1), ...) or Dict({k1: v1, ...})')
+        elements = frozenset(items)
+        obj = Basic.__new__(cls, *ordered(items))
+        obj.elements = elements
+        obj._dict = dict(items)  # In case Tuple decides it wants to sympify
+        return obj
+
+    def __getitem__(self, key):
+        """x.__getitem__(y) <==> x[y]"""
+        try:
+            key = _sympify(key)
+        except SympifyError:
+            raise KeyError(key)
+
+        return self._dict[key]
+
+    def __setitem__(self, key, value):
+        raise NotImplementedError("SymPy Dicts are Immutable")
+
+    def items(self):
+        '''Returns a set-like object providing a view on dict's items.
+        '''
+        return self._dict.items()
+
+    def keys(self):
+        '''Returns the list of the dict's keys.'''
+        return self._dict.keys()
+
+    def values(self):
+        '''Returns the list of the dict's values.'''
+        return self._dict.values()
+
+    def __iter__(self):
+        '''x.__iter__() <==> iter(x)'''
+        return iter(self._dict)
+
+    def __len__(self):
+        '''x.__len__() <==> len(x)'''
+        return self._dict.__len__()
+
+    def get(self, key, default=None):
+        '''Returns the value for key if the key is in the dictionary.'''
+        try:
+            key = _sympify(key)
+        except SympifyError:
+            return default
+        return self._dict.get(key, default)
+
+    def __contains__(self, key):
+        '''D.__contains__(k) -> True if D has a key k, else False'''
+        try:
+            key = _sympify(key)
+        except SympifyError:
+            return False
+        return key in self._dict
+
+    def __lt__(self, other):
+        return _sympify(self.args < other.args)
+
+    @property
+    def _sorted_args(self):
+        return tuple(sorted(self.args, key=default_sort_key))
+
+    def __eq__(self, other):
+        if isinstance(other, dict):
+            return self == Dict(other)
+        return super().__eq__(other)
+
+    __hash__ : Callable[[Basic], Any] = Basic.__hash__
+
+# this handles dict, defaultdict, OrderedDict
+_sympy_converter[dict] = lambda d: Dict(*d.items())
+
+class OrderedSet(MutableSet):
+    def __init__(self, iterable=None):
+        if iterable:
+            self.map = OrderedDict((item, None) for item in iterable)
+        else:
+            self.map = OrderedDict()
+
+    def __len__(self):
+        return len(self.map)
+
+    def __contains__(self, key):
+        return key in self.map
+
+    def add(self, key):
+        self.map[key] = None
+
+    def discard(self, key):
+        self.map.pop(key)
+
+    def pop(self, last=True):
+        return self.map.popitem(last=last)[0]
+
+    def __iter__(self):
+        yield from self.map.keys()
+
+    def __repr__(self):
+        if not self.map:
+            return '%s()' % (self.__class__.__name__,)
+        return '%s(%r)' % (self.__class__.__name__, list(self.map.keys()))
+
+    def intersection(self, other):
+        return self.__class__([val for val in self if val in other])
+
+    def difference(self, other):
+        return self.__class__([val for val in self if val not in other])
+
+    def update(self, iterable):
+        for val in iterable:
+            self.add(val)
+
+class TupleKind(Kind):
+    """
+    TupleKind is a subclass of Kind, which is used to define Kind of ``Tuple``.
+
+    Parameters of TupleKind will be kinds of all the arguments in Tuples, for
+    example
+
+    Parameters
+    ==========
+
+    args : tuple(element_kind)
+       element_kind is kind of element.
+       args is tuple of kinds of element
+
+    Examples
+    ========
+
+    >>> from sympy import Tuple
+    >>> Tuple(1, 2).kind
+    TupleKind(NumberKind, NumberKind)
+    >>> Tuple(1, 2).kind.element_kind
+    (NumberKind, NumberKind)
+
+    See Also
+    ========
+
+    sympy.core.kind.NumberKind
+    MatrixKind
+    sympy.sets.sets.SetKind
+    """
+    def __new__(cls, *args):
+        obj = super().__new__(cls, *args)
+        obj.element_kind = args
+        return obj
+
+    def __repr__(self):
+        return "TupleKind{}".format(self.element_kind)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/core.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/core.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a45bb06919d7a8ef88e2c9958decac705c0b8ee
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/core.py
@@ -0,0 +1,21 @@
+""" The core's core. """
+from __future__ import annotations
+
+
+class Registry:
+    """
+    Base class for registry objects.
+
+    Registries map a name to an object using attribute notation. Registry
+    classes behave singletonically: all their instances share the same state,
+    which is stored in the class object.
+
+    All subclasses should set `__slots__ = ()`.
+    """
+    __slots__ = ()
+
+    def __setattr__(self, name, obj):
+        setattr(self.__class__, name, obj)
+
+    def __delattr__(self, name):
+        delattr(self.__class__, name)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/coreerrors.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/coreerrors.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2dbdd5227d7b0495145072d31bd993f13f31f0d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/coreerrors.py
@@ -0,0 +1,23 @@
+"""Definitions of common exceptions for :mod:`sympy.core` module. """
+
+from typing import Callable
+
+
+class BaseCoreError(Exception):
+    """Base class for core related exceptions. """
+
+
+class NonCommutativeExpression(BaseCoreError):
+    """Raised when expression didn't have commutative property. """
+
+
+class LazyExceptionMessage:
+    """Wrapper class that lets you specify an expensive to compute
+    error message that is only evaluated if the error is rendered."""
+    callback: Callable[[], str]
+
+    def __init__(self, callback: Callable[[], str]):
+        self.callback = callback
+
+    def __str__(self):
+        return self.callback()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/decorators.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/decorators.py
new file mode 100644
index 0000000000000000000000000000000000000000..afd6ae0c72dc32d260586c6411507e4859a9f8ff
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/decorators.py
@@ -0,0 +1,250 @@
+"""
+SymPy core decorators.
+
+The purpose of this module is to expose decorators without any other
+dependencies, so that they can be easily imported anywhere in sympy/core.
+"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+from functools import wraps
+from .sympify import SympifyError, sympify
+
+
+if TYPE_CHECKING:
+    from typing import Callable, TypeVar, Union
+    T1 = TypeVar('T1')
+    T2 = TypeVar('T2')
+    T3 = TypeVar('T3')
+
+
+def _sympifyit(arg, retval=None) -> Callable[[Callable[[T1, T2], T3]], Callable[[T1, T2], T3]]:
+    """
+    decorator to smartly _sympify function arguments
+
+    Explanation
+    ===========
+
+    @_sympifyit('other', NotImplemented)
+    def add(self, other):
+        ...
+
+    In add, other can be thought of as already being a SymPy object.
+
+    If it is not, the code is likely to catch an exception, then other will
+    be explicitly _sympified, and the whole code restarted.
+
+    if _sympify(arg) fails, NotImplemented will be returned
+
+    See also
+    ========
+
+    __sympifyit
+    """
+    def deco(func):
+        return __sympifyit(func, arg, retval)
+
+    return deco
+
+
+def __sympifyit(func, arg, retval=None):
+    """Decorator to _sympify `arg` argument for function `func`.
+
+       Do not use directly -- use _sympifyit instead.
+    """
+
+    # we support f(a,b) only
+    if not func.__code__.co_argcount:
+        raise LookupError("func not found")
+    # only b is _sympified
+    assert func.__code__.co_varnames[1] == arg
+    if retval is None:
+        @wraps(func)
+        def __sympifyit_wrapper(a, b):
+            return func(a, sympify(b, strict=True))
+
+    else:
+        @wraps(func)
+        def __sympifyit_wrapper(a, b):
+            try:
+                # If an external class has _op_priority, it knows how to deal
+                # with SymPy objects. Otherwise, it must be converted.
+                if not hasattr(b, '_op_priority'):
+                    b = sympify(b, strict=True)
+                return func(a, b)
+            except SympifyError:
+                return retval
+
+    return __sympifyit_wrapper
+
+
+def call_highest_priority(method_name: str
+    ) -> Callable[[Callable[[T1, T2], T3]], Callable[[T1, T2], T3]]:
+    """A decorator for binary special methods to handle _op_priority.
+
+    Explanation
+    ===========
+
+    Binary special methods in Expr and its subclasses use a special attribute
+    '_op_priority' to determine whose special method will be called to
+    handle the operation. In general, the object having the highest value of
+    '_op_priority' will handle the operation. Expr and subclasses that define
+    custom binary special methods (__mul__, etc.) should decorate those
+    methods with this decorator to add the priority logic.
+
+    The ``method_name`` argument is the name of the method of the other class
+    that will be called.  Use this decorator in the following manner::
+
+        # Call other.__rmul__ if other._op_priority > self._op_priority
+        @call_highest_priority('__rmul__')
+        def __mul__(self, other):
+            ...
+
+        # Call other.__mul__ if other._op_priority > self._op_priority
+        @call_highest_priority('__mul__')
+        def __rmul__(self, other):
+        ...
+    """
+    def priority_decorator(func: Callable[[T1, T2], T3]) -> Callable[[T1, T2], T3]:
+        @wraps(func)
+        def binary_op_wrapper(self: T1, other: T2) -> T3:
+            if hasattr(other, '_op_priority'):
+                if other._op_priority > self._op_priority:  # type: ignore
+                    f: Union[Callable[[T1], T3], None] = getattr(other, method_name, None)
+                    if f is not None:
+                        return f(self)
+            return func(self, other)
+        return binary_op_wrapper
+    return priority_decorator
+
+
+def sympify_method_args(cls: type[T1]) -> type[T1]:
+    '''Decorator for a class with methods that sympify arguments.
+
+    Explanation
+    ===========
+
+    The sympify_method_args decorator is to be used with the sympify_return
+    decorator for automatic sympification of method arguments. This is
+    intended for the common idiom of writing a class like :
+
+    Examples
+    ========
+
+    >>> from sympy import Basic, SympifyError, S
+    >>> from sympy.core.sympify import _sympify
+
+    >>> class MyTuple(Basic):
+    ...     def __add__(self, other):
+    ...         try:
+    ...             other = _sympify(other)
+    ...         except SympifyError:
+    ...             return NotImplemented
+    ...         if not isinstance(other, MyTuple):
+    ...             return NotImplemented
+    ...         return MyTuple(*(self.args + other.args))
+
+    >>> MyTuple(S(1), S(2)) + MyTuple(S(3), S(4))
+    MyTuple(1, 2, 3, 4)
+
+    In the above it is important that we return NotImplemented when other is
+    not sympifiable and also when the sympified result is not of the expected
+    type. This allows the MyTuple class to be used cooperatively with other
+    classes that overload __add__ and want to do something else in combination
+    with instance of Tuple.
+
+    Using this decorator the above can be written as
+
+    >>> from sympy.core.decorators import sympify_method_args, sympify_return
+
+    >>> @sympify_method_args
+    ... class MyTuple(Basic):
+    ...     @sympify_return([('other', 'MyTuple')], NotImplemented)
+    ...     def __add__(self, other):
+    ...          return MyTuple(*(self.args + other.args))
+
+    >>> MyTuple(S(1), S(2)) + MyTuple(S(3), S(4))
+    MyTuple(1, 2, 3, 4)
+
+    The idea here is that the decorators take care of the boiler-plate code
+    for making this happen in each method that potentially needs to accept
+    unsympified arguments. Then the body of e.g. the __add__ method can be
+    written without needing to worry about calling _sympify or checking the
+    type of the resulting object.
+
+    The parameters for sympify_return are a list of tuples of the form
+    (parameter_name, expected_type) and the value to return (e.g.
+    NotImplemented). The expected_type parameter can be a type e.g. Tuple or a
+    string 'Tuple'. Using a string is useful for specifying a Type within its
+    class body (as in the above example).
+
+    Notes: Currently sympify_return only works for methods that take a single
+    argument (not including self). Specifying an expected_type as a string
+    only works for the class in which the method is defined.
+    '''
+    # Extract the wrapped methods from each of the wrapper objects created by
+    # the sympify_return decorator. Doing this here allows us to provide the
+    # cls argument which is used for forward string referencing.
+    for attrname, obj in cls.__dict__.items():
+        if isinstance(obj, _SympifyWrapper):
+            setattr(cls, attrname, obj.make_wrapped(cls))
+    return cls
+
+
+def sympify_return(*args):
+    '''Function/method decorator to sympify arguments automatically
+
+    See the docstring of sympify_method_args for explanation.
+    '''
+    # Store a wrapper object for the decorated method
+    def wrapper(func: Callable[[T1, T2], T3]) -> Callable[[T1, T2], T3]:
+        return _SympifyWrapper(func, args)  # type: ignore
+    return wrapper
+
+
+class _SympifyWrapper:
+    '''Internal class used by sympify_return and sympify_method_args'''
+
+    def __init__(self, func, args):
+        self.func = func
+        self.args = args
+
+    def make_wrapped(self, cls):
+        func = self.func
+        parameters, retval = self.args
+
+        # XXX: Handle more than one parameter?
+        [(parameter, expectedcls)] = parameters
+
+        # Handle forward references to the current class using strings
+        if expectedcls == cls.__name__:
+            expectedcls = cls
+
+        # Raise RuntimeError since this is a failure at import time and should
+        # not be recoverable.
+        nargs = func.__code__.co_argcount
+        # we support f(a, b) only
+        if nargs != 2:
+            raise RuntimeError('sympify_return can only be used with 2 argument functions')
+        # only b is _sympified
+        if func.__code__.co_varnames[1] != parameter:
+            raise RuntimeError('parameter name mismatch "%s" in %s' %
+                    (parameter, func.__name__))
+
+        @wraps(func)
+        def _func(self, other):
+            # XXX: The check for _op_priority here should be removed. It is
+            # needed to stop mutable matrices from being sympified to
+            # immutable matrices which breaks things in quantum...
+            if not hasattr(other, '_op_priority'):
+                try:
+                    other = sympify(other, strict=True)
+                except SympifyError:
+                    return retval
+            if not isinstance(other, expectedcls):
+                return retval
+            return func(self, other)
+
+        return _func
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/evalf.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/evalf.py
new file mode 100644
index 0000000000000000000000000000000000000000..55a981090360556b357ec1cade5576e226633be8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/evalf.py
@@ -0,0 +1,1808 @@
+"""
+Adaptive numerical evaluation of SymPy expressions, using mpmath
+for mathematical functions.
+"""
+from __future__ import annotations
+from typing import Callable, TYPE_CHECKING, Any, overload, Type
+
+import math
+
+import mpmath.libmp as libmp
+from mpmath import (
+    make_mpc, make_mpf, mp, mpc, mpf, nsum, quadts, quadosc, workprec)
+from mpmath import inf as mpmath_inf
+from mpmath.libmp import (from_int, from_man_exp, from_rational, fhalf,
+                          fnan, finf, fninf, fnone, fone, fzero, mpf_abs, mpf_add,
+                          mpf_atan, mpf_atan2, mpf_cmp, mpf_cos, mpf_e, mpf_exp, mpf_log, mpf_lt,
+                          mpf_mul, mpf_neg, mpf_pi, mpf_pow, mpf_pow_int, mpf_shift, mpf_sin,
+                          mpf_sqrt, normalize, round_nearest, to_int, to_str, mpf_tan)
+from mpmath.libmp import bitcount as mpmath_bitcount
+from mpmath.libmp.backend import MPZ
+from mpmath.libmp.libmpc import _infs_nan
+from mpmath.libmp.libmpf import dps_to_prec, prec_to_dps
+
+from .sympify import sympify
+from .singleton import S
+from sympy.external.gmpy import SYMPY_INTS
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.lambdify import lambdify
+from sympy.utilities.misc import as_int
+
+if TYPE_CHECKING:
+    from sympy.core.expr import Expr
+    from sympy.core.add import Add
+    from sympy.core.mul import Mul
+    from sympy.core.power import Pow
+    from sympy.core.symbol import Symbol
+    from sympy.integrals.integrals import Integral
+    from sympy.concrete.summations import Sum
+    from sympy.concrete.products import Product
+    from sympy.functions.elementary.exponential import exp, log
+    from sympy.functions.elementary.complexes import Abs, re, im
+    from sympy.functions.elementary.integers import ceiling, floor
+    from sympy.functions.elementary.trigonometric import atan
+    from .numbers import Float, Rational, Integer, AlgebraicNumber, Number
+
+LG10 = math.log2(10)
+rnd = round_nearest
+
+
+def bitcount(n):
+    """Return smallest integer, b, such that |n|/2**b < 1.
+    """
+    return mpmath_bitcount(abs(int(n)))
+
+# Used in a few places as placeholder values to denote exponents and
+# precision levels, e.g. of exact numbers. Must be careful to avoid
+# passing these to mpmath functions or returning them in final results.
+INF = float(mpmath_inf)
+MINUS_INF = float(-mpmath_inf)
+
+# ~= 100 digits. Real men set this to INF.
+DEFAULT_MAXPREC = 333
+
+
+class PrecisionExhausted(ArithmeticError):
+    pass
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#              Helper functions for arithmetic and complex parts             #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+"""
+An mpf value tuple is a tuple of integers (sign, man, exp, bc)
+representing a floating-point number: [1, -1][sign]*man*2**exp where
+sign is 0 or 1 and bc should correspond to the number of bits used to
+represent the mantissa (man) in binary notation, e.g.
+"""
+
+MPF_TUP = tuple[int, int, int, int]  # mpf value tuple
+
+"""
+Explanation
+===========
+
+>>> from sympy.core.evalf import bitcount
+>>> sign, man, exp, bc = 0, 5, 1, 3
+>>> n = [1, -1][sign]*man*2**exp
+>>> n, bitcount(man)
+(10, 3)
+
+A temporary result is a tuple (re, im, re_acc, im_acc) where
+re and im are nonzero mpf value tuples representing approximate
+numbers, or None to denote exact zeros.
+
+re_acc, im_acc are integers denoting log2(e) where e is the estimated
+relative accuracy of the respective complex part, but may be anything
+if the corresponding complex part is None.
+
+"""
+TMP_RES = Any  # temporary result, should be some variant of
+# tUnion[tTuple[Optional[MPF_TUP], Optional[MPF_TUP],
+#               Optional[int], Optional[int]],
+#        'ComplexInfinity']
+# but mypy reports error because it doesn't know as we know
+# 1. re and re_acc are either both None or both MPF_TUP
+# 2. sometimes the result can't be zoo
+
+# type of the "options" parameter in internal evalf functions
+OPT_DICT = dict[str, Any]
+
+
+def fastlog(x: MPF_TUP | None) -> int | Any:
+    """Fast approximation of log2(x) for an mpf value tuple x.
+
+    Explanation
+    ===========
+
+    Calculated as exponent + width of mantissa. This is an
+    approximation for two reasons: 1) it gives the ceil(log2(abs(x)))
+    value and 2) it is too high by 1 in the case that x is an exact
+    power of 2. Although this is easy to remedy by testing to see if
+    the odd mpf mantissa is 1 (indicating that one was dealing with
+    an exact power of 2) that would decrease the speed and is not
+    necessary as this is only being used as an approximation for the
+    number of bits in x. The correct return value could be written as
+    "x[2] + (x[3] if x[1] != 1 else 0)".
+        Since mpf tuples always have an odd mantissa, no check is done
+    to see if the mantissa is a multiple of 2 (in which case the
+    result would be too large by 1).
+
+    Examples
+    ========
+
+    >>> from sympy import log
+    >>> from sympy.core.evalf import fastlog, bitcount
+    >>> s, m, e = 0, 5, 1
+    >>> bc = bitcount(m)
+    >>> n = [1, -1][s]*m*2**e
+    >>> n, (log(n)/log(2)).evalf(2), fastlog((s, m, e, bc))
+    (10, 3.3, 4)
+    """
+
+    if not x or x == fzero:
+        return MINUS_INF
+    return x[2] + x[3]
+
+
+def pure_complex(v: Expr, or_real=False) -> tuple[Number, Number] | None:
+    """Return a and b if v matches a + I*b where b is not zero and
+    a and b are Numbers, else None. If `or_real` is True then 0 will
+    be returned for `b` if `v` is a real number.
+
+    Examples
+    ========
+
+    >>> from sympy.core.evalf import pure_complex
+    >>> from sympy import sqrt, I, S
+    >>> a, b, surd = S(2), S(3), sqrt(2)
+    >>> pure_complex(a)
+    >>> pure_complex(a, or_real=True)
+    (2, 0)
+    >>> pure_complex(surd)
+    >>> pure_complex(a + b*I)
+    (2, 3)
+    >>> pure_complex(I)
+    (0, 1)
+    """
+    h, t = v.as_coeff_Add()
+    if t:
+        c, i = t.as_coeff_Mul()
+        if i is S.ImaginaryUnit:
+            return h, c
+    elif or_real:
+        return h, S.Zero
+    return None
+
+
+# I don't know what this is, see function scaled_zero below
+SCALED_ZERO_TUP = tuple[list[int], int, int, int]
+
+
+
+@overload
+def scaled_zero(mag: SCALED_ZERO_TUP, sign=1) -> MPF_TUP:
+    ...
+@overload
+def scaled_zero(mag: int, sign=1) -> tuple[SCALED_ZERO_TUP, int]:
+    ...
+def scaled_zero(mag: SCALED_ZERO_TUP | int, sign=1) -> \
+        MPF_TUP | tuple[SCALED_ZERO_TUP, int]:
+    """Return an mpf representing a power of two with magnitude ``mag``
+    and -1 for precision. Or, if ``mag`` is a scaled_zero tuple, then just
+    remove the sign from within the list that it was initially wrapped
+    in.
+
+    Examples
+    ========
+
+    >>> from sympy.core.evalf import scaled_zero
+    >>> from sympy import Float
+    >>> z, p = scaled_zero(100)
+    >>> z, p
+    (([0], 1, 100, 1), -1)
+    >>> ok = scaled_zero(z)
+    >>> ok
+    (0, 1, 100, 1)
+    >>> Float(ok)
+    1.26765060022823e+30
+    >>> Float(ok, p)
+    0.e+30
+    >>> ok, p = scaled_zero(100, -1)
+    >>> Float(scaled_zero(ok), p)
+    -0.e+30
+    """
+    if isinstance(mag, tuple) and len(mag) == 4 and iszero(mag, scaled=True):
+        return (mag[0][0],) + mag[1:]
+    elif isinstance(mag, SYMPY_INTS):
+        if sign not in [-1, 1]:
+            raise ValueError('sign must be +/-1')
+        rv, p = mpf_shift(fone, mag), -1
+        s = 0 if sign == 1 else 1
+        rv = ([s],) + rv[1:]
+        return rv, p
+    else:
+        raise ValueError('scaled zero expects int or scaled_zero tuple.')
+
+
+def iszero(mpf: MPF_TUP | SCALED_ZERO_TUP | None, scaled=False) -> bool | None:
+    if not scaled:
+        return not mpf or not mpf[1] and not mpf[-1]
+    return mpf and isinstance(mpf[0], list) and mpf[1] == mpf[-1] == 1
+
+
+def complex_accuracy(result: TMP_RES) -> int | Any:
+    """
+    Returns relative accuracy of a complex number with given accuracies
+    for the real and imaginary parts. The relative accuracy is defined
+    in the complex norm sense as ||z|+|error|| / |z| where error
+    is equal to (real absolute error) + (imag absolute error)*i.
+
+    The full expression for the (logarithmic) error can be approximated
+    easily by using the max norm to approximate the complex norm.
+
+    In the worst case (re and im equal), this is wrong by a factor
+    sqrt(2), or by log2(sqrt(2)) = 0.5 bit.
+    """
+    if result is S.ComplexInfinity:
+        return INF
+    re, im, re_acc, im_acc = result
+    if not im:
+        if not re:
+            return INF
+        return re_acc
+    if not re:
+        return im_acc
+    re_size = fastlog(re)
+    im_size = fastlog(im)
+    absolute_error = max(re_size - re_acc, im_size - im_acc)
+    relative_error = absolute_error - max(re_size, im_size)
+    return -relative_error
+
+
+def get_abs(expr: Expr, prec: int, options: OPT_DICT) -> TMP_RES:
+    result = evalf(expr, prec + 2, options)
+    if result is S.ComplexInfinity:
+        return finf, None, prec, None
+    re, im, re_acc, im_acc = result
+    if not re:
+        re, re_acc, im, im_acc = im, im_acc, re, re_acc
+    if im:
+        if expr.is_number:
+            abs_expr, _, acc, _ = evalf(abs(N(expr, prec + 2)),
+                                        prec + 2, options)
+            return abs_expr, None, acc, None
+        else:
+            if 'subs' in options:
+                return libmp.mpc_abs((re, im), prec), None, re_acc, None
+            return abs(expr), None, prec, None
+    elif re:
+        return mpf_abs(re), None, re_acc, None
+    else:
+        return None, None, None, None
+
+
+def get_complex_part(expr: Expr, no: int, prec: int, options: OPT_DICT) -> TMP_RES:
+    """no = 0 for real part, no = 1 for imaginary part"""
+    workprec = prec
+    i = 0
+    while 1:
+        res = evalf(expr, workprec, options)
+        if res is S.ComplexInfinity:
+            return fnan, None, prec, None
+        value, accuracy = res[no::2]
+        # XXX is the last one correct? Consider re((1+I)**2).n()
+        if (not value) or accuracy >= prec or -value[2] > prec:
+            return value, None, accuracy, None
+        workprec += max(30, 2**i)
+        i += 1
+
+
+def evalf_abs(expr: 'Abs', prec: int, options: OPT_DICT) -> TMP_RES:
+    return get_abs(expr.args[0], prec, options)
+
+
+def evalf_re(expr: 're', prec: int, options: OPT_DICT) -> TMP_RES:
+    return get_complex_part(expr.args[0], 0, prec, options)
+
+
+def evalf_im(expr: 'im', prec: int, options: OPT_DICT) -> TMP_RES:
+    return get_complex_part(expr.args[0], 1, prec, options)
+
+
+def finalize_complex(re: MPF_TUP, im: MPF_TUP, prec: int) -> TMP_RES:
+    if re == fzero and im == fzero:
+        raise ValueError("got complex zero with unknown accuracy")
+    elif re == fzero:
+        return None, im, None, prec
+    elif im == fzero:
+        return re, None, prec, None
+
+    size_re = fastlog(re)
+    size_im = fastlog(im)
+    if size_re > size_im:
+        re_acc = prec
+        im_acc = prec + min(-(size_re - size_im), 0)
+    else:
+        im_acc = prec
+        re_acc = prec + min(-(size_im - size_re), 0)
+    return re, im, re_acc, im_acc
+
+
+def chop_parts(value: TMP_RES, prec: int) -> TMP_RES:
+    """
+    Chop off tiny real or complex parts.
+    """
+    if value is S.ComplexInfinity:
+        return value
+    re, im, re_acc, im_acc = value
+    # Method 1: chop based on absolute value
+    if re and re not in _infs_nan and (fastlog(re) < -prec + 4):
+        re, re_acc = None, None
+    if im and im not in _infs_nan and (fastlog(im) < -prec + 4):
+        im, im_acc = None, None
+    # Method 2: chop if inaccurate and relatively small
+    if re and im:
+        delta = fastlog(re) - fastlog(im)
+        if re_acc < 2 and (delta - re_acc <= -prec + 4):
+            re, re_acc = None, None
+        if im_acc < 2 and (delta - im_acc >= prec - 4):
+            im, im_acc = None, None
+    return re, im, re_acc, im_acc
+
+
+def check_target(expr: Expr, result: TMP_RES, prec: int):
+    a = complex_accuracy(result)
+    if a < prec:
+        raise PrecisionExhausted("Failed to distinguish the expression: \n\n%s\n\n"
+            "from zero. Try simplifying the input, using chop=True, or providing "
+            "a higher maxn for evalf" % (expr))
+
+
+def get_integer_part(expr: Expr, no: int, options: OPT_DICT, return_ints=False) -> \
+        TMP_RES | tuple[int, int]:
+    """
+    With no = 1, computes ceiling(expr)
+    With no = -1, computes floor(expr)
+
+    Note: this function either gives the exact result or signals failure.
+    """
+    from sympy.functions.elementary.complexes import re, im
+    # The expression is likely less than 2^30 or so
+    assumed_size = 30
+    result = evalf(expr, assumed_size, options)
+    if result is S.ComplexInfinity:
+        raise ValueError("Cannot get integer part of Complex Infinity")
+    ire, iim, ire_acc, iim_acc = result
+
+    # We now know the size, so we can calculate how much extra precision
+    # (if any) is needed to get within the nearest integer
+    if ire and iim:
+        gap = max(fastlog(ire) - ire_acc, fastlog(iim) - iim_acc)
+    elif ire:
+        gap = fastlog(ire) - ire_acc
+    elif iim:
+        gap = fastlog(iim) - iim_acc
+    else:
+        # ... or maybe the expression was exactly zero
+        if return_ints:
+            return 0, 0
+        else:
+            return None, None, None, None
+
+    margin = 10
+
+    if gap >= -margin:
+        prec = margin + assumed_size + gap
+        ire, iim, ire_acc, iim_acc = evalf(
+            expr, prec, options)
+    else:
+        prec = assumed_size
+
+    # We can now easily find the nearest integer, but to find floor/ceil, we
+    # must also calculate whether the difference to the nearest integer is
+    # positive or negative (which may fail if very close).
+    def calc_part(re_im: Expr, nexpr: MPF_TUP):
+        from .add import Add
+        _, _, exponent, _ = nexpr
+        is_int = exponent == 0
+        nint = int(to_int(nexpr, rnd))
+        if is_int:
+            # make sure that we had enough precision to distinguish
+            # between nint and the re or im part (re_im) of expr that
+            # was passed to calc_part
+            ire, iim, ire_acc, iim_acc = evalf(
+                re_im - nint, 10, options)  # don't need much precision
+            assert not iim
+            size = -fastlog(ire) + 2  # -ve b/c ire is less than 1
+            if size > prec:
+                ire, iim, ire_acc, iim_acc = evalf(
+                    re_im, size, options)
+                assert not iim
+                nexpr = ire
+            nint = int(to_int(nexpr, rnd))
+            _, _, new_exp, _ = ire
+            is_int = new_exp == 0
+        if not is_int:
+            # if there are subs and they all contain integer re/im parts
+            # then we can (hopefully) safely substitute them into the
+            # expression
+            s = options.get('subs', False)
+            if s:
+                # use strict=False with as_int because we take
+                # 2.0 == 2
+                def is_int_reim(x):
+                    """Check for integer or integer + I*integer."""
+                    try:
+                        as_int(x, strict=False)
+                        return True
+                    except ValueError:
+                        try:
+                            [as_int(i, strict=False) for i in x.as_real_imag()]
+                            return True
+                        except ValueError:
+                            return False
+
+                if all(is_int_reim(v) for v in s.values()):
+                    re_im = re_im.subs(s)
+
+            re_im = Add(re_im, -nint, evaluate=False)
+            x, _, x_acc, _ = evalf(re_im, 10, options)
+            try:
+                check_target(re_im, (x, None, x_acc, None), 3)
+            except PrecisionExhausted:
+                if not re_im.equals(0):
+                    raise PrecisionExhausted
+                x = fzero
+            nint += int(no*(mpf_cmp(x or fzero, fzero) == no))
+        nint = from_int(nint)
+        return nint, INF
+
+    re_, im_, re_acc, im_acc = None, None, None, None
+
+    if ire is not None and ire != fzero:
+        re_, re_acc = calc_part(re(expr, evaluate=False), ire)
+    if iim is not None and iim != fzero:
+        im_, im_acc = calc_part(im(expr, evaluate=False), iim)
+
+    if return_ints:
+        return int(to_int(re_ or fzero)), int(to_int(im_ or fzero))
+    return re_, im_, re_acc, im_acc
+
+
+def evalf_ceiling(expr: 'ceiling', prec: int, options: OPT_DICT) -> TMP_RES:
+    return get_integer_part(expr.args[0], 1, options)
+
+
+def evalf_floor(expr: 'floor', prec: int, options: OPT_DICT) -> TMP_RES:
+    return get_integer_part(expr.args[0], -1, options)
+
+
+def evalf_float(expr: 'Float', prec: int, options: OPT_DICT) -> TMP_RES:
+    return expr._mpf_, None, prec, None
+
+
+def evalf_rational(expr: 'Rational', prec: int, options: OPT_DICT) -> TMP_RES:
+    return from_rational(expr.p, expr.q, prec), None, prec, None
+
+
+def evalf_integer(expr: 'Integer', prec: int, options: OPT_DICT) -> TMP_RES:
+    return from_int(expr.p, prec), None, prec, None
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            Arithmetic operations                           #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+def add_terms(terms: list, prec: int, target_prec: int) -> \
+        tuple[MPF_TUP | SCALED_ZERO_TUP | None, int | None]:
+    """
+    Helper for evalf_add. Adds a list of (mpfval, accuracy) terms.
+
+    Returns
+    =======
+
+    - None, None if there are no non-zero terms;
+    - terms[0] if there is only 1 term;
+    - scaled_zero if the sum of the terms produces a zero by cancellation
+      e.g. mpfs representing 1 and -1 would produce a scaled zero which need
+      special handling since they are not actually zero and they are purposely
+      malformed to ensure that they cannot be used in anything but accuracy
+      calculations;
+    - a tuple that is scaled to target_prec that corresponds to the
+      sum of the terms.
+
+    The returned mpf tuple will be normalized to target_prec; the input
+    prec is used to define the working precision.
+
+    XXX explain why this is needed and why one cannot just loop using mpf_add
+    """
+
+    terms = [t for t in terms if not iszero(t[0])]
+    if not terms:
+        return None, None
+    elif len(terms) == 1:
+        return terms[0]
+
+    # see if any argument is NaN or oo and thus warrants a special return
+    special = []
+    from .numbers import Float
+    for t in terms:
+        arg = Float._new(t[0], 1)
+        if arg is S.NaN or arg.is_infinite:
+            special.append(arg)
+    if special:
+        from .add import Add
+        rv = evalf(Add(*special), prec + 4, {})
+        return rv[0], rv[2]
+
+    working_prec = 2*prec
+    sum_man, sum_exp = 0, 0
+    absolute_err: list[int] = []
+
+    for x, accuracy in terms:
+        sign, man, exp, bc = x
+        if sign:
+            man = -man
+        absolute_err.append(bc + exp - accuracy)
+        delta = exp - sum_exp
+        if exp >= sum_exp:
+            # x much larger than existing sum?
+            # first: quick test
+            if ((delta > working_prec) and
+                ((not sum_man) or
+                 delta - bitcount(abs(sum_man)) > working_prec)):
+                sum_man = man
+                sum_exp = exp
+            else:
+                sum_man += (man << delta)
+        else:
+            delta = -delta
+            # x much smaller than existing sum?
+            if delta - bc > working_prec:
+                if not sum_man:
+                    sum_man, sum_exp = man, exp
+            else:
+                sum_man = (sum_man << delta) + man
+                sum_exp = exp
+    absolute_error = max(absolute_err)
+    if not sum_man:
+        return scaled_zero(absolute_error)
+    if sum_man < 0:
+        sum_sign = 1
+        sum_man = -sum_man
+    else:
+        sum_sign = 0
+    sum_bc = bitcount(sum_man)
+    sum_accuracy = sum_exp + sum_bc - absolute_error
+    r = normalize(sum_sign, sum_man, sum_exp, sum_bc, target_prec,
+        rnd), sum_accuracy
+    return r
+
+
+def evalf_add(v: 'Add', prec: int, options: OPT_DICT) -> TMP_RES:
+    res = pure_complex(v)
+    if res:
+        h, c = res
+        re, _, re_acc, _ = evalf(h, prec, options)
+        im, _, im_acc, _ = evalf(c, prec, options)
+        return re, im, re_acc, im_acc
+
+    oldmaxprec = options.get('maxprec', DEFAULT_MAXPREC)
+
+    i = 0
+    target_prec = prec
+    while 1:
+        options['maxprec'] = min(oldmaxprec, 2*prec)
+
+        terms = [evalf(arg, prec + 10, options) for arg in v.args]
+        n = terms.count(S.ComplexInfinity)
+        if n >= 2:
+            return fnan, None, prec, None
+        re, re_acc = add_terms(
+            [a[0::2] for a in terms if isinstance(a, tuple) and a[0]], prec, target_prec)
+        im, im_acc = add_terms(
+            [a[1::2] for a in terms if isinstance(a, tuple) and a[1]], prec, target_prec)
+        if n == 1:
+            if re in (finf, fninf, fnan) or im in (finf, fninf, fnan):
+                return fnan, None, prec, None
+            return S.ComplexInfinity
+        acc = complex_accuracy((re, im, re_acc, im_acc))
+        if acc >= target_prec:
+            if options.get('verbose'):
+                print("ADD: wanted", target_prec, "accurate bits, got", re_acc, im_acc)
+            break
+        else:
+            if (prec - target_prec) > options['maxprec']:
+                break
+
+            prec = prec + max(10 + 2**i, target_prec - acc)
+            i += 1
+            if options.get('verbose'):
+                print("ADD: restarting with prec", prec)
+
+    options['maxprec'] = oldmaxprec
+    if iszero(re, scaled=True):
+        re = scaled_zero(re)
+    if iszero(im, scaled=True):
+        im = scaled_zero(im)
+    return re, im, re_acc, im_acc
+
+
+def evalf_mul(v: 'Mul', prec: int, options: OPT_DICT) -> TMP_RES:
+    res = pure_complex(v)
+    if res:
+        # the only pure complex that is a mul is h*I
+        _, h = res
+        im, _, im_acc, _ = evalf(h, prec, options)
+        return None, im, None, im_acc
+    args = list(v.args)
+
+    # see if any argument is NaN or oo and thus warrants a special return
+    has_zero = False
+    special = []
+    from .numbers import Float
+    for arg in args:
+        result = evalf(arg, prec, options)
+        if result is S.ComplexInfinity:
+            special.append(result)
+            continue
+        if result[0] is None:
+            if result[1] is None:
+                has_zero = True
+            continue
+        num = Float._new(result[0], 1)
+        if num is S.NaN:
+            return fnan, None, prec, None
+        if num.is_infinite:
+            special.append(num)
+    if special:
+        if has_zero:
+            return fnan, None, prec, None
+        from .mul import Mul
+        return evalf(Mul(*special), prec + 4, {})
+    if has_zero:
+        return None, None, None, None
+
+    # With guard digits, multiplication in the real case does not destroy
+    # accuracy. This is also true in the complex case when considering the
+    # total accuracy; however accuracy for the real or imaginary parts
+    # separately may be lower.
+    acc = prec
+
+    # XXX: big overestimate
+    working_prec = prec + len(args) + 5
+
+    # Empty product is 1
+    start = man, exp, bc = MPZ(1), 0, 1
+
+    # First, we multiply all pure real or pure imaginary numbers.
+    # direction tells us that the result should be multiplied by
+    # I**direction; all other numbers get put into complex_factors
+    # to be multiplied out after the first phase.
+    last = len(args)
+    direction = 0
+    args.append(S.One)
+    complex_factors = []
+
+    for i, arg in enumerate(args):
+        if i != last and pure_complex(arg):
+            args[-1] = (args[-1]*arg).expand()
+            continue
+        elif i == last and arg is S.One:
+            continue
+        re, im, re_acc, im_acc = evalf(arg, working_prec, options)
+        if re and im:
+            complex_factors.append((re, im, re_acc, im_acc))
+            continue
+        elif re:
+            (s, m, e, b), w_acc = re, re_acc
+        elif im:
+            (s, m, e, b), w_acc = im, im_acc
+            direction += 1
+        else:
+            return None, None, None, None
+        direction += 2*s
+        man *= m
+        exp += e
+        bc += b
+        while bc > 3*working_prec:
+            man >>= working_prec
+            exp += working_prec
+            bc -= working_prec
+        acc = min(acc, w_acc)
+    sign = (direction & 2) >> 1
+    if not complex_factors:
+        v = normalize(sign, man, exp, bitcount(man), prec, rnd)
+        # multiply by i
+        if direction & 1:
+            return None, v, None, acc
+        else:
+            return v, None, acc, None
+    else:
+        # initialize with the first term
+        if (man, exp, bc) != start:
+            # there was a real part; give it an imaginary part
+            re, im = (sign, man, exp, bitcount(man)), (0, MPZ(0), 0, 0)
+            i0 = 0
+        else:
+            # there is no real part to start (other than the starting 1)
+            wre, wim, wre_acc, wim_acc = complex_factors[0]
+            acc = min(acc,
+                      complex_accuracy((wre, wim, wre_acc, wim_acc)))
+            re = wre
+            im = wim
+            i0 = 1
+
+        for wre, wim, wre_acc, wim_acc in complex_factors[i0:]:
+            # acc is the overall accuracy of the product; we aren't
+            # computing exact accuracies of the product.
+            acc = min(acc,
+                      complex_accuracy((wre, wim, wre_acc, wim_acc)))
+
+            use_prec = working_prec
+            A = mpf_mul(re, wre, use_prec)
+            B = mpf_mul(mpf_neg(im), wim, use_prec)
+            C = mpf_mul(re, wim, use_prec)
+            D = mpf_mul(im, wre, use_prec)
+            re = mpf_add(A, B, use_prec)
+            im = mpf_add(C, D, use_prec)
+        if options.get('verbose'):
+            print("MUL: wanted", prec, "accurate bits, got", acc)
+        # multiply by I
+        if direction & 1:
+            re, im = mpf_neg(im), re
+        return re, im, acc, acc
+
+
+def evalf_pow(v: 'Pow', prec: int, options) -> TMP_RES:
+
+    target_prec = prec
+    base, exp = v.args
+
+    # We handle x**n separately. This has two purposes: 1) it is much
+    # faster, because we avoid calling evalf on the exponent, and 2) it
+    # allows better handling of real/imaginary parts that are exactly zero
+    if exp.is_Integer:
+        p: int = exp.p  # type: ignore
+        # Exact
+        if not p:
+            return fone, None, prec, None
+        # Exponentiation by p magnifies relative error by |p|, so the
+        # base must be evaluated with increased precision if p is large
+        prec += int(math.log2(abs(p)))
+        result = evalf(base, prec + 5, options)
+        if result is S.ComplexInfinity:
+            if p < 0:
+                return None, None, None, None
+            return result
+        re, im, re_acc, im_acc = result
+        # Real to integer power
+        if re and not im:
+            return mpf_pow_int(re, p, target_prec), None, target_prec, None
+        # (x*I)**n = I**n * x**n
+        if im and not re:
+            z = mpf_pow_int(im, p, target_prec)
+            case = p % 4
+            if case == 0:
+                return z, None, target_prec, None
+            if case == 1:
+                return None, z, None, target_prec
+            if case == 2:
+                return mpf_neg(z), None, target_prec, None
+            if case == 3:
+                return None, mpf_neg(z), None, target_prec
+        # Zero raised to an integer power
+        if not re:
+            if p < 0:
+                return S.ComplexInfinity
+            return None, None, None, None
+        # General complex number to arbitrary integer power
+        re, im = libmp.mpc_pow_int((re, im), p, prec)
+        # Assumes full accuracy in input
+        return finalize_complex(re, im, target_prec)
+
+    result = evalf(base, prec + 5, options)
+    if result is S.ComplexInfinity:
+        if exp.is_Rational:
+            if exp < 0:
+                return None, None, None, None
+            return result
+        raise NotImplementedError
+
+    # Pure square root
+    if exp is S.Half:
+        xre, xim, _, _ = result
+        # General complex square root
+        if xim:
+            re, im = libmp.mpc_sqrt((xre or fzero, xim), prec)
+            return finalize_complex(re, im, prec)
+        if not xre:
+            return None, None, None, None
+        # Square root of a negative real number
+        if mpf_lt(xre, fzero):
+            return None, mpf_sqrt(mpf_neg(xre), prec), None, prec
+        # Positive square root
+        return mpf_sqrt(xre, prec), None, prec, None
+
+    # We first evaluate the exponent to find its magnitude
+    # This determines the working precision that must be used
+    prec += 10
+    result = evalf(exp, prec, options)
+    if result is S.ComplexInfinity:
+        return fnan, None, prec, None
+    yre, yim, _, _ = result
+    # Special cases: x**0
+    if not (yre or yim):
+        return fone, None, prec, None
+
+    ysize = fastlog(yre)
+    # Restart if too big
+    # XXX: prec + ysize might exceed maxprec
+    if ysize > 5:
+        prec += ysize
+        yre, yim, _, _ = evalf(exp, prec, options)
+
+    # Pure exponential function; no need to evalf the base
+    if base is S.Exp1:
+        if yim:
+            re, im = libmp.mpc_exp((yre or fzero, yim), prec)
+            return finalize_complex(re, im, target_prec)
+        return mpf_exp(yre, target_prec), None, target_prec, None
+
+    xre, xim, _, _ = evalf(base, prec + 5, options)
+    # 0**y
+    if not (xre or xim):
+        if yim:
+            return fnan, None, prec, None
+        if yre[0] == 1:  # y < 0
+            return S.ComplexInfinity
+        return None, None, None, None
+
+    # (real ** complex) or (complex ** complex)
+    if yim:
+        re, im = libmp.mpc_pow(
+            (xre or fzero, xim or fzero), (yre or fzero, yim),
+            target_prec)
+        return finalize_complex(re, im, target_prec)
+    # complex ** real
+    if xim:
+        re, im = libmp.mpc_pow_mpf((xre or fzero, xim), yre, target_prec)
+        return finalize_complex(re, im, target_prec)
+    # negative ** real
+    elif mpf_lt(xre, fzero):
+        re, im = libmp.mpc_pow_mpf((xre, fzero), yre, target_prec)
+        return finalize_complex(re, im, target_prec)
+    # positive ** real
+    else:
+        return mpf_pow(xre, yre, target_prec), None, target_prec, None
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            Special functions                               #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+def evalf_exp(expr: 'exp', prec: int, options: OPT_DICT) -> TMP_RES:
+    from .power import Pow
+    return evalf_pow(Pow(S.Exp1, expr.exp, evaluate=False), prec, options)
+
+
+def evalf_trig(v: Expr, prec: int, options: OPT_DICT) -> TMP_RES:
+    """
+    This function handles sin , cos and tan of complex arguments.
+
+    """
+    from sympy.functions.elementary.trigonometric import cos, sin, tan
+    if isinstance(v, cos):
+        func = mpf_cos
+    elif isinstance(v, sin):
+        func = mpf_sin
+    elif isinstance(v,tan):
+        func = mpf_tan
+    else:
+        raise NotImplementedError
+    arg = v.args[0]
+    # 20 extra bits is possibly overkill. It does make the need
+    # to restart very unlikely
+    xprec = prec + 20
+    re, im, re_acc, im_acc = evalf(arg, xprec, options)
+    if im:
+        if 'subs' in options:
+            v = v.subs(options['subs'])
+        return evalf(v._eval_evalf(prec), prec, options)
+    if not re:
+        if isinstance(v, cos):
+            return fone, None, prec, None
+        elif isinstance(v, sin):
+            return None, None, None, None
+        elif isinstance(v,tan):
+            return None, None, None, None
+        else:
+            raise NotImplementedError
+    # For trigonometric functions, we are interested in the
+    # fixed-point (absolute) accuracy of the argument.
+    xsize = fastlog(re)
+    # Magnitude <= 1.0. OK to compute directly, because there is no
+    # danger of hitting the first root of cos (with sin, magnitude
+    # <= 2.0 would actually be ok)
+    if xsize < 1:
+        return func(re, prec, rnd), None, prec, None
+    # Very large
+    if xsize >= 10:
+        xprec = prec + xsize
+        re, im, re_acc, im_acc = evalf(arg, xprec, options)
+    # Need to repeat in case the argument is very close to a
+    # multiple of pi (or pi/2), hitting close to a root
+    while 1:
+        y = func(re, prec, rnd)
+        ysize = fastlog(y)
+        gap = -ysize
+        accuracy = (xprec - xsize) - gap
+        if accuracy < prec:
+            if options.get('verbose'):
+                print("SIN/COS/TAN", accuracy, "wanted", prec, "gap", gap)
+                print(to_str(y, 10))
+            if xprec > options.get('maxprec', DEFAULT_MAXPREC):
+                return y, None, accuracy, None
+            xprec += gap
+            re, im, re_acc, im_acc = evalf(arg, xprec, options)
+            continue
+        else:
+            return y, None, prec, None
+
+
+def evalf_log(expr: 'log', prec: int, options: OPT_DICT) -> TMP_RES:
+    if len(expr.args)>1:
+        expr = expr.doit()
+        return evalf(expr, prec, options)
+    arg = expr.args[0]
+    workprec = prec + 10
+    result = evalf(arg, workprec, options)
+    if result is S.ComplexInfinity:
+        return result
+    xre, xim, xacc, _ = result
+
+    # evalf can return NoneTypes if chop=True
+    # issue 18516, 19623
+    if xre is xim is None:
+        # Dear reviewer, I do not know what -inf is;
+        # it looks to be (1, 0, -789, -3)
+        # but I'm not sure in general,
+        # so we just let mpmath figure
+        # it out by taking log of 0 directly.
+        # It would be better to return -inf instead.
+        xre = fzero
+
+    if xim:
+        from sympy.functions.elementary.complexes import Abs
+        from sympy.functions.elementary.exponential import log
+
+        # XXX: use get_abs etc instead
+        re = evalf_log(
+            log(Abs(arg, evaluate=False), evaluate=False), prec, options)
+        im = mpf_atan2(xim, xre or fzero, prec)
+        return re[0], im, re[2], prec
+
+    imaginary_term = (mpf_cmp(xre, fzero) < 0)
+
+    re = mpf_log(mpf_abs(xre), prec, rnd)
+    size = fastlog(re)
+    if prec - size > workprec and re != fzero:
+        from .add import Add
+        # We actually need to compute 1+x accurately, not x
+        add = Add(S.NegativeOne, arg, evaluate=False)
+        xre, xim, _, _ = evalf_add(add, prec, options)
+        prec2 = workprec - fastlog(xre)
+        # xre is now x - 1 so we add 1 back here to calculate x
+        re = mpf_log(mpf_abs(mpf_add(xre, fone, prec2)), prec, rnd)
+
+    re_acc = prec
+
+    if imaginary_term:
+        return re, mpf_pi(prec), re_acc, prec
+    else:
+        return re, None, re_acc, None
+
+
+def evalf_atan(v: 'atan', prec: int, options: OPT_DICT) -> TMP_RES:
+    arg = v.args[0]
+    xre, xim, reacc, imacc = evalf(arg, prec + 5, options)
+    if xre is xim is None:
+        return (None,)*4
+    if xim:
+        raise NotImplementedError
+    return mpf_atan(xre, prec, rnd), None, prec, None
+
+
+def evalf_subs(prec: int, subs: dict) -> dict:
+    """ Change all Float entries in `subs` to have precision prec. """
+    newsubs = {}
+    for a, b in subs.items():
+        b = S(b)
+        if b.is_Float:
+            b = b._eval_evalf(prec)
+        newsubs[a] = b
+    return newsubs
+
+
+def evalf_piecewise(expr: Expr, prec: int, options: OPT_DICT) -> TMP_RES:
+    from .numbers import Float, Integer
+    if 'subs' in options:
+        expr = expr.subs(evalf_subs(prec, options['subs']))
+        newopts = options.copy()
+        del newopts['subs']
+        if hasattr(expr, 'func'):
+            return evalf(expr, prec, newopts)
+        if isinstance(expr, float):
+            return evalf(Float(expr), prec, newopts)
+        if isinstance(expr, int):
+            return evalf(Integer(expr), prec, newopts)
+
+    # We still have undefined symbols
+    raise NotImplementedError
+
+
+def evalf_alg_num(a: 'AlgebraicNumber', prec: int, options: OPT_DICT) -> TMP_RES:
+    return evalf(a.to_root(), prec, options)
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            High-level operations                           #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+def as_mpmath(x: Any, prec: int, options: OPT_DICT) -> mpc | mpf:
+    from .numbers import Infinity, NegativeInfinity, Zero
+    x = sympify(x)
+    if isinstance(x, Zero) or x == 0.0:
+        return mpf(0)
+    if isinstance(x, Infinity):
+        return mpf('inf')
+    if isinstance(x, NegativeInfinity):
+        return mpf('-inf')
+    # XXX
+    result = evalf(x, prec, options)
+    return quad_to_mpmath(result)
+
+
+def do_integral(expr: 'Integral', prec: int, options: OPT_DICT) -> TMP_RES:
+    func = expr.args[0]
+    x, xlow, xhigh = expr.args[1]
+    if xlow == xhigh:
+        xlow = xhigh = 0
+    elif x not in func.free_symbols:
+        # only the difference in limits matters in this case
+        # so if there is a symbol in common that will cancel
+        # out when taking the difference, then use that
+        # difference
+        if xhigh.free_symbols & xlow.free_symbols:
+            diff = xhigh - xlow
+            if diff.is_number:
+                xlow, xhigh = 0, diff
+
+    oldmaxprec = options.get('maxprec', DEFAULT_MAXPREC)
+    options['maxprec'] = min(oldmaxprec, 2*prec)
+
+    with workprec(prec + 5):
+        xlow = as_mpmath(xlow, prec + 15, options)
+        xhigh = as_mpmath(xhigh, prec + 15, options)
+
+        # Integration is like summation, and we can phone home from
+        # the integrand function to update accuracy summation style
+        # Note that this accuracy is inaccurate, since it fails
+        # to account for the variable quadrature weights,
+        # but it is better than nothing
+
+        from sympy.functions.elementary.trigonometric import cos, sin
+        from .symbol import Wild
+
+        have_part = [False, False]
+        max_real_term: float | int = MINUS_INF
+        max_imag_term: float | int = MINUS_INF
+
+        def f(t: Expr) -> mpc | mpf:
+            nonlocal max_real_term, max_imag_term
+            re, im, re_acc, im_acc = evalf(func, mp.prec, {'subs': {x: t}})
+
+            have_part[0] = re or have_part[0]
+            have_part[1] = im or have_part[1]
+
+            max_real_term = max(max_real_term, fastlog(re))
+            max_imag_term = max(max_imag_term, fastlog(im))
+
+            if im:
+                return mpc(re or fzero, im)
+            return mpf(re or fzero)
+
+        if options.get('quad') == 'osc':
+            A = Wild('A', exclude=[x])
+            B = Wild('B', exclude=[x])
+            D = Wild('D')
+            m = func.match(cos(A*x + B)*D)
+            if not m:
+                m = func.match(sin(A*x + B)*D)
+            if not m:
+                raise ValueError("An integrand of the form sin(A*x+B)*f(x) "
+                  "or cos(A*x+B)*f(x) is required for oscillatory quadrature")
+            period = as_mpmath(2*S.Pi/m[A], prec + 15, options)
+            result = quadosc(f, [xlow, xhigh], period=period)
+            # XXX: quadosc does not do error detection yet
+            quadrature_error = MINUS_INF
+        else:
+            result, quadrature_err = quadts(f, [xlow, xhigh], error=1)
+            quadrature_error = fastlog(quadrature_err._mpf_)
+
+    options['maxprec'] = oldmaxprec
+
+    if have_part[0]:
+        re: MPF_TUP | None = result.real._mpf_
+        re_acc: int | None
+        if re == fzero:
+            re_s, re_acc = scaled_zero(int(-max(prec, max_real_term, quadrature_error)))
+            re = scaled_zero(re_s)  # handled ok in evalf_integral
+        else:
+            re_acc = int(-max(max_real_term - fastlog(re) - prec, quadrature_error))
+    else:
+        re, re_acc = None, None
+
+    if have_part[1]:
+        im: MPF_TUP | None = result.imag._mpf_
+        im_acc: int | None
+        if im == fzero:
+            im_s, im_acc = scaled_zero(int(-max(prec, max_imag_term, quadrature_error)))
+            im = scaled_zero(im_s)  # handled ok in evalf_integral
+        else:
+            im_acc = int(-max(max_imag_term - fastlog(im) - prec, quadrature_error))
+    else:
+        im, im_acc = None, None
+
+    result = re, im, re_acc, im_acc
+    return result
+
+
+def evalf_integral(expr: 'Integral', prec: int, options: OPT_DICT) -> TMP_RES:
+    limits = expr.limits
+    if len(limits) != 1 or len(limits[0]) != 3:
+        raise NotImplementedError
+    workprec = prec
+    i = 0
+    maxprec = options.get('maxprec', INF)
+    while 1:
+        result = do_integral(expr, workprec, options)
+        accuracy = complex_accuracy(result)
+        if accuracy >= prec:  # achieved desired precision
+            break
+        if workprec >= maxprec:  # can't increase accuracy any more
+            break
+        if accuracy == -1:
+            # maybe the answer really is zero and maybe we just haven't increased
+            # the precision enough. So increase by doubling to not take too long
+            # to get to maxprec.
+            workprec *= 2
+        else:
+            workprec += max(prec, 2**i)
+        workprec = min(workprec, maxprec)
+        i += 1
+    return result
+
+
+def check_convergence(numer: Expr, denom: Expr, n: Symbol) -> tuple[int, Any, Any]:
+    """
+    Returns
+    =======
+
+    (h, g, p) where
+    -- h is:
+        > 0 for convergence of rate 1/factorial(n)**h
+        < 0 for divergence of rate factorial(n)**(-h)
+        = 0 for geometric or polynomial convergence or divergence
+
+    -- abs(g) is:
+        > 1 for geometric convergence of rate 1/h**n
+        < 1 for geometric divergence of rate h**n
+        = 1 for polynomial convergence or divergence
+
+        (g < 0 indicates an alternating series)
+
+    -- p is:
+        > 1 for polynomial convergence of rate 1/n**h
+        <= 1 for polynomial divergence of rate n**(-h)
+
+    """
+    from sympy.polys.polytools import Poly
+    npol = Poly(numer, n)
+    dpol = Poly(denom, n)
+    p = npol.degree()
+    q = dpol.degree()
+    rate = q - p
+    if rate:
+        return rate, None, None
+    constant = dpol.LC() / npol.LC()
+    from .numbers import equal_valued
+    if not equal_valued(abs(constant), 1):
+        return rate, constant, None
+    if npol.degree() == dpol.degree() == 0:
+        return rate, constant, 0
+    pc = npol.all_coeffs()[1]
+    qc = dpol.all_coeffs()[1]
+    return rate, constant, (qc - pc)/dpol.LC()
+
+
+def hypsum(expr: Expr, n: Symbol, start: int, prec: int) -> mpf:
+    """
+    Sum a rapidly convergent infinite hypergeometric series with
+    given general term, e.g. e = hypsum(1/factorial(n), n). The
+    quotient between successive terms must be a quotient of integer
+    polynomials.
+    """
+    from .numbers import Float, equal_valued
+    from sympy.simplify.simplify import hypersimp
+
+    if prec == float('inf'):
+        raise NotImplementedError('does not support inf prec')
+
+    if start:
+        expr = expr.subs(n, n + start)
+    hs = hypersimp(expr, n)
+    if hs is None:
+        raise NotImplementedError("a hypergeometric series is required")
+    num, den = hs.as_numer_denom()
+
+    func1 = lambdify(n, num)
+    func2 = lambdify(n, den)
+
+    h, g, p = check_convergence(num, den, n)
+
+    if h < 0:
+        raise ValueError("Sum diverges like (n!)^%i" % (-h))
+
+    eterm = expr.subs(n, 0)
+    if not eterm.is_Rational:
+        raise NotImplementedError("Non rational term functionality is not implemented.")
+
+    term: Rational = eterm # type: ignore
+
+    # Direct summation if geometric or faster
+    if h > 0 or (h == 0 and abs(g) > 1):
+        term = (MPZ(term.p) << prec) // term.q
+        s = term
+        k = 1
+        while abs(term) > 5:
+            term *= MPZ(func1(k - 1))
+            term //= MPZ(func2(k - 1))
+            s += term
+            k += 1
+        return from_man_exp(s, -prec)
+    else:
+        alt = g < 0
+        if abs(g) < 1:
+            raise ValueError("Sum diverges like (%i)^n" % abs(1/g))
+        if p < 1 or (equal_valued(p, 1) and not alt):
+            raise ValueError("Sum diverges like n^%i" % (-p))
+        # We have polynomial convergence: use Richardson extrapolation
+        vold = None
+        ndig = prec_to_dps(prec)
+        while True:
+            # Need to use at least quad precision because a lot of cancellation
+            # might occur in the extrapolation process; we check the answer to
+            # make sure that the desired precision has been reached, too.
+            prec2 = 4*prec
+            term0 = (MPZ(term.p) << prec2) // term.q
+
+            def summand(k, _term=[term0]):
+                if k:
+                    k = int(k)
+                    _term[0] *= MPZ(func1(k - 1))
+                    _term[0] //= MPZ(func2(k - 1))
+                return make_mpf(from_man_exp(_term[0], -prec2))
+
+            with workprec(prec):
+                v = nsum(summand, [0, mpmath_inf], method='richardson')
+            vf = Float(v, ndig)
+            if vold is not None and vold == vf:
+                break
+            prec += prec  # double precision each time
+            vold = vf
+
+        return v._mpf_
+
+
+def evalf_prod(expr: 'Product', prec: int, options: OPT_DICT) -> TMP_RES:
+    if all((l[1] - l[2]).is_Integer for l in expr.limits):
+        result = evalf(expr.doit(), prec=prec, options=options)
+    else:
+        from sympy.concrete.summations import Sum
+        result = evalf(expr.rewrite(Sum), prec=prec, options=options)
+    return result
+
+
+def evalf_sum(expr: 'Sum', prec: int, options: OPT_DICT) -> TMP_RES:
+    from .numbers import Float
+    if 'subs' in options:
+        expr = expr.subs(options['subs']) # type: ignore
+    func = expr.function
+    limits = expr.limits
+    if len(limits) != 1 or len(limits[0]) != 3:
+        raise NotImplementedError
+    if func.is_zero:
+        return None, None, prec, None
+    prec2 = prec + 10
+    try:
+        n, a, b = limits[0]
+        if b is not S.Infinity or a is S.NegativeInfinity or a != int(a):
+            raise NotImplementedError
+        # Use fast hypergeometric summation if possible
+        v = hypsum(func, n, int(a), prec2)
+        delta = prec - fastlog(v)
+        if fastlog(v) < -10:
+            v = hypsum(func, n, int(a), delta)
+        return v, None, min(prec, delta), None
+    except NotImplementedError:
+        # Euler-Maclaurin summation for general series
+        eps = Float(2.0)**(-prec)
+        for i in range(1, 5):
+            m = n = 2**i * prec
+            s, err = expr.euler_maclaurin(m=m, n=n, eps=eps,
+                eval_integral=False)
+            err = err.evalf()
+            if err is S.NaN:
+                raise NotImplementedError
+            if err <= eps:
+                break
+        err = fastlog(evalf(abs(err), 20, options)[0])
+        re, im, re_acc, im_acc = evalf(s, prec2, options)
+        if re_acc is None:
+            re_acc = -err
+        if im_acc is None:
+            im_acc = -err
+        return re, im, re_acc, im_acc
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            Symbolic interface                              #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def evalf_symbol(x: Expr, prec: int, options: OPT_DICT) -> TMP_RES:
+    val = options['subs'][x]
+    if isinstance(val, mpf):
+        if not val:
+            return None, None, None, None
+        return val._mpf_, None, prec, None
+    else:
+        if '_cache' not in options:
+            options['_cache'] = {}
+        cache = options['_cache']
+        cached, cached_prec = cache.get(x, (None, MINUS_INF))
+        if cached_prec >= prec:
+            return cached
+        v = evalf(sympify(val), prec, options)
+        cache[x] = (v, prec)
+        return v
+
+evalf_table: dict[Type[Expr], Callable[[Expr, int, OPT_DICT], TMP_RES]] = {}
+
+
+def _create_evalf_table():
+    global evalf_table
+    from sympy.concrete.products import Product
+    from sympy.concrete.summations import Sum
+    from .add import Add
+    from .mul import Mul
+    from .numbers import Exp1, Float, Half, ImaginaryUnit, Integer, NaN, NegativeOne, One, Pi, Rational, \
+        Zero, ComplexInfinity, AlgebraicNumber
+    from .power import Pow
+    from .symbol import Dummy, Symbol
+    from sympy.functions.elementary.complexes import Abs, im, re
+    from sympy.functions.elementary.exponential import exp, log
+    from sympy.functions.elementary.integers import ceiling, floor
+    from sympy.functions.elementary.piecewise import Piecewise
+    from sympy.functions.elementary.trigonometric import atan, cos, sin, tan
+    from sympy.integrals.integrals import Integral
+    evalf_table = {
+        Symbol: evalf_symbol,
+        Dummy: evalf_symbol,
+        Float: evalf_float,
+        Rational: evalf_rational,
+        Integer: evalf_integer,
+        Zero: lambda x, prec, options: (None, None, prec, None),
+        One: lambda x, prec, options: (fone, None, prec, None),
+        Half: lambda x, prec, options: (fhalf, None, prec, None),
+        Pi: lambda x, prec, options: (mpf_pi(prec), None, prec, None),
+        Exp1: lambda x, prec, options: (mpf_e(prec), None, prec, None),
+        ImaginaryUnit: lambda x, prec, options: (None, fone, None, prec),
+        NegativeOne: lambda x, prec, options: (fnone, None, prec, None),
+        ComplexInfinity: lambda x, prec, options: S.ComplexInfinity,
+        NaN: lambda x, prec, options: (fnan, None, prec, None),
+
+        exp: evalf_exp,
+
+        cos: evalf_trig,
+        sin: evalf_trig,
+        tan: evalf_trig,
+
+        Add: evalf_add,
+        Mul: evalf_mul,
+        Pow: evalf_pow,
+
+        log: evalf_log,
+        atan: evalf_atan,
+        Abs: evalf_abs,
+
+        re: evalf_re,
+        im: evalf_im,
+        floor: evalf_floor,
+        ceiling: evalf_ceiling,
+
+        Integral: evalf_integral,
+        Sum: evalf_sum,
+        Product: evalf_prod,
+        Piecewise: evalf_piecewise,
+
+        AlgebraicNumber: evalf_alg_num,
+    }
+
+
+def evalf(x: Expr, prec: int, options: OPT_DICT) -> TMP_RES:
+    """
+    Evaluate the ``Expr`` instance, ``x``
+    to a binary precision of ``prec``. This
+    function is supposed to be used internally.
+
+    Parameters
+    ==========
+
+    x : Expr
+        The formula to evaluate to a float.
+    prec : int
+        The binary precision that the output should have.
+    options : dict
+        A dictionary with the same entries as
+        ``EvalfMixin.evalf`` and in addition,
+        ``maxprec`` which is the maximum working precision.
+
+    Returns
+    =======
+
+    An optional tuple, ``(re, im, re_acc, im_acc)``
+    which are the real, imaginary, real accuracy
+    and imaginary accuracy respectively. ``re`` is
+    an mpf value tuple and so is ``im``. ``re_acc``
+    and ``im_acc`` are ints.
+
+    NB: all these return values can be ``None``.
+    If all values are ``None``, then that represents 0.
+    Note that 0 is also represented as ``fzero = (0, 0, 0, 0)``.
+    """
+    from sympy.functions.elementary.complexes import re as re_, im as im_
+    try:
+        rf = evalf_table[type(x)]
+        r = rf(x, prec, options)
+    except KeyError:
+        # Fall back to ordinary evalf if possible
+        if 'subs' in options:
+            x = x.subs(evalf_subs(prec, options['subs']))
+        xe = x._eval_evalf(prec)
+        if xe is None:
+            raise NotImplementedError
+        as_real_imag = getattr(xe, "as_real_imag", None)
+        if as_real_imag is None:
+            raise NotImplementedError # e.g. FiniteSet(-1.0, 1.0).evalf()
+        re, im = as_real_imag()
+        if re.has(re_) or im.has(im_):
+            raise NotImplementedError
+        if not re:
+            re = None
+            reprec = None
+        elif re.is_number:
+            re = re._to_mpmath(prec, allow_ints=False)._mpf_
+            reprec = prec
+        else:
+            raise NotImplementedError
+        if not im:
+            im = None
+            imprec = None
+        elif im.is_number:
+            im = im._to_mpmath(prec, allow_ints=False)._mpf_
+            imprec = prec
+        else:
+            raise NotImplementedError
+        r = re, im, reprec, imprec
+
+    if options.get("verbose"):
+        print("### input", x)
+        print("### output", to_str(r[0] or fzero, 50) if isinstance(r, tuple) else r)
+        print("### raw", r) # r[0], r[2]
+        print()
+    chop = options.get('chop', False)
+    if chop:
+        if chop is True:
+            chop_prec = prec
+        else:
+            # convert (approximately) from given tolerance;
+            # the formula here will will make 1e-i rounds to 0 for
+            # i in the range +/-27 while 2e-i will not be chopped
+            chop_prec = int(round(-3.321*math.log10(chop) + 2.5))
+            if chop_prec == 3:
+                chop_prec -= 1
+        r = chop_parts(r, chop_prec)
+    if options.get("strict"):
+        check_target(x, r, prec)
+    return r
+
+
+def quad_to_mpmath(q, ctx=None):
+    """Turn the quad returned by ``evalf`` into an ``mpf`` or ``mpc``. """
+    mpc = make_mpc if ctx is None else ctx.make_mpc
+    mpf = make_mpf if ctx is None else ctx.make_mpf
+    if q is S.ComplexInfinity:
+        raise NotImplementedError
+    re, im, _, _ = q
+    if im:
+        if not re:
+            re = fzero
+        return mpc((re, im))
+    elif re:
+        return mpf(re)
+    else:
+        return mpf(fzero)
+
+
+class EvalfMixin:
+    """Mixin class adding evalf capability."""
+
+    __slots__: tuple[str, ...] = ()
+
+    def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False):
+        """
+        Evaluate the given formula to an accuracy of *n* digits.
+
+        Parameters
+        ==========
+
+        subs : dict, optional
+            Substitute numerical values for symbols, e.g.
+            ``subs={x:3, y:1+pi}``. The substitutions must be given as a
+            dictionary.
+
+        maxn : int, optional
+            Allow a maximum temporary working precision of maxn digits.
+
+        chop : bool or number, optional
+            Specifies how to replace tiny real or imaginary parts in
+            subresults by exact zeros.
+
+            When ``True`` the chop value defaults to standard precision.
+
+            Otherwise the chop value is used to determine the
+            magnitude of "small" for purposes of chopping.
+
+            >>> from sympy import N
+            >>> x = 1e-4
+            >>> N(x, chop=True)
+            0.000100000000000000
+            >>> N(x, chop=1e-5)
+            0.000100000000000000
+            >>> N(x, chop=1e-4)
+            0
+
+        strict : bool, optional
+            Raise ``PrecisionExhausted`` if any subresult fails to
+            evaluate to full accuracy, given the available maxprec.
+
+        quad : str, optional
+            Choose algorithm for numerical quadrature. By default,
+            tanh-sinh quadrature is used. For oscillatory
+            integrals on an infinite interval, try ``quad='osc'``.
+
+        verbose : bool, optional
+            Print debug information.
+
+        Notes
+        =====
+
+        When Floats are naively substituted into an expression,
+        precision errors may adversely affect the result. For example,
+        adding 1e16 (a Float) to 1 will truncate to 1e16; if 1e16 is
+        then subtracted, the result will be 0.
+        That is exactly what happens in the following:
+
+        >>> from sympy.abc import x, y, z
+        >>> values = {x: 1e16, y: 1, z: 1e16}
+        >>> (x + y - z).subs(values)
+        0
+
+        Using the subs argument for evalf is the accurate way to
+        evaluate such an expression:
+
+        >>> (x + y - z).evalf(subs=values)
+        1.00000000000000
+        """
+        from .numbers import Float, Number
+        n = n if n is not None else 15
+
+        if subs and is_sequence(subs):
+            raise TypeError('subs must be given as a dictionary')
+
+        # for sake of sage that doesn't like evalf(1)
+        if n == 1 and isinstance(self, Number):
+            from .expr import _mag
+            rv = self.evalf(2, subs, maxn, chop, strict, quad, verbose)
+            m = _mag(rv)
+            rv = rv.round(1 - m)
+            return rv
+
+        if not evalf_table:
+            _create_evalf_table()
+        prec = dps_to_prec(n)
+        options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,
+               'strict': strict, 'verbose': verbose}
+        if subs is not None:
+            options['subs'] = subs
+        if quad is not None:
+            options['quad'] = quad
+        try:
+            result = evalf(self, prec + 4, options)
+        except NotImplementedError:
+            # Fall back to the ordinary evalf
+            if hasattr(self, 'subs') and subs is not None:  # issue 20291
+                v = self.subs(subs)._eval_evalf(prec)
+            else:
+                v = self._eval_evalf(prec)
+            if v is None:
+                return self
+            elif not v.is_number:
+                return v
+            try:
+                # If the result is numerical, normalize it
+                result = evalf(v, prec, options)
+            except NotImplementedError:
+                # Probably contains symbols or unknown functions
+                return v
+        if result is S.ComplexInfinity:
+            return result
+        re, im, re_acc, im_acc = result
+        if re is S.NaN or im is S.NaN:
+            return S.NaN
+        if re:
+            p = max(min(prec, re_acc), 1)
+            re = Float._new(re, p)
+        else:
+            re = S.Zero
+        if im:
+            p = max(min(prec, im_acc), 1)
+            im = Float._new(im, p)
+            return re + im*S.ImaginaryUnit
+        else:
+            return re
+
+    n = evalf
+
+    def _evalf(self, prec: int) -> Expr:
+        """Helper for evalf. Does the same thing but takes binary precision"""
+        r = self._eval_evalf(prec)
+        if r is None:
+            r = self # type: ignore
+        return r # type: ignore
+
+    def _eval_evalf(self, prec: int) -> Expr | None:
+        return None
+
+    def _to_mpmath(self, prec, allow_ints=True):
+        # mpmath functions accept ints as input
+        errmsg = "cannot convert to mpmath number"
+        if allow_ints and self.is_Integer:
+            return self.p
+        if hasattr(self, '_as_mpf_val'):
+            return make_mpf(self._as_mpf_val(prec))
+        try:
+            result = evalf(self, prec, {})
+            return quad_to_mpmath(result)
+        except NotImplementedError:
+            v = self._eval_evalf(prec)
+            if v is None:
+                raise ValueError(errmsg)
+            if v.is_Float:
+                return make_mpf(v._mpf_)
+            # Number + Number*I is also fine
+            re, im = v.as_real_imag()
+            if allow_ints and re.is_Integer:
+                re = from_int(re.p)
+            elif re.is_Float:
+                re = re._mpf_
+            else:
+                raise ValueError(errmsg)
+            if allow_ints and im.is_Integer:
+                im = from_int(im.p)
+            elif im.is_Float:
+                im = im._mpf_
+            else:
+                raise ValueError(errmsg)
+            return make_mpc((re, im))
+
+
+def N(x, n=15, **options):
+    r"""
+    Calls x.evalf(n, \*\*options).
+
+    Explanations
+    ============
+
+    Both .n() and N() are equivalent to .evalf(); use the one that you like better.
+    See also the docstring of .evalf() for information on the options.
+
+    Examples
+    ========
+
+    >>> from sympy import Sum, oo, N
+    >>> from sympy.abc import k
+    >>> Sum(1/k**k, (k, 1, oo))
+    Sum(k**(-k), (k, 1, oo))
+    >>> N(_, 4)
+    1.291
+
+    """
+    # by using rational=True, any evaluation of a string
+    # will be done using exact values for the Floats
+    return sympify(x, rational=True).evalf(n, **options)
+
+
+def _evalf_with_bounded_error(x: Expr, eps: Expr | None = None,
+                              m: int = 0,
+                              options: OPT_DICT | None = None) -> TMP_RES:
+    """
+    Evaluate *x* to within a bounded absolute error.
+
+    Parameters
+    ==========
+
+    x : Expr
+        The quantity to be evaluated.
+    eps : Expr, None, optional (default=None)
+        Positive real upper bound on the acceptable error.
+    m : int, optional (default=0)
+        If *eps* is None, then use 2**(-m) as the upper bound on the error.
+    options: OPT_DICT
+        As in the ``evalf`` function.
+
+    Returns
+    =======
+
+    A tuple ``(re, im, re_acc, im_acc)``, as returned by ``evalf``.
+
+    See Also
+    ========
+
+    evalf
+
+    """
+    if eps is not None:
+        if not (eps.is_Rational or eps.is_Float) or not eps > 0:
+            raise ValueError("eps must be positive")
+        r, _, _, _ = evalf(1/eps, 1, {})
+        m = fastlog(r)
+
+    c, d, _, _ = evalf(x, 1, {})
+    # Note: If x = a + b*I, then |a| <= 2|c| and |b| <= 2|d|, with equality
+    # only in the zero case.
+    # If a is non-zero, then |c| = 2**nc for some integer nc, and c has
+    # bitcount 1. Therefore 2**fastlog(c) = 2**(nc+1) = 2|c| is an upper bound
+    # on |a|. Likewise for b and d.
+    nr, ni = fastlog(c), fastlog(d)
+    n = max(nr, ni) + 1
+    # If x is 0, then n is MINUS_INF, and p will be 1. Otherwise,
+    # n - 1 bits get us past the integer parts of a and b, and +1 accounts for
+    # the factor of <= sqrt(2) that is |x|/max(|a|, |b|).
+    p = max(1, m + n + 1)
+
+    options = options or {}
+    return evalf(x, p, options)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/expr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/expr.py
new file mode 100644
index 0000000000000000000000000000000000000000..e66ff239a679942f2cc95c3f66af1fc13f7229d9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/expr.py
@@ -0,0 +1,4194 @@
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, overload
+from collections.abc import Iterable, Mapping
+from functools import reduce
+import re
+
+from .sympify import sympify, _sympify
+from .basic import Basic, Atom
+from .singleton import S
+from .evalf import EvalfMixin, pure_complex, DEFAULT_MAXPREC
+from .decorators import call_highest_priority, sympify_method_args, sympify_return
+from .cache import cacheit
+from .logic import fuzzy_or, fuzzy_not
+from .intfunc import mod_inverse
+from .sorting import default_sort_key
+from .kind import NumberKind
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.misc import as_int, func_name, filldedent
+from sympy.utilities.iterables import has_variety, sift
+from mpmath.libmp import mpf_log, prec_to_dps
+from mpmath.libmp.libintmath import giant_steps
+
+
+if TYPE_CHECKING:
+    from typing import Any
+    from typing_extensions import Self
+    from .numbers import Number
+
+from collections import defaultdict
+
+
+def _corem(eq, c):  # helper for extract_additively
+    # return co, diff from co*c + diff
+    co = []
+    non = []
+    for i in Add.make_args(eq):
+        ci = i.coeff(c)
+        if not ci:
+            non.append(i)
+        else:
+            co.append(ci)
+    return Add(*co), Add(*non)
+
+
+@sympify_method_args
+class Expr(Basic, EvalfMixin):
+    """
+    Base class for algebraic expressions.
+
+    Explanation
+    ===========
+
+    Everything that requires arithmetic operations to be defined
+    should subclass this class, instead of Basic (which should be
+    used only for argument storage and expression manipulation, i.e.
+    pattern matching, substitutions, etc).
+
+    If you want to override the comparisons of expressions:
+    Should use _eval_is_ge for inequality, or _eval_is_eq, with multiple dispatch.
+    _eval_is_ge return true if x >= y, false if x < y, and None if the two types
+    are not comparable or the comparison is indeterminate
+
+    See Also
+    ========
+
+    sympy.core.basic.Basic
+    """
+
+    __slots__: tuple[str, ...] = ()
+
+    if TYPE_CHECKING:
+
+        def __new__(cls, *args: Basic) -> Self:
+            ...
+
+        @overload # type: ignore
+        def subs(self, arg1: Mapping[Basic | complex, Expr | complex], arg2: None=None) -> Expr: ...
+        @overload
+        def subs(self, arg1: Iterable[tuple[Basic | complex, Expr | complex]], arg2: None=None, **kwargs: Any) -> Expr: ...
+        @overload
+        def subs(self, arg1: Expr | complex, arg2: Expr | complex) -> Expr: ...
+        @overload
+        def subs(self, arg1: Mapping[Basic | complex, Basic | complex], arg2: None=None, **kwargs: Any) -> Basic: ...
+        @overload
+        def subs(self, arg1: Iterable[tuple[Basic | complex, Basic | complex]], arg2: None=None, **kwargs: Any) -> Basic: ...
+        @overload
+        def subs(self, arg1: Basic | complex, arg2: Basic | complex, **kwargs: Any) -> Basic: ...
+
+        def subs(self, arg1: Mapping[Basic | complex, Basic | complex] | Basic | complex, # type: ignore
+                 arg2: Basic | complex | None = None, **kwargs: Any) -> Basic:
+            ...
+
+        def simplify(self, **kwargs) -> Expr:
+            ...
+
+        def evalf(self, n: int = 15, subs: dict[Basic, Basic | float] | None = None,
+                  maxn: int = 100, chop: bool = False, strict: bool  = False,
+                  quad: str | None = None, verbose: bool = False) -> Expr:
+            ...
+
+        n = evalf
+
+    is_scalar = True  # self derivative is 1
+
+    @property
+    def _diff_wrt(self):
+        """Return True if one can differentiate with respect to this
+        object, else False.
+
+        Explanation
+        ===========
+
+        Subclasses such as Symbol, Function and Derivative return True
+        to enable derivatives wrt them. The implementation in Derivative
+        separates the Symbol and non-Symbol (_diff_wrt=True) variables and
+        temporarily converts the non-Symbols into Symbols when performing
+        the differentiation. By default, any object deriving from Expr
+        will behave like a scalar with self.diff(self) == 1. If this is
+        not desired then the object must also set `is_scalar = False` or
+        else define an _eval_derivative routine.
+
+        Note, see the docstring of Derivative for how this should work
+        mathematically. In particular, note that expr.subs(yourclass, Symbol)
+        should be well-defined on a structural level, or this will lead to
+        inconsistent results.
+
+        Examples
+        ========
+
+        >>> from sympy import Expr
+        >>> e = Expr()
+        >>> e._diff_wrt
+        False
+        >>> class MyScalar(Expr):
+        ...     _diff_wrt = True
+        ...
+        >>> MyScalar().diff(MyScalar())
+        1
+        >>> class MySymbol(Expr):
+        ...     _diff_wrt = True
+        ...     is_scalar = False
+        ...
+        >>> MySymbol().diff(MySymbol())
+        Derivative(MySymbol(), MySymbol())
+        """
+        return False
+
+    @cacheit
+    def sort_key(self, order=None):
+
+        coeff, expr = self.as_coeff_Mul()
+
+        if expr.is_Pow:
+            base, exp = expr.as_base_exp()
+            if base is S.Exp1:
+                # If we remove this, many doctests will go crazy:
+                # (keeps E**x sorted like the exp(x) function,
+                #  part of exp(x) to E**x transition)
+                base, exp = Function("exp")(exp), S.One
+            expr = base
+        else:
+            exp = S.One
+
+        if expr.is_Dummy:
+            args = (expr.sort_key(),)
+        elif expr.is_Atom:
+            args = (str(expr),)
+        else:
+            if expr.is_Add:
+                args = expr.as_ordered_terms(order=order)
+            elif expr.is_Mul:
+                args = expr.as_ordered_factors(order=order)
+            else:
+                args = expr.args
+
+            args = tuple(
+                [ default_sort_key(arg, order=order) for arg in args ])
+
+        args = (len(args), tuple(args))
+        exp = exp.sort_key(order=order)
+
+        return expr.class_key(), args, exp, coeff
+
+    def _hashable_content(self):
+        """Return a tuple of information about self that can be used to
+        compute the hash. If a class defines additional attributes,
+        like ``name`` in Symbol, then this method should be updated
+        accordingly to return such relevant attributes.
+        Defining more than _hashable_content is necessary if __eq__ has
+        been defined by a class. See note about this in Basic.__eq__."""
+        return self._args
+
+    # ***************
+    # * Arithmetics *
+    # ***************
+    # Expr and its subclasses use _op_priority to determine which object
+    # passed to a binary special method (__mul__, etc.) will handle the
+    # operation. In general, the 'call_highest_priority' decorator will choose
+    # the object with the highest _op_priority to handle the call.
+    # Custom subclasses that want to define their own binary special methods
+    # should set an _op_priority value that is higher than the default.
+    #
+    # **NOTE**:
+    # This is a temporary fix, and will eventually be replaced with
+    # something better and more powerful.  See issue 5510.
+    _op_priority = 10.0
+
+    @property
+    def _add_handler(self):
+        return Add
+
+    @property
+    def _mul_handler(self):
+        return Mul
+
+    def __pos__(self) -> Expr:
+        return self
+
+    def __neg__(self) -> Expr:
+        # Mul has its own __neg__ routine, so we just
+        # create a 2-args Mul with the -1 in the canonical
+        # slot 0.
+        c = self.is_commutative
+        return Mul._from_args((S.NegativeOne, self), c)
+
+    def __abs__(self) -> Expr:
+        from sympy.functions.elementary.complexes import Abs
+        return Abs(self)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__radd__')
+    def __add__(self, other) -> Expr:
+        return Add(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__add__')
+    def __radd__(self, other) -> Expr:
+        return Add(other, self)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rsub__')
+    def __sub__(self, other) -> Expr:
+        return Add(self, -other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__sub__')
+    def __rsub__(self, other) -> Expr:
+        return Add(other, -self)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rmul__')
+    def __mul__(self, other) -> Expr:
+        return Mul(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__mul__')
+    def __rmul__(self, other) -> Expr:
+        return Mul(other, self)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rpow__')
+    def _pow(self, other):
+        return Pow(self, other)
+
+    def __pow__(self, other, mod=None) -> Expr:
+        if mod is None:
+            return self._pow(other)
+        try:
+            _self, other, mod = as_int(self), as_int(other), as_int(mod)
+            if other >= 0:
+                return _sympify(pow(_self, other, mod))
+            else:
+                return _sympify(mod_inverse(pow(_self, -other, mod), mod))
+        except ValueError:
+            power = self._pow(other)
+            try:
+                return power%mod
+            except TypeError:
+                return NotImplemented
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__pow__')
+    def __rpow__(self, other) -> Expr:
+        return Pow(other, self)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rtruediv__')
+    def __truediv__(self, other) -> Expr:
+        denom = Pow(other, S.NegativeOne)
+        if self is S.One:
+            return denom
+        else:
+            return Mul(self, denom)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__truediv__')
+    def __rtruediv__(self, other) -> Expr:
+        denom = Pow(self, S.NegativeOne)
+        if other is S.One:
+            return denom
+        else:
+            return Mul(other, denom)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rmod__')
+    def __mod__(self, other) -> Expr:
+        return Mod(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__mod__')
+    def __rmod__(self, other) -> Expr:
+        return Mod(other, self)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rfloordiv__')
+    def __floordiv__(self, other) -> Expr:
+        from sympy.functions.elementary.integers import floor
+        return floor(self / other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__floordiv__')
+    def __rfloordiv__(self, other) -> Expr:
+        from sympy.functions.elementary.integers import floor
+        return floor(other / self)
+
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__rdivmod__')
+    def __divmod__(self, other) -> tuple[Expr, Expr]:
+        from sympy.functions.elementary.integers import floor
+        return floor(self / other), Mod(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    @call_highest_priority('__divmod__')
+    def __rdivmod__(self, other) -> tuple[Expr, Expr]:
+        from sympy.functions.elementary.integers import floor
+        return floor(other / self), Mod(other, self)
+
+    def __int__(self) -> int:
+        if not self.is_number:
+            raise TypeError("Cannot convert symbols to int")
+        r = self.round(2)
+        if not r.is_Number:
+            raise TypeError("Cannot convert complex to int")
+        if r in (S.NaN, S.Infinity, S.NegativeInfinity):
+            raise TypeError("Cannot convert %s to int" % r)
+        i = int(r)
+        if not i:
+            return i
+        if int_valued(r):
+            # non-integer self should pass one of these tests
+            if (self > i) is S.true:
+                return i
+            if (self < i) is S.true:
+                return i - 1
+            ok = self.equals(i)
+            if ok is None:
+                raise TypeError('cannot compute int value accurately')
+            if ok:
+                return i
+            # off by one
+            return i - (1 if i > 0 else -1)
+        return i
+
+    def __float__(self) -> float:
+        # Don't bother testing if it's a number; if it's not this is going
+        # to fail, and if it is we still need to check that it evalf'ed to
+        # a number.
+        result = self.evalf()
+        if result.is_Number:
+            return float(result)
+        if result.is_number and result.as_real_imag()[1]:
+            raise TypeError("Cannot convert complex to float")
+        raise TypeError("Cannot convert expression to float")
+
+    def __complex__(self) -> complex:
+        result = self.evalf()
+        re, im = result.as_real_imag()
+        return complex(float(re), float(im))
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    def __ge__(self, other):
+        from .relational import GreaterThan
+        return GreaterThan(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    def __le__(self, other):
+        from .relational import LessThan
+        return LessThan(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    def __gt__(self, other):
+        from .relational import StrictGreaterThan
+        return StrictGreaterThan(self, other)
+
+    @sympify_return([('other', 'Expr')], NotImplemented)
+    def __lt__(self, other):
+        from .relational import StrictLessThan
+        return StrictLessThan(self, other)
+
+    def __trunc__(self):
+        if not self.is_number:
+            raise TypeError("Cannot truncate symbols and expressions")
+        else:
+            return Integer(self)
+
+    def __format__(self, format_spec: str):
+        if self.is_number:
+            mt = re.match(r'\+?\d*\.(\d+)f', format_spec)
+            if mt:
+                prec = int(mt.group(1))
+                rounded = self.round(prec)
+                if rounded.is_Integer:
+                    return format(int(rounded), format_spec)
+                if rounded.is_Float:
+                    return format(rounded, format_spec)
+        return super().__format__(format_spec)
+
+    @staticmethod
+    def _from_mpmath(x, prec):
+        if hasattr(x, "_mpf_"):
+            return Float._new(x._mpf_, prec)
+        elif hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            re = Float._new(re, prec)
+            im = Float._new(im, prec)*S.ImaginaryUnit
+            return re + im
+        else:
+            raise TypeError("expected mpmath number (mpf or mpc)")
+
+    @property
+    def is_number(self):
+        """Returns True if ``self`` has no free symbols and no
+        undefined functions (AppliedUndef, to be precise). It will be
+        faster than ``if not self.free_symbols``, however, since
+        ``is_number`` will fail as soon as it hits a free symbol
+        or undefined function.
+
+        Examples
+        ========
+
+        >>> from sympy import Function, Integral, cos, sin, pi
+        >>> from sympy.abc import x
+        >>> f = Function('f')
+
+        >>> x.is_number
+        False
+        >>> f(1).is_number
+        False
+        >>> (2*x).is_number
+        False
+        >>> (2 + Integral(2, x)).is_number
+        False
+        >>> (2 + Integral(2, (x, 1, 2))).is_number
+        True
+
+        Not all numbers are Numbers in the SymPy sense:
+
+        >>> pi.is_number, pi.is_Number
+        (True, False)
+
+        If something is a number it should evaluate to a number with
+        real and imaginary parts that are Numbers; the result may not
+        be comparable, however, since the real and/or imaginary part
+        of the result may not have precision.
+
+        >>> cos(1).is_number and cos(1).is_comparable
+        True
+
+        >>> z = cos(1)**2 + sin(1)**2 - 1
+        >>> z.is_number
+        True
+        >>> z.is_comparable
+        False
+
+        See Also
+        ========
+
+        sympy.core.basic.Basic.is_comparable
+        """
+        return all(obj.is_number for obj in self.args)
+
+    def _eval_is_comparable(self):
+        # Basic._eval_is_comparable always returns False, so we override it
+        # here
+        is_extended_real = self.is_extended_real
+        if is_extended_real is False:
+            return False
+        if not self.is_number:
+            return False
+
+        # XXX: as_real_imag() can be a very expensive operation. It should not
+        # be used here because is_comparable is used implicitly in many places.
+        # Probably this method should just return self.evalf(2).is_Number.
+
+        n, i = self.as_real_imag()
+
+        if not n.is_Number:
+            n = n.evalf(2)
+            if not n.is_Number:
+                return False
+
+        if not i.is_Number:
+            i = i.evalf(2)
+            if not i.is_Number:
+                return False
+
+        if i:
+            # if _prec = 1 we can't decide and if not,
+            # the answer is False because numbers with
+            # imaginary parts can't be compared
+            # so return False
+            return False
+        else:
+            return n._prec != 1
+
+    def _random(self, n=None, re_min=-1, im_min=-1, re_max=1, im_max=1):
+        """Return self evaluated, if possible, replacing free symbols with
+        random complex values, if necessary.
+
+        Explanation
+        ===========
+
+        The random complex value for each free symbol is generated
+        by the random_complex_number routine giving real and imaginary
+        parts in the range given by the re_min, re_max, im_min, and im_max
+        values. The returned value is evaluated to a precision of n
+        (if given) else the maximum of 15 and the precision needed
+        to get more than 1 digit of precision. If the expression
+        could not be evaluated to a number, or could not be evaluated
+        to more than 1 digit of precision, then None is returned.
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt
+        >>> from sympy.abc import x, y
+        >>> x._random()                         # doctest: +SKIP
+        0.0392918155679172 + 0.916050214307199*I
+        >>> x._random(2)                        # doctest: +SKIP
+        -0.77 - 0.87*I
+        >>> (x + y/2)._random(2)                # doctest: +SKIP
+        -0.57 + 0.16*I
+        >>> sqrt(2)._random(2)
+        1.4
+
+        See Also
+        ========
+
+        sympy.core.random.random_complex_number
+        """
+
+        free = self.free_symbols
+        prec = 1
+        if free:
+            from sympy.core.random import random_complex_number
+            a, c, b, d = re_min, re_max, im_min, im_max
+            reps = dict(list(zip(free, [random_complex_number(a, b, c, d, rational=True)
+                           for zi in free])))
+            try:
+                nmag = abs(self.evalf(2, subs=reps))
+            except (ValueError, TypeError):
+                # if an out of range value resulted in evalf problems
+                # then return None -- XXX is there a way to know how to
+                # select a good random number for a given expression?
+                # e.g. when calculating n! negative values for n should not
+                # be used
+                return None
+        else:
+            reps = {}
+            nmag = abs(self.evalf(2))
+
+        if not hasattr(nmag, '_prec'):
+            # e.g. exp_polar(2*I*pi) doesn't evaluate but is_number is True
+            return None
+
+        if nmag._prec == 1:
+            # increase the precision up to the default maximum
+            # precision to see if we can get any significance
+
+            # evaluate
+            for prec in giant_steps(2, DEFAULT_MAXPREC):
+                nmag = abs(self.evalf(prec, subs=reps))
+                if nmag._prec != 1:
+                    break
+
+        if nmag._prec != 1:
+            if n is None:
+                n = max(prec, 15)
+            return self.evalf(n, subs=reps)
+
+        # never got any significance
+        return None
+
+    def is_constant(self, *wrt, **flags):
+        """Return True if self is constant, False if not, or None if
+        the constancy could not be determined conclusively.
+
+        Explanation
+        ===========
+
+        If an expression has no free symbols then it is a constant. If
+        there are free symbols it is possible that the expression is a
+        constant, perhaps (but not necessarily) zero. To test such
+        expressions, a few strategies are tried:
+
+        1) numerical evaluation at two random points. If two such evaluations
+        give two different values and the values have a precision greater than
+        1 then self is not constant. If the evaluations agree or could not be
+        obtained with any precision, no decision is made. The numerical testing
+        is done only if ``wrt`` is different than the free symbols.
+
+        2) differentiation with respect to variables in 'wrt' (or all free
+        symbols if omitted) to see if the expression is constant or not. This
+        will not always lead to an expression that is zero even though an
+        expression is constant (see added test in test_expr.py). If
+        all derivatives are zero then self is constant with respect to the
+        given symbols.
+
+        3) finding out zeros of denominator expression with free_symbols.
+        It will not be constant if there are zeros. It gives more negative
+        answers for expression that are not constant.
+
+        If neither evaluation nor differentiation can prove the expression is
+        constant, None is returned unless two numerical values happened to be
+        the same and the flag ``failing_number`` is True -- in that case the
+        numerical value will be returned.
+
+        If flag simplify=False is passed, self will not be simplified;
+        the default is True since self should be simplified before testing.
+
+        Examples
+        ========
+
+        >>> from sympy import cos, sin, Sum, S, pi
+        >>> from sympy.abc import a, n, x, y
+        >>> x.is_constant()
+        False
+        >>> S(2).is_constant()
+        True
+        >>> Sum(x, (x, 1, 10)).is_constant()
+        True
+        >>> Sum(x, (x, 1, n)).is_constant()
+        False
+        >>> Sum(x, (x, 1, n)).is_constant(y)
+        True
+        >>> Sum(x, (x, 1, n)).is_constant(n)
+        False
+        >>> Sum(x, (x, 1, n)).is_constant(x)
+        True
+        >>> eq = a*cos(x)**2 + a*sin(x)**2 - a
+        >>> eq.is_constant()
+        True
+        >>> eq.subs({x: pi, a: 2}) == eq.subs({x: pi, a: 3}) == 0
+        True
+
+        >>> (0**x).is_constant()
+        False
+        >>> x.is_constant()
+        False
+        >>> (x**x).is_constant()
+        False
+        >>> one = cos(x)**2 + sin(x)**2
+        >>> one.is_constant()
+        True
+        >>> ((one - 1)**(x + 1)).is_constant() in (True, False) # could be 0 or 1
+        True
+        """
+
+        simplify = flags.get('simplify', True)
+
+        if self.is_number:
+            return True
+        free = self.free_symbols
+        if not free:
+            return True  # assume f(1) is some constant
+
+        # if we are only interested in some symbols and they are not in the
+        # free symbols then this expression is constant wrt those symbols
+        wrt = set(wrt)
+        if wrt and not wrt & free:
+            return True
+        wrt = wrt or free
+
+        # simplify unless this has already been done
+        expr = self
+        if simplify:
+            expr = expr.simplify()
+
+        # is_zero should be a quick assumptions check; it can be wrong for
+        # numbers (see test_is_not_constant test), giving False when it
+        # shouldn't, but hopefully it will never give True unless it is sure.
+        if expr.is_zero:
+            return True
+
+        # Don't attempt substitution or differentiation with non-number symbols
+        wrt_number = {sym for sym in wrt if sym.kind is NumberKind}
+
+        # try numerical evaluation to see if we get two different values
+        failing_number = None
+        if wrt_number == free:
+            # try 0 (for a) and 1 (for b)
+            try:
+                a = expr.subs(list(zip(free, [0]*len(free))),
+                    simultaneous=True)
+                if a is S.NaN:
+                    # evaluation may succeed when substitution fails
+                    a = expr._random(None, 0, 0, 0, 0)
+            except ZeroDivisionError:
+                a = None
+            if a is not None and a is not S.NaN:
+                try:
+                    b = expr.subs(list(zip(free, [1]*len(free))),
+                        simultaneous=True)
+                    if b is S.NaN:
+                        # evaluation may succeed when substitution fails
+                        b = expr._random(None, 1, 0, 1, 0)
+                except ZeroDivisionError:
+                    b = None
+                if b is not None and b is not S.NaN and b.equals(a) is False:
+                    return False
+                # try random real
+                b = expr._random(None, -1, 0, 1, 0)
+                if b is not None and b is not S.NaN and b.equals(a) is False:
+                    return False
+                # try random complex
+                b = expr._random()
+                if b is not None and b is not S.NaN:
+                    if b.equals(a) is False:
+                        return False
+                    failing_number = a if a.is_number else b
+
+        # now we will test each wrt symbol (or all free symbols) to see if the
+        # expression depends on them or not using differentiation. This is
+        # not sufficient for all expressions, however, so we don't return
+        # False if we get a derivative other than 0 with free symbols.
+        for w in wrt_number:
+            deriv = expr.diff(w)
+            if simplify:
+                deriv = deriv.simplify()
+            if deriv != 0:
+                if not (pure_complex(deriv, or_real=True)):
+                    if flags.get('failing_number', False):
+                        return failing_number
+                return False
+        from sympy.solvers.solvers import denoms
+        return fuzzy_not(fuzzy_or(den.is_zero for den in denoms(self)))
+
+    def equals(self, other, failing_expression=False):
+        """Return True if self == other, False if it does not, or None. If
+        failing_expression is True then the expression which did not simplify
+        to a 0 will be returned instead of None.
+
+        Explanation
+        ===========
+
+        If ``self`` is a Number (or complex number) that is not zero, then
+        the result is False.
+
+        If ``self`` is a number and has not evaluated to zero, evalf will be
+        used to test whether the expression evaluates to zero. If it does so
+        and the result has significance (i.e. the precision is either -1, for
+        a Rational result, or is greater than 1) then the evalf value will be
+        used to return True or False.
+
+        """
+        from sympy.simplify.simplify import nsimplify, simplify
+        from sympy.solvers.solvers import solve
+        from sympy.polys.polyerrors import NotAlgebraic
+        from sympy.polys.numberfields import minimal_polynomial
+
+        other = sympify(other)
+
+        if not isinstance(other, Expr):
+            return False
+
+        if self == other:
+            return True
+
+        # they aren't the same so see if we can make the difference 0;
+        # don't worry about doing simplification steps one at a time
+        # because if the expression ever goes to 0 then the subsequent
+        # simplification steps that are done will be very fast.
+        diff = factor_terms(simplify(self - other), radical=True)
+
+        if not diff:
+            return True
+
+        if not diff.has(Add, Mod):
+            # if there is no expanding to be done after simplifying
+            # then this can't be a zero
+            return False
+
+        factors = diff.as_coeff_mul()[1]
+        if len(factors) > 1:  # avoid infinity recursion
+            fac_zero = [fac.equals(0) for fac in factors]
+            if None not in fac_zero:  # every part can be decided
+                return any(fac_zero)
+
+        constant = diff.is_constant(simplify=False, failing_number=True)
+
+        if constant is False:
+            return False
+
+        if not diff.is_number:
+            if constant is None:
+                # e.g. unless the right simplification is done, a symbolic
+                # zero is possible (see expression of issue 6829: without
+                # simplification constant will be None).
+                return
+
+        if constant is True:
+            # this gives a number whether there are free symbols or not
+            ndiff = diff._random()
+            # is_comparable will work whether the result is real
+            # or complex; it could be None, however.
+            if ndiff and ndiff.is_comparable:
+                return False
+
+        # sometimes we can use a simplified result to give a clue as to
+        # what the expression should be; if the expression is *not* zero
+        # then we should have been able to compute that and so now
+        # we can just consider the cases where the approximation appears
+        # to be zero -- we try to prove it via minimal_polynomial.
+        #
+        # removed
+        # ns = nsimplify(diff)
+        # if diff.is_number and (not ns or ns == diff):
+        #
+        # The thought was that if it nsimplifies to 0 that's a sure sign
+        # to try the following to prove it; or if it changed but wasn't
+        # zero that might be a sign that it's not going to be easy to
+        # prove. But tests seem to be working without that logic.
+        #
+        if diff.is_number:
+            # try to prove via self-consistency
+            surds = [s for s in diff.atoms(Pow) if s.args[0].is_Integer]
+            # it seems to work better to try big ones first
+            surds.sort(key=lambda x: -x.args[0])
+            for s in surds:
+                try:
+                    # simplify is False here -- this expression has already
+                    # been identified as being hard to identify as zero;
+                    # we will handle the checking ourselves using nsimplify
+                    # to see if we are in the right ballpark or not and if so
+                    # *then* the simplification will be attempted.
+                    sol = solve(diff, s, simplify=False)
+                    if sol:
+                        if s in sol:
+                            # the self-consistent result is present
+                            return True
+                        if all(si.is_Integer for si in sol):
+                            # perfect powers are removed at instantiation
+                            # so surd s cannot be an integer
+                            return False
+                        if all(i.is_algebraic is False for i in sol):
+                            # a surd is algebraic
+                            return False
+                        if any(si in surds for si in sol):
+                            # it wasn't equal to s but it is in surds
+                            # and different surds are not equal
+                            return False
+                        if any(nsimplify(s - si) == 0 and
+                                simplify(s - si) == 0 for si in sol):
+                            return True
+                        if s.is_real:
+                            if any(nsimplify(si, [s]) == s and simplify(si) == s
+                                    for si in sol):
+                                return True
+                except NotImplementedError:
+                    pass
+
+            # try to prove with minimal_polynomial but know when
+            # *not* to use this or else it can take a long time. e.g. issue 8354
+            if True:  # change True to condition that assures non-hang
+                try:
+                    mp = minimal_polynomial(diff)
+                    if mp.is_Symbol:
+                        return True
+                    return False
+                except (NotAlgebraic, NotImplementedError):
+                    pass
+
+        # diff has not simplified to zero; constant is either None, True
+        # or the number with significance (is_comparable) that was randomly
+        # calculated twice as the same value.
+        if constant not in (True, None) and constant != 0:
+            return False
+
+        if failing_expression:
+            return diff
+        return None
+
+    def _eval_is_extended_positive_negative(self, positive):
+        from sympy.polys.numberfields import minimal_polynomial
+        from sympy.polys.polyerrors import NotAlgebraic
+        if self.is_number:
+            # check to see that we can get a value
+            try:
+                n2 = self._eval_evalf(2)
+            # XXX: This shouldn't be caught here
+            # Catches ValueError: hypsum() failed to converge to the requested
+            # 34 bits of accuracy
+            except ValueError:
+                return None
+            if n2 is None:
+                return None
+            if getattr(n2, '_prec', 1) == 1:  # no significance
+                return None
+            if n2 is S.NaN:
+                return None
+
+            f = self.evalf(2)
+            if f.is_Float:
+                match = f, S.Zero
+            else:
+                match = pure_complex(f)
+            if match is None:
+                return False
+            r, i = match
+            if not (i.is_Number and r.is_Number):
+                return False
+            if r._prec != 1 and i._prec != 1:
+                return bool(not i and ((r > 0) if positive else (r < 0)))
+            elif r._prec == 1 and (not i or i._prec == 1) and \
+                    self._eval_is_algebraic() and not self.has(Function):
+                try:
+                    if minimal_polynomial(self).is_Symbol:
+                        return False
+                except (NotAlgebraic, NotImplementedError):
+                    pass
+
+    def _eval_is_extended_positive(self):
+        return self._eval_is_extended_positive_negative(positive=True)
+
+    def _eval_is_extended_negative(self):
+        return self._eval_is_extended_positive_negative(positive=False)
+
+    def _eval_interval(self, x, a, b):
+        """
+        Returns evaluation over an interval.  For most functions this is:
+
+        self.subs(x, b) - self.subs(x, a),
+
+        possibly using limit() if NaN is returned from subs, or if
+        singularities are found between a and b.
+
+        If b or a is None, it only evaluates -self.subs(x, a) or self.subs(b, x),
+        respectively.
+
+        """
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.functions.elementary.exponential import log
+        from sympy.series.limits import limit, Limit
+        from sympy.sets.sets import Interval
+        from sympy.solvers.solveset import solveset
+
+        if (a is None and b is None):
+            raise ValueError('Both interval ends cannot be None.')
+
+        def _eval_endpoint(left):
+            c = a if left else b
+            if c is None:
+                return S.Zero
+            else:
+                C = self.subs(x, c)
+                if C.has(S.NaN, S.Infinity, S.NegativeInfinity,
+                         S.ComplexInfinity, AccumBounds):
+                    if (a < b) != False:
+                        C = limit(self, x, c, "+" if left else "-")
+                    else:
+                        C = limit(self, x, c, "-" if left else "+")
+
+                    if isinstance(C, Limit):
+                        raise NotImplementedError("Could not compute limit")
+            return C
+
+        if a == b:
+            return S.Zero
+
+        A = _eval_endpoint(left=True)
+        if A is S.NaN:
+            return A
+
+        B = _eval_endpoint(left=False)
+
+        if (a and b) is None:
+            return B - A
+
+        value = B - A
+
+        if a.is_comparable and b.is_comparable:
+            if a < b:
+                domain = Interval(a, b)
+            else:
+                domain = Interval(b, a)
+            # check the singularities of self within the interval
+            # if singularities is a ConditionSet (not iterable), catch the exception and pass
+            singularities = solveset(self.cancel().as_numer_denom()[1], x,
+                domain=domain)
+            for logterm in self.atoms(log):
+                singularities = singularities | solveset(logterm.args[0], x,
+                    domain=domain)
+            try:
+                for s in singularities:
+                    if value is S.NaN:
+                        # no need to keep adding, it will stay NaN
+                        break
+                    if not s.is_comparable:
+                        continue
+                    if (a < s) == (s < b) == True:
+                        value += -limit(self, x, s, "+") + limit(self, x, s, "-")
+                    elif (b < s) == (s < a) == True:
+                        value += limit(self, x, s, "+") - limit(self, x, s, "-")
+            except TypeError:
+                pass
+
+        return value
+
+    def _eval_power(self, expt) -> Expr | None:
+        # subclass to compute self**other for cases when
+        # other is not NaN, 0, or 1
+        return None
+
+    def _eval_conjugate(self):
+        if self.is_extended_real:
+            return self
+        elif self.is_imaginary:
+            return -self
+
+    def conjugate(self):
+        """Returns the complex conjugate of 'self'."""
+        from sympy.functions.elementary.complexes import conjugate as c
+        return c(self)
+
+    def dir(self, x, cdir):
+        if self.is_zero:
+            return S.Zero
+        from sympy.functions.elementary.exponential import log
+        minexp = S.Zero
+        arg = self
+        while arg:
+            minexp += S.One
+            arg = arg.diff(x)
+            coeff = arg.subs(x, 0)
+            if coeff is S.NaN:
+                coeff = arg.limit(x, 0)
+            if coeff is S.ComplexInfinity:
+                try:
+                    coeff, _ = arg.leadterm(x)
+                    if coeff.has(log(x)):
+                        raise ValueError()
+                except ValueError:
+                    coeff = arg.limit(x, 0)
+            if coeff != S.Zero:
+                break
+        return coeff*cdir**minexp
+
+    def _eval_transpose(self):
+        from sympy.functions.elementary.complexes import conjugate
+        if self.is_commutative:
+            return self
+        elif self.is_hermitian:
+            return conjugate(self)
+        elif self.is_antihermitian:
+            return -conjugate(self)
+
+    def transpose(self):
+        from sympy.functions.elementary.complexes import transpose
+        return transpose(self)
+
+    def _eval_adjoint(self):
+        from sympy.functions.elementary.complexes import conjugate, transpose
+        if self.is_hermitian:
+            return self
+        elif self.is_antihermitian:
+            return -self
+        obj = self._eval_conjugate()
+        if obj is not None:
+            return transpose(obj)
+        obj = self._eval_transpose()
+        if obj is not None:
+            return conjugate(obj)
+
+    def adjoint(self):
+        from sympy.functions.elementary.complexes import adjoint
+        return adjoint(self)
+
+    @classmethod
+    def _parse_order(cls, order):
+        """Parse and configure the ordering of terms. """
+        from sympy.polys.orderings import monomial_key
+
+        startswith = getattr(order, "startswith", None)
+        if startswith is None:
+            reverse = False
+        else:
+            reverse = startswith('rev-')
+            if reverse:
+                order = order[4:]
+
+        monom_key = monomial_key(order)
+
+        def neg(monom):
+            return tuple([neg(m) if isinstance(m, tuple) else -m for m in monom])
+
+        def key(term):
+            _, ((re, im), monom, ncpart) = term
+
+            monom = neg(monom_key(monom))
+            ncpart = tuple([e.sort_key(order=order) for e in ncpart])
+            coeff = ((bool(im), im), (re, im))
+
+            return monom, ncpart, coeff
+
+        return key, reverse
+
+    def as_ordered_factors(self, order=None):
+        """Return list of ordered factors (if Mul) else [self]."""
+        return [self]
+
+    def as_poly(self, *gens, **args):
+        """Converts ``self`` to a polynomial or returns ``None``.
+
+        Explanation
+        ===========
+
+        >>> from sympy import sin
+        >>> from sympy.abc import x, y
+
+        >>> print((x**2 + x*y).as_poly())
+        Poly(x**2 + x*y, x, y, domain='ZZ')
+
+        >>> print((x**2 + x*y).as_poly(x, y))
+        Poly(x**2 + x*y, x, y, domain='ZZ')
+
+        >>> print((x**2 + sin(y)).as_poly(x, y))
+        None
+
+        """
+        from sympy.polys.polyerrors import PolynomialError, GeneratorsNeeded
+        from sympy.polys.polytools import Poly
+
+        try:
+            poly = Poly(self, *gens, **args)
+
+            if not poly.is_Poly:
+                return None
+            else:
+                return poly
+        except (PolynomialError, GeneratorsNeeded):
+            # PolynomialError is caught for e.g. exp(x).as_poly(x)
+            # GeneratorsNeeded is caught for e.g. S(2).as_poly()
+            return None
+
+    def as_ordered_terms(self, order=None, data=False):
+        """
+        Transform an expression to an ordered list of terms.
+
+        Examples
+        ========
+
+        >>> from sympy import sin, cos
+        >>> from sympy.abc import x
+
+        >>> (sin(x)**2*cos(x) + sin(x)**2 + 1).as_ordered_terms()
+        [sin(x)**2*cos(x), sin(x)**2, 1]
+
+        """
+
+        from .numbers import Number, NumberSymbol
+
+        if order is None and self.is_Add:
+            # Spot the special case of Add(Number, Mul(Number, expr)) with the
+            # first number positive and the second number negative
+            key = lambda x:not isinstance(x, (Number, NumberSymbol))
+            add_args = sorted(Add.make_args(self), key=key)
+            if (len(add_args) == 2
+                and isinstance(add_args[0], (Number, NumberSymbol))
+                and isinstance(add_args[1], Mul)):
+                mul_args = sorted(Mul.make_args(add_args[1]), key=key)
+                if (len(mul_args) == 2
+                    and isinstance(mul_args[0], Number)
+                    and add_args[0].is_positive
+                    and mul_args[0].is_negative):
+                    return add_args
+
+        key, reverse = self._parse_order(order)
+        terms, gens = self.as_terms()
+
+        if not any(term.is_Order for term, _ in terms):
+            ordered = sorted(terms, key=key, reverse=reverse)
+        else:
+            _terms, _order = [], []
+
+            for term, repr in terms:
+                if not term.is_Order:
+                    _terms.append((term, repr))
+                else:
+                    _order.append((term, repr))
+
+            ordered = sorted(_terms, key=key, reverse=True) \
+                + sorted(_order, key=key, reverse=True)
+
+        if data:
+            return ordered, gens
+        else:
+            return [term for term, _ in ordered]
+
+    def as_terms(self):
+        """Transform an expression to a list of terms. """
+        from .exprtools import decompose_power
+
+        gens, terms = set(), []
+
+        for term in Add.make_args(self):
+            coeff, _term = term.as_coeff_Mul()
+
+            coeff = complex(coeff)
+            cpart, ncpart = {}, []
+
+            if _term is not S.One:
+                for factor in Mul.make_args(_term):
+                    if factor.is_number:
+                        try:
+                            coeff *= complex(factor)
+                        except (TypeError, ValueError):
+                            pass
+                        else:
+                            continue
+
+                    if factor.is_commutative:
+                        base, exp = decompose_power(factor)
+
+                        cpart[base] = exp
+                        gens.add(base)
+                    else:
+                        ncpart.append(factor)
+
+            coeff = coeff.real, coeff.imag
+            ncpart = tuple(ncpart)
+
+            terms.append((term, (coeff, cpart, ncpart)))
+
+        gens = sorted(gens, key=default_sort_key)
+
+        k, indices = len(gens), {}
+
+        for i, g in enumerate(gens):
+            indices[g] = i
+
+        result = []
+
+        for term, (coeff, cpart, ncpart) in terms:
+            monom = [0]*k
+
+            for base, exp in cpart.items():
+                monom[indices[base]] = exp
+
+            result.append((term, (coeff, tuple(monom), ncpart)))
+
+        return result, gens
+
+    def removeO(self) -> Expr:
+        """Removes the additive O(..) symbol if there is one"""
+        return self
+
+    def getO(self) -> Expr | None:
+        """Returns the additive O(..) symbol if there is one, else None."""
+        return None
+
+    def getn(self):
+        """
+        Returns the order of the expression.
+
+        Explanation
+        ===========
+
+        The order is determined either from the O(...) term. If there
+        is no O(...) term, it returns None.
+
+        Examples
+        ========
+
+        >>> from sympy import O
+        >>> from sympy.abc import x
+        >>> (1 + x + O(x**2)).getn()
+        2
+        >>> (1 + x).getn()
+
+        """
+        o = self.getO()
+        if o is None:
+            return None
+        elif o.is_Order:
+            o = o.expr
+            if o is S.One:
+                return S.Zero
+            if o.is_Symbol:
+                return S.One
+            if o.is_Pow:
+                return o.args[1]
+            if o.is_Mul:  # x**n*log(x)**n or x**n/log(x)**n
+                for oi in o.args:
+                    if oi.is_Symbol:
+                        return S.One
+                    if oi.is_Pow:
+                        from .symbol import Dummy, Symbol
+                        syms = oi.atoms(Symbol)
+                        if len(syms) == 1:
+                            x = syms.pop()
+                            oi = oi.subs(x, Dummy('x', positive=True))
+                            if oi.base.is_Symbol and oi.exp.is_Rational:
+                                return abs(oi.exp)
+
+        raise NotImplementedError('not sure of order of %s' % o)
+
+    def count_ops(self, visual=False):
+        from .function import count_ops
+        return count_ops(self, visual)
+
+    def args_cnc(self, cset=False, warn=True, split_1=True):
+        """Return [commutative factors, non-commutative factors] of self.
+
+        Explanation
+        ===========
+
+        self is treated as a Mul and the ordering of the factors is maintained.
+        If ``cset`` is True the commutative factors will be returned in a set.
+        If there were repeated factors (as may happen with an unevaluated Mul)
+        then an error will be raised unless it is explicitly suppressed by
+        setting ``warn`` to False.
+
+        Note: -1 is always separated from a Number unless split_1 is False.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, oo
+        >>> A, B = symbols('A B', commutative=0)
+        >>> x, y = symbols('x y')
+        >>> (-2*x*y).args_cnc()
+        [[-1, 2, x, y], []]
+        >>> (-2.5*x).args_cnc()
+        [[-1, 2.5, x], []]
+        >>> (-2*x*A*B*y).args_cnc()
+        [[-1, 2, x, y], [A, B]]
+        >>> (-2*x*A*B*y).args_cnc(split_1=False)
+        [[-2, x, y], [A, B]]
+        >>> (-2*x*y).args_cnc(cset=True)
+        [{-1, 2, x, y}, []]
+
+        The arg is always treated as a Mul:
+
+        >>> (-2 + x + A).args_cnc()
+        [[], [x - 2 + A]]
+        >>> (-oo).args_cnc() # -oo is a singleton
+        [[-1, oo], []]
+        """
+        args = list(Mul.make_args(self))
+
+        for i, mi in enumerate(args):
+            if not mi.is_commutative:
+                c = args[:i]
+                nc = args[i:]
+                break
+        else:
+            c = args
+            nc = []
+
+        if c and split_1 and (
+            c[0].is_Number and
+            c[0].is_extended_negative and
+                c[0] is not S.NegativeOne):
+            c[:1] = [S.NegativeOne, -c[0]]
+
+        if cset:
+            clen = len(c)
+            c = set(c)
+            if clen and warn and len(c) != clen:
+                raise ValueError('repeated commutative arguments: %s' %
+                                 [ci for ci in c if list(self.args).count(ci) > 1])
+        return [c, nc]
+
+    def coeff(self, x: Expr, n=1, right=False, _first=True):
+        """
+        Returns the coefficient from the term(s) containing ``x**n``. If ``n``
+        is zero then all terms independent of ``x`` will be returned.
+
+        Explanation
+        ===========
+
+        When ``x`` is noncommutative, the coefficient to the left (default) or
+        right of ``x`` can be returned. The keyword 'right' is ignored when
+        ``x`` is commutative.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.abc import x, y, z
+
+        You can select terms that have an explicit negative in front of them:
+
+        >>> (-x + 2*y).coeff(-1)
+        x
+        >>> (x - 2*y).coeff(-1)
+        2*y
+
+        You can select terms with no Rational coefficient:
+
+        >>> (x + 2*y).coeff(1)
+        x
+        >>> (3 + 2*x + 4*x**2).coeff(1)
+        0
+
+        You can select terms independent of x by making n=0; in this case
+        expr.as_independent(x)[0] is returned (and 0 will be returned instead
+        of None):
+
+        >>> (3 + 2*x + 4*x**2).coeff(x, 0)
+        3
+        >>> eq = ((x + 1)**3).expand() + 1
+        >>> eq
+        x**3 + 3*x**2 + 3*x + 2
+        >>> [eq.coeff(x, i) for i in reversed(range(4))]
+        [1, 3, 3, 2]
+        >>> eq -= 2
+        >>> [eq.coeff(x, i) for i in reversed(range(4))]
+        [1, 3, 3, 0]
+
+        You can select terms that have a numerical term in front of them:
+
+        >>> (-x - 2*y).coeff(2)
+        -y
+        >>> from sympy import sqrt
+        >>> (x + sqrt(2)*x).coeff(sqrt(2))
+        x
+
+        The matching is exact:
+
+        >>> (3 + 2*x + 4*x**2).coeff(x)
+        2
+        >>> (3 + 2*x + 4*x**2).coeff(x**2)
+        4
+        >>> (3 + 2*x + 4*x**2).coeff(x**3)
+        0
+        >>> (z*(x + y)**2).coeff((x + y)**2)
+        z
+        >>> (z*(x + y)**2).coeff(x + y)
+        0
+
+        In addition, no factoring is done, so 1 + z*(1 + y) is not obtained
+        from the following:
+
+        >>> (x + z*(x + x*y)).coeff(x)
+        1
+
+        If such factoring is desired, factor_terms can be used first:
+
+        >>> from sympy import factor_terms
+        >>> factor_terms(x + z*(x + x*y)).coeff(x)
+        z*(y + 1) + 1
+
+        >>> n, m, o = symbols('n m o', commutative=False)
+        >>> n.coeff(n)
+        1
+        >>> (3*n).coeff(n)
+        3
+        >>> (n*m + m*n*m).coeff(n) # = (1 + m)*n*m
+        1 + m
+        >>> (n*m + m*n*m).coeff(n, right=True) # = (1 + m)*n*m
+        m
+
+        If there is more than one possible coefficient 0 is returned:
+
+        >>> (n*m + m*n).coeff(n)
+        0
+
+        If there is only one possible coefficient, it is returned:
+
+        >>> (n*m + x*m*n).coeff(m*n)
+        x
+        >>> (n*m + x*m*n).coeff(m*n, right=1)
+        1
+
+        See Also
+        ========
+
+        as_coefficient: separate the expression into a coefficient and factor
+        as_coeff_Add: separate the additive constant from an expression
+        as_coeff_Mul: separate the multiplicative constant from an expression
+        as_independent: separate x-dependent terms/factors from others
+        sympy.polys.polytools.Poly.coeff_monomial: efficiently find the single coefficient of a monomial in Poly
+        sympy.polys.polytools.Poly.nth: like coeff_monomial but powers of monomial terms are used
+        """
+        x = sympify(x)
+        if not isinstance(x, Basic):
+            return S.Zero
+
+        n = as_int(n)
+
+        if not x:
+            return S.Zero
+
+        if x == self:
+            if n == 1:
+                return S.One
+            return S.Zero
+
+        co2: list[Expr]
+
+        if x is S.One:
+            co2 = [a for a in Add.make_args(self) if a.as_coeff_Mul()[0] is S.One]
+            if not co2:
+                return S.Zero
+            return Add(*co2)
+
+        if n == 0:
+            if x.is_Add and self.is_Add:
+                c = self.coeff(x, right=right)
+                if not c:
+                    return S.Zero
+                if not right:
+                    return self - Add(*[a*x for a in Add.make_args(c)])
+                return self - Add(*[x*a for a in Add.make_args(c)])
+            return self.as_independent(x, as_Add=True)[0]
+
+        # continue with the full method, looking for this power of x:
+        x = x**n
+
+        def incommon(l1, l2):
+            if not l1 or not l2:
+                return []
+            n = min(len(l1), len(l2))
+            for i in range(n):
+                if l1[i] != l2[i]:
+                    return l1[:i]
+            return l1[:]
+
+        def find(l, sub, first=True):
+            """ Find where list sub appears in list l. When ``first`` is True
+            the first occurrence from the left is returned, else the last
+            occurrence is returned. Return None if sub is not in l.
+
+            Examples
+            ========
+
+            >> l = range(5)*2
+            >> find(l, [2, 3])
+            2
+            >> find(l, [2, 3], first=0)
+            7
+            >> find(l, [2, 4])
+            None
+
+            """
+            if not sub or not l or len(sub) > len(l):
+                return None
+            n = len(sub)
+            if not first:
+                l.reverse()
+                sub.reverse()
+            for i in range(len(l) - n + 1):
+                if all(l[i + j] == sub[j] for j in range(n)):
+                    break
+            else:
+                i = None
+            if not first:
+                l.reverse()
+                sub.reverse()
+            if i is not None and not first:
+                i = len(l) - (i + n)
+            return i
+
+        co2 = []
+        co: list[tuple[set[Expr], list[Expr]]] = []
+        args = Add.make_args(self)
+        self_c = self.is_commutative
+        x_c = x.is_commutative
+        if self_c and not x_c:
+            return S.Zero
+        if _first and self.is_Add and not self_c and not x_c:
+            # get the part that depends on x exactly
+            xargs = Mul.make_args(x)
+            d = Add(*[i for i in Add.make_args(self.as_independent(x)[1])
+                if all(xi in Mul.make_args(i) for xi in xargs)])
+            rv = d.coeff(x, right=right, _first=False)
+            if not rv.is_Add or not right:
+                return rv
+            c_part, nc_part = zip(*[i.args_cnc() for i in rv.args])
+            if has_variety(c_part):
+                return rv
+            return Add(*[Mul._from_args(i) for i in nc_part])
+
+        one_c = self_c or x_c
+        xargs, nx = x.args_cnc(cset=True, warn=bool(not x_c))
+        # find the parts that pass the commutative terms
+        for a in args:
+            margs, nc = a.args_cnc(cset=True, warn=bool(not self_c))
+            if nc is None:
+                nc = []
+            if len(xargs) > len(margs):
+                continue
+            resid = margs.difference(xargs)
+            if len(resid) + len(xargs) == len(margs):
+                if one_c:
+                    co2.append(Mul(*(list(resid) + nc)))
+                else:
+                    co.append((resid, nc))
+        if one_c:
+            if co2 == []:
+                return S.Zero
+            elif co2:
+                return Add(*co2)
+        else:  # both nc
+            # now check the non-comm parts
+            if not co:
+                return S.Zero
+            if all(n == co[0][1] for r, n in co):
+                ii = find(co[0][1], nx, right)
+                if ii is not None:
+                    if not right:
+                        return Mul(Add(*[Mul(*r) for r, c in co]), Mul(*co[0][1][:ii]))
+                    else:
+                        return Mul(*co[0][1][ii + len(nx):])
+            beg = reduce(incommon, (n[1] for n in co))
+            if beg:
+                ii = find(beg, nx, right)
+                if ii is not None:
+                    if not right:
+                        gcdc = co[0][0]
+                        for i in range(1, len(co)):
+                            gcdc = gcdc.intersection(co[i][0])
+                            if not gcdc:
+                                break
+                        return Mul(*(list(gcdc) + beg[:ii]))
+                    else:
+                        m = ii + len(nx)
+                        return Add(*[Mul(*(list(r) + n[m:])) for r, n in co])
+            end = list(reversed(
+                reduce(incommon, (list(reversed(n[1])) for n in co))))
+            if end:
+                ii = find(end, nx, right)
+                if ii is not None:
+                    if not right:
+                        return Add(*[Mul(*(list(r) + n[:-len(end) + ii])) for r, n in co])
+                    else:
+                        return Mul(*end[ii + len(nx):])
+            # look for single match
+            hit = None
+            for i, (r, n) in enumerate(co):
+                ii = find(n, nx, right)
+                if ii is not None:
+                    if not hit:
+                        hit = ii, r, n
+                    else:
+                        break
+            else:
+                if hit:
+                    ii, r, n = hit
+                    if not right:
+                        return Mul(*(list(r) + n[:ii]))
+                    else:
+                        return Mul(*n[ii + len(nx):])
+
+            return S.Zero
+
+    def as_expr(self, *gens):
+        """
+        Convert a polynomial to a SymPy expression.
+
+        Examples
+        ========
+
+        >>> from sympy import sin
+        >>> from sympy.abc import x, y
+
+        >>> f = (x**2 + x*y).as_poly(x, y)
+        >>> f.as_expr()
+        x**2 + x*y
+
+        >>> sin(x).as_expr()
+        sin(x)
+
+        """
+        return self
+
+    def as_coefficient(self, expr: Expr) -> Expr | None:
+        """
+        Extracts symbolic coefficient at the given expression. In
+        other words, this functions separates 'self' into the product
+        of 'expr' and 'expr'-free coefficient. If such separation
+        is not possible it will return None.
+
+        Examples
+        ========
+
+        >>> from sympy import E, pi, sin, I, Poly
+        >>> from sympy.abc import x
+
+        >>> E.as_coefficient(E)
+        1
+        >>> (2*E).as_coefficient(E)
+        2
+        >>> (2*sin(E)*E).as_coefficient(E)
+
+        Two terms have E in them so a sum is returned. (If one were
+        desiring the coefficient of the term exactly matching E then
+        the constant from the returned expression could be selected.
+        Or, for greater precision, a method of Poly can be used to
+        indicate the desired term from which the coefficient is
+        desired.)
+
+        >>> (2*E + x*E).as_coefficient(E)
+        x + 2
+        >>> _.args[0]  # just want the exact match
+        2
+        >>> p = Poly(2*E + x*E); p
+        Poly(x*E + 2*E, x, E, domain='ZZ')
+        >>> p.coeff_monomial(E)
+        2
+        >>> p.nth(0, 1)
+        2
+
+        Since the following cannot be written as a product containing
+        E as a factor, None is returned. (If the coefficient ``2*x`` is
+        desired then the ``coeff`` method should be used.)
+
+        >>> (2*E*x + x).as_coefficient(E)
+        >>> (2*E*x + x).coeff(E)
+        2*x
+
+        >>> (E*(x + 1) + x).as_coefficient(E)
+
+        >>> (2*pi*I).as_coefficient(pi*I)
+        2
+        >>> (2*I).as_coefficient(pi*I)
+
+        See Also
+        ========
+
+        coeff: return sum of terms have a given factor
+        as_coeff_Add: separate the additive constant from an expression
+        as_coeff_Mul: separate the multiplicative constant from an expression
+        as_independent: separate x-dependent terms/factors from others
+        sympy.polys.polytools.Poly.coeff_monomial: efficiently find the single coefficient of a monomial in Poly
+        sympy.polys.polytools.Poly.nth: like coeff_monomial but powers of monomial terms are used
+
+
+        """
+
+        r = self.extract_multiplicatively(expr)
+        if r and not r.has(expr):
+            return r
+        else:
+            return None
+
+    def as_independent(self, *deps, **hint) -> tuple[Expr, Expr]:
+        """
+        A mostly naive separation of a Mul or Add into arguments that are not
+        are dependent on deps. To obtain as complete a separation of variables
+        as possible, use a separation method first, e.g.:
+
+        * separatevars() to change Mul, Add and Pow (including exp) into Mul
+        * .expand(mul=True) to change Add or Mul into Add
+        * .expand(log=True) to change log expr into an Add
+
+        The only non-naive thing that is done here is to respect noncommutative
+        ordering of variables and to always return (0, 0) for `self` of zero
+        regardless of hints.
+
+        For nonzero `self`, the returned tuple (i, d) has the
+        following interpretation:
+
+        * i will has no variable that appears in deps
+        * d will either have terms that contain variables that are in deps, or
+          be equal to 0 (when self is an Add) or 1 (when self is a Mul)
+        * if self is an Add then self = i + d
+        * if self is a Mul then self = i*d
+        * otherwise (self, S.One) or (S.One, self) is returned.
+
+        To force the expression to be treated as an Add, use the hint as_Add=True
+
+        Examples
+        ========
+
+        -- self is an Add
+
+        >>> from sympy import sin, cos, exp
+        >>> from sympy.abc import x, y, z
+
+        >>> (x + x*y).as_independent(x)
+        (0, x*y + x)
+        >>> (x + x*y).as_independent(y)
+        (x, x*y)
+        >>> (2*x*sin(x) + y + x + z).as_independent(x)
+        (y + z, 2*x*sin(x) + x)
+        >>> (2*x*sin(x) + y + x + z).as_independent(x, y)
+        (z, 2*x*sin(x) + x + y)
+
+        -- self is a Mul
+
+        >>> (x*sin(x)*cos(y)).as_independent(x)
+        (cos(y), x*sin(x))
+
+        non-commutative terms cannot always be separated out when self is a Mul
+
+        >>> from sympy import symbols
+        >>> n1, n2, n3 = symbols('n1 n2 n3', commutative=False)
+        >>> (n1 + n1*n2).as_independent(n2)
+        (n1, n1*n2)
+        >>> (n2*n1 + n1*n2).as_independent(n2)
+        (0, n1*n2 + n2*n1)
+        >>> (n1*n2*n3).as_independent(n1)
+        (1, n1*n2*n3)
+        >>> (n1*n2*n3).as_independent(n2)
+        (n1, n2*n3)
+        >>> ((x-n1)*(x-y)).as_independent(x)
+        (1, (x - y)*(x - n1))
+
+        -- self is anything else:
+
+        >>> (sin(x)).as_independent(x)
+        (1, sin(x))
+        >>> (sin(x)).as_independent(y)
+        (sin(x), 1)
+        >>> exp(x+y).as_independent(x)
+        (1, exp(x + y))
+
+        -- force self to be treated as an Add:
+
+        >>> (3*x).as_independent(x, as_Add=True)
+        (0, 3*x)
+
+        -- force self to be treated as a Mul:
+
+        >>> (3+x).as_independent(x, as_Add=False)
+        (1, x + 3)
+        >>> (-3+x).as_independent(x, as_Add=False)
+        (1, x - 3)
+
+        Note how the below differs from the above in making the
+        constant on the dep term positive.
+
+        >>> (y*(-3+x)).as_independent(x)
+        (y, x - 3)
+
+        -- use .as_independent() for true independence testing instead
+           of .has(). The former considers only symbols in the free
+           symbols while the latter considers all symbols
+
+        >>> from sympy import Integral
+        >>> I = Integral(x, (x, 1, 2))
+        >>> I.has(x)
+        True
+        >>> x in I.free_symbols
+        False
+        >>> I.as_independent(x) == (I, 1)
+        True
+        >>> (I + x).as_independent(x) == (I, x)
+        True
+
+        Note: when trying to get independent terms, a separation method
+        might need to be used first. In this case, it is important to keep
+        track of what you send to this routine so you know how to interpret
+        the returned values
+
+        >>> from sympy import separatevars, log
+        >>> separatevars(exp(x+y)).as_independent(x)
+        (exp(y), exp(x))
+        >>> (x + x*y).as_independent(y)
+        (x, x*y)
+        >>> separatevars(x + x*y).as_independent(y)
+        (x, y + 1)
+        >>> (x*(1 + y)).as_independent(y)
+        (x, y + 1)
+        >>> (x*(1 + y)).expand(mul=True).as_independent(y)
+        (x, x*y)
+        >>> a, b=symbols('a b', positive=True)
+        >>> (log(a*b).expand(log=True)).as_independent(b)
+        (log(a), log(b))
+
+        See Also
+        ========
+
+        separatevars
+        expand_log
+        sympy.core.add.Add.as_two_terms
+        sympy.core.mul.Mul.as_two_terms
+        as_coeff_mul
+        """
+        from .symbol import Symbol
+        from .add import _unevaluated_Add
+        from .mul import _unevaluated_Mul
+
+        if self is S.Zero:
+            return (self, self)
+
+        func = self.func
+        want: type[Add] | type[Mul]
+        if hint.get('as_Add', isinstance(self, Add) ):
+            want = Add
+        else:
+            want = Mul
+
+        # sift out deps into symbolic and other and ignore
+        # all symbols but those that are in the free symbols
+        sym = set()
+        other = []
+        for d in deps:
+            if isinstance(d, Symbol):  # Symbol.is_Symbol is True
+                sym.add(d)
+            else:
+                other.append(d)
+
+        def has(e):
+            """return the standard has() if there are no literal symbols, else
+            check to see that symbol-deps are in the free symbols."""
+            has_other = e.has(*other)
+            if not sym:
+                return has_other
+            return has_other or e.has(*(e.free_symbols & sym))
+
+        if (want is not func or
+                func is not Add and func is not Mul):
+            if has(self):
+                return (want.identity, self)
+            else:
+                return (self, want.identity)
+        else:
+            if func is Add:
+                args = list(self.args)
+            else:
+                args, nc = self.args_cnc()
+
+        d = sift(args, has)
+        depend = d[True]
+        indep = d[False]
+        if func is Add:  # all terms were treated as commutative
+            return (Add(*indep), _unevaluated_Add(*depend))
+        else:  # handle noncommutative by stopping at first dependent term
+            for i, n in enumerate(nc):
+                if has(n):
+                    depend.extend(nc[i:])
+                    break
+                indep.append(n)
+            return Mul(*indep), _unevaluated_Mul(*depend)
+
+    def as_real_imag(self, deep=True, **hints) -> tuple[Expr, Expr]:
+        """Performs complex expansion on 'self' and returns a tuple
+           containing collected both real and imaginary parts. This
+           method cannot be confused with re() and im() functions,
+           which does not perform complex expansion at evaluation.
+
+           However it is possible to expand both re() and im()
+           functions and get exactly the same results as with
+           a single call to this function.
+
+           >>> from sympy import symbols, I
+
+           >>> x, y = symbols('x,y', real=True)
+
+           >>> (x + y*I).as_real_imag()
+           (x, y)
+
+           >>> from sympy.abc import z, w
+
+           >>> (z + w*I).as_real_imag()
+           (re(z) - im(w), re(w) + im(z))
+
+        """
+        if hints.get('ignore') == self:
+            return None  # type: ignore
+        else:
+            from sympy.functions.elementary.complexes import im, re
+            return (re(self), im(self))
+
+    def as_powers_dict(self):
+        """Return self as a dictionary of factors with each factor being
+        treated as a power. The keys are the bases of the factors and the
+        values, the corresponding exponents. The resulting dictionary should
+        be used with caution if the expression is a Mul and contains non-
+        commutative factors since the order that they appeared will be lost in
+        the dictionary.
+
+        See Also
+        ========
+        as_ordered_factors: An alternative for noncommutative applications,
+                            returning an ordered list of factors.
+        args_cnc: Similar to as_ordered_factors, but guarantees separation
+                  of commutative and noncommutative factors.
+        """
+        d = defaultdict(int)
+        d.update([self.as_base_exp()])
+        return d
+
+    def as_coefficients_dict(self, *syms):
+        """Return a dictionary mapping terms to their Rational coefficient.
+        Since the dictionary is a defaultdict, inquiries about terms which
+        were not present will return a coefficient of 0.
+
+        If symbols ``syms`` are provided, any multiplicative terms
+        independent of them will be considered a coefficient and a
+        regular dictionary of syms-dependent generators as keys and
+        their corresponding coefficients as values will be returned.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import a, x, y
+        >>> (3*x + a*x + 4).as_coefficients_dict()
+        {1: 4, x: 3, a*x: 1}
+        >>> _[a]
+        0
+        >>> (3*a*x).as_coefficients_dict()
+        {a*x: 3}
+        >>> (3*a*x).as_coefficients_dict(x)
+        {x: 3*a}
+        >>> (3*a*x).as_coefficients_dict(y)
+        {1: 3*a*x}
+
+        """
+        d = defaultdict(list)
+        if not syms:
+            for ai in Add.make_args(self):
+                c, m = ai.as_coeff_Mul()
+                d[m].append(c)
+            for k, v in d.items():
+                if len(v) == 1:
+                    d[k] = v[0]
+                else:
+                    d[k] = Add(*v)
+        else:
+            ind, dep = self.as_independent(*syms, as_Add=True)
+            for i in Add.make_args(dep):
+                if i.is_Mul:
+                    c, x = i.as_coeff_mul(*syms)
+                    if c is S.One:
+                        d[i].append(c)
+                    else:
+                        d[i._new_rawargs(*x)].append(c)
+                elif i:
+                    d[i].append(S.One)
+            d = {k: Add(*d[k]) for k in d}
+            if ind is not S.Zero:
+                d.update({S.One: ind})
+        di = defaultdict(int)
+        di.update(d)
+        return di
+
+    def as_base_exp(self) -> tuple[Expr, Expr]:
+        # a -> b ** e
+        return self, S.One
+
+    def as_coeff_mul(self, *deps, **kwargs) -> tuple[Expr, tuple[Expr, ...]]:
+        """Return the tuple (c, args) where self is written as a Mul, ``m``.
+
+        c should be a Rational multiplied by any factors of the Mul that are
+        independent of deps.
+
+        args should be a tuple of all other factors of m; args is empty
+        if self is a Number or if self is independent of deps (when given).
+
+        This should be used when you do not know if self is a Mul or not but
+        you want to treat self as a Mul or if you want to process the
+        individual arguments of the tail of self as a Mul.
+
+        - if you know self is a Mul and want only the head, use self.args[0];
+        - if you do not want to process the arguments of the tail but need the
+          tail then use self.as_two_terms() which gives the head and tail;
+        - if you want to split self into an independent and dependent parts
+          use ``self.as_independent(*deps)``
+
+        >>> from sympy import S
+        >>> from sympy.abc import x, y
+        >>> (S(3)).as_coeff_mul()
+        (3, ())
+        >>> (3*x*y).as_coeff_mul()
+        (3, (x, y))
+        >>> (3*x*y).as_coeff_mul(x)
+        (3*y, (x,))
+        >>> (3*y).as_coeff_mul(x)
+        (3*y, ())
+        """
+        if deps:
+            if not self.has(*deps):
+                return self, ()
+        return S.One, (self,)
+
+    def as_coeff_add(self, *deps) -> tuple[Expr, tuple[Expr, ...]]:
+        """Return the tuple (c, args) where self is written as an Add, ``a``.
+
+        c should be a Rational added to any terms of the Add that are
+        independent of deps.
+
+        args should be a tuple of all other terms of ``a``; args is empty
+        if self is a Number or if self is independent of deps (when given).
+
+        This should be used when you do not know if self is an Add or not but
+        you want to treat self as an Add or if you want to process the
+        individual arguments of the tail of self as an Add.
+
+        - if you know self is an Add and want only the head, use self.args[0];
+        - if you do not want to process the arguments of the tail but need the
+          tail then use self.as_two_terms() which gives the head and tail.
+        - if you want to split self into an independent and dependent parts
+          use ``self.as_independent(*deps)``
+
+        >>> from sympy import S
+        >>> from sympy.abc import x, y
+        >>> (S(3)).as_coeff_add()
+        (3, ())
+        >>> (3 + x).as_coeff_add()
+        (3, (x,))
+        >>> (3 + x + y).as_coeff_add(x)
+        (y + 3, (x,))
+        >>> (3 + y).as_coeff_add(x)
+        (y + 3, ())
+
+        """
+        if deps:
+            if not self.has_free(*deps):
+                return self, ()
+        return S.Zero, (self,)
+
+    def primitive(self) -> tuple[Number, Expr]:
+        """Return the positive Rational that can be extracted non-recursively
+        from every term of self (i.e., self is treated like an Add). This is
+        like the as_coeff_Mul() method but primitive always extracts a positive
+        Rational (never a negative or a Float).
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> (3*(x + 1)**2).primitive()
+        (3, (x + 1)**2)
+        >>> a = (6*x + 2); a.primitive()
+        (2, 3*x + 1)
+        >>> b = (x/2 + 3); b.primitive()
+        (1/2, x + 6)
+        >>> (a*b).primitive() == (1, a*b)
+        True
+        """
+        if not self:
+            return S.One, S.Zero
+        c, r = self.as_coeff_Mul(rational=True)
+        if c.is_negative:
+            c, r = -c, -r
+        return c, r
+
+    def as_content_primitive(self, radical=False, clear=True):
+        """This method should recursively remove a Rational from all arguments
+        and return that (content) and the new self (primitive). The content
+        should always be positive and ``Mul(*foo.as_content_primitive()) == foo``.
+        The primitive need not be in canonical form and should try to preserve
+        the underlying structure if possible (i.e. expand_mul should not be
+        applied to self).
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt
+        >>> from sympy.abc import x, y, z
+
+        >>> eq = 2 + 2*x + 2*y*(3 + 3*y)
+
+        The as_content_primitive function is recursive and retains structure:
+
+        >>> eq.as_content_primitive()
+        (2, x + 3*y*(y + 1) + 1)
+
+        Integer powers will have Rationals extracted from the base:
+
+        >>> ((2 + 6*x)**2).as_content_primitive()
+        (4, (3*x + 1)**2)
+        >>> ((2 + 6*x)**(2*y)).as_content_primitive()
+        (1, (2*(3*x + 1))**(2*y))
+
+        Terms may end up joining once their as_content_primitives are added:
+
+        >>> ((5*(x*(1 + y)) + 2*x*(3 + 3*y))).as_content_primitive()
+        (11, x*(y + 1))
+        >>> ((3*(x*(1 + y)) + 2*x*(3 + 3*y))).as_content_primitive()
+        (9, x*(y + 1))
+        >>> ((3*(z*(1 + y)) + 2.0*x*(3 + 3*y))).as_content_primitive()
+        (1, 6.0*x*(y + 1) + 3*z*(y + 1))
+        >>> ((5*(x*(1 + y)) + 2*x*(3 + 3*y))**2).as_content_primitive()
+        (121, x**2*(y + 1)**2)
+        >>> ((x*(1 + y) + 0.4*x*(3 + 3*y))**2).as_content_primitive()
+        (1, 4.84*x**2*(y + 1)**2)
+
+        Radical content can also be factored out of the primitive:
+
+        >>> (2*sqrt(2) + 4*sqrt(10)).as_content_primitive(radical=True)
+        (2, sqrt(2)*(1 + 2*sqrt(5)))
+
+        If clear=False (default is True) then content will not be removed
+        from an Add if it can be distributed to leave one or more
+        terms with integer coefficients.
+
+        >>> (x/2 + y).as_content_primitive()
+        (1/2, x + 2*y)
+        >>> (x/2 + y).as_content_primitive(clear=False)
+        (1, x/2 + y)
+        """
+        return S.One, self
+
+    def as_numer_denom(self) -> tuple[Expr, Expr]:
+        """Return the numerator and the denominator of an expression.
+
+        expression -> a/b -> a, b
+
+        This is just a stub that should be defined by
+        an object's class methods to get anything else.
+
+        See Also
+        ========
+
+        normal: return ``a/b`` instead of ``(a, b)``
+
+        """
+        return self, S.One
+
+    def normal(self):
+        """Return the expression as a fraction.
+
+        expression -> a/b
+
+        See Also
+        ========
+
+        as_numer_denom: return ``(a, b)`` instead of ``a/b``
+
+        """
+        from .mul import _unevaluated_Mul
+        n, d = self.as_numer_denom()
+        if d is S.One:
+            return n
+        if d.is_Number:
+            return _unevaluated_Mul(n, 1/d)
+        else:
+            return n/d
+
+    def extract_multiplicatively(self, c: Expr) -> Expr | None:
+        """Return None if it's not possible to make self in the form
+           c * something in a nice way, i.e. preserving the properties
+           of arguments of self.
+
+           Examples
+           ========
+
+           >>> from sympy import symbols, Rational
+
+           >>> x, y = symbols('x,y', real=True)
+
+           >>> ((x*y)**3).extract_multiplicatively(x**2 * y)
+           x*y**2
+
+           >>> ((x*y)**3).extract_multiplicatively(x**4 * y)
+
+           >>> (2*x).extract_multiplicatively(2)
+           x
+
+           >>> (2*x).extract_multiplicatively(3)
+
+           >>> (Rational(1, 2)*x).extract_multiplicatively(3)
+           x/6
+
+        """
+        from sympy.functions.elementary.exponential import exp
+        from .add import _unevaluated_Add
+        c = sympify(c)
+        if self is S.NaN:
+            return None
+        if c is S.One:
+            return self
+        elif c == self:
+            return S.One
+
+        if c.is_Add:
+            cc, pc = c.primitive()
+            if cc is not S.One:
+                c = Mul(cc, pc, evaluate=False)
+
+        if c.is_Mul:
+            a, b = c.as_two_terms() # type: ignore
+            x = self.extract_multiplicatively(a)
+            if x is not None:
+                return x.extract_multiplicatively(b)
+            else:
+                return x
+
+        quotient = self / c
+        if self.is_Number:
+            if self is S.Infinity:
+                if c.is_positive:
+                    return S.Infinity
+            elif self is S.NegativeInfinity:
+                if c.is_negative:
+                    return S.Infinity
+                elif c.is_positive:
+                    return S.NegativeInfinity
+            elif self is S.ComplexInfinity:
+                if not c.is_zero:
+                    return S.ComplexInfinity
+            elif self.is_Integer:
+                if not quotient.is_Integer:
+                    return None
+                elif self.is_positive and quotient.is_negative:
+                    return None
+                else:
+                    return quotient
+            elif self.is_Rational:
+                if not quotient.is_Rational:
+                    return None
+                elif self.is_positive and quotient.is_negative:
+                    return None
+                else:
+                    return quotient
+            elif self.is_Float:
+                if not quotient.is_Float:
+                    return None
+                elif self.is_positive and quotient.is_negative:
+                    return None
+                else:
+                    return quotient
+        elif self.is_NumberSymbol or self.is_Symbol or self is S.ImaginaryUnit:
+            if quotient.is_Mul and len(quotient.args) == 2:
+                if quotient.args[0].is_Integer and quotient.args[0].is_positive and quotient.args[1] == self:
+                    return quotient
+            elif quotient.is_Integer and c.is_Number:
+                return quotient
+        elif self.is_Add:
+            cs, ps = self.primitive()
+            # assert cs >= 1
+            if c.is_Number and c is not S.NegativeOne:
+                # assert c != 1 (handled at top)
+                if cs is not S.One:
+                    if c.is_negative:
+                        xc = cs.extract_multiplicatively(-c)
+                        if xc is not None:
+                            xc = -xc
+                    else:
+                        xc = cs.extract_multiplicatively(c)
+                    if xc is not None:
+                        return xc*ps  # rely on 2-arg Mul to restore Add
+                return None # |c| != 1 can only be extracted from cs
+            if c == ps:
+                return cs
+            # check args of ps
+            newargs = []
+            arg: Expr
+            for arg in ps.args: # type: ignore
+                newarg = arg.extract_multiplicatively(c)
+                if newarg is None:
+                    return None # all or nothing
+                newargs.append(newarg)
+            if cs is not S.One:
+                args = [cs*t for t in newargs]
+                # args may be in different order
+                return _unevaluated_Add(*args)
+            else:
+                return Add._from_args(newargs)
+        elif self.is_Mul:
+            args: list[Expr] = list(self.args) # type: ignore
+            for i, arg in enumerate(args):
+                newarg = arg.extract_multiplicatively(c)
+                if newarg is not None:
+                    args[i] = newarg
+                    return Mul(*args)
+        elif self.is_Pow or isinstance(self, exp):
+            sb, se = self.as_base_exp()
+            cb, ce = c.as_base_exp()
+            if cb == sb:
+                new_exp = se.extract_additively(ce)
+                if new_exp is not None:
+                    return Pow(sb, new_exp)
+            elif c == sb:
+                new_exp = se.extract_additively(1)
+                if new_exp is not None:
+                    return Pow(sb, new_exp)
+
+        return None
+
+    def extract_additively(self, c):
+        """Return self - c if it's possible to subtract c from self and
+        make all matching coefficients move towards zero, else return None.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> e = 2*x + 3
+        >>> e.extract_additively(x + 1)
+        x + 2
+        >>> e.extract_additively(3*x)
+        >>> e.extract_additively(4)
+        >>> (y*(x + 1)).extract_additively(x + 1)
+        >>> ((x + 1)*(x + 2*y + 1) + 3).extract_additively(x + 1)
+        (x + 1)*(x + 2*y) + 3
+
+        See Also
+        ========
+        extract_multiplicatively
+        coeff
+        as_coefficient
+
+        """
+
+        c = sympify(c)
+        if self is S.NaN:
+            return None
+        if c.is_zero:
+            return self
+        elif c == self:
+            return S.Zero
+        elif self == S.Zero:
+            return None
+
+        if self.is_Number:
+            if not c.is_Number:
+                return None
+            co = self
+            diff = co - c
+            # XXX should we match types? i.e should 3 - .1 succeed?
+            if (co > 0 and diff >= 0 and diff < co or
+                    co < 0 and diff <= 0 and diff > co):
+                return diff
+            return None
+
+        if c.is_Number:
+            co, t = self.as_coeff_Add()
+            xa = co.extract_additively(c)
+            if xa is None:
+                return None
+            return xa + t
+
+        # handle the args[0].is_Number case separately
+        # since we will have trouble looking for the coeff of
+        # a number.
+        if c.is_Add and c.args[0].is_Number:
+            # whole term as a term factor
+            co = self.coeff(c)
+            xa0 = (co.extract_additively(1) or 0)*c
+            if xa0:
+                diff = self - co*c
+                return (xa0 + (diff.extract_additively(c) or diff)) or None
+            # term-wise
+            h, t = c.as_coeff_Add()
+            sh, st = self.as_coeff_Add()
+            xa = sh.extract_additively(h)
+            if xa is None:
+                return None
+            xa2 = st.extract_additively(t)
+            if xa2 is None:
+                return None
+            return xa + xa2
+
+        # whole term as a term factor
+        co, diff = _corem(self, c)
+        xa0 = (co.extract_additively(1) or 0)*c
+        if xa0:
+            return (xa0 + (diff.extract_additively(c) or diff)) or None
+        # term-wise
+        coeffs = []
+        for a in Add.make_args(c):
+            ac, at = a.as_coeff_Mul()
+            co = self.coeff(at)
+            if not co:
+                return None
+            coc, cot = co.as_coeff_Add()
+            xa = coc.extract_additively(ac)
+            if xa is None:
+                return None
+            self -= co*at
+            coeffs.append((cot + xa)*at)
+        coeffs.append(self)
+        return Add(*coeffs)
+
+    @property
+    def expr_free_symbols(self):
+        """
+        Like ``free_symbols``, but returns the free symbols only if
+        they are contained in an expression node.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> (x + y).expr_free_symbols # doctest: +SKIP
+        {x, y}
+
+        If the expression is contained in a non-expression object, do not return
+        the free symbols. Compare:
+
+        >>> from sympy import Tuple
+        >>> t = Tuple(x + y)
+        >>> t.expr_free_symbols # doctest: +SKIP
+        set()
+        >>> t.free_symbols
+        {x, y}
+        """
+        sympy_deprecation_warning("""
+        The expr_free_symbols property is deprecated. Use free_symbols to get
+        the free symbols of an expression.
+        """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-expr-free-symbols")
+        return {j for i in self.args for j in i.expr_free_symbols}
+
+    def could_extract_minus_sign(self) -> bool:
+        """Return True if self has -1 as a leading factor or has
+        more literal negative signs than positive signs in a sum,
+        otherwise False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> e = x - y
+        >>> {i.could_extract_minus_sign() for i in (e, -e)}
+        {False, True}
+
+        Though the ``y - x`` is considered like ``-(x - y)``, since it
+        is in a product without a leading factor of -1, the result is
+        false below:
+
+        >>> (x*(y - x)).could_extract_minus_sign()
+        False
+
+        To put something in canonical form wrt to sign, use `signsimp`:
+
+        >>> from sympy import signsimp
+        >>> signsimp(x*(y - x))
+        -x*(x - y)
+        >>> _.could_extract_minus_sign()
+        True
+        """
+        return False
+
+    def extract_branch_factor(self, allow_half=False):
+        """
+        Try to write self as ``exp_polar(2*pi*I*n)*z`` in a nice way.
+        Return (z, n).
+
+        >>> from sympy import exp_polar, I, pi
+        >>> from sympy.abc import x, y
+        >>> exp_polar(I*pi).extract_branch_factor()
+        (exp_polar(I*pi), 0)
+        >>> exp_polar(2*I*pi).extract_branch_factor()
+        (1, 1)
+        >>> exp_polar(-pi*I).extract_branch_factor()
+        (exp_polar(I*pi), -1)
+        >>> exp_polar(3*pi*I + x).extract_branch_factor()
+        (exp_polar(x + I*pi), 1)
+        >>> (y*exp_polar(-5*pi*I)*exp_polar(3*pi*I + 2*pi*x)).extract_branch_factor()
+        (y*exp_polar(2*pi*x), -1)
+        >>> exp_polar(-I*pi/2).extract_branch_factor()
+        (exp_polar(-I*pi/2), 0)
+
+        If allow_half is True, also extract exp_polar(I*pi):
+
+        >>> exp_polar(I*pi).extract_branch_factor(allow_half=True)
+        (1, 1/2)
+        >>> exp_polar(2*I*pi).extract_branch_factor(allow_half=True)
+        (1, 1)
+        >>> exp_polar(3*I*pi).extract_branch_factor(allow_half=True)
+        (1, 3/2)
+        >>> exp_polar(-I*pi).extract_branch_factor(allow_half=True)
+        (1, -1/2)
+        """
+        from sympy.functions.elementary.exponential import exp_polar
+        from sympy.functions.elementary.integers import ceiling
+
+        n = S.Zero
+        res = S.One
+        args = Mul.make_args(self)
+        exps = []
+        for arg in args:
+            if isinstance(arg, exp_polar):
+                exps += [arg.exp]
+            else:
+                res *= arg
+        piimult = S.Zero
+        extras = []
+
+        ipi = S.Pi*S.ImaginaryUnit
+        while exps:
+            exp = exps.pop()
+            if exp.is_Add:
+                exps += exp.args
+                continue
+            if exp.is_Mul:
+                coeff = exp.as_coefficient(ipi)
+                if coeff is not None:
+                    piimult += coeff
+                    continue
+            extras += [exp]
+        if piimult.is_number:
+            coeff = piimult
+            tail = ()
+        else:
+            coeff, tail = piimult.as_coeff_add(*piimult.free_symbols)
+        # round down to nearest multiple of 2
+        branchfact = ceiling(coeff/2 - S.Half)*2
+        n += branchfact/2
+        c = coeff - branchfact
+        if allow_half:
+            nc = c.extract_additively(1)
+            if nc is not None:
+                n += S.Half
+                c = nc
+        newexp = ipi*Add(*((c, ) + tail)) + Add(*extras)
+        if newexp != 0:
+            res *= exp_polar(newexp)
+        return res, n
+
+    def is_polynomial(self, *syms):
+        r"""
+        Return True if self is a polynomial in syms and False otherwise.
+
+        This checks if self is an exact polynomial in syms.  This function
+        returns False for expressions that are "polynomials" with symbolic
+        exponents.  Thus, you should be able to apply polynomial algorithms to
+        expressions for which this returns True, and Poly(expr, \*syms) should
+        work if and only if expr.is_polynomial(\*syms) returns True. The
+        polynomial does not have to be in expanded form.  If no symbols are
+        given, all free symbols in the expression will be used.
+
+        This is not part of the assumptions system.  You cannot do
+        Symbol('z', polynomial=True).
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Function
+        >>> x = Symbol('x')
+        >>> ((x**2 + 1)**4).is_polynomial(x)
+        True
+        >>> ((x**2 + 1)**4).is_polynomial()
+        True
+        >>> (2**x + 1).is_polynomial(x)
+        False
+        >>> (2**x + 1).is_polynomial(2**x)
+        True
+        >>> f = Function('f')
+        >>> (f(x) + 1).is_polynomial(x)
+        False
+        >>> (f(x) + 1).is_polynomial(f(x))
+        True
+        >>> (1/f(x) + 1).is_polynomial(f(x))
+        False
+
+        >>> n = Symbol('n', nonnegative=True, integer=True)
+        >>> (x**n + 1).is_polynomial(x)
+        False
+
+        This function does not attempt any nontrivial simplifications that may
+        result in an expression that does not appear to be a polynomial to
+        become one.
+
+        >>> from sympy import sqrt, factor, cancel
+        >>> y = Symbol('y', positive=True)
+        >>> a = sqrt(y**2 + 2*y + 1)
+        >>> a.is_polynomial(y)
+        False
+        >>> factor(a)
+        y + 1
+        >>> factor(a).is_polynomial(y)
+        True
+
+        >>> b = (y**2 + 2*y + 1)/(y + 1)
+        >>> b.is_polynomial(y)
+        False
+        >>> cancel(b)
+        y + 1
+        >>> cancel(b).is_polynomial(y)
+        True
+
+        See also .is_rational_function()
+
+        """
+        if syms:
+            syms = set(map(sympify, syms))
+        else:
+            syms = self.free_symbols
+            if not syms:
+                return True
+
+        return self._eval_is_polynomial(syms)
+
+    def _eval_is_polynomial(self, syms) -> bool | None:
+        if self in syms:
+            return True
+        if not self.has_free(*syms):
+            # constant polynomial
+            return True
+        # subclasses should return True or False
+        return None
+
+    def is_rational_function(self, *syms):
+        """
+        Test whether function is a ratio of two polynomials in the given
+        symbols, syms. When syms is not given, all free symbols will be used.
+        The rational function does not have to be in expanded or in any kind of
+        canonical form.
+
+        This function returns False for expressions that are "rational
+        functions" with symbolic exponents.  Thus, you should be able to call
+        .as_numer_denom() and apply polynomial algorithms to the result for
+        expressions for which this returns True.
+
+        This is not part of the assumptions system.  You cannot do
+        Symbol('z', rational_function=True).
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, sin
+        >>> from sympy.abc import x, y
+
+        >>> (x/y).is_rational_function()
+        True
+
+        >>> (x**2).is_rational_function()
+        True
+
+        >>> (x/sin(y)).is_rational_function(y)
+        False
+
+        >>> n = Symbol('n', integer=True)
+        >>> (x**n + 1).is_rational_function(x)
+        False
+
+        This function does not attempt any nontrivial simplifications that may
+        result in an expression that does not appear to be a rational function
+        to become one.
+
+        >>> from sympy import sqrt, factor
+        >>> y = Symbol('y', positive=True)
+        >>> a = sqrt(y**2 + 2*y + 1)/y
+        >>> a.is_rational_function(y)
+        False
+        >>> factor(a)
+        (y + 1)/y
+        >>> factor(a).is_rational_function(y)
+        True
+
+        See also is_algebraic_expr().
+
+        """
+        if syms:
+            syms = set(map(sympify, syms))
+        else:
+            syms = self.free_symbols
+            if not syms:
+                return self not in _illegal
+
+        return self._eval_is_rational_function(syms)
+
+    def _eval_is_rational_function(self, syms) -> bool | None:
+        if self in syms:
+            return True
+        if not self.has_xfree(syms):
+            return True
+        # subclasses should return True or False
+        return None
+
+    def is_meromorphic(self, x, a):
+        """
+        This tests whether an expression is meromorphic as
+        a function of the given symbol ``x`` at the point ``a``.
+
+        This method is intended as a quick test that will return
+        None if no decision can be made without simplification or
+        more detailed analysis.
+
+        Examples
+        ========
+
+        >>> from sympy import zoo, log, sin, sqrt
+        >>> from sympy.abc import x
+
+        >>> f = 1/x**2 + 1 - 2*x**3
+        >>> f.is_meromorphic(x, 0)
+        True
+        >>> f.is_meromorphic(x, 1)
+        True
+        >>> f.is_meromorphic(x, zoo)
+        True
+
+        >>> g = x**log(3)
+        >>> g.is_meromorphic(x, 0)
+        False
+        >>> g.is_meromorphic(x, 1)
+        True
+        >>> g.is_meromorphic(x, zoo)
+        False
+
+        >>> h = sin(1/x)*x**2
+        >>> h.is_meromorphic(x, 0)
+        False
+        >>> h.is_meromorphic(x, 1)
+        True
+        >>> h.is_meromorphic(x, zoo)
+        True
+
+        Multivalued functions are considered meromorphic when their
+        branches are meromorphic. Thus most functions are meromorphic
+        everywhere except at essential singularities and branch points.
+        In particular, they will be meromorphic also on branch cuts
+        except at their endpoints.
+
+        >>> log(x).is_meromorphic(x, -1)
+        True
+        >>> log(x).is_meromorphic(x, 0)
+        False
+        >>> sqrt(x).is_meromorphic(x, -1)
+        True
+        >>> sqrt(x).is_meromorphic(x, 0)
+        False
+
+        """
+        if not x.is_symbol:
+            raise TypeError("{} should be of symbol type".format(x))
+        a = sympify(a)
+
+        return self._eval_is_meromorphic(x, a)
+
+    def _eval_is_meromorphic(self, x, a) -> bool | None:
+        if self == x:
+            return True
+        if not self.has_free(x):
+            return True
+        # subclasses should return True or False
+        return None
+
+    def is_algebraic_expr(self, *syms):
+        """
+        This tests whether a given expression is algebraic or not, in the
+        given symbols, syms. When syms is not given, all free symbols
+        will be used. The rational function does not have to be in expanded
+        or in any kind of canonical form.
+
+        This function returns False for expressions that are "algebraic
+        expressions" with symbolic exponents. This is a simple extension to the
+        is_rational_function, including rational exponentiation.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, sqrt
+        >>> x = Symbol('x', real=True)
+        >>> sqrt(1 + x).is_rational_function()
+        False
+        >>> sqrt(1 + x).is_algebraic_expr()
+        True
+
+        This function does not attempt any nontrivial simplifications that may
+        result in an expression that does not appear to be an algebraic
+        expression to become one.
+
+        >>> from sympy import exp, factor
+        >>> a = sqrt(exp(x)**2 + 2*exp(x) + 1)/(exp(x) + 1)
+        >>> a.is_algebraic_expr(x)
+        False
+        >>> factor(a).is_algebraic_expr()
+        True
+
+        See Also
+        ========
+
+        is_rational_function
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Algebraic_expression
+
+        """
+        if syms:
+            syms = set(map(sympify, syms))
+        else:
+            syms = self.free_symbols
+            if not syms:
+                return True
+
+        return self._eval_is_algebraic_expr(syms)
+
+    def _eval_is_algebraic_expr(self, syms) -> bool | None:
+        if self in syms:
+            return True
+        if not self.has_free(*syms):
+            return True
+        # subclasses should return True or False
+        return None
+
+    ###################################################################################
+    ##################### SERIES, LEADING TERM, LIMIT, ORDER METHODS ##################
+    ###################################################################################
+
+    def series(self, x=None, x0=0, n=6, dir="+", logx=None, cdir=0):
+        """
+        Series expansion of "self" around ``x = x0`` yielding either terms of
+        the series one by one (the lazy series given when n=None), else
+        all the terms at once when n != None.
+
+        Returns the series expansion of "self" around the point ``x = x0``
+        with respect to ``x`` up to ``O((x - x0)**n, x, x0)`` (default n is 6).
+
+        If ``x=None`` and ``self`` is univariate, the univariate symbol will
+        be supplied, otherwise an error will be raised.
+
+        Parameters
+        ==========
+
+        expr : Expression
+               The expression whose series is to be expanded.
+
+        x : Symbol
+            It is the variable of the expression to be calculated.
+
+        x0 : Value
+             The value around which ``x`` is calculated. Can be any value
+             from ``-oo`` to ``oo``.
+
+        n : Value
+            The value used to represent the order in terms of ``x**n``,
+            up to which the series is to be expanded.
+
+        dir : String, optional
+              The series-expansion can be bi-directional. If ``dir="+"``,
+              then (x->x0+). If ``dir="-", then (x->x0-). For infinite
+              ``x0`` (``oo`` or ``-oo``), the ``dir`` argument is determined
+              from the direction of the infinity (i.e., ``dir="-"`` for
+              ``oo``).
+
+        logx : optional
+               It is used to replace any log(x) in the returned series with a
+               symbolic value rather than evaluating the actual value.
+
+        cdir : optional
+               It stands for complex direction, and indicates the direction
+               from which the expansion needs to be evaluated.
+
+        Examples
+        ========
+
+        >>> from sympy import cos, exp, tan
+        >>> from sympy.abc import x, y
+        >>> cos(x).series()
+        1 - x**2/2 + x**4/24 + O(x**6)
+        >>> cos(x).series(n=4)
+        1 - x**2/2 + O(x**4)
+        >>> cos(x).series(x, x0=1, n=2)
+        cos(1) - (x - 1)*sin(1) + O((x - 1)**2, (x, 1))
+        >>> e = cos(x + exp(y))
+        >>> e.series(y, n=2)
+        cos(x + 1) - y*sin(x + 1) + O(y**2)
+        >>> e.series(x, n=2)
+        cos(exp(y)) - x*sin(exp(y)) + O(x**2)
+
+        If ``n=None`` then a generator of the series terms will be returned.
+
+        >>> term=cos(x).series(n=None)
+        >>> [next(term) for i in range(2)]
+        [1, -x**2/2]
+
+        For ``dir=+`` (default) the series is calculated from the right and
+        for ``dir=-`` the series from the left. For smooth functions this
+        flag will not alter the results.
+
+        >>> abs(x).series(dir="+")
+        x
+        >>> abs(x).series(dir="-")
+        -x
+        >>> f = tan(x)
+        >>> f.series(x, 2, 6, "+")
+        tan(2) + (1 + tan(2)**2)*(x - 2) + (x - 2)**2*(tan(2)**3 + tan(2)) +
+        (x - 2)**3*(1/3 + 4*tan(2)**2/3 + tan(2)**4) + (x - 2)**4*(tan(2)**5 +
+        5*tan(2)**3/3 + 2*tan(2)/3) + (x - 2)**5*(2/15 + 17*tan(2)**2/15 +
+        2*tan(2)**4 + tan(2)**6) + O((x - 2)**6, (x, 2))
+
+        >>> f.series(x, 2, 3, "-")
+        tan(2) + (2 - x)*(-tan(2)**2 - 1) + (2 - x)**2*(tan(2)**3 + tan(2))
+        + O((x - 2)**3, (x, 2))
+
+        For rational expressions this method may return original expression without the Order term.
+        >>> (1/x).series(x, n=8)
+        1/x
+
+        Returns
+        =======
+
+        Expr : Expression
+            Series expansion of the expression about x0
+
+        Raises
+        ======
+
+        TypeError
+            If "n" and "x0" are infinity objects
+
+        PoleError
+            If "x0" is an infinity object
+
+        """
+        if x is None:
+            syms = self.free_symbols
+            if not syms:
+                return self
+            elif len(syms) > 1:
+                raise ValueError('x must be given for multivariate functions.')
+            x = syms.pop()
+
+        from .symbol import Dummy, Symbol
+        if isinstance(x, Symbol):
+            dep = x in self.free_symbols
+        else:
+            d = Dummy()
+            dep = d in self.xreplace({x: d}).free_symbols
+        if not dep:
+            if n is None:
+                return (s for s in [self])
+            else:
+                return self
+
+        if len(dir) != 1 or dir not in '+-':
+            raise ValueError("Dir must be '+' or '-'")
+
+        if n is not None:
+            n = int(n)
+            if n < 0:
+                raise ValueError("Number of terms should be nonnegative")
+
+        x0 = sympify(x0)
+        cdir = sympify(cdir)
+        from sympy.functions.elementary.complexes import im, sign
+
+        if not cdir.is_zero:
+            if cdir.is_real:
+                dir = '+' if cdir.is_positive else '-'
+            else:
+                dir = '+' if im(cdir).is_positive else '-'
+        else:
+            if x0 and x0.is_infinite:
+                cdir = sign(x0).simplify()
+            elif str(dir) == "+":
+                cdir = S.One
+            elif str(dir) == "-":
+                cdir = S.NegativeOne
+            elif cdir == S.Zero:
+                cdir = S.One
+
+        cdir = cdir/abs(cdir)
+
+        if x0 and x0.is_infinite:
+            from .function import PoleError
+            try:
+                s = self.subs(x, cdir/x).series(x, n=n, dir='+', cdir=1)
+                if n is None:
+                    return (si.subs(x, cdir/x) for si in s)
+                return s.subs(x, cdir/x)
+            except PoleError:
+                s = self.subs(x, cdir*x).aseries(x, n=n)
+                return s.subs(x, cdir*x)
+
+        # use rep to shift origin to x0 and change sign (if dir is negative)
+        # and undo the process with rep2
+        if x0 or cdir != 1:
+            s = self.subs({x: x0 + cdir*x}).series(x, x0=0, n=n, dir='+', logx=logx, cdir=1)
+            if n is None:  # lseries...
+                return (si.subs({x: x/cdir - x0/cdir}) for si in s)
+            return s.subs({x: x/cdir - x0/cdir})
+
+        # from here on it's x0=0 and dir='+' handling
+
+        if x.is_positive is x.is_negative is None or x.is_Symbol is not True:
+            # replace x with an x that has a positive assumption
+            xpos = Dummy('x', positive=True)
+            rv = self.subs(x, xpos).series(xpos, x0, n, dir, logx=logx, cdir=cdir)
+            if n is None:
+                return (s.subs(xpos, x) for s in rv)
+            else:
+                return rv.subs(xpos, x)
+
+        from sympy.series.order import Order
+        if n is not None:  # nseries handling
+            s1 = self._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+            o = s1.getO() or S.Zero
+            if o:
+                # make sure the requested order is returned
+                ngot = o.getn()
+                if ngot > n:
+                    # leave o in its current form (e.g. with x*log(x)) so
+                    # it eats terms properly, then replace it below
+                    if n != 0:
+                        s1 += o.subs(x, x**Rational(n, ngot))
+                    else:
+                        s1 += Order(1, x)
+                elif ngot < n:
+                    # increase the requested number of terms to get the desired
+                    # number keep increasing (up to 9) until the received order
+                    # is different than the original order and then predict how
+                    # many additional terms are needed
+                    from sympy.functions.elementary.integers import ceiling
+                    for more in range(1, 9):
+                        s1 = self._eval_nseries(x, n=n + more, logx=logx, cdir=cdir)
+                        newn = s1.getn()
+                        if newn != ngot:
+                            ndo = n + ceiling((n - ngot)*more/(newn - ngot))
+                            s1 = self._eval_nseries(x, n=ndo, logx=logx, cdir=cdir)
+                            while s1.getn() < n:
+                                s1 = self._eval_nseries(x, n=ndo, logx=logx, cdir=cdir)
+                                ndo += 1
+                            break
+                    else:
+                        raise ValueError('Could not calculate %s terms for %s'
+                                         % (str(n), self))
+                    s1 += Order(x**n, x)
+                o = s1.getO()
+                s1 = s1.removeO()
+            elif s1.has(Order):
+                # asymptotic expansion
+                return s1
+            else:
+                o = Order(x**n, x)
+                s1done = s1.doit()
+                try:
+                    if (s1done + o).removeO() == s1done:
+                        o = S.Zero
+                except NotImplementedError:
+                    return s1
+
+            try:
+                from sympy.simplify.radsimp import collect
+                return collect(s1, x) + o
+            except NotImplementedError:
+                return s1 + o
+
+        else:  # lseries handling
+            def yield_lseries(s):
+                """Return terms of lseries one at a time."""
+                for si in s:
+                    if not si.is_Add:
+                        yield si
+                        continue
+                    # yield terms 1 at a time if possible
+                    # by increasing order until all the
+                    # terms have been returned
+                    yielded = 0
+                    o = Order(si, x)*x
+                    ndid = 0
+                    ndo = len(si.args)
+                    while 1:
+                        do = (si - yielded + o).removeO()
+                        o *= x
+                        if not do or do.is_Order:
+                            continue
+                        if do.is_Add:
+                            ndid += len(do.args)
+                        else:
+                            ndid += 1
+                        yield do
+                        if ndid == ndo:
+                            break
+                        yielded += do
+
+            return yield_lseries(self.removeO()._eval_lseries(x, logx=logx, cdir=cdir))
+
+    def aseries(self, x=None, n=6, bound=0, hir=False):
+        """Asymptotic Series expansion of self.
+        This is equivalent to ``self.series(x, oo, n)``.
+
+        Parameters
+        ==========
+
+        self : Expression
+               The expression whose series is to be expanded.
+
+        x : Symbol
+            It is the variable of the expression to be calculated.
+
+        n : Value
+            The value used to represent the order in terms of ``x**n``,
+            up to which the series is to be expanded.
+
+        hir : Boolean
+              Set this parameter to be True to produce hierarchical series.
+              It stops the recursion at an early level and may provide nicer
+              and more useful results.
+
+        bound : Value, Integer
+                Use the ``bound`` parameter to give limit on rewriting
+                coefficients in its normalised form.
+
+        Examples
+        ========
+
+        >>> from sympy import sin, exp
+        >>> from sympy.abc import x
+
+        >>> e = sin(1/x + exp(-x)) - sin(1/x)
+
+        >>> e.aseries(x)
+        (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x)
+
+        >>> e.aseries(x, n=3, hir=True)
+        -exp(-2*x)*sin(1/x)/2 + exp(-x)*cos(1/x) + O(exp(-3*x), (x, oo))
+
+        >>> e = exp(exp(x)/(1 - 1/x))
+
+        >>> e.aseries(x)
+        exp(exp(x)/(1 - 1/x))
+
+        >>> e.aseries(x, bound=3) # doctest: +SKIP
+        exp(exp(x)/x**2)*exp(exp(x)/x)*exp(-exp(x) + exp(x)/(1 - 1/x) - exp(x)/x - exp(x)/x**2)*exp(exp(x))
+
+        For rational expressions this method may return original expression without the Order term.
+        >>> (1/x).aseries(x, n=8)
+        1/x
+
+        Returns
+        =======
+
+        Expr
+            Asymptotic series expansion of the expression.
+
+        Notes
+        =====
+
+        This algorithm is directly induced from the limit computational algorithm provided by Gruntz.
+        It majorly uses the mrv and rewrite sub-routines. The overall idea of this algorithm is first
+        to look for the most rapidly varying subexpression w of a given expression f and then expands f
+        in a series in w. Then same thing is recursively done on the leading coefficient
+        till we get constant coefficients.
+
+        If the most rapidly varying subexpression of a given expression f is f itself,
+        the algorithm tries to find a normalised representation of the mrv set and rewrites f
+        using this normalised representation.
+
+        If the expansion contains an order term, it will be either ``O(x ** (-n))`` or ``O(w ** (-n))``
+        where ``w`` belongs to the most rapidly varying expression of ``self``.
+
+        References
+        ==========
+
+        .. [1] Gruntz, Dominik. A new algorithm for computing asymptotic series.
+               In: Proc. 1993 Int. Symp. Symbolic and Algebraic Computation. 1993.
+               pp. 239-244.
+        .. [2] Gruntz thesis - p90
+        .. [3] https://en.wikipedia.org/wiki/Asymptotic_expansion
+
+        See Also
+        ========
+
+        Expr.aseries: See the docstring of this function for complete details of this wrapper.
+        """
+
+        from .symbol import Dummy
+
+        if x.is_positive is x.is_negative is None:
+            xpos = Dummy('x', positive=True)
+            return self.subs(x, xpos).aseries(xpos, n, bound, hir).subs(xpos, x)
+
+        from .function import PoleError
+        from sympy.series.gruntz import mrv, rewrite
+
+        try:
+            om, exps = mrv(self, x)
+        except PoleError:
+            return self
+
+        # We move one level up by replacing `x` by `exp(x)`, and then
+        # computing the asymptotic series for f(exp(x)). Then asymptotic series
+        # can be obtained by moving one-step back, by replacing x by ln(x).
+
+        from sympy.functions.elementary.exponential import exp, log
+        from sympy.series.order import Order
+
+        if x in om:
+            s = self.subs(x, exp(x)).aseries(x, n, bound, hir).subs(x, log(x))
+            if s.getO():
+                return s + Order(1/x**n, (x, S.Infinity))
+            return s
+
+        k = Dummy('k', positive=True)
+        # f is rewritten in terms of omega
+        func, logw = rewrite(exps, om, x, k)
+
+        if self in om:
+            if bound <= 0:
+                return self
+            s = (self.exp).aseries(x, n, bound=bound)
+            s = s.func(*[t.removeO() for t in s.args])
+            try:
+                res = exp(s.subs(x, 1/x).as_leading_term(x).subs(x, 1/x))
+            except PoleError:
+                res = self
+
+            func = exp(self.args[0] - res.args[0]) / k
+            logw = log(1/res)
+
+        s = func.series(k, 0, n)
+        from sympy.core.function import expand_mul
+        s = expand_mul(s)
+        # Hierarchical series
+        if hir:
+            return s.subs(k, exp(logw))
+
+        o = s.getO()
+        terms = sorted(Add.make_args(s.removeO()), key=lambda i: int(i.as_coeff_exponent(k)[1]))
+        s = S.Zero
+        has_ord = False
+
+        # Then we recursively expand these coefficients one by one into
+        # their asymptotic series in terms of their most rapidly varying subexpressions.
+        for t in terms:
+            coeff, expo = t.as_coeff_exponent(k)
+            if coeff.has(x):
+                # Recursive step
+                snew = coeff.aseries(x, n, bound=bound-1)
+                if has_ord and snew.getO():
+                    break
+                elif snew.getO():
+                    has_ord = True
+                s += (snew * k**expo)
+            else:
+                s += t
+
+        if not o or has_ord:
+            return s.subs(k, exp(logw))
+        return (s + o).subs(k, exp(logw))
+
+
+    def taylor_term(self, n, x, *previous_terms):
+        """General method for the taylor term.
+
+        This method is slow, because it differentiates n-times. Subclasses can
+        redefine it to make it faster by using the "previous_terms".
+        """
+        from .symbol import Dummy
+        from sympy.functions.combinatorial.factorials import factorial
+
+        x = sympify(x)
+        _x = Dummy('x')
+        return self.subs(x, _x).diff(_x, n).subs(_x, x).subs(x, 0) * x**n / factorial(n)
+
+    def lseries(self, x=None, x0=0, dir='+', logx=None, cdir=0):
+        """
+        Wrapper for series yielding an iterator of the terms of the series.
+
+        Note: an infinite series will yield an infinite iterator. The following,
+        for exaxmple, will never terminate. It will just keep printing terms
+        of the sin(x) series::
+
+          for term in sin(x).lseries(x):
+              print term
+
+        The advantage of lseries() over nseries() is that many times you are
+        just interested in the next term in the series (i.e. the first term for
+        example), but you do not know how many you should ask for in nseries()
+        using the "n" parameter.
+
+        See also nseries().
+        """
+        return self.series(x, x0, n=None, dir=dir, logx=logx, cdir=cdir)
+
+    def _eval_lseries(self, x, logx=None, cdir=0):
+        # default implementation of lseries is using nseries(), and adaptively
+        # increasing the "n". As you can see, it is not very efficient, because
+        # we are calculating the series over and over again. Subclasses should
+        # override this method and implement much more efficient yielding of
+        # terms.
+        n = 0
+        series = self._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+
+        while series.is_Order:
+            n += 1
+            series = self._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+
+        e = series.removeO()
+        yield e
+        if e is S.Zero:
+            return
+
+        while 1:
+            while 1:
+                n += 1
+                series = self._eval_nseries(x, n=n, logx=logx, cdir=cdir).removeO()
+                if e != series:
+                    break
+                if (series - self).cancel() is S.Zero:
+                    return
+            yield series - e
+            e = series
+
+    def nseries(self, x=None, x0=0, n=6, dir='+', logx=None, cdir=0):
+        """
+        Wrapper to _eval_nseries if assumptions allow, else to series.
+
+        If x is given, x0 is 0, dir='+', and self has x, then _eval_nseries is
+        called. This calculates "n" terms in the innermost expressions and
+        then builds up the final series just by "cross-multiplying" everything
+        out.
+
+        The optional ``logx`` parameter can be used to replace any log(x) in the
+        returned series with a symbolic value to avoid evaluating log(x) at 0. A
+        symbol to use in place of log(x) should be provided.
+
+        Advantage -- it's fast, because we do not have to determine how many
+        terms we need to calculate in advance.
+
+        Disadvantage -- you may end up with less terms than you may have
+        expected, but the O(x**n) term appended will always be correct and
+        so the result, though perhaps shorter, will also be correct.
+
+        If any of those assumptions is not met, this is treated like a
+        wrapper to series which will try harder to return the correct
+        number of terms.
+
+        See also lseries().
+
+        Examples
+        ========
+
+        >>> from sympy import sin, log, Symbol
+        >>> from sympy.abc import x, y
+        >>> sin(x).nseries(x, 0, 6)
+        x - x**3/6 + x**5/120 + O(x**6)
+        >>> log(x+1).nseries(x, 0, 5)
+        x - x**2/2 + x**3/3 - x**4/4 + O(x**5)
+
+        Handling of the ``logx`` parameter --- in the following example the
+        expansion fails since ``sin`` does not have an asymptotic expansion
+        at -oo (the limit of log(x) as x approaches 0):
+
+        >>> e = sin(log(x))
+        >>> e.nseries(x, 0, 6)
+        Traceback (most recent call last):
+        ...
+        PoleError: ...
+        ...
+        >>> logx = Symbol('logx')
+        >>> e.nseries(x, 0, 6, logx=logx)
+        sin(logx)
+
+        In the following example, the expansion works but only returns self
+        unless the ``logx`` parameter is used:
+
+        >>> e = x**y
+        >>> e.nseries(x, 0, 2)
+        x**y
+        >>> e.nseries(x, 0, 2, logx=logx)
+        exp(logx*y)
+
+        """
+        if x and x not in self.free_symbols:
+            return self
+        if x is None or x0 or dir != '+':  # {see XPOS above} or (x.is_positive == x.is_negative == None):
+            return self.series(x, x0, n, dir, cdir=cdir)
+        else:
+            return self._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir):
+        """
+        Return terms of series for self up to O(x**n) at x=0
+        from the positive direction.
+
+        This is a method that should be overridden in subclasses. Users should
+        never call this method directly (use .nseries() instead), so you do not
+        have to write docstrings for _eval_nseries().
+        """
+        raise NotImplementedError(filldedent("""
+                     The _eval_nseries method should be added to
+                     %s to give terms up to O(x**n) at x=0
+                     from the positive direction so it is available when
+                     nseries calls it.""" % self.func)
+                     )
+
+    def limit(self, x, xlim, dir='+'):
+        """ Compute limit x->xlim.
+        """
+        from sympy.series.limits import limit
+        return limit(self, x, xlim, dir)
+
+    @cacheit
+    def as_leading_term(self, *symbols, logx=None, cdir=0):
+        """
+        Returns the leading (nonzero) term of the series expansion of self.
+
+        The _eval_as_leading_term routines are used to do this, and they must
+        always return a non-zero value.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> (1 + x + x**2).as_leading_term(x)
+        1
+        >>> (1/x**2 + x + x**2).as_leading_term(x)
+        x**(-2)
+
+        """
+        if len(symbols) > 1:
+            c = self
+            for x in symbols:
+                c = c.as_leading_term(x, logx=logx, cdir=cdir)
+            return c
+        elif not symbols:
+            return self
+        x = sympify(symbols[0])
+        cdir = sympify(cdir)
+        if not x.is_symbol:
+            raise ValueError('expecting a Symbol but got %s' % x)
+        if x not in self.free_symbols:
+            return self
+        obj = self._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        if obj is not None:
+            from sympy.simplify.powsimp import powsimp
+            return powsimp(obj, deep=True, combine='exp')
+        raise NotImplementedError('as_leading_term(%s, %s)' % (self, x))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        return self
+
+    def as_coeff_exponent(self, x) -> tuple[Expr, Expr]:
+        """ ``c*x**e -> c,e`` where x can be any symbolic expression.
+        """
+        from sympy.simplify.radsimp import collect
+        s = collect(self, x)
+        c, p = s.as_coeff_mul(x)
+        if len(p) == 1:
+            b, e = p[0].as_base_exp()
+            if b == x:
+                return c, e
+        return s, S.Zero
+
+    def leadterm(self, x, logx=None, cdir=0):
+        """
+        Returns the leading term a*x**b as a tuple (a, b).
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> (1+x+x**2).leadterm(x)
+        (1, 0)
+        >>> (1/x**2+x+x**2).leadterm(x)
+        (1, -2)
+
+        """
+        from .symbol import Dummy
+        from sympy.functions.elementary.exponential import log
+        l = self.as_leading_term(x, logx=logx, cdir=cdir)
+        d = Dummy('logx')
+        if l.has(log(x)):
+            l = l.subs(log(x), d)
+        c, e = l.as_coeff_exponent(x)
+        if x in c.free_symbols:
+            raise ValueError(filldedent("""
+                cannot compute leadterm(%s, %s). The coefficient
+                should have been free of %s but got %s""" % (self, x, x, c)))
+        c = c.subs(d, log(x))
+        return c, e
+
+    def as_coeff_Mul(self, rational: bool = False) -> tuple['Number', Expr]:
+        """Efficiently extract the coefficient of a product."""
+        return S.One, self
+
+    def as_coeff_Add(self, rational=False) -> tuple['Number', Expr]:
+        """Efficiently extract the coefficient of a summation."""
+        return S.Zero, self
+
+    def fps(self, x=None, x0=0, dir=1, hyper=True, order=4, rational=True,
+            full=False):
+        """
+        Compute formal power power series of self.
+
+        See the docstring of the :func:`fps` function in sympy.series.formal for
+        more information.
+        """
+        from sympy.series.formal import fps
+
+        return fps(self, x, x0, dir, hyper, order, rational, full)
+
+    def fourier_series(self, limits=None):
+        """Compute fourier sine/cosine series of self.
+
+        See the docstring of the :func:`fourier_series` in sympy.series.fourier
+        for more information.
+        """
+        from sympy.series.fourier import fourier_series
+
+        return fourier_series(self, limits)
+
+    ###################################################################################
+    ##################### DERIVATIVE, INTEGRAL, FUNCTIONAL METHODS ####################
+    ###################################################################################
+
+    def diff(self, *symbols, **assumptions):
+        assumptions.setdefault("evaluate", True)
+        return _derivative_dispatch(self, *symbols, **assumptions)
+
+    ###########################################################################
+    ###################### EXPRESSION EXPANSION METHODS #######################
+    ###########################################################################
+
+    # Relevant subclasses should override _eval_expand_hint() methods.  See
+    # the docstring of expand() for more info.
+
+    def _eval_expand_complex(self, **hints):
+        real, imag = self.as_real_imag(**hints)
+        return real + S.ImaginaryUnit*imag
+
+    @staticmethod
+    def _expand_hint(expr, hint, deep=True, **hints):
+        """
+        Helper for ``expand()``.  Recursively calls ``expr._eval_expand_hint()``.
+
+        Returns ``(expr, hit)``, where expr is the (possibly) expanded
+        ``expr`` and ``hit`` is ``True`` if ``expr`` was truly expanded and
+        ``False`` otherwise.
+        """
+        hit = False
+        # XXX: Hack to support non-Basic args
+        #              |
+        #              V
+        if deep and getattr(expr, 'args', ()) and not expr.is_Atom:
+            sargs = []
+            for arg in expr.args:
+                arg, arghit = Expr._expand_hint(arg, hint, **hints)
+                hit |= arghit
+                sargs.append(arg)
+
+            if hit:
+                expr = expr.func(*sargs)
+
+        if hasattr(expr, hint):
+            newexpr = getattr(expr, hint)(**hints)
+            if newexpr != expr:
+                return (newexpr, True)
+
+        return (expr, hit)
+
+    @cacheit
+    def expand(self, deep=True, modulus=None, power_base=True, power_exp=True,
+            mul=True, log=True, multinomial=True, basic=True, **hints):
+        """
+        Expand an expression using hints.
+
+        See the docstring of the expand() function in sympy.core.function for
+        more information.
+
+        """
+        from sympy.simplify.radsimp import fraction
+
+        hints.update(power_base=power_base, power_exp=power_exp, mul=mul,
+           log=log, multinomial=multinomial, basic=basic)
+
+        expr = self
+        # default matches fraction's default
+        _fraction = lambda x: fraction(x, hints.get('exact', False))
+        if hints.pop('frac', False):
+            n, d = [a.expand(deep=deep, modulus=modulus, **hints)
+                    for a in _fraction(self)]
+            return n/d
+        elif hints.pop('denom', False):
+            n, d = _fraction(self)
+            return n/d.expand(deep=deep, modulus=modulus, **hints)
+        elif hints.pop('numer', False):
+            n, d = _fraction(self)
+            return n.expand(deep=deep, modulus=modulus, **hints)/d
+
+        # Although the hints are sorted here, an earlier hint may get applied
+        # at a given node in the expression tree before another because of how
+        # the hints are applied.  e.g. expand(log(x*(y + z))) -> log(x*y +
+        # x*z) because while applying log at the top level, log and mul are
+        # applied at the deeper level in the tree so that when the log at the
+        # upper level gets applied, the mul has already been applied at the
+        # lower level.
+
+        # Additionally, because hints are only applied once, the expression
+        # may not be expanded all the way.   For example, if mul is applied
+        # before multinomial, x*(x + 1)**2 won't be expanded all the way.  For
+        # now, we just use a special case to make multinomial run before mul,
+        # so that at least polynomials will be expanded all the way.  In the
+        # future, smarter heuristics should be applied.
+        # TODO: Smarter heuristics
+
+        def _expand_hint_key(hint):
+            """Make multinomial come before mul"""
+            if hint == 'mul':
+                return 'mulz'
+            return hint
+
+        for hint in sorted(hints.keys(), key=_expand_hint_key):
+            use_hint = hints[hint]
+            if use_hint:
+                hint = '_eval_expand_' + hint
+                expr, hit = Expr._expand_hint(expr, hint, deep=deep, **hints)
+
+        while True:
+            was = expr
+            if hints.get('multinomial', False):
+                expr, _ = Expr._expand_hint(
+                    expr, '_eval_expand_multinomial', deep=deep, **hints)
+            if hints.get('mul', False):
+                expr, _ = Expr._expand_hint(
+                    expr, '_eval_expand_mul', deep=deep, **hints)
+            if hints.get('log', False):
+                expr, _ = Expr._expand_hint(
+                    expr, '_eval_expand_log', deep=deep, **hints)
+            if expr == was:
+                break
+
+        if modulus is not None:
+            modulus = sympify(modulus)
+
+            if not modulus.is_Integer or modulus <= 0:
+                raise ValueError(
+                    "modulus must be a positive integer, got %s" % modulus)
+
+            terms = []
+
+            for term in Add.make_args(expr):
+                coeff, tail = term.as_coeff_Mul(rational=True)
+
+                coeff %= modulus
+
+                if coeff:
+                    terms.append(coeff*tail)
+
+            expr = Add(*terms)
+
+        return expr
+
+    ###########################################################################
+    ################### GLOBAL ACTION VERB WRAPPER METHODS ####################
+    ###########################################################################
+
+    def integrate(self, *args, **kwargs):
+        """See the integrate function in sympy.integrals"""
+        from sympy.integrals.integrals import integrate
+        return integrate(self, *args, **kwargs)
+
+    def nsimplify(self, constants=(), tolerance=None, full=False):
+        """See the nsimplify function in sympy.simplify"""
+        from sympy.simplify.simplify import nsimplify
+        return nsimplify(self, constants, tolerance, full)
+
+    def separate(self, deep=False, force=False):
+        """See the separate function in sympy.simplify"""
+        from .function import expand_power_base
+        return expand_power_base(self, deep=deep, force=force)
+
+    def collect(self, syms, func=None, evaluate=True, exact=False, distribute_order_term=True):
+        """See the collect function in sympy.simplify"""
+        from sympy.simplify.radsimp import collect
+        return collect(self, syms, func, evaluate, exact, distribute_order_term)
+
+    def together(self, *args, **kwargs):
+        """See the together function in sympy.polys"""
+        from sympy.polys.rationaltools import together
+        return together(self, *args, **kwargs)
+
+    def apart(self, x=None, **args):
+        """See the apart function in sympy.polys"""
+        from sympy.polys.partfrac import apart
+        return apart(self, x, **args)
+
+    def ratsimp(self):
+        """See the ratsimp function in sympy.simplify"""
+        from sympy.simplify.ratsimp import ratsimp
+        return ratsimp(self)
+
+    def trigsimp(self, **args):
+        """See the trigsimp function in sympy.simplify"""
+        from sympy.simplify.trigsimp import trigsimp
+        return trigsimp(self, **args)
+
+    def radsimp(self, **kwargs):
+        """See the radsimp function in sympy.simplify"""
+        from sympy.simplify.radsimp import radsimp
+        return radsimp(self, **kwargs)
+
+    def powsimp(self, *args, **kwargs):
+        """See the powsimp function in sympy.simplify"""
+        from sympy.simplify.powsimp import powsimp
+        return powsimp(self, *args, **kwargs)
+
+    def combsimp(self):
+        """See the combsimp function in sympy.simplify"""
+        from sympy.simplify.combsimp import combsimp
+        return combsimp(self)
+
+    def gammasimp(self):
+        """See the gammasimp function in sympy.simplify"""
+        from sympy.simplify.gammasimp import gammasimp
+        return gammasimp(self)
+
+    def factor(self, *gens, **args):
+        """See the factor() function in sympy.polys.polytools"""
+        from sympy.polys.polytools import factor
+        return factor(self, *gens, **args)
+
+    def cancel(self, *gens, **args):
+        """See the cancel function in sympy.polys"""
+        from sympy.polys.polytools import cancel
+        return cancel(self, *gens, **args)
+
+    def invert(self, g, *gens, **args):
+        """Return the multiplicative inverse of ``self`` mod ``g``
+        where ``self`` (and ``g``) may be symbolic expressions).
+
+        See Also
+        ========
+        sympy.core.intfunc.mod_inverse, sympy.polys.polytools.invert
+        """
+        if self.is_number and getattr(g, 'is_number', True):
+            return mod_inverse(self, g)
+        from sympy.polys.polytools import invert
+        return invert(self, g, *gens, **args)
+
+    def round(self, n=None):
+        """Return x rounded to the given decimal place.
+
+        If a complex number would results, apply round to the real
+        and imaginary components of the number.
+
+        Examples
+        ========
+
+        >>> from sympy import pi, E, I, S, Number
+        >>> pi.round()
+        3
+        >>> pi.round(2)
+        3.14
+        >>> (2*pi + E*I).round()
+        6 + 3*I
+
+        The round method has a chopping effect:
+
+        >>> (2*pi + I/10).round()
+        6
+        >>> (pi/10 + 2*I).round()
+        2*I
+        >>> (pi/10 + E*I).round(2)
+        0.31 + 2.72*I
+
+        Notes
+        =====
+
+        The Python ``round`` function uses the SymPy ``round`` method so it
+        will always return a SymPy number (not a Python float or int):
+
+        >>> isinstance(round(S(123), -2), Number)
+        True
+        """
+        x = self
+
+        if not x.is_number:
+            raise TypeError("Cannot round symbolic expression")
+        if not x.is_Atom:
+            if not pure_complex(x.n(2), or_real=True):
+                raise TypeError(
+                    'Expected a number but got %s:' % func_name(x))
+        elif x in _illegal:
+            return x
+        if not (xr := x.is_extended_real):
+            r, i = x.as_real_imag()
+            if xr is False:
+                return r.round(n) + S.ImaginaryUnit*i.round(n)
+            if i.equals(0):
+                return r.round(n)
+        if not x:
+            return S.Zero if n is None else x
+
+        p = as_int(n or 0)
+
+        if x.is_Integer:
+            return Integer(round(int(x), p))
+
+        digits_to_decimal = _mag(x)  # _mag(12) = 2, _mag(.012) = -1
+        allow = digits_to_decimal + p
+        precs = [f._prec for f in x.atoms(Float)]
+        dps = prec_to_dps(max(precs)) if precs else None
+        if dps is None:
+            # assume everything is exact so use the Python
+            # float default or whatever was requested
+            dps = max(15, allow)
+        else:
+            allow = min(allow, dps)
+        # this will shift all digits to right of decimal
+        # and give us dps to work with as an int
+        shift = -digits_to_decimal + dps
+        extra = 1  # how far we look past known digits
+        # NOTE
+        # mpmath will calculate the binary representation to
+        # an arbitrary number of digits but we must base our
+        # answer on a finite number of those digits, e.g.
+        # .575 2589569785738035/2**52 in binary.
+        # mpmath shows us that the first 18 digits are
+        #     >>> Float(.575).n(18)
+        #     0.574999999999999956
+        # The default precision is 15 digits and if we ask
+        # for 15 we get
+        #     >>> Float(.575).n(15)
+        #     0.575000000000000
+        # mpmath handles rounding at the 15th digit. But we
+        # need to be careful since the user might be asking
+        # for rounding at the last digit and our semantics
+        # are to round toward the even final digit when there
+        # is a tie. So the extra digit will be used to make
+        # that decision. In this case, the value is the same
+        # to 15 digits:
+        #     >>> Float(.575).n(16)
+        #     0.5750000000000000
+        # Now converting this to the 15 known digits gives
+        #     575000000000000.0
+        # which rounds to integer
+        #    5750000000000000
+        # And now we can round to the desired digt, e.g. at
+        # the second from the left and we get
+        #    5800000000000000
+        # and rescaling that gives
+        #    0.58
+        # as the final result.
+        # If the value is made slightly less than 0.575 we might
+        # still obtain the same value:
+        #    >>> Float(.575-1e-16).n(16)*10**15
+        #    574999999999999.8
+        # What 15 digits best represents the known digits (which are
+        # to the left of the decimal? 5750000000000000, the same as
+        # before. The only way we will round down (in this case) is
+        # if we declared that we had more than 15 digits of precision.
+        # For example, if we use 16 digits of precision, the integer
+        # we deal with is
+        #    >>> Float(.575-1e-16).n(17)*10**16
+        #    5749999999999998.4
+        # and this now rounds to 5749999999999998 and (if we round to
+        # the 2nd digit from the left) we get 5700000000000000.
+        #
+        xf = x.n(dps + extra)*Pow(10, shift)
+        if xf.is_Number and xf._prec == 1:  # xf.is_Add will raise below
+            # is x == 0?
+            if x.equals(0):
+                return Float(0)
+            raise ValueError('not computing with precision')
+        xi = Integer(xf)
+        # use the last digit to select the value of xi
+        # nearest to x before rounding at the desired digit
+        sign = 1 if x > 0 else -1
+        dif2 = sign*(xf - xi).n(extra)
+        if dif2 < 0:
+            raise NotImplementedError(
+                'not expecting int(x) to round away from 0')
+        if dif2 > .5:
+            xi += sign  # round away from 0
+        elif dif2 == .5:
+            xi += sign if xi%2 else -sign  # round toward even
+        # shift p to the new position
+        ip = p - shift
+        # let Python handle the int rounding then rescale
+        xr = round(xi.p, ip)
+        # restore scale
+        rv = Rational(xr, Pow(10, shift))
+        # return Float or Integer
+        if rv.is_Integer:
+            if n is None:  # the single-arg case
+                return rv
+            # use str or else it won't be a float
+            return Float(str(rv), dps)  # keep same precision
+        else:
+            if not allow and rv > self:
+                allow += 1
+            return Float(rv, allow)
+
+    __round__ = round
+
+    def _eval_derivative_matrix_lines(self, x):
+        from sympy.matrices.expressions.matexpr import _LeftRightArgs
+        return [_LeftRightArgs([S.One, S.One], higher=self._eval_derivative(x))]
+
+
+class AtomicExpr(Atom, Expr):
+    """
+    A parent class for object which are both atoms and Exprs.
+
+    For example: Symbol, Number, Rational, Integer, ...
+    But not: Add, Mul, Pow, ...
+    """
+    is_number = False
+    is_Atom = True
+
+    __slots__ = ()
+
+    def _eval_derivative(self, s):
+        if self == s:
+            return S.One
+        return S.Zero
+
+    def _eval_derivative_n_times(self, s, n):
+        from .containers import Tuple
+        from sympy.matrices.expressions.matexpr import MatrixExpr
+        from sympy.matrices.matrixbase import MatrixBase
+        if isinstance(s, (MatrixBase, Tuple, Iterable, MatrixExpr)):
+            return super()._eval_derivative_n_times(s, n)
+        from .relational import Eq
+        from sympy.functions.elementary.piecewise import Piecewise
+        if self == s:
+            return Piecewise((self, Eq(n, 0)), (1, Eq(n, 1)), (0, True))
+        else:
+            return Piecewise((self, Eq(n, 0)), (0, True))
+
+    def _eval_is_polynomial(self, syms):
+        return True
+
+    def _eval_is_rational_function(self, syms):
+        return self not in _illegal
+
+    def _eval_is_meromorphic(self, x, a):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        return (not self.is_Number or self.is_finite) and not isinstance(self, AccumBounds)
+
+    def _eval_is_algebraic_expr(self, syms):
+        return True
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        return self
+
+    @property
+    def expr_free_symbols(self):
+        sympy_deprecation_warning("""
+        The expr_free_symbols property is deprecated. Use free_symbols to get
+        the free symbols of an expression.
+        """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-expr-free-symbols")
+        return {self}
+
+
+def _mag(x):
+    r"""Return integer $i$ such that $0.1 \le x/10^i < 1$
+
+    Examples
+    ========
+
+    >>> from sympy.core.expr import _mag
+    >>> from sympy import Float
+    >>> _mag(Float(.1))
+    0
+    >>> _mag(Float(.01))
+    -1
+    >>> _mag(Float(1234))
+    4
+    """
+    from math import log10, ceil, log
+    xpos = abs(x.n())
+    if not xpos:
+        return S.Zero
+    try:
+        mag_first_dig = int(ceil(log10(xpos)))
+    except (ValueError, OverflowError):
+        mag_first_dig = int(ceil(Float(mpf_log(xpos._mpf_, 53))/log(10)))
+    # check that we aren't off by 1
+    if (xpos/S(10)**mag_first_dig) >= 1:
+        assert 1 <= (xpos/S(10)**mag_first_dig) < 10
+        mag_first_dig += 1
+    return mag_first_dig
+
+
+class UnevaluatedExpr(Expr):
+    """
+    Expression that is not evaluated unless released.
+
+    Examples
+    ========
+
+    >>> from sympy import UnevaluatedExpr
+    >>> from sympy.abc import x
+    >>> x*(1/x)
+    1
+    >>> x*UnevaluatedExpr(1/x)
+    x*1/x
+
+    """
+
+    def __new__(cls, arg, **kwargs):
+        arg = _sympify(arg)
+        obj = Expr.__new__(cls, arg, **kwargs)
+        return obj
+
+    def doit(self, **hints):
+        if hints.get("deep", True):
+            return self.args[0].doit(**hints)
+        else:
+            return self.args[0]
+
+
+
+def unchanged(func, *args):
+    """Return True if `func` applied to the `args` is unchanged.
+    Can be used instead of `assert foo == foo`.
+
+    Examples
+    ========
+
+    >>> from sympy import Piecewise, cos, pi
+    >>> from sympy.core.expr import unchanged
+    >>> from sympy.abc import x
+
+    >>> unchanged(cos, 1)  # instead of assert cos(1) == cos(1)
+    True
+
+    >>> unchanged(cos, pi)
+    False
+
+    Comparison of args uses the builtin capabilities of the object's
+    arguments to test for equality so args can be defined loosely. Here,
+    the ExprCondPair arguments of Piecewise compare as equal to the
+    tuples that can be used to create the Piecewise:
+
+    >>> unchanged(Piecewise, (x, x > 1), (0, True))
+    True
+    """
+    f = func(*args)
+    return f.func == func and f.args == args
+
+
+class ExprBuilder:
+    def __init__(self, op, args=None, validator=None, check=True):
+        if not hasattr(op, "__call__"):
+            raise TypeError("op {} needs to be callable".format(op))
+        self.op = op
+        if args is None:
+            self.args = []
+        else:
+            self.args = args
+        self.validator = validator
+        if (validator is not None) and check:
+            self.validate()
+
+    @staticmethod
+    def _build_args(args):
+        return [i.build() if isinstance(i, ExprBuilder) else i for i in args]
+
+    def validate(self):
+        if self.validator is None:
+            return
+        args = self._build_args(self.args)
+        self.validator(*args)
+
+    def build(self, check=True):
+        args = self._build_args(self.args)
+        if self.validator and check:
+            self.validator(*args)
+        return self.op(*args)
+
+    def append_argument(self, arg, check=True):
+        self.args.append(arg)
+        if self.validator and check:
+            self.validate(*self.args)
+
+    def __getitem__(self, item):
+        if item == 0:
+            return self.op
+        else:
+            return self.args[item-1]
+
+    def __repr__(self):
+        return str(self.build())
+
+    def search_element(self, elem):
+        for i, arg in enumerate(self.args):
+            if isinstance(arg, ExprBuilder):
+                ret = arg.search_index(elem)
+                if ret is not None:
+                    return (i,) + ret
+            elif id(arg) == id(elem):
+                return (i,)
+        return None
+
+
+from .mul import Mul
+from .add import Add
+from .power import Pow
+from .function import Function, _derivative_dispatch
+from .mod import Mod
+from .exprtools import factor_terms
+from .numbers import Float, Integer, Rational, _illegal, int_valued
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/exprtools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/exprtools.py
new file mode 100644
index 0000000000000000000000000000000000000000..4868e4416a72e91dc12c9113d90b9c31c5e26011
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/exprtools.py
@@ -0,0 +1,1573 @@
+"""Tools for manipulating of large commutative expressions. """
+
+from __future__ import annotations
+
+from .add import Add
+from .mul import Mul, _keep_coeff
+from .power import Pow
+from .basic import Basic
+from .expr import Expr
+from .function import expand_power_exp
+from .sympify import sympify
+from .numbers import Rational, Integer, Number, I, equal_valued
+from .singleton import S
+from .sorting import default_sort_key, ordered
+from .symbol import Dummy
+from .traversal import preorder_traversal
+from .coreerrors import NonCommutativeExpression
+from .containers import Tuple, Dict
+from sympy.external.gmpy import SYMPY_INTS
+from sympy.utilities.iterables import (common_prefix, common_suffix,
+        variations, iterable, is_sequence)
+
+from collections import defaultdict
+
+
+_eps = Dummy(positive=True)
+
+
+def _isnumber(i):
+    return isinstance(i, (SYMPY_INTS, float)) or i.is_Number
+
+
+def _monotonic_sign(self):
+    """Return the value closest to 0 that ``self`` may have if all symbols
+    are signed and the result is uniformly the same sign for all values of symbols.
+    If a symbol is only signed but not known to be an
+    integer or the result is 0 then a symbol representative of the sign of self
+    will be returned. Otherwise, None is returned if a) the sign could be positive
+    or negative or b) self is not in one of the following forms:
+
+    - L(x, y, ...) + A: a function linear in all symbols x, y, ... with an
+      additive constant; if A is zero then the function can be a monomial whose
+      sign is monotonic over the range of the variables, e.g. (x + 1)**3 if x is
+      nonnegative.
+    - A/L(x, y, ...) + B: the inverse of a function linear in all symbols x, y, ...
+      that does not have a sign change from positive to negative for any set
+      of values for the variables.
+    - M(x, y, ...) + A: a monomial M whose factors are all signed and a constant, A.
+    - A/M(x, y, ...) + B: the inverse of a monomial and constants A and B.
+    - P(x): a univariate polynomial
+
+    Examples
+    ========
+
+    >>> from sympy.core.exprtools import _monotonic_sign as F
+    >>> from sympy import Dummy
+    >>> nn = Dummy(integer=True, nonnegative=True)
+    >>> p = Dummy(integer=True, positive=True)
+    >>> p2 = Dummy(integer=True, positive=True)
+    >>> F(nn + 1)
+    1
+    >>> F(p - 1)
+    _nneg
+    >>> F(nn*p + 1)
+    1
+    >>> F(p2*p + 1)
+    2
+    >>> F(nn - 1)  # could be negative, zero or positive
+    """
+    if not self.is_extended_real:
+        return
+
+    if (-self).is_Symbol:
+        rv = _monotonic_sign(-self)
+        return rv if rv is None else -rv
+
+    if not self.is_Add and self.as_numer_denom()[1].is_number:
+        s = self
+        if s.is_prime:
+            if s.is_odd:
+                return Integer(3)
+            else:
+                return Integer(2)
+        elif s.is_composite:
+            if s.is_odd:
+                return Integer(9)
+            else:
+                return Integer(4)
+        elif s.is_positive:
+            if s.is_even:
+                if s.is_prime is False:
+                    return Integer(4)
+                else:
+                    return Integer(2)
+            elif s.is_integer:
+                return S.One
+            else:
+                return _eps
+        elif s.is_extended_negative:
+            if s.is_even:
+                return Integer(-2)
+            elif s.is_integer:
+                return S.NegativeOne
+            else:
+                return -_eps
+        if s.is_zero or s.is_extended_nonpositive or s.is_extended_nonnegative:
+            return S.Zero
+        return None
+
+    # univariate polynomial
+    free = self.free_symbols
+    if len(free) == 1:
+        if self.is_polynomial():
+            from sympy.polys.polytools import real_roots
+            from sympy.polys.polyroots import roots
+            from sympy.polys.polyerrors import PolynomialError
+            x = free.pop()
+            x0 = _monotonic_sign(x)
+            if x0 in (_eps, -_eps):
+                x0 = S.Zero
+            if x0 is not None:
+                d = self.diff(x)
+                if d.is_number:
+                    currentroots = []
+                else:
+                    try:
+                        currentroots = real_roots(d)
+                    except (PolynomialError, NotImplementedError):
+                        currentroots = [r for r in roots(d, x) if r.is_extended_real]
+                y = self.subs(x, x0)
+                if x.is_nonnegative and all(
+                        (r - x0).is_nonpositive for r in currentroots):
+                    if y.is_nonnegative and d.is_positive:
+                        if y:
+                            return y if y.is_positive else Dummy('pos', positive=True)
+                        else:
+                            return Dummy('nneg', nonnegative=True)
+                    if y.is_nonpositive and d.is_negative:
+                        if y:
+                            return y if y.is_negative else Dummy('neg', negative=True)
+                        else:
+                            return Dummy('npos', nonpositive=True)
+                elif x.is_nonpositive and all(
+                        (r - x0).is_nonnegative for r in currentroots):
+                    if y.is_nonnegative and d.is_negative:
+                        if y:
+                            return Dummy('pos', positive=True)
+                        else:
+                            return Dummy('nneg', nonnegative=True)
+                    if y.is_nonpositive and d.is_positive:
+                        if y:
+                            return Dummy('neg', negative=True)
+                        else:
+                            return Dummy('npos', nonpositive=True)
+        else:
+            n, d = self.as_numer_denom()
+            den = None
+            if n.is_number:
+                den = _monotonic_sign(d)
+            elif not d.is_number:
+                if _monotonic_sign(n) is not None:
+                    den = _monotonic_sign(d)
+            if den is not None and (den.is_positive or den.is_negative):
+                v = n*den
+                if v.is_positive:
+                    return Dummy('pos', positive=True)
+                elif v.is_nonnegative:
+                    return Dummy('nneg', nonnegative=True)
+                elif v.is_negative:
+                    return Dummy('neg', negative=True)
+                elif v.is_nonpositive:
+                    return Dummy('npos', nonpositive=True)
+        return None
+
+    # multivariate
+    c, a = self.as_coeff_Add()
+    v = None
+    if not a.is_polynomial():
+        # F/A or A/F where A is a number and F is a signed, rational monomial
+        n, d = a.as_numer_denom()
+        if not (n.is_number or d.is_number):
+            return
+        if (
+                a.is_Mul or a.is_Pow) and \
+                a.is_rational and \
+                all(p.exp.is_Integer for p in a.atoms(Pow) if p.is_Pow) and \
+                (a.is_positive or a.is_negative):
+            v = S.One
+            for ai in Mul.make_args(a):
+                if ai.is_number:
+                    v *= ai
+                    continue
+                reps = {}
+                for x in ai.free_symbols:
+                    reps[x] = _monotonic_sign(x)
+                    if reps[x] is None:
+                        return
+                v *= ai.subs(reps)
+    elif c:
+        # signed linear expression
+        if not any(p for p in a.atoms(Pow) if not p.is_number) and (a.is_nonpositive or a.is_nonnegative):
+            free = list(a.free_symbols)
+            p = {}
+            for i in free:
+                v = _monotonic_sign(i)
+                if v is None:
+                    return
+                p[i] = v or (_eps if i.is_nonnegative else -_eps)
+            v = a.xreplace(p)
+    if v is not None:
+        rv = v + c
+        if v.is_nonnegative and rv.is_positive:
+            return rv.subs(_eps, 0)
+        if v.is_nonpositive and rv.is_negative:
+            return rv.subs(_eps, 0)
+
+
+def decompose_power(expr: Expr) -> tuple[Expr, int]:
+    """
+    Decompose power into symbolic base and integer exponent.
+
+    Examples
+    ========
+
+    >>> from sympy.core.exprtools import decompose_power
+    >>> from sympy.abc import x, y
+    >>> from sympy import exp
+
+    >>> decompose_power(x)
+    (x, 1)
+    >>> decompose_power(x**2)
+    (x, 2)
+    >>> decompose_power(exp(2*y/3))
+    (exp(y/3), 2)
+
+    """
+    base, exp = expr.as_base_exp()
+
+    if exp.is_Number:
+        if exp.is_Rational:
+            if not exp.is_Integer:
+                base = Pow(base, Rational(1, exp.q))  # type: ignore
+            e = exp.p  # type: ignore
+        else:
+            base, e = expr, 1
+    else:
+        exp, tail = exp.as_coeff_Mul(rational=True)
+
+        if exp is S.NegativeOne:
+            base, e = Pow(base, tail), -1
+        elif exp is not S.One:
+            # todo: after dropping python 3.7 support, use overload and Literal
+            #  in as_coeff_Mul to make exp Rational, and remove these 2 ignores
+            tail = _keep_coeff(Rational(1, exp.q), tail)  # type: ignore
+            base, e = Pow(base, tail), exp.p  # type: ignore
+        else:
+            base, e = expr, 1
+
+    return base, e
+
+
+def decompose_power_rat(expr: Expr) -> tuple[Expr, Rational]:
+    """
+    Decompose power into symbolic base and rational exponent;
+    if the exponent is not a Rational, then separate only the
+    integer coefficient.
+
+    Examples
+    ========
+
+    >>> from sympy.core.exprtools import decompose_power_rat
+    >>> from sympy.abc import x
+    >>> from sympy import sqrt, exp
+
+    >>> decompose_power_rat(sqrt(x))
+    (x, 1/2)
+    >>> decompose_power_rat(exp(-3*x/2))
+    (exp(x/2), -3)
+
+    """
+    base, exp = expr.as_base_exp()
+    if not exp.is_Rational:
+        base, exp_i = decompose_power(expr)
+        exp = Integer(exp_i)
+    return base, exp # type: ignore
+
+
+class Factors:
+    """Efficient representation of ``f_1*f_2*...*f_n``."""
+
+    __slots__ = ('factors', 'gens')
+
+    def __init__(self, factors=None):  # Factors
+        """Initialize Factors from dict or expr.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x
+        >>> from sympy import I
+        >>> e = 2*x**3
+        >>> Factors(e)
+        Factors({2: 1, x: 3})
+        >>> Factors(e.as_powers_dict())
+        Factors({2: 1, x: 3})
+        >>> f = _
+        >>> f.factors  # underlying dictionary
+        {2: 1, x: 3}
+        >>> f.gens  # base of each factor
+        frozenset({2, x})
+        >>> Factors(0)
+        Factors({0: 1})
+        >>> Factors(I)
+        Factors({I: 1})
+
+        Notes
+        =====
+
+        Although a dictionary can be passed, only minimal checking is
+        performed: powers of -1 and I are made canonical.
+
+        """
+        if isinstance(factors, (SYMPY_INTS, float)):
+            factors = S(factors)
+        if isinstance(factors, Factors):
+            factors = factors.factors.copy()
+        elif factors in (None, S.One):
+            factors = {}
+        elif factors is S.Zero or factors == 0:
+            factors = {S.Zero: S.One}
+        elif isinstance(factors, Number):
+            n = factors
+            factors = {}
+            if n < 0:
+                factors[S.NegativeOne] = S.One
+                n = -n
+            if n is not S.One:
+                if n.is_Float or n.is_Integer or n is S.Infinity:
+                    factors[n] = S.One
+                elif n.is_Rational:
+                    # since we're processing Numbers, the denominator is
+                    # stored with a negative exponent; all other factors
+                    # are left .
+                    if n.p != 1:
+                        factors[Integer(n.p)] = S.One
+                    factors[Integer(n.q)] = S.NegativeOne
+                else:
+                    raise ValueError('Expected Float|Rational|Integer, not %s' % n)
+        elif isinstance(factors, Basic) and not factors.args:
+            factors = {factors: S.One}
+        elif isinstance(factors, Expr):
+            c, nc = factors.args_cnc()
+            i = c.count(I)
+            for _ in range(i):
+                c.remove(I)
+            factors = dict(Mul._from_args(c).as_powers_dict())
+            # Handle all rational Coefficients
+            for f in list(factors.keys()):
+                if isinstance(f, Rational) and not isinstance(f, Integer):
+                    p, q = Integer(f.p), Integer(f.q)
+                    factors[p] = (factors[p] if p in factors else S.Zero) + factors[f]
+                    factors[q] = (factors[q] if q in factors else S.Zero) - factors[f]
+                    factors.pop(f)
+            if i:
+                factors[I] = factors.get(I, S.Zero) + i
+            if nc:
+                factors[Mul(*nc, evaluate=False)] = S.One
+        else:
+            factors = factors.copy()  # /!\ should be dict-like
+
+            # tidy up -/+1 and I exponents if Rational
+
+            handle = [k for k in factors if k is I or k in (-1, 1)]
+            if handle:
+                i1 = S.One
+                for k in handle:
+                    if not _isnumber(factors[k]):
+                        continue
+                    i1 *= k**factors.pop(k)
+                if i1 is not S.One:
+                    for a in i1.args if i1.is_Mul else [i1]:  # at worst, -1.0*I*(-1)**e
+                        if a is S.NegativeOne:
+                            factors[a] = S.One
+                        elif a is I:
+                            factors[I] = S.One
+                        elif a.is_Pow:
+                            factors[a.base] = factors.get(a.base, S.Zero) + a.exp
+                        elif equal_valued(a, 1):
+                            factors[a] = S.One
+                        elif equal_valued(a, -1):
+                            factors[-a] = S.One
+                            factors[S.NegativeOne] = S.One
+                        else:
+                            raise ValueError('unexpected factor in i1: %s' % a)
+
+        self.factors = factors
+        keys = getattr(factors, 'keys', None)
+        if keys is None:
+            raise TypeError('expecting Expr or dictionary')
+        self.gens = frozenset(keys())
+
+    def __hash__(self):  # Factors
+        keys = tuple(ordered(self.factors.keys()))
+        values = [self.factors[k] for k in keys]
+        return hash((keys, values))
+
+    def __repr__(self):  # Factors
+        return "Factors({%s})" % ', '.join(
+            ['%s: %s' % (k, v) for k, v in ordered(self.factors.items())])
+
+    @property
+    def is_zero(self):  # Factors
+        """
+        >>> from sympy.core.exprtools import Factors
+        >>> Factors(0).is_zero
+        True
+        """
+        f = self.factors
+        return len(f) == 1 and S.Zero in f
+
+    @property
+    def is_one(self):  # Factors
+        """
+        >>> from sympy.core.exprtools import Factors
+        >>> Factors(1).is_one
+        True
+        """
+        return not self.factors
+
+    def as_expr(self):  # Factors
+        """Return the underlying expression.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y
+        >>> Factors((x*y**2).as_powers_dict()).as_expr()
+        x*y**2
+
+        """
+
+        args = []
+        for factor, exp in self.factors.items():
+            if exp != 1:
+                if isinstance(exp, Integer):
+                    b, e = factor.as_base_exp()
+                    e = _keep_coeff(exp, e)
+                    args.append(b**e)
+                else:
+                    args.append(factor**exp)
+            else:
+                args.append(factor)
+        return Mul(*args)
+
+    def mul(self, other):  # Factors
+        """Return Factors of ``self * other``.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y, z
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> b = Factors((x*y/z).as_powers_dict())
+        >>> a.mul(b)
+        Factors({x: 2, y: 3, z: -1})
+        >>> a*b
+        Factors({x: 2, y: 3, z: -1})
+        """
+        if not isinstance(other, Factors):
+            other = Factors(other)
+        if any(f.is_zero for f in (self, other)):
+            return Factors(S.Zero)
+        factors = dict(self.factors)
+
+        for factor, exp in other.factors.items():
+            if factor in factors:
+                exp = factors[factor] + exp
+
+                if not exp:
+                    del factors[factor]
+                    continue
+
+            factors[factor] = exp
+
+        return Factors(factors)
+
+    def normal(self, other):
+        """Return ``self`` and ``other`` with ``gcd`` removed from each.
+        The only differences between this and method ``div`` is that this
+        is 1) optimized for the case when there are few factors in common and
+        2) this does not raise an error if ``other`` is zero.
+
+        See Also
+        ========
+        div
+
+        """
+        if not isinstance(other, Factors):
+            other = Factors(other)
+            if other.is_zero:
+                return (Factors(), Factors(S.Zero))
+            if self.is_zero:
+                return (Factors(S.Zero), Factors())
+
+        self_factors = dict(self.factors)
+        other_factors = dict(other.factors)
+
+        for factor, self_exp in self.factors.items():
+            try:
+                other_exp = other.factors[factor]
+            except KeyError:
+                continue
+
+            exp = self_exp - other_exp
+
+            if not exp:
+                del self_factors[factor]
+                del other_factors[factor]
+            elif _isnumber(exp):
+                if exp > 0:
+                    self_factors[factor] = exp
+                    del other_factors[factor]
+                else:
+                    del self_factors[factor]
+                    other_factors[factor] = -exp
+            else:
+                r = self_exp.extract_additively(other_exp)
+                if r is not None:
+                    if r:
+                        self_factors[factor] = r
+                        del other_factors[factor]
+                    else:  # should be handled already
+                        del self_factors[factor]
+                        del other_factors[factor]
+                else:
+                    sc, sa = self_exp.as_coeff_Add()
+                    if sc:
+                        oc, oa = other_exp.as_coeff_Add()
+                        diff = sc - oc
+                        if diff > 0:
+                            self_factors[factor] -= oc
+                            other_exp = oa
+                        elif diff < 0:
+                            self_factors[factor] -= sc
+                            other_factors[factor] -= sc
+                            other_exp = oa - diff
+                        else:
+                            self_factors[factor] = sa
+                            other_exp = oa
+                    if other_exp:
+                        other_factors[factor] = other_exp
+                    else:
+                        del other_factors[factor]
+
+        return Factors(self_factors), Factors(other_factors)
+
+    def div(self, other):  # Factors
+        """Return ``self`` and ``other`` with ``gcd`` removed from each.
+        This is optimized for the case when there are many factors in common.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y, z
+        >>> from sympy import S
+
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> a.div(a)
+        (Factors({}), Factors({}))
+        >>> a.div(x*z)
+        (Factors({y: 2}), Factors({z: 1}))
+
+        The ``/`` operator only gives ``quo``:
+
+        >>> a/x
+        Factors({y: 2})
+
+        Factors treats its factors as though they are all in the numerator, so
+        if you violate this assumption the results will be correct but will
+        not strictly correspond to the numerator and denominator of the ratio:
+
+        >>> a.div(x/z)
+        (Factors({y: 2}), Factors({z: -1}))
+
+        Factors is also naive about bases: it does not attempt any denesting
+        of Rational-base terms, for example the following does not become
+        2**(2*x)/2.
+
+        >>> Factors(2**(2*x + 2)).div(S(8))
+        (Factors({2: 2*x + 2}), Factors({8: 1}))
+
+        factor_terms can clean up such Rational-bases powers:
+
+        >>> from sympy import factor_terms
+        >>> n, d = Factors(2**(2*x + 2)).div(S(8))
+        >>> n.as_expr()/d.as_expr()
+        2**(2*x + 2)/8
+        >>> factor_terms(_)
+        2**(2*x)/2
+
+        """
+        quo, rem = dict(self.factors), {}
+
+        if not isinstance(other, Factors):
+            other = Factors(other)
+            if other.is_zero:
+                raise ZeroDivisionError
+            if self.is_zero:
+                return (Factors(S.Zero), Factors())
+
+        for factor, exp in other.factors.items():
+            if factor in quo:
+                d = quo[factor] - exp
+                if _isnumber(d):
+                    if d <= 0:
+                        del quo[factor]
+
+                    if d >= 0:
+                        if d:
+                            quo[factor] = d
+
+                        continue
+
+                    exp = -d
+
+                else:
+                    r = quo[factor].extract_additively(exp)
+                    if r is not None:
+                        if r:
+                            quo[factor] = r
+                        else:  # should be handled already
+                            del quo[factor]
+                    else:
+                        other_exp = exp
+                        sc, sa = quo[factor].as_coeff_Add()
+                        if sc:
+                            oc, oa = other_exp.as_coeff_Add()
+                            diff = sc - oc
+                            if diff > 0:
+                                quo[factor] -= oc
+                                other_exp = oa
+                            elif diff < 0:
+                                quo[factor] -= sc
+                                other_exp = oa - diff
+                            else:
+                                quo[factor] = sa
+                                other_exp = oa
+                        if other_exp:
+                            rem[factor] = other_exp
+                        else:
+                            assert factor not in rem
+                    continue
+
+            rem[factor] = exp
+
+        return Factors(quo), Factors(rem)
+
+    def quo(self, other):  # Factors
+        """Return numerator Factor of ``self / other``.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y, z
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> b = Factors((x*y/z).as_powers_dict())
+        >>> a.quo(b)  # same as a/b
+        Factors({y: 1})
+        """
+        return self.div(other)[0]
+
+    def rem(self, other):  # Factors
+        """Return denominator Factors of ``self / other``.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y, z
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> b = Factors((x*y/z).as_powers_dict())
+        >>> a.rem(b)
+        Factors({z: -1})
+        >>> a.rem(a)
+        Factors({})
+        """
+        return self.div(other)[1]
+
+    def pow(self, other):  # Factors
+        """Return self raised to a non-negative integer power.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> a**2
+        Factors({x: 2, y: 4})
+
+        """
+        if isinstance(other, Factors):
+            other = other.as_expr()
+            if other.is_Integer:
+                other = int(other)
+        if isinstance(other, SYMPY_INTS) and other >= 0:
+            factors = {}
+
+            if other:
+                for factor, exp in self.factors.items():
+                    factors[factor] = exp*other
+
+            return Factors(factors)
+        else:
+            raise ValueError("expected non-negative integer, got %s" % other)
+
+    def gcd(self, other):  # Factors
+        """Return Factors of ``gcd(self, other)``. The keys are
+        the intersection of factors with the minimum exponent for
+        each factor.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y, z
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> b = Factors((x*y/z).as_powers_dict())
+        >>> a.gcd(b)
+        Factors({x: 1, y: 1})
+        """
+        if not isinstance(other, Factors):
+            other = Factors(other)
+            if other.is_zero:
+                return Factors(self.factors)
+
+        factors = {}
+
+        for factor, exp in self.factors.items():
+            factor, exp = sympify(factor), sympify(exp)
+            if factor in other.factors:
+                lt = (exp - other.factors[factor]).is_negative
+                if lt == True:
+                    factors[factor] = exp
+                elif lt == False:
+                    factors[factor] = other.factors[factor]
+
+        return Factors(factors)
+
+    def lcm(self, other):  # Factors
+        """Return Factors of ``lcm(self, other)`` which are
+        the union of factors with the maximum exponent for
+        each factor.
+
+        Examples
+        ========
+
+        >>> from sympy.core.exprtools import Factors
+        >>> from sympy.abc import x, y, z
+        >>> a = Factors((x*y**2).as_powers_dict())
+        >>> b = Factors((x*y/z).as_powers_dict())
+        >>> a.lcm(b)
+        Factors({x: 1, y: 2, z: -1})
+        """
+        if not isinstance(other, Factors):
+            other = Factors(other)
+            if any(f.is_zero for f in (self, other)):
+                return Factors(S.Zero)
+
+        factors = dict(self.factors)
+
+        for factor, exp in other.factors.items():
+            if factor in factors:
+                exp = max(exp, factors[factor])
+
+            factors[factor] = exp
+
+        return Factors(factors)
+
+    def __mul__(self, other):  # Factors
+        return self.mul(other)
+
+    def __divmod__(self, other):  # Factors
+        return self.div(other)
+
+    def __truediv__(self, other):  # Factors
+        return self.quo(other)
+
+    def __mod__(self, other):  # Factors
+        return self.rem(other)
+
+    def __pow__(self, other):  # Factors
+        return self.pow(other)
+
+    def __eq__(self, other):  # Factors
+        if not isinstance(other, Factors):
+            other = Factors(other)
+        return self.factors == other.factors
+
+    def __ne__(self, other):  # Factors
+        return not self == other
+
+
+class Term:
+    """Efficient representation of ``coeff*(numer/denom)``. """
+
+    __slots__ = ('coeff', 'numer', 'denom')
+
+    def __init__(self, term, numer=None, denom=None):  # Term
+        if numer is None and denom is None:
+            if not term.is_commutative:
+                raise NonCommutativeExpression(
+                    'commutative expression expected')
+
+            coeff, factors = term.as_coeff_mul()
+            numer, denom = defaultdict(int), defaultdict(int)
+
+            for factor in factors:
+                base, exp = decompose_power(factor)
+
+                if base.is_Add:
+                    cont, base = base.primitive()
+                    coeff *= cont**exp
+
+                if exp > 0:
+                    numer[base] += exp
+                else:
+                    denom[base] += -exp
+
+            numer = Factors(numer)
+            denom = Factors(denom)
+        else:
+            coeff = term
+
+            if numer is None:
+                numer = Factors()
+
+            if denom is None:
+                denom = Factors()
+
+        self.coeff = coeff
+        self.numer = numer
+        self.denom = denom
+
+    def __hash__(self):  # Term
+        return hash((self.coeff, self.numer, self.denom))
+
+    def __repr__(self):  # Term
+        return "Term(%s, %s, %s)" % (self.coeff, self.numer, self.denom)
+
+    def as_expr(self):  # Term
+        return self.coeff*(self.numer.as_expr()/self.denom.as_expr())
+
+    def mul(self, other):  # Term
+        coeff = self.coeff*other.coeff
+        numer = self.numer.mul(other.numer)
+        denom = self.denom.mul(other.denom)
+
+        numer, denom = numer.normal(denom)
+
+        return Term(coeff, numer, denom)
+
+    def inv(self):  # Term
+        return Term(1/self.coeff, self.denom, self.numer)
+
+    def quo(self, other):  # Term
+        return self.mul(other.inv())
+
+    def pow(self, other):  # Term
+        if other < 0:
+            return self.inv().pow(-other)
+        else:
+            return Term(self.coeff ** other,
+                        self.numer.pow(other),
+                        self.denom.pow(other))
+
+    def gcd(self, other):  # Term
+        return Term(self.coeff.gcd(other.coeff),
+                    self.numer.gcd(other.numer),
+                    self.denom.gcd(other.denom))
+
+    def lcm(self, other):  # Term
+        return Term(self.coeff.lcm(other.coeff),
+                    self.numer.lcm(other.numer),
+                    self.denom.lcm(other.denom))
+
+    def __mul__(self, other):  # Term
+        if isinstance(other, Term):
+            return self.mul(other)
+        else:
+            return NotImplemented
+
+    def __truediv__(self, other):  # Term
+        if isinstance(other, Term):
+            return self.quo(other)
+        else:
+            return NotImplemented
+
+    def __pow__(self, other):  # Term
+        if isinstance(other, SYMPY_INTS):
+            return self.pow(other)
+        else:
+            return NotImplemented
+
+    def __eq__(self, other):  # Term
+        return (self.coeff == other.coeff and
+                self.numer == other.numer and
+                self.denom == other.denom)
+
+    def __ne__(self, other):  # Term
+        return not self == other
+
+
+def _gcd_terms(terms, isprimitive=False, fraction=True):
+    """Helper function for :func:`gcd_terms`.
+
+    Parameters
+    ==========
+
+    isprimitive : boolean, optional
+        If ``isprimitive`` is True then the call to primitive
+        for an Add will be skipped. This is useful when the
+        content has already been extracted.
+
+    fraction : boolean, optional
+        If ``fraction`` is True then the expression will appear over a common
+        denominator, the lcm of all term denominators.
+    """
+
+    if isinstance(terms, Basic) and not isinstance(terms, Tuple):
+        terms = Add.make_args(terms)
+
+    terms = list(map(Term, [t for t in terms if t]))
+
+    # there is some simplification that may happen if we leave this
+    # here rather than duplicate it before the mapping of Term onto
+    # the terms
+    if len(terms) == 0:
+        return S.Zero, S.Zero, S.One
+
+    if len(terms) == 1:
+        cont = terms[0].coeff
+        numer = terms[0].numer.as_expr()
+        denom = terms[0].denom.as_expr()
+
+    else:
+        cont = terms[0]
+        for term in terms[1:]:
+            cont = cont.gcd(term)
+
+        for i, term in enumerate(terms):
+            terms[i] = term.quo(cont)
+
+        if fraction:
+            denom = terms[0].denom
+
+            for term in terms[1:]:
+                denom = denom.lcm(term.denom)
+
+            numers = []
+            for term in terms:
+                numer = term.numer.mul(denom.quo(term.denom))
+                numers.append(term.coeff*numer.as_expr())
+        else:
+            numers = [t.as_expr() for t in terms]
+            denom = Term(S.One).numer
+
+        cont = cont.as_expr()
+        numer = Add(*numers)
+        denom = denom.as_expr()
+
+    if not isprimitive and numer.is_Add:
+        _cont, numer = numer.primitive()
+        cont *= _cont
+
+    return cont, numer, denom
+
+
+def gcd_terms(terms, isprimitive=False, clear=True, fraction=True):
+    """Compute the GCD of ``terms`` and put them together.
+
+    Parameters
+    ==========
+
+    terms : Expr
+        Can be an expression or a non-Basic sequence of expressions
+        which will be handled as though they are terms from a sum.
+
+    isprimitive : bool, optional
+        If ``isprimitive`` is True the _gcd_terms will not run the primitive
+        method on the terms.
+
+    clear : bool, optional
+        It controls the removal of integers from the denominator of an Add
+        expression. When True (default), all numerical denominator will be cleared;
+        when False the denominators will be cleared only if all terms had numerical
+        denominators other than 1.
+
+    fraction : bool, optional
+        When True (default), will put the expression over a common
+        denominator.
+
+    Examples
+    ========
+
+    >>> from sympy import gcd_terms
+    >>> from sympy.abc import x, y
+
+    >>> gcd_terms((x + 1)**2*y + (x + 1)*y**2)
+    y*(x + 1)*(x + y + 1)
+    >>> gcd_terms(x/2 + 1)
+    (x + 2)/2
+    >>> gcd_terms(x/2 + 1, clear=False)
+    x/2 + 1
+    >>> gcd_terms(x/2 + y/2, clear=False)
+    (x + y)/2
+    >>> gcd_terms(x/2 + 1/x)
+    (x**2 + 2)/(2*x)
+    >>> gcd_terms(x/2 + 1/x, fraction=False)
+    (x + 2/x)/2
+    >>> gcd_terms(x/2 + 1/x, fraction=False, clear=False)
+    x/2 + 1/x
+
+    >>> gcd_terms(x/2/y + 1/x/y)
+    (x**2 + 2)/(2*x*y)
+    >>> gcd_terms(x/2/y + 1/x/y, clear=False)
+    (x**2/2 + 1)/(x*y)
+    >>> gcd_terms(x/2/y + 1/x/y, clear=False, fraction=False)
+    (x/2 + 1/x)/y
+
+    The ``clear`` flag was ignored in this case because the returned
+    expression was a rational expression, not a simple sum.
+
+    See Also
+    ========
+
+    factor_terms, sympy.polys.polytools.terms_gcd
+
+    """
+    def mask(terms):
+        """replace nc portions of each term with a unique Dummy symbols
+        and return the replacements to restore them"""
+        args = [(a, []) if a.is_commutative else a.args_cnc() for a in terms]
+        reps = []
+        for i, (c, nc) in enumerate(args):
+            if nc:
+                nc = Mul(*nc)
+                d = Dummy()
+                reps.append((d, nc))
+                c.append(d)
+                args[i] = Mul(*c)
+            else:
+                args[i] = c
+        return args, dict(reps)
+
+    isadd = isinstance(terms, Add)
+    addlike = isadd or not isinstance(terms, Basic) and \
+        is_sequence(terms, include=set) and \
+        not isinstance(terms, Dict)
+
+    if addlike:
+        if isadd:  # i.e. an Add
+            terms = list(terms.args)
+        else:
+            terms = sympify(terms)
+        terms, reps = mask(terms)
+        cont, numer, denom = _gcd_terms(terms, isprimitive, fraction)
+        numer = numer.xreplace(reps)
+        coeff, factors = cont.as_coeff_Mul()
+        if not clear:
+            c, _coeff = coeff.as_coeff_Mul()
+            if not c.is_Integer and not clear and numer.is_Add:
+                n, d = c.as_numer_denom()
+                _numer = numer/d
+                if any(a.as_coeff_Mul()[0].is_Integer
+                        for a in _numer.args):
+                    numer = _numer
+                    coeff = n*_coeff
+        return _keep_coeff(coeff, factors*numer/denom, clear=clear)
+
+    if not isinstance(terms, Basic):
+        return terms
+
+    if terms.is_Atom:
+        return terms
+
+    if terms.is_Mul:
+        c, args = terms.as_coeff_mul()
+        return _keep_coeff(c, Mul(*[gcd_terms(i, isprimitive, clear, fraction)
+            for i in args]), clear=clear)
+
+    def handle(a):
+        # don't treat internal args like terms of an Add
+        if not isinstance(a, Expr):
+            if isinstance(a, Basic):
+                if not a.args:
+                    return a
+                return a.func(*[handle(i) for i in a.args])
+            return type(a)([handle(i) for i in a])
+        return gcd_terms(a, isprimitive, clear, fraction)
+
+    if isinstance(terms, Dict):
+        return Dict(*[(k, handle(v)) for k, v in terms.args])
+    return terms.func(*[handle(i) for i in terms.args])
+
+
+def _factor_sum_int(expr, **kwargs):
+    """Return Sum or Integral object with factors that are not
+    in the wrt variables removed. In cases where there are additive
+    terms in the function of the object that are independent, the
+    object will be separated into two objects.
+
+    Examples
+    ========
+
+    >>> from sympy import Sum, factor_terms
+    >>> from sympy.abc import x, y
+    >>> factor_terms(Sum(x + y, (x, 1, 3)))
+    y*Sum(1, (x, 1, 3)) + Sum(x, (x, 1, 3))
+    >>> factor_terms(Sum(x*y, (x, 1, 3)))
+    y*Sum(x, (x, 1, 3))
+
+    Notes
+    =====
+
+    If a function in the summand or integrand is replaced
+    with a symbol, then this simplification should not be
+    done or else an incorrect result will be obtained when
+    the symbol is replaced with an expression that depends
+    on the variables of summation/integration:
+
+    >>> eq = Sum(y, (x, 1, 3))
+    >>> factor_terms(eq).subs(y, x).doit()
+    3*x
+    >>> eq.subs(y, x).doit()
+    6
+    """
+    result = expr.function
+    if result == 0:
+        return S.Zero
+    limits = expr.limits
+
+    # get the wrt variables
+    wrt = {i.args[0] for i in limits}
+
+    # factor out any common terms that are independent of wrt
+    f = factor_terms(result, **kwargs)
+    i, d = f.as_independent(*wrt)
+    if isinstance(f, Add):
+        return i * expr.func(1, *limits) + expr.func(d, *limits)
+    else:
+        return i * expr.func(d, *limits)
+
+
+def factor_terms(expr: Expr | complex, radical=False, clear=False, fraction=False, sign=True) -> Expr:
+    """Remove common factors from terms in all arguments without
+    changing the underlying structure of the expr. No expansion or
+    simplification (and no processing of non-commutatives) is performed.
+
+    Parameters
+    ==========
+
+    radical: bool, optional
+        If radical=True then a radical common to all terms will be factored
+        out of any Add sub-expressions of the expr.
+
+    clear : bool, optional
+        If clear=False (default) then coefficients will not be separated
+        from a single Add if they can be distributed to leave one or more
+        terms with integer coefficients.
+
+    fraction : bool, optional
+        If fraction=True (default is False) then a common denominator will be
+        constructed for the expression.
+
+    sign : bool, optional
+        If sign=True (default) then even if the only factor in common is a -1,
+        it will be factored out of the expression.
+
+    Examples
+    ========
+
+    >>> from sympy import factor_terms, Symbol
+    >>> from sympy.abc import x, y
+    >>> factor_terms(x + x*(2 + 4*y)**3)
+    x*(8*(2*y + 1)**3 + 1)
+    >>> A = Symbol('A', commutative=False)
+    >>> factor_terms(x*A + x*A + x*y*A)
+    x*(y*A + 2*A)
+
+    When ``clear`` is False, a rational will only be factored out of an
+    Add expression if all terms of the Add have coefficients that are
+    fractions:
+
+    >>> factor_terms(x/2 + 1, clear=False)
+    x/2 + 1
+    >>> factor_terms(x/2 + 1, clear=True)
+    (x + 2)/2
+
+    If a -1 is all that can be factored out, to *not* factor it out, the
+    flag ``sign`` must be False:
+
+    >>> factor_terms(-x - y)
+    -(x + y)
+    >>> factor_terms(-x - y, sign=False)
+    -x - y
+    >>> factor_terms(-2*x - 2*y, sign=False)
+    -2*(x + y)
+
+    See Also
+    ========
+
+    gcd_terms, sympy.polys.polytools.terms_gcd
+
+    """
+    def do(expr):
+        from sympy.concrete.summations import Sum
+        from sympy.integrals.integrals import Integral
+        is_iterable = iterable(expr)
+
+        if not isinstance(expr, Basic) or expr.is_Atom:
+            if is_iterable:
+                return type(expr)([do(i) for i in expr])
+            return expr
+
+        if expr.is_Pow or expr.is_Function or \
+                is_iterable or not hasattr(expr, 'args_cnc'):
+            args = expr.args
+            newargs = tuple([do(i) for i in args])
+            if newargs == args:
+                return expr
+            return expr.func(*newargs)
+
+        if isinstance(expr, (Sum, Integral)):
+            return _factor_sum_int(expr,
+                radical=radical, clear=clear,
+                fraction=fraction, sign=sign)
+
+        cont, p = expr.as_content_primitive(radical=radical, clear=clear)
+        if p.is_Add:
+            list_args = [do(a) for a in Add.make_args(p)]
+            # get a common negative (if there) which gcd_terms does not remove
+            if not any(a.as_coeff_Mul()[0].extract_multiplicatively(-1) is None
+                       for a in list_args):
+                cont = -cont
+                list_args = [-a for a in list_args]
+            # watch out for exp(-(x+2)) which gcd_terms will change to exp(-x-2)
+            special = {}
+            for i, a in enumerate(list_args):
+                b, e = a.as_base_exp()
+                if e.is_Mul and e != Mul(*e.args):
+                    list_args[i] = Dummy()
+                    special[list_args[i]] = a
+            # rebuild p not worrying about the order which gcd_terms will fix
+            p = Add._from_args(list_args)
+            p = gcd_terms(p,
+                isprimitive=True,
+                clear=clear,
+                fraction=fraction).xreplace(special)
+        elif p.args:
+            p = p.func(
+                *[do(a) for a in p.args])
+        rv = _keep_coeff(cont, p, clear=clear, sign=sign)
+        return rv
+    expr2 = sympify(expr)
+    return do(expr2)
+
+
+def _mask_nc(eq, name=None):
+    """
+    Return ``eq`` with non-commutative objects replaced with Dummy
+    symbols. A dictionary that can be used to restore the original
+    values is returned: if it is None, the expression is noncommutative
+    and cannot be made commutative. The third value returned is a list
+    of any non-commutative symbols that appear in the returned equation.
+
+    Explanation
+    ===========
+
+    All non-commutative objects other than Symbols are replaced with
+    a non-commutative Symbol. Identical objects will be identified
+    by identical symbols.
+
+    If there is only 1 non-commutative object in an expression it will
+    be replaced with a commutative symbol. Otherwise, the non-commutative
+    entities are retained and the calling routine should handle
+    replacements in this case since some care must be taken to keep
+    track of the ordering of symbols when they occur within Muls.
+
+    Parameters
+    ==========
+
+    name : str
+        ``name``, if given, is the name that will be used with numbered Dummy
+        variables that will replace the non-commutative objects and is mainly
+        used for doctesting purposes.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import Commutator, NO, F, Fd
+    >>> from sympy import symbols
+    >>> from sympy.core.exprtools import _mask_nc
+    >>> from sympy.abc import x, y
+    >>> A, B, C = symbols('A,B,C', commutative=False)
+
+    One nc-symbol:
+
+    >>> _mask_nc(A**2 - x**2, 'd')
+    (_d0**2 - x**2, {_d0: A}, [])
+
+    Multiple nc-symbols:
+
+    >>> _mask_nc(A**2 - B**2, 'd')
+    (A**2 - B**2, {}, [A, B])
+
+    An nc-object with nc-symbols but no others outside of it:
+
+    >>> _mask_nc(1 + x*Commutator(A, B), 'd')
+    (_d0*x + 1, {_d0: Commutator(A, B)}, [])
+    >>> _mask_nc(NO(Fd(x)*F(y)), 'd')
+    (_d0, {_d0: NO(CreateFermion(x)*AnnihilateFermion(y))}, [])
+
+    Multiple nc-objects:
+
+    >>> eq = x*Commutator(A, B) + x*Commutator(A, C)*Commutator(A, B)
+    >>> _mask_nc(eq, 'd')
+    (x*_d0 + x*_d1*_d0, {_d0: Commutator(A, B), _d1: Commutator(A, C)}, [_d0, _d1])
+
+    Multiple nc-objects and nc-symbols:
+
+    >>> eq = A*Commutator(A, B) + B*Commutator(A, C)
+    >>> _mask_nc(eq, 'd')
+    (A*_d0 + B*_d1, {_d0: Commutator(A, B), _d1: Commutator(A, C)}, [_d0, _d1, A, B])
+
+    """
+    name = name or 'mask'
+    # Make Dummy() append sequential numbers to the name
+
+    def numbered_names():
+        i = 0
+        while True:
+            yield name + str(i)
+            i += 1
+
+    names = numbered_names()
+
+    def Dummy(*args, **kwargs):
+        from .symbol import Dummy
+        return Dummy(next(names), *args, **kwargs)
+
+    expr = eq
+    if expr.is_commutative:
+        return eq, {}, []
+
+    # identify nc-objects; symbols and other
+    rep = []
+    nc_obj = set()
+    nc_syms = set()
+    pot = preorder_traversal(expr, keys=default_sort_key)
+    for a in pot:
+        if any(a == r[0] for r in rep):
+            pot.skip()
+        elif not a.is_commutative:
+            if a.is_symbol:
+                nc_syms.add(a)
+                pot.skip()
+            elif not (a.is_Add or a.is_Mul or a.is_Pow):
+                nc_obj.add(a)
+                pot.skip()
+
+    # If there is only one nc symbol or object, it can be factored regularly
+    # but polys is going to complain, so replace it with a Dummy.
+    if len(nc_obj) == 1 and not nc_syms:
+        rep.append((nc_obj.pop(), Dummy()))
+    elif len(nc_syms) == 1 and not nc_obj:
+        rep.append((nc_syms.pop(), Dummy()))
+
+    # Any remaining nc-objects will be replaced with an nc-Dummy and
+    # identified as an nc-Symbol to watch out for
+    nc_obj = sorted(nc_obj, key=default_sort_key)
+    for n in nc_obj:
+        nc = Dummy(commutative=False)
+        rep.append((n, nc))
+        nc_syms.add(nc)
+    expr = expr.subs(rep)
+
+    nc_syms = list(nc_syms)
+    nc_syms.sort(key=default_sort_key)
+    return expr, {v: k for k, v in rep}, nc_syms
+
+
+def factor_nc(expr):
+    """Return the factored form of ``expr`` while handling non-commutative
+    expressions.
+
+    Examples
+    ========
+
+    >>> from sympy import factor_nc, Symbol
+    >>> from sympy.abc import x
+    >>> A = Symbol('A', commutative=False)
+    >>> B = Symbol('B', commutative=False)
+    >>> factor_nc((x**2 + 2*A*x + A**2).expand())
+    (x + A)**2
+    >>> factor_nc(((x + A)*(x + B)).expand())
+    (x + A)*(x + B)
+    """
+    expr = sympify(expr)
+    if not isinstance(expr, Expr) or not expr.args:
+        return expr
+    if not expr.is_Add:
+        return expr.func(*[factor_nc(a) for a in expr.args])
+    expr = expr.func(*[expand_power_exp(i) for i in expr.args])
+
+    from sympy.polys.polytools import gcd, factor
+    expr, rep, nc_symbols = _mask_nc(expr)
+
+    if rep:
+        return factor(expr).subs(rep)
+    else:
+        args = [a.args_cnc() for a in Add.make_args(expr)]
+        c = g = l = r = S.One
+        hit = False
+        # find any commutative gcd term
+        for i, a in enumerate(args):
+            if i == 0:
+                c = Mul._from_args(a[0])
+            elif a[0]:
+                c = gcd(c, Mul._from_args(a[0]))
+            else:
+                c = S.One
+        if c is not S.One:
+            hit = True
+            c, g = c.as_coeff_Mul()
+            if g is not S.One:
+                for i, (cc, _) in enumerate(args):
+                    cc = list(Mul.make_args(Mul._from_args(list(cc))/g))
+                    args[i][0] = cc
+            for i, (cc, _) in enumerate(args):
+                if cc:
+                    cc[0] = cc[0]/c
+                else:
+                    cc = [1/c]
+                args[i][0] = cc
+        # find any noncommutative common prefix
+        for i, a in enumerate(args):
+            if i == 0:
+                n = a[1][:]
+            else:
+                n = common_prefix(n, a[1])
+            if not n:
+                # is there a power that can be extracted?
+                if not args[0][1]:
+                    break
+                b, e = args[0][1][0].as_base_exp()
+                ok = False
+                if e.is_Integer:
+                    for t in args:
+                        if not t[1]:
+                            break
+                        bt, et = t[1][0].as_base_exp()
+                        if et.is_Integer and bt == b:
+                            e = min(e, et)
+                        else:
+                            break
+                    else:
+                        ok = hit = True
+                        l = b**e
+                        il = b**-e
+                        for _ in args:
+                            _[1][0] = il*_[1][0]
+                        break
+                if not ok:
+                    break
+        else:
+            hit = True
+            lenn = len(n)
+            l = Mul(*n)
+            for _ in args:
+                _[1] = _[1][lenn:]
+        # find any noncommutative common suffix
+        for i, a in enumerate(args):
+            if i == 0:
+                n = a[1][:]
+            else:
+                n = common_suffix(n, a[1])
+            if not n:
+                # is there a power that can be extracted?
+                if not args[0][1]:
+                    break
+                b, e = args[0][1][-1].as_base_exp()
+                ok = False
+                if e.is_Integer:
+                    for t in args:
+                        if not t[1]:
+                            break
+                        bt, et = t[1][-1].as_base_exp()
+                        if et.is_Integer and bt == b:
+                            e = min(e, et)
+                        else:
+                            break
+                    else:
+                        ok = hit = True
+                        r = b**e
+                        il = b**-e
+                        for _ in args:
+                            _[1][-1] = _[1][-1]*il
+                        break
+                if not ok:
+                    break
+        else:
+            hit = True
+            lenn = len(n)
+            r = Mul(*n)
+            for _ in args:
+                _[1] = _[1][:len(_[1]) - lenn]
+        if hit:
+            mid = Add(*[Mul(*cc)*Mul(*nc) for cc, nc in args])
+        else:
+            mid = expr
+
+        from sympy.simplify.powsimp import powsimp
+
+        # sort the symbols so the Dummys would appear in the same
+        # order as the original symbols, otherwise you may introduce
+        # a factor of -1, e.g. A**2 - B**2) -- {A:y, B:x} --> y**2 - x**2
+        # and the former factors into two terms, (A - B)*(A + B) while the
+        # latter factors into 3 terms, (-1)*(x - y)*(x + y)
+        rep1 = [(n, Dummy()) for n in sorted(nc_symbols, key=default_sort_key)]
+        unrep1 = [(v, k) for k, v in rep1]
+        unrep1.reverse()
+        new_mid, r2, _ = _mask_nc(mid.subs(rep1))
+        new_mid = powsimp(factor(new_mid))
+
+        new_mid = new_mid.subs(r2).subs(unrep1)
+
+        if new_mid.is_Pow:
+            return _keep_coeff(c, g*l*new_mid*r)
+
+        if new_mid.is_Mul:
+            def _pemexpand(expr):
+                "Expand with the minimal set of hints necessary to check the result."
+                return expr.expand(deep=True, mul=True, power_exp=True,
+                    power_base=False, basic=False, multinomial=True, log=False)
+            # XXX TODO there should be a way to inspect what order the terms
+            # must be in and just select the plausible ordering without
+            # checking permutations
+            cfac = []
+            ncfac = []
+            for f in new_mid.args:
+                if f.is_commutative:
+                    cfac.append(f)
+                else:
+                    b, e = f.as_base_exp()
+                    if e.is_Integer:
+                        ncfac.extend([b]*e)
+                    else:
+                        ncfac.append(f)
+            pre_mid = g*Mul(*cfac)*l
+            target = _pemexpand(expr/c)
+            for s in variations(ncfac, len(ncfac)):
+                ok = pre_mid*Mul(*s)*r
+                if _pemexpand(ok) == target:
+                    return _keep_coeff(c, ok)
+
+        # mid was an Add that didn't factor successfully
+        return _keep_coeff(c, g*l*mid*r)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/facts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/facts.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b98d9b14bbac661d3c0fd1d1fd87977a792fb74
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/facts.py
@@ -0,0 +1,634 @@
+r"""This is rule-based deduction system for SymPy
+
+The whole thing is split into two parts
+
+ - rules compilation and preparation of tables
+ - runtime inference
+
+For rule-based inference engines, the classical work is RETE algorithm [1],
+[2] Although we are not implementing it in full (or even significantly)
+it's still worth a read to understand the underlying ideas.
+
+In short, every rule in a system of rules is one of two forms:
+
+ - atom                     -> ...      (alpha rule)
+ - And(atom1, atom2, ...)   -> ...      (beta rule)
+
+
+The major complexity is in efficient beta-rules processing and usually for an
+expert system a lot of effort goes into code that operates on beta-rules.
+
+
+Here we take minimalistic approach to get something usable first.
+
+ - (preparation)    of alpha- and beta- networks, everything except
+ - (runtime)        FactRules.deduce_all_facts
+
+             _____________________________________
+            ( Kirr: I've never thought that doing )
+            ( logic stuff is that difficult...    )
+             -------------------------------------
+                    o   ^__^
+                     o  (oo)\_______
+                        (__)\       )\/\
+                            ||----w |
+                            ||     ||
+
+
+Some references on the topic
+----------------------------
+
+[1] https://en.wikipedia.org/wiki/Rete_algorithm
+[2] http://reports-archive.adm.cs.cmu.edu/anon/1995/CMU-CS-95-113.pdf
+
+https://en.wikipedia.org/wiki/Propositional_formula
+https://en.wikipedia.org/wiki/Inference_rule
+https://en.wikipedia.org/wiki/List_of_rules_of_inference
+"""
+
+from collections import defaultdict
+from typing import Iterator
+
+from .logic import Logic, And, Or, Not
+
+
+def _base_fact(atom):
+    """Return the literal fact of an atom.
+
+    Effectively, this merely strips the Not around a fact.
+    """
+    if isinstance(atom, Not):
+        return atom.arg
+    else:
+        return atom
+
+
+def _as_pair(atom):
+    if isinstance(atom, Not):
+        return (atom.arg, False)
+    else:
+        return (atom, True)
+
+# XXX this prepares forward-chaining rules for alpha-network
+
+
+def transitive_closure(implications):
+    """
+    Computes the transitive closure of a list of implications
+
+    Uses Warshall's algorithm, as described at
+    http://www.cs.hope.edu/~cusack/Notes/Notes/DiscreteMath/Warshall.pdf.
+    """
+    full_implications = set(implications)
+    literals = set().union(*map(set, full_implications))
+
+    for k in literals:
+        for i in literals:
+            if (i, k) in full_implications:
+                for j in literals:
+                    if (k, j) in full_implications:
+                        full_implications.add((i, j))
+
+    return full_implications
+
+
+def deduce_alpha_implications(implications):
+    """deduce all implications
+
+       Description by example
+       ----------------------
+
+       given set of logic rules:
+
+         a -> b
+         b -> c
+
+       we deduce all possible rules:
+
+         a -> b, c
+         b -> c
+
+
+       implications: [] of (a,b)
+       return:       {} of a -> set([b, c, ...])
+    """
+    implications = implications + [(Not(j), Not(i)) for (i, j) in implications]
+    res = defaultdict(set)
+    full_implications = transitive_closure(implications)
+    for a, b in full_implications:
+        if a == b:
+            continue    # skip a->a cyclic input
+
+        res[a].add(b)
+
+    # Clean up tautologies and check consistency
+    for a, impl in res.items():
+        impl.discard(a)
+        na = Not(a)
+        if na in impl:
+            raise ValueError(
+                'implications are inconsistent: %s -> %s %s' % (a, na, impl))
+
+    return res
+
+
+def apply_beta_to_alpha_route(alpha_implications, beta_rules):
+    """apply additional beta-rules (And conditions) to already-built
+    alpha implication tables
+
+       TODO: write about
+
+       - static extension of alpha-chains
+       - attaching refs to beta-nodes to alpha chains
+
+
+       e.g.
+
+       alpha_implications:
+
+       a  ->  [b, !c, d]
+       b  ->  [d]
+       ...
+
+
+       beta_rules:
+
+       &(b,d) -> e
+
+
+       then we'll extend a's rule to the following
+
+       a  ->  [b, !c, d, e]
+    """
+    x_impl = {}
+    for x in alpha_implications.keys():
+        x_impl[x] = (set(alpha_implications[x]), [])
+    for bcond, bimpl in beta_rules:
+        for bk in bcond.args:
+            if bk in x_impl:
+                continue
+            x_impl[bk] = (set(), [])
+
+    # static extensions to alpha rules:
+    # A: x -> a,b   B: &(a,b) -> c  ==>  A: x -> a,b,c
+    seen_static_extension = True
+    while seen_static_extension:
+        seen_static_extension = False
+
+        for bcond, bimpl in beta_rules:
+            if not isinstance(bcond, And):
+                raise TypeError("Cond is not And")
+            bargs = set(bcond.args)
+            for x, (ximpls, bb) in x_impl.items():
+                x_all = ximpls | {x}
+                # A: ... -> a   B: &(...) -> a  is non-informative
+                if bimpl not in x_all and bargs.issubset(x_all):
+                    ximpls.add(bimpl)
+
+                    # we introduced new implication - now we have to restore
+                    # completeness of the whole set.
+                    bimpl_impl = x_impl.get(bimpl)
+                    if bimpl_impl is not None:
+                        ximpls |= bimpl_impl[0]
+                    seen_static_extension = True
+
+    # attach beta-nodes which can be possibly triggered by an alpha-chain
+    for bidx, (bcond, bimpl) in enumerate(beta_rules):
+        bargs = set(bcond.args)
+        for x, (ximpls, bb) in x_impl.items():
+            x_all = ximpls | {x}
+            # A: ... -> a   B: &(...) -> a      (non-informative)
+            if bimpl in x_all:
+                continue
+            # A: x -> a...  B: &(!a,...) -> ... (will never trigger)
+            # A: x -> a...  B: &(...) -> !a     (will never trigger)
+            if any(Not(xi) in bargs or Not(xi) == bimpl for xi in x_all):
+                continue
+
+            if bargs & x_all:
+                bb.append(bidx)
+
+    return x_impl
+
+
+def rules_2prereq(rules):
+    """build prerequisites table from rules
+
+       Description by example
+       ----------------------
+
+       given set of logic rules:
+
+         a -> b, c
+         b -> c
+
+       we build prerequisites (from what points something can be deduced):
+
+         b <- a
+         c <- a, b
+
+       rules:   {} of a -> [b, c, ...]
+       return:  {} of c <- [a, b, ...]
+
+       Note however, that this prerequisites may be *not* enough to prove a
+       fact. An example is 'a -> b' rule, where prereq(a) is b, and prereq(b)
+       is a. That's because a=T -> b=T, and b=F -> a=F, but a=F -> b=?
+    """
+    prereq = defaultdict(set)
+    for (a, _), impl in rules.items():
+        if isinstance(a, Not):
+            a = a.args[0]
+        for (i, _) in impl:
+            if isinstance(i, Not):
+                i = i.args[0]
+            prereq[i].add(a)
+    return prereq
+
+################
+# RULES PROVER #
+################
+
+
+class TautologyDetected(Exception):
+    """(internal) Prover uses it for reporting detected tautology"""
+    pass
+
+
+class Prover:
+    """ai - prover of logic rules
+
+       given a set of initial rules, Prover tries to prove all possible rules
+       which follow from given premises.
+
+       As a result proved_rules are always either in one of two forms: alpha or
+       beta:
+
+       Alpha rules
+       -----------
+
+       This are rules of the form::
+
+         a -> b & c & d & ...
+
+
+       Beta rules
+       ----------
+
+       This are rules of the form::
+
+         &(a,b,...) -> c & d & ...
+
+
+       i.e. beta rules are join conditions that say that something follows when
+       *several* facts are true at the same time.
+    """
+
+    def __init__(self):
+        self.proved_rules = []
+        self._rules_seen = set()
+
+    def split_alpha_beta(self):
+        """split proved rules into alpha and beta chains"""
+        rules_alpha = []    # a      -> b
+        rules_beta = []     # &(...) -> b
+        for a, b in self.proved_rules:
+            if isinstance(a, And):
+                rules_beta.append((a, b))
+            else:
+                rules_alpha.append((a, b))
+        return rules_alpha, rules_beta
+
+    @property
+    def rules_alpha(self):
+        return self.split_alpha_beta()[0]
+
+    @property
+    def rules_beta(self):
+        return self.split_alpha_beta()[1]
+
+    def process_rule(self, a, b):
+        """process a -> b rule"""   # TODO write more?
+        if (not a) or isinstance(b, bool):
+            return
+        if isinstance(a, bool):
+            return
+        if (a, b) in self._rules_seen:
+            return
+        else:
+            self._rules_seen.add((a, b))
+
+        # this is the core of processing
+        try:
+            self._process_rule(a, b)
+        except TautologyDetected:
+            pass
+
+    def _process_rule(self, a, b):
+        # right part first
+
+        # a -> b & c    -->  a -> b  ;  a -> c
+        # (?) FIXME this is only correct when b & c != null !
+
+        if isinstance(b, And):
+            sorted_bargs = sorted(b.args, key=str)
+            for barg in sorted_bargs:
+                self.process_rule(a, barg)
+
+        # a -> b | c    -->  !b & !c -> !a
+        #               -->   a & !b -> c
+        #               -->   a & !c -> b
+        elif isinstance(b, Or):
+            sorted_bargs = sorted(b.args, key=str)
+            # detect tautology first
+            if not isinstance(a, Logic):    # Atom
+                # tautology:  a -> a|c|...
+                if a in sorted_bargs:
+                    raise TautologyDetected(a, b, 'a -> a|c|...')
+            self.process_rule(And(*[Not(barg) for barg in b.args]), Not(a))
+
+            for bidx in range(len(sorted_bargs)):
+                barg = sorted_bargs[bidx]
+                brest = sorted_bargs[:bidx] + sorted_bargs[bidx + 1:]
+                self.process_rule(And(a, Not(barg)), Or(*brest))
+
+        # left part
+
+        # a & b -> c    -->  IRREDUCIBLE CASE -- WE STORE IT AS IS
+        #                    (this will be the basis of beta-network)
+        elif isinstance(a, And):
+            sorted_aargs = sorted(a.args, key=str)
+            if b in sorted_aargs:
+                raise TautologyDetected(a, b, 'a & b -> a')
+            self.proved_rules.append((a, b))
+            # XXX NOTE at present we ignore  !c -> !a | !b
+
+        elif isinstance(a, Or):
+            sorted_aargs = sorted(a.args, key=str)
+            if b in sorted_aargs:
+                raise TautologyDetected(a, b, 'a | b -> a')
+            for aarg in sorted_aargs:
+                self.process_rule(aarg, b)
+
+        else:
+            # both `a` and `b` are atoms
+            self.proved_rules.append((a, b))             # a  -> b
+            self.proved_rules.append((Not(b), Not(a)))   # !b -> !a
+
+########################################
+
+
+class FactRules:
+    """Rules that describe how to deduce facts in logic space
+
+       When defined, these rules allow implications to quickly be determined
+       for a set of facts. For this precomputed deduction tables are used.
+       see `deduce_all_facts`   (forward-chaining)
+
+       Also it is possible to gather prerequisites for a fact, which is tried
+       to be proven.    (backward-chaining)
+
+
+       Definition Syntax
+       -----------------
+
+       a -> b       -- a=T -> b=T  (and automatically b=F -> a=F)
+       a -> !b      -- a=T -> b=F
+       a == b       -- a -> b & b -> a
+       a -> b & c   -- a=T -> b=T & c=T
+       # TODO b | c
+
+
+       Internals
+       ---------
+
+       .full_implications[k, v]: all the implications of fact k=v
+       .beta_triggers[k, v]: beta rules that might be triggered when k=v
+       .prereq  -- {} k <- [] of k's prerequisites
+
+       .defined_facts -- set of defined fact names
+    """
+
+    def __init__(self, rules):
+        """Compile rules into internal lookup tables"""
+
+        if isinstance(rules, str):
+            rules = rules.splitlines()
+
+        # --- parse and process rules ---
+        P = Prover()
+
+        for rule in rules:
+            # XXX `a` is hardcoded to be always atom
+            a, op, b = rule.split(None, 2)
+
+            a = Logic.fromstring(a)
+            b = Logic.fromstring(b)
+
+            if op == '->':
+                P.process_rule(a, b)
+            elif op == '==':
+                P.process_rule(a, b)
+                P.process_rule(b, a)
+            else:
+                raise ValueError('unknown op %r' % op)
+
+        # --- build deduction networks ---
+        self.beta_rules = []
+        for bcond, bimpl in P.rules_beta:
+            self.beta_rules.append(
+                ({_as_pair(a) for a in bcond.args}, _as_pair(bimpl)))
+
+        # deduce alpha implications
+        impl_a = deduce_alpha_implications(P.rules_alpha)
+
+        # now:
+        # - apply beta rules to alpha chains  (static extension), and
+        # - further associate beta rules to alpha chain (for inference
+        # at runtime)
+        impl_ab = apply_beta_to_alpha_route(impl_a, P.rules_beta)
+
+        # extract defined fact names
+        self.defined_facts = {_base_fact(k) for k in impl_ab.keys()}
+
+        # build rels (forward chains)
+        full_implications = defaultdict(set)
+        beta_triggers = defaultdict(set)
+        for k, (impl, betaidxs) in impl_ab.items():
+            full_implications[_as_pair(k)] = {_as_pair(i) for i in impl}
+            beta_triggers[_as_pair(k)] = betaidxs
+
+        self.full_implications = full_implications
+        self.beta_triggers = beta_triggers
+
+        # build prereq (backward chains)
+        prereq = defaultdict(set)
+        rel_prereq = rules_2prereq(full_implications)
+        for k, pitems in rel_prereq.items():
+            prereq[k] |= pitems
+        self.prereq = prereq
+
+    def _to_python(self) -> str:
+        """ Generate a string with plain python representation of the instance """
+        return '\n'.join(self.print_rules())
+
+    @classmethod
+    def _from_python(cls, data : dict):
+        """ Generate an instance from the plain python representation """
+        self = cls('')
+        for key in ['full_implications', 'beta_triggers', 'prereq']:
+            d=defaultdict(set)
+            d.update(data[key])
+            setattr(self, key, d)
+        self.beta_rules = data['beta_rules']
+        self.defined_facts = set(data['defined_facts'])
+
+        return self
+
+    def _defined_facts_lines(self):
+        yield 'defined_facts = ['
+        for fact in sorted(self.defined_facts):
+            yield f'    {fact!r},'
+        yield '] # defined_facts'
+
+    def _full_implications_lines(self):
+        yield 'full_implications = dict( ['
+        for fact in sorted(self.defined_facts):
+            for value in (True, False):
+                yield f'    # Implications of {fact} = {value}:'
+                yield f'    (({fact!r}, {value!r}), set( ('
+                implications = self.full_implications[(fact, value)]
+                for implied in sorted(implications):
+                    yield f'        {implied!r},'
+                yield '       ) ),'
+                yield '     ),'
+        yield ' ] ) # full_implications'
+
+    def _prereq_lines(self):
+        yield 'prereq = {'
+        yield ''
+        for fact in sorted(self.prereq):
+            yield f'    # facts that could determine the value of {fact}'
+            yield f'    {fact!r}: {{'
+            for pfact in sorted(self.prereq[fact]):
+                yield f'        {pfact!r},'
+            yield '    },'
+            yield ''
+        yield '} # prereq'
+
+    def _beta_rules_lines(self):
+        reverse_implications = defaultdict(list)
+        for n, (pre, implied) in enumerate(self.beta_rules):
+            reverse_implications[implied].append((pre, n))
+
+        yield '# Note: the order of the beta rules is used in the beta_triggers'
+        yield 'beta_rules = ['
+        yield ''
+        m = 0
+        indices = {}
+        for implied in sorted(reverse_implications):
+            fact, value = implied
+            yield f'    # Rules implying {fact} = {value}'
+            for pre, n in reverse_implications[implied]:
+                indices[n] = m
+                m += 1
+                setstr = ", ".join(map(str, sorted(pre)))
+                yield f'    ({{{setstr}}},'
+                yield f'        {implied!r}),'
+            yield ''
+        yield '] # beta_rules'
+
+        yield 'beta_triggers = {'
+        for query in sorted(self.beta_triggers):
+            fact, value = query
+            triggers = [indices[n] for n in self.beta_triggers[query]]
+            yield f'    {query!r}: {triggers!r},'
+        yield '} # beta_triggers'
+
+    def print_rules(self) -> Iterator[str]:
+        """ Returns a generator with lines to represent the facts and rules """
+        yield from self._defined_facts_lines()
+        yield ''
+        yield ''
+        yield from self._full_implications_lines()
+        yield ''
+        yield ''
+        yield from self._prereq_lines()
+        yield ''
+        yield ''
+        yield from self._beta_rules_lines()
+        yield ''
+        yield ''
+        yield "generated_assumptions = {'defined_facts': defined_facts, 'full_implications': full_implications,"
+        yield "               'prereq': prereq, 'beta_rules': beta_rules, 'beta_triggers': beta_triggers}"
+
+
+class InconsistentAssumptions(ValueError):
+    def __str__(self):
+        kb, fact, value = self.args
+        return "%s, %s=%s" % (kb, fact, value)
+
+
+class FactKB(dict):
+    """
+    A simple propositional knowledge base relying on compiled inference rules.
+    """
+    def __str__(self):
+        return '{\n%s}' % ',\n'.join(
+            ["\t%s: %s" % i for i in sorted(self.items())])
+
+    def __init__(self, rules):
+        self.rules = rules
+
+    def _tell(self, k, v):
+        """Add fact k=v to the knowledge base.
+
+        Returns True if the KB has actually been updated, False otherwise.
+        """
+        if k in self and self[k] is not None:
+            if self[k] == v:
+                return False
+            else:
+                raise InconsistentAssumptions(self, k, v)
+        else:
+            self[k] = v
+            return True
+
+    # *********************************************
+    # * This is the workhorse, so keep it *fast*. *
+    # *********************************************
+    def deduce_all_facts(self, facts):
+        """
+        Update the KB with all the implications of a list of facts.
+
+        Facts can be specified as a dictionary or as a list of (key, value)
+        pairs.
+        """
+        # keep frequently used attributes locally, so we'll avoid extra
+        # attribute access overhead
+        full_implications = self.rules.full_implications
+        beta_triggers = self.rules.beta_triggers
+        beta_rules = self.rules.beta_rules
+
+        if isinstance(facts, dict):
+            facts = facts.items()
+
+        while facts:
+            beta_maytrigger = set()
+
+            # --- alpha chains ---
+            for k, v in facts:
+                if not self._tell(k, v) or v is None:
+                    continue
+
+                # lookup routing tables
+                for key, value in full_implications[k, v]:
+                    self._tell(key, value)
+
+                beta_maytrigger.update(beta_triggers[k, v])
+
+            # --- beta chains ---
+            facts = []
+            for bidx in beta_maytrigger:
+                bcond, bimpl = beta_rules[bidx]
+                if all(self.get(k) is v for k, v in bcond):
+                    facts.append(bimpl)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/function.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/function.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac850845e0bb2aaf9b535635567d6e2629527ad7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/function.py
@@ -0,0 +1,3423 @@
+"""
+There are three types of functions implemented in SymPy:
+
+    1) defined functions (in the sense that they can be evaluated) like
+       exp or sin; they have a name and a body:
+           f = exp
+    2) undefined function which have a name but no body. Undefined
+       functions can be defined using a Function class as follows:
+           f = Function('f')
+       (the result will be a Function instance)
+    3) anonymous function (or lambda function) which have a body (defined
+       with dummy variables) but have no name:
+           f = Lambda(x, exp(x)*x)
+           f = Lambda((x, y), exp(x)*y)
+    The fourth type of functions are composites, like (sin + cos)(x); these work in
+    SymPy core, but are not yet part of SymPy.
+
+    Examples
+    ========
+
+    >>> import sympy
+    >>> f = sympy.Function("f")
+    >>> from sympy.abc import x
+    >>> f(x)
+    f(x)
+    >>> print(sympy.srepr(f(x).func))
+    Function('f')
+    >>> f(x).args
+    (x,)
+
+"""
+
+from __future__ import annotations
+
+from typing import Any
+from collections.abc import Iterable
+import copyreg
+
+from .add import Add
+from .basic import Basic, _atomic
+from .cache import cacheit
+from .containers import Tuple, Dict
+from .decorators import _sympifyit
+from .evalf import pure_complex
+from .expr import Expr, AtomicExpr
+from .logic import fuzzy_and, fuzzy_or, fuzzy_not, FuzzyBool
+from .mul import Mul
+from .numbers import Rational, Float, Integer
+from .operations import LatticeOp
+from .parameters import global_parameters
+from .rules import Transform
+from .singleton import S
+from .sympify import sympify, _sympify
+
+from .sorting import default_sort_key, ordered
+from sympy.utilities.exceptions import (sympy_deprecation_warning,
+                                        SymPyDeprecationWarning, ignore_warnings)
+from sympy.utilities.iterables import (has_dups, sift, iterable,
+    is_sequence, uniq, topological_sort)
+from sympy.utilities.lambdify import MPMATH_TRANSLATIONS
+from sympy.utilities.misc import as_int, filldedent, func_name
+
+import mpmath
+from mpmath.libmp.libmpf import prec_to_dps
+
+import inspect
+from collections import Counter
+
+def _coeff_isneg(a):
+    """Return True if the leading Number is negative.
+
+    Examples
+    ========
+
+    >>> from sympy.core.function import _coeff_isneg
+    >>> from sympy import S, Symbol, oo, pi
+    >>> _coeff_isneg(-3*pi)
+    True
+    >>> _coeff_isneg(S(3))
+    False
+    >>> _coeff_isneg(-oo)
+    True
+    >>> _coeff_isneg(Symbol('n', negative=True)) # coeff is 1
+    False
+
+    For matrix expressions:
+
+    >>> from sympy import MatrixSymbol, sqrt
+    >>> A = MatrixSymbol("A", 3, 3)
+    >>> _coeff_isneg(-sqrt(2)*A)
+    True
+    >>> _coeff_isneg(sqrt(2)*A)
+    False
+    """
+
+    if a.is_MatMul:
+        a = a.args[0]
+    if a.is_Mul:
+        a = a.args[0]
+    return a.is_Number and a.is_extended_negative
+
+
+class PoleError(Exception):
+    pass
+
+
+class ArgumentIndexError(ValueError):
+    def __str__(self):
+        return ("Invalid operation with argument number %s for Function %s" %
+               (self.args[1], self.args[0]))
+
+
+class BadSignatureError(TypeError):
+    '''Raised when a Lambda is created with an invalid signature'''
+    pass
+
+
+class BadArgumentsError(TypeError):
+    '''Raised when a Lambda is called with an incorrect number of arguments'''
+    pass
+
+
+# Python 3 version that does not raise a Deprecation warning
+def arity(cls):
+    """Return the arity of the function if it is known, else None.
+
+    Explanation
+    ===========
+
+    When default values are specified for some arguments, they are
+    optional and the arity is reported as a tuple of possible values.
+
+    Examples
+    ========
+
+    >>> from sympy import arity, log
+    >>> arity(lambda x: x)
+    1
+    >>> arity(log)
+    (1, 2)
+    >>> arity(lambda *x: sum(x)) is None
+    True
+    """
+    eval_ = getattr(cls, 'eval', cls)
+
+    parameters = inspect.signature(eval_).parameters.items()
+    if [p for _, p in parameters if p.kind == p.VAR_POSITIONAL]:
+        return
+    p_or_k = [p for _, p in parameters if p.kind == p.POSITIONAL_OR_KEYWORD]
+    # how many have no default and how many have a default value
+    no, yes = map(len, sift(p_or_k,
+        lambda p:p.default == p.empty, binary=True))
+    return no if not yes else tuple(range(no, no + yes + 1))
+
+class FunctionClass(type):
+    """
+    Base class for function classes. FunctionClass is a subclass of type.
+
+    Use Function('' [ , signature ]) to create
+    undefined function classes.
+    """
+    _new = type.__new__
+
+    def __init__(cls, *args, **kwargs):
+        # honor kwarg value or class-defined value before using
+        # the number of arguments in the eval function (if present)
+        nargs = kwargs.pop('nargs', cls.__dict__.get('nargs', arity(cls)))
+        if nargs is None and 'nargs' not in cls.__dict__:
+            for supcls in cls.__mro__:
+                if hasattr(supcls, '_nargs'):
+                    nargs = supcls._nargs
+                    break
+                else:
+                    continue
+
+        # Canonicalize nargs here; change to set in nargs.
+        if is_sequence(nargs):
+            if not nargs:
+                raise ValueError(filldedent('''
+                    Incorrectly specified nargs as %s:
+                    if there are no arguments, it should be
+                    `nargs = 0`;
+                    if there are any number of arguments,
+                    it should be
+                    `nargs = None`''' % str(nargs)))
+            nargs = tuple(ordered(set(nargs)))
+        elif nargs is not None:
+            nargs = (as_int(nargs),)
+        cls._nargs = nargs
+
+        # When __init__ is called from UndefinedFunction it is called with
+        # just one arg but when it is called from subclassing Function it is
+        # called with the usual (name, bases, namespace) type() signature.
+        if len(args) == 3:
+            namespace = args[2]
+            if 'eval' in namespace and not isinstance(namespace['eval'], classmethod):
+                raise TypeError("eval on Function subclasses should be a class method (defined with @classmethod)")
+
+    @property
+    def __signature__(self):
+        """
+        Allow Python 3's inspect.signature to give a useful signature for
+        Function subclasses.
+        """
+        # Python 3 only, but backports (like the one in IPython) still might
+        # call this.
+        try:
+            from inspect import signature
+        except ImportError:
+            return None
+
+        # TODO: Look at nargs
+        return signature(self.eval)
+
+    @property
+    def free_symbols(self):
+        return set()
+
+    @property
+    def xreplace(self):
+        # Function needs args so we define a property that returns
+        # a function that takes args...and then use that function
+        # to return the right value
+        return lambda rule, **_: rule.get(self, self)
+
+    @property
+    def nargs(self):
+        """Return a set of the allowed number of arguments for the function.
+
+        Examples
+        ========
+
+        >>> from sympy import Function
+        >>> f = Function('f')
+
+        If the function can take any number of arguments, the set of whole
+        numbers is returned:
+
+        >>> Function('f').nargs
+        Naturals0
+
+        If the function was initialized to accept one or more arguments, a
+        corresponding set will be returned:
+
+        >>> Function('f', nargs=1).nargs
+        {1}
+        >>> Function('f', nargs=(2, 1)).nargs
+        {1, 2}
+
+        The undefined function, after application, also has the nargs
+        attribute; the actual number of arguments is always available by
+        checking the ``args`` attribute:
+
+        >>> f = Function('f')
+        >>> f(1).nargs
+        Naturals0
+        >>> len(f(1).args)
+        1
+        """
+        from sympy.sets.sets import FiniteSet
+        # XXX it would be nice to handle this in __init__ but there are import
+        # problems with trying to import FiniteSet there
+        return FiniteSet(*self._nargs) if self._nargs else S.Naturals0
+
+    def _valid_nargs(self, n : int) -> bool:
+        """ Return True if the specified integer is a valid number of arguments
+
+        The number of arguments n is guaranteed to be an integer and positive
+
+        """
+        if self._nargs:
+            return n in self._nargs
+
+        nargs = self.nargs
+        return nargs is S.Naturals0 or n in nargs
+
+    def __repr__(cls):
+        return cls.__name__
+
+
+class Application(Basic, metaclass=FunctionClass):
+    """
+    Base class for applied functions.
+
+    Explanation
+    ===========
+
+    Instances of Application represent the result of applying an application of
+    any type to any object.
+    """
+
+    is_Function = True
+
+    @cacheit
+    def __new__(cls, *args, **options):
+        from sympy.sets.fancysets import Naturals0
+        from sympy.sets.sets import FiniteSet
+
+        args = list(map(sympify, args))
+        evaluate = options.pop('evaluate', global_parameters.evaluate)
+        # WildFunction (and anything else like it) may have nargs defined
+        # and we throw that value away here
+        options.pop('nargs', None)
+
+        if options:
+            raise ValueError("Unknown options: %s" % options)
+
+        if evaluate:
+            evaluated = cls.eval(*args)
+            if evaluated is not None:
+                return evaluated
+
+        obj = super().__new__(cls, *args, **options)
+
+        # make nargs uniform here
+        sentinel = object()
+        objnargs = getattr(obj, "nargs", sentinel)
+        if objnargs is not sentinel:
+            # things passing through here:
+            #  - functions subclassed from Function (e.g. myfunc(1).nargs)
+            #  - functions like cos(1).nargs
+            #  - AppliedUndef with given nargs like Function('f', nargs=1)(1).nargs
+            # Canonicalize nargs here
+            if is_sequence(objnargs):
+                nargs = tuple(ordered(set(objnargs)))
+            elif objnargs is not None:
+                nargs = (as_int(objnargs),)
+            else:
+                nargs = None
+        else:
+            # things passing through here:
+            #  - WildFunction('f').nargs
+            #  - AppliedUndef with no nargs like Function('f')(1).nargs
+            nargs = obj._nargs  # note the underscore here
+        # convert to FiniteSet
+        obj.nargs = FiniteSet(*nargs) if nargs else Naturals0()
+        return obj
+
+    @classmethod
+    def eval(cls, *args):
+        """
+        Returns a canonical form of cls applied to arguments args.
+
+        Explanation
+        ===========
+
+        The ``eval()`` method is called when the class ``cls`` is about to be
+        instantiated and it should return either some simplified instance
+        (possible of some other class), or if the class ``cls`` should be
+        unmodified, return None.
+
+        Examples of ``eval()`` for the function "sign"
+
+        .. code-block:: python
+
+            @classmethod
+            def eval(cls, arg):
+                if arg is S.NaN:
+                    return S.NaN
+                if arg.is_zero: return S.Zero
+                if arg.is_positive: return S.One
+                if arg.is_negative: return S.NegativeOne
+                if isinstance(arg, Mul):
+                    coeff, terms = arg.as_coeff_Mul(rational=True)
+                    if coeff is not S.One:
+                        return cls(coeff) * cls(terms)
+
+        """
+        return
+
+    @property
+    def func(self):
+        return self.__class__
+
+    def _eval_subs(self, old, new):
+        if (old.is_Function and new.is_Function and
+            callable(old) and callable(new) and
+            old == self.func and len(self.args) in new.nargs):
+            return new(*[i._subs(old, new) for i in self.args])
+
+
+class Function(Application, Expr):
+    r"""
+    Base class for applied mathematical functions.
+
+    It also serves as a constructor for undefined function classes.
+
+    See the :ref:`custom-functions` guide for details on how to subclass
+    ``Function`` and what methods can be defined.
+
+    Examples
+    ========
+
+    **Undefined Functions**
+
+    To create an undefined function, pass a string of the function name to
+    ``Function``.
+
+    >>> from sympy import Function, Symbol
+    >>> x = Symbol('x')
+    >>> f = Function('f')
+    >>> g = Function('g')(x)
+    >>> f
+    f
+    >>> f(x)
+    f(x)
+    >>> g
+    g(x)
+    >>> f(x).diff(x)
+    Derivative(f(x), x)
+    >>> g.diff(x)
+    Derivative(g(x), x)
+
+    Assumptions can be passed to ``Function`` the same as with a
+    :class:`~.Symbol`. Alternatively, you can use a ``Symbol`` with
+    assumptions for the function name and the function will inherit the name
+    and assumptions associated with the ``Symbol``:
+
+    >>> f_real = Function('f', real=True)
+    >>> f_real(x).is_real
+    True
+    >>> f_real_inherit = Function(Symbol('f', real=True))
+    >>> f_real_inherit(x).is_real
+    True
+
+    Note that assumptions on a function are unrelated to the assumptions on
+    the variables it is called on. If you want to add a relationship, subclass
+    ``Function`` and define custom assumptions handler methods. See the
+    :ref:`custom-functions-assumptions` section of the :ref:`custom-functions`
+    guide for more details.
+
+    **Custom Function Subclasses**
+
+    The :ref:`custom-functions` guide has several
+    :ref:`custom-functions-complete-examples` of how to subclass ``Function``
+    to create a custom function.
+
+    """
+
+    @property
+    def _diff_wrt(self):
+        return False
+
+    @cacheit
+    def __new__(cls, *args, **options) -> type[AppliedUndef]:  # type: ignore
+        # Handle calls like Function('f')
+        if cls is Function:
+            return UndefinedFunction(*args, **options)  # type: ignore
+        else:
+            return cls._new_(*args, **options)  # type: ignore
+
+    @classmethod
+    def _new_(cls, *args, **options) -> Expr:
+        n = len(args)
+
+        if not cls._valid_nargs(n):
+            # XXX: exception message must be in exactly this format to
+            # make it work with NumPy's functions like vectorize(). See,
+            # for example, https://github.com/numpy/numpy/issues/1697.
+            # The ideal solution would be just to attach metadata to
+            # the exception and change NumPy to take advantage of this.
+            temp = ('%(name)s takes %(qual)s %(args)s '
+                   'argument%(plural)s (%(given)s given)')
+            raise TypeError(temp % {
+                'name': cls,
+                'qual': 'exactly' if len(cls.nargs) == 1 else 'at least',
+                'args': min(cls.nargs),
+                'plural': 's'*(min(cls.nargs) != 1),
+                'given': n})
+
+        evaluate = options.get('evaluate', global_parameters.evaluate)
+        result = super().__new__(cls, *args, **options)
+        if evaluate and isinstance(result, cls) and result.args:
+            _should_evalf = [cls._should_evalf(a) for a in result.args]
+            pr2 = min(_should_evalf)
+            if pr2 > 0:
+                pr = max(_should_evalf)
+                result = result.evalf(prec_to_dps(pr))
+
+        return _sympify(result)
+
+    @classmethod
+    def _should_evalf(cls, arg):
+        """
+        Decide if the function should automatically evalf().
+
+        Explanation
+        ===========
+
+        By default (in this implementation), this happens if (and only if) the
+        ARG is a floating point number (including complex numbers).
+        This function is used by __new__.
+
+        Returns the precision to evalf to, or -1 if it should not evalf.
+        """
+        if arg.is_Float:
+            return arg._prec
+        if not arg.is_Add:
+            return -1
+        m = pure_complex(arg)
+        if m is None:
+            return -1
+        # the elements of m are of type Number, so have a _prec
+        return max(m[0]._prec, m[1]._prec)
+
+    @classmethod
+    def class_key(cls):
+        from sympy.sets.fancysets import Naturals0
+        funcs = {
+            'exp': 10,
+            'log': 11,
+            'sin': 20,
+            'cos': 21,
+            'tan': 22,
+            'cot': 23,
+            'sinh': 30,
+            'cosh': 31,
+            'tanh': 32,
+            'coth': 33,
+            'conjugate': 40,
+            're': 41,
+            'im': 42,
+            'arg': 43,
+        }
+        name = cls.__name__
+
+        try:
+            i = funcs[name]
+        except KeyError:
+            i = 0 if isinstance(cls.nargs, Naturals0) else 10000
+
+        return 4, i, name
+
+    def _eval_evalf(self, prec):
+
+        def _get_mpmath_func(fname):
+            """Lookup mpmath function based on name"""
+            if isinstance(self, AppliedUndef):
+                # Shouldn't lookup in mpmath but might have ._imp_
+                return None
+
+            if not hasattr(mpmath, fname):
+                fname = MPMATH_TRANSLATIONS.get(fname, None)
+                if fname is None:
+                    return None
+            return getattr(mpmath, fname)
+
+        _eval_mpmath = getattr(self, '_eval_mpmath', None)
+        if _eval_mpmath is None:
+            func = _get_mpmath_func(self.func.__name__)
+            args = self.args
+        else:
+            func, args = _eval_mpmath()
+
+        # Fall-back evaluation
+        if func is None:
+            imp = getattr(self, '_imp_', None)
+            if imp is None:
+                return None
+            try:
+                return Float(imp(*[i.evalf(prec) for i in self.args]), prec)
+            except (TypeError, ValueError):
+                return None
+
+        # Convert all args to mpf or mpc
+        # Convert the arguments to *higher* precision than requested for the
+        # final result.
+        # XXX + 5 is a guess, it is similar to what is used in evalf.py. Should
+        #     we be more intelligent about it?
+        try:
+            args = [arg._to_mpmath(prec + 5) for arg in args]
+            def bad(m):
+                from mpmath import mpf, mpc
+                # the precision of an mpf value is the last element
+                # if that is 1 (and m[1] is not 1 which would indicate a
+                # power of 2), then the eval failed; so check that none of
+                # the arguments failed to compute to a finite precision.
+                # Note: An mpc value has two parts, the re and imag tuple;
+                # check each of those parts, too. Anything else is allowed to
+                # pass
+                if isinstance(m, mpf):
+                    m = m._mpf_
+                    return m[1] !=1 and m[-1] == 1
+                elif isinstance(m, mpc):
+                    m, n = m._mpc_
+                    return m[1] !=1 and m[-1] == 1 and \
+                        n[1] !=1 and n[-1] == 1
+                else:
+                    return False
+            if any(bad(a) for a in args):
+                raise ValueError  # one or more args failed to compute with significance
+        except ValueError:
+            return
+
+        with mpmath.workprec(prec):
+            v = func(*args)
+
+        return Expr._from_mpmath(v, prec)
+
+    def _eval_derivative(self, s):
+        # f(x).diff(s) -> x.diff(s) * f.fdiff(1)(s)
+        i = 0
+        l = []
+        for a in self.args:
+            i += 1
+            da = a.diff(s)
+            if da.is_zero:
+                continue
+            try:
+                df = self.fdiff(i)
+            except ArgumentIndexError:
+                df = Function.fdiff(self, i)
+            l.append(df * da)
+        return Add(*l)
+
+    def _eval_is_commutative(self):
+        return fuzzy_and(a.is_commutative for a in self.args)
+
+    def _eval_is_meromorphic(self, x, a):
+        if not self.args:
+            return True
+        if any(arg.has(x) for arg in self.args[1:]):
+            return False
+
+        arg = self.args[0]
+        if not arg._eval_is_meromorphic(x, a):
+            return None
+
+        return fuzzy_not(type(self).is_singular(arg.subs(x, a)))
+
+    _singularities: FuzzyBool | tuple[Expr, ...] = None
+
+    @classmethod
+    def is_singular(cls, a):
+        """
+        Tests whether the argument is an essential singularity
+        or a branch point, or the functions is non-holomorphic.
+        """
+        ss = cls._singularities
+        if ss in (True, None, False):
+            return ss
+
+        return fuzzy_or(a.is_infinite if s is S.ComplexInfinity
+                        else (a - s).is_zero for s in ss)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        """
+        Compute an asymptotic expansion around args0, in terms of self.args.
+        This function is only used internally by _eval_nseries and should not
+        be called directly; derived classes can overwrite this to implement
+        asymptotic expansions.
+        """
+        raise PoleError(filldedent('''
+            Asymptotic expansion of %s around %s is
+            not implemented.''' % (type(self), args0)))
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        """
+        This function does compute series for multivariate functions,
+        but the expansion is always in terms of *one* variable.
+
+        Examples
+        ========
+
+        >>> from sympy import atan2
+        >>> from sympy.abc import x, y
+        >>> atan2(x, y).series(x, n=2)
+        atan2(0, y) + x/y + O(x**2)
+        >>> atan2(x, y).series(y, n=2)
+        -y/x + atan2(x, 0) + O(y**2)
+
+        This function also computes asymptotic expansions, if necessary
+        and possible:
+
+        >>> from sympy import loggamma
+        >>> loggamma(1/x)._eval_nseries(x,0,None)
+        -1/x - log(x)/x + log(x)/2 + O(1)
+
+        """
+        from .symbol import uniquely_named_symbol
+        from sympy.series.order import Order
+        from sympy.sets.sets import FiniteSet
+        args = self.args
+        args0 = [t.limit(x, 0) for t in args]
+        if any(t.is_finite is False for t in args0):
+            from .numbers import oo, zoo, nan
+            a = [t.as_leading_term(x, logx=logx) for t in args]
+            a0 = [t.limit(x, 0) for t in a]
+            if any(t.has(oo, -oo, zoo, nan) for t in a0):
+                return self._eval_aseries(n, args0, x, logx)
+            # Careful: the argument goes to oo, but only logarithmically so. We
+            # are supposed to do a power series expansion "around the
+            # logarithmic term". e.g.
+            #      f(1+x+log(x))
+            #     -> f(1+logx) + x*f'(1+logx) + O(x**2)
+            # where 'logx' is given in the argument
+            a = [t._eval_nseries(x, n, logx) for t in args]
+            z = [r - r0 for (r, r0) in zip(a, a0)]
+            p = [Dummy() for _ in z]
+            q = []
+            v = None
+            for ai, zi, pi in zip(a0, z, p):
+                if zi.has(x):
+                    if v is not None:
+                        raise NotImplementedError
+                    q.append(ai + pi)
+                    v = pi
+                else:
+                    q.append(ai)
+            e1 = self.func(*q)
+            if v is None:
+                return e1
+            s = e1._eval_nseries(v, n, logx)
+            o = s.getO()
+            s = s.removeO()
+            s = s.subs(v, zi).expand() + Order(o.expr.subs(v, zi), x)
+            return s
+        if (self.func.nargs is S.Naturals0
+                or (self.func.nargs == FiniteSet(1) and args0[0])
+                or any(c > 1 for c in self.func.nargs)):
+            e = self
+            e1 = e.expand()
+            if e == e1:
+                #for example when e = sin(x+1) or e = sin(cos(x))
+                #let's try the general algorithm
+                if len(e.args) == 1:
+                    # issue 14411
+                    e = e.func(e.args[0].cancel())
+                term = e.subs(x, S.Zero)
+                if term.is_finite is False or term is S.NaN:
+                    raise PoleError("Cannot expand %s around 0" % (self))
+                series = term
+                fact = S.One
+
+                _x = uniquely_named_symbol('xi', self)
+                e = e.subs(x, _x)
+                for i in range(1, n):
+                    fact *= Rational(i)
+                    e = e.diff(_x)
+                    subs = e.subs(_x, S.Zero)
+                    if subs is S.NaN:
+                        # try to evaluate a limit if we have to
+                        subs = e.limit(_x, S.Zero)
+                    if subs.is_finite is False:
+                        raise PoleError("Cannot expand %s around 0" % (self))
+                    term = subs*(x**i)/fact
+                    term = term.expand()
+                    series += term
+                return series + Order(x**n, x)
+            return e1.nseries(x, n=n, logx=logx)
+        arg = self.args[0]
+        l = []
+        g = None
+        # try to predict a number of terms needed
+        nterms = n + 2
+        cf = Order(arg.as_leading_term(x), x).getn()
+        if cf != 0:
+            nterms = (n/cf).ceiling()
+        for i in range(nterms):
+            g = self.taylor_term(i, arg, g)
+            g = g.nseries(x, n=n, logx=logx)
+            l.append(g)
+        return Add(*l) + Order(x**n, x)
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of the function.
+        """
+        if not (1 <= argindex <= len(self.args)):
+            raise ArgumentIndexError(self, argindex)
+        ix = argindex - 1
+        A = self.args[ix]
+        if A._diff_wrt:
+            if len(self.args) == 1 or not A.is_Symbol:
+                return _derivative_dispatch(self, A)
+            for i, v in enumerate(self.args):
+                if i != ix and A in v.free_symbols:
+                    # it can't be in any other argument's free symbols
+                    # issue 8510
+                    break
+            else:
+                return _derivative_dispatch(self, A)
+
+        # See issue 4624 and issue 4719, 5600 and 8510
+        D = Dummy('xi_%i' % argindex, dummy_index=hash(A))
+        args = self.args[:ix] + (D,) + self.args[ix + 1:]
+        return Subs(Derivative(self.func(*args), D), D, A)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        """Stub that should be overridden by new Functions to return
+        the first non-zero term in a series if ever an x-dependent
+        argument whose leading term vanishes as x -> 0 might be encountered.
+        See, for example, cos._eval_as_leading_term.
+        """
+        from sympy.series.order import Order
+        args = [a.as_leading_term(x, logx=logx) for a in self.args]
+        o = Order(1, x)
+        if any(x in a.free_symbols and o.contains(a) for a in args):
+            # Whereas x and any finite number are contained in O(1, x),
+            # expressions like 1/x are not. If any arg simplified to a
+            # vanishing expression as x -> 0 (like x or x**2, but not
+            # 3, 1/x, etc...) then the _eval_as_leading_term is needed
+            # to supply the first non-zero term of the series,
+            #
+            # e.g. expression    leading term
+            #      ----------    ------------
+            #      cos(1/x)      cos(1/x)
+            #      cos(cos(x))   cos(1)
+            #      cos(x)        1        <- _eval_as_leading_term needed
+            #      sin(x)        x        <- _eval_as_leading_term needed
+            #
+            raise NotImplementedError(
+                '%s has no _eval_as_leading_term routine' % self.func)
+        else:
+            return self
+
+
+class DefinedFunction(Function):
+    """Base class for defined functions like ``sin``, ``cos``, ..."""
+
+    @cacheit
+    def __new__(cls, *args, **options) -> Expr:  # type: ignore
+        return cls._new_(*args, **options)
+
+
+class AppliedUndef(Function):
+    """
+    Base class for expressions resulting from the application of an undefined
+    function.
+    """
+
+    is_number = False
+
+    name: str
+
+    def __new__(cls, *args, **options) -> Expr:  # type: ignore
+        args = tuple(map(sympify, args))
+        u = [a.name for a in args if isinstance(a, UndefinedFunction)]
+        if u:
+            raise TypeError('Invalid argument: expecting an expression, not UndefinedFunction%s: %s' % (
+                's'*(len(u) > 1), ', '.join(u)))
+        obj: Expr = super().__new__(cls, *args, **options)  # type: ignore
+        return obj
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        return self
+
+    @property
+    def _diff_wrt(self):
+        """
+        Allow derivatives wrt to undefined functions.
+
+        Examples
+        ========
+
+        >>> from sympy import Function, Symbol
+        >>> f = Function('f')
+        >>> x = Symbol('x')
+        >>> f(x)._diff_wrt
+        True
+        >>> f(x).diff(x)
+        Derivative(f(x), x)
+        """
+        return True
+
+
+class UndefSageHelper:
+    """
+    Helper to facilitate Sage conversion.
+    """
+    def __get__(self, ins, typ):
+        import sage.all as sage
+        if ins is None:
+            return lambda: sage.function(typ.__name__)
+        else:
+            args = [arg._sage_() for arg in ins.args]
+            return lambda : sage.function(ins.__class__.__name__)(*args)
+
+_undef_sage_helper = UndefSageHelper()
+
+
+class UndefinedFunction(FunctionClass):
+    """
+    The (meta)class of undefined functions.
+    """
+    name: str
+    _sage_: UndefSageHelper
+
+    def __new__(mcl, name, bases=(AppliedUndef,), __dict__=None, **kwargs) -> type[AppliedUndef]:
+        from .symbol import _filter_assumptions
+        # Allow Function('f', real=True)
+        # and/or Function(Symbol('f', real=True))
+        assumptions, kwargs = _filter_assumptions(kwargs)
+        if isinstance(name, Symbol):
+            assumptions = name._merge(assumptions)
+            name = name.name
+        elif not isinstance(name, str):
+            raise TypeError('expecting string or Symbol for name')
+        else:
+            commutative = assumptions.get('commutative', None)
+            assumptions = Symbol(name, **assumptions).assumptions0
+            if commutative is None:
+                assumptions.pop('commutative')
+        __dict__ = __dict__ or {}
+        # put the `is_*` for into __dict__
+        __dict__.update({'is_%s' % k: v for k, v in assumptions.items()})
+        # You can add other attributes, although they do have to be hashable
+        # (but seriously, if you want to add anything other than assumptions,
+        # just subclass Function)
+        __dict__.update(kwargs)
+        # add back the sanitized assumptions without the is_ prefix
+        kwargs.update(assumptions)
+        # Save these for __eq__
+        __dict__.update({'_kwargs': kwargs})
+        # do this for pickling
+        __dict__['__module__'] = None
+        obj = super().__new__(mcl, name, bases, __dict__)  # type: ignore
+        obj.name = name
+        obj._sage_ = _undef_sage_helper
+        return obj  # type: ignore
+
+    def __instancecheck__(cls, instance):
+        return cls in type(instance).__mro__
+
+    _kwargs: dict[str, bool | None] = {}
+
+    def __hash__(self):
+        return hash((self.class_key(), frozenset(self._kwargs.items())))
+
+    def __eq__(self, other):
+        return (isinstance(other, self.__class__) and
+            self.class_key() == other.class_key() and
+            self._kwargs == other._kwargs)
+
+    def __ne__(self, other):
+        return not self == other
+
+    @property
+    def _diff_wrt(self):
+        return False
+
+
+# Using copyreg is the only way to make a dynamically generated instance of a
+# metaclass picklable without using a custom pickler. It is not possible to
+# define e.g. __reduce__ on the metaclass because obj.__reduce__ will retrieve
+# the __reduce__ method for reducing instances of the type rather than for the
+# type itself.
+def _reduce_undef(f):
+    return (_rebuild_undef, (f.name, f._kwargs))
+
+def _rebuild_undef(name, kwargs):
+    return Function(name, **kwargs)
+
+copyreg.pickle(UndefinedFunction, _reduce_undef)
+
+
+# XXX: The type: ignore on WildFunction is because mypy complains:
+#
+# sympy/core/function.py:939: error: Cannot determine type of 'sort_key' in
+# base class 'Expr'
+#
+# Somehow this is because of the @cacheit decorator but it is not clear how to
+# fix it.
+
+
+class WildFunction(Function, AtomicExpr):  # type: ignore
+    """
+    A WildFunction function matches any function (with its arguments).
+
+    Examples
+    ========
+
+    >>> from sympy import WildFunction, Function, cos
+    >>> from sympy.abc import x, y
+    >>> F = WildFunction('F')
+    >>> f = Function('f')
+    >>> F.nargs
+    Naturals0
+    >>> x.match(F)
+    >>> F.match(F)
+    {F_: F_}
+    >>> f(x).match(F)
+    {F_: f(x)}
+    >>> cos(x).match(F)
+    {F_: cos(x)}
+    >>> f(x, y).match(F)
+    {F_: f(x, y)}
+
+    To match functions with a given number of arguments, set ``nargs`` to the
+    desired value at instantiation:
+
+    >>> F = WildFunction('F', nargs=2)
+    >>> F.nargs
+    {2}
+    >>> f(x).match(F)
+    >>> f(x, y).match(F)
+    {F_: f(x, y)}
+
+    To match functions with a range of arguments, set ``nargs`` to a tuple
+    containing the desired number of arguments, e.g. if ``nargs = (1, 2)``
+    then functions with 1 or 2 arguments will be matched.
+
+    >>> F = WildFunction('F', nargs=(1, 2))
+    >>> F.nargs
+    {1, 2}
+    >>> f(x).match(F)
+    {F_: f(x)}
+    >>> f(x, y).match(F)
+    {F_: f(x, y)}
+    >>> f(x, y, 1).match(F)
+
+    """
+
+    # XXX: What is this class attribute used for?
+    include: set[Any] = set()
+
+    def __init__(cls, name, **assumptions):
+        from sympy.sets.sets import Set, FiniteSet
+        cls.name = name
+        nargs = assumptions.pop('nargs', S.Naturals0)
+        if not isinstance(nargs, Set):
+            # Canonicalize nargs here.  See also FunctionClass.
+            if is_sequence(nargs):
+                nargs = tuple(ordered(set(nargs)))
+            elif nargs is not None:
+                nargs = (as_int(nargs),)
+            nargs = FiniteSet(*nargs)
+        cls.nargs = nargs
+
+    def matches(self, expr, repl_dict=None, old=False):
+        if not isinstance(expr, (AppliedUndef, Function)):
+            return None
+        if len(expr.args) not in self.nargs:
+            return None
+
+        if repl_dict is None:
+            repl_dict = {}
+        else:
+            repl_dict = repl_dict.copy()
+
+        repl_dict[self] = expr
+        return repl_dict
+
+
+class Derivative(Expr):
+    """
+    Carries out differentiation of the given expression with respect to symbols.
+
+    Examples
+    ========
+
+    >>> from sympy import Derivative, Function, symbols, Subs
+    >>> from sympy.abc import x, y
+    >>> f, g = symbols('f g', cls=Function)
+
+    >>> Derivative(x**2, x, evaluate=True)
+    2*x
+
+    Denesting of derivatives retains the ordering of variables:
+
+        >>> Derivative(Derivative(f(x, y), y), x)
+        Derivative(f(x, y), y, x)
+
+    Contiguously identical symbols are merged into a tuple giving
+    the symbol and the count:
+
+        >>> Derivative(f(x), x, x, y, x)
+        Derivative(f(x), (x, 2), y, x)
+
+    If the derivative cannot be performed, and evaluate is True, the
+    order of the variables of differentiation will be made canonical:
+
+        >>> Derivative(f(x, y), y, x, evaluate=True)
+        Derivative(f(x, y), x, y)
+
+    Derivatives with respect to undefined functions can be calculated:
+
+        >>> Derivative(f(x)**2, f(x), evaluate=True)
+        2*f(x)
+
+    Such derivatives will show up when the chain rule is used to
+    evaluate a derivative:
+
+        >>> f(g(x)).diff(x)
+        Derivative(f(g(x)), g(x))*Derivative(g(x), x)
+
+    Substitution is used to represent derivatives of functions with
+    arguments that are not symbols or functions:
+
+        >>> f(2*x + 3).diff(x) == 2*Subs(f(y).diff(y), y, 2*x + 3)
+        True
+
+    Notes
+    =====
+
+    Simplification of high-order derivatives:
+
+    Because there can be a significant amount of simplification that can be
+    done when multiple differentiations are performed, results will be
+    automatically simplified in a fairly conservative fashion unless the
+    keyword ``simplify`` is set to False.
+
+        >>> from sympy import sqrt, diff, Function, symbols
+        >>> from sympy.abc import x, y, z
+        >>> f, g = symbols('f,g', cls=Function)
+
+        >>> e = sqrt((x + 1)**2 + x)
+        >>> diff(e, (x, 5), simplify=False).count_ops()
+        136
+        >>> diff(e, (x, 5)).count_ops()
+        30
+
+    Ordering of variables:
+
+    If evaluate is set to True and the expression cannot be evaluated, the
+    list of differentiation symbols will be sorted, that is, the expression is
+    assumed to have continuous derivatives up to the order asked.
+
+    Derivative wrt non-Symbols:
+
+    For the most part, one may not differentiate wrt non-symbols.
+    For example, we do not allow differentiation wrt `x*y` because
+    there are multiple ways of structurally defining where x*y appears
+    in an expression: a very strict definition would make
+    (x*y*z).diff(x*y) == 0. Derivatives wrt defined functions (like
+    cos(x)) are not allowed, either:
+
+        >>> (x*y*z).diff(x*y)
+        Traceback (most recent call last):
+        ...
+        ValueError: Can't calculate derivative wrt x*y.
+
+    To make it easier to work with variational calculus, however,
+    derivatives wrt AppliedUndef and Derivatives are allowed.
+    For example, in the Euler-Lagrange method one may write
+    F(t, u, v) where u = f(t) and v = f'(t). These variables can be
+    written explicitly as functions of time::
+
+        >>> from sympy.abc import t
+        >>> F = Function('F')
+        >>> U = f(t)
+        >>> V = U.diff(t)
+
+    The derivative wrt f(t) can be obtained directly:
+
+        >>> direct = F(t, U, V).diff(U)
+
+    When differentiation wrt a non-Symbol is attempted, the non-Symbol
+    is temporarily converted to a Symbol while the differentiation
+    is performed and the same answer is obtained:
+
+        >>> indirect = F(t, U, V).subs(U, x).diff(x).subs(x, U)
+        >>> assert direct == indirect
+
+    The implication of this non-symbol replacement is that all
+    functions are treated as independent of other functions and the
+    symbols are independent of the functions that contain them::
+
+        >>> x.diff(f(x))
+        0
+        >>> g(x).diff(f(x))
+        0
+
+    It also means that derivatives are assumed to depend only
+    on the variables of differentiation, not on anything contained
+    within the expression being differentiated::
+
+        >>> F = f(x)
+        >>> Fx = F.diff(x)
+        >>> Fx.diff(F)  # derivative depends on x, not F
+        0
+        >>> Fxx = Fx.diff(x)
+        >>> Fxx.diff(Fx)  # derivative depends on x, not Fx
+        0
+
+    The last example can be made explicit by showing the replacement
+    of Fx in Fxx with y:
+
+        >>> Fxx.subs(Fx, y)
+        Derivative(y, x)
+
+        Since that in itself will evaluate to zero, differentiating
+        wrt Fx will also be zero:
+
+        >>> _.doit()
+        0
+
+    Replacing undefined functions with concrete expressions
+
+    One must be careful to replace undefined functions with expressions
+    that contain variables consistent with the function definition and
+    the variables of differentiation or else insconsistent result will
+    be obtained. Consider the following example:
+
+    >>> eq = f(x)*g(y)
+    >>> eq.subs(f(x), x*y).diff(x, y).doit()
+    y*Derivative(g(y), y) + g(y)
+    >>> eq.diff(x, y).subs(f(x), x*y).doit()
+    y*Derivative(g(y), y)
+
+    The results differ because `f(x)` was replaced with an expression
+    that involved both variables of differentiation. In the abstract
+    case, differentiation of `f(x)` by `y` is 0; in the concrete case,
+    the presence of `y` made that derivative nonvanishing and produced
+    the extra `g(y)` term.
+
+    Defining differentiation for an object
+
+    An object must define ._eval_derivative(symbol) method that returns
+    the differentiation result. This function only needs to consider the
+    non-trivial case where expr contains symbol and it should call the diff()
+    method internally (not _eval_derivative); Derivative should be the only
+    one to call _eval_derivative.
+
+    Any class can allow derivatives to be taken with respect to
+    itself (while indicating its scalar nature). See the
+    docstring of Expr._diff_wrt.
+
+    See Also
+    ========
+    _sort_variable_count
+    """
+
+    is_Derivative = True
+
+    @property
+    def _diff_wrt(self):
+        """An expression may be differentiated wrt a Derivative if
+        it is in elementary form.
+
+        Examples
+        ========
+
+        >>> from sympy import Function, Derivative, cos
+        >>> from sympy.abc import x
+        >>> f = Function('f')
+
+        >>> Derivative(f(x), x)._diff_wrt
+        True
+        >>> Derivative(cos(x), x)._diff_wrt
+        False
+        >>> Derivative(x + 1, x)._diff_wrt
+        False
+
+        A Derivative might be an unevaluated form of what will not be
+        a valid variable of differentiation if evaluated. For example,
+
+        >>> Derivative(f(f(x)), x).doit()
+        Derivative(f(x), x)*Derivative(f(f(x)), f(x))
+
+        Such an expression will present the same ambiguities as arise
+        when dealing with any other product, like ``2*x``, so ``_diff_wrt``
+        is False:
+
+        >>> Derivative(f(f(x)), x)._diff_wrt
+        False
+        """
+        return self.expr._diff_wrt and isinstance(self.doit(), Derivative)
+
+    def __new__(cls, expr, *variables, **kwargs):
+        expr = sympify(expr)
+        if not isinstance(expr, Basic):
+            raise TypeError(f"Cannot represent derivative of {type(expr)}")
+        symbols_or_none = getattr(expr, "free_symbols", None)
+        has_symbol_set = isinstance(symbols_or_none, set)
+
+        if not has_symbol_set:
+            raise ValueError(filldedent('''
+                Since there are no variables in the expression %s,
+                it cannot be differentiated.''' % expr))
+
+        # determine value for variables if it wasn't given
+        if not variables:
+            variables = expr.free_symbols
+            if len(variables) != 1:
+                if expr.is_number:
+                    return S.Zero
+                if len(variables) == 0:
+                    raise ValueError(filldedent('''
+                        Since there are no variables in the expression,
+                        the variable(s) of differentiation must be supplied
+                        to differentiate %s''' % expr))
+                else:
+                    raise ValueError(filldedent('''
+                        Since there is more than one variable in the
+                        expression, the variable(s) of differentiation
+                        must be supplied to differentiate %s''' % expr))
+
+        # Split the list of variables into a list of the variables we are diff
+        # wrt, where each element of the list has the form (s, count) where
+        # s is the entity to diff wrt and count is the order of the
+        # derivative.
+        variable_count = []
+        array_likes = (tuple, list, Tuple)
+
+        from sympy.tensor.array import Array, NDimArray
+
+        for i, v in enumerate(variables):
+            if isinstance(v, UndefinedFunction):
+                raise TypeError(
+                    "cannot differentiate wrt "
+                    "UndefinedFunction: %s" % v)
+
+            if isinstance(v, array_likes):
+                if len(v) == 0:
+                    # Ignore empty tuples: Derivative(expr, ... , (), ... )
+                    continue
+                if isinstance(v[0], array_likes):
+                    # Derive by array: Derivative(expr, ... , [[x, y, z]], ... )
+                    if len(v) == 1:
+                        v = Array(v[0])
+                        count = 1
+                    else:
+                        v, count = v
+                        v = Array(v)
+                else:
+                    v, count = v
+                if count == 0:
+                    continue
+                variable_count.append(Tuple(v, count))
+                continue
+
+            v = sympify(v)
+            if isinstance(v, Integer):
+                if i == 0:
+                    raise ValueError("First variable cannot be a number: %i" % v)
+                count = v
+                prev, prevcount = variable_count[-1]
+                if prevcount != 1:
+                    raise TypeError("tuple {} followed by number {}".format((prev, prevcount), v))
+                if count == 0:
+                    variable_count.pop()
+                else:
+                    variable_count[-1] = Tuple(prev, count)
+            else:
+                count = 1
+                variable_count.append(Tuple(v, count))
+
+        # light evaluation of contiguous, identical
+        # items: (x, 1), (x, 1) -> (x, 2)
+        merged = []
+        for t in variable_count:
+            v, c = t
+            if c.is_negative:
+                raise ValueError(
+                    'order of differentiation must be nonnegative')
+            if merged and merged[-1][0] == v:
+                c += merged[-1][1]
+                if not c:
+                    merged.pop()
+                else:
+                    merged[-1] = Tuple(v, c)
+            else:
+                merged.append(t)
+        variable_count = merged
+
+        # sanity check of variables of differentation; we waited
+        # until the counts were computed since some variables may
+        # have been removed because the count was 0
+        for v, c in variable_count:
+            # v must have _diff_wrt True
+            if not v._diff_wrt:
+                __ = ''  # filler to make error message neater
+                raise ValueError(filldedent('''
+                    Can't calculate derivative wrt %s.%s''' % (v,
+                    __)))
+
+        # We make a special case for 0th derivative, because there is no
+        # good way to unambiguously print this.
+        if len(variable_count) == 0:
+            return expr
+
+        evaluate = kwargs.get('evaluate', False)
+
+        if evaluate:
+            if isinstance(expr, Derivative):
+                expr = expr.canonical
+            variable_count = [
+                (v.canonical if isinstance(v, Derivative) else v, c)
+                for v, c in variable_count]
+
+            # Look for a quick exit if there are symbols that don't appear in
+            # expression at all. Note, this cannot check non-symbols like
+            # Derivatives as those can be created by intermediate
+            # derivatives.
+            zero = False
+            free = expr.free_symbols
+            from sympy.matrices.expressions.matexpr import MatrixExpr
+
+            for v, c in variable_count:
+                vfree = v.free_symbols
+                if c.is_positive and vfree:
+                    if isinstance(v, AppliedUndef):
+                        # these match exactly since
+                        # x.diff(f(x)) == g(x).diff(f(x)) == 0
+                        # and are not created by differentiation
+                        D = Dummy()
+                        if not expr.xreplace({v: D}).has(D):
+                            zero = True
+                            break
+                    elif isinstance(v, MatrixExpr):
+                        zero = False
+                        break
+                    elif isinstance(v, Symbol) and v not in free:
+                        zero = True
+                        break
+                    else:
+                        if not free & vfree:
+                            # e.g. v is IndexedBase or Matrix
+                            zero = True
+                            break
+            if zero:
+                return cls._get_zero_with_shape_like(expr)
+
+            # make the order of symbols canonical
+            #TODO: check if assumption of discontinuous derivatives exist
+            variable_count = cls._sort_variable_count(variable_count)
+
+        # denest
+        if isinstance(expr, Derivative):
+            variable_count = list(expr.variable_count) + variable_count
+            expr = expr.expr
+            return _derivative_dispatch(expr, *variable_count, **kwargs)
+
+        # we return here if evaluate is False or if there is no
+        # _eval_derivative method
+        if not evaluate or not hasattr(expr, '_eval_derivative'):
+            # return an unevaluated Derivative
+            if evaluate and variable_count == [(expr, 1)] and expr.is_scalar:
+                # special hack providing evaluation for classes
+                # that have defined is_scalar=True but have no
+                # _eval_derivative defined
+                return S.One
+            return Expr.__new__(cls, expr, *variable_count)
+
+        # evaluate the derivative by calling _eval_derivative method
+        # of expr for each variable
+        # -------------------------------------------------------------
+        nderivs = 0  # how many derivatives were performed
+        unhandled = []
+        from sympy.matrices.matrixbase import MatrixBase
+        for i, (v, count) in enumerate(variable_count):
+
+            old_expr = expr
+            old_v = None
+
+            is_symbol = v.is_symbol or isinstance(v,
+                (Iterable, Tuple, MatrixBase, NDimArray))
+
+            if not is_symbol:
+                old_v = v
+                v = Dummy('xi')
+                expr = expr.xreplace({old_v: v})
+                # Derivatives and UndefinedFunctions are independent
+                # of all others
+                clashing = not (isinstance(old_v, (Derivative, AppliedUndef)))
+                if v not in expr.free_symbols and not clashing:
+                    return expr.diff(v)  # expr's version of 0
+                if not old_v.is_scalar and not hasattr(
+                        old_v, '_eval_derivative'):
+                    # special hack providing evaluation for classes
+                    # that have defined is_scalar=True but have no
+                    # _eval_derivative defined
+                    expr *= old_v.diff(old_v)
+
+            obj = cls._dispatch_eval_derivative_n_times(expr, v, count)
+            if obj is not None and obj.is_zero:
+                return obj
+
+            nderivs += count
+
+            if old_v is not None:
+                if obj is not None:
+                    # remove the dummy that was used
+                    obj = obj.subs(v, old_v)
+                # restore expr
+                expr = old_expr
+
+            if obj is None:
+                # we've already checked for quick-exit conditions
+                # that give 0 so the remaining variables
+                # are contained in the expression but the expression
+                # did not compute a derivative so we stop taking
+                # derivatives
+                unhandled = variable_count[i:]
+                break
+
+            expr = obj
+
+        # what we have so far can be made canonical
+        expr = expr.replace(
+            lambda x: isinstance(x, Derivative),
+            lambda x: x.canonical)
+
+        if unhandled:
+            if isinstance(expr, Derivative):
+                unhandled = list(expr.variable_count) + unhandled
+                expr = expr.expr
+            expr = Expr.__new__(cls, expr, *unhandled)
+
+        if (nderivs > 1) == True and kwargs.get('simplify', True):
+            from .exprtools import factor_terms
+            from sympy.simplify.simplify import signsimp
+            expr = factor_terms(signsimp(expr))
+        return expr
+
+    @property
+    def canonical(cls):
+        return cls.func(cls.expr,
+            *Derivative._sort_variable_count(cls.variable_count))
+
+    @classmethod
+    def _sort_variable_count(cls, vc):
+        """
+        Sort (variable, count) pairs into canonical order while
+        retaining order of variables that do not commute during
+        differentiation:
+
+        * symbols and functions commute with each other
+        * derivatives commute with each other
+        * a derivative does not commute with anything it contains
+        * any other object is not allowed to commute if it has
+          free symbols in common with another object
+
+        Examples
+        ========
+
+        >>> from sympy import Derivative, Function, symbols
+        >>> vsort = Derivative._sort_variable_count
+        >>> x, y, z = symbols('x y z')
+        >>> f, g, h = symbols('f g h', cls=Function)
+
+        Contiguous items are collapsed into one pair:
+
+        >>> vsort([(x, 1), (x, 1)])
+        [(x, 2)]
+        >>> vsort([(y, 1), (f(x), 1), (y, 1), (f(x), 1)])
+        [(y, 2), (f(x), 2)]
+
+        Ordering is canonical.
+
+        >>> def vsort0(*v):
+        ...     # docstring helper to
+        ...     # change vi -> (vi, 0), sort, and return vi vals
+        ...     return [i[0] for i in vsort([(i, 0) for i in v])]
+
+        >>> vsort0(y, x)
+        [x, y]
+        >>> vsort0(g(y), g(x), f(y))
+        [f(y), g(x), g(y)]
+
+        Symbols are sorted as far to the left as possible but never
+        move to the left of a derivative having the same symbol in
+        its variables; the same applies to AppliedUndef which are
+        always sorted after Symbols:
+
+        >>> dfx = f(x).diff(x)
+        >>> assert vsort0(dfx, y) == [y, dfx]
+        >>> assert vsort0(dfx, x) == [dfx, x]
+        """
+        if not vc:
+            return []
+        vc = list(vc)
+        if len(vc) == 1:
+            return [Tuple(*vc[0])]
+        V = list(range(len(vc)))
+        E = []
+        v = lambda i: vc[i][0]
+        D = Dummy()
+        def _block(d, v, wrt=False):
+            # return True if v should not come before d else False
+            if d == v:
+                return wrt
+            if d.is_Symbol:
+                return False
+            if isinstance(d, Derivative):
+                # a derivative blocks if any of it's variables contain
+                # v; the wrt flag will return True for an exact match
+                # and will cause an AppliedUndef to block if v is in
+                # the arguments
+                if any(_block(k, v, wrt=True)
+                        for k in d._wrt_variables):
+                    return True
+                return False
+            if not wrt and isinstance(d, AppliedUndef):
+                return False
+            if v.is_Symbol:
+                return v in d.free_symbols
+            if isinstance(v, AppliedUndef):
+                return _block(d.xreplace({v: D}), D)
+            return d.free_symbols & v.free_symbols
+        for i in range(len(vc)):
+            for j in range(i):
+                if _block(v(j), v(i)):
+                    E.append((j,i))
+        # this is the default ordering to use in case of ties
+        O = dict(zip(ordered(uniq([i for i, c in vc])), range(len(vc))))
+        ix = topological_sort((V, E), key=lambda i: O[v(i)])
+        # merge counts of contiguously identical items
+        merged = []
+        for v, c in [vc[i] for i in ix]:
+            if merged and merged[-1][0] == v:
+                merged[-1][1] += c
+            else:
+                merged.append([v, c])
+        return [Tuple(*i) for i in merged]
+
+    def _eval_is_commutative(self):
+        return self.expr.is_commutative
+
+    def _eval_derivative(self, v):
+        # If v (the variable of differentiation) is not in
+        # self.variables, we might be able to take the derivative.
+        if v not in self._wrt_variables:
+            dedv = self.expr.diff(v)
+            if isinstance(dedv, Derivative):
+                return dedv.func(dedv.expr, *(self.variable_count + dedv.variable_count))
+            # dedv (d(self.expr)/dv) could have simplified things such that the
+            # derivative wrt things in self.variables can now be done. Thus,
+            # we set evaluate=True to see if there are any other derivatives
+            # that can be done. The most common case is when dedv is a simple
+            # number so that the derivative wrt anything else will vanish.
+            return self.func(dedv, *self.variables, evaluate=True)
+        # In this case v was in self.variables so the derivative wrt v has
+        # already been attempted and was not computed, either because it
+        # couldn't be or evaluate=False originally.
+        variable_count = list(self.variable_count)
+        variable_count.append((v, 1))
+        return self.func(self.expr, *variable_count, evaluate=False)
+
+    def doit(self, **hints):
+        expr = self.expr
+        if hints.get('deep', True):
+            expr = expr.doit(**hints)
+        hints['evaluate'] = True
+        rv = self.func(expr, *self.variable_count, **hints)
+        if rv!= self and rv.has(Derivative):
+            rv =  rv.doit(**hints)
+        return rv
+
+    @_sympifyit('z0', NotImplementedError)
+    def doit_numerically(self, z0):
+        """
+        Evaluate the derivative at z numerically.
+
+        When we can represent derivatives at a point, this should be folded
+        into the normal evalf. For now, we need a special method.
+        """
+        if len(self.free_symbols) != 1 or len(self.variables) != 1:
+            raise NotImplementedError('partials and higher order derivatives')
+        z = list(self.free_symbols)[0]
+
+        def eval(x):
+            f0 = self.expr.subs(z, Expr._from_mpmath(x, prec=mpmath.mp.prec))
+            f0 = f0.evalf(prec_to_dps(mpmath.mp.prec))
+            return f0._to_mpmath(mpmath.mp.prec)
+        return Expr._from_mpmath(mpmath.diff(eval,
+                                             z0._to_mpmath(mpmath.mp.prec)),
+                                 mpmath.mp.prec)
+
+    @property
+    def expr(self):
+        return self._args[0]
+
+    @property
+    def _wrt_variables(self):
+        # return the variables of differentiation without
+        # respect to the type of count (int or symbolic)
+        return [i[0] for i in self.variable_count]
+
+    @property
+    def variables(self):
+        # TODO: deprecate?  YES, make this 'enumerated_variables' and
+        #       name _wrt_variables as variables
+        # TODO: support for `d^n`?
+        rv = []
+        for v, count in self.variable_count:
+            if not count.is_Integer:
+                raise TypeError(filldedent('''
+                Cannot give expansion for symbolic count. If you just
+                want a list of all variables of differentiation, use
+                _wrt_variables.'''))
+            rv.extend([v]*count)
+        return tuple(rv)
+
+    @property
+    def variable_count(self):
+        return self._args[1:]
+
+    @property
+    def derivative_count(self):
+        return sum([count for _, count in self.variable_count], 0)
+
+    @property
+    def free_symbols(self):
+        ret = self.expr.free_symbols
+        # Add symbolic counts to free_symbols
+        for _, count in self.variable_count:
+            ret.update(count.free_symbols)
+        return ret
+
+    @property
+    def kind(self):
+        return self.args[0].kind
+
+    def _eval_subs(self, old, new):
+        # The substitution (old, new) cannot be done inside
+        # Derivative(expr, vars) for a variety of reasons
+        # as handled below.
+        if old in self._wrt_variables:
+            # first handle the counts
+            expr = self.func(self.expr, *[(v, c.subs(old, new))
+                for v, c in self.variable_count])
+            if expr != self:
+                return expr._eval_subs(old, new)
+            # quick exit case
+            if not getattr(new, '_diff_wrt', False):
+                # case (0): new is not a valid variable of
+                # differentiation
+                if isinstance(old, Symbol):
+                    # don't introduce a new symbol if the old will do
+                    return Subs(self, old, new)
+                else:
+                    xi = Dummy('xi')
+                    return Subs(self.xreplace({old: xi}), xi, new)
+
+        # If both are Derivatives with the same expr, check if old is
+        # equivalent to self or if old is a subderivative of self.
+        if old.is_Derivative and old.expr == self.expr:
+            if self.canonical == old.canonical:
+                return new
+
+            # collections.Counter doesn't have __le__
+            def _subset(a, b):
+                return all((a[i] <= b[i]) == True for i in a)
+
+            old_vars = Counter(dict(reversed(old.variable_count)))
+            self_vars = Counter(dict(reversed(self.variable_count)))
+            if _subset(old_vars, self_vars):
+                return _derivative_dispatch(new, *(self_vars - old_vars).items()).canonical
+
+        args = list(self.args)
+        newargs = [x._subs(old, new) for x in args]
+        if args[0] == old:
+            # complete replacement of self.expr
+            # we already checked that the new is valid so we know
+            # it won't be a problem should it appear in variables
+            return _derivative_dispatch(*newargs)
+
+        if newargs[0] != args[0]:
+            # case (1) can't change expr by introducing something that is in
+            # the _wrt_variables if it was already in the expr
+            # e.g.
+            # for Derivative(f(x, g(y)), y), x cannot be replaced with
+            # anything that has y in it; for f(g(x), g(y)).diff(g(y))
+            # g(x) cannot be replaced with anything that has g(y)
+            syms = {vi: Dummy() for vi in self._wrt_variables
+                if not vi.is_Symbol}
+            wrt = {syms.get(vi, vi) for vi in self._wrt_variables}
+            forbidden = args[0].xreplace(syms).free_symbols & wrt
+            nfree = new.xreplace(syms).free_symbols
+            ofree = old.xreplace(syms).free_symbols
+            if (nfree - ofree) & forbidden:
+                return Subs(self, old, new)
+
+        viter = ((i, j) for ((i, _), (j, _)) in zip(newargs[1:], args[1:]))
+        if any(i != j for i, j in viter):  # a wrt-variable change
+            # case (2) can't change vars by introducing a variable
+            # that is contained in expr, e.g.
+            # for Derivative(f(z, g(h(x), y)), y), y cannot be changed to
+            # x, h(x), or g(h(x), y)
+            for a in _atomic(self.expr, recursive=True):
+                for i in range(1, len(newargs)):
+                    vi, _ = newargs[i]
+                    if a == vi and vi != args[i][0]:
+                        return Subs(self, old, new)
+            # more arg-wise checks
+            vc = newargs[1:]
+            oldv = self._wrt_variables
+            newe = self.expr
+            subs = []
+            for i, (vi, ci) in enumerate(vc):
+                if not vi._diff_wrt:
+                    # case (3) invalid differentiation expression so
+                    # create a replacement dummy
+                    xi = Dummy('xi_%i' % i)
+                    # replace the old valid variable with the dummy
+                    # in the expression
+                    newe = newe.xreplace({oldv[i]: xi})
+                    # and replace the bad variable with the dummy
+                    vc[i] = (xi, ci)
+                    # and record the dummy with the new (invalid)
+                    # differentiation expression
+                    subs.append((xi, vi))
+
+            if subs:
+                # handle any residual substitution in the expression
+                newe = newe._subs(old, new)
+                # return the Subs-wrapped derivative
+                return Subs(Derivative(newe, *vc), *zip(*subs))
+
+        # everything was ok
+        return _derivative_dispatch(*newargs)
+
+    def _eval_lseries(self, x, logx, cdir=0):
+        dx = self.variables
+        for term in self.expr.lseries(x, logx=logx, cdir=cdir):
+            yield self.func(term, *dx)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.expr.nseries(x, n=n, logx=logx)
+        o = arg.getO()
+        dx = self.variables
+        rv = [self.func(a, *dx) for a in Add.make_args(arg.removeO())]
+        if o:
+            rv.append(o/x)
+        return Add(*rv)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        series_gen = self.expr.lseries(x)
+        d = S.Zero
+        for leading_term in series_gen:
+            d = diff(leading_term, *self.variables)
+            if d != 0:
+                break
+        return d
+
+    def as_finite_difference(self, points=1, x0=None, wrt=None):
+        """ Expresses a Derivative instance as a finite difference.
+
+        Parameters
+        ==========
+
+        points : sequence or coefficient, optional
+            If sequence: discrete values (length >= order+1) of the
+            independent variable used for generating the finite
+            difference weights.
+            If it is a coefficient, it will be used as the step-size
+            for generating an equidistant sequence of length order+1
+            centered around ``x0``. Default: 1 (step-size 1)
+
+        x0 : number or Symbol, optional
+            the value of the independent variable (``wrt``) at which the
+            derivative is to be approximated. Default: same as ``wrt``.
+
+        wrt : Symbol, optional
+            "with respect to" the variable for which the (partial)
+            derivative is to be approximated for. If not provided it
+            is required that the derivative is ordinary. Default: ``None``.
+
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Function, exp, sqrt, Symbol
+        >>> x, h = symbols('x h')
+        >>> f = Function('f')
+        >>> f(x).diff(x).as_finite_difference()
+        -f(x - 1/2) + f(x + 1/2)
+
+        The default step size and number of points are 1 and
+        ``order + 1`` respectively. We can change the step size by
+        passing a symbol as a parameter:
+
+        >>> f(x).diff(x).as_finite_difference(h)
+        -f(-h/2 + x)/h + f(h/2 + x)/h
+
+        We can also specify the discretized values to be used in a
+        sequence:
+
+        >>> f(x).diff(x).as_finite_difference([x, x+h, x+2*h])
+        -3*f(x)/(2*h) + 2*f(h + x)/h - f(2*h + x)/(2*h)
+
+        The algorithm is not restricted to use equidistant spacing, nor
+        do we need to make the approximation around ``x0``, but we can get
+        an expression estimating the derivative at an offset:
+
+        >>> e, sq2 = exp(1), sqrt(2)
+        >>> xl = [x-h, x+h, x+e*h]
+        >>> f(x).diff(x, 1).as_finite_difference(xl, x+h*sq2)  # doctest: +ELLIPSIS
+        2*h*((h + sqrt(2)*h)/(2*h) - (-sqrt(2)*h + h)/(2*h))*f(E*h + x)/...
+
+        To approximate ``Derivative`` around ``x0`` using a non-equidistant
+        spacing step, the algorithm supports assignment of undefined
+        functions to ``points``:
+
+        >>> dx = Function('dx')
+        >>> f(x).diff(x).as_finite_difference(points=dx(x), x0=x-h)
+        -f(-h + x - dx(-h + x)/2)/dx(-h + x) + f(-h + x + dx(-h + x)/2)/dx(-h + x)
+
+        Partial derivatives are also supported:
+
+        >>> y = Symbol('y')
+        >>> d2fdxdy=f(x,y).diff(x,y)
+        >>> d2fdxdy.as_finite_difference(wrt=x)
+        -Derivative(f(x - 1/2, y), y) + Derivative(f(x + 1/2, y), y)
+
+        We can apply ``as_finite_difference`` to ``Derivative`` instances in
+        compound expressions using ``replace``:
+
+        >>> (1 + 42**f(x).diff(x)).replace(lambda arg: arg.is_Derivative,
+        ...     lambda arg: arg.as_finite_difference())
+        42**(-f(x - 1/2) + f(x + 1/2)) + 1
+
+
+        See also
+        ========
+
+        sympy.calculus.finite_diff.apply_finite_diff
+        sympy.calculus.finite_diff.differentiate_finite
+        sympy.calculus.finite_diff.finite_diff_weights
+
+        """
+        from sympy.calculus.finite_diff import _as_finite_diff
+        return _as_finite_diff(self, points, x0, wrt)
+
+    @classmethod
+    def _get_zero_with_shape_like(cls, expr):
+        return S.Zero
+
+    @classmethod
+    def _dispatch_eval_derivative_n_times(cls, expr, v, count):
+        # Evaluate the derivative `n` times.  If
+        # `_eval_derivative_n_times` is not overridden by the current
+        # object, the default in `Basic` will call a loop over
+        # `_eval_derivative`:
+        return expr._eval_derivative_n_times(v, count)
+
+
+def _derivative_dispatch(expr, *variables, **kwargs):
+    from sympy.matrices.matrixbase import MatrixBase
+    from sympy.matrices.expressions.matexpr import MatrixExpr
+    from sympy.tensor.array import NDimArray
+    array_types = (MatrixBase, MatrixExpr, NDimArray, list, tuple, Tuple)
+    if isinstance(expr, array_types) or any(isinstance(i[0], array_types) if isinstance(i, (tuple, list, Tuple)) else isinstance(i, array_types) for i in variables):
+        from sympy.tensor.array.array_derivatives import ArrayDerivative
+        return ArrayDerivative(expr, *variables, **kwargs)
+    return Derivative(expr, *variables, **kwargs)
+
+
+class Lambda(Expr):
+    """
+    Lambda(x, expr) represents a lambda function similar to Python's
+    'lambda x: expr'. A function of several variables is written as
+    Lambda((x, y, ...), expr).
+
+    Examples
+    ========
+
+    A simple example:
+
+    >>> from sympy import Lambda
+    >>> from sympy.abc import x
+    >>> f = Lambda(x, x**2)
+    >>> f(4)
+    16
+
+    For multivariate functions, use:
+
+    >>> from sympy.abc import y, z, t
+    >>> f2 = Lambda((x, y, z, t), x + y**z + t**z)
+    >>> f2(1, 2, 3, 4)
+    73
+
+    It is also possible to unpack tuple arguments:
+
+    >>> f = Lambda(((x, y), z), x + y + z)
+    >>> f((1, 2), 3)
+    6
+
+    A handy shortcut for lots of arguments:
+
+    >>> p = x, y, z
+    >>> f = Lambda(p, x + y*z)
+    >>> f(*p)
+    x + y*z
+
+    """
+    is_Function = True
+
+    def __new__(cls, signature, expr) -> Lambda:
+        if iterable(signature) and not isinstance(signature, (tuple, Tuple)):
+            sympy_deprecation_warning(
+                """
+                Using a non-tuple iterable as the first argument to Lambda
+                is deprecated. Use Lambda(tuple(args), expr) instead.
+                """,
+                deprecated_since_version="1.5",
+                active_deprecations_target="deprecated-non-tuple-lambda",
+            )
+            signature = tuple(signature)
+        _sig = signature if iterable(signature) else (signature,)
+        sig: Tuple = sympify(_sig) # type: ignore
+        cls._check_signature(sig)
+
+        if len(sig) == 1 and sig[0] == expr:
+            return S.IdentityFunction
+
+        return Expr.__new__(cls, sig, sympify(expr))
+
+    @classmethod
+    def _check_signature(cls, sig):
+        syms = set()
+
+        def rcheck(args):
+            for a in args:
+                if a.is_symbol:
+                    if a in syms:
+                        raise BadSignatureError("Duplicate symbol %s" % a)
+                    syms.add(a)
+                elif isinstance(a, Tuple):
+                    rcheck(a)
+                else:
+                    raise BadSignatureError("Lambda signature should be only tuples"
+                        " and symbols, not %s" % a)
+
+        if not isinstance(sig, Tuple):
+            raise BadSignatureError("Lambda signature should be a tuple not %s" % sig)
+        # Recurse through the signature:
+        rcheck(sig)
+
+    @property
+    def signature(self):
+        """The expected form of the arguments to be unpacked into variables"""
+        return self._args[0]
+
+    @property
+    def expr(self):
+        """The return value of the function"""
+        return self._args[1]
+
+    @property
+    def variables(self):
+        """The variables used in the internal representation of the function"""
+        def _variables(args):
+            if isinstance(args, Tuple):
+                for arg in args:
+                    yield from _variables(arg)
+            else:
+                yield args
+        return tuple(_variables(self.signature))
+
+    @property
+    def nargs(self):
+        from sympy.sets.sets import FiniteSet
+        return FiniteSet(len(self.signature))
+
+    bound_symbols = variables
+
+    @property
+    def free_symbols(self):
+        return self.expr.free_symbols - set(self.variables)
+
+    def __call__(self, *args):
+        n = len(args)
+        if n not in self.nargs:  # Lambda only ever has 1 value in nargs
+            # XXX: exception message must be in exactly this format to
+            # make it work with NumPy's functions like vectorize(). See,
+            # for example, https://github.com/numpy/numpy/issues/1697.
+            # The ideal solution would be just to attach metadata to
+            # the exception and change NumPy to take advantage of this.
+            ## XXX does this apply to Lambda? If not, remove this comment.
+            temp = ('%(name)s takes exactly %(args)s '
+                   'argument%(plural)s (%(given)s given)')
+            raise BadArgumentsError(temp % {
+                'name': self,
+                'args': list(self.nargs)[0],
+                'plural': 's'*(list(self.nargs)[0] != 1),
+                'given': n})
+
+        d = self._match_signature(self.signature, args)
+
+        return self.expr.xreplace(d)
+
+    def _match_signature(self, sig, args):
+
+        symargmap = {}
+
+        def rmatch(pars, args):
+            for par, arg in zip(pars, args):
+                if par.is_symbol:
+                    symargmap[par] = arg
+                elif isinstance(par, Tuple):
+                    if not isinstance(arg, (tuple, Tuple)) or len(args) != len(pars):
+                        raise BadArgumentsError("Can't match %s and %s" % (args, pars))
+                    rmatch(par, arg)
+
+        rmatch(sig, args)
+
+        return symargmap
+
+    @property
+    def is_identity(self):
+        """Return ``True`` if this ``Lambda`` is an identity function. """
+        return self.signature == self.expr
+
+    def _eval_evalf(self, prec):
+        return self.func(self.args[0], self.args[1].evalf(n=prec_to_dps(prec)))
+
+
+class Subs(Expr):
+    """
+    Represents unevaluated substitutions of an expression.
+
+    ``Subs(expr, x, x0)`` represents the expression resulting
+    from substituting x with x0 in expr.
+
+    Parameters
+    ==========
+
+    expr : Expr
+        An expression.
+
+    x : tuple, variable
+        A variable or list of distinct variables.
+
+    x0 : tuple or list of tuples
+        A point or list of evaluation points
+        corresponding to those variables.
+
+    Examples
+    ========
+
+    >>> from sympy import Subs, Function, sin, cos
+    >>> from sympy.abc import x, y, z
+    >>> f = Function('f')
+
+    Subs are created when a particular substitution cannot be made. The
+    x in the derivative cannot be replaced with 0 because 0 is not a
+    valid variables of differentiation:
+
+    >>> f(x).diff(x).subs(x, 0)
+    Subs(Derivative(f(x), x), x, 0)
+
+    Once f is known, the derivative and evaluation at 0 can be done:
+
+    >>> _.subs(f, sin).doit() == sin(x).diff(x).subs(x, 0) == cos(0)
+    True
+
+    Subs can also be created directly with one or more variables:
+
+    >>> Subs(f(x)*sin(y) + z, (x, y), (0, 1))
+    Subs(z + f(x)*sin(y), (x, y), (0, 1))
+    >>> _.doit()
+    z + f(0)*sin(1)
+
+    Notes
+    =====
+
+    ``Subs`` objects are generally useful to represent unevaluated derivatives
+    calculated at a point.
+
+    The variables may be expressions, but they are subjected to the limitations
+    of subs(), so it is usually a good practice to use only symbols for
+    variables, since in that case there can be no ambiguity.
+
+    There's no automatic expansion - use the method .doit() to effect all
+    possible substitutions of the object and also of objects inside the
+    expression.
+
+    When evaluating derivatives at a point that is not a symbol, a Subs object
+    is returned. One is also able to calculate derivatives of Subs objects - in
+    this case the expression is always expanded (for the unevaluated form, use
+    Derivative()).
+
+    In order to allow expressions to combine before doit is done, a
+    representation of the Subs expression is used internally to make
+    expressions that are superficially different compare the same:
+
+    >>> a, b = Subs(x, x, 0), Subs(y, y, 0)
+    >>> a + b
+    2*Subs(x, x, 0)
+
+    This can lead to unexpected consequences when using methods
+    like `has` that are cached:
+
+    >>> s = Subs(x, x, 0)
+    >>> s.has(x), s.has(y)
+    (True, False)
+    >>> ss = s.subs(x, y)
+    >>> ss.has(x), ss.has(y)
+    (True, False)
+    >>> s, ss
+    (Subs(x, x, 0), Subs(y, y, 0))
+    """
+    def __new__(cls, expr, variables, point, **assumptions):
+        if not is_sequence(variables, Tuple):
+            variables = [variables]
+        variables = Tuple(*variables)
+
+        if has_dups(variables):
+            repeated = [str(v) for v, i in Counter(variables).items() if i > 1]
+            __ = ', '.join(repeated)
+            raise ValueError(filldedent('''
+                The following expressions appear more than once: %s
+                ''' % __))
+
+        point = Tuple(*(point if is_sequence(point, Tuple) else [point]))
+
+        if len(point) != len(variables):
+            raise ValueError('Number of point values must be the same as '
+                             'the number of variables.')
+
+        if not point:
+            return sympify(expr)
+
+        # denest
+        if isinstance(expr, Subs):
+            variables = expr.variables + variables
+            point = expr.point + point
+            expr = expr.expr
+        else:
+            expr = sympify(expr)
+
+        # use symbols with names equal to the point value (with prepended _)
+        # to give a variable-independent expression
+        pre = "_"
+        pts = sorted(set(point), key=default_sort_key)
+        from sympy.printing.str import StrPrinter
+        class CustomStrPrinter(StrPrinter):
+            def _print_Dummy(self, expr):
+                return str(expr) + str(expr.dummy_index)
+        def mystr(expr, **settings):
+            p = CustomStrPrinter(settings)
+            return p.doprint(expr)
+        while 1:
+            s_pts = {p: Symbol(pre + mystr(p)) for p in pts}
+            reps = [(v, s_pts[p])
+                for v, p in zip(variables, point)]
+            # if any underscore-prepended symbol is already a free symbol
+            # and is a variable with a different point value, then there
+            # is a clash, e.g. _0 clashes in Subs(_0 + _1, (_0, _1), (1, 0))
+            # because the new symbol that would be created is _1 but _1
+            # is already mapped to 0 so __0 and __1 are used for the new
+            # symbols
+            if any(r in expr.free_symbols and
+                   r in variables and
+                   Symbol(pre + mystr(point[variables.index(r)])) != r
+                   for _, r in reps):
+                pre += "_"
+                continue
+            break
+
+        obj = Expr.__new__(cls, expr, Tuple(*variables), point)
+        obj._expr = expr.xreplace(dict(reps))
+        return obj
+
+    def _eval_is_commutative(self):
+        return self.expr.is_commutative
+
+    def doit(self, **hints):
+        e, v, p = self.args
+
+        # remove self mappings
+        for i, (vi, pi) in enumerate(zip(v, p)):
+            if vi == pi:
+                v = v[:i] + v[i + 1:]
+                p = p[:i] + p[i + 1:]
+        if not v:
+            return self.expr
+
+        if isinstance(e, Derivative):
+            # apply functions first, e.g. f -> cos
+            undone = []
+            for i, vi in enumerate(v):
+                if isinstance(vi, FunctionClass):
+                    e = e.subs(vi, p[i])
+                else:
+                    undone.append((vi, p[i]))
+            if not isinstance(e, Derivative):
+                e = e.doit()
+            if isinstance(e, Derivative):
+                # do Subs that aren't related to differentiation
+                undone2 = []
+                D = Dummy()
+                arg = e.args[0]
+                for vi, pi in undone:
+                    if D not in e.xreplace({vi: D}).free_symbols:
+                        if arg.has(vi):
+                            e = e.subs(vi, pi)
+                    else:
+                        undone2.append((vi, pi))
+                undone = undone2
+                # differentiate wrt variables that are present
+                wrt = []
+                D = Dummy()
+                expr = e.expr
+                free = expr.free_symbols
+                for vi, ci in e.variable_count:
+                    if isinstance(vi, Symbol) and vi in free:
+                        expr = expr.diff((vi, ci))
+                    elif D in expr.subs(vi, D).free_symbols:
+                        expr = expr.diff((vi, ci))
+                    else:
+                        wrt.append((vi, ci))
+                # inject remaining subs
+                rv = expr.subs(undone)
+                # do remaining differentiation *in order given*
+                for vc in wrt:
+                    rv = rv.diff(vc)
+            else:
+                # inject remaining subs
+                rv = e.subs(undone)
+        else:
+            rv = e.doit(**hints).subs(list(zip(v, p)))
+
+        if hints.get('deep', True) and rv != self:
+            rv = rv.doit(**hints)
+        return rv
+
+    def evalf(self, prec=None, **options):
+        return self.doit().evalf(prec, **options)
+
+    n = evalf  # type:ignore
+
+    @property
+    def variables(self):
+        """The variables to be evaluated"""
+        return self._args[1]
+
+    bound_symbols = variables
+
+    @property
+    def expr(self):
+        """The expression on which the substitution operates"""
+        return self._args[0]
+
+    @property
+    def point(self):
+        """The values for which the variables are to be substituted"""
+        return self._args[2]
+
+    @property
+    def free_symbols(self):
+        return (self.expr.free_symbols - set(self.variables) |
+            set(self.point.free_symbols))
+
+    @property
+    def expr_free_symbols(self):
+        sympy_deprecation_warning("""
+        The expr_free_symbols property is deprecated. Use free_symbols to get
+        the free symbols of an expression.
+        """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-expr-free-symbols")
+        # Don't show the warning twice from the recursive call
+        with ignore_warnings(SymPyDeprecationWarning):
+            return (self.expr.expr_free_symbols - set(self.variables) |
+                    set(self.point.expr_free_symbols))
+
+    def __eq__(self, other):
+        if not isinstance(other, Subs):
+            return False
+        return self._hashable_content() == other._hashable_content()
+
+    def __ne__(self, other):
+        return not(self == other)
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def _hashable_content(self):
+        return (self._expr.xreplace(self.canonical_variables),
+            ) + tuple(ordered([(v, p) for v, p in
+            zip(self.variables, self.point) if not self.expr.has(v)]))
+
+    def _eval_subs(self, old, new):
+        # Subs doit will do the variables in order; the semantics
+        # of subs for Subs is have the following invariant for
+        # Subs object foo:
+        #    foo.doit().subs(reps) == foo.subs(reps).doit()
+        pt = list(self.point)
+        if old in self.variables:
+            if _atomic(new) == {new} and not any(
+                    i.has(new) for i in self.args):
+                # the substitution is neutral
+                return self.xreplace({old: new})
+            # any occurrence of old before this point will get
+            # handled by replacements from here on
+            i = self.variables.index(old)
+            for j in range(i, len(self.variables)):
+                pt[j] = pt[j]._subs(old, new)
+            return self.func(self.expr, self.variables, pt)
+        v = [i._subs(old, new) for i in self.variables]
+        if v != list(self.variables):
+            return self.func(self.expr, self.variables + (old,), pt + [new])
+        expr = self.expr._subs(old, new)
+        pt = [i._subs(old, new) for i in self.point]
+        return self.func(expr, v, pt)
+
+    def _eval_derivative(self, s):
+        # Apply the chain rule of the derivative on the substitution variables:
+        f = self.expr
+        vp = V, P = self.variables, self.point
+        val = Add.fromiter(p.diff(s)*Subs(f.diff(v), *vp).doit()
+            for v, p in zip(V, P))
+
+        # these are all the free symbols in the expr
+        efree = f.free_symbols
+        # some symbols like IndexedBase include themselves and args
+        # as free symbols
+        compound = {i for i in efree if len(i.free_symbols) > 1}
+        # hide them and see what independent free symbols remain
+        dums = {Dummy() for i in compound}
+        masked = f.xreplace(dict(zip(compound, dums)))
+        ifree = masked.free_symbols - dums
+        # include the compound symbols
+        free = ifree | compound
+        # remove the variables already handled
+        free -= set(V)
+        # add back any free symbols of remaining compound symbols
+        free |= {i for j in free & compound for i in j.free_symbols}
+        # if symbols of s are in free then there is more to do
+        if free & s.free_symbols:
+            val += Subs(f.diff(s), self.variables, self.point).doit()
+        return val
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        if x in self.point:
+            # x is the variable being substituted into
+            apos = self.point.index(x)
+            other = self.variables[apos]
+        else:
+            other = x
+        arg = self.expr.nseries(other, n=n, logx=logx)
+        o = arg.getO()
+        terms = Add.make_args(arg.removeO())
+        rv = Add(*[self.func(a, *self.args[1:]) for a in terms])
+        if o:
+            rv += o.subs(other, x)
+        return rv
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        if x in self.point:
+            ipos = self.point.index(x)
+            xvar = self.variables[ipos]
+            return self.expr.as_leading_term(xvar)
+        if x in self.variables:
+            # if `x` is a dummy variable, it means it won't exist after the
+            # substitution has been performed:
+            return self
+        # The variable is independent of the substitution:
+        return self.expr.as_leading_term(x)
+
+
+def diff(f, *symbols, **kwargs):
+    """
+    Differentiate f with respect to symbols.
+
+    Explanation
+    ===========
+
+    This is just a wrapper to unify .diff() and the Derivative class; its
+    interface is similar to that of integrate().  You can use the same
+    shortcuts for multiple variables as with Derivative.  For example,
+    diff(f(x), x, x, x) and diff(f(x), x, 3) both return the third derivative
+    of f(x).
+
+    You can pass evaluate=False to get an unevaluated Derivative class.  Note
+    that if there are 0 symbols (such as diff(f(x), x, 0), then the result will
+    be the function (the zeroth derivative), even if evaluate=False.
+
+    Examples
+    ========
+
+    >>> from sympy import sin, cos, Function, diff
+    >>> from sympy.abc import x, y
+    >>> f = Function('f')
+
+    >>> diff(sin(x), x)
+    cos(x)
+    >>> diff(f(x), x, x, x)
+    Derivative(f(x), (x, 3))
+    >>> diff(f(x), x, 3)
+    Derivative(f(x), (x, 3))
+    >>> diff(sin(x)*cos(y), x, 2, y, 2)
+    sin(x)*cos(y)
+
+    >>> type(diff(sin(x), x))
+    cos
+    >>> type(diff(sin(x), x, evaluate=False))
+    
+    >>> type(diff(sin(x), x, 0))
+    sin
+    >>> type(diff(sin(x), x, 0, evaluate=False))
+    sin
+
+    >>> diff(sin(x))
+    cos(x)
+    >>> diff(sin(x*y))
+    Traceback (most recent call last):
+    ...
+    ValueError: specify differentiation variables to differentiate sin(x*y)
+
+    Note that ``diff(sin(x))`` syntax is meant only for convenience
+    in interactive sessions and should be avoided in library code.
+
+    References
+    ==========
+
+    .. [1] https://reference.wolfram.com/legacy/v5_2/Built-inFunctions/AlgebraicComputation/Calculus/D.html
+
+    See Also
+    ========
+
+    Derivative
+    idiff: computes the derivative implicitly
+
+    """
+    if hasattr(f, 'diff'):
+        return f.diff(*symbols, **kwargs)
+    kwargs.setdefault('evaluate', True)
+    return _derivative_dispatch(f, *symbols, **kwargs)
+
+
+def expand(e, deep=True, modulus=None, power_base=True, power_exp=True,
+        mul=True, log=True, multinomial=True, basic=True, **hints):
+    r"""
+    Expand an expression using methods given as hints.
+
+    Explanation
+    ===========
+
+    Hints evaluated unless explicitly set to False are:  ``basic``, ``log``,
+    ``multinomial``, ``mul``, ``power_base``, and ``power_exp`` The following
+    hints are supported but not applied unless set to True:  ``complex``,
+    ``func``, and ``trig``.  In addition, the following meta-hints are
+    supported by some or all of the other hints:  ``frac``, ``numer``,
+    ``denom``, ``modulus``, and ``force``.  ``deep`` is supported by all
+    hints.  Additionally, subclasses of Expr may define their own hints or
+    meta-hints.
+
+    The ``basic`` hint is used for any special rewriting of an object that
+    should be done automatically (along with the other hints like ``mul``)
+    when expand is called. This is a catch-all hint to handle any sort of
+    expansion that may not be described by the existing hint names. To use
+    this hint an object should override the ``_eval_expand_basic`` method.
+    Objects may also define their own expand methods, which are not run by
+    default.  See the API section below.
+
+    If ``deep`` is set to ``True`` (the default), things like arguments of
+    functions are recursively expanded.  Use ``deep=False`` to only expand on
+    the top level.
+
+    If the ``force`` hint is used, assumptions about variables will be ignored
+    in making the expansion.
+
+    Hints
+    =====
+
+    These hints are run by default
+
+    mul
+    ---
+
+    Distributes multiplication over addition:
+
+    >>> from sympy import cos, exp, sin
+    >>> from sympy.abc import x, y, z
+    >>> (y*(x + z)).expand(mul=True)
+    x*y + y*z
+
+    multinomial
+    -----------
+
+    Expand (x + y + ...)**n where n is a positive integer.
+
+    >>> ((x + y + z)**2).expand(multinomial=True)
+    x**2 + 2*x*y + 2*x*z + y**2 + 2*y*z + z**2
+
+    power_exp
+    ---------
+
+    Expand addition in exponents into multiplied bases.
+
+    >>> exp(x + y).expand(power_exp=True)
+    exp(x)*exp(y)
+    >>> (2**(x + y)).expand(power_exp=True)
+    2**x*2**y
+
+    power_base
+    ----------
+
+    Split powers of multiplied bases.
+
+    This only happens by default if assumptions allow, or if the
+    ``force`` meta-hint is used:
+
+    >>> ((x*y)**z).expand(power_base=True)
+    (x*y)**z
+    >>> ((x*y)**z).expand(power_base=True, force=True)
+    x**z*y**z
+    >>> ((2*y)**z).expand(power_base=True)
+    2**z*y**z
+
+    Note that in some cases where this expansion always holds, SymPy performs
+    it automatically:
+
+    >>> (x*y)**2
+    x**2*y**2
+
+    log
+    ---
+
+    Pull out power of an argument as a coefficient and split logs products
+    into sums of logs.
+
+    Note that these only work if the arguments of the log function have the
+    proper assumptions--the arguments must be positive and the exponents must
+    be real--or else the ``force`` hint must be True:
+
+    >>> from sympy import log, symbols
+    >>> log(x**2*y).expand(log=True)
+    log(x**2*y)
+    >>> log(x**2*y).expand(log=True, force=True)
+    2*log(x) + log(y)
+    >>> x, y = symbols('x,y', positive=True)
+    >>> log(x**2*y).expand(log=True)
+    2*log(x) + log(y)
+
+    basic
+    -----
+
+    This hint is intended primarily as a way for custom subclasses to enable
+    expansion by default.
+
+    These hints are not run by default:
+
+    complex
+    -------
+
+    Split an expression into real and imaginary parts.
+
+    >>> x, y = symbols('x,y')
+    >>> (x + y).expand(complex=True)
+    re(x) + re(y) + I*im(x) + I*im(y)
+    >>> cos(x).expand(complex=True)
+    -I*sin(re(x))*sinh(im(x)) + cos(re(x))*cosh(im(x))
+
+    Note that this is just a wrapper around ``as_real_imag()``.  Most objects
+    that wish to redefine ``_eval_expand_complex()`` should consider
+    redefining ``as_real_imag()`` instead.
+
+    func
+    ----
+
+    Expand other functions.
+
+    >>> from sympy import gamma
+    >>> gamma(x + 1).expand(func=True)
+    x*gamma(x)
+
+    trig
+    ----
+
+    Do trigonometric expansions.
+
+    >>> cos(x + y).expand(trig=True)
+    -sin(x)*sin(y) + cos(x)*cos(y)
+    >>> sin(2*x).expand(trig=True)
+    2*sin(x)*cos(x)
+
+    Note that the forms of ``sin(n*x)`` and ``cos(n*x)`` in terms of ``sin(x)``
+    and ``cos(x)`` are not unique, due to the identity `\sin^2(x) + \cos^2(x)
+    = 1`.  The current implementation uses the form obtained from Chebyshev
+    polynomials, but this may change.  See `this MathWorld article
+    `_ for more
+    information.
+
+    Notes
+    =====
+
+    - You can shut off unwanted methods::
+
+        >>> (exp(x + y)*(x + y)).expand()
+        x*exp(x)*exp(y) + y*exp(x)*exp(y)
+        >>> (exp(x + y)*(x + y)).expand(power_exp=False)
+        x*exp(x + y) + y*exp(x + y)
+        >>> (exp(x + y)*(x + y)).expand(mul=False)
+        (x + y)*exp(x)*exp(y)
+
+    - Use deep=False to only expand on the top level::
+
+        >>> exp(x + exp(x + y)).expand()
+        exp(x)*exp(exp(x)*exp(y))
+        >>> exp(x + exp(x + y)).expand(deep=False)
+        exp(x)*exp(exp(x + y))
+
+    - Hints are applied in an arbitrary, but consistent order (in the current
+      implementation, they are applied in alphabetical order, except
+      multinomial comes before mul, but this may change).  Because of this,
+      some hints may prevent expansion by other hints if they are applied
+      first. For example, ``mul`` may distribute multiplications and prevent
+      ``log`` and ``power_base`` from expanding them. Also, if ``mul`` is
+      applied before ``multinomial`, the expression might not be fully
+      distributed. The solution is to use the various ``expand_hint`` helper
+      functions or to use ``hint=False`` to this function to finely control
+      which hints are applied. Here are some examples::
+
+        >>> from sympy import expand, expand_mul, expand_power_base
+        >>> x, y, z = symbols('x,y,z', positive=True)
+
+        >>> expand(log(x*(y + z)))
+        log(x) + log(y + z)
+
+      Here, we see that ``log`` was applied before ``mul``.  To get the mul
+      expanded form, either of the following will work::
+
+        >>> expand_mul(log(x*(y + z)))
+        log(x*y + x*z)
+        >>> expand(log(x*(y + z)), log=False)
+        log(x*y + x*z)
+
+      A similar thing can happen with the ``power_base`` hint::
+
+        >>> expand((x*(y + z))**x)
+        (x*y + x*z)**x
+
+      To get the ``power_base`` expanded form, either of the following will
+      work::
+
+        >>> expand((x*(y + z))**x, mul=False)
+        x**x*(y + z)**x
+        >>> expand_power_base((x*(y + z))**x)
+        x**x*(y + z)**x
+
+        >>> expand((x + y)*y/x)
+        y + y**2/x
+
+      The parts of a rational expression can be targeted::
+
+        >>> expand((x + y)*y/x/(x + 1), frac=True)
+        (x*y + y**2)/(x**2 + x)
+        >>> expand((x + y)*y/x/(x + 1), numer=True)
+        (x*y + y**2)/(x*(x + 1))
+        >>> expand((x + y)*y/x/(x + 1), denom=True)
+        y*(x + y)/(x**2 + x)
+
+    - The ``modulus`` meta-hint can be used to reduce the coefficients of an
+      expression post-expansion::
+
+        >>> expand((3*x + 1)**2)
+        9*x**2 + 6*x + 1
+        >>> expand((3*x + 1)**2, modulus=5)
+        4*x**2 + x + 1
+
+    - Either ``expand()`` the function or ``.expand()`` the method can be
+      used.  Both are equivalent::
+
+        >>> expand((x + 1)**2)
+        x**2 + 2*x + 1
+        >>> ((x + 1)**2).expand()
+        x**2 + 2*x + 1
+
+    API
+    ===
+
+    Objects can define their own expand hints by defining
+    ``_eval_expand_hint()``.  The function should take the form::
+
+        def _eval_expand_hint(self, **hints):
+            # Only apply the method to the top-level expression
+            ...
+
+    See also the example below.  Objects should define ``_eval_expand_hint()``
+    methods only if ``hint`` applies to that specific object.  The generic
+    ``_eval_expand_hint()`` method defined in Expr will handle the no-op case.
+
+    Each hint should be responsible for expanding that hint only.
+    Furthermore, the expansion should be applied to the top-level expression
+    only.  ``expand()`` takes care of the recursion that happens when
+    ``deep=True``.
+
+    You should only call ``_eval_expand_hint()`` methods directly if you are
+    100% sure that the object has the method, as otherwise you are liable to
+    get unexpected ``AttributeError``s.  Note, again, that you do not need to
+    recursively apply the hint to args of your object: this is handled
+    automatically by ``expand()``.  ``_eval_expand_hint()`` should
+    generally not be used at all outside of an ``_eval_expand_hint()`` method.
+    If you want to apply a specific expansion from within another method, use
+    the public ``expand()`` function, method, or ``expand_hint()`` functions.
+
+    In order for expand to work, objects must be rebuildable by their args,
+    i.e., ``obj.func(*obj.args) == obj`` must hold.
+
+    Expand methods are passed ``**hints`` so that expand hints may use
+    'metahints'--hints that control how different expand methods are applied.
+    For example, the ``force=True`` hint described above that causes
+    ``expand(log=True)`` to ignore assumptions is such a metahint.  The
+    ``deep`` meta-hint is handled exclusively by ``expand()`` and is not
+    passed to ``_eval_expand_hint()`` methods.
+
+    Note that expansion hints should generally be methods that perform some
+    kind of 'expansion'.  For hints that simply rewrite an expression, use the
+    .rewrite() API.
+
+    Examples
+    ========
+
+    >>> from sympy import Expr, sympify
+    >>> class MyClass(Expr):
+    ...     def __new__(cls, *args):
+    ...         args = sympify(args)
+    ...         return Expr.__new__(cls, *args)
+    ...
+    ...     def _eval_expand_double(self, *, force=False, **hints):
+    ...         '''
+    ...         Doubles the args of MyClass.
+    ...
+    ...         If there more than four args, doubling is not performed,
+    ...         unless force=True is also used (False by default).
+    ...         '''
+    ...         if not force and len(self.args) > 4:
+    ...             return self
+    ...         return self.func(*(self.args + self.args))
+    ...
+    >>> a = MyClass(1, 2, MyClass(3, 4))
+    >>> a
+    MyClass(1, 2, MyClass(3, 4))
+    >>> a.expand(double=True)
+    MyClass(1, 2, MyClass(3, 4, 3, 4), 1, 2, MyClass(3, 4, 3, 4))
+    >>> a.expand(double=True, deep=False)
+    MyClass(1, 2, MyClass(3, 4), 1, 2, MyClass(3, 4))
+
+    >>> b = MyClass(1, 2, 3, 4, 5)
+    >>> b.expand(double=True)
+    MyClass(1, 2, 3, 4, 5)
+    >>> b.expand(double=True, force=True)
+    MyClass(1, 2, 3, 4, 5, 1, 2, 3, 4, 5)
+
+    See Also
+    ========
+
+    expand_log, expand_mul, expand_multinomial, expand_complex, expand_trig,
+    expand_power_base, expand_power_exp, expand_func, sympy.simplify.hyperexpand.hyperexpand
+
+    """
+    # don't modify this; modify the Expr.expand method
+    hints['power_base'] = power_base
+    hints['power_exp'] = power_exp
+    hints['mul'] = mul
+    hints['log'] = log
+    hints['multinomial'] = multinomial
+    hints['basic'] = basic
+    return sympify(e).expand(deep=deep, modulus=modulus, **hints)
+
+# This is a special application of two hints
+
+def _mexpand(expr, recursive=False):
+    # expand multinomials and then expand products; this may not always
+    # be sufficient to give a fully expanded expression (see
+    # test_issue_8247_8354 in test_arit)
+    if expr is None:
+        return
+    was = None
+    while was != expr:
+        was, expr = expr, expand_mul(expand_multinomial(expr))
+        if not recursive:
+            break
+    return expr
+
+
+# These are simple wrappers around single hints.
+
+
+def expand_mul(expr, deep=True):
+    """
+    Wrapper around expand that only uses the mul hint.  See the expand
+    docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, expand_mul, exp, log
+    >>> x, y = symbols('x,y', positive=True)
+    >>> expand_mul(exp(x+y)*(x+y)*log(x*y**2))
+    x*exp(x + y)*log(x*y**2) + y*exp(x + y)*log(x*y**2)
+
+    """
+    return sympify(expr).expand(deep=deep, mul=True, power_exp=False,
+    power_base=False, basic=False, multinomial=False, log=False)
+
+
+def expand_multinomial(expr, deep=True):
+    """
+    Wrapper around expand that only uses the multinomial hint.  See the expand
+    docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, expand_multinomial, exp
+    >>> x, y = symbols('x y', positive=True)
+    >>> expand_multinomial((x + exp(x + 1))**2)
+    x**2 + 2*x*exp(x + 1) + exp(2*x + 2)
+
+    """
+    return sympify(expr).expand(deep=deep, mul=False, power_exp=False,
+    power_base=False, basic=False, multinomial=True, log=False)
+
+
+def expand_log(expr, deep=True, force=False, factor=False):
+    """
+    Wrapper around expand that only uses the log hint.  See the expand
+    docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, expand_log, exp, log
+    >>> x, y = symbols('x,y', positive=True)
+    >>> expand_log(exp(x+y)*(x+y)*log(x*y**2))
+    (x + y)*(log(x) + 2*log(y))*exp(x + y)
+
+    """
+    from sympy.functions.elementary.exponential import log
+    from sympy.simplify.radsimp import fraction
+    if factor is False:
+        def _handleMul(x):
+            # look for the simple case of expanded log(b**a)/log(b) -> a in args
+            n, d = fraction(x)
+            n = [i for i in n.atoms(log) if i.args[0].is_Integer]
+            d = [i for i in d.atoms(log) if i.args[0].is_Integer]
+            if len(n) == 1 and len(d) == 1:
+                n = n[0]
+                d = d[0]
+                from sympy import multiplicity
+                m = multiplicity(d.args[0], n.args[0])
+                if m:
+                    r = m + log(n.args[0]//d.args[0]**m)/d
+                    x = x.subs(n, d*r)
+            x1 = expand_mul(expand_log(x, deep=deep, force=force, factor=True))
+            if x1.count(log) <= x.count(log):
+                return x1
+            return x
+
+        expr = expr.replace(
+        lambda x: x.is_Mul and all(any(isinstance(i, log) and i.args[0].is_Rational
+        for i in Mul.make_args(j)) for j in x.as_numer_denom()),
+        _handleMul)
+
+    return sympify(expr).expand(deep=deep, log=True, mul=False,
+        power_exp=False, power_base=False, multinomial=False,
+        basic=False, force=force, factor=factor)
+
+
+def expand_func(expr, deep=True):
+    """
+    Wrapper around expand that only uses the func hint.  See the expand
+    docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import expand_func, gamma
+    >>> from sympy.abc import x
+    >>> expand_func(gamma(x + 2))
+    x*(x + 1)*gamma(x)
+
+    """
+    return sympify(expr).expand(deep=deep, func=True, basic=False,
+    log=False, mul=False, power_exp=False, power_base=False, multinomial=False)
+
+
+def expand_trig(expr, deep=True):
+    """
+    Wrapper around expand that only uses the trig hint.  See the expand
+    docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import expand_trig, sin
+    >>> from sympy.abc import x, y
+    >>> expand_trig(sin(x+y)*(x+y))
+    (x + y)*(sin(x)*cos(y) + sin(y)*cos(x))
+
+    """
+    return sympify(expr).expand(deep=deep, trig=True, basic=False,
+    log=False, mul=False, power_exp=False, power_base=False, multinomial=False)
+
+
+def expand_complex(expr, deep=True):
+    """
+    Wrapper around expand that only uses the complex hint.  See the expand
+    docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import expand_complex, exp, sqrt, I
+    >>> from sympy.abc import z
+    >>> expand_complex(exp(z))
+    I*exp(re(z))*sin(im(z)) + exp(re(z))*cos(im(z))
+    >>> expand_complex(sqrt(I))
+    sqrt(2)/2 + sqrt(2)*I/2
+
+    See Also
+    ========
+
+    sympy.core.expr.Expr.as_real_imag
+    """
+    return sympify(expr).expand(deep=deep, complex=True, basic=False,
+    log=False, mul=False, power_exp=False, power_base=False, multinomial=False)
+
+
+def expand_power_base(expr, deep=True, force=False):
+    """
+    Wrapper around expand that only uses the power_base hint.
+
+    A wrapper to expand(power_base=True) which separates a power with a base
+    that is a Mul into a product of powers, without performing any other
+    expansions, provided that assumptions about the power's base and exponent
+    allow.
+
+    deep=False (default is True) will only apply to the top-level expression.
+
+    force=True (default is False) will cause the expansion to ignore
+    assumptions about the base and exponent. When False, the expansion will
+    only happen if the base is non-negative or the exponent is an integer.
+
+    >>> from sympy.abc import x, y, z
+    >>> from sympy import expand_power_base, sin, cos, exp, Symbol
+
+    >>> (x*y)**2
+    x**2*y**2
+
+    >>> (2*x)**y
+    (2*x)**y
+    >>> expand_power_base(_)
+    2**y*x**y
+
+    >>> expand_power_base((x*y)**z)
+    (x*y)**z
+    >>> expand_power_base((x*y)**z, force=True)
+    x**z*y**z
+    >>> expand_power_base(sin((x*y)**z), deep=False)
+    sin((x*y)**z)
+    >>> expand_power_base(sin((x*y)**z), force=True)
+    sin(x**z*y**z)
+
+    >>> expand_power_base((2*sin(x))**y + (2*cos(x))**y)
+    2**y*sin(x)**y + 2**y*cos(x)**y
+
+    >>> expand_power_base((2*exp(y))**x)
+    2**x*exp(y)**x
+
+    >>> expand_power_base((2*cos(x))**y)
+    2**y*cos(x)**y
+
+    Notice that sums are left untouched. If this is not the desired behavior,
+    apply full ``expand()`` to the expression:
+
+    >>> expand_power_base(((x+y)*z)**2)
+    z**2*(x + y)**2
+    >>> (((x+y)*z)**2).expand()
+    x**2*z**2 + 2*x*y*z**2 + y**2*z**2
+
+    >>> expand_power_base((2*y)**(1+z))
+    2**(z + 1)*y**(z + 1)
+    >>> ((2*y)**(1+z)).expand()
+    2*2**z*y**(z + 1)
+
+    The power that is unexpanded can be expanded safely when
+    ``y != 0``, otherwise different values might be obtained for the expression:
+
+    >>> prev = _
+
+    If we indicate that ``y`` is positive but then replace it with
+    a value of 0 after expansion, the expression becomes 0:
+
+    >>> p = Symbol('p', positive=True)
+    >>> prev.subs(y, p).expand().subs(p, 0)
+    0
+
+    But if ``z = -1`` the expression would not be zero:
+
+    >>> prev.subs(y, 0).subs(z, -1)
+    1
+
+    See Also
+    ========
+
+    expand
+
+    """
+    return sympify(expr).expand(deep=deep, log=False, mul=False,
+        power_exp=False, power_base=True, multinomial=False,
+        basic=False, force=force)
+
+
+def expand_power_exp(expr, deep=True):
+    """
+    Wrapper around expand that only uses the power_exp hint.
+
+    See the expand docstring for more information.
+
+    Examples
+    ========
+
+    >>> from sympy import expand_power_exp, Symbol
+    >>> from sympy.abc import x, y
+    >>> expand_power_exp(3**(y + 2))
+    9*3**y
+    >>> expand_power_exp(x**(y + 2))
+    x**(y + 2)
+
+    If ``x = 0`` the value of the expression depends on the
+    value of ``y``; if the expression were expanded the result
+    would be 0. So expansion is only done if ``x != 0``:
+
+    >>> expand_power_exp(Symbol('x', zero=False)**(y + 2))
+    x**2*x**y
+    """
+    return sympify(expr).expand(deep=deep, complex=False, basic=False,
+    log=False, mul=False, power_exp=True, power_base=False, multinomial=False)
+
+
+def count_ops(expr, visual=False):
+    """
+    Return a representation (integer or expression) of the operations in expr.
+
+    Parameters
+    ==========
+
+    expr : Expr
+        If expr is an iterable, the sum of the op counts of the
+        items will be returned.
+
+    visual : bool, optional
+        If ``False`` (default) then the sum of the coefficients of the
+        visual expression will be returned.
+        If ``True`` then the number of each type of operation is shown
+        with the core class types (or their virtual equivalent) multiplied by the
+        number of times they occur.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import a, b, x, y
+    >>> from sympy import sin, count_ops
+
+    Although there is not a SUB object, minus signs are interpreted as
+    either negations or subtractions:
+
+    >>> (x - y).count_ops(visual=True)
+    SUB
+    >>> (-x).count_ops(visual=True)
+    NEG
+
+    Here, there are two Adds and a Pow:
+
+    >>> (1 + a + b**2).count_ops(visual=True)
+    2*ADD + POW
+
+    In the following, an Add, Mul, Pow and two functions:
+
+    >>> (sin(x)*x + sin(x)**2).count_ops(visual=True)
+    ADD + MUL + POW + 2*SIN
+
+    for a total of 5:
+
+    >>> (sin(x)*x + sin(x)**2).count_ops(visual=False)
+    5
+
+    Note that "what you type" is not always what you get. The expression
+    1/x/y is translated by sympy into 1/(x*y) so it gives a DIV and MUL rather
+    than two DIVs:
+
+    >>> (1/x/y).count_ops(visual=True)
+    DIV + MUL
+
+    The visual option can be used to demonstrate the difference in
+    operations for expressions in different forms. Here, the Horner
+    representation is compared with the expanded form of a polynomial:
+
+    >>> eq=x*(1 + x*(2 + x*(3 + x)))
+    >>> count_ops(eq.expand(), visual=True) - count_ops(eq, visual=True)
+    -MUL + 3*POW
+
+    The count_ops function also handles iterables:
+
+    >>> count_ops([x, sin(x), None, True, x + 2], visual=False)
+    2
+    >>> count_ops([x, sin(x), None, True, x + 2], visual=True)
+    ADD + SIN
+    >>> count_ops({x: sin(x), x + 2: y + 1}, visual=True)
+    2*ADD + SIN
+
+    """
+    from .relational import Relational
+    from sympy.concrete.summations import Sum
+    from sympy.integrals.integrals import Integral
+    from sympy.logic.boolalg import BooleanFunction
+    from sympy.simplify.radsimp import fraction
+
+    expr = sympify(expr)
+    if isinstance(expr, Expr) and not expr.is_Relational:
+
+        ops = []
+        args = [expr]
+        NEG = Symbol('NEG')
+        DIV = Symbol('DIV')
+        SUB = Symbol('SUB')
+        ADD = Symbol('ADD')
+        EXP = Symbol('EXP')
+        while args:
+            a = args.pop()
+
+            # if the following fails because the object is
+            # not Basic type, then the object should be fixed
+            # since it is the intention that all args of Basic
+            # should themselves be Basic
+            if a.is_Rational:
+                #-1/3 = NEG + DIV
+                if a is not S.One:
+                    if a.p < 0:
+                        ops.append(NEG)
+                    if a.q != 1:
+                        ops.append(DIV)
+                    continue
+            elif a.is_Mul or a.is_MatMul:
+                if _coeff_isneg(a):
+                    ops.append(NEG)
+                    if a.args[0] is S.NegativeOne:
+                        a = a.as_two_terms()[1]
+                    else:
+                        a = -a
+                n, d = fraction(a)
+                if n.is_Integer:
+                    ops.append(DIV)
+                    if n < 0:
+                        ops.append(NEG)
+                    args.append(d)
+                    continue  # won't be -Mul but could be Add
+                elif d is not S.One:
+                    if not d.is_Integer:
+                        args.append(d)
+                    ops.append(DIV)
+                    args.append(n)
+                    continue  # could be -Mul
+            elif a.is_Add or a.is_MatAdd:
+                aargs = list(a.args)
+                negs = 0
+                for i, ai in enumerate(aargs):
+                    if _coeff_isneg(ai):
+                        negs += 1
+                        args.append(-ai)
+                        if i > 0:
+                            ops.append(SUB)
+                    else:
+                        args.append(ai)
+                        if i > 0:
+                            ops.append(ADD)
+                if negs == len(aargs):  # -x - y = NEG + SUB
+                    ops.append(NEG)
+                elif _coeff_isneg(aargs[0]):  # -x + y = SUB, but already recorded ADD
+                    ops.append(SUB - ADD)
+                continue
+            if a.is_Pow and a.exp is S.NegativeOne:
+                ops.append(DIV)
+                args.append(a.base)  # won't be -Mul but could be Add
+                continue
+            if a == S.Exp1:
+                ops.append(EXP)
+                continue
+            if a.is_Pow and a.base == S.Exp1:
+                ops.append(EXP)
+                args.append(a.exp)
+                continue
+            if a.is_Mul or isinstance(a, LatticeOp):
+                o = Symbol(a.func.__name__.upper())
+                # count the args
+                ops.append(o*(len(a.args) - 1))
+            elif a.args and (
+                    a.is_Pow or a.is_Function or isinstance(a, (Derivative, Integral, Sum))):
+                # if it's not in the list above we don't
+                # consider a.func something to count, e.g.
+                # Tuple, MatrixSymbol, etc...
+                if isinstance(a.func, UndefinedFunction):
+                    o = Symbol("FUNC_" + a.func.__name__.upper())
+                else:
+                    o = Symbol(a.func.__name__.upper())
+                ops.append(o)
+
+            if not a.is_Symbol:
+                args.extend(a.args)
+
+    elif isinstance(expr, Dict):
+        ops = [count_ops(k, visual=visual) +
+               count_ops(v, visual=visual) for k, v in expr.items()]
+    elif iterable(expr):
+        ops = [count_ops(i, visual=visual) for i in expr]
+    elif isinstance(expr, (Relational, BooleanFunction)):
+        ops = []
+        for arg in expr.args:
+            ops.append(count_ops(arg, visual=True))
+        o = Symbol(func_name(expr, short=True).upper())
+        ops.append(o)
+    elif not isinstance(expr, Basic):
+        ops = []
+    else:  # it's Basic not isinstance(expr, Expr):
+        if not isinstance(expr, Basic):
+            raise TypeError("Invalid type of expr")
+        else:
+            ops = []
+            args = [expr]
+            while args:
+                a = args.pop()
+
+                if a.args:
+                    o = Symbol(type(a).__name__.upper())
+                    if a.is_Boolean:
+                        ops.append(o*(len(a.args)-1))
+                    else:
+                        ops.append(o)
+                    args.extend(a.args)
+
+    if not ops:
+        if visual:
+            return S.Zero
+        return 0
+
+    ops = Add(*ops)
+
+    if visual:
+        return ops
+
+    if ops.is_Number:
+        return int(ops)
+
+    return sum(int((a.args or [1])[0]) for a in Add.make_args(ops))
+
+
+def nfloat(expr, n=15, exponent=False, dkeys=False):
+    """Make all Rationals in expr Floats except those in exponents
+    (unless the exponents flag is set to True) and those in undefined
+    functions. When processing dictionaries, do not modify the keys
+    unless ``dkeys=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import nfloat, cos, pi, sqrt
+    >>> from sympy.abc import x, y
+    >>> nfloat(x**4 + x/2 + cos(pi/3) + 1 + sqrt(y))
+    x**4 + 0.5*x + sqrt(y) + 1.5
+    >>> nfloat(x**4 + sqrt(y), exponent=True)
+    x**4.0 + y**0.5
+
+    Container types are not modified:
+
+    >>> type(nfloat((1, 2))) is tuple
+    True
+    """
+    from sympy.matrices.matrixbase import MatrixBase
+
+    kw = {"n": n, "exponent": exponent, "dkeys": dkeys}
+
+    if isinstance(expr, MatrixBase):
+        return expr.applyfunc(lambda e: nfloat(e, **kw))
+
+    # handling of iterable containers
+    if iterable(expr, exclude=str):
+        if isinstance(expr, (dict, Dict)):
+            if dkeys:
+                args = [tuple((nfloat(i, **kw) for i in a))
+                    for a in expr.items()]
+            else:
+                args = [(k, nfloat(v, **kw)) for k, v in expr.items()]
+            if isinstance(expr, dict):
+                return type(expr)(args)
+            else:
+                return expr.func(*args)
+        elif isinstance(expr, Basic):
+            return expr.func(*[nfloat(a, **kw) for a in expr.args])
+        return type(expr)([nfloat(a, **kw) for a in expr])
+
+    rv = sympify(expr)
+
+    if rv.is_Number:
+        return Float(rv, n)
+    elif rv.is_number:
+        # evalf doesn't always set the precision
+        rv = rv.n(n)
+        if rv.is_Number:
+            rv = Float(rv.n(n), n)
+        else:
+            pass  # pure_complex(rv) is likely True
+        return rv
+    elif rv.is_Atom:
+        return rv
+    elif rv.is_Relational:
+        args_nfloat = (nfloat(arg, **kw) for arg in rv.args)
+        return rv.func(*args_nfloat)
+
+
+    # watch out for RootOf instances that don't like to have
+    # their exponents replaced with Dummies and also sometimes have
+    # problems with evaluating at low precision (issue 6393)
+    from sympy.polys.rootoftools import RootOf
+    rv = rv.xreplace({ro: ro.n(n) for ro in rv.atoms(RootOf)})
+
+    from .power import Pow
+    if not exponent:
+        reps = [(p, Pow(p.base, Dummy())) for p in rv.atoms(Pow)]
+        rv = rv.xreplace(dict(reps))
+    rv = rv.n(n)
+    if not exponent:
+        rv = rv.xreplace({d.exp: p.exp for p, d in reps})
+    else:
+        # Pow._eval_evalf special cases Integer exponents so if
+        # exponent is suppose to be handled we have to do so here
+        rv = rv.xreplace(Transform(
+            lambda x: Pow(x.base, Float(x.exp, n)),
+            lambda x: x.is_Pow and x.exp.is_Integer))
+
+    return rv.xreplace(Transform(
+        lambda x: x.func(*nfloat(x.args, n, exponent)),
+        lambda x: isinstance(x, Function) and not isinstance(x, AppliedUndef)))
+
+
+from .symbol import Dummy, Symbol
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/intfunc.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/intfunc.py
new file mode 100644
index 0000000000000000000000000000000000000000..50cb625dafcc1e795933311780e26423ddc6015a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/intfunc.py
@@ -0,0 +1,530 @@
+"""
+The routines here were removed from numbers.py, power.py,
+digits.py and factor_.py so they could be imported into core
+without raising circular import errors.
+
+Although the name 'intfunc' was chosen to represent functions that
+work with integers, it can also be thought of as containing
+internal/core functions that are needed by the classes of the core.
+"""
+
+import math
+import sys
+from functools import lru_cache
+
+from .sympify import sympify
+from .singleton import S
+from sympy.external.gmpy import (gcd as number_gcd, lcm as number_lcm, sqrt,
+                                 iroot, bit_scan1, gcdext)
+from sympy.utilities.misc import as_int, filldedent
+
+
+def num_digits(n, base=10):
+    """Return the number of digits needed to express n in give base.
+
+    Examples
+    ========
+
+    >>> from sympy.core.intfunc import num_digits
+    >>> num_digits(10)
+    2
+    >>> num_digits(10, 2)  # 1010 -> 4 digits
+    4
+    >>> num_digits(-100, 16)  # -64 -> 2 digits
+    2
+
+
+    Parameters
+    ==========
+
+    n: integer
+        The number whose digits are counted.
+
+    b: integer
+        The base in which digits are computed.
+
+    See Also
+    ========
+    sympy.ntheory.digits.digits, sympy.ntheory.digits.count_digits
+    """
+    if base < 0:
+        raise ValueError('base must be int greater than 1')
+    if not n:
+        return 1
+    e, t = integer_log(abs(n), base)
+    return 1 + e
+
+
+def integer_log(n, b):
+    r"""
+    Returns ``(e, bool)`` where e is the largest nonnegative integer
+    such that :math:`|n| \geq |b^e|` and ``bool`` is True if $n = b^e$.
+
+    Examples
+    ========
+
+    >>> from sympy import integer_log
+    >>> integer_log(125, 5)
+    (3, True)
+    >>> integer_log(17, 9)
+    (1, False)
+
+    If the base is positive and the number negative the
+    return value will always be the same except for 2:
+
+    >>> integer_log(-4, 2)
+    (2, False)
+    >>> integer_log(-16, 4)
+    (0, False)
+
+    When the base is negative, the returned value
+    will only be True if the parity of the exponent is
+    correct for the sign of the base:
+
+    >>> integer_log(4, -2)
+    (2, True)
+    >>> integer_log(8, -2)
+    (3, False)
+    >>> integer_log(-8, -2)
+    (3, True)
+    >>> integer_log(-4, -2)
+    (2, False)
+
+    See Also
+    ========
+    integer_nthroot
+    sympy.ntheory.primetest.is_square
+    sympy.ntheory.factor_.multiplicity
+    sympy.ntheory.factor_.perfect_power
+    """
+    n = as_int(n)
+    b = as_int(b)
+
+    if b < 0:
+        e, t = integer_log(abs(n), -b)
+        # (-2)**3 == -8
+        # (-2)**2 = 4
+        t = t and e % 2 == (n < 0)
+        return e, t
+    if b <= 1:
+        raise ValueError('base must be 2 or more')
+    if n < 0:
+        if b != 2:
+            return 0, False
+        e, t = integer_log(-n, b)
+        return e, False
+    if n == 0:
+        raise ValueError('n cannot be 0')
+
+    if n < b:
+        return 0, n == 1
+    if b == 2:
+        e = n.bit_length() - 1
+        return e, trailing(n) == e
+    t = trailing(b)
+    if 2**t == b:
+        e = int(n.bit_length() - 1)//t
+        n_ = 1 << (t*e)
+        return e, n_ == n
+
+    d = math.floor(math.log10(n) / math.log10(b))
+    n_ = b ** d
+    while n_ <= n:  # this will iterate 0, 1 or 2 times
+        d += 1
+        n_ *= b
+    return d - (n_ > n), (n_ == n or n_//b == n)
+
+
+def trailing(n):
+    """Count the number of trailing zero digits in the binary
+    representation of n, i.e. determine the largest power of 2
+    that divides n.
+
+    Examples
+    ========
+
+    >>> from sympy import trailing
+    >>> trailing(128)
+    7
+    >>> trailing(63)
+    0
+
+    See Also
+    ========
+    sympy.ntheory.factor_.multiplicity
+
+    """
+    if not n:
+        return 0
+    return bit_scan1(int(n))
+
+
+@lru_cache(1024)
+def igcd(*args):
+    """Computes nonnegative integer greatest common divisor.
+
+    Explanation
+    ===========
+
+    The algorithm is based on the well known Euclid's algorithm [1]_. To
+    improve speed, ``igcd()`` has its own caching mechanism.
+    If you do not need the cache mechanism, using ``sympy.external.gmpy.gcd``.
+
+    Examples
+    ========
+
+    >>> from sympy import igcd
+    >>> igcd(2, 4)
+    2
+    >>> igcd(5, 10, 15)
+    5
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euclidean_algorithm
+
+    """
+    if len(args) < 2:
+        raise TypeError("igcd() takes at least 2 arguments (%s given)" % len(args))
+    return int(number_gcd(*map(as_int, args)))
+
+
+igcd2 = math.gcd
+
+
+def igcd_lehmer(a, b):
+    r"""Computes greatest common divisor of two integers.
+
+    Explanation
+    ===========
+
+    Euclid's algorithm for the computation of the greatest
+    common divisor ``gcd(a, b)``  of two (positive) integers
+    $a$ and $b$ is based on the division identity
+    $$ a = q \times b + r$$,
+    where the quotient  $q$  and the remainder  $r$  are integers
+    and  $0 \le r < b$. Then each common divisor of  $a$  and  $b$
+    divides  $r$, and it follows that  ``gcd(a, b) == gcd(b, r)``.
+    The algorithm works by constructing the sequence
+    r0, r1, r2, ..., where  r0 = a, r1 = b,  and each  rn
+    is the remainder from the division of the two preceding
+    elements.
+
+    In Python, ``q = a // b``  and  ``r = a % b``  are obtained by the
+    floor division and the remainder operations, respectively.
+    These are the most expensive arithmetic operations, especially
+    for large  a  and  b.
+
+    Lehmer's algorithm [1]_ is based on the observation that the quotients
+    ``qn = r(n-1) // rn``  are in general small integers even
+    when  a  and  b  are very large. Hence the quotients can be
+    usually determined from a relatively small number of most
+    significant bits.
+
+    The efficiency of the algorithm is further enhanced by not
+    computing each long remainder in Euclid's sequence. The remainders
+    are linear combinations of  a  and  b  with integer coefficients
+    derived from the quotients. The coefficients can be computed
+    as far as the quotients can be determined from the chosen
+    most significant parts of  a  and  b. Only then a new pair of
+    consecutive remainders is computed and the algorithm starts
+    anew with this pair.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Lehmer%27s_GCD_algorithm
+
+    """
+    a, b = abs(as_int(a)), abs(as_int(b))
+    if a < b:
+        a, b = b, a
+
+    # The algorithm works by using one or two digit division
+    # whenever possible. The outer loop will replace the
+    # pair (a, b) with a pair of shorter consecutive elements
+    # of the Euclidean gcd sequence until a and b
+    # fit into two Python (long) int digits.
+    nbits = 2 * sys.int_info.bits_per_digit
+
+    while a.bit_length() > nbits and b != 0:
+        # Quotients are mostly small integers that can
+        # be determined from most significant bits.
+        n = a.bit_length() - nbits
+        x, y = int(a >> n), int(b >> n)  # most significant bits
+
+        # Elements of the Euclidean gcd sequence are linear
+        # combinations of a and b with integer coefficients.
+        # Compute the coefficients of consecutive pairs
+        #     a' = A*a + B*b, b' = C*a + D*b
+        # using small integer arithmetic as far as possible.
+        A, B, C, D = 1, 0, 0, 1  # initial values
+
+        while True:
+            # The coefficients alternate in sign while looping.
+            # The inner loop combines two steps to keep track
+            # of the signs.
+
+            # At this point we have
+            #   A > 0, B <= 0, C <= 0, D > 0,
+            #   x' = x + B <= x < x" = x + A,
+            #   y' = y + C <= y < y" = y + D,
+            # and
+            #   x'*N <= a' < x"*N, y'*N <= b' < y"*N,
+            # where N = 2**n.
+
+            # Now, if y' > 0, and x"//y' and x'//y" agree,
+            # then their common value is equal to  q = a'//b'.
+            # In addition,
+            #   x'%y" = x' - q*y" < x" - q*y' = x"%y',
+            # and
+            #   (x'%y")*N < a'%b' < (x"%y')*N.
+
+            # On the other hand, we also have  x//y == q,
+            # and therefore
+            #   x'%y" = x + B - q*(y + D) = x%y + B',
+            #   x"%y' = x + A - q*(y + C) = x%y + A',
+            # where
+            #    B' = B - q*D < 0, A' = A - q*C > 0.
+
+            if y + C <= 0:
+                break
+            q = (x + A) // (y + C)
+
+            # Now  x'//y" <= q, and equality holds if
+            #   x' - q*y" = (x - q*y) + (B - q*D) >= 0.
+            # This is a minor optimization to avoid division.
+            x_qy, B_qD = x - q * y, B - q * D
+            if x_qy + B_qD < 0:
+                break
+
+            # Next step in the Euclidean sequence.
+            x, y = y, x_qy
+            A, B, C, D = C, D, A - q * C, B_qD
+
+            # At this point the signs of the coefficients
+            # change and their roles are interchanged.
+            #   A <= 0, B > 0, C > 0, D < 0,
+            #   x' = x + A <= x < x" = x + B,
+            #   y' = y + D < y < y" = y + C.
+
+            if y + D <= 0:
+                break
+            q = (x + B) // (y + D)
+            x_qy, A_qC = x - q * y, A - q * C
+            if x_qy + A_qC < 0:
+                break
+
+            x, y = y, x_qy
+            A, B, C, D = C, D, A_qC, B - q * D
+            # Now the conditions on top of the loop
+            # are again satisfied.
+            #   A > 0, B < 0, C < 0, D > 0.
+
+        if B == 0:
+            # This can only happen when y == 0 in the beginning
+            # and the inner loop does nothing.
+            # Long division is forced.
+            a, b = b, a % b
+            continue
+
+        # Compute new long arguments using the coefficients.
+        a, b = A * a + B * b, C * a + D * b
+
+    # Small divisors. Finish with the standard algorithm.
+    while b:
+        a, b = b, a % b
+
+    return a
+
+
+def ilcm(*args):
+    """Computes integer least common multiple.
+
+    Examples
+    ========
+
+    >>> from sympy import ilcm
+    >>> ilcm(5, 10)
+    10
+    >>> ilcm(7, 3)
+    21
+    >>> ilcm(5, 10, 15)
+    30
+
+    """
+    if len(args) < 2:
+        raise TypeError("ilcm() takes at least 2 arguments (%s given)" % len(args))
+    return int(number_lcm(*map(as_int, args)))
+
+
+def igcdex(a, b):
+    """Returns x, y, g such that g = x*a + y*b = gcd(a, b).
+
+    Examples
+    ========
+
+    >>> from sympy.core.intfunc import igcdex
+    >>> igcdex(2, 3)
+    (-1, 1, 1)
+    >>> igcdex(10, 12)
+    (-1, 1, 2)
+
+    >>> x, y, g = igcdex(100, 2004)
+    >>> x, y, g
+    (-20, 1, 4)
+    >>> x*100 + y*2004
+    4
+
+    """
+    g, x, y = gcdext(int(a), int(b))
+    return x, y, g
+
+
+def mod_inverse(a, m):
+    r"""
+    Return the number $c$ such that, $a \times c = 1 \pmod{m}$
+    where $c$ has the same sign as $m$. If no such value exists,
+    a ValueError is raised.
+
+    Examples
+    ========
+
+    >>> from sympy import mod_inverse, S
+
+    Suppose we wish to find multiplicative inverse $x$ of
+    3 modulo 11. This is the same as finding $x$ such
+    that $3x = 1 \pmod{11}$. One value of x that satisfies
+    this congruence is 4. Because $3 \times 4 = 12$ and $12 = 1 \pmod{11}$.
+    This is the value returned by ``mod_inverse``:
+
+    >>> mod_inverse(3, 11)
+    4
+    >>> mod_inverse(-3, 11)
+    7
+
+    When there is a common factor between the numerators of
+    `a` and `m` the inverse does not exist:
+
+    >>> mod_inverse(2, 4)
+    Traceback (most recent call last):
+    ...
+    ValueError: inverse of 2 mod 4 does not exist
+
+    >>> mod_inverse(S(2)/7, S(5)/2)
+    7/2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Modular_multiplicative_inverse
+    .. [2] https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
+    """
+    c = None
+    try:
+        a, m = as_int(a), as_int(m)
+        if m != 1 and m != -1:
+            x, _, g = igcdex(a, m)
+            if g == 1:
+                c = x % m
+    except ValueError:
+        a, m = sympify(a), sympify(m)
+        if not (a.is_number and m.is_number):
+            raise TypeError(
+                filldedent(
+                    """
+                Expected numbers for arguments; symbolic `mod_inverse`
+                is not implemented
+                but symbolic expressions can be handled with the
+                similar function,
+                sympy.polys.polytools.invert"""
+                )
+            )
+        big = m > 1
+        if big not in (S.true, S.false):
+            raise ValueError("m > 1 did not evaluate; try to simplify %s" % m)
+        elif big:
+            c = 1 / a
+    if c is None:
+        raise ValueError("inverse of %s (mod %s) does not exist" % (a, m))
+    return c
+
+
+def isqrt(n):
+    r""" Return the largest integer less than or equal to `\sqrt{n}`.
+
+    Parameters
+    ==========
+
+    n : non-negative integer
+
+    Returns
+    =======
+
+    int : `\left\lfloor\sqrt{n}\right\rfloor`
+
+    Raises
+    ======
+
+    ValueError
+        If n is negative.
+    TypeError
+        If n is of a type that cannot be compared to ``int``.
+        Therefore, a TypeError is raised for ``str``, but not for ``float``.
+
+    Examples
+    ========
+
+    >>> from sympy.core.intfunc import isqrt
+    >>> isqrt(0)
+    0
+    >>> isqrt(9)
+    3
+    >>> isqrt(10)
+    3
+    >>> isqrt("30")
+    Traceback (most recent call last):
+        ...
+    TypeError: '<' not supported between instances of 'str' and 'int'
+    >>> from sympy.core.numbers import Rational
+    >>> isqrt(Rational(-1, 2))
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be nonnegative
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative")
+    return int(sqrt(int(n)))
+
+
+def integer_nthroot(y, n):
+    """
+    Return a tuple containing x = floor(y**(1/n))
+    and a boolean indicating whether the result is exact (that is,
+    whether x**n == y).
+
+    Examples
+    ========
+
+    >>> from sympy import integer_nthroot
+    >>> integer_nthroot(16, 2)
+    (4, True)
+    >>> integer_nthroot(26, 2)
+    (5, False)
+
+    To simply determine if a number is a perfect square, the is_square
+    function should be used:
+
+    >>> from sympy.ntheory.primetest import is_square
+    >>> is_square(26)
+    False
+
+    See Also
+    ========
+    sympy.ntheory.primetest.is_square
+    integer_log
+    """
+    x, b = iroot(as_int(y), as_int(n))
+    return int(x), b
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/kind.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/kind.py
new file mode 100644
index 0000000000000000000000000000000000000000..83c5929eda14114659f2a5a72eb2d8b91a560f0e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/kind.py
@@ -0,0 +1,388 @@
+"""
+Module to efficiently partition SymPy objects.
+
+This system is introduced because class of SymPy object does not always
+represent the mathematical classification of the entity. For example,
+``Integral(1, x)`` and ``Integral(Matrix([1,2]), x)`` are both instance
+of ``Integral`` class. However the former is number and the latter is
+matrix.
+
+One way to resolve this is defining subclass for each mathematical type,
+such as ``MatAdd`` for the addition between matrices. Basic algebraic
+operation such as addition or multiplication take this approach, but
+defining every class for every mathematical object is not scalable.
+
+Therefore, we define the "kind" of the object and let the expression
+infer the kind of itself from its arguments. Function and class can
+filter the arguments by their kind, and behave differently according to
+the type of itself.
+
+This module defines basic kinds for core objects. Other kinds such as
+``ArrayKind`` or ``MatrixKind`` can be found in corresponding modules.
+
+.. notes::
+       This approach is experimental, and can be replaced or deleted in the future.
+       See https://github.com/sympy/sympy/pull/20549.
+"""
+
+from collections import defaultdict
+
+from .cache import cacheit
+from sympy.multipledispatch.dispatcher import (Dispatcher,
+    ambiguity_warn, ambiguity_register_error_ignore_dup,
+    str_signature, RaiseNotImplementedError)
+
+
+class KindMeta(type):
+    """
+    Metaclass for ``Kind``.
+
+    Assigns empty ``dict`` as class attribute ``_inst`` for every class,
+    in order to endow singleton-like behavior.
+    """
+    def __new__(cls, clsname, bases, dct):
+        dct['_inst'] = {}
+        return super().__new__(cls, clsname, bases, dct)
+
+
+class Kind(object, metaclass=KindMeta):
+    """
+    Base class for kinds.
+
+    Kind of the object represents the mathematical classification that
+    the entity falls into. It is expected that functions and classes
+    recognize and filter the argument by its kind.
+
+    Kind of every object must be carefully selected so that it shows the
+    intention of design. Expressions may have different kind according
+    to the kind of its arguments. For example, arguments of ``Add``
+    must have common kind since addition is group operator, and the
+    resulting ``Add()`` has the same kind.
+
+    For the performance, each kind is as broad as possible and is not
+    based on set theory. For example, ``NumberKind`` includes not only
+    complex number but expression containing ``S.Infinity`` or ``S.NaN``
+    which are not strictly number.
+
+    Kind may have arguments as parameter. For example, ``MatrixKind()``
+    may be constructed with one element which represents the kind of its
+    elements.
+
+    ``Kind`` behaves in singleton-like fashion. Same signature will
+    return the same object.
+
+    """
+    def __new__(cls, *args):
+        if args in cls._inst:
+            inst = cls._inst[args]
+        else:
+            inst = super().__new__(cls)
+            cls._inst[args] = inst
+        return inst
+
+
+class _UndefinedKind(Kind):
+    """
+    Default kind for all SymPy object. If the kind is not defined for
+    the object, or if the object cannot infer the kind from its
+    arguments, this will be returned.
+
+    Examples
+    ========
+
+    >>> from sympy import Expr
+    >>> Expr().kind
+    UndefinedKind
+    """
+    def __new__(cls):
+        return super().__new__(cls)
+
+    def __repr__(self):
+        return "UndefinedKind"
+
+UndefinedKind = _UndefinedKind()
+
+
+class _NumberKind(Kind):
+    """
+    Kind for all numeric object.
+
+    This kind represents every number, including complex numbers,
+    infinity and ``S.NaN``. Other objects such as quaternions do not
+    have this kind.
+
+    Most ``Expr`` are initially designed to represent the number, so
+    this will be the most common kind in SymPy core. For example
+    ``Symbol()``, which represents a scalar, has this kind as long as it
+    is commutative.
+
+    Numbers form a field. Any operation between number-kind objects will
+    result this kind as well.
+
+    Examples
+    ========
+
+    >>> from sympy import S, oo, Symbol
+    >>> S.One.kind
+    NumberKind
+    >>> (-oo).kind
+    NumberKind
+    >>> S.NaN.kind
+    NumberKind
+
+    Commutative symbol are treated as number.
+
+    >>> x = Symbol('x')
+    >>> x.kind
+    NumberKind
+    >>> Symbol('y', commutative=False).kind
+    UndefinedKind
+
+    Operation between numbers results number.
+
+    >>> (x+1).kind
+    NumberKind
+
+    See Also
+    ========
+
+    sympy.core.expr.Expr.is_Number : check if the object is strictly
+    subclass of ``Number`` class.
+
+    sympy.core.expr.Expr.is_number : check if the object is number
+    without any free symbol.
+
+    """
+    def __new__(cls):
+        return super().__new__(cls)
+
+    def __repr__(self):
+        return "NumberKind"
+
+NumberKind = _NumberKind()
+
+
+class _BooleanKind(Kind):
+    """
+    Kind for boolean objects.
+
+    SymPy's ``S.true``, ``S.false``, and built-in ``True`` and ``False``
+    have this kind. Boolean number ``1`` and ``0`` are not relevant.
+
+    Examples
+    ========
+
+    >>> from sympy import S, Q
+    >>> S.true.kind
+    BooleanKind
+    >>> Q.even(3).kind
+    BooleanKind
+    """
+    def __new__(cls):
+        return super().__new__(cls)
+
+    def __repr__(self):
+        return "BooleanKind"
+
+BooleanKind = _BooleanKind()
+
+
+class KindDispatcher:
+    """
+    Dispatcher to select a kind from multiple kinds by binary dispatching.
+
+    .. notes::
+       This approach is experimental, and can be replaced or deleted in
+       the future.
+
+    Explanation
+    ===========
+
+    SymPy object's :obj:`sympy.core.kind.Kind()` vaguely represents the
+    algebraic structure where the object belongs to. Therefore, with
+    given operation, we can always find a dominating kind among the
+    different kinds. This class selects the kind by recursive binary
+    dispatching. If the result cannot be determined, ``UndefinedKind``
+    is returned.
+
+    Examples
+    ========
+
+    Multiplication between numbers return number.
+
+    >>> from sympy import NumberKind, Mul
+    >>> Mul._kind_dispatcher(NumberKind, NumberKind)
+    NumberKind
+
+    Multiplication between number and unknown-kind object returns unknown kind.
+
+    >>> from sympy import UndefinedKind
+    >>> Mul._kind_dispatcher(NumberKind, UndefinedKind)
+    UndefinedKind
+
+    Any number and order of kinds is allowed.
+
+    >>> Mul._kind_dispatcher(UndefinedKind, NumberKind)
+    UndefinedKind
+    >>> Mul._kind_dispatcher(NumberKind, UndefinedKind, NumberKind)
+    UndefinedKind
+
+    Since matrix forms a vector space over scalar field, multiplication
+    between matrix with numeric element and number returns matrix with
+    numeric element.
+
+    >>> from sympy.matrices import MatrixKind
+    >>> Mul._kind_dispatcher(MatrixKind(NumberKind), NumberKind)
+    MatrixKind(NumberKind)
+
+    If a matrix with number element and another matrix with unknown-kind
+    element are multiplied, we know that the result is matrix but the
+    kind of its elements is unknown.
+
+    >>> Mul._kind_dispatcher(MatrixKind(NumberKind), MatrixKind(UndefinedKind))
+    MatrixKind(UndefinedKind)
+
+    Parameters
+    ==========
+
+    name : str
+
+    commutative : bool, optional
+        If True, binary dispatch will be automatically registered in
+        reversed order as well.
+
+    doc : str, optional
+
+    """
+    def __init__(self, name, commutative=False, doc=None):
+        self.name = name
+        self.doc = doc
+        self.commutative = commutative
+        self._dispatcher = Dispatcher(name)
+
+    def __repr__(self):
+        return "" % self.name
+
+    def register(self, *types, **kwargs):
+        """
+        Register the binary dispatcher for two kind classes.
+
+        If *self.commutative* is ``True``, signature in reversed order is
+        automatically registered as well.
+        """
+        on_ambiguity = kwargs.pop("on_ambiguity", None)
+        if not on_ambiguity:
+            if self.commutative:
+                on_ambiguity = ambiguity_register_error_ignore_dup
+            else:
+                on_ambiguity = ambiguity_warn
+        kwargs.update(on_ambiguity=on_ambiguity)
+
+        if not len(types) == 2:
+            raise RuntimeError(
+                "Only binary dispatch is supported, but got %s types: <%s>." % (
+                len(types), str_signature(types)
+            ))
+
+        def _(func):
+            self._dispatcher.add(types, func, **kwargs)
+            if self.commutative:
+                self._dispatcher.add(tuple(reversed(types)), func, **kwargs)
+        return _
+
+    def __call__(self, *args, **kwargs):
+        if self.commutative:
+            kinds = frozenset(args)
+        else:
+            kinds = []
+            prev = None
+            for a in args:
+                if prev is not a:
+                    kinds.append(a)
+                    prev = a
+        return self.dispatch_kinds(kinds, **kwargs)
+
+    @cacheit
+    def dispatch_kinds(self, kinds, **kwargs):
+        # Quick exit for the case where all kinds are same
+        if len(kinds) == 1:
+            result, = kinds
+            if not isinstance(result, Kind):
+                raise RuntimeError("%s is not a kind." % result)
+            return result
+
+        for i,kind in enumerate(kinds):
+            if not isinstance(kind, Kind):
+                raise RuntimeError("%s is not a kind." % kind)
+
+            if i == 0:
+                result = kind
+            else:
+                prev_kind = result
+
+                t1, t2 = type(prev_kind), type(kind)
+                k1, k2 = prev_kind, kind
+                func = self._dispatcher.dispatch(t1, t2)
+                if func is None and self.commutative:
+                    # try reversed order
+                    func = self._dispatcher.dispatch(t2, t1)
+                    k1, k2 = k2, k1
+                if func is None:
+                    # unregistered kind relation
+                    result = UndefinedKind
+                else:
+                    result = func(k1, k2)
+                if not isinstance(result, Kind):
+                    raise RuntimeError(
+                        "Dispatcher for {!r} and {!r} must return a Kind, but got {!r}".format(
+                        prev_kind, kind, result
+                    ))
+
+        return result
+
+    @property
+    def __doc__(self):
+        docs = [
+            "Kind dispatcher : %s" % self.name,
+            "Note that support for this is experimental. See the docs for :class:`KindDispatcher` for details"
+        ]
+
+        if self.doc:
+            docs.append(self.doc)
+
+        s = "Registered kind classes\n"
+        s += '=' * len(s)
+        docs.append(s)
+
+        amb_sigs = []
+
+        typ_sigs = defaultdict(list)
+        for sigs in self._dispatcher.ordering[::-1]:
+            key = self._dispatcher.funcs[sigs]
+            typ_sigs[key].append(sigs)
+
+        for func, sigs in typ_sigs.items():
+
+            sigs_str = ', '.join('<%s>' % str_signature(sig) for sig in sigs)
+
+            if isinstance(func, RaiseNotImplementedError):
+                amb_sigs.append(sigs_str)
+                continue
+
+            s = 'Inputs: %s\n' % sigs_str
+            s += '-' * len(s) + '\n'
+            if func.__doc__:
+                s += func.__doc__.strip()
+            else:
+                s += func.__name__
+            docs.append(s)
+
+        if amb_sigs:
+            s = "Ambiguous kind classes\n"
+            s += '=' * len(s)
+            docs.append(s)
+
+            s = '\n'.join(amb_sigs)
+            docs.append(s)
+
+        return '\n\n'.join(docs)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/logic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/logic.py
new file mode 100644
index 0000000000000000000000000000000000000000..1c318063049a4657952c8ca84e0f0fdeef62a207
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/logic.py
@@ -0,0 +1,425 @@
+"""Logic expressions handling
+
+NOTE
+----
+
+at present this is mainly needed for facts.py, feel free however to improve
+this stuff for general purpose.
+"""
+
+from __future__ import annotations
+from typing import Optional
+
+# Type of a fuzzy bool
+FuzzyBool = Optional[bool]
+
+
+def _torf(args):
+    """Return True if all args are True, False if they
+    are all False, else None.
+
+    >>> from sympy.core.logic import _torf
+    >>> _torf((True, True))
+    True
+    >>> _torf((False, False))
+    False
+    >>> _torf((True, False))
+    """
+    sawT = sawF = False
+    for a in args:
+        if a is True:
+            if sawF:
+                return
+            sawT = True
+        elif a is False:
+            if sawT:
+                return
+            sawF = True
+        else:
+            return
+    return sawT
+
+
+def _fuzzy_group(args, quick_exit=False):
+    """Return True if all args are True, None if there is any None else False
+    unless ``quick_exit`` is True (then return None as soon as a second False
+    is seen.
+
+     ``_fuzzy_group`` is like ``fuzzy_and`` except that it is more
+    conservative in returning a False, waiting to make sure that all
+    arguments are True or False and returning None if any arguments are
+    None. It also has the capability of permiting only a single False and
+    returning None if more than one is seen. For example, the presence of a
+    single transcendental amongst rationals would indicate that the group is
+    no longer rational; but a second transcendental in the group would make the
+    determination impossible.
+
+
+    Examples
+    ========
+
+    >>> from sympy.core.logic import _fuzzy_group
+
+    By default, multiple Falses mean the group is broken:
+
+    >>> _fuzzy_group([False, False, True])
+    False
+
+    If multiple Falses mean the group status is unknown then set
+    `quick_exit` to True so None can be returned when the 2nd False is seen:
+
+    >>> _fuzzy_group([False, False, True], quick_exit=True)
+
+    But if only a single False is seen then the group is known to
+    be broken:
+
+    >>> _fuzzy_group([False, True, True], quick_exit=True)
+    False
+
+    """
+    saw_other = False
+    for a in args:
+        if a is True:
+            continue
+        if a is None:
+            return
+        if quick_exit and saw_other:
+            return
+        saw_other = True
+    return not saw_other
+
+
+def fuzzy_bool(x):
+    """Return True, False or None according to x.
+
+    Whereas bool(x) returns True or False, fuzzy_bool allows
+    for the None value and non-false values (which become None), too.
+
+    Examples
+    ========
+
+    >>> from sympy.core.logic import fuzzy_bool
+    >>> from sympy.abc import x
+    >>> fuzzy_bool(x), fuzzy_bool(None)
+    (None, None)
+    >>> bool(x), bool(None)
+    (True, False)
+
+    """
+    if x is None:
+        return None
+    if x in (True, False):
+        return bool(x)
+
+
+def fuzzy_and(args):
+    """Return True (all True), False (any False) or None.
+
+    Examples
+    ========
+
+    >>> from sympy.core.logic import fuzzy_and
+    >>> from sympy import Dummy
+
+    If you had a list of objects to test the commutivity of
+    and you want the fuzzy_and logic applied, passing an
+    iterator will allow the commutativity to only be computed
+    as many times as necessary. With this list, False can be
+    returned after analyzing the first symbol:
+
+    >>> syms = [Dummy(commutative=False), Dummy()]
+    >>> fuzzy_and(s.is_commutative for s in syms)
+    False
+
+    That False would require less work than if a list of pre-computed
+    items was sent:
+
+    >>> fuzzy_and([s.is_commutative for s in syms])
+    False
+    """
+
+    rv = True
+    for ai in args:
+        ai = fuzzy_bool(ai)
+        if ai is False:
+            return False
+        if rv:  # this will stop updating if a None is ever trapped
+            rv = ai
+    return rv
+
+
+def fuzzy_not(v):
+    """
+    Not in fuzzy logic
+
+    Return None if `v` is None else `not v`.
+
+    Examples
+    ========
+
+    >>> from sympy.core.logic import fuzzy_not
+    >>> fuzzy_not(True)
+    False
+    >>> fuzzy_not(None)
+    >>> fuzzy_not(False)
+    True
+
+    """
+    if v is None:
+        return v
+    else:
+        return not v
+
+
+def fuzzy_or(args):
+    """
+    Or in fuzzy logic. Returns True (any True), False (all False), or None
+
+    See the docstrings of fuzzy_and and fuzzy_not for more info.  fuzzy_or is
+    related to the two by the standard De Morgan's law.
+
+    >>> from sympy.core.logic import fuzzy_or
+    >>> fuzzy_or([True, False])
+    True
+    >>> fuzzy_or([True, None])
+    True
+    >>> fuzzy_or([False, False])
+    False
+    >>> print(fuzzy_or([False, None]))
+    None
+
+    """
+    rv = False
+    for ai in args:
+        ai = fuzzy_bool(ai)
+        if ai is True:
+            return True
+        if rv is False:  # this will stop updating if a None is ever trapped
+            rv = ai
+    return rv
+
+
+def fuzzy_xor(args):
+    """Return None if any element of args is not True or False, else
+    True (if there are an odd number of True elements), else False."""
+    t = 0
+    for a in args:
+        ai = fuzzy_bool(a)
+        if ai:
+            t += 1
+        elif ai is None:
+            return
+    return t % 2 == 1
+
+
+def fuzzy_nand(args):
+    """Return False if all args are True, True if they are all False,
+    else None."""
+    return fuzzy_not(fuzzy_and(args))
+
+
+class Logic:
+    """Logical expression"""
+    # {} 'op' -> LogicClass
+    op_2class: dict[str, type[Logic]] = {}
+
+    def __new__(cls, *args):
+        obj = object.__new__(cls)
+        obj.args = args
+        return obj
+
+    def __getnewargs__(self):
+        return self.args
+
+    def __hash__(self):
+        return hash((type(self).__name__,) + tuple(self.args))
+
+    def __eq__(a, b):
+        if not isinstance(b, type(a)):
+            return False
+        else:
+            return a.args == b.args
+
+    def __ne__(a, b):
+        if not isinstance(b, type(a)):
+            return True
+        else:
+            return a.args != b.args
+
+    def __lt__(self, other):
+        if self.__cmp__(other) == -1:
+            return True
+        return False
+
+    def __cmp__(self, other):
+        if type(self) is not type(other):
+            a = str(type(self))
+            b = str(type(other))
+        else:
+            a = self.args
+            b = other.args
+        return (a > b) - (a < b)
+
+    def __str__(self):
+        return '%s(%s)' % (self.__class__.__name__,
+                           ', '.join(str(a) for a in self.args))
+
+    __repr__ = __str__
+
+    @staticmethod
+    def fromstring(text):
+        """Logic from string with space around & and | but none after !.
+
+           e.g.
+
+           !a & b | c
+        """
+        lexpr = None  # current logical expression
+        schedop = None  # scheduled operation
+        for term in text.split():
+            # operation symbol
+            if term in '&|':
+                if schedop is not None:
+                    raise ValueError(
+                        'double op forbidden: "%s %s"' % (term, schedop))
+                if lexpr is None:
+                    raise ValueError(
+                        '%s cannot be in the beginning of expression' % term)
+                schedop = term
+                continue
+            if '&' in term or '|' in term:
+                raise ValueError('& and | must have space around them')
+            if term[0] == '!':
+                if len(term) == 1:
+                    raise ValueError('do not include space after "!"')
+                term = Not(term[1:])
+
+            # already scheduled operation, e.g. '&'
+            if schedop:
+                lexpr = Logic.op_2class[schedop](lexpr, term)
+                schedop = None
+                continue
+
+            # this should be atom
+            if lexpr is not None:
+                raise ValueError(
+                    'missing op between "%s" and "%s"' % (lexpr, term))
+
+            lexpr = term
+
+        # let's check that we ended up in correct state
+        if schedop is not None:
+            raise ValueError('premature end-of-expression in "%s"' % text)
+        if lexpr is None:
+            raise ValueError('"%s" is empty' % text)
+
+        # everything looks good now
+        return lexpr
+
+
+class AndOr_Base(Logic):
+
+    def __new__(cls, *args):
+        bargs = []
+        for a in args:
+            if a == cls.op_x_notx:
+                return a
+            elif a == (not cls.op_x_notx):
+                continue    # skip this argument
+            bargs.append(a)
+
+        args = sorted(set(cls.flatten(bargs)), key=hash)
+
+        for a in args:
+            if Not(a) in args:
+                return cls.op_x_notx
+
+        if len(args) == 1:
+            return args.pop()
+        elif len(args) == 0:
+            return not cls.op_x_notx
+
+        return Logic.__new__(cls, *args)
+
+    @classmethod
+    def flatten(cls, args):
+        # quick-n-dirty flattening for And and Or
+        args_queue = list(args)
+        res = []
+
+        while True:
+            try:
+                arg = args_queue.pop(0)
+            except IndexError:
+                break
+            if isinstance(arg, Logic):
+                if isinstance(arg, cls):
+                    args_queue.extend(arg.args)
+                    continue
+            res.append(arg)
+
+        args = tuple(res)
+        return args
+
+
+class And(AndOr_Base):
+    op_x_notx = False
+
+    def _eval_propagate_not(self):
+        # !(a&b&c ...) == !a | !b | !c ...
+        return Or(*[Not(a) for a in self.args])
+
+    # (a|b|...) & c == (a&c) | (b&c) | ...
+    def expand(self):
+
+        # first locate Or
+        for i, arg in enumerate(self.args):
+            if isinstance(arg, Or):
+                arest = self.args[:i] + self.args[i + 1:]
+
+                orterms = [And(*(arest + (a,))) for a in arg.args]
+                for j in range(len(orterms)):
+                    if isinstance(orterms[j], Logic):
+                        orterms[j] = orterms[j].expand()
+
+                res = Or(*orterms)
+                return res
+
+        return self
+
+
+class Or(AndOr_Base):
+    op_x_notx = True
+
+    def _eval_propagate_not(self):
+        # !(a|b|c ...) == !a & !b & !c ...
+        return And(*[Not(a) for a in self.args])
+
+
+class Not(Logic):
+
+    def __new__(cls, arg):
+        if isinstance(arg, str):
+            return Logic.__new__(cls, arg)
+
+        elif isinstance(arg, bool):
+            return not arg
+        elif isinstance(arg, Not):
+            return arg.args[0]
+
+        elif isinstance(arg, Logic):
+            # XXX this is a hack to expand right from the beginning
+            arg = arg._eval_propagate_not()
+            return arg
+
+        else:
+            raise ValueError('Not: unknown argument %r' % (arg,))
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+
+Logic.op_2class['&'] = And
+Logic.op_2class['|'] = Or
+Logic.op_2class['!'] = Not
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/mod.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/mod.py
new file mode 100644
index 0000000000000000000000000000000000000000..8be0c56e497eb5ed0041801488044b50f907962c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/mod.py
@@ -0,0 +1,260 @@
+from .add import Add
+from .exprtools import gcd_terms
+from .function import DefinedFunction
+from .kind import NumberKind
+from .logic import fuzzy_and, fuzzy_not
+from .mul import Mul
+from .numbers import equal_valued
+from .relational import is_le, is_lt, is_ge, is_gt
+from .singleton import S
+
+
+class Mod(DefinedFunction):
+    """Represents a modulo operation on symbolic expressions.
+
+    Parameters
+    ==========
+
+    p : Expr
+        Dividend.
+
+    q : Expr
+        Divisor.
+
+    Notes
+    =====
+
+    The convention used is the same as Python's: the remainder always has the
+    same sign as the divisor.
+
+    Many objects can be evaluated modulo ``n`` much faster than they can be
+    evaluated directly (or at all).  For this, ``evaluate=False`` is
+    necessary to prevent eager evaluation:
+
+    >>> from sympy import binomial, factorial, Mod, Pow
+    >>> Mod(Pow(2, 10**16, evaluate=False), 97)
+    61
+    >>> Mod(factorial(10**9, evaluate=False), 10**9 + 9)
+    712524808
+    >>> Mod(binomial(10**18, 10**12, evaluate=False), (10**5 + 3)**2)
+    3744312326
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> x**2 % y
+    Mod(x**2, y)
+    >>> _.subs({x: 5, y: 6})
+    1
+
+    """
+
+    kind = NumberKind
+
+    @classmethod
+    def eval(cls, p, q):
+        def number_eval(p, q):
+            """Try to return p % q if both are numbers or +/-p is known
+            to be less than or equal q.
+            """
+
+            if q.is_zero:
+                raise ZeroDivisionError("Modulo by zero")
+            if p is S.NaN or q is S.NaN or p.is_finite is False or q.is_finite is False:
+                return S.NaN
+            if p is S.Zero or p in (q, -q) or (p.is_integer and q == 1):
+                return S.Zero
+
+            if q.is_Number:
+                if p.is_Number:
+                    return p%q
+                if q == 2:
+                    if p.is_even:
+                        return S.Zero
+                    elif p.is_odd:
+                        return S.One
+
+            if hasattr(p, '_eval_Mod'):
+                rv = getattr(p, '_eval_Mod')(q)
+                if rv is not None:
+                    return rv
+
+            # by ratio
+            r = p/q
+            if r.is_integer:
+                return S.Zero
+            try:
+                d = int(r)
+            except TypeError:
+                pass
+            else:
+                if isinstance(d, int):
+                    rv = p - d*q
+                    if (rv*q < 0) == True:
+                        rv += q
+                    return rv
+
+            # by difference
+            # -2|q| < p < 2|q|
+            if q.is_positive:
+                comp1, comp2 = is_le, is_lt
+            elif q.is_negative:
+                comp1, comp2 = is_ge, is_gt
+            else:
+                return
+            ls = -2*q
+            r = p - q
+            for _ in range(4):
+                if not comp1(ls, p):
+                    return
+                if comp2(r, ls):
+                    return p - ls
+                ls += q
+
+        rv = number_eval(p, q)
+        if rv is not None:
+            return rv
+
+        # denest
+        if isinstance(p, cls):
+            qinner = p.args[1]
+            if qinner % q == 0:
+                return cls(p.args[0], q)
+            elif (qinner*(q - qinner)).is_nonnegative:
+                # |qinner| < |q| and have same sign
+                return p
+        elif isinstance(-p, cls):
+            qinner = (-p).args[1]
+            if qinner % q == 0:
+                return cls(-(-p).args[0], q)
+            elif (qinner*(q + qinner)).is_nonpositive:
+                # |qinner| < |q| and have different sign
+                return p
+        elif isinstance(p, Add):
+            # separating into modulus and non modulus
+            both_l = non_mod_l, mod_l = [], []
+            for arg in p.args:
+                both_l[isinstance(arg, cls)].append(arg)
+            # if q same for all
+            if mod_l and all(inner.args[1] == q for inner in mod_l):
+                net = Add(*non_mod_l) + Add(*[i.args[0] for i in mod_l])
+                return cls(net, q)
+
+        elif isinstance(p, Mul):
+            # separating into modulus and non modulus
+            both_l = non_mod_l, mod_l = [], []
+            for arg in p.args:
+                both_l[isinstance(arg, cls)].append(arg)
+
+            if mod_l and all(inner.args[1] == q for inner in mod_l) and all(t.is_integer for t in p.args) and q.is_integer:
+                # finding distributive term
+                non_mod_l = [cls(x, q) for x in non_mod_l]
+                mod = []
+                non_mod = []
+                for j in non_mod_l:
+                    if isinstance(j, cls):
+                        mod.append(j.args[0])
+                    else:
+                        non_mod.append(j)
+                prod_mod = Mul(*mod)
+                prod_non_mod = Mul(*non_mod)
+                prod_mod1 = Mul(*[i.args[0] for i in mod_l])
+                net = prod_mod1*prod_mod
+                return prod_non_mod*cls(net, q)
+
+            if q.is_Integer and q is not S.One:
+                if all(t.is_integer for t in p.args):
+                    non_mod_l = [i % q if i.is_Integer else i for i in p.args]
+                    if any(iq is S.Zero for iq in non_mod_l):
+                        return S.Zero
+
+            p = Mul(*(non_mod_l + mod_l))
+
+        # XXX other possibilities?
+
+        from sympy.polys.polyerrors import PolynomialError
+        from sympy.polys.polytools import gcd
+
+        # extract gcd; any further simplification should be done by the user
+        try:
+            G = gcd(p, q)
+            if not equal_valued(G, 1):
+                p, q = [gcd_terms(i/G, clear=False, fraction=False)
+                        for i in (p, q)]
+        except PolynomialError:  # issue 21373
+            G = S.One
+        pwas, qwas = p, q
+
+        # simplify terms
+        # (x + y + 2) % x -> Mod(y + 2, x)
+        if p.is_Add:
+            args = []
+            for i in p.args:
+                a = cls(i, q)
+                if a.count(cls) > i.count(cls):
+                    args.append(i)
+                else:
+                    args.append(a)
+            if args != list(p.args):
+                p = Add(*args)
+
+        else:
+            # handle coefficients if they are not Rational
+            # since those are not handled by factor_terms
+            # e.g. Mod(.6*x, .3*y) -> 0.3*Mod(2*x, y)
+            cp, p = p.as_coeff_Mul()
+            cq, q = q.as_coeff_Mul()
+            ok = False
+            if not cp.is_Rational or not cq.is_Rational:
+                r = cp % cq
+                if equal_valued(r, 0):
+                    G *= cq
+                    p *= int(cp/cq)
+                    ok = True
+            if not ok:
+                p = cp*p
+                q = cq*q
+
+        # simple -1 extraction
+        if p.could_extract_minus_sign() and q.could_extract_minus_sign():
+            G, p, q = [-i for i in (G, p, q)]
+
+        # check again to see if p and q can now be handled as numbers
+        rv = number_eval(p, q)
+        if rv is not None:
+            return rv*G
+
+        # put 1.0 from G on inside
+        if G.is_Float and equal_valued(G, 1):
+            p *= G
+            return cls(p, q, evaluate=False)
+        elif G.is_Mul and G.args[0].is_Float and equal_valued(G.args[0], 1):
+            p = G.args[0]*p
+            G = Mul._from_args(G.args[1:])
+        return G*cls(p, q, evaluate=(p, q) != (pwas, qwas))
+
+    def _eval_is_integer(self):
+        p, q = self.args
+        if fuzzy_and([p.is_integer, q.is_integer, fuzzy_not(q.is_zero)]):
+            return True
+
+    def _eval_is_nonnegative(self):
+        if self.args[1].is_positive:
+            return True
+
+    def _eval_is_nonpositive(self):
+        if self.args[1].is_negative:
+            return True
+
+    def _eval_rewrite_as_floor(self, a, b, **kwargs):
+        from sympy.functions.elementary.integers import floor
+        return a - b*floor(a/b)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.functions.elementary.integers import floor
+        return self.rewrite(floor)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.functions.elementary.integers import floor
+        return self.rewrite(floor)._eval_nseries(x, n, logx=logx, cdir=cdir)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/mul.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/mul.py
new file mode 100644
index 0000000000000000000000000000000000000000..fd83c8610a76db4e7bc7a2a71b98e437bd00a28e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/mul.py
@@ -0,0 +1,2214 @@
+from __future__ import annotations
+from typing import TYPE_CHECKING, ClassVar
+
+from collections import defaultdict
+from functools import reduce
+from itertools import product
+import operator
+
+from .sympify import sympify
+from .basic import Basic, _args_sortkey
+from .singleton import S
+from .operations import AssocOp, AssocOpDispatcher
+from .cache import cacheit
+from .intfunc import integer_nthroot, trailing
+from .logic import fuzzy_not, _fuzzy_group
+from .expr import Expr
+from .parameters import global_parameters
+from .kind import KindDispatcher
+from .traversal import bottom_up
+from sympy.utilities.iterables import sift
+
+
+# internal marker to indicate:
+#   "there are still non-commutative objects -- don't forget to process them"
+class NC_Marker:
+    is_Order = False
+    is_Mul = False
+    is_Number = False
+    is_Poly = False
+
+    is_commutative = False
+
+
+def _mulsort(args):
+    # in-place sorting of args
+    args.sort(key=_args_sortkey)
+
+
+def _unevaluated_Mul(*args):
+    """Return a well-formed unevaluated Mul: Numbers are collected and
+    put in slot 0, any arguments that are Muls will be flattened, and args
+    are sorted. Use this when args have changed but you still want to return
+    an unevaluated Mul.
+
+    Examples
+    ========
+
+    >>> from sympy.core.mul import _unevaluated_Mul as uMul
+    >>> from sympy import S, sqrt, Mul
+    >>> from sympy.abc import x
+    >>> a = uMul(*[S(3.0), x, S(2)])
+    >>> a.args[0]
+    6.00000000000000
+    >>> a.args[1]
+    x
+
+    Two unevaluated Muls with the same arguments will
+    always compare as equal during testing:
+
+    >>> m = uMul(sqrt(2), sqrt(3))
+    >>> m == uMul(sqrt(3), sqrt(2))
+    True
+    >>> u = Mul(sqrt(3), sqrt(2), evaluate=False)
+    >>> m == uMul(u)
+    True
+    >>> m == Mul(*m.args)
+    False
+
+    """
+    cargs = []
+    ncargs = []
+    args = list(args)
+    co = S.One
+    for a in args:
+        if a.is_Mul:
+            a_c, a_nc = a.args_cnc()
+            args.extend(a_c)  # grow args
+            ncargs.extend(a_nc)
+        elif a.is_Number:
+            co *= a
+        elif a.is_commutative:
+            cargs.append(a)
+        else:
+            ncargs.append(a)
+    _mulsort(cargs)
+    if co is not S.One:
+        cargs.insert(0, co)
+    return Mul._from_args(cargs+ncargs)
+
+
+class Mul(Expr, AssocOp):
+    """
+    Expression representing multiplication operation for algebraic field.
+
+    .. deprecated:: 1.7
+
+       Using arguments that aren't subclasses of :class:`~.Expr` in core
+       operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is
+       deprecated. See :ref:`non-expr-args-deprecated` for details.
+
+    Every argument of ``Mul()`` must be ``Expr``. Infix operator ``*``
+    on most scalar objects in SymPy calls this class.
+
+    Another use of ``Mul()`` is to represent the structure of abstract
+    multiplication so that its arguments can be substituted to return
+    different class. Refer to examples section for this.
+
+    ``Mul()`` evaluates the argument unless ``evaluate=False`` is passed.
+    The evaluation logic includes:
+
+    1. Flattening
+        ``Mul(x, Mul(y, z))`` -> ``Mul(x, y, z)``
+
+    2. Identity removing
+        ``Mul(x, 1, y)`` -> ``Mul(x, y)``
+
+    3. Exponent collecting by ``.as_base_exp()``
+        ``Mul(x, x**2)`` -> ``Pow(x, 3)``
+
+    4. Term sorting
+        ``Mul(y, x, 2)`` -> ``Mul(2, x, y)``
+
+    Since multiplication can be vector space operation, arguments may
+    have the different :obj:`sympy.core.kind.Kind()`. Kind of the
+    resulting object is automatically inferred.
+
+    Examples
+    ========
+
+    >>> from sympy import Mul
+    >>> from sympy.abc import x, y
+    >>> Mul(x, 1)
+    x
+    >>> Mul(x, x)
+    x**2
+
+    If ``evaluate=False`` is passed, result is not evaluated.
+
+    >>> Mul(1, 2, evaluate=False)
+    1*2
+    >>> Mul(x, x, evaluate=False)
+    x*x
+
+    ``Mul()`` also represents the general structure of multiplication
+    operation.
+
+    >>> from sympy import MatrixSymbol
+    >>> A = MatrixSymbol('A', 2,2)
+    >>> expr = Mul(x,y).subs({y:A})
+    >>> expr
+    x*A
+    >>> type(expr)
+    
+
+    See Also
+    ========
+
+    MatMul
+
+    """
+    __slots__ = ()
+
+    is_Mul = True
+
+    _args_type = Expr
+    _kind_dispatcher = KindDispatcher("Mul_kind_dispatcher", commutative=True)
+
+    identity: ClassVar[Expr]
+
+    @property
+    def kind(self):
+        arg_kinds = (a.kind for a in self.args)
+        return self._kind_dispatcher(*arg_kinds)
+
+    if TYPE_CHECKING:
+
+        def __new__(cls, *args: Expr | complex, evaluate: bool=True) -> Expr: # type: ignore
+            ...
+
+        @property
+        def args(self) -> tuple[Expr, ...]:
+            ...
+
+    def could_extract_minus_sign(self):
+        if self == (-self):
+            return False  # e.g. zoo*x == -zoo*x
+        c = self.args[0]
+        return c.is_Number and c.is_extended_negative
+
+    def __neg__(self):
+        c, args = self.as_coeff_mul()
+        if args[0] is not S.ComplexInfinity:
+            c = -c
+        if c is not S.One:
+            if args[0].is_Number:
+                args = list(args)
+                if c is S.NegativeOne:
+                    args[0] = -args[0]
+                else:
+                    args[0] *= c
+            else:
+                args = (c,) + args
+        return self._from_args(args, self.is_commutative)
+
+    @classmethod
+    def flatten(cls, seq):
+        """Return commutative, noncommutative and order arguments by
+        combining related terms.
+
+        Notes
+        =====
+            * In an expression like ``a*b*c``, Python process this through SymPy
+              as ``Mul(Mul(a, b), c)``. This can have undesirable consequences.
+
+              -  Sometimes terms are not combined as one would like:
+                 {c.f. https://github.com/sympy/sympy/issues/4596}
+
+                >>> from sympy import Mul, sqrt
+                >>> from sympy.abc import x, y, z
+                >>> 2*(x + 1) # this is the 2-arg Mul behavior
+                2*x + 2
+                >>> y*(x + 1)*2
+                2*y*(x + 1)
+                >>> 2*(x + 1)*y # 2-arg result will be obtained first
+                y*(2*x + 2)
+                >>> Mul(2, x + 1, y) # all 3 args simultaneously processed
+                2*y*(x + 1)
+                >>> 2*((x + 1)*y) # parentheses can control this behavior
+                2*y*(x + 1)
+
+                Powers with compound bases may not find a single base to
+                combine with unless all arguments are processed at once.
+                Post-processing may be necessary in such cases.
+                {c.f. https://github.com/sympy/sympy/issues/5728}
+
+                >>> a = sqrt(x*sqrt(y))
+                >>> a**3
+                (x*sqrt(y))**(3/2)
+                >>> Mul(a,a,a)
+                (x*sqrt(y))**(3/2)
+                >>> a*a*a
+                x*sqrt(y)*sqrt(x*sqrt(y))
+                >>> _.subs(a.base, z).subs(z, a.base)
+                (x*sqrt(y))**(3/2)
+
+              -  If more than two terms are being multiplied then all the
+                 previous terms will be re-processed for each new argument.
+                 So if each of ``a``, ``b`` and ``c`` were :class:`Mul`
+                 expression, then ``a*b*c`` (or building up the product
+                 with ``*=``) will process all the arguments of ``a`` and
+                 ``b`` twice: once when ``a*b`` is computed and again when
+                 ``c`` is multiplied.
+
+                 Using ``Mul(a, b, c)`` will process all arguments once.
+
+            * The results of Mul are cached according to arguments, so flatten
+              will only be called once for ``Mul(a, b, c)``. If you can
+              structure a calculation so the arguments are most likely to be
+              repeats then this can save time in computing the answer. For
+              example, say you had a Mul, M, that you wished to divide by ``d[i]``
+              and multiply by ``n[i]`` and you suspect there are many repeats
+              in ``n``. It would be better to compute ``M*n[i]/d[i]`` rather
+              than ``M/d[i]*n[i]`` since every time n[i] is a repeat, the
+              product, ``M*n[i]`` will be returned without flattening -- the
+              cached value will be returned. If you divide by the ``d[i]``
+              first (and those are more unique than the ``n[i]``) then that will
+              create a new Mul, ``M/d[i]`` the args of which will be traversed
+              again when it is multiplied by ``n[i]``.
+
+              {c.f. https://github.com/sympy/sympy/issues/5706}
+
+              This consideration is moot if the cache is turned off.
+
+            NB
+            --
+              The validity of the above notes depends on the implementation
+              details of Mul and flatten which may change at any time. Therefore,
+              you should only consider them when your code is highly performance
+              sensitive.
+
+              Removal of 1 from the sequence is already handled by AssocOp.__new__.
+        """
+
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.matrices.expressions import MatrixExpr
+        rv = None
+        if len(seq) == 2:
+            a, b = seq
+            if b.is_Rational:
+                a, b = b, a
+                seq = [a, b]
+            assert a is not S.One
+            if a.is_Rational and not a.is_zero:
+                r, b = b.as_coeff_Mul()
+                if b.is_Add:
+                    if r is not S.One:  # 2-arg hack
+                        # leave the Mul as a Mul?
+                        ar = a*r
+                        if ar is S.One:
+                            arb = b
+                        else:
+                            arb = cls(a*r, b, evaluate=False)
+                        rv = [arb], [], None
+                    elif global_parameters.distribute and b.is_commutative:
+                        newb = Add(*[_keep_coeff(a, bi) for bi in b.args])
+                        rv = [newb], [], None
+            if rv:
+                return rv
+
+        # apply associativity, separate commutative part of seq
+        c_part = []         # out: commutative factors
+        nc_part = []        # out: non-commutative factors
+
+        nc_seq = []
+
+        coeff = S.One       # standalone term
+                            # e.g. 3 * ...
+
+        c_powers = []       # (base,exp)      n
+                            # e.g. (x,n) for x
+
+        num_exp = []        # (num-base, exp)           y
+                            # e.g.  (3, y)  for  ... * 3  * ...
+
+        neg1e = S.Zero      # exponent on -1 extracted from Number-based Pow and I
+
+        pnum_rat = {}       # (num-base, Rat-exp)          1/2
+                            # e.g.  (3, 1/2)  for  ... * 3     * ...
+
+        order_symbols = None
+
+        # --- PART 1 ---
+        #
+        # "collect powers and coeff":
+        #
+        # o coeff
+        # o c_powers
+        # o num_exp
+        # o neg1e
+        # o pnum_rat
+        #
+        # NOTE: this is optimized for all-objects-are-commutative case
+        for o in seq:
+            # O(x)
+            if o.is_Order:
+                o, order_symbols = o.as_expr_variables(order_symbols)
+
+            # Mul([...])
+            if o.is_Mul:
+                if o.is_commutative:
+                    seq.extend(o.args)    # XXX zerocopy?
+
+                else:
+                    # NCMul can have commutative parts as well
+                    for q in o.args:
+                        if q.is_commutative:
+                            seq.append(q)
+                        else:
+                            nc_seq.append(q)
+
+                    # append non-commutative marker, so we don't forget to
+                    # process scheduled non-commutative objects
+                    seq.append(NC_Marker)
+
+                continue
+
+            # 3
+            elif o.is_Number:
+                if o is S.NaN or coeff is S.ComplexInfinity and o.is_zero:
+                    # we know for sure the result will be nan
+                    return [S.NaN], [], None
+                elif coeff.is_Number or isinstance(coeff, AccumBounds):  # it could be zoo
+                    coeff *= o
+                    if coeff is S.NaN:
+                        # we know for sure the result will be nan
+                        return [S.NaN], [], None
+                continue
+
+            elif isinstance(o, AccumBounds):
+                coeff = o.__mul__(coeff)
+                continue
+
+            elif o is S.ComplexInfinity:
+                if not coeff:
+                    # 0 * zoo = NaN
+                    return [S.NaN], [], None
+                coeff = S.ComplexInfinity
+                continue
+
+            elif not coeff and isinstance(o, Add) and any(
+                    _ in (S.NegativeInfinity, S.ComplexInfinity, S.Infinity)
+                    for __ in o.args for _ in Mul.make_args(__)):
+                # e.g 0 * (x + oo) = NaN but not
+                # 0 * (1 + Integral(x, (x, 0, oo))) which is
+                # treated like 0 * x -> 0
+                return [S.NaN], [], None
+
+            elif o is S.ImaginaryUnit:
+                neg1e += S.Half
+                continue
+
+            elif o.is_commutative:
+                #      e
+                # o = b
+                b, e = o.as_base_exp()
+
+                #  y
+                # 3
+                if o.is_Pow:
+                    if b.is_Number:
+
+                        # get all the factors with numeric base so they can be
+                        # combined below, but don't combine negatives unless
+                        # the exponent is an integer
+                        if e.is_Rational:
+                            if e.is_Integer:
+                                coeff *= Pow(b, e)  # it is an unevaluated power
+                                continue
+                            elif e.is_negative:    # also a sign of an unevaluated power
+                                seq.append(Pow(b, e))
+                                continue
+                            elif b.is_negative:
+                                neg1e += e
+                                b = -b
+                            if b is not S.One:
+                                pnum_rat.setdefault(b, []).append(e)
+                            continue
+                        elif b.is_positive or e.is_integer:
+                            num_exp.append((b, e))
+                            continue
+
+                c_powers.append((b, e))
+
+            # NON-COMMUTATIVE
+            # TODO: Make non-commutative exponents not combine automatically
+            else:
+                if o is not NC_Marker:
+                    nc_seq.append(o)
+
+                # process nc_seq (if any)
+                while nc_seq:
+                    o = nc_seq.pop(0)
+                    if not nc_part:
+                        nc_part.append(o)
+                        continue
+
+                    #                             b    c       b+c
+                    # try to combine last terms: a  * a   ->  a
+                    o1 = nc_part.pop()
+                    b1, e1 = o1.as_base_exp()
+                    b2, e2 = o.as_base_exp()
+                    new_exp = e1 + e2
+                    # Only allow powers to combine if the new exponent is
+                    # not an Add. This allow things like a**2*b**3 == a**5
+                    # if a.is_commutative == False, but prohibits
+                    # a**x*a**y and x**a*x**b from combining (x,y commute).
+                    if b1 == b2 and (not new_exp.is_Add):
+                        o12 = b1 ** new_exp
+
+                        # now o12 could be a commutative object
+                        if o12.is_commutative:
+                            seq.append(o12)
+                            continue
+                        else:
+                            nc_seq.insert(0, o12)
+
+                    else:
+                        nc_part.extend([o1, o])
+
+        # We do want a combined exponent if it would not be an Add, such as
+        #  y    2y     3y
+        # x  * x   -> x
+        # We determine if two exponents have the same term by using
+        # as_coeff_Mul.
+        #
+        # Unfortunately, this isn't smart enough to consider combining into
+        # exponents that might already be adds, so things like:
+        #  z - y    y
+        # x      * x  will be left alone.  This is because checking every possible
+        # combination can slow things down.
+
+        # gather exponents of common bases...
+        def _gather(c_powers):
+            common_b = {}  # b:e
+            for b, e in c_powers:
+                co = e.as_coeff_Mul()
+                common_b.setdefault(b, {}).setdefault(
+                    co[1], []).append(co[0])
+            for b, d in common_b.items():
+                for di, li in d.items():
+                    d[di] = Add(*li)
+            new_c_powers = []
+            for b, e in common_b.items():
+                new_c_powers.extend([(b, c*t) for t, c in e.items()])
+            return new_c_powers
+
+        # in c_powers
+        c_powers = _gather(c_powers)
+
+        # and in num_exp
+        num_exp = _gather(num_exp)
+
+        # --- PART 2 ---
+        #
+        # o process collected powers  (x**0 -> 1; x**1 -> x; otherwise Pow)
+        # o combine collected powers  (2**x * 3**x -> 6**x)
+        #   with numeric base
+
+        # ................................
+        # now we have:
+        # - coeff:
+        # - c_powers:    (b, e)
+        # - num_exp:     (2, e)
+        # - pnum_rat:    {(1/3, [1/3, 2/3, 1/4])}
+
+        #  0             1
+        # x  -> 1       x  -> x
+
+        # this should only need to run twice; if it fails because
+        # it needs to be run more times, perhaps this should be
+        # changed to a "while True" loop -- the only reason it
+        # isn't such now is to allow a less-than-perfect result to
+        # be obtained rather than raising an error or entering an
+        # infinite loop
+        for i in range(2):
+            new_c_powers = []
+            changed = False
+            for b, e in c_powers:
+                if e.is_zero:
+                    # canceling out infinities yields NaN
+                    if (b.is_Add or b.is_Mul) and any(infty in b.args
+                        for infty in (S.ComplexInfinity, S.Infinity,
+                                      S.NegativeInfinity)):
+                        return [S.NaN], [], None
+                    continue
+                if e is S.One:
+                    if b.is_Number:
+                        coeff *= b
+                        continue
+                    p = b
+                if e is not S.One:
+                    p = Pow(b, e)
+                    # check to make sure that the base doesn't change
+                    # after exponentiation; to allow for unevaluated
+                    # Pow, we only do so if b is not already a Pow
+                    if p.is_Pow and not b.is_Pow:
+                        bi = b
+                        b, e = p.as_base_exp()
+                        if b != bi:
+                            changed = True
+                c_part.append(p)
+                new_c_powers.append((b, e))
+            # there might have been a change, but unless the base
+            # matches some other base, there is nothing to do
+            if changed and len({
+                    b for b, e in new_c_powers}) != len(new_c_powers):
+                # start over again
+                c_part = []
+                c_powers = _gather(new_c_powers)
+            else:
+                break
+
+        #  x    x     x
+        # 2  * 3  -> 6
+        inv_exp_dict = {}   # exp:Mul(num-bases)     x    x
+                            # e.g.  x:6  for  ... * 2  * 3  * ...
+        for b, e in num_exp:
+            inv_exp_dict.setdefault(e, []).append(b)
+        for e, b in inv_exp_dict.items():
+            inv_exp_dict[e] = cls(*b)
+        c_part.extend([Pow(b, e) for e, b in inv_exp_dict.items() if e])
+
+        # b, e -> e' = sum(e), b
+        # {(1/5, [1/3]), (1/2, [1/12, 1/4]} -> {(1/3, [1/5, 1/2])}
+        comb_e = {}
+        for b, e in pnum_rat.items():
+            comb_e.setdefault(Add(*e), []).append(b)
+        del pnum_rat
+        # process them, reducing exponents to values less than 1
+        # and updating coeff if necessary else adding them to
+        # num_rat for further processing
+        num_rat = []
+        for e, b in comb_e.items():
+            b = cls(*b)
+            if e.q == 1:
+                coeff *= Pow(b, e)
+                continue
+            if e.p > e.q:
+                e_i, ep = divmod(e.p, e.q)
+                coeff *= Pow(b, e_i)
+                e = Rational(ep, e.q)
+            num_rat.append((b, e))
+        del comb_e
+
+        # extract gcd of bases in num_rat
+        # 2**(1/3)*6**(1/4) -> 2**(1/3+1/4)*3**(1/4)
+        pnew = defaultdict(list)
+        i = 0  # steps through num_rat which may grow
+        while i < len(num_rat):
+            bi, ei = num_rat[i]
+            if bi == 1:
+                i += 1
+                continue
+            grow = []
+            for j in range(i + 1, len(num_rat)):
+                bj, ej = num_rat[j]
+                g = bi.gcd(bj)
+                if g is not S.One:
+                    # 4**r1*6**r2 -> 2**(r1+r2)  *  2**r1 *  3**r2
+                    # this might have a gcd with something else
+                    e = ei + ej
+                    if e.q == 1:
+                        coeff *= Pow(g, e)
+                    else:
+                        if e.p > e.q:
+                            e_i, ep = divmod(e.p, e.q)  # change e in place
+                            coeff *= Pow(g, e_i)
+                            e = Rational(ep, e.q)
+                        grow.append((g, e))
+                    # update the jth item
+                    num_rat[j] = (bj/g, ej)
+                    # update bi that we are checking with
+                    bi = bi/g
+                    if bi is S.One:
+                        break
+            if bi is not S.One:
+                obj = Pow(bi, ei)
+                if obj.is_Number:
+                    coeff *= obj
+                else:
+                    # changes like sqrt(12) -> 2*sqrt(3)
+                    for obj in Mul.make_args(obj):
+                        if obj.is_Number:
+                            coeff *= obj
+                        else:
+                            assert obj.is_Pow
+                            bi, ei = obj.args
+                            pnew[ei].append(bi)
+
+            num_rat.extend(grow)
+            i += 1
+
+        # combine bases of the new powers
+        for e, b in pnew.items():
+            pnew[e] = cls(*b)
+
+        # handle -1 and I
+        if neg1e:
+            # treat I as (-1)**(1/2) and compute -1's total exponent
+            p, q =  neg1e.as_numer_denom()
+            # if the integer part is odd, extract -1
+            n, p = divmod(p, q)
+            if n % 2:
+                coeff = -coeff
+            # if it's a multiple of 1/2 extract I
+            if q == 2:
+                c_part.append(S.ImaginaryUnit)
+            elif p:
+                # see if there is any positive base this power of
+                # -1 can join
+                neg1e = Rational(p, q)
+                for e, b in pnew.items():
+                    if e == neg1e and b.is_positive:
+                        pnew[e] = -b
+                        break
+                else:
+                    # keep it separate; we've already evaluated it as
+                    # much as possible so evaluate=False
+                    c_part.append(Pow(S.NegativeOne, neg1e, evaluate=False))
+
+        # add all the pnew powers
+        c_part.extend([Pow(b, e) for e, b in pnew.items()])
+
+        # oo, -oo
+        if coeff in (S.Infinity, S.NegativeInfinity):
+            def _handle_for_oo(c_part, coeff_sign):
+                new_c_part = []
+                for t in c_part:
+                    if t.is_extended_positive:
+                        continue
+                    if t.is_extended_negative:
+                        coeff_sign *= -1
+                        continue
+                    new_c_part.append(t)
+                return new_c_part, coeff_sign
+            c_part, coeff_sign = _handle_for_oo(c_part, 1)
+            nc_part, coeff_sign = _handle_for_oo(nc_part, coeff_sign)
+            coeff *= coeff_sign
+
+        # zoo
+        if coeff is S.ComplexInfinity:
+            # zoo might be
+            #   infinite_real + bounded_im
+            #   bounded_real + infinite_im
+            #   infinite_real + infinite_im
+            # and non-zero real or imaginary will not change that status.
+            c_part = [c for c in c_part if not (fuzzy_not(c.is_zero) and
+                                                c.is_extended_real is not None)]
+            nc_part = [c for c in nc_part if not (fuzzy_not(c.is_zero) and
+                                                  c.is_extended_real is not None)]
+
+        # 0
+        elif coeff.is_zero:
+            # we know for sure the result will be 0 except the multiplicand
+            # is infinity or a matrix
+            if any(isinstance(c, MatrixExpr) for c in nc_part):
+                return [coeff], nc_part, order_symbols
+            if any(c.is_finite == False for c in c_part):
+                return [S.NaN], [], order_symbols
+            return [coeff], [], order_symbols
+
+        # check for straggling Numbers that were produced
+        _new = []
+        for i in c_part:
+            if i.is_Number:
+                coeff *= i
+            else:
+                _new.append(i)
+        c_part = _new
+
+        # order commutative part canonically
+        _mulsort(c_part)
+
+        # current code expects coeff to be always in slot-0
+        if coeff is not S.One:
+            c_part.insert(0, coeff)
+
+        # we are done
+        if (global_parameters.distribute and not nc_part and len(c_part) == 2 and
+                c_part[0].is_Number and c_part[0].is_finite and c_part[1].is_Add):
+            # 2*(1+a) -> 2 + 2 * a
+            coeff = c_part[0]
+            c_part = [Add(*[coeff*f for f in c_part[1].args])]
+
+        return c_part, nc_part, order_symbols
+
+    def _eval_power(self, expt):
+
+        # don't break up NC terms: (A*B)**3 != A**3*B**3, it is A*B*A*B*A*B
+        cargs, nc = self.args_cnc(split_1=False)
+
+        if expt.is_Integer:
+            return Mul(*[Pow(b, expt, evaluate=False) for b in cargs]) * \
+                Pow(Mul._from_args(nc), expt, evaluate=False)
+        if expt.is_Rational and expt.q == 2:
+            if self.is_imaginary:
+                a = self.as_real_imag()[1]
+                if a.is_Rational:
+                    n, d = abs(a/2).as_numer_denom()
+                    n, t = integer_nthroot(n, 2)
+                    if t:
+                        d, t = integer_nthroot(d, 2)
+                        if t:
+                            from sympy.functions.elementary.complexes import sign
+                            r = sympify(n)/d
+                            return _unevaluated_Mul(r**expt.p, (1 + sign(a)*S.ImaginaryUnit)**expt.p)
+
+        p = Pow(self, expt, evaluate=False)
+
+        if expt.is_Rational or expt.is_Float:
+            return p._eval_expand_power_base()
+
+        return p
+
+    @classmethod
+    def class_key(cls):
+        return 3, 0, cls.__name__
+
+    def _eval_evalf(self, prec):
+        c, m = self.as_coeff_Mul()
+        if c is S.NegativeOne:
+            if m.is_Mul:
+                rv = -AssocOp._eval_evalf(m, prec)
+            else:
+                mnew = m._eval_evalf(prec)
+                if mnew is not None:
+                    m = mnew
+                rv = -m
+        else:
+            rv = AssocOp._eval_evalf(self, prec)
+        if rv.is_number:
+            return rv.expand()
+        return rv
+
+    @property
+    def _mpc_(self):
+        """
+        Convert self to an mpmath mpc if possible
+        """
+        from .numbers import Float
+        im_part, imag_unit = self.as_coeff_Mul()
+        if imag_unit is not S.ImaginaryUnit:
+            # ValueError may seem more reasonable but since it's a @property,
+            # we need to use AttributeError to keep from confusing things like
+            # hasattr.
+            raise AttributeError("Cannot convert Mul to mpc. Must be of the form Number*I")
+
+        return (Float(0)._mpf_, Float(im_part)._mpf_)
+
+    @cacheit
+    def as_two_terms(self):
+        """Return head and tail of self.
+
+        This is the most efficient way to get the head and tail of an
+        expression.
+
+        - if you want only the head, use self.args[0];
+        - if you want to process the arguments of the tail then use
+          self.as_coef_mul() which gives the head and a tuple containing
+          the arguments of the tail when treated as a Mul.
+        - if you want the coefficient when self is treated as an Add
+          then use self.as_coeff_add()[0]
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> (3*x*y).as_two_terms()
+        (3, x*y)
+        """
+        args = self.args
+
+        if len(args) == 1:
+            return S.One, self
+        elif len(args) == 2:
+            return args
+
+        else:
+            return args[0], self._new_rawargs(*args[1:])
+
+    @cacheit
+    def as_coeff_mul(self, *deps, rational=True, **kwargs):
+        if deps:
+            l1, l2 = sift(self.args, lambda x: x.has(*deps), binary=True)
+            return self._new_rawargs(*l2), tuple(l1)
+        args = self.args
+        if args[0].is_Number:
+            if not rational or args[0].is_Rational:
+                return args[0], args[1:]
+            elif args[0].is_extended_negative:
+                return S.NegativeOne, (-args[0],) + args[1:]
+        return S.One, args
+
+    def as_coeff_Mul(self, rational=False):
+        """
+        Efficiently extract the coefficient of a product.
+        """
+        coeff, args = self.args[0], self.args[1:]
+
+        if coeff.is_Number:
+            if not rational or coeff.is_Rational:
+                if len(args) == 1:
+                    return coeff, args[0]
+                else:
+                    return coeff, self._new_rawargs(*args)
+            elif coeff.is_extended_negative:
+                return S.NegativeOne, self._new_rawargs(*((-coeff,) + args))
+        return S.One, self
+
+    def as_real_imag(self, deep=True, **hints):
+        from sympy.functions.elementary.complexes import Abs, im, re
+        other = []
+        coeffr = []
+        coeffi = []
+        addterms = S.One
+        for a in self.args:
+            r, i = a.as_real_imag()
+            if i.is_zero:
+                coeffr.append(r)
+            elif r.is_zero:
+                coeffi.append(i*S.ImaginaryUnit)
+            elif a.is_commutative:
+                aconj = a.conjugate() if other else None
+                # search for complex conjugate pairs:
+                for i, x in enumerate(other):
+                    if x == aconj:
+                        coeffr.append(Abs(x)**2)
+                        del other[i]
+                        break
+                else:
+                    if a.is_Add:
+                        addterms *= a
+                    else:
+                        other.append(a)
+            else:
+                other.append(a)
+        m = self.func(*other)
+        if hints.get('ignore') == m:
+            return
+        if len(coeffi) % 2:
+            imco = im(coeffi.pop(0))
+            # all other pairs make a real factor; they will be
+            # put into reco below
+        else:
+            imco = S.Zero
+        reco = self.func(*(coeffr + coeffi))
+        r, i = (reco*re(m), reco*im(m))
+        if addterms == 1:
+            if m == 1:
+                if imco.is_zero:
+                    return (reco, S.Zero)
+                else:
+                    return (S.Zero, reco*imco)
+            if imco is S.Zero:
+                return (r, i)
+            return (-imco*i, imco*r)
+        from .function import expand_mul
+        addre, addim = expand_mul(addterms, deep=False).as_real_imag()
+        if imco is S.Zero:
+            return (r*addre - i*addim, i*addre + r*addim)
+        else:
+            r, i = -imco*i, imco*r
+            return (r*addre - i*addim, r*addim + i*addre)
+
+    @staticmethod
+    def _expandsums(sums):
+        """
+        Helper function for _eval_expand_mul.
+
+        sums must be a list of instances of Basic.
+        """
+
+        L = len(sums)
+        if L == 1:
+            return sums[0].args
+        terms = []
+        left = Mul._expandsums(sums[:L//2])
+        right = Mul._expandsums(sums[L//2:])
+
+        terms = [Mul(a, b) for a in left for b in right]
+        added = Add(*terms)
+        return Add.make_args(added)  # it may have collapsed down to one term
+
+    def _eval_expand_mul(self, **hints):
+        from sympy.simplify.radsimp import fraction
+
+        # Handle things like 1/(x*(x + 1)), which are automatically converted
+        # to 1/x*1/(x + 1)
+        expr = self
+        # default matches fraction's default
+        n, d = fraction(expr, hints.get('exact', False))
+        if d.is_Mul:
+            n, d = [i._eval_expand_mul(**hints) if i.is_Mul else i
+                for i in (n, d)]
+        expr = n/d
+        if not expr.is_Mul:
+            return expr
+
+        plain, sums, rewrite = [], [], False
+        for factor in expr.args:
+            if factor.is_Add:
+                sums.append(factor)
+                rewrite = True
+            else:
+                if factor.is_commutative:
+                    plain.append(factor)
+                else:
+                    sums.append(Basic(factor))  # Wrapper
+
+        if not rewrite:
+            return expr
+        else:
+            plain = self.func(*plain)
+            if sums:
+                deep = hints.get("deep", False)
+                terms = self.func._expandsums(sums)
+                args = []
+                for term in terms:
+                    t = self.func(plain, term)
+                    if t.is_Mul and any(a.is_Add for a in t.args) and deep:
+                        t = t._eval_expand_mul()
+                    args.append(t)
+                return Add(*args)
+            else:
+                return plain
+
+    @cacheit
+    def _eval_derivative(self, s):
+        args = list(self.args)
+        terms = []
+        for i in range(len(args)):
+            d = args[i].diff(s)
+            if d:
+                # Note: reduce is used in step of Mul as Mul is unable to
+                # handle subtypes and operation priority:
+                terms.append(reduce(lambda x, y: x*y, (args[:i] + [d] + args[i + 1:]), S.One))
+        return Add.fromiter(terms)
+
+    @cacheit
+    def _eval_derivative_n_times(self, s, n):
+        from .function import AppliedUndef
+        from .symbol import Symbol, symbols, Dummy
+        if not isinstance(s, (AppliedUndef, Symbol)):
+            # other types of s may not be well behaved, e.g.
+            # (cos(x)*sin(y)).diff([[x, y, z]])
+            return super()._eval_derivative_n_times(s, n)
+        from .numbers import Integer
+        args = self.args
+        m = len(args)
+        if isinstance(n, (int, Integer)):
+            # https://en.wikipedia.org/wiki/General_Leibniz_rule#More_than_two_factors
+            terms = []
+            from sympy.ntheory.multinomial import multinomial_coefficients_iterator
+            for kvals, c in multinomial_coefficients_iterator(m, n):
+                p = Mul(*[arg.diff((s, k)) for k, arg in zip(kvals, args)])
+                terms.append(c * p)
+            return Add(*terms)
+        from sympy.concrete.summations import Sum
+        from sympy.functions.combinatorial.factorials import factorial
+        from sympy.functions.elementary.miscellaneous import Max
+        kvals = symbols("k1:%i" % m, cls=Dummy)
+        klast = n - sum(kvals)
+        nfact = factorial(n)
+        e, l = (# better to use the multinomial?
+            nfact/prod(map(factorial, kvals))/factorial(klast)*\
+            Mul(*[args[t].diff((s, kvals[t])) for t in range(m-1)])*\
+            args[-1].diff((s, Max(0, klast))),
+            [(k, 0, n) for k in kvals])
+        return Sum(e, *l)
+
+    def _eval_difference_delta(self, n, step):
+        from sympy.series.limitseq import difference_delta as dd
+        arg0 = self.args[0]
+        rest = Mul(*self.args[1:])
+        return (arg0.subs(n, n + step) * dd(rest, n, step) + dd(arg0, n, step) *
+                rest)
+
+    def _matches_simple(self, expr, repl_dict):
+        # handle (w*3).matches('x*5') -> {w: x*5/3}
+        coeff, terms = self.as_coeff_Mul()
+        terms = Mul.make_args(terms)
+        if len(terms) == 1:
+            newexpr = self.__class__._combine_inverse(expr, coeff)
+            return terms[0].matches(newexpr, repl_dict)
+        return
+
+    def matches(self, expr, repl_dict=None, old=False):
+        expr = sympify(expr)
+        if self.is_commutative and expr.is_commutative:
+            return self._matches_commutative(expr, repl_dict, old)
+        elif self.is_commutative is not expr.is_commutative:
+            return None
+
+        # Proceed only if both both expressions are non-commutative
+        c1, nc1 = self.args_cnc()
+        c2, nc2 = expr.args_cnc()
+        c1, c2 = [c or [1] for c in [c1, c2]]
+
+        # TODO: Should these be self.func?
+        comm_mul_self = Mul(*c1)
+        comm_mul_expr = Mul(*c2)
+
+        repl_dict = comm_mul_self.matches(comm_mul_expr, repl_dict, old)
+
+        # If the commutative arguments didn't match and aren't equal, then
+        # then the expression as a whole doesn't match
+        if not repl_dict and c1 != c2:
+            return None
+
+        # Now match the non-commutative arguments, expanding powers to
+        # multiplications
+        nc1 = Mul._matches_expand_pows(nc1)
+        nc2 = Mul._matches_expand_pows(nc2)
+
+        repl_dict = Mul._matches_noncomm(nc1, nc2, repl_dict)
+
+        return repl_dict or None
+
+    @staticmethod
+    def _matches_expand_pows(arg_list):
+        new_args = []
+        for arg in arg_list:
+            if arg.is_Pow and arg.exp > 0:
+                new_args.extend([arg.base] * arg.exp)
+            else:
+                new_args.append(arg)
+        return new_args
+
+    @staticmethod
+    def _matches_noncomm(nodes, targets, repl_dict=None):
+        """Non-commutative multiplication matcher.
+
+        `nodes` is a list of symbols within the matcher multiplication
+        expression, while `targets` is a list of arguments in the
+        multiplication expression being matched against.
+        """
+        if repl_dict is None:
+            repl_dict = {}
+        else:
+            repl_dict = repl_dict.copy()
+
+        # List of possible future states to be considered
+        agenda = []
+        # The current matching state, storing index in nodes and targets
+        state = (0, 0)
+        node_ind, target_ind = state
+        # Mapping between wildcard indices and the index ranges they match
+        wildcard_dict = {}
+
+        while target_ind < len(targets) and node_ind < len(nodes):
+            node = nodes[node_ind]
+
+            if node.is_Wild:
+                Mul._matches_add_wildcard(wildcard_dict, state)
+
+            states_matches = Mul._matches_new_states(wildcard_dict, state,
+                                                     nodes, targets)
+            if states_matches:
+                new_states, new_matches = states_matches
+                agenda.extend(new_states)
+                if new_matches:
+                    for match in new_matches:
+                        repl_dict[match] = new_matches[match]
+            if not agenda:
+                return None
+            else:
+                state = agenda.pop()
+                node_ind, target_ind = state
+
+        return repl_dict
+
+    @staticmethod
+    def _matches_add_wildcard(dictionary, state):
+        node_ind, target_ind = state
+        if node_ind in dictionary:
+            begin, end = dictionary[node_ind]
+            dictionary[node_ind] = (begin, target_ind)
+        else:
+            dictionary[node_ind] = (target_ind, target_ind)
+
+    @staticmethod
+    def _matches_new_states(dictionary, state, nodes, targets):
+        node_ind, target_ind = state
+        node = nodes[node_ind]
+        target = targets[target_ind]
+
+        # Don't advance at all if we've exhausted the targets but not the nodes
+        if target_ind >= len(targets) - 1 and node_ind < len(nodes) - 1:
+            return None
+
+        if node.is_Wild:
+            match_attempt = Mul._matches_match_wilds(dictionary, node_ind,
+                                                     nodes, targets)
+            if match_attempt:
+                # If the same node has been matched before, don't return
+                # anything if the current match is diverging from the previous
+                # match
+                other_node_inds = Mul._matches_get_other_nodes(dictionary,
+                                                               nodes, node_ind)
+                for ind in other_node_inds:
+                    other_begin, other_end = dictionary[ind]
+                    curr_begin, curr_end = dictionary[node_ind]
+
+                    other_targets = targets[other_begin:other_end + 1]
+                    current_targets = targets[curr_begin:curr_end + 1]
+
+                    for curr, other in zip(current_targets, other_targets):
+                        if curr != other:
+                            return None
+
+                # A wildcard node can match more than one target, so only the
+                # target index is advanced
+                new_state = [(node_ind, target_ind + 1)]
+                # Only move on to the next node if there is one
+                if node_ind < len(nodes) - 1:
+                    new_state.append((node_ind + 1, target_ind + 1))
+                return new_state, match_attempt
+        else:
+            # If we're not at a wildcard, then make sure we haven't exhausted
+            # nodes but not targets, since in this case one node can only match
+            # one target
+            if node_ind >= len(nodes) - 1 and target_ind < len(targets) - 1:
+                return None
+
+            match_attempt = node.matches(target)
+
+            if match_attempt:
+                return [(node_ind + 1, target_ind + 1)], match_attempt
+            elif node == target:
+                return [(node_ind + 1, target_ind + 1)], None
+            else:
+                return None
+
+    @staticmethod
+    def _matches_match_wilds(dictionary, wildcard_ind, nodes, targets):
+        """Determine matches of a wildcard with sub-expression in `target`."""
+        wildcard = nodes[wildcard_ind]
+        begin, end = dictionary[wildcard_ind]
+        terms = targets[begin:end + 1]
+        # TODO: Should this be self.func?
+        mult = Mul(*terms) if len(terms) > 1 else terms[0]
+        return wildcard.matches(mult)
+
+    @staticmethod
+    def _matches_get_other_nodes(dictionary, nodes, node_ind):
+        """Find other wildcards that may have already been matched."""
+        ind_node = nodes[node_ind]
+        return [ind for ind in dictionary if nodes[ind] == ind_node]
+
+    @staticmethod
+    def _combine_inverse(lhs, rhs):
+        """
+        Returns lhs/rhs, but treats arguments like symbols, so things
+        like oo/oo return 1 (instead of a nan) and ``I`` behaves like
+        a symbol instead of sqrt(-1).
+        """
+        from sympy.simplify.simplify import signsimp
+        from .symbol import Dummy
+        if lhs == rhs:
+            return S.One
+
+        def check(l, r):
+            if l.is_Float and r.is_comparable:
+                # if both objects are added to 0 they will share the same "normalization"
+                # and are more likely to compare the same. Since Add(foo, 0) will not allow
+                # the 0 to pass, we use __add__ directly.
+                return l.__add__(0) == r.evalf().__add__(0)
+            return False
+        if check(lhs, rhs) or check(rhs, lhs):
+            return S.One
+        if any(i.is_Pow or i.is_Mul for i in (lhs, rhs)):
+            # gruntz and limit wants a literal I to not combine
+            # with a power of -1
+            d = Dummy('I')
+            _i = {S.ImaginaryUnit: d}
+            i_ = {d: S.ImaginaryUnit}
+            a = lhs.xreplace(_i).as_powers_dict()
+            b = rhs.xreplace(_i).as_powers_dict()
+            blen = len(b)
+            for bi in tuple(b.keys()):
+                if bi in a:
+                    a[bi] -= b.pop(bi)
+                    if not a[bi]:
+                        a.pop(bi)
+            if len(b) != blen:
+                lhs = Mul(*[k**v for k, v in a.items()]).xreplace(i_)
+                rhs = Mul(*[k**v for k, v in b.items()]).xreplace(i_)
+        rv = lhs/rhs
+        srv = signsimp(rv)
+        return srv if srv.is_Number else rv
+
+    def as_powers_dict(self):
+        d = defaultdict(int)
+        for term in self.args:
+            for b, e in term.as_powers_dict().items():
+                d[b] += e
+        return d
+
+    def as_numer_denom(self):
+        # don't use _from_args to rebuild the numerators and denominators
+        # as the order is not guaranteed to be the same once they have
+        # been separated from each other
+        numers, denoms = list(zip(*[f.as_numer_denom() for f in self.args]))
+        return self.func(*numers), self.func(*denoms)
+
+    def as_base_exp(self):
+        e1 = None
+        bases = []
+        nc = 0
+        for m in self.args:
+            b, e = m.as_base_exp()
+            if not b.is_commutative:
+                nc += 1
+            if e1 is None:
+                e1 = e
+            elif e != e1 or nc > 1 or not e.is_Integer:
+                return self, S.One
+            bases.append(b)
+        return self.func(*bases), e1
+
+    def _eval_is_polynomial(self, syms):
+        return all(term._eval_is_polynomial(syms) for term in self.args)
+
+    def _eval_is_rational_function(self, syms):
+        return all(term._eval_is_rational_function(syms) for term in self.args)
+
+    def _eval_is_meromorphic(self, x, a):
+        return _fuzzy_group((arg.is_meromorphic(x, a) for arg in self.args),
+                            quick_exit=True)
+
+    def _eval_is_algebraic_expr(self, syms):
+        return all(term._eval_is_algebraic_expr(syms) for term in self.args)
+
+    _eval_is_commutative = lambda self: _fuzzy_group(
+        a.is_commutative for a in self.args)
+
+    def _eval_is_complex(self):
+        comp = _fuzzy_group(a.is_complex for a in self.args)
+        if comp is False:
+            if any(a.is_infinite for a in self.args):
+                if any(a.is_zero is not False for a in self.args):
+                    return None
+                return False
+        return comp
+
+    def _eval_is_zero_infinite_helper(self):
+        #
+        # Helper used by _eval_is_zero and _eval_is_infinite.
+        #
+        # Three-valued logic is tricky so let us reason this carefully. It
+        # would be nice to say that we just check is_zero/is_infinite in all
+        # args but we need to be careful about the case that one arg is zero
+        # and another is infinite like Mul(0, oo) or more importantly a case
+        # where it is not known if the arguments are zero or infinite like
+        # Mul(y, 1/x). If either y or x could be zero then there is a
+        # *possibility* that we have Mul(0, oo) which should give None for both
+        # is_zero and is_infinite.
+        #
+        # We keep track of whether we have seen a zero or infinity but we also
+        # need to keep track of whether we have *possibly* seen one which
+        # would be indicated by None.
+        #
+        # For each argument there is the possibility that is_zero might give
+        # True, False or None and likewise that is_infinite might give True,
+        # False or None, giving 9 combinations. The True cases for is_zero and
+        # is_infinite are mutually exclusive though so there are 3 main cases:
+        #
+        # - is_zero = True
+        # - is_infinite = True
+        # - is_zero and is_infinite are both either False or None
+        #
+        # At the end seen_zero and seen_infinite can be any of 9 combinations
+        # of True/False/None. Unless one is False though we cannot return
+        # anything except None:
+        #
+        # - is_zero=True needs seen_zero=True and seen_infinite=False
+        # - is_zero=False needs seen_zero=False
+        # - is_infinite=True needs seen_infinite=True and seen_zero=False
+        # - is_infinite=False needs seen_infinite=False
+        # - anything else gives both is_zero=None and is_infinite=None
+        #
+        # The loop only sets the flags to True or None and never back to False.
+        # Hence as soon as neither flag is False we exit early returning None.
+        # In particular as soon as we encounter a single arg that has
+        # is_zero=is_infinite=None we exit. This is a common case since it is
+        # the default assumptions for a Symbol and also the case for most
+        # expressions containing such a symbol. The early exit gives a big
+        # speedup for something like Mul(*symbols('x:1000')).is_zero.
+        #
+        seen_zero = seen_infinite = False
+
+        for a in self.args:
+            if a.is_zero:
+                if seen_infinite is not False:
+                    return None, None
+                seen_zero = True
+            elif a.is_infinite:
+                if seen_zero is not False:
+                    return None, None
+                seen_infinite = True
+            else:
+                if seen_zero is False and a.is_zero is None:
+                    if seen_infinite is not False:
+                        return None, None
+                    seen_zero = None
+                if seen_infinite is False and a.is_infinite is None:
+                    if seen_zero is not False:
+                        return None, None
+                    seen_infinite = None
+
+        return seen_zero, seen_infinite
+
+    def _eval_is_zero(self):
+        # True iff any arg is zero and no arg is infinite but need to handle
+        # three valued logic carefully.
+        seen_zero, seen_infinite = self._eval_is_zero_infinite_helper()
+
+        if seen_zero is False:
+            return False
+        elif seen_zero is True and seen_infinite is False:
+            return True
+        else:
+            return None
+
+    def _eval_is_infinite(self):
+        # True iff any arg is infinite and no arg is zero but need to handle
+        # three valued logic carefully.
+        seen_zero, seen_infinite = self._eval_is_zero_infinite_helper()
+
+        if seen_infinite is True and seen_zero is False:
+            return True
+        elif seen_infinite is False:
+            return False
+        else:
+            return None
+
+    # We do not need to implement _eval_is_finite because the assumptions
+    # system can infer it from finite = not infinite.
+
+    def _eval_is_rational(self):
+        r = _fuzzy_group((a.is_rational for a in self.args), quick_exit=True)
+        if r:
+            return r
+        elif r is False:
+            # All args except one are rational
+            if all(a.is_zero is False for a in self.args):
+                return False
+
+    def _eval_is_algebraic(self):
+        r = _fuzzy_group((a.is_algebraic for a in self.args), quick_exit=True)
+        if r:
+            return r
+        elif r is False:
+            # All args except one are algebraic
+            if all(a.is_zero is False for a in self.args):
+                return False
+
+    # without involving odd/even checks this code would suffice:
+    #_eval_is_integer = lambda self: _fuzzy_group(
+    #    (a.is_integer for a in self.args), quick_exit=True)
+    def _eval_is_integer(self):
+        is_rational = self._eval_is_rational()
+        if is_rational is False:
+            return False
+
+        numerators = []
+        denominators = []
+        unknown = False
+        for a in self.args:
+            hit = False
+            if a.is_integer:
+                if abs(a) is not S.One:
+                    numerators.append(a)
+            elif a.is_Rational:
+                n, d = a.as_numer_denom()
+                if abs(n) is not S.One:
+                    numerators.append(n)
+                if d is not S.One:
+                    denominators.append(d)
+            elif a.is_Pow:
+                b, e = a.as_base_exp()
+                if not b.is_integer or not e.is_integer:
+                    hit = unknown = True
+                if e.is_negative:
+                    denominators.append(2 if a is S.Half else
+                        Pow(a, S.NegativeOne))
+                elif not hit:
+                    # int b and pos int e: a = b**e is integer
+                    assert not e.is_positive
+                    # for rational self and e equal to zero: a = b**e is 1
+                    assert not e.is_zero
+                    return # sign of e unknown -> self.is_integer unknown
+                else:
+                    # x**2, 2**x, or x**y with x and y int-unknown -> unknown
+                    return
+            else:
+                return
+
+        if not denominators and not unknown:
+            return True
+
+        allodd = lambda x: all(i.is_odd for i in x)
+        alleven = lambda x: all(i.is_even for i in x)
+        anyeven = lambda x: any(i.is_even for i in x)
+
+        from .relational import is_gt
+        if not numerators and denominators and all(
+                is_gt(_, S.One) for _ in denominators):
+            return False
+        elif unknown:
+            return
+        elif allodd(numerators) and anyeven(denominators):
+            return False
+        elif anyeven(numerators) and denominators == [2]:
+            return True
+        elif alleven(numerators) and allodd(denominators
+                ) and (Mul(*denominators, evaluate=False) - 1
+                ).is_positive:
+            return False
+        if len(denominators) == 1:
+            d = denominators[0]
+            if d.is_Integer and d.is_even:
+                # if minimal power of 2 in num vs den is not
+                # negative then we have an integer
+                if (Add(*[i.as_base_exp()[1] for i in
+                        numerators if i.is_even]) - trailing(d.p)
+                        ).is_nonnegative:
+                    return True
+        if len(numerators) == 1:
+            n = numerators[0]
+            if n.is_Integer and n.is_even:
+                # if minimal power of 2 in den vs num is positive
+                # then we have have a non-integer
+                if (Add(*[i.as_base_exp()[1] for i in
+                        denominators if i.is_even]) - trailing(n.p)
+                        ).is_positive:
+                    return False
+
+    def _eval_is_polar(self):
+        has_polar = any(arg.is_polar for arg in self.args)
+        return has_polar and \
+            all(arg.is_polar or arg.is_positive for arg in self.args)
+
+    def _eval_is_extended_real(self):
+        return self._eval_real_imag(True)
+
+    def _eval_real_imag(self, real):
+        zero = False
+        t_not_re_im = None
+
+        for t in self.args:
+            if (t.is_complex or t.is_infinite) is False and t.is_extended_real is False:
+                return False
+            elif t.is_imaginary:  # I
+                real = not real
+            elif t.is_extended_real:  # 2
+                if not zero:
+                    z = t.is_zero
+                    if not z and zero is False:
+                        zero = z
+                    elif z:
+                        if all(a.is_finite for a in self.args):
+                            return True
+                        return
+            elif t.is_extended_real is False:
+                # symbolic or literal like `2 + I` or symbolic imaginary
+                if t_not_re_im:
+                    return  # complex terms might cancel
+                t_not_re_im = t
+            elif t.is_imaginary is False:  # symbolic like `2` or `2 + I`
+                if t_not_re_im:
+                    return  # complex terms might cancel
+                t_not_re_im = t
+            else:
+                return
+
+        if t_not_re_im:
+            if t_not_re_im.is_extended_real is False:
+                if real:  # like 3
+                    return zero  # 3*(smthng like 2 + I or i) is not real
+            if t_not_re_im.is_imaginary is False:  # symbolic 2 or 2 + I
+                if not real:  # like I
+                    return zero  # I*(smthng like 2 or 2 + I) is not real
+        elif zero is False:
+            return real  # can't be trumped by 0
+        elif real:
+            return real  # doesn't matter what zero is
+
+    def _eval_is_imaginary(self):
+        if all(a.is_zero is False and a.is_finite for a in self.args):
+            return self._eval_real_imag(False)
+
+    def _eval_is_hermitian(self):
+        return self._eval_herm_antiherm(True)
+
+    def _eval_is_antihermitian(self):
+        return self._eval_herm_antiherm(False)
+
+    def _eval_herm_antiherm(self, herm):
+        for t in self.args:
+            if t.is_hermitian is None or t.is_antihermitian is None:
+                return
+            if t.is_hermitian:
+                continue
+            elif t.is_antihermitian:
+                herm = not herm
+            else:
+                return
+
+        if herm is not False:
+            return herm
+
+        is_zero = self._eval_is_zero()
+        if is_zero:
+            return True
+        elif is_zero is False:
+            return herm
+
+    def _eval_is_irrational(self):
+        for t in self.args:
+            a = t.is_irrational
+            if a:
+                others = list(self.args)
+                others.remove(t)
+                if all((x.is_rational and fuzzy_not(x.is_zero)) is True for x in others):
+                    return True
+                return
+            if a is None:
+                return
+        if all(x.is_real for x in self.args):
+            return False
+
+    def _eval_is_extended_positive(self):
+        """Return True if self is positive, False if not, and None if it
+        cannot be determined.
+
+        Explanation
+        ===========
+
+        This algorithm is non-recursive and works by keeping track of the
+        sign which changes when a negative or nonpositive is encountered.
+        Whether a nonpositive or nonnegative is seen is also tracked since
+        the presence of these makes it impossible to return True, but
+        possible to return False if the end result is nonpositive. e.g.
+
+            pos * neg * nonpositive -> pos or zero -> None is returned
+            pos * neg * nonnegative -> neg or zero -> False is returned
+        """
+        return self._eval_pos_neg(1)
+
+    def _eval_pos_neg(self, sign):
+        saw_NON = saw_NOT = False
+        for t in self.args:
+            if t.is_extended_positive:
+                continue
+            elif t.is_extended_negative:
+                sign = -sign
+            elif t.is_zero:
+                if all(a.is_finite for a in self.args):
+                    return False
+                return
+            elif t.is_extended_nonpositive:
+                sign = -sign
+                saw_NON = True
+            elif t.is_extended_nonnegative:
+                saw_NON = True
+            # FIXME: is_positive/is_negative is False doesn't take account of
+            # Symbol('x', infinite=True, extended_real=True) which has
+            # e.g. is_positive is False but has uncertain sign.
+            elif t.is_positive is False:
+                sign = -sign
+                if saw_NOT:
+                    return
+                saw_NOT = True
+            elif t.is_negative is False:
+                if saw_NOT:
+                    return
+                saw_NOT = True
+            else:
+                return
+        if sign == 1 and saw_NON is False and saw_NOT is False:
+            return True
+        if sign < 0:
+            return False
+
+    def _eval_is_extended_negative(self):
+        return self._eval_pos_neg(-1)
+
+    def _eval_is_odd(self):
+        is_integer = self._eval_is_integer()
+        if is_integer is not True:
+            return is_integer
+
+        from sympy.simplify.radsimp import fraction
+        n, d = fraction(self)
+        if d.is_Integer and d.is_even:
+            # if minimal power of 2 in num vs den is
+            # positive then we have an even number
+            if (Add(*[i.as_base_exp()[1] for i in
+                    Mul.make_args(n) if i.is_even]) - trailing(d.p)
+                    ).is_positive:
+                return False
+            return
+        r, acc = True, 1
+        for t in self.args:
+            if abs(t) is S.One:
+                continue
+            if t.is_even:
+                return False
+            if r is False:
+                pass
+            elif acc != 1 and (acc + t).is_odd:
+                r = False
+            elif t.is_even is None:
+                r = None
+            acc = t
+        return r
+
+    def _eval_is_even(self):
+        from sympy.simplify.radsimp import fraction
+        n, d = fraction(self)
+        if n.is_Integer and n.is_even:
+            # if minimal power of 2 in den vs num is not
+            # negative then this is not an integer and
+            # can't be even
+            if (Add(*[i.as_base_exp()[1] for i in
+                    Mul.make_args(d) if i.is_even]) - trailing(n.p)
+                    ).is_nonnegative:
+                return False
+
+    def _eval_is_composite(self):
+        """
+        Here we count the number of arguments that have a minimum value
+        greater than two.
+        If there are more than one of such a symbol then the result is composite.
+        Else, the result cannot be determined.
+        """
+        number_of_args = 0 # count of symbols with minimum value greater than one
+        for arg in self.args:
+            if not (arg.is_integer and arg.is_positive):
+                return None
+            if (arg-1).is_positive:
+                number_of_args += 1
+
+        if number_of_args > 1:
+            return True
+
+    def _eval_subs(self, old, new):
+        from sympy.functions.elementary.complexes import sign
+        from sympy.ntheory.factor_ import multiplicity
+        from sympy.simplify.powsimp import powdenest
+        from sympy.simplify.radsimp import fraction
+
+        if not old.is_Mul:
+            return None
+
+        # try keep replacement literal so -2*x doesn't replace 4*x
+        if old.args[0].is_Number and old.args[0] < 0:
+            if self.args[0].is_Number:
+                if self.args[0] < 0:
+                    return self._subs(-old, -new)
+                return None
+
+        def base_exp(a):
+            # if I and -1 are in a Mul, they get both end up with
+            # a -1 base (see issue 6421); all we want here are the
+            # true Pow or exp separated into base and exponent
+            from sympy.functions.elementary.exponential import exp
+            if a.is_Pow or isinstance(a, exp):
+                return a.as_base_exp()
+            return a, S.One
+
+        def breakup(eq):
+            """break up powers of eq when treated as a Mul:
+                   b**(Rational*e) -> b**e, Rational
+                commutatives come back as a dictionary {b**e: Rational}
+                noncommutatives come back as a list [(b**e, Rational)]
+            """
+
+            (c, nc) = (defaultdict(int), [])
+            for a in Mul.make_args(eq):
+                a = powdenest(a)
+                (b, e) = base_exp(a)
+                if e is not S.One:
+                    (co, _) = e.as_coeff_mul()
+                    b = Pow(b, e/co)
+                    e = co
+                if a.is_commutative:
+                    c[b] += e
+                else:
+                    nc.append([b, e])
+            return (c, nc)
+
+        def rejoin(b, co):
+            """
+            Put rational back with exponent; in general this is not ok, but
+            since we took it from the exponent for analysis, it's ok to put
+            it back.
+            """
+
+            (b, e) = base_exp(b)
+            return Pow(b, e*co)
+
+        def ndiv(a, b):
+            """if b divides a in an extractive way (like 1/4 divides 1/2
+            but not vice versa, and 2/5 does not divide 1/3) then return
+            the integer number of times it divides, else return 0.
+            """
+            if not b.q % a.q or not a.q % b.q:
+                return int(a/b)
+            return 0
+
+        # give Muls in the denominator a chance to be changed (see issue 5651)
+        # rv will be the default return value
+        rv = None
+        n, d = fraction(self)
+        self2 = self
+        if d is not S.One:
+            self2 = n._subs(old, new)/d._subs(old, new)
+            if not self2.is_Mul:
+                return self2._subs(old, new)
+            if self2 != self:
+                rv = self2
+
+        # Now continue with regular substitution.
+
+        # handle the leading coefficient and use it to decide if anything
+        # should even be started; we always know where to find the Rational
+        # so it's a quick test
+
+        co_self = self2.args[0]
+        co_old = old.args[0]
+        co_xmul = None
+        if co_old.is_Rational and co_self.is_Rational:
+            # if coeffs are the same there will be no updating to do
+            # below after breakup() step; so skip (and keep co_xmul=None)
+            if co_old != co_self:
+                co_xmul = co_self.extract_multiplicatively(co_old)
+        elif co_old.is_Rational:
+            return rv
+
+        # break self and old into factors
+
+        (c, nc) = breakup(self2)
+        (old_c, old_nc) = breakup(old)
+
+        # update the coefficients if we had an extraction
+        # e.g. if co_self were 2*(3/35*x)**2 and co_old = 3/5
+        # then co_self in c is replaced by (3/5)**2 and co_residual
+        # is 2*(1/7)**2
+
+        if co_xmul and co_xmul.is_Rational and abs(co_old) != 1:
+            mult = S(multiplicity(abs(co_old), co_self))
+            c.pop(co_self)
+            if co_old in c:
+                c[co_old] += mult
+            else:
+                c[co_old] = mult
+            co_residual = co_self/co_old**mult
+        else:
+            co_residual = 1
+
+        # do quick tests to see if we can't succeed
+
+        ok = True
+        if len(old_nc) > len(nc):
+            # more non-commutative terms
+            ok = False
+        elif len(old_c) > len(c):
+            # more commutative terms
+            ok = False
+        elif {i[0] for i in old_nc}.difference({i[0] for i in nc}):
+            # unmatched non-commutative bases
+            ok = False
+        elif set(old_c).difference(set(c)):
+            # unmatched commutative terms
+            ok = False
+        elif any(sign(c[b]) != sign(old_c[b]) for b in old_c):
+            # differences in sign
+            ok = False
+        if not ok:
+            return rv
+
+        if not old_c:
+            cdid = None
+        else:
+            rat = []
+            for (b, old_e) in old_c.items():
+                c_e = c[b]
+                rat.append(ndiv(c_e, old_e))
+                if not rat[-1]:
+                    return rv
+            cdid = min(rat)
+
+        if not old_nc:
+            ncdid = None
+            for i in range(len(nc)):
+                nc[i] = rejoin(*nc[i])
+        else:
+            ncdid = 0  # number of nc replacements we did
+            take = len(old_nc)  # how much to look at each time
+            limit = cdid or S.Infinity  # max number that we can take
+            failed = []  # failed terms will need subs if other terms pass
+            i = 0
+            while limit and i + take <= len(nc):
+                hit = False
+
+                # the bases must be equivalent in succession, and
+                # the powers must be extractively compatible on the
+                # first and last factor but equal in between.
+
+                rat = []
+                for j in range(take):
+                    if nc[i + j][0] != old_nc[j][0]:
+                        break
+                    elif j == 0:
+                        rat.append(ndiv(nc[i + j][1], old_nc[j][1]))
+                    elif j == take - 1:
+                        rat.append(ndiv(nc[i + j][1], old_nc[j][1]))
+                    elif nc[i + j][1] != old_nc[j][1]:
+                        break
+                    else:
+                        rat.append(1)
+                    j += 1
+                else:
+                    ndo = min(rat)
+                    if ndo:
+                        if take == 1:
+                            if cdid:
+                                ndo = min(cdid, ndo)
+                            nc[i] = Pow(new, ndo)*rejoin(nc[i][0],
+                                    nc[i][1] - ndo*old_nc[0][1])
+                        else:
+                            ndo = 1
+
+                            # the left residual
+
+                            l = rejoin(nc[i][0], nc[i][1] - ndo*
+                                    old_nc[0][1])
+
+                            # eliminate all middle terms
+
+                            mid = new
+
+                            # the right residual (which may be the same as the middle if take == 2)
+
+                            ir = i + take - 1
+                            r = (nc[ir][0], nc[ir][1] - ndo*
+                                 old_nc[-1][1])
+                            if r[1]:
+                                if i + take < len(nc):
+                                    nc[i:i + take] = [l*mid, r]
+                                else:
+                                    r = rejoin(*r)
+                                    nc[i:i + take] = [l*mid*r]
+                            else:
+
+                                # there was nothing left on the right
+
+                                nc[i:i + take] = [l*mid]
+
+                        limit -= ndo
+                        ncdid += ndo
+                        hit = True
+                if not hit:
+
+                    # do the subs on this failing factor
+
+                    failed.append(i)
+                i += 1
+            else:
+
+                if not ncdid:
+                    return rv
+
+                # although we didn't fail, certain nc terms may have
+                # failed so we rebuild them after attempting a partial
+                # subs on them
+
+                failed.extend(range(i, len(nc)))
+                for i in failed:
+                    nc[i] = rejoin(*nc[i]).subs(old, new)
+
+        # rebuild the expression
+
+        if cdid is None:
+            do = ncdid
+        elif ncdid is None:
+            do = cdid
+        else:
+            do = min(ncdid, cdid)
+
+        margs = []
+        for b in c:
+            if b in old_c:
+
+                # calculate the new exponent
+
+                e = c[b] - old_c[b]*do
+                margs.append(rejoin(b, e))
+            else:
+                margs.append(rejoin(b.subs(old, new), c[b]))
+        if cdid and not ncdid:
+
+            # in case we are replacing commutative with non-commutative,
+            # we want the new term to come at the front just like the
+            # rest of this routine
+
+            margs = [Pow(new, cdid)] + margs
+        return co_residual*self2.func(*margs)*self2.func(*nc)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from .function import PoleError
+        from sympy.functions.elementary.integers import ceiling
+        from sympy.series.order import Order
+
+        def coeff_exp(term, x):
+            lt = term.as_coeff_exponent(x)
+            if lt[0].has(x):
+                try:
+                    lt = term.leadterm(x)
+                except ValueError:
+                    return term, S.Zero
+            return lt
+
+        ords = []
+
+        try:
+            for t in self.args:
+                coeff, exp = t.leadterm(x)
+                if not coeff.has(x):
+                    ords.append((t, exp))
+                else:
+                    raise ValueError
+
+            n0 = sum(t[1] for t in ords if t[1].is_number)
+            facs = []
+            for t, m in ords:
+                n1 = ceiling(n - n0 + (m if m.is_number else 0))
+                s = t.nseries(x, n=n1, logx=logx, cdir=cdir)
+                ns = s.getn()
+                if ns is not None:
+                    if ns < n1:  # less than expected
+                        n -= n1 - ns    # reduce n
+                facs.append(s)
+
+        except (ValueError, NotImplementedError, TypeError, PoleError):
+            # XXX: Catching so many generic exceptions around a large block of
+            # code will mask bugs. Whatever purpose catching these exceptions
+            # serves should be handled in a different way.
+            n0 = sympify(sum(t[1] for t in ords if t[1].is_number))
+            if n0.is_nonnegative:
+                n0 = S.Zero
+            facs = [t.nseries(x, n=ceiling(n-n0), logx=logx, cdir=cdir) for t in self.args]
+            from sympy.simplify.powsimp import powsimp
+            res = powsimp(self.func(*facs).expand(), combine='exp', deep=True)
+            if res.has(Order):
+                res += Order(x**n, x)
+            return res
+
+        res = S.Zero
+        ords2 = [Add.make_args(factor) for factor in facs]
+
+        for fac in product(*ords2):
+            ords3 = [coeff_exp(term, x) for term in fac]
+            coeffs, powers = zip(*ords3)
+            power = sum(powers)
+            if (power - n).is_negative:
+                res += Mul(*coeffs)*(x**power)
+
+        def max_degree(e, x):
+            if e is x:
+                return S.One
+            if e.is_Atom:
+                return S.Zero
+            if e.is_Add:
+                return max(max_degree(a, x) for a in e.args)
+            if e.is_Mul:
+                return Add(*[max_degree(a, x) for a in e.args])
+            if e.is_Pow:
+                return max_degree(e.base, x)*e.exp
+            return S.Zero
+
+        if self.is_polynomial(x):
+            from sympy.polys.polyerrors import PolynomialError
+            from sympy.polys.polytools import degree
+            try:
+                if max_degree(self, x) >= n or degree(self, x) != degree(res, x):
+                    res += Order(x**n, x)
+            except PolynomialError:
+                pass
+            else:
+                return res
+
+        if res != self:
+            if (self - res).subs(x, 0) == S.Zero and n > 0:
+                lt = self._eval_as_leading_term(x, logx=logx, cdir=cdir)
+                if lt == S.Zero:
+                    return res
+            res += Order(x**n, x)
+        return res
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        return self.func(*[t.as_leading_term(x, logx=logx, cdir=cdir) for t in self.args])
+
+    def _eval_conjugate(self):
+        return self.func(*[t.conjugate() for t in self.args])
+
+    def _eval_transpose(self):
+        return self.func(*[t.transpose() for t in self.args[::-1]])
+
+    def _eval_adjoint(self):
+        return self.func(*[t.adjoint() for t in self.args[::-1]])
+
+    def as_content_primitive(self, radical=False, clear=True):
+        """Return the tuple (R, self/R) where R is the positive Rational
+        extracted from self.
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt
+        >>> (-3*sqrt(2)*(2 - 2*sqrt(2))).as_content_primitive()
+        (6, -sqrt(2)*(1 - sqrt(2)))
+
+        See docstring of Expr.as_content_primitive for more examples.
+        """
+
+        coef = S.One
+        args = []
+        for a in self.args:
+            c, p = a.as_content_primitive(radical=radical, clear=clear)
+            coef *= c
+            if p is not S.One:
+                args.append(p)
+        # don't use self._from_args here to reconstruct args
+        # since there may be identical args now that should be combined
+        # e.g. (2+2*x)*(3+3*x) should be (6, (1 + x)**2) not (6, (1+x)*(1+x))
+        return coef, self.func(*args)
+
+    def as_ordered_factors(self, order=None):
+        """Transform an expression into an ordered list of factors.
+
+        Examples
+        ========
+
+        >>> from sympy import sin, cos
+        >>> from sympy.abc import x, y
+
+        >>> (2*x*y*sin(x)*cos(x)).as_ordered_factors()
+        [2, x, y, sin(x), cos(x)]
+
+        """
+        cpart, ncpart = self.args_cnc()
+        cpart.sort(key=lambda expr: expr.sort_key(order=order))
+        return cpart + ncpart
+
+    @property
+    def _sorted_args(self):
+        return tuple(self.as_ordered_factors())
+
+mul = AssocOpDispatcher('mul')
+
+
+def prod(a, start=1):
+    """Return product of elements of a. Start with int 1 so if only
+       ints are included then an int result is returned.
+
+    Examples
+    ========
+
+    >>> from sympy import prod, S
+    >>> prod(range(3))
+    0
+    >>> type(_) is int
+    True
+    >>> prod([S(2), 3])
+    6
+    >>> _.is_Integer
+    True
+
+    You can start the product at something other than 1:
+
+    >>> prod([1, 2], 3)
+    6
+
+    """
+    return reduce(operator.mul, a, start)
+
+
+def _keep_coeff(coeff, factors, clear=True, sign=False):
+    """Return ``coeff*factors`` unevaluated if necessary.
+
+    If ``clear`` is False, do not keep the coefficient as a factor
+    if it can be distributed on a single factor such that one or
+    more terms will still have integer coefficients.
+
+    If ``sign`` is True, allow a coefficient of -1 to remain factored out.
+
+    Examples
+    ========
+
+    >>> from sympy.core.mul import _keep_coeff
+    >>> from sympy.abc import x, y
+    >>> from sympy import S
+
+    >>> _keep_coeff(S.Half, x + 2)
+    (x + 2)/2
+    >>> _keep_coeff(S.Half, x + 2, clear=False)
+    x/2 + 1
+    >>> _keep_coeff(S.Half, (x + 2)*y, clear=False)
+    y*(x + 2)/2
+    >>> _keep_coeff(S(-1), x + y)
+    -x - y
+    >>> _keep_coeff(S(-1), x + y, sign=True)
+    -(x + y)
+    """
+    if not coeff.is_Number:
+        if factors.is_Number:
+            factors, coeff = coeff, factors
+        else:
+            return coeff*factors
+    if factors is S.One:
+        return coeff
+    if coeff is S.One:
+        return factors
+    elif coeff is S.NegativeOne and not sign:
+        return -factors
+    elif factors.is_Add:
+        if not clear and coeff.is_Rational and coeff.q != 1:
+            args = [i.as_coeff_Mul() for i in factors.args]
+            args = [(_keep_coeff(c, coeff), m) for c, m in args]
+            if any(c.is_Integer for c, _ in args):
+                return Add._from_args([Mul._from_args(
+                    i[1:] if i[0] == 1 else i) for i in args])
+        return Mul(coeff, factors, evaluate=False)
+    elif factors.is_Mul:
+        margs = list(factors.args)
+        if margs[0].is_Number:
+            margs[0] *= coeff
+            if margs[0] == 1:
+                margs.pop(0)
+        else:
+            margs.insert(0, coeff)
+        return Mul._from_args(margs)
+    else:
+        m = coeff*factors
+        if m.is_Number and not factors.is_Number:
+            m = Mul._from_args((coeff, factors))
+        return m
+
+def expand_2arg(e):
+    def do(e):
+        if e.is_Mul:
+            c, r = e.as_coeff_Mul()
+            if c.is_Number and r.is_Add:
+                return _unevaluated_Add(*[c*ri for ri in r.args])
+        return e
+    return bottom_up(e, do)
+
+
+from .numbers import Rational
+from .power import Pow
+from .add import Add, _unevaluated_Add
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/multidimensional.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/multidimensional.py
new file mode 100644
index 0000000000000000000000000000000000000000..133e0ab6cba6a87c627feb6f6034a6daed1128c5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/multidimensional.py
@@ -0,0 +1,131 @@
+"""
+Provides functionality for multidimensional usage of scalar-functions.
+
+Read the vectorize docstring for more details.
+"""
+
+from functools import wraps
+
+
+def apply_on_element(f, args, kwargs, n):
+    """
+    Returns a structure with the same dimension as the specified argument,
+    where each basic element is replaced by the function f applied on it. All
+    other arguments stay the same.
+    """
+    # Get the specified argument.
+    if isinstance(n, int):
+        structure = args[n]
+        is_arg = True
+    elif isinstance(n, str):
+        structure = kwargs[n]
+        is_arg = False
+
+    # Define reduced function that is only dependent on the specified argument.
+    def f_reduced(x):
+        if hasattr(x, "__iter__"):
+            return list(map(f_reduced, x))
+        else:
+            if is_arg:
+                args[n] = x
+            else:
+                kwargs[n] = x
+            return f(*args, **kwargs)
+
+    # f_reduced will call itself recursively so that in the end f is applied to
+    # all basic elements.
+    return list(map(f_reduced, structure))
+
+
+def iter_copy(structure):
+    """
+    Returns a copy of an iterable object (also copying all embedded iterables).
+    """
+    return [iter_copy(i) if hasattr(i, "__iter__") else i for i in structure]
+
+
+def structure_copy(structure):
+    """
+    Returns a copy of the given structure (numpy-array, list, iterable, ..).
+    """
+    if hasattr(structure, "copy"):
+        return structure.copy()
+    return iter_copy(structure)
+
+
+class vectorize:
+    """
+    Generalizes a function taking scalars to accept multidimensional arguments.
+
+    Examples
+    ========
+
+    >>> from sympy import vectorize, diff, sin, symbols, Function
+    >>> x, y, z = symbols('x y z')
+    >>> f, g, h = list(map(Function, 'fgh'))
+
+    >>> @vectorize(0)
+    ... def vsin(x):
+    ...     return sin(x)
+
+    >>> vsin([1, x, y])
+    [sin(1), sin(x), sin(y)]
+
+    >>> @vectorize(0, 1)
+    ... def vdiff(f, y):
+    ...     return diff(f, y)
+
+    >>> vdiff([f(x, y, z), g(x, y, z), h(x, y, z)], [x, y, z])
+    [[Derivative(f(x, y, z), x), Derivative(f(x, y, z), y), Derivative(f(x, y, z), z)], [Derivative(g(x, y, z), x), Derivative(g(x, y, z), y), Derivative(g(x, y, z), z)], [Derivative(h(x, y, z), x), Derivative(h(x, y, z), y), Derivative(h(x, y, z), z)]]
+    """
+    def __init__(self, *mdargs):
+        """
+        The given numbers and strings characterize the arguments that will be
+        treated as data structures, where the decorated function will be applied
+        to every single element.
+        If no argument is given, everything is treated multidimensional.
+        """
+        for a in mdargs:
+            if not isinstance(a, (int, str)):
+                raise TypeError("a is of invalid type")
+        self.mdargs = mdargs
+
+    def __call__(self, f):
+        """
+        Returns a wrapper for the one-dimensional function that can handle
+        multidimensional arguments.
+        """
+        @wraps(f)
+        def wrapper(*args, **kwargs):
+            # Get arguments that should be treated multidimensional
+            if self.mdargs:
+                mdargs = self.mdargs
+            else:
+                mdargs = range(len(args)) + kwargs.keys()
+
+            arglength = len(args)
+
+            for n in mdargs:
+                if isinstance(n, int):
+                    if n >= arglength:
+                        continue
+                    entry = args[n]
+                    is_arg = True
+                elif isinstance(n, str):
+                    try:
+                        entry = kwargs[n]
+                    except KeyError:
+                        continue
+                    is_arg = False
+                if hasattr(entry, "__iter__"):
+                    # Create now a copy of the given array and manipulate then
+                    # the entries directly.
+                    if is_arg:
+                        args = list(args)
+                        args[n] = structure_copy(entry)
+                    else:
+                        kwargs[n] = structure_copy(entry)
+                    result = apply_on_element(wrapper, args, kwargs, n)
+                    return result
+            return f(*args, **kwargs)
+        return wrapper
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..9fa13fbb96aa25a8e60e048c0147a5e660804ccc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/numbers.py
@@ -0,0 +1,4482 @@
+from __future__ import annotations
+
+from typing import overload
+
+import numbers
+import decimal
+import fractions
+import math
+
+from .containers import Tuple
+from .sympify import (SympifyError, _sympy_converter, sympify, _convert_numpy_types,
+              _sympify, _is_numpy_instance)
+from .singleton import S, Singleton
+from .basic import Basic
+from .expr import Expr, AtomicExpr
+from .evalf import pure_complex
+from .cache import cacheit, clear_cache
+from .decorators import _sympifyit
+from .intfunc import num_digits, igcd, ilcm, mod_inverse, integer_nthroot
+from .logic import fuzzy_not
+from .kind import NumberKind
+from .sorting import ordered
+from sympy.external.gmpy import SYMPY_INTS, gmpy, flint
+from sympy.multipledispatch import dispatch
+import mpmath
+import mpmath.libmp as mlib
+from mpmath.libmp import bitcount, round_nearest as rnd
+from mpmath.libmp.backend import MPZ
+from mpmath.libmp import mpf_pow, mpf_pi, mpf_e, phi_fixed
+from mpmath.ctx_mp_python import mpnumeric
+from mpmath.libmp.libmpf import (
+    finf as _mpf_inf, fninf as _mpf_ninf,
+    fnan as _mpf_nan, fzero, _normalize as mpf_normalize,
+    prec_to_dps, dps_to_prec)
+from sympy.utilities.misc import debug
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from .parameters import global_parameters
+
+_LOG2 = math.log(2)
+
+
+def comp(z1, z2, tol=None):
+    r"""Return a bool indicating whether the error between z1 and z2
+    is $\le$ ``tol``.
+
+    Examples
+    ========
+
+    If ``tol`` is ``None`` then ``True`` will be returned if
+    :math:`|z1 - z2|\times 10^p \le 5` where $p$ is minimum value of the
+    decimal precision of each value.
+
+    >>> from sympy import comp, pi
+    >>> pi4 = pi.n(4); pi4
+    3.142
+    >>> comp(_, 3.142)
+    True
+    >>> comp(pi4, 3.141)
+    False
+    >>> comp(pi4, 3.143)
+    False
+
+    A comparison of strings will be made
+    if ``z1`` is a Number and ``z2`` is a string or ``tol`` is ''.
+
+    >>> comp(pi4, 3.1415)
+    True
+    >>> comp(pi4, 3.1415, '')
+    False
+
+    When ``tol`` is provided and $z2$ is non-zero and
+    :math:`|z1| > 1` the error is normalized by :math:`|z1|`:
+
+    >>> abs(pi4 - 3.14)/pi4
+    0.000509791731426756
+    >>> comp(pi4, 3.14, .001)  # difference less than 0.1%
+    True
+    >>> comp(pi4, 3.14, .0005)  # difference less than 0.1%
+    False
+
+    When :math:`|z1| \le 1` the absolute error is used:
+
+    >>> 1/pi4
+    0.3183
+    >>> abs(1/pi4 - 0.3183)/(1/pi4)
+    3.07371499106316e-5
+    >>> abs(1/pi4 - 0.3183)
+    9.78393554684764e-6
+    >>> comp(1/pi4, 0.3183, 1e-5)
+    True
+
+    To see if the absolute error between ``z1`` and ``z2`` is less
+    than or equal to ``tol``, call this as ``comp(z1 - z2, 0, tol)``
+    or ``comp(z1 - z2, tol=tol)``:
+
+    >>> abs(pi4 - 3.14)
+    0.00160156249999988
+    >>> comp(pi4 - 3.14, 0, .002)
+    True
+    >>> comp(pi4 - 3.14, 0, .001)
+    False
+    """
+    if isinstance(z2, str):
+        if not pure_complex(z1, or_real=True):
+            raise ValueError('when z2 is a str z1 must be a Number')
+        return str(z1) == z2
+    if not z1:
+        z1, z2 = z2, z1
+    if not z1:
+        return True
+    if not tol:
+        a, b = z1, z2
+        if tol == '':
+            return str(a) == str(b)
+        if tol is None:
+            a, b = sympify(a), sympify(b)
+            if not all(i.is_number for i in (a, b)):
+                raise ValueError('expecting 2 numbers')
+            fa = a.atoms(Float)
+            fb = b.atoms(Float)
+            if not fa and not fb:
+                # no floats -- compare exactly
+                return a == b
+            # get a to be pure_complex
+            for _ in range(2):
+                ca = pure_complex(a, or_real=True)
+                if not ca:
+                    if fa:
+                        a = a.n(prec_to_dps(min(i._prec for i in fa)))
+                        ca = pure_complex(a, or_real=True)
+                        break
+                    else:
+                        fa, fb = fb, fa
+                        a, b = b, a
+            cb = pure_complex(b)
+            if not cb and fb:
+                b = b.n(prec_to_dps(min(i._prec for i in fb)))
+                cb = pure_complex(b, or_real=True)
+            if ca and cb and (ca[1] or cb[1]):
+                return all(comp(i, j) for i, j in zip(ca, cb))
+            tol = 10**prec_to_dps(min(a._prec, getattr(b, '_prec', a._prec)))
+            return int(abs(a - b)*tol) <= 5
+    diff = abs(z1 - z2)
+    az1 = abs(z1)
+    if z2 and az1 > 1:
+        return diff/az1 <= tol
+    else:
+        return diff <= tol
+
+
+def mpf_norm(mpf, prec):
+    """Return the mpf tuple normalized appropriately for the indicated
+    precision after doing a check to see if zero should be returned or
+    not when the mantissa is 0. ``mpf_normlize`` always assumes that this
+    is zero, but it may not be since the mantissa for mpf's values "+inf",
+    "-inf" and "nan" have a mantissa of zero, too.
+
+    Note: this is not intended to validate a given mpf tuple, so sending
+    mpf tuples that were not created by mpmath may produce bad results. This
+    is only a wrapper to ``mpf_normalize`` which provides the check for non-
+    zero mpfs that have a 0 for the mantissa.
+    """
+    sign, man, expt, bc = mpf
+    if not man:
+        # hack for mpf_normalize which does not do this;
+        # it assumes that if man is zero the result is 0
+        # (see issue 6639)
+        if not bc:
+            return fzero
+        else:
+            # don't change anything; this should already
+            # be a well formed mpf tuple
+            return mpf
+
+    # Necessary if mpmath is using the gmpy backend
+    from mpmath.libmp.backend import MPZ
+    rv = mpf_normalize(sign, MPZ(man), expt, bc, prec, rnd)
+    return rv
+
+# TODO: we should use the warnings module
+_errdict = {"divide": False}
+
+
+def seterr(divide=False):
+    """
+    Should SymPy raise an exception on 0/0 or return a nan?
+
+    divide == True .... raise an exception
+    divide == False ... return nan
+    """
+    if _errdict["divide"] != divide:
+        clear_cache()
+        _errdict["divide"] = divide
+
+
+def _as_integer_ratio(p):
+    neg_pow, man, expt, _ = getattr(p, '_mpf_', mpmath.mpf(p)._mpf_)
+    p = [1, -1][neg_pow % 2]*man
+    if expt < 0:
+        q = 2**-expt
+    else:
+        q = 1
+        p *= 2**expt
+    return int(p), int(q)
+
+
+def _decimal_to_Rational_prec(dec):
+    """Convert an ordinary decimal instance to a Rational."""
+    if not dec.is_finite():
+        raise TypeError("dec must be finite, got %s." % dec)
+    s, d, e = dec.as_tuple()
+    prec = len(d)
+    if e >= 0:  # it's an integer
+        rv = Integer(int(dec))
+    else:
+        s = (-1)**s
+        d = sum(di*10**i for i, di in enumerate(reversed(d)))
+        rv = Rational(s*d, 10**-e)
+    return rv, prec
+
+_dig = str.maketrans(dict.fromkeys('1234567890'))
+
+def _literal_float(s):
+    """return True if s is space-trimmed number literal else False
+
+    Python allows underscore as digit separators: there must be a
+    digit on each side. So neither a leading underscore nor a
+    double underscore are valid as part of a number. A number does
+    not have to precede the decimal point, but there must be a
+    digit before the optional "e" or "E" that begins the signs
+    exponent of the number which must be an integer, perhaps with
+    underscore separators.
+
+    SymPy allows space as a separator; if the calling routine replaces
+    them with underscores then the same semantics will be enforced
+    for them as for underscores: there can only be 1 *between* digits.
+
+    We don't check for error from float(s) because we don't know
+    whether s is malicious or not. A regex for this could maybe
+    be written but will it be understood by most who read it?
+    """
+    # mantissa and exponent
+    parts = s.split('e')
+    if len(parts) > 2:
+        return False
+    if len(parts) == 2:
+        m, e = parts
+        if e.startswith(tuple('+-')):
+            e = e[1:]
+        if not e:
+            return False
+    else:
+        m, e = s, '1'
+    # integer and fraction of mantissa
+    parts = m.split('.')
+    if len(parts) > 2:
+        return False
+    elif len(parts) == 2:
+        i, f = parts
+    else:
+        i, f = m, '1'
+    if not i and not f:
+        return False
+    if i and i[0] in '+-':
+        i = i[1:]
+    if not i:  # -.3e4 -> -0.3e4
+        i = '1'
+    f = f or '1'
+    # check that all groups contain only digits and are not null
+    for n in (i, f, e):
+        for g in n.split('_'):
+            if not g or g.translate(_dig):
+                return False
+    return True
+
+# (a,b) -> gcd(a,b)
+
+# TODO caching with decorator, but not to degrade performance
+
+
+class Number(AtomicExpr):
+    """Represents atomic numbers in SymPy.
+
+    Explanation
+    ===========
+
+    Floating point numbers are represented by the Float class.
+    Rational numbers (of any size) are represented by the Rational class.
+    Integer numbers (of any size) are represented by the Integer class.
+    Float and Rational are subclasses of Number; Integer is a subclass
+    of Rational.
+
+    For example, ``2/3`` is represented as ``Rational(2, 3)`` which is
+    a different object from the floating point number obtained with
+    Python division ``2/3``. Even for numbers that are exactly
+    represented in binary, there is a difference between how two forms,
+    such as ``Rational(1, 2)`` and ``Float(0.5)``, are used in SymPy.
+    The rational form is to be preferred in symbolic computations.
+
+    Other kinds of numbers, such as algebraic numbers ``sqrt(2)`` or
+    complex numbers ``3 + 4*I``, are not instances of Number class as
+    they are not atomic.
+
+    See Also
+    ========
+
+    Float, Integer, Rational
+    """
+    is_commutative = True
+    is_number = True
+    is_Number = True
+
+    __slots__ = ()
+
+    # Used to make max(x._prec, y._prec) return x._prec when only x is a float
+    _prec = -1
+
+    kind = NumberKind
+
+    def __new__(cls, *obj):
+        if len(obj) == 1:
+            obj = obj[0]
+
+        if isinstance(obj, Number):
+            return obj
+        if isinstance(obj, SYMPY_INTS):
+            return Integer(obj)
+        if isinstance(obj, tuple) and len(obj) == 2:
+            return Rational(*obj)
+        if isinstance(obj, (float, mpmath.mpf, decimal.Decimal)):
+            return Float(obj)
+        if isinstance(obj, str):
+            _obj = obj.lower()  # float('INF') == float('inf')
+            if _obj == 'nan':
+                return S.NaN
+            elif _obj == 'inf':
+                return S.Infinity
+            elif _obj == '+inf':
+                return S.Infinity
+            elif _obj == '-inf':
+                return S.NegativeInfinity
+            val = sympify(obj)
+            if isinstance(val, Number):
+                return val
+            else:
+                raise ValueError('String "%s" does not denote a Number' % obj)
+        msg = "expected str|int|long|float|Decimal|Number object but got %r"
+        raise TypeError(msg % type(obj).__name__)
+
+    def could_extract_minus_sign(self):
+        return bool(self.is_extended_negative)
+
+    def invert(self, other, *gens, **args):
+        from sympy.polys.polytools import invert
+        if getattr(other, 'is_number', True):
+            return mod_inverse(self, other)
+        return invert(self, other, *gens, **args)
+
+    def __divmod__(self, other):
+        from sympy.functions.elementary.complexes import sign
+
+        try:
+            other = Number(other)
+            if self.is_infinite or S.NaN in (self, other):
+                return (S.NaN, S.NaN)
+        except TypeError:
+            return NotImplemented
+        if not other:
+            raise ZeroDivisionError('modulo by zero')
+        if self.is_Integer and other.is_Integer:
+            return Tuple(*divmod(self.p, other.p))
+        elif isinstance(other, Float):
+            rat = self/Rational(other)
+        else:
+            rat = self/other
+        if other.is_finite:
+            w = int(rat) if rat >= 0 else int(rat) - 1
+            r = self - other*w
+            if r == Float(other):
+                w += 1
+                r = 0
+            if isinstance(self, Float) or isinstance(other, Float):
+                r = Float(r)  # in case w or r is 0
+        else:
+            w = 0 if not self or (sign(self) == sign(other)) else -1
+            r = other if w else self
+        return Tuple(w, r)
+
+    def __rdivmod__(self, other):
+        try:
+            other = Number(other)
+        except TypeError:
+            return NotImplemented
+        return divmod(other, self)
+
+    def _as_mpf_val(self, prec):
+        """Evaluation of mpf tuple accurate to at least prec bits."""
+        raise NotImplementedError('%s needs ._as_mpf_val() method' %
+            (self.__class__.__name__))
+
+    def _eval_evalf(self, prec):
+        return Float._new(self._as_mpf_val(prec), prec)
+
+    def _as_mpf_op(self, prec):
+        prec = max(prec, self._prec)
+        return self._as_mpf_val(prec), prec
+
+    def __float__(self):
+        return mlib.to_float(self._as_mpf_val(53))
+
+    def floor(self):
+        raise NotImplementedError('%s needs .floor() method' %
+            (self.__class__.__name__))
+
+    def ceiling(self):
+        raise NotImplementedError('%s needs .ceiling() method' %
+            (self.__class__.__name__))
+
+    def __floor__(self):
+        return self.floor()
+
+    def __ceil__(self):
+        return self.ceiling()
+
+    def _eval_conjugate(self):
+        return self
+
+    def _eval_order(self, *symbols):
+        from sympy.series.order import Order
+        # Order(5, x, y) -> Order(1,x,y)
+        return Order(S.One, *symbols)
+
+    def _eval_subs(self, old, new):
+        if old == -self:
+            return -new
+        return self  # there is no other possibility
+
+    @classmethod
+    def class_key(cls):
+        return 1, 0, 'Number'
+
+    @cacheit
+    def sort_key(self, order=None):
+        return self.class_key(), (0, ()), (), self
+
+    def __neg__(self) -> Number:
+        raise NotImplementedError
+
+    @overload
+    def __add__(self, other: Number | int | float) -> Number: ...
+    @overload
+    def __add__(self, other: Expr) -> Expr: ...
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other) -> Expr:
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other is S.NaN:
+                return S.NaN
+            elif other is S.Infinity:
+                return S.Infinity
+            elif other is S.NegativeInfinity:
+                return S.NegativeInfinity
+        return AtomicExpr.__add__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other is S.NaN:
+                return S.NaN
+            elif other is S.Infinity:
+                return S.NegativeInfinity
+            elif other is S.NegativeInfinity:
+                return S.Infinity
+        return AtomicExpr.__sub__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other is S.NaN:
+                return S.NaN
+            elif other is S.Infinity:
+                if self.is_zero:
+                    return S.NaN
+                elif self.is_positive:
+                    return S.Infinity
+                else:
+                    return S.NegativeInfinity
+            elif other is S.NegativeInfinity:
+                if self.is_zero:
+                    return S.NaN
+                elif self.is_positive:
+                    return S.NegativeInfinity
+                else:
+                    return S.Infinity
+        elif isinstance(other, Tuple):
+            return NotImplemented
+        return AtomicExpr.__mul__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other is S.NaN:
+                return S.NaN
+            elif other in (S.Infinity, S.NegativeInfinity):
+                return S.Zero
+        return AtomicExpr.__truediv__(self, other)
+
+    def __eq__(self, other):
+        raise NotImplementedError('%s needs .__eq__() method' %
+            (self.__class__.__name__))
+
+    def __ne__(self, other):
+        raise NotImplementedError('%s needs .__ne__() method' %
+            (self.__class__.__name__))
+
+    def __lt__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            raise TypeError("Invalid comparison %s < %s" % (self, other))
+        raise NotImplementedError('%s needs .__lt__() method' %
+            (self.__class__.__name__))
+
+    def __le__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            raise TypeError("Invalid comparison %s <= %s" % (self, other))
+        raise NotImplementedError('%s needs .__le__() method' %
+            (self.__class__.__name__))
+
+    def __gt__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            raise TypeError("Invalid comparison %s > %s" % (self, other))
+        return _sympify(other).__lt__(self)
+
+    def __ge__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            raise TypeError("Invalid comparison %s >= %s" % (self, other))
+        return _sympify(other).__le__(self)
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def is_constant(self, *wrt, **flags):
+        return True
+
+    def as_coeff_mul(self, *deps, rational=True, **kwargs):
+        # a -> c*t
+        if self.is_Rational or not rational:
+            return self, ()
+        elif self.is_negative:
+            return S.NegativeOne, (-self,)
+        return S.One, (self,)
+
+    def as_coeff_add(self, *deps):
+        # a -> c + t
+        if self.is_Rational:
+            return self, ()
+        return S.Zero, (self,)
+
+    def as_coeff_Mul(self, rational=False):
+        """Efficiently extract the coefficient of a product."""
+        if not rational:
+            return self, S.One
+        return S.One, self
+
+    def as_coeff_Add(self, rational=False):
+        """Efficiently extract the coefficient of a summation."""
+        if not rational:
+            return self, S.Zero
+        return S.Zero, self
+
+    def gcd(self, other):
+        """Compute GCD of `self` and `other`. """
+        from sympy.polys.polytools import gcd
+        return gcd(self, other)
+
+    def lcm(self, other):
+        """Compute LCM of `self` and `other`. """
+        from sympy.polys.polytools import lcm
+        return lcm(self, other)
+
+    def cofactors(self, other):
+        """Compute GCD and cofactors of `self` and `other`. """
+        from sympy.polys.polytools import cofactors
+        return cofactors(self, other)
+
+
+class Float(Number):
+    """Represent a floating-point number of arbitrary precision.
+
+    Examples
+    ========
+
+    >>> from sympy import Float
+    >>> Float(3.5)
+    3.50000000000000
+    >>> Float(3)
+    3.00000000000000
+
+    Creating Floats from strings (and Python ``int`` and ``long``
+    types) will give a minimum precision of 15 digits, but the
+    precision will automatically increase to capture all digits
+    entered.
+
+    >>> Float(1)
+    1.00000000000000
+    >>> Float(10**20)
+    100000000000000000000.
+    >>> Float('1e20')
+    100000000000000000000.
+
+    However, *floating-point* numbers (Python ``float`` types) retain
+    only 15 digits of precision:
+
+    >>> Float(1e20)
+    1.00000000000000e+20
+    >>> Float(1.23456789123456789)
+    1.23456789123457
+
+    It may be preferable to enter high-precision decimal numbers
+    as strings:
+
+    >>> Float('1.23456789123456789')
+    1.23456789123456789
+
+    The desired number of digits can also be specified:
+
+    >>> Float('1e-3', 3)
+    0.00100
+    >>> Float(100, 4)
+    100.0
+
+    Float can automatically count significant figures if a null string
+    is sent for the precision; spaces or underscores are also allowed. (Auto-
+    counting is only allowed for strings, ints and longs).
+
+    >>> Float('123 456 789.123_456', '')
+    123456789.123456
+    >>> Float('12e-3', '')
+    0.012
+    >>> Float(3, '')
+    3.
+
+    If a number is written in scientific notation, only the digits before the
+    exponent are considered significant if a decimal appears, otherwise the
+    "e" signifies only how to move the decimal:
+
+    >>> Float('60.e2', '')  # 2 digits significant
+    6.0e+3
+    >>> Float('60e2', '')  # 4 digits significant
+    6000.
+    >>> Float('600e-2', '')  # 3 digits significant
+    6.00
+
+    Notes
+    =====
+
+    Floats are inexact by their nature unless their value is a binary-exact
+    value.
+
+    >>> approx, exact = Float(.1, 1), Float(.125, 1)
+
+    For calculation purposes, evalf needs to be able to change the precision
+    but this will not increase the accuracy of the inexact value. The
+    following is the most accurate 5-digit approximation of a value of 0.1
+    that had only 1 digit of precision:
+
+    >>> approx.evalf(5)
+    0.099609
+
+    By contrast, 0.125 is exact in binary (as it is in base 10) and so it
+    can be passed to Float or evalf to obtain an arbitrary precision with
+    matching accuracy:
+
+    >>> Float(exact, 5)
+    0.12500
+    >>> exact.evalf(20)
+    0.12500000000000000000
+
+    Trying to make a high-precision Float from a float is not disallowed,
+    but one must keep in mind that the *underlying float* (not the apparent
+    decimal value) is being obtained with high precision. For example, 0.3
+    does not have a finite binary representation. The closest rational is
+    the fraction 5404319552844595/2**54. So if you try to obtain a Float of
+    0.3 to 20 digits of precision you will not see the same thing as 0.3
+    followed by 19 zeros:
+
+    >>> Float(0.3, 20)
+    0.29999999999999998890
+
+    If you want a 20-digit value of the decimal 0.3 (not the floating point
+    approximation of 0.3) you should send the 0.3 as a string. The underlying
+    representation is still binary but a higher precision than Python's float
+    is used:
+
+    >>> Float('0.3', 20)
+    0.30000000000000000000
+
+    Although you can increase the precision of an existing Float using Float
+    it will not increase the accuracy -- the underlying value is not changed:
+
+    >>> def show(f): # binary rep of Float
+    ...     from sympy import Mul, Pow
+    ...     s, m, e, b = f._mpf_
+    ...     v = Mul(int(m), Pow(2, int(e), evaluate=False), evaluate=False)
+    ...     print('%s at prec=%s' % (v, f._prec))
+    ...
+    >>> t = Float('0.3', 3)
+    >>> show(t)
+    4915/2**14 at prec=13
+    >>> show(Float(t, 20)) # higher prec, not higher accuracy
+    4915/2**14 at prec=70
+    >>> show(Float(t, 2)) # lower prec
+    307/2**10 at prec=10
+
+    The same thing happens when evalf is used on a Float:
+
+    >>> show(t.evalf(20))
+    4915/2**14 at prec=70
+    >>> show(t.evalf(2))
+    307/2**10 at prec=10
+
+    Finally, Floats can be instantiated with an mpf tuple (n, c, p) to
+    produce the number (-1)**n*c*2**p:
+
+    >>> n, c, p = 1, 5, 0
+    >>> (-1)**n*c*2**p
+    -5
+    >>> Float((1, 5, 0))
+    -5.00000000000000
+
+    An actual mpf tuple also contains the number of bits in c as the last
+    element of the tuple:
+
+    >>> _._mpf_
+    (1, 5, 0, 3)
+
+    This is not needed for instantiation and is not the same thing as the
+    precision. The mpf tuple and the precision are two separate quantities
+    that Float tracks.
+
+    In SymPy, a Float is a number that can be computed with arbitrary
+    precision. Although floating point 'inf' and 'nan' are not such
+    numbers, Float can create these numbers:
+
+    >>> Float('-inf')
+    -oo
+    >>> _.is_Float
+    False
+
+    Zero in Float only has a single value. Values are not separate for
+    positive and negative zeroes.
+    """
+    __slots__ = ('_mpf_', '_prec')
+
+    _mpf_: tuple[int, int, int, int]
+
+    # A Float, though rational in form, does not behave like
+    # a rational in all Python expressions so we deal with
+    # exceptions (where we want to deal with the rational
+    # form of the Float as a rational) at the source rather
+    # than assigning a mathematically loaded category of 'rational'
+    is_rational = None
+    is_irrational = None
+    is_number = True
+
+    is_real = True
+    is_extended_real = True
+
+    is_Float = True
+
+    _remove_non_digits = str.maketrans(dict.fromkeys("-+_."))
+
+    def __new__(cls, num, dps=None, precision=None):
+        if dps is not None and precision is not None:
+            raise ValueError('Both decimal and binary precision supplied. '
+                             'Supply only one. ')
+
+        if isinstance(num, str):
+            _num = num = num.strip()  # Python ignores leading and trailing space
+            num = num.replace(' ', '_').lower()  # Float treats spaces as digit sep; E -> e
+            if num.startswith('.') and len(num) > 1:
+                num = '0' + num
+            elif num.startswith('-.') and len(num) > 2:
+                num = '-0.' + num[2:]
+            elif num in ('inf', '+inf'):
+                return S.Infinity
+            elif num == '-inf':
+                return S.NegativeInfinity
+            elif num == 'nan':
+                return S.NaN
+            elif not _literal_float(num):
+                raise ValueError('string-float not recognized: %s' % _num)
+        elif isinstance(num, float) and num == 0:
+            num = '0'
+        elif isinstance(num, float) and num == float('inf'):
+            return S.Infinity
+        elif isinstance(num, float) and num == float('-inf'):
+            return S.NegativeInfinity
+        elif isinstance(num, float) and math.isnan(num):
+            return S.NaN
+        elif isinstance(num, (SYMPY_INTS, Integer)):
+            num = str(num)
+        elif num is S.Infinity:
+            return num
+        elif num is S.NegativeInfinity:
+            return num
+        elif num is S.NaN:
+            return num
+        elif _is_numpy_instance(num):  # support for numpy datatypes
+            num = _convert_numpy_types(num)
+        elif isinstance(num, mpmath.mpf):
+            if precision is None:
+                if dps is None:
+                    precision = num.context.prec
+            num = num._mpf_
+
+        if dps is None and precision is None:
+            dps = 15
+            if isinstance(num, Float):
+                return num
+            if isinstance(num, str):
+                try:
+                    Num = decimal.Decimal(num)
+                except decimal.InvalidOperation:
+                    pass
+                else:
+                    isint = '.' not in num
+                    num, dps = _decimal_to_Rational_prec(Num)
+                    if num.is_Integer and isint:
+                        # 12e3 is shorthand for int, not float;
+                        # 12.e3 would be the float version
+                        dps = max(dps, num_digits(num))
+                    dps = max(15, dps)
+                    precision = dps_to_prec(dps)
+        elif precision == '' and dps is None or precision is None and dps == '':
+            if not isinstance(num, str):
+                raise ValueError('The null string can only be used when '
+                'the number to Float is passed as a string or an integer.')
+            try:
+                Num = decimal.Decimal(num)
+            except decimal.InvalidOperation:
+                raise ValueError('string-float not recognized by Decimal: %s' % num)
+            else:
+                isint = '.' not in num
+                num, dps = _decimal_to_Rational_prec(Num)
+                if num.is_Integer and isint:
+                    # without dec, e-notation is short for int
+                    dps = max(dps, num_digits(num))
+                    precision = dps_to_prec(dps)
+
+        # decimal precision(dps) is set and maybe binary precision(precision)
+        # as well.From here on binary precision is used to compute the Float.
+        # Hence, if supplied use binary precision else translate from decimal
+        # precision.
+
+        if precision is None or precision == '':
+            precision = dps_to_prec(dps)
+
+        precision = int(precision)
+
+        if isinstance(num, float):
+            _mpf_ = mlib.from_float(num, precision, rnd)
+        elif isinstance(num, str):
+            _mpf_ = mlib.from_str(num, precision, rnd)
+        elif isinstance(num, decimal.Decimal):
+            if num.is_finite():
+                _mpf_ = mlib.from_str(str(num), precision, rnd)
+            elif num.is_nan():
+                return S.NaN
+            elif num.is_infinite():
+                if num > 0:
+                    return S.Infinity
+                return S.NegativeInfinity
+            else:
+                raise ValueError("unexpected decimal value %s" % str(num))
+        elif isinstance(num, tuple) and len(num) in (3, 4):
+            if isinstance(num[1], str):
+                # it's a hexadecimal (coming from a pickled object)
+                num = list(num)
+                # If we're loading an object pickled in Python 2 into
+                # Python 3, we may need to strip a tailing 'L' because
+                # of a shim for int on Python 3, see issue #13470.
+                # Strip leading '0x' - gmpy2 only documents such inputs
+                # with base prefix as valid when the 2nd argument (base) is 0.
+                # When mpmath uses Sage as the backend, however, it
+                # ends up including '0x' when preparing the picklable tuple.
+                # See issue #19690.
+                num[1] = num[1].removeprefix('0x').removesuffix('L')
+                # Now we can assume that it is in standard form
+                num[1] = MPZ(num[1], 16)
+                _mpf_ = tuple(num)
+            else:
+                if len(num) == 4:
+                    # handle normalization hack
+                    return Float._new(num, precision)
+                else:
+                    if not all((
+                            num[0] in (0, 1),
+                            num[1] >= 0,
+                            all(type(i) in (int, int) for i in num)
+                            )):
+                        raise ValueError('malformed mpf: %s' % (num,))
+                    # don't compute number or else it may
+                    # over/underflow
+                    return Float._new(
+                        (num[0], num[1], num[2], bitcount(num[1])),
+                        precision)
+        elif isinstance(num, (Number, NumberSymbol)):
+            _mpf_ = num._as_mpf_val(precision)
+        else:
+            _mpf_ = mpmath.mpf(num, prec=precision)._mpf_
+
+        return cls._new(_mpf_, precision, zero=False)
+
+    @classmethod
+    def _new(cls, _mpf_, _prec, zero=True):
+        # special cases
+        if zero and _mpf_ == fzero:
+            return S.Zero  # Float(0) -> 0.0; Float._new((0,0,0,0)) -> 0
+        elif _mpf_ == _mpf_nan:
+            return S.NaN
+        elif _mpf_ == _mpf_inf:
+            return S.Infinity
+        elif _mpf_ == _mpf_ninf:
+            return S.NegativeInfinity
+
+        obj = Expr.__new__(cls)
+        obj._mpf_ = mpf_norm(_mpf_, _prec)
+        obj._prec = _prec
+        return obj
+
+    def __getnewargs_ex__(self):
+        sign, man, exp, bc = self._mpf_
+        arg = (sign, hex(man)[2:], exp, bc)
+        kwargs = {'precision': self._prec}
+        return ((arg,), kwargs)
+
+    def _hashable_content(self):
+        return (self._mpf_, self._prec)
+
+    def floor(self):
+        return Integer(int(mlib.to_int(
+            mlib.mpf_floor(self._mpf_, self._prec))))
+
+    def ceiling(self):
+        return Integer(int(mlib.to_int(
+            mlib.mpf_ceil(self._mpf_, self._prec))))
+
+    def __floor__(self):
+        return self.floor()
+
+    def __ceil__(self):
+        return self.ceiling()
+
+    @property
+    def num(self):
+        return mpmath.mpf(self._mpf_)
+
+    def _as_mpf_val(self, prec):
+        rv = mpf_norm(self._mpf_, prec)
+        if rv != self._mpf_ and self._prec == prec:
+            debug(self._mpf_, rv)
+        return rv
+
+    def _as_mpf_op(self, prec):
+        return self._mpf_, max(prec, self._prec)
+
+    def _eval_is_finite(self):
+        if self._mpf_ in (_mpf_inf, _mpf_ninf):
+            return False
+        return True
+
+    def _eval_is_infinite(self):
+        if self._mpf_ in (_mpf_inf, _mpf_ninf):
+            return True
+        return False
+
+    def _eval_is_integer(self):
+        if self._mpf_ == fzero:
+            return True
+        if not int_valued(self):
+            return False
+
+    def _eval_is_negative(self):
+        if self._mpf_ in (_mpf_ninf, _mpf_inf):
+            return False
+        return self.num < 0
+
+    def _eval_is_positive(self):
+        if self._mpf_ in (_mpf_ninf, _mpf_inf):
+            return False
+        return self.num > 0
+
+    def _eval_is_extended_negative(self):
+        if self._mpf_ == _mpf_ninf:
+            return True
+        if self._mpf_ == _mpf_inf:
+            return False
+        return self.num < 0
+
+    def _eval_is_extended_positive(self):
+        if self._mpf_ == _mpf_inf:
+            return True
+        if self._mpf_ == _mpf_ninf:
+            return False
+        return self.num > 0
+
+    def _eval_is_zero(self):
+        return self._mpf_ == fzero
+
+    def __bool__(self):
+        return self._mpf_ != fzero
+
+    def __neg__(self):
+        if not self:
+            return self
+        return Float._new(mlib.mpf_neg(self._mpf_), self._prec)
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            rhs, prec = other._as_mpf_op(self._prec)
+            return Float._new(mlib.mpf_add(self._mpf_, rhs, prec, rnd), prec)
+        return Number.__add__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            rhs, prec = other._as_mpf_op(self._prec)
+            return Float._new(mlib.mpf_sub(self._mpf_, rhs, prec, rnd), prec)
+        return Number.__sub__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            rhs, prec = other._as_mpf_op(self._prec)
+            return Float._new(mlib.mpf_mul(self._mpf_, rhs, prec, rnd), prec)
+        return Number.__mul__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        if isinstance(other, Number) and other != 0 and global_parameters.evaluate:
+            rhs, prec = other._as_mpf_op(self._prec)
+            return Float._new(mlib.mpf_div(self._mpf_, rhs, prec, rnd), prec)
+        return Number.__truediv__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __mod__(self, other):
+        if isinstance(other, Rational) and other.q != 1 and global_parameters.evaluate:
+            # calculate mod with Rationals, *then* round the result
+            return Float(Rational.__mod__(Rational(self), other),
+                         precision=self._prec)
+        if isinstance(other, Float) and global_parameters.evaluate:
+            r = self/other
+            if int_valued(r):
+                return Float(0, precision=max(self._prec, other._prec))
+        if isinstance(other, Number) and global_parameters.evaluate:
+            rhs, prec = other._as_mpf_op(self._prec)
+            return Float._new(mlib.mpf_mod(self._mpf_, rhs, prec, rnd), prec)
+        return Number.__mod__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __rmod__(self, other):
+        if isinstance(other, Float) and global_parameters.evaluate:
+            return other.__mod__(self)
+        if isinstance(other, Number) and global_parameters.evaluate:
+            rhs, prec = other._as_mpf_op(self._prec)
+            return Float._new(mlib.mpf_mod(rhs, self._mpf_, prec, rnd), prec)
+        return Number.__rmod__(self, other)
+
+    def _eval_power(self, expt):
+        """
+        expt is symbolic object but not equal to 0, 1
+
+        (-p)**r -> exp(r*log(-p)) -> exp(r*(log(p) + I*Pi)) ->
+                  -> p**r*(sin(Pi*r) + cos(Pi*r)*I)
+        """
+        if equal_valued(self, 0):
+            if expt.is_extended_positive:
+                return self
+            if expt.is_extended_negative:
+                return S.ComplexInfinity
+        if isinstance(expt, Number):
+            if isinstance(expt, Integer):
+                prec = self._prec
+                return Float._new(
+                    mlib.mpf_pow_int(self._mpf_, expt.p, prec, rnd), prec)
+            elif isinstance(expt, Rational) and \
+                    expt.p == 1 and expt.q % 2 and self.is_negative:
+                return Pow(S.NegativeOne, expt, evaluate=False)*(
+                    -self)._eval_power(expt)
+            expt, prec = expt._as_mpf_op(self._prec)
+            mpfself = self._mpf_
+            try:
+                y = mpf_pow(mpfself, expt, prec, rnd)
+                return Float._new(y, prec)
+            except mlib.ComplexResult:
+                re, im = mlib.mpc_pow(
+                    (mpfself, fzero), (expt, fzero), prec, rnd)
+                return Float._new(re, prec) + \
+                    Float._new(im, prec)*S.ImaginaryUnit
+
+    def __abs__(self):
+        return Float._new(mlib.mpf_abs(self._mpf_), self._prec)
+
+    def __int__(self):
+        if self._mpf_ == fzero:
+            return 0
+        return int(mlib.to_int(self._mpf_))  # uses round_fast = round_down
+
+    def __eq__(self, other):
+        if isinstance(other, float):
+            other = Float(other)
+        return Basic.__eq__(self, other)
+
+    def __ne__(self, other):
+        eq = self.__eq__(other)
+        if eq is NotImplemented:
+            return eq
+        else:
+            return not eq
+
+    def __hash__(self):
+        float_val = float(self)
+        if not math.isinf(float_val):
+            return hash(float_val)
+        return Basic.__hash__(self)
+
+    def _Frel(self, other, op):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if other.is_Rational:
+            # test self*other.q  other.p without losing precision
+            '''
+            >>> f = Float(.1,2)
+            >>> i = 1234567890
+            >>> (f*i)._mpf_
+            (0, 471, 18, 9)
+            >>> mlib.mpf_mul(f._mpf_, mlib.from_int(i))
+            (0, 505555550955, -12, 39)
+            '''
+            smpf = mlib.mpf_mul(self._mpf_, mlib.from_int(other.q))
+            ompf = mlib.from_int(other.p)
+            return _sympify(bool(op(smpf, ompf)))
+        elif other.is_Float:
+            return _sympify(bool(
+                        op(self._mpf_, other._mpf_)))
+        elif other.is_comparable and other not in (
+                S.Infinity, S.NegativeInfinity):
+            other = other.evalf(prec_to_dps(self._prec))
+            if other._prec > 1:
+                if other.is_Number:
+                    return _sympify(bool(
+                        op(self._mpf_, other._as_mpf_val(self._prec))))
+
+    def __gt__(self, other):
+        if isinstance(other, NumberSymbol):
+            return other.__lt__(self)
+        rv = self._Frel(other, mlib.mpf_gt)
+        if rv is None:
+            return Expr.__gt__(self, other)
+        return rv
+
+    def __ge__(self, other):
+        if isinstance(other, NumberSymbol):
+            return other.__le__(self)
+        rv = self._Frel(other, mlib.mpf_ge)
+        if rv is None:
+            return Expr.__ge__(self, other)
+        return rv
+
+    def __lt__(self, other):
+        if isinstance(other, NumberSymbol):
+            return other.__gt__(self)
+        rv = self._Frel(other, mlib.mpf_lt)
+        if rv is None:
+            return Expr.__lt__(self, other)
+        return rv
+
+    def __le__(self, other):
+        if isinstance(other, NumberSymbol):
+            return other.__ge__(self)
+        rv = self._Frel(other, mlib.mpf_le)
+        if rv is None:
+            return Expr.__le__(self, other)
+        return rv
+
+    def epsilon_eq(self, other, epsilon="1e-15"):
+        return abs(self - other) < Float(epsilon)
+
+    def __format__(self, format_spec):
+        return format(decimal.Decimal(str(self)), format_spec)
+
+
+# Add sympify converters
+_sympy_converter[float] = _sympy_converter[decimal.Decimal] = Float
+
+# this is here to work nicely in Sage
+RealNumber = Float
+
+
+class Rational(Number):
+    """Represents rational numbers (p/q) of any size.
+
+    Examples
+    ========
+
+    >>> from sympy import Rational, nsimplify, S, pi
+    >>> Rational(1, 2)
+    1/2
+
+    Rational is unprejudiced in accepting input. If a float is passed, the
+    underlying value of the binary representation will be returned:
+
+    >>> Rational(.5)
+    1/2
+    >>> Rational(.2)
+    3602879701896397/18014398509481984
+
+    If the simpler representation of the float is desired then consider
+    limiting the denominator to the desired value or convert the float to
+    a string (which is roughly equivalent to limiting the denominator to
+    10**12):
+
+    >>> Rational(str(.2))
+    1/5
+    >>> Rational(.2).limit_denominator(10**12)
+    1/5
+
+    An arbitrarily precise Rational is obtained when a string literal is
+    passed:
+
+    >>> Rational("1.23")
+    123/100
+    >>> Rational('1e-2')
+    1/100
+    >>> Rational(".1")
+    1/10
+    >>> Rational('1e-2/3.2')
+    1/320
+
+    The conversion of other types of strings can be handled by
+    the sympify() function, and conversion of floats to expressions
+    or simple fractions can be handled with nsimplify:
+
+    >>> S('.[3]')  # repeating digits in brackets
+    1/3
+    >>> S('3**2/10')  # general expressions
+    9/10
+    >>> nsimplify(.3)  # numbers that have a simple form
+    3/10
+
+    But if the input does not reduce to a literal Rational, an error will
+    be raised:
+
+    >>> Rational(pi)
+    Traceback (most recent call last):
+    ...
+    TypeError: invalid input: pi
+
+
+    Low-level
+    ---------
+
+    Access numerator and denominator as .p and .q:
+
+    >>> r = Rational(3, 4)
+    >>> r
+    3/4
+    >>> r.p
+    3
+    >>> r.q
+    4
+
+    Note that p and q return integers (not SymPy Integers) so some care
+    is needed when using them in expressions:
+
+    >>> r.p/r.q
+    0.75
+
+    See Also
+    ========
+    sympy.core.sympify.sympify, sympy.simplify.simplify.nsimplify
+    """
+    is_real = True
+    is_integer = False
+    is_rational = True
+    is_number = True
+
+    __slots__ = ('p', 'q')
+
+    p: int
+    q: int
+
+    is_Rational = True
+
+    @cacheit
+    def __new__(cls, p, q=None, gcd=None):
+        if q is None:
+            if isinstance(p, Rational):
+                return p
+
+            if isinstance(p, SYMPY_INTS):
+                pass
+            else:
+                if isinstance(p, (float, Float)):
+                    return Rational(*_as_integer_ratio(p))
+
+                if not isinstance(p, str):
+                    try:
+                        p = sympify(p)
+                    except (SympifyError, SyntaxError):
+                        pass  # error will raise below
+                else:
+                    if p.count('/') > 1:
+                        raise TypeError('invalid input: %s' % p)
+                    p = p.replace(' ', '')
+                    pq = p.rsplit('/', 1)
+                    if len(pq) == 2:
+                        p, q = pq
+                        fp = fractions.Fraction(p)
+                        fq = fractions.Fraction(q)
+                        p = fp/fq
+                    try:
+                        p = fractions.Fraction(p)
+                    except ValueError:
+                        pass  # error will raise below
+                    else:
+                        return cls._new(p.numerator, p.denominator, 1)
+
+                if not isinstance(p, Rational):
+                    raise TypeError('invalid input: %s' % p)
+
+            q = 1
+
+        Q = 1
+
+        if not isinstance(p, SYMPY_INTS):
+            p = Rational(p)
+            Q *= p.q
+            p = p.p
+        else:
+            p = int(p)
+
+        if not isinstance(q, SYMPY_INTS):
+            q = Rational(q)
+            p *= q.q
+            Q *= q.p
+        else:
+            Q *= int(q)
+        q = Q
+
+        if gcd is not None:
+            sympy_deprecation_warning(
+                "gcd is deprecated in Rational, use nsimplify instead",
+                deprecated_since_version="1.11",
+                active_deprecations_target="deprecated-rational-gcd",
+                stacklevel=4,
+            )
+            return cls._new(p, q, gcd)
+
+        # p and q are now ints
+        return cls._new(p, q)
+
+    @classmethod
+    def _new(cls, p, q, gcd=None):
+        if q == 0:
+            if p == 0:
+                if _errdict["divide"]:
+                    raise ValueError("Indeterminate 0/0")
+                else:
+                    return S.NaN
+            return S.ComplexInfinity
+
+        if q < 0:
+            q = -q
+            p = -p
+
+        if gcd is None:
+            gcd = igcd(abs(p), q)
+
+        if gcd > 1:
+            p //= gcd
+            q //= gcd
+
+        return cls.from_coprime_ints(p, q)
+
+    @classmethod
+    def from_coprime_ints(cls, p: int, q: int) -> Rational:
+        """Create a Rational from a pair of coprime integers.
+
+        Both ``p`` and ``q`` should be strictly of type ``int``.
+
+        The caller should ensure that ``gcd(p,q) == 1`` and ``q > 0``.
+
+        This may be more efficient than ``Rational(p, q)``. The validity of the
+        arguments may or may not be checked so it should not be relied upon to
+        pass unvalidated or invalid arguments to this function.
+        """
+        if q == 1:
+            return Integer(p)
+        if p == 1 and q == 2:
+            return S.Half
+
+        obj = Expr.__new__(cls)
+        obj.p = p
+        obj.q = q
+        return obj
+
+    def limit_denominator(self, max_denominator=1000000):
+        """Closest Rational to self with denominator at most max_denominator.
+
+        Examples
+        ========
+
+        >>> from sympy import Rational
+        >>> Rational('3.141592653589793').limit_denominator(10)
+        22/7
+        >>> Rational('3.141592653589793').limit_denominator(100)
+        311/99
+
+        """
+        f = fractions.Fraction(self.p, self.q)
+        return Rational(f.limit_denominator(fractions.Fraction(int(max_denominator))))
+
+    def __getnewargs__(self):
+        return (self.p, self.q)
+
+    def _hashable_content(self):
+        return (self.p, self.q)
+
+    def _eval_is_positive(self):
+        return self.p > 0
+
+    def _eval_is_zero(self):
+        return self.p == 0
+
+    def __neg__(self):
+        return Rational(-self.p, self.q)
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Integer):
+                return Rational._new(self.p + self.q*other.p, self.q, 1)
+            elif isinstance(other, Rational):
+                #TODO: this can probably be optimized more
+                return Rational(self.p*other.q + self.q*other.p, self.q*other.q)
+            elif isinstance(other, Float):
+                return other + self
+            else:
+                return Number.__add__(self, other)
+        return Number.__add__(self, other)
+    __radd__ = __add__
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Integer):
+                return Rational._new(self.p - self.q*other.p, self.q, 1)
+            elif isinstance(other, Rational):
+                return Rational(self.p*other.q - self.q*other.p, self.q*other.q)
+            elif isinstance(other, Float):
+                return -other + self
+            else:
+                return Number.__sub__(self, other)
+        return Number.__sub__(self, other)
+    @_sympifyit('other', NotImplemented)
+    def __rsub__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Integer):
+                return Rational._new(self.q*other.p - self.p, self.q, 1)
+            elif isinstance(other, Rational):
+                return Rational(self.q*other.p - self.p*other.q, self.q*other.q)
+            elif isinstance(other, Float):
+                return -self + other
+            else:
+                return Number.__rsub__(self, other)
+        return Number.__rsub__(self, other)
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Integer):
+                return Rational._new(self.p*other.p, self.q, igcd(other.p, self.q))
+            elif isinstance(other, Rational):
+                return Rational._new(self.p*other.p, self.q*other.q, igcd(self.p, other.q)*igcd(self.q, other.p))
+            elif isinstance(other, Float):
+                return other*self
+            else:
+                return Number.__mul__(self, other)
+        return Number.__mul__(self, other)
+    __rmul__ = __mul__
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Integer):
+                if self.p and other.p == S.Zero:
+                    return S.ComplexInfinity
+                else:
+                    return Rational._new(self.p, self.q*other.p, igcd(self.p, other.p))
+            elif isinstance(other, Rational):
+                return Rational._new(self.p*other.q, self.q*other.p, igcd(self.p, other.p)*igcd(self.q, other.q))
+            elif isinstance(other, Float):
+                return self*(1/other)
+            else:
+                return Number.__truediv__(self, other)
+        return Number.__truediv__(self, other)
+    @_sympifyit('other', NotImplemented)
+    def __rtruediv__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Integer):
+                return Rational._new(other.p*self.q, self.p, igcd(self.p, other.p))
+            elif isinstance(other, Rational):
+                return Rational._new(other.p*self.q, other.q*self.p, igcd(self.p, other.p)*igcd(self.q, other.q))
+            elif isinstance(other, Float):
+                return other*(1/self)
+            else:
+                return Number.__rtruediv__(self, other)
+        return Number.__rtruediv__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __mod__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, Rational):
+                n = (self.p*other.q) // (other.p*self.q)
+                return Rational(self.p*other.q - n*other.p*self.q, self.q*other.q)
+            if isinstance(other, Float):
+                # calculate mod with Rationals, *then* round the answer
+                return Float(self.__mod__(Rational(other)),
+                             precision=other._prec)
+            return Number.__mod__(self, other)
+        return Number.__mod__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __rmod__(self, other):
+        if isinstance(other, Rational):
+            return Rational.__mod__(other, self)
+        return Number.__rmod__(self, other)
+
+    def _eval_power(self, expt):
+        if isinstance(expt, Number):
+            if isinstance(expt, Float):
+                return self._eval_evalf(expt._prec)**expt
+            if expt.is_extended_negative:
+                # (3/4)**-2 -> (4/3)**2
+                ne = -expt
+                if (ne is S.One):
+                    return Rational(self.q, self.p)
+                if self.is_negative:
+                    return S.NegativeOne**expt*Rational(self.q, -self.p)**ne
+                else:
+                    return Rational(self.q, self.p)**ne
+            if expt is S.Infinity:  # -oo already caught by test for negative
+                if self.p > self.q:
+                    # (3/2)**oo -> oo
+                    return S.Infinity
+                if self.p < -self.q:
+                    # (-3/2)**oo -> oo + I*oo
+                    return S.Infinity + S.Infinity*S.ImaginaryUnit
+                return S.Zero
+            if isinstance(expt, Integer):
+                # (4/3)**2 -> 4**2 / 3**2
+                return Rational._new(self.p**expt.p, self.q**expt.p, 1)
+            if isinstance(expt, Rational):
+                intpart = expt.p // expt.q
+                if intpart:
+                    intpart += 1
+                    remfracpart = intpart*expt.q - expt.p
+                    ratfracpart = Rational(remfracpart, expt.q)
+                    if self.p != 1:
+                        return Integer(self.p)**expt*Integer(self.q)**ratfracpart*Rational._new(1, self.q**intpart, 1)
+                    return Integer(self.q)**ratfracpart*Rational._new(1, self.q**intpart, 1)
+                else:
+                    remfracpart = expt.q - expt.p
+                    ratfracpart = Rational(remfracpart, expt.q)
+                    if self.p != 1:
+                        return Integer(self.p)**expt*Integer(self.q)**ratfracpart*Rational._new(1, self.q, 1)
+                    return Integer(self.q)**ratfracpart*Rational._new(1, self.q, 1)
+
+        if self.is_extended_negative and expt.is_even:
+            return (-self)**expt
+
+        return
+
+    def _as_mpf_val(self, prec):
+        return mlib.from_rational(self.p, self.q, prec, rnd)
+
+    def _mpmath_(self, prec, rnd):
+        return mpmath.make_mpf(mlib.from_rational(self.p, self.q, prec, rnd))
+
+    def __abs__(self):
+        return Rational(abs(self.p), self.q)
+
+    def __int__(self):
+        p, q = self.p, self.q
+        if p < 0:
+            return -int(-p//q)
+        return int(p//q)
+
+    def floor(self):
+        return Integer(self.p // self.q)
+
+    def ceiling(self):
+        return -Integer(-self.p // self.q)
+
+    def __floor__(self):
+        return self.floor()
+
+    def __ceil__(self):
+        return self.ceiling()
+
+    def __eq__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if not isinstance(other, Number):
+            # S(0) == S.false is False
+            # S(0) == False is True
+            return False
+        if other.is_NumberSymbol:
+            if other.is_irrational:
+                return False
+            return other.__eq__(self)
+        if other.is_Rational:
+            # a Rational is always in reduced form so will never be 2/4
+            # so we can just check equivalence of args
+            return self.p == other.p and self.q == other.q
+        return False
+
+    def __ne__(self, other):
+        return not self == other
+
+    def _Rrel(self, other, attr):
+        # if you want self < other, pass self, other, __gt__
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if other.is_Number:
+            op = None
+            s, o = self, other
+            if other.is_NumberSymbol:
+                op = getattr(o, attr)
+            elif other.is_Float:
+                op = getattr(o, attr)
+            elif other.is_Rational:
+                s, o = Integer(s.p*o.q), Integer(s.q*o.p)
+                op = getattr(o, attr)
+            if op:
+                return op(s)
+            if o.is_number and o.is_extended_real:
+                return Integer(s.p), s.q*o
+
+    def __gt__(self, other):
+        rv = self._Rrel(other, '__lt__')
+        if rv is None:
+            rv = self, other
+        elif not isinstance(rv, tuple):
+            return rv
+        return Expr.__gt__(*rv)
+
+    def __ge__(self, other):
+        rv = self._Rrel(other, '__le__')
+        if rv is None:
+            rv = self, other
+        elif not isinstance(rv, tuple):
+            return rv
+        return Expr.__ge__(*rv)
+
+    def __lt__(self, other):
+        rv = self._Rrel(other, '__gt__')
+        if rv is None:
+            rv = self, other
+        elif not isinstance(rv, tuple):
+            return rv
+        return Expr.__lt__(*rv)
+
+    def __le__(self, other):
+        rv = self._Rrel(other, '__ge__')
+        if rv is None:
+            rv = self, other
+        elif not isinstance(rv, tuple):
+            return rv
+        return Expr.__le__(*rv)
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def factors(self, limit=None, use_trial=True, use_rho=False,
+                use_pm1=False, verbose=False, visual=False):
+        """A wrapper to factorint which return factors of self that are
+        smaller than limit (or cheap to compute). Special methods of
+        factoring are disabled by default so that only trial division is used.
+        """
+        from sympy.ntheory.factor_ import factorrat
+
+        return factorrat(self, limit=limit, use_trial=use_trial,
+                      use_rho=use_rho, use_pm1=use_pm1,
+                      verbose=verbose).copy()
+
+    @property
+    def numerator(self):
+        return self.p
+
+    @property
+    def denominator(self):
+        return self.q
+
+    @_sympifyit('other', NotImplemented)
+    def gcd(self, other):
+        if isinstance(other, Rational):
+            if other == S.Zero:
+                return other
+            return Rational(
+                igcd(self.p, other.p),
+                ilcm(self.q, other.q))
+        return Number.gcd(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def lcm(self, other):
+        if isinstance(other, Rational):
+            return Rational(
+                self.p // igcd(self.p, other.p) * other.p,
+                igcd(self.q, other.q))
+        return Number.lcm(self, other)
+
+    def as_numer_denom(self):
+        return Integer(self.p), Integer(self.q)
+
+    def as_content_primitive(self, radical=False, clear=True):
+        """Return the tuple (R, self/R) where R is the positive Rational
+        extracted from self.
+
+        Examples
+        ========
+
+        >>> from sympy import S
+        >>> (S(-3)/2).as_content_primitive()
+        (3/2, -1)
+
+        See docstring of Expr.as_content_primitive for more examples.
+        """
+
+        if self:
+            if self.is_positive:
+                return self, S.One
+            return -self, S.NegativeOne
+        return S.One, self
+
+    def as_coeff_Mul(self, rational=False):
+        """Efficiently extract the coefficient of a product."""
+        return self, S.One
+
+    def as_coeff_Add(self, rational=False):
+        """Efficiently extract the coefficient of a summation."""
+        return self, S.Zero
+
+
+class Integer(Rational):
+    """Represents integer numbers of any size.
+
+    Examples
+    ========
+
+    >>> from sympy import Integer
+    >>> Integer(3)
+    3
+
+    If a float or a rational is passed to Integer, the fractional part
+    will be discarded; the effect is of rounding toward zero.
+
+    >>> Integer(3.8)
+    3
+    >>> Integer(-3.8)
+    -3
+
+    A string is acceptable input if it can be parsed as an integer:
+
+    >>> Integer("9" * 20)
+    99999999999999999999
+
+    It is rarely needed to explicitly instantiate an Integer, because
+    Python integers are automatically converted to Integer when they
+    are used in SymPy expressions.
+    """
+    q = 1
+    is_integer = True
+    is_number = True
+
+    is_Integer = True
+
+    __slots__ = ()
+
+    def _as_mpf_val(self, prec):
+        return mlib.from_int(self.p, prec, rnd)
+
+    def _mpmath_(self, prec, rnd):
+        return mpmath.make_mpf(self._as_mpf_val(prec))
+
+    @cacheit
+    def __new__(cls, i):
+        if isinstance(i, str):
+            i = i.replace(' ', '')
+        # whereas we cannot, in general, make a Rational from an
+        # arbitrary expression, we can make an Integer unambiguously
+        # (except when a non-integer expression happens to round to
+        # an integer). So we proceed by taking int() of the input and
+        # let the int routines determine whether the expression can
+        # be made into an int or whether an error should be raised.
+        try:
+            ival = int(i)
+        except TypeError:
+            raise TypeError(
+                "Argument of Integer should be of numeric type, got %s." % i)
+        # We only work with well-behaved integer types. This converts, for
+        # example, numpy.int32 instances.
+        if ival == 1:
+            return S.One
+        if ival == -1:
+            return S.NegativeOne
+        if ival == 0:
+            return S.Zero
+        obj = Expr.__new__(cls)
+        obj.p = ival
+        return obj
+
+    def __getnewargs__(self):
+        return (self.p,)
+
+    # Arithmetic operations are here for efficiency
+    def __int__(self):
+        return self.p
+
+    def floor(self):
+        return Integer(self.p)
+
+    def ceiling(self):
+        return Integer(self.p)
+
+    def __floor__(self):
+        return self.floor()
+
+    def __ceil__(self):
+        return self.ceiling()
+
+    def __neg__(self):
+        return Integer(-self.p)
+
+    def __abs__(self):
+        if self.p >= 0:
+            return self
+        else:
+            return Integer(-self.p)
+
+    def __divmod__(self, other):
+        if isinstance(other, Integer) and global_parameters.evaluate:
+            return Tuple(*(divmod(self.p, other.p)))
+        else:
+            return Number.__divmod__(self, other)
+
+    def __rdivmod__(self, other):
+        if isinstance(other, int) and global_parameters.evaluate:
+            return Tuple(*(divmod(other, self.p)))
+        else:
+            try:
+                other = Number(other)
+            except TypeError:
+                msg = "unsupported operand type(s) for divmod(): '%s' and '%s'"
+                oname = type(other).__name__
+                sname = type(self).__name__
+                raise TypeError(msg % (oname, sname))
+            return Number.__divmod__(other, self)
+
+    # TODO make it decorator + bytecodehacks?
+    def __add__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(self.p + other)
+            elif isinstance(other, Integer):
+                return Integer(self.p + other.p)
+            elif isinstance(other, Rational):
+                return Rational._new(self.p*other.q + other.p, other.q, 1)
+            return Rational.__add__(self, other)
+        else:
+            return Add(self, other)
+
+    def __radd__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(other + self.p)
+            elif isinstance(other, Rational):
+                return Rational._new(other.p + self.p*other.q, other.q, 1)
+            return Rational.__radd__(self, other)
+        return Rational.__radd__(self, other)
+
+    def __sub__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(self.p - other)
+            elif isinstance(other, Integer):
+                return Integer(self.p - other.p)
+            elif isinstance(other, Rational):
+                return Rational._new(self.p*other.q - other.p, other.q, 1)
+            return Rational.__sub__(self, other)
+        return Rational.__sub__(self, other)
+
+    def __rsub__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(other - self.p)
+            elif isinstance(other, Rational):
+                return Rational._new(other.p - self.p*other.q, other.q, 1)
+            return Rational.__rsub__(self, other)
+        return Rational.__rsub__(self, other)
+
+    def __mul__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(self.p*other)
+            elif isinstance(other, Integer):
+                return Integer(self.p*other.p)
+            elif isinstance(other, Rational):
+                return Rational._new(self.p*other.p, other.q, igcd(self.p, other.q))
+            return Rational.__mul__(self, other)
+        return Rational.__mul__(self, other)
+
+    def __rmul__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(other*self.p)
+            elif isinstance(other, Rational):
+                return Rational._new(other.p*self.p, other.q, igcd(self.p, other.q))
+            return Rational.__rmul__(self, other)
+        return Rational.__rmul__(self, other)
+
+    def __mod__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(self.p % other)
+            elif isinstance(other, Integer):
+                return Integer(self.p % other.p)
+            return Rational.__mod__(self, other)
+        return Rational.__mod__(self, other)
+
+    def __rmod__(self, other):
+        if global_parameters.evaluate:
+            if isinstance(other, int):
+                return Integer(other % self.p)
+            elif isinstance(other, Integer):
+                return Integer(other.p % self.p)
+            return Rational.__rmod__(self, other)
+        return Rational.__rmod__(self, other)
+
+    def __eq__(self, other):
+        if isinstance(other, int):
+            return (self.p == other)
+        elif isinstance(other, Integer):
+            return (self.p == other.p)
+        return Rational.__eq__(self, other)
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __gt__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if other.is_Integer:
+            return _sympify(self.p > other.p)
+        return Rational.__gt__(self, other)
+
+    def __lt__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if other.is_Integer:
+            return _sympify(self.p < other.p)
+        return Rational.__lt__(self, other)
+
+    def __ge__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if other.is_Integer:
+            return _sympify(self.p >= other.p)
+        return Rational.__ge__(self, other)
+
+    def __le__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if other.is_Integer:
+            return _sympify(self.p <= other.p)
+        return Rational.__le__(self, other)
+
+    def __hash__(self):
+        return hash(self.p)
+
+    def __index__(self):
+        return self.p
+
+    ########################################
+
+    def _eval_is_odd(self):
+        return bool(self.p % 2)
+
+    def _eval_power(self, expt):
+        """
+        Tries to do some simplifications on self**expt
+
+        Returns None if no further simplifications can be done.
+
+        Explanation
+        ===========
+
+        When exponent is a fraction (so we have for example a square root),
+        we try to find a simpler representation by factoring the argument
+        up to factors of 2**15, e.g.
+
+          - sqrt(4) becomes 2
+          - sqrt(-4) becomes 2*I
+          - (2**(3+7)*3**(6+7))**Rational(1,7) becomes 6*18**(3/7)
+
+        Further simplification would require a special call to factorint on
+        the argument which is not done here for sake of speed.
+
+        """
+        from sympy.ntheory.factor_ import perfect_power
+
+        if expt is S.Infinity:
+            if self.p > S.One:
+                return S.Infinity
+            # cases -1, 0, 1 are done in their respective classes
+            return S.Infinity + S.ImaginaryUnit*S.Infinity
+        if expt is S.NegativeInfinity:
+            return Rational._new(1, self, 1)**S.Infinity
+        if not isinstance(expt, Number):
+            # simplify when expt is even
+            # (-2)**k --> 2**k
+            if self.is_negative and expt.is_even:
+                return (-self)**expt
+        if isinstance(expt, Float):
+            # Rational knows how to exponentiate by a Float
+            return super()._eval_power(expt)
+        if not isinstance(expt, Rational):
+            return
+        if expt is S.Half and self.is_negative:
+            # we extract I for this special case since everyone is doing so
+            return S.ImaginaryUnit*Pow(-self, expt)
+        if expt.is_negative:
+            # invert base and change sign on exponent
+            ne = -expt
+            if self.is_negative:
+                return S.NegativeOne**expt*Rational._new(1, -self.p, 1)**ne
+            else:
+                return Rational._new(1, self.p, 1)**ne
+        # see if base is a perfect root, sqrt(4) --> 2
+        x, xexact = integer_nthroot(abs(self.p), expt.q)
+        if xexact:
+            # if it's a perfect root we've finished
+            result = Integer(x**abs(expt.p))
+            if self.is_negative:
+                result *= S.NegativeOne**expt
+            return result
+
+        # The following is an algorithm where we collect perfect roots
+        # from the factors of base.
+
+        # if it's not an nth root, it still might be a perfect power
+        b_pos = int(abs(self.p))
+        p = perfect_power(b_pos)
+        if p is not False:
+            # XXX: Convert to int because perfect_power may return fmpz
+            # Ideally that should be fixed in perfect_power though...
+            dict = {int(p[0]): int(p[1])}
+        else:
+            dict = Integer(b_pos).factors(limit=2**15)
+
+        # now process the dict of factors
+        out_int = 1  # integer part
+        out_rad = 1  # extracted radicals
+        sqr_int = 1
+        sqr_gcd = 0
+        sqr_dict = {}
+        for prime, exponent in dict.items():
+            exponent *= expt.p
+            # remove multiples of expt.q: (2**12)**(1/10) -> 2*(2**2)**(1/10)
+            div_e, div_m = divmod(exponent, expt.q)
+            if div_e > 0:
+                out_int *= prime**div_e
+            if div_m > 0:
+                # see if the reduced exponent shares a gcd with e.q
+                # (2**2)**(1/10) -> 2**(1/5)
+                g = igcd(div_m, expt.q)
+                if g != 1:
+                    out_rad *= Pow(prime, Rational._new(div_m//g, expt.q//g, 1))
+                else:
+                    sqr_dict[prime] = div_m
+        # identify gcd of remaining powers
+        for p, ex in sqr_dict.items():
+            if sqr_gcd == 0:
+                sqr_gcd = ex
+            else:
+                sqr_gcd = igcd(sqr_gcd, ex)
+                if sqr_gcd == 1:
+                    break
+        for k, v in sqr_dict.items():
+            sqr_int *= k**(v//sqr_gcd)
+        if sqr_int == b_pos and out_int == 1 and out_rad == 1:
+            result = None
+        else:
+            result = out_int*out_rad*Pow(sqr_int, Rational(sqr_gcd, expt.q))
+            if self.is_negative:
+                result *= Pow(S.NegativeOne, expt)
+        return result
+
+    def _eval_is_prime(self):
+        from sympy.ntheory.primetest import isprime
+
+        return isprime(self)
+
+    def _eval_is_composite(self):
+        if self > 1:
+            return fuzzy_not(self.is_prime)
+        else:
+            return False
+
+    def as_numer_denom(self):
+        return self, S.One
+
+    @_sympifyit('other', NotImplemented)
+    def __floordiv__(self, other):
+        if not isinstance(other, Expr):
+            return NotImplemented
+        if isinstance(other, Integer):
+            return Integer(self.p // other)
+        return divmod(self, other)[0]
+
+    def __rfloordiv__(self, other):
+        return Integer(Integer(other).p // self.p)
+
+    # These bitwise operations (__lshift__, __rlshift__, ..., __invert__) are defined
+    # for Integer only and not for general SymPy expressions. This is to achieve
+    # compatibility with the numbers.Integral ABC which only defines these operations
+    # among instances of numbers.Integral. Therefore, these methods check explicitly for
+    # integer types rather than using sympify because they should not accept arbitrary
+    # symbolic expressions and there is no symbolic analogue of numbers.Integral's
+    # bitwise operations.
+    def __lshift__(self, other):
+        if isinstance(other, (int, Integer, numbers.Integral)):
+            return Integer(self.p << int(other))
+        else:
+            return NotImplemented
+
+    def __rlshift__(self, other):
+        if isinstance(other, (int, numbers.Integral)):
+            return Integer(int(other) << self.p)
+        else:
+            return NotImplemented
+
+    def __rshift__(self, other):
+        if isinstance(other, (int, Integer, numbers.Integral)):
+            return Integer(self.p >> int(other))
+        else:
+            return NotImplemented
+
+    def __rrshift__(self, other):
+        if isinstance(other, (int, numbers.Integral)):
+            return Integer(int(other) >> self.p)
+        else:
+            return NotImplemented
+
+    def __and__(self, other):
+        if isinstance(other, (int, Integer, numbers.Integral)):
+            return Integer(self.p & int(other))
+        else:
+            return NotImplemented
+
+    def __rand__(self, other):
+        if isinstance(other, (int, numbers.Integral)):
+            return Integer(int(other) & self.p)
+        else:
+            return NotImplemented
+
+    def __xor__(self, other):
+        if isinstance(other, (int, Integer, numbers.Integral)):
+            return Integer(self.p ^ int(other))
+        else:
+            return NotImplemented
+
+    def __rxor__(self, other):
+        if isinstance(other, (int, numbers.Integral)):
+            return Integer(int(other) ^ self.p)
+        else:
+            return NotImplemented
+
+    def __or__(self, other):
+        if isinstance(other, (int, Integer, numbers.Integral)):
+            return Integer(self.p | int(other))
+        else:
+            return NotImplemented
+
+    def __ror__(self, other):
+        if isinstance(other, (int, numbers.Integral)):
+            return Integer(int(other) | self.p)
+        else:
+            return NotImplemented
+
+    def __invert__(self):
+        return Integer(~self.p)
+
+# Add sympify converters
+_sympy_converter[int] = Integer
+
+
+class AlgebraicNumber(Expr):
+    r"""
+    Class for representing algebraic numbers in SymPy.
+
+    Symbolically, an instance of this class represents an element
+    $\alpha \in \mathbb{Q}(\theta) \hookrightarrow \mathbb{C}$. That is, the
+    algebraic number $\alpha$ is represented as an element of a particular
+    number field $\mathbb{Q}(\theta)$, with a particular embedding of this
+    field into the complex numbers.
+
+    Formally, the primitive element $\theta$ is given by two data points: (1)
+    its minimal polynomial (which defines $\mathbb{Q}(\theta)$), and (2) a
+    particular complex number that is a root of this polynomial (which defines
+    the embedding $\mathbb{Q}(\theta) \hookrightarrow \mathbb{C}$). Finally,
+    the algebraic number $\alpha$ which we represent is then given by the
+    coefficients of a polynomial in $\theta$.
+    """
+
+    __slots__ = ('rep', 'root', 'alias', 'minpoly', '_own_minpoly')
+
+    is_AlgebraicNumber = True
+    is_algebraic = True
+    is_number = True
+
+
+    kind = NumberKind
+
+    # Optional alias symbol is not free.
+    # Actually, alias should be a Str, but some methods
+    # expect that it be an instance of Expr.
+    free_symbols: set[Basic] = set()
+
+    def __new__(cls, expr, coeffs=None, alias=None, **args):
+        r"""
+        Construct a new algebraic number $\alpha$ belonging to a number field
+        $k = \mathbb{Q}(\theta)$.
+
+        There are four instance attributes to be determined:
+
+        ===========  ============================================================================
+        Attribute    Type/Meaning
+        ===========  ============================================================================
+        ``root``     :py:class:`~.Expr` for $\theta$ as a complex number
+        ``minpoly``  :py:class:`~.Poly`, the minimal polynomial of $\theta$
+        ``rep``      :py:class:`~sympy.polys.polyclasses.DMP` giving $\alpha$ as poly in $\theta$
+        ``alias``    :py:class:`~.Symbol` for $\theta$, or ``None``
+        ===========  ============================================================================
+
+        See Parameters section for how they are determined.
+
+        Parameters
+        ==========
+
+        expr : :py:class:`~.Expr`, or pair $(m, r)$
+            There are three distinct modes of construction, depending on what
+            is passed as *expr*.
+
+            **(1)** *expr* is an :py:class:`~.AlgebraicNumber`:
+            In this case we begin by copying all four instance attributes from
+            *expr*. If *coeffs* were also given, we compose the two coeff
+            polynomials (see below). If an *alias* was given, it overrides.
+
+            **(2)** *expr* is any other type of :py:class:`~.Expr`:
+            Then ``root`` will equal *expr*. Therefore it
+            must express an algebraic quantity, and we will compute its
+            ``minpoly``.
+
+            **(3)** *expr* is an ordered pair $(m, r)$ giving the
+            ``minpoly`` $m$, and a ``root`` $r$ thereof, which together
+            define $\theta$. In this case $m$ may be either a univariate
+            :py:class:`~.Poly` or any :py:class:`~.Expr` which represents the
+            same, while $r$ must be some :py:class:`~.Expr` representing a
+            complex number that is a root of $m$, including both explicit
+            expressions in radicals, and instances of
+            :py:class:`~.ComplexRootOf` or :py:class:`~.AlgebraicNumber`.
+
+        coeffs : list, :py:class:`~.ANP`, None, optional (default=None)
+            This defines ``rep``, giving the algebraic number $\alpha$ as a
+            polynomial in $\theta$.
+
+            If a list, the elements should be integers or rational numbers.
+            If an :py:class:`~.ANP`, we take its coefficients (using its
+            :py:meth:`~.ANP.to_list()` method). If ``None``, then the list of
+            coefficients defaults to ``[1, 0]``, meaning that $\alpha = \theta$
+            is the primitive element of the field.
+
+            If *expr* was an :py:class:`~.AlgebraicNumber`, let $g(x)$ be its
+            ``rep`` polynomial, and let $f(x)$ be the polynomial defined by
+            *coeffs*. Then ``self.rep`` will represent the composition
+            $(f \circ g)(x)$.
+
+        alias : str, :py:class:`~.Symbol`, None, optional (default=None)
+            This is a way to provide a name for the primitive element. We
+            described several ways in which the *expr* argument can define the
+            value of the primitive element, but none of these methods gave it
+            a name. Here, for example, *alias* could be set as
+            ``Symbol('theta')``, in order to make this symbol appear when
+            $\alpha$ is printed, or rendered as a polynomial, using the
+            :py:meth:`~.as_poly()` method.
+
+        Examples
+        ========
+
+        Recall that we are constructing an algebraic number as a field element
+        $\alpha \in \mathbb{Q}(\theta)$.
+
+        >>> from sympy import AlgebraicNumber, sqrt, CRootOf, S
+        >>> from sympy.abc import x
+
+        Example (1): $\alpha = \theta = \sqrt{2}$
+
+        >>> a1 = AlgebraicNumber(sqrt(2))
+        >>> a1.minpoly_of_element().as_expr(x)
+        x**2 - 2
+        >>> a1.evalf(10)
+        1.414213562
+
+        Example (2): $\alpha = 3 \sqrt{2} - 5$, $\theta = \sqrt{2}$. We can
+        either build on the last example:
+
+        >>> a2 = AlgebraicNumber(a1, [3, -5])
+        >>> a2.as_expr()
+        -5 + 3*sqrt(2)
+
+        or start from scratch:
+
+        >>> a2 = AlgebraicNumber(sqrt(2), [3, -5])
+        >>> a2.as_expr()
+        -5 + 3*sqrt(2)
+
+        Example (3): $\alpha = 6 \sqrt{2} - 11$, $\theta = \sqrt{2}$. Again we
+        can build on the previous example, and we see that the coeff polys are
+        composed:
+
+        >>> a3 = AlgebraicNumber(a2, [2, -1])
+        >>> a3.as_expr()
+        -11 + 6*sqrt(2)
+
+        reflecting the fact that $(2x - 1) \circ (3x - 5) = 6x - 11$.
+
+        Example (4): $\alpha = \sqrt{2}$, $\theta = \sqrt{2} + \sqrt{3}$. The
+        easiest way is to use the :py:func:`~.to_number_field()` function:
+
+        >>> from sympy import to_number_field
+        >>> a4 = to_number_field(sqrt(2), sqrt(2) + sqrt(3))
+        >>> a4.minpoly_of_element().as_expr(x)
+        x**2 - 2
+        >>> a4.to_root()
+        sqrt(2)
+        >>> a4.primitive_element()
+        sqrt(2) + sqrt(3)
+        >>> a4.coeffs()
+        [1/2, 0, -9/2, 0]
+
+        but if you already knew the right coefficients, you could construct it
+        directly:
+
+        >>> a4 = AlgebraicNumber(sqrt(2) + sqrt(3), [S(1)/2, 0, S(-9)/2, 0])
+        >>> a4.to_root()
+        sqrt(2)
+        >>> a4.primitive_element()
+        sqrt(2) + sqrt(3)
+
+        Example (5): Construct the Golden Ratio as an element of the 5th
+        cyclotomic field, supposing we already know its coefficients. This time
+        we introduce the alias $\zeta$ for the primitive element of the field:
+
+        >>> from sympy import cyclotomic_poly
+        >>> from sympy.abc import zeta
+        >>> a5 = AlgebraicNumber(CRootOf(cyclotomic_poly(5), -1),
+        ...                  [-1, -1, 0, 0], alias=zeta)
+        >>> a5.as_poly().as_expr()
+        -zeta**3 - zeta**2
+        >>> a5.evalf()
+        1.61803398874989
+
+        (The index ``-1`` to ``CRootOf`` selects the complex root with the
+        largest real and imaginary parts, which in this case is
+        $\mathrm{e}^{2i\pi/5}$. See :py:class:`~.ComplexRootOf`.)
+
+        Example (6): Building on the last example, construct the number
+        $2 \phi \in \mathbb{Q}(\phi)$, where $\phi$ is the Golden Ratio:
+
+        >>> from sympy.abc import phi
+        >>> a6 = AlgebraicNumber(a5.to_root(), coeffs=[2, 0], alias=phi)
+        >>> a6.as_poly().as_expr()
+        2*phi
+        >>> a6.primitive_element().evalf()
+        1.61803398874989
+
+        Note that we needed to use ``a5.to_root()``, since passing ``a5`` as
+        the first argument would have constructed the number $2 \phi$ as an
+        element of the field $\mathbb{Q}(\zeta)$:
+
+        >>> a6_wrong = AlgebraicNumber(a5, coeffs=[2, 0])
+        >>> a6_wrong.as_poly().as_expr()
+        -2*zeta**3 - 2*zeta**2
+        >>> a6_wrong.primitive_element().evalf()
+        0.309016994374947 + 0.951056516295154*I
+
+        """
+        from sympy.polys.polyclasses import ANP, DMP
+        from sympy.polys.numberfields import minimal_polynomial
+
+        expr = sympify(expr)
+        rep0 = None
+        alias0 = None
+
+        if isinstance(expr, (tuple, Tuple)):
+            minpoly, root = expr
+
+            if not minpoly.is_Poly:
+                from sympy.polys.polytools import Poly
+                minpoly = Poly(minpoly)
+        elif expr.is_AlgebraicNumber:
+            minpoly, root, rep0, alias0 = (expr.minpoly, expr.root,
+                                           expr.rep, expr.alias)
+        else:
+            minpoly, root = minimal_polynomial(
+                expr, args.get('gen'), polys=True), expr
+
+        dom = minpoly.get_domain()
+
+        if coeffs is not None:
+            if not isinstance(coeffs, ANP):
+                rep = DMP.from_sympy_list(sympify(coeffs), 0, dom)
+                scoeffs = Tuple(*coeffs)
+            else:
+                rep = DMP.from_list(coeffs.to_list(), 0, dom)
+                scoeffs = Tuple(*coeffs.to_list())
+
+        else:
+            rep = DMP.from_list([1, 0], 0, dom)
+            scoeffs = Tuple(1, 0)
+
+        if rep0 is not None:
+            from sympy.polys.densetools import dup_compose
+            c = dup_compose(rep.to_list(), rep0.to_list(), dom)
+            rep = DMP.from_list(c, 0, dom)
+            scoeffs = Tuple(*c)
+
+        if rep.degree() >= minpoly.degree():
+            rep = rep.rem(minpoly.rep)
+
+        sargs = (root, scoeffs)
+
+        alias = alias or alias0
+        if alias is not None:
+            from .symbol import Symbol
+            if not isinstance(alias, Symbol):
+                alias = Symbol(alias)
+            sargs = sargs + (alias,)
+
+        obj = Expr.__new__(cls, *sargs)
+
+        obj.rep = rep
+        obj.root = root
+        obj.alias = alias
+        obj.minpoly = minpoly
+
+        obj._own_minpoly = None
+
+        return obj
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def _eval_evalf(self, prec):
+        return self.as_expr()._evalf(prec)
+
+    @property
+    def is_aliased(self):
+        """Returns ``True`` if ``alias`` was set. """
+        return self.alias is not None
+
+    def as_poly(self, x=None):
+        """Create a Poly instance from ``self``. """
+        from sympy.polys.polytools import Poly, PurePoly
+        if x is not None:
+            return Poly.new(self.rep, x)
+        else:
+            if self.alias is not None:
+                return Poly.new(self.rep, self.alias)
+            else:
+                from .symbol import Dummy
+                return PurePoly.new(self.rep, Dummy('x'))
+
+    def as_expr(self, x=None):
+        """Create a Basic expression from ``self``. """
+        return self.as_poly(x or self.root).as_expr().expand()
+
+    def coeffs(self):
+        """Returns all SymPy coefficients of an algebraic number. """
+        return [ self.rep.dom.to_sympy(c) for c in self.rep.all_coeffs() ]
+
+    def native_coeffs(self):
+        """Returns all native coefficients of an algebraic number. """
+        return self.rep.all_coeffs()
+
+    def to_algebraic_integer(self):
+        """Convert ``self`` to an algebraic integer. """
+        from sympy.polys.polytools import Poly
+
+        f = self.minpoly
+
+        if f.LC() == 1:
+            return self
+
+        coeff = f.LC()**(f.degree() - 1)
+        poly = f.compose(Poly(f.gen/f.LC()))
+
+        minpoly = poly*coeff
+        root = f.LC()*self.root
+
+        return AlgebraicNumber((minpoly, root), self.coeffs())
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.polys.rootoftools import CRootOf
+        from sympy.polys import minpoly
+        measure, ratio = kwargs['measure'], kwargs['ratio']
+        for r in [r for r in self.minpoly.all_roots() if r.func != CRootOf]:
+            if minpoly(self.root - r).is_Symbol:
+                # use the matching root if it's simpler
+                if measure(r) < ratio*measure(self.root):
+                    return AlgebraicNumber(r)
+        return self
+
+    def field_element(self, coeffs):
+        r"""
+        Form another element of the same number field.
+
+        Explanation
+        ===========
+
+        If we represent $\alpha \in \mathbb{Q}(\theta)$, form another element
+        $\beta \in \mathbb{Q}(\theta)$ of the same number field.
+
+        Parameters
+        ==========
+
+        coeffs : list, :py:class:`~.ANP`
+            Like the *coeffs* arg to the class
+            :py:meth:`constructor<.AlgebraicNumber.__new__>`, defines the
+            new element as a polynomial in the primitive element.
+
+            If a list, the elements should be integers or rational numbers.
+            If an :py:class:`~.ANP`, we take its coefficients (using its
+            :py:meth:`~.ANP.to_list()` method).
+
+        Examples
+        ========
+
+        >>> from sympy import AlgebraicNumber, sqrt
+        >>> a = AlgebraicNumber(sqrt(5), [-1, 1])
+        >>> b = a.field_element([3, 2])
+        >>> print(a)
+        1 - sqrt(5)
+        >>> print(b)
+        2 + 3*sqrt(5)
+        >>> print(b.primitive_element() == a.primitive_element())
+        True
+
+        See Also
+        ========
+
+        AlgebraicNumber
+        """
+        return AlgebraicNumber(
+            (self.minpoly, self.root), coeffs=coeffs, alias=self.alias)
+
+    @property
+    def is_primitive_element(self):
+        r"""
+        Say whether this algebraic number $\alpha \in \mathbb{Q}(\theta)$ is
+        equal to the primitive element $\theta$ for its field.
+        """
+        c = self.coeffs()
+        # Second case occurs if self.minpoly is linear:
+        return c == [1, 0] or c == [self.root]
+
+    def primitive_element(self):
+        r"""
+        Get the primitive element $\theta$ for the number field
+        $\mathbb{Q}(\theta)$ to which this algebraic number $\alpha$ belongs.
+
+        Returns
+        =======
+
+        AlgebraicNumber
+
+        """
+        if self.is_primitive_element:
+            return self
+        return self.field_element([1, 0])
+
+    def to_primitive_element(self, radicals=True):
+        r"""
+        Convert ``self`` to an :py:class:`~.AlgebraicNumber` instance that is
+        equal to its own primitive element.
+
+        Explanation
+        ===========
+
+        If we represent $\alpha \in \mathbb{Q}(\theta)$, $\alpha \neq \theta$,
+        construct a new :py:class:`~.AlgebraicNumber` that represents
+        $\alpha \in \mathbb{Q}(\alpha)$.
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt, to_number_field
+        >>> from sympy.abc import x
+        >>> a = to_number_field(sqrt(2), sqrt(2) + sqrt(3))
+
+        The :py:class:`~.AlgebraicNumber` ``a`` represents the number
+        $\sqrt{2}$ in the field $\mathbb{Q}(\sqrt{2} + \sqrt{3})$. Rendering
+        ``a`` as a polynomial,
+
+        >>> a.as_poly().as_expr(x)
+        x**3/2 - 9*x/2
+
+        reflects the fact that $\sqrt{2} = \theta^3/2 - 9 \theta/2$, where
+        $\theta = \sqrt{2} + \sqrt{3}$.
+
+        ``a`` is not equal to its own primitive element. Its minpoly
+
+        >>> a.minpoly.as_poly().as_expr(x)
+        x**4 - 10*x**2 + 1
+
+        is that of $\theta$.
+
+        Converting to a primitive element,
+
+        >>> a_prim = a.to_primitive_element()
+        >>> a_prim.minpoly.as_poly().as_expr(x)
+        x**2 - 2
+
+        we obtain an :py:class:`~.AlgebraicNumber` whose ``minpoly`` is that of
+        the number itself.
+
+        Parameters
+        ==========
+
+        radicals : boolean, optional (default=True)
+            If ``True``, then we will try to return an
+            :py:class:`~.AlgebraicNumber` whose ``root`` is an expression
+            in radicals. If that is not possible (or if *radicals* is
+            ``False``), ``root`` will be a :py:class:`~.ComplexRootOf`.
+
+        Returns
+        =======
+
+        AlgebraicNumber
+
+        See Also
+        ========
+
+        is_primitive_element
+
+        """
+        if self.is_primitive_element:
+            return self
+        m = self.minpoly_of_element()
+        r = self.to_root(radicals=radicals)
+        return AlgebraicNumber((m, r))
+
+    def minpoly_of_element(self):
+        r"""
+        Compute the minimal polynomial for this algebraic number.
+
+        Explanation
+        ===========
+
+        Recall that we represent an element $\alpha \in \mathbb{Q}(\theta)$.
+        Our instance attribute ``self.minpoly`` is the minimal polynomial for
+        our primitive element $\theta$. This method computes the minimal
+        polynomial for $\alpha$.
+
+        """
+        if self._own_minpoly is None:
+            if self.is_primitive_element:
+                self._own_minpoly = self.minpoly
+            else:
+                from sympy.polys.numberfields.minpoly import minpoly
+                theta = self.primitive_element()
+                self._own_minpoly = minpoly(self.as_expr(theta), polys=True)
+        return self._own_minpoly
+
+    def to_root(self, radicals=True, minpoly=None):
+        """
+        Convert to an :py:class:`~.Expr` that is not an
+        :py:class:`~.AlgebraicNumber`, specifically, either a
+        :py:class:`~.ComplexRootOf`, or, optionally and where possible, an
+        expression in radicals.
+
+        Parameters
+        ==========
+
+        radicals : boolean, optional (default=True)
+            If ``True``, then we will try to return the root as an expression
+            in radicals. If that is not possible, we will return a
+            :py:class:`~.ComplexRootOf`.
+
+        minpoly : :py:class:`~.Poly`
+            If the minimal polynomial for `self` has been pre-computed, it can
+            be passed in order to save time.
+
+        """
+        if self.is_primitive_element and not isinstance(self.root, AlgebraicNumber):
+            return self.root
+        m = minpoly or self.minpoly_of_element()
+        roots = m.all_roots(radicals=radicals)
+        if len(roots) == 1:
+            return roots[0]
+        ex = self.as_expr()
+        for b in roots:
+            if m.same_root(b, ex):
+                return b
+
+
+class RationalConstant(Rational):
+    """
+    Abstract base class for rationals with specific behaviors
+
+    Derived classes must define class attributes p and q and should probably all
+    be singletons.
+    """
+    __slots__ = ()
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+
+class IntegerConstant(Integer):
+    __slots__ = ()
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+
+class Zero(IntegerConstant, metaclass=Singleton):
+    """The number zero.
+
+    Zero is a singleton, and can be accessed by ``S.Zero``
+
+    Examples
+    ========
+
+    >>> from sympy import S, Integer
+    >>> Integer(0) is S.Zero
+    True
+    >>> 1/S.Zero
+    zoo
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Zero
+    """
+
+    p = 0
+    q = 1
+    is_positive = False
+    is_negative = False
+    is_zero = True
+    is_number = True
+    is_comparable = True
+
+    __slots__ = ()
+
+    def __getnewargs__(self):
+        return ()
+
+    @staticmethod
+    def __abs__():
+        return S.Zero
+
+    @staticmethod
+    def __neg__():
+        return S.Zero
+
+    def _eval_power(self, expt):
+        if expt.is_extended_positive:
+            return self
+        if expt.is_extended_negative:
+            return S.ComplexInfinity
+        if expt.is_extended_real is False:
+            return S.NaN
+        if expt.is_zero:
+            return S.One
+
+        # infinities are already handled with pos and neg
+        # tests above; now throw away leading numbers on Mul
+        # exponent since 0**-x = zoo**x even when x == 0
+        coeff, terms = expt.as_coeff_Mul()
+        if coeff.is_negative:
+            return S.ComplexInfinity**terms
+        if coeff is not S.One:  # there is a Number to discard
+            return self**terms
+
+    def _eval_order(self, *symbols):
+        # Order(0,x) -> 0
+        return self
+
+    def __bool__(self):
+        return False
+
+
+class One(IntegerConstant, metaclass=Singleton):
+    """The number one.
+
+    One is a singleton, and can be accessed by ``S.One``.
+
+    Examples
+    ========
+
+    >>> from sympy import S, Integer
+    >>> Integer(1) is S.One
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/1_%28number%29
+    """
+    is_number = True
+    is_positive = True
+
+    p = 1
+    q = 1
+
+    __slots__ = ()
+
+    def __getnewargs__(self):
+        return ()
+
+    @staticmethod
+    def __abs__():
+        return S.One
+
+    @staticmethod
+    def __neg__():
+        return S.NegativeOne
+
+    def _eval_power(self, expt):
+        return self
+
+    def _eval_order(self, *symbols):
+        return
+
+    @staticmethod
+    def factors(limit=None, use_trial=True, use_rho=False, use_pm1=False,
+                verbose=False, visual=False):
+        if visual:
+            return S.One
+        else:
+            return {}
+
+
+class NegativeOne(IntegerConstant, metaclass=Singleton):
+    """The number negative one.
+
+    NegativeOne is a singleton, and can be accessed by ``S.NegativeOne``.
+
+    Examples
+    ========
+
+    >>> from sympy import S, Integer
+    >>> Integer(-1) is S.NegativeOne
+    True
+
+    See Also
+    ========
+
+    One
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/%E2%88%921_%28number%29
+
+    """
+    is_number = True
+
+    p = -1
+    q = 1
+
+    __slots__ = ()
+
+    def __getnewargs__(self):
+        return ()
+
+    @staticmethod
+    def __abs__():
+        return S.One
+
+    @staticmethod
+    def __neg__():
+        return S.One
+
+    def _eval_power(self, expt):
+        if expt.is_odd:
+            return S.NegativeOne
+        if expt.is_even:
+            return S.One
+        if isinstance(expt, Number):
+            if isinstance(expt, Float):
+                return Float(-1.0)**expt
+            if expt is S.NaN:
+                return S.NaN
+            if expt in (S.Infinity, S.NegativeInfinity):
+                return S.NaN
+            if expt is S.Half:
+                return S.ImaginaryUnit
+            if isinstance(expt, Rational):
+                if expt.q == 2:
+                    return S.ImaginaryUnit**Integer(expt.p)
+                i, r = divmod(expt.p, expt.q)
+                if i:
+                    return self**i*self**Rational(r, expt.q)
+        return
+
+
+class Half(RationalConstant, metaclass=Singleton):
+    """The rational number 1/2.
+
+    Half is a singleton, and can be accessed by ``S.Half``.
+
+    Examples
+    ========
+
+    >>> from sympy import S, Rational
+    >>> Rational(1, 2) is S.Half
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/One_half
+    """
+    is_number = True
+
+    p = 1
+    q = 2
+
+    __slots__ = ()
+
+    def __getnewargs__(self):
+        return ()
+
+    @staticmethod
+    def __abs__():
+        return S.Half
+
+
+class Infinity(Number, metaclass=Singleton):
+    r"""Positive infinite quantity.
+
+    Explanation
+    ===========
+
+    In real analysis the symbol `\infty` denotes an unbounded
+    limit: `x\to\infty` means that `x` grows without bound.
+
+    Infinity is often used not only to define a limit but as a value
+    in the affinely extended real number system.  Points labeled `+\infty`
+    and `-\infty` can be added to the topological space of the real numbers,
+    producing the two-point compactification of the real numbers.  Adding
+    algebraic properties to this gives us the extended real numbers.
+
+    Infinity is a singleton, and can be accessed by ``S.Infinity``,
+    or can be imported as ``oo``.
+
+    Examples
+    ========
+
+    >>> from sympy import oo, exp, limit, Symbol
+    >>> 1 + oo
+    oo
+    >>> 42/oo
+    0
+    >>> x = Symbol('x')
+    >>> limit(exp(x), x, oo)
+    oo
+
+    See Also
+    ========
+
+    NegativeInfinity, NaN
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Infinity
+    """
+
+    is_commutative = True
+    is_number = True
+    is_complex = False
+    is_extended_real = True
+    is_infinite = True
+    is_comparable = True
+    is_extended_positive = True
+    is_prime = False
+
+    __slots__ = ()
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+    def _latex(self, printer):
+        return r"\infty"
+
+    def _eval_subs(self, old, new):
+        if self == old:
+            return new
+
+    def _eval_evalf(self, prec=None):
+        return Float('inf')
+
+    def evalf(self, prec=None, **options):
+        return self._eval_evalf(prec)
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other in (S.NegativeInfinity, S.NaN):
+                return S.NaN
+            return self
+        return Number.__add__(self, other)
+    __radd__ = __add__
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other in (S.Infinity, S.NaN):
+                return S.NaN
+            return self
+        return Number.__sub__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __rsub__(self, other):
+        return (-self).__add__(other)
+
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other.is_zero or other is S.NaN:
+                return S.NaN
+            if other.is_extended_positive:
+                return self
+            return S.NegativeInfinity
+        return Number.__mul__(self, other)
+    __rmul__ = __mul__
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other is S.Infinity or \
+                other is S.NegativeInfinity or \
+                    other is S.NaN:
+                return S.NaN
+            if other.is_extended_nonnegative:
+                return self
+            return S.NegativeInfinity
+        return Number.__truediv__(self, other)
+
+    def __abs__(self):
+        return S.Infinity
+
+    def __neg__(self):
+        return S.NegativeInfinity
+
+    def _eval_power(self, expt):
+        """
+        ``expt`` is symbolic object but not equal to 0 or 1.
+
+        ================ ======= ==============================
+        Expression       Result  Notes
+        ================ ======= ==============================
+        ``oo ** nan``    ``nan``
+        ``oo ** -p``     ``0``   ``p`` is number, ``oo``
+        ================ ======= ==============================
+
+        See Also
+        ========
+        Pow
+        NaN
+        NegativeInfinity
+
+        """
+        if expt.is_extended_positive:
+            return S.Infinity
+        if expt.is_extended_negative:
+            return S.Zero
+        if expt is S.NaN:
+            return S.NaN
+        if expt is S.ComplexInfinity:
+            return S.NaN
+        if expt.is_extended_real is False and expt.is_number:
+            from sympy.functions.elementary.complexes import re
+            expt_real = re(expt)
+            if expt_real.is_positive:
+                return S.ComplexInfinity
+            if expt_real.is_negative:
+                return S.Zero
+            if expt_real.is_zero:
+                return S.NaN
+
+            return self**expt.evalf()
+
+    def _as_mpf_val(self, prec):
+        return mlib.finf
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def __eq__(self, other):
+        return other is S.Infinity or other == float('inf')
+
+    def __ne__(self, other):
+        return other is not S.Infinity and other != float('inf')
+
+    __gt__ = Expr.__gt__
+    __ge__ = Expr.__ge__
+    __lt__ = Expr.__lt__
+    __le__ = Expr.__le__
+
+    @_sympifyit('other', NotImplemented)
+    def __mod__(self, other):
+        if not isinstance(other, Expr):
+            return NotImplemented
+        return S.NaN
+
+    __rmod__ = __mod__
+
+    def floor(self):
+        return self
+
+    def ceiling(self):
+        return self
+
+oo = S.Infinity
+
+
+class NegativeInfinity(Number, metaclass=Singleton):
+    """Negative infinite quantity.
+
+    NegativeInfinity is a singleton, and can be accessed
+    by ``S.NegativeInfinity``.
+
+    See Also
+    ========
+
+    Infinity
+    """
+
+    is_extended_real = True
+    is_complex = False
+    is_commutative = True
+    is_infinite = True
+    is_comparable = True
+    is_extended_negative = True
+    is_number = True
+    is_prime = False
+
+    __slots__ = ()
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+    def _latex(self, printer):
+        return r"-\infty"
+
+    def _eval_subs(self, old, new):
+        if self == old:
+            return new
+
+    def _eval_evalf(self, prec=None):
+        return Float('-inf')
+
+    def evalf(self, prec=None, **options):
+        return self._eval_evalf(prec)
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other in (S.Infinity, S.NaN):
+                return S.NaN
+            return self
+        return Number.__add__(self, other)
+    __radd__ = __add__
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other in (S.NegativeInfinity, S.NaN):
+                return S.NaN
+            return self
+        return Number.__sub__(self, other)
+
+    @_sympifyit('other', NotImplemented)
+    def __rsub__(self, other):
+        return (-self).__add__(other)
+
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other.is_zero or other is S.NaN:
+                return S.NaN
+            if other.is_extended_positive:
+                return self
+            return S.Infinity
+        return Number.__mul__(self, other)
+    __rmul__ = __mul__
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        if isinstance(other, Number) and global_parameters.evaluate:
+            if other is S.Infinity or \
+                other is S.NegativeInfinity or \
+                    other is S.NaN:
+                return S.NaN
+            if other.is_extended_nonnegative:
+                return self
+            return S.Infinity
+        return Number.__truediv__(self, other)
+
+    def __abs__(self):
+        return S.Infinity
+
+    def __neg__(self):
+        return S.Infinity
+
+    def _eval_power(self, expt):
+        """
+        ``expt`` is symbolic object but not equal to 0 or 1.
+
+        ================ ======= ==============================
+        Expression       Result  Notes
+        ================ ======= ==============================
+        ``(-oo) ** nan`` ``nan``
+        ``(-oo) ** oo``  ``nan``
+        ``(-oo) ** -oo`` ``nan``
+        ``(-oo) ** e``   ``oo``  ``e`` is positive even integer
+        ``(-oo) ** o``   ``-oo`` ``o`` is positive odd integer
+        ================ ======= ==============================
+
+        See Also
+        ========
+
+        Infinity
+        Pow
+        NaN
+
+        """
+        if expt.is_number:
+            if expt is S.NaN or \
+                expt is S.Infinity or \
+                    expt is S.NegativeInfinity:
+                return S.NaN
+
+            if isinstance(expt, Integer) and expt.is_extended_positive:
+                if expt.is_odd:
+                    return S.NegativeInfinity
+                else:
+                    return S.Infinity
+
+            inf_part = S.Infinity**expt
+            s_part = S.NegativeOne**expt
+            if inf_part == 0 and s_part.is_finite:
+                return inf_part
+            if (inf_part is S.ComplexInfinity and
+                    s_part.is_finite and not s_part.is_zero):
+                return S.ComplexInfinity
+            return s_part*inf_part
+
+    def _as_mpf_val(self, prec):
+        return mlib.fninf
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def __eq__(self, other):
+        return other is S.NegativeInfinity or other == float('-inf')
+
+    def __ne__(self, other):
+        return other is not S.NegativeInfinity and other != float('-inf')
+
+    __gt__ = Expr.__gt__
+    __ge__ = Expr.__ge__
+    __lt__ = Expr.__lt__
+    __le__ = Expr.__le__
+
+    @_sympifyit('other', NotImplemented)
+    def __mod__(self, other):
+        if not isinstance(other, Expr):
+            return NotImplemented
+        return S.NaN
+
+    __rmod__ = __mod__
+
+    def floor(self):
+        return self
+
+    def ceiling(self):
+        return self
+
+    def as_powers_dict(self):
+        return {S.NegativeOne: 1, S.Infinity: 1}
+
+
+class NaN(Number, metaclass=Singleton):
+    """
+    Not a Number.
+
+    Explanation
+    ===========
+
+    This serves as a place holder for numeric values that are indeterminate.
+    Most operations on NaN, produce another NaN.  Most indeterminate forms,
+    such as ``0/0`` or ``oo - oo` produce NaN.  Two exceptions are ``0**0``
+    and ``oo**0``, which all produce ``1`` (this is consistent with Python's
+    float).
+
+    NaN is loosely related to floating point nan, which is defined in the
+    IEEE 754 floating point standard, and corresponds to the Python
+    ``float('nan')``.  Differences are noted below.
+
+    NaN is mathematically not equal to anything else, even NaN itself.  This
+    explains the initially counter-intuitive results with ``Eq`` and ``==`` in
+    the examples below.
+
+    NaN is not comparable so inequalities raise a TypeError.  This is in
+    contrast with floating point nan where all inequalities are false.
+
+    NaN is a singleton, and can be accessed by ``S.NaN``, or can be imported
+    as ``nan``.
+
+    Examples
+    ========
+
+    >>> from sympy import nan, S, oo, Eq
+    >>> nan is S.NaN
+    True
+    >>> oo - oo
+    nan
+    >>> nan + 1
+    nan
+    >>> Eq(nan, nan)   # mathematical equality
+    False
+    >>> nan == nan     # structural equality
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/NaN
+
+    """
+    is_commutative = True
+    is_extended_real = None
+    is_real = None
+    is_rational = None
+    is_algebraic = None
+    is_transcendental = None
+    is_integer = None
+    is_comparable = False
+    is_finite = None
+    is_zero = None
+    is_prime = None
+    is_positive = None
+    is_negative = None
+    is_number = True
+
+    __slots__ = ()
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+    def _latex(self, printer):
+        return r"\text{NaN}"
+
+    def __neg__(self):
+        return self
+
+    @_sympifyit('other', NotImplemented)
+    def __add__(self, other):
+        return self
+
+    @_sympifyit('other', NotImplemented)
+    def __sub__(self, other):
+        return self
+
+    @_sympifyit('other', NotImplemented)
+    def __mul__(self, other):
+        return self
+
+    @_sympifyit('other', NotImplemented)
+    def __truediv__(self, other):
+        return self
+
+    def floor(self):
+        return self
+
+    def ceiling(self):
+        return self
+
+    def _as_mpf_val(self, prec):
+        return _mpf_nan
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def __eq__(self, other):
+        # NaN is structurally equal to another NaN
+        return other is S.NaN
+
+    def __ne__(self, other):
+        return other is not S.NaN
+
+    # Expr will _sympify and raise TypeError
+    __gt__ = Expr.__gt__
+    __ge__ = Expr.__ge__
+    __lt__ = Expr.__lt__
+    __le__ = Expr.__le__
+
+nan = S.NaN
+
+@dispatch(NaN, Expr) # type:ignore
+def _eval_is_eq(a, b): # noqa:F811
+    return False
+
+
+class ComplexInfinity(AtomicExpr, metaclass=Singleton):
+    r"""Complex infinity.
+
+    Explanation
+    ===========
+
+    In complex analysis the symbol `\tilde\infty`, called "complex
+    infinity", represents a quantity with infinite magnitude, but
+    undetermined complex phase.
+
+    ComplexInfinity is a singleton, and can be accessed by
+    ``S.ComplexInfinity``, or can be imported as ``zoo``.
+
+    Examples
+    ========
+
+    >>> from sympy import zoo
+    >>> zoo + 42
+    zoo
+    >>> 42/zoo
+    0
+    >>> zoo + zoo
+    nan
+    >>> zoo*zoo
+    zoo
+
+    See Also
+    ========
+
+    Infinity
+    """
+
+    is_commutative = True
+    is_infinite = True
+    is_number = True
+    is_prime = False
+    is_complex = False
+    is_extended_real = False
+
+    kind = NumberKind
+
+    __slots__ = ()
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+    def _latex(self, printer):
+        return r"\tilde{\infty}"
+
+    @staticmethod
+    def __abs__():
+        return S.Infinity
+
+    def floor(self):
+        return self
+
+    def ceiling(self):
+        return self
+
+    @staticmethod
+    def __neg__():
+        return S.ComplexInfinity
+
+    def _eval_power(self, expt):
+        if expt is S.ComplexInfinity:
+            return S.NaN
+
+        if isinstance(expt, Number):
+            if expt.is_zero:
+                return S.NaN
+            else:
+                if expt.is_positive:
+                    return S.ComplexInfinity
+                else:
+                    return S.Zero
+
+
+zoo = S.ComplexInfinity
+
+
+class NumberSymbol(AtomicExpr):
+
+    is_commutative = True
+    is_finite = True
+    is_number = True
+
+    __slots__ = ()
+
+    is_NumberSymbol = True
+
+    kind = NumberKind
+
+    def __new__(cls):
+        return AtomicExpr.__new__(cls)
+
+    def approximation(self, number_cls):
+        """ Return an interval with number_cls endpoints
+        that contains the value of NumberSymbol.
+        If not implemented, then return None.
+        """
+
+    def _eval_evalf(self, prec):
+        return Float._new(self._as_mpf_val(prec), prec)
+
+    def __eq__(self, other):
+        try:
+            other = _sympify(other)
+        except SympifyError:
+            return NotImplemented
+        if self is other:
+            return True
+        if other.is_Number and self.is_irrational:
+            return False
+
+        return False    # NumberSymbol != non-(Number|self)
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __le__(self, other):
+        if self is other:
+            return S.true
+        return Expr.__le__(self, other)
+
+    def __ge__(self, other):
+        if self is other:
+            return S.true
+        return Expr.__ge__(self, other)
+
+    def __int__(self):
+        # subclass with appropriate return value
+        raise NotImplementedError
+
+    def __hash__(self):
+        return super().__hash__()
+
+
+class Exp1(NumberSymbol, metaclass=Singleton):
+    r"""The `e` constant.
+
+    Explanation
+    ===========
+
+    The transcendental number `e = 2.718281828\ldots` is the base of the
+    natural logarithm and of the exponential function, `e = \exp(1)`.
+    Sometimes called Euler's number or Napier's constant.
+
+    Exp1 is a singleton, and can be accessed by ``S.Exp1``,
+    or can be imported as ``E``.
+
+    Examples
+    ========
+
+    >>> from sympy import exp, log, E
+    >>> E is exp(1)
+    True
+    >>> log(E)
+    1
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/E_%28mathematical_constant%29
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False  # XXX Forces is_negative/is_nonnegative
+    is_irrational = True
+    is_number = True
+    is_algebraic = False
+    is_transcendental = True
+
+    __slots__ = ()
+
+    def _latex(self, printer):
+        return r"e"
+
+    @staticmethod
+    def __abs__():
+        return S.Exp1
+
+    def __int__(self):
+        return 2
+
+    def _as_mpf_val(self, prec):
+        return mpf_e(prec)
+
+    def approximation_interval(self, number_cls):
+        if issubclass(number_cls, Integer):
+            return (Integer(2), Integer(3))
+        elif issubclass(number_cls, Rational):
+            pass
+
+    def _eval_power(self, expt):
+        if global_parameters.exp_is_pow:
+            return self._eval_power_exp_is_pow(expt)
+        else:
+            from sympy.functions.elementary.exponential import exp
+            return exp(expt)
+
+    def _eval_power_exp_is_pow(self, arg):
+        if arg.is_Number:
+            if arg is oo:
+                return oo
+            elif arg == -oo:
+                return S.Zero
+        from sympy.functions.elementary.exponential import log
+        if isinstance(arg, log):
+            return arg.args[0]
+
+        # don't autoexpand Pow or Mul (see the issue 3351):
+        elif not arg.is_Add:
+            Ioo = I*oo
+            if arg in [Ioo, -Ioo]:
+                return nan
+
+            coeff = arg.coeff(pi*I)
+            if coeff:
+                if (2*coeff).is_integer:
+                    if coeff.is_even:
+                        return S.One
+                    elif coeff.is_odd:
+                        return S.NegativeOne
+                    elif (coeff + S.Half).is_even:
+                        return -I
+                    elif (coeff + S.Half).is_odd:
+                        return I
+                elif coeff.is_Rational:
+                    ncoeff = coeff % 2 # restrict to [0, 2pi)
+                    if ncoeff > 1: # restrict to (-pi, pi]
+                        ncoeff -= 2
+                    if ncoeff != coeff:
+                        return S.Exp1**(ncoeff*S.Pi*S.ImaginaryUnit)
+
+            # Warning: code in risch.py will be very sensitive to changes
+            # in this (see DifferentialExtension).
+
+            # look for a single log factor
+
+            coeff, terms = arg.as_coeff_Mul()
+
+            # but it can't be multiplied by oo
+            if coeff in (oo, -oo):
+                return
+
+            coeffs, log_term = [coeff], None
+            for term in Mul.make_args(terms):
+                if isinstance(term, log):
+                    if log_term is None:
+                        log_term = term.args[0]
+                    else:
+                        return
+                elif term.is_comparable:
+                    coeffs.append(term)
+                else:
+                    return
+
+            return log_term**Mul(*coeffs) if log_term else None
+        elif arg.is_Add:
+            out = []
+            add = []
+            argchanged = False
+            for a in arg.args:
+                if a is S.One:
+                    add.append(a)
+                    continue
+                newa = self**a
+                if isinstance(newa, Pow) and newa.base is self:
+                    if newa.exp != a:
+                        add.append(newa.exp)
+                        argchanged = True
+                    else:
+                        add.append(a)
+                else:
+                    out.append(newa)
+            if out or argchanged:
+                return Mul(*out)*Pow(self, Add(*add), evaluate=False)
+        elif arg.is_Matrix:
+            return arg.exp()
+
+    def _eval_rewrite_as_sin(self, **kwargs):
+        from sympy.functions.elementary.trigonometric import sin
+        return sin(I + S.Pi/2) - I*sin(I)
+
+    def _eval_rewrite_as_cos(self, **kwargs):
+        from sympy.functions.elementary.trigonometric import cos
+        return cos(I) + I*cos(I + S.Pi/2)
+
+E = S.Exp1
+
+
+class Pi(NumberSymbol, metaclass=Singleton):
+    r"""The `\pi` constant.
+
+    Explanation
+    ===========
+
+    The transcendental number `\pi = 3.141592654\ldots` represents the ratio
+    of a circle's circumference to its diameter, the area of the unit circle,
+    the half-period of trigonometric functions, and many other things
+    in mathematics.
+
+    Pi is a singleton, and can be accessed by ``S.Pi``, or can
+    be imported as ``pi``.
+
+    Examples
+    ========
+
+    >>> from sympy import S, pi, oo, sin, exp, integrate, Symbol
+    >>> S.Pi
+    pi
+    >>> pi > 3
+    True
+    >>> pi.is_irrational
+    True
+    >>> x = Symbol('x')
+    >>> sin(x + 2*pi)
+    sin(x)
+    >>> integrate(exp(-x**2), (x, -oo, oo))
+    sqrt(pi)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Pi
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False
+    is_irrational = True
+    is_number = True
+    is_algebraic = False
+    is_transcendental = True
+
+    __slots__ = ()
+
+    def _latex(self, printer):
+        return r"\pi"
+
+    @staticmethod
+    def __abs__():
+        return S.Pi
+
+    def __int__(self):
+        return 3
+
+    def _as_mpf_val(self, prec):
+        return mpf_pi(prec)
+
+    def approximation_interval(self, number_cls):
+        if issubclass(number_cls, Integer):
+            return (Integer(3), Integer(4))
+        elif issubclass(number_cls, Rational):
+            return (Rational(223, 71, 1), Rational(22, 7, 1))
+
+pi = S.Pi
+
+
+class GoldenRatio(NumberSymbol, metaclass=Singleton):
+    r"""The golden ratio, `\phi`.
+
+    Explanation
+    ===========
+
+    `\phi = \frac{1 + \sqrt{5}}{2}` is an algebraic number.  Two quantities
+    are in the golden ratio if their ratio is the same as the ratio of
+    their sum to the larger of the two quantities, i.e. their maximum.
+
+    GoldenRatio is a singleton, and can be accessed by ``S.GoldenRatio``.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> S.GoldenRatio > 1
+    True
+    >>> S.GoldenRatio.expand(func=True)
+    1/2 + sqrt(5)/2
+    >>> S.GoldenRatio.is_irrational
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Golden_ratio
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False
+    is_irrational = True
+    is_number = True
+    is_algebraic = True
+    is_transcendental = False
+
+    __slots__ = ()
+
+    def _latex(self, printer):
+        return r"\phi"
+
+    def __int__(self):
+        return 1
+
+    def _as_mpf_val(self, prec):
+         # XXX track down why this has to be increased
+        rv = mlib.from_man_exp(phi_fixed(prec + 10), -prec - 10)
+        return mpf_norm(rv, prec)
+
+    def _eval_expand_func(self, **hints):
+        from sympy.functions.elementary.miscellaneous import sqrt
+        return S.Half + S.Half*sqrt(5)
+
+    def approximation_interval(self, number_cls):
+        if issubclass(number_cls, Integer):
+            return (S.One, Rational(2))
+        elif issubclass(number_cls, Rational):
+            pass
+
+    _eval_rewrite_as_sqrt = _eval_expand_func
+
+
+class TribonacciConstant(NumberSymbol, metaclass=Singleton):
+    r"""The tribonacci constant.
+
+    Explanation
+    ===========
+
+    The tribonacci numbers are like the Fibonacci numbers, but instead
+    of starting with two predetermined terms, the sequence starts with
+    three predetermined terms and each term afterwards is the sum of the
+    preceding three terms.
+
+    The tribonacci constant is the ratio toward which adjacent tribonacci
+    numbers tend. It is a root of the polynomial `x^3 - x^2 - x - 1 = 0`,
+    and also satisfies the equation `x + x^{-3} = 2`.
+
+    TribonacciConstant is a singleton, and can be accessed
+    by ``S.TribonacciConstant``.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> S.TribonacciConstant > 1
+    True
+    >>> S.TribonacciConstant.expand(func=True)
+    1/3 + (19 - 3*sqrt(33))**(1/3)/3 + (3*sqrt(33) + 19)**(1/3)/3
+    >>> S.TribonacciConstant.is_irrational
+    True
+    >>> S.TribonacciConstant.n(20)
+    1.8392867552141611326
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False
+    is_irrational = True
+    is_number = True
+    is_algebraic = True
+    is_transcendental = False
+
+    __slots__ = ()
+
+    def _latex(self, printer):
+        return r"\text{TribonacciConstant}"
+
+    def __int__(self):
+        return 1
+
+    def _as_mpf_val(self, prec):
+        return self._eval_evalf(prec)._mpf_
+
+    def _eval_evalf(self, prec):
+        rv = self._eval_expand_func(function=True)._eval_evalf(prec + 4)
+        return Float(rv, precision=prec)
+
+    def _eval_expand_func(self, **hints):
+        from sympy.functions.elementary.miscellaneous import cbrt, sqrt
+        return (1 + cbrt(19 - 3*sqrt(33)) + cbrt(19 + 3*sqrt(33))) / 3
+
+    def approximation_interval(self, number_cls):
+        if issubclass(number_cls, Integer):
+            return (S.One, Rational(2))
+        elif issubclass(number_cls, Rational):
+            pass
+
+    _eval_rewrite_as_sqrt = _eval_expand_func
+
+
+class EulerGamma(NumberSymbol, metaclass=Singleton):
+    r"""The Euler-Mascheroni constant.
+
+    Explanation
+    ===========
+
+    `\gamma = 0.5772157\ldots` (also called Euler's constant) is a mathematical
+    constant recurring in analysis and number theory.  It is defined as the
+    limiting difference between the harmonic series and the
+    natural logarithm:
+
+    .. math:: \gamma = \lim\limits_{n\to\infty}
+              \left(\sum\limits_{k=1}^n\frac{1}{k} - \ln n\right)
+
+    EulerGamma is a singleton, and can be accessed by ``S.EulerGamma``.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> S.EulerGamma.is_irrational
+    >>> S.EulerGamma > 0
+    True
+    >>> S.EulerGamma > 1
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False
+    is_irrational = None
+    is_number = True
+
+    __slots__ = ()
+
+    def _latex(self, printer):
+        return r"\gamma"
+
+    def __int__(self):
+        return 0
+
+    def _as_mpf_val(self, prec):
+         # XXX track down why this has to be increased
+        v = mlib.libhyper.euler_fixed(prec + 10)
+        rv = mlib.from_man_exp(v, -prec - 10)
+        return mpf_norm(rv, prec)
+
+    def approximation_interval(self, number_cls):
+        if issubclass(number_cls, Integer):
+            return (S.Zero, S.One)
+        elif issubclass(number_cls, Rational):
+            return (S.Half, Rational(3, 5, 1))
+
+
+class Catalan(NumberSymbol, metaclass=Singleton):
+    r"""Catalan's constant.
+
+    Explanation
+    ===========
+
+    $G = 0.91596559\ldots$ is given by the infinite series
+
+    .. math:: G = \sum_{k=0}^{\infty} \frac{(-1)^k}{(2k+1)^2}
+
+    Catalan is a singleton, and can be accessed by ``S.Catalan``.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> S.Catalan.is_irrational
+    >>> S.Catalan > 0
+    True
+    >>> S.Catalan > 1
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Catalan%27s_constant
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False
+    is_irrational = None
+    is_number = True
+
+    __slots__ = ()
+
+    def __int__(self):
+        return 0
+
+    def _as_mpf_val(self, prec):
+        # XXX track down why this has to be increased
+        v = mlib.catalan_fixed(prec + 10)
+        rv = mlib.from_man_exp(v, -prec - 10)
+        return mpf_norm(rv, prec)
+
+    def approximation_interval(self, number_cls):
+        if issubclass(number_cls, Integer):
+            return (S.Zero, S.One)
+        elif issubclass(number_cls, Rational):
+            return (Rational(9, 10, 1), S.One)
+
+    def _eval_rewrite_as_Sum(self, k_sym=None, symbols=None, **hints):
+        if (k_sym is not None) or (symbols is not None):
+            return self
+        from .symbol import Dummy
+        from sympy.concrete.summations import Sum
+        k = Dummy('k', integer=True, nonnegative=True)
+        return Sum(S.NegativeOne**k / (2*k+1)**2, (k, 0, S.Infinity))
+
+    def _latex(self, printer):
+        return "G"
+
+
+class ImaginaryUnit(AtomicExpr, metaclass=Singleton):
+    r"""The imaginary unit, `i = \sqrt{-1}`.
+
+    I is a singleton, and can be accessed by ``S.I``, or can be
+    imported as ``I``.
+
+    Examples
+    ========
+
+    >>> from sympy import I, sqrt
+    >>> sqrt(-1)
+    I
+    >>> I*I
+    -1
+    >>> 1/I
+    -I
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Imaginary_unit
+    """
+
+    is_commutative = True
+    is_imaginary = True
+    is_finite = True
+    is_number = True
+    is_algebraic = True
+    is_transcendental = False
+
+    kind = NumberKind
+
+    __slots__ = ()
+
+    def _latex(self, printer):
+        return printer._settings['imaginary_unit_latex']
+
+    @staticmethod
+    def __abs__():
+        return S.One
+
+    def _eval_evalf(self, prec):
+        return self
+
+    def _eval_conjugate(self):
+        return -S.ImaginaryUnit
+
+    def _eval_power(self, expt):
+        """
+        b is I = sqrt(-1)
+        e is symbolic object but not equal to 0, 1
+
+        I**r -> (-1)**(r/2) -> exp(r/2*Pi*I) -> sin(Pi*r/2) + cos(Pi*r/2)*I, r is decimal
+        I**0 mod 4 -> 1
+        I**1 mod 4 -> I
+        I**2 mod 4 -> -1
+        I**3 mod 4 -> -I
+        """
+
+        if isinstance(expt, Integer):
+            expt = expt % 4
+            if expt == 0:
+                return S.One
+            elif expt == 1:
+                return S.ImaginaryUnit
+            elif expt == 2:
+                return S.NegativeOne
+            elif expt == 3:
+                return -S.ImaginaryUnit
+        if isinstance(expt, Rational):
+            i, r = divmod(expt, 2)
+            rv = Pow(S.ImaginaryUnit, r, evaluate=False)
+            if i % 2:
+                return Mul(S.NegativeOne, rv, evaluate=False)
+            return rv
+
+    def as_base_exp(self):
+        return S.NegativeOne, S.Half
+
+    @property
+    def _mpc_(self):
+        return (Float(0)._mpf_, Float(1)._mpf_)
+
+
+I = S.ImaginaryUnit
+
+
+def int_valued(x):
+    """return True only for a literal Number whose internal
+    representation as a fraction has a denominator of 1,
+    else False, i.e. integer, with no fractional part.
+    """
+    if isinstance(x, (SYMPY_INTS, int)):
+        return True
+    if type(x) is float:
+        return x.is_integer()
+    if isinstance(x, Integer):
+        return True
+    if isinstance(x, Float):
+        # x = s*m*2**p; _mpf_ = s,m,e,p
+        return x._mpf_[2] >= 0
+    return False  # or add new types to recognize
+
+
+def equal_valued(x, y):
+    """Compare expressions treating plain floats as rationals.
+
+    Examples
+    ========
+
+    >>> from sympy import S, symbols, Rational, Float
+    >>> from sympy.core.numbers import equal_valued
+    >>> equal_valued(1, 2)
+    False
+    >>> equal_valued(1, 1)
+    True
+
+    In SymPy expressions with Floats compare unequal to corresponding
+    expressions with rationals:
+
+    >>> x = symbols('x')
+    >>> x**2 == x**2.0
+    False
+
+    However an individual Float compares equal to a Rational:
+
+    >>> Rational(1, 2) == Float(0.5)
+    False
+
+    In a future version of SymPy this might change so that Rational and Float
+    compare unequal. This function provides the behavior currently expected of
+    ``==`` so that it could still be used if the behavior of ``==`` were to
+    change in future.
+
+    >>> equal_valued(1, 1.0) # Float vs Rational
+    True
+    >>> equal_valued(S(1).n(3), S(1).n(5)) # Floats of different precision
+    True
+
+    Explanation
+    ===========
+
+    In future SymPy versions Float and Rational might compare unequal and floats
+    with different precisions might compare unequal. In that context a function
+    is needed that can check if a number is equal to 1 or 0 etc. The idea is
+    that instead of testing ``if x == 1:`` if we want to accept floats like
+    ``1.0`` as well then the test can be written as ``if equal_valued(x, 1):``
+    or ``if equal_valued(x, 2):``. Since this function is intended to be used
+    in situations where one or both operands are expected to be concrete
+    numbers like 1 or 0 the function does not recurse through the args of any
+    compound expression to compare any nested floats.
+
+    References
+    ==========
+
+    .. [1] https://github.com/sympy/sympy/pull/20033
+    """
+    x = _sympify(x)
+    y = _sympify(y)
+
+    # Handle everything except Float/Rational first
+    if not x.is_Float and not y.is_Float:
+        return x == y
+    elif x.is_Float and y.is_Float:
+        # Compare values without regard for precision
+        return x._mpf_ == y._mpf_
+    elif x.is_Float:
+        x, y = y, x
+    if not x.is_Rational:
+        return False
+
+    # Now y is Float and x is Rational. A simple approach at this point would
+    # just be x == Rational(y) but if y has a large exponent creating a
+    # Rational could be prohibitively expensive.
+
+    sign, man, exp, _ = y._mpf_
+    p, q = x.p, x.q
+
+    if sign:
+        man = -man
+
+    if exp == 0:
+        # y odd integer
+        return q == 1 and man == p
+    elif exp > 0:
+        # y even integer
+        if q != 1:
+            return False
+        if p.bit_length() != man.bit_length() + exp:
+            return False
+        return man << exp == p
+    else:
+        # y non-integer. Need p == man and q == 2**-exp
+        if p != man:
+            return False
+        neg_exp = -exp
+        if q.bit_length() - 1 != neg_exp:
+            return False
+        return (1 << neg_exp) == q
+
+
+def all_close(expr1, expr2, rtol=1e-5, atol=1e-8):
+    """Return True if expr1 and expr2 are numerically close.
+
+    The expressions must have the same structure, but any Rational, Integer, or
+    Float numbers they contain are compared approximately using rtol and atol.
+    Any other parts of expressions are compared exactly. However, allowance is
+    made to allow for the additive and multiplicative identities.
+
+    Relative tolerance is measured with respect to expr2 so when used in
+    testing expr2 should be the expected correct answer.
+
+    Examples
+    ========
+
+    >>> from sympy import exp
+    >>> from sympy.abc import x, y
+    >>> from sympy.core.numbers import all_close
+    >>> expr1 = 0.1*exp(x - y)
+    >>> expr2 = exp(x - y)/10
+    >>> expr1
+    0.1*exp(x - y)
+    >>> expr2
+    exp(x - y)/10
+    >>> expr1 == expr2
+    False
+    >>> all_close(expr1, expr2)
+    True
+
+    Identities are automatically supplied:
+
+    >>> all_close(x, x + 1e-10)
+    True
+    >>> all_close(x, 1.0*x)
+    True
+    >>> all_close(x, 1.0*x + 1e-10)
+    True
+
+    """
+    NUM_TYPES = (Rational, Float)
+
+    def _all_close(obj1, obj2):
+        if type(obj1) == type(obj2) and isinstance(obj1, (list, tuple)):
+            if len(obj1) != len(obj2):
+                return False
+            return all(_all_close(e1, e2) for e1, e2 in zip(obj1, obj2))
+        else:
+            return _all_close_expr(_sympify(obj1), _sympify(obj2))
+
+    def _all_close_expr(expr1, expr2):
+        num1 = isinstance(expr1, NUM_TYPES)
+        num2 = isinstance(expr2, NUM_TYPES)
+        if num1 != num2:
+            return False
+        elif num1:
+            return _close_num(expr1, expr2)
+        if expr1.is_Add or expr1.is_Mul or expr2.is_Add or expr2.is_Mul:
+            return _all_close_ac(expr1, expr2)
+        if expr1.func != expr2.func or len(expr1.args) != len(expr2.args):
+            return False
+        args = zip(expr1.args, expr2.args)
+        return all(_all_close_expr(a1, a2) for a1, a2 in args)
+
+    def _close_num(num1, num2):
+        return bool(abs(num1 - num2) <= atol + rtol*abs(num2))
+
+    def _all_close_ac(expr1, expr2):
+        # compare expressions with associative commutative operators for
+        # approximate equality by seeing that all terms have equivalent
+        # coefficients (which are always Rational or Float)
+        if expr1.is_Mul or expr2.is_Mul:
+            # as_coeff_mul automatically will supply coeff of 1
+            c1, e1 = expr1.as_coeff_mul(rational=False)
+            c2, e2 = expr2.as_coeff_mul(rational=False)
+            if not _close_num(c1, c2):
+                return False
+            s1 = set(e1)
+            s2 = set(e2)
+            common = s1 & s2
+            s1 -= common
+            s2 -= common
+            if not s1:
+                return True
+            if not any(i.has(Float) for j in (s1, s2) for i in j):
+                return False
+            # factors might not be matching, e.g.
+            # x != x**1.0, exp(x) != exp(1.0*x), etc...
+            s1 = [i.as_base_exp() for i in ordered(s1)]
+            s2 = [i.as_base_exp() for i in ordered(s2)]
+            unmatched = list(range(len(s1)))
+            for be1 in s1:
+                for i in unmatched:
+                    be2 = s2[i]
+                    if _all_close(be1, be2):
+                        unmatched.remove(i)
+                        break
+                else:
+                    return False
+            return not(unmatched)
+        assert expr1.is_Add or expr2.is_Add
+        cd1 = expr1.as_coefficients_dict()
+        cd2 = expr2.as_coefficients_dict()
+        # this test will assure that the key of 1 is in
+        # each dict and that they have equal values
+        if not _close_num(cd1[1], cd2[1]):
+            return False
+        if len(cd1) != len(cd2):
+            return False
+        for k in list(cd1):
+            if k in cd2:
+                if not _close_num(cd1.pop(k), cd2.pop(k)):
+                    return False
+            # k (or a close version in cd2) might have
+            # Floats in a factor of the term which will
+            # be handled below
+        else:
+            if not cd1:
+                return True
+        for k1 in cd1:
+            for k2 in cd2:
+                if _all_close_expr(k1, k2):
+                    # found a matching key
+                    # XXX there could be a corner case where
+                    # more than 1 might match and the numbers are
+                    # such that one is better than the other
+                    # that is not being considered here
+                    if not _close_num(cd1[k1], cd2[k2]):
+                        return False
+                    break
+            else:
+                # no key matched
+                return False
+        return True
+
+    return _all_close(expr1, expr2)
+
+
+@dispatch(Tuple, Number) # type:ignore
+def _eval_is_eq(self, other): # noqa: F811
+    return False
+
+
+def sympify_fractions(f):
+    return Rational._new(f.numerator, f.denominator, 1)
+
+_sympy_converter[fractions.Fraction] = sympify_fractions
+
+
+if gmpy is not None:
+
+    def sympify_mpz(x):
+        return Integer(int(x))
+
+    def sympify_mpq(x):
+        return Rational(int(x.numerator), int(x.denominator))
+
+    _sympy_converter[type(gmpy.mpz(1))] = sympify_mpz
+    _sympy_converter[type(gmpy.mpq(1, 2))] = sympify_mpq
+
+
+if flint is not None:
+
+    def sympify_fmpz(x):
+        return Integer(int(x))
+
+    def sympify_fmpq(x):
+        return Rational(int(x.numerator), int(x.denominator))
+
+    _sympy_converter[type(flint.fmpz(1))] = sympify_fmpz
+    _sympy_converter[type(flint.fmpq(1, 2))] = sympify_fmpq
+
+
+def sympify_mpmath(x):
+    return Expr._from_mpmath(x, x.context.prec)
+
+_sympy_converter[mpnumeric] = sympify_mpmath
+
+
+def sympify_complex(a):
+    real, imag = list(map(sympify, (a.real, a.imag)))
+    return real + S.ImaginaryUnit*imag
+
+_sympy_converter[complex] = sympify_complex
+
+from .power import Pow
+from .mul import Mul
+Mul.identity = One()
+from .add import Add
+Add.identity = Zero()
+
+
+def _register_classes():
+    numbers.Number.register(Number)
+    numbers.Real.register(Float)
+    numbers.Rational.register(Rational)
+    numbers.Integral.register(Integer)
+
+_register_classes()
+
+_illegal = (S.NaN, S.Infinity, S.NegativeInfinity, S.ComplexInfinity)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/operations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/operations.py
new file mode 100644
index 0000000000000000000000000000000000000000..70d22127eb4d3f69fc5e304ab38f5cce9c4bb551
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/operations.py
@@ -0,0 +1,741 @@
+from __future__ import annotations
+
+from typing import overload, TYPE_CHECKING
+
+from operator import attrgetter
+from collections import defaultdict
+
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+from .sympify import _sympify as _sympify_, sympify
+from .basic import Basic
+from .cache import cacheit
+from .sorting import ordered
+from .logic import fuzzy_and
+from .parameters import global_parameters
+from sympy.utilities.iterables import sift
+from sympy.multipledispatch.dispatcher import (Dispatcher,
+    ambiguity_register_error_ignore_dup,
+    str_signature, RaiseNotImplementedError)
+
+
+if TYPE_CHECKING:
+    from sympy.core.expr import Expr
+    from sympy.core.add import Add
+    from sympy.core.mul import Mul
+    from sympy.logic.boolalg import Boolean, And, Or
+
+
+class AssocOp(Basic):
+    """ Associative operations, can separate noncommutative and
+    commutative parts.
+
+    (a op b) op c == a op (b op c) == a op b op c.
+
+    Base class for Add and Mul.
+
+    This is an abstract base class, concrete derived classes must define
+    the attribute `identity`.
+
+    .. deprecated:: 1.7
+
+       Using arguments that aren't subclasses of :class:`~.Expr` in core
+       operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is
+       deprecated. See :ref:`non-expr-args-deprecated` for details.
+
+    Parameters
+    ==========
+
+    *args :
+        Arguments which are operated
+
+    evaluate : bool, optional
+        Evaluate the operation. If not passed, refer to ``global_parameters.evaluate``.
+    """
+
+    # for performance reason, we don't let is_commutative go to assumptions,
+    # and keep it right here
+    __slots__: tuple[str, ...] = ('is_commutative',)
+
+    _args_type: type[Basic] | None = None
+
+    @cacheit
+    def __new__(cls, *args, evaluate=None, _sympify=True):
+        # Allow faster processing by passing ``_sympify=False``, if all arguments
+        # are already sympified.
+        if _sympify:
+            args = list(map(_sympify_, args))
+
+        # Disallow non-Expr args in Add/Mul
+        typ = cls._args_type
+        if typ is not None:
+            from .relational import Relational
+            if any(isinstance(arg, Relational) for arg in args):
+                raise TypeError("Relational cannot be used in %s" % cls.__name__)
+
+            # This should raise TypeError once deprecation period is over:
+            for arg in args:
+                if not isinstance(arg, typ):
+                    sympy_deprecation_warning(
+                        f"""
+
+Using non-Expr arguments in {cls.__name__} is deprecated (in this case, one of
+the arguments has type {type(arg).__name__!r}).
+
+If you really did intend to use a multiplication or addition operation with
+this object, use the * or + operator instead.
+
+                        """,
+                        deprecated_since_version="1.7",
+                        active_deprecations_target="non-expr-args-deprecated",
+                        stacklevel=4,
+                    )
+
+        if evaluate is None:
+            evaluate = global_parameters.evaluate
+        if not evaluate:
+            obj = cls._from_args(args)
+            obj = cls._exec_constructor_postprocessors(obj)
+            return obj
+
+        args = [a for a in args if a is not cls.identity]
+
+        if len(args) == 0:
+            return cls.identity
+        if len(args) == 1:
+            return args[0]
+
+        c_part, nc_part, order_symbols = cls.flatten(args)
+        is_commutative = not nc_part
+        obj = cls._from_args(c_part + nc_part, is_commutative)
+        obj = cls._exec_constructor_postprocessors(obj)
+
+        if order_symbols is not None:
+            from sympy.series.order import Order
+            return Order(obj, *order_symbols)
+        return obj
+
+    @classmethod
+    def _from_args(cls, args, is_commutative=None):
+        """Create new instance with already-processed args.
+        If the args are not in canonical order, then a non-canonical
+        result will be returned, so use with caution. The order of
+        args may change if the sign of the args is changed."""
+        if len(args) == 0:
+            return cls.identity
+        elif len(args) == 1:
+            return args[0]
+
+        obj = super().__new__(cls, *args)
+        if is_commutative is None:
+            is_commutative = fuzzy_and(a.is_commutative for a in args)
+        obj.is_commutative = is_commutative
+        return obj
+
+    def _new_rawargs(self, *args, reeval=True, **kwargs):
+        """Create new instance of own class with args exactly as provided by
+        caller but returning the self class identity if args is empty.
+
+        Examples
+        ========
+
+           This is handy when we want to optimize things, e.g.
+
+               >>> from sympy import Mul, S
+               >>> from sympy.abc import x, y
+               >>> e = Mul(3, x, y)
+               >>> e.args
+               (3, x, y)
+               >>> Mul(*e.args[1:])
+               x*y
+               >>> e._new_rawargs(*e.args[1:])  # the same as above, but faster
+               x*y
+
+           Note: use this with caution. There is no checking of arguments at
+           all. This is best used when you are rebuilding an Add or Mul after
+           simply removing one or more args. If, for example, modifications,
+           result in extra 1s being inserted they will show up in the result:
+
+               >>> m = (x*y)._new_rawargs(S.One, x); m
+               1*x
+               >>> m == x
+               False
+               >>> m.is_Mul
+               True
+
+           Another issue to be aware of is that the commutativity of the result
+           is based on the commutativity of self. If you are rebuilding the
+           terms that came from a commutative object then there will be no
+           problem, but if self was non-commutative then what you are
+           rebuilding may now be commutative.
+
+           Although this routine tries to do as little as possible with the
+           input, getting the commutativity right is important, so this level
+           of safety is enforced: commutativity will always be recomputed if
+           self is non-commutative and kwarg `reeval=False` has not been
+           passed.
+        """
+        if reeval and self.is_commutative is False:
+            is_commutative = None
+        else:
+            is_commutative = self.is_commutative
+        return self._from_args(args, is_commutative)
+
+    @classmethod
+    def flatten(cls, seq):
+        """Return seq so that none of the elements are of type `cls`. This is
+        the vanilla routine that will be used if a class derived from AssocOp
+        does not define its own flatten routine."""
+        # apply associativity, no commutativity property is used
+        new_seq = []
+        while seq:
+            o = seq.pop()
+            if o.__class__ is cls:  # classes must match exactly
+                seq.extend(o.args)
+            else:
+                new_seq.append(o)
+        new_seq.reverse()
+
+        # c_part, nc_part, order_symbols
+        return [], new_seq, None
+
+    def _matches_commutative(self, expr, repl_dict=None, old=False):
+        """
+        Matches Add/Mul "pattern" to an expression "expr".
+
+        repl_dict ... a dictionary of (wild: expression) pairs, that get
+                      returned with the results
+
+        This function is the main workhorse for Add/Mul.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Wild, sin
+        >>> a = Wild("a")
+        >>> b = Wild("b")
+        >>> c = Wild("c")
+        >>> x, y, z = symbols("x y z")
+        >>> (a+sin(b)*c)._matches_commutative(x+sin(y)*z)
+        {a_: x, b_: y, c_: z}
+
+        In the example above, "a+sin(b)*c" is the pattern, and "x+sin(y)*z" is
+        the expression.
+
+        The repl_dict contains parts that were already matched. For example
+        here:
+
+        >>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z, repl_dict={a: x})
+        {a_: x, b_: y, c_: z}
+
+        the only function of the repl_dict is to return it in the
+        result, e.g. if you omit it:
+
+        >>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z)
+        {b_: y, c_: z}
+
+        the "a: x" is not returned in the result, but otherwise it is
+        equivalent.
+
+        """
+        from .function import _coeff_isneg
+        # make sure expr is Expr if pattern is Expr
+        from .expr import Expr
+        if isinstance(self, Expr) and not isinstance(expr, Expr):
+            return None
+
+        if repl_dict is None:
+            repl_dict = {}
+
+        # handle simple patterns
+        if self == expr:
+            return repl_dict
+
+        d = self._matches_simple(expr, repl_dict)
+        if d is not None:
+            return d
+
+        # eliminate exact part from pattern: (2+a+w1+w2).matches(expr) -> (w1+w2).matches(expr-a-2)
+        from .function import WildFunction
+        from .symbol import Wild
+        wild_part, exact_part = sift(self.args, lambda p:
+            p.has(Wild, WildFunction) and not expr.has(p),
+            binary=True)
+        if not exact_part:
+            wild_part = list(ordered(wild_part))
+            if self.is_Add:
+                # in addition to normal ordered keys, impose
+                # sorting on Muls with leading Number to put
+                # them in order
+                wild_part = sorted(wild_part, key=lambda x:
+                    x.args[0] if x.is_Mul and x.args[0].is_Number else
+                    0)
+        else:
+            exact = self._new_rawargs(*exact_part)
+            free = expr.free_symbols
+            if free and (exact.free_symbols - free):
+                # there are symbols in the exact part that are not
+                # in the expr; but if there are no free symbols, let
+                # the matching continue
+                return None
+            newexpr = self._combine_inverse(expr, exact)
+            if not old and (expr.is_Add or expr.is_Mul):
+                check = newexpr
+                if _coeff_isneg(check):
+                    check = -check
+                if check.count_ops() > expr.count_ops():
+                    return None
+            newpattern = self._new_rawargs(*wild_part)
+            return newpattern.matches(newexpr, repl_dict)
+
+        # now to real work ;)
+        i = 0
+        saw = set()
+        while expr not in saw:
+            saw.add(expr)
+            args = tuple(ordered(self.make_args(expr)))
+            if self.is_Add and expr.is_Add:
+                # in addition to normal ordered keys, impose
+                # sorting on Muls with leading Number to put
+                # them in order
+                args = tuple(sorted(args, key=lambda x:
+                    x.args[0] if x.is_Mul and x.args[0].is_Number else
+                    0))
+            expr_list = (self.identity,) + args
+            for last_op in reversed(expr_list):
+                for w in reversed(wild_part):
+                    d1 = w.matches(last_op, repl_dict)
+                    if d1 is not None:
+                        d2 = self.xreplace(d1).matches(expr, d1)
+                        if d2 is not None:
+                            return d2
+
+            if i == 0:
+                if self.is_Mul:
+                    # make e**i look like Mul
+                    if expr.is_Pow and expr.exp.is_Integer:
+                        from .mul import Mul
+                        if expr.exp > 0:
+                            expr = Mul(*[expr.base, expr.base**(expr.exp - 1)], evaluate=False)
+                        else:
+                            expr = Mul(*[1/expr.base, expr.base**(expr.exp + 1)], evaluate=False)
+                        i += 1
+                        continue
+
+                elif self.is_Add:
+                    # make i*e look like Add
+                    c, e = expr.as_coeff_Mul()
+                    if abs(c) > 1:
+                        from .add import Add
+                        if c > 0:
+                            expr = Add(*[e, (c - 1)*e], evaluate=False)
+                        else:
+                            expr = Add(*[-e, (c + 1)*e], evaluate=False)
+                        i += 1
+                        continue
+
+                    # try collection on non-Wild symbols
+                    from sympy.simplify.radsimp import collect
+                    was = expr
+                    did = set()
+                    for w in reversed(wild_part):
+                        c, w = w.as_coeff_mul(Wild)
+                        free = c.free_symbols - did
+                        if free:
+                            did.update(free)
+                            expr = collect(expr, free)
+                    if expr != was:
+                        i += 0
+                        continue
+
+                break  # if we didn't continue, there is nothing more to do
+
+        return
+
+    def _has_matcher(self):
+        """Helper for .has() that checks for containment of
+        subexpressions within an expr by using sets of args
+        of similar nodes, e.g. x + 1 in x + y + 1 checks
+        to see that {x, 1} & {x, y, 1} == {x, 1}
+        """
+        def _ncsplit(expr):
+            # this is not the same as args_cnc because here
+            # we don't assume expr is a Mul -- hence deal with args --
+            # and always return a set.
+            cpart, ncpart = sift(expr.args,
+                lambda arg: arg.is_commutative is True, binary=True)
+            return set(cpart), ncpart
+
+        c, nc = _ncsplit(self)
+        cls = self.__class__
+
+        def is_in(expr):
+            if isinstance(expr, cls):
+                if expr == self:
+                    return True
+                _c, _nc = _ncsplit(expr)
+                if (c & _c) == c:
+                    if not nc:
+                        return True
+                    elif len(nc) <= len(_nc):
+                        for i in range(len(_nc) - len(nc) + 1):
+                            if _nc[i:i + len(nc)] == nc:
+                                return True
+            return False
+        return is_in
+
+    def _eval_evalf(self, prec):
+        """
+        Evaluate the parts of self that are numbers; if the whole thing
+        was a number with no functions it would have been evaluated, but
+        it wasn't so we must judiciously extract the numbers and reconstruct
+        the object. This is *not* simply replacing numbers with evaluated
+        numbers. Numbers should be handled in the largest pure-number
+        expression as possible. So the code below separates ``self`` into
+        number and non-number parts and evaluates the number parts and
+        walks the args of the non-number part recursively (doing the same
+        thing).
+        """
+        from .add import Add
+        from .mul import Mul
+        from .symbol import Symbol
+        from .function import AppliedUndef
+        if isinstance(self, (Mul, Add)):
+            x, tail = self.as_independent(Symbol, AppliedUndef)
+            # if x is an AssocOp Function then the _evalf below will
+            # call _eval_evalf (here) so we must break the recursion
+            if not (tail is self.identity or
+                    isinstance(x, AssocOp) and x.is_Function or
+                    x is self.identity and isinstance(tail, AssocOp)):
+                # here, we have a number so we just call to _evalf with prec;
+                # prec is not the same as n, it is the binary precision so
+                # that's why we don't call to evalf.
+                x = x._evalf(prec) if x is not self.identity else self.identity
+                args = []
+                tail_args = tuple(self.func.make_args(tail))
+                for a in tail_args:
+                    # here we call to _eval_evalf since we don't know what we
+                    # are dealing with and all other _eval_evalf routines should
+                    # be doing the same thing (i.e. taking binary prec and
+                    # finding the evalf-able args)
+                    newa = a._eval_evalf(prec)
+                    if newa is None:
+                        args.append(a)
+                    else:
+                        args.append(newa)
+                return self.func(x, *args)
+
+        # this is the same as above, but there were no pure-number args to
+        # deal with
+        args = []
+        for a in self.args:
+            newa = a._eval_evalf(prec)
+            if newa is None:
+                args.append(a)
+            else:
+                args.append(newa)
+        return self.func(*args)
+
+    @overload
+    @classmethod
+    def make_args(cls: type[Add], expr: Expr) -> tuple[Expr, ...]: ... # type: ignore
+    @overload
+    @classmethod
+    def make_args(cls: type[Mul], expr: Expr) -> tuple[Expr, ...]: ... # type: ignore
+    @overload
+    @classmethod
+    def make_args(cls: type[And], expr: Boolean) -> tuple[Boolean, ...]: ... # type: ignore
+    @overload
+    @classmethod
+    def make_args(cls: type[Or], expr: Boolean) -> tuple[Boolean, ...]: ... # type: ignore
+
+    @classmethod
+    def make_args(cls: type[Basic], expr: Basic) -> tuple[Basic, ...]:
+        """
+        Return a sequence of elements `args` such that cls(*args) == expr
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Mul, Add
+        >>> x, y = map(Symbol, 'xy')
+
+        >>> Mul.make_args(x*y)
+        (x, y)
+        >>> Add.make_args(x*y)
+        (x*y,)
+        >>> set(Add.make_args(x*y + y)) == set([y, x*y])
+        True
+
+        """
+        if isinstance(expr, cls):
+            return expr.args
+        else:
+            return (sympify(expr),)
+
+    def doit(self, **hints):
+        if hints.get('deep', True):
+            terms = [term.doit(**hints) for term in self.args]
+        else:
+            terms = self.args
+        return self.func(*terms, evaluate=True)
+
+class ShortCircuit(Exception):
+    pass
+
+
+class LatticeOp(AssocOp):
+    """
+    Join/meet operations of an algebraic lattice[1].
+
+    Explanation
+    ===========
+
+    These binary operations are associative (op(op(a, b), c) = op(a, op(b, c))),
+    commutative (op(a, b) = op(b, a)) and idempotent (op(a, a) = op(a) = a).
+    Common examples are AND, OR, Union, Intersection, max or min. They have an
+    identity element (op(identity, a) = a) and an absorbing element
+    conventionally called zero (op(zero, a) = zero).
+
+    This is an abstract base class, concrete derived classes must declare
+    attributes zero and identity. All defining properties are then respected.
+
+    Examples
+    ========
+
+    >>> from sympy import Integer
+    >>> from sympy.core.operations import LatticeOp
+    >>> class my_join(LatticeOp):
+    ...     zero = Integer(0)
+    ...     identity = Integer(1)
+    >>> my_join(2, 3) == my_join(3, 2)
+    True
+    >>> my_join(2, my_join(3, 4)) == my_join(2, 3, 4)
+    True
+    >>> my_join(0, 1, 4, 2, 3, 4)
+    0
+    >>> my_join(1, 2)
+    2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Lattice_%28order%29
+    """
+
+    is_commutative = True
+
+    def __new__(cls, *args, **options):
+        args = (_sympify_(arg) for arg in args)
+
+        try:
+            # /!\ args is a generator and _new_args_filter
+            # must be careful to handle as such; this
+            # is done so short-circuiting can be done
+            # without having to sympify all values
+            _args = frozenset(cls._new_args_filter(args))
+        except ShortCircuit:
+            return sympify(cls.zero)
+        if not _args:
+            return sympify(cls.identity)
+        elif len(_args) == 1:
+            return set(_args).pop()
+        else:
+            # XXX in almost every other case for __new__, *_args is
+            # passed along, but the expectation here is for _args
+            obj = super(AssocOp, cls).__new__(cls, *ordered(_args))
+            obj._argset = _args
+            return obj
+
+    @classmethod
+    def _new_args_filter(cls, arg_sequence, call_cls=None):
+        """Generator filtering args"""
+        ncls = call_cls or cls
+        for arg in arg_sequence:
+            if arg == ncls.zero:
+                raise ShortCircuit(arg)
+            elif arg == ncls.identity:
+                continue
+            elif arg.func == ncls:
+                yield from arg.args
+            else:
+                yield arg
+
+    @classmethod
+    def make_args(cls, expr):
+        """
+        Return a set of args such that cls(*arg_set) == expr.
+        """
+        if isinstance(expr, cls):
+            return expr._argset
+        else:
+            return frozenset([sympify(expr)])
+
+
+class AssocOpDispatcher:
+    """
+    Handler dispatcher for associative operators
+
+    .. notes::
+       This approach is experimental, and can be replaced or deleted in the future.
+       See https://github.com/sympy/sympy/pull/19463.
+
+    Explanation
+    ===========
+
+    If arguments of different types are passed, the classes which handle the operation for each type
+    are collected. Then, a class which performs the operation is selected by recursive binary dispatching.
+    Dispatching relation can be registered by ``register_handlerclass`` method.
+
+    Priority registration is unordered. You cannot make ``A*B`` and ``B*A`` refer to
+    different handler classes. All logic dealing with the order of arguments must be implemented
+    in the handler class.
+
+    Examples
+    ========
+
+    >>> from sympy import Add, Expr, Symbol
+    >>> from sympy.core.add import add
+
+    >>> class NewExpr(Expr):
+    ...     @property
+    ...     def _add_handler(self):
+    ...         return NewAdd
+    >>> class NewAdd(NewExpr, Add):
+    ...     pass
+    >>> add.register_handlerclass((Add, NewAdd), NewAdd)
+
+    >>> a, b = Symbol('a'), NewExpr()
+    >>> add(a, b) == NewAdd(a, b)
+    True
+
+    """
+    def __init__(self, name, doc=None):
+        self.name = name
+        self.doc = doc
+        self.handlerattr = "_%s_handler" % name
+        self._handlergetter = attrgetter(self.handlerattr)
+        self._dispatcher = Dispatcher(name)
+
+    def __repr__(self):
+        return "" % self.name
+
+    def register_handlerclass(self, classes, typ, on_ambiguity=ambiguity_register_error_ignore_dup):
+        """
+        Register the handler class for two classes, in both straight and reversed order.
+
+        Paramteters
+        ===========
+
+        classes : tuple of two types
+            Classes who are compared with each other.
+
+        typ:
+            Class which is registered to represent *cls1* and *cls2*.
+            Handler method of *self* must be implemented in this class.
+        """
+        if not len(classes) == 2:
+            raise RuntimeError(
+                "Only binary dispatch is supported, but got %s types: <%s>." % (
+                len(classes), str_signature(classes)
+            ))
+        if len(set(classes)) == 1:
+            raise RuntimeError(
+                "Duplicate types <%s> cannot be dispatched." % str_signature(classes)
+            )
+        self._dispatcher.add(tuple(classes), typ, on_ambiguity=on_ambiguity)
+        self._dispatcher.add(tuple(reversed(classes)), typ, on_ambiguity=on_ambiguity)
+
+    @cacheit
+    def __call__(self, *args, _sympify=True, **kwargs):
+        """
+        Parameters
+        ==========
+
+        *args :
+            Arguments which are operated
+        """
+        if _sympify:
+            args = tuple(map(_sympify_, args))
+        handlers = frozenset(map(self._handlergetter, args))
+
+        # no need to sympify again
+        return self.dispatch(handlers)(*args, _sympify=False, **kwargs)
+
+    @cacheit
+    def dispatch(self, handlers):
+        """
+        Select the handler class, and return its handler method.
+        """
+
+        # Quick exit for the case where all handlers are same
+        if len(handlers) == 1:
+            h, = handlers
+            if not isinstance(h, type):
+                raise RuntimeError("Handler {!r} is not a type.".format(h))
+            return h
+
+        # Recursively select with registered binary priority
+        for i, typ in enumerate(handlers):
+
+            if not isinstance(typ, type):
+                raise RuntimeError("Handler {!r} is not a type.".format(typ))
+
+            if i == 0:
+                handler = typ
+            else:
+                prev_handler = handler
+                handler = self._dispatcher.dispatch(prev_handler, typ)
+
+                if not isinstance(handler, type):
+                    raise RuntimeError(
+                        "Dispatcher for {!r} and {!r} must return a type, but got {!r}".format(
+                        prev_handler, typ, handler
+                    ))
+
+        # return handler class
+        return handler
+
+    @property
+    def __doc__(self):
+        docs = [
+            "Multiply dispatched associative operator: %s" % self.name,
+            "Note that support for this is experimental, see the docs for :class:`AssocOpDispatcher` for details"
+        ]
+
+        if self.doc:
+            docs.append(self.doc)
+
+        s = "Registered handler classes\n"
+        s += '=' * len(s)
+        docs.append(s)
+
+        amb_sigs = []
+
+        typ_sigs = defaultdict(list)
+        for sigs in self._dispatcher.ordering[::-1]:
+            key = self._dispatcher.funcs[sigs]
+            typ_sigs[key].append(sigs)
+
+        for typ, sigs in typ_sigs.items():
+
+            sigs_str = ', '.join('<%s>' % str_signature(sig) for sig in sigs)
+
+            if isinstance(typ, RaiseNotImplementedError):
+                amb_sigs.append(sigs_str)
+                continue
+
+            s = 'Inputs: %s\n' % sigs_str
+            s += '-' * len(s) + '\n'
+            s += typ.__name__
+            docs.append(s)
+
+        if amb_sigs:
+            s = "Ambiguous handler classes\n"
+            s += '=' * len(s)
+            docs.append(s)
+
+            s = '\n'.join(amb_sigs)
+            docs.append(s)
+
+        return '\n\n'.join(docs)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/parameters.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/parameters.py
new file mode 100644
index 0000000000000000000000000000000000000000..d911a3652bf02fa5b24c43b138035a57be687228
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/parameters.py
@@ -0,0 +1,161 @@
+"""Thread-safe global parameters"""
+
+from .cache import clear_cache
+from contextlib import contextmanager
+from threading import local
+
+class _global_parameters(local):
+    """
+    Thread-local global parameters.
+
+    Explanation
+    ===========
+
+    This class generates thread-local container for SymPy's global parameters.
+    Every global parameters must be passed as keyword argument when generating
+    its instance.
+    A variable, `global_parameters` is provided as default instance for this class.
+
+    WARNING! Although the global parameters are thread-local, SymPy's cache is not
+    by now.
+    This may lead to undesired result in multi-threading operations.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.core.cache import clear_cache
+    >>> from sympy.core.parameters import global_parameters as gp
+
+    >>> gp.evaluate
+    True
+    >>> x+x
+    2*x
+
+    >>> log = []
+    >>> def f():
+    ...     clear_cache()
+    ...     gp.evaluate = False
+    ...     log.append(x+x)
+    ...     clear_cache()
+    >>> import threading
+    >>> thread = threading.Thread(target=f)
+    >>> thread.start()
+    >>> thread.join()
+
+    >>> print(log)
+    [x + x]
+
+    >>> gp.evaluate
+    True
+    >>> x+x
+    2*x
+
+    References
+    ==========
+
+    .. [1] https://docs.python.org/3/library/threading.html
+
+    """
+    def __init__(self, **kwargs):
+        self.__dict__.update(kwargs)
+
+    def __setattr__(self, name, value):
+        if getattr(self, name) != value:
+            clear_cache()
+        return super().__setattr__(name, value)
+
+global_parameters = _global_parameters(evaluate=True, distribute=True, exp_is_pow=False)
+
+class evaluate:
+    """ Control automatic evaluation
+
+    Explanation
+    ===========
+
+    This context manager controls whether or not all SymPy functions evaluate
+    by default.
+
+    Note that much of SymPy expects evaluated expressions.  This functionality
+    is experimental and is unlikely to function as intended on large
+    expressions.
+
+    Examples
+    ========
+
+    >>> from sympy import evaluate
+    >>> from sympy.abc import x
+    >>> print(x + x)
+    2*x
+    >>> with evaluate(False):
+    ...     print(x + x)
+    x + x
+    """
+    def __init__(self, x):
+        self.x = x
+        self.old = []
+
+    def __enter__(self):
+        self.old.append(global_parameters.evaluate)
+        global_parameters.evaluate = self.x
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        global_parameters.evaluate = self.old.pop()
+
+@contextmanager
+def distribute(x):
+    """ Control automatic distribution of Number over Add
+
+    Explanation
+    ===========
+
+    This context manager controls whether or not Mul distribute Number over
+    Add. Plan is to avoid distributing Number over Add in all of sympy. Once
+    that is done, this contextmanager will be removed.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x
+    >>> from sympy.core.parameters import distribute
+    >>> print(2*(x + 1))
+    2*x + 2
+    >>> with distribute(False):
+    ...     print(2*(x + 1))
+    2*(x + 1)
+    """
+
+    old = global_parameters.distribute
+
+    try:
+        global_parameters.distribute = x
+        yield
+    finally:
+        global_parameters.distribute = old
+
+
+@contextmanager
+def _exp_is_pow(x):
+    """
+    Control whether `e^x` should be represented as ``exp(x)`` or a ``Pow(E, x)``.
+
+    Examples
+    ========
+
+    >>> from sympy import exp
+    >>> from sympy.abc import x
+    >>> from sympy.core.parameters import _exp_is_pow
+    >>> with _exp_is_pow(True): print(type(exp(x)))
+    
+    >>> with _exp_is_pow(False): print(type(exp(x)))
+    exp
+    """
+    old = global_parameters.exp_is_pow
+
+    clear_cache()
+    try:
+        global_parameters.exp_is_pow = x
+        yield
+    finally:
+        clear_cache()
+        global_parameters.exp_is_pow = old
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/power.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/power.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f257d030553ecc7b887ca9d1199ccc19b9a642f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/power.py
@@ -0,0 +1,1847 @@
+from __future__ import annotations
+from typing import Callable, TYPE_CHECKING
+from itertools import product
+
+from .sympify import _sympify
+from .cache import cacheit
+from .singleton import S
+from .expr import Expr
+from .evalf import PrecisionExhausted
+from .function import (expand_complex, expand_multinomial,
+    expand_mul, _mexpand, PoleError)
+from .logic import fuzzy_bool, fuzzy_not, fuzzy_and, fuzzy_or
+from .parameters import global_parameters
+from .relational import is_gt, is_lt
+from .kind import NumberKind, UndefinedKind
+from sympy.utilities.iterables import sift
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.misc import as_int
+from sympy.multipledispatch import Dispatcher
+
+
+class Pow(Expr):
+    """
+    Defines the expression x**y as "x raised to a power y"
+
+    .. deprecated:: 1.7
+
+       Using arguments that aren't subclasses of :class:`~.Expr` in core
+       operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is
+       deprecated. See :ref:`non-expr-args-deprecated` for details.
+
+    Singleton definitions involving (0, 1, -1, oo, -oo, I, -I):
+
+    +--------------+---------+-----------------------------------------------+
+    | expr         | value   | reason                                        |
+    +==============+=========+===============================================+
+    | z**0         | 1       | Although arguments over 0**0 exist, see [2].  |
+    +--------------+---------+-----------------------------------------------+
+    | z**1         | z       |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | (-oo)**(-1)  | 0       |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | (-1)**-1     | -1      |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | S.Zero**-1   | zoo     | This is not strictly true, as 0**-1 may be    |
+    |              |         | undefined, but is convenient in some contexts |
+    |              |         | where the base is assumed to be positive.     |
+    +--------------+---------+-----------------------------------------------+
+    | 1**-1        | 1       |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | oo**-1       | 0       |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | 0**oo        | 0       | Because for all complex numbers z near        |
+    |              |         | 0, z**oo -> 0.                                |
+    +--------------+---------+-----------------------------------------------+
+    | 0**-oo       | zoo     | This is not strictly true, as 0**oo may be    |
+    |              |         | oscillating between positive and negative     |
+    |              |         | values or rotating in the complex plane.      |
+    |              |         | It is convenient, however, when the base      |
+    |              |         | is positive.                                  |
+    +--------------+---------+-----------------------------------------------+
+    | 1**oo        | nan     | Because there are various cases where         |
+    | 1**-oo       |         | lim(x(t),t)=1, lim(y(t),t)=oo (or -oo),       |
+    |              |         | but lim( x(t)**y(t), t) != 1.  See [3].       |
+    +--------------+---------+-----------------------------------------------+
+    | b**zoo       | nan     | Because b**z has no limit as z -> zoo         |
+    +--------------+---------+-----------------------------------------------+
+    | (-1)**oo     | nan     | Because of oscillations in the limit.         |
+    | (-1)**(-oo)  |         |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | oo**oo       | oo      |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | oo**-oo      | 0       |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | (-oo)**oo    | nan     |                                               |
+    | (-oo)**-oo   |         |                                               |
+    +--------------+---------+-----------------------------------------------+
+    | oo**I        | nan     | oo**e could probably be best thought of as    |
+    | (-oo)**I     |         | the limit of x**e for real x as x tends to    |
+    |              |         | oo. If e is I, then the limit does not exist  |
+    |              |         | and nan is used to indicate that.             |
+    +--------------+---------+-----------------------------------------------+
+    | oo**(1+I)    | zoo     | If the real part of e is positive, then the   |
+    | (-oo)**(1+I) |         | limit of abs(x**e) is oo. So the limit value  |
+    |              |         | is zoo.                                       |
+    +--------------+---------+-----------------------------------------------+
+    | oo**(-1+I)   | 0       | If the real part of e is negative, then the   |
+    | -oo**(-1+I)  |         | limit is 0.                                   |
+    +--------------+---------+-----------------------------------------------+
+
+    Because symbolic computations are more flexible than floating point
+    calculations and we prefer to never return an incorrect answer,
+    we choose not to conform to all IEEE 754 conventions.  This helps
+    us avoid extra test-case code in the calculation of limits.
+
+    See Also
+    ========
+
+    sympy.core.numbers.Infinity
+    sympy.core.numbers.NegativeInfinity
+    sympy.core.numbers.NaN
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Exponentiation
+    .. [2] https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero
+    .. [3] https://en.wikipedia.org/wiki/Indeterminate_forms
+
+    """
+    is_Pow = True
+
+    __slots__ = ('is_commutative',)
+
+    if TYPE_CHECKING:
+
+        @property
+        def args(self) -> tuple[Expr, Expr]:
+            ...
+
+    @property
+    def base(self) -> Expr:
+        return self.args[0]
+
+    @property
+    def exp(self) -> Expr:
+        return self.args[1]
+
+    @property
+    def kind(self):
+        if self.exp.kind is NumberKind:
+            return self.base.kind
+        else:
+            return UndefinedKind
+
+    @cacheit
+    def __new__(cls, b: Expr | complex, e: Expr | complex, evaluate=None) -> Expr: # type: ignore
+        if evaluate is None:
+            evaluate = global_parameters.evaluate
+
+        base = _sympify(b)
+        exp = _sympify(e)
+
+        # XXX: This can be removed when non-Expr args are disallowed rather
+        # than deprecated.
+        from .relational import Relational
+        if isinstance(base, Relational) or isinstance(exp, Relational):
+            raise TypeError('Relational cannot be used in Pow')
+
+        # XXX: This should raise TypeError once deprecation period is over:
+        for arg in [base, exp]:
+            if not isinstance(arg, Expr):
+                sympy_deprecation_warning(
+                    f"""
+    Using non-Expr arguments in Pow is deprecated (in this case, one of the
+    arguments is of type {type(arg).__name__!r}).
+
+    If you really did intend to construct a power with this base, use the **
+    operator instead.""",
+                    deprecated_since_version="1.7",
+                    active_deprecations_target="non-expr-args-deprecated",
+                    stacklevel=4,
+                )
+
+        if evaluate:
+            if exp is S.ComplexInfinity:
+                return S.NaN
+            if exp is S.Infinity:
+                if is_gt(base, S.One):
+                    return S.Infinity
+                if is_gt(base, S.NegativeOne) and is_lt(base, S.One):
+                    return S.Zero
+                if is_lt(base, S.NegativeOne):
+                    if base.is_finite:
+                        return S.ComplexInfinity
+                    if base.is_finite is False:
+                        return S.NaN
+            if exp is S.Zero:
+                return S.One
+            elif exp is S.One:
+                return base
+            elif exp == -1 and not base:
+                return S.ComplexInfinity
+            elif exp.__class__.__name__ == "AccumulationBounds":
+                if base == S.Exp1:
+                    from sympy.calculus.accumulationbounds import AccumBounds
+                    return AccumBounds(Pow(base, exp.min), Pow(base, exp.max))
+            # autosimplification if base is a number and exp odd/even
+            # if base is Number then the base will end up positive; we
+            # do not do this with arbitrary expressions since symbolic
+            # cancellation might occur as in (x - 1)/(1 - x) -> -1. If
+            # we returned Piecewise((-1, Ne(x, 1))) for such cases then
+            # we could do this...but we don't
+            elif (exp.is_Symbol and exp.is_integer or exp.is_Integer
+                    ) and (base.is_number and base.is_Mul or base.is_Number
+                    ) and base.could_extract_minus_sign():
+                if exp.is_even:
+                    base = -base
+                elif exp.is_odd:
+                    return -Pow(-base, exp)
+            if S.NaN in (base, exp):  # XXX S.NaN**x -> S.NaN under assumption that x != 0
+                return S.NaN
+            elif base is S.One:
+                if abs(exp).is_infinite:
+                    return S.NaN
+                return S.One
+            else:
+                # recognize base as E
+                from sympy.functions.elementary.exponential import exp_polar
+                if not exp.is_Atom and base is not S.Exp1 and not isinstance(base, exp_polar):
+                    from .exprtools import factor_terms
+                    from sympy.functions.elementary.exponential import log
+                    from sympy.simplify.radsimp import fraction
+                    c, ex = factor_terms(exp, sign=False).as_coeff_Mul()
+                    num, den = fraction(ex)
+                    if isinstance(den, log) and den.args[0] == base:
+                        return S.Exp1**(c*num)
+                    elif den.is_Add:
+                        from sympy.functions.elementary.complexes import sign, im
+                        s = sign(im(base))
+                        if s.is_Number and s and den == \
+                                log(-factor_terms(base, sign=False)) + s*S.ImaginaryUnit*S.Pi:
+                            return S.Exp1**(c*num)
+
+                obj = base._eval_power(exp)
+                if obj is not None:
+                    return obj
+        obj = Expr.__new__(cls, base, exp)
+        obj = cls._exec_constructor_postprocessors(obj)
+        if not isinstance(obj, Pow):
+            return obj
+        obj.is_commutative = (base.is_commutative and exp.is_commutative)
+        return obj
+
+    def inverse(self, argindex=1):
+        if self.base == S.Exp1:
+            from sympy.functions.elementary.exponential import log
+            return log
+        return None
+
+    @classmethod
+    def class_key(cls):
+        return 3, 2, cls.__name__
+
+    def _eval_refine(self, assumptions):
+        from sympy.assumptions.ask import ask, Q
+        b, e = self.as_base_exp()
+        if ask(Q.integer(e), assumptions) and b.could_extract_minus_sign():
+            if ask(Q.even(e), assumptions):
+                return Pow(-b, e)
+            elif ask(Q.odd(e), assumptions):
+                return -Pow(-b, e)
+
+    def _eval_power(self, expt):
+        b, e = self.as_base_exp()
+        if b is S.NaN:
+            return (b**e)**expt  # let __new__ handle it
+
+        s = None
+        if expt.is_integer:
+            s = 1
+        elif b.is_polar:  # e.g. exp_polar, besselj, var('p', polar=True)...
+            s = 1
+        elif e.is_extended_real is not None:
+            from sympy.functions.elementary.complexes import arg, im, re, sign
+            from sympy.functions.elementary.exponential import exp, log
+            from sympy.functions.elementary.integers import floor
+            # helper functions ===========================
+            def _half(e):
+                """Return True if the exponent has a literal 2 as the
+                denominator, else None."""
+                if getattr(e, 'q', None) == 2:
+                    return True
+                n, d = e.as_numer_denom()
+                if n.is_integer and d == 2:
+                    return True
+            def _n2(e):
+                """Return ``e`` evaluated to a Number with 2 significant
+                digits, else None."""
+                try:
+                    rv = e.evalf(2, strict=True)
+                    if rv.is_Number:
+                        return rv
+                except PrecisionExhausted:
+                    pass
+            # ===================================================
+            if e.is_extended_real:
+                # we need _half(expt) with constant floor or
+                # floor(S.Half - e*arg(b)/2/pi) == 0
+
+
+                # handle -1 as special case
+                if e == -1:
+                    # floor arg. is 1/2 + arg(b)/2/pi
+                    if _half(expt):
+                        if b.is_negative is True:
+                            return S.NegativeOne**expt*Pow(-b, e*expt)
+                        elif b.is_negative is False:  # XXX ok if im(b) != 0?
+                            return Pow(b, -expt)
+                elif e.is_even:
+                    if b.is_extended_real:
+                        b = abs(b)
+                    if b.is_imaginary:
+                        b = abs(im(b))*S.ImaginaryUnit
+
+                if (abs(e) < 1) == True or e == 1:
+                    s = 1  # floor = 0
+                elif b.is_extended_nonnegative:
+                    s = 1  # floor = 0
+                elif re(b).is_extended_nonnegative and (abs(e) < 2) == True:
+                    s = 1  # floor = 0
+                elif _half(expt):
+                    s = exp(2*S.Pi*S.ImaginaryUnit*expt*floor(
+                        S.Half - e*arg(b)/(2*S.Pi)))
+                    if s.is_extended_real and _n2(sign(s) - s) == 0:
+                        s = sign(s)
+                    else:
+                        s = None
+            else:
+                # e.is_extended_real is False requires:
+                #     _half(expt) with constant floor or
+                #     floor(S.Half - im(e*log(b))/2/pi) == 0
+                try:
+                    s = exp(2*S.ImaginaryUnit*S.Pi*expt*
+                        floor(S.Half - im(e*log(b))/2/S.Pi))
+                    # be careful to test that s is -1 or 1 b/c sign(I) == I:
+                    # so check that s is real
+                    if s.is_extended_real and _n2(sign(s) - s) == 0:
+                        s = sign(s)
+                    else:
+                        s = None
+                except PrecisionExhausted:
+                    s = None
+
+        if s is not None:
+            return s*Pow(b, e*expt)
+
+    def _eval_Mod(self, q):
+        r"""A dispatched function to compute `b^e \bmod q`, dispatched
+        by ``Mod``.
+
+        Notes
+        =====
+
+        Algorithms:
+
+        1. For unevaluated integer power, use built-in ``pow`` function
+        with 3 arguments, if powers are not too large wrt base.
+
+        2. For very large powers, use totient reduction if $e \ge \log(m)$.
+        Bound on m, is for safe factorization memory wise i.e. $m^{1/4}$.
+        For pollard-rho to be faster than built-in pow $\log(e) > m^{1/4}$
+        check is added.
+
+        3. For any unevaluated power found in `b` or `e`, the step 2
+        will be recursed down to the base and the exponent
+        such that the $b \bmod q$ becomes the new base and
+        $\phi(q) + e \bmod \phi(q)$ becomes the new exponent, and then
+        the computation for the reduced expression can be done.
+        """
+
+        base, exp = self.base, self.exp
+
+        if exp.is_integer and exp.is_positive:
+            if q.is_integer and base % q == 0:
+                return S.Zero
+
+            from sympy.functions.combinatorial.numbers import totient
+
+            if base.is_Integer and exp.is_Integer and q.is_Integer:
+                b, e, m = int(base), int(exp), int(q)
+                mb = m.bit_length()
+                if mb <= 80 and e >= mb and e.bit_length()**4 >= m:
+                    phi = int(totient(m))
+                    return Integer(pow(b, phi + e%phi, m))
+                return Integer(pow(b, e, m))
+
+            from .mod import Mod
+
+            if isinstance(base, Pow) and base.is_integer and base.is_number:
+                base = Mod(base, q)
+                return Mod(Pow(base, exp, evaluate=False), q)
+
+            if isinstance(exp, Pow) and exp.is_integer and exp.is_number:
+                bit_length = int(q).bit_length()
+                # XXX Mod-Pow actually attempts to do a hanging evaluation
+                # if this dispatched function returns None.
+                # May need some fixes in the dispatcher itself.
+                if bit_length <= 80:
+                    phi = totient(q)
+                    exp = phi + Mod(exp, phi)
+                    return Mod(Pow(base, exp, evaluate=False), q)
+
+    def _eval_is_even(self):
+        if self.exp.is_integer and self.exp.is_positive:
+            return self.base.is_even
+
+    def _eval_is_negative(self):
+        ext_neg = Pow._eval_is_extended_negative(self)
+        if ext_neg is True:
+            return self.is_finite
+        return ext_neg
+
+    def _eval_is_extended_positive(self):
+        if self.base == self.exp:
+            if self.base.is_extended_nonnegative:
+                return True
+        elif self.base.is_positive:
+            if self.exp.is_real:
+                return True
+        elif self.base.is_extended_negative:
+            if self.exp.is_even:
+                return True
+            if self.exp.is_odd:
+                return False
+        elif self.base.is_zero:
+            if self.exp.is_extended_real:
+                return self.exp.is_zero
+        elif self.base.is_extended_nonpositive:
+            if self.exp.is_odd:
+                return False
+        elif self.base.is_imaginary:
+            if self.exp.is_integer:
+                m = self.exp % 4
+                if m.is_zero:
+                    return True
+                if m.is_integer and m.is_zero is False:
+                    return False
+            if self.exp.is_imaginary:
+                from sympy.functions.elementary.exponential import log
+                return log(self.base).is_imaginary
+
+    def _eval_is_extended_negative(self):
+        if self.exp is S.Half:
+            if self.base.is_complex or self.base.is_extended_real:
+                return False
+        if self.base.is_extended_negative:
+            if self.exp.is_odd and self.base.is_finite:
+                return True
+            if self.exp.is_even:
+                return False
+        elif self.base.is_extended_positive:
+            if self.exp.is_extended_real:
+                return False
+        elif self.base.is_zero:
+            if self.exp.is_extended_real:
+                return False
+        elif self.base.is_extended_nonnegative:
+            if self.exp.is_extended_nonnegative:
+                return False
+        elif self.base.is_extended_nonpositive:
+            if self.exp.is_even:
+                return False
+        elif self.base.is_extended_real:
+            if self.exp.is_even:
+                return False
+
+    def _eval_is_zero(self):
+        if self.base.is_zero:
+            if self.exp.is_extended_positive:
+                return True
+            elif self.exp.is_extended_nonpositive:
+                return False
+        elif self.base == S.Exp1:
+            return self.exp is S.NegativeInfinity
+        elif self.base.is_zero is False:
+            if self.base.is_finite and self.exp.is_finite:
+                return False
+            elif self.exp.is_negative:
+                return self.base.is_infinite
+            elif self.exp.is_nonnegative:
+                return False
+            elif self.exp.is_infinite and self.exp.is_extended_real:
+                if (1 - abs(self.base)).is_extended_positive:
+                    return self.exp.is_extended_positive
+                elif (1 - abs(self.base)).is_extended_negative:
+                    return self.exp.is_extended_negative
+        elif self.base.is_finite and self.exp.is_negative:
+            # when self.base.is_zero is None
+            return False
+
+    def _eval_is_integer(self):
+        b, e = self.args
+        if b.is_rational:
+            if b.is_integer is False and e.is_positive:
+                return False  # rat**nonneg
+        if b.is_integer and e.is_integer:
+            if b is S.NegativeOne:
+                return True
+            if e.is_nonnegative or e.is_positive:
+                return True
+        if b.is_integer and e.is_negative and (e.is_finite or e.is_integer):
+            if fuzzy_not((b - 1).is_zero) and fuzzy_not((b + 1).is_zero):
+                return False
+        if b.is_Number and e.is_Number:
+            check = self.func(*self.args)
+            return check.is_Integer
+        if e.is_negative and b.is_positive and (b - 1).is_positive:
+            return False
+        if e.is_negative and b.is_negative and (b + 1).is_negative:
+            return False
+
+    def _eval_is_extended_real(self):
+        if self.base is S.Exp1:
+            if self.exp.is_extended_real:
+                return True
+            elif self.exp.is_imaginary:
+                return (2*S.ImaginaryUnit*self.exp/S.Pi).is_even
+
+        from sympy.functions.elementary.exponential import log, exp
+        real_b = self.base.is_extended_real
+        if real_b is None:
+            if self.base.func == exp and self.base.exp.is_imaginary:
+                return self.exp.is_imaginary
+            if self.base.func == Pow and self.base.base is S.Exp1 and self.base.exp.is_imaginary:
+                return self.exp.is_imaginary
+            return
+        real_e = self.exp.is_extended_real
+        if real_e is None:
+            return
+        if real_b and real_e:
+            if self.base.is_extended_positive:
+                return True
+            elif self.base.is_extended_nonnegative and self.exp.is_extended_nonnegative:
+                return True
+            elif self.exp.is_integer and self.base.is_extended_nonzero:
+                return True
+            elif self.exp.is_integer and self.exp.is_nonnegative:
+                return True
+            elif self.base.is_extended_negative:
+                if self.exp.is_Rational:
+                    return False
+        if real_e and self.exp.is_extended_negative and self.base.is_zero is False:
+            return Pow(self.base, -self.exp).is_extended_real
+        im_b = self.base.is_imaginary
+        im_e = self.exp.is_imaginary
+        if im_b:
+            if self.exp.is_integer:
+                if self.exp.is_even:
+                    return True
+                elif self.exp.is_odd:
+                    return False
+            elif im_e and log(self.base).is_imaginary:
+                return True
+            elif self.exp.is_Add:
+                c, a = self.exp.as_coeff_Add()
+                if c and c.is_Integer:
+                    return Mul(
+                        self.base**c, self.base**a, evaluate=False).is_extended_real
+            elif self.base in (-S.ImaginaryUnit, S.ImaginaryUnit):
+                if (self.exp/2).is_integer is False:
+                    return False
+        if real_b and im_e:
+            if self.base is S.NegativeOne:
+                return True
+            c = self.exp.coeff(S.ImaginaryUnit)
+            if c:
+                if self.base.is_rational and c.is_rational:
+                    if self.base.is_nonzero and (self.base - 1).is_nonzero and c.is_nonzero:
+                        return False
+                ok = (c*log(self.base)/S.Pi).is_integer
+                if ok is not None:
+                    return ok
+
+        if real_b is False and real_e: # we already know it's not imag
+            if isinstance(self.exp, Rational) and self.exp.p == 1:
+                return False
+            from sympy.functions.elementary.complexes import arg
+            i = arg(self.base)*self.exp/S.Pi
+            if i.is_complex: # finite
+                return i.is_integer
+
+    def _eval_is_complex(self):
+
+        if self.base == S.Exp1:
+            return fuzzy_or([self.exp.is_complex, self.exp.is_extended_negative])
+
+        if all(a.is_complex for a in self.args) and self._eval_is_finite():
+            return True
+
+    def _eval_is_imaginary(self):
+        if self.base.is_commutative is False:
+            return False
+
+        if self.base.is_imaginary:
+            if self.exp.is_integer:
+                odd = self.exp.is_odd
+                if odd is not None:
+                    return odd
+                return
+
+        if self.base == S.Exp1:
+            f = 2 * self.exp / (S.Pi*S.ImaginaryUnit)
+            # exp(pi*integer) = 1 or -1, so not imaginary
+            if f.is_even:
+                return False
+            # exp(pi*integer + pi/2) = I or -I, so it is imaginary
+            if f.is_odd:
+                return True
+            return None
+
+        if self.exp.is_imaginary:
+            from sympy.functions.elementary.exponential import log
+            imlog = log(self.base).is_imaginary
+            if imlog is not None:
+                return False  # I**i -> real; (2*I)**i -> complex ==> not imaginary
+
+        if self.base.is_extended_real and self.exp.is_extended_real:
+            if self.base.is_positive:
+                return False
+            else:
+                rat = self.exp.is_rational
+                if not rat:
+                    return rat
+                if self.exp.is_integer:
+                    return False
+                else:
+                    half = (2*self.exp).is_integer
+                    if half:
+                        return self.base.is_negative
+                    return half
+
+        if self.base.is_extended_real is False:  # we already know it's not imag
+            from sympy.functions.elementary.complexes import arg
+            i = arg(self.base)*self.exp/S.Pi
+            isodd = (2*i).is_odd
+            if isodd is not None:
+                return isodd
+
+    def _eval_is_odd(self):
+        if self.exp.is_integer:
+            if self.exp.is_positive:
+                return self.base.is_odd
+            elif self.exp.is_nonnegative and self.base.is_odd:
+                return True
+            elif self.base is S.NegativeOne:
+                return True
+
+    def _eval_is_finite(self):
+        if self.exp.is_negative:
+            if self.base.is_zero:
+                return False
+            if self.base.is_infinite or self.base.is_nonzero:
+                return True
+        c1 = self.base.is_finite
+        if c1 is None:
+            return
+        c2 = self.exp.is_finite
+        if c2 is None:
+            return
+        if c1 and c2:
+            if self.exp.is_nonnegative or fuzzy_not(self.base.is_zero):
+                return True
+
+    def _eval_is_prime(self):
+        '''
+        An integer raised to the n(>=2)-th power cannot be a prime.
+        '''
+        if self.base.is_integer and self.exp.is_integer and (self.exp - 1).is_positive:
+            return False
+
+    def _eval_is_composite(self):
+        """
+        A power is composite if both base and exponent are greater than 1
+        """
+        if (self.base.is_integer and self.exp.is_integer and
+            ((self.base - 1).is_positive and (self.exp - 1).is_positive or
+            (self.base + 1).is_negative and self.exp.is_positive and self.exp.is_even)):
+            return True
+
+    def _eval_is_polar(self):
+        return self.base.is_polar
+
+    def _eval_subs(self, old, new):
+        from sympy.calculus.accumulationbounds import AccumBounds
+
+        if isinstance(self.exp, AccumBounds):
+            b = self.base.subs(old, new)
+            e = self.exp.subs(old, new)
+            if isinstance(e, AccumBounds):
+                return e.__rpow__(b)
+            return self.func(b, e)
+
+        from sympy.functions.elementary.exponential import exp, log
+
+        def _check(ct1, ct2, old):
+            """Return (bool, pow, remainder_pow) where, if bool is True, then the
+            exponent of Pow `old` will combine with `pow` so the substitution
+            is valid, otherwise bool will be False.
+
+            For noncommutative objects, `pow` will be an integer, and a factor
+            `Pow(old.base, remainder_pow)` needs to be included. If there is
+            no such factor, None is returned. For commutative objects,
+            remainder_pow is always None.
+
+            cti are the coefficient and terms of an exponent of self or old
+            In this _eval_subs routine a change like (b**(2*x)).subs(b**x, y)
+            will give y**2 since (b**x)**2 == b**(2*x); if that equality does
+            not hold then the substitution should not occur so `bool` will be
+            False.
+
+            """
+            coeff1, terms1 = ct1
+            coeff2, terms2 = ct2
+            if terms1 == terms2:
+                if old.is_commutative:
+                    # Allow fractional powers for commutative objects
+                    pow = coeff1/coeff2
+                    try:
+                        as_int(pow, strict=False)
+                        combines = True
+                    except ValueError:
+                        b, e = old.as_base_exp()
+                        # These conditions ensure that (b**e)**f == b**(e*f) for any f
+                        combines = b.is_positive and e.is_real or b.is_nonnegative and e.is_nonnegative
+
+                    return combines, pow, None
+                else:
+                    # With noncommutative symbols, substitute only integer powers
+                    if not isinstance(terms1, tuple):
+                        terms1 = (terms1,)
+                    if not all(term.is_integer for term in terms1):
+                        return False, None, None
+
+                    try:
+                        # Round pow toward zero
+                        pow, remainder = divmod(as_int(coeff1), as_int(coeff2))
+                        if pow < 0 and remainder != 0:
+                            pow += 1
+                            remainder -= as_int(coeff2)
+
+                        if remainder == 0:
+                            remainder_pow = None
+                        else:
+                            remainder_pow = Mul(remainder, *terms1)
+
+                        return True, pow, remainder_pow
+                    except ValueError:
+                        # Can't substitute
+                        pass
+
+            return False, None, None
+
+        if old == self.base or (old == exp and self.base == S.Exp1):
+            if new.is_Function and isinstance(new, Callable):
+                return new(self.exp._subs(old, new))
+            else:
+                return new**self.exp._subs(old, new)
+
+        # issue 10829: (4**x - 3*y + 2).subs(2**x, y) -> y**2 - 3*y + 2
+        if isinstance(old, self.func) and self.exp == old.exp:
+            l = log(self.base, old.base)
+            if l.is_Number:
+                return Pow(new, l)
+
+        if isinstance(old, self.func) and self.base == old.base:
+            if self.exp.is_Add is False:
+                ct1 = self.exp.as_independent(Symbol, as_Add=False)
+                ct2 = old.exp.as_independent(Symbol, as_Add=False)
+                ok, pow, remainder_pow = _check(ct1, ct2, old)
+                if ok:
+                    # issue 5180: (x**(6*y)).subs(x**(3*y),z)->z**2
+                    result = self.func(new, pow)
+                    if remainder_pow is not None:
+                        result = Mul(result, Pow(old.base, remainder_pow))
+                    return result
+            else:  # b**(6*x + a).subs(b**(3*x), y) -> y**2 * b**a
+                # exp(exp(x) + exp(x**2)).subs(exp(exp(x)), w) -> w * exp(exp(x**2))
+                oarg = old.exp
+                new_l = []
+                o_al = []
+                ct2 = oarg.as_coeff_mul()
+                for a in self.exp.args:
+                    newa = a._subs(old, new)
+                    ct1 = newa.as_coeff_mul()
+                    ok, pow, remainder_pow = _check(ct1, ct2, old)
+                    if ok:
+                        new_l.append(new**pow)
+                        if remainder_pow is not None:
+                            o_al.append(remainder_pow)
+                        continue
+                    elif not old.is_commutative and not newa.is_integer:
+                        # If any term in the exponent is non-integer,
+                        # we do not do any substitutions in the noncommutative case
+                        return
+                    o_al.append(newa)
+                if new_l:
+                    expo = Add(*o_al)
+                    new_l.append(Pow(self.base, expo, evaluate=False) if expo != 1 else self.base)
+                    return Mul(*new_l)
+
+        if (isinstance(old, exp) or (old.is_Pow and old.base is S.Exp1)) and self.exp.is_extended_real and self.base.is_positive:
+            ct1 = old.exp.as_independent(Symbol, as_Add=False)
+            ct2 = (self.exp*log(self.base)).as_independent(
+                Symbol, as_Add=False)
+            ok, pow, remainder_pow = _check(ct1, ct2, old)
+            if ok:
+                result = self.func(new, pow)  # (2**x).subs(exp(x*log(2)), z) -> z
+                if remainder_pow is not None:
+                    result = Mul(result, Pow(old.base, remainder_pow))
+                return result
+
+    def as_base_exp(self):
+        """Return base and exp of self.
+
+        Explanation
+        ===========
+
+        If base a Rational less than 1, then return 1/Rational, -exp.
+        If this extra processing is not needed, the base and exp
+        properties will give the raw arguments.
+
+        Examples
+        ========
+
+        >>> from sympy import Pow, S
+        >>> p = Pow(S.Half, 2, evaluate=False)
+        >>> p.as_base_exp()
+        (2, -2)
+        >>> p.args
+        (1/2, 2)
+        >>> p.base, p.exp
+        (1/2, 2)
+
+        """
+        b, e = self.args
+        if b.is_Rational and b.p == 1 and b.q != 1:
+            return Integer(b.q), -e
+        return b, e
+
+    def _eval_adjoint(self):
+        from sympy.functions.elementary.complexes import adjoint
+        i, p = self.exp.is_integer, self.base.is_positive
+        if i:
+            return adjoint(self.base)**self.exp
+        if p:
+            return self.base**adjoint(self.exp)
+        if i is False and p is False:
+            expanded = expand_complex(self)
+            if expanded != self:
+                return adjoint(expanded)
+
+    def _eval_conjugate(self):
+        from sympy.functions.elementary.complexes import conjugate as c
+        i, p = self.exp.is_integer, self.base.is_positive
+        if i:
+            return c(self.base)**self.exp
+        if p:
+            return self.base**c(self.exp)
+        if i is False and p is False:
+            expanded = expand_complex(self)
+            if expanded != self:
+                return c(expanded)
+        if self.is_extended_real:
+            return self
+
+    def _eval_transpose(self):
+        from sympy.functions.elementary.complexes import transpose
+        if self.base == S.Exp1:
+            return self.func(S.Exp1, self.exp.transpose())
+        i, p = self.exp.is_integer, (self.base.is_complex or self.base.is_infinite)
+        if p:
+            return self.base**self.exp
+        if i:
+            return transpose(self.base)**self.exp
+        if i is False and p is False:
+            expanded = expand_complex(self)
+            if expanded != self:
+                return transpose(expanded)
+
+    def _eval_expand_power_exp(self, **hints):
+        """a**(n + m) -> a**n*a**m"""
+        b = self.base
+        e = self.exp
+        if b == S.Exp1:
+            from sympy.concrete.summations import Sum
+            if isinstance(e, Sum) and e.is_commutative:
+                from sympy.concrete.products import Product
+                return Product(self.func(b, e.function), *e.limits)
+        if e.is_Add and (hints.get('force', False) or
+                b.is_zero is False or e._all_nonneg_or_nonppos()):
+            if e.is_commutative:
+                return Mul(*[self.func(b, x) for x in e.args])
+            if b.is_commutative:
+                c, nc = sift(e.args, lambda x: x.is_commutative, binary=True)
+                if c:
+                    return Mul(*[self.func(b, x) for x in c]
+                        )*b**Add._from_args(nc)
+        return self
+
+    def _eval_expand_power_base(self, **hints):
+        """(a*b)**n -> a**n * b**n"""
+        force = hints.get('force', False)
+
+        b = self.base
+        e = self.exp
+        if not b.is_Mul:
+            return self
+
+        cargs, nc = b.args_cnc(split_1=False)
+
+        # expand each term - this is top-level-only
+        # expansion but we have to watch out for things
+        # that don't have an _eval_expand method
+        if nc:
+            nc = [i._eval_expand_power_base(**hints)
+                if hasattr(i, '_eval_expand_power_base') else i
+                for i in nc]
+
+            if e.is_Integer:
+                if e.is_positive:
+                    rv = Mul(*nc*e)
+                else:
+                    rv = Mul(*[i**-1 for i in nc[::-1]]*-e)
+                if cargs:
+                    rv *= Mul(*cargs)**e
+                return rv
+
+            if not cargs:
+                return self.func(Mul(*nc), e, evaluate=False)
+
+            nc = [Mul(*nc)]
+
+        # sift the commutative bases
+        other, maybe_real = sift(cargs, lambda x: x.is_extended_real is False,
+            binary=True)
+        def pred(x):
+            if x is S.ImaginaryUnit:
+                return S.ImaginaryUnit
+            polar = x.is_polar
+            if polar:
+                return True
+            if polar is None:
+                return fuzzy_bool(x.is_extended_nonnegative)
+        sifted = sift(maybe_real, pred)
+        nonneg = sifted[True]
+        other += sifted[None]
+        neg = sifted[False]
+        imag = sifted[S.ImaginaryUnit]
+        if imag:
+            I = S.ImaginaryUnit
+            i = len(imag) % 4
+            if i == 0:
+                pass
+            elif i == 1:
+                other.append(I)
+            elif i == 2:
+                if neg:
+                    nonn = -neg.pop()
+                    if nonn is not S.One:
+                        nonneg.append(nonn)
+                else:
+                    neg.append(S.NegativeOne)
+            else:
+                if neg:
+                    nonn = -neg.pop()
+                    if nonn is not S.One:
+                        nonneg.append(nonn)
+                else:
+                    neg.append(S.NegativeOne)
+                other.append(I)
+            del imag
+
+        # bring out the bases that can be separated from the base
+
+        if force or e.is_integer:
+            # treat all commutatives the same and put nc in other
+            cargs = nonneg + neg + other
+            other = nc
+        else:
+            # this is just like what is happening automatically, except
+            # that now we are doing it for an arbitrary exponent for which
+            # no automatic expansion is done
+
+            assert not e.is_Integer
+
+            # handle negatives by making them all positive and putting
+            # the residual -1 in other
+            if len(neg) > 1:
+                o = S.One
+                if not other and neg[0].is_Number:
+                    o *= neg.pop(0)
+                if len(neg) % 2:
+                    o = -o
+                for n in neg:
+                    nonneg.append(-n)
+                if o is not S.One:
+                    other.append(o)
+            elif neg and other:
+                if neg[0].is_Number and neg[0] is not S.NegativeOne:
+                    other.append(S.NegativeOne)
+                    nonneg.append(-neg[0])
+                else:
+                    other.extend(neg)
+            else:
+                other.extend(neg)
+            del neg
+
+            cargs = nonneg
+            other += nc
+
+        rv = S.One
+        if cargs:
+            if e.is_Rational:
+                npow, cargs = sift(cargs, lambda x: x.is_Pow and
+                    x.exp.is_Rational and x.base.is_number,
+                    binary=True)
+                rv = Mul(*[self.func(b.func(*b.args), e) for b in npow])
+            rv *= Mul(*[self.func(b, e, evaluate=False) for b in cargs])
+        if other:
+            rv *= self.func(Mul(*other), e, evaluate=False)
+        return rv
+
+    def _eval_expand_multinomial(self, **hints):
+        """(a + b + ..)**n -> a**n + n*a**(n-1)*b + .., n is nonzero integer"""
+
+        base, exp = self.args
+        result = self
+
+        if exp.is_Rational and exp.p > 0 and base.is_Add:
+            if not exp.is_Integer:
+                n = Integer(exp.p // exp.q)
+
+                if not n:
+                    return result
+                else:
+                    radical, result = self.func(base, exp - n), []
+
+                    expanded_base_n = self.func(base, n)
+                    if expanded_base_n.is_Pow:
+                        expanded_base_n = \
+                            expanded_base_n._eval_expand_multinomial()
+                    for term in Add.make_args(expanded_base_n):
+                        result.append(term*radical)
+
+                    return Add(*result)
+
+            n = int(exp)
+
+            if base.is_commutative:
+                order_terms, other_terms = [], []
+
+                for b in base.args:
+                    if b.is_Order:
+                        order_terms.append(b)
+                    else:
+                        other_terms.append(b)
+
+                if order_terms:
+                    # (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n)
+                    f = Add(*other_terms)
+                    o = Add(*order_terms)
+
+                    if n == 2:
+                        return expand_multinomial(f**n, deep=False) + n*f*o
+                    else:
+                        g = expand_multinomial(f**(n - 1), deep=False)
+                        return expand_mul(f*g, deep=False) + n*g*o
+
+                if base.is_number:
+                    # Efficiently expand expressions of the form (a + b*I)**n
+                    # where 'a' and 'b' are real numbers and 'n' is integer.
+                    a, b = base.as_real_imag()
+
+                    if a.is_Rational and b.is_Rational:
+                        if not a.is_Integer:
+                            if not b.is_Integer:
+                                k = self.func(a.q * b.q, n)
+                                a, b = a.p*b.q, a.q*b.p
+                            else:
+                                k = self.func(a.q, n)
+                                a, b = a.p, a.q*b
+                        elif not b.is_Integer:
+                            k = self.func(b.q, n)
+                            a, b = a*b.q, b.p
+                        else:
+                            k = 1
+
+                        a, b, c, d = int(a), int(b), 1, 0
+
+                        while n:
+                            if n & 1:
+                                c, d = a*c - b*d, b*c + a*d
+                                n -= 1
+                            a, b = a*a - b*b, 2*a*b
+                            n //= 2
+
+                        I = S.ImaginaryUnit
+
+                        if k == 1:
+                            return c + I*d
+                        else:
+                            return Integer(c)/k + I*d/k
+
+                p = other_terms
+                # (x + y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3
+                # in this particular example:
+                # p = [x,y]; n = 3
+                # so now it's easy to get the correct result -- we get the
+                # coefficients first:
+                from sympy.ntheory.multinomial import multinomial_coefficients
+                from sympy.polys.polyutils import basic_from_dict
+                expansion_dict = multinomial_coefficients(len(p), n)
+                # in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
+                # and now construct the expression.
+                return basic_from_dict(expansion_dict, *p)
+            else:
+                if n == 2:
+                    return Add(*[f*g for f in base.args for g in base.args])
+                else:
+                    multi = (base**(n - 1))._eval_expand_multinomial()
+                    if multi.is_Add:
+                        return Add(*[f*g for f in base.args
+                            for g in multi.args])
+                    else:
+                        # XXX can this ever happen if base was an Add?
+                        return Add(*[f*multi for f in base.args])
+        elif (exp.is_Rational and exp.p < 0 and base.is_Add and
+                abs(exp.p) > exp.q):
+            return 1 / self.func(base, -exp)._eval_expand_multinomial()
+        elif exp.is_Add and base.is_Number and (hints.get('force', False) or
+                base.is_zero is False or exp._all_nonneg_or_nonppos()):
+            #  a + b      a  b
+            #  n      --> n  n, where n, a, b are Numbers
+            # XXX should be in expand_power_exp?
+            coeff, tail = [], []
+            for term in exp.args:
+                if term.is_Number:
+                    coeff.append(self.func(base, term))
+                else:
+                    tail.append(term)
+            return Mul(*(coeff + [self.func(base, Add._from_args(tail))]))
+        else:
+            return result
+
+    def as_real_imag(self, deep=True, **hints):
+        if self.exp.is_Integer:
+            from sympy.polys.polytools import poly
+
+            exp = self.exp
+            re_e, im_e = self.base.as_real_imag(deep=deep)
+            if not im_e:
+                return self, S.Zero
+            a, b = symbols('a b', cls=Dummy)
+            if exp >= 0:
+                if re_e.is_Number and im_e.is_Number:
+                    # We can be more efficient in this case
+                    expr = expand_multinomial(self.base**exp)
+                    if expr != self:
+                        return expr.as_real_imag()
+
+                expr = poly(
+                    (a + b)**exp)  # a = re, b = im; expr = (a + b*I)**exp
+            else:
+                mag = re_e**2 + im_e**2
+                re_e, im_e = re_e/mag, -im_e/mag
+                if re_e.is_Number and im_e.is_Number:
+                    # We can be more efficient in this case
+                    expr = expand_multinomial((re_e + im_e*S.ImaginaryUnit)**-exp)
+                    if expr != self:
+                        return expr.as_real_imag()
+
+                expr = poly((a + b)**-exp)
+
+            # Terms with even b powers will be real
+            r = [i for i in expr.terms() if not i[0][1] % 2]
+            re_part = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
+            # Terms with odd b powers will be imaginary
+            r = [i for i in expr.terms() if i[0][1] % 4 == 1]
+            im_part1 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
+            r = [i for i in expr.terms() if i[0][1] % 4 == 3]
+            im_part3 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
+
+            return (re_part.subs({a: re_e, b: S.ImaginaryUnit*im_e}),
+            im_part1.subs({a: re_e, b: im_e}) + im_part3.subs({a: re_e, b: -im_e}))
+
+        from sympy.functions.elementary.trigonometric import atan2, cos, sin
+
+        if self.exp.is_Rational:
+            re_e, im_e = self.base.as_real_imag(deep=deep)
+
+            if im_e.is_zero and self.exp is S.Half:
+                if re_e.is_extended_nonnegative:
+                    return self, S.Zero
+                if re_e.is_extended_nonpositive:
+                    return S.Zero, (-self.base)**self.exp
+
+            # XXX: This is not totally correct since for x**(p/q) with
+            #      x being imaginary there are actually q roots, but
+            #      only a single one is returned from here.
+            r = self.func(self.func(re_e, 2) + self.func(im_e, 2), S.Half)
+
+            t = atan2(im_e, re_e)
+
+            rp, tp = self.func(r, self.exp), t*self.exp
+
+            return rp*cos(tp), rp*sin(tp)
+        elif self.base is S.Exp1:
+            from sympy.functions.elementary.exponential import exp
+            re_e, im_e = self.exp.as_real_imag()
+            if deep:
+                re_e = re_e.expand(deep, **hints)
+                im_e = im_e.expand(deep, **hints)
+            c, s = cos(im_e), sin(im_e)
+            return exp(re_e)*c, exp(re_e)*s
+        else:
+            from sympy.functions.elementary.complexes import im, re
+            if deep:
+                hints['complex'] = False
+
+                expanded = self.expand(deep, **hints)
+                if hints.get('ignore') == expanded:
+                    return None
+                else:
+                    return (re(expanded), im(expanded))
+            else:
+                return re(self), im(self)
+
+    def _eval_derivative(self, s):
+        from sympy.functions.elementary.exponential import log
+        dbase = self.base.diff(s)
+        dexp = self.exp.diff(s)
+        return self * (dexp * log(self.base) + dbase * self.exp/self.base)
+
+    def _eval_evalf(self, prec):
+        base, exp = self.as_base_exp()
+        if base == S.Exp1:
+            # Use mpmath function associated to class "exp":
+            from sympy.functions.elementary.exponential import exp as exp_function
+            return exp_function(self.exp, evaluate=False)._eval_evalf(prec)
+        base = base._evalf(prec)
+        if not exp.is_Integer:
+            exp = exp._evalf(prec)
+        if exp.is_negative and base.is_number and base.is_extended_real is False:
+            base = base.conjugate() / (base * base.conjugate())._evalf(prec)
+            exp = -exp
+            return self.func(base, exp).expand()
+        return self.func(base, exp)
+
+    def _eval_is_polynomial(self, syms):
+        if self.exp.has(*syms):
+            return False
+
+        if self.base.has(*syms):
+            return bool(self.base._eval_is_polynomial(syms) and
+                self.exp.is_Integer and (self.exp >= 0))
+        else:
+            return True
+
+    def _eval_is_rational(self):
+        # The evaluation of self.func below can be very expensive in the case
+        # of integer**integer if the exponent is large.  We should try to exit
+        # before that if possible:
+        if (self.exp.is_integer and self.base.is_rational
+                and fuzzy_not(fuzzy_and([self.exp.is_negative, self.base.is_zero]))):
+            return True
+        p = self.func(*self.as_base_exp())  # in case it's unevaluated
+        if not p.is_Pow:
+            return p.is_rational
+        b, e = p.as_base_exp()
+        if e.is_Rational and b.is_Rational:
+            # we didn't check that e is not an Integer
+            # because Rational**Integer autosimplifies
+            return False
+        if e.is_integer:
+            if b.is_rational:
+                if fuzzy_not(b.is_zero) or e.is_nonnegative:
+                    return True
+                if b == e:  # always rational, even for 0**0
+                    return True
+            elif b.is_irrational:
+                return e.is_zero
+        if b is S.Exp1:
+            if e.is_rational and e.is_nonzero:
+                return False
+
+    def _eval_is_algebraic(self):
+        def _is_one(expr):
+            try:
+                return (expr - 1).is_zero
+            except ValueError:
+                # when the operation is not allowed
+                return False
+
+        if self.base.is_zero or _is_one(self.base):
+            return True
+        elif self.base is S.Exp1:
+            s = self.func(*self.args)
+            if s.func == self.func:
+                if self.exp.is_nonzero:
+                    if self.exp.is_algebraic:
+                        return False
+                    elif (self.exp/S.Pi).is_rational:
+                        return False
+                    elif (self.exp/(S.ImaginaryUnit*S.Pi)).is_rational:
+                        return True
+            else:
+                return s.is_algebraic
+        elif self.exp.is_rational:
+            if self.base.is_algebraic is False:
+                return self.exp.is_zero
+            if self.base.is_zero is False:
+                if self.exp.is_nonzero:
+                    return self.base.is_algebraic
+                elif self.base.is_algebraic:
+                    return True
+            if self.exp.is_positive:
+                return self.base.is_algebraic
+        elif self.base.is_algebraic and self.exp.is_algebraic:
+            if ((fuzzy_not(self.base.is_zero)
+                and fuzzy_not(_is_one(self.base)))
+                or self.base.is_integer is False
+                or self.base.is_irrational):
+                return self.exp.is_rational
+
+    def _eval_is_rational_function(self, syms):
+        if self.exp.has(*syms):
+            return False
+
+        if self.base.has(*syms):
+            return self.base._eval_is_rational_function(syms) and \
+                self.exp.is_Integer
+        else:
+            return True
+
+    def _eval_is_meromorphic(self, x, a):
+        # f**g is meromorphic if g is an integer and f is meromorphic.
+        # E**(log(f)*g) is meromorphic if log(f)*g is meromorphic
+        # and finite.
+        base_merom = self.base._eval_is_meromorphic(x, a)
+        exp_integer = self.exp.is_Integer
+        if exp_integer:
+            return base_merom
+
+        exp_merom = self.exp._eval_is_meromorphic(x, a)
+        if base_merom is False:
+            # f**g = E**(log(f)*g) may be meromorphic if the
+            # singularities of log(f) and g cancel each other,
+            # for example, if g = 1/log(f). Hence,
+            return False if exp_merom else None
+        elif base_merom is None:
+            return None
+
+        b = self.base.subs(x, a)
+        # b is extended complex as base is meromorphic.
+        # log(base) is finite and meromorphic when b != 0, zoo.
+        b_zero = b.is_zero
+        if b_zero:
+            log_defined = False
+        else:
+            log_defined = fuzzy_and((b.is_finite, fuzzy_not(b_zero)))
+
+        if log_defined is False: # zero or pole of base
+            return exp_integer  # False or None
+        elif log_defined is None:
+            return None
+
+        if not exp_merom:
+            return exp_merom  # False or None
+
+        return self.exp.subs(x, a).is_finite
+
+    def _eval_is_algebraic_expr(self, syms):
+        if self.exp.has(*syms):
+            return False
+
+        if self.base.has(*syms):
+            return self.base._eval_is_algebraic_expr(syms) and \
+                self.exp.is_Rational
+        else:
+            return True
+
+    def _eval_rewrite_as_exp(self, base, expo, **kwargs):
+        from sympy.functions.elementary.exponential import exp, log
+
+        if base.is_zero or base.has(exp) or expo.has(exp):
+            return base**expo
+
+        evaluate = expo.has(Symbol)
+
+        if base.has(Symbol):
+            # delay evaluation if expo is non symbolic
+            # (as exp(x*log(5)) automatically reduces to x**5)
+            if global_parameters.exp_is_pow:
+                return Pow(S.Exp1, log(base)*expo, evaluate=evaluate)
+            else:
+                return exp(log(base)*expo, evaluate=evaluate)
+
+        else:
+            from sympy.functions.elementary.complexes import arg, Abs
+            return exp((log(Abs(base)) + S.ImaginaryUnit*arg(base))*expo)
+
+    def as_numer_denom(self):
+        if not self.is_commutative:
+            return self, S.One
+        base, exp = self.as_base_exp()
+        n, d = base.as_numer_denom()
+        # this should be the same as ExpBase.as_numer_denom wrt
+        # exponent handling
+        neg_exp = exp.is_negative
+        if exp.is_Mul and not neg_exp and not exp.is_positive:
+            neg_exp = exp.could_extract_minus_sign()
+        int_exp = exp.is_integer
+        # the denominator cannot be separated from the numerator if
+        # its sign is unknown unless the exponent is an integer, e.g.
+        # sqrt(a/b) != sqrt(a)/sqrt(b) when a=1 and b=-1. But if the
+        # denominator is negative the numerator and denominator can
+        # be negated and the denominator (now positive) separated.
+        if not (d.is_extended_real or int_exp):
+            n = base
+            d = S.One
+        dnonpos = d.is_nonpositive
+        if dnonpos:
+            n, d = -n, -d
+        elif dnonpos is None and not int_exp:
+            n = base
+            d = S.One
+        if neg_exp:
+            n, d = d, n
+            exp = -exp
+        if exp.is_infinite:
+            if n is S.One and d is not S.One:
+                return n, self.func(d, exp)
+            if n is not S.One and d is S.One:
+                return self.func(n, exp), d
+        return self.func(n, exp), self.func(d, exp)
+
+    def matches(self, expr, repl_dict=None, old=False):
+        expr = _sympify(expr)
+        if repl_dict is None:
+            repl_dict = {}
+
+        # special case, pattern = 1 and expr.exp can match to 0
+        if expr is S.One:
+            d = self.exp.matches(S.Zero, repl_dict)
+            if d is not None:
+                return d
+
+        # make sure the expression to be matched is an Expr
+        if not isinstance(expr, Expr):
+            return None
+
+        b, e = expr.as_base_exp()
+
+        # special case number
+        sb, se = self.as_base_exp()
+        if sb.is_Symbol and se.is_Integer and expr:
+            if e.is_rational:
+                return sb.matches(b**(e/se), repl_dict)
+            return sb.matches(expr**(1/se), repl_dict)
+
+        d = repl_dict.copy()
+        d = self.base.matches(b, d)
+        if d is None:
+            return None
+
+        d = self.exp.xreplace(d).matches(e, d)
+        if d is None:
+            return Expr.matches(self, expr, repl_dict)
+        return d
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # NOTE! This function is an important part of the gruntz algorithm
+        #       for computing limits. It has to return a generalized power
+        #       series with coefficients in C(log, log(x)). In more detail:
+        # It has to return an expression
+        #     c_0*x**e_0 + c_1*x**e_1 + ... (finitely many terms)
+        # where e_i are numbers (not necessarily integers) and c_i are
+        # expressions involving only numbers, the log function, and log(x).
+        # The series expansion of b**e is computed as follows:
+        # 1) We express b as f*(1 + g) where f is the leading term of b.
+        #    g has order O(x**d) where d is strictly positive.
+        # 2) Then b**e = (f**e)*((1 + g)**e).
+        #    (1 + g)**e is computed using binomial series.
+        from sympy.functions.elementary.exponential import exp, log
+        from sympy.series.limits import limit
+        from sympy.series.order import Order
+        from sympy.core.sympify import sympify
+        if self.base is S.Exp1:
+            e_series = self.exp.nseries(x, n=n, logx=logx)
+            if e_series.is_Order:
+                return 1 + e_series
+            e0 = limit(e_series.removeO(), x, 0)
+            if e0 is S.NegativeInfinity:
+                return Order(x**n, x)
+            if e0 is S.Infinity:
+                return self
+            t = e_series - e0
+            exp_series = term = exp(e0)
+            # series of exp(e0 + t) in t
+            for i in range(1, n):
+                term *= t/i
+                term = term.nseries(x, n=n, logx=logx)
+                exp_series += term
+            exp_series += Order(t**n, x)
+            from sympy.simplify.powsimp import powsimp
+            return powsimp(exp_series, deep=True, combine='exp')
+        from sympy.simplify.powsimp import powdenest
+        from .numbers import _illegal
+        self = powdenest(self, force=True).trigsimp()
+        b, e = self.as_base_exp()
+
+        if e.has(*_illegal):
+            raise PoleError()
+
+        if e.has(x):
+            return exp(e*log(b))._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+
+        if logx is not None and b.has(log):
+            from .symbol import Wild
+            c, ex = symbols('c, ex', cls=Wild, exclude=[x])
+            b = b.replace(log(c*x**ex), log(c) + ex*logx)
+            self = b**e
+
+        b = b.removeO()
+        try:
+            from sympy.functions.special.gamma_functions import polygamma
+            if b.has(polygamma, S.EulerGamma) and logx is not None:
+                raise ValueError()
+            _, m = b.leadterm(x)
+        except (ValueError, NotImplementedError, PoleError):
+            b = b._eval_nseries(x, n=max(2, n), logx=logx, cdir=cdir).removeO()
+            if b.has(S.NaN, S.ComplexInfinity):
+                raise NotImplementedError()
+            _, m = b.leadterm(x)
+
+        if e.has(log):
+            from sympy.simplify.simplify import logcombine
+            e = logcombine(e).cancel()
+
+        if not (m.is_zero or e.is_number and e.is_real):
+            if self == self._eval_as_leading_term(x, logx=logx, cdir=cdir):
+                res = exp(e*log(b))._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+                if res == exp(e*log(b)):
+                    return self
+                return res
+
+        f = b.as_leading_term(x, logx=logx)
+        g = (_mexpand(b) - f).cancel()
+        g = g/f
+        if not m.is_number:
+            raise NotImplementedError()
+        maxpow = n - m*e
+        if maxpow.has(Symbol):
+            maxpow = sympify(n)
+
+        if maxpow.is_negative:
+            return Order(x**(m*e), x)
+
+        if g.is_zero:
+            r = f**e
+            if r != self:
+                r += Order(x**n, x)
+            return r
+
+        def coeff_exp(term, x):
+            coeff, exp = S.One, S.Zero
+            for factor in Mul.make_args(term):
+                if factor.has(x):
+                    base, exp = factor.as_base_exp()
+                    if base != x:
+                        try:
+                            return term.leadterm(x)
+                        except ValueError:
+                            return term, S.Zero
+                else:
+                    coeff *= factor
+            return coeff, exp
+
+        def mul(d1, d2):
+            res = {}
+            for e1, e2 in product(d1, d2):
+                ex = e1 + e2
+                if ex < maxpow:
+                    res[ex] = res.get(ex, S.Zero) + d1[e1]*d2[e2]
+            return res
+
+        try:
+            c, d = g.leadterm(x, logx=logx)
+        except (ValueError, NotImplementedError):
+            if limit(g/x**maxpow, x, 0) == 0:
+                # g has higher order zero
+                return f**e + e*f**e*g  # first term of binomial series
+            else:
+                raise NotImplementedError()
+        if c.is_Float and d == S.Zero:
+            # Convert floats like 0.5 to exact SymPy numbers like S.Half, to
+            # prevent rounding errors which can induce wrong values of d leading
+            # to a NotImplementedError being returned from the block below.
+            g = g.replace(lambda x: x.is_Float, lambda x: Rational(x))
+            _, d = g.leadterm(x, logx=logx)
+        if not d.is_positive:
+            g = g.simplify()
+            if g.is_zero:
+                return f**e
+            _, d = g.leadterm(x, logx=logx)
+            if not d.is_positive:
+                g = ((b - f)/f).expand()
+                _, d = g.leadterm(x, logx=logx)
+                if not d.is_positive:
+                    raise NotImplementedError()
+
+        from sympy.functions.elementary.integers import ceiling
+        gpoly = g._eval_nseries(x, n=ceiling(maxpow), logx=logx, cdir=cdir).removeO()
+        gterms = {}
+
+        for term in Add.make_args(gpoly):
+            co1, e1 = coeff_exp(term, x)
+            gterms[e1] = gterms.get(e1, S.Zero) + co1
+
+        k = S.One
+        terms = {S.Zero: S.One}
+        tk = gterms
+
+        from sympy.functions.combinatorial.factorials import factorial, ff
+
+        while (k*d - maxpow).is_negative:
+            coeff = ff(e, k)/factorial(k)
+            for ex in tk:
+                terms[ex] = terms.get(ex, S.Zero) + coeff*tk[ex]
+            tk = mul(tk, gterms)
+            k += S.One
+
+        from sympy.functions.elementary.complexes import im
+
+        if not e.is_integer and m.is_zero and f.is_negative:
+            ndir = (b - f).dir(x, cdir)
+            if im(ndir).is_negative:
+                inco, inex = coeff_exp(f**e*(-1)**(-2*e), x)
+            elif im(ndir).is_zero:
+                inco, inex = coeff_exp(exp(e*log(b)).as_leading_term(x, logx=logx, cdir=cdir), x)
+            else:
+                inco, inex = coeff_exp(f**e, x)
+        else:
+            inco, inex = coeff_exp(f**e, x)
+        res = S.Zero
+
+        for e1 in terms:
+            ex = e1 + inex
+            res += terms[e1]*inco*x**(ex)
+
+        if not (e.is_integer and e.is_positive and (e*d - n).is_nonpositive and
+                res == _mexpand(self)):
+            try:
+                res += Order(x**n, x)
+            except NotImplementedError:
+                return exp(e*log(b))._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.functions.elementary.exponential import exp, log
+        e = self.exp
+        b = self.base
+        if self.base is S.Exp1:
+            arg = e.as_leading_term(x, logx=logx)
+            arg0 = arg.subs(x, 0)
+            if arg0 is S.NaN:
+                arg0 = arg.limit(x, 0)
+            if arg0.is_infinite is False:
+                return S.Exp1**arg0
+            raise PoleError("Cannot expand %s around 0" % (self))
+        elif e.has(x):
+            lt = exp(e * log(b))
+            return lt.as_leading_term(x, logx=logx, cdir=cdir)
+        else:
+            from sympy.functions.elementary.complexes import im
+            try:
+                f = b.as_leading_term(x, logx=logx, cdir=cdir)
+            except PoleError:
+                return self
+            if not e.is_integer and f.is_negative and not f.has(x):
+                ndir = (b - f).dir(x, cdir)
+                if im(ndir).is_negative:
+                    # Normally, f**e would evaluate to exp(e*log(f)) but on branch cuts
+                    # an other value is expected through the following computation
+                    # exp(e*(log(f) - 2*pi*I)) == f**e*exp(-2*e*pi*I) == f**e*(-1)**(-2*e).
+                    return self.func(f, e) * (-1)**(-2*e)
+                elif im(ndir).is_zero:
+                    log_leadterm = log(b)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+                    if log_leadterm.is_infinite is False:
+                        return exp(e*log_leadterm)
+            return self.func(f, e)
+
+    @cacheit
+    def _taylor_term(self, n, x, *previous_terms): # of (1 + x)**e
+        from sympy.functions.combinatorial.factorials import binomial
+        return binomial(self.exp, n) * self.func(x, n)
+
+    def taylor_term(self, n, x, *previous_terms):
+        if self.base is not S.Exp1:
+            return super().taylor_term(n, x, *previous_terms)
+        if n < 0:
+            return S.Zero
+        if n == 0:
+            return S.One
+        from .sympify import sympify
+        x = sympify(x)
+        if previous_terms:
+            p = previous_terms[-1]
+            if p is not None:
+                return p * x / n
+        from sympy.functions.combinatorial.factorials import factorial
+        return x**n/factorial(n)
+
+    def _eval_rewrite_as_sin(self, base, exp, **hints):
+        if self.base is S.Exp1:
+            from sympy.functions.elementary.trigonometric import sin
+            return sin(S.ImaginaryUnit*self.exp + S.Pi/2) - S.ImaginaryUnit*sin(S.ImaginaryUnit*self.exp)
+
+    def _eval_rewrite_as_cos(self, base, exp, **hints):
+        if self.base is S.Exp1:
+            from sympy.functions.elementary.trigonometric import cos
+            return cos(S.ImaginaryUnit*self.exp) + S.ImaginaryUnit*cos(S.ImaginaryUnit*self.exp + S.Pi/2)
+
+    def _eval_rewrite_as_tanh(self, base, exp, **hints):
+        if self.base is S.Exp1:
+            from sympy.functions.elementary.hyperbolic import tanh
+            return (1 + tanh(self.exp/2))/(1 - tanh(self.exp/2))
+
+    def _eval_rewrite_as_sqrt(self, base, exp, **kwargs):
+        from sympy.functions.elementary.trigonometric import sin, cos
+        if base is not S.Exp1:
+            return None
+        if exp.is_Mul:
+            coeff = exp.coeff(S.Pi * S.ImaginaryUnit)
+            if coeff and coeff.is_number:
+                cosine, sine = cos(S.Pi*coeff), sin(S.Pi*coeff)
+                if not isinstance(cosine, cos) and not isinstance (sine, sin):
+                    return cosine + S.ImaginaryUnit*sine
+
+    def as_content_primitive(self, radical=False, clear=True):
+        """Return the tuple (R, self/R) where R is the positive Rational
+        extracted from self.
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt
+        >>> sqrt(4 + 4*sqrt(2)).as_content_primitive()
+        (2, sqrt(1 + sqrt(2)))
+        >>> sqrt(3 + 3*sqrt(2)).as_content_primitive()
+        (1, sqrt(3)*sqrt(1 + sqrt(2)))
+
+        >>> from sympy import expand_power_base, powsimp, Mul
+        >>> from sympy.abc import x, y
+
+        >>> ((2*x + 2)**2).as_content_primitive()
+        (4, (x + 1)**2)
+        >>> (4**((1 + y)/2)).as_content_primitive()
+        (2, 4**(y/2))
+        >>> (3**((1 + y)/2)).as_content_primitive()
+        (1, 3**((y + 1)/2))
+        >>> (3**((5 + y)/2)).as_content_primitive()
+        (9, 3**((y + 1)/2))
+        >>> eq = 3**(2 + 2*x)
+        >>> powsimp(eq) == eq
+        True
+        >>> eq.as_content_primitive()
+        (9, 3**(2*x))
+        >>> powsimp(Mul(*_))
+        3**(2*x + 2)
+
+        >>> eq = (2 + 2*x)**y
+        >>> s = expand_power_base(eq); s.is_Mul, s
+        (False, (2*x + 2)**y)
+        >>> eq.as_content_primitive()
+        (1, (2*(x + 1))**y)
+        >>> s = expand_power_base(_[1]); s.is_Mul, s
+        (True, 2**y*(x + 1)**y)
+
+        See docstring of Expr.as_content_primitive for more examples.
+        """
+
+        b, e = self.as_base_exp()
+        b = _keep_coeff(*b.as_content_primitive(radical=radical, clear=clear))
+        ce, pe = e.as_content_primitive(radical=radical, clear=clear)
+        if b.is_Rational:
+            #e
+            #= ce*pe
+            #= ce*(h + t)
+            #= ce*h + ce*t
+            #=> self
+            #= b**(ce*h)*b**(ce*t)
+            #= b**(cehp/cehq)*b**(ce*t)
+            #= b**(iceh + r/cehq)*b**(ce*t)
+            #= b**(iceh)*b**(r/cehq)*b**(ce*t)
+            #= b**(iceh)*b**(ce*t + r/cehq)
+            h, t = pe.as_coeff_Add()
+            if h.is_Rational and b != S.Zero:
+                ceh = ce*h
+                c = self.func(b, ceh)
+                r = S.Zero
+                if not c.is_Rational:
+                    iceh, r = divmod(ceh.p, ceh.q)
+                    c = self.func(b, iceh)
+                return c, self.func(b, _keep_coeff(ce, t + r/ce/ceh.q))
+        e = _keep_coeff(ce, pe)
+        # b**e = (h*t)**e = h**e*t**e = c*m*t**e
+        if e.is_Rational and b.is_Mul:
+            h, t = b.as_content_primitive(radical=radical, clear=clear)  # h is positive
+            c, m = self.func(h, e).as_coeff_Mul()  # so c is positive
+            m, me = m.as_base_exp()
+            if m is S.One or me == e:  # probably always true
+                # return the following, not return c, m*Pow(t, e)
+                # which would change Pow into Mul; we let SymPy
+                # decide what to do by using the unevaluated Mul, e.g
+                # should it stay as sqrt(2 + 2*sqrt(5)) or become
+                # sqrt(2)*sqrt(1 + sqrt(5))
+                return c, self.func(_keep_coeff(m, t), e)
+        return S.One, self.func(b, e)
+
+    def is_constant(self, *wrt, **flags):
+        expr = self
+        if flags.get('simplify', True):
+            expr = expr.simplify()
+        b, e = expr.as_base_exp()
+        bz = b.equals(0)
+        if bz:  # recalculate with assumptions in case it's unevaluated
+            new = b**e
+            if new != expr:
+                return new.is_constant()
+        econ = e.is_constant(*wrt)
+        bcon = b.is_constant(*wrt)
+        if bcon:
+            if econ:
+                return True
+            bz = b.equals(0)
+            if bz is False:
+                return False
+        elif bcon is None:
+            return None
+
+        return e.equals(0)
+
+    def _eval_difference_delta(self, n, step):
+        b, e = self.args
+        if e.has(n) and not b.has(n):
+            new_e = e.subs(n, n + step)
+            return (b**(new_e - e) - 1) * self
+
+power = Dispatcher('power')
+power.add((object, object), Pow)
+
+from .add import Add
+from .numbers import Integer, Rational
+from .mul import Mul, _keep_coeff
+from .symbol import Symbol, Dummy, symbols
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/random.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/random.py
new file mode 100644
index 0000000000000000000000000000000000000000..c02986283523b39462a1e2c0b97e3fb230cff100
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/random.py
@@ -0,0 +1,227 @@
+"""
+When you need to use random numbers in SymPy library code, import from here
+so there is only one generator working for SymPy. Imports from here should
+behave the same as if they were being imported from Python's random module.
+But only the routines currently used in SymPy are included here. To use others
+import ``rng`` and access the method directly. For example, to capture the
+current state of the generator use ``rng.getstate()``.
+
+There is intentionally no Random to import from here. If you want
+to control the state of the generator, import ``seed`` and call it
+with or without an argument to set the state.
+
+Examples
+========
+
+>>> from sympy.core.random import random, seed
+>>> assert random() < 1
+>>> seed(1); a = random()
+>>> b = random()
+>>> seed(1); c = random()
+>>> assert a == c
+>>> assert a != b  # remote possibility this will fail
+
+"""
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.misc import as_int
+
+import random as _random
+rng = _random.Random()
+
+choice = rng.choice
+random = rng.random
+randint = rng.randint
+randrange = rng.randrange
+sample = rng.sample
+# seed = rng.seed
+shuffle = rng.shuffle
+uniform = rng.uniform
+
+_assumptions_rng = _random.Random()
+_assumptions_shuffle = _assumptions_rng.shuffle
+
+
+def seed(a=None, version=2):
+    rng.seed(a=a, version=version)
+    _assumptions_rng.seed(a=a, version=version)
+
+
+def random_complex_number(a=2, b=-1, c=3, d=1, rational=False, tolerance=None):
+    """
+    Return a random complex number.
+
+    To reduce chance of hitting branch cuts or anything, we guarantee
+    b <= Im z <= d, a <= Re z <= c
+
+    When rational is True, a rational approximation to a random number
+    is obtained within specified tolerance, if any.
+    """
+    from sympy.core.numbers import I
+    from sympy.simplify.simplify import nsimplify
+    A, B = uniform(a, c), uniform(b, d)
+    if not rational:
+        return A + I*B
+    return (nsimplify(A, rational=True, tolerance=tolerance) +
+        I*nsimplify(B, rational=True, tolerance=tolerance))
+
+
+def verify_numerically(f, g, z=None, tol=1.0e-6, a=2, b=-1, c=3, d=1):
+    """
+    Test numerically that f and g agree when evaluated in the argument z.
+
+    If z is None, all symbols will be tested. This routine does not test
+    whether there are Floats present with precision higher than 15 digits
+    so if there are, your results may not be what you expect due to round-
+    off errors.
+
+    Examples
+    ========
+
+    >>> from sympy import sin, cos
+    >>> from sympy.abc import x
+    >>> from sympy.core.random import verify_numerically as tn
+    >>> tn(sin(x)**2 + cos(x)**2, 1, x)
+    True
+    """
+    from sympy.core.symbol import Symbol
+    from sympy.core.sympify import sympify
+    from sympy.core.numbers import comp
+    f, g = (sympify(i) for i in (f, g))
+    if z is None:
+        z = f.free_symbols | g.free_symbols
+    elif isinstance(z, Symbol):
+        z = [z]
+    reps = list(zip(z, [random_complex_number(a, b, c, d) for _ in z]))
+    z1 = f.subs(reps).n()
+    z2 = g.subs(reps).n()
+    return comp(z1, z2, tol)
+
+
+def test_derivative_numerically(f, z, tol=1.0e-6, a=2, b=-1, c=3, d=1):
+    """
+    Test numerically that the symbolically computed derivative of f
+    with respect to z is correct.
+
+    This routine does not test whether there are Floats present with
+    precision higher than 15 digits so if there are, your results may
+    not be what you expect due to round-off errors.
+
+    Examples
+    ========
+
+    >>> from sympy import sin
+    >>> from sympy.abc import x
+    >>> from sympy.core.random import test_derivative_numerically as td
+    >>> td(sin(x), x)
+    True
+    """
+    from sympy.core.numbers import comp
+    from sympy.core.function import Derivative
+    z0 = random_complex_number(a, b, c, d)
+    f1 = f.diff(z).subs(z, z0)
+    f2 = Derivative(f, z).doit_numerically(z0)
+    return comp(f1.n(), f2.n(), tol)
+
+
+def _randrange(seed=None):
+    """Return a randrange generator.
+
+    ``seed`` can be
+
+    * None - return randomly seeded generator
+    * int - return a generator seeded with the int
+    * list - the values to be returned will be taken from the list
+      in the order given; the provided list is not modified.
+
+    Examples
+    ========
+
+    >>> from sympy.core.random import _randrange
+    >>> rr = _randrange()
+    >>> rr(1000) # doctest: +SKIP
+    999
+    >>> rr = _randrange(3)
+    >>> rr(1000) # doctest: +SKIP
+    238
+    >>> rr = _randrange([0, 5, 1, 3, 4])
+    >>> rr(3), rr(3)
+    (0, 1)
+    """
+    if seed is None:
+        return randrange
+    elif isinstance(seed, int):
+        rng.seed(seed)
+        return randrange
+    elif is_sequence(seed):
+        seed = list(seed)  # make a copy
+        seed.reverse()
+
+        def give(a, b=None, seq=seed):
+            if b is None:
+                a, b = 0, a
+            a, b = as_int(a), as_int(b)
+            w = b - a
+            if w < 1:
+                raise ValueError('_randrange got empty range')
+            try:
+                x = seq.pop()
+            except IndexError:
+                raise ValueError('_randrange sequence was too short')
+            if a <= x < b:
+                return x
+            else:
+                return give(a, b, seq)
+        return give
+    else:
+        raise ValueError('_randrange got an unexpected seed')
+
+
+def _randint(seed=None):
+    """Return a randint generator.
+
+    ``seed`` can be
+
+    * None - return randomly seeded generator
+    * int - return a generator seeded with the int
+    * list - the values to be returned will be taken from the list
+      in the order given; the provided list is not modified.
+
+    Examples
+    ========
+
+    >>> from sympy.core.random import _randint
+    >>> ri = _randint()
+    >>> ri(1, 1000) # doctest: +SKIP
+    999
+    >>> ri = _randint(3)
+    >>> ri(1, 1000) # doctest: +SKIP
+    238
+    >>> ri = _randint([0, 5, 1, 2, 4])
+    >>> ri(1, 3), ri(1, 3)
+    (1, 2)
+    """
+    if seed is None:
+        return randint
+    elif isinstance(seed, int):
+        rng.seed(seed)
+        return randint
+    elif is_sequence(seed):
+        seed = list(seed)  # make a copy
+        seed.reverse()
+
+        def give(a, b, seq=seed):
+            a, b = as_int(a), as_int(b)
+            w = b - a
+            if w < 0:
+                raise ValueError('_randint got empty range')
+            try:
+                x = seq.pop()
+            except IndexError:
+                raise ValueError('_randint sequence was too short')
+            if a <= x <= b:
+                return x
+            else:
+                return give(a, b, seq)
+        return give
+    else:
+        raise ValueError('_randint got an unexpected seed')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/relational.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/relational.py
new file mode 100644
index 0000000000000000000000000000000000000000..28bf039c9be67a6f5cd6f11df1968961c0760373
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/relational.py
@@ -0,0 +1,1622 @@
+from __future__ import annotations
+
+from .basic import Atom, Basic
+from .coreerrors import LazyExceptionMessage
+from .sorting import ordered
+from .evalf import EvalfMixin
+from .function import AppliedUndef
+from .numbers import int_valued
+from .singleton import S
+from .sympify import _sympify, SympifyError
+from .parameters import global_parameters
+from .logic import fuzzy_bool, fuzzy_xor, fuzzy_and, fuzzy_not
+from sympy.logic.boolalg import Boolean, BooleanAtom
+from sympy.utilities.iterables import sift
+from sympy.utilities.misc import filldedent
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+
+__all__ = (
+    'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge',
+    'Relational', 'Equality', 'Unequality', 'StrictLessThan', 'LessThan',
+    'StrictGreaterThan', 'GreaterThan',
+)
+
+from .expr import Expr
+from sympy.multipledispatch import dispatch
+from .containers import Tuple
+from .symbol import Symbol
+
+
+def _nontrivBool(side):
+    return isinstance(side, Boolean) and \
+           not isinstance(side, Atom)
+
+
+# Note, see issue 4986.  Ideally, we wouldn't want to subclass both Boolean
+# and Expr.
+# from .. import Expr
+
+
+def _canonical(cond):
+    # return a condition in which all relationals are canonical
+    reps = {r: r.canonical for r in cond.atoms(Relational)}
+    return cond.xreplace(reps)
+    # XXX: AttributeError was being caught here but it wasn't triggered by any of
+    # the tests so I've removed it...
+
+
+def _canonical_coeff(rel):
+    # return -2*x + 1 < 0 as x > 1/2
+    # XXX make this part of Relational.canonical?
+    rel = rel.canonical
+    if not rel.is_Relational or rel.rhs.is_Boolean:
+        return rel  # Eq(x, True)
+    if not isinstance(rel.lhs, Expr):
+        return rel.reversed  # e.g.: Eq(True, x) -> Eq(x, True)
+    b, l = rel.lhs.as_coeff_Add(rational=True)
+    m, lhs = l.as_coeff_Mul(rational=True)
+    rhs = (rel.rhs - b)/m
+    if m < 0:
+        return rel.reversed.func(lhs, rhs)
+    return rel.func(lhs, rhs)
+
+
+class Relational(Boolean, EvalfMixin):
+    """Base class for all relation types.
+
+    Explanation
+    ===========
+
+    Subclasses of Relational should generally be instantiated directly, but
+    Relational can be instantiated with a valid ``rop`` value to dispatch to
+    the appropriate subclass.
+
+    Parameters
+    ==========
+
+    rop : str or None
+        Indicates what subclass to instantiate.  Valid values can be found
+        in the keys of Relational.ValidRelationOperator.
+
+    Examples
+    ========
+
+    >>> from sympy import Rel
+    >>> from sympy.abc import x, y
+    >>> Rel(y, x + x**2, '==')
+    Eq(y, x**2 + x)
+
+    A relation's type can be defined upon creation using ``rop``.
+    The relation type of an existing expression can be obtained
+    using its ``rel_op`` property.
+    Here is a table of all the relation types, along with their
+    ``rop`` and ``rel_op`` values:
+
+    +---------------------+----------------------------+------------+
+    |Relation             |``rop``                     |``rel_op``  |
+    +=====================+============================+============+
+    |``Equality``         |``==`` or ``eq`` or ``None``|``==``      |
+    +---------------------+----------------------------+------------+
+    |``Unequality``       |``!=`` or ``ne``            |``!=``      |
+    +---------------------+----------------------------+------------+
+    |``GreaterThan``      |``>=`` or ``ge``            |``>=``      |
+    +---------------------+----------------------------+------------+
+    |``LessThan``         |``<=`` or ``le``            |``<=``      |
+    +---------------------+----------------------------+------------+
+    |``StrictGreaterThan``|``>`` or ``gt``             |``>``       |
+    +---------------------+----------------------------+------------+
+    |``StrictLessThan``   |``<`` or ``lt``             |``<``       |
+    +---------------------+----------------------------+------------+
+
+    For example, setting ``rop`` to ``==`` produces an
+    ``Equality`` relation, ``Eq()``.
+    So does setting ``rop`` to ``eq``, or leaving ``rop`` unspecified.
+    That is, the first three ``Rel()`` below all produce the same result.
+    Using a ``rop`` from a different row in the table produces a
+    different relation type.
+    For example, the fourth ``Rel()`` below using ``lt`` for ``rop``
+    produces a ``StrictLessThan`` inequality:
+
+    >>> from sympy import Rel
+    >>> from sympy.abc import x, y
+    >>> Rel(y, x + x**2, '==')
+        Eq(y, x**2 + x)
+    >>> Rel(y, x + x**2, 'eq')
+        Eq(y, x**2 + x)
+    >>> Rel(y, x + x**2)
+        Eq(y, x**2 + x)
+    >>> Rel(y, x + x**2, 'lt')
+        y < x**2 + x
+
+    To obtain the relation type of an existing expression,
+    get its ``rel_op`` property.
+    For example, ``rel_op`` is ``==`` for the ``Equality`` relation above,
+    and ``<`` for the strict less than inequality above:
+
+    >>> from sympy import Rel
+    >>> from sympy.abc import x, y
+    >>> my_equality = Rel(y, x + x**2, '==')
+    >>> my_equality.rel_op
+        '=='
+    >>> my_inequality = Rel(y, x + x**2, 'lt')
+    >>> my_inequality.rel_op
+        '<'
+
+    """
+    __slots__ = ()
+
+    ValidRelationOperator: dict[str | None, type[Relational]] = {}
+
+    is_Relational = True
+
+    # ValidRelationOperator - Defined below, because the necessary classes
+    #   have not yet been defined
+
+    def __new__(cls, lhs, rhs, rop=None, **assumptions):
+        # If called by a subclass, do nothing special and pass on to Basic.
+        if cls is not Relational:
+            return Basic.__new__(cls, lhs, rhs, **assumptions)
+
+        # XXX: Why do this? There should be a separate function to make a
+        # particular subclass of Relational from a string.
+        #
+        # If called directly with an operator, look up the subclass
+        # corresponding to that operator and delegate to it
+        cls = cls.ValidRelationOperator.get(rop, None)
+        if cls is None:
+            raise ValueError("Invalid relational operator symbol: %r" % rop)
+
+        if not issubclass(cls, (Eq, Ne)):
+            # validate that Booleans are not being used in a relational
+            # other than Eq/Ne;
+            # Note: Symbol is a subclass of Boolean but is considered
+            # acceptable here.
+            if any(map(_nontrivBool, (lhs, rhs))):
+                raise TypeError(filldedent('''
+                    A Boolean argument can only be used in
+                    Eq and Ne; all other relationals expect
+                    real expressions.
+                '''))
+
+        return cls(lhs, rhs, **assumptions)
+
+    @property
+    def lhs(self):
+        """The left-hand side of the relation."""
+        return self._args[0]
+
+    @property
+    def rhs(self):
+        """The right-hand side of the relation."""
+        return self._args[1]
+
+    @property
+    def reversed(self):
+        """Return the relationship with sides reversed.
+
+        Examples
+        ========
+
+        >>> from sympy import Eq
+        >>> from sympy.abc import x
+        >>> Eq(x, 1)
+        Eq(x, 1)
+        >>> _.reversed
+        Eq(1, x)
+        >>> x < 1
+        x < 1
+        >>> _.reversed
+        1 > x
+        """
+        ops = {Eq: Eq, Gt: Lt, Ge: Le, Lt: Gt, Le: Ge, Ne: Ne}
+        a, b = self.args
+        return Relational.__new__(ops.get(self.func, self.func), b, a)
+
+    @property
+    def reversedsign(self):
+        """Return the relationship with signs reversed.
+
+        Examples
+        ========
+
+        >>> from sympy import Eq
+        >>> from sympy.abc import x
+        >>> Eq(x, 1)
+        Eq(x, 1)
+        >>> _.reversedsign
+        Eq(-x, -1)
+        >>> x < 1
+        x < 1
+        >>> _.reversedsign
+        -x > -1
+        """
+        a, b = self.args
+        if not (isinstance(a, BooleanAtom) or isinstance(b, BooleanAtom)):
+            ops = {Eq: Eq, Gt: Lt, Ge: Le, Lt: Gt, Le: Ge, Ne: Ne}
+            return Relational.__new__(ops.get(self.func, self.func), -a, -b)
+        else:
+            return self
+
+    @property
+    def negated(self):
+        """Return the negated relationship.
+
+        Examples
+        ========
+
+        >>> from sympy import Eq
+        >>> from sympy.abc import x
+        >>> Eq(x, 1)
+        Eq(x, 1)
+        >>> _.negated
+        Ne(x, 1)
+        >>> x < 1
+        x < 1
+        >>> _.negated
+        x >= 1
+
+        Notes
+        =====
+
+        This works more or less identical to ``~``/``Not``. The difference is
+        that ``negated`` returns the relationship even if ``evaluate=False``.
+        Hence, this is useful in code when checking for e.g. negated relations
+        to existing ones as it will not be affected by the `evaluate` flag.
+
+        """
+        ops = {Eq: Ne, Ge: Lt, Gt: Le, Le: Gt, Lt: Ge, Ne: Eq}
+        # If there ever will be new Relational subclasses, the following line
+        # will work until it is properly sorted out
+        # return ops.get(self.func, lambda a, b, evaluate=False: ~(self.func(a,
+        #      b, evaluate=evaluate)))(*self.args, evaluate=False)
+        return Relational.__new__(ops.get(self.func), *self.args)
+
+    @property
+    def weak(self):
+        """return the non-strict version of the inequality or self
+
+        EXAMPLES
+        ========
+
+        >>> from sympy.abc import x
+        >>> (x < 1).weak
+        x <= 1
+        >>> _.weak
+        x <= 1
+        """
+        return self
+
+    @property
+    def strict(self):
+        """return the strict version of the inequality or self
+
+        EXAMPLES
+        ========
+
+        >>> from sympy.abc import x
+        >>> (x <= 1).strict
+        x < 1
+        >>> _.strict
+        x < 1
+        """
+        return self
+
+    def _eval_evalf(self, prec):
+        return self.func(*[s._evalf(prec) for s in self.args])
+
+    @property
+    def canonical(self):
+        """Return a canonical form of the relational by putting a
+        number on the rhs, canonically removing a sign or else
+        ordering the args canonically. No other simplification is
+        attempted.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> x < 2
+        x < 2
+        >>> _.reversed.canonical
+        x < 2
+        >>> (-y < x).canonical
+        x > -y
+        >>> (-y > x).canonical
+        x < -y
+        >>> (-y < -x).canonical
+        x < y
+
+        The canonicalization is recursively applied:
+
+        >>> from sympy import Eq
+        >>> Eq(x < y, y > x).canonical
+        True
+        """
+        args = tuple([i.canonical if isinstance(i, Relational) else i for i in self.args])
+        if args != self.args:
+            r = self.func(*args)
+            if not isinstance(r, Relational):
+                return r
+        else:
+            r = self
+        if r.rhs.is_number:
+            if r.rhs.is_Number and r.lhs.is_Number and r.lhs > r.rhs:
+                r = r.reversed
+        elif r.lhs.is_number:
+            r = r.reversed
+        elif tuple(ordered(args)) != args:
+            r = r.reversed
+
+        LHS_CEMS = getattr(r.lhs, 'could_extract_minus_sign', None)
+        RHS_CEMS = getattr(r.rhs, 'could_extract_minus_sign', None)
+
+        if isinstance(r.lhs, BooleanAtom) or isinstance(r.rhs, BooleanAtom):
+            return r
+
+        # Check if first value has negative sign
+        if LHS_CEMS and LHS_CEMS():
+            return r.reversedsign
+        elif not r.rhs.is_number and RHS_CEMS and RHS_CEMS():
+            # Right hand side has a minus, but not lhs.
+            # How does the expression with reversed signs behave?
+            # This is so that expressions of the type
+            # Eq(x, -y) and Eq(-x, y)
+            # have the same canonical representation
+            expr1, _ = ordered([r.lhs, -r.rhs])
+            if expr1 != r.lhs:
+                return r.reversed.reversedsign
+
+        return r
+
+    def equals(self, other, failing_expression=False):
+        """Return True if the sides of the relationship are mathematically
+        identical and the type of relationship is the same.
+        If failing_expression is True, return the expression whose truth value
+        was unknown."""
+        if isinstance(other, Relational):
+            if other in (self, self.reversed):
+                return True
+            a, b = self, other
+            if a.func in (Eq, Ne) or b.func in (Eq, Ne):
+                if a.func != b.func:
+                    return False
+                left, right = [i.equals(j,
+                                        failing_expression=failing_expression)
+                               for i, j in zip(a.args, b.args)]
+                if left is True:
+                    return right
+                if right is True:
+                    return left
+                lr, rl = [i.equals(j, failing_expression=failing_expression)
+                          for i, j in zip(a.args, b.reversed.args)]
+                if lr is True:
+                    return rl
+                if rl is True:
+                    return lr
+                e = (left, right, lr, rl)
+                if all(i is False for i in e):
+                    return False
+                for i in e:
+                    if i not in (True, False):
+                        return i
+            else:
+                if b.func != a.func:
+                    b = b.reversed
+                if a.func != b.func:
+                    return False
+                left = a.lhs.equals(b.lhs,
+                                    failing_expression=failing_expression)
+                if left is False:
+                    return False
+                right = a.rhs.equals(b.rhs,
+                                     failing_expression=failing_expression)
+                if right is False:
+                    return False
+                if left is True:
+                    return right
+                return left
+
+    def _eval_simplify(self, **kwargs):
+        from .add import Add
+        from .expr import Expr
+        r = self
+        r = r.func(*[i.simplify(**kwargs) for i in r.args])
+        if r.is_Relational:
+            if not isinstance(r.lhs, Expr) or not isinstance(r.rhs, Expr):
+                return r
+            dif = r.lhs - r.rhs
+            # replace dif with a valid Number that will
+            # allow a definitive comparison with 0
+            v = None
+            if dif.is_comparable:
+                v = dif.n(2)
+                if any(i._prec == 1 for i in v.as_real_imag()):
+                    rv, iv = [i.n(2) for i in dif.as_real_imag()]
+                    v = rv + S.ImaginaryUnit*iv
+            elif dif.equals(0):  # XXX this is expensive
+                v = S.Zero
+            if v is not None:
+                r = r.func._eval_relation(v, S.Zero)
+            r = r.canonical
+            # If there is only one symbol in the expression,
+            # try to write it on a simplified form
+            free = list(filter(lambda x: x.is_real is not False, r.free_symbols))
+            if len(free) == 1:
+                try:
+                    from sympy.solvers.solveset import linear_coeffs
+                    x = free.pop()
+                    dif = r.lhs - r.rhs
+                    m, b = linear_coeffs(dif, x)
+                    if m.is_zero is False:
+                        if m.is_negative:
+                            # Dividing with a negative number, so change order of arguments
+                            # canonical will put the symbol back on the lhs later
+                            r = r.func(-b / m, x)
+                        else:
+                            r = r.func(x, -b / m)
+                    else:
+                        r = r.func(b, S.Zero)
+                except ValueError:
+                    # maybe not a linear function, try polynomial
+                    from sympy.polys.polyerrors import PolynomialError
+                    from sympy.polys.polytools import gcd, Poly, poly
+                    try:
+                        p = poly(dif, x)
+                        c = p.all_coeffs()
+                        constant = c[-1]
+                        c[-1] = 0
+                        scale = gcd(c)
+                        c = [ctmp / scale for ctmp in c]
+                        r = r.func(Poly.from_list(c, x).as_expr(), -constant / scale)
+                    except PolynomialError:
+                        pass
+            elif len(free) >= 2:
+                try:
+                    from sympy.solvers.solveset import linear_coeffs
+                    from sympy.polys.polytools import gcd
+                    free = list(ordered(free))
+                    dif = r.lhs - r.rhs
+                    m = linear_coeffs(dif, *free)
+                    constant = m[-1]
+                    del m[-1]
+                    scale = gcd(m)
+                    m = [mtmp / scale for mtmp in m]
+                    nzm = list(filter(lambda f: f[0] != 0, list(zip(m, free))))
+                    if scale.is_zero is False:
+                        if constant != 0:
+                            # lhs: expression, rhs: constant
+                            newexpr = Add(*[i * j for i, j in nzm])
+                            r = r.func(newexpr, -constant / scale)
+                        else:
+                            # keep first term on lhs
+                            lhsterm = nzm[0][0] * nzm[0][1]
+                            del nzm[0]
+                            newexpr = Add(*[i * j for i, j in nzm])
+                            r = r.func(lhsterm, -newexpr)
+
+                    else:
+                        r = r.func(constant, S.Zero)
+                except ValueError:
+                    pass
+        # Did we get a simplified result?
+        r = r.canonical
+        measure = kwargs['measure']
+        if measure(r) < kwargs['ratio'] * measure(self):
+            return r
+        else:
+            return self
+
+    def _eval_trigsimp(self, **opts):
+        from sympy.simplify.trigsimp import trigsimp
+        return self.func(trigsimp(self.lhs, **opts), trigsimp(self.rhs, **opts))
+
+    def expand(self, **kwargs):
+        args = (arg.expand(**kwargs) for arg in self.args)
+        return self.func(*args)
+
+    def __bool__(self) -> bool:
+        raise TypeError(
+            LazyExceptionMessage(
+                lambda: f"cannot determine truth value of Relational: {self}"
+            )
+        )
+
+    def _eval_as_set(self):
+        # self is univariate and periodicity(self, x) in (0, None)
+        from sympy.solvers.inequalities import solve_univariate_inequality
+        from sympy.sets.conditionset import ConditionSet
+        syms = self.free_symbols
+        assert len(syms) == 1
+        x = syms.pop()
+        try:
+            xset = solve_univariate_inequality(self, x, relational=False)
+        except NotImplementedError:
+            # solve_univariate_inequality raises NotImplementedError for
+            # unsolvable equations/inequalities.
+            xset = ConditionSet(x, self, S.Reals)
+        return xset
+
+    @property
+    def binary_symbols(self):
+        # override where necessary
+        return set()
+
+
+Rel = Relational
+
+
+class Equality(Relational):
+    """
+    An equal relation between two objects.
+
+    Explanation
+    ===========
+
+    Represents that two objects are equal.  If they can be easily shown
+    to be definitively equal (or unequal), this will reduce to True (or
+    False).  Otherwise, the relation is maintained as an unevaluated
+    Equality object.  Use the ``simplify`` function on this object for
+    more nontrivial evaluation of the equality relation.
+
+    As usual, the keyword argument ``evaluate=False`` can be used to
+    prevent any evaluation.
+
+    Examples
+    ========
+
+    >>> from sympy import Eq, simplify, exp, cos
+    >>> from sympy.abc import x, y
+    >>> Eq(y, x + x**2)
+    Eq(y, x**2 + x)
+    >>> Eq(2, 5)
+    False
+    >>> Eq(2, 5, evaluate=False)
+    Eq(2, 5)
+    >>> _.doit()
+    False
+    >>> Eq(exp(x), exp(x).rewrite(cos))
+    Eq(exp(x), sinh(x) + cosh(x))
+    >>> simplify(_)
+    True
+
+    See Also
+    ========
+
+    sympy.logic.boolalg.Equivalent : for representing equality between two
+        boolean expressions
+
+    Notes
+    =====
+
+    Python treats 1 and True (and 0 and False) as being equal; SymPy
+    does not. And integer will always compare as unequal to a Boolean:
+
+    >>> Eq(True, 1), True == 1
+    (False, True)
+
+    This class is not the same as the == operator.  The == operator tests
+    for exact structural equality between two expressions; this class
+    compares expressions mathematically.
+
+    If either object defines an ``_eval_Eq`` method, it can be used in place of
+    the default algorithm.  If ``lhs._eval_Eq(rhs)`` or ``rhs._eval_Eq(lhs)``
+    returns anything other than None, that return value will be substituted for
+    the Equality.  If None is returned by ``_eval_Eq``, an Equality object will
+    be created as usual.
+
+    Since this object is already an expression, it does not respond to
+    the method ``as_expr`` if one tries to create `x - y` from ``Eq(x, y)``.
+    If ``eq = Eq(x, y)`` then write `eq.lhs - eq.rhs` to get ``x - y``.
+
+    .. deprecated:: 1.5
+
+       ``Eq(expr)`` with a single argument is a shorthand for ``Eq(expr, 0)``,
+       but this behavior is deprecated and will be removed in a future version
+       of SymPy.
+
+    """
+    rel_op = '=='
+
+    __slots__ = ()
+
+    is_Equality = True
+
+    def __new__(cls, lhs, rhs, **options):
+        evaluate = options.pop('evaluate', global_parameters.evaluate)
+        lhs = _sympify(lhs)
+        rhs = _sympify(rhs)
+        if evaluate:
+            val = is_eq(lhs, rhs)
+            if val is None:
+                return cls(lhs, rhs, evaluate=False)
+            else:
+                return _sympify(val)
+
+        return Relational.__new__(cls, lhs, rhs)
+
+    @classmethod
+    def _eval_relation(cls, lhs, rhs):
+        return _sympify(lhs == rhs)
+
+    def _eval_rewrite_as_Add(self, L, R, evaluate=True, **kwargs):
+        """
+        return Eq(L, R) as L - R. To control the evaluation of
+        the result set pass `evaluate=True` to give L - R;
+        if `evaluate=None` then terms in L and R will not cancel
+        but they will be listed in canonical order; otherwise
+        non-canonical args will be returned. If one side is 0, the
+        non-zero side will be returned.
+
+        .. deprecated:: 1.13
+
+           The method ``Eq.rewrite(Add)`` is deprecated.
+           See :ref:`eq-rewrite-Add` for details.
+
+        Examples
+        ========
+
+        >>> from sympy import Eq, Add
+        >>> from sympy.abc import b, x
+        >>> eq = Eq(x + b, x - b)
+        >>> eq.rewrite(Add)  #doctest: +SKIP
+        2*b
+        >>> eq.rewrite(Add, evaluate=None).args  #doctest: +SKIP
+        (b, b, x, -x)
+        >>> eq.rewrite(Add, evaluate=False).args  #doctest: +SKIP
+        (b, x, b, -x)
+        """
+        sympy_deprecation_warning("""
+        Eq.rewrite(Add) is deprecated.
+
+        For ``eq = Eq(a, b)`` use ``eq.lhs - eq.rhs`` to obtain
+        ``a - b``.
+        """,
+            deprecated_since_version="1.13",
+            active_deprecations_target="eq-rewrite-Add",
+            stacklevel=5,
+        )
+        from .add import _unevaluated_Add, Add
+        if L == 0:
+            return R
+        if R == 0:
+            return L
+        if evaluate:
+            # allow cancellation of args
+            return L - R
+        args = Add.make_args(L) + Add.make_args(-R)
+        if evaluate is None:
+            # no cancellation, but canonical
+            return _unevaluated_Add(*args)
+        # no cancellation, not canonical
+        return Add._from_args(args)
+
+    @property
+    def binary_symbols(self):
+        if S.true in self.args or S.false in self.args:
+            if self.lhs.is_Symbol:
+                return {self.lhs}
+            elif self.rhs.is_Symbol:
+                return {self.rhs}
+        return set()
+
+    def _eval_simplify(self, **kwargs):
+        # standard simplify
+        e = super()._eval_simplify(**kwargs)
+        if not isinstance(e, Equality):
+            return e
+        from .expr import Expr
+        if not isinstance(e.lhs, Expr) or not isinstance(e.rhs, Expr):
+            return e
+        free = self.free_symbols
+        if len(free) == 1:
+            try:
+                from .add import Add
+                from sympy.solvers.solveset import linear_coeffs
+                x = free.pop()
+                m, b = linear_coeffs(
+                    Add(e.lhs, -e.rhs, evaluate=False), x)
+                if m.is_zero is False:
+                    enew = e.func(x, -b / m)
+                else:
+                    enew = e.func(m * x, -b)
+                measure = kwargs['measure']
+                if measure(enew) <= kwargs['ratio'] * measure(e):
+                    e = enew
+            except ValueError:
+                pass
+        return e.canonical
+
+    def integrate(self, *args, **kwargs):
+        """See the integrate function in sympy.integrals"""
+        from sympy.integrals.integrals import integrate
+        return integrate(self, *args, **kwargs)
+
+    def as_poly(self, *gens, **kwargs):
+        '''Returns lhs-rhs as a Poly
+
+        Examples
+        ========
+
+        >>> from sympy import Eq
+        >>> from sympy.abc import x
+        >>> Eq(x**2, 1).as_poly(x)
+        Poly(x**2 - 1, x, domain='ZZ')
+        '''
+        return (self.lhs - self.rhs).as_poly(*gens, **kwargs)
+
+
+Eq = Equality
+
+
+class Unequality(Relational):
+    """An unequal relation between two objects.
+
+    Explanation
+    ===========
+
+    Represents that two objects are not equal.  If they can be shown to be
+    definitively equal, this will reduce to False; if definitively unequal,
+    this will reduce to True.  Otherwise, the relation is maintained as an
+    Unequality object.
+
+    Examples
+    ========
+
+    >>> from sympy import Ne
+    >>> from sympy.abc import x, y
+    >>> Ne(y, x+x**2)
+    Ne(y, x**2 + x)
+
+    See Also
+    ========
+    Equality
+
+    Notes
+    =====
+    This class is not the same as the != operator.  The != operator tests
+    for exact structural equality between two expressions; this class
+    compares expressions mathematically.
+
+    This class is effectively the inverse of Equality.  As such, it uses the
+    same algorithms, including any available `_eval_Eq` methods.
+
+    """
+    rel_op = '!='
+
+    __slots__ = ()
+
+    def __new__(cls, lhs, rhs, **options):
+        lhs = _sympify(lhs)
+        rhs = _sympify(rhs)
+        evaluate = options.pop('evaluate', global_parameters.evaluate)
+        if evaluate:
+            val = is_neq(lhs, rhs)
+            if val is None:
+                return cls(lhs, rhs, evaluate=False)
+            else:
+                return _sympify(val)
+
+        return Relational.__new__(cls, lhs, rhs, **options)
+
+    @classmethod
+    def _eval_relation(cls, lhs, rhs):
+        return _sympify(lhs != rhs)
+
+    @property
+    def binary_symbols(self):
+        if S.true in self.args or S.false in self.args:
+            if self.lhs.is_Symbol:
+                return {self.lhs}
+            elif self.rhs.is_Symbol:
+                return {self.rhs}
+        return set()
+
+    def _eval_simplify(self, **kwargs):
+        # simplify as an equality
+        eq = Equality(*self.args)._eval_simplify(**kwargs)
+        if isinstance(eq, Equality):
+            # send back Ne with the new args
+            return self.func(*eq.args)
+        return eq.negated  # result of Ne is the negated Eq
+
+
+Ne = Unequality
+
+
+class _Inequality(Relational):
+    """Internal base class for all *Than types.
+
+    Each subclass must implement _eval_relation to provide the method for
+    comparing two real numbers.
+
+    """
+    __slots__ = ()
+
+    def __new__(cls, lhs, rhs, **options):
+
+        try:
+            lhs = _sympify(lhs)
+            rhs = _sympify(rhs)
+        except SympifyError:
+            return NotImplemented
+
+        evaluate = options.pop('evaluate', global_parameters.evaluate)
+        if evaluate:
+            for me in (lhs, rhs):
+                if me.is_extended_real is False:
+                    raise TypeError("Invalid comparison of non-real %s" % me)
+                if me is S.NaN:
+                    raise TypeError("Invalid NaN comparison")
+            # First we invoke the appropriate inequality method of `lhs`
+            # (e.g., `lhs.__lt__`).  That method will try to reduce to
+            # boolean or raise an exception.  It may keep calling
+            # superclasses until it reaches `Expr` (e.g., `Expr.__lt__`).
+            # In some cases, `Expr` will just invoke us again (if neither it
+            # nor a subclass was able to reduce to boolean or raise an
+            # exception).  In that case, it must call us with
+            # `evaluate=False` to prevent infinite recursion.
+            return cls._eval_relation(lhs, rhs, **options)
+
+        # make a "non-evaluated" Expr for the inequality
+        return Relational.__new__(cls, lhs, rhs, **options)
+
+    @classmethod
+    def _eval_relation(cls, lhs, rhs, **options):
+        val = cls._eval_fuzzy_relation(lhs, rhs)
+        if val is None:
+            return cls(lhs, rhs, evaluate=False)
+        else:
+            return _sympify(val)
+
+
+class _Greater(_Inequality):
+    """Not intended for general use
+
+    _Greater is only used so that GreaterThan and StrictGreaterThan may
+    subclass it for the .gts and .lts properties.
+
+    """
+    __slots__ = ()
+
+    @property
+    def gts(self):
+        return self._args[0]
+
+    @property
+    def lts(self):
+        return self._args[1]
+
+
+class _Less(_Inequality):
+    """Not intended for general use.
+
+    _Less is only used so that LessThan and StrictLessThan may subclass it for
+    the .gts and .lts properties.
+
+    """
+    __slots__ = ()
+
+    @property
+    def gts(self):
+        return self._args[1]
+
+    @property
+    def lts(self):
+        return self._args[0]
+
+
+class GreaterThan(_Greater):
+    r"""Class representations of inequalities.
+
+    Explanation
+    ===========
+
+    The ``*Than`` classes represent inequal relationships, where the left-hand
+    side is generally bigger or smaller than the right-hand side.  For example,
+    the GreaterThan class represents an inequal relationship where the
+    left-hand side is at least as big as the right side, if not bigger.  In
+    mathematical notation:
+
+    lhs $\ge$ rhs
+
+    In total, there are four ``*Than`` classes, to represent the four
+    inequalities:
+
+    +-----------------+--------+
+    |Class Name       | Symbol |
+    +=================+========+
+    |GreaterThan      | ``>=`` |
+    +-----------------+--------+
+    |LessThan         | ``<=`` |
+    +-----------------+--------+
+    |StrictGreaterThan| ``>``  |
+    +-----------------+--------+
+    |StrictLessThan   | ``<``  |
+    +-----------------+--------+
+
+    All classes take two arguments, lhs and rhs.
+
+    +----------------------------+-----------------+
+    |Signature Example           | Math Equivalent |
+    +============================+=================+
+    |GreaterThan(lhs, rhs)       |   lhs $\ge$ rhs |
+    +----------------------------+-----------------+
+    |LessThan(lhs, rhs)          |   lhs $\le$ rhs |
+    +----------------------------+-----------------+
+    |StrictGreaterThan(lhs, rhs) |   lhs $>$ rhs   |
+    +----------------------------+-----------------+
+    |StrictLessThan(lhs, rhs)    |   lhs $<$ rhs   |
+    +----------------------------+-----------------+
+
+    In addition to the normal .lhs and .rhs of Relations, ``*Than`` inequality
+    objects also have the .lts and .gts properties, which represent the "less
+    than side" and "greater than side" of the operator.  Use of .lts and .gts
+    in an algorithm rather than .lhs and .rhs as an assumption of inequality
+    direction will make more explicit the intent of a certain section of code,
+    and will make it similarly more robust to client code changes:
+
+    >>> from sympy import GreaterThan, StrictGreaterThan
+    >>> from sympy import LessThan, StrictLessThan
+    >>> from sympy import And, Ge, Gt, Le, Lt, Rel, S
+    >>> from sympy.abc import x, y, z
+    >>> from sympy.core.relational import Relational
+
+    >>> e = GreaterThan(x, 1)
+    >>> e
+    x >= 1
+    >>> '%s >= %s is the same as %s <= %s' % (e.gts, e.lts, e.lts, e.gts)
+    'x >= 1 is the same as 1 <= x'
+
+    Examples
+    ========
+
+    One generally does not instantiate these classes directly, but uses various
+    convenience methods:
+
+    >>> for f in [Ge, Gt, Le, Lt]:  # convenience wrappers
+    ...     print(f(x, 2))
+    x >= 2
+    x > 2
+    x <= 2
+    x < 2
+
+    Another option is to use the Python inequality operators (``>=``, ``>``,
+    ``<=``, ``<``) directly.  Their main advantage over the ``Ge``, ``Gt``,
+    ``Le``, and ``Lt`` counterparts, is that one can write a more
+    "mathematical looking" statement rather than littering the math with
+    oddball function calls.  However there are certain (minor) caveats of
+    which to be aware (search for 'gotcha', below).
+
+    >>> x >= 2
+    x >= 2
+    >>> _ == Ge(x, 2)
+    True
+
+    However, it is also perfectly valid to instantiate a ``*Than`` class less
+    succinctly and less conveniently:
+
+    >>> Rel(x, 1, ">")
+    x > 1
+    >>> Relational(x, 1, ">")
+    x > 1
+
+    >>> StrictGreaterThan(x, 1)
+    x > 1
+    >>> GreaterThan(x, 1)
+    x >= 1
+    >>> LessThan(x, 1)
+    x <= 1
+    >>> StrictLessThan(x, 1)
+    x < 1
+
+    Notes
+    =====
+
+    There are a couple of "gotchas" to be aware of when using Python's
+    operators.
+
+    The first is that what your write is not always what you get:
+
+        >>> 1 < x
+        x > 1
+
+        Due to the order that Python parses a statement, it may
+        not immediately find two objects comparable.  When ``1 < x``
+        is evaluated, Python recognizes that the number 1 is a native
+        number and that x is *not*.  Because a native Python number does
+        not know how to compare itself with a SymPy object
+        Python will try the reflective operation, ``x > 1`` and that is the
+        form that gets evaluated, hence returned.
+
+        If the order of the statement is important (for visual output to
+        the console, perhaps), one can work around this annoyance in a
+        couple ways:
+
+        (1) "sympify" the literal before comparison
+
+        >>> S(1) < x
+        1 < x
+
+        (2) use one of the wrappers or less succinct methods described
+        above
+
+        >>> Lt(1, x)
+        1 < x
+        >>> Relational(1, x, "<")
+        1 < x
+
+    The second gotcha involves writing equality tests between relationals
+    when one or both sides of the test involve a literal relational:
+
+        >>> e = x < 1; e
+        x < 1
+        >>> e == e  # neither side is a literal
+        True
+        >>> e == x < 1  # expecting True, too
+        False
+        >>> e != x < 1  # expecting False
+        x < 1
+        >>> x < 1 != x < 1  # expecting False or the same thing as before
+        Traceback (most recent call last):
+        ...
+        TypeError: cannot determine truth value of Relational
+
+        The solution for this case is to wrap literal relationals in
+        parentheses:
+
+        >>> e == (x < 1)
+        True
+        >>> e != (x < 1)
+        False
+        >>> (x < 1) != (x < 1)
+        False
+
+    The third gotcha involves chained inequalities not involving
+    ``==`` or ``!=``. Occasionally, one may be tempted to write:
+
+        >>> e = x < y < z
+        Traceback (most recent call last):
+        ...
+        TypeError: symbolic boolean expression has no truth value.
+
+        Due to an implementation detail or decision of Python [1]_,
+        there is no way for SymPy to create a chained inequality with
+        that syntax so one must use And:
+
+        >>> e = And(x < y, y < z)
+        >>> type( e )
+        And
+        >>> e
+        (x < y) & (y < z)
+
+        Although this can also be done with the '&' operator, it cannot
+        be done with the 'and' operarator:
+
+        >>> (x < y) & (y < z)
+        (x < y) & (y < z)
+        >>> (x < y) and (y < z)
+        Traceback (most recent call last):
+        ...
+        TypeError: cannot determine truth value of Relational
+
+    .. [1] This implementation detail is that Python provides no reliable
+       method to determine that a chained inequality is being built.
+       Chained comparison operators are evaluated pairwise, using "and"
+       logic (see
+       https://docs.python.org/3/reference/expressions.html#not-in). This
+       is done in an efficient way, so that each object being compared
+       is only evaluated once and the comparison can short-circuit. For
+       example, ``1 > 2 > 3`` is evaluated by Python as ``(1 > 2) and (2
+       > 3)``. The ``and`` operator coerces each side into a bool,
+       returning the object itself when it short-circuits. The bool of
+       the --Than operators will raise TypeError on purpose, because
+       SymPy cannot determine the mathematical ordering of symbolic
+       expressions. Thus, if we were to compute ``x > y > z``, with
+       ``x``, ``y``, and ``z`` being Symbols, Python converts the
+       statement (roughly) into these steps:
+
+        (1) x > y > z
+        (2) (x > y) and (y > z)
+        (3) (GreaterThanObject) and (y > z)
+        (4) (GreaterThanObject.__bool__()) and (y > z)
+        (5) TypeError
+
+       Because of the ``and`` added at step 2, the statement gets turned into a
+       weak ternary statement, and the first object's ``__bool__`` method will
+       raise TypeError.  Thus, creating a chained inequality is not possible.
+
+           In Python, there is no way to override the ``and`` operator, or to
+           control how it short circuits, so it is impossible to make something
+           like ``x > y > z`` work.  There was a PEP to change this,
+           :pep:`335`, but it was officially closed in March, 2012.
+
+    """
+    __slots__ = ()
+
+    rel_op = '>='
+
+    @classmethod
+    def _eval_fuzzy_relation(cls, lhs, rhs):
+        return is_ge(lhs, rhs)
+
+    @property
+    def strict(self):
+        return Gt(*self.args)
+
+Ge = GreaterThan
+
+
+class LessThan(_Less):
+    __doc__ = GreaterThan.__doc__
+    __slots__ = ()
+
+    rel_op = '<='
+
+    @classmethod
+    def _eval_fuzzy_relation(cls, lhs, rhs):
+        return is_le(lhs, rhs)
+
+    @property
+    def strict(self):
+        return Lt(*self.args)
+
+Le = LessThan
+
+
+class StrictGreaterThan(_Greater):
+    __doc__ = GreaterThan.__doc__
+    __slots__ = ()
+
+    rel_op = '>'
+
+    @classmethod
+    def _eval_fuzzy_relation(cls, lhs, rhs):
+        return is_gt(lhs, rhs)
+
+    @property
+    def weak(self):
+        return Ge(*self.args)
+
+
+Gt = StrictGreaterThan
+
+
+class StrictLessThan(_Less):
+    __doc__ = GreaterThan.__doc__
+    __slots__ = ()
+
+    rel_op = '<'
+
+    @classmethod
+    def _eval_fuzzy_relation(cls, lhs, rhs):
+        return is_lt(lhs, rhs)
+
+    @property
+    def weak(self):
+        return Le(*self.args)
+
+Lt = StrictLessThan
+
+# A class-specific (not object-specific) data item used for a minor speedup.
+# It is defined here, rather than directly in the class, because the classes
+# that it references have not been defined until now (e.g. StrictLessThan).
+Relational.ValidRelationOperator = {
+    None: Equality,
+    '==': Equality,
+    'eq': Equality,
+    '!=': Unequality,
+    '<>': Unequality,
+    'ne': Unequality,
+    '>=': GreaterThan,
+    'ge': GreaterThan,
+    '<=': LessThan,
+    'le': LessThan,
+    '>': StrictGreaterThan,
+    'gt': StrictGreaterThan,
+    '<': StrictLessThan,
+    'lt': StrictLessThan,
+}
+
+
+def _n2(a, b):
+    """Return (a - b).evalf(2) if a and b are comparable, else None.
+    This should only be used when a and b are already sympified.
+    """
+    # /!\ it is very important (see issue 8245) not to
+    # use a re-evaluated number in the calculation of dif
+    if a.is_comparable and b.is_comparable:
+        dif = (a - b).evalf(2)
+        if dif.is_comparable:
+            return dif
+
+
+@dispatch(Expr, Expr)
+def _eval_is_ge(lhs, rhs):
+    return None
+
+
+@dispatch(Basic, Basic)
+def _eval_is_eq(lhs, rhs):
+    return None
+
+
+@dispatch(Tuple, Expr) # type: ignore
+def _eval_is_eq(lhs, rhs):  # noqa:F811
+    return False
+
+
+@dispatch(Tuple, AppliedUndef) # type: ignore
+def _eval_is_eq(lhs, rhs):  # noqa:F811
+    return None
+
+
+@dispatch(Tuple, Symbol) # type: ignore
+def _eval_is_eq(lhs, rhs):  # noqa:F811
+    return None
+
+
+@dispatch(Tuple, Tuple) # type: ignore
+def _eval_is_eq(lhs, rhs):  # noqa:F811
+    if len(lhs) != len(rhs):
+        return False
+
+    return fuzzy_and(fuzzy_bool(is_eq(s, o)) for s, o in zip(lhs, rhs))
+
+
+def is_lt(lhs, rhs, assumptions=None):
+    """Fuzzy bool for lhs is strictly less than rhs.
+
+    See the docstring for :func:`~.is_ge` for more.
+    """
+    return fuzzy_not(is_ge(lhs, rhs, assumptions))
+
+
+def is_gt(lhs, rhs, assumptions=None):
+    """Fuzzy bool for lhs is strictly greater than rhs.
+
+    See the docstring for :func:`~.is_ge` for more.
+    """
+    return fuzzy_not(is_le(lhs, rhs, assumptions))
+
+
+def is_le(lhs, rhs, assumptions=None):
+    """Fuzzy bool for lhs is less than or equal to rhs.
+
+    See the docstring for :func:`~.is_ge` for more.
+    """
+    return is_ge(rhs, lhs, assumptions)
+
+
+def is_ge(lhs, rhs, assumptions=None):
+    """
+    Fuzzy bool for *lhs* is greater than or equal to *rhs*.
+
+    Parameters
+    ==========
+
+    lhs : Expr
+        The left-hand side of the expression, must be sympified,
+        and an instance of expression. Throws an exception if
+        lhs is not an instance of expression.
+
+    rhs : Expr
+        The right-hand side of the expression, must be sympified
+        and an instance of expression. Throws an exception if
+        lhs is not an instance of expression.
+
+    assumptions: Boolean, optional
+        Assumptions taken to evaluate the inequality.
+
+    Returns
+    =======
+
+    ``True`` if *lhs* is greater than or equal to *rhs*, ``False`` if *lhs*
+    is less than *rhs*, and ``None`` if the comparison between *lhs* and
+    *rhs* is indeterminate.
+
+    Explanation
+    ===========
+
+    This function is intended to give a relatively fast determination and
+    deliberately does not attempt slow calculations that might help in
+    obtaining a determination of True or False in more difficult cases.
+
+    The four comparison functions ``is_le``, ``is_lt``, ``is_ge``, and ``is_gt`` are
+    each implemented in terms of ``is_ge`` in the following way:
+
+    is_ge(x, y) := is_ge(x, y)
+    is_le(x, y) := is_ge(y, x)
+    is_lt(x, y) := fuzzy_not(is_ge(x, y))
+    is_gt(x, y) := fuzzy_not(is_ge(y, x))
+
+    Therefore, supporting new type with this function will ensure behavior for
+    other three functions as well.
+
+    To maintain these equivalences in fuzzy logic it is important that in cases where
+    either x or y is non-real all comparisons will give None.
+
+    Examples
+    ========
+
+    >>> from sympy import S, Q
+    >>> from sympy.core.relational import is_ge, is_le, is_gt, is_lt
+    >>> from sympy.abc import x
+    >>> is_ge(S(2), S(0))
+    True
+    >>> is_ge(S(0), S(2))
+    False
+    >>> is_le(S(0), S(2))
+    True
+    >>> is_gt(S(0), S(2))
+    False
+    >>> is_lt(S(2), S(0))
+    False
+
+    Assumptions can be passed to evaluate the quality which is otherwise
+    indeterminate.
+
+    >>> print(is_ge(x, S(0)))
+    None
+    >>> is_ge(x, S(0), assumptions=Q.positive(x))
+    True
+
+    New types can be supported by dispatching to ``_eval_is_ge``.
+
+    >>> from sympy import Expr, sympify
+    >>> from sympy.multipledispatch import dispatch
+    >>> class MyExpr(Expr):
+    ...     def __new__(cls, arg):
+    ...         return super().__new__(cls, sympify(arg))
+    ...     @property
+    ...     def value(self):
+    ...         return self.args[0]
+    >>> @dispatch(MyExpr, MyExpr)
+    ... def _eval_is_ge(a, b):
+    ...     return is_ge(a.value, b.value)
+    >>> a = MyExpr(1)
+    >>> b = MyExpr(2)
+    >>> is_ge(b, a)
+    True
+    >>> is_le(a, b)
+    True
+    """
+    from sympy.assumptions.wrapper import AssumptionsWrapper, is_extended_nonnegative
+
+    if not (isinstance(lhs, Expr) and isinstance(rhs, Expr)):
+        raise TypeError("Can only compare inequalities with Expr")
+
+    retval = _eval_is_ge(lhs, rhs)
+
+    if retval is not None:
+        return retval
+    else:
+        n2 = _n2(lhs, rhs)
+        if n2 is not None:
+            # use float comparison for infinity.
+            # otherwise get stuck in infinite recursion
+            if n2 in (S.Infinity, S.NegativeInfinity):
+                n2 = float(n2)
+            return n2 >= 0
+
+        _lhs = AssumptionsWrapper(lhs, assumptions)
+        _rhs = AssumptionsWrapper(rhs, assumptions)
+        if _lhs.is_extended_real and _rhs.is_extended_real:
+            if (_lhs.is_infinite and _lhs.is_extended_positive) or (_rhs.is_infinite and _rhs.is_extended_negative):
+                return True
+            diff = lhs - rhs
+            if diff is not S.NaN:
+                rv = is_extended_nonnegative(diff, assumptions)
+                if rv is not None:
+                    return rv
+
+
+def is_neq(lhs, rhs, assumptions=None):
+    """Fuzzy bool for lhs does not equal rhs.
+
+    See the docstring for :func:`~.is_eq` for more.
+    """
+    return fuzzy_not(is_eq(lhs, rhs, assumptions))
+
+
+def is_eq(lhs, rhs, assumptions=None):
+    """
+    Fuzzy bool representing mathematical equality between *lhs* and *rhs*.
+
+    Parameters
+    ==========
+
+    lhs : Expr
+        The left-hand side of the expression, must be sympified.
+
+    rhs : Expr
+        The right-hand side of the expression, must be sympified.
+
+    assumptions: Boolean, optional
+        Assumptions taken to evaluate the equality.
+
+    Returns
+    =======
+
+    ``True`` if *lhs* is equal to *rhs*, ``False`` is *lhs* is not equal to *rhs*,
+    and ``None`` if the comparison between *lhs* and *rhs* is indeterminate.
+
+    Explanation
+    ===========
+
+    This function is intended to give a relatively fast determination and
+    deliberately does not attempt slow calculations that might help in
+    obtaining a determination of True or False in more difficult cases.
+
+    :func:`~.is_neq` calls this function to return its value, so supporting
+    new type with this function will ensure correct behavior for ``is_neq``
+    as well.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, S
+    >>> from sympy.core.relational import is_eq, is_neq
+    >>> from sympy.abc import x
+    >>> is_eq(S(0), S(0))
+    True
+    >>> is_neq(S(0), S(0))
+    False
+    >>> is_eq(S(0), S(2))
+    False
+    >>> is_neq(S(0), S(2))
+    True
+
+    Assumptions can be passed to evaluate the equality which is otherwise
+    indeterminate.
+
+    >>> print(is_eq(x, S(0)))
+    None
+    >>> is_eq(x, S(0), assumptions=Q.zero(x))
+    True
+
+    New types can be supported by dispatching to ``_eval_is_eq``.
+
+    >>> from sympy import Basic, sympify
+    >>> from sympy.multipledispatch import dispatch
+    >>> class MyBasic(Basic):
+    ...     def __new__(cls, arg):
+    ...         return Basic.__new__(cls, sympify(arg))
+    ...     @property
+    ...     def value(self):
+    ...         return self.args[0]
+    ...
+    >>> @dispatch(MyBasic, MyBasic)
+    ... def _eval_is_eq(a, b):
+    ...     return is_eq(a.value, b.value)
+    ...
+    >>> a = MyBasic(1)
+    >>> b = MyBasic(1)
+    >>> is_eq(a, b)
+    True
+    >>> is_neq(a, b)
+    False
+
+    """
+    # here, _eval_Eq is only called for backwards compatibility
+    # new code should use is_eq with multiple dispatch as
+    # outlined in the docstring
+    for side1, side2 in (lhs, rhs), (rhs, lhs):
+        eval_func = getattr(side1, '_eval_Eq', None)
+        if eval_func is not None:
+            retval = eval_func(side2)
+            if retval is not None:
+                return retval
+
+    retval = _eval_is_eq(lhs, rhs)
+    if retval is not None:
+        return retval
+
+    if dispatch(type(lhs), type(rhs)) != dispatch(type(rhs), type(lhs)):
+        retval = _eval_is_eq(rhs, lhs)
+        if retval is not None:
+            return retval
+
+    # retval is still None, so go through the equality logic
+    # If expressions have the same structure, they must be equal.
+    if lhs == rhs:
+        return True  # e.g. True == True
+    elif all(isinstance(i, BooleanAtom) for i in (rhs, lhs)):
+        return False  # True != False
+    elif not (lhs.is_Symbol or rhs.is_Symbol) and (
+        isinstance(lhs, Boolean) !=
+        isinstance(rhs, Boolean)):
+        return False  # only Booleans can equal Booleans
+
+    from sympy.assumptions.wrapper import (AssumptionsWrapper,
+        is_infinite, is_extended_real)
+    from .add import Add
+
+    _lhs = AssumptionsWrapper(lhs, assumptions)
+    _rhs = AssumptionsWrapper(rhs, assumptions)
+
+    if _lhs.is_infinite or _rhs.is_infinite:
+        if fuzzy_xor([_lhs.is_infinite, _rhs.is_infinite]):
+            return False
+        if fuzzy_xor([_lhs.is_extended_real, _rhs.is_extended_real]):
+            return False
+        if fuzzy_and([_lhs.is_extended_real, _rhs.is_extended_real]):
+            return fuzzy_xor([_lhs.is_extended_positive, fuzzy_not(_rhs.is_extended_positive)])
+
+        # Try to split real/imaginary parts and equate them
+        I = S.ImaginaryUnit
+
+        def split_real_imag(expr):
+            real_imag = lambda t: (
+                'real' if is_extended_real(t, assumptions) else
+                'imag' if is_extended_real(I*t, assumptions) else None)
+            return sift(Add.make_args(expr), real_imag)
+
+        lhs_ri = split_real_imag(lhs)
+        if not lhs_ri[None]:
+            rhs_ri = split_real_imag(rhs)
+            if not rhs_ri[None]:
+                eq_real = is_eq(Add(*lhs_ri['real']), Add(*rhs_ri['real']), assumptions)
+                eq_imag = is_eq(I * Add(*lhs_ri['imag']), I * Add(*rhs_ri['imag']), assumptions)
+                return fuzzy_and(map(fuzzy_bool, [eq_real, eq_imag]))
+
+        from sympy.functions.elementary.complexes import arg
+        # Compare e.g. zoo with 1+I*oo by comparing args
+        arglhs = arg(lhs)
+        argrhs = arg(rhs)
+        # Guard against Eq(nan, nan) -> False
+        if not (arglhs == S.NaN and argrhs == S.NaN):
+            return fuzzy_bool(is_eq(arglhs, argrhs, assumptions))
+
+    if all(isinstance(i, Expr) for i in (lhs, rhs)):
+        # see if the difference evaluates
+        dif = lhs - rhs
+        _dif = AssumptionsWrapper(dif, assumptions)
+        z = _dif.is_zero
+        if z is not None:
+            if z is False and _dif.is_commutative:  # issue 10728
+                return False
+            if z:
+                return True
+
+        # is_zero cannot help decide integer/rational with Float
+        c, t = dif.as_coeff_Add()
+        if c.is_Float:
+            if int_valued(c):
+                if t.is_integer is False:
+                    return False
+            elif t.is_rational is False:
+                return False
+
+        n2 = _n2(lhs, rhs)
+        if n2 is not None:
+            return _sympify(n2 == 0)
+
+        # see if the ratio evaluates
+        n, d = dif.as_numer_denom()
+        rv = None
+        _n = AssumptionsWrapper(n, assumptions)
+        _d = AssumptionsWrapper(d, assumptions)
+        if _n.is_zero:
+            rv = _d.is_nonzero
+        elif _n.is_finite:
+            if _d.is_infinite:
+                rv = True
+            elif _n.is_zero is False:
+                rv = _d.is_infinite
+                if rv is None:
+                    # if the condition that makes the denominator
+                    # infinite does not make the original expression
+                    # True then False can be returned
+                    from sympy.simplify.simplify import clear_coefficients
+                    l, r = clear_coefficients(d, S.Infinity)
+                    args = [_.subs(l, r) for _ in (lhs, rhs)]
+                    if args != [lhs, rhs]:
+                        rv = fuzzy_bool(is_eq(*args, assumptions))
+                        if rv is True:
+                            rv = None
+        elif any(is_infinite(a, assumptions) for a in Add.make_args(n)):
+            # (inf or nan)/x != 0
+            rv = False
+        if rv is not None:
+            return rv
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/rules.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/rules.py
new file mode 100644
index 0000000000000000000000000000000000000000..5ae331f71b21c8a6ef35f499c5c5c89239349e9c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/rules.py
@@ -0,0 +1,66 @@
+"""
+Replacement rules.
+"""
+
+class Transform:
+    """
+    Immutable mapping that can be used as a generic transformation rule.
+
+    Parameters
+    ==========
+
+    transform : callable
+        Computes the value corresponding to any key.
+
+    filter : callable, optional
+        If supplied, specifies which objects are in the mapping.
+
+    Examples
+    ========
+
+    >>> from sympy.core.rules import Transform
+    >>> from sympy.abc import x
+
+    This Transform will return, as a value, one more than the key:
+
+    >>> add1 = Transform(lambda x: x + 1)
+    >>> add1[1]
+    2
+    >>> add1[x]
+    x + 1
+
+    By default, all values are considered to be in the dictionary. If a filter
+    is supplied, only the objects for which it returns True are considered as
+    being in the dictionary:
+
+    >>> add1_odd = Transform(lambda x: x + 1, lambda x: x%2 == 1)
+    >>> 2 in add1_odd
+    False
+    >>> add1_odd.get(2, 0)
+    0
+    >>> 3 in add1_odd
+    True
+    >>> add1_odd[3]
+    4
+    >>> add1_odd.get(3, 0)
+    4
+    """
+
+    def __init__(self, transform, filter=lambda x: True):
+        self._transform = transform
+        self._filter = filter
+
+    def __contains__(self, item):
+        return self._filter(item)
+
+    def __getitem__(self, key):
+        if self._filter(key):
+            return self._transform(key)
+        else:
+            raise KeyError(key)
+
+    def get(self, item, default=None):
+        if item in self:
+            return self[item]
+        else:
+            return default
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/singleton.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/singleton.py
new file mode 100644
index 0000000000000000000000000000000000000000..e8b9df959393270140bc3ef11b3d9a4e948c5e80
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/singleton.py
@@ -0,0 +1,199 @@
+"""Singleton mechanism"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+from .core import Registry
+from .sympify import sympify
+
+
+if TYPE_CHECKING:
+    from sympy.core.numbers import (
+        Zero as _Zero,
+        One as _One,
+        NegativeOne as _NegativeOne,
+        Half as _Half,
+        Infinity as _Infinity,
+        NegativeInfinity as _NegativeInfinity,
+        ComplexInfinity as _ComplexInfinity,
+        NaN as _NaN,
+    )
+
+
+class SingletonRegistry(Registry):
+    """
+    The registry for the singleton classes (accessible as ``S``).
+
+    Explanation
+    ===========
+
+    This class serves as two separate things.
+
+    The first thing it is is the ``SingletonRegistry``. Several classes in
+    SymPy appear so often that they are singletonized, that is, using some
+    metaprogramming they are made so that they can only be instantiated once
+    (see the :class:`sympy.core.singleton.Singleton` class for details). For
+    instance, every time you create ``Integer(0)``, this will return the same
+    instance, :class:`sympy.core.numbers.Zero`. All singleton instances are
+    attributes of the ``S`` object, so ``Integer(0)`` can also be accessed as
+    ``S.Zero``.
+
+    Singletonization offers two advantages: it saves memory, and it allows
+    fast comparison. It saves memory because no matter how many times the
+    singletonized objects appear in expressions in memory, they all point to
+    the same single instance in memory. The fast comparison comes from the
+    fact that you can use ``is`` to compare exact instances in Python
+    (usually, you need to use ``==`` to compare things). ``is`` compares
+    objects by memory address, and is very fast.
+
+    Examples
+    ========
+
+    >>> from sympy import S, Integer
+    >>> a = Integer(0)
+    >>> a is S.Zero
+    True
+
+    For the most part, the fact that certain objects are singletonized is an
+    implementation detail that users should not need to worry about. In SymPy
+    library code, ``is`` comparison is often used for performance purposes
+    The primary advantage of ``S`` for end users is the convenient access to
+    certain instances that are otherwise difficult to type, like ``S.Half``
+    (instead of ``Rational(1, 2)``).
+
+    When using ``is`` comparison, make sure the argument is sympified. For
+    instance,
+
+    >>> x = 0
+    >>> x is S.Zero
+    False
+
+    This problem is not an issue when using ``==``, which is recommended for
+    most use-cases:
+
+    >>> 0 == S.Zero
+    True
+
+    The second thing ``S`` is is a shortcut for
+    :func:`sympy.core.sympify.sympify`. :func:`sympy.core.sympify.sympify` is
+    the function that converts Python objects such as ``int(1)`` into SymPy
+    objects such as ``Integer(1)``. It also converts the string form of an
+    expression into a SymPy expression, like ``sympify("x**2")`` ->
+    ``Symbol("x")**2``. ``S(1)`` is the same thing as ``sympify(1)``
+    (basically, ``S.__call__`` has been defined to call ``sympify``).
+
+    This is for convenience, since ``S`` is a single letter. It's mostly
+    useful for defining rational numbers. Consider an expression like ``x +
+    1/2``. If you enter this directly in Python, it will evaluate the ``1/2``
+    and give ``0.5``, because both arguments are ints (see also
+    :ref:`tutorial-gotchas-final-notes`). However, in SymPy, you usually want
+    the quotient of two integers to give an exact rational number. The way
+    Python's evaluation works, at least one side of an operator needs to be a
+    SymPy object for the SymPy evaluation to take over. You could write this
+    as ``x + Rational(1, 2)``, but this is a lot more typing. A shorter
+    version is ``x + S(1)/2``. Since ``S(1)`` returns ``Integer(1)``, the
+    division will return a ``Rational`` type, since it will call
+    ``Integer.__truediv__``, which knows how to return a ``Rational``.
+
+    """
+    __slots__ = ()
+
+    Zero: _Zero
+    One: _One
+    NegativeOne: _NegativeOne
+    Half: _Half
+    Infinity: _Infinity
+    NegativeInfinity: _NegativeInfinity
+    ComplexInfinity: _ComplexInfinity
+    NaN: _NaN
+
+    # Also allow things like S(5)
+    __call__ = staticmethod(sympify)
+
+    def __init__(self):
+        self._classes_to_install = {}
+        # Dict of classes that have been registered, but that have not have been
+        # installed as an attribute of this SingletonRegistry.
+        # Installation automatically happens at the first attempt to access the
+        # attribute.
+        # The purpose of this is to allow registration during class
+        # initialization during import, but not trigger object creation until
+        # actual use (which should not happen until after all imports are
+        # finished).
+
+    def register(self, cls):
+        # Make sure a duplicate class overwrites the old one
+        if hasattr(self, cls.__name__):
+            delattr(self, cls.__name__)
+        self._classes_to_install[cls.__name__] = cls
+
+    def __getattr__(self, name):
+        """Python calls __getattr__ if no attribute of that name was installed
+        yet.
+
+        Explanation
+        ===========
+
+        This __getattr__ checks whether a class with the requested name was
+        already registered but not installed; if no, raises an AttributeError.
+        Otherwise, retrieves the class, calculates its singleton value, installs
+        it as an attribute of the given name, and unregisters the class."""
+        if name not in self._classes_to_install:
+            raise AttributeError(
+                "Attribute '%s' was not installed on SymPy registry %s" % (
+                name, self))
+        class_to_install = self._classes_to_install[name]
+        value_to_install = class_to_install()
+        self.__setattr__(name, value_to_install)
+        del self._classes_to_install[name]
+        return value_to_install
+
+    def __repr__(self):
+        return "S"
+
+S = SingletonRegistry()
+
+
+class Singleton(type):
+    """
+    Metaclass for singleton classes.
+
+    Explanation
+    ===========
+
+    A singleton class has only one instance which is returned every time the
+    class is instantiated. Additionally, this instance can be accessed through
+    the global registry object ``S`` as ``S.``.
+
+    Examples
+    ========
+
+        >>> from sympy import S, Basic
+        >>> from sympy.core.singleton import Singleton
+        >>> class MySingleton(Basic, metaclass=Singleton):
+        ...     pass
+        >>> Basic() is Basic()
+        False
+        >>> MySingleton() is MySingleton()
+        True
+        >>> S.MySingleton is MySingleton()
+        True
+
+    Notes
+    =====
+
+    Instance creation is delayed until the first time the value is accessed.
+    (SymPy versions before 1.0 would create the instance during class
+    creation time, which would be prone to import cycles.)
+    """
+    def __init__(cls, *args, **kwargs):
+        cls._instance = obj = Basic.__new__(cls)
+        cls.__new__ = lambda cls: obj
+        cls.__getnewargs__ = lambda obj: ()
+        cls.__getstate__ = lambda obj: None
+        S.register(cls)
+
+
+# Delayed to avoid cyclic import
+from .basic import Basic
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/sorting.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/sorting.py
new file mode 100644
index 0000000000000000000000000000000000000000..399a7efa1f6cbe1ebdf6307c14b411df36fc7de0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/sorting.py
@@ -0,0 +1,312 @@
+from collections import defaultdict
+
+from .sympify import sympify, SympifyError
+from sympy.utilities.iterables import iterable, uniq
+
+
+__all__ = ['default_sort_key', 'ordered']
+
+
+def default_sort_key(item, order=None):
+    """Return a key that can be used for sorting.
+
+    The key has the structure:
+
+    (class_key, (len(args), args), exponent.sort_key(), coefficient)
+
+    This key is supplied by the sort_key routine of Basic objects when
+    ``item`` is a Basic object or an object (other than a string) that
+    sympifies to a Basic object. Otherwise, this function produces the
+    key.
+
+    The ``order`` argument is passed along to the sort_key routine and is
+    used to determine how the terms *within* an expression are ordered.
+    (See examples below) ``order`` options are: 'lex', 'grlex', 'grevlex',
+    and reversed values of the same (e.g. 'rev-lex'). The default order
+    value is None (which translates to 'lex').
+
+    Examples
+    ========
+
+    >>> from sympy import S, I, default_sort_key, sin, cos, sqrt
+    >>> from sympy.core.function import UndefinedFunction
+    >>> from sympy.abc import x
+
+    The following are equivalent ways of getting the key for an object:
+
+    >>> x.sort_key() == default_sort_key(x)
+    True
+
+    Here are some examples of the key that is produced:
+
+    >>> default_sort_key(UndefinedFunction('f'))
+    ((0, 0, 'UndefinedFunction'), (1, ('f',)), ((1, 0, 'Number'),
+        (0, ()), (), 1), 1)
+    >>> default_sort_key('1')
+    ((0, 0, 'str'), (1, ('1',)), ((1, 0, 'Number'), (0, ()), (), 1), 1)
+    >>> default_sort_key(S.One)
+    ((1, 0, 'Number'), (0, ()), (), 1)
+    >>> default_sort_key(2)
+    ((1, 0, 'Number'), (0, ()), (), 2)
+
+    While sort_key is a method only defined for SymPy objects,
+    default_sort_key will accept anything as an argument so it is
+    more robust as a sorting key. For the following, using key=
+    lambda i: i.sort_key() would fail because 2 does not have a sort_key
+    method; that's why default_sort_key is used. Note, that it also
+    handles sympification of non-string items likes ints:
+
+    >>> a = [2, I, -I]
+    >>> sorted(a, key=default_sort_key)
+    [2, -I, I]
+
+    The returned key can be used anywhere that a key can be specified for
+    a function, e.g. sort, min, max, etc...:
+
+    >>> a.sort(key=default_sort_key); a[0]
+    2
+    >>> min(a, key=default_sort_key)
+    2
+
+    Notes
+    =====
+
+    The key returned is useful for getting items into a canonical order
+    that will be the same across platforms. It is not directly useful for
+    sorting lists of expressions:
+
+    >>> a, b = x, 1/x
+
+    Since ``a`` has only 1 term, its value of sort_key is unaffected by
+    ``order``:
+
+    >>> a.sort_key() == a.sort_key('rev-lex')
+    True
+
+    If ``a`` and ``b`` are combined then the key will differ because there
+    are terms that can be ordered:
+
+    >>> eq = a + b
+    >>> eq.sort_key() == eq.sort_key('rev-lex')
+    False
+    >>> eq.as_ordered_terms()
+    [x, 1/x]
+    >>> eq.as_ordered_terms('rev-lex')
+    [1/x, x]
+
+    But since the keys for each of these terms are independent of ``order``'s
+    value, they do not sort differently when they appear separately in a list:
+
+    >>> sorted(eq.args, key=default_sort_key)
+    [1/x, x]
+    >>> sorted(eq.args, key=lambda i: default_sort_key(i, order='rev-lex'))
+    [1/x, x]
+
+    The order of terms obtained when using these keys is the order that would
+    be obtained if those terms were *factors* in a product.
+
+    Although it is useful for quickly putting expressions in canonical order,
+    it does not sort expressions based on their complexity defined by the
+    number of operations, power of variables and others:
+
+    >>> sorted([sin(x)*cos(x), sin(x)], key=default_sort_key)
+    [sin(x)*cos(x), sin(x)]
+    >>> sorted([x, x**2, sqrt(x), x**3], key=default_sort_key)
+    [sqrt(x), x, x**2, x**3]
+
+    See Also
+    ========
+
+    ordered, sympy.core.expr.Expr.as_ordered_factors, sympy.core.expr.Expr.as_ordered_terms
+
+    """
+    from .basic import Basic
+    from .singleton import S
+
+    if isinstance(item, Basic):
+        return item.sort_key(order=order)
+
+    if iterable(item, exclude=str):
+        if isinstance(item, dict):
+            args = item.items()
+            unordered = True
+        elif isinstance(item, set):
+            args = item
+            unordered = True
+        else:
+            # e.g. tuple, list
+            args = list(item)
+            unordered = False
+
+        args = [default_sort_key(arg, order=order) for arg in args]
+
+        if unordered:
+            # e.g. dict, set
+            args = sorted(args)
+
+        cls_index, args = 10, (len(args), tuple(args))
+    else:
+        if not isinstance(item, str):
+            try:
+                item = sympify(item, strict=True)
+            except SympifyError:
+                # e.g. lambda x: x
+                pass
+            else:
+                if isinstance(item, Basic):
+                    # e.g int -> Integer
+                    return default_sort_key(item)
+                # e.g. UndefinedFunction
+
+        # e.g. str
+        cls_index, args = 0, (1, (str(item),))
+
+    return (cls_index, 0, item.__class__.__name__
+            ), args, S.One.sort_key(), S.One
+
+
+def _node_count(e):
+    # this not only counts nodes, it affirms that the
+    # args are Basic (i.e. have an args property). If
+    # some object has a non-Basic arg, it needs to be
+    # fixed since it is intended that all Basic args
+    # are of Basic type (though this is not easy to enforce).
+    if e.is_Float:
+        return 0.5
+    return 1 + sum(map(_node_count, e.args))
+
+
+def _nodes(e):
+    """
+    A helper for ordered() which returns the node count of ``e`` which
+    for Basic objects is the number of Basic nodes in the expression tree
+    but for other objects is 1 (unless the object is an iterable or dict
+    for which the sum of nodes is returned).
+    """
+    from .basic import Basic
+    from .function import Derivative
+
+    if isinstance(e, Basic):
+        if isinstance(e, Derivative):
+            return _nodes(e.expr) + sum(i[1] if i[1].is_Number else
+                _nodes(i[1]) for i in e.variable_count)
+        return _node_count(e)
+    elif iterable(e):
+        return 1 + sum(_nodes(ei) for ei in e)
+    elif isinstance(e, dict):
+        return 1 + sum(_nodes(k) + _nodes(v) for k, v in e.items())
+    else:
+        return 1
+
+
+def ordered(seq, keys=None, default=True, warn=False):
+    """Return an iterator of the seq where keys are used to break ties
+    in a conservative fashion: if, after applying a key, there are no
+    ties then no other keys will be computed.
+
+    Two default keys will be applied if 1) keys are not provided or
+    2) the given keys do not resolve all ties (but only if ``default``
+    is True). The two keys are ``_nodes`` (which places smaller
+    expressions before large) and ``default_sort_key`` which (if the
+    ``sort_key`` for an object is defined properly) should resolve
+    any ties. This strategy is similar to sorting done by
+    ``Basic.compare``, but differs in that ``ordered`` never makes a
+    decision based on an objects name.
+
+    If ``warn`` is True then an error will be raised if there were no
+    keys remaining to break ties. This can be used if it was expected that
+    there should be no ties between items that are not identical.
+
+    Examples
+    ========
+
+    >>> from sympy import ordered, count_ops
+    >>> from sympy.abc import x, y
+
+    The count_ops is not sufficient to break ties in this list and the first
+    two items appear in their original order (i.e. the sorting is stable):
+
+    >>> list(ordered([y + 2, x + 2, x**2 + y + 3],
+    ...    count_ops, default=False, warn=False))
+    ...
+    [y + 2, x + 2, x**2 + y + 3]
+
+    The default_sort_key allows the tie to be broken:
+
+    >>> list(ordered([y + 2, x + 2, x**2 + y + 3]))
+    ...
+    [x + 2, y + 2, x**2 + y + 3]
+
+    Here, sequences are sorted by length, then sum:
+
+    >>> seq, keys = [[[1, 2, 1], [0, 3, 1], [1, 1, 3], [2], [1]], [
+    ...    lambda x: len(x),
+    ...    lambda x: sum(x)]]
+    ...
+    >>> list(ordered(seq, keys, default=False, warn=False))
+    [[1], [2], [1, 2, 1], [0, 3, 1], [1, 1, 3]]
+
+    If ``warn`` is True, an error will be raised if there were not
+    enough keys to break ties:
+
+    >>> list(ordered(seq, keys, default=False, warn=True))
+    Traceback (most recent call last):
+    ...
+    ValueError: not enough keys to break ties
+
+
+    Notes
+    =====
+
+    The decorated sort is one of the fastest ways to sort a sequence for
+    which special item comparison is desired: the sequence is decorated,
+    sorted on the basis of the decoration (e.g. making all letters lower
+    case) and then undecorated. If one wants to break ties for items that
+    have the same decorated value, a second key can be used. But if the
+    second key is expensive to compute then it is inefficient to decorate
+    all items with both keys: only those items having identical first key
+    values need to be decorated. This function applies keys successively
+    only when needed to break ties. By yielding an iterator, use of the
+    tie-breaker is delayed as long as possible.
+
+    This function is best used in cases when use of the first key is
+    expected to be a good hashing function; if there are no unique hashes
+    from application of a key, then that key should not have been used. The
+    exception, however, is that even if there are many collisions, if the
+    first group is small and one does not need to process all items in the
+    list then time will not be wasted sorting what one was not interested
+    in. For example, if one were looking for the minimum in a list and
+    there were several criteria used to define the sort order, then this
+    function would be good at returning that quickly if the first group
+    of candidates is small relative to the number of items being processed.
+
+    """
+
+    d = defaultdict(list)
+    if keys:
+        if isinstance(keys, (list, tuple)):
+            keys = list(keys)
+            f = keys.pop(0)
+        else:
+            f = keys
+            keys = []
+        for a in seq:
+            d[f(a)].append(a)
+    else:
+        if not default:
+            raise ValueError('if default=False then keys must be provided')
+        d[None].extend(seq)
+
+    for k, value in sorted(d.items()):
+        if len(value) > 1:
+            if keys:
+                value = ordered(value, keys, default, warn)
+            elif default:
+                value = ordered(value, (_nodes, default_sort_key,),
+                               default=False, warn=warn)
+            elif warn:
+                u = list(uniq(value))
+                if len(u) > 1:
+                    raise ValueError(
+                        'not enough keys to break ties: %s' % u)
+        yield from value
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/symbol.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/symbol.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e03ff0c84c1668b70ec5b3d7f8bc854a2e5e4ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/symbol.py
@@ -0,0 +1,993 @@
+from __future__ import annotations
+
+
+from .assumptions import StdFactKB, _assume_defined
+from .basic import Basic, Atom
+from .cache import cacheit
+from .containers import Tuple
+from .expr import Expr, AtomicExpr
+from .function import AppliedUndef, FunctionClass
+from .kind import NumberKind, UndefinedKind
+from .logic import fuzzy_bool
+from .singleton import S
+from .sorting import ordered
+from .sympify import sympify
+from sympy.logic.boolalg import Boolean
+from sympy.utilities.iterables import sift, is_sequence
+from sympy.utilities.misc import filldedent
+
+import string
+import re as _re
+import random
+from itertools import product
+from typing import Any
+
+
+class Str(Atom):
+    """
+    Represents string in SymPy.
+
+    Explanation
+    ===========
+
+    Previously, ``Symbol`` was used where string is needed in ``args`` of SymPy
+    objects, e.g. denoting the name of the instance. However, since ``Symbol``
+    represents mathematical scalar, this class should be used instead.
+
+    """
+    __slots__ = ('name',)
+
+    def __new__(cls, name, **kwargs):
+        if not isinstance(name, str):
+            raise TypeError("name should be a string, not %s" % repr(type(name)))
+        obj = Expr.__new__(cls, **kwargs)
+        obj.name = name
+        return obj
+
+    def __getnewargs__(self):
+        return (self.name,)
+
+    def _hashable_content(self):
+        return (self.name,)
+
+
+def _filter_assumptions(kwargs):
+    """Split the given dict into assumptions and non-assumptions.
+    Keys are taken as assumptions if they correspond to an
+    entry in ``_assume_defined``.
+    """
+    assumptions, nonassumptions = map(dict, sift(kwargs.items(),
+        lambda i: i[0] in _assume_defined,
+        binary=True))
+    Symbol._sanitize(assumptions)
+    return assumptions, nonassumptions
+
+def _symbol(s, matching_symbol=None, **assumptions):
+    """Return s if s is a Symbol, else if s is a string, return either
+    the matching_symbol if the names are the same or else a new symbol
+    with the same assumptions as the matching symbol (or the
+    assumptions as provided).
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol
+    >>> from sympy.core.symbol import _symbol
+    >>> _symbol('y')
+    y
+    >>> _.is_real is None
+    True
+    >>> _symbol('y', real=True).is_real
+    True
+
+    >>> x = Symbol('x')
+    >>> _symbol(x, real=True)
+    x
+    >>> _.is_real is None  # ignore attribute if s is a Symbol
+    True
+
+    Below, the variable sym has the name 'foo':
+
+    >>> sym = Symbol('foo', real=True)
+
+    Since 'x' is not the same as sym's name, a new symbol is created:
+
+    >>> _symbol('x', sym).name
+    'x'
+
+    It will acquire any assumptions give:
+
+    >>> _symbol('x', sym, real=False).is_real
+    False
+
+    Since 'foo' is the same as sym's name, sym is returned
+
+    >>> _symbol('foo', sym)
+    foo
+
+    Any assumptions given are ignored:
+
+    >>> _symbol('foo', sym, real=False).is_real
+    True
+
+    NB: the symbol here may not be the same as a symbol with the same
+    name defined elsewhere as a result of different assumptions.
+
+    See Also
+    ========
+
+    sympy.core.symbol.Symbol
+
+    """
+    if isinstance(s, str):
+        if matching_symbol and matching_symbol.name == s:
+            return matching_symbol
+        return Symbol(s, **assumptions)
+    elif isinstance(s, Symbol):
+        return s
+    else:
+        raise ValueError('symbol must be string for symbol name or Symbol')
+
+def uniquely_named_symbol(xname, exprs=(), compare=str, modify=None, **assumptions):
+    """
+    Return a symbol whose name is derivated from *xname* but is unique
+    from any other symbols in *exprs*.
+
+    *xname* and symbol names in *exprs* are passed to *compare* to be
+    converted to comparable forms. If ``compare(xname)`` is not unique,
+    it is recursively passed to *modify* until unique name is acquired.
+
+    Parameters
+    ==========
+
+    xname : str or Symbol
+        Base name for the new symbol.
+
+    exprs : Expr or iterable of Expr
+        Expressions whose symbols are compared to *xname*.
+
+    compare : function
+        Unary function which transforms *xname* and symbol names from
+        *exprs* to comparable form.
+
+    modify : function
+        Unary function which modifies the string. Default is appending
+        the number, or increasing the number if exists.
+
+    Examples
+    ========
+
+    By default, a number is appended to *xname* to generate unique name.
+    If the number already exists, it is recursively increased.
+
+    >>> from sympy.core.symbol import uniquely_named_symbol, Symbol
+    >>> uniquely_named_symbol('x', Symbol('x'))
+    x0
+    >>> uniquely_named_symbol('x', (Symbol('x'), Symbol('x0')))
+    x1
+    >>> uniquely_named_symbol('x0', (Symbol('x1'), Symbol('x0')))
+    x2
+
+    Name generation can be controlled by passing *modify* parameter.
+
+    >>> from sympy.abc import x
+    >>> uniquely_named_symbol('x', x, modify=lambda s: 2*s)
+    xx
+
+    """
+    def numbered_string_incr(s, start=0):
+        if not s:
+            return str(start)
+        i = len(s) - 1
+        while i != -1:
+            if not s[i].isdigit():
+                break
+            i -= 1
+        n = str(int(s[i + 1:] or start - 1) + 1)
+        return s[:i + 1] + n
+
+    default = None
+    if is_sequence(xname):
+        xname, default = xname
+    x = compare(xname)
+    if not exprs:
+        return _symbol(x, default, **assumptions)
+    if not is_sequence(exprs):
+        exprs = [exprs]
+    names = set().union(
+        [i.name for e in exprs for i in e.atoms(Symbol)] +
+        [i.func.name for e in exprs for i in e.atoms(AppliedUndef)])
+    if modify is None:
+        modify = numbered_string_incr
+    while any(x == compare(s) for s in names):
+        x = modify(x)
+    return _symbol(x, default, **assumptions)
+_uniquely_named_symbol = uniquely_named_symbol
+
+
+# XXX: We need type: ignore below because Expr and Boolean are incompatible as
+# superclasses. Really Symbol should not be a subclass of Boolean.
+
+
+class Symbol(AtomicExpr, Boolean): # type: ignore
+    """
+    Symbol class is used to create symbolic variables.
+
+    Explanation
+    ===========
+
+    Symbolic variables are placeholders for mathematical symbols that can represent numbers, constants, or any other mathematical entities and can be used in mathematical expressions and to perform symbolic computations.
+
+    Assumptions:
+
+    commutative = True
+    positive = True
+    real = True
+    imaginary = True
+    complex = True
+    complete list of more assumptions- :ref:`predicates`
+
+    You can override the default assumptions in the constructor.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol
+    >>> x = Symbol("x", positive=True)
+    >>> x.is_positive
+    True
+    >>> x.is_negative
+    False
+
+    passing in greek letters:
+
+    >>> from sympy import Symbol
+    >>> alpha = Symbol('alpha')
+    >>> alpha #doctest: +SKIP
+    α
+
+    Trailing digits are automatically treated like subscripts of what precedes them in the name.
+    General format to add subscript to a symbol :
+    `` = Symbol('_')``
+
+    >>> from sympy import Symbol
+    >>> alpha_i = Symbol('alpha_i')
+    >>> alpha_i #doctest: +SKIP
+    αᵢ
+
+    Parameters
+    ==========
+
+    AtomicExpr: variable name
+    Boolean: Assumption with a boolean value(True or False)
+    """
+
+    is_comparable = False
+
+    __slots__ = ('name', '_assumptions_orig', '_assumptions0')
+
+    name: str
+
+    is_Symbol = True
+    is_symbol = True
+
+    @property
+    def kind(self):
+        if self.is_commutative:
+            return NumberKind
+        return UndefinedKind
+
+    @property
+    def _diff_wrt(self):
+        """Allow derivatives wrt Symbols.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> x = Symbol('x')
+        >>> x._diff_wrt
+        True
+        """
+        return True
+
+    @staticmethod
+    def _sanitize(assumptions, obj=None):
+        """Remove None, convert values to bool, check commutativity *in place*.
+        """
+
+        # be strict about commutativity: cannot be None
+        is_commutative = fuzzy_bool(assumptions.get('commutative', True))
+        if is_commutative is None:
+            whose = '%s ' % obj.__name__ if obj else ''
+            raise ValueError(
+                '%scommutativity must be True or False.' % whose)
+
+        # sanitize other assumptions so 1 -> True and 0 -> False
+        for key in list(assumptions.keys()):
+            v = assumptions[key]
+            if v is None:
+                assumptions.pop(key)
+                continue
+            assumptions[key] = bool(v)
+
+    def _merge(self, assumptions):
+        base = self.assumptions0
+        for k in set(assumptions) & set(base):
+            if assumptions[k] != base[k]:
+                raise ValueError(filldedent('''
+                    non-matching assumptions for %s: existing value
+                    is %s and new value is %s''' % (
+                    k, base[k], assumptions[k])))
+        base.update(assumptions)
+        return base
+
+    def __new__(cls, name, **assumptions):
+        """Symbols are identified by name and assumptions::
+
+        >>> from sympy import Symbol
+        >>> Symbol("x") == Symbol("x")
+        True
+        >>> Symbol("x", real=True) == Symbol("x", real=False)
+        False
+
+        """
+        cls._sanitize(assumptions, cls)
+        return Symbol.__xnew_cached_(cls, name, **assumptions)
+
+
+    @staticmethod
+    @cacheit
+    def _canonical_assumptions(**assumptions):
+        # This is retained purely so that srepr can include commutative=True if
+        # that was explicitly specified but not if it was not. Ideally srepr
+        # should not distinguish these cases because the symbols otherwise
+        # compare equal and are considered equivalent.
+        #
+        # See https://github.com/sympy/sympy/issues/8873
+        #
+        assumptions_orig = assumptions.copy()
+
+        # The only assumption that is assumed by default is commutative=True:
+        assumptions.setdefault('commutative', True)
+
+        assumptions_kb = StdFactKB(assumptions)
+        assumptions0 = dict(assumptions_kb)
+
+        return assumptions_kb, assumptions_orig, assumptions0
+
+    @staticmethod
+    def __xnew__(cls, name, **assumptions):  # never cached (e.g. dummy)
+        if not isinstance(name, str):
+            raise TypeError("name should be a string, not %s" % repr(type(name)))
+
+
+        obj = Expr.__new__(cls)
+        obj.name = name
+
+        assumptions_kb, assumptions_orig, assumptions0 = Symbol._canonical_assumptions(**assumptions)
+
+        obj._assumptions = assumptions_kb
+        obj._assumptions_orig = assumptions_orig
+        obj._assumptions0 = tuple(sorted(assumptions0.items()))
+
+        # The three assumptions dicts are all a little different:
+        #
+        #   >>> from sympy import Symbol
+        #   >>> x = Symbol('x', finite=True)
+        #   >>> x.is_positive  # query an assumption
+        #   >>> x._assumptions
+        #   {'finite': True, 'infinite': False, 'commutative': True, 'positive': None}
+        #   >>> x._assumptions0
+        #   {'finite': True, 'infinite': False, 'commutative': True}
+        #   >>> x._assumptions_orig
+        #   {'finite': True}
+        #
+        # Two symbols with the same name are equal if their _assumptions0 are
+        # the same. Arguably it should be _assumptions_orig that is being
+        # compared because that is more transparent to the user (it is
+        # what was passed to the constructor modulo changes made by _sanitize).
+
+        return obj
+
+    @staticmethod
+    @cacheit
+    def __xnew_cached_(cls, name, **assumptions):  # symbols are always cached
+        return Symbol.__xnew__(cls, name, **assumptions)
+
+    def __getnewargs_ex__(self):
+        return ((self.name,), self._assumptions_orig)
+
+    # NOTE: __setstate__ is not needed for pickles created by __getnewargs_ex__
+    # but was used before Symbol was changed to use __getnewargs_ex__ in v1.9.
+    # Pickles created in previous SymPy versions will still need __setstate__
+    # so that they can be unpickled in SymPy > v1.9.
+
+    def __setstate__(self, state):
+        for name, value in state.items():
+            setattr(self, name, value)
+
+    def _hashable_content(self):
+        return (self.name,) + self._assumptions0
+
+    def _eval_subs(self, old, new):
+        if old.is_Pow:
+            from sympy.core.power import Pow
+            return Pow(self, S.One, evaluate=False)._eval_subs(old, new)
+
+    def _eval_refine(self, assumptions):
+        return self
+
+    @property
+    def assumptions0(self):
+        return dict(self._assumptions0)
+
+    @cacheit
+    def sort_key(self, order=None):
+        return self.class_key(), (1, (self.name,)), S.One.sort_key(), S.One
+
+    def as_dummy(self):
+        # only put commutativity in explicitly if it is False
+        return Dummy(self.name) if self.is_commutative is not False \
+            else Dummy(self.name, commutative=self.is_commutative)
+
+    def as_real_imag(self, deep=True, **hints):
+        if hints.get('ignore') == self:
+            return None
+        else:
+            from sympy.functions.elementary.complexes import im, re
+            return (re(self), im(self))
+
+    def is_constant(self, *wrt, **flags):
+        if not wrt:
+            return False
+        return self not in wrt
+
+    @property
+    def free_symbols(self):
+        return {self}
+
+    binary_symbols = free_symbols  # in this case, not always
+
+    def as_set(self):
+        return S.UniversalSet
+
+
+class Dummy(Symbol):
+    """Dummy symbols are each unique, even if they have the same name:
+
+    Examples
+    ========
+
+    >>> from sympy import Dummy
+    >>> Dummy("x") == Dummy("x")
+    False
+
+    If a name is not supplied then a string value of an internal count will be
+    used. This is useful when a temporary variable is needed and the name
+    of the variable used in the expression is not important.
+
+    >>> Dummy() #doctest: +SKIP
+    _Dummy_10
+
+    """
+
+    # In the rare event that a Dummy object needs to be recreated, both the
+    # `name` and `dummy_index` should be passed.  This is used by `srepr` for
+    # example:
+    # >>> d1 = Dummy()
+    # >>> d2 = eval(srepr(d1))
+    # >>> d2 == d1
+    # True
+    #
+    # If a new session is started between `srepr` and `eval`, there is a very
+    # small chance that `d2` will be equal to a previously-created Dummy.
+
+    _count = 0
+    _prng = random.Random()
+    _base_dummy_index = _prng.randint(10**6, 9*10**6)
+
+    __slots__ = ('dummy_index',)
+
+    is_Dummy = True
+
+    def __new__(cls, name=None, dummy_index=None, **assumptions):
+        if dummy_index is not None:
+            assert name is not None, "If you specify a dummy_index, you must also provide a name"
+
+        if name is None:
+            name = "Dummy_" + str(Dummy._count)
+
+        if dummy_index is None:
+            dummy_index = Dummy._base_dummy_index + Dummy._count
+            Dummy._count += 1
+
+        cls._sanitize(assumptions, cls)
+        obj = Symbol.__xnew__(cls, name, **assumptions)
+
+        obj.dummy_index = dummy_index
+
+        return obj
+
+    def __getnewargs_ex__(self):
+        return ((self.name, self.dummy_index), self._assumptions_orig)
+
+    @cacheit
+    def sort_key(self, order=None):
+        return self.class_key(), (
+            2, (self.name, self.dummy_index)), S.One.sort_key(), S.One
+
+    def _hashable_content(self):
+        return Symbol._hashable_content(self) + (self.dummy_index,)
+
+
+class Wild(Symbol):
+    """
+    A Wild symbol matches anything, or anything
+    without whatever is explicitly excluded.
+
+    Parameters
+    ==========
+
+    name : str
+        Name of the Wild instance.
+
+    exclude : iterable, optional
+        Instances in ``exclude`` will not be matched.
+
+    properties : iterable of functions, optional
+        Functions, each taking an expressions as input
+        and returns a ``bool``. All functions in ``properties``
+        need to return ``True`` in order for the Wild instance
+        to match the expression.
+
+    Examples
+    ========
+
+    >>> from sympy import Wild, WildFunction, cos, pi
+    >>> from sympy.abc import x, y, z
+    >>> a = Wild('a')
+    >>> x.match(a)
+    {a_: x}
+    >>> pi.match(a)
+    {a_: pi}
+    >>> (3*x**2).match(a*x)
+    {a_: 3*x}
+    >>> cos(x).match(a)
+    {a_: cos(x)}
+    >>> b = Wild('b', exclude=[x])
+    >>> (3*x**2).match(b*x)
+    >>> b.match(a)
+    {a_: b_}
+    >>> A = WildFunction('A')
+    >>> A.match(a)
+    {a_: A_}
+
+    Tips
+    ====
+
+    When using Wild, be sure to use the exclude
+    keyword to make the pattern more precise.
+    Without the exclude pattern, you may get matches
+    that are technically correct, but not what you
+    wanted. For example, using the above without
+    exclude:
+
+    >>> from sympy import symbols
+    >>> a, b = symbols('a b', cls=Wild)
+    >>> (2 + 3*y).match(a*x + b*y)
+    {a_: 2/x, b_: 3}
+
+    This is technically correct, because
+    (2/x)*x + 3*y == 2 + 3*y, but you probably
+    wanted it to not match at all. The issue is that
+    you really did not want a and b to include x and y,
+    and the exclude parameter lets you specify exactly
+    this.  With the exclude parameter, the pattern will
+    not match.
+
+    >>> a = Wild('a', exclude=[x, y])
+    >>> b = Wild('b', exclude=[x, y])
+    >>> (2 + 3*y).match(a*x + b*y)
+
+    Exclude also helps remove ambiguity from matches.
+
+    >>> E = 2*x**3*y*z
+    >>> a, b = symbols('a b', cls=Wild)
+    >>> E.match(a*b)
+    {a_: 2*y*z, b_: x**3}
+    >>> a = Wild('a', exclude=[x, y])
+    >>> E.match(a*b)
+    {a_: z, b_: 2*x**3*y}
+    >>> a = Wild('a', exclude=[x, y, z])
+    >>> E.match(a*b)
+    {a_: 2, b_: x**3*y*z}
+
+    Wild also accepts a ``properties`` parameter:
+
+    >>> a = Wild('a', properties=[lambda k: k.is_Integer])
+    >>> E.match(a*b)
+    {a_: 2, b_: x**3*y*z}
+
+    """
+    is_Wild = True
+
+    __slots__ = ('exclude', 'properties')
+
+    def __new__(cls, name, exclude=(), properties=(), **assumptions):
+        exclude = tuple([sympify(x) for x in exclude])
+        properties = tuple(properties)
+        cls._sanitize(assumptions, cls)
+        return Wild.__xnew__(cls, name, exclude, properties, **assumptions)
+
+    def __getnewargs__(self):
+        return (self.name, self.exclude, self.properties)
+
+    @staticmethod
+    @cacheit
+    def __xnew__(cls, name, exclude, properties, **assumptions):
+        obj = Symbol.__xnew__(cls, name, **assumptions)
+        obj.exclude = exclude
+        obj.properties = properties
+        return obj
+
+    def _hashable_content(self):
+        return super()._hashable_content() + (self.exclude, self.properties)
+
+    # TODO add check against another Wild
+    def matches(self, expr, repl_dict=None, old=False):
+        if any(expr.has(x) for x in self.exclude):
+            return None
+        if not all(f(expr) for f in self.properties):
+            return None
+        if repl_dict is None:
+            repl_dict = {}
+        else:
+            repl_dict = repl_dict.copy()
+        repl_dict[self] = expr
+        return repl_dict
+
+
+_range = _re.compile('([0-9]*:[0-9]+|[a-zA-Z]?:[a-zA-Z])')
+
+
+def symbols(names, *, cls=Symbol, **args) -> Any:
+    r"""
+    Transform strings into instances of :class:`Symbol` class.
+
+    :func:`symbols` function returns a sequence of symbols with names taken
+    from ``names`` argument, which can be a comma or whitespace delimited
+    string, or a sequence of strings::
+
+        >>> from sympy import symbols, Function
+
+        >>> x, y, z = symbols('x,y,z')
+        >>> a, b, c = symbols('a b c')
+
+    The type of output is dependent on the properties of input arguments::
+
+        >>> symbols('x')
+        x
+        >>> symbols('x,')
+        (x,)
+        >>> symbols('x,y')
+        (x, y)
+        >>> symbols(('a', 'b', 'c'))
+        (a, b, c)
+        >>> symbols(['a', 'b', 'c'])
+        [a, b, c]
+        >>> symbols({'a', 'b', 'c'})
+        {a, b, c}
+
+    If an iterable container is needed for a single symbol, set the ``seq``
+    argument to ``True`` or terminate the symbol name with a comma::
+
+        >>> symbols('x', seq=True)
+        (x,)
+
+    To reduce typing, range syntax is supported to create indexed symbols.
+    Ranges are indicated by a colon and the type of range is determined by
+    the character to the right of the colon. If the character is a digit
+    then all contiguous digits to the left are taken as the nonnegative
+    starting value (or 0 if there is no digit left of the colon) and all
+    contiguous digits to the right are taken as 1 greater than the ending
+    value::
+
+        >>> symbols('x:10')
+        (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
+
+        >>> symbols('x5:10')
+        (x5, x6, x7, x8, x9)
+        >>> symbols('x5(:2)')
+        (x50, x51)
+
+        >>> symbols('x5:10,y:5')
+        (x5, x6, x7, x8, x9, y0, y1, y2, y3, y4)
+
+        >>> symbols(('x5:10', 'y:5'))
+        ((x5, x6, x7, x8, x9), (y0, y1, y2, y3, y4))
+
+    If the character to the right of the colon is a letter, then the single
+    letter to the left (or 'a' if there is none) is taken as the start
+    and all characters in the lexicographic range *through* the letter to
+    the right are used as the range::
+
+        >>> symbols('x:z')
+        (x, y, z)
+        >>> symbols('x:c')  # null range
+        ()
+        >>> symbols('x(:c)')
+        (xa, xb, xc)
+
+        >>> symbols(':c')
+        (a, b, c)
+
+        >>> symbols('a:d, x:z')
+        (a, b, c, d, x, y, z)
+
+        >>> symbols(('a:d', 'x:z'))
+        ((a, b, c, d), (x, y, z))
+
+    Multiple ranges are supported; contiguous numerical ranges should be
+    separated by parentheses to disambiguate the ending number of one
+    range from the starting number of the next::
+
+        >>> symbols('x:2(1:3)')
+        (x01, x02, x11, x12)
+        >>> symbols(':3:2')  # parsing is from left to right
+        (00, 01, 10, 11, 20, 21)
+
+    Only one pair of parentheses surrounding ranges are removed, so to
+    include parentheses around ranges, double them. And to include spaces,
+    commas, or colons, escape them with a backslash::
+
+        >>> symbols('x((a:b))')
+        (x(a), x(b))
+        >>> symbols(r'x(:1\,:2)')  # or r'x((:1)\,(:2))'
+        (x(0,0), x(0,1))
+
+    All newly created symbols have assumptions set according to ``args``::
+
+        >>> a = symbols('a', integer=True)
+        >>> a.is_integer
+        True
+
+        >>> x, y, z = symbols('x,y,z', real=True)
+        >>> x.is_real and y.is_real and z.is_real
+        True
+
+    Despite its name, :func:`symbols` can create symbol-like objects like
+    instances of Function or Wild classes. To achieve this, set ``cls``
+    keyword argument to the desired type::
+
+        >>> symbols('f,g,h', cls=Function)
+        (f, g, h)
+
+        >>> type(_[0])
+        
+
+    """
+    result = []
+
+    if isinstance(names, str):
+        marker = 0
+        splitters = r'\,', r'\:', r'\ '
+        literals: list[tuple[str, str]] = []
+        for splitter in splitters:
+            if splitter in names:
+                while chr(marker) in names:
+                    marker += 1
+                lit_char = chr(marker)
+                marker += 1
+                names = names.replace(splitter, lit_char)
+                literals.append((lit_char, splitter[1:]))
+        def literal(s):
+            if literals:
+                for c, l in literals:
+                    s = s.replace(c, l)
+            return s
+
+        names = names.strip()
+        as_seq = names.endswith(',')
+        if as_seq:
+            names = names[:-1].rstrip()
+        if not names:
+            raise ValueError('no symbols given')
+
+        # split on commas
+        names = [n.strip() for n in names.split(',')]
+        if not all(n for n in names):
+            raise ValueError('missing symbol between commas')
+        # split on spaces
+        for i in range(len(names) - 1, -1, -1):
+            names[i: i + 1] = names[i].split()
+
+        seq = args.pop('seq', as_seq)
+
+        for name in names:
+            if not name:
+                raise ValueError('missing symbol')
+
+            if ':' not in name:
+                symbol = cls(literal(name), **args)
+                result.append(symbol)
+                continue
+
+            split: list[str] = _range.split(name)
+            split_list: list[list[str]] = []
+            # remove 1 layer of bounding parentheses around ranges
+            for i in range(len(split) - 1):
+                if i and ':' in split[i] and split[i] != ':' and \
+                        split[i - 1].endswith('(') and \
+                        split[i + 1].startswith(')'):
+                    split[i - 1] = split[i - 1][:-1]
+                    split[i + 1] = split[i + 1][1:]
+            for s in split:
+                if ':' in s:
+                    if s.endswith(':'):
+                        raise ValueError('missing end range')
+                    a, b = s.split(':')
+                    if b[-1] in string.digits:
+                        a_i = 0 if not a else int(a)
+                        b_i = int(b)
+                        split_list.append([str(c) for c in range(a_i, b_i)])
+                    else:
+                        a = a or 'a'
+                        split_list.append([string.ascii_letters[c] for c in range(
+                            string.ascii_letters.index(a),
+                            string.ascii_letters.index(b) + 1)])  # inclusive
+                    if not split_list[-1]:
+                        break
+                else:
+                    split_list.append([s])
+            else:
+                seq = True
+                if len(split_list) == 1:
+                    names = split_list[0]
+                else:
+                    names = [''.join(s) for s in product(*split_list)]
+                if literals:
+                    result.extend([cls(literal(s), **args) for s in names])
+                else:
+                    result.extend([cls(s, **args) for s in names])
+
+        if not seq and len(result) <= 1:
+            if not result:
+                return ()
+            return result[0]
+
+        return tuple(result)
+    else:
+        for name in names:
+            result.append(symbols(name, cls=cls, **args))
+
+        return type(names)(result)
+
+
+def var(names, **args):
+    """
+    Create symbols and inject them into the global namespace.
+
+    Explanation
+    ===========
+
+    This calls :func:`symbols` with the same arguments and puts the results
+    into the *global* namespace. It's recommended not to use :func:`var` in
+    library code, where :func:`symbols` has to be used::
+
+    Examples
+    ========
+
+    >>> from sympy import var
+
+    >>> var('x')
+    x
+    >>> x # noqa: F821
+    x
+
+    >>> var('a,ab,abc')
+    (a, ab, abc)
+    >>> abc # noqa: F821
+    abc
+
+    >>> var('x,y', real=True)
+    (x, y)
+    >>> x.is_real and y.is_real # noqa: F821
+    True
+
+    See :func:`symbols` documentation for more details on what kinds of
+    arguments can be passed to :func:`var`.
+
+    """
+    def traverse(symbols, frame):
+        """Recursively inject symbols to the global namespace. """
+        for symbol in symbols:
+            if isinstance(symbol, Basic):
+                frame.f_globals[symbol.name] = symbol
+            elif isinstance(symbol, FunctionClass):
+                frame.f_globals[symbol.__name__] = symbol
+            else:
+                traverse(symbol, frame)
+
+    from inspect import currentframe
+    frame = currentframe().f_back
+
+    try:
+        syms = symbols(names, **args)
+
+        if syms is not None:
+            if isinstance(syms, Basic):
+                frame.f_globals[syms.name] = syms
+            elif isinstance(syms, FunctionClass):
+                frame.f_globals[syms.__name__] = syms
+            else:
+                traverse(syms, frame)
+    finally:
+        del frame  # break cyclic dependencies as stated in inspect docs
+
+    return syms
+
+def disambiguate(*iter):
+    """
+    Return a Tuple containing the passed expressions with symbols
+    that appear the same when printed replaced with numerically
+    subscripted symbols, and all Dummy symbols replaced with Symbols.
+
+    Parameters
+    ==========
+
+    iter: list of symbols or expressions.
+
+    Examples
+    ========
+
+    >>> from sympy.core.symbol import disambiguate
+    >>> from sympy import Dummy, Symbol, Tuple
+    >>> from sympy.abc import y
+
+    >>> tup = Symbol('_x'), Dummy('x'), Dummy('x')
+    >>> disambiguate(*tup)
+    (x_2, x, x_1)
+
+    >>> eqs = Tuple(Symbol('x')/y, Dummy('x')/y)
+    >>> disambiguate(*eqs)
+    (x_1/y, x/y)
+
+    >>> ix = Symbol('x', integer=True)
+    >>> vx = Symbol('x')
+    >>> disambiguate(vx + ix)
+    (x + x_1,)
+
+    To make your own mapping of symbols to use, pass only the free symbols
+    of the expressions and create a dictionary:
+
+    >>> free = eqs.free_symbols
+    >>> mapping = dict(zip(free, disambiguate(*free)))
+    >>> eqs.xreplace(mapping)
+    (x_1/y, x/y)
+
+    """
+    new_iter = Tuple(*iter)
+    key = lambda x:tuple(sorted(x.assumptions0.items()))
+    syms = ordered(new_iter.free_symbols, keys=key)
+    mapping = {}
+    for s in syms:
+        mapping.setdefault(str(s).lstrip('_'), []).append(s)
+    reps = {}
+    for k in mapping:
+        # the first or only symbol doesn't get subscripted but make
+        # sure that it's a Symbol, not a Dummy
+        mapk0 = Symbol("%s" % (k), **mapping[k][0].assumptions0)
+        if mapping[k][0] != mapk0:
+            reps[mapping[k][0]] = mapk0
+        # the others get subscripts (and are made into Symbols)
+        skip = 0
+        for i in range(1, len(mapping[k])):
+            while True:
+                name = "%s_%i" % (k, i + skip)
+                if name not in mapping:
+                    break
+                skip += 1
+            ki = mapping[k][i]
+            reps[ki] = Symbol(name, **ki.assumptions0)
+    return new_iter.xreplace(reps)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/sympify.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/sympify.py
new file mode 100644
index 0000000000000000000000000000000000000000..df30fbb85d5f160540312de4eef1d0e6702fc974
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/sympify.py
@@ -0,0 +1,646 @@
+"""sympify -- convert objects SymPy internal format"""
+
+from __future__ import annotations
+
+from typing import Any, Callable, overload, TYPE_CHECKING, TypeVar
+
+import mpmath.libmp as mlib
+
+from inspect import getmro
+import string
+from sympy.core.random import choice
+
+from .parameters import global_parameters
+
+from sympy.utilities.iterables import iterable
+
+
+if TYPE_CHECKING:
+
+    from sympy.core.basic import Basic
+    from sympy.core.expr import Expr
+    from sympy.core.numbers import Integer, Float
+
+    Tbasic = TypeVar('Tbasic', bound=Basic)
+
+
+class SympifyError(ValueError):
+    def __init__(self, expr, base_exc=None):
+        self.expr = expr
+        self.base_exc = base_exc
+
+    def __str__(self):
+        if self.base_exc is None:
+            return "SympifyError: %r" % (self.expr,)
+
+        return ("Sympify of expression '%s' failed, because of exception being "
+            "raised:\n%s: %s" % (self.expr, self.base_exc.__class__.__name__,
+            str(self.base_exc)))
+
+
+converter: dict[type[Any], Callable[[Any], Basic]] = {}
+
+#holds the conversions defined in SymPy itself, i.e. non-user defined conversions
+_sympy_converter: dict[type[Any], Callable[[Any], Basic]] = {}
+
+#alias for clearer use in the library
+_external_converter = converter
+
+class CantSympify:
+    """
+    Mix in this trait to a class to disallow sympification of its instances.
+
+    Examples
+    ========
+
+    >>> from sympy import sympify
+    >>> from sympy.core.sympify import CantSympify
+
+    >>> class Something(dict):
+    ...     pass
+    ...
+    >>> sympify(Something())
+    {}
+
+    >>> class Something(dict, CantSympify):
+    ...     pass
+    ...
+    >>> sympify(Something())
+    Traceback (most recent call last):
+    ...
+    SympifyError: SympifyError: {}
+
+    """
+
+    __slots__ = ()
+
+
+def _is_numpy_instance(a):
+    """
+    Checks if an object is an instance of a type from the numpy module.
+    """
+    # This check avoids unnecessarily importing NumPy.  We check the whole
+    # __mro__ in case any base type is a numpy type.
+    return any(type_.__module__ == 'numpy'
+               for type_ in type(a).__mro__)
+
+
+def _convert_numpy_types(a, **sympify_args):
+    """
+    Converts a numpy datatype input to an appropriate SymPy type.
+    """
+    import numpy as np
+    if not isinstance(a, np.floating):
+        if np.iscomplex(a):
+            return _sympy_converter[complex](a.item())
+        else:
+            return sympify(a.item(), **sympify_args)
+    else:
+        from .numbers import Float
+        prec = np.finfo(a).nmant + 1
+        # E.g. double precision means prec=53 but nmant=52
+        # Leading bit of mantissa is always 1, so is not stored
+        if np.isposinf(a):
+            return Float('inf')
+        elif np.isneginf(a):
+            return Float('-inf')
+        else:
+            p, q = a.as_integer_ratio()
+            a = mlib.from_rational(p, q, prec)
+            return Float(a, precision=prec)
+
+
+@overload
+def sympify(a: int, *, strict: bool = False) -> Integer: ... # type: ignore
+@overload
+def sympify(a: float, *, strict: bool = False) -> Float: ...
+@overload
+def sympify(a: Expr | complex, *, strict: bool = False) -> Expr: ...
+@overload
+def sympify(a: Tbasic, *, strict: bool = False) -> Tbasic: ...
+@overload
+def sympify(a: Any, *, strict: bool = False) -> Basic: ...
+
+def sympify(a, locals=None, convert_xor=True, strict=False, rational=False,
+        evaluate=None):
+    """
+    Converts an arbitrary expression to a type that can be used inside SymPy.
+
+    Explanation
+    ===========
+
+    It will convert Python ints into instances of :class:`~.Integer`, floats
+    into instances of :class:`~.Float`, etc. It is also able to coerce
+    symbolic expressions which inherit from :class:`~.Basic`. This can be
+    useful in cooperation with SAGE.
+
+    .. warning::
+        Note that this function uses ``eval``, and thus shouldn't be used on
+        unsanitized input.
+
+    If the argument is already a type that SymPy understands, it will do
+    nothing but return that value. This can be used at the beginning of a
+    function to ensure you are working with the correct type.
+
+    Examples
+    ========
+
+    >>> from sympy import sympify
+
+    >>> sympify(2).is_integer
+    True
+    >>> sympify(2).is_real
+    True
+
+    >>> sympify(2.0).is_real
+    True
+    >>> sympify("2.0").is_real
+    True
+    >>> sympify("2e-45").is_real
+    True
+
+    If the expression could not be converted, a SympifyError is raised.
+
+    >>> sympify("x***2")
+    Traceback (most recent call last):
+    ...
+    SympifyError: SympifyError: "could not parse 'x***2'"
+
+    When attempting to parse non-Python syntax using ``sympify``, it raises a
+    ``SympifyError``:
+
+    >>> sympify("2x+1")
+    Traceback (most recent call last):
+    ...
+    SympifyError: Sympify of expression 'could not parse '2x+1'' failed
+
+    To parse non-Python syntax, use ``parse_expr`` from ``sympy.parsing.sympy_parser``.
+
+    >>> from sympy.parsing.sympy_parser import parse_expr
+    >>> parse_expr("2x+1", transformations="all")
+    2*x + 1
+
+    For more details about ``transformations``: see :func:`~sympy.parsing.sympy_parser.parse_expr`
+
+    Locals
+    ------
+
+    The sympification happens with access to everything that is loaded
+    by ``from sympy import *``; anything used in a string that is not
+    defined by that import will be converted to a symbol. In the following,
+    the ``bitcount`` function is treated as a symbol and the ``O`` is
+    interpreted as the :class:`~.Order` object (used with series) and it raises
+    an error when used improperly:
+
+    >>> s = 'bitcount(42)'
+    >>> sympify(s)
+    bitcount(42)
+    >>> sympify("O(x)")
+    O(x)
+    >>> sympify("O + 1")
+    Traceback (most recent call last):
+    ...
+    TypeError: unbound method...
+
+    In order to have ``bitcount`` be recognized it can be imported into a
+    namespace dictionary and passed as locals:
+
+    >>> ns = {}
+    >>> exec('from sympy.core.evalf import bitcount', ns)
+    >>> sympify(s, locals=ns)
+    6
+
+    In order to have the ``O`` interpreted as a Symbol, identify it as such
+    in the namespace dictionary. This can be done in a variety of ways; all
+    three of the following are possibilities:
+
+    >>> from sympy import Symbol
+    >>> ns["O"] = Symbol("O")  # method 1
+    >>> exec('from sympy.abc import O', ns)  # method 2
+    >>> ns.update(dict(O=Symbol("O")))  # method 3
+    >>> sympify("O + 1", locals=ns)
+    O + 1
+
+    If you want *all* single-letter and Greek-letter variables to be symbols
+    then you can use the clashing-symbols dictionaries that have been defined
+    there as private variables: ``_clash1`` (single-letter variables),
+    ``_clash2`` (the multi-letter Greek names) or ``_clash`` (both single and
+    multi-letter names that are defined in ``abc``).
+
+    >>> from sympy.abc import _clash1
+    >>> set(_clash1)  # if this fails, see issue #23903
+    {'E', 'I', 'N', 'O', 'Q', 'S'}
+    >>> sympify('I & Q', _clash1)
+    I & Q
+
+    Strict
+    ------
+
+    If the option ``strict`` is set to ``True``, only the types for which an
+    explicit conversion has been defined are converted. In the other
+    cases, a SympifyError is raised.
+
+    >>> print(sympify(None))
+    None
+    >>> sympify(None, strict=True)
+    Traceback (most recent call last):
+    ...
+    SympifyError: SympifyError: None
+
+    .. deprecated:: 1.6
+
+       ``sympify(obj)`` automatically falls back to ``str(obj)`` when all
+       other conversion methods fail, but this is deprecated. ``strict=True``
+       will disable this deprecated behavior. See
+       :ref:`deprecated-sympify-string-fallback`.
+
+    Evaluation
+    ----------
+
+    If the option ``evaluate`` is set to ``False``, then arithmetic and
+    operators will be converted into their SymPy equivalents and the
+    ``evaluate=False`` option will be added. Nested ``Add`` or ``Mul`` will
+    be denested first. This is done via an AST transformation that replaces
+    operators with their SymPy equivalents, so if an operand redefines any
+    of those operations, the redefined operators will not be used. If
+    argument a is not a string, the mathematical expression is evaluated
+    before being passed to sympify, so adding ``evaluate=False`` will still
+    return the evaluated result of expression.
+
+    >>> sympify('2**2 / 3 + 5')
+    19/3
+    >>> sympify('2**2 / 3 + 5', evaluate=False)
+    2**2/3 + 5
+    >>> sympify('4/2+7', evaluate=True)
+    9
+    >>> sympify('4/2+7', evaluate=False)
+    4/2 + 7
+    >>> sympify(4/2+7, evaluate=False)
+    9.00000000000000
+
+    Extending
+    ---------
+
+    To extend ``sympify`` to convert custom objects (not derived from ``Basic``),
+    just define a ``_sympy_`` method to your class. You can do that even to
+    classes that you do not own by subclassing or adding the method at runtime.
+
+    >>> from sympy import Matrix
+    >>> class MyList1(object):
+    ...     def __iter__(self):
+    ...         yield 1
+    ...         yield 2
+    ...         return
+    ...     def __getitem__(self, i): return list(self)[i]
+    ...     def _sympy_(self): return Matrix(self)
+    >>> sympify(MyList1())
+    Matrix([
+    [1],
+    [2]])
+
+    If you do not have control over the class definition you could also use the
+    ``converter`` global dictionary. The key is the class and the value is a
+    function that takes a single argument and returns the desired SymPy
+    object, e.g. ``converter[MyList] = lambda x: Matrix(x)``.
+
+    >>> class MyList2(object):   # XXX Do not do this if you control the class!
+    ...     def __iter__(self):  #     Use _sympy_!
+    ...         yield 1
+    ...         yield 2
+    ...         return
+    ...     def __getitem__(self, i): return list(self)[i]
+    >>> from sympy.core.sympify import converter
+    >>> converter[MyList2] = lambda x: Matrix(x)
+    >>> sympify(MyList2())
+    Matrix([
+    [1],
+    [2]])
+
+    Notes
+    =====
+
+    The keywords ``rational`` and ``convert_xor`` are only used
+    when the input is a string.
+
+    convert_xor
+    -----------
+
+    >>> sympify('x^y',convert_xor=True)
+    x**y
+    >>> sympify('x^y',convert_xor=False)
+    x ^ y
+
+    rational
+    --------
+
+    >>> sympify('0.1',rational=False)
+    0.1
+    >>> sympify('0.1',rational=True)
+    1/10
+
+    Sometimes autosimplification during sympification results in expressions
+    that are very different in structure than what was entered. Until such
+    autosimplification is no longer done, the ``kernS`` function might be of
+    some use. In the example below you can see how an expression reduces to
+    $-1$ by autosimplification, but does not do so when ``kernS`` is used.
+
+    >>> from sympy.core.sympify import kernS
+    >>> from sympy.abc import x
+    >>> -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1
+    -1
+    >>> s = '-2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1'
+    >>> sympify(s)
+    -1
+    >>> kernS(s)
+    -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1
+
+    Parameters
+    ==========
+
+    a :
+        - any object defined in SymPy
+        - standard numeric Python types: ``int``, ``long``, ``float``, ``Decimal``
+        - strings (like ``"0.09"``, ``"2e-19"`` or ``'sin(x)'``)
+        - booleans, including ``None`` (will leave ``None`` unchanged)
+        - dicts, lists, sets or tuples containing any of the above
+
+    convert_xor : bool, optional
+        If true, treats ``^`` as exponentiation.
+        If False, treats ``^`` as XOR itself.
+        Used only when input is a string.
+
+    locals : any object defined in SymPy, optional
+        In order to have strings be recognized it can be imported
+        into a namespace dictionary and passed as locals.
+
+    strict : bool, optional
+        If the option strict is set to ``True``, only the types for which
+        an explicit conversion has been defined are converted. In the
+        other cases, a SympifyError is raised.
+
+    rational : bool, optional
+        If ``True``, converts floats into :class:`~.Rational`.
+        If ``False``, it lets floats remain as it is.
+        Used only when input is a string.
+
+    evaluate : bool, optional
+        If False, then arithmetic and operators will be converted into
+        their SymPy equivalents. If True the expression will be evaluated
+        and the result will be returned.
+
+    """
+    # XXX: If a is a Basic subclass rather than instance (e.g. sin rather than
+    # sin(x)) then a.__sympy__ will be the property. Only on the instance will
+    # a.__sympy__ give the *value* of the property (True). Since sympify(sin)
+    # was used for a long time we allow it to pass. However if strict=True as
+    # is the case in internal calls to _sympify then we only allow
+    # is_sympy=True.
+    #
+    # https://github.com/sympy/sympy/issues/20124
+    is_sympy = getattr(a, '__sympy__', None)
+    if is_sympy is True:
+        return a
+    elif is_sympy is not None:
+        if not strict:
+            return a
+        else:
+            raise SympifyError(a)
+
+    if isinstance(a, CantSympify):
+        raise SympifyError(a)
+
+    cls = getattr(a, "__class__", None)
+
+    #Check if there exists a converter for any of the types in the mro
+    for superclass in getmro(cls):
+        #First check for user defined converters
+        conv = _external_converter.get(superclass)
+        if conv is None:
+            #if none exists, check for SymPy defined converters
+            conv = _sympy_converter.get(superclass)
+        if conv is not None:
+            return conv(a)
+
+    if cls is type(None):
+        if strict:
+            raise SympifyError(a)
+        else:
+            return a
+
+    if evaluate is None:
+        evaluate = global_parameters.evaluate
+
+    # Support for basic numpy datatypes
+    if _is_numpy_instance(a):
+        import numpy as np
+        if np.isscalar(a):
+            return _convert_numpy_types(a, locals=locals,
+                convert_xor=convert_xor, strict=strict, rational=rational,
+                evaluate=evaluate)
+
+    _sympy_ = getattr(a, "_sympy_", None)
+    if _sympy_ is not None:
+        return a._sympy_()
+
+    if not strict:
+        # Put numpy array conversion _before_ float/int, see
+        # .
+        flat = getattr(a, "flat", None)
+        if flat is not None:
+            shape = getattr(a, "shape", None)
+            if shape is not None:
+                from sympy.tensor.array import Array
+                return Array(a.flat, a.shape)  # works with e.g. NumPy arrays
+
+    if not isinstance(a, str):
+        if _is_numpy_instance(a):
+            import numpy as np
+            assert not isinstance(a, np.number)
+            if isinstance(a, np.ndarray):
+                # Scalar arrays (those with zero dimensions) have sympify
+                # called on the scalar element.
+                if a.ndim == 0:
+                    try:
+                        return sympify(a.item(),
+                                       locals=locals,
+                                       convert_xor=convert_xor,
+                                       strict=strict,
+                                       rational=rational,
+                                       evaluate=evaluate)
+                    except SympifyError:
+                        pass
+        elif hasattr(a, '__float__'):
+            # float and int can coerce size-one numpy arrays to their lone
+            # element.  See issue https://github.com/numpy/numpy/issues/10404.
+            return sympify(float(a))
+        elif hasattr(a, '__int__'):
+            return sympify(int(a))
+
+    if strict:
+        raise SympifyError(a)
+
+    if iterable(a):
+        try:
+            return type(a)([sympify(x, locals=locals, convert_xor=convert_xor,
+                rational=rational, evaluate=evaluate) for x in a])
+        except TypeError:
+            # Not all iterables are rebuildable with their type.
+            pass
+
+    if not isinstance(a, str):
+        raise SympifyError('cannot sympify object of type %r' % type(a))
+
+    from sympy.parsing.sympy_parser import (parse_expr, TokenError,
+                                            standard_transformations)
+    from sympy.parsing.sympy_parser import convert_xor as t_convert_xor
+    from sympy.parsing.sympy_parser import rationalize as t_rationalize
+
+    transformations = standard_transformations
+
+    if rational:
+        transformations += (t_rationalize,)
+    if convert_xor:
+        transformations += (t_convert_xor,)
+
+    try:
+        a = a.replace('\n', '')
+        expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate)
+    except (TokenError, SyntaxError) as exc:
+        raise SympifyError('could not parse %r' % a, exc)
+
+    return expr
+
+
+def _sympify(a):
+    """
+    Short version of :func:`~.sympify` for internal usage for ``__add__`` and
+    ``__eq__`` methods where it is ok to allow some things (like Python
+    integers and floats) in the expression. This excludes things (like strings)
+    that are unwise to allow into such an expression.
+
+    >>> from sympy import Integer
+    >>> Integer(1) == 1
+    True
+
+    >>> Integer(1) == '1'
+    False
+
+    >>> from sympy.abc import x
+    >>> x + 1
+    x + 1
+
+    >>> x + '1'
+    Traceback (most recent call last):
+    ...
+    TypeError: unsupported operand type(s) for +: 'Symbol' and 'str'
+
+    see: sympify
+
+    """
+    return sympify(a, strict=True)
+
+
+def kernS(s):
+    """Use a hack to try keep autosimplification from distributing a
+    a number into an Add; this modification does not
+    prevent the 2-arg Mul from becoming an Add, however.
+
+    Examples
+    ========
+
+    >>> from sympy.core.sympify import kernS
+    >>> from sympy.abc import x, y
+
+    The 2-arg Mul distributes a number (or minus sign) across the terms
+    of an expression, but kernS will prevent that:
+
+    >>> 2*(x + y), -(x + 1)
+    (2*x + 2*y, -x - 1)
+    >>> kernS('2*(x + y)')
+    2*(x + y)
+    >>> kernS('-(x + 1)')
+    -(x + 1)
+
+    If use of the hack fails, the un-hacked string will be passed to sympify...
+    and you get what you get.
+
+    XXX This hack should not be necessary once issue 4596 has been resolved.
+    """
+    hit = False
+    quoted = '"' in s or "'" in s
+    if '(' in s and not quoted:
+        if s.count('(') != s.count(")"):
+            raise SympifyError('unmatched left parenthesis')
+
+        # strip all space from s
+        s = ''.join(s.split())
+        olds = s
+        # now use space to represent a symbol that
+        # will
+        # step 1. turn potential 2-arg Muls into 3-arg versions
+        # 1a. *( -> * *(
+        s = s.replace('*(', '* *(')
+        # 1b. close up exponentials
+        s = s.replace('** *', '**')
+        # 2. handle the implied multiplication of a negated
+        # parenthesized expression in two steps
+        # 2a:  -(...)  -->  -( *(...)
+        target = '-( *('
+        s = s.replace('-(', target)
+        # 2b: double the matching closing parenthesis
+        # -( *(...)  -->  -( *(...))
+        i = nest = 0
+        assert target.endswith('(')  # assumption below
+        while True:
+            j = s.find(target, i)
+            if j == -1:
+                break
+            j += len(target) - 1
+            for j in range(j, len(s)):
+                if s[j] == "(":
+                    nest += 1
+                elif s[j] == ")":
+                    nest -= 1
+                if nest == 0:
+                    break
+            s = s[:j] + ")" + s[j:]
+            i = j + 2  # the first char after 2nd )
+        if ' ' in s:
+            # get a unique kern
+            kern = '_'
+            while kern in s:
+                kern += choice(string.ascii_letters + string.digits)
+            s = s.replace(' ', kern)
+            hit = kern in s
+        else:
+            hit = False
+
+    for i in range(2):
+        try:
+            expr = sympify(s)
+            break
+        except TypeError:  # the kern might cause unknown errors...
+            if hit:
+                s = olds  # maybe it didn't like the kern; use un-kerned s
+                hit = False
+                continue
+            expr = sympify(s)  # let original error raise
+
+    if not hit:
+        return expr
+
+    from .symbol import Symbol
+    rep = {Symbol(kern): 1}
+    def _clear(expr):
+        if isinstance(expr, (list, tuple, set)):
+            return type(expr)([_clear(e) for e in expr])
+        if hasattr(expr, 'subs'):
+            return expr.subs(rep, hack2=True)
+        return expr
+    expr = _clear(expr)
+    # hope that kern is not there anymore
+    return expr
+
+
+# Avoid circular import
+from .basic import Basic
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_args.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_args.py
new file mode 100644
index 0000000000000000000000000000000000000000..75b326146e1cc645a27e26ba13d44c92d56d5efb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_args.py
@@ -0,0 +1,5517 @@
+"""Test whether all elements of cls.args are instances of Basic. """
+
+# NOTE: keep tests sorted by (module, class name) key. If a class can't
+# be instantiated, add it here anyway with @SKIP("abstract class) (see
+# e.g. Function).
+
+import os
+import re
+from pathlib import Path
+
+from sympy.assumptions.ask import Q
+from sympy.core.basic import Basic
+from sympy.core.function import (Function, Lambda)
+from sympy.core.numbers import (Rational, oo, pi)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+
+from sympy.testing.pytest import SKIP, warns_deprecated_sympy
+
+a, b, c, x, y, z, s = symbols('a,b,c,x,y,z,s')
+
+
+whitelist = [
+     "sympy.assumptions.predicates",    # tested by test_predicates()
+     "sympy.assumptions.relation.equality",    # tested by test_predicates()
+]
+
+def test_all_classes_are_tested():
+    this = os.path.split(__file__)[0]
+    path = os.path.join(this, os.pardir, os.pardir)
+    sympy_path = os.path.abspath(path)
+    prefix = os.path.split(sympy_path)[0] + os.sep
+
+    re_cls = re.compile(r"^class ([A-Za-z][A-Za-z0-9_]*)\s*\(", re.MULTILINE)
+
+    modules = {}
+
+    for root, dirs, files in os.walk(sympy_path):
+        module = root.replace(prefix, "").replace(os.sep, ".")
+
+        for file in files:
+            if file.startswith(("_", "test_", "bench_")):
+                continue
+            if not file.endswith(".py"):
+                continue
+
+            text = Path(os.path.join(root, file)).read_text(encoding='utf-8')
+
+            submodule = module + '.' + file[:-3]
+
+            if any(submodule.startswith(wpath) for wpath in whitelist):
+                continue
+
+            names = re_cls.findall(text)
+
+            if not names:
+                continue
+
+            try:
+                mod = __import__(submodule, fromlist=names)
+            except ImportError:
+                continue
+
+            def is_Basic(name):
+                cls = getattr(mod, name)
+                if hasattr(cls, '_sympy_deprecated_func'):
+                    cls = cls._sympy_deprecated_func
+                if not isinstance(cls, type):
+                    # check instance of singleton class with same name
+                    cls = type(cls)
+                return issubclass(cls, Basic)
+
+            names = list(filter(is_Basic, names))
+
+            if names:
+                modules[submodule] = names
+
+    ns = globals()
+    failed = []
+
+    for module, names in modules.items():
+        mod = module.replace('.', '__')
+
+        for name in names:
+            test = 'test_' + mod + '__' + name
+
+            if test not in ns:
+                failed.append(module + '.' + name)
+
+    assert not failed, "Missing classes: %s.  Please add tests for these to sympy/core/tests/test_args.py." % ", ".join(failed)
+
+
+def _test_args(obj):
+    all_basic = all(isinstance(arg, Basic) for arg in obj.args)
+    # Ideally obj.func(*obj.args) would always recreate the object, but for
+    # now, we only require it for objects with non-empty .args
+    recreatable = not obj.args or obj.func(*obj.args) == obj
+    return all_basic and recreatable
+
+
+def test_sympy__algebras__quaternion__Quaternion():
+    from sympy.algebras.quaternion import Quaternion
+    assert _test_args(Quaternion(x, 1, 2, 3))
+
+
+def test_sympy__assumptions__assume__AppliedPredicate():
+    from sympy.assumptions.assume import AppliedPredicate, Predicate
+    assert _test_args(AppliedPredicate(Predicate("test"), 2))
+    assert _test_args(Q.is_true(True))
+
+@SKIP("abstract class")
+def test_sympy__assumptions__assume__Predicate():
+    pass
+
+def test_predicates():
+    predicates = [
+        getattr(Q, attr)
+        for attr in Q.__class__.__dict__
+        if not attr.startswith('__')]
+    for p in predicates:
+        assert _test_args(p)
+
+def test_sympy__assumptions__assume__UndefinedPredicate():
+    from sympy.assumptions.assume import Predicate
+    assert _test_args(Predicate("test"))
+
+@SKIP('abstract class')
+def test_sympy__assumptions__relation__binrel__BinaryRelation():
+    pass
+
+def test_sympy__assumptions__relation__binrel__AppliedBinaryRelation():
+    assert _test_args(Q.eq(1, 2))
+
+def test_sympy__assumptions__wrapper__AssumptionsWrapper():
+    from sympy.assumptions.wrapper import AssumptionsWrapper
+    assert _test_args(AssumptionsWrapper(x, Q.positive(x)))
+
+@SKIP("abstract Class")
+def test_sympy__codegen__ast__CodegenAST():
+    from sympy.codegen.ast import CodegenAST
+    assert _test_args(CodegenAST())
+
+@SKIP("abstract Class")
+def test_sympy__codegen__ast__AssignmentBase():
+    from sympy.codegen.ast import AssignmentBase
+    assert _test_args(AssignmentBase(x, 1))
+
+@SKIP("abstract Class")
+def test_sympy__codegen__ast__AugmentedAssignment():
+    from sympy.codegen.ast import AugmentedAssignment
+    assert _test_args(AugmentedAssignment(x, 1))
+
+def test_sympy__codegen__ast__AddAugmentedAssignment():
+    from sympy.codegen.ast import AddAugmentedAssignment
+    assert _test_args(AddAugmentedAssignment(x, 1))
+
+def test_sympy__codegen__ast__SubAugmentedAssignment():
+    from sympy.codegen.ast import SubAugmentedAssignment
+    assert _test_args(SubAugmentedAssignment(x, 1))
+
+def test_sympy__codegen__ast__MulAugmentedAssignment():
+    from sympy.codegen.ast import MulAugmentedAssignment
+    assert _test_args(MulAugmentedAssignment(x, 1))
+
+def test_sympy__codegen__ast__DivAugmentedAssignment():
+    from sympy.codegen.ast import DivAugmentedAssignment
+    assert _test_args(DivAugmentedAssignment(x, 1))
+
+def test_sympy__codegen__ast__ModAugmentedAssignment():
+    from sympy.codegen.ast import ModAugmentedAssignment
+    assert _test_args(ModAugmentedAssignment(x, 1))
+
+def test_sympy__codegen__ast__CodeBlock():
+    from sympy.codegen.ast import CodeBlock, Assignment
+    assert _test_args(CodeBlock(Assignment(x, 1), Assignment(y, 2)))
+
+def test_sympy__codegen__ast__For():
+    from sympy.codegen.ast import For, CodeBlock, AddAugmentedAssignment
+    from sympy.sets import Range
+    assert _test_args(For(x, Range(10), CodeBlock(AddAugmentedAssignment(y, 1))))
+
+
+def test_sympy__codegen__ast__Token():
+    from sympy.codegen.ast import Token
+    assert _test_args(Token())
+
+
+def test_sympy__codegen__ast__ContinueToken():
+    from sympy.codegen.ast import ContinueToken
+    assert _test_args(ContinueToken())
+
+def test_sympy__codegen__ast__BreakToken():
+    from sympy.codegen.ast import BreakToken
+    assert _test_args(BreakToken())
+
+def test_sympy__codegen__ast__NoneToken():
+    from sympy.codegen.ast import NoneToken
+    assert _test_args(NoneToken())
+
+def test_sympy__codegen__ast__String():
+    from sympy.codegen.ast import String
+    assert _test_args(String('foobar'))
+
+def test_sympy__codegen__ast__QuotedString():
+    from sympy.codegen.ast import QuotedString
+    assert _test_args(QuotedString('foobar'))
+
+def test_sympy__codegen__ast__Comment():
+    from sympy.codegen.ast import Comment
+    assert _test_args(Comment('this is a comment'))
+
+def test_sympy__codegen__ast__Node():
+    from sympy.codegen.ast import Node
+    assert _test_args(Node())
+    assert _test_args(Node(attrs={1, 2, 3}))
+
+
+def test_sympy__codegen__ast__Type():
+    from sympy.codegen.ast import Type
+    assert _test_args(Type('float128'))
+
+
+def test_sympy__codegen__ast__IntBaseType():
+    from sympy.codegen.ast import IntBaseType
+    assert _test_args(IntBaseType('bigint'))
+
+
+def test_sympy__codegen__ast___SizedIntType():
+    from sympy.codegen.ast import _SizedIntType
+    assert _test_args(_SizedIntType('int128', 128))
+
+
+def test_sympy__codegen__ast__SignedIntType():
+    from sympy.codegen.ast import SignedIntType
+    assert _test_args(SignedIntType('int128_with_sign', 128))
+
+
+def test_sympy__codegen__ast__UnsignedIntType():
+    from sympy.codegen.ast import UnsignedIntType
+    assert _test_args(UnsignedIntType('unt128', 128))
+
+
+def test_sympy__codegen__ast__FloatBaseType():
+    from sympy.codegen.ast import FloatBaseType
+    assert _test_args(FloatBaseType('positive_real'))
+
+
+def test_sympy__codegen__ast__FloatType():
+    from sympy.codegen.ast import FloatType
+    assert _test_args(FloatType('float242', 242, nmant=142, nexp=99))
+
+
+def test_sympy__codegen__ast__ComplexBaseType():
+    from sympy.codegen.ast import ComplexBaseType
+    assert _test_args(ComplexBaseType('positive_cmplx'))
+
+def test_sympy__codegen__ast__ComplexType():
+    from sympy.codegen.ast import ComplexType
+    assert _test_args(ComplexType('complex42', 42, nmant=15, nexp=5))
+
+
+def test_sympy__codegen__ast__Attribute():
+    from sympy.codegen.ast import Attribute
+    assert _test_args(Attribute('noexcept'))
+
+
+def test_sympy__codegen__ast__Variable():
+    from sympy.codegen.ast import Variable, Type, value_const
+    assert _test_args(Variable(x))
+    assert _test_args(Variable(y, Type('float32'), {value_const}))
+    assert _test_args(Variable(z, type=Type('float64')))
+
+
+def test_sympy__codegen__ast__Pointer():
+    from sympy.codegen.ast import Pointer, Type, pointer_const
+    assert _test_args(Pointer(x))
+    assert _test_args(Pointer(y, type=Type('float32')))
+    assert _test_args(Pointer(z, Type('float64'), {pointer_const}))
+
+
+def test_sympy__codegen__ast__Declaration():
+    from sympy.codegen.ast import Declaration, Variable, Type
+    vx = Variable(x, type=Type('float'))
+    assert _test_args(Declaration(vx))
+
+
+def test_sympy__codegen__ast__While():
+    from sympy.codegen.ast import While, AddAugmentedAssignment
+    assert _test_args(While(abs(x) < 1, [AddAugmentedAssignment(x, -1)]))
+
+
+def test_sympy__codegen__ast__Scope():
+    from sympy.codegen.ast import Scope, AddAugmentedAssignment
+    assert _test_args(Scope([AddAugmentedAssignment(x, -1)]))
+
+
+def test_sympy__codegen__ast__Stream():
+    from sympy.codegen.ast import Stream
+    assert _test_args(Stream('stdin'))
+
+def test_sympy__codegen__ast__Print():
+    from sympy.codegen.ast import Print
+    assert _test_args(Print([x, y]))
+    assert _test_args(Print([x, y], "%d %d"))
+
+
+def test_sympy__codegen__ast__FunctionPrototype():
+    from sympy.codegen.ast import FunctionPrototype, real, Declaration, Variable
+    inp_x = Declaration(Variable(x, type=real))
+    assert _test_args(FunctionPrototype(real, 'pwer', [inp_x]))
+
+
+def test_sympy__codegen__ast__FunctionDefinition():
+    from sympy.codegen.ast import FunctionDefinition, real, Declaration, Variable, Assignment
+    inp_x = Declaration(Variable(x, type=real))
+    assert _test_args(FunctionDefinition(real, 'pwer', [inp_x], [Assignment(x, x**2)]))
+
+
+def test_sympy__codegen__ast__Raise():
+    from sympy.codegen.ast import Raise
+    assert _test_args(Raise(x))
+
+
+def test_sympy__codegen__ast__Return():
+    from sympy.codegen.ast import Return
+    assert _test_args(Return(x))
+
+
+def test_sympy__codegen__ast__RuntimeError_():
+    from sympy.codegen.ast import RuntimeError_
+    assert _test_args(RuntimeError_('"message"'))
+
+
+def test_sympy__codegen__ast__FunctionCall():
+    from sympy.codegen.ast import FunctionCall
+    assert _test_args(FunctionCall('pwer', [x]))
+
+
+def test_sympy__codegen__ast__Element():
+    from sympy.codegen.ast import Element
+    assert _test_args(Element('x', range(3)))
+
+
+def test_sympy__codegen__cnodes__CommaOperator():
+    from sympy.codegen.cnodes import CommaOperator
+    assert _test_args(CommaOperator(1, 2))
+
+
+def test_sympy__codegen__cnodes__goto():
+    from sympy.codegen.cnodes import goto
+    assert _test_args(goto('early_exit'))
+
+
+def test_sympy__codegen__cnodes__Label():
+    from sympy.codegen.cnodes import Label
+    assert _test_args(Label('early_exit'))
+
+
+def test_sympy__codegen__cnodes__PreDecrement():
+    from sympy.codegen.cnodes import PreDecrement
+    assert _test_args(PreDecrement(x))
+
+
+def test_sympy__codegen__cnodes__PostDecrement():
+    from sympy.codegen.cnodes import PostDecrement
+    assert _test_args(PostDecrement(x))
+
+
+def test_sympy__codegen__cnodes__PreIncrement():
+    from sympy.codegen.cnodes import PreIncrement
+    assert _test_args(PreIncrement(x))
+
+
+def test_sympy__codegen__cnodes__PostIncrement():
+    from sympy.codegen.cnodes import PostIncrement
+    assert _test_args(PostIncrement(x))
+
+
+def test_sympy__codegen__cnodes__struct():
+    from sympy.codegen.ast import real, Variable
+    from sympy.codegen.cnodes import struct
+    assert _test_args(struct(declarations=[
+        Variable(x, type=real),
+        Variable(y, type=real)
+    ]))
+
+
+def test_sympy__codegen__cnodes__union():
+    from sympy.codegen.ast import float32, int32, Variable
+    from sympy.codegen.cnodes import union
+    assert _test_args(union(declarations=[
+        Variable(x, type=float32),
+        Variable(y, type=int32)
+    ]))
+
+
+def test_sympy__codegen__cxxnodes__using():
+    from sympy.codegen.cxxnodes import using
+    assert _test_args(using('std::vector'))
+    assert _test_args(using('std::vector', 'vec'))
+
+
+def test_sympy__codegen__fnodes__Program():
+    from sympy.codegen.fnodes import Program
+    assert _test_args(Program('foobar', []))
+
+def test_sympy__codegen__fnodes__Module():
+    from sympy.codegen.fnodes import Module
+    assert _test_args(Module('foobar', [], []))
+
+
+def test_sympy__codegen__fnodes__Subroutine():
+    from sympy.codegen.fnodes import Subroutine
+    x = symbols('x', real=True)
+    assert _test_args(Subroutine('foo', [x], []))
+
+
+def test_sympy__codegen__fnodes__GoTo():
+    from sympy.codegen.fnodes import GoTo
+    assert _test_args(GoTo([10]))
+    assert _test_args(GoTo([10, 20], x > 1))
+
+
+def test_sympy__codegen__fnodes__FortranReturn():
+    from sympy.codegen.fnodes import FortranReturn
+    assert _test_args(FortranReturn(10))
+
+
+def test_sympy__codegen__fnodes__Extent():
+    from sympy.codegen.fnodes import Extent
+    assert _test_args(Extent())
+    assert _test_args(Extent(None))
+    assert _test_args(Extent(':'))
+    assert _test_args(Extent(-3, 4))
+    assert _test_args(Extent(x, y))
+
+
+def test_sympy__codegen__fnodes__use_rename():
+    from sympy.codegen.fnodes import use_rename
+    assert _test_args(use_rename('loc', 'glob'))
+
+
+def test_sympy__codegen__fnodes__use():
+    from sympy.codegen.fnodes import use
+    assert _test_args(use('modfoo', only='bar'))
+
+
+def test_sympy__codegen__fnodes__SubroutineCall():
+    from sympy.codegen.fnodes import SubroutineCall
+    assert _test_args(SubroutineCall('foo', ['bar', 'baz']))
+
+
+def test_sympy__codegen__fnodes__Do():
+    from sympy.codegen.fnodes import Do
+    assert _test_args(Do([], 'i', 1, 42))
+
+
+def test_sympy__codegen__fnodes__ImpliedDoLoop():
+    from sympy.codegen.fnodes import ImpliedDoLoop
+    assert _test_args(ImpliedDoLoop('i', 'i', 1, 42))
+
+
+def test_sympy__codegen__fnodes__ArrayConstructor():
+    from sympy.codegen.fnodes import ArrayConstructor
+    assert _test_args(ArrayConstructor([1, 2, 3]))
+    from sympy.codegen.fnodes import ImpliedDoLoop
+    idl = ImpliedDoLoop('i', 'i', 1, 42)
+    assert _test_args(ArrayConstructor([1, idl, 3]))
+
+
+def test_sympy__codegen__fnodes__sum_():
+    from sympy.codegen.fnodes import sum_
+    assert _test_args(sum_('arr'))
+
+
+def test_sympy__codegen__fnodes__product_():
+    from sympy.codegen.fnodes import product_
+    assert _test_args(product_('arr'))
+
+
+def test_sympy__codegen__numpy_nodes__logaddexp():
+    from sympy.codegen.numpy_nodes import logaddexp
+    assert _test_args(logaddexp(x, y))
+
+
+def test_sympy__codegen__numpy_nodes__logaddexp2():
+    from sympy.codegen.numpy_nodes import logaddexp2
+    assert _test_args(logaddexp2(x, y))
+
+
+def test_sympy__codegen__numpy_nodes__amin():
+    from sympy.codegen.numpy_nodes import amin
+    assert _test_args(amin(x))
+
+
+def test_sympy__codegen__numpy_nodes__amax():
+    from sympy.codegen.numpy_nodes import amax
+    assert _test_args(amax(x))
+
+
+def test_sympy__codegen__numpy_nodes__minimum():
+    from sympy.codegen.numpy_nodes import minimum
+    assert _test_args(minimum(x, y, z))
+
+
+def test_sympy__codegen__numpy_nodes__maximum():
+    from sympy.codegen.numpy_nodes import maximum
+    assert _test_args(maximum(x, y, z))
+
+
+def test_sympy__codegen__pynodes__List():
+    from sympy.codegen.pynodes import List
+    assert _test_args(List(1, 2, 3))
+
+
+def test_sympy__codegen__pynodes__NumExprEvaluate():
+    from sympy.codegen.pynodes import NumExprEvaluate
+    assert _test_args(NumExprEvaluate(x))
+
+
+def test_sympy__codegen__scipy_nodes__cosm1():
+    from sympy.codegen.scipy_nodes import cosm1
+    assert _test_args(cosm1(x))
+
+
+def test_sympy__codegen__scipy_nodes__powm1():
+    from sympy.codegen.scipy_nodes import powm1
+    assert _test_args(powm1(x, y))
+
+
+def test_sympy__codegen__abstract_nodes__List():
+    from sympy.codegen.abstract_nodes import List
+    assert _test_args(List(1, 2, 3))
+
+def test_sympy__combinatorics__graycode__GrayCode():
+    from sympy.combinatorics.graycode import GrayCode
+    # an integer is given and returned from GrayCode as the arg
+    assert _test_args(GrayCode(3, start='100'))
+    assert _test_args(GrayCode(3, rank=1))
+
+
+def test_sympy__combinatorics__permutations__Permutation():
+    from sympy.combinatorics.permutations import Permutation
+    assert _test_args(Permutation([0, 1, 2, 3]))
+
+def test_sympy__combinatorics__permutations__AppliedPermutation():
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.combinatorics.permutations import AppliedPermutation
+    p = Permutation([0, 1, 2, 3])
+    assert _test_args(AppliedPermutation(p, x))
+
+def test_sympy__combinatorics__perm_groups__PermutationGroup():
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.combinatorics.perm_groups import PermutationGroup
+    assert _test_args(PermutationGroup([Permutation([0, 1])]))
+
+
+def test_sympy__combinatorics__polyhedron__Polyhedron():
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.combinatorics.polyhedron import Polyhedron
+    from sympy.abc import w, x, y, z
+    pgroup = [Permutation([[0, 1, 2], [3]]),
+              Permutation([[0, 1, 3], [2]]),
+              Permutation([[0, 2, 3], [1]]),
+              Permutation([[1, 2, 3], [0]]),
+              Permutation([[0, 1], [2, 3]]),
+              Permutation([[0, 2], [1, 3]]),
+              Permutation([[0, 3], [1, 2]]),
+              Permutation([[0, 1, 2, 3]])]
+    corners = [w, x, y, z]
+    faces = [(w, x, y), (w, y, z), (w, z, x), (x, y, z)]
+    assert _test_args(Polyhedron(corners, faces, pgroup))
+
+
+def test_sympy__combinatorics__prufer__Prufer():
+    from sympy.combinatorics.prufer import Prufer
+    assert _test_args(Prufer([[0, 1], [0, 2], [0, 3]], 4))
+
+
+def test_sympy__combinatorics__partitions__Partition():
+    from sympy.combinatorics.partitions import Partition
+    assert _test_args(Partition([1]))
+
+
+def test_sympy__combinatorics__partitions__IntegerPartition():
+    from sympy.combinatorics.partitions import IntegerPartition
+    assert _test_args(IntegerPartition([1]))
+
+
+def test_sympy__concrete__products__Product():
+    from sympy.concrete.products import Product
+    assert _test_args(Product(x, (x, 0, 10)))
+    assert _test_args(Product(x, (x, 0, y), (y, 0, 10)))
+
+
+@SKIP("abstract Class")
+def test_sympy__concrete__expr_with_limits__ExprWithLimits():
+    from sympy.concrete.expr_with_limits import ExprWithLimits
+    assert _test_args(ExprWithLimits(x, (x, 0, 10)))
+    assert _test_args(ExprWithLimits(x*y, (x, 0, 10.),(y,1.,3)))
+
+
+@SKIP("abstract Class")
+def test_sympy__concrete__expr_with_limits__AddWithLimits():
+    from sympy.concrete.expr_with_limits import AddWithLimits
+    assert _test_args(AddWithLimits(x, (x, 0, 10)))
+    assert _test_args(AddWithLimits(x*y, (x, 0, 10),(y,1,3)))
+
+
+@SKIP("abstract Class")
+def test_sympy__concrete__expr_with_intlimits__ExprWithIntLimits():
+    from sympy.concrete.expr_with_intlimits import ExprWithIntLimits
+    assert _test_args(ExprWithIntLimits(x, (x, 0, 10)))
+    assert _test_args(ExprWithIntLimits(x*y, (x, 0, 10),(y,1,3)))
+
+
+def test_sympy__concrete__summations__Sum():
+    from sympy.concrete.summations import Sum
+    assert _test_args(Sum(x, (x, 0, 10)))
+    assert _test_args(Sum(x, (x, 0, y), (y, 0, 10)))
+
+
+def test_sympy__core__add__Add():
+    from sympy.core.add import Add
+    assert _test_args(Add(x, y, z, 2))
+
+
+def test_sympy__core__basic__Atom():
+    from sympy.core.basic import Atom
+    assert _test_args(Atom())
+
+
+def test_sympy__core__basic__Basic():
+    from sympy.core.basic import Basic
+    assert _test_args(Basic())
+
+
+def test_sympy__core__containers__Dict():
+    from sympy.core.containers import Dict
+    assert _test_args(Dict({x: y, y: z}))
+
+
+def test_sympy__core__containers__Tuple():
+    from sympy.core.containers import Tuple
+    assert _test_args(Tuple(x, y, z, 2))
+
+
+def test_sympy__core__expr__AtomicExpr():
+    from sympy.core.expr import AtomicExpr
+    assert _test_args(AtomicExpr())
+
+
+def test_sympy__core__expr__Expr():
+    from sympy.core.expr import Expr
+    assert _test_args(Expr())
+
+
+def test_sympy__core__expr__UnevaluatedExpr():
+    from sympy.core.expr import UnevaluatedExpr
+    from sympy.abc import x
+    assert _test_args(UnevaluatedExpr(x))
+
+
+def test_sympy__core__function__Application():
+    from sympy.core.function import Application
+    assert _test_args(Application(1, 2, 3))
+
+
+def test_sympy__core__function__AppliedUndef():
+    from sympy.core.function import AppliedUndef
+    assert _test_args(AppliedUndef(1, 2, 3))
+
+
+def test_sympy__core__function__DefinedFunction():
+    from sympy.core.function import DefinedFunction
+    assert _test_args(DefinedFunction(1, 2, 3))
+
+
+def test_sympy__core__function__Derivative():
+    from sympy.core.function import Derivative
+    assert _test_args(Derivative(2, x, y, 3))
+
+
+@SKIP("abstract class")
+def test_sympy__core__function__Function():
+    pass
+
+
+def test_sympy__core__function__Lambda():
+    assert _test_args(Lambda((x, y), x + y + z))
+
+
+def test_sympy__core__function__Subs():
+    from sympy.core.function import Subs
+    assert _test_args(Subs(x + y, x, 2))
+
+
+def test_sympy__core__function__WildFunction():
+    from sympy.core.function import WildFunction
+    assert _test_args(WildFunction('f'))
+
+
+def test_sympy__core__mod__Mod():
+    from sympy.core.mod import Mod
+    assert _test_args(Mod(x, 2))
+
+
+def test_sympy__core__mul__Mul():
+    from sympy.core.mul import Mul
+    assert _test_args(Mul(2, x, y, z))
+
+
+def test_sympy__core__numbers__Catalan():
+    from sympy.core.numbers import Catalan
+    assert _test_args(Catalan())
+
+
+def test_sympy__core__numbers__ComplexInfinity():
+    from sympy.core.numbers import ComplexInfinity
+    assert _test_args(ComplexInfinity())
+
+
+def test_sympy__core__numbers__EulerGamma():
+    from sympy.core.numbers import EulerGamma
+    assert _test_args(EulerGamma())
+
+
+def test_sympy__core__numbers__Exp1():
+    from sympy.core.numbers import Exp1
+    assert _test_args(Exp1())
+
+
+def test_sympy__core__numbers__Float():
+    from sympy.core.numbers import Float
+    assert _test_args(Float(1.23))
+
+
+def test_sympy__core__numbers__GoldenRatio():
+    from sympy.core.numbers import GoldenRatio
+    assert _test_args(GoldenRatio())
+
+
+def test_sympy__core__numbers__TribonacciConstant():
+    from sympy.core.numbers import TribonacciConstant
+    assert _test_args(TribonacciConstant())
+
+
+def test_sympy__core__numbers__Half():
+    from sympy.core.numbers import Half
+    assert _test_args(Half())
+
+
+def test_sympy__core__numbers__ImaginaryUnit():
+    from sympy.core.numbers import ImaginaryUnit
+    assert _test_args(ImaginaryUnit())
+
+
+def test_sympy__core__numbers__Infinity():
+    from sympy.core.numbers import Infinity
+    assert _test_args(Infinity())
+
+
+def test_sympy__core__numbers__Integer():
+    from sympy.core.numbers import Integer
+    assert _test_args(Integer(7))
+
+
+@SKIP("abstract class")
+def test_sympy__core__numbers__IntegerConstant():
+    pass
+
+
+def test_sympy__core__numbers__NaN():
+    from sympy.core.numbers import NaN
+    assert _test_args(NaN())
+
+
+def test_sympy__core__numbers__NegativeInfinity():
+    from sympy.core.numbers import NegativeInfinity
+    assert _test_args(NegativeInfinity())
+
+
+def test_sympy__core__numbers__NegativeOne():
+    from sympy.core.numbers import NegativeOne
+    assert _test_args(NegativeOne())
+
+
+def test_sympy__core__numbers__Number():
+    from sympy.core.numbers import Number
+    assert _test_args(Number(1, 7))
+
+
+def test_sympy__core__numbers__NumberSymbol():
+    from sympy.core.numbers import NumberSymbol
+    assert _test_args(NumberSymbol())
+
+
+def test_sympy__core__numbers__One():
+    from sympy.core.numbers import One
+    assert _test_args(One())
+
+
+def test_sympy__core__numbers__Pi():
+    from sympy.core.numbers import Pi
+    assert _test_args(Pi())
+
+
+def test_sympy__core__numbers__Rational():
+    from sympy.core.numbers import Rational
+    assert _test_args(Rational(1, 7))
+
+
+@SKIP("abstract class")
+def test_sympy__core__numbers__RationalConstant():
+    pass
+
+
+def test_sympy__core__numbers__Zero():
+    from sympy.core.numbers import Zero
+    assert _test_args(Zero())
+
+
+@SKIP("abstract class")
+def test_sympy__core__operations__AssocOp():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__core__operations__LatticeOp():
+    pass
+
+
+def test_sympy__core__power__Pow():
+    from sympy.core.power import Pow
+    assert _test_args(Pow(x, 2))
+
+
+def test_sympy__core__relational__Equality():
+    from sympy.core.relational import Equality
+    assert _test_args(Equality(x, 2))
+
+
+def test_sympy__core__relational__GreaterThan():
+    from sympy.core.relational import GreaterThan
+    assert _test_args(GreaterThan(x, 2))
+
+
+def test_sympy__core__relational__LessThan():
+    from sympy.core.relational import LessThan
+    assert _test_args(LessThan(x, 2))
+
+
+@SKIP("abstract class")
+def test_sympy__core__relational__Relational():
+    pass
+
+
+def test_sympy__core__relational__StrictGreaterThan():
+    from sympy.core.relational import StrictGreaterThan
+    assert _test_args(StrictGreaterThan(x, 2))
+
+
+def test_sympy__core__relational__StrictLessThan():
+    from sympy.core.relational import StrictLessThan
+    assert _test_args(StrictLessThan(x, 2))
+
+
+def test_sympy__core__relational__Unequality():
+    from sympy.core.relational import Unequality
+    assert _test_args(Unequality(x, 2))
+
+
+def test_sympy__sandbox__indexed_integrals__IndexedIntegral():
+    from sympy.tensor import IndexedBase, Idx
+    from sympy.sandbox.indexed_integrals import IndexedIntegral
+    A = IndexedBase('A')
+    i, j = symbols('i j', integer=True)
+    a1, a2 = symbols('a1:3', cls=Idx)
+    assert _test_args(IndexedIntegral(A[a1], A[a2]))
+    assert _test_args(IndexedIntegral(A[i], A[j]))
+
+
+def test_sympy__calculus__accumulationbounds__AccumulationBounds():
+    from sympy.calculus.accumulationbounds import AccumulationBounds
+    assert _test_args(AccumulationBounds(0, 1))
+
+
+def test_sympy__sets__ordinals__OmegaPower():
+    from sympy.sets.ordinals import OmegaPower
+    assert _test_args(OmegaPower(1, 1))
+
+def test_sympy__sets__ordinals__Ordinal():
+    from sympy.sets.ordinals import Ordinal, OmegaPower
+    assert _test_args(Ordinal(OmegaPower(2, 1)))
+
+def test_sympy__sets__ordinals__OrdinalOmega():
+    from sympy.sets.ordinals import OrdinalOmega
+    assert _test_args(OrdinalOmega())
+
+def test_sympy__sets__ordinals__OrdinalZero():
+    from sympy.sets.ordinals import OrdinalZero
+    assert _test_args(OrdinalZero())
+
+
+def test_sympy__sets__powerset__PowerSet():
+    from sympy.sets.powerset import PowerSet
+    from sympy.core.singleton import S
+    assert _test_args(PowerSet(S.EmptySet))
+
+
+def test_sympy__sets__sets__EmptySet():
+    from sympy.sets.sets import EmptySet
+    assert _test_args(EmptySet())
+
+
+def test_sympy__sets__sets__UniversalSet():
+    from sympy.sets.sets import UniversalSet
+    assert _test_args(UniversalSet())
+
+
+def test_sympy__sets__sets__FiniteSet():
+    from sympy.sets.sets import FiniteSet
+    assert _test_args(FiniteSet(x, y, z))
+
+
+def test_sympy__sets__sets__Interval():
+    from sympy.sets.sets import Interval
+    assert _test_args(Interval(0, 1))
+
+
+def test_sympy__sets__sets__ProductSet():
+    from sympy.sets.sets import ProductSet, Interval
+    assert _test_args(ProductSet(Interval(0, 1), Interval(0, 1)))
+
+
+@SKIP("does it make sense to test this?")
+def test_sympy__sets__sets__Set():
+    from sympy.sets.sets import Set
+    assert _test_args(Set())
+
+
+def test_sympy__sets__sets__Intersection():
+    from sympy.sets.sets import Intersection, Interval
+    from sympy.core.symbol import Symbol
+    x = Symbol('x')
+    y = Symbol('y')
+    S = Intersection(Interval(0, x), Interval(y, 1))
+    assert isinstance(S, Intersection)
+    assert _test_args(S)
+
+
+def test_sympy__sets__sets__Union():
+    from sympy.sets.sets import Union, Interval
+    assert _test_args(Union(Interval(0, 1), Interval(2, 3)))
+
+
+def test_sympy__sets__sets__Complement():
+    from sympy.sets.sets import Complement, Interval
+    assert _test_args(Complement(Interval(0, 2), Interval(0, 1)))
+
+
+def test_sympy__sets__sets__SymmetricDifference():
+    from sympy.sets.sets import FiniteSet, SymmetricDifference
+    assert _test_args(SymmetricDifference(FiniteSet(1, 2, 3), \
+           FiniteSet(2, 3, 4)))
+
+def test_sympy__sets__sets__DisjointUnion():
+    from sympy.sets.sets import FiniteSet, DisjointUnion
+    assert _test_args(DisjointUnion(FiniteSet(1, 2, 3), \
+           FiniteSet(2, 3, 4)))
+
+
+def test_sympy__physics__quantum__trace__Tr():
+    from sympy.physics.quantum.trace import Tr
+    a, b = symbols('a b', commutative=False)
+    assert _test_args(Tr(a + b))
+
+
+def test_sympy__sets__setexpr__SetExpr():
+    from sympy.sets.setexpr import SetExpr
+    from sympy.sets.sets import Interval
+    assert _test_args(SetExpr(Interval(0, 1)))
+
+
+def test_sympy__sets__fancysets__Rationals():
+    from sympy.sets.fancysets import Rationals
+    assert _test_args(Rationals())
+
+
+def test_sympy__sets__fancysets__Naturals():
+    from sympy.sets.fancysets import Naturals
+    assert _test_args(Naturals())
+
+
+def test_sympy__sets__fancysets__Naturals0():
+    from sympy.sets.fancysets import Naturals0
+    assert _test_args(Naturals0())
+
+
+def test_sympy__sets__fancysets__Integers():
+    from sympy.sets.fancysets import Integers
+    assert _test_args(Integers())
+
+
+def test_sympy__sets__fancysets__Reals():
+    from sympy.sets.fancysets import Reals
+    assert _test_args(Reals())
+
+
+def test_sympy__sets__fancysets__Complexes():
+    from sympy.sets.fancysets import Complexes
+    assert _test_args(Complexes())
+
+
+def test_sympy__sets__fancysets__ComplexRegion():
+    from sympy.sets.fancysets import ComplexRegion
+    from sympy.core.singleton import S
+    from sympy.sets import Interval
+    a = Interval(0, 1)
+    b = Interval(2, 3)
+    theta = Interval(0, 2*S.Pi)
+    assert _test_args(ComplexRegion(a*b))
+    assert _test_args(ComplexRegion(a*theta, polar=True))
+
+
+def test_sympy__sets__fancysets__CartesianComplexRegion():
+    from sympy.sets.fancysets import CartesianComplexRegion
+    from sympy.sets import Interval
+    a = Interval(0, 1)
+    b = Interval(2, 3)
+    assert _test_args(CartesianComplexRegion(a*b))
+
+
+def test_sympy__sets__fancysets__PolarComplexRegion():
+    from sympy.sets.fancysets import PolarComplexRegion
+    from sympy.core.singleton import S
+    from sympy.sets import Interval
+    a = Interval(0, 1)
+    theta = Interval(0, 2*S.Pi)
+    assert _test_args(PolarComplexRegion(a*theta))
+
+
+def test_sympy__sets__fancysets__ImageSet():
+    from sympy.sets.fancysets import ImageSet
+    from sympy.core.singleton import S
+    from sympy.core.symbol import Symbol
+    x = Symbol('x')
+    assert _test_args(ImageSet(Lambda(x, x**2), S.Naturals))
+
+
+def test_sympy__sets__fancysets__Range():
+    from sympy.sets.fancysets import Range
+    assert _test_args(Range(1, 5, 1))
+
+
+def test_sympy__sets__conditionset__ConditionSet():
+    from sympy.sets.conditionset import ConditionSet
+    from sympy.core.singleton import S
+    from sympy.core.symbol import Symbol
+    x = Symbol('x')
+    assert _test_args(ConditionSet(x, Eq(x**2, 1), S.Reals))
+
+
+def test_sympy__sets__contains__Contains():
+    from sympy.sets.fancysets import Range
+    from sympy.sets.contains import Contains
+    assert _test_args(Contains(x, Range(0, 10, 2)))
+
+
+# STATS
+
+
+from sympy.stats.crv_types import NormalDistribution
+nd = NormalDistribution(0, 1)
+from sympy.stats.frv_types import DieDistribution
+die = DieDistribution(6)
+
+
+def test_sympy__stats__crv__ContinuousDomain():
+    from sympy.sets.sets import Interval
+    from sympy.stats.crv import ContinuousDomain
+    assert _test_args(ContinuousDomain({x}, Interval(-oo, oo)))
+
+
+def test_sympy__stats__crv__SingleContinuousDomain():
+    from sympy.sets.sets import Interval
+    from sympy.stats.crv import SingleContinuousDomain
+    assert _test_args(SingleContinuousDomain(x, Interval(-oo, oo)))
+
+
+def test_sympy__stats__crv__ProductContinuousDomain():
+    from sympy.sets.sets import Interval
+    from sympy.stats.crv import SingleContinuousDomain, ProductContinuousDomain
+    D = SingleContinuousDomain(x, Interval(-oo, oo))
+    E = SingleContinuousDomain(y, Interval(0, oo))
+    assert _test_args(ProductContinuousDomain(D, E))
+
+
+def test_sympy__stats__crv__ConditionalContinuousDomain():
+    from sympy.sets.sets import Interval
+    from sympy.stats.crv import (SingleContinuousDomain,
+            ConditionalContinuousDomain)
+    D = SingleContinuousDomain(x, Interval(-oo, oo))
+    assert _test_args(ConditionalContinuousDomain(D, x > 0))
+
+
+def test_sympy__stats__crv__ContinuousPSpace():
+    from sympy.sets.sets import Interval
+    from sympy.stats.crv import ContinuousPSpace, SingleContinuousDomain
+    D = SingleContinuousDomain(x, Interval(-oo, oo))
+    assert _test_args(ContinuousPSpace(D, nd))
+
+
+def test_sympy__stats__crv__SingleContinuousPSpace():
+    from sympy.stats.crv import SingleContinuousPSpace
+    assert _test_args(SingleContinuousPSpace(x, nd))
+
+@SKIP("abstract class")
+def test_sympy__stats__rv__Distribution():
+    pass
+
+@SKIP("abstract class")
+def test_sympy__stats__crv__SingleContinuousDistribution():
+    pass
+
+
+def test_sympy__stats__drv__SingleDiscreteDomain():
+    from sympy.stats.drv import SingleDiscreteDomain
+    assert _test_args(SingleDiscreteDomain(x, S.Naturals))
+
+
+def test_sympy__stats__drv__ProductDiscreteDomain():
+    from sympy.stats.drv import SingleDiscreteDomain, ProductDiscreteDomain
+    X = SingleDiscreteDomain(x, S.Naturals)
+    Y = SingleDiscreteDomain(y, S.Integers)
+    assert _test_args(ProductDiscreteDomain(X, Y))
+
+
+def test_sympy__stats__drv__SingleDiscretePSpace():
+    from sympy.stats.drv import SingleDiscretePSpace
+    from sympy.stats.drv_types import PoissonDistribution
+    assert _test_args(SingleDiscretePSpace(x, PoissonDistribution(1)))
+
+def test_sympy__stats__drv__DiscretePSpace():
+    from sympy.stats.drv import DiscretePSpace, SingleDiscreteDomain
+    density = Lambda(x, 2**(-x))
+    domain = SingleDiscreteDomain(x, S.Naturals)
+    assert _test_args(DiscretePSpace(domain, density))
+
+def test_sympy__stats__drv__ConditionalDiscreteDomain():
+    from sympy.stats.drv import ConditionalDiscreteDomain, SingleDiscreteDomain
+    X = SingleDiscreteDomain(x, S.Naturals0)
+    assert _test_args(ConditionalDiscreteDomain(X, x > 2))
+
+def test_sympy__stats__joint_rv__JointPSpace():
+    from sympy.stats.joint_rv import JointPSpace, JointDistribution
+    assert _test_args(JointPSpace('X', JointDistribution(1)))
+
+def test_sympy__stats__joint_rv__JointRandomSymbol():
+    from sympy.stats.joint_rv import JointRandomSymbol
+    assert _test_args(JointRandomSymbol(x))
+
+def test_sympy__stats__joint_rv_types__JointDistributionHandmade():
+    from sympy.tensor.indexed import Indexed
+    from sympy.stats.joint_rv_types import JointDistributionHandmade
+    x1, x2 = (Indexed('x', i) for i in (1, 2))
+    assert _test_args(JointDistributionHandmade(x1 + x2, S.Reals**2))
+
+
+def test_sympy__stats__joint_rv__MarginalDistribution():
+    from sympy.stats.rv import RandomSymbol
+    from sympy.stats.joint_rv import MarginalDistribution
+    r = RandomSymbol(S('r'))
+    assert _test_args(MarginalDistribution(r, (r,)))
+
+
+def test_sympy__stats__compound_rv__CompoundDistribution():
+    from sympy.stats.compound_rv import CompoundDistribution
+    from sympy.stats.drv_types import PoissonDistribution, Poisson
+    r = Poisson('r', 10)
+    assert _test_args(CompoundDistribution(PoissonDistribution(r)))
+
+
+def test_sympy__stats__compound_rv__CompoundPSpace():
+    from sympy.stats.compound_rv import CompoundPSpace, CompoundDistribution
+    from sympy.stats.drv_types import PoissonDistribution, Poisson
+    r = Poisson('r', 5)
+    C = CompoundDistribution(PoissonDistribution(r))
+    assert _test_args(CompoundPSpace('C', C))
+
+
+@SKIP("abstract class")
+def test_sympy__stats__drv__SingleDiscreteDistribution():
+    pass
+
+@SKIP("abstract class")
+def test_sympy__stats__drv__DiscreteDistribution():
+    pass
+
+@SKIP("abstract class")
+def test_sympy__stats__drv__DiscreteDomain():
+    pass
+
+
+def test_sympy__stats__rv__RandomDomain():
+    from sympy.stats.rv import RandomDomain
+    from sympy.sets.sets import FiniteSet
+    assert _test_args(RandomDomain(FiniteSet(x), FiniteSet(1, 2, 3)))
+
+
+def test_sympy__stats__rv__SingleDomain():
+    from sympy.stats.rv import SingleDomain
+    from sympy.sets.sets import FiniteSet
+    assert _test_args(SingleDomain(x, FiniteSet(1, 2, 3)))
+
+
+def test_sympy__stats__rv__ConditionalDomain():
+    from sympy.stats.rv import ConditionalDomain, RandomDomain
+    from sympy.sets.sets import FiniteSet
+    D = RandomDomain(FiniteSet(x), FiniteSet(1, 2))
+    assert _test_args(ConditionalDomain(D, x > 1))
+
+def test_sympy__stats__rv__MatrixDomain():
+    from sympy.stats.rv import MatrixDomain
+    from sympy.matrices import MatrixSet
+    from sympy.core.singleton import S
+    assert _test_args(MatrixDomain(x, MatrixSet(2, 2, S.Reals)))
+
+def test_sympy__stats__rv__PSpace():
+    from sympy.stats.rv import PSpace, RandomDomain
+    from sympy.sets.sets import FiniteSet
+    D = RandomDomain(FiniteSet(x), FiniteSet(1, 2, 3, 4, 5, 6))
+    assert _test_args(PSpace(D, die))
+
+
+@SKIP("abstract Class")
+def test_sympy__stats__rv__SinglePSpace():
+    pass
+
+
+def test_sympy__stats__rv__RandomSymbol():
+    from sympy.stats.rv import RandomSymbol
+    from sympy.stats.crv import SingleContinuousPSpace
+    A = SingleContinuousPSpace(x, nd)
+    assert _test_args(RandomSymbol(x, A))
+
+
+@SKIP("abstract Class")
+def test_sympy__stats__rv__ProductPSpace():
+    pass
+
+
+def test_sympy__stats__rv__IndependentProductPSpace():
+    from sympy.stats.rv import IndependentProductPSpace
+    from sympy.stats.crv import SingleContinuousPSpace
+    A = SingleContinuousPSpace(x, nd)
+    B = SingleContinuousPSpace(y, nd)
+    assert _test_args(IndependentProductPSpace(A, B))
+
+
+def test_sympy__stats__rv__ProductDomain():
+    from sympy.sets.sets import Interval
+    from sympy.stats.rv import ProductDomain, SingleDomain
+    D = SingleDomain(x, Interval(-oo, oo))
+    E = SingleDomain(y, Interval(0, oo))
+    assert _test_args(ProductDomain(D, E))
+
+
+def test_sympy__stats__symbolic_probability__Probability():
+    from sympy.stats.symbolic_probability import Probability
+    from sympy.stats import Normal
+    X = Normal('X', 0, 1)
+    assert _test_args(Probability(X > 0))
+
+
+def test_sympy__stats__symbolic_probability__Expectation():
+    from sympy.stats.symbolic_probability import Expectation
+    from sympy.stats import Normal
+    X = Normal('X', 0, 1)
+    assert _test_args(Expectation(X > 0))
+
+
+def test_sympy__stats__symbolic_probability__Covariance():
+    from sympy.stats.symbolic_probability import Covariance
+    from sympy.stats import Normal
+    X = Normal('X', 0, 1)
+    Y = Normal('Y', 0, 3)
+    assert _test_args(Covariance(X, Y))
+
+
+def test_sympy__stats__symbolic_probability__Variance():
+    from sympy.stats.symbolic_probability import Variance
+    from sympy.stats import Normal
+    X = Normal('X', 0, 1)
+    assert _test_args(Variance(X))
+
+
+def test_sympy__stats__symbolic_probability__Moment():
+    from sympy.stats.symbolic_probability import Moment
+    from sympy.stats import Normal
+    X = Normal('X', 0, 1)
+    assert _test_args(Moment(X, 3, 2, X > 3))
+
+
+def test_sympy__stats__symbolic_probability__CentralMoment():
+    from sympy.stats.symbolic_probability import CentralMoment
+    from sympy.stats import Normal
+    X = Normal('X', 0, 1)
+    assert _test_args(CentralMoment(X, 2, X > 1))
+
+
+def test_sympy__stats__frv_types__DiscreteUniformDistribution():
+    from sympy.stats.frv_types import DiscreteUniformDistribution
+    from sympy.core.containers import Tuple
+    assert _test_args(DiscreteUniformDistribution(Tuple(*list(range(6)))))
+
+
+def test_sympy__stats__frv_types__DieDistribution():
+    assert _test_args(die)
+
+
+def test_sympy__stats__frv_types__BernoulliDistribution():
+    from sympy.stats.frv_types import BernoulliDistribution
+    assert _test_args(BernoulliDistribution(S.Half, 0, 1))
+
+
+def test_sympy__stats__frv_types__BinomialDistribution():
+    from sympy.stats.frv_types import BinomialDistribution
+    assert _test_args(BinomialDistribution(5, S.Half, 1, 0))
+
+def test_sympy__stats__frv_types__BetaBinomialDistribution():
+    from sympy.stats.frv_types import BetaBinomialDistribution
+    assert _test_args(BetaBinomialDistribution(5, 1, 1))
+
+
+def test_sympy__stats__frv_types__HypergeometricDistribution():
+    from sympy.stats.frv_types import HypergeometricDistribution
+    assert _test_args(HypergeometricDistribution(10, 5, 3))
+
+
+def test_sympy__stats__frv_types__RademacherDistribution():
+    from sympy.stats.frv_types import RademacherDistribution
+    assert _test_args(RademacherDistribution())
+
+def test_sympy__stats__frv_types__IdealSolitonDistribution():
+    from sympy.stats.frv_types import IdealSolitonDistribution
+    assert _test_args(IdealSolitonDistribution(10))
+
+def test_sympy__stats__frv_types__RobustSolitonDistribution():
+    from sympy.stats.frv_types import RobustSolitonDistribution
+    assert _test_args(RobustSolitonDistribution(1000, 0.5, 0.1))
+
+def test_sympy__stats__frv__FiniteDomain():
+    from sympy.stats.frv import FiniteDomain
+    assert _test_args(FiniteDomain({(x, 1), (x, 2)}))  # x can be 1 or 2
+
+
+def test_sympy__stats__frv__SingleFiniteDomain():
+    from sympy.stats.frv import SingleFiniteDomain
+    assert _test_args(SingleFiniteDomain(x, {1, 2}))  # x can be 1 or 2
+
+
+def test_sympy__stats__frv__ProductFiniteDomain():
+    from sympy.stats.frv import SingleFiniteDomain, ProductFiniteDomain
+    xd = SingleFiniteDomain(x, {1, 2})
+    yd = SingleFiniteDomain(y, {1, 2})
+    assert _test_args(ProductFiniteDomain(xd, yd))
+
+
+def test_sympy__stats__frv__ConditionalFiniteDomain():
+    from sympy.stats.frv import SingleFiniteDomain, ConditionalFiniteDomain
+    xd = SingleFiniteDomain(x, {1, 2})
+    assert _test_args(ConditionalFiniteDomain(xd, x > 1))
+
+
+def test_sympy__stats__frv__FinitePSpace():
+    from sympy.stats.frv import FinitePSpace, SingleFiniteDomain
+    xd = SingleFiniteDomain(x, {1, 2, 3, 4, 5, 6})
+    assert _test_args(FinitePSpace(xd, {(x, 1): S.Half, (x, 2): S.Half}))
+
+    xd = SingleFiniteDomain(x, {1, 2})
+    assert _test_args(FinitePSpace(xd, {(x, 1): S.Half, (x, 2): S.Half}))
+
+
+def test_sympy__stats__frv__SingleFinitePSpace():
+    from sympy.stats.frv import SingleFinitePSpace
+    from sympy.core.symbol import Symbol
+
+    assert _test_args(SingleFinitePSpace(Symbol('x'), die))
+
+
+def test_sympy__stats__frv__ProductFinitePSpace():
+    from sympy.stats.frv import SingleFinitePSpace, ProductFinitePSpace
+    from sympy.core.symbol import Symbol
+    xp = SingleFinitePSpace(Symbol('x'), die)
+    yp = SingleFinitePSpace(Symbol('y'), die)
+    assert _test_args(ProductFinitePSpace(xp, yp))
+
+@SKIP("abstract class")
+def test_sympy__stats__frv__SingleFiniteDistribution():
+    pass
+
+@SKIP("abstract class")
+def test_sympy__stats__crv__ContinuousDistribution():
+    pass
+
+
+def test_sympy__stats__frv_types__FiniteDistributionHandmade():
+    from sympy.stats.frv_types import FiniteDistributionHandmade
+    from sympy.core.containers import Dict
+    assert _test_args(FiniteDistributionHandmade(Dict({1: 1})))
+
+
+def test_sympy__stats__crv_types__ContinuousDistributionHandmade():
+    from sympy.stats.crv_types import ContinuousDistributionHandmade
+    from sympy.core.function import Lambda
+    from sympy.sets.sets import Interval
+    from sympy.abc import x
+    assert _test_args(ContinuousDistributionHandmade(Lambda(x, 2*x),
+                                                     Interval(0, 1)))
+
+
+def test_sympy__stats__drv_types__DiscreteDistributionHandmade():
+    from sympy.stats.drv_types import DiscreteDistributionHandmade
+    from sympy.core.function import Lambda
+    from sympy.sets.sets import FiniteSet
+    from sympy.abc import x
+    assert _test_args(DiscreteDistributionHandmade(Lambda(x, Rational(1, 10)),
+                                                    FiniteSet(*range(10))))
+
+
+def test_sympy__stats__rv__Density():
+    from sympy.stats.rv import Density
+    from sympy.stats.crv_types import Normal
+    assert _test_args(Density(Normal('x', 0, 1)))
+
+
+def test_sympy__stats__crv_types__ArcsinDistribution():
+    from sympy.stats.crv_types import ArcsinDistribution
+    assert _test_args(ArcsinDistribution(0, 1))
+
+
+def test_sympy__stats__crv_types__BeniniDistribution():
+    from sympy.stats.crv_types import BeniniDistribution
+    assert _test_args(BeniniDistribution(1, 1, 1))
+
+
+def test_sympy__stats__crv_types__BetaDistribution():
+    from sympy.stats.crv_types import BetaDistribution
+    assert _test_args(BetaDistribution(1, 1))
+
+def test_sympy__stats__crv_types__BetaNoncentralDistribution():
+    from sympy.stats.crv_types import BetaNoncentralDistribution
+    assert _test_args(BetaNoncentralDistribution(1, 1, 1))
+
+
+def test_sympy__stats__crv_types__BetaPrimeDistribution():
+    from sympy.stats.crv_types import BetaPrimeDistribution
+    assert _test_args(BetaPrimeDistribution(1, 1))
+
+def test_sympy__stats__crv_types__BoundedParetoDistribution():
+    from sympy.stats.crv_types import BoundedParetoDistribution
+    assert _test_args(BoundedParetoDistribution(1, 1, 2))
+
+def test_sympy__stats__crv_types__CauchyDistribution():
+    from sympy.stats.crv_types import CauchyDistribution
+    assert _test_args(CauchyDistribution(0, 1))
+
+
+def test_sympy__stats__crv_types__ChiDistribution():
+    from sympy.stats.crv_types import ChiDistribution
+    assert _test_args(ChiDistribution(1))
+
+
+def test_sympy__stats__crv_types__ChiNoncentralDistribution():
+    from sympy.stats.crv_types import ChiNoncentralDistribution
+    assert _test_args(ChiNoncentralDistribution(1,1))
+
+
+def test_sympy__stats__crv_types__ChiSquaredDistribution():
+    from sympy.stats.crv_types import ChiSquaredDistribution
+    assert _test_args(ChiSquaredDistribution(1))
+
+
+def test_sympy__stats__crv_types__DagumDistribution():
+    from sympy.stats.crv_types import DagumDistribution
+    assert _test_args(DagumDistribution(1, 1, 1))
+
+
+def test_sympy__stats__crv_types__DavisDistribution():
+    from sympy.stats.crv_types import DavisDistribution
+    assert _test_args(DavisDistribution(1, 1, 1))
+
+
+def test_sympy__stats__crv_types__ExGaussianDistribution():
+    from sympy.stats.crv_types import ExGaussianDistribution
+    assert _test_args(ExGaussianDistribution(1, 1, 1))
+
+
+def test_sympy__stats__crv_types__ExponentialDistribution():
+    from sympy.stats.crv_types import ExponentialDistribution
+    assert _test_args(ExponentialDistribution(1))
+
+
+def test_sympy__stats__crv_types__ExponentialPowerDistribution():
+    from sympy.stats.crv_types import ExponentialPowerDistribution
+    assert _test_args(ExponentialPowerDistribution(0, 1, 1))
+
+
+def test_sympy__stats__crv_types__FDistributionDistribution():
+    from sympy.stats.crv_types import FDistributionDistribution
+    assert _test_args(FDistributionDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__FisherZDistribution():
+    from sympy.stats.crv_types import FisherZDistribution
+    assert _test_args(FisherZDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__FrechetDistribution():
+    from sympy.stats.crv_types import FrechetDistribution
+    assert _test_args(FrechetDistribution(1, 1, 1))
+
+
+def test_sympy__stats__crv_types__GammaInverseDistribution():
+    from sympy.stats.crv_types import GammaInverseDistribution
+    assert _test_args(GammaInverseDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__GammaDistribution():
+    from sympy.stats.crv_types import GammaDistribution
+    assert _test_args(GammaDistribution(1, 1))
+
+def test_sympy__stats__crv_types__GumbelDistribution():
+    from sympy.stats.crv_types import GumbelDistribution
+    assert _test_args(GumbelDistribution(1, 1, False))
+
+def test_sympy__stats__crv_types__GompertzDistribution():
+    from sympy.stats.crv_types import GompertzDistribution
+    assert _test_args(GompertzDistribution(1, 1))
+
+def test_sympy__stats__crv_types__KumaraswamyDistribution():
+    from sympy.stats.crv_types import KumaraswamyDistribution
+    assert _test_args(KumaraswamyDistribution(1, 1))
+
+def test_sympy__stats__crv_types__LaplaceDistribution():
+    from sympy.stats.crv_types import LaplaceDistribution
+    assert _test_args(LaplaceDistribution(0, 1))
+
+def test_sympy__stats__crv_types__LevyDistribution():
+    from sympy.stats.crv_types import LevyDistribution
+    assert _test_args(LevyDistribution(0, 1))
+
+def test_sympy__stats__crv_types__LogCauchyDistribution():
+    from sympy.stats.crv_types import LogCauchyDistribution
+    assert _test_args(LogCauchyDistribution(0, 1))
+
+def test_sympy__stats__crv_types__LogisticDistribution():
+    from sympy.stats.crv_types import LogisticDistribution
+    assert _test_args(LogisticDistribution(0, 1))
+
+def test_sympy__stats__crv_types__LogLogisticDistribution():
+    from sympy.stats.crv_types import LogLogisticDistribution
+    assert _test_args(LogLogisticDistribution(1, 1))
+
+def test_sympy__stats__crv_types__LogitNormalDistribution():
+    from sympy.stats.crv_types import LogitNormalDistribution
+    assert _test_args(LogitNormalDistribution(0, 1))
+
+def test_sympy__stats__crv_types__LogNormalDistribution():
+    from sympy.stats.crv_types import LogNormalDistribution
+    assert _test_args(LogNormalDistribution(0, 1))
+
+def test_sympy__stats__crv_types__LomaxDistribution():
+    from sympy.stats.crv_types import LomaxDistribution
+    assert _test_args(LomaxDistribution(1, 2))
+
+def test_sympy__stats__crv_types__MaxwellDistribution():
+    from sympy.stats.crv_types import MaxwellDistribution
+    assert _test_args(MaxwellDistribution(1))
+
+def test_sympy__stats__crv_types__MoyalDistribution():
+    from sympy.stats.crv_types import MoyalDistribution
+    assert _test_args(MoyalDistribution(1,2))
+
+def test_sympy__stats__crv_types__NakagamiDistribution():
+    from sympy.stats.crv_types import NakagamiDistribution
+    assert _test_args(NakagamiDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__NormalDistribution():
+    from sympy.stats.crv_types import NormalDistribution
+    assert _test_args(NormalDistribution(0, 1))
+
+def test_sympy__stats__crv_types__GaussianInverseDistribution():
+    from sympy.stats.crv_types import GaussianInverseDistribution
+    assert _test_args(GaussianInverseDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__ParetoDistribution():
+    from sympy.stats.crv_types import ParetoDistribution
+    assert _test_args(ParetoDistribution(1, 1))
+
+def test_sympy__stats__crv_types__PowerFunctionDistribution():
+    from sympy.stats.crv_types import PowerFunctionDistribution
+    assert _test_args(PowerFunctionDistribution(2,0,1))
+
+def test_sympy__stats__crv_types__QuadraticUDistribution():
+    from sympy.stats.crv_types import QuadraticUDistribution
+    assert _test_args(QuadraticUDistribution(1, 2))
+
+def test_sympy__stats__crv_types__RaisedCosineDistribution():
+    from sympy.stats.crv_types import RaisedCosineDistribution
+    assert _test_args(RaisedCosineDistribution(1, 1))
+
+def test_sympy__stats__crv_types__RayleighDistribution():
+    from sympy.stats.crv_types import RayleighDistribution
+    assert _test_args(RayleighDistribution(1))
+
+def test_sympy__stats__crv_types__ReciprocalDistribution():
+    from sympy.stats.crv_types import ReciprocalDistribution
+    assert _test_args(ReciprocalDistribution(5, 30))
+
+def test_sympy__stats__crv_types__ShiftedGompertzDistribution():
+    from sympy.stats.crv_types import ShiftedGompertzDistribution
+    assert _test_args(ShiftedGompertzDistribution(1, 1))
+
+def test_sympy__stats__crv_types__StudentTDistribution():
+    from sympy.stats.crv_types import StudentTDistribution
+    assert _test_args(StudentTDistribution(1))
+
+def test_sympy__stats__crv_types__TrapezoidalDistribution():
+    from sympy.stats.crv_types import TrapezoidalDistribution
+    assert _test_args(TrapezoidalDistribution(1, 2, 3, 4))
+
+def test_sympy__stats__crv_types__TriangularDistribution():
+    from sympy.stats.crv_types import TriangularDistribution
+    assert _test_args(TriangularDistribution(-1, 0, 1))
+
+
+def test_sympy__stats__crv_types__UniformDistribution():
+    from sympy.stats.crv_types import UniformDistribution
+    assert _test_args(UniformDistribution(0, 1))
+
+
+def test_sympy__stats__crv_types__UniformSumDistribution():
+    from sympy.stats.crv_types import UniformSumDistribution
+    assert _test_args(UniformSumDistribution(1))
+
+
+def test_sympy__stats__crv_types__VonMisesDistribution():
+    from sympy.stats.crv_types import VonMisesDistribution
+    assert _test_args(VonMisesDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__WeibullDistribution():
+    from sympy.stats.crv_types import WeibullDistribution
+    assert _test_args(WeibullDistribution(1, 1))
+
+
+def test_sympy__stats__crv_types__WignerSemicircleDistribution():
+    from sympy.stats.crv_types import WignerSemicircleDistribution
+    assert _test_args(WignerSemicircleDistribution(1))
+
+
+def test_sympy__stats__drv_types__GeometricDistribution():
+    from sympy.stats.drv_types import GeometricDistribution
+    assert _test_args(GeometricDistribution(.5))
+
+def test_sympy__stats__drv_types__HermiteDistribution():
+    from sympy.stats.drv_types import HermiteDistribution
+    assert _test_args(HermiteDistribution(1, 2))
+
+def test_sympy__stats__drv_types__LogarithmicDistribution():
+    from sympy.stats.drv_types import LogarithmicDistribution
+    assert _test_args(LogarithmicDistribution(.5))
+
+
+def test_sympy__stats__drv_types__NegativeBinomialDistribution():
+    from sympy.stats.drv_types import NegativeBinomialDistribution
+    assert _test_args(NegativeBinomialDistribution(.5, .5))
+
+def test_sympy__stats__drv_types__FlorySchulzDistribution():
+    from sympy.stats.drv_types import FlorySchulzDistribution
+    assert _test_args(FlorySchulzDistribution(.5))
+
+def test_sympy__stats__drv_types__PoissonDistribution():
+    from sympy.stats.drv_types import PoissonDistribution
+    assert _test_args(PoissonDistribution(1))
+
+
+def test_sympy__stats__drv_types__SkellamDistribution():
+    from sympy.stats.drv_types import SkellamDistribution
+    assert _test_args(SkellamDistribution(1, 1))
+
+
+def test_sympy__stats__drv_types__YuleSimonDistribution():
+    from sympy.stats.drv_types import YuleSimonDistribution
+    assert _test_args(YuleSimonDistribution(.5))
+
+
+def test_sympy__stats__drv_types__ZetaDistribution():
+    from sympy.stats.drv_types import ZetaDistribution
+    assert _test_args(ZetaDistribution(1.5))
+
+
+def test_sympy__stats__joint_rv__JointDistribution():
+    from sympy.stats.joint_rv import JointDistribution
+    assert _test_args(JointDistribution(1, 2, 3, 4))
+
+
+def test_sympy__stats__joint_rv_types__MultivariateNormalDistribution():
+    from sympy.stats.joint_rv_types import MultivariateNormalDistribution
+    assert _test_args(
+        MultivariateNormalDistribution([0, 1], [[1, 0],[0, 1]]))
+
+def test_sympy__stats__joint_rv_types__MultivariateLaplaceDistribution():
+    from sympy.stats.joint_rv_types import MultivariateLaplaceDistribution
+    assert _test_args(MultivariateLaplaceDistribution([0, 1], [[1, 0],[0, 1]]))
+
+
+def test_sympy__stats__joint_rv_types__MultivariateTDistribution():
+    from sympy.stats.joint_rv_types import MultivariateTDistribution
+    assert _test_args(MultivariateTDistribution([0, 1], [[1, 0],[0, 1]], 1))
+
+
+def test_sympy__stats__joint_rv_types__NormalGammaDistribution():
+    from sympy.stats.joint_rv_types import NormalGammaDistribution
+    assert _test_args(NormalGammaDistribution(1, 2, 3, 4))
+
+def test_sympy__stats__joint_rv_types__GeneralizedMultivariateLogGammaDistribution():
+    from sympy.stats.joint_rv_types import GeneralizedMultivariateLogGammaDistribution
+    v, l, mu = (4, [1, 2, 3, 4], [1, 2, 3, 4])
+    assert _test_args(GeneralizedMultivariateLogGammaDistribution(S.Half, v, l, mu))
+
+def test_sympy__stats__joint_rv_types__MultivariateBetaDistribution():
+    from sympy.stats.joint_rv_types import MultivariateBetaDistribution
+    assert _test_args(MultivariateBetaDistribution([1, 2, 3]))
+
+def test_sympy__stats__joint_rv_types__MultivariateEwensDistribution():
+    from sympy.stats.joint_rv_types import MultivariateEwensDistribution
+    assert _test_args(MultivariateEwensDistribution(5, 1))
+
+def test_sympy__stats__joint_rv_types__MultinomialDistribution():
+    from sympy.stats.joint_rv_types import MultinomialDistribution
+    assert _test_args(MultinomialDistribution(5, [0.5, 0.1, 0.3]))
+
+def test_sympy__stats__joint_rv_types__NegativeMultinomialDistribution():
+    from sympy.stats.joint_rv_types import NegativeMultinomialDistribution
+    assert _test_args(NegativeMultinomialDistribution(5, [0.5, 0.1, 0.3]))
+
+def test_sympy__stats__rv__RandomIndexedSymbol():
+    from sympy.stats.rv import RandomIndexedSymbol, pspace
+    from sympy.stats.stochastic_process_types import DiscreteMarkovChain
+    X = DiscreteMarkovChain("X")
+    assert _test_args(RandomIndexedSymbol(X[0].symbol, pspace(X[0])))
+
+def test_sympy__stats__rv__RandomMatrixSymbol():
+    from sympy.stats.rv import RandomMatrixSymbol
+    from sympy.stats.random_matrix import RandomMatrixPSpace
+    pspace = RandomMatrixPSpace('P')
+    assert _test_args(RandomMatrixSymbol('M', 3, 3, pspace))
+
+def test_sympy__stats__stochastic_process__StochasticPSpace():
+    from sympy.stats.stochastic_process import StochasticPSpace
+    from sympy.stats.stochastic_process_types import StochasticProcess
+    from sympy.stats.frv_types import BernoulliDistribution
+    assert _test_args(StochasticPSpace("Y", StochasticProcess("Y", [1, 2, 3]), BernoulliDistribution(S.Half, 1, 0)))
+
+def test_sympy__stats__stochastic_process_types__StochasticProcess():
+    from sympy.stats.stochastic_process_types import StochasticProcess
+    assert _test_args(StochasticProcess("Y", [1, 2, 3]))
+
+def test_sympy__stats__stochastic_process_types__MarkovProcess():
+    from sympy.stats.stochastic_process_types import MarkovProcess
+    assert _test_args(MarkovProcess("Y", [1, 2, 3]))
+
+def test_sympy__stats__stochastic_process_types__DiscreteTimeStochasticProcess():
+    from sympy.stats.stochastic_process_types import DiscreteTimeStochasticProcess
+    assert _test_args(DiscreteTimeStochasticProcess("Y", [1, 2, 3]))
+
+def test_sympy__stats__stochastic_process_types__ContinuousTimeStochasticProcess():
+    from sympy.stats.stochastic_process_types import ContinuousTimeStochasticProcess
+    assert _test_args(ContinuousTimeStochasticProcess("Y", [1, 2, 3]))
+
+def test_sympy__stats__stochastic_process_types__TransitionMatrixOf():
+    from sympy.stats.stochastic_process_types import TransitionMatrixOf, DiscreteMarkovChain
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    DMC = DiscreteMarkovChain("Y")
+    assert _test_args(TransitionMatrixOf(DMC, MatrixSymbol('T', 3, 3)))
+
+def test_sympy__stats__stochastic_process_types__GeneratorMatrixOf():
+    from sympy.stats.stochastic_process_types import GeneratorMatrixOf, ContinuousMarkovChain
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    DMC = ContinuousMarkovChain("Y")
+    assert _test_args(GeneratorMatrixOf(DMC, MatrixSymbol('T', 3, 3)))
+
+def test_sympy__stats__stochastic_process_types__StochasticStateSpaceOf():
+    from sympy.stats.stochastic_process_types import StochasticStateSpaceOf, DiscreteMarkovChain
+    DMC = DiscreteMarkovChain("Y")
+    assert _test_args(StochasticStateSpaceOf(DMC, [0, 1, 2]))
+
+def test_sympy__stats__stochastic_process_types__DiscreteMarkovChain():
+    from sympy.stats.stochastic_process_types import DiscreteMarkovChain
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    assert _test_args(DiscreteMarkovChain("Y", [0, 1, 2], MatrixSymbol('T', 3, 3)))
+
+def test_sympy__stats__stochastic_process_types__ContinuousMarkovChain():
+    from sympy.stats.stochastic_process_types import ContinuousMarkovChain
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    assert _test_args(ContinuousMarkovChain("Y", [0, 1, 2], MatrixSymbol('T', 3, 3)))
+
+def test_sympy__stats__stochastic_process_types__BernoulliProcess():
+    from sympy.stats.stochastic_process_types import BernoulliProcess
+    assert _test_args(BernoulliProcess("B", 0.5, 1, 0))
+
+def test_sympy__stats__stochastic_process_types__CountingProcess():
+    from sympy.stats.stochastic_process_types import CountingProcess
+    assert _test_args(CountingProcess("C"))
+
+def test_sympy__stats__stochastic_process_types__PoissonProcess():
+    from sympy.stats.stochastic_process_types import PoissonProcess
+    assert _test_args(PoissonProcess("X", 2))
+
+def test_sympy__stats__stochastic_process_types__WienerProcess():
+    from sympy.stats.stochastic_process_types import WienerProcess
+    assert _test_args(WienerProcess("X"))
+
+def test_sympy__stats__stochastic_process_types__GammaProcess():
+    from sympy.stats.stochastic_process_types import GammaProcess
+    assert _test_args(GammaProcess("X", 1, 2))
+
+def test_sympy__stats__random_matrix__RandomMatrixPSpace():
+    from sympy.stats.random_matrix import RandomMatrixPSpace
+    from sympy.stats.random_matrix_models import RandomMatrixEnsembleModel
+    model = RandomMatrixEnsembleModel('R', 3)
+    assert _test_args(RandomMatrixPSpace('P', model=model))
+
+def test_sympy__stats__random_matrix_models__RandomMatrixEnsembleModel():
+    from sympy.stats.random_matrix_models import RandomMatrixEnsembleModel
+    assert _test_args(RandomMatrixEnsembleModel('R', 3))
+
+def test_sympy__stats__random_matrix_models__GaussianEnsembleModel():
+    from sympy.stats.random_matrix_models import GaussianEnsembleModel
+    assert _test_args(GaussianEnsembleModel('G', 3))
+
+def test_sympy__stats__random_matrix_models__GaussianUnitaryEnsembleModel():
+    from sympy.stats.random_matrix_models import GaussianUnitaryEnsembleModel
+    assert _test_args(GaussianUnitaryEnsembleModel('U', 3))
+
+def test_sympy__stats__random_matrix_models__GaussianOrthogonalEnsembleModel():
+    from sympy.stats.random_matrix_models import GaussianOrthogonalEnsembleModel
+    assert _test_args(GaussianOrthogonalEnsembleModel('U', 3))
+
+def test_sympy__stats__random_matrix_models__GaussianSymplecticEnsembleModel():
+    from sympy.stats.random_matrix_models import GaussianSymplecticEnsembleModel
+    assert _test_args(GaussianSymplecticEnsembleModel('U', 3))
+
+def test_sympy__stats__random_matrix_models__CircularEnsembleModel():
+    from sympy.stats.random_matrix_models import CircularEnsembleModel
+    assert _test_args(CircularEnsembleModel('C', 3))
+
+def test_sympy__stats__random_matrix_models__CircularUnitaryEnsembleModel():
+    from sympy.stats.random_matrix_models import CircularUnitaryEnsembleModel
+    assert _test_args(CircularUnitaryEnsembleModel('U', 3))
+
+def test_sympy__stats__random_matrix_models__CircularOrthogonalEnsembleModel():
+    from sympy.stats.random_matrix_models import CircularOrthogonalEnsembleModel
+    assert _test_args(CircularOrthogonalEnsembleModel('O', 3))
+
+def test_sympy__stats__random_matrix_models__CircularSymplecticEnsembleModel():
+    from sympy.stats.random_matrix_models import CircularSymplecticEnsembleModel
+    assert _test_args(CircularSymplecticEnsembleModel('S', 3))
+
+def test_sympy__stats__symbolic_multivariate_probability__ExpectationMatrix():
+    from sympy.stats import ExpectationMatrix
+    from sympy.stats.rv import RandomMatrixSymbol
+    assert _test_args(ExpectationMatrix(RandomMatrixSymbol('R', 2, 1)))
+
+def test_sympy__stats__symbolic_multivariate_probability__VarianceMatrix():
+    from sympy.stats import VarianceMatrix
+    from sympy.stats.rv import RandomMatrixSymbol
+    assert _test_args(VarianceMatrix(RandomMatrixSymbol('R', 3, 1)))
+
+def test_sympy__stats__symbolic_multivariate_probability__CrossCovarianceMatrix():
+    from sympy.stats import CrossCovarianceMatrix
+    from sympy.stats.rv import RandomMatrixSymbol
+    assert _test_args(CrossCovarianceMatrix(RandomMatrixSymbol('R', 3, 1),
+                        RandomMatrixSymbol('X', 3, 1)))
+
+def test_sympy__stats__matrix_distributions__MatrixPSpace():
+    from sympy.stats.matrix_distributions import MatrixDistribution, MatrixPSpace
+    from sympy.matrices.dense import Matrix
+    M = MatrixDistribution(1, Matrix([[1, 0], [0, 1]]))
+    assert _test_args(MatrixPSpace('M', M, 2, 2))
+
+def test_sympy__stats__matrix_distributions__MatrixDistribution():
+    from sympy.stats.matrix_distributions import MatrixDistribution
+    from sympy.matrices.dense import Matrix
+    assert _test_args(MatrixDistribution(1, Matrix([[1, 0], [0, 1]])))
+
+def test_sympy__stats__matrix_distributions__MatrixGammaDistribution():
+    from sympy.stats.matrix_distributions import MatrixGammaDistribution
+    from sympy.matrices.dense import Matrix
+    assert _test_args(MatrixGammaDistribution(3, 4, Matrix([[1, 0], [0, 1]])))
+
+def test_sympy__stats__matrix_distributions__WishartDistribution():
+    from sympy.stats.matrix_distributions import WishartDistribution
+    from sympy.matrices.dense import Matrix
+    assert _test_args(WishartDistribution(3, Matrix([[1, 0], [0, 1]])))
+
+def test_sympy__stats__matrix_distributions__MatrixNormalDistribution():
+    from sympy.stats.matrix_distributions import MatrixNormalDistribution
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    L = MatrixSymbol('L', 1, 2)
+    S1 = MatrixSymbol('S1', 1, 1)
+    S2 = MatrixSymbol('S2', 2, 2)
+    assert _test_args(MatrixNormalDistribution(L, S1, S2))
+
+def test_sympy__stats__matrix_distributions__MatrixStudentTDistribution():
+    from sympy.stats.matrix_distributions import MatrixStudentTDistribution
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    v = symbols('v', positive=True)
+    Omega = MatrixSymbol('Omega', 3, 3)
+    Sigma = MatrixSymbol('Sigma', 1, 1)
+    Location = MatrixSymbol('Location', 1, 3)
+    assert _test_args(MatrixStudentTDistribution(v, Location, Omega, Sigma))
+
+def test_sympy__utilities__matchpy_connector__WildDot():
+    from sympy.utilities.matchpy_connector import WildDot
+    assert _test_args(WildDot("w_"))
+
+
+def test_sympy__utilities__matchpy_connector__WildPlus():
+    from sympy.utilities.matchpy_connector import WildPlus
+    assert _test_args(WildPlus("w__"))
+
+
+def test_sympy__utilities__matchpy_connector__WildStar():
+    from sympy.utilities.matchpy_connector import WildStar
+    assert _test_args(WildStar("w___"))
+
+
+def test_sympy__core__symbol__Str():
+    from sympy.core.symbol import Str
+    assert _test_args(Str('t'))
+
+def test_sympy__core__symbol__Dummy():
+    from sympy.core.symbol import Dummy
+    assert _test_args(Dummy('t'))
+
+
+def test_sympy__core__symbol__Symbol():
+    from sympy.core.symbol import Symbol
+    assert _test_args(Symbol('t'))
+
+
+def test_sympy__core__symbol__Wild():
+    from sympy.core.symbol import Wild
+    assert _test_args(Wild('x', exclude=[x]))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__combinatorial__factorials__CombinatorialFunction():
+    pass
+
+
+def test_sympy__functions__combinatorial__factorials__FallingFactorial():
+    from sympy.functions.combinatorial.factorials import FallingFactorial
+    assert _test_args(FallingFactorial(2, x))
+
+
+def test_sympy__functions__combinatorial__factorials__MultiFactorial():
+    from sympy.functions.combinatorial.factorials import MultiFactorial
+    assert _test_args(MultiFactorial(x))
+
+
+def test_sympy__functions__combinatorial__factorials__RisingFactorial():
+    from sympy.functions.combinatorial.factorials import RisingFactorial
+    assert _test_args(RisingFactorial(2, x))
+
+
+def test_sympy__functions__combinatorial__factorials__binomial():
+    from sympy.functions.combinatorial.factorials import binomial
+    assert _test_args(binomial(2, x))
+
+
+def test_sympy__functions__combinatorial__factorials__subfactorial():
+    from sympy.functions.combinatorial.factorials import subfactorial
+    assert _test_args(subfactorial(x))
+
+
+def test_sympy__functions__combinatorial__factorials__factorial():
+    from sympy.functions.combinatorial.factorials import factorial
+    assert _test_args(factorial(x))
+
+
+def test_sympy__functions__combinatorial__factorials__factorial2():
+    from sympy.functions.combinatorial.factorials import factorial2
+    assert _test_args(factorial2(x))
+
+
+def test_sympy__functions__combinatorial__numbers__bell():
+    from sympy.functions.combinatorial.numbers import bell
+    assert _test_args(bell(x, y))
+
+
+def test_sympy__functions__combinatorial__numbers__bernoulli():
+    from sympy.functions.combinatorial.numbers import bernoulli
+    assert _test_args(bernoulli(x))
+
+
+def test_sympy__functions__combinatorial__numbers__catalan():
+    from sympy.functions.combinatorial.numbers import catalan
+    assert _test_args(catalan(x))
+
+
+def test_sympy__functions__combinatorial__numbers__genocchi():
+    from sympy.functions.combinatorial.numbers import genocchi
+    assert _test_args(genocchi(x))
+
+
+def test_sympy__functions__combinatorial__numbers__euler():
+    from sympy.functions.combinatorial.numbers import euler
+    assert _test_args(euler(x))
+
+
+def test_sympy__functions__combinatorial__numbers__andre():
+    from sympy.functions.combinatorial.numbers import andre
+    assert _test_args(andre(x))
+
+
+def test_sympy__functions__combinatorial__numbers__carmichael():
+    from sympy.functions.combinatorial.numbers import carmichael
+    assert _test_args(carmichael(x))
+
+
+def test_sympy__functions__combinatorial__numbers__divisor_sigma():
+    from sympy.functions.combinatorial.numbers import divisor_sigma
+    k = symbols('k', integer=True)
+    n = symbols('n', integer=True)
+    t = divisor_sigma(n, k)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__fibonacci():
+    from sympy.functions.combinatorial.numbers import fibonacci
+    assert _test_args(fibonacci(x))
+
+
+def test_sympy__functions__combinatorial__numbers__jacobi_symbol():
+    from sympy.functions.combinatorial.numbers import jacobi_symbol
+    assert _test_args(jacobi_symbol(2, 3))
+
+
+def test_sympy__functions__combinatorial__numbers__kronecker_symbol():
+    from sympy.functions.combinatorial.numbers import kronecker_symbol
+    assert _test_args(kronecker_symbol(2, 3))
+
+
+def test_sympy__functions__combinatorial__numbers__legendre_symbol():
+    from sympy.functions.combinatorial.numbers import legendre_symbol
+    assert _test_args(legendre_symbol(2, 3))
+
+
+def test_sympy__functions__combinatorial__numbers__mobius():
+    from sympy.functions.combinatorial.numbers import mobius
+    assert _test_args(mobius(2))
+
+
+def test_sympy__functions__combinatorial__numbers__motzkin():
+    from sympy.functions.combinatorial.numbers import motzkin
+    assert _test_args(motzkin(5))
+
+
+def test_sympy__functions__combinatorial__numbers__partition():
+    from sympy.core.symbol import Symbol
+    from sympy.functions.combinatorial.numbers import partition
+    assert _test_args(partition(Symbol('a', integer=True)))
+
+
+def test_sympy__functions__combinatorial__numbers__primenu():
+    from sympy.functions.combinatorial.numbers import primenu
+    n = symbols('n', integer=True)
+    t = primenu(n)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__primeomega():
+    from sympy.functions.combinatorial.numbers import primeomega
+    n = symbols('n', integer=True)
+    t = primeomega(n)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__primepi():
+    from sympy.functions.combinatorial.numbers import primepi
+    n = symbols('n')
+    t = primepi(n)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__reduced_totient():
+    from sympy.functions.combinatorial.numbers import reduced_totient
+    k = symbols('k', integer=True)
+    t = reduced_totient(k)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__totient():
+    from sympy.functions.combinatorial.numbers import totient
+    k = symbols('k', integer=True)
+    t = totient(k)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__tribonacci():
+    from sympy.functions.combinatorial.numbers import tribonacci
+    assert _test_args(tribonacci(x))
+
+
+def test_sympy__functions__combinatorial__numbers__udivisor_sigma():
+    from sympy.functions.combinatorial.numbers import udivisor_sigma
+    k = symbols('k', integer=True)
+    n = symbols('n', integer=True)
+    t = udivisor_sigma(n, k)
+    assert _test_args(t)
+
+
+def test_sympy__functions__combinatorial__numbers__harmonic():
+    from sympy.functions.combinatorial.numbers import harmonic
+    assert _test_args(harmonic(x, 2))
+
+
+def test_sympy__functions__combinatorial__numbers__lucas():
+    from sympy.functions.combinatorial.numbers import lucas
+    assert _test_args(lucas(x))
+
+
+def test_sympy__functions__elementary__complexes__Abs():
+    from sympy.functions.elementary.complexes import Abs
+    assert _test_args(Abs(x))
+
+
+def test_sympy__functions__elementary__complexes__adjoint():
+    from sympy.functions.elementary.complexes import adjoint
+    assert _test_args(adjoint(x))
+
+
+def test_sympy__functions__elementary__complexes__arg():
+    from sympy.functions.elementary.complexes import arg
+    assert _test_args(arg(x))
+
+
+def test_sympy__functions__elementary__complexes__conjugate():
+    from sympy.functions.elementary.complexes import conjugate
+    assert _test_args(conjugate(x))
+
+
+def test_sympy__functions__elementary__complexes__im():
+    from sympy.functions.elementary.complexes import im
+    assert _test_args(im(x))
+
+
+def test_sympy__functions__elementary__complexes__re():
+    from sympy.functions.elementary.complexes import re
+    assert _test_args(re(x))
+
+
+def test_sympy__functions__elementary__complexes__sign():
+    from sympy.functions.elementary.complexes import sign
+    assert _test_args(sign(x))
+
+
+def test_sympy__functions__elementary__complexes__polar_lift():
+    from sympy.functions.elementary.complexes import polar_lift
+    assert _test_args(polar_lift(x))
+
+
+def test_sympy__functions__elementary__complexes__periodic_argument():
+    from sympy.functions.elementary.complexes import periodic_argument
+    assert _test_args(periodic_argument(x, y))
+
+
+def test_sympy__functions__elementary__complexes__principal_branch():
+    from sympy.functions.elementary.complexes import principal_branch
+    assert _test_args(principal_branch(x, y))
+
+
+def test_sympy__functions__elementary__complexes__transpose():
+    from sympy.functions.elementary.complexes import transpose
+    assert _test_args(transpose(x))
+
+
+def test_sympy__functions__elementary__exponential__LambertW():
+    from sympy.functions.elementary.exponential import LambertW
+    assert _test_args(LambertW(2))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__exponential__ExpBase():
+    pass
+
+
+def test_sympy__functions__elementary__exponential__exp():
+    from sympy.functions.elementary.exponential import exp
+    assert _test_args(exp(2))
+
+
+def test_sympy__functions__elementary__exponential__exp_polar():
+    from sympy.functions.elementary.exponential import exp_polar
+    assert _test_args(exp_polar(2))
+
+
+def test_sympy__functions__elementary__exponential__log():
+    from sympy.functions.elementary.exponential import log
+    assert _test_args(log(2))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__hyperbolic__HyperbolicFunction():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__hyperbolic__ReciprocalHyperbolicFunction():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__hyperbolic__InverseHyperbolicFunction():
+    pass
+
+
+def test_sympy__functions__elementary__hyperbolic__acosh():
+    from sympy.functions.elementary.hyperbolic import acosh
+    assert _test_args(acosh(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__acoth():
+    from sympy.functions.elementary.hyperbolic import acoth
+    assert _test_args(acoth(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__asinh():
+    from sympy.functions.elementary.hyperbolic import asinh
+    assert _test_args(asinh(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__atanh():
+    from sympy.functions.elementary.hyperbolic import atanh
+    assert _test_args(atanh(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__asech():
+    from sympy.functions.elementary.hyperbolic import asech
+    assert _test_args(asech(x))
+
+def test_sympy__functions__elementary__hyperbolic__acsch():
+    from sympy.functions.elementary.hyperbolic import acsch
+    assert _test_args(acsch(x))
+
+def test_sympy__functions__elementary__hyperbolic__cosh():
+    from sympy.functions.elementary.hyperbolic import cosh
+    assert _test_args(cosh(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__coth():
+    from sympy.functions.elementary.hyperbolic import coth
+    assert _test_args(coth(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__csch():
+    from sympy.functions.elementary.hyperbolic import csch
+    assert _test_args(csch(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__sech():
+    from sympy.functions.elementary.hyperbolic import sech
+    assert _test_args(sech(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__sinh():
+    from sympy.functions.elementary.hyperbolic import sinh
+    assert _test_args(sinh(2))
+
+
+def test_sympy__functions__elementary__hyperbolic__tanh():
+    from sympy.functions.elementary.hyperbolic import tanh
+    assert _test_args(tanh(2))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__integers__RoundFunction():
+    pass
+
+
+def test_sympy__functions__elementary__integers__ceiling():
+    from sympy.functions.elementary.integers import ceiling
+    assert _test_args(ceiling(x))
+
+
+def test_sympy__functions__elementary__integers__floor():
+    from sympy.functions.elementary.integers import floor
+    assert _test_args(floor(x))
+
+
+def test_sympy__functions__elementary__integers__frac():
+    from sympy.functions.elementary.integers import frac
+    assert _test_args(frac(x))
+
+
+def test_sympy__functions__elementary__miscellaneous__IdentityFunction():
+    from sympy.functions.elementary.miscellaneous import IdentityFunction
+    assert _test_args(IdentityFunction())
+
+
+def test_sympy__functions__elementary__miscellaneous__Max():
+    from sympy.functions.elementary.miscellaneous import Max
+    assert _test_args(Max(x, 2))
+
+
+def test_sympy__functions__elementary__miscellaneous__Min():
+    from sympy.functions.elementary.miscellaneous import Min
+    assert _test_args(Min(x, 2))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__miscellaneous__MinMaxBase():
+    pass
+
+
+def test_sympy__functions__elementary__miscellaneous__Rem():
+    from sympy.functions.elementary.miscellaneous import Rem
+    assert _test_args(Rem(x, 2))
+
+
+def test_sympy__functions__elementary__piecewise__ExprCondPair():
+    from sympy.functions.elementary.piecewise import ExprCondPair
+    assert _test_args(ExprCondPair(1, True))
+
+
+def test_sympy__functions__elementary__piecewise__Piecewise():
+    from sympy.functions.elementary.piecewise import Piecewise
+    assert _test_args(Piecewise((1, x >= 0), (0, True)))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__trigonometric__TrigonometricFunction():
+    pass
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__trigonometric__ReciprocalTrigonometricFunction():
+    pass
+
+@SKIP("abstract class")
+def test_sympy__functions__elementary__trigonometric__InverseTrigonometricFunction():
+    pass
+
+def test_sympy__functions__elementary__trigonometric__acos():
+    from sympy.functions.elementary.trigonometric import acos
+    assert _test_args(acos(2))
+
+
+def test_sympy__functions__elementary__trigonometric__acot():
+    from sympy.functions.elementary.trigonometric import acot
+    assert _test_args(acot(2))
+
+
+def test_sympy__functions__elementary__trigonometric__asin():
+    from sympy.functions.elementary.trigonometric import asin
+    assert _test_args(asin(2))
+
+
+def test_sympy__functions__elementary__trigonometric__asec():
+    from sympy.functions.elementary.trigonometric import asec
+    assert _test_args(asec(x))
+
+
+def test_sympy__functions__elementary__trigonometric__acsc():
+    from sympy.functions.elementary.trigonometric import acsc
+    assert _test_args(acsc(x))
+
+
+def test_sympy__functions__elementary__trigonometric__atan():
+    from sympy.functions.elementary.trigonometric import atan
+    assert _test_args(atan(2))
+
+
+def test_sympy__functions__elementary__trigonometric__atan2():
+    from sympy.functions.elementary.trigonometric import atan2
+    assert _test_args(atan2(2, 3))
+
+
+def test_sympy__functions__elementary__trigonometric__cos():
+    from sympy.functions.elementary.trigonometric import cos
+    assert _test_args(cos(2))
+
+
+def test_sympy__functions__elementary__trigonometric__csc():
+    from sympy.functions.elementary.trigonometric import csc
+    assert _test_args(csc(2))
+
+
+def test_sympy__functions__elementary__trigonometric__cot():
+    from sympy.functions.elementary.trigonometric import cot
+    assert _test_args(cot(2))
+
+
+def test_sympy__functions__elementary__trigonometric__sin():
+    assert _test_args(sin(2))
+
+
+def test_sympy__functions__elementary__trigonometric__sinc():
+    from sympy.functions.elementary.trigonometric import sinc
+    assert _test_args(sinc(2))
+
+
+def test_sympy__functions__elementary__trigonometric__sec():
+    from sympy.functions.elementary.trigonometric import sec
+    assert _test_args(sec(2))
+
+
+def test_sympy__functions__elementary__trigonometric__tan():
+    from sympy.functions.elementary.trigonometric import tan
+    assert _test_args(tan(2))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__bessel__BesselBase():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__bessel__SphericalBesselBase():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__bessel__SphericalHankelBase():
+    pass
+
+
+def test_sympy__functions__special__bessel__besseli():
+    from sympy.functions.special.bessel import besseli
+    assert _test_args(besseli(x, 1))
+
+
+def test_sympy__functions__special__bessel__besselj():
+    from sympy.functions.special.bessel import besselj
+    assert _test_args(besselj(x, 1))
+
+
+def test_sympy__functions__special__bessel__besselk():
+    from sympy.functions.special.bessel import besselk
+    assert _test_args(besselk(x, 1))
+
+
+def test_sympy__functions__special__bessel__bessely():
+    from sympy.functions.special.bessel import bessely
+    assert _test_args(bessely(x, 1))
+
+
+def test_sympy__functions__special__bessel__hankel1():
+    from sympy.functions.special.bessel import hankel1
+    assert _test_args(hankel1(x, 1))
+
+
+def test_sympy__functions__special__bessel__hankel2():
+    from sympy.functions.special.bessel import hankel2
+    assert _test_args(hankel2(x, 1))
+
+
+def test_sympy__functions__special__bessel__jn():
+    from sympy.functions.special.bessel import jn
+    assert _test_args(jn(0, x))
+
+
+def test_sympy__functions__special__bessel__yn():
+    from sympy.functions.special.bessel import yn
+    assert _test_args(yn(0, x))
+
+
+def test_sympy__functions__special__bessel__hn1():
+    from sympy.functions.special.bessel import hn1
+    assert _test_args(hn1(0, x))
+
+
+def test_sympy__functions__special__bessel__hn2():
+    from sympy.functions.special.bessel import hn2
+    assert _test_args(hn2(0, x))
+
+
+def test_sympy__functions__special__bessel__AiryBase():
+    pass
+
+
+def test_sympy__functions__special__bessel__airyai():
+    from sympy.functions.special.bessel import airyai
+    assert _test_args(airyai(2))
+
+
+def test_sympy__functions__special__bessel__airybi():
+    from sympy.functions.special.bessel import airybi
+    assert _test_args(airybi(2))
+
+
+def test_sympy__functions__special__bessel__airyaiprime():
+    from sympy.functions.special.bessel import airyaiprime
+    assert _test_args(airyaiprime(2))
+
+
+def test_sympy__functions__special__bessel__airybiprime():
+    from sympy.functions.special.bessel import airybiprime
+    assert _test_args(airybiprime(2))
+
+
+def test_sympy__functions__special__bessel__marcumq():
+    from sympy.functions.special.bessel import marcumq
+    assert _test_args(marcumq(x, y, z))
+
+
+def test_sympy__functions__special__elliptic_integrals__elliptic_k():
+    from sympy.functions.special.elliptic_integrals import elliptic_k as K
+    assert _test_args(K(x))
+
+
+def test_sympy__functions__special__elliptic_integrals__elliptic_f():
+    from sympy.functions.special.elliptic_integrals import elliptic_f as F
+    assert _test_args(F(x, y))
+
+
+def test_sympy__functions__special__elliptic_integrals__elliptic_e():
+    from sympy.functions.special.elliptic_integrals import elliptic_e as E
+    assert _test_args(E(x))
+    assert _test_args(E(x, y))
+
+
+def test_sympy__functions__special__elliptic_integrals__elliptic_pi():
+    from sympy.functions.special.elliptic_integrals import elliptic_pi as P
+    assert _test_args(P(x, y))
+    assert _test_args(P(x, y, z))
+
+
+def test_sympy__functions__special__delta_functions__DiracDelta():
+    from sympy.functions.special.delta_functions import DiracDelta
+    assert _test_args(DiracDelta(x, 1))
+
+
+def test_sympy__functions__special__singularity_functions__SingularityFunction():
+    from sympy.functions.special.singularity_functions import SingularityFunction
+    assert _test_args(SingularityFunction(x, y, z))
+
+
+def test_sympy__functions__special__delta_functions__Heaviside():
+    from sympy.functions.special.delta_functions import Heaviside
+    assert _test_args(Heaviside(x))
+
+
+def test_sympy__functions__special__error_functions__erf():
+    from sympy.functions.special.error_functions import erf
+    assert _test_args(erf(2))
+
+def test_sympy__functions__special__error_functions__erfc():
+    from sympy.functions.special.error_functions import erfc
+    assert _test_args(erfc(2))
+
+def test_sympy__functions__special__error_functions__erfi():
+    from sympy.functions.special.error_functions import erfi
+    assert _test_args(erfi(2))
+
+def test_sympy__functions__special__error_functions__erf2():
+    from sympy.functions.special.error_functions import erf2
+    assert _test_args(erf2(2, 3))
+
+def test_sympy__functions__special__error_functions__erfinv():
+    from sympy.functions.special.error_functions import erfinv
+    assert _test_args(erfinv(2))
+
+def test_sympy__functions__special__error_functions__erfcinv():
+    from sympy.functions.special.error_functions import erfcinv
+    assert _test_args(erfcinv(2))
+
+def test_sympy__functions__special__error_functions__erf2inv():
+    from sympy.functions.special.error_functions import erf2inv
+    assert _test_args(erf2inv(2, 3))
+
+@SKIP("abstract class")
+def test_sympy__functions__special__error_functions__FresnelIntegral():
+    pass
+
+
+def test_sympy__functions__special__error_functions__fresnels():
+    from sympy.functions.special.error_functions import fresnels
+    assert _test_args(fresnels(2))
+
+
+def test_sympy__functions__special__error_functions__fresnelc():
+    from sympy.functions.special.error_functions import fresnelc
+    assert _test_args(fresnelc(2))
+
+
+def test_sympy__functions__special__error_functions__erfs():
+    from sympy.functions.special.error_functions import _erfs
+    assert _test_args(_erfs(2))
+
+
+def test_sympy__functions__special__error_functions__Ei():
+    from sympy.functions.special.error_functions import Ei
+    assert _test_args(Ei(2))
+
+
+def test_sympy__functions__special__error_functions__li():
+    from sympy.functions.special.error_functions import li
+    assert _test_args(li(2))
+
+
+def test_sympy__functions__special__error_functions__Li():
+    from sympy.functions.special.error_functions import Li
+    assert _test_args(Li(5))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__error_functions__TrigonometricIntegral():
+    pass
+
+
+def test_sympy__functions__special__error_functions__Si():
+    from sympy.functions.special.error_functions import Si
+    assert _test_args(Si(2))
+
+
+def test_sympy__functions__special__error_functions__Ci():
+    from sympy.functions.special.error_functions import Ci
+    assert _test_args(Ci(2))
+
+
+def test_sympy__functions__special__error_functions__Shi():
+    from sympy.functions.special.error_functions import Shi
+    assert _test_args(Shi(2))
+
+
+def test_sympy__functions__special__error_functions__Chi():
+    from sympy.functions.special.error_functions import Chi
+    assert _test_args(Chi(2))
+
+
+def test_sympy__functions__special__error_functions__expint():
+    from sympy.functions.special.error_functions import expint
+    assert _test_args(expint(y, x))
+
+
+def test_sympy__functions__special__gamma_functions__gamma():
+    from sympy.functions.special.gamma_functions import gamma
+    assert _test_args(gamma(x))
+
+
+def test_sympy__functions__special__gamma_functions__loggamma():
+    from sympy.functions.special.gamma_functions import loggamma
+    assert _test_args(loggamma(x))
+
+
+def test_sympy__functions__special__gamma_functions__lowergamma():
+    from sympy.functions.special.gamma_functions import lowergamma
+    assert _test_args(lowergamma(x, 2))
+
+
+def test_sympy__functions__special__gamma_functions__polygamma():
+    from sympy.functions.special.gamma_functions import polygamma
+    assert _test_args(polygamma(x, 2))
+
+def test_sympy__functions__special__gamma_functions__digamma():
+    from sympy.functions.special.gamma_functions import digamma
+    assert _test_args(digamma(x))
+
+def test_sympy__functions__special__gamma_functions__trigamma():
+    from sympy.functions.special.gamma_functions import trigamma
+    assert _test_args(trigamma(x))
+
+def test_sympy__functions__special__gamma_functions__uppergamma():
+    from sympy.functions.special.gamma_functions import uppergamma
+    assert _test_args(uppergamma(x, 2))
+
+def test_sympy__functions__special__gamma_functions__multigamma():
+    from sympy.functions.special.gamma_functions import multigamma
+    assert _test_args(multigamma(x, 1))
+
+
+def test_sympy__functions__special__beta_functions__beta():
+    from sympy.functions.special.beta_functions import beta
+    assert _test_args(beta(x))
+    assert _test_args(beta(x, x))
+
+def test_sympy__functions__special__beta_functions__betainc():
+    from sympy.functions.special.beta_functions import betainc
+    assert _test_args(betainc(a, b, x, y))
+
+def test_sympy__functions__special__beta_functions__betainc_regularized():
+    from sympy.functions.special.beta_functions import betainc_regularized
+    assert _test_args(betainc_regularized(a, b, x, y))
+
+
+def test_sympy__functions__special__mathieu_functions__MathieuBase():
+    pass
+
+
+def test_sympy__functions__special__mathieu_functions__mathieus():
+    from sympy.functions.special.mathieu_functions import mathieus
+    assert _test_args(mathieus(1, 1, 1))
+
+
+def test_sympy__functions__special__mathieu_functions__mathieuc():
+    from sympy.functions.special.mathieu_functions import mathieuc
+    assert _test_args(mathieuc(1, 1, 1))
+
+
+def test_sympy__functions__special__mathieu_functions__mathieusprime():
+    from sympy.functions.special.mathieu_functions import mathieusprime
+    assert _test_args(mathieusprime(1, 1, 1))
+
+
+def test_sympy__functions__special__mathieu_functions__mathieucprime():
+    from sympy.functions.special.mathieu_functions import mathieucprime
+    assert _test_args(mathieucprime(1, 1, 1))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__hyper__TupleParametersBase():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__hyper__TupleArg():
+    pass
+
+
+def test_sympy__functions__special__hyper__hyper():
+    from sympy.functions.special.hyper import hyper
+    assert _test_args(hyper([1, 2, 3], [4, 5], x))
+
+
+def test_sympy__functions__special__hyper__meijerg():
+    from sympy.functions.special.hyper import meijerg
+    assert _test_args(meijerg([1, 2, 3], [4, 5], [6], [], x))
+
+
+@SKIP("abstract class")
+def test_sympy__functions__special__hyper__HyperRep():
+    pass
+
+
+def test_sympy__functions__special__hyper__HyperRep_power1():
+    from sympy.functions.special.hyper import HyperRep_power1
+    assert _test_args(HyperRep_power1(x, y))
+
+
+def test_sympy__functions__special__hyper__HyperRep_power2():
+    from sympy.functions.special.hyper import HyperRep_power2
+    assert _test_args(HyperRep_power2(x, y))
+
+
+def test_sympy__functions__special__hyper__HyperRep_log1():
+    from sympy.functions.special.hyper import HyperRep_log1
+    assert _test_args(HyperRep_log1(x))
+
+
+def test_sympy__functions__special__hyper__HyperRep_atanh():
+    from sympy.functions.special.hyper import HyperRep_atanh
+    assert _test_args(HyperRep_atanh(x))
+
+
+def test_sympy__functions__special__hyper__HyperRep_asin1():
+    from sympy.functions.special.hyper import HyperRep_asin1
+    assert _test_args(HyperRep_asin1(x))
+
+
+def test_sympy__functions__special__hyper__HyperRep_asin2():
+    from sympy.functions.special.hyper import HyperRep_asin2
+    assert _test_args(HyperRep_asin2(x))
+
+
+def test_sympy__functions__special__hyper__HyperRep_sqrts1():
+    from sympy.functions.special.hyper import HyperRep_sqrts1
+    assert _test_args(HyperRep_sqrts1(x, y))
+
+
+def test_sympy__functions__special__hyper__HyperRep_sqrts2():
+    from sympy.functions.special.hyper import HyperRep_sqrts2
+    assert _test_args(HyperRep_sqrts2(x, y))
+
+
+def test_sympy__functions__special__hyper__HyperRep_log2():
+    from sympy.functions.special.hyper import HyperRep_log2
+    assert _test_args(HyperRep_log2(x))
+
+
+def test_sympy__functions__special__hyper__HyperRep_cosasin():
+    from sympy.functions.special.hyper import HyperRep_cosasin
+    assert _test_args(HyperRep_cosasin(x, y))
+
+
+def test_sympy__functions__special__hyper__HyperRep_sinasin():
+    from sympy.functions.special.hyper import HyperRep_sinasin
+    assert _test_args(HyperRep_sinasin(x, y))
+
+def test_sympy__functions__special__hyper__appellf1():
+    from sympy.functions.special.hyper import appellf1
+    a, b1, b2, c, x, y = symbols('a b1 b2 c x y')
+    assert _test_args(appellf1(a, b1, b2, c, x, y))
+
+@SKIP("abstract class")
+def test_sympy__functions__special__polynomials__OrthogonalPolynomial():
+    pass
+
+
+def test_sympy__functions__special__polynomials__jacobi():
+    from sympy.functions.special.polynomials import jacobi
+    assert _test_args(jacobi(x, y, 2, 2))
+
+
+def test_sympy__functions__special__polynomials__gegenbauer():
+    from sympy.functions.special.polynomials import gegenbauer
+    assert _test_args(gegenbauer(x, 2, 2))
+
+
+def test_sympy__functions__special__polynomials__chebyshevt():
+    from sympy.functions.special.polynomials import chebyshevt
+    assert _test_args(chebyshevt(x, 2))
+
+
+def test_sympy__functions__special__polynomials__chebyshevt_root():
+    from sympy.functions.special.polynomials import chebyshevt_root
+    assert _test_args(chebyshevt_root(3, 2))
+
+
+def test_sympy__functions__special__polynomials__chebyshevu():
+    from sympy.functions.special.polynomials import chebyshevu
+    assert _test_args(chebyshevu(x, 2))
+
+
+def test_sympy__functions__special__polynomials__chebyshevu_root():
+    from sympy.functions.special.polynomials import chebyshevu_root
+    assert _test_args(chebyshevu_root(3, 2))
+
+
+def test_sympy__functions__special__polynomials__hermite():
+    from sympy.functions.special.polynomials import hermite
+    assert _test_args(hermite(x, 2))
+
+
+def test_sympy__functions__special__polynomials__hermite_prob():
+    from sympy.functions.special.polynomials import hermite_prob
+    assert _test_args(hermite_prob(x, 2))
+
+
+def test_sympy__functions__special__polynomials__legendre():
+    from sympy.functions.special.polynomials import legendre
+    assert _test_args(legendre(x, 2))
+
+
+def test_sympy__functions__special__polynomials__assoc_legendre():
+    from sympy.functions.special.polynomials import assoc_legendre
+    assert _test_args(assoc_legendre(x, 0, y))
+
+
+def test_sympy__functions__special__polynomials__laguerre():
+    from sympy.functions.special.polynomials import laguerre
+    assert _test_args(laguerre(x, 2))
+
+
+def test_sympy__functions__special__polynomials__assoc_laguerre():
+    from sympy.functions.special.polynomials import assoc_laguerre
+    assert _test_args(assoc_laguerre(x, 0, y))
+
+
+def test_sympy__functions__special__spherical_harmonics__Ynm():
+    from sympy.functions.special.spherical_harmonics import Ynm
+    assert _test_args(Ynm(1, 1, x, y))
+
+
+def test_sympy__functions__special__spherical_harmonics__Znm():
+    from sympy.functions.special.spherical_harmonics import Znm
+    assert _test_args(Znm(x, y, 1, 1))
+
+
+def test_sympy__functions__special__tensor_functions__LeviCivita():
+    from sympy.functions.special.tensor_functions import LeviCivita
+    assert _test_args(LeviCivita(x, y, 2))
+
+
+def test_sympy__functions__special__tensor_functions__KroneckerDelta():
+    from sympy.functions.special.tensor_functions import KroneckerDelta
+    assert _test_args(KroneckerDelta(x, y))
+
+
+def test_sympy__functions__special__zeta_functions__dirichlet_eta():
+    from sympy.functions.special.zeta_functions import dirichlet_eta
+    assert _test_args(dirichlet_eta(x))
+
+
+def test_sympy__functions__special__zeta_functions__riemann_xi():
+    from sympy.functions.special.zeta_functions import riemann_xi
+    assert _test_args(riemann_xi(x))
+
+
+def test_sympy__functions__special__zeta_functions__zeta():
+    from sympy.functions.special.zeta_functions import zeta
+    assert _test_args(zeta(101))
+
+
+def test_sympy__functions__special__zeta_functions__lerchphi():
+    from sympy.functions.special.zeta_functions import lerchphi
+    assert _test_args(lerchphi(x, y, z))
+
+
+def test_sympy__functions__special__zeta_functions__polylog():
+    from sympy.functions.special.zeta_functions import polylog
+    assert _test_args(polylog(x, y))
+
+
+def test_sympy__functions__special__zeta_functions__stieltjes():
+    from sympy.functions.special.zeta_functions import stieltjes
+    assert _test_args(stieltjes(x, y))
+
+
+def test_sympy__integrals__integrals__Integral():
+    from sympy.integrals.integrals import Integral
+    assert _test_args(Integral(2, (x, 0, 1)))
+
+
+def test_sympy__integrals__risch__NonElementaryIntegral():
+    from sympy.integrals.risch import NonElementaryIntegral
+    assert _test_args(NonElementaryIntegral(exp(-x**2), x))
+
+
+@SKIP("abstract class")
+def test_sympy__integrals__transforms__IntegralTransform():
+    pass
+
+
+def test_sympy__integrals__transforms__MellinTransform():
+    from sympy.integrals.transforms import MellinTransform
+    assert _test_args(MellinTransform(2, x, y))
+
+
+def test_sympy__integrals__transforms__InverseMellinTransform():
+    from sympy.integrals.transforms import InverseMellinTransform
+    assert _test_args(InverseMellinTransform(2, x, y, 0, 1))
+
+
+def test_sympy__integrals__laplace__LaplaceTransform():
+    from sympy.integrals.laplace import LaplaceTransform
+    assert _test_args(LaplaceTransform(2, x, y))
+
+
+def test_sympy__integrals__laplace__InverseLaplaceTransform():
+    from sympy.integrals.laplace import InverseLaplaceTransform
+    assert _test_args(InverseLaplaceTransform(2, x, y, 0))
+
+
+@SKIP("abstract class")
+def test_sympy__integrals__transforms__FourierTypeTransform():
+    pass
+
+
+def test_sympy__integrals__transforms__InverseFourierTransform():
+    from sympy.integrals.transforms import InverseFourierTransform
+    assert _test_args(InverseFourierTransform(2, x, y))
+
+
+def test_sympy__integrals__transforms__FourierTransform():
+    from sympy.integrals.transforms import FourierTransform
+    assert _test_args(FourierTransform(2, x, y))
+
+
+@SKIP("abstract class")
+def test_sympy__integrals__transforms__SineCosineTypeTransform():
+    pass
+
+
+def test_sympy__integrals__transforms__InverseSineTransform():
+    from sympy.integrals.transforms import InverseSineTransform
+    assert _test_args(InverseSineTransform(2, x, y))
+
+
+def test_sympy__integrals__transforms__SineTransform():
+    from sympy.integrals.transforms import SineTransform
+    assert _test_args(SineTransform(2, x, y))
+
+
+def test_sympy__integrals__transforms__InverseCosineTransform():
+    from sympy.integrals.transforms import InverseCosineTransform
+    assert _test_args(InverseCosineTransform(2, x, y))
+
+
+def test_sympy__integrals__transforms__CosineTransform():
+    from sympy.integrals.transforms import CosineTransform
+    assert _test_args(CosineTransform(2, x, y))
+
+
+@SKIP("abstract class")
+def test_sympy__integrals__transforms__HankelTypeTransform():
+    pass
+
+
+def test_sympy__integrals__transforms__InverseHankelTransform():
+    from sympy.integrals.transforms import InverseHankelTransform
+    assert _test_args(InverseHankelTransform(2, x, y, 0))
+
+
+def test_sympy__integrals__transforms__HankelTransform():
+    from sympy.integrals.transforms import HankelTransform
+    assert _test_args(HankelTransform(2, x, y, 0))
+
+
+def test_sympy__liealgebras__cartan_type__Standard_Cartan():
+    from sympy.liealgebras.cartan_type import Standard_Cartan
+    assert _test_args(Standard_Cartan("A", 2))
+
+def test_sympy__liealgebras__weyl_group__WeylGroup():
+    from sympy.liealgebras.weyl_group import WeylGroup
+    assert _test_args(WeylGroup("B4"))
+
+def test_sympy__liealgebras__root_system__RootSystem():
+    from sympy.liealgebras.root_system import RootSystem
+    assert _test_args(RootSystem("A2"))
+
+def test_sympy__liealgebras__type_a__TypeA():
+    from sympy.liealgebras.type_a import TypeA
+    assert _test_args(TypeA(2))
+
+def test_sympy__liealgebras__type_b__TypeB():
+    from sympy.liealgebras.type_b import TypeB
+    assert _test_args(TypeB(4))
+
+def test_sympy__liealgebras__type_c__TypeC():
+    from sympy.liealgebras.type_c import TypeC
+    assert _test_args(TypeC(4))
+
+def test_sympy__liealgebras__type_d__TypeD():
+    from sympy.liealgebras.type_d import TypeD
+    assert _test_args(TypeD(4))
+
+def test_sympy__liealgebras__type_e__TypeE():
+    from sympy.liealgebras.type_e import TypeE
+    assert _test_args(TypeE(6))
+
+def test_sympy__liealgebras__type_f__TypeF():
+    from sympy.liealgebras.type_f import TypeF
+    assert _test_args(TypeF(4))
+
+def test_sympy__liealgebras__type_g__TypeG():
+    from sympy.liealgebras.type_g import TypeG
+    assert _test_args(TypeG(2))
+
+
+def test_sympy__logic__boolalg__And():
+    from sympy.logic.boolalg import And
+    assert _test_args(And(x, y, 1))
+
+
+@SKIP("abstract class")
+def test_sympy__logic__boolalg__Boolean():
+    pass
+
+
+def test_sympy__logic__boolalg__BooleanFunction():
+    from sympy.logic.boolalg import BooleanFunction
+    assert _test_args(BooleanFunction(1, 2, 3))
+
+@SKIP("abstract class")
+def test_sympy__logic__boolalg__BooleanAtom():
+    pass
+
+def test_sympy__logic__boolalg__BooleanTrue():
+    from sympy.logic.boolalg import true
+    assert _test_args(true)
+
+def test_sympy__logic__boolalg__BooleanFalse():
+    from sympy.logic.boolalg import false
+    assert _test_args(false)
+
+def test_sympy__logic__boolalg__Equivalent():
+    from sympy.logic.boolalg import Equivalent
+    assert _test_args(Equivalent(x, 2))
+
+
+def test_sympy__logic__boolalg__ITE():
+    from sympy.logic.boolalg import ITE
+    assert _test_args(ITE(x, y, 1))
+
+
+def test_sympy__logic__boolalg__Implies():
+    from sympy.logic.boolalg import Implies
+    assert _test_args(Implies(x, y))
+
+
+def test_sympy__logic__boolalg__Nand():
+    from sympy.logic.boolalg import Nand
+    assert _test_args(Nand(x, y, 1))
+
+
+def test_sympy__logic__boolalg__Nor():
+    from sympy.logic.boolalg import Nor
+    assert _test_args(Nor(x, y))
+
+
+def test_sympy__logic__boolalg__Not():
+    from sympy.logic.boolalg import Not
+    assert _test_args(Not(x))
+
+
+def test_sympy__logic__boolalg__Or():
+    from sympy.logic.boolalg import Or
+    assert _test_args(Or(x, y))
+
+
+def test_sympy__logic__boolalg__Xor():
+    from sympy.logic.boolalg import Xor
+    assert _test_args(Xor(x, y, 2))
+
+def test_sympy__logic__boolalg__Xnor():
+    from sympy.logic.boolalg import Xnor
+    assert _test_args(Xnor(x, y, 2))
+
+def test_sympy__logic__boolalg__Exclusive():
+    from sympy.logic.boolalg import Exclusive
+    assert _test_args(Exclusive(x, y, z))
+
+
+def test_sympy__matrices__matrixbase__DeferredVector():
+    from sympy.matrices.matrixbase import DeferredVector
+    assert _test_args(DeferredVector("X"))
+
+
+@SKIP("abstract class")
+def test_sympy__matrices__expressions__matexpr__MatrixBase():
+    pass
+
+
+@SKIP("abstract class")
+def test_sympy__matrices__immutable__ImmutableRepMatrix():
+    pass
+
+
+def test_sympy__matrices__immutable__ImmutableDenseMatrix():
+    from sympy.matrices.immutable import ImmutableDenseMatrix
+    m = ImmutableDenseMatrix([[1, 2], [3, 4]])
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+    m = ImmutableDenseMatrix(1, 1, [1])
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+    m = ImmutableDenseMatrix(2, 2, lambda i, j: 1)
+    assert m[0, 0] is S.One
+    m = ImmutableDenseMatrix(2, 2, lambda i, j: 1/(1 + i) + 1/(1 + j))
+    assert m[1, 1] is S.One  # true div. will give 1.0 if i,j not sympified
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+
+
+def test_sympy__matrices__immutable__ImmutableSparseMatrix():
+    from sympy.matrices.immutable import ImmutableSparseMatrix
+    m = ImmutableSparseMatrix([[1, 2], [3, 4]])
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+    m = ImmutableSparseMatrix(1, 1, {(0, 0): 1})
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+    m = ImmutableSparseMatrix(1, 1, [1])
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+    m = ImmutableSparseMatrix(2, 2, lambda i, j: 1)
+    assert m[0, 0] is S.One
+    m = ImmutableSparseMatrix(2, 2, lambda i, j: 1/(1 + i) + 1/(1 + j))
+    assert m[1, 1] is S.One  # true div. will give 1.0 if i,j not sympified
+    assert _test_args(m)
+    assert _test_args(Basic(*list(m)))
+
+
+def test_sympy__matrices__expressions__slice__MatrixSlice():
+    from sympy.matrices.expressions.slice import MatrixSlice
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', 4, 4)
+    assert _test_args(MatrixSlice(X, (0, 2), (0, 2)))
+
+
+def test_sympy__matrices__expressions__applyfunc__ElementwiseApplyFunction():
+    from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol("X", x, x)
+    func = Lambda(x, x**2)
+    assert _test_args(ElementwiseApplyFunction(func, X))
+
+
+def test_sympy__matrices__expressions__blockmatrix__BlockDiagMatrix():
+    from sympy.matrices.expressions.blockmatrix import BlockDiagMatrix
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, x)
+    Y = MatrixSymbol('Y', y, y)
+    assert _test_args(BlockDiagMatrix(X, Y))
+
+
+def test_sympy__matrices__expressions__blockmatrix__BlockMatrix():
+    from sympy.matrices.expressions.blockmatrix import BlockMatrix
+    from sympy.matrices.expressions import MatrixSymbol, ZeroMatrix
+    X = MatrixSymbol('X', x, x)
+    Y = MatrixSymbol('Y', y, y)
+    Z = MatrixSymbol('Z', x, y)
+    O = ZeroMatrix(y, x)
+    assert _test_args(BlockMatrix([[X, Z], [O, Y]]))
+
+
+def test_sympy__matrices__expressions__inverse__Inverse():
+    from sympy.matrices.expressions.inverse import Inverse
+    from sympy.matrices.expressions import MatrixSymbol
+    assert _test_args(Inverse(MatrixSymbol('A', 3, 3)))
+
+
+def test_sympy__matrices__expressions__matadd__MatAdd():
+    from sympy.matrices.expressions.matadd import MatAdd
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, y)
+    Y = MatrixSymbol('Y', x, y)
+    assert _test_args(MatAdd(X, Y))
+
+
+@SKIP("abstract class")
+def test_sympy__matrices__expressions__matexpr__MatrixExpr():
+    pass
+
+def test_sympy__matrices__expressions__matexpr__MatrixElement():
+    from sympy.matrices.expressions.matexpr import MatrixSymbol, MatrixElement
+    from sympy.core.singleton import S
+    assert _test_args(MatrixElement(MatrixSymbol('A', 3, 5), S(2), S(3)))
+
+def test_sympy__matrices__expressions__matexpr__MatrixSymbol():
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    assert _test_args(MatrixSymbol('A', 3, 5))
+
+
+def test_sympy__matrices__expressions__special__OneMatrix():
+    from sympy.matrices.expressions.special import OneMatrix
+    assert _test_args(OneMatrix(3, 5))
+
+
+def test_sympy__matrices__expressions__special__ZeroMatrix():
+    from sympy.matrices.expressions.special import ZeroMatrix
+    assert _test_args(ZeroMatrix(3, 5))
+
+
+def test_sympy__matrices__expressions__special__GenericZeroMatrix():
+    from sympy.matrices.expressions.special import GenericZeroMatrix
+    assert _test_args(GenericZeroMatrix())
+
+
+def test_sympy__matrices__expressions__special__Identity():
+    from sympy.matrices.expressions.special import Identity
+    assert _test_args(Identity(3))
+
+
+def test_sympy__matrices__expressions__special__GenericIdentity():
+    from sympy.matrices.expressions.special import GenericIdentity
+    assert _test_args(GenericIdentity())
+
+
+def test_sympy__matrices__expressions__sets__MatrixSet():
+    from sympy.matrices.expressions.sets import MatrixSet
+    from sympy.core.singleton import S
+    assert _test_args(MatrixSet(2, 2, S.Reals))
+
+def test_sympy__matrices__expressions__matmul__MatMul():
+    from sympy.matrices.expressions.matmul import MatMul
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, y)
+    Y = MatrixSymbol('Y', y, x)
+    assert _test_args(MatMul(X, Y))
+
+
+def test_sympy__matrices__expressions__dotproduct__DotProduct():
+    from sympy.matrices.expressions.dotproduct import DotProduct
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, 1)
+    Y = MatrixSymbol('Y', x, 1)
+    assert _test_args(DotProduct(X, Y))
+
+def test_sympy__matrices__expressions__diagonal__DiagonalMatrix():
+    from sympy.matrices.expressions.diagonal import DiagonalMatrix
+    from sympy.matrices.expressions import MatrixSymbol
+    x = MatrixSymbol('x', 10, 1)
+    assert _test_args(DiagonalMatrix(x))
+
+def test_sympy__matrices__expressions__diagonal__DiagonalOf():
+    from sympy.matrices.expressions.diagonal import DiagonalOf
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('x', 10, 10)
+    assert _test_args(DiagonalOf(X))
+
+def test_sympy__matrices__expressions__diagonal__DiagMatrix():
+    from sympy.matrices.expressions.diagonal import DiagMatrix
+    from sympy.matrices.expressions import MatrixSymbol
+    x = MatrixSymbol('x', 10, 1)
+    assert _test_args(DiagMatrix(x))
+
+def test_sympy__matrices__expressions__hadamard__HadamardProduct():
+    from sympy.matrices.expressions.hadamard import HadamardProduct
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, y)
+    Y = MatrixSymbol('Y', x, y)
+    assert _test_args(HadamardProduct(X, Y))
+
+def test_sympy__matrices__expressions__hadamard__HadamardPower():
+    from sympy.matrices.expressions.hadamard import HadamardPower
+    from sympy.matrices.expressions import MatrixSymbol
+    from sympy.core.symbol import Symbol
+    X = MatrixSymbol('X', x, y)
+    n = Symbol("n")
+    assert _test_args(HadamardPower(X, n))
+
+def test_sympy__matrices__expressions__kronecker__KroneckerProduct():
+    from sympy.matrices.expressions.kronecker import KroneckerProduct
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, y)
+    Y = MatrixSymbol('Y', x, y)
+    assert _test_args(KroneckerProduct(X, Y))
+
+
+def test_sympy__matrices__expressions__matpow__MatPow():
+    from sympy.matrices.expressions.matpow import MatPow
+    from sympy.matrices.expressions import MatrixSymbol
+    X = MatrixSymbol('X', x, x)
+    assert _test_args(MatPow(X, 2))
+
+
+def test_sympy__matrices__expressions__transpose__Transpose():
+    from sympy.matrices.expressions.transpose import Transpose
+    from sympy.matrices.expressions import MatrixSymbol
+    assert _test_args(Transpose(MatrixSymbol('A', 3, 5)))
+
+
+def test_sympy__matrices__expressions__adjoint__Adjoint():
+    from sympy.matrices.expressions.adjoint import Adjoint
+    from sympy.matrices.expressions import MatrixSymbol
+    assert _test_args(Adjoint(MatrixSymbol('A', 3, 5)))
+
+
+def test_sympy__matrices__expressions__trace__Trace():
+    from sympy.matrices.expressions.trace import Trace
+    from sympy.matrices.expressions import MatrixSymbol
+    assert _test_args(Trace(MatrixSymbol('A', 3, 3)))
+
+def test_sympy__matrices__expressions__determinant__Determinant():
+    from sympy.matrices.expressions.determinant import Determinant
+    from sympy.matrices.expressions import MatrixSymbol
+    assert _test_args(Determinant(MatrixSymbol('A', 3, 3)))
+
+def test_sympy__matrices__expressions__determinant__Permanent():
+    from sympy.matrices.expressions.determinant import Permanent
+    from sympy.matrices.expressions import MatrixSymbol
+    assert _test_args(Permanent(MatrixSymbol('A', 3, 4)))
+
+def test_sympy__matrices__expressions__funcmatrix__FunctionMatrix():
+    from sympy.matrices.expressions.funcmatrix import FunctionMatrix
+    from sympy.core.symbol import symbols
+    i, j = symbols('i,j')
+    assert _test_args(FunctionMatrix(3, 3, Lambda((i, j), i - j) ))
+
+def test_sympy__matrices__expressions__fourier__DFT():
+    from sympy.matrices.expressions.fourier import DFT
+    from sympy.core.singleton import S
+    assert _test_args(DFT(S(2)))
+
+def test_sympy__matrices__expressions__fourier__IDFT():
+    from sympy.matrices.expressions.fourier import IDFT
+    from sympy.core.singleton import S
+    assert _test_args(IDFT(S(2)))
+
+from sympy.matrices.expressions import MatrixSymbol
+X = MatrixSymbol('X', 10, 10)
+
+def test_sympy__matrices__expressions__factorizations__LofLU():
+    from sympy.matrices.expressions.factorizations import LofLU
+    assert _test_args(LofLU(X))
+
+def test_sympy__matrices__expressions__factorizations__UofLU():
+    from sympy.matrices.expressions.factorizations import UofLU
+    assert _test_args(UofLU(X))
+
+def test_sympy__matrices__expressions__factorizations__QofQR():
+    from sympy.matrices.expressions.factorizations import QofQR
+    assert _test_args(QofQR(X))
+
+def test_sympy__matrices__expressions__factorizations__RofQR():
+    from sympy.matrices.expressions.factorizations import RofQR
+    assert _test_args(RofQR(X))
+
+def test_sympy__matrices__expressions__factorizations__LofCholesky():
+    from sympy.matrices.expressions.factorizations import LofCholesky
+    assert _test_args(LofCholesky(X))
+
+def test_sympy__matrices__expressions__factorizations__UofCholesky():
+    from sympy.matrices.expressions.factorizations import UofCholesky
+    assert _test_args(UofCholesky(X))
+
+def test_sympy__matrices__expressions__factorizations__EigenVectors():
+    from sympy.matrices.expressions.factorizations import EigenVectors
+    assert _test_args(EigenVectors(X))
+
+def test_sympy__matrices__expressions__factorizations__EigenValues():
+    from sympy.matrices.expressions.factorizations import EigenValues
+    assert _test_args(EigenValues(X))
+
+def test_sympy__matrices__expressions__factorizations__UofSVD():
+    from sympy.matrices.expressions.factorizations import UofSVD
+    assert _test_args(UofSVD(X))
+
+def test_sympy__matrices__expressions__factorizations__VofSVD():
+    from sympy.matrices.expressions.factorizations import VofSVD
+    assert _test_args(VofSVD(X))
+
+def test_sympy__matrices__expressions__factorizations__SofSVD():
+    from sympy.matrices.expressions.factorizations import SofSVD
+    assert _test_args(SofSVD(X))
+
+@SKIP("abstract class")
+def test_sympy__matrices__expressions__factorizations__Factorization():
+    pass
+
+def test_sympy__matrices__expressions__permutation__PermutationMatrix():
+    from sympy.combinatorics import Permutation
+    from sympy.matrices.expressions.permutation import PermutationMatrix
+    assert _test_args(PermutationMatrix(Permutation([2, 0, 1])))
+
+def test_sympy__matrices__expressions__permutation__MatrixPermute():
+    from sympy.combinatorics import Permutation
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    from sympy.matrices.expressions.permutation import MatrixPermute
+    A = MatrixSymbol('A', 3, 3)
+    assert _test_args(MatrixPermute(A, Permutation([2, 0, 1])))
+
+def test_sympy__matrices__expressions__companion__CompanionMatrix():
+    from sympy.core.symbol import Symbol
+    from sympy.matrices.expressions.companion import CompanionMatrix
+    from sympy.polys.polytools import Poly
+
+    x = Symbol('x')
+    p = Poly([1, 2, 3], x)
+    assert _test_args(CompanionMatrix(p))
+
+def test_sympy__physics__vector__frame__CoordinateSym():
+    from sympy.physics.vector import CoordinateSym
+    from sympy.physics.vector import ReferenceFrame
+    assert _test_args(CoordinateSym('R_x', ReferenceFrame('R'), 0))
+
+
+@SKIP("abstract class")
+def test_sympy__physics__biomechanics__curve__CharacteristicCurveFunction():
+    pass
+
+
+def test_sympy__physics__biomechanics__curve__TendonForceLengthDeGroote2016():
+    from sympy.physics.biomechanics import TendonForceLengthDeGroote2016
+    l_T_tilde, c0, c1, c2, c3 = symbols('l_T_tilde, c0, c1, c2, c3')
+    assert _test_args(TendonForceLengthDeGroote2016(l_T_tilde, c0, c1, c2, c3))
+
+
+def test_sympy__physics__biomechanics__curve__TendonForceLengthInverseDeGroote2016():
+    from sympy.physics.biomechanics import TendonForceLengthInverseDeGroote2016
+    fl_T, c0, c1, c2, c3 = symbols('fl_T, c0, c1, c2, c3')
+    assert _test_args(TendonForceLengthInverseDeGroote2016(fl_T, c0, c1, c2, c3))
+
+
+def test_sympy__physics__biomechanics__curve__FiberForceLengthPassiveDeGroote2016():
+    from sympy.physics.biomechanics import FiberForceLengthPassiveDeGroote2016
+    l_M_tilde, c0, c1 = symbols('l_M_tilde, c0, c1')
+    assert _test_args(FiberForceLengthPassiveDeGroote2016(l_M_tilde, c0, c1))
+
+
+def test_sympy__physics__biomechanics__curve__FiberForceLengthPassiveInverseDeGroote2016():
+    from sympy.physics.biomechanics import FiberForceLengthPassiveInverseDeGroote2016
+    fl_M_pas, c0, c1 = symbols('fl_M_pas, c0, c1')
+    assert _test_args(FiberForceLengthPassiveInverseDeGroote2016(fl_M_pas, c0, c1))
+
+
+def test_sympy__physics__biomechanics__curve__FiberForceLengthActiveDeGroote2016():
+    from sympy.physics.biomechanics import FiberForceLengthActiveDeGroote2016
+    l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11 = symbols('l_M_tilde, c0:12')
+    assert _test_args(FiberForceLengthActiveDeGroote2016(l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11))
+
+
+def test_sympy__physics__biomechanics__curve__FiberForceVelocityDeGroote2016():
+    from sympy.physics.biomechanics import FiberForceVelocityDeGroote2016
+    v_M_tilde, c0, c1, c2, c3 = symbols('v_M_tilde, c0, c1, c2, c3')
+    assert _test_args(FiberForceVelocityDeGroote2016(v_M_tilde, c0, c1, c2, c3))
+
+
+def test_sympy__physics__biomechanics__curve__FiberForceVelocityInverseDeGroote2016():
+    from sympy.physics.biomechanics import FiberForceVelocityInverseDeGroote2016
+    fv_M, c0, c1, c2, c3 = symbols('fv_M, c0, c1, c2, c3')
+    assert _test_args(FiberForceVelocityInverseDeGroote2016(fv_M, c0, c1, c2, c3))
+
+
+def test_sympy__physics__paulialgebra__Pauli():
+    from sympy.physics.paulialgebra import Pauli
+    assert _test_args(Pauli(1))
+
+
+def test_sympy__physics__quantum__anticommutator__AntiCommutator():
+    from sympy.physics.quantum.anticommutator import AntiCommutator
+    assert _test_args(AntiCommutator(x, y))
+
+
+def test_sympy__physics__quantum__cartesian__PositionBra3D():
+    from sympy.physics.quantum.cartesian import PositionBra3D
+    assert _test_args(PositionBra3D(x, y, z))
+
+
+def test_sympy__physics__quantum__cartesian__PositionKet3D():
+    from sympy.physics.quantum.cartesian import PositionKet3D
+    assert _test_args(PositionKet3D(x, y, z))
+
+
+def test_sympy__physics__quantum__cartesian__PositionState3D():
+    from sympy.physics.quantum.cartesian import PositionState3D
+    assert _test_args(PositionState3D(x, y, z))
+
+
+def test_sympy__physics__quantum__cartesian__PxBra():
+    from sympy.physics.quantum.cartesian import PxBra
+    assert _test_args(PxBra(x, y, z))
+
+
+def test_sympy__physics__quantum__cartesian__PxKet():
+    from sympy.physics.quantum.cartesian import PxKet
+    assert _test_args(PxKet(x, y, z))
+
+
+def test_sympy__physics__quantum__cartesian__PxOp():
+    from sympy.physics.quantum.cartesian import PxOp
+    assert _test_args(PxOp(x, y, z))
+
+
+def test_sympy__physics__quantum__cartesian__XBra():
+    from sympy.physics.quantum.cartesian import XBra
+    assert _test_args(XBra(x))
+
+
+def test_sympy__physics__quantum__cartesian__XKet():
+    from sympy.physics.quantum.cartesian import XKet
+    assert _test_args(XKet(x))
+
+
+def test_sympy__physics__quantum__cartesian__XOp():
+    from sympy.physics.quantum.cartesian import XOp
+    assert _test_args(XOp(x))
+
+
+def test_sympy__physics__quantum__cartesian__YOp():
+    from sympy.physics.quantum.cartesian import YOp
+    assert _test_args(YOp(x))
+
+
+def test_sympy__physics__quantum__cartesian__ZOp():
+    from sympy.physics.quantum.cartesian import ZOp
+    assert _test_args(ZOp(x))
+
+
+def test_sympy__physics__quantum__cg__CG():
+    from sympy.physics.quantum.cg import CG
+    from sympy.core.singleton import S
+    assert _test_args(CG(Rational(3, 2), Rational(3, 2), S.Half, Rational(-1, 2), 1, 1))
+
+
+def test_sympy__physics__quantum__cg__Wigner3j():
+    from sympy.physics.quantum.cg import Wigner3j
+    assert _test_args(Wigner3j(6, 0, 4, 0, 2, 0))
+
+
+def test_sympy__physics__quantum__cg__Wigner6j():
+    from sympy.physics.quantum.cg import Wigner6j
+    assert _test_args(Wigner6j(1, 2, 3, 2, 1, 2))
+
+
+def test_sympy__physics__quantum__cg__Wigner9j():
+    from sympy.physics.quantum.cg import Wigner9j
+    assert _test_args(Wigner9j(2, 1, 1, Rational(3, 2), S.Half, 1, S.Half, S.Half, 0))
+
+def test_sympy__physics__quantum__circuitplot__Mz():
+    from sympy.physics.quantum.circuitplot import Mz
+    assert _test_args(Mz(0))
+
+def test_sympy__physics__quantum__circuitplot__Mx():
+    from sympy.physics.quantum.circuitplot import Mx
+    assert _test_args(Mx(0))
+
+def test_sympy__physics__quantum__commutator__Commutator():
+    from sympy.physics.quantum.commutator import Commutator
+    A, B = symbols('A,B', commutative=False)
+    assert _test_args(Commutator(A, B))
+
+
+def test_sympy__physics__quantum__constants__HBar():
+    from sympy.physics.quantum.constants import HBar
+    assert _test_args(HBar())
+
+
+def test_sympy__physics__quantum__dagger__Dagger():
+    from sympy.physics.quantum.dagger import Dagger
+    from sympy.physics.quantum.state import Ket
+    assert _test_args(Dagger(Dagger(Ket('psi'))))
+
+
+def test_sympy__physics__quantum__gate__CGate():
+    from sympy.physics.quantum.gate import CGate, Gate
+    assert _test_args(CGate((0, 1), Gate(2)))
+
+
+def test_sympy__physics__quantum__gate__CGateS():
+    from sympy.physics.quantum.gate import CGateS, Gate
+    assert _test_args(CGateS((0, 1), Gate(2)))
+
+
+def test_sympy__physics__quantum__gate__CNotGate():
+    from sympy.physics.quantum.gate import CNotGate
+    assert _test_args(CNotGate(0, 1))
+
+
+def test_sympy__physics__quantum__gate__Gate():
+    from sympy.physics.quantum.gate import Gate
+    assert _test_args(Gate(0))
+
+
+def test_sympy__physics__quantum__gate__HadamardGate():
+    from sympy.physics.quantum.gate import HadamardGate
+    assert _test_args(HadamardGate(0))
+
+
+def test_sympy__physics__quantum__gate__IdentityGate():
+    from sympy.physics.quantum.gate import IdentityGate
+    assert _test_args(IdentityGate(0))
+
+
+def test_sympy__physics__quantum__gate__OneQubitGate():
+    from sympy.physics.quantum.gate import OneQubitGate
+    assert _test_args(OneQubitGate(0))
+
+
+def test_sympy__physics__quantum__gate__PhaseGate():
+    from sympy.physics.quantum.gate import PhaseGate
+    assert _test_args(PhaseGate(0))
+
+
+def test_sympy__physics__quantum__gate__SwapGate():
+    from sympy.physics.quantum.gate import SwapGate
+    assert _test_args(SwapGate(0, 1))
+
+
+def test_sympy__physics__quantum__gate__TGate():
+    from sympy.physics.quantum.gate import TGate
+    assert _test_args(TGate(0))
+
+
+def test_sympy__physics__quantum__gate__TwoQubitGate():
+    from sympy.physics.quantum.gate import TwoQubitGate
+    assert _test_args(TwoQubitGate(0))
+
+
+def test_sympy__physics__quantum__gate__UGate():
+    from sympy.physics.quantum.gate import UGate
+    from sympy.matrices.immutable import ImmutableDenseMatrix
+    from sympy.core.containers import Tuple
+    from sympy.core.numbers import Integer
+    assert _test_args(
+        UGate(Tuple(Integer(1)), ImmutableDenseMatrix([[1, 0], [0, 2]])))
+
+
+def test_sympy__physics__quantum__gate__XGate():
+    from sympy.physics.quantum.gate import XGate
+    assert _test_args(XGate(0))
+
+
+def test_sympy__physics__quantum__gate__YGate():
+    from sympy.physics.quantum.gate import YGate
+    assert _test_args(YGate(0))
+
+
+def test_sympy__physics__quantum__gate__ZGate():
+    from sympy.physics.quantum.gate import ZGate
+    assert _test_args(ZGate(0))
+
+
+def test_sympy__physics__quantum__grover__OracleGateFunction():
+    from sympy.physics.quantum.grover import OracleGateFunction
+    @OracleGateFunction
+    def f(qubit):
+        return
+    assert _test_args(f)
+
+def test_sympy__physics__quantum__grover__OracleGate():
+    from sympy.physics.quantum.grover import OracleGate
+    def f(qubit):
+        return
+    assert _test_args(OracleGate(1,f))
+
+
+def test_sympy__physics__quantum__grover__WGate():
+    from sympy.physics.quantum.grover import WGate
+    assert _test_args(WGate(1))
+
+
+def test_sympy__physics__quantum__hilbert__ComplexSpace():
+    from sympy.physics.quantum.hilbert import ComplexSpace
+    assert _test_args(ComplexSpace(x))
+
+
+def test_sympy__physics__quantum__hilbert__DirectSumHilbertSpace():
+    from sympy.physics.quantum.hilbert import DirectSumHilbertSpace, ComplexSpace, FockSpace
+    c = ComplexSpace(2)
+    f = FockSpace()
+    assert _test_args(DirectSumHilbertSpace(c, f))
+
+
+def test_sympy__physics__quantum__hilbert__FockSpace():
+    from sympy.physics.quantum.hilbert import FockSpace
+    assert _test_args(FockSpace())
+
+
+def test_sympy__physics__quantum__hilbert__HilbertSpace():
+    from sympy.physics.quantum.hilbert import HilbertSpace
+    assert _test_args(HilbertSpace())
+
+
+def test_sympy__physics__quantum__hilbert__L2():
+    from sympy.physics.quantum.hilbert import L2
+    from sympy.core.numbers import oo
+    from sympy.sets.sets import Interval
+    assert _test_args(L2(Interval(0, oo)))
+
+
+def test_sympy__physics__quantum__hilbert__TensorPowerHilbertSpace():
+    from sympy.physics.quantum.hilbert import TensorPowerHilbertSpace, FockSpace
+    f = FockSpace()
+    assert _test_args(TensorPowerHilbertSpace(f, 2))
+
+
+def test_sympy__physics__quantum__hilbert__TensorProductHilbertSpace():
+    from sympy.physics.quantum.hilbert import TensorProductHilbertSpace, FockSpace, ComplexSpace
+    c = ComplexSpace(2)
+    f = FockSpace()
+    assert _test_args(TensorProductHilbertSpace(f, c))
+
+
+def test_sympy__physics__quantum__innerproduct__InnerProduct():
+    from sympy.physics.quantum import Bra, Ket, InnerProduct
+    b = Bra('b')
+    k = Ket('k')
+    assert _test_args(InnerProduct(b, k))
+
+
+def test_sympy__physics__quantum__operator__DifferentialOperator():
+    from sympy.physics.quantum.operator import DifferentialOperator
+    from sympy.core.function import (Derivative, Function)
+    f = Function('f')
+    assert _test_args(DifferentialOperator(1/x*Derivative(f(x), x), f(x)))
+
+
+def test_sympy__physics__quantum__operator__HermitianOperator():
+    from sympy.physics.quantum.operator import HermitianOperator
+    assert _test_args(HermitianOperator('H'))
+
+
+def test_sympy__physics__quantum__operator__IdentityOperator():
+    with warns_deprecated_sympy():
+        from sympy.physics.quantum.operator import IdentityOperator
+        assert _test_args(IdentityOperator(5))
+
+
+def test_sympy__physics__quantum__operator__Operator():
+    from sympy.physics.quantum.operator import Operator
+    assert _test_args(Operator('A'))
+
+
+def test_sympy__physics__quantum__operator__OuterProduct():
+    from sympy.physics.quantum.operator import OuterProduct
+    from sympy.physics.quantum import Ket, Bra
+    b = Bra('b')
+    k = Ket('k')
+    assert _test_args(OuterProduct(k, b))
+
+
+def test_sympy__physics__quantum__operator__UnitaryOperator():
+    from sympy.physics.quantum.operator import UnitaryOperator
+    assert _test_args(UnitaryOperator('U'))
+
+
+def test_sympy__physics__quantum__piab__PIABBra():
+    from sympy.physics.quantum.piab import PIABBra
+    assert _test_args(PIABBra('B'))
+
+
+def test_sympy__physics__quantum__boson__BosonOp():
+    from sympy.physics.quantum.boson import BosonOp
+    assert _test_args(BosonOp('a'))
+    assert _test_args(BosonOp('a', False))
+
+
+def test_sympy__physics__quantum__boson__BosonFockKet():
+    from sympy.physics.quantum.boson import BosonFockKet
+    assert _test_args(BosonFockKet(1))
+
+
+def test_sympy__physics__quantum__boson__BosonFockBra():
+    from sympy.physics.quantum.boson import BosonFockBra
+    assert _test_args(BosonFockBra(1))
+
+
+def test_sympy__physics__quantum__boson__BosonCoherentKet():
+    from sympy.physics.quantum.boson import BosonCoherentKet
+    assert _test_args(BosonCoherentKet(1))
+
+
+def test_sympy__physics__quantum__boson__BosonCoherentBra():
+    from sympy.physics.quantum.boson import BosonCoherentBra
+    assert _test_args(BosonCoherentBra(1))
+
+
+def test_sympy__physics__quantum__fermion__FermionOp():
+    from sympy.physics.quantum.fermion import FermionOp
+    assert _test_args(FermionOp('c'))
+    assert _test_args(FermionOp('c', False))
+
+
+def test_sympy__physics__quantum__fermion__FermionFockKet():
+    from sympy.physics.quantum.fermion import FermionFockKet
+    assert _test_args(FermionFockKet(1))
+
+
+def test_sympy__physics__quantum__fermion__FermionFockBra():
+    from sympy.physics.quantum.fermion import FermionFockBra
+    assert _test_args(FermionFockBra(1))
+
+
+def test_sympy__physics__quantum__pauli__SigmaOpBase():
+    from sympy.physics.quantum.pauli import SigmaOpBase
+    assert _test_args(SigmaOpBase())
+
+
+def test_sympy__physics__quantum__pauli__SigmaX():
+    from sympy.physics.quantum.pauli import SigmaX
+    assert _test_args(SigmaX())
+
+
+def test_sympy__physics__quantum__pauli__SigmaY():
+    from sympy.physics.quantum.pauli import SigmaY
+    assert _test_args(SigmaY())
+
+
+def test_sympy__physics__quantum__pauli__SigmaZ():
+    from sympy.physics.quantum.pauli import SigmaZ
+    assert _test_args(SigmaZ())
+
+
+def test_sympy__physics__quantum__pauli__SigmaMinus():
+    from sympy.physics.quantum.pauli import SigmaMinus
+    assert _test_args(SigmaMinus())
+
+
+def test_sympy__physics__quantum__pauli__SigmaPlus():
+    from sympy.physics.quantum.pauli import SigmaPlus
+    assert _test_args(SigmaPlus())
+
+
+def test_sympy__physics__quantum__pauli__SigmaZKet():
+    from sympy.physics.quantum.pauli import SigmaZKet
+    assert _test_args(SigmaZKet(0))
+
+
+def test_sympy__physics__quantum__pauli__SigmaZBra():
+    from sympy.physics.quantum.pauli import SigmaZBra
+    assert _test_args(SigmaZBra(0))
+
+
+def test_sympy__physics__quantum__piab__PIABHamiltonian():
+    from sympy.physics.quantum.piab import PIABHamiltonian
+    assert _test_args(PIABHamiltonian('P'))
+
+
+def test_sympy__physics__quantum__piab__PIABKet():
+    from sympy.physics.quantum.piab import PIABKet
+    assert _test_args(PIABKet('K'))
+
+
+def test_sympy__physics__quantum__qexpr__QExpr():
+    from sympy.physics.quantum.qexpr import QExpr
+    assert _test_args(QExpr(0))
+
+
+def test_sympy__physics__quantum__qft__Fourier():
+    from sympy.physics.quantum.qft import Fourier
+    assert _test_args(Fourier(0, 1))
+
+
+def test_sympy__physics__quantum__qft__IQFT():
+    from sympy.physics.quantum.qft import IQFT
+    assert _test_args(IQFT(0, 1))
+
+
+def test_sympy__physics__quantum__qft__QFT():
+    from sympy.physics.quantum.qft import QFT
+    assert _test_args(QFT(0, 1))
+
+
+def test_sympy__physics__quantum__qft__RkGate():
+    from sympy.physics.quantum.qft import RkGate
+    assert _test_args(RkGate(0, 1))
+
+
+def test_sympy__physics__quantum__qubit__IntQubit():
+    from sympy.physics.quantum.qubit import IntQubit
+    assert _test_args(IntQubit(0))
+
+
+def test_sympy__physics__quantum__qubit__IntQubitBra():
+    from sympy.physics.quantum.qubit import IntQubitBra
+    assert _test_args(IntQubitBra(0))
+
+
+def test_sympy__physics__quantum__qubit__IntQubitState():
+    from sympy.physics.quantum.qubit import IntQubitState, QubitState
+    assert _test_args(IntQubitState(QubitState(0, 1)))
+
+
+def test_sympy__physics__quantum__qubit__Qubit():
+    from sympy.physics.quantum.qubit import Qubit
+    assert _test_args(Qubit(0, 0, 0))
+
+
+def test_sympy__physics__quantum__qubit__QubitBra():
+    from sympy.physics.quantum.qubit import QubitBra
+    assert _test_args(QubitBra('1', 0))
+
+
+def test_sympy__physics__quantum__qubit__QubitState():
+    from sympy.physics.quantum.qubit import QubitState
+    assert _test_args(QubitState(0, 1))
+
+
+def test_sympy__physics__quantum__density__Density():
+    from sympy.physics.quantum.density import Density
+    from sympy.physics.quantum.state import Ket
+    assert _test_args(Density([Ket(0), 0.5], [Ket(1), 0.5]))
+
+
+@SKIP("TODO: sympy.physics.quantum.shor: Cmod Not Implemented")
+def test_sympy__physics__quantum__shor__CMod():
+    from sympy.physics.quantum.shor import CMod
+    assert _test_args(CMod())
+
+
+def test_sympy__physics__quantum__spin__CoupledSpinState():
+    from sympy.physics.quantum.spin import CoupledSpinState
+    assert _test_args(CoupledSpinState(1, 0, (1, 1)))
+    assert _test_args(CoupledSpinState(1, 0, (1, S.Half, S.Half)))
+    assert _test_args(CoupledSpinState(
+        1, 0, (1, S.Half, S.Half), ((2, 3, S.Half), (1, 2, 1)) ))
+    j, m, j1, j2, j3, j12, x = symbols('j m j1:4 j12 x')
+    assert CoupledSpinState(
+        j, m, (j1, j2, j3)).subs(j2, x) == CoupledSpinState(j, m, (j1, x, j3))
+    assert CoupledSpinState(j, m, (j1, j2, j3), ((1, 3, j12), (1, 2, j)) ).subs(j12, x) == \
+        CoupledSpinState(j, m, (j1, j2, j3), ((1, 3, x), (1, 2, j)) )
+
+
+def test_sympy__physics__quantum__spin__J2Op():
+    from sympy.physics.quantum.spin import J2Op
+    assert _test_args(J2Op('J'))
+
+
+def test_sympy__physics__quantum__spin__JminusOp():
+    from sympy.physics.quantum.spin import JminusOp
+    assert _test_args(JminusOp('J'))
+
+
+def test_sympy__physics__quantum__spin__JplusOp():
+    from sympy.physics.quantum.spin import JplusOp
+    assert _test_args(JplusOp('J'))
+
+
+def test_sympy__physics__quantum__spin__JxBra():
+    from sympy.physics.quantum.spin import JxBra
+    assert _test_args(JxBra(1, 0))
+
+
+def test_sympy__physics__quantum__spin__JxBraCoupled():
+    from sympy.physics.quantum.spin import JxBraCoupled
+    assert _test_args(JxBraCoupled(1, 0, (1, 1)))
+
+
+def test_sympy__physics__quantum__spin__JxKet():
+    from sympy.physics.quantum.spin import JxKet
+    assert _test_args(JxKet(1, 0))
+
+
+def test_sympy__physics__quantum__spin__JxKetCoupled():
+    from sympy.physics.quantum.spin import JxKetCoupled
+    assert _test_args(JxKetCoupled(1, 0, (1, 1)))
+
+
+def test_sympy__physics__quantum__spin__JxOp():
+    from sympy.physics.quantum.spin import JxOp
+    assert _test_args(JxOp('J'))
+
+
+def test_sympy__physics__quantum__spin__JyBra():
+    from sympy.physics.quantum.spin import JyBra
+    assert _test_args(JyBra(1, 0))
+
+
+def test_sympy__physics__quantum__spin__JyBraCoupled():
+    from sympy.physics.quantum.spin import JyBraCoupled
+    assert _test_args(JyBraCoupled(1, 0, (1, 1)))
+
+
+def test_sympy__physics__quantum__spin__JyKet():
+    from sympy.physics.quantum.spin import JyKet
+    assert _test_args(JyKet(1, 0))
+
+
+def test_sympy__physics__quantum__spin__JyKetCoupled():
+    from sympy.physics.quantum.spin import JyKetCoupled
+    assert _test_args(JyKetCoupled(1, 0, (1, 1)))
+
+
+def test_sympy__physics__quantum__spin__JyOp():
+    from sympy.physics.quantum.spin import JyOp
+    assert _test_args(JyOp('J'))
+
+
+def test_sympy__physics__quantum__spin__JzBra():
+    from sympy.physics.quantum.spin import JzBra
+    assert _test_args(JzBra(1, 0))
+
+
+def test_sympy__physics__quantum__spin__JzBraCoupled():
+    from sympy.physics.quantum.spin import JzBraCoupled
+    assert _test_args(JzBraCoupled(1, 0, (1, 1)))
+
+
+def test_sympy__physics__quantum__spin__JzKet():
+    from sympy.physics.quantum.spin import JzKet
+    assert _test_args(JzKet(1, 0))
+
+
+def test_sympy__physics__quantum__spin__JzKetCoupled():
+    from sympy.physics.quantum.spin import JzKetCoupled
+    assert _test_args(JzKetCoupled(1, 0, (1, 1)))
+
+
+def test_sympy__physics__quantum__spin__JzOp():
+    from sympy.physics.quantum.spin import JzOp
+    assert _test_args(JzOp('J'))
+
+
+def test_sympy__physics__quantum__spin__Rotation():
+    from sympy.physics.quantum.spin import Rotation
+    assert _test_args(Rotation(pi, 0, pi/2))
+
+
+def test_sympy__physics__quantum__spin__SpinState():
+    from sympy.physics.quantum.spin import SpinState
+    assert _test_args(SpinState(1, 0))
+
+
+def test_sympy__physics__quantum__spin__WignerD():
+    from sympy.physics.quantum.spin import WignerD
+    assert _test_args(WignerD(0, 1, 2, 3, 4, 5))
+
+
+def test_sympy__physics__quantum__state__Bra():
+    from sympy.physics.quantum.state import Bra
+    assert _test_args(Bra(0))
+
+
+def test_sympy__physics__quantum__state__BraBase():
+    from sympy.physics.quantum.state import BraBase
+    assert _test_args(BraBase(0))
+
+
+def test_sympy__physics__quantum__state__Ket():
+    from sympy.physics.quantum.state import Ket
+    assert _test_args(Ket(0))
+
+
+def test_sympy__physics__quantum__state__KetBase():
+    from sympy.physics.quantum.state import KetBase
+    assert _test_args(KetBase(0))
+
+
+def test_sympy__physics__quantum__state__State():
+    from sympy.physics.quantum.state import State
+    assert _test_args(State(0))
+
+
+def test_sympy__physics__quantum__state__StateBase():
+    from sympy.physics.quantum.state import StateBase
+    assert _test_args(StateBase(0))
+
+
+def test_sympy__physics__quantum__state__OrthogonalBra():
+    from sympy.physics.quantum.state import OrthogonalBra
+    assert _test_args(OrthogonalBra(0))
+
+
+def test_sympy__physics__quantum__state__OrthogonalKet():
+    from sympy.physics.quantum.state import OrthogonalKet
+    assert _test_args(OrthogonalKet(0))
+
+
+def test_sympy__physics__quantum__state__OrthogonalState():
+    from sympy.physics.quantum.state import OrthogonalState
+    assert _test_args(OrthogonalState(0))
+
+
+def test_sympy__physics__quantum__state__TimeDepBra():
+    from sympy.physics.quantum.state import TimeDepBra
+    assert _test_args(TimeDepBra('psi', 't'))
+
+
+def test_sympy__physics__quantum__state__TimeDepKet():
+    from sympy.physics.quantum.state import TimeDepKet
+    assert _test_args(TimeDepKet('psi', 't'))
+
+
+def test_sympy__physics__quantum__state__TimeDepState():
+    from sympy.physics.quantum.state import TimeDepState
+    assert _test_args(TimeDepState('psi', 't'))
+
+
+def test_sympy__physics__quantum__state__Wavefunction():
+    from sympy.physics.quantum.state import Wavefunction
+    from sympy.functions import sin
+    from sympy.functions.elementary.piecewise import Piecewise
+    n = 1
+    L = 1
+    g = Piecewise((0, x < 0), (0, x > L), (sqrt(2//L)*sin(n*pi*x/L), True))
+    assert _test_args(Wavefunction(g, x))
+
+
+def test_sympy__physics__quantum__tensorproduct__TensorProduct():
+    from sympy.physics.quantum.tensorproduct import TensorProduct
+    x, y = symbols("x y", commutative=False)
+    assert _test_args(TensorProduct(x, y))
+
+
+def test_sympy__physics__quantum__identitysearch__GateIdentity():
+    from sympy.physics.quantum.gate import X
+    from sympy.physics.quantum.identitysearch import GateIdentity
+    assert _test_args(GateIdentity(X(0), X(0)))
+
+
+def test_sympy__physics__quantum__sho1d__SHOOp():
+    from sympy.physics.quantum.sho1d import SHOOp
+    assert _test_args(SHOOp('a'))
+
+
+def test_sympy__physics__quantum__sho1d__RaisingOp():
+    from sympy.physics.quantum.sho1d import RaisingOp
+    assert _test_args(RaisingOp('a'))
+
+
+def test_sympy__physics__quantum__sho1d__LoweringOp():
+    from sympy.physics.quantum.sho1d import LoweringOp
+    assert _test_args(LoweringOp('a'))
+
+
+def test_sympy__physics__quantum__sho1d__NumberOp():
+    from sympy.physics.quantum.sho1d import NumberOp
+    assert _test_args(NumberOp('N'))
+
+
+def test_sympy__physics__quantum__sho1d__Hamiltonian():
+    from sympy.physics.quantum.sho1d import Hamiltonian
+    assert _test_args(Hamiltonian('H'))
+
+
+def test_sympy__physics__quantum__sho1d__SHOState():
+    from sympy.physics.quantum.sho1d import SHOState
+    assert _test_args(SHOState(0))
+
+
+def test_sympy__physics__quantum__sho1d__SHOKet():
+    from sympy.physics.quantum.sho1d import SHOKet
+    assert _test_args(SHOKet(0))
+
+
+def test_sympy__physics__quantum__sho1d__SHOBra():
+    from sympy.physics.quantum.sho1d import SHOBra
+    assert _test_args(SHOBra(0))
+
+
+def test_sympy__physics__secondquant__AnnihilateBoson():
+    from sympy.physics.secondquant import AnnihilateBoson
+    assert _test_args(AnnihilateBoson(0))
+
+
+def test_sympy__physics__secondquant__AnnihilateFermion():
+    from sympy.physics.secondquant import AnnihilateFermion
+    assert _test_args(AnnihilateFermion(0))
+
+
+@SKIP("abstract class")
+def test_sympy__physics__secondquant__Annihilator():
+    pass
+
+
+def test_sympy__physics__secondquant__AntiSymmetricTensor():
+    from sympy.physics.secondquant import AntiSymmetricTensor
+    i, j = symbols('i j', below_fermi=True)
+    a, b = symbols('a b', above_fermi=True)
+    assert _test_args(AntiSymmetricTensor('v', (a, i), (b, j)))
+
+
+def test_sympy__physics__secondquant__BosonState():
+    from sympy.physics.secondquant import BosonState
+    assert _test_args(BosonState((0, 1)))
+
+
+@SKIP("abstract class")
+def test_sympy__physics__secondquant__BosonicOperator():
+    pass
+
+
+def test_sympy__physics__secondquant__Commutator():
+    from sympy.physics.secondquant import Commutator
+    x, y = symbols('x y', commutative=False)
+    assert _test_args(Commutator(x, y))
+
+
+def test_sympy__physics__secondquant__CreateBoson():
+    from sympy.physics.secondquant import CreateBoson
+    assert _test_args(CreateBoson(0))
+
+
+def test_sympy__physics__secondquant__CreateFermion():
+    from sympy.physics.secondquant import CreateFermion
+    assert _test_args(CreateFermion(0))
+
+
+@SKIP("abstract class")
+def test_sympy__physics__secondquant__Creator():
+    pass
+
+
+def test_sympy__physics__secondquant__Dagger():
+    from sympy.physics.secondquant import Dagger
+    assert _test_args(Dagger(x))
+
+
+def test_sympy__physics__secondquant__FermionState():
+    from sympy.physics.secondquant import FermionState
+    assert _test_args(FermionState((0, 1)))
+
+
+def test_sympy__physics__secondquant__FermionicOperator():
+    from sympy.physics.secondquant import FermionicOperator
+    assert _test_args(FermionicOperator(0))
+
+
+def test_sympy__physics__secondquant__FockState():
+    from sympy.physics.secondquant import FockState
+    assert _test_args(FockState((0, 1)))
+
+
+def test_sympy__physics__secondquant__FockStateBosonBra():
+    from sympy.physics.secondquant import FockStateBosonBra
+    assert _test_args(FockStateBosonBra((0, 1)))
+
+
+def test_sympy__physics__secondquant__FockStateBosonKet():
+    from sympy.physics.secondquant import FockStateBosonKet
+    assert _test_args(FockStateBosonKet((0, 1)))
+
+
+def test_sympy__physics__secondquant__FockStateBra():
+    from sympy.physics.secondquant import FockStateBra
+    assert _test_args(FockStateBra((0, 1)))
+
+
+def test_sympy__physics__secondquant__FockStateFermionBra():
+    from sympy.physics.secondquant import FockStateFermionBra
+    assert _test_args(FockStateFermionBra((0, 1)))
+
+
+def test_sympy__physics__secondquant__FockStateFermionKet():
+    from sympy.physics.secondquant import FockStateFermionKet
+    assert _test_args(FockStateFermionKet((0, 1)))
+
+
+def test_sympy__physics__secondquant__FockStateKet():
+    from sympy.physics.secondquant import FockStateKet
+    assert _test_args(FockStateKet((0, 1)))
+
+
+def test_sympy__physics__secondquant__InnerProduct():
+    from sympy.physics.secondquant import InnerProduct
+    from sympy.physics.secondquant import FockStateKet, FockStateBra
+    assert _test_args(InnerProduct(FockStateBra((0, 1)), FockStateKet((0, 1))))
+
+
+def test_sympy__physics__secondquant__NO():
+    from sympy.physics.secondquant import NO, F, Fd
+    assert _test_args(NO(Fd(x)*F(y)))
+
+
+def test_sympy__physics__secondquant__PermutationOperator():
+    from sympy.physics.secondquant import PermutationOperator
+    assert _test_args(PermutationOperator(0, 1))
+
+
+def test_sympy__physics__secondquant__SqOperator():
+    from sympy.physics.secondquant import SqOperator
+    assert _test_args(SqOperator(0))
+
+
+def test_sympy__physics__secondquant__TensorSymbol():
+    from sympy.physics.secondquant import TensorSymbol
+    assert _test_args(TensorSymbol(x))
+
+
+def test_sympy__physics__control__lti__LinearTimeInvariant():
+    # Direct instances of LinearTimeInvariant class are not allowed.
+    # func(*args) tests for its derived classes (TransferFunction,
+    # Series, Parallel and TransferFunctionMatrix) should pass.
+    pass
+
+
+def test_sympy__physics__control__lti__SISOLinearTimeInvariant():
+    # Direct instances of SISOLinearTimeInvariant class are not allowed.
+    pass
+
+
+def test_sympy__physics__control__lti__MIMOLinearTimeInvariant():
+    # Direct instances of MIMOLinearTimeInvariant class are not allowed.
+    pass
+
+
+def test_sympy__physics__control__lti__TransferFunction():
+    from sympy.physics.control.lti import TransferFunction
+    assert _test_args(TransferFunction(2, 3, x))
+
+
+def _test_args_PIDController(obj):
+    from sympy.physics.control.lti import PIDController
+    if isinstance(obj, PIDController):
+        kp, ki, kd, tf = obj.kp, obj.ki, obj.kd, obj.tf
+        recreated_pid = PIDController(kp, ki, kd, tf, s)
+        return recreated_pid == obj
+    return False
+
+
+def test_sympy__physics__control__lti__PIDController():
+    from sympy.physics.control.lti import PIDController
+    kp, ki, kd, tf = 1, 0.1, 0.01, 0
+    assert _test_args_PIDController(PIDController(kp, ki, kd, tf, s))
+
+
+def test_sympy__physics__control__lti__Series():
+    from sympy.physics.control import Series, TransferFunction
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    assert _test_args(Series(tf1, tf2))
+
+
+def test_sympy__physics__control__lti__MIMOSeries():
+    from sympy.physics.control import MIMOSeries, TransferFunction, TransferFunctionMatrix
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    tfm_1 = TransferFunctionMatrix([[tf2, tf1]])
+    tfm_2 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+    tfm_3 = TransferFunctionMatrix([[tf1], [tf2]])
+    assert _test_args(MIMOSeries(tfm_3, tfm_2, tfm_1))
+
+
+def test_sympy__physics__control__lti__Parallel():
+    from sympy.physics.control import Parallel, TransferFunction
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    assert _test_args(Parallel(tf1, tf2))
+
+
+def test_sympy__physics__control__lti__MIMOParallel():
+    from sympy.physics.control import MIMOParallel, TransferFunction, TransferFunctionMatrix
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+    tfm_2 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf2]])
+    assert _test_args(MIMOParallel(tfm_1, tfm_2))
+
+
+def test_sympy__physics__control__lti__Feedback():
+    from sympy.physics.control import TransferFunction, Feedback
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    assert _test_args(Feedback(tf1, tf2))
+    assert _test_args(Feedback(tf1, tf2, 1))
+
+
+def test_sympy__physics__control__lti__MIMOFeedback():
+    from sympy.physics.control import TransferFunction, MIMOFeedback, TransferFunctionMatrix
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    tfm_1 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf2]])
+    tfm_2 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+    assert _test_args(MIMOFeedback(tfm_1, tfm_2))
+    assert _test_args(MIMOFeedback(tfm_1, tfm_2, 1))
+
+
+def test_sympy__physics__control__lti__TransferFunctionMatrix():
+    from sympy.physics.control import TransferFunction, TransferFunctionMatrix
+    tf1 = TransferFunction(x**2 - y**3, y - z, x)
+    tf2 = TransferFunction(y - x, z + y, x)
+    assert _test_args(TransferFunctionMatrix([[tf1, tf2]]))
+
+
+def test_sympy__physics__control__lti__StateSpace():
+    from sympy.matrices.dense import Matrix
+    from sympy.physics.control import StateSpace
+    A = Matrix([[-5, -1], [3, -1]])
+    B = Matrix([2, 5])
+    C = Matrix([[1, 2]])
+    D = Matrix([0])
+    assert _test_args(StateSpace(A, B, C, D))
+
+
+def test_sympy__physics__units__dimensions__Dimension():
+    from sympy.physics.units.dimensions import Dimension
+    assert _test_args(Dimension("length", "L"))
+
+
+def test_sympy__physics__units__dimensions__DimensionSystem():
+    from sympy.physics.units.dimensions import DimensionSystem
+    from sympy.physics.units.definitions.dimension_definitions import length, time, velocity
+    assert _test_args(DimensionSystem((length, time), (velocity,)))
+
+
+def test_sympy__physics__units__quantities__Quantity():
+    from sympy.physics.units.quantities import Quantity
+    assert _test_args(Quantity("dam"))
+
+
+def test_sympy__physics__units__quantities__PhysicalConstant():
+    from sympy.physics.units.quantities import PhysicalConstant
+    assert _test_args(PhysicalConstant("foo"))
+
+
+def test_sympy__physics__units__prefixes__Prefix():
+    from sympy.physics.units.prefixes import Prefix
+    assert _test_args(Prefix('kilo', 'k', 3))
+
+
+def test_sympy__core__numbers__AlgebraicNumber():
+    from sympy.core.numbers import AlgebraicNumber
+    assert _test_args(AlgebraicNumber(sqrt(2), [1, 2, 3]))
+
+
+def test_sympy__polys__polytools__GroebnerBasis():
+    from sympy.polys.polytools import GroebnerBasis
+    assert _test_args(GroebnerBasis([x, y, z], x, y, z))
+
+
+def test_sympy__polys__polytools__Poly():
+    from sympy.polys.polytools import Poly
+    assert _test_args(Poly(2, x, y))
+
+
+def test_sympy__polys__polytools__PurePoly():
+    from sympy.polys.polytools import PurePoly
+    assert _test_args(PurePoly(2, x, y))
+
+
+@SKIP('abstract class')
+def test_sympy__polys__rootoftools__RootOf():
+    pass
+
+
+def test_sympy__polys__rootoftools__ComplexRootOf():
+    from sympy.polys.rootoftools import ComplexRootOf
+    assert _test_args(ComplexRootOf(x**3 + x + 1, 0))
+
+
+def test_sympy__polys__rootoftools__RootSum():
+    from sympy.polys.rootoftools import RootSum
+    assert _test_args(RootSum(x**3 + x + 1, sin))
+
+
+def test_sympy__series__limits__Limit():
+    from sympy.series.limits import Limit
+    assert _test_args(Limit(x, x, 0, dir='-'))
+
+
+def test_sympy__series__order__Order():
+    from sympy.series.order import Order
+    assert _test_args(Order(1, x, y))
+
+
+@SKIP('Abstract Class')
+def test_sympy__series__sequences__SeqBase():
+    pass
+
+
+def test_sympy__series__sequences__EmptySequence():
+    # Need to import the instance from series not the class from
+    # series.sequence
+    from sympy.series import EmptySequence
+    assert _test_args(EmptySequence)
+
+
+@SKIP('Abstract Class')
+def test_sympy__series__sequences__SeqExpr():
+    pass
+
+
+def test_sympy__series__sequences__SeqPer():
+    from sympy.series.sequences import SeqPer
+    assert _test_args(SeqPer((1, 2, 3), (0, 10)))
+
+
+def test_sympy__series__sequences__SeqFormula():
+    from sympy.series.sequences import SeqFormula
+    assert _test_args(SeqFormula(x**2, (0, 10)))
+
+
+def test_sympy__series__sequences__RecursiveSeq():
+    from sympy.series.sequences import RecursiveSeq
+    y = Function("y")
+    n = symbols("n")
+    assert _test_args(RecursiveSeq(y(n - 1) + y(n - 2), y(n), n, (0, 1)))
+    assert _test_args(RecursiveSeq(y(n - 1) + y(n - 2), y(n), n))
+
+
+def test_sympy__series__sequences__SeqExprOp():
+    from sympy.series.sequences import SeqExprOp, sequence
+    s1 = sequence((1, 2, 3))
+    s2 = sequence(x**2)
+    assert _test_args(SeqExprOp(s1, s2))
+
+
+def test_sympy__series__sequences__SeqAdd():
+    from sympy.series.sequences import SeqAdd, sequence
+    s1 = sequence((1, 2, 3))
+    s2 = sequence(x**2)
+    assert _test_args(SeqAdd(s1, s2))
+
+
+def test_sympy__series__sequences__SeqMul():
+    from sympy.series.sequences import SeqMul, sequence
+    s1 = sequence((1, 2, 3))
+    s2 = sequence(x**2)
+    assert _test_args(SeqMul(s1, s2))
+
+
+@SKIP('Abstract Class')
+def test_sympy__series__series_class__SeriesBase():
+    pass
+
+
+def test_sympy__series__fourier__FourierSeries():
+    from sympy.series.fourier import fourier_series
+    assert _test_args(fourier_series(x, (x, -pi, pi)))
+
+def test_sympy__series__fourier__FiniteFourierSeries():
+    from sympy.series.fourier import fourier_series
+    assert _test_args(fourier_series(sin(pi*x), (x, -1, 1)))
+
+
+def test_sympy__series__formal__FormalPowerSeries():
+    from sympy.series.formal import fps
+    assert _test_args(fps(log(1 + x), x))
+
+
+def test_sympy__series__formal__Coeff():
+    from sympy.series.formal import fps
+    assert _test_args(fps(x**2 + x + 1, x))
+
+
+@SKIP('Abstract Class')
+def test_sympy__series__formal__FiniteFormalPowerSeries():
+    pass
+
+
+def test_sympy__series__formal__FormalPowerSeriesProduct():
+    from sympy.series.formal import fps
+    f1, f2 = fps(sin(x)), fps(exp(x))
+    assert _test_args(f1.product(f2, x))
+
+
+def test_sympy__series__formal__FormalPowerSeriesCompose():
+    from sympy.series.formal import fps
+    f1, f2 = fps(exp(x)), fps(sin(x))
+    assert _test_args(f1.compose(f2, x))
+
+
+def test_sympy__series__formal__FormalPowerSeriesInverse():
+    from sympy.series.formal import fps
+    f1 = fps(exp(x))
+    assert _test_args(f1.inverse(x))
+
+
+def test_sympy__simplify__hyperexpand__Hyper_Function():
+    from sympy.simplify.hyperexpand import Hyper_Function
+    assert _test_args(Hyper_Function([2], [1]))
+
+
+def test_sympy__simplify__hyperexpand__G_Function():
+    from sympy.simplify.hyperexpand import G_Function
+    assert _test_args(G_Function([2], [1], [], []))
+
+
+@SKIP("abstract class")
+def test_sympy__tensor__array__ndim_array__ImmutableNDimArray():
+    pass
+
+
+def test_sympy__tensor__array__dense_ndim_array__ImmutableDenseNDimArray():
+    from sympy.tensor.array.dense_ndim_array import ImmutableDenseNDimArray
+    densarr = ImmutableDenseNDimArray(range(10, 34), (2, 3, 4))
+    assert _test_args(densarr)
+
+
+def test_sympy__tensor__array__sparse_ndim_array__ImmutableSparseNDimArray():
+    from sympy.tensor.array.sparse_ndim_array import ImmutableSparseNDimArray
+    sparr = ImmutableSparseNDimArray(range(10, 34), (2, 3, 4))
+    assert _test_args(sparr)
+
+
+def test_sympy__tensor__array__array_comprehension__ArrayComprehension():
+    from sympy.tensor.array.array_comprehension import ArrayComprehension
+    arrcom = ArrayComprehension(x, (x, 1, 5))
+    assert _test_args(arrcom)
+
+def test_sympy__tensor__array__array_comprehension__ArrayComprehensionMap():
+    from sympy.tensor.array.array_comprehension import ArrayComprehensionMap
+    arrcomma = ArrayComprehensionMap(lambda: 0, (x, 1, 5))
+    assert _test_args(arrcomma)
+
+
+def test_sympy__tensor__array__array_derivatives__ArrayDerivative():
+    from sympy.tensor.array.array_derivatives import ArrayDerivative
+    A = MatrixSymbol("A", 2, 2)
+    arrder = ArrayDerivative(A, A, evaluate=False)
+    assert _test_args(arrder)
+
+def test_sympy__tensor__array__expressions__array_expressions__ArraySymbol():
+    from sympy.tensor.array.expressions.array_expressions import ArraySymbol
+    m, n, k = symbols("m n k")
+    array = ArraySymbol("A", (m, n, k, 2))
+    assert _test_args(array)
+
+def test_sympy__tensor__array__expressions__array_expressions__ArrayElement():
+    from sympy.tensor.array.expressions.array_expressions import ArrayElement
+    m, n, k = symbols("m n k")
+    ae = ArrayElement("A", (m, n, k, 2))
+    assert _test_args(ae)
+
+def test_sympy__tensor__array__expressions__array_expressions__ZeroArray():
+    from sympy.tensor.array.expressions.array_expressions import ZeroArray
+    m, n, k = symbols("m n k")
+    za = ZeroArray(m, n, k, 2)
+    assert _test_args(za)
+
+def test_sympy__tensor__array__expressions__array_expressions__OneArray():
+    from sympy.tensor.array.expressions.array_expressions import OneArray
+    m, n, k = symbols("m n k")
+    za = OneArray(m, n, k, 2)
+    assert _test_args(za)
+
+def test_sympy__tensor__functions__TensorProduct():
+    from sympy.tensor.functions import TensorProduct
+    A = MatrixSymbol('A', 3, 3)
+    B = MatrixSymbol('B', 3, 3)
+    tp = TensorProduct(A, B)
+    assert _test_args(tp)
+
+
+def test_sympy__tensor__indexed__Idx():
+    from sympy.tensor.indexed import Idx
+    assert _test_args(Idx('test'))
+    assert _test_args(Idx('test', (0, 10)))
+    assert _test_args(Idx('test', 2))
+    assert _test_args(Idx('test', x))
+
+
+def test_sympy__tensor__indexed__Indexed():
+    from sympy.tensor.indexed import Indexed, Idx
+    assert _test_args(Indexed('A', Idx('i'), Idx('j')))
+
+
+def test_sympy__tensor__indexed__IndexedBase():
+    from sympy.tensor.indexed import IndexedBase
+    assert _test_args(IndexedBase('A', shape=(x, y)))
+    assert _test_args(IndexedBase('A', 1))
+    assert _test_args(IndexedBase('A')[0, 1])
+
+
+def test_sympy__tensor__tensor__TensorIndexType():
+    from sympy.tensor.tensor import TensorIndexType
+    assert _test_args(TensorIndexType('Lorentz'))
+
+
+@SKIP("deprecated class")
+def test_sympy__tensor__tensor__TensorType():
+    pass
+
+
+def test_sympy__tensor__tensor__TensorSymmetry():
+    from sympy.tensor.tensor import TensorSymmetry, get_symmetric_group_sgs
+    assert _test_args(TensorSymmetry(get_symmetric_group_sgs(2)))
+
+
+def test_sympy__tensor__tensor__TensorHead():
+    from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, TensorHead
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    sym = TensorSymmetry(get_symmetric_group_sgs(1))
+    assert _test_args(TensorHead('p', [Lorentz], sym, 0))
+
+
+def test_sympy__tensor__tensor__TensorIndex():
+    from sympy.tensor.tensor import TensorIndexType, TensorIndex
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    assert _test_args(TensorIndex('i', Lorentz))
+
+@SKIP("abstract class")
+def test_sympy__tensor__tensor__TensExpr():
+    pass
+
+def test_sympy__tensor__tensor__TensAdd():
+    from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, tensor_indices, TensAdd, tensor_heads
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    a, b = tensor_indices('a,b', Lorentz)
+    sym = TensorSymmetry(get_symmetric_group_sgs(1))
+    p, q = tensor_heads('p,q', [Lorentz], sym)
+    t1 = p(a)
+    t2 = q(a)
+    assert _test_args(TensAdd(t1, t2))
+
+
+def test_sympy__tensor__tensor__Tensor():
+    from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, tensor_indices, TensorHead
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    a, b = tensor_indices('a,b', Lorentz)
+    sym = TensorSymmetry(get_symmetric_group_sgs(1))
+    p = TensorHead('p', [Lorentz], sym)
+    assert _test_args(p(a))
+
+
+def test_sympy__tensor__tensor__TensMul():
+    from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, tensor_indices, tensor_heads
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    a, b = tensor_indices('a,b', Lorentz)
+    sym = TensorSymmetry(get_symmetric_group_sgs(1))
+    p, q = tensor_heads('p, q', [Lorentz], sym)
+    assert _test_args(3*p(a)*q(b))
+
+
+def test_sympy__tensor__tensor__TensorElement():
+    from sympy.tensor.tensor import TensorIndexType, TensorHead, TensorElement
+    L = TensorIndexType("L")
+    A = TensorHead("A", [L, L])
+    telem = TensorElement(A(x, y), {x: 1})
+    assert _test_args(telem)
+
+def test_sympy__tensor__tensor__WildTensor():
+    from sympy.tensor.tensor import TensorIndexType, WildTensorHead, TensorIndex
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    a = TensorIndex('a', Lorentz)
+    p = WildTensorHead('p')
+    assert _test_args(p(a))
+
+def test_sympy__tensor__tensor__WildTensorHead():
+    from sympy.tensor.tensor import WildTensorHead
+    assert _test_args(WildTensorHead('p'))
+
+def test_sympy__tensor__tensor__WildTensorIndex():
+    from sympy.tensor.tensor import TensorIndexType, WildTensorIndex
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    assert _test_args(WildTensorIndex('i', Lorentz))
+
+def test_sympy__tensor__toperators__PartialDerivative():
+    from sympy.tensor.tensor import TensorIndexType, tensor_indices, TensorHead
+    from sympy.tensor.toperators import PartialDerivative
+    Lorentz = TensorIndexType('Lorentz', dummy_name='L')
+    a, b = tensor_indices('a,b', Lorentz)
+    A = TensorHead("A", [Lorentz])
+    assert _test_args(PartialDerivative(A(a), A(b)))
+
+
+def test_as_coeff_add():
+    assert (7, (3*x, 4*x**2)) == (7 + 3*x + 4*x**2).as_coeff_add()
+
+
+def test_sympy__geometry__curve__Curve():
+    from sympy.geometry.curve import Curve
+    assert _test_args(Curve((x, 1), (x, 0, 1)))
+
+
+def test_sympy__geometry__point__Point():
+    from sympy.geometry.point import Point
+    assert _test_args(Point(0, 1))
+
+
+def test_sympy__geometry__point__Point2D():
+    from sympy.geometry.point import Point2D
+    assert _test_args(Point2D(0, 1))
+
+
+def test_sympy__geometry__point__Point3D():
+    from sympy.geometry.point import Point3D
+    assert _test_args(Point3D(0, 1, 2))
+
+
+def test_sympy__geometry__ellipse__Ellipse():
+    from sympy.geometry.ellipse import Ellipse
+    assert _test_args(Ellipse((0, 1), 2, 3))
+
+
+def test_sympy__geometry__ellipse__Circle():
+    from sympy.geometry.ellipse import Circle
+    assert _test_args(Circle((0, 1), 2))
+
+
+def test_sympy__geometry__parabola__Parabola():
+    from sympy.geometry.parabola import Parabola
+    from sympy.geometry.line import Line
+    assert _test_args(Parabola((0, 0), Line((2, 3), (4, 3))))
+
+
+@SKIP("abstract class")
+def test_sympy__geometry__line__LinearEntity():
+    pass
+
+
+def test_sympy__geometry__line__Line():
+    from sympy.geometry.line import Line
+    assert _test_args(Line((0, 1), (2, 3)))
+
+
+def test_sympy__geometry__line__Ray():
+    from sympy.geometry.line import Ray
+    assert _test_args(Ray((0, 1), (2, 3)))
+
+
+def test_sympy__geometry__line__Segment():
+    from sympy.geometry.line import Segment
+    assert _test_args(Segment((0, 1), (2, 3)))
+
+@SKIP("abstract class")
+def test_sympy__geometry__line__LinearEntity2D():
+    pass
+
+
+def test_sympy__geometry__line__Line2D():
+    from sympy.geometry.line import Line2D
+    assert _test_args(Line2D((0, 1), (2, 3)))
+
+
+def test_sympy__geometry__line__Ray2D():
+    from sympy.geometry.line import Ray2D
+    assert _test_args(Ray2D((0, 1), (2, 3)))
+
+
+def test_sympy__geometry__line__Segment2D():
+    from sympy.geometry.line import Segment2D
+    assert _test_args(Segment2D((0, 1), (2, 3)))
+
+
+@SKIP("abstract class")
+def test_sympy__geometry__line__LinearEntity3D():
+    pass
+
+
+def test_sympy__geometry__line__Line3D():
+    from sympy.geometry.line import Line3D
+    assert _test_args(Line3D((0, 1, 1), (2, 3, 4)))
+
+
+def test_sympy__geometry__line__Segment3D():
+    from sympy.geometry.line import Segment3D
+    assert _test_args(Segment3D((0, 1, 1), (2, 3, 4)))
+
+
+def test_sympy__geometry__line__Ray3D():
+    from sympy.geometry.line import Ray3D
+    assert _test_args(Ray3D((0, 1, 1), (2, 3, 4)))
+
+
+def test_sympy__geometry__plane__Plane():
+    from sympy.geometry.plane import Plane
+    assert _test_args(Plane((1, 1, 1), (-3, 4, -2), (1, 2, 3)))
+
+
+def test_sympy__geometry__polygon__Polygon():
+    from sympy.geometry.polygon import Polygon
+    assert _test_args(Polygon((0, 1), (2, 3), (4, 5), (6, 7)))
+
+
+def test_sympy__geometry__polygon__RegularPolygon():
+    from sympy.geometry.polygon import RegularPolygon
+    assert _test_args(RegularPolygon((0, 1), 2, 3, 4))
+
+
+def test_sympy__geometry__polygon__Triangle():
+    from sympy.geometry.polygon import Triangle
+    assert _test_args(Triangle((0, 1), (2, 3), (4, 5)))
+
+
+def test_sympy__geometry__entity__GeometryEntity():
+    from sympy.geometry.entity import GeometryEntity
+    from sympy.geometry.point import Point
+    assert _test_args(GeometryEntity(Point(1, 0), 1, [1, 2]))
+
+@SKIP("abstract class")
+def test_sympy__geometry__entity__GeometrySet():
+    pass
+
+def test_sympy__diffgeom__diffgeom__Manifold():
+    from sympy.diffgeom import Manifold
+    assert _test_args(Manifold('name', 3))
+
+
+def test_sympy__diffgeom__diffgeom__Patch():
+    from sympy.diffgeom import Manifold, Patch
+    assert _test_args(Patch('name', Manifold('name', 3)))
+
+
+def test_sympy__diffgeom__diffgeom__CoordSystem():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem
+    assert _test_args(CoordSystem('name', Patch('name', Manifold('name', 3))))
+    assert _test_args(CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]))
+
+
+def test_sympy__diffgeom__diffgeom__CoordinateSymbol():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, CoordinateSymbol
+    assert _test_args(CoordinateSymbol(CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]), 0))
+
+
+def test_sympy__diffgeom__diffgeom__Point():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, Point
+    assert _test_args(Point(
+        CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]), [x, y]))
+
+
+def test_sympy__diffgeom__diffgeom__BaseScalarField():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    assert _test_args(BaseScalarField(cs, 0))
+
+
+def test_sympy__diffgeom__diffgeom__BaseVectorField():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseVectorField
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    assert _test_args(BaseVectorField(cs, 0))
+
+
+def test_sympy__diffgeom__diffgeom__Differential():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    assert _test_args(Differential(BaseScalarField(cs, 0)))
+
+
+def test_sympy__diffgeom__diffgeom__Commutator():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseVectorField, Commutator
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    cs1 = CoordSystem('name1', Patch('name', Manifold('name', 3)), [a, b, c])
+    v = BaseVectorField(cs, 0)
+    v1 = BaseVectorField(cs1, 0)
+    assert _test_args(Commutator(v, v1))
+
+
+def test_sympy__diffgeom__diffgeom__TensorProduct():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential, TensorProduct
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    d = Differential(BaseScalarField(cs, 0))
+    assert _test_args(TensorProduct(d, d))
+
+
+def test_sympy__diffgeom__diffgeom__WedgeProduct():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential, WedgeProduct
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    d = Differential(BaseScalarField(cs, 0))
+    d1 = Differential(BaseScalarField(cs, 1))
+    assert _test_args(WedgeProduct(d, d1))
+
+
+def test_sympy__diffgeom__diffgeom__LieDerivative():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential, BaseVectorField, LieDerivative
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    d = Differential(BaseScalarField(cs, 0))
+    v = BaseVectorField(cs, 0)
+    assert _test_args(LieDerivative(v, d))
+
+
+def test_sympy__diffgeom__diffgeom__BaseCovarDerivativeOp():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseCovarDerivativeOp
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    assert _test_args(BaseCovarDerivativeOp(cs, 0, [[[0, ]*3, ]*3, ]*3))
+
+
+def test_sympy__diffgeom__diffgeom__CovarDerivativeOp():
+    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseVectorField, CovarDerivativeOp
+    cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])
+    v = BaseVectorField(cs, 0)
+    _test_args(CovarDerivativeOp(v, [[[0, ]*3, ]*3, ]*3))
+
+
+def test_sympy__categories__baseclasses__Class():
+    from sympy.categories.baseclasses import Class
+    assert _test_args(Class())
+
+
+def test_sympy__categories__baseclasses__Object():
+    from sympy.categories import Object
+    assert _test_args(Object("A"))
+
+
+@SKIP("abstract class")
+def test_sympy__categories__baseclasses__Morphism():
+    pass
+
+
+def test_sympy__categories__baseclasses__IdentityMorphism():
+    from sympy.categories import Object, IdentityMorphism
+    assert _test_args(IdentityMorphism(Object("A")))
+
+
+def test_sympy__categories__baseclasses__NamedMorphism():
+    from sympy.categories import Object, NamedMorphism
+    assert _test_args(NamedMorphism(Object("A"), Object("B"), "f"))
+
+
+def test_sympy__categories__baseclasses__CompositeMorphism():
+    from sympy.categories import Object, NamedMorphism, CompositeMorphism
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    assert _test_args(CompositeMorphism(f, g))
+
+
+def test_sympy__categories__baseclasses__Diagram():
+    from sympy.categories import Object, NamedMorphism, Diagram
+    A = Object("A")
+    B = Object("B")
+    f = NamedMorphism(A, B, "f")
+    d = Diagram([f])
+    assert _test_args(d)
+
+
+def test_sympy__categories__baseclasses__Category():
+    from sympy.categories import Object, NamedMorphism, Diagram, Category
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    d1 = Diagram([f, g])
+    d2 = Diagram([f])
+    K = Category("K", commutative_diagrams=[d1, d2])
+    assert _test_args(K)
+
+
+def test_sympy__physics__optics__waves__TWave():
+    from sympy.physics.optics import TWave
+    A, f, phi = symbols('A, f, phi')
+    assert _test_args(TWave(A, f, phi))
+
+
+def test_sympy__physics__optics__gaussopt__BeamParameter():
+    from sympy.physics.optics import BeamParameter
+    assert _test_args(BeamParameter(530e-9, 1, w=1e-3, n=1))
+
+
+def test_sympy__physics__optics__medium__Medium():
+    from sympy.physics.optics import Medium
+    assert _test_args(Medium('m'))
+
+
+def test_sympy__physics__optics__medium__MediumN():
+    from sympy.physics.optics.medium import Medium
+    assert _test_args(Medium('m', n=2))
+
+
+def test_sympy__physics__optics__medium__MediumPP():
+    from sympy.physics.optics.medium import Medium
+    assert _test_args(Medium('m', permittivity=2, permeability=2))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__ArrayContraction():
+    from sympy.tensor.array.expressions.array_expressions import ArrayContraction
+    from sympy.tensor.indexed import IndexedBase
+    A = symbols("A", cls=IndexedBase)
+    assert _test_args(ArrayContraction(A, (0, 1)))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__ArrayDiagonal():
+    from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal
+    from sympy.tensor.indexed import IndexedBase
+    A = symbols("A", cls=IndexedBase)
+    assert _test_args(ArrayDiagonal(A, (0, 1)))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__ArrayTensorProduct():
+    from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+    from sympy.tensor.indexed import IndexedBase
+    A, B = symbols("A B", cls=IndexedBase)
+    assert _test_args(ArrayTensorProduct(A, B))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__ArrayAdd():
+    from sympy.tensor.array.expressions.array_expressions import ArrayAdd
+    from sympy.tensor.indexed import IndexedBase
+    A, B = symbols("A B", cls=IndexedBase)
+    assert _test_args(ArrayAdd(A, B))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__PermuteDims():
+    from sympy.tensor.array.expressions.array_expressions import PermuteDims
+    A = MatrixSymbol("A", 4, 4)
+    assert _test_args(PermuteDims(A, (1, 0)))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__ArrayElementwiseApplyFunc():
+    from sympy.tensor.array.expressions.array_expressions import ArraySymbol, ArrayElementwiseApplyFunc
+    A = ArraySymbol("A", (4,))
+    assert _test_args(ArrayElementwiseApplyFunc(exp, A))
+
+
+def test_sympy__tensor__array__expressions__array_expressions__Reshape():
+    from sympy.tensor.array.expressions.array_expressions import ArraySymbol, Reshape
+    A = ArraySymbol("A", (4,))
+    assert _test_args(Reshape(A, (2, 2)))
+
+
+def test_sympy__codegen__ast__Assignment():
+    from sympy.codegen.ast import Assignment
+    assert _test_args(Assignment(x, y))
+
+
+def test_sympy__codegen__cfunctions__expm1():
+    from sympy.codegen.cfunctions import expm1
+    assert _test_args(expm1(x))
+
+
+def test_sympy__codegen__cfunctions__log1p():
+    from sympy.codegen.cfunctions import log1p
+    assert _test_args(log1p(x))
+
+
+def test_sympy__codegen__cfunctions__exp2():
+    from sympy.codegen.cfunctions import exp2
+    assert _test_args(exp2(x))
+
+
+def test_sympy__codegen__cfunctions__log2():
+    from sympy.codegen.cfunctions import log2
+    assert _test_args(log2(x))
+
+
+def test_sympy__codegen__cfunctions__fma():
+    from sympy.codegen.cfunctions import fma
+    assert _test_args(fma(x, y, z))
+
+
+def test_sympy__codegen__cfunctions__log10():
+    from sympy.codegen.cfunctions import log10
+    assert _test_args(log10(x))
+
+
+def test_sympy__codegen__cfunctions__Sqrt():
+    from sympy.codegen.cfunctions import Sqrt
+    assert _test_args(Sqrt(x))
+
+def test_sympy__codegen__cfunctions__Cbrt():
+    from sympy.codegen.cfunctions import Cbrt
+    assert _test_args(Cbrt(x))
+
+def test_sympy__codegen__cfunctions__hypot():
+    from sympy.codegen.cfunctions import hypot
+    assert _test_args(hypot(x, y))
+
+
+def test_sympy__codegen__cfunctions__isnan():
+    from sympy.codegen.cfunctions import isnan
+    assert _test_args(isnan(x))
+
+
+def test_sympy__codegen__cfunctions__isinf():
+    from sympy.codegen.cfunctions import isinf
+    assert _test_args(isinf(x))
+
+
+def test_sympy__codegen__fnodes__FFunction():
+    from sympy.codegen.fnodes import FFunction
+    assert _test_args(FFunction('f'))
+
+
+def test_sympy__codegen__fnodes__F95Function():
+    from sympy.codegen.fnodes import F95Function
+    assert _test_args(F95Function('f'))
+
+
+def test_sympy__codegen__fnodes__isign():
+    from sympy.codegen.fnodes import isign
+    assert _test_args(isign(1, x))
+
+
+def test_sympy__codegen__fnodes__dsign():
+    from sympy.codegen.fnodes import dsign
+    assert _test_args(dsign(1, x))
+
+
+def test_sympy__codegen__fnodes__cmplx():
+    from sympy.codegen.fnodes import cmplx
+    assert _test_args(cmplx(x, y))
+
+
+def test_sympy__codegen__fnodes__kind():
+    from sympy.codegen.fnodes import kind
+    assert _test_args(kind(x))
+
+
+def test_sympy__codegen__fnodes__merge():
+    from sympy.codegen.fnodes import merge
+    assert _test_args(merge(1, 2, Eq(x, 0)))
+
+
+def test_sympy__codegen__fnodes___literal():
+    from sympy.codegen.fnodes import _literal
+    assert _test_args(_literal(1))
+
+
+def test_sympy__codegen__fnodes__literal_sp():
+    from sympy.codegen.fnodes import literal_sp
+    assert _test_args(literal_sp(1))
+
+
+def test_sympy__codegen__fnodes__literal_dp():
+    from sympy.codegen.fnodes import literal_dp
+    assert _test_args(literal_dp(1))
+
+
+def test_sympy__codegen__matrix_nodes__MatrixSolve():
+    from sympy.matrices import MatrixSymbol
+    from sympy.codegen.matrix_nodes import MatrixSolve
+    A = MatrixSymbol('A', 3, 3)
+    v = MatrixSymbol('x', 3, 1)
+    assert _test_args(MatrixSolve(A, v))
+
+
+def test_sympy__printing__rust__TypeCast():
+    from sympy.printing.rust import TypeCast
+    from sympy.codegen.ast import real
+    assert _test_args(TypeCast(x, real))
+
+
+def test_sympy__printing__rust__float_floor():
+    from sympy.printing.rust import float_floor
+    assert _test_args(float_floor(x))
+
+
+def test_sympy__printing__rust__float_ceiling():
+    from sympy.printing.rust import float_ceiling
+    assert _test_args(float_ceiling(x))
+
+
+def test_sympy__vector__coordsysrect__CoordSys3D():
+    from sympy.vector.coordsysrect import CoordSys3D
+    assert _test_args(CoordSys3D('C'))
+
+
+def test_sympy__vector__point__Point():
+    from sympy.vector.point import Point
+    assert _test_args(Point('P'))
+
+
+def test_sympy__vector__basisdependent__BasisDependent():
+    #from sympy.vector.basisdependent import BasisDependent
+    #These classes have been created to maintain an OOP hierarchy
+    #for Vectors and Dyadics. Are NOT meant to be initialized
+    pass
+
+
+def test_sympy__vector__basisdependent__BasisDependentMul():
+    #from sympy.vector.basisdependent import BasisDependentMul
+    #These classes have been created to maintain an OOP hierarchy
+    #for Vectors and Dyadics. Are NOT meant to be initialized
+    pass
+
+
+def test_sympy__vector__basisdependent__BasisDependentAdd():
+    #from sympy.vector.basisdependent import BasisDependentAdd
+    #These classes have been created to maintain an OOP hierarchy
+    #for Vectors and Dyadics. Are NOT meant to be initialized
+    pass
+
+
+def test_sympy__vector__basisdependent__BasisDependentZero():
+    #from sympy.vector.basisdependent import BasisDependentZero
+    #These classes have been created to maintain an OOP hierarchy
+    #for Vectors and Dyadics. Are NOT meant to be initialized
+    pass
+
+
+def test_sympy__vector__vector__BaseVector():
+    from sympy.vector.vector import BaseVector
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(BaseVector(0, C, ' ', ' '))
+
+
+def test_sympy__vector__vector__VectorAdd():
+    from sympy.vector.vector import VectorAdd, VectorMul
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    from sympy.abc import a, b, c, x, y, z
+    v1 = a*C.i + b*C.j + c*C.k
+    v2 = x*C.i + y*C.j + z*C.k
+    assert _test_args(VectorAdd(v1, v2))
+    assert _test_args(VectorMul(x, v1))
+
+
+def test_sympy__vector__vector__VectorMul():
+    from sympy.vector.vector import VectorMul
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    from sympy.abc import a
+    assert _test_args(VectorMul(a, C.i))
+
+
+def test_sympy__vector__vector__VectorZero():
+    from sympy.vector.vector import VectorZero
+    assert _test_args(VectorZero())
+
+
+def test_sympy__vector__vector__Vector():
+    #from sympy.vector.vector import Vector
+    #Vector is never to be initialized using args
+    pass
+
+
+def test_sympy__vector__vector__Cross():
+    from sympy.vector.vector import Cross
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    _test_args(Cross(C.i, C.j))
+
+
+def test_sympy__vector__vector__Dot():
+    from sympy.vector.vector import Dot
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    _test_args(Dot(C.i, C.j))
+
+
+def test_sympy__vector__dyadic__Dyadic():
+    #from sympy.vector.dyadic import Dyadic
+    #Dyadic is never to be initialized using args
+    pass
+
+
+def test_sympy__vector__dyadic__BaseDyadic():
+    from sympy.vector.dyadic import BaseDyadic
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(BaseDyadic(C.i, C.j))
+
+
+def test_sympy__vector__dyadic__DyadicMul():
+    from sympy.vector.dyadic import BaseDyadic, DyadicMul
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(DyadicMul(3, BaseDyadic(C.i, C.j)))
+
+
+def test_sympy__vector__dyadic__DyadicAdd():
+    from sympy.vector.dyadic import BaseDyadic, DyadicAdd
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(2 * DyadicAdd(BaseDyadic(C.i, C.i),
+                                    BaseDyadic(C.i, C.j)))
+
+
+def test_sympy__vector__dyadic__DyadicZero():
+    from sympy.vector.dyadic import DyadicZero
+    assert _test_args(DyadicZero())
+
+
+def test_sympy__vector__deloperator__Del():
+    from sympy.vector.deloperator import Del
+    assert _test_args(Del())
+
+
+def test_sympy__vector__implicitregion__ImplicitRegion():
+    from sympy.vector.implicitregion import ImplicitRegion
+    from sympy.abc import x, y
+    assert _test_args(ImplicitRegion((x, y), y**3 - 4*x))
+
+
+def test_sympy__vector__integrals__ParametricIntegral():
+    from sympy.vector.integrals import ParametricIntegral
+    from sympy.vector.parametricregion import ParametricRegion
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(ParametricIntegral(C.y*C.i - 10*C.j,\
+                    ParametricRegion((x, y), (x, 1, 3), (y, -2, 2))))
+
+def test_sympy__vector__operators__Curl():
+    from sympy.vector.operators import Curl
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(Curl(C.i))
+
+
+def test_sympy__vector__operators__Laplacian():
+    from sympy.vector.operators import Laplacian
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(Laplacian(C.i))
+
+
+def test_sympy__vector__operators__Divergence():
+    from sympy.vector.operators import Divergence
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(Divergence(C.i))
+
+
+def test_sympy__vector__operators__Gradient():
+    from sympy.vector.operators import Gradient
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(Gradient(C.x))
+
+
+def test_sympy__vector__orienters__Orienter():
+    #from sympy.vector.orienters import Orienter
+    #Not to be initialized
+    pass
+
+
+def test_sympy__vector__orienters__ThreeAngleOrienter():
+    #from sympy.vector.orienters import ThreeAngleOrienter
+    #Not to be initialized
+    pass
+
+
+def test_sympy__vector__orienters__AxisOrienter():
+    from sympy.vector.orienters import AxisOrienter
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(AxisOrienter(x, C.i))
+
+
+def test_sympy__vector__orienters__BodyOrienter():
+    from sympy.vector.orienters import BodyOrienter
+    assert _test_args(BodyOrienter(x, y, z, '123'))
+
+
+def test_sympy__vector__orienters__SpaceOrienter():
+    from sympy.vector.orienters import SpaceOrienter
+    assert _test_args(SpaceOrienter(x, y, z, '123'))
+
+
+def test_sympy__vector__orienters__QuaternionOrienter():
+    from sympy.vector.orienters import QuaternionOrienter
+    a, b, c, d = symbols('a b c d')
+    assert _test_args(QuaternionOrienter(a, b, c, d))
+
+
+def test_sympy__vector__parametricregion__ParametricRegion():
+    from sympy.abc import t
+    from sympy.vector.parametricregion import ParametricRegion
+    assert _test_args(ParametricRegion((t, t**3), (t, 0, 2)))
+
+
+def test_sympy__vector__scalar__BaseScalar():
+    from sympy.vector.scalar import BaseScalar
+    from sympy.vector.coordsysrect import CoordSys3D
+    C = CoordSys3D('C')
+    assert _test_args(BaseScalar(0, C, ' ', ' '))
+
+
+def test_sympy__physics__wigner__Wigner3j():
+    from sympy.physics.wigner import Wigner3j
+    assert _test_args(Wigner3j(0, 0, 0, 0, 0, 0))
+
+
+def test_sympy__combinatorics__schur_number__SchurNumber():
+    from sympy.combinatorics.schur_number import SchurNumber
+    assert _test_args(SchurNumber(x))
+
+
+def test_sympy__combinatorics__perm_groups__SymmetricPermutationGroup():
+    from sympy.combinatorics.perm_groups import SymmetricPermutationGroup
+    assert _test_args(SymmetricPermutationGroup(5))
+
+
+def test_sympy__combinatorics__perm_groups__Coset():
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.combinatorics.perm_groups import PermutationGroup, Coset
+    a = Permutation(1, 2)
+    b = Permutation(0, 1)
+    G = PermutationGroup([a, b])
+    assert _test_args(Coset(a, G))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_arit.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_arit.py
new file mode 100644
index 0000000000000000000000000000000000000000..251fc4c4234cbd6e82adc9a24ccea536ed6a37b7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_arit.py
@@ -0,0 +1,2489 @@
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.mod import Mod
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Float, I, Integer, Rational, comp, nan,
+    oo, pi, zoo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import (im, re, sign)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import (Max, sqrt)
+from sympy.functions.elementary.trigonometric import (atan, cos, sin)
+from sympy.integrals.integrals import Integral
+from sympy.polys.polytools import Poly
+from sympy.sets.sets import FiniteSet
+
+from sympy.core.parameters import distribute, evaluate
+from sympy.core.expr import unchanged
+from sympy.utilities.iterables import permutations
+from sympy.testing.pytest import XFAIL, raises, warns
+from sympy.utilities.exceptions import SymPyDeprecationWarning
+from sympy.core.random import verify_numerically
+from sympy.functions.elementary.trigonometric import asin
+
+from itertools import product
+
+a, c, x, y, z = symbols('a,c,x,y,z')
+b = Symbol("b", positive=True)
+
+
+def same_and_same_prec(a, b):
+    # stricter matching for Floats
+    return a == b and a._prec == b._prec
+
+
+def test_bug1():
+    assert re(x) != x
+    x.series(x, 0, 1)
+    assert re(x) != x
+
+
+def test_Symbol():
+    e = a*b
+    assert e == a*b
+    assert a*b*b == a*b**2
+    assert a*b*b + c == c + a*b**2
+    assert a*b*b - c == -c + a*b**2
+
+    x = Symbol('x', complex=True, real=False)
+    assert x.is_imaginary is None  # could be I or 1 + I
+    x = Symbol('x', complex=True, imaginary=False)
+    assert x.is_real is None  # could be 1 or 1 + I
+    x = Symbol('x', real=True)
+    assert x.is_complex
+    x = Symbol('x', imaginary=True)
+    assert x.is_complex
+    x = Symbol('x', real=False, imaginary=False)
+    assert x.is_complex is None  # might be a non-number
+
+
+def test_arit0():
+    p = Rational(5)
+    e = a*b
+    assert e == a*b
+    e = a*b + b*a
+    assert e == 2*a*b
+    e = a*b + b*a + a*b + p*b*a
+    assert e == 8*a*b
+    e = a*b + b*a + a*b + p*b*a + a
+    assert e == a + 8*a*b
+    e = a + a
+    assert e == 2*a
+    e = a + b + a
+    assert e == b + 2*a
+    e = a + b*b + a + b*b
+    assert e == 2*a + 2*b**2
+    e = a + Rational(2) + b*b + a + b*b + p
+    assert e == 7 + 2*a + 2*b**2
+    e = (a + b*b + a + b*b)*p
+    assert e == 5*(2*a + 2*b**2)
+    e = (a*b*c + c*b*a + b*a*c)*p
+    assert e == 15*a*b*c
+    e = (a*b*c + c*b*a + b*a*c)*p - Rational(15)*a*b*c
+    assert e == Rational(0)
+    e = Rational(50)*(a - a)
+    assert e == Rational(0)
+    e = b*a - b - a*b + b
+    assert e == Rational(0)
+    e = a*b + c**p
+    assert e == a*b + c**5
+    e = a/b
+    assert e == a*b**(-1)
+    e = a*2*2
+    assert e == 4*a
+    e = 2 + a*2/2
+    assert e == 2 + a
+    e = 2 - a - 2
+    assert e == -a
+    e = 2*a*2
+    assert e == 4*a
+    e = 2/a/2
+    assert e == a**(-1)
+    e = 2**a**2
+    assert e == 2**(a**2)
+    e = -(1 + a)
+    assert e == -1 - a
+    e = S.Half*(1 + a)
+    assert e == S.Half + a/2
+
+
+def test_div():
+    e = a/b
+    assert e == a*b**(-1)
+    e = a/b + c/2
+    assert e == a*b**(-1) + Rational(1)/2*c
+    e = (1 - b)/(b - 1)
+    assert e == (1 + -b)*((-1) + b)**(-1)
+
+
+def test_pow_arit():
+    n1 = Rational(1)
+    n2 = Rational(2)
+    n5 = Rational(5)
+    e = a*a
+    assert e == a**2
+    e = a*a*a
+    assert e == a**3
+    e = a*a*a*a**Rational(6)
+    assert e == a**9
+    e = a*a*a*a**Rational(6) - a**Rational(9)
+    assert e == Rational(0)
+    e = a**(b - b)
+    assert e == Rational(1)
+    e = (a + Rational(1) - a)**b
+    assert e == Rational(1)
+
+    e = (a + b + c)**n2
+    assert e == (a + b + c)**2
+    assert e.expand() == 2*b*c + 2*a*c + 2*a*b + a**2 + c**2 + b**2
+
+    e = (a + b)**n2
+    assert e == (a + b)**2
+    assert e.expand() == 2*a*b + a**2 + b**2
+
+    e = (a + b)**(n1/n2)
+    assert e == sqrt(a + b)
+    assert e.expand() == sqrt(a + b)
+
+    n = n5**(n1/n2)
+    assert n == sqrt(5)
+    e = n*a*b - n*b*a
+    assert e == Rational(0)
+    e = n*a*b + n*b*a
+    assert e == 2*a*b*sqrt(5)
+    assert e.diff(a) == 2*b*sqrt(5)
+    assert e.diff(a) == 2*b*sqrt(5)
+    e = a/b**2
+    assert e == a*b**(-2)
+
+    assert sqrt(2*(1 + sqrt(2))) == (2*(1 + 2**S.Half))**S.Half
+
+    x = Symbol('x')
+    y = Symbol('y')
+
+    assert ((x*y)**3).expand() == y**3 * x**3
+    assert ((x*y)**-3).expand() == y**-3 * x**-3
+
+    assert (x**5*(3*x)**(3)).expand() == 27 * x**8
+    assert (x**5*(-3*x)**(3)).expand() == -27 * x**8
+    assert (x**5*(3*x)**(-3)).expand() == x**2 * Rational(1, 27)
+    assert (x**5*(-3*x)**(-3)).expand() == x**2 * Rational(-1, 27)
+
+    # expand_power_exp
+    _x = Symbol('x', zero=False)
+    _y = Symbol('y', zero=False)
+    assert (_x**(y**(x + exp(x + y)) + z)).expand(deep=False) == \
+        _x**z*_x**(y**(x + exp(x + y)))
+    assert (_x**(_y**(x + exp(x + y)) + z)).expand() == \
+        _x**z*_x**(_y**x*_y**(exp(x)*exp(y)))
+
+    n = Symbol('n', even=False)
+    k = Symbol('k', even=True)
+    o = Symbol('o', odd=True)
+
+    assert unchanged(Pow, -1, x)
+    assert unchanged(Pow, -1, n)
+    assert (-2)**k == 2**k
+    assert (-1)**k == 1
+    assert (-1)**o == -1
+
+
+def test_pow2():
+    # x**(2*y) is always (x**y)**2 but is only (x**2)**y if
+    #                                  x.is_positive or y.is_integer
+    # let x = 1 to see why the following are not true.
+    assert (-x)**Rational(2, 3) != x**Rational(2, 3)
+    assert (-x)**Rational(5, 7) != -x**Rational(5, 7)
+    assert ((-x)**2)**Rational(1, 3) != ((-x)**Rational(1, 3))**2
+    assert sqrt(x**2) != x
+
+
+def test_pow3():
+    assert sqrt(2)**3 == 2 * sqrt(2)
+    assert sqrt(2)**3 == sqrt(8)
+
+
+def test_mod_pow():
+    for s, t, u, v in [(4, 13, 497, 445), (4, -3, 497, 365),
+            (3.2, 2.1, 1.9, 0.1031015682350942), (S(3)/2, 5, S(5)/6, S(3)/32)]:
+        assert pow(S(s), t, u) == v
+        assert pow(S(s), S(t), u) == v
+        assert pow(S(s), t, S(u)) == v
+        assert pow(S(s), S(t), S(u)) == v
+    assert pow(S(2), S(10000000000), S(3)) == 1
+    assert pow(x, y, z) == x**y%z
+    raises(TypeError, lambda: pow(S(4), "13", 497))
+    raises(TypeError, lambda: pow(S(4), 13, "497"))
+
+
+def test_pow_E():
+    assert 2**(y/log(2)) == S.Exp1**y
+    assert 2**(y/log(2)/3) == S.Exp1**(y/3)
+    assert 3**(1/log(-3)) != S.Exp1
+    assert (3 + 2*I)**(1/(log(-3 - 2*I) + I*pi)) == S.Exp1
+    assert (4 + 2*I)**(1/(log(-4 - 2*I) + I*pi)) == S.Exp1
+    assert (3 + 2*I)**(1/(log(-3 - 2*I, 3)/2 + I*pi/log(3)/2)) == 9
+    assert (3 + 2*I)**(1/(log(3 + 2*I, 3)/2)) == 9
+    # every time tests are run they will affirm with a different random
+    # value that this identity holds
+    while 1:
+        b = x._random()
+        r, i = b.as_real_imag()
+        if i:
+            break
+    assert verify_numerically(b**(1/(log(-b) + sign(i)*I*pi).n()), S.Exp1)
+
+
+def test_pow_issue_3516():
+    assert 4**Rational(1, 4) == sqrt(2)
+
+
+def test_pow_im():
+    for m in (-2, -1, 2):
+        for d in (3, 4, 5):
+            b = m*I
+            for i in range(1, 4*d + 1):
+                e = Rational(i, d)
+                assert (b**e - b.n()**e.n()).n(2, chop=1e-10) == 0
+
+    e = Rational(7, 3)
+    assert (2*x*I)**e == 4*2**Rational(1, 3)*(I*x)**e  # same as Wolfram Alpha
+    im = symbols('im', imaginary=True)
+    assert (2*im*I)**e == 4*2**Rational(1, 3)*(I*im)**e
+
+    args = [I, I, I, I, 2]
+    e = Rational(1, 3)
+    ans = 2**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+    args = [I, I, I, 2]
+    e = Rational(1, 3)
+    ans = 2**e*(-I)**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+    args.append(-3)
+    ans = (6*I)**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+    args.append(-1)
+    ans = (-6*I)**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+
+    args = [I, I, 2]
+    e = Rational(1, 3)
+    ans = (-2)**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+    args.append(-3)
+    ans = (6)**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+    args.append(-1)
+    ans = (-6)**e
+    assert Mul(*args, evaluate=False)**e == ans
+    assert Mul(*args)**e == ans
+    assert Mul(Pow(-1, Rational(3, 2), evaluate=False), I, I) == I
+    assert Mul(I*Pow(I, S.Half, evaluate=False)) == sqrt(I)*I
+
+
+def test_real_mul():
+    assert Float(0) * pi * x == 0
+    assert set((Float(1) * pi * x).args) == {Float(1), pi, x}
+
+
+def test_ncmul():
+    A = Symbol("A", commutative=False)
+    B = Symbol("B", commutative=False)
+    C = Symbol("C", commutative=False)
+    assert A*B != B*A
+    assert A*B*C != C*B*A
+    assert A*b*B*3*C == 3*b*A*B*C
+    assert A*b*B*3*C != 3*b*B*A*C
+    assert A*b*B*3*C == 3*A*B*C*b
+
+    assert A + B == B + A
+    assert (A + B)*C != C*(A + B)
+
+    assert C*(A + B)*C != C*C*(A + B)
+
+    assert A*A == A**2
+    assert (A + B)*(A + B) == (A + B)**2
+
+    assert A**-1 * A == 1
+    assert A/A == 1
+    assert A/(A**2) == 1/A
+
+    assert A/(1 + A) == A/(1 + A)
+
+    assert set((A + B + 2*(A + B)).args) == \
+        {A, B, 2*(A + B)}
+
+
+def test_mul_add_identity():
+    m = Mul(1, 2)
+    assert isinstance(m, Rational) and m.p == 2 and m.q == 1
+    m = Mul(1, 2, evaluate=False)
+    assert isinstance(m, Mul) and m.args == (1, 2)
+    m = Mul(0, 1)
+    assert m is S.Zero
+    m = Mul(0, 1, evaluate=False)
+    assert isinstance(m, Mul) and m.args == (0, 1)
+    m = Add(0, 1)
+    assert m is S.One
+    m = Add(0, 1, evaluate=False)
+    assert isinstance(m, Add) and m.args == (0, 1)
+
+
+def test_ncpow():
+    x = Symbol('x', commutative=False)
+    y = Symbol('y', commutative=False)
+    z = Symbol('z', commutative=False)
+    a = Symbol('a')
+    b = Symbol('b')
+    c = Symbol('c')
+
+    assert (x**2)*(y**2) != (y**2)*(x**2)
+    assert (x**-2)*y != y*(x**2)
+    assert 2**x*2**y != 2**(x + y)
+    assert 2**x*2**y*2**z != 2**(x + y + z)
+    assert 2**x*2**(2*x) == 2**(3*x)
+    assert 2**x*2**(2*x)*2**x == 2**(4*x)
+    assert exp(x)*exp(y) != exp(y)*exp(x)
+    assert exp(x)*exp(y)*exp(z) != exp(y)*exp(x)*exp(z)
+    assert exp(x)*exp(y)*exp(z) != exp(x + y + z)
+    assert x**a*x**b != x**(a + b)
+    assert x**a*x**b*x**c != x**(a + b + c)
+    assert x**3*x**4 == x**7
+    assert x**3*x**4*x**2 == x**9
+    assert x**a*x**(4*a) == x**(5*a)
+    assert x**a*x**(4*a)*x**a == x**(6*a)
+
+
+def test_powerbug():
+    x = Symbol("x")
+    assert x**1 != (-x)**1
+    assert x**2 == (-x)**2
+    assert x**3 != (-x)**3
+    assert x**4 == (-x)**4
+    assert x**5 != (-x)**5
+    assert x**6 == (-x)**6
+
+    assert x**128 == (-x)**128
+    assert x**129 != (-x)**129
+
+    assert (2*x)**2 == (-2*x)**2
+
+
+def test_Mul_doesnt_expand_exp():
+    x = Symbol('x')
+    y = Symbol('y')
+    assert unchanged(Mul, exp(x), exp(y))
+    assert unchanged(Mul, 2**x, 2**y)
+    assert x**2*x**3 == x**5
+    assert 2**x*3**x == 6**x
+    assert x**(y)*x**(2*y) == x**(3*y)
+    assert sqrt(2)*sqrt(2) == 2
+    assert 2**x*2**(2*x) == 2**(3*x)
+    assert sqrt(2)*2**Rational(1, 4)*5**Rational(3, 4) == 10**Rational(3, 4)
+    assert (x**(-log(5)/log(3))*x)/(x*x**( - log(5)/log(3))) == sympify(1)
+
+
+def test_Mul_is_integer():
+    k = Symbol('k', integer=True)
+    n = Symbol('n', integer=True)
+    nr = Symbol('nr', rational=False)
+    ir = Symbol('ir', irrational=True)
+    nz = Symbol('nz', integer=True, zero=False)
+    e = Symbol('e', even=True)
+    o = Symbol('o', odd=True)
+    i2 = Symbol('2', prime=True, even=True)
+
+    assert (k/3).is_integer is None
+    assert (nz/3).is_integer is None
+    assert (nr/3).is_integer is False
+    assert (ir/3).is_integer is False
+    assert (x*k*n).is_integer is None
+    assert (e/2).is_integer is True
+    assert (e**2/2).is_integer is True
+    assert (2/k).is_integer is None
+    assert (2/k**2).is_integer is None
+    assert ((-1)**k*n).is_integer is True
+    assert (3*k*e/2).is_integer is True
+    assert (2*k*e/3).is_integer is None
+    assert (e/o).is_integer is None
+    assert (o/e).is_integer is False
+    assert (o/i2).is_integer is False
+    assert Mul(k, 1/k, evaluate=False).is_integer is None
+    assert Mul(2., S.Half, evaluate=False).is_integer is None
+    assert (2*sqrt(k)).is_integer is None
+    assert (2*k**n).is_integer is None
+
+    s = 2**2**2**Pow(2, 1000, evaluate=False)
+    m = Mul(s, s, evaluate=False)
+    assert m.is_integer
+
+    # broken in 1.6 and before, see #20161
+    xq = Symbol('xq', rational=True)
+    yq = Symbol('yq', rational=True)
+    assert (xq*yq).is_integer is None
+    e_20161 = Mul(-1,Mul(1,Pow(2,-1,evaluate=False),evaluate=False),evaluate=False)
+    assert e_20161.is_integer is not True # expand(e_20161) -> -1/2, but no need to see that in the assumption without evaluation
+
+
+def test_Add_Mul_is_integer():
+    x = Symbol('x')
+
+    k = Symbol('k', integer=True)
+    n = Symbol('n', integer=True)
+    nk = Symbol('nk', integer=False)
+    nr = Symbol('nr', rational=False)
+    nz = Symbol('nz', integer=True, zero=False)
+
+    assert (-nk).is_integer is None
+    assert (-nr).is_integer is False
+    assert (2*k).is_integer is True
+    assert (-k).is_integer is True
+
+    assert (k + nk).is_integer is False
+    assert (k + n).is_integer is True
+    assert (k + x).is_integer is None
+    assert (k + n*x).is_integer is None
+    assert (k + n/3).is_integer is None
+    assert (k + nz/3).is_integer is None
+    assert (k + nr/3).is_integer is False
+
+    assert ((1 + sqrt(3))*(-sqrt(3) + 1)).is_integer is not False
+    assert (1 + (1 + sqrt(3))*(-sqrt(3) + 1)).is_integer is not False
+
+
+def test_Add_Mul_is_finite():
+    x = Symbol('x', extended_real=True, finite=False)
+
+    assert sin(x).is_finite is True
+    assert (x*sin(x)).is_finite is None
+    assert (x*atan(x)).is_finite is False
+    assert (1024*sin(x)).is_finite is True
+    assert (sin(x)*exp(x)).is_finite is None
+    assert (sin(x)*cos(x)).is_finite is True
+    assert (x*sin(x)*exp(x)).is_finite is None
+
+    assert (sin(x) - 67).is_finite is True
+    assert (sin(x) + exp(x)).is_finite is not True
+    assert (1 + x).is_finite is False
+    assert (1 + x**2 + (1 + x)*(1 - x)).is_finite is None
+    assert (sqrt(2)*(1 + x)).is_finite is False
+    assert (sqrt(2)*(1 + x)*(1 - x)).is_finite is False
+
+
+def test_Mul_is_even_odd():
+    x = Symbol('x', integer=True)
+    y = Symbol('y', integer=True)
+
+    k = Symbol('k', odd=True)
+    n = Symbol('n', odd=True)
+    m = Symbol('m', even=True)
+
+    assert (2*x).is_even is True
+    assert (2*x).is_odd is False
+
+    assert (3*x).is_even is None
+    assert (3*x).is_odd is None
+
+    assert (k/3).is_integer is None
+    assert (k/3).is_even is None
+    assert (k/3).is_odd is None
+
+    assert (2*n).is_even is True
+    assert (2*n).is_odd is False
+
+    assert (2*m).is_even is True
+    assert (2*m).is_odd is False
+
+    assert (-n).is_even is False
+    assert (-n).is_odd is True
+
+    assert (k*n).is_even is False
+    assert (k*n).is_odd is True
+
+    assert (k*m).is_even is True
+    assert (k*m).is_odd is False
+
+    assert (k*n*m).is_even is True
+    assert (k*n*m).is_odd is False
+
+    assert (k*m*x).is_even is True
+    assert (k*m*x).is_odd is False
+
+    # issue 6791:
+    assert (x/2).is_integer is None
+    assert (k/2).is_integer is False
+    assert (m/2).is_integer is True
+
+    assert (x*y).is_even is None
+    assert (x*x).is_even is None
+    assert (x*(x + k)).is_even is True
+    assert (x*(x + m)).is_even is None
+
+    assert (x*y).is_odd is None
+    assert (x*x).is_odd is None
+    assert (x*(x + k)).is_odd is False
+    assert (x*(x + m)).is_odd is None
+
+    # issue 8648
+    assert (m**2/2).is_even
+    assert (m**2/3).is_even is False
+    assert (2/m**2).is_odd is False
+    assert (2/m).is_odd is None
+
+
+@XFAIL
+def test_evenness_in_ternary_integer_product_with_odd():
+    # Tests that oddness inference is independent of term ordering.
+    # Term ordering at the point of testing depends on SymPy's symbol order, so
+    # we try to force a different order by modifying symbol names.
+    x = Symbol('x', integer=True)
+    y = Symbol('y', integer=True)
+    k = Symbol('k', odd=True)
+    assert (x*y*(y + k)).is_even is True
+    assert (y*x*(x + k)).is_even is True
+
+
+def test_evenness_in_ternary_integer_product_with_even():
+    x = Symbol('x', integer=True)
+    y = Symbol('y', integer=True)
+    m = Symbol('m', even=True)
+    assert (x*y*(y + m)).is_even is None
+
+
+@XFAIL
+def test_oddness_in_ternary_integer_product_with_odd():
+    # Tests that oddness inference is independent of term ordering.
+    # Term ordering at the point of testing depends on SymPy's symbol order, so
+    # we try to force a different order by modifying symbol names.
+    x = Symbol('x', integer=True)
+    y = Symbol('y', integer=True)
+    k = Symbol('k', odd=True)
+    assert (x*y*(y + k)).is_odd is False
+    assert (y*x*(x + k)).is_odd is False
+
+
+def test_oddness_in_ternary_integer_product_with_even():
+    x = Symbol('x', integer=True)
+    y = Symbol('y', integer=True)
+    m = Symbol('m', even=True)
+    assert (x*y*(y + m)).is_odd is None
+
+
+def test_Mul_is_rational():
+    x = Symbol('x')
+    n = Symbol('n', integer=True)
+    m = Symbol('m', integer=True, nonzero=True)
+
+    assert (n/m).is_rational is True
+    assert (x/pi).is_rational is None
+    assert (x/n).is_rational is None
+    assert (m/pi).is_rational is False
+
+    r = Symbol('r', rational=True)
+    assert (pi*r).is_rational is None
+
+    # issue 8008
+    z = Symbol('z', zero=True)
+    i = Symbol('i', imaginary=True)
+    assert (z*i).is_rational is True
+    bi = Symbol('i', imaginary=True, finite=True)
+    assert (z*bi).is_zero is True
+
+
+def test_Add_is_rational():
+    x = Symbol('x')
+    n = Symbol('n', rational=True)
+    m = Symbol('m', rational=True)
+
+    assert (n + m).is_rational is True
+    assert (x + pi).is_rational is None
+    assert (x + n).is_rational is None
+    assert (n + pi).is_rational is False
+
+
+def test_Add_is_even_odd():
+    x = Symbol('x', integer=True)
+
+    k = Symbol('k', odd=True)
+    n = Symbol('n', odd=True)
+    m = Symbol('m', even=True)
+
+    assert (k + 7).is_even is True
+    assert (k + 7).is_odd is False
+
+    assert (-k + 7).is_even is True
+    assert (-k + 7).is_odd is False
+
+    assert (k - 12).is_even is False
+    assert (k - 12).is_odd is True
+
+    assert (-k - 12).is_even is False
+    assert (-k - 12).is_odd is True
+
+    assert (k + n).is_even is True
+    assert (k + n).is_odd is False
+
+    assert (k + m).is_even is False
+    assert (k + m).is_odd is True
+
+    assert (k + n + m).is_even is True
+    assert (k + n + m).is_odd is False
+
+    assert (k + n + x + m).is_even is None
+    assert (k + n + x + m).is_odd is None
+
+
+def test_Mul_is_negative_positive():
+    x = Symbol('x', real=True)
+    y = Symbol('y', extended_real=False, complex=True)
+    z = Symbol('z', zero=True)
+
+    e = 2*z
+    assert e.is_Mul and e.is_positive is False and e.is_negative is False
+
+    neg = Symbol('neg', negative=True)
+    pos = Symbol('pos', positive=True)
+    nneg = Symbol('nneg', nonnegative=True)
+    npos = Symbol('npos', nonpositive=True)
+
+    assert neg.is_negative is True
+    assert (-neg).is_negative is False
+    assert (2*neg).is_negative is True
+
+    assert (2*pos)._eval_is_extended_negative() is False
+    assert (2*pos).is_negative is False
+
+    assert pos.is_negative is False
+    assert (-pos).is_negative is True
+    assert (2*pos).is_negative is False
+
+    assert (pos*neg).is_negative is True
+    assert (2*pos*neg).is_negative is True
+    assert (-pos*neg).is_negative is False
+    assert (pos*neg*y).is_negative is False     # y.is_real=F;  !real -> !neg
+
+    assert nneg.is_negative is False
+    assert (-nneg).is_negative is None
+    assert (2*nneg).is_negative is False
+
+    assert npos.is_negative is None
+    assert (-npos).is_negative is False
+    assert (2*npos).is_negative is None
+
+    assert (nneg*npos).is_negative is None
+
+    assert (neg*nneg).is_negative is None
+    assert (neg*npos).is_negative is False
+
+    assert (pos*nneg).is_negative is False
+    assert (pos*npos).is_negative is None
+
+    assert (npos*neg*nneg).is_negative is False
+    assert (npos*pos*nneg).is_negative is None
+
+    assert (-npos*neg*nneg).is_negative is None
+    assert (-npos*pos*nneg).is_negative is False
+
+    assert (17*npos*neg*nneg).is_negative is False
+    assert (17*npos*pos*nneg).is_negative is None
+
+    assert (neg*npos*pos*nneg).is_negative is False
+
+    assert (x*neg).is_negative is None
+    assert (nneg*npos*pos*x*neg).is_negative is None
+
+    assert neg.is_positive is False
+    assert (-neg).is_positive is True
+    assert (2*neg).is_positive is False
+
+    assert pos.is_positive is True
+    assert (-pos).is_positive is False
+    assert (2*pos).is_positive is True
+
+    assert (pos*neg).is_positive is False
+    assert (2*pos*neg).is_positive is False
+    assert (-pos*neg).is_positive is True
+    assert (-pos*neg*y).is_positive is False    # y.is_real=F;  !real -> !neg
+
+    assert nneg.is_positive is None
+    assert (-nneg).is_positive is False
+    assert (2*nneg).is_positive is None
+
+    assert npos.is_positive is False
+    assert (-npos).is_positive is None
+    assert (2*npos).is_positive is False
+
+    assert (nneg*npos).is_positive is False
+
+    assert (neg*nneg).is_positive is False
+    assert (neg*npos).is_positive is None
+
+    assert (pos*nneg).is_positive is None
+    assert (pos*npos).is_positive is False
+
+    assert (npos*neg*nneg).is_positive is None
+    assert (npos*pos*nneg).is_positive is False
+
+    assert (-npos*neg*nneg).is_positive is False
+    assert (-npos*pos*nneg).is_positive is None
+
+    assert (17*npos*neg*nneg).is_positive is None
+    assert (17*npos*pos*nneg).is_positive is False
+
+    assert (neg*npos*pos*nneg).is_positive is None
+
+    assert (x*neg).is_positive is None
+    assert (nneg*npos*pos*x*neg).is_positive is None
+
+
+def test_Mul_is_negative_positive_2():
+    a = Symbol('a', nonnegative=True)
+    b = Symbol('b', nonnegative=True)
+    c = Symbol('c', nonpositive=True)
+    d = Symbol('d', nonpositive=True)
+
+    assert (a*b).is_nonnegative is True
+    assert (a*b).is_negative is False
+    assert (a*b).is_zero is None
+    assert (a*b).is_positive is None
+
+    assert (c*d).is_nonnegative is True
+    assert (c*d).is_negative is False
+    assert (c*d).is_zero is None
+    assert (c*d).is_positive is None
+
+    assert (a*c).is_nonpositive is True
+    assert (a*c).is_positive is False
+    assert (a*c).is_zero is None
+    assert (a*c).is_negative is None
+
+
+def test_Mul_is_nonpositive_nonnegative():
+    x = Symbol('x', real=True)
+
+    k = Symbol('k', negative=True)
+    n = Symbol('n', positive=True)
+    u = Symbol('u', nonnegative=True)
+    v = Symbol('v', nonpositive=True)
+
+    assert k.is_nonpositive is True
+    assert (-k).is_nonpositive is False
+    assert (2*k).is_nonpositive is True
+
+    assert n.is_nonpositive is False
+    assert (-n).is_nonpositive is True
+    assert (2*n).is_nonpositive is False
+
+    assert (n*k).is_nonpositive is True
+    assert (2*n*k).is_nonpositive is True
+    assert (-n*k).is_nonpositive is False
+
+    assert u.is_nonpositive is None
+    assert (-u).is_nonpositive is True
+    assert (2*u).is_nonpositive is None
+
+    assert v.is_nonpositive is True
+    assert (-v).is_nonpositive is None
+    assert (2*v).is_nonpositive is True
+
+    assert (u*v).is_nonpositive is True
+
+    assert (k*u).is_nonpositive is True
+    assert (k*v).is_nonpositive is None
+
+    assert (n*u).is_nonpositive is None
+    assert (n*v).is_nonpositive is True
+
+    assert (v*k*u).is_nonpositive is None
+    assert (v*n*u).is_nonpositive is True
+
+    assert (-v*k*u).is_nonpositive is True
+    assert (-v*n*u).is_nonpositive is None
+
+    assert (17*v*k*u).is_nonpositive is None
+    assert (17*v*n*u).is_nonpositive is True
+
+    assert (k*v*n*u).is_nonpositive is None
+
+    assert (x*k).is_nonpositive is None
+    assert (u*v*n*x*k).is_nonpositive is None
+
+    assert k.is_nonnegative is False
+    assert (-k).is_nonnegative is True
+    assert (2*k).is_nonnegative is False
+
+    assert n.is_nonnegative is True
+    assert (-n).is_nonnegative is False
+    assert (2*n).is_nonnegative is True
+
+    assert (n*k).is_nonnegative is False
+    assert (2*n*k).is_nonnegative is False
+    assert (-n*k).is_nonnegative is True
+
+    assert u.is_nonnegative is True
+    assert (-u).is_nonnegative is None
+    assert (2*u).is_nonnegative is True
+
+    assert v.is_nonnegative is None
+    assert (-v).is_nonnegative is True
+    assert (2*v).is_nonnegative is None
+
+    assert (u*v).is_nonnegative is None
+
+    assert (k*u).is_nonnegative is None
+    assert (k*v).is_nonnegative is True
+
+    assert (n*u).is_nonnegative is True
+    assert (n*v).is_nonnegative is None
+
+    assert (v*k*u).is_nonnegative is True
+    assert (v*n*u).is_nonnegative is None
+
+    assert (-v*k*u).is_nonnegative is None
+    assert (-v*n*u).is_nonnegative is True
+
+    assert (17*v*k*u).is_nonnegative is True
+    assert (17*v*n*u).is_nonnegative is None
+
+    assert (k*v*n*u).is_nonnegative is True
+
+    assert (x*k).is_nonnegative is None
+    assert (u*v*n*x*k).is_nonnegative is None
+
+
+def test_Add_is_negative_positive():
+    x = Symbol('x', real=True)
+
+    k = Symbol('k', negative=True)
+    n = Symbol('n', positive=True)
+    u = Symbol('u', nonnegative=True)
+    v = Symbol('v', nonpositive=True)
+
+    assert (k - 2).is_negative is True
+    assert (k + 17).is_negative is None
+    assert (-k - 5).is_negative is None
+    assert (-k + 123).is_negative is False
+
+    assert (k - n).is_negative is True
+    assert (k + n).is_negative is None
+    assert (-k - n).is_negative is None
+    assert (-k + n).is_negative is False
+
+    assert (k - n - 2).is_negative is True
+    assert (k + n + 17).is_negative is None
+    assert (-k - n - 5).is_negative is None
+    assert (-k + n + 123).is_negative is False
+
+    assert (-2*k + 123*n + 17).is_negative is False
+
+    assert (k + u).is_negative is None
+    assert (k + v).is_negative is True
+    assert (n + u).is_negative is False
+    assert (n + v).is_negative is None
+
+    assert (u - v).is_negative is False
+    assert (u + v).is_negative is None
+    assert (-u - v).is_negative is None
+    assert (-u + v).is_negative is None
+
+    assert (u - v + n + 2).is_negative is False
+    assert (u + v + n + 2).is_negative is None
+    assert (-u - v + n + 2).is_negative is None
+    assert (-u + v + n + 2).is_negative is None
+
+    assert (k + x).is_negative is None
+    assert (k + x - n).is_negative is None
+
+    assert (k - 2).is_positive is False
+    assert (k + 17).is_positive is None
+    assert (-k - 5).is_positive is None
+    assert (-k + 123).is_positive is True
+
+    assert (k - n).is_positive is False
+    assert (k + n).is_positive is None
+    assert (-k - n).is_positive is None
+    assert (-k + n).is_positive is True
+
+    assert (k - n - 2).is_positive is False
+    assert (k + n + 17).is_positive is None
+    assert (-k - n - 5).is_positive is None
+    assert (-k + n + 123).is_positive is True
+
+    assert (-2*k + 123*n + 17).is_positive is True
+
+    assert (k + u).is_positive is None
+    assert (k + v).is_positive is False
+    assert (n + u).is_positive is True
+    assert (n + v).is_positive is None
+
+    assert (u - v).is_positive is None
+    assert (u + v).is_positive is None
+    assert (-u - v).is_positive is None
+    assert (-u + v).is_positive is False
+
+    assert (u - v - n - 2).is_positive is None
+    assert (u + v - n - 2).is_positive is None
+    assert (-u - v - n - 2).is_positive is None
+    assert (-u + v - n - 2).is_positive is False
+
+    assert (n + x).is_positive is None
+    assert (n + x - k).is_positive is None
+
+    z = (-3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2)
+    assert z.is_zero
+    z = sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) - sqrt(10 + 6*sqrt(3))
+    assert z.is_zero
+
+
+def test_Add_is_nonpositive_nonnegative():
+    x = Symbol('x', real=True)
+
+    k = Symbol('k', negative=True)
+    n = Symbol('n', positive=True)
+    u = Symbol('u', nonnegative=True)
+    v = Symbol('v', nonpositive=True)
+
+    assert (u - 2).is_nonpositive is None
+    assert (u + 17).is_nonpositive is False
+    assert (-u - 5).is_nonpositive is True
+    assert (-u + 123).is_nonpositive is None
+
+    assert (u - v).is_nonpositive is None
+    assert (u + v).is_nonpositive is None
+    assert (-u - v).is_nonpositive is None
+    assert (-u + v).is_nonpositive is True
+
+    assert (u - v - 2).is_nonpositive is None
+    assert (u + v + 17).is_nonpositive is None
+    assert (-u - v - 5).is_nonpositive is None
+    assert (-u + v - 123).is_nonpositive is True
+
+    assert (-2*u + 123*v - 17).is_nonpositive is True
+
+    assert (k + u).is_nonpositive is None
+    assert (k + v).is_nonpositive is True
+    assert (n + u).is_nonpositive is False
+    assert (n + v).is_nonpositive is None
+
+    assert (k - n).is_nonpositive is True
+    assert (k + n).is_nonpositive is None
+    assert (-k - n).is_nonpositive is None
+    assert (-k + n).is_nonpositive is False
+
+    assert (k - n + u + 2).is_nonpositive is None
+    assert (k + n + u + 2).is_nonpositive is None
+    assert (-k - n + u + 2).is_nonpositive is None
+    assert (-k + n + u + 2).is_nonpositive is False
+
+    assert (u + x).is_nonpositive is None
+    assert (v - x - n).is_nonpositive is None
+
+    assert (u - 2).is_nonnegative is None
+    assert (u + 17).is_nonnegative is True
+    assert (-u - 5).is_nonnegative is False
+    assert (-u + 123).is_nonnegative is None
+
+    assert (u - v).is_nonnegative is True
+    assert (u + v).is_nonnegative is None
+    assert (-u - v).is_nonnegative is None
+    assert (-u + v).is_nonnegative is None
+
+    assert (u - v + 2).is_nonnegative is True
+    assert (u + v + 17).is_nonnegative is None
+    assert (-u - v - 5).is_nonnegative is None
+    assert (-u + v - 123).is_nonnegative is False
+
+    assert (2*u - 123*v + 17).is_nonnegative is True
+
+    assert (k + u).is_nonnegative is None
+    assert (k + v).is_nonnegative is False
+    assert (n + u).is_nonnegative is True
+    assert (n + v).is_nonnegative is None
+
+    assert (k - n).is_nonnegative is False
+    assert (k + n).is_nonnegative is None
+    assert (-k - n).is_nonnegative is None
+    assert (-k + n).is_nonnegative is True
+
+    assert (k - n - u - 2).is_nonnegative is False
+    assert (k + n - u - 2).is_nonnegative is None
+    assert (-k - n - u - 2).is_nonnegative is None
+    assert (-k + n - u - 2).is_nonnegative is None
+
+    assert (u - x).is_nonnegative is None
+    assert (v + x + n).is_nonnegative is None
+
+
+def test_Pow_is_integer():
+    x = Symbol('x')
+
+    k = Symbol('k', integer=True)
+    n = Symbol('n', integer=True, nonnegative=True)
+    m = Symbol('m', integer=True, positive=True)
+
+    assert (k**2).is_integer is True
+    assert (k**(-2)).is_integer is None
+    assert ((m + 1)**(-2)).is_integer is False
+    assert (m**(-1)).is_integer is None  # issue 8580
+
+    assert (2**k).is_integer is None
+    assert (2**(-k)).is_integer is None
+
+    assert (2**n).is_integer is True
+    assert (2**(-n)).is_integer is None
+
+    assert (2**m).is_integer is True
+    assert (2**(-m)).is_integer is False
+
+    assert (x**2).is_integer is None
+    assert (2**x).is_integer is None
+
+    assert (k**n).is_integer is True
+    assert (k**(-n)).is_integer is None
+
+    assert (k**x).is_integer is None
+    assert (x**k).is_integer is None
+
+    assert (k**(n*m)).is_integer is True
+    assert (k**(-n*m)).is_integer is None
+
+    assert sqrt(3).is_integer is False
+    assert sqrt(.3).is_integer is False
+    assert Pow(3, 2, evaluate=False).is_integer is True
+    assert Pow(3, 0, evaluate=False).is_integer is True
+    assert Pow(3, -2, evaluate=False).is_integer is False
+    assert Pow(S.Half, 3, evaluate=False).is_integer is False
+    # decided by re-evaluating
+    assert Pow(3, S.Half, evaluate=False).is_integer is False
+    assert Pow(3, S.Half, evaluate=False).is_integer is False
+    assert Pow(4, S.Half, evaluate=False).is_integer is True
+    assert Pow(S.Half, -2, evaluate=False).is_integer is True
+
+    assert ((-1)**k).is_integer
+
+    # issue 8641
+    x = Symbol('x', real=True, integer=False)
+    assert (x**2).is_integer is None
+
+    # issue 10458
+    x = Symbol('x', positive=True)
+    assert (1/(x + 1)).is_integer is False
+    assert (1/(-x - 1)).is_integer is False
+    assert (-1/(x + 1)).is_integer is False
+    # issue 23287
+    assert (x**2/2).is_integer is None
+
+    # issue 8648-like
+    k = Symbol('k', even=True)
+    assert (k**3/2).is_integer
+    assert (k**3/8).is_integer
+    assert (k**3/16).is_integer is None
+    assert (2/k).is_integer is None
+    assert (2/k**2).is_integer is False
+    o = Symbol('o', odd=True)
+    assert (k/o).is_integer is None
+    o = Symbol('o', odd=True, prime=True)
+    assert (k/o).is_integer is False
+
+
+def test_Pow_is_real():
+    x = Symbol('x', real=True)
+    y = Symbol('y', positive=True)
+
+    assert (x**2).is_real is True
+    assert (x**3).is_real is True
+    assert (x**x).is_real is None
+    assert (y**x).is_real is True
+
+    assert (x**Rational(1, 3)).is_real is None
+    assert (y**Rational(1, 3)).is_real is True
+
+    assert sqrt(-1 - sqrt(2)).is_real is False
+
+    i = Symbol('i', imaginary=True)
+    assert (i**i).is_real is None
+    assert (I**i).is_extended_real is True
+    assert ((-I)**i).is_extended_real is True
+    assert (2**i).is_real is None  # (2**(pi/log(2) * I)) is real, 2**I is not
+    assert (2**I).is_real is False
+    assert (2**-I).is_real is False
+    assert (i**2).is_extended_real is True
+    assert (i**3).is_extended_real is False
+    assert (i**x).is_real is None  # could be (-I)**(2/3)
+    e = Symbol('e', even=True)
+    o = Symbol('o', odd=True)
+    k = Symbol('k', integer=True)
+    assert (i**e).is_extended_real is True
+    assert (i**o).is_extended_real is False
+    assert (i**k).is_real is None
+    assert (i**(4*k)).is_extended_real is True
+
+    x = Symbol("x", nonnegative=True)
+    y = Symbol("y", nonnegative=True)
+    assert im(x**y).expand(complex=True) is S.Zero
+    assert (x**y).is_real is True
+    i = Symbol('i', imaginary=True)
+    assert (exp(i)**I).is_extended_real is True
+    assert log(exp(i)).is_imaginary is None  # i could be 2*pi*I
+    c = Symbol('c', complex=True)
+    assert log(c).is_real is None  # c could be 0 or 2, too
+    assert log(exp(c)).is_real is None  # log(0), log(E), ...
+    n = Symbol('n', negative=False)
+    assert log(n).is_real is None
+    n = Symbol('n', nonnegative=True)
+    assert log(n).is_real is None
+
+    assert sqrt(-I).is_real is False  # issue 7843
+
+    i = Symbol('i', integer=True)
+    assert (1/(i-1)).is_real is None
+    assert (1/(i-1)).is_extended_real is None
+
+    # test issue 20715
+    from sympy.core.parameters import evaluate
+    x = S(-1)
+    with evaluate(False):
+        assert x.is_negative is True
+
+    f = Pow(x, -1)
+    with evaluate(False):
+        assert f.is_imaginary is False
+
+
+def test_real_Pow():
+    k = Symbol('k', integer=True, nonzero=True)
+    assert (k**(I*pi/log(k))).is_real
+
+
+def test_Pow_is_finite():
+    xe = Symbol('xe', extended_real=True)
+    xr = Symbol('xr', real=True)
+    p = Symbol('p', positive=True)
+    n = Symbol('n', negative=True)
+    i = Symbol('i', integer=True)
+
+    assert (xe**2).is_finite is None  # xe could be oo
+    assert (xr**2).is_finite is True
+
+    assert (xe**xe).is_finite is None
+    assert (xr**xe).is_finite is None
+    assert (xe**xr).is_finite is None
+    # FIXME: The line below should be True rather than None
+    # assert (xr**xr).is_finite is True
+    assert (xr**xr).is_finite is None
+
+    assert (p**xe).is_finite is None
+    assert (p**xr).is_finite is True
+
+    assert (n**xe).is_finite is None
+    assert (n**xr).is_finite is True
+
+    assert (sin(xe)**2).is_finite is True
+    assert (sin(xr)**2).is_finite is True
+
+    assert (sin(xe)**xe).is_finite is None  # xe, xr could be -pi
+    assert (sin(xr)**xr).is_finite is None
+
+    # FIXME: Should the line below be True rather than None?
+    assert (sin(xe)**exp(xe)).is_finite is None
+    assert (sin(xr)**exp(xr)).is_finite is True
+
+    assert (1/sin(xe)).is_finite is None  # if zero, no, otherwise yes
+    assert (1/sin(xr)).is_finite is None
+
+    assert (1/exp(xe)).is_finite is None  # xe could be -oo
+    assert (1/exp(xr)).is_finite is True
+
+    assert (1/S.Pi).is_finite is True
+
+    assert (1/(i-1)).is_finite is None
+
+
+def test_Pow_is_even_odd():
+    x = Symbol('x')
+
+    k = Symbol('k', even=True)
+    n = Symbol('n', odd=True)
+    m = Symbol('m', integer=True, nonnegative=True)
+    p = Symbol('p', integer=True, positive=True)
+
+    assert ((-1)**n).is_odd
+    assert ((-1)**k).is_odd
+    assert ((-1)**(m - p)).is_odd
+
+    assert (k**2).is_even is True
+    assert (n**2).is_even is False
+    assert (2**k).is_even is None
+    assert (x**2).is_even is None
+
+    assert (k**m).is_even is None
+    assert (n**m).is_even is False
+
+    assert (k**p).is_even is True
+    assert (n**p).is_even is False
+
+    assert (m**k).is_even is None
+    assert (p**k).is_even is None
+
+    assert (m**n).is_even is None
+    assert (p**n).is_even is None
+
+    assert (k**x).is_even is None
+    assert (n**x).is_even is None
+
+    assert (k**2).is_odd is False
+    assert (n**2).is_odd is True
+    assert (3**k).is_odd is None
+
+    assert (k**m).is_odd is None
+    assert (n**m).is_odd is True
+
+    assert (k**p).is_odd is False
+    assert (n**p).is_odd is True
+
+    assert (m**k).is_odd is None
+    assert (p**k).is_odd is None
+
+    assert (m**n).is_odd is None
+    assert (p**n).is_odd is None
+
+    assert (k**x).is_odd is None
+    assert (n**x).is_odd is None
+
+
+def test_Pow_is_negative_positive():
+    r = Symbol('r', real=True)
+
+    k = Symbol('k', integer=True, positive=True)
+    n = Symbol('n', even=True)
+    m = Symbol('m', odd=True)
+
+    x = Symbol('x')
+
+    assert (2**r).is_positive is True
+    assert ((-2)**r).is_positive is None
+    assert ((-2)**n).is_positive is True
+    assert ((-2)**m).is_positive is False
+
+    assert (k**2).is_positive is True
+    assert (k**(-2)).is_positive is True
+
+    assert (k**r).is_positive is True
+    assert ((-k)**r).is_positive is None
+    assert ((-k)**n).is_positive is True
+    assert ((-k)**m).is_positive is False
+
+    assert (2**r).is_negative is False
+    assert ((-2)**r).is_negative is None
+    assert ((-2)**n).is_negative is False
+    assert ((-2)**m).is_negative is True
+
+    assert (k**2).is_negative is False
+    assert (k**(-2)).is_negative is False
+
+    assert (k**r).is_negative is False
+    assert ((-k)**r).is_negative is None
+    assert ((-k)**n).is_negative is False
+    assert ((-k)**m).is_negative is True
+
+    assert (2**x).is_positive is None
+    assert (2**x).is_negative is None
+
+
+def test_Pow_is_zero():
+    z = Symbol('z', zero=True)
+    e = z**2
+    assert e.is_zero
+    assert e.is_positive is False
+    assert e.is_negative is False
+
+    assert Pow(0, 0, evaluate=False).is_zero is False
+    assert Pow(0, 3, evaluate=False).is_zero
+    assert Pow(0, oo, evaluate=False).is_zero
+    assert Pow(0, -3, evaluate=False).is_zero is False
+    assert Pow(0, -oo, evaluate=False).is_zero is False
+    assert Pow(2, 2, evaluate=False).is_zero is False
+
+    a = Symbol('a', zero=False)
+    assert Pow(a, 3).is_zero is False  # issue 7965
+
+    assert Pow(2, oo, evaluate=False).is_zero is False
+    assert Pow(2, -oo, evaluate=False).is_zero
+    assert Pow(S.Half, oo, evaluate=False).is_zero
+    assert Pow(S.Half, -oo, evaluate=False).is_zero is False
+
+    # All combinations of real/complex base/exponent
+    h = S.Half
+    T = True
+    F = False
+    N = None
+
+    pow_iszero = [
+        ['**',  0,  h,  1,  2, -h, -1,-2,-2*I,-I/2,I/2,1+I,oo,-oo,zoo],
+        [   0,  F,  T,  T,  T,  F,  F,  F,  F,  F,  F,  N,  T,  F,  N],
+        [   h,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  F,  N],
+        [   1,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  N],
+        [   2,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  N],
+        [  -h,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  F,  N],
+        [  -1,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  N],
+        [  -2,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  N],
+        [-2*I,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  N],
+        [-I/2,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  F,  N],
+        [ I/2,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  F,  N],
+        [ 1+I,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  F,  T,  N],
+        [  oo,  F,  F,  F,  F,  T,  T,  T,  F,  F,  F,  F,  F,  T,  N],
+        [ -oo,  F,  F,  F,  F,  T,  T,  T,  F,  F,  F,  F,  F,  T,  N],
+        [ zoo,  F,  F,  F,  F,  T,  T,  T,  N,  N,  N,  N,  F,  T,  N]
+    ]
+
+    def test_table(table):
+        n = len(table[0])
+        for row in range(1, n):
+            base = table[row][0]
+            for col in range(1, n):
+                exp = table[0][col]
+                is_zero = table[row][col]
+                # The actual test here:
+                assert Pow(base, exp, evaluate=False).is_zero is is_zero
+
+    test_table(pow_iszero)
+
+    # A zero symbol...
+    zo, zo2 = symbols('zo, zo2', zero=True)
+
+    # All combinations of finite symbols
+    zf, zf2 = symbols('zf, zf2', finite=True)
+    wf, wf2 = symbols('wf, wf2', nonzero=True)
+    xf, xf2 = symbols('xf, xf2', real=True)
+    yf, yf2 = symbols('yf, yf2', nonzero=True)
+    af, af2 = symbols('af, af2', positive=True)
+    bf, bf2 = symbols('bf, bf2', nonnegative=True)
+    cf, cf2 = symbols('cf, cf2', negative=True)
+    df, df2 = symbols('df, df2', nonpositive=True)
+
+    # Without finiteness:
+    zi, zi2 = symbols('zi, zi2')
+    wi, wi2 = symbols('wi, wi2', zero=False)
+    xi, xi2 = symbols('xi, xi2', extended_real=True)
+    yi, yi2 = symbols('yi, yi2', zero=False, extended_real=True)
+    ai, ai2 = symbols('ai, ai2', extended_positive=True)
+    bi, bi2 = symbols('bi, bi2', extended_nonnegative=True)
+    ci, ci2 = symbols('ci, ci2', extended_negative=True)
+    di, di2 = symbols('di, di2', extended_nonpositive=True)
+
+    pow_iszero_sym = [
+        ['**',zo,wf,yf,af,cf,zf,xf,bf,df,zi,wi,xi,yi,ai,bi,ci,di],
+        [ zo2, F, N, N, T, F, N, N, N, F, N, N, N, N, T, N, F, F],
+        [ wf2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N],
+        [ yf2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N],
+        [ af2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N],
+        [ cf2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N],
+        [ zf2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ xf2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ bf2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ df2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ zi2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ wi2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N],
+        [ xi2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ yi2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N],
+        [ ai2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N],
+        [ bi2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N],
+        [ ci2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N],
+        [ di2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N]
+    ]
+
+    test_table(pow_iszero_sym)
+
+    # In some cases (x**x).is_zero is different from (x**y).is_zero even if y
+    # has the same assumptions as x.
+    assert (zo ** zo).is_zero is False
+    assert (wf ** wf).is_zero is False
+    assert (yf ** yf).is_zero is False
+    assert (af ** af).is_zero is False
+    assert (cf ** cf).is_zero is False
+    assert (zf ** zf).is_zero is None
+    assert (xf ** xf).is_zero is None
+    assert (bf ** bf).is_zero is False # None in table
+    assert (df ** df).is_zero is None
+    assert (zi ** zi).is_zero is None
+    assert (wi ** wi).is_zero is None
+    assert (xi ** xi).is_zero is None
+    assert (yi ** yi).is_zero is None
+    assert (ai ** ai).is_zero is False # None in table
+    assert (bi ** bi).is_zero is False # None in table
+    assert (ci ** ci).is_zero is None
+    assert (di ** di).is_zero is None
+
+
+def test_Pow_is_nonpositive_nonnegative():
+    x = Symbol('x', real=True)
+
+    k = Symbol('k', integer=True, nonnegative=True)
+    l = Symbol('l', integer=True, positive=True)
+    n = Symbol('n', even=True)
+    m = Symbol('m', odd=True)
+
+    assert (x**(4*k)).is_nonnegative is True
+    assert (2**x).is_nonnegative is True
+    assert ((-2)**x).is_nonnegative is None
+    assert ((-2)**n).is_nonnegative is True
+    assert ((-2)**m).is_nonnegative is False
+
+    assert (k**2).is_nonnegative is True
+    assert (k**(-2)).is_nonnegative is None
+    assert (k**k).is_nonnegative is True
+
+    assert (k**x).is_nonnegative is None    # NOTE (0**x).is_real = U
+    assert (l**x).is_nonnegative is True
+    assert (l**x).is_positive is True
+    assert ((-k)**x).is_nonnegative is None
+
+    assert ((-k)**m).is_nonnegative is None
+
+    assert (2**x).is_nonpositive is False
+    assert ((-2)**x).is_nonpositive is None
+    assert ((-2)**n).is_nonpositive is False
+    assert ((-2)**m).is_nonpositive is True
+
+    assert (k**2).is_nonpositive is None
+    assert (k**(-2)).is_nonpositive is None
+
+    assert (k**x).is_nonpositive is None
+    assert ((-k)**x).is_nonpositive is None
+    assert ((-k)**n).is_nonpositive is None
+
+
+    assert (x**2).is_nonnegative is True
+    i = symbols('i', imaginary=True)
+    assert (i**2).is_nonpositive is True
+    assert (i**4).is_nonpositive is False
+    assert (i**3).is_nonpositive is False
+    assert (I**i).is_nonnegative is True
+    assert (exp(I)**i).is_nonnegative is True
+
+    assert ((-l)**n).is_nonnegative is True
+    assert ((-l)**m).is_nonpositive is True
+    assert ((-k)**n).is_nonnegative is None
+    assert ((-k)**m).is_nonpositive is None
+
+
+def test_Mul_is_imaginary_real():
+    r = Symbol('r', real=True)
+    p = Symbol('p', positive=True)
+    i1 = Symbol('i1', imaginary=True)
+    i2 = Symbol('i2', imaginary=True)
+    x = Symbol('x')
+
+    assert I.is_imaginary is True
+    assert I.is_real is False
+    assert (-I).is_imaginary is True
+    assert (-I).is_real is False
+    assert (3*I).is_imaginary is True
+    assert (3*I).is_real is False
+    assert (I*I).is_imaginary is False
+    assert (I*I).is_real is True
+
+    e = (p + p*I)
+    j = Symbol('j', integer=True, zero=False)
+    assert (e**j).is_real is None
+    assert (e**(2*j)).is_real is None
+    assert (e**j).is_imaginary is None
+    assert (e**(2*j)).is_imaginary is None
+
+    assert (e**-1).is_imaginary is False
+    assert (e**2).is_imaginary
+    assert (e**3).is_imaginary is False
+    assert (e**4).is_imaginary is False
+    assert (e**5).is_imaginary is False
+    assert (e**-1).is_real is False
+    assert (e**2).is_real is False
+    assert (e**3).is_real is False
+    assert (e**4).is_real is True
+    assert (e**5).is_real is False
+    assert (e**3).is_complex
+
+    assert (r*i1).is_imaginary is None
+    assert (r*i1).is_real is None
+
+    assert (x*i1).is_imaginary is None
+    assert (x*i1).is_real is None
+
+    assert (i1*i2).is_imaginary is False
+    assert (i1*i2).is_real is True
+
+    assert (r*i1*i2).is_imaginary is False
+    assert (r*i1*i2).is_real is True
+
+    # Github's issue 5874:
+    nr = Symbol('nr', real=False, complex=True)  # e.g. I or 1 + I
+    a = Symbol('a', real=True, nonzero=True)
+    b = Symbol('b', real=True)
+    assert (i1*nr).is_real is None
+    assert (a*nr).is_real is False
+    assert (b*nr).is_real is None
+
+    ni = Symbol('ni', imaginary=False, complex=True)  # e.g. 2 or 1 + I
+    a = Symbol('a', real=True, nonzero=True)
+    b = Symbol('b', real=True)
+    assert (i1*ni).is_real is False
+    assert (a*ni).is_real is None
+    assert (b*ni).is_real is None
+
+
+def test_Mul_hermitian_antihermitian():
+    xz, yz = symbols('xz, yz', zero=True, antihermitian=True)
+    xf, yf = symbols('xf, yf', hermitian=False, antihermitian=False, finite=True)
+    xh, yh = symbols('xh, yh', hermitian=True, antihermitian=False, nonzero=True)
+    xa, ya = symbols('xa, ya', hermitian=False, antihermitian=True, zero=False, finite=True)
+    assert (xz*xh).is_hermitian is True
+    assert (xz*xh).is_antihermitian is True
+    assert (xz*xa).is_hermitian is True
+    assert (xz*xa).is_antihermitian is True
+    assert (xf*yf).is_hermitian is None
+    assert (xf*yf).is_antihermitian is None
+    assert (xh*yh).is_hermitian is True
+    assert (xh*yh).is_antihermitian is False
+    assert (xh*ya).is_hermitian is False
+    assert (xh*ya).is_antihermitian is True
+    assert (xa*ya).is_hermitian is True
+    assert (xa*ya).is_antihermitian is False
+
+    a = Symbol('a', hermitian=True, zero=False)
+    b = Symbol('b', hermitian=True)
+    c = Symbol('c', hermitian=False)
+    d = Symbol('d', antihermitian=True)
+    e1 = Mul(a, b, c, evaluate=False)
+    e2 = Mul(b, a, c, evaluate=False)
+    e3 = Mul(a, b, c, d, evaluate=False)
+    e4 = Mul(b, a, c, d, evaluate=False)
+    e5 = Mul(a, c, evaluate=False)
+    e6 = Mul(a, c, d, evaluate=False)
+    assert e1.is_hermitian is None
+    assert e2.is_hermitian is None
+    assert e1.is_antihermitian is None
+    assert e2.is_antihermitian is None
+    assert e3.is_antihermitian is None
+    assert e4.is_antihermitian is None
+    assert e5.is_antihermitian is None
+    assert e6.is_antihermitian is None
+
+
+def test_Add_is_comparable():
+    assert (x + y).is_comparable is False
+    assert (x + 1).is_comparable is False
+    assert (Rational(1, 3) - sqrt(8)).is_comparable is True
+
+
+def test_Mul_is_comparable():
+    assert (x*y).is_comparable is False
+    assert (x*2).is_comparable is False
+    assert (sqrt(2)*Rational(1, 3)).is_comparable is True
+
+
+def test_Pow_is_comparable():
+    assert (x**y).is_comparable is False
+    assert (x**2).is_comparable is False
+    assert (sqrt(Rational(1, 3))).is_comparable is True
+
+
+def test_Add_is_positive_2():
+    e = Rational(1, 3) - sqrt(8)
+    assert e.is_positive is False
+    assert e.is_negative is True
+
+    e = pi - 1
+    assert e.is_positive is True
+    assert e.is_negative is False
+
+
+def test_Add_is_irrational():
+    i = Symbol('i', irrational=True)
+
+    assert i.is_irrational is True
+    assert i.is_rational is False
+
+    assert (i + 1).is_irrational is True
+    assert (i + 1).is_rational is False
+
+
+def test_Mul_is_irrational():
+    expr = Mul(1, 2, 3, evaluate=False)
+    assert expr.is_irrational is False
+    expr = Mul(1, I, I, evaluate=False)
+    assert expr.is_rational is None # I * I = -1 but *no evaluation allowed*
+    # sqrt(2) * I * I = -sqrt(2) is irrational but
+    # this can't be determined without evaluating the
+    # expression and the eval_is routines shouldn't do that
+    expr = Mul(sqrt(2), I, I, evaluate=False)
+    assert expr.is_irrational is None
+
+
+def test_issue_3531():
+    # https://github.com/sympy/sympy/issues/3531
+    # https://github.com/sympy/sympy/pull/18116
+    class MightyNumeric(tuple):
+        __slots__ = ()
+
+        def __rtruediv__(self, other):
+            return "something"
+
+    assert sympify(1)/MightyNumeric((1, 2)) == "something"
+
+
+def test_issue_3531b():
+    class Foo:
+        def __init__(self):
+            self.field = 1.0
+
+        def __mul__(self, other):
+            self.field = self.field * other
+
+        def __rmul__(self, other):
+            self.field = other * self.field
+    f = Foo()
+    x = Symbol("x")
+    assert f*x == x*f
+
+
+def test_bug3():
+    a = Symbol("a")
+    b = Symbol("b", positive=True)
+    e = 2*a + b
+    f = b + 2*a
+    assert e == f
+
+
+def test_suppressed_evaluation():
+    a = Add(0, 3, 2, evaluate=False)
+    b = Mul(1, 3, 2, evaluate=False)
+    c = Pow(3, 2, evaluate=False)
+    assert a != 6
+    assert a.func is Add
+    assert a.args == (0, 3, 2)
+    assert b != 6
+    assert b.func is Mul
+    assert b.args == (1, 3, 2)
+    assert c != 9
+    assert c.func is Pow
+    assert c.args == (3, 2)
+
+
+def test_AssocOp_doit():
+    a = Add(x,x, evaluate=False)
+    b = Mul(y,y, evaluate=False)
+    c = Add(b,b, evaluate=False)
+    d = Mul(a,a, evaluate=False)
+    assert c.doit(deep=False).func == Mul
+    assert c.doit(deep=False).args == (2,y,y)
+    assert c.doit().func == Mul
+    assert c.doit().args == (2, Pow(y,2))
+    assert d.doit(deep=False).func == Pow
+    assert d.doit(deep=False).args == (a, 2*S.One)
+    assert d.doit().func == Mul
+    assert d.doit().args == (4*S.One, Pow(x,2))
+
+
+def test_Add_Mul_Expr_args():
+    nonexpr = [Basic(), Poly(x, x), FiniteSet(x)]
+    for typ in [Add, Mul]:
+        for obj in nonexpr:
+            # The cache can mess with the stacklevel check
+            with warns(SymPyDeprecationWarning, test_stacklevel=False):
+                typ(obj, 1)
+
+
+def test_Add_as_coeff_mul():
+    # issue 5524.  These should all be (1, self)
+    assert (x + 1).as_coeff_mul() == (1, (x + 1,))
+    assert (x + 2).as_coeff_mul() == (1, (x + 2,))
+    assert (x + 3).as_coeff_mul() == (1, (x + 3,))
+
+    assert (x - 1).as_coeff_mul() == (1, (x - 1,))
+    assert (x - 2).as_coeff_mul() == (1, (x - 2,))
+    assert (x - 3).as_coeff_mul() == (1, (x - 3,))
+
+    n = Symbol('n', integer=True)
+    assert (n + 1).as_coeff_mul() == (1, (n + 1,))
+    assert (n + 2).as_coeff_mul() == (1, (n + 2,))
+    assert (n + 3).as_coeff_mul() == (1, (n + 3,))
+
+    assert (n - 1).as_coeff_mul() == (1, (n - 1,))
+    assert (n - 2).as_coeff_mul() == (1, (n - 2,))
+    assert (n - 3).as_coeff_mul() == (1, (n - 3,))
+
+
+def test_Pow_as_coeff_mul_doesnt_expand():
+    assert exp(x + y).as_coeff_mul() == (1, (exp(x + y),))
+    assert exp(x + exp(x + y)) != exp(x + exp(x)*exp(y))
+
+def test_issue_24751():
+    expr = Add(-2, -3, evaluate=False)
+    expr1 = Add(-1, expr, evaluate=False)
+    assert int(expr1) == int((-3 - 2) - 1)
+
+
+def test_issue_3514_18626():
+    assert sqrt(S.Half) * sqrt(6) == 2 * sqrt(3)/2
+    assert S.Half*sqrt(6)*sqrt(2) == sqrt(3)
+    assert sqrt(6)/2*sqrt(2) == sqrt(3)
+    assert sqrt(6)*sqrt(2)/2 == sqrt(3)
+    assert sqrt(8)**Rational(2, 3) == 2
+
+
+def test_make_args():
+    assert Add.make_args(x) == (x,)
+    assert Mul.make_args(x) == (x,)
+
+    assert Add.make_args(x*y*z) == (x*y*z,)
+    assert Mul.make_args(x*y*z) == (x*y*z).args
+
+    assert Add.make_args(x + y + z) == (x + y + z).args
+    assert Mul.make_args(x + y + z) == (x + y + z,)
+
+    assert Add.make_args((x + y)**z) == ((x + y)**z,)
+    assert Mul.make_args((x + y)**z) == ((x + y)**z,)
+
+
+def test_issue_5126():
+    assert (-2)**x*(-3)**x != 6**x
+    i = Symbol('i', integer=1)
+    assert (-2)**i*(-3)**i == 6**i
+
+
+def test_Rational_as_content_primitive():
+    c, p = S.One, S.Zero
+    assert (c*p).as_content_primitive() == (c, p)
+    c, p = S.Half, S.One
+    assert (c*p).as_content_primitive() == (c, p)
+
+
+def test_Add_as_content_primitive():
+    assert (x + 2).as_content_primitive() == (1, x + 2)
+
+    assert (3*x + 2).as_content_primitive() == (1, 3*x + 2)
+    assert (3*x + 3).as_content_primitive() == (3, x + 1)
+    assert (3*x + 6).as_content_primitive() == (3, x + 2)
+
+    assert (3*x + 2*y).as_content_primitive() == (1, 3*x + 2*y)
+    assert (3*x + 3*y).as_content_primitive() == (3, x + y)
+    assert (3*x + 6*y).as_content_primitive() == (3, x + 2*y)
+
+    assert (3/x + 2*x*y*z**2).as_content_primitive() == (1, 3/x + 2*x*y*z**2)
+    assert (3/x + 3*x*y*z**2).as_content_primitive() == (3, 1/x + x*y*z**2)
+    assert (3/x + 6*x*y*z**2).as_content_primitive() == (3, 1/x + 2*x*y*z**2)
+
+    assert (2*x/3 + 4*y/9).as_content_primitive() == \
+        (Rational(2, 9), 3*x + 2*y)
+    assert (2*x/3 + 2.5*y).as_content_primitive() == \
+        (Rational(1, 3), 2*x + 7.5*y)
+
+    # the coefficient may sort to a position other than 0
+    p = 3 + x + y
+    assert (2*p).expand().as_content_primitive() == (2, p)
+    assert (2.0*p).expand().as_content_primitive() == (1, 2.*p)
+    p *= -1
+    assert (2*p).expand().as_content_primitive() == (2, p)
+
+
+def test_Mul_as_content_primitive():
+    assert (2*x).as_content_primitive() == (2, x)
+    assert (x*(2 + 2*x)).as_content_primitive() == (2, x*(1 + x))
+    assert (x*(2 + 2*y)*(3*x + 3)**2).as_content_primitive() == \
+        (18, x*(1 + y)*(x + 1)**2)
+    assert ((2 + 2*x)**2*(3 + 6*x) + S.Half).as_content_primitive() == \
+        (S.Half, 24*(x + 1)**2*(2*x + 1) + 1)
+
+
+def test_Pow_as_content_primitive():
+    assert (x**y).as_content_primitive() == (1, x**y)
+    assert ((2*x + 2)**y).as_content_primitive() == \
+        (1, (Mul(2, (x + 1), evaluate=False))**y)
+    assert ((2*x + 2)**3).as_content_primitive() == (8, (x + 1)**3)
+
+
+def test_issue_5460():
+    u = Mul(2, (1 + x), evaluate=False)
+    assert (2 + u).args == (2, u)
+
+
+def test_product_irrational():
+    assert (I*pi).is_irrational is False
+    # The following used to be deduced from the above bug:
+    assert (I*pi).is_positive is False
+
+
+def test_issue_5919():
+    assert (x/(y*(1 + y))).expand() == x/(y**2 + y)
+
+
+def test_Mod():
+    assert Mod(x, 1).func is Mod
+    assert pi % pi is S.Zero
+    assert Mod(5, 3) == 2
+    assert Mod(-5, 3) == 1
+    assert Mod(5, -3) == -1
+    assert Mod(-5, -3) == -2
+    assert type(Mod(3.2, 2, evaluate=False)) == Mod
+    assert 5 % x == Mod(5, x)
+    assert x % 5 == Mod(x, 5)
+    assert x % y == Mod(x, y)
+    assert (x % y).subs({x: 5, y: 3}) == 2
+    assert Mod(nan, 1) is nan
+    assert Mod(1, nan) is nan
+    assert Mod(nan, nan) is nan
+
+    assert Mod(0, x) == 0
+    with raises(ZeroDivisionError):
+        Mod(x, 0)
+
+    k = Symbol('k', integer=True)
+    m = Symbol('m', integer=True, positive=True)
+    assert (x**m % x).func is Mod
+    assert (k**(-m) % k).func is Mod
+    assert k**m % k == 0
+    assert (-2*k)**m % k == 0
+
+    # Float handling
+    point3 = Float(3.3) % 1
+    assert (x - 3.3) % 1 == Mod(1.*x + 1 - point3, 1)
+    assert Mod(-3.3, 1) == 1 - point3
+    assert Mod(0.7, 1) == Float(0.7)
+    e = Mod(1.3, 1)
+    assert comp(e, .3) and e.is_Float
+    e = Mod(1.3, .7)
+    assert comp(e, .6) and e.is_Float
+    e = Mod(1.3, Rational(7, 10))
+    assert comp(e, .6) and e.is_Float
+    e = Mod(Rational(13, 10), 0.7)
+    assert comp(e, .6) and e.is_Float
+    e = Mod(Rational(13, 10), Rational(7, 10))
+    assert comp(e, .6) and e.is_Rational
+
+    # check that sign is right
+    r2 = sqrt(2)
+    r3 = sqrt(3)
+    for i in [-r3, -r2, r2, r3]:
+        for j in [-r3, -r2, r2, r3]:
+            assert verify_numerically(i % j, i.n() % j.n())
+    for _x in range(4):
+        for _y in range(9):
+            reps = [(x, _x), (y, _y)]
+            assert Mod(3*x + y, 9).subs(reps) == (3*_x + _y) % 9
+
+    # denesting
+    t = Symbol('t', real=True)
+    assert Mod(Mod(x, t), t) == Mod(x, t)
+    assert Mod(-Mod(x, t), t) == Mod(-x, t)
+    assert Mod(Mod(x, 2*t), t) == Mod(x, t)
+    assert Mod(-Mod(x, 2*t), t) == Mod(-x, t)
+    assert Mod(Mod(x, t), 2*t) == Mod(x, t)
+    assert Mod(-Mod(x, t), -2*t) == -Mod(x, t)
+    for i in [-4, -2, 2, 4]:
+        for j in [-4, -2, 2, 4]:
+            for k in range(4):
+                assert Mod(Mod(x, i), j).subs({x: k}) == (k % i) % j
+                assert Mod(-Mod(x, i), j).subs({x: k}) == -(k % i) % j
+
+    # known difference
+    assert Mod(5*sqrt(2), sqrt(5)) == 5*sqrt(2) - 3*sqrt(5)
+    p = symbols('p', positive=True)
+    assert Mod(2, p + 3) == 2
+    assert Mod(-2, p + 3) == p + 1
+    assert Mod(2, -p - 3) == -p - 1
+    assert Mod(-2, -p - 3) == -2
+    assert Mod(p + 5, p + 3) == 2
+    assert Mod(-p - 5, p + 3) == p + 1
+    assert Mod(p + 5, -p - 3) == -p - 1
+    assert Mod(-p - 5, -p - 3) == -2
+    assert Mod(p + 1, p - 1).func is Mod
+
+    # issue 27749
+    n = symbols('n', integer=True, positive=True)
+    assert unchanged(Mod, 1, n)
+    n = symbols('n', prime=True)
+    assert Mod(1, n) == 1
+
+    # handling sums
+    assert (x + 3) % 1 == Mod(x, 1)
+    assert (x + 3.0) % 1 == Mod(1.*x, 1)
+    assert (x - S(33)/10) % 1 == Mod(x + S(7)/10, 1)
+
+    a = Mod(.6*x + y, .3*y)
+    b = Mod(0.1*y + 0.6*x, 0.3*y)
+    # Test that a, b are equal, with 1e-14 accuracy in coefficients
+    eps = 1e-14
+    assert abs((a.args[0] - b.args[0]).subs({x: 1, y: 1})) < eps
+    assert abs((a.args[1] - b.args[1]).subs({x: 1, y: 1})) < eps
+
+    assert (x + 1) % x == 1 % x
+    assert (x + y) % x == y % x
+    assert (x + y + 2) % x == (y + 2) % x
+    assert (a + 3*x + 1) % (2*x) == Mod(a + x + 1, 2*x)
+    assert (12*x + 18*y) % (3*x) == 3*Mod(6*y, x)
+
+    # gcd extraction
+    assert (-3*x) % (-2*y) == -Mod(3*x, 2*y)
+    assert (.6*pi) % (.3*x*pi) == 0.3*pi*Mod(2, x)
+    assert (.6*pi) % (.31*x*pi) == pi*Mod(0.6, 0.31*x)
+    assert (6*pi) % (.3*x*pi) == 0.3*pi*Mod(20, x)
+    assert (6*pi) % (.31*x*pi) == pi*Mod(6, 0.31*x)
+    assert (6*pi) % (.42*x*pi) == pi*Mod(6, 0.42*x)
+    assert (12*x) % (2*y) == 2*Mod(6*x, y)
+    assert (12*x) % (3*5*y) == 3*Mod(4*x, 5*y)
+    assert (12*x) % (15*x*y) == 3*x*Mod(4, 5*y)
+    assert (-2*pi) % (3*pi) == pi
+    assert (2*x + 2) % (x + 1) == 0
+    assert (x*(x + 1)) % (x + 1) == (x + 1)*Mod(x, 1)
+    assert Mod(5.0*x, 0.1*y) == 0.1*Mod(50*x, y)
+    i = Symbol('i', integer=True)
+    assert (3*i*x) % (2*i*y) == i*Mod(3*x, 2*y)
+    assert Mod(4*i, 4) == 0
+
+    # issue 8677
+    n = Symbol('n', integer=True, positive=True)
+    assert factorial(n) % n == 0
+    assert factorial(n + 2) % n == 0
+    assert (factorial(n + 4) % (n + 5)).func is Mod
+
+    # Wilson's theorem
+    assert factorial(18042, evaluate=False) % 18043 == 18042
+    p = Symbol('n', prime=True)
+    assert factorial(p - 1) % p == p - 1
+    assert factorial(p - 1) % -p == -1
+    assert (factorial(3, evaluate=False) % 4).doit() == 2
+    n = Symbol('n', composite=True, odd=True)
+    assert factorial(n - 1) % n == 0
+
+    # symbolic with known parity
+    n = Symbol('n', even=True)
+    assert Mod(n, 2) == 0
+    n = Symbol('n', odd=True)
+    assert Mod(n, 2) == 1
+
+    # issue 10963
+    assert (x**6000%400).args[1] == 400
+
+    #issue 13543
+    assert Mod(Mod(x + 1, 2) + 1, 2) == Mod(x, 2)
+
+    x1 = Symbol('x1', integer=True)
+    assert Mod(Mod(x1 + 2, 4)*(x1 + 4), 4) == Mod(x1*(x1 + 2), 4)
+    assert Mod(Mod(x1 + 2, 4)*4, 4) == 0
+
+    # issue 15493
+    i, j = symbols('i j', integer=True, positive=True)
+    assert Mod(3*i, 2) == Mod(i, 2)
+    assert Mod(8*i/j, 4) == 4*Mod(2*i/j, 1)
+    assert Mod(8*i, 4) == 0
+
+    # rewrite
+    assert Mod(x, y).rewrite(floor) == x - y*floor(x/y)
+    assert ((x - Mod(x, y))/y).rewrite(floor) == floor(x/y)
+
+    # issue 21373
+    from sympy.functions.elementary.hyperbolic import sinh
+    from sympy.functions.elementary.piecewise import Piecewise
+
+    x_r, y_r = symbols('x_r y_r', real=True)
+    assert (Piecewise((x_r, y_r > x_r), (y_r, True)) / z) % 1
+    expr = exp(sinh(Piecewise((x_r, y_r > x_r), (y_r, True)) / z))
+    expr.subs({1: 1.0})
+    sinh(Piecewise((x_r, y_r > x_r), (y_r, True)) * z ** -1.0).is_zero
+
+    # issue 24215
+    from sympy.abc import phi
+    assert Mod(4.0*Mod(phi, 1) , 2) == 2.0*(Mod(2*(Mod(phi, 1)), 1))
+
+    xi = symbols('x', integer=True)
+    assert unchanged(Mod, xi, 2)
+    assert Mod(3*xi, 2) == Mod(xi, 2)
+    assert unchanged(Mod, 3*x, 2)
+
+
+def test_Mod_Pow():
+    # modular exponentiation
+    assert isinstance(Mod(Pow(2, 2, evaluate=False), 3), Integer)
+
+    assert Mod(Pow(4, 13, evaluate=False), 497) == Mod(Pow(4, 13), 497)
+    assert Mod(Pow(2, 10000000000, evaluate=False), 3) == 1
+    assert Mod(Pow(32131231232, 9**10**6, evaluate=False),10**12) == \
+        pow(32131231232,9**10**6,10**12)
+    assert Mod(Pow(33284959323, 123**999, evaluate=False),11**13) == \
+        pow(33284959323,123**999,11**13)
+    assert Mod(Pow(78789849597, 333**555, evaluate=False),12**9) == \
+        pow(78789849597,333**555,12**9)
+
+    # modular nested exponentiation
+    expr = Pow(2, 2, evaluate=False)
+    expr = Pow(2, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 16
+    expr = Pow(2, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 6487
+    expr = Pow(2, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 32191
+    expr = Pow(2, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 18016
+    expr = Pow(2, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 5137
+
+    expr = Pow(2, 2, evaluate=False)
+    expr = Pow(expr, 2, evaluate=False)
+    assert Mod(expr, 3**10) == 16
+    expr = Pow(expr, 2, evaluate=False)
+    assert Mod(expr, 3**10) == 256
+    expr = Pow(expr, 2, evaluate=False)
+    assert Mod(expr, 3**10) == 6487
+    expr = Pow(expr, 2, evaluate=False)
+    assert Mod(expr, 3**10) == 38281
+    expr = Pow(expr, 2, evaluate=False)
+    assert Mod(expr, 3**10) == 15928
+
+    expr = Pow(2, 2, evaluate=False)
+    expr = Pow(expr, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 256
+    expr = Pow(expr, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 9229
+    expr = Pow(expr, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 25708
+    expr = Pow(expr, expr, evaluate=False)
+    assert Mod(expr, 3**10) == 26608
+    expr = Pow(expr, expr, evaluate=False)
+    # XXX This used to fail in a nondeterministic way because of overflow
+    # error.
+    assert Mod(expr, 3**10) == 1966
+
+
+def test_Mod_is_integer():
+    p = Symbol('p', integer=True)
+    q1 = Symbol('q1', integer=True)
+    q2 = Symbol('q2', integer=True, nonzero=True)
+    assert Mod(x, y).is_integer is None
+    assert Mod(p, q1).is_integer is None
+    assert Mod(x, q2).is_integer is None
+    assert Mod(p, q2).is_integer
+
+
+def test_Mod_is_nonposneg():
+    n = Symbol('n', integer=True)
+    k = Symbol('k', integer=True, positive=True)
+    assert (n%3).is_nonnegative
+    assert Mod(n, -3).is_nonpositive
+    assert Mod(n, k).is_nonnegative
+    assert Mod(n, -k).is_nonpositive
+    assert Mod(k, n).is_nonnegative is None
+
+
+def test_issue_6001():
+    A = Symbol("A", commutative=False)
+    eq = A + A**2
+    # it doesn't matter whether it's True or False; they should
+    # just all be the same
+    assert (
+        eq.is_commutative ==
+        (eq + 1).is_commutative ==
+        (A + 1).is_commutative)
+
+    B = Symbol("B", commutative=False)
+    # Although commutative terms could cancel we return True
+    # meaning "there are non-commutative symbols; aftersubstitution
+    # that definition can change, e.g. (A*B).subs(B,A**-1) -> 1
+    assert (sqrt(2)*A).is_commutative is False
+    assert (sqrt(2)*A*B).is_commutative is False
+
+
+def test_polar():
+    from sympy.functions.elementary.complexes import polar_lift
+    p = Symbol('p', polar=True)
+    x = Symbol('x')
+    assert p.is_polar
+    assert x.is_polar is None
+    assert S.One.is_polar is None
+    assert (p**x).is_polar is True
+    assert (x**p).is_polar is None
+    assert ((2*p)**x).is_polar is True
+    assert (2*p).is_polar is True
+    assert (-2*p).is_polar is not True
+    assert (polar_lift(-2)*p).is_polar is True
+
+    q = Symbol('q', polar=True)
+    assert (p*q)**2 == p**2 * q**2
+    assert (2*q)**2 == 4 * q**2
+    assert ((p*q)**x).expand() == p**x * q**x
+
+
+def test_issue_6040():
+    a, b = Pow(1, 2, evaluate=False), S.One
+    assert a != b
+    assert b != a
+    assert not (a == b)
+    assert not (b == a)
+
+
+def test_issue_6082():
+    # Comparison is symmetric
+    assert Basic.compare(Max(x, 1), Max(x, 2)) == \
+      - Basic.compare(Max(x, 2), Max(x, 1))
+    # Equal expressions compare equal
+    assert Basic.compare(Max(x, 1), Max(x, 1)) == 0
+    # Basic subtypes (such as Max) compare different than standard types
+    assert Basic.compare(Max(1, x), frozenset((1, x))) != 0
+
+
+def test_issue_6077():
+    assert x**2.0/x == x**1.0
+    assert x/x**2.0 == x**-1.0
+    assert x*x**2.0 == x**3.0
+    assert x**1.5*x**2.5 == x**4.0
+
+    assert 2**(2.0*x)/2**x == 2**(1.0*x)
+    assert 2**x/2**(2.0*x) == 2**(-1.0*x)
+    assert 2**x*2**(2.0*x) == 2**(3.0*x)
+    assert 2**(1.5*x)*2**(2.5*x) == 2**(4.0*x)
+
+
+def test_mul_flatten_oo():
+    p = symbols('p', positive=True)
+    n, m = symbols('n,m', negative=True)
+    x_im = symbols('x_im', imaginary=True)
+    assert n*oo is -oo
+    assert n*m*oo is oo
+    assert p*oo is oo
+    assert x_im*oo != I*oo  # i could be +/- 3*I -> +/-oo
+
+
+def test_add_flatten():
+    # see https://github.com/sympy/sympy/issues/2633#issuecomment-29545524
+    a = oo + I*oo
+    b = oo - I*oo
+    assert a + b is nan
+    assert a - b is nan
+    # FIXME: This evaluates as:
+    #   >>> 1/a
+    #   0*(oo + oo*I)
+    # which should not simplify to 0. Should be fixed in Pow.eval
+    #assert (1/a).simplify() == (1/b).simplify() == 0
+
+    a = Pow(2, 3, evaluate=False)
+    assert a + a == 16
+
+
+def test_issue_5160_6087_6089_6090():
+    # issue 6087
+    assert ((-2*x*y**y)**3.2).n(2) == (2**3.2*(-x*y**y)**3.2).n(2)
+    # issue 6089
+    A, B, C = symbols('A,B,C', commutative=False)
+    assert (2.*B*C)**3 == 8.0*(B*C)**3
+    assert (-2.*B*C)**3 == -8.0*(B*C)**3
+    assert (-2*B*C)**2 == 4*(B*C)**2
+    # issue 5160
+    assert sqrt(-1.0*x) == 1.0*sqrt(-x)
+    assert sqrt(1.0*x) == 1.0*sqrt(x)
+    # issue 6090
+    assert (-2*x*y*A*B)**2 == 4*x**2*y**2*(A*B)**2
+
+
+def test_float_int_round():
+    assert int(float(sqrt(10))) == int(sqrt(10))
+    assert int(pi**1000) % 10 == 2
+    assert int(Float('1.123456789012345678901234567890e20', '')) == \
+        int(112345678901234567890)
+    assert int(Float('1.123456789012345678901234567890e25', '')) == \
+        int(11234567890123456789012345)
+    # decimal forces float so it's not an exact integer ending in 000000
+    assert int(Float('1.123456789012345678901234567890e35', '')) == \
+        112345678901234567890123456789000192
+    assert int(Float('123456789012345678901234567890e5', '')) == \
+        12345678901234567890123456789000000
+    assert Integer(Float('1.123456789012345678901234567890e20', '')) == \
+        112345678901234567890
+    assert Integer(Float('1.123456789012345678901234567890e25', '')) == \
+        11234567890123456789012345
+    # decimal forces float so it's not an exact integer ending in 000000
+    assert Integer(Float('1.123456789012345678901234567890e35', '')) == \
+        112345678901234567890123456789000192
+    assert Integer(Float('123456789012345678901234567890e5', '')) == \
+        12345678901234567890123456789000000
+    assert same_and_same_prec(Float('123000e-2',''), Float('1230.00', ''))
+    assert same_and_same_prec(Float('123000e2',''), Float('12300000', ''))
+
+    assert int(1 + Rational('.9999999999999999999999999')) == 1
+    assert int(pi/1e20) == 0
+    assert int(1 + pi/1e20) == 1
+    assert int(Add(1.2, -2, evaluate=False)) == int(1.2 - 2)
+    assert int(Add(1.2, +2, evaluate=False)) == int(1.2 + 2)
+    assert int(Add(1 + Float('.99999999999999999', ''), evaluate=False)) == 1
+    raises(TypeError, lambda: float(x))
+    raises(TypeError, lambda: float(sqrt(-1)))
+
+    assert int(12345678901234567890 + cos(1)**2 + sin(1)**2) == \
+        12345678901234567891
+
+
+def test_issue_6611a():
+    assert Mul.flatten([3**Rational(1, 3),
+        Pow(-Rational(1, 9), Rational(2, 3), evaluate=False)]) == \
+        ([Rational(1, 3), (-1)**Rational(2, 3)], [], None)
+
+
+def test_denest_add_mul():
+    # when working with evaluated expressions make sure they denest
+    eq = x + 1
+    eq = Add(eq, 2, evaluate=False)
+    eq = Add(eq, 2, evaluate=False)
+    assert Add(*eq.args) == x + 5
+    eq = x*2
+    eq = Mul(eq, 2, evaluate=False)
+    eq = Mul(eq, 2, evaluate=False)
+    assert Mul(*eq.args) == 8*x
+    # but don't let them denest unnecessarily
+    eq = Mul(-2, x - 2, evaluate=False)
+    assert 2*eq == Mul(-4, x - 2, evaluate=False)
+    assert -eq == Mul(2, x - 2, evaluate=False)
+
+
+def test_mul_coeff():
+    # It is important that all Numbers be removed from the seq;
+    # This can be tricky when powers combine to produce those numbers
+    p = exp(I*pi/3)
+    assert p**2*x*p*y*p*x*p**2 == x**2*y
+
+
+def test_mul_zero_detection():
+    nz = Dummy(real=True, zero=False)
+    r = Dummy(extended_real=True)
+    c = Dummy(real=False, complex=True)
+    c2 = Dummy(real=False, complex=True)
+    i = Dummy(imaginary=True)
+    e = nz*r*c
+    assert e.is_imaginary is None
+    assert e.is_extended_real is None
+    e = nz*c
+    assert e.is_imaginary is None
+    assert e.is_extended_real is False
+    e = nz*i*c
+    assert e.is_imaginary is False
+    assert e.is_extended_real is None
+    # check for more than one complex; it is important to use
+    # uniquely named Symbols to ensure that two factors appear
+    # e.g. if the symbols have the same name they just become
+    # a single factor, a power.
+    e = nz*i*c*c2
+    assert e.is_imaginary is None
+    assert e.is_extended_real is None
+
+    # _eval_is_extended_real and _eval_is_zero both employ trapping of the
+    # zero value so args should be tested in both directions and
+    # TO AVOID GETTING THE CACHED RESULT, Dummy MUST BE USED
+
+    # real is unknown
+    def test(z, b, e):
+        if z.is_zero and b.is_finite:
+            assert e.is_extended_real and e.is_zero
+        else:
+            assert e.is_extended_real is None
+            if b.is_finite:
+                if z.is_zero:
+                    assert e.is_zero
+                else:
+                    assert e.is_zero is None
+            elif b.is_finite is False:
+                if z.is_zero is None:
+                    assert e.is_zero is None
+                else:
+                    assert e.is_zero is False
+
+
+    for iz, ib in product(*[[True, False, None]]*2):
+        z = Dummy('z', nonzero=iz)
+        b = Dummy('f', finite=ib)
+        e = Mul(z, b, evaluate=False)
+        test(z, b, e)
+        z = Dummy('nz', nonzero=iz)
+        b = Dummy('f', finite=ib)
+        e = Mul(b, z, evaluate=False)
+        test(z, b, e)
+
+    # real is True
+    def test(z, b, e):
+        if z.is_zero and not b.is_finite:
+            assert e.is_extended_real is None
+        else:
+            assert e.is_extended_real is True
+
+    for iz, ib in product(*[[True, False, None]]*2):
+        z = Dummy('z', nonzero=iz, extended_real=True)
+        b = Dummy('b', finite=ib, extended_real=True)
+        e = Mul(z, b, evaluate=False)
+        test(z, b, e)
+        z = Dummy('z', nonzero=iz, extended_real=True)
+        b = Dummy('b', finite=ib, extended_real=True)
+        e = Mul(b, z, evaluate=False)
+        test(z, b, e)
+
+
+def test_Mul_with_zero_infinite():
+    zer = Dummy(zero=True)
+    inf = Dummy(finite=False)
+
+    e = Mul(zer, inf, evaluate=False)
+    assert e.is_extended_positive is None
+    assert e.is_hermitian is None
+
+    e = Mul(inf, zer, evaluate=False)
+    assert e.is_extended_positive is None
+    assert e.is_hermitian is None
+
+
+def test_Mul_does_not_cancel_infinities():
+    a, b = symbols('a b')
+    assert ((zoo + 3*a)/(3*a + zoo)) is nan
+    assert ((b - oo)/(b - oo)) is nan
+    # issue 13904
+    expr = (1/(a+b) + 1/(a-b))/(1/(a+b) - 1/(a-b))
+    assert expr.subs(b, a) is nan
+
+
+def test_Mul_does_not_distribute_infinity():
+    a, b = symbols('a b')
+    assert ((1 + I)*oo).is_Mul
+    assert ((a + b)*(-oo)).is_Mul
+    assert ((a + 1)*zoo).is_Mul
+    assert ((1 + I)*oo).is_finite is False
+    z = (1 + I)*oo
+    assert ((1 - I)*z).expand() is oo
+
+
+def test_Mul_does_not_let_0_trump_inf():
+    assert Mul(*[0, a + zoo]) is S.NaN
+    assert Mul(*[0, a + oo]) is S.NaN
+    assert Mul(*[0, a + Integral(1/x**2, (x, 1, oo))]) is S.Zero
+    # Integral is treated like an unknown like 0*x -> 0
+    assert Mul(*[0, a + Integral(x, (x, 1, oo))]) is S.Zero
+
+
+def test_issue_8247_8354():
+    from sympy.functions.elementary.trigonometric import tan
+    z = sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) - sqrt(10 + 6*sqrt(3))
+    assert z.is_positive is False  # it's 0
+    z = S('''-2**(1/3)*(3*sqrt(93) + 29)**2 - 4*(3*sqrt(93) + 29)**(4/3) +
+        12*sqrt(93)*(3*sqrt(93) + 29)**(1/3) + 116*(3*sqrt(93) + 29)**(1/3) +
+        174*2**(1/3)*sqrt(93) + 1678*2**(1/3)''')
+    assert z.is_positive is False  # it's 0
+    z = 2*(-3*tan(19*pi/90) + sqrt(3))*cos(11*pi/90)*cos(19*pi/90) - \
+        sqrt(3)*(-3 + 4*cos(19*pi/90)**2)
+    assert z.is_positive is not True  # it's zero and it shouldn't hang
+    z = S('''9*(3*sqrt(93) + 29)**(2/3)*((3*sqrt(93) +
+        29)**(1/3)*(-2**(2/3)*(3*sqrt(93) + 29)**(1/3) - 2) - 2*2**(1/3))**3 +
+        72*(3*sqrt(93) + 29)**(2/3)*(81*sqrt(93) + 783) + (162*sqrt(93) +
+        1566)*((3*sqrt(93) + 29)**(1/3)*(-2**(2/3)*(3*sqrt(93) + 29)**(1/3) -
+        2) - 2*2**(1/3))**2''')
+    assert z.is_positive is False  # it's 0 (and a single _mexpand isn't enough)
+
+
+def test_Add_is_zero():
+    x, y = symbols('x y', zero=True)
+    assert (x + y).is_zero
+
+    # Issue 15873
+    e = -2*I + (1 + I)**2
+    assert e.is_zero is None
+
+
+def test_issue_14392():
+    assert (sin(zoo)**2).as_real_imag() == (nan, nan)
+
+
+def test_divmod():
+    assert divmod(x, y) == (x//y, x % y)
+    assert divmod(x, 3) == (x//3, x % 3)
+    assert divmod(3, x) == (3//x, 3 % x)
+
+
+def test__neg__():
+    assert -(x*y) == -x*y
+    assert -(-x*y) == x*y
+    assert -(1.*x) == -1.*x
+    assert -(-1.*x) == 1.*x
+    assert -(2.*x) == -2.*x
+    assert -(-2.*x) == 2.*x
+    with distribute(False):
+        eq = -(x + y)
+        assert eq.is_Mul and eq.args == (-1, x + y)
+    with evaluate(False):
+        eq = -(x + y)
+        assert eq.is_Mul and eq.args == (-1, x + y)
+
+
+def test_issue_18507():
+    assert Mul(zoo, zoo, 0) is nan
+
+
+def test_issue_17130():
+    e = Add(b, -b, I, -I, evaluate=False)
+    assert e.is_zero is None # ideally this would be True
+
+
+def test_issue_21034():
+    e = -I*log((re(asin(5)) + I*im(asin(5)))/sqrt(re(asin(5))**2 + im(asin(5))**2))/pi
+    assert e.round(2)
+
+
+def test_issue_22021():
+    from sympy.calculus.accumulationbounds import AccumBounds
+    # these objects are special cases in Mul
+    from sympy.tensor.tensor import TensorIndexType, tensor_indices, tensor_heads
+    L = TensorIndexType("L")
+    i = tensor_indices("i", L)
+    A, B = tensor_heads("A B", [L])
+    e = A(i) + B(i)
+    assert -e == -1*e
+    e = zoo + x
+    assert -e == -1*e
+    a = AccumBounds(1, 2)
+    e = a + x
+    assert -e == -1*e
+    for args in permutations((zoo, a, x)):
+        e = Add(*args, evaluate=False)
+        assert -e == -1*e
+    assert 2*Add(1, x, x, evaluate=False) == 4*x + 2
+
+
+def test_issue_22244():
+    assert -(zoo*x) == zoo*x
+
+
+def test_issue_22453():
+    from sympy.utilities.iterables import cartes
+    e = Symbol('e', extended_positive=True)
+    for a, b in cartes(*[[oo, -oo, 3]]*2):
+        if a == b == 3:
+            continue
+        i = a + I*b
+        assert i**(1 + e) is S.ComplexInfinity
+        assert i**-e is S.Zero
+        assert unchanged(Pow, i, e)
+    assert 1/(oo + I*oo) is S.Zero
+    r, i = [Dummy(infinite=True, extended_real=True) for _ in range(2)]
+    assert 1/(r + I*i) is S.Zero
+    assert 1/(3 + I*i) is S.Zero
+    assert 1/(r + I*3) is S.Zero
+
+
+def test_issue_22613():
+    assert (0**(x - 2)).as_content_primitive() == (1, 0**(x - 2))
+    assert (0**(x + 2)).as_content_primitive() == (1, 0**(x + 2))
+
+
+def test_issue_25176():
+    assert sqrt(-4*3**(S(3)/4)*I/3) == 2*3**(S(7)/8)*sqrt(-I)/3
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_assumptions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_assumptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..574e90178fb489fe99c99ea0c72df57ceec4b249
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_assumptions.py
@@ -0,0 +1,1335 @@
+from sympy.core.mod import Mod
+from sympy.core.numbers import (I, oo, pi)
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (asin, sin)
+from sympy.simplify.simplify import simplify
+from sympy.core import Symbol, S, Rational, Integer, Dummy, Wild, Pow
+from sympy.core.assumptions import (assumptions, check_assumptions,
+    failing_assumptions, common_assumptions, _generate_assumption_rules,
+    _load_pre_generated_assumption_rules)
+from sympy.core.facts import InconsistentAssumptions
+from sympy.core.random import seed
+from sympy.combinatorics import Permutation
+from sympy.combinatorics.perm_groups import PermutationGroup
+
+from sympy.testing.pytest import raises, XFAIL
+
+
+def test_symbol_unset():
+    x = Symbol('x', real=True, integer=True)
+    assert x.is_real is True
+    assert x.is_integer is True
+    assert x.is_imaginary is False
+    assert x.is_noninteger is False
+    assert x.is_number is False
+
+
+def test_zero():
+    z = Integer(0)
+    assert z.is_commutative is True
+    assert z.is_integer is True
+    assert z.is_rational is True
+    assert z.is_algebraic is True
+    assert z.is_transcendental is False
+    assert z.is_real is True
+    assert z.is_complex is True
+    assert z.is_noninteger is False
+    assert z.is_irrational is False
+    assert z.is_imaginary is False
+    assert z.is_positive is False
+    assert z.is_negative is False
+    assert z.is_nonpositive is True
+    assert z.is_nonnegative is True
+    assert z.is_even is True
+    assert z.is_odd is False
+    assert z.is_finite is True
+    assert z.is_infinite is False
+    assert z.is_comparable is True
+    assert z.is_prime is False
+    assert z.is_composite is False
+    assert z.is_number is True
+
+
+def test_one():
+    z = Integer(1)
+    assert z.is_commutative is True
+    assert z.is_integer is True
+    assert z.is_rational is True
+    assert z.is_algebraic is True
+    assert z.is_transcendental is False
+    assert z.is_real is True
+    assert z.is_complex is True
+    assert z.is_noninteger is False
+    assert z.is_irrational is False
+    assert z.is_imaginary is False
+    assert z.is_positive is True
+    assert z.is_negative is False
+    assert z.is_nonpositive is False
+    assert z.is_nonnegative is True
+    assert z.is_even is False
+    assert z.is_odd is True
+    assert z.is_finite is True
+    assert z.is_infinite is False
+    assert z.is_comparable is True
+    assert z.is_prime is False
+    assert z.is_number is True
+    assert z.is_composite is False  # issue 8807
+
+
+def test_negativeone():
+    z = Integer(-1)
+    assert z.is_commutative is True
+    assert z.is_integer is True
+    assert z.is_rational is True
+    assert z.is_algebraic is True
+    assert z.is_transcendental is False
+    assert z.is_real is True
+    assert z.is_complex is True
+    assert z.is_noninteger is False
+    assert z.is_irrational is False
+    assert z.is_imaginary is False
+    assert z.is_positive is False
+    assert z.is_negative is True
+    assert z.is_nonpositive is True
+    assert z.is_nonnegative is False
+    assert z.is_even is False
+    assert z.is_odd is True
+    assert z.is_finite is True
+    assert z.is_infinite is False
+    assert z.is_comparable is True
+    assert z.is_prime is False
+    assert z.is_composite is False
+    assert z.is_number is True
+
+
+def test_infinity():
+    oo = S.Infinity
+
+    assert oo.is_commutative is True
+    assert oo.is_integer is False
+    assert oo.is_rational is False
+    assert oo.is_algebraic is False
+    assert oo.is_transcendental is False
+    assert oo.is_extended_real is True
+    assert oo.is_real is False
+    assert oo.is_complex is False
+    assert oo.is_noninteger is True
+    assert oo.is_irrational is False
+    assert oo.is_imaginary is False
+    assert oo.is_nonzero is False
+    assert oo.is_positive is False
+    assert oo.is_negative is False
+    assert oo.is_nonpositive is False
+    assert oo.is_nonnegative is False
+    assert oo.is_extended_nonzero is True
+    assert oo.is_extended_positive is True
+    assert oo.is_extended_negative is False
+    assert oo.is_extended_nonpositive is False
+    assert oo.is_extended_nonnegative is True
+    assert oo.is_even is False
+    assert oo.is_odd is False
+    assert oo.is_finite is False
+    assert oo.is_infinite is True
+    assert oo.is_comparable is True
+    assert oo.is_prime is False
+    assert oo.is_composite is False
+    assert oo.is_number is True
+
+
+def test_neg_infinity():
+    mm = S.NegativeInfinity
+
+    assert mm.is_commutative is True
+    assert mm.is_integer is False
+    assert mm.is_rational is False
+    assert mm.is_algebraic is False
+    assert mm.is_transcendental is False
+    assert mm.is_extended_real is True
+    assert mm.is_real is False
+    assert mm.is_complex is False
+    assert mm.is_noninteger is True
+    assert mm.is_irrational is False
+    assert mm.is_imaginary is False
+    assert mm.is_nonzero is False
+    assert mm.is_positive is False
+    assert mm.is_negative is False
+    assert mm.is_nonpositive is False
+    assert mm.is_nonnegative is False
+    assert mm.is_extended_nonzero is True
+    assert mm.is_extended_positive is False
+    assert mm.is_extended_negative is True
+    assert mm.is_extended_nonpositive is True
+    assert mm.is_extended_nonnegative is False
+    assert mm.is_even is False
+    assert mm.is_odd is False
+    assert mm.is_finite is False
+    assert mm.is_infinite is True
+    assert mm.is_comparable is True
+    assert mm.is_prime is False
+    assert mm.is_composite is False
+    assert mm.is_number is True
+
+
+def test_zoo():
+    zoo = S.ComplexInfinity
+    assert zoo.is_complex is False
+    assert zoo.is_real is False
+    assert zoo.is_prime is False
+
+
+def test_nan():
+    nan = S.NaN
+
+    assert nan.is_commutative is True
+    assert nan.is_integer is None
+    assert nan.is_rational is None
+    assert nan.is_algebraic is None
+    assert nan.is_transcendental is None
+    assert nan.is_real is None
+    assert nan.is_complex is None
+    assert nan.is_noninteger is None
+    assert nan.is_irrational is None
+    assert nan.is_imaginary is None
+    assert nan.is_positive is None
+    assert nan.is_negative is None
+    assert nan.is_nonpositive is None
+    assert nan.is_nonnegative is None
+    assert nan.is_even is None
+    assert nan.is_odd is None
+    assert nan.is_finite is None
+    assert nan.is_infinite is None
+    assert nan.is_comparable is False
+    assert nan.is_prime is None
+    assert nan.is_composite is None
+    assert nan.is_number is True
+
+
+def test_pos_rational():
+    r = Rational(3, 4)
+    assert r.is_commutative is True
+    assert r.is_integer is False
+    assert r.is_rational is True
+    assert r.is_algebraic is True
+    assert r.is_transcendental is False
+    assert r.is_real is True
+    assert r.is_complex is True
+    assert r.is_noninteger is True
+    assert r.is_irrational is False
+    assert r.is_imaginary is False
+    assert r.is_positive is True
+    assert r.is_negative is False
+    assert r.is_nonpositive is False
+    assert r.is_nonnegative is True
+    assert r.is_even is False
+    assert r.is_odd is False
+    assert r.is_finite is True
+    assert r.is_infinite is False
+    assert r.is_comparable is True
+    assert r.is_prime is False
+    assert r.is_composite is False
+
+    r = Rational(1, 4)
+    assert r.is_nonpositive is False
+    assert r.is_positive is True
+    assert r.is_negative is False
+    assert r.is_nonnegative is True
+    r = Rational(5, 4)
+    assert r.is_negative is False
+    assert r.is_positive is True
+    assert r.is_nonpositive is False
+    assert r.is_nonnegative is True
+    r = Rational(5, 3)
+    assert r.is_nonnegative is True
+    assert r.is_positive is True
+    assert r.is_negative is False
+    assert r.is_nonpositive is False
+
+
+def test_neg_rational():
+    r = Rational(-3, 4)
+    assert r.is_positive is False
+    assert r.is_nonpositive is True
+    assert r.is_negative is True
+    assert r.is_nonnegative is False
+    r = Rational(-1, 4)
+    assert r.is_nonpositive is True
+    assert r.is_positive is False
+    assert r.is_negative is True
+    assert r.is_nonnegative is False
+    r = Rational(-5, 4)
+    assert r.is_negative is True
+    assert r.is_positive is False
+    assert r.is_nonpositive is True
+    assert r.is_nonnegative is False
+    r = Rational(-5, 3)
+    assert r.is_nonnegative is False
+    assert r.is_positive is False
+    assert r.is_negative is True
+    assert r.is_nonpositive is True
+
+
+def test_pi():
+    z = S.Pi
+    assert z.is_commutative is True
+    assert z.is_integer is False
+    assert z.is_rational is False
+    assert z.is_algebraic is False
+    assert z.is_transcendental is True
+    assert z.is_real is True
+    assert z.is_complex is True
+    assert z.is_noninteger is True
+    assert z.is_irrational is True
+    assert z.is_imaginary is False
+    assert z.is_positive is True
+    assert z.is_negative is False
+    assert z.is_nonpositive is False
+    assert z.is_nonnegative is True
+    assert z.is_even is False
+    assert z.is_odd is False
+    assert z.is_finite is True
+    assert z.is_infinite is False
+    assert z.is_comparable is True
+    assert z.is_prime is False
+    assert z.is_composite is False
+
+
+def test_E():
+    z = S.Exp1
+    assert z.is_commutative is True
+    assert z.is_integer is False
+    assert z.is_rational is False
+    assert z.is_algebraic is False
+    assert z.is_transcendental is True
+    assert z.is_real is True
+    assert z.is_complex is True
+    assert z.is_noninteger is True
+    assert z.is_irrational is True
+    assert z.is_imaginary is False
+    assert z.is_positive is True
+    assert z.is_negative is False
+    assert z.is_nonpositive is False
+    assert z.is_nonnegative is True
+    assert z.is_even is False
+    assert z.is_odd is False
+    assert z.is_finite is True
+    assert z.is_infinite is False
+    assert z.is_comparable is True
+    assert z.is_prime is False
+    assert z.is_composite is False
+
+
+def test_I():
+    z = S.ImaginaryUnit
+    assert z.is_commutative is True
+    assert z.is_integer is False
+    assert z.is_rational is False
+    assert z.is_algebraic is True
+    assert z.is_transcendental is False
+    assert z.is_real is False
+    assert z.is_complex is True
+    assert z.is_noninteger is False
+    assert z.is_irrational is False
+    assert z.is_imaginary is True
+    assert z.is_positive is False
+    assert z.is_negative is False
+    assert z.is_nonpositive is False
+    assert z.is_nonnegative is False
+    assert z.is_even is False
+    assert z.is_odd is False
+    assert z.is_finite is True
+    assert z.is_infinite is False
+    assert z.is_comparable is False
+    assert z.is_prime is False
+    assert z.is_composite is False
+
+
+def test_symbol_real_false():
+    # issue 3848
+    a = Symbol('a', real=False)
+
+    assert a.is_real is False
+    assert a.is_integer is False
+    assert a.is_zero is False
+
+    assert a.is_negative is False
+    assert a.is_positive is False
+    assert a.is_nonnegative is False
+    assert a.is_nonpositive is False
+    assert a.is_nonzero is False
+
+    assert a.is_extended_negative is None
+    assert a.is_extended_positive is None
+    assert a.is_extended_nonnegative is None
+    assert a.is_extended_nonpositive is None
+    assert a.is_extended_nonzero is None
+
+
+def test_symbol_extended_real_false():
+    # issue 3848
+    a = Symbol('a', extended_real=False)
+
+    assert a.is_real is False
+    assert a.is_integer is False
+    assert a.is_zero is False
+
+    assert a.is_negative is False
+    assert a.is_positive is False
+    assert a.is_nonnegative is False
+    assert a.is_nonpositive is False
+    assert a.is_nonzero is False
+
+    assert a.is_extended_negative is False
+    assert a.is_extended_positive is False
+    assert a.is_extended_nonnegative is False
+    assert a.is_extended_nonpositive is False
+    assert a.is_extended_nonzero is False
+
+
+def test_symbol_imaginary():
+    a = Symbol('a', imaginary=True)
+
+    assert a.is_real is False
+    assert a.is_integer is False
+    assert a.is_negative is False
+    assert a.is_positive is False
+    assert a.is_nonnegative is False
+    assert a.is_nonpositive is False
+    assert a.is_zero is False
+    assert a.is_nonzero is False  # since nonzero -> real
+
+
+def test_symbol_zero():
+    x = Symbol('x', zero=True)
+    assert x.is_positive is False
+    assert x.is_nonpositive
+    assert x.is_negative is False
+    assert x.is_nonnegative
+    assert x.is_zero is True
+    # TODO Change to x.is_nonzero is None
+    # See https://github.com/sympy/sympy/pull/9583
+    assert x.is_nonzero is False
+    assert x.is_finite is True
+
+
+def test_symbol_positive():
+    x = Symbol('x', positive=True)
+    assert x.is_positive is True
+    assert x.is_nonpositive is False
+    assert x.is_negative is False
+    assert x.is_nonnegative is True
+    assert x.is_zero is False
+    assert x.is_nonzero is True
+
+
+def test_neg_symbol_positive():
+    x = -Symbol('x', positive=True)
+    assert x.is_positive is False
+    assert x.is_nonpositive is True
+    assert x.is_negative is True
+    assert x.is_nonnegative is False
+    assert x.is_zero is False
+    assert x.is_nonzero is True
+
+
+def test_symbol_nonpositive():
+    x = Symbol('x', nonpositive=True)
+    assert x.is_positive is False
+    assert x.is_nonpositive is True
+    assert x.is_negative is None
+    assert x.is_nonnegative is None
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_neg_symbol_nonpositive():
+    x = -Symbol('x', nonpositive=True)
+    assert x.is_positive is None
+    assert x.is_nonpositive is None
+    assert x.is_negative is False
+    assert x.is_nonnegative is True
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_symbol_falsepositive():
+    x = Symbol('x', positive=False)
+    assert x.is_positive is False
+    assert x.is_nonpositive is None
+    assert x.is_negative is None
+    assert x.is_nonnegative is None
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_symbol_falsepositive_mul():
+    # To test pull request 9379
+    # Explicit handling of arg.is_positive=False was added to Mul._eval_is_positive
+    x = 2*Symbol('x', positive=False)
+    assert x.is_positive is False  # This was None before
+    assert x.is_nonpositive is None
+    assert x.is_negative is None
+    assert x.is_nonnegative is None
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+@XFAIL
+def test_symbol_infinitereal_mul():
+    ix = Symbol('ix', infinite=True, extended_real=True)
+    assert (-ix).is_extended_positive is None
+
+
+def test_neg_symbol_falsepositive():
+    x = -Symbol('x', positive=False)
+    assert x.is_positive is None
+    assert x.is_nonpositive is None
+    assert x.is_negative is False
+    assert x.is_nonnegative is None
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_neg_symbol_falsenegative():
+    # To test pull request 9379
+    # Explicit handling of arg.is_negative=False was added to Mul._eval_is_positive
+    x = -Symbol('x', negative=False)
+    assert x.is_positive is False  # This was None before
+    assert x.is_nonpositive is None
+    assert x.is_negative is None
+    assert x.is_nonnegative is None
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_symbol_falsepositive_real():
+    x = Symbol('x', positive=False, real=True)
+    assert x.is_positive is False
+    assert x.is_nonpositive is True
+    assert x.is_negative is None
+    assert x.is_nonnegative is None
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_neg_symbol_falsepositive_real():
+    x = -Symbol('x', positive=False, real=True)
+    assert x.is_positive is None
+    assert x.is_nonpositive is None
+    assert x.is_negative is False
+    assert x.is_nonnegative is True
+    assert x.is_zero is None
+    assert x.is_nonzero is None
+
+
+def test_symbol_falsenonnegative():
+    x = Symbol('x', nonnegative=False)
+    assert x.is_positive is False
+    assert x.is_nonpositive is None
+    assert x.is_negative is None
+    assert x.is_nonnegative is False
+    assert x.is_zero is False
+    assert x.is_nonzero is None
+
+
+@XFAIL
+def test_neg_symbol_falsenonnegative():
+    x = -Symbol('x', nonnegative=False)
+    assert x.is_positive is None
+    assert x.is_nonpositive is False  # this currently returns None
+    assert x.is_negative is False  # this currently returns None
+    assert x.is_nonnegative is None
+    assert x.is_zero is False  # this currently returns None
+    assert x.is_nonzero is True  # this currently returns None
+
+
+def test_symbol_falsenonnegative_real():
+    x = Symbol('x', nonnegative=False, real=True)
+    assert x.is_positive is False
+    assert x.is_nonpositive is True
+    assert x.is_negative is True
+    assert x.is_nonnegative is False
+    assert x.is_zero is False
+    assert x.is_nonzero is True
+
+
+def test_neg_symbol_falsenonnegative_real():
+    x = -Symbol('x', nonnegative=False, real=True)
+    assert x.is_positive is True
+    assert x.is_nonpositive is False
+    assert x.is_negative is False
+    assert x.is_nonnegative is True
+    assert x.is_zero is False
+    assert x.is_nonzero is True
+
+
+def test_prime():
+    assert S.NegativeOne.is_prime is False
+    assert S(-2).is_prime is False
+    assert S(-4).is_prime is False
+    assert S.Zero.is_prime is False
+    assert S.One.is_prime is False
+    assert S(2).is_prime is True
+    assert S(17).is_prime is True
+    assert S(4).is_prime is False
+
+
+def test_composite():
+    assert S.NegativeOne.is_composite is False
+    assert S(-2).is_composite is False
+    assert S(-4).is_composite is False
+    assert S.Zero.is_composite is False
+    assert S(2).is_composite is False
+    assert S(17).is_composite is False
+    assert S(4).is_composite is True
+    x = Dummy(integer=True, positive=True, prime=False)
+    assert x.is_composite is None # x could be 1
+    assert (x + 1).is_composite is None
+    x = Dummy(positive=True, even=True, prime=False)
+    assert x.is_integer is True
+    assert x.is_composite is True
+
+
+def test_prime_symbol():
+    x = Symbol('x', prime=True)
+    assert x.is_prime is True
+    assert x.is_integer is True
+    assert x.is_positive is True
+    assert x.is_negative is False
+    assert x.is_nonpositive is False
+    assert x.is_nonnegative is True
+
+    x = Symbol('x', prime=False)
+    assert x.is_prime is False
+    assert x.is_integer is None
+    assert x.is_positive is None
+    assert x.is_negative is None
+    assert x.is_nonpositive is None
+    assert x.is_nonnegative is None
+
+
+def test_symbol_noncommutative():
+    x = Symbol('x', commutative=True)
+    assert x.is_complex is None
+
+    x = Symbol('x', commutative=False)
+    assert x.is_integer is False
+    assert x.is_rational is False
+    assert x.is_algebraic is False
+    assert x.is_irrational is False
+    assert x.is_real is False
+    assert x.is_complex is False
+
+
+def test_other_symbol():
+    x = Symbol('x', integer=True)
+    assert x.is_integer is True
+    assert x.is_real is True
+    assert x.is_finite is True
+
+    x = Symbol('x', integer=True, nonnegative=True)
+    assert x.is_integer is True
+    assert x.is_nonnegative is True
+    assert x.is_negative is False
+    assert x.is_positive is None
+    assert x.is_finite is True
+
+    x = Symbol('x', integer=True, nonpositive=True)
+    assert x.is_integer is True
+    assert x.is_nonpositive is True
+    assert x.is_positive is False
+    assert x.is_negative is None
+    assert x.is_finite is True
+
+    x = Symbol('x', odd=True)
+    assert x.is_odd is True
+    assert x.is_even is False
+    assert x.is_integer is True
+    assert x.is_finite is True
+
+    x = Symbol('x', odd=False)
+    assert x.is_odd is False
+    assert x.is_even is None
+    assert x.is_integer is None
+    assert x.is_finite is None
+
+    x = Symbol('x', even=True)
+    assert x.is_even is True
+    assert x.is_odd is False
+    assert x.is_integer is True
+    assert x.is_finite is True
+
+    x = Symbol('x', even=False)
+    assert x.is_even is False
+    assert x.is_odd is None
+    assert x.is_integer is None
+    assert x.is_finite is None
+
+    x = Symbol('x', integer=True, nonnegative=True)
+    assert x.is_integer is True
+    assert x.is_nonnegative is True
+    assert x.is_finite is True
+
+    x = Symbol('x', integer=True, nonpositive=True)
+    assert x.is_integer is True
+    assert x.is_nonpositive is True
+    assert x.is_finite is True
+
+    x = Symbol('x', rational=True)
+    assert x.is_real is True
+    assert x.is_finite is True
+
+    x = Symbol('x', rational=False)
+    assert x.is_real is None
+    assert x.is_finite is None
+
+    x = Symbol('x', irrational=True)
+    assert x.is_real is True
+    assert x.is_finite is True
+
+    x = Symbol('x', irrational=False)
+    assert x.is_real is None
+    assert x.is_finite is None
+
+    with raises(AttributeError):
+        x.is_real = False
+
+    x = Symbol('x', algebraic=True)
+    assert x.is_transcendental is False
+    x = Symbol('x', transcendental=True)
+    assert x.is_algebraic is False
+    assert x.is_rational is False
+    assert x.is_integer is False
+
+
+def test_evaluate_false():
+    # Previously this failed because the assumptions query would make new
+    # expressions and some of the evaluation logic would fail under
+    # evaluate(False).
+    from sympy.core.parameters import evaluate
+    from sympy.abc import x, h
+    f = 2**x**7
+    with evaluate(False):
+        fh = f.xreplace({x: x+h})
+        assert fh.exp.is_rational is None
+
+
+def test_issue_3825():
+    """catch: hash instability"""
+    x = Symbol("x")
+    y = Symbol("y")
+    a1 = x + y
+    a2 = y + x
+    a2.is_comparable
+
+    h1 = hash(a1)
+    h2 = hash(a2)
+    assert h1 == h2
+
+
+def test_issue_4822():
+    z = (-1)**Rational(1, 3)*(1 - I*sqrt(3))
+    assert z.is_real in [True, None]
+
+
+def test_hash_vs_typeinfo():
+    """seemingly different typeinfo, but in fact equal"""
+
+    # the following two are semantically equal
+    x1 = Symbol('x', even=True)
+    x2 = Symbol('x', integer=True, odd=False)
+
+    assert hash(x1) == hash(x2)
+    assert x1 == x2
+
+
+def test_hash_vs_typeinfo_2():
+    """different typeinfo should mean !eq"""
+    # the following two are semantically different
+    x = Symbol('x')
+    x1 = Symbol('x', even=True)
+
+    assert x != x1
+    assert hash(x) != hash(x1)  # This might fail with very low probability
+
+
+def test_hash_vs_eq():
+    """catch: different hash for equal objects"""
+    a = 1 + S.Pi    # important: do not fold it into a Number instance
+    ha = hash(a)  # it should be Add/Mul/... to trigger the bug
+
+    a.is_positive   # this uses .evalf() and deduces it is positive
+    assert a.is_positive is True
+
+    # be sure that hash stayed the same
+    assert ha == hash(a)
+
+    # now b should be the same expression
+    b = a.expand(trig=True)
+    hb = hash(b)
+
+    assert a == b
+    assert ha == hb
+
+
+def test_Add_is_pos_neg():
+    # these cover lines not covered by the rest of tests in core
+    n = Symbol('n', extended_negative=True, infinite=True)
+    nn = Symbol('n', extended_nonnegative=True, infinite=True)
+    np = Symbol('n', extended_nonpositive=True, infinite=True)
+    p = Symbol('p', extended_positive=True, infinite=True)
+    r = Dummy(extended_real=True, finite=False)
+    x = Symbol('x')
+    xf = Symbol('xf', finite=True)
+    assert (n + p).is_extended_positive is None
+    assert (n + x).is_extended_positive is None
+    assert (p + x).is_extended_positive is None
+    assert (n + p).is_extended_negative is None
+    assert (n + x).is_extended_negative is None
+    assert (p + x).is_extended_negative is None
+
+    assert (n + xf).is_extended_positive is False
+    assert (p + xf).is_extended_positive is True
+    assert (n + xf).is_extended_negative is True
+    assert (p + xf).is_extended_negative is False
+
+    assert (x - S.Infinity).is_extended_negative is None  # issue 7798
+    # issue 8046, 16.2
+    assert (p + nn).is_extended_positive
+    assert (n + np).is_extended_negative
+    assert (p + r).is_extended_positive is None
+
+
+def test_Add_is_imaginary():
+    nn = Dummy(nonnegative=True)
+    assert (I*nn + I).is_imaginary  # issue 8046, 17
+
+
+def test_Add_is_algebraic():
+    a = Symbol('a', algebraic=True)
+    b = Symbol('a', algebraic=True)
+    na = Symbol('na', algebraic=False)
+    nb = Symbol('nb', algebraic=False)
+    x = Symbol('x')
+    assert (a + b).is_algebraic
+    assert (na + nb).is_algebraic is None
+    assert (a + na).is_algebraic is False
+    assert (a + x).is_algebraic is None
+    assert (na + x).is_algebraic is None
+
+
+def test_Mul_is_algebraic():
+    a = Symbol('a', algebraic=True)
+    b = Symbol('b', algebraic=True)
+    na = Symbol('na', algebraic=False)
+    an = Symbol('an', algebraic=True, nonzero=True)
+    nb = Symbol('nb', algebraic=False)
+    x = Symbol('x')
+    assert (a*b).is_algebraic is True
+    assert (na*nb).is_algebraic is None
+    assert (a*na).is_algebraic is None
+    assert (an*na).is_algebraic is False
+    assert (a*x).is_algebraic is None
+    assert (na*x).is_algebraic is None
+
+
+def test_Pow_is_algebraic():
+    e = Symbol('e', algebraic=True)
+
+    assert Pow(1, e, evaluate=False).is_algebraic
+    assert Pow(0, e, evaluate=False).is_algebraic
+
+    a = Symbol('a', algebraic=True)
+    azf = Symbol('azf', algebraic=True, zero=False)
+    na = Symbol('na', algebraic=False)
+    ia = Symbol('ia', algebraic=True, irrational=True)
+    ib = Symbol('ib', algebraic=True, irrational=True)
+    r = Symbol('r', rational=True)
+    x = Symbol('x')
+    assert (a**2).is_algebraic is True
+    assert (a**r).is_algebraic is None
+    assert (azf**r).is_algebraic is True
+    assert (a**x).is_algebraic is None
+    assert (na**r).is_algebraic is None
+    assert (ia**r).is_algebraic is True
+    assert (ia**ib).is_algebraic is False
+
+    assert (a**e).is_algebraic is None
+
+    # Gelfond-Schneider constant:
+    assert Pow(2, sqrt(2), evaluate=False).is_algebraic is False
+
+    assert Pow(S.GoldenRatio, sqrt(3), evaluate=False).is_algebraic is False
+
+    # issue 8649
+    t = Symbol('t', real=True, transcendental=True)
+    n = Symbol('n', integer=True)
+    assert (t**n).is_algebraic is None
+    assert (t**n).is_integer is None
+
+    assert (pi**3).is_algebraic is False
+    r = Symbol('r', zero=True)
+    assert (pi**r).is_algebraic is True
+
+
+def test_Mul_is_prime_composite():
+    x = Symbol('x', positive=True, integer=True)
+    y = Symbol('y', positive=True, integer=True)
+    assert (x*y).is_prime is None
+    assert ( (x+1)*(y+1) ).is_prime is False
+    assert ( (x+1)*(y+1) ).is_composite is True
+
+    x = Symbol('x', positive=True)
+    assert ( (x+1)*(y+1) ).is_prime is None
+    assert ( (x+1)*(y+1) ).is_composite is None
+
+
+def test_Pow_is_pos_neg():
+    z = Symbol('z', real=True)
+    w = Symbol('w', nonpositive=True)
+
+    assert (S.NegativeOne**S(2)).is_positive is True
+    assert (S.One**z).is_positive is True
+    assert (S.NegativeOne**S(3)).is_positive is False
+    assert (S.Zero**S.Zero).is_positive is True  # 0**0 is 1
+    assert (w**S(3)).is_positive is False
+    assert (w**S(2)).is_positive is None
+    assert (I**2).is_positive is False
+    assert (I**4).is_positive is True
+
+    # tests emerging from #16332 issue
+    p = Symbol('p', zero=True)
+    q = Symbol('q', zero=False, real=True)
+    j = Symbol('j', zero=False, even=True)
+    x = Symbol('x', zero=True)
+    y = Symbol('y', zero=True)
+    assert (p**q).is_positive is False
+    assert (p**q).is_negative is False
+    assert (p**j).is_positive is False
+    assert (x**y).is_positive is True   # 0**0
+    assert (x**y).is_negative is False
+
+
+def test_Pow_is_prime_composite():
+    x = Symbol('x', positive=True, integer=True)
+    y = Symbol('y', positive=True, integer=True)
+    assert (x**y).is_prime is None
+    assert ( x**(y+1) ).is_prime is False
+    assert ( x**(y+1) ).is_composite is None
+    assert ( (x+1)**(y+1) ).is_composite is True
+    assert ( (-x-1)**(2*y) ).is_composite is True
+
+    x = Symbol('x', positive=True)
+    assert (x**y).is_prime is None
+
+
+def test_Mul_is_infinite():
+    x = Symbol('x')
+    f = Symbol('f', finite=True)
+    i = Symbol('i', infinite=True)
+    z = Dummy(zero=True)
+    nzf = Dummy(finite=True, zero=False)
+    from sympy.core.mul import Mul
+    assert (x*f).is_finite is None
+    assert (x*i).is_finite is None
+    assert (f*i).is_finite is None
+    assert (x*f*i).is_finite is None
+    assert (z*i).is_finite is None
+    assert (nzf*i).is_finite is False
+    assert (z*f).is_finite is True
+    assert Mul(0, f, evaluate=False).is_finite is True
+    assert Mul(0, i, evaluate=False).is_finite is None
+
+    assert (x*f).is_infinite is None
+    assert (x*i).is_infinite is None
+    assert (f*i).is_infinite is None
+    assert (x*f*i).is_infinite is None
+    assert (z*i).is_infinite is S.NaN.is_infinite
+    assert (nzf*i).is_infinite is True
+    assert (z*f).is_infinite is False
+    assert Mul(0, f, evaluate=False).is_infinite is False
+    assert Mul(0, i, evaluate=False).is_infinite is S.NaN.is_infinite
+
+
+def test_Add_is_infinite():
+    x = Symbol('x')
+    f = Symbol('f', finite=True)
+    i = Symbol('i', infinite=True)
+    i2 = Symbol('i2', infinite=True)
+    z = Dummy(zero=True)
+    nzf = Dummy(finite=True, zero=False)
+    from sympy.core.add import Add
+    assert (x+f).is_finite is None
+    assert (x+i).is_finite is None
+    assert (f+i).is_finite is False
+    assert (x+f+i).is_finite is None
+    assert (z+i).is_finite is False
+    assert (nzf+i).is_finite is False
+    assert (z+f).is_finite is True
+    assert (i+i2).is_finite is None
+    assert Add(0, f, evaluate=False).is_finite is True
+    assert Add(0, i, evaluate=False).is_finite is False
+
+    assert (x+f).is_infinite is None
+    assert (x+i).is_infinite is None
+    assert (f+i).is_infinite is True
+    assert (x+f+i).is_infinite is None
+    assert (z+i).is_infinite is True
+    assert (nzf+i).is_infinite is True
+    assert (z+f).is_infinite is False
+    assert (i+i2).is_infinite is None
+    assert Add(0, f, evaluate=False).is_infinite is False
+    assert Add(0, i, evaluate=False).is_infinite is True
+
+
+def test_special_is_rational():
+    i = Symbol('i', integer=True)
+    i2 = Symbol('i2', integer=True)
+    ni = Symbol('ni', integer=True, nonzero=True)
+    r = Symbol('r', rational=True)
+    rn = Symbol('r', rational=True, nonzero=True)
+    nr = Symbol('nr', irrational=True)
+    x = Symbol('x')
+    assert sqrt(3).is_rational is False
+    assert (3 + sqrt(3)).is_rational is False
+    assert (3*sqrt(3)).is_rational is False
+    assert exp(3).is_rational is False
+    assert exp(ni).is_rational is False
+    assert exp(rn).is_rational is False
+    assert exp(x).is_rational is None
+    assert exp(log(3), evaluate=False).is_rational is True
+    assert log(exp(3), evaluate=False).is_rational is True
+    assert log(3).is_rational is False
+    assert log(ni + 1).is_rational is False
+    assert log(rn + 1).is_rational is False
+    assert log(x).is_rational is None
+    assert (sqrt(3) + sqrt(5)).is_rational is None
+    assert (sqrt(3) + S.Pi).is_rational is False
+    assert (x**i).is_rational is None
+    assert (i**i).is_rational is True
+    assert (i**i2).is_rational is None
+    assert (r**i).is_rational is None
+    assert (r**r).is_rational is None
+    assert (r**x).is_rational is None
+    assert (nr**i).is_rational is None  # issue 8598
+    assert (nr**Symbol('z', zero=True)).is_rational
+    assert sin(1).is_rational is False
+    assert sin(ni).is_rational is False
+    assert sin(rn).is_rational is False
+    assert sin(x).is_rational is None
+    assert asin(r).is_rational is False
+    assert sin(asin(3), evaluate=False).is_rational is True
+
+
+@XFAIL
+def test_issue_6275():
+    x = Symbol('x')
+    # both zero or both Muls...but neither "change would be very appreciated.
+    # This is similar to x/x => 1 even though if x = 0, it is really nan.
+    assert isinstance(x*0, type(0*S.Infinity))
+    if 0*S.Infinity is S.NaN:
+        b = Symbol('b', finite=None)
+        assert (b*0).is_zero is None
+
+
+def test_sanitize_assumptions():
+    # issue 6666
+    for cls in (Symbol, Dummy, Wild):
+        x = cls('x', real=1, positive=0)
+        assert x.is_real is True
+        assert x.is_positive is False
+        assert cls('', real=True, positive=None).is_positive is None
+        raises(ValueError, lambda: cls('', commutative=None))
+    raises(ValueError, lambda: Symbol._sanitize({"commutative": None}))
+
+
+def test_special_assumptions():
+    e = -3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2
+    assert simplify(e < 0) is S.false
+    assert simplify(e > 0) is S.false
+    assert (e == 0) is False  # it's not a literal 0
+    assert e.equals(0) is True
+
+
+def test_inconsistent():
+    # cf. issues 5795 and 5545
+    raises(InconsistentAssumptions, lambda: Symbol('x', real=True,
+           commutative=False))
+
+
+def test_issue_6631():
+    assert ((-1)**(I)).is_real is True
+    assert ((-1)**(I*2)).is_real is True
+    assert ((-1)**(I/2)).is_real is True
+    assert ((-1)**(I*S.Pi)).is_real is True
+    assert (I**(I + 2)).is_real is True
+
+
+def test_issue_2730():
+    assert (1/(1 + I)).is_real is False
+
+
+def test_issue_4149():
+    assert (3 + I).is_complex
+    assert (3 + I).is_imaginary is False
+    assert (3*I + S.Pi*I).is_imaginary
+    # as Zero.is_imaginary is False, see issue 7649
+    y = Symbol('y', real=True)
+    assert (3*I + S.Pi*I + y*I).is_imaginary is None
+    p = Symbol('p', positive=True)
+    assert (3*I + S.Pi*I + p*I).is_imaginary
+    n = Symbol('n', negative=True)
+    assert (-3*I - S.Pi*I + n*I).is_imaginary
+
+    i = Symbol('i', imaginary=True)
+    assert ([(i**a).is_imaginary for a in range(4)] ==
+            [False, True, False, True])
+
+    # tests from the PR #7887:
+    e = S("-sqrt(3)*I/2 + 0.866025403784439*I")
+    assert e.is_real is False
+    assert e.is_imaginary
+
+
+def test_issue_2920():
+    n = Symbol('n', negative=True)
+    assert sqrt(n).is_imaginary
+
+
+def test_issue_7899():
+    x = Symbol('x', real=True)
+    assert (I*x).is_real is None
+    assert ((x - I)*(x - 1)).is_zero is None
+    assert ((x - I)*(x - 1)).is_real is None
+
+
+@XFAIL
+def test_issue_7993():
+    x = Dummy(integer=True)
+    y = Dummy(noninteger=True)
+    assert (x - y).is_zero is False
+
+
+def test_issue_8075():
+    raises(InconsistentAssumptions, lambda: Dummy(zero=True, finite=False))
+    raises(InconsistentAssumptions, lambda: Dummy(zero=True, infinite=True))
+
+
+def test_issue_8642():
+    x = Symbol('x', real=True, integer=False)
+    assert (x*2).is_integer is None, (x*2).is_integer
+
+
+def test_issues_8632_8633_8638_8675_8992():
+    p = Dummy(integer=True, positive=True)
+    nn = Dummy(integer=True, nonnegative=True)
+    assert (p - S.Half).is_positive
+    assert (p - 1).is_nonnegative
+    assert (nn + 1).is_positive
+    assert (-p + 1).is_nonpositive
+    assert (-nn - 1).is_negative
+    prime = Dummy(prime=True)
+    assert (prime - 2).is_nonnegative
+    assert (prime - 3).is_nonnegative is None
+    even = Dummy(positive=True, even=True)
+    assert (even - 2).is_nonnegative
+
+    p = Dummy(positive=True)
+    assert (p/(p + 1) - 1).is_negative
+    assert ((p + 2)**3 - S.Half).is_positive
+    n = Dummy(negative=True)
+    assert (n - 3).is_nonpositive
+
+
+def test_issue_9115_9150():
+    n = Dummy('n', integer=True, nonnegative=True)
+    assert (factorial(n) >= 1) == True
+    assert (factorial(n) < 1) == False
+
+    assert factorial(n + 1).is_even is None
+    assert factorial(n + 2).is_even is True
+    assert factorial(n + 2) >= 2
+
+
+def test_issue_9165():
+    z = Symbol('z', zero=True)
+    f = Symbol('f', finite=False)
+    assert 0/z is S.NaN
+    assert 0*(1/z) is S.NaN
+    assert 0*f is S.NaN
+
+
+def test_issue_10024():
+    x = Dummy('x')
+    assert Mod(x, 2*pi).is_zero is None
+
+
+def test_issue_10302():
+    x = Symbol('x')
+    r = Symbol('r', real=True)
+    u = -(3*2**pi)**(1/pi) + 2*3**(1/pi)
+    i = u + u*I
+
+    assert i.is_real is None  # w/o simplification this should fail
+    assert (u + i).is_zero is None
+    assert (1 + i).is_zero is False
+
+    a = Dummy('a', zero=True)
+    assert (a + I).is_zero is False
+    assert (a + r*I).is_zero is None
+    assert (a + I).is_imaginary
+    assert (a + x + I).is_imaginary is None
+    assert (a + r*I + I).is_imaginary is None
+
+
+def test_complex_reciprocal_imaginary():
+    assert (1 / (4 + 3*I)).is_imaginary is False
+
+
+def test_issue_16313():
+    x = Symbol('x', extended_real=False)
+    k = Symbol('k', real=True)
+    l = Symbol('l', real=True, zero=False)
+    assert (-x).is_real is False
+    assert (k*x).is_real is None  # k can be zero also
+    assert (l*x).is_real is False
+    assert (l*x*x).is_real is None  # since x*x can be a real number
+    assert (-x).is_positive is False
+
+
+def test_issue_16579():
+    # extended_real -> finite | infinite
+    x = Symbol('x', extended_real=True, infinite=False)
+    y = Symbol('y', extended_real=True, finite=False)
+    assert x.is_finite is True
+    assert y.is_infinite is True
+
+    # With PR 16978, complex now implies finite
+    c = Symbol('c', complex=True)
+    assert c.is_finite is True
+    raises(InconsistentAssumptions, lambda: Dummy(complex=True, finite=False))
+
+    # Now infinite == !finite
+    nf = Symbol('nf', finite=False)
+    assert nf.is_infinite is True
+
+
+def test_issue_17556():
+    z = I*oo
+    assert z.is_imaginary is False
+    assert z.is_finite is False
+
+
+def test_issue_21651():
+    k = Symbol('k', positive=True, integer=True)
+    exp = 2*2**(-k)
+    assert exp.is_integer is None
+
+
+def test_assumptions_copy():
+    assert assumptions(Symbol('x'), {"commutative": True}
+        ) == {'commutative': True}
+    assert assumptions(Symbol('x'), ['integer']) == {}
+    assert assumptions(Symbol('x'), ['commutative']
+        ) == {'commutative': True}
+    assert assumptions(Symbol('x')) == {'commutative': True}
+    assert assumptions(1)['positive']
+    assert assumptions(3 + I) == {
+        'algebraic': True,
+        'commutative': True,
+        'complex': True,
+        'composite': False,
+        'even': False,
+        'extended_negative': False,
+        'extended_nonnegative': False,
+        'extended_nonpositive': False,
+        'extended_nonzero': False,
+        'extended_positive': False,
+        'extended_real': False,
+        'finite': True,
+        'imaginary': False,
+        'infinite': False,
+        'integer': False,
+        'irrational': False,
+        'negative': False,
+        'noninteger': False,
+        'nonnegative': False,
+        'nonpositive': False,
+        'nonzero': False,
+        'odd': False,
+        'positive': False,
+        'prime': False,
+        'rational': False,
+        'real': False,
+        'transcendental': False,
+        'zero': False}
+
+
+def test_check_assumptions():
+    assert check_assumptions(1, 0) is False
+    x = Symbol('x', positive=True)
+    assert check_assumptions(1, x) is True
+    assert check_assumptions(1, 1) is True
+    assert check_assumptions(-1, 1) is False
+    i = Symbol('i', integer=True)
+    # don't know if i is positive (or prime, etc...)
+    assert check_assumptions(i, 1) is None
+    assert check_assumptions(Dummy(integer=None), integer=True) is None
+    assert check_assumptions(Dummy(integer=None), integer=False) is None
+    assert check_assumptions(Dummy(integer=False), integer=True) is False
+    assert check_assumptions(Dummy(integer=True), integer=False) is False
+    # no T/F assumptions to check
+    assert check_assumptions(Dummy(integer=False), integer=None) is True
+    raises(ValueError, lambda: check_assumptions(2*x, x, positive=True))
+
+
+def test_failing_assumptions():
+    x = Symbol('x', positive=True)
+    y = Symbol('y')
+    assert failing_assumptions(6*x + y, **x.assumptions0) == \
+    {'real': None, 'imaginary': None, 'complex': None, 'hermitian': None,
+    'positive': None, 'nonpositive': None, 'nonnegative': None, 'nonzero': None,
+    'negative': None, 'zero': None, 'extended_real': None, 'finite': None,
+    'infinite': None, 'extended_negative': None, 'extended_nonnegative': None,
+    'extended_nonpositive': None, 'extended_nonzero': None,
+    'extended_positive': None }
+
+
+def test_common_assumptions():
+    assert common_assumptions([0, 1, 2]
+        ) == {'algebraic': True, 'irrational': False, 'hermitian':
+        True, 'extended_real': True, 'real': True, 'extended_negative':
+        False, 'extended_nonnegative': True, 'integer': True,
+        'rational': True, 'imaginary': False, 'complex': True,
+        'commutative': True,'noninteger': False, 'composite': False,
+        'infinite': False, 'nonnegative': True, 'finite': True,
+        'transcendental': False,'negative': False}
+    assert common_assumptions([0, 1, 2], 'positive integer'.split()
+        ) == {'integer': True}
+    assert common_assumptions([0, 1, 2], []) == {}
+    assert common_assumptions([], ['integer']) == {}
+    assert common_assumptions([0], ['integer']) == {'integer': True}
+
+def test_pre_generated_assumption_rules_are_valid():
+    # check the pre-generated assumptions match freshly generated assumptions
+    # if this check fails, consider updating the assumptions
+    # see sympy.core.assumptions._generate_assumption_rules
+    pre_generated_assumptions =_load_pre_generated_assumption_rules()
+    generated_assumptions =_generate_assumption_rules()
+    assert pre_generated_assumptions._to_python() == generated_assumptions._to_python(), "pre-generated assumptions are invalid, see sympy.core.assumptions._generate_assumption_rules"
+
+
+def test_ask_shuffle():
+    grp = PermutationGroup(Permutation(1, 0, 2), Permutation(2, 1, 3))
+
+    seed(123)
+    first = grp.random()
+    seed(123)
+    simplify(I)
+    second = grp.random()
+    seed(123)
+    simplify(-I)
+    third = grp.random()
+
+    assert first == second == third
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_basic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a7adbb5dcf0d70089ff79028afa943b24ee0c42
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_basic.py
@@ -0,0 +1,343 @@
+"""This tests sympy/core/basic.py with (ideally) no reference to subclasses
+of Basic or Atom."""
+import collections
+from typing import TypeVar, Generic
+
+from sympy.assumptions.ask import Q
+from sympy.core.basic import (Basic, Atom, as_Basic,
+    _atomic, _aresame)
+from sympy.core.containers import Tuple
+from sympy.core.function import Function, Lambda
+from sympy.core.numbers import I, pi, Float
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols, Symbol, Dummy
+from sympy.concrete.summations import Sum
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.gamma_functions import gamma
+from sympy.integrals.integrals import Integral
+from sympy.functions.elementary.exponential import exp
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+from sympy.functions.elementary.complexes import Abs, sign
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.core.relational import Eq
+
+b1 = Basic()
+b2 = Basic(b1)
+b3 = Basic(b2)
+b21 = Basic(b2, b1)
+T = TypeVar('T')
+
+
+def test__aresame():
+    assert not _aresame(Basic(Tuple()), Basic())
+    for i, j in [(S(2), S(2.)), (1., Float(1))]:
+        for do in range(2):
+            assert not _aresame(Basic(i), Basic(j))
+            assert not _aresame(i, j)
+            i, j = j, i
+
+
+def test_structure():
+    assert b21.args == (b2, b1)
+    assert b21.func(*b21.args) == b21
+    assert bool(b1)
+
+
+def test_immutable():
+    assert not hasattr(b1, '__dict__')
+    with raises(AttributeError):
+        b1.x = 1
+
+
+def test_equality():
+    instances = [b1, b2, b3, b21, Basic(b1, b1, b1), Basic]
+    for i, b_i in enumerate(instances):
+        for j, b_j in enumerate(instances):
+            assert (b_i == b_j) == (i == j)
+            assert (b_i != b_j) == (i != j)
+
+    assert Basic() != []
+    assert not(Basic() == [])
+    assert Basic() != 0
+    assert not(Basic() == 0)
+
+    class Foo:
+        """
+        Class that is unaware of Basic, and relies on both classes returning
+        the NotImplemented singleton for equivalence to evaluate to False.
+
+        """
+
+    b = Basic()
+    foo = Foo()
+
+    assert b != foo
+    assert foo != b
+    assert not b == foo
+    assert not foo == b
+
+    class Bar:
+        """
+        Class that considers itself equal to any instance of Basic, and relies
+        on Basic returning the NotImplemented singleton in order to achieve
+        a symmetric equivalence relation.
+
+        """
+        def __eq__(self, other):
+            if isinstance(other, Basic):
+                return True
+            return NotImplemented
+
+        def __ne__(self, other):
+            return not self == other
+
+    bar = Bar()
+
+    assert b == bar
+    assert bar == b
+    assert not b != bar
+    assert not bar != b
+
+
+def test_matches_basic():
+    instances = [Basic(b1, b1, b2), Basic(b1, b2, b1), Basic(b2, b1, b1),
+                 Basic(b1, b2), Basic(b2, b1), b2, b1]
+    for i, b_i in enumerate(instances):
+        for j, b_j in enumerate(instances):
+            if i == j:
+                assert b_i.matches(b_j) == {}
+            else:
+                assert b_i.matches(b_j) is None
+    assert b1.match(b1) == {}
+
+
+def test_has():
+    assert b21.has(b1)
+    assert b21.has(b3, b1)
+    assert b21.has(Basic)
+    assert not b1.has(b21, b3)
+    assert not b21.has()
+    assert not b21.has(str)
+    assert not Symbol("x").has("x")
+
+
+def test_subs():
+    assert b21.subs(b2, b1) == Basic(b1, b1)
+    assert b21.subs(b2, b21) == Basic(b21, b1)
+    assert b3.subs(b2, b1) == b2
+
+    assert b21.subs([(b2, b1), (b1, b2)]) == Basic(b2, b2)
+
+    assert b21.subs({b1: b2, b2: b1}) == Basic(b2, b2)
+    assert b21.subs(collections.ChainMap({b1: b2}, {b2: b1})) == Basic(b2, b2)
+    assert b21.subs(collections.OrderedDict([(b2, b1), (b1, b2)])) == Basic(b2, b2)
+
+    raises(ValueError, lambda: b21.subs('bad arg'))
+    raises(TypeError, lambda: b21.subs(b1, b2, b3))
+    # dict(b1=foo) creates a string 'b1' but leaves foo unchanged; subs
+    # will convert the first to a symbol but will raise an error if foo
+    # cannot be sympified; sympification is strict if foo is not string
+    raises(TypeError, lambda: b21.subs(b1='bad arg'))
+
+    assert Symbol("text").subs({"text": b1}) == b1
+    assert Symbol("s").subs({"s": 1}) == 1
+
+
+def test_subs_with_unicode_symbols():
+    expr = Symbol('var1')
+    replaced = expr.subs('var1', 'x')
+    assert replaced.name == 'x'
+
+    replaced = expr.subs('var1', 'x')
+    assert replaced.name == 'x'
+
+
+def test_atoms():
+    assert b21.atoms() == {Basic()}
+
+
+def test_free_symbols_empty():
+    assert b21.free_symbols == set()
+
+
+def test_doit():
+    assert b21.doit() == b21
+    assert b21.doit(deep=False) == b21
+
+
+def test_S():
+    assert repr(S) == 'S'
+
+
+def test_xreplace():
+    assert b21.xreplace({b2: b1}) == Basic(b1, b1)
+    assert b21.xreplace({b2: b21}) == Basic(b21, b1)
+    assert b3.xreplace({b2: b1}) == b2
+    assert Basic(b1, b2).xreplace({b1: b2, b2: b1}) == Basic(b2, b1)
+    assert Atom(b1).xreplace({b1: b2}) == Atom(b1)
+    assert Atom(b1).xreplace({Atom(b1): b2}) == b2
+    raises(TypeError, lambda: b1.xreplace())
+    raises(TypeError, lambda: b1.xreplace([b1, b2]))
+    for f in (exp, Function('f')):
+        assert f.xreplace({}) == f
+        assert f.xreplace({}, hack2=True) == f
+        assert f.xreplace({f: b1}) == b1
+        assert f.xreplace({f: b1}, hack2=True) == b1
+
+
+def test_sorted_args():
+    x = symbols('x')
+    assert b21._sorted_args == b21.args
+    raises(AttributeError, lambda: x._sorted_args)
+
+def test_call():
+    x, y = symbols('x y')
+    # See the long history of this in issues 5026 and 5105.
+
+    raises(TypeError, lambda: sin(x)({ x : 1, sin(x) : 2}))
+    raises(TypeError, lambda: sin(x)(1))
+
+    # No effect as there are no callables
+    assert sin(x).rcall(1) == sin(x)
+    assert (1 + sin(x)).rcall(1) == 1 + sin(x)
+
+    # Effect in the presence of callables
+    l = Lambda(x, 2*x)
+    assert (l + x).rcall(y) == 2*y + x
+    assert (x**l).rcall(2) == x**4
+    # TODO UndefinedFunction does not subclass Expr
+    #f = Function('f')
+    #assert (2*f)(x) == 2*f(x)
+
+    assert (Q.real & Q.positive).rcall(x) == Q.real(x) & Q.positive(x)
+
+
+def test_rewrite():
+    x, y, z = symbols('x y z')
+    a, b = symbols('a b')
+    f1 = sin(x) + cos(x)
+    assert f1.rewrite(cos,exp) == exp(I*x)/2 + sin(x) + exp(-I*x)/2
+    assert f1.rewrite([cos],sin) == sin(x) + sin(x + pi/2, evaluate=False)
+    f2 = sin(x) + cos(y)/gamma(z)
+    assert f2.rewrite(sin,exp) == -I*(exp(I*x) - exp(-I*x))/2 + cos(y)/gamma(z)
+
+    assert f1.rewrite() == f1
+
+def test_literal_evalf_is_number_is_zero_is_comparable():
+    x = symbols('x')
+    f = Function('f')
+
+    # issue 5033
+    assert f.is_number is False
+    # issue 6646
+    assert f(1).is_number is False
+    i = Integral(0, (x, x, x))
+    # expressions that are symbolically 0 can be difficult to prove
+    # so in case there is some easy way to know if something is 0
+    # it should appear in the is_zero property for that object;
+    # if is_zero is true evalf should always be able to compute that
+    # zero
+    assert i.n() == 0
+    assert i.is_zero
+    assert i.is_number is False
+    assert i.evalf(2, strict=False) == 0
+
+    # issue 10268
+    n = sin(1)**2 + cos(1)**2 - 1
+    assert n.is_comparable is False
+    assert n.n(2).is_comparable is False
+    assert n.n(2).n(2).is_comparable
+
+
+def test_as_Basic():
+    assert as_Basic(1) is S.One
+    assert as_Basic(()) == Tuple()
+    raises(TypeError, lambda: as_Basic([]))
+
+
+def test_atomic():
+    g, h = map(Function, 'gh')
+    x = symbols('x')
+    assert _atomic(g(x + h(x))) == {g(x + h(x))}
+    assert _atomic(g(x + h(x)), recursive=True) == {h(x), x, g(x + h(x))}
+    assert _atomic(1) == set()
+    assert _atomic(Basic(S(1), S(2))) == set()
+
+
+def test_as_dummy():
+    u, v, x, y, z, _0, _1 = symbols('u v x y z _0 _1')
+    assert Lambda(x, x + 1).as_dummy() == Lambda(_0, _0 + 1)
+    assert Lambda(x, x + _0).as_dummy() == Lambda(_1, _0 + _1)
+    eq = (1 + Sum(x, (x, 1, x)))
+    ans = 1 + Sum(_0, (_0, 1, x))
+    once = eq.as_dummy()
+    assert once == ans
+    twice = once.as_dummy()
+    assert twice == ans
+    assert Integral(x + _0, (x, x + 1), (_0, 1, 2)
+        ).as_dummy() == Integral(_0 + _1, (_0, x + 1), (_1, 1, 2))
+    for T in (Symbol, Dummy):
+        d = T('x', real=True)
+        D = d.as_dummy()
+        assert D != d and D.func == Dummy and D.is_real is None
+    assert Dummy().as_dummy().is_commutative
+    assert Dummy(commutative=False).as_dummy().is_commutative is False
+
+
+def test_canonical_variables():
+    x, i0, i1 = symbols('x _:2')
+    assert Integral(x, (x, x + 1)).canonical_variables == {x: i0}
+    assert Integral(x, (x, x + 1), (i0, 1, 2)).canonical_variables == {
+        x: i0, i0: i1}
+    assert Integral(x, (x, x + i0)).canonical_variables == {x: i1}
+
+
+def test_replace_exceptions():
+    from sympy.core.symbol import Wild
+    x, y = symbols('x y')
+    e = (x**2 + x*y)
+    raises(TypeError, lambda: e.replace(sin, 2))
+    b = Wild('b')
+    c = Wild('c')
+    raises(TypeError, lambda: e.replace(b*c, c.is_real))
+    raises(TypeError, lambda: e.replace(b.is_real, 1))
+    raises(TypeError, lambda: e.replace(lambda d: d.is_Number, 1))
+
+
+def test_ManagedProperties():
+    # ManagedProperties is now deprecated. Here we do our best to check that if
+    # someone is using it then it does work in the way that it previously did
+    # but gives a deprecation warning.
+    from sympy.core.assumptions import ManagedProperties
+
+    myclasses = []
+
+    class MyMeta(ManagedProperties):
+        def __init__(cls, *args, **kwargs):
+            myclasses.append('executed')
+            super().__init__(*args, **kwargs)
+
+    code = """
+class MySubclass(Basic, metaclass=MyMeta):
+    pass
+"""
+    with warns_deprecated_sympy():
+        exec(code)
+
+    assert myclasses == ['executed']
+
+
+def test_generic():
+    # https://github.com/sympy/sympy/issues/25399
+    class A(Symbol, Generic[T]):
+        pass
+
+    class B(A[T]):
+        pass
+
+
+def test_rewrite_abs():
+    # https://github.com/sympy/sympy/issues/27323
+    x = Symbol('x')
+    assert sign(x).rewrite(abs) == sign(x).rewrite(Abs)
+    assert sign(x).rewrite(abs) == Piecewise((0, Eq(x, 0)), (x / Abs(x), True))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_cache.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_cache.py
new file mode 100644
index 0000000000000000000000000000000000000000..9124fca70718299252929a9923f335dde25256eb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_cache.py
@@ -0,0 +1,91 @@
+import sys
+from sympy.core.cache import cacheit, cached_property, lazy_function
+from sympy.testing.pytest import raises
+
+def test_cacheit_doc():
+    @cacheit
+    def testfn():
+        "test docstring"
+        pass
+
+    assert testfn.__doc__ == "test docstring"
+    assert testfn.__name__ == "testfn"
+
+def test_cacheit_unhashable():
+    @cacheit
+    def testit(x):
+        return x
+
+    assert testit(1) == 1
+    assert testit(1) == 1
+    a = {}
+    assert testit(a) == {}
+    a[1] = 2
+    assert testit(a) == {1: 2}
+
+def test_cachit_exception():
+    # Make sure the cache doesn't call functions multiple times when they
+    # raise TypeError
+
+    a = []
+
+    @cacheit
+    def testf(x):
+        a.append(0)
+        raise TypeError
+
+    raises(TypeError, lambda: testf(1))
+    assert len(a) == 1
+
+    a.clear()
+    # Unhashable type
+    raises(TypeError, lambda: testf([]))
+    assert len(a) == 1
+
+    @cacheit
+    def testf2(x):
+        a.append(0)
+        raise TypeError("Error")
+
+    a.clear()
+    raises(TypeError, lambda: testf2(1))
+    assert len(a) == 1
+
+    a.clear()
+    # Unhashable type
+    raises(TypeError, lambda: testf2([]))
+    assert len(a) == 1
+
+def test_cached_property():
+    class A:
+        def __init__(self, value):
+            self.value = value
+            self.calls = 0
+
+        @cached_property
+        def prop(self):
+            self.calls = self.calls + 1
+            return self.value
+
+    a = A(2)
+    assert a.calls == 0
+    assert a.prop == 2
+    assert a.calls == 1
+    assert a.prop == 2
+    assert a.calls == 1
+    b = A(None)
+    assert b.prop == None
+
+
+def test_lazy_function():
+    module_name='xmlrpc.client'
+    function_name = 'gzip_decode'
+    lazy = lazy_function(module_name, function_name)
+    assert lazy(b'') == b''
+    assert module_name in sys.modules
+    assert function_name in str(lazy)
+    repr_lazy = repr(lazy)
+    assert 'LazyFunction' in repr_lazy
+    assert function_name in repr_lazy
+
+    lazy = lazy_function('sympy.core.cache', 'cheap')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_compatibility.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_compatibility.py
new file mode 100644
index 0000000000000000000000000000000000000000..31d2bed07b21aa2fa489273dca9edfc9993cfd86
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_compatibility.py
@@ -0,0 +1,6 @@
+from sympy.testing.pytest import warns_deprecated_sympy
+
+def test_compatibility_submodule():
+    # Test the sympy.core.compatibility deprecation warning
+    with warns_deprecated_sympy():
+        import sympy.core.compatibility # noqa:F401
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_complex.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_complex.py
new file mode 100644
index 0000000000000000000000000000000000000000..a607e0bdb4db859336aa30aa61f43bfb57d5df88
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_complex.py
@@ -0,0 +1,226 @@
+from sympy.core.function import expand_complex
+from sympy.core.numbers import (I, Integer, Rational, pi)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (Abs, conjugate, im, re, sign)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.hyperbolic import (cosh, coth, sinh, tanh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, cot, sin, tan)
+
+def test_complex():
+    a = Symbol("a", real=True)
+    b = Symbol("b", real=True)
+    e = (a + I*b)*(a - I*b)
+    assert e.expand() == a**2 + b**2
+    assert sqrt(I) == Pow(I, S.Half)
+
+
+def test_conjugate():
+    a = Symbol("a", real=True)
+    b = Symbol("b", real=True)
+    c = Symbol("c", imaginary=True)
+    d = Symbol("d", imaginary=True)
+    x = Symbol('x')
+    z = a + I*b + c + I*d
+    zc = a - I*b - c + I*d
+    assert conjugate(z) == zc
+    assert conjugate(exp(z)) == exp(zc)
+    assert conjugate(exp(I*x)) == exp(-I*conjugate(x))
+    assert conjugate(z**5) == zc**5
+    assert conjugate(abs(x)) == abs(x)
+    assert conjugate(sign(z)) == sign(zc)
+    assert conjugate(sin(z)) == sin(zc)
+    assert conjugate(cos(z)) == cos(zc)
+    assert conjugate(tan(z)) == tan(zc)
+    assert conjugate(cot(z)) == cot(zc)
+    assert conjugate(sinh(z)) == sinh(zc)
+    assert conjugate(cosh(z)) == cosh(zc)
+    assert conjugate(tanh(z)) == tanh(zc)
+    assert conjugate(coth(z)) == coth(zc)
+
+
+def test_abs1():
+    a = Symbol("a", real=True)
+    b = Symbol("b", real=True)
+    assert abs(a) == Abs(a)
+    assert abs(-a) == abs(a)
+    assert abs(a + I*b) == sqrt(a**2 + b**2)
+
+
+def test_abs2():
+    a = Symbol("a", real=False)
+    b = Symbol("b", real=False)
+    assert abs(a) != a
+    assert abs(-a) != a
+    assert abs(a + I*b) != sqrt(a**2 + b**2)
+
+
+def test_evalc():
+    x = Symbol("x", real=True)
+    y = Symbol("y", real=True)
+    z = Symbol("z")
+    assert ((x + I*y)**2).expand(complex=True) == x**2 + 2*I*x*y - y**2
+    assert expand_complex(z**(2*I)) == (re((re(z) + I*im(z))**(2*I)) +
+        I*im((re(z) + I*im(z))**(2*I)))
+    assert expand_complex(
+        z**(2*I), deep=False) == I*im(z**(2*I)) + re(z**(2*I))
+
+    assert exp(I*x) != cos(x) + I*sin(x)
+    assert exp(I*x).expand(complex=True) == cos(x) + I*sin(x)
+    assert exp(I*x + y).expand(complex=True) == exp(y)*cos(x) + I*sin(x)*exp(y)
+
+    assert sin(I*x).expand(complex=True) == I * sinh(x)
+    assert sin(x + I*y).expand(complex=True) == sin(x)*cosh(y) + \
+        I * sinh(y) * cos(x)
+
+    assert cos(I*x).expand(complex=True) == cosh(x)
+    assert cos(x + I*y).expand(complex=True) == cos(x)*cosh(y) - \
+        I * sinh(y) * sin(x)
+
+    assert tan(I*x).expand(complex=True) == tanh(x) * I
+    assert tan(x + I*y).expand(complex=True) == (
+        sin(2*x)/(cos(2*x) + cosh(2*y)) +
+        I*sinh(2*y)/(cos(2*x) + cosh(2*y)))
+
+    assert sinh(I*x).expand(complex=True) == I * sin(x)
+    assert sinh(x + I*y).expand(complex=True) == sinh(x)*cos(y) + \
+        I * sin(y) * cosh(x)
+
+    assert cosh(I*x).expand(complex=True) == cos(x)
+    assert cosh(x + I*y).expand(complex=True) == cosh(x)*cos(y) + \
+        I * sin(y) * sinh(x)
+
+    assert tanh(I*x).expand(complex=True) == tan(x) * I
+    assert tanh(x + I*y).expand(complex=True) == (
+        (sinh(x)*cosh(x) + I*cos(y)*sin(y)) /
+        (sinh(x)**2 + cos(y)**2)).expand()
+
+
+def test_pythoncomplex():
+    x = Symbol("x")
+    assert 4j*x != 4*x*I
+    assert 4j*x == 4.0*x*I
+    assert 4.1j*x != 4*x*I
+
+
+def test_rootcomplex():
+    R = Rational
+    assert ((+1 + I)**R(1, 2)).expand(
+        complex=True) == 2**R(1, 4)*cos(  pi/8) + 2**R(1, 4)*sin(  pi/8)*I
+    assert ((-1 - I)**R(1, 2)).expand(
+        complex=True) == 2**R(1, 4)*cos(3*pi/8) - 2**R(1, 4)*sin(3*pi/8)*I
+    assert (sqrt(-10)*I).as_real_imag() == (-sqrt(10), 0)
+
+
+def test_expand_inverse():
+    assert (1/(1 + I)).expand(complex=True) == (1 - I)/2
+    assert ((1 + 2*I)**(-2)).expand(complex=True) == (-3 - 4*I)/25
+    assert ((1 + I)**(-8)).expand(complex=True) == Rational(1, 16)
+
+
+def test_expand_complex():
+    assert ((2 + 3*I)**10).expand(complex=True) == -341525 - 145668*I
+    # the following two tests are to ensure the SymPy uses an efficient
+    # algorithm for calculating powers of complex numbers. They should execute
+    # in something like 0.01s.
+    assert ((2 + 3*I)**1000).expand(complex=True) == \
+        -81079464736246615951519029367296227340216902563389546989376269312984127074385455204551402940331021387412262494620336565547972162814110386834027871072723273110439771695255662375718498785908345629702081336606863762777939617745464755635193139022811989314881997210583159045854968310911252660312523907616129080027594310008539817935736331124833163907518549408018652090650537035647520296539436440394920287688149200763245475036722326561143851304795139005599209239350981457301460233967137708519975586996623552182807311159141501424576682074392689622074945519232029999 + \
+        46938745946789557590804551905243206242164799136976022474337918748798900569942573265747576032611189047943842446167719177749107138603040963603119861476016947257034472364028585381714774667326478071264878108114128915685688115488744955550920239128462489496563930809677159214598114273887061533057125164518549173898349061972857446844052995037423459472376202251620778517659247970283904820245958198842631651569984310559418135975795868314764489884749573052997832686979294085577689571149679540256349988338406458116270429842222666345146926395233040564229555893248370000*I
+    assert ((2 + 3*I/4)**1000).expand(complex=True) == \
+        Integer(1)*37079892761199059751745775382463070250205990218394308874593455293485167797989691280095867197640410033222367257278387021789651672598831503296531725827158233077451476545928116965316544607115843772405184272449644892857783761260737279675075819921259597776770965829089907990486964515784097181964312256560561065607846661496055417619388874421218472707497847700629822858068783288579581649321248495739224020822198695759609598745114438265083593711851665996586461937988748911532242908776883696631067311443171682974330675406616373422505939887984366289623091300746049101284856530270685577940283077888955692921951247230006346681086274961362500646889925803654263491848309446197554307105991537357310209426736453173441104334496173618419659521888945605315751089087820455852582920963561495787655250624781448951403353654348109893478206364632640344111022531861683064175862889459084900614967785405977231549003280842218501570429860550379522498497412180001/114813069527425452423283320117768198402231770208869520047764273682576626139237031385665948631650626991844596463898746277344711896086305533142593135616665318539129989145312280000688779148240044871428926990063486244781615463646388363947317026040466353970904996558162398808944629605623311649536164221970332681344168908984458505602379484807914058900934776500429002716706625830522008132236281291761267883317206598995396418127021779858404042159853183251540889433902091920554957783589672039160081957216630582755380425583726015528348786419432054508915275783882625175435528800822842770817965453762184851149029376 + \
+        I*421638390580169706973991429333213477486930178424989246669892530737775352519112934278994501272111385966211392610029433824534634841747911783746811994443436271013377059560245191441549885048056920190833693041257216263519792201852046825443439142932464031501882145407459174948712992271510309541474392303461939389368955986650538525895866713074543004916049550090364398070215427272240155060576252568700906004691224321432509053286859100920489253598392100207663785243368195857086816912514025693453058403158416856847185079684216151337200057494966741268925263085619240941610301610538225414050394612058339070756009433535451561664522479191267503989904464718368605684297071150902631208673621618217106272361061676184840810762902463998065947687814692402219182668782278472952758690939877465065070481351343206840649517150634973307937551168752642148704904383991876969408056379195860410677814566225456558230131911142229028179902418223009651437985670625/1793954211366022694113801876840128100034871409513586250746316776290259783425578615401030447369541046747571819748417910583511123376348523955353017744010395602173906080395504375010762174191250701116076984219741972574712741619474818186676828531882286780795390571221287481389759837587864244524002565968286448146002639202882164150037179450123657170327105882819203167448541028601906377066191895183769810676831353109303069033234715310287563158747705988305326397404720186258671215368588625611876280581509852855552819149745718992630449787803625851701801184123166018366180137512856918294030710215034138299203584
+    assert ((2 + 3*I)**-1000).expand(complex=True) == \
+        Integer(1)*-81079464736246615951519029367296227340216902563389546989376269312984127074385455204551402940331021387412262494620336565547972162814110386834027871072723273110439771695255662375718498785908345629702081336606863762777939617745464755635193139022811989314881997210583159045854968310911252660312523907616129080027594310008539817935736331124833163907518549408018652090650537035647520296539436440394920287688149200763245475036722326561143851304795139005599209239350981457301460233967137708519975586996623552182807311159141501424576682074392689622074945519232029999/8777125472973511649630750050295188683351430110097915876250894978429797369155961290321829625004920141758416719066805645579710744290541337680113772670040386863849283653078324415471816788604945889094925784900885812724984087843737442111926413818245854362613018058774368703971604921858023116665586358870612944209398056562604561248859926344335598822815885851096698226775053153403320782439987679978321289537645645163767251396759519805603090332694449553371530571613352311006350058217982509738362083094920649452123351717366337410243853659113315547584871655479914439219520157174729130746351059075207407866012574386726064196992865627149566238044625779078186624347183905913357718850537058578084932880569701242598663149911276357125355850792073635533676541250531086757377369962506979378337216411188347761901006460813413505861461267545723590468627854202034450569581626648934062198718362303420281555886394558137408159453103395918783625713213314350531051312551733021627153081075080140680608080529736975658786227362251632725009435866547613598753584705455955419696609282059191031962604169242974038517575645939316377801594539335940001 - Integer(1)*46938745946789557590804551905243206242164799136976022474337918748798900569942573265747576032611189047943842446167719177749107138603040963603119861476016947257034472364028585381714774667326478071264878108114128915685688115488744955550920239128462489496563930809677159214598114273887061533057125164518549173898349061972857446844052995037423459472376202251620778517659247970283904820245958198842631651569984310559418135975795868314764489884749573052997832686979294085577689571149679540256349988338406458116270429842222666345146926395233040564229555893248370000*I/8777125472973511649630750050295188683351430110097915876250894978429797369155961290321829625004920141758416719066805645579710744290541337680113772670040386863849283653078324415471816788604945889094925784900885812724984087843737442111926413818245854362613018058774368703971604921858023116665586358870612944209398056562604561248859926344335598822815885851096698226775053153403320782439987679978321289537645645163767251396759519805603090332694449553371530571613352311006350058217982509738362083094920649452123351717366337410243853659113315547584871655479914439219520157174729130746351059075207407866012574386726064196992865627149566238044625779078186624347183905913357718850537058578084932880569701242598663149911276357125355850792073635533676541250531086757377369962506979378337216411188347761901006460813413505861461267545723590468627854202034450569581626648934062198718362303420281555886394558137408159453103395918783625713213314350531051312551733021627153081075080140680608080529736975658786227362251632725009435866547613598753584705455955419696609282059191031962604169242974038517575645939316377801594539335940001
+    assert ((2 + 3*I/4)**-1000).expand(complex=True) == \
+        Integer(1)*4257256305661027385394552848555894604806501409793288342610746813288539790051927148781268212212078237301273165351052934681382567968787279534591114913777456610214738290619922068269909423637926549603264174216950025398244509039145410016404821694746262142525173737175066432954496592560621330313807235750500564940782099283410261748370262433487444897446779072067625787246390824312580440138770014838135245148574339248259670887549732495841810961088930810608893772914812838358159009303794863047635845688453859317690488124382253918725010358589723156019888846606295866740117645571396817375322724096486161308083462637370825829567578309445855481578518239186117686659177284332344643124760453112513611749309168470605289172320376911472635805822082051716625171429727162039621902266619821870482519063133136820085579315127038372190224739238686708451840610064871885616258831386810233957438253532027049148030157164346719204500373766157143311767338973363806106967439378604898250533766359989107510507493549529158818602327525235240510049484816090584478644771183158342479140194633579061295740839490629457435283873180259847394582069479062820225159699506175855369539201399183443253793905149785994830358114153241481884290274629611529758663543080724574566578220908907477622643689220814376054314972190402285121776593824615083669045183404206291739005554569305329760211752815718335731118664756831942466773261465213581616104242113894521054475516019456867271362053692785300826523328020796670205463390909136593859765912483565093461468865534470710132881677639651348709376/2103100954337624833663208713697737151593634525061637972297915388685604042449504336765884978184588688426595940401280828953096857809292320006227881797146858511436638446932833617514351442216409828605662238790280753075176269765767010004889778647709740770757817960711900340755635772183674511158570690702969774966791073165467918123298694584729211212414462628433370481195120564586361368504153395406845170075275051749019600057116719726628746724489572189061061036426955163696859127711110719502594479795200686212257570291758725259007379710596548777812659422174199194837355646482046783616494013289495563083118517507178847555801163089723056310287760875135196081975602765511153122381201303871673391366630940702817360340900568748719988954847590748960761446218262344767250783946365392689256634180417145926390656439421745644011831124277463643383712803287985472471755648426749842410972650924240795946699346613614779460399530274263580007672855851663196114585312432954432654691485867618908420370875753749297487803461900447407917655296784879220450937110470920633595689721819488638484547259978337741496090602390463594556401615298457456112485536498177883358587125449801777718900375736758266215245325999241624148841915093787519330809347240990363802360596034171167818310322276373120180985148650099673289383722502488957717848531612020897298448601714154586319660314294591620415272119454982220034319689607295960162971300417552364254983071768070124456169427638371140064235083443242844616326538396503937972586505546495649094344512270582463639152160238137952390380581401171977159154009407415523525096743009110916334144716516647041176989758534635251844947906038080852185583742296318878233394998111078843229681030277039104786225656992262073797524057992347971177720807155842376332851559276430280477639539393920006008737472164850104411971830120295750221200029811143140323763349636629725073624360001 - Integer(1)*3098214262599218784594285246258841485430681674561917573155883806818465520660668045042109232930382494608383663464454841313154390741655282039877410154577448327874989496074260116195788919037407420625081798124301494353693248757853222257918294662198297114746822817460991242508743651430439120439020484502408313310689912381846149597061657483084652685283853595100434135149479564507015504022249330340259111426799121454516345905101620532787348293877485702600390665276070250119465888154331218827342488849948540687659846652377277250614246402784754153678374932540789808703029043827352976139228402417432199779415751301480406673762521987999573209628597459357964214510139892316208670927074795773830798600837815329291912002136924506221066071242281626618211060464126372574400100990746934953437169840312584285942093951405864225230033279614235191326102697164613004299868695519642598882914862568516635347204441042798206770888274175592401790040170576311989738272102077819127459014286741435419468254146418098278519775722104890854275995510700298782146199325790002255362719776098816136732897323406228294203133323296591166026338391813696715894870956511298793595675308998014158717167429941371979636895553724830981754579086664608880698350866487717403917070872269853194118364230971216854931998642990452908852258008095741042117326241406479532880476938937997238098399302185675832474590293188864060116934035867037219176916416481757918864533515526389079998129329045569609325290897577497835388451456680707076072624629697883854217331728051953671643278797380171857920000*I/2103100954337624833663208713697737151593634525061637972297915388685604042449504336765884978184588688426595940401280828953096857809292320006227881797146858511436638446932833617514351442216409828605662238790280753075176269765767010004889778647709740770757817960711900340755635772183674511158570690702969774966791073165467918123298694584729211212414462628433370481195120564586361368504153395406845170075275051749019600057116719726628746724489572189061061036426955163696859127711110719502594479795200686212257570291758725259007379710596548777812659422174199194837355646482046783616494013289495563083118517507178847555801163089723056310287760875135196081975602765511153122381201303871673391366630940702817360340900568748719988954847590748960761446218262344767250783946365392689256634180417145926390656439421745644011831124277463643383712803287985472471755648426749842410972650924240795946699346613614779460399530274263580007672855851663196114585312432954432654691485867618908420370875753749297487803461900447407917655296784879220450937110470920633595689721819488638484547259978337741496090602390463594556401615298457456112485536498177883358587125449801777718900375736758266215245325999241624148841915093787519330809347240990363802360596034171167818310322276373120180985148650099673289383722502488957717848531612020897298448601714154586319660314294591620415272119454982220034319689607295960162971300417552364254983071768070124456169427638371140064235083443242844616326538396503937972586505546495649094344512270582463639152160238137952390380581401171977159154009407415523525096743009110916334144716516647041176989758534635251844947906038080852185583742296318878233394998111078843229681030277039104786225656992262073797524057992347971177720807155842376332851559276430280477639539393920006008737472164850104411971830120295750221200029811143140323763349636629725073624360001
+
+    a = Symbol('a', real=True)
+    b = Symbol('b', real=True)
+    assert exp(a*(2 + I*b)).expand(complex=True) == \
+        I*exp(2*a)*sin(a*b) + exp(2*a)*cos(a*b)
+
+
+def test_expand():
+    f = (16 - 2*sqrt(29))**2
+    assert f.expand() == 372 - 64*sqrt(29)
+    f = (Integer(1)/2 + I/2)**10
+    assert f.expand() == I/32
+    f = (Integer(1)/2 + I)**10
+    assert f.expand() == Integer(237)/1024 - 779*I/256
+
+
+def test_re_im1652():
+    x = Symbol('x')
+    assert re(x) == re(conjugate(x))
+    assert im(x) == - im(conjugate(x))
+    assert im(x)*re(conjugate(x)) + im(conjugate(x)) * re(x) == 0
+
+
+def test_issue_5084():
+    x = Symbol('x')
+    assert ((x + x*I)/(1 + I)).as_real_imag() == (re((x + I*x)/(1 + I)
+            ), im((x + I*x)/(1 + I)))
+
+
+def test_issue_5236():
+    assert (cos(1 + I)**3).as_real_imag() == (-3*sin(1)**2*sinh(1)**2*cos(1)*cosh(1) +
+        cos(1)**3*cosh(1)**3, -3*cos(1)**2*cosh(1)**2*sin(1)*sinh(1) + sin(1)**3*sinh(1)**3)
+
+
+def test_real_imag():
+    x, y, z = symbols('x, y, z')
+    X, Y, Z = symbols('X, Y, Z', commutative=False)
+    a = Symbol('a', real=True)
+    assert (2*a*x).as_real_imag() == (2*a*re(x), 2*a*im(x))
+
+    # issue 5395:
+    assert (x*x.conjugate()).as_real_imag() == (Abs(x)**2, 0)
+    assert im(x*x.conjugate()) == 0
+    assert im(x*y.conjugate()*z*y) == im(x*z)*Abs(y)**2
+    assert im(x*y.conjugate()*x*y) == im(x**2)*Abs(y)**2
+    assert im(Z*y.conjugate()*X*y) == im(Z*X)*Abs(y)**2
+    assert im(X*X.conjugate()) == im(X*X.conjugate(), evaluate=False)
+    assert (sin(x)*sin(x).conjugate()).as_real_imag() == \
+        (Abs(sin(x))**2, 0)
+
+    # issue 6573:
+    assert (x**2).as_real_imag() == (re(x)**2 - im(x)**2, 2*re(x)*im(x))
+
+    # issue 6428:
+    r = Symbol('r', real=True)
+    i = Symbol('i', imaginary=True)
+    assert (i*r*x).as_real_imag() == (I*i*r*im(x), -I*i*r*re(x))
+    assert (i*r*x*(y + 2)).as_real_imag() == (
+        I*i*r*(re(y) + 2)*im(x) + I*i*r*re(x)*im(y),
+        -I*i*r*(re(y) + 2)*re(x) + I*i*r*im(x)*im(y))
+
+    # issue 7106:
+    assert ((1 + I)/(1 - I)).as_real_imag() == (0, 1)
+    assert ((1 + 2*I)*(1 + 3*I)).as_real_imag() == (-5, 5)
+
+
+def test_pow_issue_1724():
+    e = ((S.NegativeOne)**(S.One/3))
+    assert e.conjugate().n() == e.n().conjugate()
+    e = S('-2/3 - (-29/54 + sqrt(93)/18)**(1/3) - 1/(9*(-29/54 + sqrt(93)/18)**(1/3))')
+    assert e.conjugate().n() == e.n().conjugate()
+    e = 2**I
+    assert e.conjugate().n() == e.n().conjugate()
+
+
+def test_issue_5429():
+    assert sqrt(I).conjugate() != sqrt(I)
+
+def test_issue_4124():
+    from sympy.core.numbers import oo
+    assert expand_complex(I*oo) == oo*I
+
+def test_issue_11518():
+    x = Symbol("x", real=True)
+    y = Symbol("y", real=True)
+    r = sqrt(x**2 + y**2)
+    assert conjugate(r) == r
+    s = abs(x + I * y)
+    assert conjugate(s) == r
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_constructor_postprocessor.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_constructor_postprocessor.py
new file mode 100644
index 0000000000000000000000000000000000000000..c199e24eddf8ef7c2a14e38d1ad2dc95e4acc0cc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_constructor_postprocessor.py
@@ -0,0 +1,87 @@
+from sympy.core.basic import Basic
+from sympy.core.mul import Mul
+from sympy.core.symbol import (Symbol, symbols)
+
+from sympy.testing.pytest import XFAIL
+
+class SymbolInMulOnce(Symbol):
+    # Test class for a symbol that can only appear once in a `Mul` expression.
+    pass
+
+
+Basic._constructor_postprocessor_mapping[SymbolInMulOnce] = {
+    "Mul": [lambda x: x],
+    "Pow": [lambda x: x.base if isinstance(x.base, SymbolInMulOnce) else x],
+    "Add": [lambda x: x],
+}
+
+
+def _postprocess_SymbolRemovesOtherSymbols(expr):
+    args = tuple(i for i in expr.args if not isinstance(i, Symbol) or isinstance(i, SymbolRemovesOtherSymbols))
+    if args == expr.args:
+        return expr
+    return Mul.fromiter(args)
+
+
+class SymbolRemovesOtherSymbols(Symbol):
+    # Test class for a symbol that removes other symbols in `Mul`.
+    pass
+
+Basic._constructor_postprocessor_mapping[SymbolRemovesOtherSymbols] = {
+    "Mul": [_postprocess_SymbolRemovesOtherSymbols],
+}
+
+class SubclassSymbolInMulOnce(SymbolInMulOnce):
+    pass
+
+class SubclassSymbolRemovesOtherSymbols(SymbolRemovesOtherSymbols):
+    pass
+
+
+def test_constructor_postprocessors1():
+    x = SymbolInMulOnce("x")
+    y = SymbolInMulOnce("y")
+    assert isinstance(3*x, Mul)
+    assert (3*x).args == (3, x)
+    assert x*x == x
+    assert 3*x*x == 3*x
+    assert 2*x*x + x == 3*x
+    assert x**3*y*y == x*y
+    assert x**5 + y*x**3 == x + x*y
+
+    w = SymbolRemovesOtherSymbols("w")
+    assert x*w == w
+    assert (3*w).args == (3, w)
+    assert set((w + x).args) == {x, w}
+
+def test_constructor_postprocessors2():
+    x = SubclassSymbolInMulOnce("x")
+    y = SubclassSymbolInMulOnce("y")
+    assert isinstance(3*x, Mul)
+    assert (3*x).args == (3, x)
+    assert x*x == x
+    assert 3*x*x == 3*x
+    assert 2*x*x + x == 3*x
+    assert x**3*y*y == x*y
+    assert x**5 + y*x**3 == x + x*y
+
+    w = SubclassSymbolRemovesOtherSymbols("w")
+    assert x*w == w
+    assert (3*w).args == (3, w)
+    assert set((w + x).args) == {x, w}
+
+
+@XFAIL
+def test_subexpression_postprocessors():
+    # The postprocessors used to work with subexpressions, but the
+    # functionality was removed. See #15948.
+    a = symbols("a")
+    x = SymbolInMulOnce("x")
+    w = SymbolRemovesOtherSymbols("w")
+    assert 3*a*w**2 == 3*w**2
+    assert 3*a*x**3*w**2 == 3*w**2
+
+    x = SubclassSymbolInMulOnce("x")
+    w = SubclassSymbolRemovesOtherSymbols("w")
+    assert 3*a*w**2 == 3*w**2
+    assert 3*a*x**3*w**2 == 3*w**2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_containers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_containers.py
new file mode 100644
index 0000000000000000000000000000000000000000..23357b9f667fffc82d93b2b1adb42b495114c67e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_containers.py
@@ -0,0 +1,217 @@
+from collections import defaultdict
+
+from sympy.core.basic import Basic
+from sympy.core.containers import (Dict, Tuple)
+from sympy.core.numbers import Integer
+from sympy.core.kind import NumberKind
+from sympy.matrices.kind import MatrixKind
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.core.sympify import sympify
+from sympy.matrices.dense import Matrix
+from sympy.sets.sets import FiniteSet
+from sympy.core.containers import tuple_wrapper, TupleKind
+from sympy.core.expr import unchanged
+from sympy.core.function import Function, Lambda
+from sympy.core.relational import Eq
+from sympy.testing.pytest import raises
+from sympy.utilities.iterables import is_sequence, iterable
+
+from sympy.abc import x, y
+
+
+def test_Tuple():
+    t = (1, 2, 3, 4)
+    st = Tuple(*t)
+    assert set(sympify(t)) == set(st)
+    assert len(t) == len(st)
+    assert set(sympify(t[:2])) == set(st[:2])
+    assert isinstance(st[:], Tuple)
+    assert st == Tuple(1, 2, 3, 4)
+    assert st.func(*st.args) == st
+    p, q, r, s = symbols('p q r s')
+    t2 = (p, q, r, s)
+    st2 = Tuple(*t2)
+    assert st2.atoms() == set(t2)
+    assert st == st2.subs({p: 1, q: 2, r: 3, s: 4})
+    # issue 5505
+    assert all(isinstance(arg, Basic) for arg in st.args)
+    assert Tuple(p, 1).subs(p, 0) == Tuple(0, 1)
+    assert Tuple(p, Tuple(p, 1)).subs(p, 0) == Tuple(0, Tuple(0, 1))
+
+    assert Tuple(t2) == Tuple(Tuple(*t2))
+    assert Tuple.fromiter(t2) == Tuple(*t2)
+    assert Tuple.fromiter(x for x in range(4)) == Tuple(0, 1, 2, 3)
+    assert st2.fromiter(st2.args) == st2
+
+
+def test_Tuple_contains():
+    t1, t2 = Tuple(1), Tuple(2)
+    assert t1 in Tuple(1, 2, 3, t1, Tuple(t2))
+    assert t2 not in Tuple(1, 2, 3, t1, Tuple(t2))
+
+
+def test_Tuple_concatenation():
+    assert Tuple(1, 2) + Tuple(3, 4) == Tuple(1, 2, 3, 4)
+    assert (1, 2) + Tuple(3, 4) == Tuple(1, 2, 3, 4)
+    assert Tuple(1, 2) + (3, 4) == Tuple(1, 2, 3, 4)
+    raises(TypeError, lambda: Tuple(1, 2) + 3)
+    raises(TypeError, lambda: 1 + Tuple(2, 3))
+
+    #the Tuple case in __radd__ is only reached when a subclass is involved
+    class Tuple2(Tuple):
+        def __radd__(self, other):
+            return Tuple.__radd__(self, other + other)
+    assert Tuple(1, 2) + Tuple2(3, 4) == Tuple(1, 2, 1, 2, 3, 4)
+    assert Tuple2(1, 2) + Tuple(3, 4) == Tuple(1, 2, 3, 4)
+
+
+def test_Tuple_equality():
+    assert not isinstance(Tuple(1, 2), tuple)
+    assert (Tuple(1, 2) == (1, 2)) is True
+    assert (Tuple(1, 2) != (1, 2)) is False
+    assert (Tuple(1, 2) == (1, 3)) is False
+    assert (Tuple(1, 2) != (1, 3)) is True
+    assert (Tuple(1, 2) == Tuple(1, 2)) is True
+    assert (Tuple(1, 2) != Tuple(1, 2)) is False
+    assert (Tuple(1, 2) == Tuple(1, 3)) is False
+    assert (Tuple(1, 2) != Tuple(1, 3)) is True
+
+
+def test_Tuple_Eq():
+    assert Eq(Tuple(), Tuple()) is S.true
+    assert Eq(Tuple(1), 1) is S.false
+    assert Eq(Tuple(1, 2), Tuple(1)) is S.false
+    assert Eq(Tuple(1), Tuple(1)) is S.true
+    assert Eq(Tuple(1, 2), Tuple(1, 3)) is S.false
+    assert Eq(Tuple(1, 2), Tuple(1, 2)) is S.true
+    assert unchanged(Eq, Tuple(1, x), Tuple(1, 2))
+    assert Eq(Tuple(1, x), Tuple(1, 2)).subs(x, 2) is S.true
+    assert unchanged(Eq, Tuple(1, 2), x)
+    f = Function('f')
+    assert unchanged(Eq, Tuple(1), f(x))
+    assert Eq(Tuple(1), f(x)).subs(x, 1).subs(f, Lambda(y, (y,))) is S.true
+
+
+def test_Tuple_comparision():
+    assert (Tuple(1, 3) >= Tuple(-10, 30)) is S.true
+    assert (Tuple(1, 3) <= Tuple(-10, 30)) is S.false
+    assert (Tuple(1, 3) >= Tuple(1, 3)) is S.true
+    assert (Tuple(1, 3) <= Tuple(1, 3)) is S.true
+
+
+def test_Tuple_tuple_count():
+    assert Tuple(0, 1, 2, 3).tuple_count(4) == 0
+    assert Tuple(0, 4, 1, 2, 3).tuple_count(4) == 1
+    assert Tuple(0, 4, 1, 4, 2, 3).tuple_count(4) == 2
+    assert Tuple(0, 4, 1, 4, 2, 4, 3).tuple_count(4) == 3
+
+
+def test_Tuple_index():
+    assert Tuple(4, 0, 1, 2, 3).index(4) == 0
+    assert Tuple(0, 4, 1, 2, 3).index(4) == 1
+    assert Tuple(0, 1, 4, 2, 3).index(4) == 2
+    assert Tuple(0, 1, 2, 4, 3).index(4) == 3
+    assert Tuple(0, 1, 2, 3, 4).index(4) == 4
+
+    raises(ValueError, lambda: Tuple(0, 1, 2, 3).index(4))
+    raises(ValueError, lambda: Tuple(4, 0, 1, 2, 3).index(4, 1))
+    raises(ValueError, lambda: Tuple(0, 1, 2, 3, 4).index(4, 1, 4))
+
+
+def test_Tuple_mul():
+    assert Tuple(1, 2, 3)*2 == Tuple(1, 2, 3, 1, 2, 3)
+    assert 2*Tuple(1, 2, 3) == Tuple(1, 2, 3, 1, 2, 3)
+    assert Tuple(1, 2, 3)*Integer(2) == Tuple(1, 2, 3, 1, 2, 3)
+    assert Integer(2)*Tuple(1, 2, 3) == Tuple(1, 2, 3, 1, 2, 3)
+
+    raises(TypeError, lambda: Tuple(1, 2, 3)*S.Half)
+    raises(TypeError, lambda: S.Half*Tuple(1, 2, 3))
+
+
+def test_tuple_wrapper():
+
+    @tuple_wrapper
+    def wrap_tuples_and_return(*t):
+        return t
+
+    p = symbols('p')
+    assert wrap_tuples_and_return(p, 1) == (p, 1)
+    assert wrap_tuples_and_return((p, 1)) == (Tuple(p, 1),)
+    assert wrap_tuples_and_return(1, (p, 2), 3) == (1, Tuple(p, 2), 3)
+
+
+def test_iterable_is_sequence():
+    ordered = [[], (), Tuple(), Matrix([[]])]
+    unordered = [set()]
+    not_sympy_iterable = [{}, '', '']
+    assert all(is_sequence(i) for i in ordered)
+    assert all(not is_sequence(i) for i in unordered)
+    assert all(iterable(i) for i in ordered + unordered)
+    assert all(not iterable(i) for i in not_sympy_iterable)
+    assert all(iterable(i, exclude=None) for i in not_sympy_iterable)
+
+
+def test_TupleKind():
+    kind = TupleKind(NumberKind, MatrixKind(NumberKind))
+    assert Tuple(1, Matrix([1, 2])).kind is kind
+    assert Tuple(1, 2).kind is TupleKind(NumberKind, NumberKind)
+    assert Tuple(1, 2).kind.element_kind == (NumberKind, NumberKind)
+
+
+def test_Dict():
+    x, y, z = symbols('x y z')
+    d = Dict({x: 1, y: 2, z: 3})
+    assert d[x] == 1
+    assert d[y] == 2
+    raises(KeyError, lambda: d[2])
+    raises(KeyError, lambda: d['2'])
+    assert len(d) == 3
+    assert set(d.keys()) == {x, y, z}
+    assert set(d.values()) == {S.One, S(2), S(3)}
+    assert d.get(5, 'default') == 'default'
+    assert d.get('5', 'default') == 'default'
+    assert x in d and z in d and 5 not in d and '5' not in d
+    assert d.has(x) and d.has(1)  # SymPy Basic .has method
+
+    # Test input types
+    # input - a Python dict
+    # input - items as args - SymPy style
+    assert (Dict({x: 1, y: 2, z: 3}) ==
+            Dict((x, 1), (y, 2), (z, 3)))
+
+    raises(TypeError, lambda: Dict(((x, 1), (y, 2), (z, 3))))
+    with raises(NotImplementedError):
+        d[5] = 6  # assert immutability
+
+    assert set(
+        d.items()) == {Tuple(x, S.One), Tuple(y, S(2)), Tuple(z, S(3))}
+    assert set(d) == {x, y, z}
+    assert str(d) == '{x: 1, y: 2, z: 3}'
+    assert d.__repr__() == '{x: 1, y: 2, z: 3}'
+
+    # Test creating a Dict from a Dict.
+    d = Dict({x: 1, y: 2, z: 3})
+    assert d == Dict(d)
+
+    # Test for supporting defaultdict
+    d = defaultdict(int)
+    assert d[x] == 0
+    assert d[y] == 0
+    assert d[z] == 0
+    assert Dict(d)
+    d = Dict(d)
+    assert len(d) == 3
+    assert set(d.keys()) == {x, y, z}
+    assert set(d.values()) == {S.Zero, S.Zero, S.Zero}
+
+
+def test_issue_5788():
+    args = [(1, 2), (2, 1)]
+    for o in [Dict, Tuple, FiniteSet]:
+        # __eq__ and arg handling
+        if o != Tuple:
+            assert o(*args) == o(*reversed(args))
+        pair = [o(*args), o(*reversed(args))]
+        assert sorted(pair) == sorted(pair)
+        assert set(o(*args))  # doesn't fail
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_count_ops.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_count_ops.py
new file mode 100644
index 0000000000000000000000000000000000000000..bc95004ef5ba4421927289a049a9197d208c30d0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_count_ops.py
@@ -0,0 +1,155 @@
+from sympy.concrete.summations import Sum
+from sympy.core.basic import Basic
+from sympy.core.function import (Derivative, Function, count_ops)
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.relational import (Eq, Rel)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.integrals.integrals import Integral
+from sympy.logic.boolalg import (And, Equivalent, ITE, Implies, Nand,
+    Nor, Not, Or, Xor)
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.core.containers import Tuple
+
+x, y, z = symbols('x,y,z')
+a, b, c = symbols('a,b,c')
+
+def test_count_ops_non_visual():
+    def count(val):
+        return count_ops(val, visual=False)
+    assert count(x) == 0
+    assert count(x) is not S.Zero
+    assert count(x + y) == 1
+    assert count(x + y) is not S.One
+    assert count(x + y*x + 2*y) == 4
+    assert count({x + y: x}) == 1
+    assert count({x + y: S(2) + x}) is not S.One
+    assert count(x < y) == 1
+    assert count(Or(x,y)) == 1
+    assert count(And(x,y)) == 1
+    assert count(Not(x)) == 1
+    assert count(Nor(x,y)) == 2
+    assert count(Nand(x,y)) == 2
+    assert count(Xor(x,y)) == 1
+    assert count(Implies(x,y)) == 1
+    assert count(Equivalent(x,y)) == 1
+    assert count(ITE(x,y,z)) == 1
+    assert count(ITE(True,x,y)) == 0
+
+
+def test_count_ops_visual():
+    ADD, MUL, POW, SIN, COS, EXP, AND, D, G, M = symbols(
+        'Add Mul Pow sin cos exp And Derivative Integral Sum'.upper())
+    DIV, SUB, NEG = symbols('DIV SUB NEG')
+    LT, LE, GT, GE, EQ, NE = symbols('LT LE GT GE EQ NE')
+    NOT, OR, AND, XOR, IMPLIES, EQUIVALENT, _ITE, BASIC, TUPLE = symbols(
+        'Not Or And Xor Implies Equivalent ITE Basic Tuple'.upper())
+
+    def count(val):
+        return count_ops(val, visual=True)
+
+    assert count(7) is S.Zero
+    assert count(S(7)) is S.Zero
+    assert count(-1) == NEG
+    assert count(-2) == NEG
+    assert count(S(2)/3) == DIV
+    assert count(Rational(2, 3)) == DIV
+    assert count(pi/3) == DIV
+    assert count(-pi/3) == DIV + NEG
+    assert count(I - 1) == SUB
+    assert count(1 - I) == SUB
+    assert count(1 - 2*I) == SUB + MUL
+
+    assert count(x) is S.Zero
+    assert count(-x) == NEG
+    assert count(-2*x/3) == NEG + DIV + MUL
+    assert count(Rational(-2, 3)*x) == NEG + DIV + MUL
+    assert count(1/x) == DIV
+    assert count(1/(x*y)) == DIV + MUL
+    assert count(-1/x) == NEG + DIV
+    assert count(-2/x) == NEG + DIV
+    assert count(x/y) == DIV
+    assert count(-x/y) == NEG + DIV
+
+    assert count(x**2) == POW
+    assert count(-x**2) == POW + NEG
+    assert count(-2*x**2) == POW + MUL + NEG
+
+    assert count(x + pi/3) == ADD + DIV
+    assert count(x + S.One/3) == ADD + DIV
+    assert count(x + Rational(1, 3)) == ADD + DIV
+    assert count(x + y) == ADD
+    assert count(x - y) == SUB
+    assert count(y - x) == SUB
+    assert count(-1/(x - y)) == DIV + NEG + SUB
+    assert count(-1/(y - x)) == DIV + NEG + SUB
+    assert count(1 + x**y) == ADD + POW
+    assert count(1 + x + y) == 2*ADD
+    assert count(1 + x + y + z) == 3*ADD
+    assert count(1 + x**y + 2*x*y + y**2) == 3*ADD + 2*POW + 2*MUL
+    assert count(2*z + y + x + 1) == 3*ADD + MUL
+    assert count(2*z + y**17 + x + 1) == 3*ADD + MUL + POW
+    assert count(2*z + y**17 + x + sin(x)) == 3*ADD + POW + MUL + SIN
+    assert count(2*z + y**17 + x + sin(x**2)) == 3*ADD + MUL + 2*POW + SIN
+    assert count(2*z + y**17 + x + sin(
+        x**2) + exp(cos(x))) == 4*ADD + MUL + 2*POW + EXP + COS + SIN
+
+    assert count(Derivative(x, x)) == D
+    assert count(Integral(x, x) + 2*x/(1 + x)) == G + DIV + MUL + 2*ADD
+    assert count(Sum(x, (x, 1, x + 1)) + 2*x/(1 + x)) == M + DIV + MUL + 3*ADD
+    assert count(Basic()) is S.Zero
+
+    assert count({x + 1: sin(x)}) == ADD + SIN
+    assert count([x + 1, sin(x) + y, None]) == ADD + SIN + ADD
+    assert count({x + 1: sin(x), y: cos(x) + 1}) == SIN + COS + 2*ADD
+    assert count({}) is S.Zero
+    assert count([x + 1, sin(x)*y, None]) == SIN + ADD + MUL
+    assert count([]) is S.Zero
+
+    assert count(Basic()) == 0
+    assert count(Basic(Basic(),Basic(x,x+y))) == ADD + 2*BASIC
+    assert count(Basic(x, x + y)) == ADD + BASIC
+    assert [count(Rel(x, y, op)) for op in '< <= > >= == <> !='.split()
+        ] == [LT, LE, GT, GE, EQ, NE, NE]
+    assert count(Or(x, y)) == OR
+    assert count(And(x, y)) == AND
+    assert count(Or(x, Or(y, And(z, a)))) == AND + OR
+    assert count(Nor(x, y)) == NOT + OR
+    assert count(Nand(x, y)) == NOT + AND
+    assert count(Xor(x, y)) == XOR
+    assert count(Implies(x, y)) == IMPLIES
+    assert count(Equivalent(x, y)) == EQUIVALENT
+    assert count(ITE(x, y, z)) == _ITE
+    assert count([Or(x, y), And(x, y), Basic(x + y)]
+        ) == ADD + AND + BASIC + OR
+
+    assert count(Basic(Tuple(x))) == BASIC + TUPLE
+    #It checks that TUPLE is counted as an operation.
+
+    assert count(Eq(x + y, S(2))) == ADD + EQ
+
+
+def test_issue_9324():
+    def count(val):
+        return count_ops(val, visual=False)
+
+    M = MatrixSymbol('M', 10, 10)
+    assert count(M[0, 0]) == 0
+    assert count(2 * M[0, 0] + M[5, 7]) == 2
+    P = MatrixSymbol('P', 3, 3)
+    Q = MatrixSymbol('Q', 3, 3)
+    assert count(P + Q) == 1
+    m = Symbol('m', integer=True)
+    n = Symbol('n', integer=True)
+    M = MatrixSymbol('M', m + n, m * m)
+    assert count(M[0, 1]) == 2
+
+
+def test_issue_21532():
+    f = Function('f')
+    g = Function('g')
+    FUNC_F, FUNC_G = symbols('FUNC_F, FUNC_G')
+    assert f(x).count_ops(visual=True) == FUNC_F
+    assert g(x).count_ops(visual=True) == FUNC_G
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_diff.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_diff.py
new file mode 100644
index 0000000000000000000000000000000000000000..effc9cd91d2e7b6f8f8e5fd04bb667ed71c0ffaf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_diff.py
@@ -0,0 +1,160 @@
+from sympy.concrete.summations import Sum
+from sympy.core.expr import Expr
+from sympy.core.function import (Derivative, Function, diff, Subs)
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import (im, re)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import Max
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (cos, cot, sin, tan)
+from sympy.tensor.array.ndim_array import NDimArray
+from sympy.testing.pytest import raises
+from sympy.abc import a, b, c, x, y, z
+
+def test_diff():
+    assert Rational(1, 3).diff(x) is S.Zero
+    assert I.diff(x) is S.Zero
+    assert pi.diff(x) is S.Zero
+    assert x.diff(x, 0) == x
+    assert (x**2).diff(x, 2, x) == 0
+    assert (x**2).diff((x, 2), x) == 0
+    assert (x**2).diff((x, 1), x) == 2
+    assert (x**2).diff((x, 1), (x, 1)) == 2
+    assert (x**2).diff((x, 2)) == 2
+    assert (x**2).diff(x, y, 0) == 2*x
+    assert (x**2).diff(x, (y, 0)) == 2*x
+    assert (x**2).diff(x, y) == 0
+    raises(ValueError, lambda: x.diff(1, x))
+
+    p = Rational(5)
+    e = a*b + b**p
+    assert e.diff(a) == b
+    assert e.diff(b) == a + 5*b**4
+    assert e.diff(b).diff(a) == Rational(1)
+    e = a*(b + c)
+    assert e.diff(a) == b + c
+    assert e.diff(b) == a
+    assert e.diff(b).diff(a) == Rational(1)
+    e = c**p
+    assert e.diff(c, 6) == Rational(0)
+    assert e.diff(c, 5) == Rational(120)
+    e = c**Rational(2)
+    assert e.diff(c) == 2*c
+    e = a*b*c
+    assert e.diff(c) == a*b
+
+
+def test_diff2():
+    n3 = Rational(3)
+    n2 = Rational(2)
+    n6 = Rational(6)
+
+    e = n3*(-n2 + x**n2)*cos(x) + x*(-n6 + x**n2)*sin(x)
+    assert e == 3*(-2 + x**2)*cos(x) + x*(-6 + x**2)*sin(x)
+    assert e.diff(x).expand() == x**3*cos(x)
+
+    e = (x + 1)**3
+    assert e.diff(x) == 3*(x + 1)**2
+    e = x*(x + 1)**3
+    assert e.diff(x) == (x + 1)**3 + 3*x*(x + 1)**2
+    e = 2*exp(x*x)*x
+    assert e.diff(x) == 2*exp(x**2) + 4*x**2*exp(x**2)
+
+
+def test_diff3():
+    p = Rational(5)
+    e = a*b + sin(b**p)
+    assert e == a*b + sin(b**5)
+    assert e.diff(a) == b
+    assert e.diff(b) == a + 5*b**4*cos(b**5)
+    e = tan(c)
+    assert e == tan(c)
+    assert e.diff(c) in [cos(c)**(-2), 1 + sin(c)**2/cos(c)**2, 1 + tan(c)**2]
+    e = c*log(c) - c
+    assert e == -c + c*log(c)
+    assert e.diff(c) == log(c)
+    e = log(sin(c))
+    assert e == log(sin(c))
+    assert e.diff(c) in [sin(c)**(-1)*cos(c), cot(c)]
+    e = (Rational(2)**a/log(Rational(2)))
+    assert e == 2**a*log(Rational(2))**(-1)
+    assert e.diff(a) == 2**a
+
+
+def test_diff_no_eval_derivative():
+    class My(Expr):
+        def __new__(cls, x):
+            return Expr.__new__(cls, x)
+
+    # My doesn't have its own _eval_derivative method
+    assert My(x).diff(x).func is Derivative
+    assert My(x).diff(x, 3).func is Derivative
+    assert re(x).diff(x, 2) == Derivative(re(x), (x, 2))  # issue 15518
+    assert diff(NDimArray([re(x), im(x)]), (x, 2)) == NDimArray(
+        [Derivative(re(x), (x, 2)), Derivative(im(x), (x, 2))])
+    # it doesn't have y so it shouldn't need a method for this case
+    assert My(x).diff(y) == 0
+
+
+def test_speed():
+    # this should return in 0.0s. If it takes forever, it's wrong.
+    assert x.diff(x, 10**8) == 0
+
+
+def test_deriv_noncommutative():
+    A = Symbol("A", commutative=False)
+    f = Function("f")
+    assert A*f(x)*A == f(x)*A**2
+    assert A*f(x).diff(x)*A == f(x).diff(x) * A**2
+
+
+def test_diff_nth_derivative():
+    f =  Function("f")
+    n = Symbol("n", integer=True)
+
+    expr = diff(sin(x), (x, n))
+    expr2 = diff(f(x), (x, 2))
+    expr3 = diff(f(x), (x, n))
+
+    assert expr.subs(sin(x), cos(-x)) == Derivative(cos(-x), (x, n))
+    assert expr.subs(n, 1).doit() == cos(x)
+    assert expr.subs(n, 2).doit() == -sin(x)
+
+    assert expr2.subs(Derivative(f(x), x), y) == Derivative(y, x)
+    # Currently not supported (cannot determine if `n > 1`):
+    #assert expr3.subs(Derivative(f(x), x), y) == Derivative(y, (x, n-1))
+    assert expr3 == Derivative(f(x), (x, n))
+
+    assert diff(x, (x, n)) == Piecewise((x, Eq(n, 0)), (1, Eq(n, 1)), (0, True))
+    assert diff(2*x, (x, n)).dummy_eq(
+        Sum(Piecewise((2*x*factorial(n)/(factorial(y)*factorial(-y + n)),
+        Eq(y, 0) & Eq(Max(0, -y + n), 0)),
+        (2*factorial(n)/(factorial(y)*factorial(-y + n)), Eq(y, 0) & Eq(Max(0,
+        -y + n), 1)), (0, True)), (y, 0, n)))
+    # TODO: assert diff(x**2, (x, n)) == x**(2-n)*ff(2, n)
+    exprm = x*sin(x)
+    mul_diff = diff(exprm, (x, n))
+    assert isinstance(mul_diff, Sum)
+    for i in range(5):
+        assert mul_diff.subs(n, i).doit() == exprm.diff((x, i)).expand()
+
+    exprm2 = 2*y*x*sin(x)*cos(x)*log(x)*exp(x)
+    dex = exprm2.diff((x, n))
+    assert isinstance(dex, Sum)
+    for i in range(7):
+        assert dex.subs(n, i).doit().expand() == \
+        exprm2.diff((x, i)).expand()
+
+    assert (cos(x)*sin(y)).diff([[x, y, z]]) == NDimArray([
+        -sin(x)*sin(y), cos(x)*cos(y), 0])
+
+
+def test_issue_16160():
+    assert Derivative(x**3, (x, x)).subs(x, 2) == Subs(
+        Derivative(x**3, (x, 2)), x, 2)
+    assert Derivative(1 + x**3, (x, x)).subs(x, 0
+        ) == Derivative(1 + y**3, (y, 0)).subs(y, 0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_equal.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_equal.py
new file mode 100644
index 0000000000000000000000000000000000000000..82213b757cda5fbd80310e387bdf00cc1c9c25fe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_equal.py
@@ -0,0 +1,89 @@
+from sympy.core.numbers import Rational
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.elementary.exponential import exp
+
+
+def test_equal():
+    b = Symbol("b")
+    a = Symbol("a")
+    e1 = a + b
+    e2 = 2*a*b
+    e3 = a**3*b**2
+    e4 = a*b + b*a
+    assert not e1 == e2
+    assert not e1 == e2
+    assert e1 != e2
+    assert e2 == e4
+    assert e2 != e3
+    assert not e2 == e3
+
+    x = Symbol("x")
+    e1 = exp(x + 1/x)
+    y = Symbol("x")
+    e2 = exp(y + 1/y)
+    assert e1 == e2
+    assert not e1 != e2
+    y = Symbol("y")
+    e2 = exp(y + 1/y)
+    assert not e1 == e2
+    assert e1 != e2
+
+    e5 = Rational(3) + 2*x - x - x
+    assert e5 == 3
+    assert 3 == e5
+    assert e5 != 4
+    assert 4 != e5
+    assert e5 != 3 + x
+    assert 3 + x != e5
+
+
+def test_expevalbug():
+    x = Symbol("x")
+    e1 = exp(1*x)
+    e3 = exp(x)
+    assert e1 == e3
+
+
+def test_cmp_bug1():
+    class T:
+        pass
+
+    t = T()
+    x = Symbol("x")
+
+    assert not (x == t)
+    assert (x != t)
+
+
+def test_cmp_bug2():
+    class T:
+        pass
+
+    t = T()
+
+    assert not (Symbol == t)
+    assert (Symbol != t)
+
+
+def test_cmp_issue_4357():
+    """ Check that Basic subclasses can be compared with sympifiable objects.
+
+    https://github.com/sympy/sympy/issues/4357
+    """
+    assert not (Symbol == 1)
+    assert (Symbol != 1)
+    assert not (Symbol == 'x')
+    assert (Symbol != 'x')
+
+
+def test_dummy_eq():
+    x = Symbol('x')
+    y = Symbol('y')
+
+    u = Dummy('u')
+
+    assert (u**2 + 1).dummy_eq(x**2 + 1) is True
+    assert ((u**2 + 1) == (x**2 + 1)) is False
+
+    assert (u**2 + y).dummy_eq(x**2 + y, x) is True
+    assert (u**2 + y).dummy_eq(x**2 + y, y) is False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_eval.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_eval.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c1633f77b50483afee21c6d9fca232b1279d2b9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_eval.py
@@ -0,0 +1,95 @@
+from sympy.core.function import Function
+from sympy.core.numbers import (I, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, tan)
+from sympy.testing.pytest import XFAIL
+
+
+def test_add_eval():
+    a = Symbol("a")
+    b = Symbol("b")
+    c = Rational(1)
+    p = Rational(5)
+    assert a*b + c + p == a*b + 6
+    assert c + a + p == a + 6
+    assert c + a - p == a + (-4)
+    assert a + a == 2*a
+    assert a + p + a == 2*a + 5
+    assert c + p == Rational(6)
+    assert b + a - b == a
+
+
+def test_addmul_eval():
+    a = Symbol("a")
+    b = Symbol("b")
+    c = Rational(1)
+    p = Rational(5)
+    assert c + a + b*c + a - p == 2*a + b + (-4)
+    assert a*2 + p + a == a*2 + 5 + a
+    assert a*2 + p + a == 3*a + 5
+    assert a*2 + a == 3*a
+
+
+def test_pow_eval():
+    # XXX Pow does not fully support conversion of negative numbers
+    #     to their complex equivalent
+
+    assert sqrt(-1) == I
+
+    assert sqrt(-4) == 2*I
+    assert sqrt( 4) == 2
+    assert (8)**Rational(1, 3) == 2
+    assert (-8)**Rational(1, 3) == 2*((-1)**Rational(1, 3))
+
+    assert sqrt(-2) == I*sqrt(2)
+    assert (-1)**Rational(1, 3) != I
+    assert (-10)**Rational(1, 3) != I*((10)**Rational(1, 3))
+    assert (-2)**Rational(1, 4) != (2)**Rational(1, 4)
+
+    assert 64**Rational(1, 3) == 4
+    assert 64**Rational(2, 3) == 16
+    assert 24/sqrt(64) == 3
+    assert (-27)**Rational(1, 3) == 3*(-1)**Rational(1, 3)
+
+    assert (cos(2) / tan(2))**2 == (cos(2) / tan(2))**2
+
+
+@XFAIL
+def test_pow_eval_X1():
+    assert (-1)**Rational(1, 3) == S.Half + S.Half*I*sqrt(3)
+
+
+def test_mulpow_eval():
+    x = Symbol('x')
+    assert sqrt(50)/(sqrt(2)*x) == 5/x
+    assert sqrt(27)/sqrt(3) == 3
+
+
+def test_evalpow_bug():
+    x = Symbol("x")
+    assert 1/(1/x) == x
+    assert 1/(-1/x) == -x
+
+
+def test_symbol_expand():
+    x = Symbol('x')
+    y = Symbol('y')
+
+    f = x**4*y**4
+    assert f == x**4*y**4
+    assert f == f.expand()
+
+    g = (x*y)**4
+    assert g == f
+    assert g.expand() == f
+    assert g.expand() == g.expand().expand()
+
+
+def test_function():
+    f, l = map(Function, 'fl')
+    x = Symbol('x')
+    assert exp(l(x))*l(x)/exp(l(x)) == l(x)
+    assert exp(f(x))*f(x)/exp(f(x)) == f(x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_evalf.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_evalf.py
new file mode 100644
index 0000000000000000000000000000000000000000..2c3c26a2d265da9ea2daa73a9eea3091b2af1999
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_evalf.py
@@ -0,0 +1,738 @@
+import math
+
+from sympy.concrete.products import (Product, product)
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.evalf import N
+from sympy.core.function import (Function, nfloat)
+from sympy.core.mul import Mul
+from sympy.core import (GoldenRatio)
+from sympy.core.numbers import (AlgebraicNumber, E, Float, I, Rational,
+                                oo, zoo, nan, pi)
+from sympy.core.power import Pow
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.combinatorial.numbers import fibonacci
+from sympy.functions.elementary.complexes import (Abs, re, im)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (acosh, cosh)
+from sympy.functions.elementary.integers import (ceiling, floor)
+from sympy.functions.elementary.miscellaneous import (Max, sqrt)
+from sympy.functions.elementary.trigonometric import (acos, atan, cos, sin, tan)
+from sympy.integrals.integrals import (Integral, integrate)
+from sympy.polys.polytools import factor
+from sympy.polys.rootoftools import CRootOf
+from sympy.polys.specialpolys import cyclotomic_poly
+from sympy.printing import srepr
+from sympy.printing.str import sstr
+from sympy.simplify.simplify import simplify
+from sympy.core.numbers import comp
+from sympy.core.evalf import (complex_accuracy, PrecisionExhausted,
+                              scaled_zero, get_integer_part, as_mpmath, evalf, _evalf_with_bounded_error)
+from mpmath import inf, ninf, make_mpc
+from mpmath.libmp.libmpf import from_float, fzero
+from sympy.core.expr import unchanged
+from sympy.testing.pytest import raises, XFAIL
+from sympy.abc import n, x, y
+
+
+def NS(e, n=15, **options):
+    return sstr(sympify(e).evalf(n, **options), full_prec=True)
+
+
+def test_evalf_helpers():
+    from mpmath.libmp import finf
+    assert complex_accuracy((from_float(2.0), None, 35, None)) == 35
+    assert complex_accuracy((from_float(2.0), from_float(10.0), 35, 100)) == 37
+    assert complex_accuracy(
+        (from_float(2.0), from_float(1000.0), 35, 100)) == 43
+    assert complex_accuracy((from_float(2.0), from_float(10.0), 100, 35)) == 35
+    assert complex_accuracy(
+        (from_float(2.0), from_float(1000.0), 100, 35)) == 35
+    assert complex_accuracy(finf) == math.inf
+    assert complex_accuracy(zoo) == math.inf
+    raises(ValueError, lambda: get_integer_part(zoo, 1, {}))
+
+
+def test_evalf_basic():
+    assert NS('pi', 15) == '3.14159265358979'
+    assert NS('2/3', 10) == '0.6666666667'
+    assert NS('355/113-pi', 6) == '2.66764e-7'
+    assert NS('16*atan(1/5)-4*atan(1/239)', 15) == '3.14159265358979'
+
+
+def test_cancellation():
+    assert NS(Add(pi, Rational(1, 10**1000), -pi, evaluate=False), 15,
+              maxn=1200) == '1.00000000000000e-1000'
+
+
+def test_evalf_powers():
+    assert NS('pi**(10**20)', 10) == '1.339148777e+49714987269413385435'
+    assert NS(pi**(10**100), 10) == ('4.946362032e+4971498726941338543512682882'
+          '9089887365167832438044244613405349992494711208'
+          '95526746555473864642912223')
+    assert NS('2**(1/10**50)', 15) == '1.00000000000000'
+    assert NS('2**(1/10**50)-1', 15) == '6.93147180559945e-51'
+
+# Evaluation of Rump's ill-conditioned polynomial
+
+
+def test_evalf_rump():
+    a = 1335*y**6/4 + x**2*(11*x**2*y**2 - y**6 - 121*y**4 - 2) + 11*y**8/2 + x/(2*y)
+    assert NS(a, 15, subs={x: 77617, y: 33096}) == '-0.827396059946821'
+
+
+def test_evalf_complex():
+    assert NS('2*sqrt(pi)*I', 10) == '3.544907702*I'
+    assert NS('3+3*I', 15) == '3.00000000000000 + 3.00000000000000*I'
+    assert NS('E+pi*I', 15) == '2.71828182845905 + 3.14159265358979*I'
+    assert NS('pi * (3+4*I)', 15) == '9.42477796076938 + 12.5663706143592*I'
+    assert NS('I*(2+I)', 15) == '-1.00000000000000 + 2.00000000000000*I'
+
+
+@XFAIL
+def test_evalf_complex_bug():
+    assert NS('(pi+E*I)*(E+pi*I)', 15) in ('0.e-15 + 17.25866050002*I',
+              '0.e-17 + 17.25866050002*I', '-0.e-17 + 17.25866050002*I')
+
+
+def test_evalf_complex_powers():
+    assert NS('(E+pi*I)**100000000000000000') == \
+        '-3.58896782867793e+61850354284995199 + 4.58581754997159e+61850354284995199*I'
+    # XXX: rewrite if a+a*I simplification introduced in SymPy
+    #assert NS('(pi + pi*I)**2') in ('0.e-15 + 19.7392088021787*I', '0.e-16 + 19.7392088021787*I')
+    assert NS('(pi + pi*I)**2', chop=True) == '19.7392088021787*I'
+    assert NS(
+        '(pi + 1/10**8 + pi*I)**2') == '6.2831853e-8 + 19.7392088650106*I'
+    assert NS('(pi + 1/10**12 + pi*I)**2') == '6.283e-12 + 19.7392088021850*I'
+    assert NS('(pi + pi*I)**4', chop=True) == '-389.636364136010'
+    assert NS(
+        '(pi + 1/10**8 + pi*I)**4') == '-389.636366616512 + 2.4805021e-6*I'
+    assert NS('(pi + 1/10**12 + pi*I)**4') == '-389.636364136258 + 2.481e-10*I'
+    assert NS(
+        '(10000*pi + 10000*pi*I)**4', chop=True) == '-3.89636364136010e+18'
+
+
+@XFAIL
+def test_evalf_complex_powers_bug():
+    assert NS('(pi + pi*I)**4') == '-389.63636413601 + 0.e-14*I'
+
+
+def test_evalf_exponentiation():
+    assert NS(sqrt(-pi)) == '1.77245385090552*I'
+    assert NS(Pow(pi*I, Rational(
+        1, 2), evaluate=False)) == '1.25331413731550 + 1.25331413731550*I'
+    assert NS(pi**I) == '0.413292116101594 + 0.910598499212615*I'
+    assert NS(pi**(E + I/3)) == '20.8438653991931 + 8.36343473930031*I'
+    assert NS((pi + I/3)**(E + I/3)) == '17.2442906093590 + 13.6839376767037*I'
+    assert NS(exp(pi)) == '23.1406926327793'
+    assert NS(exp(pi + E*I)) == '-21.0981542849657 + 9.50576358282422*I'
+    assert NS(pi**pi) == '36.4621596072079'
+    assert NS((-pi)**pi) == '-32.9138577418939 - 15.6897116534332*I'
+    assert NS((-pi)**(-pi)) == '-0.0247567717232697 + 0.0118013091280262*I'
+
+# An example from Smith, "Multiple Precision Complex Arithmetic and Functions"
+
+
+def test_evalf_complex_cancellation():
+    A = Rational('63287/100000')
+    B = Rational('52498/100000')
+    C = Rational('69301/100000')
+    D = Rational('83542/100000')
+    F = Rational('2231321613/2500000000')
+    # XXX: the number of returned mantissa digits in the real part could
+    # change with the implementation. What matters is that the returned digits are
+    # correct; those that are showing now are correct.
+    # >>> ((A+B*I)*(C+D*I)).expand()
+    # 64471/10000000000 + 2231321613*I/2500000000
+    # >>> 2231321613*4
+    # 8925286452L
+    assert NS((A + B*I)*(C + D*I), 6) == '6.44710e-6 + 0.892529*I'
+    assert NS((A + B*I)*(C + D*I), 10) == '6.447100000e-6 + 0.8925286452*I'
+    assert NS((A + B*I)*(
+        C + D*I) - F*I, 5) in ('6.4471e-6 + 0.e-14*I', '6.4471e-6 - 0.e-14*I')
+
+
+def test_evalf_logs():
+    assert NS("log(3+pi*I)", 15) == '1.46877619736226 + 0.808448792630022*I'
+    assert NS("log(pi*I)", 15) == '1.14472988584940 + 1.57079632679490*I'
+    assert NS('log(-1 + 0.00001)', 2) == '-1.0e-5 + 3.1*I'
+    assert NS('log(100, 10, evaluate=False)', 15) == '2.00000000000000'
+    assert NS('-2*I*log(-(-1)**(S(1)/9))', 15) == '-5.58505360638185'
+
+
+def test_evalf_trig():
+    assert NS('sin(1)', 15) == '0.841470984807897'
+    assert NS('cos(1)', 15) == '0.540302305868140'
+    assert NS('tan(1)', 15) == '1.55740772465490'
+    assert NS('sin(10**-6)', 15) == '9.99999999999833e-7'
+    assert NS('cos(10**-6)', 15) == '0.999999999999500'
+    assert NS('tan(10**-6)', 15) == '1.00000000000033e-6'
+    assert NS('sin(E*10**100)', 15) == '0.409160531722613'
+    assert NS('tan(I)',15) =='0.761594155955765*I'
+    assert NS('tan(1000*I)',15)== '1.00000000000000*I'
+    # Some input near roots
+    assert NS(sin(exp(pi*sqrt(163))*pi), 15) == '-2.35596641936785e-12'
+    assert NS(sin(pi*10**100 + Rational(7, 10**5), evaluate=False), 15, maxn=120) == \
+        '6.99999999428333e-5'
+    assert NS(sin(Rational(7, 10**5), evaluate=False), 15) == \
+        '6.99999999428333e-5'
+
+# Check detection of various false identities
+
+
+def test_evalf_near_integers():
+    # Binet's formula
+    f = lambda n: ((1 + sqrt(5))**n)/(2**n * sqrt(5))
+    assert NS(f(5000) - fibonacci(5000), 10, maxn=1500) == '5.156009964e-1046'
+    # Some near-integer identities from
+    # http://mathworld.wolfram.com/AlmostInteger.html
+    assert NS('sin(2017*2**(1/5))', 15) == '-1.00000000000000'
+    assert NS('sin(2017*2**(1/5))', 20) == '-0.99999999999999997857'
+    assert NS('1+sin(2017*2**(1/5))', 15) == '2.14322287389390e-17'
+    assert NS('45 - 613*E/37 + 35/991', 15) == '6.03764498766326e-11'
+
+
+def test_evalf_ramanujan():
+    assert NS(exp(pi*sqrt(163)) - 640320**3 - 744, 10) == '-7.499274028e-13'
+    # A related identity
+    A = 262537412640768744*exp(-pi*sqrt(163))
+    B = 196884*exp(-2*pi*sqrt(163))
+    C = 103378831900730205293632*exp(-3*pi*sqrt(163))
+    assert NS(1 - A - B + C, 10) == '1.613679005e-59'
+
+# Input that for various reasons have failed at some point
+
+
+def test_evalf_bugs():
+    assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10)
+    assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10)
+    assert NS('expand_log(log(1+1/10**50))', 20) == '1.0000000000000000000e-50'
+    assert NS('log(10**100,10)', 10) == '100.0000000'
+    assert NS('log(2)', 10) == '0.6931471806'
+    assert NS(
+        '(sin(x)-x)/x**3', 15, subs={x: '1/10**50'}) == '-0.166666666666667'
+    assert NS(sin(1) + Rational(
+        1, 10**100)*I, 15) == '0.841470984807897 + 1.00000000000000e-100*I'
+    assert x.evalf() == x
+    assert NS((1 + I)**2*I, 6) == '-2.00000'
+    d = {n: (
+        -1)**Rational(6, 7), y: (-1)**Rational(4, 7), x: (-1)**Rational(2, 7)}
+    assert NS((x*(1 + y*(1 + n))).subs(d).evalf(), 6) == '0.346011 + 0.433884*I'
+    assert NS(((-I - sqrt(2)*I)**2).evalf()) == '-5.82842712474619'
+    assert NS((1 + I)**2*I, 15) == '-2.00000000000000'
+    # issue 4758 (1/2):
+    assert NS(pi.evalf(69) - pi) == '-4.43863937855894e-71'
+    # issue 4758 (2/2): With the bug present, this still only fails if the
+    # terms are in the order given here. This is not generally the case,
+    # because the order depends on the hashes of the terms.
+    assert NS(20 - 5008329267844*n**25 - 477638700*n**37 - 19*n,
+              subs={n: .01}) == '19.8100000000000'
+    assert NS(((x - 1)*(1 - x)**1000).n()
+              ) == '(1.00000000000000 - x)**1000*(x - 1.00000000000000)'
+    assert NS((-x).n()) == '-x'
+    assert NS((-2*x).n()) == '-2.00000000000000*x'
+    assert NS((-2*x*y).n()) == '-2.00000000000000*x*y'
+    assert cos(x).n(subs={x: 1+I}) == cos(x).subs(x, 1+I).n()
+    # issue 6660. Also NaN != mpmath.nan
+    # In this order:
+    # 0*nan, 0/nan, 0*inf, 0/inf
+    # 0+nan, 0-nan, 0+inf, 0-inf
+    # >>> n = Some Number
+    # n*nan, n/nan, n*inf, n/inf
+    # n+nan, n-nan, n+inf, n-inf
+    assert (0*E**(oo)).n() is S.NaN
+    assert (0/E**(oo)).n() is S.Zero
+
+    assert (0+E**(oo)).n() is S.Infinity
+    assert (0-E**(oo)).n() is S.NegativeInfinity
+
+    assert (5*E**(oo)).n() is S.Infinity
+    assert (5/E**(oo)).n() is S.Zero
+
+    assert (5+E**(oo)).n() is S.Infinity
+    assert (5-E**(oo)).n() is S.NegativeInfinity
+
+    #issue 7416
+    assert as_mpmath(0.0, 10, {'chop': True}) == 0
+
+    #issue 5412
+    assert ((oo*I).n() == S.Infinity*I)
+    assert ((oo+oo*I).n() == S.Infinity + S.Infinity*I)
+
+    #issue 11518
+    assert NS(2*x**2.5, 5) == '2.0000*x**2.5000'
+
+    #issue 13076
+    assert NS(Mul(Max(0, y), x, evaluate=False).evalf()) == 'x*Max(0, y)'
+
+    #issue 18516
+    assert NS(log(S(3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376)/36360291795869936842385267079543319118023385026001623040346035832580600191583895484198508262979388783308179702534403855752855931517013066142992430916562025780021771247847643450125342836565813209972590371590152578728008385990139795377610001).evalf(15, chop=True)) == '-oo'
+
+
+def test_evalf_integer_parts():
+    a = floor(log(8)/log(2) - exp(-1000), evaluate=False)
+    b = floor(log(8)/log(2), evaluate=False)
+    assert a.evalf() == 3.0
+    assert b.evalf() == 3.0
+    # equals, as a fallback, can still fail but it might succeed as here
+    assert ceiling(10*(sin(1)**2 + cos(1)**2)) == 10
+
+    assert int(floor(factorial(50)/E, evaluate=False).evalf(70)) == \
+        int(11188719610782480504630258070757734324011354208865721592720336800)
+    assert int(ceiling(factorial(50)/E, evaluate=False).evalf(70)) == \
+        int(11188719610782480504630258070757734324011354208865721592720336801)
+    assert int(floor(GoldenRatio**999 / sqrt(5) + S.Half)
+               .evalf(1000)) == fibonacci(999)
+    assert int(floor(GoldenRatio**1000 / sqrt(5) + S.Half)
+               .evalf(1000)) == fibonacci(1000)
+
+    assert ceiling(x).evalf(subs={x: 3}) == 3.0
+    assert ceiling(x).evalf(subs={x: 3*I}) == 3.0*I
+    assert ceiling(x).evalf(subs={x: 2 + 3*I}) == 2.0 + 3.0*I
+    assert ceiling(x).evalf(subs={x: 3.}) == 3.0
+    assert ceiling(x).evalf(subs={x: 3.*I}) == 3.0*I
+    assert ceiling(x).evalf(subs={x: 2. + 3*I}) == 2.0 + 3.0*I
+
+    assert float((floor(1.5, evaluate=False)+1/9).evalf()) == 1 + 1/9
+    assert float((floor(0.5, evaluate=False)+20).evalf()) == 20
+
+    # issue 19991
+    n = 1169809367327212570704813632106852886389036911
+    r = 744723773141314414542111064094745678855643068
+
+    assert floor(n / (pi / 2)) == r
+    assert floor(80782 * sqrt(2)) == 114242
+
+    # issue 20076
+    assert 260515 - floor(260515/pi + 1/2) * pi == atan(tan(260515))
+
+    assert floor(x).evalf(subs={x: sqrt(2)}) == 1.0
+
+
+def test_evalf_trig_zero_detection():
+    a = sin(160*pi, evaluate=False)
+    t = a.evalf(maxn=100)
+    assert abs(t) < 1e-100
+    assert t._prec < 2
+    assert a.evalf(chop=True) == 0
+    raises(PrecisionExhausted, lambda: a.evalf(strict=True))
+
+
+def test_evalf_sum():
+    assert Sum(n,(n,1,2)).evalf() == 3.
+    assert Sum(n,(n,1,2)).doit().evalf() == 3.
+    # the next test should return instantly
+    assert Sum(1/n,(n,1,2)).evalf() == 1.5
+
+    # issue 8219
+    assert Sum(E/factorial(n), (n, 0, oo)).evalf() == (E*E).evalf()
+    # issue 8254
+    assert Sum(2**n*n/factorial(n), (n, 0, oo)).evalf() == (2*E*E).evalf()
+    # issue 8411
+    s = Sum(1/x**2, (x, 100, oo))
+    assert s.n() == s.doit().n()
+
+
+def test_evalf_divergent_series():
+    raises(ValueError, lambda: Sum(1/n, (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum(n/(n**2 + 1), (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum((-1)**n, (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum((-1)**n, (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum(n**2, (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum(2**n, (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum((-2)**n, (n, 1, oo)).evalf())
+    raises(ValueError, lambda: Sum((2*n + 3)/(3*n**2 + 4), (n, 0, oo)).evalf())
+    raises(ValueError, lambda: Sum((0.5*n**3)/(n**4 + 1), (n, 0, oo)).evalf())
+
+
+def test_evalf_product():
+    assert Product(n, (n, 1, 10)).evalf() == 3628800.
+    assert comp(Product(1 - S.Half**2/n**2, (n, 1, oo)).n(5), 0.63662)
+    assert Product(n, (n, -1, 3)).evalf() == 0
+
+
+def test_evalf_py_methods():
+    assert abs(float(pi + 1) - 4.1415926535897932) < 1e-10
+    assert abs(complex(pi + 1) - 4.1415926535897932) < 1e-10
+    assert abs(
+        complex(pi + E*I) - (3.1415926535897931 + 2.7182818284590451j)) < 1e-10
+    raises(TypeError, lambda: float(pi + x))
+
+
+def test_evalf_power_subs_bugs():
+    assert (x**2).evalf(subs={x: 0}) == 0
+    assert sqrt(x).evalf(subs={x: 0}) == 0
+    assert (x**Rational(2, 3)).evalf(subs={x: 0}) == 0
+    assert (x**x).evalf(subs={x: 0}) == 1.0
+    assert (3**x).evalf(subs={x: 0}) == 1.0
+    assert exp(x).evalf(subs={x: 0}) == 1.0
+    assert ((2 + I)**x).evalf(subs={x: 0}) == 1.0
+    assert (0**x).evalf(subs={x: 0}) == 1.0
+
+
+def test_evalf_arguments():
+    raises(TypeError, lambda: pi.evalf(method="garbage"))
+
+
+def test_implemented_function_evalf():
+    from sympy.utilities.lambdify import implemented_function
+    f = Function('f')
+    f = implemented_function(f, lambda x: x + 1)
+    assert str(f(x)) == "f(x)"
+    assert str(f(2)) == "f(2)"
+    assert f(2).evalf() == 3.0
+    assert f(x).evalf() == f(x)
+    f = implemented_function(Function('sin'), lambda x: x + 1)
+    assert f(2).evalf() != sin(2)
+    del f._imp_     # XXX: due to caching _imp_ would influence all other tests
+
+
+def test_evaluate_false():
+    for no in [0, False]:
+        assert Add(3, 2, evaluate=no).is_Add
+        assert Mul(3, 2, evaluate=no).is_Mul
+        assert Pow(3, 2, evaluate=no).is_Pow
+    assert Pow(y, 2, evaluate=True) - Pow(y, 2, evaluate=True) == 0
+
+
+def test_evalf_relational():
+    assert Eq(x/5, y/10).evalf() == Eq(0.2*x, 0.1*y)
+    # if this first assertion fails it should be replaced with
+    # one that doesn't
+    assert unchanged(Eq, (3 - I)**2/2 + I, 0)
+    assert Eq((3 - I)**2/2 + I, 0).n() is S.false
+    assert nfloat(Eq((3 - I)**2 + I, 0)) == S.false
+
+
+def test_issue_5486():
+    assert not cos(sqrt(0.5 + I)).n().is_Function
+
+
+def test_issue_5486_bug():
+    from sympy.core.expr import Expr
+    from sympy.core.numbers import I
+    assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15
+
+
+def test_bugs():
+    from sympy.functions.elementary.complexes import (polar_lift, re)
+
+    assert abs(re((1 + I)**2)) < 1e-15
+
+    # anything that evalf's to 0 will do in place of polar_lift
+    assert abs(polar_lift(0)).n() == 0
+
+
+def test_subs():
+    assert NS('besseli(-x, y) - besseli(x, y)', subs={x: 3.5, y: 20.0}) == \
+        '-4.92535585957223e-10'
+    assert NS('Piecewise((x, x>0)) + Piecewise((1-x, x>0))', subs={x: 0.1}) == \
+        '1.00000000000000'
+    raises(TypeError, lambda: x.evalf(subs=(x, 1)))
+
+
+def test_issue_4956_5204():
+    # issue 4956
+    v = S('''(-27*12**(1/3)*sqrt(31)*I +
+    27*2**(2/3)*3**(1/3)*sqrt(31)*I)/(-2511*2**(2/3)*3**(1/3) +
+    (29*18**(1/3) + 9*2**(1/3)*3**(2/3)*sqrt(31)*I +
+    87*2**(1/3)*3**(1/6)*I)**2)''')
+    assert NS(v, 1) == '0.e-118 - 0.e-118*I'
+
+    # issue 5204
+    v = S('''-(357587765856 + 18873261792*249**(1/2) + 56619785376*I*83**(1/2) +
+    108755765856*I*3**(1/2) + 41281887168*6**(1/3)*(1422 +
+    54*249**(1/2))**(1/3) - 1239810624*6**(1/3)*249**(1/2)*(1422 +
+    54*249**(1/2))**(1/3) - 3110400000*I*6**(1/3)*83**(1/2)*(1422 +
+    54*249**(1/2))**(1/3) + 13478400000*I*3**(1/2)*6**(1/3)*(1422 +
+    54*249**(1/2))**(1/3) + 1274950152*6**(2/3)*(1422 +
+    54*249**(1/2))**(2/3) + 32347944*6**(2/3)*249**(1/2)*(1422 +
+    54*249**(1/2))**(2/3) - 1758790152*I*3**(1/2)*6**(2/3)*(1422 +
+    54*249**(1/2))**(2/3) - 304403832*I*6**(2/3)*83**(1/2)*(1422 +
+    4*249**(1/2))**(2/3))/(175732658352 + (1106028 + 25596*249**(1/2) +
+    76788*I*83**(1/2))**2)''')
+    assert NS(v, 5) == '0.077284 + 1.1104*I'
+    assert NS(v, 1) == '0.08 + 1.*I'
+
+
+def test_old_docstring():
+    a = (E + pi*I)*(E - pi*I)
+    assert NS(a) == '17.2586605000200'
+    assert a.n() == 17.25866050002001
+
+
+def test_issue_4806():
+    assert integrate(atan(x)**2, (x, -1, 1)).evalf().round(1) == Float(0.5, 1)
+    assert atan(0, evaluate=False).n() == 0
+
+
+def test_evalf_mul():
+    # SymPy should not try to expand this; it should be handled term-wise
+    # in evalf through mpmath
+    assert NS(product(1 + sqrt(n)*I, (n, 1, 500)), 1) == '5.e+567 + 2.e+568*I'
+
+
+def test_scaled_zero():
+    a, b = (([0], 1, 100, 1), -1)
+    assert scaled_zero(100) == (a, b)
+    assert scaled_zero(a) == (0, 1, 100, 1)
+    a, b = (([1], 1, 100, 1), -1)
+    assert scaled_zero(100, -1) == (a, b)
+    assert scaled_zero(a) == (1, 1, 100, 1)
+    raises(ValueError, lambda: scaled_zero(scaled_zero(100)))
+    raises(ValueError, lambda: scaled_zero(100, 2))
+    raises(ValueError, lambda: scaled_zero(100, 0))
+    raises(ValueError, lambda: scaled_zero((1, 5, 1, 3)))
+
+
+def test_chop_value():
+    for i in range(-27, 28):
+        assert (Pow(10, i)*2).n(chop=10**i) and not (Pow(10, i)).n(chop=10**i)
+
+
+def test_infinities():
+    assert oo.evalf(chop=True) == inf
+    assert (-oo).evalf(chop=True) == ninf
+
+
+def test_to_mpmath():
+    assert sqrt(3)._to_mpmath(20)._mpf_ == (0, int(908093), -19, 20)
+    assert S(3.2)._to_mpmath(20)._mpf_ == (0, int(838861), -18, 20)
+
+
+def test_issue_6632_evalf():
+    add = (-100000*sqrt(2500000001) + 5000000001)
+    assert add.n() == 9.999999998e-11
+    assert (add*add).n() == 9.999999996e-21
+
+
+def test_issue_4945():
+    from sympy.abc import H
+    assert (H/0).evalf(subs={H:1}) == zoo
+
+
+def test_evalf_integral():
+    # test that workprec has to increase in order to get a result other than 0
+    eps = Rational(1, 1000000)
+    assert Integral(sin(x), (x, -pi, pi + eps)).n(2)._prec == 10
+
+
+def test_issue_8821_highprec_from_str():
+    s = str(pi.evalf(128))
+    p = N(s)
+    assert Abs(sin(p)) < 1e-15
+    p = N(s, 64)
+    assert Abs(sin(p)) < 1e-64
+
+
+def test_issue_8853():
+    p = Symbol('x', even=True, positive=True)
+    assert floor(-p - S.Half).is_even == False
+    assert floor(-p + S.Half).is_even == True
+    assert ceiling(p - S.Half).is_even == True
+    assert ceiling(p + S.Half).is_even == False
+
+    assert get_integer_part(S.Half, -1, {}, True) == (0, 0)
+    assert get_integer_part(S.Half, 1, {}, True) == (1, 0)
+    assert get_integer_part(Rational(-1, 2), -1, {}, True) == (-1, 0)
+    assert get_integer_part(Rational(-1, 2), 1, {}, True) == (0, 0)
+
+
+def test_issue_17681():
+    class identity_func(Function):
+
+        def _eval_evalf(self, *args, **kwargs):
+            return self.args[0].evalf(*args, **kwargs)
+
+    assert floor(identity_func(S(0))) == 0
+    assert get_integer_part(S(0), 1, {}, True) == (0, 0)
+
+
+def test_issue_9326():
+    from sympy.core.symbol import Dummy
+    d1 = Dummy('d')
+    d2 = Dummy('d')
+    e = d1 + d2
+    assert e.evalf(subs = {d1: 1, d2: 2}) == 3.0
+
+
+def test_issue_10323():
+    assert ceiling(sqrt(2**30 + 1)) == 2**15 + 1
+
+
+def test_AssocOp_Function():
+    # the first arg of Min is not comparable in the imaginary part
+    raises(ValueError, lambda: S('''
+    Min(-sqrt(3)*cos(pi/18)/6 + re(1/((-1/2 - sqrt(3)*I/2)*(1/6 +
+    sqrt(3)*I/18)**(1/3)))/3 + sin(pi/18)/2 + 2 + I*(-cos(pi/18)/2 -
+    sqrt(3)*sin(pi/18)/6 + im(1/((-1/2 - sqrt(3)*I/2)*(1/6 +
+    sqrt(3)*I/18)**(1/3)))/3), re(1/((-1/2 + sqrt(3)*I/2)*(1/6 +
+    sqrt(3)*I/18)**(1/3)))/3 - sqrt(3)*cos(pi/18)/6 - sin(pi/18)/2 + 2 +
+    I*(im(1/((-1/2 + sqrt(3)*I/2)*(1/6 + sqrt(3)*I/18)**(1/3)))/3 -
+    sqrt(3)*sin(pi/18)/6 + cos(pi/18)/2))'''))
+    # if that is changed so a non-comparable number remains as
+    # an arg, then the Min/Max instantiation needs to be changed
+    # to watch out for non-comparable args when making simplifications
+    # and the following test should be added instead (with e being
+    # the sympified expression above):
+    # raises(ValueError, lambda: e._eval_evalf(2))
+
+
+def test_issue_10395():
+    eq = x*Max(0, y)
+    assert nfloat(eq) == eq
+    eq = x*Max(y, -1.1)
+    assert nfloat(eq) == eq
+    assert Max(y, 4).n() == Max(4.0, y)
+
+
+def test_issue_13098():
+    assert floor(log(S('9.'+'9'*20), 10)) == 0
+    assert ceiling(log(S('9.'+'9'*20), 10)) == 1
+    assert floor(log(20 - S('9.'+'9'*20), 10)) == 1
+    assert ceiling(log(20 - S('9.'+'9'*20), 10)) == 2
+
+
+def test_issue_14601():
+    e = 5*x*y/2 - y*(35*(x**3)/2 - 15*x/2)
+    subst = {x:0.0, y:0.0}
+    e2 = e.evalf(subs=subst)
+    assert float(e2) == 0.0
+    assert float((x + x*(x**2 + x)).evalf(subs={x: 0.0})) == 0.0
+
+
+def test_issue_11151():
+    z = S.Zero
+    e = Sum(z, (x, 1, 2))
+    assert e != z  # it shouldn't evaluate
+    # when it does evaluate, this is what it should give
+    assert evalf(e, 15, {}) == \
+        evalf(z, 15, {}) == (None, None, 15, None)
+    # so this shouldn't fail
+    assert (e/2).n() == 0
+    # this was where the issue appeared
+    expr0 = Sum(x**2 + x, (x, 1, 2))
+    expr1 = Sum(0, (x, 1, 2))
+    expr2 = expr1/expr0
+    assert simplify(factor(expr2) - expr2) == 0
+
+
+def test_issue_13425():
+    assert N('2**.5', 30) == N('sqrt(2)', 30)
+    assert N('x - x', 30) == 0
+    assert abs((N('pi*.1', 22)*10 - pi).n()) < 1e-22
+
+
+def test_issue_17421():
+    assert N(acos(-I + acosh(cosh(cosh(1) + I)))) == 1.0*I
+
+
+def test_issue_20291():
+    from sympy.sets import EmptySet, Reals
+    from sympy.sets.sets import (Complement, FiniteSet, Intersection)
+    a = Symbol('a')
+    b = Symbol('b')
+    A = FiniteSet(a, b)
+    assert A.evalf(subs={a: 1, b: 2}) == FiniteSet(1.0, 2.0)
+    B = FiniteSet(a-b, 1)
+    assert B.evalf(subs={a: 1, b: 2}) == FiniteSet(-1.0, 1.0)
+
+    sol = Complement(Intersection(FiniteSet(-b/2 - sqrt(b**2-4*pi)/2), Reals), FiniteSet(0))
+    assert sol.evalf(subs={b: 1}) == EmptySet
+
+
+def test_evalf_with_zoo():
+    assert (1/x).evalf(subs={x: 0}) == zoo  # issue 8242
+    assert (-1/x).evalf(subs={x: 0}) == zoo  # PR 16150
+    assert (0 ** x).evalf(subs={x: -1}) == zoo  # PR 16150
+    assert (0 ** x).evalf(subs={x: -1 + I}) == nan
+    assert Mul(2, Pow(0, -1, evaluate=False), evaluate=False).evalf() == zoo  # issue 21147
+    assert Mul(x, 1/x, evaluate=False).evalf(subs={x: 0}) == Mul(x, 1/x, evaluate=False).subs(x, 0) == nan
+    assert Mul(1/x, 1/x, evaluate=False).evalf(subs={x: 0}) == zoo
+    assert Mul(1/x, Abs(1/x), evaluate=False).evalf(subs={x: 0}) == zoo
+    assert Abs(zoo, evaluate=False).evalf() == oo
+    assert re(zoo, evaluate=False).evalf() == nan
+    assert im(zoo, evaluate=False).evalf() == nan
+    assert Add(zoo, zoo, evaluate=False).evalf() == nan
+    assert Add(oo, zoo, evaluate=False).evalf() == nan
+    assert Pow(zoo, -1, evaluate=False).evalf() == 0
+    assert Pow(zoo, Rational(-1, 3), evaluate=False).evalf() == 0
+    assert Pow(zoo, Rational(1, 3), evaluate=False).evalf() == zoo
+    assert Pow(zoo, S.Half, evaluate=False).evalf() == zoo
+    assert Pow(zoo, 2, evaluate=False).evalf() == zoo
+    assert Pow(0, zoo, evaluate=False).evalf() == nan
+    assert log(zoo, evaluate=False).evalf() == zoo
+    assert zoo.evalf(chop=True) == zoo
+    assert x.evalf(subs={x: zoo}) == zoo
+
+
+def test_evalf_with_bounded_error():
+    cases = [
+        # zero
+        (Rational(0), None, 1),
+        # zero im part
+        (pi, None, 10),
+        # zero real part
+        (pi*I, None, 10),
+        # re and im nonzero
+        (2-3*I, None, 5),
+        # similar tests again, but using eps instead of m
+        (Rational(0), Rational(1, 2), None),
+        (pi, Rational(1, 1000), None),
+        (pi * I, Rational(1, 1000), None),
+        (2 - 3 * I, Rational(1, 1000), None),
+        # very large eps
+        (2 - 3 * I, Rational(1000), None),
+        # case where x already small, hence some cancellation in p = m + n - 1
+        (Rational(1234, 10**8), Rational(1, 10**12), None),
+    ]
+    for x0, eps, m in cases:
+        a, b, _, _ = evalf(x0, 53, {})
+        c, d, _, _ = _evalf_with_bounded_error(x0, eps, m)
+        if eps is None:
+            eps = 2**(-m)
+        z = make_mpc((a or fzero, b or fzero))
+        w = make_mpc((c or fzero, d or fzero))
+        assert abs(w - z) < eps
+
+    # eps must be positive
+    raises(ValueError, lambda: _evalf_with_bounded_error(pi, Rational(0)))
+    raises(ValueError, lambda: _evalf_with_bounded_error(pi, -pi))
+    raises(ValueError, lambda: _evalf_with_bounded_error(pi, I))
+
+
+def test_issue_22849():
+    a = -8 + 3 * sqrt(3)
+    x = AlgebraicNumber(a)
+    assert evalf(a, 1, {}) == evalf(x, 1, {})
+
+
+def test_evalf_real_alg_num():
+    # This test demonstrates why the entry for `AlgebraicNumber` in
+    # `sympy.core.evalf._create_evalf_table()` has to use `x.to_root()`,
+    # instead of `x.as_expr()`. If the latter is used, then `z` will be
+    # a complex number with `0.e-20` for imaginary part, even though `a5`
+    # is a real number.
+    zeta = Symbol('zeta')
+    a5 = AlgebraicNumber(CRootOf(cyclotomic_poly(5), -1), [-1, -1, 0, 0], alias=zeta)
+    z = a5.evalf()
+    assert isinstance(z, Float)
+    assert not hasattr(z, '_mpc_')
+    assert hasattr(z, '_mpf_')
+
+
+def test_issue_20733():
+    expr = 1/((x - 9)*(x - 8)*(x - 7)*(x - 4)**2*(x - 3)**3*(x - 2))
+    assert str(expr.evalf(1, subs={x:1})) == '-4.e-5'
+    assert str(expr.evalf(2, subs={x:1})) == '-4.1e-5'
+    assert str(expr.evalf(11, subs={x:1})) == '-4.1335978836e-5'
+    assert str(expr.evalf(20, subs={x:1})) == '-0.000041335978835978835979'
+
+    expr = Mul(*((x - i) for i in range(2, 1000)))
+    assert srepr(expr.evalf(2, subs={x: 1})) == "Float('4.0271e+2561', precision=10)"
+    assert srepr(expr.evalf(10, subs={x: 1})) == "Float('4.02790050126e+2561', precision=37)"
+    assert srepr(expr.evalf(53, subs={x: 1})) == "Float('4.0279005012722099453824067459760158730668154575647110393e+2561', precision=179)"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_expand.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_expand.py
new file mode 100644
index 0000000000000000000000000000000000000000..e7abb5daacebbe81664b3de3a7ac35a490ab31bc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_expand.py
@@ -0,0 +1,364 @@
+from sympy.core.expr import unchanged
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Rational as R, pi)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.series.order import O
+from sympy.simplify.radsimp import expand_numer
+from sympy.core.function import (expand, expand_multinomial,
+    expand_power_base, expand_log)
+
+from sympy.testing.pytest import raises
+from sympy.core.random import verify_numerically
+
+from sympy.abc import x, y, z
+
+
+def test_expand_no_log():
+    assert (
+        (1 + log(x**4))**2).expand(log=False) == 1 + 2*log(x**4) + log(x**4)**2
+    assert ((1 + log(x**4))*(1 + log(x**3))).expand(
+        log=False) == 1 + log(x**4) + log(x**3) + log(x**4)*log(x**3)
+
+
+def test_expand_no_multinomial():
+    assert ((1 + x)*(1 + (1 + x)**4)).expand(multinomial=False) == \
+        1 + x + (1 + x)**4 + x*(1 + x)**4
+
+
+def test_expand_negative_integer_powers():
+    expr = (x + y)**(-2)
+    assert expr.expand() == 1 / (2*x*y + x**2 + y**2)
+    assert expr.expand(multinomial=False) == (x + y)**(-2)
+    expr = (x + y)**(-3)
+    assert expr.expand() == 1 / (3*x*x*y + 3*x*y*y + x**3 + y**3)
+    assert expr.expand(multinomial=False) == (x + y)**(-3)
+    expr = (x + y)**(2) * (x + y)**(-4)
+    assert expr.expand() == 1 / (2*x*y + x**2 + y**2)
+    assert expr.expand(multinomial=False) == (x + y)**(-2)
+
+
+def test_expand_non_commutative():
+    A = Symbol('A', commutative=False)
+    B = Symbol('B', commutative=False)
+    C = Symbol('C', commutative=False)
+    a = Symbol('a')
+    b = Symbol('b')
+    i = Symbol('i', integer=True)
+    n = Symbol('n', negative=True)
+    m = Symbol('m', negative=True)
+    p = Symbol('p', polar=True)
+    np = Symbol('p', polar=False)
+
+    assert (C*(A + B)).expand() == C*A + C*B
+    assert (C*(A + B)).expand() != A*C + B*C
+    assert ((A + B)**2).expand() == A**2 + A*B + B*A + B**2
+    assert ((A + B)**3).expand() == (A**2*B + B**2*A + A*B**2 + B*A**2 +
+                                     A**3 + B**3 + A*B*A + B*A*B)
+    # issue 6219
+    assert ((a*A*B*A**-1)**2).expand() == a**2*A*B**2/A
+    # Note that (a*A*B*A**-1)**2 is automatically converted to a**2*(A*B*A**-1)**2
+    assert ((a*A*B*A**-1)**2).expand(deep=False) == a**2*(A*B*A**-1)**2
+    assert ((a*A*B*A**-1)**2).expand() == a**2*(A*B**2*A**-1)
+    assert ((a*A*B*A**-1)**2).expand(force=True) == a**2*A*B**2*A**(-1)
+    assert ((a*A*B)**2).expand() == a**2*A*B*A*B
+    assert ((a*A)**2).expand() == a**2*A**2
+    assert ((a*A*B)**i).expand() == a**i*(A*B)**i
+    assert ((a*A*(B*(A*B/A)**2))**i).expand() == a**i*(A*B*A*B**2/A)**i
+    # issue 6558
+    assert (A*B*(A*B)**-1).expand() == 1
+    assert ((a*A)**i).expand() == a**i*A**i
+    assert ((a*A*B*A**-1)**3).expand() == a**3*A*B**3/A
+    assert ((a*A*B*A*B/A)**3).expand() == \
+        a**3*A*B*(A*B**2)*(A*B**2)*A*B*A**(-1)
+    assert ((a*A*B*A*B/A)**-2).expand() == \
+        A*B**-1*A**-1*B**-2*A**-1*B**-1*A**-1/a**2
+    assert ((a*b*A*B*A**-1)**i).expand() == a**i*b**i*(A*B/A)**i
+    assert ((a*(a*b)**i)**i).expand() == a**i*a**(i**2)*b**(i**2)
+    e = Pow(Mul(a, 1/a, A, B, evaluate=False), S(2), evaluate=False)
+    assert e.expand() == A*B*A*B
+    assert sqrt(a*(A*b)**i).expand() == sqrt(a*b**i*A**i)
+    assert (sqrt(-a)**a).expand() == sqrt(-a)**a
+    assert expand((-2*n)**(i/3)) == 2**(i/3)*(-n)**(i/3)
+    assert expand((-2*n*m)**(i/a)) == (-2)**(i/a)*(-n)**(i/a)*(-m)**(i/a)
+    assert expand((-2*a*p)**b) == 2**b*p**b*(-a)**b
+    assert expand((-2*a*np)**b) == 2**b*(-a*np)**b
+    assert expand(sqrt(A*B)) == sqrt(A*B)
+    assert expand(sqrt(-2*a*b)) == sqrt(2)*sqrt(-a*b)
+
+
+def test_expand_radicals():
+    a = (x + y)**R(1, 2)
+
+    assert (a**1).expand() == a
+    assert (a**3).expand() == x*a + y*a
+    assert (a**5).expand() == x**2*a + 2*x*y*a + y**2*a
+
+    assert (1/a**1).expand() == 1/a
+    assert (1/a**3).expand() == 1/(x*a + y*a)
+    assert (1/a**5).expand() == 1/(x**2*a + 2*x*y*a + y**2*a)
+
+    a = (x + y)**R(1, 3)
+
+    assert (a**1).expand() == a
+    assert (a**2).expand() == a**2
+    assert (a**4).expand() == x*a + y*a
+    assert (a**5).expand() == x*a**2 + y*a**2
+    assert (a**7).expand() == x**2*a + 2*x*y*a + y**2*a
+
+
+def test_expand_modulus():
+    assert ((x + y)**11).expand(modulus=11) == x**11 + y**11
+    assert ((x + sqrt(2)*y)**11).expand(modulus=11) == x**11 + 10*sqrt(2)*y**11
+    assert (x + y/2).expand(modulus=1) == y/2
+
+    raises(ValueError, lambda: ((x + y)**11).expand(modulus=0))
+    raises(ValueError, lambda: ((x + y)**11).expand(modulus=x))
+
+
+def test_issue_5743():
+    assert (x*sqrt(
+        x + y)*(1 + sqrt(x + y))).expand() == x**2 + x*y + x*sqrt(x + y)
+    assert (x*sqrt(
+        x + y)*(1 + x*sqrt(x + y))).expand() == x**3 + x**2*y + x*sqrt(x + y)
+
+
+def test_expand_frac():
+    assert expand((x + y)*y/x/(x + 1), frac=True) == \
+        (x*y + y**2)/(x**2 + x)
+    assert expand((x + y)*y/x/(x + 1), numer=True) == \
+        (x*y + y**2)/(x*(x + 1))
+    assert expand((x + y)*y/x/(x + 1), denom=True) == \
+        y*(x + y)/(x**2 + x)
+    eq = (x + 1)**2/y
+    assert expand_numer(eq, multinomial=False) == eq
+    # issue 26329
+    eq = (exp(x*z) - exp(y*z))/exp(z*(x + y))
+    ans = exp(-y*z) - exp(-x*z)
+    assert eq.expand(numer=True) != ans
+    assert eq.expand(numer=True, exact=True) == ans
+    assert expand_numer(eq) != ans
+    assert expand_numer(eq, exact=True) == ans
+
+
+def test_issue_6121():
+    eq = -I*exp(-3*I*pi/4)/(4*pi**(S(3)/2)*sqrt(x))
+    assert eq.expand(complex=True)  # does not give oo recursion
+    eq = -I*exp(-3*I*pi/4)/(4*pi**(R(3, 2))*sqrt(x))
+    assert eq.expand(complex=True)  # does not give oo recursion
+
+
+def test_expand_power_base():
+    assert expand_power_base((x*y*z)**4) == x**4*y**4*z**4
+    assert expand_power_base((x*y*z)**x).is_Pow
+    assert expand_power_base((x*y*z)**x, force=True) == x**x*y**x*z**x
+    assert expand_power_base((x*(y*z)**2)**3) == x**3*y**6*z**6
+
+    assert expand_power_base((sin((x*y)**2)*y)**z).is_Pow
+    assert expand_power_base(
+        (sin((x*y)**2)*y)**z, force=True) == sin((x*y)**2)**z*y**z
+    assert expand_power_base(
+        (sin((x*y)**2)*y)**z, deep=True) == (sin(x**2*y**2)*y)**z
+
+    assert expand_power_base(exp(x)**2) == exp(2*x)
+    assert expand_power_base((exp(x)*exp(y))**2) == exp(2*x)*exp(2*y)
+
+    assert expand_power_base(
+        (exp((x*y)**z)*exp(y))**2) == exp(2*(x*y)**z)*exp(2*y)
+    assert expand_power_base((exp((x*y)**z)*exp(
+        y))**2, deep=True, force=True) == exp(2*x**z*y**z)*exp(2*y)
+
+    assert expand_power_base((exp(x)*exp(y))**z).is_Pow
+    assert expand_power_base(
+        (exp(x)*exp(y))**z, force=True) == exp(x)**z*exp(y)**z
+
+
+def test_expand_arit():
+    a = Symbol("a")
+    b = Symbol("b", positive=True)
+    c = Symbol("c")
+
+    p = R(5)
+    e = (a + b)*c
+    assert e == c*(a + b)
+    assert (e.expand() - a*c - b*c) == R(0)
+    e = (a + b)*(a + b)
+    assert e == (a + b)**2
+    assert e.expand() == 2*a*b + a**2 + b**2
+    e = (a + b)*(a + b)**R(2)
+    assert e == (a + b)**3
+    assert e.expand() == 3*b*a**2 + 3*a*b**2 + a**3 + b**3
+    assert e.expand() == 3*b*a**2 + 3*a*b**2 + a**3 + b**3
+    e = (a + b)*(a + c)*(b + c)
+    assert e == (a + c)*(a + b)*(b + c)
+    assert e.expand() == 2*a*b*c + b*a**2 + c*a**2 + b*c**2 + a*c**2 + c*b**2 + a*b**2
+    e = (a + R(1))**p
+    assert e == (1 + a)**5
+    assert e.expand() == 1 + 5*a + 10*a**2 + 10*a**3 + 5*a**4 + a**5
+    e = (a + b + c)*(a + c + p)
+    assert e == (5 + a + c)*(a + b + c)
+    assert e.expand() == 5*a + 5*b + 5*c + 2*a*c + b*c + a*b + a**2 + c**2
+    x = Symbol("x")
+    s = exp(x*x) - 1
+    e = s.nseries(x, 0, 6)/x**2
+    assert e.expand() == 1 + x**2/2 + O(x**4)
+
+    e = (x*(y + z))**(x*(y + z))*(x + y)
+    assert e.expand(power_exp=False, power_base=False) == x*(x*y + x*
+                    z)**(x*y + x*z) + y*(x*y + x*z)**(x*y + x*z)
+    assert e.expand(power_exp=False, power_base=False, deep=False) == x* \
+        (x*(y + z))**(x*(y + z)) + y*(x*(y + z))**(x*(y + z))
+    e = x * (x + (y + 1)**2)
+    assert e.expand(deep=False) == x**2 + x*(y + 1)**2
+    e = (x*(y + z))**z
+    assert e.expand(power_base=True, mul=True, deep=True) in [x**z*(y +
+                    z)**z, (x*y + x*z)**z]
+    assert ((2*y)**z).expand() == 2**z*y**z
+    p = Symbol('p', positive=True)
+    assert sqrt(-x).expand().is_Pow
+    assert sqrt(-x).expand(force=True) == I*sqrt(x)
+    assert ((2*y*p)**z).expand() == 2**z*p**z*y**z
+    assert ((2*y*p*x)**z).expand() == 2**z*p**z*(x*y)**z
+    assert ((2*y*p*x)**z).expand(force=True) == 2**z*p**z*x**z*y**z
+    assert ((2*y*p*-pi)**z).expand() == 2**z*pi**z*p**z*(-y)**z
+    assert ((2*y*p*-pi*x)**z).expand() == 2**z*pi**z*p**z*(-x*y)**z
+    n = Symbol('n', negative=True)
+    m = Symbol('m', negative=True)
+    assert ((-2*x*y*n)**z).expand() == 2**z*(-n)**z*(x*y)**z
+    assert ((-2*x*y*n*m)**z).expand() == 2**z*(-m)**z*(-n)**z*(-x*y)**z
+    # issue 5482
+    assert sqrt(-2*x*n) == sqrt(2)*sqrt(-n)*sqrt(x)
+    # issue 5605 (2)
+    assert (cos(x + y)**2).expand(trig=True) in [
+        (-sin(x)*sin(y) + cos(x)*cos(y))**2,
+        sin(x)**2*sin(y)**2 - 2*sin(x)*sin(y)*cos(x)*cos(y) + cos(x)**2*cos(y)**2
+    ]
+
+    # Check that this isn't too slow
+    x = Symbol('x')
+    W = 1
+    for i in range(1, 21):
+        W = W * (x - i)
+    W = W.expand()
+    assert W.has(-1672280820*x**15)
+
+def test_expand_mul():
+    # part of issue 20597
+    e = Mul(2, 3, evaluate=False)
+    assert e.expand() == 6
+
+    e = Mul(2, 3, 1/x, evaluate=False)
+    assert e.expand() == 6/x
+    e = Mul(2, R(1, 3), evaluate=False)
+    assert e.expand() == R(2, 3)
+
+def test_power_expand():
+    """Test for Pow.expand()"""
+    a = Symbol('a')
+    b = Symbol('b')
+    p = (a + b)**2
+    assert p.expand() == a**2 + b**2 + 2*a*b
+
+    p = (1 + 2*(1 + a))**2
+    assert p.expand() == 9 + 4*(a**2) + 12*a
+
+    p = 2**(a + b)
+    assert p.expand() == 2**a*2**b
+
+    A = Symbol('A', commutative=False)
+    B = Symbol('B', commutative=False)
+    assert (2**(A + B)).expand() == 2**(A + B)
+    assert (A**(a + b)).expand() != A**(a + b)
+
+
+def test_issues_5919_6830():
+    # issue 5919
+    n = -1 + 1/x
+    z = n/x/(-n)**2 - 1/n/x
+    assert expand(z) == 1/(x**2 - 2*x + 1) - 1/(x - 2 + 1/x) - 1/(-x + 1)
+
+    # issue 6830
+    p = (1 + x)**2
+    assert expand_multinomial((1 + x*p)**2) == (
+        x**2*(x**4 + 4*x**3 + 6*x**2 + 4*x + 1) + 2*x*(x**2 + 2*x + 1) + 1)
+    assert expand_multinomial((1 + (y + x)*p)**2) == (
+        2*((x + y)*(x**2 + 2*x + 1)) + (x**2 + 2*x*y + y**2)*
+        (x**4 + 4*x**3 + 6*x**2 + 4*x + 1) + 1)
+    A = Symbol('A', commutative=False)
+    p = (1 + A)**2
+    assert expand_multinomial((1 + x*p)**2) == (
+        x**2*(1 + 4*A + 6*A**2 + 4*A**3 + A**4) + 2*x*(1 + 2*A + A**2) + 1)
+    assert expand_multinomial((1 + (y + x)*p)**2) == (
+        (x + y)*(1 + 2*A + A**2)*2 + (x**2 + 2*x*y + y**2)*
+        (1 + 4*A + 6*A**2 + 4*A**3 + A**4) + 1)
+    assert expand_multinomial((1 + (y + x)*p)**3) == (
+        (x + y)*(1 + 2*A + A**2)*3 + (x**2 + 2*x*y + y**2)*(1 + 4*A +
+        6*A**2 + 4*A**3 + A**4)*3 + (x**3 + 3*x**2*y + 3*x*y**2 + y**3)*(1 + 6*A
+        + 15*A**2 + 20*A**3 + 15*A**4 + 6*A**5 + A**6) + 1)
+    # unevaluate powers
+    eq = (Pow((x + 1)*((A + 1)**2), 2, evaluate=False))
+    # - in this case the base is not an Add so no further
+    #   expansion is done
+    assert expand_multinomial(eq) == \
+        (x**2 + 2*x + 1)*(1 + 4*A + 6*A**2 + 4*A**3 + A**4)
+    # - but here, the expanded base *is* an Add so it gets expanded
+    eq = (Pow(((A + 1)**2), 2, evaluate=False))
+    assert expand_multinomial(eq) == 1 + 4*A + 6*A**2 + 4*A**3 + A**4
+
+    # coverage
+    def ok(a, b, n):
+        e = (a + I*b)**n
+        return verify_numerically(e, expand_multinomial(e))
+
+    for a in [2, S.Half]:
+        for b in [3, R(1, 3)]:
+            for n in range(2, 6):
+                assert ok(a, b, n)
+
+    assert expand_multinomial((x + 1 + O(z))**2) == \
+        1 + 2*x + x**2 + O(z)
+    assert expand_multinomial((x + 1 + O(z))**3) == \
+        1 + 3*x + 3*x**2 + x**3 + O(z)
+
+    assert expand_multinomial(3**(x + y + 3)) == 27*3**(x + y)
+
+def test_expand_log():
+    t = Symbol('t', positive=True)
+    # after first expansion, -2*log(2) + log(4); then 0 after second
+    assert expand(log(t**2) - log(t**2/4) - 2*log(2)) == 0
+    assert expand_log(log(7*6)/log(6)) == 1 + log(7)/log(6)
+    b = factorial(10)
+    assert expand_log(log(7*b**4)/log(b)
+        ) == 4 + log(7)/log(b)
+
+
+def test_issue_23952():
+    assert (x**(y + z)).expand(force=True) == x**y*x**z
+    one = Symbol('1', integer=True, prime=True, odd=True, positive=True)
+    two = Symbol('2', integer=True, prime=True, even=True)
+    e = two - one
+    for b in (0, x):
+        # 0**e = 0, 0**-e = zoo; but if expanded then nan
+        assert unchanged(Pow, b, e)  # power_exp
+        assert unchanged(Pow, b, -e)  # power_exp
+        assert unchanged(Pow, b, y - x)  # power_exp
+        assert unchanged(Pow, b, 3 - x)  # multinomial
+        assert (b**e).expand().is_Pow  # power_exp
+        assert (b**-e).expand().is_Pow  # power_exp
+        assert (b**(y - x)).expand().is_Pow  # power_exp
+        assert (b**(3 - x)).expand().is_Pow  # multinomial
+    nn1 = Symbol('nn1', nonnegative=True)
+    nn2 = Symbol('nn2', nonnegative=True)
+    nn3 = Symbol('nn3', nonnegative=True)
+    assert (x**(nn1 + nn2)).expand() == x**nn1*x**nn2
+    assert (x**(-nn1 - nn2)).expand() == x**-nn1*x**-nn2
+    assert unchanged(Pow, x, nn1 + nn2 - nn3)
+    assert unchanged(Pow, x, 1 + nn2 - nn3)
+    assert unchanged(Pow, x, nn1 - nn2)
+    assert unchanged(Pow, x, 1 - nn2)
+    assert unchanged(Pow, x, -1 + nn2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_expr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_expr.py
new file mode 100644
index 0000000000000000000000000000000000000000..af63823345e2b0564ebb7e9015bfe1b423c9bafa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_expr.py
@@ -0,0 +1,2313 @@
+from sympy.assumptions.refine import refine
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.expr import (ExprBuilder, unchanged, Expr,
+    UnevaluatedExpr)
+from sympy.core.function import (Function, expand, WildFunction,
+    AppliedUndef, Derivative, diff, Subs)
+from sympy.core.mul import Mul, _unevaluated_Mul
+from sympy.core.numbers import (NumberSymbol, E, zoo, oo, Float, I,
+    Rational, nan, Integer, Number, pi, _illegal)
+from sympy.core.power import Pow
+from sympy.core.relational import Ge, Lt, Gt, Le
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import Symbol, symbols, Dummy, Wild
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.exponential import exp_polar, exp, log
+from sympy.functions.elementary.hyperbolic import sinh, tanh
+from sympy.functions.elementary.miscellaneous import sqrt, Max
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import tan, sin, cos
+from sympy.functions.special.delta_functions import (Heaviside,
+    DiracDelta)
+from sympy.functions.special.error_functions import Si
+from sympy.functions.special.gamma_functions import gamma
+from sympy.integrals.integrals import integrate, Integral
+from sympy.physics.secondquant import FockState
+from sympy.polys.partfrac import apart
+from sympy.polys.polytools import factor, cancel, Poly
+from sympy.polys.rationaltools import together
+from sympy.series.order import O
+from sympy.sets.sets import FiniteSet
+from sympy.simplify.combsimp import combsimp
+from sympy.simplify.gammasimp import gammasimp
+from sympy.simplify.powsimp import powsimp
+from sympy.simplify.radsimp import collect, radsimp
+from sympy.simplify.ratsimp import ratsimp
+from sympy.simplify.simplify import simplify, nsimplify
+from sympy.simplify.trigsimp import trigsimp
+from sympy.tensor.indexed import Indexed
+from sympy.physics.units import meter
+
+from sympy.testing.pytest import raises, XFAIL
+
+from sympy.abc import a, b, c, n, t, u, x, y, z
+
+
+f, g, h = symbols('f,g,h', cls=Function)
+
+
+class DummyNumber:
+    """
+    Minimal implementation of a number that works with SymPy.
+
+    If one has a Number class (e.g. Sage Integer, or some other custom class)
+    that one wants to work well with SymPy, one has to implement at least the
+    methods of this class DummyNumber, resp. its subclasses I5 and F1_1.
+
+    Basically, one just needs to implement either __int__() or __float__() and
+    then one needs to make sure that the class works with Python integers and
+    with itself.
+    """
+
+    def __radd__(self, a):
+        if isinstance(a, (int, float)):
+            return a + self.number
+        return NotImplemented
+
+    def __add__(self, a):
+        if isinstance(a, (int, float, DummyNumber)):
+            return self.number + a
+        return NotImplemented
+
+    def __rsub__(self, a):
+        if isinstance(a, (int, float)):
+            return a - self.number
+        return NotImplemented
+
+    def __sub__(self, a):
+        if isinstance(a, (int, float, DummyNumber)):
+            return self.number - a
+        return NotImplemented
+
+    def __rmul__(self, a):
+        if isinstance(a, (int, float)):
+            return a * self.number
+        return NotImplemented
+
+    def __mul__(self, a):
+        if isinstance(a, (int, float, DummyNumber)):
+            return self.number * a
+        return NotImplemented
+
+    def __rtruediv__(self, a):
+        if isinstance(a, (int, float)):
+            return a / self.number
+        return NotImplemented
+
+    def __truediv__(self, a):
+        if isinstance(a, (int, float, DummyNumber)):
+            return self.number / a
+        return NotImplemented
+
+    def __rpow__(self, a):
+        if isinstance(a, (int, float)):
+            return a ** self.number
+        return NotImplemented
+
+    def __pow__(self, a):
+        if isinstance(a, (int, float, DummyNumber)):
+            return self.number ** a
+        return NotImplemented
+
+    def __pos__(self):
+        return self.number
+
+    def __neg__(self):
+        return - self.number
+
+
+class I5(DummyNumber):
+    number = 5
+
+    def __int__(self):
+        return self.number
+
+
+class F1_1(DummyNumber):
+    number = 1.1
+
+    def __float__(self):
+        return self.number
+
+i5 = I5()
+f1_1 = F1_1()
+
+# basic SymPy objects
+basic_objs = [
+    Rational(2),
+    Float("1.3"),
+    x,
+    y,
+    pow(x, y)*y,
+]
+
+# all supported objects
+all_objs = basic_objs + [
+    5,
+    5.5,
+    i5,
+    f1_1
+]
+
+
+def dotest(s):
+    for xo in all_objs:
+        for yo in all_objs:
+            s(xo, yo)
+    return True
+
+
+def test_basic():
+    def j(a, b):
+        x = a
+        x = +a
+        x = -a
+        x = a + b
+        x = a - b
+        x = a*b
+        x = a/b
+        x = a**b
+        del x
+    assert dotest(j)
+
+
+def test_ibasic():
+    def s(a, b):
+        x = a
+        x += b
+        x = a
+        x -= b
+        x = a
+        x *= b
+        x = a
+        x /= b
+    assert dotest(s)
+
+
+class NonBasic:
+    '''This class represents an object that knows how to implement binary
+    operations like +, -, etc with Expr but is not a subclass of Basic itself.
+    The NonExpr subclass below does subclass Basic but not Expr.
+
+    For both NonBasic and NonExpr it should be possible for them to override
+    Expr.__add__ etc because Expr.__add__ should be returning NotImplemented
+    for non Expr classes. Otherwise Expr.__add__ would create meaningless
+    objects like Add(Integer(1), FiniteSet(2)) and it wouldn't be possible for
+    other classes to override these operations when interacting with Expr.
+    '''
+    def __add__(self, other):
+        return SpecialOp('+', self, other)
+
+    def __radd__(self, other):
+        return SpecialOp('+', other, self)
+
+    def __sub__(self, other):
+        return SpecialOp('-', self, other)
+
+    def __rsub__(self, other):
+        return SpecialOp('-', other, self)
+
+    def __mul__(self, other):
+        return SpecialOp('*', self, other)
+
+    def __rmul__(self, other):
+        return SpecialOp('*', other, self)
+
+    def __truediv__(self, other):
+        return SpecialOp('/', self, other)
+
+    def __rtruediv__(self, other):
+        return SpecialOp('/', other, self)
+
+    def __floordiv__(self, other):
+        return SpecialOp('//', self, other)
+
+    def __rfloordiv__(self, other):
+        return SpecialOp('//', other, self)
+
+    def __mod__(self, other):
+        return SpecialOp('%', self, other)
+
+    def __rmod__(self, other):
+        return SpecialOp('%', other, self)
+
+    def __divmod__(self, other):
+        return SpecialOp('divmod', self, other)
+
+    def __rdivmod__(self, other):
+        return SpecialOp('divmod', other, self)
+
+    def __pow__(self, other):
+        return SpecialOp('**', self, other)
+
+    def __rpow__(self, other):
+        return SpecialOp('**', other, self)
+
+    def __lt__(self, other):
+        return SpecialOp('<', self, other)
+
+    def __gt__(self, other):
+        return SpecialOp('>', self, other)
+
+    def __le__(self, other):
+        return SpecialOp('<=', self, other)
+
+    def __ge__(self, other):
+        return SpecialOp('>=', self, other)
+
+
+class NonExpr(Basic, NonBasic):
+    '''Like NonBasic above except this is a subclass of Basic but not Expr'''
+    pass
+
+
+class SpecialOp():
+    '''Represents the results of operations with NonBasic and NonExpr'''
+    def __new__(cls, op, arg1, arg2):
+        obj = object.__new__(cls)
+        obj.args = (op, arg1, arg2)
+        return obj
+
+
+class NonArithmetic(Basic):
+    '''Represents a Basic subclass that does not support arithmetic operations'''
+    pass
+
+
+def test_cooperative_operations():
+    '''Tests that Expr uses binary operations cooperatively.
+
+    In particular it should be possible for non-Expr classes to override
+    binary operators like +, - etc when used with Expr instances. This should
+    work for non-Expr classes whether they are Basic subclasses or not. Also
+    non-Expr classes that do not define binary operators with Expr should give
+    TypeError.
+    '''
+    # A bunch of instances of Expr subclasses
+    exprs = [
+        Expr(),
+        S.Zero,
+        S.One,
+        S.Infinity,
+        S.NegativeInfinity,
+        S.ComplexInfinity,
+        S.Half,
+        Float(0.5),
+        Integer(2),
+        Symbol('x'),
+        Mul(2, Symbol('x')),
+        Add(2, Symbol('x')),
+        Pow(2, Symbol('x')),
+    ]
+
+    for e in exprs:
+        # Test that these classes can override arithmetic operations in
+        # combination with various Expr types.
+        for ne in [NonBasic(), NonExpr()]:
+
+            results = [
+                (ne + e, ('+', ne, e)),
+                (e + ne, ('+', e, ne)),
+                (ne - e, ('-', ne, e)),
+                (e - ne, ('-', e, ne)),
+                (ne * e, ('*', ne, e)),
+                (e * ne, ('*', e, ne)),
+                (ne / e, ('/', ne, e)),
+                (e / ne, ('/', e, ne)),
+                (ne // e, ('//', ne, e)),
+                (e // ne, ('//', e, ne)),
+                (ne % e, ('%', ne, e)),
+                (e % ne, ('%', e, ne)),
+                (divmod(ne, e), ('divmod', ne, e)),
+                (divmod(e, ne), ('divmod', e, ne)),
+                (ne ** e, ('**', ne, e)),
+                (e ** ne, ('**', e, ne)),
+                (e < ne, ('>', ne, e)),
+                (ne < e, ('<', ne, e)),
+                (e > ne, ('<', ne, e)),
+                (ne > e, ('>', ne, e)),
+                (e <= ne, ('>=', ne, e)),
+                (ne <= e, ('<=', ne, e)),
+                (e >= ne, ('<=', ne, e)),
+                (ne >= e, ('>=', ne, e)),
+            ]
+
+            for res, args in results:
+                assert type(res) is SpecialOp and res.args == args
+
+        # These classes do not support binary operators with Expr. Every
+        # operation should raise in combination with any of the Expr types.
+        for na in [NonArithmetic(), object()]:
+
+            raises(TypeError, lambda : e + na)
+            raises(TypeError, lambda : na + e)
+            raises(TypeError, lambda : e - na)
+            raises(TypeError, lambda : na - e)
+            raises(TypeError, lambda : e * na)
+            raises(TypeError, lambda : na * e)
+            raises(TypeError, lambda : e / na)
+            raises(TypeError, lambda : na / e)
+            raises(TypeError, lambda : e // na)
+            raises(TypeError, lambda : na // e)
+            raises(TypeError, lambda : e % na)
+            raises(TypeError, lambda : na % e)
+            raises(TypeError, lambda : divmod(e, na))
+            raises(TypeError, lambda : divmod(na, e))
+            raises(TypeError, lambda : e ** na)
+            raises(TypeError, lambda : na ** e)
+            raises(TypeError, lambda : e > na)
+            raises(TypeError, lambda : na > e)
+            raises(TypeError, lambda : e < na)
+            raises(TypeError, lambda : na < e)
+            raises(TypeError, lambda : e >= na)
+            raises(TypeError, lambda : na >= e)
+            raises(TypeError, lambda : e <= na)
+            raises(TypeError, lambda : na <= e)
+
+
+def test_relational():
+    from sympy.core.relational import Lt
+    assert (pi < 3) is S.false
+    assert (pi <= 3) is S.false
+    assert (pi > 3) is S.true
+    assert (pi >= 3) is S.true
+    assert (-pi < 3) is S.true
+    assert (-pi <= 3) is S.true
+    assert (-pi > 3) is S.false
+    assert (-pi >= 3) is S.false
+    r = Symbol('r', real=True)
+    assert (r - 2 < r - 3) is S.false
+    assert Lt(x + I, x + I + 2).func == Lt  # issue 8288
+
+
+def test_relational_assumptions():
+    m1 = Symbol("m1", nonnegative=False)
+    m2 = Symbol("m2", positive=False)
+    m3 = Symbol("m3", nonpositive=False)
+    m4 = Symbol("m4", negative=False)
+    assert (m1 < 0) == Lt(m1, 0)
+    assert (m2 <= 0) == Le(m2, 0)
+    assert (m3 > 0) == Gt(m3, 0)
+    assert (m4 >= 0) == Ge(m4, 0)
+    m1 = Symbol("m1", nonnegative=False, real=True)
+    m2 = Symbol("m2", positive=False, real=True)
+    m3 = Symbol("m3", nonpositive=False, real=True)
+    m4 = Symbol("m4", negative=False, real=True)
+    assert (m1 < 0) is S.true
+    assert (m2 <= 0) is S.true
+    assert (m3 > 0) is S.true
+    assert (m4 >= 0) is S.true
+    m1 = Symbol("m1", negative=True)
+    m2 = Symbol("m2", nonpositive=True)
+    m3 = Symbol("m3", positive=True)
+    m4 = Symbol("m4", nonnegative=True)
+    assert (m1 < 0) is S.true
+    assert (m2 <= 0) is S.true
+    assert (m3 > 0) is S.true
+    assert (m4 >= 0) is S.true
+    m1 = Symbol("m1", negative=False, real=True)
+    m2 = Symbol("m2", nonpositive=False, real=True)
+    m3 = Symbol("m3", positive=False, real=True)
+    m4 = Symbol("m4", nonnegative=False, real=True)
+    assert (m1 < 0) is S.false
+    assert (m2 <= 0) is S.false
+    assert (m3 > 0) is S.false
+    assert (m4 >= 0) is S.false
+
+
+# See https://github.com/sympy/sympy/issues/17708
+#def test_relational_noncommutative():
+#    from sympy import Lt, Gt, Le, Ge
+#    A, B = symbols('A,B', commutative=False)
+#    assert (A < B) == Lt(A, B)
+#    assert (A <= B) == Le(A, B)
+#    assert (A > B) == Gt(A, B)
+#    assert (A >= B) == Ge(A, B)
+
+
+def test_basic_nostr():
+    for obj in basic_objs:
+        raises(TypeError, lambda: obj + '1')
+        raises(TypeError, lambda: obj - '1')
+        if obj == 2:
+            assert obj * '1' == '11'
+        else:
+            raises(TypeError, lambda: obj * '1')
+        raises(TypeError, lambda: obj / '1')
+        raises(TypeError, lambda: obj ** '1')
+
+
+def test_series_expansion_for_uniform_order():
+    assert (1/x + y + x).series(x, 0, 0) == 1/x + O(1, x)
+    assert (1/x + y + x).series(x, 0, 1) == 1/x + y + O(x)
+    assert (1/x + 1 + x).series(x, 0, 0) == 1/x + O(1, x)
+    assert (1/x + 1 + x).series(x, 0, 1) == 1/x + 1 + O(x)
+    assert (1/x + x).series(x, 0, 0) == 1/x + O(1, x)
+    assert (1/x + y + y*x + x).series(x, 0, 0) == 1/x + O(1, x)
+    assert (1/x + y + y*x + x).series(x, 0, 1) == 1/x + y + O(x)
+
+
+def test_leadterm():
+    assert (3 + 2*x**(log(3)/log(2) - 1)).leadterm(x) == (3, 0)
+
+    assert (1/x**2 + 1 + x + x**2).leadterm(x)[1] == -2
+    assert (1/x + 1 + x + x**2).leadterm(x)[1] == -1
+    assert (x**2 + 1/x).leadterm(x)[1] == -1
+    assert (1 + x**2).leadterm(x)[1] == 0
+    assert (x + 1).leadterm(x)[1] == 0
+    assert (x + x**2).leadterm(x)[1] == 1
+    assert (x**2).leadterm(x)[1] == 2
+
+
+def test_as_leading_term():
+    assert (3 + 2*x**(log(3)/log(2) - 1)).as_leading_term(x) == 3
+    assert (1/x**2 + 1 + x + x**2).as_leading_term(x) == 1/x**2
+    assert (1/x + 1 + x + x**2).as_leading_term(x) == 1/x
+    assert (x**2 + 1/x).as_leading_term(x) == 1/x
+    assert (1 + x**2).as_leading_term(x) == 1
+    assert (x + 1).as_leading_term(x) == 1
+    assert (x + x**2).as_leading_term(x) == x
+    assert (x**2).as_leading_term(x) == x**2
+    assert (x + oo).as_leading_term(x) is oo
+
+    raises(ValueError, lambda: (x + 1).as_leading_term(1))
+
+    # https://github.com/sympy/sympy/issues/21177
+    e = -3*x + (x + Rational(3, 2) - sqrt(3)*S.ImaginaryUnit/2)**2\
+        - Rational(3, 2) + 3*sqrt(3)*S.ImaginaryUnit/2
+    assert e.as_leading_term(x) == -sqrt(3)*I*x
+
+    # https://github.com/sympy/sympy/issues/21245
+    e = 1 - x - x**2
+    d = (1 + sqrt(5))/2
+    assert e.subs(x, y + 1/d).as_leading_term(y) == \
+        (-40*y - 16*sqrt(5)*y)/(16 + 8*sqrt(5))
+
+    # https://github.com/sympy/sympy/issues/26991
+    assert sinh(tanh(3/(100*x))).as_leading_term(x, cdir = 1) == sinh(1)
+
+
+def test_leadterm2():
+    assert (x*cos(1)*cos(1 + sin(1)) + sin(1 + sin(1))).leadterm(x) == \
+           (sin(1 + sin(1)), 0)
+
+
+def test_leadterm3():
+    assert (y + z + x).leadterm(x) == (y + z, 0)
+
+
+def test_as_leading_term2():
+    assert (x*cos(1)*cos(1 + sin(1)) + sin(1 + sin(1))).as_leading_term(x) == \
+        sin(1 + sin(1))
+
+
+def test_as_leading_term3():
+    assert (2 + pi + x).as_leading_term(x) == 2 + pi
+    assert (2*x + pi*x + x**2).as_leading_term(x) == 2*x + pi*x
+
+
+def test_as_leading_term4():
+    # see issue 6843
+    n = Symbol('n', integer=True, positive=True)
+    r = -n**3/(2*n**2 + 4*n + 2) - n**2/(n**2 + 2*n + 1) + \
+        n**2/(n + 1) - n/(2*n**2 + 4*n + 2) + n/(n*x + x) + 2*n/(n + 1) - \
+        1 + 1/(n*x + x) + 1/(n + 1) - 1/x
+    assert r.as_leading_term(x).cancel() == n/2
+
+
+def test_as_leading_term_stub():
+    class foo(Function):
+        pass
+    assert foo(1/x).as_leading_term(x) == foo(1/x)
+    assert foo(1).as_leading_term(x) == foo(1)
+    raises(NotImplementedError, lambda: foo(x).as_leading_term(x))
+
+
+def test_as_leading_term_deriv_integral():
+    # related to issue 11313
+    assert Derivative(x ** 3, x).as_leading_term(x) == 3*x**2
+    assert Derivative(x ** 3, y).as_leading_term(x) == 0
+
+    assert Integral(x ** 3, x).as_leading_term(x) == x**4/4
+    assert Integral(x ** 3, y).as_leading_term(x) == y*x**3
+
+    assert Derivative(exp(x), x).as_leading_term(x) == 1
+    assert Derivative(log(x), x).as_leading_term(x) == (1/x).as_leading_term(x)
+
+
+def test_atoms():
+    assert x.atoms() == {x}
+    assert (1 + x).atoms() == {x, S.One}
+
+    assert (1 + 2*cos(x)).atoms(Symbol) == {x}
+    assert (1 + 2*cos(x)).atoms(Symbol, Number) == {S.One, S(2), x}
+
+    assert (2*(x**(y**x))).atoms() == {S(2), x, y}
+
+    assert S.Half.atoms() == {S.Half}
+    assert S.Half.atoms(Symbol) == set()
+
+    assert sin(oo).atoms(oo) == set()
+
+    assert Poly(0, x).atoms() == {S.Zero, x}
+    assert Poly(1, x).atoms() == {S.One, x}
+
+    assert Poly(x, x).atoms() == {x}
+    assert Poly(x, x, y).atoms() == {x, y}
+    assert Poly(x + y, x, y).atoms() == {x, y}
+    assert Poly(x + y, x, y, z).atoms() == {x, y, z}
+    assert Poly(x + y*t, x, y, z).atoms() == {t, x, y, z}
+
+    assert (I*pi).atoms(NumberSymbol) == {pi}
+    assert (I*pi).atoms(NumberSymbol, I) == \
+        (I*pi).atoms(I, NumberSymbol) == {pi, I}
+
+    assert exp(exp(x)).atoms(exp) == {exp(exp(x)), exp(x)}
+    assert (1 + x*(2 + y) + exp(3 + z)).atoms(Add) == \
+        {1 + x*(2 + y) + exp(3 + z), 2 + y, 3 + z}
+
+    # issue 6132
+    e = (f(x) + sin(x) + 2)
+    assert e.atoms(AppliedUndef) == \
+        {f(x)}
+    assert e.atoms(AppliedUndef, Function) == \
+        {f(x), sin(x)}
+    assert e.atoms(Function) == \
+        {f(x), sin(x)}
+    assert e.atoms(AppliedUndef, Number) == \
+        {f(x), S(2)}
+    assert e.atoms(Function, Number) == \
+        {S(2), sin(x), f(x)}
+
+
+def test_is_polynomial():
+    k = Symbol('k', nonnegative=True, integer=True)
+
+    assert Rational(2).is_polynomial(x, y, z) is True
+    assert (S.Pi).is_polynomial(x, y, z) is True
+
+    assert x.is_polynomial(x) is True
+    assert x.is_polynomial(y) is True
+
+    assert (x**2).is_polynomial(x) is True
+    assert (x**2).is_polynomial(y) is True
+
+    assert (x**(-2)).is_polynomial(x) is False
+    assert (x**(-2)).is_polynomial(y) is True
+
+    assert (2**x).is_polynomial(x) is False
+    assert (2**x).is_polynomial(y) is True
+
+    assert (x**k).is_polynomial(x) is False
+    assert (x**k).is_polynomial(k) is False
+    assert (x**x).is_polynomial(x) is False
+    assert (k**k).is_polynomial(k) is False
+    assert (k**x).is_polynomial(k) is False
+
+    assert (x**(-k)).is_polynomial(x) is False
+    assert ((2*x)**k).is_polynomial(x) is False
+
+    assert (x**2 + 3*x - 8).is_polynomial(x) is True
+    assert (x**2 + 3*x - 8).is_polynomial(y) is True
+
+    assert (x**2 + 3*x - 8).is_polynomial() is True
+
+    assert sqrt(x).is_polynomial(x) is False
+    assert (sqrt(x)**3).is_polynomial(x) is False
+
+    assert (x**2 + 3*x*sqrt(y) - 8).is_polynomial(x) is True
+    assert (x**2 + 3*x*sqrt(y) - 8).is_polynomial(y) is False
+
+    assert ((x**2)*(y**2) + x*(y**2) + y*x + exp(2)).is_polynomial() is True
+    assert ((x**2)*(y**2) + x*(y**2) + y*x + exp(x)).is_polynomial() is False
+
+    assert (
+        (x**2)*(y**2) + x*(y**2) + y*x + exp(2)).is_polynomial(x, y) is True
+    assert (
+        (x**2)*(y**2) + x*(y**2) + y*x + exp(x)).is_polynomial(x, y) is False
+
+    assert (1/f(x) + 1).is_polynomial(f(x)) is False
+
+
+def test_is_rational_function():
+    assert Integer(1).is_rational_function() is True
+    assert Integer(1).is_rational_function(x) is True
+
+    assert Rational(17, 54).is_rational_function() is True
+    assert Rational(17, 54).is_rational_function(x) is True
+
+    assert (12/x).is_rational_function() is True
+    assert (12/x).is_rational_function(x) is True
+
+    assert (x/y).is_rational_function() is True
+    assert (x/y).is_rational_function(x) is True
+    assert (x/y).is_rational_function(x, y) is True
+
+    assert (x**2 + 1/x/y).is_rational_function() is True
+    assert (x**2 + 1/x/y).is_rational_function(x) is True
+    assert (x**2 + 1/x/y).is_rational_function(x, y) is True
+
+    assert (sin(y)/x).is_rational_function() is False
+    assert (sin(y)/x).is_rational_function(y) is False
+    assert (sin(y)/x).is_rational_function(x) is True
+    assert (sin(y)/x).is_rational_function(x, y) is False
+
+    for i in _illegal:
+        assert not i.is_rational_function()
+        for d in (1, x):
+            assert not (i/d).is_rational_function()
+
+
+def test_is_meromorphic():
+    f = a/x**2 + b + x + c*x**2
+    assert f.is_meromorphic(x, 0) is True
+    assert f.is_meromorphic(x, 1) is True
+    assert f.is_meromorphic(x, zoo) is True
+
+    g = 3 + 2*x**(log(3)/log(2) - 1)
+    assert g.is_meromorphic(x, 0) is False
+    assert g.is_meromorphic(x, 1) is True
+    assert g.is_meromorphic(x, zoo) is False
+
+    n = Symbol('n', integer=True)
+    e = sin(1/x)**n*x
+    assert e.is_meromorphic(x, 0) is False
+    assert e.is_meromorphic(x, 1) is True
+    assert e.is_meromorphic(x, zoo) is False
+
+    e = log(x)**pi
+    assert e.is_meromorphic(x, 0) is False
+    assert e.is_meromorphic(x, 1) is False
+    assert e.is_meromorphic(x, 2) is True
+    assert e.is_meromorphic(x, zoo) is False
+
+    assert (log(x)**a).is_meromorphic(x, 0) is False
+    assert (log(x)**a).is_meromorphic(x, 1) is False
+    assert (a**log(x)).is_meromorphic(x, 0) is None
+    assert (3**log(x)).is_meromorphic(x, 0) is False
+    assert (3**log(x)).is_meromorphic(x, 1) is True
+
+def test_is_algebraic_expr():
+    assert sqrt(3).is_algebraic_expr(x) is True
+    assert sqrt(3).is_algebraic_expr() is True
+
+    eq = ((1 + x**2)/(1 - y**2))**(S.One/3)
+    assert eq.is_algebraic_expr(x) is True
+    assert eq.is_algebraic_expr(y) is True
+
+    assert (sqrt(x) + y**(S(2)/3)).is_algebraic_expr(x) is True
+    assert (sqrt(x) + y**(S(2)/3)).is_algebraic_expr(y) is True
+    assert (sqrt(x) + y**(S(2)/3)).is_algebraic_expr() is True
+
+    assert (cos(y)/sqrt(x)).is_algebraic_expr() is False
+    assert (cos(y)/sqrt(x)).is_algebraic_expr(x) is True
+    assert (cos(y)/sqrt(x)).is_algebraic_expr(y) is False
+    assert (cos(y)/sqrt(x)).is_algebraic_expr(x, y) is False
+
+
+def test_SAGE1():
+    #see https://github.com/sympy/sympy/issues/3346
+    class MyInt:
+        def _sympy_(self):
+            return Integer(5)
+    m = MyInt()
+    e = Rational(2)*m
+    assert e == 10
+
+    raises(TypeError, lambda: Rational(2)*MyInt)
+
+
+def test_SAGE2():
+    class MyInt:
+        def __int__(self):
+            return 5
+    assert sympify(MyInt()) == 5
+    e = Rational(2)*MyInt()
+    assert e == 10
+
+    raises(TypeError, lambda: Rational(2)*MyInt)
+
+
+def test_SAGE3():
+    class MySymbol:
+        def __rmul__(self, other):
+            return ('mys', other, self)
+
+    o = MySymbol()
+    e = x*o
+
+    assert e == ('mys', x, o)
+
+
+def test_len():
+    e = x*y
+    assert len(e.args) == 2
+    e = x + y + z
+    assert len(e.args) == 3
+
+
+def test_doit():
+    a = Integral(x**2, x)
+
+    assert isinstance(a.doit(), Integral) is False
+
+    assert isinstance(a.doit(integrals=True), Integral) is False
+    assert isinstance(a.doit(integrals=False), Integral) is True
+
+    assert (2*Integral(x, x)).doit() == x**2
+
+
+def test_attribute_error():
+    raises(AttributeError, lambda: x.cos())
+    raises(AttributeError, lambda: x.sin())
+    raises(AttributeError, lambda: x.exp())
+
+
+def test_args():
+    assert (x*y).args in ((x, y), (y, x))
+    assert (x + y).args in ((x, y), (y, x))
+    assert (x*y + 1).args in ((x*y, 1), (1, x*y))
+    assert sin(x*y).args == (x*y,)
+    assert sin(x*y).args[0] == x*y
+    assert (x**y).args == (x, y)
+    assert (x**y).args[0] == x
+    assert (x**y).args[1] == y
+
+
+def test_noncommutative_expand_issue_3757():
+    A, B, C = symbols('A,B,C', commutative=False)
+    assert A*B - B*A != 0
+    assert (A*(A + B)*B).expand() == A**2*B + A*B**2
+    assert (A*(A + B + C)*B).expand() == A**2*B + A*B**2 + A*C*B
+
+
+def test_as_numer_denom():
+    a, b, c = symbols('a, b, c')
+
+    assert nan.as_numer_denom() == (nan, 1)
+    assert oo.as_numer_denom() == (oo, 1)
+    assert (-oo).as_numer_denom() == (-oo, 1)
+    assert zoo.as_numer_denom() == (zoo, 1)
+    assert (-zoo).as_numer_denom() == (zoo, 1)
+
+    assert x.as_numer_denom() == (x, 1)
+    assert (1/x).as_numer_denom() == (1, x)
+    assert (x/y).as_numer_denom() == (x, y)
+    assert (x/2).as_numer_denom() == (x, 2)
+    assert (x*y/z).as_numer_denom() == (x*y, z)
+    assert (x/(y*z)).as_numer_denom() == (x, y*z)
+    assert S.Half.as_numer_denom() == (1, 2)
+    assert (1/y**2).as_numer_denom() == (1, y**2)
+    assert (x/y**2).as_numer_denom() == (x, y**2)
+    assert ((x**2 + 1)/y).as_numer_denom() == (x**2 + 1, y)
+    assert (x*(y + 1)/y**7).as_numer_denom() == (x*(y + 1), y**7)
+    assert (x**-2).as_numer_denom() == (1, x**2)
+    assert (a/x + b/2/x + c/3/x).as_numer_denom() == \
+        (6*a + 3*b + 2*c, 6*x)
+    assert (a/x + b/2/x + c/3/y).as_numer_denom() == \
+        (2*c*x + y*(6*a + 3*b), 6*x*y)
+    assert (a/x + b/2/x + c/.5/x).as_numer_denom() == \
+        (2*a + b + 4.0*c, 2*x)
+    # this should take no more than a few seconds
+    assert int(log(Add(*[Dummy()/i/x for i in range(1, 705)]
+                       ).as_numer_denom()[1]/x).n(4)) == 705
+    for i in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]:
+        assert (i + x/3).as_numer_denom() == \
+            (x + i, 3)
+    assert (S.Infinity + x/3 + y/4).as_numer_denom() == \
+        (4*x + 3*y + S.Infinity, 12)
+    assert (oo*x + zoo*y).as_numer_denom() == \
+        (zoo*y + oo*x, 1)
+
+    A, B, C = symbols('A,B,C', commutative=False)
+
+    assert (A*B*C**-1).as_numer_denom() == (A*B*C**-1, 1)
+    assert (A*B*C**-1/x).as_numer_denom() == (A*B*C**-1, x)
+    assert (C**-1*A*B).as_numer_denom() == (C**-1*A*B, 1)
+    assert (C**-1*A*B/x).as_numer_denom() == (C**-1*A*B, x)
+    assert ((A*B*C)**-1).as_numer_denom() == ((A*B*C)**-1, 1)
+    assert ((A*B*C)**-1/x).as_numer_denom() == ((A*B*C)**-1, x)
+
+    # the following morphs from Add to Mul during processing
+    assert Add(0, (x + y)/z/-2, evaluate=False).as_numer_denom(
+        ) == (-x - y, 2*z)
+
+
+def test_trunc():
+    import math
+    x, y = symbols('x y')
+    assert math.trunc(2) == 2
+    assert math.trunc(4.57) == 4
+    assert math.trunc(-5.79) == -5
+    assert math.trunc(pi) == 3
+    assert math.trunc(log(7)) == 1
+    assert math.trunc(exp(5)) == 148
+    assert math.trunc(cos(pi)) == -1
+    assert math.trunc(sin(5)) == 0
+
+    raises(TypeError, lambda: math.trunc(x))
+    raises(TypeError, lambda: math.trunc(x + y**2))
+    raises(TypeError, lambda: math.trunc(oo))
+
+
+def test_as_independent():
+    assert S.Zero.as_independent(x, as_Add=True) == (0, 0)
+    assert S.Zero.as_independent(x, as_Add=False) == (0, 0)
+    assert (2*x*sin(x) + y + x).as_independent(x) == (y, x + 2*x*sin(x))
+    assert (2*x*sin(x) + y + x).as_independent(y) == (x + 2*x*sin(x), y)
+
+    assert (2*x*sin(x) + y + x).as_independent(x, y) == (0, y + x + 2*x*sin(x))
+
+    assert (x*sin(x)*cos(y)).as_independent(x) == (cos(y), x*sin(x))
+    assert (x*sin(x)*cos(y)).as_independent(y) == (x*sin(x), cos(y))
+
+    assert (x*sin(x)*cos(y)).as_independent(x, y) == (1, x*sin(x)*cos(y))
+
+    assert (sin(x)).as_independent(x) == (1, sin(x))
+    assert (sin(x)).as_independent(y) == (sin(x), 1)
+
+    assert (2*sin(x)).as_independent(x) == (2, sin(x))
+    assert (2*sin(x)).as_independent(y) == (2*sin(x), 1)
+
+    # issue 4903 = 1766b
+    n1, n2, n3 = symbols('n1 n2 n3', commutative=False)
+    assert (n1 + n1*n2).as_independent(n2) == (n1, n1*n2)
+    assert (n2*n1 + n1*n2).as_independent(n2) == (0, n1*n2 + n2*n1)
+    assert (n1*n2*n1).as_independent(n2) == (n1, n2*n1)
+    assert (n1*n2*n1).as_independent(n1) == (1, n1*n2*n1)
+
+    assert (3*x).as_independent(x, as_Add=True) == (0, 3*x)
+    assert (3*x).as_independent(x, as_Add=False) == (3, x)
+    assert (3 + x).as_independent(x, as_Add=True) == (3, x)
+    assert (3 + x).as_independent(x, as_Add=False) == (1, 3 + x)
+
+    # issue 5479
+    assert (3*x).as_independent(Symbol) == (3, x)
+
+    # issue 5648
+    assert (n1*x*y).as_independent(x) == (n1*y, x)
+    assert ((x + n1)*(x - y)).as_independent(x) == (1, (x + n1)*(x - y))
+    assert ((x + n1)*(x - y)).as_independent(y) == (x + n1, x - y)
+    assert (DiracDelta(x - n1)*DiracDelta(x - y)).as_independent(x) \
+        == (1, DiracDelta(x - n1)*DiracDelta(x - y))
+    assert (x*y*n1*n2*n3).as_independent(n2) == (x*y*n1, n2*n3)
+    assert (x*y*n1*n2*n3).as_independent(n1) == (x*y, n1*n2*n3)
+    assert (x*y*n1*n2*n3).as_independent(n3) == (x*y*n1*n2, n3)
+    assert (DiracDelta(x - n1)*DiracDelta(y - n1)*DiracDelta(x - n2)).as_independent(y) == \
+           (DiracDelta(x - n1)*DiracDelta(x - n2), DiracDelta(y - n1))
+
+    # issue 5784
+    assert (x + Integral(x, (x, 1, 2))).as_independent(x, strict=True) == \
+           (Integral(x, (x, 1, 2)), x)
+
+    eq = Add(x, -x, 2, -3, evaluate=False)
+    assert eq.as_independent(x) == (-1, Add(x, -x, evaluate=False))
+    eq = Mul(x, 1/x, 2, -3, evaluate=False)
+    assert eq.as_independent(x) == (-6, Mul(x, 1/x, evaluate=False))
+
+    assert (x*y).as_independent(z, as_Add=True) == (x*y, 0)
+
+@XFAIL
+def test_call_2():
+    # TODO UndefinedFunction does not subclass Expr
+    assert (2*f)(x) == 2*f(x)
+
+
+def test_replace():
+    e = log(sin(x)) + tan(sin(x**2))
+
+    assert e.replace(sin, cos) == log(cos(x)) + tan(cos(x**2))
+    assert e.replace(
+        sin, lambda a: sin(2*a)) == log(sin(2*x)) + tan(sin(2*x**2))
+
+    a = Wild('a')
+    b = Wild('b')
+
+    assert e.replace(sin(a), cos(a)) == log(cos(x)) + tan(cos(x**2))
+    assert e.replace(
+        sin(a), lambda a: sin(2*a)) == log(sin(2*x)) + tan(sin(2*x**2))
+    # test exact
+    assert (2*x).replace(a*x + b, b - a, exact=True) == 2*x
+    assert (2*x).replace(a*x + b, b - a) == 2*x
+    assert (2*x).replace(a*x + b, b - a, exact=False) == 2/x
+    assert (2*x).replace(a*x + b, lambda a, b: b - a, exact=True) == 2*x
+    assert (2*x).replace(a*x + b, lambda a, b: b - a) == 2*x
+    assert (2*x).replace(a*x + b, lambda a, b: b - a, exact=False) == 2/x
+
+    g = 2*sin(x**3)
+
+    assert g.replace(
+        lambda expr: expr.is_Number, lambda expr: expr**2) == 4*sin(x**9)
+
+    assert cos(x).replace(cos, sin, map=True) == (sin(x), {cos(x): sin(x)})
+    assert sin(x).replace(cos, sin) == sin(x)
+
+    cond, func = lambda x: x.is_Mul, lambda x: 2*x
+    assert (x*y).replace(cond, func, map=True) == (2*x*y, {x*y: 2*x*y})
+    assert (x*(1 + x*y)).replace(cond, func, map=True) == \
+        (2*x*(2*x*y + 1), {x*(2*x*y + 1): 2*x*(2*x*y + 1), x*y: 2*x*y})
+    assert (y*sin(x)).replace(sin, lambda expr: sin(expr)/y, map=True) == \
+        (sin(x), {sin(x): sin(x)/y})
+    # if not simultaneous then y*sin(x) -> y*sin(x)/y = sin(x) -> sin(x)/y
+    assert (y*sin(x)).replace(sin, lambda expr: sin(expr)/y,
+        simultaneous=False) == sin(x)/y
+    assert (x**2 + O(x**3)).replace(Pow, lambda b, e: b**e/e
+        ) == x**2/2 + O(x**3)
+    assert (x**2 + O(x**3)).replace(Pow, lambda b, e: b**e/e,
+        simultaneous=False) == x**2/2 + O(x**3)
+    assert (x*(x*y + 3)).replace(lambda x: x.is_Mul, lambda x: 2 + x) == \
+        x*(x*y + 5) + 2
+    e = (x*y + 1)*(2*x*y + 1) + 1
+    assert e.replace(cond, func, map=True) == (
+        2*((2*x*y + 1)*(4*x*y + 1)) + 1,
+        {2*x*y: 4*x*y, x*y: 2*x*y, (2*x*y + 1)*(4*x*y + 1):
+        2*((2*x*y + 1)*(4*x*y + 1))})
+    assert x.replace(x, y) == y
+    assert (x + 1).replace(1, 2) == x + 2
+
+    # https://groups.google.com/forum/#!topic/sympy/8wCgeC95tz0
+    n1, n2, n3 = symbols('n1:4', commutative=False)
+    assert (n1*f(n2)).replace(f, lambda x: x) == n1*n2
+    assert (n3*f(n2)).replace(f, lambda x: x) == n3*n2
+
+    # issue 16725
+    assert S.Zero.replace(Wild('x'), 1) == 1
+    # let the user override the default decision of False
+    assert S.Zero.replace(Wild('x'), 1, exact=True) == 0
+
+
+def test_replace_integral():
+    # https://github.com/sympy/sympy/issues/27142
+    q, p, s, t = symbols('q p s t', cls=Wild)
+    a, b, c, d = symbols('a b c d')
+    i = Integral(a + b, (b, c, d))
+    pattern = Integral(q, (p, s, t))
+    assert i.replace(pattern, q) == a + b
+
+
+def test_find():
+    expr = (x + y + 2 + sin(3*x))
+
+    assert expr.find(lambda u: u.is_Integer) == {S(2), S(3)}
+    assert expr.find(lambda u: u.is_Symbol) == {x, y}
+
+    assert expr.find(lambda u: u.is_Integer, group=True) == {S(2): 1, S(3): 1}
+    assert expr.find(lambda u: u.is_Symbol, group=True) == {x: 2, y: 1}
+
+    assert expr.find(Integer) == {S(2), S(3)}
+    assert expr.find(Symbol) == {x, y}
+
+    assert expr.find(Integer, group=True) == {S(2): 1, S(3): 1}
+    assert expr.find(Symbol, group=True) == {x: 2, y: 1}
+
+    a = Wild('a')
+
+    expr = sin(sin(x)) + sin(x) + cos(x) + x
+
+    assert expr.find(lambda u: type(u) is sin) == {sin(x), sin(sin(x))}
+    assert expr.find(
+        lambda u: type(u) is sin, group=True) == {sin(x): 2, sin(sin(x)): 1}
+
+    assert expr.find(sin(a)) == {sin(x), sin(sin(x))}
+    assert expr.find(sin(a), group=True) == {sin(x): 2, sin(sin(x)): 1}
+
+    assert expr.find(sin) == {sin(x), sin(sin(x))}
+    assert expr.find(sin, group=True) == {sin(x): 2, sin(sin(x)): 1}
+
+
+def test_count():
+    expr = (x + y + 2 + sin(3*x))
+
+    assert expr.count(lambda u: u.is_Integer) == 2
+    assert expr.count(lambda u: u.is_Symbol) == 3
+
+    assert expr.count(Integer) == 2
+    assert expr.count(Symbol) == 3
+    assert expr.count(2) == 1
+
+    a = Wild('a')
+
+    assert expr.count(sin) == 1
+    assert expr.count(sin(a)) == 1
+    assert expr.count(lambda u: type(u) is sin) == 1
+
+    assert f(x).count(f(x)) == 1
+    assert f(x).diff(x).count(f(x)) == 1
+    assert f(x).diff(x).count(x) == 2
+
+
+def test_has_basics():
+    p = Wild('p')
+
+    assert sin(x).has(x)
+    assert sin(x).has(sin)
+    assert not sin(x).has(y)
+    assert not sin(x).has(cos)
+    assert f(x).has(x)
+    assert f(x).has(f)
+    assert not f(x).has(y)
+    assert not f(x).has(g)
+
+    assert f(x).diff(x).has(x)
+    assert f(x).diff(x).has(f)
+    assert f(x).diff(x).has(Derivative)
+    assert not f(x).diff(x).has(y)
+    assert not f(x).diff(x).has(g)
+    assert not f(x).diff(x).has(sin)
+
+    assert (x**2).has(Symbol)
+    assert not (x**2).has(Wild)
+    assert (2*p).has(Wild)
+
+    assert not x.has()
+
+    # see issue at https://github.com/sympy/sympy/issues/5190
+    assert not S(1).has(Wild)
+    assert not x.has(Wild)
+
+
+def test_has_multiple():
+    f = x**2*y + sin(2**t + log(z))
+
+    assert f.has(x)
+    assert f.has(y)
+    assert f.has(z)
+    assert f.has(t)
+
+    assert not f.has(u)
+
+    assert f.has(x, y, z, t)
+    assert f.has(x, y, z, t, u)
+
+    i = Integer(4400)
+
+    assert not i.has(x)
+
+    assert (i*x**i).has(x)
+    assert not (i*y**i).has(x)
+    assert (i*y**i).has(x, y)
+    assert not (i*y**i).has(x, z)
+
+
+def test_has_piecewise():
+    f = (x*y + 3/y)**(3 + 2)
+    p = Piecewise((g(x), x < -1), (1, x <= 1), (f, True))
+
+    assert p.has(x)
+    assert p.has(y)
+    assert not p.has(z)
+    assert p.has(1)
+    assert p.has(3)
+    assert not p.has(4)
+    assert p.has(f)
+    assert p.has(g)
+    assert not p.has(h)
+
+
+def test_has_iterative():
+    A, B, C = symbols('A,B,C', commutative=False)
+    f = x*gamma(x)*sin(x)*exp(x*y)*A*B*C*cos(x*A*B)
+
+    assert f.has(x)
+    assert f.has(x*y)
+    assert f.has(x*sin(x))
+    assert not f.has(x*sin(y))
+    assert f.has(x*A)
+    assert f.has(x*A*B)
+    assert not f.has(x*A*C)
+    assert f.has(x*A*B*C)
+    assert not f.has(x*A*C*B)
+    assert f.has(x*sin(x)*A*B*C)
+    assert not f.has(x*sin(x)*A*C*B)
+    assert not f.has(x*sin(y)*A*B*C)
+    assert f.has(x*gamma(x))
+    assert not f.has(x + sin(x))
+
+    assert (x & y & z).has(x & z)
+
+
+def test_has_integrals():
+    f = Integral(x**2 + sin(x*y*z), (x, 0, x + y + z))
+
+    assert f.has(x + y)
+    assert f.has(x + z)
+    assert f.has(y + z)
+
+    assert f.has(x*y)
+    assert f.has(x*z)
+    assert f.has(y*z)
+
+    assert not f.has(2*x + y)
+    assert not f.has(2*x*y)
+
+
+def test_has_tuple():
+    assert Tuple(x, y).has(x)
+    assert not Tuple(x, y).has(z)
+    assert Tuple(f(x), g(x)).has(x)
+    assert not Tuple(f(x), g(x)).has(y)
+    assert Tuple(f(x), g(x)).has(f)
+    assert Tuple(f(x), g(x)).has(f(x))
+    # XXX to be deprecated
+    #assert not Tuple(f, g).has(x)
+    #assert Tuple(f, g).has(f)
+    #assert not Tuple(f, g).has(h)
+    assert Tuple(True).has(True)
+    assert Tuple(True).has(S.true)
+    assert not Tuple(True).has(1)
+
+
+def test_has_units():
+    from sympy.physics.units import m, s
+
+    assert (x*m/s).has(x)
+    assert (x*m/s).has(y, z) is False
+
+
+def test_has_polys():
+    poly = Poly(x**2 + x*y*sin(z), x, y, t)
+
+    assert poly.has(x)
+    assert poly.has(x, y, z)
+    assert poly.has(x, y, z, t)
+
+
+def test_has_physics():
+    assert FockState((x, y)).has(x)
+
+
+def test_as_poly_as_expr():
+    f = x**2 + 2*x*y
+
+    assert f.as_poly().as_expr() == f
+    assert f.as_poly(x, y).as_expr() == f
+
+    assert (f + sin(x)).as_poly(x, y) is None
+
+    p = Poly(f, x, y)
+
+    assert p.as_poly() == p
+
+    # https://github.com/sympy/sympy/issues/20610
+    assert S(2).as_poly() is None
+    assert sqrt(2).as_poly(extension=True) is None
+
+    raises(AttributeError, lambda: Tuple(x, x).as_poly(x))
+    raises(AttributeError, lambda: Tuple(x ** 2, x, y).as_poly(x))
+
+
+def test_nonzero():
+    assert bool(S.Zero) is False
+    assert bool(S.One) is True
+    assert bool(x) is True
+    assert bool(x + y) is True
+    assert bool(x - x) is False
+    assert bool(x*y) is True
+    assert bool(x*1) is True
+    assert bool(x*0) is False
+
+
+def test_is_number():
+    assert Float(3.14).is_number is True
+    assert Integer(737).is_number is True
+    assert Rational(3, 2).is_number is True
+    assert Rational(8).is_number is True
+    assert x.is_number is False
+    assert (2*x).is_number is False
+    assert (x + y).is_number is False
+    assert log(2).is_number is True
+    assert log(x).is_number is False
+    assert (2 + log(2)).is_number is True
+    assert (8 + log(2)).is_number is True
+    assert (2 + log(x)).is_number is False
+    assert (8 + log(2) + x).is_number is False
+    assert (1 + x**2/x - x).is_number is True
+    assert Tuple(Integer(1)).is_number is False
+    assert Add(2, x).is_number is False
+    assert Mul(3, 4).is_number is True
+    assert Pow(log(2), 2).is_number is True
+    assert oo.is_number is True
+    g = WildFunction('g')
+    assert g.is_number is False
+    assert (2*g).is_number is False
+    assert (x**2).subs(x, 3).is_number is True
+
+    # test extensibility of .is_number
+    # on subinstances of Basic
+    class A(Basic):
+        pass
+    a = A()
+    assert a.is_number is False
+
+
+def test_as_coeff_add():
+    assert S(2).as_coeff_add() == (2, ())
+    assert S(3.0).as_coeff_add() == (0, (S(3.0),))
+    assert S(-3.0).as_coeff_add() == (0, (S(-3.0),))
+    assert x.as_coeff_add() == (0, (x,))
+    assert (x - 1).as_coeff_add() == (-1, (x,))
+    assert (x + 1).as_coeff_add() == (1, (x,))
+    assert (x + 2).as_coeff_add() == (2, (x,))
+    assert (x + y).as_coeff_add(y) == (x, (y,))
+    assert (3*x).as_coeff_add(y) == (3*x, ())
+    # don't do expansion
+    e = (x + y)**2
+    assert e.as_coeff_add(y) == (0, (e,))
+
+
+def test_as_coeff_mul():
+    assert S(2).as_coeff_mul() == (2, ())
+    assert S(3.0).as_coeff_mul() == (1, (S(3.0),))
+    assert S(-3.0).as_coeff_mul() == (-1, (S(3.0),))
+    assert S(-3.0).as_coeff_mul(rational=False) == (-S(3.0), ())
+    assert x.as_coeff_mul() == (1, (x,))
+    assert (-x).as_coeff_mul() == (-1, (x,))
+    assert (2*x).as_coeff_mul() == (2, (x,))
+    assert (x*y).as_coeff_mul(y) == (x, (y,))
+    assert (3 + x).as_coeff_mul() == (1, (3 + x,))
+    assert (3 + x).as_coeff_mul(y) == (3 + x, ())
+    # don't do expansion
+    e = exp(x + y)
+    assert e.as_coeff_mul(y) == (1, (e,))
+    e = 2**(x + y)
+    assert e.as_coeff_mul(y) == (1, (e,))
+    assert (1.1*x).as_coeff_mul(rational=False) == (1.1, (x,))
+    assert (1.1*x).as_coeff_mul() == (1, (1.1, x))
+    assert (-oo*x).as_coeff_mul(rational=True) == (-1, (oo, x))
+
+
+def test_as_coeff_exponent():
+    assert (3*x**4).as_coeff_exponent(x) == (3, 4)
+    assert (2*x**3).as_coeff_exponent(x) == (2, 3)
+    assert (4*x**2).as_coeff_exponent(x) == (4, 2)
+    assert (6*x**1).as_coeff_exponent(x) == (6, 1)
+    assert (3*x**0).as_coeff_exponent(x) == (3, 0)
+    assert (2*x**0).as_coeff_exponent(x) == (2, 0)
+    assert (1*x**0).as_coeff_exponent(x) == (1, 0)
+    assert (0*x**0).as_coeff_exponent(x) == (0, 0)
+    assert (-1*x**0).as_coeff_exponent(x) == (-1, 0)
+    assert (-2*x**0).as_coeff_exponent(x) == (-2, 0)
+    assert (2*x**3 + pi*x**3).as_coeff_exponent(x) == (2 + pi, 3)
+    assert (x*log(2)/(2*x + pi*x)).as_coeff_exponent(x) == \
+        (log(2)/(2 + pi), 0)
+    # issue 4784
+    D = Derivative
+    fx = D(f(x), x)
+    assert fx.as_coeff_exponent(f(x)) == (fx, 0)
+
+
+def test_extractions():
+    for base in (2, S.Exp1):
+        assert Pow(base**x, 3, evaluate=False
+            ).extract_multiplicatively(base**x) == base**(2*x)
+        assert (base**(5*x)).extract_multiplicatively(
+            base**(3*x)) == base**(2*x)
+    assert ((x*y)**3).extract_multiplicatively(x**2 * y) == x*y**2
+    assert ((x*y)**3).extract_multiplicatively(x**4 * y) is None
+    assert (2*x).extract_multiplicatively(2) == x
+    assert (2*x).extract_multiplicatively(3) is None
+    assert (2*x).extract_multiplicatively(-1) is None
+    assert (S.Half*x).extract_multiplicatively(3) == x/6
+    assert (sqrt(x)).extract_multiplicatively(x) is None
+    assert (sqrt(x)).extract_multiplicatively(1/x) is None
+    assert x.extract_multiplicatively(-x) is None
+    assert (-2 - 4*I).extract_multiplicatively(-2) == 1 + 2*I
+    assert (-2 - 4*I).extract_multiplicatively(3) is None
+    assert (-2*x - 4*y - 8).extract_multiplicatively(-2) == x + 2*y + 4
+    assert (-2*x*y - 4*x**2*y).extract_multiplicatively(-2*y) == 2*x**2 + x
+    assert (2*x*y + 4*x**2*y).extract_multiplicatively(2*y) == 2*x**2 + x
+    assert (-4*y**2*x).extract_multiplicatively(-3*y) is None
+    assert (2*x).extract_multiplicatively(1) == 2*x
+    assert (-oo).extract_multiplicatively(5) is -oo
+    assert (oo).extract_multiplicatively(5) is oo
+
+    assert ((x*y)**3).extract_additively(1) is None
+    assert (x + 1).extract_additively(x) == 1
+    assert (x + 1).extract_additively(2*x) is None
+    assert (x + 1).extract_additively(-x) is None
+    assert (-x + 1).extract_additively(2*x) is None
+    assert (2*x + 3).extract_additively(x) == x + 3
+    assert (2*x + 3).extract_additively(2) == 2*x + 1
+    assert (2*x + 3).extract_additively(3) == 2*x
+    assert (2*x + 3).extract_additively(-2) is None
+    assert (2*x + 3).extract_additively(3*x) is None
+    assert (2*x + 3).extract_additively(2*x) == 3
+    assert x.extract_additively(0) == x
+    assert S(2).extract_additively(x) is None
+    assert S(2.).extract_additively(2.) is S.Zero
+    assert S(2.).extract_additively(2) is S.Zero
+    assert S(2*x + 3).extract_additively(x + 1) == x + 2
+    assert S(2*x + 3).extract_additively(y + 1) is None
+    assert S(2*x - 3).extract_additively(x + 1) is None
+    assert S(2*x - 3).extract_additively(y + z) is None
+    assert ((a + 1)*x*4 + y).extract_additively(x).expand() == \
+        4*a*x + 3*x + y
+    assert ((a + 1)*x*4 + 3*y).extract_additively(x + 2*y).expand() == \
+        4*a*x + 3*x + y
+    assert (y*(x + 1)).extract_additively(x + 1) is None
+    assert ((y + 1)*(x + 1) + 3).extract_additively(x + 1) == \
+        y*(x + 1) + 3
+    assert ((x + y)*(x + 1) + x + y + 3).extract_additively(x + y) == \
+        x*(x + y) + 3
+    assert (x + y + 2*((x + y)*(x + 1)) + 3).extract_additively((x + y)*(x + 1)) == \
+        x + y + (x + 1)*(x + y) + 3
+    assert ((y + 1)*(x + 2*y + 1) + 3).extract_additively(y + 1) == \
+        (x + 2*y)*(y + 1) + 3
+    assert (-x - x*I).extract_additively(-x) == -I*x
+    # extraction does not leave artificats, now
+    assert (4*x*(y + 1) + y).extract_additively(x) == x*(4*y + 3) + y
+
+    n = Symbol("n", integer=True)
+    assert (Integer(-3)).could_extract_minus_sign() is True
+    assert (-n*x + x).could_extract_minus_sign() != \
+        (n*x - x).could_extract_minus_sign()
+    assert (x - y).could_extract_minus_sign() != \
+        (-x + y).could_extract_minus_sign()
+    assert (1 - x - y).could_extract_minus_sign() is True
+    assert (1 - x + y).could_extract_minus_sign() is False
+    assert ((-x - x*y)/y).could_extract_minus_sign() is False
+    assert ((x + x*y)/(-y)).could_extract_minus_sign() is True
+    assert ((x + x*y)/y).could_extract_minus_sign() is False
+    assert ((-x - y)/(x + y)).could_extract_minus_sign() is False
+
+    class sign_invariant(Function, Expr):
+        nargs = 1
+        def __neg__(self):
+            return self
+    foo = sign_invariant(x)
+    assert foo == -foo
+    assert foo.could_extract_minus_sign() is False
+    assert (x - y).could_extract_minus_sign() is False
+    assert (-x + y).could_extract_minus_sign() is True
+    assert (x - 1).could_extract_minus_sign() is False
+    assert (1 - x).could_extract_minus_sign() is True
+    assert (sqrt(2) - 1).could_extract_minus_sign() is True
+    assert (1 - sqrt(2)).could_extract_minus_sign() is False
+    # check that result is canonical
+    eq = (3*x + 15*y).extract_multiplicatively(3)
+    assert eq.args == eq.func(*eq.args).args
+
+
+def test_nan_extractions():
+    for r in (1, 0, I, nan):
+        assert nan.extract_additively(r) is None
+        assert nan.extract_multiplicatively(r) is None
+
+
+def test_coeff():
+    assert (x + 1).coeff(x + 1) == 1
+    assert (3*x).coeff(0) == 0
+    assert (z*(1 + x)*x**2).coeff(1 + x) == z*x**2
+    assert (1 + 2*x*x**(1 + x)).coeff(x*x**(1 + x)) == 2
+    assert (1 + 2*x**(y + z)).coeff(x**(y + z)) == 2
+    assert (3 + 2*x + 4*x**2).coeff(1) == 0
+    assert (3 + 2*x + 4*x**2).coeff(-1) == 0
+    assert (3 + 2*x + 4*x**2).coeff(x) == 2
+    assert (3 + 2*x + 4*x**2).coeff(x**2) == 4
+    assert (3 + 2*x + 4*x**2).coeff(x**3) == 0
+
+    assert (-x/8 + x*y).coeff(x) == Rational(-1, 8) + y
+    assert (-x/8 + x*y).coeff(-x) == S.One/8
+    assert (4*x).coeff(2*x) == 0
+    assert (2*x).coeff(2*x) == 1
+    assert (-oo*x).coeff(x*oo) == -1
+    assert (10*x).coeff(x, 0) == 0
+    assert (10*x).coeff(10*x, 0) == 0
+
+    n1, n2 = symbols('n1 n2', commutative=False)
+    assert (n1*n2).coeff(n1) == 1
+    assert (n1*n2).coeff(n2) == n1
+    assert (n1*n2 + x*n1).coeff(n1) == 1  # 1*n1*(n2+x)
+    assert (n2*n1 + x*n1).coeff(n1) == n2 + x
+    assert (n2*n1 + x*n1**2).coeff(n1) == n2
+    assert (n1**x).coeff(n1) == 0
+    assert (n1*n2 + n2*n1).coeff(n1) == 0
+    assert (2*(n1 + n2)*n2).coeff(n1 + n2, right=1) == n2
+    assert (2*(n1 + n2)*n2).coeff(n1 + n2, right=0) == 2
+
+    assert (2*f(x) + 3*f(x).diff(x)).coeff(f(x)) == 2
+
+    expr = z*(x + y)**2
+    expr2 = z*(x + y)**2 + z*(2*x + 2*y)**2
+    assert expr.coeff(z) == (x + y)**2
+    assert expr.coeff(x + y) == 0
+    assert expr2.coeff(z) == (x + y)**2 + (2*x + 2*y)**2
+
+    assert (x + y + 3*z).coeff(1) == x + y
+    assert (-x + 2*y).coeff(-1) == x
+    assert (x - 2*y).coeff(-1) == 2*y
+    assert (3 + 2*x + 4*x**2).coeff(1) == 0
+    assert (-x - 2*y).coeff(2) == -y
+    assert (x + sqrt(2)*x).coeff(sqrt(2)) == x
+    assert (3 + 2*x + 4*x**2).coeff(x) == 2
+    assert (3 + 2*x + 4*x**2).coeff(x**2) == 4
+    assert (3 + 2*x + 4*x**2).coeff(x**3) == 0
+    assert (z*(x + y)**2).coeff((x + y)**2) == z
+    assert (z*(x + y)**2).coeff(x + y) == 0
+    assert (2 + 2*x + (x + 1)*y).coeff(x + 1) == y
+
+    assert (x + 2*y + 3).coeff(1) == x
+    assert (x + 2*y + 3).coeff(x, 0) == 2*y + 3
+    assert (x**2 + 2*y + 3*x).coeff(x**2, 0) == 2*y + 3*x
+    assert x.coeff(0, 0) == 0
+    assert x.coeff(x, 0) == 0
+
+    n, m, o, l = symbols('n m o l', commutative=False)
+    assert n.coeff(n) == 1
+    assert y.coeff(n) == 0
+    assert (3*n).coeff(n) == 3
+    assert (2 + n).coeff(x*m) == 0
+    assert (2*x*n*m).coeff(x) == 2*n*m
+    assert (2 + n).coeff(x*m*n + y) == 0
+    assert (2*x*n*m).coeff(3*n) == 0
+    assert (n*m + m*n*m).coeff(n) == 1 + m
+    assert (n*m + m*n*m).coeff(n, right=True) == m  # = (1 + m)*n*m
+    assert (n*m + m*n).coeff(n) == 0
+    assert (n*m + o*m*n).coeff(m*n) == o
+    assert (n*m + o*m*n).coeff(m*n, right=True) == 1
+    assert (n*m + n*m*n).coeff(n*m, right=True) == 1 + n  # = n*m*(n + 1)
+
+    assert (x*y).coeff(z, 0) == x*y
+
+    assert (x*n + y*n + z*m).coeff(n) == x + y
+    assert (n*m + n*o + o*l).coeff(n, right=True) == m + o
+    assert (x*n*m*n + y*n*m*o + z*l).coeff(m, right=True) == x*n + y*o
+    assert (x*n*m*n + x*n*m*o + z*l).coeff(m, right=True) == n + o
+    assert (x*n*m*n + x*n*m*o + z*l).coeff(m) == x*n
+
+
+def test_coeff2():
+    r, kappa = symbols('r, kappa')
+    psi = Function("psi")
+    g = 1/r**2 * (2*r*psi(r).diff(r, 1) + r**2 * psi(r).diff(r, 2))
+    g = g.expand()
+    assert g.coeff(psi(r).diff(r)) == 2/r
+
+
+def test_coeff2_0():
+    r, kappa = symbols('r, kappa')
+    psi = Function("psi")
+    g = 1/r**2 * (2*r*psi(r).diff(r, 1) + r**2 * psi(r).diff(r, 2))
+    g = g.expand()
+
+    assert g.coeff(psi(r).diff(r, 2)) == 1
+
+
+def test_coeff_expand():
+    expr = z*(x + y)**2
+    expr2 = z*(x + y)**2 + z*(2*x + 2*y)**2
+    assert expr.coeff(z) == (x + y)**2
+    assert expr2.coeff(z) == (x + y)**2 + (2*x + 2*y)**2
+
+
+def test_integrate():
+    assert x.integrate(x) == x**2/2
+    assert x.integrate((x, 0, 1)) == S.Half
+
+
+def test_as_base_exp():
+    assert x.as_base_exp() == (x, S.One)
+    assert (x*y*z).as_base_exp() == (x*y*z, S.One)
+    assert (x + y + z).as_base_exp() == (x + y + z, S.One)
+    assert ((x + y)**z).as_base_exp() == (x + y, z)
+    assert (x**2*y**2).as_base_exp() == (x*y, 2)
+    assert (x**z*y**z).as_base_exp() == (x**z*y**z, S.One)
+
+
+def test_issue_4963():
+    assert hasattr(Mul(x, y), "is_commutative")
+    assert hasattr(Mul(x, y, evaluate=False), "is_commutative")
+    assert hasattr(Pow(x, y), "is_commutative")
+    assert hasattr(Pow(x, y, evaluate=False), "is_commutative")
+    expr = Mul(Pow(2, 2, evaluate=False), 3, evaluate=False) + 1
+    assert hasattr(expr, "is_commutative")
+
+
+def test_action_verbs():
+    assert nsimplify(1/(exp(3*pi*x/5) + 1)) == \
+        (1/(exp(3*pi*x/5) + 1)).nsimplify()
+    assert ratsimp(1/x + 1/y) == (1/x + 1/y).ratsimp()
+    assert trigsimp(log(x), deep=True) == (log(x)).trigsimp(deep=True)
+    assert radsimp(1/(2 + sqrt(2))) == (1/(2 + sqrt(2))).radsimp()
+    assert radsimp(1/(a + b*sqrt(c)), symbolic=False) == \
+        (1/(a + b*sqrt(c))).radsimp(symbolic=False)
+    assert powsimp(x**y*x**z*y**z, combine='all') == \
+        (x**y*x**z*y**z).powsimp(combine='all')
+    assert (x**t*y**t).powsimp(force=True) == (x*y)**t
+    assert simplify(x**y*x**z*y**z) == (x**y*x**z*y**z).simplify()
+    assert together(1/x + 1/y) == (1/x + 1/y).together()
+    assert collect(a*x**2 + b*x**2 + a*x - b*x + c, x) == \
+        (a*x**2 + b*x**2 + a*x - b*x + c).collect(x)
+    assert apart(y/(y + 2)/(y + 1), y) == (y/(y + 2)/(y + 1)).apart(y)
+    assert combsimp(y/(x + 2)/(x + 1)) == (y/(x + 2)/(x + 1)).combsimp()
+    assert gammasimp(gamma(x)/gamma(x-5)) == (gamma(x)/gamma(x-5)).gammasimp()
+    assert factor(x**2 + 5*x + 6) == (x**2 + 5*x + 6).factor()
+    assert refine(sqrt(x**2)) == sqrt(x**2).refine()
+    assert cancel((x**2 + 5*x + 6)/(x + 2)) == ((x**2 + 5*x + 6)/(x + 2)).cancel()
+
+
+def test_as_powers_dict():
+    assert x.as_powers_dict() == {x: 1}
+    assert (x**y*z).as_powers_dict() == {x: y, z: 1}
+    assert Mul(2, 2, evaluate=False).as_powers_dict() == {S(2): S(2)}
+    assert (x*y).as_powers_dict()[z] == 0
+    assert (x + y).as_powers_dict()[z] == 0
+
+
+def test_as_coefficients_dict():
+    check = [S.One, x, y, x*y, 1]
+    assert [Add(3*x, 2*x, y, 3).as_coefficients_dict()[i] for i in check] == \
+        [3, 5, 1, 0, 3]
+    assert [Add(3*x, 2*x, y, 3, evaluate=False).as_coefficients_dict()[i]
+            for i in check] == [3, 5, 1, 0, 3]
+    assert [(3*x*y).as_coefficients_dict()[i] for i in check] == \
+        [0, 0, 0, 3, 0]
+    assert [(3.0*x*y).as_coefficients_dict()[i] for i in check] == \
+        [0, 0, 0, 3.0, 0]
+    assert (3.0*x*y).as_coefficients_dict()[3.0*x*y] == 0
+    eq = x*(x + 1)*a + x*b + c/x
+    assert eq.as_coefficients_dict(x) == {x: b, 1/x: c,
+        x*(x + 1): a}
+    assert eq.expand().as_coefficients_dict(x) == {x**2: a, x: a + b, 1/x: c}
+    assert x.as_coefficients_dict() == {x: S.One}
+
+
+def test_args_cnc():
+    A = symbols('A', commutative=False)
+    assert (x + A).args_cnc() == \
+        [[], [x + A]]
+    assert (x + a).args_cnc() == \
+        [[a + x], []]
+    assert (x*a).args_cnc() == \
+        [[a, x], []]
+    assert (x*y*A*(A + 1)).args_cnc(cset=True) == \
+        [{x, y}, [A, 1 + A]]
+    assert Mul(x, x, evaluate=False).args_cnc(cset=True, warn=False) == \
+        [{x}, []]
+    assert Mul(x, x**2, evaluate=False).args_cnc(cset=True, warn=False) == \
+        [{x, x**2}, []]
+    raises(ValueError, lambda: Mul(x, x, evaluate=False).args_cnc(cset=True))
+    assert Mul(x, y, x, evaluate=False).args_cnc() == \
+        [[x, y, x], []]
+    # always split -1 from leading number
+    assert (-1.*x).args_cnc() == [[-1, 1.0, x], []]
+
+
+def test_new_rawargs():
+    n = Symbol('n', commutative=False)
+    a = x + n
+    assert a.is_commutative is False
+    assert a._new_rawargs(x).is_commutative
+    assert a._new_rawargs(x, y).is_commutative
+    assert a._new_rawargs(x, n).is_commutative is False
+    assert a._new_rawargs(x, y, n).is_commutative is False
+    m = x*n
+    assert m.is_commutative is False
+    assert m._new_rawargs(x).is_commutative
+    assert m._new_rawargs(n).is_commutative is False
+    assert m._new_rawargs(x, y).is_commutative
+    assert m._new_rawargs(x, n).is_commutative is False
+    assert m._new_rawargs(x, y, n).is_commutative is False
+
+    assert m._new_rawargs(x, n, reeval=False).is_commutative is False
+    assert m._new_rawargs(S.One) is S.One
+
+
+def test_issue_5226():
+    assert Add(evaluate=False) == 0
+    assert Mul(evaluate=False) == 1
+    assert Mul(x + y, evaluate=False).is_Add
+
+
+def test_free_symbols():
+    # free_symbols should return the free symbols of an object
+    assert S.One.free_symbols == set()
+    assert x.free_symbols == {x}
+    assert Integral(x, (x, 1, y)).free_symbols == {y}
+    assert (-Integral(x, (x, 1, y))).free_symbols == {y}
+    assert meter.free_symbols == set()
+    assert (meter**x).free_symbols == {x}
+
+
+def test_has_free():
+    assert x.has_free(x)
+    assert not x.has_free(y)
+    assert (x + y).has_free(x)
+    assert (x + y).has_free(*(x, z))
+    assert f(x).has_free(x)
+    assert f(x).has_free(f(x))
+    assert Integral(f(x), (f(x), 1, y)).has_free(y)
+    assert not Integral(f(x), (f(x), 1, y)).has_free(x)
+    assert not Integral(f(x), (f(x), 1, y)).has_free(f(x))
+    # simple extraction
+    assert (x + 1 + y).has_free(x + 1)
+    assert not (x + 2 + y).has_free(x + 1)
+    assert (2 + 3*x*y).has_free(3*x)
+    raises(TypeError, lambda: x.has_free({x, y}))
+    s = FiniteSet(1, 2)
+    assert Piecewise((s, x > 3), (4, True)).has_free(s)
+    assert not Piecewise((1, x > 3), (4, True)).has_free(s)
+    # can't make set of these, but fallback will handle
+    raises(TypeError, lambda: x.has_free(y, []))
+
+
+def test_has_xfree():
+    assert (x + 1).has_xfree({x})
+    assert ((x + 1)**2).has_xfree({x + 1})
+    assert not (x + y + 1).has_xfree({x + 1})
+    raises(TypeError, lambda: x.has_xfree(x))
+    raises(TypeError, lambda: x.has_xfree([x]))
+
+
+def test_issue_5300():
+    x = Symbol('x', commutative=False)
+    assert x*sqrt(2)/sqrt(6) == x*sqrt(3)/3
+
+
+def test_floordiv():
+    from sympy.functions.elementary.integers import floor
+    assert x // y == floor(x / y)
+
+
+def test_as_coeff_Mul():
+    assert Integer(3).as_coeff_Mul() == (Integer(3), Integer(1))
+    assert Rational(3, 4).as_coeff_Mul() == (Rational(3, 4), Integer(1))
+    assert Float(5.0).as_coeff_Mul() == (Float(5.0), Integer(1))
+    assert Float(0.0).as_coeff_Mul() == (Float(0.0), Integer(1))
+
+    assert (Integer(3)*x).as_coeff_Mul() == (Integer(3), x)
+    assert (Rational(3, 4)*x).as_coeff_Mul() == (Rational(3, 4), x)
+    assert (Float(5.0)*x).as_coeff_Mul() == (Float(5.0), x)
+
+    assert (Integer(3)*x*y).as_coeff_Mul() == (Integer(3), x*y)
+    assert (Rational(3, 4)*x*y).as_coeff_Mul() == (Rational(3, 4), x*y)
+    assert (Float(5.0)*x*y).as_coeff_Mul() == (Float(5.0), x*y)
+
+    assert (x).as_coeff_Mul() == (S.One, x)
+    assert (x*y).as_coeff_Mul() == (S.One, x*y)
+    assert (-oo*x).as_coeff_Mul(rational=True) == (-1, oo*x)
+
+
+def test_as_coeff_Add():
+    assert Integer(3).as_coeff_Add() == (Integer(3), Integer(0))
+    assert Rational(3, 4).as_coeff_Add() == (Rational(3, 4), Integer(0))
+    assert Float(5.0).as_coeff_Add() == (Float(5.0), Integer(0))
+
+    assert (Integer(3) + x).as_coeff_Add() == (Integer(3), x)
+    assert (Rational(3, 4) + x).as_coeff_Add() == (Rational(3, 4), x)
+    assert (Float(5.0) + x).as_coeff_Add() == (Float(5.0), x)
+    assert (Float(5.0) + x).as_coeff_Add(rational=True) == (0, Float(5.0) + x)
+
+    assert (Integer(3) + x + y).as_coeff_Add() == (Integer(3), x + y)
+    assert (Rational(3, 4) + x + y).as_coeff_Add() == (Rational(3, 4), x + y)
+    assert (Float(5.0) + x + y).as_coeff_Add() == (Float(5.0), x + y)
+
+    assert (x).as_coeff_Add() == (S.Zero, x)
+    assert (x*y).as_coeff_Add() == (S.Zero, x*y)
+
+
+def test_expr_sorting():
+
+    exprs = [1/x**2, 1/x, sqrt(sqrt(x)), sqrt(x), x, sqrt(x)**3, x**2]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [x, 2*x, 2*x**2, 2*x**3, x**n, 2*x**n, sin(x), sin(x)**n,
+             sin(x**2), cos(x), cos(x**2), tan(x)]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [x + 1, x**2 + x + 1, x**3 + x**2 + x + 1]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [S(4), x - 3*I/2, x + 3*I/2, x - 4*I + 1, x + 4*I + 1]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [f(1), f(2), f(3), f(1, 2, 3), g(1), g(2), g(3), g(1, 2, 3)]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [f(x), g(x), exp(x), sin(x), cos(x), factorial(x)]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [Tuple(x, y), Tuple(x, z), Tuple(x, y, z)]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [[3], [1, 2]]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [[1, 2], [2, 3]]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [[1, 2], [1, 2, 3]]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [{x: -y}, {x: y}]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    exprs = [{1}, {1, 2}]
+    assert sorted(exprs, key=default_sort_key) == exprs
+
+    a, b = exprs = [Dummy('x'), Dummy('x')]
+    assert sorted([b, a], key=default_sort_key) == exprs
+
+
+def test_as_ordered_factors():
+
+    assert x.as_ordered_factors() == [x]
+    assert (2*x*x**n*sin(x)*cos(x)).as_ordered_factors() \
+        == [Integer(2), x, x**n, sin(x), cos(x)]
+
+    args = [f(1), f(2), f(3), f(1, 2, 3), g(1), g(2), g(3), g(1, 2, 3)]
+    expr = Mul(*args)
+
+    assert expr.as_ordered_factors() == args
+
+    A, B = symbols('A,B', commutative=False)
+
+    assert (A*B).as_ordered_factors() == [A, B]
+    assert (B*A).as_ordered_factors() == [B, A]
+
+
+def test_as_ordered_terms():
+
+    assert x.as_ordered_terms() == [x]
+    assert (sin(x)**2*cos(x) + sin(x)*cos(x)**2 + 1).as_ordered_terms() \
+        == [sin(x)**2*cos(x), sin(x)*cos(x)**2, 1]
+
+    args = [f(1), f(2), f(3), f(1, 2, 3), g(1), g(2), g(3), g(1, 2, 3)]
+    expr = Add(*args)
+
+    assert expr.as_ordered_terms() == args
+
+    assert (1 + 4*sqrt(3)*pi*x).as_ordered_terms() == [4*pi*x*sqrt(3), 1]
+
+    assert ( 2 + 3*I).as_ordered_terms() == [2, 3*I]
+    assert (-2 + 3*I).as_ordered_terms() == [-2, 3*I]
+    assert ( 2 - 3*I).as_ordered_terms() == [2, -3*I]
+    assert (-2 - 3*I).as_ordered_terms() == [-2, -3*I]
+
+    assert ( 4 + 3*I).as_ordered_terms() == [4, 3*I]
+    assert (-4 + 3*I).as_ordered_terms() == [-4, 3*I]
+    assert ( 4 - 3*I).as_ordered_terms() == [4, -3*I]
+    assert (-4 - 3*I).as_ordered_terms() == [-4, -3*I]
+
+    e = x**2*y**2 + x*y**4 + y + 2
+
+    assert e.as_ordered_terms(order="lex") == [x**2*y**2, x*y**4, y, 2]
+    assert e.as_ordered_terms(order="grlex") == [x*y**4, x**2*y**2, y, 2]
+    assert e.as_ordered_terms(order="rev-lex") == [2, y, x*y**4, x**2*y**2]
+    assert e.as_ordered_terms(order="rev-grlex") == [2, y, x**2*y**2, x*y**4]
+
+    k = symbols('k')
+    assert k.as_ordered_terms(data=True) == ([(k, ((1.0, 0.0), (1,), ()))], [k])
+
+
+def test_sort_key_atomic_expr():
+    from sympy.physics.units import m, s
+    assert sorted([-m, s], key=lambda arg: arg.sort_key()) == [-m, s]
+
+
+def test_eval_interval():
+    assert exp(x)._eval_interval(*Tuple(x, 0, 1)) == exp(1) - exp(0)
+
+    # issue 4199
+    a = x/y
+    raises(NotImplementedError, lambda: a._eval_interval(x, S.Zero, oo)._eval_interval(y, oo, S.Zero))
+    raises(NotImplementedError, lambda: a._eval_interval(x, S.Zero, oo)._eval_interval(y, S.Zero, oo))
+    a = x - y
+    raises(NotImplementedError, lambda: a._eval_interval(x, S.One, oo)._eval_interval(y, oo, S.One))
+    raises(ValueError, lambda: x._eval_interval(x, None, None))
+    a = -y*Heaviside(x - y)
+    assert a._eval_interval(x, -oo, oo) == -y
+    assert a._eval_interval(x, oo, -oo) == y
+
+
+def test_eval_interval_zoo():
+    # Test that limit is used when zoo is returned
+    assert Si(1/x)._eval_interval(x, S.Zero, S.One) == -pi/2 + Si(1)
+
+
+def test_primitive():
+    assert (3*(x + 1)**2).primitive() == (3, (x + 1)**2)
+    assert (6*x + 2).primitive() == (2, 3*x + 1)
+    assert (x/2 + 3).primitive() == (S.Half, x + 6)
+    eq = (6*x + 2)*(x/2 + 3)
+    assert eq.primitive()[0] == 1
+    eq = (2 + 2*x)**2
+    assert eq.primitive()[0] == 1
+    assert (4.0*x).primitive() == (1, 4.0*x)
+    assert (4.0*x + y/2).primitive() == (S.Half, 8.0*x + y)
+    assert (-2*x).primitive() == (2, -x)
+    assert Add(5*z/7, 0.5*x, 3*y/2, evaluate=False).primitive() == \
+        (S.One/14, 7.0*x + 21*y + 10*z)
+    for i in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]:
+        assert (i + x/3).primitive() == \
+            (S.One/3, i + x)
+    assert (S.Infinity + 2*x/3 + 4*y/7).primitive() == \
+        (S.One/21, 14*x + 12*y + oo)
+    assert S.Zero.primitive() == (S.One, S.Zero)
+
+
+def test_issue_5843():
+    a = 1 + x
+    assert (2*a).extract_multiplicatively(a) == 2
+    assert (4*a).extract_multiplicatively(2*a) == 2
+    assert ((3*a)*(2*a)).extract_multiplicatively(a) == 6*a
+
+
+def test_is_constant():
+    from sympy.solvers.solvers import checksol
+    assert Sum(x, (x, 1, 10)).is_constant() is True
+    assert Sum(x, (x, 1, n)).is_constant() is False
+    assert Sum(x, (x, 1, n)).is_constant(y) is True
+    assert Sum(x, (x, 1, n)).is_constant(n) is False
+    assert Sum(x, (x, 1, n)).is_constant(x) is True
+    eq = a*cos(x)**2 + a*sin(x)**2 - a
+    assert eq.is_constant() is True
+    assert eq.subs({x: pi, a: 2}) == eq.subs({x: pi, a: 3}) == 0
+    assert x.is_constant() is False
+    assert x.is_constant(y) is True
+    assert log(x/y).is_constant() is False
+
+    assert checksol(x, x, Sum(x, (x, 1, n))) is False
+    assert checksol(x, x, Sum(x, (x, 1, n))) is False
+    assert f(1).is_constant
+    assert checksol(x, x, f(x)) is False
+
+    assert Pow(x, S.Zero, evaluate=False).is_constant() is True  # == 1
+    assert Pow(S.Zero, x, evaluate=False).is_constant() is False  # == 0 or 1
+    assert (2**x).is_constant() is False
+    assert Pow(S(2), S(3), evaluate=False).is_constant() is True
+
+    z1, z2 = symbols('z1 z2', zero=True)
+    assert (z1 + 2*z2).is_constant() is True
+
+    assert meter.is_constant() is True
+    assert (3*meter).is_constant() is True
+    assert (x*meter).is_constant() is False
+
+
+def test_equals():
+    assert (-3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2).equals(0)
+    assert (x**2 - 1).equals((x + 1)*(x - 1))
+    assert (cos(x)**2 + sin(x)**2).equals(1)
+    assert (a*cos(x)**2 + a*sin(x)**2).equals(a)
+    r = sqrt(2)
+    assert (-1/(r + r*x) + 1/r/(1 + x)).equals(0)
+    assert factorial(x + 1).equals((x + 1)*factorial(x))
+    assert sqrt(3).equals(2*sqrt(3)) is False
+    assert (sqrt(5)*sqrt(3)).equals(sqrt(3)) is False
+    assert (sqrt(5) + sqrt(3)).equals(0) is False
+    assert (sqrt(5) + pi).equals(0) is False
+    assert meter.equals(0) is False
+    assert (3*meter**2).equals(0) is False
+    eq = -(-1)**(S(3)/4)*6**(S.One/4) + (-6)**(S.One/4)*I
+    if eq != 0:  # if canonicalization makes this zero, skip the test
+        assert eq.equals(0)
+    assert sqrt(x).equals(0) is False
+
+    # from integrate(x*sqrt(1 + 2*x), x);
+    # diff is zero only when assumptions allow
+    i = 2*sqrt(2)*x**(S(5)/2)*(1 + 1/(2*x))**(S(5)/2)/5 + \
+        2*sqrt(2)*x**(S(3)/2)*(1 + 1/(2*x))**(S(5)/2)/(-6 - 3/x)
+    ans = sqrt(2*x + 1)*(6*x**2 + x - 1)/15
+    diff = i - ans
+    assert diff.equals(0) is None  # should be False, but previously this was False due to wrong intermediate result
+    assert diff.subs(x, Rational(-1, 2)/2) == 7*sqrt(2)/120
+    # there are regions for x for which the expression is True, for
+    # example, when x < -1/2 or x > 0 the expression is zero
+    p = Symbol('p', positive=True)
+    assert diff.subs(x, p).equals(0) is True
+    assert diff.subs(x, -1).equals(0) is True
+
+    # prove via minimal_polynomial or self-consistency
+    eq = sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) - sqrt(10 + 6*sqrt(3))
+    assert eq.equals(0)
+    q = 3**Rational(1, 3) + 3
+    p = expand(q**3)**Rational(1, 3)
+    assert (p - q).equals(0)
+
+    # issue 6829
+    # eq = q*x + q/4 + x**4 + x**3 + 2*x**2 - S.One/3
+    # z = eq.subs(x, solve(eq, x)[0])
+    q = symbols('q')
+    z = (q*(-sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/12)/2 - sqrt((2*q - S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 -
+    S(2197)/13824)**(S.One/3) - S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 -
+    S(2197)/13824)**(S.One/3) - S(13)/6)/2 - S.One/4) + q/4 + (-sqrt(-2*(-(q
+    - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - S(13)/12)/2 - sqrt((2*q
+    - S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/6)/2 - S.One/4)**4 + (-sqrt(-2*(-(q - S(7)/8)**S(2)/8 -
+    S(2197)/13824)**(S.One/3) - S(13)/12)/2 - sqrt((2*q -
+    S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/6)/2 - S.One/4)**3 + 2*(-sqrt(-2*(-(q - S(7)/8)**S(2)/8 -
+    S(2197)/13824)**(S.One/3) - S(13)/12)/2 - sqrt((2*q -
+    S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) -
+    S(13)/6)/2 - S.One/4)**2 - Rational(1, 3))
+    assert z.equals(0)
+
+
+def test_random():
+    from sympy.functions.combinatorial.numbers import lucas
+    from sympy.simplify.simplify import posify
+    assert posify(x)[0]._random() is not None
+    assert lucas(n)._random(2, -2, 0, -1, 1) is None
+
+    # issue 8662
+    assert Piecewise((Max(x, y), z))._random() is None
+
+
+def test_round():
+    assert str(Float('0.1249999').round(2)) == '0.12'
+    d20 = 12345678901234567890
+    ans = S(d20).round(2)
+    assert ans.is_Integer and ans == d20
+    ans = S(d20).round(-2)
+    assert ans.is_Integer and ans == 12345678901234567900
+    assert str(S('1/7').round(4)) == '0.1429'
+    assert str(S('.[12345]').round(4)) == '0.1235'
+    assert str(S('.1349').round(2)) == '0.13'
+    n = S(12345)
+    ans = n.round()
+    assert ans.is_Integer
+    assert ans == n
+    ans = n.round(1)
+    assert ans.is_Integer
+    assert ans == n
+    ans = n.round(4)
+    assert ans.is_Integer
+    assert ans == n
+    assert n.round(-1) == 12340
+
+    r = Float(str(n)).round(-4)
+    assert r == 10000.0
+
+    assert n.round(-5) == 0
+
+    assert str((pi + sqrt(2)).round(2)) == '4.56'
+    assert (10*(pi + sqrt(2))).round(-1) == 50.0
+    raises(TypeError, lambda: round(x + 2, 2))
+    assert str(S(2.3).round(1)) == '2.3'
+    # rounding in SymPy (as in Decimal) should be
+    # exact for the given precision; we check here
+    # that when a 5 follows the last digit that
+    # the rounded digit will be even.
+    for i in range(-99, 100):
+        # construct a decimal that ends in 5, e.g. 123 -> 0.1235
+        s = str(abs(i))
+        p = len(s)  # we are going to round to the last digit of i
+        n = '0.%s5' % s  # put a 5 after i's digits
+        j = p + 2  # 2 for '0.'
+        if i < 0:  # 1 for '-'
+            j += 1
+            n = '-' + n
+        v = str(Float(n).round(p))[:j]  # pertinent digits
+        if v.endswith('.'):
+            continue  # it ends with 0 which is even
+        L = int(v[-1])  # last digit
+        assert L % 2 == 0, (n, '->', v)
+
+    assert (Float(.3, 3) + 2*pi).round() == 7
+    assert (Float(.3, 3) + 2*pi*100).round() == 629
+    assert (pi + 2*E*I).round() == 3 + 5*I
+    # don't let request for extra precision give more than
+    # what is known (in this case, only 3 digits)
+    assert str((Float(.03, 3) + 2*pi/100).round(5)) == '0.0928'
+    assert str((Float(.03, 3) + 2*pi/100).round(4)) == '0.0928'
+
+    assert S.Zero.round() == 0
+
+    a = (Add(1, Float('1.' + '9'*27, ''), evaluate=False))
+    assert a.round(10) == Float('3.000000000000000000000000000', '')
+    assert a.round(25) == Float('3.000000000000000000000000000', '')
+    assert a.round(26) == Float('3.000000000000000000000000000', '')
+    assert a.round(27) == Float('2.999999999999999999999999999', '')
+    assert a.round(30) == Float('2.999999999999999999999999999', '')
+    #assert a.round(10) == Float('3.0000000000', '')
+    #assert a.round(25) == Float('3.0000000000000000000000000', '')
+    #assert a.round(26) == Float('3.00000000000000000000000000', '')
+    #assert a.round(27) == Float('2.999999999999999999999999999', '')
+    #assert a.round(30) == Float('2.999999999999999999999999999', '')
+
+    # XXX: Should round set the precision of the result?
+    #      The previous version of the tests above is this but they only pass
+    #      because Floats with unequal precision compare equal:
+    #
+    # assert a.round(10) == Float('3.0000000000', '')
+    # assert a.round(25) == Float('3.0000000000000000000000000', '')
+    # assert a.round(26) == Float('3.00000000000000000000000000', '')
+    # assert a.round(27) == Float('2.999999999999999999999999999', '')
+    # assert a.round(30) == Float('2.999999999999999999999999999', '')
+
+    raises(TypeError, lambda: x.round())
+    raises(TypeError, lambda: f(1).round())
+
+    # exact magnitude of 10
+    assert str(S.One.round()) == '1'
+    assert str(S(100).round()) == '100'
+
+    # applied to real and imaginary portions
+    assert (2*pi + E*I).round() == 6 + 3*I
+    assert (2*pi + I/10).round() == 6
+    assert (pi/10 + 2*I).round() == 2*I
+    # the lhs re and im parts are Float with dps of 2
+    # and those on the right have dps of 15 so they won't compare
+    # equal unless we use string or compare components (which will
+    # then coerce the floats to the same precision) or re-create
+    # the floats
+    assert str((pi/10 + E*I).round(2)) == '0.31 + 2.72*I'
+    assert str((pi/10 + E*I).round(2).as_real_imag()) == '(0.31, 2.72)'
+    assert str((pi/10 + E*I).round(2)) == '0.31 + 2.72*I'
+
+    # issue 6914
+    assert (I**(I + 3)).round(3) == Float('-0.208', '')*I
+
+    # issue 8720
+    assert S(-123.6).round() == -124
+    assert S(-1.5).round() == -2
+    assert S(-100.5).round() == -100
+    assert S(-1.5 - 10.5*I).round() == -2 - 10*I
+
+    # issue 7961
+    assert str(S(0.006).round(2)) == '0.01'
+    assert str(S(0.00106).round(4)) == '0.0011'
+
+    # issue 8147
+    assert S.NaN.round() is S.NaN
+    assert S.Infinity.round() is S.Infinity
+    assert S.NegativeInfinity.round() is S.NegativeInfinity
+    assert S.ComplexInfinity.round() is S.ComplexInfinity
+
+    # check that types match
+    for i in range(2):
+        fi = float(i)
+        # 2 args
+        assert all(type(round(i, p)) is int for p in (-1, 0, 1))
+        assert all(S(i).round(p).is_Integer for p in (-1, 0, 1))
+        assert all(type(round(fi, p)) is float for p in (-1, 0, 1))
+        assert all(S(fi).round(p).is_Float for p in (-1, 0, 1))
+        # 1 arg (p is None)
+        assert type(round(i)) is int
+        assert S(i).round().is_Integer
+        assert type(round(fi)) is int
+        assert S(fi).round().is_Integer
+
+        # issue 25698
+        n = 6000002
+        assert int(n*(log(n) + log(log(n)))) == 110130079
+        one = cos(2)**2 + sin(2)**2
+        eq = exp(one*I*pi)
+        qr, qi = eq.as_real_imag()
+        assert qi.round(2) == 0.0
+        assert eq.round(2) == -1.0
+        eq = one - 1/S(10**120)
+        assert S.true not in (eq > 1, eq < 1)
+        assert int(eq) == int(.9) == 0
+        assert int(-eq) == int(-.9) == 0
+
+
+def test_held_expression_UnevaluatedExpr():
+    x = symbols("x")
+    he = UnevaluatedExpr(1/x)
+    e1 = x*he
+
+    assert isinstance(e1, Mul)
+    assert e1.args == (x, he)
+    assert e1.doit() == 1
+    assert UnevaluatedExpr(Derivative(x, x)).doit(deep=False
+        ) == Derivative(x, x)
+    assert UnevaluatedExpr(Derivative(x, x)).doit() == 1
+
+    xx = Mul(x, x, evaluate=False)
+    assert xx != x**2
+
+    ue2 = UnevaluatedExpr(xx)
+    assert isinstance(ue2, UnevaluatedExpr)
+    assert ue2.args == (xx,)
+    assert ue2.doit() == x**2
+    assert ue2.doit(deep=False) == xx
+
+    x2 = UnevaluatedExpr(2)*2
+    assert type(x2) is Mul
+    assert x2.args == (2, UnevaluatedExpr(2))
+
+def test_round_exception_nostr():
+    # Don't use the string form of the expression in the round exception, as
+    # it's too slow
+    s = Symbol('bad')
+    try:
+        s.round()
+    except TypeError as e:
+        assert 'bad' not in str(e)
+    else:
+        # Did not raise
+        raise AssertionError("Did not raise")
+
+
+def test_extract_branch_factor():
+    assert exp_polar(2.0*I*pi).extract_branch_factor() == (1, 1)
+
+
+def test_identity_removal():
+    assert Add.make_args(x + 0) == (x,)
+    assert Mul.make_args(x*1) == (x,)
+
+
+def test_float_0():
+    assert Float(0.0) + 1 == Float(1.0)
+
+
+@XFAIL
+def test_float_0_fail():
+    assert Float(0.0)*x == Float(0.0)
+    assert (x + Float(0.0)).is_Add
+
+
+def test_issue_6325():
+    ans = (b**2 + z**2 - (b*(a + b*t) + z*(c + t*z))**2/(
+        (a + b*t)**2 + (c + t*z)**2))/sqrt((a + b*t)**2 + (c + t*z)**2)
+    e = sqrt((a + b*t)**2 + (c + z*t)**2)
+    assert diff(e, t, 2) == ans
+    assert e.diff(t, 2) == ans
+    assert diff(e, t, 2, simplify=False) != ans
+
+
+def test_issue_7426():
+    f1 = a % c
+    f2 = x % z
+    assert f1.equals(f2) is None
+
+
+def test_issue_11122():
+    x = Symbol('x', extended_positive=False)
+    assert unchanged(Gt, x, 0)  # (x > 0)
+    # (x > 0) should remain unevaluated after PR #16956
+
+    x = Symbol('x', positive=False, real=True)
+    assert (x > 0) is S.false
+
+
+def test_issue_10651():
+    x = Symbol('x', real=True)
+    e1 = (-1 + x)/(1 - x)
+    e3 = (4*x**2 - 4)/((1 - x)*(1 + x))
+    e4 = 1/(cos(x)**2) - (tan(x))**2
+    x = Symbol('x', positive=True)
+    e5 = (1 + x)/x
+    assert e1.is_constant() is None
+    assert e3.is_constant() is None
+    assert e4.is_constant() is None
+    assert e5.is_constant() is False
+
+
+def test_issue_10161():
+    x = symbols('x', real=True)
+    assert x*abs(x)*abs(x) == x**3
+
+
+def test_issue_10755():
+    x = symbols('x')
+    raises(TypeError, lambda: int(log(x)))
+    raises(TypeError, lambda: log(x).round(2))
+
+
+def test_issue_11877():
+    x = symbols('x')
+    assert integrate(log(S.Half - x), (x, 0, S.Half)) == Rational(-1, 2) -log(2)/2
+
+
+def test_normal():
+    x = symbols('x')
+    e = Mul(S.Half, 1 + x, evaluate=False)
+    assert e.normal() == e
+
+
+def test_expr():
+    x = symbols('x')
+    raises(TypeError, lambda: tan(x).series(x, 2, oo, "+"))
+
+
+def test_ExprBuilder():
+    eb = ExprBuilder(Mul)
+    eb.args.extend([x, x])
+    assert eb.build() == x**2
+
+
+def test_issue_22020():
+    from sympy.parsing.sympy_parser import parse_expr
+    x = parse_expr("log((2*V/3-V)/C)/-(R+r)*C")
+    y = parse_expr("log((2*V/3-V)/C)/-(R+r)*2")
+    assert x.equals(y) is False
+
+
+def test_non_string_equality():
+    # Expressions should not compare equal to strings
+    x = symbols('x')
+    one = sympify(1)
+    assert (x == 'x') is False
+    assert (x != 'x') is True
+    assert (one == '1') is False
+    assert (one != '1') is True
+    assert (x + 1 == 'x + 1') is False
+    assert (x + 1 != 'x + 1') is True
+
+    # Make sure == doesn't try to convert the resulting expression to a string
+    # (e.g., by calling sympify() instead of _sympify())
+
+    class BadRepr:
+        def __repr__(self):
+            raise RuntimeError
+
+    assert (x == BadRepr()) is False
+    assert (x != BadRepr()) is True
+
+
+def test_21494():
+    from sympy.testing.pytest import warns_deprecated_sympy
+
+    with warns_deprecated_sympy():
+        assert x.expr_free_symbols == {x}
+
+    with warns_deprecated_sympy():
+        assert Basic().expr_free_symbols == set()
+
+    with warns_deprecated_sympy():
+        assert S(2).expr_free_symbols == {S(2)}
+
+    with warns_deprecated_sympy():
+        assert Indexed("A", x).expr_free_symbols == {Indexed("A", x)}
+
+    with warns_deprecated_sympy():
+        assert Subs(x, x, 0).expr_free_symbols == set()
+
+
+def test_Expr__eq__iterable_handling():
+    assert x != range(3)
+
+
+def test_format():
+    assert '{:1.2f}'.format(S.Zero) == '0.00'
+    assert '{:+3.0f}'.format(S(3)) == ' +3'
+    assert '{:23.20f}'.format(pi) == ' 3.14159265358979323846'
+    assert '{:50.48f}'.format(exp(sin(1))) == '2.319776824715853173956590377503266813254904772376'
+
+
+def test_issue_24045():
+    assert powsimp(exp(a)/((c*a - c*b)*(Float(1.0)*c*a - Float(1.0)*c*b)))  # doesn't raise
+
+
+def test__unevaluated_Mul():
+    A, B = symbols('A B', commutative=False)
+    assert _unevaluated_Mul(x, A, B, S(2), A).args == (2, x, A, B, A)
+    assert _unevaluated_Mul(-x*A*B, S(2), A).args == (-2, x, A, B, A)
+
+
+def test_Float_zero_division_error():
+    # issue 27165
+    assert Float('1.7567e-1417').round(15) == Float(0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_exprtools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_exprtools.py
new file mode 100644
index 0000000000000000000000000000000000000000..b550db1606866fb76442980ea2139aaf61219525
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_exprtools.py
@@ -0,0 +1,493 @@
+"""Tests for tools for manipulating of large commutative expressions. """
+
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import (Dict, Tuple)
+from sympy.core.function import Function
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Rational, oo)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import (root, sqrt)
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.integrals.integrals import Integral
+from sympy.series.order import O
+from sympy.sets.sets import Interval
+from sympy.simplify.radsimp import collect
+from sympy.simplify.simplify import simplify
+from sympy.core.exprtools import (decompose_power, Factors, Term, _gcd_terms,
+                                  gcd_terms, factor_terms, factor_nc, _mask_nc,
+                                  _monotonic_sign)
+from sympy.core.mul import _keep_coeff as _keep_coeff
+from sympy.simplify.cse_opts import sub_pre
+from sympy.testing.pytest import raises
+
+from sympy.abc import a, b, t, x, y, z
+
+
+def test_decompose_power():
+    assert decompose_power(x) == (x, 1)
+    assert decompose_power(x**2) == (x, 2)
+    assert decompose_power(x**(2*y)) == (x**y, 2)
+    assert decompose_power(x**(2*y/3)) == (x**(y/3), 2)
+    assert decompose_power(x**(y*Rational(2, 3))) == (x**(y/3), 2)
+
+
+def test_Factors():
+    assert Factors() == Factors({}) == Factors(S.One)
+    assert Factors().as_expr() is S.One
+    assert Factors({x: 2, y: 3, sin(x): 4}).as_expr() == x**2*y**3*sin(x)**4
+    assert Factors(S.Infinity) == Factors({oo: 1})
+    assert Factors(S.NegativeInfinity) == Factors({oo: 1, -1: 1})
+    # issue #18059:
+    assert Factors((x**2)**S.Half).as_expr() == (x**2)**S.Half
+
+    a = Factors({x: 5, y: 3, z: 7})
+    b = Factors({      y: 4, z: 3, t: 10})
+
+    assert a.mul(b) == a*b == Factors({x: 5, y: 7, z: 10, t: 10})
+
+    assert a.div(b) == divmod(a, b) == \
+        (Factors({x: 5, z: 4}), Factors({y: 1, t: 10}))
+    assert a.quo(b) == a/b == Factors({x: 5, z: 4})
+    assert a.rem(b) == a % b == Factors({y: 1, t: 10})
+
+    assert a.pow(3) == a**3 == Factors({x: 15, y: 9, z: 21})
+    assert b.pow(3) == b**3 == Factors({y: 12, z: 9, t: 30})
+
+    assert a.gcd(b) == Factors({y: 3, z: 3})
+    assert a.lcm(b) == Factors({x: 5, y: 4, z: 7, t: 10})
+
+    a = Factors({x: 4, y: 7, t: 7})
+    b = Factors({z: 1, t: 3})
+
+    assert a.normal(b) == (Factors({x: 4, y: 7, t: 4}), Factors({z: 1}))
+
+    assert Factors(sqrt(2)*x).as_expr() == sqrt(2)*x
+
+    assert Factors(-I)*I == Factors()
+    assert Factors({S.NegativeOne: S(3)})*Factors({S.NegativeOne: S.One, I: S(5)}) == \
+        Factors(I)
+    assert Factors(sqrt(I)*I) == Factors(I**(S(3)/2)) == Factors({I: S(3)/2})
+    assert Factors({I: S(3)/2}).as_expr() == I**(S(3)/2)
+
+    assert Factors(S(2)**x).div(S(3)**x) == \
+        (Factors({S(2): x}), Factors({S(3): x}))
+    assert Factors(2**(2*x + 2)).div(S(8)) == \
+        (Factors({S(2): 2*x + 2}), Factors({S(8): S.One}))
+
+    # coverage
+    # /!\ things break if this is not True
+    assert Factors({S.NegativeOne: Rational(3, 2)}) == Factors({I: S.One, S.NegativeOne: S.One})
+    assert Factors({I: S.One, S.NegativeOne: Rational(1, 3)}).as_expr() == I*(-1)**Rational(1, 3)
+
+    assert Factors(-1.) == Factors({S.NegativeOne: S.One, S(1.): 1})
+    assert Factors(-2.) == Factors({S.NegativeOne: S.One, S(2.): 1})
+    assert Factors((-2.)**x) == Factors({S(-2.): x})
+    assert Factors(S(-2)) == Factors({S.NegativeOne: S.One, S(2): 1})
+    assert Factors(S.Half) == Factors({S(2): -S.One})
+    assert Factors(Rational(3, 2)) == Factors({S(3): S.One, S(2): S.NegativeOne})
+    assert Factors({I: S.One}) == Factors(I)
+    assert Factors({-1.0: 2, I: 1}) == Factors({S(1.0): 1, I: 1})
+    assert Factors({S.NegativeOne: Rational(-3, 2)}).as_expr() == I
+    A = symbols('A', commutative=False)
+    assert Factors(2*A**2) == Factors({S(2): 1, A**2: 1})
+    assert Factors(I) == Factors({I: S.One})
+    assert Factors(x).normal(S(2)) == (Factors(x), Factors(S(2)))
+    assert Factors(x).normal(S.Zero) == (Factors(), Factors(S.Zero))
+    raises(ZeroDivisionError, lambda: Factors(x).div(S.Zero))
+    assert Factors(x).mul(S(2)) == Factors(2*x)
+    assert Factors(x).mul(S.Zero).is_zero
+    assert Factors(x).mul(1/x).is_one
+    assert Factors(x**sqrt(2)**3).as_expr() == x**(2*sqrt(2))
+    assert Factors(x)**Factors(S(2)) == Factors(x**2)
+    assert Factors(x).gcd(S.Zero) == Factors(x)
+    assert Factors(x).lcm(S.Zero).is_zero
+    assert Factors(S.Zero).div(x) == (Factors(S.Zero), Factors())
+    assert Factors(x).div(x) == (Factors(), Factors())
+    assert Factors({x: .2})/Factors({x: .2}) == Factors()
+    assert Factors(x) != Factors()
+    assert Factors(S.Zero).normal(x) == (Factors(S.Zero), Factors())
+    n, d = x**(2 + y), x**2
+    f = Factors(n)
+    assert f.div(d) == f.normal(d) == (Factors(x**y), Factors())
+    assert f.gcd(d) == Factors()
+    d = x**y
+    assert f.div(d) == f.normal(d) == (Factors(x**2), Factors())
+    assert f.gcd(d) == Factors(d)
+    n = d = 2**x
+    f = Factors(n)
+    assert f.div(d) == f.normal(d) == (Factors(), Factors())
+    assert f.gcd(d) == Factors(d)
+    n, d = 2**x, 2**y
+    f = Factors(n)
+    assert f.div(d) == f.normal(d) == (Factors({S(2): x}), Factors({S(2): y}))
+    assert f.gcd(d) == Factors()
+
+    # extraction of constant only
+    n = x**(x + 3)
+    assert Factors(n).normal(x**-3) == (Factors({x: x + 6}), Factors({}))
+    assert Factors(n).normal(x**3) == (Factors({x: x}), Factors({}))
+    assert Factors(n).normal(x**4) == (Factors({x: x}), Factors({x: 1}))
+    assert Factors(n).normal(x**(y - 3)) == \
+        (Factors({x: x + 6}), Factors({x: y}))
+    assert Factors(n).normal(x**(y + 3)) == (Factors({x: x}), Factors({x: y}))
+    assert Factors(n).normal(x**(y + 4)) == \
+        (Factors({x: x}), Factors({x: y + 1}))
+
+    assert Factors(n).div(x**-3) == (Factors({x: x + 6}), Factors({}))
+    assert Factors(n).div(x**3) == (Factors({x: x}), Factors({}))
+    assert Factors(n).div(x**4) == (Factors({x: x}), Factors({x: 1}))
+    assert Factors(n).div(x**(y - 3)) == \
+        (Factors({x: x + 6}), Factors({x: y}))
+    assert Factors(n).div(x**(y + 3)) == (Factors({x: x}), Factors({x: y}))
+    assert Factors(n).div(x**(y + 4)) == \
+        (Factors({x: x}), Factors({x: y + 1}))
+
+    assert Factors(3 * x / 2) == Factors({3: 1, 2: -1, x: 1})
+    assert Factors(x * x / y) == Factors({x: 2, y: -1})
+    assert Factors(27 * x / y**9) == Factors({27: 1, x: 1, y: -9})
+
+
+def test_Term():
+    a = Term(4*x*y**2/z/t**3)
+    b = Term(2*x**3*y**5/t**3)
+
+    assert a == Term(4, Factors({x: 1, y: 2}), Factors({z: 1, t: 3}))
+    assert b == Term(2, Factors({x: 3, y: 5}), Factors({t: 3}))
+
+    assert a.as_expr() == 4*x*y**2/z/t**3
+    assert b.as_expr() == 2*x**3*y**5/t**3
+
+    assert a.inv() == \
+        Term(S.One/4, Factors({z: 1, t: 3}), Factors({x: 1, y: 2}))
+    assert b.inv() == Term(S.Half, Factors({t: 3}), Factors({x: 3, y: 5}))
+
+    assert a.mul(b) == a*b == \
+        Term(8, Factors({x: 4, y: 7}), Factors({z: 1, t: 6}))
+    assert a.quo(b) == a/b == Term(2, Factors({}), Factors({x: 2, y: 3, z: 1}))
+
+    assert a.pow(3) == a**3 == \
+        Term(64, Factors({x: 3, y: 6}), Factors({z: 3, t: 9}))
+    assert b.pow(3) == b**3 == Term(8, Factors({x: 9, y: 15}), Factors({t: 9}))
+
+    assert a.pow(-3) == a**(-3) == \
+        Term(S.One/64, Factors({z: 3, t: 9}), Factors({x: 3, y: 6}))
+    assert b.pow(-3) == b**(-3) == \
+        Term(S.One/8, Factors({t: 9}), Factors({x: 9, y: 15}))
+
+    assert a.gcd(b) == Term(2, Factors({x: 1, y: 2}), Factors({t: 3}))
+    assert a.lcm(b) == Term(4, Factors({x: 3, y: 5}), Factors({z: 1, t: 3}))
+
+    a = Term(4*x*y**2/z/t**3)
+    b = Term(2*x**3*y**5*t**7)
+
+    assert a.mul(b) == Term(8, Factors({x: 4, y: 7, t: 4}), Factors({z: 1}))
+
+    assert Term((2*x + 2)**3) == Term(8, Factors({x + 1: 3}), Factors({}))
+    assert Term((2*x + 2)*(3*x + 6)**2) == \
+        Term(18, Factors({x + 1: 1, x + 2: 2}), Factors({}))
+
+
+def test_gcd_terms():
+    f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + \
+        (2*x + 2)*(x + 6)/(5*x**2 + 5)
+
+    assert _gcd_terms(f) == ((Rational(6, 5))*((1 + x)/(1 + x**2)), 5 + x, 1)
+    assert _gcd_terms(Add.make_args(f)) == \
+        ((Rational(6, 5))*((1 + x)/(1 + x**2)), 5 + x, 1)
+
+    newf = (Rational(6, 5))*((1 + x)*(5 + x)/(1 + x**2))
+    assert gcd_terms(f) == newf
+    args = Add.make_args(f)
+    # non-Basic sequences of terms treated as terms of Add
+    assert gcd_terms(list(args)) == newf
+    assert gcd_terms(tuple(args)) == newf
+    assert gcd_terms(set(args)) == newf
+    # but a Basic sequence is treated as a container
+    assert gcd_terms(Tuple(*args)) != newf
+    assert gcd_terms(Basic(Tuple(S(1), 3*y + 3*x*y), Tuple(S(1), S(3)))) == \
+        Basic(Tuple(S(1), 3*y*(x + 1)), Tuple(S(1), S(3)))
+    # but we shouldn't change keys of a dictionary or some may be lost
+    assert gcd_terms(Dict((x*(1 + y), S(2)), (x + x*y, y + x*y))) == \
+        Dict({x*(y + 1): S(2), x + x*y: y*(1 + x)})
+
+    assert gcd_terms((2*x + 2)**3 + (2*x + 2)**2) == 4*(x + 1)**2*(2*x + 3)
+
+    assert gcd_terms(0) == 0
+    assert gcd_terms(1) == 1
+    assert gcd_terms(x) == x
+    assert gcd_terms(2 + 2*x) == Mul(2, 1 + x, evaluate=False)
+    arg = x*(2*x + 4*y)
+    garg = 2*x*(x + 2*y)
+    assert gcd_terms(arg) == garg
+    assert gcd_terms(sin(arg)) == sin(garg)
+
+    # issue 6139-like
+    alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
+    a = alpha**2 - alpha*x**2 + alpha + x**3 - x*(alpha + 1)
+    rep = (alpha, (1 + sqrt(5))/2 + alpha1*x + alpha2*x**2 + alpha3*x**3)
+    s = (a/(x - alpha)).subs(*rep).series(x, 0, 1)
+    assert simplify(collect(s, x)) == -sqrt(5)/2 - Rational(3, 2) + O(x)
+
+    # issue 5917
+    assert _gcd_terms([S.Zero, S.Zero]) == (0, 0, 1)
+    assert _gcd_terms([2*x + 4]) == (2, x + 2, 1)
+
+    eq = x/(x + 1/x)
+    assert gcd_terms(eq, fraction=False) == eq
+    eq = x/2/y + 1/x/y
+    assert gcd_terms(eq, fraction=True, clear=True) == \
+        (x**2 + 2)/(2*x*y)
+    assert gcd_terms(eq, fraction=True, clear=False) == \
+        (x**2/2 + 1)/(x*y)
+    assert gcd_terms(eq, fraction=False, clear=True) == \
+        (x + 2/x)/(2*y)
+    assert gcd_terms(eq, fraction=False, clear=False) == \
+        (x/2 + 1/x)/y
+
+
+def test_factor_terms():
+    A = Symbol('A', commutative=False)
+    assert factor_terms(9*(x + x*y + 1) + (3*x + 3)**(2 + 2*x)) == \
+        9*x*y + 9*x + _keep_coeff(S(3), x + 1)**_keep_coeff(S(2), x + 1) + 9
+    assert factor_terms(9*(x + x*y + 1) + (3)**(2 + 2*x)) == \
+        _keep_coeff(S(9), 3**(2*x) + x*y + x + 1)
+    assert factor_terms(3**(2 + 2*x) + a*3**(2 + 2*x)) == \
+        9*3**(2*x)*(a + 1)
+    assert factor_terms(x + x*A) == \
+        x*(1 + A)
+    assert factor_terms(sin(x + x*A)) == \
+        sin(x*(1 + A))
+    assert factor_terms((3*x + 3)**((2 + 2*x)/3)) == \
+        _keep_coeff(S(3), x + 1)**_keep_coeff(Rational(2, 3), x + 1)
+    assert factor_terms(x + (x*y + x)**(3*x + 3)) == \
+        x + (x*(y + 1))**_keep_coeff(S(3), x + 1)
+    assert factor_terms(a*(x + x*y) + b*(x*2 + y*x*2)) == \
+        x*(a + 2*b)*(y + 1)
+    i = Integral(x, (x, 0, oo))
+    assert factor_terms(i) == i
+
+    assert factor_terms(x/2 + y) == x/2 + y
+    # fraction doesn't apply to integer denominators
+    assert factor_terms(x/2 + y, fraction=True) == x/2 + y
+    # clear *does* apply to the integer denominators
+    assert factor_terms(x/2 + y, clear=True) == Mul(S.Half, x + 2*y, evaluate=False)
+
+    # check radical extraction
+    eq = sqrt(2) + sqrt(10)
+    assert factor_terms(eq) == eq
+    assert factor_terms(eq, radical=True) == sqrt(2)*(1 + sqrt(5))
+    eq = root(-6, 3) + root(6, 3)
+    assert factor_terms(eq, radical=True) == 6**(S.One/3)*(1 + (-1)**(S.One/3))
+
+    eq = [x + x*y]
+    ans = [x*(y + 1)]
+    for c in [list, tuple, set]:
+        assert factor_terms(c(eq)) == c(ans)
+    assert factor_terms(Tuple(x + x*y)) == Tuple(x*(y + 1))
+    assert factor_terms(Interval(0, 1)) == Interval(0, 1)
+    e = 1/sqrt(a/2 + 1)
+    assert factor_terms(e, clear=False) == 1/sqrt(a/2 + 1)
+    assert factor_terms(e, clear=True) == sqrt(2)/sqrt(a + 2)
+
+    eq = x/(x + 1/x) + 1/(x**2 + 1)
+    assert factor_terms(eq, fraction=False) == eq
+    assert factor_terms(eq, fraction=True) == 1
+
+    assert factor_terms((1/(x**3 + x**2) + 2/x**2)*y) == \
+        y*(2 + 1/(x + 1))/x**2
+
+    # if not True, then processesing for this in factor_terms is not necessary
+    assert gcd_terms(-x - y) == -x - y
+    assert factor_terms(-x - y) == Mul(-1, x + y, evaluate=False)
+
+    # if not True, then "special" processesing in factor_terms is not necessary
+    assert gcd_terms(exp(Mul(-1, x + 1))) == exp(-x - 1)
+    e = exp(-x - 2) + x
+    assert factor_terms(e) == exp(Mul(-1, x + 2, evaluate=False)) + x
+    assert factor_terms(e, sign=False) == e
+    assert factor_terms(exp(-4*x - 2) - x) == -x + exp(Mul(-2, 2*x + 1, evaluate=False))
+
+    # sum/integral tests
+    for F in (Sum, Integral):
+        assert factor_terms(F(x, (y, 1, 10))) == x * F(1, (y, 1, 10))
+        assert factor_terms(F(x, (y, 1, 10)) + x) == x * (1 + F(1, (y, 1, 10)))
+        assert factor_terms(F(x*y + x*y**2, (y, 1, 10))) == x*F(y*(y + 1), (y, 1, 10))
+
+    # expressions involving Pow terms with base 0
+    assert factor_terms(0**(x - 2) - 1) == 0**(x - 2) - 1
+    assert factor_terms(0**(x + 2) - 1) == 0**(x + 2) - 1
+    assert factor_terms((0**(x + 2) - 1).subs(x,-2)) == 0
+
+
+def test_xreplace():
+    e = Mul(2, 1 + x, evaluate=False)
+    assert e.xreplace({}) == e
+    assert e.xreplace({y: x}) == e
+
+
+def test_factor_nc():
+    x, y = symbols('x,y')
+    k = symbols('k', integer=True)
+    n, m, o = symbols('n,m,o', commutative=False)
+
+    # mul and multinomial expansion is needed
+    from sympy.core.function import _mexpand
+    e = x*(1 + y)**2
+    assert _mexpand(e) == x + x*2*y + x*y**2
+
+    def factor_nc_test(e):
+        ex = _mexpand(e)
+        assert ex.is_Add
+        f = factor_nc(ex)
+        assert not f.is_Add and _mexpand(f) == ex
+
+    factor_nc_test(x*(1 + y))
+    factor_nc_test(n*(x + 1))
+    factor_nc_test(n*(x + m))
+    factor_nc_test((x + m)*n)
+    factor_nc_test(n*m*(x*o + n*o*m)*n)
+    s = Sum(x, (x, 1, 2))
+    factor_nc_test(x*(1 + s))
+    factor_nc_test(x*(1 + s)*s)
+    factor_nc_test(x*(1 + sin(s)))
+    factor_nc_test((1 + n)**2)
+
+    factor_nc_test((x + n)*(x + m)*(x + y))
+    factor_nc_test(x*(n*m + 1))
+    factor_nc_test(x*(n*m + x))
+    factor_nc_test(x*(x*n*m + 1))
+    factor_nc_test(n*(m/x + o))
+    factor_nc_test(m*(n + o/2))
+    factor_nc_test(x*n*(x*m + 1))
+    factor_nc_test(x*(m*n + x*n*m))
+    factor_nc_test(n*(1 - m)*n**2)
+
+    factor_nc_test((n + m)**2)
+    factor_nc_test((n - m)*(n + m)**2)
+    factor_nc_test((n + m)**2*(n - m))
+    factor_nc_test((m - n)*(n + m)**2*(n - m))
+
+    assert factor_nc(n*(n + n*m)) == n**2*(1 + m)
+    assert factor_nc(m*(m*n + n*m*n**2)) == m*(m + n*m*n)*n
+    eq = m*sin(n) - sin(n)*m
+    assert factor_nc(eq) == eq
+
+    # for coverage:
+    from sympy.physics.secondquant import Commutator
+    from sympy.polys.polytools import factor
+    eq = 1 + x*Commutator(m, n)
+    assert factor_nc(eq) == eq
+    eq = x*Commutator(m, n) + x*Commutator(m, o)*Commutator(m, n)
+    assert factor(eq) == x*(1 + Commutator(m, o))*Commutator(m, n)
+
+    # issue 6534
+    assert (2*n + 2*m).factor() == 2*(n + m)
+
+    # issue 6701
+    _n = symbols('nz', zero=False, commutative=False)
+    assert factor_nc(_n**k + _n**(k + 1)) == _n**k*(1 + _n)
+    assert factor_nc((m*n)**k + (m*n)**(k + 1)) == (1 + m*n)*(m*n)**k
+
+    # issue 6918
+    assert factor_nc(-n*(2*x**2 + 2*x)) == -2*n*x*(x + 1)
+
+
+def test_issue_6360():
+    a, b = symbols("a b")
+    apb = a + b
+    eq = apb + apb**2*(-2*a - 2*b)
+    assert factor_terms(sub_pre(eq)) == a + b - 2*(a + b)**3
+
+
+def test_issue_7903():
+    a = symbols(r'a', real=True)
+    t = exp(I*cos(a)) + exp(-I*sin(a))
+    assert t.simplify()
+
+def test_issue_8263():
+    F, G = symbols('F, G', commutative=False, cls=Function)
+    x, y = symbols('x, y')
+    expr, dummies, _ = _mask_nc(F(x)*G(y) - G(y)*F(x))
+    for v in dummies.values():
+        assert not v.is_commutative
+    assert not expr.is_zero
+
+def test_monotonic_sign():
+    F = _monotonic_sign
+    x = symbols('x')
+    assert F(x) is None
+    assert F(-x) is None
+    assert F(Dummy(prime=True)) == 2
+    assert F(Dummy(prime=True, odd=True)) == 3
+    assert F(Dummy(composite=True)) == 4
+    assert F(Dummy(composite=True, odd=True)) == 9
+    assert F(Dummy(positive=True, integer=True)) == 1
+    assert F(Dummy(positive=True, even=True)) == 2
+    assert F(Dummy(positive=True, even=True, prime=False)) == 4
+    assert F(Dummy(negative=True, integer=True)) == -1
+    assert F(Dummy(negative=True, even=True)) == -2
+    assert F(Dummy(zero=True)) == 0
+    assert F(Dummy(nonnegative=True)) == 0
+    assert F(Dummy(nonpositive=True)) == 0
+
+    assert F(Dummy(positive=True) + 1).is_positive
+    assert F(Dummy(positive=True, integer=True) - 1).is_nonnegative
+    assert F(Dummy(positive=True) - 1) is None
+    assert F(Dummy(negative=True) + 1) is None
+    assert F(Dummy(negative=True, integer=True) - 1).is_nonpositive
+    assert F(Dummy(negative=True) - 1).is_negative
+    assert F(-Dummy(positive=True) + 1) is None
+    assert F(-Dummy(positive=True, integer=True) - 1).is_negative
+    assert F(-Dummy(positive=True) - 1).is_negative
+    assert F(-Dummy(negative=True) + 1).is_positive
+    assert F(-Dummy(negative=True, integer=True) - 1).is_nonnegative
+    assert F(-Dummy(negative=True) - 1) is None
+    x = Dummy(negative=True)
+    assert F(x**3).is_nonpositive
+    assert F(x**3 + log(2)*x - 1).is_negative
+    x = Dummy(positive=True)
+    assert F(-x**3).is_nonpositive
+
+    p = Dummy(positive=True)
+    assert F(1/p).is_positive
+    assert F(p/(p + 1)).is_positive
+    p = Dummy(nonnegative=True)
+    assert F(p/(p + 1)).is_nonnegative
+    p = Dummy(positive=True)
+    assert F(-1/p).is_negative
+    p = Dummy(nonpositive=True)
+    assert F(p/(-p + 1)).is_nonpositive
+
+    p = Dummy(positive=True, integer=True)
+    q = Dummy(positive=True, integer=True)
+    assert F(-2/p/q).is_negative
+    assert F(-2/(p - 1)/q) is None
+
+    assert F((p - 1)*q + 1).is_positive
+    assert F(-(p - 1)*q - 1).is_negative
+
+def test_issue_17256():
+    from sympy.sets.fancysets import Range
+    x = Symbol('x')
+    s1 = Sum(x + 1, (x, 1, 9))
+    s2 = Sum(x + 1, (x, Range(1, 10)))
+    a = Symbol('a')
+    r1 = s1.xreplace({x:a})
+    r2 = s2.xreplace({x:a})
+
+    assert r1.doit() == r2.doit()
+    s1 = Sum(x + 1, (x, 0, 9))
+    s2 = Sum(x + 1, (x, Range(10)))
+    a = Symbol('a')
+    r1 = s1.xreplace({x:a})
+    r2 = s2.xreplace({x:a})
+    assert r1 == r2
+
+def test_issue_21623():
+    from sympy.matrices.expressions.matexpr import MatrixSymbol
+    M = MatrixSymbol('X', 2, 2)
+    assert gcd_terms(M[0,0], 1) == M[0,0]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_facts.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_facts.py
new file mode 100644
index 0000000000000000000000000000000000000000..7ca04877d0bdaf8124258ea1d25a10bcfa0f5f3a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_facts.py
@@ -0,0 +1,312 @@
+from sympy.core.facts import (deduce_alpha_implications,
+        apply_beta_to_alpha_route, rules_2prereq, FactRules, FactKB)
+from sympy.core.logic import And, Not
+from sympy.testing.pytest import raises
+
+T = True
+F = False
+U = None
+
+
+def test_deduce_alpha_implications():
+    def D(i):
+        I = deduce_alpha_implications(i)
+        P = rules_2prereq({
+            (k, True): {(v, True) for v in S} for k, S in I.items()})
+        return I, P
+
+    # transitivity
+    I, P = D([('a', 'b'), ('b', 'c')])
+    assert I == {'a': {'b', 'c'}, 'b': {'c'}, Not('b'):
+        {Not('a')}, Not('c'): {Not('a'), Not('b')}}
+    assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}}
+
+    # Duplicate entry
+    I, P = D([('a', 'b'), ('b', 'c'), ('b', 'c')])
+    assert I == {'a': {'b', 'c'}, 'b': {'c'}, Not('b'): {Not('a')}, Not('c'): {Not('a'), Not('b')}}
+    assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}}
+
+    # see if it is tolerant to cycles
+    assert D([('a', 'a'), ('a', 'a')]) == ({}, {})
+    assert D([('a', 'b'), ('b', 'a')]) == (
+        {'a': {'b'}, 'b': {'a'}, Not('a'): {Not('b')}, Not('b'): {Not('a')}},
+        {'a': {'b'}, 'b': {'a'}})
+
+    # see if it catches inconsistency
+    raises(ValueError, lambda: D([('a', Not('a'))]))
+    raises(ValueError, lambda: D([('a', 'b'), ('b', Not('a'))]))
+    raises(ValueError, lambda: D([('a', 'b'), ('b', 'c'), ('b', 'na'),
+           ('na', Not('a'))]))
+
+    # see if it handles implications with negations
+    I, P = D([('a', Not('b')), ('c', 'b')])
+    assert I == {'a': {Not('b'), Not('c')}, 'b': {Not('a')}, 'c': {'b', Not('a')}, Not('b'): {Not('c')}}
+    assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}}
+    I, P = D([(Not('a'), 'b'), ('a', 'c')])
+    assert I == {'a': {'c'}, Not('a'): {'b'}, Not('b'): {'a',
+    'c'}, Not('c'): {Not('a'), 'b'},}
+    assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}}
+
+
+    # Long deductions
+    I, P = D([('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'e')])
+    assert I == {'a': {'b', 'c', 'd', 'e'}, 'b': {'c', 'd', 'e'},
+        'c': {'d', 'e'}, 'd': {'e'}, Not('b'): {Not('a')},
+        Not('c'): {Not('a'), Not('b')}, Not('d'): {Not('a'), Not('b'),
+            Not('c')}, Not('e'): {Not('a'), Not('b'), Not('c'), Not('d')}}
+    assert P == {'a': {'b', 'c', 'd', 'e'}, 'b': {'a', 'c', 'd',
+        'e'}, 'c': {'a', 'b', 'd', 'e'}, 'd': {'a', 'b', 'c', 'e'},
+        'e': {'a', 'b', 'c', 'd'}}
+
+    # something related to real-world
+    I, P = D([('rat', 'real'), ('int', 'rat')])
+
+    assert I == {'int': {'rat', 'real'}, 'rat': {'real'},
+        Not('real'): {Not('rat'), Not('int')}, Not('rat'): {Not('int')}}
+    assert P == {'rat': {'int', 'real'}, 'real': {'int', 'rat'},
+        'int': {'rat', 'real'}}
+
+
+# TODO move me to appropriate place
+def test_apply_beta_to_alpha_route():
+    APPLY = apply_beta_to_alpha_route
+
+    # indicates empty alpha-chain with attached beta-rule #bidx
+    def Q(bidx):
+        return (set(), [bidx])
+
+    # x -> a        &(a,b) -> x     --  x -> a
+    A = {'x': {'a'}}
+    B = [(And('a', 'b'), 'x')]
+    assert APPLY(A, B) == {'x': ({'a'}, []), 'a': Q(0), 'b': Q(0)}
+
+    # x -> a        &(a,!x) -> b    --  x -> a
+    A = {'x': {'a'}}
+    B = [(And('a', Not('x')), 'b')]
+    assert APPLY(A, B) == {'x': ({'a'}, []), Not('x'): Q(0), 'a': Q(0)}
+
+    # x -> a b      &(a,b) -> c     --  x -> a b c
+    A = {'x': {'a', 'b'}}
+    B = [(And('a', 'b'), 'c')]
+    assert APPLY(A, B) == \
+        {'x': ({'a', 'b', 'c'}, []), 'a': Q(0), 'b': Q(0)}
+
+    # x -> a        &(a,b) -> y     --  x -> a [#0]
+    A = {'x': {'a'}}
+    B = [(And('a', 'b'), 'y')]
+    assert APPLY(A, B) == {'x': ({'a'}, [0]), 'a': Q(0), 'b': Q(0)}
+
+    # x -> a b c    &(a,b) -> c     --  x -> a b c
+    A = {'x': {'a', 'b', 'c'}}
+    B = [(And('a', 'b'), 'c')]
+    assert APPLY(A, B) == \
+        {'x': ({'a', 'b', 'c'}, []), 'a': Q(0), 'b': Q(0)}
+
+    # x -> a b      &(a,b,c) -> y   --  x -> a b [#0]
+    A = {'x': {'a', 'b'}}
+    B = [(And('a', 'b', 'c'), 'y')]
+    assert APPLY(A, B) == \
+        {'x': ({'a', 'b'}, [0]), 'a': Q(0), 'b': Q(0), 'c': Q(0)}
+
+    # x -> a b      &(a,b) -> c     --  x -> a b c d
+    # c -> d                            c -> d
+    A = {'x': {'a', 'b'}, 'c': {'d'}}
+    B = [(And('a', 'b'), 'c')]
+    assert APPLY(A, B) == {'x': ({'a', 'b', 'c', 'd'}, []),
+        'c': ({'d'}, []), 'a': Q(0), 'b': Q(0)}
+
+    # x -> a b      &(a,b) -> c     --  x -> a b c d e
+    # c -> d        &(c,d) -> e         c -> d e
+    A = {'x': {'a', 'b'}, 'c': {'d'}}
+    B = [(And('a', 'b'), 'c'), (And('c', 'd'), 'e')]
+    assert APPLY(A, B) == {'x': ({'a', 'b', 'c', 'd', 'e'}, []),
+        'c': ({'d', 'e'}, []), 'a': Q(0), 'b': Q(0), 'd': Q(1)}
+
+    # x -> a b      &(a,y) -> z     --  x -> a b y z
+    #               &(a,b) -> y
+    A = {'x': {'a', 'b'}}
+    B = [(And('a', 'y'), 'z'), (And('a', 'b'), 'y')]
+    assert APPLY(A, B) == {'x': ({'a', 'b', 'y', 'z'}, []),
+        'a': (set(), [0, 1]), 'y': Q(0), 'b': Q(1)}
+
+    # x -> a b      &(a,!b) -> c    --  x -> a b
+    A = {'x': {'a', 'b'}}
+    B = [(And('a', Not('b')), 'c')]
+    assert APPLY(A, B) == \
+        {'x': ({'a', 'b'}, []), 'a': Q(0), Not('b'): Q(0)}
+
+    # !x -> !a !b   &(!a,b) -> c    --  !x -> !a !b
+    A = {Not('x'): {Not('a'), Not('b')}}
+    B = [(And(Not('a'), 'b'), 'c')]
+    assert APPLY(A, B) == \
+        {Not('x'): ({Not('a'), Not('b')}, []), Not('a'): Q(0), 'b': Q(0)}
+
+    # x -> a b      &(b,c) -> !a    --  x -> a b
+    A = {'x': {'a', 'b'}}
+    B = [(And('b', 'c'), Not('a'))]
+    assert APPLY(A, B) == {'x': ({'a', 'b'}, []), 'b': Q(0), 'c': Q(0)}
+
+    # x -> a b      &(a, b) -> c    --  x -> a b c p
+    # c -> p a
+    A = {'x': {'a', 'b'}, 'c': {'p', 'a'}}
+    B = [(And('a', 'b'), 'c')]
+    assert APPLY(A, B) == {'x': ({'a', 'b', 'c', 'p'}, []),
+        'c': ({'p', 'a'}, []), 'a': Q(0), 'b': Q(0)}
+
+
+def test_FactRules_parse():
+    f = FactRules('a -> b')
+    assert f.prereq == {'b': {'a'}, 'a': {'b'}}
+
+    f = FactRules('a -> !b')
+    assert f.prereq == {'b': {'a'}, 'a': {'b'}}
+
+    f = FactRules('!a -> b')
+    assert f.prereq == {'b': {'a'}, 'a': {'b'}}
+
+    f = FactRules('!a -> !b')
+    assert f.prereq == {'b': {'a'}, 'a': {'b'}}
+
+    f = FactRules('!z == nz')
+    assert f.prereq == {'z': {'nz'}, 'nz': {'z'}}
+
+
+def test_FactRules_parse2():
+    raises(ValueError, lambda: FactRules('a -> !a'))
+
+
+def test_FactRules_deduce():
+    f = FactRules(['a -> b', 'b -> c', 'b -> d', 'c -> e'])
+
+    def D(facts):
+        kb = FactKB(f)
+        kb.deduce_all_facts(facts)
+        return kb
+
+    assert D({'a': T}) == {'a': T, 'b': T, 'c': T, 'd': T, 'e': T}
+    assert D({'b': T}) == {        'b': T, 'c': T, 'd': T, 'e': T}
+    assert D({'c': T}) == {                'c': T,         'e': T}
+    assert D({'d': T}) == {                        'd': T        }
+    assert D({'e': T}) == {                                'e': T}
+
+    assert D({'a': F}) == {'a': F                                }
+    assert D({'b': F}) == {'a': F, 'b': F                        }
+    assert D({'c': F}) == {'a': F, 'b': F, 'c': F                }
+    assert D({'d': F}) == {'a': F, 'b': F,         'd': F        }
+
+    assert D({'a': U}) == {'a': U}  # XXX ok?
+
+
+def test_FactRules_deduce2():
+    # pos/neg/zero, but the rules are not sufficient to derive all relations
+    f = FactRules(['pos -> !neg', 'pos -> !z'])
+
+    def D(facts):
+        kb = FactKB(f)
+        kb.deduce_all_facts(facts)
+        return kb
+
+    assert D({'pos': T}) == {'pos': T, 'neg': F, 'z': F}
+    assert D({'pos': F}) == {'pos': F                  }
+    assert D({'neg': T}) == {'pos': F, 'neg': T        }
+    assert D({'neg': F}) == {          'neg': F        }
+    assert D({'z': T}) == {'pos': F,           'z': T}
+    assert D({'z': F}) == {                    'z': F}
+
+    # pos/neg/zero. rules are sufficient to derive all relations
+    f = FactRules(['pos -> !neg', 'neg -> !pos', 'pos -> !z', 'neg -> !z'])
+
+    assert D({'pos': T}) == {'pos': T, 'neg': F, 'z': F}
+    assert D({'pos': F}) == {'pos': F                  }
+    assert D({'neg': T}) == {'pos': F, 'neg': T, 'z': F}
+    assert D({'neg': F}) == {          'neg': F        }
+    assert D({'z': T}) == {'pos': F, 'neg': F, 'z': T}
+    assert D({'z': F}) == {                    'z': F}
+
+
+def test_FactRules_deduce_multiple():
+    # deduction that involves _several_ starting points
+    f = FactRules(['real == pos | npos'])
+
+    def D(facts):
+        kb = FactKB(f)
+        kb.deduce_all_facts(facts)
+        return kb
+
+    assert D({'real': T}) == {'real': T}
+    assert D({'real': F}) == {'real': F, 'pos': F, 'npos': F}
+    assert D({'pos': T}) == {'real': T, 'pos': T}
+    assert D({'npos': T}) == {'real': T, 'npos': T}
+
+    # --- key tests below ---
+    assert D({'pos': F, 'npos': F}) == {'real': F, 'pos': F, 'npos': F}
+    assert D({'real': T, 'pos': F}) == {'real': T, 'pos': F, 'npos': T}
+    assert D({'real': T, 'npos': F}) == {'real': T, 'pos': T, 'npos': F}
+
+    assert D({'pos': T, 'npos': F}) == {'real': T, 'pos': T, 'npos': F}
+    assert D({'pos': F, 'npos': T}) == {'real': T, 'pos': F, 'npos': T}
+
+
+def test_FactRules_deduce_multiple2():
+    f = FactRules(['real == neg | zero | pos'])
+
+    def D(facts):
+        kb = FactKB(f)
+        kb.deduce_all_facts(facts)
+        return kb
+
+    assert D({'real': T}) == {'real': T}
+    assert D({'real': F}) == {'real': F, 'neg': F, 'zero': F, 'pos': F}
+    assert D({'neg': T}) == {'real': T, 'neg': T}
+    assert D({'zero': T}) == {'real': T, 'zero': T}
+    assert D({'pos': T}) == {'real': T, 'pos': T}
+
+    # --- key tests below ---
+    assert D({'neg': F, 'zero': F, 'pos': F}) == {'real': F, 'neg': F,
+             'zero': F, 'pos': F}
+    assert D({'real': T, 'neg': F}) == {'real': T, 'neg': F}
+    assert D({'real': T, 'zero': F}) == {'real': T, 'zero': F}
+    assert D({'real': T, 'pos': F}) == {'real': T, 'pos': F}
+
+    assert D({'real': T,           'zero': F, 'pos': F}) == {'real': T,
+             'neg': T, 'zero': F, 'pos': F}
+    assert D({'real': T, 'neg': F,            'pos': F}) == {'real': T,
+             'neg': F, 'zero': T, 'pos': F}
+    assert D({'real': T, 'neg': F, 'zero': F          }) == {'real': T,
+             'neg': F, 'zero': F, 'pos': T}
+
+    assert D({'neg': T, 'zero': F, 'pos': F}) == {'real': T, 'neg': T,
+             'zero': F, 'pos': F}
+    assert D({'neg': F, 'zero': T, 'pos': F}) == {'real': T, 'neg': F,
+             'zero': T, 'pos': F}
+    assert D({'neg': F, 'zero': F, 'pos': T}) == {'real': T, 'neg': F,
+             'zero': F, 'pos': T}
+
+
+def test_FactRules_deduce_base():
+    # deduction that starts from base
+
+    f = FactRules(['real  == neg | zero | pos',
+                   'neg   -> real & !zero & !pos',
+                   'pos   -> real & !zero & !neg'])
+    base = FactKB(f)
+
+    base.deduce_all_facts({'real': T, 'neg': F})
+    assert base == {'real': T, 'neg': F}
+
+    base.deduce_all_facts({'zero': F})
+    assert base == {'real': T, 'neg': F, 'zero': F, 'pos': T}
+
+
+def test_FactRules_deduce_staticext():
+    # verify that static beta-extensions deduction takes place
+    f = FactRules(['real  == neg | zero | pos',
+                   'neg   -> real & !zero & !pos',
+                   'pos   -> real & !zero & !neg',
+                   'nneg  == real & !neg',
+                   'npos  == real & !pos'])
+
+    assert ('npos', True) in f.full_implications[('neg', True)]
+    assert ('nneg', True) in f.full_implications[('pos', True)]
+    assert ('nneg', True) in f.full_implications[('zero', True)]
+    assert ('npos', True) in f.full_implications[('zero', True)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_function.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_function.py
new file mode 100644
index 0000000000000000000000000000000000000000..a69c6b81b786ab0f0592367eaf402c2165a615dc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_function.py
@@ -0,0 +1,1459 @@
+from sympy.concrete.summations import Sum
+from sympy.core.basic import Basic, _aresame
+from sympy.core.cache import clear_cache
+from sympy.core.containers import Dict, Tuple
+from sympy.core.expr import Expr, unchanged
+from sympy.core.function import (Subs, Function, diff, Lambda, expand,
+    nfloat, Derivative)
+from sympy.core.numbers import E, Float, zoo, Rational, pi, I, oo, nan
+from sympy.core.power import Pow
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols, Dummy, Symbol
+from sympy.functions.elementary.complexes import im, re
+from sympy.functions.elementary.exponential import log, exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import sin, cos, acos
+from sympy.functions.special.error_functions import expint
+from sympy.functions.special.gamma_functions import loggamma, polygamma
+from sympy.matrices.dense import Matrix
+from sympy.printing.str import sstr
+from sympy.series.order import O
+from sympy.tensor.indexed import Indexed
+from sympy.core.function import (PoleError, _mexpand, arity,
+        BadSignatureError, BadArgumentsError)
+from sympy.core.parameters import _exp_is_pow
+from sympy.core.sympify import sympify, SympifyError
+from sympy.matrices import MutableMatrix, ImmutableMatrix
+from sympy.sets.sets import FiniteSet
+from sympy.solvers.solveset import solveset
+from sympy.tensor.array import NDimArray
+from sympy.utilities.iterables import subsets, variations
+from sympy.testing.pytest import XFAIL, raises, warns_deprecated_sympy, _both_exp_pow
+
+from sympy.abc import t, w, x, y, z
+f, g, h = symbols('f g h', cls=Function)
+_xi_1, _xi_2, _xi_3 = [Dummy() for i in range(3)]
+
+def test_f_expand_complex():
+    x = Symbol('x', real=True)
+
+    assert f(x).expand(complex=True) == I*im(f(x)) + re(f(x))
+    assert exp(x).expand(complex=True) == exp(x)
+    assert exp(I*x).expand(complex=True) == cos(x) + I*sin(x)
+    assert exp(z).expand(complex=True) == cos(im(z))*exp(re(z)) + \
+        I*sin(im(z))*exp(re(z))
+
+
+def test_bug1():
+    e = sqrt(-log(w))
+    assert e.subs(log(w), -x) == sqrt(x)
+
+    e = sqrt(-5*log(w))
+    assert e.subs(log(w), -x) == sqrt(5*x)
+
+
+def test_general_function():
+    nu = Function('nu')
+
+    e = nu(x)
+    edx = e.diff(x)
+    edy = e.diff(y)
+    edxdx = e.diff(x).diff(x)
+    edxdy = e.diff(x).diff(y)
+    assert e == nu(x)
+    assert edx != nu(x)
+    assert edx == diff(nu(x), x)
+    assert edy == 0
+    assert edxdx == diff(diff(nu(x), x), x)
+    assert edxdy == 0
+
+def test_general_function_nullary():
+    nu = Function('nu')
+
+    e = nu()
+    edx = e.diff(x)
+    edxdx = e.diff(x).diff(x)
+    assert e == nu()
+    assert edx != nu()
+    assert edx == 0
+    assert edxdx == 0
+
+
+def test_derivative_subs_bug():
+    e = diff(g(x), x)
+    assert e.subs(g(x), f(x)) != e
+    assert e.subs(g(x), f(x)) == Derivative(f(x), x)
+    assert e.subs(g(x), -f(x)) == Derivative(-f(x), x)
+
+    assert e.subs(x, y) == Derivative(g(y), y)
+
+
+def test_derivative_subs_self_bug():
+    d = diff(f(x), x)
+
+    assert d.subs(d, y) == y
+
+
+def test_derivative_linearity():
+    assert diff(-f(x), x) == -diff(f(x), x)
+    assert diff(8*f(x), x) == 8*diff(f(x), x)
+    assert diff(8*f(x), x) != 7*diff(f(x), x)
+    assert diff(8*f(x)*x, x) == 8*f(x) + 8*x*diff(f(x), x)
+    assert diff(8*f(x)*y*x, x).expand() == 8*y*f(x) + 8*y*x*diff(f(x), x)
+
+
+def test_derivative_evaluate():
+    assert Derivative(sin(x), x) != diff(sin(x), x)
+    assert Derivative(sin(x), x).doit() == diff(sin(x), x)
+
+    assert Derivative(Derivative(f(x), x), x) == diff(f(x), x, x)
+    assert Derivative(sin(x), x, 0) == sin(x)
+    assert Derivative(sin(x), (x, y), (x, -y)) == sin(x)
+
+
+def test_diff_symbols():
+    assert diff(f(x, y, z), x, y, z) == Derivative(f(x, y, z), x, y, z)
+    assert diff(f(x, y, z), x, x, x) == Derivative(f(x, y, z), x, x, x) == Derivative(f(x, y, z), (x, 3))
+    assert diff(f(x, y, z), x, 3) == Derivative(f(x, y, z), x, 3)
+
+    # issue 5028
+    assert [diff(-z + x/y, sym) for sym in (z, x, y)] == [-1, 1/y, -x/y**2]
+    assert diff(f(x, y, z), x, y, z, 2) == Derivative(f(x, y, z), x, y, z, z)
+    assert diff(f(x, y, z), x, y, z, 2, evaluate=False) == \
+        Derivative(f(x, y, z), x, y, z, z)
+    assert Derivative(f(x, y, z), x, y, z)._eval_derivative(z) == \
+        Derivative(f(x, y, z), x, y, z, z)
+    assert Derivative(Derivative(f(x, y, z), x), y)._eval_derivative(z) == \
+        Derivative(f(x, y, z), x, y, z)
+
+    raises(TypeError, lambda: cos(x).diff((x, y)).variables)
+    assert cos(x).diff((x, y))._wrt_variables == [x]
+
+    # issue 23222
+    assert sympify("a*x+b").diff("x") == sympify("a")
+
+def test_Function():
+    class myfunc(Function):
+        @classmethod
+        def eval(cls):  # zero args
+            return
+
+    assert myfunc.nargs == FiniteSet(0)
+    assert myfunc().nargs == FiniteSet(0)
+    raises(TypeError, lambda: myfunc(x).nargs)
+
+    class myfunc(Function):
+        @classmethod
+        def eval(cls, x):  # one arg
+            return
+
+    assert myfunc.nargs == FiniteSet(1)
+    assert myfunc(x).nargs == FiniteSet(1)
+    raises(TypeError, lambda: myfunc(x, y).nargs)
+
+    class myfunc(Function):
+        @classmethod
+        def eval(cls, *x):  # star args
+            return
+
+    assert myfunc.nargs == S.Naturals0
+    assert myfunc(x).nargs == S.Naturals0
+
+
+def test_nargs():
+    f = Function('f')
+    assert f.nargs == S.Naturals0
+    assert f(1).nargs == S.Naturals0
+    assert Function('f', nargs=2)(1, 2).nargs == FiniteSet(2)
+    assert sin.nargs == FiniteSet(1)
+    assert sin(2).nargs == FiniteSet(1)
+    assert log.nargs == FiniteSet(1, 2)
+    assert log(2).nargs == FiniteSet(1, 2)
+    assert Function('f', nargs=2).nargs == FiniteSet(2)
+    assert Function('f', nargs=0).nargs == FiniteSet(0)
+    assert Function('f', nargs=(0, 1)).nargs == FiniteSet(0, 1)
+    assert Function('f', nargs=None).nargs == S.Naturals0
+    raises(ValueError, lambda: Function('f', nargs=()))
+
+def test_nargs_inheritance():
+    class f1(Function):
+        nargs = 2
+    class f2(f1):
+        pass
+    class f3(f2):
+        pass
+    class f4(f3):
+        nargs = 1,2
+    class f5(f4):
+        pass
+    class f6(f5):
+        pass
+    class f7(f6):
+        nargs=None
+    class f8(f7):
+        pass
+    class f9(f8):
+        pass
+    class f10(f9):
+        nargs = 1
+    class f11(f10):
+        pass
+    assert f1.nargs == FiniteSet(2)
+    assert f2.nargs == FiniteSet(2)
+    assert f3.nargs == FiniteSet(2)
+    assert f4.nargs == FiniteSet(1, 2)
+    assert f5.nargs == FiniteSet(1, 2)
+    assert f6.nargs == FiniteSet(1, 2)
+    assert f7.nargs == S.Naturals0
+    assert f8.nargs == S.Naturals0
+    assert f9.nargs == S.Naturals0
+    assert f10.nargs == FiniteSet(1)
+    assert f11.nargs == FiniteSet(1)
+
+def test_arity():
+    f = lambda x, y: 1
+    assert arity(f) == 2
+    def f(x, y, z=None):
+        pass
+    assert arity(f) == (2, 3)
+    assert arity(lambda *x: x) is None
+    assert arity(log) == (1, 2)
+
+
+def test_Lambda():
+    e = Lambda(x, x**2)
+    assert e(4) == 16
+    assert e(x) == x**2
+    assert e(y) == y**2
+
+    assert Lambda((), 42)() == 42
+    assert unchanged(Lambda, (), 42)
+    assert Lambda((), 42) != Lambda((), 43)
+    assert Lambda((), f(x))() == f(x)
+    assert Lambda((), 42).nargs == FiniteSet(0)
+
+    assert unchanged(Lambda, (x,), x**2)
+    assert Lambda(x, x**2) == Lambda((x,), x**2)
+    assert Lambda(x, x**2) != Lambda(x, x**2 + 1)
+    assert Lambda((x, y), x**y) != Lambda((y, x), y**x)
+    assert Lambda((x, y), x**y) != Lambda((x, y), y**x)
+
+    assert Lambda((x, y), x**y)(x, y) == x**y
+    assert Lambda((x, y), x**y)(3, 3) == 3**3
+    assert Lambda((x, y), x**y)(x, 3) == x**3
+    assert Lambda((x, y), x**y)(3, y) == 3**y
+    assert Lambda(x, f(x))(x) == f(x)
+    assert Lambda(x, x**2)(e(x)) == x**4
+    assert e(e(x)) == x**4
+
+    x1, x2 = (Indexed('x', i) for i in (1, 2))
+    assert Lambda((x1, x2), x1 + x2)(x, y) == x + y
+
+    assert Lambda((x, y), x + y).nargs == FiniteSet(2)
+
+    p = x, y, z, t
+    assert Lambda(p, t*(x + y + z))(*p) == t * (x + y + z)
+
+    eq = Lambda(x, 2*x) + Lambda(y, 2*y)
+    assert eq != 2*Lambda(x, 2*x)
+    assert eq.as_dummy() == 2*Lambda(x, 2*x).as_dummy()
+    assert Lambda(x, 2*x) not in [ Lambda(x, x) ]
+    raises(BadSignatureError, lambda: Lambda(1, x))
+    assert Lambda(x, 1)(1) is S.One
+
+    raises(BadSignatureError, lambda: Lambda((x, x), x + 2))
+    raises(BadSignatureError, lambda: Lambda(((x, x), y), x))
+    raises(BadSignatureError, lambda: Lambda(((y, x), x), x))
+    raises(BadSignatureError, lambda: Lambda(((y, 1), 2), x))
+
+    with warns_deprecated_sympy():
+        assert Lambda([x, y], x+y) == Lambda((x, y), x+y)
+
+    flam = Lambda(((x, y),), x + y)
+    assert flam((2, 3)) == 5
+    flam = Lambda(((x, y), z), x + y + z)
+    assert flam((2, 3), 1) == 6
+    flam = Lambda((((x, y), z),), x + y + z)
+    assert flam(((2, 3), 1)) == 6
+    raises(BadArgumentsError, lambda: flam(1, 2, 3))
+    flam = Lambda( (x,), (x, x))
+    assert flam(1,) == (1, 1)
+    assert flam((1,)) == ((1,), (1,))
+    flam = Lambda( ((x,),), (x, x))
+    raises(BadArgumentsError, lambda: flam(1))
+    assert flam((1,)) == (1, 1)
+
+    # Previously TypeError was raised so this is potentially needed for
+    # backwards compatibility.
+    assert issubclass(BadSignatureError, TypeError)
+    assert issubclass(BadArgumentsError, TypeError)
+
+    # These are tested to see they don't raise:
+    hash(Lambda(x, 2*x))
+    hash(Lambda(x, x))  # IdentityFunction subclass
+
+
+def test_IdentityFunction():
+    assert Lambda(x, x) is Lambda(y, y) is S.IdentityFunction
+    assert Lambda(x, 2*x) is not S.IdentityFunction
+    assert Lambda((x, y), x) is not S.IdentityFunction
+
+
+def test_Lambda_symbols():
+    assert Lambda(x, 2*x).free_symbols == set()
+    assert Lambda(x, x*y).free_symbols == {y}
+    assert Lambda((), 42).free_symbols == set()
+    assert Lambda((), x*y).free_symbols == {x,y}
+
+
+def test_functionclas_symbols():
+    assert f.free_symbols == set()
+
+
+def test_Lambda_arguments():
+    raises(TypeError, lambda: Lambda(x, 2*x)(x, y))
+    raises(TypeError, lambda: Lambda((x, y), x + y)(x))
+    raises(TypeError, lambda: Lambda((), 42)(x))
+
+
+def test_Lambda_equality():
+    assert Lambda((x, y), 2*x) == Lambda((x, y), 2*x)
+    # these, of course, should never be equal
+    assert Lambda(x, 2*x) != Lambda((x, y), 2*x)
+    assert Lambda(x, 2*x) != 2*x
+    # But it is tempting to want expressions that differ only
+    # in bound symbols to compare the same.  But this is not what
+    # Python's `==` is intended to do; two objects that compare
+    # as equal means that they are indistibguishable and cache to the
+    # same value.  We wouldn't want to expression that are
+    # mathematically the same but written in different variables to be
+    # interchanged else what is the point of allowing for different
+    # variable names?
+    assert Lambda(x, 2*x) != Lambda(y, 2*y)
+
+
+def test_Subs():
+    assert Subs(1, (), ()) is S.One
+    # check null subs influence on hashing
+    assert Subs(x, y, z) != Subs(x, y, 1)
+    # neutral subs works
+    assert Subs(x, x, 1).subs(x, y).has(y)
+    # self mapping var/point
+    assert Subs(Derivative(f(x), (x, 2)), x, x).doit() == f(x).diff(x, x)
+    assert Subs(x, x, 0).has(x)  # it's a structural answer
+    assert not Subs(x, x, 0).free_symbols
+    assert Subs(Subs(x + y, x, 2), y, 1) == Subs(x + y, (x, y), (2, 1))
+    assert Subs(x, (x,), (0,)) == Subs(x, x, 0)
+    assert Subs(x, x, 0) == Subs(y, y, 0)
+    assert Subs(x, x, 0).subs(x, 1) == Subs(x, x, 0)
+    assert Subs(y, x, 0).subs(y, 1) == Subs(1, x, 0)
+    assert Subs(f(x), x, 0).doit() == f(0)
+    assert Subs(f(x**2), x**2, 0).doit() == f(0)
+    assert Subs(f(x, y, z), (x, y, z), (0, 1, 1)) != \
+        Subs(f(x, y, z), (x, y, z), (0, 0, 1))
+    assert Subs(x, y, 2).subs(x, y).doit() == 2
+    assert Subs(f(x, y), (x, y, z), (0, 1, 1)) != \
+        Subs(f(x, y) + z, (x, y, z), (0, 1, 0))
+    assert Subs(f(x, y), (x, y), (0, 1)).doit() == f(0, 1)
+    assert Subs(Subs(f(x, y), x, 0), y, 1).doit() == f(0, 1)
+    raises(ValueError, lambda: Subs(f(x, y), (x, y), (0, 0, 1)))
+    raises(ValueError, lambda: Subs(f(x, y), (x, x, y), (0, 0, 1)))
+
+    assert len(Subs(f(x, y), (x, y), (0, 1)).variables) == 2
+    assert Subs(f(x, y), (x, y), (0, 1)).point == Tuple(0, 1)
+
+    assert Subs(f(x), x, 0) == Subs(f(y), y, 0)
+    assert Subs(f(x, y), (x, y), (0, 1)) == Subs(f(x, y), (y, x), (1, 0))
+    assert Subs(f(x)*y, (x, y), (0, 1)) == Subs(f(y)*x, (y, x), (0, 1))
+    assert Subs(f(x)*y, (x, y), (1, 1)) == Subs(f(y)*x, (x, y), (1, 1))
+
+    assert Subs(f(x), x, 0).subs(x, 1).doit() == f(0)
+    assert Subs(f(x), x, y).subs(y, 0) == Subs(f(x), x, 0)
+    assert Subs(y*f(x), x, y).subs(y, 2) == Subs(2*f(x), x, 2)
+    assert (2 * Subs(f(x), x, 0)).subs(Subs(f(x), x, 0), y) == 2*y
+
+    assert Subs(f(x), x, 0).free_symbols == set()
+    assert Subs(f(x, y), x, z).free_symbols == {y, z}
+
+    assert Subs(f(x).diff(x), x, 0).doit(), Subs(f(x).diff(x), x, 0)
+    assert Subs(1 + f(x).diff(x), x, 0).doit(), 1 + Subs(f(x).diff(x), x, 0)
+    assert Subs(y*f(x, y).diff(x), (x, y), (0, 2)).doit() == \
+        2*Subs(Derivative(f(x, 2), x), x, 0)
+    assert Subs(y**2*f(x), x, 0).diff(y) == 2*y*f(0)
+
+    e = Subs(y**2*f(x), x, y)
+    assert e.diff(y) == e.doit().diff(y) == y**2*Derivative(f(y), y) + 2*y*f(y)
+
+    assert Subs(f(x), x, 0) + Subs(f(x), x, 0) == 2*Subs(f(x), x, 0)
+    e1 = Subs(z*f(x), x, 1)
+    e2 = Subs(z*f(y), y, 1)
+    assert e1 + e2 == 2*e1
+    assert e1.__hash__() == e2.__hash__()
+    assert Subs(z*f(x + 1), x, 1) not in [ e1, e2 ]
+    assert Derivative(f(x), x).subs(x, g(x)) == Derivative(f(g(x)), g(x))
+    assert Derivative(f(x), x).subs(x, x + y) == Subs(Derivative(f(x), x),
+        x, x + y)
+    assert Subs(f(x)*cos(y) + z, (x, y), (0, pi/3)).n(2) == \
+        Subs(f(x)*cos(y) + z, (x, y), (0, pi/3)).evalf(2) == \
+        z + Rational('1/2').n(2)*f(0)
+
+    assert f(x).diff(x).subs(x, 0).subs(x, y) == f(x).diff(x).subs(x, 0)
+    assert (x*f(x).diff(x).subs(x, 0)).subs(x, y) == y*f(x).diff(x).subs(x, 0)
+    assert Subs(Derivative(g(x)**2, g(x), x), g(x), exp(x)
+        ).doit() == 2*exp(x)
+    assert Subs(Derivative(g(x)**2, g(x), x), g(x), exp(x)
+        ).doit(deep=False) == 2*Derivative(exp(x), x)
+    assert Derivative(f(x, g(x)), x).doit() == Derivative(
+        f(x, g(x)), g(x))*Derivative(g(x), x) + Subs(Derivative(
+        f(y, g(x)), y), y, x)
+
+def test_doitdoit():
+    done = Derivative(f(x, g(x)), x, g(x)).doit()
+    assert done == done.doit()
+
+
+@XFAIL
+def test_Subs2():
+    # this reflects a limitation of subs(), probably won't fix
+    assert Subs(f(x), x**2, x).doit() == f(sqrt(x))
+
+
+def test_expand_function():
+    assert expand(x + y) == x + y
+    assert expand(x + y, complex=True) == I*im(x) + I*im(y) + re(x) + re(y)
+    assert expand((x + y)**11, modulus=11) == x**11 + y**11
+
+
+def test_function_comparable():
+    assert sin(x).is_comparable is False
+    assert cos(x).is_comparable is False
+
+    assert sin(Float('0.1')).is_comparable is True
+    assert cos(Float('0.1')).is_comparable is True
+
+    assert sin(E).is_comparable is True
+    assert cos(E).is_comparable is True
+
+    assert sin(Rational(1, 3)).is_comparable is True
+    assert cos(Rational(1, 3)).is_comparable is True
+
+
+def test_function_comparable_infinities():
+    assert sin(oo).is_comparable is False
+    assert sin(-oo).is_comparable is False
+    assert sin(zoo).is_comparable is False
+    assert sin(nan).is_comparable is False
+
+
+def test_deriv1():
+    # These all require derivatives evaluated at a point (issue 4719) to work.
+    # See issue 4624
+    assert f(2*x).diff(x) == 2*Subs(Derivative(f(x), x), x, 2*x)
+    assert (f(x)**3).diff(x) == 3*f(x)**2*f(x).diff(x)
+    assert (f(2*x)**3).diff(x) == 6*f(2*x)**2*Subs(
+        Derivative(f(x), x), x, 2*x)
+
+    assert f(2 + x).diff(x) == Subs(Derivative(f(x), x), x, x + 2)
+    assert f(2 + 3*x).diff(x) == 3*Subs(
+        Derivative(f(x), x), x, 3*x + 2)
+    assert f(3*sin(x)).diff(x) == 3*cos(x)*Subs(
+        Derivative(f(x), x), x, 3*sin(x))
+
+    # See issue 8510
+    assert f(x, x + z).diff(x) == (
+        Subs(Derivative(f(y, x + z), y), y, x) +
+        Subs(Derivative(f(x, y), y), y, x + z))
+    assert f(x, x**2).diff(x) == (
+        2*x*Subs(Derivative(f(x, y), y), y, x**2) +
+        Subs(Derivative(f(y, x**2), y), y, x))
+    # but Subs is not always necessary
+    assert f(x, g(y)).diff(g(y)) == Derivative(f(x, g(y)), g(y))
+
+
+def test_deriv2():
+    assert (x**3).diff(x) == 3*x**2
+    assert (x**3).diff(x, evaluate=False) != 3*x**2
+    assert (x**3).diff(x, evaluate=False) == Derivative(x**3, x)
+
+    assert diff(x**3, x) == 3*x**2
+    assert diff(x**3, x, evaluate=False) != 3*x**2
+    assert diff(x**3, x, evaluate=False) == Derivative(x**3, x)
+
+
+def test_func_deriv():
+    assert f(x).diff(x) == Derivative(f(x), x)
+    # issue 4534
+    assert f(x, y).diff(x, y) - f(x, y).diff(y, x) == 0
+    assert Derivative(f(x, y), x, y).args[1:] == ((x, 1), (y, 1))
+    assert Derivative(f(x, y), y, x).args[1:] == ((y, 1), (x, 1))
+    assert (Derivative(f(x, y), x, y) - Derivative(f(x, y), y, x)).doit() == 0
+
+
+def test_suppressed_evaluation():
+    a = sin(0, evaluate=False)
+    assert a != 0
+    assert a.func is sin
+    assert a.args == (0,)
+
+
+def test_function_evalf():
+    def eq(a, b, eps):
+        return abs(a - b) < eps
+    assert eq(sin(1).evalf(15), Float("0.841470984807897"), 1e-13)
+    assert eq(
+        sin(2).evalf(25), Float("0.9092974268256816953960199", 25), 1e-23)
+    assert eq(sin(1 + I).evalf(
+        15), Float("1.29845758141598") + Float("0.634963914784736")*I, 1e-13)
+    assert eq(exp(1 + I).evalf(15), Float(
+        "1.46869393991588") + Float("2.28735528717884239")*I, 1e-13)
+    assert eq(exp(-0.5 + 1.5*I).evalf(15), Float(
+        "0.0429042815937374") + Float("0.605011292285002")*I, 1e-13)
+    assert eq(log(pi + sqrt(2)*I).evalf(
+        15), Float("1.23699044022052") + Float("0.422985442737893")*I, 1e-13)
+    assert eq(cos(100).evalf(15), Float("0.86231887228768"), 1e-13)
+
+
+def test_extensibility_eval():
+    class MyFunc(Function):
+        @classmethod
+        def eval(cls, *args):
+            return (0, 0, 0)
+    assert MyFunc(0) == (0, 0, 0)
+
+
+@_both_exp_pow
+def test_function_non_commutative():
+    x = Symbol('x', commutative=False)
+    assert f(x).is_commutative is False
+    assert sin(x).is_commutative is False
+    assert exp(x).is_commutative is False
+    assert log(x).is_commutative is False
+    assert f(x).is_complex is False
+    assert sin(x).is_complex is False
+    assert exp(x).is_complex is False
+    assert log(x).is_complex is False
+
+
+def test_function_complex():
+    x = Symbol('x', complex=True)
+    xzf = Symbol('x', complex=True, zero=False)
+    assert f(x).is_commutative is True
+    assert sin(x).is_commutative is True
+    assert exp(x).is_commutative is True
+    assert log(x).is_commutative is True
+    assert f(x).is_complex is None
+    assert sin(x).is_complex is True
+    assert exp(x).is_complex is True
+    assert log(x).is_complex is None
+    assert log(xzf).is_complex is True
+
+
+def test_function__eval_nseries():
+    n = Symbol('n')
+
+    assert sin(x)._eval_nseries(x, 2, None) == x + O(x**2)
+    assert sin(x + 1)._eval_nseries(x, 2, None) == x*cos(1) + sin(1) + O(x**2)
+    assert sin(pi*(1 - x))._eval_nseries(x, 2, None) == pi*x + O(x**2)
+    assert acos(1 - x**2)._eval_nseries(x, 2, None) == sqrt(2)*sqrt(x**2) + O(x**2)
+    assert polygamma(n, x + 1)._eval_nseries(x, 2, None) == \
+        polygamma(n, 1) + polygamma(n + 1, 1)*x + O(x**2)
+    raises(PoleError, lambda: sin(1/x)._eval_nseries(x, 2, None))
+    assert acos(1 - x)._eval_nseries(x, 2, None) == sqrt(2)*sqrt(x) + sqrt(2)*x**(S(3)/2)/12 + O(x**2)
+    assert acos(1 + x)._eval_nseries(x, 2, None) == sqrt(2)*sqrt(-x) + sqrt(2)*(-x)**(S(3)/2)/12 + O(x**2)
+    assert loggamma(1/x)._eval_nseries(x, 0, None) == \
+        log(x)/2 - log(x)/x - 1/x + O(1, x)
+    assert loggamma(log(1/x)).nseries(x, n=1, logx=y) == loggamma(-y)
+
+    # issue 6725:
+    assert expint(Rational(3, 2), -x)._eval_nseries(x, 5, None) == \
+        2 - 2*x - x**2/3 - x**3/15 - x**4/84 - 2*I*sqrt(pi)*sqrt(x) + O(x**5)
+    assert sin(sqrt(x))._eval_nseries(x, 3, None) == \
+        sqrt(x) - x**Rational(3, 2)/6 + x**Rational(5, 2)/120 + O(x**3)
+
+    # issue 19065:
+    s1 = f(x,y).series(y, n=2)
+    assert {i.name for i in s1.atoms(Symbol)} == {'x', 'xi', 'y'}
+    xi = Symbol('xi')
+    s2 = f(xi, y).series(y, n=2)
+    assert {i.name for i in s2.atoms(Symbol)} == {'xi', 'xi0', 'y'}
+
+def test_doit():
+    n = Symbol('n', integer=True)
+    f = Sum(2 * n * x, (n, 1, 3))
+    d = Derivative(f, x)
+    assert d.doit() == 12
+    assert d.doit(deep=False) == Sum(2*n, (n, 1, 3))
+
+
+def test_evalf_default():
+    from sympy.functions.special.gamma_functions import polygamma
+    assert type(sin(4.0)) == Float
+    assert type(re(sin(I + 1.0))) == Float
+    assert type(im(sin(I + 1.0))) == Float
+    assert type(sin(4)) == sin
+    assert type(polygamma(2.0, 4.0)) == Float
+    assert type(sin(Rational(1, 4))) == sin
+
+
+def test_issue_5399():
+    args = [x, y, S(2), S.Half]
+
+    def ok(a):
+        """Return True if the input args for diff are ok"""
+        if not a:
+            return False
+        if a[0].is_Symbol is False:
+            return False
+        s_at = [i for i in range(len(a)) if a[i].is_Symbol]
+        n_at = [i for i in range(len(a)) if not a[i].is_Symbol]
+        # every symbol is followed by symbol or int
+        # every number is followed by a symbol
+        return (all(a[i + 1].is_Symbol or a[i + 1].is_Integer
+            for i in s_at if i + 1 < len(a)) and
+            all(a[i + 1].is_Symbol
+            for i in n_at if i + 1 < len(a)))
+    eq = x**10*y**8
+    for a in subsets(args):
+        for v in variations(a, len(a)):
+            if ok(v):
+                eq.diff(*v) # does not raise
+            else:
+                raises(ValueError, lambda: eq.diff(*v))
+
+
+def test_derivative_numerically():
+    z0 = x._random()
+    assert abs(Derivative(sin(x), x).doit_numerically(z0) - cos(z0)) < 1e-15
+
+
+def test_fdiff_argument_index_error():
+    from sympy.core.function import ArgumentIndexError
+
+    class myfunc(Function):
+        nargs = 1  # define since there is no eval routine
+
+        def fdiff(self, idx):
+            raise ArgumentIndexError
+    mf = myfunc(x)
+    assert mf.diff(x) == Derivative(mf, x)
+    raises(TypeError, lambda: myfunc(x, x))
+
+
+def test_deriv_wrt_function():
+    x = f(t)
+    xd = diff(x, t)
+    xdd = diff(xd, t)
+    y = g(t)
+    yd = diff(y, t)
+
+    assert diff(x, t) == xd
+    assert diff(2 * x + 4, t) == 2 * xd
+    assert diff(2 * x + 4 + y, t) == 2 * xd + yd
+    assert diff(2 * x + 4 + y * x, t) == 2 * xd + x * yd + xd * y
+    assert diff(2 * x + 4 + y * x, x) == 2 + y
+    assert (diff(4 * x**2 + 3 * x + x * y, t) == 3 * xd + x * yd + xd * y +
+            8 * x * xd)
+    assert (diff(4 * x**2 + 3 * xd + x * y, t) == 3 * xdd + x * yd + xd * y +
+            8 * x * xd)
+    assert diff(4 * x**2 + 3 * xd + x * y, xd) == 3
+    assert diff(4 * x**2 + 3 * xd + x * y, xdd) == 0
+    assert diff(sin(x), t) == xd * cos(x)
+    assert diff(exp(x), t) == xd * exp(x)
+    assert diff(sqrt(x), t) == xd / (2 * sqrt(x))
+
+
+def test_diff_wrt_value():
+    assert Expr()._diff_wrt is False
+    assert x._diff_wrt is True
+    assert f(x)._diff_wrt is True
+    assert Derivative(f(x), x)._diff_wrt is True
+    assert Derivative(x**2, x)._diff_wrt is False
+
+
+def test_diff_wrt():
+    fx = f(x)
+    dfx = diff(f(x), x)
+    ddfx = diff(f(x), x, x)
+
+    assert diff(sin(fx) + fx**2, fx) == cos(fx) + 2*fx
+    assert diff(sin(dfx) + dfx**2, dfx) == cos(dfx) + 2*dfx
+    assert diff(sin(ddfx) + ddfx**2, ddfx) == cos(ddfx) + 2*ddfx
+    assert diff(fx**2, dfx) == 0
+    assert diff(fx**2, ddfx) == 0
+    assert diff(dfx**2, fx) == 0
+    assert diff(dfx**2, ddfx) == 0
+    assert diff(ddfx**2, dfx) == 0
+
+    assert diff(fx*dfx*ddfx, fx) == dfx*ddfx
+    assert diff(fx*dfx*ddfx, dfx) == fx*ddfx
+    assert diff(fx*dfx*ddfx, ddfx) == fx*dfx
+
+    assert diff(f(x), x).diff(f(x)) == 0
+    assert (sin(f(x)) - cos(diff(f(x), x))).diff(f(x)) == cos(f(x))
+
+    assert diff(sin(fx), fx, x) == diff(sin(fx), x, fx)
+
+    # Chain rule cases
+    assert f(g(x)).diff(x) == \
+        Derivative(g(x), x)*Derivative(f(g(x)), g(x))
+    assert diff(f(g(x), h(y)), x) == \
+        Derivative(g(x), x)*Derivative(f(g(x), h(y)), g(x))
+    assert diff(f(g(x), h(x)), x) == (
+        Derivative(f(g(x), h(x)), g(x))*Derivative(g(x), x) +
+        Derivative(f(g(x), h(x)), h(x))*Derivative(h(x), x))
+    assert f(
+        sin(x)).diff(x) == cos(x)*Subs(Derivative(f(x), x), x, sin(x))
+
+    assert diff(f(g(x)), g(x)) == Derivative(f(g(x)), g(x))
+
+
+def test_diff_wrt_func_subs():
+    assert f(g(x)).diff(x).subs(g, Lambda(x, 2*x)).doit() == f(2*x).diff(x)
+
+
+def test_subs_in_derivative():
+    expr = sin(x*exp(y))
+    u = Function('u')
+    v = Function('v')
+    assert Derivative(expr, y).subs(expr, y) == Derivative(y, y)
+    assert Derivative(expr, y).subs(y, x).doit() == \
+        Derivative(expr, y).doit().subs(y, x)
+    assert Derivative(f(x, y), y).subs(y, x) == Subs(Derivative(f(x, y), y), y, x)
+    assert Derivative(f(x, y), y).subs(x, y) == Subs(Derivative(f(x, y), y), x, y)
+    assert Derivative(f(x, y), y).subs(y, g(x, y)) == Subs(Derivative(f(x, y), y), y, g(x, y)).doit()
+    assert Derivative(f(x, y), y).subs(x, g(x, y)) == Subs(Derivative(f(x, y), y), x, g(x, y))
+    assert Derivative(f(x, y), g(y)).subs(x, g(x, y)) == Derivative(f(g(x, y), y), g(y))
+    assert Derivative(f(u(x), h(y)), h(y)).subs(h(y), g(x, y)) == \
+        Subs(Derivative(f(u(x), h(y)), h(y)), h(y), g(x, y)).doit()
+    assert Derivative(f(x, y), y).subs(y, z) == Derivative(f(x, z), z)
+    assert Derivative(f(x, y), y).subs(y, g(y)) == Derivative(f(x, g(y)), g(y))
+    assert Derivative(f(g(x), h(y)), h(y)).subs(h(y), u(y)) == \
+        Derivative(f(g(x), u(y)), u(y))
+    assert Derivative(f(x, f(x, x)), f(x, x)).subs(
+        f, Lambda((x, y), x + y)) == Subs(
+        Derivative(z + x, z), z, 2*x)
+    assert Subs(Derivative(f(f(x)), x), f, cos).doit() == sin(x)*sin(cos(x))
+    assert Subs(Derivative(f(f(x)), f(x)), f, cos).doit() == -sin(cos(x))
+    # Issue 13791. No comparison (it's a long formula) but this used to raise an exception.
+    assert isinstance(v(x, y, u(x, y)).diff(y).diff(x).diff(y), Expr)
+    # This is also related to issues 13791 and 13795; issue 15190
+    F = Lambda((x, y), exp(2*x + 3*y))
+    abstract = f(x, f(x, x)).diff(x, 2)
+    concrete = F(x, F(x, x)).diff(x, 2)
+    assert (abstract.subs(f, F).doit() - concrete).simplify() == 0
+    # don't introduce a new symbol if not necessary
+    assert x in f(x).diff(x).subs(x, 0).atoms()
+    # case (4)
+    assert Derivative(f(x,f(x,y)), x, y).subs(x, g(y)
+        ) == Subs(Derivative(f(x, f(x, y)), x, y), x, g(y))
+
+    assert Derivative(f(x, x), x).subs(x, 0
+        ) == Subs(Derivative(f(x, x), x), x, 0)
+    # issue 15194
+    assert Derivative(f(y, g(x)), (x, z)).subs(z, x
+        ) == Derivative(f(y, g(x)), (x, x))
+
+    df = f(x).diff(x)
+    assert df.subs(df, 1) is S.One
+    assert df.diff(df) is S.One
+    dxy = Derivative(f(x, y), x, y)
+    dyx = Derivative(f(x, y), y, x)
+    assert dxy.subs(Derivative(f(x, y), y, x), 1) is S.One
+    assert dxy.diff(dyx) is S.One
+    assert Derivative(f(x, y), x, 2, y, 3).subs(
+        dyx, g(x, y)) == Derivative(g(x, y), x, 1, y, 2)
+    assert Derivative(f(x, x - y), y).subs(x, x + y) == Subs(
+        Derivative(f(x, x - y), y), x, x + y)
+
+
+def test_diff_wrt_not_allowed():
+    # issue 7027 included
+    for wrt in (
+            cos(x), re(x), x**2, x*y, 1 + x,
+            Derivative(cos(x), x), Derivative(f(f(x)), x)):
+        raises(ValueError, lambda: diff(f(x), wrt))
+    # if we don't differentiate wrt then don't raise error
+    assert diff(exp(x*y), x*y, 0) == exp(x*y)
+
+
+def test_diff_wrt_intlike():
+    class Two:
+        def __int__(self):
+            return 2
+
+    assert cos(x).diff(x, Two()) == -cos(x)
+
+
+def test_klein_gordon_lagrangian():
+    m = Symbol('m')
+    phi = f(x, t)
+
+    L = -(diff(phi, t)**2 - diff(phi, x)**2 - m**2*phi**2)/2
+    eqna = Eq(
+        diff(L, phi) - diff(L, diff(phi, x), x) - diff(L, diff(phi, t), t), 0)
+    eqnb = Eq(diff(phi, t, t) - diff(phi, x, x) + m**2*phi, 0)
+    assert eqna == eqnb
+
+
+def test_sho_lagrangian():
+    m = Symbol('m')
+    k = Symbol('k')
+    x = f(t)
+
+    L = m*diff(x, t)**2/2 - k*x**2/2
+    eqna = Eq(diff(L, x), diff(L, diff(x, t), t))
+    eqnb = Eq(-k*x, m*diff(x, t, t))
+    assert eqna == eqnb
+
+    assert diff(L, x, t) == diff(L, t, x)
+    assert diff(L, diff(x, t), t) == m*diff(x, t, 2)
+    assert diff(L, t, diff(x, t)) == -k*x + m*diff(x, t, 2)
+
+
+def test_straight_line():
+    F = f(x)
+    Fd = F.diff(x)
+    L = sqrt(1 + Fd**2)
+    assert diff(L, F) == 0
+    assert diff(L, Fd) == Fd/sqrt(1 + Fd**2)
+
+
+def test_sort_variable():
+    vsort = Derivative._sort_variable_count
+    def vsort0(*v, reverse=False):
+        return [i[0] for i in vsort([(i, 0) for i in (
+            reversed(v) if reverse else v)])]
+
+    for R in range(2):
+        assert vsort0(y, x, reverse=R) == [x, y]
+        assert vsort0(f(x), x, reverse=R) == [x, f(x)]
+        assert vsort0(f(y), f(x), reverse=R) == [f(x), f(y)]
+        assert vsort0(g(x), f(y), reverse=R) == [f(y), g(x)]
+        assert vsort0(f(x, y), f(x), reverse=R) == [f(x), f(x, y)]
+        fx = f(x).diff(x)
+        assert vsort0(fx, y, reverse=R) == [y, fx]
+        fy = f(y).diff(y)
+        assert vsort0(fy, fx, reverse=R) == [fx, fy]
+        fxx = fx.diff(x)
+        assert vsort0(fxx, fx, reverse=R) == [fx, fxx]
+        assert vsort0(Basic(x), f(x), reverse=R) == [f(x), Basic(x)]
+        assert vsort0(Basic(y), Basic(x), reverse=R) == [Basic(x), Basic(y)]
+        assert vsort0(Basic(y, z), Basic(x), reverse=R) == [
+            Basic(x), Basic(y, z)]
+        assert vsort0(fx, x, reverse=R) == [
+            x, fx] if R else [fx, x]
+        assert vsort0(Basic(x), x, reverse=R) == [
+            x, Basic(x)] if R else [Basic(x), x]
+        assert vsort0(Basic(f(x)), f(x), reverse=R) == [
+            f(x), Basic(f(x))] if R else [Basic(f(x)), f(x)]
+        assert vsort0(Basic(x, z), Basic(x), reverse=R) == [
+            Basic(x), Basic(x, z)] if R else [Basic(x, z), Basic(x)]
+    assert vsort([]) == []
+    assert _aresame(vsort([(x, 1)]), [Tuple(x, 1)])
+    assert vsort([(x, y), (x, z)]) == [(x, y + z)]
+    assert vsort([(y, 1), (x, 1 + y)]) == [(x, 1 + y), (y, 1)]
+    # coverage complete; legacy tests below
+    assert vsort([(x, 3), (y, 2), (z, 1)]) == [(x, 3), (y, 2), (z, 1)]
+    assert vsort([(h(x), 1), (g(x), 1), (f(x), 1)]) == [
+        (f(x), 1), (g(x), 1), (h(x), 1)]
+    assert vsort([(z, 1), (y, 2), (x, 3), (h(x), 1), (g(x), 1),
+        (f(x), 1)]) == [(x, 3), (y, 2), (z, 1), (f(x), 1), (g(x), 1),
+        (h(x), 1)]
+    assert vsort([(x, 1), (f(x), 1), (y, 1), (f(y), 1)]) == [(x, 1),
+        (y, 1), (f(x), 1), (f(y), 1)]
+    assert vsort([(y, 1), (x, 2), (g(x), 1), (f(x), 1), (z, 1),
+        (h(x), 1), (y, 2), (x, 1)]) == [(x, 3), (y, 3), (z, 1),
+        (f(x), 1), (g(x), 1), (h(x), 1)]
+    assert vsort([(z, 1), (y, 1), (f(x), 1), (x, 1), (f(x), 1),
+        (g(x), 1)]) == [(x, 1), (y, 1), (z, 1), (f(x), 2), (g(x), 1)]
+    assert vsort([(z, 1), (y, 2), (f(x), 1), (x, 2), (f(x), 2),
+        (g(x), 1), (z, 2), (z, 1), (y, 1), (x, 1)]) == [(x, 3), (y, 3),
+        (z, 4), (f(x), 3), (g(x), 1)]
+    assert vsort(((y, 2), (x, 1), (y, 1), (x, 1))) == [(x, 2), (y, 3)]
+    assert isinstance(vsort([(x, 3), (y, 2), (z, 1)])[0], Tuple)
+    assert vsort([(x, 1), (f(x), 1), (x, 1)]) == [(x, 2), (f(x), 1)]
+    assert vsort([(y, 2), (x, 3), (z, 1)]) == [(x, 3), (y, 2), (z, 1)]
+    assert vsort([(h(y), 1), (g(x), 1), (f(x), 1)]) == [
+        (f(x), 1), (g(x), 1), (h(y), 1)]
+    assert vsort([(x, 1), (y, 1), (x, 1)]) == [(x, 2), (y, 1)]
+    assert vsort([(f(x), 1), (f(y), 1), (f(x), 1)]) == [
+        (f(x), 2), (f(y), 1)]
+    dfx = f(x).diff(x)
+    self = [(dfx, 1), (x, 1)]
+    assert vsort(self) == self
+    assert vsort([
+        (dfx, 1), (y, 1), (f(x), 1), (x, 1), (f(y), 1), (x, 1)]) == [
+        (y, 1), (f(x), 1), (f(y), 1), (dfx, 1), (x, 2)]
+    dfy = f(y).diff(y)
+    assert vsort([(dfy, 1), (dfx, 1)]) == [(dfx, 1), (dfy, 1)]
+    d2fx = dfx.diff(x)
+    assert vsort([(d2fx, 1), (dfx, 1)]) == [(dfx, 1), (d2fx, 1)]
+
+
+def test_multiple_derivative():
+    # Issue #15007
+    assert f(x, y).diff(y, y, x, y, x
+        ) == Derivative(f(x, y), (x, 2), (y, 3))
+
+
+def test_unhandled():
+    class MyExpr(Expr):
+        def _eval_derivative(self, s):
+            if not s.name.startswith('xi'):
+                return self
+            else:
+                return None
+
+    eq = MyExpr(f(x), y, z)
+    assert diff(eq, x, y, f(x), z) == Derivative(eq, f(x))
+    assert diff(eq, f(x), x) == Derivative(eq, f(x))
+    assert f(x, y).diff(x,(y, z)) == Derivative(f(x, y), x, (y, z))
+    assert f(x, y).diff(x,(y, 0)) == Derivative(f(x, y), x)
+
+
+def test_nfloat():
+    from sympy.core.basic import _aresame
+    from sympy.polys.rootoftools import rootof
+
+    x = Symbol("x")
+    eq = x**Rational(4, 3) + 4*x**(S.One/3)/3
+    assert _aresame(nfloat(eq), x**Rational(4, 3) + (4.0/3)*x**(S.One/3))
+    assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3))
+    eq = x**Rational(4, 3) + 4*x**(x/3)/3
+    assert _aresame(nfloat(eq), x**Rational(4, 3) + (4.0/3)*x**(x/3))
+    big = 12345678901234567890
+    # specify precision to match value used in nfloat
+    Float_big = Float(big, 15)
+    assert _aresame(nfloat(big), Float_big)
+    assert _aresame(nfloat(big*x), Float_big*x)
+    assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
+    assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
+
+    # issue 6342
+    f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
+    assert not any(a.free_symbols for a in solveset(f.subs(x, -0.139)))
+
+    # issue 6632
+    assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
+        9.99999999800000e-11
+
+    # issue 7122
+    eq = cos(3*x**4 + y)*rootof(x**5 + 3*x**3 + 1, 0)
+    assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)'
+
+    # issue 10933
+    for ti in (dict, Dict):
+        d = ti({S.Half: S.Half})
+        n = nfloat(d)
+        assert isinstance(n, ti)
+        assert _aresame(list(n.items()).pop(), (S.Half, Float(.5)))
+    for ti in (dict, Dict):
+        d = ti({S.Half: S.Half})
+        n = nfloat(d, dkeys=True)
+        assert isinstance(n, ti)
+        assert _aresame(list(n.items()).pop(), (Float(.5), Float(.5)))
+    d = [S.Half]
+    n = nfloat(d)
+    assert type(n) is list
+    assert _aresame(n[0], Float(.5))
+    assert _aresame(nfloat(Eq(x, S.Half)).rhs, Float(.5))
+    assert _aresame(nfloat(S(True)), S(True))
+    assert _aresame(nfloat(Tuple(S.Half))[0], Float(.5))
+    assert nfloat(Eq((3 - I)**2/2 + I, 0)) == S.false
+    # pass along kwargs
+    assert nfloat([{S.Half: x}], dkeys=True) == [{Float(0.5): x}]
+
+    # Issue 17706
+    A = MutableMatrix([[1, 2], [3, 4]])
+    B = MutableMatrix(
+        [[Float('1.0', precision=53), Float('2.0', precision=53)],
+        [Float('3.0', precision=53), Float('4.0', precision=53)]])
+    assert _aresame(nfloat(A), B)
+    A = ImmutableMatrix([[1, 2], [3, 4]])
+    B = ImmutableMatrix(
+        [[Float('1.0', precision=53), Float('2.0', precision=53)],
+        [Float('3.0', precision=53), Float('4.0', precision=53)]])
+    assert _aresame(nfloat(A), B)
+
+    # issue 22524
+    f = Function('f')
+    assert not nfloat(f(2)).atoms(Float)
+
+
+def test_issue_7068():
+    from sympy.abc import a, b
+    f = Function('f')
+    y1 = Dummy('y')
+    y2 = Dummy('y')
+    func1 = f(a + y1 * b)
+    func2 = f(a + y2 * b)
+    func1_y = func1.diff(y1)
+    func2_y = func2.diff(y2)
+    assert func1_y != func2_y
+    z1 = Subs(f(a), a, y1)
+    z2 = Subs(f(a), a, y2)
+    assert z1 != z2
+
+
+def test_issue_7231():
+    from sympy.abc import a
+    ans1 = f(x).series(x, a)
+    res = (f(a) + (-a + x)*Subs(Derivative(f(y), y), y, a) +
+           (-a + x)**2*Subs(Derivative(f(y), y, y), y, a)/2 +
+           (-a + x)**3*Subs(Derivative(f(y), y, y, y),
+                            y, a)/6 +
+           (-a + x)**4*Subs(Derivative(f(y), y, y, y, y),
+                            y, a)/24 +
+           (-a + x)**5*Subs(Derivative(f(y), y, y, y, y, y),
+                            y, a)/120 + O((-a + x)**6, (x, a)))
+    assert res == ans1
+    ans2 = f(x).series(x, a)
+    assert res == ans2
+
+
+def test_issue_7687():
+    from sympy.core.function import Function
+    from sympy.abc import x
+    f = Function('f')(x)
+    ff = Function('f')(x)
+    match_with_cache = ff.matches(f)
+    assert isinstance(f, type(ff))
+    clear_cache()
+    ff = Function('f')(x)
+    assert isinstance(f, type(ff))
+    assert match_with_cache == ff.matches(f)
+
+
+def test_issue_7688():
+    from sympy.core.function import Function, UndefinedFunction
+
+    f = Function('f')  # actually an UndefinedFunction
+    clear_cache()
+    class A(UndefinedFunction):
+        pass
+    a = A('f')
+    assert isinstance(a, type(f))
+
+
+def test_mexpand():
+    from sympy.abc import x
+    assert _mexpand(None) is None
+    assert _mexpand(1) is S.One
+    assert _mexpand(x*(x + 1)**2) == (x*(x + 1)**2).expand()
+
+
+def test_issue_8469():
+    # This should not take forever to run
+    N = 40
+    def g(w, theta):
+        return 1/(1+exp(w-theta))
+
+    ws = symbols(['w%i'%i for i in range(N)])
+    import functools
+    expr = functools.reduce(g, ws)
+    assert isinstance(expr, Pow)
+
+
+def test_issue_12996():
+    # foo=True imitates the sort of arguments that Derivative can get
+    # from Integral when it passes doit to the expression
+    assert Derivative(im(x), x).doit(foo=True) == Derivative(im(x), x)
+
+
+def test_should_evalf():
+    # This should not take forever to run (see #8506)
+    assert isinstance(sin((1.0 + 1.0*I)**10000 + 1), sin)
+
+
+def test_Derivative_as_finite_difference():
+    # Central 1st derivative at gridpoint
+    x, h = symbols('x h', real=True)
+    dfdx = f(x).diff(x)
+    assert (dfdx.as_finite_difference([x-2, x-1, x, x+1, x+2]) -
+            (S.One/12*(f(x-2)-f(x+2)) + Rational(2, 3)*(f(x+1)-f(x-1)))).simplify() == 0
+
+    # Central 1st derivative "half-way"
+    assert (dfdx.as_finite_difference() -
+            (f(x + S.Half)-f(x - S.Half))).simplify() == 0
+    assert (dfdx.as_finite_difference(h) -
+            (f(x + h/S(2))-f(x - h/S(2)))/h).simplify() == 0
+    assert (dfdx.as_finite_difference([x - 3*h, x-h, x+h, x + 3*h]) -
+            (S(9)/(8*2*h)*(f(x+h) - f(x-h)) +
+             S.One/(24*2*h)*(f(x - 3*h) - f(x + 3*h)))).simplify() == 0
+
+    # One sided 1st derivative at gridpoint
+    assert (dfdx.as_finite_difference([0, 1, 2], 0) -
+            (Rational(-3, 2)*f(0) + 2*f(1) - f(2)/2)).simplify() == 0
+    assert (dfdx.as_finite_difference([x, x+h], x) -
+            (f(x+h) - f(x))/h).simplify() == 0
+    assert (dfdx.as_finite_difference([x-h, x, x+h], x-h) -
+            (-S(3)/(2*h)*f(x-h) + 2/h*f(x) -
+             S.One/(2*h)*f(x+h))).simplify() == 0
+
+    # One sided 1st derivative "half-way"
+    assert (dfdx.as_finite_difference([x-h, x+h, x + 3*h, x + 5*h, x + 7*h])
+            - 1/(2*h)*(-S(11)/(12)*f(x-h) + S(17)/(24)*f(x+h)
+                       + Rational(3, 8)*f(x + 3*h) - Rational(5, 24)*f(x + 5*h)
+                       + S.One/24*f(x + 7*h))).simplify() == 0
+
+    d2fdx2 = f(x).diff(x, 2)
+    # Central 2nd derivative at gridpoint
+    assert (d2fdx2.as_finite_difference([x-h, x, x+h]) -
+            h**-2 * (f(x-h) + f(x+h) - 2*f(x))).simplify() == 0
+
+    assert (d2fdx2.as_finite_difference([x - 2*h, x-h, x, x+h, x + 2*h]) -
+            h**-2 * (Rational(-1, 12)*(f(x - 2*h) + f(x + 2*h)) +
+                     Rational(4, 3)*(f(x+h) + f(x-h)) - Rational(5, 2)*f(x))).simplify() == 0
+
+    # Central 2nd derivative "half-way"
+    assert (d2fdx2.as_finite_difference([x - 3*h, x-h, x+h, x + 3*h]) -
+            (2*h)**-2 * (S.Half*(f(x - 3*h) + f(x + 3*h)) -
+                         S.Half*(f(x+h) + f(x-h)))).simplify() == 0
+
+    # One sided 2nd derivative at gridpoint
+    assert (d2fdx2.as_finite_difference([x, x+h, x + 2*h, x + 3*h]) -
+            h**-2 * (2*f(x) - 5*f(x+h) +
+                     4*f(x+2*h) - f(x+3*h))).simplify() == 0
+
+    # One sided 2nd derivative at "half-way"
+    assert (d2fdx2.as_finite_difference([x-h, x+h, x + 3*h, x + 5*h]) -
+            (2*h)**-2 * (Rational(3, 2)*f(x-h) - Rational(7, 2)*f(x+h) + Rational(5, 2)*f(x + 3*h) -
+                         S.Half*f(x + 5*h))).simplify() == 0
+
+    d3fdx3 = f(x).diff(x, 3)
+    # Central 3rd derivative at gridpoint
+    assert (d3fdx3.as_finite_difference() -
+            (-f(x - Rational(3, 2)) + 3*f(x - S.Half) -
+             3*f(x + S.Half) + f(x + Rational(3, 2)))).simplify() == 0
+
+    assert (d3fdx3.as_finite_difference(
+        [x - 3*h, x - 2*h, x-h, x, x+h, x + 2*h, x + 3*h]) -
+        h**-3 * (S.One/8*(f(x - 3*h) - f(x + 3*h)) - f(x - 2*h) +
+                 f(x + 2*h) + Rational(13, 8)*(f(x-h) - f(x+h)))).simplify() == 0
+
+    # Central 3rd derivative at "half-way"
+    assert (d3fdx3.as_finite_difference([x - 3*h, x-h, x+h, x + 3*h]) -
+            (2*h)**-3 * (f(x + 3*h)-f(x - 3*h) +
+                         3*(f(x-h)-f(x+h)))).simplify() == 0
+
+    # One sided 3rd derivative at gridpoint
+    assert (d3fdx3.as_finite_difference([x, x+h, x + 2*h, x + 3*h]) -
+            h**-3 * (f(x + 3*h)-f(x) + 3*(f(x+h)-f(x + 2*h)))).simplify() == 0
+
+    # One sided 3rd derivative at "half-way"
+    assert (d3fdx3.as_finite_difference([x-h, x+h, x + 3*h, x + 5*h]) -
+            (2*h)**-3 * (f(x + 5*h)-f(x-h) +
+                         3*(f(x+h)-f(x + 3*h)))).simplify() == 0
+
+    # issue 11007
+    y = Symbol('y', real=True)
+    d2fdxdy = f(x, y).diff(x, y)
+
+    ref0 = Derivative(f(x + S.Half, y), y) - Derivative(f(x - S.Half, y), y)
+    assert (d2fdxdy.as_finite_difference(wrt=x) - ref0).simplify() == 0
+
+    half = S.Half
+    xm, xp, ym, yp = x-half, x+half, y-half, y+half
+    ref2 = f(xm, ym) + f(xp, yp) - f(xp, ym) - f(xm, yp)
+    assert (d2fdxdy.as_finite_difference() - ref2).simplify() == 0
+
+
+def test_issue_11159():
+    # Tests Application._eval_subs
+    with _exp_is_pow(False):
+        expr1 = E
+        expr0 = expr1 * expr1
+        expr1 = expr0.subs(expr1,expr0)
+        assert expr0 == expr1
+    with _exp_is_pow(True):
+        expr1 = E
+        expr0 = expr1 * expr1
+        expr2 = expr0.subs(expr1, expr0)
+        assert expr2 == E ** 4
+
+
+def test_issue_12005():
+    e1 = Subs(Derivative(f(x), x), x, x)
+    assert e1.diff(x) == Derivative(f(x), x, x)
+    e2 = Subs(Derivative(f(x), x), x, x**2 + 1)
+    assert e2.diff(x) == 2*x*Subs(Derivative(f(x), x, x), x, x**2 + 1)
+    e3 = Subs(Derivative(f(x) + y**2 - y, y), y, y**2)
+    assert e3.diff(y) == 4*y
+    e4 = Subs(Derivative(f(x + y), y), y, (x**2))
+    assert e4.diff(y) is S.Zero
+    e5 = Subs(Derivative(f(x), x), (y, z), (y, z))
+    assert e5.diff(x) == Derivative(f(x), x, x)
+    assert f(g(x)).diff(g(x), g(x)) == Derivative(f(g(x)), g(x), g(x))
+
+
+def test_issue_13843():
+    x = symbols('x')
+    f = Function('f')
+    m, n = symbols('m n', integer=True)
+    assert Derivative(Derivative(f(x), (x, m)), (x, n)) == Derivative(f(x), (x, m + n))
+    assert Derivative(Derivative(f(x), (x, m+5)), (x, n+3)) == Derivative(f(x), (x, m + n + 8))
+
+    assert Derivative(f(x), (x, n)).doit() == Derivative(f(x), (x, n))
+
+
+def test_order_could_be_zero():
+    x, y = symbols('x, y')
+    n = symbols('n', integer=True, nonnegative=True)
+    m = symbols('m', integer=True, positive=True)
+    assert diff(y, (x, n)) == Piecewise((y, Eq(n, 0)), (0, True))
+    assert diff(y, (x, n + 1)) is S.Zero
+    assert diff(y, (x, m)) is S.Zero
+
+
+def test_undefined_function_eq():
+    f = Function('f')
+    f2 = Function('f')
+    g = Function('g')
+    f_real = Function('f', is_real=True)
+
+    # This test may only be meaningful if the cache is turned off
+    assert f == f2
+    assert hash(f) == hash(f2)
+    assert f == f
+
+    assert f != g
+
+    assert f != f_real
+
+
+def test_function_assumptions():
+    x = Symbol('x')
+    f = Function('f')
+    f_real = Function('f', real=True)
+    f_real1 = Function('f', real=1)
+    f_real_inherit = Function(Symbol('f', real=True))
+
+    assert f_real == f_real1  # assumptions are sanitized
+    assert f != f_real
+    assert f(x) != f_real(x)
+
+    assert f(x).is_real is None
+    assert f_real(x).is_real is True
+    assert f_real_inherit(x).is_real is True and f_real_inherit.name == 'f'
+
+    # Can also do it this way, but it won't be equal to f_real because of the
+    # way UndefinedFunction.__new__ works. Any non-recognized assumptions
+    # are just added literally as something which is used in the hash
+    f_real2 = Function('f', is_real=True)
+    assert f_real2(x).is_real is True
+
+
+def test_undef_fcn_float_issue_6938():
+    f = Function('ceil')
+    assert not f(0.3).is_number
+    f = Function('sin')
+    assert not f(0.3).is_number
+    assert not f(pi).evalf().is_number
+    x = Symbol('x')
+    assert not f(x).evalf(subs={x:1.2}).is_number
+
+
+def test_undefined_function_eval():
+    # Issue 15170. Make sure UndefinedFunction with eval defined works
+    # properly.
+
+    fdiff = lambda self, argindex=1: cos(self.args[argindex - 1])
+    eval = classmethod(lambda cls, t: None)
+    _imp_ = classmethod(lambda cls, t: sin(t))
+
+    temp = Function('temp', fdiff=fdiff, eval=eval, _imp_=_imp_)
+
+    expr = temp(t)
+    assert sympify(expr) == expr
+    assert type(sympify(expr)).fdiff.__name__ == ""
+    assert expr.diff(t) == cos(t)
+
+
+def test_issue_15241():
+    F = f(x)
+    Fx = F.diff(x)
+    assert (F + x*Fx).diff(x, Fx) == 2
+    assert (F + x*Fx).diff(Fx, x) == 1
+    assert (x*F + x*Fx*F).diff(F, x) == x*Fx.diff(x) + Fx + 1
+    assert (x*F + x*Fx*F).diff(x, F) == x*Fx.diff(x) + Fx + 1
+    y = f(x)
+    G = f(y)
+    Gy = G.diff(y)
+    assert (G + y*Gy).diff(y, Gy) == 2
+    assert (G + y*Gy).diff(Gy, y) == 1
+    assert (y*G + y*Gy*G).diff(G, y) == y*Gy.diff(y) + Gy + 1
+    assert (y*G + y*Gy*G).diff(y, G) == y*Gy.diff(y) + Gy + 1
+
+
+def test_issue_15226():
+    assert Subs(Derivative(f(y), x, y), y, g(x)).doit() != 0
+
+
+def test_issue_7027():
+    for wrt in (cos(x), re(x), Derivative(cos(x), x)):
+        raises(ValueError, lambda: diff(f(x), wrt))
+
+
+def test_derivative_quick_exit():
+    assert f(x).diff(y) == 0
+    assert f(x).diff(y, f(x)) == 0
+    assert f(x).diff(x, f(y)) == 0
+    assert f(f(x)).diff(x, f(x), f(y)) == 0
+    assert f(f(x)).diff(x, f(x), y) == 0
+    assert f(x).diff(g(x)) == 0
+    assert f(x).diff(x, f(x).diff(x)) == 1
+    df = f(x).diff(x)
+    assert f(x).diff(df) == 0
+    dg = g(x).diff(x)
+    assert dg.diff(df).doit() == 0
+
+
+def test_issue_15084_13166():
+    eq = f(x, g(x))
+    assert eq.diff((g(x), y)) == Derivative(f(x, g(x)), (g(x), y))
+    # issue 13166
+    assert eq.diff(x, 2).doit() == (
+        (Derivative(f(x, g(x)), (g(x), 2))*Derivative(g(x), x) +
+        Subs(Derivative(f(x, _xi_2), _xi_2, x), _xi_2, g(x)))*Derivative(g(x),
+        x) + Derivative(f(x, g(x)), g(x))*Derivative(g(x), (x, 2)) +
+        Derivative(g(x), x)*Subs(Derivative(f(_xi_1, g(x)), _xi_1, g(x)),
+        _xi_1, x) + Subs(Derivative(f(_xi_1, g(x)), (_xi_1, 2)), _xi_1, x))
+    # issue 6681
+    assert diff(f(x, t, g(x, t)), x).doit() == (
+        Derivative(f(x, t, g(x, t)), g(x, t))*Derivative(g(x, t), x) +
+        Subs(Derivative(f(_xi_1, t, g(x, t)), _xi_1), _xi_1, x))
+    # make sure the order doesn't matter when using diff
+    assert eq.diff(x, g(x)) == eq.diff(g(x), x)
+
+
+def test_negative_counts():
+    # issue 13873
+    raises(ValueError, lambda: sin(x).diff(x, -1))
+
+
+def test_Derivative__new__():
+    raises(TypeError, lambda: f(x).diff((x, 2), 0))
+    assert f(x, y).diff([(x, y), 0]) == f(x, y)
+    assert f(x, y).diff([(x, y), 1]) == NDimArray([
+        Derivative(f(x, y), x), Derivative(f(x, y), y)])
+    assert f(x,y).diff(y, (x, z), y, x) == Derivative(
+        f(x, y), (x, z + 1), (y, 2))
+    assert Matrix([x]).diff(x, 2) == Matrix([0])  # is_zero exit
+
+
+def test_issue_14719_10150():
+    class V(Expr):
+        _diff_wrt = True
+        is_scalar = False
+    assert V().diff(V()) == Derivative(V(), V())
+    assert (2*V()).diff(V()) == 2*Derivative(V(), V())
+    class X(Expr):
+        _diff_wrt = True
+    assert X().diff(X()) == 1
+    assert (2*X()).diff(X()) == 2
+
+
+def test_noncommutative_issue_15131():
+    x = Symbol('x', commutative=False)
+    t = Symbol('t', commutative=False)
+    fx = Function('Fx', commutative=False)(x)
+    ft = Function('Ft', commutative=False)(t)
+    A = Symbol('A', commutative=False)
+    eq = fx * A * ft
+    eqdt = eq.diff(t)
+    assert eqdt.args[-1] == ft.diff(t)
+
+
+def test_Subs_Derivative():
+    a = Derivative(f(g(x), h(x)), g(x), h(x),x)
+    b = Derivative(Derivative(f(g(x), h(x)), g(x), h(x)),x)
+    c = f(g(x), h(x)).diff(g(x), h(x), x)
+    d = f(g(x), h(x)).diff(g(x), h(x)).diff(x)
+    e = Derivative(f(g(x), h(x)), x)
+    eqs = (a, b, c, d, e)
+    subs = lambda arg: arg.subs(f, Lambda((x, y), exp(x + y))
+        ).subs(g(x), 1/x).subs(h(x), x**3)
+    ans = 3*x**2*exp(1/x)*exp(x**3) - exp(1/x)*exp(x**3)/x**2
+    assert all(subs(i).doit().expand() == ans for i in eqs)
+    assert all(subs(i.doit()).doit().expand() == ans for i in eqs)
+
+def test_issue_15360():
+    f = Function('f')
+    assert f.name == 'f'
+
+
+def test_issue_15947():
+    assert f._diff_wrt is False
+    raises(TypeError, lambda: f(f))
+    raises(TypeError, lambda: f(x).diff(f))
+
+
+def test_Derivative_free_symbols():
+    f = Function('f')
+    n = Symbol('n', integer=True, positive=True)
+    assert diff(f(x), (x, n)).free_symbols == {n, x}
+
+
+def test_issue_20683():
+    x = Symbol('x')
+    y = Symbol('y')
+    z = Symbol('z')
+    y = Derivative(z, x).subs(x,0)
+    assert y.doit() == 0
+    y = Derivative(8, x).subs(x,0)
+    assert y.doit() == 0
+
+
+def test_issue_10503():
+    f = exp(x**3)*cos(x**6)
+    assert f.series(x, 0, 14) == 1 + x**3 + x**6/2 + x**9/6 - 11*x**12/24 + O(x**14)
+
+
+def test_issue_17382():
+    # copied from sympy/core/tests/test_evalf.py
+    def NS(e, n=15, **options):
+        return sstr(sympify(e).evalf(n, **options), full_prec=True)
+
+    x = Symbol('x')
+    expr = solveset(2 * cos(x) * cos(2 * x) - 1, x, S.Reals)
+    expected = "Union(" \
+               "ImageSet(Lambda(_n, 6.28318530717959*_n + 5.79812359592087), Integers), " \
+               "ImageSet(Lambda(_n, 6.28318530717959*_n + 0.485061711258717), Integers))"
+    assert NS(expr) == expected
+
+def test_eval_sympified():
+    # Check both arguments and return types from eval are sympified
+
+    class F(Function):
+        @classmethod
+        def eval(cls, x):
+            assert x is S.One
+            return 1
+
+    assert F(1) is S.One
+
+    # String arguments are not allowed
+    class F2(Function):
+        @classmethod
+        def eval(cls, x):
+            if x == 0:
+                return '1'
+
+    raises(SympifyError, lambda: F2(0))
+    F2(1) # Doesn't raise
+
+    # TODO: Disable string inputs (https://github.com/sympy/sympy/issues/11003)
+    # raises(SympifyError, lambda: F2('2'))
+
+def test_eval_classmethod_check():
+    with raises(TypeError):
+        class F(Function):
+            def eval(self, x):
+                pass
+
+
+def test_issue_27163():
+    # https://github.com/sympy/sympy/issues/27163
+    raises(TypeError, lambda: Derivative(f, t))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_kind.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_kind.py
new file mode 100644
index 0000000000000000000000000000000000000000..cbfdffb9304b49488756752ca198fd4067087437
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_kind.py
@@ -0,0 +1,57 @@
+from sympy.core.add import Add
+from sympy.core.kind import NumberKind, UndefinedKind
+from sympy.core.mul import Mul
+from sympy.core.numbers import pi, zoo, I, AlgebraicNumber
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.integrals.integrals import Integral
+from sympy.core.function import Derivative
+from sympy.matrices import (Matrix, SparseMatrix, ImmutableMatrix,
+    ImmutableSparseMatrix, MatrixSymbol, MatrixKind, MatMul)
+
+comm_x = Symbol('x')
+noncomm_x = Symbol('x', commutative=False)
+
+def test_NumberKind():
+    assert S.One.kind is NumberKind
+    assert pi.kind is NumberKind
+    assert S.NaN.kind is NumberKind
+    assert zoo.kind is NumberKind
+    assert I.kind is NumberKind
+    assert AlgebraicNumber(1).kind is NumberKind
+
+def test_Add_kind():
+    assert Add(2, 3, evaluate=False).kind is NumberKind
+    assert Add(2,comm_x).kind is NumberKind
+    assert Add(2,noncomm_x).kind is UndefinedKind
+
+def test_mul_kind():
+    assert Mul(2,comm_x, evaluate=False).kind is NumberKind
+    assert Mul(2,3, evaluate=False).kind is NumberKind
+    assert Mul(noncomm_x,2, evaluate=False).kind is UndefinedKind
+    assert Mul(2,noncomm_x, evaluate=False).kind is UndefinedKind
+
+def test_Symbol_kind():
+    assert comm_x.kind is NumberKind
+    assert noncomm_x.kind is UndefinedKind
+
+def test_Integral_kind():
+    A = MatrixSymbol('A', 2,2)
+    assert Integral(comm_x, comm_x).kind is NumberKind
+    assert Integral(A, comm_x).kind is MatrixKind(NumberKind)
+
+def test_Derivative_kind():
+    A = MatrixSymbol('A', 2,2)
+    assert Derivative(comm_x, comm_x).kind is NumberKind
+    assert Derivative(A, comm_x).kind is MatrixKind(NumberKind)
+
+def test_Matrix_kind():
+    classes = (Matrix, SparseMatrix, ImmutableMatrix, ImmutableSparseMatrix)
+    for cls in classes:
+        m = cls.zeros(3, 2)
+        assert m.kind is MatrixKind(NumberKind)
+
+def test_MatMul_kind():
+    M = Matrix([[1,2],[3,4]])
+    assert MatMul(2, M).kind is MatrixKind(NumberKind)
+    assert MatMul(comm_x, M).kind is MatrixKind(NumberKind)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_logic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_logic.py
new file mode 100644
index 0000000000000000000000000000000000000000..df5647f32ea7c4e326eb4e3aec6a7b2987f32aee
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_logic.py
@@ -0,0 +1,198 @@
+from sympy.core.logic import (fuzzy_not, Logic, And, Or, Not, fuzzy_and,
+    fuzzy_or, _fuzzy_group, _torf, fuzzy_nand, fuzzy_xor)
+from sympy.testing.pytest import raises
+
+from itertools import product
+
+T = True
+F = False
+U = None
+
+
+
+def test_torf():
+    v = [T, F, U]
+    for i in product(*[v]*3):
+        assert _torf(i) is (True if all(j for j in i) else
+                            (False if all(j is False for j in i) else None))
+
+
+def test_fuzzy_group():
+    v = [T, F, U]
+    for i in product(*[v]*3):
+        assert _fuzzy_group(i) is (None if None in i else
+                                   (True if all(j for j in i) else False))
+        assert _fuzzy_group(i, quick_exit=True) is \
+            (None if (i.count(False) > 1) else
+             (None if None in i else (True if all(j for j in i) else False)))
+    it = (True if (i == 0) else None for i in range(2))
+    assert _torf(it) is None
+    it = (True if (i == 1) else None for i in range(2))
+    assert _torf(it) is None
+
+
+def test_fuzzy_not():
+    assert fuzzy_not(T) == F
+    assert fuzzy_not(F) == T
+    assert fuzzy_not(U) == U
+
+
+def test_fuzzy_and():
+    assert fuzzy_and([T, T]) == T
+    assert fuzzy_and([T, F]) == F
+    assert fuzzy_and([T, U]) == U
+    assert fuzzy_and([F, F]) == F
+    assert fuzzy_and([F, U]) == F
+    assert fuzzy_and([U, U]) == U
+    assert [fuzzy_and([w]) for w in [U, T, F]] == [U, T, F]
+    assert fuzzy_and([T, F, U]) == F
+    assert fuzzy_and([]) == T
+    raises(TypeError, lambda: fuzzy_and())
+
+
+def test_fuzzy_or():
+    assert fuzzy_or([T, T]) == T
+    assert fuzzy_or([T, F]) == T
+    assert fuzzy_or([T, U]) == T
+    assert fuzzy_or([F, F]) == F
+    assert fuzzy_or([F, U]) == U
+    assert fuzzy_or([U, U]) == U
+    assert [fuzzy_or([w]) for w in [U, T, F]] == [U, T, F]
+    assert fuzzy_or([T, F, U]) == T
+    assert fuzzy_or([]) == F
+    raises(TypeError, lambda: fuzzy_or())
+
+
+def test_logic_cmp():
+    l1 = And('a', Not('b'))
+    l2 = And('a', Not('b'))
+
+    assert hash(l1) == hash(l2)
+    assert (l1 == l2) == T
+    assert (l1 != l2) == F
+
+    assert And('a', 'b', 'c') == And('b', 'a', 'c')
+    assert And('a', 'b', 'c') == And('c', 'b', 'a')
+    assert And('a', 'b', 'c') == And('c', 'a', 'b')
+
+    assert Not('a') < Not('b')
+    assert (Not('b') < Not('a')) is False
+    assert (Not('a') < 2) is False
+
+
+def test_logic_onearg():
+    assert And() is True
+    assert Or() is False
+
+    assert And(T) == T
+    assert And(F) == F
+    assert Or(T) == T
+    assert Or(F) == F
+
+    assert And('a') == 'a'
+    assert Or('a') == 'a'
+
+
+def test_logic_xnotx():
+    assert And('a', Not('a')) == F
+    assert Or('a', Not('a')) == T
+
+
+def test_logic_eval_TF():
+    assert And(F, F) == F
+    assert And(F, T) == F
+    assert And(T, F) == F
+    assert And(T, T) == T
+
+    assert Or(F, F) == F
+    assert Or(F, T) == T
+    assert Or(T, F) == T
+    assert Or(T, T) == T
+
+    assert And('a', T) == 'a'
+    assert And('a', F) == F
+    assert Or('a', T) == T
+    assert Or('a', F) == 'a'
+
+
+def test_logic_combine_args():
+    assert And('a', 'b', 'a') == And('a', 'b')
+    assert Or('a', 'b', 'a') == Or('a', 'b')
+
+    assert And(And('a', 'b'), And('c', 'd')) == And('a', 'b', 'c', 'd')
+    assert Or(Or('a', 'b'), Or('c', 'd')) == Or('a', 'b', 'c', 'd')
+
+    assert Or('t', And('n', 'p', 'r'), And('n', 'r'), And('n', 'p', 'r'), 't',
+              And('n', 'r')) == Or('t', And('n', 'p', 'r'), And('n', 'r'))
+
+
+def test_logic_expand():
+    t = And(Or('a', 'b'), 'c')
+    assert t.expand() == Or(And('a', 'c'), And('b', 'c'))
+
+    t = And(Or('a', Not('b')), 'b')
+    assert t.expand() == And('a', 'b')
+
+    t = And(Or('a', 'b'), Or('c', 'd'))
+    assert t.expand() == \
+        Or(And('a', 'c'), And('a', 'd'), And('b', 'c'), And('b', 'd'))
+
+
+def test_logic_fromstring():
+    S = Logic.fromstring
+
+    assert S('a') == 'a'
+    assert S('!a') == Not('a')
+    assert S('a & b') == And('a', 'b')
+    assert S('a | b') == Or('a', 'b')
+    assert S('a | b & c') == And(Or('a', 'b'), 'c')
+    assert S('a & b | c') == Or(And('a', 'b'), 'c')
+    assert S('a & b & c') == And('a', 'b', 'c')
+    assert S('a | b | c') == Or('a', 'b', 'c')
+
+    raises(ValueError, lambda: S('| a'))
+    raises(ValueError, lambda: S('& a'))
+    raises(ValueError, lambda: S('a | | b'))
+    raises(ValueError, lambda: S('a | & b'))
+    raises(ValueError, lambda: S('a & & b'))
+    raises(ValueError, lambda: S('a |'))
+    raises(ValueError, lambda: S('a|b'))
+    raises(ValueError, lambda: S('!'))
+    raises(ValueError, lambda: S('! a'))
+    raises(ValueError, lambda: S('!(a + 1)'))
+    raises(ValueError, lambda: S(''))
+
+
+def test_logic_not():
+    assert Not('a') != '!a'
+    assert Not('!a') != 'a'
+    assert Not(True) == False
+    assert Not(False) == True
+
+    # NOTE: we may want to change default Not behaviour and put this
+    # functionality into some method.
+    assert Not(And('a', 'b')) == Or(Not('a'), Not('b'))
+    assert Not(Or('a', 'b')) == And(Not('a'), Not('b'))
+
+    raises(ValueError, lambda: Not(1))
+
+
+def test_formatting():
+    S = Logic.fromstring
+    raises(ValueError, lambda: S('a&b'))
+    raises(ValueError, lambda: S('a|b'))
+    raises(ValueError, lambda: S('! a'))
+
+
+def test_fuzzy_xor():
+    assert fuzzy_xor((None,)) is None
+    assert fuzzy_xor((None, True)) is None
+    assert fuzzy_xor((None, False)) is None
+    assert fuzzy_xor((True, False)) is True
+    assert fuzzy_xor((True, True)) is False
+    assert fuzzy_xor((True, True, False)) is False
+    assert fuzzy_xor((True, True, False, True)) is True
+
+def test_fuzzy_nand():
+    for args in [(1, 0), (1, 1), (0, 0)]:
+        assert fuzzy_nand(args) == fuzzy_not(fuzzy_and(args))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_match.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_match.py
new file mode 100644
index 0000000000000000000000000000000000000000..b44012bebc4a5f3ec413c236dca1dec71da78cf5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_match.py
@@ -0,0 +1,766 @@
+from sympy import abc
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Float, I, Integer, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, Wild, symbols)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.hyper import meijerg
+from sympy.polys.polytools import Poly
+from sympy.simplify.radsimp import collect
+from sympy.simplify.simplify import signsimp
+
+from sympy.testing.pytest import XFAIL
+
+
+def test_symbol():
+    x = Symbol('x')
+    a, b, c, p, q = map(Wild, 'abcpq')
+
+    e = x
+    assert e.match(x) == {}
+    assert e.matches(x) == {}
+    assert e.match(a) == {a: x}
+
+    e = Rational(5)
+    assert e.match(c) == {c: 5}
+    assert e.match(e) == {}
+    assert e.match(e + 1) is None
+
+
+def test_add():
+    x, y, a, b, c = map(Symbol, 'xyabc')
+    p, q, r = map(Wild, 'pqr')
+
+    e = a + b
+    assert e.match(p + b) == {p: a}
+    assert e.match(p + a) == {p: b}
+
+    e = 1 + b
+    assert e.match(p + b) == {p: 1}
+
+    e = a + b + c
+    assert e.match(a + p + c) == {p: b}
+    assert e.match(b + p + c) == {p: a}
+
+    e = a + b + c + x
+    assert e.match(a + p + x + c) == {p: b}
+    assert e.match(b + p + c + x) == {p: a}
+    assert e.match(b) is None
+    assert e.match(b + p) == {p: a + c + x}
+    assert e.match(a + p + c) == {p: b + x}
+    assert e.match(b + p + c) == {p: a + x}
+
+    e = 4*x + 5
+    assert e.match(4*x + p) == {p: 5}
+    assert e.match(3*x + p) == {p: x + 5}
+    assert e.match(p*x + 5) == {p: 4}
+
+
+def test_power():
+    x, y, a, b, c = map(Symbol, 'xyabc')
+    p, q, r = map(Wild, 'pqr')
+
+    e = (x + y)**a
+    assert e.match(p**q) == {p: x + y, q: a}
+    assert e.match(p**p) is None
+
+    e = (x + y)**(x + y)
+    assert e.match(p**p) == {p: x + y}
+    assert e.match(p**q) == {p: x + y, q: x + y}
+
+    e = (2*x)**2
+    assert e.match(p*q**r) == {p: 4, q: x, r: 2}
+
+    e = Integer(1)
+    assert e.match(x**p) == {p: 0}
+
+
+def test_match_exclude():
+    x = Symbol('x')
+    y = Symbol('y')
+    p = Wild("p")
+    q = Wild("q")
+    r = Wild("r")
+
+    e = Rational(6)
+    assert e.match(2*p) == {p: 3}
+
+    e = 3/(4*x + 5)
+    assert e.match(3/(p*x + q)) == {p: 4, q: 5}
+
+    e = 3/(4*x + 5)
+    assert e.match(p/(q*x + r)) == {p: 3, q: 4, r: 5}
+
+    e = 2/(x + 1)
+    assert e.match(p/(q*x + r)) == {p: 2, q: 1, r: 1}
+
+    e = 1/(x + 1)
+    assert e.match(p/(q*x + r)) == {p: 1, q: 1, r: 1}
+
+    e = 4*x + 5
+    assert e.match(p*x + q) == {p: 4, q: 5}
+
+    e = 4*x + 5*y + 6
+    assert e.match(p*x + q*y + r) == {p: 4, q: 5, r: 6}
+
+    a = Wild('a', exclude=[x])
+
+    e = 3*x
+    assert e.match(p*x) == {p: 3}
+    assert e.match(a*x) == {a: 3}
+
+    e = 3*x**2
+    assert e.match(p*x) == {p: 3*x}
+    assert e.match(a*x) is None
+
+    e = 3*x + 3 + 6/x
+    assert e.match(p*x**2 + p*x + 2*p) == {p: 3/x}
+    assert e.match(a*x**2 + a*x + 2*a) is None
+
+
+def test_mul():
+    x, y, a, b, c = map(Symbol, 'xyabc')
+    p, q = map(Wild, 'pq')
+
+    e = 4*x
+    assert e.match(p*x) == {p: 4}
+    assert e.match(p*y) is None
+    assert e.match(e + p*y) == {p: 0}
+
+    e = a*x*b*c
+    assert e.match(p*x) == {p: a*b*c}
+    assert e.match(c*p*x) == {p: a*b}
+
+    e = (a + b)*(a + c)
+    assert e.match((p + b)*(p + c)) == {p: a}
+
+    e = x
+    assert e.match(p*x) == {p: 1}
+
+    e = exp(x)
+    assert e.match(x**p*exp(x*q)) == {p: 0, q: 1}
+
+    e = I*Poly(x, x)
+    assert e.match(I*p) == {p: x}
+
+
+def test_mul_noncommutative():
+    x, y = symbols('x y')
+    A, B, C = symbols('A B C', commutative=False)
+    u, v = symbols('u v', cls=Wild)
+    w, z = symbols('w z', cls=Wild, commutative=False)
+
+    assert (u*v).matches(x) in ({v: x, u: 1}, {u: x, v: 1})
+    assert (u*v).matches(x*y) in ({v: y, u: x}, {u: y, v: x})
+    assert (u*v).matches(A) is None
+    assert (u*v).matches(A*B) is None
+    assert (u*v).matches(x*A) is None
+    assert (u*v).matches(x*y*A) is None
+    assert (u*v).matches(x*A*B) is None
+    assert (u*v).matches(x*y*A*B) is None
+
+    assert (v*w).matches(x) is None
+    assert (v*w).matches(x*y) is None
+    assert (v*w).matches(A) == {w: A, v: 1}
+    assert (v*w).matches(A*B) == {w: A*B, v: 1}
+    assert (v*w).matches(x*A) == {w: A, v: x}
+    assert (v*w).matches(x*y*A) == {w: A, v: x*y}
+    assert (v*w).matches(x*A*B) == {w: A*B, v: x}
+    assert (v*w).matches(x*y*A*B) == {w: A*B, v: x*y}
+
+    assert (v*w).matches(-x) is None
+    assert (v*w).matches(-x*y) is None
+    assert (v*w).matches(-A) == {w: A, v: -1}
+    assert (v*w).matches(-A*B) == {w: A*B, v: -1}
+    assert (v*w).matches(-x*A) == {w: A, v: -x}
+    assert (v*w).matches(-x*y*A) == {w: A, v: -x*y}
+    assert (v*w).matches(-x*A*B) == {w: A*B, v: -x}
+    assert (v*w).matches(-x*y*A*B) == {w: A*B, v: -x*y}
+
+    assert (w*z).matches(x) is None
+    assert (w*z).matches(x*y) is None
+    assert (w*z).matches(A) is None
+    assert (w*z).matches(A*B) == {w: A, z: B}
+    assert (w*z).matches(B*A) == {w: B, z: A}
+    assert (w*z).matches(A*B*C) in [{w: A, z: B*C}, {w: A*B, z: C}]
+    assert (w*z).matches(x*A) is None
+    assert (w*z).matches(x*y*A) is None
+    assert (w*z).matches(x*A*B) is None
+    assert (w*z).matches(x*y*A*B) is None
+
+    assert (w*A).matches(A) is None
+    assert (A*w*B).matches(A*B) is None
+
+    assert (u*w*z).matches(x) is None
+    assert (u*w*z).matches(x*y) is None
+    assert (u*w*z).matches(A) is None
+    assert (u*w*z).matches(A*B) == {u: 1, w: A, z: B}
+    assert (u*w*z).matches(B*A) == {u: 1, w: B, z: A}
+    assert (u*w*z).matches(x*A) is None
+    assert (u*w*z).matches(x*y*A) is None
+    assert (u*w*z).matches(x*A*B) == {u: x, w: A, z: B}
+    assert (u*w*z).matches(x*B*A) == {u: x, w: B, z: A}
+    assert (u*w*z).matches(x*y*A*B) == {u: x*y, w: A, z: B}
+    assert (u*w*z).matches(x*y*B*A) == {u: x*y, w: B, z: A}
+
+    assert (u*A).matches(x*A) == {u: x}
+    assert (u*A).matches(x*A*B) is None
+    assert (u*B).matches(x*A) is None
+    assert (u*A*B).matches(x*A*B) == {u: x}
+    assert (u*A*B).matches(x*B*A) is None
+    assert (u*A*B).matches(x*A) is None
+
+    assert (u*w*A).matches(x*A*B) is None
+    assert (u*w*B).matches(x*A*B) == {u: x, w: A}
+
+    assert (u*v*A*B).matches(x*A*B) in [{u: x, v: 1}, {v: x, u: 1}]
+    assert (u*v*A*B).matches(x*B*A) is None
+    assert (u*v*A*B).matches(u*v*A*C) is None
+
+
+def test_mul_noncommutative_mismatch():
+    A, B, C = symbols('A B C', commutative=False)
+    w = symbols('w', cls=Wild, commutative=False)
+
+    assert (w*B*w).matches(A*B*A) == {w: A}
+    assert (w*B*w).matches(A*C*B*A*C) == {w: A*C}
+    assert (w*B*w).matches(A*C*B*A*B) is None
+    assert (w*B*w).matches(A*B*C) is None
+    assert (w*w*C).matches(A*B*C) is None
+
+
+def test_mul_noncommutative_pow():
+    A, B, C = symbols('A B C', commutative=False)
+    w = symbols('w', cls=Wild, commutative=False)
+
+    assert (A*B*w).matches(A*B**2) == {w: B}
+    assert (A*(B**2)*w*(B**3)).matches(A*B**8) == {w: B**3}
+    assert (A*B*w*C).matches(A*(B**4)*C) == {w: B**3}
+
+    assert (A*B*(w**(-1))).matches(A*B*(C**(-1))) == {w: C}
+    assert (A*(B*w)**(-1)*C).matches(A*(B*C)**(-1)*C) == {w: C}
+
+    assert ((w**2)*B*C).matches((A**2)*B*C) == {w: A}
+    assert ((w**2)*B*(w**3)).matches((A**2)*B*(A**3)) == {w: A}
+    assert ((w**2)*B*(w**4)).matches((A**2)*B*(A**2)) is None
+
+def test_complex():
+    a, b, c = map(Symbol, 'abc')
+    x, y = map(Wild, 'xy')
+
+    assert (1 + I).match(x + I) == {x: 1}
+    assert (a + I).match(x + I) == {x: a}
+    assert (2*I).match(x*I) == {x: 2}
+    assert (a*I).match(x*I) == {x: a}
+    assert (a*I).match(x*y) == {x: I, y: a}
+    assert (2*I).match(x*y) == {x: 2, y: I}
+    assert (a + b*I).match(x + y*I) == {x: a, y: b}
+
+
+def test_functions():
+    from sympy.core.function import WildFunction
+    x = Symbol('x')
+    g = WildFunction('g')
+    p = Wild('p')
+    q = Wild('q')
+
+    f = cos(5*x)
+    notf = x
+    assert f.match(p*cos(q*x)) == {p: 1, q: 5}
+    assert f.match(p*g) == {p: 1, g: cos(5*x)}
+    assert notf.match(g) is None
+
+
+@XFAIL
+def test_functions_X1():
+    from sympy.core.function import WildFunction
+    x = Symbol('x')
+    g = WildFunction('g')
+    p = Wild('p')
+    q = Wild('q')
+
+    f = cos(5*x)
+    assert f.match(p*g(q*x)) == {p: 1, g: cos, q: 5}
+
+
+def test_interface():
+    x, y = map(Symbol, 'xy')
+    p, q = map(Wild, 'pq')
+
+    assert (x + 1).match(p + 1) == {p: x}
+    assert (x*3).match(p*3) == {p: x}
+    assert (x**3).match(p**3) == {p: x}
+    assert (x*cos(y)).match(p*cos(q)) == {p: x, q: y}
+
+    assert (x*y).match(p*q) in [{p:x, q:y}, {p:y, q:x}]
+    assert (x + y).match(p + q) in [{p:x, q:y}, {p:y, q:x}]
+    assert (x*y + 1).match(p*q) in [{p:1, q:1 + x*y}, {p:1 + x*y, q:1}]
+
+
+def test_derivative1():
+    x, y = map(Symbol, 'xy')
+    p, q = map(Wild, 'pq')
+
+    f = Function('f', nargs=1)
+    fd = Derivative(f(x), x)
+
+    assert fd.match(p) == {p: fd}
+    assert (fd + 1).match(p + 1) == {p: fd}
+    assert (fd).match(fd) == {}
+    assert (3*fd).match(p*fd) is not None
+    assert (3*fd - 1).match(p*fd + q) == {p: 3, q: -1}
+
+
+def test_derivative_bug1():
+    f = Function("f")
+    x = Symbol("x")
+    a = Wild("a", exclude=[f, x])
+    b = Wild("b", exclude=[f])
+    pattern = a * Derivative(f(x), x, x) + b
+    expr = Derivative(f(x), x) + x**2
+    d1 = {b: x**2}
+    d2 = pattern.xreplace(d1).matches(expr, d1)
+    assert d2 is None
+
+
+def test_derivative2():
+    f = Function("f")
+    x = Symbol("x")
+    a = Wild("a", exclude=[f, x])
+    b = Wild("b", exclude=[f])
+    e = Derivative(f(x), x)
+    assert e.match(Derivative(f(x), x)) == {}
+    assert e.match(Derivative(f(x), x, x)) is None
+    e = Derivative(f(x), x, x)
+    assert e.match(Derivative(f(x), x)) is None
+    assert e.match(Derivative(f(x), x, x)) == {}
+    e = Derivative(f(x), x) + x**2
+    assert e.match(a*Derivative(f(x), x) + b) == {a: 1, b: x**2}
+    assert e.match(a*Derivative(f(x), x, x) + b) is None
+    e = Derivative(f(x), x, x) + x**2
+    assert e.match(a*Derivative(f(x), x) + b) is None
+    assert e.match(a*Derivative(f(x), x, x) + b) == {a: 1, b: x**2}
+
+
+def test_match_deriv_bug1():
+    n = Function('n')
+    l = Function('l')
+
+    x = Symbol('x')
+    p = Wild('p')
+
+    e = diff(l(x), x)/x - diff(diff(n(x), x), x)/2 - \
+        diff(n(x), x)**2/4 + diff(n(x), x)*diff(l(x), x)/4
+    e = e.subs(n(x), -l(x)).doit()
+    t = x*exp(-l(x))
+    t2 = t.diff(x, x)/t
+    assert e.match( (p*t2).expand() ) == {p: Rational(-1, 2)}
+
+
+def test_match_bug2():
+    x, y = map(Symbol, 'xy')
+    p, q, r = map(Wild, 'pqr')
+    res = (x + y).match(p + q + r)
+    assert (p + q + r).subs(res) == x + y
+
+
+def test_match_bug3():
+    x, a, b = map(Symbol, 'xab')
+    p = Wild('p')
+    assert (b*x*exp(a*x)).match(x*exp(p*x)) is None
+
+
+def test_match_bug4():
+    x = Symbol('x')
+    p = Wild('p')
+    e = x
+    assert e.match(-p*x) == {p: -1}
+
+
+def test_match_bug5():
+    x = Symbol('x')
+    p = Wild('p')
+    e = -x
+    assert e.match(-p*x) == {p: 1}
+
+
+def test_match_bug6():
+    x = Symbol('x')
+    p = Wild('p')
+    e = x
+    assert e.match(3*p*x) == {p: Rational(1)/3}
+
+
+def test_match_polynomial():
+    x = Symbol('x')
+    a = Wild('a', exclude=[x])
+    b = Wild('b', exclude=[x])
+    c = Wild('c', exclude=[x])
+    d = Wild('d', exclude=[x])
+
+    eq = 4*x**3 + 3*x**2 + 2*x + 1
+    pattern = a*x**3 + b*x**2 + c*x + d
+    assert eq.match(pattern) == {a: 4, b: 3, c: 2, d: 1}
+    assert (eq - 3*x**2).match(pattern) == {a: 4, b: 0, c: 2, d: 1}
+    assert (x + sqrt(2) + 3).match(a + b*x + c*x**2) == \
+        {b: 1, a: sqrt(2) + 3, c: 0}
+
+
+def test_exclude():
+    x, y, a = map(Symbol, 'xya')
+    p = Wild('p', exclude=[1, x])
+    q = Wild('q')
+    r = Wild('r', exclude=[sin, y])
+
+    assert sin(x).match(r) is None
+    assert cos(y).match(r) is None
+
+    e = 3*x**2 + y*x + a
+    assert e.match(p*x**2 + q*x + r) == {p: 3, q: y, r: a}
+
+    e = x + 1
+    assert e.match(x + p) is None
+    assert e.match(p + 1) is None
+    assert e.match(x + 1 + p) == {p: 0}
+
+    e = cos(x) + 5*sin(y)
+    assert e.match(r) is None
+    assert e.match(cos(y) + r) is None
+    assert e.match(r + p*sin(q)) == {r: cos(x), p: 5, q: y}
+
+
+def test_floats():
+    a, b = map(Wild, 'ab')
+
+    e = cos(0.12345, evaluate=False)**2
+    r = e.match(a*cos(b)**2)
+    assert r == {a: 1, b: Float(0.12345)}
+
+
+def test_Derivative_bug1():
+    f = Function("f")
+    x = abc.x
+    a = Wild("a", exclude=[f(x)])
+    b = Wild("b", exclude=[f(x)])
+    eq = f(x).diff(x)
+    assert eq.match(a*Derivative(f(x), x) + b) == {a: 1, b: 0}
+
+
+def test_match_wild_wild():
+    p = Wild('p')
+    q = Wild('q')
+    r = Wild('r')
+
+    assert p.match(q + r) in [ {q: p, r: 0}, {q: 0, r: p} ]
+    assert p.match(q*r) in [ {q: p, r: 1}, {q: 1, r: p} ]
+
+    p = Wild('p')
+    q = Wild('q', exclude=[p])
+    r = Wild('r')
+
+    assert p.match(q + r) == {q: 0, r: p}
+    assert p.match(q*r) == {q: 1, r: p}
+
+    p = Wild('p')
+    q = Wild('q', exclude=[p])
+    r = Wild('r', exclude=[p])
+
+    assert p.match(q + r) is None
+    assert p.match(q*r) is None
+
+
+def test__combine_inverse():
+    x, y = symbols("x y")
+    assert Mul._combine_inverse(x*I*y, x*I) == y
+    assert Mul._combine_inverse(x*x**(1 + y), x**(1 + y)) == x
+    assert Mul._combine_inverse(x*I*y, y*I) == x
+    assert Mul._combine_inverse(oo*I*y, y*I) is oo
+    assert Mul._combine_inverse(oo*I*y, oo*I) == y
+    assert Mul._combine_inverse(oo*I*y, oo*I) == y
+    assert Mul._combine_inverse(oo*y, -oo) == -y
+    assert Mul._combine_inverse(-oo*y, oo) == -y
+    assert Mul._combine_inverse((1-exp(x/y)),(exp(x/y)-1)) == -1
+    assert Add._combine_inverse(oo, oo) is S.Zero
+    assert Add._combine_inverse(oo*I, oo*I) is S.Zero
+    assert Add._combine_inverse(x*oo, x*oo) is S.Zero
+    assert Add._combine_inverse(-x*oo, -x*oo) is S.Zero
+    assert Add._combine_inverse((x - oo)*(x + oo), -oo)
+
+
+def test_issue_3773():
+    x = symbols('x')
+    z, phi, r = symbols('z phi r')
+    c, A, B, N = symbols('c A B N', cls=Wild)
+    l = Wild('l', exclude=(0,))
+
+    eq = z * sin(2*phi) * r**7
+    matcher = c * sin(phi*N)**l * r**A * log(r)**B
+
+    assert eq.match(matcher) == {c: z, l: 1, N: 2, A: 7, B: 0}
+    assert (-eq).match(matcher) == {c: -z, l: 1, N: 2, A: 7, B: 0}
+    assert (x*eq).match(matcher) == {c: x*z, l: 1, N: 2, A: 7, B: 0}
+    assert (-7*x*eq).match(matcher) == {c: -7*x*z, l: 1, N: 2, A: 7, B: 0}
+
+    matcher = c*sin(phi*N)**l * r**A
+
+    assert eq.match(matcher) == {c: z, l: 1, N: 2, A: 7}
+    assert (-eq).match(matcher) == {c: -z, l: 1, N: 2, A: 7}
+    assert (x*eq).match(matcher) == {c: x*z, l: 1, N: 2, A: 7}
+    assert (-7*x*eq).match(matcher) == {c: -7*x*z, l: 1, N: 2, A: 7}
+
+
+def test_issue_3883():
+    from sympy.abc import gamma, mu, x
+    f = (-gamma * (x - mu)**2 - log(gamma) + log(2*pi))/2
+    a, b, c = symbols('a b c', cls=Wild, exclude=(gamma,))
+
+    assert f.match(a * log(gamma) + b * gamma + c) == \
+        {a: Rational(-1, 2), b: -(-mu + x)**2/2, c: log(2*pi)/2}
+    assert f.expand().collect(gamma).match(a * log(gamma) + b * gamma + c) == \
+        {a: Rational(-1, 2), b: (-(x - mu)**2/2).expand(), c: (log(2*pi)/2).expand()}
+    g1 = Wild('g1', exclude=[gamma])
+    g2 = Wild('g2', exclude=[gamma])
+    g3 = Wild('g3', exclude=[gamma])
+    assert f.expand().match(g1 * log(gamma) + g2 * gamma + g3) == \
+    {g3: log(2)/2 + log(pi)/2, g1: Rational(-1, 2), g2: -mu**2/2 + mu*x - x**2/2}
+
+
+def test_issue_4418():
+    x = Symbol('x')
+    a, b, c = symbols('a b c', cls=Wild, exclude=(x,))
+    f, g = symbols('f g', cls=Function)
+
+    eq = diff(g(x)*f(x).diff(x), x)
+
+    assert eq.match(
+        g(x).diff(x)*f(x).diff(x) + g(x)*f(x).diff(x, x) + c) == {c: 0}
+    assert eq.match(a*g(x).diff(
+        x)*f(x).diff(x) + b*g(x)*f(x).diff(x, x) + c) == {a: 1, b: 1, c: 0}
+
+
+def test_issue_4700():
+    f = Function('f')
+    x = Symbol('x')
+    a, b = symbols('a b', cls=Wild, exclude=(f(x),))
+
+    p = a*f(x) + b
+    eq1 = sin(x)
+    eq2 = f(x) + sin(x)
+    eq3 = f(x) + x + sin(x)
+    eq4 = x + sin(x)
+
+    assert eq1.match(p) == {a: 0, b: sin(x)}
+    assert eq2.match(p) == {a: 1, b: sin(x)}
+    assert eq3.match(p) == {a: 1, b: x + sin(x)}
+    assert eq4.match(p) == {a: 0, b: x + sin(x)}
+
+
+def test_issue_5168():
+    a, b, c = symbols('a b c', cls=Wild)
+    x = Symbol('x')
+    f = Function('f')
+
+    assert x.match(a) == {a: x}
+    assert x.match(a*f(x)**c) == {a: x, c: 0}
+    assert x.match(a*b) == {a: 1, b: x}
+    assert x.match(a*b*f(x)**c) == {a: 1, b: x, c: 0}
+
+    assert (-x).match(a) == {a: -x}
+    assert (-x).match(a*f(x)**c) == {a: -x, c: 0}
+    assert (-x).match(a*b) == {a: -1, b: x}
+    assert (-x).match(a*b*f(x)**c) == {a: -1, b: x, c: 0}
+
+    assert (2*x).match(a) == {a: 2*x}
+    assert (2*x).match(a*f(x)**c) == {a: 2*x, c: 0}
+    assert (2*x).match(a*b) == {a: 2, b: x}
+    assert (2*x).match(a*b*f(x)**c) == {a: 2, b: x, c: 0}
+
+    assert (-2*x).match(a) == {a: -2*x}
+    assert (-2*x).match(a*f(x)**c) == {a: -2*x, c: 0}
+    assert (-2*x).match(a*b) == {a: -2, b: x}
+    assert (-2*x).match(a*b*f(x)**c) == {a: -2, b: x, c: 0}
+
+
+def test_issue_4559():
+    x = Symbol('x')
+    e = Symbol('e')
+    w = Wild('w', exclude=[x])
+    y = Wild('y')
+
+    # this is as it should be
+
+    assert (3/x).match(w/y) == {w: 3, y: x}
+    assert (3*x).match(w*y) == {w: 3, y: x}
+    assert (x/3).match(y/w) == {w: 3, y: x}
+    assert (3*x).match(y/w) == {w: S.One/3, y: x}
+    assert (3*x).match(y/w) == {w: Rational(1, 3), y: x}
+
+    # these could be allowed to fail
+
+    assert (x/3).match(w/y) == {w: S.One/3, y: 1/x}
+    assert (3*x).match(w/y) == {w: 3, y: 1/x}
+    assert (3/x).match(w*y) == {w: 3, y: 1/x}
+
+    # Note that solve will give
+    # multiple roots but match only gives one:
+    #
+    # >>> solve(x**r-y**2,y)
+    # [-x**(r/2), x**(r/2)]
+
+    r = Symbol('r', rational=True)
+    assert (x**r).match(y**2) == {y: x**(r/2)}
+    assert (x**e).match(y**2) == {y: sqrt(x**e)}
+
+    # since (x**i = y) -> x = y**(1/i) where i is an integer
+    # the following should also be valid as long as y is not
+    # zero when i is negative.
+
+    a = Wild('a')
+
+    e = S.Zero
+    assert e.match(a) == {a: e}
+    assert e.match(1/a) is None
+    assert e.match(a**.3) is None
+
+    e = S(3)
+    assert e.match(1/a) == {a: 1/e}
+    assert e.match(1/a**2) == {a: 1/sqrt(e)}
+    e = pi
+    assert e.match(1/a) == {a: 1/e}
+    assert e.match(1/a**2) == {a: 1/sqrt(e)}
+    assert (-e).match(sqrt(a)) is None
+    assert (-e).match(a**2) == {a: I*sqrt(pi)}
+
+# The pattern matcher doesn't know how to handle (x - a)**2 == (a - x)**2. To
+# avoid ambiguity in actual applications, don't put a coefficient (including a
+# minus sign) in front of a wild.
+@XFAIL
+def test_issue_4883():
+    a = Wild('a')
+    x = Symbol('x')
+
+    e = [i**2 for i in (x - 2, 2 - x)]
+    p = [i**2 for i in (x - a, a- x)]
+    for eq in e:
+        for pat in p:
+            assert eq.match(pat) == {a: 2}
+
+
+def test_issue_4319():
+    x, y = symbols('x y')
+
+    p = -x*(S.One/8 - y)
+    ans = {S.Zero, y - S.One/8}
+
+    def ok(pat):
+        assert set(p.match(pat).values()) == ans
+
+    ok(Wild("coeff", exclude=[x])*x + Wild("rest"))
+    ok(Wild("w", exclude=[x])*x + Wild("rest"))
+    ok(Wild("coeff", exclude=[x])*x + Wild("rest"))
+    ok(Wild("w", exclude=[x])*x + Wild("rest"))
+    ok(Wild("e", exclude=[x])*x + Wild("rest"))
+    ok(Wild("ress", exclude=[x])*x + Wild("rest"))
+    ok(Wild("resu", exclude=[x])*x + Wild("rest"))
+
+
+def test_issue_3778():
+    p, c, q = symbols('p c q', cls=Wild)
+    x = Symbol('x')
+
+    assert (sin(x)**2).match(sin(p)*sin(q)*c) == {q: x, c: 1, p: x}
+    assert (2*sin(x)).match(sin(p) + sin(q) + c) == {q: x, c: 0, p: x}
+
+
+def test_issue_6103():
+    x = Symbol('x')
+    a = Wild('a')
+    assert (-I*x*oo).match(I*a*oo) == {a: -x}
+
+
+def test_issue_3539():
+    a = Wild('a')
+    x = Symbol('x')
+    assert (x - 2).match(a - x) is None
+    assert (6/x).match(a*x) is None
+    assert (6/x**2).match(a/x) == {a: 6/x}
+
+def test_gh_issue_2711():
+    x = Symbol('x')
+    f = meijerg(((), ()), ((0,), ()), x)
+    a = Wild('a')
+    b = Wild('b')
+
+    assert f.find(a) == {(S.Zero,), ((), ()), ((S.Zero,), ()), x, S.Zero,
+                             (), meijerg(((), ()), ((S.Zero,), ()), x)}
+    assert f.find(a + b) == \
+        {meijerg(((), ()), ((S.Zero,), ()), x), x, S.Zero}
+    assert f.find(a**2) == {meijerg(((), ()), ((S.Zero,), ()), x), x}
+
+
+def test_issue_17354():
+    from sympy.core.symbol import (Wild, symbols)
+    x, y = symbols("x y", real=True)
+    a, b = symbols("a b", cls=Wild)
+    assert ((0 <= x).reversed | (y <= x)).match((1/a <= b) | (a <= b)) is None
+
+
+def test_match_issue_17397():
+    f = Function("f")
+    x = Symbol("x")
+    a3 = Wild('a3', exclude=[f(x), f(x).diff(x), f(x).diff(x, 2)])
+    b3 = Wild('b3', exclude=[f(x), f(x).diff(x), f(x).diff(x, 2)])
+    c3 = Wild('c3', exclude=[f(x), f(x).diff(x), f(x).diff(x, 2)])
+    deq = a3*(f(x).diff(x, 2)) + b3*f(x).diff(x) + c3*f(x)
+
+    eq = (x-2)**2*(f(x).diff(x, 2)) + (x-2)*(f(x).diff(x)) + ((x-2)**2 - 4)*f(x)
+    r = collect(eq, [f(x).diff(x, 2), f(x).diff(x), f(x)]).match(deq)
+    assert r == {a3: (x - 2)**2, c3: (x - 2)**2 - 4, b3: x - 2}
+
+    eq =x*f(x) + x*Derivative(f(x), (x, 2)) - 4*f(x) + Derivative(f(x), x) \
+        - 4*Derivative(f(x), (x, 2)) - 2*Derivative(f(x), x)/x + 4*Derivative(f(x), (x, 2))/x
+    r = collect(eq, [f(x).diff(x, 2), f(x).diff(x), f(x)]).match(deq)
+    assert r == {a3: x - 4 + 4/x, b3: 1 - 2/x, c3: x - 4}
+
+
+def test_match_issue_21942():
+    a, r, w = symbols('a, r, w', nonnegative=True)
+    p = symbols('p', positive=True)
+    g_ = Wild('g')
+    pattern = g_ ** (1 / (1 - p))
+    eq = (a * r ** (1 - p) + w ** (1 - p) * (1 - a)) ** (1 / (1 - p))
+    m = {g_: a * r ** (1 - p) + w ** (1 - p) * (1 - a)}
+    assert pattern.matches(eq) == m
+    assert (-pattern).matches(-eq) == m
+    assert pattern.matches(signsimp(eq)) is None
+
+
+def test_match_terms():
+    X, Y = map(Wild, "XY")
+    x, y, z = symbols('x y z')
+    assert (5*y - x).match(5*X - Y) == {X: y, Y: x}
+    # 15907
+    assert (x + (y - 1)*z).match(x + X*z) == {X: y - 1}
+    # 20747
+    assert (x - log(x/y)*(1-exp(x/y))).match(x - log(X/y)*(1-exp(x/y))) == {X: x}
+
+
+def test_match_bound():
+    V, W = map(Wild, "VW")
+    x, y = symbols('x y')
+    assert Sum(x, (x, 1, 2)).match(Sum(y, (y, 1, W))) is None
+    assert Sum(x, (x, 1, 2)).match(Sum(V, (V, 1, W))) == {W: 2, V:x}
+    assert Sum(x, (x, 1, 2)).match(Sum(V, (V, 1, 2))) == {V:x}
+
+
+def test_issue_22462():
+    x, f = symbols('x'), Function('f')
+    n, Q = symbols('n Q', cls=Wild)
+    pattern = -Q*f(x)**n
+    eq = 5*f(x)**2
+    assert pattern.matches(eq) == {n: 2, Q: -5}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_multidimensional.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_multidimensional.py
new file mode 100644
index 0000000000000000000000000000000000000000..765c78adf8dbed2ead43721ca4ab9510dbeeb282
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_multidimensional.py
@@ -0,0 +1,24 @@
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import sin
+from sympy.core.multidimensional import vectorize
+x, y, z = symbols('x y z')
+f, g, h = list(map(Function, 'fgh'))
+
+
+def test_vectorize():
+    @vectorize(0)
+    def vsin(x):
+        return sin(x)
+
+    assert vsin([1, x, y]) == [sin(1), sin(x), sin(y)]
+
+    @vectorize(0, 1)
+    def vdiff(f, y):
+        return diff(f, y)
+
+    assert vdiff([f(x, y, z), g(x, y, z), h(x, y, z)], [x, y, z]) == \
+         [[Derivative(f(x, y, z), x), Derivative(f(x, y, z), y),
+           Derivative(f(x, y, z), z)], [Derivative(g(x, y, z), x),
+                     Derivative(g(x, y, z), y), Derivative(g(x, y, z), z)],
+         [Derivative(h(x, y, z), x), Derivative(h(x, y, z), y), Derivative(h(x, y, z), z)]]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_noncommutative.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_noncommutative.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3d3a3cec2ef64aa500aad08b438c90cc8987581
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_noncommutative.py
@@ -0,0 +1,140 @@
+"""Tests for noncommutative symbols and expressions."""
+
+from sympy.core.function import expand
+from sympy.core.numbers import I
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.complexes import (adjoint, conjugate, transpose)
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.polys.polytools import (cancel, factor)
+from sympy.simplify.combsimp import combsimp
+from sympy.simplify.gammasimp import gammasimp
+from sympy.simplify.radsimp import (collect, radsimp, rcollect)
+from sympy.simplify.ratsimp import ratsimp
+from sympy.simplify.simplify import (posify, simplify)
+from sympy.simplify.trigsimp import trigsimp
+from sympy.abc import x, y, z
+from sympy.testing.pytest import XFAIL
+
+A, B, C = symbols("A B C", commutative=False)
+X = symbols("X", commutative=False, hermitian=True)
+Y = symbols("Y", commutative=False, antihermitian=True)
+
+
+def test_adjoint():
+    assert adjoint(A).is_commutative is False
+    assert adjoint(A*A) == adjoint(A)**2
+    assert adjoint(A*B) == adjoint(B)*adjoint(A)
+    assert adjoint(A*B**2) == adjoint(B)**2*adjoint(A)
+    assert adjoint(A*B - B*A) == adjoint(B)*adjoint(A) - adjoint(A)*adjoint(B)
+    assert adjoint(A + I*B) == adjoint(A) - I*adjoint(B)
+
+    assert adjoint(X) == X
+    assert adjoint(-I*X) == I*X
+    assert adjoint(Y) == -Y
+    assert adjoint(-I*Y) == -I*Y
+
+    assert adjoint(X) == conjugate(transpose(X))
+    assert adjoint(Y) == conjugate(transpose(Y))
+    assert adjoint(X) == transpose(conjugate(X))
+    assert adjoint(Y) == transpose(conjugate(Y))
+
+
+def test_cancel():
+    assert cancel(A*B - B*A) == A*B - B*A
+    assert cancel(A*B*(x - 1)) == A*B*(x - 1)
+    assert cancel(A*B*(x**2 - 1)/(x + 1)) == A*B*(x - 1)
+    assert cancel(A*B*(x**2 - 1)/(x + 1) - B*A*(x - 1)) == A*B*(x - 1) + (1 - x)*B*A
+
+
+@XFAIL
+def test_collect():
+    assert collect(A*B - B*A, A) == A*B - B*A
+    assert collect(A*B - B*A, B) == A*B - B*A
+    assert collect(A*B - B*A, x) == A*B - B*A
+
+
+def test_combsimp():
+    assert combsimp(A*B - B*A) == A*B - B*A
+
+
+def test_gammasimp():
+    assert gammasimp(A*B - B*A) == A*B - B*A
+
+
+def test_conjugate():
+    assert conjugate(A).is_commutative is False
+    assert (A*A).conjugate() == conjugate(A)**2
+    assert (A*B).conjugate() == conjugate(A)*conjugate(B)
+    assert (A*B**2).conjugate() == conjugate(A)*conjugate(B)**2
+    assert (A*B - B*A).conjugate() == \
+        conjugate(A)*conjugate(B) - conjugate(B)*conjugate(A)
+    assert (A*B).conjugate() - (B*A).conjugate() == \
+        conjugate(A)*conjugate(B) - conjugate(B)*conjugate(A)
+    assert (A + I*B).conjugate() == conjugate(A) - I*conjugate(B)
+
+
+def test_expand():
+    assert expand((A*B)**2) == A*B*A*B
+    assert expand(A*B - B*A) == A*B - B*A
+    assert expand((A*B/A)**2) == A*B*B/A
+    assert expand(B*A*(A + B)*B) == B*A**2*B + B*A*B**2
+    assert expand(B*A*(A + C)*B) == B*A**2*B + B*A*C*B
+
+
+def test_factor():
+    assert factor(A*B - B*A) == A*B - B*A
+
+
+def test_posify():
+    assert posify(A)[0].is_commutative is False
+    for q in (A*B/A, (A*B/A)**2, (A*B)**2, A*B - B*A):
+        p = posify(q)
+        assert p[0].subs(p[1]) == q
+
+
+def test_radsimp():
+    assert radsimp(A*B - B*A) == A*B - B*A
+
+
+@XFAIL
+def test_ratsimp():
+    assert ratsimp(A*B - B*A) == A*B - B*A
+
+
+@XFAIL
+def test_rcollect():
+    assert rcollect(A*B - B*A, A) == A*B - B*A
+    assert rcollect(A*B - B*A, B) == A*B - B*A
+    assert rcollect(A*B - B*A, x) == A*B - B*A
+
+
+def test_simplify():
+    assert simplify(A*B - B*A) == A*B - B*A
+
+
+def test_subs():
+    assert (x*y*A).subs(x*y, z) == A*z
+    assert (x*A*B).subs(x*A, C) == C*B
+    assert (x*A*x*x).subs(x**2*A, C) == x*C
+    assert (x*A*x*B).subs(x**2*A, C) == C*B
+    assert (A**2*B**2).subs(A*B**2, C) == A*C
+    assert (A*A*A + A*B*A).subs(A*A*A, C) == C + A*B*A
+
+
+def test_transpose():
+    assert transpose(A).is_commutative is False
+    assert transpose(A*A) == transpose(A)**2
+    assert transpose(A*B) == transpose(B)*transpose(A)
+    assert transpose(A*B**2) == transpose(B)**2*transpose(A)
+    assert transpose(A*B - B*A) == \
+        transpose(B)*transpose(A) - transpose(A)*transpose(B)
+    assert transpose(A + I*B) == transpose(A) + I*transpose(B)
+
+    assert transpose(X) == conjugate(X)
+    assert transpose(-I*X) == -I*conjugate(X)
+    assert transpose(Y) == -conjugate(Y)
+    assert transpose(-I*Y) == I*conjugate(Y)
+
+
+def test_trigsimp():
+    assert trigsimp(A*sin(x)**2 + A*cos(x)**2) == A
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..10d14b6ac09fb0ab102c37cb99405440bd0bbffb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_numbers.py
@@ -0,0 +1,2335 @@
+import numbers as nums
+import decimal
+from sympy.concrete.summations import Sum
+from sympy.core import (EulerGamma, Catalan, TribonacciConstant,
+    GoldenRatio)
+from sympy.core.containers import Tuple
+from sympy.core.expr import unchanged
+from sympy.core.logic import fuzzy_not
+from sympy.core.mul import Mul
+from sympy.core.numbers import (mpf_norm, seterr,
+    Integer, I, pi, comp, Rational, E, nan,
+    oo, AlgebraicNumber, Number, Float, zoo, equal_valued,
+    int_valued, all_close)
+from sympy.core.intfunc import (igcd, igcdex, igcd2, igcd_lehmer,
+    ilcm, integer_nthroot, isqrt, integer_log, mod_inverse)
+from sympy.core.power import Pow
+from sympy.core.relational import Ge, Gt, Le, Lt
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy, Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.integers import floor
+from sympy.functions.combinatorial.numbers import fibonacci
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.miscellaneous import sqrt, cbrt
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.polys.domains.realfield import RealField
+from sympy.printing.latex import latex
+from sympy.printing.repr import srepr
+from sympy.simplify import simplify
+from sympy.polys.domains.groundtypes import PythonRational
+from sympy.utilities.decorator import conserve_mpmath_dps
+from sympy.utilities.iterables import permutations
+from sympy.testing.pytest import (XFAIL, raises, _both_exp_pow,
+                                  warns_deprecated_sympy)
+from sympy import Add
+
+from mpmath import mpf
+import mpmath
+from sympy.core import numbers
+t = Symbol('t', real=False)
+
+_ninf = float(-oo)
+_inf = float(oo)
+
+
+def same_and_same_prec(a, b):
+    # stricter matching for Floats
+    return a == b and a._prec == b._prec
+
+
+def test_seterr():
+    seterr(divide=True)
+    raises(ValueError, lambda: S.Zero/S.Zero)
+    seterr(divide=False)
+    assert S.Zero / S.Zero is S.NaN
+
+
+def test_mod():
+    x = S.Half
+    y = Rational(3, 4)
+    z = Rational(5, 18043)
+
+    assert x % x == 0
+    assert x % y == S.Half
+    assert x % z == Rational(3, 36086)
+    assert y % x == Rational(1, 4)
+    assert y % y == 0
+    assert y % z == Rational(9, 72172)
+    assert z % x == Rational(5, 18043)
+    assert z % y == Rational(5, 18043)
+    assert z % z == 0
+
+    a = Float(2.6)
+
+    assert (a % .2) == 0.0
+    assert (a % 2).round(15) == 0.6
+    assert (a % 0.5).round(15) == 0.1
+
+    p = Symbol('p', infinite=True)
+
+    assert oo % oo is nan
+    assert zoo % oo is nan
+    assert 5 % oo is nan
+    assert p % 5 is nan
+
+    # In these two tests, if the precision of m does
+    # not match the precision of the ans, then it is
+    # likely that the change made now gives an answer
+    # with degraded accuracy.
+    r = Rational(500, 41)
+    f = Float('.36', 3)
+    m = r % f
+    ans = Float(r % Rational(f), 3)
+    assert m == ans and m._prec == ans._prec
+    f = Float('8.36', 3)
+    m = f % r
+    ans = Float(Rational(f) % r, 3)
+    assert m == ans and m._prec == ans._prec
+
+    s = S.Zero
+
+    assert s % float(1) == 0.0
+
+    # No rounding required since these numbers can be represented
+    # exactly.
+    assert Rational(3, 4) % Float(1.1) == 0.75
+    assert Float(1.5) % Rational(5, 4) == 0.25
+    assert Rational(5, 4).__rmod__(Float('1.5')) == 0.25
+    assert Float('1.5').__rmod__(Float('2.75')) == Float('1.25')
+    assert 2.75 % Float('1.5') == Float('1.25')
+
+    a = Integer(7)
+    b = Integer(4)
+
+    assert type(a % b) == Integer
+    assert a % b == Integer(3)
+    assert Integer(1) % Rational(2, 3) == Rational(1, 3)
+    assert Rational(7, 5) % Integer(1) == Rational(2, 5)
+    assert Integer(2) % 1.5 == 0.5
+
+    assert Integer(3).__rmod__(Integer(10)) == Integer(1)
+    assert Integer(10) % 4 == Integer(2)
+    assert 15 % Integer(4) == Integer(3)
+
+
+def test_divmod():
+    x = Symbol("x")
+    assert divmod(S(12), S(8)) == Tuple(1, 4)
+    assert divmod(-S(12), S(8)) == Tuple(-2, 4)
+    assert divmod(S.Zero, S.One) == Tuple(0, 0)
+    raises(ZeroDivisionError, lambda: divmod(S.Zero, S.Zero))
+    raises(ZeroDivisionError, lambda: divmod(S.One, S.Zero))
+    assert divmod(S(12), 8) == Tuple(1, 4)
+    assert divmod(12, S(8)) == Tuple(1, 4)
+    assert S(1024)//x == 1024//x == floor(1024/x)
+
+    assert divmod(S("2"), S("3/2")) == Tuple(S("1"), S("1/2"))
+    assert divmod(S("3/2"), S("2")) == Tuple(S("0"), S("3/2"))
+    assert divmod(S("2"), S("3.5")) == Tuple(S("0"), S("2."))
+    assert divmod(S("3.5"), S("2")) == Tuple(S("1"), S("1.5"))
+    assert divmod(S("2"), S("1/3")) == Tuple(S("6"), S("0"))
+    assert divmod(S("1/3"), S("2")) == Tuple(S("0"), S("1/3"))
+    assert divmod(S("2"), S("1/10")) == Tuple(S("20"), S("0"))
+    assert divmod(S("2"), S(".1"))[0] == 19
+    assert divmod(S("0.1"), S("2")) == Tuple(S("0"), S("0.1"))
+    assert divmod(S("2"), 2) == Tuple(S("1"), S("0"))
+    assert divmod(2, S("2")) == Tuple(S("1"), S("0"))
+    assert divmod(S("2"), 1.5) == Tuple(S("1"), S("0.5"))
+    assert divmod(1.5, S("2")) == Tuple(S("0"), S("1.5"))
+    assert divmod(0.3, S("2")) == Tuple(S("0"), S("0.3"))
+    assert divmod(S("3/2"), S("3.5")) == Tuple(S("0"), S(3/2))
+    assert divmod(S("3.5"), S("3/2")) == Tuple(S("2"), S("0.5"))
+    assert divmod(S("3/2"), S("1/3")) == Tuple(S("4"), S("1/6"))
+    assert divmod(S("1/3"), S("3/2")) == Tuple(S("0"), S("1/3"))
+    assert divmod(S("3/2"), S("0.1"))[0] == 14
+    assert divmod(S("0.1"), S("3/2")) == Tuple(S("0"), S("0.1"))
+    assert divmod(S("3/2"), 2) == Tuple(S("0"), S("3/2"))
+    assert divmod(2, S("3/2")) == Tuple(S("1"), S("1/2"))
+    assert divmod(S("3/2"), 1.5) == Tuple(S("1"), S("0."))
+    assert divmod(1.5, S("3/2")) == Tuple(S("1"), S("0."))
+    assert divmod(S("3/2"), 0.3) == Tuple(S("5"), S("0."))
+    assert divmod(0.3, S("3/2")) == Tuple(S("0"), S("0.3"))
+    assert divmod(S("1/3"), S("3.5")) == (0, 1/3)
+    assert divmod(S("3.5"), S("0.1")) == Tuple(S("35"), S("0."))
+    assert divmod(S("0.1"), S("3.5")) == Tuple(S("0"), S("0.1"))
+    assert divmod(S("3.5"), 2) == Tuple(S("1"), S("1.5"))
+    assert divmod(2, S("3.5")) == Tuple(S("0"), S("2."))
+    assert divmod(S("3.5"), 1.5) == Tuple(S("2"), S("0.5"))
+    assert divmod(1.5, S("3.5")) == Tuple(S("0"), S("1.5"))
+    assert divmod(0.3, S("3.5")) == Tuple(S("0"), S("0.3"))
+    assert divmod(S("0.1"), S("1/3")) == Tuple(S("0"), S("0.1"))
+    assert divmod(S("1/3"), 2) == Tuple(S("0"), S("1/3"))
+    assert divmod(2, S("1/3")) == Tuple(S("6"), S("0"))
+    assert divmod(S("1/3"), 1.5) == (0, 1/3)
+    assert divmod(0.3, S("1/3")) == (0, 0.3)
+    assert divmod(S("0.1"), 2) == (0, 0.1)
+    assert divmod(2, S("0.1"))[0] == 19
+    assert divmod(S("0.1"), 1.5) == (0, 0.1)
+    assert divmod(1.5, S("0.1")) == Tuple(S("15"), S("0."))
+    assert divmod(S("0.1"), 0.3) == Tuple(S("0"), S("0.1"))
+
+    assert str(divmod(S("2"), 0.3)) == '(6, 0.2)'
+    assert str(divmod(S("3.5"), S("1/3"))) == '(10, 0.166666666666667)'
+    assert str(divmod(S("3.5"), 0.3)) == '(11, 0.2)'
+    assert str(divmod(S("1/3"), S("0.1"))) == '(3, 0.0333333333333333)'
+    assert str(divmod(1.5, S("1/3"))) == '(4, 0.166666666666667)'
+    assert str(divmod(S("1/3"), 0.3)) == '(1, 0.0333333333333333)'
+    assert str(divmod(0.3, S("0.1"))) == '(2, 0.1)'
+
+    assert divmod(-3, S(2)) == (-2, 1)
+    assert divmod(S(-3), S(2)) == (-2, 1)
+    assert divmod(S(-3), 2) == (-2, 1)
+
+    assert divmod(oo, 1) == (S.NaN, S.NaN)
+    assert divmod(S.NaN, 1) == (S.NaN, S.NaN)
+    assert divmod(1, S.NaN) == (S.NaN, S.NaN)
+    ans = [(-1, oo), (-1, oo), (0, 0), (0, 1), (0, 2)]
+    OO = float('inf')
+    ANS = [tuple(map(float, i)) for i in ans]
+    assert [divmod(i, oo) for i in range(-2, 3)] == ans
+    ans = [(0, -2), (0, -1), (0, 0), (-1, -oo), (-1, -oo)]
+    ANS = [tuple(map(float, i)) for i in ans]
+    assert [divmod(i, -oo) for i in range(-2, 3)] == ans
+    assert [divmod(i, -OO) for i in range(-2, 3)] == ANS
+
+    # sympy's divmod gives an Integer for the quotient rather than a float
+    dmod = lambda a, b: tuple([j if i else int(j) for i, j in enumerate(divmod(a, b))])
+    for a in (4, 4., 4.25, 0, 0., -4, -4. -4.25):
+        for b in (2, 2., 2.5, -2, -2., -2.5):
+            assert divmod(S(a), S(b)) == dmod(a, b)
+
+
+def test_igcd():
+    assert igcd(0, 0) == 0
+    assert igcd(0, 1) == 1
+    assert igcd(1, 0) == 1
+    assert igcd(0, 7) == 7
+    assert igcd(7, 0) == 7
+    assert igcd(7, 1) == 1
+    assert igcd(1, 7) == 1
+    assert igcd(-1, 0) == 1
+    assert igcd(0, -1) == 1
+    assert igcd(-1, -1) == 1
+    assert igcd(-1, 7) == 1
+    assert igcd(7, -1) == 1
+    assert igcd(8, 2) == 2
+    assert igcd(4, 8) == 4
+    assert igcd(8, 16) == 8
+    assert igcd(7, -3) == 1
+    assert igcd(-7, 3) == 1
+    assert igcd(-7, -3) == 1
+    assert igcd(*[10, 20, 30]) == 10
+    raises(TypeError, lambda: igcd())
+    raises(TypeError, lambda: igcd(2))
+    raises(ValueError, lambda: igcd(0, None))
+    raises(ValueError, lambda: igcd(1, 2.2))
+    for args in permutations((45.1, 1, 30)):
+        raises(ValueError, lambda: igcd(*args))
+    for args in permutations((1, 2, None)):
+        raises(ValueError, lambda: igcd(*args))
+
+
+def test_igcd_lehmer():
+    a, b = fibonacci(10001), fibonacci(10000)
+    # len(str(a)) == 2090
+    # small divisors, long Euclidean sequence
+    assert igcd_lehmer(a, b) == 1
+    c = fibonacci(100)
+    assert igcd_lehmer(a*c, b*c) == c
+    # big divisor
+    assert igcd_lehmer(a, 10**1000) == 1
+    # swapping argument
+    assert igcd_lehmer(1, 2) == igcd_lehmer(2, 1)
+
+
+def test_igcd2():
+    # short loop
+    assert igcd2(2**100 - 1, 2**99 - 1) == 1
+    # Lehmer's algorithm
+    a, b = int(fibonacci(10001)), int(fibonacci(10000))
+    assert igcd2(a, b) == 1
+
+
+def test_ilcm():
+    assert ilcm(0, 0) == 0
+    assert ilcm(1, 0) == 0
+    assert ilcm(0, 1) == 0
+    assert ilcm(1, 1) == 1
+    assert ilcm(2, 1) == 2
+    assert ilcm(8, 2) == 8
+    assert ilcm(8, 6) == 24
+    assert ilcm(8, 7) == 56
+    assert ilcm(*[10, 20, 30]) == 60
+    raises(ValueError, lambda: ilcm(8.1, 7))
+    raises(ValueError, lambda: ilcm(8, 7.1))
+    raises(TypeError, lambda: ilcm(8))
+
+
+def test_igcdex():
+    assert igcdex(2, 3) == (-1, 1, 1)
+    assert igcdex(10, 12) == (-1, 1, 2)
+    assert igcdex(100, 2004) == (-20, 1, 4)
+    assert igcdex(0, 0) == (0, 0, 0)
+    assert igcdex(1, 0) == (1, 0, 1)
+
+
+def _strictly_equal(a, b):
+    return (a.p, a.q, type(a.p), type(a.q)) == \
+           (b.p, b.q, type(b.p), type(b.q))
+
+
+def _test_rational_new(cls):
+    """
+    Tests that are common between Integer and Rational.
+    """
+    assert cls(0) is S.Zero
+    assert cls(1) is S.One
+    assert cls(-1) is S.NegativeOne
+    # These look odd, but are similar to int():
+    assert cls('1') is S.One
+    assert cls('-1') is S.NegativeOne
+
+    i = Integer(10)
+    assert _strictly_equal(i, cls('10'))
+    assert _strictly_equal(i, cls('10'))
+    assert _strictly_equal(i, cls(int(10)))
+    assert _strictly_equal(i, cls(i))
+
+    raises(TypeError, lambda: cls(Symbol('x')))
+
+
+def test_Integer_new():
+    """
+    Test for Integer constructor
+    """
+    _test_rational_new(Integer)
+
+    assert _strictly_equal(Integer(0.9), S.Zero)
+    assert _strictly_equal(Integer(10.5), Integer(10))
+    raises(ValueError, lambda: Integer("10.5"))
+    assert Integer(Rational('1.' + '9'*20)) == 1
+
+
+def test_Rational_new():
+    """"
+    Test for Rational constructor
+    """
+    _test_rational_new(Rational)
+
+    n1 = S.Half
+    assert n1 == Rational(Integer(1), 2)
+    assert n1 == Rational(Integer(1), Integer(2))
+    assert n1 == Rational(1, Integer(2))
+    assert n1 == Rational(S.Half)
+    assert 1 == Rational(n1, n1)
+    assert Rational(3, 2) == Rational(S.Half, Rational(1, 3))
+    assert Rational(3, 1) == Rational(1, Rational(1, 3))
+    n3_4 = Rational(3, 4)
+    assert Rational('3/4') == n3_4
+    assert -Rational('-3/4') == n3_4
+    assert Rational('.76').limit_denominator(4) == n3_4
+    assert Rational(19, 25).limit_denominator(4) == n3_4
+    assert Rational('19/25').limit_denominator(4) == n3_4
+    assert Rational(1.0, 3) == Rational(1, 3)
+    assert Rational(1, 3.0) == Rational(1, 3)
+    assert Rational(Float(0.5)) == S.Half
+    assert Rational('1e2/1e-2') == Rational(10000)
+    assert Rational('1 234') == Rational(1234)
+    assert Rational('1/1 234') == Rational(1, 1234)
+    assert Rational(-1, 0) is S.ComplexInfinity
+    assert Rational(1, 0) is S.ComplexInfinity
+    # Make sure Rational doesn't lose precision on Floats
+    assert Rational(pi.evalf(100)).evalf(100) == pi.evalf(100)
+    raises(TypeError, lambda: Rational('3**3'))
+    raises(TypeError, lambda: Rational('1/2 + 2/3'))
+
+    # handle fractions.Fraction instances
+    try:
+        import fractions
+        assert Rational(fractions.Fraction(1, 2)) == S.Half
+    except ImportError:
+        pass
+
+    assert Rational(PythonRational(2, 6)) == Rational(1, 3)
+
+    with warns_deprecated_sympy():
+        assert Rational(2, 4, gcd=1).q == 4
+    with warns_deprecated_sympy():
+        n = Rational(2, -4, gcd=1)
+    assert n.q == 4
+    assert n.p == -2
+
+    assert Rational.from_coprime_ints(3, 5) == Rational(3, 5)
+
+
+def test_issue_24543():
+    for p in ('1.5', 1.5, 2):
+        for q in ('1.5', 1.5, 2):
+            assert Rational(p, q).as_numer_denom() == Rational('%s/%s'%(p,q)).as_numer_denom()
+
+    assert Rational('0.5', '100') == Rational(1, 200)
+
+
+def test_Number_new():
+    """"
+    Test for Number constructor
+    """
+    # Expected behavior on numbers and strings
+    assert Number(1) is S.One
+    assert Number(2).__class__ is Integer
+    assert Number(-622).__class__ is Integer
+    assert Number(5, 3).__class__ is Rational
+    assert Number(5.3).__class__ is Float
+    assert Number('1') is S.One
+    assert Number('2').__class__ is Integer
+    assert Number('-622').__class__ is Integer
+    assert Number('5/3').__class__ is Rational
+    assert Number('5.3').__class__ is Float
+    raises(ValueError, lambda: Number('cos'))
+    raises(TypeError, lambda: Number(cos))
+    a = Rational(3, 5)
+    assert Number(a) is a  # Check idempotence on Numbers
+    u = ['inf', '-inf', 'nan', 'iNF', '+inf']
+    v = [oo, -oo, nan, oo, oo]
+    for i, a in zip(u, v):
+        assert Number(i) is a, (i, Number(i), a)
+
+
+def test_Number_cmp():
+    n1 = Number(1)
+    n2 = Number(2)
+    n3 = Number(-3)
+
+    assert n1 < n2
+    assert n1 <= n2
+    assert n3 < n1
+    assert n2 > n3
+    assert n2 >= n3
+
+    raises(TypeError, lambda: n1 < S.NaN)
+    raises(TypeError, lambda: n1 <= S.NaN)
+    raises(TypeError, lambda: n1 > S.NaN)
+    raises(TypeError, lambda: n1 >= S.NaN)
+
+
+def test_Rational_cmp():
+    n1 = Rational(1, 4)
+    n2 = Rational(1, 3)
+    n3 = Rational(2, 4)
+    n4 = Rational(2, -4)
+    n5 = Rational(0)
+    n6 = Rational(1)
+    n7 = Rational(3)
+    n8 = Rational(-3)
+
+    assert n8 < n5
+    assert n5 < n6
+    assert n6 < n7
+    assert n8 < n7
+    assert n7 > n8
+    assert (n1 + 1)**n2 < 2
+    assert ((n1 + n6)/n7) < 1
+
+    assert n4 < n3
+    assert n2 < n3
+    assert n1 < n2
+    assert n3 > n1
+    assert not n3 < n1
+    assert not (Rational(-1) > 0)
+    assert Rational(-1) < 0
+
+    raises(TypeError, lambda: n1 < S.NaN)
+    raises(TypeError, lambda: n1 <= S.NaN)
+    raises(TypeError, lambda: n1 > S.NaN)
+    raises(TypeError, lambda: n1 >= S.NaN)
+
+
+def test_Float():
+    def eq(a, b):
+        t = Float("1.0E-15")
+        return (-t < a - b < t)
+
+    equal_pairs = [
+        (0, 0.0), # This is just how Python works...
+        (0, S.Zero),
+        (0.0, Float(0)),
+    ]
+    unequal_pairs = [
+        (0.0, S.Zero),
+        (0, Float(0)),
+        (S.Zero, Float(0)),
+    ]
+    for p1, p2 in equal_pairs:
+        assert (p1 == p2) is True
+        assert (p1 != p2) is False
+        assert (p2 == p1) is True
+        assert (p2 != p1) is False
+    for p1, p2 in unequal_pairs:
+        assert (p1 == p2) is False
+        assert (p1 != p2) is True
+        assert (p2 == p1) is False
+        assert (p2 != p1) is True
+
+    assert S.Zero.is_zero
+
+    a = Float(2) ** Float(3)
+    assert eq(a.evalf(), Float(8))
+    assert eq((pi ** -1).evalf(), Float("0.31830988618379067"))
+    a = Float(2) ** Float(4)
+    assert eq(a.evalf(), Float(16))
+    assert (S(.3) == S(.5)) is False
+
+    mpf = (0, 5404319552844595, -52, 53)
+    x_str = Float((0, '13333333333333', -52, 53))
+    x_0xstr = Float((0, '0x13333333333333', -52, 53))
+    x2_str = Float((0, '26666666666666', -53, 54))
+    x_hex = Float((0, int(0x13333333333333), -52, 53))
+    x_dec = Float(mpf)
+    assert x_str == x_0xstr == x_hex == x_dec == Float(1.2)
+    # x2_str was entered slightly malformed in that the mantissa
+    # was even -- it should be odd and the even part should be
+    # included with the exponent, but this is resolved by normalization
+    # ONLY IF REQUIREMENTS of mpf_norm are met: the bitcount must
+    # be exact: double the mantissa ==> increase bc by 1
+    assert Float(1.2)._mpf_ == mpf
+    assert x2_str._mpf_ == mpf
+
+    assert Float((0, int(0), -123, -1)) is S.NaN
+    assert Float((0, int(0), -456, -2)) is S.Infinity
+    assert Float((1, int(0), -789, -3)) is S.NegativeInfinity
+    # if you don't give the full signature, it's not special
+    assert Float((0, int(0), -123)) == Float(0)
+    assert Float((0, int(0), -456)) == Float(0)
+    assert Float((1, int(0), -789)) == Float(0)
+
+    raises(ValueError, lambda: Float((0, 7, 1, 3), ''))
+
+    assert Float('0.0').is_finite is True
+    assert Float('0.0').is_negative is False
+    assert Float('0.0').is_positive is False
+    assert Float('0.0').is_infinite is False
+    assert Float('0.0').is_zero is True
+
+    # rationality properties
+    # if the integer test fails then the use of intlike
+    # should be removed from gamma_functions.py
+    assert Float(1).is_integer is None
+    assert Float(1).is_rational is None
+    assert Float(1).is_irrational is None
+    assert sqrt(2).n(15).is_rational is None
+    assert sqrt(2).n(15).is_irrational is None
+
+    # do not automatically evalf
+    def teq(a):
+        assert (a.evalf() == a) is False
+        assert (a.evalf() != a) is True
+        assert (a == a.evalf()) is False
+        assert (a != a.evalf()) is True
+
+    teq(pi)
+    teq(2*pi)
+    teq(cos(0.1, evaluate=False))
+
+    # long integer
+    i = 12345678901234567890
+    assert same_and_same_prec(Float(12, ''), Float('12', ''))
+    assert same_and_same_prec(Float(Integer(i), ''), Float(i, ''))
+    assert same_and_same_prec(Float(i, ''), Float(str(i), 20))
+    assert same_and_same_prec(Float(str(i)), Float(i, ''))
+    assert same_and_same_prec(Float(i), Float(i, ''))
+
+    # inexact floats (repeating binary = denom not multiple of 2)
+    # cannot have precision greater than 15
+    assert Float(.125, 22)._prec == 76
+    assert Float(2.0, 22)._prec == 76
+    # only default prec is equal, even for exactly representable float
+    assert Float(.125, 22) != .125
+    #assert Float(2.0, 22) == 2
+    assert float(Float('.12500000000000001', '')) == .125
+    raises(ValueError, lambda: Float(.12500000000000001, ''))
+
+    # allow spaces
+    assert Float('123 456.123 456') == Float('123456.123456')
+    assert Integer('123 456') == Integer('123456')
+    assert Rational('123 456.123 456') == Rational('123456.123456')
+    assert Float(' .3e2') == Float('0.3e2')
+    # but treat them as strictly ass underscore between digits: only 1
+    raises(ValueError, lambda: Float('1  2'))
+
+    # allow underscore between digits
+    assert Float('1_23.4_56') == Float('123.456')
+    # assert Float('1_23.4_5_6', 12) == Float('123.456', 12)
+    # ...but not in all cases (per Py 3.6)
+    raises(ValueError, lambda: Float('1_'))
+    raises(ValueError, lambda: Float('1__2'))
+    raises(ValueError, lambda: Float('_1'))
+    raises(ValueError, lambda: Float('_inf'))
+
+    # allow auto precision detection
+    assert Float('.1', '') == Float(.1, 1)
+    assert Float('.125', '') == Float(.125, 3)
+    assert Float('.100', '') == Float(.1, 3)
+    assert Float('2.0', '') == Float('2', 2)
+
+    raises(ValueError, lambda: Float("12.3d-4", ""))
+    raises(ValueError, lambda: Float(12.3, ""))
+    raises(ValueError, lambda: Float('.'))
+    raises(ValueError, lambda: Float('-.'))
+
+    zero = Float('0.0')
+    assert Float('-0') == zero
+    assert Float('.0') == zero
+    assert Float('-.0') == zero
+    assert Float('-0.0') == zero
+    assert Float(0.0) == zero
+    assert Float(0) == zero
+    assert Float(0, '') == Float('0', '')
+    assert Float(1) == Float(1.0)
+    assert Float(S.Zero) == zero
+    assert Float(S.One) == Float(1.0)
+
+    assert Float(decimal.Decimal('0.1'), 3) == Float('.1', 3)
+    assert Float(decimal.Decimal('nan')) is S.NaN
+    assert Float(decimal.Decimal('Infinity')) is S.Infinity
+    assert Float(decimal.Decimal('-Infinity')) is S.NegativeInfinity
+
+    assert '{:.3f}'.format(Float(4.236622)) == '4.237'
+    assert '{:.35f}'.format(Float(pi.n(40), 40)) == \
+        '3.14159265358979323846264338327950288'
+
+    # unicode
+    assert Float('0.73908513321516064100000000') == \
+        Float('0.73908513321516064100000000')
+    assert Float('0.73908513321516064100000000', 28) == \
+        Float('0.73908513321516064100000000', 28)
+
+    # binary precision
+    # Decimal value 0.1 cannot be expressed precisely as a base 2 fraction
+    a = Float(S.One/10, dps=15)
+    b = Float(S.One/10, dps=16)
+    p = Float(S.One/10, precision=53)
+    q = Float(S.One/10, precision=54)
+    assert a._mpf_ == p._mpf_
+    assert not a._mpf_ == q._mpf_
+    assert not b._mpf_ == q._mpf_
+
+    # Precision specifying errors
+    raises(ValueError, lambda: Float("1.23", dps=3, precision=10))
+    raises(ValueError, lambda: Float("1.23", dps="", precision=10))
+    raises(ValueError, lambda: Float("1.23", dps=3, precision=""))
+    raises(ValueError, lambda: Float("1.23", dps="", precision=""))
+
+    # from NumberSymbol
+    assert same_and_same_prec(Float(pi, 32), pi.evalf(32))
+    assert same_and_same_prec(Float(Catalan), Catalan.evalf())
+
+    # oo and nan
+    u = ['inf', '-inf', 'nan', 'iNF', '+inf']
+    v = [oo, -oo, nan, oo, oo]
+    for i, a in zip(u, v):
+        assert Float(i) is a
+
+
+def test_zero_not_false():
+    # https://github.com/sympy/sympy/issues/20796
+    assert (S(0.0) == S.false) is False
+    assert (S.false == S(0.0)) is False
+    assert (S(0) == S.false) is False
+    assert (S.false == S(0)) is False
+
+
+@conserve_mpmath_dps
+def test_float_mpf():
+    import mpmath
+    mpmath.mp.dps = 100
+    mp_pi = mpmath.pi()
+
+    assert Float(mp_pi, 100) == Float(mp_pi._mpf_, 100) == pi.evalf(100)
+
+    mpmath.mp.dps = 15
+
+    assert Float(mp_pi, 100) == Float(mp_pi._mpf_, 100) == pi.evalf(100)
+
+
+def test_Float_RealElement():
+    repi = RealField(dps=100)(pi.evalf(100))
+    # We still have to pass the precision because Float doesn't know what
+    # RealElement is, but make sure it keeps full precision from the result.
+    assert Float(repi, 100) == pi.evalf(100)
+
+
+def test_Float_default_to_highprec_from_str():
+    s = str(pi.evalf(128))
+    assert same_and_same_prec(Float(s), Float(s, ''))
+
+
+def test_Float_eval():
+    a = Float(3.2)
+    assert (a**2).is_Float
+
+
+def test_Float_issue_2107():
+    a = Float(0.1, 10)
+    b = Float("0.1", 10)
+
+    assert a - a == 0
+    assert a + (-a) == 0
+    assert S.Zero + a - a == 0
+    assert S.Zero + a + (-a) == 0
+
+    assert b - b == 0
+    assert b + (-b) == 0
+    assert S.Zero + b - b == 0
+    assert S.Zero + b + (-b) == 0
+
+
+def test_issue_14289():
+    from sympy.polys.numberfields import to_number_field
+
+    a = 1 - sqrt(2)
+    b = to_number_field(a)
+    assert b.as_expr() == a
+    assert b.minpoly(a).expand() == 0
+
+
+def test_Float_from_tuple():
+    a = Float((0, '1L', 0, 1))
+    b = Float((0, '1', 0, 1))
+    assert a == b
+
+
+def test_Infinity():
+    assert oo != 1
+    assert 1*oo is oo
+    assert 1 != oo
+    assert oo != -oo
+    assert oo != Symbol("x")**3
+    assert oo + 1 is oo
+    assert 2 + oo is oo
+    assert 3*oo + 2 is oo
+    assert S.Half**oo == 0
+    assert S.Half**(-oo) is oo
+    assert -oo*3 is -oo
+    assert oo + oo is oo
+    assert -oo + oo*(-5) is -oo
+    assert 1/oo == 0
+    assert 1/(-oo) == 0
+    assert 8/oo == 0
+    assert oo % 2 is nan
+    assert 2 % oo is nan
+    assert oo/oo is nan
+    assert oo/-oo is nan
+    assert -oo/oo is nan
+    assert -oo/-oo is nan
+    assert oo - oo is nan
+    assert oo - -oo is oo
+    assert -oo - oo is -oo
+    assert -oo - -oo is nan
+    assert oo + -oo is nan
+    assert -oo + oo is nan
+    assert oo + oo is oo
+    assert -oo + oo is nan
+    assert oo + -oo is nan
+    assert -oo + -oo is -oo
+    assert oo*oo is oo
+    assert -oo*oo is -oo
+    assert oo*-oo is -oo
+    assert -oo*-oo is oo
+    assert oo/0 is oo
+    assert -oo/0 is -oo
+    assert 0/oo == 0
+    assert 0/-oo == 0
+    assert oo*0 is nan
+    assert -oo*0 is nan
+    assert 0*oo is nan
+    assert 0*-oo is nan
+    assert oo + 0 is oo
+    assert -oo + 0 is -oo
+    assert 0 + oo is oo
+    assert 0 + -oo is -oo
+    assert oo - 0 is oo
+    assert -oo - 0 is -oo
+    assert 0 - oo is -oo
+    assert 0 - -oo is oo
+    assert oo/2 is oo
+    assert -oo/2 is -oo
+    assert oo/-2 is -oo
+    assert -oo/-2 is oo
+    assert oo*2 is oo
+    assert -oo*2 is -oo
+    assert oo*-2 is -oo
+    assert 2/oo == 0
+    assert 2/-oo == 0
+    assert -2/oo == 0
+    assert -2/-oo == 0
+    assert 2*oo is oo
+    assert 2*-oo is -oo
+    assert -2*oo is -oo
+    assert -2*-oo is oo
+    assert 2 + oo is oo
+    assert 2 - oo is -oo
+    assert -2 + oo is oo
+    assert -2 - oo is -oo
+    assert 2 + -oo is -oo
+    assert 2 - -oo is oo
+    assert -2 + -oo is -oo
+    assert -2 - -oo is oo
+    assert S(2) + oo is oo
+    assert S(2) - oo is -oo
+    assert oo/I == -oo*I
+    assert -oo/I == oo*I
+    assert oo*float(1) == _inf and (oo*float(1)) is oo
+    assert -oo*float(1) == _ninf and (-oo*float(1)) is -oo
+    assert oo/float(1) == _inf and (oo/float(1)) is oo
+    assert -oo/float(1) == _ninf and (-oo/float(1)) is -oo
+    assert oo*float(-1) == _ninf and (oo*float(-1)) is -oo
+    assert -oo*float(-1) == _inf and (-oo*float(-1)) is oo
+    assert oo/float(-1) == _ninf and (oo/float(-1)) is -oo
+    assert -oo/float(-1) == _inf and (-oo/float(-1)) is oo
+    assert oo + float(1) == _inf and (oo + float(1)) is oo
+    assert -oo + float(1) == _ninf and (-oo + float(1)) is -oo
+    assert oo - float(1) == _inf and (oo - float(1)) is oo
+    assert -oo - float(1) == _ninf and (-oo - float(1)) is -oo
+    assert float(1)*oo == _inf and (float(1)*oo) is oo
+    assert float(1)*-oo == _ninf and (float(1)*-oo) is -oo
+    assert float(1)/oo == 0
+    assert float(1)/-oo == 0
+    assert float(-1)*oo == _ninf and (float(-1)*oo) is -oo
+    assert float(-1)*-oo == _inf and (float(-1)*-oo) is oo
+    assert float(-1)/oo == 0
+    assert float(-1)/-oo == 0
+    assert float(1) + oo is oo
+    assert float(1) + -oo is -oo
+    assert float(1) - oo is -oo
+    assert float(1) - -oo is oo
+    assert oo == float(oo)
+    assert (oo != float(oo)) is False
+    assert type(float(oo)) is float
+    assert -oo == float(-oo)
+    assert (-oo != float(-oo)) is False
+    assert type(float(-oo)) is float
+
+    assert Float('nan') is nan
+    assert nan*1.0 is nan
+    assert -1.0*nan is nan
+    assert nan*oo is nan
+    assert nan*-oo is nan
+    assert nan/oo is nan
+    assert nan/-oo is nan
+    assert nan + oo is nan
+    assert nan + -oo is nan
+    assert nan - oo is nan
+    assert nan - -oo is nan
+    assert -oo * S.Zero is nan
+
+    assert oo*nan is nan
+    assert -oo*nan is nan
+    assert oo/nan is nan
+    assert -oo/nan is nan
+    assert oo + nan is nan
+    assert -oo + nan is nan
+    assert oo - nan is nan
+    assert -oo - nan is nan
+    assert S.Zero * oo is nan
+    assert oo.is_Rational is False
+    assert isinstance(oo, Rational) is False
+
+    assert S.One/oo == 0
+    assert -S.One/oo == 0
+    assert S.One/-oo == 0
+    assert -S.One/-oo == 0
+    assert S.One*oo is oo
+    assert -S.One*oo is -oo
+    assert S.One*-oo is -oo
+    assert -S.One*-oo is oo
+    assert S.One/nan is nan
+    assert S.One - -oo is oo
+    assert S.One + nan is nan
+    assert S.One - nan is nan
+    assert nan - S.One is nan
+    assert nan/S.One is nan
+    assert -oo - S.One is -oo
+
+
+def test_Infinity_2():
+    x = Symbol('x')
+    assert oo*x != oo
+    assert oo*(pi - 1) is oo
+    assert oo*(1 - pi) is -oo
+
+    assert (-oo)*x != -oo
+    assert (-oo)*(pi - 1) is -oo
+    assert (-oo)*(1 - pi) is oo
+
+    assert (-1)**S.NaN is S.NaN
+    assert oo - _inf is S.NaN
+    assert oo + _ninf is S.NaN
+    assert oo*0 is S.NaN
+    assert oo/_inf is S.NaN
+    assert oo/_ninf is S.NaN
+    assert oo**S.NaN is S.NaN
+    assert -oo + _inf is S.NaN
+    assert -oo - _ninf is S.NaN
+    assert -oo*S.NaN is S.NaN
+    assert -oo*0 is S.NaN
+    assert -oo/_inf is S.NaN
+    assert -oo/_ninf is S.NaN
+    assert -oo/S.NaN is S.NaN
+    assert abs(-oo) is oo
+    assert all((-oo)**i is S.NaN for i in (oo, -oo, S.NaN))
+    assert (-oo)**3 is -oo
+    assert (-oo)**2 is oo
+    assert abs(S.ComplexInfinity) is oo
+
+
+def test_Mul_Infinity_Zero():
+    assert Float(0)*_inf is nan
+    assert Float(0)*_ninf is nan
+    assert Float(0)*_inf is nan
+    assert Float(0)*_ninf is nan
+    assert _inf*Float(0) is nan
+    assert _ninf*Float(0) is nan
+    assert _inf*Float(0) is nan
+    assert _ninf*Float(0) is nan
+
+
+def test_Div_By_Zero():
+    assert 1/S.Zero is zoo
+    assert 1/Float(0) is zoo
+    assert 0/S.Zero is nan
+    assert 0/Float(0) is nan
+    assert S.Zero/0 is nan
+    assert Float(0)/0 is nan
+    assert -1/S.Zero is zoo
+    assert -1/Float(0) is zoo
+
+
+@_both_exp_pow
+def test_Infinity_inequations():
+    assert oo > pi
+    assert not (oo < pi)
+    assert exp(-3) < oo
+
+    assert _inf > pi
+    assert not (_inf < pi)
+    assert exp(-3) < _inf
+
+    raises(TypeError, lambda: oo < I)
+    raises(TypeError, lambda: oo <= I)
+    raises(TypeError, lambda: oo > I)
+    raises(TypeError, lambda: oo >= I)
+    raises(TypeError, lambda: -oo < I)
+    raises(TypeError, lambda: -oo <= I)
+    raises(TypeError, lambda: -oo > I)
+    raises(TypeError, lambda: -oo >= I)
+
+    raises(TypeError, lambda: I < oo)
+    raises(TypeError, lambda: I <= oo)
+    raises(TypeError, lambda: I > oo)
+    raises(TypeError, lambda: I >= oo)
+    raises(TypeError, lambda: I < -oo)
+    raises(TypeError, lambda: I <= -oo)
+    raises(TypeError, lambda: I > -oo)
+    raises(TypeError, lambda: I >= -oo)
+
+    assert oo > -oo and oo >= -oo
+    assert (oo < -oo) == False and (oo <= -oo) == False
+    assert -oo < oo and -oo <= oo
+    assert (-oo > oo) == False and (-oo >= oo) == False
+
+    assert (oo < oo) == False  # issue 7775
+    assert (oo > oo) == False
+    assert (-oo > -oo) == False and (-oo < -oo) == False
+    assert oo >= oo and oo <= oo and -oo >= -oo and -oo <= -oo
+    assert (-oo < -_inf) ==  False
+    assert (oo > _inf) == False
+    assert -oo >= -_inf
+    assert oo <= _inf
+
+    x = Symbol('x')
+    b = Symbol('b', finite=True, real=True)
+    assert (x < oo) == Lt(x, oo)  # issue 7775
+    assert b < oo and b > -oo and b <= oo and b >= -oo
+    assert oo > b and oo >= b and (oo < b) == False and (oo <= b) == False
+    assert (-oo > b) == False and (-oo >= b) == False and -oo < b and -oo <= b
+    assert (oo < x) == Lt(oo, x) and (oo > x) == Gt(oo, x)
+    assert (oo <= x) == Le(oo, x) and (oo >= x) == Ge(oo, x)
+    assert (-oo < x) == Lt(-oo, x) and (-oo > x) == Gt(-oo, x)
+    assert (-oo <= x) == Le(-oo, x) and (-oo >= x) == Ge(-oo, x)
+
+
+def test_NaN():
+    assert nan is nan
+    assert nan != 1
+    assert 1*nan is nan
+    assert 1 != nan
+    assert -nan is nan
+    assert oo != Symbol("x")**3
+    assert 2 + nan is nan
+    assert 3*nan + 2 is nan
+    assert -nan*3 is nan
+    assert nan + nan is nan
+    assert -nan + nan*(-5) is nan
+    assert 8/nan is nan
+    raises(TypeError, lambda: nan > 0)
+    raises(TypeError, lambda: nan < 0)
+    raises(TypeError, lambda: nan >= 0)
+    raises(TypeError, lambda: nan <= 0)
+    raises(TypeError, lambda: 0 < nan)
+    raises(TypeError, lambda: 0 > nan)
+    raises(TypeError, lambda: 0 <= nan)
+    raises(TypeError, lambda: 0 >= nan)
+    assert nan**0 == 1  # as per IEEE 754
+    assert 1**nan is nan # IEEE 754 is not the best choice for symbolic work
+    # test Pow._eval_power's handling of NaN
+    assert Pow(nan, 0, evaluate=False)**2 == 1
+    for n in (1, 1., S.One, S.NegativeOne, Float(1)):
+        assert n + nan is nan
+        assert n - nan is nan
+        assert nan + n is nan
+        assert nan - n is nan
+        assert n/nan is nan
+        assert nan/n is nan
+
+
+def test_special_numbers():
+    assert isinstance(S.NaN, Number) is True
+    assert isinstance(S.Infinity, Number) is True
+    assert isinstance(S.NegativeInfinity, Number) is True
+
+    assert S.NaN.is_number is True
+    assert S.Infinity.is_number is True
+    assert S.NegativeInfinity.is_number is True
+    assert S.ComplexInfinity.is_number is True
+
+    assert isinstance(S.NaN, Rational) is False
+    assert isinstance(S.Infinity, Rational) is False
+    assert isinstance(S.NegativeInfinity, Rational) is False
+
+    assert S.NaN.is_rational is not True
+    assert S.Infinity.is_rational is not True
+    assert S.NegativeInfinity.is_rational is not True
+
+
+def test_powers():
+    assert integer_nthroot(1, 2) == (1, True)
+    assert integer_nthroot(1, 5) == (1, True)
+    assert integer_nthroot(2, 1) == (2, True)
+    assert integer_nthroot(2, 2) == (1, False)
+    assert integer_nthroot(2, 5) == (1, False)
+    assert integer_nthroot(4, 2) == (2, True)
+    assert integer_nthroot(123**25, 25) == (123, True)
+    assert integer_nthroot(123**25 + 1, 25) == (123, False)
+    assert integer_nthroot(123**25 - 1, 25) == (122, False)
+    assert integer_nthroot(1, 1) == (1, True)
+    assert integer_nthroot(0, 1) == (0, True)
+    assert integer_nthroot(0, 3) == (0, True)
+    assert integer_nthroot(10000, 1) == (10000, True)
+    assert integer_nthroot(4, 2) == (2, True)
+    assert integer_nthroot(16, 2) == (4, True)
+    assert integer_nthroot(26, 2) == (5, False)
+    assert integer_nthroot(1234567**7, 7) == (1234567, True)
+    assert integer_nthroot(1234567**7 + 1, 7) == (1234567, False)
+    assert integer_nthroot(1234567**7 - 1, 7) == (1234566, False)
+    b = 25**1000
+    assert integer_nthroot(b, 1000) == (25, True)
+    assert integer_nthroot(b + 1, 1000) == (25, False)
+    assert integer_nthroot(b - 1, 1000) == (24, False)
+    c = 10**400
+    c2 = c**2
+    assert integer_nthroot(c2, 2) == (c, True)
+    assert integer_nthroot(c2 + 1, 2) == (c, False)
+    assert integer_nthroot(c2 - 1, 2) == (c - 1, False)
+    assert integer_nthroot(2, 10**10) == (1, False)
+
+    p, r = integer_nthroot(int(factorial(10000)), 100)
+    assert p % (10**10) == 5322420655
+    assert not r
+
+    # Test that this is fast
+    assert integer_nthroot(2, 10**10) == (1, False)
+
+    # output should be int if possible
+    assert type(integer_nthroot(2**61, 2)[0]) is int
+
+
+def test_integer_nthroot_overflow():
+    assert integer_nthroot(10**(50*50), 50) == (10**50, True)
+    assert integer_nthroot(10**100000, 10000) == (10**10, True)
+
+
+def test_integer_log():
+    raises(ValueError, lambda: integer_log(2, 1))
+    raises(ValueError, lambda: integer_log(0, 2))
+    raises(ValueError, lambda: integer_log(1.1, 2))
+    raises(ValueError, lambda: integer_log(1, 2.2))
+
+    assert integer_log(1, 2) == (0, True)
+    assert integer_log(1, 3) == (0, True)
+    assert integer_log(2, 3) == (0, False)
+    assert integer_log(3, 3) == (1, True)
+    assert integer_log(3*2, 3) == (1, False)
+    assert integer_log(3**2, 3) == (2, True)
+    assert integer_log(3*4, 3) == (2, False)
+    assert integer_log(3**3, 3) == (3, True)
+    assert integer_log(27, 5) == (2, False)
+    assert integer_log(2, 3) == (0, False)
+    assert integer_log(-4, 2) == (2, False)
+    assert integer_log(-16, 4) == (0, False)
+    assert integer_log(-4, -2) == (2, False)
+    assert integer_log(4, -2) == (2, True)
+    assert integer_log(-8, -2) == (3, True)
+    assert integer_log(8, -2) == (3, False)
+    assert integer_log(-9, 3) == (0, False)
+    assert integer_log(-9, -3) == (2, False)
+    assert integer_log(9, -3) == (2, True)
+    assert integer_log(-27, -3) == (3, True)
+    assert integer_log(27, -3) == (3, False)
+
+
+def test_isqrt():
+    from math import sqrt as _sqrt
+    limit = 4503599761588223
+    assert int(_sqrt(limit)) == integer_nthroot(limit, 2)[0]
+    assert int(_sqrt(limit + 1)) != integer_nthroot(limit + 1, 2)[0]
+    assert isqrt(limit + 1) == integer_nthroot(limit + 1, 2)[0]
+    assert isqrt(limit + S.Half) == integer_nthroot(limit, 2)[0]
+    assert isqrt(limit + 1 + S.Half) == integer_nthroot(limit + 1, 2)[0]
+    assert isqrt(limit + 2 + S.Half) == integer_nthroot(limit + 2, 2)[0]
+
+    # Regression tests for https://github.com/sympy/sympy/issues/17034
+    assert isqrt(4503599761588224) == 67108864
+    assert isqrt(9999999999999999) == 99999999
+
+    # Other corner cases, especially involving non-integers.
+    raises(ValueError, lambda: isqrt(-1))
+    raises(ValueError, lambda: isqrt(-10**1000))
+    raises(ValueError, lambda: isqrt(Rational(-1, 2)))
+
+    tiny = Rational(1, 10**1000)
+    raises(ValueError, lambda: isqrt(-tiny))
+    assert isqrt(1-tiny) == 0
+    assert isqrt(4503599761588224-tiny) == 67108864
+    assert isqrt(10**100 - tiny) == 10**50 - 1
+
+
+def test_powers_Integer():
+    """Test Integer._eval_power"""
+    # check infinity
+    assert S.One ** S.Infinity is S.NaN
+    assert S.NegativeOne** S.Infinity is S.NaN
+    assert S(2) ** S.Infinity is S.Infinity
+    assert S(-2)** S.Infinity == zoo
+    assert S(0) ** S.Infinity is S.Zero
+
+    # check Nan
+    assert S.One ** S.NaN is S.NaN
+    assert S.NegativeOne ** S.NaN is S.NaN
+
+    # check for exact roots
+    assert S.NegativeOne ** Rational(6, 5) == - (-1)**(S.One/5)
+    assert sqrt(S(4)) == 2
+    assert sqrt(S(-4)) == I * 2
+    assert S(16) ** Rational(1, 4) == 2
+    assert S(-16) ** Rational(1, 4) == 2 * (-1)**Rational(1, 4)
+    assert S(9) ** Rational(3, 2) == 27
+    assert S(-9) ** Rational(3, 2) == -27*I
+    assert S(27) ** Rational(2, 3) == 9
+    assert S(-27) ** Rational(2, 3) == 9 * (S.NegativeOne ** Rational(2, 3))
+    assert (-2) ** Rational(-2, 1) == Rational(1, 4)
+
+    # not exact roots
+    assert sqrt(-3) == I*sqrt(3)
+    assert (3) ** (Rational(3, 2)) == 3 * sqrt(3)
+    assert (-3) ** (Rational(3, 2)) == - 3 * sqrt(-3)
+    assert (-3) ** (Rational(5, 2)) == 9 * I * sqrt(3)
+    assert (-3) ** (Rational(7, 2)) == - I * 27 * sqrt(3)
+    assert (2) ** (Rational(3, 2)) == 2 * sqrt(2)
+    assert (2) ** (Rational(-3, 2)) == sqrt(2) / 4
+    assert (81) ** (Rational(2, 3)) == 9 * (S(3) ** (Rational(2, 3)))
+    assert (-81) ** (Rational(2, 3)) == 9 * (S(-3) ** (Rational(2, 3)))
+    assert (-3) ** Rational(-7, 3) == \
+        -(-1)**Rational(2, 3)*3**Rational(2, 3)/27
+    assert (-3) ** Rational(-2, 3) == \
+        -(-1)**Rational(1, 3)*3**Rational(1, 3)/3
+
+    # join roots
+    assert sqrt(6) + sqrt(24) == 3*sqrt(6)
+    assert sqrt(2) * sqrt(3) == sqrt(6)
+
+    # separate symbols & constansts
+    x = Symbol("x")
+    assert sqrt(49 * x) == 7 * sqrt(x)
+    assert sqrt((3 - sqrt(pi)) ** 2) == 3 - sqrt(pi)
+
+    # check that it is fast for big numbers
+    assert (2**64 + 1) ** Rational(4, 3)
+    assert (2**64 + 1) ** Rational(17, 25)
+
+    # negative rational power and negative base
+    assert (-3) ** Rational(-7, 3) == \
+        -(-1)**Rational(2, 3)*3**Rational(2, 3)/27
+    assert (-3) ** Rational(-2, 3) == \
+        -(-1)**Rational(1, 3)*3**Rational(1, 3)/3
+    assert (-2) ** Rational(-10, 3) == \
+        (-1)**Rational(2, 3)*2**Rational(2, 3)/16
+    assert abs(Pow(-2, Rational(-10, 3)).n() -
+        Pow(-2, Rational(-10, 3), evaluate=False).n()) < 1e-16
+
+    # negative base and rational power with some simplification
+    assert (-8) ** Rational(2, 5) == \
+        2*(-1)**Rational(2, 5)*2**Rational(1, 5)
+    assert (-4) ** Rational(9, 5) == \
+        -8*(-1)**Rational(4, 5)*2**Rational(3, 5)
+
+    assert S(1234).factors() == {617: 1, 2: 1}
+    assert Rational(2*3, 3*5*7).factors() == {2: 1, 5: -1, 7: -1}
+
+    # test that eval_power factors numbers bigger than
+    # the current limit in factor_trial_division (2**15)
+    from sympy.ntheory.generate import nextprime
+    n = nextprime(2**15)
+    assert sqrt(n**2) == n
+    assert sqrt(n**3) == n*sqrt(n)
+    assert sqrt(4*n) == 2*sqrt(n)
+
+    # check that factors of base with powers sharing gcd with power are removed
+    assert (2**4*3)**Rational(1, 6) == 2**Rational(2, 3)*3**Rational(1, 6)
+    assert (2**4*3)**Rational(5, 6) == 8*2**Rational(1, 3)*3**Rational(5, 6)
+
+    # check that bases sharing a gcd are exptracted
+    assert 2**Rational(1, 3)*3**Rational(1, 4)*6**Rational(1, 5) == \
+        2**Rational(8, 15)*3**Rational(9, 20)
+    assert sqrt(8)*24**Rational(1, 3)*6**Rational(1, 5) == \
+        4*2**Rational(7, 10)*3**Rational(8, 15)
+    assert sqrt(8)*(-24)**Rational(1, 3)*(-6)**Rational(1, 5) == \
+        4*(-3)**Rational(8, 15)*2**Rational(7, 10)
+    assert 2**Rational(1, 3)*2**Rational(8, 9) == 2*2**Rational(2, 9)
+    assert 2**Rational(2, 3)*6**Rational(1, 3) == 2*3**Rational(1, 3)
+    assert 2**Rational(2, 3)*6**Rational(8, 9) == \
+        2*2**Rational(5, 9)*3**Rational(8, 9)
+    assert (-2)**Rational(2, S(3))*(-4)**Rational(1, S(3)) == -2*2**Rational(1, 3)
+    assert 3*Pow(3, 2, evaluate=False) == 3**3
+    assert 3*Pow(3, Rational(-1, 3), evaluate=False) == 3**Rational(2, 3)
+    assert (-2)**Rational(1, 3)*(-3)**Rational(1, 4)*(-5)**Rational(5, 6) == \
+        -(-1)**Rational(5, 12)*2**Rational(1, 3)*3**Rational(1, 4) * \
+        5**Rational(5, 6)
+
+    assert Integer(-2)**Symbol('', even=True) == \
+        Integer(2)**Symbol('', even=True)
+    assert (-1)**Float(.5) == 1.0*I
+
+
+def test_powers_Rational():
+    """Test Rational._eval_power"""
+    # check infinity
+    assert S.Half ** S.Infinity == 0
+    assert Rational(3, 2) ** S.Infinity is S.Infinity
+    assert Rational(-1, 2) ** S.Infinity == 0
+    assert Rational(-3, 2) ** S.Infinity == zoo
+
+    # check Nan
+    assert Rational(3, 4) ** S.NaN is S.NaN
+    assert Rational(-2, 3) ** S.NaN is S.NaN
+
+    # exact roots on numerator
+    assert sqrt(Rational(4, 3)) == 2 * sqrt(3) / 3
+    assert Rational(4, 3) ** Rational(3, 2) == 8 * sqrt(3) / 9
+    assert sqrt(Rational(-4, 3)) == I * 2 * sqrt(3) / 3
+    assert Rational(-4, 3) ** Rational(3, 2) == - I * 8 * sqrt(3) / 9
+    assert Rational(27, 2) ** Rational(1, 3) == 3 * (2 ** Rational(2, 3)) / 2
+    assert Rational(5**3, 8**3) ** Rational(4, 3) == Rational(5**4, 8**4)
+
+    # exact root on denominator
+    assert sqrt(Rational(1, 4)) == S.Half
+    assert sqrt(Rational(1, -4)) == I * S.Half
+    assert sqrt(Rational(3, 4)) == sqrt(3) / 2
+    assert sqrt(Rational(3, -4)) == I * sqrt(3) / 2
+    assert Rational(5, 27) ** Rational(1, 3) == (5 ** Rational(1, 3)) / 3
+
+    # not exact roots
+    assert sqrt(S.Half) == sqrt(2) / 2
+    assert sqrt(Rational(-4, 7)) == I * sqrt(Rational(4, 7))
+    assert Rational(-3, 2)**Rational(-7, 3) == \
+        -4*(-1)**Rational(2, 3)*2**Rational(1, 3)*3**Rational(2, 3)/27
+    assert Rational(-3, 2)**Rational(-2, 3) == \
+        -(-1)**Rational(1, 3)*2**Rational(2, 3)*3**Rational(1, 3)/3
+    assert Rational(-3, 2)**Rational(-10, 3) == \
+        8*(-1)**Rational(2, 3)*2**Rational(1, 3)*3**Rational(2, 3)/81
+    assert abs(Pow(Rational(-2, 3), Rational(-7, 4)).n() -
+        Pow(Rational(-2, 3), Rational(-7, 4), evaluate=False).n()) < 1e-16
+
+    # negative integer power and negative rational base
+    assert Rational(-2, 3) ** Rational(-2, 1) == Rational(9, 4)
+
+    a = Rational(1, 10)
+    assert a**Float(a, 2) == Float(a, 2)**Float(a, 2)
+    assert Rational(-2, 3)**Symbol('', even=True) == \
+        Rational(2, 3)**Symbol('', even=True)
+
+
+def test_powers_Float():
+    assert str((S('-1/10')**S('3/10')).n()) == str(Float(-.1)**(.3))
+
+
+def test_lshift_Integer():
+    assert Integer(0) << Integer(2) == Integer(0)
+    assert Integer(0) << 2 == Integer(0)
+    assert 0 << Integer(2) == Integer(0)
+
+    assert Integer(0b11) << Integer(0) == Integer(0b11)
+    assert Integer(0b11) << 0 == Integer(0b11)
+    assert 0b11 << Integer(0) == Integer(0b11)
+
+    assert Integer(0b11) << Integer(2) == Integer(0b11 << 2)
+    assert Integer(0b11) << 2 == Integer(0b11 << 2)
+    assert 0b11 << Integer(2) == Integer(0b11 << 2)
+
+    assert Integer(-0b11) << Integer(2) == Integer(-0b11 << 2)
+    assert Integer(-0b11) << 2 == Integer(-0b11 << 2)
+    assert -0b11 << Integer(2) == Integer(-0b11 << 2)
+
+    raises(TypeError, lambda: Integer(2) << 0.0)
+    raises(TypeError, lambda: 0.0 << Integer(2))
+    raises(ValueError, lambda: Integer(1) << Integer(-1))
+
+
+def test_rshift_Integer():
+    assert Integer(0) >> Integer(2) == Integer(0)
+    assert Integer(0) >> 2 == Integer(0)
+    assert 0 >> Integer(2) == Integer(0)
+
+    assert Integer(0b11) >> Integer(0) == Integer(0b11)
+    assert Integer(0b11) >> 0 == Integer(0b11)
+    assert 0b11 >> Integer(0) == Integer(0b11)
+
+    assert Integer(0b11) >> Integer(2) == Integer(0)
+    assert Integer(0b11) >> 2 == Integer(0)
+    assert 0b11 >> Integer(2) == Integer(0)
+
+    assert Integer(-0b11) >> Integer(2) == Integer(-1)
+    assert Integer(-0b11) >> 2 == Integer(-1)
+    assert -0b11 >> Integer(2) == Integer(-1)
+
+    assert Integer(0b1100) >> Integer(2) == Integer(0b1100 >> 2)
+    assert Integer(0b1100) >> 2 == Integer(0b1100 >> 2)
+    assert 0b1100 >> Integer(2) == Integer(0b1100 >> 2)
+
+    assert Integer(-0b1100) >> Integer(2) == Integer(-0b1100 >> 2)
+    assert Integer(-0b1100) >> 2 == Integer(-0b1100 >> 2)
+    assert -0b1100 >> Integer(2) == Integer(-0b1100 >> 2)
+
+    raises(TypeError, lambda: Integer(0b10) >> 0.0)
+    raises(TypeError, lambda: 0.0 >> Integer(2))
+    raises(ValueError, lambda: Integer(1) >> Integer(-1))
+
+
+def test_and_Integer():
+    assert Integer(0b01010101) & Integer(0b10101010) == Integer(0)
+    assert Integer(0b01010101) & 0b10101010 == Integer(0)
+    assert 0b01010101 & Integer(0b10101010) == Integer(0)
+
+    assert Integer(0b01010101) & Integer(0b11011011) == Integer(0b01010001)
+    assert Integer(0b01010101) & 0b11011011 == Integer(0b01010001)
+    assert 0b01010101 & Integer(0b11011011) == Integer(0b01010001)
+
+    assert -Integer(0b01010101) & Integer(0b11011011) == Integer(-0b01010101 & 0b11011011)
+    assert Integer(-0b01010101) & 0b11011011 == Integer(-0b01010101 & 0b11011011)
+    assert -0b01010101 & Integer(0b11011011) == Integer(-0b01010101 & 0b11011011)
+
+    assert Integer(0b01010101) & -Integer(0b11011011) == Integer(0b01010101 & -0b11011011)
+    assert Integer(0b01010101) & -0b11011011 == Integer(0b01010101 & -0b11011011)
+    assert 0b01010101 & Integer(-0b11011011) == Integer(0b01010101 & -0b11011011)
+
+    raises(TypeError, lambda: Integer(2) & 0.0)
+    raises(TypeError, lambda: 0.0 & Integer(2))
+
+
+def test_xor_Integer():
+    assert Integer(0b01010101) ^ Integer(0b11111111) == Integer(0b10101010)
+    assert Integer(0b01010101) ^ 0b11111111 == Integer(0b10101010)
+    assert 0b01010101 ^ Integer(0b11111111) == Integer(0b10101010)
+
+    assert Integer(0b01010101) ^ Integer(0b11011011) == Integer(0b10001110)
+    assert Integer(0b01010101) ^ 0b11011011 == Integer(0b10001110)
+    assert 0b01010101 ^ Integer(0b11011011) == Integer(0b10001110)
+
+    assert -Integer(0b01010101) ^ Integer(0b11011011) == Integer(-0b01010101 ^ 0b11011011)
+    assert Integer(-0b01010101) ^ 0b11011011 == Integer(-0b01010101 ^ 0b11011011)
+    assert -0b01010101 ^ Integer(0b11011011) == Integer(-0b01010101 ^ 0b11011011)
+
+    assert Integer(0b01010101) ^ -Integer(0b11011011) == Integer(0b01010101 ^ -0b11011011)
+    assert Integer(0b01010101) ^ -0b11011011 == Integer(0b01010101 ^ -0b11011011)
+    assert 0b01010101 ^ Integer(-0b11011011) == Integer(0b01010101 ^ -0b11011011)
+
+    raises(TypeError, lambda: Integer(2) ^ 0.0)
+    raises(TypeError, lambda: 0.0 ^ Integer(2))
+
+
+def test_or_Integer():
+    assert Integer(0b01010101) | Integer(0b10101010) == Integer(0b11111111)
+    assert Integer(0b01010101) | 0b10101010 == Integer(0b11111111)
+    assert 0b01010101 | Integer(0b10101010) == Integer(0b11111111)
+
+    assert Integer(0b01010101) | Integer(0b11011011) == Integer(0b11011111)
+    assert Integer(0b01010101) | 0b11011011 == Integer(0b11011111)
+    assert 0b01010101 | Integer(0b11011011) == Integer(0b11011111)
+
+    assert -Integer(0b01010101) | Integer(0b11011011) == Integer(-0b01010101 | 0b11011011)
+    assert Integer(-0b01010101) | 0b11011011 == Integer(-0b01010101 | 0b11011011)
+    assert -0b01010101 | Integer(0b11011011) == Integer(-0b01010101 | 0b11011011)
+
+    assert Integer(0b01010101) | -Integer(0b11011011) == Integer(0b01010101 | -0b11011011)
+    assert Integer(0b01010101) | -0b11011011 == Integer(0b01010101 | -0b11011011)
+    assert 0b01010101 | Integer(-0b11011011) == Integer(0b01010101 | -0b11011011)
+
+    raises(TypeError, lambda: Integer(2) | 0.0)
+    raises(TypeError, lambda: 0.0 | Integer(2))
+
+
+def test_invert_Integer():
+    assert ~Integer(0b01010101) == Integer(-0b01010110)
+    assert ~Integer(0b01010101) == Integer(~0b01010101)
+    assert ~(~Integer(0b01010101)) == Integer(0b01010101)
+
+
+def test_abs1():
+    assert Rational(1, 6) != Rational(-1, 6)
+    assert abs(Rational(1, 6)) == abs(Rational(-1, 6))
+
+
+def test_accept_int():
+    assert not Float(4) == 4
+    assert Float(4) != 4
+    assert Float(4) == 4.0
+
+
+def test_dont_accept_str():
+    assert Float("0.2") != "0.2"
+    assert not (Float("0.2") == "0.2")
+
+
+def test_int():
+    a = Rational(5)
+    assert int(a) == 5
+    a = Rational(9, 10)
+    assert int(a) == int(-a) == 0
+    assert 1/(-1)**Rational(2, 3) == -(-1)**Rational(1, 3)
+    # issue 10368
+    a = Rational(32442016954, 78058255275)
+    assert type(int(a)) is type(int(-a)) is int
+
+
+def test_int_NumberSymbols():
+    assert int(Catalan) == 0
+    assert int(EulerGamma) == 0
+    assert int(pi) == 3
+    assert int(E) == 2
+    assert int(GoldenRatio) == 1
+    assert int(TribonacciConstant) == 1
+    for i in [Catalan, E, EulerGamma, GoldenRatio, TribonacciConstant, pi]:
+        a, b = i.approximation_interval(Integer)
+        ia = int(i)
+        assert ia == a
+        assert isinstance(ia, int)
+        assert b == a + 1
+        assert a.is_Integer and b.is_Integer
+
+
+def test_real_bug():
+    x = Symbol("x")
+    assert str(2.0*x*x) in ["(2.0*x)*x", "2.0*x**2", "2.00000000000000*x**2"]
+    assert str(2.1*x*x) != "(2.0*x)*x"
+
+
+def test_bug_sqrt():
+    assert ((sqrt(Rational(2)) + 1)*(sqrt(Rational(2)) - 1)).expand() == 1
+
+
+def test_pi_Pi():
+    "Test that pi (instance) is imported, but Pi (class) is not"
+    from sympy import pi  # noqa
+    with raises(ImportError):
+        from sympy import Pi  # noqa
+
+
+def test_no_len():
+    # there should be no len for numbers
+    raises(TypeError, lambda: len(Rational(2)))
+    raises(TypeError, lambda: len(Rational(2, 3)))
+    raises(TypeError, lambda: len(Integer(2)))
+
+
+def test_issue_3321():
+    assert sqrt(Rational(1, 5)) == Rational(1, 5)**S.Half
+    assert 5 * sqrt(Rational(1, 5)) == sqrt(5)
+
+
+def test_issue_3692():
+    assert ((-1)**Rational(1, 6)).expand(complex=True) == I/2 + sqrt(3)/2
+    assert ((-5)**Rational(1, 6)).expand(complex=True) == \
+        5**Rational(1, 6)*I/2 + 5**Rational(1, 6)*sqrt(3)/2
+    assert ((-64)**Rational(1, 6)).expand(complex=True) == I + sqrt(3)
+
+
+def test_issue_3423():
+    x = Symbol("x")
+    assert sqrt(x - 1).as_base_exp() == (x - 1, S.Half)
+    assert sqrt(x - 1) != I*sqrt(1 - x)
+
+
+def test_issue_3449():
+    x = Symbol("x")
+    assert sqrt(x - 1).subs(x, 5) == 2
+
+
+def test_issue_13890():
+    x = Symbol("x")
+    e = (-x/4 - S.One/12)**x - 1
+    f = simplify(e)
+    a = Rational(9, 5)
+    assert abs(e.subs(x,a).evalf() - f.subs(x,a).evalf()) < 1e-15
+
+
+def test_Integer_factors():
+    def F(i):
+        return Integer(i).factors()
+
+    assert F(1) == {}
+    assert F(2) == {2: 1}
+    assert F(3) == {3: 1}
+    assert F(4) == {2: 2}
+    assert F(5) == {5: 1}
+    assert F(6) == {2: 1, 3: 1}
+    assert F(7) == {7: 1}
+    assert F(8) == {2: 3}
+    assert F(9) == {3: 2}
+    assert F(10) == {2: 1, 5: 1}
+    assert F(11) == {11: 1}
+    assert F(12) == {2: 2, 3: 1}
+    assert F(13) == {13: 1}
+    assert F(14) == {2: 1, 7: 1}
+    assert F(15) == {3: 1, 5: 1}
+    assert F(16) == {2: 4}
+    assert F(17) == {17: 1}
+    assert F(18) == {2: 1, 3: 2}
+    assert F(19) == {19: 1}
+    assert F(20) == {2: 2, 5: 1}
+    assert F(21) == {3: 1, 7: 1}
+    assert F(22) == {2: 1, 11: 1}
+    assert F(23) == {23: 1}
+    assert F(24) == {2: 3, 3: 1}
+    assert F(25) == {5: 2}
+    assert F(26) == {2: 1, 13: 1}
+    assert F(27) == {3: 3}
+    assert F(28) == {2: 2, 7: 1}
+    assert F(29) == {29: 1}
+    assert F(30) == {2: 1, 3: 1, 5: 1}
+    assert F(31) == {31: 1}
+    assert F(32) == {2: 5}
+    assert F(33) == {3: 1, 11: 1}
+    assert F(34) == {2: 1, 17: 1}
+    assert F(35) == {5: 1, 7: 1}
+    assert F(36) == {2: 2, 3: 2}
+    assert F(37) == {37: 1}
+    assert F(38) == {2: 1, 19: 1}
+    assert F(39) == {3: 1, 13: 1}
+    assert F(40) == {2: 3, 5: 1}
+    assert F(41) == {41: 1}
+    assert F(42) == {2: 1, 3: 1, 7: 1}
+    assert F(43) == {43: 1}
+    assert F(44) == {2: 2, 11: 1}
+    assert F(45) == {3: 2, 5: 1}
+    assert F(46) == {2: 1, 23: 1}
+    assert F(47) == {47: 1}
+    assert F(48) == {2: 4, 3: 1}
+    assert F(49) == {7: 2}
+    assert F(50) == {2: 1, 5: 2}
+    assert F(51) == {3: 1, 17: 1}
+
+
+def test_Rational_factors():
+    def F(p, q, visual=None):
+        return Rational(p, q).factors(visual=visual)
+
+    assert F(2, 3) == {2: 1, 3: -1}
+    assert F(2, 9) == {2: 1, 3: -2}
+    assert F(2, 15) == {2: 1, 3: -1, 5: -1}
+    assert F(6, 10) == {3: 1, 5: -1}
+
+
+def test_issue_4107():
+    assert pi*(E + 10) + pi*(-E - 10) != 0
+    assert pi*(E + 10**10) + pi*(-E - 10**10) != 0
+    assert pi*(E + 10**20) + pi*(-E - 10**20) != 0
+    assert pi*(E + 10**80) + pi*(-E - 10**80) != 0
+
+    assert (pi*(E + 10) + pi*(-E - 10)).expand() == 0
+    assert (pi*(E + 10**10) + pi*(-E - 10**10)).expand() == 0
+    assert (pi*(E + 10**20) + pi*(-E - 10**20)).expand() == 0
+    assert (pi*(E + 10**80) + pi*(-E - 10**80)).expand() == 0
+
+
+def test_IntegerInteger():
+    a = Integer(4)
+    b = Integer(a)
+
+    assert a == b
+
+
+def test_Rational_gcd_lcm_cofactors():
+    assert Integer(4).gcd(2) == Integer(2)
+    assert Integer(4).lcm(2) == Integer(4)
+    assert Integer(4).gcd(Integer(2)) == Integer(2)
+    assert Integer(4).lcm(Integer(2)) == Integer(4)
+    a, b = 720**99911, 480**12342
+    assert Integer(a).lcm(b) == a*b/Integer(a).gcd(b)
+
+    assert Integer(4).gcd(3) == Integer(1)
+    assert Integer(4).lcm(3) == Integer(12)
+    assert Integer(4).gcd(Integer(3)) == Integer(1)
+    assert Integer(4).lcm(Integer(3)) == Integer(12)
+
+    assert Rational(4, 3).gcd(2) == Rational(2, 3)
+    assert Rational(4, 3).lcm(2) == Integer(4)
+    assert Rational(4, 3).gcd(Integer(2)) == Rational(2, 3)
+    assert Rational(4, 3).lcm(Integer(2)) == Integer(4)
+
+    assert Integer(4).gcd(Rational(2, 9)) == Rational(2, 9)
+    assert Integer(4).lcm(Rational(2, 9)) == Integer(4)
+
+    assert Rational(4, 3).gcd(Rational(2, 9)) == Rational(2, 9)
+    assert Rational(4, 3).lcm(Rational(2, 9)) == Rational(4, 3)
+    assert Rational(4, 5).gcd(Rational(2, 9)) == Rational(2, 45)
+    assert Rational(4, 5).lcm(Rational(2, 9)) == Integer(4)
+    assert Rational(5, 9).lcm(Rational(3, 7)) == Rational(Integer(5).lcm(3),Integer(9).gcd(7))
+
+    assert Integer(4).cofactors(2) == (Integer(2), Integer(2), Integer(1))
+    assert Integer(4).cofactors(Integer(2)) == \
+        (Integer(2), Integer(2), Integer(1))
+
+    assert Integer(4).gcd(Float(2.0)) == Float(1.0)
+    assert Integer(4).lcm(Float(2.0)) == Float(8.0)
+    assert Integer(4).cofactors(Float(2.0)) == (Float(1.0), Float(4.0), Float(2.0))
+
+    assert S.Half.gcd(Float(2.0)) == Float(1.0)
+    assert S.Half.lcm(Float(2.0)) == Float(1.0)
+    assert S.Half.cofactors(Float(2.0)) == \
+        (Float(1.0), Float(0.5), Float(2.0))
+
+
+def test_Float_gcd_lcm_cofactors():
+    assert Float(2.0).gcd(Integer(4)) == Float(1.0)
+    assert Float(2.0).lcm(Integer(4)) == Float(8.0)
+    assert Float(2.0).cofactors(Integer(4)) == (Float(1.0), Float(2.0), Float(4.0))
+
+    assert Float(2.0).gcd(S.Half) == Float(1.0)
+    assert Float(2.0).lcm(S.Half) == Float(1.0)
+    assert Float(2.0).cofactors(S.Half) == \
+        (Float(1.0), Float(2.0), Float(0.5))
+
+
+def test_issue_4611():
+    assert abs(pi._evalf(50) - 3.14159265358979) < 1e-10
+    assert abs(E._evalf(50) - 2.71828182845905) < 1e-10
+    assert abs(Catalan._evalf(50) - 0.915965594177219) < 1e-10
+    assert abs(EulerGamma._evalf(50) - 0.577215664901533) < 1e-10
+    assert abs(GoldenRatio._evalf(50) - 1.61803398874989) < 1e-10
+    assert abs(TribonacciConstant._evalf(50) - 1.83928675521416) < 1e-10
+
+    x = Symbol("x")
+    assert (pi + x).evalf() == pi.evalf() + x
+    assert (E + x).evalf() == E.evalf() + x
+    assert (Catalan + x).evalf() == Catalan.evalf() + x
+    assert (EulerGamma + x).evalf() == EulerGamma.evalf() + x
+    assert (GoldenRatio + x).evalf() == GoldenRatio.evalf() + x
+    assert (TribonacciConstant + x).evalf() == TribonacciConstant.evalf() + x
+
+
+@conserve_mpmath_dps
+def test_conversion_to_mpmath():
+    assert mpmath.mpmathify(Integer(1)) == mpmath.mpf(1)
+    assert mpmath.mpmathify(S.Half) == mpmath.mpf(0.5)
+    assert mpmath.mpmathify(Float('1.23', 15)) == mpmath.mpf('1.23')
+
+    assert mpmath.mpmathify(I) == mpmath.mpc(1j)
+
+    assert mpmath.mpmathify(1 + 2*I) == mpmath.mpc(1 + 2j)
+    assert mpmath.mpmathify(1.0 + 2*I) == mpmath.mpc(1 + 2j)
+    assert mpmath.mpmathify(1 + 2.0*I) == mpmath.mpc(1 + 2j)
+    assert mpmath.mpmathify(1.0 + 2.0*I) == mpmath.mpc(1 + 2j)
+    assert mpmath.mpmathify(S.Half + S.Half*I) == mpmath.mpc(0.5 + 0.5j)
+
+    assert mpmath.mpmathify(2*I) == mpmath.mpc(2j)
+    assert mpmath.mpmathify(2.0*I) == mpmath.mpc(2j)
+    assert mpmath.mpmathify(S.Half*I) == mpmath.mpc(0.5j)
+
+    mpmath.mp.dps = 100
+    assert mpmath.mpmathify(pi.evalf(100) + pi.evalf(100)*I) == mpmath.pi + mpmath.pi*mpmath.j
+    assert mpmath.mpmathify(pi.evalf(100)*I) == mpmath.pi*mpmath.j
+
+
+def test_relational():
+    # real
+    x = S(.1)
+    assert (x != cos) is True
+    assert (x == cos) is False
+
+    # rational
+    x = Rational(1, 3)
+    assert (x != cos) is True
+    assert (x == cos) is False
+
+    # integer defers to rational so these tests are omitted
+
+    # number symbol
+    x = pi
+    assert (x != cos) is True
+    assert (x == cos) is False
+
+
+def test_Integer_as_index():
+    assert 'hello'[Integer(2):] == 'llo'
+
+
+def test_Rational_int():
+    assert int( Rational(7, 5)) == 1
+    assert int( S.Half) == 0
+    assert int(Rational(-1, 2)) == 0
+    assert int(-Rational(7, 5)) == -1
+
+
+def test_zoo():
+    b = Symbol('b', finite=True)
+    nz = Symbol('nz', nonzero=True)
+    p = Symbol('p', positive=True)
+    n = Symbol('n', negative=True)
+    im = Symbol('i', imaginary=True)
+    c = Symbol('c', complex=True)
+    pb = Symbol('pb', positive=True)
+    nb = Symbol('nb', negative=True)
+    imb = Symbol('ib', imaginary=True, finite=True)
+    for i in [I, S.Infinity, S.NegativeInfinity, S.Zero, S.One, S.Pi, S.Half, S(3), log(3),
+              b, nz, p, n, im, pb, nb, imb, c]:
+        if i.is_finite and (i.is_real or i.is_imaginary):
+            assert i + zoo is zoo
+            assert i - zoo is zoo
+            assert zoo + i is zoo
+            assert zoo - i is zoo
+        elif i.is_finite is not False:
+            assert (i + zoo).is_Add
+            assert (i - zoo).is_Add
+            assert (zoo + i).is_Add
+            assert (zoo - i).is_Add
+        else:
+            assert (i + zoo) is S.NaN
+            assert (i - zoo) is S.NaN
+            assert (zoo + i) is S.NaN
+            assert (zoo - i) is S.NaN
+
+        if fuzzy_not(i.is_zero) and (i.is_extended_real or i.is_imaginary):
+            assert i*zoo is zoo
+            assert zoo*i is zoo
+        elif i.is_zero:
+            assert i*zoo is S.NaN
+            assert zoo*i is S.NaN
+        else:
+            assert (i*zoo).is_Mul
+            assert (zoo*i).is_Mul
+
+        if fuzzy_not((1/i).is_zero) and (i.is_real or i.is_imaginary):
+            assert zoo/i is zoo
+        elif (1/i).is_zero:
+            assert zoo/i is S.NaN
+        elif i.is_zero:
+            assert zoo/i is zoo
+        else:
+            assert (zoo/i).is_Mul
+
+    assert (I*oo).is_Mul  # allow directed infinity
+    assert zoo + zoo is S.NaN
+    assert zoo * zoo is zoo
+    assert zoo - zoo is S.NaN
+    assert zoo/zoo is S.NaN
+    assert zoo**zoo is S.NaN
+    assert zoo**0 is S.One
+    assert zoo**2 is zoo
+    assert 1/zoo is S.Zero
+
+    assert Mul.flatten([S.NegativeOne, oo, S(0)]) == ([S.NaN], [], None)
+
+
+def test_issue_4122():
+    x = Symbol('x', nonpositive=True)
+    assert oo + x is oo
+    x = Symbol('x', extended_nonpositive=True)
+    assert (oo + x).is_Add
+    x = Symbol('x', finite=True)
+    assert (oo + x).is_Add  # x could be imaginary
+    x = Symbol('x', nonnegative=True)
+    assert oo + x is oo
+    x = Symbol('x', extended_nonnegative=True)
+    assert oo + x is oo
+    x = Symbol('x', finite=True, real=True)
+    assert oo + x is oo
+
+    # similarly for negative infinity
+    x = Symbol('x', nonnegative=True)
+    assert -oo + x is -oo
+    x = Symbol('x', extended_nonnegative=True)
+    assert (-oo + x).is_Add
+    x = Symbol('x', finite=True)
+    assert (-oo + x).is_Add
+    x = Symbol('x', nonpositive=True)
+    assert -oo + x is -oo
+    x = Symbol('x', extended_nonpositive=True)
+    assert -oo + x is -oo
+    x = Symbol('x', finite=True, real=True)
+    assert -oo + x is -oo
+
+
+def test_GoldenRatio_expand():
+    assert GoldenRatio.expand(func=True) == S.Half + sqrt(5)/2
+
+
+def test_TribonacciConstant_expand():
+        assert TribonacciConstant.expand(func=True) == \
+          (1 + cbrt(19 - 3*sqrt(33)) + cbrt(19 + 3*sqrt(33))) / 3
+
+
+def test_as_content_primitive():
+    assert S.Zero.as_content_primitive() == (1, 0)
+    assert S.Half.as_content_primitive() == (S.Half, 1)
+    assert (Rational(-1, 2)).as_content_primitive() == (S.Half, -1)
+    assert S(3).as_content_primitive() == (3, 1)
+    assert S(3.1).as_content_primitive() == (1, 3.1)
+
+
+def test_hashing_sympy_integers():
+    # Test for issue 5072
+    assert {Integer(3)} == {int(3)}
+    assert hash(Integer(4)) == hash(int(4))
+
+
+def test_rounding_issue_4172():
+    assert int((E**100).round()) == \
+        26881171418161354484126255515800135873611119
+    assert int((pi**100).round()) == \
+        51878483143196131920862615246303013562686760680406
+    assert int((Rational(1)/EulerGamma**100).round()) == \
+        734833795660954410469466
+
+
+@XFAIL
+def test_mpmath_issues():
+    from mpmath.libmp.libmpf import _normalize
+    import mpmath.libmp as mlib
+    rnd = mlib.round_nearest
+    mpf = (0, int(0), -123, -1, 53, rnd)  # nan
+    assert _normalize(mpf, 53) != (0, int(0), 0, 0)
+    mpf = (0, int(0), -456, -2, 53, rnd)  # +inf
+    assert _normalize(mpf, 53) != (0, int(0), 0, 0)
+    mpf = (1, int(0), -789, -3, 53, rnd)  # -inf
+    assert _normalize(mpf, 53) != (0, int(0), 0, 0)
+
+    from mpmath.libmp.libmpf import fnan
+    assert mlib.mpf_eq(fnan, fnan)
+
+
+def test_Catalan_EulerGamma_prec():
+    n = GoldenRatio
+    f = Float(n.n(), 5)
+    assert f._mpf_ == (0, int(212079), -17, 18)
+    assert f._prec == 20
+    assert n._as_mpf_val(20) == f._mpf_
+
+    n = EulerGamma
+    f = Float(n.n(), 5)
+    assert f._mpf_ == (0, int(302627), -19, 19)
+    assert f._prec == 20
+    assert n._as_mpf_val(20) == f._mpf_
+
+
+def test_Catalan_rewrite():
+    k = Dummy('k', integer=True, nonnegative=True)
+    assert Catalan.rewrite(Sum).dummy_eq(
+            Sum((-1)**k/(2*k + 1)**2, (k, 0, oo)))
+    assert Catalan.rewrite() == Catalan
+
+
+def test_bool_eq():
+    assert 0 == False
+    assert S(0) == False
+    assert S(0) != S.false
+    assert 1 == True
+    assert S.One == True
+    assert S.One != S.true
+
+
+def test_Float_eq():
+    # Floats with different precision should not compare equal
+    assert Float(.5, 10) != Float(.5, 11) != Float(.5, 1)
+    # but floats that aren't exact in base-2 still
+    # don't compare the same because they have different
+    # underlying mpf values
+    assert Float(.12, 3) != Float(.12, 4)
+    assert Float(.12, 3) != .12
+    assert 0.12 != Float(.12, 3)
+    assert Float('.12', 22) != .12
+    # issue 11707
+    # but Float/Rational -- except for 0 --
+    # are exact so Rational(x) = Float(y) only if
+    # Rational(x) == Rational(Float(y))
+    assert Float('1.1') != Rational(11, 10)
+    assert Rational(11, 10) != Float('1.1')
+    # coverage
+    assert not Float(3) == 2
+    assert not Float(3) == Float(2)
+    assert not Float(3) == 3
+    assert not Float(2**2) == S.Half
+    assert Float(2**2) == 4.0
+    assert not Float(2**-2) == 1
+    assert Float(2**-1) == 0.5
+    assert not Float(2*3) == 3
+    assert not Float(2*3) == 0.5
+    assert Float(2*3) == 6.0
+    assert not Float(2*3) == 6
+    assert not Float(2*3) == 8
+    assert not Float(.75) == Rational(3, 4)
+    assert Float(.75) == 0.75
+    assert Float(5/18) == 5/18
+    # 4473
+    assert Float(2.) != 3
+    assert not Float((0,1,-3)) == S.One/8
+    assert Float((0,1,-3)) == 1/8
+    assert Float((0,1,-3)) != S.One/9
+    # 16196
+    assert not 2 == Float(2)  # unlike Python
+    assert t**2 != t**2.0
+
+
+def test_issue_6640():
+    from mpmath.libmp.libmpf import finf, fninf
+    # fnan is not included because Float no longer returns fnan,
+    # but otherwise, the same sort of test could apply
+    assert Float(finf).is_zero is False
+    assert Float(fninf).is_zero is False
+    assert bool(Float(0)) is False
+
+
+def test_issue_6349():
+    assert Float('23.e3', '')._prec == 10
+    assert Float('23e3', '')._prec == 20
+    assert Float('23000', '')._prec == 20
+    assert Float('-23000', '')._prec == 20
+
+
+def test_mpf_norm():
+    assert mpf_norm((1, 0, 1, 0), 10) == mpf('0')._mpf_
+    assert Float._new((1, 0, 1, 0), 10)._mpf_ == mpf('0')._mpf_
+
+
+def test_latex():
+    assert latex(pi) == r"\pi"
+    assert latex(E) == r"e"
+    assert latex(GoldenRatio) == r"\phi"
+    assert latex(TribonacciConstant) == r"\text{TribonacciConstant}"
+    assert latex(EulerGamma) == r"\gamma"
+    assert latex(oo) == r"\infty"
+    assert latex(-oo) == r"-\infty"
+    assert latex(zoo) == r"\tilde{\infty}"
+    assert latex(nan) == r"\text{NaN}"
+    assert latex(I) == r"i"
+
+
+def test_issue_7742():
+    assert -oo % 1 is nan
+
+
+def test_simplify_AlgebraicNumber():
+    A = AlgebraicNumber
+    e = 3**(S.One/6)*(3 + (135 + 78*sqrt(3))**Rational(2, 3))/(45 + 26*sqrt(3))**(S.One/3)
+    assert simplify(A(e)) == A(12)  # wester test_C20
+
+    e = (41 + 29*sqrt(2))**(S.One/5)
+    assert simplify(A(e)) == A(1 + sqrt(2))  # wester test_C21
+
+    e = (3 + 4*I)**Rational(3, 2)
+    assert simplify(A(e)) == A(2 + 11*I)  # issue 4401
+
+
+def test_Float_idempotence():
+    x = Float('1.23', '')
+    y = Float(x)
+    z = Float(x, 15)
+    assert same_and_same_prec(y, x)
+    assert not same_and_same_prec(z, x)
+    x = Float(10**20)
+    y = Float(x)
+    z = Float(x, 15)
+    assert same_and_same_prec(y, x)
+    assert not same_and_same_prec(z, x)
+
+
+def test_comp1():
+    # sqrt(2) = 1.414213 5623730950...
+    a = sqrt(2).n(7)
+    assert comp(a, 1.4142129) is False
+    assert comp(a, 1.4142130)
+    #                  ...
+    assert comp(a, 1.4142141)
+    assert comp(a, 1.4142142) is False
+    assert comp(sqrt(2).n(2), '1.4')
+    assert comp(sqrt(2).n(2), Float(1.4, 2), '')
+    assert comp(sqrt(2).n(2), 1.4, '')
+    assert comp(sqrt(2).n(2), Float(1.4, 3), '') is False
+    assert comp(sqrt(2) + sqrt(3)*I, 1.4 + 1.7*I, .1)
+    assert not comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*0.89, .1)
+    assert comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*0.90, .1)
+    assert comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*1.07, .1)
+    assert not comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*1.08, .1)
+    assert [(i, j)
+            for i in range(130, 150)
+            for j in range(170, 180)
+            if comp((sqrt(2)+ I*sqrt(3)).n(3), i/100. + I*j/100.)] == [
+        (141, 173), (142, 173)]
+    raises(ValueError, lambda: comp(t, '1'))
+    raises(ValueError, lambda: comp(t, 1))
+    assert comp(0, 0.0)
+    assert comp(.5, S.Half)
+    assert comp(2 + sqrt(2), 2.0 + sqrt(2))
+    assert not comp(0, 1)
+    assert not comp(2, sqrt(2))
+    assert not comp(2 + I, 2.0 + sqrt(2))
+    assert not comp(2.0 + sqrt(2), 2 + I)
+    assert not comp(2.0 + sqrt(2), sqrt(3))
+    assert comp(1/pi.n(4), 0.3183, 1e-5)
+    assert not comp(1/pi.n(4), 0.3183, 8e-6)
+
+
+def test_issue_9491():
+    assert oo**zoo is nan
+
+
+def test_issue_10063():
+    assert 2**Float(3) == Float(8)
+
+
+def test_issue_10020():
+    assert oo**I is S.NaN
+    assert oo**(1 + I) is S.ComplexInfinity
+    assert oo**(-1 + I) is S.Zero
+    assert (-oo)**I is S.NaN
+    assert (-oo)**(-1 + I) is S.Zero
+    assert oo**t == Pow(oo, t, evaluate=False)
+    assert (-oo)**t == Pow(-oo, t, evaluate=False)
+
+
+def test_invert_numbers():
+    assert S(2).invert(5) == 3
+    assert S(2).invert(Rational(5, 2)) == S.Half
+    assert S(2).invert(5.) == S.Half
+    assert S(2).invert(S(5)) == 3
+    assert S(2.).invert(5) == 0.5
+    assert S(sqrt(2)).invert(5) == 1/sqrt(2)
+    assert S(sqrt(2)).invert(sqrt(3)) == 1/sqrt(2)
+
+
+def test_mod_inverse():
+    assert mod_inverse(3, 11) == 4
+    assert mod_inverse(5, 11) == 9
+    assert mod_inverse(21124921, 521512) == 7713
+    assert mod_inverse(124215421, 5125) == 2981
+    assert mod_inverse(214, 12515) == 1579
+    assert mod_inverse(5823991, 3299) == 1442
+    assert mod_inverse(123, 44) == 39
+    assert mod_inverse(2, 5) == 3
+    assert mod_inverse(-2, 5) == 2
+    assert mod_inverse(2, -5) == -2
+    assert mod_inverse(-2, -5) == -3
+    assert mod_inverse(-3, -7) == -5
+    x = Symbol('x')
+    assert S(2).invert(x) == S.Half
+    raises(TypeError, lambda: mod_inverse(2, x))
+    raises(ValueError, lambda: mod_inverse(2, S.Half))
+    raises(ValueError, lambda: mod_inverse(2, cos(1)**2 + sin(1)**2))
+
+
+def test_golden_ratio_rewrite_as_sqrt():
+    assert GoldenRatio.rewrite(sqrt) == S.Half + sqrt(5)*S.Half
+
+
+def test_tribonacci_constant_rewrite_as_sqrt():
+    assert TribonacciConstant.rewrite(sqrt) == \
+      (1 + cbrt(19 - 3*sqrt(33)) + cbrt(19 + 3*sqrt(33))) / 3
+
+
+def test_comparisons_with_unknown_type():
+    class Foo:
+        """
+        Class that is unaware of Basic, and relies on both classes returning
+        the NotImplemented singleton for equivalence to evaluate to False.
+
+        """
+
+    ni, nf, nr = Integer(3), Float(1.0), Rational(1, 3)
+    foo = Foo()
+
+    for n in ni, nf, nr, oo, -oo, zoo, nan:
+        assert n != foo
+        assert foo != n
+        assert not n == foo
+        assert not foo == n
+        raises(TypeError, lambda: n < foo)
+        raises(TypeError, lambda: foo > n)
+        raises(TypeError, lambda: n > foo)
+        raises(TypeError, lambda: foo < n)
+        raises(TypeError, lambda: n <= foo)
+        raises(TypeError, lambda: foo >= n)
+        raises(TypeError, lambda: n >= foo)
+        raises(TypeError, lambda: foo <= n)
+
+    class Bar:
+        """
+        Class that considers itself equal to any instance of Number except
+        infinities and nans, and relies on SymPy types returning the
+        NotImplemented singleton for symmetric equality relations.
+
+        """
+        def __eq__(self, other):
+            if other in (oo, -oo, zoo, nan):
+                return False
+            if isinstance(other, Number):
+                return True
+            return NotImplemented
+
+        def __ne__(self, other):
+            return not self == other
+
+    bar = Bar()
+
+    for n in ni, nf, nr:
+        assert n == bar
+        assert bar == n
+        assert not n != bar
+        assert not bar != n
+
+    for n in oo, -oo, zoo, nan:
+        assert n != bar
+        assert bar != n
+        assert not n == bar
+        assert not bar == n
+
+    for n in ni, nf, nr, oo, -oo, zoo, nan:
+        raises(TypeError, lambda: n < bar)
+        raises(TypeError, lambda: bar > n)
+        raises(TypeError, lambda: n > bar)
+        raises(TypeError, lambda: bar < n)
+        raises(TypeError, lambda: n <= bar)
+        raises(TypeError, lambda: bar >= n)
+        raises(TypeError, lambda: n >= bar)
+        raises(TypeError, lambda: bar <= n)
+
+
+def test_NumberSymbol_comparison():
+    from sympy.core.tests.test_relational import rel_check
+    rpi = Rational('905502432259640373/288230376151711744')
+    fpi = Float(float(pi))
+    assert rel_check(rpi, fpi)
+
+
+def test_Integer_precision():
+    # Make sure Integer inputs for keyword args work
+    assert Float('1.0', dps=Integer(15))._prec == 53
+    assert Float('1.0', precision=Integer(15))._prec == 15
+    assert type(Float('1.0', precision=Integer(15))._prec) == int
+    assert sympify(srepr(Float('1.0', precision=15))) == Float('1.0', precision=15)
+
+
+def test_numpy_to_float():
+    from sympy.testing.pytest import skip
+    from sympy.external import import_module
+    np = import_module('numpy')
+    if not np:
+        skip('numpy not installed. Abort numpy tests.')
+
+    def check_prec_and_relerr(npval, ratval):
+        prec = np.finfo(npval).nmant + 1
+        x = Float(npval)
+        assert x._prec == prec
+        y = Float(ratval, precision=prec)
+        assert abs((x - y)/y) < 2**(-(prec + 1))
+
+    check_prec_and_relerr(np.float16(2.0/3), Rational(2, 3))
+    check_prec_and_relerr(np.float32(2.0/3), Rational(2, 3))
+    check_prec_and_relerr(np.float64(2.0/3), Rational(2, 3))
+    # extended precision, on some arch/compilers:
+    x = np.longdouble(2)/3
+    check_prec_and_relerr(x, Rational(2, 3))
+    y = Float(x, precision=10)
+    assert same_and_same_prec(y, Float(Rational(2, 3), precision=10))
+
+    raises(TypeError, lambda: Float(np.complex64(1+2j)))
+    raises(TypeError, lambda: Float(np.complex128(1+2j)))
+
+
+def test_Integer_ceiling_floor():
+    a = Integer(4)
+
+    assert a.floor() == a
+    assert a.ceiling() == a
+
+
+def test_ComplexInfinity():
+    assert zoo.floor() is zoo
+    assert zoo.ceiling() is zoo
+    assert zoo**zoo is S.NaN
+
+
+def test_Infinity_floor_ceiling_power():
+    assert oo.floor() is oo
+    assert oo.ceiling() is oo
+    assert oo**S.NaN is S.NaN
+    assert oo**zoo is S.NaN
+
+
+def test_One_power():
+    assert S.One**12 is S.One
+    assert S.NegativeOne**S.NaN is S.NaN
+
+
+def test_NegativeInfinity():
+    assert (-oo).floor() is -oo
+    assert (-oo).ceiling() is -oo
+    assert (-oo)**11 is -oo
+    assert (-oo)**12 is oo
+
+
+def test_issue_6133():
+    raises(TypeError, lambda: (-oo < None))
+    raises(TypeError, lambda: (S(-2) < None))
+    raises(TypeError, lambda: (oo < None))
+    raises(TypeError, lambda: (oo > None))
+    raises(TypeError, lambda: (S(2) < None))
+
+
+def test_abc():
+    x = numbers.Float(5)
+    assert(isinstance(x, nums.Number))
+    assert(isinstance(x, numbers.Number))
+    assert(isinstance(x, nums.Real))
+    y = numbers.Rational(1, 3)
+    assert(isinstance(y, nums.Number))
+    assert(y.numerator == 1)
+    assert(y.denominator == 3)
+    assert(isinstance(y, nums.Rational))
+    z = numbers.Integer(3)
+    assert(isinstance(z, nums.Number))
+    assert(isinstance(z, numbers.Number))
+    assert(isinstance(z, nums.Rational))
+    assert(isinstance(z, numbers.Rational))
+    assert(isinstance(z, nums.Integral))
+
+
+def test_floordiv():
+    assert S(2)//S.Half == 4
+
+
+def test_negation():
+    assert -S.Zero is S.Zero
+    assert -Float(0) is not S.Zero and -Float(0) == 0.0
+
+
+def test_exponentiation_of_0():
+    x = Symbol('x')
+    assert 0**-x == zoo**x
+    assert unchanged(Pow, 0, x)
+    x = Symbol('x', zero=True)
+    assert 0**-x == S.One
+    assert 0**x == S.One
+
+
+def test_int_valued():
+    x = Symbol('x')
+    assert int_valued(x) == False
+    assert int_valued(S.Half) == False
+    assert int_valued(S.One) == True
+    assert int_valued(Float(1)) == True
+    assert int_valued(Float(1.1)) == False
+    assert int_valued(pi) == False
+
+
+def test_equal_valued():
+    x = Symbol('x')
+
+    equal_values = [
+        [1, 1.0, S(1), S(1.0), S(1).n(5)],
+        [2, 2.0, S(2), S(2.0), S(2).n(5)],
+        [-1, -1.0, -S(1), -S(1.0), -S(1).n(5)],
+        [0.5, S(0.5), S(1)/2],
+        [-0.5, -S(0.5), -S(1)/2],
+        [0, 0.0, S(0), S(0.0), S(0).n()],
+        [pi], [pi.n()],           # <-- not equal
+        [S(1)/10], [0.1, S(0.1)], # <-- not equal
+        [S(0.1).n(5)],
+        [oo],
+        [cos(x/2)], [cos(0.5*x)], # <-- no recursion
+    ]
+
+    for m, values_m in enumerate(equal_values):
+        for value_i in values_m:
+
+            # All values in same list equal
+            for value_j in values_m:
+                assert equal_valued(value_i, value_j) is True
+
+            # Not equal to anything in any other list:
+            for n, values_n in enumerate(equal_values):
+                if n == m:
+                    continue
+                for value_j in values_n:
+                    assert equal_valued(value_i, value_j) is False
+
+
+def test_all_close():
+    x = Symbol('x')
+    y = Symbol('y')
+    z = Symbol('z')
+    assert all_close(2, 2) is True
+    assert all_close(2, 2.0000) is True
+    assert all_close(2, 2.0001) is False
+    assert all_close(1/3, 1/3.0001) is False
+    assert all_close(1/3, 1/3.0001, 1e-3, 1e-3) is True
+    assert all_close(1/3, Rational(1, 3)) is True
+    assert all_close(0.1*exp(0.2*x), exp(x/5)/10) is True
+    # The expressions should be structurally the same modulo identity:
+    assert all_close(1.4142135623730951, sqrt(2)) is False
+    assert all_close(1.4142135623730951, sqrt(2).evalf()) is True
+    assert all_close(x + 1e-20, x) is True
+    # We should be able to match terms of an Add/Mul in any order
+    assert all_close(Add(1, 2, evaluate=False), Add(2, 1, evaluate=False))
+    # coverage
+    assert not all_close(2*x, 3*x)
+    assert all_close(2*x, 3*x, 1)
+    assert not all_close(2*x, 3*x, 0, 0.5)
+    assert all_close(2*x, 3*x, 0, 1)
+    assert not all_close(y*x, z*x)
+    assert all_close(2*x*exp(1.0*x), 2.0*x*exp(x))
+    assert not all_close(2*x*exp(1.0*x), 2.0*x*exp(2.*x))
+    assert all_close(x + 2.*y, 1.*x + 2*y)
+    assert all_close(x + exp(2.*x)*y, 1.*x + exp(2*x)*y)
+    assert not all_close(x + exp(2.*x)*y, 1.*x + 2*exp(2*x)*y)
+    assert not all_close(x + exp(2.*x)*y, 1.*x + exp(3*x)*y)
+    assert not all_close(x + 2.*y, 1.*x + 3*y)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_operations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_operations.py
new file mode 100644
index 0000000000000000000000000000000000000000..c60d691ef00ee9601ada04ef68e2db37794a81ad
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_operations.py
@@ -0,0 +1,110 @@
+from sympy.core.expr import Expr
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.operations import AssocOp, LatticeOp
+from sympy.testing.pytest import raises
+from sympy.core.sympify import SympifyError
+from sympy.core.add import Add, add
+from sympy.core.mul import Mul, mul
+
+# create the simplest possible Lattice class
+
+
+class join(LatticeOp):
+    zero = Integer(0)
+    identity = Integer(1)
+
+
+def test_lattice_simple():
+    assert join(join(2, 3), 4) == join(2, join(3, 4))
+    assert join(2, 3) == join(3, 2)
+    assert join(0, 2) == 0
+    assert join(1, 2) == 2
+    assert join(2, 2) == 2
+
+    assert join(join(2, 3), 4) == join(2, 3, 4)
+    assert join() == 1
+    assert join(4) == 4
+    assert join(1, 4, 2, 3, 1, 3, 2) == join(2, 3, 4)
+
+
+def test_lattice_shortcircuit():
+    raises(SympifyError, lambda: join(object))
+    assert join(0, object) == 0
+
+
+def test_lattice_print():
+    assert str(join(5, 4, 3, 2)) == 'join(2, 3, 4, 5)'
+
+
+def test_lattice_make_args():
+    assert join.make_args(join(2, 3, 4)) == {S(2), S(3), S(4)}
+    assert join.make_args(0) == {0}
+    assert list(join.make_args(0))[0] is S.Zero
+    assert Add.make_args(0)[0] is S.Zero
+
+
+def test_issue_14025():
+    a, b, c, d = symbols('a,b,c,d', commutative=False)
+    assert Mul(a, b, c).has(c*b) == False
+    assert Mul(a, b, c).has(b*c) == True
+    assert Mul(a, b, c, d).has(b*c*d) == True
+
+
+def test_AssocOp_flatten():
+    a, b, c, d = symbols('a,b,c,d')
+
+    class MyAssoc(AssocOp):
+        identity = S.One
+
+    assert MyAssoc(a, MyAssoc(b, c)).args == \
+        MyAssoc(MyAssoc(a, b), c).args == \
+        MyAssoc(MyAssoc(a, b, c)).args == \
+        MyAssoc(a, b, c).args == \
+            (a, b, c)
+    u = MyAssoc(b, c)
+    v = MyAssoc(u, d, evaluate=False)
+    assert v.args == (u, d)
+    # like Add, any unevaluated outer call will flatten inner args
+    assert MyAssoc(a, v).args == (a, b, c, d)
+
+
+def test_add_dispatcher():
+
+    class NewBase(Expr):
+        @property
+        def _add_handler(self):
+            return NewAdd
+    class NewAdd(NewBase, Add):
+        pass
+    add.register_handlerclass((Add, NewAdd), NewAdd)
+
+    a, b = Symbol('a'), NewBase()
+
+    # Add called as fallback
+    assert add(1, 2) == Add(1, 2)
+    assert add(a, a) == Add(a, a)
+
+    # selection by registered priority
+    assert add(a,b,a) == NewAdd(2*a, b)
+
+
+def test_mul_dispatcher():
+
+    class NewBase(Expr):
+        @property
+        def _mul_handler(self):
+            return NewMul
+    class NewMul(NewBase, Mul):
+        pass
+    mul.register_handlerclass((Mul, NewMul), NewMul)
+
+    a, b = Symbol('a'), NewBase()
+
+    # Mul called as fallback
+    assert mul(1, 2) == Mul(1, 2)
+    assert mul(a, a) == Mul(a, a)
+
+    # selection by registered priority
+    assert mul(a,b,a) == NewMul(a**2, b)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_parameters.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_parameters.py
new file mode 100644
index 0000000000000000000000000000000000000000..21e03d717872a9a8165ceeebf7ef58e9842702c0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_parameters.py
@@ -0,0 +1,126 @@
+from sympy.abc import x, y
+from sympy.core.parameters import evaluate
+from sympy.core import Mul, Add, Pow, S
+from sympy.core.numbers import oo
+from sympy.functions.elementary.miscellaneous import sqrt
+
+def test_add():
+    with evaluate(False):
+        p = oo - oo
+        assert isinstance(p, Add) and p.args == (oo, -oo)
+        p = 5 - oo
+        assert isinstance(p, Add) and p.args == (-oo, 5)
+        p = oo - 5
+        assert isinstance(p, Add) and p.args == (oo, -5)
+        p = oo + 5
+        assert isinstance(p, Add) and p.args == (oo, 5)
+        p = 5 + oo
+        assert isinstance(p, Add) and p.args == (oo, 5)
+        p = -oo + 5
+        assert isinstance(p, Add) and p.args == (-oo, 5)
+        p = -5 - oo
+        assert isinstance(p, Add) and p.args == (-oo, -5)
+
+    with evaluate(False):
+        expr = x + x
+        assert isinstance(expr, Add)
+        assert expr.args == (x, x)
+
+        with evaluate(True):
+            assert (x + x).args == (2, x)
+
+        assert (x + x).args == (x, x)
+
+    assert isinstance(x + x, Mul)
+
+    with evaluate(False):
+        assert S.One + 1 == Add(1, 1)
+        assert 1 + S.One == Add(1, 1)
+
+        assert S(4) - 3 == Add(4, -3)
+        assert -3 + S(4) == Add(4, -3)
+
+        assert S(2) * 4 == Mul(2, 4)
+        assert 4 * S(2) == Mul(2, 4)
+
+        assert S(6) / 3 == Mul(6, Pow(3, -1))
+        assert S.One / 3 * 6 == Mul(S.One / 3, 6)
+
+        assert 9 ** S(2) == Pow(9, 2)
+        assert S(2) ** 9 == Pow(2, 9)
+
+        assert S(2) / 2 == Mul(2, Pow(2, -1))
+        assert S.One / 2 * 2 == Mul(S.One / 2, 2)
+
+        assert S(2) / 3 + 1 == Add(S(2) / 3, 1)
+        assert 1 + S(2) / 3 == Add(1, S(2) / 3)
+
+        assert S(4) / 7 - 3 == Add(S(4) / 7, -3)
+        assert -3 + S(4) / 7 == Add(-3, S(4) / 7)
+
+        assert S(2) / 4 * 4 == Mul(S(2) / 4, 4)
+        assert 4 * (S(2) / 4) == Mul(4, S(2) / 4)
+
+        assert S(6) / 3 == Mul(6, Pow(3, -1))
+        assert S.One / 3 * 6 == Mul(S.One / 3, 6)
+
+        assert S.One / 3 + sqrt(3) == Add(S.One / 3, sqrt(3))
+        assert sqrt(3) + S.One / 3 == Add(sqrt(3), S.One / 3)
+
+        assert S.One / 2 * 10.333 == Mul(S.One / 2, 10.333)
+        assert 10.333 * (S.One / 2) == Mul(10.333, S.One / 2)
+
+        assert sqrt(2) * sqrt(2) == Mul(sqrt(2), sqrt(2))
+
+        assert S.One / 2 + x == Add(S.One / 2, x)
+        assert x + S.One / 2 == Add(x, S.One / 2)
+
+        assert S.One / x * x == Mul(S.One / x, x)
+        assert x * (S.One / x) == Mul(x, Pow(x, -1))
+
+        assert S.One / 3 == Pow(3, -1)
+        assert S.One / x == Pow(x, -1)
+        assert 1 / S(3) == Pow(3, -1)
+        assert 1 / x == Pow(x, -1)
+
+def test_nested():
+    with evaluate(False):
+        expr = (x + x) + (y + y)
+        assert expr.args == ((x + x), (y + y))
+        assert expr.args[0].args == (x, x)
+
+def test_reentrantcy():
+    with evaluate(False):
+        expr = x + x
+        assert expr.args == (x, x)
+        with evaluate(True):
+            expr = x + x
+            assert expr.args == (2, x)
+        expr = x + x
+        assert expr.args == (x, x)
+
+def test_reusability():
+    f = evaluate(False)
+
+    with f:
+        expr = x + x
+        assert expr.args == (x, x)
+
+    expr = x + x
+    assert expr.args == (2, x)
+
+    with f:
+        expr = x + x
+        assert expr.args == (x, x)
+
+    # Assure reentrancy with reusability
+    ctx = evaluate(False)
+    with ctx:
+        expr = x + x
+        assert expr.args == (x, x)
+        with ctx:
+            expr = x + x
+            assert expr.args == (x, x)
+
+    expr = x + x
+    assert expr.args == (2, x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_power.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_power.py
new file mode 100644
index 0000000000000000000000000000000000000000..80ae48c525c20da6153deffbc9feadef81acf527
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_power.py
@@ -0,0 +1,670 @@
+from sympy.core import (
+    Basic, Rational, Symbol, S, Float, Integer, Mul, Number, Pow,
+    Expr, I, nan, pi, symbols, oo, zoo, N)
+from sympy.core.parameters import global_parameters
+from sympy.core.tests.test_evalf import NS
+from sympy.core.function import expand_multinomial
+from sympy.functions.elementary.miscellaneous import sqrt, cbrt
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.special.error_functions import erf
+from sympy.functions.elementary.trigonometric import (
+    sin, cos, tan, sec, csc, atan)
+from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh
+from sympy.polys import Poly
+from sympy.series.order import O
+from sympy.sets import FiniteSet
+from sympy.core.power import power
+from sympy.core.intfunc import integer_nthroot
+from sympy.testing.pytest import warns, _both_exp_pow
+from sympy.utilities.exceptions import SymPyDeprecationWarning
+from sympy.abc import a, b, c, x, y
+from sympy.core.numbers import all_close
+
+def test_rational():
+    a = Rational(1, 5)
+
+    r = sqrt(5)/5
+    assert sqrt(a) == r
+    assert 2*sqrt(a) == 2*r
+
+    r = a*a**S.Half
+    assert a**Rational(3, 2) == r
+    assert 2*a**Rational(3, 2) == 2*r
+
+    r = a**5*a**Rational(2, 3)
+    assert a**Rational(17, 3) == r
+    assert 2 * a**Rational(17, 3) == 2*r
+
+
+def test_large_rational():
+    e = (Rational(123712**12 - 1, 7) + Rational(1, 7))**Rational(1, 3)
+    assert e == 234232585392159195136 * (Rational(1, 7)**Rational(1, 3))
+
+
+def test_negative_real():
+    def feq(a, b):
+        return abs(a - b) < 1E-10
+
+    assert feq(S.One / Float(-0.5), -Integer(2))
+
+
+def test_expand():
+    assert (2**(-1 - x)).expand() == S.Half*2**(-x)
+
+
+def test_issue_3449():
+    #test if powers are simplified correctly
+    #see also issue 3995
+    assert ((x**Rational(1, 3))**Rational(2)) == x**Rational(2, 3)
+    assert (
+        (x**Rational(3))**Rational(2, 5)) == (x**Rational(3))**Rational(2, 5)
+
+    a = Symbol('a', real=True)
+    b = Symbol('b', real=True)
+    assert (a**2)**b == (abs(a)**b)**2
+    assert sqrt(1/a) != 1/sqrt(a)  # e.g. for a = -1
+    assert (a**3)**Rational(1, 3) != a
+    assert (x**a)**b != x**(a*b)  # e.g. x = -1, a=2, b=1/2
+    assert (x**.5)**b == x**(.5*b)
+    assert (x**.5)**.5 == x**.25
+    assert (x**2.5)**.5 != x**1.25  # e.g. for x = 5*I
+
+    k = Symbol('k', integer=True)
+    m = Symbol('m', integer=True)
+    assert (x**k)**m == x**(k*m)
+    assert Number(5)**Rational(2, 3) == Number(25)**Rational(1, 3)
+
+    assert (x**.5)**2 == x**1.0
+    assert (x**2)**k == (x**k)**2 == x**(2*k)
+
+    a = Symbol('a', positive=True)
+    assert (a**3)**Rational(2, 5) == a**Rational(6, 5)
+    assert (a**2)**b == (a**b)**2
+    assert (a**Rational(2, 3))**x == a**(x*Rational(2, 3)) != (a**x)**Rational(2, 3)
+
+
+def test_issue_3866():
+    assert --sqrt(sqrt(5) - 1) == sqrt(sqrt(5) - 1)
+
+
+def test_negative_one():
+    x = Symbol('x', complex=True)
+    y = Symbol('y', complex=True)
+    assert 1/x**y == x**(-y)
+
+
+def test_issue_4362():
+    neg = Symbol('neg', negative=True)
+    nonneg = Symbol('nonneg', nonnegative=True)
+    any = Symbol('any')
+    num, den = sqrt(1/neg).as_numer_denom()
+    assert num == sqrt(-1)
+    assert den == sqrt(-neg)
+    num, den = sqrt(1/nonneg).as_numer_denom()
+    assert num == 1
+    assert den == sqrt(nonneg)
+    num, den = sqrt(1/any).as_numer_denom()
+    assert num == sqrt(1/any)
+    assert den == 1
+
+    def eqn(num, den, pow):
+        return (num/den)**pow
+    npos = 1
+    nneg = -1
+    dpos = 2 - sqrt(3)
+    dneg = 1 - sqrt(3)
+    assert dpos > 0 and dneg < 0 and npos > 0 and nneg < 0
+    # pos or neg integer
+    eq = eqn(npos, dpos, 2)
+    assert eq.is_Pow and eq.as_numer_denom() == (1, dpos**2)
+    eq = eqn(npos, dneg, 2)
+    assert eq.is_Pow and eq.as_numer_denom() == (1, dneg**2)
+    eq = eqn(nneg, dpos, 2)
+    assert eq.is_Pow and eq.as_numer_denom() == (1, dpos**2)
+    eq = eqn(nneg, dneg, 2)
+    assert eq.is_Pow and eq.as_numer_denom() == (1, dneg**2)
+    eq = eqn(npos, dpos, -2)
+    assert eq.is_Pow and eq.as_numer_denom() == (dpos**2, 1)
+    eq = eqn(npos, dneg, -2)
+    assert eq.is_Pow and eq.as_numer_denom() == (dneg**2, 1)
+    eq = eqn(nneg, dpos, -2)
+    assert eq.is_Pow and eq.as_numer_denom() == (dpos**2, 1)
+    eq = eqn(nneg, dneg, -2)
+    assert eq.is_Pow and eq.as_numer_denom() == (dneg**2, 1)
+    # pos or neg rational
+    pow = S.Half
+    eq = eqn(npos, dpos, pow)
+    assert eq.is_Pow and eq.as_numer_denom() == (npos**pow, dpos**pow)
+    eq = eqn(npos, dneg, pow)
+    assert eq.is_Pow is False and eq.as_numer_denom() == ((-npos)**pow, (-dneg)**pow)
+    eq = eqn(nneg, dpos, pow)
+    assert not eq.is_Pow or eq.as_numer_denom() == (nneg**pow, dpos**pow)
+    eq = eqn(nneg, dneg, pow)
+    assert eq.is_Pow and eq.as_numer_denom() == ((-nneg)**pow, (-dneg)**pow)
+    eq = eqn(npos, dpos, -pow)
+    assert eq.is_Pow and eq.as_numer_denom() == (dpos**pow, npos**pow)
+    eq = eqn(npos, dneg, -pow)
+    assert eq.is_Pow is False and eq.as_numer_denom() == (-(-npos)**pow*(-dneg)**pow, npos)
+    eq = eqn(nneg, dpos, -pow)
+    assert not eq.is_Pow or eq.as_numer_denom() == (dpos**pow, nneg**pow)
+    eq = eqn(nneg, dneg, -pow)
+    assert eq.is_Pow and eq.as_numer_denom() == ((-dneg)**pow, (-nneg)**pow)
+    # unknown exponent
+    pow = 2*any
+    eq = eqn(npos, dpos, pow)
+    assert eq.is_Pow and eq.as_numer_denom() == (npos**pow, dpos**pow)
+    eq = eqn(npos, dneg, pow)
+    assert eq.is_Pow and eq.as_numer_denom() == ((-npos)**pow, (-dneg)**pow)
+    eq = eqn(nneg, dpos, pow)
+    assert eq.is_Pow and eq.as_numer_denom() == (nneg**pow, dpos**pow)
+    eq = eqn(nneg, dneg, pow)
+    assert eq.is_Pow and eq.as_numer_denom() == ((-nneg)**pow, (-dneg)**pow)
+    eq = eqn(npos, dpos, -pow)
+    assert eq.as_numer_denom() == (dpos**pow, npos**pow)
+    eq = eqn(npos, dneg, -pow)
+    assert eq.is_Pow and eq.as_numer_denom() == ((-dneg)**pow, (-npos)**pow)
+    eq = eqn(nneg, dpos, -pow)
+    assert eq.is_Pow and eq.as_numer_denom() == (dpos**pow, nneg**pow)
+    eq = eqn(nneg, dneg, -pow)
+    assert eq.is_Pow and eq.as_numer_denom() == ((-dneg)**pow, (-nneg)**pow)
+
+    assert ((1/(1 + x/3))**(-S.One)).as_numer_denom() == (3 + x, 3)
+    notp = Symbol('notp', positive=False)  # not positive does not imply real
+    b = ((1 + x/notp)**-2)
+    assert (b**(-y)).as_numer_denom() == (1, b**y)
+    assert (b**(-S.One)).as_numer_denom() == ((notp + x)**2, notp**2)
+    nonp = Symbol('nonp', nonpositive=True)
+    assert (((1 + x/nonp)**-2)**(-S.One)).as_numer_denom() == ((-nonp -
+            x)**2, nonp**2)
+
+    n = Symbol('n', negative=True)
+    assert (x**n).as_numer_denom() == (1, x**-n)
+    assert sqrt(1/n).as_numer_denom() == (S.ImaginaryUnit, sqrt(-n))
+    n = Symbol('0 or neg', nonpositive=True)
+    # if x and n are split up without negating each term and n is negative
+    # then the answer might be wrong; if n is 0 it won't matter since
+    # 1/oo and 1/zoo are both zero as is sqrt(0)/sqrt(-x) unless x is also
+    # zero (in which case the negative sign doesn't matter):
+    # 1/sqrt(1/-1) = -I but sqrt(-1)/sqrt(1) = I
+    assert (1/sqrt(x/n)).as_numer_denom() == (sqrt(-n), sqrt(-x))
+    c = Symbol('c', complex=True)
+    e = sqrt(1/c)
+    assert e.as_numer_denom() == (e, 1)
+    i = Symbol('i', integer=True)
+    assert ((1 + x/y)**i).as_numer_denom() == ((x + y)**i, y**i)
+
+
+def test_Pow_Expr_args():
+    bases = [Basic(), Poly(x, x), FiniteSet(x)]
+    for base in bases:
+        # The cache can mess with the stacklevel test
+        with warns(SymPyDeprecationWarning, test_stacklevel=False):
+            Pow(base, S.One)
+
+
+def test_Pow_signs():
+    """Cf. issues 4595 and 5250"""
+    n = Symbol('n', even=True)
+    assert (3 - y)**2 != (y - 3)**2
+    assert (3 - y)**n != (y - 3)**n
+    assert (-3 + y - x)**2 != (3 - y + x)**2
+    assert (y - 3)**3 != -(3 - y)**3
+
+
+def test_power_with_noncommutative_mul_as_base():
+    x = Symbol('x', commutative=False)
+    y = Symbol('y', commutative=False)
+    assert not (x*y)**3 == x**3*y**3
+    assert (2*x*y)**3 == 8*(x*y)**3
+
+
+@_both_exp_pow
+def test_power_rewrite_exp():
+    assert (I**I).rewrite(exp) == exp(-pi/2)
+
+    expr = (2 + 3*I)**(4 + 5*I)
+    assert expr.rewrite(exp) == exp((4 + 5*I)*(log(sqrt(13)) + I*atan(Rational(3, 2))))
+    assert expr.rewrite(exp).expand() == \
+        169*exp(5*I*log(13)/2)*exp(4*I*atan(Rational(3, 2)))*exp(-5*atan(Rational(3, 2)))
+
+    assert ((6 + 7*I)**5).rewrite(exp) == 7225*sqrt(85)*exp(5*I*atan(Rational(7, 6)))
+
+    expr = 5**(6 + 7*I)
+    assert expr.rewrite(exp) == exp((6 + 7*I)*log(5))
+    assert expr.rewrite(exp).expand() == 15625*exp(7*I*log(5))
+
+    assert Pow(123, 789, evaluate=False).rewrite(exp) == 123**789
+    assert (1**I).rewrite(exp) == 1**I
+    assert (0**I).rewrite(exp) == 0**I
+
+    expr = (-2)**(2 + 5*I)
+    assert expr.rewrite(exp) == exp((2 + 5*I)*(log(2) + I*pi))
+    assert expr.rewrite(exp).expand() == 4*exp(-5*pi)*exp(5*I*log(2))
+
+    assert ((-2)**S(-5)).rewrite(exp) == (-2)**S(-5)
+
+    x, y = symbols('x y')
+    assert (x**y).rewrite(exp) == exp(y*log(x))
+    if global_parameters.exp_is_pow:
+        assert (7**x).rewrite(exp) == Pow(S.Exp1, x*log(7), evaluate=False)
+    else:
+        assert (7**x).rewrite(exp) == exp(x*log(7), evaluate=False)
+    assert ((2 + 3*I)**x).rewrite(exp) == exp(x*(log(sqrt(13)) + I*atan(Rational(3, 2))))
+    assert (y**(5 + 6*I)).rewrite(exp) == exp(log(y)*(5 + 6*I))
+
+    assert all((1/func(x)).rewrite(exp) == 1/(func(x).rewrite(exp)) for func in
+                    (sin, cos, tan, sec, csc, sinh, cosh, tanh))
+
+
+def test_zero():
+    assert 0**x != 0
+    assert 0**(2*x) == 0**x
+    assert 0**(1.0*x) == 0**x
+    assert 0**(2.0*x) == 0**x
+    assert (0**(2 - x)).as_base_exp() == (0, 2 - x)
+    assert 0**(x - 2) != S.Infinity**(2 - x)
+    assert 0**(2*x*y) == 0**(x*y)
+    assert 0**(-2*x*y) == S.ComplexInfinity**(x*y)
+    assert Float(0)**2 is not S.Zero
+    assert Float(0)**2 == 0.0
+    assert Float(0)**-2 is zoo
+    assert Float(0)**oo is S.Zero
+
+    #Test issue 19572
+    assert 0 ** -oo is zoo
+    assert power(0, -oo) is zoo
+    assert Float(0)**-oo is zoo
+
+def test_pow_as_base_exp():
+    assert (S.Infinity**(2 - x)).as_base_exp() == (S.Infinity, 2 - x)
+    assert (S.Infinity**(x - 2)).as_base_exp() == (S.Infinity, x - 2)
+    p = S.Half**x
+    assert p.base, p.exp == p.as_base_exp() == (S(2), -x)
+    p = (S(3)/2)**x
+    assert p.base, p.exp == p.as_base_exp() == (3*S.Half, x)
+    p = (S(2)/3)**x
+    assert p.as_base_exp() == (S(2)/3, x)
+    assert p.base, p.exp == (S(2)/3, x)
+    # issue 8344:
+    assert Pow(1, 2, evaluate=False).as_base_exp() == (S.One, S(2))
+
+
+def test_nseries():
+    assert sqrt(I*x - 1)._eval_nseries(x, 4, None, 1) == I + x/2 + I*x**2/8 - x**3/16 + O(x**4)
+    assert sqrt(I*x - 1)._eval_nseries(x, 4, None, -1) == -I - x/2 - I*x**2/8 + x**3/16 + O(x**4)
+    assert cbrt(I*x - 1)._eval_nseries(x, 4, None, 1) == (-1)**(S(1)/3) - (-1)**(S(5)/6)*x/3 + \
+    (-1)**(S(1)/3)*x**2/9 + 5*(-1)**(S(5)/6)*x**3/81 + O(x**4)
+    assert cbrt(I*x - 1)._eval_nseries(x, 4, None, -1) == -(-1)**(S(2)/3) - (-1)**(S(1)/6)*x/3 - \
+    (-1)**(S(2)/3)*x**2/9 + 5*(-1)**(S(1)/6)*x**3/81 + O(x**4)
+    assert (1 / (exp(-1/x) + 1/x))._eval_nseries(x, 2, None) == x + O(x**2)
+    # test issue 23752
+    assert sqrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, 1) == -sqrt(3)*I + sqrt(3)*I*x/6 - \
+    sqrt(3)*I*x**2*(-S(1)/72 + I/6) - sqrt(3)*I*x**3*(-S(1)/432 + I/36) + O(x**4)
+    assert sqrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, -1) == -sqrt(3)*I + sqrt(3)*I*x/6 - \
+    sqrt(3)*I*x**2*(-S(1)/72 + I/6) - sqrt(3)*I*x**3*(-S(1)/432 + I/36) + O(x**4)
+    assert cbrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, 1) == -(-1)**(S(2)/3)*3**(S(1)/3) + \
+    (-1)**(S(2)/3)*3**(S(1)/3)*x/9 - (-1)**(S(2)/3)*3**(S(1)/3)*x**2*(-S(1)/81 + I/9) - \
+    (-1)**(S(2)/3)*3**(S(1)/3)*x**3*(-S(5)/2187 + 2*I/81) + O(x**4)
+    assert cbrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, -1) == -(-1)**(S(2)/3)*3**(S(1)/3) + \
+    (-1)**(S(2)/3)*3**(S(1)/3)*x/9 - (-1)**(S(2)/3)*3**(S(1)/3)*x**2*(-S(1)/81 + I/9) - \
+    (-1)**(S(2)/3)*3**(S(1)/3)*x**3*(-S(5)/2187 + 2*I/81) + O(x**4)
+
+
+def test_issue_6100_12942_4473():
+    assert x**1.0 != x
+    assert x != x**1.0
+    assert True != x**1.0
+    assert x**1.0 is not True
+    assert x is not True
+    assert x*y != (x*y)**1.0
+    # Pow != Symbol
+    assert (x**1.0)**1.0 != x
+    assert (x**1.0)**2.0 != x**2
+    b = Expr()
+    assert Pow(b, 1.0, evaluate=False) != b
+    # if the following gets distributed as a Mul (x**1.0*y**1.0 then
+    # __eq__ methods could be added to Symbol and Pow to detect the
+    # power-of-1.0 case.
+    assert ((x*y)**1.0).func is Pow
+
+
+def test_issue_6208():
+    from sympy.functions.elementary.miscellaneous import root
+    assert sqrt(33**(I*9/10)) == -33**(I*9/20)
+    assert root((6*I)**(2*I), 3).as_base_exp()[1] == Rational(1, 3)  # != 2*I/3
+    assert root((6*I)**(I/3), 3).as_base_exp()[1] == I/9
+    assert sqrt(exp(3*I)) == exp(3*I/2)
+    assert sqrt(-sqrt(3)*(1 + 2*I)) == sqrt(sqrt(3))*sqrt(-1 - 2*I)
+    assert sqrt(exp(5*I)) == -exp(5*I/2)
+    assert root(exp(5*I), 3).exp == Rational(1, 3)
+
+
+def test_issue_6990():
+    assert (sqrt(a + b*x + x**2)).series(x, 0, 3).removeO() == \
+        sqrt(a)*x**2*(1/(2*a) - b**2/(8*a**2)) + sqrt(a) + b*x/(2*sqrt(a))
+
+
+def test_issue_6068():
+    assert sqrt(sin(x)).series(x, 0, 7) == \
+        sqrt(x) - x**Rational(5, 2)/12 + x**Rational(9, 2)/1440 - \
+        x**Rational(13, 2)/24192 + O(x**7)
+    assert sqrt(sin(x)).series(x, 0, 9) == \
+        sqrt(x) - x**Rational(5, 2)/12 + x**Rational(9, 2)/1440 - \
+        x**Rational(13, 2)/24192 - 67*x**Rational(17, 2)/29030400 + O(x**9)
+    assert sqrt(sin(x**3)).series(x, 0, 19) == \
+        x**Rational(3, 2) - x**Rational(15, 2)/12 + x**Rational(27, 2)/1440 + O(x**19)
+    assert sqrt(sin(x**3)).series(x, 0, 20) == \
+        x**Rational(3, 2) - x**Rational(15, 2)/12 + x**Rational(27, 2)/1440 - \
+        x**Rational(39, 2)/24192 + O(x**20)
+
+
+def test_issue_6782():
+    assert sqrt(sin(x**3)).series(x, 0, 7) == x**Rational(3, 2) + O(x**7)
+    assert sqrt(sin(x**4)).series(x, 0, 3) == x**2 + O(x**3)
+
+
+def test_issue_6653():
+    assert (1 / sqrt(1 + sin(x**2))).series(x, 0, 3) == 1 - x**2/2 + O(x**3)
+
+
+def test_issue_6429():
+    f = (c**2 + x)**(0.5)
+    assert f.series(x, x0=0, n=1) == (c**2)**0.5 + O(x)
+    assert f.taylor_term(0, x) == (c**2)**0.5
+    assert f.taylor_term(1, x) == 0.5*x*(c**2)**(-0.5)
+    assert f.taylor_term(2, x) == -0.125*x**2*(c**2)**(-1.5)
+
+
+def test_issue_7638():
+    f = pi/log(sqrt(2))
+    assert ((1 + I)**(I*f/2))**0.3 == (1 + I)**(0.15*I*f)
+    # if 1/3 -> 1.0/3 this should fail since it cannot be shown that the
+    # sign will be +/-1; for the previous "small arg" case, it didn't matter
+    # that this could not be proved
+    assert (1 + I)**(4*I*f) == ((1 + I)**(12*I*f))**Rational(1, 3)
+
+    assert (((1 + I)**(I*(1 + 7*f)))**Rational(1, 3)).exp == Rational(1, 3)
+    r = symbols('r', real=True)
+    assert sqrt(r**2) == abs(r)
+    assert cbrt(r**3) != r
+    assert sqrt(Pow(2*I, 5*S.Half)) != (2*I)**Rational(5, 4)
+    p = symbols('p', positive=True)
+    assert cbrt(p**2) == p**Rational(2, 3)
+    assert NS(((0.2 + 0.7*I)**(0.7 + 1.0*I))**(0.5 - 0.1*I), 1) == '0.4 + 0.2*I'
+    assert sqrt(1/(1 + I)) == sqrt(1 - I)/sqrt(2)  # or 1/sqrt(1 + I)
+    e = 1/(1 - sqrt(2))
+    assert sqrt(e) == I/sqrt(-1 + sqrt(2))
+    assert e**Rational(-1, 2) == -I*sqrt(-1 + sqrt(2))
+    assert sqrt((cos(1)**2 + sin(1)**2 - 1)**(3 + I)).exp in [S.Half,
+                                                              Rational(3, 2) + I/2]
+    assert sqrt(r**Rational(4, 3)) != r**Rational(2, 3)
+    assert sqrt((p + I)**Rational(4, 3)) == (p + I)**Rational(2, 3)
+
+    for q in 1+I, 1-I:
+        assert sqrt(q**2) == q
+    for q in -1+I, -1-I:
+        assert sqrt(q**2) == -q
+
+    assert sqrt((p + r*I)**2) != p + r*I
+    e = (1 + I/5)
+    assert sqrt(e**5) == e**(5*S.Half)
+    assert sqrt(e**6) == e**3
+    assert sqrt((1 + I*r)**6) != (1 + I*r)**3
+
+
+def test_issue_8582():
+    assert 1**oo is nan
+    assert 1**(-oo) is nan
+    assert 1**zoo is nan
+    assert 1**(oo + I) is nan
+    assert 1**(1 + I*oo) is nan
+    assert 1**(oo + I*oo) is nan
+
+
+def test_issue_8650():
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert (n**n).is_positive is True
+    x = 5*n + 5
+    assert (x**(5*(n + 1))).is_positive is True
+
+
+def test_issue_13914():
+    b = Symbol('b')
+    assert (-1)**zoo is nan
+    assert 2**zoo is nan
+    assert (S.Half)**(1 + zoo) is nan
+    assert I**(zoo + I) is nan
+    assert b**(I + zoo) is nan
+
+
+def test_better_sqrt():
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert sqrt(3 + 4*I) == 2 + I
+    assert sqrt(3 - 4*I) == 2 - I
+    assert sqrt(-3 - 4*I) == 1 - 2*I
+    assert sqrt(-3 + 4*I) == 1 + 2*I
+    assert sqrt(32 + 24*I) == 6 + 2*I
+    assert sqrt(32 - 24*I) == 6 - 2*I
+    assert sqrt(-32 - 24*I) == 2 - 6*I
+    assert sqrt(-32 + 24*I) == 2 + 6*I
+
+    # triple (3, 4, 5):
+    # parity of 3 matches parity of 5 and
+    # den, 4, is a square
+    assert sqrt((3 + 4*I)/4) == 1 + I/2
+    # triple (8, 15, 17)
+    # parity of 8 doesn't match parity of 17 but
+    # den/2, 8/2, is a square
+    assert sqrt((8 + 15*I)/8) == (5 + 3*I)/4
+    # handle the denominator
+    assert sqrt((3 - 4*I)/25) == (2 - I)/5
+    assert sqrt((3 - 4*I)/26) == (2 - I)/sqrt(26)
+    # mul
+    #  issue #12739
+    assert sqrt((3 + 4*I)/(3 - 4*I)) == (3 + 4*I)/5
+    assert sqrt(2/(3 + 4*I)) == sqrt(2)/5*(2 - I)
+    assert sqrt(n/(3 + 4*I)).subs(n, 2) == sqrt(2)/5*(2 - I)
+    assert sqrt(-2/(3 + 4*I)) == sqrt(2)/5*(1 + 2*I)
+    assert sqrt(-n/(3 + 4*I)).subs(n, 2) == sqrt(2)/5*(1 + 2*I)
+    # power
+    assert sqrt(1/(3 + I*4)) == (2 - I)/5
+    assert sqrt(1/(3 - I)) == sqrt(10)*sqrt(3 + I)/10
+    # symbolic
+    i = symbols('i', imaginary=True)
+    assert sqrt(3/i) == Mul(sqrt(3), 1/sqrt(i), evaluate=False)
+    # multiples of 1/2; don't make this too automatic
+    assert sqrt(3 + 4*I)**3 == (2 + I)**3
+    assert Pow(3 + 4*I, Rational(3, 2)) == 2 + 11*I
+    assert Pow(6 + 8*I, Rational(3, 2)) == 2*sqrt(2)*(2 + 11*I)
+    n, d = (3 + 4*I), (3 - 4*I)**3
+    a = n/d
+    assert a.args == (1/d, n)
+    eq = sqrt(a)
+    assert eq.args == (a, S.Half)
+    assert expand_multinomial(eq) == sqrt((-117 + 44*I)*(3 + 4*I))/125
+    assert eq.expand() == (7 - 24*I)/125
+
+    # issue 12775
+    # pos im part
+    assert sqrt(2*I) == (1 + I)
+    assert sqrt(2*9*I) == Mul(3, 1 + I, evaluate=False)
+    assert Pow(2*I, 3*S.Half) == (1 + I)**3
+    # neg im part
+    assert sqrt(-I/2) == Mul(S.Half, 1 - I, evaluate=False)
+    # fractional im part
+    assert Pow(Rational(-9, 2)*I, Rational(3, 2)) == 27*(1 - I)**3/8
+
+
+def test_issue_2993():
+    assert str((2.3*x - 4)**0.3) == '(2.3*x - 4)**0.3'
+    assert str((2.3*x + 4)**0.3) == '(2.3*x + 4)**0.3'
+    assert str((-2.3*x + 4)**0.3) == '(4 - 2.3*x)**0.3'
+    assert str((-2.3*x - 4)**0.3) == '(-2.3*x - 4)**0.3'
+    assert str((2.3*x - 2)**0.3) == '(2.3*x - 2)**0.3'
+    assert str((-2.3*x - 2)**0.3) == '(-2.3*x - 2)**0.3'
+    assert str((-2.3*x + 2)**0.3) == '(2 - 2.3*x)**0.3'
+    assert str((2.3*x + 2)**0.3) == '(2.3*x + 2)**0.3'
+    assert str((2.3*x - 4)**Rational(1, 3)) == '(2.3*x - 4)**(1/3)'
+    eq = (2.3*x + 4)
+    assert str(eq**2) == '(2.3*x + 4)**2'
+    assert (1/eq).args == (eq, -1)  # don't change trivial power
+    # issue 17735
+    q=.5*exp(x) - .5*exp(-x) + 0.1
+    assert int((q**2).subs(x, 1)) == 1
+    # issue 17756
+    y = Symbol('y')
+    assert len(sqrt(x/(x + y)**2 + Float('0.008', 30)).subs(y, pi.n(25)).atoms(Float)) == 2
+    # issue 17756
+    a, b, c, d, e, f, g = symbols('a:g')
+    expr = sqrt(1 + a*(c**4 + g*d - 2*g*e - f*(-g + d))**2/
+        (c**3*b**2*(d - 3*e + 2*f)**2))/2
+    r = [
+    (a, N('0.0170992456333788667034850458615', 30)),
+    (b, N('0.0966594956075474769169134801223', 30)),
+    (c, N('0.390911862903463913632151616184', 30)),
+    (d, N('0.152812084558656566271750185933', 30)),
+    (e, N('0.137562344465103337106561623432', 30)),
+    (f, N('0.174259178881496659302933610355', 30)),
+    (g, N('0.220745448491223779615401870086', 30))]
+    tru = expr.n(30, subs=dict(r))
+    seq = expr.subs(r)
+    # although `tru` is the right way to evaluate
+    # expr with numerical values, `seq` will have
+    # significant loss of precision if extraction of
+    # the largest coefficient of a power's base's terms
+    # is done improperly
+    assert seq == tru
+
+def test_issue_17450():
+    assert (erf(cosh(1)**7)**I).is_real is None
+    assert (erf(cosh(1)**7)**I).is_imaginary is False
+    assert (Pow(exp(1+sqrt(2)), ((1-sqrt(2))*I*pi), evaluate=False)).is_real is None
+    assert ((-10)**(10*I*pi/3)).is_real is False
+    assert ((-5)**(4*I*pi)).is_real is False
+
+
+def test_issue_18190():
+    assert sqrt(1 / tan(1 + I)) == 1 / sqrt(tan(1 + I))
+
+
+def test_issue_14815():
+    x = Symbol('x', real=True)
+    assert sqrt(x).is_extended_negative is False
+    x = Symbol('x', real=False)
+    assert sqrt(x).is_extended_negative is None
+    x = Symbol('x', complex=True)
+    assert sqrt(x).is_extended_negative is False
+    x = Symbol('x', extended_real=True)
+    assert sqrt(x).is_extended_negative is False
+    assert sqrt(zoo, evaluate=False).is_extended_negative is False
+    assert sqrt(nan, evaluate=False).is_extended_negative is None
+
+
+def test_issue_18509():
+    x = Symbol('x', prime=True)
+    assert x**oo is oo
+    assert (1/x)**oo is S.Zero
+    assert (-1/x)**oo is S.Zero
+    assert (-x)**oo is zoo
+    assert (-oo)**(-1 + I) is S.Zero
+    assert (-oo)**(1 + I) is zoo
+    assert (oo)**(-1 + I) is S.Zero
+    assert (oo)**(1 + I) is zoo
+
+
+def test_issue_18762():
+    e, p = symbols('e p')
+    g0 = sqrt(1 + e**2 - 2*e*cos(p))
+    assert len(g0.series(e, 1, 3).args) == 4
+
+
+def test_issue_21860():
+    e = 3*2**Rational(66666666667,200000000000)*3**Rational(16666666667,50000000000)*x**Rational(66666666667, 200000000000)
+    ans = Mul(Rational(3, 2),
+              Pow(Integer(2), Rational(33333333333, 100000000000)),
+              Pow(Integer(3), Rational(26666666667, 40000000000)))
+    assert e.xreplace({x: Rational(3,8)}) == ans
+
+
+def test_issue_21647():
+    e = log((Integer(567)/500)**(811*(Integer(567)/500)**x/100))
+    ans = log(Mul(Rational(64701150190720499096094005280169087619821081527,
+                           76293945312500000000000000000000000000000000000),
+                  Pow(Integer(2), Rational(396204892125479941, 781250000000000000)),
+                  Pow(Integer(3), Rational(385045107874520059, 390625000000000000)),
+                  Pow(Integer(5), Rational(407364676376439823, 1562500000000000000)),
+                  Pow(Integer(7), Rational(385045107874520059, 1562500000000000000))))
+    assert e.xreplace({x: 6}) == ans
+
+
+def test_issue_21762():
+    e = (x**2 + 6)**(Integer(33333333333333333)/50000000000000000)
+    ans = Mul(Rational(5, 4),
+              Pow(Integer(2), Rational(16666666666666667, 25000000000000000)),
+              Pow(Integer(5), Rational(8333333333333333, 25000000000000000)))
+    assert e.xreplace({x: S.Half}) == ans
+
+
+def test_issue_14704():
+    a = 144**144
+    x, xexact = integer_nthroot(a,a)
+    assert x == 1 and xexact is False
+
+
+def test_rational_powers_larger_than_one():
+    assert Rational(2, 3)**Rational(3, 2) == 2*sqrt(6)/9
+    assert Rational(1, 6)**Rational(9, 4) == 6**Rational(3, 4)/216
+    assert Rational(3, 7)**Rational(7, 3) == 9*3**Rational(1, 3)*7**Rational(2, 3)/343
+
+
+def test_power_dispatcher():
+
+    class NewBase(Expr):
+        pass
+    class NewPow(NewBase, Pow):
+        pass
+    a, b = Symbol('a'), NewBase()
+
+    @power.register(Expr, NewBase)
+    @power.register(NewBase, Expr)
+    @power.register(NewBase, NewBase)
+    def _(a, b):
+        return NewPow(a, b)
+
+    # Pow called as fallback
+    assert power(2, 3) == 8*S.One
+    assert power(a, 2) == Pow(a, 2)
+    assert power(a, a) == Pow(a, a)
+
+    # NewPow called by dispatch
+    assert power(a, b) == NewPow(a, b)
+    assert power(b, a) == NewPow(b, a)
+    assert power(b, b) == NewPow(b, b)
+
+
+def test_powers_of_I():
+    assert [sqrt(I)**i for i in range(13)] == [
+        1, sqrt(I), I, sqrt(I)**3, -1, -sqrt(I), -I, -sqrt(I)**3,
+        1, sqrt(I), I, sqrt(I)**3, -1]
+    assert sqrt(I)**(S(9)/2) == -I**(S(1)/4)
+
+
+def test_issue_23918():
+    b = S(2)/3
+    assert (b**x).as_base_exp() == (b, x)
+
+
+def test_issue_26546():
+    x = Symbol('x', real=True)
+    assert x.is_extended_real is True
+    assert sqrt(x+I).is_extended_real is False
+    assert Pow(x+I, S.Half).is_extended_real is False
+    assert Pow(x+I, Rational(1,2)).is_extended_real is False
+    assert Pow(x+I, Rational(1,13)).is_extended_real is False
+    assert Pow(x+I, Rational(2,3)).is_extended_real is None
+
+
+def test_issue_25165():
+    e1 = (1/sqrt(( - x + 1)**2 + (x - 0.23)**4)).series(x, 0, 2)
+    e2 = 0.998603724830355 + 1.02004923189934*x + O(x**2)
+    assert all_close(e1, e2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_priority.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_priority.py
new file mode 100644
index 0000000000000000000000000000000000000000..276e653100f886243e07b866b699b8da53cdaf88
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_priority.py
@@ -0,0 +1,145 @@
+from sympy.core.decorators import call_highest_priority
+from sympy.core.expr import Expr
+from sympy.core.mod import Mod
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.integers import floor
+
+
+class Higher(Integer):
+    '''
+    Integer of value 1 and _op_priority 20
+
+    Operations handled by this class return 1 and reverse operations return 2
+    '''
+
+    _op_priority = 20.0
+    result: Expr = S.One
+
+    def __new__(cls):
+        obj = Expr.__new__(cls)
+        obj.p = 1
+        return obj
+
+    @call_highest_priority('__rmul__')
+    def __mul__(self, other):
+        return self.result
+
+    @call_highest_priority('__mul__')
+    def __rmul__(self, other):
+        return 2*self.result
+
+    @call_highest_priority('__radd__')
+    def __add__(self, other):
+        return self.result
+
+    @call_highest_priority('__add__')
+    def __radd__(self, other):
+        return 2*self.result
+
+    @call_highest_priority('__rsub__')
+    def __sub__(self, other):
+        return self.result
+
+    @call_highest_priority('__sub__')
+    def __rsub__(self, other):
+        return 2*self.result
+
+    @call_highest_priority('__rpow__')
+    def __pow__(self, other):
+        return self.result
+
+    @call_highest_priority('__pow__')
+    def __rpow__(self, other):
+        return 2*self.result
+
+    @call_highest_priority('__rtruediv__')
+    def __truediv__(self, other):
+        return self.result
+
+    @call_highest_priority('__truediv__')
+    def __rtruediv__(self, other):
+        return 2*self.result
+
+    @call_highest_priority('__rmod__')
+    def __mod__(self, other):
+        return self.result
+
+    @call_highest_priority('__mod__')
+    def __rmod__(self, other):
+        return 2*self.result
+
+    @call_highest_priority('__rfloordiv__')
+    def __floordiv__(self, other):
+        return self.result
+
+    @call_highest_priority('__floordiv__')
+    def __rfloordiv__(self, other):
+        return 2*self.result
+
+
+class Lower(Higher):
+    '''
+    Integer of value -1 and _op_priority 5
+
+    Operations handled by this class return -1 and reverse operations return -2
+    '''
+
+    _op_priority = 5.0
+    result: Expr = S.NegativeOne
+
+    def __new__(cls):
+        obj = Expr.__new__(cls)
+        obj.p = -1
+        return obj
+
+
+x = Symbol('x')
+h = Higher()
+l = Lower()
+
+
+def test_mul():
+    assert h*l == h*x == 1
+    assert l*h == x*h == 2
+    assert x*l == l*x == -x
+
+
+def test_add():
+    assert h + l == h + x == 1
+    assert l + h == x + h == 2
+    assert x + l == l + x == x - 1
+
+
+def test_sub():
+    assert h - l == h - x == 1
+    assert l - h == x - h == 2
+    assert x - l == -(l - x) == x + 1
+
+
+def test_pow():
+    assert h**l == h**x == 1
+    assert l**h == x**h == 2
+    assert (x**l).args == (1/x).args and (x**l).is_Pow
+    assert (l**x).args == ((-1)**x).args and (l**x).is_Pow
+
+
+def test_div():
+    assert h/l == h/x == 1
+    assert l/h == x/h == 2
+    assert x/l == 1/(l/x) == -x
+
+
+def test_mod():
+    assert h%l == h%x == 1
+    assert l%h == x%h == 2
+    assert x%l == Mod(x, -1)
+    assert l%x == Mod(-1, x)
+
+
+def test_floordiv():
+    assert h//l == h//x == 1
+    assert l//h == x//h == 2
+    assert x//l == floor(-x)
+    assert l//x == floor(-1/x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_random.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_random.py
new file mode 100644
index 0000000000000000000000000000000000000000..01c677126285eb66349253368b94b3270fb97793
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_random.py
@@ -0,0 +1,61 @@
+import random
+from sympy.core.random import random as rand, seed, shuffle, _assumptions_shuffle
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions.elementary.trigonometric import sin, acos
+from sympy.abc import x
+
+
+def test_random():
+    random.seed(42)
+    a = random.random()
+    random.seed(42)
+    Symbol('z').is_finite
+    b = random.random()
+    assert a == b
+
+    got = set()
+    for i in range(2):
+        random.seed(28)
+        m0, m1 = symbols('m_0 m_1', real=True)
+        _ = acos(-m0/m1)
+        got.add(random.uniform(0,1))
+    assert len(got) == 1
+
+    random.seed(10)
+    y = 0
+    for i in range(4):
+        y += sin(random.uniform(-10,10) * x)
+    random.seed(10)
+    z = 0
+    for i in range(4):
+        z += sin(random.uniform(-10,10) * x)
+    assert y == z
+
+
+def test_seed():
+    assert rand() < 1
+    seed(1)
+    a = rand()
+    b = rand()
+    seed(1)
+    c = rand()
+    d = rand()
+    assert a == c
+    if not c == d:
+        assert a != b
+    else:
+        assert a == b
+
+    abc = 'abc'
+    first = list(abc)
+    second = list(abc)
+    third = list(abc)
+
+    seed(123)
+    shuffle(first)
+
+    seed(123)
+    shuffle(second)
+    _assumptions_shuffle(third)
+
+    assert first == second == third
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_relational.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_relational.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c026fd5f5b8cee2e90e00582047cc7763bb8a4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_relational.py
@@ -0,0 +1,1271 @@
+from sympy.core.logic import fuzzy_and
+from sympy.core.sympify import _sympify
+from sympy.multipledispatch import dispatch
+from sympy.testing.pytest import XFAIL, raises
+from sympy.assumptions.ask import Q
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr, unchanged
+from sympy.core.function import Function
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Float, I, Rational, nan, oo, pi, zoo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import sign, Abs
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.integers import (ceiling, floor)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.logic.boolalg import (And, Implies, Not, Or, Xor)
+from sympy.sets import Reals
+from sympy.simplify.simplify import simplify
+from sympy.simplify.trigsimp import trigsimp
+from sympy.core.relational import (Relational, Equality, Unequality,
+                                   GreaterThan, LessThan, StrictGreaterThan,
+                                   StrictLessThan, Rel, Eq, Lt, Le,
+                                   Gt, Ge, Ne, is_le, is_gt, is_ge, is_lt, is_eq, is_neq)
+from sympy.sets.sets import Interval, FiniteSet
+
+from itertools import combinations
+
+x, y, z, t = symbols('x,y,z,t')
+
+
+def rel_check(a, b):
+    from sympy.testing.pytest import raises
+    assert a.is_number and b.is_number
+    for do in range(len({type(a), type(b)})):
+        if S.NaN in (a, b):
+            v = [(a == b), (a != b)]
+            assert len(set(v)) == 1 and v[0] == False
+            assert not (a != b) and not (a == b)
+            assert raises(TypeError, lambda: a < b)
+            assert raises(TypeError, lambda: a <= b)
+            assert raises(TypeError, lambda: a > b)
+            assert raises(TypeError, lambda: a >= b)
+        else:
+            E = [(a == b), (a != b)]
+            assert len(set(E)) == 2
+            v = [
+            (a < b), (a <= b), (a > b), (a >= b)]
+            i = [
+            [True,    True,     False,   False],
+            [False,   True,     False,   True], # <-- i == 1
+            [False,   False,    True,    True]].index(v)
+            if i == 1:
+                assert E[0] or (a.is_Float != b.is_Float) # ugh
+            else:
+                assert E[1]
+        a, b = b, a
+    return True
+
+
+def test_rel_ne():
+    assert Relational(x, y, '!=') == Ne(x, y)
+
+    # issue 6116
+    p = Symbol('p', positive=True)
+    assert Ne(p, 0) is S.true
+
+
+def test_rel_subs():
+    e = Relational(x, y, '==')
+    e = e.subs(x, z)
+
+    assert isinstance(e, Equality)
+    assert e.lhs == z
+    assert e.rhs == y
+
+    e = Relational(x, y, '>=')
+    e = e.subs(x, z)
+
+    assert isinstance(e, GreaterThan)
+    assert e.lhs == z
+    assert e.rhs == y
+
+    e = Relational(x, y, '<=')
+    e = e.subs(x, z)
+
+    assert isinstance(e, LessThan)
+    assert e.lhs == z
+    assert e.rhs == y
+
+    e = Relational(x, y, '>')
+    e = e.subs(x, z)
+
+    assert isinstance(e, StrictGreaterThan)
+    assert e.lhs == z
+    assert e.rhs == y
+
+    e = Relational(x, y, '<')
+    e = e.subs(x, z)
+
+    assert isinstance(e, StrictLessThan)
+    assert e.lhs == z
+    assert e.rhs == y
+
+    e = Eq(x, 0)
+    assert e.subs(x, 0) is S.true
+    assert e.subs(x, 1) is S.false
+
+
+def test_wrappers():
+    e = x + x**2
+
+    res = Relational(y, e, '==')
+    assert Rel(y, x + x**2, '==') == res
+    assert Eq(y, x + x**2) == res
+
+    res = Relational(y, e, '<')
+    assert Lt(y, x + x**2) == res
+
+    res = Relational(y, e, '<=')
+    assert Le(y, x + x**2) == res
+
+    res = Relational(y, e, '>')
+    assert Gt(y, x + x**2) == res
+
+    res = Relational(y, e, '>=')
+    assert Ge(y, x + x**2) == res
+
+    res = Relational(y, e, '!=')
+    assert Ne(y, x + x**2) == res
+
+
+def test_Eq_Ne():
+
+    assert Eq(x, x)  # issue 5719
+
+    # issue 6116
+    p = Symbol('p', positive=True)
+    assert Eq(p, 0) is S.false
+
+    # issue 13348; 19048
+    # SymPy is strict about 0 and 1 not being
+    # interpreted as Booleans
+    assert Eq(True, 1) is S.false
+    assert Eq(False, 0) is S.false
+    assert Eq(~x, 0) is S.false
+    assert Eq(~x, 1) is S.false
+    assert Ne(True, 1) is S.true
+    assert Ne(False, 0) is S.true
+    assert Ne(~x, 0) is S.true
+    assert Ne(~x, 1) is S.true
+
+    assert Eq((), 1) is S.false
+    assert Ne((), 1) is S.true
+
+
+def test_as_poly():
+    from sympy.polys.polytools import Poly
+    # Only Eq should have an as_poly method:
+    assert Eq(x, 1).as_poly() == Poly(x - 1, x, domain='ZZ')
+    raises(AttributeError, lambda: Ne(x, 1).as_poly())
+    raises(AttributeError, lambda: Ge(x, 1).as_poly())
+    raises(AttributeError, lambda: Gt(x, 1).as_poly())
+    raises(AttributeError, lambda: Le(x, 1).as_poly())
+    raises(AttributeError, lambda: Lt(x, 1).as_poly())
+
+
+def test_rel_Infinity():
+    # NOTE: All of these are actually handled by sympy.core.Number, and do
+    # not create Relational objects.
+    assert (oo > oo) is S.false
+    assert (oo > -oo) is S.true
+    assert (oo > 1) is S.true
+    assert (oo < oo) is S.false
+    assert (oo < -oo) is S.false
+    assert (oo < 1) is S.false
+    assert (oo >= oo) is S.true
+    assert (oo >= -oo) is S.true
+    assert (oo >= 1) is S.true
+    assert (oo <= oo) is S.true
+    assert (oo <= -oo) is S.false
+    assert (oo <= 1) is S.false
+    assert (-oo > oo) is S.false
+    assert (-oo > -oo) is S.false
+    assert (-oo > 1) is S.false
+    assert (-oo < oo) is S.true
+    assert (-oo < -oo) is S.false
+    assert (-oo < 1) is S.true
+    assert (-oo >= oo) is S.false
+    assert (-oo >= -oo) is S.true
+    assert (-oo >= 1) is S.false
+    assert (-oo <= oo) is S.true
+    assert (-oo <= -oo) is S.true
+    assert (-oo <= 1) is S.true
+
+
+def test_infinite_symbol_inequalities():
+    x = Symbol('x', extended_positive=True, infinite=True)
+    y = Symbol('y', extended_positive=True, infinite=True)
+    z = Symbol('z', extended_negative=True, infinite=True)
+    w = Symbol('w', extended_negative=True, infinite=True)
+
+    inf_set = (x, y, oo)
+    ninf_set = (z, w, -oo)
+
+    for inf1 in inf_set:
+        assert (inf1 < 1) is S.false
+        assert (inf1 > 1) is S.true
+        assert (inf1 <= 1) is S.false
+        assert (inf1 >= 1) is S.true
+
+        for inf2 in inf_set:
+            assert (inf1 < inf2) is S.false
+            assert (inf1 > inf2) is S.false
+            assert (inf1 <= inf2) is S.true
+            assert (inf1 >= inf2) is S.true
+
+        for ninf1 in ninf_set:
+            assert (inf1 < ninf1) is S.false
+            assert (inf1 > ninf1) is S.true
+            assert (inf1 <= ninf1) is S.false
+            assert (inf1 >= ninf1) is S.true
+            assert (ninf1 < inf1) is S.true
+            assert (ninf1 > inf1) is S.false
+            assert (ninf1 <= inf1) is S.true
+            assert (ninf1 >= inf1) is S.false
+
+    for ninf1 in ninf_set:
+        assert (ninf1 < 1) is S.true
+        assert (ninf1 > 1) is S.false
+        assert (ninf1 <= 1) is S.true
+        assert (ninf1 >= 1) is S.false
+
+        for ninf2 in ninf_set:
+            assert (ninf1 < ninf2) is S.false
+            assert (ninf1 > ninf2) is S.false
+            assert (ninf1 <= ninf2) is S.true
+            assert (ninf1 >= ninf2) is S.true
+
+
+def test_bool():
+    assert Eq(0, 0) is S.true
+    assert Eq(1, 0) is S.false
+    assert Ne(0, 0) is S.false
+    assert Ne(1, 0) is S.true
+    assert Lt(0, 1) is S.true
+    assert Lt(1, 0) is S.false
+    assert Le(0, 1) is S.true
+    assert Le(1, 0) is S.false
+    assert Le(0, 0) is S.true
+    assert Gt(1, 0) is S.true
+    assert Gt(0, 1) is S.false
+    assert Ge(1, 0) is S.true
+    assert Ge(0, 1) is S.false
+    assert Ge(1, 1) is S.true
+    assert Eq(I, 2) is S.false
+    assert Ne(I, 2) is S.true
+    raises(TypeError, lambda: Gt(I, 2))
+    raises(TypeError, lambda: Ge(I, 2))
+    raises(TypeError, lambda: Lt(I, 2))
+    raises(TypeError, lambda: Le(I, 2))
+    a = Float('.000000000000000000001', '')
+    b = Float('.0000000000000000000001', '')
+    assert Eq(pi + a, pi + b) is S.false
+
+
+def test_rich_cmp():
+    assert (x < y) == Lt(x, y)
+    assert (x <= y) == Le(x, y)
+    assert (x > y) == Gt(x, y)
+    assert (x >= y) == Ge(x, y)
+
+
+def test_doit():
+    from sympy.core.symbol import Symbol
+    p = Symbol('p', positive=True)
+    n = Symbol('n', negative=True)
+    np = Symbol('np', nonpositive=True)
+    nn = Symbol('nn', nonnegative=True)
+
+    assert Gt(p, 0).doit() is S.true
+    assert Gt(p, 1).doit() == Gt(p, 1)
+    assert Ge(p, 0).doit() is S.true
+    assert Le(p, 0).doit() is S.false
+    assert Lt(n, 0).doit() is S.true
+    assert Le(np, 0).doit() is S.true
+    assert Gt(nn, 0).doit() == Gt(nn, 0)
+    assert Lt(nn, 0).doit() is S.false
+
+    assert Eq(x, 0).doit() == Eq(x, 0)
+
+
+def test_new_relational():
+    x = Symbol('x')
+
+    assert Eq(x, 0) == Relational(x, 0)       # None ==> Equality
+    assert Eq(x, 0) == Relational(x, 0, '==')
+    assert Eq(x, 0) == Relational(x, 0, 'eq')
+    assert Eq(x, 0) == Equality(x, 0)
+
+    assert Eq(x, 0) != Relational(x, 1)       # None ==> Equality
+    assert Eq(x, 0) != Relational(x, 1, '==')
+    assert Eq(x, 0) != Relational(x, 1, 'eq')
+    assert Eq(x, 0) != Equality(x, 1)
+
+    assert Eq(x, -1) == Relational(x, -1)       # None ==> Equality
+    assert Eq(x, -1) == Relational(x, -1, '==')
+    assert Eq(x, -1) == Relational(x, -1, 'eq')
+    assert Eq(x, -1) == Equality(x, -1)
+    assert Eq(x, -1) != Relational(x, 1)       # None ==> Equality
+    assert Eq(x, -1) != Relational(x, 1, '==')
+    assert Eq(x, -1) != Relational(x, 1, 'eq')
+    assert Eq(x, -1) != Equality(x, 1)
+
+    assert Ne(x, 0) == Relational(x, 0, '!=')
+    assert Ne(x, 0) == Relational(x, 0, '<>')
+    assert Ne(x, 0) == Relational(x, 0, 'ne')
+    assert Ne(x, 0) == Unequality(x, 0)
+    assert Ne(x, 0) != Relational(x, 1, '!=')
+    assert Ne(x, 0) != Relational(x, 1, '<>')
+    assert Ne(x, 0) != Relational(x, 1, 'ne')
+    assert Ne(x, 0) != Unequality(x, 1)
+
+    assert Ge(x, 0) == Relational(x, 0, '>=')
+    assert Ge(x, 0) == Relational(x, 0, 'ge')
+    assert Ge(x, 0) == GreaterThan(x, 0)
+    assert Ge(x, 1) != Relational(x, 0, '>=')
+    assert Ge(x, 1) != Relational(x, 0, 'ge')
+    assert Ge(x, 1) != GreaterThan(x, 0)
+    assert (x >= 1) == Relational(x, 1, '>=')
+    assert (x >= 1) == Relational(x, 1, 'ge')
+    assert (x >= 1) == GreaterThan(x, 1)
+    assert (x >= 0) != Relational(x, 1, '>=')
+    assert (x >= 0) != Relational(x, 1, 'ge')
+    assert (x >= 0) != GreaterThan(x, 1)
+
+    assert Le(x, 0) == Relational(x, 0, '<=')
+    assert Le(x, 0) == Relational(x, 0, 'le')
+    assert Le(x, 0) == LessThan(x, 0)
+    assert Le(x, 1) != Relational(x, 0, '<=')
+    assert Le(x, 1) != Relational(x, 0, 'le')
+    assert Le(x, 1) != LessThan(x, 0)
+    assert (x <= 1) == Relational(x, 1, '<=')
+    assert (x <= 1) == Relational(x, 1, 'le')
+    assert (x <= 1) == LessThan(x, 1)
+    assert (x <= 0) != Relational(x, 1, '<=')
+    assert (x <= 0) != Relational(x, 1, 'le')
+    assert (x <= 0) != LessThan(x, 1)
+
+    assert Gt(x, 0) == Relational(x, 0, '>')
+    assert Gt(x, 0) == Relational(x, 0, 'gt')
+    assert Gt(x, 0) == StrictGreaterThan(x, 0)
+    assert Gt(x, 1) != Relational(x, 0, '>')
+    assert Gt(x, 1) != Relational(x, 0, 'gt')
+    assert Gt(x, 1) != StrictGreaterThan(x, 0)
+    assert (x > 1) == Relational(x, 1, '>')
+    assert (x > 1) == Relational(x, 1, 'gt')
+    assert (x > 1) == StrictGreaterThan(x, 1)
+    assert (x > 0) != Relational(x, 1, '>')
+    assert (x > 0) != Relational(x, 1, 'gt')
+    assert (x > 0) != StrictGreaterThan(x, 1)
+
+    assert Lt(x, 0) == Relational(x, 0, '<')
+    assert Lt(x, 0) == Relational(x, 0, 'lt')
+    assert Lt(x, 0) == StrictLessThan(x, 0)
+    assert Lt(x, 1) != Relational(x, 0, '<')
+    assert Lt(x, 1) != Relational(x, 0, 'lt')
+    assert Lt(x, 1) != StrictLessThan(x, 0)
+    assert (x < 1) == Relational(x, 1, '<')
+    assert (x < 1) == Relational(x, 1, 'lt')
+    assert (x < 1) == StrictLessThan(x, 1)
+    assert (x < 0) != Relational(x, 1, '<')
+    assert (x < 0) != Relational(x, 1, 'lt')
+    assert (x < 0) != StrictLessThan(x, 1)
+
+    # finally, some fuzz testing
+    from sympy.core.random import randint
+    for i in range(100):
+        while 1:
+            strtype, length = (chr, 65535) if randint(0, 1) else (chr, 255)
+            relation_type = strtype(randint(0, length))
+            if randint(0, 1):
+                relation_type += strtype(randint(0, length))
+            if relation_type not in ('==', 'eq', '!=', '<>', 'ne', '>=', 'ge',
+                                     '<=', 'le', '>', 'gt', '<', 'lt', ':=',
+                                     '+=', '-=', '*=', '/=', '%='):
+                break
+
+        raises(ValueError, lambda: Relational(x, 1, relation_type))
+    assert all(Relational(x, 0, op).rel_op == '==' for op in ('eq', '=='))
+    assert all(Relational(x, 0, op).rel_op == '!='
+               for op in ('ne', '<>', '!='))
+    assert all(Relational(x, 0, op).rel_op == '>' for op in ('gt', '>'))
+    assert all(Relational(x, 0, op).rel_op == '<' for op in ('lt', '<'))
+    assert all(Relational(x, 0, op).rel_op == '>=' for op in ('ge', '>='))
+    assert all(Relational(x, 0, op).rel_op == '<=' for op in ('le', '<='))
+
+
+def test_relational_arithmetic():
+    for cls in [Eq, Ne, Le, Lt, Ge, Gt]:
+        rel = cls(x, y)
+        raises(TypeError, lambda: 0+rel)
+        raises(TypeError, lambda: 1*rel)
+        raises(TypeError, lambda: 1**rel)
+        raises(TypeError, lambda: rel**1)
+        raises(TypeError, lambda: Add(0, rel))
+        raises(TypeError, lambda: Mul(1, rel))
+        raises(TypeError, lambda: Pow(1, rel))
+        raises(TypeError, lambda: Pow(rel, 1))
+
+
+def test_relational_bool_output():
+    # https://github.com/sympy/sympy/issues/5931
+    raises(TypeError, lambda: bool(x > 3))
+    raises(TypeError, lambda: bool(x >= 3))
+    raises(TypeError, lambda: bool(x < 3))
+    raises(TypeError, lambda: bool(x <= 3))
+    raises(TypeError, lambda: bool(Eq(x, 3)))
+    raises(TypeError, lambda: bool(Ne(x, 3)))
+
+
+def test_relational_logic_symbols():
+    # See issue 6204
+    assert (x < y) & (z < t) == And(x < y, z < t)
+    assert (x < y) | (z < t) == Or(x < y, z < t)
+    assert ~(x < y) == Not(x < y)
+    assert (x < y) >> (z < t) == Implies(x < y, z < t)
+    assert (x < y) << (z < t) == Implies(z < t, x < y)
+    assert (x < y) ^ (z < t) == Xor(x < y, z < t)
+
+    assert isinstance((x < y) & (z < t), And)
+    assert isinstance((x < y) | (z < t), Or)
+    assert isinstance(~(x < y), GreaterThan)
+    assert isinstance((x < y) >> (z < t), Implies)
+    assert isinstance((x < y) << (z < t), Implies)
+    assert isinstance((x < y) ^ (z < t), (Or, Xor))
+
+
+def test_univariate_relational_as_set():
+    assert (x > 0).as_set() == Interval(0, oo, True, True)
+    assert (x >= 0).as_set() == Interval(0, oo)
+    assert (x < 0).as_set() == Interval(-oo, 0, True, True)
+    assert (x <= 0).as_set() == Interval(-oo, 0)
+    assert Eq(x, 0).as_set() == FiniteSet(0)
+    assert Ne(x, 0).as_set() == Interval(-oo, 0, True, True) + \
+        Interval(0, oo, True, True)
+
+    assert (x**2 >= 4).as_set() == Interval(-oo, -2) + Interval(2, oo)
+
+
+@XFAIL
+def test_multivariate_relational_as_set():
+    assert (x*y >= 0).as_set() == Interval(0, oo)*Interval(0, oo) + \
+        Interval(-oo, 0)*Interval(-oo, 0)
+
+
+def test_Not():
+    assert Not(Equality(x, y)) == Unequality(x, y)
+    assert Not(Unequality(x, y)) == Equality(x, y)
+    assert Not(StrictGreaterThan(x, y)) == LessThan(x, y)
+    assert Not(StrictLessThan(x, y)) == GreaterThan(x, y)
+    assert Not(GreaterThan(x, y)) == StrictLessThan(x, y)
+    assert Not(LessThan(x, y)) == StrictGreaterThan(x, y)
+
+
+def test_evaluate():
+    assert str(Eq(x, x, evaluate=False)) == 'Eq(x, x)'
+    assert Eq(x, x, evaluate=False).doit() == S.true
+    assert str(Ne(x, x, evaluate=False)) == 'Ne(x, x)'
+    assert Ne(x, x, evaluate=False).doit() == S.false
+
+    assert str(Ge(x, x, evaluate=False)) == 'x >= x'
+    assert str(Le(x, x, evaluate=False)) == 'x <= x'
+    assert str(Gt(x, x, evaluate=False)) == 'x > x'
+    assert str(Lt(x, x, evaluate=False)) == 'x < x'
+
+
+def assert_all_ineq_raise_TypeError(a, b):
+    raises(TypeError, lambda: a > b)
+    raises(TypeError, lambda: a >= b)
+    raises(TypeError, lambda: a < b)
+    raises(TypeError, lambda: a <= b)
+    raises(TypeError, lambda: b > a)
+    raises(TypeError, lambda: b >= a)
+    raises(TypeError, lambda: b < a)
+    raises(TypeError, lambda: b <= a)
+
+
+def assert_all_ineq_give_class_Inequality(a, b):
+    """All inequality operations on `a` and `b` result in class Inequality."""
+    from sympy.core.relational import _Inequality as Inequality
+    assert isinstance(a > b,  Inequality)
+    assert isinstance(a >= b, Inequality)
+    assert isinstance(a < b,  Inequality)
+    assert isinstance(a <= b, Inequality)
+    assert isinstance(b > a,  Inequality)
+    assert isinstance(b >= a, Inequality)
+    assert isinstance(b < a,  Inequality)
+    assert isinstance(b <= a, Inequality)
+
+
+def test_imaginary_compare_raises_TypeError():
+    # See issue #5724
+    assert_all_ineq_raise_TypeError(I, x)
+
+
+def test_complex_compare_not_real():
+    # two cases which are not real
+    y = Symbol('y', imaginary=True)
+    z = Symbol('z', complex=True, extended_real=False)
+    for w in (y, z):
+        assert_all_ineq_raise_TypeError(2, w)
+    # some cases which should remain un-evaluated
+    t = Symbol('t')
+    x = Symbol('x', real=True)
+    z = Symbol('z', complex=True)
+    for w in (x, z, t):
+        assert_all_ineq_give_class_Inequality(2, w)
+
+
+def test_imaginary_and_inf_compare_raises_TypeError():
+    # See pull request #7835
+    y = Symbol('y', imaginary=True)
+    assert_all_ineq_raise_TypeError(oo, y)
+    assert_all_ineq_raise_TypeError(-oo, y)
+
+
+def test_complex_pure_imag_not_ordered():
+    raises(TypeError, lambda: 2*I < 3*I)
+
+    # more generally
+    x = Symbol('x', real=True, nonzero=True)
+    y = Symbol('y', imaginary=True)
+    z = Symbol('z', complex=True)
+    assert_all_ineq_raise_TypeError(I, y)
+
+    t = I*x   # an imaginary number, should raise errors
+    assert_all_ineq_raise_TypeError(2, t)
+
+    t = -I*y   # a real number, so no errors
+    assert_all_ineq_give_class_Inequality(2, t)
+
+    t = I*z   # unknown, should be unevaluated
+    assert_all_ineq_give_class_Inequality(2, t)
+
+
+def test_x_minus_y_not_same_as_x_lt_y():
+    """
+    A consequence of pull request #7792 is that `x - y < 0` and `x < y`
+    are not synonymous.
+    """
+    x = I + 2
+    y = I + 3
+    raises(TypeError, lambda: x < y)
+    assert x - y < 0
+
+    ineq = Lt(x, y, evaluate=False)
+    raises(TypeError, lambda: ineq.doit())
+    assert ineq.lhs - ineq.rhs < 0
+
+    t = Symbol('t', imaginary=True)
+    x = 2 + t
+    y = 3 + t
+    ineq = Lt(x, y, evaluate=False)
+    raises(TypeError, lambda: ineq.doit())
+    assert ineq.lhs - ineq.rhs < 0
+
+    # this one should give error either way
+    x = I + 2
+    y = 2*I + 3
+    raises(TypeError, lambda: x < y)
+    raises(TypeError, lambda: x - y < 0)
+
+
+def test_nan_equality_exceptions():
+    # See issue #7774
+    import random
+    assert Equality(nan, nan) is S.false
+    assert Unequality(nan, nan) is S.true
+
+    # See issue #7773
+    A = (x, S.Zero, S.One/3, pi, oo, -oo)
+    assert Equality(nan, random.choice(A)) is S.false
+    assert Equality(random.choice(A), nan) is S.false
+    assert Unequality(nan, random.choice(A)) is S.true
+    assert Unequality(random.choice(A), nan) is S.true
+
+
+def test_nan_inequality_raise_errors():
+    # See discussion in pull request #7776.  We test inequalities with
+    # a set including examples of various classes.
+    for q in (x, S.Zero, S(10), S.One/3, pi, S(1.3), oo, -oo, nan):
+        assert_all_ineq_raise_TypeError(q, nan)
+
+
+def test_nan_complex_inequalities():
+    # Comparisons of NaN with non-real raise errors, we're not too
+    # fussy whether its the NaN error or complex error.
+    for r in (I, zoo, Symbol('z', imaginary=True)):
+        assert_all_ineq_raise_TypeError(r, nan)
+
+
+def test_complex_infinity_inequalities():
+    raises(TypeError, lambda: zoo > 0)
+    raises(TypeError, lambda: zoo >= 0)
+    raises(TypeError, lambda: zoo < 0)
+    raises(TypeError, lambda: zoo <= 0)
+
+
+def test_inequalities_symbol_name_same():
+    """Using the operator and functional forms should give same results."""
+    # We test all combinations from a set
+    # FIXME: could replace with random selection after test passes
+    A = (x, y, S.Zero, S.One/3, pi, oo, -oo)
+    for a in A:
+        for b in A:
+            assert Gt(a, b) == (a > b)
+            assert Lt(a, b) == (a < b)
+            assert Ge(a, b) == (a >= b)
+            assert Le(a, b) == (a <= b)
+
+    for b in (y, S.Zero, S.One/3, pi, oo, -oo):
+        assert Gt(x, b, evaluate=False) == (x > b)
+        assert Lt(x, b, evaluate=False) == (x < b)
+        assert Ge(x, b, evaluate=False) == (x >= b)
+        assert Le(x, b, evaluate=False) == (x <= b)
+
+    for b in (y, S.Zero, S.One/3, pi, oo, -oo):
+        assert Gt(b, x, evaluate=False) == (b > x)
+        assert Lt(b, x, evaluate=False) == (b < x)
+        assert Ge(b, x, evaluate=False) == (b >= x)
+        assert Le(b, x, evaluate=False) == (b <= x)
+
+
+def test_inequalities_symbol_name_same_complex():
+    """Using the operator and functional forms should give same results.
+    With complex non-real numbers, both should raise errors.
+    """
+    # FIXME: could replace with random selection after test passes
+    for a in (x, S.Zero, S.One/3, pi, oo, Rational(1, 3)):
+        raises(TypeError, lambda: Gt(a, I))
+        raises(TypeError, lambda: a > I)
+        raises(TypeError, lambda: Lt(a, I))
+        raises(TypeError, lambda: a < I)
+        raises(TypeError, lambda: Ge(a, I))
+        raises(TypeError, lambda: a >= I)
+        raises(TypeError, lambda: Le(a, I))
+        raises(TypeError, lambda: a <= I)
+
+
+def test_inequalities_cant_sympify_other():
+    # see issue 7833
+    from operator import gt, lt, ge, le
+
+    bar = "foo"
+
+    for a in (x, S.Zero, S.One/3, pi, I, zoo, oo, -oo, nan, Rational(1, 3)):
+        for op in (lt, gt, le, ge):
+            raises(TypeError, lambda: op(a, bar))
+
+
+def test_ineq_avoid_wild_symbol_flip():
+    # see issue #7951, we try to avoid this internally, e.g., by using
+    # __lt__ instead of "<".
+    from sympy.core.symbol import Wild
+    p = symbols('p', cls=Wild)
+    # x > p might flip, but Gt should not:
+    assert Gt(x, p) == Gt(x, p, evaluate=False)
+    # Previously failed as 'p > x':
+    e = Lt(x, y).subs({y: p})
+    assert e == Lt(x, p, evaluate=False)
+    # Previously failed as 'p <= x':
+    e = Ge(x, p).doit()
+    assert e == Ge(x, p, evaluate=False)
+
+
+def test_issue_8245():
+    a = S("6506833320952669167898688709329/5070602400912917605986812821504")
+    assert rel_check(a, a.n(10))
+    assert rel_check(a, a.n(20))
+    assert rel_check(a, a.n())
+    # prec of 31 is enough to fully capture a as mpf
+    assert Float(a, 31) == Float(str(a.p), '')/Float(str(a.q), '')
+    for i in range(31):
+        r = Rational(Float(a, i))
+        f = Float(r)
+        assert (f < a) == (Rational(f) < a)
+    # test sign handling
+    assert (-f < -a) == (Rational(-f) < -a)
+    # test equivalence handling
+    isa = Float(a.p,'')/Float(a.q,'')
+    assert isa <= a
+    assert not isa < a
+    assert isa >= a
+    assert not isa > a
+    assert isa > 0
+
+    a = sqrt(2)
+    r = Rational(str(a.n(30)))
+    assert rel_check(a, r)
+
+    a = sqrt(2)
+    r = Rational(str(a.n(29)))
+    assert rel_check(a, r)
+
+    assert Eq(log(cos(2)**2 + sin(2)**2), 0) is S.true
+
+
+def test_issue_8449():
+    p = Symbol('p', nonnegative=True)
+    assert Lt(-oo, p)
+    assert Ge(-oo, p) is S.false
+    assert Gt(oo, -p)
+    assert Le(oo, -p) is S.false
+
+
+def test_simplify_relational():
+    assert simplify(x*(y + 1) - x*y - x + 1 < x) == (x > 1)
+    assert simplify(x*(y + 1) - x*y - x - 1 < x) == (x > -1)
+    assert simplify(x < x*(y + 1) - x*y - x + 1) == (x < 1)
+    q, r = symbols("q r")
+    assert (((-q + r) - (q - r)) <= 0).simplify() == (q >= r)
+    root2 = sqrt(2)
+    equation = ((root2 * (-q + r) - root2 * (q - r)) <= 0).simplify()
+    assert equation == (q >= r)
+    r = S.One < x
+    # canonical operations are not the same as simplification,
+    # so if there is no simplification, canonicalization will
+    # be done unless the measure forbids it
+    assert simplify(r) == r.canonical
+    assert simplify(r, ratio=0) != r.canonical
+    # this is not a random test; in _eval_simplify
+    # this will simplify to S.false and that is the
+    # reason for the 'if r.is_Relational' in Relational's
+    # _eval_simplify routine
+    assert simplify(-(2**(pi*Rational(3, 2)) + 6**pi)**(1/pi) +
+                    2*(2**(pi/2) + 3**pi)**(1/pi) < 0) is S.false
+    # canonical at least
+    assert Eq(y, x).simplify() == Eq(x, y)
+    assert Eq(x - 1, 0).simplify() == Eq(x, 1)
+    assert Eq(x - 1, x).simplify() == S.false
+    assert Eq(2*x - 1, x).simplify() == Eq(x, 1)
+    assert Eq(2*x, 4).simplify() == Eq(x, 2)
+    z = cos(1)**2 + sin(1)**2 - 1  # z.is_zero is None
+    assert Eq(z*x, 0).simplify() == S.true
+
+    assert Ne(y, x).simplify() == Ne(x, y)
+    assert Ne(x - 1, 0).simplify() == Ne(x, 1)
+    assert Ne(x - 1, x).simplify() == S.true
+    assert Ne(2*x - 1, x).simplify() == Ne(x, 1)
+    assert Ne(2*x, 4).simplify() == Ne(x, 2)
+    assert Ne(z*x, 0).simplify() == S.false
+
+    # No real-valued assumptions
+    assert Ge(y, x).simplify() == Le(x, y)
+    assert Ge(x - 1, 0).simplify() == Ge(x, 1)
+    assert Ge(x - 1, x).simplify() == S.false
+    assert Ge(2*x - 1, x).simplify() == Ge(x, 1)
+    assert Ge(2*x, 4).simplify() == Ge(x, 2)
+    assert Ge(z*x, 0).simplify() == S.true
+    assert Ge(x, -2).simplify() == Ge(x, -2)
+    assert Ge(-x, -2).simplify() == Le(x, 2)
+    assert Ge(x, 2).simplify() == Ge(x, 2)
+    assert Ge(-x, 2).simplify() == Le(x, -2)
+
+    assert Le(y, x).simplify() == Ge(x, y)
+    assert Le(x - 1, 0).simplify() == Le(x, 1)
+    assert Le(x - 1, x).simplify() == S.true
+    assert Le(2*x - 1, x).simplify() == Le(x, 1)
+    assert Le(2*x, 4).simplify() == Le(x, 2)
+    assert Le(z*x, 0).simplify() == S.true
+    assert Le(x, -2).simplify() == Le(x, -2)
+    assert Le(-x, -2).simplify() == Ge(x, 2)
+    assert Le(x, 2).simplify() == Le(x, 2)
+    assert Le(-x, 2).simplify() == Ge(x, -2)
+
+    assert Gt(y, x).simplify() == Lt(x, y)
+    assert Gt(x - 1, 0).simplify() == Gt(x, 1)
+    assert Gt(x - 1, x).simplify() == S.false
+    assert Gt(2*x - 1, x).simplify() == Gt(x, 1)
+    assert Gt(2*x, 4).simplify() == Gt(x, 2)
+    assert Gt(z*x, 0).simplify() == S.false
+    assert Gt(x, -2).simplify() == Gt(x, -2)
+    assert Gt(-x, -2).simplify() == Lt(x, 2)
+    assert Gt(x, 2).simplify() == Gt(x, 2)
+    assert Gt(-x, 2).simplify() == Lt(x, -2)
+
+    assert Lt(y, x).simplify() == Gt(x, y)
+    assert Lt(x - 1, 0).simplify() == Lt(x, 1)
+    assert Lt(x - 1, x).simplify() == S.true
+    assert Lt(2*x - 1, x).simplify() == Lt(x, 1)
+    assert Lt(2*x, 4).simplify() == Lt(x, 2)
+    assert Lt(z*x, 0).simplify() == S.false
+    assert Lt(x, -2).simplify() == Lt(x, -2)
+    assert Lt(-x, -2).simplify() == Gt(x, 2)
+    assert Lt(x, 2).simplify() == Lt(x, 2)
+    assert Lt(-x, 2).simplify() == Gt(x, -2)
+
+    # Test particular branches of _eval_simplify
+    m = exp(1) - exp_polar(1)
+    assert simplify(m*x > 1) is S.false
+    # These two test the same branch
+    assert simplify(m*x + 2*m*y > 1) is S.false
+    assert simplify(m*x + y > 1 + y) is S.false
+
+
+def test_equals():
+    w, x, y, z = symbols('w:z')
+    f = Function('f')
+    assert Eq(x, 1).equals(Eq(x*(y + 1) - x*y - x + 1, x))
+    assert Eq(x, y).equals(x < y, True) == False
+    assert Eq(x, f(1)).equals(Eq(x, f(2)), True) == f(1) - f(2)
+    assert Eq(f(1), y).equals(Eq(f(2), y), True) == f(1) - f(2)
+    assert Eq(x, f(1)).equals(Eq(f(2), x), True) == f(1) - f(2)
+    assert Eq(f(1), x).equals(Eq(x, f(2)), True) == f(1) - f(2)
+    assert Eq(w, x).equals(Eq(y, z), True) == False
+    assert Eq(f(1), f(2)).equals(Eq(f(3), f(4)), True) == f(1) - f(3)
+    assert (x < y).equals(y > x, True) == True
+    assert (x < y).equals(y >= x, True) == False
+    assert (x < y).equals(z < y, True) == False
+    assert (x < y).equals(x < z, True) == False
+    assert (x < f(1)).equals(x < f(2), True) == f(1) - f(2)
+    assert (f(1) < x).equals(f(2) < x, True) == f(1) - f(2)
+
+
+def test_reversed():
+    assert (x < y).reversed == (y > x)
+    assert (x <= y).reversed == (y >= x)
+    assert Eq(x, y, evaluate=False).reversed == Eq(y, x, evaluate=False)
+    assert Ne(x, y, evaluate=False).reversed == Ne(y, x, evaluate=False)
+    assert (x >= y).reversed == (y <= x)
+    assert (x > y).reversed == (y < x)
+
+
+def test_canonical():
+    c = [i.canonical for i in (
+        x + y < z,
+        x + 2 > 3,
+        x < 2,
+        S(2) > x,
+        x**2 > -x/y,
+        Gt(3, 2, evaluate=False)
+        )]
+    assert [i.canonical for i in c] == c
+    assert [i.reversed.canonical for i in c] == c
+    assert not any(i.lhs.is_Number and not i.rhs.is_Number for i in c)
+
+    c = [i.reversed.func(i.rhs, i.lhs, evaluate=False).canonical for i in c]
+    assert [i.canonical for i in c] == c
+    assert [i.reversed.canonical for i in c] == c
+    assert not any(i.lhs.is_Number and not i.rhs.is_Number for i in c)
+    assert Eq(y < x, x > y).canonical is S.true
+
+
+@XFAIL
+def test_issue_8444_nonworkingtests():
+    x = symbols('x', real=True)
+    assert (x <= oo) == (x >= -oo) == True
+
+    x = symbols('x')
+    assert x >= floor(x)
+    assert (x < floor(x)) == False
+    assert x <= ceiling(x)
+    assert (x > ceiling(x)) == False
+
+
+def test_issue_8444_workingtests():
+    x = symbols('x')
+    assert Gt(x, floor(x)) == Gt(x, floor(x), evaluate=False)
+    assert Ge(x, floor(x)) == Ge(x, floor(x), evaluate=False)
+    assert Lt(x, ceiling(x)) == Lt(x, ceiling(x), evaluate=False)
+    assert Le(x, ceiling(x)) == Le(x, ceiling(x), evaluate=False)
+    i = symbols('i', integer=True)
+    assert (i > floor(i)) == False
+    assert (i < ceiling(i)) == False
+
+
+def test_issue_10304():
+    d = cos(1)**2 + sin(1)**2 - 1
+    assert d.is_comparable is False  # if this fails, find a new d
+    e = 1 + d*I
+    assert simplify(Eq(e, 0)) is S.false
+
+
+def test_issue_18412():
+    d = (Rational(1, 6) + z / 4 / y)
+    assert Eq(x, pi * y**3 * d).replace(y**3, z) == Eq(x, pi * z * d)
+
+
+def test_issue_10401():
+    x = symbols('x')
+    fin = symbols('inf', finite=True)
+    inf = symbols('inf', infinite=True)
+    inf2 = symbols('inf2', infinite=True)
+    infx = symbols('infx', infinite=True, extended_real=True)
+    # Used in the commented tests below:
+    #infx2 = symbols('infx2', infinite=True, extended_real=True)
+    infnx = symbols('inf~x', infinite=True, extended_real=False)
+    infnx2 = symbols('inf~x2', infinite=True, extended_real=False)
+    infp = symbols('infp', infinite=True, extended_positive=True)
+    infp1 = symbols('infp1', infinite=True, extended_positive=True)
+    infn = symbols('infn', infinite=True, extended_negative=True)
+    zero = symbols('z', zero=True)
+    nonzero = symbols('nz', zero=False, finite=True)
+
+    assert Eq(1/(1/x + 1), 1).func is Eq
+    assert Eq(1/(1/x + 1), 1).subs(x, S.ComplexInfinity) is S.true
+    assert Eq(1/(1/fin + 1), 1) is S.false
+
+    T, F = S.true, S.false
+    assert Eq(fin, inf) is F
+    assert Eq(inf, inf2) not in (T, F) and inf != inf2
+    assert Eq(1 + inf, 2 + inf2) not in (T, F) and inf != inf2
+    assert Eq(infp, infp1) is T
+    assert Eq(infp, infn) is F
+    assert Eq(1 + I*oo, I*oo) is F
+    assert Eq(I*oo, 1 + I*oo) is F
+    assert Eq(1 + I*oo, 2 + I*oo) is F
+    assert Eq(1 + I*oo, 2 + I*infx) is F
+    assert Eq(1 + I*oo, 2 + infx) is F
+    # FIXME: The test below fails because (-infx).is_extended_positive is True
+    # (should be None)
+    #assert Eq(1 + I*infx, 1 + I*infx2) not in (T, F) and infx != infx2
+    #
+    assert Eq(zoo, sqrt(2) + I*oo) is F
+    assert Eq(zoo, oo) is F
+    r = Symbol('r', real=True)
+    i = Symbol('i', imaginary=True)
+    assert Eq(i*I, r) not in (T, F)
+    assert Eq(infx, infnx) is F
+    assert Eq(infnx, infnx2) not in (T, F) and infnx != infnx2
+    assert Eq(zoo, oo) is F
+    assert Eq(inf/inf2, 0) is F
+    assert Eq(inf/fin, 0) is F
+    assert Eq(fin/inf, 0) is T
+    assert Eq(zero/nonzero, 0) is T and ((zero/nonzero) != 0)
+    # The commented out test below is incorrect because:
+    assert zoo == -zoo
+    assert Eq(zoo, -zoo) is T
+    assert Eq(oo, -oo) is F
+    assert Eq(inf, -inf) not in (T, F)
+
+    assert Eq(fin/(fin + 1), 1) is S.false
+
+    o = symbols('o', odd=True)
+    assert Eq(o, 2*o) is S.false
+
+    p = symbols('p', positive=True)
+    assert Eq(p/(p - 1), 1) is F
+
+
+def test_issue_10633():
+    assert Eq(True, False) == False
+    assert Eq(False, True) == False
+    assert Eq(True, True) == True
+    assert Eq(False, False) == True
+
+
+def test_issue_10927():
+    x = symbols('x')
+    assert str(Eq(x, oo)) == 'Eq(x, oo)'
+    assert str(Eq(x, -oo)) == 'Eq(x, -oo)'
+
+
+def test_issues_13081_12583_12534():
+    # 13081
+    r = Rational('905502432259640373/288230376151711744')
+    assert (r < pi) is S.false
+    assert (r > pi) is S.true
+    # 12583
+    v = sqrt(2)
+    u = sqrt(v) + 2/sqrt(10 - 8/sqrt(2 - v) + 4*v*(1/sqrt(2 - v) - 1))
+    assert (u >= 0) is S.true
+    # 12534; Rational vs NumberSymbol
+    # here are some precisions for which Rational forms
+    # at a lower and higher precision bracket the value of pi
+    # e.g. for p = 20:
+    # Rational(pi.n(p + 1)).n(25) = 3.14159265358979323846 2834
+    #                    pi.n(25) = 3.14159265358979323846 2643
+    # Rational(pi.n(p    )).n(25) = 3.14159265358979323846 1987
+    assert [p for p in range(20, 50) if
+            (Rational(pi.n(p)) < pi) and
+            (pi < Rational(pi.n(p + 1)))] == [20, 24, 27, 33, 37, 43, 48]
+    # pick one such precision and affirm that the reversed operation
+    # gives the opposite result, i.e. if x < y is true then x > y
+    # must be false
+    for i in (20, 21):
+        v = pi.n(i)
+        assert rel_check(Rational(v), pi)
+        assert rel_check(v, pi)
+    assert rel_check(pi.n(20), pi.n(21))
+    # Float vs Rational
+    # the rational form is less than the floating representation
+    # at the same precision
+    assert [i for i in range(15, 50) if Rational(pi.n(i)) > pi.n(i)] == []
+    # this should be the same if we reverse the relational
+    assert [i for i in range(15, 50) if pi.n(i) < Rational(pi.n(i))] == []
+
+def test_issue_18188():
+    from sympy.sets.conditionset import ConditionSet
+    result1 = Eq(x*cos(x) - 3*sin(x), 0)
+    assert result1.as_set() == ConditionSet(x, Eq(x*cos(x) - 3*sin(x), 0), Reals)
+
+    result2 = Eq(x**2 + sqrt(x*2) + sin(x), 0)
+    assert result2.as_set() == ConditionSet(x, Eq(sqrt(2)*sqrt(x) + x**2 + sin(x), 0), Reals)
+
+def test_binary_symbols():
+    ans = {x}
+    for f in Eq, Ne:
+        for t in S.true, S.false:
+            eq = f(x, S.true)
+            assert eq.binary_symbols == ans
+            assert eq.reversed.binary_symbols == ans
+        assert f(x, 1).binary_symbols == set()
+
+
+def test_rel_args():
+    # can't have Boolean args; this is automatic for True/False
+    # with Python 3 and we confirm that SymPy does the same
+    # for true/false
+    for op in ['<', '<=', '>', '>=']:
+        for b in (S.true, x < 1, And(x, y)):
+            for v in (0.1, 1, 2**32, t, S.One):
+                raises(TypeError, lambda: Relational(b, v, op))
+
+
+def test_nothing_happens_to_Eq_condition_during_simplify():
+    # issue 25701
+    r = symbols('r', real=True)
+    assert Eq(2*sign(r + 3)/(5*Abs(r + 3)**Rational(3, 5)), 0
+        ).simplify() == Eq(Piecewise(
+        (0, Eq(r, -3)), ((r + 3)/(5*Abs((r + 3)**Rational(8, 5)))*2, True)), 0)
+
+
+def test_issue_15847():
+    a = Ne(x*(x + y), x**2 + x*y)
+    assert simplify(a) == False
+
+
+def test_negated_property():
+    eq = Eq(x, y)
+    assert eq.negated == Ne(x, y)
+
+    eq = Ne(x, y)
+    assert eq.negated == Eq(x, y)
+
+    eq = Ge(x + y, y - x)
+    assert eq.negated == Lt(x + y, y - x)
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(x, y).negated.negated == f(x, y)
+
+
+def test_reversedsign_property():
+    eq = Eq(x, y)
+    assert eq.reversedsign == Eq(-x, -y)
+
+    eq = Ne(x, y)
+    assert eq.reversedsign == Ne(-x, -y)
+
+    eq = Ge(x + y, y - x)
+    assert eq.reversedsign == Le(-x - y, x - y)
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(x, y).reversedsign.reversedsign == f(x, y)
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(-x, y).reversedsign.reversedsign == f(-x, y)
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(x, -y).reversedsign.reversedsign == f(x, -y)
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(-x, -y).reversedsign.reversedsign == f(-x, -y)
+
+
+def test_reversed_reversedsign_property():
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(x, y).reversed.reversedsign == f(x, y).reversedsign.reversed
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(-x, y).reversed.reversedsign == f(-x, y).reversedsign.reversed
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(x, -y).reversed.reversedsign == f(x, -y).reversedsign.reversed
+
+    for f in (Eq, Ne, Ge, Gt, Le, Lt):
+        assert f(-x, -y).reversed.reversedsign == \
+            f(-x, -y).reversedsign.reversed
+
+
+def test_improved_canonical():
+    def test_different_forms(listofforms):
+        for form1, form2 in combinations(listofforms, 2):
+            assert form1.canonical == form2.canonical
+
+    def generate_forms(expr):
+        return [expr, expr.reversed, expr.reversedsign,
+                expr.reversed.reversedsign]
+
+    test_different_forms(generate_forms(x > -y))
+    test_different_forms(generate_forms(x >= -y))
+    test_different_forms(generate_forms(Eq(x, -y)))
+    test_different_forms(generate_forms(Ne(x, -y)))
+    test_different_forms(generate_forms(pi < x))
+    test_different_forms(generate_forms(pi - 5*y < -x + 2*y**2 - 7))
+
+    assert (pi >= x).canonical == (x <= pi)
+
+
+def test_set_equality_canonical():
+    a, b, c = symbols('a b c')
+
+    A = Eq(FiniteSet(a, b, c), FiniteSet(1, 2, 3))
+    B = Ne(FiniteSet(a, b, c), FiniteSet(4, 5, 6))
+
+    assert A.canonical == A.reversed
+    assert B.canonical == B.reversed
+
+
+def test_trigsimp():
+    # issue 16736
+    s, c = sin(2*x), cos(2*x)
+    eq = Eq(s, c)
+    assert trigsimp(eq) == eq  # no rearrangement of sides
+    # simplification of sides might result in
+    # an unevaluated Eq
+    changed = trigsimp(Eq(s + c, sqrt(2)))
+    assert isinstance(changed, Eq)
+    assert changed.subs(x, pi/8) is S.true
+    # or an evaluated one
+    assert trigsimp(Eq(cos(x)**2 + sin(x)**2, 1)) is S.true
+
+
+def test_polynomial_relation_simplification():
+    assert Ge(3*x*(x + 1) + 4, 3*x).simplify() in [Ge(x**2, -Rational(4,3)), Le(-x**2, Rational(4, 3))]
+    assert Le(-(3*x*(x + 1) + 4), -3*x).simplify() in [Ge(x**2, -Rational(4,3)), Le(-x**2, Rational(4, 3))]
+    assert ((x**2+3)*(x**2-1)+3*x >= 2*x**2).simplify() in [(x**4 + 3*x >= 3), (-x**4 - 3*x <= -3)]
+
+
+def test_multivariate_linear_function_simplification():
+    assert Ge(x + y, x - y).simplify() == Ge(y, 0)
+    assert Le(-x + y, -x - y).simplify() == Le(y, 0)
+    assert Eq(2*x + y, 2*x + y - 3).simplify() == False
+    assert (2*x + y > 2*x + y - 3).simplify() == True
+    assert (2*x + y < 2*x + y - 3).simplify() == False
+    assert (2*x + y < 2*x + y + 3).simplify() == True
+    a, b, c, d, e, f, g = symbols('a b c d e f g')
+    assert Lt(a + b + c + 2*d, 3*d - f + g). simplify() == Lt(a, -b - c + d - f + g)
+
+
+def test_nonpolymonial_relations():
+    assert Eq(cos(x), 0).simplify() == Eq(cos(x), 0)
+
+def test_18778():
+    raises(TypeError, lambda: is_le(Basic(), Basic()))
+    raises(TypeError, lambda: is_gt(Basic(), Basic()))
+    raises(TypeError, lambda: is_ge(Basic(), Basic()))
+    raises(TypeError, lambda: is_lt(Basic(), Basic()))
+
+def test_EvalEq():
+    """
+
+    This test exists to ensure backwards compatibility.
+    The method to use is _eval_is_eq
+    """
+    from sympy.core.expr import Expr
+
+    class PowTest(Expr):
+        def __new__(cls, base, exp):
+            return Basic.__new__(PowTest, _sympify(base), _sympify(exp))
+
+        def _eval_Eq(lhs, rhs):
+            if type(lhs) == PowTest and type(rhs) == PowTest:
+                return lhs.args[0] == rhs.args[0] and lhs.args[1] == rhs.args[1]
+
+    assert is_eq(PowTest(3, 4), PowTest(3,4))
+    assert is_eq(PowTest(3, 4), _sympify(4)) is None
+    assert is_neq(PowTest(3, 4), PowTest(3,7))
+
+
+def test_is_eq():
+    # test assumptions
+    assert is_eq(x, y, Q.infinite(x) & Q.finite(y)) is False
+    assert is_eq(x, y, Q.infinite(x) & Q.infinite(y) & Q.extended_real(x) & ~Q.extended_real(y)) is False
+    assert is_eq(x, y, Q.infinite(x) & Q.infinite(y) & Q.extended_positive(x) & Q.extended_negative(y)) is False
+
+    assert is_eq(x+I, y+I, Q.infinite(x) & Q.finite(y)) is False
+    assert is_eq(1+x*I, 1+y*I, Q.infinite(x) & Q.finite(y)) is False
+
+    assert is_eq(x, S(0), assumptions=Q.zero(x))
+    assert is_eq(x, S(0), assumptions=~Q.zero(x)) is False
+    assert is_eq(x, S(0), assumptions=Q.nonzero(x)) is False
+    assert is_neq(x, S(0), assumptions=Q.zero(x)) is False
+    assert is_neq(x, S(0), assumptions=~Q.zero(x))
+    assert is_neq(x, S(0), assumptions=Q.nonzero(x))
+
+    # test registration
+    class PowTest(Expr):
+        def __new__(cls, base, exp):
+            return Basic.__new__(cls, _sympify(base), _sympify(exp))
+
+    @dispatch(PowTest, PowTest)
+    def _eval_is_eq(lhs, rhs):
+        if type(lhs) == PowTest and type(rhs) == PowTest:
+            return fuzzy_and([is_eq(lhs.args[0], rhs.args[0]), is_eq(lhs.args[1], rhs.args[1])])
+
+    assert is_eq(PowTest(3, 4), PowTest(3,4))
+    assert is_eq(PowTest(3, 4), _sympify(4)) is None
+    assert is_neq(PowTest(3, 4), PowTest(3,7))
+
+
+def test_is_ge_le():
+    # test assumptions
+    assert is_ge(x, S(0), Q.nonnegative(x)) is True
+    assert is_ge(x, S(0), Q.negative(x)) is False
+
+    # test registration
+    class PowTest(Expr):
+        def __new__(cls, base, exp):
+            return Basic.__new__(cls, _sympify(base), _sympify(exp))
+
+    @dispatch(PowTest, PowTest)
+    def _eval_is_ge(lhs, rhs):
+        if type(lhs) == PowTest and type(rhs) == PowTest:
+            return fuzzy_and([is_ge(lhs.args[0], rhs.args[0]), is_ge(lhs.args[1], rhs.args[1])])
+
+    assert is_ge(PowTest(3, 9), PowTest(3,2))
+    assert is_gt(PowTest(3, 9), PowTest(3,2))
+    assert is_le(PowTest(3, 2), PowTest(3,9))
+    assert is_lt(PowTest(3, 2), PowTest(3,9))
+
+
+def test_weak_strict():
+    for func in (Eq, Ne):
+        eq = func(x, 1)
+        assert eq.strict == eq.weak == eq
+    eq = Gt(x, 1)
+    assert eq.weak == Ge(x, 1)
+    assert eq.strict == eq
+    eq = Lt(x, 1)
+    assert eq.weak == Le(x, 1)
+    assert eq.strict == eq
+    eq = Ge(x, 1)
+    assert eq.strict == Gt(x, 1)
+    assert eq.weak == eq
+    eq = Le(x, 1)
+    assert eq.strict == Lt(x, 1)
+    assert eq.weak == eq
+
+
+def test_issue_23731():
+    i = symbols('i', integer=True)
+    assert unchanged(Eq, i, 1.0)
+    assert unchanged(Eq, i/2, 0.5)
+    ni = symbols('ni', integer=False)
+    assert Eq(ni, 1) == False
+    assert unchanged(Eq, ni, .1)
+    assert Eq(ni, 1.0) == False
+    nr = symbols('nr', rational=False)
+    assert Eq(nr, .1) == False
+
+
+def test_rewrite_Add():
+    from sympy.testing.pytest import warns_deprecated_sympy
+    with warns_deprecated_sympy():
+        assert Eq(x, y).rewrite(Add) == x - y
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_rules.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_rules.py
new file mode 100644
index 0000000000000000000000000000000000000000..31cb88b52db21f39653033b4567526e992be99f0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_rules.py
@@ -0,0 +1,14 @@
+from sympy.core.rules import Transform
+
+from sympy.testing.pytest import raises
+
+
+def test_Transform():
+    add1 = Transform(lambda x: x + 1, lambda x: x % 2 == 1)
+    assert add1[1] == 2
+    assert (1 in add1) is True
+    assert add1.get(1) == 2
+
+    raises(KeyError, lambda: add1[2])
+    assert (2 in add1) is False
+    assert add1.get(2) is None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_singleton.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_singleton.py
new file mode 100644
index 0000000000000000000000000000000000000000..893713f27d74b884391ad800d186eafe5337ab1c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_singleton.py
@@ -0,0 +1,76 @@
+from sympy.core.basic import Basic
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S, Singleton
+
+def test_Singleton():
+
+    class MySingleton(Basic, metaclass=Singleton):
+        pass
+
+    MySingleton() # force instantiation
+    assert MySingleton() is not Basic()
+    assert MySingleton() is MySingleton()
+    assert S.MySingleton is MySingleton()
+
+    class MySingleton_sub(MySingleton):
+        pass
+
+    MySingleton_sub()
+    assert MySingleton_sub() is not MySingleton()
+    assert MySingleton_sub() is MySingleton_sub()
+
+def test_singleton_redefinition():
+    class TestSingleton(Basic, metaclass=Singleton):
+        pass
+
+    assert TestSingleton() is S.TestSingleton
+
+    class TestSingleton(Basic, metaclass=Singleton):
+        pass
+
+    assert TestSingleton() is S.TestSingleton
+
+def test_names_in_namespace():
+    # Every singleton name should be accessible from the 'from sympy import *'
+    # namespace in addition to the S object. However, it does not need to be
+    # by the same name (e.g., oo instead of S.Infinity).
+
+    # As a general rule, things should only be added to the singleton registry
+    # if they are used often enough that code can benefit either from the
+    # performance benefit of being able to use 'is' (this only matters in very
+    # tight loops), or from the memory savings of having exactly one instance
+    # (this matters for the numbers singletons, but very little else). The
+    # singleton registry is already a bit overpopulated, and things cannot be
+    # removed from it without breaking backwards compatibility. So if you got
+    # here by adding something new to the singletons, ask yourself if it
+    # really needs to be singletonized. Note that SymPy classes compare to one
+    # another just fine, so Class() == Class() will give True even if each
+    # Class() returns a new instance. Having unique instances is only
+    # necessary for the above noted performance gains. It should not be needed
+    # for any behavioral purposes.
+
+    # If you determine that something really should be a singleton, it must be
+    # accessible to sympify() without using 'S' (hence this test). Also, its
+    # str printer should print a form that does not use S. This is because
+    # sympify() disables attribute lookups by default for safety purposes.
+    d = {}
+    exec('from sympy import *', d)
+
+    for name in dir(S) + list(S._classes_to_install):
+        if name.startswith('_'):
+            continue
+        if name == 'register':
+            continue
+        if isinstance(getattr(S, name), Rational):
+            continue
+        if getattr(S, name).__module__.startswith('sympy.physics'):
+            continue
+        if name in ['MySingleton', 'MySingleton_sub', 'TestSingleton']:
+            # From the tests above
+            continue
+        if name == 'NegativeInfinity':
+            # Accessible by -oo
+            continue
+
+        # Use is here to ensure it is the exact same object
+        assert any(getattr(S, name) is i for i in d.values()), name
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_sorting.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_sorting.py
new file mode 100644
index 0000000000000000000000000000000000000000..a18dbfb624552cf2fa11bb7f3c3a9e865caeb0c4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_sorting.py
@@ -0,0 +1,28 @@
+from sympy.core.sorting import default_sort_key, ordered
+from sympy.testing.pytest import raises
+
+from sympy.abc import x
+
+
+def test_default_sort_key():
+    func = lambda x: x
+    assert sorted([func, x, func], key=default_sort_key) == [func, func, x]
+
+    class C:
+        def __repr__(self):
+            return 'x.y'
+    func = C()
+    assert sorted([x, func], key=default_sort_key) == [func, x]
+
+
+def test_ordered():
+    # Issue 7210 - this had been failing with python2/3 problems
+    assert (list(ordered([{1:3, 2:4, 9:10}, {1:3}])) == \
+               [{1: 3}, {1: 3, 2: 4, 9: 10}])
+    # warnings should not be raised for identical items
+    l = [1, 1]
+    assert list(ordered(l, warn=True)) == l
+    l = [[1], [2], [1]]
+    assert list(ordered(l, warn=True)) == [[1], [1], [2]]
+    raises(ValueError, lambda: list(ordered(['a', 'ab'], keys=[lambda x: x[0]],
+        default=False, warn=True)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_subs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_subs.py
new file mode 100644
index 0000000000000000000000000000000000000000..0803a4b1b5e93b8a35f43516ccef3ab9a16f08ec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_subs.py
@@ -0,0 +1,895 @@
+from sympy.calculus.accumulationbounds import AccumBounds
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import (Dict, Tuple)
+from sympy.core.function import (Derivative, Function, Lambda, Subs)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Float, I, Integer, Rational, oo, pi, zoo)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, Wild, symbols)
+from sympy.core.sympify import SympifyError
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (atan2, cos, cot, sin, tan)
+from sympy.matrices.dense import (Matrix, zeros)
+from sympy.matrices.expressions.special import ZeroMatrix
+from sympy.polys.polytools import factor
+from sympy.polys.rootoftools import RootOf
+from sympy.simplify.cse_main import cse
+from sympy.simplify.simplify import nsimplify
+from sympy.core.basic import _aresame
+from sympy.testing.pytest import XFAIL, raises
+from sympy.abc import a, x, y, z, t
+
+
+def test_subs():
+    n3 = Rational(3)
+    e = x
+    e = e.subs(x, n3)
+    assert e == Rational(3)
+
+    e = 2*x
+    assert e == 2*x
+    e = e.subs(x, n3)
+    assert e == Rational(6)
+
+
+def test_subs_Matrix():
+    z = zeros(2)
+    z1 = ZeroMatrix(2, 2)
+    assert (x*y).subs({x:z, y:0}) in [z, z1]
+    assert (x*y).subs({y:z, x:0}) == 0
+    assert (x*y).subs({y:z, x:0}, simultaneous=True) in [z, z1]
+    assert (x + y).subs({x: z, y: z}, simultaneous=True) in [z, z1]
+    assert (x + y).subs({x: z, y: z}) in [z, z1]
+
+    # Issue #15528
+    assert Mul(Matrix([[3]]), x).subs(x, 2.0) == Matrix([[6.0]])
+    # Does not raise a TypeError, see comment on the MatAdd postprocessor
+    assert Add(Matrix([[3]]), x).subs(x, 2.0) == Add(Matrix([[3]]), 2.0)
+
+
+def test_subs_AccumBounds():
+    e = x
+    e = e.subs(x, AccumBounds(1, 3))
+    assert e == AccumBounds(1, 3)
+
+    e = 2*x
+    e = e.subs(x, AccumBounds(1, 3))
+    assert e == AccumBounds(2, 6)
+
+    e = x + x**2
+    e = e.subs(x, AccumBounds(-1, 1))
+    assert e == AccumBounds(-1, 2)
+
+
+def test_trigonometric():
+    n3 = Rational(3)
+    e = (sin(x)**2).diff(x)
+    assert e == 2*sin(x)*cos(x)
+    e = e.subs(x, n3)
+    assert e == 2*cos(n3)*sin(n3)
+
+    e = (sin(x)**2).diff(x)
+    assert e == 2*sin(x)*cos(x)
+    e = e.subs(sin(x), cos(x))
+    assert e == 2*cos(x)**2
+
+    assert exp(pi).subs(exp, sin) == 0
+    assert cos(exp(pi)).subs(exp, sin) == 1
+
+    i = Symbol('i', integer=True)
+    zoo = S.ComplexInfinity
+    assert tan(x).subs(x, pi/2) is zoo
+    assert cot(x).subs(x, pi) is zoo
+    assert cot(i*x).subs(x, pi) is zoo
+    assert tan(i*x).subs(x, pi/2) == tan(i*pi/2)
+    assert tan(i*x).subs(x, pi/2).subs(i, 1) is zoo
+    o = Symbol('o', odd=True)
+    assert tan(o*x).subs(x, pi/2) == tan(o*pi/2)
+
+
+def test_powers():
+    assert sqrt(1 - sqrt(x)).subs(x, 4) == I
+    assert (sqrt(1 - x**2)**3).subs(x, 2) == - 3*I*sqrt(3)
+    assert (x**Rational(1, 3)).subs(x, 27) == 3
+    assert (x**Rational(1, 3)).subs(x, -27) == 3*(-1)**Rational(1, 3)
+    assert ((-x)**Rational(1, 3)).subs(x, 27) == 3*(-1)**Rational(1, 3)
+    n = Symbol('n', negative=True)
+    assert (x**n).subs(x, 0) is S.ComplexInfinity
+    assert exp(-1).subs(S.Exp1, 0) is S.ComplexInfinity
+    assert (x**(4.0*y)).subs(x**(2.0*y), n) == n**2.0
+    assert (2**(x + 2)).subs(2, 3) == 3**(x + 3)
+
+
+def test_logexppow():   # no eval()
+    x = Symbol('x', real=True)
+    w = Symbol('w')
+    e = (3**(1 + x) + 2**(1 + x))/(3**x + 2**x)
+    assert e.subs(2**x, w) != e
+    assert e.subs(exp(x*log(Rational(2))), w) != e
+
+
+def test_bug():
+    x1 = Symbol('x1')
+    x2 = Symbol('x2')
+    y = x1*x2
+    assert y.subs(x1, Float(3.0)) == Float(3.0)*x2
+
+
+def test_subbug1():
+    # see that they don't fail
+    (x**x).subs(x, 1)
+    (x**x).subs(x, 1.0)
+
+
+def test_subbug2():
+    # Ensure this does not cause infinite recursion
+    assert Float(7.7).epsilon_eq(abs(x).subs(x, -7.7))
+
+
+def test_dict_set():
+    a, b, c = map(Wild, 'abc')
+
+    f = 3*cos(4*x)
+    r = f.match(a*cos(b*x))
+    assert r == {a: 3, b: 4}
+    e = a/b*sin(b*x)
+    assert e.subs(r) == r[a]/r[b]*sin(r[b]*x)
+    assert e.subs(r) == 3*sin(4*x) / 4
+    s = set(r.items())
+    assert e.subs(s) == r[a]/r[b]*sin(r[b]*x)
+    assert e.subs(s) == 3*sin(4*x) / 4
+
+    assert e.subs(r) == r[a]/r[b]*sin(r[b]*x)
+    assert e.subs(r) == 3*sin(4*x) / 4
+    assert x.subs(Dict((x, 1))) == 1
+
+
+def test_dict_ambigous():   # see issue 3566
+    f = x*exp(x)
+    g = z*exp(z)
+
+    df = {x: y, exp(x): y}
+    dg = {z: y, exp(z): y}
+
+    assert f.subs(df) == y**2
+    assert g.subs(dg) == y**2
+
+    # and this is how order can affect the result
+    assert f.subs(x, y).subs(exp(x), y) == y*exp(y)
+    assert f.subs(exp(x), y).subs(x, y) == y**2
+
+    # length of args and count_ops are the same so
+    # default_sort_key resolves ordering...if one
+    # doesn't want this result then an unordered
+    # sequence should not be used.
+    e = 1 + x*y
+    assert e.subs({x: y, y: 2}) == 5
+    # here, there are no obviously clashing keys or values
+    # but the results depend on the order
+    assert exp(x/2 + y).subs({exp(y + 1): 2, x: 2}) == exp(y + 1)
+
+
+def test_deriv_sub_bug3():
+    f = Function('f')
+    pat = Derivative(f(x), x, x)
+    assert pat.subs(y, y**2) == Derivative(f(x), x, x)
+    assert pat.subs(y, y**2) != Derivative(f(x), x)
+
+
+def test_equality_subs1():
+    f = Function('f')
+    eq = Eq(f(x)**2, x)
+    res = Eq(Integer(16), x)
+    assert eq.subs(f(x), 4) == res
+
+
+def test_equality_subs2():
+    f = Function('f')
+    eq = Eq(f(x)**2, 16)
+    assert bool(eq.subs(f(x), 3)) is False
+    assert bool(eq.subs(f(x), 4)) is True
+
+
+def test_issue_3742():
+    e = sqrt(x)*exp(y)
+    assert e.subs(sqrt(x), 1) == exp(y)
+
+
+def test_subs_dict1():
+    assert (1 + x*y).subs(x, pi) == 1 + pi*y
+    assert (1 + x*y).subs({x: pi, y: 2}) == 1 + 2*pi
+
+    c2, c3, q1p, q2p, c1, s1, s2, s3 = symbols('c2 c3 q1p q2p c1 s1 s2 s3')
+    test = (c2**2*q2p*c3 + c1**2*s2**2*q2p*c3 + s1**2*s2**2*q2p*c3
+            - c1**2*q1p*c2*s3 - s1**2*q1p*c2*s3)
+    assert (test.subs({c1**2: 1 - s1**2, c2**2: 1 - s2**2, c3**3: 1 - s3**2})
+        == c3*q2p*(1 - s2**2) + c3*q2p*s2**2*(1 - s1**2)
+            - c2*q1p*s3*(1 - s1**2) + c3*q2p*s1**2*s2**2 - c2*q1p*s3*s1**2)
+
+
+def test_mul():
+    x, y, z, a, b, c = symbols('x y z a b c')
+    A, B, C = symbols('A B C', commutative=0)
+    assert (x*y*z).subs(z*x, y) == y**2
+    assert (z*x).subs(1/x, z) == 1
+    assert (x*y/z).subs(1/z, a) == a*x*y
+    assert (x*y/z).subs(x/z, a) == a*y
+    assert (x*y/z).subs(y/z, a) == a*x
+    assert (x*y/z).subs(x/z, 1/a) == y/a
+    assert (x*y/z).subs(x, 1/a) == y/(z*a)
+    assert (2*x*y).subs(5*x*y, z) != z*Rational(2, 5)
+    assert (x*y*A).subs(x*y, a) == a*A
+    assert (x**2*y**(x*Rational(3, 2))).subs(x*y**(x/2), 2) == 4*y**(x/2)
+    assert (x*exp(x*2)).subs(x*exp(x), 2) == 2*exp(x)
+    assert ((x**(2*y))**3).subs(x**y, 2) == 64
+    assert (x*A*B).subs(x*A, y) == y*B
+    assert (x*y*(1 + x)*(1 + x*y)).subs(x*y, 2) == 6*(1 + x)
+    assert ((1 + A*B)*A*B).subs(A*B, x*A*B)
+    assert (x*a/z).subs(x/z, A) == a*A
+    assert (x**3*A).subs(x**2*A, a) == a*x
+    assert (x**2*A*B).subs(x**2*B, a) == a*A
+    assert (x**2*A*B).subs(x**2*A, a) == a*B
+    assert (b*A**3/(a**3*c**3)).subs(a**4*c**3*A**3/b**4, z) == \
+        b*A**3/(a**3*c**3)
+    assert (6*x).subs(2*x, y) == 3*y
+    assert (y*exp(x*Rational(3, 2))).subs(y*exp(x), 2) == 2*exp(x/2)
+    assert (y*exp(x*Rational(3, 2))).subs(y*exp(x), 2) == 2*exp(x/2)
+    assert (A**2*B*A**2*B*A**2).subs(A*B*A, C) == A*C**2*A
+    assert (x*A**3).subs(x*A, y) == y*A**2
+    assert (x**2*A**3).subs(x*A, y) == y**2*A
+    assert (x*A**3).subs(x*A, B) == B*A**2
+    assert (x*A*B*A*exp(x*A*B)).subs(x*A, B) == B**2*A*exp(B*B)
+    assert (x**2*A*B*A*exp(x*A*B)).subs(x*A, B) == B**3*exp(B**2)
+    assert (x**3*A*exp(x*A*B)*A*exp(x*A*B)).subs(x*A, B) == \
+        x*B*exp(B**2)*B*exp(B**2)
+    assert (x*A*B*C*A*B).subs(x*A*B, C) == C**2*A*B
+    assert (-I*a*b).subs(a*b, 2) == -2*I
+
+    # issue 6361
+    assert (-8*I*a).subs(-2*a, 1) == 4*I
+    assert (-I*a).subs(-a, 1) == I
+
+    # issue 6441
+    assert (4*x**2).subs(2*x, y) == y**2
+    assert (2*4*x**2).subs(2*x, y) == 2*y**2
+    assert (-x**3/9).subs(-x/3, z) == -z**2*x
+    assert (-x**3/9).subs(x/3, z) == -z**2*x
+    assert (-2*x**3/9).subs(x/3, z) == -2*x*z**2
+    assert (-2*x**3/9).subs(-x/3, z) == -2*x*z**2
+    assert (-2*x**3/9).subs(-2*x, z) == z*x**2/9
+    assert (-2*x**3/9).subs(2*x, z) == -z*x**2/9
+    assert (2*(3*x/5/7)**2).subs(3*x/5, z) == 2*(Rational(1, 7))**2*z**2
+    assert (4*x).subs(-2*x, z) == 4*x  # try keep subs literal
+
+
+def test_subs_simple():
+    a = symbols('a', commutative=True)
+    x = symbols('x', commutative=False)
+
+    assert (2*a).subs(1, 3) == 2*a
+    assert (2*a).subs(2, 3) == 3*a
+    assert (2*a).subs(a, 3) == 6
+    assert sin(2).subs(1, 3) == sin(2)
+    assert sin(2).subs(2, 3) == sin(3)
+    assert sin(a).subs(a, 3) == sin(3)
+
+    assert (2*x).subs(1, 3) == 2*x
+    assert (2*x).subs(2, 3) == 3*x
+    assert (2*x).subs(x, 3) == 6
+    assert sin(x).subs(x, 3) == sin(3)
+
+
+def test_subs_constants():
+    a, b = symbols('a b', commutative=True)
+    x, y = symbols('x y', commutative=False)
+
+    assert (a*b).subs(2*a, 1) == a*b
+    assert (1.5*a*b).subs(a, 1) == 1.5*b
+    assert (2*a*b).subs(2*a, 1) == b
+    assert (2*a*b).subs(4*a, 1) == 2*a*b
+
+    assert (x*y).subs(2*x, 1) == x*y
+    assert (1.5*x*y).subs(x, 1) == 1.5*y
+    assert (2*x*y).subs(2*x, 1) == y
+    assert (2*x*y).subs(4*x, 1) == 2*x*y
+
+
+def test_subs_commutative():
+    a, b, c, d, K = symbols('a b c d K', commutative=True)
+
+    assert (a*b).subs(a*b, K) == K
+    assert (a*b*a*b).subs(a*b, K) == K**2
+    assert (a*a*b*b).subs(a*b, K) == K**2
+    assert (a*b*c*d).subs(a*b*c, K) == d*K
+    assert (a*b**c).subs(a, K) == K*b**c
+    assert (a*b**c).subs(b, K) == a*K**c
+    assert (a*b**c).subs(c, K) == a*b**K
+    assert (a*b*c*b*a).subs(a*b, K) == c*K**2
+    assert (a**3*b**2*a).subs(a*b, K) == a**2*K**2
+
+
+def test_subs_noncommutative():
+    w, x, y, z, L = symbols('w x y z L', commutative=False)
+    alpha = symbols('alpha', commutative=True)
+    someint = symbols('someint', commutative=True, integer=True)
+
+    assert (x*y).subs(x*y, L) == L
+    assert (w*y*x).subs(x*y, L) == w*y*x
+    assert (w*x*y*z).subs(x*y, L) == w*L*z
+    assert (x*y*x*y).subs(x*y, L) == L**2
+    assert (x*x*y).subs(x*y, L) == x*L
+    assert (x*x*y*y).subs(x*y, L) == x*L*y
+    assert (w*x*y).subs(x*y*z, L) == w*x*y
+    assert (x*y**z).subs(x, L) == L*y**z
+    assert (x*y**z).subs(y, L) == x*L**z
+    assert (x*y**z).subs(z, L) == x*y**L
+    assert (w*x*y*z*x*y).subs(x*y*z, L) == w*L*x*y
+    assert (w*x*y*y*w*x*x*y*x*y*y*x*y).subs(x*y, L) == w*L*y*w*x*L**2*y*L
+
+    # Check fractional power substitutions. It should not do
+    # substitutions that choose a value for noncommutative log,
+    # or inverses that don't already appear in the expressions.
+    assert (x*x*x).subs(x*x, L) == L*x
+    assert (x*x*x*y*x*x*x*x).subs(x*x, L) == L*x*y*L**2
+    for p in range(1, 5):
+        for k in range(10):
+            assert (y * x**k).subs(x**p, L) == y * L**(k//p) * x**(k % p)
+    assert (x**Rational(3, 2)).subs(x**S.Half, L) == x**Rational(3, 2)
+    assert (x**S.Half).subs(x**S.Half, L) == L
+    assert (x**Rational(-1, 2)).subs(x**S.Half, L) == x**Rational(-1, 2)
+    assert (x**Rational(-1, 2)).subs(x**Rational(-1, 2), L) == L
+
+    assert (x**(2*someint)).subs(x**someint, L) == L**2
+    assert (x**(2*someint + 3)).subs(x**someint, L) == L**2*x**3
+    assert (x**(3*someint + 3)).subs(x**someint, L) == L**3*x**3
+    assert (x**(3*someint)).subs(x**(2*someint), L) == L * x**someint
+    assert (x**(4*someint)).subs(x**(2*someint), L) == L**2
+    assert (x**(4*someint + 1)).subs(x**(2*someint), L) == L**2 * x
+    assert (x**(4*someint)).subs(x**(3*someint), L) == L * x**someint
+    assert (x**(4*someint + 1)).subs(x**(3*someint), L) == L * x**(someint + 1)
+
+    assert (x**(2*alpha)).subs(x**alpha, L) == x**(2*alpha)
+    assert (x**(2*alpha + 2)).subs(x**2, L) == x**(2*alpha + 2)
+    assert ((2*z)**alpha).subs(z**alpha, y) == (2*z)**alpha
+    assert (x**(2*someint*alpha)).subs(x**someint, L) == x**(2*someint*alpha)
+    assert (x**(2*someint + alpha)).subs(x**someint, L) == x**(2*someint + alpha)
+
+    # This could in principle be substituted, but is not currently
+    # because it requires recognizing that someint**2 is divisible by
+    # someint.
+    assert (x**(someint**2 + 3)).subs(x**someint, L) == x**(someint**2 + 3)
+
+    # alpha**z := exp(log(alpha) z) is usually well-defined
+    assert (4**z).subs(2**z, y) == y**2
+
+    # Negative powers
+    assert (x**(-1)).subs(x**3, L) == x**(-1)
+    assert (x**(-2)).subs(x**3, L) == x**(-2)
+    assert (x**(-3)).subs(x**3, L) == L**(-1)
+    assert (x**(-4)).subs(x**3, L) == L**(-1) * x**(-1)
+    assert (x**(-5)).subs(x**3, L) == L**(-1) * x**(-2)
+
+    assert (x**(-1)).subs(x**(-3), L) == x**(-1)
+    assert (x**(-2)).subs(x**(-3), L) == x**(-2)
+    assert (x**(-3)).subs(x**(-3), L) == L
+    assert (x**(-4)).subs(x**(-3), L) == L * x**(-1)
+    assert (x**(-5)).subs(x**(-3), L) == L * x**(-2)
+
+    assert (x**1).subs(x**(-3), L) == x
+    assert (x**2).subs(x**(-3), L) == x**2
+    assert (x**3).subs(x**(-3), L) == L**(-1)
+    assert (x**4).subs(x**(-3), L) == L**(-1) * x
+    assert (x**5).subs(x**(-3), L) == L**(-1) * x**2
+
+
+def test_subs_basic_funcs():
+    a, b, c, d, K = symbols('a b c d K', commutative=True)
+    w, x, y, z, L = symbols('w x y z L', commutative=False)
+
+    assert (x + y).subs(x + y, L) == L
+    assert (x - y).subs(x - y, L) == L
+    assert (x/y).subs(x, L) == L/y
+    assert (x**y).subs(x, L) == L**y
+    assert (x**y).subs(y, L) == x**L
+    assert ((a - c)/b).subs(b, K) == (a - c)/K
+    assert (exp(x*y - z)).subs(x*y, L) == exp(L - z)
+    assert (a*exp(x*y - w*z) + b*exp(x*y + w*z)).subs(z, 0) == \
+        a*exp(x*y) + b*exp(x*y)
+    assert ((a - b)/(c*d - a*b)).subs(c*d - a*b, K) == (a - b)/K
+    assert (w*exp(a*b - c)*x*y/4).subs(x*y, L) == w*exp(a*b - c)*L/4
+
+
+def test_subs_wild():
+    R, S, T, U = symbols('R S T U', cls=Wild)
+
+    assert (R*S).subs(R*S, T) == T
+    assert (S*R).subs(R*S, T) == T
+    assert (R + S).subs(R + S, T) == T
+    assert (R**S).subs(R, T) == T**S
+    assert (R**S).subs(S, T) == R**T
+    assert (R*S**T).subs(R, U) == U*S**T
+    assert (R*S**T).subs(S, U) == R*U**T
+    assert (R*S**T).subs(T, U) == R*S**U
+
+
+def test_subs_mixed():
+    a, b, c, d, K = symbols('a b c d K', commutative=True)
+    w, x, y, z, L = symbols('w x y z L', commutative=False)
+    R, S, T, U = symbols('R S T U', cls=Wild)
+
+    assert (a*x*y).subs(x*y, L) == a*L
+    assert (a*b*x*y*x).subs(x*y, L) == a*b*L*x
+    assert (R*x*y*exp(x*y)).subs(x*y, L) == R*L*exp(L)
+    assert (a*x*y*y*x - x*y*z*exp(a*b)).subs(x*y, L) == a*L*y*x - L*z*exp(a*b)
+    e = c*y*x*y*x**(R*S - a*b) - T*(a*R*b*S)
+    assert e.subs(x*y, L).subs(a*b, K).subs(R*S, U) == \
+        c*y*L*x**(U - K) - T*(U*K)
+
+
+def test_division():
+    a, b, c = symbols('a b c', commutative=True)
+    x, y, z = symbols('x y z', commutative=True)
+
+    assert (1/a).subs(a, c) == 1/c
+    assert (1/a**2).subs(a, c) == 1/c**2
+    assert (1/a**2).subs(a, -2) == Rational(1, 4)
+    assert (-(1/a**2)).subs(a, -2) == Rational(-1, 4)
+
+    assert (1/x).subs(x, z) == 1/z
+    assert (1/x**2).subs(x, z) == 1/z**2
+    assert (1/x**2).subs(x, -2) == Rational(1, 4)
+    assert (-(1/x**2)).subs(x, -2) == Rational(-1, 4)
+
+    #issue 5360
+    assert (1/x).subs(x, 0) == 1/S.Zero
+
+
+def test_add():
+    a, b, c, d, x, y, t = symbols('a b c d x y t')
+
+    assert (a**2 - b - c).subs(a**2 - b, d) in [d - c, a**2 - b - c]
+    assert (a**2 - c).subs(a**2 - c, d) == d
+    assert (a**2 - b - c).subs(a**2 - c, d) in [d - b, a**2 - b - c]
+    assert (a**2 - x - c).subs(a**2 - c, d) in [d - x, a**2 - x - c]
+    assert (a**2 - b - sqrt(a)).subs(a**2 - sqrt(a), c) == c - b
+    assert (a + b + exp(a + b)).subs(a + b, c) == c + exp(c)
+    assert (c + b + exp(c + b)).subs(c + b, a) == a + exp(a)
+    assert (a + b + c + d).subs(b + c, x) == a + d + x
+    assert (a + b + c + d).subs(-b - c, x) == a + d - x
+    assert ((x + 1)*y).subs(x + 1, t) == t*y
+    assert ((-x - 1)*y).subs(x + 1, t) == -t*y
+    assert ((x - 1)*y).subs(x + 1, t) == y*(t - 2)
+    assert ((-x + 1)*y).subs(x + 1, t) == y*(-t + 2)
+
+    # this should work every time:
+    e = a**2 - b - c
+    assert e.subs(Add(*e.args[:2]), d) == d + e.args[2]
+    assert e.subs(a**2 - c, d) == d - b
+
+    # the fallback should recognize when a change has
+    # been made; while .1 == Rational(1, 10) they are not the same
+    # and the change should be made
+    assert (0.1 + a).subs(0.1, Rational(1, 10)) == Rational(1, 10) + a
+
+    e = (-x*(-y + 1) - y*(y - 1))
+    ans = (-x*(x) - y*(-x)).expand()
+    assert e.subs(-y + 1, x) == ans
+
+    #Test issue 18747
+    assert (exp(x) + cos(x)).subs(x, oo) == oo
+    assert Add(*[AccumBounds(-1, 1), oo]) == oo
+    assert Add(*[oo, AccumBounds(-1, 1)]) == oo
+
+
+def test_subs_issue_4009():
+    assert (I*Symbol('a')).subs(1, 2) == I*Symbol('a')
+
+
+def test_functions_subs():
+    f, g = symbols('f g', cls=Function)
+    l = Lambda((x, y), sin(x) + y)
+    assert (g(y, x) + cos(x)).subs(g, l) == sin(y) + x + cos(x)
+    assert (f(x)**2).subs(f, sin) == sin(x)**2
+    assert (f(x, y)).subs(f, log) == log(x, y)
+    assert (f(x, y)).subs(f, sin) == f(x, y)
+    assert (sin(x) + atan2(x, y)).subs([[atan2, f], [sin, g]]) == \
+        f(x, y) + g(x)
+    assert (g(f(x + y, x))).subs([[f, l], [g, exp]]) == exp(x + sin(x + y))
+
+
+def test_derivative_subs():
+    f = Function('f')
+    g = Function('g')
+    assert Derivative(f(x), x).subs(f(x), y) != 0
+    # need xreplace to put the function back, see #13803
+    assert Derivative(f(x), x).subs(f(x), y).xreplace({y: f(x)}) == \
+        Derivative(f(x), x)
+    # issues 5085, 5037
+    assert cse(Derivative(f(x), x) + f(x))[1][0].has(Derivative)
+    assert cse(Derivative(f(x, y), x) +
+               Derivative(f(x, y), y))[1][0].has(Derivative)
+    eq = Derivative(g(x), g(x))
+    assert eq.subs(g, f) == Derivative(f(x), f(x))
+    assert eq.subs(g(x), f(x)) == Derivative(f(x), f(x))
+    assert eq.subs(g, cos) == Subs(Derivative(y, y), y, cos(x))
+
+
+def test_derivative_subs2():
+    f_func, g_func = symbols('f g', cls=Function)
+    f, g = f_func(x, y, z), g_func(x, y, z)
+    assert Derivative(f, x, y).subs(Derivative(f, x, y), g) == g
+    assert Derivative(f, y, x).subs(Derivative(f, x, y), g) == g
+    assert Derivative(f, x, y).subs(Derivative(f, x), g) == Derivative(g, y)
+    assert Derivative(f, x, y).subs(Derivative(f, y), g) == Derivative(g, x)
+    assert (Derivative(f, x, y, z).subs(
+                Derivative(f, x, z), g) == Derivative(g, y))
+    assert (Derivative(f, x, y, z).subs(
+                Derivative(f, z, y), g) == Derivative(g, x))
+    assert (Derivative(f, x, y, z).subs(
+                Derivative(f, z, y, x), g) == g)
+
+    # Issue 9135
+    assert (Derivative(f, x, x, y).subs(
+                Derivative(f, y, y), g) == Derivative(f, x, x, y))
+    assert (Derivative(f, x, y, y, z).subs(
+                Derivative(f, x, y, y, y), g) == Derivative(f, x, y, y, z))
+
+    assert Derivative(f, x, y).subs(Derivative(f_func(x), x, y), g) == Derivative(f, x, y)
+
+
+def test_derivative_subs3():
+    dex = Derivative(exp(x), x)
+    assert Derivative(dex, x).subs(dex, exp(x)) == dex
+    assert dex.subs(exp(x), dex) == Derivative(exp(x), x, x)
+
+
+def test_issue_5284():
+    A, B = symbols('A B', commutative=False)
+    assert (x*A).subs(x**2*A, B) == x*A
+    assert (A**2).subs(A**3, B) == A**2
+    assert (A**6).subs(A**3, B) == B**2
+
+
+def test_subs_iter():
+    assert x.subs(reversed([[x, y]])) == y
+    it = iter([[x, y]])
+    assert x.subs(it) == y
+    assert x.subs(Tuple((x, y))) == y
+
+
+def test_subs_dict():
+    a, b, c, d, e = symbols('a b c d e')
+
+    assert (2*x + y + z).subs({"x": 1, "y": 2}) == 4 + z
+
+    l = [(sin(x), 2), (x, 1)]
+    assert (sin(x)).subs(l) == \
+           (sin(x)).subs(dict(l)) == 2
+    assert sin(x).subs(reversed(l)) == sin(1)
+
+    expr = sin(2*x) + sqrt(sin(2*x))*cos(2*x)*sin(exp(x)*x)
+    reps = {sin(2*x): c,
+               sqrt(sin(2*x)): a,
+               cos(2*x): b,
+               exp(x): e,
+               x: d,}
+    assert expr.subs(reps) == c + a*b*sin(d*e)
+
+    l = [(x, 3), (y, x**2)]
+    assert (x + y).subs(l) == 3 + x**2
+    assert (x + y).subs(reversed(l)) == 12
+
+    # If changes are made to convert lists into dictionaries and do
+    # a dictionary-lookup replacement, these tests will help to catch
+    # some logical errors that might occur
+    l = [(y, z + 2), (1 + z, 5), (z, 2)]
+    assert (y - 1 + 3*x).subs(l) == 5 + 3*x
+    l = [(y, z + 2), (z, 3)]
+    assert (y - 2).subs(l) == 3
+
+
+def test_no_arith_subs_on_floats():
+    assert (x + 3).subs(x + 3, a) == a
+    assert (x + 3).subs(x + 2, a) == a + 1
+
+    assert (x + y + 3).subs(x + 3, a) == a + y
+    assert (x + y + 3).subs(x + 2, a) == a + y + 1
+
+    assert (x + 3.0).subs(x + 3.0, a) == a
+    assert (x + 3.0).subs(x + 2.0, a) == x + 3.0
+
+    assert (x + y + 3.0).subs(x + 3.0, a) == a + y
+    assert (x + y + 3.0).subs(x + 2.0, a) == x + y + 3.0
+
+
+def test_issue_5651():
+    a, b, c, K = symbols('a b c K', commutative=True)
+    assert (a/(b*c)).subs(b*c, K) == a/K
+    assert (a/(b**2*c**3)).subs(b*c, K) == a/(c*K**2)
+    assert (1/(x*y)).subs(x*y, 2) == S.Half
+    assert ((1 + x*y)/(x*y)).subs(x*y, 1) == 2
+    assert (x*y*z).subs(x*y, 2) == 2*z
+    assert ((1 + x*y)/(x*y)/z).subs(x*y, 1) == 2/z
+
+
+def test_issue_6075():
+    assert Tuple(1, True).subs(1, 2) == Tuple(2, True)
+
+
+def test_issue_6079():
+    # since x + 2.0 == x + 2 we can't do a simple equality test
+    assert _aresame((x + 2.0).subs(2, 3), x + 2.0)
+    assert _aresame((x + 2.0).subs(2.0, 3), x + 3)
+    assert not _aresame(x + 2, x + 2.0)
+    assert not _aresame(Basic(cos(x), S(1)), Basic(cos(x), S(1.)))
+    assert _aresame(cos, cos)
+    assert not _aresame(1, S.One)
+    assert not _aresame(x, symbols('x', positive=True))
+
+
+def test_issue_4680():
+    N = Symbol('N')
+    assert N.subs({"N": 3}) == 3
+
+
+def test_issue_6158():
+    assert (x - 1).subs(1, y) == x - y
+    assert (x - 1).subs(-1, y) == x + y
+    assert (x - oo).subs(oo, y) == x - y
+    assert (x - oo).subs(-oo, y) == x + y
+
+
+def test_Function_subs():
+    f, g, h, i = symbols('f g h i', cls=Function)
+    p = Piecewise((g(f(x, y)), x < -1), (g(x), x <= 1))
+    assert p.subs(g, h) == Piecewise((h(f(x, y)), x < -1), (h(x), x <= 1))
+    assert (f(y) + g(x)).subs({f: h, g: i}) == i(x) + h(y)
+
+
+def test_simultaneous_subs():
+    reps = {x: 0, y: 0}
+    assert (x/y).subs(reps) != (y/x).subs(reps)
+    assert (x/y).subs(reps, simultaneous=True) == \
+        (y/x).subs(reps, simultaneous=True)
+    reps = reps.items()
+    assert (x/y).subs(reps) != (y/x).subs(reps)
+    assert (x/y).subs(reps, simultaneous=True) == \
+        (y/x).subs(reps, simultaneous=True)
+    assert Derivative(x, y, z).subs(reps, simultaneous=True) == \
+        Subs(Derivative(0, y, z), y, 0)
+
+
+def test_issue_6419_6421():
+    assert (1/(1 + x/y)).subs(x/y, x) == 1/(1 + x)
+    assert (-2*I).subs(2*I, x) == -x
+    assert (-I*x).subs(I*x, x) == -x
+    assert (-3*I*y**4).subs(3*I*y**2, x) == -x*y**2
+
+
+def test_issue_6559():
+    assert (-12*x + y).subs(-x, 1) == 12 + y
+    # though this involves cse it generated a failure in Mul._eval_subs
+    x0, x1 = symbols('x0 x1')
+    e = -log(-12*sqrt(2) + 17)/24 - log(-2*sqrt(2) + 3)/12 + sqrt(2)/3
+    # XXX modify cse so x1 is eliminated and x0 = -sqrt(2)?
+    assert cse(e) == (
+        [(x0, sqrt(2))], [x0/3 - log(-12*x0 + 17)/24 - log(-2*x0 + 3)/12])
+
+
+def test_issue_5261():
+    x = symbols('x', real=True)
+    e = I*x
+    assert exp(e).subs(exp(x), y) == y**I
+    assert (2**e).subs(2**x, y) == y**I
+    eq = (-2)**e
+    assert eq.subs((-2)**x, y) == eq
+
+
+def test_issue_6923():
+    assert (-2*x*sqrt(2)).subs(2*x, y) == -sqrt(2)*y
+
+
+def test_2arg_hack():
+    N = Symbol('N', commutative=False)
+    ans = Mul(2, y + 1, evaluate=False)
+    assert (2*x*(y + 1)).subs(x, 1, hack2=True) == ans
+    assert (2*(y + 1 + N)).subs(N, 0, hack2=True) == ans
+
+
+@XFAIL
+def test_mul2():
+    """When this fails, remove things labelled "2-arg hack"
+    1) remove special handling in the fallback of subs that
+    was added in the same commit as this test
+    2) remove the special handling in Mul.flatten
+    """
+    assert (2*(x + 1)).is_Mul
+
+
+def test_noncommutative_subs():
+    x,y = symbols('x,y', commutative=False)
+    assert (x*y*x).subs([(x, x*y), (y, x)], simultaneous=True) == (x*y*x**2*y)
+
+
+def test_issue_2877():
+    f = Float(2.0)
+    assert (x + f).subs({f: 2}) == x + 2
+
+    def r(a, b, c):
+        return factor(a*x**2 + b*x + c)
+    e = r(5.0/6, 10, 5)
+    assert nsimplify(e) == 5*x**2/6 + 10*x + 5
+
+
+def test_issue_5910():
+    t = Symbol('t')
+    assert (1/(1 - t)).subs(t, 1) is zoo
+    n = t
+    d = t - 1
+    assert (n/d).subs(t, 1) is zoo
+    assert (-n/-d).subs(t, 1) is zoo
+
+
+def test_issue_5217():
+    s = Symbol('s')
+    z = (1 - 2*x*x)
+    w = (1 + 2*x*x)
+    q = 2*x*x*2*y*y
+    sub = {2*x*x: s}
+    assert w.subs(sub) == 1 + s
+    assert z.subs(sub) == 1 - s
+    assert q == 4*x**2*y**2
+    assert q.subs(sub) == 2*y**2*s
+
+
+def test_issue_10829():
+    assert (4**x).subs(2**x, y) == y**2
+    assert (9**x).subs(3**x, y) == y**2
+
+
+def test_pow_eval_subs_no_cache():
+    # Tests pull request 9376 is working
+    from sympy.core.cache import clear_cache
+
+    s = 1/sqrt(x**2)
+    # This bug only appeared when the cache was turned off.
+    # We need to approximate running this test without the cache.
+    # This creates approximately the same situation.
+    clear_cache()
+
+    # This used to fail with a wrong result.
+    # It incorrectly returned 1/sqrt(x**2) before this pull request.
+    result = s.subs(sqrt(x**2), y)
+    assert result == 1/y
+
+
+def test_RootOf_issue_10092():
+    x = Symbol('x', real=True)
+    eq = x**3 - 17*x**2 + 81*x - 118
+    r = RootOf(eq, 0)
+    assert (x < r).subs(x, r) is S.false
+
+
+def test_issue_8886():
+    from sympy.physics.mechanics import ReferenceFrame as R
+    # if something can't be sympified we assume that it
+    # doesn't play well with SymPy and disallow the
+    # substitution
+    v = R('A').x
+    raises(SympifyError, lambda: x.subs(x, v))
+    raises(SympifyError, lambda: v.subs(v, x))
+    assert v.__eq__(x) is False
+
+
+def test_issue_12657():
+    # treat -oo like the atom that it is
+    reps = [(-oo, 1), (oo, 2)]
+    assert (x < -oo).subs(reps) == (x < 1)
+    assert (x < -oo).subs(list(reversed(reps))) == (x < 1)
+    reps = [(-oo, 2), (oo, 1)]
+    assert (x < oo).subs(reps) == (x < 1)
+    assert (x < oo).subs(list(reversed(reps))) == (x < 1)
+
+
+def test_recurse_Application_args():
+    F = Lambda((x, y), exp(2*x + 3*y))
+    f = Function('f')
+    A = f(x, f(x, x))
+    C = F(x, F(x, x))
+    assert A.subs(f, F) == A.replace(f, F) == C
+
+
+def test_Subs_subs():
+    assert Subs(x*y, x, x).subs(x, y) == Subs(x*y, x, y)
+    assert Subs(x*y, x, x + 1).subs(x, y) == \
+        Subs(x*y, x, y + 1)
+    assert Subs(x*y, y, x + 1).subs(x, y) == \
+        Subs(y**2, y, y + 1)
+    a = Subs(x*y*z, (y, x, z), (x + 1, x + z, x))
+    b = Subs(x*y*z, (y, x, z), (x + 1, y + z, y))
+    assert a.subs(x, y) == b and \
+        a.doit().subs(x, y) == a.subs(x, y).doit()
+    f = Function('f')
+    g = Function('g')
+    assert Subs(2*f(x, y) + g(x), f(x, y), 1).subs(y, 2) == Subs(
+        2*f(x, y) + g(x), (f(x, y), y), (1, 2))
+
+
+def test_issue_13333():
+    eq = 1/x
+    assert eq.subs({"x": '1/2'}) == 2
+    assert eq.subs({"x": '(1/2)'}) == 2
+
+
+def test_issue_15234():
+    x, y = symbols('x y', real=True)
+    p = 6*x**5 + x**4 - 4*x**3 + 4*x**2 - 2*x + 3
+    p_subbed = 6*x**5 - 4*x**3 - 2*x + y**4 + 4*y**2 + 3
+    assert p.subs([(x**i, y**i) for i in [2, 4]]) == p_subbed
+    x, y = symbols('x y', complex=True)
+    p = 6*x**5 + x**4 - 4*x**3 + 4*x**2 - 2*x + 3
+    p_subbed = 6*x**5 - 4*x**3 - 2*x + y**4 + 4*y**2 + 3
+    assert p.subs([(x**i, y**i) for i in [2, 4]]) == p_subbed
+
+
+def test_issue_6976():
+    x, y = symbols('x y')
+    assert (sqrt(x)**3 + sqrt(x) + x + x**2).subs(sqrt(x), y) == \
+        y**4 + y**3 + y**2 + y
+    assert (x**4 + x**3 + x**2 + x + sqrt(x)).subs(x**2, y) == \
+        sqrt(x) + x**3 + x + y**2 + y
+    assert x.subs(x**3, y) == x
+    assert x.subs(x**Rational(1, 3), y) == y**3
+
+    # More substitutions are possible with nonnegative symbols
+    x, y = symbols('x y', nonnegative=True)
+    assert (x**4 + x**3 + x**2 + x + sqrt(x)).subs(x**2, y) == \
+        y**Rational(1, 4) + y**Rational(3, 2) + sqrt(y) + y**2 + y
+    assert x.subs(x**3, y) == y**Rational(1, 3)
+
+
+def test_issue_11746():
+    assert (1/x).subs(x**2, 1) == 1/x
+    assert (1/(x**3)).subs(x**2, 1) == x**(-3)
+    assert (1/(x**4)).subs(x**2, 1) == 1
+    assert (1/(x**3)).subs(x**4, 1) == x**(-3)
+    assert (1/(y**5)).subs(x**5, 1) == y**(-5)
+
+
+def test_issue_17823():
+    from sympy.physics.mechanics import dynamicsymbols
+    q1, q2 = dynamicsymbols('q1, q2')
+    expr = q1.diff().diff()**2*q1 + q1.diff()*q2.diff()
+    reps={q1: a, q1.diff(): a*x*y, q1.diff().diff(): z}
+    assert expr.subs(reps) == a*x*y*Derivative(q2, t) + a*z**2
+
+
+def test_issue_19326():
+    x, y = [i(t) for i in map(Function, 'xy')]
+    assert (x*y).subs({x: 1 + x, y: x}) == (1 + x)*x
+
+
+def test_issue_19558():
+    e = (7*x*cos(x) - 12*log(x)**3)*(-log(x)**4 + 2*sin(x) + 1)**2/ \
+    (2*(x*cos(x) - 2*log(x)**3)*(3*log(x)**4 - 7*sin(x) + 3)**2)
+
+    assert e.subs(x, oo) == AccumBounds(-oo, oo)
+    assert (sin(x) + cos(x)).subs(x, oo) == AccumBounds(-2, 2)
+
+
+def test_issue_22033():
+    xr = Symbol('xr', real=True)
+    e = (1/xr)
+    assert e.subs(xr**2, y) == e
+
+
+def test_guard_against_indeterminate_evaluation():
+    eq = x**y
+    assert eq.subs([(x, 1), (y, oo)]) == 1  # because 1**y == 1
+    assert eq.subs([(y, oo), (x, 1)]) is S.NaN
+    assert eq.subs({x: 1, y: oo}) is S.NaN
+    assert eq.subs([(x, 1), (y, oo)], simultaneous=True) is S.NaN
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_symbol.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_symbol.py
new file mode 100644
index 0000000000000000000000000000000000000000..acf27700825c4822456207afe95108480505ce2c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_symbol.py
@@ -0,0 +1,421 @@
+import threading
+
+from sympy.core.function import Function, UndefinedFunction
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.relational import (GreaterThan, LessThan, StrictGreaterThan, StrictLessThan)
+from sympy.core.symbol import (Dummy, Symbol, Wild, symbols)
+from sympy.core.sympify import sympify  # can't import as S yet
+from sympy.core.symbol import uniquely_named_symbol, _symbol, Str
+
+from sympy.testing.pytest import raises, skip_under_pyodide
+from sympy.core.symbol import disambiguate
+
+
+def test_Str():
+    a1 = Str('a')
+    a2 = Str('a')
+    b = Str('b')
+    assert a1 == a2 != b
+    raises(TypeError, lambda: Str())
+
+
+def test_Symbol():
+    a = Symbol("a")
+    x1 = Symbol("x")
+    x2 = Symbol("x")
+    xdummy1 = Dummy("x")
+    xdummy2 = Dummy("x")
+
+    assert a != x1
+    assert a != x2
+    assert x1 == x2
+    assert x1 != xdummy1
+    assert xdummy1 != xdummy2
+
+    assert Symbol("x") == Symbol("x")
+    assert Dummy("x") != Dummy("x")
+    d = symbols('d', cls=Dummy)
+    assert isinstance(d, Dummy)
+    c, d = symbols('c,d', cls=Dummy)
+    assert isinstance(c, Dummy)
+    assert isinstance(d, Dummy)
+    raises(TypeError, lambda: Symbol())
+
+
+def test_Dummy():
+    assert Dummy() != Dummy()
+
+
+def test_Dummy_force_dummy_index():
+    raises(AssertionError, lambda: Dummy(dummy_index=1))
+    assert Dummy('d', dummy_index=2) == Dummy('d', dummy_index=2)
+    assert Dummy('d1', dummy_index=2) != Dummy('d2', dummy_index=2)
+    d1 = Dummy('d', dummy_index=3)
+    d2 = Dummy('d')
+    # might fail if d1 were created with dummy_index >= 10**6
+    assert d1 != d2
+    d3 = Dummy('d', dummy_index=3)
+    assert d1 == d3
+    assert Dummy()._count == Dummy('d', dummy_index=3)._count
+
+
+def test_lt_gt():
+    S = sympify
+    x, y = Symbol('x'), Symbol('y')
+
+    assert (x >= y) == GreaterThan(x, y)
+    assert (x >= 0) == GreaterThan(x, 0)
+    assert (x <= y) == LessThan(x, y)
+    assert (x <= 0) == LessThan(x, 0)
+
+    assert (0 <= x) == GreaterThan(x, 0)
+    assert (0 >= x) == LessThan(x, 0)
+    assert (S(0) >= x) == GreaterThan(0, x)
+    assert (S(0) <= x) == LessThan(0, x)
+
+    assert (x > y) == StrictGreaterThan(x, y)
+    assert (x > 0) == StrictGreaterThan(x, 0)
+    assert (x < y) == StrictLessThan(x, y)
+    assert (x < 0) == StrictLessThan(x, 0)
+
+    assert (0 < x) == StrictGreaterThan(x, 0)
+    assert (0 > x) == StrictLessThan(x, 0)
+    assert (S(0) > x) == StrictGreaterThan(0, x)
+    assert (S(0) < x) == StrictLessThan(0, x)
+
+    e = x**2 + 4*x + 1
+    assert (e >= 0) == GreaterThan(e, 0)
+    assert (0 <= e) == GreaterThan(e, 0)
+    assert (e > 0) == StrictGreaterThan(e, 0)
+    assert (0 < e) == StrictGreaterThan(e, 0)
+
+    assert (e <= 0) == LessThan(e, 0)
+    assert (0 >= e) == LessThan(e, 0)
+    assert (e < 0) == StrictLessThan(e, 0)
+    assert (0 > e) == StrictLessThan(e, 0)
+
+    assert (S(0) >= e) == GreaterThan(0, e)
+    assert (S(0) <= e) == LessThan(0, e)
+    assert (S(0) < e) == StrictLessThan(0, e)
+    assert (S(0) > e) == StrictGreaterThan(0, e)
+
+
+def test_no_len():
+    # there should be no len for numbers
+    x = Symbol('x')
+    raises(TypeError, lambda: len(x))
+
+
+def test_ineq_unequal():
+    S = sympify
+    x, y, z = symbols('x,y,z')
+
+    e = (
+        S(-1) >= x, S(-1) >= y, S(-1) >= z,
+        S(-1) > x, S(-1) > y, S(-1) > z,
+        S(-1) <= x, S(-1) <= y, S(-1) <= z,
+        S(-1) < x, S(-1) < y, S(-1) < z,
+        S(0) >= x, S(0) >= y, S(0) >= z,
+        S(0) > x, S(0) > y, S(0) > z,
+        S(0) <= x, S(0) <= y, S(0) <= z,
+        S(0) < x, S(0) < y, S(0) < z,
+        S('3/7') >= x, S('3/7') >= y, S('3/7') >= z,
+        S('3/7') > x, S('3/7') > y, S('3/7') > z,
+        S('3/7') <= x, S('3/7') <= y, S('3/7') <= z,
+        S('3/7') < x, S('3/7') < y, S('3/7') < z,
+        S(1.5) >= x, S(1.5) >= y, S(1.5) >= z,
+        S(1.5) > x, S(1.5) > y, S(1.5) > z,
+        S(1.5) <= x, S(1.5) <= y, S(1.5) <= z,
+        S(1.5) < x, S(1.5) < y, S(1.5) < z,
+        S(2) >= x, S(2) >= y, S(2) >= z,
+        S(2) > x, S(2) > y, S(2) > z,
+        S(2) <= x, S(2) <= y, S(2) <= z,
+        S(2) < x, S(2) < y, S(2) < z,
+        x >= -1, y >= -1, z >= -1,
+        x > -1, y > -1, z > -1,
+        x <= -1, y <= -1, z <= -1,
+        x < -1, y < -1, z < -1,
+        x >= 0, y >= 0, z >= 0,
+        x > 0, y > 0, z > 0,
+        x <= 0, y <= 0, z <= 0,
+        x < 0, y < 0, z < 0,
+        x >= 1.5, y >= 1.5, z >= 1.5,
+        x > 1.5, y > 1.5, z > 1.5,
+        x <= 1.5, y <= 1.5, z <= 1.5,
+        x < 1.5, y < 1.5, z < 1.5,
+        x >= 2, y >= 2, z >= 2,
+        x > 2, y > 2, z > 2,
+        x <= 2, y <= 2, z <= 2,
+        x < 2, y < 2, z < 2,
+
+        x >= y, x >= z, y >= x, y >= z, z >= x, z >= y,
+        x > y, x > z, y > x, y > z, z > x, z > y,
+        x <= y, x <= z, y <= x, y <= z, z <= x, z <= y,
+        x < y, x < z, y < x, y < z, z < x, z < y,
+
+        x - pi >= y + z, y - pi >= x + z, z - pi >= x + y,
+        x - pi > y + z, y - pi > x + z, z - pi > x + y,
+        x - pi <= y + z, y - pi <= x + z, z - pi <= x + y,
+        x - pi < y + z, y - pi < x + z, z - pi < x + y,
+        True, False
+    )
+
+    left_e = e[:-1]
+    for i, e1 in enumerate( left_e ):
+        for e2 in e[i + 1:]:
+            assert e1 != e2
+
+
+def test_Wild_properties():
+    S = sympify
+    # these tests only include Atoms
+    x = Symbol("x")
+    y = Symbol("y")
+    p = Symbol("p", positive=True)
+    k = Symbol("k", integer=True)
+    n = Symbol("n", integer=True, positive=True)
+
+    given_patterns = [ x, y, p, k, -k, n, -n, S(-3), S(3),
+                       pi, Rational(3, 2), I ]
+
+    integerp = lambda k: k.is_integer
+    positivep = lambda k: k.is_positive
+    symbolp = lambda k: k.is_Symbol
+    realp = lambda k: k.is_extended_real
+
+    S = Wild("S", properties=[symbolp])
+    R = Wild("R", properties=[realp])
+    Y = Wild("Y", exclude=[x, p, k, n])
+    P = Wild("P", properties=[positivep])
+    K = Wild("K", properties=[integerp])
+    N = Wild("N", properties=[positivep, integerp])
+
+    given_wildcards = [ S, R, Y, P, K, N ]
+
+    goodmatch = {
+        S: (x, y, p, k, n),
+        R: (p, k, -k, n, -n, -3, 3, pi, Rational(3, 2)),
+        Y: (y, -3, 3, pi, Rational(3, 2), I ),
+        P: (p, n, 3, pi, Rational(3, 2)),
+        K: (k, -k, n, -n, -3, 3),
+        N: (n, 3)}
+
+    for A in given_wildcards:
+        for pat in given_patterns:
+            d = pat.match(A)
+            if pat in goodmatch[A]:
+                assert d[A] in goodmatch[A]
+            else:
+                assert d is None
+
+
+def test_symbols():
+    x = Symbol('x')
+    y = Symbol('y')
+    z = Symbol('z')
+
+    assert symbols('x') == x
+    assert symbols('x ') == x
+    assert symbols(' x ') == x
+    assert symbols('x,') == (x,)
+    assert symbols('x, ') == (x,)
+    assert symbols('x ,') == (x,)
+
+    assert symbols('x , y') == (x, y)
+
+    assert symbols('x,y,z') == (x, y, z)
+    assert symbols('x y z') == (x, y, z)
+
+    assert symbols('x,y,z,') == (x, y, z)
+    assert symbols('x y z ') == (x, y, z)
+
+    xyz = Symbol('xyz')
+    abc = Symbol('abc')
+
+    assert symbols('xyz') == xyz
+    assert symbols('xyz,') == (xyz,)
+    assert symbols('xyz,abc') == (xyz, abc)
+
+    assert symbols(('xyz',)) == (xyz,)
+    assert symbols(('xyz,',)) == ((xyz,),)
+    assert symbols(('x,y,z,',)) == ((x, y, z),)
+    assert symbols(('xyz', 'abc')) == (xyz, abc)
+    assert symbols(('xyz,abc',)) == ((xyz, abc),)
+    assert symbols(('xyz,abc', 'x,y,z')) == ((xyz, abc), (x, y, z))
+
+    assert symbols(('x', 'y', 'z')) == (x, y, z)
+    assert symbols(['x', 'y', 'z']) == [x, y, z]
+    assert symbols({'x', 'y', 'z'}) == {x, y, z}
+
+    raises(ValueError, lambda: symbols(''))
+    raises(ValueError, lambda: symbols(','))
+    raises(ValueError, lambda: symbols('x,,y,,z'))
+    raises(ValueError, lambda: symbols(('x', '', 'y', '', 'z')))
+
+    a, b = symbols('x,y', real=True)
+    assert a.is_real and b.is_real
+
+    x0 = Symbol('x0')
+    x1 = Symbol('x1')
+    x2 = Symbol('x2')
+
+    y0 = Symbol('y0')
+    y1 = Symbol('y1')
+
+    assert symbols('x0:0') == ()
+    assert symbols('x0:1') == (x0,)
+    assert symbols('x0:2') == (x0, x1)
+    assert symbols('x0:3') == (x0, x1, x2)
+
+    assert symbols('x:0') == ()
+    assert symbols('x:1') == (x0,)
+    assert symbols('x:2') == (x0, x1)
+    assert symbols('x:3') == (x0, x1, x2)
+
+    assert symbols('x1:1') == ()
+    assert symbols('x1:2') == (x1,)
+    assert symbols('x1:3') == (x1, x2)
+
+    assert symbols('x1:3,x,y,z') == (x1, x2, x, y, z)
+
+    assert symbols('x:3,y:2') == (x0, x1, x2, y0, y1)
+    assert symbols(('x:3', 'y:2')) == ((x0, x1, x2), (y0, y1))
+
+    a = Symbol('a')
+    b = Symbol('b')
+    c = Symbol('c')
+    d = Symbol('d')
+
+    assert symbols('x:z') == (x, y, z)
+    assert symbols('a:d,x:z') == (a, b, c, d, x, y, z)
+    assert symbols(('a:d', 'x:z')) == ((a, b, c, d), (x, y, z))
+
+    aa = Symbol('aa')
+    ab = Symbol('ab')
+    ac = Symbol('ac')
+    ad = Symbol('ad')
+
+    assert symbols('aa:d') == (aa, ab, ac, ad)
+    assert symbols('aa:d,x:z') == (aa, ab, ac, ad, x, y, z)
+    assert symbols(('aa:d','x:z')) == ((aa, ab, ac, ad), (x, y, z))
+
+    assert type(symbols(('q:2', 'u:2'), cls=Function)[0][0]) == UndefinedFunction  # issue 23532
+
+    # issue 6675
+    def sym(s):
+        return str(symbols(s))
+    assert sym('a0:4') == '(a0, a1, a2, a3)'
+    assert sym('a2:4,b1:3') == '(a2, a3, b1, b2)'
+    assert sym('a1(2:4)') == '(a12, a13)'
+    assert sym('a0:2.0:2') == '(a0.0, a0.1, a1.0, a1.1)'
+    assert sym('aa:cz') == '(aaz, abz, acz)'
+    assert sym('aa:c0:2') == '(aa0, aa1, ab0, ab1, ac0, ac1)'
+    assert sym('aa:ba:b') == '(aaa, aab, aba, abb)'
+    assert sym('a:3b') == '(a0b, a1b, a2b)'
+    assert sym('a-1:3b') == '(a-1b, a-2b)'
+    assert sym(r'a:2\,:2' + chr(0)) == '(a0,0%s, a0,1%s, a1,0%s, a1,1%s)' % (
+        (chr(0),)*4)
+    assert sym('x(:a:3)') == '(x(a0), x(a1), x(a2))'
+    assert sym('x(:c):1') == '(xa0, xb0, xc0)'
+    assert sym('x((:a)):3') == '(x(a)0, x(a)1, x(a)2)'
+    assert sym('x(:a:3') == '(x(a0, x(a1, x(a2)'
+    assert sym(':2') == '(0, 1)'
+    assert sym(':b') == '(a, b)'
+    assert sym(':b:2') == '(a0, a1, b0, b1)'
+    assert sym(':2:2') == '(00, 01, 10, 11)'
+    assert sym(':b:b') == '(aa, ab, ba, bb)'
+
+    raises(ValueError, lambda: symbols(':'))
+    raises(ValueError, lambda: symbols('a:'))
+    raises(ValueError, lambda: symbols('::'))
+    raises(ValueError, lambda: symbols('a::'))
+    raises(ValueError, lambda: symbols(':a:'))
+    raises(ValueError, lambda: symbols('::a'))
+
+
+def test_symbols_become_functions_issue_3539():
+    from sympy.abc import alpha, phi, beta, t
+    raises(TypeError, lambda: beta(2))
+    raises(TypeError, lambda: beta(2.5))
+    raises(TypeError, lambda: phi(2.5))
+    raises(TypeError, lambda: alpha(2.5))
+    raises(TypeError, lambda: phi(t))
+
+
+def test_unicode():
+    xu = Symbol('x')
+    x = Symbol('x')
+    assert x == xu
+
+    raises(TypeError, lambda: Symbol(1))
+
+
+def test_uniquely_named_symbol_and_Symbol():
+    F = uniquely_named_symbol
+    x = Symbol('x')
+    assert F(x) == x
+    assert F('x') == x
+    assert str(F('x', x)) == 'x0'
+    assert str(F('x', (x + 1, 1/x))) == 'x0'
+    _x = Symbol('x', real=True)
+    assert F(('x', _x)) == _x
+    assert F((x, _x)) == _x
+    assert F('x', real=True).is_real
+    y = Symbol('y')
+    assert F(('x', y), real=True).is_real
+    r = Symbol('x', real=True)
+    assert F(('x', r)).is_real
+    assert F(('x', r), real=False).is_real
+    assert F('x1', Symbol('x1'),
+        compare=lambda i: str(i).rstrip('1')).name == 'x0'
+    assert F('x1', Symbol('x1'),
+        modify=lambda i: i + '_').name == 'x1_'
+    assert _symbol(x, _x) == x
+
+
+def test_disambiguate():
+    x, y, y_1, _x, x_1, x_2 = symbols('x y y_1 _x x_1 x_2')
+    t1 = Dummy('y'), _x, Dummy('x'), Dummy('x')
+    t2 = Dummy('x'), Dummy('x')
+    t3 = Dummy('x'), Dummy('y')
+    t4 = x, Dummy('x')
+    t5 = Symbol('x', integer=True), x, Symbol('x_1')
+
+    assert disambiguate(*t1) == (y, x_2, x, x_1)
+    assert disambiguate(*t2) == (x, x_1)
+    assert disambiguate(*t3) == (x, y)
+    assert disambiguate(*t4) == (x_1, x)
+    assert disambiguate(*t5) == (t5[0], x_2, x_1)
+    assert disambiguate(*t5)[0] != x  # assumptions are retained
+
+    t6 = _x, Dummy('x')/y
+    t7 = y*Dummy('y'), y
+
+    assert disambiguate(*t6) == (x_1, x/y)
+    assert disambiguate(*t7) == (y*y_1, y_1)
+    assert disambiguate(Dummy('x_1'), Dummy('x_1')
+        ) == (x_1, Symbol('x_1_1'))
+
+
+@skip_under_pyodide("Cannot create threads under pyodide.")
+def test_issue_gh_16734():
+    # https://github.com/sympy/sympy/issues/16734
+
+    syms = list(symbols('x, y'))
+
+    def thread1():
+        for n in range(1000):
+            syms[0], syms[1] = symbols(f'x{n}, y{n}')
+            syms[0].is_positive # Check an assumption in this thread.
+        syms[0] = None
+
+    def thread2():
+        while syms[0] is not None:
+            # Compare the symbol in this thread.
+            result = (syms[0] == syms[1])  # noqa
+
+    # Previously this would be very likely to raise an exception:
+    thread = threading.Thread(target=thread1)
+    thread.start()
+    thread2()
+    thread.join()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_sympify.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_sympify.py
new file mode 100644
index 0000000000000000000000000000000000000000..40be30c25d5826ceadde6d176c160a0090967659
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_sympify.py
@@ -0,0 +1,892 @@
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.function import (Function, Lambda)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Float, I, Integer, Rational, pi, oo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.logic.boolalg import (false, Or, true, Xor)
+from sympy.matrices.dense import Matrix
+from sympy.parsing.sympy_parser import null
+from sympy.polys.polytools import Poly
+from sympy.printing.repr import srepr
+from sympy.sets.fancysets import Range
+from sympy.sets.sets import Interval
+from sympy.abc import x, y
+from sympy.core.sympify import (sympify, _sympify, SympifyError, kernS,
+    CantSympify, converter)
+from sympy.core.decorators import _sympifyit
+from sympy.external import import_module
+from sympy.testing.pytest import raises, XFAIL, skip
+from sympy.utilities.decorator import conserve_mpmath_dps
+from sympy.geometry import Point, Line
+from sympy.functions.combinatorial.factorials import factorial, factorial2
+from sympy.abc import _clash, _clash1, _clash2
+from sympy.external.gmpy import gmpy as _gmpy, flint as _flint
+from sympy.sets import FiniteSet, EmptySet
+from sympy.tensor.array.dense_ndim_array import ImmutableDenseNDimArray
+
+import mpmath
+from collections import defaultdict, OrderedDict
+
+
+numpy = import_module('numpy')
+
+
+def test_issue_3538():
+    v = sympify("exp(x)")
+    assert v == exp(x)
+    assert type(v) == type(exp(x))
+    assert str(type(v)) == str(type(exp(x)))
+
+
+def test_sympify1():
+    assert sympify("x") == Symbol("x")
+    assert sympify("   x") == Symbol("x")
+    assert sympify("   x   ") == Symbol("x")
+    # issue 4877
+    assert sympify('--.5') == 0.5
+    assert sympify('-1/2') == -S.Half
+    assert sympify('-+--.5') == -0.5
+    assert sympify('-.[3]') == Rational(-1, 3)
+    assert sympify('.[3]') == Rational(1, 3)
+    assert sympify('+.[3]') == Rational(1, 3)
+    assert sympify('+0.[3]*10**-2') == Rational(1, 300)
+    assert sympify('.[052631578947368421]') == Rational(1, 19)
+    assert sympify('.0[526315789473684210]') == Rational(1, 19)
+    assert sympify('.034[56]') == Rational(1711, 49500)
+    # options to make reals into rationals
+    assert sympify('1.22[345]', rational=True) == \
+        1 + Rational(22, 100) + Rational(345, 99900)
+    assert sympify('2/2.6', rational=True) == Rational(10, 13)
+    assert sympify('2.6/2', rational=True) == Rational(13, 10)
+    assert sympify('2.6e2/17', rational=True) == Rational(260, 17)
+    assert sympify('2.6e+2/17', rational=True) == Rational(260, 17)
+    assert sympify('2.6e-2/17', rational=True) == Rational(26, 17000)
+    assert sympify('2.1+3/4', rational=True) == \
+        Rational(21, 10) + Rational(3, 4)
+    assert sympify('2.234456', rational=True) == Rational(279307, 125000)
+    assert sympify('2.234456e23', rational=True) == 223445600000000000000000
+    assert sympify('2.234456e-23', rational=True) == \
+        Rational(279307, 12500000000000000000000000000)
+    assert sympify('-2.234456e-23', rational=True) == \
+        Rational(-279307, 12500000000000000000000000000)
+    assert sympify('12345678901/17', rational=True) == \
+        Rational(12345678901, 17)
+    assert sympify('1/.3 + x', rational=True) == Rational(10, 3) + x
+    # make sure longs in fractions work
+    assert sympify('222222222222/11111111111') == \
+        Rational(222222222222, 11111111111)
+    # ... even if they come from repetend notation
+    assert sympify('1/.2[123456789012]') == Rational(333333333333, 70781892967)
+    # ... or from high precision reals
+    assert sympify('.1234567890123456', rational=True) == \
+        Rational(19290123283179, 156250000000000)
+
+
+def test_sympify_Fraction():
+    try:
+        import fractions
+    except ImportError:
+        pass
+    else:
+        value = sympify(fractions.Fraction(101, 127))
+        assert value == Rational(101, 127) and type(value) is Rational
+
+
+def test_sympify_gmpy():
+    if _gmpy is not None:
+        import gmpy2
+
+        value = sympify(gmpy2.mpz(1000001))
+        assert value == Integer(1000001) and type(value) is Integer
+
+        value = sympify(gmpy2.mpq(101, 127))
+        assert value == Rational(101, 127) and type(value) is Rational
+
+
+def test_sympify_flint():
+    if _flint is not None:
+        import flint
+
+        value = sympify(flint.fmpz(1000001))
+        assert value == Integer(1000001) and type(value) is Integer
+
+        value = sympify(flint.fmpq(101, 127))
+        assert value == Rational(101, 127) and type(value) is Rational
+
+
+@conserve_mpmath_dps
+def test_sympify_mpmath():
+    value = sympify(mpmath.mpf(1.0))
+    assert value == Float(1.0) and type(value) is Float
+
+    mpmath.mp.dps = 12
+    assert sympify(
+        mpmath.pi).epsilon_eq(Float("3.14159265359"), Float("1e-12")) == True
+    assert sympify(
+        mpmath.pi).epsilon_eq(Float("3.14159265359"), Float("1e-13")) == False
+
+    mpmath.mp.dps = 6
+    assert sympify(
+        mpmath.pi).epsilon_eq(Float("3.14159"), Float("1e-5")) == True
+    assert sympify(
+        mpmath.pi).epsilon_eq(Float("3.14159"), Float("1e-6")) == False
+
+    mpmath.mp.dps = 15
+    assert sympify(mpmath.mpc(1.0 + 2.0j)) == Float(1.0) + Float(2.0)*I
+
+
+def test_sympify2():
+    class A:
+        def _sympy_(self):
+            return Symbol("x")**3
+
+    a = A()
+
+    assert _sympify(a) == x**3
+    assert sympify(a) == x**3
+    assert a == x**3
+
+
+def test_sympify3():
+    assert sympify("x**3") == x**3
+    assert sympify("x^3") == x**3
+    assert sympify("1/2") == Integer(1)/2
+
+    raises(SympifyError, lambda: _sympify('x**3'))
+    raises(SympifyError, lambda: _sympify('1/2'))
+
+
+def test_sympify_keywords():
+    raises(SympifyError, lambda: sympify('if'))
+    raises(SympifyError, lambda: sympify('for'))
+    raises(SympifyError, lambda: sympify('while'))
+    raises(SympifyError, lambda: sympify('lambda'))
+
+
+def test_sympify_float():
+    assert sympify("1e-64") != 0
+    assert sympify("1e-20000") != 0
+
+
+def test_sympify_bool():
+    assert sympify(True) is true
+    assert sympify(False) is false
+
+
+def test_sympify_iterables():
+    ans = [Rational(3, 10), Rational(1, 5)]
+    assert sympify(['.3', '.2'], rational=True) == ans
+    assert sympify({"x": 0, "y": 1}) == {x: 0, y: 1}
+    assert sympify(['1', '2', ['3', '4']]) == [S(1), S(2), [S(3), S(4)]]
+
+
+@XFAIL
+def test_issue_16772():
+    # because there is a converter for tuple, the
+    # args are only sympified without the flags being passed
+    # along; list, on the other hand, is not converted
+    # with a converter so its args are traversed later
+    ans = [Rational(3, 10), Rational(1, 5)]
+    assert sympify(('.3', '.2'), rational=True) == Tuple(*ans)
+
+
+def test_issue_16859():
+    class no(float, CantSympify):
+        pass
+    raises(SympifyError, lambda: sympify(no(1.2)))
+
+
+def test_sympify4():
+    class A:
+        def _sympy_(self):
+            return Symbol("x")
+
+    a = A()
+
+    assert _sympify(a)**3 == x**3
+    assert sympify(a)**3 == x**3
+    assert a == x
+
+
+def test_sympify_text():
+    assert sympify('some') == Symbol('some')
+    assert sympify('core') == Symbol('core')
+
+    assert sympify('True') is True
+    assert sympify('False') is False
+
+    assert sympify('Poly') == Poly
+    assert sympify('sin') == sin
+
+
+def test_sympify_function():
+    assert sympify('factor(x**2-1, x)') == -(1 - x)*(x + 1)
+    assert sympify('sin(pi/2)*cos(pi)') == -Integer(1)
+
+
+def test_sympify_poly():
+    p = Poly(x**2 + x + 1, x)
+
+    assert _sympify(p) is p
+    assert sympify(p) is p
+
+
+def test_sympify_factorial():
+    assert sympify('x!') == factorial(x)
+    assert sympify('(x+1)!') == factorial(x + 1)
+    assert sympify('(1 + y*(x + 1))!') == factorial(1 + y*(x + 1))
+    assert sympify('(1 + y*(x + 1)!)^2') == (1 + y*factorial(x + 1))**2
+    assert sympify('y*x!') == y*factorial(x)
+    assert sympify('x!!') == factorial2(x)
+    assert sympify('(x+1)!!') == factorial2(x + 1)
+    assert sympify('(1 + y*(x + 1))!!') == factorial2(1 + y*(x + 1))
+    assert sympify('(1 + y*(x + 1)!!)^2') == (1 + y*factorial2(x + 1))**2
+    assert sympify('y*x!!') == y*factorial2(x)
+    assert sympify('factorial2(x)!') == factorial(factorial2(x))
+
+    raises(SympifyError, lambda: sympify("+!!"))
+    raises(SympifyError, lambda: sympify(")!!"))
+    raises(SympifyError, lambda: sympify("!"))
+    raises(SympifyError, lambda: sympify("(!)"))
+    raises(SympifyError, lambda: sympify("x!!!"))
+
+
+def test_issue_3595():
+    assert sympify("a_") == Symbol("a_")
+    assert sympify("_a") == Symbol("_a")
+
+
+def test_lambda():
+    x = Symbol('x')
+    assert sympify('lambda: 1') == Lambda((), 1)
+    assert sympify('lambda x: x') == Lambda(x, x)
+    assert sympify('lambda x: 2*x') == Lambda(x, 2*x)
+    assert sympify('lambda x, y: 2*x+y') == Lambda((x, y), 2*x + y)
+
+
+def test_lambda_raises():
+    raises(SympifyError, lambda: sympify("lambda *args: args")) # args argument error
+    raises(SympifyError, lambda: sympify("lambda **kwargs: kwargs[0]")) # kwargs argument error
+    raises(SympifyError, lambda: sympify("lambda x = 1: x"))    # Keyword argument error
+    with raises(SympifyError):
+        _sympify('lambda: 1')
+
+
+def test_sympify_raises():
+    raises(SympifyError, lambda: sympify("fx)"))
+
+    class A:
+        def __str__(self):
+            return 'x'
+
+    raises(SympifyError, lambda: sympify(A()))
+
+
+def test__sympify():
+    x = Symbol('x')
+    f = Function('f')
+
+    # positive _sympify
+    assert _sympify(x) is x
+    assert _sympify(1) == Integer(1)
+    assert _sympify(0.5) == Float("0.5")
+    assert _sympify(1 + 1j) == 1.0 + I*1.0
+
+    # Function f is not Basic and can't sympify to Basic. We allow it to pass
+    # with sympify but not with _sympify.
+    # https://github.com/sympy/sympy/issues/20124
+    assert sympify(f) is f
+    raises(SympifyError, lambda: _sympify(f))
+
+    class A:
+        def _sympy_(self):
+            return Integer(5)
+
+    a = A()
+    assert _sympify(a) == Integer(5)
+
+    # negative _sympify
+    raises(SympifyError, lambda: _sympify('1'))
+    raises(SympifyError, lambda: _sympify([1, 2, 3]))
+
+
+def test_sympifyit():
+    x = Symbol('x')
+    y = Symbol('y')
+
+    @_sympifyit('b', NotImplemented)
+    def add(a, b):
+        return a + b
+
+    assert add(x, 1) == x + 1
+    assert add(x, 0.5) == x + Float('0.5')
+    assert add(x, y) == x + y
+
+    assert add(x, '1') == NotImplemented
+
+    @_sympifyit('b')
+    def add_raises(a, b):
+        return a + b
+
+    assert add_raises(x, 1) == x + 1
+    assert add_raises(x, 0.5) == x + Float('0.5')
+    assert add_raises(x, y) == x + y
+
+    raises(SympifyError, lambda: add_raises(x, '1'))
+
+
+def test_int_float():
+    class F1_1:
+        def __float__(self):
+            return 1.1
+
+    class F1_1b:
+        """
+        This class is still a float, even though it also implements __int__().
+        """
+        def __float__(self):
+            return 1.1
+
+        def __int__(self):
+            return 1
+
+    class F1_1c:
+        """
+        This class is still a float, because it implements _sympy_()
+        """
+        def __float__(self):
+            return 1.1
+
+        def __int__(self):
+            return 1
+
+        def _sympy_(self):
+            return Float(1.1)
+
+    class I5:
+        def __int__(self):
+            return 5
+
+    class I5b:
+        """
+        This class implements both __int__() and __float__(), so it will be
+        treated as Float in SymPy. One could change this behavior, by using
+        float(a) == int(a), but deciding that integer-valued floats represent
+        exact numbers is arbitrary and often not correct, so we do not do it.
+        If, in the future, we decide to do it anyway, the tests for I5b need to
+        be changed.
+        """
+        def __float__(self):
+            return 5.0
+
+        def __int__(self):
+            return 5
+
+    class I5c:
+        """
+        This class implements both __int__() and __float__(), but also
+        a _sympy_() method, so it will be Integer.
+        """
+        def __float__(self):
+            return 5.0
+
+        def __int__(self):
+            return 5
+
+        def _sympy_(self):
+            return Integer(5)
+
+    i5 = I5()
+    i5b = I5b()
+    i5c = I5c()
+    f1_1 = F1_1()
+    f1_1b = F1_1b()
+    f1_1c = F1_1c()
+    assert sympify(i5) == 5
+    assert isinstance(sympify(i5), Integer)
+    assert sympify(i5b) == 5.0
+    assert isinstance(sympify(i5b), Float)
+    assert sympify(i5c) == 5
+    assert isinstance(sympify(i5c), Integer)
+    assert abs(sympify(f1_1) - 1.1) < 1e-5
+    assert abs(sympify(f1_1b) - 1.1) < 1e-5
+    assert abs(sympify(f1_1c) - 1.1) < 1e-5
+
+    assert _sympify(i5) == 5
+    assert isinstance(_sympify(i5), Integer)
+    assert _sympify(i5b) == 5.0
+    assert isinstance(_sympify(i5b), Float)
+    assert _sympify(i5c) == 5
+    assert isinstance(_sympify(i5c), Integer)
+    assert abs(_sympify(f1_1) - 1.1) < 1e-5
+    assert abs(_sympify(f1_1b) - 1.1) < 1e-5
+    assert abs(_sympify(f1_1c) - 1.1) < 1e-5
+
+
+def test_evaluate_false():
+    cases = {
+        '2 + 3': Add(2, 3, evaluate=False),
+        '2**2 / 3': Mul(Pow(2, 2, evaluate=False), Pow(3, -1, evaluate=False), evaluate=False),
+        '2 + 3 * 5': Add(2, Mul(3, 5, evaluate=False), evaluate=False),
+        '2 - 3 * 5': Add(2, Mul(-1, Mul(3, 5,evaluate=False), evaluate=False), evaluate=False),
+        '1 / 3': Mul(1, Pow(3, -1, evaluate=False), evaluate=False),
+        'True | False': Or(True, False, evaluate=False),
+        '1 + 2 + 3 + 5*3 + integrate(x)': Add(1, 2, 3, Mul(5, 3, evaluate=False), x**2/2, evaluate=False),
+        '2 * 4 * 6 + 8': Add(Mul(2, 4, 6, evaluate=False), 8, evaluate=False),
+        '2 - 8 / 4': Add(2, Mul(-1, Mul(8, Pow(4, -1, evaluate=False), evaluate=False), evaluate=False), evaluate=False),
+        '2 - 2**2': Add(2, Mul(-1, Pow(2, 2, evaluate=False), evaluate=False), evaluate=False),
+    }
+    for case, result in cases.items():
+        assert sympify(case, evaluate=False) == result
+
+
+def test_issue_4133():
+    a = sympify('Integer(4)')
+
+    assert a == Integer(4)
+    assert a.is_Integer
+
+
+def test_issue_3982():
+    a = [3, 2.0]
+    assert sympify(a) == [Integer(3), Float(2.0)]
+    assert sympify(tuple(a)) == Tuple(Integer(3), Float(2.0))
+    assert sympify(set(a)) == FiniteSet(Integer(3), Float(2.0))
+
+
+def test_S_sympify():
+    assert S(1)/2 == sympify(1)/2 == S.Half
+    assert (-2)**(S(1)/2) == sqrt(2)*I
+
+
+def test_issue_4788():
+    assert srepr(S(1.0 + 0J)) == srepr(S(1.0)) == srepr(Float(1.0))
+
+
+def test_issue_4798_None():
+    assert S(None) is None
+
+
+def test_issue_3218():
+    assert sympify("x+\ny") == x + y
+
+def test_issue_19399():
+    if not numpy:
+        skip("numpy not installed.")
+
+    a = numpy.array(Rational(1, 2))
+    b = Rational(1, 3)
+    assert (a * b, type(a * b)) == (b * a, type(b * a))
+
+
+def test_issue_4988_builtins():
+    C = Symbol('C')
+    vars = {'C': C}
+    exp1 = sympify('C')
+    assert exp1 == C  # Make sure it did not get mixed up with sympy.C
+
+    exp2 = sympify('C', vars)
+    assert exp2 == C  # Make sure it did not get mixed up with sympy.C
+
+
+def test_geometry():
+    p = sympify(Point(0, 1))
+    assert p == Point(0, 1) and isinstance(p, Point)
+    L = sympify(Line(p, (1, 0)))
+    assert L == Line((0, 1), (1, 0)) and isinstance(L, Line)
+
+
+def test_kernS():
+    s =   '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'
+    # when 1497 is fixed, this no longer should pass: the expression
+    # should be unchanged
+    assert -1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) == -1
+    # sympification should not allow the constant to enter a Mul
+    # or else the structure can change dramatically
+    ss = kernS(s)
+    assert ss != -1 and ss.simplify() == -1
+    s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace(
+        'x', '_kern')
+    ss = kernS(s)
+    assert ss != -1 and ss.simplify() == -1
+    # issue 6687
+    assert (kernS('Interval(-1,-2 - 4*(-3))')
+        == Interval(-1, Add(-2, Mul(12, 1, evaluate=False), evaluate=False)))
+    assert kernS('_kern') == Symbol('_kern')
+    assert kernS('E**-(x)') == exp(-x)
+    e = 2*(x + y)*y
+    assert kernS(['2*(x + y)*y', ('2*(x + y)*y',)]) == [e, (e,)]
+    assert kernS('-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2') == \
+        -y*(2*sin(x)**2 + 2*sin(x)*cos(x))/2
+    # issue 15132
+    assert kernS('(1 - x)/(1 - x*(1-y))') == kernS('(1-x)/(1-(1-y)*x)')
+    assert kernS('(1-2**-(4+1)*(1-y)*x)') == (1 - x*(1 - y)/32)
+    assert kernS('(1-2**(4+1)*(1-y)*x)') == (1 - 32*x*(1 - y))
+    assert kernS('(1-2.*(1-y)*x)') == 1 - 2.*x*(1 - y)
+    one = kernS('x - (x - 1)')
+    assert one != 1 and one.expand() == 1
+    assert kernS("(2*x)/(x-1)") == 2*x/(x-1)
+
+
+def test_issue_6540_6552():
+    assert S('[[1/3,2], (2/5,)]') == [[Rational(1, 3), 2], (Rational(2, 5),)]
+    assert S('[[2/6,2], (2/4,)]') == [[Rational(1, 3), 2], (S.Half,)]
+    assert S('[[[2*(1)]]]') == [[[2]]]
+    assert S('Matrix([2*(1)])') == Matrix([2])
+
+
+def test_issue_6046():
+    assert str(S("Q & C", locals=_clash1)) == 'C & Q'
+    assert str(S('pi(x)', locals=_clash2)) == 'pi(x)'
+    locals = {}
+    exec("from sympy.abc import Q, C", locals)
+    assert str(S('C&Q', locals)) == 'C & Q'
+    # clash can act as Symbol or Function
+    assert str(S('pi(C, Q)', locals=_clash)) == 'pi(C, Q)'
+    assert len(S('pi + x', locals=_clash2).free_symbols) == 2
+    # but not both
+    raises(TypeError, lambda: S('pi + pi(x)', locals=_clash2))
+    assert all(set(i.values()) == {null} for i in (
+        _clash, _clash1, _clash2))
+
+
+def test_issue_8821_highprec_from_str():
+    s = str(pi.evalf(128))
+    p = sympify(s)
+    assert Abs(sin(p)) < 1e-127
+
+
+def test_issue_10295():
+    if not numpy:
+        skip("numpy not installed.")
+
+    A = numpy.array([[1, 3, -1],
+                     [0, 1, 7]])
+    sA = S(A)
+    assert sA.shape == (2, 3)
+    for (ri, ci), val in numpy.ndenumerate(A):
+        assert sA[ri, ci] == val
+
+    B = numpy.array([-7, x, 3*y**2])
+    sB = S(B)
+    assert sB.shape == (3,)
+    assert B[0] == sB[0] == -7
+    assert B[1] == sB[1] == x
+    assert B[2] == sB[2] == 3*y**2
+
+    C = numpy.arange(0, 24)
+    C.resize(2,3,4)
+    sC = S(C)
+    assert sC[0, 0, 0].is_integer
+    assert sC[0, 0, 0] == 0
+
+    a1 = numpy.array([1, 2, 3])
+    a2 = numpy.array(list(range(24)))
+    a2.resize(2, 4, 3)
+    assert sympify(a1) == ImmutableDenseNDimArray([1, 2, 3])
+    assert sympify(a2) == ImmutableDenseNDimArray(list(range(24)), (2, 4, 3))
+
+
+def test_Range():
+    # Only works in Python 3 where range returns a range type
+    assert sympify(range(10)) == Range(10)
+    assert _sympify(range(10)) == Range(10)
+
+
+def test_sympify_set():
+    n = Symbol('n')
+    assert sympify({n}) == FiniteSet(n)
+    assert sympify(set()) == EmptySet
+
+
+def test_sympify_numpy():
+    if not numpy:
+        skip('numpy not installed. Abort numpy tests.')
+    np = numpy
+
+    def equal(x, y):
+        return x == y and type(x) == type(y)
+
+    assert sympify(np.bool_(1)) is S(True)
+    try:
+        assert equal(
+            sympify(np.int_(1234567891234567891)), S(1234567891234567891))
+        assert equal(
+            sympify(np.intp(1234567891234567891)), S(1234567891234567891))
+    except OverflowError:
+        # May fail on 32-bit systems: Python int too large to convert to C long
+        pass
+    assert equal(sympify(np.intc(1234567891)), S(1234567891))
+    assert equal(sympify(np.int8(-123)), S(-123))
+    assert equal(sympify(np.int16(-12345)), S(-12345))
+    assert equal(sympify(np.int32(-1234567891)), S(-1234567891))
+    assert equal(
+        sympify(np.int64(-1234567891234567891)), S(-1234567891234567891))
+    assert equal(sympify(np.uint8(123)), S(123))
+    assert equal(sympify(np.uint16(12345)), S(12345))
+    assert equal(sympify(np.uint32(1234567891)), S(1234567891))
+    assert equal(
+        sympify(np.uint64(1234567891234567891)), S(1234567891234567891))
+    assert equal(sympify(np.float32(1.123456)), Float(1.123456, precision=24))
+    assert equal(sympify(np.float64(1.1234567891234)),
+                Float(1.1234567891234, precision=53))
+
+    # The exact precision of np.longdouble, npfloat128 and other extended
+    # precision dtypes is platform dependent.
+    ldprec = np.finfo(np.longdouble(1)).nmant + 1
+    assert equal(sympify(np.longdouble(1.123456789)),
+                 Float(1.123456789, precision=ldprec))
+
+    assert equal(sympify(np.complex64(1 + 2j)), S(1.0 + 2.0*I))
+    assert equal(sympify(np.complex128(1 + 2j)), S(1.0 + 2.0*I))
+
+    lcprec = np.finfo(np.clongdouble(1)).nmant + 1
+    assert equal(sympify(np.clongdouble(1 + 2j)),
+                Float(1.0, precision=lcprec) + Float(2.0, precision=lcprec)*I)
+
+    #float96 does not exist on all platforms
+    if hasattr(np, 'float96'):
+        f96prec = np.finfo(np.float96(1)).nmant + 1
+        assert equal(sympify(np.float96(1.123456789)),
+                    Float(1.123456789, precision=f96prec))
+
+    #float128 does not exist on all platforms
+    if hasattr(np, 'float128'):
+        f128prec = np.finfo(np.float128(1)).nmant + 1
+        assert equal(sympify(np.float128(1.123456789123)),
+                    Float(1.123456789123, precision=f128prec))
+
+
+@XFAIL
+def test_sympify_rational_numbers_set():
+    ans = [Rational(3, 10), Rational(1, 5)]
+    assert sympify({'.3', '.2'}, rational=True) == FiniteSet(*ans)
+
+
+def test_sympify_mro():
+    """Tests the resolution order for classes that implement _sympy_"""
+    class a:
+        def _sympy_(self):
+            return Integer(1)
+    class b(a):
+        def _sympy_(self):
+            return Integer(2)
+    class c(a):
+        pass
+
+    assert sympify(a()) == Integer(1)
+    assert sympify(b()) == Integer(2)
+    assert sympify(c()) == Integer(1)
+
+
+def test_sympify_converter():
+    """Tests the resolution order for classes in converter"""
+    class a:
+        pass
+    class b(a):
+        pass
+    class c(a):
+        pass
+
+    converter[a] = lambda x: Integer(1)
+    converter[b] = lambda x: Integer(2)
+
+    assert sympify(a()) == Integer(1)
+    assert sympify(b()) == Integer(2)
+    assert sympify(c()) == Integer(1)
+
+    class MyInteger(Integer):
+        pass
+
+    if int in converter:
+        int_converter = converter[int]
+    else:
+        int_converter = None
+
+    try:
+        converter[int] = MyInteger
+        assert sympify(1) == MyInteger(1)
+    finally:
+        if int_converter is None:
+            del converter[int]
+        else:
+            converter[int] = int_converter
+
+
+def test_issue_13924():
+    if not numpy:
+        skip("numpy not installed.")
+
+    a = sympify(numpy.array([1]))
+    assert isinstance(a, ImmutableDenseNDimArray)
+    assert a[0] == 1
+
+
+def test_numpy_sympify_args():
+    # Issue 15098. Make sure sympify args work with numpy types (like numpy.str_)
+    if not numpy:
+        skip("numpy not installed.")
+
+    a = sympify(numpy.str_('a'))
+    assert type(a) is Symbol
+    assert a == Symbol('a')
+
+    class CustomSymbol(Symbol):
+        pass
+
+    a = sympify(numpy.str_('a'), {"Symbol": CustomSymbol})
+    assert isinstance(a, CustomSymbol)
+
+    a = sympify(numpy.str_('x^y'))
+    assert a == x**y
+    a = sympify(numpy.str_('x^y'), convert_xor=False)
+    assert a == Xor(x, y)
+
+    raises(SympifyError, lambda: sympify(numpy.str_('x'), strict=True))
+
+    a = sympify(numpy.str_('1.1'))
+    assert isinstance(a, Float)
+    assert a == 1.1
+
+    a = sympify(numpy.str_('1.1'), rational=True)
+    assert isinstance(a, Rational)
+    assert a == Rational(11, 10)
+
+    a = sympify(numpy.str_('x + x'))
+    assert isinstance(a, Mul)
+    assert a == 2*x
+
+    a = sympify(numpy.str_('x + x'), evaluate=False)
+    assert isinstance(a, Add)
+    assert a == Add(x, x, evaluate=False)
+
+
+def test_issue_5939():
+    a = Symbol('a')
+    b = Symbol('b')
+    assert sympify('''a+\nb''') == a + b
+
+
+def test_issue_16759():
+    d = sympify({.5: 1})
+    assert S.Half not in d
+    assert Float(.5) in d
+    assert d[.5] is S.One
+    d = sympify(OrderedDict({.5: 1}))
+    assert S.Half not in d
+    assert Float(.5) in d
+    assert d[.5] is S.One
+    d = sympify(defaultdict(int, {.5: 1}))
+    assert S.Half not in d
+    assert Float(.5) in d
+    assert d[.5] is S.One
+
+
+def test_issue_17811():
+    a = Function('a')
+    assert sympify('a(x)*5', evaluate=False) == Mul(a(x), 5, evaluate=False)
+
+
+def test_issue_8439():
+    assert sympify(float('inf')) == oo
+    assert x + float('inf') == x + oo
+    assert S(float('inf')) == oo
+
+
+def test_issue_14706():
+    if not numpy:
+        skip("numpy not installed.")
+
+    z1 = numpy.zeros((1, 1), dtype=numpy.float64)
+    z2 = numpy.zeros((2, 2), dtype=numpy.float64)
+    z3 = numpy.zeros((), dtype=numpy.float64)
+
+    y1 = numpy.ones((1, 1), dtype=numpy.float64)
+    y2 = numpy.ones((2, 2), dtype=numpy.float64)
+    y3 = numpy.ones((), dtype=numpy.float64)
+
+    assert numpy.all(x + z1 == numpy.full((1, 1), x))
+    assert numpy.all(x + z2 == numpy.full((2, 2), x))
+    assert numpy.all(z1 + x == numpy.full((1, 1), x))
+    assert numpy.all(z2 + x == numpy.full((2, 2), x))
+    for z in [z3,
+              numpy.int64(0),
+              numpy.float64(0),
+              numpy.complex64(0)]:
+        assert x + z == x
+        assert z + x == x
+        assert isinstance(x + z, Symbol)
+        assert isinstance(z + x, Symbol)
+
+    # If these tests fail, then it means that numpy has finally
+    # fixed the issue of scalar conversion for rank>0 arrays
+    # which is mentioned in numpy/numpy#10404. In that case,
+    # some changes have to be made in sympify.py.
+    # Note: For future reference, for anyone who takes up this
+    # issue when numpy has finally fixed their side of the problem,
+    # the changes for this temporary fix were introduced in PR 18651
+    assert numpy.all(x + y1 == numpy.full((1, 1), x + 1.0))
+    assert numpy.all(x + y2 == numpy.full((2, 2), x + 1.0))
+    assert numpy.all(y1 + x == numpy.full((1, 1), x + 1.0))
+    assert numpy.all(y2 + x == numpy.full((2, 2), x + 1.0))
+    for y_ in [y3,
+              numpy.int64(1),
+              numpy.float64(1),
+              numpy.complex64(1)]:
+        assert x + y_ == y_ + x
+        assert isinstance(x + y_, Add)
+        assert isinstance(y_ + x, Add)
+
+    assert x + numpy.array(x) == 2 * x
+    assert x + numpy.array([x]) == numpy.array([2*x], dtype=object)
+
+    assert sympify(numpy.array([1])) == ImmutableDenseNDimArray([1], 1)
+    assert sympify(numpy.array([[[1]]])) == ImmutableDenseNDimArray([1], (1, 1, 1))
+    assert sympify(z1) == ImmutableDenseNDimArray([0.0], (1, 1))
+    assert sympify(z2) == ImmutableDenseNDimArray([0.0, 0.0, 0.0, 0.0], (2, 2))
+    assert sympify(z3) == ImmutableDenseNDimArray([0.0], ())
+    assert sympify(z3, strict=True) == 0.0
+
+    raises(SympifyError, lambda: sympify(numpy.array([1]), strict=True))
+    raises(SympifyError, lambda: sympify(z1, strict=True))
+    raises(SympifyError, lambda: sympify(z2, strict=True))
+
+
+def test_issue_21536():
+    #test to check evaluate=False in case of iterable input
+    u = sympify("x+3*x+2", evaluate=False)
+    v = sympify("2*x+4*x+2+4", evaluate=False)
+
+    assert u.is_Add and set(u.args) == {x, 3*x, 2}
+    assert v.is_Add and set(v.args) == {2*x, 4*x, 2, 4}
+    assert sympify(["x+3*x+2", "2*x+4*x+2+4"], evaluate=False) == [u, v]
+
+    #test to check evaluate=True in case of iterable input
+    u = sympify("x+3*x+2", evaluate=True)
+    v = sympify("2*x+4*x+2+4", evaluate=True)
+
+    assert u.is_Add and set(u.args) == {4*x, 2}
+    assert v.is_Add and set(v.args) == {6*x, 6}
+    assert sympify(["x+3*x+2", "2*x+4*x+2+4"], evaluate=True) == [u, v]
+
+    #test to check evaluate with no input in case of iterable input
+    u = sympify("x+3*x+2")
+    v = sympify("2*x+4*x+2+4")
+
+    assert u.is_Add and set(u.args) == {4*x, 2}
+    assert v.is_Add and set(v.args) == {6*x, 6}
+    assert sympify(["x+3*x+2", "2*x+4*x+2+4"]) == [u, v]
+
+def test_issue_27284():
+    if not numpy:
+        skip("numpy not installed.")
+
+    assert Float(numpy.float32(float('inf'))) == S.Infinity
+    assert Float(numpy.float32(float('-inf'))) == S.NegativeInfinity
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_traversal.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_traversal.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bf067283eaba5d4a073a73feb07aac199055a7f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_traversal.py
@@ -0,0 +1,119 @@
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import symbols
+from sympy.core.singleton import S
+from sympy.core.function import expand, Function
+from sympy.core.numbers import I
+from sympy.integrals.integrals import Integral
+from sympy.polys.polytools import factor
+from sympy.core.traversal import preorder_traversal, use, postorder_traversal, iterargs, iterfreeargs
+from sympy.functions.elementary.piecewise import ExprCondPair, Piecewise
+from sympy.testing.pytest import warns_deprecated_sympy
+from sympy.utilities.iterables import capture
+
+b1 = Basic()
+b2 = Basic(b1)
+b3 = Basic(b2)
+b21 = Basic(b2, b1)
+
+
+def test_preorder_traversal():
+    expr = Basic(b21, b3)
+    assert list(
+        preorder_traversal(expr)) == [expr, b21, b2, b1, b1, b3, b2, b1]
+    assert list(preorder_traversal(('abc', ('d', 'ef')))) == [
+        ('abc', ('d', 'ef')), 'abc', ('d', 'ef'), 'd', 'ef']
+
+    result = []
+    pt = preorder_traversal(expr)
+    for i in pt:
+        result.append(i)
+        if i == b2:
+            pt.skip()
+    assert result == [expr, b21, b2, b1, b3, b2]
+
+    w, x, y, z = symbols('w:z')
+    expr = z + w*(x + y)
+    assert list(preorder_traversal([expr], keys=default_sort_key)) == \
+        [[w*(x + y) + z], w*(x + y) + z, z, w*(x + y), w, x + y, x, y]
+    assert list(preorder_traversal((x + y)*z, keys=True)) == \
+        [z*(x + y), z, x + y, x, y]
+
+
+def test_use():
+    x, y = symbols('x y')
+
+    assert use(0, expand) == 0
+
+    f = (x + y)**2*x + 1
+
+    assert use(f, expand, level=0) == x**3 + 2*x**2*y + x*y**2 + + 1
+    assert use(f, expand, level=1) == x**3 + 2*x**2*y + x*y**2 + + 1
+    assert use(f, expand, level=2) == 1 + x*(2*x*y + x**2 + y**2)
+    assert use(f, expand, level=3) == (x + y)**2*x + 1
+
+    f = (x**2 + 1)**2 - 1
+    kwargs = {'gaussian': True}
+
+    assert use(f, factor, level=0, kwargs=kwargs) == x**2*(x**2 + 2)
+    assert use(f, factor, level=1, kwargs=kwargs) == (x + I)**2*(x - I)**2 - 1
+    assert use(f, factor, level=2, kwargs=kwargs) == (x + I)**2*(x - I)**2 - 1
+    assert use(f, factor, level=3, kwargs=kwargs) == (x**2 + 1)**2 - 1
+
+
+def test_postorder_traversal():
+    x, y, z, w = symbols('x y z w')
+    expr = z + w*(x + y)
+    expected = [z, w, x, y, x + y, w*(x + y), w*(x + y) + z]
+    assert list(postorder_traversal(expr, keys=default_sort_key)) == expected
+    assert list(postorder_traversal(expr, keys=True)) == expected
+
+    expr = Piecewise((x, x < 1), (x**2, True))
+    expected = [
+        x, 1, x, x < 1, ExprCondPair(x, x < 1),
+        2, x, x**2, S.true,
+        ExprCondPair(x**2, True), Piecewise((x, x < 1), (x**2, True))
+    ]
+    assert list(postorder_traversal(expr, keys=default_sort_key)) == expected
+    assert list(postorder_traversal(
+        [expr], keys=default_sort_key)) == expected + [[expr]]
+
+    assert list(postorder_traversal(Integral(x**2, (x, 0, 1)),
+        keys=default_sort_key)) == [
+            2, x, x**2, 0, 1, x, Tuple(x, 0, 1),
+            Integral(x**2, Tuple(x, 0, 1))
+        ]
+    assert list(postorder_traversal(('abc', ('d', 'ef')))) == [
+        'abc', 'd', 'ef', ('d', 'ef'), ('abc', ('d', 'ef'))]
+
+
+def test_iterargs():
+    f = Function('f')
+    x = symbols('x')
+    assert list(iterfreeargs(Integral(f(x), (f(x), 1)))) == [
+        Integral(f(x), (f(x), 1)), 1]
+    assert list(iterargs(Integral(f(x), (f(x), 1)))) == [
+        Integral(f(x), (f(x), 1)), f(x), (f(x), 1), x, f(x), 1, x]
+
+def test_deprecated_imports():
+    x = symbols('x')
+
+    with warns_deprecated_sympy():
+        from sympy.core.basic import preorder_traversal
+        preorder_traversal(x)
+    with warns_deprecated_sympy():
+        from sympy.simplify.simplify import bottom_up
+        bottom_up(x, lambda x: x)
+    with warns_deprecated_sympy():
+        from sympy.simplify.simplify import walk
+        walk(x, lambda x: x)
+    with warns_deprecated_sympy():
+        from sympy.simplify.traversaltools import use
+        use(x, lambda x: x)
+    with warns_deprecated_sympy():
+        from sympy.utilities.iterables import postorder_traversal
+        postorder_traversal(x)
+    with warns_deprecated_sympy():
+        from sympy.utilities.iterables import interactive_traversal
+        capture(lambda: interactive_traversal(x))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_truediv.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_truediv.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fcf9e1ab754d05a3b47e7ec0c2be5ea9929da02
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_truediv.py
@@ -0,0 +1,54 @@
+#this module tests that SymPy works with true division turned on
+
+from sympy.core.numbers import (Float, Rational)
+from sympy.core.symbol import Symbol
+
+
+def test_truediv():
+    assert 1/2 != 0
+    assert Rational(1)/2 != 0
+
+
+def dotest(s):
+    x = Symbol("x")
+    y = Symbol("y")
+    l = [
+        Rational(2),
+        Float("1.3"),
+        x,
+        y,
+        pow(x, y)*y,
+        5,
+        5.5
+    ]
+    for x in l:
+        for y in l:
+            s(x, y)
+    return True
+
+
+def test_basic():
+    def s(a, b):
+        x = a
+        x = +a
+        x = -a
+        x = a + b
+        x = a - b
+        x = a*b
+        x = a/b
+        x = a**b
+        del x
+    assert dotest(s)
+
+
+def test_ibasic():
+    def s(a, b):
+        x = a
+        x += b
+        x = a
+        x -= b
+        x = a
+        x *= b
+        x = a
+        x /= b
+    assert dotest(s)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_var.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_var.py
new file mode 100644
index 0000000000000000000000000000000000000000..a02709464c9878082fecaf70fa47067ac8838ac6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/tests/test_var.py
@@ -0,0 +1,62 @@
+from sympy.core.function import (Function, FunctionClass)
+from sympy.core.symbol import (Symbol, var)
+from sympy.testing.pytest import raises
+
+def test_var():
+    ns = {"var": var, "raises": raises}
+    eval("var('a')", ns)
+    assert ns["a"] == Symbol("a")
+
+    eval("var('b bb cc zz _x')", ns)
+    assert ns["b"] == Symbol("b")
+    assert ns["bb"] == Symbol("bb")
+    assert ns["cc"] == Symbol("cc")
+    assert ns["zz"] == Symbol("zz")
+    assert ns["_x"] == Symbol("_x")
+
+    v = eval("var(['d', 'e', 'fg'])", ns)
+    assert ns['d'] == Symbol('d')
+    assert ns['e'] == Symbol('e')
+    assert ns['fg'] == Symbol('fg')
+
+# check return value
+    assert v != ['d', 'e', 'fg']
+    assert v == [Symbol('d'), Symbol('e'), Symbol('fg')]
+
+
+def test_var_return():
+    ns = {"var": var, "raises": raises}
+    "raises(ValueError, lambda: var(''))"
+    v2 = eval("var('q')", ns)
+    v3 = eval("var('q p')", ns)
+
+    assert v2 == Symbol('q')
+    assert v3 == (Symbol('q'), Symbol('p'))
+
+
+def test_var_accepts_comma():
+    ns = {"var": var}
+    v1 = eval("var('x y z')", ns)
+    v2 = eval("var('x,y,z')", ns)
+    v3 = eval("var('x,y z')", ns)
+
+    assert v1 == v2
+    assert v1 == v3
+
+
+def test_var_keywords():
+    ns = {"var": var}
+    eval("var('x y', real=True)", ns)
+    assert ns['x'].is_real and ns['y'].is_real
+
+
+def test_var_cls():
+    ns = {"var": var, "Function": Function}
+    eval("var('f', cls=Function)", ns)
+
+    assert isinstance(ns['f'], FunctionClass)
+
+    eval("var('g,h', cls=Function)", ns)
+
+    assert isinstance(ns['g'], FunctionClass)
+    assert isinstance(ns['h'], FunctionClass)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/trace.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/trace.py
new file mode 100644
index 0000000000000000000000000000000000000000..58326ce1fdd5038f0b5805afe7c453314a22cb6a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/trace.py
@@ -0,0 +1,12 @@
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+sympy_deprecation_warning(
+    """
+    sympy.core.trace is deprecated. Use sympy.physics.quantum.trace
+    instead.
+    """,
+    deprecated_since_version="1.10",
+    active_deprecations_target="sympy-core-trace-deprecated",
+)
+
+from sympy.physics.quantum.trace import Tr # noqa:F401
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/traversal.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/traversal.py
new file mode 100644
index 0000000000000000000000000000000000000000..e4e000ef44bf636b9adc700964a7ee4c2372a019
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/core/traversal.py
@@ -0,0 +1,304 @@
+from __future__ import annotations
+
+from typing import Iterator
+
+from .basic import Basic
+from .sorting import ordered
+from .sympify import sympify
+from sympy.utilities.iterables import iterable
+
+
+
+def iterargs(expr):
+    """Yield the args of a Basic object in a breadth-first traversal.
+    Depth-traversal stops if `arg.args` is either empty or is not
+    an iterable.
+
+    Examples
+    ========
+
+    >>> from sympy import Integral, Function
+    >>> from sympy.abc import x
+    >>> f = Function('f')
+    >>> from sympy.core.traversal import iterargs
+    >>> list(iterargs(Integral(f(x), (f(x), 1))))
+    [Integral(f(x), (f(x), 1)), f(x), (f(x), 1), x, f(x), 1, x]
+
+    See Also
+    ========
+    iterfreeargs, preorder_traversal
+    """
+    args = [expr]
+    for i in args:
+        yield i
+        args.extend(i.args)
+
+
+def iterfreeargs(expr, _first=True):
+    """Yield the args of a Basic object in a breadth-first traversal.
+    Depth-traversal stops if `arg.args` is either empty or is not
+    an iterable. The bound objects of an expression will be returned
+    as canonical variables.
+
+    Examples
+    ========
+
+    >>> from sympy import Integral, Function
+    >>> from sympy.abc import x
+    >>> f = Function('f')
+    >>> from sympy.core.traversal import iterfreeargs
+    >>> list(iterfreeargs(Integral(f(x), (f(x), 1))))
+    [Integral(f(x), (f(x), 1)), 1]
+
+    See Also
+    ========
+    iterargs, preorder_traversal
+    """
+    args = [expr]
+    for i in args:
+        yield i
+        if _first and hasattr(i, 'bound_symbols'):
+            void = i.canonical_variables.values()
+            for i in iterfreeargs(i.as_dummy(), _first=False):
+                if not i.has(*void):
+                    yield i
+        args.extend(i.args)
+
+
+class preorder_traversal:
+    """
+    Do a pre-order traversal of a tree.
+
+    This iterator recursively yields nodes that it has visited in a pre-order
+    fashion. That is, it yields the current node then descends through the
+    tree breadth-first to yield all of a node's children's pre-order
+    traversal.
+
+
+    For an expression, the order of the traversal depends on the order of
+    .args, which in many cases can be arbitrary.
+
+    Parameters
+    ==========
+    node : SymPy expression
+        The expression to traverse.
+    keys : (default None) sort key(s)
+        The key(s) used to sort args of Basic objects. When None, args of Basic
+        objects are processed in arbitrary order. If key is defined, it will
+        be passed along to ordered() as the only key(s) to use to sort the
+        arguments; if ``key`` is simply True then the default keys of ordered
+        will be used.
+
+    Yields
+    ======
+    subtree : SymPy expression
+        All of the subtrees in the tree.
+
+    Examples
+    ========
+
+    >>> from sympy import preorder_traversal, symbols
+    >>> x, y, z = symbols('x y z')
+
+    The nodes are returned in the order that they are encountered unless key
+    is given; simply passing key=True will guarantee that the traversal is
+    unique.
+
+    >>> list(preorder_traversal((x + y)*z, keys=None)) # doctest: +SKIP
+    [z*(x + y), z, x + y, y, x]
+    >>> list(preorder_traversal((x + y)*z, keys=True))
+    [z*(x + y), z, x + y, x, y]
+
+    """
+    def __init__(self, node, keys=None):
+        self._skip_flag = False
+        self._pt = self._preorder_traversal(node, keys)
+
+    def _preorder_traversal(self, node, keys):
+        yield node
+        if self._skip_flag:
+            self._skip_flag = False
+            return
+        if isinstance(node, Basic):
+            if not keys and hasattr(node, '_argset'):
+                # LatticeOp keeps args as a set. We should use this if we
+                # don't care about the order, to prevent unnecessary sorting.
+                args = node._argset
+            else:
+                args = node.args
+            if keys:
+                if keys != True:
+                    args = ordered(args, keys, default=False)
+                else:
+                    args = ordered(args)
+            for arg in args:
+                yield from self._preorder_traversal(arg, keys)
+        elif iterable(node):
+            for item in node:
+                yield from self._preorder_traversal(item, keys)
+
+    def skip(self):
+        """
+        Skip yielding current node's (last yielded node's) subtrees.
+
+        Examples
+        ========
+
+        >>> from sympy import preorder_traversal, symbols
+        >>> x, y, z = symbols('x y z')
+        >>> pt = preorder_traversal((x + y*z)*z)
+        >>> for i in pt:
+        ...     print(i)
+        ...     if i == x + y*z:
+        ...             pt.skip()
+        z*(x + y*z)
+        z
+        x + y*z
+        """
+        self._skip_flag = True
+
+    def __next__(self):
+        return next(self._pt)
+
+    def __iter__(self) -> Iterator[Basic]:
+        return self
+
+
+def use(expr, func, level=0, args=(), kwargs={}):
+    """
+    Use ``func`` to transform ``expr`` at the given level.
+
+    Examples
+    ========
+
+    >>> from sympy import use, expand
+    >>> from sympy.abc import x, y
+
+    >>> f = (x + y)**2*x + 1
+
+    >>> use(f, expand, level=2)
+    x*(x**2 + 2*x*y + y**2) + 1
+    >>> expand(f)
+    x**3 + 2*x**2*y + x*y**2 + 1
+
+    """
+    def _use(expr, level):
+        if not level:
+            return func(expr, *args, **kwargs)
+        else:
+            if expr.is_Atom:
+                return expr
+            else:
+                level -= 1
+                _args = [_use(arg, level) for arg in expr.args]
+                return expr.__class__(*_args)
+
+    return _use(sympify(expr), level)
+
+
+def walk(e, *target):
+    """Iterate through the args that are the given types (target) and
+    return a list of the args that were traversed; arguments
+    that are not of the specified types are not traversed.
+
+    Examples
+    ========
+
+    >>> from sympy.core.traversal import walk
+    >>> from sympy import Min, Max
+    >>> from sympy.abc import x, y, z
+    >>> list(walk(Min(x, Max(y, Min(1, z))), Min))
+    [Min(x, Max(y, Min(1, z)))]
+    >>> list(walk(Min(x, Max(y, Min(1, z))), Min, Max))
+    [Min(x, Max(y, Min(1, z))), Max(y, Min(1, z)), Min(1, z)]
+
+    See Also
+    ========
+
+    bottom_up
+    """
+    if isinstance(e, target):
+        yield e
+        for i in e.args:
+            yield from walk(i, *target)
+
+
+def bottom_up(rv, F, atoms=False, nonbasic=False):
+    """Apply ``F`` to all expressions in an expression tree from the
+    bottom up. If ``atoms`` is True, apply ``F`` even if there are no args;
+    if ``nonbasic`` is True, try to apply ``F`` to non-Basic objects.
+    """
+    args = getattr(rv, 'args', None)
+    if args is not None:
+        if args:
+            args = tuple([bottom_up(a, F, atoms, nonbasic) for a in args])
+            if args != rv.args:
+                rv = rv.func(*args)
+            rv = F(rv)
+        elif atoms:
+            rv = F(rv)
+    else:
+        if nonbasic:
+            try:
+                rv = F(rv)
+            except TypeError:
+                pass
+
+    return rv
+
+
+def postorder_traversal(node, keys=None):
+    """
+    Do a postorder traversal of a tree.
+
+    This generator recursively yields nodes that it has visited in a postorder
+    fashion. That is, it descends through the tree depth-first to yield all of
+    a node's children's postorder traversal before yielding the node itself.
+
+    Parameters
+    ==========
+
+    node : SymPy expression
+        The expression to traverse.
+    keys : (default None) sort key(s)
+        The key(s) used to sort args of Basic objects. When None, args of Basic
+        objects are processed in arbitrary order. If key is defined, it will
+        be passed along to ordered() as the only key(s) to use to sort the
+        arguments; if ``key`` is simply True then the default keys of
+        ``ordered`` will be used (node count and default_sort_key).
+
+    Yields
+    ======
+    subtree : SymPy expression
+        All of the subtrees in the tree.
+
+    Examples
+    ========
+
+    >>> from sympy import postorder_traversal
+    >>> from sympy.abc import w, x, y, z
+
+    The nodes are returned in the order that they are encountered unless key
+    is given; simply passing key=True will guarantee that the traversal is
+    unique.
+
+    >>> list(postorder_traversal(w + (x + y)*z)) # doctest: +SKIP
+    [z, y, x, x + y, z*(x + y), w, w + z*(x + y)]
+    >>> list(postorder_traversal(w + (x + y)*z, keys=True))
+    [w, z, x, y, x + y, z*(x + y), w + z*(x + y)]
+
+
+    """
+    if isinstance(node, Basic):
+        args = node.args
+        if keys:
+            if keys != True:
+                args = ordered(args, keys, default=False)
+            else:
+                args = ordered(args)
+        for arg in args:
+            yield from postorder_traversal(arg, keys)
+    elif iterable(node):
+        for item in node:
+            yield from postorder_traversal(item, keys)
+    yield node
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b27b4b036e5f2ed93a1ea88cd7d7144eb5615d4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/__init__.py
@@ -0,0 +1,35 @@
+from sympy.crypto.crypto import (cycle_list,
+        encipher_shift, encipher_affine, encipher_substitution,
+        check_and_join, encipher_vigenere, decipher_vigenere, bifid5_square,
+        bifid6_square, encipher_hill, decipher_hill,
+        encipher_bifid5, encipher_bifid6, decipher_bifid5,
+        decipher_bifid6, encipher_kid_rsa, decipher_kid_rsa,
+        kid_rsa_private_key, kid_rsa_public_key, decipher_rsa, rsa_private_key,
+        rsa_public_key, encipher_rsa, lfsr_connection_polynomial,
+        lfsr_autocorrelation, lfsr_sequence, encode_morse, decode_morse,
+        elgamal_private_key, elgamal_public_key, decipher_elgamal,
+        encipher_elgamal, dh_private_key, dh_public_key, dh_shared_key,
+        padded_key, encipher_bifid, decipher_bifid, bifid_square, bifid5,
+        bifid6, bifid10, decipher_gm, encipher_gm, gm_public_key,
+        gm_private_key, bg_private_key, bg_public_key, encipher_bg, decipher_bg,
+        encipher_rot13, decipher_rot13, encipher_atbash, decipher_atbash,
+        encipher_railfence, decipher_railfence)
+
+__all__ = [
+    'cycle_list', 'encipher_shift', 'encipher_affine',
+    'encipher_substitution', 'check_and_join', 'encipher_vigenere',
+    'decipher_vigenere', 'bifid5_square', 'bifid6_square', 'encipher_hill',
+    'decipher_hill', 'encipher_bifid5', 'encipher_bifid6', 'decipher_bifid5',
+    'decipher_bifid6', 'encipher_kid_rsa', 'decipher_kid_rsa',
+    'kid_rsa_private_key', 'kid_rsa_public_key', 'decipher_rsa',
+    'rsa_private_key', 'rsa_public_key', 'encipher_rsa',
+    'lfsr_connection_polynomial', 'lfsr_autocorrelation', 'lfsr_sequence',
+    'encode_morse', 'decode_morse', 'elgamal_private_key',
+    'elgamal_public_key', 'decipher_elgamal', 'encipher_elgamal',
+    'dh_private_key', 'dh_public_key', 'dh_shared_key', 'padded_key',
+    'encipher_bifid', 'decipher_bifid', 'bifid_square', 'bifid5', 'bifid6',
+    'bifid10', 'decipher_gm', 'encipher_gm', 'gm_public_key',
+    'gm_private_key', 'bg_private_key', 'bg_public_key', 'encipher_bg',
+    'decipher_bg', 'encipher_rot13', 'decipher_rot13', 'encipher_atbash',
+    'decipher_atbash', 'encipher_railfence', 'decipher_railfence',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/crypto.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/crypto.py
new file mode 100644
index 0000000000000000000000000000000000000000..2c298e4ac08616dbe7d607a9d56d33b7fe9d5e2d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/crypto.py
@@ -0,0 +1,3368 @@
+"""
+This file contains some classical ciphers and routines
+implementing a linear-feedback shift register (LFSR)
+and the Diffie-Hellman key exchange.
+
+.. warning::
+
+   This module is intended for educational purposes only. Do not use the
+   functions in this module for real cryptographic applications. If you wish
+   to encrypt real data, we recommend using something like the `cryptography
+   `_ module.
+
+"""
+
+from string import whitespace, ascii_uppercase as uppercase, printable
+from functools import reduce
+import string
+import warnings
+
+from itertools import cycle
+
+from sympy.external.gmpy import GROUND_TYPES
+from sympy.core import Symbol
+from sympy.core.numbers import Rational
+from sympy.core.random import _randrange, _randint
+from sympy.external.gmpy import gcd, invert
+from sympy.functions.combinatorial.numbers import (totient as _euler,
+                                                   reduced_totient as _carmichael)
+from sympy.matrices import Matrix
+from sympy.ntheory import isprime, primitive_root, factorint
+from sympy.ntheory.generate import nextprime
+from sympy.ntheory.modular import crt
+from sympy.polys.domains import FF
+from sympy.polys.polytools import Poly
+from sympy.utilities.misc import as_int, filldedent, translate
+from sympy.utilities.iterables import uniq, multiset
+from sympy.utilities.decorator import doctest_depends_on
+
+
+if GROUND_TYPES == 'flint':
+    __doctest_skip__ = ['lfsr_sequence']
+
+
+class NonInvertibleCipherWarning(RuntimeWarning):
+    """A warning raised if the cipher is not invertible."""
+    def __init__(self, msg):
+        self.fullMessage = msg
+
+    def __str__(self):
+        return '\n\t' + self.fullMessage
+
+    def warn(self, stacklevel=3):
+        warnings.warn(self, stacklevel=stacklevel)
+
+
+def AZ(s=None):
+    """Return the letters of ``s`` in uppercase. In case more than
+    one string is passed, each of them will be processed and a list
+    of upper case strings will be returned.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import AZ
+    >>> AZ('Hello, world!')
+    'HELLOWORLD'
+    >>> AZ('Hello, world!'.split())
+    ['HELLO', 'WORLD']
+
+    See Also
+    ========
+
+    check_and_join
+
+    """
+    if not s:
+        return uppercase
+    t = isinstance(s, str)
+    if t:
+        s = [s]
+    rv = [check_and_join(i.upper().split(), uppercase, filter=True)
+        for i in s]
+    if t:
+        return rv[0]
+    return rv
+
+bifid5 = AZ().replace('J', '')
+bifid6 = AZ() + string.digits
+bifid10 = printable
+
+
+def padded_key(key, symbols):
+    """Return a string of the distinct characters of ``symbols`` with
+    those of ``key`` appearing first. A ValueError is raised if
+    a) there are duplicate characters in ``symbols`` or
+    b) there are characters in ``key`` that are  not in ``symbols``.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import padded_key
+    >>> padded_key('PUPPY', 'OPQRSTUVWXY')
+    'PUYOQRSTVWX'
+    >>> padded_key('RSA', 'ARTIST')
+    Traceback (most recent call last):
+    ...
+    ValueError: duplicate characters in symbols: T
+
+    """
+    syms = list(uniq(symbols))
+    if len(syms) != len(symbols):
+        extra = ''.join(sorted({
+            i for i in symbols if symbols.count(i) > 1}))
+        raise ValueError('duplicate characters in symbols: %s' % extra)
+    extra = set(key) - set(syms)
+    if extra:
+        raise ValueError(
+            'characters in key but not symbols: %s' % ''.join(
+            sorted(extra)))
+    key0 = ''.join(list(uniq(key)))
+    # remove from syms characters in key0
+    return key0 + translate(''.join(syms), None, key0)
+
+
+def check_and_join(phrase, symbols=None, filter=None):
+    """
+    Joins characters of ``phrase`` and if ``symbols`` is given, raises
+    an error if any character in ``phrase`` is not in ``symbols``.
+
+    Parameters
+    ==========
+
+    phrase
+        String or list of strings to be returned as a string.
+
+    symbols
+        Iterable of characters allowed in ``phrase``.
+
+        If ``symbols`` is ``None``, no checking is performed.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import check_and_join
+    >>> check_and_join('a phrase')
+    'a phrase'
+    >>> check_and_join('a phrase'.upper().split())
+    'APHRASE'
+    >>> check_and_join('a phrase!'.upper().split(), 'ARE', filter=True)
+    'ARAE'
+    >>> check_and_join('a phrase!'.upper().split(), 'ARE')
+    Traceback (most recent call last):
+    ...
+    ValueError: characters in phrase but not symbols: "!HPS"
+
+    """
+    rv = ''.join(''.join(phrase))
+    if symbols is not None:
+        symbols = check_and_join(symbols)
+        missing = ''.join(sorted(set(rv) - set(symbols)))
+        if missing:
+            if not filter:
+                raise ValueError(
+                    'characters in phrase but not symbols: "%s"' % missing)
+            rv = translate(rv, None, missing)
+    return rv
+
+
+def _prep(msg, key, alp, default=None):
+    if not alp:
+        if not default:
+            alp = AZ()
+            msg = AZ(msg)
+            key = AZ(key)
+        else:
+            alp = default
+    else:
+        alp = ''.join(alp)
+    key = check_and_join(key, alp, filter=True)
+    msg = check_and_join(msg, alp, filter=True)
+    return msg, key, alp
+
+
+def cycle_list(k, n):
+    """
+    Returns the elements of the list ``range(n)`` shifted to the
+    left by ``k`` (so the list starts with ``k`` (mod ``n``)).
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import cycle_list
+    >>> cycle_list(3, 10)
+    [3, 4, 5, 6, 7, 8, 9, 0, 1, 2]
+
+    """
+    k = k % n
+    return list(range(k, n)) + list(range(k))
+
+
+######## shift cipher examples ############
+
+
+def encipher_shift(msg, key, symbols=None):
+    """
+    Performs shift cipher encryption on plaintext msg, and returns the
+    ciphertext.
+
+    Parameters
+    ==========
+
+    key : int
+        The secret key.
+
+    msg : str
+        Plaintext of upper-case letters.
+
+    Returns
+    =======
+
+    str
+        Ciphertext of upper-case letters.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_shift, decipher_shift
+    >>> msg = "GONAVYBEATARMY"
+    >>> ct = encipher_shift(msg, 1); ct
+    'HPOBWZCFBUBSNZ'
+
+    To decipher the shifted text, change the sign of the key:
+
+    >>> encipher_shift(ct, -1)
+    'GONAVYBEATARMY'
+
+    There is also a convenience function that does this with the
+    original key:
+
+    >>> decipher_shift(ct, 1)
+    'GONAVYBEATARMY'
+
+    Notes
+    =====
+
+    ALGORITHM:
+
+        STEPS:
+            0. Number the letters of the alphabet from 0, ..., N
+            1. Compute from the string ``msg`` a list ``L1`` of
+               corresponding integers.
+            2. Compute from the list ``L1`` a new list ``L2``, given by
+               adding ``(k mod 26)`` to each element in ``L1``.
+            3. Compute from the list ``L2`` a string ``ct`` of
+               corresponding letters.
+
+    The shift cipher is also called the Caesar cipher, after
+    Julius Caesar, who, according to Suetonius, used it with a
+    shift of three to protect messages of military significance.
+    Caesar's nephew Augustus reportedly used a similar cipher, but
+    with a right shift of 1.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Caesar_cipher
+    .. [2] https://mathworld.wolfram.com/CaesarsMethod.html
+
+    See Also
+    ========
+
+    decipher_shift
+
+    """
+    msg, _, A = _prep(msg, '', symbols)
+    shift = len(A) - key % len(A)
+    key = A[shift:] + A[:shift]
+    return translate(msg, key, A)
+
+
+def decipher_shift(msg, key, symbols=None):
+    """
+    Return the text by shifting the characters of ``msg`` to the
+    left by the amount given by ``key``.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_shift, decipher_shift
+    >>> msg = "GONAVYBEATARMY"
+    >>> ct = encipher_shift(msg, 1); ct
+    'HPOBWZCFBUBSNZ'
+
+    To decipher the shifted text, change the sign of the key:
+
+    >>> encipher_shift(ct, -1)
+    'GONAVYBEATARMY'
+
+    Or use this function with the original key:
+
+    >>> decipher_shift(ct, 1)
+    'GONAVYBEATARMY'
+
+    """
+    return encipher_shift(msg, -key, symbols)
+
+def encipher_rot13(msg, symbols=None):
+    """
+    Performs the ROT13 encryption on a given plaintext ``msg``.
+
+    Explanation
+    ===========
+
+    ROT13 is a substitution cipher which substitutes each letter
+    in the plaintext message for the letter furthest away from it
+    in the English alphabet.
+
+    Equivalently, it is just a Caeser (shift) cipher with a shift
+    key of 13 (midway point of the alphabet).
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/ROT13
+
+    See Also
+    ========
+
+    decipher_rot13
+    encipher_shift
+
+    """
+    return encipher_shift(msg, 13, symbols)
+
+def decipher_rot13(msg, symbols=None):
+    """
+    Performs the ROT13 decryption on a given plaintext ``msg``.
+
+    Explanation
+    ============
+
+    ``decipher_rot13`` is equivalent to ``encipher_rot13`` as both
+    ``decipher_shift`` with a key of 13 and ``encipher_shift`` key with a
+    key of 13 will return the same results. Nonetheless,
+    ``decipher_rot13`` has nonetheless been explicitly defined here for
+    consistency.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_rot13, decipher_rot13
+    >>> msg = 'GONAVYBEATARMY'
+    >>> ciphertext = encipher_rot13(msg);ciphertext
+    'TBANILORNGNEZL'
+    >>> decipher_rot13(ciphertext)
+    'GONAVYBEATARMY'
+    >>> encipher_rot13(msg) == decipher_rot13(msg)
+    True
+    >>> msg == decipher_rot13(ciphertext)
+    True
+
+    """
+    return decipher_shift(msg, 13, symbols)
+
+######## affine cipher examples ############
+
+
+def encipher_affine(msg, key, symbols=None, _inverse=False):
+    r"""
+    Performs the affine cipher encryption on plaintext ``msg``, and
+    returns the ciphertext.
+
+    Explanation
+    ===========
+
+    Encryption is based on the map `x \rightarrow ax+b` (mod `N`)
+    where ``N`` is the number of characters in the alphabet.
+    Decryption is based on the map `x \rightarrow cx+d` (mod `N`),
+    where `c = a^{-1}` (mod `N`) and `d = -a^{-1}b` (mod `N`).
+    In particular, for the map to be invertible, we need
+    `\mathrm{gcd}(a, N) = 1` and an error will be raised if this is
+    not true.
+
+    Parameters
+    ==========
+
+    msg : str
+        Characters that appear in ``symbols``.
+
+    a, b : int, int
+        A pair integers, with ``gcd(a, N) = 1`` (the secret key).
+
+    symbols
+        String of characters (default = uppercase letters).
+
+        When no symbols are given, ``msg`` is converted to upper case
+        letters and all other characters are ignored.
+
+    Returns
+    =======
+
+    ct
+        String of characters (the ciphertext message)
+
+    Notes
+    =====
+
+    ALGORITHM:
+
+        STEPS:
+            0. Number the letters of the alphabet from 0, ..., N
+            1. Compute from the string ``msg`` a list ``L1`` of
+               corresponding integers.
+            2. Compute from the list ``L1`` a new list ``L2``, given by
+               replacing ``x`` by ``a*x + b (mod N)``, for each element
+               ``x`` in ``L1``.
+            3. Compute from the list ``L2`` a string ``ct`` of
+               corresponding letters.
+
+    This is a straightforward generalization of the shift cipher with
+    the added complexity of requiring 2 characters to be deciphered in
+    order to recover the key.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Affine_cipher
+
+    See Also
+    ========
+
+    decipher_affine
+
+    """
+    msg, _, A = _prep(msg, '', symbols)
+    N = len(A)
+    a, b = key
+    assert gcd(a, N) == 1
+    if _inverse:
+        c = invert(a, N)
+        d = -b*c
+        a, b = c, d
+    B = ''.join([A[(a*i + b) % N] for i in range(N)])
+    return translate(msg, A, B)
+
+
+def decipher_affine(msg, key, symbols=None):
+    r"""
+    Return the deciphered text that was made from the mapping,
+    `x \rightarrow ax+b` (mod `N`), where ``N`` is the
+    number of characters in the alphabet. Deciphering is done by
+    reciphering with a new key: `x \rightarrow cx+d` (mod `N`),
+    where `c = a^{-1}` (mod `N`) and `d = -a^{-1}b` (mod `N`).
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_affine, decipher_affine
+    >>> msg = "GO NAVY BEAT ARMY"
+    >>> key = (3, 1)
+    >>> encipher_affine(msg, key)
+    'TROBMVENBGBALV'
+    >>> decipher_affine(_, key)
+    'GONAVYBEATARMY'
+
+    See Also
+    ========
+
+    encipher_affine
+
+    """
+    return encipher_affine(msg, key, symbols, _inverse=True)
+
+
+def encipher_atbash(msg, symbols=None):
+    r"""
+    Enciphers a given ``msg`` into its Atbash ciphertext and returns it.
+
+    Explanation
+    ===========
+
+    Atbash is a substitution cipher originally used to encrypt the Hebrew
+    alphabet. Atbash works on the principle of mapping each alphabet to its
+    reverse / counterpart (i.e. a would map to z, b to y etc.)
+
+    Atbash is functionally equivalent to the affine cipher with ``a = 25``
+    and ``b = 25``
+
+    See Also
+    ========
+
+    decipher_atbash
+
+    """
+    return encipher_affine(msg, (25, 25), symbols)
+
+
+def decipher_atbash(msg, symbols=None):
+    r"""
+    Deciphers a given ``msg`` using Atbash cipher and returns it.
+
+    Explanation
+    ===========
+
+    ``decipher_atbash`` is functionally equivalent to ``encipher_atbash``.
+    However, it has still been added as a separate function to maintain
+    consistency.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_atbash, decipher_atbash
+    >>> msg = 'GONAVYBEATARMY'
+    >>> encipher_atbash(msg)
+    'TLMZEBYVZGZINB'
+    >>> decipher_atbash(msg)
+    'TLMZEBYVZGZINB'
+    >>> encipher_atbash(msg) == decipher_atbash(msg)
+    True
+    >>> msg == encipher_atbash(encipher_atbash(msg))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Atbash
+
+    See Also
+    ========
+
+    encipher_atbash
+
+    """
+    return decipher_affine(msg, (25, 25), symbols)
+
+#################### substitution cipher ###########################
+
+
+def encipher_substitution(msg, old, new=None):
+    r"""
+    Returns the ciphertext obtained by replacing each character that
+    appears in ``old`` with the corresponding character in ``new``.
+    If ``old`` is a mapping, then new is ignored and the replacements
+    defined by ``old`` are used.
+
+    Explanation
+    ===========
+
+    This is a more general than the affine cipher in that the key can
+    only be recovered by determining the mapping for each symbol.
+    Though in practice, once a few symbols are recognized the mappings
+    for other characters can be quickly guessed.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_substitution, AZ
+    >>> old = 'OEYAG'
+    >>> new = '034^6'
+    >>> msg = AZ("go navy! beat army!")
+    >>> ct = encipher_substitution(msg, old, new); ct
+    '60N^V4B3^T^RM4'
+
+    To decrypt a substitution, reverse the last two arguments:
+
+    >>> encipher_substitution(ct, new, old)
+    'GONAVYBEATARMY'
+
+    In the special case where ``old`` and ``new`` are a permutation of
+    order 2 (representing a transposition of characters) their order
+    is immaterial:
+
+    >>> old = 'NAVY'
+    >>> new = 'ANYV'
+    >>> encipher = lambda x: encipher_substitution(x, old, new)
+    >>> encipher('NAVY')
+    'ANYV'
+    >>> encipher(_)
+    'NAVY'
+
+    The substitution cipher, in general, is a method
+    whereby "units" (not necessarily single characters) of plaintext
+    are replaced with ciphertext according to a regular system.
+
+    >>> ords = dict(zip('abc', ['\\%i' % ord(i) for i in 'abc']))
+    >>> print(encipher_substitution('abc', ords))
+    \97\98\99
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Substitution_cipher
+
+    """
+    return translate(msg, old, new)
+
+
+######################################################################
+#################### Vigenere cipher examples ########################
+######################################################################
+
+def encipher_vigenere(msg, key, symbols=None):
+    """
+    Performs the Vigenere cipher encryption on plaintext ``msg``, and
+    returns the ciphertext.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_vigenere, AZ
+    >>> key = "encrypt"
+    >>> msg = "meet me on monday"
+    >>> encipher_vigenere(msg, key)
+    'QRGKKTHRZQEBPR'
+
+    Section 1 of the Kryptos sculpture at the CIA headquarters
+    uses this cipher and also changes the order of the
+    alphabet [2]_. Here is the first line of that section of
+    the sculpture:
+
+    >>> from sympy.crypto.crypto import decipher_vigenere, padded_key
+    >>> alp = padded_key('KRYPTOS', AZ())
+    >>> key = 'PALIMPSEST'
+    >>> msg = 'EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJ'
+    >>> decipher_vigenere(msg, key, alp)
+    'BETWEENSUBTLESHADINGANDTHEABSENC'
+
+    Explanation
+    ===========
+
+    The Vigenere cipher is named after Blaise de Vigenere, a sixteenth
+    century diplomat and cryptographer, by a historical accident.
+    Vigenere actually invented a different and more complicated cipher.
+    The so-called *Vigenere cipher* was actually invented
+    by Giovan Batista Belaso in 1553.
+
+    This cipher was used in the 1800's, for example, during the American
+    Civil War. The Confederacy used a brass cipher disk to implement the
+    Vigenere cipher (now on display in the NSA Museum in Fort
+    Meade) [1]_.
+
+    The Vigenere cipher is a generalization of the shift cipher.
+    Whereas the shift cipher shifts each letter by the same amount
+    (that amount being the key of the shift cipher) the Vigenere
+    cipher shifts a letter by an amount determined by the key (which is
+    a word or phrase known only to the sender and receiver).
+
+    For example, if the key was a single letter, such as "C", then the
+    so-called Vigenere cipher is actually a shift cipher with a
+    shift of `2` (since "C" is the 2nd letter of the alphabet, if
+    you start counting at `0`). If the key was a word with two
+    letters, such as "CA", then the so-called Vigenere cipher will
+    shift letters in even positions by `2` and letters in odd positions
+    are left alone (shifted by `0`, since "A" is the 0th letter, if
+    you start counting at `0`).
+
+
+    ALGORITHM:
+
+        INPUT:
+
+            ``msg``: string of characters that appear in ``symbols``
+            (the plaintext)
+
+            ``key``: a string of characters that appear in ``symbols``
+            (the secret key)
+
+            ``symbols``: a string of letters defining the alphabet
+
+
+        OUTPUT:
+
+            ``ct``: string of characters (the ciphertext message)
+
+        STEPS:
+            0. Number the letters of the alphabet from 0, ..., N
+            1. Compute from the string ``key`` a list ``L1`` of
+               corresponding integers. Let ``n1 = len(L1)``.
+            2. Compute from the string ``msg`` a list ``L2`` of
+               corresponding integers. Let ``n2 = len(L2)``.
+            3. Break ``L2`` up sequentially into sublists of size
+               ``n1``; the last sublist may be smaller than ``n1``
+            4. For each of these sublists ``L`` of ``L2``, compute a
+               new list ``C`` given by ``C[i] = L[i] + L1[i] (mod N)``
+               to the ``i``-th element in the sublist, for each ``i``.
+            5. Assemble these lists ``C`` by concatenation into a new
+               list of length ``n2``.
+            6. Compute from the new list a string ``ct`` of
+               corresponding letters.
+
+    Once it is known that the key is, say, `n` characters long,
+    frequency analysis can be applied to every `n`-th letter of
+    the ciphertext to determine the plaintext. This method is
+    called *Kasiski examination* (although it was first discovered
+    by Babbage). If they key is as long as the message and is
+    comprised of randomly selected characters -- a one-time pad -- the
+    message is theoretically unbreakable.
+
+    The cipher Vigenere actually discovered is an "auto-key" cipher
+    described as follows.
+
+    ALGORITHM:
+
+        INPUT:
+
+          ``key``: a string of letters (the secret key)
+
+          ``msg``: string of letters (the plaintext message)
+
+        OUTPUT:
+
+          ``ct``: string of upper-case letters (the ciphertext message)
+
+        STEPS:
+            0. Number the letters of the alphabet from 0, ..., N
+            1. Compute from the string ``msg`` a list ``L2`` of
+               corresponding integers. Let ``n2 = len(L2)``.
+            2. Let ``n1`` be the length of the key. Append to the
+               string ``key`` the first ``n2 - n1`` characters of
+               the plaintext message. Compute from this string (also of
+               length ``n2``) a list ``L1`` of integers corresponding
+               to the letter numbers in the first step.
+            3. Compute a new list ``C`` given by
+               ``C[i] = L1[i] + L2[i] (mod N)``.
+            4. Compute from the new list a string ``ct`` of letters
+               corresponding to the new integers.
+
+    To decipher the auto-key ciphertext, the key is used to decipher
+    the first ``n1`` characters and then those characters become the
+    key to  decipher the next ``n1`` characters, etc...:
+
+    >>> m = AZ('go navy, beat army! yes you can'); m
+    'GONAVYBEATARMYYESYOUCAN'
+    >>> key = AZ('gold bug'); n1 = len(key); n2 = len(m)
+    >>> auto_key = key + m[:n2 - n1]; auto_key
+    'GOLDBUGGONAVYBEATARMYYE'
+    >>> ct = encipher_vigenere(m, auto_key); ct
+    'MCYDWSHKOGAMKZCELYFGAYR'
+    >>> n1 = len(key)
+    >>> pt = []
+    >>> while ct:
+    ...     part, ct = ct[:n1], ct[n1:]
+    ...     pt.append(decipher_vigenere(part, key))
+    ...     key = pt[-1]
+    ...
+    >>> ''.join(pt) == m
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Vigenere_cipher
+    .. [2] https://web.archive.org/web/20071116100808/https://filebox.vt.edu/users/batman/kryptos.html
+       (short URL: https://goo.gl/ijr22d)
+
+    """
+    msg, key, A = _prep(msg, key, symbols)
+    map = {c: i for i, c in enumerate(A)}
+    key = [map[c] for c in key]
+    N = len(map)
+    k = len(key)
+    rv = []
+    for i, m in enumerate(msg):
+        rv.append(A[(map[m] + key[i % k]) % N])
+    rv = ''.join(rv)
+    return rv
+
+
+def decipher_vigenere(msg, key, symbols=None):
+    """
+    Decode using the Vigenere cipher.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import decipher_vigenere
+    >>> key = "encrypt"
+    >>> ct = "QRGK kt HRZQE BPR"
+    >>> decipher_vigenere(ct, key)
+    'MEETMEONMONDAY'
+
+    """
+    msg, key, A = _prep(msg, key, symbols)
+    map = {c: i for i, c in enumerate(A)}
+    N = len(A)   # normally, 26
+    K = [map[c] for c in key]
+    n = len(K)
+    C = [map[c] for c in msg]
+    rv = ''.join([A[(-K[i % n] + c) % N] for i, c in enumerate(C)])
+    return rv
+
+
+#################### Hill cipher  ########################
+
+
+def encipher_hill(msg, key, symbols=None, pad="Q"):
+    r"""
+    Return the Hill cipher encryption of ``msg``.
+
+    Explanation
+    ===========
+
+    The Hill cipher [1]_, invented by Lester S. Hill in the 1920's [2]_,
+    was the first polygraphic cipher in which it was practical
+    (though barely) to operate on more than three symbols at once.
+    The following discussion assumes an elementary knowledge of
+    matrices.
+
+    First, each letter is first encoded as a number starting with 0.
+    Suppose your message `msg` consists of `n` capital letters, with no
+    spaces. This may be regarded an `n`-tuple M of elements of
+    `Z_{26}` (if the letters are those of the English alphabet). A key
+    in the Hill cipher is a `k x k` matrix `K`, all of whose entries
+    are in `Z_{26}`, such that the matrix `K` is invertible (i.e., the
+    linear transformation `K: Z_{N}^k \rightarrow Z_{N}^k`
+    is one-to-one).
+
+
+    Parameters
+    ==========
+
+    msg
+        Plaintext message of `n` upper-case letters.
+
+    key
+        A `k \times k` invertible matrix `K`, all of whose entries are
+        in `Z_{26}` (or whatever number of symbols are being used).
+
+    pad
+        Character (default "Q") to use to make length of text be a
+        multiple of ``k``.
+
+    Returns
+    =======
+
+    ct
+        Ciphertext of upper-case letters.
+
+    Notes
+    =====
+
+    ALGORITHM:
+
+        STEPS:
+            0. Number the letters of the alphabet from 0, ..., N
+            1. Compute from the string ``msg`` a list ``L`` of
+               corresponding integers. Let ``n = len(L)``.
+            2. Break the list ``L`` up into ``t = ceiling(n/k)``
+               sublists ``L_1``, ..., ``L_t`` of size ``k`` (with
+               the last list "padded" to ensure its size is
+               ``k``).
+            3. Compute new list ``C_1``, ..., ``C_t`` given by
+               ``C[i] = K*L_i`` (arithmetic is done mod N), for each
+               ``i``.
+            4. Concatenate these into a list ``C = C_1 + ... + C_t``.
+            5. Compute from ``C`` a string ``ct`` of corresponding
+               letters. This has length ``k*t``.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hill_cipher
+    .. [2] Lester S. Hill, Cryptography in an Algebraic Alphabet,
+       The American Mathematical Monthly Vol.36, June-July 1929,
+       pp.306-312.
+
+    See Also
+    ========
+
+    decipher_hill
+
+    """
+    assert key.is_square
+    assert len(pad) == 1
+    msg, pad, A = _prep(msg, pad, symbols)
+    map = {c: i for i, c in enumerate(A)}
+    P = [map[c] for c in msg]
+    N = len(A)
+    k = key.cols
+    n = len(P)
+    m, r = divmod(n, k)
+    if r:
+        P = P + [map[pad]]*(k - r)
+        m += 1
+    rv = ''.join([A[c % N] for j in range(m) for c in
+        list(key*Matrix(k, 1, [P[i]
+        for i in range(k*j, k*(j + 1))]))])
+    return rv
+
+
+def decipher_hill(msg, key, symbols=None):
+    """
+    Deciphering is the same as enciphering but using the inverse of the
+    key matrix.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_hill, decipher_hill
+    >>> from sympy import Matrix
+
+    >>> key = Matrix([[1, 2], [3, 5]])
+    >>> encipher_hill("meet me on monday", key)
+    'UEQDUEODOCTCWQ'
+    >>> decipher_hill(_, key)
+    'MEETMEONMONDAY'
+
+    When the length of the plaintext (stripped of invalid characters)
+    is not a multiple of the key dimension, extra characters will
+    appear at the end of the enciphered and deciphered text. In order to
+    decipher the text, those characters must be included in the text to
+    be deciphered. In the following, the key has a dimension of 4 but
+    the text is 2 short of being a multiple of 4 so two characters will
+    be added.
+
+    >>> key = Matrix([[1, 1, 1, 2], [0, 1, 1, 0],
+    ...               [2, 2, 3, 4], [1, 1, 0, 1]])
+    >>> msg = "ST"
+    >>> encipher_hill(msg, key)
+    'HJEB'
+    >>> decipher_hill(_, key)
+    'STQQ'
+    >>> encipher_hill(msg, key, pad="Z")
+    'ISPK'
+    >>> decipher_hill(_, key)
+    'STZZ'
+
+    If the last two characters of the ciphertext were ignored in
+    either case, the wrong plaintext would be recovered:
+
+    >>> decipher_hill("HD", key)
+    'ORMV'
+    >>> decipher_hill("IS", key)
+    'UIKY'
+
+    See Also
+    ========
+
+    encipher_hill
+
+    """
+    assert key.is_square
+    msg, _, A = _prep(msg, '', symbols)
+    map = {c: i for i, c in enumerate(A)}
+    C = [map[c] for c in msg]
+    N = len(A)
+    k = key.cols
+    n = len(C)
+    m, r = divmod(n, k)
+    if r:
+        C = C + [0]*(k - r)
+        m += 1
+    key_inv = key.inv_mod(N)
+    rv = ''.join([A[p % N] for j in range(m) for p in
+        list(key_inv*Matrix(
+        k, 1, [C[i] for i in range(k*j, k*(j + 1))]))])
+    return rv
+
+
+#################### Bifid cipher  ########################
+
+
+def encipher_bifid(msg, key, symbols=None):
+    r"""
+    Performs the Bifid cipher encryption on plaintext ``msg``, and
+    returns the ciphertext.
+
+    This is the version of the Bifid cipher that uses an `n \times n`
+    Polybius square.
+
+    Parameters
+    ==========
+
+    msg
+        Plaintext string.
+
+    key
+        Short string for key.
+
+        Duplicate characters are ignored and then it is padded with the
+        characters in ``symbols`` that were not in the short key.
+
+    symbols
+        `n \times n` characters defining the alphabet.
+
+        (default is string.printable)
+
+    Returns
+    =======
+
+    ciphertext
+        Ciphertext using Bifid5 cipher without spaces.
+
+    See Also
+    ========
+
+    decipher_bifid, encipher_bifid5, encipher_bifid6
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Bifid_cipher
+
+    """
+    msg, key, A = _prep(msg, key, symbols, bifid10)
+    long_key = ''.join(uniq(key)) or A
+
+    n = len(A)**.5
+    if n != int(n):
+        raise ValueError(
+            'Length of alphabet (%s) is not a square number.' % len(A))
+    N = int(n)
+    if len(long_key) < N**2:
+        long_key = list(long_key) + [x for x in A if x not in long_key]
+
+    # the fractionalization
+    row_col = {ch: divmod(i, N) for i, ch in enumerate(long_key)}
+    r, c = zip(*[row_col[x] for x in msg])
+    rc = r + c
+    ch = {i: ch for ch, i in row_col.items()}
+    rv = ''.join(ch[i] for i in zip(rc[::2], rc[1::2]))
+    return rv
+
+
+def decipher_bifid(msg, key, symbols=None):
+    r"""
+    Performs the Bifid cipher decryption on ciphertext ``msg``, and
+    returns the plaintext.
+
+    This is the version of the Bifid cipher that uses the `n \times n`
+    Polybius square.
+
+    Parameters
+    ==========
+
+    msg
+        Ciphertext string.
+
+    key
+        Short string for key.
+
+        Duplicate characters are ignored and then it is padded with the
+        characters in symbols that were not in the short key.
+
+    symbols
+        `n \times n` characters defining the alphabet.
+
+        (default=string.printable, a `10 \times 10` matrix)
+
+    Returns
+    =======
+
+    deciphered
+        Deciphered text.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     encipher_bifid, decipher_bifid, AZ)
+
+    Do an encryption using the bifid5 alphabet:
+
+    >>> alp = AZ().replace('J', '')
+    >>> ct = AZ("meet me on monday!")
+    >>> key = AZ("gold bug")
+    >>> encipher_bifid(ct, key, alp)
+    'IEILHHFSTSFQYE'
+
+    When entering the text or ciphertext, spaces are ignored so it
+    can be formatted as desired. Re-entering the ciphertext from the
+    preceding, putting 4 characters per line and padding with an extra
+    J, does not cause problems for the deciphering:
+
+    >>> decipher_bifid('''
+    ... IEILH
+    ... HFSTS
+    ... FQYEJ''', key, alp)
+    'MEETMEONMONDAY'
+
+    When no alphabet is given, all 100 printable characters will be
+    used:
+
+    >>> key = ''
+    >>> encipher_bifid('hello world!', key)
+    'bmtwmg-bIo*w'
+    >>> decipher_bifid(_, key)
+    'hello world!'
+
+    If the key is changed, a different encryption is obtained:
+
+    >>> key = 'gold bug'
+    >>> encipher_bifid('hello world!', 'gold_bug')
+    'hg2sfuei7t}w'
+
+    And if the key used to decrypt the message is not exact, the
+    original text will not be perfectly obtained:
+
+    >>> decipher_bifid(_, 'gold pug')
+    'heldo~wor6d!'
+
+    """
+    msg, _, A = _prep(msg, '', symbols, bifid10)
+    long_key = ''.join(uniq(key)) or A
+
+    n = len(A)**.5
+    if n != int(n):
+        raise ValueError(
+            'Length of alphabet (%s) is not a square number.' % len(A))
+    N = int(n)
+    if len(long_key) < N**2:
+        long_key = list(long_key) + [x for x in A if x not in long_key]
+
+    # the reverse fractionalization
+    row_col = {
+        ch: divmod(i, N) for i, ch in enumerate(long_key)}
+    rc = [i for c in msg for i in row_col[c]]
+    n = len(msg)
+    rc = zip(*(rc[:n], rc[n:]))
+    ch = {i: ch for ch, i in row_col.items()}
+    rv = ''.join(ch[i] for i in rc)
+    return rv
+
+
+def bifid_square(key):
+    """Return characters of ``key`` arranged in a square.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...    bifid_square, AZ, padded_key, bifid5)
+    >>> bifid_square(AZ().replace('J', ''))
+    Matrix([
+    [A, B, C, D, E],
+    [F, G, H, I, K],
+    [L, M, N, O, P],
+    [Q, R, S, T, U],
+    [V, W, X, Y, Z]])
+
+    >>> bifid_square(padded_key(AZ('gold bug!'), bifid5))
+    Matrix([
+    [G, O, L, D, B],
+    [U, A, C, E, F],
+    [H, I, K, M, N],
+    [P, Q, R, S, T],
+    [V, W, X, Y, Z]])
+
+    See Also
+    ========
+
+    padded_key
+
+    """
+    A = ''.join(uniq(''.join(key)))
+    n = len(A)**.5
+    if n != int(n):
+        raise ValueError(
+            'Length of alphabet (%s) is not a square number.' % len(A))
+    n = int(n)
+    f = lambda i, j: Symbol(A[n*i + j])
+    rv = Matrix(n, n, f)
+    return rv
+
+
+def encipher_bifid5(msg, key):
+    r"""
+    Performs the Bifid cipher encryption on plaintext ``msg``, and
+    returns the ciphertext.
+
+    Explanation
+    ===========
+
+    This is the version of the Bifid cipher that uses the `5 \times 5`
+    Polybius square. The letter "J" is ignored so it must be replaced
+    with something else (traditionally an "I") before encryption.
+
+    ALGORITHM: (5x5 case)
+
+        STEPS:
+            0. Create the `5 \times 5` Polybius square ``S`` associated
+               to ``key`` as follows:
+
+                a) moving from left-to-right, top-to-bottom,
+                   place the letters of the key into a `5 \times 5`
+                   matrix,
+                b) if the key has less than 25 letters, add the
+                   letters of the alphabet not in the key until the
+                   `5 \times 5` square is filled.
+
+            1. Create a list ``P`` of pairs of numbers which are the
+               coordinates in the Polybius square of the letters in
+               ``msg``.
+            2. Let ``L1`` be the list of all first coordinates of ``P``
+               (length of ``L1 = n``), let ``L2`` be the list of all
+               second coordinates of ``P`` (so the length of ``L2``
+               is also ``n``).
+            3. Let ``L`` be the concatenation of ``L1`` and ``L2``
+               (length ``L = 2*n``), except that consecutive numbers
+               are paired ``(L[2*i], L[2*i + 1])``. You can regard
+               ``L`` as a list of pairs of length ``n``.
+            4. Let ``C`` be the list of all letters which are of the
+               form ``S[i, j]``, for all ``(i, j)`` in ``L``. As a
+               string, this is the ciphertext of ``msg``.
+
+    Parameters
+    ==========
+
+    msg : str
+        Plaintext string.
+
+        Converted to upper case and filtered of anything but all letters
+        except J.
+
+    key
+        Short string for key; non-alphabetic letters, J and duplicated
+        characters are ignored and then, if the length is less than 25
+        characters, it is padded with other letters of the alphabet
+        (in alphabetical order).
+
+    Returns
+    =======
+
+    ct
+        Ciphertext (all caps, no spaces).
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     encipher_bifid5, decipher_bifid5)
+
+    "J" will be omitted unless it is replaced with something else:
+
+    >>> round_trip = lambda m, k: \
+    ...     decipher_bifid5(encipher_bifid5(m, k), k)
+    >>> key = 'a'
+    >>> msg = "JOSIE"
+    >>> round_trip(msg, key)
+    'OSIE'
+    >>> round_trip(msg.replace("J", "I"), key)
+    'IOSIE'
+    >>> j = "QIQ"
+    >>> round_trip(msg.replace("J", j), key).replace(j, "J")
+    'JOSIE'
+
+
+    Notes
+    =====
+
+    The Bifid cipher was invented around 1901 by Felix Delastelle.
+    It is a *fractional substitution* cipher, where letters are
+    replaced by pairs of symbols from a smaller alphabet. The
+    cipher uses a `5 \times 5` square filled with some ordering of the
+    alphabet, except that "J" is replaced with "I" (this is a so-called
+    Polybius square; there is a `6 \times 6` analog if you add back in
+    "J" and also append onto the usual 26 letter alphabet, the digits
+    0, 1, ..., 9).
+    According to Helen Gaines' book *Cryptanalysis*, this type of cipher
+    was used in the field by the German Army during World War I.
+
+    See Also
+    ========
+
+    decipher_bifid5, encipher_bifid
+
+    """
+    msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid5)
+    key = padded_key(key, bifid5)
+    return encipher_bifid(msg, '', key)
+
+
+def decipher_bifid5(msg, key):
+    r"""
+    Return the Bifid cipher decryption of ``msg``.
+
+    Explanation
+    ===========
+
+    This is the version of the Bifid cipher that uses the `5 \times 5`
+    Polybius square; the letter "J" is ignored unless a ``key`` of
+    length 25 is used.
+
+    Parameters
+    ==========
+
+    msg
+        Ciphertext string.
+
+    key
+        Short string for key; duplicated characters are ignored and if
+        the length is less then 25 characters, it will be padded with
+        other letters from the alphabet omitting "J".
+        Non-alphabetic characters are ignored.
+
+    Returns
+    =======
+
+    plaintext
+        Plaintext from Bifid5 cipher (all caps, no spaces).
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_bifid5, decipher_bifid5
+    >>> key = "gold bug"
+    >>> encipher_bifid5('meet me on friday', key)
+    'IEILEHFSTSFXEE'
+    >>> encipher_bifid5('meet me on monday', key)
+    'IEILHHFSTSFQYE'
+    >>> decipher_bifid5(_, key)
+    'MEETMEONMONDAY'
+
+    """
+    msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid5)
+    key = padded_key(key, bifid5)
+    return decipher_bifid(msg, '', key)
+
+
+def bifid5_square(key=None):
+    r"""
+    5x5 Polybius square.
+
+    Produce the Polybius square for the `5 \times 5` Bifid cipher.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import bifid5_square
+    >>> bifid5_square("gold bug")
+    Matrix([
+    [G, O, L, D, B],
+    [U, A, C, E, F],
+    [H, I, K, M, N],
+    [P, Q, R, S, T],
+    [V, W, X, Y, Z]])
+
+    """
+    if not key:
+        key = bifid5
+    else:
+        _, key, _ = _prep('', key.upper(), None, bifid5)
+        key = padded_key(key, bifid5)
+    return bifid_square(key)
+
+
+def encipher_bifid6(msg, key):
+    r"""
+    Performs the Bifid cipher encryption on plaintext ``msg``, and
+    returns the ciphertext.
+
+    This is the version of the Bifid cipher that uses the `6 \times 6`
+    Polybius square.
+
+    Parameters
+    ==========
+
+    msg
+        Plaintext string (digits okay).
+
+    key
+        Short string for key (digits okay).
+
+        If ``key`` is less than 36 characters long, the square will be
+        filled with letters A through Z and digits 0 through 9.
+
+    Returns
+    =======
+
+    ciphertext
+        Ciphertext from Bifid cipher (all caps, no spaces).
+
+    See Also
+    ========
+
+    decipher_bifid6, encipher_bifid
+
+    """
+    msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid6)
+    key = padded_key(key, bifid6)
+    return encipher_bifid(msg, '', key)
+
+
+def decipher_bifid6(msg, key):
+    r"""
+    Performs the Bifid cipher decryption on ciphertext ``msg``, and
+    returns the plaintext.
+
+    This is the version of the Bifid cipher that uses the `6 \times 6`
+    Polybius square.
+
+    Parameters
+    ==========
+
+    msg
+        Ciphertext string (digits okay); converted to upper case
+
+    key
+        Short string for key (digits okay).
+
+        If ``key`` is less than 36 characters long, the square will be
+        filled with letters A through Z and digits 0 through 9.
+        All letters are converted to uppercase.
+
+    Returns
+    =======
+
+    plaintext
+        Plaintext from Bifid cipher (all caps, no spaces).
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_bifid6, decipher_bifid6
+    >>> key = "gold bug"
+    >>> encipher_bifid6('meet me on monday at 8am', key)
+    'KFKLJJHF5MMMKTFRGPL'
+    >>> decipher_bifid6(_, key)
+    'MEETMEONMONDAYAT8AM'
+
+    """
+    msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid6)
+    key = padded_key(key, bifid6)
+    return decipher_bifid(msg, '', key)
+
+
+def bifid6_square(key=None):
+    r"""
+    6x6 Polybius square.
+
+    Produces the Polybius square for the `6 \times 6` Bifid cipher.
+    Assumes alphabet of symbols is "A", ..., "Z", "0", ..., "9".
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import bifid6_square
+    >>> key = "gold bug"
+    >>> bifid6_square(key)
+    Matrix([
+    [G, O, L, D, B, U],
+    [A, C, E, F, H, I],
+    [J, K, M, N, P, Q],
+    [R, S, T, V, W, X],
+    [Y, Z, 0, 1, 2, 3],
+    [4, 5, 6, 7, 8, 9]])
+
+    """
+    if not key:
+        key = bifid6
+    else:
+        _, key, _ = _prep('', key.upper(), None, bifid6)
+        key = padded_key(key, bifid6)
+    return bifid_square(key)
+
+
+#################### RSA  #############################
+
+def _decipher_rsa_crt(i, d, factors):
+    """Decipher RSA using chinese remainder theorem from the information
+    of the relatively-prime factors of the modulus.
+
+    Parameters
+    ==========
+
+    i : integer
+        Ciphertext
+
+    d : integer
+        The exponent component.
+
+    factors : list of relatively-prime integers
+        The integers given must be coprime and the product must equal
+        the modulus component of the original RSA key.
+
+    Examples
+    ========
+
+    How to decrypt RSA with CRT:
+
+    >>> from sympy.crypto.crypto import rsa_public_key, rsa_private_key
+    >>> primes = [61, 53]
+    >>> e = 17
+    >>> args = primes + [e]
+    >>> puk = rsa_public_key(*args)
+    >>> prk = rsa_private_key(*args)
+
+    >>> from sympy.crypto.crypto import encipher_rsa, _decipher_rsa_crt
+    >>> msg = 65
+    >>> crt_primes = primes
+    >>> encrypted = encipher_rsa(msg, puk)
+    >>> decrypted = _decipher_rsa_crt(encrypted, prk[1], primes)
+    >>> decrypted
+    65
+    """
+    moduluses = [pow(i, d, p) for p in factors]
+
+    result = crt(factors, moduluses)
+    if not result:
+        raise ValueError("CRT failed")
+    return result[0]
+
+
+def _rsa_key(*args, public=True, private=True, totient='Euler', index=None, multipower=None):
+    r"""A private subroutine to generate RSA key
+
+    Parameters
+    ==========
+
+    public, private : bool, optional
+        Flag to generate either a public key, a private key.
+
+    totient : 'Euler' or 'Carmichael'
+        Different notation used for totient.
+
+    multipower : bool, optional
+        Flag to bypass warning for multipower RSA.
+    """
+
+    if len(args) < 2:
+        return False
+
+    if totient not in ('Euler', 'Carmichael'):
+        raise ValueError(
+            "The argument totient={} should either be " \
+            "'Euler', 'Carmichalel'." \
+            .format(totient))
+
+    if totient == 'Euler':
+        _totient = _euler
+    else:
+        _totient = _carmichael
+
+    if index is not None:
+        index = as_int(index)
+        if totient != 'Carmichael':
+            raise ValueError(
+                "Setting the 'index' keyword argument requires totient"
+                "notation to be specified as 'Carmichael'.")
+
+    primes, e = args[:-1], args[-1]
+
+    if not all(isprime(p) for p in primes):
+        new_primes = []
+        for i in primes:
+            new_primes.extend(factorint(i, multiple=True))
+        primes = new_primes
+
+    n = reduce(lambda i, j: i*j, primes)
+
+    tally = multiset(primes)
+    if all(v == 1 for v in tally.values()):
+        phi = int(_totient(tally))
+
+    else:
+        if not multipower:
+            NonInvertibleCipherWarning(
+                'Non-distinctive primes found in the factors {}. '
+                'The cipher may not be decryptable for some numbers '
+                'in the complete residue system Z[{}], but the cipher '
+                'can still be valid if you restrict the domain to be '
+                'the reduced residue system Z*[{}]. You can pass '
+                'the flag multipower=True if you want to suppress this '
+                'warning.'
+                .format(primes, n, n)
+                # stacklevel=4 because most users will call a function that
+                # calls this function
+                ).warn(stacklevel=4)
+        phi = int(_totient(tally))
+
+    if gcd(e, phi) == 1:
+        if public and not private:
+            if isinstance(index, int):
+                e = e % phi
+                e += index * phi
+            return n, e
+
+        if private and not public:
+            d = invert(e, phi)
+            if isinstance(index, int):
+                d += index * phi
+            return n, d
+
+    return False
+
+
+def rsa_public_key(*args, **kwargs):
+    r"""Return the RSA *public key* pair, `(n, e)`
+
+    Parameters
+    ==========
+
+    args : naturals
+        If specified as `p, q, e` where `p` and `q` are distinct primes
+        and `e` is a desired public exponent of the RSA, `n = p q` and
+        `e` will be verified against the totient
+        `\phi(n)` (Euler totient) or `\lambda(n)` (Carmichael totient)
+        to be `\gcd(e, \phi(n)) = 1` or `\gcd(e, \lambda(n)) = 1`.
+
+        If specified as `p_1, p_2, \dots, p_n, e` where
+        `p_1, p_2, \dots, p_n` are specified as primes,
+        and `e` is specified as a desired public exponent of the RSA,
+        it will be able to form a multi-prime RSA, which is a more
+        generalized form of the popular 2-prime RSA.
+
+        It can also be possible to form a single-prime RSA by specifying
+        the argument as `p, e`, which can be considered a trivial case
+        of a multiprime RSA.
+
+        Furthermore, it can be possible to form a multi-power RSA by
+        specifying two or more pairs of the primes to be same.
+        However, unlike the two-distinct prime RSA or multi-prime
+        RSA, not every numbers in the complete residue system
+        (`\mathbb{Z}_n`) will be decryptable since the mapping
+        `\mathbb{Z}_{n} \rightarrow \mathbb{Z}_{n}`
+        will not be bijective.
+        (Only except for the trivial case when
+        `e = 1`
+        or more generally,
+
+        .. math::
+            e \in \left \{ 1 + k \lambda(n)
+            \mid k \in \mathbb{Z} \land k \geq 0 \right \}
+
+        when RSA reduces to the identity.)
+        However, the RSA can still be decryptable for the numbers in the
+        reduced residue system (`\mathbb{Z}_n^{\times}`), since the
+        mapping
+        `\mathbb{Z}_{n}^{\times} \rightarrow \mathbb{Z}_{n}^{\times}`
+        can still be bijective.
+
+        If you pass a non-prime integer to the arguments
+        `p_1, p_2, \dots, p_n`, the particular number will be
+        prime-factored and it will become either a multi-prime RSA or a
+        multi-power RSA in its canonical form, depending on whether the
+        product equals its radical or not.
+        `p_1 p_2 \dots p_n = \text{rad}(p_1 p_2 \dots p_n)`
+
+    totient : bool, optional
+        If ``'Euler'``, it uses Euler's totient `\phi(n)` which is
+        :meth:`sympy.functions.combinatorial.numbers.totient` in SymPy.
+
+        If ``'Carmichael'``, it uses Carmichael's totient `\lambda(n)`
+        which is :meth:`sympy.functions.combinatorial.numbers.reduced_totient` in SymPy.
+
+        Unlike private key generation, this is a trivial keyword for
+        public key generation because
+        `\gcd(e, \phi(n)) = 1 \iff \gcd(e, \lambda(n)) = 1`.
+
+    index : nonnegative integer, optional
+        Returns an arbitrary solution of a RSA public key at the index
+        specified at `0, 1, 2, \dots`. This parameter needs to be
+        specified along with ``totient='Carmichael'``.
+
+        Similarly to the non-uniquenss of a RSA private key as described
+        in the ``index`` parameter documentation in
+        :meth:`rsa_private_key`, RSA public key is also not unique and
+        there is an infinite number of RSA public exponents which
+        can behave in the same manner.
+
+        From any given RSA public exponent `e`, there are can be an
+        another RSA public exponent `e + k \lambda(n)` where `k` is an
+        integer, `\lambda` is a Carmichael's totient function.
+
+        However, considering only the positive cases, there can be
+        a principal solution of a RSA public exponent `e_0` in
+        `0 < e_0 < \lambda(n)`, and all the other solutions
+        can be canonicalzed in a form of `e_0 + k \lambda(n)`.
+
+        ``index`` specifies the `k` notation to yield any possible value
+        an RSA public key can have.
+
+        An example of computing any arbitrary RSA public key:
+
+        >>> from sympy.crypto.crypto import rsa_public_key
+        >>> rsa_public_key(61, 53, 17, totient='Carmichael', index=0)
+        (3233, 17)
+        >>> rsa_public_key(61, 53, 17, totient='Carmichael', index=1)
+        (3233, 797)
+        >>> rsa_public_key(61, 53, 17, totient='Carmichael', index=2)
+        (3233, 1577)
+
+    multipower : bool, optional
+        Any pair of non-distinct primes found in the RSA specification
+        will restrict the domain of the cryptosystem, as noted in the
+        explanation of the parameter ``args``.
+
+        SymPy RSA key generator may give a warning before dispatching it
+        as a multi-power RSA, however, you can disable the warning if
+        you pass ``True`` to this keyword.
+
+    Returns
+    =======
+
+    (n, e) : int, int
+        `n` is a product of any arbitrary number of primes given as
+        the argument.
+
+        `e` is relatively prime (coprime) to the Euler totient
+        `\phi(n)`.
+
+    False
+        Returned if less than two arguments are given, or `e` is
+        not relatively prime to the modulus.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import rsa_public_key
+
+    A public key of a two-prime RSA:
+
+    >>> p, q, e = 3, 5, 7
+    >>> rsa_public_key(p, q, e)
+    (15, 7)
+    >>> rsa_public_key(p, q, 30)
+    False
+
+    A public key of a multiprime RSA:
+
+    >>> primes = [2, 3, 5, 7, 11, 13]
+    >>> e = 7
+    >>> args = primes + [e]
+    >>> rsa_public_key(*args)
+    (30030, 7)
+
+    Notes
+    =====
+
+    Although the RSA can be generalized over any modulus `n`, using
+    two large primes had became the most popular specification because a
+    product of two large primes is usually the hardest to factor
+    relatively to the digits of `n` can have.
+
+    However, it may need further understanding of the time complexities
+    of each prime-factoring algorithms to verify the claim.
+
+    See Also
+    ========
+
+    rsa_private_key
+    encipher_rsa
+    decipher_rsa
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29
+
+    .. [2] https://cacr.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
+
+    .. [3] https://link.springer.com/content/pdf/10.1007/BFb0055738.pdf
+
+    .. [4] https://www.itiis.org/digital-library/manuscript/1381
+    """
+    return _rsa_key(*args, public=True, private=False, **kwargs)
+
+
+def rsa_private_key(*args, **kwargs):
+    r"""Return the RSA *private key* pair, `(n, d)`
+
+    Parameters
+    ==========
+
+    args : naturals
+        The keyword is identical to the ``args`` in
+        :meth:`rsa_public_key`.
+
+    totient : bool, optional
+        If ``'Euler'``, it uses Euler's totient convention `\phi(n)`
+        which is :meth:`sympy.functions.combinatorial.numbers.totient` in SymPy.
+
+        If ``'Carmichael'``, it uses Carmichael's totient convention
+        `\lambda(n)` which is
+        :meth:`sympy.functions.combinatorial.numbers.reduced_totient` in SymPy.
+
+        There can be some output differences for private key generation
+        as examples below.
+
+        Example using Euler's totient:
+
+        >>> from sympy.crypto.crypto import rsa_private_key
+        >>> rsa_private_key(61, 53, 17, totient='Euler')
+        (3233, 2753)
+
+        Example using Carmichael's totient:
+
+        >>> from sympy.crypto.crypto import rsa_private_key
+        >>> rsa_private_key(61, 53, 17, totient='Carmichael')
+        (3233, 413)
+
+    index : nonnegative integer, optional
+        Returns an arbitrary solution of a RSA private key at the index
+        specified at `0, 1, 2, \dots`. This parameter needs to be
+        specified along with ``totient='Carmichael'``.
+
+        RSA private exponent is a non-unique solution of
+        `e d \mod \lambda(n) = 1` and it is possible in any form of
+        `d + k \lambda(n)`, where `d` is an another
+        already-computed private exponent, and `\lambda` is a
+        Carmichael's totient function, and `k` is any integer.
+
+        However, considering only the positive cases, there can be
+        a principal solution of a RSA private exponent `d_0` in
+        `0 < d_0 < \lambda(n)`, and all the other solutions
+        can be canonicalzed in a form of `d_0 + k \lambda(n)`.
+
+        ``index`` specifies the `k` notation to yield any possible value
+        an RSA private key can have.
+
+        An example of computing any arbitrary RSA private key:
+
+        >>> from sympy.crypto.crypto import rsa_private_key
+        >>> rsa_private_key(61, 53, 17, totient='Carmichael', index=0)
+        (3233, 413)
+        >>> rsa_private_key(61, 53, 17, totient='Carmichael', index=1)
+        (3233, 1193)
+        >>> rsa_private_key(61, 53, 17, totient='Carmichael', index=2)
+        (3233, 1973)
+
+    multipower : bool, optional
+        The keyword is identical to the ``multipower`` in
+        :meth:`rsa_public_key`.
+
+    Returns
+    =======
+
+    (n, d) : int, int
+        `n` is a product of any arbitrary number of primes given as
+        the argument.
+
+        `d` is the inverse of `e` (mod `\phi(n)`) where `e` is the
+        exponent given, and `\phi` is a Euler totient.
+
+    False
+        Returned if less than two arguments are given, or `e` is
+        not relatively prime to the totient of the modulus.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import rsa_private_key
+
+    A private key of a two-prime RSA:
+
+    >>> p, q, e = 3, 5, 7
+    >>> rsa_private_key(p, q, e)
+    (15, 7)
+    >>> rsa_private_key(p, q, 30)
+    False
+
+    A private key of a multiprime RSA:
+
+    >>> primes = [2, 3, 5, 7, 11, 13]
+    >>> e = 7
+    >>> args = primes + [e]
+    >>> rsa_private_key(*args)
+    (30030, 823)
+
+    See Also
+    ========
+
+    rsa_public_key
+    encipher_rsa
+    decipher_rsa
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29
+
+    .. [2] https://cacr.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
+
+    .. [3] https://link.springer.com/content/pdf/10.1007/BFb0055738.pdf
+
+    .. [4] https://www.itiis.org/digital-library/manuscript/1381
+    """
+    return _rsa_key(*args, public=False, private=True, **kwargs)
+
+
+def _encipher_decipher_rsa(i, key, factors=None):
+    n, d = key
+    if not factors:
+        return pow(i, d, n)
+
+    def _is_coprime_set(l):
+        is_coprime_set = True
+        for i in range(len(l)):
+            for j in range(i+1, len(l)):
+                if gcd(l[i], l[j]) != 1:
+                    is_coprime_set = False
+                    break
+        return is_coprime_set
+
+    prod = reduce(lambda i, j: i*j, factors)
+    if prod == n and _is_coprime_set(factors):
+        return _decipher_rsa_crt(i, d, factors)
+    return _encipher_decipher_rsa(i, key, factors=None)
+
+
+def encipher_rsa(i, key, factors=None):
+    r"""Encrypt the plaintext with RSA.
+
+    Parameters
+    ==========
+
+    i : integer
+        The plaintext to be encrypted for.
+
+    key : (n, e) where n, e are integers
+        `n` is the modulus of the key and `e` is the exponent of the
+        key. The encryption is computed by `i^e \bmod n`.
+
+        The key can either be a public key or a private key, however,
+        the message encrypted by a public key can only be decrypted by
+        a private key, and vice versa, as RSA is an asymmetric
+        cryptography system.
+
+    factors : list of coprime integers
+        This is identical to the keyword ``factors`` in
+        :meth:`decipher_rsa`.
+
+    Notes
+    =====
+
+    Some specifications may make the RSA not cryptographically
+    meaningful.
+
+    For example, `0`, `1` will remain always same after taking any
+    number of exponentiation, thus, should be avoided.
+
+    Furthermore, if `i^e < n`, `i` may easily be figured out by taking
+    `e` th root.
+
+    And also, specifying the exponent as `1` or in more generalized form
+    as `1 + k \lambda(n)` where `k` is an nonnegative integer,
+    `\lambda` is a carmichael totient, the RSA becomes an identity
+    mapping.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_rsa
+    >>> from sympy.crypto.crypto import rsa_public_key, rsa_private_key
+
+    Public Key Encryption:
+
+    >>> p, q, e = 3, 5, 7
+    >>> puk = rsa_public_key(p, q, e)
+    >>> msg = 12
+    >>> encipher_rsa(msg, puk)
+    3
+
+    Private Key Encryption:
+
+    >>> p, q, e = 3, 5, 7
+    >>> prk = rsa_private_key(p, q, e)
+    >>> msg = 12
+    >>> encipher_rsa(msg, prk)
+    3
+
+    Encryption using chinese remainder theorem:
+
+    >>> encipher_rsa(msg, prk, factors=[p, q])
+    3
+    """
+    return _encipher_decipher_rsa(i, key, factors=factors)
+
+
+def decipher_rsa(i, key, factors=None):
+    r"""Decrypt the ciphertext with RSA.
+
+    Parameters
+    ==========
+
+    i : integer
+        The ciphertext to be decrypted for.
+
+    key : (n, d) where n, d are integers
+        `n` is the modulus of the key and `d` is the exponent of the
+        key. The decryption is computed by `i^d \bmod n`.
+
+        The key can either be a public key or a private key, however,
+        the message encrypted by a public key can only be decrypted by
+        a private key, and vice versa, as RSA is an asymmetric
+        cryptography system.
+
+    factors : list of coprime integers
+        As the modulus `n` created from RSA key generation is composed
+        of arbitrary prime factors
+        `n = {p_1}^{k_1}{p_2}^{k_2}\dots{p_n}^{k_n}` where
+        `p_1, p_2, \dots, p_n` are distinct primes and
+        `k_1, k_2, \dots, k_n` are positive integers, chinese remainder
+        theorem can be used to compute `i^d \bmod n` from the
+        fragmented modulo operations like
+
+        .. math::
+            i^d \bmod {p_1}^{k_1}, i^d \bmod {p_2}^{k_2}, \dots,
+            i^d \bmod {p_n}^{k_n}
+
+        or like
+
+        .. math::
+            i^d \bmod {p_1}^{k_1}{p_2}^{k_2},
+            i^d \bmod {p_3}^{k_3}, \dots ,
+            i^d \bmod {p_n}^{k_n}
+
+        as long as every moduli does not share any common divisor each
+        other.
+
+        The raw primes used in generating the RSA key pair can be a good
+        option.
+
+        Note that the speed advantage of using this is only viable for
+        very large cases (Like 2048-bit RSA keys) since the
+        overhead of using pure Python implementation of
+        :meth:`sympy.ntheory.modular.crt` may overcompensate the
+        theoretical speed advantage.
+
+    Notes
+    =====
+
+    See the ``Notes`` section in the documentation of
+    :meth:`encipher_rsa`
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import decipher_rsa, encipher_rsa
+    >>> from sympy.crypto.crypto import rsa_public_key, rsa_private_key
+
+    Public Key Encryption and Decryption:
+
+    >>> p, q, e = 3, 5, 7
+    >>> prk = rsa_private_key(p, q, e)
+    >>> puk = rsa_public_key(p, q, e)
+    >>> msg = 12
+    >>> new_msg = encipher_rsa(msg, prk)
+    >>> new_msg
+    3
+    >>> decipher_rsa(new_msg, puk)
+    12
+
+    Private Key Encryption and Decryption:
+
+    >>> p, q, e = 3, 5, 7
+    >>> prk = rsa_private_key(p, q, e)
+    >>> puk = rsa_public_key(p, q, e)
+    >>> msg = 12
+    >>> new_msg = encipher_rsa(msg, puk)
+    >>> new_msg
+    3
+    >>> decipher_rsa(new_msg, prk)
+    12
+
+    Decryption using chinese remainder theorem:
+
+    >>> decipher_rsa(new_msg, prk, factors=[p, q])
+    12
+
+    See Also
+    ========
+
+    encipher_rsa
+    """
+    return _encipher_decipher_rsa(i, key, factors=factors)
+
+
+#################### kid krypto (kid RSA) #############################
+
+
+def kid_rsa_public_key(a, b, A, B):
+    r"""
+    Kid RSA is a version of RSA useful to teach grade school children
+    since it does not involve exponentiation.
+
+    Explanation
+    ===========
+
+    Alice wants to talk to Bob. Bob generates keys as follows.
+    Key generation:
+
+    * Select positive integers `a, b, A, B` at random.
+    * Compute `M = a b - 1`, `e = A M + a`, `d = B M + b`,
+      `n = (e d - 1)//M`.
+    * The *public key* is `(n, e)`. Bob sends these to Alice.
+    * The *private key* is `(n, d)`, which Bob keeps secret.
+
+    Encryption: If `p` is the plaintext message then the
+    ciphertext is `c = p e \pmod n`.
+
+    Decryption: If `c` is the ciphertext message then the
+    plaintext is `p = c d \pmod n`.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import kid_rsa_public_key
+    >>> a, b, A, B = 3, 4, 5, 6
+    >>> kid_rsa_public_key(a, b, A, B)
+    (369, 58)
+
+    """
+    M = a*b - 1
+    e = A*M + a
+    d = B*M + b
+    n = (e*d - 1)//M
+    return n, e
+
+
+def kid_rsa_private_key(a, b, A, B):
+    """
+    Compute `M = a b - 1`, `e = A M + a`, `d = B M + b`,
+    `n = (e d - 1) / M`. The *private key* is `d`, which Bob
+    keeps secret.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import kid_rsa_private_key
+    >>> a, b, A, B = 3, 4, 5, 6
+    >>> kid_rsa_private_key(a, b, A, B)
+    (369, 70)
+
+    """
+    M = a*b - 1
+    e = A*M + a
+    d = B*M + b
+    n = (e*d - 1)//M
+    return n, d
+
+
+def encipher_kid_rsa(msg, key):
+    """
+    Here ``msg`` is the plaintext and ``key`` is the public key.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     encipher_kid_rsa, kid_rsa_public_key)
+    >>> msg = 200
+    >>> a, b, A, B = 3, 4, 5, 6
+    >>> key = kid_rsa_public_key(a, b, A, B)
+    >>> encipher_kid_rsa(msg, key)
+    161
+
+    """
+    n, e = key
+    return (msg*e) % n
+
+
+def decipher_kid_rsa(msg, key):
+    """
+    Here ``msg`` is the plaintext and ``key`` is the private key.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     kid_rsa_public_key, kid_rsa_private_key,
+    ...     decipher_kid_rsa, encipher_kid_rsa)
+    >>> a, b, A, B = 3, 4, 5, 6
+    >>> d = kid_rsa_private_key(a, b, A, B)
+    >>> msg = 200
+    >>> pub = kid_rsa_public_key(a, b, A, B)
+    >>> pri = kid_rsa_private_key(a, b, A, B)
+    >>> ct = encipher_kid_rsa(msg, pub)
+    >>> decipher_kid_rsa(ct, pri)
+    200
+
+    """
+    n, d = key
+    return (msg*d) % n
+
+
+#################### Morse Code ######################################
+
+morse_char = {
+    ".-": "A", "-...": "B",
+    "-.-.": "C", "-..": "D",
+    ".": "E", "..-.": "F",
+    "--.": "G", "....": "H",
+    "..": "I", ".---": "J",
+    "-.-": "K", ".-..": "L",
+    "--": "M", "-.": "N",
+    "---": "O", ".--.": "P",
+    "--.-": "Q", ".-.": "R",
+    "...": "S", "-": "T",
+    "..-": "U", "...-": "V",
+    ".--": "W", "-..-": "X",
+    "-.--": "Y", "--..": "Z",
+    "-----": "0", ".----": "1",
+    "..---": "2", "...--": "3",
+    "....-": "4", ".....": "5",
+    "-....": "6", "--...": "7",
+    "---..": "8", "----.": "9",
+    ".-.-.-": ".", "--..--": ",",
+    "---...": ":", "-.-.-.": ";",
+    "..--..": "?", "-....-": "-",
+    "..--.-": "_", "-.--.": "(",
+    "-.--.-": ")", ".----.": "'",
+    "-...-": "=", ".-.-.": "+",
+    "-..-.": "/", ".--.-.": "@",
+    "...-..-": "$", "-.-.--": "!"}
+char_morse = {v: k for k, v in morse_char.items()}
+
+
+def encode_morse(msg, sep='|', mapping=None):
+    """
+    Encodes a plaintext into popular Morse Code with letters
+    separated by ``sep`` and words by a double ``sep``.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encode_morse
+    >>> msg = 'ATTACK RIGHT FLANK'
+    >>> encode_morse(msg)
+    '.-|-|-|.-|-.-.|-.-||.-.|..|--.|....|-||..-.|.-..|.-|-.|-.-'
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Morse_code
+
+    """
+
+    mapping = mapping or char_morse
+    assert sep not in mapping
+    word_sep = 2*sep
+    mapping[" "] = word_sep
+    suffix = msg and msg[-1] in whitespace
+
+    # normalize whitespace
+    msg = (' ' if word_sep else '').join(msg.split())
+    # omit unmapped chars
+    chars = set(''.join(msg.split()))
+    ok = set(mapping.keys())
+    msg = translate(msg, None, ''.join(chars - ok))
+
+    morsestring = []
+    words = msg.split()
+    for word in words:
+        morseword = []
+        for letter in word:
+            morseletter = mapping[letter]
+            morseword.append(morseletter)
+
+        word = sep.join(morseword)
+        morsestring.append(word)
+
+    return word_sep.join(morsestring) + (word_sep if suffix else '')
+
+
+def decode_morse(msg, sep='|', mapping=None):
+    """
+    Decodes a Morse Code with letters separated by ``sep``
+    (default is '|') and words by `word_sep` (default is '||)
+    into plaintext.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import decode_morse
+    >>> mc = '--|---|...-|.||.|.-|...|-'
+    >>> decode_morse(mc)
+    'MOVE EAST'
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Morse_code
+
+    """
+
+    mapping = mapping or morse_char
+    word_sep = 2*sep
+    characterstring = []
+    words = msg.strip(word_sep).split(word_sep)
+    for word in words:
+        letters = word.split(sep)
+        chars = [mapping[c] for c in letters]
+        word = ''.join(chars)
+        characterstring.append(word)
+    rv = " ".join(characterstring)
+    return rv
+
+
+#################### LFSRs  ##########################################
+
+
+@doctest_depends_on(ground_types=['python', 'gmpy'])
+def lfsr_sequence(key, fill, n):
+    r"""
+    This function creates an LFSR sequence.
+
+    Parameters
+    ==========
+
+    key : list
+        A list of finite field elements, `[c_0, c_1, \ldots, c_k].`
+
+    fill : list
+        The list of the initial terms of the LFSR sequence,
+        `[x_0, x_1, \ldots, x_k].`
+
+    n
+        Number of terms of the sequence that the function returns.
+
+    Returns
+    =======
+
+    L
+        The LFSR sequence defined by
+        `x_{n+1} = c_k x_n + \ldots + c_0 x_{n-k}`, for
+        `n \leq k`.
+
+    Notes
+    =====
+
+    S. Golomb [G]_ gives a list of three statistical properties a
+    sequence of numbers `a = \{a_n\}_{n=1}^\infty`,
+    `a_n \in \{0,1\}`, should display to be considered
+    "random". Define the autocorrelation of `a` to be
+
+    .. math::
+
+        C(k) = C(k,a) = \lim_{N\rightarrow \infty} {1\over N}\sum_{n=1}^N (-1)^{a_n + a_{n+k}}.
+
+    In the case where `a` is periodic with period
+    `P` then this reduces to
+
+    .. math::
+
+        C(k) = {1\over P}\sum_{n=1}^P (-1)^{a_n + a_{n+k}}.
+
+    Assume `a` is periodic with period `P`.
+
+    - balance:
+
+      .. math::
+
+        \left|\sum_{n=1}^P(-1)^{a_n}\right| \leq 1.
+
+    - low autocorrelation:
+
+       .. math::
+
+         C(k) = \left\{ \begin{array}{cc} 1,& k = 0,\\ \epsilon, & k \ne 0. \end{array} \right.
+
+      (For sequences satisfying these first two properties, it is known
+      that `\epsilon = -1/P` must hold.)
+
+    - proportional runs property: In each period, half the runs have
+      length `1`, one-fourth have length `2`, etc.
+      Moreover, there are as many runs of `1`'s as there are of
+      `0`'s.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import lfsr_sequence
+    >>> from sympy.polys.domains import FF
+    >>> F = FF(2)
+    >>> fill = [F(1), F(1), F(0), F(1)]
+    >>> key = [F(1), F(0), F(0), F(1)]
+    >>> lfsr_sequence(key, fill, 10)
+    [1 mod 2, 1 mod 2, 0 mod 2, 1 mod 2, 0 mod 2,
+    1 mod 2, 1 mod 2, 0 mod 2, 0 mod 2, 1 mod 2]
+
+    References
+    ==========
+
+    .. [G] Solomon Golomb, Shift register sequences, Aegean Park Press,
+       Laguna Hills, Ca, 1967
+
+    """
+    if not isinstance(key, list):
+        raise TypeError("key must be a list")
+    if not isinstance(fill, list):
+        raise TypeError("fill must be a list")
+    p = key[0].modulus()
+    F = FF(p)
+    s = fill
+    k = len(fill)
+    L = []
+    for i in range(n):
+        s0 = s[:]
+        L.append(s[0])
+        s = s[1:k]
+        x = sum(int(key[i]*s0[i]) for i in range(k))
+        s.append(F(x))
+    return L       # use [int(x) for x in L] for int version
+
+
+def lfsr_autocorrelation(L, P, k):
+    """
+    This function computes the LFSR autocorrelation function.
+
+    Parameters
+    ==========
+
+    L
+        A periodic sequence of elements of `GF(2)`.
+        L must have length larger than P.
+
+    P
+        The period of L.
+
+    k : int
+        An integer `k` (`0 < k < P`).
+
+    Returns
+    =======
+
+    autocorrelation
+        The k-th value of the autocorrelation of the LFSR L.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     lfsr_sequence, lfsr_autocorrelation)
+    >>> from sympy.polys.domains import FF
+    >>> F = FF(2)
+    >>> fill = [F(1), F(1), F(0), F(1)]
+    >>> key = [F(1), F(0), F(0), F(1)]
+    >>> s = lfsr_sequence(key, fill, 20)
+    >>> lfsr_autocorrelation(s, 15, 7)
+    -1/15
+    >>> lfsr_autocorrelation(s, 15, 0)
+    1
+
+    """
+    if not isinstance(L, list):
+        raise TypeError("L (=%s) must be a list" % L)
+    P = int(P)
+    k = int(k)
+    L0 = L[:P]     # slices makes a copy
+    L1 = L0 + L0[:k]
+    L2 = [(-1)**(int(L1[i]) + int(L1[i + k])) for i in range(P)]
+    tot = sum(L2)
+    return Rational(tot, P)
+
+
+def lfsr_connection_polynomial(s):
+    """
+    This function computes the LFSR connection polynomial.
+
+    Parameters
+    ==========
+
+    s
+        A sequence of elements of even length, with entries in a finite
+        field.
+
+    Returns
+    =======
+
+    C(x)
+        The connection polynomial of a minimal LFSR yielding s.
+
+        This implements the algorithm in section 3 of J. L. Massey's
+        article [M]_.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     lfsr_sequence, lfsr_connection_polynomial)
+    >>> from sympy.polys.domains import FF
+    >>> F = FF(2)
+    >>> fill = [F(1), F(1), F(0), F(1)]
+    >>> key = [F(1), F(0), F(0), F(1)]
+    >>> s = lfsr_sequence(key, fill, 20)
+    >>> lfsr_connection_polynomial(s)
+    x**4 + x + 1
+    >>> fill = [F(1), F(0), F(0), F(1)]
+    >>> key = [F(1), F(1), F(0), F(1)]
+    >>> s = lfsr_sequence(key, fill, 20)
+    >>> lfsr_connection_polynomial(s)
+    x**3 + 1
+    >>> fill = [F(1), F(0), F(1)]
+    >>> key = [F(1), F(1), F(0)]
+    >>> s = lfsr_sequence(key, fill, 20)
+    >>> lfsr_connection_polynomial(s)
+    x**3 + x**2 + 1
+    >>> fill = [F(1), F(0), F(1)]
+    >>> key = [F(1), F(0), F(1)]
+    >>> s = lfsr_sequence(key, fill, 20)
+    >>> lfsr_connection_polynomial(s)
+    x**3 + x + 1
+
+    References
+    ==========
+
+    .. [M] James L. Massey, "Shift-Register Synthesis and BCH Decoding."
+        IEEE Trans. on Information Theory, vol. 15(1), pp. 122-127,
+        Jan 1969.
+
+    """
+    # Initialization:
+    p = s[0].modulus()
+    x = Symbol("x")
+    C = 1*x**0
+    B = 1*x**0
+    m = 1
+    b = 1*x**0
+    L = 0
+    N = 0
+    while N < len(s):
+        if L > 0:
+            dC = Poly(C).degree()
+            r = min(L + 1, dC + 1)
+            coeffsC = [C.subs(x, 0)] + [C.coeff(x**i)
+                for i in range(1, dC + 1)]
+            d = (int(s[N]) + sum(coeffsC[i]*int(s[N - i])
+                for i in range(1, r))) % p
+        if L == 0:
+            d = int(s[N])*x**0
+        if d == 0:
+            m += 1
+            N += 1
+        if d > 0:
+            if 2*L > N:
+                C = (C - d*((b**(p - 2)) % p)*x**m*B).expand()
+                m += 1
+                N += 1
+            else:
+                T = C
+                C = (C - d*((b**(p - 2)) % p)*x**m*B).expand()
+                L = N + 1 - L
+                m = 1
+                b = d
+                B = T
+                N += 1
+    dC = Poly(C).degree()
+    coeffsC = [C.subs(x, 0)] + [C.coeff(x**i) for i in range(1, dC + 1)]
+    return sum(coeffsC[i] % p*x**i for i in range(dC + 1)
+        if coeffsC[i] is not None)
+
+
+#################### ElGamal  #############################
+
+
+def elgamal_private_key(digit=10, seed=None):
+    r"""
+    Return three number tuple as private key.
+
+    Explanation
+    ===========
+
+    Elgamal encryption is based on the mathematical problem
+    called the Discrete Logarithm Problem (DLP). For example,
+
+    `a^{b} \equiv c \pmod p`
+
+    In general, if ``a`` and ``b`` are known, ``ct`` is easily
+    calculated. If ``b`` is unknown, it is hard to use
+    ``a`` and ``ct`` to get ``b``.
+
+    Parameters
+    ==========
+
+    digit : int
+        Minimum number of binary digits for key.
+
+    Returns
+    =======
+
+    tuple : (p, r, d)
+        p = prime number.
+
+        r = primitive root.
+
+        d = random number.
+
+    Notes
+    =====
+
+    For testing purposes, the ``seed`` parameter may be set to control
+    the output of this routine. See sympy.core.random._randrange.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import elgamal_private_key
+    >>> from sympy.ntheory import is_primitive_root, isprime
+    >>> a, b, _ = elgamal_private_key()
+    >>> isprime(a)
+    True
+    >>> is_primitive_root(b, a)
+    True
+
+    """
+    randrange = _randrange(seed)
+    p = nextprime(2**digit)
+    return p, primitive_root(p), randrange(2, p)
+
+
+def elgamal_public_key(key):
+    r"""
+    Return three number tuple as public key.
+
+    Parameters
+    ==========
+
+    key : (p, r, e)
+        Tuple generated by ``elgamal_private_key``.
+
+    Returns
+    =======
+
+    tuple : (p, r, e)
+        `e = r**d \bmod p`
+
+        `d` is a random number in private key.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import elgamal_public_key
+    >>> elgamal_public_key((1031, 14, 636))
+    (1031, 14, 212)
+
+    """
+    p, r, e = key
+    return p, r, pow(r, e, p)
+
+
+def encipher_elgamal(i, key, seed=None):
+    r"""
+    Encrypt message with public key.
+
+    Explanation
+    ===========
+
+    ``i`` is a plaintext message expressed as an integer.
+    ``key`` is public key (p, r, e). In order to encrypt
+    a message, a random number ``a`` in ``range(2, p)``
+    is generated and the encrypted message is returned as
+    `c_{1}` and `c_{2}` where:
+
+    `c_{1} \equiv r^{a} \pmod p`
+
+    `c_{2} \equiv m e^{a} \pmod p`
+
+    Parameters
+    ==========
+
+    msg
+        int of encoded message.
+
+    key
+        Public key.
+
+    Returns
+    =======
+
+    tuple : (c1, c2)
+        Encipher into two number.
+
+    Notes
+    =====
+
+    For testing purposes, the ``seed`` parameter may be set to control
+    the output of this routine. See sympy.core.random._randrange.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_elgamal, elgamal_private_key, elgamal_public_key
+    >>> pri = elgamal_private_key(5, seed=[3]); pri
+    (37, 2, 3)
+    >>> pub = elgamal_public_key(pri); pub
+    (37, 2, 8)
+    >>> msg = 36
+    >>> encipher_elgamal(msg, pub, seed=[3])
+    (8, 6)
+
+    """
+    p, r, e = key
+    if i < 0 or i >= p:
+        raise ValueError(
+            'Message (%s) should be in range(%s)' % (i, p))
+    randrange = _randrange(seed)
+    a = randrange(2, p)
+    return pow(r, a, p), i*pow(e, a, p) % p
+
+
+def decipher_elgamal(msg, key):
+    r"""
+    Decrypt message with private key.
+
+    `msg = (c_{1}, c_{2})`
+
+    `key = (p, r, d)`
+
+    According to extended Eucliden theorem,
+    `u c_{1}^{d} + p n = 1`
+
+    `u \equiv 1/{{c_{1}}^d} \pmod p`
+
+    `u c_{2} \equiv \frac{1}{c_{1}^d} c_{2} \equiv \frac{1}{r^{ad}} c_{2} \pmod p`
+
+    `\frac{1}{r^{ad}} m e^a \equiv \frac{1}{r^{ad}} m {r^{d a}} \equiv m \pmod p`
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import decipher_elgamal
+    >>> from sympy.crypto.crypto import encipher_elgamal
+    >>> from sympy.crypto.crypto import elgamal_private_key
+    >>> from sympy.crypto.crypto import elgamal_public_key
+
+    >>> pri = elgamal_private_key(5, seed=[3])
+    >>> pub = elgamal_public_key(pri); pub
+    (37, 2, 8)
+    >>> msg = 17
+    >>> decipher_elgamal(encipher_elgamal(msg, pub), pri) == msg
+    True
+
+    """
+    p, _, d = key
+    c1, c2 = msg
+    u = pow(c1, -d, p)
+    return u * c2 % p
+
+
+################ Diffie-Hellman Key Exchange  #########################
+
+def dh_private_key(digit=10, seed=None):
+    r"""
+    Return three integer tuple as private key.
+
+    Explanation
+    ===========
+
+    Diffie-Hellman key exchange is based on the mathematical problem
+    called the Discrete Logarithm Problem (see ElGamal).
+
+    Diffie-Hellman key exchange is divided into the following steps:
+
+    *   Alice and Bob agree on a base that consist of a prime ``p``
+        and a primitive root of ``p`` called ``g``
+    *   Alice choses a number ``a`` and Bob choses a number ``b`` where
+        ``a`` and ``b`` are random numbers in range `[2, p)`. These are
+        their private keys.
+    *   Alice then publicly sends Bob `g^{a} \pmod p` while Bob sends
+        Alice `g^{b} \pmod p`
+    *   They both raise the received value to their secretly chosen
+        number (``a`` or ``b``) and now have both as their shared key
+        `g^{ab} \pmod p`
+
+    Parameters
+    ==========
+
+    digit
+        Minimum number of binary digits required in key.
+
+    Returns
+    =======
+
+    tuple : (p, g, a)
+        p = prime number.
+
+        g = primitive root of p.
+
+        a = random number from 2 through p - 1.
+
+    Notes
+    =====
+
+    For testing purposes, the ``seed`` parameter may be set to control
+    the output of this routine. See sympy.core.random._randrange.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import dh_private_key
+    >>> from sympy.ntheory import isprime, is_primitive_root
+    >>> p, g, _ = dh_private_key()
+    >>> isprime(p)
+    True
+    >>> is_primitive_root(g, p)
+    True
+    >>> p, g, _ = dh_private_key(5)
+    >>> isprime(p)
+    True
+    >>> is_primitive_root(g, p)
+    True
+
+    """
+    p = nextprime(2**digit)
+    g = primitive_root(p)
+    randrange = _randrange(seed)
+    a = randrange(2, p)
+    return p, g, a
+
+
+def dh_public_key(key):
+    r"""
+    Return three number tuple as public key.
+
+    This is the tuple that Alice sends to Bob.
+
+    Parameters
+    ==========
+
+    key : (p, g, a)
+        A tuple generated by ``dh_private_key``.
+
+    Returns
+    =======
+
+    tuple : int, int, int
+        A tuple of `(p, g, g^a \mod p)` with `p`, `g` and `a` given as
+        parameters.s
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import dh_private_key, dh_public_key
+    >>> p, g, a = dh_private_key();
+    >>> _p, _g, x = dh_public_key((p, g, a))
+    >>> p == _p and g == _g
+    True
+    >>> x == pow(g, a, p)
+    True
+
+    """
+    p, g, a = key
+    return p, g, pow(g, a, p)
+
+
+def dh_shared_key(key, b):
+    """
+    Return an integer that is the shared key.
+
+    This is what Bob and Alice can both calculate using the public
+    keys they received from each other and their private keys.
+
+    Parameters
+    ==========
+
+    key : (p, g, x)
+        Tuple `(p, g, x)` generated by ``dh_public_key``.
+
+    b
+        Random number in the range of `2` to `p - 1`
+        (Chosen by second key exchange member (Bob)).
+
+    Returns
+    =======
+
+    int
+        A shared key.
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import (
+    ...     dh_private_key, dh_public_key, dh_shared_key)
+    >>> prk = dh_private_key();
+    >>> p, g, x = dh_public_key(prk);
+    >>> sk = dh_shared_key((p, g, x), 1000)
+    >>> sk == pow(x, 1000, p)
+    True
+
+    """
+    p, _, x = key
+    if 1 >= b or b >= p:
+        raise ValueError(filldedent('''
+            Value of b should be greater 1 and less
+            than prime %s.''' % p))
+
+    return pow(x, b, p)
+
+
+################ Goldwasser-Micali Encryption  #########################
+
+
+def _legendre(a, p):
+    """
+    Returns the legendre symbol of a and p
+    assuming that p is a prime.
+
+    i.e. 1 if a is a quadratic residue mod p
+        -1 if a is not a quadratic residue mod p
+         0 if a is divisible by p
+
+    Parameters
+    ==========
+
+    a : int
+        The number to test.
+
+    p : prime
+        The prime to test ``a`` against.
+
+    Returns
+    =======
+
+    int
+        Legendre symbol (a / p).
+
+    """
+    sig = pow(a, (p - 1)//2, p)
+    if sig == 1:
+        return 1
+    elif sig == 0:
+        return 0
+    else:
+        return -1
+
+
+def _random_coprime_stream(n, seed=None):
+    randrange = _randrange(seed)
+    while True:
+        y = randrange(n)
+        if gcd(y, n) == 1:
+            yield y
+
+
+def gm_private_key(p, q, a=None):
+    r"""
+    Check if ``p`` and ``q`` can be used as private keys for
+    the Goldwasser-Micali encryption. The method works
+    roughly as follows.
+
+    Explanation
+    ===========
+
+    #. Pick two large primes $p$ and $q$.
+    #. Call their product $N$.
+    #. Given a message as an integer $i$, write $i$ in its bit representation $b_0, \dots, b_n$.
+    #. For each $k$,
+
+     if $b_k = 0$:
+        let $a_k$ be a random square
+        (quadratic residue) modulo $p q$
+        such that ``jacobi_symbol(a, p*q) = 1``
+     if $b_k = 1$:
+        let $a_k$ be a random non-square
+        (non-quadratic residue) modulo $p q$
+        such that ``jacobi_symbol(a, p*q) = 1``
+
+    returns $\left[a_1, a_2, \dots\right]$
+
+    $b_k$ can be recovered by checking whether or not
+    $a_k$ is a residue. And from the $b_k$'s, the message
+    can be reconstructed.
+
+    The idea is that, while ``jacobi_symbol(a, p*q)``
+    can be easily computed (and when it is equal to $-1$ will
+    tell you that $a$ is not a square mod $p q$), quadratic
+    residuosity modulo a composite number is hard to compute
+    without knowing its factorization.
+
+    Moreover, approximately half the numbers coprime to $p q$ have
+    :func:`~.jacobi_symbol` equal to $1$ . And among those, approximately half
+    are residues and approximately half are not. This maximizes the
+    entropy of the code.
+
+    Parameters
+    ==========
+
+    p, q, a
+        Initialization variables.
+
+    Returns
+    =======
+
+    tuple : (p, q)
+        The input value ``p`` and ``q``.
+
+    Raises
+    ======
+
+    ValueError
+        If ``p`` and ``q`` are not distinct odd primes.
+
+    """
+    if p == q:
+        raise ValueError("expected distinct primes, "
+                         "got two copies of %i" % p)
+    elif not isprime(p) or not isprime(q):
+        raise ValueError("first two arguments must be prime, "
+                         "got %i of %i" % (p, q))
+    elif p == 2 or q == 2:
+        raise ValueError("first two arguments must not be even, "
+                         "got %i of %i" % (p, q))
+    return p, q
+
+
+def gm_public_key(p, q, a=None, seed=None):
+    """
+    Compute public keys for ``p`` and ``q``.
+    Note that in Goldwasser-Micali Encryption,
+    public keys are randomly selected.
+
+    Parameters
+    ==========
+
+    p, q, a : int, int, int
+        Initialization variables.
+
+    Returns
+    =======
+
+    tuple : (a, N)
+        ``a`` is the input ``a`` if it is not ``None`` otherwise
+        some random integer coprime to ``p`` and ``q``.
+
+        ``N`` is the product of ``p`` and ``q``.
+
+    """
+
+    p, q = gm_private_key(p, q)
+    N = p * q
+
+    if a is None:
+        randrange = _randrange(seed)
+        while True:
+            a = randrange(N)
+            if _legendre(a, p) == _legendre(a, q) == -1:
+                break
+    else:
+        if _legendre(a, p) != -1 or _legendre(a, q) != -1:
+            return False
+    return (a, N)
+
+
+def encipher_gm(i, key, seed=None):
+    """
+    Encrypt integer 'i' using public_key 'key'
+    Note that gm uses random encryption.
+
+    Parameters
+    ==========
+
+    i : int
+        The message to encrypt.
+
+    key : (a, N)
+        The public key.
+
+    Returns
+    =======
+
+    list : list of int
+        The randomized encrypted message.
+
+    """
+    if i < 0:
+        raise ValueError(
+            "message must be a non-negative "
+            "integer: got %d instead" % i)
+    a, N = key
+    bits = []
+    while i > 0:
+        bits.append(i % 2)
+        i //= 2
+
+    gen = _random_coprime_stream(N, seed)
+    rev = reversed(bits)
+    encode = lambda b: next(gen)**2*pow(a, b) % N
+    return [ encode(b) for b in rev ]
+
+
+
+def decipher_gm(message, key):
+    """
+    Decrypt message 'message' using public_key 'key'.
+
+    Parameters
+    ==========
+
+    message : list of int
+        The randomized encrypted message.
+
+    key : (p, q)
+        The private key.
+
+    Returns
+    =======
+
+    int
+        The encrypted message.
+
+    """
+    p, q = key
+    res = lambda m, p: _legendre(m, p) > 0
+    bits = [res(m, p) * res(m, q) for m in message]
+    m = 0
+    for b in bits:
+        m <<= 1
+        m += not b
+    return m
+
+
+
+########### RailFence Cipher #############
+
+def encipher_railfence(message,rails):
+    """
+    Performs Railfence Encryption on plaintext and returns ciphertext
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import encipher_railfence
+    >>> message = "hello world"
+    >>> encipher_railfence(message,3)
+    'horel ollwd'
+
+    Parameters
+    ==========
+
+    message : string, the message to encrypt.
+    rails : int, the number of rails.
+
+    Returns
+    =======
+
+    The Encrypted string message.
+
+    References
+    ==========
+    .. [1] https://en.wikipedia.org/wiki/Rail_fence_cipher
+
+    """
+    r = list(range(rails))
+    p = cycle(r + r[-2:0:-1])
+    return ''.join(sorted(message, key=lambda i: next(p)))
+
+
+def decipher_railfence(ciphertext,rails):
+    """
+    Decrypt the message using the given rails
+
+    Examples
+    ========
+
+    >>> from sympy.crypto.crypto import decipher_railfence
+    >>> decipher_railfence("horel ollwd",3)
+    'hello world'
+
+    Parameters
+    ==========
+
+    message : string, the message to encrypt.
+    rails : int, the number of rails.
+
+    Returns
+    =======
+
+    The Decrypted string message.
+
+    """
+    r = list(range(rails))
+    p = cycle(r + r[-2:0:-1])
+
+    idx = sorted(range(len(ciphertext)), key=lambda i: next(p))
+    res = [''] * len(ciphertext)
+    for i, c in zip(idx, ciphertext):
+        res[i] = c
+    return ''.join(res)
+
+
+################ Blum-Goldwasser cryptosystem  #########################
+
+def bg_private_key(p, q):
+    """
+    Check if p and q can be used as private keys for
+    the Blum-Goldwasser cryptosystem.
+
+    Explanation
+    ===========
+
+    The three necessary checks for p and q to pass
+    so that they can be used as private keys:
+
+        1. p and q must both be prime
+        2. p and q must be distinct
+        3. p and q must be congruent to 3 mod 4
+
+    Parameters
+    ==========
+
+    p, q
+        The keys to be checked.
+
+    Returns
+    =======
+
+    p, q
+        Input values.
+
+    Raises
+    ======
+
+    ValueError
+        If p and q do not pass the above conditions.
+
+    """
+
+    if not isprime(p) or not isprime(q):
+        raise ValueError("the two arguments must be prime, "
+                         "got %i and %i" %(p, q))
+    elif p == q:
+        raise ValueError("the two arguments must be distinct, "
+                         "got two copies of %i. " %p)
+    elif (p - 3) % 4 != 0 or (q - 3) % 4 != 0:
+        raise ValueError("the two arguments must be congruent to 3 mod 4, "
+                         "got %i and %i" %(p, q))
+    return p, q
+
+def bg_public_key(p, q):
+    """
+    Calculates public keys from private keys.
+
+    Explanation
+    ===========
+
+    The function first checks the validity of
+    private keys passed as arguments and
+    then returns their product.
+
+    Parameters
+    ==========
+
+    p, q
+        The private keys.
+
+    Returns
+    =======
+
+    N
+        The public key.
+
+    """
+    p, q = bg_private_key(p, q)
+    N = p * q
+    return N
+
+def encipher_bg(i, key, seed=None):
+    """
+    Encrypts the message using public key and seed.
+
+    Explanation
+    ===========
+
+    ALGORITHM:
+        1. Encodes i as a string of L bits, m.
+        2. Select a random element r, where 1 < r < key, and computes
+           x = r^2 mod key.
+        3. Use BBS pseudo-random number generator to generate L random bits, b,
+        using the initial seed as x.
+        4. Encrypted message, c_i = m_i XOR b_i, 1 <= i <= L.
+        5. x_L = x^(2^L) mod key.
+        6. Return (c, x_L)
+
+    Parameters
+    ==========
+
+    i
+        Message, a non-negative integer
+
+    key
+        The public key
+
+    Returns
+    =======
+
+    Tuple
+        (encrypted_message, x_L)
+
+    Raises
+    ======
+
+    ValueError
+        If i is negative.
+
+    """
+
+    if i < 0:
+        raise ValueError(
+            "message must be a non-negative "
+            "integer: got %d instead" % i)
+
+    enc_msg = []
+    while i > 0:
+        enc_msg.append(i % 2)
+        i //= 2
+    enc_msg.reverse()
+    L = len(enc_msg)
+
+    r = _randint(seed)(2, key - 1)
+    x = r**2 % key
+    x_L = pow(int(x), int(2**L), int(key))
+
+    rand_bits = []
+    for _ in range(L):
+        rand_bits.append(x % 2)
+        x = x**2 % key
+
+    encrypt_msg = [m ^ b for (m, b) in zip(enc_msg, rand_bits)]
+
+    return (encrypt_msg, x_L)
+
+def decipher_bg(message, key):
+    """
+    Decrypts the message using private keys.
+
+    Explanation
+    ===========
+
+    ALGORITHM:
+        1. Let, c be the encrypted message, y the second number received,
+        and p and q be the private keys.
+        2. Compute, r_p = y^((p+1)/4 ^ L) mod p and
+        r_q = y^((q+1)/4 ^ L) mod q.
+        3. Compute x_0 = (q(q^-1 mod p)r_p + p(p^-1 mod q)r_q) mod N.
+        4. From, recompute the bits using the BBS generator, as in the
+        encryption algorithm.
+        5. Compute original message by XORing c and b.
+
+    Parameters
+    ==========
+
+    message
+        Tuple of encrypted message and a non-negative integer.
+
+    key
+        Tuple of private keys.
+
+    Returns
+    =======
+
+    orig_msg
+        The original message
+
+    """
+
+    p, q = key
+    encrypt_msg, y = message
+    public_key = p * q
+    L = len(encrypt_msg)
+    p_t = ((p + 1)/4)**L
+    q_t = ((q + 1)/4)**L
+    r_p = pow(int(y), int(p_t), int(p))
+    r_q = pow(int(y), int(q_t), int(q))
+
+    x = (q * invert(q, p) * r_p + p * invert(p, q) * r_q) % public_key
+
+    orig_bits = []
+    for _ in range(L):
+        orig_bits.append(x % 2)
+        x = x**2 % public_key
+
+    orig_msg = 0
+    for (m, b) in zip(encrypt_msg, orig_bits):
+        orig_msg = orig_msg * 2
+        orig_msg += (m ^ b)
+
+    return orig_msg
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/tests/test_crypto.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/tests/test_crypto.py
new file mode 100644
index 0000000000000000000000000000000000000000..c671138f9a61325f6e65cc7cafddc7cd46f19229
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/crypto/tests/test_crypto.py
@@ -0,0 +1,562 @@
+from sympy.core import symbols
+from sympy.crypto.crypto import (cycle_list,
+      encipher_shift, encipher_affine, encipher_substitution,
+      check_and_join, encipher_vigenere, decipher_vigenere,
+      encipher_hill, decipher_hill, encipher_bifid5, encipher_bifid6,
+      bifid5_square, bifid6_square, bifid5, bifid6,
+      decipher_bifid5, decipher_bifid6, encipher_kid_rsa,
+      decipher_kid_rsa, kid_rsa_private_key, kid_rsa_public_key,
+      decipher_rsa, rsa_private_key, rsa_public_key, encipher_rsa,
+      lfsr_connection_polynomial, lfsr_autocorrelation, lfsr_sequence,
+      encode_morse, decode_morse, elgamal_private_key, elgamal_public_key,
+      encipher_elgamal, decipher_elgamal, dh_private_key, dh_public_key,
+      dh_shared_key, decipher_shift, decipher_affine, encipher_bifid,
+      decipher_bifid, bifid_square, padded_key, uniq, decipher_gm,
+      encipher_gm, gm_public_key, gm_private_key, encipher_bg, decipher_bg,
+      bg_private_key, bg_public_key, encipher_rot13, decipher_rot13,
+      encipher_atbash, decipher_atbash, NonInvertibleCipherWarning,
+      encipher_railfence, decipher_railfence)
+from sympy.external.gmpy import gcd
+from sympy.matrices import Matrix
+from sympy.ntheory import isprime, is_primitive_root
+from sympy.polys.domains import FF
+
+from sympy.testing.pytest import raises, warns
+
+from sympy.core.random import randrange
+
+def test_encipher_railfence():
+    assert encipher_railfence("hello world",2) == "hlowrdel ol"
+    assert encipher_railfence("hello world",3) == "horel ollwd"
+    assert encipher_railfence("hello world",4) == "hwe olordll"
+
+def test_decipher_railfence():
+    assert decipher_railfence("hlowrdel ol",2) == "hello world"
+    assert decipher_railfence("horel ollwd",3) == "hello world"
+    assert decipher_railfence("hwe olordll",4) == "hello world"
+
+
+def test_cycle_list():
+    assert cycle_list(3, 4) == [3, 0, 1, 2]
+    assert cycle_list(-1, 4) == [3, 0, 1, 2]
+    assert cycle_list(1, 4) == [1, 2, 3, 0]
+
+
+def test_encipher_shift():
+    assert encipher_shift("ABC", 0) == "ABC"
+    assert encipher_shift("ABC", 1) == "BCD"
+    assert encipher_shift("ABC", -1) == "ZAB"
+    assert decipher_shift("ZAB", -1) == "ABC"
+
+def test_encipher_rot13():
+    assert encipher_rot13("ABC") == "NOP"
+    assert encipher_rot13("NOP") == "ABC"
+    assert decipher_rot13("ABC") == "NOP"
+    assert decipher_rot13("NOP") == "ABC"
+
+
+def test_encipher_affine():
+    assert encipher_affine("ABC", (1, 0)) == "ABC"
+    assert encipher_affine("ABC", (1, 1)) == "BCD"
+    assert encipher_affine("ABC", (-1, 0)) == "AZY"
+    assert encipher_affine("ABC", (-1, 1), symbols="ABCD") == "BAD"
+    assert encipher_affine("123", (-1, 1), symbols="1234") == "214"
+    assert encipher_affine("ABC", (3, 16)) == "QTW"
+    assert decipher_affine("QTW", (3, 16)) == "ABC"
+
+def test_encipher_atbash():
+    assert encipher_atbash("ABC") == "ZYX"
+    assert encipher_atbash("ZYX") == "ABC"
+    assert decipher_atbash("ABC") == "ZYX"
+    assert decipher_atbash("ZYX") == "ABC"
+
+def test_encipher_substitution():
+    assert encipher_substitution("ABC", "BAC", "ABC") == "BAC"
+    assert encipher_substitution("123", "1243", "1234") == "124"
+
+
+def test_check_and_join():
+    assert check_and_join("abc") == "abc"
+    assert check_and_join(uniq("aaabc")) == "abc"
+    assert check_and_join("ab c".split()) == "abc"
+    assert check_and_join("abc", "a", filter=True) == "a"
+    raises(ValueError, lambda: check_and_join('ab', 'a'))
+
+
+def test_encipher_vigenere():
+    assert encipher_vigenere("ABC", "ABC") == "ACE"
+    assert encipher_vigenere("ABC", "ABC", symbols="ABCD") == "ACA"
+    assert encipher_vigenere("ABC", "AB", symbols="ABCD") == "ACC"
+    assert encipher_vigenere("AB", "ABC", symbols="ABCD") == "AC"
+    assert encipher_vigenere("A", "ABC", symbols="ABCD") == "A"
+
+
+def test_decipher_vigenere():
+    assert decipher_vigenere("ABC", "ABC") == "AAA"
+    assert decipher_vigenere("ABC", "ABC", symbols="ABCD") == "AAA"
+    assert decipher_vigenere("ABC", "AB", symbols="ABCD") == "AAC"
+    assert decipher_vigenere("AB", "ABC", symbols="ABCD") == "AA"
+    assert decipher_vigenere("A", "ABC", symbols="ABCD") == "A"
+
+
+def test_encipher_hill():
+    A = Matrix(2, 2, [1, 2, 3, 5])
+    assert encipher_hill("ABCD", A) == "CFIV"
+    A = Matrix(2, 2, [1, 0, 0, 1])
+    assert encipher_hill("ABCD", A) == "ABCD"
+    assert encipher_hill("ABCD", A, symbols="ABCD") == "ABCD"
+    A = Matrix(2, 2, [1, 2, 3, 5])
+    assert encipher_hill("ABCD", A, symbols="ABCD") == "CBAB"
+    assert encipher_hill("AB", A, symbols="ABCD") == "CB"
+    # message length, n, does not need to be a multiple of k;
+    # it is padded
+    assert encipher_hill("ABA", A) == "CFGC"
+    assert encipher_hill("ABA", A, pad="Z") == "CFYV"
+
+
+def test_decipher_hill():
+    A = Matrix(2, 2, [1, 2, 3, 5])
+    assert decipher_hill("CFIV", A) == "ABCD"
+    A = Matrix(2, 2, [1, 0, 0, 1])
+    assert decipher_hill("ABCD", A) == "ABCD"
+    assert decipher_hill("ABCD", A, symbols="ABCD") == "ABCD"
+    A = Matrix(2, 2, [1, 2, 3, 5])
+    assert decipher_hill("CBAB", A, symbols="ABCD") == "ABCD"
+    assert decipher_hill("CB", A, symbols="ABCD") == "AB"
+    # n does not need to be a multiple of k
+    assert decipher_hill("CFA", A) == "ABAA"
+
+
+def test_encipher_bifid5():
+    assert encipher_bifid5("AB", "AB") == "AB"
+    assert encipher_bifid5("AB", "CD") == "CO"
+    assert encipher_bifid5("ab", "c") == "CH"
+    assert encipher_bifid5("a bc", "b") == "BAC"
+
+
+def test_bifid5_square():
+    A = bifid5
+    f = lambda i, j: symbols(A[5*i + j])
+    M = Matrix(5, 5, f)
+    assert bifid5_square("") == M
+
+
+def test_decipher_bifid5():
+    assert decipher_bifid5("AB", "AB") == "AB"
+    assert decipher_bifid5("CO", "CD") == "AB"
+    assert decipher_bifid5("ch", "c") == "AB"
+    assert decipher_bifid5("b ac", "b") == "ABC"
+
+
+def test_encipher_bifid6():
+    assert encipher_bifid6("AB", "AB") == "AB"
+    assert encipher_bifid6("AB", "CD") == "CP"
+    assert encipher_bifid6("ab", "c") == "CI"
+    assert encipher_bifid6("a bc", "b") == "BAC"
+
+
+def test_decipher_bifid6():
+    assert decipher_bifid6("AB", "AB") == "AB"
+    assert decipher_bifid6("CP", "CD") == "AB"
+    assert decipher_bifid6("ci", "c") == "AB"
+    assert decipher_bifid6("b ac", "b") == "ABC"
+
+
+def test_bifid6_square():
+    A = bifid6
+    f = lambda i, j: symbols(A[6*i + j])
+    M = Matrix(6, 6, f)
+    assert bifid6_square("") == M
+
+
+def test_rsa_public_key():
+    assert rsa_public_key(2, 3, 1) == (6, 1)
+    assert rsa_public_key(5, 3, 3) == (15, 3)
+
+    with warns(NonInvertibleCipherWarning):
+        assert rsa_public_key(2, 2, 1) == (4, 1)
+        assert rsa_public_key(8, 8, 8) is False
+
+
+def test_rsa_private_key():
+    assert rsa_private_key(2, 3, 1) == (6, 1)
+    assert rsa_private_key(5, 3, 3) == (15, 3)
+    assert rsa_private_key(23,29,5) == (667,493)
+
+    with warns(NonInvertibleCipherWarning):
+        assert rsa_private_key(2, 2, 1) == (4, 1)
+        assert rsa_private_key(8, 8, 8) is False
+
+
+def test_rsa_large_key():
+    # Sample from
+    # http://www.herongyang.com/Cryptography/JCE-Public-Key-RSA-Private-Public-Key-Pair-Sample.html
+    p = int('101565610013301240713207239558950144682174355406589305284428666'\
+        '903702505233009')
+    q = int('894687191887545488935455605955948413812376003053143521429242133'\
+        '12069293984003')
+    e = int('65537')
+    d = int('893650581832704239530398858744759129594796235440844479456143566'\
+        '6999402846577625762582824202269399672579058991442587406384754958587'\
+        '400493169361356902030209')
+    assert rsa_public_key(p, q, e) == (p*q, e)
+    assert rsa_private_key(p, q, e) == (p*q, d)
+
+
+def test_encipher_rsa():
+    puk = rsa_public_key(2, 3, 1)
+    assert encipher_rsa(2, puk) == 2
+    puk = rsa_public_key(5, 3, 3)
+    assert encipher_rsa(2, puk) == 8
+
+    with warns(NonInvertibleCipherWarning):
+        puk = rsa_public_key(2, 2, 1)
+        assert encipher_rsa(2, puk) == 2
+
+
+def test_decipher_rsa():
+    prk = rsa_private_key(2, 3, 1)
+    assert decipher_rsa(2, prk) == 2
+    prk = rsa_private_key(5, 3, 3)
+    assert decipher_rsa(8, prk) == 2
+
+    with warns(NonInvertibleCipherWarning):
+        prk = rsa_private_key(2, 2, 1)
+        assert decipher_rsa(2, prk) == 2
+
+
+def test_mutltiprime_rsa_full_example():
+    # Test example from
+    # https://iopscience.iop.org/article/10.1088/1742-6596/995/1/012030
+    puk = rsa_public_key(2, 3, 5, 7, 11, 13, 7)
+    prk = rsa_private_key(2, 3, 5, 7, 11, 13, 7)
+    assert puk == (30030, 7)
+    assert prk == (30030, 823)
+
+    msg = 10
+    encrypted = encipher_rsa(2 * msg - 15, puk)
+    assert encrypted == 18065
+    decrypted = (decipher_rsa(encrypted, prk) + 15) / 2
+    assert decrypted == msg
+
+    # Test example from
+    # https://www.scirp.org/pdf/JCC_2018032215502008.pdf
+    puk1 = rsa_public_key(53, 41, 43, 47, 41)
+    prk1 = rsa_private_key(53, 41, 43, 47, 41)
+    puk2 = rsa_public_key(53, 41, 43, 47, 97)
+    prk2 = rsa_private_key(53, 41, 43, 47, 97)
+
+    assert puk1 == (4391633, 41)
+    assert prk1 == (4391633, 294041)
+    assert puk2 == (4391633, 97)
+    assert prk2 == (4391633, 455713)
+
+    msg = 12321
+    encrypted = encipher_rsa(encipher_rsa(msg, puk1), puk2)
+    assert encrypted == 1081588
+    decrypted = decipher_rsa(decipher_rsa(encrypted, prk2), prk1)
+    assert decrypted == msg
+
+
+def test_rsa_crt_extreme():
+    p = int(
+        '10177157607154245068023861503693082120906487143725062283406501' \
+        '54082258226204046999838297167140821364638180697194879500245557' \
+        '65445186962893346463841419427008800341257468600224049986260471' \
+        '92257248163014468841725476918639415726709736077813632961290911' \
+        '0256421232977833028677441206049309220354796014376698325101693')
+
+    q = int(
+        '28752342353095132872290181526607275886182793241660805077850801' \
+        '75689512797754286972952273553128181861830576836289738668745250' \
+        '34028199691128870676414118458442900035778874482624765513861643' \
+        '27966696316822188398336199002306588703902894100476186823849595' \
+        '103239410527279605442148285816149368667083114802852804976893')
+
+    r = int(
+        '17698229259868825776879500736350186838850961935956310134378261' \
+        '89771862186717463067541369694816245225291921138038800171125596' \
+        '07315449521981157084370187887650624061033066022458512942411841' \
+        '18747893789972315277160085086164119879536041875335384844820566' \
+        '0287479617671726408053319619892052000850883994343378882717849')
+
+    s = int(
+        '68925428438585431029269182233502611027091755064643742383515623' \
+        '64321310582896893395529367074942808353187138794422745718419645' \
+        '28291231865157212604266903677599180789896916456120289112752835' \
+        '98502265889669730331688206825220074713977607415178738015831030' \
+        '364290585369150502819743827343552098197095520550865360159439'
+    )
+
+    t = int(
+        '69035483433453632820551311892368908779778144568711455301541094' \
+        '31487047642322695357696860925747923189635033183069823820910521' \
+        '71172909106797748883261493224162414050106920442445896819806600' \
+        '15448444826108008217972129130625571421904893252804729877353352' \
+        '739420480574842850202181462656251626522910618936534699566291'
+    )
+
+    e = 65537
+    puk = rsa_public_key(p, q, r, s, t, e)
+    prk = rsa_private_key(p, q, r, s, t, e)
+
+    plaintext = 1000
+    ciphertext_1 = encipher_rsa(plaintext, puk)
+    ciphertext_2 = encipher_rsa(plaintext, puk, [p, q, r, s, t])
+    assert ciphertext_1 == ciphertext_2
+    assert decipher_rsa(ciphertext_1, prk) == \
+        decipher_rsa(ciphertext_1, prk, [p, q, r, s, t])
+
+
+def test_rsa_exhaustive():
+    p, q = 61, 53
+    e = 17
+    puk = rsa_public_key(p, q, e, totient='Carmichael')
+    prk = rsa_private_key(p, q, e, totient='Carmichael')
+
+    for msg in range(puk[0]):
+        encrypted = encipher_rsa(msg, puk)
+        decrypted = decipher_rsa(encrypted, prk)
+        try:
+            assert decrypted == msg
+        except AssertionError:
+            raise AssertionError(
+                "The RSA is not correctly decrypted " \
+                "(Original : {}, Encrypted : {}, Decrypted : {})" \
+                .format(msg, encrypted, decrypted)
+                )
+
+
+def test_rsa_multiprime_exhanstive():
+    primes = [3, 5, 7, 11]
+    e = 7
+    args = primes + [e]
+    puk = rsa_public_key(*args, totient='Carmichael')
+    prk = rsa_private_key(*args, totient='Carmichael')
+    n = puk[0]
+
+    for msg in range(n):
+        encrypted = encipher_rsa(msg, puk)
+        decrypted = decipher_rsa(encrypted, prk)
+        try:
+            assert decrypted == msg
+        except AssertionError:
+            raise AssertionError(
+                "The RSA is not correctly decrypted " \
+                "(Original : {}, Encrypted : {}, Decrypted : {})" \
+                .format(msg, encrypted, decrypted)
+                )
+
+
+def test_rsa_multipower_exhanstive():
+    primes = [5, 5, 7]
+    e = 7
+    args = primes + [e]
+    puk = rsa_public_key(*args, multipower=True)
+    prk = rsa_private_key(*args, multipower=True)
+    n = puk[0]
+
+    for msg in range(n):
+        if gcd(msg, n) != 1:
+            continue
+
+        encrypted = encipher_rsa(msg, puk)
+        decrypted = decipher_rsa(encrypted, prk)
+        try:
+            assert decrypted == msg
+        except AssertionError:
+            raise AssertionError(
+                "The RSA is not correctly decrypted " \
+                "(Original : {}, Encrypted : {}, Decrypted : {})" \
+                .format(msg, encrypted, decrypted)
+                )
+
+
+def test_kid_rsa_public_key():
+    assert kid_rsa_public_key(1, 2, 1, 1) == (5, 2)
+    assert kid_rsa_public_key(1, 2, 2, 1) == (8, 3)
+    assert kid_rsa_public_key(1, 2, 1, 2) == (7, 2)
+
+
+def test_kid_rsa_private_key():
+    assert kid_rsa_private_key(1, 2, 1, 1) == (5, 3)
+    assert kid_rsa_private_key(1, 2, 2, 1) == (8, 3)
+    assert kid_rsa_private_key(1, 2, 1, 2) == (7, 4)
+
+
+def test_encipher_kid_rsa():
+    assert encipher_kid_rsa(1, (5, 2)) == 2
+    assert encipher_kid_rsa(1, (8, 3)) == 3
+    assert encipher_kid_rsa(1, (7, 2)) == 2
+
+
+def test_decipher_kid_rsa():
+    assert decipher_kid_rsa(2, (5, 3)) == 1
+    assert decipher_kid_rsa(3, (8, 3)) == 1
+    assert decipher_kid_rsa(2, (7, 4)) == 1
+
+
+def test_encode_morse():
+    assert encode_morse('ABC') == '.-|-...|-.-.'
+    assert encode_morse('SMS ') == '...|--|...||'
+    assert encode_morse('SMS\n') == '...|--|...||'
+    assert encode_morse('') == ''
+    assert encode_morse(' ') == '||'
+    assert encode_morse(' ', sep='`') == '``'
+    assert encode_morse(' ', sep='``') == '````'
+    assert encode_morse('!@#$%^&*()_+') == '-.-.--|.--.-.|...-..-|-.--.|-.--.-|..--.-|.-.-.'
+    assert encode_morse('12345') == '.----|..---|...--|....-|.....'
+    assert encode_morse('67890') == '-....|--...|---..|----.|-----'
+
+
+def test_decode_morse():
+    assert decode_morse('-.-|.|-.--') == 'KEY'
+    assert decode_morse('.-.|..-|-.||') == 'RUN'
+    raises(KeyError, lambda: decode_morse('.....----'))
+
+
+def test_lfsr_sequence():
+    raises(TypeError, lambda: lfsr_sequence(1, [1], 1))
+    raises(TypeError, lambda: lfsr_sequence([1], 1, 1))
+    F = FF(2)
+    assert lfsr_sequence([F(1)], [F(1)], 2) == [F(1), F(1)]
+    assert lfsr_sequence([F(0)], [F(1)], 2) == [F(1), F(0)]
+    F = FF(3)
+    assert lfsr_sequence([F(1)], [F(1)], 2) == [F(1), F(1)]
+    assert lfsr_sequence([F(0)], [F(2)], 2) == [F(2), F(0)]
+    assert lfsr_sequence([F(1)], [F(2)], 2) == [F(2), F(2)]
+
+
+def test_lfsr_autocorrelation():
+    raises(TypeError, lambda: lfsr_autocorrelation(1, 2, 3))
+    F = FF(2)
+    s = lfsr_sequence([F(1), F(0)], [F(0), F(1)], 5)
+    assert lfsr_autocorrelation(s, 2, 0) == 1
+    assert lfsr_autocorrelation(s, 2, 1) == -1
+
+
+def test_lfsr_connection_polynomial():
+    F = FF(2)
+    x = symbols("x")
+    s = lfsr_sequence([F(1), F(0)], [F(0), F(1)], 5)
+    assert lfsr_connection_polynomial(s) == x**2 + 1
+    s = lfsr_sequence([F(1), F(1)], [F(0), F(1)], 5)
+    assert lfsr_connection_polynomial(s) == x**2 + x + 1
+
+
+def test_elgamal_private_key():
+    a, b, _ = elgamal_private_key(digit=100)
+    assert isprime(a)
+    assert is_primitive_root(b, a)
+    assert len(bin(a)) >= 102
+
+
+def test_elgamal():
+    dk = elgamal_private_key(5)
+    ek = elgamal_public_key(dk)
+    P = ek[0]
+    assert P - 1 == decipher_elgamal(encipher_elgamal(P - 1, ek), dk)
+    raises(ValueError, lambda: encipher_elgamal(P, dk))
+    raises(ValueError, lambda: encipher_elgamal(-1, dk))
+
+
+def test_dh_private_key():
+    p, g, _ = dh_private_key(digit = 100)
+    assert isprime(p)
+    assert is_primitive_root(g, p)
+    assert len(bin(p)) >= 102
+
+
+def test_dh_public_key():
+    p1, g1, a = dh_private_key(digit = 100)
+    p2, g2, ga = dh_public_key((p1, g1, a))
+    assert p1 == p2
+    assert g1 == g2
+    assert ga == pow(g1, a, p1)
+
+
+def test_dh_shared_key():
+    prk = dh_private_key(digit = 100)
+    p, _, ga = dh_public_key(prk)
+    b = randrange(2, p)
+    sk = dh_shared_key((p, _, ga), b)
+    assert sk == pow(ga, b, p)
+    raises(ValueError, lambda: dh_shared_key((1031, 14, 565), 2000))
+
+
+def test_padded_key():
+    assert padded_key('b', 'ab') == 'ba'
+    raises(ValueError, lambda: padded_key('ab', 'ace'))
+    raises(ValueError, lambda: padded_key('ab', 'abba'))
+
+
+def test_bifid():
+    raises(ValueError, lambda: encipher_bifid('abc', 'b', 'abcde'))
+    assert encipher_bifid('abc', 'b', 'abcd') == 'bdb'
+    raises(ValueError, lambda: decipher_bifid('bdb', 'b', 'abcde'))
+    assert encipher_bifid('bdb', 'b', 'abcd') == 'abc'
+    raises(ValueError, lambda: bifid_square('abcde'))
+    assert bifid5_square("B") == \
+        bifid5_square('BACDEFGHIKLMNOPQRSTUVWXYZ')
+    assert bifid6_square('B0') == \
+        bifid6_square('B0ACDEFGHIJKLMNOPQRSTUVWXYZ123456789')
+
+
+def test_encipher_decipher_gm():
+    ps = [131, 137, 139, 149, 151, 157, 163, 167,
+          173, 179, 181, 191, 193, 197, 199]
+    qs = [89, 97, 101, 103, 107, 109, 113, 127,
+          131, 137, 139, 149, 151, 157, 47]
+    messages = [
+        0, 32855, 34303, 14805, 1280, 75859, 38368,
+        724, 60356, 51675, 76697, 61854, 18661,
+    ]
+    for p, q in zip(ps, qs):
+        pri = gm_private_key(p, q)
+        for msg in messages:
+            pub = gm_public_key(p, q)
+            enc = encipher_gm(msg, pub)
+            dec = decipher_gm(enc, pri)
+            assert dec == msg
+
+
+def test_gm_private_key():
+    raises(ValueError, lambda: gm_public_key(13, 15))
+    raises(ValueError, lambda: gm_public_key(0, 0))
+    raises(ValueError, lambda: gm_public_key(0, 5))
+    assert 17, 19 == gm_public_key(17, 19)
+
+
+def test_gm_public_key():
+    assert 323 == gm_public_key(17, 19)[1]
+    assert 15  == gm_public_key(3, 5)[1]
+    raises(ValueError, lambda: gm_public_key(15, 19))
+
+def test_encipher_decipher_bg():
+    ps = [67, 7, 71, 103, 11, 43, 107, 47,
+          79, 19, 83, 23, 59, 127, 31]
+    qs = qs = [7, 71, 103, 11, 43, 107, 47,
+               79, 19, 83, 23, 59, 127, 31, 67]
+    messages = [
+        0, 328, 343, 148, 1280, 758, 383,
+        724, 603, 516, 766, 618, 186,
+    ]
+
+    for p, q in zip(ps, qs):
+        pri = bg_private_key(p, q)
+        for msg in messages:
+            pub = bg_public_key(p, q)
+            enc = encipher_bg(msg, pub)
+            dec = decipher_bg(enc, pri)
+            assert dec == msg
+
+def test_bg_private_key():
+    raises(ValueError, lambda: bg_private_key(8, 16))
+    raises(ValueError, lambda: bg_private_key(8, 8))
+    raises(ValueError, lambda: bg_private_key(13, 17))
+    assert 23, 31 == bg_private_key(23, 31)
+
+def test_bg_public_key():
+    assert 5293 == bg_public_key(67, 79)
+    assert 713 == bg_public_key(23, 31)
+    raises(ValueError, lambda: bg_private_key(13, 17))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..8846a99510601c9675103e21ef5a0a1e839fdd11
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/__init__.py
@@ -0,0 +1,19 @@
+from .diffgeom import (
+    BaseCovarDerivativeOp, BaseScalarField, BaseVectorField, Commutator,
+    contravariant_order, CoordSystem, CoordinateSymbol,
+    CovarDerivativeOp, covariant_order, Differential, intcurve_diffequ,
+    intcurve_series, LieDerivative, Manifold, metric_to_Christoffel_1st,
+    metric_to_Christoffel_2nd, metric_to_Ricci_components,
+    metric_to_Riemann_components, Patch, Point, TensorProduct, twoform_to_matrix,
+    vectors_in_basis, WedgeProduct,
+)
+
+__all__ = [
+    'BaseCovarDerivativeOp', 'BaseScalarField', 'BaseVectorField', 'Commutator',
+    'contravariant_order', 'CoordSystem', 'CoordinateSymbol',
+    'CovarDerivativeOp', 'covariant_order', 'Differential', 'intcurve_diffequ',
+    'intcurve_series', 'LieDerivative', 'Manifold', 'metric_to_Christoffel_1st',
+    'metric_to_Christoffel_2nd', 'metric_to_Ricci_components',
+    'metric_to_Riemann_components', 'Patch', 'Point', 'TensorProduct',
+    'twoform_to_matrix', 'vectors_in_basis', 'WedgeProduct',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/diffgeom.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/diffgeom.py
new file mode 100644
index 0000000000000000000000000000000000000000..a95f83122d6de0b7015b9a3ad0573cbfd97a7ef3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/diffgeom.py
@@ -0,0 +1,2270 @@
+from __future__ import annotations
+from typing import Any
+
+from functools import reduce
+from itertools import permutations
+
+from sympy.combinatorics import Permutation
+from sympy.core import (
+    Basic, Expr, Function, diff,
+    Pow, Mul, Add, Lambda, S, Tuple, Dict
+)
+from sympy.core.cache import cacheit
+
+from sympy.core.symbol import Symbol, Dummy
+from sympy.core.symbol import Str
+from sympy.core.sympify import _sympify
+from sympy.functions import factorial
+from sympy.matrices import ImmutableDenseMatrix as Matrix
+from sympy.solvers import solve
+
+from sympy.utilities.exceptions import (sympy_deprecation_warning,
+                                        SymPyDeprecationWarning,
+                                        ignore_warnings)
+
+
+# TODO you are a bit excessive in the use of Dummies
+# TODO dummy point, literal field
+# TODO too often one needs to call doit or simplify on the output, check the
+# tests and find out why
+from sympy.tensor.array import ImmutableDenseNDimArray
+
+
+class Manifold(Basic):
+    """
+    A mathematical manifold.
+
+    Explanation
+    ===========
+
+    A manifold is a topological space that locally resembles
+    Euclidean space near each point [1].
+    This class does not provide any means to study the topological
+    characteristics of the manifold that it represents, though.
+
+    Parameters
+    ==========
+
+    name : str
+        The name of the manifold.
+
+    dim : int
+        The dimension of the manifold.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom import Manifold
+    >>> m = Manifold('M', 2)
+    >>> m
+    M
+    >>> m.dim
+    2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Manifold
+    """
+
+    def __new__(cls, name, dim, **kwargs):
+        if not isinstance(name, Str):
+            name = Str(name)
+        dim = _sympify(dim)
+        obj = super().__new__(cls, name, dim)
+
+        obj.patches = _deprecated_list(
+            """
+            Manifold.patches is deprecated. The Manifold object is now
+            immutable. Instead use a separate list to keep track of the
+            patches.
+            """, [])
+        return obj
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def dim(self):
+        return self.args[1]
+
+
+class Patch(Basic):
+    """
+    A patch on a manifold.
+
+    Explanation
+    ===========
+
+    Coordinate patch, or patch in short, is a simply-connected open set around
+    a point in the manifold [1]. On a manifold one can have many patches that
+    do not always include the whole manifold. On these patches coordinate
+    charts can be defined that permit the parameterization of any point on the
+    patch in terms of a tuple of real numbers (the coordinates).
+
+    This class does not provide any means to study the topological
+    characteristics of the patch that it represents.
+
+    Parameters
+    ==========
+
+    name : str
+        The name of the patch.
+
+    manifold : Manifold
+        The manifold on which the patch is defined.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom import Manifold, Patch
+    >>> m = Manifold('M', 2)
+    >>> p = Patch('P', m)
+    >>> p
+    P
+    >>> p.dim
+    2
+
+    References
+    ==========
+
+    .. [1] G. Sussman, J. Wisdom, W. Farr, Functional Differential Geometry
+           (2013)
+
+    """
+    def __new__(cls, name, manifold, **kwargs):
+        if not isinstance(name, Str):
+            name = Str(name)
+        obj = super().__new__(cls, name, manifold)
+
+        obj.manifold.patches.append(obj) # deprecated
+        obj.coord_systems = _deprecated_list(
+            """
+            Patch.coord_systms is deprecated. The Patch class is now
+            immutable. Instead use a separate list to keep track of coordinate
+            systems.
+            """, [])
+        return obj
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def manifold(self):
+        return self.args[1]
+
+    @property
+    def dim(self):
+        return self.manifold.dim
+
+
+class CoordSystem(Basic):
+    """
+    A coordinate system defined on the patch.
+
+    Explanation
+    ===========
+
+    Coordinate system is a system that uses one or more coordinates to uniquely
+    determine the position of the points or other geometric elements on a
+    manifold [1].
+
+    By passing ``Symbols`` to *symbols* parameter, user can define the name and
+    assumptions of coordinate symbols of the coordinate system. If not passed,
+    these symbols are generated automatically and are assumed to be real valued.
+
+    By passing *relations* parameter, user can define the transform relations of
+    coordinate systems. Inverse transformation and indirect transformation can
+    be found automatically. If this parameter is not passed, coordinate
+    transformation cannot be done.
+
+    Parameters
+    ==========
+
+    name : str
+        The name of the coordinate system.
+
+    patch : Patch
+        The patch where the coordinate system is defined.
+
+    symbols : list of Symbols, optional
+        Defines the names and assumptions of coordinate symbols.
+
+    relations : dict, optional
+        Key is a tuple of two strings, who are the names of the systems where
+        the coordinates transform from and transform to.
+        Value is a tuple of the symbols before transformation and a tuple of
+        the expressions after transformation.
+
+    Examples
+    ========
+
+    We define two-dimensional Cartesian coordinate system and polar coordinate
+    system.
+
+    >>> from sympy import symbols, pi, sqrt, atan2, cos, sin
+    >>> from sympy.diffgeom import Manifold, Patch, CoordSystem
+    >>> m = Manifold('M', 2)
+    >>> p = Patch('P', m)
+    >>> x, y = symbols('x y', real=True)
+    >>> r, theta = symbols('r theta', nonnegative=True)
+    >>> relation_dict = {
+    ... ('Car2D', 'Pol'): [(x, y), (sqrt(x**2 + y**2), atan2(y, x))],
+    ... ('Pol', 'Car2D'): [(r, theta), (r*cos(theta), r*sin(theta))]
+    ... }
+    >>> Car2D = CoordSystem('Car2D', p, (x, y), relation_dict)
+    >>> Pol = CoordSystem('Pol', p, (r, theta), relation_dict)
+
+    ``symbols`` property returns ``CoordinateSymbol`` instances. These symbols
+    are not same with the symbols used to construct the coordinate system.
+
+    >>> Car2D
+    Car2D
+    >>> Car2D.dim
+    2
+    >>> Car2D.symbols
+    (x, y)
+    >>> _[0].func
+    
+
+    ``transformation()`` method returns the transformation function from
+    one coordinate system to another. ``transform()`` method returns the
+    transformed coordinates.
+
+    >>> Car2D.transformation(Pol)
+    Lambda((x, y), Matrix([
+    [sqrt(x**2 + y**2)],
+    [      atan2(y, x)]]))
+    >>> Car2D.transform(Pol)
+    Matrix([
+    [sqrt(x**2 + y**2)],
+    [      atan2(y, x)]])
+    >>> Car2D.transform(Pol, [1, 2])
+    Matrix([
+    [sqrt(5)],
+    [atan(2)]])
+
+    ``jacobian()`` method returns the Jacobian matrix of coordinate
+    transformation between two systems. ``jacobian_determinant()`` method
+    returns the Jacobian determinant of coordinate transformation between two
+    systems.
+
+    >>> Pol.jacobian(Car2D)
+    Matrix([
+    [cos(theta), -r*sin(theta)],
+    [sin(theta),  r*cos(theta)]])
+    >>> Pol.jacobian(Car2D, [1, pi/2])
+    Matrix([
+    [0, -1],
+    [1,  0]])
+    >>> Car2D.jacobian_determinant(Pol)
+    1/sqrt(x**2 + y**2)
+    >>> Car2D.jacobian_determinant(Pol, [1,0])
+    1
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Coordinate_system
+
+    """
+    def __new__(cls, name, patch, symbols=None, relations={}, **kwargs):
+        if not isinstance(name, Str):
+            name = Str(name)
+
+        # canonicallize the symbols
+        if symbols is None:
+            names = kwargs.get('names', None)
+            if names is None:
+                symbols = Tuple(
+                    *[Symbol('%s_%s' % (name.name, i), real=True)
+                      for i in range(patch.dim)]
+                )
+            else:
+                sympy_deprecation_warning(
+                    f"""
+The 'names' argument to CoordSystem is deprecated. Use 'symbols' instead. That
+is, replace
+
+    CoordSystem(..., names={names})
+
+with
+
+    CoordSystem(..., symbols=[{', '.join(["Symbol(" + repr(n) + ", real=True)" for n in names])}])
+                    """,
+                    deprecated_since_version="1.7",
+                    active_deprecations_target="deprecated-diffgeom-mutable",
+                )
+                symbols = Tuple(
+                    *[Symbol(n, real=True) for n in names]
+                )
+        else:
+            syms = []
+            for s in symbols:
+                if isinstance(s, Symbol):
+                    syms.append(Symbol(s.name, **s._assumptions.generator))
+                elif isinstance(s, str):
+                    sympy_deprecation_warning(
+                        f"""
+
+Passing a string as the coordinate symbol name to CoordSystem is deprecated.
+Pass a Symbol with the appropriate name and assumptions instead.
+
+That is, replace {s} with Symbol({s!r}, real=True).
+                        """,
+
+                        deprecated_since_version="1.7",
+                        active_deprecations_target="deprecated-diffgeom-mutable",
+                    )
+                    syms.append(Symbol(s, real=True))
+            symbols = Tuple(*syms)
+
+        # canonicallize the relations
+        rel_temp = {}
+        for k,v in relations.items():
+            s1, s2 = k
+            if not isinstance(s1, Str):
+                s1 = Str(s1)
+            if not isinstance(s2, Str):
+                s2 = Str(s2)
+            key = Tuple(s1, s2)
+
+            # Old version used Lambda as a value.
+            if isinstance(v, Lambda):
+                v = (tuple(v.signature), tuple(v.expr))
+            else:
+                v = (tuple(v[0]), tuple(v[1]))
+            rel_temp[key] = v
+        relations = Dict(rel_temp)
+
+        # construct the object
+        obj = super().__new__(cls, name, patch, symbols, relations)
+
+        # Add deprecated attributes
+        obj.transforms = _deprecated_dict(
+            """
+            CoordSystem.transforms is deprecated. The CoordSystem class is now
+            immutable. Use the 'relations' keyword argument to the
+            CoordSystems() constructor to specify relations.
+            """, {})
+        obj._names = [str(n) for n in symbols]
+        obj.patch.coord_systems.append(obj) # deprecated
+        obj._dummies = [Dummy(str(n)) for n in symbols] # deprecated
+        obj._dummy = Dummy()
+
+        return obj
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def patch(self):
+        return self.args[1]
+
+    @property
+    def manifold(self):
+        return self.patch.manifold
+
+    @property
+    def symbols(self):
+        return tuple(CoordinateSymbol(self, i, **s._assumptions.generator)
+            for i,s in enumerate(self.args[2]))
+
+    @property
+    def relations(self):
+        return self.args[3]
+
+    @property
+    def dim(self):
+        return self.patch.dim
+
+    ##########################################################################
+    # Finding transformation relation
+    ##########################################################################
+
+    def transformation(self, sys):
+        """
+        Return coordinate transformation function from *self* to *sys*.
+
+        Parameters
+        ==========
+
+        sys : CoordSystem
+
+        Returns
+        =======
+
+        sympy.Lambda
+
+        Examples
+        ========
+
+        >>> from sympy.diffgeom.rn import R2_r, R2_p
+        >>> R2_r.transformation(R2_p)
+        Lambda((x, y), Matrix([
+        [sqrt(x**2 + y**2)],
+        [      atan2(y, x)]]))
+
+        """
+        signature = self.args[2]
+
+        key = Tuple(self.name, sys.name)
+        if self == sys:
+            expr = Matrix(self.symbols)
+        elif key in self.relations:
+            expr = Matrix(self.relations[key][1])
+        elif key[::-1] in self.relations:
+            expr = Matrix(self._inverse_transformation(sys, self))
+        else:
+            expr = Matrix(self._indirect_transformation(self, sys))
+        return Lambda(signature, expr)
+
+    @staticmethod
+    def _solve_inverse(sym1, sym2, exprs, sys1_name, sys2_name):
+        ret = solve(
+            [t[0] - t[1] for t in zip(sym2, exprs)],
+            list(sym1), dict=True)
+
+        if len(ret) == 0:
+            temp = "Cannot solve inverse relation from {} to {}."
+            raise NotImplementedError(temp.format(sys1_name, sys2_name))
+        elif len(ret) > 1:
+            temp = "Obtained multiple inverse relation from {} to {}."
+            raise ValueError(temp.format(sys1_name, sys2_name))
+
+        return ret[0]
+
+    @classmethod
+    def _inverse_transformation(cls, sys1, sys2):
+        # Find the transformation relation from sys2 to sys1
+        forward = sys1.transform(sys2)
+        inv_results = cls._solve_inverse(sys1.symbols, sys2.symbols, forward,
+                                         sys1.name, sys2.name)
+        signature = tuple(sys1.symbols)
+        return [inv_results[s] for s in signature]
+
+    @classmethod
+    @cacheit
+    def _indirect_transformation(cls, sys1, sys2):
+        # Find the transformation relation between two indirectly connected
+        # coordinate systems
+        rel = sys1.relations
+        path = cls._dijkstra(sys1, sys2)
+
+        transforms = []
+        for s1, s2 in zip(path, path[1:]):
+            if (s1, s2) in rel:
+                transforms.append(rel[(s1, s2)])
+            else:
+                sym2, inv_exprs = rel[(s2, s1)]
+                sym1 = tuple(Dummy() for i in sym2)
+                ret = cls._solve_inverse(sym2, sym1, inv_exprs, s2, s1)
+                ret = tuple(ret[s] for s in sym2)
+                transforms.append((sym1, ret))
+        syms = sys1.args[2]
+        exprs = syms
+        for newsyms, newexprs in transforms:
+            exprs = tuple(e.subs(zip(newsyms, exprs)) for e in newexprs)
+        return exprs
+
+    @staticmethod
+    def _dijkstra(sys1, sys2):
+        # Use Dijkstra algorithm to find the shortest path between two indirectly-connected
+        # coordinate systems
+        # return value is the list of the names of the systems.
+        relations = sys1.relations
+        graph = {}
+        for s1, s2 in relations.keys():
+            if s1 not in graph:
+                graph[s1] = {s2}
+            else:
+                graph[s1].add(s2)
+            if s2 not in graph:
+                graph[s2] = {s1}
+            else:
+                graph[s2].add(s1)
+
+        path_dict = {sys:[0, [], 0] for sys in graph} # minimum distance, path, times of visited
+
+        def visit(sys):
+            path_dict[sys][2] = 1
+            for newsys in graph[sys]:
+                distance = path_dict[sys][0] + 1
+                if path_dict[newsys][0] >= distance or not path_dict[newsys][1]:
+                    path_dict[newsys][0] = distance
+                    path_dict[newsys][1] = list(path_dict[sys][1])
+                    path_dict[newsys][1].append(sys)
+
+        visit(sys1.name)
+
+        while True:
+            min_distance = max(path_dict.values(), key=lambda x:x[0])[0]
+            newsys = None
+            for sys, lst in path_dict.items():
+                if 0 < lst[0] <= min_distance and not lst[2]:
+                    min_distance = lst[0]
+                    newsys = sys
+            if newsys is None:
+                break
+            visit(newsys)
+
+        result = path_dict[sys2.name][1]
+        result.append(sys2.name)
+
+        if result == [sys2.name]:
+            raise KeyError("Two coordinate systems are not connected.")
+        return result
+
+    def connect_to(self, to_sys, from_coords, to_exprs, inverse=True, fill_in_gaps=False):
+        sympy_deprecation_warning(
+            """
+            The CoordSystem.connect_to() method is deprecated. Instead,
+            generate a new instance of CoordSystem with the 'relations'
+            keyword argument (CoordSystem classes are now immutable).
+            """,
+            deprecated_since_version="1.7",
+            active_deprecations_target="deprecated-diffgeom-mutable",
+        )
+
+        from_coords, to_exprs = dummyfy(from_coords, to_exprs)
+        self.transforms[to_sys] = Matrix(from_coords), Matrix(to_exprs)
+
+        if inverse:
+            to_sys.transforms[self] = self._inv_transf(from_coords, to_exprs)
+
+        if fill_in_gaps:
+            self._fill_gaps_in_transformations()
+
+    @staticmethod
+    def _inv_transf(from_coords, to_exprs):
+        # Will be removed when connect_to is removed
+        inv_from = [i.as_dummy() for i in from_coords]
+        inv_to = solve(
+            [t[0] - t[1] for t in zip(inv_from, to_exprs)],
+            list(from_coords), dict=True)[0]
+        inv_to = [inv_to[fc] for fc in from_coords]
+        return Matrix(inv_from), Matrix(inv_to)
+
+    @staticmethod
+    def _fill_gaps_in_transformations():
+        # Will be removed when connect_to is removed
+        raise NotImplementedError
+
+    ##########################################################################
+    # Coordinate transformations
+    ##########################################################################
+
+    def transform(self, sys, coordinates=None):
+        """
+        Return the result of coordinate transformation from *self* to *sys*.
+        If coordinates are not given, coordinate symbols of *self* are used.
+
+        Parameters
+        ==========
+
+        sys : CoordSystem
+
+        coordinates : Any iterable, optional.
+
+        Returns
+        =======
+
+        sympy.ImmutableDenseMatrix containing CoordinateSymbol
+
+        Examples
+        ========
+
+        >>> from sympy.diffgeom.rn import R2_r, R2_p
+        >>> R2_r.transform(R2_p)
+        Matrix([
+        [sqrt(x**2 + y**2)],
+        [      atan2(y, x)]])
+        >>> R2_r.transform(R2_p, [0, 1])
+        Matrix([
+        [   1],
+        [pi/2]])
+
+        """
+        if coordinates is None:
+            coordinates = self.symbols
+        if self != sys:
+            transf = self.transformation(sys)
+            coordinates = transf(*coordinates)
+        else:
+            coordinates = Matrix(coordinates)
+        return coordinates
+
+    def coord_tuple_transform_to(self, to_sys, coords):
+        """Transform ``coords`` to coord system ``to_sys``."""
+        sympy_deprecation_warning(
+            """
+            The CoordSystem.coord_tuple_transform_to() method is deprecated.
+            Use the CoordSystem.transform() method instead.
+            """,
+            deprecated_since_version="1.7",
+            active_deprecations_target="deprecated-diffgeom-mutable",
+        )
+
+        coords = Matrix(coords)
+        if self != to_sys:
+            with ignore_warnings(SymPyDeprecationWarning):
+                transf = self.transforms[to_sys]
+            coords = transf[1].subs(list(zip(transf[0], coords)))
+        return coords
+
+    def jacobian(self, sys, coordinates=None):
+        """
+        Return the jacobian matrix of a transformation on given coordinates.
+        If coordinates are not given, coordinate symbols of *self* are used.
+
+        Parameters
+        ==========
+
+        sys : CoordSystem
+
+        coordinates : Any iterable, optional.
+
+        Returns
+        =======
+
+        sympy.ImmutableDenseMatrix
+
+        Examples
+        ========
+
+        >>> from sympy.diffgeom.rn import R2_r, R2_p
+        >>> R2_p.jacobian(R2_r)
+        Matrix([
+        [cos(theta), -rho*sin(theta)],
+        [sin(theta),  rho*cos(theta)]])
+        >>> R2_p.jacobian(R2_r, [1, 0])
+        Matrix([
+        [1, 0],
+        [0, 1]])
+
+        """
+        result = self.transform(sys).jacobian(self.symbols)
+        if coordinates is not None:
+            result = result.subs(list(zip(self.symbols, coordinates)))
+        return result
+    jacobian_matrix = jacobian
+
+    def jacobian_determinant(self, sys, coordinates=None):
+        """
+        Return the jacobian determinant of a transformation on given
+        coordinates. If coordinates are not given, coordinate symbols of *self*
+        are used.
+
+        Parameters
+        ==========
+
+        sys : CoordSystem
+
+        coordinates : Any iterable, optional.
+
+        Returns
+        =======
+
+        sympy.Expr
+
+        Examples
+        ========
+
+        >>> from sympy.diffgeom.rn import R2_r, R2_p
+        >>> R2_r.jacobian_determinant(R2_p)
+        1/sqrt(x**2 + y**2)
+        >>> R2_r.jacobian_determinant(R2_p, [1, 0])
+        1
+
+        """
+        return self.jacobian(sys, coordinates).det()
+
+
+    ##########################################################################
+    # Points
+    ##########################################################################
+
+    def point(self, coords):
+        """Create a ``Point`` with coordinates given in this coord system."""
+        return Point(self, coords)
+
+    def point_to_coords(self, point):
+        """Calculate the coordinates of a point in this coord system."""
+        return point.coords(self)
+
+    ##########################################################################
+    # Base fields.
+    ##########################################################################
+
+    def base_scalar(self, coord_index):
+        """Return ``BaseScalarField`` that takes a point and returns one of the coordinates."""
+        return BaseScalarField(self, coord_index)
+    coord_function = base_scalar
+
+    def base_scalars(self):
+        """Returns a list of all coordinate functions.
+        For more details see the ``base_scalar`` method of this class."""
+        return [self.base_scalar(i) for i in range(self.dim)]
+    coord_functions = base_scalars
+
+    def base_vector(self, coord_index):
+        """Return a basis vector field.
+        The basis vector field for this coordinate system. It is also an
+        operator on scalar fields."""
+        return BaseVectorField(self, coord_index)
+
+    def base_vectors(self):
+        """Returns a list of all base vectors.
+        For more details see the ``base_vector`` method of this class."""
+        return [self.base_vector(i) for i in range(self.dim)]
+
+    def base_oneform(self, coord_index):
+        """Return a basis 1-form field.
+        The basis one-form field for this coordinate system. It is also an
+        operator on vector fields."""
+        return Differential(self.coord_function(coord_index))
+
+    def base_oneforms(self):
+        """Returns a list of all base oneforms.
+        For more details see the ``base_oneform`` method of this class."""
+        return [self.base_oneform(i) for i in range(self.dim)]
+
+
+class CoordinateSymbol(Symbol):
+    """A symbol which denotes an abstract value of i-th coordinate of
+    the coordinate system with given context.
+
+    Explanation
+    ===========
+
+    Each coordinates in coordinate system are represented by unique symbol,
+    such as x, y, z in Cartesian coordinate system.
+
+    You may not construct this class directly. Instead, use `symbols` method
+    of CoordSystem.
+
+    Parameters
+    ==========
+
+    coord_sys : CoordSystem
+
+    index : integer
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Lambda, Matrix, sqrt, atan2, cos, sin
+    >>> from sympy.diffgeom import Manifold, Patch, CoordSystem
+    >>> m = Manifold('M', 2)
+    >>> p = Patch('P', m)
+    >>> x, y = symbols('x y', real=True)
+    >>> r, theta = symbols('r theta', nonnegative=True)
+    >>> relation_dict = {
+    ... ('Car2D', 'Pol'): Lambda((x, y), Matrix([sqrt(x**2 + y**2), atan2(y, x)])),
+    ... ('Pol', 'Car2D'): Lambda((r, theta), Matrix([r*cos(theta), r*sin(theta)]))
+    ... }
+    >>> Car2D = CoordSystem('Car2D', p, [x, y], relation_dict)
+    >>> Pol = CoordSystem('Pol', p, [r, theta], relation_dict)
+    >>> x, y = Car2D.symbols
+
+    ``CoordinateSymbol`` contains its coordinate symbol and index.
+
+    >>> x.name
+    'x'
+    >>> x.coord_sys == Car2D
+    True
+    >>> x.index
+    0
+    >>> x.is_real
+    True
+
+    You can transform ``CoordinateSymbol`` into other coordinate system using
+    ``rewrite()`` method.
+
+    >>> x.rewrite(Pol)
+    r*cos(theta)
+    >>> sqrt(x**2 + y**2).rewrite(Pol).simplify()
+    r
+
+    """
+    def __new__(cls, coord_sys, index, **assumptions):
+        name = coord_sys.args[2][index].name
+        obj = super().__new__(cls, name, **assumptions)
+        obj.coord_sys = coord_sys
+        obj.index = index
+        return obj
+
+    def __getnewargs__(self):
+        return (self.coord_sys, self.index)
+
+    def _hashable_content(self):
+        return (
+            self.coord_sys, self.index
+        ) + tuple(sorted(self.assumptions0.items()))
+
+    def _eval_rewrite(self, rule, args, **hints):
+        if isinstance(rule, CoordSystem):
+            return rule.transform(self.coord_sys)[self.index]
+        return super()._eval_rewrite(rule, args, **hints)
+
+
+class Point(Basic):
+    """Point defined in a coordinate system.
+
+    Explanation
+    ===========
+
+    Mathematically, point is defined in the manifold and does not have any coordinates
+    by itself. Coordinate system is what imbues the coordinates to the point by coordinate
+    chart. However, due to the difficulty of realizing such logic, you must supply
+    a coordinate system and coordinates to define a Point here.
+
+    The usage of this object after its definition is independent of the
+    coordinate system that was used in order to define it, however due to
+    limitations in the simplification routines you can arrive at complicated
+    expressions if you use inappropriate coordinate systems.
+
+    Parameters
+    ==========
+
+    coord_sys : CoordSystem
+
+    coords : list
+        The coordinates of the point.
+
+    Examples
+    ========
+
+    >>> from sympy import pi
+    >>> from sympy.diffgeom import Point
+    >>> from sympy.diffgeom.rn import R2, R2_r, R2_p
+    >>> rho, theta = R2_p.symbols
+
+    >>> p = Point(R2_p, [rho, 3*pi/4])
+
+    >>> p.manifold == R2
+    True
+
+    >>> p.coords()
+    Matrix([
+    [   rho],
+    [3*pi/4]])
+    >>> p.coords(R2_r)
+    Matrix([
+    [-sqrt(2)*rho/2],
+    [ sqrt(2)*rho/2]])
+
+    """
+
+    def __new__(cls, coord_sys, coords, **kwargs):
+        coords = Matrix(coords)
+        obj = super().__new__(cls, coord_sys, coords)
+        obj._coord_sys = coord_sys
+        obj._coords = coords
+        return obj
+
+    @property
+    def patch(self):
+        return self._coord_sys.patch
+
+    @property
+    def manifold(self):
+        return self._coord_sys.manifold
+
+    @property
+    def dim(self):
+        return self.manifold.dim
+
+    def coords(self, sys=None):
+        """
+        Coordinates of the point in given coordinate system. If coordinate system
+        is not passed, it returns the coordinates in the coordinate system in which
+        the point was defined.
+        """
+        if sys is None:
+            return self._coords
+        else:
+            return self._coord_sys.transform(sys, self._coords)
+
+    @property
+    def free_symbols(self):
+        return self._coords.free_symbols
+
+
+class BaseScalarField(Expr):
+    """Base scalar field over a manifold for a given coordinate system.
+
+    Explanation
+    ===========
+
+    A scalar field takes a point as an argument and returns a scalar.
+    A base scalar field of a coordinate system takes a point and returns one of
+    the coordinates of that point in the coordinate system in question.
+
+    To define a scalar field you need to choose the coordinate system and the
+    index of the coordinate.
+
+    The use of the scalar field after its definition is independent of the
+    coordinate system in which it was defined, however due to limitations in
+    the simplification routines you may arrive at more complicated
+    expression if you use unappropriate coordinate systems.
+    You can build complicated scalar fields by just building up SymPy
+    expressions containing ``BaseScalarField`` instances.
+
+    Parameters
+    ==========
+
+    coord_sys : CoordSystem
+
+    index : integer
+
+    Examples
+    ========
+
+    >>> from sympy import Function, pi
+    >>> from sympy.diffgeom import BaseScalarField
+    >>> from sympy.diffgeom.rn import R2_r, R2_p
+    >>> rho, _ = R2_p.symbols
+    >>> point = R2_p.point([rho, 0])
+    >>> fx, fy = R2_r.base_scalars()
+    >>> ftheta = BaseScalarField(R2_r, 1)
+
+    >>> fx(point)
+    rho
+    >>> fy(point)
+    0
+
+    >>> (fx**2+fy**2).rcall(point)
+    rho**2
+
+    >>> g = Function('g')
+    >>> fg = g(ftheta-pi)
+    >>> fg.rcall(point)
+    g(-pi)
+
+    """
+
+    is_commutative = True
+
+    def __new__(cls, coord_sys, index, **kwargs):
+        index = _sympify(index)
+        obj = super().__new__(cls, coord_sys, index)
+        obj._coord_sys = coord_sys
+        obj._index = index
+        return obj
+
+    @property
+    def coord_sys(self):
+        return self.args[0]
+
+    @property
+    def index(self):
+        return self.args[1]
+
+    @property
+    def patch(self):
+        return self.coord_sys.patch
+
+    @property
+    def manifold(self):
+        return self.coord_sys.manifold
+
+    @property
+    def dim(self):
+        return self.manifold.dim
+
+    def __call__(self, *args):
+        """Evaluating the field at a point or doing nothing.
+        If the argument is a ``Point`` instance, the field is evaluated at that
+        point. The field is returned itself if the argument is any other
+        object. It is so in order to have working recursive calling mechanics
+        for all fields (check the ``__call__`` method of ``Expr``).
+        """
+        point = args[0]
+        if len(args) != 1 or not isinstance(point, Point):
+            return self
+        coords = point.coords(self._coord_sys)
+        # XXX Calling doit  is necessary with all the Subs expressions
+        # XXX Calling simplify is necessary with all the trig expressions
+        return simplify(coords[self._index]).doit()
+
+    # XXX Workaround for limitations on the content of args
+    free_symbols: set[Any] = set()
+
+
+class BaseVectorField(Expr):
+    r"""Base vector field over a manifold for a given coordinate system.
+
+    Explanation
+    ===========
+
+    A vector field is an operator taking a scalar field and returning a
+    directional derivative (which is also a scalar field).
+    A base vector field is the same type of operator, however the derivation is
+    specifically done with respect to a chosen coordinate.
+
+    To define a base vector field you need to choose the coordinate system and
+    the index of the coordinate.
+
+    The use of the vector field after its definition is independent of the
+    coordinate system in which it was defined, however due to limitations in the
+    simplification routines you may arrive at more complicated expression if you
+    use unappropriate coordinate systems.
+
+    Parameters
+    ==========
+    coord_sys : CoordSystem
+
+    index : integer
+
+    Examples
+    ========
+
+    >>> from sympy import Function
+    >>> from sympy.diffgeom.rn import R2_p, R2_r
+    >>> from sympy.diffgeom import BaseVectorField
+    >>> from sympy import pprint
+
+    >>> x, y = R2_r.symbols
+    >>> rho, theta = R2_p.symbols
+    >>> fx, fy = R2_r.base_scalars()
+    >>> point_p = R2_p.point([rho, theta])
+    >>> point_r = R2_r.point([x, y])
+
+    >>> g = Function('g')
+    >>> s_field = g(fx, fy)
+
+    >>> v = BaseVectorField(R2_r, 1)
+    >>> pprint(v(s_field))
+    / d           \|
+    |---(g(x, xi))||
+    \dxi          /|xi=y
+    >>> pprint(v(s_field).rcall(point_r).doit())
+    d
+    --(g(x, y))
+    dy
+    >>> pprint(v(s_field).rcall(point_p))
+    / d                        \|
+    |---(g(rho*cos(theta), xi))||
+    \dxi                       /|xi=rho*sin(theta)
+
+    """
+
+    is_commutative = False
+
+    def __new__(cls, coord_sys, index, **kwargs):
+        index = _sympify(index)
+        obj = super().__new__(cls, coord_sys, index)
+        obj._coord_sys = coord_sys
+        obj._index = index
+        return obj
+
+    @property
+    def coord_sys(self):
+        return self.args[0]
+
+    @property
+    def index(self):
+        return self.args[1]
+
+    @property
+    def patch(self):
+        return self.coord_sys.patch
+
+    @property
+    def manifold(self):
+        return self.coord_sys.manifold
+
+    @property
+    def dim(self):
+        return self.manifold.dim
+
+    def __call__(self, scalar_field):
+        """Apply on a scalar field.
+        The action of a vector field on a scalar field is a directional
+        differentiation.
+        If the argument is not a scalar field an error is raised.
+        """
+        if covariant_order(scalar_field) or contravariant_order(scalar_field):
+            raise ValueError('Only scalar fields can be supplied as arguments to vector fields.')
+
+        if scalar_field is None:
+            return self
+
+        base_scalars = list(scalar_field.atoms(BaseScalarField))
+
+        # First step: e_x(x+r**2) -> e_x(x) + 2*r*e_x(r)
+        d_var = self._coord_sys._dummy
+        # TODO: you need a real dummy function for the next line
+        d_funcs = [Function('_#_%s' % i)(d_var) for i,
+                   b in enumerate(base_scalars)]
+        d_result = scalar_field.subs(list(zip(base_scalars, d_funcs)))
+        d_result = d_result.diff(d_var)
+
+        # Second step: e_x(x) -> 1 and e_x(r) -> cos(atan2(x, y))
+        coords = self._coord_sys.symbols
+        d_funcs_deriv = [f.diff(d_var) for f in d_funcs]
+        d_funcs_deriv_sub = []
+        for b in base_scalars:
+            jac = self._coord_sys.jacobian(b._coord_sys, coords)
+            d_funcs_deriv_sub.append(jac[b._index, self._index])
+        d_result = d_result.subs(list(zip(d_funcs_deriv, d_funcs_deriv_sub)))
+
+        # Remove the dummies
+        result = d_result.subs(list(zip(d_funcs, base_scalars)))
+        result = result.subs(list(zip(coords, self._coord_sys.coord_functions())))
+        return result.doit()
+
+
+def _find_coords(expr):
+    # Finds CoordinateSystems existing in expr
+    fields = expr.atoms(BaseScalarField, BaseVectorField)
+    return {f._coord_sys for f in fields}
+
+
+class Commutator(Expr):
+    r"""Commutator of two vector fields.
+
+    Explanation
+    ===========
+
+    The commutator of two vector fields `v_1` and `v_2` is defined as the
+    vector field `[v_1, v_2]` that evaluated on each scalar field `f` is equal
+    to `v_1(v_2(f)) - v_2(v_1(f))`.
+
+    Examples
+    ========
+
+
+    >>> from sympy.diffgeom.rn import R2_p, R2_r
+    >>> from sympy.diffgeom import Commutator
+    >>> from sympy import simplify
+
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> e_r = R2_p.base_vector(0)
+
+    >>> c_xy = Commutator(e_x, e_y)
+    >>> c_xr = Commutator(e_x, e_r)
+    >>> c_xy
+    0
+
+    Unfortunately, the current code is not able to compute everything:
+
+    >>> c_xr
+    Commutator(e_x, e_rho)
+    >>> simplify(c_xr(fy**2))
+    -2*cos(theta)*y**2/(x**2 + y**2)
+
+    """
+    def __new__(cls, v1, v2):
+        if (covariant_order(v1) or contravariant_order(v1) != 1
+                or covariant_order(v2) or contravariant_order(v2) != 1):
+            raise ValueError(
+                'Only commutators of vector fields are supported.')
+        if v1 == v2:
+            return S.Zero
+        coord_sys = set().union(*[_find_coords(v) for v in (v1, v2)])
+        if len(coord_sys) == 1:
+            # Only one coordinate systems is used, hence it is easy enough to
+            # actually evaluate the commutator.
+            if all(isinstance(v, BaseVectorField) for v in (v1, v2)):
+                return S.Zero
+            bases_1, bases_2 = [list(v.atoms(BaseVectorField))
+                                for v in (v1, v2)]
+            coeffs_1 = [v1.expand().coeff(b) for b in bases_1]
+            coeffs_2 = [v2.expand().coeff(b) for b in bases_2]
+            res = 0
+            for c1, b1 in zip(coeffs_1, bases_1):
+                for c2, b2 in zip(coeffs_2, bases_2):
+                    res += c1*b1(c2)*b2 - c2*b2(c1)*b1
+            return res
+        else:
+            obj = super().__new__(cls, v1, v2)
+            obj._v1 = v1 # deprecated assignment
+            obj._v2 = v2 # deprecated assignment
+            return obj
+
+    @property
+    def v1(self):
+        return self.args[0]
+
+    @property
+    def v2(self):
+        return self.args[1]
+
+    def __call__(self, scalar_field):
+        """Apply on a scalar field.
+        If the argument is not a scalar field an error is raised.
+        """
+        return self.v1(self.v2(scalar_field)) - self.v2(self.v1(scalar_field))
+
+
+class Differential(Expr):
+    r"""Return the differential (exterior derivative) of a form field.
+
+    Explanation
+    ===========
+
+    The differential of a form (i.e. the exterior derivative) has a complicated
+    definition in the general case.
+    The differential `df` of the 0-form `f` is defined for any vector field `v`
+    as `df(v) = v(f)`.
+
+    Examples
+    ========
+
+    >>> from sympy import Function
+    >>> from sympy.diffgeom.rn import R2_r
+    >>> from sympy.diffgeom import Differential
+    >>> from sympy import pprint
+
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> g = Function('g')
+    >>> s_field = g(fx, fy)
+    >>> dg = Differential(s_field)
+
+    >>> dg
+    d(g(x, y))
+    >>> pprint(dg(e_x))
+    / d           \|
+    |---(g(xi, y))||
+    \dxi          /|xi=x
+    >>> pprint(dg(e_y))
+    / d           \|
+    |---(g(x, xi))||
+    \dxi          /|xi=y
+
+    Applying the exterior derivative operator twice always results in:
+
+    >>> Differential(dg)
+    0
+    """
+
+    is_commutative = False
+
+    def __new__(cls, form_field):
+        if contravariant_order(form_field):
+            raise ValueError(
+                'A vector field was supplied as an argument to Differential.')
+        if isinstance(form_field, Differential):
+            return S.Zero
+        else:
+            obj = super().__new__(cls, form_field)
+            obj._form_field = form_field # deprecated assignment
+            return obj
+
+    @property
+    def form_field(self):
+        return self.args[0]
+
+    def __call__(self, *vector_fields):
+        """Apply on a list of vector_fields.
+
+        Explanation
+        ===========
+
+        If the number of vector fields supplied is not equal to 1 + the order of
+        the form field inside the differential the result is undefined.
+
+        For 1-forms (i.e. differentials of scalar fields) the evaluation is
+        done as `df(v)=v(f)`. However if `v` is ``None`` instead of a vector
+        field, the differential is returned unchanged. This is done in order to
+        permit partial contractions for higher forms.
+
+        In the general case the evaluation is done by applying the form field
+        inside the differential on a list with one less elements than the number
+        of elements in the original list. Lowering the number of vector fields
+        is achieved through replacing each pair of fields by their
+        commutator.
+
+        If the arguments are not vectors or ``None``s an error is raised.
+        """
+        if any((contravariant_order(a) != 1 or covariant_order(a)) and a is not None
+                for a in vector_fields):
+            raise ValueError('The arguments supplied to Differential should be vector fields or Nones.')
+        k = len(vector_fields)
+        if k == 1:
+            if vector_fields[0]:
+                return vector_fields[0].rcall(self._form_field)
+            return self
+        else:
+            # For higher form it is more complicated:
+            # Invariant formula:
+            # https://en.wikipedia.org/wiki/Exterior_derivative#Invariant_formula
+            # df(v1, ... vn) = +/- vi(f(v1..no i..vn))
+            #                  +/- f([vi,vj],v1..no i, no j..vn)
+            f = self._form_field
+            v = vector_fields
+            ret = 0
+            for i in range(k):
+                t = v[i].rcall(f.rcall(*v[:i] + v[i + 1:]))
+                ret += (-1)**i*t
+                for j in range(i + 1, k):
+                    c = Commutator(v[i], v[j])
+                    if c:  # TODO this is ugly - the Commutator can be Zero and
+                        # this causes the next line to fail
+                        t = f.rcall(*(c,) + v[:i] + v[i + 1:j] + v[j + 1:])
+                        ret += (-1)**(i + j)*t
+            return ret
+
+
+class TensorProduct(Expr):
+    """Tensor product of forms.
+
+    Explanation
+    ===========
+
+    The tensor product permits the creation of multilinear functionals (i.e.
+    higher order tensors) out of lower order fields (e.g. 1-forms and vector
+    fields). However, the higher tensors thus created lack the interesting
+    features provided by the other type of product, the wedge product, namely
+    they are not antisymmetric and hence are not form fields.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2_r
+    >>> from sympy.diffgeom import TensorProduct
+
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> dx, dy = R2_r.base_oneforms()
+
+    >>> TensorProduct(dx, dy)(e_x, e_y)
+    1
+    >>> TensorProduct(dx, dy)(e_y, e_x)
+    0
+    >>> TensorProduct(dx, fx*dy)(fx*e_x, e_y)
+    x**2
+    >>> TensorProduct(e_x, e_y)(fx**2, fy**2)
+    4*x*y
+    >>> TensorProduct(e_y, dx)(fy)
+    dx
+
+    You can nest tensor products.
+
+    >>> tp1 = TensorProduct(dx, dy)
+    >>> TensorProduct(tp1, dx)(e_x, e_y, e_x)
+    1
+
+    You can make partial contraction for instance when 'raising an index'.
+    Putting ``None`` in the second argument of ``rcall`` means that the
+    respective position in the tensor product is left as it is.
+
+    >>> TP = TensorProduct
+    >>> metric = TP(dx, dx) + 3*TP(dy, dy)
+    >>> metric.rcall(e_y, None)
+    3*dy
+
+    Or automatically pad the args with ``None`` without specifying them.
+
+    >>> metric.rcall(e_y)
+    3*dy
+
+    """
+    def __new__(cls, *args):
+        scalar = Mul(*[m for m in args if covariant_order(m) + contravariant_order(m) == 0])
+        multifields = [m for m in args if covariant_order(m) + contravariant_order(m)]
+        if multifields:
+            if len(multifields) == 1:
+                return scalar*multifields[0]
+            return scalar*super().__new__(cls, *multifields)
+        else:
+            return scalar
+
+    def __call__(self, *fields):
+        """Apply on a list of fields.
+
+        If the number of input fields supplied is not equal to the order of
+        the tensor product field, the list of arguments is padded with ``None``'s.
+
+        The list of arguments is divided in sublists depending on the order of
+        the forms inside the tensor product. The sublists are provided as
+        arguments to these forms and the resulting expressions are given to the
+        constructor of ``TensorProduct``.
+
+        """
+        tot_order = covariant_order(self) + contravariant_order(self)
+        tot_args = len(fields)
+        if tot_args != tot_order:
+            fields = list(fields) + [None]*(tot_order - tot_args)
+        orders = [covariant_order(f) + contravariant_order(f) for f in self._args]
+        indices = [sum(orders[:i + 1]) for i in range(len(orders) - 1)]
+        fields = [fields[i:j] for i, j in zip([0] + indices, indices + [None])]
+        multipliers = [t[0].rcall(*t[1]) for t in zip(self._args, fields)]
+        return TensorProduct(*multipliers)
+
+
+class WedgeProduct(TensorProduct):
+    """Wedge product of forms.
+
+    Explanation
+    ===========
+
+    In the context of integration only completely antisymmetric forms make
+    sense. The wedge product permits the creation of such forms.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2_r
+    >>> from sympy.diffgeom import WedgeProduct
+
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> dx, dy = R2_r.base_oneforms()
+
+    >>> WedgeProduct(dx, dy)(e_x, e_y)
+    1
+    >>> WedgeProduct(dx, dy)(e_y, e_x)
+    -1
+    >>> WedgeProduct(dx, fx*dy)(fx*e_x, e_y)
+    x**2
+    >>> WedgeProduct(e_x, e_y)(fy, None)
+    -e_x
+
+    You can nest wedge products.
+
+    >>> wp1 = WedgeProduct(dx, dy)
+    >>> WedgeProduct(wp1, dx)(e_x, e_y, e_x)
+    0
+
+    """
+    # TODO the calculation of signatures is slow
+    # TODO you do not need all these permutations (neither the prefactor)
+    def __call__(self, *fields):
+        """Apply on a list of vector_fields.
+        The expression is rewritten internally in terms of tensor products and evaluated."""
+        orders = (covariant_order(e) + contravariant_order(e) for e in self.args)
+        mul = 1/Mul(*(factorial(o) for o in orders))
+        perms = permutations(fields)
+        perms_par = (Permutation(
+            p).signature() for p in permutations(range(len(fields))))
+        tensor_prod = TensorProduct(*self.args)
+        return mul*Add(*[tensor_prod(*p[0])*p[1] for p in zip(perms, perms_par)])
+
+
+class LieDerivative(Expr):
+    """Lie derivative with respect to a vector field.
+
+    Explanation
+    ===========
+
+    The transport operator that defines the Lie derivative is the pushforward of
+    the field to be derived along the integral curve of the field with respect
+    to which one derives.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2_r, R2_p
+    >>> from sympy.diffgeom import (LieDerivative, TensorProduct)
+
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> e_rho, e_theta = R2_p.base_vectors()
+    >>> dx, dy = R2_r.base_oneforms()
+
+    >>> LieDerivative(e_x, fy)
+    0
+    >>> LieDerivative(e_x, fx)
+    1
+    >>> LieDerivative(e_x, e_x)
+    0
+
+    The Lie derivative of a tensor field by another tensor field is equal to
+    their commutator:
+
+    >>> LieDerivative(e_x, e_rho)
+    Commutator(e_x, e_rho)
+    >>> LieDerivative(e_x + e_y, fx)
+    1
+
+    >>> tp = TensorProduct(dx, dy)
+    >>> LieDerivative(e_x, tp)
+    LieDerivative(e_x, TensorProduct(dx, dy))
+    >>> LieDerivative(e_x, tp)
+    LieDerivative(e_x, TensorProduct(dx, dy))
+
+    """
+    def __new__(cls, v_field, expr):
+        expr_form_ord = covariant_order(expr)
+        if contravariant_order(v_field) != 1 or covariant_order(v_field):
+            raise ValueError('Lie derivatives are defined only with respect to'
+                             ' vector fields. The supplied argument was not a '
+                             'vector field.')
+        if expr_form_ord > 0:
+            obj = super().__new__(cls, v_field, expr)
+            # deprecated assignments
+            obj._v_field = v_field
+            obj._expr = expr
+            return obj
+        if expr.atoms(BaseVectorField):
+            return Commutator(v_field, expr)
+        else:
+            return v_field.rcall(expr)
+
+    @property
+    def v_field(self):
+        return self.args[0]
+
+    @property
+    def expr(self):
+        return self.args[1]
+
+    def __call__(self, *args):
+        v = self.v_field
+        expr = self.expr
+        lead_term = v(expr(*args))
+        rest = Add(*[Mul(*args[:i] + (Commutator(v, args[i]),) + args[i + 1:])
+                     for i in range(len(args))])
+        return lead_term - rest
+
+
+class BaseCovarDerivativeOp(Expr):
+    """Covariant derivative operator with respect to a base vector.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2_r
+    >>> from sympy.diffgeom import BaseCovarDerivativeOp
+    >>> from sympy.diffgeom import metric_to_Christoffel_2nd, TensorProduct
+
+    >>> TP = TensorProduct
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> dx, dy = R2_r.base_oneforms()
+
+    >>> ch = metric_to_Christoffel_2nd(TP(dx, dx) + TP(dy, dy))
+    >>> ch
+    [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
+    >>> cvd = BaseCovarDerivativeOp(R2_r, 0, ch)
+    >>> cvd(fx)
+    1
+    >>> cvd(fx*e_x)
+    e_x
+    """
+
+    def __new__(cls, coord_sys, index, christoffel):
+        index = _sympify(index)
+        christoffel = ImmutableDenseNDimArray(christoffel)
+        obj = super().__new__(cls, coord_sys, index, christoffel)
+        # deprecated assignments
+        obj._coord_sys = coord_sys
+        obj._index = index
+        obj._christoffel = christoffel
+        return obj
+
+    @property
+    def coord_sys(self):
+        return self.args[0]
+
+    @property
+    def index(self):
+        return self.args[1]
+
+    @property
+    def christoffel(self):
+        return self.args[2]
+
+    def __call__(self, field):
+        """Apply on a scalar field.
+
+        The action of a vector field on a scalar field is a directional
+        differentiation.
+        If the argument is not a scalar field the behaviour is undefined.
+        """
+        if covariant_order(field) != 0:
+            raise NotImplementedError()
+
+        field = vectors_in_basis(field, self._coord_sys)
+
+        wrt_vector = self._coord_sys.base_vector(self._index)
+        wrt_scalar = self._coord_sys.coord_function(self._index)
+        vectors = list(field.atoms(BaseVectorField))
+
+        # First step: replace all vectors with something susceptible to
+        # derivation and do the derivation
+        # TODO: you need a real dummy function for the next line
+        d_funcs = [Function('_#_%s' % i)(wrt_scalar) for i,
+                   b in enumerate(vectors)]
+        d_result = field.subs(list(zip(vectors, d_funcs)))
+        d_result = wrt_vector(d_result)
+
+        # Second step: backsubstitute the vectors in
+        d_result = d_result.subs(list(zip(d_funcs, vectors)))
+
+        # Third step: evaluate the derivatives of the vectors
+        derivs = []
+        for v in vectors:
+            d = Add(*[(self._christoffel[k, wrt_vector._index, v._index]
+                       *v._coord_sys.base_vector(k))
+                      for k in range(v._coord_sys.dim)])
+            derivs.append(d)
+        to_subs = [wrt_vector(d) for d in d_funcs]
+        # XXX: This substitution can fail when there are Dummy symbols and the
+        # cache is disabled: https://github.com/sympy/sympy/issues/17794
+        result = d_result.subs(list(zip(to_subs, derivs)))
+
+        # Remove the dummies
+        result = result.subs(list(zip(d_funcs, vectors)))
+        return result.doit()
+
+
+class CovarDerivativeOp(Expr):
+    """Covariant derivative operator.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2_r
+    >>> from sympy.diffgeom import CovarDerivativeOp
+    >>> from sympy.diffgeom import metric_to_Christoffel_2nd, TensorProduct
+    >>> TP = TensorProduct
+    >>> fx, fy = R2_r.base_scalars()
+    >>> e_x, e_y = R2_r.base_vectors()
+    >>> dx, dy = R2_r.base_oneforms()
+    >>> ch = metric_to_Christoffel_2nd(TP(dx, dx) + TP(dy, dy))
+
+    >>> ch
+    [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
+    >>> cvd = CovarDerivativeOp(fx*e_x, ch)
+    >>> cvd(fx)
+    x
+    >>> cvd(fx*e_x)
+    x*e_x
+
+    """
+
+    def __new__(cls, wrt, christoffel):
+        if len({v._coord_sys for v in wrt.atoms(BaseVectorField)}) > 1:
+            raise NotImplementedError()
+        if contravariant_order(wrt) != 1 or covariant_order(wrt):
+            raise ValueError('Covariant derivatives are defined only with '
+                             'respect to vector fields. The supplied argument '
+                             'was not a vector field.')
+        christoffel = ImmutableDenseNDimArray(christoffel)
+        obj = super().__new__(cls, wrt, christoffel)
+        # deprecated assignments
+        obj._wrt = wrt
+        obj._christoffel = christoffel
+        return obj
+
+    @property
+    def wrt(self):
+        return self.args[0]
+
+    @property
+    def christoffel(self):
+        return self.args[1]
+
+    def __call__(self, field):
+        vectors = list(self._wrt.atoms(BaseVectorField))
+        base_ops = [BaseCovarDerivativeOp(v._coord_sys, v._index, self._christoffel)
+                    for v in vectors]
+        return self._wrt.subs(list(zip(vectors, base_ops))).rcall(field)
+
+
+###############################################################################
+# Integral curves on vector fields
+###############################################################################
+def intcurve_series(vector_field, param, start_point, n=6, coord_sys=None, coeffs=False):
+    r"""Return the series expansion for an integral curve of the field.
+
+    Explanation
+    ===========
+
+    Integral curve is a function `\gamma` taking a parameter in `R` to a point
+    in the manifold. It verifies the equation:
+
+    `V(f)\big(\gamma(t)\big) = \frac{d}{dt}f\big(\gamma(t)\big)`
+
+    where the given ``vector_field`` is denoted as `V`. This holds for any
+    value `t` for the parameter and any scalar field `f`.
+
+    This equation can also be decomposed of a basis of coordinate functions
+    `V(f_i)\big(\gamma(t)\big) = \frac{d}{dt}f_i\big(\gamma(t)\big) \quad \forall i`
+
+    This function returns a series expansion of `\gamma(t)` in terms of the
+    coordinate system ``coord_sys``. The equations and expansions are necessarily
+    done in coordinate-system-dependent way as there is no other way to
+    represent movement between points on the manifold (i.e. there is no such
+    thing as a difference of points for a general manifold).
+
+    Parameters
+    ==========
+    vector_field
+        the vector field for which an integral curve will be given
+
+    param
+        the argument of the function `\gamma` from R to the curve
+
+    start_point
+        the point which corresponds to `\gamma(0)`
+
+    n
+        the order to which to expand
+
+    coord_sys
+        the coordinate system in which to expand
+        coeffs (default False) - if True return a list of elements of the expansion
+
+    Examples
+    ========
+
+    Use the predefined R2 manifold:
+
+    >>> from sympy.abc import t, x, y
+    >>> from sympy.diffgeom.rn import R2_p, R2_r
+    >>> from sympy.diffgeom import intcurve_series
+
+    Specify a starting point and a vector field:
+
+    >>> start_point = R2_r.point([x, y])
+    >>> vector_field = R2_r.e_x
+
+    Calculate the series:
+
+    >>> intcurve_series(vector_field, t, start_point, n=3)
+    Matrix([
+    [t + x],
+    [    y]])
+
+    Or get the elements of the expansion in a list:
+
+    >>> series = intcurve_series(vector_field, t, start_point, n=3, coeffs=True)
+    >>> series[0]
+    Matrix([
+    [x],
+    [y]])
+    >>> series[1]
+    Matrix([
+    [t],
+    [0]])
+    >>> series[2]
+    Matrix([
+    [0],
+    [0]])
+
+    The series in the polar coordinate system:
+
+    >>> series = intcurve_series(vector_field, t, start_point,
+    ...             n=3, coord_sys=R2_p, coeffs=True)
+    >>> series[0]
+    Matrix([
+    [sqrt(x**2 + y**2)],
+    [      atan2(y, x)]])
+    >>> series[1]
+    Matrix([
+    [t*x/sqrt(x**2 + y**2)],
+    [   -t*y/(x**2 + y**2)]])
+    >>> series[2]
+    Matrix([
+    [t**2*(-x**2/(x**2 + y**2)**(3/2) + 1/sqrt(x**2 + y**2))/2],
+    [                                t**2*x*y/(x**2 + y**2)**2]])
+
+    See Also
+    ========
+
+    intcurve_diffequ
+
+    """
+    if contravariant_order(vector_field) != 1 or covariant_order(vector_field):
+        raise ValueError('The supplied field was not a vector field.')
+
+    def iter_vfield(scalar_field, i):
+        """Return ``vector_field`` called `i` times on ``scalar_field``."""
+        return reduce(lambda s, v: v.rcall(s), [vector_field, ]*i, scalar_field)
+
+    def taylor_terms_per_coord(coord_function):
+        """Return the series for one of the coordinates."""
+        return [param**i*iter_vfield(coord_function, i).rcall(start_point)/factorial(i)
+                for i in range(n)]
+    coord_sys = coord_sys if coord_sys else start_point._coord_sys
+    coord_functions = coord_sys.coord_functions()
+    taylor_terms = [taylor_terms_per_coord(f) for f in coord_functions]
+    if coeffs:
+        return [Matrix(t) for t in zip(*taylor_terms)]
+    else:
+        return Matrix([sum(c) for c in taylor_terms])
+
+
+def intcurve_diffequ(vector_field, param, start_point, coord_sys=None):
+    r"""Return the differential equation for an integral curve of the field.
+
+    Explanation
+    ===========
+
+    Integral curve is a function `\gamma` taking a parameter in `R` to a point
+    in the manifold. It verifies the equation:
+
+    `V(f)\big(\gamma(t)\big) = \frac{d}{dt}f\big(\gamma(t)\big)`
+
+    where the given ``vector_field`` is denoted as `V`. This holds for any
+    value `t` for the parameter and any scalar field `f`.
+
+    This function returns the differential equation of `\gamma(t)` in terms of the
+    coordinate system ``coord_sys``. The equations and expansions are necessarily
+    done in coordinate-system-dependent way as there is no other way to
+    represent movement between points on the manifold (i.e. there is no such
+    thing as a difference of points for a general manifold).
+
+    Parameters
+    ==========
+
+    vector_field
+        the vector field for which an integral curve will be given
+
+    param
+        the argument of the function `\gamma` from R to the curve
+
+    start_point
+        the point which corresponds to `\gamma(0)`
+
+    coord_sys
+        the coordinate system in which to give the equations
+
+    Returns
+    =======
+
+    a tuple of (equations, initial conditions)
+
+    Examples
+    ========
+
+    Use the predefined R2 manifold:
+
+    >>> from sympy.abc import t
+    >>> from sympy.diffgeom.rn import R2, R2_p, R2_r
+    >>> from sympy.diffgeom import intcurve_diffequ
+
+    Specify a starting point and a vector field:
+
+    >>> start_point = R2_r.point([0, 1])
+    >>> vector_field = -R2.y*R2.e_x + R2.x*R2.e_y
+
+    Get the equation:
+
+    >>> equations, init_cond = intcurve_diffequ(vector_field, t, start_point)
+    >>> equations
+    [f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]
+    >>> init_cond
+    [f_0(0), f_1(0) - 1]
+
+    The series in the polar coordinate system:
+
+    >>> equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p)
+    >>> equations
+    [Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]
+    >>> init_cond
+    [f_0(0) - 1, f_1(0) - pi/2]
+
+    See Also
+    ========
+
+    intcurve_series
+
+    """
+    if contravariant_order(vector_field) != 1 or covariant_order(vector_field):
+        raise ValueError('The supplied field was not a vector field.')
+    coord_sys = coord_sys if coord_sys else start_point._coord_sys
+    gammas = [Function('f_%d' % i)(param) for i in range(
+        start_point._coord_sys.dim)]
+    arbitrary_p = Point(coord_sys, gammas)
+    coord_functions = coord_sys.coord_functions()
+    equations = [simplify(diff(cf.rcall(arbitrary_p), param) - vector_field.rcall(cf).rcall(arbitrary_p))
+                 for cf in coord_functions]
+    init_cond = [simplify(cf.rcall(arbitrary_p).subs(param, 0) - cf.rcall(start_point))
+                 for cf in coord_functions]
+    return equations, init_cond
+
+
+###############################################################################
+# Helpers
+###############################################################################
+def dummyfy(args, exprs):
+    # TODO Is this a good idea?
+    d_args = Matrix([s.as_dummy() for s in args])
+    reps = dict(zip(args, d_args))
+    d_exprs = Matrix([_sympify(expr).subs(reps) for expr in exprs])
+    return d_args, d_exprs
+
+###############################################################################
+# Helpers
+###############################################################################
+def contravariant_order(expr, _strict=False):
+    """Return the contravariant order of an expression.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom import contravariant_order
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.abc import a
+
+    >>> contravariant_order(a)
+    0
+    >>> contravariant_order(a*R2.x + 2)
+    0
+    >>> contravariant_order(a*R2.x*R2.e_y + R2.e_x)
+    1
+
+    """
+    # TODO move some of this to class methods.
+    # TODO rewrite using the .as_blah_blah methods
+    if isinstance(expr, Add):
+        orders = [contravariant_order(e) for e in expr.args]
+        if len(set(orders)) != 1:
+            raise ValueError('Misformed expression containing contravariant fields of varying order.')
+        return orders[0]
+    elif isinstance(expr, Mul):
+        orders = [contravariant_order(e) for e in expr.args]
+        not_zero = [o for o in orders if o != 0]
+        if len(not_zero) > 1:
+            raise ValueError('Misformed expression containing multiplication between vectors.')
+        return 0 if not not_zero else not_zero[0]
+    elif isinstance(expr, Pow):
+        if covariant_order(expr.base) or covariant_order(expr.exp):
+            raise ValueError(
+                'Misformed expression containing a power of a vector.')
+        return 0
+    elif isinstance(expr, BaseVectorField):
+        return 1
+    elif isinstance(expr, TensorProduct):
+        return sum(contravariant_order(a) for a in expr.args)
+    elif not _strict or expr.atoms(BaseScalarField):
+        return 0
+    else:  # If it does not contain anything related to the diffgeom module and it is _strict
+        return -1
+
+
+def covariant_order(expr, _strict=False):
+    """Return the covariant order of an expression.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom import covariant_order
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.abc import a
+
+    >>> covariant_order(a)
+    0
+    >>> covariant_order(a*R2.x + 2)
+    0
+    >>> covariant_order(a*R2.x*R2.dy + R2.dx)
+    1
+
+    """
+    # TODO move some of this to class methods.
+    # TODO rewrite using the .as_blah_blah methods
+    if isinstance(expr, Add):
+        orders = [covariant_order(e) for e in expr.args]
+        if len(set(orders)) != 1:
+            raise ValueError('Misformed expression containing form fields of varying order.')
+        return orders[0]
+    elif isinstance(expr, Mul):
+        orders = [covariant_order(e) for e in expr.args]
+        not_zero = [o for o in orders if o != 0]
+        if len(not_zero) > 1:
+            raise ValueError('Misformed expression containing multiplication between forms.')
+        return 0 if not not_zero else not_zero[0]
+    elif isinstance(expr, Pow):
+        if covariant_order(expr.base) or covariant_order(expr.exp):
+            raise ValueError(
+                'Misformed expression containing a power of a form.')
+        return 0
+    elif isinstance(expr, Differential):
+        return covariant_order(*expr.args) + 1
+    elif isinstance(expr, TensorProduct):
+        return sum(covariant_order(a) for a in expr.args)
+    elif not _strict or expr.atoms(BaseScalarField):
+        return 0
+    else:  # If it does not contain anything related to the diffgeom module and it is _strict
+        return -1
+
+
+###############################################################################
+# Coordinate transformation functions
+###############################################################################
+def vectors_in_basis(expr, to_sys):
+    """Transform all base vectors in base vectors of a specified coord basis.
+    While the new base vectors are in the new coordinate system basis, any
+    coefficients are kept in the old system.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom import vectors_in_basis
+    >>> from sympy.diffgeom.rn import R2_r, R2_p
+
+    >>> vectors_in_basis(R2_r.e_x, R2_p)
+    -y*e_theta/(x**2 + y**2) + x*e_rho/sqrt(x**2 + y**2)
+    >>> vectors_in_basis(R2_p.e_r, R2_r)
+    sin(theta)*e_y + cos(theta)*e_x
+
+    """
+    vectors = list(expr.atoms(BaseVectorField))
+    new_vectors = []
+    for v in vectors:
+        cs = v._coord_sys
+        jac = cs.jacobian(to_sys, cs.coord_functions())
+        new = (jac.T*Matrix(to_sys.base_vectors()))[v._index]
+        new_vectors.append(new)
+    return expr.subs(list(zip(vectors, new_vectors)))
+
+
+###############################################################################
+# Coordinate-dependent functions
+###############################################################################
+def twoform_to_matrix(expr):
+    """Return the matrix representing the twoform.
+
+    For the twoform `w` return the matrix `M` such that `M[i,j]=w(e_i, e_j)`,
+    where `e_i` is the i-th base vector field for the coordinate system in
+    which the expression of `w` is given.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.diffgeom import twoform_to_matrix, TensorProduct
+    >>> TP = TensorProduct
+
+    >>> twoform_to_matrix(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    >>> twoform_to_matrix(R2.x*TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    Matrix([
+    [x, 0],
+    [0, 1]])
+    >>> twoform_to_matrix(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy) - TP(R2.dx, R2.dy)/2)
+    Matrix([
+    [   1, 0],
+    [-1/2, 1]])
+
+    """
+    if covariant_order(expr) != 2 or contravariant_order(expr):
+        raise ValueError('The input expression is not a two-form.')
+    coord_sys = _find_coords(expr)
+    if len(coord_sys) != 1:
+        raise ValueError('The input expression concerns more than one '
+                         'coordinate systems, hence there is no unambiguous '
+                         'way to choose a coordinate system for the matrix.')
+    coord_sys = coord_sys.pop()
+    vectors = coord_sys.base_vectors()
+    expr = expr.expand()
+    matrix_content = [[expr.rcall(v1, v2) for v1 in vectors]
+                      for v2 in vectors]
+    return Matrix(matrix_content)
+
+
+def metric_to_Christoffel_1st(expr):
+    """Return the nested list of Christoffel symbols for the given metric.
+    This returns the Christoffel symbol of first kind that represents the
+    Levi-Civita connection for the given metric.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.diffgeom import metric_to_Christoffel_1st, TensorProduct
+    >>> TP = TensorProduct
+
+    >>> metric_to_Christoffel_1st(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
+    >>> metric_to_Christoffel_1st(R2.x*TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    [[[1/2, 0], [0, 0]], [[0, 0], [0, 0]]]
+
+    """
+    matrix = twoform_to_matrix(expr)
+    if not matrix.is_symmetric():
+        raise ValueError(
+            'The two-form representing the metric is not symmetric.')
+    coord_sys = _find_coords(expr).pop()
+    deriv_matrices = [matrix.applyfunc(d) for d in coord_sys.base_vectors()]
+    indices = list(range(coord_sys.dim))
+    christoffel = [[[(deriv_matrices[k][i, j] + deriv_matrices[j][i, k] - deriv_matrices[i][j, k])/2
+                     for k in indices]
+                    for j in indices]
+                   for i in indices]
+    return ImmutableDenseNDimArray(christoffel)
+
+
+def metric_to_Christoffel_2nd(expr):
+    """Return the nested list of Christoffel symbols for the given metric.
+    This returns the Christoffel symbol of second kind that represents the
+    Levi-Civita connection for the given metric.
+
+    Examples
+    ========
+
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.diffgeom import metric_to_Christoffel_2nd, TensorProduct
+    >>> TP = TensorProduct
+
+    >>> metric_to_Christoffel_2nd(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
+    >>> metric_to_Christoffel_2nd(R2.x*TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    [[[1/(2*x), 0], [0, 0]], [[0, 0], [0, 0]]]
+
+    """
+    ch_1st = metric_to_Christoffel_1st(expr)
+    coord_sys = _find_coords(expr).pop()
+    indices = list(range(coord_sys.dim))
+    # XXX workaround, inverting a matrix does not work if it contains non
+    # symbols
+    #matrix = twoform_to_matrix(expr).inv()
+    matrix = twoform_to_matrix(expr)
+    s_fields = set()
+    for e in matrix:
+        s_fields.update(e.atoms(BaseScalarField))
+    s_fields = list(s_fields)
+    dums = coord_sys.symbols
+    matrix = matrix.subs(list(zip(s_fields, dums))).inv().subs(list(zip(dums, s_fields)))
+    # XXX end of workaround
+    christoffel = [[[Add(*[matrix[i, l]*ch_1st[l, j, k] for l in indices])
+                     for k in indices]
+                    for j in indices]
+                   for i in indices]
+    return ImmutableDenseNDimArray(christoffel)
+
+
+def metric_to_Riemann_components(expr):
+    """Return the components of the Riemann tensor expressed in a given basis.
+
+    Given a metric it calculates the components of the Riemann tensor in the
+    canonical basis of the coordinate system in which the metric expression is
+    given.
+
+    Examples
+    ========
+
+    >>> from sympy import exp
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.diffgeom import metric_to_Riemann_components, TensorProduct
+    >>> TP = TensorProduct
+
+    >>> metric_to_Riemann_components(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    [[[[0, 0], [0, 0]], [[0, 0], [0, 0]]], [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]]
+    >>> non_trivial_metric = exp(2*R2.r)*TP(R2.dr, R2.dr) + \
+        R2.r**2*TP(R2.dtheta, R2.dtheta)
+    >>> non_trivial_metric
+    exp(2*rho)*TensorProduct(drho, drho) + rho**2*TensorProduct(dtheta, dtheta)
+    >>> riemann = metric_to_Riemann_components(non_trivial_metric)
+    >>> riemann[0, :, :, :]
+    [[[0, 0], [0, 0]], [[0, exp(-2*rho)*rho], [-exp(-2*rho)*rho, 0]]]
+    >>> riemann[1, :, :, :]
+    [[[0, -1/rho], [1/rho, 0]], [[0, 0], [0, 0]]]
+
+    """
+    ch_2nd = metric_to_Christoffel_2nd(expr)
+    coord_sys = _find_coords(expr).pop()
+    indices = list(range(coord_sys.dim))
+    deriv_ch = [[[[d(ch_2nd[i, j, k])
+                   for d in coord_sys.base_vectors()]
+                  for k in indices]
+                 for j in indices]
+                for i in indices]
+    riemann_a = [[[[deriv_ch[rho][sig][nu][mu] - deriv_ch[rho][sig][mu][nu]
+                    for nu in indices]
+                   for mu in indices]
+                  for sig in indices]
+                     for rho in indices]
+    riemann_b = [[[[Add(*[ch_2nd[rho, l, mu]*ch_2nd[l, sig, nu] - ch_2nd[rho, l, nu]*ch_2nd[l, sig, mu] for l in indices])
+                    for nu in indices]
+                   for mu in indices]
+                  for sig in indices]
+                 for rho in indices]
+    riemann = [[[[riemann_a[rho][sig][mu][nu] + riemann_b[rho][sig][mu][nu]
+                  for nu in indices]
+                     for mu in indices]
+                for sig in indices]
+               for rho in indices]
+    return ImmutableDenseNDimArray(riemann)
+
+
+def metric_to_Ricci_components(expr):
+
+    """Return the components of the Ricci tensor expressed in a given basis.
+
+    Given a metric it calculates the components of the Ricci tensor in the
+    canonical basis of the coordinate system in which the metric expression is
+    given.
+
+    Examples
+    ========
+
+    >>> from sympy import exp
+    >>> from sympy.diffgeom.rn import R2
+    >>> from sympy.diffgeom import metric_to_Ricci_components, TensorProduct
+    >>> TP = TensorProduct
+
+    >>> metric_to_Ricci_components(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    [[0, 0], [0, 0]]
+    >>> non_trivial_metric = exp(2*R2.r)*TP(R2.dr, R2.dr) + \
+                             R2.r**2*TP(R2.dtheta, R2.dtheta)
+    >>> non_trivial_metric
+    exp(2*rho)*TensorProduct(drho, drho) + rho**2*TensorProduct(dtheta, dtheta)
+    >>> metric_to_Ricci_components(non_trivial_metric)
+    [[1/rho, 0], [0, exp(-2*rho)*rho]]
+
+    """
+    riemann = metric_to_Riemann_components(expr)
+    coord_sys = _find_coords(expr).pop()
+    indices = list(range(coord_sys.dim))
+    ricci = [[Add(*[riemann[k, i, k, j] for k in indices])
+              for j in indices]
+             for i in indices]
+    return ImmutableDenseNDimArray(ricci)
+
+###############################################################################
+# Classes for deprecation
+###############################################################################
+
+class _deprecated_container:
+    # This class gives deprecation warning.
+    # When deprecated features are completely deleted, this should be removed as well.
+    # See https://github.com/sympy/sympy/pull/19368
+    def __init__(self, message, data):
+        super().__init__(data)
+        self.message = message
+
+    def warn(self):
+        sympy_deprecation_warning(
+            self.message,
+            deprecated_since_version="1.7",
+            active_deprecations_target="deprecated-diffgeom-mutable",
+            stacklevel=4
+        )
+
+    def __iter__(self):
+        self.warn()
+        return super().__iter__()
+
+    def __getitem__(self, key):
+        self.warn()
+        return super().__getitem__(key)
+
+    def __contains__(self, key):
+        self.warn()
+        return super().__contains__(key)
+
+
+class _deprecated_list(_deprecated_container, list):
+    pass
+
+
+class _deprecated_dict(_deprecated_container, dict):
+    pass
+
+
+# Import at end to avoid cyclic imports
+from sympy.simplify.simplify import simplify
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/rn.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/rn.py
new file mode 100644
index 0000000000000000000000000000000000000000..897c7e82bc804d260612f79c820af92632f3b281
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/rn.py
@@ -0,0 +1,143 @@
+"""Predefined R^n manifolds together with common coord. systems.
+
+Coordinate systems are predefined as well as the transformation laws between
+them.
+
+Coordinate functions can be accessed as attributes of the manifold (eg `R2.x`),
+as attributes of the coordinate systems (eg `R2_r.x` and `R2_p.theta`), or by
+using the usual `coord_sys.coord_function(index, name)` interface.
+"""
+
+from typing import Any
+import warnings
+
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, atan2, cos, sin)
+from .diffgeom import Manifold, Patch, CoordSystem
+
+__all__ = [
+    'R2', 'R2_origin', 'relations_2d', 'R2_r', 'R2_p',
+    'R3', 'R3_origin', 'relations_3d', 'R3_r', 'R3_c', 'R3_s'
+]
+
+###############################################################################
+# R2
+###############################################################################
+R2: Any = Manifold('R^2', 2)
+
+R2_origin: Any = Patch('origin', R2)
+
+x, y = symbols('x y', real=True)
+r, theta = symbols('rho theta', nonnegative=True)
+
+relations_2d = {
+    ('rectangular', 'polar'): [(x, y), (sqrt(x**2 + y**2), atan2(y, x))],
+    ('polar', 'rectangular'): [(r, theta), (r*cos(theta), r*sin(theta))],
+}
+
+R2_r: Any = CoordSystem('rectangular', R2_origin, (x, y), relations_2d)
+R2_p: Any = CoordSystem('polar', R2_origin, (r, theta), relations_2d)
+
+# support deprecated feature
+with warnings.catch_warnings():
+    warnings.simplefilter("ignore")
+    x, y, r, theta = symbols('x y r theta', cls=Dummy)
+    R2_r.connect_to(R2_p, [x, y],
+                        [sqrt(x**2 + y**2), atan2(y, x)],
+                    inverse=False, fill_in_gaps=False)
+    R2_p.connect_to(R2_r, [r, theta],
+                        [r*cos(theta), r*sin(theta)],
+                    inverse=False, fill_in_gaps=False)
+
+# Defining the basis coordinate functions and adding shortcuts for them to the
+# manifold and the patch.
+R2.x, R2.y = R2_origin.x, R2_origin.y = R2_r.x, R2_r.y = R2_r.coord_functions()
+R2.r, R2.theta = R2_origin.r, R2_origin.theta = R2_p.r, R2_p.theta = R2_p.coord_functions()
+
+# Defining the basis vector fields and adding shortcuts for them to the
+# manifold and the patch.
+R2.e_x, R2.e_y = R2_origin.e_x, R2_origin.e_y = R2_r.e_x, R2_r.e_y = R2_r.base_vectors()
+R2.e_r, R2.e_theta = R2_origin.e_r, R2_origin.e_theta = R2_p.e_r, R2_p.e_theta = R2_p.base_vectors()
+
+# Defining the basis oneform fields and adding shortcuts for them to the
+# manifold and the patch.
+R2.dx, R2.dy = R2_origin.dx, R2_origin.dy = R2_r.dx, R2_r.dy = R2_r.base_oneforms()
+R2.dr, R2.dtheta = R2_origin.dr, R2_origin.dtheta = R2_p.dr, R2_p.dtheta = R2_p.base_oneforms()
+
+###############################################################################
+# R3
+###############################################################################
+R3: Any = Manifold('R^3', 3)
+
+R3_origin: Any = Patch('origin', R3)
+
+x, y, z = symbols('x y z', real=True)
+rho, psi, r, theta, phi = symbols('rho psi r theta phi', nonnegative=True)
+
+relations_3d = {
+    ('rectangular', 'cylindrical'): [(x, y, z),
+                                     (sqrt(x**2 + y**2), atan2(y, x), z)],
+    ('cylindrical', 'rectangular'): [(rho, psi, z),
+                                     (rho*cos(psi), rho*sin(psi), z)],
+    ('rectangular', 'spherical'): [(x, y, z),
+                                   (sqrt(x**2 + y**2 + z**2),
+                                    acos(z/sqrt(x**2 + y**2 + z**2)),
+                                    atan2(y, x))],
+    ('spherical', 'rectangular'): [(r, theta, phi),
+                                   (r*sin(theta)*cos(phi),
+                                    r*sin(theta)*sin(phi),
+                                    r*cos(theta))],
+    ('cylindrical', 'spherical'): [(rho, psi, z),
+                                   (sqrt(rho**2 + z**2),
+                                    acos(z/sqrt(rho**2 + z**2)),
+                                    psi)],
+    ('spherical', 'cylindrical'): [(r, theta, phi),
+                                   (r*sin(theta), phi, r*cos(theta))],
+}
+
+R3_r: Any = CoordSystem('rectangular', R3_origin, (x, y, z), relations_3d)
+R3_c: Any = CoordSystem('cylindrical', R3_origin, (rho, psi, z), relations_3d)
+R3_s: Any = CoordSystem('spherical', R3_origin, (r, theta, phi), relations_3d)
+
+# support deprecated feature
+with warnings.catch_warnings():
+    warnings.simplefilter("ignore")
+    x, y, z, rho, psi, r, theta, phi = symbols('x y z rho psi r theta phi', cls=Dummy)
+    R3_r.connect_to(R3_c, [x, y, z],
+                        [sqrt(x**2 + y**2), atan2(y, x), z],
+                    inverse=False, fill_in_gaps=False)
+    R3_c.connect_to(R3_r, [rho, psi, z],
+                        [rho*cos(psi), rho*sin(psi), z],
+                    inverse=False, fill_in_gaps=False)
+    ## rectangular <-> spherical
+    R3_r.connect_to(R3_s, [x, y, z],
+                        [sqrt(x**2 + y**2 + z**2), acos(z/
+                                sqrt(x**2 + y**2 + z**2)), atan2(y, x)],
+                    inverse=False, fill_in_gaps=False)
+    R3_s.connect_to(R3_r, [r, theta, phi],
+                        [r*sin(theta)*cos(phi), r*sin(
+                            theta)*sin(phi), r*cos(theta)],
+                    inverse=False, fill_in_gaps=False)
+    ## cylindrical <-> spherical
+    R3_c.connect_to(R3_s, [rho, psi, z],
+                        [sqrt(rho**2 + z**2), acos(z/sqrt(rho**2 + z**2)), psi],
+                    inverse=False, fill_in_gaps=False)
+    R3_s.connect_to(R3_c, [r, theta, phi],
+                        [r*sin(theta), phi, r*cos(theta)],
+                    inverse=False, fill_in_gaps=False)
+
+# Defining the basis coordinate functions.
+R3_r.x, R3_r.y, R3_r.z = R3_r.coord_functions()
+R3_c.rho, R3_c.psi, R3_c.z = R3_c.coord_functions()
+R3_s.r, R3_s.theta, R3_s.phi = R3_s.coord_functions()
+
+# Defining the basis vector fields.
+R3_r.e_x, R3_r.e_y, R3_r.e_z = R3_r.base_vectors()
+R3_c.e_rho, R3_c.e_psi, R3_c.e_z = R3_c.base_vectors()
+R3_s.e_r, R3_s.e_theta, R3_s.e_phi = R3_s.base_vectors()
+
+# Defining the basis oneform fields.
+R3_r.dx, R3_r.dy, R3_r.dz = R3_r.base_oneforms()
+R3_c.drho, R3_c.dpsi, R3_c.dz = R3_c.base_oneforms()
+R3_s.dr, R3_s.dtheta, R3_s.dphi = R3_s.base_oneforms()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_class_structure.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_class_structure.py
new file mode 100644
index 0000000000000000000000000000000000000000..c649fd9fcb9acdf1f410a021966c6e0fee62cc2b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_class_structure.py
@@ -0,0 +1,33 @@
+from sympy.diffgeom import Manifold, Patch, CoordSystem, Point
+from sympy.core.function import Function
+from sympy.core.symbol import symbols
+from sympy.testing.pytest import warns_deprecated_sympy
+
+m = Manifold('m', 2)
+p = Patch('p', m)
+a, b = symbols('a b')
+cs = CoordSystem('cs', p, [a, b])
+x, y = symbols('x y')
+f = Function('f')
+s1, s2 = cs.coord_functions()
+v1, v2 = cs.base_vectors()
+f1, f2 = cs.base_oneforms()
+
+def test_point():
+    point = Point(cs, [x, y])
+    assert point != Point(cs, [2, y])
+    #TODO assert point.subs(x, 2) == Point(cs, [2, y])
+    #TODO assert point.free_symbols == set([x, y])
+
+def test_subs():
+    assert s1.subs(s1, s2) == s2
+    assert v1.subs(v1, v2) == v2
+    assert f1.subs(f1, f2) == f2
+    assert (x*f(s1) + y).subs(s1, s2) == x*f(s2) + y
+    assert (f(s1)*v1).subs(v1, v2) == f(s1)*v2
+    assert (y*f(s1)*f1).subs(f1, f2) == y*f(s1)*f2
+
+def test_deprecated():
+    with warns_deprecated_sympy():
+        cs_wname = CoordSystem('cs', p, ['a', 'b'])
+        assert cs_wname == cs_wname.func(*cs_wname.args)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_diffgeom.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_diffgeom.py
new file mode 100644
index 0000000000000000000000000000000000000000..7c3c9265785896b8f4ffa3a2b41816ca90579758
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_diffgeom.py
@@ -0,0 +1,342 @@
+from sympy.core import Lambda, Symbol, symbols
+from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r, R3_c, R3_s, R2_origin
+from sympy.diffgeom import (Manifold, Patch, CoordSystem, Commutator, Differential, TensorProduct,
+        WedgeProduct, BaseCovarDerivativeOp, CovarDerivativeOp, LieDerivative,
+        covariant_order, contravariant_order, twoform_to_matrix, metric_to_Christoffel_1st,
+        metric_to_Christoffel_2nd, metric_to_Riemann_components,
+        metric_to_Ricci_components, intcurve_diffequ, intcurve_series)
+from sympy.simplify import trigsimp, simplify
+from sympy.functions import sqrt, atan2, sin
+from sympy.matrices import Matrix
+from sympy.testing.pytest import raises, nocache_fail
+from sympy.testing.pytest import warns_deprecated_sympy
+
+TP = TensorProduct
+
+
+def test_coordsys_transform():
+    # test inverse transforms
+    p, q, r, s = symbols('p q r s')
+    rel = {('first', 'second'): [(p, q), (q, -p)]}
+    R2_pq = CoordSystem('first', R2_origin, [p, q], rel)
+    R2_rs = CoordSystem('second', R2_origin, [r, s], rel)
+    r, s = R2_rs.symbols
+    assert R2_rs.transform(R2_pq) == Matrix([[-s], [r]])
+
+    # inverse transform impossible case
+    a, b = symbols('a b', positive=True)
+    rel = {('first', 'second'): [(a,), (-a,)]}
+    R2_a = CoordSystem('first', R2_origin, [a], rel)
+    R2_b = CoordSystem('second', R2_origin, [b], rel)
+    # This transformation is uninvertible because there is no positive a, b satisfying a = -b
+    with raises(NotImplementedError):
+        R2_b.transform(R2_a)
+
+    # inverse transform ambiguous case
+    c, d = symbols('c d')
+    rel = {('first', 'second'): [(c,), (c**2,)]}
+    R2_c = CoordSystem('first', R2_origin, [c], rel)
+    R2_d = CoordSystem('second', R2_origin, [d], rel)
+    # The transform method should throw if it finds multiple inverses for a coordinate transformation.
+    with raises(ValueError):
+        R2_d.transform(R2_c)
+
+    # test indirect transformation
+    a, b, c, d, e, f = symbols('a, b, c, d, e, f')
+    rel = {('C1', 'C2'): [(a, b), (2*a, 3*b)],
+        ('C2', 'C3'): [(c, d), (3*c, 2*d)]}
+    C1 = CoordSystem('C1', R2_origin, (a, b), rel)
+    C2 = CoordSystem('C2', R2_origin, (c, d), rel)
+    C3 = CoordSystem('C3', R2_origin, (e, f), rel)
+    a, b = C1.symbols
+    c, d = C2.symbols
+    e, f = C3.symbols
+    assert C2.transform(C1) == Matrix([c/2, d/3])
+    assert C1.transform(C3) == Matrix([6*a, 6*b])
+    assert C3.transform(C1) == Matrix([e/6, f/6])
+    assert C3.transform(C2) == Matrix([e/3, f/2])
+
+    a, b, c, d, e, f = symbols('a, b, c, d, e, f')
+    rel = {('C1', 'C2'): [(a, b), (2*a, 3*b + 1)],
+        ('C3', 'C2'): [(e, f), (-e - 2, 2*f)]}
+    C1 = CoordSystem('C1', R2_origin, (a, b), rel)
+    C2 = CoordSystem('C2', R2_origin, (c, d), rel)
+    C3 = CoordSystem('C3', R2_origin, (e, f), rel)
+    a, b = C1.symbols
+    c, d = C2.symbols
+    e, f = C3.symbols
+    assert C2.transform(C1) == Matrix([c/2, (d - 1)/3])
+    assert C1.transform(C3) == Matrix([-2*a - 2, (3*b + 1)/2])
+    assert C3.transform(C1) == Matrix([-e/2 - 1, (2*f - 1)/3])
+    assert C3.transform(C2) == Matrix([-e - 2, 2*f])
+
+    # old signature uses Lambda
+    a, b, c, d, e, f = symbols('a, b, c, d, e, f')
+    rel = {('C1', 'C2'): Lambda((a, b), (2*a, 3*b + 1)),
+        ('C3', 'C2'): Lambda((e, f), (-e - 2, 2*f))}
+    C1 = CoordSystem('C1', R2_origin, (a, b), rel)
+    C2 = CoordSystem('C2', R2_origin, (c, d), rel)
+    C3 = CoordSystem('C3', R2_origin, (e, f), rel)
+    a, b = C1.symbols
+    c, d = C2.symbols
+    e, f = C3.symbols
+    assert C2.transform(C1) == Matrix([c/2, (d - 1)/3])
+    assert C1.transform(C3) == Matrix([-2*a - 2, (3*b + 1)/2])
+    assert C3.transform(C1) == Matrix([-e/2 - 1, (2*f - 1)/3])
+    assert C3.transform(C2) == Matrix([-e - 2, 2*f])
+
+
+def test_R2():
+    x0, y0, r0, theta0 = symbols('x0, y0, r0, theta0', real=True)
+    point_r = R2_r.point([x0, y0])
+    point_p = R2_p.point([r0, theta0])
+
+    # r**2 = x**2 + y**2
+    assert (R2.r**2 - R2.x**2 - R2.y**2).rcall(point_r) == 0
+    assert trigsimp( (R2.r**2 - R2.x**2 - R2.y**2).rcall(point_p) ) == 0
+    assert trigsimp(R2.e_r(R2.x**2 + R2.y**2).rcall(point_p).doit()) == 2*r0
+
+    # polar->rect->polar == Id
+    a, b = symbols('a b', positive=True)
+    m = Matrix([[a], [b]])
+
+    #TODO assert m == R2_r.transform(R2_p, R2_p.transform(R2_r, [a, b])).applyfunc(simplify)
+    assert m == R2_p.transform(R2_r, R2_r.transform(R2_p, m)).applyfunc(simplify)
+
+    # deprecated method
+    with warns_deprecated_sympy():
+        assert m == R2_p.coord_tuple_transform_to(
+            R2_r, R2_r.coord_tuple_transform_to(R2_p, m)).applyfunc(simplify)
+
+
+def test_R3():
+    a, b, c = symbols('a b c', positive=True)
+    m = Matrix([[a], [b], [c]])
+
+    assert m == R3_c.transform(R3_r, R3_r.transform(R3_c, m)).applyfunc(simplify)
+    #TODO assert m == R3_r.transform(R3_c, R3_c.transform(R3_r, m)).applyfunc(simplify)
+    assert m == R3_s.transform(
+        R3_r, R3_r.transform(R3_s, m)).applyfunc(simplify)
+    #TODO assert m == R3_r.transform(R3_s, R3_s.transform(R3_r, m)).applyfunc(simplify)
+    assert m == R3_s.transform(
+        R3_c, R3_c.transform(R3_s, m)).applyfunc(simplify)
+    #TODO assert m == R3_c.transform(R3_s, R3_s.transform(R3_c, m)).applyfunc(simplify)
+
+    with warns_deprecated_sympy():
+        assert m == R3_c.coord_tuple_transform_to(
+            R3_r, R3_r.coord_tuple_transform_to(R3_c, m)).applyfunc(simplify)
+        #TODO assert m == R3_r.coord_tuple_transform_to(R3_c, R3_c.coord_tuple_transform_to(R3_r, m)).applyfunc(simplify)
+        assert m == R3_s.coord_tuple_transform_to(
+            R3_r, R3_r.coord_tuple_transform_to(R3_s, m)).applyfunc(simplify)
+        #TODO assert m == R3_r.coord_tuple_transform_to(R3_s, R3_s.coord_tuple_transform_to(R3_r, m)).applyfunc(simplify)
+        assert m == R3_s.coord_tuple_transform_to(
+            R3_c, R3_c.coord_tuple_transform_to(R3_s, m)).applyfunc(simplify)
+        #TODO assert m == R3_c.coord_tuple_transform_to(R3_s, R3_s.coord_tuple_transform_to(R3_c, m)).applyfunc(simplify)
+
+
+def test_CoordinateSymbol():
+    x, y = R2_r.symbols
+    r, theta = R2_p.symbols
+    assert y.rewrite(R2_p) == r*sin(theta)
+
+
+def test_point():
+    x, y = symbols('x, y')
+    p = R2_r.point([x, y])
+    assert p.free_symbols == {x, y}
+    assert p.coords(R2_r) == p.coords() == Matrix([x, y])
+    assert p.coords(R2_p) == Matrix([sqrt(x**2 + y**2), atan2(y, x)])
+
+
+def test_commutator():
+    assert Commutator(R2.e_x, R2.e_y) == 0
+    assert Commutator(R2.x*R2.e_x, R2.x*R2.e_x) == 0
+    assert Commutator(R2.x*R2.e_x, R2.x*R2.e_y) == R2.x*R2.e_y
+    c = Commutator(R2.e_x, R2.e_r)
+    assert c(R2.x) == R2.y*(R2.x**2 + R2.y**2)**(-1)*sin(R2.theta)
+
+
+def test_differential():
+    xdy = R2.x*R2.dy
+    dxdy = Differential(xdy)
+    assert xdy.rcall(None) == xdy
+    assert dxdy(R2.e_x, R2.e_y) == 1
+    assert dxdy(R2.e_x, R2.x*R2.e_y) == R2.x
+    assert Differential(dxdy) == 0
+
+
+def test_products():
+    assert TensorProduct(
+        R2.dx, R2.dy)(R2.e_x, R2.e_y) == R2.dx(R2.e_x)*R2.dy(R2.e_y) == 1
+    assert TensorProduct(R2.dx, R2.dy)(None, R2.e_y) == R2.dx
+    assert TensorProduct(R2.dx, R2.dy)(R2.e_x, None) == R2.dy
+    assert TensorProduct(R2.dx, R2.dy)(R2.e_x) == R2.dy
+    assert TensorProduct(R2.x, R2.dx) == R2.x*R2.dx
+    assert TensorProduct(
+        R2.e_x, R2.e_y)(R2.x, R2.y) == R2.e_x(R2.x) * R2.e_y(R2.y) == 1
+    assert TensorProduct(R2.e_x, R2.e_y)(None, R2.y) == R2.e_x
+    assert TensorProduct(R2.e_x, R2.e_y)(R2.x, None) == R2.e_y
+    assert TensorProduct(R2.e_x, R2.e_y)(R2.x) == R2.e_y
+    assert TensorProduct(R2.x, R2.e_x) == R2.x * R2.e_x
+    assert TensorProduct(
+        R2.dx, R2.e_y)(R2.e_x, R2.y) == R2.dx(R2.e_x) * R2.e_y(R2.y) == 1
+    assert TensorProduct(R2.dx, R2.e_y)(None, R2.y) == R2.dx
+    assert TensorProduct(R2.dx, R2.e_y)(R2.e_x, None) == R2.e_y
+    assert TensorProduct(R2.dx, R2.e_y)(R2.e_x) == R2.e_y
+    assert TensorProduct(R2.x, R2.e_x) == R2.x * R2.e_x
+    assert TensorProduct(
+        R2.e_x, R2.dy)(R2.x, R2.e_y) == R2.e_x(R2.x) * R2.dy(R2.e_y) == 1
+    assert TensorProduct(R2.e_x, R2.dy)(None, R2.e_y) == R2.e_x
+    assert TensorProduct(R2.e_x, R2.dy)(R2.x, None) == R2.dy
+    assert TensorProduct(R2.e_x, R2.dy)(R2.x) == R2.dy
+    assert TensorProduct(R2.e_y,R2.e_x)(R2.x**2 + R2.y**2,R2.x**2 + R2.y**2) == 4*R2.x*R2.y
+
+    assert WedgeProduct(R2.dx, R2.dy)(R2.e_x, R2.e_y) == 1
+    assert WedgeProduct(R2.e_x, R2.e_y)(R2.x, R2.y) == 1
+
+
+def test_lie_derivative():
+    assert LieDerivative(R2.e_x, R2.y) == R2.e_x(R2.y) == 0
+    assert LieDerivative(R2.e_x, R2.x) == R2.e_x(R2.x) == 1
+    assert LieDerivative(R2.e_x, R2.e_x) == Commutator(R2.e_x, R2.e_x) == 0
+    assert LieDerivative(R2.e_x, R2.e_r) == Commutator(R2.e_x, R2.e_r)
+    assert LieDerivative(R2.e_x + R2.e_y, R2.x) == 1
+    assert LieDerivative(
+        R2.e_x, TensorProduct(R2.dx, R2.dy))(R2.e_x, R2.e_y) == 0
+
+
+@nocache_fail
+def test_covar_deriv():
+    ch = metric_to_Christoffel_2nd(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy))
+    cvd = BaseCovarDerivativeOp(R2_r, 0, ch)
+    assert cvd(R2.x) == 1
+    # This line fails if the cache is disabled:
+    assert cvd(R2.x*R2.e_x) == R2.e_x
+    cvd = CovarDerivativeOp(R2.x*R2.e_x, ch)
+    assert cvd(R2.x) == R2.x
+    assert cvd(R2.x*R2.e_x) == R2.x*R2.e_x
+
+
+def test_intcurve_diffequ():
+    t = symbols('t')
+    start_point = R2_r.point([1, 0])
+    vector_field = -R2.y*R2.e_x + R2.x*R2.e_y
+    equations, init_cond = intcurve_diffequ(vector_field, t, start_point)
+    assert str(equations) == '[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]'
+    assert str(init_cond) == '[f_0(0) - 1, f_1(0)]'
+    equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p)
+    assert str(
+        equations) == '[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]'
+    assert str(init_cond) == '[f_0(0) - 1, f_1(0)]'
+
+
+def test_helpers_and_coordinate_dependent():
+    one_form = R2.dr + R2.dx
+    two_form = Differential(R2.x*R2.dr + R2.r*R2.dx)
+    three_form = Differential(
+        R2.y*two_form) + Differential(R2.x*Differential(R2.r*R2.dr))
+    metric = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dy, R2.dy)
+    metric_ambig = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dr, R2.dr)
+    misform_a = TensorProduct(R2.dr, R2.dr) + R2.dr
+    misform_b = R2.dr**4
+    misform_c = R2.dx*R2.dy
+    twoform_not_sym = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dx, R2.dy)
+    twoform_not_TP = WedgeProduct(R2.dx, R2.dy)
+
+    one_vector = R2.e_x + R2.e_y
+    two_vector = TensorProduct(R2.e_x, R2.e_y)
+    three_vector = TensorProduct(R2.e_x, R2.e_y, R2.e_x)
+    two_wp = WedgeProduct(R2.e_x,R2.e_y)
+
+    assert covariant_order(one_form) == 1
+    assert covariant_order(two_form) == 2
+    assert covariant_order(three_form) == 3
+    assert covariant_order(two_form + metric) == 2
+    assert covariant_order(two_form + metric_ambig) == 2
+    assert covariant_order(two_form + twoform_not_sym) == 2
+    assert covariant_order(two_form + twoform_not_TP) == 2
+
+    assert contravariant_order(one_vector) == 1
+    assert contravariant_order(two_vector) == 2
+    assert contravariant_order(three_vector) == 3
+    assert contravariant_order(two_vector + two_wp) == 2
+
+    raises(ValueError, lambda: covariant_order(misform_a))
+    raises(ValueError, lambda: covariant_order(misform_b))
+    raises(ValueError, lambda: covariant_order(misform_c))
+
+    assert twoform_to_matrix(metric) == Matrix([[1, 0], [0, 1]])
+    assert twoform_to_matrix(twoform_not_sym) == Matrix([[1, 0], [1, 0]])
+    assert twoform_to_matrix(twoform_not_TP) == Matrix([[0, -1], [1, 0]])
+
+    raises(ValueError, lambda: twoform_to_matrix(one_form))
+    raises(ValueError, lambda: twoform_to_matrix(three_form))
+    raises(ValueError, lambda: twoform_to_matrix(metric_ambig))
+
+    raises(ValueError, lambda: metric_to_Christoffel_1st(twoform_not_sym))
+    raises(ValueError, lambda: metric_to_Christoffel_2nd(twoform_not_sym))
+    raises(ValueError, lambda: metric_to_Riemann_components(twoform_not_sym))
+    raises(ValueError, lambda: metric_to_Ricci_components(twoform_not_sym))
+
+
+def test_correct_arguments():
+    raises(ValueError, lambda: R2.e_x(R2.e_x))
+    raises(ValueError, lambda: R2.e_x(R2.dx))
+
+    raises(ValueError, lambda: Commutator(R2.e_x, R2.x))
+    raises(ValueError, lambda: Commutator(R2.dx, R2.e_x))
+
+    raises(ValueError, lambda: Differential(Differential(R2.e_x)))
+
+    raises(ValueError, lambda: R2.dx(R2.x))
+
+    raises(ValueError, lambda: LieDerivative(R2.dx, R2.dx))
+    raises(ValueError, lambda: LieDerivative(R2.x, R2.dx))
+
+    raises(ValueError, lambda: CovarDerivativeOp(R2.dx, []))
+    raises(ValueError, lambda: CovarDerivativeOp(R2.x, []))
+
+    a = Symbol('a')
+    raises(ValueError, lambda: intcurve_series(R2.dx, a, R2_r.point([1, 2])))
+    raises(ValueError, lambda: intcurve_series(R2.x, a, R2_r.point([1, 2])))
+
+    raises(ValueError, lambda: intcurve_diffequ(R2.dx, a, R2_r.point([1, 2])))
+    raises(ValueError, lambda: intcurve_diffequ(R2.x, a, R2_r.point([1, 2])))
+
+    raises(ValueError, lambda: contravariant_order(R2.e_x + R2.dx))
+    raises(ValueError, lambda: covariant_order(R2.e_x + R2.dx))
+
+    raises(ValueError, lambda: contravariant_order(R2.e_x*R2.e_y))
+    raises(ValueError, lambda: covariant_order(R2.dx*R2.dy))
+
+def test_simplify():
+    x, y = R2_r.coord_functions()
+    dx, dy = R2_r.base_oneforms()
+    ex, ey = R2_r.base_vectors()
+    assert simplify(x) == x
+    assert simplify(x*y) == x*y
+    assert simplify(dx*dy) == dx*dy
+    assert simplify(ex*ey) == ex*ey
+    assert ((1-x)*dx)/(1-x)**2 == dx/(1-x)
+
+
+def test_issue_17917():
+    X = R2.x*R2.e_x - R2.y*R2.e_y
+    Y = (R2.x**2 + R2.y**2)*R2.e_x - R2.x*R2.y*R2.e_y
+    assert LieDerivative(X, Y).expand() == (
+        R2.x**2*R2.e_x - 3*R2.y**2*R2.e_x - R2.x*R2.y*R2.e_y)
+
+def test_deprecations():
+    m = Manifold('M', 2)
+    p = Patch('P', m)
+    with warns_deprecated_sympy():
+        CoordSystem('Car2d', p, names=['x', 'y'])
+
+    with warns_deprecated_sympy():
+        c = CoordSystem('Car2d', p, ['x', 'y'])
+
+    with warns_deprecated_sympy():
+        list(m.patches)
+
+    with warns_deprecated_sympy():
+        list(c.transforms)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_function_diffgeom_book.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_function_diffgeom_book.py
new file mode 100644
index 0000000000000000000000000000000000000000..44d9623bc34ab73c7d575d9d9fd5b6d84f8e4a94
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_function_diffgeom_book.py
@@ -0,0 +1,145 @@
+from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r
+from sympy.diffgeom import intcurve_series, Differential, WedgeProduct
+from sympy.core import symbols, Function, Derivative
+from sympy.simplify import trigsimp, simplify
+from sympy.functions import sqrt, atan2, sin, cos
+from sympy.matrices import Matrix
+
+# Most of the functionality is covered in the
+# test_functional_diffgeom_ch* tests which are based on the
+# example from the paper of Sussman and Wisdom.
+# If they do not cover something, additional tests are added in other test
+# functions.
+
+# From "Functional Differential Geometry" as of 2011
+# by Sussman and Wisdom.
+
+
+def test_functional_diffgeom_ch2():
+    x0, y0, r0, theta0 = symbols('x0, y0, r0, theta0', real=True)
+    x, y = symbols('x, y', real=True)
+    f = Function('f')
+
+    assert (R2_p.point_to_coords(R2_r.point([x0, y0])) ==
+           Matrix([sqrt(x0**2 + y0**2), atan2(y0, x0)]))
+    assert (R2_r.point_to_coords(R2_p.point([r0, theta0])) ==
+           Matrix([r0*cos(theta0), r0*sin(theta0)]))
+
+    assert R2_p.jacobian(R2_r, [r0, theta0]) == Matrix(
+        [[cos(theta0), -r0*sin(theta0)], [sin(theta0), r0*cos(theta0)]])
+
+    field = f(R2.x, R2.y)
+    p1_in_rect = R2_r.point([x0, y0])
+    p1_in_polar = R2_p.point([sqrt(x0**2 + y0**2), atan2(y0, x0)])
+    assert field.rcall(p1_in_rect) == f(x0, y0)
+    assert field.rcall(p1_in_polar) == f(x0, y0)
+
+    p_r = R2_r.point([x0, y0])
+    p_p = R2_p.point([r0, theta0])
+    assert R2.x(p_r) == x0
+    assert R2.x(p_p) == r0*cos(theta0)
+    assert R2.r(p_p) == r0
+    assert R2.r(p_r) == sqrt(x0**2 + y0**2)
+    assert R2.theta(p_r) == atan2(y0, x0)
+
+    h = R2.x*R2.r**2 + R2.y**3
+    assert h.rcall(p_r) == x0*(x0**2 + y0**2) + y0**3
+    assert h.rcall(p_p) == r0**3*sin(theta0)**3 + r0**3*cos(theta0)
+
+
+def test_functional_diffgeom_ch3():
+    x0, y0 = symbols('x0, y0', real=True)
+    x, y, t = symbols('x, y, t', real=True)
+    f = Function('f')
+    b1 = Function('b1')
+    b2 = Function('b2')
+    p_r = R2_r.point([x0, y0])
+
+    s_field = f(R2.x, R2.y)
+    v_field = b1(R2.x)*R2.e_x + b2(R2.y)*R2.e_y
+    assert v_field.rcall(s_field).rcall(p_r).doit() == b1(
+        x0)*Derivative(f(x0, y0), x0) + b2(y0)*Derivative(f(x0, y0), y0)
+
+    assert R2.e_x(R2.r**2).rcall(p_r) == 2*x0
+    v = R2.e_x + 2*R2.e_y
+    s = R2.r**2 + 3*R2.x
+    assert v.rcall(s).rcall(p_r).doit() == 2*x0 + 4*y0 + 3
+
+    circ = -R2.y*R2.e_x + R2.x*R2.e_y
+    series = intcurve_series(circ, t, R2_r.point([1, 0]), coeffs=True)
+    series_x, series_y = zip(*series)
+    assert all(
+        term == cos(t).taylor_term(i, t) for i, term in enumerate(series_x))
+    assert all(
+        term == sin(t).taylor_term(i, t) for i, term in enumerate(series_y))
+
+
+def test_functional_diffgeom_ch4():
+    x0, y0, theta0 = symbols('x0, y0, theta0', real=True)
+    x, y, r, theta = symbols('x, y, r, theta', real=True)
+    r0 = symbols('r0', positive=True)
+    f = Function('f')
+    b1 = Function('b1')
+    b2 = Function('b2')
+    p_r = R2_r.point([x0, y0])
+    p_p = R2_p.point([r0, theta0])
+
+    f_field = b1(R2.x, R2.y)*R2.dx + b2(R2.x, R2.y)*R2.dy
+    assert f_field.rcall(R2.e_x).rcall(p_r) == b1(x0, y0)
+    assert f_field.rcall(R2.e_y).rcall(p_r) == b2(x0, y0)
+
+    s_field_r = f(R2.x, R2.y)
+    df = Differential(s_field_r)
+    assert df(R2.e_x).rcall(p_r).doit() == Derivative(f(x0, y0), x0)
+    assert df(R2.e_y).rcall(p_r).doit() == Derivative(f(x0, y0), y0)
+
+    s_field_p = f(R2.r, R2.theta)
+    df = Differential(s_field_p)
+    assert trigsimp(df(R2.e_x).rcall(p_p).doit()) == (
+        cos(theta0)*Derivative(f(r0, theta0), r0) -
+        sin(theta0)*Derivative(f(r0, theta0), theta0)/r0)
+    assert trigsimp(df(R2.e_y).rcall(p_p).doit()) == (
+        sin(theta0)*Derivative(f(r0, theta0), r0) +
+        cos(theta0)*Derivative(f(r0, theta0), theta0)/r0)
+
+    assert R2.dx(R2.e_x).rcall(p_r) == 1
+    assert R2.dx(R2.e_x) == 1
+    assert R2.dx(R2.e_y).rcall(p_r) == 0
+    assert R2.dx(R2.e_y) == 0
+
+    circ = -R2.y*R2.e_x + R2.x*R2.e_y
+    assert R2.dx(circ).rcall(p_r).doit() == -y0
+    assert R2.dy(circ).rcall(p_r) == x0
+    assert R2.dr(circ).rcall(p_r) == 0
+    assert simplify(R2.dtheta(circ).rcall(p_r)) == 1
+
+    assert (circ - R2.e_theta).rcall(s_field_r).rcall(p_r) == 0
+
+
+def test_functional_diffgeom_ch6():
+    u0, u1, u2, v0, v1, v2, w0, w1, w2 = symbols('u0:3, v0:3, w0:3', real=True)
+
+    u = u0*R2.e_x + u1*R2.e_y
+    v = v0*R2.e_x + v1*R2.e_y
+    wp = WedgeProduct(R2.dx, R2.dy)
+    assert wp(u, v) == u0*v1 - u1*v0
+
+    u = u0*R3_r.e_x + u1*R3_r.e_y + u2*R3_r.e_z
+    v = v0*R3_r.e_x + v1*R3_r.e_y + v2*R3_r.e_z
+    w = w0*R3_r.e_x + w1*R3_r.e_y + w2*R3_r.e_z
+    wp = WedgeProduct(R3_r.dx, R3_r.dy, R3_r.dz)
+    assert wp(
+        u, v, w) == Matrix(3, 3, [u0, u1, u2, v0, v1, v2, w0, w1, w2]).det()
+
+    a, b, c = symbols('a, b, c', cls=Function)
+    a_f = a(R3_r.x, R3_r.y, R3_r.z)
+    b_f = b(R3_r.x, R3_r.y, R3_r.z)
+    c_f = c(R3_r.x, R3_r.y, R3_r.z)
+    theta = a_f*R3_r.dx + b_f*R3_r.dy + c_f*R3_r.dz
+    dtheta = Differential(theta)
+    da = Differential(a_f)
+    db = Differential(b_f)
+    dc = Differential(c_f)
+    expr = dtheta - WedgeProduct(
+        da, R3_r.dx) - WedgeProduct(db, R3_r.dy) - WedgeProduct(dc, R3_r.dz)
+    assert expr.rcall(R3_r.e_x, R3_r.e_y) == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.py
new file mode 100644
index 0000000000000000000000000000000000000000..48ddc7f8065f2b69bcd8eca4726a21c5901514ec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.py
@@ -0,0 +1,91 @@
+r'''
+unit test describing the hyperbolic half-plane with the Poincare metric. This
+is a basic model of hyperbolic geometry on the (positive) half-space
+
+{(x,y) \in R^2 | y > 0}
+
+with the Riemannian metric
+
+ds^2 = (dx^2 + dy^2)/y^2
+
+It has constant negative scalar curvature = -2
+
+https://en.wikipedia.org/wiki/Poincare_half-plane_model
+'''
+from sympy.matrices.dense import diag
+from sympy.diffgeom import (twoform_to_matrix,
+                            metric_to_Christoffel_1st, metric_to_Christoffel_2nd,
+                            metric_to_Riemann_components, metric_to_Ricci_components)
+import sympy.diffgeom.rn
+from sympy.tensor.array import ImmutableDenseNDimArray
+
+
+def test_H2():
+    TP = sympy.diffgeom.TensorProduct
+    R2 = sympy.diffgeom.rn.R2
+    y = R2.y
+    dy = R2.dy
+    dx = R2.dx
+    g = (TP(dx, dx) + TP(dy, dy))*y**(-2)
+    automat = twoform_to_matrix(g)
+    mat = diag(y**(-2), y**(-2))
+    assert mat == automat
+
+    gamma1 = metric_to_Christoffel_1st(g)
+    assert gamma1[0, 0, 0] == 0
+    assert gamma1[0, 0, 1] == -y**(-3)
+    assert gamma1[0, 1, 0] == -y**(-3)
+    assert gamma1[0, 1, 1] == 0
+
+    assert gamma1[1, 1, 1] == -y**(-3)
+    assert gamma1[1, 1, 0] == 0
+    assert gamma1[1, 0, 1] == 0
+    assert gamma1[1, 0, 0] == y**(-3)
+
+    gamma2 = metric_to_Christoffel_2nd(g)
+    assert gamma2[0, 0, 0] == 0
+    assert gamma2[0, 0, 1] == -y**(-1)
+    assert gamma2[0, 1, 0] == -y**(-1)
+    assert gamma2[0, 1, 1] == 0
+
+    assert gamma2[1, 1, 1] == -y**(-1)
+    assert gamma2[1, 1, 0] == 0
+    assert gamma2[1, 0, 1] == 0
+    assert gamma2[1, 0, 0] == y**(-1)
+
+    Rm = metric_to_Riemann_components(g)
+    assert Rm[0, 0, 0, 0] == 0
+    assert Rm[0, 0, 0, 1] == 0
+    assert Rm[0, 0, 1, 0] == 0
+    assert Rm[0, 0, 1, 1] == 0
+
+    assert Rm[0, 1, 0, 0] == 0
+    assert Rm[0, 1, 0, 1] == -y**(-2)
+    assert Rm[0, 1, 1, 0] == y**(-2)
+    assert Rm[0, 1, 1, 1] == 0
+
+    assert Rm[1, 0, 0, 0] == 0
+    assert Rm[1, 0, 0, 1] == y**(-2)
+    assert Rm[1, 0, 1, 0] == -y**(-2)
+    assert Rm[1, 0, 1, 1] == 0
+
+    assert Rm[1, 1, 0, 0] == 0
+    assert Rm[1, 1, 0, 1] == 0
+    assert Rm[1, 1, 1, 0] == 0
+    assert Rm[1, 1, 1, 1] == 0
+
+    Ric = metric_to_Ricci_components(g)
+    assert Ric[0, 0] == -y**(-2)
+    assert Ric[0, 1] == 0
+    assert Ric[1, 0] == 0
+    assert Ric[0, 0] == -y**(-2)
+
+    assert Ric == ImmutableDenseNDimArray([-y**(-2), 0, 0, -y**(-2)], (2, 2))
+
+    ## scalar curvature is -2
+    #TODO - it would be nice to have index contraction built-in
+    R = (Ric[0, 0] + Ric[1, 1])*y**2
+    assert R == -2
+
+    ## Gauss curvature is -1
+    assert R/2 == -1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..968c4caa0d4562b71285f414bfb70f43d0b35111
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/__init__.py
@@ -0,0 +1,20 @@
+"""This module contains functions which operate on discrete sequences.
+
+Transforms - ``fft``, ``ifft``, ``ntt``, ``intt``, ``fwht``, ``ifwht``,
+            ``mobius_transform``, ``inverse_mobius_transform``
+
+Convolutions - ``convolution``, ``convolution_fft``, ``convolution_ntt``,
+            ``convolution_fwht``, ``convolution_subset``,
+            ``covering_product``, ``intersecting_product``
+"""
+
+from .transforms import (fft, ifft, ntt, intt, fwht, ifwht,
+    mobius_transform, inverse_mobius_transform)
+from .convolutions import convolution, covering_product, intersecting_product
+
+__all__ = [
+    'fft', 'ifft', 'ntt', 'intt', 'fwht', 'ifwht', 'mobius_transform',
+    'inverse_mobius_transform',
+
+    'convolution', 'covering_product', 'intersecting_product',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/convolutions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/convolutions.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac9a3dbbb26b8b117ea1ee99cf7ebabbd21322cc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/convolutions.py
@@ -0,0 +1,597 @@
+"""
+Convolution (using **FFT**, **NTT**, **FWHT**), Subset Convolution,
+Covering Product, Intersecting Product
+"""
+
+from sympy.core import S, sympify, Rational
+from sympy.core.function import expand_mul
+from sympy.discrete.transforms import (
+    fft, ifft, ntt, intt, fwht, ifwht,
+    mobius_transform, inverse_mobius_transform)
+from sympy.external.gmpy import MPZ, lcm
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import as_int
+
+
+def convolution(a, b, cycle=0, dps=None, prime=None, dyadic=None, subset=None):
+    """
+    Performs convolution by determining the type of desired
+    convolution using hints.
+
+    Exactly one of ``dps``, ``prime``, ``dyadic``, ``subset`` arguments
+    should be specified explicitly for identifying the type of convolution,
+    and the argument ``cycle`` can be specified optionally.
+
+    For the default arguments, linear convolution is performed using **FFT**.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which convolution is performed.
+    cycle : Integer
+        Specifies the length for doing cyclic convolution.
+    dps : Integer
+        Specifies the number of decimal digits for precision for
+        performing **FFT** on the sequence.
+    prime : Integer
+        Prime modulus of the form `(m 2^k + 1)` to be used for
+        performing **NTT** on the sequence.
+    dyadic : bool
+        Identifies the convolution type as dyadic (*bitwise-XOR*)
+        convolution, which is performed using **FWHT**.
+    subset : bool
+        Identifies the convolution type as subset convolution.
+
+    Examples
+    ========
+
+    >>> from sympy import convolution, symbols, S, I
+    >>> u, v, w, x, y, z = symbols('u v w x y z')
+
+    >>> convolution([1 + 2*I, 4 + 3*I], [S(5)/4, 6], dps=3)
+    [1.25 + 2.5*I, 11.0 + 15.8*I, 24.0 + 18.0*I]
+    >>> convolution([1, 2, 3], [4, 5, 6], cycle=3)
+    [31, 31, 28]
+
+    >>> convolution([111, 777], [888, 444], prime=19*2**10 + 1)
+    [1283, 19351, 14219]
+    >>> convolution([111, 777], [888, 444], prime=19*2**10 + 1, cycle=2)
+    [15502, 19351]
+
+    >>> convolution([u, v], [x, y, z], dyadic=True)
+    [u*x + v*y, u*y + v*x, u*z, v*z]
+    >>> convolution([u, v], [x, y, z], dyadic=True, cycle=2)
+    [u*x + u*z + v*y, u*y + v*x + v*z]
+
+    >>> convolution([u, v, w], [x, y, z], subset=True)
+    [u*x, u*y + v*x, u*z + w*x, v*z + w*y]
+    >>> convolution([u, v, w], [x, y, z], subset=True, cycle=3)
+    [u*x + v*z + w*y, u*y + v*x, u*z + w*x]
+
+    """
+
+    c = as_int(cycle)
+    if c < 0:
+        raise ValueError("The length for cyclic convolution "
+                        "must be non-negative")
+
+    dyadic = True if dyadic else None
+    subset = True if subset else None
+    if sum(x is not None for x in (prime, dps, dyadic, subset)) > 1:
+        raise TypeError("Ambiguity in determining the type of convolution")
+
+    if prime is not None:
+        ls = convolution_ntt(a, b, prime=prime)
+        return ls if not c else [sum(ls[i::c]) % prime for i in range(c)]
+
+    if dyadic:
+        ls = convolution_fwht(a, b)
+    elif subset:
+        ls = convolution_subset(a, b)
+    else:
+        def loop(a):
+            dens = []
+            for i in a:
+                if isinstance(i, Rational) and i.q - 1:
+                    dens.append(i.q)
+                elif not isinstance(i, int):
+                    return
+            if dens:
+                l = lcm(*dens)
+                return [i*l if type(i) is int else i.p*(l//i.q) for i in a], l
+            # no lcm of den to deal with
+            return a, 1
+        ls = None
+        da = loop(a)
+        if da is not None:
+            db = loop(b)
+            if db is not None:
+                (ia, ma), (ib, mb) = da, db
+                den = ma*mb
+                ls = convolution_int(ia, ib)
+                if den != 1:
+                    ls = [Rational(i, den) for i in ls]
+        if ls is None:
+            ls = convolution_fft(a, b, dps)
+
+    return ls if not c else [sum(ls[i::c]) for i in range(c)]
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                       Convolution for Complex domain                       #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def convolution_fft(a, b, dps=None):
+    """
+    Performs linear convolution using Fast Fourier Transform.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which convolution is performed.
+    dps : Integer
+        Specifies the number of decimal digits for precision.
+
+    Examples
+    ========
+
+    >>> from sympy import S, I
+    >>> from sympy.discrete.convolutions import convolution_fft
+
+    >>> convolution_fft([2, 3], [4, 5])
+    [8, 22, 15]
+    >>> convolution_fft([2, 5], [6, 7, 3])
+    [12, 44, 41, 15]
+    >>> convolution_fft([1 + 2*I, 4 + 3*I], [S(5)/4, 6])
+    [5/4 + 5*I/2, 11 + 63*I/4, 24 + 18*I]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Convolution_theorem
+    .. [2] https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general%29
+
+    """
+
+    a, b = a[:], b[:]
+    n = m = len(a) + len(b) - 1 # convolution size
+
+    if n > 0 and n&(n - 1): # not a power of 2
+        n = 2**n.bit_length()
+
+    # padding with zeros
+    a += [S.Zero]*(n - len(a))
+    b += [S.Zero]*(n - len(b))
+
+    a, b = fft(a, dps), fft(b, dps)
+    a = [expand_mul(x*y) for x, y in zip(a, b)]
+    a = ifft(a, dps)[:m]
+
+    return a
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Convolution for GF(p)                            #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def convolution_ntt(a, b, prime):
+    """
+    Performs linear convolution using Number Theoretic Transform.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which convolution is performed.
+    prime : Integer
+        Prime modulus of the form `(m 2^k + 1)` to be used for performing
+        **NTT** on the sequence.
+
+    Examples
+    ========
+
+    >>> from sympy.discrete.convolutions import convolution_ntt
+    >>> convolution_ntt([2, 3], [4, 5], prime=19*2**10 + 1)
+    [8, 22, 15]
+    >>> convolution_ntt([2, 5], [6, 7, 3], prime=19*2**10 + 1)
+    [12, 44, 41, 15]
+    >>> convolution_ntt([333, 555], [222, 666], prime=19*2**10 + 1)
+    [15555, 14219, 19404]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Convolution_theorem
+    .. [2] https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general%29
+
+    """
+
+    a, b, p = a[:], b[:], as_int(prime)
+    n = m = len(a) + len(b) - 1 # convolution size
+
+    if n > 0 and n&(n - 1): # not a power of 2
+        n = 2**n.bit_length()
+
+    # padding with zeros
+    a += [0]*(n - len(a))
+    b += [0]*(n - len(b))
+
+    a, b = ntt(a, p), ntt(b, p)
+    a = [x*y % p for x, y in zip(a, b)]
+    a = intt(a, p)[:m]
+
+    return a
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                         Convolution for 2**n-group                         #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def convolution_fwht(a, b):
+    """
+    Performs dyadic (*bitwise-XOR*) convolution using Fast Walsh Hadamard
+    Transform.
+
+    The convolution is automatically padded to the right with zeros, as the
+    *radix-2 FWHT* requires the number of sample points to be a power of 2.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which convolution is performed.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, S, I
+    >>> from sympy.discrete.convolutions import convolution_fwht
+
+    >>> u, v, x, y = symbols('u v x y')
+    >>> convolution_fwht([u, v], [x, y])
+    [u*x + v*y, u*y + v*x]
+
+    >>> convolution_fwht([2, 3], [4, 5])
+    [23, 22]
+    >>> convolution_fwht([2, 5 + 4*I, 7], [6*I, 7, 3 + 4*I])
+    [56 + 68*I, -10 + 30*I, 6 + 50*I, 48 + 32*I]
+
+    >>> convolution_fwht([S(33)/7, S(55)/6, S(7)/4], [S(2)/3, 5])
+    [2057/42, 1870/63, 7/6, 35/4]
+
+    References
+    ==========
+
+    .. [1] https://www.radioeng.cz/fulltexts/2002/02_03_40_42.pdf
+    .. [2] https://en.wikipedia.org/wiki/Hadamard_transform
+
+    """
+
+    if not a or not b:
+        return []
+
+    a, b = a[:], b[:]
+    n = max(len(a), len(b))
+
+    if n&(n - 1): # not a power of 2
+        n = 2**n.bit_length()
+
+    # padding with zeros
+    a += [S.Zero]*(n - len(a))
+    b += [S.Zero]*(n - len(b))
+
+    a, b = fwht(a), fwht(b)
+    a = [expand_mul(x*y) for x, y in zip(a, b)]
+    a = ifwht(a)
+
+    return a
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            Subset Convolution                              #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def convolution_subset(a, b):
+    """
+    Performs Subset Convolution of given sequences.
+
+    The indices of each argument, considered as bit strings, correspond to
+    subsets of a finite set.
+
+    The sequence is automatically padded to the right with zeros, as the
+    definition of subset based on bitmasks (indices) requires the size of
+    sequence to be a power of 2.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which convolution is performed.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, S
+    >>> from sympy.discrete.convolutions import convolution_subset
+    >>> u, v, x, y, z = symbols('u v x y z')
+
+    >>> convolution_subset([u, v], [x, y])
+    [u*x, u*y + v*x]
+    >>> convolution_subset([u, v, x], [y, z])
+    [u*y, u*z + v*y, x*y, x*z]
+
+    >>> convolution_subset([1, S(2)/3], [3, 4])
+    [3, 6]
+    >>> convolution_subset([1, 3, S(5)/7], [7])
+    [7, 21, 5, 0]
+
+    References
+    ==========
+
+    .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf
+
+    """
+
+    if not a or not b:
+        return []
+
+    if not iterable(a) or not iterable(b):
+        raise TypeError("Expected a sequence of coefficients for convolution")
+
+    a = [sympify(arg) for arg in a]
+    b = [sympify(arg) for arg in b]
+    n = max(len(a), len(b))
+
+    if n&(n - 1): # not a power of 2
+        n = 2**n.bit_length()
+
+    # padding with zeros
+    a += [S.Zero]*(n - len(a))
+    b += [S.Zero]*(n - len(b))
+
+    c = [S.Zero]*n
+
+    for mask in range(n):
+        smask = mask
+        while smask > 0:
+            c[mask] += expand_mul(a[smask] * b[mask^smask])
+            smask = (smask - 1)&mask
+
+        c[mask] += expand_mul(a[smask] * b[mask^smask])
+
+    return c
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                              Covering Product                              #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def covering_product(a, b):
+    """
+    Returns the covering product of given sequences.
+
+    The indices of each argument, considered as bit strings, correspond to
+    subsets of a finite set.
+
+    The covering product of given sequences is a sequence which contains
+    the sum of products of the elements of the given sequences grouped by
+    the *bitwise-OR* of the corresponding indices.
+
+    The sequence is automatically padded to the right with zeros, as the
+    definition of subset based on bitmasks (indices) requires the size of
+    sequence to be a power of 2.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which covering product is to be obtained.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, S, I, covering_product
+    >>> u, v, x, y, z = symbols('u v x y z')
+
+    >>> covering_product([u, v], [x, y])
+    [u*x, u*y + v*x + v*y]
+    >>> covering_product([u, v, x], [y, z])
+    [u*y, u*z + v*y + v*z, x*y, x*z]
+
+    >>> covering_product([1, S(2)/3], [3, 4 + 5*I])
+    [3, 26/3 + 25*I/3]
+    >>> covering_product([1, 3, S(5)/7], [7, 8])
+    [7, 53, 5, 40/7]
+
+    References
+    ==========
+
+    .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf
+
+    """
+
+    if not a or not b:
+        return []
+
+    a, b = a[:], b[:]
+    n = max(len(a), len(b))
+
+    if n&(n - 1): # not a power of 2
+        n = 2**n.bit_length()
+
+    # padding with zeros
+    a += [S.Zero]*(n - len(a))
+    b += [S.Zero]*(n - len(b))
+
+    a, b = mobius_transform(a), mobius_transform(b)
+    a = [expand_mul(x*y) for x, y in zip(a, b)]
+    a = inverse_mobius_transform(a)
+
+    return a
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            Intersecting Product                            #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def intersecting_product(a, b):
+    """
+    Returns the intersecting product of given sequences.
+
+    The indices of each argument, considered as bit strings, correspond to
+    subsets of a finite set.
+
+    The intersecting product of given sequences is the sequence which
+    contains the sum of products of the elements of the given sequences
+    grouped by the *bitwise-AND* of the corresponding indices.
+
+    The sequence is automatically padded to the right with zeros, as the
+    definition of subset based on bitmasks (indices) requires the size of
+    sequence to be a power of 2.
+
+    Parameters
+    ==========
+
+    a, b : iterables
+        The sequences for which intersecting product is to be obtained.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, S, I, intersecting_product
+    >>> u, v, x, y, z = symbols('u v x y z')
+
+    >>> intersecting_product([u, v], [x, y])
+    [u*x + u*y + v*x, v*y]
+    >>> intersecting_product([u, v, x], [y, z])
+    [u*y + u*z + v*y + x*y + x*z, v*z, 0, 0]
+
+    >>> intersecting_product([1, S(2)/3], [3, 4 + 5*I])
+    [9 + 5*I, 8/3 + 10*I/3]
+    >>> intersecting_product([1, 3, S(5)/7], [7, 8])
+    [327/7, 24, 0, 0]
+
+    References
+    ==========
+
+    .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf
+
+    """
+
+    if not a or not b:
+        return []
+
+    a, b = a[:], b[:]
+    n = max(len(a), len(b))
+
+    if n&(n - 1): # not a power of 2
+        n = 2**n.bit_length()
+
+    # padding with zeros
+    a += [S.Zero]*(n - len(a))
+    b += [S.Zero]*(n - len(b))
+
+    a, b = mobius_transform(a, subset=False), mobius_transform(b, subset=False)
+    a = [expand_mul(x*y) for x, y in zip(a, b)]
+    a = inverse_mobius_transform(a, subset=False)
+
+    return a
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                            Integer Convolutions                            #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def convolution_int(a, b):
+    """Return the convolution of two sequences as a list.
+
+    The iterables must consist solely of integers.
+
+    Parameters
+    ==========
+
+    a, b : Sequence
+        The sequences for which convolution is performed.
+
+    Explanation
+    ===========
+
+    This function performs the convolution of ``a`` and ``b`` by packing
+    each into a single integer, multiplying them together, and then
+    unpacking the result from the product.  The intuition behind this is
+    that if we evaluate some polynomial [1]:
+
+    .. math ::
+        1156x^6 + 3808x^5 + 8440x^4 + 14856x^3 + 16164x^2 + 14040x + 8100
+
+    at say $x = 10^5$ we obtain $1156038080844014856161641404008100$.
+    Note we can read of the coefficients for each term every five digits.
+    If the $x$ we chose to evaluate at is large enough, the same will hold
+    for the product.
+
+    The idea now is since big integer multiplication in libraries such
+    as GMP is highly optimised, this will be reasonably fast.
+
+    Examples
+    ========
+
+    >>> from sympy.discrete.convolutions import convolution_int
+
+    >>> convolution_int([2, 3], [4, 5])
+    [8, 22, 15]
+    >>> convolution_int([1, 1, -1], [1, 1])
+    [1, 2, 0, -1]
+
+    References
+    ==========
+
+    .. [1] Fateman, Richard J.
+           Can you save time in multiplying polynomials by encoding them as integers?
+           University of California, Berkeley, California (2004).
+           https://people.eecs.berkeley.edu/~fateman/papers/polysbyGMP.pdf
+    """
+    # An upper bound on the largest coefficient in p(x)q(x) is given by (1 + min(dp, dq))N(p)N(q)
+    # where dp = deg(p), dq = deg(q), N(f) denotes the coefficient of largest modulus in f [1]
+    B = max(abs(c) for c in a)*max(abs(c) for c in b)*(1 + min(len(a) - 1, len(b) - 1))
+    x, power = MPZ(1), 0
+    while x <= (2*B):  # multiply by two for negative coefficients, see [1]
+        x <<= 1
+        power += 1
+
+    def to_integer(poly):
+        n, mul = MPZ(0), 0
+        for c in reversed(poly):
+            if c and not mul: mul = -1 if c < 0 else 1
+            n <<= power
+            n += mul*int(c)
+        return mul, n
+
+    # Perform packing and multiplication
+    (a_mul, a_packed), (b_mul, b_packed) = to_integer(a), to_integer(b)
+    result = a_packed * b_packed
+
+    # Perform unpacking
+    mul = a_mul * b_mul
+    mask, half, borrow, poly = x - 1, x >> 1, 0, []
+    while result or borrow:
+        coeff = (result & mask) + borrow
+        result >>= power
+        borrow = coeff >= half
+        poly.append(mul * int(coeff if coeff < half else coeff - x))
+    return poly or [0]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/recurrences.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/recurrences.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b0ed80d304161cf9ca298321aedc094c8cae1b3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/recurrences.py
@@ -0,0 +1,166 @@
+"""
+Recurrences
+"""
+
+from sympy.core import S, sympify
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import as_int
+
+
+def linrec(coeffs, init, n):
+    r"""
+    Evaluation of univariate linear recurrences of homogeneous type
+    having coefficients independent of the recurrence variable.
+
+    Parameters
+    ==========
+
+    coeffs : iterable
+        Coefficients of the recurrence
+    init : iterable
+        Initial values of the recurrence
+    n : Integer
+        Point of evaluation for the recurrence
+
+    Notes
+    =====
+
+    Let `y(n)` be the recurrence of given type, ``c`` be the sequence
+    of coefficients, ``b`` be the sequence of initial/base values of the
+    recurrence and ``k`` (equal to ``len(c)``) be the order of recurrence.
+    Then,
+
+    .. math :: y(n) = \begin{cases} b_n & 0 \le n < k \\
+        c_0 y(n-1) + c_1 y(n-2) + \cdots + c_{k-1} y(n-k) & n \ge k
+        \end{cases}
+
+    Let `x_0, x_1, \ldots, x_n` be a sequence and consider the transformation
+    that maps each polynomial `f(x)` to `T(f(x))` where each power `x^i` is
+    replaced by the corresponding value `x_i`. The sequence is then a solution
+    of the recurrence if and only if `T(x^i p(x)) = 0` for each `i \ge 0` where
+    `p(x) = x^k - c_0 x^(k-1) - \cdots - c_{k-1}` is the characteristic
+    polynomial.
+
+    Then `T(f(x)p(x)) = 0` for each polynomial `f(x)` (as it is a linear
+    combination of powers `x^i`). Now, if `x^n` is congruent to
+    `g(x) = a_0 x^0 + a_1 x^1 + \cdots + a_{k-1} x^{k-1}` modulo `p(x)`, then
+    `T(x^n) = x_n` is equal to
+    `T(g(x)) = a_0 x_0 + a_1 x_1 + \cdots + a_{k-1} x_{k-1}`.
+
+    Computation of `x^n`,
+    given `x^k = c_0 x^{k-1} + c_1 x^{k-2} + \cdots + c_{k-1}`
+    is performed using exponentiation by squaring (refer to [1_]) with
+    an additional reduction step performed to retain only first `k` powers
+    of `x` in the representation of `x^n`.
+
+    Examples
+    ========
+
+    >>> from sympy.discrete.recurrences import linrec
+    >>> from sympy.abc import x, y, z
+
+    >>> linrec(coeffs=[1, 1], init=[0, 1], n=10)
+    55
+
+    >>> linrec(coeffs=[1, 1], init=[x, y], n=10)
+    34*x + 55*y
+
+    >>> linrec(coeffs=[x, y], init=[0, 1], n=5)
+    x**2*y + x*(x**3 + 2*x*y) + y**2
+
+    >>> linrec(coeffs=[1, 2, 3, 0, 0, 4], init=[x, y, z], n=16)
+    13576*x + 5676*y + 2356*z
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Exponentiation_by_squaring
+    .. [2] https://en.wikipedia.org/w/index.php?title=Modular_exponentiation§ion=6#Matrices
+
+    See Also
+    ========
+
+    sympy.polys.agca.extensions.ExtensionElement.__pow__
+
+    """
+
+    if not coeffs:
+        return S.Zero
+
+    if not iterable(coeffs):
+        raise TypeError("Expected a sequence of coefficients for"
+                        " the recurrence")
+
+    if not iterable(init):
+        raise TypeError("Expected a sequence of values for the initialization"
+                        " of the recurrence")
+
+    n = as_int(n)
+    if n < 0:
+        raise ValueError("Point of evaluation of recurrence must be a "
+                        "non-negative integer")
+
+    c = [sympify(arg) for arg in coeffs]
+    b = [sympify(arg) for arg in init]
+    k = len(c)
+
+    if len(b) > k:
+        raise TypeError("Count of initial values should not exceed the "
+                        "order of the recurrence")
+    else:
+        b += [S.Zero]*(k - len(b)) # remaining initial values default to zero
+
+    if n < k:
+        return b[n]
+    terms = [u*v for u, v in zip(linrec_coeffs(c, n), b)]
+    return sum(terms[:-1], terms[-1])
+
+
+def linrec_coeffs(c, n):
+    r"""
+    Compute the coefficients of n'th term in linear recursion
+    sequence defined by c.
+
+    `x^k = c_0 x^{k-1} + c_1 x^{k-2} + \cdots + c_{k-1}`.
+
+    It computes the coefficients by using binary exponentiation.
+    This function is used by `linrec` and `_eval_pow_by_cayley`.
+
+    Parameters
+    ==========
+
+    c = coefficients of the divisor polynomial
+    n = exponent of x, so dividend is x^n
+
+    """
+
+    k = len(c)
+
+    def _square_and_reduce(u, offset):
+        # squares `(u_0 + u_1 x + u_2 x^2 + \cdots + u_{k-1} x^k)` (and
+        # multiplies by `x` if offset is 1) and reduces the above result of
+        # length upto `2k` to `k` using the characteristic equation of the
+        # recurrence given by, `x^k = c_0 x^{k-1} + c_1 x^{k-2} + \cdots + c_{k-1}`
+
+        w = [S.Zero]*(2*len(u) - 1 + offset)
+        for i, p in enumerate(u):
+            for j, q in enumerate(u):
+                w[offset + i + j] += p*q
+
+        for j in range(len(w) - 1, k - 1, -1):
+            for i in range(k):
+                w[j - i - 1] += w[j]*c[i]
+
+        return w[:k]
+
+    def _final_coeffs(n):
+        # computes the final coefficient list - `cf` corresponding to the
+        # point at which recurrence is to be evalauted - `n`, such that,
+        # `y(n) = cf_0 y(k-1) + cf_1 y(k-2) + \cdots + cf_{k-1} y(0)`
+
+        if n < k:
+            return [S.Zero]*n + [S.One] + [S.Zero]*(k - n - 1)
+        else:
+            return _square_and_reduce(_final_coeffs(n // 2), n % 2)
+
+    return _final_coeffs(n)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_convolutions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_convolutions.py
new file mode 100644
index 0000000000000000000000000000000000000000..96e5fc801ac63f95c01eb18d48143ae3a1ac6222
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_convolutions.py
@@ -0,0 +1,392 @@
+from sympy.core.numbers import (E, Rational, pi)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.core import S, symbols, I
+from sympy.discrete.convolutions import (
+    convolution, convolution_fft, convolution_ntt, convolution_fwht,
+    convolution_subset, covering_product, intersecting_product,
+    convolution_int)
+from sympy.testing.pytest import raises
+from sympy.abc import x, y
+
+def test_convolution():
+    # fft
+    a = [1, Rational(5, 3), sqrt(3), Rational(7, 5)]
+    b = [9, 5, 5, 4, 3, 2]
+    c = [3, 5, 3, 7, 8]
+    d = [1422, 6572, 3213, 5552]
+    e = [-1, Rational(5, 3), Rational(7, 5)]
+
+    assert convolution(a, b) == convolution_fft(a, b)
+    assert convolution(a, b, dps=9) == convolution_fft(a, b, dps=9)
+    assert convolution(a, d, dps=7) == convolution_fft(d, a, dps=7)
+    assert convolution(a, d[1:], dps=3) == convolution_fft(d[1:], a, dps=3)
+
+    # prime moduli of the form (m*2**k + 1), sequence length
+    # should be a divisor of 2**k
+    p = 7*17*2**23 + 1
+    q = 19*2**10 + 1
+
+    # ntt
+    assert convolution(d, b, prime=q) == convolution_ntt(b, d, prime=q)
+    assert convolution(c, b, prime=p) == convolution_ntt(b, c, prime=p)
+    assert convolution(d, c, prime=p) == convolution_ntt(c, d, prime=p)
+    raises(TypeError, lambda: convolution(b, d, dps=5, prime=q))
+    raises(TypeError, lambda: convolution(b, d, dps=6, prime=q))
+
+    # fwht
+    assert convolution(a, b, dyadic=True) == convolution_fwht(a, b)
+    assert convolution(a, b, dyadic=False) == convolution(a, b)
+    raises(TypeError, lambda: convolution(b, d, dps=2, dyadic=True))
+    raises(TypeError, lambda: convolution(b, d, prime=p, dyadic=True))
+    raises(TypeError, lambda: convolution(a, b, dps=2, dyadic=True))
+    raises(TypeError, lambda: convolution(b, c, prime=p, dyadic=True))
+
+    # subset
+    assert convolution(a, b, subset=True) == convolution_subset(a, b) == \
+            convolution(a, b, subset=True, dyadic=False) == \
+                convolution(a, b, subset=True)
+    assert convolution(a, b, subset=False) == convolution(a, b)
+    raises(TypeError, lambda: convolution(a, b, subset=True, dyadic=True))
+    raises(TypeError, lambda: convolution(c, d, subset=True, dps=6))
+    raises(TypeError, lambda: convolution(a, c, subset=True, prime=q))
+
+    # integer
+    assert convolution([0], [0]) == convolution_int([0], [0])
+    assert convolution(b, c) == convolution_int(b, c)
+
+    # rational
+    assert convolution([Rational(1,2)], [Rational(1,2)]) == [Rational(1, 4)]
+    assert convolution(b, e) == [-9, 10, Rational(239, 15), Rational(34, 3),
+                                 Rational(32, 3), Rational(43, 5), Rational(113, 15),
+                                 Rational(14, 5)]
+
+
+def test_cyclic_convolution():
+    # fft
+    a = [1, Rational(5, 3), sqrt(3), Rational(7, 5)]
+    b = [9, 5, 5, 4, 3, 2]
+
+    assert convolution([1, 2, 3], [4, 5, 6], cycle=0) == \
+            convolution([1, 2, 3], [4, 5, 6], cycle=5) == \
+                convolution([1, 2, 3], [4, 5, 6])
+
+    assert convolution([1, 2, 3], [4, 5, 6], cycle=3) == [31, 31, 28]
+
+    a = [Rational(1, 3), Rational(7, 3), Rational(5, 9), Rational(2, 7), Rational(5, 8)]
+    b = [Rational(3, 5), Rational(4, 7), Rational(7, 8), Rational(8, 9)]
+
+    assert convolution(a, b, cycle=0) == \
+            convolution(a, b, cycle=len(a) + len(b) - 1)
+
+    assert convolution(a, b, cycle=4) == [Rational(87277, 26460), Rational(30521, 11340),
+                            Rational(11125, 4032), Rational(3653, 1080)]
+
+    assert convolution(a, b, cycle=6) == [Rational(20177, 20160), Rational(676, 315), Rational(47, 24),
+                            Rational(3053, 1080), Rational(16397, 5292), Rational(2497, 2268)]
+
+    assert convolution(a, b, cycle=9) == \
+                convolution(a, b, cycle=0) + [S.Zero]
+
+    # ntt
+    a = [2313, 5323532, S(3232), 42142, 42242421]
+    b = [S(33456), 56757, 45754, 432423]
+
+    assert convolution(a, b, prime=19*2**10 + 1, cycle=0) == \
+            convolution(a, b, prime=19*2**10 + 1, cycle=8) == \
+                convolution(a, b, prime=19*2**10 + 1)
+
+    assert convolution(a, b, prime=19*2**10 + 1, cycle=5) == [96, 17146, 2664,
+                                                                    15534, 3517]
+
+    assert convolution(a, b, prime=19*2**10 + 1, cycle=7) == [4643, 3458, 1260,
+                                                        15534, 3517, 16314, 13688]
+
+    assert convolution(a, b, prime=19*2**10 + 1, cycle=9) == \
+            convolution(a, b, prime=19*2**10 + 1) + [0]
+
+    # fwht
+    u, v, w, x, y = symbols('u v w x y')
+    p, q, r, s, t = symbols('p q r s t')
+    c = [u, v, w, x, y]
+    d = [p, q, r, s, t]
+
+    assert convolution(a, b, dyadic=True, cycle=3) == \
+                        [2499522285783, 19861417974796, 4702176579021]
+
+    assert convolution(a, b, dyadic=True, cycle=5) == [2718149225143,
+            2114320852171, 20571217906407, 246166418903, 1413262436976]
+
+    assert convolution(c, d, dyadic=True, cycle=4) == \
+            [p*u + p*y + q*v + r*w + s*x + t*u + t*y,
+             p*v + q*u + q*y + r*x + s*w + t*v,
+             p*w + q*x + r*u + r*y + s*v + t*w,
+             p*x + q*w + r*v + s*u + s*y + t*x]
+
+    assert convolution(c, d, dyadic=True, cycle=6) == \
+            [p*u + q*v + r*w + r*y + s*x + t*w + t*y,
+             p*v + q*u + r*x + s*w + s*y + t*x,
+             p*w + q*x + r*u + s*v,
+             p*x + q*w + r*v + s*u,
+             p*y + t*u,
+             q*y + t*v]
+
+    # subset
+    assert convolution(a, b, subset=True, cycle=7) == [18266671799811,
+                    178235365533, 213958794, 246166418903, 1413262436976,
+                    2397553088697, 1932759730434]
+
+    assert convolution(a[1:], b, subset=True, cycle=4) == \
+            [178104086592, 302255835516, 244982785880, 3717819845434]
+
+    assert convolution(a, b[:-1], subset=True, cycle=6) == [1932837114162,
+            178235365533, 213958794, 245166224504, 1413262436976, 2397553088697]
+
+    assert convolution(c, d, subset=True, cycle=3) == \
+            [p*u + p*x + q*w + r*v + r*y + s*u + t*w,
+             p*v + p*y + q*u + s*y + t*u + t*x,
+             p*w + q*y + r*u + t*v]
+
+    assert convolution(c, d, subset=True, cycle=5) == \
+            [p*u + q*y + t*v,
+             p*v + q*u + r*y + t*w,
+             p*w + r*u + s*y + t*x,
+             p*x + q*w + r*v + s*u,
+             p*y + t*u]
+
+    raises(ValueError, lambda: convolution([1, 2, 3], [4, 5, 6], cycle=-1))
+
+
+def test_convolution_fft():
+    assert all(convolution_fft([], x, dps=y) == [] for x in ([], [1]) for y in (None, 3))
+    assert convolution_fft([1, 2, 3], [4, 5, 6]) == [4, 13, 28, 27, 18]
+    assert convolution_fft([1], [5, 6, 7]) == [5, 6, 7]
+    assert convolution_fft([1, 3], [5, 6, 7]) == [5, 21, 25, 21]
+
+    assert convolution_fft([1 + 2*I], [2 + 3*I]) == [-4 + 7*I]
+    assert convolution_fft([1 + 2*I, 3 + 4*I, 5 + 3*I/5], [Rational(2, 5) + 4*I/7]) == \
+            [Rational(-26, 35) + I*48/35, Rational(-38, 35) + I*116/35, Rational(58, 35) + I*542/175]
+
+    assert convolution_fft([Rational(3, 4), Rational(5, 6)], [Rational(7, 8), Rational(1, 3), Rational(2, 5)]) == \
+                                    [Rational(21, 32), Rational(47, 48), Rational(26, 45), Rational(1, 3)]
+
+    assert convolution_fft([Rational(1, 9), Rational(2, 3), Rational(3, 5)], [Rational(2, 5), Rational(3, 7), Rational(4, 9)]) == \
+                                [Rational(2, 45), Rational(11, 35), Rational(8152, 14175), Rational(523, 945), Rational(4, 15)]
+
+    assert convolution_fft([pi, E, sqrt(2)], [sqrt(3), 1/pi, 1/E]) == \
+                    [sqrt(3)*pi, 1 + sqrt(3)*E, E/pi + pi*exp(-1) + sqrt(6),
+                                            sqrt(2)/pi + 1, sqrt(2)*exp(-1)]
+
+    assert convolution_fft([2321, 33123], [5321, 6321, 71323]) == \
+                        [12350041, 190918524, 374911166, 2362431729]
+
+    assert convolution_fft([312313, 31278232], [32139631, 319631]) == \
+                        [10037624576503, 1005370659728895, 9997492572392]
+
+    raises(TypeError, lambda: convolution_fft(x, y))
+    raises(ValueError, lambda: convolution_fft([x, y], [y, x]))
+
+
+def test_convolution_ntt():
+    # prime moduli of the form (m*2**k + 1), sequence length
+    # should be a divisor of 2**k
+    p = 7*17*2**23 + 1
+    q = 19*2**10 + 1
+    r = 2*500000003 + 1 # only for sequences of length 1 or 2
+    # s = 2*3*5*7 # composite modulus
+
+    assert all(convolution_ntt([], x, prime=y) == [] for x in ([], [1]) for y in (p, q, r))
+    assert convolution_ntt([2], [3], r) == [6]
+    assert convolution_ntt([2, 3], [4], r) == [8, 12]
+
+    assert convolution_ntt([32121, 42144, 4214, 4241], [32132, 3232, 87242], p) == [33867619,
+                                    459741727, 79180879, 831885249, 381344700, 369993322]
+    assert convolution_ntt([121913, 3171831, 31888131, 12], [17882, 21292, 29921, 312], q) == \
+                                                [8158, 3065, 3682, 7090, 1239, 2232, 3744]
+
+    assert convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], p) == \
+                    convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], q)
+    assert convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], p) == \
+                    convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], q)
+
+    raises(ValueError, lambda: convolution_ntt([2, 3], [4, 5], r))
+    raises(ValueError, lambda: convolution_ntt([x, y], [y, x], q))
+    raises(TypeError, lambda: convolution_ntt(x, y, p))
+
+
+def test_convolution_fwht():
+    assert convolution_fwht([], []) == []
+    assert convolution_fwht([], [1]) == []
+    assert convolution_fwht([1, 2, 3], [4, 5, 6]) == [32, 13, 18, 27]
+
+    assert convolution_fwht([Rational(5, 7), Rational(6, 8), Rational(7, 3)], [2, 4, Rational(6, 7)]) == \
+                                    [Rational(45, 7), Rational(61, 14), Rational(776, 147), Rational(419, 42)]
+
+    a = [1, Rational(5, 3), sqrt(3), Rational(7, 5), 4 + 5*I]
+    b = [94, 51, 53, 45, 31, 27, 13]
+    c = [3 + 4*I, 5 + 7*I, 3, Rational(7, 6), 8]
+
+    assert convolution_fwht(a, b) == [53*sqrt(3) + 366 + 155*I,
+                                    45*sqrt(3) + Rational(5848, 15) + 135*I,
+                                    94*sqrt(3) + Rational(1257, 5) + 65*I,
+                                    51*sqrt(3) + Rational(3974, 15),
+                                    13*sqrt(3) + 452 + 470*I,
+                                    Rational(4513, 15) + 255*I,
+                                    31*sqrt(3) + Rational(1314, 5) + 265*I,
+                                    27*sqrt(3) + Rational(3676, 15) + 225*I]
+
+    assert convolution_fwht(b, c) == [Rational(1993, 2) + 733*I, Rational(6215, 6) + 862*I,
+        Rational(1659, 2) + 527*I, Rational(1988, 3) + 551*I, 1019 + 313*I, Rational(3955, 6) + 325*I,
+        Rational(1175, 2) + 52*I, Rational(3253, 6) + 91*I]
+
+    assert convolution_fwht(a[3:], c) == [Rational(-54, 5) + I*293/5, -1 + I*204/5,
+            Rational(133, 15) + I*35/6, Rational(409, 30) + 15*I, Rational(56, 5), 32 + 40*I, 0, 0]
+
+    u, v, w, x, y, z = symbols('u v w x y z')
+
+    assert convolution_fwht([u, v], [x, y]) == [u*x + v*y, u*y + v*x]
+
+    assert convolution_fwht([u, v, w], [x, y]) == \
+        [u*x + v*y, u*y + v*x, w*x, w*y]
+
+    assert convolution_fwht([u, v, w], [x, y, z]) == \
+        [u*x + v*y + w*z, u*y + v*x, u*z + w*x, v*z + w*y]
+
+    raises(TypeError, lambda: convolution_fwht(x, y))
+    raises(TypeError, lambda: convolution_fwht(x*y, u + v))
+
+
+def test_convolution_subset():
+    assert convolution_subset([], []) == []
+    assert convolution_subset([], [Rational(1, 3)]) == []
+    assert convolution_subset([6 + I*3/7], [Rational(2, 3)]) == [4 + I*2/7]
+
+    a = [1, Rational(5, 3), sqrt(3), 4 + 5*I]
+    b = [64, 71, 55, 47, 33, 29, 15]
+    c = [3 + I*2/3, 5 + 7*I, 7, Rational(7, 5), 9]
+
+    assert convolution_subset(a, b) == [64, Rational(533, 3), 55 + 64*sqrt(3),
+                                        71*sqrt(3) + Rational(1184, 3) + 320*I, 33, 84,
+                                        15 + 33*sqrt(3), 29*sqrt(3) + 157 + 165*I]
+
+    assert convolution_subset(b, c) == [192 + I*128/3, 533 + I*1486/3,
+                                        613 + I*110/3, Rational(5013, 5) + I*1249/3,
+                                        675 + 22*I, 891 + I*751/3,
+                                        771 + 10*I, Rational(3736, 5) + 105*I]
+
+    assert convolution_subset(a, c) == convolution_subset(c, a)
+    assert convolution_subset(a[:2], b) == \
+            [64, Rational(533, 3), 55, Rational(416, 3), 33, 84, 15, 25]
+
+    assert convolution_subset(a[:2], c) == \
+            [3 + I*2/3, 10 + I*73/9, 7, Rational(196, 15), 9, 15, 0, 0]
+
+    u, v, w, x, y, z = symbols('u v w x y z')
+
+    assert convolution_subset([u, v, w], [x, y]) == [u*x, u*y + v*x, w*x, w*y]
+    assert convolution_subset([u, v, w, x], [y, z]) == \
+                            [u*y, u*z + v*y, w*y, w*z + x*y]
+
+    assert convolution_subset([u, v], [x, y, z]) == \
+                    convolution_subset([x, y, z], [u, v])
+
+    raises(TypeError, lambda: convolution_subset(x, z))
+    raises(TypeError, lambda: convolution_subset(Rational(7, 3), u))
+
+
+def test_covering_product():
+    assert covering_product([], []) == []
+    assert covering_product([], [Rational(1, 3)]) == []
+    assert covering_product([6 + I*3/7], [Rational(2, 3)]) == [4 + I*2/7]
+
+    a = [1, Rational(5, 8), sqrt(7), 4 + 9*I]
+    b = [66, 81, 95, 49, 37, 89, 17]
+    c = [3 + I*2/3, 51 + 72*I, 7, Rational(7, 15), 91]
+
+    assert covering_product(a, b) == [66, Rational(1383, 8), 95 + 161*sqrt(7),
+                                        130*sqrt(7) + 1303 + 2619*I, 37,
+                                        Rational(671, 4), 17 + 54*sqrt(7),
+                                        89*sqrt(7) + Rational(4661, 8) + 1287*I]
+
+    assert covering_product(b, c) == [198 + 44*I, 7740 + 10638*I,
+                                        1412 + I*190/3, Rational(42684, 5) + I*31202/3,
+                                        9484 + I*74/3, 22163 + I*27394/3,
+                                        10621 + I*34/3, Rational(90236, 15) + 1224*I]
+
+    assert covering_product(a, c) == covering_product(c, a)
+    assert covering_product(b, c[:-1]) == [198 + 44*I, 7740 + 10638*I,
+                                         1412 + I*190/3, Rational(42684, 5) + I*31202/3,
+                                         111 + I*74/3, 6693 + I*27394/3,
+                                         429 + I*34/3, Rational(23351, 15) + 1224*I]
+
+    assert covering_product(a, c[:-1]) == [3 + I*2/3,
+                            Rational(339, 4) + I*1409/12, 7 + 10*sqrt(7) + 2*sqrt(7)*I/3,
+                            -403 + 772*sqrt(7)/15 + 72*sqrt(7)*I + I*12658/15]
+
+    u, v, w, x, y, z = symbols('u v w x y z')
+
+    assert covering_product([u, v, w], [x, y]) == \
+                            [u*x, u*y + v*x + v*y, w*x, w*y]
+
+    assert covering_product([u, v, w, x], [y, z]) == \
+                            [u*y, u*z + v*y + v*z, w*y, w*z + x*y + x*z]
+
+    assert covering_product([u, v], [x, y, z]) == \
+                    covering_product([x, y, z], [u, v])
+
+    raises(TypeError, lambda: covering_product(x, z))
+    raises(TypeError, lambda: covering_product(Rational(7, 3), u))
+
+
+def test_intersecting_product():
+    assert intersecting_product([], []) == []
+    assert intersecting_product([], [Rational(1, 3)]) == []
+    assert intersecting_product([6 + I*3/7], [Rational(2, 3)]) == [4 + I*2/7]
+
+    a = [1, sqrt(5), Rational(3, 8) + 5*I, 4 + 7*I]
+    b = [67, 51, 65, 48, 36, 79, 27]
+    c = [3 + I*2/5, 5 + 9*I, 7, Rational(7, 19), 13]
+
+    assert intersecting_product(a, b) == [195*sqrt(5) + Rational(6979, 8) + 1886*I,
+                                178*sqrt(5) + 520 + 910*I, Rational(841, 2) + 1344*I,
+                                192 + 336*I, 0, 0, 0, 0]
+
+    assert intersecting_product(b, c) == [Rational(128553, 19) + I*9521/5,
+                Rational(17820, 19) + 1602*I, Rational(19264, 19), Rational(336, 19), 1846, 0, 0, 0]
+
+    assert intersecting_product(a, c) == intersecting_product(c, a)
+    assert intersecting_product(b[1:], c[:-1]) == [Rational(64788, 19) + I*8622/5,
+                    Rational(12804, 19) + 1152*I, Rational(11508, 19), Rational(252, 19), 0, 0, 0, 0]
+
+    assert intersecting_product(a, c[:-2]) == \
+                    [Rational(-99, 5) + 10*sqrt(5) + 2*sqrt(5)*I/5 + I*3021/40,
+                    -43 + 5*sqrt(5) + 9*sqrt(5)*I + 71*I, Rational(245, 8) + 84*I, 0]
+
+    u, v, w, x, y, z = symbols('u v w x y z')
+
+    assert intersecting_product([u, v, w], [x, y]) == \
+                            [u*x + u*y + v*x + w*x + w*y, v*y, 0, 0]
+
+    assert intersecting_product([u, v, w, x], [y, z]) == \
+                        [u*y + u*z + v*y + w*y + w*z + x*y, v*z + x*z, 0, 0]
+
+    assert intersecting_product([u, v], [x, y, z]) == \
+                    intersecting_product([x, y, z], [u, v])
+
+    raises(TypeError, lambda: intersecting_product(x, z))
+    raises(TypeError, lambda: intersecting_product(u, Rational(8, 3)))
+
+
+def test_convolution_int():
+    assert convolution_int([1], [1]) == [1]
+    assert convolution_int([1, 1], [0]) == [0]
+    assert convolution_int([1, 2, 3], [4, 5, 6]) == [4, 13, 28, 27, 18]
+    assert convolution_int([1], [5, 6, 7]) == [5, 6, 7]
+    assert convolution_int([1, 3], [5, 6, 7]) == [5, 21, 25, 21]
+    assert convolution_int([10, -5, 1, 3], [-5, 6, 7]) == [-50, 85, 35, -44, 25, 21]
+    assert convolution_int([0, 1, 0, -1], [1, 0, -1, 0]) == [0, 1, 0, -2, 0, 1]
+    assert convolution_int(
+        [-341, -5, 1, 3, -71, -99, 43, 87],
+        [5, 6, 7, 12, 345, 21, -78, -7, -89]
+    ) == [-1705, -2071, -2412, -4106, -118035, -9774, 25998, 2981, 5509,
+          -34317, 19228, 38870, 5485, 1724, -4436, -7743]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_recurrences.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_recurrences.py
new file mode 100644
index 0000000000000000000000000000000000000000..2c2186ca525b6680350a03edbe44ca88f8f95c3c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_recurrences.py
@@ -0,0 +1,59 @@
+from sympy.core.numbers import Rational
+from sympy.functions.combinatorial.numbers import fibonacci
+from sympy.core import S, symbols
+from sympy.testing.pytest import raises
+from sympy.discrete.recurrences import linrec
+
+def test_linrec():
+    assert linrec(coeffs=[1, 1], init=[1, 1], n=20) == 10946
+    assert linrec(coeffs=[1, 2, 3, 4, 5], init=[1, 1, 0, 2], n=10) == 1040
+    assert linrec(coeffs=[0, 0, 11, 13], init=[23, 27], n=25) == 59628567384
+    assert linrec(coeffs=[0, 0, 1, 1, 2], init=[1, 5, 3], n=15) == 165
+    assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=70) == \
+        56889923441670659718376223533331214868804815612050381493741233489928913241
+    assert linrec(coeffs=[0]*55 + [1, 1, 2, 3], init=[0]*50 + [1, 2, 3], n=4000) == \
+        702633573874937994980598979769135096432444135301118916539
+
+    assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=10**4)
+    assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=10**5)
+
+    assert all(linrec(coeffs=[1, 1], init=[0, 1], n=n) == fibonacci(n)
+                                                    for n in range(95, 115))
+
+    assert all(linrec(coeffs=[1, 1], init=[1, 1], n=n) == fibonacci(n + 1)
+                                                    for n in range(595, 615))
+
+    a = [S.Half, Rational(3, 4), Rational(5, 6), 7, Rational(8, 9), Rational(3, 5)]
+    b = [1, 2, 8, Rational(5, 7), Rational(3, 7), Rational(2, 9), 6]
+    x, y, z = symbols('x y z')
+
+    assert linrec(coeffs=a[:5], init=b[:4], n=80) == \
+        Rational(1726244235456268979436592226626304376013002142588105090705187189,
+            1960143456748895967474334873705475211264)
+
+    assert linrec(coeffs=a[:4], init=b[:4], n=50) == \
+        Rational(368949940033050147080268092104304441, 504857282956046106624)
+
+    assert linrec(coeffs=a[3:], init=b[:3], n=35) == \
+        Rational(97409272177295731943657945116791049305244422833125109,
+            814315512679031689453125)
+
+    assert linrec(coeffs=[0]*60 + [Rational(2, 3), Rational(4, 5)], init=b, n=3000) == \
+        Rational(26777668739896791448594650497024, 48084516708184142230517578125)
+
+    raises(TypeError, lambda: linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4, 5], n=1))
+    raises(TypeError, lambda: linrec(coeffs=a[:4], init=b[:5], n=10000))
+    raises(ValueError, lambda: linrec(coeffs=a[:4], init=b[:4], n=-10000))
+    raises(TypeError, lambda: linrec(x, b, n=10000))
+    raises(TypeError, lambda: linrec(a, y, n=10000))
+
+    assert linrec(coeffs=[x, y, z], init=[1, 1, 1], n=4) == \
+        x**2  + x*y + x*z + y + z
+    assert linrec(coeffs=[1, 2, 1], init=[x, y, z], n=20) == \
+        269542*x + 664575*y + 578949*z
+    assert linrec(coeffs=[0, 3, 1, 2], init=[x, y], n=30) == \
+        58516436*x + 56372788*y
+    assert linrec(coeffs=[0]*50 + [1, 2, 3], init=[x, y, z], n=1000) == \
+        11477135884896*x + 25999077948732*y + 41975630244216*z
+    assert linrec(coeffs=[], init=[1, 1], n=20) == 0
+    assert linrec(coeffs=[x, y, z], init=[1, 2, 3], n=2) == 3
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_transforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..385514be4cdec2f19cf3a750bdbe0f4f6e21cc6e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/tests/test_transforms.py
@@ -0,0 +1,154 @@
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.core import S, Symbol, symbols, I, Rational
+from sympy.discrete import (fft, ifft, ntt, intt, fwht, ifwht,
+    mobius_transform, inverse_mobius_transform)
+from sympy.testing.pytest import raises
+
+
+def test_fft_ifft():
+    assert all(tf(ls) == ls for tf in (fft, ifft)
+                            for ls in ([], [Rational(5, 3)]))
+
+    ls = list(range(6))
+    fls = [15, -7*sqrt(2)/2 - 4 - sqrt(2)*I/2 + 2*I, 2 + 3*I,
+             -4 + 7*sqrt(2)/2 - 2*I - sqrt(2)*I/2, -3,
+             -4 + 7*sqrt(2)/2 + sqrt(2)*I/2 + 2*I,
+              2 - 3*I, -7*sqrt(2)/2 - 4 - 2*I + sqrt(2)*I/2]
+
+    assert fft(ls) == fls
+    assert ifft(fls) == ls + [S.Zero]*2
+
+    ls = [1 + 2*I, 3 + 4*I, 5 + 6*I]
+    ifls = [Rational(9, 4) + 3*I, I*Rational(-7, 4), Rational(3, 4) + I, -2 - I/4]
+
+    assert ifft(ls) == ifls
+    assert fft(ifls) == ls + [S.Zero]
+
+    x = Symbol('x', real=True)
+    raises(TypeError, lambda: fft(x))
+    raises(ValueError, lambda: ifft([x, 2*x, 3*x**2, 4*x**3]))
+
+
+def test_ntt_intt():
+    # prime moduli of the form (m*2**k + 1), sequence length
+    # should be a divisor of 2**k
+    p = 7*17*2**23 + 1
+    q = 2*500000003 + 1 # only for sequences of length 1 or 2
+    r = 2*3*5*7 # composite modulus
+
+    assert all(tf(ls, p) == ls for tf in (ntt, intt)
+                                for ls in ([], [5]))
+
+    ls = list(range(6))
+    nls = [15, 801133602, 738493201, 334102277, 998244350, 849020224,
+            259751156, 12232587]
+
+    assert ntt(ls, p) == nls
+    assert intt(nls, p) == ls + [0]*2
+
+    ls = [1 + 2*I, 3 + 4*I, 5 + 6*I]
+    x = Symbol('x', integer=True)
+
+    raises(TypeError, lambda: ntt(x, p))
+    raises(ValueError, lambda: intt([x, 2*x, 3*x**2, 4*x**3], p))
+    raises(ValueError, lambda: intt(ls, p))
+    raises(ValueError, lambda: ntt([1.2, 2.1, 3.5], p))
+    raises(ValueError, lambda: ntt([3, 5, 6], q))
+    raises(ValueError, lambda: ntt([4, 5, 7], r))
+    raises(ValueError, lambda: ntt([1.0, 2.0, 3.0], p))
+
+
+def test_fwht_ifwht():
+    assert all(tf(ls) == ls for tf in (fwht, ifwht) \
+                        for ls in ([], [Rational(7, 4)]))
+
+    ls = [213, 321, 43235, 5325, 312, 53]
+    fls = [49459, 38061, -47661, -37759, 48729, 37543, -48391, -38277]
+
+    assert fwht(ls) == fls
+    assert ifwht(fls) == ls + [S.Zero]*2
+
+    ls = [S.Half + 2*I, Rational(3, 7) + 4*I, Rational(5, 6) + 6*I, Rational(7, 3), Rational(9, 4)]
+    ifls = [Rational(533, 672) + I*3/2, Rational(23, 224) + I/2, Rational(1, 672), Rational(107, 224) - I,
+        Rational(155, 672) + I*3/2, Rational(-103, 224) + I/2, Rational(-377, 672), Rational(-19, 224) - I]
+
+    assert ifwht(ls) == ifls
+    assert fwht(ifls) == ls + [S.Zero]*3
+
+    x, y = symbols('x y')
+
+    raises(TypeError, lambda: fwht(x))
+
+    ls = [x, 2*x, 3*x**2, 4*x**3]
+    ifls = [x**3 + 3*x**2/4 + x*Rational(3, 4),
+        -x**3 + 3*x**2/4 - x/4,
+        -x**3 - 3*x**2/4 + x*Rational(3, 4),
+        x**3 - 3*x**2/4 - x/4]
+
+    assert ifwht(ls) == ifls
+    assert fwht(ifls) == ls
+
+    ls = [x, y, x**2, y**2, x*y]
+    fls = [x**2 + x*y + x + y**2 + y,
+        x**2 + x*y + x - y**2 - y,
+        -x**2 + x*y + x - y**2 + y,
+        -x**2 + x*y + x + y**2 - y,
+        x**2 - x*y + x + y**2 + y,
+        x**2 - x*y + x - y**2 - y,
+        -x**2 - x*y + x - y**2 + y,
+        -x**2 - x*y + x + y**2 - y]
+
+    assert fwht(ls) == fls
+    assert ifwht(fls) == ls + [S.Zero]*3
+
+    ls = list(range(6))
+
+    assert fwht(ls) == [x*8 for x in ifwht(ls)]
+
+
+def test_mobius_transform():
+    assert all(tf(ls, subset=subset) == ls
+                for ls in ([], [Rational(7, 4)]) for subset in (True, False)
+                for tf in (mobius_transform, inverse_mobius_transform))
+
+    w, x, y, z = symbols('w x y z')
+
+    assert mobius_transform([x, y]) == [x, x + y]
+    assert inverse_mobius_transform([x, x + y]) == [x, y]
+    assert mobius_transform([x, y], subset=False) == [x + y, y]
+    assert inverse_mobius_transform([x + y, y], subset=False) == [x, y]
+
+    assert mobius_transform([w, x, y, z]) == [w, w + x, w + y, w + x + y + z]
+    assert inverse_mobius_transform([w, w + x, w + y, w + x + y + z]) == \
+            [w, x, y, z]
+    assert mobius_transform([w, x, y, z], subset=False) == \
+            [w + x + y + z, x + z, y + z, z]
+    assert inverse_mobius_transform([w + x + y + z, x + z, y + z, z], subset=False) == \
+            [w, x, y, z]
+
+    ls = [Rational(2, 3), Rational(6, 7), Rational(5, 8), 9, Rational(5, 3) + 7*I]
+    mls = [Rational(2, 3), Rational(32, 21), Rational(31, 24), Rational(1873, 168),
+            Rational(7, 3) + 7*I, Rational(67, 21) + 7*I, Rational(71, 24) + 7*I,
+            Rational(2153, 168) + 7*I]
+
+    assert mobius_transform(ls) == mls
+    assert inverse_mobius_transform(mls) == ls + [S.Zero]*3
+
+    mls = [Rational(2153, 168) + 7*I, Rational(69, 7), Rational(77, 8), 9, Rational(5, 3) + 7*I, 0, 0, 0]
+
+    assert mobius_transform(ls, subset=False) == mls
+    assert inverse_mobius_transform(mls, subset=False) == ls + [S.Zero]*3
+
+    ls = ls[:-1]
+    mls = [Rational(2, 3), Rational(32, 21), Rational(31, 24), Rational(1873, 168)]
+
+    assert mobius_transform(ls) == mls
+    assert inverse_mobius_transform(mls) == ls
+
+    mls = [Rational(1873, 168), Rational(69, 7), Rational(77, 8), 9]
+
+    assert mobius_transform(ls, subset=False) == mls
+    assert inverse_mobius_transform(mls, subset=False) == ls
+
+    raises(TypeError, lambda: mobius_transform(x, subset=True))
+    raises(TypeError, lambda: inverse_mobius_transform(y, subset=False))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/transforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..cb3550837021a4cf99e38c6b15f89ce8bb69b25a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/discrete/transforms.py
@@ -0,0 +1,425 @@
+"""
+Discrete Fourier Transform, Number Theoretic Transform,
+Walsh Hadamard Transform, Mobius Transform
+"""
+
+from sympy.core import S, Symbol, sympify
+from sympy.core.function import expand_mul
+from sympy.core.numbers import pi, I
+from sympy.functions.elementary.trigonometric import sin, cos
+from sympy.ntheory import isprime, primitive_root
+from sympy.utilities.iterables import ibin, iterable
+from sympy.utilities.misc import as_int
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                         Discrete Fourier Transform                         #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def _fourier_transform(seq, dps, inverse=False):
+    """Utility function for the Discrete Fourier Transform"""
+
+    if not iterable(seq):
+        raise TypeError("Expected a sequence of numeric coefficients "
+                        "for Fourier Transform")
+
+    a = [sympify(arg) for arg in seq]
+    if any(x.has(Symbol) for x in a):
+        raise ValueError("Expected non-symbolic coefficients")
+
+    n = len(a)
+    if n < 2:
+        return a
+
+    b = n.bit_length() - 1
+    if n&(n - 1): # not a power of 2
+        b += 1
+        n = 2**b
+
+    a += [S.Zero]*(n - len(a))
+    for i in range(1, n):
+        j = int(ibin(i, b, str=True)[::-1], 2)
+        if i < j:
+            a[i], a[j] = a[j], a[i]
+
+    ang = -2*pi/n if inverse else 2*pi/n
+
+    if dps is not None:
+        ang = ang.evalf(dps + 2)
+
+    w = [cos(ang*i) + I*sin(ang*i) for i in range(n // 2)]
+
+    h = 2
+    while h <= n:
+        hf, ut = h // 2, n // h
+        for i in range(0, n, h):
+            for j in range(hf):
+                u, v = a[i + j], expand_mul(a[i + j + hf]*w[ut * j])
+                a[i + j], a[i + j + hf] = u + v, u - v
+        h *= 2
+
+    if inverse:
+        a = [(x/n).evalf(dps) for x in a] if dps is not None \
+                            else [x/n for x in a]
+
+    return a
+
+
+def fft(seq, dps=None):
+    r"""
+    Performs the Discrete Fourier Transform (**DFT**) in the complex domain.
+
+    The sequence is automatically padded to the right with zeros, as the
+    *radix-2 FFT* requires the number of sample points to be a power of 2.
+
+    This method should be used with default arguments only for short sequences
+    as the complexity of expressions increases with the size of the sequence.
+
+    Parameters
+    ==========
+
+    seq : iterable
+        The sequence on which **DFT** is to be applied.
+    dps : Integer
+        Specifies the number of decimal digits for precision.
+
+    Examples
+    ========
+
+    >>> from sympy import fft, ifft
+
+    >>> fft([1, 2, 3, 4])
+    [10, -2 - 2*I, -2, -2 + 2*I]
+    >>> ifft(_)
+    [1, 2, 3, 4]
+
+    >>> ifft([1, 2, 3, 4])
+    [5/2, -1/2 + I/2, -1/2, -1/2 - I/2]
+    >>> fft(_)
+    [1, 2, 3, 4]
+
+    >>> ifft([1, 7, 3, 4], dps=15)
+    [3.75, -0.5 - 0.75*I, -1.75, -0.5 + 0.75*I]
+    >>> fft(_)
+    [1.0, 7.0, 3.0, 4.0]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm
+    .. [2] https://mathworld.wolfram.com/FastFourierTransform.html
+
+    """
+
+    return _fourier_transform(seq, dps=dps)
+
+
+def ifft(seq, dps=None):
+    return _fourier_transform(seq, dps=dps, inverse=True)
+
+ifft.__doc__ = fft.__doc__
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                         Number Theoretic Transform                         #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def _number_theoretic_transform(seq, prime, inverse=False):
+    """Utility function for the Number Theoretic Transform"""
+
+    if not iterable(seq):
+        raise TypeError("Expected a sequence of integer coefficients "
+                        "for Number Theoretic Transform")
+
+    p = as_int(prime)
+    if not isprime(p):
+        raise ValueError("Expected prime modulus for "
+                        "Number Theoretic Transform")
+
+    a = [as_int(x) % p for x in seq]
+
+    n = len(a)
+    if n < 1:
+        return a
+
+    b = n.bit_length() - 1
+    if n&(n - 1):
+        b += 1
+        n = 2**b
+
+    if (p - 1) % n:
+        raise ValueError("Expected prime modulus of the form (m*2**k + 1)")
+
+    a += [0]*(n - len(a))
+    for i in range(1, n):
+        j = int(ibin(i, b, str=True)[::-1], 2)
+        if i < j:
+            a[i], a[j] = a[j], a[i]
+
+    pr = primitive_root(p)
+
+    rt = pow(pr, (p - 1) // n, p)
+    if inverse:
+        rt = pow(rt, p - 2, p)
+
+    w = [1]*(n // 2)
+    for i in range(1, n // 2):
+        w[i] = w[i - 1]*rt % p
+
+    h = 2
+    while h <= n:
+        hf, ut = h // 2, n // h
+        for i in range(0, n, h):
+            for j in range(hf):
+                u, v = a[i + j], a[i + j + hf]*w[ut * j]
+                a[i + j], a[i + j + hf] = (u + v) % p, (u - v) % p
+        h *= 2
+
+    if inverse:
+        rv = pow(n, p - 2, p)
+        a = [x*rv % p for x in a]
+
+    return a
+
+
+def ntt(seq, prime):
+    r"""
+    Performs the Number Theoretic Transform (**NTT**), which specializes the
+    Discrete Fourier Transform (**DFT**) over quotient ring `Z/pZ` for prime
+    `p` instead of complex numbers `C`.
+
+    The sequence is automatically padded to the right with zeros, as the
+    *radix-2 NTT* requires the number of sample points to be a power of 2.
+
+    Parameters
+    ==========
+
+    seq : iterable
+        The sequence on which **DFT** is to be applied.
+    prime : Integer
+        Prime modulus of the form `(m 2^k + 1)` to be used for performing
+        **NTT** on the sequence.
+
+    Examples
+    ========
+
+    >>> from sympy import ntt, intt
+    >>> ntt([1, 2, 3, 4], prime=3*2**8 + 1)
+    [10, 643, 767, 122]
+    >>> intt(_, 3*2**8 + 1)
+    [1, 2, 3, 4]
+    >>> intt([1, 2, 3, 4], prime=3*2**8 + 1)
+    [387, 415, 384, 353]
+    >>> ntt(_, prime=3*2**8 + 1)
+    [1, 2, 3, 4]
+
+    References
+    ==========
+
+    .. [1] http://www.apfloat.org/ntt.html
+    .. [2] https://mathworld.wolfram.com/NumberTheoreticTransform.html
+    .. [3] https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general%29
+
+    """
+
+    return _number_theoretic_transform(seq, prime=prime)
+
+
+def intt(seq, prime):
+    return _number_theoretic_transform(seq, prime=prime, inverse=True)
+
+intt.__doc__ = ntt.__doc__
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                          Walsh Hadamard Transform                          #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def _walsh_hadamard_transform(seq, inverse=False):
+    """Utility function for the Walsh Hadamard Transform"""
+
+    if not iterable(seq):
+        raise TypeError("Expected a sequence of coefficients "
+                        "for Walsh Hadamard Transform")
+
+    a = [sympify(arg) for arg in seq]
+    n = len(a)
+    if n < 2:
+        return a
+
+    if n&(n - 1):
+        n = 2**n.bit_length()
+
+    a += [S.Zero]*(n - len(a))
+    h = 2
+    while h <= n:
+        hf = h // 2
+        for i in range(0, n, h):
+            for j in range(hf):
+                u, v = a[i + j], a[i + j + hf]
+                a[i + j], a[i + j + hf] = u + v, u - v
+        h *= 2
+
+    if inverse:
+        a = [x/n for x in a]
+
+    return a
+
+
+def fwht(seq):
+    r"""
+    Performs the Walsh Hadamard Transform (**WHT**), and uses Hadamard
+    ordering for the sequence.
+
+    The sequence is automatically padded to the right with zeros, as the
+    *radix-2 FWHT* requires the number of sample points to be a power of 2.
+
+    Parameters
+    ==========
+
+    seq : iterable
+        The sequence on which WHT is to be applied.
+
+    Examples
+    ========
+
+    >>> from sympy import fwht, ifwht
+    >>> fwht([4, 2, 2, 0, 0, 2, -2, 0])
+    [8, 0, 8, 0, 8, 8, 0, 0]
+    >>> ifwht(_)
+    [4, 2, 2, 0, 0, 2, -2, 0]
+
+    >>> ifwht([19, -1, 11, -9, -7, 13, -15, 5])
+    [2, 0, 4, 0, 3, 10, 0, 0]
+    >>> fwht(_)
+    [19, -1, 11, -9, -7, 13, -15, 5]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hadamard_transform
+    .. [2] https://en.wikipedia.org/wiki/Fast_Walsh%E2%80%93Hadamard_transform
+
+    """
+
+    return _walsh_hadamard_transform(seq)
+
+
+def ifwht(seq):
+    return _walsh_hadamard_transform(seq, inverse=True)
+
+ifwht.__doc__ = fwht.__doc__
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                    Mobius Transform for Subset Lattice                     #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+def _mobius_transform(seq, sgn, subset):
+    r"""Utility function for performing Mobius Transform using
+    Yate's Dynamic Programming method"""
+
+    if not iterable(seq):
+        raise TypeError("Expected a sequence of coefficients")
+
+    a = [sympify(arg) for arg in seq]
+
+    n = len(a)
+    if n < 2:
+        return a
+
+    if n&(n - 1):
+        n = 2**n.bit_length()
+
+    a += [S.Zero]*(n - len(a))
+
+    if subset:
+        i = 1
+        while i < n:
+            for j in range(n):
+                if j & i:
+                    a[j] += sgn*a[j ^ i]
+            i *= 2
+
+    else:
+        i = 1
+        while i < n:
+            for j in range(n):
+                if j & i:
+                    continue
+                a[j] += sgn*a[j ^ i]
+            i *= 2
+
+    return a
+
+
+def mobius_transform(seq, subset=True):
+    r"""
+    Performs the Mobius Transform for subset lattice with indices of
+    sequence as bitmasks.
+
+    The indices of each argument, considered as bit strings, correspond
+    to subsets of a finite set.
+
+    The sequence is automatically padded to the right with zeros, as the
+    definition of subset/superset based on bitmasks (indices) requires
+    the size of sequence to be a power of 2.
+
+    Parameters
+    ==========
+
+    seq : iterable
+        The sequence on which Mobius Transform is to be applied.
+    subset : bool
+        Specifies if Mobius Transform is applied by enumerating subsets
+        or supersets of the given set.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy import mobius_transform, inverse_mobius_transform
+    >>> x, y, z = symbols('x y z')
+
+    >>> mobius_transform([x, y, z])
+    [x, x + y, x + z, x + y + z]
+    >>> inverse_mobius_transform(_)
+    [x, y, z, 0]
+
+    >>> mobius_transform([x, y, z], subset=False)
+    [x + y + z, y, z, 0]
+    >>> inverse_mobius_transform(_, subset=False)
+    [x, y, z, 0]
+
+    >>> mobius_transform([1, 2, 3, 4])
+    [1, 3, 4, 10]
+    >>> inverse_mobius_transform(_)
+    [1, 2, 3, 4]
+    >>> mobius_transform([1, 2, 3, 4], subset=False)
+    [10, 6, 7, 4]
+    >>> inverse_mobius_transform(_, subset=False)
+    [1, 2, 3, 4]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula
+    .. [2] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf
+    .. [3] https://arxiv.org/pdf/1211.0189.pdf
+
+    """
+
+    return _mobius_transform(seq, sgn=+1, subset=subset)
+
+def inverse_mobius_transform(seq, subset=True):
+    return _mobius_transform(seq, sgn=-1, subset=subset)
+
+inverse_mobius_transform.__doc__ = mobius_transform.__doc__
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..549b4b96cdce0ee4d31960e89cb9dc26af0e105d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/__init__.py
@@ -0,0 +1,20 @@
+"""
+Unified place for determining if external dependencies are installed or not.
+
+You should import all external modules using the import_module() function.
+
+For example
+
+>>> from sympy.external import import_module
+>>> numpy = import_module('numpy')
+
+If the resulting library is not installed, or if the installed version
+is less than a given minimum version, the function will return None.
+Otherwise, it will return the library. See the docstring of
+import_module() for more information.
+
+"""
+
+from sympy.external.importtools import import_module
+
+__all__ = ['import_module']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/gmpy.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/gmpy.py
new file mode 100644
index 0000000000000000000000000000000000000000..d26942864bf4786e72198d3640d488857b3313f4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/gmpy.py
@@ -0,0 +1,342 @@
+from __future__ import annotations
+import os
+from ctypes import c_long, sizeof
+from functools import reduce
+from typing import Type
+from warnings import warn
+
+from sympy.external import import_module
+
+from .pythonmpq import PythonMPQ
+
+from .ntheory import (
+    bit_scan1 as python_bit_scan1,
+    bit_scan0 as python_bit_scan0,
+    remove as python_remove,
+    factorial as python_factorial,
+    sqrt as python_sqrt,
+    sqrtrem as python_sqrtrem,
+    gcd as python_gcd,
+    lcm as python_lcm,
+    gcdext as python_gcdext,
+    is_square as python_is_square,
+    invert as python_invert,
+    legendre as python_legendre,
+    jacobi as python_jacobi,
+    kronecker as python_kronecker,
+    iroot as python_iroot,
+    is_fermat_prp as python_is_fermat_prp,
+    is_euler_prp as python_is_euler_prp,
+    is_strong_prp as python_is_strong_prp,
+    is_fibonacci_prp as python_is_fibonacci_prp,
+    is_lucas_prp as python_is_lucas_prp,
+    is_selfridge_prp as python_is_selfridge_prp,
+    is_strong_lucas_prp as python_is_strong_lucas_prp,
+    is_strong_selfridge_prp as python_is_strong_selfridge_prp,
+    is_bpsw_prp as python_is_bpsw_prp,
+    is_strong_bpsw_prp as python_is_strong_bpsw_prp,
+)
+
+
+__all__ = [
+    # GROUND_TYPES is either 'gmpy' or 'python' depending on which is used. If
+    # gmpy is installed then it will be used unless the environment variable
+    # SYMPY_GROUND_TYPES is set to something other than 'auto', 'gmpy', or
+    # 'gmpy2'.
+    'GROUND_TYPES',
+
+    # If HAS_GMPY is 0, no supported version of gmpy is available. Otherwise,
+    # HAS_GMPY will be 2 for gmpy2 if GROUND_TYPES is 'gmpy'. It used to be
+    # possible for HAS_GMPY to be 1 for gmpy but gmpy is no longer supported.
+    'HAS_GMPY',
+
+    # SYMPY_INTS is a tuple containing the base types for valid integer types.
+    # This is either (int,) or (int, type(mpz(0))) depending on GROUND_TYPES.
+    'SYMPY_INTS',
+
+    # MPQ is either gmpy.mpq or the Python equivalent from
+    # sympy.external.pythonmpq
+    'MPQ',
+
+    # MPZ is either gmpy.mpz or int.
+    'MPZ',
+
+    'bit_scan1',
+    'bit_scan0',
+    'remove',
+    'factorial',
+    'sqrt',
+    'is_square',
+    'sqrtrem',
+    'gcd',
+    'lcm',
+    'gcdext',
+    'invert',
+    'legendre',
+    'jacobi',
+    'kronecker',
+    'iroot',
+    'is_fermat_prp',
+    'is_euler_prp',
+    'is_strong_prp',
+    'is_fibonacci_prp',
+    'is_lucas_prp',
+    'is_selfridge_prp',
+    'is_strong_lucas_prp',
+    'is_strong_selfridge_prp',
+    'is_bpsw_prp',
+    'is_strong_bpsw_prp',
+]
+
+
+#
+# Tested python-flint version. Future versions might work but we will only use
+# them if explicitly requested by SYMPY_GROUND_TYPES=flint.
+#
+_PYTHON_FLINT_VERSION_NEEDED = ["0.6", "0.7", "0.8", "0.9", "0.10"]
+
+
+def _flint_version_okay(flint_version):
+    major, minor = flint_version.split('.')[:2]
+    flint_ver = f'{major}.{minor}'
+    return flint_ver in _PYTHON_FLINT_VERSION_NEEDED
+
+#
+# We will only use gmpy2 >= 2.0.0
+#
+_GMPY2_MIN_VERSION = '2.0.0'
+
+
+def _get_flint(sympy_ground_types):
+    if sympy_ground_types not in ('auto', 'flint'):
+        return None
+
+    try:
+        import flint
+        # Earlier versions of python-flint may not have __version__.
+        from flint import __version__ as _flint_version
+    except ImportError:
+        if sympy_ground_types == 'flint':
+            warn("SYMPY_GROUND_TYPES was set to flint but python-flint is not "
+                 "installed. Falling back to other ground types.")
+        return None
+
+    if _flint_version_okay(_flint_version):
+        return flint
+    elif sympy_ground_types == 'auto':
+        return None
+    else:
+        warn(f"Using python-flint {_flint_version} because SYMPY_GROUND_TYPES "
+             f"is set to flint but this version of SymPy is only tested "
+             f"with python-flint versions {_PYTHON_FLINT_VERSION_NEEDED}.")
+        return flint
+
+
+def _get_gmpy2(sympy_ground_types):
+    if sympy_ground_types not in ('auto', 'gmpy', 'gmpy2'):
+        return None
+
+    gmpy = import_module('gmpy2', min_module_version=_GMPY2_MIN_VERSION,
+            module_version_attr='version', module_version_attr_call_args=())
+
+    if sympy_ground_types != 'auto' and gmpy is None:
+        warn("gmpy2 library is not installed, switching to 'python' ground types")
+
+    return gmpy
+
+
+#
+# SYMPY_GROUND_TYPES can be flint, gmpy, gmpy2, python or auto (default)
+#
+_SYMPY_GROUND_TYPES = os.environ.get('SYMPY_GROUND_TYPES', 'auto').lower()
+_flint = None
+_gmpy = None
+
+#
+# First handle auto-detection of flint/gmpy2. We will prefer flint if available
+# or otherwise gmpy2 if available and then lastly the python types.
+#
+if _SYMPY_GROUND_TYPES in ('auto', 'flint'):
+    _flint = _get_flint(_SYMPY_GROUND_TYPES)
+    if _flint is not None:
+        _SYMPY_GROUND_TYPES = 'flint'
+    else:
+        _SYMPY_GROUND_TYPES = 'auto'
+
+if _SYMPY_GROUND_TYPES in ('auto', 'gmpy', 'gmpy2'):
+    _gmpy = _get_gmpy2(_SYMPY_GROUND_TYPES)
+    if _gmpy is not None:
+        _SYMPY_GROUND_TYPES = 'gmpy'
+    else:
+        _SYMPY_GROUND_TYPES = 'python'
+
+if _SYMPY_GROUND_TYPES not in ('flint', 'gmpy', 'python'):
+    warn("SYMPY_GROUND_TYPES environment variable unrecognised. "
+         "Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'.")
+    _SYMPY_GROUND_TYPES = 'python'
+
+#
+# At this point _SYMPY_GROUND_TYPES is either flint, gmpy or python. The blocks
+# below define the values exported by this module in each case.
+#
+
+#
+# In gmpy2 and flint, there are functions that take a long (or unsigned long)
+# argument. That is, it is not possible to input a value larger than that.
+#
+LONG_MAX = (1 << (8*sizeof(c_long) - 1)) - 1
+
+#
+# Type checkers are confused by what SYMPY_INTS is. There may be a better type
+# hint for this like Type[Integral] or something.
+#
+SYMPY_INTS: tuple[Type, ...]
+
+if _SYMPY_GROUND_TYPES == 'gmpy':
+
+    assert _gmpy is not None
+
+    flint = None
+    gmpy = _gmpy
+
+    HAS_GMPY = 2
+    GROUND_TYPES = 'gmpy'
+    SYMPY_INTS = (int, type(gmpy.mpz(0)))
+    MPZ = gmpy.mpz
+    MPQ = gmpy.mpq
+
+    bit_scan1 = gmpy.bit_scan1
+    bit_scan0 = gmpy.bit_scan0
+    remove = gmpy.remove
+    factorial = gmpy.fac
+    sqrt = gmpy.isqrt
+    is_square = gmpy.is_square
+    sqrtrem = gmpy.isqrt_rem
+    gcd = gmpy.gcd
+    lcm = gmpy.lcm
+    gcdext = gmpy.gcdext
+    invert = gmpy.invert
+    legendre = gmpy.legendre
+    jacobi = gmpy.jacobi
+    kronecker = gmpy.kronecker
+
+    def iroot(x, n):
+        # In the latest gmpy2, the threshold for n is ULONG_MAX,
+        # but adjust to the older one.
+        if n <= LONG_MAX:
+            return gmpy.iroot(x, n)
+        return python_iroot(x, n)
+
+    is_fermat_prp = gmpy.is_fermat_prp
+    is_euler_prp = gmpy.is_euler_prp
+    is_strong_prp = gmpy.is_strong_prp
+    is_fibonacci_prp = gmpy.is_fibonacci_prp
+    is_lucas_prp = gmpy.is_lucas_prp
+    is_selfridge_prp = gmpy.is_selfridge_prp
+    is_strong_lucas_prp = gmpy.is_strong_lucas_prp
+    is_strong_selfridge_prp = gmpy.is_strong_selfridge_prp
+    is_bpsw_prp = gmpy.is_bpsw_prp
+    is_strong_bpsw_prp = gmpy.is_strong_bpsw_prp
+
+elif _SYMPY_GROUND_TYPES == 'flint':
+
+    assert _flint is not None
+
+    flint = _flint
+    gmpy = None
+
+    HAS_GMPY = 0
+    GROUND_TYPES = 'flint'
+    SYMPY_INTS = (int, flint.fmpz) # type: ignore
+    MPZ = flint.fmpz # type: ignore
+    MPQ = flint.fmpq # type: ignore
+
+    bit_scan1 = python_bit_scan1
+    bit_scan0 = python_bit_scan0
+    remove = python_remove
+    factorial = python_factorial
+
+    def sqrt(x):
+        return flint.fmpz(x).isqrt()
+
+    def is_square(x):
+        if x < 0:
+            return False
+        return flint.fmpz(x).sqrtrem()[1] == 0
+
+    def sqrtrem(x):
+        return flint.fmpz(x).sqrtrem()
+
+    def gcd(*args):
+        return reduce(flint.fmpz.gcd, args, flint.fmpz(0))
+
+    def lcm(*args):
+        return reduce(flint.fmpz.lcm, args, flint.fmpz(1))
+
+    gcdext = python_gcdext
+    invert = python_invert
+    legendre = python_legendre
+
+    def jacobi(x, y):
+        if y <= 0 or not y % 2:
+            raise ValueError("y should be an odd positive integer")
+        return flint.fmpz(x).jacobi(y)
+
+    kronecker = python_kronecker
+
+    def iroot(x, n):
+        if n <= LONG_MAX:
+            y = flint.fmpz(x).root(n)
+            return y, y**n == x
+        return python_iroot(x, n)
+
+    is_fermat_prp = python_is_fermat_prp
+    is_euler_prp = python_is_euler_prp
+    is_strong_prp = python_is_strong_prp
+    is_fibonacci_prp = python_is_fibonacci_prp
+    is_lucas_prp = python_is_lucas_prp
+    is_selfridge_prp = python_is_selfridge_prp
+    is_strong_lucas_prp = python_is_strong_lucas_prp
+    is_strong_selfridge_prp = python_is_strong_selfridge_prp
+    is_bpsw_prp = python_is_bpsw_prp
+    is_strong_bpsw_prp = python_is_strong_bpsw_prp
+
+elif _SYMPY_GROUND_TYPES == 'python':
+
+    flint = None
+    gmpy = None
+
+    HAS_GMPY = 0
+    GROUND_TYPES = 'python'
+    SYMPY_INTS = (int,)
+    MPZ = int
+    MPQ = PythonMPQ
+
+    bit_scan1 = python_bit_scan1
+    bit_scan0 = python_bit_scan0
+    remove = python_remove
+    factorial = python_factorial
+    sqrt = python_sqrt
+    is_square = python_is_square
+    sqrtrem = python_sqrtrem
+    gcd = python_gcd
+    lcm = python_lcm
+    gcdext = python_gcdext
+    invert = python_invert
+    legendre = python_legendre
+    jacobi = python_jacobi
+    kronecker = python_kronecker
+    iroot = python_iroot
+    is_fermat_prp = python_is_fermat_prp
+    is_euler_prp = python_is_euler_prp
+    is_strong_prp = python_is_strong_prp
+    is_fibonacci_prp = python_is_fibonacci_prp
+    is_lucas_prp = python_is_lucas_prp
+    is_selfridge_prp = python_is_selfridge_prp
+    is_strong_lucas_prp = python_is_strong_lucas_prp
+    is_strong_selfridge_prp = python_is_strong_selfridge_prp
+    is_bpsw_prp = python_is_bpsw_prp
+    is_strong_bpsw_prp = python_is_strong_bpsw_prp
+
+else:
+    assert False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/importtools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/importtools.py
new file mode 100644
index 0000000000000000000000000000000000000000..5008b3dd4634d3cee10744a0a92b1204051f07cc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/importtools.py
@@ -0,0 +1,187 @@
+"""Tools to assist importing optional external modules."""
+
+import sys
+import re
+
+# Override these in the module to change the default warning behavior.
+# For example, you might set both to False before running the tests so that
+# warnings are not printed to the console, or set both to True for debugging.
+
+WARN_NOT_INSTALLED = None  # Default is False
+WARN_OLD_VERSION = None  # Default is True
+
+
+def __sympy_debug():
+    # helper function from sympy/__init__.py
+    # We don't just import SYMPY_DEBUG from that file because we don't want to
+    # import all of SymPy just to use this module.
+    import os
+    debug_str = os.getenv('SYMPY_DEBUG', 'False')
+    if debug_str in ('True', 'False'):
+        return eval(debug_str)
+    else:
+        raise RuntimeError("unrecognized value for SYMPY_DEBUG: %s" %
+                           debug_str)
+
+if __sympy_debug():
+    WARN_OLD_VERSION = True
+    WARN_NOT_INSTALLED = True
+
+
+_component_re = re.compile(r'(\d+ | [a-z]+ | \.)', re.VERBOSE)
+
+def version_tuple(vstring):
+    # Parse a version string to a tuple e.g. '1.2' -> (1, 2)
+    # Simplified from distutils.version.LooseVersion which was deprecated in
+    # Python 3.10.
+    components = []
+    for x in _component_re.split(vstring):
+        if x and x != '.':
+            try:
+                x = int(x)
+            except ValueError:
+                pass
+            components.append(x)
+    return tuple(components)
+
+
+def import_module(module, min_module_version=None, min_python_version=None,
+        warn_not_installed=None, warn_old_version=None,
+        module_version_attr='__version__', module_version_attr_call_args=None,
+        import_kwargs={}, catch=()):
+    """
+    Import and return a module if it is installed.
+
+    If the module is not installed, it returns None.
+
+    A minimum version for the module can be given as the keyword argument
+    min_module_version.  This should be comparable against the module version.
+    By default, module.__version__ is used to get the module version.  To
+    override this, set the module_version_attr keyword argument.  If the
+    attribute of the module to get the version should be called (e.g.,
+    module.version()), then set module_version_attr_call_args to the args such
+    that module.module_version_attr(*module_version_attr_call_args) returns the
+    module's version.
+
+    If the module version is less than min_module_version using the Python <
+    comparison, None will be returned, even if the module is installed. You can
+    use this to keep from importing an incompatible older version of a module.
+
+    You can also specify a minimum Python version by using the
+    min_python_version keyword argument.  This should be comparable against
+    sys.version_info.
+
+    If the keyword argument warn_not_installed is set to True, the function will
+    emit a UserWarning when the module is not installed.
+
+    If the keyword argument warn_old_version is set to True, the function will
+    emit a UserWarning when the library is installed, but cannot be imported
+    because of the min_module_version or min_python_version options.
+
+    Note that because of the way warnings are handled, a warning will be
+    emitted for each module only once.  You can change the default warning
+    behavior by overriding the values of WARN_NOT_INSTALLED and WARN_OLD_VERSION
+    in sympy.external.importtools.  By default, WARN_NOT_INSTALLED is False and
+    WARN_OLD_VERSION is True.
+
+    This function uses __import__() to import the module.  To pass additional
+    options to __import__(), use the import_kwargs keyword argument.  For
+    example, to import a submodule A.B, you must pass a nonempty fromlist option
+    to __import__.  See the docstring of __import__().
+
+    This catches ImportError to determine if the module is not installed.  To
+    catch additional errors, pass them as a tuple to the catch keyword
+    argument.
+
+    Examples
+    ========
+
+    >>> from sympy.external import import_module
+
+    >>> numpy = import_module('numpy')
+
+    >>> numpy = import_module('numpy', min_python_version=(2, 7),
+    ... warn_old_version=False)
+
+    >>> numpy = import_module('numpy', min_module_version='1.5',
+    ... warn_old_version=False) # numpy.__version__ is a string
+
+    >>> # gmpy does not have __version__, but it does have gmpy.version()
+
+    >>> gmpy = import_module('gmpy', min_module_version='1.14',
+    ... module_version_attr='version', module_version_attr_call_args=(),
+    ... warn_old_version=False)
+
+    >>> # To import a submodule, you must pass a nonempty fromlist to
+    >>> # __import__().  The values do not matter.
+    >>> p3 = import_module('mpl_toolkits.mplot3d',
+    ... import_kwargs={'fromlist':['something']})
+
+    >>> # matplotlib.pyplot can raise RuntimeError when the display cannot be opened
+    >>> matplotlib = import_module('matplotlib',
+    ... import_kwargs={'fromlist':['pyplot']}, catch=(RuntimeError,))
+
+    """
+    # keyword argument overrides default, and global variable overrides
+    # keyword argument.
+    warn_old_version = (WARN_OLD_VERSION if WARN_OLD_VERSION is not None
+        else warn_old_version or True)
+    warn_not_installed = (WARN_NOT_INSTALLED if WARN_NOT_INSTALLED is not None
+        else warn_not_installed or False)
+
+    import warnings
+
+    # Check Python first so we don't waste time importing a module we can't use
+    if min_python_version:
+        if sys.version_info < min_python_version:
+            if warn_old_version:
+                warnings.warn("Python version is too old to use %s "
+                    "(%s or newer required)" % (
+                        module, '.'.join(map(str, min_python_version))),
+                    UserWarning, stacklevel=2)
+            return
+
+    try:
+        mod = __import__(module, **import_kwargs)
+
+        ## there's something funny about imports with matplotlib and py3k. doing
+        ##    from matplotlib import collections
+        ## gives python's stdlib collections module. explicitly re-importing
+        ## the module fixes this.
+        from_list = import_kwargs.get('fromlist', ())
+        for submod in from_list:
+            if submod == 'collections' and mod.__name__ == 'matplotlib':
+                __import__(module + '.' + submod)
+    except ImportError:
+        if warn_not_installed:
+            warnings.warn("%s module is not installed" % module, UserWarning,
+                    stacklevel=2)
+        return
+    except catch as e:
+        if warn_not_installed:
+            warnings.warn(
+                "%s module could not be used (%s)" % (module, repr(e)),
+                stacklevel=2)
+        return
+
+    if min_module_version:
+        modversion = getattr(mod, module_version_attr)
+        if module_version_attr_call_args is not None:
+            modversion = modversion(*module_version_attr_call_args)
+        if version_tuple(modversion) < version_tuple(min_module_version):
+            if warn_old_version:
+                # Attempt to create a pretty string version of the version
+                if isinstance(min_module_version, str):
+                    verstr = min_module_version
+                elif isinstance(min_module_version, (tuple, list)):
+                    verstr = '.'.join(map(str, min_module_version))
+                else:
+                    # Either don't know what this is.  Hopefully
+                    # it's something that has a nice str version, like an int.
+                    verstr = str(min_module_version)
+                warnings.warn("%s version is too old to use "
+                    "(%s or newer required)" % (module, verstr),
+                    UserWarning, stacklevel=2)
+            return
+
+    return mod
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/ntheory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/ntheory.py
new file mode 100644
index 0000000000000000000000000000000000000000..a0c9bf813cf02b311f9a12ee7fbc4932ed551f3b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/ntheory.py
@@ -0,0 +1,618 @@
+# sympy.external.ntheory
+#
+# This module provides pure Python implementations of some number theory
+# functions that are alternately used from gmpy2 if it is installed.
+
+import math
+
+import mpmath.libmp as mlib
+
+
+_small_trailing = [0] * 256
+for j in range(1, 8):
+    _small_trailing[1 << j :: 1 << (j + 1)] = [j] * (1 << (7 - j))
+
+
+def bit_scan1(x, n=0):
+    if not x:
+        return
+    x = abs(x >> n)
+    low_byte = x & 0xFF
+    if low_byte:
+        return _small_trailing[low_byte] + n
+
+    t = 8 + n
+    x >>= 8
+    # 2**m is quick for z up through 2**30
+    z = x.bit_length() - 1
+    if x == 1 << z:
+        return z + t
+
+    if z < 300:
+        # fixed 8-byte reduction
+        while not x & 0xFF:
+            x >>= 8
+            t += 8
+    else:
+        # binary reduction important when there might be a large
+        # number of trailing 0s
+        p = z >> 1
+        while not x & 0xFF:
+            while x & ((1 << p) - 1):
+                p >>= 1
+            x >>= p
+            t += p
+    return t + _small_trailing[x & 0xFF]
+
+
+def bit_scan0(x, n=0):
+    return bit_scan1(x + (1 << n), n)
+
+
+def remove(x, f):
+    if f < 2:
+        raise ValueError("factor must be > 1")
+    if x == 0:
+        return 0, 0
+    if f == 2:
+        b = bit_scan1(x)
+        return x >> b, b
+    m = 0
+    y, rem = divmod(x, f)
+    while not rem:
+        x = y
+        m += 1
+        if m > 5:
+            pow_list = [f**2]
+            while pow_list:
+                _f = pow_list[-1]
+                y, rem = divmod(x, _f)
+                if not rem:
+                    m += 1 << len(pow_list)
+                    x = y
+                    pow_list.append(_f**2)
+                else:
+                    pow_list.pop()
+        y, rem = divmod(x, f)
+    return x, m
+
+
+def factorial(x):
+    """Return x!."""
+    return int(mlib.ifac(int(x)))
+
+
+def sqrt(x):
+    """Integer square root of x."""
+    return int(mlib.isqrt(int(x)))
+
+
+def sqrtrem(x):
+    """Integer square root of x and remainder."""
+    s, r = mlib.sqrtrem(int(x))
+    return (int(s), int(r))
+
+
+gcd = math.gcd
+lcm = math.lcm
+
+
+def _sign(n):
+    if n < 0:
+        return -1, -n
+    return 1, n
+
+
+def gcdext(a, b):
+    if not a or not b:
+        g = abs(a) or abs(b)
+        if not g:
+            return (0, 0, 0)
+        return (g, a // g, b // g)
+
+    x_sign, a = _sign(a)
+    y_sign, b = _sign(b)
+    x, r = 1, 0
+    y, s = 0, 1
+
+    while b:
+        q, c = divmod(a, b)
+        a, b = b, c
+        x, r = r, x - q*r
+        y, s = s, y - q*s
+
+    return (a, x * x_sign, y * y_sign)
+
+
+def is_square(x):
+    """Return True if x is a square number."""
+    if x < 0:
+        return False
+
+    # Note that the possible values of y**2 % n for a given n are limited.
+    # For example, when n=4, y**2 % n can only take 0 or 1.
+    # In other words, if x % 4 is 2 or 3, then x is not a square number.
+    # Mathematically, it determines if it belongs to the set {y**2 % n},
+    # but implementationally, it can be realized as a logical conjunction
+    # with an n-bit integer.
+    # see https://mersenneforum.org/showpost.php?p=110896
+    # def magic(n):
+    #     s = {y**2 % n for y in range(n)}
+    #     s = set(range(n)) - s
+    #     return sum(1 << bit for bit in s)
+    # >>> print(hex(magic(128)))
+    # 0xfdfdfdedfdfdfdecfdfdfdedfdfcfdec
+    # >>> print(hex(magic(99)))
+    # 0x5f6f9ffb6fb7ddfcb75befdec
+    # >>> print(hex(magic(91)))
+    # 0x6fd1bfcfed5f3679d3ebdec
+    # >>> print(hex(magic(85)))
+    # 0xdef9ae771ffe3b9d67dec
+    if 0xfdfdfdedfdfdfdecfdfdfdedfdfcfdec & (1 << (x & 127)):
+        return False  # e.g. 2, 3
+    m = x % 765765 # 765765 = 99 * 91 * 85
+    if 0x5f6f9ffb6fb7ddfcb75befdec & (1 << (m % 99)):
+        return False  # e.g. 17, 68
+    if 0x6fd1bfcfed5f3679d3ebdec & (1 << (m % 91)):
+        return False  # e.g. 97, 388
+    if 0xdef9ae771ffe3b9d67dec & (1 << (m % 85)):
+        return False  # e.g. 793, 1408
+    return mlib.sqrtrem(int(x))[1] == 0
+
+
+def invert(x, m):
+    """Modular inverse of x modulo m.
+
+    Returns y such that x*y == 1 mod m.
+
+    Uses ``math.pow`` but reproduces the behaviour of ``gmpy2.invert``
+    which raises ZeroDivisionError if no inverse exists.
+    """
+    try:
+        return pow(x, -1, m)
+    except ValueError:
+        raise ZeroDivisionError("invert() no inverse exists")
+
+
+def legendre(x, y):
+    """Legendre symbol (x / y).
+
+    Following the implementation of gmpy2,
+    the error is raised only when y is an even number.
+    """
+    if y <= 0 or not y % 2:
+        raise ValueError("y should be an odd prime")
+    x %= y
+    if not x:
+        return 0
+    if pow(x, (y - 1) // 2, y) == 1:
+        return 1
+    return -1
+
+
+def jacobi(x, y):
+    """Jacobi symbol (x / y)."""
+    if y <= 0 or not y % 2:
+        raise ValueError("y should be an odd positive integer")
+    x %= y
+    if not x:
+        return int(y == 1)
+    if y == 1 or x == 1:
+        return 1
+    if gcd(x, y) != 1:
+        return 0
+    j = 1
+    while x != 0:
+        while x % 2 == 0 and x > 0:
+            x >>= 1
+            if y % 8 in [3, 5]:
+                j = -j
+        x, y = y, x
+        if x % 4 == y % 4 == 3:
+            j = -j
+        x %= y
+    return j
+
+
+def kronecker(x, y):
+    """Kronecker symbol (x / y)."""
+    if gcd(x, y) != 1:
+        return 0
+    if y == 0:
+        return 1
+    sign = -1 if y < 0 and x < 0 else 1
+    y = abs(y)
+    s = bit_scan1(y)
+    y >>= s
+    if s % 2 and x % 8 in [3, 5]:
+        sign = -sign
+    return sign * jacobi(x, y)
+
+
+def iroot(y, n):
+    if y < 0:
+        raise ValueError("y must be nonnegative")
+    if n < 1:
+        raise ValueError("n must be positive")
+    if y in (0, 1):
+        return y, True
+    if n == 1:
+        return y, True
+    if n == 2:
+        x, rem = mlib.sqrtrem(y)
+        return int(x), not rem
+    if n >= y.bit_length():
+        return 1, False
+    # Get initial estimate for Newton's method. Care must be taken to
+    # avoid overflow
+    try:
+        guess = int(y**(1./n) + 0.5)
+    except OverflowError:
+        exp = math.log2(y)/n
+        if exp > 53:
+            shift = int(exp - 53)
+            guess = int(2.0**(exp - shift) + 1) << shift
+        else:
+            guess = int(2.0**exp)
+    if guess > 2**50:
+        # Newton iteration
+        xprev, x = -1, guess
+        while 1:
+            t = x**(n - 1)
+            xprev, x = x, ((n - 1)*x + y//t)//n
+            if abs(x - xprev) < 2:
+                break
+    else:
+        x = guess
+    # Compensate
+    t = x**n
+    while t < y:
+        x += 1
+        t = x**n
+    while t > y:
+        x -= 1
+        t = x**n
+    return x, t == y
+
+
+def is_fermat_prp(n, a):
+    if a < 2:
+        raise ValueError("is_fermat_prp() requires 'a' greater than or equal to 2")
+    if n < 1:
+        raise ValueError("is_fermat_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    a %= n
+    if gcd(n, a) != 1:
+        raise ValueError("is_fermat_prp() requires gcd(n,a) == 1")
+    return pow(a, n - 1, n) == 1
+
+
+def is_euler_prp(n, a):
+    if a < 2:
+        raise ValueError("is_euler_prp() requires 'a' greater than or equal to 2")
+    if n < 1:
+        raise ValueError("is_euler_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    a %= n
+    if gcd(n, a) != 1:
+        raise ValueError("is_euler_prp() requires gcd(n,a) == 1")
+    return pow(a, n >> 1, n) == jacobi(a, n) % n
+
+
+def _is_strong_prp(n, a):
+    s = bit_scan1(n - 1)
+    a = pow(a, n >> s, n)
+    if a == 1 or a == n - 1:
+        return True
+    for _ in range(s - 1):
+        a = pow(a, 2, n)
+        if a == n - 1:
+            return True
+        if a == 1:
+            return False
+    return False
+
+
+def is_strong_prp(n, a):
+    if a < 2:
+        raise ValueError("is_strong_prp() requires 'a' greater than or equal to 2")
+    if n < 1:
+        raise ValueError("is_strong_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    a %= n
+    if gcd(n, a) != 1:
+        raise ValueError("is_strong_prp() requires gcd(n,a) == 1")
+    return _is_strong_prp(n, a)
+
+
+def _lucas_sequence(n, P, Q, k):
+    r"""Return the modular Lucas sequence (U_k, V_k, Q_k).
+
+    Explanation
+    ===========
+
+    Given a Lucas sequence defined by P, Q, returns the kth values for
+    U and V, along with Q^k, all modulo n. This is intended for use with
+    possibly very large values of n and k, where the combinatorial functions
+    would be completely unusable.
+
+    .. math ::
+        U_k = \begin{cases}
+             0 & \text{if } k = 0\\
+             1 & \text{if } k = 1\\
+             PU_{k-1} - QU_{k-2} & \text{if } k > 1
+        \end{cases}\\
+        V_k = \begin{cases}
+             2 & \text{if } k = 0\\
+             P & \text{if } k = 1\\
+             PV_{k-1} - QV_{k-2} & \text{if } k > 1
+        \end{cases}
+
+    The modular Lucas sequences are used in numerous places in number theory,
+    especially in the Lucas compositeness tests and the various n + 1 proofs.
+
+    Parameters
+    ==========
+
+    n : int
+        n is an odd number greater than or equal to 3
+    P : int
+    Q : int
+        D determined by D = P**2 - 4*Q is non-zero
+    k : int
+        k is a nonnegative integer
+
+    Returns
+    =======
+
+    U, V, Qk : (int, int, int)
+        `(U_k \bmod{n}, V_k \bmod{n}, Q^k \bmod{n})`
+
+    Examples
+    ========
+
+    >>> from sympy.external.ntheory import _lucas_sequence
+    >>> N = 10**2000 + 4561
+    >>> sol = U, V, Qk = _lucas_sequence(N, 3, 1, N//2); sol
+    (0, 2, 1)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Lucas_sequence
+
+    """
+    if k == 0:
+        return (0, 2, 1)
+    D = P**2 - 4*Q
+    U = 1
+    V = P
+    Qk = Q % n
+    if Q == 1:
+        # Optimization for extra strong tests.
+        for b in bin(k)[3:]:
+            U = (U*V) % n
+            V = (V*V - 2) % n
+            if b == "1":
+                U, V = U*P + V, V*P + U*D
+                if U & 1:
+                    U += n
+                if V & 1:
+                    V += n
+                U, V = U >> 1, V >> 1
+    elif P == 1 and Q == -1:
+        # Small optimization for 50% of Selfridge parameters.
+        for b in bin(k)[3:]:
+            U = (U*V) % n
+            if Qk == 1:
+                V = (V*V - 2) % n
+            else:
+                V = (V*V + 2) % n
+                Qk = 1
+            if b == "1":
+                # new_U = (U + V) // 2
+                # new_V = (5*U + V) // 2 = 2*U + new_U
+                U, V  = U + V, U << 1
+                if U & 1:
+                    U += n
+                U >>= 1
+                V += U
+                Qk = -1
+        Qk %= n
+    elif P == 1:
+        for b in bin(k)[3:]:
+            U = (U*V) % n
+            V = (V*V - 2*Qk) % n
+            Qk *= Qk
+            if b == "1":
+                # new_U = (U + V) // 2
+                # new_V = new_U - 2*Q*U
+                U, V  = U + V, (Q*U) << 1
+                if U & 1:
+                    U += n
+                U >>= 1
+                V = U - V
+                Qk *= Q
+            Qk %= n
+    else:
+        # The general case with any P and Q.
+        for b in bin(k)[3:]:
+            U = (U*V) % n
+            V = (V*V - 2*Qk) % n
+            Qk *= Qk
+            if b == "1":
+                U, V = U*P + V, V*P + U*D
+                if U & 1:
+                    U += n
+                if V & 1:
+                    V += n
+                U, V = U >> 1, V >> 1
+                Qk *= Q
+            Qk %= n
+    return (U % n, V % n, Qk)
+
+
+def is_fibonacci_prp(n, p, q):
+    d = p**2 - 4*q
+    if d == 0 or p <= 0 or q not in [1, -1]:
+        raise ValueError("invalid values for p,q in is_fibonacci_prp()")
+    if n < 1:
+        raise ValueError("is_fibonacci_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    return _lucas_sequence(n, p, q, n)[1] == p % n
+
+
+def is_lucas_prp(n, p, q):
+    d = p**2 - 4*q
+    if d == 0:
+        raise ValueError("invalid values for p,q in is_lucas_prp()")
+    if n < 1:
+        raise ValueError("is_lucas_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    if gcd(n, q*d) not in [1, n]:
+        raise ValueError("is_lucas_prp() requires gcd(n,2*q*D) == 1")
+    return _lucas_sequence(n, p, q, n - jacobi(d, n))[0] == 0
+
+
+def _is_selfridge_prp(n):
+    """Lucas compositeness test with the Selfridge parameters for n.
+
+    Explanation
+    ===========
+
+    The Lucas compositeness test checks whether n is a prime number.
+    The test can be run with arbitrary parameters ``P`` and ``Q``, which also change the performance of the test.
+    So, which parameters are most effective for running the Lucas compositeness test?
+    As an algorithm for determining ``P`` and ``Q``, Selfridge proposed method A [1]_ page 1401
+    (Since two methods were proposed, referred to simply as A and B in the paper,
+    we will refer to one of them as "method A").
+
+    method A fixes ``P = 1``. Then, ``D`` defined by ``D = P**2 - 4Q`` is varied from 5, -7, 9, -11, 13, and so on,
+    with the first ``D`` being ``jacobi(D, n) == -1``. Once ``D`` is determined,
+    ``Q`` is determined to be ``(P**2 - D)//4``.
+
+    References
+    ==========
+
+    .. [1] Robert Baillie, Samuel S. Wagstaff, Lucas Pseudoprimes,
+           Math. Comp. Vol 35, Number 152 (1980), pp. 1391-1417,
+           https://doi.org/10.1090%2FS0025-5718-1980-0583518-6
+           http://mpqs.free.fr/LucasPseudoprimes.pdf
+
+    """
+    for D in range(5, 1_000_000, 2):
+        if D & 2: # if D % 4 == 3
+            D = -D
+        j = jacobi(D, n)
+        if j == -1:
+            return _lucas_sequence(n, 1, (1-D) // 4, n + 1)[0] == 0
+        if j == 0 and D % n:
+            return False
+        # When j == -1 is hard to find, suspect a square number
+        if D == 13 and is_square(n):
+            return False
+    raise ValueError("appropriate value for D cannot be found in is_selfridge_prp()")
+
+
+def is_selfridge_prp(n):
+    if n < 1:
+        raise ValueError("is_selfridge_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    return _is_selfridge_prp(n)
+
+
+def is_strong_lucas_prp(n, p, q):
+    D = p**2 - 4*q
+    if D == 0:
+        raise ValueError("invalid values for p,q in is_strong_lucas_prp()")
+    if n < 1:
+        raise ValueError("is_selfridge_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    if gcd(n, q*D) not in [1, n]:
+        raise ValueError("is_strong_lucas_prp() requires gcd(n,2*q*D) == 1")
+    j = jacobi(D, n)
+    s = bit_scan1(n - j)
+    U, V, Qk = _lucas_sequence(n, p, q, (n - j) >> s)
+    if U == 0 or V == 0:
+        return True
+    for _ in range(s - 1):
+        V = (V*V - 2*Qk) % n
+        if V == 0:
+            return True
+        Qk = pow(Qk, 2, n)
+    return False
+
+
+def _is_strong_selfridge_prp(n):
+    for D in range(5, 1_000_000, 2):
+        if D & 2: # if D % 4 == 3
+            D = -D
+        j = jacobi(D, n)
+        if j == -1:
+            s = bit_scan1(n + 1)
+            U, V, Qk = _lucas_sequence(n, 1, (1-D) // 4, (n + 1) >> s)
+            if U == 0 or V == 0:
+                return True
+            for _ in range(s - 1):
+                V = (V*V - 2*Qk) % n
+                if V == 0:
+                    return True
+                Qk = pow(Qk, 2, n)
+            return False
+        if j == 0 and D % n:
+            return False
+        # When j == -1 is hard to find, suspect a square number
+        if D == 13 and is_square(n):
+            return False
+    raise ValueError("appropriate value for D cannot be found in is_strong_selfridge_prp()")
+
+
+def is_strong_selfridge_prp(n):
+    if n < 1:
+        raise ValueError("is_strong_selfridge_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    return _is_strong_selfridge_prp(n)
+
+
+def is_bpsw_prp(n):
+    if n < 1:
+        raise ValueError("is_bpsw_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    return _is_strong_prp(n, 2) and _is_selfridge_prp(n)
+
+
+def is_strong_bpsw_prp(n):
+    if n < 1:
+        raise ValueError("is_strong_bpsw_prp() requires 'n' be greater than 0")
+    if n == 1:
+        return False
+    if n % 2 == 0:
+        return n == 2
+    return _is_strong_prp(n, 2) and _is_strong_selfridge_prp(n)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/pythonmpq.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/pythonmpq.py
new file mode 100644
index 0000000000000000000000000000000000000000..4f2d102974e04e139c00a39057976b5a5bf90776
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/pythonmpq.py
@@ -0,0 +1,341 @@
+"""
+PythonMPQ: Rational number type based on Python integers.
+
+This class is intended as a pure Python fallback for when gmpy2 is not
+installed. If gmpy2 is installed then its mpq type will be used instead. The
+mpq type is around 20x faster. We could just use the stdlib Fraction class
+here but that is slower:
+
+    from fractions import Fraction
+    from sympy.external.pythonmpq import PythonMPQ
+    nums = range(1000)
+    dens = range(5, 1005)
+    rats = [Fraction(n, d) for n, d in zip(nums, dens)]
+    sum(rats) # <--- 24 milliseconds
+    rats = [PythonMPQ(n, d) for n, d in zip(nums, dens)]
+    sum(rats) # <---  7 milliseconds
+
+Both mpq and Fraction have some awkward features like the behaviour of
+division with // and %:
+
+    >>> from fractions import Fraction
+    >>> Fraction(2, 3) % Fraction(1, 4)
+    1/6
+
+For the QQ domain we do not want this behaviour because there should be no
+remainder when dividing rational numbers. SymPy does not make use of this
+aspect of mpq when gmpy2 is installed. Since this class is a fallback for that
+case we do not bother implementing e.g. __mod__ so that we can be sure we
+are not using it when gmpy2 is installed either.
+"""
+
+from __future__ import annotations
+import operator
+from math import gcd
+from decimal import Decimal
+from fractions import Fraction
+import sys
+from typing import Type
+
+
+# Used for __hash__
+_PyHASH_MODULUS = sys.hash_info.modulus
+_PyHASH_INF = sys.hash_info.inf
+
+
+class PythonMPQ:
+    """Rational number implementation that is intended to be compatible with
+    gmpy2's mpq.
+
+    Also slightly faster than fractions.Fraction.
+
+    PythonMPQ should be treated as immutable although no effort is made to
+    prevent mutation (since that might slow down calculations).
+    """
+    __slots__ = ('numerator', 'denominator')
+
+    def __new__(cls, numerator, denominator=None):
+        """Construct PythonMPQ with gcd computation and checks"""
+        if denominator is not None:
+            #
+            # PythonMPQ(n, d): require n and d to be int and d != 0
+            #
+            if isinstance(numerator, int) and isinstance(denominator, int):
+                # This is the slow part:
+                divisor = gcd(numerator, denominator)
+                numerator //= divisor
+                denominator //= divisor
+                return cls._new_check(numerator, denominator)
+        else:
+            #
+            # PythonMPQ(q)
+            #
+            # Here q can be PythonMPQ, int, Decimal, float, Fraction or str
+            #
+            if isinstance(numerator, int):
+                return cls._new(numerator, 1)
+            elif isinstance(numerator, PythonMPQ):
+                return cls._new(numerator.numerator, numerator.denominator)
+
+            # Let Fraction handle Decimal/float conversion and str parsing
+            if isinstance(numerator, (Decimal, float, str)):
+                numerator = Fraction(numerator)
+            if isinstance(numerator, Fraction):
+                return cls._new(numerator.numerator, numerator.denominator)
+        #
+        # Reject everything else. This is more strict than mpq which allows
+        # things like mpq(Fraction, Fraction) or mpq(Decimal, any). The mpq
+        # behaviour is somewhat inconsistent so we choose to accept only a
+        # more strict subset of what mpq allows.
+        #
+        raise TypeError("PythonMPQ() requires numeric or string argument")
+
+    @classmethod
+    def _new_check(cls, numerator, denominator):
+        """Construct PythonMPQ, check divide by zero and canonicalize signs"""
+        if not denominator:
+            raise ZeroDivisionError(f'Zero divisor {numerator}/{denominator}')
+        elif denominator < 0:
+            numerator = -numerator
+            denominator = -denominator
+        return cls._new(numerator, denominator)
+
+    @classmethod
+    def _new(cls, numerator, denominator):
+        """Construct PythonMPQ efficiently (no checks)"""
+        obj = super().__new__(cls)
+        obj.numerator = numerator
+        obj.denominator = denominator
+        return obj
+
+    def __int__(self):
+        """Convert to int (truncates towards zero)"""
+        p, q = self.numerator, self.denominator
+        if p < 0:
+            return -(-p//q)
+        return p//q
+
+    def __float__(self):
+        """Convert to float (approximately)"""
+        return self.numerator / self.denominator
+
+    def __bool__(self):
+        """True/False if nonzero/zero"""
+        return bool(self.numerator)
+
+    def __eq__(self, other):
+        """Compare equal with PythonMPQ, int, float, Decimal or Fraction"""
+        if isinstance(other, PythonMPQ):
+            return (self.numerator == other.numerator
+                and self.denominator == other.denominator)
+        elif isinstance(other, self._compatible_types):
+            return self.__eq__(PythonMPQ(other))
+        else:
+            return NotImplemented
+
+    def __hash__(self):
+        """hash - same as mpq/Fraction"""
+        try:
+            dinv = pow(self.denominator, -1, _PyHASH_MODULUS)
+        except ValueError:
+            hash_ = _PyHASH_INF
+        else:
+            hash_ = hash(hash(abs(self.numerator)) * dinv)
+        result = hash_ if self.numerator >= 0 else -hash_
+        return -2 if result == -1 else result
+
+    def __reduce__(self):
+        """Deconstruct for pickling"""
+        return type(self), (self.numerator, self.denominator)
+
+    def __str__(self):
+        """Convert to string"""
+        if self.denominator != 1:
+            return f"{self.numerator}/{self.denominator}"
+        else:
+            return f"{self.numerator}"
+
+    def __repr__(self):
+        """Convert to string"""
+        return f"MPQ({self.numerator},{self.denominator})"
+
+    def _cmp(self, other, op):
+        """Helper for lt/le/gt/ge"""
+        if not isinstance(other, self._compatible_types):
+            return NotImplemented
+        lhs = self.numerator * other.denominator
+        rhs = other.numerator * self.denominator
+        return op(lhs, rhs)
+
+    def __lt__(self, other):
+        """self < other"""
+        return self._cmp(other, operator.lt)
+
+    def __le__(self, other):
+        """self <= other"""
+        return self._cmp(other, operator.le)
+
+    def __gt__(self, other):
+        """self > other"""
+        return self._cmp(other, operator.gt)
+
+    def __ge__(self, other):
+        """self >= other"""
+        return self._cmp(other, operator.ge)
+
+    def __abs__(self):
+        """abs(q)"""
+        return self._new(abs(self.numerator), self.denominator)
+
+    def __pos__(self):
+        """+q"""
+        return self
+
+    def __neg__(self):
+        """-q"""
+        return self._new(-self.numerator, self.denominator)
+
+    def __add__(self, other):
+        """q1 + q2"""
+        if isinstance(other, PythonMPQ):
+            #
+            # This is much faster than the naive method used in the stdlib
+            # fractions module. Not sure where this method comes from
+            # though...
+            #
+            # Compare timings for something like:
+            #   nums = range(1000)
+            #   rats = [PythonMPQ(n, d) for n, d in zip(nums[:-5], nums[5:])]
+            #   sum(rats) # <-- time this
+            #
+            ap, aq = self.numerator, self.denominator
+            bp, bq = other.numerator, other.denominator
+            g = gcd(aq, bq)
+            if g == 1:
+                p = ap*bq + aq*bp
+                q = bq*aq
+            else:
+                q1, q2 = aq//g, bq//g
+                p, q = ap*q2 + bp*q1, q1*q2
+                g2 = gcd(p, g)
+                p, q = (p // g2), q * (g // g2)
+
+        elif isinstance(other, int):
+            p = self.numerator + self.denominator * other
+            q = self.denominator
+        else:
+            return NotImplemented
+
+        return self._new(p, q)
+
+    def __radd__(self, other):
+        """z1 + q2"""
+        if isinstance(other, int):
+            p = self.numerator + self.denominator * other
+            q = self.denominator
+            return self._new(p, q)
+        else:
+            return NotImplemented
+
+    def __sub__(self ,other):
+        """q1 - q2"""
+        if isinstance(other, PythonMPQ):
+            ap, aq = self.numerator, self.denominator
+            bp, bq = other.numerator, other.denominator
+            g = gcd(aq, bq)
+            if g == 1:
+                p = ap*bq - aq*bp
+                q = bq*aq
+            else:
+                q1, q2 = aq//g, bq//g
+                p, q = ap*q2 - bp*q1, q1*q2
+                g2 = gcd(p, g)
+                p, q = (p // g2), q * (g // g2)
+        elif isinstance(other, int):
+            p = self.numerator - self.denominator*other
+            q = self.denominator
+        else:
+            return NotImplemented
+
+        return self._new(p, q)
+
+    def __rsub__(self, other):
+        """z1 - q2"""
+        if isinstance(other, int):
+            p = self.denominator * other - self.numerator
+            q = self.denominator
+            return self._new(p, q)
+        else:
+            return NotImplemented
+
+    def __mul__(self, other):
+        """q1 * q2"""
+        if isinstance(other, PythonMPQ):
+            ap, aq = self.numerator, self.denominator
+            bp, bq = other.numerator, other.denominator
+            x1 = gcd(ap, bq)
+            x2 = gcd(bp, aq)
+            p, q = ((ap//x1)*(bp//x2), (aq//x2)*(bq//x1))
+        elif isinstance(other, int):
+            x = gcd(other, self.denominator)
+            p = self.numerator*(other//x)
+            q = self.denominator//x
+        else:
+            return NotImplemented
+
+        return self._new(p, q)
+
+    def __rmul__(self, other):
+        """z1 * q2"""
+        if isinstance(other, int):
+            x = gcd(self.denominator, other)
+            p = self.numerator*(other//x)
+            q = self.denominator//x
+            return self._new(p, q)
+        else:
+            return NotImplemented
+
+    def __pow__(self, exp):
+        """q ** z"""
+        p, q = self.numerator, self.denominator
+
+        if exp < 0:
+            p, q, exp = q, p, -exp
+
+        return self._new_check(p**exp, q**exp)
+
+    def __truediv__(self, other):
+        """q1 / q2"""
+        if isinstance(other, PythonMPQ):
+            ap, aq = self.numerator, self.denominator
+            bp, bq = other.numerator, other.denominator
+            x1 = gcd(ap, bp)
+            x2 = gcd(bq, aq)
+            p, q = ((ap//x1)*(bq//x2), (aq//x2)*(bp//x1))
+        elif isinstance(other, int):
+            x = gcd(other, self.numerator)
+            p = self.numerator//x
+            q = self.denominator*(other//x)
+        else:
+            return NotImplemented
+
+        return self._new_check(p, q)
+
+    def __rtruediv__(self, other):
+        """z / q"""
+        if isinstance(other, int):
+            x = gcd(self.numerator, other)
+            p = self.denominator*(other//x)
+            q = self.numerator//x
+            return self._new_check(p, q)
+        else:
+            return NotImplemented
+
+    _compatible_types: tuple[Type, ...] = ()
+
+#
+# These are the types that PythonMPQ will interoperate with for operations
+# and comparisons such as ==, + etc. We define this down here so that we can
+# include PythonMPQ in the list as well.
+#
+PythonMPQ._compatible_types = (PythonMPQ, int, Decimal, Fraction)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_autowrap.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_autowrap.py
new file mode 100644
index 0000000000000000000000000000000000000000..d469b552995b7625f786f3296089e41f42da75cb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_autowrap.py
@@ -0,0 +1,313 @@
+import sympy
+import tempfile
+import os
+from pathlib import Path
+from sympy.core.mod import Mod
+from sympy.core.relational import Eq
+from sympy.core.symbol import symbols
+from sympy.external import import_module
+from sympy.tensor import IndexedBase, Idx
+from sympy.utilities.autowrap import autowrap, ufuncify, CodeWrapError
+from sympy.testing.pytest import skip
+
+numpy = import_module('numpy', min_module_version='1.6.1')
+Cython = import_module('Cython', min_module_version='0.15.1')
+f2py = import_module('numpy.f2py', import_kwargs={'fromlist': ['f2py']})
+
+f2pyworks = False
+if f2py:
+    try:
+        autowrap(symbols('x'), 'f95', 'f2py')
+    except (CodeWrapError, ImportError, OSError):
+        f2pyworks = False
+    else:
+        f2pyworks = True
+
+a, b, c = symbols('a b c')
+n, m, d = symbols('n m d', integer=True)
+A, B, C = symbols('A B C', cls=IndexedBase)
+i = Idx('i', m)
+j = Idx('j', n)
+k = Idx('k', d)
+
+
+def has_module(module):
+    """
+    Return True if module exists, otherwise run skip().
+
+    module should be a string.
+    """
+    # To give a string of the module name to skip(), this function takes a
+    # string.  So we don't waste time running import_module() more than once,
+    # just map the three modules tested here in this dict.
+    modnames = {'numpy': numpy, 'Cython': Cython, 'f2py': f2py}
+
+    if modnames[module]:
+        if module == 'f2py' and not f2pyworks:
+            skip("Couldn't run f2py.")
+        return True
+    skip("Couldn't import %s." % module)
+
+#
+# test runners used by several language-backend combinations
+#
+
+def runtest_autowrap_twice(language, backend):
+    f = autowrap((((a + b)/c)**5).expand(), language, backend)
+    g = autowrap((((a + b)/c)**4).expand(), language, backend)
+
+    # check that autowrap updates the module name.  Else, g gives the same as f
+    assert f(1, -2, 1) == -1.0
+    assert g(1, -2, 1) == 1.0
+
+
+def runtest_autowrap_trace(language, backend):
+    has_module('numpy')
+    trace = autowrap(A[i, i], language, backend)
+    assert trace(numpy.eye(100)) == 100
+
+
+def runtest_autowrap_matrix_vector(language, backend):
+    has_module('numpy')
+    x, y = symbols('x y', cls=IndexedBase)
+    expr = Eq(y[i], A[i, j]*x[j])
+    mv = autowrap(expr, language, backend)
+
+    # compare with numpy's dot product
+    M = numpy.random.rand(10, 20)
+    x = numpy.random.rand(20)
+    y = numpy.dot(M, x)
+    assert numpy.sum(numpy.abs(y - mv(M, x))) < 1e-13
+
+
+def runtest_autowrap_matrix_matrix(language, backend):
+    has_module('numpy')
+    expr = Eq(C[i, j], A[i, k]*B[k, j])
+    matmat = autowrap(expr, language, backend)
+
+    # compare with numpy's dot product
+    M1 = numpy.random.rand(10, 20)
+    M2 = numpy.random.rand(20, 15)
+    M3 = numpy.dot(M1, M2)
+    assert numpy.sum(numpy.abs(M3 - matmat(M1, M2))) < 1e-13
+
+
+def runtest_ufuncify(language, backend):
+    has_module('numpy')
+    a, b, c = symbols('a b c')
+    fabc = ufuncify([a, b, c], a*b + c, backend=backend)
+    facb = ufuncify([a, c, b], a*b + c, backend=backend)
+    grid = numpy.linspace(-2, 2, 50)
+    b = numpy.linspace(-5, 4, 50)
+    c = numpy.linspace(-1, 1, 50)
+    expected = grid*b + c
+    numpy.testing.assert_allclose(fabc(grid, b, c), expected)
+    numpy.testing.assert_allclose(facb(grid, c, b), expected)
+
+
+def runtest_issue_10274(language, backend):
+    expr = (a - b + c)**(13)
+    tmp = tempfile.mkdtemp()
+    f = autowrap(expr, language, backend, tempdir=tmp,
+                 helpers=('helper', a - b + c, (a, b, c)))
+    assert f(1, 1, 1) == 1
+
+    for file in os.listdir(tmp):
+        if not (file.startswith("wrapped_code_") and file.endswith(".c")):
+            continue
+
+        with open(tmp + '/' + file) as fil:
+            lines = fil.readlines()
+            assert lines[0] == "/******************************************************************************\n"
+            assert "Code generated with SymPy " + sympy.__version__ in lines[1]
+            assert lines[2:] == [
+                " *                                                                            *\n",
+                " *              See http://www.sympy.org/ for more information.               *\n",
+                " *                                                                            *\n",
+                " *                      This file is part of 'autowrap'                       *\n",
+                " ******************************************************************************/\n",
+                "#include " + '"' + file[:-1]+ 'h"' + "\n",
+                "#include \n",
+                "\n",
+                "double helper(double a, double b, double c) {\n",
+                "\n",
+                "   double helper_result;\n",
+                "   helper_result = a - b + c;\n",
+                "   return helper_result;\n",
+                "\n",
+                "}\n",
+                "\n",
+                "double autofunc(double a, double b, double c) {\n",
+                "\n",
+                "   double autofunc_result;\n",
+                "   autofunc_result = pow(helper(a, b, c), 13);\n",
+                "   return autofunc_result;\n",
+                "\n",
+                "}\n",
+                ]
+
+
+def runtest_issue_15337(language, backend):
+    has_module('numpy')
+    # NOTE : autowrap was originally designed to only accept an iterable for
+    # the kwarg "helpers", but in issue 10274 the user mistakenly thought that
+    # if there was only a single helper it did not need to be passed via an
+    # iterable that wrapped the helper tuple. There were no tests for this
+    # behavior so when the code was changed to accept a single tuple it broke
+    # the original behavior. These tests below ensure that both now work.
+    a, b, c, d, e = symbols('a, b, c, d, e')
+    expr = (a - b + c - d + e)**13
+    exp_res = (1. - 2. + 3. - 4. + 5.)**13
+
+    f = autowrap(expr, language, backend, args=(a, b, c, d, e),
+                 helpers=('f1', a - b + c, (a, b, c)))
+    numpy.testing.assert_allclose(f(1, 2, 3, 4, 5), exp_res)
+
+    f = autowrap(expr, language, backend, args=(a, b, c, d, e),
+                 helpers=(('f1', a - b, (a, b)), ('f2', c - d, (c, d))))
+    numpy.testing.assert_allclose(f(1, 2, 3, 4, 5), exp_res)
+
+
+def test_issue_15230():
+    has_module('f2py')
+
+    x, y = symbols('x, y')
+    expr = Mod(x, 3.0) - Mod(y, -2.0)
+    f = autowrap(expr, args=[x, y], language='F95')
+    exp_res = float(expr.xreplace({x: 3.5, y: 2.7}).evalf())
+    assert abs(f(3.5, 2.7) - exp_res) < 1e-14
+
+    x, y = symbols('x, y', integer=True)
+    expr = Mod(x, 3) - Mod(y, -2)
+    f = autowrap(expr, args=[x, y], language='F95')
+    assert f(3, 2) == expr.xreplace({x: 3, y: 2})
+
+#
+# tests of language-backend combinations
+#
+
+# f2py
+
+
+def test_wrap_twice_f95_f2py():
+    has_module('f2py')
+    runtest_autowrap_twice('f95', 'f2py')
+
+
+def test_autowrap_trace_f95_f2py():
+    has_module('f2py')
+    runtest_autowrap_trace('f95', 'f2py')
+
+
+def test_autowrap_matrix_vector_f95_f2py():
+    has_module('f2py')
+    runtest_autowrap_matrix_vector('f95', 'f2py')
+
+
+def test_autowrap_matrix_matrix_f95_f2py():
+    has_module('f2py')
+    runtest_autowrap_matrix_matrix('f95', 'f2py')
+
+
+def test_ufuncify_f95_f2py():
+    has_module('f2py')
+    runtest_ufuncify('f95', 'f2py')
+
+
+def test_issue_15337_f95_f2py():
+    has_module('f2py')
+    runtest_issue_15337('f95', 'f2py')
+
+# Cython
+
+
+def test_wrap_twice_c_cython():
+    has_module('Cython')
+    runtest_autowrap_twice('C', 'cython')
+
+
+def test_autowrap_trace_C_Cython():
+    has_module('Cython')
+    runtest_autowrap_trace('C99', 'cython')
+
+
+def test_autowrap_matrix_vector_C_cython():
+    has_module('Cython')
+    runtest_autowrap_matrix_vector('C99', 'cython')
+
+
+def test_autowrap_matrix_matrix_C_cython():
+    has_module('Cython')
+    runtest_autowrap_matrix_matrix('C99', 'cython')
+
+
+def test_ufuncify_C_Cython():
+    has_module('Cython')
+    runtest_ufuncify('C99', 'cython')
+
+
+def test_issue_10274_C_cython():
+    has_module('Cython')
+    runtest_issue_10274('C89', 'cython')
+
+
+def test_issue_15337_C_cython():
+    has_module('Cython')
+    runtest_issue_15337('C89', 'cython')
+
+
+def test_autowrap_custom_printer():
+    has_module('Cython')
+
+    from sympy.core.numbers import pi
+    from sympy.utilities.codegen import C99CodeGen
+    from sympy.printing.c import C99CodePrinter
+
+    class PiPrinter(C99CodePrinter):
+        def _print_Pi(self, expr):
+            return "S_PI"
+
+    printer = PiPrinter()
+    gen = C99CodeGen(printer=printer)
+    gen.preprocessor_statements.append('#include "shortpi.h"')
+
+    expr = pi * a
+
+    expected = (
+        '#include "%s"\n'
+        '#include \n'
+        '#include "shortpi.h"\n'
+        '\n'
+        'double autofunc(double a) {\n'
+        '\n'
+        '   double autofunc_result;\n'
+        '   autofunc_result = S_PI*a;\n'
+        '   return autofunc_result;\n'
+        '\n'
+        '}\n'
+    )
+
+    tmpdir = tempfile.mkdtemp()
+    # write a trivial header file to use in the generated code
+    Path(os.path.join(tmpdir, 'shortpi.h')).write_text('#define S_PI 3.14')
+
+    func = autowrap(expr, backend='cython', tempdir=tmpdir, code_gen=gen)
+
+    assert func(4.2) == 3.14 * 4.2
+
+    # check that the generated code is correct
+    for filename in os.listdir(tmpdir):
+        if filename.startswith('wrapped_code') and filename.endswith('.c'):
+            with open(os.path.join(tmpdir, filename)) as f:
+                lines = f.readlines()
+                expected = expected % filename.replace('.c', '.h')
+                assert ''.join(lines[7:]) == expected
+
+
+# Numpy
+
+def test_ufuncify_numpy():
+    # This test doesn't use Cython, but if Cython works, then there is a valid
+    # C compiler, which is needed.
+    has_module('Cython')
+    runtest_ufuncify('C99', 'numpy')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_codegen.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_codegen.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a4fe28300b86fb0b38d98fcf2fcbbe514cf720f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_codegen.py
@@ -0,0 +1,375 @@
+# This tests the compilation and execution of the source code generated with
+# utilities.codegen. The compilation takes place in a temporary directory that
+# is removed after the test. By default the test directory is always removed,
+# but this behavior can be changed by setting the environment variable
+# SYMPY_TEST_CLEAN_TEMP to:
+#   export SYMPY_TEST_CLEAN_TEMP=always   : the default behavior.
+#   export SYMPY_TEST_CLEAN_TEMP=success  : only remove the directories of working tests.
+#   export SYMPY_TEST_CLEAN_TEMP=never    : never remove the directories with the test code.
+# When a directory is not removed, the necessary information is printed on
+# screen to find the files that belong to the (failed) tests. If a test does
+# not fail, py.test captures all the output and you will not see the directories
+# corresponding to the successful tests. Use the --nocapture option to see all
+# the output.
+
+# All tests below have a counterpart in utilities/test/test_codegen.py. In the
+# latter file, the resulting code is compared with predefined strings, without
+# compilation or execution.
+
+# All the generated Fortran code should conform with the Fortran 95 standard,
+# and all the generated C code should be ANSI C, which facilitates the
+# incorporation in various projects. The tests below assume that the binary cc
+# is somewhere in the path and that it can compile ANSI C code.
+
+from sympy.abc import x, y, z
+from sympy.testing.pytest import IS_WASM, skip
+from sympy.utilities.codegen import codegen, make_routine, get_code_generator
+import sys
+import os
+import tempfile
+import subprocess
+from pathlib import Path
+
+
+# templates for the main program that will test the generated code.
+
+main_template = {}
+main_template['F95'] = """
+program main
+  include "codegen.h"
+  integer :: result;
+  result = 0
+
+  %(statements)s
+
+  call exit(result)
+end program
+"""
+
+main_template['C89'] = """
+#include "codegen.h"
+#include 
+#include 
+
+int main() {
+  int result = 0;
+
+  %(statements)s
+
+  return result;
+}
+"""
+main_template['C99'] = main_template['C89']
+# templates for the numerical tests
+
+numerical_test_template = {}
+numerical_test_template['C89'] = """
+  if (fabs(%(call)s)>%(threshold)s) {
+    printf("Numerical validation failed: %(call)s=%%e threshold=%(threshold)s\\n", %(call)s);
+    result = -1;
+  }
+"""
+numerical_test_template['C99'] = numerical_test_template['C89']
+
+numerical_test_template['F95'] = """
+  if (abs(%(call)s)>%(threshold)s) then
+    write(6,"('Numerical validation failed:')")
+    write(6,"('%(call)s=',e15.5,'threshold=',e15.5)") %(call)s, %(threshold)s
+    result = -1;
+  end if
+"""
+# command sequences for supported compilers
+
+compile_commands = {}
+compile_commands['cc'] = [
+    "cc -c codegen.c -o codegen.o",
+    "cc -c main.c -o main.o",
+    "cc main.o codegen.o -lm -o test.exe"
+]
+
+compile_commands['gfortran'] = [
+    "gfortran -c codegen.f90 -o codegen.o",
+    "gfortran -ffree-line-length-none -c main.f90 -o main.o",
+    "gfortran main.o codegen.o -o test.exe"
+]
+
+compile_commands['g95'] = [
+    "g95 -c codegen.f90 -o codegen.o",
+    "g95 -ffree-line-length-huge -c main.f90 -o main.o",
+    "g95 main.o codegen.o -o test.exe"
+]
+
+compile_commands['ifort'] = [
+    "ifort -c codegen.f90 -o codegen.o",
+    "ifort -c main.f90 -o main.o",
+    "ifort main.o codegen.o -o test.exe"
+]
+
+combinations_lang_compiler = [
+    ('C89', 'cc'),
+    ('C99', 'cc'),
+    ('F95', 'ifort'),
+    ('F95', 'gfortran'),
+    ('F95', 'g95')
+]
+
+def try_run(commands):
+    """Run a series of commands and only return True if all ran fine."""
+    if IS_WASM:
+        return False
+    with open(os.devnull, 'w') as null:
+        for command in commands:
+            retcode = subprocess.call(command, stdout=null, shell=True,
+                    stderr=subprocess.STDOUT)
+            if retcode != 0:
+                return False
+    return True
+
+
+def run_test(label, routines, numerical_tests, language, commands, friendly=True):
+    """A driver for the codegen tests.
+
+       This driver assumes that a compiler ifort is present in the PATH and that
+       ifort is (at least) a Fortran 90 compiler. The generated code is written in
+       a temporary directory, together with a main program that validates the
+       generated code. The test passes when the compilation and the validation
+       run correctly.
+    """
+
+    # Check input arguments before touching the file system
+    language = language.upper()
+    assert language in main_template
+    assert language in numerical_test_template
+
+    # Check that environment variable makes sense
+    clean = os.getenv('SYMPY_TEST_CLEAN_TEMP', 'always').lower()
+    if clean not in ('always', 'success', 'never'):
+        raise ValueError("SYMPY_TEST_CLEAN_TEMP must be one of the following: 'always', 'success' or 'never'.")
+
+    # Do all the magic to compile, run and validate the test code
+    # 1) prepare the temporary working directory, switch to that dir
+    work = tempfile.mkdtemp("_sympy_%s_test" % language, "%s_" % label)
+    oldwork = os.getcwd()
+    os.chdir(work)
+
+    # 2) write the generated code
+    if friendly:
+        # interpret the routines as a name_expr list and call the friendly
+        # function codegen
+        codegen(routines, language, "codegen", to_files=True)
+    else:
+        code_gen = get_code_generator(language, "codegen")
+        code_gen.write(routines, "codegen", to_files=True)
+
+    # 3) write a simple main program that links to the generated code, and that
+    #    includes the numerical tests
+    test_strings = []
+    for fn_name, args, expected, threshold in numerical_tests:
+        call_string = "%s(%s)-(%s)" % (
+            fn_name, ",".join(str(arg) for arg in args), expected)
+        if language == "F95":
+            call_string = fortranize_double_constants(call_string)
+            threshold = fortranize_double_constants(str(threshold))
+        test_strings.append(numerical_test_template[language] % {
+            "call": call_string,
+            "threshold": threshold,
+        })
+
+    if language == "F95":
+        f_name = "main.f90"
+    elif language.startswith("C"):
+        f_name = "main.c"
+    else:
+        raise NotImplementedError(
+            "FIXME: filename extension unknown for language: %s" % language)
+
+    Path(f_name).write_text(
+        main_template[language] % {'statements': "".join(test_strings)})
+
+    # 4) Compile and link
+    compiled = try_run(commands)
+
+    # 5) Run if compiled
+    if compiled:
+        executed = try_run(["./test.exe"])
+    else:
+        executed = False
+
+    # 6) Clean up stuff
+    if clean == 'always' or (clean == 'success' and compiled and executed):
+        def safe_remove(filename):
+            if os.path.isfile(filename):
+                os.remove(filename)
+        safe_remove("codegen.f90")
+        safe_remove("codegen.c")
+        safe_remove("codegen.h")
+        safe_remove("codegen.o")
+        safe_remove("main.f90")
+        safe_remove("main.c")
+        safe_remove("main.o")
+        safe_remove("test.exe")
+        os.chdir(oldwork)
+        os.rmdir(work)
+    else:
+        print("TEST NOT REMOVED: %s" % work, file=sys.stderr)
+        os.chdir(oldwork)
+
+    # 7) Do the assertions in the end
+    assert compiled, "failed to compile %s code with:\n%s" % (
+        language, "\n".join(commands))
+    assert executed, "failed to execute %s code from:\n%s" % (
+        language, "\n".join(commands))
+
+
+def fortranize_double_constants(code_string):
+    """
+    Replaces every literal float with literal doubles
+    """
+    import re
+    pattern_exp = re.compile(r'\d+(\.)?\d*[eE]-?\d+')
+    pattern_float = re.compile(r'\d+\.\d*(?!\d*d)')
+
+    def subs_exp(matchobj):
+        return re.sub('[eE]', 'd', matchobj.group(0))
+
+    def subs_float(matchobj):
+        return "%sd0" % matchobj.group(0)
+
+    code_string = pattern_exp.sub(subs_exp, code_string)
+    code_string = pattern_float.sub(subs_float, code_string)
+
+    return code_string
+
+
+def is_feasible(language, commands):
+    # This test should always work, otherwise the compiler is not present.
+    routine = make_routine("test", x)
+    numerical_tests = [
+        ("test", ( 1.0,), 1.0, 1e-15),
+        ("test", (-1.0,), -1.0, 1e-15),
+    ]
+    try:
+        run_test("is_feasible", [routine], numerical_tests, language, commands,
+                 friendly=False)
+        return True
+    except AssertionError:
+        return False
+
+valid_lang_commands = []
+invalid_lang_compilers = []
+for lang, compiler in combinations_lang_compiler:
+    commands = compile_commands[compiler]
+    if is_feasible(lang, commands):
+        valid_lang_commands.append((lang, commands))
+    else:
+        invalid_lang_compilers.append((lang, compiler))
+
+# We test all language-compiler combinations, just to report what is skipped
+
+def test_C89_cc():
+    if ("C89", 'cc') in invalid_lang_compilers:
+        skip("`cc' command didn't work as expected (C89)")
+
+
+def test_C99_cc():
+    if ("C99", 'cc') in invalid_lang_compilers:
+        skip("`cc' command didn't work as expected (C99)")
+
+
+def test_F95_ifort():
+    if ("F95", 'ifort') in invalid_lang_compilers:
+        skip("`ifort' command didn't work as expected")
+
+
+def test_F95_gfortran():
+    if ("F95", 'gfortran') in invalid_lang_compilers:
+        skip("`gfortran' command didn't work as expected")
+
+
+def test_F95_g95():
+    if ("F95", 'g95') in invalid_lang_compilers:
+        skip("`g95' command didn't work as expected")
+
+# Here comes the actual tests
+
+
+def test_basic_codegen():
+    numerical_tests = [
+        ("test", (1.0, 6.0, 3.0), 21.0, 1e-15),
+        ("test", (-1.0, 2.0, -2.5), -2.5, 1e-15),
+    ]
+    name_expr = [("test", (x + y)*z)]
+    for lang, commands in valid_lang_commands:
+        run_test("basic_codegen", name_expr, numerical_tests, lang, commands)
+
+
+def test_intrinsic_math1_codegen():
+    # not included: log10
+    from sympy.core.evalf import N
+    from sympy.functions import ln
+    from sympy.functions.elementary.exponential import log
+    from sympy.functions.elementary.hyperbolic import (cosh, sinh, tanh)
+    from sympy.functions.elementary.integers import (ceiling, floor)
+    from sympy.functions.elementary.miscellaneous import sqrt
+    from sympy.functions.elementary.trigonometric import (acos, asin, atan, cos, sin, tan)
+    name_expr = [
+        ("test_fabs", abs(x)),
+        ("test_acos", acos(x)),
+        ("test_asin", asin(x)),
+        ("test_atan", atan(x)),
+        ("test_cos", cos(x)),
+        ("test_cosh", cosh(x)),
+        ("test_log", log(x)),
+        ("test_ln", ln(x)),
+        ("test_sin", sin(x)),
+        ("test_sinh", sinh(x)),
+        ("test_sqrt", sqrt(x)),
+        ("test_tan", tan(x)),
+        ("test_tanh", tanh(x)),
+    ]
+    numerical_tests = []
+    for name, expr in name_expr:
+        for xval in 0.2, 0.5, 0.8:
+            expected = N(expr.subs(x, xval))
+            numerical_tests.append((name, (xval,), expected, 1e-14))
+    for lang, commands in valid_lang_commands:
+        if lang.startswith("C"):
+            name_expr_C = [("test_floor", floor(x)), ("test_ceil", ceiling(x))]
+        else:
+            name_expr_C = []
+        run_test("intrinsic_math1", name_expr + name_expr_C,
+                 numerical_tests, lang, commands)
+
+
+def test_instrinsic_math2_codegen():
+    # not included: frexp, ldexp, modf, fmod
+    from sympy.core.evalf import N
+    from sympy.functions.elementary.trigonometric import atan2
+    name_expr = [
+        ("test_atan2", atan2(x, y)),
+        ("test_pow", x**y),
+    ]
+    numerical_tests = []
+    for name, expr in name_expr:
+        for xval, yval in (0.2, 1.3), (0.5, -0.2), (0.8, 0.8):
+            expected = N(expr.subs(x, xval).subs(y, yval))
+            numerical_tests.append((name, (xval, yval), expected, 1e-14))
+    for lang, commands in valid_lang_commands:
+        run_test("intrinsic_math2", name_expr, numerical_tests, lang, commands)
+
+
+def test_complicated_codegen():
+    from sympy.core.evalf import N
+    from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+    name_expr = [
+        ("test1", ((sin(x) + cos(y) + tan(z))**7).expand()),
+        ("test2", cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))),
+    ]
+    numerical_tests = []
+    for name, expr in name_expr:
+        for xval, yval, zval in (0.2, 1.3, -0.3), (0.5, -0.2, 0.0), (0.8, 2.1, 0.8):
+            expected = N(expr.subs(x, xval).subs(y, yval).subs(z, zval))
+            numerical_tests.append((name, (xval, yval, zval), expected, 1e-12))
+    for lang, commands in valid_lang_commands:
+        run_test(
+            "complicated_codegen", name_expr, numerical_tests, lang, commands)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_gmpy.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_gmpy.py
new file mode 100644
index 0000000000000000000000000000000000000000..d88f9da0c6c26c15f529ce485fff5b72342170ea
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_gmpy.py
@@ -0,0 +1,12 @@
+from sympy.external.gmpy import LONG_MAX, iroot
+from sympy.testing.pytest import raises
+
+
+def test_iroot():
+    assert iroot(2, LONG_MAX) == (1, False)
+    assert iroot(2, LONG_MAX + 1) == (1, False)
+    for x in range(3):
+        assert iroot(x, 1) == (x, True)
+    raises(ValueError, lambda: iroot(-1, 1))
+    raises(ValueError, lambda: iroot(0, 0))
+    raises(ValueError, lambda: iroot(0, -1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_importtools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_importtools.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b954070c179282ed2bcf5735d802c5f22a3a261
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_importtools.py
@@ -0,0 +1,40 @@
+from sympy.external import import_module
+from sympy.testing.pytest import warns
+
+# fixes issue that arose in addressing issue 6533
+def test_no_stdlib_collections():
+    '''
+    make sure we get the right collections when it is not part of a
+    larger list
+    '''
+    import collections
+    matplotlib = import_module('matplotlib',
+        import_kwargs={'fromlist': ['cm', 'collections']},
+        min_module_version='1.1.0', catch=(RuntimeError,))
+    if matplotlib:
+        assert collections != matplotlib.collections
+
+def test_no_stdlib_collections2():
+    '''
+    make sure we get the right collections when it is not part of a
+    larger list
+    '''
+    import collections
+    matplotlib = import_module('matplotlib',
+        import_kwargs={'fromlist': ['collections']},
+        min_module_version='1.1.0', catch=(RuntimeError,))
+    if matplotlib:
+        assert collections != matplotlib.collections
+
+def test_no_stdlib_collections3():
+    '''make sure we get the right collections with no catch'''
+    import collections
+    matplotlib = import_module('matplotlib',
+        import_kwargs={'fromlist': ['cm', 'collections']},
+        min_module_version='1.1.0')
+    if matplotlib:
+        assert collections != matplotlib.collections
+
+def test_min_module_version_python3_basestring_error():
+    with warns(UserWarning):
+        import_module('mpmath', min_module_version='1000.0.1')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_ntheory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_ntheory.py
new file mode 100644
index 0000000000000000000000000000000000000000..00824481ad27aa9071ea5801fb3bde75cacbc3c8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_ntheory.py
@@ -0,0 +1,307 @@
+from itertools import permutations
+
+from sympy.external.ntheory import (bit_scan1, remove, bit_scan0, is_fermat_prp,
+                                    is_euler_prp, is_strong_prp, gcdext, _lucas_sequence,
+                                    is_fibonacci_prp, is_lucas_prp, is_selfridge_prp,
+                                    is_strong_lucas_prp, is_strong_selfridge_prp,
+                                    is_bpsw_prp, is_strong_bpsw_prp)
+from sympy.testing.pytest import raises
+
+
+def test_bit_scan1():
+    assert bit_scan1(0) is None
+    assert bit_scan1(1) == 0
+    assert bit_scan1(-1) == 0
+    assert bit_scan1(2) == 1
+    assert bit_scan1(7) == 0
+    assert bit_scan1(-7) == 0
+    for i in range(100):
+        assert bit_scan1(1 << i) == i
+        assert bit_scan1((1 << i) * 31337) == i
+    for i in range(500):
+        n = (1 << 500) + (1 << i)
+        assert bit_scan1(n) == i
+    assert bit_scan1(1 << 1000001) == 1000001
+    assert bit_scan1((1 << 273956)*7**37) == 273956
+    # issue 12709
+    for i in range(1, 10):
+        big = 1 << i
+        assert bit_scan1(-big) == bit_scan1(big)
+
+
+def test_bit_scan0():
+    assert bit_scan0(-1) is None
+    assert bit_scan0(0) == 0
+    assert bit_scan0(1) == 1
+    assert bit_scan0(-2) == 0
+
+
+def test_remove():
+    raises(ValueError, lambda: remove(1, 1))
+    assert remove(0, 3) == (0, 0)
+    for f in range(2, 10):
+        for y in range(2, 1000):
+            for z in [1, 17, 101, 1009]:
+                assert remove(z*f**y, f) == (z, y)
+
+
+def test_gcdext():
+    assert gcdext(0, 0) == (0, 0, 0)
+    assert gcdext(3, 0) == (3, 1, 0)
+    assert gcdext(0, 4) == (4, 0, 1)
+
+    for n in range(1, 10):
+        assert gcdext(n, 1) == gcdext(-n, 1) == (1, 0, 1)
+        assert gcdext(n, -1) == gcdext(-n, -1) == (1, 0, -1)
+        assert gcdext(n, n) == gcdext(-n, n) == (n, 0, 1)
+        assert gcdext(n, -n) == gcdext(-n, -n) == (n, 0, -1)
+
+    for n in range(2, 10):
+        assert gcdext(1, n) == gcdext(1, -n) == (1, 1, 0)
+        assert gcdext(-1, n) == gcdext(-1, -n) == (1, -1, 0)
+
+    for a, b in permutations([2**5, 3, 5, 7**2, 11], 2):
+        g, x, y = gcdext(a, b)
+        assert g == a*x + b*y == 1
+
+
+def test_is_fermat_prp():
+    # invalid input
+    raises(ValueError, lambda: is_fermat_prp(0, 10))
+    raises(ValueError, lambda: is_fermat_prp(5, 1))
+
+    # n = 1
+    assert not is_fermat_prp(1, 3)
+
+    # n is prime
+    assert is_fermat_prp(2, 4)
+    assert is_fermat_prp(3, 2)
+    assert is_fermat_prp(11, 3)
+    assert is_fermat_prp(2**31-1, 5)
+
+    # A001567
+    pseudorpime = [341, 561, 645, 1105, 1387, 1729, 1905, 2047,
+                   2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681]
+    for n in pseudorpime:
+        assert is_fermat_prp(n, 2)
+
+    # A020136
+    pseudorpime = [15, 85, 91, 341, 435, 451, 561, 645, 703, 1105,
+                   1247, 1271, 1387, 1581, 1695, 1729, 1891, 1905]
+    for n in pseudorpime:
+        assert is_fermat_prp(n, 4)
+
+
+def test_is_euler_prp():
+    # invalid input
+    raises(ValueError, lambda: is_euler_prp(0, 10))
+    raises(ValueError, lambda: is_euler_prp(5, 1))
+
+    # n = 1
+    assert not is_euler_prp(1, 3)
+
+    # n is prime
+    assert is_euler_prp(2, 4)
+    assert is_euler_prp(3, 2)
+    assert is_euler_prp(11, 3)
+    assert is_euler_prp(2**31-1, 5)
+
+    # A047713
+    pseudorpime = [561, 1105, 1729, 1905, 2047, 2465, 3277, 4033,
+                   4681, 6601, 8321, 8481, 10585, 12801, 15841]
+    for n in pseudorpime:
+        assert is_euler_prp(n, 2)
+
+    # A048950
+    pseudorpime = [121, 703, 1729, 1891, 2821, 3281, 7381, 8401,
+                   8911, 10585, 12403, 15457, 15841, 16531, 18721]
+    for n in pseudorpime:
+        assert is_euler_prp(n, 3)
+
+
+def test_is_strong_prp():
+    # invalid input
+    raises(ValueError, lambda: is_strong_prp(0, 10))
+    raises(ValueError, lambda: is_strong_prp(5, 1))
+
+    # n = 1
+    assert not is_strong_prp(1, 3)
+
+    # n is prime
+    assert is_strong_prp(2, 4)
+    assert is_strong_prp(3, 2)
+    assert is_strong_prp(11, 3)
+    assert is_strong_prp(2**31-1, 5)
+
+    # A001262
+    pseudorpime = [2047, 3277, 4033, 4681, 8321, 15841, 29341,
+                   42799, 49141, 52633, 65281, 74665, 80581]
+    for n in pseudorpime:
+        assert is_strong_prp(n, 2)
+
+    # A020229
+    pseudorpime = [121, 703, 1891, 3281, 8401, 8911, 10585, 12403,
+                   16531, 18721, 19345, 23521, 31621, 44287, 47197]
+    for n in pseudorpime:
+        assert is_strong_prp(n, 3)
+
+
+def test_lucas_sequence():
+    def lucas_u(P, Q, length):
+        array = [0] * length
+        array[1] = 1
+        for k in range(2, length):
+            array[k] = P * array[k - 1] - Q * array[k - 2]
+        return array
+
+    def lucas_v(P, Q, length):
+        array = [0] * length
+        array[0] = 2
+        array[1] = P
+        for k in range(2, length):
+            array[k] = P * array[k - 1] - Q * array[k - 2]
+        return array
+
+    length = 20
+    for P in range(-10, 10):
+        for Q in range(-10, 10):
+            D = P**2 - 4*Q
+            if D == 0:
+                continue
+            us = lucas_u(P, Q, length)
+            vs = lucas_v(P, Q, length)
+            for n in range(3, 100, 2):
+                for k in range(length):
+                    U, V, Qk = _lucas_sequence(n, P, Q, k)
+                    assert U == us[k] % n
+                    assert V == vs[k] % n
+                    assert pow(Q, k, n) == Qk
+
+
+def test_is_fibonacci_prp():
+    # invalid input
+    raises(ValueError, lambda: is_fibonacci_prp(3, 2, 1))
+    raises(ValueError, lambda: is_fibonacci_prp(3, -5, 1))
+    raises(ValueError, lambda: is_fibonacci_prp(3, 5, 2))
+    raises(ValueError, lambda: is_fibonacci_prp(0, 5, -1))
+
+    # n = 1
+    assert not is_fibonacci_prp(1, 3, 1)
+
+    # n is prime
+    assert is_fibonacci_prp(2, 5, 1)
+    assert is_fibonacci_prp(3, 6, -1)
+    assert is_fibonacci_prp(11, 7, 1)
+    assert is_fibonacci_prp(2**31-1, 8, -1)
+
+    # A005845
+    pseudorpime = [705, 2465, 2737, 3745, 4181, 5777, 6721,
+                   10877, 13201, 15251, 24465, 29281, 34561]
+    for n in pseudorpime:
+        assert is_fibonacci_prp(n, 1, -1)
+
+
+def test_is_lucas_prp():
+    # invalid input
+    raises(ValueError, lambda: is_lucas_prp(3, 2, 1))
+    raises(ValueError, lambda: is_lucas_prp(0, 5, -1))
+    raises(ValueError, lambda: is_lucas_prp(15, 3, 1))
+
+    # n = 1
+    assert not is_lucas_prp(1, 3, 1)
+
+    # n is prime
+    assert is_lucas_prp(2, 5, 2)
+    assert is_lucas_prp(3, 6, -1)
+    assert is_lucas_prp(11, 7, 5)
+    assert is_lucas_prp(2**31-1, 8, -3)
+
+    # A081264
+    pseudorpime = [323, 377, 1891, 3827, 4181, 5777, 6601, 6721,
+                   8149, 10877, 11663, 13201, 13981, 15251, 17119]
+    for n in pseudorpime:
+        assert is_lucas_prp(n, 1, -1)
+
+
+def test_is_selfridge_prp():
+    # invalid input
+    raises(ValueError, lambda: is_selfridge_prp(0))
+
+    # n = 1
+    assert not is_selfridge_prp(1)
+
+    # n is prime
+    assert is_selfridge_prp(2)
+    assert is_selfridge_prp(3)
+    assert is_selfridge_prp(11)
+    assert is_selfridge_prp(2**31-1)
+
+    # A217120
+    pseudorpime = [323, 377, 1159, 1829, 3827, 5459, 5777, 9071,
+                   9179, 10877, 11419, 11663, 13919, 14839, 16109]
+    for n in pseudorpime:
+        assert is_selfridge_prp(n)
+
+
+def test_is_strong_lucas_prp():
+    # invalid input
+    raises(ValueError, lambda: is_strong_lucas_prp(3, 2, 1))
+    raises(ValueError, lambda: is_strong_lucas_prp(0, 5, -1))
+    raises(ValueError, lambda: is_strong_lucas_prp(15, 3, 1))
+
+    # n = 1
+    assert not is_strong_lucas_prp(1, 3, 1)
+
+    # n is prime
+    assert is_strong_lucas_prp(2, 5, 2)
+    assert is_strong_lucas_prp(3, 6, -1)
+    assert is_strong_lucas_prp(11, 7, 5)
+    assert is_strong_lucas_prp(2**31-1, 8, -3)
+
+
+def test_is_strong_selfridge_prp():
+    # invalid input
+    raises(ValueError, lambda: is_strong_selfridge_prp(0))
+
+    # n = 1
+    assert not is_strong_selfridge_prp(1)
+
+    # n is prime
+    assert is_strong_selfridge_prp(2)
+    assert is_strong_selfridge_prp(3)
+    assert is_strong_selfridge_prp(11)
+    assert is_strong_selfridge_prp(2**31-1)
+
+    # A217255
+    pseudorpime = [5459, 5777, 10877, 16109, 18971, 22499, 24569,
+                   25199, 40309, 58519, 75077, 97439, 100127, 113573]
+    for n in pseudorpime:
+        assert is_strong_selfridge_prp(n)
+
+
+def test_is_bpsw_prp():
+    # invalid input
+    raises(ValueError, lambda: is_bpsw_prp(0))
+
+    # n = 1
+    assert not is_bpsw_prp(1)
+
+    # n is prime
+    assert is_bpsw_prp(2)
+    assert is_bpsw_prp(3)
+    assert is_bpsw_prp(11)
+    assert is_bpsw_prp(2**31-1)
+
+
+def test_is_strong_bpsw_prp():
+    # invalid input
+    raises(ValueError, lambda: is_strong_bpsw_prp(0))
+
+    # n = 1
+    assert not is_strong_bpsw_prp(1)
+
+    # n is prime
+    assert is_strong_bpsw_prp(2)
+    assert is_strong_bpsw_prp(3)
+    assert is_strong_bpsw_prp(11)
+    assert is_strong_bpsw_prp(2**31-1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_numpy.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_numpy.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd456d0d6cc49138c29d7ab28ee02694448d578f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_numpy.py
@@ -0,0 +1,335 @@
+# This testfile tests SymPy <-> NumPy compatibility
+
+# Don't test any SymPy features here. Just pure interaction with NumPy.
+# Always write regular SymPy tests for anything, that can be tested in pure
+# Python (without numpy). Here we test everything, that a user may need when
+# using SymPy with NumPy
+from sympy.external.importtools import version_tuple
+from sympy.external import import_module
+
+numpy = import_module('numpy')
+if numpy:
+    array, matrix, ndarray = numpy.array, numpy.matrix, numpy.ndarray
+else:
+    #bin/test will not execute any tests now
+    disabled = True
+
+
+from sympy.core.numbers import (Float, Integer, Rational)
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.trigonometric import sin
+from sympy.matrices.dense import (Matrix, list2numpy, matrix2numpy, symarray)
+from sympy.utilities.lambdify import lambdify
+import sympy
+
+import mpmath
+from sympy.abc import x, y, z
+from sympy.utilities.decorator import conserve_mpmath_dps
+from sympy.utilities.exceptions import ignore_warnings
+from sympy.testing.pytest import raises
+
+
+# first, systematically check, that all operations are implemented and don't
+# raise an exception
+
+
+def test_systematic_basic():
+    def s(sympy_object, numpy_array):
+        _ = [sympy_object + numpy_array,
+        numpy_array + sympy_object,
+        sympy_object - numpy_array,
+        numpy_array - sympy_object,
+        sympy_object * numpy_array,
+        numpy_array * sympy_object,
+        sympy_object / numpy_array,
+        numpy_array / sympy_object,
+        sympy_object ** numpy_array,
+        numpy_array ** sympy_object]
+    x = Symbol("x")
+    y = Symbol("y")
+    sympy_objs = [
+        Rational(2, 3),
+        Float("1.3"),
+        x,
+        y,
+        pow(x, y)*y,
+        Integer(5),
+        Float(5.5),
+    ]
+    numpy_objs = [
+        array([1]),
+        array([3, 8, -1]),
+        array([x, x**2, Rational(5)]),
+        array([x/y*sin(y), 5, Rational(5)]),
+    ]
+    for x in sympy_objs:
+        for y in numpy_objs:
+            s(x, y)
+
+
+# now some random tests, that test particular problems and that also
+# check that the results of the operations are correct
+
+def test_basics():
+    one = Rational(1)
+    zero = Rational(0)
+    assert array(1) == array(one)
+    assert array([one]) == array([one])
+    assert array([x]) == array([x])
+    assert array(x) == array(Symbol("x"))
+    assert array(one + x) == array(1 + x)
+
+    X = array([one, zero, zero])
+    assert (X == array([one, zero, zero])).all()
+    assert (X == array([one, 0, 0])).all()
+
+
+def test_arrays():
+    one = Rational(1)
+    zero = Rational(0)
+    X = array([one, zero, zero])
+    Y = one*X
+    X = array([Symbol("a") + Rational(1, 2)])
+    Y = X + X
+    assert Y == array([1 + 2*Symbol("a")])
+    Y = Y + 1
+    assert Y == array([2 + 2*Symbol("a")])
+    Y = X - X
+    assert Y == array([0])
+
+
+def test_conversion1():
+    a = list2numpy([x**2, x])
+    #looks like an array?
+    assert isinstance(a, ndarray)
+    assert a[0] == x**2
+    assert a[1] == x
+    assert len(a) == 2
+    #yes, it's the array
+
+
+def test_conversion2():
+    a = 2*list2numpy([x**2, x])
+    b = list2numpy([2*x**2, 2*x])
+    assert (a == b).all()
+
+    one = Rational(1)
+    zero = Rational(0)
+    X = list2numpy([one, zero, zero])
+    Y = one*X
+    X = list2numpy([Symbol("a") + Rational(1, 2)])
+    Y = X + X
+    assert Y == array([1 + 2*Symbol("a")])
+    Y = Y + 1
+    assert Y == array([2 + 2*Symbol("a")])
+    Y = X - X
+    assert Y == array([0])
+
+
+def test_list2numpy():
+    assert (array([x**2, x]) == list2numpy([x**2, x])).all()
+
+
+def test_Matrix1():
+    m = Matrix([[x, x**2], [5, 2/x]])
+    assert (array(m.subs(x, 2)) == array([[2, 4], [5, 1]])).all()
+    m = Matrix([[sin(x), x**2], [5, 2/x]])
+    assert (array(m.subs(x, 2)) == array([[sin(2), 4], [5, 1]])).all()
+
+
+def test_Matrix2():
+    m = Matrix([[x, x**2], [5, 2/x]])
+    with ignore_warnings(PendingDeprecationWarning):
+        assert (matrix(m.subs(x, 2)) == matrix([[2, 4], [5, 1]])).all()
+    m = Matrix([[sin(x), x**2], [5, 2/x]])
+    with ignore_warnings(PendingDeprecationWarning):
+        assert (matrix(m.subs(x, 2)) == matrix([[sin(2), 4], [5, 1]])).all()
+
+
+def test_Matrix3():
+    a = array([[2, 4], [5, 1]])
+    assert Matrix(a) == Matrix([[2, 4], [5, 1]])
+    assert Matrix(a) != Matrix([[2, 4], [5, 2]])
+    a = array([[sin(2), 4], [5, 1]])
+    assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]])
+    assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]])
+
+
+def test_Matrix4():
+    with ignore_warnings(PendingDeprecationWarning):
+        a = matrix([[2, 4], [5, 1]])
+    assert Matrix(a) == Matrix([[2, 4], [5, 1]])
+    assert Matrix(a) != Matrix([[2, 4], [5, 2]])
+    with ignore_warnings(PendingDeprecationWarning):
+        a = matrix([[sin(2), 4], [5, 1]])
+    assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]])
+    assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]])
+
+
+def test_Matrix_sum():
+    M = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
+    with ignore_warnings(PendingDeprecationWarning):
+        m = matrix([[2, 3, 4], [x, 5, 6], [x, y, z**2]])
+    assert M + m == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]])
+    assert m + M == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]])
+    assert M + m == M.add(m)
+
+
+def test_Matrix_mul():
+    M = Matrix([[1, 2, 3], [x, y, x]])
+    with ignore_warnings(PendingDeprecationWarning):
+        m = matrix([[2, 4], [x, 6], [x, z**2]])
+    assert M*m == Matrix([
+        [         2 + 5*x,        16 + 3*z**2],
+        [2*x + x*y + x**2, 4*x + 6*y + x*z**2],
+    ])
+
+    assert m*M == Matrix([
+        [   2 + 4*x,      4 + 4*y,      6 + 4*x],
+        [       7*x,    2*x + 6*y,          9*x],
+        [x + x*z**2, 2*x + y*z**2, 3*x + x*z**2],
+    ])
+    a = array([2])
+    assert a[0] * M == 2 * M
+    assert M * a[0] == 2 * M
+
+
+def test_Matrix_array():
+    class matarray:
+        def __array__(self, dtype=object, copy=None):
+            if copy is not None and not copy:
+                raise TypeError("Cannot implement copy=False when converting Matrix to ndarray")
+            from numpy import array
+            return array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    matarr = matarray()
+    assert Matrix(matarr) == Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+
+
+def test_matrix2numpy():
+    a = matrix2numpy(Matrix([[1, x**2], [3*sin(x), 0]]))
+    assert isinstance(a, ndarray)
+    assert a.shape == (2, 2)
+    assert a[0, 0] == 1
+    assert a[0, 1] == x**2
+    assert a[1, 0] == 3*sin(x)
+    assert a[1, 1] == 0
+
+
+def test_matrix2numpy_conversion():
+    a = Matrix([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]])
+    b = array([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]])
+    assert (matrix2numpy(a) == b).all()
+    assert matrix2numpy(a).dtype == numpy.dtype('object')
+
+    c = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='int8')
+    d = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='float64')
+    assert c.dtype == numpy.dtype('int8')
+    assert d.dtype == numpy.dtype('float64')
+
+
+def test_issue_3728():
+    assert (Rational(1, 2)*array([2*x, 0]) == array([x, 0])).all()
+    assert (Rational(1, 2) + array(
+        [2*x, 0]) == array([2*x + Rational(1, 2), Rational(1, 2)])).all()
+    assert (Float("0.5")*array([2*x, 0]) == array([Float("1.0")*x, 0])).all()
+    assert (Float("0.5") + array(
+        [2*x, 0]) == array([2*x + Float("0.5"), Float("0.5")])).all()
+
+
+@conserve_mpmath_dps
+def test_lambdify():
+    mpmath.mp.dps = 16
+    sin02 = mpmath.mpf("0.198669330795061215459412627")
+    f = lambdify(x, sin(x), "numpy")
+    prec = 1e-15
+    assert -prec < f(0.2) - sin02 < prec
+
+    # if this succeeds, it can't be a numpy function
+
+    if version_tuple(numpy.__version__) >= version_tuple('1.17'):
+        with raises(TypeError):
+            f(x)
+    else:
+        with raises(AttributeError):
+            f(x)
+
+
+def test_lambdify_matrix():
+    f = lambdify(x, Matrix([[x, 2*x], [1, 2]]), [{'ImmutableMatrix': numpy.array}, "numpy"])
+    assert (f(1) == array([[1, 2], [1, 2]])).all()
+
+
+def test_lambdify_matrix_multi_input():
+    M = sympy.Matrix([[x**2, x*y, x*z],
+                      [y*x, y**2, y*z],
+                      [z*x, z*y, z**2]])
+    f = lambdify((x, y, z), M, [{'ImmutableMatrix': numpy.array}, "numpy"])
+
+    xh, yh, zh = 1.0, 2.0, 3.0
+    expected = array([[xh**2, xh*yh, xh*zh],
+                      [yh*xh, yh**2, yh*zh],
+                      [zh*xh, zh*yh, zh**2]])
+    actual = f(xh, yh, zh)
+    assert numpy.allclose(actual, expected)
+
+
+def test_lambdify_matrix_vec_input():
+    X = sympy.DeferredVector('X')
+    M = Matrix([
+        [X[0]**2, X[0]*X[1], X[0]*X[2]],
+        [X[1]*X[0], X[1]**2, X[1]*X[2]],
+        [X[2]*X[0], X[2]*X[1], X[2]**2]])
+    f = lambdify(X, M, [{'ImmutableMatrix': numpy.array}, "numpy"])
+
+    Xh = array([1.0, 2.0, 3.0])
+    expected = array([[Xh[0]**2, Xh[0]*Xh[1], Xh[0]*Xh[2]],
+                      [Xh[1]*Xh[0], Xh[1]**2, Xh[1]*Xh[2]],
+                      [Xh[2]*Xh[0], Xh[2]*Xh[1], Xh[2]**2]])
+    actual = f(Xh)
+    assert numpy.allclose(actual, expected)
+
+
+def test_lambdify_transl():
+    from sympy.utilities.lambdify import NUMPY_TRANSLATIONS
+    for sym, mat in NUMPY_TRANSLATIONS.items():
+        assert sym in sympy.__dict__
+        assert mat in numpy.__dict__
+
+
+def test_symarray():
+    """Test creation of numpy arrays of SymPy symbols."""
+
+    import numpy as np
+    import numpy.testing as npt
+
+    syms = symbols('_0,_1,_2')
+    s1 = symarray("", 3)
+    s2 = symarray("", 3)
+    npt.assert_array_equal(s1, np.array(syms, dtype=object))
+    assert s1[0] == s2[0]
+
+    a = symarray('a', 3)
+    b = symarray('b', 3)
+    assert not(a[0] == b[0])
+
+    asyms = symbols('a_0,a_1,a_2')
+    npt.assert_array_equal(a, np.array(asyms, dtype=object))
+
+    # Multidimensional checks
+    a2d = symarray('a', (2, 3))
+    assert a2d.shape == (2, 3)
+    a00, a12 = symbols('a_0_0,a_1_2')
+    assert a2d[0, 0] == a00
+    assert a2d[1, 2] == a12
+
+    a3d = symarray('a', (2, 3, 2))
+    assert a3d.shape == (2, 3, 2)
+    a000, a120, a121 = symbols('a_0_0_0,a_1_2_0,a_1_2_1')
+    assert a3d[0, 0, 0] == a000
+    assert a3d[1, 2, 0] == a120
+    assert a3d[1, 2, 1] == a121
+
+
+def test_vectorize():
+    assert (numpy.vectorize(
+        sin)([1, 2, 3]) == numpy.array([sin(1), sin(2), sin(3)])).all()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_pythonmpq.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_pythonmpq.py
new file mode 100644
index 0000000000000000000000000000000000000000..137cfdf5c858544f0811ae666f000cfb368787a0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_pythonmpq.py
@@ -0,0 +1,176 @@
+"""
+test_pythonmpq.py
+
+Test the PythonMPQ class for consistency with gmpy2's mpq type. If gmpy2 is
+installed run the same tests for both.
+"""
+from fractions import Fraction
+from decimal import Decimal
+import pickle
+from typing import Callable, List, Tuple, Type
+
+from sympy.testing.pytest import raises
+
+from sympy.external.pythonmpq import PythonMPQ
+
+#
+# If gmpy2 is installed then run the tests for both mpq and PythonMPQ.
+# That should ensure consistency between the implementation here and mpq.
+#
+rational_types: List[Tuple[Callable, Type, Callable, Type]]
+rational_types = [(PythonMPQ, PythonMPQ, int, int)]
+try:
+    from gmpy2 import mpq, mpz
+    rational_types.append((mpq, type(mpq(1)), mpz, type(mpz(1))))
+except ImportError:
+    pass
+
+
+def test_PythonMPQ():
+    #
+    # Test PythonMPQ and also mpq if gmpy/gmpy2 is installed.
+    #
+    for Q, TQ, Z, TZ in rational_types:
+
+        def check_Q(q):
+            assert isinstance(q, TQ)
+            assert isinstance(q.numerator, TZ)
+            assert isinstance(q.denominator, TZ)
+            return q.numerator, q.denominator
+
+        # Check construction from different types
+        assert check_Q(Q(3)) == (3, 1)
+        assert check_Q(Q(3, 5)) == (3, 5)
+        assert check_Q(Q(Q(3, 5))) == (3, 5)
+        assert check_Q(Q(0.5)) == (1, 2)
+        assert check_Q(Q('0.5')) == (1, 2)
+        assert check_Q(Q(Fraction(3, 5))) == (3, 5)
+
+        # https://github.com/aleaxit/gmpy/issues/327
+        if Q is PythonMPQ:
+            assert check_Q(Q(Decimal('0.6'))) == (3, 5)
+
+        # Invalid types
+        raises(TypeError, lambda: Q([]))
+        raises(TypeError, lambda: Q([], []))
+
+        # Check normalisation of signs
+        assert check_Q(Q(2, 3)) == (2, 3)
+        assert check_Q(Q(-2, 3)) == (-2, 3)
+        assert check_Q(Q(2, -3)) == (-2, 3)
+        assert check_Q(Q(-2, -3)) == (2, 3)
+
+        # Check gcd calculation
+        assert check_Q(Q(12, 8)) == (3, 2)
+
+        # __int__/__float__
+        assert int(Q(5, 3)) == 1
+        assert int(Q(-5, 3)) == -1
+        assert float(Q(5, 2)) == 2.5
+        assert float(Q(-5, 2)) == -2.5
+
+        # __str__/__repr__
+        assert str(Q(2, 1)) == "2"
+        assert str(Q(1, 2)) == "1/2"
+        if Q is PythonMPQ:
+            assert repr(Q(2, 1)) == "MPQ(2,1)"
+            assert repr(Q(1, 2)) == "MPQ(1,2)"
+        else:
+            assert repr(Q(2, 1)) == "mpq(2,1)"
+            assert repr(Q(1, 2)) == "mpq(1,2)"
+
+        # __bool__
+        assert bool(Q(1, 2)) is True
+        assert bool(Q(0)) is False
+
+        # __eq__/__ne__
+        assert (Q(2, 3) == Q(2, 3)) is True
+        assert (Q(2, 3) == Q(2, 5)) is False
+        assert (Q(2, 3) != Q(2, 3)) is False
+        assert (Q(2, 3) != Q(2, 5)) is True
+
+        # __hash__
+        assert hash(Q(3, 5)) == hash(Fraction(3, 5))
+
+        # __reduce__
+        q = Q(2, 3)
+        assert pickle.loads(pickle.dumps(q)) == q
+
+        # __ge__/__gt__/__le__/__lt__
+        assert (Q(1, 3) < Q(2, 3)) is True
+        assert (Q(2, 3) < Q(2, 3)) is False
+        assert (Q(2, 3) < Q(1, 3)) is False
+        assert (Q(-2, 3) < Q(1, 3)) is True
+        assert (Q(1, 3) < Q(-2, 3)) is False
+
+        assert (Q(1, 3) <= Q(2, 3)) is True
+        assert (Q(2, 3) <= Q(2, 3)) is True
+        assert (Q(2, 3) <= Q(1, 3)) is False
+        assert (Q(-2, 3) <= Q(1, 3)) is True
+        assert (Q(1, 3) <= Q(-2, 3)) is False
+
+        assert (Q(1, 3) > Q(2, 3)) is False
+        assert (Q(2, 3) > Q(2, 3)) is False
+        assert (Q(2, 3) > Q(1, 3)) is True
+        assert (Q(-2, 3) > Q(1, 3)) is False
+        assert (Q(1, 3) > Q(-2, 3)) is True
+
+        assert (Q(1, 3) >= Q(2, 3)) is False
+        assert (Q(2, 3) >= Q(2, 3)) is True
+        assert (Q(2, 3) >= Q(1, 3)) is True
+        assert (Q(-2, 3) >= Q(1, 3)) is False
+        assert (Q(1, 3) >= Q(-2, 3)) is True
+
+        # __abs__/__pos__/__neg__
+        assert abs(Q(2, 3)) == abs(Q(-2, 3)) == Q(2, 3)
+        assert +Q(2, 3) == Q(2, 3)
+        assert -Q(2, 3) == Q(-2, 3)
+
+        # __add__/__radd__
+        assert Q(2, 3) + Q(5, 7) == Q(29, 21)
+        assert Q(2, 3) + 1 == Q(5, 3)
+        assert 1 + Q(2, 3) == Q(5, 3)
+        raises(TypeError, lambda: [] + Q(1))
+        raises(TypeError, lambda: Q(1) + [])
+
+        # __sub__/__rsub__
+        assert Q(2, 3) - Q(5, 7) == Q(-1, 21)
+        assert Q(2, 3) - 1 == Q(-1, 3)
+        assert 1 - Q(2, 3) == Q(1, 3)
+        raises(TypeError, lambda: [] - Q(1))
+        raises(TypeError, lambda: Q(1) - [])
+
+        # __mul__/__rmul__
+        assert Q(2, 3) * Q(5, 7) == Q(10, 21)
+        assert Q(2, 3) * 1 == Q(2, 3)
+        assert 1 * Q(2, 3) == Q(2, 3)
+        raises(TypeError, lambda: [] * Q(1))
+        raises(TypeError, lambda: Q(1) * [])
+
+        # __pow__/__rpow__
+        assert Q(2, 3) ** 2 == Q(4, 9)
+        assert Q(2, 3) ** 1 == Q(2, 3)
+        assert Q(-2, 3) ** 2 == Q(4, 9)
+        assert Q(-2, 3) ** -1 == Q(-3, 2)
+        if Q is PythonMPQ:
+            raises(TypeError, lambda: 1 ** Q(2, 3))
+            raises(TypeError, lambda: Q(1, 4) ** Q(1, 2))
+        raises(TypeError, lambda: [] ** Q(1))
+        raises(TypeError, lambda: Q(1) ** [])
+
+        # __div__/__rdiv__
+        assert Q(2, 3) / Q(5, 7) == Q(14, 15)
+        assert Q(2, 3) / 1 == Q(2, 3)
+        assert 1 / Q(2, 3) == Q(3, 2)
+        raises(TypeError, lambda: [] / Q(1))
+        raises(TypeError, lambda: Q(1) / [])
+        raises(ZeroDivisionError, lambda: Q(1, 2) / Q(0))
+
+        # __divmod__
+        if Q is PythonMPQ:
+            raises(TypeError, lambda: Q(2, 3) // Q(1, 3))
+            raises(TypeError, lambda: Q(2, 3) % Q(1, 3))
+            raises(TypeError, lambda: 1 // Q(1, 3))
+            raises(TypeError, lambda: 1 % Q(1, 3))
+            raises(TypeError, lambda: Q(2, 3) // 1)
+            raises(TypeError, lambda: Q(2, 3) % 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_scipy.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_scipy.py
new file mode 100644
index 0000000000000000000000000000000000000000..3746d1a311eb68bb1af16e18ab152c7236b42bb5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/external/tests/test_scipy.py
@@ -0,0 +1,35 @@
+# This testfile tests SymPy <-> SciPy compatibility
+
+# Don't test any SymPy features here. Just pure interaction with SciPy.
+# Always write regular SymPy tests for anything, that can be tested in pure
+# Python (without scipy). Here we test everything, that a user may need when
+# using SymPy with SciPy
+
+from sympy.external import import_module
+
+scipy = import_module('scipy')
+if not scipy:
+    #bin/test will not execute any tests now
+    disabled = True
+
+from sympy.functions.special.bessel import jn_zeros
+
+
+def eq(a, b, tol=1e-6):
+    for x, y in zip(a, b):
+        if not (abs(x - y) < tol):
+            return False
+    return True
+
+
+def test_jn_zeros():
+    assert eq(jn_zeros(0, 4, method="scipy"),
+            [3.141592, 6.283185, 9.424777, 12.566370])
+    assert eq(jn_zeros(1, 4, method="scipy"),
+            [4.493409, 7.725251, 10.904121, 14.066193])
+    assert eq(jn_zeros(2, 4, method="scipy"),
+            [5.763459, 9.095011, 12.322940, 15.514603])
+    assert eq(jn_zeros(3, 4, method="scipy"),
+            [6.987932, 10.417118, 13.698023, 16.923621])
+    assert eq(jn_zeros(4, 4, method="scipy"),
+            [8.182561, 11.704907, 15.039664, 18.301255])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..ed93b2a11754aa26af5eef3932d177374b3ddfd6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/__init__.py
@@ -0,0 +1,115 @@
+"""A functions module, includes all the standard functions.
+
+Combinatorial - factorial, fibonacci, harmonic, bernoulli...
+Elementary - hyperbolic, trigonometric, exponential, floor and ceiling, sqrt...
+Special - gamma, zeta,spherical harmonics...
+"""
+
+from sympy.functions.combinatorial.factorials import (factorial, factorial2,
+        rf, ff, binomial, RisingFactorial, FallingFactorial, subfactorial)
+from sympy.functions.combinatorial.numbers import (carmichael, fibonacci, lucas, tribonacci,
+        harmonic, bernoulli, bell, euler, catalan, genocchi, andre, partition, divisor_sigma,
+        udivisor_sigma, legendre_symbol, jacobi_symbol, kronecker_symbol, mobius,
+        primenu, primeomega, totient, reduced_totient, primepi, motzkin)
+from sympy.functions.elementary.miscellaneous import (sqrt, root, Min, Max,
+        Id, real_root, cbrt, Rem)
+from sympy.functions.elementary.complexes import (re, im, sign, Abs,
+        conjugate, arg, polar_lift, periodic_argument, unbranched_argument,
+        principal_branch, transpose, adjoint, polarify, unpolarify)
+from sympy.functions.elementary.trigonometric import (sin, cos, tan,
+        sec, csc, cot, sinc, asin, acos, atan, asec, acsc, acot, atan2)
+from sympy.functions.elementary.exponential import (exp_polar, exp, log,
+        LambertW)
+from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth,
+        sech, csch, asinh, acosh, atanh, acoth, asech, acsch)
+from sympy.functions.elementary.integers import floor, ceiling, frac
+from sympy.functions.elementary.piecewise import (Piecewise, piecewise_fold,
+                                                  piecewise_exclusive)
+from sympy.functions.special.error_functions import (erf, erfc, erfi, erf2,
+        erfinv, erfcinv, erf2inv, Ei, expint, E1, li, Li, Si, Ci, Shi, Chi,
+        fresnels, fresnelc)
+from sympy.functions.special.gamma_functions import (gamma, lowergamma,
+        uppergamma, polygamma, loggamma, digamma, trigamma, multigamma)
+from sympy.functions.special.zeta_functions import (dirichlet_eta, zeta,
+        lerchphi, polylog, stieltjes, riemann_xi)
+from sympy.functions.special.tensor_functions import (Eijk, LeviCivita,
+        KroneckerDelta)
+from sympy.functions.special.singularity_functions import SingularityFunction
+from sympy.functions.special.delta_functions import DiracDelta, Heaviside
+from sympy.functions.special.bsplines import bspline_basis, bspline_basis_set, interpolating_spline
+from sympy.functions.special.bessel import (besselj, bessely, besseli, besselk,
+        hankel1, hankel2, jn, yn, jn_zeros, hn1, hn2, airyai, airybi, airyaiprime, airybiprime, marcumq)
+from sympy.functions.special.hyper import hyper, meijerg, appellf1
+from sympy.functions.special.polynomials import (legendre, assoc_legendre,
+        hermite, hermite_prob, chebyshevt, chebyshevu, chebyshevu_root,
+        chebyshevt_root, laguerre, assoc_laguerre, gegenbauer, jacobi, jacobi_normalized)
+from sympy.functions.special.spherical_harmonics import Ynm, Ynm_c, Znm
+from sympy.functions.special.elliptic_integrals import (elliptic_k,
+        elliptic_f, elliptic_e, elliptic_pi)
+from sympy.functions.special.beta_functions import beta, betainc, betainc_regularized
+from sympy.functions.special.mathieu_functions import (mathieus, mathieuc,
+        mathieusprime, mathieucprime)
+ln = log
+
+__all__ = [
+    'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial',
+    'FallingFactorial', 'subfactorial',
+
+    'carmichael', 'fibonacci', 'lucas', 'motzkin', 'tribonacci', 'harmonic',
+    'bernoulli', 'bell', 'euler', 'catalan', 'genocchi', 'andre', 'partition',
+    'divisor_sigma', 'udivisor_sigma', 'legendre_symbol', 'jacobi_symbol', 'kronecker_symbol',
+    'mobius', 'primenu', 'primeomega', 'totient', 'reduced_totient', 'primepi',
+
+    'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root', 'cbrt', 'Rem',
+
+    're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift',
+    'periodic_argument', 'unbranched_argument', 'principal_branch',
+    'transpose', 'adjoint', 'polarify', 'unpolarify',
+
+    'sin', 'cos', 'tan', 'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan',
+    'asec', 'acsc', 'acot', 'atan2',
+
+    'exp_polar', 'exp', 'ln', 'log', 'LambertW',
+
+    'sinh', 'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh',
+    'acoth', 'asech', 'acsch',
+
+    'floor', 'ceiling', 'frac',
+
+    'Piecewise', 'piecewise_fold', 'piecewise_exclusive',
+
+    'erf', 'erfc', 'erfi', 'erf2', 'erfinv', 'erfcinv', 'erf2inv', 'Ei',
+    'expint', 'E1', 'li', 'Li', 'Si', 'Ci', 'Shi', 'Chi', 'fresnels',
+    'fresnelc',
+
+    'gamma', 'lowergamma', 'uppergamma', 'polygamma', 'loggamma', 'digamma',
+    'trigamma', 'multigamma',
+
+    'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'riemann_xi',
+
+    'Eijk', 'LeviCivita', 'KroneckerDelta',
+
+    'SingularityFunction',
+
+    'DiracDelta', 'Heaviside',
+
+    'bspline_basis', 'bspline_basis_set', 'interpolating_spline',
+
+    'besselj', 'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn',
+    'yn', 'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime',
+    'airybiprime', 'marcumq',
+
+    'hyper', 'meijerg', 'appellf1',
+
+    'legendre', 'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt',
+    'chebyshevu', 'chebyshevu_root', 'chebyshevt_root', 'laguerre',
+    'assoc_laguerre', 'gegenbauer', 'jacobi', 'jacobi_normalized',
+
+    'Ynm', 'Ynm_c', 'Znm',
+
+    'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi',
+
+    'beta', 'betainc', 'betainc_regularized',
+
+    'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..584b3c8d46b5c7600d85efc7db46d7aa190397f8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/__init__.py
@@ -0,0 +1 @@
+# Stub __init__.py for sympy.functions.combinatorial
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/factorials.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/factorials.py
new file mode 100644
index 0000000000000000000000000000000000000000..0c6d2f09524debca29d3040b28a019127a244b33
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/factorials.py
@@ -0,0 +1,1133 @@
+from __future__ import annotations
+from functools import reduce
+
+from sympy.core import S, sympify, Dummy, Mod
+from sympy.core.cache import cacheit
+from sympy.core.function import DefinedFunction, ArgumentIndexError, PoleError
+from sympy.core.logic import fuzzy_and
+from sympy.core.numbers import Integer, pi, I
+from sympy.core.relational import Eq
+from sympy.external.gmpy import gmpy as _gmpy
+from sympy.ntheory import sieve
+from sympy.ntheory.residue_ntheory import binomial_mod
+from sympy.polys.polytools import Poly
+
+from math import factorial as _factorial, prod, sqrt as _sqrt
+
+class CombinatorialFunction(DefinedFunction):
+    """Base class for combinatorial functions. """
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.simplify.combsimp import combsimp
+        # combinatorial function with non-integer arguments is
+        # automatically passed to gammasimp
+        expr = combsimp(self)
+        measure = kwargs['measure']
+        if measure(expr) <= kwargs['ratio']*measure(self):
+            return expr
+        return self
+
+
+###############################################################################
+######################## FACTORIAL and MULTI-FACTORIAL ########################
+###############################################################################
+
+
+class factorial(CombinatorialFunction):
+    r"""Implementation of factorial function over nonnegative integers.
+       By convention (consistent with the gamma function and the binomial
+       coefficients), factorial of a negative integer is complex infinity.
+
+       The factorial is very important in combinatorics where it gives
+       the number of ways in which `n` objects can be permuted. It also
+       arises in calculus, probability, number theory, etc.
+
+       There is strict relation of factorial with gamma function. In
+       fact `n! = gamma(n+1)` for nonnegative integers. Rewrite of this
+       kind is very useful in case of combinatorial simplification.
+
+       Computation of the factorial is done using two algorithms. For
+       small arguments a precomputed look up table is used. However for bigger
+       input algorithm Prime-Swing is used. It is the fastest algorithm
+       known and computes `n!` via prime factorization of special class
+       of numbers, called here the 'Swing Numbers'.
+
+       Examples
+       ========
+
+       >>> from sympy import Symbol, factorial, S
+       >>> n = Symbol('n', integer=True)
+
+       >>> factorial(0)
+       1
+
+       >>> factorial(7)
+       5040
+
+       >>> factorial(-2)
+       zoo
+
+       >>> factorial(n)
+       factorial(n)
+
+       >>> factorial(2*n)
+       factorial(2*n)
+
+       >>> factorial(S(1)/2)
+       factorial(1/2)
+
+       See Also
+       ========
+
+       factorial2, RisingFactorial, FallingFactorial
+    """
+
+    def fdiff(self, argindex=1):
+        from sympy.functions.special.gamma_functions import (gamma, polygamma)
+        if argindex == 1:
+            return gamma(self.args[0] + 1)*polygamma(0, self.args[0] + 1)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    _small_swing = [
+        1, 1, 1, 3, 3, 15, 5, 35, 35, 315, 63, 693, 231, 3003, 429, 6435, 6435, 109395,
+        12155, 230945, 46189, 969969, 88179, 2028117, 676039, 16900975, 1300075,
+        35102025, 5014575, 145422675, 9694845, 300540195, 300540195
+    ]
+
+    _small_factorials: list[int] = []
+
+    @classmethod
+    def _swing(cls, n):
+        if n < 33:
+            return cls._small_swing[n]
+        else:
+            N, primes = int(_sqrt(n)), []
+
+            for prime in sieve.primerange(3, N + 1):
+                p, q = 1, n
+
+                while True:
+                    q //= prime
+
+                    if q > 0:
+                        if q & 1 == 1:
+                            p *= prime
+                    else:
+                        break
+
+                if p > 1:
+                    primes.append(p)
+
+            for prime in sieve.primerange(N + 1, n//3 + 1):
+                if (n // prime) & 1 == 1:
+                    primes.append(prime)
+
+            L_product = prod(sieve.primerange(n//2 + 1, n + 1))
+            R_product = prod(primes)
+
+            return L_product*R_product
+
+    @classmethod
+    def _recursive(cls, n):
+        if n < 2:
+            return 1
+        else:
+            return (cls._recursive(n//2)**2)*cls._swing(n)
+
+    @classmethod
+    def eval(cls, n):
+        n = sympify(n)
+
+        if n.is_Number:
+            if n.is_zero:
+                return S.One
+            elif n is S.Infinity:
+                return S.Infinity
+            elif n.is_Integer:
+                if n.is_negative:
+                    return S.ComplexInfinity
+                else:
+                    n = n.p
+
+                    if n < 20:
+                        if not cls._small_factorials:
+                            result = 1
+                            for i in range(1, 20):
+                                result *= i
+                                cls._small_factorials.append(result)
+                        result = cls._small_factorials[n-1]
+
+                    # GMPY factorial is faster, use it when available
+                    #
+                    # XXX: There is a sympy.external.gmpy.factorial function
+                    # which provides gmpy.fac if available or the flint version
+                    # if flint is used. It could be used here to avoid the
+                    # conditional logic but it needs to be checked whether the
+                    # pure Python fallback used there is as fast as the
+                    # fallback used here (perhaps the fallback here should be
+                    # moved to sympy.external.ntheory).
+                    elif _gmpy is not None:
+                        result = _gmpy.fac(n)
+
+                    else:
+                        bits = bin(n).count('1')
+                        result = cls._recursive(n)*2**(n - bits)
+
+                    return Integer(result)
+
+    def _facmod(self, n, q):
+        res, N = 1, int(_sqrt(n))
+
+        # Exponent of prime p in n! is e_p(n) = [n/p] + [n/p**2] + ...
+        # for p > sqrt(n), e_p(n) < sqrt(n), the primes with [n/p] = m,
+        # occur consecutively and are grouped together in pw[m] for
+        # simultaneous exponentiation at a later stage
+        pw = [1]*N
+
+        m = 2 # to initialize the if condition below
+        for prime in sieve.primerange(2, n + 1):
+            if m > 1:
+                m, y = 0, n // prime
+                while y:
+                    m += y
+                    y //= prime
+            if m < N:
+                pw[m] = pw[m]*prime % q
+            else:
+                res = res*pow(prime, m, q) % q
+
+        for ex, bs in enumerate(pw):
+            if ex == 0 or bs == 1:
+                continue
+            if bs == 0:
+                return 0
+            res = res*pow(bs, ex, q) % q
+
+        return res
+
+    def _eval_Mod(self, q):
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative and q.is_integer:
+            aq = abs(q)
+            d = aq - n
+            if d.is_nonpositive:
+                return S.Zero
+            else:
+                isprime = aq.is_prime
+                if d == 1:
+                    # Apply Wilson's theorem (if a natural number n > 1
+                    # is a prime number, then (n-1)! = -1 mod n) and
+                    # its inverse (if n > 4 is a composite number, then
+                    # (n-1)! = 0 mod n)
+                    if isprime:
+                        return -1 % q
+                    elif isprime is False and (aq - 6).is_nonnegative:
+                        return S.Zero
+                elif n.is_Integer and q.is_Integer:
+                    n, d, aq = map(int, (n, d, aq))
+                    if isprime and (d - 1 < n):
+                        fc = self._facmod(d - 1, aq)
+                        fc = pow(fc, aq - 2, aq)
+                        if d%2:
+                            fc = -fc
+                    else:
+                        fc = self._facmod(n, aq)
+
+                    return fc % q
+
+    def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma
+        return gamma(n + 1)
+
+    def _eval_rewrite_as_Product(self, n, **kwargs):
+        from sympy.concrete.products import Product
+        if n.is_nonnegative and n.is_integer:
+            i = Dummy('i', integer=True)
+            return Product(i, (i, 1, n))
+
+    def _eval_is_integer(self):
+        if self.args[0].is_integer and self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_positive(self):
+        if self.args[0].is_integer and self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_even(self):
+        x = self.args[0]
+        if x.is_integer and x.is_nonnegative:
+            return (x - 2).is_nonnegative
+
+    def _eval_is_composite(self):
+        x = self.args[0]
+        if x.is_integer and x.is_nonnegative:
+            return (x - 3).is_nonnegative
+
+    def _eval_is_real(self):
+        x = self.args[0]
+        if x.is_nonnegative or x.is_noninteger:
+            return True
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x)
+        arg0 = arg.subs(x, 0)
+        if arg0.is_zero:
+            return S.One
+        elif not arg0.is_infinite:
+            return self.func(arg)
+        raise PoleError("Cannot expand %s around 0" % (self))
+
+class MultiFactorial(CombinatorialFunction):
+    pass
+
+
+class subfactorial(CombinatorialFunction):
+    r"""The subfactorial counts the derangements of $n$ items and is
+    defined for non-negative integers as:
+
+    .. math:: !n = \begin{cases} 1 & n = 0 \\ 0 & n = 1 \\
+                    (n-1)(!(n-1) + !(n-2)) & n > 1 \end{cases}
+
+    It can also be written as ``int(round(n!/exp(1)))`` but the
+    recursive definition with caching is implemented for this function.
+
+    An interesting analytic expression is the following [2]_
+
+    .. math:: !x = \Gamma(x + 1, -1)/e
+
+    which is valid for non-negative integers `x`. The above formula
+    is not very useful in case of non-integers. `\Gamma(x + 1, -1)` is
+    single-valued only for integral arguments `x`, elsewhere on the positive
+    real axis it has an infinite number of branches none of which are real.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Subfactorial
+    .. [2] https://mathworld.wolfram.com/Subfactorial.html
+
+    Examples
+    ========
+
+    >>> from sympy import subfactorial
+    >>> from sympy.abc import n
+    >>> subfactorial(n + 1)
+    subfactorial(n + 1)
+    >>> subfactorial(5)
+    44
+
+    See Also
+    ========
+
+    factorial, uppergamma,
+    sympy.utilities.iterables.generate_derangements
+    """
+
+    @classmethod
+    @cacheit
+    def _eval(self, n):
+        if not n:
+            return S.One
+        elif n == 1:
+            return S.Zero
+        else:
+            z1, z2 = 1, 0
+            for i in range(2, n + 1):
+                z1, z2 = z2, (i - 1)*(z2 + z1)
+            return z2
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg.is_Integer and arg.is_nonnegative:
+                return cls._eval(arg)
+            elif arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+
+    def _eval_is_even(self):
+        if self.args[0].is_odd and self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_integer(self):
+        if self.args[0].is_integer and self.args[0].is_nonnegative:
+            return True
+
+    def _eval_rewrite_as_factorial(self, arg, **kwargs):
+        from sympy.concrete.summations import summation
+        i = Dummy('i')
+        f = S.NegativeOne**i / factorial(i)
+        return factorial(arg) * summation(f, (i, 0, arg))
+
+    def _eval_rewrite_as_gamma(self, arg, piecewise=True, **kwargs):
+        from sympy.functions.elementary.exponential import exp
+        from sympy.functions.special.gamma_functions import (gamma, lowergamma)
+        return (S.NegativeOne**(arg + 1)*exp(-I*pi*arg)*lowergamma(arg + 1, -1)
+                + gamma(arg + 1))*exp(-1)
+
+    def _eval_rewrite_as_uppergamma(self, arg, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return uppergamma(arg + 1, -1)/S.Exp1
+
+    def _eval_is_nonnegative(self):
+        if self.args[0].is_integer and self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_odd(self):
+        if self.args[0].is_even and self.args[0].is_nonnegative:
+            return True
+
+
+class factorial2(CombinatorialFunction):
+    r"""The double factorial `n!!`, not to be confused with `(n!)!`
+
+    The double factorial is defined for nonnegative integers and for odd
+    negative integers as:
+
+    .. math:: n!! = \begin{cases} 1 & n = 0 \\
+                    n(n-2)(n-4) \cdots 1 & n\ \text{positive odd} \\
+                    n(n-2)(n-4) \cdots 2 & n\ \text{positive even} \\
+                    (n+2)!!/(n+2) & n\ \text{negative odd} \end{cases}
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Double_factorial
+
+    Examples
+    ========
+
+    >>> from sympy import factorial2, var
+    >>> n = var('n')
+    >>> n
+    n
+    >>> factorial2(n + 1)
+    factorial2(n + 1)
+    >>> factorial2(5)
+    15
+    >>> factorial2(-1)
+    1
+    >>> factorial2(-5)
+    1/3
+
+    See Also
+    ========
+
+    factorial, RisingFactorial, FallingFactorial
+    """
+
+    @classmethod
+    def eval(cls, arg):
+        # TODO: extend this to complex numbers?
+
+        if arg.is_Number:
+            if not arg.is_Integer:
+                raise ValueError("argument must be nonnegative integer "
+                                    "or negative odd integer")
+
+            # This implementation is faster than the recursive one
+            # It also avoids "maximum recursion depth exceeded" runtime error
+            if arg.is_nonnegative:
+                if arg.is_even:
+                    k = arg / 2
+                    return 2**k * factorial(k)
+                return factorial(arg) / factorial2(arg - 1)
+
+
+            if arg.is_odd:
+                return arg*(S.NegativeOne)**((1 - arg)/2) / factorial2(-arg)
+            raise ValueError("argument must be nonnegative integer "
+                                "or negative odd integer")
+
+
+    def _eval_is_even(self):
+        # Double factorial is even for every positive even input
+        n = self.args[0]
+        if n.is_integer:
+            if n.is_odd:
+                return False
+            if n.is_even:
+                if n.is_positive:
+                    return True
+                if n.is_zero:
+                    return False
+
+    def _eval_is_integer(self):
+        # Double factorial is an integer for every nonnegative input, and for
+        # -1 and -3
+        n = self.args[0]
+        if n.is_integer:
+            if (n + 1).is_nonnegative:
+                return True
+            if n.is_odd:
+                return (n + 3).is_nonnegative
+
+    def _eval_is_odd(self):
+        # Double factorial is odd for every odd input not smaller than -3, and
+        # for 0
+        n = self.args[0]
+        if n.is_odd:
+            return (n + 3).is_nonnegative
+        if n.is_even:
+            if n.is_positive:
+                return False
+            if n.is_zero:
+                return True
+
+    def _eval_is_positive(self):
+        # Double factorial is positive for every nonnegative input, and for
+        # every odd negative input which is of the form -1-4k for an
+        # nonnegative integer k
+        n = self.args[0]
+        if n.is_integer:
+            if (n + 1).is_nonnegative:
+                return True
+            if n.is_odd:
+                return ((n + 1) / 2).is_even
+
+    def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs):
+        from sympy.functions.elementary.miscellaneous import sqrt
+        from sympy.functions.elementary.piecewise import Piecewise
+        from sympy.functions.special.gamma_functions import gamma
+        return 2**(n/2)*gamma(n/2 + 1) * Piecewise((1, Eq(Mod(n, 2), 0)),
+                (sqrt(2/pi), Eq(Mod(n, 2), 1)))
+
+
+###############################################################################
+######################## RISING and FALLING FACTORIALS ########################
+###############################################################################
+
+
+class RisingFactorial(CombinatorialFunction):
+    r"""
+    Rising factorial (also called Pochhammer symbol [1]_) is a double valued
+    function arising in concrete mathematics, hypergeometric functions
+    and series expansions. It is defined by:
+
+    .. math:: \texttt{rf(y, k)} = (x)^k = x \cdot (x+1) \cdots (x+k-1)
+
+    where `x` can be arbitrary expression and `k` is an integer. For
+    more information check "Concrete mathematics" by Graham, pp. 66
+    or visit https://mathworld.wolfram.com/RisingFactorial.html page.
+
+    When `x` is a `~.Poly` instance of degree $\ge 1$ with a single variable,
+    `(x)^k = x(y) \cdot x(y+1) \cdots x(y+k-1)`, where `y` is the
+    variable of `x`. This is as described in [2]_.
+
+    Examples
+    ========
+
+    >>> from sympy import rf, Poly
+    >>> from sympy.abc import x
+    >>> rf(x, 0)
+    1
+    >>> rf(1, 5)
+    120
+    >>> rf(x, 5) == x*(1 + x)*(2 + x)*(3 + x)*(4 + x)
+    True
+    >>> rf(Poly(x**3, x), 2)
+    Poly(x**6 + 3*x**5 + 3*x**4 + x**3, x, domain='ZZ')
+
+    Rewriting is complicated unless the relationship between
+    the arguments is known, but rising factorial can
+    be rewritten in terms of gamma, factorial, binomial,
+    and falling factorial.
+
+    >>> from sympy import Symbol, factorial, ff, binomial, gamma
+    >>> n = Symbol('n', integer=True, positive=True)
+    >>> R = rf(n, n + 2)
+    >>> for i in (rf, ff, factorial, binomial, gamma):
+    ...  R.rewrite(i)
+    ...
+    RisingFactorial(n, n + 2)
+    FallingFactorial(2*n + 1, n + 2)
+    factorial(2*n + 1)/factorial(n - 1)
+    binomial(2*n + 1, n + 2)*factorial(n + 2)
+    gamma(2*n + 2)/gamma(n)
+
+    See Also
+    ========
+
+    factorial, factorial2, FallingFactorial
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Pochhammer_symbol
+    .. [2] Peter Paule, "Greatest Factorial Factorization and Symbolic
+           Summation", Journal of Symbolic Computation, vol. 20, pp. 235-268,
+           1995.
+
+    """
+
+    @classmethod
+    def eval(cls, x, k):
+        x = sympify(x)
+        k = sympify(k)
+
+        if x is S.NaN or k is S.NaN:
+            return S.NaN
+        elif x is S.One:
+            return factorial(k)
+        elif k.is_Integer:
+            if k.is_zero:
+                return S.One
+            else:
+                if k.is_positive:
+                    if x is S.Infinity:
+                        return S.Infinity
+                    elif x is S.NegativeInfinity:
+                        if k.is_odd:
+                            return S.NegativeInfinity
+                        else:
+                            return S.Infinity
+                    else:
+                        if isinstance(x, Poly):
+                            gens = x.gens
+                            if len(gens)!= 1:
+                                raise ValueError("rf only defined for "
+                                            "polynomials on one generator")
+                            else:
+                                return reduce(lambda r, i:
+                                              r*(x.shift(i)),
+                                              range(int(k)), 1)
+                        else:
+                            return reduce(lambda r, i: r*(x + i),
+                                          range(int(k)), 1)
+
+                else:
+                    if x is S.Infinity:
+                        return S.Infinity
+                    elif x is S.NegativeInfinity:
+                        return S.Infinity
+                    else:
+                        if isinstance(x, Poly):
+                            gens = x.gens
+                            if len(gens)!= 1:
+                                raise ValueError("rf only defined for "
+                                            "polynomials on one generator")
+                            else:
+                                return 1/reduce(lambda r, i:
+                                                r*(x.shift(-i)),
+                                                range(1, abs(int(k)) + 1), 1)
+                        else:
+                            return 1/reduce(lambda r, i:
+                                            r*(x - i),
+                                            range(1, abs(int(k)) + 1), 1)
+
+        if k.is_integer == False:
+            if x.is_integer and x.is_negative:
+                return S.Zero
+
+    def _eval_rewrite_as_gamma(self, x, k, piecewise=True, **kwargs):
+        from sympy.functions.elementary.piecewise import Piecewise
+        from sympy.functions.special.gamma_functions import gamma
+        if not piecewise:
+            if (x <= 0) == True:
+                return S.NegativeOne**k*gamma(1 - x) / gamma(-k - x + 1)
+            return gamma(x + k) / gamma(x)
+        return Piecewise(
+            (gamma(x + k) / gamma(x), x > 0),
+            (S.NegativeOne**k*gamma(1 - x) / gamma(-k - x + 1), True))
+
+    def _eval_rewrite_as_FallingFactorial(self, x, k, **kwargs):
+        return FallingFactorial(x + k - 1, k)
+
+    def _eval_rewrite_as_factorial(self, x, k, **kwargs):
+        from sympy.functions.elementary.piecewise import Piecewise
+        if x.is_integer and k.is_integer:
+            return Piecewise(
+                (factorial(k + x - 1)/factorial(x - 1), x > 0),
+                (S.NegativeOne**k*factorial(-x)/factorial(-k - x), True))
+
+    def _eval_rewrite_as_binomial(self, x, k, **kwargs):
+        if k.is_integer:
+            return factorial(k) * binomial(x + k - 1, k)
+
+    def _eval_rewrite_as_tractable(self, x, k, limitvar=None, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma
+        if limitvar:
+            k_lim = k.subs(limitvar, S.Infinity)
+            if k_lim is S.Infinity:
+                return (gamma(x + k).rewrite('tractable', deep=True) / gamma(x))
+            elif k_lim is S.NegativeInfinity:
+                return (S.NegativeOne**k*gamma(1 - x) / gamma(-k - x + 1).rewrite('tractable', deep=True))
+        return self.rewrite(gamma).rewrite('tractable', deep=True)
+
+    def _eval_is_integer(self):
+        return fuzzy_and((self.args[0].is_integer, self.args[1].is_integer,
+                          self.args[1].is_nonnegative))
+
+
+class FallingFactorial(CombinatorialFunction):
+    r"""
+    Falling factorial (related to rising factorial) is a double valued
+    function arising in concrete mathematics, hypergeometric functions
+    and series expansions. It is defined by
+
+    .. math:: \texttt{ff(x, k)} = (x)_k = x \cdot (x-1) \cdots (x-k+1)
+
+    where `x` can be arbitrary expression and `k` is an integer. For
+    more information check "Concrete mathematics" by Graham, pp. 66
+    or [1]_.
+
+    When `x` is a `~.Poly` instance of degree $\ge 1$ with single variable,
+    `(x)_k = x(y) \cdot x(y-1) \cdots x(y-k+1)`, where `y` is the
+    variable of `x`. This is as described in
+
+    >>> from sympy import ff, Poly, Symbol
+    >>> from sympy.abc import x
+    >>> n = Symbol('n', integer=True)
+
+    >>> ff(x, 0)
+    1
+    >>> ff(5, 5)
+    120
+    >>> ff(x, 5) == x*(x - 1)*(x - 2)*(x - 3)*(x - 4)
+    True
+    >>> ff(Poly(x**2, x), 2)
+    Poly(x**4 - 2*x**3 + x**2, x, domain='ZZ')
+    >>> ff(n, n)
+    factorial(n)
+
+    Rewriting is complicated unless the relationship between
+    the arguments is known, but falling factorial can
+    be rewritten in terms of gamma, factorial and binomial
+    and rising factorial.
+
+    >>> from sympy import factorial, rf, gamma, binomial, Symbol
+    >>> n = Symbol('n', integer=True, positive=True)
+    >>> F = ff(n, n - 2)
+    >>> for i in (rf, ff, factorial, binomial, gamma):
+    ...  F.rewrite(i)
+    ...
+    RisingFactorial(3, n - 2)
+    FallingFactorial(n, n - 2)
+    factorial(n)/2
+    binomial(n, n - 2)*factorial(n - 2)
+    gamma(n + 1)/2
+
+    See Also
+    ========
+
+    factorial, factorial2, RisingFactorial
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/FallingFactorial.html
+    .. [2] Peter Paule, "Greatest Factorial Factorization and Symbolic
+           Summation", Journal of Symbolic Computation, vol. 20, pp. 235-268,
+           1995.
+
+    """
+
+    @classmethod
+    def eval(cls, x, k):
+        x = sympify(x)
+        k = sympify(k)
+
+        if x is S.NaN or k is S.NaN:
+            return S.NaN
+        elif k.is_integer and x == k:
+            return factorial(x)
+        elif k.is_Integer:
+            if k.is_zero:
+                return S.One
+            else:
+                if k.is_positive:
+                    if x is S.Infinity:
+                        return S.Infinity
+                    elif x is S.NegativeInfinity:
+                        if k.is_odd:
+                            return S.NegativeInfinity
+                        else:
+                            return S.Infinity
+                    else:
+                        if isinstance(x, Poly):
+                            gens = x.gens
+                            if len(gens)!= 1:
+                                raise ValueError("ff only defined for "
+                                            "polynomials on one generator")
+                            else:
+                                return reduce(lambda r, i:
+                                              r*(x.shift(-i)),
+                                              range(int(k)), 1)
+                        else:
+                            return reduce(lambda r, i: r*(x - i),
+                                          range(int(k)), 1)
+                else:
+                    if x is S.Infinity:
+                        return S.Infinity
+                    elif x is S.NegativeInfinity:
+                        return S.Infinity
+                    else:
+                        if isinstance(x, Poly):
+                            gens = x.gens
+                            if len(gens)!= 1:
+                                raise ValueError("rf only defined for "
+                                            "polynomials on one generator")
+                            else:
+                                return 1/reduce(lambda r, i:
+                                                r*(x.shift(i)),
+                                                range(1, abs(int(k)) + 1), 1)
+                        else:
+                            return 1/reduce(lambda r, i: r*(x + i),
+                                            range(1, abs(int(k)) + 1), 1)
+
+    def _eval_rewrite_as_gamma(self, x, k, piecewise=True, **kwargs):
+        from sympy.functions.elementary.piecewise import Piecewise
+        from sympy.functions.special.gamma_functions import gamma
+        if not piecewise:
+            if (x < 0) == True:
+                return S.NegativeOne**k*gamma(k - x) / gamma(-x)
+            return gamma(x + 1) / gamma(x - k + 1)
+        return Piecewise(
+            (gamma(x + 1) / gamma(x - k + 1), x >= 0),
+            (S.NegativeOne**k*gamma(k - x) / gamma(-x), True))
+
+    def _eval_rewrite_as_RisingFactorial(self, x, k, **kwargs):
+        return rf(x - k + 1, k)
+
+    def _eval_rewrite_as_binomial(self, x, k, **kwargs):
+        if k.is_integer:
+            return factorial(k) * binomial(x, k)
+
+    def _eval_rewrite_as_factorial(self, x, k, **kwargs):
+        from sympy.functions.elementary.piecewise import Piecewise
+        if x.is_integer and k.is_integer:
+            return Piecewise(
+                (factorial(x)/factorial(-k + x), x >= 0),
+                (S.NegativeOne**k*factorial(k - x - 1)/factorial(-x - 1), True))
+
+    def _eval_rewrite_as_tractable(self, x, k, limitvar=None, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma
+        if limitvar:
+            k_lim = k.subs(limitvar, S.Infinity)
+            if k_lim is S.Infinity:
+                return (S.NegativeOne**k*gamma(k - x).rewrite('tractable', deep=True) / gamma(-x))
+            elif k_lim is S.NegativeInfinity:
+                return (gamma(x + 1) / gamma(x - k + 1).rewrite('tractable', deep=True))
+        return self.rewrite(gamma).rewrite('tractable', deep=True)
+
+    def _eval_is_integer(self):
+        return fuzzy_and((self.args[0].is_integer, self.args[1].is_integer,
+                          self.args[1].is_nonnegative))
+
+
+rf = RisingFactorial
+ff = FallingFactorial
+
+###############################################################################
+########################### BINOMIAL COEFFICIENTS #############################
+###############################################################################
+
+
+class binomial(CombinatorialFunction):
+    r"""Implementation of the binomial coefficient. It can be defined
+    in two ways depending on its desired interpretation:
+
+    .. math:: \binom{n}{k} = \frac{n!}{k!(n-k)!}\ \text{or}\
+                \binom{n}{k} = \frac{(n)_k}{k!}
+
+    First, in a strict combinatorial sense it defines the
+    number of ways we can choose `k` elements from a set of
+    `n` elements. In this case both arguments are nonnegative
+    integers and binomial is computed using an efficient
+    algorithm based on prime factorization.
+
+    The other definition is generalization for arbitrary `n`,
+    however `k` must also be nonnegative. This case is very
+    useful when evaluating summations.
+
+    For the sake of convenience, for negative integer `k` this function
+    will return zero no matter the other argument.
+
+    To expand the binomial when `n` is a symbol, use either
+    ``expand_func()`` or ``expand(func=True)``. The former will keep
+    the polynomial in factored form while the latter will expand the
+    polynomial itself. See examples for details.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, Rational, binomial, expand_func
+    >>> n = Symbol('n', integer=True, positive=True)
+
+    >>> binomial(15, 8)
+    6435
+
+    >>> binomial(n, -1)
+    0
+
+    Rows of Pascal's triangle can be generated with the binomial function:
+
+    >>> for N in range(8):
+    ...     print([binomial(N, i) for i in range(N + 1)])
+    ...
+    [1]
+    [1, 1]
+    [1, 2, 1]
+    [1, 3, 3, 1]
+    [1, 4, 6, 4, 1]
+    [1, 5, 10, 10, 5, 1]
+    [1, 6, 15, 20, 15, 6, 1]
+    [1, 7, 21, 35, 35, 21, 7, 1]
+
+    As can a given diagonal, e.g. the 4th diagonal:
+
+    >>> N = -4
+    >>> [binomial(N, i) for i in range(1 - N)]
+    [1, -4, 10, -20, 35]
+
+    >>> binomial(Rational(5, 4), 3)
+    -5/128
+    >>> binomial(Rational(-5, 4), 3)
+    -195/128
+
+    >>> binomial(n, 3)
+    binomial(n, 3)
+
+    >>> binomial(n, 3).expand(func=True)
+    n**3/6 - n**2/2 + n/3
+
+    >>> expand_func(binomial(n, 3))
+    n*(n - 2)*(n - 1)/6
+
+    In many cases, we can also compute binomial coefficients modulo a
+    prime p quickly using Lucas' Theorem [2]_, though we need to include
+    `evaluate=False` to postpone evaluation:
+
+    >>> from sympy import Mod
+    >>> Mod(binomial(156675, 4433, evaluate=False), 10**5 + 3)
+    28625
+
+    Using a generalisation of Lucas's Theorem given by Granville [3]_,
+    we can extend this to arbitrary n:
+
+    >>> Mod(binomial(10**18, 10**12, evaluate=False), (10**5 + 3)**2)
+    3744312326
+
+    References
+    ==========
+
+    .. [1] https://www.johndcook.com/blog/binomial_coefficients/
+    .. [2] https://en.wikipedia.org/wiki/Lucas%27s_theorem
+    .. [3] Binomial coefficients modulo prime powers, Andrew Granville,
+        Available: https://web.archive.org/web/20170202003812/http://www.dms.umontreal.ca/~andrew/PDF/BinCoeff.pdf
+    """
+
+    def fdiff(self, argindex=1):
+        from sympy.functions.special.gamma_functions import polygamma
+        if argindex == 1:
+            # https://functions.wolfram.com/GammaBetaErf/Binomial/20/01/01/
+            n, k = self.args
+            return binomial(n, k)*(polygamma(0, n + 1) - \
+                polygamma(0, n - k + 1))
+        elif argindex == 2:
+            # https://functions.wolfram.com/GammaBetaErf/Binomial/20/01/02/
+            n, k = self.args
+            return binomial(n, k)*(polygamma(0, n - k + 1) - \
+                polygamma(0, k + 1))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def _eval(self, n, k):
+        # n.is_Number and k.is_Integer and k != 1 and n != k
+
+        if k.is_Integer:
+            if n.is_Integer and n >= 0:
+                n, k = int(n), int(k)
+
+                if k > n:
+                    return S.Zero
+                elif k > n // 2:
+                    k = n - k
+
+                # XXX: This conditional logic should be moved to
+                # sympy.external.gmpy and the pure Python version of bincoef
+                # should be moved to sympy.external.ntheory.
+                if _gmpy is not None:
+                    return Integer(_gmpy.bincoef(n, k))
+
+                d, result = n - k, 1
+                for i in range(1, k + 1):
+                    d += 1
+                    result = result * d // i
+                return Integer(result)
+            else:
+                d, result = n - k, 1
+                for i in range(1, k + 1):
+                    d += 1
+                    result *= d
+                return result / _factorial(k)
+
+    @classmethod
+    def eval(cls, n, k):
+        n, k = map(sympify, (n, k))
+        d = n - k
+        n_nonneg, n_isint = n.is_nonnegative, n.is_integer
+        if k.is_zero or ((n_nonneg or n_isint is False)
+                and d.is_zero):
+            return S.One
+        if (k - 1).is_zero or ((n_nonneg or n_isint is False)
+                and (d - 1).is_zero):
+            return n
+        if k.is_integer:
+            if k.is_negative or (n_nonneg and n_isint and d.is_negative):
+                return S.Zero
+            elif n.is_number:
+                res = cls._eval(n, k)
+                return res.expand(basic=True) if res else res
+        elif n_nonneg is False and n_isint:
+            # a special case when binomial evaluates to complex infinity
+            return S.ComplexInfinity
+        elif k.is_number:
+            from sympy.functions.special.gamma_functions import gamma
+            return gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1))
+
+    def _eval_Mod(self, q):
+        n, k = self.args
+
+        if any(x.is_integer is False for x in (n, k, q)):
+            raise ValueError("Integers expected for binomial Mod")
+
+        if all(x.is_Integer for x in (n, k, q)):
+            n, k = map(int, (n, k))
+            aq, res = abs(q), 1
+
+            # handle negative integers k or n
+            if k < 0:
+                return S.Zero
+            if n < 0:
+                n = -n + k - 1
+                res = -1 if k%2 else 1
+
+            # non negative integers k and n
+            if k > n:
+                return S.Zero
+
+            isprime = aq.is_prime
+            aq = int(aq)
+            if isprime:
+                if aq < n:
+                    # use Lucas Theorem
+                    N, K = n, k
+                    while N or K:
+                        res = res*binomial(N % aq, K % aq) % aq
+                        N, K = N // aq, K // aq
+
+                else:
+                    # use Factorial Modulo
+                    d = n - k
+                    if k > d:
+                        k, d = d, k
+                    kf = 1
+                    for i in range(2, k + 1):
+                        kf = kf*i % aq
+                    df = kf
+                    for i in range(k + 1, d + 1):
+                        df = df*i % aq
+                    res *= df
+                    for i in range(d + 1, n + 1):
+                        res = res*i % aq
+
+                    res *= pow(kf*df % aq, aq - 2, aq)
+                    res %= aq
+
+            elif _sqrt(q) < k and q != 1:
+                res = binomial_mod(n, k, q)
+
+            else:
+                # Binomial Factorization is performed by calculating the
+                # exponents of primes <= n in `n! /(k! (n - k)!)`,
+                # for non-negative integers n and k. As the exponent of
+                # prime in n! is e_p(n) = [n/p] + [n/p**2] + ...
+                # the exponent of prime in binomial(n, k) would be
+                # e_p(n) - e_p(k) - e_p(n - k)
+                M = int(_sqrt(n))
+                for prime in sieve.primerange(2, n + 1):
+                    if prime > n - k:
+                        res = res*prime % aq
+                    elif prime > n // 2:
+                        continue
+                    elif prime > M:
+                        if n % prime < k % prime:
+                            res = res*prime % aq
+                    else:
+                        N, K = n, k
+                        exp = a = 0
+
+                        while N > 0:
+                            a = int((N % prime) < (K % prime + a))
+                            N, K = N // prime, K // prime
+                            exp += a
+
+                        if exp > 0:
+                            res *= pow(prime, exp, aq)
+                            res %= aq
+
+            return S(res % q)
+
+    def _eval_expand_func(self, **hints):
+        """
+        Function to expand binomial(n, k) when m is positive integer
+        Also,
+        n is self.args[0] and k is self.args[1] while using binomial(n, k)
+        """
+        n = self.args[0]
+        if n.is_Number:
+            return binomial(*self.args)
+
+        k = self.args[1]
+        if (n-k).is_Integer:
+            k = n - k
+
+        if k.is_Integer:
+            if k.is_zero:
+                return S.One
+            elif k.is_negative:
+                return S.Zero
+            else:
+                n, result = self.args[0], 1
+                for i in range(1, k + 1):
+                    result *= n - k + i
+                return result / _factorial(k)
+        else:
+            return binomial(*self.args)
+
+    def _eval_rewrite_as_factorial(self, n, k, **kwargs):
+        return factorial(n)/(factorial(k)*factorial(n - k))
+
+    def _eval_rewrite_as_gamma(self, n, k, piecewise=True, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma
+        return gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1))
+
+    def _eval_rewrite_as_tractable(self, n, k, limitvar=None, **kwargs):
+        return self._eval_rewrite_as_gamma(n, k).rewrite('tractable')
+
+    def _eval_rewrite_as_FallingFactorial(self, n, k, **kwargs):
+        if k.is_integer:
+            return ff(n, k) / factorial(k)
+
+    def _eval_is_integer(self):
+        n, k = self.args
+        if n.is_integer and k.is_integer:
+            return True
+        elif k.is_integer is False:
+            return False
+
+    def _eval_is_nonnegative(self):
+        n, k = self.args
+        if n.is_integer and k.is_integer:
+            if n.is_nonnegative or k.is_negative or k.is_even:
+                return True
+            elif k.is_even is False:
+                return  False
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.functions.special.gamma_functions import gamma
+        return self.rewrite(gamma)._eval_as_leading_term(x, logx=logx, cdir=cdir)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..c0dfc518d4a6784712341edaa5731145469a8d1e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/numbers.py
@@ -0,0 +1,3196 @@
+"""
+This module implements some special functions that commonly appear in
+combinatorial contexts (e.g. in power series); in particular,
+sequences of rational numbers such as Bernoulli and Fibonacci numbers.
+
+Factorials, binomial coefficients and related functions are located in
+the separate 'factorials' module.
+"""
+from __future__ import annotations
+from math import prod
+from collections import defaultdict
+from typing import Callable
+
+from sympy.core import S, Symbol, Add, Dummy
+from sympy.core.cache import cacheit
+from sympy.core.containers import Dict
+from sympy.core.expr import Expr
+from sympy.core.function import ArgumentIndexError, DefinedFunction, expand_mul
+from sympy.core.logic import fuzzy_not
+from sympy.core.mul import Mul
+from sympy.core.numbers import E, I, pi, oo, Rational, Integer
+from sympy.core.relational import Eq, is_le, is_gt, is_lt
+from sympy.external.gmpy import SYMPY_INTS, remove, lcm, legendre, jacobi, kronecker
+from sympy.functions.combinatorial.factorials import (binomial,
+    factorial, subfactorial)
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.ntheory.factor_ import (factorint, _divisor_sigma, is_carmichael,
+                                   find_carmichael_numbers_in_range, find_first_n_carmichaels)
+from sympy.ntheory.generate import _primepi
+from sympy.ntheory.partitions_ import _partition, _partition_rec
+from sympy.ntheory.primetest import isprime, is_square
+from sympy.polys.appellseqs import bernoulli_poly, euler_poly, genocchi_poly
+from sympy.polys.polytools import cancel
+from sympy.utilities.enumerative import MultisetPartitionTraverser
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import multiset, multiset_derangements, iterable
+from sympy.utilities.memoization import recurrence_memo
+from sympy.utilities.misc import as_int
+
+from mpmath import mp, workprec
+from mpmath.libmp import ifib as _ifib
+
+
+def _product(a, b):
+    return prod(range(a, b + 1))
+
+
+# Dummy symbol used for computing polynomial sequences
+_sym = Symbol('x')
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Carmichael numbers                               #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+class carmichael(DefinedFunction):
+    r"""
+    Carmichael Numbers:
+
+    Certain cryptographic algorithms make use of big prime numbers.
+    However, checking whether a big number is prime is not so easy.
+    Randomized prime number checking tests exist that offer a high degree of
+    confidence of accurate determination at low cost, such as the Fermat test.
+
+    Let 'a' be a random number between $2$ and $n - 1$, where $n$ is the
+    number whose primality we are testing. Then, $n$ is probably prime if it
+    satisfies the modular arithmetic congruence relation:
+
+    .. math :: a^{n-1} = 1 \pmod{n}
+
+    (where mod refers to the modulo operation)
+
+    If a number passes the Fermat test several times, then it is prime with a
+    high probability.
+
+    Unfortunately, certain composite numbers (non-primes) still pass the Fermat
+    test with every number smaller than themselves.
+    These numbers are called Carmichael numbers.
+
+    A Carmichael number will pass a Fermat primality test to every base $b$
+    relatively prime to the number, even though it is not actually prime.
+    This makes tests based on Fermat's Little Theorem less effective than
+    strong probable prime tests such as the Baillie-PSW primality test and
+    the Miller-Rabin primality test.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import find_first_n_carmichaels, find_carmichael_numbers_in_range
+    >>> find_first_n_carmichaels(5)
+    [561, 1105, 1729, 2465, 2821]
+    >>> find_carmichael_numbers_in_range(0, 562)
+    [561]
+    >>> find_carmichael_numbers_in_range(0,1000)
+    [561]
+    >>> find_carmichael_numbers_in_range(0,2000)
+    [561, 1105, 1729]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Carmichael_number
+    .. [2] https://en.wikipedia.org/wiki/Fermat_primality_test
+    .. [3] https://www.jstor.org/stable/23248683?seq=1#metadata_info_tab_contents
+    """
+
+    @staticmethod
+    def is_perfect_square(n):
+        sympy_deprecation_warning(
+        """
+is_perfect_square is just a wrapper around sympy.ntheory.primetest.is_square
+so use that directly instead.
+        """,
+        deprecated_since_version="1.11",
+        active_deprecations_target='deprecated-carmichael-static-methods',
+        )
+        return is_square(n)
+
+    @staticmethod
+    def divides(p, n):
+        sympy_deprecation_warning(
+        """
+        divides can be replaced by directly testing n % p == 0.
+        """,
+        deprecated_since_version="1.11",
+        active_deprecations_target='deprecated-carmichael-static-methods',
+        )
+        return n % p == 0
+
+    @staticmethod
+    def is_prime(n):
+        sympy_deprecation_warning(
+        """
+is_prime is just a wrapper around sympy.ntheory.primetest.isprime so use that
+directly instead.
+        """,
+        deprecated_since_version="1.11",
+        active_deprecations_target='deprecated-carmichael-static-methods',
+        )
+        return isprime(n)
+
+    @staticmethod
+    def is_carmichael(n):
+        sympy_deprecation_warning(
+        """
+is_carmichael is just a wrapper around sympy.ntheory.factor_.is_carmichael so use that
+directly instead.
+        """,
+        deprecated_since_version="1.13",
+        active_deprecations_target='deprecated-ntheory-symbolic-functions',
+        )
+        return is_carmichael(n)
+
+    @staticmethod
+    def find_carmichael_numbers_in_range(x, y):
+        sympy_deprecation_warning(
+        """
+find_carmichael_numbers_in_range is just a wrapper around sympy.ntheory.factor_.find_carmichael_numbers_in_range so use that
+directly instead.
+        """,
+        deprecated_since_version="1.13",
+        active_deprecations_target='deprecated-ntheory-symbolic-functions',
+        )
+        return find_carmichael_numbers_in_range(x, y)
+
+    @staticmethod
+    def find_first_n_carmichaels(n):
+        sympy_deprecation_warning(
+        """
+find_first_n_carmichaels is just a wrapper around sympy.ntheory.factor_.find_first_n_carmichaels so use that
+directly instead.
+        """,
+        deprecated_since_version="1.13",
+        active_deprecations_target='deprecated-ntheory-symbolic-functions',
+        )
+        return find_first_n_carmichaels(n)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Fibonacci numbers                                #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class fibonacci(DefinedFunction):
+    r"""
+    Fibonacci numbers / Fibonacci polynomials
+
+    The Fibonacci numbers are the integer sequence defined by the
+    initial terms `F_0 = 0`, `F_1 = 1` and the two-term recurrence
+    relation `F_n = F_{n-1} + F_{n-2}`.  This definition
+    extended to arbitrary real and complex arguments using
+    the formula
+
+    .. math :: F_z = \frac{\phi^z - \cos(\pi z) \phi^{-z}}{\sqrt 5}
+
+    The Fibonacci polynomials are defined by `F_1(x) = 1`,
+    `F_2(x) = x`, and `F_n(x) = x*F_{n-1}(x) + F_{n-2}(x)` for `n > 2`.
+    For all positive integers `n`, `F_n(1) = F_n`.
+
+    * ``fibonacci(n)`` gives the `n^{th}` Fibonacci number, `F_n`
+    * ``fibonacci(n, x)`` gives the `n^{th}` Fibonacci polynomial in `x`, `F_n(x)`
+
+    Examples
+    ========
+
+    >>> from sympy import fibonacci, Symbol
+
+    >>> [fibonacci(x) for x in range(11)]
+    [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
+    >>> fibonacci(5, Symbol('t'))
+    t**4 + 3*t**2 + 1
+
+    See Also
+    ========
+
+    bell, bernoulli, catalan, euler, harmonic, lucas, genocchi, partition, tribonacci
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fibonacci_number
+    .. [2] https://mathworld.wolfram.com/FibonacciNumber.html
+
+    """
+
+    @staticmethod
+    def _fib(n):
+        return _ifib(n)
+
+    @staticmethod
+    @recurrence_memo([None, S.One, _sym])
+    def _fibpoly(n, prev):
+        return (prev[-2] + _sym*prev[-1]).expand()
+
+    @classmethod
+    def eval(cls, n, sym=None):
+        if n is S.Infinity:
+            return S.Infinity
+
+        if n.is_Integer:
+            if sym is None:
+                n = int(n)
+                if n < 0:
+                    return S.NegativeOne**(n + 1) * fibonacci(-n)
+                else:
+                    return Integer(cls._fib(n))
+            else:
+                if n < 1:
+                    raise ValueError("Fibonacci polynomials are defined "
+                       "only for positive integer indices.")
+                return cls._fibpoly(n).subs(_sym, sym)
+
+    def _eval_rewrite_as_tractable(self, n, **kwargs):
+        from sympy.functions import sqrt, cos
+        return (S.GoldenRatio**n - cos(S.Pi*n)/S.GoldenRatio**n)/sqrt(5)
+
+    def _eval_rewrite_as_sqrt(self, n, **kwargs):
+        from sympy.functions.elementary.miscellaneous import sqrt
+        return 2**(-n)*sqrt(5)*((1 + sqrt(5))**n - (-sqrt(5) + 1)**n) / 5
+
+    def _eval_rewrite_as_GoldenRatio(self,n, **kwargs):
+        return (S.GoldenRatio**n - 1/(-S.GoldenRatio)**n)/(2*S.GoldenRatio-1)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                               Lucas numbers                                #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class lucas(DefinedFunction):
+    """
+    Lucas numbers
+
+    Lucas numbers satisfy a recurrence relation similar to that of
+    the Fibonacci sequence, in which each term is the sum of the
+    preceding two. They are generated by choosing the initial
+    values `L_0 = 2` and `L_1 = 1`.
+
+    * ``lucas(n)`` gives the `n^{th}` Lucas number
+
+    Examples
+    ========
+
+    >>> from sympy import lucas
+
+    >>> [lucas(x) for x in range(11)]
+    [2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123]
+
+    See Also
+    ========
+
+    bell, bernoulli, catalan, euler, fibonacci, harmonic, genocchi, partition, tribonacci
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Lucas_number
+    .. [2] https://mathworld.wolfram.com/LucasNumber.html
+
+    """
+
+    @classmethod
+    def eval(cls, n):
+        if n is S.Infinity:
+            return S.Infinity
+
+        if n.is_Integer:
+            return fibonacci(n + 1) + fibonacci(n - 1)
+
+    def _eval_rewrite_as_sqrt(self, n, **kwargs):
+        from sympy.functions.elementary.miscellaneous import sqrt
+        return 2**(-n)*((1 + sqrt(5))**n + (-sqrt(5) + 1)**n)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                             Tribonacci numbers                             #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class tribonacci(DefinedFunction):
+    r"""
+    Tribonacci numbers / Tribonacci polynomials
+
+    The Tribonacci numbers are the integer sequence defined by the
+    initial terms `T_0 = 0`, `T_1 = 1`, `T_2 = 1` and the three-term
+    recurrence relation `T_n = T_{n-1} + T_{n-2} + T_{n-3}`.
+
+    The Tribonacci polynomials are defined by `T_0(x) = 0`, `T_1(x) = 1`,
+    `T_2(x) = x^2`, and `T_n(x) = x^2 T_{n-1}(x) + x T_{n-2}(x) + T_{n-3}(x)`
+    for `n > 2`.  For all positive integers `n`, `T_n(1) = T_n`.
+
+    * ``tribonacci(n)`` gives the `n^{th}` Tribonacci number, `T_n`
+    * ``tribonacci(n, x)`` gives the `n^{th}` Tribonacci polynomial in `x`, `T_n(x)`
+
+    Examples
+    ========
+
+    >>> from sympy import tribonacci, Symbol
+
+    >>> [tribonacci(x) for x in range(11)]
+    [0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149]
+    >>> tribonacci(5, Symbol('t'))
+    t**8 + 3*t**5 + 3*t**2
+
+    See Also
+    ========
+
+    bell, bernoulli, catalan, euler, fibonacci, harmonic, lucas, genocchi, partition
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers
+    .. [2] https://mathworld.wolfram.com/TribonacciNumber.html
+    .. [3] https://oeis.org/A000073
+
+    """
+
+    @staticmethod
+    @recurrence_memo([S.Zero, S.One, S.One])
+    def _trib(n, prev):
+        return (prev[-3] + prev[-2] + prev[-1])
+
+    @staticmethod
+    @recurrence_memo([S.Zero, S.One, _sym**2])
+    def _tribpoly(n, prev):
+        return (prev[-3] + _sym*prev[-2] + _sym**2*prev[-1]).expand()
+
+    @classmethod
+    def eval(cls, n, sym=None):
+        if n is S.Infinity:
+            return S.Infinity
+
+        if n.is_Integer:
+            n = int(n)
+            if n < 0:
+                raise ValueError("Tribonacci polynomials are defined "
+                       "only for non-negative integer indices.")
+            if sym is None:
+                return Integer(cls._trib(n))
+            else:
+                return cls._tribpoly(n).subs(_sym, sym)
+
+    def _eval_rewrite_as_sqrt(self, n, **kwargs):
+        from sympy.functions.elementary.miscellaneous import cbrt, sqrt
+        w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2
+        a = (1 + cbrt(19 + 3*sqrt(33)) + cbrt(19 - 3*sqrt(33))) / 3
+        b = (1 + w*cbrt(19 + 3*sqrt(33)) + w**2*cbrt(19 - 3*sqrt(33))) / 3
+        c = (1 + w**2*cbrt(19 + 3*sqrt(33)) + w*cbrt(19 - 3*sqrt(33))) / 3
+        Tn = (a**(n + 1)/((a - b)*(a - c))
+            + b**(n + 1)/((b - a)*(b - c))
+            + c**(n + 1)/((c - a)*(c - b)))
+        return Tn
+
+    def _eval_rewrite_as_TribonacciConstant(self, n, **kwargs):
+        from sympy.functions.elementary.integers import floor
+        from sympy.functions.elementary.miscellaneous import cbrt, sqrt
+        b = cbrt(586 + 102*sqrt(33))
+        Tn = 3 * b * S.TribonacciConstant**n / (b**2 - 2*b + 4)
+        return floor(Tn + S.Half)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Bernoulli numbers                                #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class bernoulli(DefinedFunction):
+    r"""
+    Bernoulli numbers / Bernoulli polynomials / Bernoulli function
+
+    The Bernoulli numbers are a sequence of rational numbers
+    defined by `B_0 = 1` and the recursive relation (`n > 0`):
+
+    .. math :: n+1 = \sum_{k=0}^n \binom{n+1}{k} B_k
+
+    They are also commonly defined by their exponential generating
+    function, which is `\frac{x}{1 - e^{-x}}`. For odd indices > 1,
+    the Bernoulli numbers are zero.
+
+    The Bernoulli polynomials satisfy the analogous formula:
+
+    .. math :: B_n(x) = \sum_{k=0}^n (-1)^k \binom{n}{k} B_k x^{n-k}
+
+    Bernoulli numbers and Bernoulli polynomials are related as
+    `B_n(1) = B_n`.
+
+    The generalized Bernoulli function `\operatorname{B}(s, a)`
+    is defined for any complex `s` and `a`, except where `a` is a
+    nonpositive integer and `s` is not a nonnegative integer. It is
+    an entire function of `s` for fixed `a`, related to the Hurwitz
+    zeta function by
+
+    .. math:: \operatorname{B}(s, a) = \begin{cases}
+              -s \zeta(1-s, a) & s \ne 0 \\ 1 & s = 0 \end{cases}
+
+    When `s` is a nonnegative integer this function reduces to the
+    Bernoulli polynomials: `\operatorname{B}(n, x) = B_n(x)`. When
+    `a` is omitted it is assumed to be 1, yielding the (ordinary)
+    Bernoulli function which interpolates the Bernoulli numbers and is
+    related to the Riemann zeta function.
+
+    We compute Bernoulli numbers using Ramanujan's formula:
+
+    .. math :: B_n = \frac{A(n) - S(n)}{\binom{n+3}{n}}
+
+    where:
+
+    .. math :: A(n) = \begin{cases} \frac{n+3}{3} &
+        n \equiv 0\ \text{or}\ 2 \pmod{6} \\
+        -\frac{n+3}{6} & n \equiv 4 \pmod{6} \end{cases}
+
+    and:
+
+    .. math :: S(n) = \sum_{k=1}^{[n/6]} \binom{n+3}{n-6k} B_{n-6k}
+
+    This formula is similar to the sum given in the definition, but
+    cuts `\frac{2}{3}` of the terms. For Bernoulli polynomials, we use
+    Appell sequences.
+
+    For `n` a nonnegative integer and `s`, `a`, `x` arbitrary complex numbers,
+
+    * ``bernoulli(n)`` gives the nth Bernoulli number, `B_n`
+    * ``bernoulli(s)`` gives the Bernoulli function `\operatorname{B}(s)`
+    * ``bernoulli(n, x)`` gives the nth Bernoulli polynomial in `x`, `B_n(x)`
+    * ``bernoulli(s, a)`` gives the generalized Bernoulli function
+      `\operatorname{B}(s, a)`
+
+    .. versionchanged:: 1.12
+        ``bernoulli(1)`` gives `+\frac{1}{2}` instead of `-\frac{1}{2}`.
+        This choice of value confers several theoretical advantages [5]_,
+        including the extension to complex parameters described above
+        which this function now implements. The previous behavior, defined
+        only for nonnegative integers `n`, can be obtained with
+        ``(-1)**n*bernoulli(n)``.
+
+    Examples
+    ========
+
+    >>> from sympy import bernoulli
+    >>> from sympy.abc import x
+    >>> [bernoulli(n) for n in range(11)]
+    [1, 1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66]
+    >>> bernoulli(1000001)
+    0
+    >>> bernoulli(3, x)
+    x**3 - 3*x**2/2 + x/2
+
+    See Also
+    ========
+
+    andre, bell, catalan, euler, fibonacci, harmonic, lucas, genocchi,
+    partition, tribonacci, sympy.polys.appellseqs.bernoulli_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Bernoulli_number
+    .. [2] https://en.wikipedia.org/wiki/Bernoulli_polynomial
+    .. [3] https://mathworld.wolfram.com/BernoulliNumber.html
+    .. [4] https://mathworld.wolfram.com/BernoulliPolynomial.html
+    .. [5] Peter Luschny, "The Bernoulli Manifesto",
+           https://luschny.de/math/zeta/The-Bernoulli-Manifesto.html
+    .. [6] Peter Luschny, "An introduction to the Bernoulli function",
+           https://arxiv.org/abs/2009.06743
+
+    """
+
+    args: tuple[Integer]
+
+    # Calculates B_n for positive even n
+    @staticmethod
+    def _calc_bernoulli(n):
+        s = 0
+        a = int(binomial(n + 3, n - 6))
+        for j in range(1, n//6 + 1):
+            s += a * bernoulli(n - 6*j)
+            # Avoid computing each binomial coefficient from scratch
+            a *= _product(n - 6 - 6*j + 1, n - 6*j)
+            a //= _product(6*j + 4, 6*j + 9)
+        if n % 6 == 4:
+            s = -Rational(n + 3, 6) - s
+        else:
+            s = Rational(n + 3, 3) - s
+        return s / binomial(n + 3, n)
+
+    # We implement a specialized memoization scheme to handle each
+    # case modulo 6 separately
+    _cache = {0: S.One, 1: Rational(1, 2), 2: Rational(1, 6), 4: Rational(-1, 30)}
+    _highest = {0: 0, 1: 1, 2: 2, 4: 4}
+
+    @classmethod
+    def eval(cls, n, x=None):
+        if x is S.One:
+            return cls(n)
+        elif n.is_zero:
+            return S.One
+        elif n.is_integer is False or n.is_nonnegative is False:
+            if x is not None and x.is_Integer and x.is_nonpositive:
+                return S.NaN
+            return
+        # Bernoulli numbers
+        elif x is None:
+            if n is S.One:
+                return S.Half
+            elif n.is_odd and (n-1).is_positive:
+                return S.Zero
+            elif n.is_Number:
+                n = int(n)
+                # Use mpmath for enormous Bernoulli numbers
+                if n > 500:
+                    p, q = mp.bernfrac(n)
+                    return Rational(int(p), int(q))
+                case = n % 6
+                highest_cached = cls._highest[case]
+                if n <= highest_cached:
+                    return cls._cache[n]
+                # To avoid excessive recursion when, say, bernoulli(1000) is
+                # requested, calculate and cache the entire sequence ... B_988,
+                # B_994, B_1000 in increasing order
+                for i in range(highest_cached + 6, n + 6, 6):
+                    b = cls._calc_bernoulli(i)
+                    cls._cache[i] = b
+                    cls._highest[case] = i
+                return b
+        # Bernoulli polynomials
+        elif n.is_Number:
+            return bernoulli_poly(n, x)
+
+    def _eval_rewrite_as_zeta(self, n, x=1, **kwargs):
+        from sympy.functions.special.zeta_functions import zeta
+        return Piecewise((1, Eq(n, 0)), (-n * zeta(1-n, x), True))
+
+    def _eval_evalf(self, prec):
+        if not all(x.is_number for x in self.args):
+            return
+        n = self.args[0]._to_mpmath(prec)
+        x = (self.args[1] if len(self.args) > 1 else S.One)._to_mpmath(prec)
+        with workprec(prec):
+            if n == 0:
+                res = mp.mpf(1)
+            elif n == 1:
+                res = x - mp.mpf(0.5)
+            elif mp.isint(n) and n >= 0:
+                res = mp.bernoulli(n) if x == 1 else mp.bernpoly(n, x)
+            else:
+                res = -n * mp.zeta(1-n, x)
+        return Expr._from_mpmath(res, prec)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                                Bell numbers                                #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class bell(DefinedFunction):
+    r"""
+    Bell numbers / Bell polynomials
+
+    The Bell numbers satisfy `B_0 = 1` and
+
+    .. math:: B_n = \sum_{k=0}^{n-1} \binom{n-1}{k} B_k.
+
+    They are also given by:
+
+    .. math:: B_n = \frac{1}{e} \sum_{k=0}^{\infty} \frac{k^n}{k!}.
+
+    The Bell polynomials are given by `B_0(x) = 1` and
+
+    .. math:: B_n(x) = x \sum_{k=1}^{n-1} \binom{n-1}{k-1} B_{k-1}(x).
+
+    The second kind of Bell polynomials (are sometimes called "partial" Bell
+    polynomials or incomplete Bell polynomials) are defined as
+
+    .. math:: B_{n,k}(x_1, x_2,\dotsc x_{n-k+1}) =
+            \sum_{j_1+j_2+j_2+\dotsb=k \atop j_1+2j_2+3j_2+\dotsb=n}
+                \frac{n!}{j_1!j_2!\dotsb j_{n-k+1}!}
+                \left(\frac{x_1}{1!} \right)^{j_1}
+                \left(\frac{x_2}{2!} \right)^{j_2} \dotsb
+                \left(\frac{x_{n-k+1}}{(n-k+1)!} \right) ^{j_{n-k+1}}.
+
+    * ``bell(n)`` gives the `n^{th}` Bell number, `B_n`.
+    * ``bell(n, x)`` gives the `n^{th}` Bell polynomial, `B_n(x)`.
+    * ``bell(n, k, (x1, x2, ...))`` gives Bell polynomials of the second kind,
+      `B_{n,k}(x_1, x_2, \dotsc, x_{n-k+1})`.
+
+    Notes
+    =====
+
+    Not to be confused with Bernoulli numbers and Bernoulli polynomials,
+    which use the same notation.
+
+    Examples
+    ========
+
+    >>> from sympy import bell, Symbol, symbols
+
+    >>> [bell(n) for n in range(11)]
+    [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975]
+    >>> bell(30)
+    846749014511809332450147
+    >>> bell(4, Symbol('t'))
+    t**4 + 6*t**3 + 7*t**2 + t
+    >>> bell(6, 2, symbols('x:6')[1:])
+    6*x1*x5 + 15*x2*x4 + 10*x3**2
+
+    See Also
+    ========
+
+    bernoulli, catalan, euler, fibonacci, harmonic, lucas, genocchi, partition, tribonacci
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Bell_number
+    .. [2] https://mathworld.wolfram.com/BellNumber.html
+    .. [3] https://mathworld.wolfram.com/BellPolynomial.html
+
+    """
+
+    @staticmethod
+    @recurrence_memo([1, 1])
+    def _bell(n, prev):
+        s = 1
+        a = 1
+        for k in range(1, n):
+            a = a * (n - k) // k
+            s += a * prev[k]
+        return s
+
+    @staticmethod
+    @recurrence_memo([S.One, _sym])
+    def _bell_poly(n, prev):
+        s = 1
+        a = 1
+        for k in range(2, n + 1):
+            a = a * (n - k + 1) // (k - 1)
+            s += a * prev[k - 1]
+        return expand_mul(_sym * s)
+
+    @staticmethod
+    def _bell_incomplete_poly(n, k, symbols):
+        r"""
+        The second kind of Bell polynomials (incomplete Bell polynomials).
+
+        Calculated by recurrence formula:
+
+        .. math:: B_{n,k}(x_1, x_2, \dotsc, x_{n-k+1}) =
+                \sum_{m=1}^{n-k+1}
+                \x_m \binom{n-1}{m-1} B_{n-m,k-1}(x_1, x_2, \dotsc, x_{n-m-k})
+
+        where
+            `B_{0,0} = 1;`
+            `B_{n,0} = 0; for n \ge 1`
+            `B_{0,k} = 0; for k \ge 1`
+
+        """
+        if (n == 0) and (k == 0):
+            return S.One
+        elif (n == 0) or (k == 0):
+            return S.Zero
+        s = S.Zero
+        a = S.One
+        for m in range(1, n - k + 2):
+            s += a * bell._bell_incomplete_poly(
+                n - m, k - 1, symbols) * symbols[m - 1]
+            a = a * (n - m) / m
+        return expand_mul(s)
+
+    @classmethod
+    def eval(cls, n, k_sym=None, symbols=None):
+        if n is S.Infinity:
+            if k_sym is None:
+                return S.Infinity
+            else:
+                raise ValueError("Bell polynomial is not defined")
+
+        if n.is_negative or n.is_integer is False:
+            raise ValueError("a non-negative integer expected")
+
+        if n.is_Integer and n.is_nonnegative:
+            if k_sym is None:
+                return Integer(cls._bell(int(n)))
+            elif symbols is None:
+                return cls._bell_poly(int(n)).subs(_sym, k_sym)
+            else:
+                r = cls._bell_incomplete_poly(int(n), int(k_sym), symbols)
+                return r
+
+    def _eval_rewrite_as_Sum(self, n, k_sym=None, symbols=None, **kwargs):
+        from sympy.concrete.summations import Sum
+        if (k_sym is not None) or (symbols is not None):
+            return self
+
+        # Dobinski's formula
+        if not n.is_nonnegative:
+            return self
+        k = Dummy('k', integer=True, nonnegative=True)
+        return 1 / E * Sum(k**n / factorial(k), (k, 0, S.Infinity))
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                              Harmonic numbers                              #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class harmonic(DefinedFunction):
+    r"""
+    Harmonic numbers
+
+    The nth harmonic number is given by `\operatorname{H}_{n} =
+    1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}`.
+
+    More generally:
+
+    .. math:: \operatorname{H}_{n,m} = \sum_{k=1}^{n} \frac{1}{k^m}
+
+    As `n \rightarrow \infty`, `\operatorname{H}_{n,m} \rightarrow \zeta(m)`,
+    the Riemann zeta function.
+
+    * ``harmonic(n)`` gives the nth harmonic number, `\operatorname{H}_n`
+
+    * ``harmonic(n, m)`` gives the nth generalized harmonic number
+      of order `m`, `\operatorname{H}_{n,m}`, where
+      ``harmonic(n) == harmonic(n, 1)``
+
+    This function can be extended to complex `n` and `m` where `n` is not a
+    negative integer or `m` is a nonpositive integer as
+
+    .. math:: \operatorname{H}_{n,m} = \begin{cases} \zeta(m) - \zeta(m, n+1)
+            & m \ne 1 \\ \psi(n+1) + \gamma & m = 1 \end{cases}
+
+    Examples
+    ========
+
+    >>> from sympy import harmonic, oo
+
+    >>> [harmonic(n) for n in range(6)]
+    [0, 1, 3/2, 11/6, 25/12, 137/60]
+    >>> [harmonic(n, 2) for n in range(6)]
+    [0, 1, 5/4, 49/36, 205/144, 5269/3600]
+    >>> harmonic(oo, 2)
+    pi**2/6
+
+    >>> from sympy import Symbol, Sum
+    >>> n = Symbol("n")
+
+    >>> harmonic(n).rewrite(Sum)
+    Sum(1/_k, (_k, 1, n))
+
+    We can evaluate harmonic numbers for all integral and positive
+    rational arguments:
+
+    >>> from sympy import S, expand_func, simplify
+    >>> harmonic(8)
+    761/280
+    >>> harmonic(11)
+    83711/27720
+
+    >>> H = harmonic(1/S(3))
+    >>> H
+    harmonic(1/3)
+    >>> He = expand_func(H)
+    >>> He
+    -log(6) - sqrt(3)*pi/6 + 2*Sum(log(sin(_k*pi/3))*cos(2*_k*pi/3), (_k, 1, 1))
+                           + 3*Sum(1/(3*_k + 1), (_k, 0, 0))
+    >>> He.doit()
+    -log(6) - sqrt(3)*pi/6 - log(sqrt(3)/2) + 3
+    >>> H = harmonic(25/S(7))
+    >>> He = simplify(expand_func(H).doit())
+    >>> He
+    log(sin(2*pi/7)**(2*cos(16*pi/7))/(14*sin(pi/7)**(2*cos(pi/7))*cos(pi/14)**(2*sin(pi/14)))) + pi*tan(pi/14)/2 + 30247/9900
+    >>> He.n(40)
+    1.983697455232980674869851942390639915940
+    >>> harmonic(25/S(7)).n(40)
+    1.983697455232980674869851942390639915940
+
+    We can rewrite harmonic numbers in terms of polygamma functions:
+
+    >>> from sympy import digamma, polygamma
+    >>> m = Symbol("m", integer=True, positive=True)
+
+    >>> harmonic(n).rewrite(digamma)
+    polygamma(0, n + 1) + EulerGamma
+
+    >>> harmonic(n).rewrite(polygamma)
+    polygamma(0, n + 1) + EulerGamma
+
+    >>> harmonic(n,3).rewrite(polygamma)
+    polygamma(2, n + 1)/2 + zeta(3)
+
+    >>> simplify(harmonic(n,m).rewrite(polygamma))
+    Piecewise((polygamma(0, n + 1) + EulerGamma, Eq(m, 1)),
+    (-(-1)**m*polygamma(m - 1, n + 1)/factorial(m - 1) + zeta(m), True))
+
+    Integer offsets in the argument can be pulled out:
+
+    >>> from sympy import expand_func
+
+    >>> expand_func(harmonic(n+4))
+    harmonic(n) + 1/(n + 4) + 1/(n + 3) + 1/(n + 2) + 1/(n + 1)
+
+    >>> expand_func(harmonic(n-4))
+    harmonic(n) - 1/(n - 1) - 1/(n - 2) - 1/(n - 3) - 1/n
+
+    Some limits can be computed as well:
+
+    >>> from sympy import limit, oo
+
+    >>> limit(harmonic(n), n, oo)
+    oo
+
+    >>> limit(harmonic(n, 2), n, oo)
+    pi**2/6
+
+    >>> limit(harmonic(n, 3), n, oo)
+    zeta(3)
+
+    For `m > 1`, `H_{n,m}` tends to `\zeta(m)` in the limit of infinite `n`:
+
+    >>> m = Symbol("m", positive=True)
+    >>> limit(harmonic(n, m+1), n, oo)
+    zeta(m + 1)
+
+    See Also
+    ========
+
+    bell, bernoulli, catalan, euler, fibonacci, lucas, genocchi, partition, tribonacci
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Harmonic_number
+    .. [2] https://functions.wolfram.com/GammaBetaErf/HarmonicNumber/
+    .. [3] https://functions.wolfram.com/GammaBetaErf/HarmonicNumber2/
+
+    """
+
+    # This prevents redundant recalculations and speeds up harmonic number computations.
+    harmonic_cache: dict[Integer, Callable[[int], Rational]] = {}
+
+    @classmethod
+    def eval(cls, n, m=None):
+        from sympy.functions.special.zeta_functions import zeta
+        if m is S.One:
+            return cls(n)
+        if m is None:
+            m = S.One
+        if n.is_zero:
+            return S.Zero
+        elif m.is_zero:
+            return n
+        elif n is S.Infinity:
+            if m.is_negative:
+                return S.NaN
+            elif is_le(m, S.One):
+                return S.Infinity
+            elif is_gt(m, S.One):
+                return zeta(m)
+        elif m.is_Integer and m.is_nonpositive:
+            return (bernoulli(1-m, n+1) - bernoulli(1-m)) / (1-m)
+        elif n.is_Integer:
+            if n.is_negative and (m.is_integer is False or m.is_nonpositive is False):
+                return S.ComplexInfinity if m is S.One else S.NaN
+            if n.is_nonnegative:
+                if m.is_Integer:
+                    if m not in cls.harmonic_cache:
+                        @recurrence_memo([0])
+                        def f(n, prev):
+                            return prev[-1] + S.One / n**m
+                        cls.harmonic_cache[m] = f
+                    return cls.harmonic_cache[m](int(n))
+                return Add(*(k**(-m) for k in range(1, int(n) + 1)))
+
+    def _eval_rewrite_as_polygamma(self, n, m=S.One, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma, polygamma
+        if m.is_integer and m.is_positive:
+            return Piecewise((polygamma(0, n+1) + S.EulerGamma, Eq(m, 1)),
+                    (S.NegativeOne**m * (polygamma(m-1, 1) - polygamma(m-1, n+1)) /
+                    gamma(m), True))
+
+    def _eval_rewrite_as_digamma(self, n, m=1, **kwargs):
+        from sympy.functions.special.gamma_functions import polygamma
+        return self.rewrite(polygamma)
+
+    def _eval_rewrite_as_trigamma(self, n, m=1, **kwargs):
+        from sympy.functions.special.gamma_functions import polygamma
+        return self.rewrite(polygamma)
+
+    def _eval_rewrite_as_Sum(self, n, m=None, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k", integer=True)
+        if m is None:
+            m = S.One
+        return Sum(k**(-m), (k, 1, n))
+
+    def _eval_rewrite_as_zeta(self, n, m=S.One, **kwargs):
+        from sympy.functions.special.zeta_functions import zeta
+        from sympy.functions.special.gamma_functions import digamma
+        return Piecewise((digamma(n + 1) + S.EulerGamma, Eq(m, 1)),
+                         (zeta(m) - zeta(m, n+1), True))
+
+    def _eval_expand_func(self, **hints):
+        from sympy.concrete.summations import Sum
+        n = self.args[0]
+        m = self.args[1] if len(self.args) == 2 else 1
+
+        if m == S.One:
+            if n.is_Add:
+                off = n.args[0]
+                nnew = n - off
+                if off.is_Integer and off.is_positive:
+                    result = [S.One/(nnew + i) for i in range(off, 0, -1)] + [harmonic(nnew)]
+                    return Add(*result)
+                elif off.is_Integer and off.is_negative:
+                    result = [-S.One/(nnew + i) for i in range(0, off, -1)] + [harmonic(nnew)]
+                    return Add(*result)
+
+            if n.is_Rational:
+                # Expansions for harmonic numbers at general rational arguments (u + p/q)
+                # Split n as u + p/q with p < q
+                p, q = n.as_numer_denom()
+                u = p // q
+                p = p - u * q
+                if u.is_nonnegative and p.is_positive and q.is_positive and p < q:
+                    from sympy.functions.elementary.exponential import log
+                    from sympy.functions.elementary.integers import floor
+                    from sympy.functions.elementary.trigonometric import sin, cos, cot
+                    k = Dummy("k")
+                    t1 = q * Sum(1 / (q * k + p), (k, 0, u))
+                    t2 = 2 * Sum(cos((2 * pi * p * k) / S(q)) *
+                                   log(sin((pi * k) / S(q))),
+                                   (k, 1, floor((q - 1) / S(2))))
+                    t3 = (pi / 2) * cot((pi * p) / q) + log(2 * q)
+                    return t1 + t2 - t3
+
+        return self
+
+    def _eval_rewrite_as_tractable(self, n, m=1, limitvar=None, **kwargs):
+        from sympy.functions.special.zeta_functions import zeta
+        from sympy.functions.special.gamma_functions import polygamma
+        pg = self.rewrite(polygamma)
+        if not isinstance(pg, harmonic):
+            return pg.rewrite("tractable", deep=True)
+        arg = m - S.One
+        if arg.is_nonzero:
+            return (zeta(m) - zeta(m, n+1)).rewrite("tractable", deep=True)
+
+    def _eval_evalf(self, prec):
+        if not all(x.is_number for x in self.args):
+            return
+        n = self.args[0]._to_mpmath(prec)
+        m = (self.args[1] if len(self.args) > 1 else S.One)._to_mpmath(prec)
+        if mp.isint(n) and n < 0:
+            return S.NaN
+        with workprec(prec):
+            if m == 1:
+                res = mp.harmonic(n)
+            else:
+                res = mp.zeta(m) - mp.zeta(m, n+1)
+        return Expr._from_mpmath(res, prec)
+
+    def fdiff(self, argindex=1):
+        from sympy.functions.special.zeta_functions import zeta
+        if len(self.args) == 2:
+            n, m = self.args
+        else:
+            n, m = self.args + (1,)
+        if argindex == 1:
+            return m * zeta(m+1, n+1)
+        else:
+            raise ArgumentIndexError
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Euler numbers                                    #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class euler(DefinedFunction):
+    r"""
+    Euler numbers / Euler polynomials / Euler function
+
+    The Euler numbers are given by:
+
+    .. math:: E_{2n} = I \sum_{k=1}^{2n+1} \sum_{j=0}^k \binom{k}{j}
+        \frac{(-1)^j (k-2j)^{2n+1}}{2^k I^k k}
+
+    .. math:: E_{2n+1} = 0
+
+    Euler numbers and Euler polynomials are related by
+
+    .. math:: E_n = 2^n E_n\left(\frac{1}{2}\right).
+
+    We compute symbolic Euler polynomials using Appell sequences,
+    but numerical evaluation of the Euler polynomial is computed
+    more efficiently (and more accurately) using the mpmath library.
+
+    The Euler polynomials are special cases of the generalized Euler function,
+    related to the Genocchi function as
+
+    .. math:: \operatorname{E}(s, a) = -\frac{\operatorname{G}(s+1, a)}{s+1}
+
+    with the limit of `\psi\left(\frac{a+1}{2}\right) - \psi\left(\frac{a}{2}\right)`
+    being taken when `s = -1`. The (ordinary) Euler function interpolating
+    the Euler numbers is then obtained as
+    `\operatorname{E}(s) = 2^s \operatorname{E}\left(s, \frac{1}{2}\right)`.
+
+    * ``euler(n)`` gives the nth Euler number `E_n`.
+    * ``euler(s)`` gives the Euler function `\operatorname{E}(s)`.
+    * ``euler(n, x)`` gives the nth Euler polynomial `E_n(x)`.
+    * ``euler(s, a)`` gives the generalized Euler function `\operatorname{E}(s, a)`.
+
+    Examples
+    ========
+
+    >>> from sympy import euler, Symbol, S
+    >>> [euler(n) for n in range(10)]
+    [1, 0, -1, 0, 5, 0, -61, 0, 1385, 0]
+    >>> [2**n*euler(n,1) for n in range(10)]
+    [1, 1, 0, -2, 0, 16, 0, -272, 0, 7936]
+    >>> n = Symbol("n")
+    >>> euler(n + 2*n)
+    euler(3*n)
+
+    >>> x = Symbol("x")
+    >>> euler(n, x)
+    euler(n, x)
+
+    >>> euler(0, x)
+    1
+    >>> euler(1, x)
+    x - 1/2
+    >>> euler(2, x)
+    x**2 - x
+    >>> euler(3, x)
+    x**3 - 3*x**2/2 + 1/4
+    >>> euler(4, x)
+    x**4 - 2*x**3 + x
+
+    >>> euler(12, S.Half)
+    2702765/4096
+    >>> euler(12)
+    2702765
+
+    See Also
+    ========
+
+    andre, bell, bernoulli, catalan, fibonacci, harmonic, lucas, genocchi,
+    partition, tribonacci, sympy.polys.appellseqs.euler_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler_numbers
+    .. [2] https://mathworld.wolfram.com/EulerNumber.html
+    .. [3] https://en.wikipedia.org/wiki/Alternating_permutation
+    .. [4] https://mathworld.wolfram.com/AlternatingPermutation.html
+
+    """
+
+    @classmethod
+    def eval(cls, n, x=None):
+        if n.is_zero:
+            return S.One
+        elif n is S.NegativeOne:
+            if x is None:
+                return S.Pi/2
+            from sympy.functions.special.gamma_functions import digamma
+            return digamma((x+1)/2) - digamma(x/2)
+        elif n.is_integer is False or n.is_nonnegative is False:
+            return
+        # Euler numbers
+        elif x is None:
+            if n.is_odd and n.is_positive:
+                return S.Zero
+            elif n.is_Number:
+                from mpmath import mp
+                n = n._to_mpmath(mp.prec)
+                res = mp.eulernum(n, exact=True)
+                return Integer(res)
+        # Euler polynomials
+        elif n.is_Number:
+            from sympy.core.evalf import pure_complex
+            n = int(n)
+            reim = pure_complex(x, or_real=True)
+            if reim and all(a.is_Float or a.is_Integer for a in reim) \
+                    and any(a.is_Float for a in reim):
+                from mpmath import mp
+                prec = min([a._prec for a in reim if a.is_Float])
+                with workprec(prec):
+                    res = mp.eulerpoly(n, x)
+                return Expr._from_mpmath(res, prec)
+            return euler_poly(n, x)
+
+    def _eval_rewrite_as_Sum(self, n, x=None, **kwargs):
+        from sympy.concrete.summations import Sum
+        if x is None and n.is_even:
+            k = Dummy("k", integer=True)
+            j = Dummy("j", integer=True)
+            n = n / 2
+            Em = (S.ImaginaryUnit * Sum(Sum(binomial(k, j) * (S.NegativeOne**j *
+                                                              (k - 2*j)**(2*n + 1)) /
+                  (2**k*S.ImaginaryUnit**k * k), (j, 0, k)), (k, 1, 2*n + 1)))
+            return Em
+        if x:
+            k = Dummy("k", integer=True)
+            return Sum(binomial(n, k)*euler(k)/2**k*(x - S.Half)**(n - k), (k, 0, n))
+
+    def _eval_rewrite_as_genocchi(self, n, x=None, **kwargs):
+        if x is None:
+            return Piecewise((S.Pi/2, Eq(n, -1)),
+                             (-2**n * genocchi(n+1, S.Half) / (n+1), True))
+        from sympy.functions.special.gamma_functions import digamma
+        return Piecewise((digamma((x+1)/2) - digamma(x/2), Eq(n, -1)),
+                         (-genocchi(n+1, x) / (n+1), True))
+
+    def _eval_evalf(self, prec):
+        if not all(i.is_number for i in self.args):
+            return
+        from mpmath import mp
+        m, x = (self.args[0], None) if len(self.args) == 1 else self.args
+        m = m._to_mpmath(prec)
+        if x is not None:
+            x = x._to_mpmath(prec)
+        with workprec(prec):
+            if mp.isint(m) and m >= 0:
+                res = mp.eulernum(m) if x is None else mp.eulerpoly(m, x)
+            else:
+                if m == -1:
+                    res = mp.pi if x is None else mp.digamma((x+1)/2) - mp.digamma(x/2)
+                else:
+                    y = 0.5 if x is None else x
+                    res = 2 * (mp.zeta(-m, y) - 2**(m+1) * mp.zeta(-m, (y+1)/2))
+                if x is None:
+                    res *= 2**m
+        return Expr._from_mpmath(res, prec)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                              Catalan numbers                               #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class catalan(DefinedFunction):
+    r"""
+    Catalan numbers
+
+    The `n^{th}` catalan number is given by:
+
+    .. math :: C_n = \frac{1}{n+1} \binom{2n}{n}
+
+    * ``catalan(n)`` gives the `n^{th}` Catalan number, `C_n`
+
+    Examples
+    ========
+
+    >>> from sympy import (Symbol, binomial, gamma, hyper,
+    ...     catalan, diff, combsimp, Rational, I)
+
+    >>> [catalan(i) for i in range(1,10)]
+    [1, 2, 5, 14, 42, 132, 429, 1430, 4862]
+
+    >>> n = Symbol("n", integer=True)
+
+    >>> catalan(n)
+    catalan(n)
+
+    Catalan numbers can be transformed into several other, identical
+    expressions involving other mathematical functions
+
+    >>> catalan(n).rewrite(binomial)
+    binomial(2*n, n)/(n + 1)
+
+    >>> catalan(n).rewrite(gamma)
+    4**n*gamma(n + 1/2)/(sqrt(pi)*gamma(n + 2))
+
+    >>> catalan(n).rewrite(hyper)
+    hyper((-n, 1 - n), (2,), 1)
+
+    For some non-integer values of n we can get closed form
+    expressions by rewriting in terms of gamma functions:
+
+    >>> catalan(Rational(1, 2)).rewrite(gamma)
+    8/(3*pi)
+
+    We can differentiate the Catalan numbers C(n) interpreted as a
+    continuous real function in n:
+
+    >>> diff(catalan(n), n)
+    (polygamma(0, n + 1/2) - polygamma(0, n + 2) + log(4))*catalan(n)
+
+    As a more advanced example consider the following ratio
+    between consecutive numbers:
+
+    >>> combsimp((catalan(n + 1)/catalan(n)).rewrite(binomial))
+    2*(2*n + 1)/(n + 2)
+
+    The Catalan numbers can be generalized to complex numbers:
+
+    >>> catalan(I).rewrite(gamma)
+    4**I*gamma(1/2 + I)/(sqrt(pi)*gamma(2 + I))
+
+    and evaluated with arbitrary precision:
+
+    >>> catalan(I).evalf(20)
+    0.39764993382373624267 - 0.020884341620842555705*I
+
+    See Also
+    ========
+
+    andre, bell, bernoulli, euler, fibonacci, harmonic, lucas, genocchi,
+    partition, tribonacci, sympy.functions.combinatorial.factorials.binomial
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Catalan_number
+    .. [2] https://mathworld.wolfram.com/CatalanNumber.html
+    .. [3] https://functions.wolfram.com/GammaBetaErf/CatalanNumber/
+    .. [4] http://geometer.org/mathcircles/catalan.pdf
+
+    """
+
+    @classmethod
+    def eval(cls, n):
+        from sympy.functions.special.gamma_functions import gamma
+        if (n.is_Integer and n.is_nonnegative) or \
+           (n.is_noninteger and n.is_negative):
+            return 4**n*gamma(n + S.Half)/(gamma(S.Half)*gamma(n + 2))
+
+        if (n.is_integer and n.is_negative):
+            if (n + 1).is_negative:
+                return S.Zero
+            if (n + 1).is_zero:
+                return Rational(-1, 2)
+
+    def fdiff(self, argindex=1):
+        from sympy.functions.elementary.exponential import log
+        from sympy.functions.special.gamma_functions import polygamma
+        n = self.args[0]
+        return catalan(n)*(polygamma(0, n + S.Half) - polygamma(0, n + 2) + log(4))
+
+    def _eval_rewrite_as_binomial(self, n, **kwargs):
+        return binomial(2*n, n)/(n + 1)
+
+    def _eval_rewrite_as_factorial(self, n, **kwargs):
+        return factorial(2*n) / (factorial(n+1) * factorial(n))
+
+    def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma
+        # The gamma function allows to generalize Catalan numbers to complex n
+        return 4**n*gamma(n + S.Half)/(gamma(S.Half)*gamma(n + 2))
+
+    def _eval_rewrite_as_hyper(self, n, **kwargs):
+        from sympy.functions.special.hyper import hyper
+        return hyper([1 - n, -n], [2], 1)
+
+    def _eval_rewrite_as_Product(self, n, **kwargs):
+        from sympy.concrete.products import Product
+        if not (n.is_integer and n.is_nonnegative):
+            return self
+        k = Dummy('k', integer=True, positive=True)
+        return Product((n + k) / k, (k, 2, n))
+
+    def _eval_is_integer(self):
+        if self.args[0].is_integer and self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_positive(self):
+        if self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_composite(self):
+        if self.args[0].is_integer and (self.args[0] - 3).is_positive:
+            return True
+
+    def _eval_evalf(self, prec):
+        from sympy.functions.special.gamma_functions import gamma
+        if self.args[0].is_number:
+            return self.rewrite(gamma)._eval_evalf(prec)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Genocchi numbers                                 #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class genocchi(DefinedFunction):
+    r"""
+    Genocchi numbers / Genocchi polynomials / Genocchi function
+
+    The Genocchi numbers are a sequence of integers `G_n` that satisfy the
+    relation:
+
+    .. math:: \frac{-2t}{1 + e^{-t}} = \sum_{n=0}^\infty \frac{G_n t^n}{n!}
+
+    They are related to the Bernoulli numbers by
+
+    .. math:: G_n = 2 (1 - 2^n) B_n
+
+    and generalize like the Bernoulli numbers to the Genocchi polynomials and
+    function as
+
+    .. math:: \operatorname{G}(s, a) = 2 \left(\operatorname{B}(s, a) -
+              2^s \operatorname{B}\left(s, \frac{a+1}{2}\right)\right)
+
+    .. versionchanged:: 1.12
+        ``genocchi(1)`` gives `-1` instead of `1`.
+
+    Examples
+    ========
+
+    >>> from sympy import genocchi, Symbol
+    >>> [genocchi(n) for n in range(9)]
+    [0, -1, -1, 0, 1, 0, -3, 0, 17]
+    >>> n = Symbol('n', integer=True, positive=True)
+    >>> genocchi(2*n + 1)
+    0
+    >>> x = Symbol('x')
+    >>> genocchi(4, x)
+    -4*x**3 + 6*x**2 - 1
+
+    See Also
+    ========
+
+    bell, bernoulli, catalan, euler, fibonacci, harmonic, lucas, partition, tribonacci
+    sympy.polys.appellseqs.genocchi_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Genocchi_number
+    .. [2] https://mathworld.wolfram.com/GenocchiNumber.html
+    .. [3] Peter Luschny, "An introduction to the Bernoulli function",
+           https://arxiv.org/abs/2009.06743
+
+    """
+
+    @classmethod
+    def eval(cls, n, x=None):
+        if x is S.One:
+            return cls(n)
+        elif n.is_integer is False or n.is_nonnegative is False:
+            return
+        # Genocchi numbers
+        elif x is None:
+            if n.is_odd and (n-1).is_positive:
+                return S.Zero
+            elif n.is_Number:
+                return 2 * (1-S(2)**n) * bernoulli(n)
+        # Genocchi polynomials
+        elif n.is_Number:
+            return genocchi_poly(n, x)
+
+    def _eval_rewrite_as_bernoulli(self, n, x=1, **kwargs):
+        if x == 1 and n.is_integer and n.is_nonnegative:
+            return 2 * (1-S(2)**n) * bernoulli(n)
+        return 2 * (bernoulli(n, x) - 2**n * bernoulli(n, (x+1) / 2))
+
+    def _eval_rewrite_as_dirichlet_eta(self, n, x=1, **kwargs):
+        from sympy.functions.special.zeta_functions import dirichlet_eta
+        return -2*n * dirichlet_eta(1-n, x)
+
+    def _eval_is_integer(self):
+        if len(self.args) > 1 and self.args[1] != 1:
+            return
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative:
+            return True
+
+    def _eval_is_negative(self):
+        if len(self.args) > 1 and self.args[1] != 1:
+            return
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative:
+            if n.is_odd:
+                return fuzzy_not((n-1).is_positive)
+            return (n/2).is_odd
+
+    def _eval_is_positive(self):
+        if len(self.args) > 1 and self.args[1] != 1:
+            return
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative:
+            if n.is_zero or n.is_odd:
+                return False
+            return (n/2).is_even
+
+    def _eval_is_even(self):
+        if len(self.args) > 1 and self.args[1] != 1:
+            return
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative:
+            if n.is_even:
+                return n.is_zero
+            return (n-1).is_positive
+
+    def _eval_is_odd(self):
+        if len(self.args) > 1 and self.args[1] != 1:
+            return
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative:
+            if n.is_even:
+                return fuzzy_not(n.is_zero)
+            return fuzzy_not((n-1).is_positive)
+
+    def _eval_is_prime(self):
+        if len(self.args) > 1 and self.args[1] != 1:
+            return
+        n = self.args[0]
+        # only G_6 = -3 and G_8 = 17 are prime,
+        # but SymPy does not consider negatives as prime
+        # so only n=8 is tested
+        return (n-8).is_zero
+
+    def _eval_evalf(self, prec):
+        if all(i.is_number for i in self.args):
+            return self.rewrite(bernoulli)._eval_evalf(prec)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                              Andre numbers                                 #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class andre(DefinedFunction):
+    r"""
+    Andre numbers / Andre function
+
+    The Andre number `\mathcal{A}_n` is Luschny's name for half the number of
+    *alternating permutations* on `n` elements, where a permutation is alternating
+    if adjacent elements alternately compare "greater" and "smaller" going from
+    left to right. For example, `2 < 3 > 1 < 4` is an alternating permutation.
+
+    This sequence is A000111 in the OEIS, which assigns the names *up/down numbers*
+    and *Euler zigzag numbers*. It satisfies a recurrence relation similar to that
+    for the Catalan numbers, with `\mathcal{A}_0 = 1` and
+
+    .. math:: 2 \mathcal{A}_{n+1} = \sum_{k=0}^n \binom{n}{k} \mathcal{A}_k \mathcal{A}_{n-k}
+
+    The Bernoulli and Euler numbers are signed transformations of the odd- and
+    even-indexed elements of this sequence respectively:
+
+    .. math :: \operatorname{B}_{2k} = \frac{2k \mathcal{A}_{2k-1}}{(-4)^k - (-16)^k}
+
+    .. math :: \operatorname{E}_{2k} = (-1)^k \mathcal{A}_{2k}
+
+    Like the Bernoulli and Euler numbers, the Andre numbers are interpolated by the
+    entire Andre function:
+
+    .. math :: \mathcal{A}(s) = (-i)^{s+1} \operatorname{Li}_{-s}(i) +
+            i^{s+1} \operatorname{Li}_{-s}(-i) = \\ \frac{2 \Gamma(s+1)}{(2\pi)^{s+1}}
+            (\zeta(s+1, 1/4) - \zeta(s+1, 3/4) \cos{\pi s})
+
+    Examples
+    ========
+
+    >>> from sympy import andre, euler, bernoulli
+    >>> [andre(n) for n in range(11)]
+    [1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521]
+    >>> [(-1)**k * andre(2*k) for k in range(7)]
+    [1, -1, 5, -61, 1385, -50521, 2702765]
+    >>> [euler(2*k) for k in range(7)]
+    [1, -1, 5, -61, 1385, -50521, 2702765]
+    >>> [andre(2*k-1) * (2*k) / ((-4)**k - (-16)**k) for k in range(1, 8)]
+    [1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6]
+    >>> [bernoulli(2*k) for k in range(1, 8)]
+    [1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6]
+
+    See Also
+    ========
+
+    bernoulli, catalan, euler, sympy.polys.appellseqs.andre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Alternating_permutation
+    .. [2] https://mathworld.wolfram.com/EulerZigzagNumber.html
+    .. [3] Peter Luschny, "An introduction to the Bernoulli function",
+           https://arxiv.org/abs/2009.06743
+    """
+
+    @classmethod
+    def eval(cls, n):
+        if n is S.NaN:
+            return S.NaN
+        elif n is S.Infinity:
+            return S.Infinity
+        if n.is_zero:
+            return S.One
+        elif n == -1:
+            return -log(2)
+        elif n == -2:
+            return -2*S.Catalan
+        elif n.is_Integer:
+            if n.is_nonnegative and n.is_even:
+                return abs(euler(n))
+            elif n.is_odd:
+                from sympy.functions.special.zeta_functions import zeta
+                m = -n-1
+                return I**m * Rational(1-2**m, 4**m) * zeta(-n)
+
+    def _eval_rewrite_as_zeta(self, s, **kwargs):
+        from sympy.functions.elementary.trigonometric import cos
+        from sympy.functions.special.gamma_functions import gamma
+        from sympy.functions.special.zeta_functions import zeta
+        return 2 * gamma(s+1) / (2*pi)**(s+1) * \
+                (zeta(s+1, S.One/4) - cos(pi*s) * zeta(s+1, S(3)/4))
+
+    def _eval_rewrite_as_polylog(self, s, **kwargs):
+        from sympy.functions.special.zeta_functions import polylog
+        return (-I)**(s+1) * polylog(-s, I) + I**(s+1) * polylog(-s, -I)
+
+    def _eval_is_integer(self):
+        n = self.args[0]
+        if n.is_integer and n.is_nonnegative:
+            return True
+
+    def _eval_is_positive(self):
+        if self.args[0].is_nonnegative:
+            return True
+
+    def _eval_evalf(self, prec):
+        if not self.args[0].is_number:
+            return
+        s = self.args[0]._to_mpmath(prec+12)
+        with workprec(prec+12):
+            sp, cp = mp.sinpi(s/2), mp.cospi(s/2)
+            res = 2*mp.dirichlet(-s, (-sp, cp, sp, -cp))
+        return Expr._from_mpmath(res, prec)
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                           Partition numbers                                #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+class partition(DefinedFunction):
+    r"""
+    Partition numbers
+
+    The Partition numbers are a sequence of integers `p_n` that represent the
+    number of distinct ways of representing `n` as a sum of natural numbers
+    (with order irrelevant). The generating function for `p_n` is given by:
+
+    .. math:: \sum_{n=0}^\infty p_n x^n = \prod_{k=1}^\infty (1 - x^k)^{-1}
+
+    Examples
+    ========
+
+    >>> from sympy import partition, Symbol
+    >>> [partition(n) for n in range(9)]
+    [1, 1, 2, 3, 5, 7, 11, 15, 22]
+    >>> n = Symbol('n', integer=True, negative=True)
+    >>> partition(n)
+    0
+
+    See Also
+    ========
+
+    bell, bernoulli, catalan, euler, fibonacci, harmonic, lucas, genocchi, tribonacci
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Partition_(number_theory%29
+    .. [2] https://en.wikipedia.org/wiki/Pentagonal_number_theorem
+
+    """
+    is_integer = True
+    is_nonnegative = True
+
+    @classmethod
+    def eval(cls, n):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_negative is True:
+            return S.Zero
+        if n.is_zero is True or n is S.One:
+            return S.One
+        if n.is_Integer is True:
+            return S(_partition(as_int(n)))
+
+    def _eval_is_positive(self):
+        if self.args[0].is_nonnegative is True:
+            return True
+
+    def _eval_Mod(self, q):
+        # Ramanujan's congruences
+        n = self.args[0]
+        for p, rem in [(5, 4), (7, 5), (11, 6)]:
+            if q == p and n % q == rem:
+                return S.Zero
+
+
+class divisor_sigma(DefinedFunction):
+    r"""
+    Calculate the divisor function `\sigma_k(n)` for positive integer n
+
+    ``divisor_sigma(n, k)`` is equal to ``sum([x**k for x in divisors(n)])``
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^\omega p_i^{m_i},
+
+    then
+
+    .. math ::
+        \sigma_k(n) = \prod_{i=1}^\omega (1+p_i^k+p_i^{2k}+\cdots
+        + p_i^{m_ik}).
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import divisor_sigma
+    >>> divisor_sigma(18, 0)
+    6
+    >>> divisor_sigma(39, 1)
+    56
+    >>> divisor_sigma(12, 2)
+    210
+    >>> divisor_sigma(37)
+    38
+
+    See Also
+    ========
+
+    sympy.ntheory.factor_.divisor_count, totient, sympy.ntheory.factor_.divisors, sympy.ntheory.factor_.factorint
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Divisor_function
+
+    """
+    is_integer = True
+    is_positive = True
+
+    @classmethod
+    def eval(cls, n, k=S.One):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if k.is_integer is False:
+            raise TypeError("k should be an integer")
+        if k.is_nonnegative is False:
+            raise ValueError("k should be a nonnegative integer")
+        if n.is_prime is True:
+            return 1 + n**k
+        if n is S.One:
+            return S.One
+        if n.is_Integer is True:
+            if k.is_zero is True:
+                return Mul(*[e + 1 for e in factorint(n).values()])
+            if k.is_Integer is True:
+                return S(_divisor_sigma(as_int(n), as_int(k)))
+            if k.is_zero is False:
+                return Mul(*[cancel((p**(k*(e + 1)) - 1) / (p**k - 1)) for p, e in factorint(n).items()])
+
+
+class udivisor_sigma(DefinedFunction):
+    r"""
+    Calculate the unitary divisor function `\sigma_k^*(n)` for positive integer n
+
+    ``udivisor_sigma(n, k)`` is equal to ``sum([x**k for x in udivisors(n)])``
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^\omega p_i^{m_i},
+
+    then
+
+    .. math ::
+        \sigma_k^*(n) = \prod_{i=1}^\omega (1+ p_i^{m_ik}).
+
+    Parameters
+    ==========
+
+    k : power of divisors in the sum
+
+        for k = 0, 1:
+        ``udivisor_sigma(n, 0)`` is equal to ``udivisor_count(n)``
+        ``udivisor_sigma(n, 1)`` is equal to ``sum(udivisors(n))``
+
+        Default for k is 1.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import udivisor_sigma
+    >>> udivisor_sigma(18, 0)
+    4
+    >>> udivisor_sigma(74, 1)
+    114
+    >>> udivisor_sigma(36, 3)
+    47450
+    >>> udivisor_sigma(111)
+    152
+
+    See Also
+    ========
+
+    sympy.ntheory.factor_.divisor_count, totient, sympy.ntheory.factor_.divisors,
+    sympy.ntheory.factor_.udivisors, sympy.ntheory.factor_.udivisor_count, divisor_sigma,
+    sympy.ntheory.factor_.factorint
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/UnitaryDivisorFunction.html
+
+    """
+    is_integer = True
+    is_positive = True
+
+    @classmethod
+    def eval(cls, n, k=S.One):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if k.is_integer is False:
+            raise TypeError("k should be an integer")
+        if k.is_nonnegative is False:
+            raise ValueError("k should be a nonnegative integer")
+        if n.is_prime is True:
+            return 1 + n**k
+        if n.is_Integer:
+            return Mul(*[1+p**(k*e) for p, e in factorint(n).items()])
+
+
+class legendre_symbol(DefinedFunction):
+    r"""
+    Returns the Legendre symbol `(a / p)`.
+
+    For an integer ``a`` and an odd prime ``p``, the Legendre symbol is
+    defined as
+
+    .. math ::
+        \genfrac(){}{}{a}{p} = \begin{cases}
+             0 & \text{if } p \text{ divides } a\\
+             1 & \text{if } a \text{ is a quadratic residue modulo } p\\
+            -1 & \text{if } a \text{ is a quadratic nonresidue modulo } p
+        \end{cases}
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import legendre_symbol
+    >>> [legendre_symbol(i, 7) for i in range(7)]
+    [0, 1, 1, -1, 1, -1, -1]
+    >>> sorted(set([i**2 % 7 for i in range(7)]))
+    [0, 1, 2, 4]
+
+    See Also
+    ========
+
+    sympy.ntheory.residue_ntheory.is_quad_residue, jacobi_symbol
+
+    """
+    is_integer = True
+    is_prime = False
+
+    @classmethod
+    def eval(cls, a, p):
+        if a.is_integer is False:
+            raise TypeError("a should be an integer")
+        if p.is_integer is False:
+            raise TypeError("p should be an integer")
+        if p.is_prime is False or p.is_odd is False:
+            raise ValueError("p should be an odd prime integer")
+        if (a % p).is_zero is True:
+            return S.Zero
+        if a is S.One:
+            return S.One
+        if a.is_Integer is True and p.is_Integer is True:
+            return S(legendre(as_int(a), as_int(p)))
+
+
+class jacobi_symbol(DefinedFunction):
+    r"""
+    Returns the Jacobi symbol `(m / n)`.
+
+    For any integer ``m`` and any positive odd integer ``n`` the Jacobi symbol
+    is defined as the product of the Legendre symbols corresponding to the
+    prime factors of ``n``:
+
+    .. math ::
+        \genfrac(){}{}{m}{n} =
+            \genfrac(){}{}{m}{p^{1}}^{\alpha_1}
+            \genfrac(){}{}{m}{p^{2}}^{\alpha_2}
+            ...
+            \genfrac(){}{}{m}{p^{k}}^{\alpha_k}
+            \text{ where } n =
+                p_1^{\alpha_1}
+                p_2^{\alpha_2}
+                ...
+                p_k^{\alpha_k}
+
+    Like the Legendre symbol, if the Jacobi symbol `\genfrac(){}{}{m}{n} = -1`
+    then ``m`` is a quadratic nonresidue modulo ``n``.
+
+    But, unlike the Legendre symbol, if the Jacobi symbol
+    `\genfrac(){}{}{m}{n} = 1` then ``m`` may or may not be a quadratic residue
+    modulo ``n``.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import jacobi_symbol, legendre_symbol
+    >>> from sympy import S
+    >>> jacobi_symbol(45, 77)
+    -1
+    >>> jacobi_symbol(60, 121)
+    1
+
+    The relationship between the ``jacobi_symbol`` and ``legendre_symbol`` can
+    be demonstrated as follows:
+
+    >>> L = legendre_symbol
+    >>> S(45).factors()
+    {3: 2, 5: 1}
+    >>> jacobi_symbol(7, 45) == L(7, 3)**2 * L(7, 5)**1
+    True
+
+    See Also
+    ========
+
+    sympy.ntheory.residue_ntheory.is_quad_residue, legendre_symbol
+
+    """
+    is_integer = True
+    is_prime = False
+
+    @classmethod
+    def eval(cls, m, n):
+        if m.is_integer is False:
+            raise TypeError("m should be an integer")
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False or n.is_odd is False:
+            raise ValueError("n should be an odd positive integer")
+        if m is S.One or n is S.One:
+            return S.One
+        if (m % n).is_zero is True:
+            return S.Zero
+        if m.is_Integer is True and n.is_Integer is True:
+            return S(jacobi(as_int(m), as_int(n)))
+
+
+class kronecker_symbol(DefinedFunction):
+    r"""
+    Returns the Kronecker symbol `(a / n)`.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import kronecker_symbol
+    >>> kronecker_symbol(45, 77)
+    -1
+    >>> kronecker_symbol(13, -120)
+    1
+
+    See Also
+    ========
+
+    jacobi_symbol, legendre_symbol
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Kronecker_symbol
+
+    """
+    is_integer = True
+    is_prime = False
+
+    @classmethod
+    def eval(cls, a, n):
+        if a.is_integer is False:
+            raise TypeError("a should be an integer")
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if a is S.One or n is S.One:
+            return S.One
+        if a.is_Integer is True and n.is_Integer is True:
+            return S(kronecker(as_int(a), as_int(n)))
+
+
+class mobius(DefinedFunction):
+    """
+    Mobius function maps natural number to {-1, 0, 1}
+
+    It is defined as follows:
+        1) `1` if `n = 1`.
+        2) `0` if `n` has a squared prime factor.
+        3) `(-1)^k` if `n` is a square-free positive integer with `k`
+           number of prime factors.
+
+    It is an important multiplicative function in number theory
+    and combinatorics.  It has applications in mathematical series,
+    algebraic number theory and also physics (Fermion operator has very
+    concrete realization with Mobius Function model).
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import mobius
+    >>> mobius(13*7)
+    1
+    >>> mobius(1)
+    1
+    >>> mobius(13*7*5)
+    -1
+    >>> mobius(13**2)
+    0
+
+    Even in the case of a symbol, if it clearly contains a squared prime factor, it will be zero.
+
+    >>> from sympy import Symbol
+    >>> n = Symbol("n", integer=True, positive=True)
+    >>> mobius(4*n)
+    0
+    >>> mobius(n**2)
+    0
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/M%C3%B6bius_function
+    .. [2] Thomas Koshy "Elementary Number Theory with Applications"
+    .. [3] https://oeis.org/A008683
+
+    """
+    is_integer = True
+    is_prime = False
+
+    @classmethod
+    def eval(cls, n):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if n.is_prime is True:
+            return S.NegativeOne
+        if n is S.One:
+            return S.One
+        result = None
+        for m, e in (_.as_base_exp() for _ in Mul.make_args(n)):
+            if m.is_integer is True and m.is_positive is True and \
+               e.is_integer is True and e.is_positive is True:
+                lt = is_lt(S.One, e) # 1 < e
+                if lt is True:
+                    result = S.Zero
+                elif m.is_Integer is True:
+                    factors = factorint(m)
+                    if any(v > 1 for v in factors.values()):
+                        result = S.Zero
+                    elif lt is False:
+                        s = S.NegativeOne if len(factors) % 2 else S.One
+                        if result is None:
+                            result = s
+                        else:
+                            result *= s
+            else:
+                return
+        return result
+
+
+class primenu(DefinedFunction):
+    r"""
+    Calculate the number of distinct prime factors for a positive integer n.
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^k p_i^{m_i},
+
+    then ``primenu(n)`` or `\nu(n)` is:
+
+    .. math ::
+        \nu(n) = k.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import primenu
+    >>> primenu(1)
+    0
+    >>> primenu(30)
+    3
+
+    See Also
+    ========
+
+    sympy.ntheory.factor_.factorint
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PrimeFactor.html
+    .. [2] https://oeis.org/A001221
+
+    """
+    is_integer = True
+    is_nonnegative = True
+
+    @classmethod
+    def eval(cls, n):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if n.is_prime is True:
+            return S.One
+        if n is S.One:
+            return S.Zero
+        if n.is_Integer is True:
+            return S(len(factorint(n)))
+
+
+class primeomega(DefinedFunction):
+    r"""
+    Calculate the number of prime factors counting multiplicities for a
+    positive integer n.
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^k p_i^{m_i},
+
+    then ``primeomega(n)``  or `\Omega(n)` is:
+
+    .. math ::
+        \Omega(n) = \sum_{i=1}^k m_i.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import primeomega
+    >>> primeomega(1)
+    0
+    >>> primeomega(20)
+    3
+
+    See Also
+    ========
+
+    sympy.ntheory.factor_.factorint
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PrimeFactor.html
+    .. [2] https://oeis.org/A001222
+
+    """
+    is_integer = True
+    is_nonnegative = True
+
+    @classmethod
+    def eval(cls, n):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if n.is_prime is True:
+            return S.One
+        if n is S.One:
+            return S.Zero
+        if n.is_Integer is True:
+            return S(sum(factorint(n).values()))
+
+
+class totient(DefinedFunction):
+    r"""
+    Calculate the Euler totient function phi(n)
+
+    ``totient(n)`` or `\phi(n)` is the number of positive integers `\leq` n
+    that are relatively prime to n.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import totient
+    >>> totient(1)
+    1
+    >>> totient(25)
+    20
+    >>> totient(45) == totient(5)*totient(9)
+    True
+
+    See Also
+    ========
+
+    sympy.ntheory.factor_.divisor_count
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler%27s_totient_function
+    .. [2] https://mathworld.wolfram.com/TotientFunction.html
+    .. [3] https://oeis.org/A000010
+
+    """
+    is_integer = True
+    is_positive = True
+
+    @classmethod
+    def eval(cls, n):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if n is S.One:
+            return S.One
+        if n.is_prime is True:
+            return n - 1
+        if isinstance(n, Dict):
+            return S(prod(p**(k-1)*(p-1) for p, k in n.items()))
+        if n.is_Integer is True:
+            return S(prod(p**(k-1)*(p-1) for p, k in factorint(n).items()))
+
+
+class reduced_totient(DefinedFunction):
+    r"""
+    Calculate the Carmichael reduced totient function lambda(n)
+
+    ``reduced_totient(n)`` or `\lambda(n)` is the smallest m > 0 such that
+    `k^m \equiv 1 \mod n` for all k relatively prime to n.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import reduced_totient
+    >>> reduced_totient(1)
+    1
+    >>> reduced_totient(8)
+    2
+    >>> reduced_totient(30)
+    4
+
+    See Also
+    ========
+
+    totient
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Carmichael_function
+    .. [2] https://mathworld.wolfram.com/CarmichaelFunction.html
+    .. [3] https://oeis.org/A002322
+
+    """
+    is_integer = True
+    is_positive = True
+
+    @classmethod
+    def eval(cls, n):
+        if n.is_integer is False:
+            raise TypeError("n should be an integer")
+        if n.is_positive is False:
+            raise ValueError("n should be a positive integer")
+        if n is S.One:
+            return S.One
+        if n.is_prime is True:
+            return n - 1
+        if isinstance(n, Dict):
+            t = 1
+            if 2 in n:
+                t = (1 << (n[2] - 2)) if 2 < n[2] else n[2]
+            return S(lcm(int(t), *(int(p-1)*int(p)**int(k-1) for p, k in n.items() if p != 2)))
+        if n.is_Integer is True:
+            n, t = remove(int(n), 2)
+            if not t:
+                t = 1
+            elif 2 < t:
+                t = 1 << (t - 2)
+            return S(lcm(t, *((p-1)*p**(k-1) for p, k in factorint(n).items())))
+
+
+class primepi(DefinedFunction):
+    r""" Represents the prime counting function pi(n) = the number
+    of prime numbers less than or equal to n.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import primepi
+    >>> from sympy import prime, prevprime, isprime
+    >>> primepi(25)
+    9
+
+    So there are 9 primes less than or equal to 25. Is 25 prime?
+
+    >>> isprime(25)
+    False
+
+    It is not. So the first prime less than 25 must be the
+    9th prime:
+
+    >>> prevprime(25) == prime(9)
+    True
+
+    See Also
+    ========
+
+    sympy.ntheory.primetest.isprime : Test if n is prime
+    sympy.ntheory.generate.primerange : Generate all primes in a given range
+    sympy.ntheory.generate.prime : Return the nth prime
+
+    References
+    ==========
+
+    .. [1] https://oeis.org/A000720
+
+    """
+    is_integer = True
+    is_nonnegative = True
+
+    @classmethod
+    def eval(cls, n):
+        if n is S.Infinity:
+            return S.Infinity
+        if n is S.NegativeInfinity:
+            return S.Zero
+        if n.is_real is False:
+            raise TypeError("n should be a real")
+        if is_lt(n, S(2)) is True:
+            return S.Zero
+        try:
+            n = int(n)
+        except TypeError:
+            return
+        return S(_primepi(n))
+
+
+#######################################################################
+###
+### Functions for enumerating partitions, permutations and combinations
+###
+#######################################################################
+
+
+class _MultisetHistogram(tuple):
+    __slots__ = ()
+
+
+_N = -1
+_ITEMS = -2
+_M = slice(None, _ITEMS)
+
+
+def _multiset_histogram(n):
+    """Return tuple used in permutation and combination counting. Input
+    is a dictionary giving items with counts as values or a sequence of
+    items (which need not be sorted).
+
+    The data is stored in a class deriving from tuple so it is easily
+    recognized and so it can be converted easily to a list.
+    """
+    if isinstance(n, dict):  # item: count
+        if not all(isinstance(v, int) and v >= 0 for v in n.values()):
+            raise ValueError
+        tot = sum(n.values())
+        items = sum(1 for k in n if n[k] > 0)
+        return _MultisetHistogram([n[k] for k in n if n[k] > 0] + [items, tot])
+    else:
+        n = list(n)
+        s = set(n)
+        lens = len(s)
+        lenn = len(n)
+        if lens == lenn:
+            n = [1]*lenn + [lenn, lenn]
+            return _MultisetHistogram(n)
+        m = dict(zip(s, range(lens)))
+        d = dict(zip(range(lens), (0,)*lens))
+        for i in n:
+            d[m[i]] += 1
+        return _multiset_histogram(d)
+
+
+def nP(n, k=None, replacement=False):
+    """Return the number of permutations of ``n`` items taken ``k`` at a time.
+
+    Possible values for ``n``:
+
+        integer - set of length ``n``
+
+        sequence - converted to a multiset internally
+
+        multiset - {element: multiplicity}
+
+    If ``k`` is None then the total of all permutations of length 0
+    through the number of items represented by ``n`` will be returned.
+
+    If ``replacement`` is True then a given item can appear more than once
+    in the ``k`` items. (For example, for 'ab' permutations of 2 would
+    include 'aa', 'ab', 'ba' and 'bb'.) The multiplicity of elements in
+    ``n`` is ignored when ``replacement`` is True but the total number
+    of elements is considered since no element can appear more times than
+    the number of elements in ``n``.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import nP
+    >>> from sympy.utilities.iterables import multiset_permutations, multiset
+    >>> nP(3, 2)
+    6
+    >>> nP('abc', 2) == nP(multiset('abc'), 2) == 6
+    True
+    >>> nP('aab', 2)
+    3
+    >>> nP([1, 2, 2], 2)
+    3
+    >>> [nP(3, i) for i in range(4)]
+    [1, 3, 6, 6]
+    >>> nP(3) == sum(_)
+    True
+
+    When ``replacement`` is True, each item can have multiplicity
+    equal to the length represented by ``n``:
+
+    >>> nP('aabc', replacement=True)
+    121
+    >>> [len(list(multiset_permutations('aaaabbbbcccc', i))) for i in range(5)]
+    [1, 3, 9, 27, 81]
+    >>> sum(_)
+    121
+
+    See Also
+    ========
+    sympy.utilities.iterables.multiset_permutations
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Permutation
+
+    """
+    try:
+        n = as_int(n)
+    except ValueError:
+        return Integer(_nP(_multiset_histogram(n), k, replacement))
+    return Integer(_nP(n, k, replacement))
+
+
+@cacheit
+def _nP(n, k=None, replacement=False):
+
+    if k == 0:
+        return 1
+    if isinstance(n, SYMPY_INTS):  # n different items
+        # assert n >= 0
+        if k is None:
+            return sum(_nP(n, i, replacement) for i in range(n + 1))
+        elif replacement:
+            return n**k
+        elif k > n:
+            return 0
+        elif k == n:
+            return factorial(k)
+        elif k == 1:
+            return n
+        else:
+            # assert k >= 0
+            return _product(n - k + 1, n)
+    elif isinstance(n, _MultisetHistogram):
+        if k is None:
+            return sum(_nP(n, i, replacement) for i in range(n[_N] + 1))
+        elif replacement:
+            return n[_ITEMS]**k
+        elif k == n[_N]:
+            return factorial(k)/prod([factorial(i) for i in n[_M] if i > 1])
+        elif k > n[_N]:
+            return 0
+        elif k == 1:
+            return n[_ITEMS]
+        else:
+            # assert k >= 0
+            tot = 0
+            n = list(n)
+            for i in range(len(n[_M])):
+                if not n[i]:
+                    continue
+                n[_N] -= 1
+                if n[i] == 1:
+                    n[i] = 0
+                    n[_ITEMS] -= 1
+                    tot += _nP(_MultisetHistogram(n), k - 1)
+                    n[_ITEMS] += 1
+                    n[i] = 1
+                else:
+                    n[i] -= 1
+                    tot += _nP(_MultisetHistogram(n), k - 1)
+                    n[i] += 1
+                n[_N] += 1
+            return tot
+
+
+@cacheit
+def _AOP_product(n):
+    """for n = (m1, m2, .., mk) return the coefficients of the polynomial,
+    prod(sum(x**i for i in range(nj + 1)) for nj in n); i.e. the coefficients
+    of the product of AOPs (all-one polynomials) or order given in n.  The
+    resulting coefficient corresponding to x**r is the number of r-length
+    combinations of sum(n) elements with multiplicities given in n.
+    The coefficients are given as a default dictionary (so if a query is made
+    for a key that is not present, 0 will be returned).
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import _AOP_product
+    >>> from sympy.abc import x
+    >>> n = (2, 2, 3)  # e.g. aabbccc
+    >>> prod = ((x**2 + x + 1)*(x**2 + x + 1)*(x**3 + x**2 + x + 1)).expand()
+    >>> c = _AOP_product(n); dict(c)
+    {0: 1, 1: 3, 2: 6, 3: 8, 4: 8, 5: 6, 6: 3, 7: 1}
+    >>> [c[i] for i in range(8)] == [prod.coeff(x, i) for i in range(8)]
+    True
+
+    The generating poly used here is the same as that listed in
+    https://tinyurl.com/cep849r, but in a refactored form.
+
+    """
+
+    n = list(n)
+    ord = sum(n)
+    need = (ord + 2)//2
+    rv = [1]*(n.pop() + 1)
+    rv.extend((0,) * (need - len(rv)))
+    rv = rv[:need]
+    while n:
+        ni = n.pop()
+        N = ni + 1
+        was = rv[:]
+        for i in range(1, min(N, len(rv))):
+            rv[i] += rv[i - 1]
+        for i in range(N, need):
+            rv[i] += rv[i - 1] - was[i - N]
+    rev = list(reversed(rv))
+    if ord % 2:
+        rv = rv + rev
+    else:
+        rv[-1:] = rev
+    d = defaultdict(int)
+    for i, r in enumerate(rv):
+        d[i] = r
+    return d
+
+
+def nC(n, k=None, replacement=False):
+    """Return the number of combinations of ``n`` items taken ``k`` at a time.
+
+    Possible values for ``n``:
+
+        integer - set of length ``n``
+
+        sequence - converted to a multiset internally
+
+        multiset - {element: multiplicity}
+
+    If ``k`` is None then the total of all combinations of length 0
+    through the number of items represented in ``n`` will be returned.
+
+    If ``replacement`` is True then a given item can appear more than once
+    in the ``k`` items. (For example, for 'ab' sets of 2 would include 'aa',
+    'ab', and 'bb'.) The multiplicity of elements in ``n`` is ignored when
+    ``replacement`` is True but the total number of elements is considered
+    since no element can appear more times than the number of elements in
+    ``n``.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import nC
+    >>> from sympy.utilities.iterables import multiset_combinations
+    >>> nC(3, 2)
+    3
+    >>> nC('abc', 2)
+    3
+    >>> nC('aab', 2)
+    2
+
+    When ``replacement`` is True, each item can have multiplicity
+    equal to the length represented by ``n``:
+
+    >>> nC('aabc', replacement=True)
+    35
+    >>> [len(list(multiset_combinations('aaaabbbbcccc', i))) for i in range(5)]
+    [1, 3, 6, 10, 15]
+    >>> sum(_)
+    35
+
+    If there are ``k`` items with multiplicities ``m_1, m_2, ..., m_k``
+    then the total of all combinations of length 0 through ``k`` is the
+    product, ``(m_1 + 1)*(m_2 + 1)*...*(m_k + 1)``. When the multiplicity
+    of each item is 1 (i.e., k unique items) then there are 2**k
+    combinations. For example, if there are 4 unique items, the total number
+    of combinations is 16:
+
+    >>> sum(nC(4, i) for i in range(5))
+    16
+
+    See Also
+    ========
+
+    sympy.utilities.iterables.multiset_combinations
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Combination
+    .. [2] https://tinyurl.com/cep849r
+
+    """
+
+    if isinstance(n, SYMPY_INTS):
+        if k is None:
+            if not replacement:
+                return 2**n
+            return sum(nC(n, i, replacement) for i in range(n + 1))
+        if k < 0:
+            raise ValueError("k cannot be negative")
+        if replacement:
+            return binomial(n + k - 1, k)
+        return binomial(n, k)
+    if isinstance(n, _MultisetHistogram):
+        N = n[_N]
+        if k is None:
+            if not replacement:
+                return prod(m + 1 for m in n[_M])
+            return sum(nC(n, i, replacement) for i in range(N + 1))
+        elif replacement:
+            return nC(n[_ITEMS], k, replacement)
+        # assert k >= 0
+        elif k in (1, N - 1):
+            return n[_ITEMS]
+        elif k in (0, N):
+            return 1
+        return _AOP_product(tuple(n[_M]))[k]
+    else:
+        return nC(_multiset_histogram(n), k, replacement)
+
+
+def _eval_stirling1(n, k):
+    if n == k == 0:
+        return S.One
+    if 0 in (n, k):
+        return S.Zero
+
+    # some special values
+    if n == k:
+        return S.One
+    elif k == n - 1:
+        return binomial(n, 2)
+    elif k == n - 2:
+        return (3*n - 1)*binomial(n, 3)/4
+    elif k == n - 3:
+        return binomial(n, 2)*binomial(n, 4)
+
+    return _stirling1(n, k)
+
+
+@cacheit
+def _stirling1(n, k):
+    row = [0, 1]+[0]*(k-1) # for n = 1
+    for i in range(2, n+1):
+        for j in range(min(k,i), 0, -1):
+            row[j] = (i-1) * row[j] + row[j-1]
+    return Integer(row[k])
+
+
+def _eval_stirling2(n, k):
+    if n == k == 0:
+        return S.One
+    if 0 in (n, k):
+        return S.Zero
+
+    # some special values
+    if n == k:
+        return S.One
+    elif k == n - 1:
+        return binomial(n, 2)
+    elif k == 1:
+        return S.One
+    elif k == 2:
+        return Integer(2**(n - 1) - 1)
+
+    return _stirling2(n, k)
+
+
+@cacheit
+def _stirling2(n, k):
+    row = [0, 1]+[0]*(k-1) # for n = 1
+    for i in range(2, n+1):
+        for j in range(min(k,i), 0, -1):
+            row[j] = j * row[j] + row[j-1]
+    return Integer(row[k])
+
+
+def stirling(n, k, d=None, kind=2, signed=False):
+    r"""Return Stirling number $S(n, k)$ of the first or second (default) kind.
+
+    The sum of all Stirling numbers of the second kind for $k = 1$
+    through $n$ is ``bell(n)``. The recurrence relationship for these numbers
+    is:
+
+    .. math :: {0 \brace 0} = 1; {n \brace 0} = {0 \brace k} = 0;
+
+    .. math :: {{n+1} \brace k} = j {n \brace k} + {n \brace {k-1}}
+
+    where $j$ is:
+        $n$ for Stirling numbers of the first kind,
+        $-n$ for signed Stirling numbers of the first kind,
+        $k$ for Stirling numbers of the second kind.
+
+    The first kind of Stirling number counts the number of permutations of
+    ``n`` distinct items that have ``k`` cycles; the second kind counts the
+    ways in which ``n`` distinct items can be partitioned into ``k`` parts.
+    If ``d`` is given, the "reduced Stirling number of the second kind" is
+    returned: $S^{d}(n, k) = S(n - d + 1, k - d + 1)$ with $n \ge k \ge d$.
+    (This counts the ways to partition $n$ consecutive integers into $k$
+    groups with no pairwise difference less than $d$. See example below.)
+
+    To obtain the signed Stirling numbers of the first kind, use keyword
+    ``signed=True``. Using this keyword automatically sets ``kind`` to 1.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import stirling, bell
+    >>> from sympy.combinatorics import Permutation
+    >>> from sympy.utilities.iterables import multiset_partitions, permutations
+
+    First kind (unsigned by default):
+
+    >>> [stirling(6, i, kind=1) for i in range(7)]
+    [0, 120, 274, 225, 85, 15, 1]
+    >>> perms = list(permutations(range(4)))
+    >>> [sum(Permutation(p).cycles == i for p in perms) for i in range(5)]
+    [0, 6, 11, 6, 1]
+    >>> [stirling(4, i, kind=1) for i in range(5)]
+    [0, 6, 11, 6, 1]
+
+    First kind (signed):
+
+    >>> [stirling(4, i, signed=True) for i in range(5)]
+    [0, -6, 11, -6, 1]
+
+    Second kind:
+
+    >>> [stirling(10, i) for i in range(12)]
+    [0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1, 0]
+    >>> sum(_) == bell(10)
+    True
+    >>> len(list(multiset_partitions(range(4), 2))) == stirling(4, 2)
+    True
+
+    Reduced second kind:
+
+    >>> from sympy import subsets, oo
+    >>> def delta(p):
+    ...    if len(p) == 1:
+    ...        return oo
+    ...    return min(abs(i[0] - i[1]) for i in subsets(p, 2))
+    >>> parts = multiset_partitions(range(5), 3)
+    >>> d = 2
+    >>> sum(1 for p in parts if all(delta(i) >= d for i in p))
+    7
+    >>> stirling(5, 3, 2)
+    7
+
+    See Also
+    ========
+    sympy.utilities.iterables.multiset_partitions
+
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
+    .. [2] https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
+
+    """
+    # TODO: make this a class like bell()
+
+    n = as_int(n)
+    k = as_int(k)
+    if n < 0:
+        raise ValueError('n must be nonnegative')
+    if k > n:
+        return S.Zero
+    if d:
+        # assert k >= d
+        # kind is ignored -- only kind=2 is supported
+        return _eval_stirling2(n - d + 1, k - d + 1)
+    elif signed:
+        # kind is ignored -- only kind=1 is supported
+        return S.NegativeOne**(n - k)*_eval_stirling1(n, k)
+
+    if kind == 1:
+        return _eval_stirling1(n, k)
+    elif kind == 2:
+        return _eval_stirling2(n, k)
+    else:
+        raise ValueError('kind must be 1 or 2, not %s' % k)
+
+
+@cacheit
+def _nT(n, k):
+    """Return the partitions of ``n`` items into ``k`` parts. This
+    is used by ``nT`` for the case when ``n`` is an integer."""
+    # really quick exits
+    if k > n or k < 0:
+        return 0
+    if k in (1, n):
+        return 1
+    if k == 0:
+        return 0
+    # exits that could be done below but this is quicker
+    if k == 2:
+        return n//2
+    d = n - k
+    if d <= 3:
+        return d
+    # quick exit
+    if 3*k >= n:  # or, equivalently, 2*k >= d
+        # all the information needed in this case
+        # will be in the cache needed to calculate
+        # partition(d), so...
+        # update cache
+        tot = _partition_rec(d)
+        # and correct for values not needed
+        if d - k > 0:
+            tot -= sum(_partition_rec.fetch_item(slice(d - k)))
+        return tot
+    # regular exit
+    # nT(n, k) = Sum(nT(n - k, m), (m, 1, k));
+    # calculate needed nT(i, j) values
+    p = [1]*d
+    for i in range(2, k + 1):
+        for m  in range(i + 1, d):
+            p[m] += p[m - i]
+        d -= 1
+    # if p[0] were appended to the end of p then the last
+    # k values of p are the nT(n, j) values for 0 < j < k in reverse
+    # order p[-1] = nT(n, 1), p[-2] = nT(n, 2), etc.... Instead of
+    # putting the 1 from p[0] there, however, it is simply added to
+    # the sum below which is valid for 1 < k <= n//2
+    return (1 + sum(p[1 - k:]))
+
+
+def nT(n, k=None):
+    """Return the number of ``k``-sized partitions of ``n`` items.
+
+    Possible values for ``n``:
+
+        integer - ``n`` identical items
+
+        sequence - converted to a multiset internally
+
+        multiset - {element: multiplicity}
+
+    Note: the convention for ``nT`` is different than that of ``nC`` and
+    ``nP`` in that
+    here an integer indicates ``n`` *identical* items instead of a set of
+    length ``n``; this is in keeping with the ``partitions`` function which
+    treats its integer-``n`` input like a list of ``n`` 1s. One can use
+    ``range(n)`` for ``n`` to indicate ``n`` distinct items.
+
+    If ``k`` is None then the total number of ways to partition the elements
+    represented in ``n`` will be returned.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import nT
+
+    Partitions of the given multiset:
+
+    >>> [nT('aabbc', i) for i in range(1, 7)]
+    [1, 8, 11, 5, 1, 0]
+    >>> nT('aabbc') == sum(_)
+    True
+
+    >>> [nT("mississippi", i) for i in range(1, 12)]
+    [1, 74, 609, 1521, 1768, 1224, 579, 197, 50, 9, 1]
+
+    Partitions when all items are identical:
+
+    >>> [nT(5, i) for i in range(1, 6)]
+    [1, 2, 2, 1, 1]
+    >>> nT('1'*5) == sum(_)
+    True
+
+    When all items are different:
+
+    >>> [nT(range(5), i) for i in range(1, 6)]
+    [1, 15, 25, 10, 1]
+    >>> nT(range(5)) == sum(_)
+    True
+
+    Partitions of an integer expressed as a sum of positive integers:
+
+    >>> from sympy import partition
+    >>> partition(4)
+    5
+    >>> nT(4, 1) + nT(4, 2) + nT(4, 3) + nT(4, 4)
+    5
+    >>> nT('1'*4)
+    5
+
+    See Also
+    ========
+    sympy.utilities.iterables.partitions
+    sympy.utilities.iterables.multiset_partitions
+    sympy.functions.combinatorial.numbers.partition
+
+    References
+    ==========
+
+    .. [1] https://web.archive.org/web/20210507012732/https://teaching.csse.uwa.edu.au/units/CITS7209/partition.pdf
+
+    """
+
+    if isinstance(n, SYMPY_INTS):
+        # n identical items
+        if k is None:
+            return partition(n)
+        if isinstance(k, SYMPY_INTS):
+            n = as_int(n)
+            k = as_int(k)
+            return Integer(_nT(n, k))
+    if not isinstance(n, _MultisetHistogram):
+        try:
+            # if n contains hashable items there is some
+            # quick handling that can be done
+            u = len(set(n))
+            if u <= 1:
+                return nT(len(n), k)
+            elif u == len(n):
+                n = range(u)
+            raise TypeError
+        except TypeError:
+            n = _multiset_histogram(n)
+    N = n[_N]
+    if k is None and N == 1:
+        return 1
+    if k in (1, N):
+        return 1
+    if k == 2 or N == 2 and k is None:
+        m, r = divmod(N, 2)
+        rv = sum(nC(n, i) for i in range(1, m + 1))
+        if not r:
+            rv -= nC(n, m)//2
+        if k is None:
+            rv += 1  # for k == 1
+        return rv
+    if N == n[_ITEMS]:
+        # all distinct
+        if k is None:
+            return bell(N)
+        return stirling(N, k)
+    m = MultisetPartitionTraverser()
+    if k is None:
+        return m.count_partitions(n[_M])
+    # MultisetPartitionTraverser does not have a range-limited count
+    # method, so need to enumerate and count
+    tot = 0
+    for discard in m.enum_range(n[_M], k-1, k):
+        tot += 1
+    return tot
+
+
+#-----------------------------------------------------------------------------#
+#                                                                             #
+#                          Motzkin numbers                                    #
+#                                                                             #
+#-----------------------------------------------------------------------------#
+
+
+class motzkin(DefinedFunction):
+    """
+    The nth Motzkin number is the number
+    of ways of drawing non-intersecting chords
+    between n points on a circle (not necessarily touching
+    every point by a chord). The Motzkin numbers are named
+    after Theodore Motzkin and have diverse applications
+    in geometry, combinatorics and number theory.
+
+    Motzkin numbers are the integer sequence defined by the
+    initial terms `M_0 = 1`, `M_1 = 1` and the two-term recurrence relation
+    `M_n = \frac{2*n + 1}{n + 2} * M_{n-1} + \frac{3n - 3}{n + 2} * M_{n-2}`.
+
+
+    Examples
+    ========
+
+    >>> from sympy import motzkin
+
+    >>> motzkin.is_motzkin(5)
+    False
+    >>> motzkin.find_motzkin_numbers_in_range(2,300)
+    [2, 4, 9, 21, 51, 127]
+    >>> motzkin.find_motzkin_numbers_in_range(2,900)
+    [2, 4, 9, 21, 51, 127, 323, 835]
+    >>> motzkin.find_first_n_motzkins(10)
+    [1, 1, 2, 4, 9, 21, 51, 127, 323, 835]
+
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Motzkin_number
+    .. [2] https://mathworld.wolfram.com/MotzkinNumber.html
+
+    """
+
+    @staticmethod
+    def is_motzkin(n):
+        try:
+            n = as_int(n)
+        except ValueError:
+            return False
+        if n > 0:
+            if n in (1, 2):
+                return True
+
+            tn1 = 1
+            tn = 2
+            i = 3
+            while tn < n:
+                a = ((2*i + 1)*tn + (3*i - 3)*tn1)/(i + 2)
+                i += 1
+                tn1 = tn
+                tn = a
+
+            if tn == n:
+                return True
+            else:
+                return False
+
+        else:
+            return False
+
+    @staticmethod
+    def find_motzkin_numbers_in_range(x, y):
+        if 0 <= x <= y:
+            motzkins = []
+            if x <= 1 <= y:
+                motzkins.append(1)
+            tn1 = 1
+            tn = 2
+            i = 3
+            while tn <= y:
+                if tn >= x:
+                    motzkins.append(tn)
+                a = ((2*i + 1)*tn + (3*i - 3)*tn1)/(i + 2)
+                i += 1
+                tn1 = tn
+                tn = int(a)
+
+            return motzkins
+
+        else:
+            raise ValueError('The provided range is not valid. This condition should satisfy x <= y')
+
+    @staticmethod
+    def find_first_n_motzkins(n):
+        try:
+            n = as_int(n)
+        except ValueError:
+            raise ValueError('The provided number must be a positive integer')
+        if n < 0:
+            raise ValueError('The provided number must be a positive integer')
+        motzkins = [1]
+        if n >= 1:
+            motzkins.append(1)
+        tn1 = 1
+        tn = 2
+        i = 3
+        while i <= n:
+            motzkins.append(tn)
+            a = ((2*i + 1)*tn + (3*i - 3)*tn1)/(i + 2)
+            i += 1
+            tn1 = tn
+            tn = int(a)
+
+        return motzkins
+
+    @staticmethod
+    @recurrence_memo([S.One, S.One])
+    def _motzkin(n, prev):
+        return ((2*n + 1)*prev[-1] + (3*n - 3)*prev[-2]) // (n + 2)
+
+    @classmethod
+    def eval(cls, n):
+        try:
+            n = as_int(n)
+        except ValueError:
+            raise ValueError('The provided number must be a positive integer')
+        if n < 0:
+            raise ValueError('The provided number must be a positive integer')
+        return Integer(cls._motzkin(n - 1))
+
+
+def nD(i=None, brute=None, *, n=None, m=None):
+    """return the number of derangements for: ``n`` unique items, ``i``
+    items (as a sequence or multiset), or multiplicities, ``m`` given
+    as a sequence or multiset.
+
+    Examples
+    ========
+
+    >>> from sympy.utilities.iterables import generate_derangements as enum
+    >>> from sympy.functions.combinatorial.numbers import nD
+
+    A derangement ``d`` of sequence ``s`` has all ``d[i] != s[i]``:
+
+    >>> set([''.join(i) for i in enum('abc')])
+    {'bca', 'cab'}
+    >>> nD('abc')
+    2
+
+    Input as iterable or dictionary (multiset form) is accepted:
+
+    >>> assert nD([1, 2, 2, 3, 3, 3]) == nD({1: 1, 2: 2, 3: 3})
+
+    By default, a brute-force enumeration and count of multiset permutations
+    is only done if there are fewer than 9 elements. There may be cases when
+    there is high multiplicity with few unique elements that will benefit
+    from a brute-force enumeration, too. For this reason, the `brute`
+    keyword (default None) is provided. When False, the brute-force
+    enumeration will never be used. When True, it will always be used.
+
+    >>> nD('1111222233', brute=True)
+    44
+
+    For convenience, one may specify ``n`` distinct items using the
+    ``n`` keyword:
+
+    >>> assert nD(n=3) == nD('abc') == 2
+
+    Since the number of derangments depends on the multiplicity of the
+    elements and not the elements themselves, it may be more convenient
+    to give a list or multiset of multiplicities using keyword ``m``:
+
+    >>> assert nD('abc') == nD(m=(1,1,1)) == nD(m={1:3}) == 2
+
+    """
+    from sympy.integrals.integrals import integrate
+    from sympy.functions.special.polynomials import laguerre
+    from sympy.abc import x
+    def ok(x):
+        if not isinstance(x, SYMPY_INTS):
+            raise TypeError('expecting integer values')
+        if x < 0:
+            raise ValueError('value must not be negative')
+        return True
+
+    if (i, n, m).count(None) != 2:
+        raise ValueError('enter only 1 of i, n, or m')
+    if i is not None:
+        if isinstance(i, SYMPY_INTS):
+            raise TypeError('items must be a list or dictionary')
+        if not i:
+            return S.Zero
+        if type(i) is not dict:
+            s = list(i)
+            ms = multiset(s)
+        elif type(i) is dict:
+            all(ok(_) for _ in i.values())
+            ms = {k: v for k, v in i.items() if v}
+            s = None
+        if not ms:
+            return S.Zero
+        N = sum(ms.values())
+        counts = multiset(ms.values())
+        nkey = len(ms)
+    elif n is not None:
+        ok(n)
+        if not n:
+            return S.Zero
+        return subfactorial(n)
+    elif m is not None:
+        if isinstance(m, dict):
+            all(ok(i) and ok(j) for i, j in m.items())
+            counts = {k: v for k, v in m.items() if k*v}
+        elif iterable(m) or isinstance(m, str):
+            m = list(m)
+            all(ok(i) for i in m)
+            counts = multiset([i for i in m if i])
+        else:
+            raise TypeError('expecting iterable')
+        if not counts:
+            return S.Zero
+        N = sum(k*v for k, v in counts.items())
+        nkey = sum(counts.values())
+        s = None
+    big = int(max(counts))
+    if big == 1:  # no repetition
+        return subfactorial(nkey)
+    nval = len(counts)
+    if big*2 > N:
+        return S.Zero
+    if big*2 == N:
+        if nkey == 2 and nval == 1:
+            return S.One  # aaabbb
+        if nkey - 1 == big:  # one element repeated
+            return factorial(big)  # e.g. abc part of abcddd
+    if N < 9 and brute is None or brute:
+        # for all possibilities, this was found to be faster
+        if s is None:
+            s = []
+            i = 0
+            for m, v in counts.items():
+                for j in range(v):
+                    s.extend([i]*m)
+                    i += 1
+        return Integer(sum(1 for i in multiset_derangements(s)))
+    from sympy.functions.elementary.exponential import exp
+    return Integer(abs(integrate(exp(-x)*Mul(*[
+        laguerre(i, x)**m for i, m in counts.items()]), (x, 0, oo))))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/test_comb_factorials.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/test_comb_factorials.py
new file mode 100644
index 0000000000000000000000000000000000000000..6e3986c56736cccec0b3370007e047a1f38f06d1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/test_comb_factorials.py
@@ -0,0 +1,653 @@
+from sympy.concrete.products import Product
+from sympy.core.function import expand_func
+from sympy.core.mod import Mod
+from sympy.core.mul import Mul
+from sympy.core import EulerGamma
+from sympy.core.numbers import (Float, I, Rational, nan, oo, pi, zoo)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.combinatorial.factorials import (ff, rf, binomial, factorial, factorial2)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.special.gamma_functions import (gamma, polygamma)
+from sympy.polys.polytools import Poly
+from sympy.series.order import O
+from sympy.simplify.simplify import simplify
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.functions.combinatorial.factorials import subfactorial
+from sympy.functions.special.gamma_functions import uppergamma
+from sympy.testing.pytest import XFAIL, raises, slow
+
+#Solves and Fixes Issue #10388 - This is the updated test for the same solved issue
+
+def test_rf_eval_apply():
+    x, y = symbols('x,y')
+    n, k = symbols('n k', integer=True)
+    m = Symbol('m', integer=True, nonnegative=True)
+
+    assert rf(nan, y) is nan
+    assert rf(x, nan) is nan
+
+    assert unchanged(rf, x, y)
+
+    assert rf(oo, 0) == 1
+    assert rf(-oo, 0) == 1
+
+    assert rf(oo, 6) is oo
+    assert rf(-oo, 7) is -oo
+    assert rf(-oo, 6) is oo
+
+    assert rf(oo, -6) is oo
+    assert rf(-oo, -7) is oo
+
+    assert rf(-1, pi) == 0
+    assert rf(-5, 1 + I) == 0
+
+    assert unchanged(rf, -3, k)
+    assert unchanged(rf, x, Symbol('k', integer=False))
+    assert rf(-3, Symbol('k', integer=False)) == 0
+    assert rf(Symbol('x', negative=True, integer=True), Symbol('k', integer=False)) == 0
+
+    assert rf(x, 0) == 1
+    assert rf(x, 1) == x
+    assert rf(x, 2) == x*(x + 1)
+    assert rf(x, 3) == x*(x + 1)*(x + 2)
+    assert rf(x, 5) == x*(x + 1)*(x + 2)*(x + 3)*(x + 4)
+
+    assert rf(x, -1) == 1/(x - 1)
+    assert rf(x, -2) == 1/((x - 1)*(x - 2))
+    assert rf(x, -3) == 1/((x - 1)*(x - 2)*(x - 3))
+
+    assert rf(1, 100) == factorial(100)
+
+    assert rf(x**2 + 3*x, 2) == (x**2 + 3*x)*(x**2 + 3*x + 1)
+    assert isinstance(rf(x**2 + 3*x, 2), Mul)
+    assert rf(x**3 + x, -2) == 1/((x**3 + x - 1)*(x**3 + x - 2))
+
+    assert rf(Poly(x**2 + 3*x, x), 2) == Poly(x**4 + 8*x**3 + 19*x**2 + 12*x, x)
+    assert isinstance(rf(Poly(x**2 + 3*x, x), 2), Poly)
+    raises(ValueError, lambda: rf(Poly(x**2 + 3*x, x, y), 2))
+    assert rf(Poly(x**3 + x, x), -2) == 1/(x**6 - 9*x**5 + 35*x**4 - 75*x**3 + 94*x**2 - 66*x + 20)
+    raises(ValueError, lambda: rf(Poly(x**3 + x, x, y), -2))
+
+    assert rf(x, m).is_integer is None
+    assert rf(n, k).is_integer is None
+    assert rf(n, m).is_integer is True
+    assert rf(n, k + pi).is_integer is False
+    assert rf(n, m + pi).is_integer is False
+    assert rf(pi, m).is_integer is False
+
+    def check(x, k, o, n):
+        a, b = Dummy(), Dummy()
+        r = lambda x, k: o(a, b).rewrite(n).subs({a:x,b:k})
+        for i in range(-5,5):
+            for j in range(-5,5):
+                assert o(i, j) == r(i, j), (o, n, i, j)
+    check(x, k, rf, ff)
+    check(x, k, rf, binomial)
+    check(n, k, rf, factorial)
+    check(x, y, rf, factorial)
+    check(x, y, rf, binomial)
+
+    assert rf(x, k).rewrite(ff) == ff(x + k - 1, k)
+    assert rf(x, k).rewrite(gamma) == Piecewise(
+        (gamma(k + x)/gamma(x), x > 0),
+        ((-1)**k*gamma(1 - x)/gamma(-k - x + 1), True))
+    assert rf(5, k).rewrite(gamma) == gamma(k + 5)/24
+    assert rf(x, k).rewrite(binomial) == factorial(k)*binomial(x + k - 1, k)
+    assert rf(n, k).rewrite(factorial) == Piecewise(
+        (factorial(k + n - 1)/factorial(n - 1), n > 0),
+        ((-1)**k*factorial(-n)/factorial(-k - n), True))
+    assert rf(5, k).rewrite(factorial) == factorial(k + 4)/24
+    assert rf(x, y).rewrite(factorial) == rf(x, y)
+    assert rf(x, y).rewrite(binomial) == rf(x, y)
+
+    import random
+    from mpmath import rf as mpmath_rf
+    for i in range(100):
+        x = -500 + 500 * random.random()
+        k = -500 + 500 * random.random()
+        assert (abs(mpmath_rf(x, k) - rf(x, k)) < 10**(-15))
+
+
+def test_ff_eval_apply():
+    x, y = symbols('x,y')
+    n, k = symbols('n k', integer=True)
+    m = Symbol('m', integer=True, nonnegative=True)
+
+    assert ff(nan, y) is nan
+    assert ff(x, nan) is nan
+
+    assert unchanged(ff, x, y)
+
+    assert ff(oo, 0) == 1
+    assert ff(-oo, 0) == 1
+
+    assert ff(oo, 6) is oo
+    assert ff(-oo, 7) is -oo
+    assert ff(-oo, 6) is oo
+
+    assert ff(oo, -6) is oo
+    assert ff(-oo, -7) is oo
+
+    assert ff(x, 0) == 1
+    assert ff(x, 1) == x
+    assert ff(x, 2) == x*(x - 1)
+    assert ff(x, 3) == x*(x - 1)*(x - 2)
+    assert ff(x, 5) == x*(x - 1)*(x - 2)*(x - 3)*(x - 4)
+
+    assert ff(x, -1) == 1/(x + 1)
+    assert ff(x, -2) == 1/((x + 1)*(x + 2))
+    assert ff(x, -3) == 1/((x + 1)*(x + 2)*(x + 3))
+
+    assert ff(100, 100) == factorial(100)
+
+    assert ff(2*x**2 - 5*x, 2) == (2*x**2  - 5*x)*(2*x**2 - 5*x - 1)
+    assert isinstance(ff(2*x**2 - 5*x, 2), Mul)
+    assert ff(x**2 + 3*x, -2) == 1/((x**2 + 3*x + 1)*(x**2 + 3*x + 2))
+
+    assert ff(Poly(2*x**2 - 5*x, x), 2) == Poly(4*x**4 - 28*x**3 + 59*x**2 - 35*x, x)
+    assert isinstance(ff(Poly(2*x**2 - 5*x, x), 2), Poly)
+    raises(ValueError, lambda: ff(Poly(2*x**2 - 5*x, x, y), 2))
+    assert ff(Poly(x**2 + 3*x, x), -2) == 1/(x**4 + 12*x**3 + 49*x**2 + 78*x + 40)
+    raises(ValueError, lambda: ff(Poly(x**2 + 3*x, x, y), -2))
+
+
+    assert ff(x, m).is_integer is None
+    assert ff(n, k).is_integer is None
+    assert ff(n, m).is_integer is True
+    assert ff(n, k + pi).is_integer is False
+    assert ff(n, m + pi).is_integer is False
+    assert ff(pi, m).is_integer is False
+
+    assert isinstance(ff(x, x), ff)
+    assert ff(n, n) == factorial(n)
+
+    def check(x, k, o, n):
+        a, b = Dummy(), Dummy()
+        r = lambda x, k: o(a, b).rewrite(n).subs({a:x,b:k})
+        for i in range(-5,5):
+            for j in range(-5,5):
+                assert o(i, j) == r(i, j), (o, n)
+    check(x, k, ff, rf)
+    check(x, k, ff, gamma)
+    check(n, k, ff, factorial)
+    check(x, k, ff, binomial)
+    check(x, y, ff, factorial)
+    check(x, y, ff, binomial)
+
+    assert ff(x, k).rewrite(rf) == rf(x - k + 1, k)
+    assert ff(x, k).rewrite(gamma) == Piecewise(
+        (gamma(x + 1)/gamma(-k + x + 1), x >= 0),
+        ((-1)**k*gamma(k - x)/gamma(-x), True))
+    assert ff(5, k).rewrite(gamma) == 120/gamma(6 - k)
+    assert ff(n, k).rewrite(factorial) == Piecewise(
+        (factorial(n)/factorial(-k + n), n >= 0),
+        ((-1)**k*factorial(k - n - 1)/factorial(-n - 1), True))
+    assert ff(5, k).rewrite(factorial) == 120/factorial(5 - k)
+    assert ff(x, k).rewrite(binomial) == factorial(k) * binomial(x, k)
+    assert ff(x, y).rewrite(factorial) == ff(x, y)
+    assert ff(x, y).rewrite(binomial) == ff(x, y)
+
+    import random
+    from mpmath import ff as mpmath_ff
+    for i in range(100):
+        x = -500 + 500 * random.random()
+        k = -500 + 500 * random.random()
+        a = mpmath_ff(x, k)
+        b = ff(x, k)
+        assert (abs(a - b) < abs(a) * 10**(-15))
+
+
+def test_rf_ff_eval_hiprec():
+    maple = Float('6.9109401292234329956525265438452')
+    us = ff(18, Rational(2, 3)).evalf(32)
+    assert abs(us - maple)/us < 1e-31
+
+    maple = Float('6.8261540131125511557924466355367')
+    us = rf(18, Rational(2, 3)).evalf(32)
+    assert abs(us - maple)/us < 1e-31
+
+    maple = Float('34.007346127440197150854651814225')
+    us = rf(Float('4.4', 32), Float('2.2', 32))
+    assert abs(us - maple)/us < 1e-31
+
+
+def test_rf_lambdify_mpmath():
+    from sympy.utilities.lambdify import lambdify
+    x, y = symbols('x,y')
+    f = lambdify((x,y), rf(x, y), 'mpmath')
+    maple = Float('34.007346127440197')
+    us = f(4.4, 2.2)
+    assert abs(us - maple)/us < 1e-15
+
+
+def test_factorial():
+    x = Symbol('x')
+    n = Symbol('n', integer=True)
+    k = Symbol('k', integer=True, nonnegative=True)
+    r = Symbol('r', integer=False)
+    s = Symbol('s', integer=False, negative=True)
+    t = Symbol('t', nonnegative=True)
+    u = Symbol('u', noninteger=True)
+
+    assert factorial(-2) is zoo
+    assert factorial(0) == 1
+    assert factorial(7) == 5040
+    assert factorial(19) == 121645100408832000
+    assert factorial(31) == 8222838654177922817725562880000000
+    assert factorial(n).func == factorial
+    assert factorial(2*n).func == factorial
+
+    assert factorial(x).is_integer is None
+    assert factorial(n).is_integer is None
+    assert factorial(k).is_integer
+    assert factorial(r).is_integer is None
+
+    assert factorial(n).is_positive is None
+    assert factorial(k).is_positive
+
+    assert factorial(x).is_real is None
+    assert factorial(n).is_real is None
+    assert factorial(k).is_real is True
+    assert factorial(r).is_real is None
+    assert factorial(s).is_real is True
+    assert factorial(t).is_real is True
+    assert factorial(u).is_real is True
+
+    assert factorial(x).is_composite is None
+    assert factorial(n).is_composite is None
+    assert factorial(k).is_composite is None
+    assert factorial(k + 3).is_composite is True
+    assert factorial(r).is_composite is None
+    assert factorial(s).is_composite is None
+    assert factorial(t).is_composite is None
+    assert factorial(u).is_composite is None
+
+    assert factorial(oo) is oo
+
+
+def test_factorial_Mod():
+    pr = Symbol('pr', prime=True)
+    p, q = 10**9 + 9, 10**9 + 33 # prime modulo
+    r, s = 10**7 + 5, 33333333 # composite modulo
+    assert Mod(factorial(pr - 1), pr) == pr - 1
+    assert Mod(factorial(pr - 1), -pr) == -1
+    assert Mod(factorial(r - 1, evaluate=False), r) == 0
+    assert Mod(factorial(s - 1, evaluate=False), s) == 0
+    assert Mod(factorial(p - 1, evaluate=False), p) == p - 1
+    assert Mod(factorial(q - 1, evaluate=False), q) == q - 1
+    assert Mod(factorial(p - 50, evaluate=False), p) == 854928834
+    assert Mod(factorial(q - 1800, evaluate=False), q) == 905504050
+    assert Mod(factorial(153, evaluate=False), r) == Mod(factorial(153), r)
+    assert Mod(factorial(255, evaluate=False), s) == Mod(factorial(255), s)
+    assert Mod(factorial(4, evaluate=False), 3) == S.Zero
+    assert Mod(factorial(5, evaluate=False), 6) == S.Zero
+
+
+def test_factorial_diff():
+    n = Symbol('n', integer=True)
+
+    assert factorial(n).diff(n) == \
+        gamma(1 + n)*polygamma(0, 1 + n)
+    assert factorial(n**2).diff(n) == \
+        2*n*gamma(1 + n**2)*polygamma(0, 1 + n**2)
+    raises(ArgumentIndexError, lambda: factorial(n**2).fdiff(2))
+
+
+def test_factorial_series():
+    n = Symbol('n', integer=True)
+
+    assert factorial(n).series(n, 0, 3) == \
+        1 - n*EulerGamma + n**2*(EulerGamma**2/2 + pi**2/12) + O(n**3)
+
+
+def test_factorial_rewrite():
+    n = Symbol('n', integer=True)
+    k = Symbol('k', integer=True, nonnegative=True)
+
+    assert factorial(n).rewrite(gamma) == gamma(n + 1)
+    _i = Dummy('i')
+    assert factorial(k).rewrite(Product).dummy_eq(Product(_i, (_i, 1, k)))
+    assert factorial(n).rewrite(Product) == factorial(n)
+
+
+def test_factorial2():
+    n = Symbol('n', integer=True)
+
+    assert factorial2(-1) == 1
+    assert factorial2(0) == 1
+    assert factorial2(7) == 105
+    assert factorial2(8) == 384
+
+    # The following is exhaustive
+    tt = Symbol('tt', integer=True, nonnegative=True)
+    tte = Symbol('tte', even=True, nonnegative=True)
+    tpe = Symbol('tpe', even=True, positive=True)
+    tto = Symbol('tto', odd=True, nonnegative=True)
+    tf = Symbol('tf', integer=True, nonnegative=False)
+    tfe = Symbol('tfe', even=True, nonnegative=False)
+    tfo = Symbol('tfo', odd=True, nonnegative=False)
+    ft = Symbol('ft', integer=False, nonnegative=True)
+    ff = Symbol('ff', integer=False, nonnegative=False)
+    fn = Symbol('fn', integer=False)
+    nt = Symbol('nt', nonnegative=True)
+    nf = Symbol('nf', nonnegative=False)
+    nn = Symbol('nn')
+    z = Symbol('z', zero=True)
+    #Solves and Fixes Issue #10388 - This is the updated test for the same solved issue
+    raises(ValueError, lambda: factorial2(oo))
+    raises(ValueError, lambda: factorial2(Rational(5, 2)))
+    raises(ValueError, lambda: factorial2(-4))
+    assert factorial2(n).is_integer is None
+    assert factorial2(tt - 1).is_integer
+    assert factorial2(tte - 1).is_integer
+    assert factorial2(tpe - 3).is_integer
+    assert factorial2(tto - 4).is_integer
+    assert factorial2(tto - 2).is_integer
+    assert factorial2(tf).is_integer is None
+    assert factorial2(tfe).is_integer is None
+    assert factorial2(tfo).is_integer is None
+    assert factorial2(ft).is_integer is None
+    assert factorial2(ff).is_integer is None
+    assert factorial2(fn).is_integer is None
+    assert factorial2(nt).is_integer is None
+    assert factorial2(nf).is_integer is None
+    assert factorial2(nn).is_integer is None
+
+    assert factorial2(n).is_positive is None
+    assert factorial2(tt - 1).is_positive is True
+    assert factorial2(tte - 1).is_positive is True
+    assert factorial2(tpe - 3).is_positive is True
+    assert factorial2(tpe - 1).is_positive is True
+    assert factorial2(tto - 2).is_positive is True
+    assert factorial2(tto - 1).is_positive is True
+    assert factorial2(tf).is_positive is None
+    assert factorial2(tfe).is_positive is None
+    assert factorial2(tfo).is_positive is None
+    assert factorial2(ft).is_positive is None
+    assert factorial2(ff).is_positive is None
+    assert factorial2(fn).is_positive is None
+    assert factorial2(nt).is_positive is None
+    assert factorial2(nf).is_positive is None
+    assert factorial2(nn).is_positive is None
+
+    assert factorial2(tt).is_even is None
+    assert factorial2(tt).is_odd is None
+    assert factorial2(tte).is_even is None
+    assert factorial2(tte).is_odd is None
+    assert factorial2(tte + 2).is_even is True
+    assert factorial2(tpe).is_even is True
+    assert factorial2(tpe).is_odd is False
+    assert factorial2(tto).is_odd is True
+    assert factorial2(tf).is_even is None
+    assert factorial2(tf).is_odd is None
+    assert factorial2(tfe).is_even is None
+    assert factorial2(tfe).is_odd is None
+    assert factorial2(tfo).is_even is False
+    assert factorial2(tfo).is_odd is None
+    assert factorial2(z).is_even is False
+    assert factorial2(z).is_odd is True
+
+
+def test_factorial2_rewrite():
+    n = Symbol('n', integer=True)
+    assert factorial2(n).rewrite(gamma) == \
+        2**(n/2)*Piecewise((1, Eq(Mod(n, 2), 0)), (sqrt(2)/sqrt(pi), Eq(Mod(n, 2), 1)))*gamma(n/2 + 1)
+    assert factorial2(2*n).rewrite(gamma) == 2**n*gamma(n + 1)
+    assert factorial2(2*n + 1).rewrite(gamma) == \
+        sqrt(2)*2**(n + S.Half)*gamma(n + Rational(3, 2))/sqrt(pi)
+
+
+def test_binomial():
+    x = Symbol('x')
+    n = Symbol('n', integer=True)
+    nz = Symbol('nz', integer=True, nonzero=True)
+    k = Symbol('k', integer=True)
+    kp = Symbol('kp', integer=True, positive=True)
+    kn = Symbol('kn', integer=True, negative=True)
+    u = Symbol('u', negative=True)
+    v = Symbol('v', nonnegative=True)
+    p = Symbol('p', positive=True)
+    z = Symbol('z', zero=True)
+    nt = Symbol('nt', integer=False)
+    kt = Symbol('kt', integer=False)
+    a = Symbol('a', integer=True, nonnegative=True)
+    b = Symbol('b', integer=True, nonnegative=True)
+
+    assert binomial(0, 0) == 1
+    assert binomial(1, 1) == 1
+    assert binomial(10, 10) == 1
+    assert binomial(n, z) == 1
+    assert binomial(1, 2) == 0
+    assert binomial(-1, 2) == 1
+    assert binomial(1, -1) == 0
+    assert binomial(-1, 1) == -1
+    assert binomial(-1, -1) == 0
+    assert binomial(S.Half, S.Half) == 1
+    assert binomial(-10, 1) == -10
+    assert binomial(-10, 7) == -11440
+    assert binomial(n, -1) == 0 # holds for all integers (negative, zero, positive)
+    assert binomial(kp, -1) == 0
+    assert binomial(nz, 0) == 1
+    assert expand_func(binomial(n, 1)) == n
+    assert expand_func(binomial(n, 2)) == n*(n - 1)/2
+    assert expand_func(binomial(n, n - 2)) == n*(n - 1)/2
+    assert expand_func(binomial(n, n - 1)) == n
+    assert binomial(n, 3).func == binomial
+    assert binomial(n, 3).expand(func=True) ==  n**3/6 - n**2/2 + n/3
+    assert expand_func(binomial(n, 3)) ==  n*(n - 2)*(n - 1)/6
+    assert binomial(n, n).func == binomial # e.g. (-1, -1) == 0, (2, 2) == 1
+    assert binomial(n, n + 1).func == binomial  # e.g. (-1, 0) == 1
+    assert binomial(kp, kp + 1) == 0
+    assert binomial(kn, kn) == 0 # issue #14529
+    assert binomial(n, u).func == binomial
+    assert binomial(kp, u).func == binomial
+    assert binomial(n, p).func == binomial
+    assert binomial(n, k).func == binomial
+    assert binomial(n, n + p).func == binomial
+    assert binomial(kp, kp + p).func == binomial
+
+    assert expand_func(binomial(n, n - 3)) == n*(n - 2)*(n - 1)/6
+
+    assert binomial(n, k).is_integer
+    assert binomial(nt, k).is_integer is None
+    assert binomial(x, nt).is_integer is False
+
+    assert binomial(gamma(25), 6) == 79232165267303928292058750056084441948572511312165380965440075720159859792344339983120618959044048198214221915637090855535036339620413440000
+    assert binomial(1324, 47) == 906266255662694632984994480774946083064699457235920708992926525848438478406790323869952
+    assert binomial(1735, 43) == 190910140420204130794758005450919715396159959034348676124678207874195064798202216379800
+    assert binomial(2512, 53) == 213894469313832631145798303740098720367984955243020898718979538096223399813295457822575338958939834177325304000
+    assert binomial(3383, 52) == 27922807788818096863529701501764372757272890613101645521813434902890007725667814813832027795881839396839287659777235
+    assert binomial(4321, 51) == 124595639629264868916081001263541480185227731958274383287107643816863897851139048158022599533438936036467601690983780576
+
+    assert binomial(a, b).is_nonnegative is True
+    assert binomial(-1, 2, evaluate=False).is_nonnegative is True
+    assert binomial(10, 5, evaluate=False).is_nonnegative is True
+    assert binomial(10, -3, evaluate=False).is_nonnegative is True
+    assert binomial(-10, -3, evaluate=False).is_nonnegative is True
+    assert binomial(-10, 2, evaluate=False).is_nonnegative is True
+    assert binomial(-10, 1, evaluate=False).is_nonnegative is False
+    assert binomial(-10, 7, evaluate=False).is_nonnegative is False
+
+    # issue #14625
+    for _ in (pi, -pi, nt, v, a):
+        assert binomial(_, _) == 1
+        assert binomial(_, _ - 1) == _
+    assert isinstance(binomial(u, u), binomial)
+    assert isinstance(binomial(u, u - 1), binomial)
+    assert isinstance(binomial(x, x), binomial)
+    assert isinstance(binomial(x, x - 1), binomial)
+
+    #issue #18802
+    assert expand_func(binomial(x + 1, x)) == x + 1
+    assert expand_func(binomial(x, x - 1)) == x
+    assert expand_func(binomial(x + 1, x - 1)) == x*(x + 1)/2
+    assert expand_func(binomial(x**2 + 1, x**2)) == x**2 + 1
+
+    # issue #13980 and #13981
+    assert binomial(-7, -5) == 0
+    assert binomial(-23, -12) == 0
+    assert binomial(Rational(13, 2), -10) == 0
+    assert binomial(-49, -51) == 0
+
+    assert binomial(19, Rational(-7, 2)) == S(-68719476736)/(911337863661225*pi)
+    assert binomial(0, Rational(3, 2)) == S(-2)/(3*pi)
+    assert binomial(-3, Rational(-7, 2)) is zoo
+    assert binomial(kn, kt) is zoo
+
+    assert binomial(nt, kt).func == binomial
+    assert binomial(nt, Rational(15, 6)) == 8*gamma(nt + 1)/(15*sqrt(pi)*gamma(nt - Rational(3, 2)))
+    assert binomial(Rational(20, 3), Rational(-10, 8)) == gamma(Rational(23, 3))/(gamma(Rational(-1, 4))*gamma(Rational(107, 12)))
+    assert binomial(Rational(19, 2), Rational(-7, 2)) == Rational(-1615, 8388608)
+    assert binomial(Rational(-13, 5), Rational(-7, 8)) == gamma(Rational(-8, 5))/(gamma(Rational(-29, 40))*gamma(Rational(1, 8)))
+    assert binomial(Rational(-19, 8), Rational(-13, 5)) == gamma(Rational(-11, 8))/(gamma(Rational(-8, 5))*gamma(Rational(49, 40)))
+
+    # binomial for complexes
+    assert binomial(I, Rational(-89, 8)) == gamma(1 + I)/(gamma(Rational(-81, 8))*gamma(Rational(97, 8) + I))
+    assert binomial(I, 2*I) == gamma(1 + I)/(gamma(1 - I)*gamma(1 + 2*I))
+    assert binomial(-7, I) is zoo
+    assert binomial(Rational(-7, 6), I) == gamma(Rational(-1, 6))/(gamma(Rational(-1, 6) - I)*gamma(1 + I))
+    assert binomial((1+2*I), (1+3*I)) == gamma(2 + 2*I)/(gamma(1 - I)*gamma(2 + 3*I))
+    assert binomial(I, 5) == Rational(1, 3) - I/S(12)
+    assert binomial((2*I + 3), 7) == -13*I/S(63)
+    assert isinstance(binomial(I, n), binomial)
+    assert expand_func(binomial(3, 2, evaluate=False)) == 3
+    assert expand_func(binomial(n, 0, evaluate=False)) == 1
+    assert expand_func(binomial(n, -2, evaluate=False)) == 0
+    assert expand_func(binomial(n, k)) == binomial(n, k)
+
+
+def test_binomial_Mod():
+    p, q = 10**5 + 3, 10**9 + 33 # prime modulo
+    r = 10**7 + 5 # composite modulo
+
+    # A few tests to get coverage
+    # Lucas Theorem
+    assert Mod(binomial(156675, 4433, evaluate=False), p) == Mod(binomial(156675, 4433), p)
+
+    # factorial Mod
+    assert Mod(binomial(1234, 432, evaluate=False), q) == Mod(binomial(1234, 432), q)
+
+    # binomial factorize
+    assert Mod(binomial(253, 113, evaluate=False), r) == Mod(binomial(253, 113), r)
+
+    # using Granville's generalisation of Lucas' Theorem
+    assert Mod(binomial(10**18, 10**12, evaluate=False), p*p) == 3744312326
+
+
+@slow
+def test_binomial_Mod_slow():
+    p, q = 10**5 + 3, 10**9 + 33 # prime modulo
+    r, s = 10**7 + 5, 33333333 # composite modulo
+
+    n, k, m = symbols('n k m')
+    assert (binomial(n, k) % q).subs({n: s, k: p}) == Mod(binomial(s, p), q)
+    assert (binomial(n, k) % m).subs({n: 8, k: 5, m: 13}) == 4
+    assert (binomial(9, k) % 7).subs(k, 2) == 1
+
+    # Lucas Theorem
+    assert Mod(binomial(123456, 43253, evaluate=False), p) == Mod(binomial(123456, 43253), p)
+    assert Mod(binomial(-178911, 237, evaluate=False), p) == Mod(-binomial(178911 + 237 - 1, 237), p)
+    assert Mod(binomial(-178911, 238, evaluate=False), p) == Mod(binomial(178911 + 238 - 1, 238), p)
+
+    # factorial Mod
+    assert Mod(binomial(9734, 451, evaluate=False), q) == Mod(binomial(9734, 451), q)
+    assert Mod(binomial(-10733, 4459, evaluate=False), q) == Mod(binomial(-10733, 4459), q)
+    assert Mod(binomial(-15733, 4458, evaluate=False), q) == Mod(binomial(-15733, 4458), q)
+    assert Mod(binomial(23, -38, evaluate=False), q) is S.Zero
+    assert Mod(binomial(23, 38, evaluate=False), q) is S.Zero
+
+    # binomial factorize
+    assert Mod(binomial(753, 119, evaluate=False), r) == Mod(binomial(753, 119), r)
+    assert Mod(binomial(3781, 948, evaluate=False), s) == Mod(binomial(3781, 948), s)
+    assert Mod(binomial(25773, 1793, evaluate=False), s) == Mod(binomial(25773, 1793), s)
+    assert Mod(binomial(-753, 118, evaluate=False), r) == Mod(binomial(-753, 118), r)
+    assert Mod(binomial(-25773, 1793, evaluate=False), s) == Mod(binomial(-25773, 1793), s)
+
+
+def test_binomial_diff():
+    n = Symbol('n', integer=True)
+    k = Symbol('k', integer=True)
+
+    assert binomial(n, k).diff(n) == \
+        (-polygamma(0, 1 + n - k) + polygamma(0, 1 + n))*binomial(n, k)
+    assert binomial(n**2, k**3).diff(n) == \
+        2*n*(-polygamma(
+            0, 1 + n**2 - k**3) + polygamma(0, 1 + n**2))*binomial(n**2, k**3)
+
+    assert binomial(n, k).diff(k) == \
+        (-polygamma(0, 1 + k) + polygamma(0, 1 + n - k))*binomial(n, k)
+    assert binomial(n**2, k**3).diff(k) == \
+        3*k**2*(-polygamma(
+            0, 1 + k**3) + polygamma(0, 1 + n**2 - k**3))*binomial(n**2, k**3)
+    raises(ArgumentIndexError, lambda: binomial(n, k).fdiff(3))
+
+
+def test_binomial_rewrite():
+    n = Symbol('n', integer=True)
+    k = Symbol('k', integer=True)
+    x = Symbol('x')
+
+    assert binomial(n, k).rewrite(
+        factorial) == factorial(n)/(factorial(k)*factorial(n - k))
+    assert binomial(
+        n, k).rewrite(gamma) == gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1))
+    assert binomial(n, k).rewrite(ff) == ff(n, k) / factorial(k)
+    assert binomial(n, x).rewrite(ff) == binomial(n, x)
+
+
+@XFAIL
+def test_factorial_simplify_fail():
+    # simplify(factorial(x + 1).diff(x) - ((x + 1)*factorial(x)).diff(x))) == 0
+    from sympy.abc import x
+    assert simplify(x*polygamma(0, x + 1) - x*polygamma(0, x + 2) +
+                    polygamma(0, x + 1) - polygamma(0, x + 2) + 1) == 0
+
+
+def test_subfactorial():
+    assert all(subfactorial(i) == ans for i, ans in enumerate(
+        [1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496]))
+    assert subfactorial(oo) is oo
+    assert subfactorial(nan) is nan
+    assert subfactorial(23) == 9510425471055777937262
+    assert unchanged(subfactorial, 2.2)
+
+    x = Symbol('x')
+    assert subfactorial(x).rewrite(uppergamma) == uppergamma(x + 1, -1)/S.Exp1
+
+    tt = Symbol('tt', integer=True, nonnegative=True)
+    tf = Symbol('tf', integer=True, nonnegative=False)
+    tn = Symbol('tf', integer=True)
+    ft = Symbol('ft', integer=False, nonnegative=True)
+    ff = Symbol('ff', integer=False, nonnegative=False)
+    fn = Symbol('ff', integer=False)
+    nt = Symbol('nt', nonnegative=True)
+    nf = Symbol('nf', nonnegative=False)
+    nn = Symbol('nf')
+    te = Symbol('te', even=True, nonnegative=True)
+    to = Symbol('to', odd=True, nonnegative=True)
+    assert subfactorial(tt).is_integer
+    assert subfactorial(tf).is_integer is None
+    assert subfactorial(tn).is_integer is None
+    assert subfactorial(ft).is_integer is None
+    assert subfactorial(ff).is_integer is None
+    assert subfactorial(fn).is_integer is None
+    assert subfactorial(nt).is_integer is None
+    assert subfactorial(nf).is_integer is None
+    assert subfactorial(nn).is_integer is None
+    assert subfactorial(tt).is_nonnegative
+    assert subfactorial(tf).is_nonnegative is None
+    assert subfactorial(tn).is_nonnegative is None
+    assert subfactorial(ft).is_nonnegative is None
+    assert subfactorial(ff).is_nonnegative is None
+    assert subfactorial(fn).is_nonnegative is None
+    assert subfactorial(nt).is_nonnegative is None
+    assert subfactorial(nf).is_nonnegative is None
+    assert subfactorial(nn).is_nonnegative is None
+    assert subfactorial(tt).is_even is None
+    assert subfactorial(tt).is_odd is None
+    assert subfactorial(te).is_odd is True
+    assert subfactorial(to).is_even is True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/test_comb_numbers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/test_comb_numbers.py
new file mode 100644
index 0000000000000000000000000000000000000000..83a7de89ed8e4fcc433d29f41fc87b9d0d397539
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/combinatorial/tests/test_comb_numbers.py
@@ -0,0 +1,1250 @@
+import string
+
+from sympy.concrete.products import Product
+from sympy.concrete.summations import Sum
+from sympy.core.function import (diff, expand_func)
+from sympy.core import (EulerGamma, TribonacciConstant)
+from sympy.core.numbers import (Float, I, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.combinatorial.numbers import carmichael
+from sympy.functions.elementary.complexes import (im, re)
+from sympy.functions.elementary.integers import floor
+from sympy.polys.polytools import cancel
+from sympy.series.limits import limit, Limit
+from sympy.series.order import O
+from sympy.functions import (
+    bernoulli, harmonic, bell, fibonacci, tribonacci, lucas, euler, catalan,
+    genocchi, andre, partition, divisor_sigma, udivisor_sigma, legendre_symbol,
+    jacobi_symbol, kronecker_symbol, mobius,
+    primenu, primeomega, totient, reduced_totient, primepi,
+    motzkin, binomial, gamma, sqrt, cbrt, hyper, log, digamma,
+    trigamma, polygamma, factorial, sin, cos, cot, polylog, zeta, dirichlet_eta)
+from sympy.functions.combinatorial.numbers import _nT
+from sympy.ntheory.factor_ import factorint
+
+from sympy.core.expr import unchanged
+from sympy.core.numbers import GoldenRatio, Integer
+
+from sympy.testing.pytest import raises, nocache_fail, warns_deprecated_sympy
+from sympy.abc import x
+
+
+def test_carmichael():
+    with warns_deprecated_sympy():
+        assert carmichael.is_prime(2821) == False
+
+
+def test_bernoulli():
+    assert bernoulli(0) == 1
+    assert bernoulli(1) == Rational(1, 2)
+    assert bernoulli(2) == Rational(1, 6)
+    assert bernoulli(3) == 0
+    assert bernoulli(4) == Rational(-1, 30)
+    assert bernoulli(5) == 0
+    assert bernoulli(6) == Rational(1, 42)
+    assert bernoulli(7) == 0
+    assert bernoulli(8) == Rational(-1, 30)
+    assert bernoulli(10) == Rational(5, 66)
+    assert bernoulli(1000001) == 0
+
+    assert bernoulli(0, x) == 1
+    assert bernoulli(1, x) == x - S.Half
+    assert bernoulli(2, x) == x**2 - x + Rational(1, 6)
+    assert bernoulli(3, x) == x**3 - (3*x**2)/2 + x/2
+
+    # Should be fast; computed with mpmath
+    b = bernoulli(1000)
+    assert b.p % 10**10 == 7950421099
+    assert b.q == 342999030
+
+    b = bernoulli(10**6, evaluate=False).evalf()
+    assert str(b) == '-2.23799235765713e+4767529'
+
+    # Issue #8527
+    l = Symbol('l', integer=True)
+    m = Symbol('m', integer=True, nonnegative=True)
+    n = Symbol('n', integer=True, positive=True)
+    assert isinstance(bernoulli(2 * l + 1), bernoulli)
+    assert isinstance(bernoulli(2 * m + 1), bernoulli)
+    assert bernoulli(2 * n + 1) == 0
+
+    assert bernoulli(x, 1) == bernoulli(x)
+
+    assert str(bernoulli(0.0, 2.3).evalf(n=10)) == '1.000000000'
+    assert str(bernoulli(1.0).evalf(n=10)) == '0.5000000000'
+    assert str(bernoulli(1.2).evalf(n=10)) == '0.4195995367'
+    assert str(bernoulli(1.2, 0.8).evalf(n=10)) == '0.2144830348'
+    assert str(bernoulli(1.2, -0.8).evalf(n=10)) == '-1.158865646 - 0.6745558744*I'
+    assert str(bernoulli(3.0, 1j).evalf(n=10)) == '1.5 - 0.5*I'
+    assert str(bernoulli(I).evalf(n=10)) == '0.9268485643 - 0.5821580598*I'
+    assert str(bernoulli(I, I).evalf(n=10)) == '0.1267792071 + 0.01947413152*I'
+    assert bernoulli(x).evalf() == bernoulli(x)
+
+
+def test_bernoulli_rewrite():
+    from sympy.functions.elementary.piecewise import Piecewise
+    n = Symbol('n', integer=True, nonnegative=True)
+
+    assert bernoulli(-1).rewrite(zeta) == pi**2/6
+    assert bernoulli(-2).rewrite(zeta) == 2*zeta(3)
+    assert not bernoulli(n, -3).rewrite(zeta).has(harmonic)
+    assert bernoulli(-4, x).rewrite(zeta) == 4*zeta(5, x)
+    assert isinstance(bernoulli(n, x).rewrite(zeta), Piecewise)
+    assert bernoulli(n+1, x).rewrite(zeta) == -(n+1) * zeta(-n, x)
+
+
+def test_fibonacci():
+    assert [fibonacci(n) for n in range(-3, 5)] == [2, -1, 1, 0, 1, 1, 2, 3]
+    assert fibonacci(100) == 354224848179261915075
+    assert [lucas(n) for n in range(-3, 5)] == [-4, 3, -1, 2, 1, 3, 4, 7]
+    assert lucas(100) == 792070839848372253127
+
+    assert fibonacci(1, x) == 1
+    assert fibonacci(2, x) == x
+    assert fibonacci(3, x) == x**2 + 1
+    assert fibonacci(4, x) == x**3 + 2*x
+
+    # issue #8800
+    n = Dummy('n')
+    assert fibonacci(n).limit(n, S.Infinity) is S.Infinity
+    assert lucas(n).limit(n, S.Infinity) is S.Infinity
+
+    assert fibonacci(n).rewrite(sqrt) == \
+        2**(-n)*sqrt(5)*((1 + sqrt(5))**n - (-sqrt(5) + 1)**n) / 5
+    assert fibonacci(n).rewrite(sqrt).subs(n, 10).expand() == fibonacci(10)
+    assert fibonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \
+        Float(fibonacci(10))
+    assert lucas(n).rewrite(sqrt) == \
+        (fibonacci(n-1).rewrite(sqrt) + fibonacci(n+1).rewrite(sqrt)).simplify()
+    assert lucas(n).rewrite(sqrt).subs(n, 10).expand() == lucas(10)
+    raises(ValueError, lambda: fibonacci(-3, x))
+
+
+def test_tribonacci():
+    assert [tribonacci(n) for n in range(8)] == [0, 1, 1, 2, 4, 7, 13, 24]
+    assert tribonacci(100) == 98079530178586034536500564
+
+    assert tribonacci(0, x) == 0
+    assert tribonacci(1, x) == 1
+    assert tribonacci(2, x) == x**2
+    assert tribonacci(3, x) == x**4 + x
+    assert tribonacci(4, x) == x**6 + 2*x**3 + 1
+    assert tribonacci(5, x) == x**8 + 3*x**5 + 3*x**2
+
+    n = Dummy('n')
+    assert tribonacci(n).limit(n, S.Infinity) is S.Infinity
+
+    w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2
+    a = (1 + cbrt(19 + 3*sqrt(33)) + cbrt(19 - 3*sqrt(33))) / 3
+    b = (1 + w*cbrt(19 + 3*sqrt(33)) + w**2*cbrt(19 - 3*sqrt(33))) / 3
+    c = (1 + w**2*cbrt(19 + 3*sqrt(33)) + w*cbrt(19 - 3*sqrt(33))) / 3
+    assert tribonacci(n).rewrite(sqrt) == \
+      (a**(n + 1)/((a - b)*(a - c))
+      + b**(n + 1)/((b - a)*(b - c))
+      + c**(n + 1)/((c - a)*(c - b)))
+    assert tribonacci(n).rewrite(sqrt).subs(n, 4).simplify() == tribonacci(4)
+    assert tribonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \
+        Float(tribonacci(10))
+    assert tribonacci(n).rewrite(TribonacciConstant) == floor(
+            3*TribonacciConstant**n*(102*sqrt(33) + 586)**Rational(1, 3)/
+            (-2*(102*sqrt(33) + 586)**Rational(1, 3) + 4 + (102*sqrt(33)
+            + 586)**Rational(2, 3)) + S.Half)
+    raises(ValueError, lambda: tribonacci(-1, x))
+
+
+@nocache_fail
+def test_bell():
+    assert [bell(n) for n in range(8)] == [1, 1, 2, 5, 15, 52, 203, 877]
+
+    assert bell(0, x) == 1
+    assert bell(1, x) == x
+    assert bell(2, x) == x**2 + x
+    assert bell(5, x) == x**5 + 10*x**4 + 25*x**3 + 15*x**2 + x
+    assert bell(oo) is S.Infinity
+    raises(ValueError, lambda: bell(oo, x))
+
+    raises(ValueError, lambda: bell(-1))
+    raises(ValueError, lambda: bell(S.Half))
+
+    X = symbols('x:6')
+    # X = (x0, x1, .. x5)
+    # at the same time: X[1] = x1, X[2] = x2 for standard readablity.
+    # but we must supply zero-based indexed object X[1:] = (x1, .. x5)
+
+    assert bell(6, 2, X[1:]) == 6*X[5]*X[1] + 15*X[4]*X[2] + 10*X[3]**2
+    assert bell(
+        6, 3, X[1:]) == 15*X[4]*X[1]**2 + 60*X[3]*X[2]*X[1] + 15*X[2]**3
+
+    X = (1, 10, 100, 1000, 10000)
+    assert bell(6, 2, X) == (6 + 15 + 10)*10000
+
+    X = (1, 2, 3, 3, 5)
+    assert bell(6, 2, X) == 6*5 + 15*3*2 + 10*3**2
+
+    X = (1, 2, 3, 5)
+    assert bell(6, 3, X) == 15*5 + 60*3*2 + 15*2**3
+
+    # Dobinski's formula
+    n = Symbol('n', integer=True, nonnegative=True)
+    # For large numbers, this is too slow
+    # For nonintegers, there are significant precision errors
+    for i in [0, 2, 3, 7, 13, 42, 55]:
+        # Running without the cache this is either very slow or goes into an
+        # infinite loop.
+        assert bell(i).evalf() == bell(n).rewrite(Sum).evalf(subs={n: i})
+
+    m = Symbol("m")
+    assert bell(m).rewrite(Sum) == bell(m)
+    assert bell(n, m).rewrite(Sum) == bell(n, m)
+    # issue 9184
+    n = Dummy('n')
+    assert bell(n).limit(n, S.Infinity) is S.Infinity
+
+
+def test_harmonic():
+    n = Symbol("n")
+    m = Symbol("m")
+
+    assert harmonic(n, 0) == n
+    assert harmonic(n).evalf() == harmonic(n)
+    assert harmonic(n, 1) == harmonic(n)
+    assert harmonic(1, n) == 1
+
+    assert harmonic(0, 1) == 0
+    assert harmonic(1, 1) == 1
+    assert harmonic(2, 1) == Rational(3, 2)
+    assert harmonic(3, 1) == Rational(11, 6)
+    assert harmonic(4, 1) == Rational(25, 12)
+    assert harmonic(0, 2) == 0
+    assert harmonic(1, 2) == 1
+    assert harmonic(2, 2) == Rational(5, 4)
+    assert harmonic(3, 2) == Rational(49, 36)
+    assert harmonic(4, 2) == Rational(205, 144)
+    assert harmonic(0, 3) == 0
+    assert harmonic(1, 3) == 1
+    assert harmonic(2, 3) == Rational(9, 8)
+    assert harmonic(3, 3) == Rational(251, 216)
+    assert harmonic(4, 3) == Rational(2035, 1728)
+
+    assert harmonic(oo, -1) is S.NaN
+    assert harmonic(oo, 0) is oo
+    assert harmonic(oo, S.Half) is oo
+    assert harmonic(oo, 1) is oo
+    assert harmonic(oo, 2) == (pi**2)/6
+    assert harmonic(oo, 3) == zeta(3)
+    assert harmonic(oo, Dummy(negative=True)) is S.NaN
+    ip = Dummy(integer=True, positive=True)
+    if (1/ip <= 1) is True:  #---------------------------------+
+        assert None, 'delete this if-block and the next line' #|
+    ip = Dummy(even=True, positive=True)  #--------------------+
+    assert harmonic(oo, 1/ip) is oo
+    assert harmonic(oo, 1 + ip) is zeta(1 + ip)
+
+    assert harmonic(0, m) == 0
+    assert harmonic(-1, -1) == 0
+    assert harmonic(-1, 0) == -1
+    assert harmonic(-1, 1) is S.ComplexInfinity
+    assert harmonic(-1, 2) is S.NaN
+    assert harmonic(-3, -2) == -5
+    assert harmonic(-3, -3) == 9
+
+
+def test_harmonic_rational():
+    ne = S(6)
+    no = S(5)
+    pe = S(8)
+    po = S(9)
+    qe = S(10)
+    qo = S(13)
+
+    Heee = harmonic(ne + pe/qe)
+    Aeee = (-log(10) + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8)))
+             + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8)))
+             + pi*sqrt(2*sqrt(5)/5 + 1)/2 + Rational(13944145, 4720968))
+
+    Heeo = harmonic(ne + pe/qo)
+    Aeeo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(4, 13)) + 2*log(sin(pi*Rational(2, 13)))*cos(pi*Rational(32, 13))
+             + 2*log(sin(pi*Rational(5, 13)))*cos(pi*Rational(80, 13)) - 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(5, 13))
+             - 2*log(sin(pi*Rational(4, 13)))*cos(pi/13) + pi*cot(pi*Rational(5, 13))/2 - 2*log(sin(pi/13))*cos(pi*Rational(3, 13))
+             + Rational(2422020029, 702257080))
+
+    Heoe = harmonic(ne + po/qe)
+    Aeoe = (-log(20) + 2*(Rational(1, 4) + sqrt(5)/4)*log(Rational(-1, 4) + sqrt(5)/4)
+             + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8)))
+             + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8)))
+             + 2*(-sqrt(5)/4 + Rational(1, 4))*log(Rational(1, 4) + sqrt(5)/4)
+             + Rational(11818877030, 4286604231) + pi*sqrt(2*sqrt(5) + 5)/2)
+
+    Heoo = harmonic(ne + po/qo)
+    Aeoo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(54, 13)) + 2*log(sin(pi*Rational(4, 13)))*cos(pi*Rational(6, 13))
+             + 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(108, 13)) - 2*log(sin(pi*Rational(5, 13)))*cos(pi/13)
+             - 2*log(sin(pi/13))*cos(pi*Rational(5, 13)) + pi*cot(pi*Rational(4, 13))/2
+             - 2*log(sin(pi*Rational(2, 13)))*cos(pi*Rational(3, 13)) + Rational(11669332571, 3628714320))
+
+    Hoee = harmonic(no + pe/qe)
+    Aoee = (-log(10) + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8)))
+             + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8)))
+             + pi*sqrt(2*sqrt(5)/5 + 1)/2 + Rational(779405, 277704))
+
+    Hoeo = harmonic(no + pe/qo)
+    Aoeo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(4, 13)) + 2*log(sin(pi*Rational(2, 13)))*cos(pi*Rational(32, 13))
+             + 2*log(sin(pi*Rational(5, 13)))*cos(pi*Rational(80, 13)) - 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(5, 13))
+             - 2*log(sin(pi*Rational(4, 13)))*cos(pi/13) + pi*cot(pi*Rational(5, 13))/2
+             - 2*log(sin(pi/13))*cos(pi*Rational(3, 13)) + Rational(53857323, 16331560))
+
+    Hooe = harmonic(no + po/qe)
+    Aooe = (-log(20) + 2*(Rational(1, 4) + sqrt(5)/4)*log(Rational(-1, 4) + sqrt(5)/4)
+             + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8)))
+             + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8)))
+             + 2*(-sqrt(5)/4 + Rational(1, 4))*log(Rational(1, 4) + sqrt(5)/4)
+             + Rational(486853480, 186374097) + pi*sqrt(2*sqrt(5) + 5)/2)
+
+    Hooo = harmonic(no + po/qo)
+    Aooo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(54, 13)) + 2*log(sin(pi*Rational(4, 13)))*cos(pi*Rational(6, 13))
+             + 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(108, 13)) - 2*log(sin(pi*Rational(5, 13)))*cos(pi/13)
+             - 2*log(sin(pi/13))*cos(pi*Rational(5, 13)) + pi*cot(pi*Rational(4, 13))/2
+             - 2*log(sin(pi*Rational(2, 13)))*cos(3*pi/13) + Rational(383693479, 125128080))
+
+    H = [Heee, Heeo, Heoe, Heoo, Hoee, Hoeo, Hooe, Hooo]
+    A = [Aeee, Aeeo, Aeoe, Aeoo, Aoee, Aoeo, Aooe, Aooo]
+    for h, a in zip(H, A):
+        e = expand_func(h).doit()
+        assert cancel(e/a) == 1
+        assert abs(h.n() - a.n()) < 1e-12
+
+
+def test_harmonic_evalf():
+    assert str(harmonic(1.5).evalf(n=10)) == '1.280372306'
+    assert str(harmonic(1.5, 2).evalf(n=10)) == '1.154576311'  # issue 7443
+    assert str(harmonic(4.0, -3).evalf(n=10)) == '100.0000000'
+    assert str(harmonic(7.0, 1.0).evalf(n=10)) == '2.592857143'
+    assert str(harmonic(1, pi).evalf(n=10)) == '1.000000000'
+    assert str(harmonic(2, pi).evalf(n=10)) == '1.113314732'
+    assert str(harmonic(1000.0, pi).evalf(n=10)) == '1.176241563'
+    assert str(harmonic(I).evalf(n=10)) == '0.6718659855 + 1.076674047*I'
+    assert str(harmonic(I, I).evalf(n=10)) == '-0.3970915266 + 1.9629689*I'
+
+    assert harmonic(-1.0, 1).evalf() is S.NaN
+    assert harmonic(-2.0, 2.0).evalf() is S.NaN
+
+def test_harmonic_rewrite():
+    from sympy.functions.elementary.piecewise import Piecewise
+    n = Symbol("n")
+    m = Symbol("m", integer=True, positive=True)
+    x1 = Symbol("x1", positive=True)
+    x2 = Symbol("x2", negative=True)
+
+    assert harmonic(n).rewrite(digamma) == polygamma(0, n + 1) + EulerGamma
+    assert harmonic(n).rewrite(trigamma) == polygamma(0, n + 1) + EulerGamma
+    assert harmonic(n).rewrite(polygamma) == polygamma(0, n + 1) + EulerGamma
+
+    assert harmonic(n,3).rewrite(polygamma) == polygamma(2, n + 1)/2 - polygamma(2, 1)/2
+    assert isinstance(harmonic(n,m).rewrite(polygamma), Piecewise)
+
+    assert expand_func(harmonic(n+4)) == harmonic(n) + 1/(n + 4) + 1/(n + 3) + 1/(n + 2) + 1/(n + 1)
+    assert expand_func(harmonic(n-4)) == harmonic(n) - 1/(n - 1) - 1/(n - 2) - 1/(n - 3) - 1/n
+
+    assert harmonic(n, m).rewrite("tractable") == harmonic(n, m).rewrite(polygamma)
+    assert harmonic(n, x1).rewrite("tractable") == harmonic(n, x1)
+    assert harmonic(n, x1 + 1).rewrite("tractable") == zeta(x1 + 1) - zeta(x1 + 1, n + 1)
+    assert harmonic(n, x2).rewrite("tractable") == zeta(x2) - zeta(x2, n + 1)
+
+    _k = Dummy("k")
+    assert harmonic(n).rewrite(Sum).dummy_eq(Sum(1/_k, (_k, 1, n)))
+    assert harmonic(n, m).rewrite(Sum).dummy_eq(Sum(_k**(-m), (_k, 1, n)))
+
+
+def test_harmonic_calculus():
+    y = Symbol("y", positive=True)
+    z = Symbol("z", negative=True)
+    assert harmonic(x, 1).limit(x, 0) == 0
+    assert harmonic(x, y).limit(x, 0) == 0
+    assert harmonic(x, 1).series(x, y, 2) == \
+            harmonic(y) + (x - y)*zeta(2, y + 1) + O((x - y)**2, (x, y))
+    assert limit(harmonic(x, y), x, oo) == harmonic(oo, y)
+    assert limit(harmonic(x, y + 1), x, oo) == zeta(y + 1)
+    assert limit(harmonic(x, y - 1), x, oo) == harmonic(oo, y - 1)
+    assert limit(harmonic(x, z), x, oo) == Limit(harmonic(x, z), x, oo, dir='-')
+    assert limit(harmonic(x, z + 1), x, oo) == oo
+    assert limit(harmonic(x, z + 2), x, oo) == harmonic(oo, z + 2)
+    assert limit(harmonic(x, z - 1), x, oo) == Limit(harmonic(x, z - 1), x, oo, dir='-')
+
+
+def test_euler():
+    assert euler(0) == 1
+    assert euler(1) == 0
+    assert euler(2) == -1
+    assert euler(3) == 0
+    assert euler(4) == 5
+    assert euler(6) == -61
+    assert euler(8) == 1385
+
+    assert euler(20, evaluate=False) != 370371188237525
+
+    n = Symbol('n', integer=True)
+    assert euler(n) != -1
+    assert euler(n).subs(n, 2) == -1
+
+    assert euler(-1) == S.Pi / 2
+    assert euler(-1, 1) == 2*log(2)
+    assert euler(-2).evalf() == (2*S.Catalan).evalf()
+    assert euler(-3).evalf() == (S.Pi**3 / 16).evalf()
+    assert str(euler(2.3).evalf(n=10)) == '-1.052850274'
+    assert str(euler(1.2, 3.4).evalf(n=10)) == '3.575613489'
+    assert str(euler(I).evalf(n=10)) == '1.248446443 - 0.7675445124*I'
+    assert str(euler(I, I).evalf(n=10)) == '0.04812930469 + 0.01052411008*I'
+
+    assert euler(20).evalf() == 370371188237525.0
+    assert euler(20, evaluate=False).evalf() == 370371188237525.0
+
+    assert euler(n).rewrite(Sum) == euler(n)
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert euler(2*n + 1).rewrite(Sum) == 0
+    _j = Dummy('j')
+    _k = Dummy('k')
+    assert euler(2*n).rewrite(Sum).dummy_eq(
+            I*Sum((-1)**_j*2**(-_k)*I**(-_k)*(-2*_j + _k)**(2*n + 1)*
+                  binomial(_k, _j)/_k, (_j, 0, _k), (_k, 1, 2*n + 1)))
+
+
+def test_euler_odd():
+    n = Symbol('n', odd=True, positive=True)
+    assert euler(n) == 0
+    n = Symbol('n', odd=True)
+    assert euler(n) != 0
+
+
+def test_euler_polynomials():
+    assert euler(0, x) == 1
+    assert euler(1, x) == x - S.Half
+    assert euler(2, x) == x**2 - x
+    assert euler(3, x) == x**3 - (3*x**2)/2 + Rational(1, 4)
+    m = Symbol('m')
+    assert isinstance(euler(m, x), euler)
+    from sympy.core.numbers import Float
+    A = Float('-0.46237208575048694923364757452876131e8')  # from Maple
+    B = euler(19, S.Pi).evalf(32)
+    assert abs((A - B)/A) < 1e-31
+    z = Float(0.1) + Float(0.2)*I
+    expected = Float(-3126.54721663773 ) + Float(565.736261497056) * I
+    assert abs(euler(13, z) - expected) < 1e-10
+
+
+def test_euler_polynomial_rewrite():
+    m = Symbol('m')
+    A = euler(m, x).rewrite('Sum')
+    assert A.subs({m:3, x:5}).doit() == euler(3, 5)
+
+
+def test_catalan():
+    n = Symbol('n', integer=True)
+    m = Symbol('m', integer=True, positive=True)
+    k = Symbol('k', integer=True, nonnegative=True)
+    p = Symbol('p', nonnegative=True)
+
+    catalans = [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786]
+    for i, c in enumerate(catalans):
+        assert catalan(i) == c
+        assert catalan(n).rewrite(factorial).subs(n, i) == c
+        assert catalan(n).rewrite(Product).subs(n, i).doit() == c
+
+    assert unchanged(catalan, x)
+    assert catalan(2*x).rewrite(binomial) == binomial(4*x, 2*x)/(2*x + 1)
+    assert catalan(S.Half).rewrite(gamma) == 8/(3*pi)
+    assert catalan(S.Half).rewrite(factorial).rewrite(gamma) ==\
+        8 / (3 * pi)
+    assert catalan(3*x).rewrite(gamma) == 4**(
+        3*x)*gamma(3*x + S.Half)/(sqrt(pi)*gamma(3*x + 2))
+    assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2,), 1)
+
+    assert catalan(n).rewrite(factorial) == factorial(2*n) / (factorial(n + 1)
+                                                              * factorial(n))
+    assert isinstance(catalan(n).rewrite(Product), catalan)
+    assert isinstance(catalan(m).rewrite(Product), Product)
+
+    assert diff(catalan(x), x) == (polygamma(
+        0, x + S.Half) - polygamma(0, x + 2) + log(4))*catalan(x)
+
+    assert catalan(x).evalf() == catalan(x)
+    c = catalan(S.Half).evalf()
+    assert str(c) == '0.848826363156775'
+    c = catalan(I).evalf(3)
+    assert str((re(c), im(c))) == '(0.398, -0.0209)'
+
+    # Assumptions
+    assert catalan(p).is_positive is True
+    assert catalan(k).is_integer is True
+    assert catalan(m+3).is_composite is True
+
+
+def test_genocchi():
+    genocchis = [0, -1, -1, 0, 1, 0, -3, 0, 17]
+    for n, g in enumerate(genocchis):
+        assert genocchi(n) == g
+
+    m = Symbol('m', integer=True)
+    n = Symbol('n', integer=True, positive=True)
+    assert unchanged(genocchi, m)
+    assert genocchi(2*n + 1) == 0
+    gn = 2 * (1 - 2**n) * bernoulli(n)
+    assert genocchi(n).rewrite(bernoulli).factor() == gn.factor()
+    gnx = 2 * (bernoulli(n, x) - 2**n * bernoulli(n, (x+1) / 2))
+    assert genocchi(n, x).rewrite(bernoulli).factor() == gnx.factor()
+    assert genocchi(2 * n).is_odd
+    assert genocchi(2 * n).is_even is False
+    assert genocchi(2 * n + 1).is_even
+    assert genocchi(n).is_integer
+    assert genocchi(4 * n).is_positive
+    # these are the only 2 prime Genocchi numbers
+    assert genocchi(6, evaluate=False).is_prime == S(-3).is_prime
+    assert genocchi(8, evaluate=False).is_prime
+    assert genocchi(4 * n + 2).is_negative
+    assert genocchi(4 * n + 1).is_negative is False
+    assert genocchi(4 * n - 2).is_negative
+
+    g0 = genocchi(0, evaluate=False)
+    assert g0.is_positive is False
+    assert g0.is_negative is False
+    assert g0.is_even is True
+    assert g0.is_odd is False
+
+    assert genocchi(0, x) == 0
+    assert genocchi(1, x) == -1
+    assert genocchi(2, x) == 1 - 2*x
+    assert genocchi(3, x) == 3*x - 3*x**2
+    assert genocchi(4, x) == -1 + 6*x**2 - 4*x**3
+    y = Symbol("y")
+    assert genocchi(5, (x+y)**100) == -5*(x+y)**400 + 10*(x+y)**300 - 5*(x+y)**100
+
+    assert str(genocchi(5.0, 4.0).evalf(n=10)) == '-660.0000000'
+    assert str(genocchi(Rational(5, 4)).evalf(n=10)) == '-1.104286457'
+    assert str(genocchi(-2).evalf(n=10)) == '3.606170709'
+    assert str(genocchi(1.3, 3.7).evalf(n=10)) == '-1.847375373'
+    assert str(genocchi(I, 1.0).evalf(n=10)) == '-0.3161917278 - 1.45311955*I'
+
+    n = Symbol('n')
+    assert genocchi(n, x).rewrite(dirichlet_eta) == -2*n * dirichlet_eta(1-n, x)
+
+
+def test_andre():
+    nums = [1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521]
+    for n, a in enumerate(nums):
+        assert andre(n) == a
+    assert andre(S.Infinity) == S.Infinity
+    assert andre(-1) == -log(2)
+    assert andre(-2) == -2*S.Catalan
+    assert andre(-3) == 3*zeta(3)/16
+    assert andre(-5) == -15*zeta(5)/256
+    # In fact andre(-2*n) is related to the Dirichlet *beta* function
+    # at 2*n, but SymPy doesn't implement that (or general L-functions)
+    assert unchanged(andre, -4)
+
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert unchanged(andre, n)
+    assert andre(n).is_integer is True
+    assert andre(n).is_positive is True
+
+    assert str(andre(10, evaluate=False).evalf(n=10)) == '50521.00000'
+    assert str(andre(-1, evaluate=False).evalf(n=10)) == '-0.6931471806'
+    assert str(andre(-2, evaluate=False).evalf(n=10)) == '-1.831931188'
+    assert str(andre(-4, evaluate=False).evalf(n=10)) == '1.977889103'
+    assert str(andre(I, evaluate=False).evalf(n=10)) == '2.378417833 + 0.6343322845*I'
+
+    assert andre(x).rewrite(polylog) == \
+            (-I)**(x+1) * polylog(-x, I) + I**(x+1) * polylog(-x, -I)
+    assert andre(x).rewrite(zeta) == \
+            2 * gamma(x+1) / (2*pi)**(x+1) * \
+            (zeta(x+1, Rational(1,4)) - cos(pi*x) * zeta(x+1, Rational(3,4)))
+
+
+@nocache_fail
+def test_partition():
+    partition_nums = [1, 1, 2, 3, 5, 7, 11, 15, 22]
+    for n, p in enumerate(partition_nums):
+        assert partition(n) == p
+
+    x = Symbol('x')
+    y = Symbol('y', real=True)
+    m = Symbol('m', integer=True)
+    n = Symbol('n', integer=True, negative=True)
+    p = Symbol('p', integer=True, nonnegative=True)
+    assert partition(m).is_integer
+    assert not partition(m).is_negative
+    assert partition(m).is_nonnegative
+    assert partition(n).is_zero
+    assert partition(p).is_positive
+    assert partition(x).subs(x, 7) == 15
+    assert partition(y).subs(y, 8) == 22
+    raises(TypeError, lambda: partition(Rational(5, 4)))
+    assert partition(9, evaluate=False) % 5 == 0
+    assert partition(5*m + 4) % 5 == 0
+    assert partition(47, evaluate=False) % 7 == 0
+    assert partition(7*m + 5) % 7 == 0
+    assert partition(50, evaluate=False) % 11 == 0
+    assert partition(11*m + 6) % 11 == 0
+
+
+def test_divisor_sigma():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: divisor_sigma(m))
+    raises(TypeError, lambda: divisor_sigma(4.5))
+    raises(TypeError, lambda: divisor_sigma(1, m))
+    raises(TypeError, lambda: divisor_sigma(1, 4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: divisor_sigma(m))
+    raises(ValueError, lambda: divisor_sigma(0))
+    m = Symbol('m', negative=True)
+    raises(ValueError, lambda: divisor_sigma(1, m))
+    raises(ValueError, lambda: divisor_sigma(1, -1))
+
+    # special case
+    p = Symbol('p', prime=True)
+    k = Symbol('k', integer=True)
+    assert divisor_sigma(p, 1) == p + 1
+    assert divisor_sigma(p, k) == p**k + 1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert divisor_sigma(n).is_integer is True
+    assert divisor_sigma(n).is_positive is True
+
+    # symbolic
+    k = Symbol('k', integer=True, zero=False)
+    assert divisor_sigma(4, k) == 2**(2*k) + 2**k + 1
+    assert divisor_sigma(6, k) == (2**k + 1) * (3**k + 1)
+
+    # Integer
+    assert divisor_sigma(23450) == 50592
+    assert divisor_sigma(23450, 0) == 24
+    assert divisor_sigma(23450, 1) == 50592
+    assert divisor_sigma(23450, 2) == 730747500
+    assert divisor_sigma(23450, 3) == 14666785333344
+
+
+def test_udivisor_sigma():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: udivisor_sigma(m))
+    raises(TypeError, lambda: udivisor_sigma(4.5))
+    raises(TypeError, lambda: udivisor_sigma(1, m))
+    raises(TypeError, lambda: udivisor_sigma(1, 4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: udivisor_sigma(m))
+    raises(ValueError, lambda: udivisor_sigma(0))
+    m = Symbol('m', negative=True)
+    raises(ValueError, lambda: udivisor_sigma(1, m))
+    raises(ValueError, lambda: udivisor_sigma(1, -1))
+
+    # special case
+    p = Symbol('p', prime=True)
+    k = Symbol('k', integer=True)
+    assert udivisor_sigma(p, 1) == p + 1
+    assert udivisor_sigma(p, k) == p**k + 1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert udivisor_sigma(n).is_integer is True
+    assert udivisor_sigma(n).is_positive is True
+
+    # Integer
+    A034444 = [1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4,
+               4, 4, 2, 4, 2, 4, 2, 4, 2, 8, 2, 2, 4, 4, 4, 4, 2, 4, 4, 4,
+               2, 8, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 8]
+    for n, val in enumerate(A034444, 1):
+        assert udivisor_sigma(n, 0) == val
+    A034448 = [1, 3, 4, 5, 6, 12, 8, 9, 10, 18, 12, 20, 14, 24, 24, 17, 18,
+               30, 20, 30, 32, 36, 24, 36, 26, 42, 28, 40, 30, 72, 32, 33,
+               48, 54, 48, 50, 38, 60, 56, 54, 42, 96, 44, 60, 60, 72, 48]
+    for n, val in enumerate(A034448, 1):
+        assert udivisor_sigma(n, 1) == val
+    A034676 = [1, 5, 10, 17, 26, 50, 50, 65, 82, 130, 122, 170, 170, 250,
+               260, 257, 290, 410, 362, 442, 500, 610, 530, 650, 626, 850,
+               730, 850, 842, 1300, 962, 1025, 1220, 1450, 1300, 1394, 1370]
+    for n, val in enumerate(A034676, 1):
+        assert udivisor_sigma(n, 2) == val
+
+
+def test_legendre_symbol():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: legendre_symbol(m, 3))
+    raises(TypeError, lambda: legendre_symbol(4.5, 3))
+    raises(TypeError, lambda: legendre_symbol(1, m))
+    raises(TypeError, lambda: legendre_symbol(1, 4.5))
+    m = Symbol('m', prime=False)
+    raises(ValueError, lambda: legendre_symbol(1, m))
+    raises(ValueError, lambda: legendre_symbol(1, 6))
+    m = Symbol('m', odd=False)
+    raises(ValueError, lambda: legendre_symbol(1, m))
+    raises(ValueError, lambda: legendre_symbol(1, 2))
+
+    # special case
+    p = Symbol('p', prime=True)
+    k = Symbol('k', integer=True)
+    assert legendre_symbol(p*k, p) == 0
+    assert legendre_symbol(1, p) == 1
+
+    # property
+    n = Symbol('n')
+    m = Symbol('m')
+    assert legendre_symbol(m, n).is_integer is True
+    assert legendre_symbol(m, n).is_prime is False
+
+    # Integer
+    assert legendre_symbol(5, 11) == 1
+    assert legendre_symbol(25, 41) == 1
+    assert legendre_symbol(67, 101) == -1
+    assert legendre_symbol(0, 13) == 0
+    assert legendre_symbol(9, 3) == 0
+
+
+def test_jacobi_symbol():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: jacobi_symbol(m, 3))
+    raises(TypeError, lambda: jacobi_symbol(4.5, 3))
+    raises(TypeError, lambda: jacobi_symbol(1, m))
+    raises(TypeError, lambda: jacobi_symbol(1, 4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: jacobi_symbol(1, m))
+    raises(ValueError, lambda: jacobi_symbol(1, -6))
+    m = Symbol('m', odd=False)
+    raises(ValueError, lambda: jacobi_symbol(1, m))
+    raises(ValueError, lambda: jacobi_symbol(1, 2))
+
+    # special case
+    p = Symbol('p', integer=True)
+    k = Symbol('k', integer=True)
+    assert jacobi_symbol(p*k, p) == 0
+    assert jacobi_symbol(1, p) == 1
+    assert jacobi_symbol(1, 1) == 1
+    assert jacobi_symbol(0, 1) == 1
+
+    # property
+    n = Symbol('n')
+    m = Symbol('m')
+    assert jacobi_symbol(m, n).is_integer is True
+    assert jacobi_symbol(m, n).is_prime is False
+
+    # Integer
+    assert jacobi_symbol(25, 41) == 1
+    assert jacobi_symbol(-23, 83) == -1
+    assert jacobi_symbol(3, 9) == 0
+    assert jacobi_symbol(42, 97) == -1
+    assert jacobi_symbol(3, 5) == -1
+    assert jacobi_symbol(7, 9) == 1
+    assert jacobi_symbol(0, 3) == 0
+    assert jacobi_symbol(0, 1) == 1
+    assert jacobi_symbol(2, 1) == 1
+    assert jacobi_symbol(1, 3) == 1
+
+
+def test_kronecker_symbol():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: kronecker_symbol(m, 3))
+    raises(TypeError, lambda: kronecker_symbol(4.5, 3))
+    raises(TypeError, lambda: kronecker_symbol(1, m))
+    raises(TypeError, lambda: kronecker_symbol(1, 4.5))
+
+    # special case
+    p = Symbol('p', integer=True)
+    assert kronecker_symbol(1, p) == 1
+    assert kronecker_symbol(1, 1) == 1
+    assert kronecker_symbol(0, 1) == 1
+
+    # property
+    n = Symbol('n')
+    m = Symbol('m')
+    assert kronecker_symbol(m, n).is_integer is True
+    assert kronecker_symbol(m, n).is_prime is False
+
+    # Integer
+    for n in range(3, 10, 2):
+        for a in range(-n, n):
+            val = kronecker_symbol(a, n)
+            assert val == jacobi_symbol(a, n)
+            minus = kronecker_symbol(a, -n)
+            if a < 0:
+                assert -minus == val
+            else:
+                assert minus == val
+            even = kronecker_symbol(a, 2 * n)
+            if a % 2 == 0:
+                assert even == 0
+            elif a % 8 in [1, 7]:
+                assert even == val
+            else:
+                assert -even == val
+    assert kronecker_symbol(1, 0) == kronecker_symbol(-1, 0) == 1
+    assert kronecker_symbol(0, 0) == 0
+
+
+def test_mobius():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: mobius(m))
+    raises(TypeError, lambda: mobius(4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: mobius(m))
+    raises(ValueError, lambda: mobius(-3))
+
+    # special case
+    p = Symbol('p', prime=True)
+    assert mobius(p) == -1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert mobius(n).is_integer is True
+    assert mobius(n).is_prime is False
+
+    # symbolic
+    n = Symbol('n', integer=True, positive=True)
+    k = Symbol('k', integer=True, positive=True)
+    assert mobius(n**2) == 0
+    assert mobius(4*n) == 0
+    assert isinstance(mobius(n**k), mobius)
+    assert mobius(n**(k+1)) == 0
+    assert isinstance(mobius(3**k), mobius)
+    assert mobius(3**(k+1)) == 0
+    m = Symbol('m')
+    assert isinstance(mobius(4*m), mobius)
+
+    # Integer
+    assert mobius(13*7) == 1
+    assert mobius(1) == 1
+    assert mobius(13*7*5) == -1
+    assert mobius(13**2) == 0
+    A008683 = [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0,
+               -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1,
+               1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0]
+    for n, val in enumerate(A008683, 1):
+        assert mobius(n) == val
+
+
+def test_primenu():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: primenu(m))
+    raises(TypeError, lambda: primenu(4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: primenu(m))
+    raises(ValueError, lambda: primenu(0))
+
+    # special case
+    p = Symbol('p', prime=True)
+    assert primenu(p) == 1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert primenu(n).is_integer is True
+    assert primenu(n).is_nonnegative is True
+
+    # Integer
+    assert primenu(7*13) == 2
+    assert primenu(2*17*19) == 3
+    assert primenu(2**3 * 17 * 19**2) == 3
+    A001221 = [0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2,
+               1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 2]
+    for n, val in enumerate(A001221, 1):
+        assert primenu(n) == val
+
+
+def test_primeomega():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: primeomega(m))
+    raises(TypeError, lambda: primeomega(4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: primeomega(m))
+    raises(ValueError, lambda: primeomega(0))
+
+    # special case
+    p = Symbol('p', prime=True)
+    assert primeomega(p) == 1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert primeomega(n).is_integer is True
+    assert primeomega(n).is_nonnegative is True
+
+    # Integer
+    assert primeomega(7*13) == 2
+    assert primeomega(2*17*19) == 3
+    assert primeomega(2**3 * 17 * 19**2) == 6
+    A001222 = [0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3,
+               1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4]
+    for n, val in enumerate(A001222, 1):
+        assert primeomega(n) == val
+
+
+def test_totient():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: totient(m))
+    raises(TypeError, lambda: totient(4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: totient(m))
+    raises(ValueError, lambda: totient(0))
+
+    # special case
+    p = Symbol('p', prime=True)
+    assert totient(p) == p - 1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert totient(n).is_integer is True
+    assert totient(n).is_positive is True
+
+    # Integer
+    assert totient(7*13) == totient(factorint(7*13)) == (7-1)*(13-1)
+    assert totient(2*17*19) == totient(factorint(2*17*19)) == (17-1)*(19-1)
+    assert totient(2**3 * 17 * 19**2) == totient({2: 3, 17: 1, 19: 2}) == 2**2 * (17-1) * 19*(19-1)
+    A000010 = [1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16,
+               6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16,
+               20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22]
+    for n, val in enumerate(A000010, 1):
+        assert totient(n) == val
+
+
+def test_reduced_totient():
+    # error
+    m = Symbol('m', integer=False)
+    raises(TypeError, lambda: reduced_totient(m))
+    raises(TypeError, lambda: reduced_totient(4.5))
+    m = Symbol('m', positive=False)
+    raises(ValueError, lambda: reduced_totient(m))
+    raises(ValueError, lambda: reduced_totient(0))
+
+    # special case
+    p = Symbol('p', prime=True)
+    assert reduced_totient(p) == p - 1
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert reduced_totient(n).is_integer is True
+    assert reduced_totient(n).is_positive is True
+
+    # Integer
+    assert reduced_totient(7*13) == reduced_totient(factorint(7*13)) == 12
+    assert reduced_totient(2*17*19) == reduced_totient(factorint(2*17*19)) == 144
+    assert reduced_totient(2**2 * 11) == reduced_totient({2: 2, 11: 1}) == 10
+    assert reduced_totient(2**3 * 17 * 19**2) == reduced_totient({2: 3, 17: 1, 19: 2}) == 2736
+    A002322 = [1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 4, 4, 16, 6,
+               18, 4, 6, 10, 22, 2, 20, 12, 18, 6, 28, 4, 30, 8, 10, 16,
+               12, 6, 36, 18, 12, 4, 40, 6, 42, 10, 12, 22, 46, 4, 42]
+    for n, val in enumerate(A002322, 1):
+        assert reduced_totient(n) == val
+
+
+def test_primepi():
+    # error
+    z = Symbol('z', real=False)
+    raises(TypeError, lambda: primepi(z))
+    raises(TypeError, lambda: primepi(I))
+
+    # property
+    n = Symbol('n', integer=True, positive=True)
+    assert primepi(n).is_integer is True
+    assert primepi(n).is_nonnegative is True
+
+    # infinity
+    assert primepi(oo) == oo
+    assert primepi(-oo) == 0
+
+    # symbol
+    x = Symbol('x')
+    assert isinstance(primepi(x), primepi)
+
+    # Integer
+    assert primepi(0) == 0
+    A000720 = [0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8,
+               8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11,
+               12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15]
+    for n, val in enumerate(A000720, 1):
+        assert primepi(n) == primepi(n + 0.5) == val
+
+
+def test__nT():
+    assert [_nT(i, j) for i in range(5) for j in range(i + 2)] == [
+            1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0]
+    check = [_nT(10, i) for i in range(11)]
+    assert check == [0, 1, 5, 8, 9, 7, 5, 3, 2, 1, 1]
+    assert all(type(i) is int for i in check)
+    assert _nT(10, 5) == 7
+    assert _nT(100, 98) == 2
+    assert _nT(100, 100) == 1
+    assert _nT(10, 3) == 8
+
+
+def test_nC_nP_nT():
+    from sympy.utilities.iterables import (
+        multiset_permutations, multiset_combinations, multiset_partitions,
+        partitions, subsets, permutations)
+    from sympy.functions.combinatorial.numbers import (
+        nP, nC, nT, stirling, _stirling1, _stirling2, _multiset_histogram, _AOP_product)
+
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.core.random import choice
+
+    c = string.ascii_lowercase
+    for i in range(100):
+        s = ''.join(choice(c) for i in range(7))
+        u = len(s) == len(set(s))
+        try:
+            tot = 0
+            for i in range(8):
+                check = nP(s, i)
+                tot += check
+                assert len(list(multiset_permutations(s, i))) == check
+                if u:
+                    assert nP(len(s), i) == check
+            assert nP(s) == tot
+        except AssertionError:
+            print(s, i, 'failed perm test')
+            raise ValueError()
+
+    for i in range(100):
+        s = ''.join(choice(c) for i in range(7))
+        u = len(s) == len(set(s))
+        try:
+            tot = 0
+            for i in range(8):
+                check = nC(s, i)
+                tot += check
+                assert len(list(multiset_combinations(s, i))) == check
+                if u:
+                    assert nC(len(s), i) == check
+            assert nC(s) == tot
+            if u:
+                assert nC(len(s)) == tot
+        except AssertionError:
+            print(s, i, 'failed combo test')
+            raise ValueError()
+
+    for i in range(1, 10):
+        tot = 0
+        for j in range(1, i + 2):
+            check = nT(i, j)
+            assert check.is_Integer
+            tot += check
+            assert sum(1 for p in partitions(i, j, size=True) if p[0] == j) == check
+        assert nT(i) == tot
+
+    for i in range(1, 10):
+        tot = 0
+        for j in range(1, i + 2):
+            check = nT(range(i), j)
+            tot += check
+            assert len(list(multiset_partitions(list(range(i)), j))) == check
+        assert nT(range(i)) == tot
+
+    for i in range(100):
+        s = ''.join(choice(c) for i in range(7))
+        u = len(s) == len(set(s))
+        try:
+            tot = 0
+            for i in range(1, 8):
+                check = nT(s, i)
+                tot += check
+                assert len(list(multiset_partitions(s, i))) == check
+                if u:
+                    assert nT(range(len(s)), i) == check
+            if u:
+                assert nT(range(len(s))) == tot
+            assert nT(s) == tot
+        except AssertionError:
+            print(s, i, 'failed partition test')
+            raise ValueError()
+
+    # tests for Stirling numbers of the first kind that are not tested in the
+    # above
+    assert [stirling(9, i, kind=1) for i in range(11)] == [
+        0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1, 0]
+    perms = list(permutations(range(4)))
+    assert [sum(1 for p in perms if Permutation(p).cycles == i)
+            for i in range(5)] == [0, 6, 11, 6, 1] == [
+            stirling(4, i, kind=1) for i in range(5)]
+    # http://oeis.org/A008275
+    assert [stirling(n, k, signed=1)
+        for n in range(10) for k in range(1, n + 1)] == [
+            1, -1,
+            1, 2, -3,
+            1, -6, 11, -6,
+            1, 24, -50, 35, -10,
+            1, -120, 274, -225, 85, -15,
+            1, 720, -1764, 1624, -735, 175, -21,
+            1, -5040, 13068, -13132, 6769, -1960, 322, -28,
+            1, 40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1]
+    # https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
+    assert  [stirling(n, k, kind=1)
+        for n in range(10) for k in range(n+1)] == [
+            1,
+            0, 1,
+            0, 1, 1,
+            0, 2, 3, 1,
+            0, 6, 11, 6, 1,
+            0, 24, 50, 35, 10, 1,
+            0, 120, 274, 225, 85, 15, 1,
+            0, 720, 1764, 1624, 735, 175, 21, 1,
+            0, 5040, 13068, 13132, 6769, 1960, 322, 28, 1,
+            0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1]
+    # https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
+    assert [stirling(n, k, kind=2)
+        for n in range(10) for k in range(n+1)] == [
+            1,
+            0, 1,
+            0, 1, 1,
+            0, 1, 3, 1,
+            0, 1, 7, 6, 1,
+            0, 1, 15, 25, 10, 1,
+            0, 1, 31, 90, 65, 15, 1,
+            0, 1, 63, 301, 350, 140, 21, 1,
+            0, 1, 127, 966, 1701, 1050, 266, 28, 1,
+            0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1]
+    assert stirling(3, 4, kind=1) == stirling(3, 4, kind=1) == 0
+    raises(ValueError, lambda: stirling(-2, 2))
+
+    # Assertion that the return type is SymPy Integer.
+    assert isinstance(_stirling1(6, 3), Integer)
+    assert isinstance(_stirling2(6, 3), Integer)
+
+    def delta(p):
+        if len(p) == 1:
+            return oo
+        return min(abs(i[0] - i[1]) for i in subsets(p, 2))
+    parts = multiset_partitions(range(5), 3)
+    d = 2
+    assert (sum(1 for p in parts if all(delta(i) >= d for i in p)) ==
+            stirling(5, 3, d=d) == 7)
+
+    # other coverage tests
+    assert nC('abb', 2) == nC('aab', 2) == 2
+    assert nP(3, 3, replacement=True) == nP('aabc', 3, replacement=True) == 27
+    assert nP(3, 4) == 0
+    assert nP('aabc', 5) == 0
+    assert nC(4, 2, replacement=True) == nC('abcdd', 2, replacement=True) == \
+        len(list(multiset_combinations('aabbccdd', 2))) == 10
+    assert nC('abcdd') == sum(nC('abcdd', i) for i in range(6)) == 24
+    assert nC(list('abcdd'), 4) == 4
+    assert nT('aaaa') == nT(4) == len(list(partitions(4))) == 5
+    assert nT('aaab') == len(list(multiset_partitions('aaab'))) == 7
+    assert nC('aabb'*3, 3) == 4  # aaa, bbb, abb, baa
+    assert dict(_AOP_product((4,1,1,1))) == {
+        0: 1, 1: 4, 2: 7, 3: 8, 4: 8, 5: 7, 6: 4, 7: 1}
+    # the following was the first t that showed a problem in a previous form of
+    # the function, so it's not as random as it may appear
+    t = (3, 9, 4, 6, 6, 5, 5, 2, 10, 4)
+    assert sum(_AOP_product(t)[i] for i in range(55)) == 58212000
+    raises(ValueError, lambda: _multiset_histogram({1:'a'}))
+
+
+def test_PR_14617():
+    from sympy.functions.combinatorial.numbers import nT
+    for n in (0, []):
+        for k in (-1, 0, 1):
+            if k == 0:
+                assert nT(n, k) == 1
+            else:
+                assert nT(n, k) == 0
+
+
+def test_issue_8496():
+    n = Symbol("n")
+    k = Symbol("k")
+
+    raises(TypeError, lambda: catalan(n, k))
+
+
+def test_issue_8601():
+    n = Symbol('n', integer=True, negative=True)
+
+    assert catalan(n - 1) is S.Zero
+    assert catalan(Rational(-1, 2)) is S.ComplexInfinity
+    assert catalan(-S.One) == Rational(-1, 2)
+    c1 = catalan(-5.6).evalf()
+    assert str(c1) == '6.93334070531408e-5'
+    c2 = catalan(-35.4).evalf()
+    assert str(c2) == '-4.14189164517449e-24'
+
+
+def test_motzkin():
+    assert motzkin.is_motzkin(4) == True
+    assert motzkin.is_motzkin(9) == True
+    assert motzkin.is_motzkin(10) == False
+    assert motzkin.find_motzkin_numbers_in_range(10,200) == [21, 51, 127]
+    assert motzkin.find_motzkin_numbers_in_range(10,400) == [21, 51, 127, 323]
+    assert motzkin.find_motzkin_numbers_in_range(10,1600) == [21, 51, 127, 323, 835]
+    assert motzkin.find_first_n_motzkins(5) == [1, 1, 2, 4, 9]
+    assert motzkin.find_first_n_motzkins(7) == [1, 1, 2, 4, 9, 21, 51]
+    assert motzkin.find_first_n_motzkins(10) == [1, 1, 2, 4, 9, 21, 51, 127, 323, 835]
+    raises(ValueError, lambda: motzkin.eval(77.58))
+    raises(ValueError, lambda: motzkin.eval(-8))
+    raises(ValueError, lambda: motzkin.find_motzkin_numbers_in_range(-2,7))
+    raises(ValueError, lambda: motzkin.find_motzkin_numbers_in_range(13,7))
+    raises(ValueError, lambda: motzkin.find_first_n_motzkins(112.8))
+
+
+def test_nD_derangements():
+    from sympy.utilities.iterables import (partitions, multiset,
+        multiset_derangements, multiset_permutations)
+    from sympy.functions.combinatorial.numbers import nD
+
+    got = []
+    for i in partitions(8, k=4):
+        s = []
+        it = 0
+        for k, v in i.items():
+            for i in range(v):
+                s.extend([it]*k)
+                it += 1
+        ms = multiset(s)
+        c1 = sum(1 for i in multiset_permutations(s) if
+            all(i != j for i, j in zip(i, s)))
+        assert c1 == nD(ms) == nD(ms, 0) == nD(ms, 1)
+        v = [tuple(i) for i in multiset_derangements(s)]
+        c2 = len(v)
+        assert c2 == len(set(v))
+        assert c1 == c2
+        got.append(c1)
+    assert got == [1, 4, 6, 12, 24, 24, 61, 126, 315, 780, 297, 772,
+        2033, 5430, 14833]
+
+    assert nD('1112233456', brute=True) == nD('1112233456') == 16356
+    assert nD('') == nD([]) == nD({}) == 0
+    assert nD({1: 0}) == 0
+    raises(ValueError, lambda: nD({1: -1}))
+    assert nD('112') == 0
+    assert nD(i='112') == 0
+    assert [nD(n=i) for i in range(6)] == [0, 0, 1, 2, 9, 44]
+    assert nD((i for i in range(4))) == nD('0123') == 9
+    assert nD(m=(i for i in range(4))) == 3
+    assert nD(m={0: 1, 1: 1, 2: 1, 3: 1}) == 3
+    assert nD(m=[0, 1, 2, 3]) == 3
+    raises(TypeError, lambda: nD(m=0))
+    raises(TypeError, lambda: nD(-1))
+    assert nD({-1: 1, -2: 1}) == 1
+    assert nD(m={0: 3}) == 0
+    raises(ValueError, lambda: nD(i='123', n=3))
+    raises(ValueError, lambda: nD(i='123', m=(1,2)))
+    raises(ValueError, lambda: nD(n=0, m=(1,2)))
+    raises(ValueError, lambda: nD({1: -1}))
+    raises(ValueError, lambda: nD(m={-1: 1, 2: 1}))
+    raises(ValueError, lambda: nD(m={1: -1, 2: 1}))
+    raises(ValueError, lambda: nD(m=[-1, 2]))
+    raises(TypeError, lambda: nD({1: x}))
+    raises(TypeError, lambda: nD(m={1: x}))
+    raises(TypeError, lambda: nD(m={x: 1}))
+
+
+def test_deprecated_ntheory_symbolic_functions():
+    from sympy.testing.pytest import warns_deprecated_sympy
+
+    with warns_deprecated_sympy():
+        assert not carmichael.is_carmichael(3)
+    with warns_deprecated_sympy():
+        assert carmichael.find_carmichael_numbers_in_range(10, 20) == []
+    with warns_deprecated_sympy():
+        assert carmichael.find_first_n_carmichaels(1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..78034e72ef2ed722c3ae685a87cf4df618a982b0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/__init__.py
@@ -0,0 +1 @@
+# Stub __init__.py for sympy.functions.elementary
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/_trigonometric_special.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/_trigonometric_special.py
new file mode 100644
index 0000000000000000000000000000000000000000..fdf8c9d06241b46e791afe76836ea33e6d4fb1c8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/_trigonometric_special.py
@@ -0,0 +1,261 @@
+r"""A module for special angle formulas for trigonometric functions
+
+TODO
+====
+
+This module should be developed in the future to contain direct square root
+representation of
+
+.. math
+    F(\frac{n}{m} \pi)
+
+for every
+
+- $m \in \{ 3, 5, 17, 257, 65537 \}$
+- $n \in \mathbb{N}$, $0 \le n < m$
+- $F \in \{\sin, \cos, \tan, \csc, \sec, \cot\}$
+
+Without multi-step rewrites
+(e.g. $\tan \to \cos/\sin \to \cos/\sqrt \to \ sqrt$)
+or using chebyshev identities
+(e.g. $\cos \to \cos + \cos^2 + \cdots \to \sqrt{} + \sqrt{}^2 + \cdots $),
+which are trivial to implement in sympy,
+and had used to give overly complicated expressions.
+
+The reference can be found below, if anyone may need help implementing them.
+
+References
+==========
+
+.. [*] Gottlieb, Christian. (1999). The Simple and straightforward construction
+   of the regular 257-gon. The Mathematical Intelligencer. 21. 31-37.
+   10.1007/BF03024829.
+.. [*] https://resources.wolframcloud.com/FunctionRepository/resources/Cos2PiOverFermatPrime
+"""
+from __future__ import annotations
+from typing import Callable
+from functools import reduce
+from sympy.core.expr import Expr
+from sympy.core.singleton import S
+from sympy.core.intfunc import igcdex
+from sympy.core.numbers import Integer
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.core.cache import cacheit
+
+
+def migcdex(*x: int) -> tuple[tuple[int, ...], int]:
+    r"""Compute extended gcd for multiple integers.
+
+    Explanation
+    ===========
+
+    Given the integers $x_1, \cdots, x_n$ and
+    an extended gcd for multiple arguments are defined as a solution
+    $(y_1, \cdots, y_n), g$ for the diophantine equation
+    $x_1 y_1 + \cdots + x_n y_n = g$ such that
+    $g = \gcd(x_1, \cdots, x_n)$.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.elementary._trigonometric_special import migcdex
+    >>> migcdex()
+    ((), 0)
+    >>> migcdex(4)
+    ((1,), 4)
+    >>> migcdex(4, 6)
+    ((-1, 1), 2)
+    >>> migcdex(6, 10, 15)
+    ((1, 1, -1), 1)
+    """
+    if not x:
+        return (), 0
+
+    if len(x) == 1:
+        return (1,), x[0]
+
+    if len(x) == 2:
+        u, v, h = igcdex(x[0], x[1])
+        return (u, v), h
+
+    y, g = migcdex(*x[1:])
+    u, v, h = igcdex(x[0], g)
+    return (u, *(v * i for i in y)), h
+
+
+def ipartfrac(*denoms: int) -> tuple[int, ...]:
+    r"""Compute the partial fraction decomposition.
+
+    Explanation
+    ===========
+
+    Given a rational number $\frac{1}{q_1 \cdots q_n}$ where all
+    $q_1, \cdots, q_n$ are pairwise coprime,
+
+    A partial fraction decomposition is defined as
+
+    .. math::
+        \frac{1}{q_1 \cdots q_n} = \frac{p_1}{q_1} + \cdots + \frac{p_n}{q_n}
+
+    And it can be derived from solving the following diophantine equation for
+    the $p_1, \cdots, p_n$
+
+    .. math::
+        1 = p_1 \prod_{i \ne 1}q_i + \cdots + p_n \prod_{i \ne n}q_i
+
+    Where $q_1, \cdots, q_n$ being pairwise coprime implies
+    $\gcd(\prod_{i \ne 1}q_i, \cdots, \prod_{i \ne n}q_i) = 1$,
+    which guarantees the existence of the solution.
+
+    It is sufficient to compute partial fraction decomposition only
+    for numerator $1$ because partial fraction decomposition for any
+    $\frac{n}{q_1 \cdots q_n}$ can be easily computed by multiplying
+    the result by $n$ afterwards.
+
+    Parameters
+    ==========
+
+    denoms : int
+        The pairwise coprime integer denominators $q_i$ which defines the
+        rational number $\frac{1}{q_1 \cdots q_n}$
+
+    Returns
+    =======
+
+    tuple[int, ...]
+        The list of numerators which semantically corresponds to $p_i$ of the
+        partial fraction decomposition
+        $\frac{1}{q_1 \cdots q_n} = \frac{p_1}{q_1} + \cdots + \frac{p_n}{q_n}$
+
+    Examples
+    ========
+
+    >>> from sympy import Rational, Mul
+    >>> from sympy.functions.elementary._trigonometric_special import ipartfrac
+
+    >>> denoms = 2, 3, 5
+    >>> numers = ipartfrac(2, 3, 5)
+    >>> numers
+    (1, 7, -14)
+
+    >>> Rational(1, Mul(*denoms))
+    1/30
+    >>> out = 0
+    >>> for n, d in zip(numers, denoms):
+    ...    out += Rational(n, d)
+    >>> out
+    1/30
+    """
+    if not denoms:
+        return ()
+
+    def mul(x: int, y: int) -> int:
+        return x * y
+
+    denom = reduce(mul, denoms)
+    a = [denom // x for x in denoms]
+    h, _ = migcdex(*a)
+    return h
+
+
+def fermat_coords(n: int) -> list[int] | None:
+    """If n can be factored in terms of Fermat primes with
+    multiplicity of each being 1, return those primes, else
+    None
+    """
+    primes = []
+    for p in [3, 5, 17, 257, 65537]:
+        quotient, remainder = divmod(n, p)
+        if remainder == 0:
+            n = quotient
+            primes.append(p)
+            if n == 1:
+                return primes
+    return None
+
+
+@cacheit
+def cos_3() -> Expr:
+    r"""Computes $\cos \frac{\pi}{3}$ in square roots"""
+    return S.Half
+
+
+@cacheit
+def cos_5() -> Expr:
+    r"""Computes $\cos \frac{\pi}{5}$ in square roots"""
+    return (sqrt(5) + 1) / 4
+
+
+@cacheit
+def cos_17() -> Expr:
+    r"""Computes $\cos \frac{\pi}{17}$ in square roots"""
+    return sqrt(
+        (15 + sqrt(17)) / 32 + sqrt(2) * (sqrt(17 - sqrt(17)) +
+        sqrt(sqrt(2) * (-8 * sqrt(17 + sqrt(17)) - (1 - sqrt(17))
+        * sqrt(17 - sqrt(17))) + 6 * sqrt(17) + 34)) / 32)
+
+
+@cacheit
+def cos_257() -> Expr:
+    r"""Computes $\cos \frac{\pi}{257}$ in square roots
+
+    References
+    ==========
+
+    .. [*] https://math.stackexchange.com/questions/516142/how-does-cos2-pi-257-look-like-in-real-radicals
+    .. [*] https://r-knott.surrey.ac.uk/Fibonacci/simpleTrig.html
+    """
+    def f1(a: Expr, b: Expr) -> tuple[Expr, Expr]:
+        return (a + sqrt(a**2 + b)) / 2, (a - sqrt(a**2 + b)) / 2
+
+    def f2(a: Expr, b: Expr) -> Expr:
+        return (a - sqrt(a**2 + b))/2
+
+    t1, t2 = f1(S.NegativeOne, Integer(256))
+    z1, z3 = f1(t1, Integer(64))
+    z2, z4 = f1(t2, Integer(64))
+    y1, y5 = f1(z1, 4*(5 + t1 + 2*z1))
+    y6, y2 = f1(z2, 4*(5 + t2 + 2*z2))
+    y3, y7 = f1(z3, 4*(5 + t1 + 2*z3))
+    y8, y4 = f1(z4, 4*(5 + t2 + 2*z4))
+    x1, x9 = f1(y1, -4*(t1 + y1 + y3 + 2*y6))
+    x2, x10 = f1(y2, -4*(t2 + y2 + y4 + 2*y7))
+    x3, x11 = f1(y3, -4*(t1 + y3 + y5 + 2*y8))
+    x4, x12 = f1(y4, -4*(t2 + y4 + y6 + 2*y1))
+    x5, x13 = f1(y5, -4*(t1 + y5 + y7 + 2*y2))
+    x6, x14 = f1(y6, -4*(t2 + y6 + y8 + 2*y3))
+    x15, x7 = f1(y7, -4*(t1 + y7 + y1 + 2*y4))
+    x8, x16 = f1(y8, -4*(t2 + y8 + y2 + 2*y5))
+    v1 = f2(x1, -4*(x1 + x2 + x3 + x6))
+    v2 = f2(x2, -4*(x2 + x3 + x4 + x7))
+    v3 = f2(x8, -4*(x8 + x9 + x10 + x13))
+    v4 = f2(x9, -4*(x9 + x10 + x11 + x14))
+    v5 = f2(x10, -4*(x10 + x11 + x12 + x15))
+    v6 = f2(x16, -4*(x16 + x1 + x2 + x5))
+    u1 = -f2(-v1, -4*(v2 + v3))
+    u2 = -f2(-v4, -4*(v5 + v6))
+    w1 = -2*f2(-u1, -4*u2)
+    return sqrt(sqrt(2)*sqrt(w1 + 4)/8 + S.Half)
+
+
+def cos_table() -> dict[int, Callable[[], Expr]]:
+    r"""Lazily evaluated table for $\cos \frac{\pi}{n}$ in square roots for
+    $n \in \{3, 5, 17, 257, 65537\}$.
+
+    Notes
+    =====
+
+    65537 is the only other known Fermat prime and it is nearly impossible to
+    build in the current SymPy due to performance issues.
+
+    References
+    ==========
+
+    https://r-knott.surrey.ac.uk/Fibonacci/simpleTrig.html
+    """
+    return {
+        3: cos_3,
+        5: cos_5,
+        17: cos_17,
+        257: cos_257
+    }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/benchmarks/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/benchmarks/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/benchmarks/bench_exp.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/benchmarks/bench_exp.py
new file mode 100644
index 0000000000000000000000000000000000000000..fa18d29f87bcd249baec1d278a030fa7a133c3ba
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/benchmarks/bench_exp.py
@@ -0,0 +1,11 @@
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+
+x, y = symbols('x,y')
+
+e = exp(2*x)
+q = exp(3*x)
+
+
+def timeit_exp_subs():
+    e.subs(q, y)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/complexes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/complexes.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd837e4e242057050370f38c4b4e9c26aa5d06c9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/complexes.py
@@ -0,0 +1,1492 @@
+from __future__ import annotations
+
+from sympy.core import S, Add, Mul, sympify, Symbol, Dummy, Basic
+from sympy.core.expr import Expr
+from sympy.core.exprtools import factor_terms
+from sympy.core.function import (DefinedFunction, Derivative, ArgumentIndexError,
+    AppliedUndef, expand_mul, PoleError)
+from sympy.core.logic import fuzzy_not, fuzzy_or
+from sympy.core.numbers import pi, I, oo
+from sympy.core.power import Pow
+from sympy.core.relational import Eq
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+
+###############################################################################
+######################### REAL and IMAGINARY PARTS ############################
+###############################################################################
+
+
+class re(DefinedFunction):
+    """
+    Returns real part of expression. This function performs only
+    elementary analysis and so it will fail to decompose properly
+    more complicated expressions. If completely simplified result
+    is needed then use ``Basic.as_real_imag()`` or perform complex
+    expansion on instance of this function.
+
+    Examples
+    ========
+
+    >>> from sympy import re, im, I, E, symbols
+    >>> x, y = symbols('x y', real=True)
+    >>> re(2*E)
+    2*E
+    >>> re(2*I + 17)
+    17
+    >>> re(2*I)
+    0
+    >>> re(im(x) + x*I + 2)
+    2
+    >>> re(5 + I + 2)
+    7
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or complex expression.
+
+    Returns
+    =======
+
+    expr : Expr
+        Real part of expression.
+
+    See Also
+    ========
+
+    im
+    """
+
+    args: tuple[Expr]
+
+    is_extended_real = True
+    unbranched = True  # implicitly works on the projection to C
+    _singularities = True  # non-holomorphic
+
+    @classmethod
+    def eval(cls, arg):
+        if arg is S.NaN:
+            return S.NaN
+        elif arg is S.ComplexInfinity:
+            return S.NaN
+        elif arg.is_extended_real:
+            return arg
+        elif arg.is_imaginary or (I*arg).is_extended_real:
+            return S.Zero
+        elif arg.is_Matrix:
+            return arg.as_real_imag()[0]
+        elif arg.is_Function and isinstance(arg, conjugate):
+            return re(arg.args[0])
+        else:
+
+            included, reverted, excluded = [], [], []
+            args = Add.make_args(arg)
+            for term in args:
+                coeff = term.as_coefficient(I)
+
+                if coeff is not None:
+                    if not coeff.is_extended_real:
+                        reverted.append(coeff)
+                elif not term.has(I) and term.is_extended_real:
+                    excluded.append(term)
+                else:
+                    # Try to do some advanced expansion.  If
+                    # impossible, don't try to do re(arg) again
+                    # (because this is what we are trying to do now).
+                    real_imag = term.as_real_imag(ignore=arg)
+                    if real_imag:
+                        excluded.append(real_imag[0])
+                    else:
+                        included.append(term)
+
+            if len(args) != len(included):
+                a, b, c = (Add(*xs) for xs in [included, reverted, excluded])
+
+                return cls(a) - im(b) + c
+
+    def as_real_imag(self, deep=True, **hints):
+        """
+        Returns the real number with a zero imaginary part.
+
+        """
+        return (self, S.Zero)
+
+    def _eval_derivative(self, x):
+        if x.is_extended_real or self.args[0].is_extended_real:
+            return re(Derivative(self.args[0], x, evaluate=True))
+        if x.is_imaginary or self.args[0].is_imaginary:
+            return -I \
+                * im(Derivative(self.args[0], x, evaluate=True))
+
+    def _eval_rewrite_as_im(self, arg, **kwargs):
+        return self.args[0] - I*im(self.args[0])
+
+    def _eval_is_algebraic(self):
+        return self.args[0].is_algebraic
+
+    def _eval_is_zero(self):
+        # is_imaginary implies nonzero
+        return fuzzy_or([self.args[0].is_imaginary, self.args[0].is_zero])
+
+    def _eval_is_finite(self):
+        if self.args[0].is_finite:
+            return True
+
+    def _eval_is_complex(self):
+        if self.args[0].is_finite:
+            return True
+
+
+class im(DefinedFunction):
+    """
+    Returns imaginary part of expression. This function performs only
+    elementary analysis and so it will fail to decompose properly more
+    complicated expressions. If completely simplified result is needed then
+    use ``Basic.as_real_imag()`` or perform complex expansion on instance of
+    this function.
+
+    Examples
+    ========
+
+    >>> from sympy import re, im, E, I
+    >>> from sympy.abc import x, y
+    >>> im(2*E)
+    0
+    >>> im(2*I + 17)
+    2
+    >>> im(x*I)
+    re(x)
+    >>> im(re(x) + y)
+    im(y)
+    >>> im(2 + 3*I)
+    3
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or complex expression.
+
+    Returns
+    =======
+
+    expr : Expr
+        Imaginary part of expression.
+
+    See Also
+    ========
+
+    re
+    """
+
+    args: tuple[Expr]
+
+    is_extended_real = True
+    unbranched = True  # implicitly works on the projection to C
+    _singularities = True  # non-holomorphic
+
+    @classmethod
+    def eval(cls, arg):
+        if arg is S.NaN:
+            return S.NaN
+        elif arg is S.ComplexInfinity:
+            return S.NaN
+        elif arg.is_extended_real:
+            return S.Zero
+        elif arg.is_imaginary or (I*arg).is_extended_real:
+            return -I * arg
+        elif arg.is_Matrix:
+            return arg.as_real_imag()[1]
+        elif arg.is_Function and isinstance(arg, conjugate):
+            return -im(arg.args[0])
+        else:
+            included, reverted, excluded = [], [], []
+            args = Add.make_args(arg)
+            for term in args:
+                coeff = term.as_coefficient(I)
+
+                if coeff is not None:
+                    if not coeff.is_extended_real:
+                        reverted.append(coeff)
+                    else:
+                        excluded.append(coeff)
+                elif term.has(I) or not term.is_extended_real:
+                    # Try to do some advanced expansion.  If
+                    # impossible, don't try to do im(arg) again
+                    # (because this is what we are trying to do now).
+                    real_imag = term.as_real_imag(ignore=arg)
+                    if real_imag:
+                        excluded.append(real_imag[1])
+                    else:
+                        included.append(term)
+
+            if len(args) != len(included):
+                a, b, c = (Add(*xs) for xs in [included, reverted, excluded])
+
+                return cls(a) + re(b) + c
+
+    def as_real_imag(self, deep=True, **hints):
+        """
+        Return the imaginary part with a zero real part.
+
+        """
+        return (self, S.Zero)
+
+    def _eval_derivative(self, x):
+        if x.is_extended_real or self.args[0].is_extended_real:
+            return im(Derivative(self.args[0], x, evaluate=True))
+        if x.is_imaginary or self.args[0].is_imaginary:
+            return -I \
+                * re(Derivative(self.args[0], x, evaluate=True))
+
+    def _eval_rewrite_as_re(self, arg, **kwargs):
+        return -I*(self.args[0] - re(self.args[0]))
+
+    def _eval_is_algebraic(self):
+        return self.args[0].is_algebraic
+
+    def _eval_is_zero(self):
+        return self.args[0].is_extended_real
+
+    def _eval_is_finite(self):
+        if self.args[0].is_finite:
+            return True
+
+    def _eval_is_complex(self):
+        if self.args[0].is_finite:
+            return True
+
+###############################################################################
+############### SIGN, ABSOLUTE VALUE, ARGUMENT and CONJUGATION ################
+###############################################################################
+
+class sign(DefinedFunction):
+    """
+    Returns the complex sign of an expression:
+
+    Explanation
+    ===========
+
+    If the expression is real the sign will be:
+
+        * $1$ if expression is positive
+        * $0$ if expression is equal to zero
+        * $-1$ if expression is negative
+
+    If the expression is imaginary the sign will be:
+
+        * $I$ if im(expression) is positive
+        * $-I$ if im(expression) is negative
+
+    Otherwise an unevaluated expression will be returned. When evaluated, the
+    result (in general) will be ``cos(arg(expr)) + I*sin(arg(expr))``.
+
+    Examples
+    ========
+
+    >>> from sympy import sign, I
+
+    >>> sign(-1)
+    -1
+    >>> sign(0)
+    0
+    >>> sign(-3*I)
+    -I
+    >>> sign(1 + I)
+    sign(1 + I)
+    >>> _.evalf()
+    0.707106781186548 + 0.707106781186548*I
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or imaginary expression.
+
+    Returns
+    =======
+
+    expr : Expr
+        Complex sign of expression.
+
+    See Also
+    ========
+
+    Abs, conjugate
+    """
+
+    is_complex = True
+    _singularities = True
+
+    def doit(self, **hints):
+        s = super().doit()
+        if s == self and self.args[0].is_zero is False:
+            return self.args[0] / Abs(self.args[0])
+        return s
+
+    @classmethod
+    def eval(cls, arg):
+        # handle what we can
+        if arg.is_Mul:
+            c, args = arg.as_coeff_mul()
+            unk = []
+            s = sign(c)
+            for a in args:
+                if a.is_extended_negative:
+                    s = -s
+                elif a.is_extended_positive:
+                    pass
+                else:
+                    if a.is_imaginary:
+                        ai = im(a)
+                        if ai.is_comparable:  # i.e. a = I*real
+                            s *= I
+                            if ai.is_extended_negative:
+                                # can't use sign(ai) here since ai might not be
+                                # a Number
+                                s = -s
+                        else:
+                            unk.append(a)
+                    else:
+                        unk.append(a)
+            if c is S.One and len(unk) == len(args):
+                return None
+            return s * cls(arg._new_rawargs(*unk))
+        if arg is S.NaN:
+            return S.NaN
+        if arg.is_zero:  # it may be an Expr that is zero
+            return S.Zero
+        if arg.is_extended_positive:
+            return S.One
+        if arg.is_extended_negative:
+            return S.NegativeOne
+        if arg.is_Function:
+            if isinstance(arg, sign):
+                return arg
+        if arg.is_imaginary:
+            if arg.is_Pow and arg.exp is S.Half:
+                # we catch this because non-trivial sqrt args are not expanded
+                # e.g. sqrt(1-sqrt(2)) --x-->  to I*sqrt(sqrt(2) - 1)
+                return I
+            arg2 = -I * arg
+            if arg2.is_extended_positive:
+                return I
+            if arg2.is_extended_negative:
+                return -I
+
+    def _eval_Abs(self):
+        if fuzzy_not(self.args[0].is_zero):
+            return S.One
+
+    def _eval_conjugate(self):
+        return sign(conjugate(self.args[0]))
+
+    def _eval_derivative(self, x):
+        if self.args[0].is_extended_real:
+            from sympy.functions.special.delta_functions import DiracDelta
+            return 2 * Derivative(self.args[0], x, evaluate=True) \
+                * DiracDelta(self.args[0])
+        elif self.args[0].is_imaginary:
+            from sympy.functions.special.delta_functions import DiracDelta
+            return 2 * Derivative(self.args[0], x, evaluate=True) \
+                * DiracDelta(-I * self.args[0])
+
+    def _eval_is_nonnegative(self):
+        if self.args[0].is_nonnegative:
+            return True
+
+    def _eval_is_nonpositive(self):
+        if self.args[0].is_nonpositive:
+            return True
+
+    def _eval_is_imaginary(self):
+        return self.args[0].is_imaginary
+
+    def _eval_is_integer(self):
+        return self.args[0].is_extended_real
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+    def _eval_power(self, other):
+        if (
+            fuzzy_not(self.args[0].is_zero) and
+            other.is_integer and
+            other.is_even
+        ):
+            return S.One
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg0 = self.args[0]
+        x0 = arg0.subs(x, 0)
+        if x0 != 0:
+            return self.func(x0)
+        if cdir != 0:
+            cdir = arg0.dir(x, cdir)
+        return -S.One if re(cdir) < 0 else S.One
+
+    def _eval_rewrite_as_Piecewise(self, arg, **kwargs):
+        if arg.is_extended_real:
+            return Piecewise((1, arg > 0), (-1, arg < 0), (0, True))
+
+    def _eval_rewrite_as_Heaviside(self, arg, **kwargs):
+        from sympy.functions.special.delta_functions import Heaviside
+        if arg.is_extended_real:
+            return Heaviside(arg) * 2 - 1
+
+    def _eval_rewrite_as_Abs(self, arg, **kwargs):
+        return Piecewise((0, Eq(arg, 0)), (arg / Abs(arg), True))
+
+    def _eval_simplify(self, **kwargs):
+        return self.func(factor_terms(self.args[0]))  # XXX include doit?
+
+
+class Abs(DefinedFunction):
+    """
+    Return the absolute value of the argument.
+
+    Explanation
+    ===========
+
+    This is an extension of the built-in function ``abs()`` to accept symbolic
+    values.  If you pass a SymPy expression to the built-in ``abs()``, it will
+    pass it automatically to ``Abs()``.
+
+    Examples
+    ========
+
+    >>> from sympy import Abs, Symbol, S, I
+    >>> Abs(-1)
+    1
+    >>> x = Symbol('x', real=True)
+    >>> Abs(-x)
+    Abs(x)
+    >>> Abs(x**2)
+    x**2
+    >>> abs(-x) # The Python built-in
+    Abs(x)
+    >>> Abs(3*x + 2*I)
+    sqrt(9*x**2 + 4)
+    >>> Abs(8*I)
+    8
+
+    Note that the Python built-in will return either an Expr or int depending on
+    the argument::
+
+        >>> type(abs(-1))
+        <... 'int'>
+        >>> type(abs(S.NegativeOne))
+        
+
+    Abs will always return a SymPy object.
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or complex expression.
+
+    Returns
+    =======
+
+    expr : Expr
+        Absolute value returned can be an expression or integer depending on
+        input arg.
+
+    See Also
+    ========
+
+    sign, conjugate
+    """
+
+    args: tuple[Expr]
+
+    is_extended_real = True
+    is_extended_negative = False
+    is_extended_nonnegative = True
+    unbranched = True
+    _singularities = True  # non-holomorphic
+
+    def fdiff(self, argindex=1):
+        """
+        Get the first derivative of the argument to Abs().
+
+        """
+        if argindex == 1:
+            return sign(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.simplify.simplify import signsimp
+
+        if hasattr(arg, '_eval_Abs'):
+            obj = arg._eval_Abs()
+            if obj is not None:
+                return obj
+        if not isinstance(arg, Expr):
+            raise TypeError("Bad argument type for Abs(): %s" % type(arg))
+
+        # handle what we can
+        arg = signsimp(arg, evaluate=False)
+        n, d = arg.as_numer_denom()
+        if d.free_symbols and not n.free_symbols:
+            return cls(n)/cls(d)
+
+        if arg.is_Mul:
+            known = []
+            unk = []
+            for t in arg.args:
+                if t.is_Pow and t.exp.is_integer and t.exp.is_negative:
+                    bnew = cls(t.base)
+                    if isinstance(bnew, cls):
+                        unk.append(t)
+                    else:
+                        known.append(Pow(bnew, t.exp))
+                else:
+                    tnew = cls(t)
+                    if isinstance(tnew, cls):
+                        unk.append(t)
+                    else:
+                        known.append(tnew)
+            known = Mul(*known)
+            unk = cls(Mul(*unk), evaluate=False) if unk else S.One
+            return known*unk
+        if arg is S.NaN:
+            return S.NaN
+        if arg is S.ComplexInfinity:
+            return oo
+        from sympy.functions.elementary.exponential import exp, log
+
+        if arg.is_Pow:
+            base, exponent = arg.as_base_exp()
+            if base.is_extended_real:
+                if exponent.is_integer:
+                    if exponent.is_even:
+                        return arg
+                    if base is S.NegativeOne:
+                        return S.One
+                    return Abs(base)**exponent
+                if base.is_extended_nonnegative:
+                    return base**re(exponent)
+                if base.is_extended_negative:
+                    return (-base)**re(exponent)*exp(-pi*im(exponent))
+                return
+            elif not base.has(Symbol): # complex base
+                # express base**exponent as exp(exponent*log(base))
+                a, b = log(base).as_real_imag()
+                z = a + I*b
+                return exp(re(exponent*z))
+        if isinstance(arg, exp):
+            return exp(re(arg.args[0]))
+        if isinstance(arg, AppliedUndef):
+            if arg.is_positive:
+                return arg
+            elif arg.is_negative:
+                return -arg
+            return
+        if arg.is_Add and arg.has(oo, S.NegativeInfinity):
+            if any(a.is_infinite for a in arg.as_real_imag()):
+                return oo
+        if arg.is_zero:
+            return S.Zero
+        if arg.is_extended_nonnegative:
+            return arg
+        if arg.is_extended_nonpositive:
+            return -arg
+        if arg.is_imaginary:
+            arg2 = -I * arg
+            if arg2.is_extended_nonnegative:
+                return arg2
+        if arg.is_extended_real:
+            return
+        # reject result if all new conjugates are just wrappers around
+        # an expression that was already in the arg
+        conj = signsimp(arg.conjugate(), evaluate=False)
+        new_conj = conj.atoms(conjugate) - arg.atoms(conjugate)
+        if new_conj and all(arg.has(i.args[0]) for i in new_conj):
+            return
+        if arg != conj and arg != -conj:
+            ignore = arg.atoms(Abs)
+            abs_free_arg = arg.xreplace({i: Dummy(real=True) for i in ignore})
+            unk = [a for a in abs_free_arg.free_symbols if a.is_extended_real is None]
+            if not unk or not all(conj.has(conjugate(u)) for u in unk):
+                return sqrt(expand_mul(arg*conj))
+
+    def _eval_is_real(self):
+        if self.args[0].is_finite:
+            return True
+
+    def _eval_is_integer(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_integer
+
+    def _eval_is_extended_nonzero(self):
+        return fuzzy_not(self._args[0].is_zero)
+
+    def _eval_is_zero(self):
+        return self._args[0].is_zero
+
+    def _eval_is_extended_positive(self):
+        return fuzzy_not(self._args[0].is_zero)
+
+    def _eval_is_rational(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_rational
+
+    def _eval_is_even(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_even
+
+    def _eval_is_odd(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_odd
+
+    def _eval_is_algebraic(self):
+        return self.args[0].is_algebraic
+
+    def _eval_power(self, exponent):
+        if self.args[0].is_extended_real and exponent.is_integer:
+            if exponent.is_even:
+                return self.args[0]**exponent
+            elif exponent is not S.NegativeOne and exponent.is_Integer:
+                return self.args[0]**(exponent - 1)*self
+        return
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.functions.elementary.exponential import log
+        direction = self.args[0].leadterm(x)[0]
+        if direction.has(log(x)):
+            direction = direction.subs(log(x), logx)
+        s = self.args[0]._eval_nseries(x, n=n, logx=logx)
+        return (sign(direction)*s).expand()
+
+    def _eval_derivative(self, x):
+        if self.args[0].is_extended_real or self.args[0].is_imaginary:
+            return Derivative(self.args[0], x, evaluate=True) \
+                * sign(conjugate(self.args[0]))
+        rv = (re(self.args[0]) * Derivative(re(self.args[0]), x,
+            evaluate=True) + im(self.args[0]) * Derivative(im(self.args[0]),
+                x, evaluate=True)) / Abs(self.args[0])
+        return rv.rewrite(sign)
+
+    def _eval_rewrite_as_Heaviside(self, arg, **kwargs):
+        # Note this only holds for real arg (since Heaviside is not defined
+        # for complex arguments).
+        from sympy.functions.special.delta_functions import Heaviside
+        if arg.is_extended_real:
+            return arg*(Heaviside(arg) - Heaviside(-arg))
+
+    def _eval_rewrite_as_Piecewise(self, arg, **kwargs):
+        if arg.is_extended_real:
+            return Piecewise((arg, arg >= 0), (-arg, True))
+        elif arg.is_imaginary:
+            return Piecewise((I*arg, I*arg >= 0), (-I*arg, True))
+
+    def _eval_rewrite_as_sign(self, arg, **kwargs):
+        return arg/sign(arg)
+
+    def _eval_rewrite_as_conjugate(self, arg, **kwargs):
+        return sqrt(arg*conjugate(arg))
+
+
+class arg(DefinedFunction):
+    r"""
+    Returns the argument (in radians) of a complex number. The argument is
+    evaluated in consistent convention with ``atan2`` where the branch-cut is
+    taken along the negative real axis and ``arg(z)`` is in the interval
+    $(-\pi,\pi]$. For a positive number, the argument is always 0; the
+    argument of a negative number is $\pi$; and the argument of 0
+    is undefined and returns ``nan``. So the ``arg`` function will never nest
+    greater than 3 levels since at the 4th application, the result must be
+    nan; for a real number, nan is returned on the 3rd application.
+
+    Examples
+    ========
+
+    >>> from sympy import arg, I, sqrt, Dummy
+    >>> from sympy.abc import x
+    >>> arg(2.0)
+    0
+    >>> arg(I)
+    pi/2
+    >>> arg(sqrt(2) + I*sqrt(2))
+    pi/4
+    >>> arg(sqrt(3)/2 + I/2)
+    pi/6
+    >>> arg(4 + 3*I)
+    atan(3/4)
+    >>> arg(0.8 + 0.6*I)
+    0.643501108793284
+    >>> arg(arg(arg(arg(x))))
+    nan
+    >>> real = Dummy(real=True)
+    >>> arg(arg(arg(real)))
+    nan
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or complex expression.
+
+    Returns
+    =======
+
+    value : Expr
+        Returns arc tangent of arg measured in radians.
+
+    """
+
+    is_extended_real = True
+    is_real = True
+    is_finite = True
+    _singularities = True  # non-holomorphic
+
+    @classmethod
+    def eval(cls, arg):
+        a = arg
+        for i in range(3):
+            if isinstance(a, cls):
+                a = a.args[0]
+            else:
+                if i == 2 and a.is_extended_real:
+                    return S.NaN
+                break
+        else:
+            return S.NaN
+        from sympy.functions.elementary.exponential import exp, exp_polar
+        if isinstance(arg, exp_polar):
+            return periodic_argument(arg, oo)
+        elif isinstance(arg, exp):
+            i_ = im(arg.args[0])
+            if i_.is_comparable:
+                i_ %= 2*S.Pi
+                if i_ > S.Pi:
+                    i_ -= 2*S.Pi
+                return i_
+
+        if not arg.is_Atom:
+            c, arg_ = factor_terms(arg).as_coeff_Mul()
+            if arg_.is_Mul:
+                arg_ = Mul(*[a if (sign(a) not in (-1, 1)) else
+                    sign(a) for a in arg_.args])
+            arg_ = sign(c)*arg_
+        else:
+            arg_ = arg
+        if any(i.is_extended_positive is None for i in arg_.atoms(AppliedUndef)):
+            return
+        from sympy.functions.elementary.trigonometric import atan2
+        x, y = arg_.as_real_imag()
+        rv = atan2(y, x)
+        if rv.is_number:
+            return rv
+        if arg_ != arg:
+            return cls(arg_, evaluate=False)
+
+    def _eval_derivative(self, t):
+        x, y = self.args[0].as_real_imag()
+        return (x * Derivative(y, t, evaluate=True) - y *
+                    Derivative(x, t, evaluate=True)) / (x**2 + y**2)
+
+    def _eval_rewrite_as_atan2(self, arg, **kwargs):
+        from sympy.functions.elementary.trigonometric import atan2
+        x, y = self.args[0].as_real_imag()
+        return atan2(y, x)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg0 = self.args[0]
+        t = Dummy('t', positive=True)
+        if cdir == 0:
+            cdir = 1
+        z = arg0.subs(x, cdir*t)
+        if z.is_positive:
+            return S.Zero
+        elif z.is_negative:
+            return S.Pi
+        else:
+            raise PoleError("Cannot expand %s around 0" % (self))
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.series.order import Order
+        if n <= 0:
+            return Order(1)
+        return self._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+
+class conjugate(DefinedFunction):
+    """
+    Returns the *complex conjugate* [1]_ of an argument.
+    In mathematics, the complex conjugate of a complex number
+    is given by changing the sign of the imaginary part.
+
+    Thus, the conjugate of the complex number
+    :math:`a + ib` (where $a$ and $b$ are real numbers) is :math:`a - ib`
+
+    Examples
+    ========
+
+    >>> from sympy import conjugate, I
+    >>> conjugate(2)
+    2
+    >>> conjugate(I)
+    -I
+    >>> conjugate(3 + 2*I)
+    3 - 2*I
+    >>> conjugate(5 - I)
+    5 + I
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or complex expression.
+
+    Returns
+    =======
+
+    arg : Expr
+        Complex conjugate of arg as real, imaginary or mixed expression.
+
+    See Also
+    ========
+
+    sign, Abs
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Complex_conjugation
+    """
+    _singularities = True  # non-holomorphic
+
+    @classmethod
+    def eval(cls, arg):
+        obj = arg._eval_conjugate()
+        if obj is not None:
+            return obj
+
+    def inverse(self):
+        return conjugate
+
+    def _eval_Abs(self):
+        return Abs(self.args[0], evaluate=True)
+
+    def _eval_adjoint(self):
+        return transpose(self.args[0])
+
+    def _eval_conjugate(self):
+        return self.args[0]
+
+    def _eval_derivative(self, x):
+        if x.is_real:
+            return conjugate(Derivative(self.args[0], x, evaluate=True))
+        elif x.is_imaginary:
+            return -conjugate(Derivative(self.args[0], x, evaluate=True))
+
+    def _eval_transpose(self):
+        return adjoint(self.args[0])
+
+    def _eval_is_algebraic(self):
+        return self.args[0].is_algebraic
+
+
+class transpose(DefinedFunction):
+    """
+    Linear map transposition.
+
+    Examples
+    ========
+
+    >>> from sympy import transpose, Matrix, MatrixSymbol
+    >>> A = MatrixSymbol('A', 25, 9)
+    >>> transpose(A)
+    A.T
+    >>> B = MatrixSymbol('B', 9, 22)
+    >>> transpose(B)
+    B.T
+    >>> transpose(A*B)
+    B.T*A.T
+    >>> M = Matrix([[4, 5], [2, 1], [90, 12]])
+    >>> M
+    Matrix([
+    [ 4,  5],
+    [ 2,  1],
+    [90, 12]])
+    >>> transpose(M)
+    Matrix([
+    [4, 2, 90],
+    [5, 1, 12]])
+
+    Parameters
+    ==========
+
+    arg : Matrix
+         Matrix or matrix expression to take the transpose of.
+
+    Returns
+    =======
+
+    value : Matrix
+        Transpose of arg.
+
+    """
+
+    @classmethod
+    def eval(cls, arg):
+        obj = arg._eval_transpose()
+        if obj is not None:
+            return obj
+
+    def _eval_adjoint(self):
+        return conjugate(self.args[0])
+
+    def _eval_conjugate(self):
+        return adjoint(self.args[0])
+
+    def _eval_transpose(self):
+        return self.args[0]
+
+
+class adjoint(DefinedFunction):
+    """
+    Conjugate transpose or Hermite conjugation.
+
+    Examples
+    ========
+
+    >>> from sympy import adjoint, MatrixSymbol
+    >>> A = MatrixSymbol('A', 10, 5)
+    >>> adjoint(A)
+    Adjoint(A)
+
+    Parameters
+    ==========
+
+    arg : Matrix
+        Matrix or matrix expression to take the adjoint of.
+
+    Returns
+    =======
+
+    value : Matrix
+        Represents the conjugate transpose or Hermite
+        conjugation of arg.
+
+    """
+
+    @classmethod
+    def eval(cls, arg):
+        obj = arg._eval_adjoint()
+        if obj is not None:
+            return obj
+        obj = arg._eval_transpose()
+        if obj is not None:
+            return conjugate(obj)
+
+    def _eval_adjoint(self):
+        return self.args[0]
+
+    def _eval_conjugate(self):
+        return transpose(self.args[0])
+
+    def _eval_transpose(self):
+        return conjugate(self.args[0])
+
+    def _latex(self, printer, exp=None, *args):
+        arg = printer._print(self.args[0])
+        tex = r'%s^{\dagger}' % arg
+        if exp:
+            tex = r'\left(%s\right)^{%s}' % (tex, exp)
+        return tex
+
+    def _pretty(self, printer, *args):
+        from sympy.printing.pretty.stringpict import prettyForm
+        pform = printer._print(self.args[0], *args)
+        if printer._use_unicode:
+            pform = pform**prettyForm('\N{DAGGER}')
+        else:
+            pform = pform**prettyForm('+')
+        return pform
+
+###############################################################################
+############### HANDLING OF POLAR NUMBERS #####################################
+###############################################################################
+
+
+class polar_lift(DefinedFunction):
+    """
+    Lift argument to the Riemann surface of the logarithm, using the
+    standard branch.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, polar_lift, I
+    >>> p = Symbol('p', polar=True)
+    >>> x = Symbol('x')
+    >>> polar_lift(4)
+    4*exp_polar(0)
+    >>> polar_lift(-4)
+    4*exp_polar(I*pi)
+    >>> polar_lift(-I)
+    exp_polar(-I*pi/2)
+    >>> polar_lift(I + 2)
+    polar_lift(2 + I)
+
+    >>> polar_lift(4*x)
+    4*polar_lift(x)
+    >>> polar_lift(4*p)
+    4*p
+
+    Parameters
+    ==========
+
+    arg : Expr
+        Real or complex expression.
+
+    See Also
+    ========
+
+    sympy.functions.elementary.exponential.exp_polar
+    periodic_argument
+    """
+
+    is_polar = True
+    is_comparable = False  # Cannot be evalf'd.
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.functions.elementary.complexes import arg as argument
+        if arg.is_number:
+            ar = argument(arg)
+            # In general we want to affirm that something is known,
+            # e.g. `not ar.has(argument) and not ar.has(atan)`
+            # but for now we will just be more restrictive and
+            # see that it has evaluated to one of the known values.
+            if ar in (0, pi/2, -pi/2, pi):
+                from sympy.functions.elementary.exponential import exp_polar
+                return exp_polar(I*ar)*abs(arg)
+
+        if arg.is_Mul:
+            args = arg.args
+        else:
+            args = [arg]
+        included = []
+        excluded = []
+        positive = []
+        for arg in args:
+            if arg.is_polar:
+                included += [arg]
+            elif arg.is_positive:
+                positive += [arg]
+            else:
+                excluded += [arg]
+        if len(excluded) < len(args):
+            if excluded:
+                return Mul(*(included + positive))*polar_lift(Mul(*excluded))
+            elif included:
+                return Mul(*(included + positive))
+            else:
+                from sympy.functions.elementary.exponential import exp_polar
+                return Mul(*positive)*exp_polar(0)
+
+    def _eval_evalf(self, prec):
+        """ Careful! any evalf of polar numbers is flaky """
+        return self.args[0]._eval_evalf(prec)
+
+    def _eval_Abs(self):
+        return Abs(self.args[0], evaluate=True)
+
+
+class periodic_argument(DefinedFunction):
+    r"""
+    Represent the argument on a quotient of the Riemann surface of the
+    logarithm. That is, given a period $P$, always return a value in
+    $(-P/2, P/2]$, by using $\exp(PI) = 1$.
+
+    Examples
+    ========
+
+    >>> from sympy import exp_polar, periodic_argument
+    >>> from sympy import I, pi
+    >>> periodic_argument(exp_polar(10*I*pi), 2*pi)
+    0
+    >>> periodic_argument(exp_polar(5*I*pi), 4*pi)
+    pi
+    >>> from sympy import exp_polar, periodic_argument
+    >>> from sympy import I, pi
+    >>> periodic_argument(exp_polar(5*I*pi), 2*pi)
+    pi
+    >>> periodic_argument(exp_polar(5*I*pi), 3*pi)
+    -pi
+    >>> periodic_argument(exp_polar(5*I*pi), pi)
+    0
+
+    Parameters
+    ==========
+
+    ar : Expr
+        A polar number.
+
+    period : Expr
+        The period $P$.
+
+    See Also
+    ========
+
+    sympy.functions.elementary.exponential.exp_polar
+    polar_lift : Lift argument to the Riemann surface of the logarithm
+    principal_branch
+    """
+
+    @classmethod
+    def _getunbranched(cls, ar):
+        from sympy.functions.elementary.exponential import exp_polar, log
+        if ar.is_Mul:
+            args = ar.args
+        else:
+            args = [ar]
+        unbranched = 0
+        for a in args:
+            if not a.is_polar:
+                unbranched += arg(a)
+            elif isinstance(a, exp_polar):
+                unbranched += a.exp.as_real_imag()[1]
+            elif a.is_Pow:
+                re, im = a.exp.as_real_imag()
+                unbranched += re*unbranched_argument(
+                    a.base) + im*log(abs(a.base))
+            elif isinstance(a, polar_lift):
+                unbranched += arg(a.args[0])
+            else:
+                return None
+        return unbranched
+
+    @classmethod
+    def eval(cls, ar, period):
+        # Our strategy is to evaluate the argument on the Riemann surface of the
+        # logarithm, and then reduce.
+        # NOTE evidently this means it is a rather bad idea to use this with
+        # period != 2*pi and non-polar numbers.
+        if not period.is_extended_positive:
+            return None
+        if period == oo and isinstance(ar, principal_branch):
+            return periodic_argument(*ar.args)
+        if isinstance(ar, polar_lift) and period >= 2*pi:
+            return periodic_argument(ar.args[0], period)
+        if ar.is_Mul:
+            newargs = [x for x in ar.args if not x.is_positive]
+            if len(newargs) != len(ar.args):
+                return periodic_argument(Mul(*newargs), period)
+        unbranched = cls._getunbranched(ar)
+        if unbranched is None:
+            return None
+        from sympy.functions.elementary.trigonometric import atan, atan2
+        if unbranched.has(periodic_argument, atan2, atan):
+            return None
+        if period == oo:
+            return unbranched
+        if period != oo:
+            from sympy.functions.elementary.integers import ceiling
+            n = ceiling(unbranched/period - S.Half)*period
+            if not n.has(ceiling):
+                return unbranched - n
+
+    def _eval_evalf(self, prec):
+        z, period = self.args
+        if period == oo:
+            unbranched = periodic_argument._getunbranched(z)
+            if unbranched is None:
+                return self
+            return unbranched._eval_evalf(prec)
+        ub = periodic_argument(z, oo)._eval_evalf(prec)
+        from sympy.functions.elementary.integers import ceiling
+        return (ub - ceiling(ub/period - S.Half)*period)._eval_evalf(prec)
+
+
+def unbranched_argument(arg):
+    '''
+    Returns periodic argument of arg with period as infinity.
+
+    Examples
+    ========
+
+    >>> from sympy import exp_polar, unbranched_argument
+    >>> from sympy import I, pi
+    >>> unbranched_argument(exp_polar(15*I*pi))
+    15*pi
+    >>> unbranched_argument(exp_polar(7*I*pi))
+    7*pi
+
+    See also
+    ========
+
+    periodic_argument
+    '''
+    return periodic_argument(arg, oo)
+
+
+class principal_branch(DefinedFunction):
+    """
+    Represent a polar number reduced to its principal branch on a quotient
+    of the Riemann surface of the logarithm.
+
+    Explanation
+    ===========
+
+    This is a function of two arguments. The first argument is a polar
+    number `z`, and the second one a positive real number or infinity, `p`.
+    The result is ``z mod exp_polar(I*p)``.
+
+    Examples
+    ========
+
+    >>> from sympy import exp_polar, principal_branch, oo, I, pi
+    >>> from sympy.abc import z
+    >>> principal_branch(z, oo)
+    z
+    >>> principal_branch(exp_polar(2*pi*I)*3, 2*pi)
+    3*exp_polar(0)
+    >>> principal_branch(exp_polar(2*pi*I)*3*z, 2*pi)
+    3*principal_branch(z, 2*pi)
+
+    Parameters
+    ==========
+
+    x : Expr
+        A polar number.
+
+    period : Expr
+        Positive real number or infinity.
+
+    See Also
+    ========
+
+    sympy.functions.elementary.exponential.exp_polar
+    polar_lift : Lift argument to the Riemann surface of the logarithm
+    periodic_argument
+    """
+
+    is_polar = True
+    is_comparable = False  # cannot always be evalf'd
+
+    @classmethod
+    def eval(self, x, period):
+        from sympy.functions.elementary.exponential import exp_polar
+        if isinstance(x, polar_lift):
+            return principal_branch(x.args[0], period)
+        if period == oo:
+            return x
+        ub = periodic_argument(x, oo)
+        barg = periodic_argument(x, period)
+        if ub != barg and not ub.has(periodic_argument) \
+                and not barg.has(periodic_argument):
+            pl = polar_lift(x)
+
+            def mr(expr):
+                if not isinstance(expr, Symbol):
+                    return polar_lift(expr)
+                return expr
+            pl = pl.replace(polar_lift, mr)
+            # Recompute unbranched argument
+            ub = periodic_argument(pl, oo)
+            if not pl.has(polar_lift):
+                if ub != barg:
+                    res = exp_polar(I*(barg - ub))*pl
+                else:
+                    res = pl
+                if not res.is_polar and not res.has(exp_polar):
+                    res *= exp_polar(0)
+                return res
+
+        if not x.free_symbols:
+            c, m = x, ()
+        else:
+            c, m = x.as_coeff_mul(*x.free_symbols)
+        others = []
+        for y in m:
+            if y.is_positive:
+                c *= y
+            else:
+                others += [y]
+        m = tuple(others)
+        arg = periodic_argument(c, period)
+        if arg.has(periodic_argument):
+            return None
+        if arg.is_number and (unbranched_argument(c) != arg or
+                              (arg == 0 and m != () and c != 1)):
+            if arg == 0:
+                return abs(c)*principal_branch(Mul(*m), period)
+            return principal_branch(exp_polar(I*arg)*Mul(*m), period)*abs(c)
+        if arg.is_number and ((abs(arg) < period/2) == True or arg == period/2) \
+                and m == ():
+            return exp_polar(arg*I)*abs(c)
+
+    def _eval_evalf(self, prec):
+        z, period = self.args
+        p = periodic_argument(z, period)._eval_evalf(prec)
+        if abs(p) > pi or p == -pi:
+            return self  # Cannot evalf for this argument.
+        from sympy.functions.elementary.exponential import exp
+        return (abs(z)*exp(I*p))._eval_evalf(prec)
+
+
+def _polarify(eq, lift, pause=False):
+    from sympy.integrals.integrals import Integral
+    if eq.is_polar:
+        return eq
+    if eq.is_number and not pause:
+        return polar_lift(eq)
+    if isinstance(eq, Symbol) and not pause and lift:
+        return polar_lift(eq)
+    elif eq.is_Atom:
+        return eq
+    elif eq.is_Add:
+        r = eq.func(*[_polarify(arg, lift, pause=True) for arg in eq.args])
+        if lift:
+            return polar_lift(r)
+        return r
+    elif eq.is_Pow and eq.base == S.Exp1:
+        return eq.func(S.Exp1, _polarify(eq.exp, lift, pause=False))
+    elif eq.is_Function:
+        return eq.func(*[_polarify(arg, lift, pause=False) for arg in eq.args])
+    elif isinstance(eq, Integral):
+        # Don't lift the integration variable
+        func = _polarify(eq.function, lift, pause=pause)
+        limits = []
+        for limit in eq.args[1:]:
+            var = _polarify(limit[0], lift=False, pause=pause)
+            rest = _polarify(limit[1:], lift=lift, pause=pause)
+            limits.append((var,) + rest)
+        return Integral(*((func,) + tuple(limits)))
+    else:
+        return eq.func(*[_polarify(arg, lift, pause=pause)
+                         if isinstance(arg, Expr) else arg for arg in eq.args])
+
+
+def polarify(eq, subs=True, lift=False):
+    """
+    Turn all numbers in eq into their polar equivalents (under the standard
+    choice of argument).
+
+    Note that no attempt is made to guess a formal convention of adding
+    polar numbers, expressions like $1 + x$ will generally not be altered.
+
+    Note also that this function does not promote ``exp(x)`` to ``exp_polar(x)``.
+
+    If ``subs`` is ``True``, all symbols which are not already polar will be
+    substituted for polar dummies; in this case the function behaves much
+    like :func:`~.posify`.
+
+    If ``lift`` is ``True``, both addition statements and non-polar symbols are
+    changed to their ``polar_lift()``ed versions.
+    Note that ``lift=True`` implies ``subs=False``.
+
+    Examples
+    ========
+
+    >>> from sympy import polarify, sin, I
+    >>> from sympy.abc import x, y
+    >>> expr = (-x)**y
+    >>> expr.expand()
+    (-x)**y
+    >>> polarify(expr)
+    ((_x*exp_polar(I*pi))**_y, {_x: x, _y: y})
+    >>> polarify(expr)[0].expand()
+    _x**_y*exp_polar(_y*I*pi)
+    >>> polarify(x, lift=True)
+    polar_lift(x)
+    >>> polarify(x*(1+y), lift=True)
+    polar_lift(x)*polar_lift(y + 1)
+
+    Adds are treated carefully:
+
+    >>> polarify(1 + sin((1 + I)*x))
+    (sin(_x*polar_lift(1 + I)) + 1, {_x: x})
+    """
+    if lift:
+        subs = False
+    eq = _polarify(sympify(eq), lift)
+    if not subs:
+        return eq
+    reps = {s: Dummy(s.name, polar=True) for s in eq.free_symbols}
+    eq = eq.subs(reps)
+    return eq, {r: s for s, r in reps.items()}
+
+
+def _unpolarify(eq, exponents_only, pause=False):
+    if not isinstance(eq, Basic) or eq.is_Atom:
+        return eq
+
+    if not pause:
+        from sympy.functions.elementary.exponential import exp, exp_polar
+        if isinstance(eq, exp_polar):
+            return exp(_unpolarify(eq.exp, exponents_only))
+        if isinstance(eq, principal_branch) and eq.args[1] == 2*pi:
+            return _unpolarify(eq.args[0], exponents_only)
+        if (
+            eq.is_Add or eq.is_Mul or eq.is_Boolean or
+            eq.is_Relational and (
+                eq.rel_op in ('==', '!=') and 0 in eq.args or
+                eq.rel_op not in ('==', '!='))
+        ):
+            return eq.func(*[_unpolarify(x, exponents_only) for x in eq.args])
+        if isinstance(eq, polar_lift):
+            return _unpolarify(eq.args[0], exponents_only)
+
+    if eq.is_Pow:
+        expo = _unpolarify(eq.exp, exponents_only)
+        base = _unpolarify(eq.base, exponents_only,
+            not (expo.is_integer and not pause))
+        return base**expo
+
+    if eq.is_Function and getattr(eq.func, 'unbranched', False):
+        return eq.func(*[_unpolarify(x, exponents_only, exponents_only)
+            for x in eq.args])
+
+    return eq.func(*[_unpolarify(x, exponents_only, True) for x in eq.args])
+
+
+def unpolarify(eq, subs=None, exponents_only=False):
+    """
+    If `p` denotes the projection from the Riemann surface of the logarithm to
+    the complex line, return a simplified version `eq'` of `eq` such that
+    `p(eq') = p(eq)`.
+    Also apply the substitution subs in the end. (This is a convenience, since
+    ``unpolarify``, in a certain sense, undoes :func:`polarify`.)
+
+    Examples
+    ========
+
+    >>> from sympy import unpolarify, polar_lift, sin, I
+    >>> unpolarify(polar_lift(I + 2))
+    2 + I
+    >>> unpolarify(sin(polar_lift(I + 7)))
+    sin(7 + I)
+    """
+    if isinstance(eq, bool):
+        return eq
+
+    eq = sympify(eq)
+    if subs is not None:
+        return unpolarify(eq.subs(subs))
+    changed = True
+    pause = False
+    if exponents_only:
+        pause = True
+    while changed:
+        changed = False
+        res = _unpolarify(eq, exponents_only, pause)
+        if res != eq:
+            changed = True
+            eq = res
+        if isinstance(res, bool):
+            return res
+    # Finally, replacing Exp(0) by 1 is always correct.
+    # So is polar_lift(0) -> 0.
+    from sympy.functions.elementary.exponential import exp_polar
+    return res.subs({exp_polar(0): 1, polar_lift(0): 0})
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/exponential.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/exponential.py
new file mode 100644
index 0000000000000000000000000000000000000000..2bb0333cb34a35a96248c12a4640e848986f2feb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/exponential.py
@@ -0,0 +1,1286 @@
+from __future__ import annotations
+from itertools import product
+
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.expr import Expr
+from sympy.core.function import (DefinedFunction, ArgumentIndexError, expand_log,
+    expand_mul, FunctionClass, PoleError, expand_multinomial, expand_complex)
+from sympy.core.logic import fuzzy_and, fuzzy_not, fuzzy_or
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer, Rational, pi, I
+from sympy.core.parameters import global_parameters
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Wild, Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import arg, unpolarify, im, re, Abs
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.ntheory import multiplicity, perfect_power
+from sympy.ntheory.factor_ import factorint
+
+# NOTE IMPORTANT
+# The series expansion code in this file is an important part of the gruntz
+# algorithm for determining limits. _eval_nseries has to return a generalized
+# power series with coefficients in C(log(x), log).
+# In more detail, the result of _eval_nseries(self, x, n) must be
+#   c_0*x**e_0 + ... (finitely many terms)
+# where e_i are numbers (not necessarily integers) and c_i involve only
+# numbers, the function log, and log(x). [This also means it must not contain
+# log(x(1+p)), this *has* to be expanded to log(x)+log(1+p) if x.is_positive and
+# p.is_positive.]
+
+
+class ExpBase(DefinedFunction):
+
+    unbranched = True
+    _singularities = (S.ComplexInfinity,)
+
+    @property
+    def kind(self):
+        return self.exp.kind
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse function of ``exp(x)``.
+        """
+        return log
+
+    def as_numer_denom(self):
+        """
+        Returns this with a positive exponent as a 2-tuple (a fraction).
+
+        Examples
+        ========
+
+        >>> from sympy import exp
+        >>> from sympy.abc import x
+        >>> exp(-x).as_numer_denom()
+        (1, exp(x))
+        >>> exp(x).as_numer_denom()
+        (exp(x), 1)
+        """
+        # this should be the same as Pow.as_numer_denom wrt
+        # exponent handling
+        if not self.is_commutative:
+            return self, S.One
+        exp = self.exp
+        neg_exp = exp.is_negative
+        if not neg_exp and not (-exp).is_negative:
+            neg_exp = exp.could_extract_minus_sign()
+        if neg_exp:
+            return S.One, self.func(-exp)
+        return self, S.One
+
+    @property
+    def exp(self):
+        """
+        Returns the exponent of the function.
+        """
+        return self.args[0]
+
+    def as_base_exp(self):
+        """
+        Returns the 2-tuple (base, exponent).
+        """
+        return self.func(1), Mul(*self.args)
+
+    def _eval_adjoint(self):
+        return self.func(self.exp.adjoint())
+
+    def _eval_conjugate(self):
+        return self.func(self.exp.conjugate())
+
+    def _eval_transpose(self):
+        return self.func(self.exp.transpose())
+
+    def _eval_is_finite(self):
+        arg = self.exp
+        if arg.is_infinite:
+            if arg.is_extended_negative:
+                return True
+            if arg.is_extended_positive:
+                return False
+        if arg.is_finite:
+            return True
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            z = s.exp.is_zero
+            if z:
+                return True
+            elif s.exp.is_rational and fuzzy_not(z):
+                return False
+        else:
+            return s.is_rational
+
+    def _eval_is_zero(self):
+        return self.exp is S.NegativeInfinity
+
+    def _eval_power(self, other):
+        """exp(arg)**e -> exp(arg*e) if assumptions allow it.
+        """
+        b, e = self.as_base_exp()
+        return Pow._eval_power(Pow(b, e, evaluate=False), other)
+
+    def _eval_expand_power_exp(self, **hints):
+        from sympy.concrete.products import Product
+        from sympy.concrete.summations import Sum
+        arg = self.args[0]
+        if arg.is_Add and arg.is_commutative:
+            return Mul.fromiter(self.func(x) for x in arg.args)
+        elif isinstance(arg, Sum) and arg.is_commutative:
+            return Product(self.func(arg.function), *arg.limits)
+        return self.func(arg)
+
+
+class exp_polar(ExpBase):
+    r"""
+    Represent a *polar number* (see g-function Sphinx documentation).
+
+    Explanation
+    ===========
+
+    ``exp_polar`` represents the function
+    `Exp: \mathbb{C} \rightarrow \mathcal{S}`, sending the complex number
+    `z = a + bi` to the polar number `r = exp(a), \theta = b`. It is one of
+    the main functions to construct polar numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import exp_polar, pi, I, exp
+
+    The main difference is that polar numbers do not "wrap around" at `2 \pi`:
+
+    >>> exp(2*pi*I)
+    1
+    >>> exp_polar(2*pi*I)
+    exp_polar(2*I*pi)
+
+    apart from that they behave mostly like classical complex numbers:
+
+    >>> exp_polar(2)*exp_polar(3)
+    exp_polar(5)
+
+    See Also
+    ========
+
+    sympy.simplify.powsimp.powsimp
+    polar_lift
+    periodic_argument
+    principal_branch
+    """
+
+    is_polar = True
+    is_comparable = False  # cannot be evalf'd
+
+    def _eval_Abs(self):   # Abs is never a polar number
+        return exp(re(self.args[0]))
+
+    def _eval_evalf(self, prec):
+        """ Careful! any evalf of polar numbers is flaky """
+        i = im(self.args[0])
+        try:
+            bad = (i <= -pi or i > pi)
+        except TypeError:
+            bad = True
+        if bad:
+            return self  # cannot evalf for this argument
+        res = exp(self.args[0])._eval_evalf(prec)
+        if i > 0 and im(res) < 0:
+            # i ~ pi, but exp(I*i) evaluated to argument slightly bigger than pi
+            return re(res)
+        return res
+
+    def _eval_power(self, other):
+        return self.func(self.args[0]*other)
+
+    def _eval_is_extended_real(self):
+        if self.args[0].is_extended_real:
+            return True
+
+    def as_base_exp(self):
+        # XXX exp_polar(0) is special!
+        if self.args[0] == 0:
+            return self, S.One
+        return ExpBase.as_base_exp(self)
+
+
+class ExpMeta(FunctionClass):
+    def __instancecheck__(cls, instance):
+        if exp in instance.__class__.__mro__:
+            return True
+        return isinstance(instance, Pow) and instance.base is S.Exp1
+
+
+class exp(ExpBase, metaclass=ExpMeta):
+    """
+    The exponential function, :math:`e^x`.
+
+    Examples
+    ========
+
+    >>> from sympy import exp, I, pi
+    >>> from sympy.abc import x
+    >>> exp(x)
+    exp(x)
+    >>> exp(x).diff(x)
+    exp(x)
+    >>> exp(I*pi)
+    -1
+
+    Parameters
+    ==========
+
+    arg : Expr
+
+    See Also
+    ========
+
+    log
+    """
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return self
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_refine(self, assumptions):
+        from sympy.assumptions import ask, Q
+        arg = self.args[0]
+        if arg.is_Mul:
+            Ioo = I*S.Infinity
+            if arg in [Ioo, -Ioo]:
+                return S.NaN
+
+            coeff = arg.as_coefficient(pi*I)
+            if coeff:
+                if ask(Q.integer(2*coeff)):
+                    if ask(Q.even(coeff)):
+                        return S.One
+                    elif ask(Q.odd(coeff)):
+                        return S.NegativeOne
+                    elif ask(Q.even(coeff + S.Half)):
+                        return -I
+                    elif ask(Q.odd(coeff + S.Half)):
+                        return I
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.calculus import AccumBounds
+        from sympy.matrices.matrixbase import MatrixBase
+        from sympy.sets.setexpr import SetExpr
+        from sympy.simplify.simplify import logcombine
+        if isinstance(arg, MatrixBase):
+            return arg.exp()
+        elif global_parameters.exp_is_pow:
+            return Pow(S.Exp1, arg)
+        elif arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg.is_zero:
+                return S.One
+            elif arg is S.One:
+                return S.Exp1
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+        elif arg is S.ComplexInfinity:
+            return S.NaN
+        elif isinstance(arg, log):
+            return arg.args[0]
+        elif isinstance(arg, AccumBounds):
+            return AccumBounds(exp(arg.min), exp(arg.max))
+        elif isinstance(arg, SetExpr):
+            return arg._eval_func(cls)
+        elif arg.is_Mul:
+            coeff = arg.as_coefficient(pi*I)
+            if coeff:
+                if (2*coeff).is_integer:
+                    if coeff.is_even:
+                        return S.One
+                    elif coeff.is_odd:
+                        return S.NegativeOne
+                    elif (coeff + S.Half).is_even:
+                        return -I
+                    elif (coeff + S.Half).is_odd:
+                        return I
+                elif coeff.is_Rational:
+                    ncoeff = coeff % 2 # restrict to [0, 2pi)
+                    if ncoeff > 1: # restrict to (-pi, pi]
+                        ncoeff -= 2
+                    if ncoeff != coeff:
+                        return cls(ncoeff*pi*I)
+
+            # Warning: code in risch.py will be very sensitive to changes
+            # in this (see DifferentialExtension).
+
+            # look for a single log factor
+
+            coeff, terms = arg.as_coeff_Mul()
+
+            # but it can't be multiplied by oo
+            if coeff in [S.NegativeInfinity, S.Infinity]:
+                if terms.is_number:
+                    if coeff is S.NegativeInfinity:
+                        terms = -terms
+                    if re(terms).is_zero and terms is not S.Zero:
+                        return S.NaN
+                    if re(terms).is_positive and im(terms) is not S.Zero:
+                        return S.ComplexInfinity
+                    if re(terms).is_negative:
+                        return S.Zero
+                return None
+
+            coeffs, log_term = [coeff], None
+            for term in Mul.make_args(terms):
+                term_ = logcombine(term)
+                if isinstance(term_, log):
+                    if log_term is None:
+                        log_term = term_.args[0]
+                    else:
+                        return None
+                elif term.is_comparable:
+                    coeffs.append(term)
+                else:
+                    return None
+
+            return log_term**Mul(*coeffs) if log_term else None
+
+        elif arg.is_Add:
+            out = []
+            add = []
+            argchanged = False
+            for a in arg.args:
+                if a is S.One:
+                    add.append(a)
+                    continue
+                newa = cls(a)
+                if isinstance(newa, cls):
+                    if newa.args[0] != a:
+                        add.append(newa.args[0])
+                        argchanged = True
+                    else:
+                        add.append(a)
+                else:
+                    out.append(newa)
+            if out or argchanged:
+                return Mul(*out)*cls(Add(*add), evaluate=False)
+
+        if arg.is_zero:
+            return S.One
+
+    @property
+    def base(self):
+        """
+        Returns the base of the exponential function.
+        """
+        return S.Exp1
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        """
+        Calculates the next term in the Taylor series expansion.
+        """
+        if n < 0:
+            return S.Zero
+        if n == 0:
+            return S.One
+        x = sympify(x)
+        if previous_terms:
+            p = previous_terms[-1]
+            if p is not None:
+                return p * x / n
+        return x**n/factorial(n)
+
+    def as_real_imag(self, deep=True, **hints):
+        """
+        Returns this function as a 2-tuple representing a complex number.
+
+        Examples
+        ========
+
+        >>> from sympy import exp, I
+        >>> from sympy.abc import x
+        >>> exp(x).as_real_imag()
+        (exp(re(x))*cos(im(x)), exp(re(x))*sin(im(x)))
+        >>> exp(1).as_real_imag()
+        (E, 0)
+        >>> exp(I).as_real_imag()
+        (cos(1), sin(1))
+        >>> exp(1+I).as_real_imag()
+        (E*cos(1), E*sin(1))
+
+        See Also
+        ========
+
+        sympy.functions.elementary.complexes.re
+        sympy.functions.elementary.complexes.im
+        """
+        from sympy.functions.elementary.trigonometric import cos, sin
+        re, im = self.args[0].as_real_imag()
+        if deep:
+            re = re.expand(deep, **hints)
+            im = im.expand(deep, **hints)
+        cos, sin = cos(im), sin(im)
+        return (exp(re)*cos, exp(re)*sin)
+
+    def _eval_subs(self, old, new):
+        # keep processing of power-like args centralized in Pow
+        if old.is_Pow:  # handle (exp(3*log(x))).subs(x**2, z) -> z**(3/2)
+            old = exp(old.exp*log(old.base))
+        elif old is S.Exp1 and new.is_Function:
+            old = exp
+        if isinstance(old, exp) or old is S.Exp1:
+            f = lambda a: Pow(*a.as_base_exp(), evaluate=False) if (
+                a.is_Pow or isinstance(a, exp)) else a
+            return Pow._eval_subs(f(self), f(old), new)
+
+        if old is exp and not new.is_Function:
+            return new**self.exp._subs(old, new)
+        return super()._eval_subs(old, new)
+
+    def _eval_is_extended_real(self):
+        if self.args[0].is_extended_real:
+            return True
+        elif self.args[0].is_imaginary:
+            arg2 = -S(2) * I * self.args[0] / pi
+            return arg2.is_even
+
+    def _eval_is_complex(self):
+        def complex_extended_negative(arg):
+            yield arg.is_complex
+            yield arg.is_extended_negative
+        return fuzzy_or(complex_extended_negative(self.args[0]))
+
+    def _eval_is_algebraic(self):
+        if (self.exp / pi / I).is_rational:
+            return True
+        if fuzzy_not(self.exp.is_zero):
+            if self.exp.is_algebraic:
+                return False
+            elif (self.exp / pi).is_rational:
+                return False
+
+    def _eval_is_extended_positive(self):
+        if self.exp.is_extended_real:
+            return self.args[0] is not S.NegativeInfinity
+        elif self.exp.is_imaginary:
+            arg2 = -I * self.args[0] / pi
+            return arg2.is_even
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # NOTE Please see the comment at the beginning of this file, labelled
+        #      IMPORTANT.
+        from sympy.functions.elementary.complexes import sign
+        from sympy.functions.elementary.integers import ceiling
+        from sympy.series.limits import limit
+        from sympy.series.order import Order
+        from sympy.simplify.powsimp import powsimp
+        arg = self.exp
+        arg_series = arg._eval_nseries(x, n=n, logx=logx)
+        if arg_series.is_Order:
+            return 1 + arg_series
+        arg0 = limit(arg_series.removeO(), x, 0)
+        if arg0 is S.NegativeInfinity:
+            return Order(x**n, x)
+        if arg0 is S.Infinity:
+            return self
+        if arg0.is_infinite:
+            raise PoleError("Cannot expand %s around 0" % (self))
+        # checking for indecisiveness/ sign terms in arg0
+        if any(isinstance(arg, sign) for arg in arg0.args):
+            return self
+        t = Dummy("t")
+        nterms = n
+        try:
+            cf = Order(arg.as_leading_term(x, logx=logx), x).getn()
+        except (NotImplementedError, PoleError):
+            cf = 0
+        if cf and cf > 0:
+            nterms = ceiling(n/cf)
+        exp_series = exp(t)._taylor(t, nterms)
+        r = exp(arg0)*exp_series.subs(t, arg_series - arg0)
+        rep = {logx: log(x)} if logx is not None else {}
+        if r.subs(rep) == self:
+            return r
+        if cf and cf > 1:
+            r += Order((arg_series - arg0)**n, x)/x**((cf-1)*n)
+        else:
+            r += Order((arg_series - arg0)**n, x)
+        r = r.expand()
+        r = powsimp(r, deep=True, combine='exp')
+        # powsimp may introduce unexpanded (-1)**Rational; see PR #17201
+        simplerat = lambda x: x.is_Rational and x.q in [3, 4, 6]
+        w = Wild('w', properties=[simplerat])
+        r = r.replace(S.NegativeOne**w, expand_complex(S.NegativeOne**w))
+        return r
+
+    def _taylor(self, x, n):
+        l = []
+        g = None
+        for i in range(n):
+            g = self.taylor_term(i, self.args[0], g)
+            g = g.nseries(x, n=n)
+            l.append(g.removeO())
+        return Add(*l)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.util import AccumBounds
+        arg = self.args[0].cancel().as_leading_term(x, logx=logx)
+        arg0 = arg.subs(x, 0)
+        if arg is S.NaN:
+            return S.NaN
+        if isinstance(arg0, AccumBounds):
+            # This check addresses a corner case involving AccumBounds.
+            # if isinstance(arg, AccumBounds) is True, then arg0 can either be 0,
+            # AccumBounds(-oo, 0) or AccumBounds(-oo, oo).
+            # Check out function: test_issue_18473() in test_exponential.py and
+            # test_limits.py for more information.
+            if re(cdir) < S.Zero:
+                return exp(-arg0)
+            return exp(arg0)
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0)
+        if arg0.is_infinite is False:
+            return exp(arg0)
+        raise PoleError("Cannot expand %s around 0" % (self))
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        from sympy.functions.elementary.trigonometric import sin
+        return sin(I*arg + pi/2) - I*sin(I*arg)
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        from sympy.functions.elementary.trigonometric import cos
+        return cos(I*arg) + I*cos(I*arg + pi/2)
+
+    def _eval_rewrite_as_tanh(self, arg, **kwargs):
+        from sympy.functions.elementary.hyperbolic import tanh
+        return (1 + tanh(arg/2))/(1 - tanh(arg/2))
+
+    def _eval_rewrite_as_sqrt(self, arg, **kwargs):
+        from sympy.functions.elementary.trigonometric import sin, cos
+        if arg.is_Mul:
+            coeff = arg.coeff(pi*I)
+            if coeff and coeff.is_number:
+                cosine, sine = cos(pi*coeff), sin(pi*coeff)
+                if not isinstance(cosine, cos) and not isinstance (sine, sin):
+                    return cosine + I*sine
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        if arg.is_Mul:
+            logs = [a for a in arg.args if isinstance(a, log) and len(a.args) == 1]
+            if logs:
+                return Pow(logs[0].args[0], arg.coeff(logs[0]))
+
+
+def match_real_imag(expr):
+    r"""
+    Try to match expr with $a + Ib$ for real $a$ and $b$.
+
+    ``match_real_imag`` returns a tuple containing the real and imaginary
+    parts of expr or ``(None, None)`` if direct matching is not possible. Contrary
+    to :func:`~.re`, :func:`~.im``, and ``as_real_imag()``, this helper will not force things
+    by returning expressions themselves containing ``re()`` or ``im()`` and it
+    does not expand its argument either.
+
+    """
+    r_, i_ = expr.as_independent(I, as_Add=True)
+    if i_ == 0 and r_.is_real:
+        return (r_, i_)
+    i_ = i_.as_coefficient(I)
+    if i_ and i_.is_real and r_.is_real:
+        return (r_, i_)
+    else:
+        return (None, None) # simpler to check for than None
+
+
+class log(DefinedFunction):
+    r"""
+    The natural logarithm function `\ln(x)` or `\log(x)`.
+
+    Explanation
+    ===========
+
+    Logarithms are taken with the natural base, `e`. To get
+    a logarithm of a different base ``b``, use ``log(x, b)``,
+    which is essentially short-hand for ``log(x)/log(b)``.
+
+    ``log`` represents the principal branch of the natural
+    logarithm. As such it has a branch cut along the negative
+    real axis and returns values having a complex argument in
+    `(-\pi, \pi]`.
+
+    Examples
+    ========
+
+    >>> from sympy import log, sqrt, S, I
+    >>> log(8, 2)
+    3
+    >>> log(S(8)/3, 2)
+    -log(3)/log(2) + 3
+    >>> log(-1 + I*sqrt(3))
+    log(2) + 2*I*pi/3
+
+    See Also
+    ========
+
+    exp
+
+    """
+
+    args: tuple[Expr]
+
+    _singularities = (S.Zero, S.ComplexInfinity)
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of the function.
+        """
+        if argindex == 1:
+            return 1/self.args[0]
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        r"""
+        Returns `e^x`, the inverse function of `\log(x)`.
+        """
+        return exp
+
+    @classmethod
+    def eval(cls, arg, base=None):
+        from sympy.calculus import AccumBounds
+        from sympy.sets.setexpr import SetExpr
+
+        arg = sympify(arg)
+
+        if base is not None:
+            base = sympify(base)
+            if base == 1:
+                if arg == 1:
+                    return S.NaN
+                else:
+                    return S.ComplexInfinity
+            try:
+                # handle extraction of powers of the base now
+                # or else expand_log in Mul would have to handle this
+                n = multiplicity(base, arg)
+                if n:
+                    return n + log(arg / base**n) / log(base)
+                else:
+                    return log(arg)/log(base)
+            except ValueError:
+                pass
+            if base is not S.Exp1:
+                return cls(arg)/cls(base)
+            else:
+                return cls(arg)
+
+        if arg.is_Number:
+            if arg.is_zero:
+                return S.ComplexInfinity
+            elif arg is S.One:
+                return S.Zero
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.Infinity
+            elif arg is S.NaN:
+                return S.NaN
+            elif arg.is_Rational and arg.p == 1:
+                return -cls(arg.q)
+
+        if arg.is_Pow and arg.base is S.Exp1 and arg.exp.is_extended_real:
+            return arg.exp
+        if isinstance(arg, exp) and arg.exp.is_extended_real:
+            return arg.exp
+        elif isinstance(arg, exp) and arg.exp.is_number:
+            r_, i_ = match_real_imag(arg.exp)
+            if i_ and i_.is_comparable:
+                i_ %= 2*pi
+                if i_ > pi:
+                    i_ -= 2*pi
+                return r_ + expand_mul(i_ * I, deep=False)
+        elif isinstance(arg, exp_polar):
+            return unpolarify(arg.exp)
+        elif isinstance(arg, AccumBounds):
+            if arg.min.is_positive:
+                return AccumBounds(log(arg.min), log(arg.max))
+            elif arg.min.is_zero:
+                return AccumBounds(S.NegativeInfinity, log(arg.max))
+            else:
+                return S.NaN
+        elif isinstance(arg, SetExpr):
+            return arg._eval_func(cls)
+
+        if arg.is_number:
+            if arg.is_negative:
+                return pi * I + cls(-arg)
+            elif arg is S.ComplexInfinity:
+                return S.ComplexInfinity
+            elif arg is S.Exp1:
+                return S.One
+
+        if arg.is_zero:
+            return S.ComplexInfinity
+
+        # don't autoexpand Pow or Mul (see the issue 3351):
+        if not arg.is_Add:
+            coeff = arg.as_coefficient(I)
+
+            if coeff is not None:
+                if coeff is S.Infinity:
+                    return S.Infinity
+                elif coeff is S.NegativeInfinity:
+                    return S.Infinity
+                elif coeff.is_Rational:
+                    if coeff.is_nonnegative:
+                        return pi * I * S.Half + cls(coeff)
+                    else:
+                        return -pi * I * S.Half + cls(-coeff)
+
+        if arg.is_number and arg.is_algebraic:
+            # Match arg = coeff*(r_ + i_*I) with coeff>0, r_ and i_ real.
+            coeff, arg_ = arg.as_independent(I, as_Add=False)
+            if coeff.is_negative:
+                coeff *= -1
+                arg_ *= -1
+            arg_ = expand_mul(arg_, deep=False)
+            r_, i_ = arg_.as_independent(I, as_Add=True)
+            i_ = i_.as_coefficient(I)
+            if coeff.is_real and i_ and i_.is_real and r_.is_real:
+                if r_.is_zero:
+                    if i_.is_positive:
+                        return pi * I * S.Half + cls(coeff * i_)
+                    elif i_.is_negative:
+                        return -pi * I * S.Half + cls(coeff * -i_)
+                else:
+                    from sympy.simplify import ratsimp
+                    # Check for arguments involving rational multiples of pi
+                    t = (i_/r_).cancel()
+                    t1 = (-t).cancel()
+                    atan_table = _log_atan_table()
+                    if t in atan_table:
+                        modulus = ratsimp(coeff * Abs(arg_))
+                        if r_.is_positive:
+                            return cls(modulus) + I * atan_table[t]
+                        else:
+                            return cls(modulus) + I * (atan_table[t] - pi)
+                    elif t1 in atan_table:
+                        modulus = ratsimp(coeff * Abs(arg_))
+                        if r_.is_positive:
+                            return cls(modulus) + I * (-atan_table[t1])
+                        else:
+                            return cls(modulus) + I * (pi - atan_table[t1])
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):  # of log(1+x)
+        r"""
+        Returns the next term in the Taylor series expansion of `\log(1+x)`.
+        """
+        from sympy.simplify.powsimp import powsimp
+        if n < 0:
+            return S.Zero
+        x = sympify(x)
+        if n == 0:
+            return x
+        if previous_terms:
+            p = previous_terms[-1]
+            if p is not None:
+                return powsimp((-n) * p * x / (n + 1), deep=True, combine='exp')
+        return (1 - 2*(n % 2)) * x**(n + 1)/(n + 1)
+
+    def _eval_expand_log(self, deep=True, **hints):
+        from sympy.concrete import Sum, Product
+        force = hints.get('force', False)
+        factor = hints.get('factor', False)
+        if (len(self.args) == 2):
+            return expand_log(self.func(*self.args), deep=deep, force=force)
+        arg = self.args[0]
+        if arg.is_Integer:
+            # remove perfect powers
+            p = perfect_power(arg)
+            logarg = None
+            coeff = 1
+            if p is not False:
+                arg, coeff = p
+                logarg = self.func(arg)
+            # expand as product of its prime factors if factor=True
+            if factor:
+                p = factorint(arg)
+                if arg not in p.keys():
+                    logarg = sum(n*log(val) for val, n in p.items())
+            if logarg is not None:
+                return coeff*logarg
+        elif arg.is_Rational:
+            return log(arg.p) - log(arg.q)
+        elif arg.is_Mul:
+            expr = []
+            nonpos = []
+            for x in arg.args:
+                if force or x.is_positive or x.is_polar:
+                    a = self.func(x)
+                    if isinstance(a, log):
+                        expr.append(self.func(x)._eval_expand_log(**hints))
+                    else:
+                        expr.append(a)
+                elif x.is_negative:
+                    a = self.func(-x)
+                    expr.append(a)
+                    nonpos.append(S.NegativeOne)
+                else:
+                    nonpos.append(x)
+            return Add(*expr) + log(Mul(*nonpos))
+        elif arg.is_Pow or isinstance(arg, exp):
+            if force or (arg.exp.is_extended_real and (arg.base.is_positive or ((arg.exp+1)
+                .is_positive and (arg.exp-1).is_nonpositive))) or arg.base.is_polar:
+                b = arg.base
+                e = arg.exp
+                a = self.func(b)
+                if isinstance(a, log):
+                    return unpolarify(e) * a._eval_expand_log(**hints)
+                else:
+                    return unpolarify(e) * a
+        elif isinstance(arg, Product):
+            if force or arg.function.is_positive:
+                return Sum(log(arg.function), *arg.limits)
+
+        return self.func(arg)
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.simplify.simplify import expand_log, simplify, inversecombine
+        if len(self.args) == 2:  # it's unevaluated
+            return simplify(self.func(*self.args), **kwargs)
+
+        expr = self.func(simplify(self.args[0], **kwargs))
+        if kwargs['inverse']:
+            expr = inversecombine(expr)
+        expr = expand_log(expr, deep=True)
+        return min([expr, self], key=kwargs['measure'])
+
+    def as_real_imag(self, deep=True, **hints):
+        """
+        Returns this function as a complex coordinate.
+
+        Examples
+        ========
+
+        >>> from sympy import I, log
+        >>> from sympy.abc import x
+        >>> log(x).as_real_imag()
+        (log(Abs(x)), arg(x))
+        >>> log(I).as_real_imag()
+        (0, pi/2)
+        >>> log(1 + I).as_real_imag()
+        (log(sqrt(2)), pi/4)
+        >>> log(I*x).as_real_imag()
+        (log(Abs(x)), arg(I*x))
+
+        """
+        sarg = self.args[0]
+        if deep:
+            sarg = self.args[0].expand(deep, **hints)
+        sarg_abs = Abs(sarg)
+        if sarg_abs == sarg:
+            return self, S.Zero
+        sarg_arg = arg(sarg)
+        if hints.get('log', False):  # Expand the log
+            hints['complex'] = False
+            return (log(sarg_abs).expand(deep, **hints), sarg_arg)
+        else:
+            return log(sarg_abs), sarg_arg
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if (self.args[0] - 1).is_zero:
+                return True
+            if s.args[0].is_rational and fuzzy_not((self.args[0] - 1).is_zero):
+                return False
+        else:
+            return s.is_rational
+
+    def _eval_is_algebraic(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if (self.args[0] - 1).is_zero:
+                return True
+            elif fuzzy_not((self.args[0] - 1).is_zero):
+                if self.args[0].is_algebraic:
+                    return False
+        else:
+            return s.is_algebraic
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_positive
+
+    def _eval_is_complex(self):
+        z = self.args[0]
+        return fuzzy_and([z.is_complex, fuzzy_not(z.is_zero)])
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+        if arg.is_zero:
+            return False
+        return arg.is_finite
+
+    def _eval_is_extended_positive(self):
+        return (self.args[0] - 1).is_extended_positive
+
+    def _eval_is_zero(self):
+        return (self.args[0] - 1).is_zero
+
+    def _eval_is_extended_nonnegative(self):
+        return (self.args[0] - 1).is_extended_nonnegative
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # NOTE Please see the comment at the beginning of this file, labelled
+        #      IMPORTANT.
+        from sympy.series.order import Order
+        from sympy.simplify.simplify import logcombine
+        from sympy.core.symbol import Dummy
+
+        if self.args[0] == x:
+            return log(x) if logx is None else logx
+        arg = self.args[0]
+        t = Dummy('t', positive=True)
+        if cdir == 0:
+            cdir = 1
+        z = arg.subs(x, cdir*t)
+
+        k, l = Wild("k"), Wild("l")
+        r = z.match(k*t**l)
+        if r is not None:
+            k, l = r[k], r[l]
+            if l != 0 and not l.has(t) and not k.has(t):
+                r = l*log(x) if logx is None else l*logx
+                r += log(k) - l*log(cdir) # XXX true regardless of assumptions?
+                return r
+
+        def coeff_exp(term, x):
+            coeff, exp = S.One, S.Zero
+            for factor in Mul.make_args(term):
+                if factor.has(x):
+                    base, exp = factor.as_base_exp()
+                    if base != x:
+                        try:
+                            return term.leadterm(x)
+                        except ValueError:
+                            return term, S.Zero
+                else:
+                    coeff *= factor
+            return coeff, exp
+
+        # TODO new and probably slow
+        try:
+            a, b = z.leadterm(t, logx=logx, cdir=1)
+        except (ValueError, NotImplementedError, PoleError):
+            s = z._eval_nseries(t, n=n, logx=logx, cdir=1)
+            while s.is_Order:
+                n += 1
+                s = z._eval_nseries(t, n=n, logx=logx, cdir=1)
+            try:
+                a, b = s.removeO().leadterm(t, cdir=1)
+            except ValueError:
+                a, b = s.removeO().as_leading_term(t, cdir=1), S.Zero
+
+        p = (z/(a*t**b) - 1).cancel()._eval_nseries(t, n=n, logx=logx, cdir=1)
+        if p.has(exp):
+            p = logcombine(p)
+        if isinstance(p, Order):
+            n = p.getn()
+        _, d = coeff_exp(p, t)
+        logx = log(x) if logx is None else logx
+
+        if not d.is_positive:
+            res = log(a) - b*log(cdir) + b*logx
+            _res = res
+            logflags = {"deep": True, "log": True, "mul": False, "power_exp": False,
+                "power_base": False, "multinomial": False, "basic": False, "force": True,
+                "factor": False}
+            expr = self.expand(**logflags)
+            if (not a.could_extract_minus_sign() and
+                logx.could_extract_minus_sign()):
+                _res = _res.subs(-logx, -log(x)).expand(**logflags)
+            else:
+                _res = _res.subs(logx, log(x)).expand(**logflags)
+            if _res == expr:
+                return res
+            return res + Order(x**n, x)
+
+        def mul(d1, d2):
+            res = {}
+            for e1, e2 in product(d1, d2):
+                ex = e1 + e2
+                if ex < n:
+                    res[ex] = res.get(ex, S.Zero) + d1[e1]*d2[e2]
+            return res
+
+        pterms = {}
+
+        for term in Add.make_args(p.removeO()):
+            co1, e1 = coeff_exp(term, t)
+            pterms[e1] = pterms.get(e1, S.Zero) + co1
+
+        k = S.One
+        terms = {}
+        pk = pterms
+
+        while k*d < n:
+            coeff = -S.NegativeOne**k/k
+            for ex in pk:
+                terms[ex] = terms.get(ex, S.Zero) + coeff*pk[ex]
+            pk = mul(pk, pterms)
+            k += S.One
+
+        res = log(a) - b*log(cdir) + b*logx
+        for ex in terms:
+            res += terms[ex].cancel()*t**(ex)
+
+        if a.is_negative and im(z) != 0:
+            from sympy.functions.special.delta_functions import Heaviside
+            for i, term in enumerate(z.lseries(t)):
+                if not term.is_real or i == 5:
+                    break
+            if i < 5:
+                coeff, _ = term.as_coeff_exponent(t)
+                res += -2*I*pi*Heaviside(-im(coeff), 0)
+
+        res = res.subs(t, x/cdir)
+        return res + Order(x**n, x)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        # NOTE
+        # Refer https://github.com/sympy/sympy/pull/23592 for more information
+        # on each of the following steps involved in this method.
+        arg0 = self.args[0].together()
+
+        # STEP 1
+        t = Dummy('t', positive=True)
+        if cdir == 0:
+            cdir = 1
+        z = arg0.subs(x, cdir*t)
+
+        # STEP 2
+        try:
+            c, e = z.leadterm(t, logx=logx, cdir=1)
+        except ValueError:
+            arg = arg0.as_leading_term(x, logx=logx, cdir=cdir)
+            return log(arg)
+        if c.has(t):
+            c = c.subs(t, x/cdir)
+            if e != 0:
+                raise PoleError("Cannot expand %s around 0" % (self))
+            return log(c)
+
+        # STEP 3
+        if c == S.One and e == S.Zero:
+            return (arg0 - S.One).as_leading_term(x, logx=logx)
+
+        # STEP 4
+        res = log(c) - e*log(cdir)
+        logx = log(x) if logx is None else logx
+        res += e*logx
+
+        # STEP 5
+        if c.is_negative and im(z) != 0:
+            from sympy.functions.special.delta_functions import Heaviside
+            for i, term in enumerate(z.lseries(t)):
+                if not term.is_real or i == 5:
+                    break
+            if i < 5:
+                coeff, _ = term.as_coeff_exponent(t)
+                res += -2*I*pi*Heaviside(-im(coeff), 0)
+        return res
+
+
+class LambertW(DefinedFunction):
+    r"""
+    The Lambert W function $W(z)$ is defined as the inverse
+    function of $w \exp(w)$ [1]_.
+
+    Explanation
+    ===========
+
+    In other words, the value of $W(z)$ is such that $z = W(z) \exp(W(z))$
+    for any complex number $z$.  The Lambert W function is a multivalued
+    function with infinitely many branches $W_k(z)$, indexed by
+    $k \in \mathbb{Z}$.  Each branch gives a different solution $w$
+    of the equation $z = w \exp(w)$.
+
+    The Lambert W function has two partially real branches: the
+    principal branch ($k = 0$) is real for real $z > -1/e$, and the
+    $k = -1$ branch is real for $-1/e < z < 0$. All branches except
+    $k = 0$ have a logarithmic singularity at $z = 0$.
+
+    Examples
+    ========
+
+    >>> from sympy import LambertW
+    >>> LambertW(1.2)
+    0.635564016364870
+    >>> LambertW(1.2, -1).n()
+    -1.34747534407696 - 4.41624341514535*I
+    >>> LambertW(-1).is_real
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Lambert_W_function
+    """
+    _singularities = (-Pow(S.Exp1, -1, evaluate=False), S.ComplexInfinity)
+
+    @classmethod
+    def eval(cls, x, k=None):
+        if k == S.Zero:
+            return cls(x)
+        elif k is None:
+            k = S.Zero
+
+        if k.is_zero:
+            if x.is_zero:
+                return S.Zero
+            if x is S.Exp1:
+                return S.One
+            if x == -1/S.Exp1:
+                return S.NegativeOne
+            if x == -log(2)/2:
+                return -log(2)
+            if x == 2*log(2):
+                return log(2)
+            if x == -pi/2:
+                return I*pi/2
+            if x == exp(1 + S.Exp1):
+                return S.Exp1
+            if x is S.Infinity:
+                return S.Infinity
+
+        if fuzzy_not(k.is_zero):
+            if x.is_zero:
+                return S.NegativeInfinity
+        if k is S.NegativeOne:
+            if x == -pi/2:
+                return -I*pi/2
+            elif x == -1/S.Exp1:
+                return S.NegativeOne
+            elif x == -2*exp(-2):
+                return -Integer(2)
+
+    def fdiff(self, argindex=1):
+        """
+        Return the first derivative of this function.
+        """
+        x = self.args[0]
+
+        if len(self.args) == 1:
+            if argindex == 1:
+                return LambertW(x)/(x*(1 + LambertW(x)))
+        else:
+            k = self.args[1]
+            if argindex == 1:
+                return LambertW(x, k)/(x*(1 + LambertW(x, k)))
+
+        raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_extended_real(self):
+        x = self.args[0]
+        if len(self.args) == 1:
+            k = S.Zero
+        else:
+            k = self.args[1]
+        if k.is_zero:
+            if (x + 1/S.Exp1).is_positive:
+                return True
+            elif (x + 1/S.Exp1).is_nonpositive:
+                return False
+        elif (k + 1).is_zero:
+            if x.is_negative and (x + 1/S.Exp1).is_positive:
+                return True
+            elif x.is_nonpositive or (x + 1/S.Exp1).is_nonnegative:
+                return False
+        elif fuzzy_not(k.is_zero) and fuzzy_not((k + 1).is_zero):
+            if x.is_extended_real:
+                return False
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+    def _eval_is_algebraic(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if fuzzy_not(self.args[0].is_zero) and self.args[0].is_algebraic:
+                return False
+        else:
+            return s.is_algebraic
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        if len(self.args) == 1:
+            arg = self.args[0]
+            arg0 = arg.subs(x, 0).cancel()
+            if not arg0.is_zero:
+                return self.func(arg0)
+            return arg.as_leading_term(x)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        if len(self.args) == 1:
+            from sympy.functions.elementary.integers import ceiling
+            from sympy.series.order import Order
+            arg = self.args[0].nseries(x, n=n, logx=logx)
+            lt = arg.as_leading_term(x, logx=logx)
+            lte = 1
+            if lt.is_Pow:
+                lte = lt.exp
+            if ceiling(n/lte) >= 1:
+                s = Add(*[(-S.One)**(k - 1)*Integer(k)**(k - 2)/
+                          factorial(k - 1)*arg**k for k in range(1, ceiling(n/lte))])
+                s = expand_multinomial(s)
+            else:
+                s = S.Zero
+
+            return s + Order(x**n, x)
+        return super()._eval_nseries(x, n, logx)
+
+    def _eval_is_zero(self):
+        x = self.args[0]
+        if len(self.args) == 1:
+            return x.is_zero
+        else:
+            return fuzzy_and([x.is_zero, self.args[1].is_zero])
+
+
+@cacheit
+def _log_atan_table():
+    return {
+        # first quadrant only
+        sqrt(3): pi / 3,
+        1: pi / 4,
+        sqrt(5 - 2 * sqrt(5)): pi / 5,
+        sqrt(2) * sqrt(5 - sqrt(5)) / (1 + sqrt(5)): pi / 5,
+        sqrt(5 + 2 * sqrt(5)): pi * Rational(2, 5),
+        sqrt(2) * sqrt(sqrt(5) + 5) / (-1 + sqrt(5)): pi * Rational(2, 5),
+        sqrt(3) / 3: pi / 6,
+        sqrt(2) - 1: pi / 8,
+        sqrt(2 - sqrt(2)) / sqrt(sqrt(2) + 2): pi / 8,
+        sqrt(2) + 1: pi * Rational(3, 8),
+        sqrt(sqrt(2) + 2) / sqrt(2 - sqrt(2)): pi * Rational(3, 8),
+        sqrt(1 - 2 * sqrt(5) / 5): pi / 10,
+        (-sqrt(2) + sqrt(10)) / (2 * sqrt(sqrt(5) + 5)): pi / 10,
+        sqrt(1 + 2 * sqrt(5) / 5): pi * Rational(3, 10),
+        (sqrt(2) + sqrt(10)) / (2 * sqrt(5 - sqrt(5))): pi * Rational(3, 10),
+        2 - sqrt(3): pi / 12,
+        (-1 + sqrt(3)) / (1 + sqrt(3)): pi / 12,
+        2 + sqrt(3): pi * Rational(5, 12),
+        (1 + sqrt(3)) / (-1 + sqrt(3)): pi * Rational(5, 12)
+    }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/hyperbolic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/hyperbolic.py
new file mode 100644
index 0000000000000000000000000000000000000000..1031d035373bb641d26e61a395e6048906285bfe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/hyperbolic.py
@@ -0,0 +1,2285 @@
+from sympy.core import S, sympify, cacheit
+from sympy.core.add import Add
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.logic import fuzzy_or, fuzzy_and, fuzzy_not, FuzzyBool
+from sympy.core.numbers import I, pi, Rational
+from sympy.core.symbol import Dummy
+from sympy.functions.combinatorial.factorials import (binomial, factorial,
+                                                      RisingFactorial)
+from sympy.functions.combinatorial.numbers import bernoulli, euler, nC
+from sympy.functions.elementary.complexes import Abs, im, re
+from sympy.functions.elementary.exponential import exp, log, match_real_imag
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (
+    acos, acot, asin, atan, cos, cot, csc, sec, sin, tan,
+    _imaginary_unit_as_coefficient)
+from sympy.polys.specialpolys import symmetric_poly
+
+
+def _rewrite_hyperbolics_as_exp(expr):
+    return expr.xreplace({h: h.rewrite(exp)
+        for h in expr.atoms(HyperbolicFunction)})
+
+
+@cacheit
+def _acosh_table():
+    return {
+        I: log(I*(1 + sqrt(2))),
+        -I: log(-I*(1 + sqrt(2))),
+        S.Half: pi/3,
+        Rational(-1, 2): pi*Rational(2, 3),
+        sqrt(2)/2: pi/4,
+        -sqrt(2)/2: pi*Rational(3, 4),
+        1/sqrt(2): pi/4,
+        -1/sqrt(2): pi*Rational(3, 4),
+        sqrt(3)/2: pi/6,
+        -sqrt(3)/2: pi*Rational(5, 6),
+        (sqrt(3) - 1)/sqrt(2**3): pi*Rational(5, 12),
+        -(sqrt(3) - 1)/sqrt(2**3): pi*Rational(7, 12),
+        sqrt(2 + sqrt(2))/2: pi/8,
+        -sqrt(2 + sqrt(2))/2: pi*Rational(7, 8),
+        sqrt(2 - sqrt(2))/2: pi*Rational(3, 8),
+        -sqrt(2 - sqrt(2))/2: pi*Rational(5, 8),
+        (1 + sqrt(3))/(2*sqrt(2)): pi/12,
+        -(1 + sqrt(3))/(2*sqrt(2)): pi*Rational(11, 12),
+        (sqrt(5) + 1)/4: pi/5,
+        -(sqrt(5) + 1)/4: pi*Rational(4, 5)
+    }
+
+
+@cacheit
+def _acsch_table():
+    return {
+            I: -pi / 2,
+            I*(sqrt(2) + sqrt(6)): -pi / 12,
+            I*(1 + sqrt(5)): -pi / 10,
+            I*2 / sqrt(2 - sqrt(2)): -pi / 8,
+            I*2: -pi / 6,
+            I*sqrt(2 + 2/sqrt(5)): -pi / 5,
+            I*sqrt(2): -pi / 4,
+            I*(sqrt(5)-1): -3*pi / 10,
+            I*2 / sqrt(3): -pi / 3,
+            I*2 / sqrt(2 + sqrt(2)): -3*pi / 8,
+            I*sqrt(2 - 2/sqrt(5)): -2*pi / 5,
+            I*(sqrt(6) - sqrt(2)): -5*pi / 12,
+            S(2): -I*log((1+sqrt(5))/2),
+        }
+
+
+@cacheit
+def _asech_table():
+        return {
+            I: - (pi*I / 2) + log(1 + sqrt(2)),
+            -I: (pi*I / 2) + log(1 + sqrt(2)),
+            (sqrt(6) - sqrt(2)): pi / 12,
+            (sqrt(2) - sqrt(6)): 11*pi / 12,
+            sqrt(2 - 2/sqrt(5)): pi / 10,
+            -sqrt(2 - 2/sqrt(5)): 9*pi / 10,
+            2 / sqrt(2 + sqrt(2)): pi / 8,
+            -2 / sqrt(2 + sqrt(2)): 7*pi / 8,
+            2 / sqrt(3): pi / 6,
+            -2 / sqrt(3): 5*pi / 6,
+            (sqrt(5) - 1): pi / 5,
+            (1 - sqrt(5)): 4*pi / 5,
+            sqrt(2): pi / 4,
+            -sqrt(2): 3*pi / 4,
+            sqrt(2 + 2/sqrt(5)): 3*pi / 10,
+            -sqrt(2 + 2/sqrt(5)): 7*pi / 10,
+            S(2): pi / 3,
+            -S(2): 2*pi / 3,
+            sqrt(2*(2 + sqrt(2))): 3*pi / 8,
+            -sqrt(2*(2 + sqrt(2))): 5*pi / 8,
+            (1 + sqrt(5)): 2*pi / 5,
+            (-1 - sqrt(5)): 3*pi / 5,
+            (sqrt(6) + sqrt(2)): 5*pi / 12,
+            (-sqrt(6) - sqrt(2)): 7*pi / 12,
+            I*S.Infinity: -pi*I / 2,
+            I*S.NegativeInfinity: pi*I / 2,
+        }
+
+###############################################################################
+########################### HYPERBOLIC FUNCTIONS ##############################
+###############################################################################
+
+
+class HyperbolicFunction(DefinedFunction):
+    """
+    Base class for hyperbolic functions.
+
+    See Also
+    ========
+
+    sinh, cosh, tanh, coth
+    """
+
+    unbranched = True
+
+
+def _peeloff_ipi(arg):
+    r"""
+    Split ARG into two parts, a "rest" and a multiple of $I\pi$.
+    This assumes ARG to be an ``Add``.
+    The multiple of $I\pi$ returned in the second position is always a ``Rational``.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.elementary.hyperbolic import _peeloff_ipi as peel
+    >>> from sympy import pi, I
+    >>> from sympy.abc import x, y
+    >>> peel(x + I*pi/2)
+    (x, 1/2)
+    >>> peel(x + I*2*pi/3 + I*pi*y)
+    (x + I*pi*y + I*pi/6, 1/2)
+    """
+    ipi = pi*I
+    for a in Add.make_args(arg):
+        if a == ipi:
+            K = S.One
+            break
+        elif a.is_Mul:
+            K, p = a.as_two_terms()
+            if p == ipi and K.is_Rational:
+                break
+    else:
+        return arg, S.Zero
+
+    m1 = (K % S.Half)
+    m2 = K - m1
+    return arg - m2*ipi, m2
+
+
+class sinh(HyperbolicFunction):
+    r"""
+    ``sinh(x)`` is the hyperbolic sine of ``x``.
+
+    The hyperbolic sine function is $\frac{e^x - e^{-x}}{2}$.
+
+    Examples
+    ========
+
+    >>> from sympy import sinh
+    >>> from sympy.abc import x
+    >>> sinh(x)
+    sinh(x)
+
+    See Also
+    ========
+
+    cosh, tanh, asinh
+    """
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return cosh(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return asinh
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.NegativeInfinity
+            elif arg.is_zero:
+                return S.Zero
+            elif arg.is_negative:
+                return -cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                return S.NaN
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                return I * sin(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return -cls(-arg)
+
+            if arg.is_Add:
+                x, m = _peeloff_ipi(arg)
+                if m:
+                    m = m*pi*I
+                    return sinh(m)*cosh(x) + cosh(m)*sinh(x)
+
+            if arg.is_zero:
+                return S.Zero
+
+            if arg.func == asinh:
+                return arg.args[0]
+
+            if arg.func == acosh:
+                x = arg.args[0]
+                return sqrt(x - 1) * sqrt(x + 1)
+
+            if arg.func == atanh:
+                x = arg.args[0]
+                return x/sqrt(1 - x**2)
+
+            if arg.func == acoth:
+                x = arg.args[0]
+                return 1/(sqrt(x - 1) * sqrt(x + 1))
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        """
+        Returns the next term in the Taylor series expansion.
+        """
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            if len(previous_terms) > 2:
+                p = previous_terms[-2]
+                return p * x**2 / (n*(n - 1))
+            else:
+                return x**(n) / factorial(n)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        """
+        Returns this function as a complex coordinate.
+        """
+        if self.args[0].is_extended_real:
+            if deep:
+                hints['complex'] = False
+                return (self.expand(deep, **hints), S.Zero)
+            else:
+                return (self, S.Zero)
+        if deep:
+            re, im = self.args[0].expand(deep, **hints).as_real_imag()
+        else:
+            re, im = self.args[0].as_real_imag()
+        return (sinh(re)*cos(im), cosh(re)*sin(im))
+
+    def _eval_expand_complex(self, deep=True, **hints):
+        re_part, im_part = self.as_real_imag(deep=deep, **hints)
+        return re_part + im_part*I
+
+    def _eval_expand_trig(self, deep=True, **hints):
+        if deep:
+            arg = self.args[0].expand(deep, **hints)
+        else:
+            arg = self.args[0]
+        x = None
+        if arg.is_Add: # TODO, implement more if deep stuff here
+            x, y = arg.as_two_terms()
+        else:
+            coeff, terms = arg.as_coeff_Mul(rational=True)
+            if coeff is not S.One and coeff.is_Integer and terms is not S.One:
+                x = terms
+                y = (coeff - 1)*x
+        if x is not None:
+            return (sinh(x)*cosh(y) + sinh(y)*cosh(x)).expand(trig=True)
+        return sinh(arg)
+
+    def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs):
+        return (exp(arg) - exp(-arg)) / 2
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return (exp(arg) - exp(-arg)) / 2
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return -I * sin(I * arg)
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        return -I / csc(I * arg)
+
+    def _eval_rewrite_as_cosh(self, arg, **kwargs):
+        return -I*cosh(arg + pi*I/2)
+
+    def _eval_rewrite_as_tanh(self, arg, **kwargs):
+        tanh_half = tanh(S.Half*arg)
+        return 2*tanh_half/(1 - tanh_half**2)
+
+    def _eval_rewrite_as_coth(self, arg, **kwargs):
+        coth_half = coth(S.Half*arg)
+        return 2*coth_half/(coth_half**2 - 1)
+
+    def _eval_rewrite_as_csch(self, arg, **kwargs):
+        return 1 / csch(arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if cdir.is_negative else '+')
+        if arg0.is_zero:
+            return arg
+        elif arg0.is_finite:
+            return self.func(arg0)
+        else:
+            return self
+
+    def _eval_is_real(self):
+        arg = self.args[0]
+        if arg.is_real:
+            return True
+
+        # if `im` is of the form n*pi
+        # else, check if it is a number
+        re, im = arg.as_real_imag()
+        return (im%pi).is_zero
+
+    def _eval_is_extended_real(self):
+        if self.args[0].is_extended_real:
+            return True
+
+    def _eval_is_positive(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_positive
+
+    def _eval_is_negative(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_negative
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+        return arg.is_finite
+
+    def _eval_is_zero(self):
+        rest, ipi_mult = _peeloff_ipi(self.args[0])
+        if rest.is_zero:
+            return ipi_mult.is_integer
+
+
+class cosh(HyperbolicFunction):
+    r"""
+    ``cosh(x)`` is the hyperbolic cosine of ``x``.
+
+    The hyperbolic cosine function is $\frac{e^x + e^{-x}}{2}$.
+
+    Examples
+    ========
+
+    >>> from sympy import cosh
+    >>> from sympy.abc import x
+    >>> cosh(x)
+    cosh(x)
+
+    See Also
+    ========
+
+    sinh, tanh, acosh
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return sinh(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.functions.elementary.trigonometric import cos
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.Infinity
+            elif arg.is_zero:
+                return S.One
+            elif arg.is_negative:
+                return cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                return S.NaN
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                return cos(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return cls(-arg)
+
+            if arg.is_Add:
+                x, m = _peeloff_ipi(arg)
+                if m:
+                    m = m*pi*I
+                    return cosh(m)*cosh(x) + sinh(m)*sinh(x)
+
+            if arg.is_zero:
+                return S.One
+
+            if arg.func == asinh:
+                return sqrt(1 + arg.args[0]**2)
+
+            if arg.func == acosh:
+                return arg.args[0]
+
+            if arg.func == atanh:
+                return 1/sqrt(1 - arg.args[0]**2)
+
+            if arg.func == acoth:
+                x = arg.args[0]
+                return x/(sqrt(x - 1) * sqrt(x + 1))
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            if len(previous_terms) > 2:
+                p = previous_terms[-2]
+                return p * x**2 / (n*(n - 1))
+            else:
+                return x**(n)/factorial(n)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        if self.args[0].is_extended_real:
+            if deep:
+                hints['complex'] = False
+                return (self.expand(deep, **hints), S.Zero)
+            else:
+                return (self, S.Zero)
+        if deep:
+            re, im = self.args[0].expand(deep, **hints).as_real_imag()
+        else:
+            re, im = self.args[0].as_real_imag()
+
+        return (cosh(re)*cos(im), sinh(re)*sin(im))
+
+    def _eval_expand_complex(self, deep=True, **hints):
+        re_part, im_part = self.as_real_imag(deep=deep, **hints)
+        return re_part + im_part*I
+
+    def _eval_expand_trig(self, deep=True, **hints):
+        if deep:
+            arg = self.args[0].expand(deep, **hints)
+        else:
+            arg = self.args[0]
+        x = None
+        if arg.is_Add: # TODO, implement more if deep stuff here
+            x, y = arg.as_two_terms()
+        else:
+            coeff, terms = arg.as_coeff_Mul(rational=True)
+            if coeff is not S.One and coeff.is_Integer and terms is not S.One:
+                x = terms
+                y = (coeff - 1)*x
+        if x is not None:
+            return (cosh(x)*cosh(y) + sinh(x)*sinh(y)).expand(trig=True)
+        return cosh(arg)
+
+    def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs):
+        return (exp(arg) + exp(-arg)) / 2
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return (exp(arg) + exp(-arg)) / 2
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        return cos(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        return 1 / sec(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_sinh(self, arg, **kwargs):
+        return -I*sinh(arg + pi*I/2, evaluate=False)
+
+    def _eval_rewrite_as_tanh(self, arg, **kwargs):
+        tanh_half = tanh(S.Half*arg)**2
+        return (1 + tanh_half)/(1 - tanh_half)
+
+    def _eval_rewrite_as_coth(self, arg, **kwargs):
+        coth_half = coth(S.Half*arg)**2
+        return (coth_half + 1)/(coth_half - 1)
+
+    def _eval_rewrite_as_sech(self, arg, **kwargs):
+        return 1 / sech(arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if cdir.is_negative else '+')
+        if arg0.is_zero:
+            return S.One
+        elif arg0.is_finite:
+            return self.func(arg0)
+        else:
+            return self
+
+    def _eval_is_real(self):
+        arg = self.args[0]
+
+        # `cosh(x)` is real for real OR purely imaginary `x`
+        if arg.is_real or arg.is_imaginary:
+            return True
+
+        # cosh(a+ib) = cos(b)*cosh(a) + i*sin(b)*sinh(a)
+        # the imaginary part can be an expression like n*pi
+        # if not, check if the imaginary part is a number
+        re, im = arg.as_real_imag()
+        return (im%pi).is_zero
+
+    def _eval_is_positive(self):
+        # cosh(x+I*y) = cos(y)*cosh(x) + I*sin(y)*sinh(x)
+        # cosh(z) is positive iff it is real and the real part is positive.
+        # So we need sin(y)*sinh(x) = 0 which gives x=0 or y=n*pi
+        # Case 1 (y=n*pi): cosh(z) = (-1)**n * cosh(x) -> positive for n even
+        # Case 2 (x=0): cosh(z) = cos(y) -> positive when cos(y) is positive
+        z = self.args[0]
+
+        x, y = z.as_real_imag()
+        ymod = y % (2*pi)
+
+        yzero = ymod.is_zero
+        # shortcut if ymod is zero
+        if yzero:
+            return True
+
+        xzero = x.is_zero
+        # shortcut x is not zero
+        if xzero is False:
+            return yzero
+
+        return fuzzy_or([
+                # Case 1:
+                yzero,
+                # Case 2:
+                fuzzy_and([
+                    xzero,
+                    fuzzy_or([ymod < pi/2, ymod > 3*pi/2])
+                ])
+            ])
+
+
+    def _eval_is_nonnegative(self):
+        z = self.args[0]
+
+        x, y = z.as_real_imag()
+        ymod = y % (2*pi)
+
+        yzero = ymod.is_zero
+        # shortcut if ymod is zero
+        if yzero:
+            return True
+
+        xzero = x.is_zero
+        # shortcut x is not zero
+        if xzero is False:
+            return yzero
+
+        return fuzzy_or([
+                # Case 1:
+                yzero,
+                # Case 2:
+                fuzzy_and([
+                    xzero,
+                    fuzzy_or([ymod <= pi/2, ymod >= 3*pi/2])
+                ])
+            ])
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+        return arg.is_finite
+
+    def _eval_is_zero(self):
+        rest, ipi_mult = _peeloff_ipi(self.args[0])
+        if ipi_mult and rest.is_zero:
+            return (ipi_mult - S.Half).is_integer
+
+
+class tanh(HyperbolicFunction):
+    r"""
+    ``tanh(x)`` is the hyperbolic tangent of ``x``.
+
+    The hyperbolic tangent function is $\frac{\sinh(x)}{\cosh(x)}$.
+
+    Examples
+    ========
+
+    >>> from sympy import tanh
+    >>> from sympy.abc import x
+    >>> tanh(x)
+    tanh(x)
+
+    See Also
+    ========
+
+    sinh, cosh, atanh
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return S.One - tanh(self.args[0])**2
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return atanh
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.One
+            elif arg is S.NegativeInfinity:
+                return S.NegativeOne
+            elif arg.is_zero:
+                return S.Zero
+            elif arg.is_negative:
+                return -cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                return S.NaN
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                if i_coeff.could_extract_minus_sign():
+                    return -I * tan(-i_coeff)
+                return I * tan(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return -cls(-arg)
+
+            if arg.is_Add:
+                x, m = _peeloff_ipi(arg)
+                if m:
+                    tanhm = tanh(m*pi*I)
+                    if tanhm is S.ComplexInfinity:
+                        return coth(x)
+                    else: # tanhm == 0
+                        return tanh(x)
+
+            if arg.is_zero:
+                return S.Zero
+
+            if arg.func == asinh:
+                x = arg.args[0]
+                return x/sqrt(1 + x**2)
+
+            if arg.func == acosh:
+                x = arg.args[0]
+                return sqrt(x - 1) * sqrt(x + 1) / x
+
+            if arg.func == atanh:
+                return arg.args[0]
+
+            if arg.func == acoth:
+                return 1/arg.args[0]
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            a = 2**(n + 1)
+
+            B = bernoulli(n + 1)
+            F = factorial(n + 1)
+
+            return a*(a - 1) * B/F * x**n
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        if self.args[0].is_extended_real:
+            if deep:
+                hints['complex'] = False
+                return (self.expand(deep, **hints), S.Zero)
+            else:
+                return (self, S.Zero)
+        if deep:
+            re, im = self.args[0].expand(deep, **hints).as_real_imag()
+        else:
+            re, im = self.args[0].as_real_imag()
+        denom = sinh(re)**2 + cos(im)**2
+        return (sinh(re)*cosh(re)/denom, sin(im)*cos(im)/denom)
+
+    def _eval_expand_trig(self, **hints):
+        arg = self.args[0]
+        if arg.is_Add:
+            n = len(arg.args)
+            TX = [tanh(x, evaluate=False)._eval_expand_trig()
+                for x in arg.args]
+            p = [0, 0]  # [den, num]
+            for i in range(n + 1):
+                p[i % 2] += symmetric_poly(i, TX)
+            return p[1]/p[0]
+        elif arg.is_Mul:
+            coeff, terms = arg.as_coeff_Mul()
+            if coeff.is_Integer and coeff > 1:
+                T = tanh(terms)
+                n = [nC(range(coeff), k)*T**k for k in range(1, coeff + 1, 2)]
+                d = [nC(range(coeff), k)*T**k for k in range(0, coeff + 1, 2)]
+                return Add(*n)/Add(*d)
+        return tanh(arg)
+
+    def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs):
+        neg_exp, pos_exp = exp(-arg), exp(arg)
+        return (pos_exp - neg_exp)/(pos_exp + neg_exp)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        neg_exp, pos_exp = exp(-arg), exp(arg)
+        return (pos_exp - neg_exp)/(pos_exp + neg_exp)
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        return -I * tan(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_cot(self, arg, **kwargs):
+        return -I / cot(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_sinh(self, arg, **kwargs):
+        return I*sinh(arg)/sinh(pi*I/2 - arg, evaluate=False)
+
+    def _eval_rewrite_as_cosh(self, arg, **kwargs):
+        return I*cosh(pi*I/2 - arg, evaluate=False)/cosh(arg)
+
+    def _eval_rewrite_as_coth(self, arg, **kwargs):
+        return 1/coth(arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.series.order import Order
+        arg = self.args[0].as_leading_term(x)
+
+        if x in arg.free_symbols and Order(1, x).contains(arg):
+            return arg
+        else:
+            return self.func(arg)
+
+    def _eval_is_real(self):
+        arg = self.args[0]
+        if arg.is_real:
+            return True
+
+        re, im = arg.as_real_imag()
+
+        # if denom = 0, tanh(arg) = zoo
+        if re == 0 and im % pi == pi/2:
+            return None
+
+        # check if im is of the form n*pi/2 to make sin(2*im) = 0
+        # if not, im could be a number, return False in that case
+        return (im % (pi/2)).is_zero
+
+    def _eval_is_extended_real(self):
+        if self.args[0].is_extended_real:
+            return True
+
+    def _eval_is_positive(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_positive
+
+    def _eval_is_negative(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_negative
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+
+        re, im = arg.as_real_imag()
+        denom = cos(im)**2 + sinh(re)**2
+        if denom == 0:
+            return False
+        elif denom.is_number:
+            return True
+        if arg.is_extended_real:
+            return True
+
+    def _eval_is_zero(self):
+        arg = self.args[0]
+        if arg.is_zero:
+            return True
+
+
+class coth(HyperbolicFunction):
+    r"""
+    ``coth(x)`` is the hyperbolic cotangent of ``x``.
+
+    The hyperbolic cotangent function is $\frac{\cosh(x)}{\sinh(x)}$.
+
+    Examples
+    ========
+
+    >>> from sympy import coth
+    >>> from sympy.abc import x
+    >>> coth(x)
+    coth(x)
+
+    See Also
+    ========
+
+    sinh, cosh, acoth
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -1/sinh(self.args[0])**2
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return acoth
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.One
+            elif arg is S.NegativeInfinity:
+                return S.NegativeOne
+            elif arg.is_zero:
+                return S.ComplexInfinity
+            elif arg.is_negative:
+                return -cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                return S.NaN
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                if i_coeff.could_extract_minus_sign():
+                    return I * cot(-i_coeff)
+                return -I * cot(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return -cls(-arg)
+
+            if arg.is_Add:
+                x, m = _peeloff_ipi(arg)
+                if m:
+                    cothm = coth(m*pi*I)
+                    if cothm is S.ComplexInfinity:
+                        return coth(x)
+                    else: # cothm == 0
+                        return tanh(x)
+
+            if arg.is_zero:
+                return S.ComplexInfinity
+
+            if arg.func == asinh:
+                x = arg.args[0]
+                return sqrt(1 + x**2)/x
+
+            if arg.func == acosh:
+                x = arg.args[0]
+                return x/(sqrt(x - 1) * sqrt(x + 1))
+
+            if arg.func == atanh:
+                return 1/arg.args[0]
+
+            if arg.func == acoth:
+                return arg.args[0]
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return 1 / sympify(x)
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            B = bernoulli(n + 1)
+            F = factorial(n + 1)
+
+            return 2**(n + 1) * B/F * x**n
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        from sympy.functions.elementary.trigonometric import (cos, sin)
+        if self.args[0].is_extended_real:
+            if deep:
+                hints['complex'] = False
+                return (self.expand(deep, **hints), S.Zero)
+            else:
+                return (self, S.Zero)
+        if deep:
+            re, im = self.args[0].expand(deep, **hints).as_real_imag()
+        else:
+            re, im = self.args[0].as_real_imag()
+        denom = sinh(re)**2 + sin(im)**2
+        return (sinh(re)*cosh(re)/denom, -sin(im)*cos(im)/denom)
+
+    def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs):
+        neg_exp, pos_exp = exp(-arg), exp(arg)
+        return (pos_exp + neg_exp)/(pos_exp - neg_exp)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        neg_exp, pos_exp = exp(-arg), exp(arg)
+        return (pos_exp + neg_exp)/(pos_exp - neg_exp)
+
+    def _eval_rewrite_as_sinh(self, arg, **kwargs):
+        return -I*sinh(pi*I/2 - arg, evaluate=False)/sinh(arg)
+
+    def _eval_rewrite_as_cosh(self, arg, **kwargs):
+        return -I*cosh(arg)/cosh(pi*I/2 - arg, evaluate=False)
+
+    def _eval_rewrite_as_tanh(self, arg, **kwargs):
+        return 1/tanh(arg)
+
+    def _eval_is_positive(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_positive
+
+    def _eval_is_negative(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_negative
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.series.order import Order
+        arg = self.args[0].as_leading_term(x)
+
+        if x in arg.free_symbols and Order(1, x).contains(arg):
+            return 1/arg
+        else:
+            return self.func(arg)
+
+    def _eval_expand_trig(self, **hints):
+        arg = self.args[0]
+        if arg.is_Add:
+            CX = [coth(x, evaluate=False)._eval_expand_trig() for x in arg.args]
+            p = [[], []]
+            n = len(arg.args)
+            for i in range(n, -1, -1):
+                p[(n - i) % 2].append(symmetric_poly(i, CX))
+            return Add(*p[0])/Add(*p[1])
+        elif arg.is_Mul:
+            coeff, x = arg.as_coeff_Mul(rational=True)
+            if coeff.is_Integer and coeff > 1:
+                c = coth(x, evaluate=False)
+                p = [[], []]
+                for i in range(coeff, -1, -1):
+                    p[(coeff - i) % 2].append(binomial(coeff, i)*c**i)
+                return Add(*p[0])/Add(*p[1])
+        return coth(arg)
+
+
+class ReciprocalHyperbolicFunction(HyperbolicFunction):
+    """Base class for reciprocal functions of hyperbolic functions. """
+
+    #To be defined in class
+    _reciprocal_of = None
+    _is_even: FuzzyBool = None
+    _is_odd: FuzzyBool = None
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.could_extract_minus_sign():
+            if cls._is_even:
+                return cls(-arg)
+            if cls._is_odd:
+                return -cls(-arg)
+
+        t = cls._reciprocal_of.eval(arg)
+        if hasattr(arg, 'inverse') and arg.inverse() == cls:
+            return arg.args[0]
+        return 1/t if t is not None else t
+
+    def _call_reciprocal(self, method_name, *args, **kwargs):
+        # Calls method_name on _reciprocal_of
+        o = self._reciprocal_of(self.args[0])
+        return getattr(o, method_name)(*args, **kwargs)
+
+    def _calculate_reciprocal(self, method_name, *args, **kwargs):
+        # If calling method_name on _reciprocal_of returns a value != None
+        # then return the reciprocal of that value
+        t = self._call_reciprocal(method_name, *args, **kwargs)
+        return 1/t if t is not None else t
+
+    def _rewrite_reciprocal(self, method_name, arg):
+        # Special handling for rewrite functions. If reciprocal rewrite returns
+        # unmodified expression, then return None
+        t = self._call_reciprocal(method_name, arg)
+        if t is not None and t != self._reciprocal_of(arg):
+            return 1/t
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_exp", arg)
+
+    def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_tractable", arg)
+
+    def _eval_rewrite_as_tanh(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_tanh", arg)
+
+    def _eval_rewrite_as_coth(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_coth", arg)
+
+    def as_real_imag(self, deep = True, **hints):
+        return (1 / self._reciprocal_of(self.args[0])).as_real_imag(deep, **hints)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def _eval_expand_complex(self, deep=True, **hints):
+        re_part, im_part = self.as_real_imag(deep=True, **hints)
+        return re_part + I*im_part
+
+    def _eval_expand_trig(self, **hints):
+        return self._calculate_reciprocal("_eval_expand_trig", **hints)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        return (1/self._reciprocal_of(self.args[0]))._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_is_extended_real(self):
+        return self._reciprocal_of(self.args[0]).is_extended_real
+
+    def _eval_is_finite(self):
+        return (1/self._reciprocal_of(self.args[0])).is_finite
+
+
+class csch(ReciprocalHyperbolicFunction):
+    r"""
+    ``csch(x)`` is the hyperbolic cosecant of ``x``.
+
+    The hyperbolic cosecant function is $\frac{2}{e^x - e^{-x}}$
+
+    Examples
+    ========
+
+    >>> from sympy import csch
+    >>> from sympy.abc import x
+    >>> csch(x)
+    csch(x)
+
+    See Also
+    ========
+
+    sinh, cosh, tanh, sech, asinh, acosh
+    """
+
+    _reciprocal_of = sinh
+    _is_odd = True
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function
+        """
+        if argindex == 1:
+            return -coth(self.args[0]) * csch(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        """
+        Returns the next term in the Taylor series expansion
+        """
+        if n == 0:
+            return 1/sympify(x)
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            B = bernoulli(n + 1)
+            F = factorial(n + 1)
+
+            return 2 * (1 - 2**n) * B/F * x**n
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return I / sin(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        return I * csc(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_cosh(self, arg, **kwargs):
+        return I / cosh(arg + I * pi / 2, evaluate=False)
+
+    def _eval_rewrite_as_sinh(self, arg, **kwargs):
+        return 1 / sinh(arg)
+
+    def _eval_is_positive(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_positive
+
+    def _eval_is_negative(self):
+        if self.args[0].is_extended_real:
+            return self.args[0].is_negative
+
+
+class sech(ReciprocalHyperbolicFunction):
+    r"""
+    ``sech(x)`` is the hyperbolic secant of ``x``.
+
+    The hyperbolic secant function is $\frac{2}{e^x + e^{-x}}$
+
+    Examples
+    ========
+
+    >>> from sympy import sech
+    >>> from sympy.abc import x
+    >>> sech(x)
+    sech(x)
+
+    See Also
+    ========
+
+    sinh, cosh, tanh, coth, csch, asinh, acosh
+    """
+
+    _reciprocal_of = cosh
+    _is_even = True
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return - tanh(self.args[0])*sech(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+            return euler(n) / factorial(n) * x**(n)
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        return 1 / cos(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        return sec(I * arg, evaluate=False)
+
+    def _eval_rewrite_as_sinh(self, arg, **kwargs):
+        return I / sinh(arg + I * pi /2, evaluate=False)
+
+    def _eval_rewrite_as_cosh(self, arg, **kwargs):
+        return 1 / cosh(arg)
+
+    def _eval_is_positive(self):
+        if self.args[0].is_extended_real:
+            return True
+
+
+###############################################################################
+############################# HYPERBOLIC INVERSES #############################
+###############################################################################
+
+class InverseHyperbolicFunction(DefinedFunction):
+    """Base class for inverse hyperbolic functions."""
+
+    pass
+
+
+class asinh(InverseHyperbolicFunction):
+    """
+    ``asinh(x)`` is the inverse hyperbolic sine of ``x``.
+
+    The inverse hyperbolic sine function.
+
+    Examples
+    ========
+
+    >>> from sympy import asinh
+    >>> from sympy.abc import x
+    >>> asinh(x).diff(x)
+    1/sqrt(x**2 + 1)
+    >>> asinh(1)
+    log(1 + sqrt(2))
+
+    See Also
+    ========
+
+    acosh, atanh, sinh
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 1/sqrt(self.args[0]**2 + 1)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.NegativeInfinity
+            elif arg.is_zero:
+                return S.Zero
+            elif arg is S.One:
+                return log(sqrt(2) + 1)
+            elif arg is S.NegativeOne:
+                return log(sqrt(2) - 1)
+            elif arg.is_negative:
+                return -cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                return S.ComplexInfinity
+
+            if arg.is_zero:
+                return S.Zero
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                return I * asin(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return -cls(-arg)
+
+        if isinstance(arg, sinh) and arg.args[0].is_number:
+            z = arg.args[0]
+            if z.is_real:
+                return z
+            r, i = match_real_imag(z)
+            if r is not None and i is not None:
+                f = floor((i + pi/2)/pi)
+                m = z - I*pi*f
+                even = f.is_even
+                if even is True:
+                    return m
+                elif even is False:
+                    return -m
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) >= 2 and n > 2:
+                p = previous_terms[-2]
+                return -p * (n - 2)**2/(n*(n - 1)) * x**2
+            else:
+                k = (n - 1) // 2
+                R = RisingFactorial(S.Half, k)
+                F = factorial(k)
+                return S.NegativeOne**k * R / F * x**n / n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0.is_zero:
+            return arg.as_leading_term(x)
+
+        if x0 is S.NaN:
+            expr = self.func(arg.as_leading_term(x))
+            if expr.is_finite:
+                return expr
+            else:
+                return self
+
+        # Handling branch points
+        if x0 in (-I, I, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo)
+        if (1 + x0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if re(ndir).is_positive:
+                if im(x0).is_negative:
+                    return -self.func(x0) - I*pi
+            elif re(ndir).is_negative:
+                if im(x0).is_positive:
+                    return -self.func(x0) + I*pi
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # asinh
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+
+        # Handling branch points
+        if arg0 in (I, -I):
+            return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+
+        # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo)
+        if (1 + arg0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if re(ndir).is_positive:
+                if im(arg0).is_negative:
+                    return -res - I*pi
+            elif re(ndir).is_negative:
+                if im(arg0).is_positive:
+                    return -res + I*pi
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return log(x + sqrt(x**2 + 1))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_atanh(self, x, **kwargs):
+        return atanh(x/sqrt(1 + x**2))
+
+    def _eval_rewrite_as_acosh(self, x, **kwargs):
+        ix = I*x
+        return I*(sqrt(1 - ix)/sqrt(ix - 1) * acosh(ix) - pi/2)
+
+    def _eval_rewrite_as_asin(self, x, **kwargs):
+        return -I * asin(I * x, evaluate=False)
+
+    def _eval_rewrite_as_acos(self, x, **kwargs):
+        return I * acos(I * x, evaluate=False) - I*pi/2
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return sinh
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+
+class acosh(InverseHyperbolicFunction):
+    """
+    ``acosh(x)`` is the inverse hyperbolic cosine of ``x``.
+
+    The inverse hyperbolic cosine function.
+
+    Examples
+    ========
+
+    >>> from sympy import acosh
+    >>> from sympy.abc import x
+    >>> acosh(x).diff(x)
+    1/(sqrt(x - 1)*sqrt(x + 1))
+    >>> acosh(1)
+    0
+
+    See Also
+    ========
+
+    asinh, atanh, cosh
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            arg = self.args[0]
+            return 1/(sqrt(arg - 1)*sqrt(arg + 1))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.Infinity
+            elif arg.is_zero:
+                return pi*I / 2
+            elif arg is S.One:
+                return S.Zero
+            elif arg is S.NegativeOne:
+                return pi*I
+
+        if arg.is_number:
+            cst_table = _acosh_table()
+
+            if arg in cst_table:
+                if arg.is_extended_real:
+                    return cst_table[arg]*I
+                return cst_table[arg]
+
+        if arg is S.ComplexInfinity:
+            return S.ComplexInfinity
+        if arg == I*S.Infinity:
+            return S.Infinity + I*pi/2
+        if arg == -I*S.Infinity:
+            return S.Infinity - I*pi/2
+
+        if arg.is_zero:
+            return pi*I*S.Half
+
+        if isinstance(arg, cosh) and arg.args[0].is_number:
+            z = arg.args[0]
+            if z.is_real:
+                return Abs(z)
+            r, i = match_real_imag(z)
+            if r is not None and i is not None:
+                f = floor(i/pi)
+                m = z - I*pi*f
+                even = f.is_even
+                if even is True:
+                    if r.is_nonnegative:
+                        return m
+                    elif r.is_negative:
+                        return -m
+                elif even is False:
+                    m -= I*pi
+                    if r.is_nonpositive:
+                        return -m
+                    elif r.is_positive:
+                        return m
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return I*pi/2
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) >= 2 and n > 2:
+                p = previous_terms[-2]
+                return p * (n - 2)**2/(n*(n - 1)) * x**2
+            else:
+                k = (n - 1) // 2
+                R = RisingFactorial(S.Half, k)
+                F = factorial(k)
+                return -R / F * I * x**n / n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        # Handling branch points
+        if x0 in (-S.One, S.Zero, S.One, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+        if x0 is S.NaN:
+            expr = self.func(arg.as_leading_term(x))
+            if expr.is_finite:
+                return expr
+            else:
+                return self
+
+        # Handling points lying on branch cuts (-oo, 1)
+        if (x0 - 1).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if (x0 + 1).is_negative:
+                    return self.func(x0) - 2*I*pi
+                return -self.func(x0)
+            elif not im(ndir).is_positive:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # acosh
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+
+        # Handling branch points
+        if arg0 in (S.One, S.NegativeOne):
+            return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+
+        # Handling points lying on branch cuts (-oo, 1)
+        if (arg0 - 1).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if (arg0 + 1).is_negative:
+                    return res - 2*I*pi
+                return -res
+            elif not im(ndir).is_positive:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return log(x + sqrt(x + 1) * sqrt(x - 1))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_acos(self, x, **kwargs):
+        return sqrt(x - 1)/sqrt(1 - x) * acos(x)
+
+    def _eval_rewrite_as_asin(self, x, **kwargs):
+        return sqrt(x - 1)/sqrt(1 - x) * (pi/2 - asin(x))
+
+    def _eval_rewrite_as_asinh(self, x, **kwargs):
+        return sqrt(x - 1)/sqrt(1 - x) * (pi/2 + I*asinh(I*x, evaluate=False))
+
+    def _eval_rewrite_as_atanh(self, x, **kwargs):
+        sxm1 = sqrt(x - 1)
+        s1mx = sqrt(1 - x)
+        sx2m1 = sqrt(x**2 - 1)
+        return (pi/2*sxm1/s1mx*(1 - x * sqrt(1/x**2)) +
+                sxm1*sqrt(x + 1)/sx2m1 * atanh(sx2m1/x))
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return cosh
+
+    def _eval_is_zero(self):
+        if (self.args[0] - 1).is_zero:
+            return True
+
+    def _eval_is_extended_real(self):
+        return fuzzy_and([self.args[0].is_extended_real, (self.args[0] - 1).is_extended_nonnegative])
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+
+class atanh(InverseHyperbolicFunction):
+    """
+    ``atanh(x)`` is the inverse hyperbolic tangent of ``x``.
+
+    The inverse hyperbolic tangent function.
+
+    Examples
+    ========
+
+    >>> from sympy import atanh
+    >>> from sympy.abc import x
+    >>> atanh(x).diff(x)
+    1/(1 - x**2)
+
+    See Also
+    ========
+
+    asinh, acosh, tanh
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 1/(1 - self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg.is_zero:
+                return S.Zero
+            elif arg is S.One:
+                return S.Infinity
+            elif arg is S.NegativeOne:
+                return S.NegativeInfinity
+            elif arg is S.Infinity:
+                return -I * atan(arg)
+            elif arg is S.NegativeInfinity:
+                return I * atan(-arg)
+            elif arg.is_negative:
+                return -cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                from sympy.calculus.accumulationbounds import AccumBounds
+                return I*AccumBounds(-pi/2, pi/2)
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                return I * atan(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return -cls(-arg)
+
+        if arg.is_zero:
+            return S.Zero
+
+        if isinstance(arg, tanh) and arg.args[0].is_number:
+            z = arg.args[0]
+            if z.is_real:
+                return z
+            r, i = match_real_imag(z)
+            if r is not None and i is not None:
+                f = floor(2*i/pi)
+                even = f.is_even
+                m = z - I*f*pi/2
+                if even is True:
+                    return m
+                elif even is False:
+                    return m - I*pi/2
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            return x**n / n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0.is_zero:
+            return arg.as_leading_term(x)
+        if x0 is S.NaN:
+            expr = self.func(arg.as_leading_term(x))
+            if expr.is_finite:
+                return expr
+            else:
+                return self
+
+        # Handling branch points
+        if x0 in (-S.One, S.One, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        # Handling points lying on branch cuts (-oo, -1] U [1, oo)
+        if (1 - x0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if x0.is_negative:
+                    return self.func(x0) - I*pi
+            elif im(ndir).is_positive:
+                if x0.is_positive:
+                    return self.func(x0) + I*pi
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # atanh
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+
+        # Handling branch points
+        if arg0 in (S.One, S.NegativeOne):
+            return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+
+        # Handling points lying on branch cuts (-oo, -1] U [1, oo)
+        if (1 - arg0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if arg0.is_negative:
+                    return res - I*pi
+            elif im(ndir).is_positive:
+                if arg0.is_positive:
+                    return res + I*pi
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return (log(1 + x) - log(1 - x)) / 2
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_asinh(self, x, **kwargs):
+        f = sqrt(1/(x**2 - 1))
+        return (pi*x/(2*sqrt(-x**2)) -
+                sqrt(-x)*sqrt(1 - x**2)/sqrt(x)*f*asinh(f))
+
+    def _eval_is_zero(self):
+        if self.args[0].is_zero:
+            return True
+
+    def _eval_is_extended_real(self):
+        return fuzzy_and([self.args[0].is_extended_real, (1 - self.args[0]).is_nonnegative, (self.args[0] + 1).is_nonnegative])
+
+    def _eval_is_finite(self):
+        return fuzzy_not(fuzzy_or([(self.args[0] - 1).is_zero, (self.args[0] + 1).is_zero]))
+
+    def _eval_is_imaginary(self):
+        return self.args[0].is_imaginary
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return tanh
+
+
+class acoth(InverseHyperbolicFunction):
+    """
+    ``acoth(x)`` is the inverse hyperbolic cotangent of ``x``.
+
+    The inverse hyperbolic cotangent function.
+
+    Examples
+    ========
+
+    >>> from sympy import acoth
+    >>> from sympy.abc import x
+    >>> acoth(x).diff(x)
+    1/(1 - x**2)
+
+    See Also
+    ========
+
+    asinh, acosh, coth
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 1/(1 - self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Zero
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+            elif arg.is_zero:
+                return pi*I / 2
+            elif arg is S.One:
+                return S.Infinity
+            elif arg is S.NegativeOne:
+                return S.NegativeInfinity
+            elif arg.is_negative:
+                return -cls(-arg)
+        else:
+            if arg is S.ComplexInfinity:
+                return S.Zero
+
+            i_coeff = _imaginary_unit_as_coefficient(arg)
+
+            if i_coeff is not None:
+                return -I * acot(i_coeff)
+            else:
+                if arg.could_extract_minus_sign():
+                    return -cls(-arg)
+
+        if arg.is_zero:
+            return pi*I*S.Half
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return -I*pi/2
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            return x**n / n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.ComplexInfinity:
+            return (1/arg).as_leading_term(x)
+        if x0 is S.NaN:
+            expr = self.func(arg.as_leading_term(x))
+            if expr.is_finite:
+                return expr
+            else:
+                return self
+
+        # Handling branch points
+        if x0 in (-S.One, S.One, S.Zero):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        # Handling points lying on branch cuts [-1, 1]
+        if x0.is_real and (1 - x0**2).is_positive:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if x0.is_positive:
+                    return self.func(x0) + I*pi
+            elif im(ndir).is_positive:
+                if x0.is_negative:
+                    return self.func(x0) - I*pi
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # acoth
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+
+        # Handling branch points
+        if arg0 in (S.One, S.NegativeOne):
+            return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+
+        # Handling points lying on branch cuts [-1, 1]
+        if arg0.is_real and (1 - arg0**2).is_positive:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if arg0.is_positive:
+                    return res + I*pi
+            elif im(ndir).is_positive:
+                if arg0.is_negative:
+                    return res - I*pi
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return (log(1 + 1/x) - log(1 - 1/x)) / 2
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_atanh(self, x, **kwargs):
+        return atanh(1/x)
+
+    def _eval_rewrite_as_asinh(self, x, **kwargs):
+        return (pi*I/2*(sqrt((x - 1)/x)*sqrt(x/(x - 1)) - sqrt(1 + 1/x)*sqrt(x/(x + 1))) +
+                x*sqrt(1/x**2)*asinh(sqrt(1/(x**2 - 1))))
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return coth
+
+    def _eval_is_extended_real(self):
+        return fuzzy_and([self.args[0].is_extended_real, fuzzy_or([(self.args[0] - 1).is_extended_nonnegative, (self.args[0] + 1).is_extended_nonpositive])])
+
+    def _eval_is_finite(self):
+        return fuzzy_not(fuzzy_or([(self.args[0] - 1).is_zero, (self.args[0] + 1).is_zero]))
+
+
+class asech(InverseHyperbolicFunction):
+    """
+    ``asech(x)`` is the inverse hyperbolic secant of ``x``.
+
+    The inverse hyperbolic secant function.
+
+    Examples
+    ========
+
+    >>> from sympy import asech, sqrt, S
+    >>> from sympy.abc import x
+    >>> asech(x).diff(x)
+    -1/(x*sqrt(1 - x**2))
+    >>> asech(1).diff(x)
+    0
+    >>> asech(1)
+    0
+    >>> asech(S(2))
+    I*pi/3
+    >>> asech(-sqrt(2))
+    3*I*pi/4
+    >>> asech((sqrt(6) - sqrt(2)))
+    I*pi/12
+
+    See Also
+    ========
+
+    asinh, atanh, cosh, acoth
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hyperbolic_function
+    .. [2] https://dlmf.nist.gov/4.37
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcSech/
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            z = self.args[0]
+            return -1/(z*sqrt(1 - z**2))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return pi*I / 2
+            elif arg is S.NegativeInfinity:
+                return pi*I / 2
+            elif arg.is_zero:
+                return S.Infinity
+            elif arg is S.One:
+                return S.Zero
+            elif arg is S.NegativeOne:
+                return pi*I
+
+        if arg.is_number:
+            cst_table = _asech_table()
+
+            if arg in cst_table:
+                if arg.is_extended_real:
+                    return cst_table[arg]*I
+                return cst_table[arg]
+
+        if arg is S.ComplexInfinity:
+            from sympy.calculus.accumulationbounds import AccumBounds
+            return I*AccumBounds(-pi/2, pi/2)
+
+        if arg.is_zero:
+            return S.Infinity
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return log(2 / x)
+        elif n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 2 and n > 2:
+                p = previous_terms[-2]
+                return p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2)
+            else:
+                k = n // 2
+                R = RisingFactorial(S.Half, k) * n
+                F = factorial(k) * n // 2 * n // 2
+                return -1 * R / F * x**n / 4
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        # Handling branch points
+        if x0 in (-S.One, S.Zero, S.One, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+        if x0 is S.NaN:
+            expr = self.func(arg.as_leading_term(x))
+            if expr.is_finite:
+                return expr
+            else:
+                return self
+
+        # Handling points lying on branch cuts (-oo, 0] U (1, oo)
+        if x0.is_negative or (1 - x0).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_positive:
+                if x0.is_positive or (x0 + 1).is_negative:
+                    return -self.func(x0)
+                return self.func(x0) - 2*I*pi
+            elif not im(ndir).is_negative:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # asech
+        from sympy.series.order import O
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+
+        # Handling branch points
+        if arg0 is S.One:
+            t = Dummy('t', positive=True)
+            ser = asech(S.One - t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.One - self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        if arg0 is S.NegativeOne:
+            t = Dummy('t', positive=True)
+            ser = asech(S.NegativeOne + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.One + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else I*pi + O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+
+        # Handling points lying on branch cuts (-oo, 0] U (1, oo)
+        if arg0.is_negative or (1 - arg0).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_positive:
+                if arg0.is_positive or (arg0 + 1).is_negative:
+                    return -res
+                return res - 2*I*pi
+            elif not im(ndir).is_negative:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return sech
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return log(1/arg + sqrt(1/arg - 1) * sqrt(1/arg + 1))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_acosh(self, arg, **kwargs):
+        return acosh(1/arg)
+
+    def _eval_rewrite_as_asinh(self, arg, **kwargs):
+        return sqrt(1/arg - 1)/sqrt(1 - 1/arg)*(I*asinh(I/arg, evaluate=False)
+                                                + pi*S.Half)
+
+    def _eval_rewrite_as_atanh(self, x, **kwargs):
+        return (I*pi*(1 - sqrt(x)*sqrt(1/x) - I/2*sqrt(-x)/sqrt(x) - I/2*sqrt(x**2)/sqrt(-x**2))
+                + sqrt(1/(x + 1))*sqrt(x + 1)*atanh(sqrt(1 - x**2)))
+
+    def _eval_rewrite_as_acsch(self, x, **kwargs):
+        return sqrt(1/x - 1)/sqrt(1 - 1/x)*(pi/2 - I*acsch(I*x, evaluate=False))
+
+    def _eval_is_extended_real(self):
+        return fuzzy_and([self.args[0].is_extended_real, self.args[0].is_nonnegative, (1 - self.args[0]).is_nonnegative])
+
+    def _eval_is_finite(self):
+        return fuzzy_not(self.args[0].is_zero)
+
+
+class acsch(InverseHyperbolicFunction):
+    """
+    ``acsch(x)`` is the inverse hyperbolic cosecant of ``x``.
+
+    The inverse hyperbolic cosecant function.
+
+    Examples
+    ========
+
+    >>> from sympy import acsch, sqrt, I
+    >>> from sympy.abc import x
+    >>> acsch(x).diff(x)
+    -1/(x**2*sqrt(1 + x**(-2)))
+    >>> acsch(1).diff(x)
+    0
+    >>> acsch(1)
+    log(1 + sqrt(2))
+    >>> acsch(I)
+    -I*pi/2
+    >>> acsch(-2*I)
+    I*pi/6
+    >>> acsch(I*(sqrt(6) - sqrt(2)))
+    -5*I*pi/12
+
+    See Also
+    ========
+
+    asinh
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hyperbolic_function
+    .. [2] https://dlmf.nist.gov/4.37
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcCsch/
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            z = self.args[0]
+            return -1/(z**2*sqrt(1 + 1/z**2))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Zero
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+            elif arg.is_zero:
+                return S.ComplexInfinity
+            elif arg is S.One:
+                return log(1 + sqrt(2))
+            elif arg is S.NegativeOne:
+                return - log(1 + sqrt(2))
+
+        if arg.is_number:
+            cst_table = _acsch_table()
+
+            if arg in cst_table:
+                return cst_table[arg]*I
+
+        if arg is S.ComplexInfinity:
+            return S.Zero
+
+        if arg.is_infinite:
+            return S.Zero
+
+        if arg.is_zero:
+            return S.ComplexInfinity
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return log(2 / x)
+        elif n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 2 and n > 2:
+                p = previous_terms[-2]
+                return -p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2)
+            else:
+                k = n // 2
+                R = RisingFactorial(S.Half, k) *  n
+                F = factorial(k) * n // 2 * n // 2
+                return S.NegativeOne**(k +1) * R / F * x**n / 4
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        # Handling branch points
+        if x0 in (-I, I, S.Zero):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+        if x0 is S.NaN:
+            expr = self.func(arg.as_leading_term(x))
+            if expr.is_finite:
+                return expr
+            else:
+                return self
+
+        if x0 is S.ComplexInfinity:
+            return (1/arg).as_leading_term(x)
+        # Handling points lying on branch cuts (-I, I)
+        if x0.is_imaginary and (1 + x0**2).is_positive:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if re(ndir).is_positive:
+                if im(x0).is_positive:
+                    return -self.func(x0) - I*pi
+            elif re(ndir).is_negative:
+                if im(x0).is_negative:
+                    return -self.func(x0) + I*pi
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # acsch
+        from sympy.series.order import O
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+
+        # Handling branch points
+        if arg0 is I:
+            t = Dummy('t', positive=True)
+            ser = acsch(I + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = -I + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else -I*pi/2 + O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            res = ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+            return res
+
+        if arg0 == S.NegativeOne*I:
+            t = Dummy('t', positive=True)
+            ser = acsch(-I + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = I + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else I*pi/2 + O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+
+        # Handling points lying on branch cuts (-I, I)
+        if arg0.is_imaginary and (1 + arg0**2).is_positive:
+            ndir = self.args[0].dir(x, cdir if cdir else 1)
+            if re(ndir).is_positive:
+                if im(arg0).is_positive:
+                    return -res - I*pi
+            elif re(ndir).is_negative:
+                if im(arg0).is_negative:
+                    return -res + I*pi
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return csch
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return log(1/arg + sqrt(1/arg**2 + 1))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_asinh(self, arg, **kwargs):
+        return asinh(1/arg)
+
+    def _eval_rewrite_as_acosh(self, arg, **kwargs):
+        return I*(sqrt(1 - I/arg)/sqrt(I/arg - 1)*
+                                acosh(I/arg, evaluate=False) - pi*S.Half)
+
+    def _eval_rewrite_as_atanh(self, arg, **kwargs):
+        arg2 = arg**2
+        arg2p1 = arg2 + 1
+        return sqrt(-arg2)/arg*(pi*S.Half -
+                                sqrt(-arg2p1**2)/arg2p1*atanh(sqrt(arg2p1)))
+
+    def _eval_is_zero(self):
+        return self.args[0].is_infinite
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    def _eval_is_finite(self):
+        return fuzzy_not(self.args[0].is_zero)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/integers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/integers.py
new file mode 100644
index 0000000000000000000000000000000000000000..d0b58d32399144c39133855475d70c01b70b1a3f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/integers.py
@@ -0,0 +1,710 @@
+from __future__ import annotations
+
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+
+from sympy.core import Add, S
+from sympy.core.evalf import get_integer_part, PrecisionExhausted
+from sympy.core.function import DefinedFunction
+from sympy.core.logic import fuzzy_or, fuzzy_and
+from sympy.core.numbers import Integer, int_valued
+from sympy.core.relational import Gt, Lt, Ge, Le, Relational, is_eq, is_le, is_lt
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.complexes import im, re
+from sympy.multipledispatch import dispatch
+
+###############################################################################
+######################### FLOOR and CEILING FUNCTIONS #########################
+###############################################################################
+
+
+class RoundFunction(DefinedFunction):
+    """Abstract base class for rounding functions."""
+
+    args: tuple[Expr]
+
+    @classmethod
+    def eval(cls, arg):
+        if (v := cls._eval_number(arg)) is not None:
+            return v
+        if (v := cls._eval_const_number(arg)) is not None:
+            return v
+
+        if arg.is_integer or arg.is_finite is False:
+            return arg
+        if arg.is_imaginary or (S.ImaginaryUnit*arg).is_real:
+            i = im(arg)
+            if not i.has(S.ImaginaryUnit):
+                return cls(i)*S.ImaginaryUnit
+            return cls(arg, evaluate=False)
+
+        # Integral, numerical, symbolic part
+        ipart = npart = spart = S.Zero
+
+        # Extract integral (or complex integral) terms
+        intof = lambda x: int(x) if int_valued(x) else (
+            x if x.is_integer else None)
+        for t in Add.make_args(arg):
+            if t.is_imaginary and (i := intof(im(t))) is not None:
+                ipart += i*S.ImaginaryUnit
+            elif (i := intof(t)) is not None:
+                ipart += i
+            elif t.is_number:
+                npart += t
+            else:
+                spart += t
+
+        if not (npart or spart):
+            return ipart
+
+        # Evaluate npart numerically if independent of spart
+        if npart and (
+            not spart or
+            npart.is_real and (spart.is_imaginary or (S.ImaginaryUnit*spart).is_real) or
+                npart.is_imaginary and spart.is_real):
+            try:
+                r, i = get_integer_part(
+                    npart, cls._dir, {}, return_ints=True)
+                ipart += Integer(r) + Integer(i)*S.ImaginaryUnit
+                npart = S.Zero
+            except (PrecisionExhausted, NotImplementedError):
+                pass
+
+        spart += npart
+        if not spart:
+            return ipart
+        elif spart.is_imaginary or (S.ImaginaryUnit*spart).is_real:
+            return ipart + cls(im(spart), evaluate=False)*S.ImaginaryUnit
+        elif isinstance(spart, (floor, ceiling)):
+            return ipart + spart
+        else:
+            return ipart + cls(spart, evaluate=False)
+
+    @classmethod
+    def _eval_number(cls, arg):
+        raise NotImplementedError()
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+    def _eval_is_real(self):
+        return self.args[0].is_real
+
+    def _eval_is_integer(self):
+        return self.args[0].is_real
+
+
+class floor(RoundFunction):
+    """
+    Floor is a univariate function which returns the largest integer
+    value not greater than its argument. This implementation
+    generalizes floor to complex numbers by taking the floor of the
+    real and imaginary parts separately.
+
+    Examples
+    ========
+
+    >>> from sympy import floor, E, I, S, Float, Rational
+    >>> floor(17)
+    17
+    >>> floor(Rational(23, 10))
+    2
+    >>> floor(2*E)
+    5
+    >>> floor(-Float(0.567))
+    -1
+    >>> floor(-I/2)
+    -I
+    >>> floor(S(5)/2 + 5*I/2)
+    2 + 2*I
+
+    See Also
+    ========
+
+    sympy.functions.elementary.integers.ceiling
+
+    References
+    ==========
+
+    .. [1] "Concrete mathematics" by Graham, pp. 87
+    .. [2] https://mathworld.wolfram.com/FloorFunction.html
+
+    """
+    _dir = -1
+
+    @classmethod
+    def _eval_number(cls, arg):
+        if arg.is_Number:
+            return arg.floor()
+        if any(isinstance(i, j)
+                for i in (arg, -arg) for j in (floor, ceiling)):
+            return arg
+        if arg.is_NumberSymbol:
+            return arg.approximation_interval(Integer)[0]
+
+    @classmethod
+    def _eval_const_number(cls, arg):
+        if arg.is_real:
+            if arg.is_zero:
+                return S.Zero
+            if arg.is_positive:
+                num, den = arg.as_numer_denom()
+                s = den.is_negative
+                if s is None:
+                    return None
+                if s:
+                    num, den = -num, -den
+                # 0 <= num/den < 1 -> 0
+                if is_lt(num, den):
+                    return S.Zero
+                # 1 <= num/den < 2 -> 1
+                if fuzzy_and([is_le(den, num), is_lt(num, 2*den)]):
+                    return S.One
+            if arg.is_negative:
+                num, den = arg.as_numer_denom()
+                s = den.is_negative
+                if s is None:
+                    return None
+                if s:
+                    num, den = -num, -den
+                # -1 <= num/den < 0 -> -1
+                if is_le(-den, num):
+                    return S.NegativeOne
+                # -2 <= num/den < -1 -> -2
+                if fuzzy_and([is_le(-2*den, num), is_lt(num, -den)]):
+                    return Integer(-2)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+        r = self.subs(x, 0)
+        if arg0 is S.NaN or isinstance(arg0, AccumBounds):
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+            r = floor(arg0)
+        if arg0.is_finite:
+            if arg0 == r:
+                ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1)
+                if ndir.is_negative:
+                    return r - 1
+                elif ndir.is_positive:
+                    return r
+                else:
+                    raise NotImplementedError("Not sure of sign of %s" % ndir)
+            else:
+                return r
+        return arg.as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+        r = self.subs(x, 0)
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+            r = floor(arg0)
+        if arg0.is_infinite:
+            from sympy.calculus.accumulationbounds import AccumBounds
+            from sympy.series.order import Order
+            s = arg._eval_nseries(x, n, logx, cdir)
+            o = Order(1, (x, 0)) if n <= 0 else AccumBounds(-1, 0)
+            return s + o
+        if arg0 == r:
+            ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1)
+            if ndir.is_negative:
+                return r - 1
+            elif ndir.is_positive:
+                return r
+            else:
+                raise NotImplementedError("Not sure of sign of %s" % ndir)
+        else:
+            return r
+
+    def _eval_is_negative(self):
+        return self.args[0].is_negative
+
+    def _eval_is_nonnegative(self):
+        return self.args[0].is_nonnegative
+
+    def _eval_rewrite_as_ceiling(self, arg, **kwargs):
+        return -ceiling(-arg)
+
+    def _eval_rewrite_as_frac(self, arg, **kwargs):
+        return arg - frac(arg)
+
+    def __le__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] < other + 1
+            if other.is_number and other.is_real:
+                return self.args[0] < ceiling(other)
+        if self.args[0] == other and other.is_real:
+            return S.true
+        if other is S.Infinity and self.is_finite:
+            return S.true
+
+        return Le(self, other, evaluate=False)
+
+    def __ge__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] >= other
+            if other.is_number and other.is_real:
+                return self.args[0] >= ceiling(other)
+        if self.args[0] == other and other.is_real and other.is_noninteger:
+            return S.false
+        if other is S.NegativeInfinity and self.is_finite:
+            return S.true
+
+        return Ge(self, other, evaluate=False)
+
+    def __gt__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] >= other + 1
+            if other.is_number and other.is_real:
+                return self.args[0] >= ceiling(other)
+        if self.args[0] == other and other.is_real:
+            return S.false
+        if other is S.NegativeInfinity and self.is_finite:
+            return S.true
+
+        return Gt(self, other, evaluate=False)
+
+    def __lt__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] < other
+            if other.is_number and other.is_real:
+                return self.args[0] < ceiling(other)
+        if self.args[0] == other and other.is_real and other.is_noninteger:
+            return S.true
+        if other is S.Infinity and self.is_finite:
+            return S.true
+
+        return Lt(self, other, evaluate=False)
+
+
+@dispatch(floor, Expr)
+def _eval_is_eq(lhs, rhs): # noqa:F811
+    return is_eq(lhs.rewrite(ceiling), rhs) or \
+        is_eq(lhs.rewrite(frac),rhs)
+
+
+class ceiling(RoundFunction):
+    """
+    Ceiling is a univariate function which returns the smallest integer
+    value not less than its argument. This implementation
+    generalizes ceiling to complex numbers by taking the ceiling of the
+    real and imaginary parts separately.
+
+    Examples
+    ========
+
+    >>> from sympy import ceiling, E, I, S, Float, Rational
+    >>> ceiling(17)
+    17
+    >>> ceiling(Rational(23, 10))
+    3
+    >>> ceiling(2*E)
+    6
+    >>> ceiling(-Float(0.567))
+    0
+    >>> ceiling(I/2)
+    I
+    >>> ceiling(S(5)/2 + 5*I/2)
+    3 + 3*I
+
+    See Also
+    ========
+
+    sympy.functions.elementary.integers.floor
+
+    References
+    ==========
+
+    .. [1] "Concrete mathematics" by Graham, pp. 87
+    .. [2] https://mathworld.wolfram.com/CeilingFunction.html
+
+    """
+    _dir = 1
+
+    @classmethod
+    def _eval_number(cls, arg):
+        if arg.is_Number:
+            return arg.ceiling()
+        if any(isinstance(i, j)
+                for i in (arg, -arg) for j in (floor, ceiling)):
+            return arg
+        if arg.is_NumberSymbol:
+            return arg.approximation_interval(Integer)[1]
+
+    @classmethod
+    def _eval_const_number(cls, arg):
+        if arg.is_real:
+            if arg.is_zero:
+                return S.Zero
+            if arg.is_positive:
+                num, den = arg.as_numer_denom()
+                s = den.is_negative
+                if s is None:
+                    return None
+                if s:
+                    num, den = -num, -den
+                # 0 < num/den <= 1 -> 1
+                if is_le(num, den):
+                    return S.One
+                # 1 < num/den <= 2 -> 2
+                if fuzzy_and([is_lt(den, num), is_le(num, 2*den)]):
+                    return Integer(2)
+            if arg.is_negative:
+                num, den = arg.as_numer_denom()
+                s = den.is_negative
+                if s is None:
+                    return None
+                if s:
+                    num, den = -num, -den
+                # -1 < num/den <= 0 -> 0
+                if is_lt(-den, num):
+                    return S.Zero
+                # -2 < num/den <= -1 -> -1
+                if fuzzy_and([is_lt(-2*den, num), is_le(num, -den)]):
+                    return S.NegativeOne
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+        r = self.subs(x, 0)
+        if arg0 is S.NaN or isinstance(arg0, AccumBounds):
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+            r = ceiling(arg0)
+        if arg0.is_finite:
+            if arg0 == r:
+                ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1)
+                if ndir.is_negative:
+                    return r
+                elif ndir.is_positive:
+                    return r + 1
+                else:
+                    raise NotImplementedError("Not sure of sign of %s" % ndir)
+            else:
+                return r
+        return arg.as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+        r = self.subs(x, 0)
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+            r = ceiling(arg0)
+        if arg0.is_infinite:
+            from sympy.calculus.accumulationbounds import AccumBounds
+            from sympy.series.order import Order
+            s = arg._eval_nseries(x, n, logx, cdir)
+            o = Order(1, (x, 0)) if n <= 0 else AccumBounds(0, 1)
+            return s + o
+        if arg0 == r:
+            ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1)
+            if ndir.is_negative:
+                return r
+            elif ndir.is_positive:
+                return r + 1
+            else:
+                raise NotImplementedError("Not sure of sign of %s" % ndir)
+        else:
+            return r
+
+    def _eval_rewrite_as_floor(self, arg, **kwargs):
+        return -floor(-arg)
+
+    def _eval_rewrite_as_frac(self, arg, **kwargs):
+        return arg + frac(-arg)
+
+    def _eval_is_positive(self):
+        return self.args[0].is_positive
+
+    def _eval_is_nonpositive(self):
+        return self.args[0].is_nonpositive
+
+    def __lt__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] <= other - 1
+            if other.is_number and other.is_real:
+                return self.args[0] <= floor(other)
+        if self.args[0] == other and other.is_real:
+            return S.false
+        if other is S.Infinity and self.is_finite:
+            return S.true
+
+        return Lt(self, other, evaluate=False)
+
+    def __gt__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] > other
+            if other.is_number and other.is_real:
+                return self.args[0] > floor(other)
+        if self.args[0] == other and other.is_real and other.is_noninteger:
+            return S.true
+        if other is S.NegativeInfinity and self.is_finite:
+            return S.true
+
+        return Gt(self, other, evaluate=False)
+
+    def __ge__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] > other - 1
+            if other.is_number and other.is_real:
+                return self.args[0] > floor(other)
+        if self.args[0] == other and other.is_real:
+            return S.true
+        if other is S.NegativeInfinity and self.is_finite:
+            return S.true
+
+        return Ge(self, other, evaluate=False)
+
+    def __le__(self, other):
+        other = S(other)
+        if self.args[0].is_real:
+            if other.is_integer:
+                return self.args[0] <= other
+            if other.is_number and other.is_real:
+                return self.args[0] <= floor(other)
+        if self.args[0] == other and other.is_real and other.is_noninteger:
+            return S.false
+        if other is S.Infinity and self.is_finite:
+            return S.true
+
+        return Le(self, other, evaluate=False)
+
+
+@dispatch(ceiling, Basic)  # type:ignore
+def _eval_is_eq(lhs, rhs): # noqa:F811
+    return is_eq(lhs.rewrite(floor), rhs) or is_eq(lhs.rewrite(frac),rhs)
+
+
+class frac(DefinedFunction):
+    r"""Represents the fractional part of x
+
+    For real numbers it is defined [1]_ as
+
+    .. math::
+        x - \left\lfloor{x}\right\rfloor
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, frac, Rational, floor, I
+    >>> frac(Rational(4, 3))
+    1/3
+    >>> frac(-Rational(4, 3))
+    2/3
+
+    returns zero for integer arguments
+
+    >>> n = Symbol('n', integer=True)
+    >>> frac(n)
+    0
+
+    rewrite as floor
+
+    >>> x = Symbol('x')
+    >>> frac(x).rewrite(floor)
+    x - floor(x)
+
+    for complex arguments
+
+    >>> r = Symbol('r', real=True)
+    >>> t = Symbol('t', real=True)
+    >>> frac(t + I*r)
+    I*frac(r) + frac(t)
+
+    See Also
+    ========
+
+    sympy.functions.elementary.integers.floor
+    sympy.functions.elementary.integers.ceiling
+
+    References
+    ===========
+
+    .. [1] https://en.wikipedia.org/wiki/Fractional_part
+    .. [2] https://mathworld.wolfram.com/FractionalPart.html
+
+    """
+    @classmethod
+    def eval(cls, arg):
+        from sympy.calculus.accumulationbounds import AccumBounds
+
+        def _eval(arg):
+            if arg in (S.Infinity, S.NegativeInfinity):
+                return AccumBounds(0, 1)
+            if arg.is_integer:
+                return S.Zero
+            if arg.is_number:
+                if arg is S.NaN:
+                    return S.NaN
+                elif arg is S.ComplexInfinity:
+                    return S.NaN
+                else:
+                    return arg - floor(arg)
+            return cls(arg, evaluate=False)
+
+        real, imag = S.Zero, S.Zero
+        for t in Add.make_args(arg):
+            # Two checks are needed for complex arguments
+            # see issue-7649 for details
+            if t.is_imaginary or (S.ImaginaryUnit*t).is_real:
+                i = im(t)
+                if not i.has(S.ImaginaryUnit):
+                    imag += i
+                else:
+                    real += t
+            else:
+                real += t
+
+        real = _eval(real)
+        imag = _eval(imag)
+        return real + S.ImaginaryUnit*imag
+
+    def _eval_rewrite_as_floor(self, arg, **kwargs):
+        return arg - floor(arg)
+
+    def _eval_rewrite_as_ceiling(self, arg, **kwargs):
+        return arg + ceiling(-arg)
+
+    def _eval_is_finite(self):
+        return True
+
+    def _eval_is_real(self):
+        return self.args[0].is_extended_real
+
+    def _eval_is_imaginary(self):
+        return self.args[0].is_imaginary
+
+    def _eval_is_integer(self):
+        return self.args[0].is_integer
+
+    def _eval_is_zero(self):
+        return fuzzy_or([self.args[0].is_zero, self.args[0].is_integer])
+
+    def _eval_is_negative(self):
+        return False
+
+    def __ge__(self, other):
+        if self.is_extended_real:
+            other = _sympify(other)
+            # Check if other <= 0
+            if other.is_extended_nonpositive:
+                return S.true
+            # Check if other >= 1
+            res = self._value_one_or_more(other)
+            if res is not None:
+                return not(res)
+        return Ge(self, other, evaluate=False)
+
+    def __gt__(self, other):
+        if self.is_extended_real:
+            other = _sympify(other)
+            # Check if other < 0
+            res = self._value_one_or_more(other)
+            if res is not None:
+                return not(res)
+            # Check if other >= 1
+            if other.is_extended_negative:
+                return S.true
+        return Gt(self, other, evaluate=False)
+
+    def __le__(self, other):
+        if self.is_extended_real:
+            other = _sympify(other)
+            # Check if other < 0
+            if other.is_extended_negative:
+                return S.false
+            # Check if other >= 1
+            res = self._value_one_or_more(other)
+            if res is not None:
+                return res
+        return Le(self, other, evaluate=False)
+
+    def __lt__(self, other):
+        if self.is_extended_real:
+            other = _sympify(other)
+            # Check if other <= 0
+            if other.is_extended_nonpositive:
+                return S.false
+            # Check if other >= 1
+            res = self._value_one_or_more(other)
+            if res is not None:
+                return res
+        return Lt(self, other, evaluate=False)
+
+    def _value_one_or_more(self, other):
+        if other.is_extended_real:
+            if other.is_number:
+                res = other >= 1
+                if res and not isinstance(res, Relational):
+                    return S.true
+            if other.is_integer and other.is_positive:
+                return S.true
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+        r = self.subs(x, 0)
+
+        if arg0.is_finite:
+            if r.is_zero:
+                ndir = arg.dir(x, cdir=cdir)
+                if ndir.is_negative:
+                    return S.One
+                return (arg - arg0).as_leading_term(x, logx=logx, cdir=cdir)
+            else:
+                return r
+        elif arg0 in (S.ComplexInfinity, S.Infinity, S.NegativeInfinity):
+            return AccumBounds(0, 1)
+        return arg.as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.series.order import Order
+        arg = self.args[0]
+        arg0 = arg.subs(x, 0)
+        r = self.subs(x, 0)
+
+        if arg0.is_infinite:
+            from sympy.calculus.accumulationbounds import AccumBounds
+            o = Order(1, (x, 0)) if n <= 0 else AccumBounds(0, 1) + Order(x**n, (x, 0))
+            return o
+        else:
+            res = (arg - arg0)._eval_nseries(x, n, logx=logx, cdir=cdir)
+            if r.is_zero:
+                ndir = arg.dir(x, cdir=cdir)
+                res += S.One if ndir.is_negative else S.Zero
+            else:
+                res += r
+            return res
+
+
+@dispatch(frac, Basic)  # type:ignore
+def _eval_is_eq(lhs, rhs): # noqa:F811
+    if (lhs.rewrite(floor) == rhs) or \
+        (lhs.rewrite(ceiling) == rhs):
+        return True
+    # Check if other < 0
+    if rhs.is_extended_negative:
+        return False
+    # Check if other >= 1
+    res = lhs._value_one_or_more(rhs)
+    if res is not None:
+        return False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/miscellaneous.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/miscellaneous.py
new file mode 100644
index 0000000000000000000000000000000000000000..c7f3016bc7ea0d5c4ad778cf9922c941acb7fc44
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/miscellaneous.py
@@ -0,0 +1,915 @@
+from sympy.core import S, sympify, NumberKind
+from sympy.utilities.iterables import sift
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.operations import LatticeOp, ShortCircuit
+from sympy.core.function import (Application, Lambda,
+    ArgumentIndexError, DefinedFunction)
+from sympy.core.expr import Expr
+from sympy.core.exprtools import factor_terms
+from sympy.core.mod import Mod
+from sympy.core.mul import Mul
+from sympy.core.numbers import Rational
+from sympy.core.power import Pow
+from sympy.core.relational import Eq, Relational
+from sympy.core.singleton import Singleton
+from sympy.core.sorting import ordered
+from sympy.core.symbol import Dummy
+from sympy.core.rules import Transform
+from sympy.core.logic import fuzzy_and, fuzzy_or, _torf
+from sympy.core.traversal import walk
+from sympy.core.numbers import Integer
+from sympy.logic.boolalg import And, Or
+
+
+def _minmax_as_Piecewise(op, *args):
+    # helper for Min/Max rewrite as Piecewise
+    from sympy.functions.elementary.piecewise import Piecewise
+    ec = []
+    for i, a in enumerate(args):
+        c = [Relational(a, args[j], op) for j in range(i + 1, len(args))]
+        ec.append((a, And(*c)))
+    return Piecewise(*ec)
+
+
+class IdentityFunction(Lambda, metaclass=Singleton):
+    """
+    The identity function
+
+    Examples
+    ========
+
+    >>> from sympy import Id, Symbol
+    >>> x = Symbol('x')
+    >>> Id(x)
+    x
+
+    """
+
+    _symbol = Dummy('x')
+
+    @property
+    def signature(self):
+        return Tuple(self._symbol)
+
+    @property
+    def expr(self):
+        return self._symbol
+
+
+Id = S.IdentityFunction
+
+###############################################################################
+############################# ROOT and SQUARE ROOT FUNCTION ###################
+###############################################################################
+
+
+def sqrt(arg, evaluate=None):
+    """Returns the principal square root.
+
+    Parameters
+    ==========
+
+    evaluate : bool, optional
+        The parameter determines if the expression should be evaluated.
+        If ``None``, its value is taken from
+        ``global_parameters.evaluate``.
+
+    Examples
+    ========
+
+    >>> from sympy import sqrt, Symbol, S
+    >>> x = Symbol('x')
+
+    >>> sqrt(x)
+    sqrt(x)
+
+    >>> sqrt(x)**2
+    x
+
+    Note that sqrt(x**2) does not simplify to x.
+
+    >>> sqrt(x**2)
+    sqrt(x**2)
+
+    This is because the two are not equal to each other in general.
+    For example, consider x == -1:
+
+    >>> from sympy import Eq
+    >>> Eq(sqrt(x**2), x).subs(x, -1)
+    False
+
+    This is because sqrt computes the principal square root, so the square may
+    put the argument in a different branch.  This identity does hold if x is
+    positive:
+
+    >>> y = Symbol('y', positive=True)
+    >>> sqrt(y**2)
+    y
+
+    You can force this simplification by using the powdenest() function with
+    the force option set to True:
+
+    >>> from sympy import powdenest
+    >>> sqrt(x**2)
+    sqrt(x**2)
+    >>> powdenest(sqrt(x**2), force=True)
+    x
+
+    To get both branches of the square root you can use the rootof function:
+
+    >>> from sympy import rootof
+
+    >>> [rootof(x**2-3,i) for i in (0,1)]
+    [-sqrt(3), sqrt(3)]
+
+    Although ``sqrt`` is printed, there is no ``sqrt`` function so looking for
+    ``sqrt`` in an expression will fail:
+
+    >>> from sympy.utilities.misc import func_name
+    >>> func_name(sqrt(x))
+    'Pow'
+    >>> sqrt(x).has(sqrt)
+    False
+
+    To find ``sqrt`` look for ``Pow`` with an exponent of ``1/2``:
+
+    >>> (x + 1/sqrt(x)).find(lambda i: i.is_Pow and abs(i.exp) is S.Half)
+    {1/sqrt(x)}
+
+    See Also
+    ========
+
+    sympy.polys.rootoftools.rootof, root, real_root
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Square_root
+    .. [2] https://en.wikipedia.org/wiki/Principal_value
+    """
+    # arg = sympify(arg) is handled by Pow
+    return Pow(arg, S.Half, evaluate=evaluate)
+
+
+def cbrt(arg, evaluate=None):
+    """Returns the principal cube root.
+
+    Parameters
+    ==========
+
+    evaluate : bool, optional
+        The parameter determines if the expression should be evaluated.
+        If ``None``, its value is taken from
+        ``global_parameters.evaluate``.
+
+    Examples
+    ========
+
+    >>> from sympy import cbrt, Symbol
+    >>> x = Symbol('x')
+
+    >>> cbrt(x)
+    x**(1/3)
+
+    >>> cbrt(x)**3
+    x
+
+    Note that cbrt(x**3) does not simplify to x.
+
+    >>> cbrt(x**3)
+    (x**3)**(1/3)
+
+    This is because the two are not equal to each other in general.
+    For example, consider `x == -1`:
+
+    >>> from sympy import Eq
+    >>> Eq(cbrt(x**3), x).subs(x, -1)
+    False
+
+    This is because cbrt computes the principal cube root, this
+    identity does hold if `x` is positive:
+
+    >>> y = Symbol('y', positive=True)
+    >>> cbrt(y**3)
+    y
+
+    See Also
+    ========
+
+    sympy.polys.rootoftools.rootof, root, real_root
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Cube_root
+    .. [2] https://en.wikipedia.org/wiki/Principal_value
+
+    """
+    return Pow(arg, Rational(1, 3), evaluate=evaluate)
+
+
+def root(arg, n, k=0, evaluate=None):
+    r"""Returns the *k*-th *n*-th root of ``arg``.
+
+    Parameters
+    ==========
+
+    k : int, optional
+        Should be an integer in $\{0, 1, ..., n-1\}$.
+        Defaults to the principal root if $0$.
+
+    evaluate : bool, optional
+        The parameter determines if the expression should be evaluated.
+        If ``None``, its value is taken from
+        ``global_parameters.evaluate``.
+
+    Examples
+    ========
+
+    >>> from sympy import root, Rational
+    >>> from sympy.abc import x, n
+
+    >>> root(x, 2)
+    sqrt(x)
+
+    >>> root(x, 3)
+    x**(1/3)
+
+    >>> root(x, n)
+    x**(1/n)
+
+    >>> root(x, -Rational(2, 3))
+    x**(-3/2)
+
+    To get the k-th n-th root, specify k:
+
+    >>> root(-2, 3, 2)
+    -(-1)**(2/3)*2**(1/3)
+
+    To get all n n-th roots you can use the rootof function.
+    The following examples show the roots of unity for n
+    equal 2, 3 and 4:
+
+    >>> from sympy import rootof
+
+    >>> [rootof(x**2 - 1, i) for i in range(2)]
+    [-1, 1]
+
+    >>> [rootof(x**3 - 1,i) for i in range(3)]
+    [1, -1/2 - sqrt(3)*I/2, -1/2 + sqrt(3)*I/2]
+
+    >>> [rootof(x**4 - 1,i) for i in range(4)]
+    [-1, 1, -I, I]
+
+    SymPy, like other symbolic algebra systems, returns the
+    complex root of negative numbers. This is the principal
+    root and differs from the text-book result that one might
+    be expecting. For example, the cube root of -8 does not
+    come back as -2:
+
+    >>> root(-8, 3)
+    2*(-1)**(1/3)
+
+    The real_root function can be used to either make the principal
+    result real (or simply to return the real root directly):
+
+    >>> from sympy import real_root
+    >>> real_root(_)
+    -2
+    >>> real_root(-32, 5)
+    -2
+
+    Alternatively, the n//2-th n-th root of a negative number can be
+    computed with root:
+
+    >>> root(-32, 5, 5//2)
+    -2
+
+    See Also
+    ========
+
+    sympy.polys.rootoftools.rootof
+    sympy.core.intfunc.integer_nthroot
+    sqrt, real_root
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Square_root
+    .. [2] https://en.wikipedia.org/wiki/Real_root
+    .. [3] https://en.wikipedia.org/wiki/Root_of_unity
+    .. [4] https://en.wikipedia.org/wiki/Principal_value
+    .. [5] https://mathworld.wolfram.com/CubeRoot.html
+
+    """
+    n = sympify(n)
+    if k:
+        return Mul(Pow(arg, S.One/n, evaluate=evaluate), S.NegativeOne**(2*k/n), evaluate=evaluate)
+    return Pow(arg, 1/n, evaluate=evaluate)
+
+
+def real_root(arg, n=None, evaluate=None):
+    r"""Return the real *n*'th-root of *arg* if possible.
+
+    Parameters
+    ==========
+
+    n : int or None, optional
+        If *n* is ``None``, then all instances of
+        $(-n)^{1/\text{odd}}$ will be changed to $-n^{1/\text{odd}}$.
+        This will only create a real root of a principal root.
+        The presence of other factors may cause the result to not be
+        real.
+
+    evaluate : bool, optional
+        The parameter determines if the expression should be evaluated.
+        If ``None``, its value is taken from
+        ``global_parameters.evaluate``.
+
+    Examples
+    ========
+
+    >>> from sympy import root, real_root
+
+    >>> real_root(-8, 3)
+    -2
+    >>> root(-8, 3)
+    2*(-1)**(1/3)
+    >>> real_root(_)
+    -2
+
+    If one creates a non-principal root and applies real_root, the
+    result will not be real (so use with caution):
+
+    >>> root(-8, 3, 2)
+    -2*(-1)**(2/3)
+    >>> real_root(_)
+    -2*(-1)**(2/3)
+
+    See Also
+    ========
+
+    sympy.polys.rootoftools.rootof
+    sympy.core.intfunc.integer_nthroot
+    root, sqrt
+    """
+    from sympy.functions.elementary.complexes import Abs, im, sign
+    from sympy.functions.elementary.piecewise import Piecewise
+    if n is not None:
+        return Piecewise(
+            (root(arg, n, evaluate=evaluate), Or(Eq(n, S.One), Eq(n, S.NegativeOne))),
+            (Mul(sign(arg), root(Abs(arg), n, evaluate=evaluate), evaluate=evaluate),
+            And(Eq(im(arg), S.Zero), Eq(Mod(n, 2), S.One))),
+            (root(arg, n, evaluate=evaluate), True))
+    rv = sympify(arg)
+    n1pow = Transform(lambda x: -(-x.base)**x.exp,
+                      lambda x:
+                      x.is_Pow and
+                      x.base.is_negative and
+                      x.exp.is_Rational and
+                      x.exp.p == 1 and x.exp.q % 2)
+    return rv.xreplace(n1pow)
+
+###############################################################################
+############################# MINIMUM and MAXIMUM #############################
+###############################################################################
+
+
+class MinMaxBase(Expr, LatticeOp):
+    def __new__(cls, *args, **assumptions):
+        from sympy.core.parameters import global_parameters
+        evaluate = assumptions.pop('evaluate', global_parameters.evaluate)
+        args = (sympify(arg) for arg in args)
+
+        # first standard filter, for cls.zero and cls.identity
+        # also reshape Max(a, Max(b, c)) to Max(a, b, c)
+
+        if evaluate:
+            try:
+                args = frozenset(cls._new_args_filter(args))
+            except ShortCircuit:
+                return cls.zero
+            # remove redundant args that are easily identified
+            args = cls._collapse_arguments(args, **assumptions)
+            # find local zeros
+            args = cls._find_localzeros(args, **assumptions)
+        args = frozenset(args)
+
+        if not args:
+            return cls.identity
+
+        if len(args) == 1:
+            return list(args).pop()
+
+        # base creation
+        obj = Expr.__new__(cls, *ordered(args), **assumptions)
+        obj._argset = args
+        return obj
+
+    @classmethod
+    def _collapse_arguments(cls, args, **assumptions):
+        """Remove redundant args.
+
+        Examples
+        ========
+
+        >>> from sympy import Min, Max
+        >>> from sympy.abc import a, b, c, d, e
+
+        Any arg in parent that appears in any
+        parent-like function in any of the flat args
+        of parent can be removed from that sub-arg:
+
+        >>> Min(a, Max(b, Min(a, c, d)))
+        Min(a, Max(b, Min(c, d)))
+
+        If the arg of parent appears in an opposite-than parent
+        function in any of the flat args of parent that function
+        can be replaced with the arg:
+
+        >>> Min(a, Max(b, Min(c, d, Max(a, e))))
+        Min(a, Max(b, Min(a, c, d)))
+        """
+        if not args:
+            return args
+        args = list(ordered(args))
+        if cls == Min:
+            other = Max
+        else:
+            other = Min
+
+        # find global comparable max of Max and min of Min if a new
+        # value is being introduced in these args at position 0 of
+        # the ordered args
+        if args[0].is_number:
+            sifted = mins, maxs = [], []
+            for i in args:
+                for v in walk(i, Min, Max):
+                    if v.args[0].is_comparable:
+                        sifted[isinstance(v, Max)].append(v)
+            small = Min.identity
+            for i in mins:
+                v = i.args[0]
+                if v.is_number and (v < small) == True:
+                    small = v
+            big = Max.identity
+            for i in maxs:
+                v = i.args[0]
+                if v.is_number and (v > big) == True:
+                    big = v
+            # at the point when this function is called from __new__,
+            # there may be more than one numeric arg present since
+            # local zeros have not been handled yet, so look through
+            # more than the first arg
+            if cls == Min:
+                for arg in args:
+                    if not arg.is_number:
+                        break
+                    if (arg < small) == True:
+                        small = arg
+            elif cls == Max:
+                for arg in args:
+                    if not arg.is_number:
+                        break
+                    if (arg > big) == True:
+                        big = arg
+            T = None
+            if cls == Min:
+                if small != Min.identity:
+                    other = Max
+                    T = small
+            elif big != Max.identity:
+                other = Min
+                T = big
+            if T is not None:
+                # remove numerical redundancy
+                for i in range(len(args)):
+                    a = args[i]
+                    if isinstance(a, other):
+                        a0 = a.args[0]
+                        if ((a0 > T) if other == Max else (a0 < T)) == True:
+                            args[i] = cls.identity
+
+        # remove redundant symbolic args
+        def do(ai, a):
+            if not isinstance(ai, (Min, Max)):
+                return ai
+            cond = a in ai.args
+            if not cond:
+                return ai.func(*[do(i, a) for i in ai.args],
+                    evaluate=False)
+            if isinstance(ai, cls):
+                return ai.func(*[do(i, a) for i in ai.args if i != a],
+                    evaluate=False)
+            return a
+        for i, a in enumerate(args):
+            args[i + 1:] = [do(ai, a) for ai in args[i + 1:]]
+
+        # factor out common elements as for
+        # Min(Max(x, y), Max(x, z)) -> Max(x, Min(y, z))
+        # and vice versa when swapping Min/Max -- do this only for the
+        # easy case where all functions contain something in common;
+        # trying to find some optimal subset of args to modify takes
+        # too long
+
+        def factor_minmax(args):
+            is_other = lambda arg: isinstance(arg, other)
+            other_args, remaining_args = sift(args, is_other, binary=True)
+            if not other_args:
+                return args
+
+            # Min(Max(x, y, z), Max(x, y, u, v)) -> {x,y}, ({z}, {u,v})
+            arg_sets = [set(arg.args) for arg in other_args]
+            common = set.intersection(*arg_sets)
+            if not common:
+                return args
+
+            new_other_args = list(common)
+            arg_sets_diff = [arg_set - common for arg_set in arg_sets]
+
+            # If any set is empty after removing common then all can be
+            # discarded e.g. Min(Max(a, b, c), Max(a, b)) -> Max(a, b)
+            if all(arg_sets_diff):
+                other_args_diff = [other(*s, evaluate=False) for s in arg_sets_diff]
+                new_other_args.append(cls(*other_args_diff, evaluate=False))
+
+            other_args_factored = other(*new_other_args, evaluate=False)
+            return remaining_args + [other_args_factored]
+
+        if len(args) > 1:
+            args = factor_minmax(args)
+
+        return args
+
+    @classmethod
+    def _new_args_filter(cls, arg_sequence):
+        """
+        Generator filtering args.
+
+        first standard filter, for cls.zero and cls.identity.
+        Also reshape ``Max(a, Max(b, c))`` to ``Max(a, b, c)``,
+        and check arguments for comparability
+        """
+        for arg in arg_sequence:
+            # pre-filter, checking comparability of arguments
+            if not isinstance(arg, Expr) or arg.is_extended_real is False or (
+                    arg.is_number and
+                    not arg.is_comparable):
+                raise ValueError("The argument '%s' is not comparable." % arg)
+
+            if arg == cls.zero:
+                raise ShortCircuit(arg)
+            elif arg == cls.identity:
+                continue
+            elif arg.func == cls:
+                yield from arg.args
+            else:
+                yield arg
+
+    @classmethod
+    def _find_localzeros(cls, values, **options):
+        """
+        Sequentially allocate values to localzeros.
+
+        When a value is identified as being more extreme than another member it
+        replaces that member; if this is never true, then the value is simply
+        appended to the localzeros.
+        """
+        localzeros = set()
+        for v in values:
+            is_newzero = True
+            localzeros_ = list(localzeros)
+            for z in localzeros_:
+                if id(v) == id(z):
+                    is_newzero = False
+                else:
+                    con = cls._is_connected(v, z)
+                    if con:
+                        is_newzero = False
+                        if con is True or con == cls:
+                            localzeros.remove(z)
+                            localzeros.update([v])
+            if is_newzero:
+                localzeros.update([v])
+        return localzeros
+
+    @classmethod
+    def _is_connected(cls, x, y):
+        """
+        Check if x and y are connected somehow.
+        """
+        for i in range(2):
+            if x == y:
+                return True
+            t, f = Max, Min
+            for op in "><":
+                for j in range(2):
+                    try:
+                        if op == ">":
+                            v = x >= y
+                        else:
+                            v = x <= y
+                    except TypeError:
+                        return False  # non-real arg
+                    if not v.is_Relational:
+                        return t if v else f
+                    t, f = f, t
+                    x, y = y, x
+                x, y = y, x  # run next pass with reversed order relative to start
+            # simplification can be expensive, so be conservative
+            # in what is attempted
+            x = factor_terms(x - y)
+            y = S.Zero
+
+        return False
+
+    def _eval_derivative(self, s):
+        # f(x).diff(s) -> x.diff(s) * f.fdiff(1)(s)
+        i = 0
+        l = []
+        for a in self.args:
+            i += 1
+            da = a.diff(s)
+            if da.is_zero:
+                continue
+            try:
+                df = self.fdiff(i)
+            except ArgumentIndexError:
+                df = super().fdiff(i)
+            l.append(df * da)
+        return Add(*l)
+
+    def _eval_rewrite_as_Abs(self, *args, **kwargs):
+        from sympy.functions.elementary.complexes import Abs
+        s = (args[0] + self.func(*args[1:]))/2
+        d = abs(args[0] - self.func(*args[1:]))/2
+        return (s + d if isinstance(self, Max) else s - d).rewrite(Abs)
+
+    def evalf(self, n=15, **options):
+        return self.func(*[a.evalf(n, **options) for a in self.args])
+
+    def n(self, *args, **kwargs):
+        return self.evalf(*args, **kwargs)
+
+    _eval_is_algebraic = lambda s: _torf(i.is_algebraic for i in s.args)
+    _eval_is_antihermitian = lambda s: _torf(i.is_antihermitian for i in s.args)
+    _eval_is_commutative = lambda s: _torf(i.is_commutative for i in s.args)
+    _eval_is_complex = lambda s: _torf(i.is_complex for i in s.args)
+    _eval_is_composite = lambda s: _torf(i.is_composite for i in s.args)
+    _eval_is_even = lambda s: _torf(i.is_even for i in s.args)
+    _eval_is_finite = lambda s: _torf(i.is_finite for i in s.args)
+    _eval_is_hermitian = lambda s: _torf(i.is_hermitian for i in s.args)
+    _eval_is_imaginary = lambda s: _torf(i.is_imaginary for i in s.args)
+    _eval_is_infinite = lambda s: _torf(i.is_infinite for i in s.args)
+    _eval_is_integer = lambda s: _torf(i.is_integer for i in s.args)
+    _eval_is_irrational = lambda s: _torf(i.is_irrational for i in s.args)
+    _eval_is_negative = lambda s: _torf(i.is_negative for i in s.args)
+    _eval_is_noninteger = lambda s: _torf(i.is_noninteger for i in s.args)
+    _eval_is_nonnegative = lambda s: _torf(i.is_nonnegative for i in s.args)
+    _eval_is_nonpositive = lambda s: _torf(i.is_nonpositive for i in s.args)
+    _eval_is_nonzero = lambda s: _torf(i.is_nonzero for i in s.args)
+    _eval_is_odd = lambda s: _torf(i.is_odd for i in s.args)
+    _eval_is_polar = lambda s: _torf(i.is_polar for i in s.args)
+    _eval_is_positive = lambda s: _torf(i.is_positive for i in s.args)
+    _eval_is_prime = lambda s: _torf(i.is_prime for i in s.args)
+    _eval_is_rational = lambda s: _torf(i.is_rational for i in s.args)
+    _eval_is_real = lambda s: _torf(i.is_real for i in s.args)
+    _eval_is_extended_real = lambda s: _torf(i.is_extended_real for i in s.args)
+    _eval_is_transcendental = lambda s: _torf(i.is_transcendental for i in s.args)
+    _eval_is_zero = lambda s: _torf(i.is_zero for i in s.args)
+
+
+class Max(MinMaxBase, Application):
+    r"""
+    Return, if possible, the maximum value of the list.
+
+    When number of arguments is equal one, then
+    return this argument.
+
+    When number of arguments is equal two, then
+    return, if possible, the value from (a, b) that is $\ge$ the other.
+
+    In common case, when the length of list greater than 2, the task
+    is more complicated. Return only the arguments, which are greater
+    than others, if it is possible to determine directional relation.
+
+    If is not possible to determine such a relation, return a partially
+    evaluated result.
+
+    Assumptions are used to make the decision too.
+
+    Also, only comparable arguments are permitted.
+
+    It is named ``Max`` and not ``max`` to avoid conflicts
+    with the built-in function ``max``.
+
+
+    Examples
+    ========
+
+    >>> from sympy import Max, Symbol, oo
+    >>> from sympy.abc import x, y, z
+    >>> p = Symbol('p', positive=True)
+    >>> n = Symbol('n', negative=True)
+
+    >>> Max(x, -2)
+    Max(-2, x)
+    >>> Max(x, -2).subs(x, 3)
+    3
+    >>> Max(p, -2)
+    p
+    >>> Max(x, y)
+    Max(x, y)
+    >>> Max(x, y) == Max(y, x)
+    True
+    >>> Max(x, Max(y, z))
+    Max(x, y, z)
+    >>> Max(n, 8, p, 7, -oo)
+    Max(8, p)
+    >>> Max (1, x, oo)
+    oo
+
+    * Algorithm
+
+    The task can be considered as searching of supremums in the
+    directed complete partial orders [1]_.
+
+    The source values are sequentially allocated by the isolated subsets
+    in which supremums are searched and result as Max arguments.
+
+    If the resulted supremum is single, then it is returned.
+
+    The isolated subsets are the sets of values which are only the comparable
+    with each other in the current set. E.g. natural numbers are comparable with
+    each other, but not comparable with the `x` symbol. Another example: the
+    symbol `x` with negative assumption is comparable with a natural number.
+
+    Also there are "least" elements, which are comparable with all others,
+    and have a zero property (maximum or minimum for all elements).
+    For example, in case of $\infty$, the allocation operation is terminated
+    and only this value is returned.
+
+    Assumption:
+       - if $A > B > C$ then $A > C$
+       - if $A = B$ then $B$ can be removed
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Directed_complete_partial_order
+    .. [2] https://en.wikipedia.org/wiki/Lattice_%28order%29
+
+    See Also
+    ========
+
+    Min : find minimum values
+    """
+    zero = S.Infinity
+    identity = S.NegativeInfinity
+
+    def fdiff( self, argindex ):
+        from sympy.functions.special.delta_functions import Heaviside
+        n = len(self.args)
+        if 0 < argindex and argindex <= n:
+            argindex -= 1
+            if n == 2:
+                return Heaviside(self.args[argindex] - self.args[1 - argindex])
+            newargs = tuple([self.args[i] for i in range(n) if i != argindex])
+            return Heaviside(self.args[argindex] - Max(*newargs))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Heaviside(self, *args, **kwargs):
+        from sympy.functions.special.delta_functions import Heaviside
+        return Add(*[j*Mul(*[Heaviside(j - i) for i in args if i!=j]) \
+                for j in args])
+
+    def _eval_rewrite_as_Piecewise(self, *args, **kwargs):
+        return _minmax_as_Piecewise('>=', *args)
+
+    def _eval_is_positive(self):
+        return fuzzy_or(a.is_positive for a in self.args)
+
+    def _eval_is_nonnegative(self):
+        return fuzzy_or(a.is_nonnegative for a in self.args)
+
+    def _eval_is_negative(self):
+        return fuzzy_and(a.is_negative for a in self.args)
+
+
+class Min(MinMaxBase, Application):
+    """
+    Return, if possible, the minimum value of the list.
+    It is named ``Min`` and not ``min`` to avoid conflicts
+    with the built-in function ``min``.
+
+    Examples
+    ========
+
+    >>> from sympy import Min, Symbol, oo
+    >>> from sympy.abc import x, y
+    >>> p = Symbol('p', positive=True)
+    >>> n = Symbol('n', negative=True)
+
+    >>> Min(x, -2)
+    Min(-2, x)
+    >>> Min(x, -2).subs(x, 3)
+    -2
+    >>> Min(p, -3)
+    -3
+    >>> Min(x, y)
+    Min(x, y)
+    >>> Min(n, 8, p, -7, p, oo)
+    Min(-7, n)
+
+    See Also
+    ========
+
+    Max : find maximum values
+    """
+    zero = S.NegativeInfinity
+    identity = S.Infinity
+
+    def fdiff( self, argindex ):
+        from sympy.functions.special.delta_functions import Heaviside
+        n = len(self.args)
+        if 0 < argindex and argindex <= n:
+            argindex -= 1
+            if n == 2:
+                return Heaviside( self.args[1-argindex] - self.args[argindex] )
+            newargs = tuple([ self.args[i] for i in range(n) if i != argindex])
+            return Heaviside( Min(*newargs) - self.args[argindex] )
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Heaviside(self, *args, **kwargs):
+        from sympy.functions.special.delta_functions import Heaviside
+        return Add(*[j*Mul(*[Heaviside(i-j) for i in args if i!=j]) \
+                for j in args])
+
+    def _eval_rewrite_as_Piecewise(self, *args, **kwargs):
+        return _minmax_as_Piecewise('<=', *args)
+
+    def _eval_is_positive(self):
+        return fuzzy_and(a.is_positive for a in self.args)
+
+    def _eval_is_nonnegative(self):
+        return fuzzy_and(a.is_nonnegative for a in self.args)
+
+    def _eval_is_negative(self):
+        return fuzzy_or(a.is_negative for a in self.args)
+
+
+class Rem(DefinedFunction):
+    """Returns the remainder when ``p`` is divided by ``q`` where ``p`` is finite
+    and ``q`` is not equal to zero. The result, ``p - int(p/q)*q``, has the same sign
+    as the divisor.
+
+    Parameters
+    ==========
+
+    p : Expr
+        Dividend.
+
+    q : Expr
+        Divisor.
+
+    Notes
+    =====
+
+    ``Rem`` corresponds to the ``%`` operator in C.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy import Rem
+    >>> Rem(x**3, y)
+    Rem(x**3, y)
+    >>> Rem(x**3, y).subs({x: -5, y: 3})
+    -2
+
+    See Also
+    ========
+
+    Mod
+    """
+    kind = NumberKind
+
+    @classmethod
+    def eval(cls, p, q):
+        """Return the function remainder if both p, q are numbers and q is not
+        zero.
+        """
+
+        if q.is_zero:
+            raise ZeroDivisionError("Division by zero")
+        if p is S.NaN or q is S.NaN or p.is_finite is False or q.is_finite is False:
+            return S.NaN
+        if p is S.Zero or p in (q, -q) or (p.is_integer and q == 1):
+            return S.Zero
+
+        if q.is_Number:
+            if p.is_Number:
+                return p - Integer(p/q)*q
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/piecewise.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/piecewise.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe4a4d4f57e2c3af170dac994e11782b9ed54b8f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/piecewise.py
@@ -0,0 +1,1517 @@
+from sympy.core import S, diff, Tuple, Dummy, Mul
+from sympy.core.basic import Basic, as_Basic
+from sympy.core.function import DefinedFunction
+from sympy.core.numbers import Rational, NumberSymbol, _illegal
+from sympy.core.parameters import global_parameters
+from sympy.core.relational import (Lt, Gt, Eq, Ne, Relational,
+    _canonical, _canonical_coeff)
+from sympy.core.sorting import ordered
+from sympy.functions.elementary.miscellaneous import Max, Min
+from sympy.logic.boolalg import (And, Boolean, distribute_and_over_or, Not,
+    true, false, Or, ITE, simplify_logic, to_cnf, distribute_or_over_and)
+from sympy.utilities.iterables import uniq, sift, common_prefix
+from sympy.utilities.misc import filldedent, func_name
+
+from itertools import product
+
+Undefined = S.NaN  # Piecewise()
+
+class ExprCondPair(Tuple):
+    """Represents an expression, condition pair."""
+
+    def __new__(cls, expr, cond):
+        expr = as_Basic(expr)
+        if cond == True:
+            return Tuple.__new__(cls, expr, true)
+        elif cond == False:
+            return Tuple.__new__(cls, expr, false)
+        elif isinstance(cond, Basic) and cond.has(Piecewise):
+            cond = piecewise_fold(cond)
+            if isinstance(cond, Piecewise):
+                cond = cond.rewrite(ITE)
+
+        if not isinstance(cond, Boolean):
+            raise TypeError(filldedent('''
+                Second argument must be a Boolean,
+                not `%s`''' % func_name(cond)))
+        return Tuple.__new__(cls, expr, cond)
+
+    @property
+    def expr(self):
+        """
+        Returns the expression of this pair.
+        """
+        return self.args[0]
+
+    @property
+    def cond(self):
+        """
+        Returns the condition of this pair.
+        """
+        return self.args[1]
+
+    @property
+    def is_commutative(self):
+        return self.expr.is_commutative
+
+    def __iter__(self):
+        yield self.expr
+        yield self.cond
+
+    def _eval_simplify(self, **kwargs):
+        return self.func(*[a.simplify(**kwargs) for a in self.args])
+
+
+class Piecewise(DefinedFunction):
+    """
+    Represents a piecewise function.
+
+    Usage:
+
+      Piecewise( (expr,cond), (expr,cond), ... )
+        - Each argument is a 2-tuple defining an expression and condition
+        - The conds are evaluated in turn returning the first that is True.
+          If any of the evaluated conds are not explicitly False,
+          e.g. ``x < 1``, the function is returned in symbolic form.
+        - If the function is evaluated at a place where all conditions are False,
+          nan will be returned.
+        - Pairs where the cond is explicitly False, will be removed and no pair
+          appearing after a True condition will ever be retained. If a single
+          pair with a True condition remains, it will be returned, even when
+          evaluation is False.
+
+    Examples
+    ========
+
+    >>> from sympy import Piecewise, log, piecewise_fold
+    >>> from sympy.abc import x, y
+    >>> f = x**2
+    >>> g = log(x)
+    >>> p = Piecewise((0, x < -1), (f, x <= 1), (g, True))
+    >>> p.subs(x,1)
+    1
+    >>> p.subs(x,5)
+    log(5)
+
+    Booleans can contain Piecewise elements:
+
+    >>> cond = (x < y).subs(x, Piecewise((2, x < 0), (3, True))); cond
+    Piecewise((2, x < 0), (3, True)) < y
+
+    The folded version of this results in a Piecewise whose
+    expressions are Booleans:
+
+    >>> folded_cond = piecewise_fold(cond); folded_cond
+    Piecewise((2 < y, x < 0), (3 < y, True))
+
+    When a Boolean containing Piecewise (like cond) or a Piecewise
+    with Boolean expressions (like folded_cond) is used as a condition,
+    it is converted to an equivalent :class:`~.ITE` object:
+
+    >>> Piecewise((1, folded_cond))
+    Piecewise((1, ITE(x < 0, y > 2, y > 3)))
+
+    When a condition is an ``ITE``, it will be converted to a simplified
+    Boolean expression:
+
+    >>> piecewise_fold(_)
+    Piecewise((1, ((x >= 0) | (y > 2)) & ((y > 3) | (x < 0))))
+
+    See Also
+    ========
+
+    piecewise_fold
+    piecewise_exclusive
+    ITE
+    """
+
+    nargs = None
+    is_Piecewise = True
+
+    def __new__(cls, *args, **options):
+        if len(args) == 0:
+            raise TypeError("At least one (expr, cond) pair expected.")
+        # (Try to) sympify args first
+        newargs = []
+        for ec in args:
+            # ec could be a ExprCondPair or a tuple
+            pair = ExprCondPair(*getattr(ec, 'args', ec))
+            cond = pair.cond
+            if cond is false:
+                continue
+            newargs.append(pair)
+            if cond is true:
+                break
+
+        eval = options.pop('evaluate', global_parameters.evaluate)
+        if eval:
+            r = cls.eval(*newargs)
+            if r is not None:
+                return r
+        elif len(newargs) == 1 and newargs[0].cond == True:
+            return newargs[0].expr
+
+        return Basic.__new__(cls, *newargs, **options)
+
+    @classmethod
+    def eval(cls, *_args):
+        """Either return a modified version of the args or, if no
+        modifications were made, return None.
+
+        Modifications that are made here:
+
+        1. relationals are made canonical
+        2. any False conditions are dropped
+        3. any repeat of a previous condition is ignored
+        4. any args past one with a true condition are dropped
+
+        If there are no args left, nan will be returned.
+        If there is a single arg with a True condition, its
+        corresponding expression will be returned.
+
+        EXAMPLES
+        ========
+
+        >>> from sympy import Piecewise
+        >>> from sympy.abc import x
+        >>> cond = -x < -1
+        >>> args = [(1, cond), (4, cond), (3, False), (2, True), (5, x < 1)]
+        >>> Piecewise(*args, evaluate=False)
+        Piecewise((1, -x < -1), (4, -x < -1), (2, True))
+        >>> Piecewise(*args)
+        Piecewise((1, x > 1), (2, True))
+        """
+        if not _args:
+            return Undefined
+
+        if len(_args) == 1 and _args[0][-1] == True:
+            return _args[0][0]
+
+        newargs = _piecewise_collapse_arguments(_args)
+
+        # some conditions may have been redundant
+        missing = len(newargs) != len(_args)
+        # some conditions may have changed
+        same = all(a == b for a, b in zip(newargs, _args))
+        # if either change happened we return the expr with the
+        # updated args
+        if not newargs:
+            raise ValueError(filldedent('''
+                There are no conditions (or none that
+                are not trivially false) to define an
+                expression.'''))
+        if missing or not same:
+            return cls(*newargs)
+
+    def doit(self, **hints):
+        """
+        Evaluate this piecewise function.
+        """
+        newargs = []
+        for e, c in self.args:
+            if hints.get('deep', True):
+                if isinstance(e, Basic):
+                    newe = e.doit(**hints)
+                    if newe != self:
+                        e = newe
+                if isinstance(c, Basic):
+                    c = c.doit(**hints)
+            newargs.append((e, c))
+        return self.func(*newargs)
+
+    def _eval_simplify(self, **kwargs):
+        return piecewise_simplify(self, **kwargs)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        for e, c in self.args:
+            if c == True or c.subs(x, 0) == True:
+                return e.as_leading_term(x)
+
+    def _eval_adjoint(self):
+        return self.func(*[(e.adjoint(), c) for e, c in self.args])
+
+    def _eval_conjugate(self):
+        return self.func(*[(e.conjugate(), c) for e, c in self.args])
+
+    def _eval_derivative(self, x):
+        return self.func(*[(diff(e, x), c) for e, c in self.args])
+
+    def _eval_evalf(self, prec):
+        return self.func(*[(e._evalf(prec), c) for e, c in self.args])
+
+    def _eval_is_meromorphic(self, x, a):
+        # Conditions often implicitly assume that the argument is real.
+        # Hence, there needs to be some check for as_set.
+        if not a.is_real:
+            return None
+
+        # Then, scan ExprCondPairs in the given order to find a piece that would contain a,
+        # possibly as a boundary point.
+        for e, c in self.args:
+            cond = c.subs(x, a)
+
+            if cond.is_Relational:
+                return None
+            if a in c.as_set().boundary:
+                return None
+            # Apply expression if a is an interior point of the domain of e.
+            if cond:
+                return e._eval_is_meromorphic(x, a)
+
+    def piecewise_integrate(self, x, **kwargs):
+        """Return the Piecewise with each expression being
+        replaced with its antiderivative. To obtain a continuous
+        antiderivative, use the :func:`~.integrate` function or method.
+
+        Examples
+        ========
+
+        >>> from sympy import Piecewise
+        >>> from sympy.abc import x
+        >>> p = Piecewise((0, x < 0), (1, x < 1), (2, True))
+        >>> p.piecewise_integrate(x)
+        Piecewise((0, x < 0), (x, x < 1), (2*x, True))
+
+        Note that this does not give a continuous function, e.g.
+        at x = 1 the 3rd condition applies and the antiderivative
+        there is 2*x so the value of the antiderivative is 2:
+
+        >>> anti = _
+        >>> anti.subs(x, 1)
+        2
+
+        The continuous derivative accounts for the integral *up to*
+        the point of interest, however:
+
+        >>> p.integrate(x)
+        Piecewise((0, x < 0), (x, x < 1), (2*x - 1, True))
+        >>> _.subs(x, 1)
+        1
+
+        See Also
+        ========
+        Piecewise._eval_integral
+        """
+        from sympy.integrals import integrate
+        return self.func(*[(integrate(e, x, **kwargs), c) for e, c in self.args])
+
+    def _handle_irel(self, x, handler):
+        """Return either None (if the conditions of self depend only on x) else
+        a Piecewise expression whose expressions (handled by the handler that
+        was passed) are paired with the governing x-independent relationals,
+        e.g. Piecewise((A, a(x) & b(y)), (B, c(x) | c(y)) ->
+        Piecewise(
+            (handler(Piecewise((A, a(x) & True), (B, c(x) | True)), b(y) & c(y)),
+            (handler(Piecewise((A, a(x) & True), (B, c(x) | False)), b(y)),
+            (handler(Piecewise((A, a(x) & False), (B, c(x) | True)), c(y)),
+            (handler(Piecewise((A, a(x) & False), (B, c(x) | False)), True))
+        """
+        # identify governing relationals
+        rel = self.atoms(Relational)
+        irel = list(ordered([r for r in rel if x not in r.free_symbols
+            and r not in (S.true, S.false)]))
+        if irel:
+            args = {}
+            exprinorder = []
+            for truth in product((1, 0), repeat=len(irel)):
+                reps = dict(zip(irel, truth))
+                # only store the true conditions since the false are implied
+                # when they appear lower in the Piecewise args
+                if 1 not in truth:
+                    cond = None  # flag this one so it doesn't get combined
+                else:
+                    andargs = Tuple(*[i for i in reps if reps[i]])
+                    free = list(andargs.free_symbols)
+                    if len(free) == 1:
+                        from sympy.solvers.inequalities import (
+                            reduce_inequalities, _solve_inequality)
+                        try:
+                            t = reduce_inequalities(andargs, free[0])
+                            # ValueError when there are potentially
+                            # nonvanishing imaginary parts
+                        except (ValueError, NotImplementedError):
+                            # at least isolate free symbol on left
+                            t = And(*[_solve_inequality(
+                                a, free[0], linear=True)
+                                for a in andargs])
+                    else:
+                        t = And(*andargs)
+                    if t is S.false:
+                        continue  # an impossible combination
+                    cond = t
+                expr = handler(self.xreplace(reps))
+                if isinstance(expr, self.func) and len(expr.args) == 1:
+                    expr, econd = expr.args[0]
+                    cond = And(econd, True if cond is None else cond)
+                # the ec pairs are being collected since all possibilities
+                # are being enumerated, but don't put the last one in since
+                # its expr might match a previous expression and it
+                # must appear last in the args
+                if cond is not None:
+                    args.setdefault(expr, []).append(cond)
+                    # but since we only store the true conditions we must maintain
+                    # the order so that the expression with the most true values
+                    # comes first
+                    exprinorder.append(expr)
+            # convert collected conditions as args of Or
+            for k in args:
+                args[k] = Or(*args[k])
+            # take them in the order obtained
+            args = [(e, args[e]) for e in uniq(exprinorder)]
+            # add in the last arg
+            args.append((expr, True))
+            return Piecewise(*args)
+
+    def _eval_integral(self, x, _first=True, **kwargs):
+        """Return the indefinite integral of the
+        Piecewise such that subsequent substitution of x with a
+        value will give the value of the integral (not including
+        the constant of integration) up to that point. To only
+        integrate the individual parts of Piecewise, use the
+        ``piecewise_integrate`` method.
+
+        Examples
+        ========
+
+        >>> from sympy import Piecewise
+        >>> from sympy.abc import x
+        >>> p = Piecewise((0, x < 0), (1, x < 1), (2, True))
+        >>> p.integrate(x)
+        Piecewise((0, x < 0), (x, x < 1), (2*x - 1, True))
+        >>> p.piecewise_integrate(x)
+        Piecewise((0, x < 0), (x, x < 1), (2*x, True))
+
+        See Also
+        ========
+        Piecewise.piecewise_integrate
+        """
+        from sympy.integrals.integrals import integrate
+
+        if _first:
+            def handler(ipw):
+                if isinstance(ipw, self.func):
+                    return ipw._eval_integral(x, _first=False, **kwargs)
+                else:
+                    return ipw.integrate(x, **kwargs)
+            irv = self._handle_irel(x, handler)
+            if irv is not None:
+                return irv
+
+        # handle a Piecewise from -oo to oo with and no x-independent relationals
+        # -----------------------------------------------------------------------
+        ok, abei = self._intervals(x)
+        if not ok:
+            from sympy.integrals.integrals import Integral
+            return Integral(self, x)  # unevaluated
+
+        pieces = [(a, b) for a, b, _, _ in abei]
+        oo = S.Infinity
+        done = [(-oo, oo, -1)]
+        for k, p in enumerate(pieces):
+            if p == (-oo, oo):
+                # all undone intervals will get this key
+                for j, (a, b, i) in enumerate(done):
+                    if i == -1:
+                        done[j] = a, b, k
+                break  # nothing else to consider
+            N = len(done) - 1
+            for j, (a, b, i) in enumerate(reversed(done)):
+                if i == -1:
+                    j = N - j
+                    done[j: j + 1] = _clip(p, (a, b), k)
+        done = [(a, b, i) for a, b, i in done if a != b]
+
+        # append an arg if there is a hole so a reference to
+        # argument -1 will give Undefined
+        if any(i == -1 for (a, b, i) in done):
+            abei.append((-oo, oo, Undefined, -1))
+
+        # return the sum of the intervals
+        args = []
+        sum = None
+        for a, b, i in done:
+            anti = integrate(abei[i][-2], x, **kwargs)
+            if sum is None:
+                sum = anti
+            else:
+                sum = sum.subs(x, a)
+                e = anti._eval_interval(x, a, x)
+                if sum.has(*_illegal) or e.has(*_illegal):
+                    sum = anti
+                else:
+                    sum += e
+            # see if we know whether b is contained in original
+            # condition
+            if b is S.Infinity:
+                cond = True
+            elif self.args[abei[i][-1]].cond.subs(x, b) == False:
+                cond = (x < b)
+            else:
+                cond = (x <= b)
+            args.append((sum, cond))
+        return Piecewise(*args)
+
+    def _eval_interval(self, sym, a, b, _first=True):
+        """Evaluates the function along the sym in a given interval [a, b]"""
+        # FIXME: Currently complex intervals are not supported.  A possible
+        # replacement algorithm, discussed in issue 5227, can be found in the
+        # following papers;
+        #     http://portal.acm.org/citation.cfm?id=281649
+        #     http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.4127&rep=rep1&type=pdf
+
+        if a is None or b is None:
+            # In this case, it is just simple substitution
+            return super()._eval_interval(sym, a, b)
+        else:
+            x, lo, hi = map(as_Basic, (sym, a, b))
+
+        if _first:  # get only x-dependent relationals
+            def handler(ipw):
+                if isinstance(ipw, self.func):
+                    return ipw._eval_interval(x, lo, hi, _first=None)
+                else:
+                    return ipw._eval_interval(x, lo, hi)
+            irv = self._handle_irel(x, handler)
+            if irv is not None:
+                return irv
+
+            if (lo < hi) is S.false or (
+                    lo is S.Infinity or hi is S.NegativeInfinity):
+                rv = self._eval_interval(x, hi, lo, _first=False)
+                if isinstance(rv, Piecewise):
+                    rv = Piecewise(*[(-e, c) for e, c in rv.args])
+                else:
+                    rv = -rv
+                return rv
+
+            if (lo < hi) is S.true or (
+                    hi is S.Infinity or lo is S.NegativeInfinity):
+                pass
+            else:
+                _a = Dummy('lo')
+                _b = Dummy('hi')
+                a = lo if lo.is_comparable else _a
+                b = hi if hi.is_comparable else _b
+                pos = self._eval_interval(x, a, b, _first=False)
+                if a == _a and b == _b:
+                    # it's purely symbolic so just swap lo and hi and
+                    # change the sign to get the value for when lo > hi
+                    neg, pos = (-pos.xreplace({_a: hi, _b: lo}),
+                        pos.xreplace({_a: lo, _b: hi}))
+                else:
+                    # at least one of the bounds was comparable, so allow
+                    # _eval_interval to use that information when computing
+                    # the interval with lo and hi reversed
+                    neg, pos = (-self._eval_interval(x, hi, lo, _first=False),
+                        pos.xreplace({_a: lo, _b: hi}))
+
+                # allow simplification based on ordering of lo and hi
+                p = Dummy('', positive=True)
+                if lo.is_Symbol:
+                    pos = pos.xreplace({lo: hi - p}).xreplace({p: hi - lo})
+                    neg = neg.xreplace({lo: hi + p}).xreplace({p: lo - hi})
+                elif hi.is_Symbol:
+                    pos = pos.xreplace({hi: lo + p}).xreplace({p: hi - lo})
+                    neg = neg.xreplace({hi: lo - p}).xreplace({p: lo - hi})
+                # evaluate limits that may have unevaluate Min/Max
+                touch = lambda _: _.replace(
+                    lambda x: isinstance(x, (Min, Max)),
+                    lambda x: x.func(*x.args))
+                neg = touch(neg)
+                pos = touch(pos)
+                # assemble return expression; make the first condition be Lt
+                # b/c then the first expression will look the same whether
+                # the lo or hi limit is symbolic
+                if a == _a:  # the lower limit was symbolic
+                    rv = Piecewise(
+                        (pos,
+                            lo < hi),
+                        (neg,
+                            True))
+                else:
+                    rv = Piecewise(
+                        (neg,
+                            hi < lo),
+                        (pos,
+                            True))
+
+                if rv == Undefined:
+                    raise ValueError("Can't integrate across undefined region.")
+                if any(isinstance(i, Piecewise) for i in (pos, neg)):
+                    rv = piecewise_fold(rv)
+                return rv
+
+        # handle a Piecewise with lo <= hi and no x-independent relationals
+        # -----------------------------------------------------------------
+        ok, abei = self._intervals(x)
+        if not ok:
+            from sympy.integrals.integrals import Integral
+            # not being able to do the interval of f(x) can
+            # be stated as not being able to do the integral
+            # of f'(x) over the same range
+            return Integral(self.diff(x), (x, lo, hi))  # unevaluated
+
+        pieces = [(a, b) for a, b, _, _ in abei]
+        done = [(lo, hi, -1)]
+        oo = S.Infinity
+        for k, p in enumerate(pieces):
+            if p[:2] == (-oo, oo):
+                # all undone intervals will get this key
+                for j, (a, b, i) in enumerate(done):
+                    if i == -1:
+                        done[j] = a, b, k
+                break  # nothing else to consider
+            N = len(done) - 1
+            for j, (a, b, i) in enumerate(reversed(done)):
+                if i == -1:
+                    j = N - j
+                    done[j: j + 1] = _clip(p, (a, b), k)
+        done = [(a, b, i) for a, b, i in done if a != b]
+
+        # return the sum of the intervals
+        sum = S.Zero
+        upto = None
+        for a, b, i in done:
+            if i == -1:
+                if upto is None:
+                    return Undefined
+                # TODO simplify hi <= upto
+                return Piecewise((sum, hi <= upto), (Undefined, True))
+            sum += abei[i][-2]._eval_interval(x, a, b)
+            upto = b
+        return sum
+
+    def _intervals(self, sym, err_on_Eq=False):
+        r"""Return a bool and a message (when bool is False), else a
+        list of unique tuples, (a, b, e, i), where a and b
+        are the lower and upper bounds in which the expression e of
+        argument i in self is defined and $a < b$ (when involving
+        numbers) or $a \le b$ when involving symbols.
+
+        If there are any relationals not involving sym, or any
+        relational cannot be solved for sym, the bool will be False
+        a message be given as the second return value. The calling
+        routine should have removed such relationals before calling
+        this routine.
+
+        The evaluated conditions will be returned as ranges.
+        Discontinuous ranges will be returned separately with
+        identical expressions. The first condition that evaluates to
+        True will be returned as the last tuple with a, b = -oo, oo.
+        """
+        from sympy.solvers.inequalities import _solve_inequality
+
+        assert isinstance(self, Piecewise)
+
+        def nonsymfail(cond):
+            return False, filldedent('''
+                A condition not involving
+                %s appeared: %s''' % (sym, cond))
+
+        def _solve_relational(r):
+            if sym not in r.free_symbols:
+                return nonsymfail(r)
+            try:
+                rv = _solve_inequality(r, sym)
+            except NotImplementedError:
+                return False, 'Unable to solve relational %s for %s.' % (r, sym)
+            if isinstance(rv, Relational):
+                free = rv.args[1].free_symbols
+                if rv.args[0] != sym or sym in free:
+                    return False, 'Unable to solve relational %s for %s.' % (r, sym)
+                if rv.rel_op == '==':
+                    # this equality has been affirmed to have the form
+                    # Eq(sym, rhs) where rhs is sym-free; it represents
+                    # a zero-width interval which will be ignored
+                    # whether it is an isolated condition or contained
+                    # within an And or an Or
+                    rv = S.false
+                elif rv.rel_op == '!=':
+                    try:
+                        rv = Or(sym < rv.rhs, sym > rv.rhs)
+                    except TypeError:
+                        # e.g. x != I ==> all real x satisfy
+                        rv = S.true
+            elif rv == (S.NegativeInfinity < sym) & (sym < S.Infinity):
+                rv = S.true
+            return True, rv
+
+        args = list(self.args)
+        # make self canonical wrt Relationals
+        keys = self.atoms(Relational)
+        reps = {}
+        for r in keys:
+            ok, s = _solve_relational(r)
+            if ok != True:
+                return False, ok
+            reps[r] = s
+        # process args individually so if any evaluate, their position
+        # in the original Piecewise will be known
+        args = [i.xreplace(reps) for i in self.args]
+
+        # precondition args
+        expr_cond = []
+        default = idefault = None
+        for i, (expr, cond) in enumerate(args):
+            if cond is S.false:
+                continue
+            if cond is S.true:
+                default = expr
+                idefault = i
+                break
+            if isinstance(cond, Eq):
+                # unanticipated condition, but it is here in case a
+                # replacement caused an Eq to appear
+                if err_on_Eq:
+                    return False, 'encountered Eq condition: %s' % cond
+                continue  # zero width interval
+
+            cond = to_cnf(cond)
+            if isinstance(cond, And):
+                cond = distribute_or_over_and(cond)
+
+            if isinstance(cond, Or):
+                expr_cond.extend(
+                    [(i, expr, o) for o in cond.args
+                    if not isinstance(o, Eq)])
+            elif cond is not S.false:
+                expr_cond.append((i, expr, cond))
+            elif cond is S.true:
+                default = expr
+                idefault = i
+                break
+
+        # determine intervals represented by conditions
+        int_expr = []
+        for iarg, expr, cond in expr_cond:
+            if isinstance(cond, And):
+                lower = S.NegativeInfinity
+                upper = S.Infinity
+                exclude = []
+                for cond2 in cond.args:
+                    if not isinstance(cond2, Relational):
+                        return False, 'expecting only Relationals'
+                    if isinstance(cond2, Eq):
+                        lower = upper  # ignore
+                        if err_on_Eq:
+                            return False, 'encountered secondary Eq condition'
+                        break
+                    elif isinstance(cond2, Ne):
+                        l, r = cond2.args
+                        if l == sym:
+                            exclude.append(r)
+                        elif r == sym:
+                            exclude.append(l)
+                        else:
+                            return nonsymfail(cond2)
+                        continue
+                    elif cond2.lts == sym:
+                        upper = Min(cond2.gts, upper)
+                    elif cond2.gts == sym:
+                        lower = Max(cond2.lts, lower)
+                    else:
+                        return nonsymfail(cond2)  # should never get here
+                if exclude:
+                    exclude = list(ordered(exclude))
+                    newcond = []
+                    for i, e in enumerate(exclude):
+                        if e < lower == True or e > upper == True:
+                            continue
+                        if not newcond:
+                            newcond.append((None, lower))  # add a primer
+                        newcond.append((newcond[-1][1], e))
+                    newcond.append((newcond[-1][1], upper))
+                    newcond.pop(0)  # remove the primer
+                    expr_cond.extend([(iarg, expr, And(i[0] < sym, sym < i[1])) for i in newcond])
+                    continue
+            elif isinstance(cond, Relational) and cond.rel_op != '!=':
+                lower, upper = cond.lts, cond.gts  # part 1: initialize with givens
+                if cond.lts == sym:                # part 1a: expand the side ...
+                    lower = S.NegativeInfinity   # e.g. x <= 0 ---> -oo <= 0
+                elif cond.gts == sym:            # part 1a: ... that can be expanded
+                    upper = S.Infinity           # e.g. x >= 0 --->  oo >= 0
+                else:
+                    return nonsymfail(cond)
+            else:
+                return False, 'unrecognized condition: %s' % cond
+
+            upper = Max(lower, upper)
+            if err_on_Eq and lower == upper:
+                return False, 'encountered Eq condition'
+            if (lower >= upper) is not S.true:
+                int_expr.append((lower, upper, expr, iarg))
+
+        if default is not None:
+            int_expr.append(
+                (S.NegativeInfinity, S.Infinity, default, idefault))
+
+        return True, list(uniq(int_expr))
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        args = [(ec.expr._eval_nseries(x, n, logx), ec.cond) for ec in self.args]
+        return self.func(*args)
+
+    def _eval_power(self, s):
+        return self.func(*[(e**s, c) for e, c in self.args])
+
+    def _eval_subs(self, old, new):
+        # this is strictly not necessary, but we can keep track
+        # of whether True or False conditions arise and be
+        # somewhat more efficient by avoiding other substitutions
+        # and avoiding invalid conditions that appear after a
+        # True condition
+        args = list(self.args)
+        args_exist = False
+        for i, (e, c) in enumerate(args):
+            c = c._subs(old, new)
+            if c != False:
+                args_exist = True
+                e = e._subs(old, new)
+            args[i] = (e, c)
+            if c == True:
+                break
+        if not args_exist:
+            args = ((Undefined, True),)
+        return self.func(*args)
+
+    def _eval_transpose(self):
+        return self.func(*[(e.transpose(), c) for e, c in self.args])
+
+    def _eval_template_is_attr(self, is_attr):
+        b = None
+        for expr, _ in self.args:
+            a = getattr(expr, is_attr)
+            if a is None:
+                return
+            if b is None:
+                b = a
+            elif b is not a:
+                return
+        return b
+
+    _eval_is_finite = lambda self: self._eval_template_is_attr(
+        'is_finite')
+    _eval_is_complex = lambda self: self._eval_template_is_attr('is_complex')
+    _eval_is_even = lambda self: self._eval_template_is_attr('is_even')
+    _eval_is_imaginary = lambda self: self._eval_template_is_attr(
+        'is_imaginary')
+    _eval_is_integer = lambda self: self._eval_template_is_attr('is_integer')
+    _eval_is_irrational = lambda self: self._eval_template_is_attr(
+        'is_irrational')
+    _eval_is_negative = lambda self: self._eval_template_is_attr('is_negative')
+    _eval_is_nonnegative = lambda self: self._eval_template_is_attr(
+        'is_nonnegative')
+    _eval_is_nonpositive = lambda self: self._eval_template_is_attr(
+        'is_nonpositive')
+    _eval_is_nonzero = lambda self: self._eval_template_is_attr(
+        'is_nonzero')
+    _eval_is_odd = lambda self: self._eval_template_is_attr('is_odd')
+    _eval_is_polar = lambda self: self._eval_template_is_attr('is_polar')
+    _eval_is_positive = lambda self: self._eval_template_is_attr('is_positive')
+    _eval_is_extended_real = lambda self: self._eval_template_is_attr(
+            'is_extended_real')
+    _eval_is_extended_positive = lambda self: self._eval_template_is_attr(
+            'is_extended_positive')
+    _eval_is_extended_negative = lambda self: self._eval_template_is_attr(
+            'is_extended_negative')
+    _eval_is_extended_nonzero = lambda self: self._eval_template_is_attr(
+            'is_extended_nonzero')
+    _eval_is_extended_nonpositive = lambda self: self._eval_template_is_attr(
+            'is_extended_nonpositive')
+    _eval_is_extended_nonnegative = lambda self: self._eval_template_is_attr(
+            'is_extended_nonnegative')
+    _eval_is_real = lambda self: self._eval_template_is_attr('is_real')
+    _eval_is_zero = lambda self: self._eval_template_is_attr(
+        'is_zero')
+
+    @classmethod
+    def __eval_cond(cls, cond):
+        """Return the truth value of the condition."""
+        if cond == True:
+            return True
+        if isinstance(cond, Eq):
+            try:
+                diff = cond.lhs - cond.rhs
+                if diff.is_commutative:
+                    return diff.is_zero
+            except TypeError:
+                pass
+
+    def as_expr_set_pairs(self, domain=None):
+        """Return tuples for each argument of self that give
+        the expression and the interval in which it is valid
+        which is contained within the given domain.
+        If a condition cannot be converted to a set, an error
+        will be raised. The variable of the conditions is
+        assumed to be real; sets of real values are returned.
+
+        Examples
+        ========
+
+        >>> from sympy import Piecewise, Interval
+        >>> from sympy.abc import x
+        >>> p = Piecewise(
+        ...     (1, x < 2),
+        ...     (2,(x > 0) & (x < 4)),
+        ...     (3, True))
+        >>> p.as_expr_set_pairs()
+        [(1, Interval.open(-oo, 2)),
+         (2, Interval.Ropen(2, 4)),
+         (3, Interval(4, oo))]
+        >>> p.as_expr_set_pairs(Interval(0, 3))
+        [(1, Interval.Ropen(0, 2)),
+         (2, Interval(2, 3))]
+        """
+        if domain is None:
+            domain = S.Reals
+        exp_sets = []
+        U = domain
+        complex = not domain.is_subset(S.Reals)
+        cond_free = set()
+        for expr, cond in self.args:
+            cond_free |= cond.free_symbols
+            if len(cond_free) > 1:
+                raise NotImplementedError(filldedent('''
+                    multivariate conditions are not handled.'''))
+            if complex:
+                for i in cond.atoms(Relational):
+                    if not isinstance(i, (Eq, Ne)):
+                        raise ValueError(filldedent('''
+                            Inequalities in the complex domain are
+                            not supported. Try the real domain by
+                            setting domain=S.Reals'''))
+            cond_int = U.intersect(cond.as_set())
+            U = U - cond_int
+            if cond_int != S.EmptySet:
+                exp_sets.append((expr, cond_int))
+        return exp_sets
+
+    def _eval_rewrite_as_ITE(self, *args, **kwargs):
+        byfree = {}
+        args = list(args)
+        default = any(c == True for b, c in args)
+        for i, (b, c) in enumerate(args):
+            if not isinstance(b, Boolean) and b != True:
+                raise TypeError(filldedent('''
+                    Expecting Boolean or bool but got `%s`
+                    ''' % func_name(b)))
+            if c == True:
+                break
+            # loop over independent conditions for this b
+            for c in c.args if isinstance(c, Or) else [c]:
+                free = c.free_symbols
+                x = free.pop()
+                try:
+                    byfree[x] = byfree.setdefault(
+                        x, S.EmptySet).union(c.as_set())
+                except NotImplementedError:
+                    if not default:
+                        raise NotImplementedError(filldedent('''
+                            A method to determine whether a multivariate
+                            conditional is consistent with a complete coverage
+                            of all variables has not been implemented so the
+                            rewrite is being stopped after encountering `%s`.
+                            This error would not occur if a default expression
+                            like `(foo, True)` were given.
+                            ''' % c))
+                if byfree[x] in (S.UniversalSet, S.Reals):
+                    # collapse the ith condition to True and break
+                    args[i] = list(args[i])
+                    c = args[i][1] = True
+                    break
+            if c == True:
+                break
+        if c != True:
+            raise ValueError(filldedent('''
+                Conditions must cover all reals or a final default
+                condition `(foo, True)` must be given.
+                '''))
+        last, _ = args[i]  # ignore all past ith arg
+        for a, c in reversed(args[:i]):
+            last = ITE(c, a, last)
+        return _canonical(last)
+
+    def _eval_rewrite_as_KroneckerDelta(self, *args, **kwargs):
+        from sympy.functions.special.tensor_functions import KroneckerDelta
+
+        rules = {
+            And: [False, False],
+            Or: [True, True],
+            Not: [True, False],
+            Eq: [None, None],
+            Ne: [None, None]
+        }
+
+        class UnrecognizedCondition(Exception):
+            pass
+
+        def rewrite(cond):
+            if isinstance(cond, Eq):
+                return KroneckerDelta(*cond.args)
+            if isinstance(cond, Ne):
+                return 1 - KroneckerDelta(*cond.args)
+
+            cls, args = type(cond), cond.args
+            if cls not in rules:
+                raise UnrecognizedCondition(cls)
+
+            b1, b2 = rules[cls]
+            k = Mul(*[1 - rewrite(c) for c in args]) if b1 else Mul(*[rewrite(c) for c in args])
+
+            if b2:
+                return 1 - k
+            return k
+
+        conditions = []
+        true_value = None
+        for value, cond in args:
+            if type(cond) in rules:
+                conditions.append((value, cond))
+            elif cond is S.true:
+                if true_value is None:
+                    true_value = value
+            else:
+                return
+
+        if true_value is not None:
+            result = true_value
+
+            for value, cond in conditions[::-1]:
+                try:
+                    k = rewrite(cond)
+                    result = k * value + (1 - k) * result
+                except UnrecognizedCondition:
+                    return
+
+            return result
+
+
+def piecewise_fold(expr, evaluate=True):
+    """
+    Takes an expression containing a piecewise function and returns the
+    expression in piecewise form. In addition, any ITE conditions are
+    rewritten in negation normal form and simplified.
+
+    The final Piecewise is evaluated (default) but if the raw form
+    is desired, send ``evaluate=False``; if trivial evaluation is
+    desired, send ``evaluate=None`` and duplicate conditions and
+    processing of True and False will be handled.
+
+    Examples
+    ========
+
+    >>> from sympy import Piecewise, piecewise_fold, S
+    >>> from sympy.abc import x
+    >>> p = Piecewise((x, x < 1), (1, S(1) <= x))
+    >>> piecewise_fold(x*p)
+    Piecewise((x**2, x < 1), (x, True))
+
+    See Also
+    ========
+
+    Piecewise
+    piecewise_exclusive
+    """
+    if not isinstance(expr, Basic) or not expr.has(Piecewise):
+        return expr
+
+    new_args = []
+    if isinstance(expr, (ExprCondPair, Piecewise)):
+        for e, c in expr.args:
+            if not isinstance(e, Piecewise):
+                e = piecewise_fold(e)
+            # we don't keep Piecewise in condition because
+            # it has to be checked to see that it's complete
+            # and we convert it to ITE at that time
+            assert not c.has(Piecewise)  # pragma: no cover
+            if isinstance(c, ITE):
+                c = c.to_nnf()
+                c = simplify_logic(c, form='cnf')
+            if isinstance(e, Piecewise):
+                new_args.extend([(piecewise_fold(ei), And(ci, c))
+                    for ei, ci in e.args])
+            else:
+                new_args.append((e, c))
+    else:
+        # Given
+        #     P1 = Piecewise((e11, c1), (e12, c2), A)
+        #     P2 = Piecewise((e21, c1), (e22, c2), B)
+        #     ...
+        # the folding of f(P1, P2) is trivially
+        # Piecewise(
+        #   (f(e11, e21), c1),
+        #   (f(e12, e22), c2),
+        #   (f(Piecewise(A), Piecewise(B)), True))
+        # Certain objects end up rewriting themselves as thus, so
+        # we do that grouping before the more generic folding.
+        # The following applies this idea when f = Add or f = Mul
+        # (and the expression is commutative).
+        if expr.is_Add or expr.is_Mul and expr.is_commutative:
+            p, args = sift(expr.args, lambda x: x.is_Piecewise, binary=True)
+            pc = sift(p, lambda x: tuple([c for e,c in x.args]))
+            for c in list(ordered(pc)):
+                if len(pc[c]) > 1:
+                    pargs = [list(i.args) for i in pc[c]]
+                    # the first one is the same; there may be more
+                    com = common_prefix(*[
+                        [i.cond for i in j] for j in pargs])
+                    n = len(com)
+                    collected = []
+                    for i in range(n):
+                        collected.append((
+                            expr.func(*[ai[i].expr for ai in pargs]),
+                            com[i]))
+                    remains = []
+                    for a in pargs:
+                        if n == len(a):  # no more args
+                            continue
+                        if a[n].cond == True:  # no longer Piecewise
+                            remains.append(a[n].expr)
+                        else:  # restore the remaining Piecewise
+                            remains.append(
+                                Piecewise(*a[n:], evaluate=False))
+                    if remains:
+                        collected.append((expr.func(*remains), True))
+                    args.append(Piecewise(*collected, evaluate=False))
+                    continue
+                args.extend(pc[c])
+        else:
+            args = expr.args
+        # fold
+        folded = list(map(piecewise_fold, args))
+        for ec in product(*[
+                (i.args if isinstance(i, Piecewise) else
+                 [(i, true)]) for i in folded]):
+            e, c = zip(*ec)
+            new_args.append((expr.func(*e), And(*c)))
+
+    if evaluate is None:
+        # don't return duplicate conditions, otherwise don't evaluate
+        new_args = list(reversed([(e, c) for c, e in {
+            c: e for e, c in reversed(new_args)}.items()]))
+    rv = Piecewise(*new_args, evaluate=evaluate)
+    if evaluate is None and len(rv.args) == 1 and rv.args[0].cond == True:
+        return rv.args[0].expr
+    if any(s.expr.has(Piecewise) for p in rv.atoms(Piecewise) for s in p.args):
+        return piecewise_fold(rv)
+    return rv
+
+
+def _clip(A, B, k):
+    """Return interval B as intervals that are covered by A (keyed
+    to k) and all other intervals of B not covered by A keyed to -1.
+
+    The reference point of each interval is the rhs; if the lhs is
+    greater than the rhs then an interval of zero width interval will
+    result, e.g. (4, 1) is treated like (1, 1).
+
+    Examples
+    ========
+
+    >>> from sympy.functions.elementary.piecewise import _clip
+    >>> from sympy import Tuple
+    >>> A = Tuple(1, 3)
+    >>> B = Tuple(2, 4)
+    >>> _clip(A, B, 0)
+    [(2, 3, 0), (3, 4, -1)]
+
+    Interpretation: interval portion (2, 3) of interval (2, 4) is
+    covered by interval (1, 3) and is keyed to 0 as requested;
+    interval (3, 4) was not covered by (1, 3) and is keyed to -1.
+    """
+    a, b = B
+    c, d = A
+    c, d = Min(Max(c, a), b), Min(Max(d, a), b)
+    a = Min(a, b)
+    p = []
+    if a != c:
+        p.append((a, c, -1))
+    else:
+        pass
+    if c != d:
+        p.append((c, d, k))
+    else:
+        pass
+    if b != d:
+        if d == c and p and p[-1][-1] == -1:
+            p[-1] = p[-1][0], b, -1
+        else:
+            p.append((d, b, -1))
+    else:
+        pass
+
+    return p
+
+
+def piecewise_simplify_arguments(expr, **kwargs):
+    from sympy.simplify.simplify import simplify
+
+    # simplify conditions
+    f1 = expr.args[0].cond.free_symbols
+    args = None
+    if len(f1) == 1 and not expr.atoms(Eq):
+        x = f1.pop()
+        # this won't return intervals involving Eq
+        # and it won't handle symbols treated as
+        # booleans
+        ok, abe_ = expr._intervals(x, err_on_Eq=True)
+        def include(c, x, a):
+            "return True if c.subs(x, a) is True, else False"
+            try:
+                return c.subs(x, a) == True
+            except TypeError:
+                return False
+        if ok:
+            args = []
+            covered = S.EmptySet
+            from sympy.sets.sets import Interval
+            for a, b, e, i in abe_:
+                c = expr.args[i].cond
+                incl_a = include(c, x, a)
+                incl_b = include(c, x, b)
+                iv = Interval(a, b, not incl_a, not incl_b)
+                cset = iv - covered
+                if not cset:
+                    continue
+                try:
+                    a = cset.inf
+                except NotImplementedError:
+                    pass # continue with the given `a`
+                else:
+                    incl_a = include(c, x, a)
+                if incl_a and incl_b:
+                    if a.is_infinite and b.is_infinite:
+                        c = S.true
+                    elif b.is_infinite:
+                        c = (x > a) if a in covered else (x >= a)
+                    elif a.is_infinite:
+                        c = (x <= b)
+                    elif a in covered:
+                        c = And(a < x, x <= b)
+                    else:
+                        c = And(a <= x, x <= b)
+                elif incl_a:
+                    if a.is_infinite:
+                        c = (x < b)
+                    elif a in covered:
+                        c = And(a < x, x < b)
+                    else:
+                        c = And(a <= x, x < b)
+                elif incl_b:
+                    if b.is_infinite:
+                        c = (x > a)
+                    else:
+                        c = And(a < x, x <= b)
+                else:
+                    if a in covered:
+                        c = (x < b)
+                    else:
+                        c = And(a < x, x < b)
+                covered |= iv
+                if a is S.NegativeInfinity and incl_a:
+                    covered |= {S.NegativeInfinity}
+                if b is S.Infinity and incl_b:
+                    covered |= {S.Infinity}
+                args.append((e, c))
+            if not S.Reals.is_subset(covered):
+                args.append((Undefined, True))
+    if args is None:
+        args = list(expr.args)
+        for i in range(len(args)):
+            e, c  = args[i]
+            if isinstance(c, Basic):
+                c = simplify(c, **kwargs)
+            args[i] = (e, c)
+
+    # simplify expressions
+    doit = kwargs.pop('doit', None)
+    for i in range(len(args)):
+        e, c  = args[i]
+        if isinstance(e, Basic):
+            # Skip doit to avoid growth at every call for some integrals
+            # and sums, see sympy/sympy#17165
+            newe = simplify(e, doit=False, **kwargs)
+            if newe != e:
+                e = newe
+        args[i] = (e, c)
+
+    # restore kwargs flag
+    if doit is not None:
+        kwargs['doit'] = doit
+
+    return Piecewise(*args)
+
+
+def _piecewise_collapse_arguments(_args):
+    newargs = []  # the unevaluated conditions
+    current_cond = set()  # the conditions up to a given e, c pair
+    for expr, cond in _args:
+        cond = cond.replace(
+            lambda _: _.is_Relational, _canonical_coeff)
+        # Check here if expr is a Piecewise and collapse if one of
+        # the conds in expr matches cond. This allows the collapsing
+        # of Piecewise((Piecewise((x,x<0)),x<0)) to Piecewise((x,x<0)).
+        # This is important when using piecewise_fold to simplify
+        # multiple Piecewise instances having the same conds.
+        # Eventually, this code should be able to collapse Piecewise's
+        # having different intervals, but this will probably require
+        # using the new assumptions.
+        if isinstance(expr, Piecewise):
+            unmatching = []
+            for i, (e, c) in enumerate(expr.args):
+                if c in current_cond:
+                    # this would already have triggered
+                    continue
+                if c == cond:
+                    if c != True:
+                        # nothing past this condition will ever
+                        # trigger and only those args before this
+                        # that didn't match a previous condition
+                        # could possibly trigger
+                        if unmatching:
+                            expr = Piecewise(*(
+                                unmatching + [(e, c)]))
+                        else:
+                            expr = e
+                    break
+                else:
+                    unmatching.append((e, c))
+
+        # check for condition repeats
+        got = False
+        # -- if an And contains a condition that was
+        #    already encountered, then the And will be
+        #    False: if the previous condition was False
+        #    then the And will be False and if the previous
+        #    condition is True then then we wouldn't get to
+        #    this point. In either case, we can skip this condition.
+        for i in ([cond] +
+                  (list(cond.args) if isinstance(cond, And) else
+                  [])):
+            if i in current_cond:
+                got = True
+                break
+        if got:
+            continue
+
+        # -- if not(c) is already in current_cond then c is
+        #    a redundant condition in an And. This does not
+        #    apply to Or, however: (e1, c), (e2, Or(~c, d))
+        #    is not (e1, c), (e2, d) because if c and d are
+        #    both False this would give no results when the
+        #    true answer should be (e2, True)
+        if isinstance(cond, And):
+            nonredundant = []
+            for c in cond.args:
+                if isinstance(c, Relational):
+                    if c.negated.canonical in current_cond:
+                        continue
+                    # if a strict inequality appears after
+                    # a non-strict one, then the condition is
+                    # redundant
+                    if isinstance(c, (Lt, Gt)) and (
+                        c.weak in current_cond):
+                        cond = False
+                        break
+                nonredundant.append(c)
+            else:
+                cond = cond.func(*nonredundant)
+        elif isinstance(cond, Relational):
+            if cond.negated.canonical in current_cond:
+                cond = S.true
+
+        current_cond.add(cond)
+
+        # collect successive e,c pairs when exprs or cond match
+        if newargs:
+            if newargs[-1].expr == expr:
+                orcond = Or(cond, newargs[-1].cond)
+                if isinstance(orcond, (And, Or)):
+                    orcond = distribute_and_over_or(orcond)
+                newargs[-1] = ExprCondPair(expr, orcond)
+                continue
+            elif newargs[-1].cond == cond:
+                continue
+        newargs.append(ExprCondPair(expr, cond))
+    return newargs
+
+
+_blessed = lambda e: getattr(e.lhs, '_diff_wrt', False) and (
+    getattr(e.rhs, '_diff_wrt', None) or
+    isinstance(e.rhs, (Rational, NumberSymbol)))
+
+
+def piecewise_simplify(expr, **kwargs):
+    expr = piecewise_simplify_arguments(expr, **kwargs)
+    if not isinstance(expr, Piecewise):
+        return expr
+    args = list(expr.args)
+
+    args = _piecewise_simplify_eq_and(args)
+    args = _piecewise_simplify_equal_to_next_segment(args)
+    return Piecewise(*args)
+
+
+def _piecewise_simplify_equal_to_next_segment(args):
+    """
+    See if expressions valid for an Equal expression happens to evaluate
+    to the same function as in the next piecewise segment, see:
+    https://github.com/sympy/sympy/issues/8458
+    """
+    prevexpr = None
+    for i, (expr, cond) in reversed(list(enumerate(args))):
+        if prevexpr is not None:
+            if isinstance(cond, And):
+                eqs, other = sift(cond.args,
+                                  lambda i: isinstance(i, Eq), binary=True)
+            elif isinstance(cond, Eq):
+                eqs, other = [cond], []
+            else:
+                eqs = other = []
+            _prevexpr = prevexpr
+            _expr = expr
+            if eqs and not other:
+                eqs = list(ordered(eqs))
+                for e in eqs:
+                    # allow 2 args to collapse into 1 for any e
+                    # otherwise limit simplification to only simple-arg
+                    # Eq instances
+                    if len(args) == 2 or _blessed(e):
+                        _prevexpr = _prevexpr.subs(*e.args)
+                        _expr = _expr.subs(*e.args)
+            # Did it evaluate to the same?
+            if _prevexpr == _expr:
+                # Set the expression for the Not equal section to the same
+                # as the next. These will be merged when creating the new
+                # Piecewise
+                args[i] = args[i].func(args[i + 1][0], cond)
+            else:
+                # Update the expression that we compare against
+                prevexpr = expr
+        else:
+            prevexpr = expr
+    return args
+
+
+def _piecewise_simplify_eq_and(args):
+    """
+    Try to simplify conditions and the expression for
+    equalities that are part of the condition, e.g.
+    Piecewise((n, And(Eq(n,0), Eq(n + m, 0))), (1, True))
+    -> Piecewise((0, And(Eq(n, 0), Eq(m, 0))), (1, True))
+    """
+    for i, (expr, cond) in enumerate(args):
+        if isinstance(cond, And):
+            eqs, other = sift(cond.args,
+                              lambda i: isinstance(i, Eq), binary=True)
+        elif isinstance(cond, Eq):
+            eqs, other = [cond], []
+        else:
+            eqs = other = []
+        if eqs:
+            eqs = list(ordered(eqs))
+            for j, e in enumerate(eqs):
+                # these blessed lhs objects behave like Symbols
+                # and the rhs are simple replacements for the "symbols"
+                if _blessed(e):
+                    expr = expr.subs(*e.args)
+                    eqs[j + 1:] = [ei.subs(*e.args) for ei in eqs[j + 1:]]
+                    other = [ei.subs(*e.args) for ei in other]
+            cond = And(*(eqs + other))
+            args[i] = args[i].func(expr, cond)
+    return args
+
+
+def piecewise_exclusive(expr, *, skip_nan=False, deep=True):
+    """
+    Rewrite :class:`Piecewise` with mutually exclusive conditions.
+
+    Explanation
+    ===========
+
+    SymPy represents the conditions of a :class:`Piecewise` in an
+    "if-elif"-fashion, allowing more than one condition to be simultaneously
+    True. The interpretation is that the first condition that is True is the
+    case that holds. While this is a useful representation computationally it
+    is not how a piecewise formula is typically shown in a mathematical text.
+    The :func:`piecewise_exclusive` function can be used to rewrite any
+    :class:`Piecewise` with more typical mutually exclusive conditions.
+
+    Note that further manipulation of the resulting :class:`Piecewise`, e.g.
+    simplifying it, will most likely make it non-exclusive. Hence, this is
+    primarily a function to be used in conjunction with printing the Piecewise
+    or if one would like to reorder the expression-condition pairs.
+
+    If it is not possible to determine that all possibilities are covered by
+    the different cases of the :class:`Piecewise` then a final
+    :class:`~sympy.core.numbers.NaN` case will be included explicitly. This
+    can be prevented by passing ``skip_nan=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import piecewise_exclusive, Symbol, Piecewise, S
+    >>> x = Symbol('x', real=True)
+    >>> p = Piecewise((0, x < 0), (S.Half, x <= 0), (1, True))
+    >>> piecewise_exclusive(p)
+    Piecewise((0, x < 0), (1/2, Eq(x, 0)), (1, x > 0))
+    >>> piecewise_exclusive(Piecewise((2, x > 1)))
+    Piecewise((2, x > 1), (nan, x <= 1))
+    >>> piecewise_exclusive(Piecewise((2, x > 1)), skip_nan=True)
+    Piecewise((2, x > 1))
+
+    Parameters
+    ==========
+
+    expr: a SymPy expression.
+        Any :class:`Piecewise` in the expression will be rewritten.
+    skip_nan: ``bool`` (default ``False``)
+        If ``skip_nan`` is set to ``True`` then a final
+        :class:`~sympy.core.numbers.NaN` case will not be included.
+    deep:  ``bool`` (default ``True``)
+        If ``deep`` is ``True`` then :func:`piecewise_exclusive` will rewrite
+        any :class:`Piecewise` subexpressions in ``expr`` rather than just
+        rewriting ``expr`` itself.
+
+    Returns
+    =======
+
+    An expression equivalent to ``expr`` but where all :class:`Piecewise` have
+    been rewritten with mutually exclusive conditions.
+
+    See Also
+    ========
+
+    Piecewise
+    piecewise_fold
+    """
+
+    def make_exclusive(*pwargs):
+
+        cumcond = false
+        newargs = []
+
+        # Handle the first n-1 cases
+        for expr_i, cond_i in pwargs[:-1]:
+            cancond = And(cond_i, Not(cumcond)).simplify()
+            cumcond = Or(cond_i, cumcond).simplify()
+            newargs.append((expr_i, cancond))
+
+        # For the nth case defer simplification of cumcond
+        expr_n, cond_n = pwargs[-1]
+        cancond_n = And(cond_n, Not(cumcond)).simplify()
+        newargs.append((expr_n, cancond_n))
+
+        if not skip_nan:
+            cumcond = Or(cond_n, cumcond).simplify()
+            if cumcond is not true:
+                newargs.append((Undefined, Not(cumcond).simplify()))
+
+        return Piecewise(*newargs, evaluate=False)
+
+    if deep:
+        return expr.replace(Piecewise, make_exclusive)
+    elif isinstance(expr, Piecewise):
+        return make_exclusive(*expr.args)
+    else:
+        return expr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_complexes.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_complexes.py
new file mode 100644
index 0000000000000000000000000000000000000000..699c0fef966c99147b713aaa80710b7b8cf21c73
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_complexes.py
@@ -0,0 +1,1030 @@
+from sympy.core.function import (Derivative, Function, Lambda, expand, PoleError)
+from sympy.core.numbers import (E, I, Rational, comp, nan, oo, pi, zoo)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (Abs, adjoint, arg, conjugate, im, re, sign, transpose)
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (acos, atan, atan2, cos, sin)
+from sympy.functions.elementary.hyperbolic import sinh
+from sympy.functions.special.delta_functions import (DiracDelta, Heaviside)
+from sympy.integrals.integrals import Integral
+from sympy.matrices.dense import Matrix
+from sympy.matrices.expressions.funcmatrix import FunctionMatrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.immutable import (ImmutableMatrix, ImmutableSparseMatrix)
+from sympy.matrices import SparseMatrix
+from sympy.sets.sets import Interval
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.series.order import Order
+from sympy.testing.pytest import XFAIL, raises, _both_exp_pow
+
+
+def N_equals(a, b):
+    """Check whether two complex numbers are numerically close"""
+    return comp(a.n(), b.n(), 1.e-6)
+
+
+def test_re():
+    x, y = symbols('x,y')
+    a, b = symbols('a,b', real=True)
+
+    r = Symbol('r', real=True)
+    i = Symbol('i', imaginary=True)
+
+    assert re(nan) is nan
+
+    assert re(oo) is oo
+    assert re(-oo) is -oo
+
+    assert re(0) == 0
+
+    assert re(1) == 1
+    assert re(-1) == -1
+
+    assert re(E) == E
+    assert re(-E) == -E
+
+    assert unchanged(re, x)
+    assert re(x*I) == -im(x)
+    assert re(r*I) == 0
+    assert re(r) == r
+    assert re(i*I) == I * i
+    assert re(i) == 0
+
+    assert re(x + y) == re(x) + re(y)
+    assert re(x + r) == re(x) + r
+
+    assert re(re(x)) == re(x)
+
+    assert re(2 + I) == 2
+    assert re(x + I) == re(x)
+
+    assert re(x + y*I) == re(x) - im(y)
+    assert re(x + r*I) == re(x)
+
+    assert re(log(2*I)) == log(2)
+
+    assert re((2 + I)**2).expand(complex=True) == 3
+
+    assert re(conjugate(x)) == re(x)
+    assert conjugate(re(x)) == re(x)
+
+    assert re(x).as_real_imag() == (re(x), 0)
+
+    assert re(i*r*x).diff(r) == re(i*x)
+    assert re(i*r*x).diff(i) == I*r*im(x)
+
+    assert re(
+        sqrt(a + b*I)) == (a**2 + b**2)**Rational(1, 4)*cos(atan2(b, a)/2)
+    assert re(a * (2 + b*I)) == 2*a
+
+    assert re((1 + sqrt(a + b*I))/2) == \
+        (a**2 + b**2)**Rational(1, 4)*cos(atan2(b, a)/2)/2 + S.Half
+
+    assert re(x).rewrite(im) == x - S.ImaginaryUnit*im(x)
+    assert (x + re(y)).rewrite(re, im) == x + y - S.ImaginaryUnit*im(y)
+
+    a = Symbol('a', algebraic=True)
+    t = Symbol('t', transcendental=True)
+    x = Symbol('x')
+    assert re(a).is_algebraic
+    assert re(x).is_algebraic is None
+    assert re(t).is_algebraic is False
+
+    assert re(S.ComplexInfinity) is S.NaN
+
+    n, m, l = symbols('n m l')
+    A = MatrixSymbol('A',n,m)
+    assert re(A) == (S.Half) * (A + conjugate(A))
+
+    A = Matrix([[1 + 4*I,2],[0, -3*I]])
+    assert re(A) == Matrix([[1, 2],[0, 0]])
+
+    A = ImmutableMatrix([[1 + 3*I, 3-2*I],[0, 2*I]])
+    assert re(A) == ImmutableMatrix([[1, 3],[0, 0]])
+
+    X = SparseMatrix([[2*j + i*I for i in range(5)] for j in range(5)])
+    assert re(X) - Matrix([[0, 0, 0, 0, 0],
+                           [2, 2, 2, 2, 2],
+                           [4, 4, 4, 4, 4],
+                           [6, 6, 6, 6, 6],
+                           [8, 8, 8, 8, 8]]) == Matrix.zeros(5)
+
+    assert im(X) - Matrix([[0, 1, 2, 3, 4],
+                           [0, 1, 2, 3, 4],
+                           [0, 1, 2, 3, 4],
+                           [0, 1, 2, 3, 4],
+                           [0, 1, 2, 3, 4]]) == Matrix.zeros(5)
+
+    X = FunctionMatrix(3, 3, Lambda((n, m), n + m*I))
+    assert re(X) == Matrix([[0, 0, 0], [1, 1, 1], [2, 2, 2]])
+
+
+def test_im():
+    x, y = symbols('x,y')
+    a, b = symbols('a,b', real=True)
+
+    r = Symbol('r', real=True)
+    i = Symbol('i', imaginary=True)
+
+    assert im(nan) is nan
+
+    assert im(oo*I) is oo
+    assert im(-oo*I) is -oo
+
+    assert im(0) == 0
+
+    assert im(1) == 0
+    assert im(-1) == 0
+
+    assert im(E*I) == E
+    assert im(-E*I) == -E
+
+    assert unchanged(im, x)
+    assert im(x*I) == re(x)
+    assert im(r*I) == r
+    assert im(r) == 0
+    assert im(i*I) == 0
+    assert im(i) == -I * i
+
+    assert im(x + y) == im(x) + im(y)
+    assert im(x + r) == im(x)
+    assert im(x + r*I) == im(x) + r
+
+    assert im(im(x)*I) == im(x)
+
+    assert im(2 + I) == 1
+    assert im(x + I) == im(x) + 1
+
+    assert im(x + y*I) == im(x) + re(y)
+    assert im(x + r*I) == im(x) + r
+
+    assert im(log(2*I)) == pi/2
+
+    assert im((2 + I)**2).expand(complex=True) == 4
+
+    assert im(conjugate(x)) == -im(x)
+    assert conjugate(im(x)) == im(x)
+
+    assert im(x).as_real_imag() == (im(x), 0)
+
+    assert im(i*r*x).diff(r) == im(i*x)
+    assert im(i*r*x).diff(i) == -I * re(r*x)
+
+    assert im(
+        sqrt(a + b*I)) == (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)
+    assert im(a * (2 + b*I)) == a*b
+
+    assert im((1 + sqrt(a + b*I))/2) == \
+        (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)/2
+
+    assert im(x).rewrite(re) == -S.ImaginaryUnit * (x - re(x))
+    assert (x + im(y)).rewrite(im, re) == x - S.ImaginaryUnit * (y - re(y))
+
+    a = Symbol('a', algebraic=True)
+    t = Symbol('t', transcendental=True)
+    x = Symbol('x')
+    assert re(a).is_algebraic
+    assert re(x).is_algebraic is None
+    assert re(t).is_algebraic is False
+
+    assert im(S.ComplexInfinity) is S.NaN
+
+    n, m, l = symbols('n m l')
+    A = MatrixSymbol('A',n,m)
+
+    assert im(A) == (S.One/(2*I)) * (A - conjugate(A))
+
+    A = Matrix([[1 + 4*I, 2],[0, -3*I]])
+    assert im(A) == Matrix([[4, 0],[0, -3]])
+
+    A = ImmutableMatrix([[1 + 3*I, 3-2*I],[0, 2*I]])
+    assert im(A) == ImmutableMatrix([[3, -2],[0, 2]])
+
+    X = ImmutableSparseMatrix(
+            [[i*I + i for i in range(5)] for i in range(5)])
+    Y = SparseMatrix([list(range(5)) for i in range(5)])
+    assert im(X).as_immutable() == Y
+
+    X = FunctionMatrix(3, 3, Lambda((n, m), n + m*I))
+    assert im(X) == Matrix([[0, 1, 2], [0, 1, 2], [0, 1, 2]])
+
+def test_sign():
+    assert sign(1.2) == 1
+    assert sign(-1.2) == -1
+    assert sign(3*I) == I
+    assert sign(-3*I) == -I
+    assert sign(0) == 0
+    assert sign(0, evaluate=False).doit() == 0
+    assert sign(oo, evaluate=False).doit() == 1
+    assert sign(nan) is nan
+    assert sign(2 + 2*I).doit() == sqrt(2)*(2 + 2*I)/4
+    assert sign(2 + 3*I).simplify() == sign(2 + 3*I)
+    assert sign(2 + 2*I).simplify() == sign(1 + I)
+    assert sign(im(sqrt(1 - sqrt(3)))) == 1
+    assert sign(sqrt(1 - sqrt(3))) == I
+
+    x = Symbol('x')
+    assert sign(x).is_finite is True
+    assert sign(x).is_complex is True
+    assert sign(x).is_imaginary is None
+    assert sign(x).is_integer is None
+    assert sign(x).is_real is None
+    assert sign(x).is_zero is None
+    assert sign(x).doit() == sign(x)
+    assert sign(1.2*x) == sign(x)
+    assert sign(2*x) == sign(x)
+    assert sign(I*x) == I*sign(x)
+    assert sign(-2*I*x) == -I*sign(x)
+    assert sign(conjugate(x)) == conjugate(sign(x))
+
+    p = Symbol('p', positive=True)
+    n = Symbol('n', negative=True)
+    m = Symbol('m', negative=True)
+    assert sign(2*p*x) == sign(x)
+    assert sign(n*x) == -sign(x)
+    assert sign(n*m*x) == sign(x)
+
+    x = Symbol('x', imaginary=True)
+    assert sign(x).is_imaginary is True
+    assert sign(x).is_integer is False
+    assert sign(x).is_real is False
+    assert sign(x).is_zero is False
+    assert sign(x).diff(x) == 2*DiracDelta(-I*x)
+    assert sign(x).doit() == x / Abs(x)
+    assert conjugate(sign(x)) == -sign(x)
+
+    x = Symbol('x', real=True)
+    assert sign(x).is_imaginary is False
+    assert sign(x).is_integer is True
+    assert sign(x).is_real is True
+    assert sign(x).is_zero is None
+    assert sign(x).diff(x) == 2*DiracDelta(x)
+    assert sign(x).doit() == sign(x)
+    assert conjugate(sign(x)) == sign(x)
+
+    x = Symbol('x', nonzero=True)
+    assert sign(x).is_imaginary is False
+    assert sign(x).is_integer is True
+    assert sign(x).is_real is True
+    assert sign(x).is_zero is False
+    assert sign(x).doit() == x / Abs(x)
+    assert sign(Abs(x)) == 1
+    assert Abs(sign(x)) == 1
+
+    x = Symbol('x', positive=True)
+    assert sign(x).is_imaginary is False
+    assert sign(x).is_integer is True
+    assert sign(x).is_real is True
+    assert sign(x).is_zero is False
+    assert sign(x).doit() == x / Abs(x)
+    assert sign(Abs(x)) == 1
+    assert Abs(sign(x)) == 1
+
+    x = 0
+    assert sign(x).is_imaginary is False
+    assert sign(x).is_integer is True
+    assert sign(x).is_real is True
+    assert sign(x).is_zero is True
+    assert sign(x).doit() == 0
+    assert sign(Abs(x)) == 0
+    assert Abs(sign(x)) == 0
+
+    nz = Symbol('nz', nonzero=True, integer=True)
+    assert sign(nz).is_imaginary is False
+    assert sign(nz).is_integer is True
+    assert sign(nz).is_real is True
+    assert sign(nz).is_zero is False
+    assert sign(nz)**2 == 1
+    assert (sign(nz)**3).args == (sign(nz), 3)
+
+    assert sign(Symbol('x', nonnegative=True)).is_nonnegative
+    assert sign(Symbol('x', nonnegative=True)).is_nonpositive is None
+    assert sign(Symbol('x', nonpositive=True)).is_nonnegative is None
+    assert sign(Symbol('x', nonpositive=True)).is_nonpositive
+    assert sign(Symbol('x', real=True)).is_nonnegative is None
+    assert sign(Symbol('x', real=True)).is_nonpositive is None
+    assert sign(Symbol('x', real=True, zero=False)).is_nonpositive is None
+
+    x, y = Symbol('x', real=True), Symbol('y')
+    f = Function('f')
+    assert sign(x).rewrite(Piecewise) == \
+        Piecewise((1, x > 0), (-1, x < 0), (0, True))
+    assert sign(y).rewrite(Piecewise) == sign(y)
+    assert sign(x).rewrite(Heaviside) == 2*Heaviside(x, H0=S(1)/2) - 1
+    assert sign(y).rewrite(Heaviside) == sign(y)
+    assert sign(y).rewrite(Abs) == Piecewise((0, Eq(y, 0)), (y/Abs(y), True))
+    assert sign(f(y)).rewrite(Abs) == Piecewise((0, Eq(f(y), 0)), (f(y)/Abs(f(y)), True))
+
+    # evaluate what can be evaluated
+    assert sign(exp_polar(I*pi)*pi) is S.NegativeOne
+
+    eq = -sqrt(10 + 6*sqrt(3)) + sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3))
+    # if there is a fast way to know when and when you cannot prove an
+    # expression like this is zero then the equality to zero is ok
+    assert sign(eq).func is sign or sign(eq) == 0
+    # but sometimes it's hard to do this so it's better not to load
+    # abs down with tests that will be very slow
+    q = 1 + sqrt(2) - 2*sqrt(3) + 1331*sqrt(6)
+    p = expand(q**3)**Rational(1, 3)
+    d = p - q
+    assert sign(d).func is sign or sign(d) == 0
+
+
+def test_as_real_imag():
+    n = pi**1000
+    # the special code for working out the real
+    # and complex parts of a power with Integer exponent
+    # should not run if there is no imaginary part, hence
+    # this should not hang
+    assert n.as_real_imag() == (n, 0)
+
+    # issue 6261
+    x = Symbol('x')
+    assert sqrt(x).as_real_imag() == \
+        ((re(x)**2 + im(x)**2)**Rational(1, 4)*cos(atan2(im(x), re(x))/2),
+     (re(x)**2 + im(x)**2)**Rational(1, 4)*sin(atan2(im(x), re(x))/2))
+
+    # issue 3853
+    a, b = symbols('a,b', real=True)
+    assert ((1 + sqrt(a + b*I))/2).as_real_imag() == \
+           (
+               (a**2 + b**2)**Rational(
+                   1, 4)*cos(atan2(b, a)/2)/2 + S.Half,
+               (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)/2)
+
+    assert sqrt(a**2).as_real_imag() == (sqrt(a**2), 0)
+    i = symbols('i', imaginary=True)
+    assert sqrt(i**2).as_real_imag() == (0, abs(i))
+
+    assert ((1 + I)/(1 - I)).as_real_imag() == (0, 1)
+    assert ((1 + I)**3/(1 - I)).as_real_imag() == (-2, 0)
+
+
+@XFAIL
+def test_sign_issue_3068():
+    n = pi**1000
+    i = int(n)
+    x = Symbol('x')
+    assert (n - i).round() == 1  # doesn't hang
+    assert sign(n - i) == 1
+    # perhaps it's not possible to get the sign right when
+    # only 1 digit is being requested for this situation;
+    # 2 digits works
+    assert (n - x).n(1, subs={x: i}) > 0
+    assert (n - x).n(2, subs={x: i}) > 0
+
+
+def test_Abs():
+    raises(TypeError, lambda: Abs(Interval(2, 3)))  # issue 8717
+
+    x, y = symbols('x,y')
+    assert sign(sign(x)) == sign(x)
+    assert sign(x*y).func is sign
+    assert Abs(0) == 0
+    assert Abs(1) == 1
+    assert Abs(-1) == 1
+    assert Abs(I) == 1
+    assert Abs(-I) == 1
+    assert Abs(nan) is nan
+    assert Abs(zoo) is oo
+    assert Abs(I * pi) == pi
+    assert Abs(-I * pi) == pi
+    assert Abs(I * x) == Abs(x)
+    assert Abs(-I * x) == Abs(x)
+    assert Abs(-2*x) == 2*Abs(x)
+    assert Abs(-2.0*x) == 2.0*Abs(x)
+    assert Abs(2*pi*x*y) == 2*pi*Abs(x*y)
+    assert Abs(conjugate(x)) == Abs(x)
+    assert conjugate(Abs(x)) == Abs(x)
+    assert Abs(x).expand(complex=True) == sqrt(re(x)**2 + im(x)**2)
+
+    a = Symbol('a', positive=True)
+    assert Abs(2*pi*x*a) == 2*pi*a*Abs(x)
+    assert Abs(2*pi*I*x*a) == 2*pi*a*Abs(x)
+
+    x = Symbol('x', real=True)
+    n = Symbol('n', integer=True)
+    assert Abs((-1)**n) == 1
+    assert x**(2*n) == Abs(x)**(2*n)
+    assert Abs(x).diff(x) == sign(x)
+    assert abs(x) == Abs(x)  # Python built-in
+    assert Abs(x)**3 == x**2*Abs(x)
+    assert Abs(x)**4 == x**4
+    assert (
+        Abs(x)**(3*n)).args == (Abs(x), 3*n)  # leave symbolic odd unchanged
+    assert (1/Abs(x)).args == (Abs(x), -1)
+    assert 1/Abs(x)**3 == 1/(x**2*Abs(x))
+    assert Abs(x)**-3 == Abs(x)/(x**4)
+    assert Abs(x**3) == x**2*Abs(x)
+    assert Abs(I**I) == exp(-pi/2)
+    assert Abs((4 + 5*I)**(6 + 7*I)) == 68921*exp(-7*atan(Rational(5, 4)))
+    y = Symbol('y', real=True)
+    assert Abs(I**y) == 1
+    y = Symbol('y')
+    assert Abs(I**y) == exp(-pi*im(y)/2)
+
+    x = Symbol('x', imaginary=True)
+    assert Abs(x).diff(x) == -sign(x)
+
+    eq = -sqrt(10 + 6*sqrt(3)) + sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3))
+    # if there is a fast way to know when you can and when you cannot prove an
+    # expression like this is zero then the equality to zero is ok
+    assert abs(eq).func is Abs or abs(eq) == 0
+    # but sometimes it's hard to do this so it's better not to load
+    # abs down with tests that will be very slow
+    q = 1 + sqrt(2) - 2*sqrt(3) + 1331*sqrt(6)
+    p = expand(q**3)**Rational(1, 3)
+    d = p - q
+    assert abs(d).func is Abs or abs(d) == 0
+
+    assert Abs(4*exp(pi*I/4)) == 4
+    assert Abs(3**(2 + I)) == 9
+    assert Abs((-3)**(1 - I)) == 3*exp(pi)
+
+    assert Abs(oo) is oo
+    assert Abs(-oo) is oo
+    assert Abs(oo + I) is oo
+    assert Abs(oo + I*oo) is oo
+
+    a = Symbol('a', algebraic=True)
+    t = Symbol('t', transcendental=True)
+    x = Symbol('x')
+    assert re(a).is_algebraic
+    assert re(x).is_algebraic is None
+    assert re(t).is_algebraic is False
+    assert Abs(x).fdiff() == sign(x)
+    raises(ArgumentIndexError, lambda: Abs(x).fdiff(2))
+
+    # doesn't have recursion error
+    arg = sqrt(acos(1 - I)*acos(1 + I))
+    assert abs(arg) == arg
+
+    # special handling to put Abs in denom
+    assert abs(1/x) == 1/Abs(x)
+    e = abs(2/x**2)
+    assert e.is_Mul and e == 2/Abs(x**2)
+    assert unchanged(Abs, y/x)
+    assert unchanged(Abs, x/(x + 1))
+    assert unchanged(Abs, x*y)
+    p = Symbol('p', positive=True)
+    assert abs(x/p) == abs(x)/p
+
+    # coverage
+    assert unchanged(Abs, Symbol('x', real=True)**y)
+    # issue 19627
+    f = Function('f', positive=True)
+    assert sqrt(f(x)**2) == f(x)
+    # issue 21625
+    assert unchanged(Abs, S("im(acos(-i + acosh(-g + i)))"))
+
+
+def test_Abs_rewrite():
+    x = Symbol('x', real=True)
+    a = Abs(x).rewrite(Heaviside).expand()
+    assert a == x*Heaviside(x) - x*Heaviside(-x)
+    for i in [-2, -1, 0, 1, 2]:
+        assert a.subs(x, i) == abs(i)
+    y = Symbol('y')
+    assert Abs(y).rewrite(Heaviside) == Abs(y)
+
+    x, y = Symbol('x', real=True), Symbol('y')
+    assert Abs(x).rewrite(Piecewise) == Piecewise((x, x >= 0), (-x, True))
+    assert Abs(y).rewrite(Piecewise) == Abs(y)
+    assert Abs(y).rewrite(sign) == y/sign(y)
+
+    i = Symbol('i', imaginary=True)
+    assert abs(i).rewrite(Piecewise) == Piecewise((I*i, I*i >= 0), (-I*i, True))
+
+
+    assert Abs(y).rewrite(conjugate) == sqrt(y*conjugate(y))
+    assert Abs(i).rewrite(conjugate) == sqrt(-i**2) #  == -I*i
+
+    y = Symbol('y', extended_real=True)
+    assert  (Abs(exp(-I*x)-exp(-I*y))**2).rewrite(conjugate) == \
+        -exp(I*x)*exp(-I*y) + 2 - exp(-I*x)*exp(I*y)
+
+
+def test_Abs_real():
+    # test some properties of abs that only apply
+    # to real numbers
+    x = Symbol('x', complex=True)
+    assert sqrt(x**2) != Abs(x)
+    assert Abs(x**2) != x**2
+
+    x = Symbol('x', real=True)
+    assert sqrt(x**2) == Abs(x)
+    assert Abs(x**2) == x**2
+
+    # if the symbol is zero, the following will still apply
+    nn = Symbol('nn', nonnegative=True, real=True)
+    np = Symbol('np', nonpositive=True, real=True)
+    assert Abs(nn) == nn
+    assert Abs(np) == -np
+
+
+def test_Abs_properties():
+    x = Symbol('x')
+    assert Abs(x).is_real is None
+    assert Abs(x).is_extended_real is True
+    assert Abs(x).is_rational is None
+    assert Abs(x).is_positive is None
+    assert Abs(x).is_nonnegative is None
+    assert Abs(x).is_extended_positive is None
+    assert Abs(x).is_extended_nonnegative is True
+
+    f = Symbol('x', finite=True)
+    assert Abs(f).is_real is True
+    assert Abs(f).is_extended_real is True
+    assert Abs(f).is_rational is None
+    assert Abs(f).is_positive is None
+    assert Abs(f).is_nonnegative is True
+    assert Abs(f).is_extended_positive is None
+    assert Abs(f).is_extended_nonnegative is True
+
+    z = Symbol('z', complex=True, zero=False)
+    assert Abs(z).is_real is True # since complex implies finite
+    assert Abs(z).is_extended_real is True
+    assert Abs(z).is_rational is None
+    assert Abs(z).is_positive is True
+    assert Abs(z).is_extended_positive is True
+    assert Abs(z).is_zero is False
+
+    p = Symbol('p', positive=True)
+    assert Abs(p).is_real is True
+    assert Abs(p).is_extended_real is True
+    assert Abs(p).is_rational is None
+    assert Abs(p).is_positive is True
+    assert Abs(p).is_zero is False
+
+    q = Symbol('q', rational=True)
+    assert Abs(q).is_real is True
+    assert Abs(q).is_rational is True
+    assert Abs(q).is_integer is None
+    assert Abs(q).is_positive is None
+    assert Abs(q).is_nonnegative is True
+
+    i = Symbol('i', integer=True)
+    assert Abs(i).is_real is True
+    assert Abs(i).is_integer is True
+    assert Abs(i).is_positive is None
+    assert Abs(i).is_nonnegative is True
+
+    e = Symbol('n', even=True)
+    ne = Symbol('ne', real=True, even=False)
+    assert Abs(e).is_even is True
+    assert Abs(ne).is_even is False
+    assert Abs(i).is_even is None
+
+    o = Symbol('n', odd=True)
+    no = Symbol('no', real=True, odd=False)
+    assert Abs(o).is_odd is True
+    assert Abs(no).is_odd is False
+    assert Abs(i).is_odd is None
+
+
+def test_abs():
+    # this tests that abs calls Abs; don't rename to
+    # test_Abs since that test is already above
+    a = Symbol('a', positive=True)
+    assert abs(I*(1 + a)**2) == (1 + a)**2
+
+
+def test_arg():
+    assert arg(0) is nan
+    assert arg(1) == 0
+    assert arg(-1) == pi
+    assert arg(I) == pi/2
+    assert arg(-I) == -pi/2
+    assert arg(1 + I) == pi/4
+    assert arg(-1 + I) == pi*Rational(3, 4)
+    assert arg(1 - I) == -pi/4
+    assert arg(exp_polar(4*pi*I)) == 4*pi
+    assert arg(exp_polar(-7*pi*I)) == -7*pi
+    assert arg(exp_polar(5 - 3*pi*I/4)) == pi*Rational(-3, 4)
+
+    assert arg(exp(I*pi/7)) == pi/7     # issue 17300
+    assert arg(exp(16*I)) == 16 - 6*pi
+    assert arg(exp(13*I*pi/12)) == -11*pi/12
+    assert arg(exp(123 - 5*I)) == -5 + 2*pi
+    assert arg(exp(sin(1 + 3*I))) == -2*pi + cos(1)*sinh(3)
+    r = Symbol('r', real=True)
+    assert arg(exp(r - 2*I)) == -2
+
+    f = Function('f')
+    assert not arg(f(0) + I*f(1)).atoms(re)
+
+    # check nesting
+    x = Symbol('x')
+    assert arg(arg(arg(x))) is not S.NaN
+    assert arg(arg(arg(arg(x)))) is S.NaN
+    r = Symbol('r', extended_real=True)
+    assert arg(arg(r)) is not S.NaN
+    assert arg(arg(arg(r))) is S.NaN
+
+    p = Function('p', extended_positive=True)
+    assert arg(p(x)) == 0
+    assert arg((3 + I)*p(x)) == arg(3  + I)
+
+    p = Symbol('p', positive=True)
+    assert arg(p) == 0
+    assert arg(p*I) == pi/2
+
+    n = Symbol('n', negative=True)
+    assert arg(n) == pi
+    assert arg(n*I) == -pi/2
+
+    x = Symbol('x')
+    assert conjugate(arg(x)) == arg(x)
+
+    e = p + I*p**2
+    assert arg(e) == arg(1 + p*I)
+    # make sure sign doesn't swap
+    e = -2*p + 4*I*p**2
+    assert arg(e) == arg(-1 + 2*p*I)
+    # make sure sign isn't lost
+    x = symbols('x', real=True)  # could be zero
+    e = x + I*x
+    assert arg(e) == arg(x*(1 + I))
+    assert arg(e/p) == arg(x*(1 + I))
+    e = p*cos(p) + I*log(p)*exp(p)
+    assert arg(e).args[0] == e
+    # keep it simple -- let the user do more advanced cancellation
+    e = (p + 1) + I*(p**2 - 1)
+    assert arg(e).args[0] == e
+
+    f = Function('f')
+    e = 2*x*(f(0) - 1) - 2*x*f(0)
+    assert arg(e) == arg(-2*x)
+    assert arg(f(0)).func == arg and arg(f(0)).args == (f(0),)
+
+
+def test_arg_rewrite():
+    assert arg(1 + I) == atan2(1, 1)
+
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    assert arg(x + I*y).rewrite(atan2) == atan2(y, x)
+
+
+def test_arg_leading_term_and_series():
+    x = Symbol('x')
+    assert arg(x).as_leading_term(x, cdir = 1) == 0
+    assert arg(x).as_leading_term(x, cdir = -1) == pi
+    raises(PoleError, lambda: arg(x + I).as_leading_term(x, cdir = 1))
+    raises(PoleError, lambda: arg(2*x).as_leading_term(x, cdir = I))
+
+    assert arg(x).nseries(x) == 0
+    assert arg(x).nseries(x, n=0) == Order(1)
+
+
+def test_adjoint():
+    a = Symbol('a', antihermitian=True)
+    b = Symbol('b', hermitian=True)
+    assert adjoint(a) == -a
+    assert adjoint(I*a) == I*a
+    assert adjoint(b) == b
+    assert adjoint(I*b) == -I*b
+    assert adjoint(a*b) == -b*a
+    assert adjoint(I*a*b) == I*b*a
+
+    x, y = symbols('x y')
+    assert adjoint(adjoint(x)) == x
+    assert adjoint(x + y) == conjugate(x) + conjugate(y)
+    assert adjoint(x - y) == conjugate(x) - conjugate(y)
+    assert adjoint(x * y) == conjugate(x) * conjugate(y)
+    assert adjoint(x / y) == conjugate(x) / conjugate(y)
+    assert adjoint(-x) == -conjugate(x)
+
+    x, y = symbols('x y', commutative=False)
+    assert adjoint(adjoint(x)) == x
+    assert adjoint(x + y) == adjoint(x) + adjoint(y)
+    assert adjoint(x - y) == adjoint(x) - adjoint(y)
+    assert adjoint(x * y) == adjoint(y) * adjoint(x)
+    assert adjoint(x / y) == 1 / adjoint(y) * adjoint(x)
+    assert adjoint(-x) == -adjoint(x)
+
+
+def test_conjugate():
+    a = Symbol('a', real=True)
+    b = Symbol('b', imaginary=True)
+    assert conjugate(a) == a
+    assert conjugate(I*a) == -I*a
+    assert conjugate(b) == -b
+    assert conjugate(I*b) == I*b
+    assert conjugate(a*b) == -a*b
+    assert conjugate(I*a*b) == I*a*b
+
+    x, y = symbols('x y')
+    assert conjugate(conjugate(x)) == x
+    assert conjugate(x).inverse() == conjugate
+    assert conjugate(x + y) == conjugate(x) + conjugate(y)
+    assert conjugate(x - y) == conjugate(x) - conjugate(y)
+    assert conjugate(x * y) == conjugate(x) * conjugate(y)
+    assert conjugate(x / y) == conjugate(x) / conjugate(y)
+    assert conjugate(-x) == -conjugate(x)
+
+    a = Symbol('a', algebraic=True)
+    t = Symbol('t', transcendental=True)
+    assert re(a).is_algebraic
+    assert re(x).is_algebraic is None
+    assert re(t).is_algebraic is False
+
+
+def test_conjugate_transpose():
+    x = Symbol('x', commutative=False)
+    assert conjugate(transpose(x)) == adjoint(x)
+    assert transpose(conjugate(x)) == adjoint(x)
+    assert adjoint(transpose(x)) == conjugate(x)
+    assert transpose(adjoint(x)) == conjugate(x)
+    assert adjoint(conjugate(x)) == transpose(x)
+    assert conjugate(adjoint(x)) == transpose(x)
+
+    x = Symbol('x')
+    assert conjugate(x) == adjoint(x)
+    assert transpose(x) == x
+
+
+def test_transpose():
+    a = Symbol('a', complex=True)
+    assert transpose(a) == a
+    assert transpose(I*a) == I*a
+
+    x, y = symbols('x y')
+    assert transpose(transpose(x)) == x
+    assert transpose(x + y) == x + y
+    assert transpose(x - y) == x - y
+    assert transpose(x * y) == x * y
+    assert transpose(x / y) == x / y
+    assert transpose(-x) == -x
+
+    x, y = symbols('x y', commutative=False)
+    assert transpose(transpose(x)) == x
+    assert transpose(x + y) == transpose(x) + transpose(y)
+    assert transpose(x - y) == transpose(x) - transpose(y)
+    assert transpose(x * y) == transpose(y) * transpose(x)
+    assert transpose(x / y) == 1 / transpose(y) * transpose(x)
+    assert transpose(-x) == -transpose(x)
+
+
+@_both_exp_pow
+def test_polarify():
+    from sympy.functions.elementary.complexes import (polar_lift, polarify)
+    x = Symbol('x')
+    z = Symbol('z', polar=True)
+    f = Function('f')
+    ES = {}
+
+    assert polarify(-1) == (polar_lift(-1), ES)
+    assert polarify(1 + I) == (polar_lift(1 + I), ES)
+
+    assert polarify(exp(x), subs=False) == exp(x)
+    assert polarify(1 + x, subs=False) == 1 + x
+    assert polarify(f(I) + x, subs=False) == f(polar_lift(I)) + x
+
+    assert polarify(x, lift=True) == polar_lift(x)
+    assert polarify(z, lift=True) == z
+    assert polarify(f(x), lift=True) == f(polar_lift(x))
+    assert polarify(1 + x, lift=True) == polar_lift(1 + x)
+    assert polarify(1 + f(x), lift=True) == polar_lift(1 + f(polar_lift(x)))
+
+    newex, subs = polarify(f(x) + z)
+    assert newex.subs(subs) == f(x) + z
+
+    mu = Symbol("mu")
+    sigma = Symbol("sigma", positive=True)
+
+    # Make sure polarify(lift=True) doesn't try to lift the integration
+    # variable
+    assert polarify(
+        Integral(sqrt(2)*x*exp(-(-mu + x)**2/(2*sigma**2))/(2*sqrt(pi)*sigma),
+        (x, -oo, oo)), lift=True) == Integral(sqrt(2)*(sigma*exp_polar(0))**exp_polar(I*pi)*
+        exp((sigma*exp_polar(0))**(2*exp_polar(I*pi))*exp_polar(I*pi)*polar_lift(-mu + x)**
+        (2*exp_polar(0))/2)*exp_polar(0)*polar_lift(x)/(2*sqrt(pi)), (x, -oo, oo))
+
+
+def test_unpolarify():
+    from sympy.functions.elementary.complexes import (polar_lift, principal_branch, unpolarify)
+    from sympy.core.relational import Ne
+    from sympy.functions.elementary.hyperbolic import tanh
+    from sympy.functions.special.error_functions import erf
+    from sympy.functions.special.gamma_functions import (gamma, uppergamma)
+    from sympy.abc import x
+    p = exp_polar(7*I) + 1
+    u = exp(7*I) + 1
+
+    assert unpolarify(1) == 1
+    assert unpolarify(p) == u
+    assert unpolarify(p**2) == u**2
+    assert unpolarify(p**x) == p**x
+    assert unpolarify(p*x) == u*x
+    assert unpolarify(p + x) == u + x
+    assert unpolarify(sqrt(sin(p))) == sqrt(sin(u))
+
+    # Test reduction to principal branch 2*pi.
+    t = principal_branch(x, 2*pi)
+    assert unpolarify(t) == x
+    assert unpolarify(sqrt(t)) == sqrt(t)
+
+    # Test exponents_only.
+    assert unpolarify(p**p, exponents_only=True) == p**u
+    assert unpolarify(uppergamma(x, p**p)) == uppergamma(x, p**u)
+
+    # Test functions.
+    assert unpolarify(sin(p)) == sin(u)
+    assert unpolarify(tanh(p)) == tanh(u)
+    assert unpolarify(gamma(p)) == gamma(u)
+    assert unpolarify(erf(p)) == erf(u)
+    assert unpolarify(uppergamma(x, p)) == uppergamma(x, p)
+
+    assert unpolarify(uppergamma(sin(p), sin(p + exp_polar(0)))) == \
+        uppergamma(sin(u), sin(u + 1))
+    assert unpolarify(uppergamma(polar_lift(0), 2*exp_polar(0))) == \
+        uppergamma(0, 2)
+
+    assert unpolarify(Eq(p, 0)) == Eq(u, 0)
+    assert unpolarify(Ne(p, 0)) == Ne(u, 0)
+    assert unpolarify(polar_lift(x) > 0) == (x > 0)
+
+    # Test bools
+    assert unpolarify(True) is True
+
+
+def test_issue_4035():
+    x = Symbol('x')
+    assert Abs(x).expand(trig=True) == Abs(x)
+    assert sign(x).expand(trig=True) == sign(x)
+    assert arg(x).expand(trig=True) == arg(x)
+
+
+def test_issue_3206():
+    x = Symbol('x')
+    assert Abs(Abs(x)) == Abs(x)
+
+
+def test_issue_4754_derivative_conjugate():
+    x = Symbol('x', real=True)
+    y = Symbol('y', imaginary=True)
+    f = Function('f')
+    assert (f(x).conjugate()).diff(x) == (f(x).diff(x)).conjugate()
+    assert (f(y).conjugate()).diff(y) == -(f(y).diff(y)).conjugate()
+
+
+def test_derivatives_issue_4757():
+    x = Symbol('x', real=True)
+    y = Symbol('y', imaginary=True)
+    f = Function('f')
+    assert re(f(x)).diff(x) == re(f(x).diff(x))
+    assert im(f(x)).diff(x) == im(f(x).diff(x))
+    assert re(f(y)).diff(y) == -I*im(f(y).diff(y))
+    assert im(f(y)).diff(y) == -I*re(f(y).diff(y))
+    assert Abs(f(x)).diff(x).subs(f(x), 1 + I*x).doit() == x/sqrt(1 + x**2)
+    assert arg(f(x)).diff(x).subs(f(x), 1 + I*x**2).doit() == 2*x/(1 + x**4)
+    assert Abs(f(y)).diff(y).subs(f(y), 1 + y).doit() == -y/sqrt(1 - y**2)
+    assert arg(f(y)).diff(y).subs(f(y), I + y**2).doit() == 2*y/(1 + y**4)
+
+
+def test_issue_11413():
+    from sympy.simplify.simplify import simplify
+    v0 = Symbol('v0')
+    v1 = Symbol('v1')
+    v2 = Symbol('v2')
+    V = Matrix([[v0],[v1],[v2]])
+    U = V.normalized()
+    assert U == Matrix([
+    [v0/sqrt(Abs(v0)**2 + Abs(v1)**2 + Abs(v2)**2)],
+    [v1/sqrt(Abs(v0)**2 + Abs(v1)**2 + Abs(v2)**2)],
+    [v2/sqrt(Abs(v0)**2 + Abs(v1)**2 + Abs(v2)**2)]])
+    U.norm = sqrt(v0**2/(v0**2 + v1**2 + v2**2) + v1**2/(v0**2 + v1**2 + v2**2) + v2**2/(v0**2 + v1**2 + v2**2))
+    assert simplify(U.norm) == 1
+
+
+def test_periodic_argument():
+    from sympy.functions.elementary.complexes import (periodic_argument, polar_lift, principal_branch, unbranched_argument)
+    x = Symbol('x')
+    p = Symbol('p', positive=True)
+
+    assert unbranched_argument(2 + I) == periodic_argument(2 + I, oo)
+    assert unbranched_argument(1 + x) == periodic_argument(1 + x, oo)
+    assert N_equals(unbranched_argument((1 + I)**2), pi/2)
+    assert N_equals(unbranched_argument((1 - I)**2), -pi/2)
+    assert N_equals(periodic_argument((1 + I)**2, 3*pi), pi/2)
+    assert N_equals(periodic_argument((1 - I)**2, 3*pi), -pi/2)
+
+    assert unbranched_argument(principal_branch(x, pi)) == \
+        periodic_argument(x, pi)
+
+    assert unbranched_argument(polar_lift(2 + I)) == unbranched_argument(2 + I)
+    assert periodic_argument(polar_lift(2 + I), 2*pi) == \
+        periodic_argument(2 + I, 2*pi)
+    assert periodic_argument(polar_lift(2 + I), 3*pi) == \
+        periodic_argument(2 + I, 3*pi)
+    assert periodic_argument(polar_lift(2 + I), pi) == \
+        periodic_argument(polar_lift(2 + I), pi)
+
+    assert unbranched_argument(polar_lift(1 + I)) == pi/4
+    assert periodic_argument(2*p, p) == periodic_argument(p, p)
+    assert periodic_argument(pi*p, p) == periodic_argument(p, p)
+
+    assert Abs(polar_lift(1 + I)) == Abs(1 + I)
+
+
+@XFAIL
+def test_principal_branch_fail():
+    # TODO XXX why does abs(x)._eval_evalf() not fall back to global evalf?
+    from sympy.functions.elementary.complexes import principal_branch
+    assert N_equals(principal_branch((1 + I)**2, pi/2), 0)
+
+
+def test_principal_branch():
+    from sympy.functions.elementary.complexes import (polar_lift, principal_branch)
+    p = Symbol('p', positive=True)
+    x = Symbol('x')
+    neg = Symbol('x', negative=True)
+
+    assert principal_branch(polar_lift(x), p) == principal_branch(x, p)
+    assert principal_branch(polar_lift(2 + I), p) == principal_branch(2 + I, p)
+    assert principal_branch(2*x, p) == 2*principal_branch(x, p)
+    assert principal_branch(1, pi) == exp_polar(0)
+    assert principal_branch(-1, 2*pi) == exp_polar(I*pi)
+    assert principal_branch(-1, pi) == exp_polar(0)
+    assert principal_branch(exp_polar(3*pi*I)*x, 2*pi) == \
+        principal_branch(exp_polar(I*pi)*x, 2*pi)
+    assert principal_branch(neg*exp_polar(pi*I), 2*pi) == neg*exp_polar(-I*pi)
+    # related to issue #14692
+    assert principal_branch(exp_polar(-I*pi/2)/polar_lift(neg), 2*pi) == \
+        exp_polar(-I*pi/2)/neg
+
+    assert N_equals(principal_branch((1 + I)**2, 2*pi), 2*I)
+    assert N_equals(principal_branch((1 + I)**2, 3*pi), 2*I)
+    assert N_equals(principal_branch((1 + I)**2, 1*pi), 2*I)
+
+    # test argument sanitization
+    assert principal_branch(x, I).func is principal_branch
+    assert principal_branch(x, -4).func is principal_branch
+    assert principal_branch(x, -oo).func is principal_branch
+    assert principal_branch(x, zoo).func is principal_branch
+
+
+@XFAIL
+def test_issue_6167_6151():
+    n = pi**1000
+    i = int(n)
+    assert sign(n - i) == 1
+    assert abs(n - i) == n - i
+    x = Symbol('x')
+    eps = pi**-1500
+    big = pi**1000
+    one = cos(x)**2 + sin(x)**2
+    e = big*one - big + eps
+    from sympy.simplify.simplify import simplify
+    assert sign(simplify(e)) == 1
+    for xi in (111, 11, 1, Rational(1, 10)):
+        assert sign(e.subs(x, xi)) == 1
+
+
+def test_issue_14216():
+    from sympy.functions.elementary.complexes import unpolarify
+    A = MatrixSymbol("A", 2, 2)
+    assert unpolarify(A[0, 0]) == A[0, 0]
+    assert unpolarify(A[0, 0]*A[1, 0]) == A[0, 0]*A[1, 0]
+
+
+def test_issue_14238():
+    # doesn't cause recursion error
+    r = Symbol('r', real=True)
+    assert Abs(r + Piecewise((0, r > 0), (1 - r, True)))
+
+
+def test_issue_22189():
+    x = Symbol('x')
+    for a in (sqrt(7 - 2*x) - 2, 1 - x):
+        assert Abs(a) - Abs(-a) == 0, a
+
+
+def test_zero_assumptions():
+    nr = Symbol('nonreal', real=False, finite=True)
+    ni = Symbol('nonimaginary', imaginary=False)
+    # imaginary implies not zero
+    nzni = Symbol('nonzerononimaginary', zero=False, imaginary=False)
+
+    assert re(nr).is_zero is None
+    assert im(nr).is_zero is False
+
+    assert re(ni).is_zero is None
+    assert im(ni).is_zero is None
+
+    assert re(nzni).is_zero is False
+    assert im(nzni).is_zero is None
+
+
+@_both_exp_pow
+def test_issue_15893():
+    f = Function('f', real=True)
+    x = Symbol('x', real=True)
+    eq = Derivative(Abs(f(x)), f(x))
+    assert eq.doit() == sign(f(x))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_exponential.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_exponential.py
new file mode 100644
index 0000000000000000000000000000000000000000..ee8c311d01e98d7fd6831ad754e854fae409aa0c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_exponential.py
@@ -0,0 +1,810 @@
+from sympy.assumptions.refine import refine
+from sympy.calculus.accumulationbounds import AccumBounds
+from sympy.concrete.products import Product
+from sympy.concrete.summations import Sum
+from sympy.core.function import expand_log
+from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi, zoo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (adjoint, conjugate, re, sign, transpose)
+from sympy.functions.elementary.exponential import (LambertW, exp, exp_polar, log)
+from sympy.functions.elementary.hyperbolic import (cosh, sinh, tanh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.polys.polytools import gcd
+from sympy.series.order import O
+from sympy.simplify.simplify import simplify
+from sympy.core.parameters import global_parameters
+from sympy.functions.elementary.exponential import match_real_imag
+from sympy.abc import x, y, z
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.testing.pytest import raises, XFAIL, _both_exp_pow
+
+
+@_both_exp_pow
+def test_exp_values():
+    if global_parameters.exp_is_pow:
+        assert type(exp(x)) is Pow
+    else:
+        assert type(exp(x)) is exp
+
+    k = Symbol('k', integer=True)
+
+    assert exp(nan) is nan
+
+    assert exp(oo) is oo
+    assert exp(-oo) == 0
+
+    assert exp(0) == 1
+    assert exp(1) == E
+    assert exp(-1 + x).as_base_exp() == (S.Exp1, x - 1)
+    assert exp(1 + x).as_base_exp() == (S.Exp1, x + 1)
+
+    assert exp(pi*I/2) == I
+    assert exp(pi*I) == -1
+    assert exp(pi*I*Rational(3, 2)) == -I
+    assert exp(2*pi*I) == 1
+
+    assert refine(exp(pi*I*2*k)) == 1
+    assert refine(exp(pi*I*2*(k + S.Half))) == -1
+    assert refine(exp(pi*I*2*(k + Rational(1, 4)))) == I
+    assert refine(exp(pi*I*2*(k + Rational(3, 4)))) == -I
+
+    assert exp(log(x)) == x
+    assert exp(2*log(x)) == x**2
+    assert exp(pi*log(x)) == x**pi
+
+    assert exp(17*log(x) + E*log(y)) == x**17 * y**E
+
+    assert exp(x*log(x)) != x**x
+    assert exp(sin(x)*log(x)) != x
+
+    assert exp(3*log(x) + oo*x) == exp(oo*x) * x**3
+    assert exp(4*log(x)*log(y) + 3*log(x)) == x**3 * exp(4*log(x)*log(y))
+
+    assert exp(-oo, evaluate=False).is_finite is True
+    assert exp(oo, evaluate=False).is_finite is False
+
+
+@_both_exp_pow
+def test_exp_period():
+    assert exp(I*pi*Rational(9, 4)) == exp(I*pi/4)
+    assert exp(I*pi*Rational(46, 18)) == exp(I*pi*Rational(5, 9))
+    assert exp(I*pi*Rational(25, 7)) == exp(I*pi*Rational(-3, 7))
+    assert exp(I*pi*Rational(-19, 3)) == exp(-I*pi/3)
+    assert exp(I*pi*Rational(37, 8)) - exp(I*pi*Rational(-11, 8)) == 0
+    assert exp(I*pi*Rational(-5, 3)) / exp(I*pi*Rational(11, 5)) * exp(I*pi*Rational(148, 15)) == 1
+
+    assert exp(2 - I*pi*Rational(17, 5)) == exp(2 + I*pi*Rational(3, 5))
+    assert exp(log(3) + I*pi*Rational(29, 9)) == 3 * exp(I*pi*Rational(-7, 9))
+
+    n = Symbol('n', integer=True)
+    e = Symbol('e', even=True)
+    assert exp(e*I*pi) == 1
+    assert exp((e + 1)*I*pi) == -1
+    assert exp((1 + 4*n)*I*pi/2) == I
+    assert exp((-1 + 4*n)*I*pi/2) == -I
+
+
+@_both_exp_pow
+def test_exp_log():
+    x = Symbol("x", real=True)
+    assert log(exp(x)) == x
+    assert exp(log(x)) == x
+
+    if not global_parameters.exp_is_pow:
+        assert log(x).inverse() == exp
+        assert exp(x).inverse() == log
+
+    y = Symbol("y", polar=True)
+    assert log(exp_polar(z)) == z
+    assert exp(log(y)) == y
+
+
+@_both_exp_pow
+def test_exp_expand():
+    e = exp(log(Rational(2))*(1 + x) - log(Rational(2))*x)
+    assert e.expand() == 2
+    assert exp(x + y) != exp(x)*exp(y)
+    assert exp(x + y).expand() == exp(x)*exp(y)
+
+
+@_both_exp_pow
+def test_exp__as_base_exp():
+    assert exp(x).as_base_exp() == (E, x)
+    assert exp(2*x).as_base_exp() == (E, 2*x)
+    assert exp(x*y).as_base_exp() == (E, x*y)
+    assert exp(-x).as_base_exp() == (E, -x)
+
+    # Pow( *expr.as_base_exp() ) == expr    invariant should hold
+    assert E**x == exp(x)
+    assert E**(2*x) == exp(2*x)
+    assert E**(x*y) == exp(x*y)
+
+    assert exp(x).base is S.Exp1
+    assert exp(x).exp == x
+
+
+@_both_exp_pow
+def test_exp_infinity():
+    assert exp(I*y) != nan
+    assert refine(exp(I*oo)) is nan
+    assert refine(exp(-I*oo)) is nan
+    assert exp(y*I*oo) != nan
+    assert exp(zoo) is nan
+    x = Symbol('x', extended_real=True, finite=False)
+    assert exp(x).is_complex is None
+
+
+@_both_exp_pow
+def test_exp_subs():
+    x = Symbol('x')
+    e = (exp(3*log(x), evaluate=False))  # evaluates to x**3
+    assert e.subs(x**3, y**3) == e
+    assert e.subs(x**2, 5) == e
+    assert (x**3).subs(x**2, y) != y**Rational(3, 2)
+    assert exp(exp(x) + exp(x**2)).subs(exp(exp(x)), y) == y * exp(exp(x**2))
+    assert exp(x).subs(E, y) == y**x
+    x = symbols('x', real=True)
+    assert exp(5*x).subs(exp(7*x), y) == y**Rational(5, 7)
+    assert exp(2*x + 7).subs(exp(3*x), y) == y**Rational(2, 3) * exp(7)
+    x = symbols('x', positive=True)
+    assert exp(3*log(x)).subs(x**2, y) == y**Rational(3, 2)
+    # differentiate between E and exp
+    assert exp(exp(x + E)).subs(exp, 3) == 3**(3**(x + E))
+    assert exp(exp(x + E)).subs(exp, sin) == sin(sin(x + E))
+    assert exp(exp(x + E)).subs(E, 3) == 3**(3**(x + 3))
+    assert exp(3).subs(E, sin) == sin(3)
+
+
+def test_exp_adjoint():
+    x = Symbol('x', commutative=False)
+    assert adjoint(exp(x)) == exp(adjoint(x))
+
+
+def test_exp_conjugate():
+    assert conjugate(exp(x)) == exp(conjugate(x))
+
+
+@_both_exp_pow
+def test_exp_transpose():
+    assert transpose(exp(x)) == exp(transpose(x))
+
+
+@_both_exp_pow
+def test_exp_rewrite():
+    assert exp(x).rewrite(sin) == sinh(x) + cosh(x)
+    assert exp(x*I).rewrite(cos) == cos(x) + I*sin(x)
+    assert exp(1).rewrite(cos) == sinh(1) + cosh(1)
+    assert exp(1).rewrite(sin) == sinh(1) + cosh(1)
+    assert exp(1).rewrite(sin) == sinh(1) + cosh(1)
+    assert exp(x).rewrite(tanh) == (1 + tanh(x/2))/(1 - tanh(x/2))
+    assert exp(pi*I/4).rewrite(sqrt) == sqrt(2)/2 + sqrt(2)*I/2
+    assert exp(pi*I/3).rewrite(sqrt) == S.Half + sqrt(3)*I/2
+    if not global_parameters.exp_is_pow:
+        assert exp(x*log(y)).rewrite(Pow) == y**x
+        assert exp(log(x)*log(y)).rewrite(Pow) in [x**log(y), y**log(x)]
+        assert exp(log(log(x))*y).rewrite(Pow) == log(x)**y
+
+    n = Symbol('n', integer=True)
+
+    assert Sum((exp(pi*I/2)/2)**n, (n, 0, oo)).rewrite(sqrt).doit() == Rational(4, 5) + I*2/5
+    assert Sum((exp(pi*I/4)/2)**n, (n, 0, oo)).rewrite(sqrt).doit() == 1/(1 - sqrt(2)*(1 + I)/4)
+    assert (Sum((exp(pi*I/3)/2)**n, (n, 0, oo)).rewrite(sqrt).doit().cancel()
+            == 4*I/(sqrt(3) + 3*I))
+
+
+@_both_exp_pow
+def test_exp_leading_term():
+    assert exp(x).as_leading_term(x) == 1
+    assert exp(2 + x).as_leading_term(x) == exp(2)
+    assert exp((2*x + 3) / (x+1)).as_leading_term(x) == exp(3)
+
+    # The following tests are commented, since now SymPy returns the
+    # original function when the leading term in the series expansion does
+    # not exist.
+    # raises(NotImplementedError, lambda: exp(1/x).as_leading_term(x))
+    # raises(NotImplementedError, lambda: exp((x + 1) / x**2).as_leading_term(x))
+    # raises(NotImplementedError, lambda: exp(x + 1/x).as_leading_term(x))
+
+
+@_both_exp_pow
+def test_exp_taylor_term():
+    x = symbols('x')
+    assert exp(x).taylor_term(1, x) == x
+    assert exp(x).taylor_term(3, x) == x**3/6
+    assert exp(x).taylor_term(4, x) == x**4/24
+    assert exp(x).taylor_term(-1, x) is S.Zero
+
+
+def test_exp_MatrixSymbol():
+    A = MatrixSymbol("A", 2, 2)
+    assert exp(A).has(exp)
+
+
+def test_exp_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: exp(x).fdiff(2))
+
+
+def test_log_values():
+    assert log(nan) is nan
+
+    assert log(oo) is oo
+    assert log(-oo) is oo
+
+    assert log(zoo) is zoo
+    assert log(-zoo) is zoo
+
+    assert log(0) is zoo
+
+    assert log(1) == 0
+    assert log(-1) == I*pi
+
+    assert log(E) == 1
+    assert log(-E).expand() == 1 + I*pi
+
+    assert unchanged(log, pi)
+    assert log(-pi).expand() == log(pi) + I*pi
+
+    assert unchanged(log, 17)
+    assert log(-17) == log(17) + I*pi
+
+    assert log(I) == I*pi/2
+    assert log(-I) == -I*pi/2
+
+    assert log(17*I) == I*pi/2 + log(17)
+    assert log(-17*I).expand() == -I*pi/2 + log(17)
+
+    assert log(oo*I) is oo
+    assert log(-oo*I) is oo
+    assert log(0, 2) is zoo
+    assert log(0, 5) is zoo
+
+    assert exp(-log(3))**(-1) == 3
+
+    assert log(S.Half) == -log(2)
+    assert log(2*3).func is log
+    assert log(2*3**2).func is log
+
+
+def test_match_real_imag():
+    x, y = symbols('x,y', real=True)
+    i = Symbol('i', imaginary=True)
+    assert match_real_imag(S.One) == (1, 0)
+    assert match_real_imag(I) == (0, 1)
+    assert match_real_imag(3 - 5*I) == (3, -5)
+    assert match_real_imag(-sqrt(3) + S.Half*I) == (-sqrt(3), S.Half)
+    assert match_real_imag(x + y*I) == (x, y)
+    assert match_real_imag(x*I + y*I) == (0, x + y)
+    assert match_real_imag((x + y)*I) == (0, x + y)
+    assert match_real_imag(Rational(-2, 3)*i*I) == (None, None)
+    assert match_real_imag(1 - 2*i) == (None, None)
+    assert match_real_imag(sqrt(2)*(3 - 5*I)) == (None, None)
+
+
+def test_log_exact():
+    # check for pi/2, pi/3, pi/4, pi/6, pi/8, pi/12; pi/5, pi/10:
+    for n in range(-23, 24):
+        if gcd(n, 24) != 1:
+            assert log(exp(n*I*pi/24).rewrite(sqrt)) == n*I*pi/24
+        for n in range(-9, 10):
+            assert log(exp(n*I*pi/10).rewrite(sqrt)) == n*I*pi/10
+
+    assert log(S.Half - I*sqrt(3)/2) == -I*pi/3
+    assert log(Rational(-1, 2) + I*sqrt(3)/2) == I*pi*Rational(2, 3)
+    assert log(-sqrt(2)/2 - I*sqrt(2)/2) == -I*pi*Rational(3, 4)
+    assert log(-sqrt(3)/2 - I*S.Half) == -I*pi*Rational(5, 6)
+
+    assert log(Rational(-1, 4) + sqrt(5)/4 - I*sqrt(sqrt(5)/8 + Rational(5, 8))) == -I*pi*Rational(2, 5)
+    assert log(sqrt(Rational(5, 8) - sqrt(5)/8) + I*(Rational(1, 4) + sqrt(5)/4)) == I*pi*Rational(3, 10)
+    assert log(-sqrt(sqrt(2)/4 + S.Half) + I*sqrt(S.Half - sqrt(2)/4)) == I*pi*Rational(7, 8)
+    assert log(-sqrt(6)/4 - sqrt(2)/4 + I*(-sqrt(6)/4 + sqrt(2)/4)) == -I*pi*Rational(11, 12)
+
+    assert log(-1 + I*sqrt(3)) == log(2) + I*pi*Rational(2, 3)
+    assert log(5 + 5*I) == log(5*sqrt(2)) + I*pi/4
+    assert log(sqrt(-12)) == log(2*sqrt(3)) + I*pi/2
+    assert log(-sqrt(6) + sqrt(2) - I*sqrt(6) - I*sqrt(2)) == log(4) - I*pi*Rational(7, 12)
+    assert log(-sqrt(6-3*sqrt(2)) - I*sqrt(6+3*sqrt(2))) == log(2*sqrt(3)) - I*pi*Rational(5, 8)
+    assert log(1 + I*sqrt(2-sqrt(2))/sqrt(2+sqrt(2))) == log(2/sqrt(sqrt(2) + 2)) + I*pi/8
+    assert log(cos(pi*Rational(7, 12)) + I*sin(pi*Rational(7, 12))) == I*pi*Rational(7, 12)
+    assert log(cos(pi*Rational(6, 5)) + I*sin(pi*Rational(6, 5))) == I*pi*Rational(-4, 5)
+
+    assert log(5*(1 + I)/sqrt(2)) == log(5) + I*pi/4
+    assert log(sqrt(2)*(-sqrt(3) + 1 - sqrt(3)*I - I)) == log(4) - I*pi*Rational(7, 12)
+    assert log(-sqrt(2)*(1 - I*sqrt(3))) == log(2*sqrt(2)) + I*pi*Rational(2, 3)
+    assert log(sqrt(3)*I*(-sqrt(6 - 3*sqrt(2)) - I*sqrt(3*sqrt(2) + 6))) == log(6) - I*pi/8
+
+    zero = (1 + sqrt(2))**2 - 3 - 2*sqrt(2)
+    assert log(zero - I*sqrt(3)) == log(sqrt(3)) - I*pi/2
+    assert unchanged(log, zero + I*zero) or log(zero + zero*I) is zoo
+
+    # bail quickly if no obvious simplification is possible:
+    assert unchanged(log, (sqrt(2)-1/sqrt(sqrt(3)+I))**1000)
+    # beware of non-real coefficients
+    assert unchanged(log, sqrt(2-sqrt(5))*(1 + I))
+
+
+def test_log_base():
+    assert log(1, 2) == 0
+    assert log(2, 2) == 1
+    assert log(3, 2) == log(3)/log(2)
+    assert log(6, 2) == 1 + log(3)/log(2)
+    assert log(6, 3) == 1 + log(2)/log(3)
+    assert log(2**3, 2) == 3
+    assert log(3**3, 3) == 3
+    assert log(5, 1) is zoo
+    assert log(1, 1) is nan
+    assert log(Rational(2, 3), 10) == log(Rational(2, 3))/log(10)
+    assert log(Rational(2, 3), Rational(1, 3)) == -log(2)/log(3) + 1
+    assert log(Rational(2, 3), Rational(2, 5)) == \
+        log(Rational(2, 3))/log(Rational(2, 5))
+    # issue 17148
+    assert log(Rational(8, 3), 2) == -log(3)/log(2) + 3
+
+
+def test_log_symbolic():
+    assert log(x, exp(1)) == log(x)
+    assert log(exp(x)) != x
+
+    assert log(x, exp(1)) == log(x)
+    assert log(x*y) != log(x) + log(y)
+    assert log(x/y).expand() != log(x) - log(y)
+    assert log(x/y).expand(force=True) == log(x) - log(y)
+    assert log(x**y).expand() != y*log(x)
+    assert log(x**y).expand(force=True) == y*log(x)
+
+    assert log(x, 2) == log(x)/log(2)
+    assert log(E, 2) == 1/log(2)
+
+    p, q = symbols('p,q', positive=True)
+    r = Symbol('r', real=True)
+
+    assert log(p**2) != 2*log(p)
+    assert log(p**2).expand() == 2*log(p)
+    assert log(x**2).expand() != 2*log(x)
+    assert log(p**q) != q*log(p)
+    assert log(exp(p)) == p
+    assert log(p*q) != log(p) + log(q)
+    assert log(p*q).expand() == log(p) + log(q)
+
+    assert log(-sqrt(3)) == log(sqrt(3)) + I*pi
+    assert log(-exp(p)) != p + I*pi
+    assert log(-exp(x)).expand() != x + I*pi
+    assert log(-exp(r)).expand() == r + I*pi
+
+    assert log(x**y) != y*log(x)
+
+    assert (log(x**-5)**-1).expand() != -1/log(x)/5
+    assert (log(p**-5)**-1).expand() == -1/log(p)/5
+    assert log(-x).func is log and log(-x).args[0] == -x
+    assert log(-p).func is log and log(-p).args[0] == -p
+
+
+def test_log_exp():
+    assert log(exp(4*I*pi)) == 0     # exp evaluates
+    assert log(exp(-5*I*pi)) == I*pi # exp evaluates
+    assert log(exp(I*pi*Rational(19, 4))) == I*pi*Rational(3, 4)
+    assert log(exp(I*pi*Rational(25, 7))) == I*pi*Rational(-3, 7)
+    assert log(exp(-5*I)) == -5*I + 2*I*pi
+
+
+@_both_exp_pow
+def test_exp_assumptions():
+    r = Symbol('r', real=True)
+    i = Symbol('i', imaginary=True)
+    for e in exp, exp_polar:
+        assert e(x).is_real is None
+        assert e(x).is_imaginary is None
+        assert e(i).is_real is None
+        assert e(i).is_imaginary is None
+        assert e(r).is_real is True
+        assert e(r).is_imaginary is False
+        assert e(re(x)).is_extended_real is True
+        assert e(re(x)).is_imaginary is False
+
+    assert Pow(E, I*pi, evaluate=False).is_imaginary == False
+    assert Pow(E, 2*I*pi, evaluate=False).is_imaginary == False
+    assert Pow(E, I*pi/2, evaluate=False).is_imaginary == True
+    assert Pow(E, I*pi/3, evaluate=False).is_imaginary is None
+
+    assert exp(0, evaluate=False).is_algebraic
+
+    a = Symbol('a', algebraic=True)
+    an = Symbol('an', algebraic=True, nonzero=True)
+    r = Symbol('r', rational=True)
+    rn = Symbol('rn', rational=True, nonzero=True)
+    assert exp(a).is_algebraic is None
+    assert exp(an).is_algebraic is False
+    assert exp(pi*r).is_algebraic is None
+    assert exp(pi*rn).is_algebraic is False
+
+    assert exp(0, evaluate=False).is_algebraic is True
+    assert exp(I*pi/3, evaluate=False).is_algebraic is True
+    assert exp(I*pi*r, evaluate=False).is_algebraic is True
+
+
+@_both_exp_pow
+def test_exp_AccumBounds():
+    assert exp(AccumBounds(1, 2)) == AccumBounds(E, E**2)
+
+
+def test_log_assumptions():
+    p = symbols('p', positive=True)
+    n = symbols('n', negative=True)
+    z = symbols('z', zero=True)
+    x = symbols('x', infinite=True, extended_positive=True)
+
+    assert log(z).is_positive is False
+    assert log(x).is_extended_positive is True
+    assert log(2) > 0
+    assert log(1, evaluate=False).is_zero
+    assert log(1 + z).is_zero
+    assert log(p).is_zero is None
+    assert log(n).is_zero is False
+    assert log(0.5).is_negative is True
+    assert log(exp(p) + 1).is_positive
+
+    assert log(1, evaluate=False).is_algebraic
+    assert log(42, evaluate=False).is_algebraic is False
+
+    assert log(1 + z).is_rational
+
+
+def test_log_hashing():
+    assert x != log(log(x))
+    assert hash(x) != hash(log(log(x)))
+    assert log(x) != log(log(log(x)))
+
+    e = 1/log(log(x) + log(log(x)))
+    assert e.base.func is log
+    e = 1/log(log(x) + log(log(log(x))))
+    assert e.base.func is log
+
+    e = log(log(x))
+    assert e.func is log
+    assert x.func is not log
+    assert hash(log(log(x))) != hash(x)
+    assert e != x
+
+
+def test_log_sign():
+    assert sign(log(2)) == 1
+
+
+def test_log_expand_complex():
+    assert log(1 + I).expand(complex=True) == log(2)/2 + I*pi/4
+    assert log(1 - sqrt(2)).expand(complex=True) == log(sqrt(2) - 1) + I*pi
+
+
+def test_log_apply_evalf():
+    value = (log(3)/log(2) - 1).evalf()
+    assert value.epsilon_eq(Float("0.58496250072115618145373"))
+
+
+def test_log_leading_term():
+    p = Symbol('p')
+
+    # Test for STEP 3
+    assert log(1 + x + x**2).as_leading_term(x, cdir=1) == x
+    # Test for STEP 4
+    assert log(2*x).as_leading_term(x, cdir=1) == log(x) + log(2)
+    assert log(2*x).as_leading_term(x, cdir=-1) == log(x) + log(2)
+    assert log(-2*x).as_leading_term(x, cdir=1, logx=p) == p + log(2) + I*pi
+    assert log(-2*x).as_leading_term(x, cdir=-1, logx=p) == p + log(2) - I*pi
+    # Test for STEP 5
+    assert log(-2*x + (3 - I)*x**2).as_leading_term(x, cdir=1) == log(x) + log(2) - I*pi
+    assert log(-2*x + (3 - I)*x**2).as_leading_term(x, cdir=-1) == log(x) + log(2) - I*pi
+    assert log(2*x + (3 - I)*x**2).as_leading_term(x, cdir=1) == log(x) + log(2)
+    assert log(2*x + (3 - I)*x**2).as_leading_term(x, cdir=-1) == log(x) + log(2) - 2*I*pi
+    assert log(-1 + x - I*x**2 + I*x**3).as_leading_term(x, cdir=1) == -I*pi
+    assert log(-1 + x - I*x**2 + I*x**3).as_leading_term(x, cdir=-1) == -I*pi
+    assert log(-1/(1 - x)).as_leading_term(x, cdir=1) == I*pi
+    assert log(-1/(1 - x)).as_leading_term(x, cdir=-1) == I*pi
+
+
+def test_log_nseries():
+    p = Symbol('p')
+    assert log(1/x)._eval_nseries(x, 4, logx=-p, cdir=1) == p
+    assert log(1/x)._eval_nseries(x, 4, logx=-p, cdir=-1) == p + 2*I*pi
+    assert log(x - 1)._eval_nseries(x, 4, None, I) == I*pi - x - x**2/2 - x**3/3 + O(x**4)
+    assert log(x - 1)._eval_nseries(x, 4, None, -I) == -I*pi - x - x**2/2 - x**3/3 + O(x**4)
+    assert log(I*x + I*x**3 - 1)._eval_nseries(x, 3, None, 1) == I*pi - I*x + x**2/2 + O(x**3)
+    assert log(I*x + I*x**3 - 1)._eval_nseries(x, 3, None, -1) == -I*pi - I*x + x**2/2 + O(x**3)
+    assert log(I*x**2 + I*x**3 - 1)._eval_nseries(x, 3, None, 1) == I*pi - I*x**2 + O(x**3)
+    assert log(I*x**2 + I*x**3 - 1)._eval_nseries(x, 3, None, -1) == I*pi - I*x**2 + O(x**3)
+    assert log(2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, 1) == log(2) + log(x) + \
+    x*(S(3)/2 - I/2) + x**2*(-1 + 3*I/4) + O(x**3)
+    assert log(2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, -1) == -2*I*pi + log(2) + \
+    log(x) - x*(-S(3)/2 + I/2) + x**2*(-1 + 3*I/4) + O(x**3)
+    assert log(-2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, 1) == -I*pi + log(2) + log(x) + \
+    x*(-S(3)/2 + I/2) + x**2*(-1 + 3*I/4) + O(x**3)
+    assert log(-2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, -1) == -I*pi + log(2) + log(x) - \
+    x*(S(3)/2 - I/2) + x**2*(-1 + 3*I/4) + O(x**3)
+    assert log(sqrt(-I*x**2 - 3)*sqrt(-I*x**2 - 1) - 2)._eval_nseries(x, 3, None, 1) == -I*pi + \
+    log(sqrt(3) + 2) + 2*sqrt(3)*I*x**2/(3*sqrt(3) + 6) + O(x**3)
+    assert log(-1/(1 - x))._eval_nseries(x, 3, None, 1) == I*pi + x + x**2/2 + O(x**3)
+    assert log(-1/(1 - x))._eval_nseries(x, 3, None, -1) == I*pi + x + x**2/2 + O(x**3)
+
+
+def test_log_series():
+    # Note Series at infinities other than oo/-oo were introduced as a part of
+    # pull request 23798. Refer https://github.com/sympy/sympy/pull/23798 for
+    # more information.
+    expr1 = log(1 + x)
+    expr2 = log(x + sqrt(x**2 + 1))
+
+    assert expr1.series(x, x0=I*oo, n=4) == 1/(3*x**3) - 1/(2*x**2) + 1/x + \
+    I*pi/2 - log(I/x) + O(x**(-4), (x, oo*I))
+    assert expr1.series(x, x0=-I*oo, n=4) == 1/(3*x**3) - 1/(2*x**2) + 1/x - \
+    I*pi/2 - log(-I/x) + O(x**(-4), (x, -oo*I))
+    assert expr2.series(x, x0=I*oo, n=4) == 1/(4*x**2) + I*pi/2 + log(2) - \
+    log(I/x) + O(x**(-4), (x, oo*I))
+    assert expr2.series(x, x0=-I*oo, n=4) == -1/(4*x**2) - I*pi/2 - log(2) + \
+    log(-I/x) + O(x**(-4), (x, -oo*I))
+
+
+def test_log_expand():
+    w = Symbol("w", positive=True)
+    e = log(w**(log(5)/log(3)))
+    assert e.expand() == log(5)/log(3) * log(w)
+    x, y, z = symbols('x,y,z', positive=True)
+    assert log(x*(y + z)).expand(mul=False) == log(x) + log(y + z)
+    assert log(log(x**2)*log(y*z)).expand() in [log(2*log(x)*log(y) +
+        2*log(x)*log(z)), log(log(x)*log(z) + log(y)*log(x)) + log(2),
+        log((log(y) + log(z))*log(x)) + log(2)]
+    assert log(x**log(x**2)).expand(deep=False) == log(x)*log(x**2)
+    assert log(x**log(x**2)).expand() == 2*log(x)**2
+    x, y = symbols('x,y')
+    assert log(x*y).expand(force=True) == log(x) + log(y)
+    assert log(x**y).expand(force=True) == y*log(x)
+    assert log(exp(x)).expand(force=True) == x
+
+    # there's generally no need to expand out logs since this requires
+    # factoring and if simplification is sought, it's cheaper to put
+    # logs together than it is to take them apart.
+    assert log(2*3**2).expand() != 2*log(3) + log(2)
+
+
+@XFAIL
+def test_log_expand_fail():
+    x, y, z = symbols('x,y,z', positive=True)
+    assert (log(x*(y + z))*(x + y)).expand(mul=True, log=True) == y*log(
+        x) + y*log(y + z) + z*log(x) + z*log(y + z)
+
+
+def test_log_simplify():
+    x = Symbol("x", positive=True)
+    assert log(x**2).expand() == 2*log(x)
+    assert expand_log(log(x**(2 + log(2)))) == (2 + log(2))*log(x)
+
+    z = Symbol('z')
+    assert log(sqrt(z)).expand() == log(z)/2
+    assert expand_log(log(z**(log(2) - 1))) == (log(2) - 1)*log(z)
+    assert log(z**(-1)).expand() != -log(z)
+    assert log(z**(x/(x+1))).expand() == x*log(z)/(x + 1)
+
+
+def test_log_AccumBounds():
+    assert log(AccumBounds(1, E)) == AccumBounds(0, 1)
+    assert log(AccumBounds(0, E)) == AccumBounds(-oo, 1)
+    assert log(AccumBounds(-1, E)) == S.NaN
+    assert log(AccumBounds(0, oo)) == AccumBounds(-oo, oo)
+    assert log(AccumBounds(-oo, 0)) == S.NaN
+    assert log(AccumBounds(-oo, oo)) == S.NaN
+
+
+@_both_exp_pow
+def test_lambertw():
+    k = Symbol('k')
+
+    assert LambertW(x, 0) == LambertW(x)
+    assert LambertW(x, 0, evaluate=False) != LambertW(x)
+    assert LambertW(0) == 0
+    assert LambertW(E) == 1
+    assert LambertW(-1/E) == -1
+    assert LambertW(-log(2)/2) == -log(2)
+    assert LambertW(oo) is oo
+    assert LambertW(0, 1) is -oo
+    assert LambertW(0, 42) is -oo
+    assert LambertW(-pi/2, -1) == -I*pi/2
+    assert LambertW(-1/E, -1) == -1
+    assert LambertW(-2*exp(-2), -1) == -2
+    assert LambertW(2*log(2)) == log(2)
+    assert LambertW(-pi/2) == I*pi/2
+    assert LambertW(exp(1 + E)) == E
+
+    assert LambertW(x**2).diff(x) == 2*LambertW(x**2)/x/(1 + LambertW(x**2))
+    assert LambertW(x, k).diff(x) == LambertW(x, k)/x/(1 + LambertW(x, k))
+
+    assert LambertW(sqrt(2)).evalf(30).epsilon_eq(
+        Float("0.701338383413663009202120278965", 30), 1e-29)
+    assert re(LambertW(2, -1)).evalf().epsilon_eq(Float("-0.834310366631110"))
+
+    assert LambertW(-1).is_real is False  # issue 5215
+    assert LambertW(2, evaluate=False).is_real
+    p = Symbol('p', positive=True)
+    assert LambertW(p, evaluate=False).is_real
+    assert LambertW(p - 1, evaluate=False).is_real is None
+    assert LambertW(-p - 2/S.Exp1, evaluate=False).is_real is False
+    assert LambertW(S.Half, -1, evaluate=False).is_real is False
+    assert LambertW(Rational(-1, 10), -1, evaluate=False).is_real
+    assert LambertW(-10, -1, evaluate=False).is_real is False
+    assert LambertW(-2, 2, evaluate=False).is_real is False
+
+    assert LambertW(0, evaluate=False).is_algebraic
+    na = Symbol('na', nonzero=True, algebraic=True)
+    assert LambertW(na).is_algebraic is False
+    assert LambertW(p).is_zero is False
+    n = Symbol('n', negative=True)
+    assert LambertW(n).is_zero is False
+
+
+def test_issue_5673():
+    e = LambertW(-1)
+    assert e.is_comparable is False
+    assert e.is_positive is not True
+    e2 = 1 - 1/(1 - exp(-1000))
+    assert e2.is_positive is not True
+    e3 = -2 + exp(exp(LambertW(log(2)))*LambertW(log(2)))
+    assert e3.is_nonzero is not True
+
+
+def test_log_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: log(x).fdiff(2))
+
+
+def test_log_taylor_term():
+    x = symbols('x')
+    assert log(x).taylor_term(0, x) == x
+    assert log(x).taylor_term(1, x) == -x**2/2
+    assert log(x).taylor_term(4, x) == x**5/5
+    assert log(x).taylor_term(-1, x) is S.Zero
+
+
+def test_exp_expand_NC():
+    A, B, C = symbols('A,B,C', commutative=False)
+
+    assert exp(A + B).expand() == exp(A + B)
+    assert exp(A + B + C).expand() == exp(A + B + C)
+    assert exp(x + y).expand() == exp(x)*exp(y)
+    assert exp(x + y + z).expand() == exp(x)*exp(y)*exp(z)
+
+
+@_both_exp_pow
+def test_as_numer_denom():
+    n = symbols('n', negative=True)
+    assert exp(x).as_numer_denom() == (exp(x), 1)
+    assert exp(-x).as_numer_denom() == (1, exp(x))
+    assert exp(-2*x).as_numer_denom() == (1, exp(2*x))
+    assert exp(-2).as_numer_denom() == (1, exp(2))
+    assert exp(n).as_numer_denom() == (1, exp(-n))
+    assert exp(-n).as_numer_denom() == (exp(-n), 1)
+    assert exp(-I*x).as_numer_denom() == (1, exp(I*x))
+    assert exp(-I*n).as_numer_denom() == (1, exp(I*n))
+    assert exp(-n).as_numer_denom() == (exp(-n), 1)
+    # Check noncommutativity
+    a = symbols('a', commutative=False)
+    assert exp(-a).as_numer_denom() == (exp(-a), 1)
+
+
+@_both_exp_pow
+def test_polar():
+    x, y = symbols('x y', polar=True)
+
+    assert abs(exp_polar(I*4)) == 1
+    assert abs(exp_polar(0)) == 1
+    assert abs(exp_polar(2 + 3*I)) == exp(2)
+    assert exp_polar(I*10).n() == exp_polar(I*10)
+
+    assert log(exp_polar(z)) == z
+    assert log(x*y).expand() == log(x) + log(y)
+    assert log(x**z).expand() == z*log(x)
+
+    assert exp_polar(3).exp == 3
+
+    # Compare exp(1.0*pi*I).
+    assert (exp_polar(1.0*pi*I).n(n=5)).as_real_imag()[1] >= 0
+
+    assert exp_polar(0).is_rational is True  # issue 8008
+
+
+def test_exp_summation():
+    w = symbols("w")
+    m, n, i, j = symbols("m n i j")
+    expr = exp(Sum(w*i, (i, 0, n), (j, 0, m)))
+    assert expr.expand() == Product(exp(w*i), (i, 0, n), (j, 0, m))
+
+
+def test_log_product():
+    from sympy.abc import n, m
+
+    i, j = symbols('i,j', positive=True, integer=True)
+    x, y = symbols('x,y', positive=True)
+    z = symbols('z', real=True)
+    w = symbols('w')
+
+    expr = log(Product(x**i, (i, 1, n)))
+    assert simplify(expr) == expr
+    assert expr.expand() == Sum(i*log(x), (i, 1, n))
+    expr = log(Product(x**i*y**j, (i, 1, n), (j, 1, m)))
+    assert simplify(expr) == expr
+    assert expr.expand() == Sum(i*log(x) + j*log(y), (i, 1, n), (j, 1, m))
+
+    expr = log(Product(-2, (n, 0, 4)))
+    assert simplify(expr) == expr
+    assert expr.expand() == expr
+    assert expr.expand(force=True) == Sum(log(-2), (n, 0, 4))
+
+    expr = log(Product(exp(z*i), (i, 0, n)))
+    assert expr.expand() == Sum(z*i, (i, 0, n))
+
+    expr = log(Product(exp(w*i), (i, 0, n)))
+    assert expr.expand() == expr
+    assert expr.expand(force=True) == Sum(w*i, (i, 0, n))
+
+    expr = log(Product(i**2*abs(j), (i, 1, n), (j, 1, m)))
+    assert expr.expand() == Sum(2*log(i) + log(j), (i, 1, n), (j, 1, m))
+
+
+@XFAIL
+def test_log_product_simplify_to_sum():
+    from sympy.abc import n, m
+    i, j = symbols('i,j', positive=True, integer=True)
+    x, y = symbols('x,y', positive=True)
+    assert simplify(log(Product(x**i, (i, 1, n)))) == Sum(i*log(x), (i, 1, n))
+    assert simplify(log(Product(x**i*y**j, (i, 1, n), (j, 1, m)))) == \
+            Sum(i*log(x) + j*log(y), (i, 1, n), (j, 1, m))
+
+
+def test_issue_8866():
+    assert simplify(log(x, 10, evaluate=False)) == simplify(log(x, 10))
+    assert expand_log(log(x, 10, evaluate=False)) == expand_log(log(x, 10))
+
+    y = Symbol('y', positive=True)
+    l1 = log(exp(y), exp(10))
+    b1 = log(exp(y), exp(5))
+    l2 = log(exp(y), exp(10), evaluate=False)
+    b2 = log(exp(y), exp(5), evaluate=False)
+    assert simplify(log(l1, b1)) == simplify(log(l2, b2))
+    assert expand_log(log(l1, b1)) == expand_log(log(l2, b2))
+
+
+def test_log_expand_factor():
+    assert (log(18)/log(3) - 2).expand(factor=True) == log(2)/log(3)
+    assert (log(12)/log(2)).expand(factor=True) == log(3)/log(2) + 2
+    assert (log(15)/log(3)).expand(factor=True) == 1 + log(5)/log(3)
+    assert (log(2)/(-log(12) + log(24))).expand(factor=True) == 1
+
+    assert expand_log(log(12), factor=True) == log(3) + 2*log(2)
+    assert expand_log(log(21)/log(7), factor=False) == log(3)/log(7) + 1
+    assert expand_log(log(45)/log(5) + log(20), factor=False) == \
+        1 + 2*log(3)/log(5) + log(20)
+    assert expand_log(log(45)/log(5) + log(26), factor=True) == \
+        log(2) + log(13) + (log(5) + 2*log(3))/log(5)
+
+
+def test_issue_9116():
+    n = Symbol('n', positive=True, integer=True)
+    assert log(n).is_nonnegative is True
+
+
+def test_issue_18473():
+    assert exp(x*log(cos(1/x))).as_leading_term(x) == S.NaN
+    assert exp(x*log(tan(1/x))).as_leading_term(x) == S.NaN
+    assert log(cos(1/x)).as_leading_term(x) == S.NaN
+    assert log(tan(1/x)).as_leading_term(x) == S.NaN
+    assert log(cos(1/x) + 2).as_leading_term(x) == AccumBounds(0, log(3))
+    assert exp(x*log(cos(1/x) + 2)).as_leading_term(x) == 1
+    assert log(cos(1/x) - 2).as_leading_term(x) == S.NaN
+    assert exp(x*log(cos(1/x) - 2)).as_leading_term(x) == S.NaN
+    assert log(cos(1/x) + 1).as_leading_term(x) == AccumBounds(-oo, log(2))
+    assert exp(x*log(cos(1/x) + 1)).as_leading_term(x) == AccumBounds(0, 1)
+    assert log(sin(1/x)**2).as_leading_term(x) == AccumBounds(-oo, 0)
+    assert exp(x*log(sin(1/x)**2)).as_leading_term(x) == AccumBounds(0, 1)
+    assert log(tan(1/x)**2).as_leading_term(x) == AccumBounds(-oo, oo)
+    assert exp(2*x*(log(tan(1/x)**2))).as_leading_term(x) == AccumBounds(0, oo)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_hyperbolic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_hyperbolic.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ad9f1d51598b9d605b0472e254c5a710d4ed4f5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_hyperbolic.py
@@ -0,0 +1,1553 @@
+from sympy.calculus.accumulationbounds import AccumBounds
+from sympy.core.function import (expand_mul, expand_trig)
+from sympy.core.numbers import (E, I, Integer, Rational, nan, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (im, re)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (acosh, acoth, acsch, asech, asinh, atanh, cosh, coth, csch, sech, sinh, tanh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, asin, cos, cot, sec, sin, tan)
+from sympy.series.order import O
+
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError, PoleError
+from sympy.testing.pytest import raises
+
+
+def test_sinh():
+    x, y = symbols('x,y')
+
+    k = Symbol('k', integer=True)
+
+    assert sinh(nan) is nan
+    assert sinh(zoo) is nan
+
+    assert sinh(oo) is oo
+    assert sinh(-oo) is -oo
+
+    assert sinh(0) == 0
+
+    assert unchanged(sinh, 1)
+    assert sinh(-1) == -sinh(1)
+
+    assert unchanged(sinh, x)
+    assert sinh(-x) == -sinh(x)
+
+    assert unchanged(sinh, pi)
+    assert sinh(-pi) == -sinh(pi)
+
+    assert unchanged(sinh, 2**1024 * E)
+    assert sinh(-2**1024 * E) == -sinh(2**1024 * E)
+
+    assert sinh(pi*I) == 0
+    assert sinh(-pi*I) == 0
+    assert sinh(2*pi*I) == 0
+    assert sinh(-2*pi*I) == 0
+    assert sinh(-3*10**73*pi*I) == 0
+    assert sinh(7*10**103*pi*I) == 0
+
+    assert sinh(pi*I/2) == I
+    assert sinh(-pi*I/2) == -I
+    assert sinh(pi*I*Rational(5, 2)) == I
+    assert sinh(pi*I*Rational(7, 2)) == -I
+
+    assert sinh(pi*I/3) == S.Half*sqrt(3)*I
+    assert sinh(pi*I*Rational(-2, 3)) == Rational(-1, 2)*sqrt(3)*I
+
+    assert sinh(pi*I/4) == S.Half*sqrt(2)*I
+    assert sinh(-pi*I/4) == Rational(-1, 2)*sqrt(2)*I
+    assert sinh(pi*I*Rational(17, 4)) == S.Half*sqrt(2)*I
+    assert sinh(pi*I*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2)*I
+
+    assert sinh(pi*I/6) == S.Half*I
+    assert sinh(-pi*I/6) == Rational(-1, 2)*I
+    assert sinh(pi*I*Rational(7, 6)) == Rational(-1, 2)*I
+    assert sinh(pi*I*Rational(-5, 6)) == Rational(-1, 2)*I
+
+    assert sinh(pi*I/105) == sin(pi/105)*I
+    assert sinh(-pi*I/105) == -sin(pi/105)*I
+
+    assert unchanged(sinh, 2 + 3*I)
+
+    assert sinh(x*I) == sin(x)*I
+
+    assert sinh(k*pi*I) == 0
+    assert sinh(17*k*pi*I) == 0
+
+    assert sinh(k*pi*I/2) == sin(k*pi/2)*I
+
+    assert sinh(x).as_real_imag(deep=False) == (cos(im(x))*sinh(re(x)),
+                sin(im(x))*cosh(re(x)))
+    x = Symbol('x', extended_real=True)
+    assert sinh(x).as_real_imag(deep=False) == (sinh(x), 0)
+
+    x = Symbol('x', real=True)
+    assert sinh(I*x).is_finite is True
+    assert sinh(x).is_real is True
+    assert sinh(I).is_real is False
+    p = Symbol('p', positive=True)
+    assert sinh(p).is_zero is False
+    assert sinh(0, evaluate=False).is_zero is True
+    assert sinh(2*pi*I, evaluate=False).is_zero is True
+
+
+def test_sinh_series():
+    x = Symbol('x')
+    assert sinh(x).series(x, 0, 10) == \
+        x + x**3/6 + x**5/120 + x**7/5040 + x**9/362880 + O(x**10)
+
+
+def test_sinh_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: sinh(x).fdiff(2))
+
+
+def test_cosh():
+    x, y = symbols('x,y')
+
+    k = Symbol('k', integer=True)
+
+    assert cosh(nan) is nan
+    assert cosh(zoo) is nan
+
+    assert cosh(oo) is oo
+    assert cosh(-oo) is oo
+
+    assert cosh(0) == 1
+
+    assert unchanged(cosh, 1)
+    assert cosh(-1) == cosh(1)
+
+    assert unchanged(cosh, x)
+    assert cosh(-x) == cosh(x)
+
+    assert cosh(pi*I) == cos(pi)
+    assert cosh(-pi*I) == cos(pi)
+
+    assert unchanged(cosh, 2**1024 * E)
+    assert cosh(-2**1024 * E) == cosh(2**1024 * E)
+
+    assert cosh(pi*I/2) == 0
+    assert cosh(-pi*I/2) == 0
+    assert cosh((-3*10**73 + 1)*pi*I/2) == 0
+    assert cosh((7*10**103 + 1)*pi*I/2) == 0
+
+    assert cosh(pi*I) == -1
+    assert cosh(-pi*I) == -1
+    assert cosh(5*pi*I) == -1
+    assert cosh(8*pi*I) == 1
+
+    assert cosh(pi*I/3) == S.Half
+    assert cosh(pi*I*Rational(-2, 3)) == Rational(-1, 2)
+
+    assert cosh(pi*I/4) == S.Half*sqrt(2)
+    assert cosh(-pi*I/4) == S.Half*sqrt(2)
+    assert cosh(pi*I*Rational(11, 4)) == Rational(-1, 2)*sqrt(2)
+    assert cosh(pi*I*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2)
+
+    assert cosh(pi*I/6) == S.Half*sqrt(3)
+    assert cosh(-pi*I/6) == S.Half*sqrt(3)
+    assert cosh(pi*I*Rational(7, 6)) == Rational(-1, 2)*sqrt(3)
+    assert cosh(pi*I*Rational(-5, 6)) == Rational(-1, 2)*sqrt(3)
+
+    assert cosh(pi*I/105) == cos(pi/105)
+    assert cosh(-pi*I/105) == cos(pi/105)
+
+    assert unchanged(cosh, 2 + 3*I)
+
+    assert cosh(x*I) == cos(x)
+
+    assert cosh(k*pi*I) == cos(k*pi)
+    assert cosh(17*k*pi*I) == cos(17*k*pi)
+
+    assert unchanged(cosh, k*pi)
+
+    assert cosh(x).as_real_imag(deep=False) == (cos(im(x))*cosh(re(x)),
+                sin(im(x))*sinh(re(x)))
+    x = Symbol('x', extended_real=True)
+    assert cosh(x).as_real_imag(deep=False) == (cosh(x), 0)
+
+    x = Symbol('x', real=True)
+    assert cosh(I*x).is_finite is True
+    assert cosh(I*x).is_real is True
+    assert cosh(I*2 + 1).is_real is False
+    assert cosh(5*I*S.Pi/2, evaluate=False).is_zero is True
+    assert cosh(x).is_zero is False
+
+
+def test_cosh_series():
+    x = Symbol('x')
+    assert cosh(x).series(x, 0, 10) == \
+        1 + x**2/2 + x**4/24 + x**6/720 + x**8/40320 + O(x**10)
+
+
+def test_cosh_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: cosh(x).fdiff(2))
+
+
+def test_tanh():
+    x, y = symbols('x,y')
+
+    k = Symbol('k', integer=True)
+
+    assert tanh(nan) is nan
+    assert tanh(zoo) is nan
+
+    assert tanh(oo) == 1
+    assert tanh(-oo) == -1
+
+    assert tanh(0) == 0
+
+    assert unchanged(tanh, 1)
+    assert tanh(-1) == -tanh(1)
+
+    assert unchanged(tanh, x)
+    assert tanh(-x) == -tanh(x)
+
+    assert unchanged(tanh, pi)
+    assert tanh(-pi) == -tanh(pi)
+
+    assert unchanged(tanh, 2**1024 * E)
+    assert tanh(-2**1024 * E) == -tanh(2**1024 * E)
+
+    assert tanh(pi*I) == 0
+    assert tanh(-pi*I) == 0
+    assert tanh(2*pi*I) == 0
+    assert tanh(-2*pi*I) == 0
+    assert tanh(-3*10**73*pi*I) == 0
+    assert tanh(7*10**103*pi*I) == 0
+
+    assert tanh(pi*I/2) is zoo
+    assert tanh(-pi*I/2) is zoo
+    assert tanh(pi*I*Rational(5, 2)) is zoo
+    assert tanh(pi*I*Rational(7, 2)) is zoo
+
+    assert tanh(pi*I/3) == sqrt(3)*I
+    assert tanh(pi*I*Rational(-2, 3)) == sqrt(3)*I
+
+    assert tanh(pi*I/4) == I
+    assert tanh(-pi*I/4) == -I
+    assert tanh(pi*I*Rational(17, 4)) == I
+    assert tanh(pi*I*Rational(-3, 4)) == I
+
+    assert tanh(pi*I/6) == I/sqrt(3)
+    assert tanh(-pi*I/6) == -I/sqrt(3)
+    assert tanh(pi*I*Rational(7, 6)) == I/sqrt(3)
+    assert tanh(pi*I*Rational(-5, 6)) == I/sqrt(3)
+
+    assert tanh(pi*I/105) == tan(pi/105)*I
+    assert tanh(-pi*I/105) == -tan(pi/105)*I
+
+    assert unchanged(tanh, 2 + 3*I)
+
+    assert tanh(x*I) == tan(x)*I
+
+    assert tanh(k*pi*I) == 0
+    assert tanh(17*k*pi*I) == 0
+
+    assert tanh(k*pi*I/2) == tan(k*pi/2)*I
+
+    assert tanh(x).as_real_imag(deep=False) == (sinh(re(x))*cosh(re(x))/(cos(im(x))**2
+                                + sinh(re(x))**2),
+                                sin(im(x))*cos(im(x))/(cos(im(x))**2 + sinh(re(x))**2))
+    x = Symbol('x', extended_real=True)
+    assert tanh(x).as_real_imag(deep=False) == (tanh(x), 0)
+    assert tanh(I*pi/3 + 1).is_real is False
+    assert tanh(x).is_real is True
+    assert tanh(I*pi*x/2).is_real is None
+
+
+def test_tanh_series():
+    x = Symbol('x')
+    assert tanh(x).series(x, 0, 10) == \
+        x - x**3/3 + 2*x**5/15 - 17*x**7/315 + 62*x**9/2835 + O(x**10)
+
+
+def test_tanh_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: tanh(x).fdiff(2))
+
+
+def test_coth():
+    x, y = symbols('x,y')
+
+    k = Symbol('k', integer=True)
+
+    assert coth(nan) is nan
+    assert coth(zoo) is nan
+
+    assert coth(oo) == 1
+    assert coth(-oo) == -1
+
+    assert coth(0) is zoo
+    assert unchanged(coth, 1)
+    assert coth(-1) == -coth(1)
+
+    assert unchanged(coth, x)
+    assert coth(-x) == -coth(x)
+
+    assert coth(pi*I) == -I*cot(pi)
+    assert coth(-pi*I) == cot(pi)*I
+
+    assert unchanged(coth, 2**1024 * E)
+    assert coth(-2**1024 * E) == -coth(2**1024 * E)
+
+    assert coth(pi*I) == -I*cot(pi)
+    assert coth(-pi*I) == I*cot(pi)
+    assert coth(2*pi*I) == -I*cot(2*pi)
+    assert coth(-2*pi*I) == I*cot(2*pi)
+    assert coth(-3*10**73*pi*I) == I*cot(3*10**73*pi)
+    assert coth(7*10**103*pi*I) == -I*cot(7*10**103*pi)
+
+    assert coth(pi*I/2) == 0
+    assert coth(-pi*I/2) == 0
+    assert coth(pi*I*Rational(5, 2)) == 0
+    assert coth(pi*I*Rational(7, 2)) == 0
+
+    assert coth(pi*I/3) == -I/sqrt(3)
+    assert coth(pi*I*Rational(-2, 3)) == -I/sqrt(3)
+
+    assert coth(pi*I/4) == -I
+    assert coth(-pi*I/4) == I
+    assert coth(pi*I*Rational(17, 4)) == -I
+    assert coth(pi*I*Rational(-3, 4)) == -I
+
+    assert coth(pi*I/6) == -sqrt(3)*I
+    assert coth(-pi*I/6) == sqrt(3)*I
+    assert coth(pi*I*Rational(7, 6)) == -sqrt(3)*I
+    assert coth(pi*I*Rational(-5, 6)) == -sqrt(3)*I
+
+    assert coth(pi*I/105) == -cot(pi/105)*I
+    assert coth(-pi*I/105) == cot(pi/105)*I
+
+    assert unchanged(coth, 2 + 3*I)
+
+    assert coth(x*I) == -cot(x)*I
+
+    assert coth(k*pi*I) == -cot(k*pi)*I
+    assert coth(17*k*pi*I) == -cot(17*k*pi)*I
+
+    assert coth(k*pi*I) == -cot(k*pi)*I
+
+    assert coth(log(tan(2))) == coth(log(-tan(2)))
+    assert coth(1 + I*pi/2) == tanh(1)
+
+    assert coth(x).as_real_imag(deep=False) == (sinh(re(x))*cosh(re(x))/(sin(im(x))**2
+                                + sinh(re(x))**2),
+                                -sin(im(x))*cos(im(x))/(sin(im(x))**2 + sinh(re(x))**2))
+    x = Symbol('x', extended_real=True)
+    assert coth(x).as_real_imag(deep=False) == (coth(x), 0)
+
+    assert expand_trig(coth(2*x)) == (coth(x)**2 + 1)/(2*coth(x))
+    assert expand_trig(coth(3*x)) == (coth(x)**3 + 3*coth(x))/(1 + 3*coth(x)**2)
+
+    assert expand_trig(coth(x + y)) == (1 + coth(x)*coth(y))/(coth(x) + coth(y))
+
+
+def test_coth_series():
+    x = Symbol('x')
+    assert coth(x).series(x, 0, 8) == \
+        1/x + x/3 - x**3/45 + 2*x**5/945 - x**7/4725 + O(x**8)
+
+
+def test_coth_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: coth(x).fdiff(2))
+
+
+def test_csch():
+    x, y = symbols('x,y')
+
+    k = Symbol('k', integer=True)
+    n = Symbol('n', positive=True)
+
+    assert csch(nan) is nan
+    assert csch(zoo) is nan
+
+    assert csch(oo) == 0
+    assert csch(-oo) == 0
+
+    assert csch(0) is zoo
+
+    assert csch(-1) == -csch(1)
+
+    assert csch(-x) == -csch(x)
+    assert csch(-pi) == -csch(pi)
+    assert csch(-2**1024 * E) == -csch(2**1024 * E)
+
+    assert csch(pi*I) is zoo
+    assert csch(-pi*I) is zoo
+    assert csch(2*pi*I) is zoo
+    assert csch(-2*pi*I) is zoo
+    assert csch(-3*10**73*pi*I) is zoo
+    assert csch(7*10**103*pi*I) is zoo
+
+    assert csch(pi*I/2) == -I
+    assert csch(-pi*I/2) == I
+    assert csch(pi*I*Rational(5, 2)) == -I
+    assert csch(pi*I*Rational(7, 2)) == I
+
+    assert csch(pi*I/3) == -2/sqrt(3)*I
+    assert csch(pi*I*Rational(-2, 3)) == 2/sqrt(3)*I
+
+    assert csch(pi*I/4) == -sqrt(2)*I
+    assert csch(-pi*I/4) == sqrt(2)*I
+    assert csch(pi*I*Rational(7, 4)) == sqrt(2)*I
+    assert csch(pi*I*Rational(-3, 4)) == sqrt(2)*I
+
+    assert csch(pi*I/6) == -2*I
+    assert csch(-pi*I/6) == 2*I
+    assert csch(pi*I*Rational(7, 6)) == 2*I
+    assert csch(pi*I*Rational(-7, 6)) == -2*I
+    assert csch(pi*I*Rational(-5, 6)) == 2*I
+
+    assert csch(pi*I/105) == -1/sin(pi/105)*I
+    assert csch(-pi*I/105) == 1/sin(pi/105)*I
+
+    assert csch(x*I) == -1/sin(x)*I
+
+    assert csch(k*pi*I) is zoo
+    assert csch(17*k*pi*I) is zoo
+
+    assert csch(k*pi*I/2) == -1/sin(k*pi/2)*I
+
+    assert csch(n).is_real is True
+
+    assert expand_trig(csch(x + y)) == 1/(sinh(x)*cosh(y) + cosh(x)*sinh(y))
+
+
+def test_csch_series():
+    x = Symbol('x')
+    assert csch(x).series(x, 0, 10) == \
+       1/ x - x/6 + 7*x**3/360 - 31*x**5/15120 + 127*x**7/604800 \
+          - 73*x**9/3421440 + O(x**10)
+
+
+def test_csch_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: csch(x).fdiff(2))
+
+
+def test_sech():
+    x, y = symbols('x, y')
+
+    k = Symbol('k', integer=True)
+    n = Symbol('n', positive=True)
+
+    assert sech(nan) is nan
+    assert sech(zoo) is nan
+
+    assert sech(oo) == 0
+    assert sech(-oo) == 0
+
+    assert sech(0) == 1
+
+    assert sech(-1) == sech(1)
+    assert sech(-x) == sech(x)
+
+    assert sech(pi*I) == sec(pi)
+
+    assert sech(-pi*I) == sec(pi)
+    assert sech(-2**1024 * E) == sech(2**1024 * E)
+
+    assert sech(pi*I/2) is zoo
+    assert sech(-pi*I/2) is zoo
+    assert sech((-3*10**73 + 1)*pi*I/2) is zoo
+    assert sech((7*10**103 + 1)*pi*I/2) is zoo
+
+    assert sech(pi*I) == -1
+    assert sech(-pi*I) == -1
+    assert sech(5*pi*I) == -1
+    assert sech(8*pi*I) == 1
+
+    assert sech(pi*I/3) == 2
+    assert sech(pi*I*Rational(-2, 3)) == -2
+
+    assert sech(pi*I/4) == sqrt(2)
+    assert sech(-pi*I/4) == sqrt(2)
+    assert sech(pi*I*Rational(5, 4)) == -sqrt(2)
+    assert sech(pi*I*Rational(-5, 4)) == -sqrt(2)
+
+    assert sech(pi*I/6) == 2/sqrt(3)
+    assert sech(-pi*I/6) == 2/sqrt(3)
+    assert sech(pi*I*Rational(7, 6)) == -2/sqrt(3)
+    assert sech(pi*I*Rational(-5, 6)) == -2/sqrt(3)
+
+    assert sech(pi*I/105) == 1/cos(pi/105)
+    assert sech(-pi*I/105) == 1/cos(pi/105)
+
+    assert sech(x*I) == 1/cos(x)
+
+    assert sech(k*pi*I) == 1/cos(k*pi)
+    assert sech(17*k*pi*I) == 1/cos(17*k*pi)
+
+    assert sech(n).is_real is True
+
+    assert expand_trig(sech(x + y)) == 1/(cosh(x)*cosh(y) + sinh(x)*sinh(y))
+
+
+def test_sech_series():
+    x = Symbol('x')
+    assert sech(x).series(x, 0, 10) == \
+        1 - x**2/2 + 5*x**4/24 - 61*x**6/720 + 277*x**8/8064 + O(x**10)
+
+
+def test_sech_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: sech(x).fdiff(2))
+
+
+def test_asinh():
+    x, y = symbols('x,y')
+    assert unchanged(asinh, x)
+    assert asinh(-x) == -asinh(x)
+
+    # at specific points
+    assert asinh(nan) is nan
+    assert asinh( 0) == 0
+    assert asinh(+1) == log(sqrt(2) + 1)
+
+    assert asinh(-1) == log(sqrt(2) - 1)
+    assert asinh(I) == pi*I/2
+    assert asinh(-I) == -pi*I/2
+    assert asinh(I/2) == pi*I/6
+    assert asinh(-I/2) == -pi*I/6
+
+    # at infinites
+    assert asinh(oo) is oo
+    assert asinh(-oo) is -oo
+
+    assert asinh(I*oo) is oo
+    assert asinh(-I *oo) is -oo
+
+    assert asinh(zoo) is zoo
+
+    # properties
+    assert asinh(I *(sqrt(3) - 1)/(2**Rational(3, 2))) == pi*I/12
+    assert asinh(-I *(sqrt(3) - 1)/(2**Rational(3, 2))) == -pi*I/12
+
+    assert asinh(I*(sqrt(5) - 1)/4) == pi*I/10
+    assert asinh(-I*(sqrt(5) - 1)/4) == -pi*I/10
+
+    assert asinh(I*(sqrt(5) + 1)/4) == pi*I*Rational(3, 10)
+    assert asinh(-I*(sqrt(5) + 1)/4) == pi*I*Rational(-3, 10)
+
+    # reality
+    assert asinh(S(2)).is_real is True
+    assert asinh(S(2)).is_finite is True
+    assert asinh(S(-2)).is_real is True
+    assert asinh(S(oo)).is_extended_real is True
+    assert asinh(-S(oo)).is_real is False
+    assert (asinh(2) - oo) == -oo
+    assert asinh(symbols('y', real=True)).is_real is True
+
+    # Symmetry
+    assert asinh(Rational(-1, 2)) == -asinh(S.Half)
+
+    # inverse composition
+    assert unchanged(asinh, sinh(Symbol('v1')))
+
+    assert asinh(sinh(0, evaluate=False)) == 0
+    assert asinh(sinh(-3, evaluate=False)) == -3
+    assert asinh(sinh(2, evaluate=False)) == 2
+    assert asinh(sinh(I, evaluate=False)) == I
+    assert asinh(sinh(-I, evaluate=False)) == -I
+    assert asinh(sinh(5*I, evaluate=False)) == -2*I*pi + 5*I
+    assert asinh(sinh(15 + 11*I)) == 15 - 4*I*pi + 11*I
+    assert asinh(sinh(-73 + 97*I)) == 73 - 97*I + 31*I*pi
+    assert asinh(sinh(-7 - 23*I)) == 7 - 7*I*pi + 23*I
+    assert asinh(sinh(13 - 3*I)) == -13 - I*pi + 3*I
+    p = Symbol('p', positive=True)
+    assert asinh(p).is_zero is False
+    assert asinh(sinh(0, evaluate=False), evaluate=False).is_zero is True
+
+
+def test_asinh_rewrite():
+    x = Symbol('x')
+    assert asinh(x).rewrite(log) == log(x + sqrt(x**2 + 1))
+    assert asinh(x).rewrite(atanh) == atanh(x/sqrt(1 + x**2))
+    assert asinh(x).rewrite(asin) == -I*asin(I*x, evaluate=False)
+    assert asinh(x*(1 + I)).rewrite(asin) == -I*asin(I*x*(1+I))
+    assert asinh(x).rewrite(acos) == I*acos(I*x, evaluate=False) - I*pi/2
+
+
+def test_asinh_leading_term():
+    x = Symbol('x')
+    assert asinh(x).as_leading_term(x, cdir=1) == x
+    # Tests concerning branch points
+    assert asinh(x + I).as_leading_term(x, cdir=1) == I*pi/2
+    assert asinh(x - I).as_leading_term(x, cdir=1) == -I*pi/2
+    assert asinh(1/x).as_leading_term(x, cdir=1) == -log(x) + log(2)
+    assert asinh(1/x).as_leading_term(x, cdir=-1) == log(x) - log(2) - I*pi
+    # Tests concerning points lying on branch cuts
+    assert asinh(x + 2*I).as_leading_term(x, cdir=1) == I*asin(2)
+    assert asinh(x + 2*I).as_leading_term(x, cdir=-1) == -I*asin(2) + I*pi
+    assert asinh(x - 2*I).as_leading_term(x, cdir=1) == -I*pi + I*asin(2)
+    assert asinh(x - 2*I).as_leading_term(x, cdir=-1) == -I*asin(2)
+    # Tests concerning re(ndir) == 0
+    assert asinh(2*I + I*x - x**2).as_leading_term(x, cdir=1) == log(2 - sqrt(3)) + I*pi/2
+    assert asinh(2*I + I*x - x**2).as_leading_term(x, cdir=-1) == log(2 - sqrt(3)) + I*pi/2
+
+
+def test_asinh_series():
+    x = Symbol('x')
+    assert asinh(x).series(x, 0, 8) == \
+        x - x**3/6 + 3*x**5/40 - 5*x**7/112 + O(x**8)
+    t5 = asinh(x).taylor_term(5, x)
+    assert t5 == 3*x**5/40
+    assert asinh(x).taylor_term(7, x, t5, 0) == -5*x**7/112
+
+
+def test_asinh_nseries():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert asinh(x + I)._eval_nseries(x, 4, None) == I*pi/2 - \
+    sqrt(2)*sqrt(I)*I*sqrt(x) + sqrt(2)*sqrt(I)*x**(S(3)/2)/12 + 3*sqrt(2)*sqrt(I)*I*x**(S(5)/2)/160 - \
+    5*sqrt(2)*sqrt(I)*x**(S(7)/2)/896 + O(x**4)
+    assert asinh(x - I)._eval_nseries(x, 4, None) == -I*pi/2 + \
+    sqrt(2)*I*sqrt(x)*sqrt(-I) + sqrt(2)*x**(S(3)/2)*sqrt(-I)/12 - \
+    3*sqrt(2)*I*x**(S(5)/2)*sqrt(-I)/160 - 5*sqrt(2)*x**(S(7)/2)*sqrt(-I)/896 + O(x**4)
+    # Tests concerning points lying on branch cuts
+    assert asinh(x + 2*I)._eval_nseries(x, 4, None, cdir=1) == I*asin(2) - \
+    sqrt(3)*I*x/3 + sqrt(3)*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    assert asinh(x + 2*I)._eval_nseries(x, 4, None, cdir=-1) == I*pi - I*asin(2) + \
+    sqrt(3)*I*x/3 - sqrt(3)*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    assert asinh(x - 2*I)._eval_nseries(x, 4, None, cdir=1) == I*asin(2) - I*pi + \
+    sqrt(3)*I*x/3 + sqrt(3)*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    assert asinh(x - 2*I)._eval_nseries(x, 4, None, cdir=-1) == -I*asin(2) - \
+    sqrt(3)*I*x/3 - sqrt(3)*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    # Tests concerning re(ndir) == 0
+    assert asinh(2*I + I*x - x**2)._eval_nseries(x, 4, None) == I*pi/2 + log(2 - sqrt(3)) + \
+    x*(-3 + 2*sqrt(3))/(-6 + 3*sqrt(3)) + x**2*(12 - 36*I + sqrt(3)*(-7 + 21*I))/(-63 + \
+    36*sqrt(3)) + x**3*(-168 + sqrt(3)*(97 - 388*I) + 672*I)/(-1746 + 1008*sqrt(3)) + O(x**4)
+
+
+def test_asinh_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: asinh(x).fdiff(2))
+
+
+def test_acosh():
+    x = Symbol('x')
+
+    assert unchanged(acosh, -x)
+
+    #at specific points
+    assert acosh(1) == 0
+    assert acosh(-1) == pi*I
+    assert acosh(0) == I*pi/2
+    assert acosh(S.Half) == I*pi/3
+    assert acosh(Rational(-1, 2)) == pi*I*Rational(2, 3)
+    assert acosh(nan) is nan
+
+    # at infinites
+    assert acosh(oo) is oo
+    assert acosh(-oo) is oo
+
+    assert acosh(I*oo) == oo + I*pi/2
+    assert acosh(-I*oo) == oo - I*pi/2
+
+    assert acosh(zoo) is zoo
+
+    assert acosh(I) == log(I*(1 + sqrt(2)))
+    assert acosh(-I) == log(-I*(1 + sqrt(2)))
+    assert acosh((sqrt(3) - 1)/(2*sqrt(2))) == pi*I*Rational(5, 12)
+    assert acosh(-(sqrt(3) - 1)/(2*sqrt(2))) == pi*I*Rational(7, 12)
+    assert acosh(sqrt(2)/2) == I*pi/4
+    assert acosh(-sqrt(2)/2) == I*pi*Rational(3, 4)
+    assert acosh(sqrt(3)/2) == I*pi/6
+    assert acosh(-sqrt(3)/2) == I*pi*Rational(5, 6)
+    assert acosh(sqrt(2 + sqrt(2))/2) == I*pi/8
+    assert acosh(-sqrt(2 + sqrt(2))/2) == I*pi*Rational(7, 8)
+    assert acosh(sqrt(2 - sqrt(2))/2) == I*pi*Rational(3, 8)
+    assert acosh(-sqrt(2 - sqrt(2))/2) == I*pi*Rational(5, 8)
+    assert acosh((1 + sqrt(3))/(2*sqrt(2))) == I*pi/12
+    assert acosh(-(1 + sqrt(3))/(2*sqrt(2))) == I*pi*Rational(11, 12)
+    assert acosh((sqrt(5) + 1)/4) == I*pi/5
+    assert acosh(-(sqrt(5) + 1)/4) == I*pi*Rational(4, 5)
+
+    assert str(acosh(5*I).n(6)) == '2.31244 + 1.5708*I'
+    assert str(acosh(-5*I).n(6)) == '2.31244 - 1.5708*I'
+
+    # inverse composition
+    assert unchanged(acosh, Symbol('v1'))
+
+    assert acosh(cosh(-3, evaluate=False)) == 3
+    assert acosh(cosh(3, evaluate=False)) == 3
+    assert acosh(cosh(0, evaluate=False)) == 0
+    assert acosh(cosh(I, evaluate=False)) == I
+    assert acosh(cosh(-I, evaluate=False)) == I
+    assert acosh(cosh(7*I, evaluate=False)) == -2*I*pi + 7*I
+    assert acosh(cosh(1 + I)) == 1 + I
+    assert acosh(cosh(3 - 3*I)) == 3 - 3*I
+    assert acosh(cosh(-3 + 2*I)) == 3 - 2*I
+    assert acosh(cosh(-5 - 17*I)) == 5 - 6*I*pi + 17*I
+    assert acosh(cosh(-21 + 11*I)) == 21 - 11*I + 4*I*pi
+    assert acosh(cosh(cosh(1) + I)) == cosh(1) + I
+    assert acosh(1, evaluate=False).is_zero is True
+
+    # Reality
+    assert acosh(S(2)).is_real is True
+    assert acosh(S(2)).is_extended_real is True
+    assert acosh(oo).is_extended_real is True
+    assert acosh(S(2)).is_finite is True
+    assert acosh(S(1) / 5).is_real is False
+    assert (acosh(2) - oo) == -oo
+    assert acosh(symbols('y', real=True)).is_real is None
+
+
+def test_acosh_rewrite():
+    x = Symbol('x')
+    assert acosh(x).rewrite(log) == log(x + sqrt(x - 1)*sqrt(x + 1))
+    assert acosh(x).rewrite(asin) == sqrt(x - 1)*(-asin(x) + pi/2)/sqrt(1 - x)
+    assert acosh(x).rewrite(asinh) == sqrt(x - 1)*(I*asinh(I*x, evaluate=False) + pi/2)/sqrt(1 - x)
+    assert acosh(x).rewrite(atanh) == \
+        (sqrt(x - 1)*sqrt(x + 1)*atanh(sqrt(x**2 - 1)/x)/sqrt(x**2 - 1) +
+         pi*sqrt(x - 1)*(-x*sqrt(x**(-2)) + 1)/(2*sqrt(1 - x)))
+    x = Symbol('x', positive=True)
+    assert acosh(x).rewrite(atanh) == \
+        sqrt(x - 1)*sqrt(x + 1)*atanh(sqrt(x**2 - 1)/x)/sqrt(x**2 - 1)
+
+
+def test_acosh_leading_term():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert acosh(x).as_leading_term(x) == I*pi/2
+    assert acosh(x + 1).as_leading_term(x) == sqrt(2)*sqrt(x)
+    assert acosh(x - 1).as_leading_term(x) == I*pi
+    assert acosh(1/x).as_leading_term(x, cdir=1) == -log(x) + log(2)
+    assert acosh(1/x).as_leading_term(x, cdir=-1) == -log(x) + log(2) + 2*I*pi
+    # Tests concerning points lying on branch cuts
+    assert acosh(I*x - 2).as_leading_term(x, cdir=1) == acosh(-2)
+    assert acosh(-I*x - 2).as_leading_term(x, cdir=1) == -2*I*pi + acosh(-2)
+    assert acosh(x**2 - I*x + S(1)/3).as_leading_term(x, cdir=1) == -acosh(S(1)/3)
+    assert acosh(x**2 - I*x + S(1)/3).as_leading_term(x, cdir=-1) == acosh(S(1)/3)
+    assert acosh(1/(I*x - 3)).as_leading_term(x, cdir=1) == -acosh(-S(1)/3)
+    assert acosh(1/(I*x - 3)).as_leading_term(x, cdir=-1) == acosh(-S(1)/3)
+    # Tests concerning im(ndir) == 0
+    assert acosh(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == log(sqrt(3) + 2) - I*pi
+    assert acosh(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == log(sqrt(3) + 2) - I*pi
+
+
+def test_acosh_series():
+    x = Symbol('x')
+    assert acosh(x).series(x, 0, 8) == \
+        -I*x + pi*I/2 - I*x**3/6 - 3*I*x**5/40 - 5*I*x**7/112 + O(x**8)
+    t5 = acosh(x).taylor_term(5, x)
+    assert t5 == - 3*I*x**5/40
+    assert acosh(x).taylor_term(7, x, t5, 0) == - 5*I*x**7/112
+
+
+def test_acosh_nseries():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert acosh(x + 1)._eval_nseries(x, 4, None) == sqrt(2)*sqrt(x) - \
+    sqrt(2)*x**(S(3)/2)/12 + 3*sqrt(2)*x**(S(5)/2)/160 - 5*sqrt(2)*x**(S(7)/2)/896 + O(x**4)
+    # Tests concerning points lying on branch cuts
+    assert acosh(x - 1)._eval_nseries(x, 4, None) == I*pi - \
+    sqrt(2)*I*sqrt(x) - sqrt(2)*I*x**(S(3)/2)/12 - 3*sqrt(2)*I*x**(S(5)/2)/160 - \
+    5*sqrt(2)*I*x**(S(7)/2)/896 + O(x**4)
+    assert acosh(I*x - 2)._eval_nseries(x, 4, None, cdir=1) == acosh(-2) - \
+    sqrt(3)*I*x/3 + sqrt(3)*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    assert acosh(-I*x - 2)._eval_nseries(x, 4, None, cdir=1) == acosh(-2) - \
+    2*I*pi + sqrt(3)*I*x/3 + sqrt(3)*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    assert acosh(1/(I*x - 3))._eval_nseries(x, 4, None, cdir=1) == -acosh(-S(1)/3) + \
+    sqrt(2)*x/12 + 17*sqrt(2)*I*x**2/576 - 443*sqrt(2)*x**3/41472 + O(x**4)
+    assert acosh(1/(I*x - 3))._eval_nseries(x, 4, None, cdir=-1) == acosh(-S(1)/3) - \
+    sqrt(2)*x/12 - 17*sqrt(2)*I*x**2/576 + 443*sqrt(2)*x**3/41472 + O(x**4)
+    # Tests concerning im(ndir) == 0
+    assert acosh(-I*x**2 + x - 2)._eval_nseries(x, 4, None) == -I*pi + log(sqrt(3) + 2) + \
+    x*(-2*sqrt(3) - 3)/(3*sqrt(3) + 6) + x**2*(-12 + 36*I + sqrt(3)*(-7 + 21*I))/(36*sqrt(3) + \
+    63) + x**3*(-168 + 672*I + sqrt(3)*(-97 + 388*I))/(1008*sqrt(3) + 1746) + O(x**4)
+
+
+def test_acosh_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: acosh(x).fdiff(2))
+
+
+def test_asech():
+    x = Symbol('x')
+
+    assert unchanged(asech, -x)
+
+    # values at fixed points
+    assert asech(1) == 0
+    assert asech(-1) == pi*I
+    assert asech(0) is oo
+    assert asech(2) == I*pi/3
+    assert asech(-2) == 2*I*pi / 3
+    assert asech(nan) is nan
+
+    # at infinites
+    assert asech(oo) == I*pi/2
+    assert asech(-oo) == I*pi/2
+    assert asech(zoo) == I*AccumBounds(-pi/2, pi/2)
+
+    assert asech(I) == log(1 + sqrt(2)) - I*pi/2
+    assert asech(-I) == log(1 + sqrt(2)) + I*pi/2
+    assert asech(sqrt(2) - sqrt(6)) == 11*I*pi / 12
+    assert asech(sqrt(2 - 2/sqrt(5))) == I*pi / 10
+    assert asech(-sqrt(2 - 2/sqrt(5))) == 9*I*pi / 10
+    assert asech(2 / sqrt(2 + sqrt(2))) == I*pi / 8
+    assert asech(-2 / sqrt(2 + sqrt(2))) == 7*I*pi / 8
+    assert asech(sqrt(5) - 1) == I*pi / 5
+    assert asech(1 - sqrt(5)) == 4*I*pi / 5
+    assert asech(-sqrt(2*(2 + sqrt(2)))) == 5*I*pi / 8
+
+    # properties
+    # asech(x) == acosh(1/x)
+    assert asech(sqrt(2)) == acosh(1/sqrt(2))
+    assert asech(2/sqrt(3)) == acosh(sqrt(3)/2)
+    assert asech(2/sqrt(2 + sqrt(2))) == acosh(sqrt(2 + sqrt(2))/2)
+    assert asech(2) == acosh(S.Half)
+
+    # reality
+    assert asech(S(2)).is_real is False
+    assert asech(-S(1) / 3).is_real is False
+    assert asech(S(2) / 3).is_finite is True
+    assert asech(S(0)).is_real is False
+    assert asech(S(0)).is_extended_real is True
+    assert asech(symbols('y', real=True)).is_real is None
+
+    # asech(x) == I*acos(1/x)
+    # (Note: the exact formula is asech(x) == +/- I*acos(1/x))
+    assert asech(-sqrt(2)) == I*acos(-1/sqrt(2))
+    assert asech(-2/sqrt(3)) == I*acos(-sqrt(3)/2)
+    assert asech(-S(2)) == I*acos(Rational(-1, 2))
+    assert asech(-2/sqrt(2)) == I*acos(-sqrt(2)/2)
+
+    # sech(asech(x)) / x == 1
+    assert expand_mul(sech(asech(sqrt(6) - sqrt(2))) / (sqrt(6) - sqrt(2))) == 1
+    assert expand_mul(sech(asech(sqrt(6) + sqrt(2))) / (sqrt(6) + sqrt(2))) == 1
+    assert (sech(asech(sqrt(2 + 2/sqrt(5)))) / (sqrt(2 + 2/sqrt(5)))).simplify() == 1
+    assert (sech(asech(-sqrt(2 + 2/sqrt(5)))) / (-sqrt(2 + 2/sqrt(5)))).simplify() == 1
+    assert (sech(asech(sqrt(2*(2 + sqrt(2))))) / (sqrt(2*(2 + sqrt(2))))).simplify() == 1
+    assert expand_mul(sech(asech(1 + sqrt(5))) / (1 + sqrt(5))) == 1
+    assert expand_mul(sech(asech(-1 - sqrt(5))) / (-1 - sqrt(5))) == 1
+    assert expand_mul(sech(asech(-sqrt(6) - sqrt(2))) / (-sqrt(6) - sqrt(2))) == 1
+
+    # numerical evaluation
+    assert str(asech(5*I).n(6)) == '0.19869 - 1.5708*I'
+    assert str(asech(-5*I).n(6)) == '0.19869 + 1.5708*I'
+
+
+def test_asech_leading_term():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert asech(x).as_leading_term(x, cdir=1) == -log(x) + log(2)
+    assert asech(x).as_leading_term(x, cdir=-1) == -log(x) + log(2) + 2*I*pi
+    assert asech(x + 1).as_leading_term(x, cdir=1) == sqrt(2)*I*sqrt(x)
+    assert asech(1/x).as_leading_term(x, cdir=1) == I*pi/2
+    # Tests concerning points lying on branch cuts
+    assert asech(x - 1).as_leading_term(x, cdir=1) == I*pi
+    assert asech(I*x + 3).as_leading_term(x, cdir=1) == -asech(3)
+    assert asech(-I*x + 3).as_leading_term(x, cdir=1) == asech(3)
+    assert asech(I*x - 3).as_leading_term(x, cdir=1) == -asech(-3)
+    assert asech(-I*x - 3).as_leading_term(x, cdir=1) == asech(-3)
+    assert asech(I*x - S(1)/3).as_leading_term(x, cdir=1) == -2*I*pi + asech(-S(1)/3)
+    assert asech(I*x - S(1)/3).as_leading_term(x, cdir=-1) == asech(-S(1)/3)
+    # Tests concerning im(ndir) == 0
+    assert asech(-I*x**2 + x - 3).as_leading_term(x, cdir=1) == log(-S(1)/3 + 2*sqrt(2)*I/3)
+    assert asech(-I*x**2 + x - 3).as_leading_term(x, cdir=-1) == log(-S(1)/3 + 2*sqrt(2)*I/3)
+
+
+def test_asech_series():
+    x = Symbol('x')
+    assert asech(x).series(x, 0, 9, cdir=1) == log(2) - log(x) - x**2/4 - 3*x**4/32 \
+    - 5*x**6/96 - 35*x**8/1024 + O(x**9)
+    assert asech(x).series(x, 0, 9, cdir=-1) == I*pi + log(2) - log(-x) - x**2/4 - \
+    3*x**4/32 - 5*x**6/96 - 35*x**8/1024 + O(x**9)
+    t6 = asech(x).taylor_term(6, x)
+    assert t6 == -5*x**6/96
+    assert asech(x).taylor_term(8, x, t6, 0) == -35*x**8/1024
+
+
+def test_asech_nseries():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert asech(x + 1)._eval_nseries(x, 4, None) == sqrt(2)*sqrt(-x) + 5*sqrt(2)*(-x)**(S(3)/2)/12 + \
+    43*sqrt(2)*(-x)**(S(5)/2)/160 + 177*sqrt(2)*(-x)**(S(7)/2)/896 + O(x**4)
+    # Tests concerning points lying on branch cuts
+    assert asech(x - 1)._eval_nseries(x, 4, None) == I*pi + sqrt(2)*sqrt(x) + \
+    5*sqrt(2)*x**(S(3)/2)/12 + 43*sqrt(2)*x**(S(5)/2)/160 + 177*sqrt(2)*x**(S(7)/2)/896 + O(x**4)
+    assert asech(I*x + 3)._eval_nseries(x, 4, None) == -asech(3) + sqrt(2)*x/12 - \
+    17*sqrt(2)*I*x**2/576 - 443*sqrt(2)*x**3/41472 + O(x**4)
+    assert asech(-I*x + 3)._eval_nseries(x, 4, None) == asech(3) + sqrt(2)*x/12 + \
+    17*sqrt(2)*I*x**2/576 - 443*sqrt(2)*x**3/41472 + O(x**4)
+    assert asech(I*x - 3)._eval_nseries(x, 4, None) == -asech(-3) - sqrt(2)*x/12 - \
+    17*sqrt(2)*I*x**2/576 + 443*sqrt(2)*x**3/41472 + O(x**4)
+    assert asech(-I*x - 3)._eval_nseries(x, 4, None) == asech(-3) - sqrt(2)*x/12 + \
+    17*sqrt(2)*I*x**2/576 + 443*sqrt(2)*x**3/41472 + O(x**4)
+    # Tests concerning im(ndir) == 0
+    assert asech(-I*x**2 + x - 2)._eval_nseries(x, 3, None) == 2*I*pi/3 + \
+    x*(-sqrt(3) + 3*I)/(6*sqrt(3) + 6*I) + x**2*(36 + sqrt(3)*(7 - 12*I) + 21*I)/(72*sqrt(3) - \
+    72*I) + O(x**3)
+
+
+def test_asech_rewrite():
+    x = Symbol('x')
+    assert asech(x).rewrite(log) == log(1/x + sqrt(1/x - 1) * sqrt(1/x + 1))
+    assert asech(x).rewrite(acosh) == acosh(1/x)
+    assert asech(x).rewrite(asinh) == sqrt(-1 + 1/x)*(I*asinh(I/x, evaluate=False) + pi/2)/sqrt(1 - 1/x)
+    assert asech(x).rewrite(atanh) == \
+        sqrt(x + 1)*sqrt(1/(x + 1))*atanh(sqrt(1 - x**2)) + I*pi*(-sqrt(x)*sqrt(1/x) + 1 - I*sqrt(x**2)/(2*sqrt(-x**2)) - I*sqrt(-x)/(2*sqrt(x)))
+
+
+def test_asech_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: asech(x).fdiff(2))
+
+
+def test_acsch():
+    x = Symbol('x')
+
+    assert unchanged(acsch, x)
+    assert acsch(-x) == -acsch(x)
+
+    # values at fixed points
+    assert acsch(1) == log(1 + sqrt(2))
+    assert acsch(-1) == - log(1 + sqrt(2))
+    assert acsch(0) is zoo
+    assert acsch(2) == log((1+sqrt(5))/2)
+    assert acsch(-2) == - log((1+sqrt(5))/2)
+
+    assert acsch(I) == - I*pi/2
+    assert acsch(-I) == I*pi/2
+    assert acsch(-I*(sqrt(6) + sqrt(2))) == I*pi / 12
+    assert acsch(I*(sqrt(2) + sqrt(6))) == -I*pi / 12
+    assert acsch(-I*(1 + sqrt(5))) == I*pi / 10
+    assert acsch(I*(1 + sqrt(5))) == -I*pi / 10
+    assert acsch(-I*2 / sqrt(2 - sqrt(2))) == I*pi / 8
+    assert acsch(I*2 / sqrt(2 - sqrt(2))) == -I*pi / 8
+    assert acsch(-I*2) == I*pi / 6
+    assert acsch(I*2) == -I*pi / 6
+    assert acsch(-I*sqrt(2 + 2/sqrt(5))) == I*pi / 5
+    assert acsch(I*sqrt(2 + 2/sqrt(5))) == -I*pi / 5
+    assert acsch(-I*sqrt(2)) == I*pi / 4
+    assert acsch(I*sqrt(2)) == -I*pi / 4
+    assert acsch(-I*(sqrt(5)-1)) == 3*I*pi / 10
+    assert acsch(I*(sqrt(5)-1)) == -3*I*pi / 10
+    assert acsch(-I*2 / sqrt(3)) == I*pi / 3
+    assert acsch(I*2 / sqrt(3)) == -I*pi / 3
+    assert acsch(-I*2 / sqrt(2 + sqrt(2))) == 3*I*pi / 8
+    assert acsch(I*2 / sqrt(2 + sqrt(2))) == -3*I*pi / 8
+    assert acsch(-I*sqrt(2 - 2/sqrt(5))) == 2*I*pi / 5
+    assert acsch(I*sqrt(2 - 2/sqrt(5))) == -2*I*pi / 5
+    assert acsch(-I*(sqrt(6) - sqrt(2))) == 5*I*pi / 12
+    assert acsch(I*(sqrt(6) - sqrt(2))) == -5*I*pi / 12
+    assert acsch(nan) is nan
+
+    # properties
+    # acsch(x) == asinh(1/x)
+    assert acsch(-I*sqrt(2)) == asinh(I/sqrt(2))
+    assert acsch(-I*2 / sqrt(3)) == asinh(I*sqrt(3) / 2)
+
+    # reality
+    assert acsch(S(2)).is_real is True
+    assert acsch(S(2)).is_finite is True
+    assert acsch(S(-2)).is_real is True
+    assert acsch(S(oo)).is_extended_real is True
+    assert acsch(-S(oo)).is_real is True
+    assert (acsch(2) - oo) == -oo
+    assert acsch(symbols('y', extended_real=True)).is_extended_real is True
+
+    # acsch(x) == -I*asin(I/x)
+    assert acsch(-I*sqrt(2)) == -I*asin(-1/sqrt(2))
+    assert acsch(-I*2 / sqrt(3)) == -I*asin(-sqrt(3)/2)
+
+    # csch(acsch(x)) / x == 1
+    assert expand_mul(csch(acsch(-I*(sqrt(6) + sqrt(2)))) / (-I*(sqrt(6) + sqrt(2)))) == 1
+    assert expand_mul(csch(acsch(I*(1 + sqrt(5)))) / (I*(1 + sqrt(5)))) == 1
+    assert (csch(acsch(I*sqrt(2 - 2/sqrt(5)))) / (I*sqrt(2 - 2/sqrt(5)))).simplify() == 1
+    assert (csch(acsch(-I*sqrt(2 - 2/sqrt(5)))) / (-I*sqrt(2 - 2/sqrt(5)))).simplify() == 1
+
+    # numerical evaluation
+    assert str(acsch(5*I+1).n(6)) == '0.0391819 - 0.193363*I'
+    assert str(acsch(-5*I+1).n(6)) == '0.0391819 + 0.193363*I'
+
+
+def test_acsch_infinities():
+    assert acsch(oo) == 0
+    assert acsch(-oo) == 0
+    assert acsch(zoo) == 0
+
+
+def test_acsch_leading_term():
+    x = Symbol('x')
+    assert acsch(1/x).as_leading_term(x) == x
+    # Tests concerning branch points
+    assert acsch(x + I).as_leading_term(x) == -I*pi/2
+    assert acsch(x - I).as_leading_term(x) == I*pi/2
+    # Tests concerning points lying on branch cuts
+    assert acsch(x).as_leading_term(x, cdir=1) == -log(x) + log(2)
+    assert acsch(x).as_leading_term(x, cdir=-1) == log(x) - log(2) - I*pi
+    assert acsch(x + I/2).as_leading_term(x, cdir=1) == -I*pi - acsch(I/2)
+    assert acsch(x + I/2).as_leading_term(x, cdir=-1) == acsch(I/2)
+    assert acsch(x - I/2).as_leading_term(x, cdir=1) == -acsch(I/2)
+    assert acsch(x - I/2).as_leading_term(x, cdir=-1) == acsch(I/2) + I*pi
+    # Tests concerning re(ndir) == 0
+    assert acsch(I/2 + I*x - x**2).as_leading_term(x, cdir=1) == log(2 - sqrt(3)) - I*pi/2
+    assert acsch(I/2 + I*x - x**2).as_leading_term(x, cdir=-1) == log(2 - sqrt(3)) - I*pi/2
+
+
+def test_acsch_series():
+    x = Symbol('x')
+    assert acsch(x).series(x, 0, 9) == log(2) - log(x) + x**2/4 - 3*x**4/32 \
+    + 5*x**6/96 - 35*x**8/1024 + O(x**9)
+    t4 = acsch(x).taylor_term(4, x)
+    assert t4 == -3*x**4/32
+    assert acsch(x).taylor_term(6, x, t4, 0) == 5*x**6/96
+
+
+def test_acsch_nseries():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert acsch(x + I)._eval_nseries(x, 4, None) == -I*pi/2 + \
+    sqrt(2)*I*sqrt(x)*sqrt(-I) - 5*x**(S(3)/2)*(1 - I)/12 - \
+    43*sqrt(2)*I*x**(S(5)/2)*sqrt(-I)/160 + 177*x**(S(7)/2)*(1 - I)/896 + O(x**4)
+    assert acsch(x - I)._eval_nseries(x, 4, None) == I*pi/2 - \
+    sqrt(2)*sqrt(I)*I*sqrt(x) - 5*x**(S(3)/2)*(1 + I)/12 + \
+    43*sqrt(2)*sqrt(I)*I*x**(S(5)/2)/160 + 177*x**(S(7)/2)*(1 + I)/896 + O(x**4)
+    # Tests concerning points lying on branch cuts
+    assert acsch(x + I/2)._eval_nseries(x, 4, None, cdir=1) == -acsch(I/2) - \
+    I*pi + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert acsch(x + I/2)._eval_nseries(x, 4, None, cdir=-1) == acsch(I/2) - \
+    4*sqrt(3)*I*x/3 + 8*sqrt(3)*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert acsch(x - I/2)._eval_nseries(x, 4, None, cdir=1) == -acsch(I/2) - \
+    4*sqrt(3)*I*x/3 - 8*sqrt(3)*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert acsch(x - I/2)._eval_nseries(x, 4, None, cdir=-1) == I*pi + \
+    acsch(I/2) + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4)
+    # Tests concerning re(ndir) == 0
+    assert acsch(I/2 + I*x - x**2)._eval_nseries(x, 4, None) == -I*pi/2 + \
+    log(2 - sqrt(3)) + x*(12 - 8*sqrt(3))/(-6 + 3*sqrt(3)) + x**2*(-96 + \
+    sqrt(3)*(56 - 84*I) + 144*I)/(-63 + 36*sqrt(3)) + x**3*(2688 - 2688*I + \
+    sqrt(3)*(-1552 + 1552*I))/(-873 + 504*sqrt(3)) + O(x**4)
+
+
+def test_acsch_rewrite():
+    x = Symbol('x')
+    assert acsch(x).rewrite(log) == log(1/x + sqrt(1/x**2 + 1))
+    assert acsch(x).rewrite(asinh) == asinh(1/x)
+    assert acsch(x).rewrite(atanh) == (sqrt(-x**2)*(-sqrt(-(x**2 + 1)**2)
+                                                    *atanh(sqrt(x**2 + 1))/(x**2 + 1)
+                                                    + pi/2)/x)
+
+
+def test_acsch_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: acsch(x).fdiff(2))
+
+
+def test_atanh():
+    x = Symbol('x')
+
+    # at specific points
+    assert atanh(0) == 0
+    assert atanh(I) == I*pi/4
+    assert atanh(-I) == -I*pi/4
+    assert atanh(1) is oo
+    assert atanh(-1) is -oo
+    assert atanh(nan) is nan
+
+    # at infinites
+    assert atanh(oo) == -I*pi/2
+    assert atanh(-oo) == I*pi/2
+
+    assert atanh(I*oo) == I*pi/2
+    assert atanh(-I*oo) == -I*pi/2
+
+    assert atanh(zoo) == I*AccumBounds(-pi/2, pi/2)
+
+    # properties
+    assert atanh(-x) == -atanh(x)
+
+    # reality
+    assert atanh(S(2)).is_real is False
+    assert atanh(S(-1)/5).is_real is True
+    assert atanh(symbols('y', extended_real=True)).is_real is None
+    assert atanh(S(1)).is_real is False
+    assert atanh(S(1)).is_extended_real is True
+    assert atanh(S(-1)).is_real is False
+
+    # special values
+    assert atanh(I/sqrt(3)) == I*pi/6
+    assert atanh(-I/sqrt(3)) == -I*pi/6
+    assert atanh(I*sqrt(3)) == I*pi/3
+    assert atanh(-I*sqrt(3)) == -I*pi/3
+    assert atanh(I*(1 + sqrt(2))) == pi*I*Rational(3, 8)
+    assert atanh(I*(sqrt(2) - 1)) == pi*I/8
+    assert atanh(I*(1 - sqrt(2))) == -pi*I/8
+    assert atanh(-I*(1 + sqrt(2))) == pi*I*Rational(-3, 8)
+    assert atanh(I*sqrt(5 + 2*sqrt(5))) == I*pi*Rational(2, 5)
+    assert atanh(-I*sqrt(5 + 2*sqrt(5))) == I*pi*Rational(-2, 5)
+    assert atanh(I*(2 - sqrt(3))) == pi*I/12
+    assert atanh(I*(sqrt(3) - 2)) == -pi*I/12
+    assert atanh(oo) == -I*pi/2
+
+    # Symmetry
+    assert atanh(Rational(-1, 2)) == -atanh(S.Half)
+
+    # inverse composition
+    assert unchanged(atanh, tanh(Symbol('v1')))
+
+    assert atanh(tanh(-5, evaluate=False)) == -5
+    assert atanh(tanh(0, evaluate=False)) == 0
+    assert atanh(tanh(7, evaluate=False)) == 7
+    assert atanh(tanh(I, evaluate=False)) == I
+    assert atanh(tanh(-I, evaluate=False)) == -I
+    assert atanh(tanh(-11*I, evaluate=False)) == -11*I + 4*I*pi
+    assert atanh(tanh(3 + I)) == 3 + I
+    assert atanh(tanh(4 + 5*I)) == 4 - 2*I*pi + 5*I
+    assert atanh(tanh(pi/2)) == pi/2
+    assert atanh(tanh(pi)) == pi
+    assert atanh(tanh(-3 + 7*I)) == -3 - 2*I*pi + 7*I
+    assert atanh(tanh(9 - I*2/3)) == 9 - I*2/3
+    assert atanh(tanh(-32 - 123*I)) == -32 - 123*I + 39*I*pi
+
+
+def test_atanh_rewrite():
+    x = Symbol('x')
+    assert atanh(x).rewrite(log) == (log(1 + x) - log(1 - x)) / 2
+    assert atanh(x).rewrite(asinh) == \
+        pi*x/(2*sqrt(-x**2)) - sqrt(-x)*sqrt(1 - x**2)*sqrt(1/(x**2 - 1))*asinh(sqrt(1/(x**2 - 1)))/sqrt(x)
+
+
+def test_atanh_leading_term():
+    x = Symbol('x')
+    assert atanh(x).as_leading_term(x) == x
+    # Tests concerning branch points
+    assert atanh(x + 1).as_leading_term(x, cdir=1) == -log(x)/2 + log(2)/2 - I*pi/2
+    assert atanh(x + 1).as_leading_term(x, cdir=-1) == -log(x)/2 + log(2)/2 + I*pi/2
+    assert atanh(x - 1).as_leading_term(x, cdir=1) == log(x)/2 - log(2)/2
+    assert atanh(x - 1).as_leading_term(x, cdir=-1) == log(x)/2 - log(2)/2
+    assert atanh(1/x).as_leading_term(x, cdir=1) == -I*pi/2
+    assert atanh(1/x).as_leading_term(x, cdir=-1) == I*pi/2
+    # Tests concerning points lying on branch cuts
+    assert atanh(I*x + 2).as_leading_term(x, cdir=1) == atanh(2) + I*pi
+    assert atanh(-I*x + 2).as_leading_term(x, cdir=1) == atanh(2)
+    assert atanh(I*x - 2).as_leading_term(x, cdir=1) == -atanh(2)
+    assert atanh(-I*x - 2).as_leading_term(x, cdir=1) == -I*pi - atanh(2)
+    # Tests concerning im(ndir) == 0
+    assert atanh(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == -log(3)/2 - I*pi/2
+    assert atanh(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == -log(3)/2 - I*pi/2
+
+
+def test_atanh_series():
+    x = Symbol('x')
+    assert atanh(x).series(x, 0, 10) == \
+        x + x**3/3 + x**5/5 + x**7/7 + x**9/9 + O(x**10)
+
+
+def test_atanh_nseries():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert atanh(x + 1)._eval_nseries(x, 4, None, cdir=1) == -I*pi/2 + log(2)/2 - \
+    log(x)/2 + x/4 - x**2/16 + x**3/48 + O(x**4)
+    assert atanh(x + 1)._eval_nseries(x, 4, None, cdir=-1) == I*pi/2 + log(2)/2 - \
+    log(x)/2 + x/4 - x**2/16 + x**3/48 + O(x**4)
+    assert atanh(x - 1)._eval_nseries(x, 4, None, cdir=1) == -log(2)/2 + log(x)/2 + \
+    x/4 + x**2/16 + x**3/48 + O(x**4)
+    assert atanh(x - 1)._eval_nseries(x, 4, None, cdir=-1) == -log(2)/2 + log(x)/2 + \
+    x/4 + x**2/16 + x**3/48 + O(x**4)
+    # Tests concerning points lying on branch cuts
+    assert atanh(I*x + 2)._eval_nseries(x, 4, None, cdir=1) == I*pi + atanh(2) - \
+    I*x/3 - 2*x**2/9 + 13*I*x**3/81 + O(x**4)
+    assert atanh(I*x + 2)._eval_nseries(x, 4, None, cdir=-1) == atanh(2) - I*x/3 - \
+    2*x**2/9 + 13*I*x**3/81 + O(x**4)
+    assert atanh(I*x - 2)._eval_nseries(x, 4, None, cdir=1) == -atanh(2) - I*x/3 + \
+    2*x**2/9 + 13*I*x**3/81 + O(x**4)
+    assert atanh(I*x - 2)._eval_nseries(x, 4, None, cdir=-1) == -atanh(2) - I*pi - \
+    I*x/3 + 2*x**2/9 + 13*I*x**3/81 + O(x**4)
+    # Tests concerning im(ndir) == 0
+    assert atanh(-I*x**2 + x - 2)._eval_nseries(x, 4, None) == -I*pi/2 - log(3)/2 - x/3 + \
+    x**2*(-S(1)/4 + I/2) + x**2*(S(1)/36 - I/6) + x**3*(-S(1)/6 + I/2) + x**3*(S(1)/162 - I/18) + O(x**4)
+
+
+def test_atanh_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: atanh(x).fdiff(2))
+
+
+def test_acoth():
+    x = Symbol('x')
+
+    #at specific points
+    assert acoth(0) == I*pi/2
+    assert acoth(I) == -I*pi/4
+    assert acoth(-I) == I*pi/4
+    assert acoth(1) is oo
+    assert acoth(-1) is -oo
+    assert acoth(nan) is nan
+
+    # at infinites
+    assert acoth(oo) == 0
+    assert acoth(-oo) == 0
+    assert acoth(I*oo) == 0
+    assert acoth(-I*oo) == 0
+    assert acoth(zoo) == 0
+
+    #properties
+    assert acoth(-x) == -acoth(x)
+
+    assert acoth(I/sqrt(3)) == -I*pi/3
+    assert acoth(-I/sqrt(3)) == I*pi/3
+    assert acoth(I*sqrt(3)) == -I*pi/6
+    assert acoth(-I*sqrt(3)) == I*pi/6
+    assert acoth(I*(1 + sqrt(2))) == -pi*I/8
+    assert acoth(-I*(sqrt(2) + 1)) == pi*I/8
+    assert acoth(I*(1 - sqrt(2))) == pi*I*Rational(3, 8)
+    assert acoth(I*(sqrt(2) - 1)) == pi*I*Rational(-3, 8)
+    assert acoth(I*sqrt(5 + 2*sqrt(5))) == -I*pi/10
+    assert acoth(-I*sqrt(5 + 2*sqrt(5))) == I*pi/10
+    assert acoth(I*(2 + sqrt(3))) == -pi*I/12
+    assert acoth(-I*(2 + sqrt(3))) == pi*I/12
+    assert acoth(I*(2 - sqrt(3))) == pi*I*Rational(-5, 12)
+    assert acoth(I*(sqrt(3) - 2)) == pi*I*Rational(5, 12)
+
+    # reality
+    assert acoth(S(2)).is_real is True
+    assert acoth(S(2)).is_finite is True
+    assert acoth(S(2)).is_extended_real is True
+    assert acoth(S(-2)).is_real is True
+    assert acoth(S(1)).is_real is False
+    assert acoth(S(1)).is_extended_real is True
+    assert acoth(S(-1)).is_real is False
+    assert acoth(symbols('y', real=True)).is_real is None
+
+    # Symmetry
+    assert acoth(Rational(-1, 2)) == -acoth(S.Half)
+
+
+def test_acoth_rewrite():
+    x = Symbol('x')
+    assert acoth(x).rewrite(log) == (log(1 + 1/x) - log(1 - 1/x)) / 2
+    assert acoth(x).rewrite(atanh) == atanh(1/x)
+    assert acoth(x).rewrite(asinh) == \
+        x*sqrt(x**(-2))*asinh(sqrt(1/(x**2 - 1))) + I*pi*(sqrt((x - 1)/x)*sqrt(x/(x - 1)) - sqrt(x/(x + 1))*sqrt(1 + 1/x))/2
+
+
+def test_acoth_leading_term():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert acoth(x + 1).as_leading_term(x, cdir=1) == -log(x)/2 + log(2)/2
+    assert acoth(x + 1).as_leading_term(x, cdir=-1) == -log(x)/2 + log(2)/2
+    assert acoth(x - 1).as_leading_term(x, cdir=1) == log(x)/2 - log(2)/2 + I*pi/2
+    assert acoth(x - 1).as_leading_term(x, cdir=-1) == log(x)/2 - log(2)/2 - I*pi/2
+    # Tests concerning points lying on branch cuts
+    assert acoth(x).as_leading_term(x, cdir=-1) == I*pi/2
+    assert acoth(x).as_leading_term(x, cdir=1) == -I*pi/2
+    assert acoth(I*x + 1/2).as_leading_term(x, cdir=1) == acoth(1/2)
+    assert acoth(-I*x + 1/2).as_leading_term(x, cdir=1) == acoth(1/2) + I*pi
+    assert acoth(I*x - 1/2).as_leading_term(x, cdir=1) == -I*pi - acoth(1/2)
+    assert acoth(-I*x - 1/2).as_leading_term(x, cdir=1) == -acoth(1/2)
+    # Tests concerning im(ndir) == 0
+    assert acoth(-I*x**2 - x - S(1)/2).as_leading_term(x, cdir=1) == -log(3)/2 + I*pi/2
+    assert acoth(-I*x**2 - x - S(1)/2).as_leading_term(x, cdir=-1) == -log(3)/2 + I*pi/2
+
+
+def test_acoth_series():
+    x = Symbol('x')
+    assert acoth(x).series(x, 0, 10) == \
+        -I*pi/2 + x + x**3/3 + x**5/5 + x**7/7 + x**9/9 + O(x**10)
+
+
+def test_acoth_nseries():
+    x = Symbol('x')
+    # Tests concerning branch points
+    assert acoth(x + 1)._eval_nseries(x, 4, None) == log(2)/2 - log(x)/2 + x/4 - \
+    x**2/16 + x**3/48 + O(x**4)
+    assert acoth(x - 1)._eval_nseries(x, 4, None, cdir=1) == I*pi/2 - log(2)/2 + \
+    log(x)/2 + x/4 + x**2/16 + x**3/48 + O(x**4)
+    assert acoth(x - 1)._eval_nseries(x, 4, None, cdir=-1) == -I*pi/2 - log(2)/2 + \
+    log(x)/2 + x/4 + x**2/16 + x**3/48 + O(x**4)
+    # Tests concerning points lying on branch cuts
+    assert acoth(I*x + S(1)/2)._eval_nseries(x, 4, None, cdir=1) == acoth(S(1)/2) + \
+    4*I*x/3 - 8*x**2/9 - 112*I*x**3/81 + O(x**4)
+    assert acoth(I*x + S(1)/2)._eval_nseries(x, 4, None, cdir=-1) == I*pi + \
+    acoth(S(1)/2) + 4*I*x/3 - 8*x**2/9 - 112*I*x**3/81 + O(x**4)
+    assert acoth(I*x - S(1)/2)._eval_nseries(x, 4, None, cdir=1) == -acoth(S(1)/2) - \
+    I*pi + 4*I*x/3 + 8*x**2/9 - 112*I*x**3/81 + O(x**4)
+    assert acoth(I*x - S(1)/2)._eval_nseries(x, 4, None, cdir=-1) == -acoth(S(1)/2) + \
+    4*I*x/3 + 8*x**2/9 - 112*I*x**3/81 + O(x**4)
+    # Tests concerning im(ndir) == 0
+    assert acoth(-I*x**2 - x - S(1)/2)._eval_nseries(x, 4, None) == I*pi/2 - log(3)/2 - \
+    4*x/3 + x**2*(-S(8)/9 + 2*I/3) - 2*I*x**2 + x**3*(S(104)/81 - 16*I/9) - 8*x**3/3 + O(x**4)
+
+
+def test_acoth_fdiff():
+    x = Symbol('x')
+    raises(ArgumentIndexError, lambda: acoth(x).fdiff(2))
+
+
+def test_inverses():
+    x = Symbol('x')
+    assert sinh(x).inverse() == asinh
+    raises(AttributeError, lambda: cosh(x).inverse())
+    assert tanh(x).inverse() == atanh
+    assert coth(x).inverse() == acoth
+    assert asinh(x).inverse() == sinh
+    assert acosh(x).inverse() == cosh
+    assert atanh(x).inverse() == tanh
+    assert acoth(x).inverse() == coth
+    assert asech(x).inverse() == sech
+    assert acsch(x).inverse() == csch
+
+
+def test_leading_term():
+    x = Symbol('x')
+    assert cosh(x).as_leading_term(x) == 1
+    assert coth(x).as_leading_term(x) == 1/x
+    for func in [sinh, tanh]:
+        assert func(x).as_leading_term(x) == x
+    for func in [sinh, cosh, tanh, coth]:
+        for ar in (1/x, S.Half):
+            eq = func(ar)
+            assert eq.as_leading_term(x) == eq
+    for func in [csch, sech]:
+        eq = func(S.Half)
+        assert eq.as_leading_term(x) == eq
+
+
+def test_complex():
+    a, b = symbols('a,b', real=True)
+    z = a + b*I
+    for func in [sinh, cosh, tanh, coth, sech, csch]:
+        assert func(z).conjugate() == func(a - b*I)
+    for deep in [True, False]:
+        assert sinh(z).expand(
+            complex=True, deep=deep) == sinh(a)*cos(b) + I*cosh(a)*sin(b)
+        assert cosh(z).expand(
+            complex=True, deep=deep) == cosh(a)*cos(b) + I*sinh(a)*sin(b)
+        assert tanh(z).expand(complex=True, deep=deep) == sinh(a)*cosh(
+            a)/(cos(b)**2 + sinh(a)**2) + I*sin(b)*cos(b)/(cos(b)**2 + sinh(a)**2)
+        assert coth(z).expand(complex=True, deep=deep) == sinh(a)*cosh(
+            a)/(sin(b)**2 + sinh(a)**2) - I*sin(b)*cos(b)/(sin(b)**2 + sinh(a)**2)
+        assert csch(z).expand(complex=True, deep=deep) == cos(b) * sinh(a) / (sin(b)**2\
+            *cosh(a)**2 + cos(b)**2 * sinh(a)**2) - I*sin(b) * cosh(a) / (sin(b)**2\
+            *cosh(a)**2 + cos(b)**2 * sinh(a)**2)
+        assert sech(z).expand(complex=True, deep=deep) == cos(b) * cosh(a) / (sin(b)**2\
+            *sinh(a)**2 + cos(b)**2 * cosh(a)**2) - I*sin(b) * sinh(a) / (sin(b)**2\
+            *sinh(a)**2 + cos(b)**2 * cosh(a)**2)
+
+
+def test_complex_2899():
+    a, b = symbols('a,b', real=True)
+    for deep in [True, False]:
+        for func in [sinh, cosh, tanh, coth]:
+            assert func(a).expand(complex=True, deep=deep) == func(a)
+
+
+def test_simplifications():
+    x = Symbol('x')
+    assert sinh(asinh(x)) == x
+    assert sinh(acosh(x)) == sqrt(x - 1) * sqrt(x + 1)
+    assert sinh(atanh(x)) == x/sqrt(1 - x**2)
+    assert sinh(acoth(x)) == 1/(sqrt(x - 1) * sqrt(x + 1))
+
+    assert cosh(asinh(x)) == sqrt(1 + x**2)
+    assert cosh(acosh(x)) == x
+    assert cosh(atanh(x)) == 1/sqrt(1 - x**2)
+    assert cosh(acoth(x)) == x/(sqrt(x - 1) * sqrt(x + 1))
+
+    assert tanh(asinh(x)) == x/sqrt(1 + x**2)
+    assert tanh(acosh(x)) == sqrt(x - 1) * sqrt(x + 1) / x
+    assert tanh(atanh(x)) == x
+    assert tanh(acoth(x)) == 1/x
+
+    assert coth(asinh(x)) == sqrt(1 + x**2)/x
+    assert coth(acosh(x)) == x/(sqrt(x - 1) * sqrt(x + 1))
+    assert coth(atanh(x)) == 1/x
+    assert coth(acoth(x)) == x
+
+    assert csch(asinh(x)) == 1/x
+    assert csch(acosh(x)) == 1/(sqrt(x - 1) * sqrt(x + 1))
+    assert csch(atanh(x)) == sqrt(1 - x**2)/x
+    assert csch(acoth(x)) == sqrt(x - 1) * sqrt(x + 1)
+
+    assert sech(asinh(x)) == 1/sqrt(1 + x**2)
+    assert sech(acosh(x)) == 1/x
+    assert sech(atanh(x)) == sqrt(1 - x**2)
+    assert sech(acoth(x)) == sqrt(x - 1) * sqrt(x + 1)/x
+
+
+def test_issue_4136():
+    assert cosh(asinh(Integer(3)/2)) == sqrt(Integer(13)/4)
+
+
+def test_sinh_rewrite():
+    x = Symbol('x')
+    assert sinh(x).rewrite(exp) == (exp(x) - exp(-x))/2 \
+        == sinh(x).rewrite('tractable')
+    assert sinh(x).rewrite(cosh) == -I*cosh(x + I*pi/2)
+    tanh_half = tanh(S.Half*x)
+    assert sinh(x).rewrite(tanh) == 2*tanh_half/(1 - tanh_half**2)
+    coth_half = coth(S.Half*x)
+    assert sinh(x).rewrite(coth) == 2*coth_half/(coth_half**2 - 1)
+
+
+def test_cosh_rewrite():
+    x = Symbol('x')
+    assert cosh(x).rewrite(exp) == (exp(x) + exp(-x))/2 \
+        == cosh(x).rewrite('tractable')
+    assert cosh(x).rewrite(sinh) == -I*sinh(x + I*pi/2, evaluate=False)
+    tanh_half = tanh(S.Half*x)**2
+    assert cosh(x).rewrite(tanh) == (1 + tanh_half)/(1 - tanh_half)
+    coth_half = coth(S.Half*x)**2
+    assert cosh(x).rewrite(coth) == (coth_half + 1)/(coth_half - 1)
+
+
+def test_tanh_rewrite():
+    x = Symbol('x')
+    assert tanh(x).rewrite(exp) == (exp(x) - exp(-x))/(exp(x) + exp(-x)) \
+        == tanh(x).rewrite('tractable')
+    assert tanh(x).rewrite(sinh) == I*sinh(x)/sinh(I*pi/2 - x, evaluate=False)
+    assert tanh(x).rewrite(cosh) == I*cosh(I*pi/2 - x, evaluate=False)/cosh(x)
+    assert tanh(x).rewrite(coth) == 1/coth(x)
+
+
+def test_coth_rewrite():
+    x = Symbol('x')
+    assert coth(x).rewrite(exp) == (exp(x) + exp(-x))/(exp(x) - exp(-x)) \
+        == coth(x).rewrite('tractable')
+    assert coth(x).rewrite(sinh) == -I*sinh(I*pi/2 - x, evaluate=False)/sinh(x)
+    assert coth(x).rewrite(cosh) == -I*cosh(x)/cosh(I*pi/2 - x, evaluate=False)
+    assert coth(x).rewrite(tanh) == 1/tanh(x)
+
+
+def test_csch_rewrite():
+    x = Symbol('x')
+    assert csch(x).rewrite(exp) == 1 / (exp(x)/2 - exp(-x)/2) \
+        == csch(x).rewrite('tractable')
+    assert csch(x).rewrite(cosh) == I/cosh(x + I*pi/2, evaluate=False)
+    tanh_half = tanh(S.Half*x)
+    assert csch(x).rewrite(tanh) == (1 - tanh_half**2)/(2*tanh_half)
+    coth_half = coth(S.Half*x)
+    assert csch(x).rewrite(coth) == (coth_half**2 - 1)/(2*coth_half)
+
+
+def test_sech_rewrite():
+    x = Symbol('x')
+    assert sech(x).rewrite(exp) == 1 / (exp(x)/2 + exp(-x)/2) \
+        == sech(x).rewrite('tractable')
+    assert sech(x).rewrite(sinh) == I/sinh(x + I*pi/2, evaluate=False)
+    tanh_half = tanh(S.Half*x)**2
+    assert sech(x).rewrite(tanh) == (1 - tanh_half)/(1 + tanh_half)
+    coth_half = coth(S.Half*x)**2
+    assert sech(x).rewrite(coth) == (coth_half - 1)/(coth_half + 1)
+
+
+def test_derivs():
+    x = Symbol('x')
+    assert coth(x).diff(x) == -sinh(x)**(-2)
+    assert sinh(x).diff(x) == cosh(x)
+    assert cosh(x).diff(x) == sinh(x)
+    assert tanh(x).diff(x) == -tanh(x)**2 + 1
+    assert csch(x).diff(x) == -coth(x)*csch(x)
+    assert sech(x).diff(x) == -tanh(x)*sech(x)
+    assert acoth(x).diff(x) == 1/(-x**2 + 1)
+    assert asinh(x).diff(x) == 1/sqrt(x**2 + 1)
+    assert acosh(x).diff(x) == 1/(sqrt(x - 1)*sqrt(x + 1))
+    assert acosh(x).diff(x) == acosh(x).rewrite(log).diff(x).together()
+    assert atanh(x).diff(x) == 1/(-x**2 + 1)
+    assert asech(x).diff(x) == -1/(x*sqrt(1 - x**2))
+    assert acsch(x).diff(x) == -1/(x**2*sqrt(1 + x**(-2)))
+
+
+def test_sinh_expansion():
+    x, y = symbols('x,y')
+    assert sinh(x+y).expand(trig=True) == sinh(x)*cosh(y) + cosh(x)*sinh(y)
+    assert sinh(2*x).expand(trig=True) == 2*sinh(x)*cosh(x)
+    assert sinh(3*x).expand(trig=True).expand() == \
+        sinh(x)**3 + 3*sinh(x)*cosh(x)**2
+
+
+def test_cosh_expansion():
+    x, y = symbols('x,y')
+    assert cosh(x+y).expand(trig=True) == cosh(x)*cosh(y) + sinh(x)*sinh(y)
+    assert cosh(2*x).expand(trig=True) == cosh(x)**2 + sinh(x)**2
+    assert cosh(3*x).expand(trig=True).expand() == \
+        3*sinh(x)**2*cosh(x) + cosh(x)**3
+
+def test_cosh_positive():
+    # See issue 11721
+    # cosh(x) is positive for real values of x
+    k = symbols('k', real=True)
+    n = symbols('n', integer=True)
+
+    assert cosh(k, evaluate=False).is_positive is True
+    assert cosh(k + 2*n*pi*I, evaluate=False).is_positive is True
+    assert cosh(I*pi/4, evaluate=False).is_positive is True
+    assert cosh(3*I*pi/4, evaluate=False).is_positive is False
+
+def test_cosh_nonnegative():
+    k = symbols('k', real=True)
+    n = symbols('n', integer=True)
+
+    assert cosh(k, evaluate=False).is_nonnegative is True
+    assert cosh(k + 2*n*pi*I, evaluate=False).is_nonnegative is True
+    assert cosh(I*pi/4, evaluate=False).is_nonnegative is True
+    assert cosh(3*I*pi/4, evaluate=False).is_nonnegative is False
+    assert cosh(S.Zero, evaluate=False).is_nonnegative is True
+
+def test_real_assumptions():
+    z = Symbol('z', real=False)
+    assert sinh(z).is_real is None
+    assert cosh(z).is_real is None
+    assert tanh(z).is_real is None
+    assert sech(z).is_real is None
+    assert csch(z).is_real is None
+    assert coth(z).is_real is None
+
+def test_sign_assumptions():
+    p = Symbol('p', positive=True)
+    n = Symbol('n', negative=True)
+    assert sinh(n).is_negative is True
+    assert sinh(p).is_positive is True
+    assert cosh(n).is_positive is True
+    assert cosh(p).is_positive is True
+    assert tanh(n).is_negative is True
+    assert tanh(p).is_positive is True
+    assert csch(n).is_negative is True
+    assert csch(p).is_positive is True
+    assert sech(n).is_positive is True
+    assert sech(p).is_positive is True
+    assert coth(n).is_negative is True
+    assert coth(p).is_positive is True
+
+
+def test_issue_25847():
+    x = Symbol('x')
+
+    #atanh
+    assert atanh(sin(x)/x).as_leading_term(x) == atanh(sin(x)/x)
+    raises(PoleError, lambda: atanh(exp(1/x)).as_leading_term(x))
+
+    #asinh
+    assert asinh(sin(x)/x).as_leading_term(x) == log(1 + sqrt(2))
+    raises(PoleError, lambda: asinh(exp(1/x)).as_leading_term(x))
+
+    #acosh
+    assert acosh(sin(x)/x).as_leading_term(x) == 0
+    raises(PoleError, lambda: acosh(exp(1/x)).as_leading_term(x))
+
+    #acoth
+    assert acoth(sin(x)/x).as_leading_term(x) == acoth(sin(x)/x)
+    raises(PoleError, lambda: acoth(exp(1/x)).as_leading_term(x))
+
+    #asech
+    assert asech(sinh(x)/x).as_leading_term(x) == 0
+    raises(PoleError, lambda: asech(exp(1/x)).as_leading_term(x))
+
+    #acsch
+    assert acsch(sin(x)/x).as_leading_term(x) == log(1 + sqrt(2))
+    raises(PoleError, lambda: acsch(exp(1/x)).as_leading_term(x))
+
+
+def test_issue_25175():
+    x = Symbol('x')
+    g1 = 2*acosh(1 + 2*x/3) - acosh(S(5)/3 - S(8)/3/(x + 4))
+    g2 = 2*log(sqrt((x + 4)/3)*(sqrt(x + 3)+sqrt(x))**2/(2*sqrt(x + 3) + sqrt(x)))
+    assert (g1 - g2).series(x) == O(x**6)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_integers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_integers.py
new file mode 100644
index 0000000000000000000000000000000000000000..a48ad2ac24c4a857d57b2f24e3308ac90078a9b1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_integers.py
@@ -0,0 +1,688 @@
+from sympy.calculus.accumulationbounds import AccumBounds
+from sympy.core.numbers import (E, Float, I, Rational, Integer, nan, oo, pi, zoo)
+from sympy.core.relational import (Eq, Ge, Gt, Le, Lt, Ne)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.integers import (ceiling, floor, frac)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin, cos, tan, asin
+from sympy.polys.rootoftools import RootOf, CRootOf
+from sympy import Integers
+from sympy.sets.sets import Interval
+from sympy.sets.fancysets import ImageSet
+from sympy.core.function import Lambda
+
+from sympy.core.expr import unchanged
+from sympy.testing.pytest import XFAIL, raises
+
+x = Symbol('x')
+i = Symbol('i', imaginary=True)
+y = Symbol('y', real=True)
+k, n = symbols('k,n', integer=True)
+b = Symbol('b', real=True, noninteger=True)
+m = Symbol('m', positive=True)
+
+
+def test_floor():
+
+    assert floor(nan) is nan
+
+    assert floor(oo) is oo
+    assert floor(-oo) is -oo
+    assert floor(zoo) is zoo
+
+    assert floor(0) == 0
+
+    assert floor(1) == 1
+    assert floor(-1) == -1
+
+    assert floor(I*log(asin(5)/abs(asin(5)))) == 0
+    assert floor(-I*log(asin(7)/abs(asin(7)))) == -2
+
+    assert floor(E) == 2
+    assert floor(-E) == -3
+
+    assert floor(2*E) == 5
+    assert floor(-2*E) == -6
+
+    assert floor(pi) == 3
+    assert floor(-pi) == -4
+
+    assert floor(S.Half) == 0
+    assert floor(Rational(-1, 2)) == -1
+
+    assert floor(Rational(7, 3)) == 2
+    assert floor(Rational(-7, 3)) == -3
+    assert floor(-Rational(7, 3)) == -3
+
+    assert floor(Float(17.0)) == 17
+    assert floor(-Float(17.0)) == -17
+
+    assert floor(Float(7.69)) == 7
+    assert floor(-Float(7.69)) == -8
+
+    assert floor(1/(m+1)) == S.Zero
+    assert floor((m+2)/(m+1)) == S.One
+    assert floor(-1/(m+1)) == S.NegativeOne
+    assert floor((m+2)/(-m-1)) == Integer(-2)
+
+    assert floor(I) == I
+    assert floor(-I) == -I
+    e = floor(i)
+    assert e.func is floor and e.args[0] == i
+
+    assert floor(oo*I) == oo*I
+    assert floor(-oo*I) == -oo*I
+    assert floor(exp(I*pi/4)*oo) == exp(I*pi/4)*oo
+
+    assert floor(2*I) == 2*I
+    assert floor(-2*I) == -2*I
+
+    assert floor(I/2) == 0
+    assert floor(-I/2) == -I
+
+    assert floor(E + 17) == 19
+    assert floor(pi + 2) == 5
+
+    assert floor(E + pi) == 5
+    assert floor(I + pi) == 3 + I
+
+    assert floor(floor(pi)) == 3
+    assert floor(floor(y)) == floor(y)
+    assert floor(floor(x)) == floor(x)
+
+    assert unchanged(floor, x)
+    assert unchanged(floor, 2*x)
+    assert unchanged(floor, k*x)
+
+    assert floor(k) == k
+    assert floor(2*k) == 2*k
+    assert floor(k*n) == k*n
+
+    assert unchanged(floor, k/2)
+
+    assert unchanged(floor, x + y)
+
+    assert floor(x + 3) == floor(x) + 3
+    assert floor(x + k) == floor(x) + k
+
+    assert floor(y + 3) == floor(y) + 3
+    assert floor(y + k) == floor(y) + k
+
+    assert floor(3 + I*y + pi) == 6 + floor(y)*I
+
+    assert floor(k + n) == k + n
+
+    assert unchanged(floor, x*I)
+    assert floor(k*I) == k*I
+
+    assert floor(Rational(23, 10) - E*I) == 2 - 3*I
+
+    assert floor(sin(1)) == 0
+    assert floor(sin(-1)) == -1
+
+    assert floor(exp(2)) == 7
+
+    assert floor(log(8)/log(2)) != 2
+    assert int(floor(log(8)/log(2)).evalf(chop=True)) == 3
+
+    assert floor(factorial(50)/exp(1)) == \
+        11188719610782480504630258070757734324011354208865721592720336800
+
+    assert (floor(y) < y).is_Relational
+    assert (floor(y) <= y) == True
+    assert (floor(y) > y) == False
+    assert (floor(y) >= y).is_Relational
+    assert (floor(x) <= x).is_Relational  # x could be non-real
+    assert (floor(x) > x).is_Relational
+    assert (floor(x) <= y).is_Relational  # arg is not same as rhs
+    assert (floor(x) > y).is_Relational
+    assert (floor(y) <= oo) == True
+    assert (floor(y) < oo) == True
+    assert (floor(y) >= -oo) == True
+    assert (floor(y) > -oo) == True
+    assert (floor(b) < b) == True
+    assert (floor(b) <= b) == True
+    assert (floor(b) > b) == False
+    assert (floor(b) >= b) == False
+
+    assert floor(y).rewrite(frac) == y - frac(y)
+    assert floor(y).rewrite(ceiling) == -ceiling(-y)
+    assert floor(y).rewrite(frac).subs(y, -pi) == floor(-pi)
+    assert floor(y).rewrite(frac).subs(y, E) == floor(E)
+    assert floor(y).rewrite(ceiling).subs(y, E) == -ceiling(-E)
+    assert floor(y).rewrite(ceiling).subs(y, -pi) == -ceiling(pi)
+
+    assert Eq(floor(y), y - frac(y))
+    assert Eq(floor(y), -ceiling(-y))
+
+    neg = Symbol('neg', negative=True)
+    nn = Symbol('nn', nonnegative=True)
+    pos = Symbol('pos', positive=True)
+    np = Symbol('np', nonpositive=True)
+
+    assert (floor(neg) < 0) == True
+    assert (floor(neg) <= 0) == True
+    assert (floor(neg) > 0) == False
+    assert (floor(neg) >= 0) == False
+    assert (floor(neg) <= -1) == True
+    assert (floor(neg) >= -3) == (neg >= -3)
+    assert (floor(neg) < 5) == (neg < 5)
+
+    assert (floor(nn) < 0) == False
+    assert (floor(nn) >= 0) == True
+
+    assert (floor(pos) < 0) == False
+    assert (floor(pos) <= 0) == (pos < 1)
+    assert (floor(pos) > 0) == (pos >= 1)
+    assert (floor(pos) >= 0) == True
+    assert (floor(pos) >= 3) == (pos >= 3)
+
+    assert (floor(np) <= 0) == True
+    assert (floor(np) > 0) == False
+
+    assert floor(neg).is_negative == True
+    assert floor(neg).is_nonnegative == False
+    assert floor(nn).is_negative == False
+    assert floor(nn).is_nonnegative == True
+    assert floor(pos).is_negative == False
+    assert floor(pos).is_nonnegative == True
+    assert floor(np).is_negative is None
+    assert floor(np).is_nonnegative is None
+
+    assert (floor(7, evaluate=False) >= 7) == True
+    assert (floor(7, evaluate=False) > 7) == False
+    assert (floor(7, evaluate=False) <= 7) == True
+    assert (floor(7, evaluate=False) < 7) == False
+
+    assert (floor(7, evaluate=False) >= 6) == True
+    assert (floor(7, evaluate=False) > 6) == True
+    assert (floor(7, evaluate=False) <= 6) == False
+    assert (floor(7, evaluate=False) < 6) == False
+
+    assert (floor(7, evaluate=False) >= 8) == False
+    assert (floor(7, evaluate=False) > 8) == False
+    assert (floor(7, evaluate=False) <= 8) == True
+    assert (floor(7, evaluate=False) < 8) == True
+
+    assert (floor(x) <= 5.5) == Le(floor(x), 5.5, evaluate=False)
+    assert (floor(x) >= -3.2) == Ge(floor(x), -3.2, evaluate=False)
+    assert (floor(x) < 2.9) == Lt(floor(x), 2.9, evaluate=False)
+    assert (floor(x) > -1.7) == Gt(floor(x), -1.7, evaluate=False)
+
+    assert (floor(y) <= 5.5) == (y < 6)
+    assert (floor(y) >= -3.2) == (y >= -3)
+    assert (floor(y) < 2.9) == (y < 3)
+    assert (floor(y) > -1.7) == (y >= -1)
+
+    assert (floor(y) <= n) == (y < n + 1)
+    assert (floor(y) >= n) == (y >= n)
+    assert (floor(y) < n) == (y < n)
+    assert (floor(y) > n) == (y >= n + 1)
+
+    assert floor(RootOf(x**3 - 27*x, 2)) == 5
+
+
+def test_ceiling():
+
+    assert ceiling(nan) is nan
+
+    assert ceiling(oo) is oo
+    assert ceiling(-oo) is -oo
+    assert ceiling(zoo) is zoo
+
+    assert ceiling(0) == 0
+
+    assert ceiling(1) == 1
+    assert ceiling(-1) == -1
+
+    assert ceiling(I*log(asin(5)/abs(asin(5)))) == 1
+    assert ceiling(-I*log(asin(7)/abs(asin(7)))) == -1
+
+    assert ceiling(E) == 3
+    assert ceiling(-E) == -2
+
+    assert ceiling(2*E) == 6
+    assert ceiling(-2*E) == -5
+
+    assert ceiling(pi) == 4
+    assert ceiling(-pi) == -3
+
+    assert ceiling(S.Half) == 1
+    assert ceiling(Rational(-1, 2)) == 0
+
+    assert ceiling(Rational(7, 3)) == 3
+    assert ceiling(-Rational(7, 3)) == -2
+
+    assert ceiling(Float(17.0)) == 17
+    assert ceiling(-Float(17.0)) == -17
+
+    assert ceiling(Float(7.69)) == 8
+    assert ceiling(-Float(7.69)) == -7
+
+    assert ceiling(1/(m+1)) == S.One
+    assert ceiling((m+2)/(m+1)) == Integer(2)
+    assert ceiling(-1/(m+1)) == S.Zero
+    assert ceiling((m+2)/(-m-1)) == S.NegativeOne
+
+    assert ceiling(I) == I
+    assert ceiling(-I) == -I
+    e = ceiling(i)
+    assert e.func is ceiling and e.args[0] == i
+
+    assert ceiling(oo*I) == oo*I
+    assert ceiling(-oo*I) == -oo*I
+    assert ceiling(exp(I*pi/4)*oo) == exp(I*pi/4)*oo
+
+    assert ceiling(2*I) == 2*I
+    assert ceiling(-2*I) == -2*I
+
+    assert ceiling(I/2) == I
+    assert ceiling(-I/2) == 0
+
+    assert ceiling(E + 17) == 20
+    assert ceiling(pi + 2) == 6
+
+    assert ceiling(E + pi) == 6
+    assert ceiling(I + pi) == I + 4
+
+    assert ceiling(ceiling(pi)) == 4
+    assert ceiling(ceiling(y)) == ceiling(y)
+    assert ceiling(ceiling(x)) == ceiling(x)
+
+    assert unchanged(ceiling, x)
+    assert unchanged(ceiling, 2*x)
+    assert unchanged(ceiling, k*x)
+
+    assert ceiling(k) == k
+    assert ceiling(2*k) == 2*k
+    assert ceiling(k*n) == k*n
+
+    assert unchanged(ceiling, k/2)
+
+    assert unchanged(ceiling, x + y)
+
+    assert ceiling(x + 3) == ceiling(x) + 3
+    assert ceiling(x + 3.0) == ceiling(x) + 3
+    assert ceiling(x + 3.0*I) == ceiling(x) + 3*I
+    assert ceiling(x + k) == ceiling(x) + k
+
+    assert ceiling(y + 3) == ceiling(y) + 3
+    assert ceiling(y + k) == ceiling(y) + k
+
+    assert ceiling(3 + pi + y*I) == 7 + ceiling(y)*I
+
+    assert ceiling(k + n) == k + n
+
+    assert unchanged(ceiling, x*I)
+    assert ceiling(k*I) == k*I
+
+    assert ceiling(Rational(23, 10) - E*I) == 3 - 2*I
+
+    assert ceiling(sin(1)) == 1
+    assert ceiling(sin(-1)) == 0
+
+    assert ceiling(exp(2)) == 8
+
+    assert ceiling(-log(8)/log(2)) != -2
+    assert int(ceiling(-log(8)/log(2)).evalf(chop=True)) == -3
+
+    assert ceiling(factorial(50)/exp(1)) == \
+        11188719610782480504630258070757734324011354208865721592720336801
+
+    assert (ceiling(y) >= y) == True
+    assert (ceiling(y) > y).is_Relational
+    assert (ceiling(y) < y) == False
+    assert (ceiling(y) <= y).is_Relational
+    assert (ceiling(x) >= x).is_Relational  # x could be non-real
+    assert (ceiling(x) < x).is_Relational
+    assert (ceiling(x) >= y).is_Relational  # arg is not same as rhs
+    assert (ceiling(x) < y).is_Relational
+    assert (ceiling(y) >= -oo) == True
+    assert (ceiling(y) > -oo) == True
+    assert (ceiling(y) <= oo) == True
+    assert (ceiling(y) < oo) == True
+    assert (ceiling(b) < b) == False
+    assert (ceiling(b) <= b) == False
+    assert (ceiling(b) > b) == True
+    assert (ceiling(b) >= b) == True
+
+    assert ceiling(y).rewrite(floor) == -floor(-y)
+    assert ceiling(y).rewrite(frac) == y + frac(-y)
+    assert ceiling(y).rewrite(floor).subs(y, -pi) == -floor(pi)
+    assert ceiling(y).rewrite(floor).subs(y, E) == -floor(-E)
+    assert ceiling(y).rewrite(frac).subs(y, pi) == ceiling(pi)
+    assert ceiling(y).rewrite(frac).subs(y, -E) == ceiling(-E)
+
+    assert Eq(ceiling(y), y + frac(-y))
+    assert Eq(ceiling(y), -floor(-y))
+
+    neg = Symbol('neg', negative=True)
+    nn = Symbol('nn', nonnegative=True)
+    pos = Symbol('pos', positive=True)
+    np = Symbol('np', nonpositive=True)
+
+    assert (ceiling(neg) <= 0) == True
+    assert (ceiling(neg) < 0) == (neg <= -1)
+    assert (ceiling(neg) > 0) == False
+    assert (ceiling(neg) >= 0) == (neg > -1)
+    assert (ceiling(neg) > -3) == (neg > -3)
+    assert (ceiling(neg) <= 10) == (neg <= 10)
+
+    assert (ceiling(nn) < 0) == False
+    assert (ceiling(nn) >= 0) == True
+
+    assert (ceiling(pos) < 0) == False
+    assert (ceiling(pos) <= 0) == False
+    assert (ceiling(pos) > 0) == True
+    assert (ceiling(pos) >= 0) == True
+    assert (ceiling(pos) >= 1) == True
+    assert (ceiling(pos) > 5) == (pos > 5)
+
+    assert (ceiling(np) <= 0) == True
+    assert (ceiling(np) > 0) == False
+
+    assert ceiling(neg).is_positive == False
+    assert ceiling(neg).is_nonpositive == True
+    assert ceiling(nn).is_positive is None
+    assert ceiling(nn).is_nonpositive is None
+    assert ceiling(pos).is_positive == True
+    assert ceiling(pos).is_nonpositive == False
+    assert ceiling(np).is_positive == False
+    assert ceiling(np).is_nonpositive == True
+
+    assert (ceiling(7, evaluate=False) >= 7) == True
+    assert (ceiling(7, evaluate=False) > 7) == False
+    assert (ceiling(7, evaluate=False) <= 7) == True
+    assert (ceiling(7, evaluate=False) < 7) == False
+
+    assert (ceiling(7, evaluate=False) >= 6) == True
+    assert (ceiling(7, evaluate=False) > 6) == True
+    assert (ceiling(7, evaluate=False) <= 6) == False
+    assert (ceiling(7, evaluate=False) < 6) == False
+
+    assert (ceiling(7, evaluate=False) >= 8) == False
+    assert (ceiling(7, evaluate=False) > 8) == False
+    assert (ceiling(7, evaluate=False) <= 8) == True
+    assert (ceiling(7, evaluate=False) < 8) == True
+
+    assert (ceiling(x) <= 5.5) == Le(ceiling(x), 5.5, evaluate=False)
+    assert (ceiling(x) >= -3.2) == Ge(ceiling(x), -3.2, evaluate=False)
+    assert (ceiling(x) < 2.9) == Lt(ceiling(x), 2.9, evaluate=False)
+    assert (ceiling(x) > -1.7) == Gt(ceiling(x), -1.7, evaluate=False)
+
+    assert (ceiling(y) <= 5.5) == (y <= 5)
+    assert (ceiling(y) >= -3.2) == (y > -4)
+    assert (ceiling(y) < 2.9) == (y <= 2)
+    assert (ceiling(y) > -1.7) == (y > -2)
+
+    assert (ceiling(y) <= n) == (y <= n)
+    assert (ceiling(y) >= n) == (y > n - 1)
+    assert (ceiling(y) < n) == (y <= n - 1)
+    assert (ceiling(y) > n) == (y > n)
+
+    assert ceiling(RootOf(x**3 - 27*x, 2)) == 6
+    s = ImageSet(Lambda(n, n + (CRootOf(x**5 - x**2 + 1, 0))), Integers)
+    f = CRootOf(x**5 - x**2 + 1, 0)
+    s = ImageSet(Lambda(n, n + f), Integers)
+    assert s.intersect(Interval(-10, 10)) == {i + f for i in range(-9, 11)}
+
+
+def test_frac():
+    assert isinstance(frac(x), frac)
+    assert frac(oo) == AccumBounds(0, 1)
+    assert frac(-oo) == AccumBounds(0, 1)
+    assert frac(zoo) is nan
+
+    assert frac(n) == 0
+    assert frac(nan) is nan
+    assert frac(Rational(4, 3)) == Rational(1, 3)
+    assert frac(-Rational(4, 3)) == Rational(2, 3)
+    assert frac(Rational(-4, 3)) == Rational(2, 3)
+
+    r = Symbol('r', real=True)
+    assert frac(I*r) == I*frac(r)
+    assert frac(1 + I*r) == I*frac(r)
+    assert frac(0.5 + I*r) == 0.5 + I*frac(r)
+    assert frac(n + I*r) == I*frac(r)
+    assert frac(n + I*k) == 0
+    assert unchanged(frac, x + I*x)
+    assert frac(x + I*n) == frac(x)
+
+    assert frac(x).rewrite(floor) == x - floor(x)
+    assert frac(x).rewrite(ceiling) == x + ceiling(-x)
+    assert frac(y).rewrite(floor).subs(y, pi) == frac(pi)
+    assert frac(y).rewrite(floor).subs(y, -E) == frac(-E)
+    assert frac(y).rewrite(ceiling).subs(y, -pi) == frac(-pi)
+    assert frac(y).rewrite(ceiling).subs(y, E) == frac(E)
+
+    assert Eq(frac(y), y - floor(y))
+    assert Eq(frac(y), y + ceiling(-y))
+
+    r = Symbol('r', real=True)
+    p_i = Symbol('p_i', integer=True, positive=True)
+    n_i = Symbol('p_i', integer=True, negative=True)
+    np_i = Symbol('np_i', integer=True, nonpositive=True)
+    nn_i = Symbol('nn_i', integer=True, nonnegative=True)
+    p_r = Symbol('p_r', positive=True)
+    n_r = Symbol('n_r', negative=True)
+    np_r = Symbol('np_r', real=True, nonpositive=True)
+    nn_r = Symbol('nn_r', real=True, nonnegative=True)
+
+    # Real frac argument, integer rhs
+    assert frac(r) <= p_i
+    assert not frac(r) <= n_i
+    assert (frac(r) <= np_i).has(Le)
+    assert (frac(r) <= nn_i).has(Le)
+    assert frac(r) < p_i
+    assert not frac(r) < n_i
+    assert not frac(r) < np_i
+    assert (frac(r) < nn_i).has(Lt)
+    assert not frac(r) >= p_i
+    assert frac(r) >= n_i
+    assert frac(r) >= np_i
+    assert (frac(r) >= nn_i).has(Ge)
+    assert not frac(r) > p_i
+    assert frac(r) > n_i
+    assert (frac(r) > np_i).has(Gt)
+    assert (frac(r) > nn_i).has(Gt)
+
+    assert not Eq(frac(r), p_i)
+    assert not Eq(frac(r), n_i)
+    assert Eq(frac(r), np_i).has(Eq)
+    assert Eq(frac(r), nn_i).has(Eq)
+
+    assert Ne(frac(r), p_i)
+    assert Ne(frac(r), n_i)
+    assert Ne(frac(r), np_i).has(Ne)
+    assert Ne(frac(r), nn_i).has(Ne)
+
+
+    # Real frac argument, real rhs
+    assert (frac(r) <= p_r).has(Le)
+    assert not frac(r) <= n_r
+    assert (frac(r) <= np_r).has(Le)
+    assert (frac(r) <= nn_r).has(Le)
+    assert (frac(r) < p_r).has(Lt)
+    assert not frac(r) < n_r
+    assert not frac(r) < np_r
+    assert (frac(r) < nn_r).has(Lt)
+    assert (frac(r) >= p_r).has(Ge)
+    assert frac(r) >= n_r
+    assert frac(r) >= np_r
+    assert (frac(r) >= nn_r).has(Ge)
+    assert (frac(r) > p_r).has(Gt)
+    assert frac(r) > n_r
+    assert (frac(r) > np_r).has(Gt)
+    assert (frac(r) > nn_r).has(Gt)
+
+    assert not Eq(frac(r), n_r)
+    assert Eq(frac(r), p_r).has(Eq)
+    assert Eq(frac(r), np_r).has(Eq)
+    assert Eq(frac(r), nn_r).has(Eq)
+
+    assert Ne(frac(r), p_r).has(Ne)
+    assert Ne(frac(r), n_r)
+    assert Ne(frac(r), np_r).has(Ne)
+    assert Ne(frac(r), nn_r).has(Ne)
+
+    # Real frac argument, +/- oo rhs
+    assert frac(r) < oo
+    assert frac(r) <= oo
+    assert not frac(r) > oo
+    assert not frac(r) >= oo
+
+    assert not frac(r) < -oo
+    assert not frac(r) <= -oo
+    assert frac(r) > -oo
+    assert frac(r) >= -oo
+
+    assert frac(r) < 1
+    assert frac(r) <= 1
+    assert not frac(r) > 1
+    assert not frac(r) >= 1
+
+    assert not frac(r) < 0
+    assert (frac(r) <= 0).has(Le)
+    assert (frac(r) > 0).has(Gt)
+    assert frac(r) >= 0
+
+    # Some test for numbers
+    assert frac(r) <= sqrt(2)
+    assert (frac(r) <= sqrt(3) - sqrt(2)).has(Le)
+    assert not frac(r) <= sqrt(2) - sqrt(3)
+    assert not frac(r) >= sqrt(2)
+    assert (frac(r) >= sqrt(3) - sqrt(2)).has(Ge)
+    assert frac(r) >= sqrt(2) - sqrt(3)
+
+    assert not Eq(frac(r), sqrt(2))
+    assert Eq(frac(r), sqrt(3) - sqrt(2)).has(Eq)
+    assert not Eq(frac(r), sqrt(2) - sqrt(3))
+    assert Ne(frac(r), sqrt(2))
+    assert Ne(frac(r), sqrt(3) - sqrt(2)).has(Ne)
+    assert Ne(frac(r), sqrt(2) - sqrt(3))
+
+    assert frac(p_i, evaluate=False).is_zero
+    assert frac(p_i, evaluate=False).is_finite
+    assert frac(p_i, evaluate=False).is_integer
+    assert frac(p_i, evaluate=False).is_real
+    assert frac(r).is_finite
+    assert frac(r).is_real
+    assert frac(r).is_zero is None
+    assert frac(r).is_integer is None
+
+    assert frac(oo).is_finite
+    assert frac(oo).is_real
+
+
+def test_series():
+    x, y = symbols('x,y')
+    assert floor(x).nseries(x, y, 100) == floor(y)
+    assert ceiling(x).nseries(x, y, 100) == ceiling(y)
+    assert floor(x).nseries(x, pi, 100) == 3
+    assert ceiling(x).nseries(x, pi, 100) == 4
+    assert floor(x).nseries(x, 0, 100) == 0
+    assert ceiling(x).nseries(x, 0, 100) == 1
+    assert floor(-x).nseries(x, 0, 100) == -1
+    assert ceiling(-x).nseries(x, 0, 100) == 0
+
+
+def test_issue_14355():
+    # This test checks the leading term and series for the floor and ceil
+    # function when arg0 evaluates to S.NaN.
+    assert floor((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = 1) == -2
+    assert floor((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = -1) == -1
+    assert floor((cos(x) - 1)/x).as_leading_term(x, cdir = 1) == -1
+    assert floor((cos(x) - 1)/x).as_leading_term(x, cdir = -1) == 0
+    assert floor(sin(x)/x).as_leading_term(x, cdir = 1) == 0
+    assert floor(sin(x)/x).as_leading_term(x, cdir = -1) == 0
+    assert floor(-tan(x)/x).as_leading_term(x, cdir = 1) == -2
+    assert floor(-tan(x)/x).as_leading_term(x, cdir = -1) == -2
+    assert floor(sin(x)/x/3).as_leading_term(x, cdir = 1) == 0
+    assert floor(sin(x)/x/3).as_leading_term(x, cdir = -1) == 0
+    assert ceiling((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = 1) == -1
+    assert ceiling((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = -1) == 0
+    assert ceiling((cos(x) - 1)/x).as_leading_term(x, cdir = 1) == 0
+    assert ceiling((cos(x) - 1)/x).as_leading_term(x, cdir = -1) == 1
+    assert ceiling(sin(x)/x).as_leading_term(x, cdir = 1) == 1
+    assert ceiling(sin(x)/x).as_leading_term(x, cdir = -1) == 1
+    assert ceiling(-tan(x)/x).as_leading_term(x, cdir = 1) == -1
+    assert ceiling(-tan(x)/x).as_leading_term(x, cdir = 1) == -1
+    assert ceiling(sin(x)/x/3).as_leading_term(x, cdir = 1) == 1
+    assert ceiling(sin(x)/x/3).as_leading_term(x, cdir = -1) == 1
+    # test for series
+    assert floor(sin(x)/x).series(x, 0, 100, cdir = 1) == 0
+    assert floor(sin(x)/x).series(x, 0, 100, cdir = 1) == 0
+    assert floor((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = 1) == -2
+    assert floor((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = -1) == -1
+    assert ceiling(sin(x)/x).series(x, 0, 100, cdir = 1) == 1
+    assert ceiling(sin(x)/x).series(x, 0, 100, cdir = -1) == 1
+    assert ceiling((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = 1) == -1
+    assert ceiling((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = -1) == 0
+
+
+def test_frac_leading_term():
+    assert frac(x).as_leading_term(x) == x
+    assert frac(x).as_leading_term(x, cdir = 1) == x
+    assert frac(x).as_leading_term(x, cdir = -1) == 1
+    assert frac(x + S.Half).as_leading_term(x, cdir = 1) == S.Half
+    assert frac(x + S.Half).as_leading_term(x, cdir = -1) == S.Half
+    assert frac(-2*x + 1).as_leading_term(x, cdir = 1) == S.One
+    assert frac(-2*x + 1).as_leading_term(x, cdir = -1) == -2*x
+    assert frac(sin(x) + 5).as_leading_term(x, cdir = 1) == x
+    assert frac(sin(x) + 5).as_leading_term(x, cdir = -1) == S.One
+    assert frac(sin(x**2) + 5).as_leading_term(x, cdir = 1) == x**2
+    assert frac(sin(x**2) + 5).as_leading_term(x, cdir = -1) == x**2
+
+
+@XFAIL
+def test_issue_4149():
+    assert floor(3 + pi*I + y*I) == 3 + floor(pi + y)*I
+    assert floor(3*I + pi*I + y*I) == floor(3 + pi + y)*I
+    assert floor(3 + E + pi*I + y*I) == 5 + floor(pi + y)*I
+
+
+def test_issue_21651():
+    k = Symbol('k', positive=True, integer=True)
+    exp = 2*2**(-k)
+    assert isinstance(floor(exp), floor)
+
+
+def test_issue_11207():
+    assert floor(floor(x)) == floor(x)
+    assert floor(ceiling(x)) == ceiling(x)
+    assert ceiling(floor(x)) == floor(x)
+    assert ceiling(ceiling(x)) == ceiling(x)
+
+
+def test_nested_floor_ceiling():
+    assert floor(-floor(ceiling(x**3)/y)) == -floor(ceiling(x**3)/y)
+    assert ceiling(-floor(ceiling(x**3)/y)) == -floor(ceiling(x**3)/y)
+    assert floor(ceiling(-floor(x**Rational(7, 2)/y))) == -floor(x**Rational(7, 2)/y)
+    assert -ceiling(-ceiling(floor(x)/y)) == ceiling(floor(x)/y)
+
+def test_issue_18689():
+    assert floor(floor(floor(x)) + 3) == floor(x) + 3
+    assert ceiling(ceiling(ceiling(x)) + 1) == ceiling(x) + 1
+    assert ceiling(ceiling(floor(x)) + 3) == floor(x) + 3
+
+def test_issue_18421():
+    assert floor(float(0)) is S.Zero
+    assert ceiling(float(0)) is S.Zero
+
+def test_issue_25230():
+    a = Symbol('a', real = True)
+    b = Symbol('b', positive = True)
+    c = Symbol('c', negative = True)
+    raises(NotImplementedError, lambda: floor(x/a).as_leading_term(x, cdir = 1))
+    raises(NotImplementedError, lambda: ceiling(x/a).as_leading_term(x, cdir = 1))
+    assert floor(x/b).as_leading_term(x, cdir = 1) == 0
+    assert floor(x/b).as_leading_term(x, cdir = -1) == -1
+    assert floor(x/c).as_leading_term(x, cdir = 1) == -1
+    assert floor(x/c).as_leading_term(x, cdir = -1) == 0
+    assert ceiling(x/b).as_leading_term(x, cdir = 1) == 1
+    assert ceiling(x/b).as_leading_term(x, cdir = -1) == 0
+    assert ceiling(x/c).as_leading_term(x, cdir = 1) == 0
+    assert ceiling(x/c).as_leading_term(x, cdir = -1) == 1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_interface.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_interface.py
new file mode 100644
index 0000000000000000000000000000000000000000..6ae2f78b50bea24c64079066076971e315660d69
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_interface.py
@@ -0,0 +1,82 @@
+# This test file tests the SymPy function interface, that people use to create
+# their own new functions. It should be as easy as possible.
+#
+# We test that it works with both Function and DefinedFunction. New code should
+# use DefinedFunction because it has better type inference. Old code still
+# using Function should continue to work though.
+from sympy.core.function import Function, DefinedFunction
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.hyperbolic import tanh
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.series.limits import limit
+from sympy.abc import x
+
+
+def test_function_series1():
+    """Create our new "sin" function."""
+
+    for F in [Function, DefinedFunction]:
+
+        class my_function(F):
+
+            def fdiff(self, argindex=1):
+                return cos(self.args[0])
+
+            @classmethod
+            def eval(cls, arg):
+                arg = sympify(arg)
+                if arg == 0:
+                    return sympify(0)
+
+        #Test that the taylor series is correct
+        assert my_function(x).series(x, 0, 10) == sin(x).series(x, 0, 10)
+        assert limit(my_function(x)/x, x, 0) == 1
+
+
+def test_function_series2():
+    """Create our new "cos" function."""
+
+    for F in [Function, DefinedFunction]:
+
+        class my_function2(F):
+
+            def fdiff(self, argindex=1):
+                return -sin(self.args[0])
+
+            @classmethod
+            def eval(cls, arg):
+                arg = sympify(arg)
+                if arg == 0:
+                    return sympify(1)
+
+        #Test that the taylor series is correct
+        assert my_function2(x).series(x, 0, 10) == cos(x).series(x, 0, 10)
+
+
+def test_function_series3():
+    """
+    Test our easy "tanh" function.
+
+    This test tests two things:
+      * that the Function interface works as expected and it's easy to use
+      * that the general algorithm for the series expansion works even when the
+        derivative is defined recursively in terms of the original function,
+        since tanh(x).diff(x) == 1-tanh(x)**2
+    """
+
+    for F in [Function, DefinedFunction]:
+
+        class mytanh(F):
+
+            def fdiff(self, argindex=1):
+                return 1 - mytanh(self.args[0])**2
+
+            @classmethod
+            def eval(cls, arg):
+                arg = sympify(arg)
+                if arg == 0:
+                    return sympify(0)
+
+        e = tanh(x)
+        f = mytanh(x)
+        assert e.series(x, 0, 6) == f.series(x, 0, 6)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py
new file mode 100644
index 0000000000000000000000000000000000000000..374c4fb50eaae54a9884015c124c245385e1761e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py
@@ -0,0 +1,504 @@
+import itertools as it
+
+from sympy.core.expr import unchanged
+from sympy.core.function import Function
+from sympy.core.numbers import I, oo, Rational
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.external import import_module
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.integers import floor, ceiling
+from sympy.functions.elementary.miscellaneous import (sqrt, cbrt, root, Min,
+                                                      Max, real_root, Rem)
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.functions.special.delta_functions import Heaviside
+
+from sympy.utilities.lambdify import lambdify
+from sympy.testing.pytest import raises, skip, ignore_warnings
+
+def test_Min():
+    from sympy.abc import x, y, z
+    n = Symbol('n', negative=True)
+    n_ = Symbol('n_', negative=True)
+    nn = Symbol('nn', nonnegative=True)
+    nn_ = Symbol('nn_', nonnegative=True)
+    p = Symbol('p', positive=True)
+    p_ = Symbol('p_', positive=True)
+    np = Symbol('np', nonpositive=True)
+    np_ = Symbol('np_', nonpositive=True)
+    r = Symbol('r', real=True)
+
+    assert Min(5, 4) == 4
+    assert Min(-oo, -oo) is -oo
+    assert Min(-oo, n) is -oo
+    assert Min(n, -oo) is -oo
+    assert Min(-oo, np) is -oo
+    assert Min(np, -oo) is -oo
+    assert Min(-oo, 0) is -oo
+    assert Min(0, -oo) is -oo
+    assert Min(-oo, nn) is -oo
+    assert Min(nn, -oo) is -oo
+    assert Min(-oo, p) is -oo
+    assert Min(p, -oo) is -oo
+    assert Min(-oo, oo) is -oo
+    assert Min(oo, -oo) is -oo
+    assert Min(n, n) == n
+    assert unchanged(Min, n, np)
+    assert Min(np, n) == Min(n, np)
+    assert Min(n, 0) == n
+    assert Min(0, n) == n
+    assert Min(n, nn) == n
+    assert Min(nn, n) == n
+    assert Min(n, p) == n
+    assert Min(p, n) == n
+    assert Min(n, oo) == n
+    assert Min(oo, n) == n
+    assert Min(np, np) == np
+    assert Min(np, 0) == np
+    assert Min(0, np) == np
+    assert Min(np, nn) == np
+    assert Min(nn, np) == np
+    assert Min(np, p) == np
+    assert Min(p, np) == np
+    assert Min(np, oo) == np
+    assert Min(oo, np) == np
+    assert Min(0, 0) == 0
+    assert Min(0, nn) == 0
+    assert Min(nn, 0) == 0
+    assert Min(0, p) == 0
+    assert Min(p, 0) == 0
+    assert Min(0, oo) == 0
+    assert Min(oo, 0) == 0
+    assert Min(nn, nn) == nn
+    assert unchanged(Min, nn, p)
+    assert Min(p, nn) == Min(nn, p)
+    assert Min(nn, oo) == nn
+    assert Min(oo, nn) == nn
+    assert Min(p, p) == p
+    assert Min(p, oo) == p
+    assert Min(oo, p) == p
+    assert Min(oo, oo) is oo
+
+    assert Min(n, n_).func is Min
+    assert Min(nn, nn_).func is Min
+    assert Min(np, np_).func is Min
+    assert Min(p, p_).func is Min
+
+    # lists
+    assert Min() is S.Infinity
+    assert Min(x) == x
+    assert Min(x, y) == Min(y, x)
+    assert Min(x, y, z) == Min(z, y, x)
+    assert Min(x, Min(y, z)) == Min(z, y, x)
+    assert Min(x, Max(y, -oo)) == Min(x, y)
+    assert Min(p, oo, n, p, p, p_) == n
+    assert Min(p_, n_, p) == n_
+    assert Min(n, oo, -7, p, p, 2) == Min(n, -7)
+    assert Min(2, x, p, n, oo, n_, p, 2, -2, -2) == Min(-2, x, n, n_)
+    assert Min(0, x, 1, y) == Min(0, x, y)
+    assert Min(1000, 100, -100, x, p, n) == Min(n, x, -100)
+    assert unchanged(Min, sin(x), cos(x))
+    assert Min(sin(x), cos(x)) == Min(cos(x), sin(x))
+    assert Min(cos(x), sin(x)).subs(x, 1) == cos(1)
+    assert Min(cos(x), sin(x)).subs(x, S.Half) == sin(S.Half)
+    raises(ValueError, lambda: Min(cos(x), sin(x)).subs(x, I))
+    raises(ValueError, lambda: Min(I))
+    raises(ValueError, lambda: Min(I, x))
+    raises(ValueError, lambda: Min(S.ComplexInfinity, x))
+
+    assert Min(1, x).diff(x) == Heaviside(1 - x)
+    assert Min(x, 1).diff(x) == Heaviside(1 - x)
+    assert Min(0, -x, 1 - 2*x).diff(x) == -Heaviside(x + Min(0, -2*x + 1)) \
+        - 2*Heaviside(2*x + Min(0, -x) - 1)
+
+    # issue 7619
+    f = Function('f')
+    assert Min(1, 2*Min(f(1), 2))  # doesn't fail
+
+    # issue 7233
+    e = Min(0, x)
+    assert e.n().args == (0, x)
+
+    # issue 8643
+    m = Min(n, p_, n_, r)
+    assert m.is_positive is False
+    assert m.is_nonnegative is False
+    assert m.is_negative is True
+
+    m = Min(p, p_)
+    assert m.is_positive is True
+    assert m.is_nonnegative is True
+    assert m.is_negative is False
+
+    m = Min(p, nn_, p_)
+    assert m.is_positive is None
+    assert m.is_nonnegative is True
+    assert m.is_negative is False
+
+    m = Min(nn, p, r)
+    assert m.is_positive is None
+    assert m.is_nonnegative is None
+    assert m.is_negative is None
+
+
+def test_Max():
+    from sympy.abc import x, y, z
+    n = Symbol('n', negative=True)
+    n_ = Symbol('n_', negative=True)
+    nn = Symbol('nn', nonnegative=True)
+    p = Symbol('p', positive=True)
+    p_ = Symbol('p_', positive=True)
+    r = Symbol('r', real=True)
+
+    assert Max(5, 4) == 5
+
+    # lists
+
+    assert Max() is S.NegativeInfinity
+    assert Max(x) == x
+    assert Max(x, y) == Max(y, x)
+    assert Max(x, y, z) == Max(z, y, x)
+    assert Max(x, Max(y, z)) == Max(z, y, x)
+    assert Max(x, Min(y, oo)) == Max(x, y)
+    assert Max(n, -oo, n_, p, 2) == Max(p, 2)
+    assert Max(n, -oo, n_, p) == p
+    assert Max(2, x, p, n, -oo, S.NegativeInfinity, n_, p, 2) == Max(2, x, p)
+    assert Max(0, x, 1, y) == Max(1, x, y)
+    assert Max(r, r + 1, r - 1) == 1 + r
+    assert Max(1000, 100, -100, x, p, n) == Max(p, x, 1000)
+    assert Max(cos(x), sin(x)) == Max(sin(x), cos(x))
+    assert Max(cos(x), sin(x)).subs(x, 1) == sin(1)
+    assert Max(cos(x), sin(x)).subs(x, S.Half) == cos(S.Half)
+    raises(ValueError, lambda: Max(cos(x), sin(x)).subs(x, I))
+    raises(ValueError, lambda: Max(I))
+    raises(ValueError, lambda: Max(I, x))
+    raises(ValueError, lambda: Max(S.ComplexInfinity, 1))
+    assert Max(n, -oo, n_,  p, 2) == Max(p, 2)
+    assert Max(n, -oo, n_,  p, 1000) == Max(p, 1000)
+
+    assert Max(1, x).diff(x) == Heaviside(x - 1)
+    assert Max(x, 1).diff(x) == Heaviside(x - 1)
+    assert Max(x**2, 1 + x, 1).diff(x) == \
+        2*x*Heaviside(x**2 - Max(1, x + 1)) \
+        + Heaviside(x - Max(1, x**2) + 1)
+
+    e = Max(0, x)
+    assert e.n().args == (0, x)
+
+    # issue 8643
+    m = Max(p, p_, n, r)
+    assert m.is_positive is True
+    assert m.is_nonnegative is True
+    assert m.is_negative is False
+
+    m = Max(n, n_)
+    assert m.is_positive is False
+    assert m.is_nonnegative is False
+    assert m.is_negative is True
+
+    m = Max(n, n_, r)
+    assert m.is_positive is None
+    assert m.is_nonnegative is None
+    assert m.is_negative is None
+
+    m = Max(n, nn, r)
+    assert m.is_positive is None
+    assert m.is_nonnegative is True
+    assert m.is_negative is False
+
+
+def test_minmax_assumptions():
+    r = Symbol('r', real=True)
+    a = Symbol('a', real=True, algebraic=True)
+    t = Symbol('t', real=True, transcendental=True)
+    q = Symbol('q', rational=True)
+    p = Symbol('p', irrational=True)
+    n = Symbol('n', rational=True, integer=False)
+    i = Symbol('i', integer=True)
+    o = Symbol('o', odd=True)
+    e = Symbol('e', even=True)
+    k = Symbol('k', prime=True)
+    reals = [r, a, t, q, p, n, i, o, e, k]
+
+    for ext in (Max, Min):
+        for x, y in it.product(reals, repeat=2):
+
+            # Must be real
+            assert ext(x, y).is_real
+
+            # Algebraic?
+            if x.is_algebraic and y.is_algebraic:
+                assert ext(x, y).is_algebraic
+            elif x.is_transcendental and y.is_transcendental:
+                assert ext(x, y).is_transcendental
+            else:
+                assert ext(x, y).is_algebraic is None
+
+            # Rational?
+            if x.is_rational and y.is_rational:
+                assert ext(x, y).is_rational
+            elif x.is_irrational and y.is_irrational:
+                assert ext(x, y).is_irrational
+            else:
+                assert ext(x, y).is_rational is None
+
+            # Integer?
+            if x.is_integer and y.is_integer:
+                assert ext(x, y).is_integer
+            elif x.is_noninteger and y.is_noninteger:
+                assert ext(x, y).is_noninteger
+            else:
+                assert ext(x, y).is_integer is None
+
+            # Odd?
+            if x.is_odd and y.is_odd:
+                assert ext(x, y).is_odd
+            elif x.is_odd is False and y.is_odd is False:
+                assert ext(x, y).is_odd is False
+            else:
+                assert ext(x, y).is_odd is None
+
+            # Even?
+            if x.is_even and y.is_even:
+                assert ext(x, y).is_even
+            elif x.is_even is False and y.is_even is False:
+                assert ext(x, y).is_even is False
+            else:
+                assert ext(x, y).is_even is None
+
+            # Prime?
+            if x.is_prime and y.is_prime:
+                assert ext(x, y).is_prime
+            elif x.is_prime is False and y.is_prime is False:
+                assert ext(x, y).is_prime is False
+            else:
+                assert ext(x, y).is_prime is None
+
+
+def test_issue_8413():
+    x = Symbol('x', real=True)
+    # we can't evaluate in general because non-reals are not
+    # comparable: Min(floor(3.2 + I), 3.2 + I) -> ValueError
+    assert Min(floor(x), x) == floor(x)
+    assert Min(ceiling(x), x) == x
+    assert Max(floor(x), x) == x
+    assert Max(ceiling(x), x) == ceiling(x)
+
+
+def test_root():
+    from sympy.abc import x
+    n = Symbol('n', integer=True)
+    k = Symbol('k', integer=True)
+
+    assert root(2, 2) == sqrt(2)
+    assert root(2, 1) == 2
+    assert root(2, 3) == 2**Rational(1, 3)
+    assert root(2, 3) == cbrt(2)
+    assert root(2, -5) == 2**Rational(4, 5)/2
+
+    assert root(-2, 1) == -2
+
+    assert root(-2, 2) == sqrt(2)*I
+    assert root(-2, 1) == -2
+
+    assert root(x, 2) == sqrt(x)
+    assert root(x, 1) == x
+    assert root(x, 3) == x**Rational(1, 3)
+    assert root(x, 3) == cbrt(x)
+    assert root(x, -5) == x**Rational(-1, 5)
+
+    assert root(x, n) == x**(1/n)
+    assert root(x, -n) == x**(-1/n)
+
+    assert root(x, n, k) == (-1)**(2*k/n)*x**(1/n)
+
+
+def test_real_root():
+    assert real_root(-8, 3) == -2
+    assert real_root(-16, 4) == root(-16, 4)
+    r = root(-7, 4)
+    assert real_root(r) == r
+    r1 = root(-1, 3)
+    r2 = r1**2
+    r3 = root(-1, 4)
+    assert real_root(r1 + r2 + r3) == -1 + r2 + r3
+    assert real_root(root(-2, 3)) == -root(2, 3)
+    assert real_root(-8., 3) == -2.0
+    x = Symbol('x')
+    n = Symbol('n')
+    g = real_root(x, n)
+    assert g.subs({"x": -8, "n": 3}) == -2
+    assert g.subs({"x": 8, "n": 3}) == 2
+    # give principle root if there is no real root -- if this is not desired
+    # then maybe a Root class is needed to raise an error instead
+    assert g.subs({"x": I, "n": 3}) == cbrt(I)
+    assert g.subs({"x": -8, "n": 2}) == sqrt(-8)
+    assert g.subs({"x": I, "n": 2}) == sqrt(I)
+
+
+def test_issue_11463():
+    numpy = import_module('numpy')
+    if not numpy:
+        skip("numpy not installed.")
+    x = Symbol('x')
+    f = lambdify(x, real_root((log(x/(x-2))), 3), 'numpy')
+    # numpy.select evaluates all options before considering conditions,
+    # so it raises a warning about root of negative number which does
+    # not affect the outcome. This warning is suppressed here
+    with ignore_warnings(RuntimeWarning):
+        assert f(numpy.array(-1)) < -1
+
+
+def test_rewrite_MaxMin_as_Heaviside():
+    from sympy.abc import x
+    assert Max(0, x).rewrite(Heaviside) == x*Heaviside(x)
+    assert Max(3, x).rewrite(Heaviside) == x*Heaviside(x - 3) + \
+        3*Heaviside(-x + 3)
+    assert Max(0, x+2, 2*x).rewrite(Heaviside) == \
+        2*x*Heaviside(2*x)*Heaviside(x - 2) + \
+        (x + 2)*Heaviside(-x + 2)*Heaviside(x + 2)
+
+    assert Min(0, x).rewrite(Heaviside) == x*Heaviside(-x)
+    assert Min(3, x).rewrite(Heaviside) == x*Heaviside(-x + 3) + \
+        3*Heaviside(x - 3)
+    assert Min(x, -x, -2).rewrite(Heaviside) == \
+        x*Heaviside(-2*x)*Heaviside(-x - 2) - \
+        x*Heaviside(2*x)*Heaviside(x - 2) \
+        - 2*Heaviside(-x + 2)*Heaviside(x + 2)
+
+
+def test_rewrite_MaxMin_as_Piecewise():
+    from sympy.core.symbol import symbols
+    from sympy.functions.elementary.piecewise import Piecewise
+    x, y, z, a, b = symbols('x y z a b', real=True)
+    vx, vy, va = symbols('vx vy va')
+    assert Max(a, b).rewrite(Piecewise) == Piecewise((a, a >= b), (b, True))
+    assert Max(x, y, z).rewrite(Piecewise) == Piecewise((x, (x >= y) & (x >= z)), (y, y >= z), (z, True))
+    assert Max(x, y, a, b).rewrite(Piecewise) == Piecewise((a, (a >= b) & (a >= x) & (a >= y)),
+        (b, (b >= x) & (b >= y)), (x, x >= y), (y, True))
+    assert Min(a, b).rewrite(Piecewise) == Piecewise((a, a <= b), (b, True))
+    assert Min(x, y, z).rewrite(Piecewise) == Piecewise((x, (x <= y) & (x <= z)), (y, y <= z), (z, True))
+    assert Min(x,  y, a, b).rewrite(Piecewise) ==  Piecewise((a, (a <= b) & (a <= x) & (a <= y)),
+        (b, (b <= x) & (b <= y)), (x, x <= y), (y, True))
+
+    # Piecewise rewriting of Min/Max does also takes place for not explicitly real arguments
+    assert Max(vx, vy).rewrite(Piecewise) == Piecewise((vx, vx >= vy), (vy, True))
+    assert Min(va, vx, vy).rewrite(Piecewise) == Piecewise((va, (va <= vx) & (va <= vy)), (vx, vx <= vy), (vy, True))
+
+
+def test_issue_11099():
+    from sympy.abc import x, y
+    # some fixed value tests
+    fixed_test_data = {x: -2, y: 3}
+    assert Min(x, y).evalf(subs=fixed_test_data) == \
+        Min(x, y).subs(fixed_test_data).evalf()
+    assert Max(x, y).evalf(subs=fixed_test_data) == \
+        Max(x, y).subs(fixed_test_data).evalf()
+    # randomly generate some test data
+    from sympy.core.random import randint
+    for i in range(20):
+        random_test_data = {x: randint(-100, 100), y: randint(-100, 100)}
+        assert Min(x, y).evalf(subs=random_test_data) == \
+            Min(x, y).subs(random_test_data).evalf()
+        assert Max(x, y).evalf(subs=random_test_data) == \
+            Max(x, y).subs(random_test_data).evalf()
+
+
+def test_issue_12638():
+    from sympy.abc import a, b, c
+    assert Min(a, b, c, Max(a, b)) == Min(a, b, c)
+    assert Min(a, b, Max(a, b, c)) == Min(a, b)
+    assert Min(a, b, Max(a, c)) == Min(a, b)
+
+def test_issue_21399():
+    from sympy.abc import a, b, c
+    assert Max(Min(a, b), Min(a, b, c)) == Min(a, b)
+
+
+def test_instantiation_evaluation():
+    from sympy.abc import v, w, x, y, z
+    assert Min(1, Max(2, x)) == 1
+    assert Max(3, Min(2, x)) == 3
+    assert Min(Max(x, y), Max(x, z)) == Max(x, Min(y, z))
+    assert set(Min(Max(w, x), Max(y, z)).args) == {
+        Max(w, x), Max(y, z)}
+    assert Min(Max(x, y), Max(x, z), w) == Min(
+        w, Max(x, Min(y, z)))
+    A, B = Min, Max
+    for i in range(2):
+        assert A(x, B(x, y)) == x
+        assert A(x, B(y, A(x, w, z))) == A(x, B(y, A(w, z)))
+        A, B = B, A
+    assert Min(w, Max(x, y), Max(v, x, z)) == Min(
+        w, Max(x, Min(y, Max(v, z))))
+
+def test_rewrite_as_Abs():
+    from itertools import permutations
+    from sympy.functions.elementary.complexes import Abs
+    from sympy.abc import x, y, z, w
+    def test(e):
+        free = e.free_symbols
+        a = e.rewrite(Abs)
+        assert not a.has(Min, Max)
+        for i in permutations(range(len(free))):
+            reps = dict(zip(free, i))
+            assert a.xreplace(reps) == e.xreplace(reps)
+    test(Min(x, y))
+    test(Max(x, y))
+    test(Min(x, y, z))
+    test(Min(Max(w, x), Max(y, z)))
+
+def test_issue_14000():
+    assert isinstance(sqrt(4, evaluate=False), Pow) == True
+    assert isinstance(cbrt(3.5, evaluate=False), Pow) == True
+    assert isinstance(root(16, 4, evaluate=False), Pow) == True
+
+    assert sqrt(4, evaluate=False) == Pow(4, S.Half, evaluate=False)
+    assert cbrt(3.5, evaluate=False) == Pow(3.5, Rational(1, 3), evaluate=False)
+    assert root(4, 2, evaluate=False) == Pow(4, S.Half, evaluate=False)
+
+    assert root(16, 4, 2, evaluate=False).has(Pow) == True
+    assert real_root(-8, 3, evaluate=False).has(Pow) == True
+
+def test_issue_6899():
+    from sympy.core.function import Lambda
+    x = Symbol('x')
+    eqn = Lambda(x, x)
+    assert eqn.func(*eqn.args) == eqn
+
+def test_Rem():
+    from sympy.abc import x, y
+    assert Rem(5, 3) == 2
+    assert Rem(-5, 3) == -2
+    assert Rem(5, -3) == 2
+    assert Rem(-5, -3) == -2
+    assert Rem(x**3, y) == Rem(x**3, y)
+    assert Rem(Rem(-5, 3) + 3, 3) == 1
+
+
+def test_minmax_no_evaluate():
+    from sympy import evaluate
+    p = Symbol('p', positive=True)
+
+    assert Max(1, 3) == 3
+    assert Max(1, 3).args == ()
+    assert Max(0, p) == p
+    assert Max(0, p).args == ()
+    assert Min(0, p) == 0
+    assert Min(0, p).args == ()
+
+    assert Max(1, 3, evaluate=False) != 3
+    assert Max(1, 3, evaluate=False).args == (1, 3)
+    assert Max(0, p, evaluate=False) != p
+    assert Max(0, p, evaluate=False).args == (0, p)
+    assert Min(0, p, evaluate=False) != 0
+    assert Min(0, p, evaluate=False).args == (0, p)
+
+    with evaluate(False):
+        assert Max(1, 3) != 3
+        assert Max(1, 3).args == (1, 3)
+        assert Max(0, p) != p
+        assert Max(0, p).args == (0, p)
+        assert Min(0, p) != 0
+        assert Min(0, p).args == (0, p)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_piecewise.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_piecewise.py
new file mode 100644
index 0000000000000000000000000000000000000000..7d0728095578b49480a1334857a1c237012d2534
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_piecewise.py
@@ -0,0 +1,1639 @@
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.expr import unchanged
+from sympy.core.function import (Function, diff, expand)
+from sympy.core.mul import Mul
+from sympy.core.mod import Mod
+from sympy.core.numbers import (Float, I, Rational, oo, pi, zoo)
+from sympy.core.relational import (Eq, Ge, Gt, Ne)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import (Abs, adjoint, arg, conjugate, im, re, transpose)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt)
+from sympy.functions.elementary.piecewise import (Piecewise,
+    piecewise_fold, piecewise_exclusive, Undefined, ExprCondPair)
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.delta_functions import (DiracDelta, Heaviside)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.integrals.integrals import (Integral, integrate)
+from sympy.logic.boolalg import (And, ITE, Not, Or)
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.printing import srepr
+from sympy.sets.contains import Contains
+from sympy.sets.sets import Interval
+from sympy.solvers.solvers import solve
+from sympy.testing.pytest import raises, slow
+from sympy.utilities.lambdify import lambdify
+
+a, b, c, d, x, y = symbols('a:d, x, y')
+z = symbols('z', nonzero=True)
+
+
+def test_piecewise1():
+
+    # Test canonicalization
+    assert Piecewise((x, x < 1.)).has(1.0)  # doesn't get changed to x < 1
+    assert unchanged(Piecewise, ExprCondPair(x, x < 1), ExprCondPair(0, True))
+    assert Piecewise((x, x < 1), (0, True)) == Piecewise(ExprCondPair(x, x < 1),
+                                                         ExprCondPair(0, True))
+    assert Piecewise((x, x < 1), (0, True), (1, True)) == \
+        Piecewise((x, x < 1), (0, True))
+    assert Piecewise((x, x < 1), (0, False), (-1, 1 > 2)) == \
+        Piecewise((x, x < 1))
+    assert Piecewise((x, x < 1), (0, x < 1), (0, True)) == \
+        Piecewise((x, x < 1), (0, True))
+    assert Piecewise((x, x < 1), (0, x < 2), (0, True)) == \
+        Piecewise((x, x < 1), (0, True))
+    assert Piecewise((x, x < 1), (x, x < 2), (0, True)) == \
+        Piecewise((x, Or(x < 1, x < 2)), (0, True))
+    assert Piecewise((x, x < 1), (x, x < 2), (x, True)) == x
+    assert Piecewise((x, True)) == x
+    # Explicitly constructed empty Piecewise not accepted
+    raises(TypeError, lambda: Piecewise())
+    # False condition is never retained
+    assert Piecewise((2*x, x < 0), (x, False)) == \
+        Piecewise((2*x, x < 0), (x, False), evaluate=False) == \
+        Piecewise((2*x, x < 0))
+    assert Piecewise((x, False)) == Undefined
+    raises(TypeError, lambda: Piecewise(x))
+    assert Piecewise((x, 1)) == x  # 1 and 0 are accepted as True/False
+    raises(TypeError, lambda: Piecewise((x, 2)))
+    raises(TypeError, lambda: Piecewise((x, x**2)))
+    raises(TypeError, lambda: Piecewise(([1], True)))
+    assert Piecewise(((1, 2), True)) == Tuple(1, 2)
+    cond = (Piecewise((1, x < 0), (2, True)) < y)
+    assert Piecewise((1, cond)
+        ) == Piecewise((1, ITE(x < 0, y > 1, y > 2)))
+
+    assert Piecewise((1, x > 0), (2, And(x <= 0, x > -1))
+        ) == Piecewise((1, x > 0), (2, x > -1))
+    assert Piecewise((1, x <= 0), (2, (x < 0) & (x > -1))
+        ) == Piecewise((1, x <= 0))
+
+    # test for supporting Contains in Piecewise
+    pwise = Piecewise(
+        (1, And(x <= 6, x > 1, Contains(x, S.Integers))),
+        (0, True))
+    assert pwise.subs(x, pi) == 0
+    assert pwise.subs(x, 2) == 1
+    assert pwise.subs(x, 7) == 0
+
+    # Test subs
+    p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), x >= 0))
+    p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), x**2 >= 0))
+    assert p.subs(x, x**2) == p_x2
+    assert p.subs(x, -5) == -1
+    assert p.subs(x, -1) == 1
+    assert p.subs(x, 1) == log(1)
+
+    # More subs tests
+    p2 = Piecewise((1, x < pi), (-1, x < 2*pi), (0, x > 2*pi))
+    p3 = Piecewise((1, Eq(x, 0)), (1/x, True))
+    p4 = Piecewise((1, Eq(x, 0)), (2, 1/x>2))
+    assert p2.subs(x, 2) == 1
+    assert p2.subs(x, 4) == -1
+    assert p2.subs(x, 10) == 0
+    assert p3.subs(x, 0.0) == 1
+    assert p4.subs(x, 0.0) == 1
+
+
+    f, g, h = symbols('f,g,h', cls=Function)
+    pf = Piecewise((f(x), x < -1), (f(x) + h(x) + 2, x <= 1))
+    pg = Piecewise((g(x), x < -1), (g(x) + h(x) + 2, x <= 1))
+    assert pg.subs(g, f) == pf
+
+    assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 0) == 1
+    assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 1) == 0
+    assert Piecewise((1, Eq(x, y)), (0, True)).subs(x, y) == 1
+    assert Piecewise((1, Eq(x, z)), (0, True)).subs(x, z) == 1
+    assert Piecewise((1, Eq(exp(x), cos(z))), (0, True)).subs(x, z) == \
+        Piecewise((1, Eq(exp(z), cos(z))), (0, True))
+
+    p5 = Piecewise( (0, Eq(cos(x) + y, 0)), (1, True))
+    assert p5.subs(y, 0) == Piecewise( (0, Eq(cos(x), 0)), (1, True))
+
+    assert Piecewise((-1, y < 1), (0, x < 0), (1, Eq(x, 0)), (2, True)
+        ).subs(x, 1) == Piecewise((-1, y < 1), (2, True))
+    assert Piecewise((1, Eq(x**2, -1)), (2, x < 0)).subs(x, I) == 1
+
+    p6 = Piecewise((x, x > 0))
+    n = symbols('n', negative=True)
+    assert p6.subs(x, n) == Undefined
+
+    # Test evalf
+    assert p.evalf() == Piecewise((-1.0, x < -1), (x**2, x < 0), (log(x), True))
+    assert p.evalf(subs={x: -2}) == -1.0
+    assert p.evalf(subs={x: -1}) == 1.0
+    assert p.evalf(subs={x: 1}) == log(1)
+    assert p6.evalf(subs={x: -5}) == Undefined
+
+    # Test doit
+    f_int = Piecewise((Integral(x, (x, 0, 1)), x < 1))
+    assert f_int.doit() == Piecewise( (S.Half, x < 1) )
+
+    # Test differentiation
+    f = x
+    fp = x*p
+    dp = Piecewise((0, x < -1), (2*x, x < 0), (1/x, x >= 0))
+    fp_dx = x*dp + p
+    assert diff(p, x) == dp
+    assert diff(f*p, x) == fp_dx
+
+    # Test simple arithmetic
+    assert x*p == fp
+    assert x*p + p == p + x*p
+    assert p + f == f + p
+    assert p + dp == dp + p
+    assert p - dp == -(dp - p)
+
+    # Test power
+    dp2 = Piecewise((0, x < -1), (4*x**2, x < 0), (1/x**2, x >= 0))
+    assert dp**2 == dp2
+
+    # Test _eval_interval
+    f1 = x*y + 2
+    f2 = x*y**2 + 3
+    peval = Piecewise((f1, x < 0), (f2, x > 0))
+    peval_interval = f1.subs(
+        x, 0) - f1.subs(x, -1) + f2.subs(x, 1) - f2.subs(x, 0)
+    assert peval._eval_interval(x, 0, 0) == 0
+    assert peval._eval_interval(x, -1, 1) == peval_interval
+    peval2 = Piecewise((f1, x < 0), (f2, True))
+    assert peval2._eval_interval(x, 0, 0) == 0
+    assert peval2._eval_interval(x, 1, -1) == -peval_interval
+    assert peval2._eval_interval(x, -1, -2) == f1.subs(x, -2) - f1.subs(x, -1)
+    assert peval2._eval_interval(x, -1, 1) == peval_interval
+    assert peval2._eval_interval(x, None, 0) == peval2.subs(x, 0)
+    assert peval2._eval_interval(x, -1, None) == -peval2.subs(x, -1)
+
+    # Test integration
+    assert p.integrate() == Piecewise(
+        (-x, x < -1),
+        (x**3/3 + Rational(4, 3), x < 0),
+        (x*log(x) - x + Rational(4, 3), True))
+    p = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
+    assert integrate(p, (x, -2, 2)) == Rational(5, 6)
+    assert integrate(p, (x, 2, -2)) == Rational(-5, 6)
+    p = Piecewise((0, x < 0), (1, x < 1), (0, x < 2), (1, x < 3), (0, True))
+    assert integrate(p, (x, -oo, oo)) == 2
+    p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x))
+    assert integrate(p, (x, -2, 2)) == Undefined
+
+    # Test commutativity
+    assert isinstance(p, Piecewise) and p.is_commutative is True
+
+
+def test_piecewise_free_symbols():
+    f = Piecewise((x, a < 0), (y, True))
+    assert f.free_symbols == {x, y, a}
+
+
+def test_piecewise_integrate1():
+    x, y = symbols('x y', real=True)
+
+    f = Piecewise(((x - 2)**2, x >= 0), (1, True))
+    assert integrate(f, (x, -2, 2)) == Rational(14, 3)
+
+    g = Piecewise(((x - 5)**5, x >= 4), (f, True))
+    assert integrate(g, (x, -2, 2)) == Rational(14, 3)
+    assert integrate(g, (x, -2, 5)) == Rational(43, 6)
+
+    assert g == Piecewise(((x - 5)**5, x >= 4), (f, x < 4))
+
+    g = Piecewise(((x - 5)**5, 2 <= x), (f, x < 2))
+    assert integrate(g, (x, -2, 2)) == Rational(14, 3)
+    assert integrate(g, (x, -2, 5)) == Rational(-701, 6)
+
+    assert g == Piecewise(((x - 5)**5, 2 <= x), (f, True))
+
+    g = Piecewise(((x - 5)**5, 2 <= x), (2*f, True))
+    assert integrate(g, (x, -2, 2)) == Rational(28, 3)
+    assert integrate(g, (x, -2, 5)) == Rational(-673, 6)
+
+
+def test_piecewise_integrate1b():
+    g = Piecewise((1, x > 0), (0, Eq(x, 0)), (-1, x < 0))
+    assert integrate(g, (x, -1, 1)) == 0
+
+    g = Piecewise((1, x - y < 0), (0, True))
+    assert integrate(g, (y, -oo, 0)) == -Min(0, x)
+    assert g.subs(x, -3).integrate((y, -oo, 0)) == 3
+    assert integrate(g, (y, 0, -oo)) == Min(0, x)
+    assert integrate(g, (y, 0, oo)) == -Max(0, x) + oo
+    assert integrate(g, (y, -oo, 42)) == -Min(42, x) + 42
+    assert integrate(g, (y, -oo, oo)) == -x + oo
+
+    g = Piecewise((0, x < 0), (x, x <= 1), (1, True))
+    gy1 = g.integrate((x, y, 1))
+    g1y = g.integrate((x, 1, y))
+    for yy in (-1, S.Half, 2):
+        assert g.integrate((x, yy, 1)) == gy1.subs(y, yy)
+        assert g.integrate((x, 1, yy)) == g1y.subs(y, yy)
+    assert gy1 == Piecewise(
+        (-Min(1, Max(0, y))**2/2 + S.Half, y < 1),
+        (-y + 1, True))
+    assert g1y == Piecewise(
+        (Min(1, Max(0, y))**2/2 - S.Half, y < 1),
+        (y - 1, True))
+
+
+@slow
+def test_piecewise_integrate1ca():
+    y = symbols('y', real=True)
+    g = Piecewise(
+        (1 - x, Interval(0, 1).contains(x)),
+        (1 + x, Interval(-1, 0).contains(x)),
+        (0, True)
+        )
+    gy1 = g.integrate((x, y, 1))
+    g1y = g.integrate((x, 1, y))
+
+    assert g.integrate((x, -2, 1)) == gy1.subs(y, -2)
+    assert g.integrate((x, 1, -2)) == g1y.subs(y, -2)
+    assert g.integrate((x, 0, 1)) == gy1.subs(y, 0)
+    assert g.integrate((x, 1, 0)) == g1y.subs(y, 0)
+    assert g.integrate((x, 2, 1)) == gy1.subs(y, 2)
+    assert g.integrate((x, 1, 2)) == g1y.subs(y, 2)
+    assert piecewise_fold(gy1.rewrite(Piecewise)
+        ).simplify() == Piecewise(
+            (1, y <= -1),
+            (-y**2/2 - y + S.Half, y <= 0),
+            (y**2/2 - y + S.Half, y < 1),
+            (0, True))
+    assert piecewise_fold(g1y.rewrite(Piecewise)
+        ).simplify() == Piecewise(
+            (-1, y <= -1),
+            (y**2/2 + y - S.Half, y <= 0),
+            (-y**2/2 + y - S.Half, y < 1),
+            (0, True))
+    assert gy1 == Piecewise(
+        (
+            -Min(1, Max(-1, y))**2/2 - Min(1, Max(-1, y)) +
+            Min(1, Max(0, y))**2 + S.Half, y < 1),
+        (0, True)
+        )
+    assert g1y == Piecewise(
+        (
+            Min(1, Max(-1, y))**2/2 + Min(1, Max(-1, y)) -
+            Min(1, Max(0, y))**2 - S.Half, y < 1),
+        (0, True))
+
+
+@slow
+def test_piecewise_integrate1cb():
+    y = symbols('y', real=True)
+    g = Piecewise(
+        (0, Or(x <= -1, x >= 1)),
+        (1 - x, x > 0),
+        (1 + x, True)
+        )
+    gy1 = g.integrate((x, y, 1))
+    g1y = g.integrate((x, 1, y))
+
+    assert g.integrate((x, -2, 1)) == gy1.subs(y, -2)
+    assert g.integrate((x, 1, -2)) == g1y.subs(y, -2)
+    assert g.integrate((x, 0, 1)) == gy1.subs(y, 0)
+    assert g.integrate((x, 1, 0)) == g1y.subs(y, 0)
+    assert g.integrate((x, 2, 1)) == gy1.subs(y, 2)
+    assert g.integrate((x, 1, 2)) == g1y.subs(y, 2)
+
+    assert piecewise_fold(gy1.rewrite(Piecewise)
+        ).simplify() == Piecewise(
+            (1, y <= -1),
+            (-y**2/2 - y + S.Half, y <= 0),
+            (y**2/2 - y + S.Half, y < 1),
+            (0, True))
+    assert piecewise_fold(g1y.rewrite(Piecewise)
+        ).simplify() == Piecewise(
+            (-1, y <= -1),
+            (y**2/2 + y - S.Half, y <= 0),
+            (-y**2/2 + y - S.Half, y < 1),
+            (0, True))
+
+    # g1y and gy1 should simplify if the condition that y < 1
+    # is applied, e.g. Min(1, Max(-1, y)) --> Max(-1, y)
+    assert gy1 == Piecewise(
+        (
+            -Min(1, Max(-1, y))**2/2 - Min(1, Max(-1, y)) +
+            Min(1, Max(0, y))**2 + S.Half, y < 1),
+        (0, True)
+        )
+    assert g1y == Piecewise(
+        (
+            Min(1, Max(-1, y))**2/2 + Min(1, Max(-1, y)) -
+            Min(1, Max(0, y))**2 - S.Half, y < 1),
+        (0, True))
+
+
+def test_piecewise_integrate2():
+    from itertools import permutations
+    lim = Tuple(x, c, d)
+    p = Piecewise((1, x < a), (2, x > b), (3, True))
+    q = p.integrate(lim)
+    assert q == Piecewise(
+        (-c + 2*d - 2*Min(d, Max(a, c)) + Min(d, Max(a, b, c)), c < d),
+        (-2*c + d + 2*Min(c, Max(a, d)) - Min(c, Max(a, b, d)), True))
+    for v in permutations((1, 2, 3, 4)):
+        r = dict(zip((a, b, c, d), v))
+        assert p.subs(r).integrate(lim.subs(r)) == q.subs(r)
+
+
+def test_meijer_bypass():
+    # totally bypass meijerg machinery when dealing
+    # with Piecewise in integrate
+    assert Piecewise((1, x < 4), (0, True)).integrate((x, oo, 1)) == -3
+
+
+def test_piecewise_integrate3_inequality_conditions():
+    from sympy.utilities.iterables import cartes
+    lim = (x, 0, 5)
+    # set below includes two pts below range, 2 pts in range,
+    # 2 pts above range, and the boundaries
+    N = (-2, -1, 0, 1, 2, 5, 6, 7)
+
+    p = Piecewise((1, x > a), (2, x > b), (0, True))
+    ans = p.integrate(lim)
+    for i, j in cartes(N, repeat=2):
+        reps = dict(zip((a, b), (i, j)))
+        assert ans.subs(reps) == p.subs(reps).integrate(lim)
+    assert ans.subs(a, 4).subs(b, 1) == 0 + 2*3 + 1
+
+    p = Piecewise((1, x > a), (2, x < b), (0, True))
+    ans = p.integrate(lim)
+    for i, j in cartes(N, repeat=2):
+        reps = dict(zip((a, b), (i, j)))
+        assert ans.subs(reps) == p.subs(reps).integrate(lim)
+
+    # delete old tests that involved c1 and c2 since those
+    # reduce to the above except that a value of 0 was used
+    # for two expressions whereas the above uses 3 different
+    # values
+
+
+@slow
+def test_piecewise_integrate4_symbolic_conditions():
+    a = Symbol('a', real=True)
+    b = Symbol('b', real=True)
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    p0 = Piecewise((0, Or(x < a, x > b)), (1, True))
+    p1 = Piecewise((0, x < a), (0, x > b), (1, True))
+    p2 = Piecewise((0, x > b), (0, x < a), (1, True))
+    p3 = Piecewise((0, x < a), (1, x < b), (0, True))
+    p4 = Piecewise((0, x > b), (1, x > a), (0, True))
+    p5 = Piecewise((1, And(a < x, x < b)), (0, True))
+
+    # check values of a=1, b=3 (and reversed) with values
+    # of y of 0, 1, 2, 3, 4
+    lim = Tuple(x, -oo, y)
+    for p in (p0, p1, p2, p3, p4, p5):
+        ans = p.integrate(lim)
+        for i in range(5):
+            reps = {a:1, b:3, y:i}
+            assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps))
+            reps = {a: 3, b:1, y:i}
+            assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps))
+    lim = Tuple(x, y, oo)
+    for p in (p0, p1, p2, p3, p4, p5):
+        ans = p.integrate(lim)
+        for i in range(5):
+            reps = {a:1, b:3, y:i}
+            assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps))
+            reps = {a:3, b:1, y:i}
+            assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps))
+
+    ans = Piecewise(
+        (0, x <= Min(a, b)),
+        (x - Min(a, b), x <= b),
+        (b - Min(a, b), True))
+    for i in (p0, p1, p2, p4):
+        assert i.integrate(x) == ans
+    assert p3.integrate(x) == Piecewise(
+        (0, x < a),
+        (-a + x, x <= Max(a, b)),
+        (-a + Max(a, b), True))
+    assert p5.integrate(x) == Piecewise(
+        (0, x <= a),
+        (-a + x, x <= Max(a, b)),
+        (-a + Max(a, b), True))
+
+    p1 = Piecewise((0, x < a), (S.Half, x > b), (1, True))
+    p2 = Piecewise((S.Half, x > b), (0, x < a), (1, True))
+    p3 = Piecewise((0, x < a), (1, x < b), (S.Half, True))
+    p4 = Piecewise((S.Half, x > b), (1, x > a), (0, True))
+    p5 = Piecewise((1, And(a < x, x < b)), (S.Half, x > b), (0, True))
+
+    # check values of a=1, b=3 (and reversed) with values
+    # of y of 0, 1, 2, 3, 4
+    lim = Tuple(x, -oo, y)
+    for p in (p1, p2, p3, p4, p5):
+        ans = p.integrate(lim)
+        for i in range(5):
+            reps = {a:1, b:3, y:i}
+            assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps))
+            reps = {a: 3, b:1, y:i}
+            assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps))
+
+
+def test_piecewise_integrate5_independent_conditions():
+    p = Piecewise((0, Eq(y, 0)), (x*y, True))
+    assert integrate(p, (x, 1, 3)) == Piecewise((0, Eq(y, 0)), (4*y, True))
+
+
+def test_issue_22917():
+    p = (Piecewise((0, ITE((x - y > 1) | (2 * x - 2 * y > 1), False,
+                           ITE(x - y > 1, 2 * y - 2 < -1, 2 * x - 2 * y > 1))),
+                   (Piecewise((0, ITE(x - y > 1, True, 2 * x - 2 * y > 1)),
+                              (2 * Piecewise((0, x - y > 1), (y, True)), True)), True))
+         + 2 * Piecewise((1, ITE((x - y > 1) | (2 * x - 2 * y > 1), False,
+                                 ITE(x - y > 1, 2 * y - 2 < -1, 2 * x - 2 * y > 1))),
+                         (Piecewise((1, ITE(x - y > 1, True, 2 * x - 2 * y > 1)),
+                                    (2 * Piecewise((1, x - y > 1), (x, True)), True)), True)))
+    assert piecewise_fold(p) == Piecewise((2, (x - y > S.Half) | (x - y > 1)),
+                                          (2*y + 4, x - y > 1),
+                                          (4*x + 2*y, True))
+    assert piecewise_fold(p > 1).rewrite(ITE) == ITE((x - y > S.Half) | (x - y > 1), True,
+                                                     ITE(x - y > 1, 2*y + 4 > 1, 4*x + 2*y > 1))
+
+
+def test_piecewise_simplify():
+    p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
+                  ((-1)**x*(-1), True))
+    assert p.simplify() == \
+        Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
+    # simplify when there are Eq in conditions
+    assert Piecewise(
+        (a, And(Eq(a, 0), Eq(a + b, 0))), (1, True)).simplify(
+        ) == Piecewise(
+        (0, And(Eq(a, 0), Eq(b, 0))), (1, True))
+    assert Piecewise((2*x*factorial(a)/(factorial(y)*factorial(-y + a)),
+        Eq(y, 0) & Eq(-y + a, 0)), (2*factorial(a)/(factorial(y)*factorial(-y
+        + a)), Eq(y, 0) & Eq(-y + a, 1)), (0, True)).simplify(
+        ) == Piecewise(
+            (2*x, And(Eq(a, 0), Eq(y, 0))),
+            (2, And(Eq(a, 1), Eq(y, 0))),
+            (0, True))
+    args = (2, And(Eq(x, 2), Ge(y, 0))), (x, True)
+    assert Piecewise(*args).simplify() == Piecewise(*args)
+    args = (1, Eq(x, 0)), (sin(x)/x, True)
+    assert Piecewise(*args).simplify() == Piecewise(*args)
+    assert Piecewise((2 + y, And(Eq(x, 2), Eq(y, 0))), (x, True)
+        ).simplify() == x
+    # check that x or f(x) are recognized as being Symbol-like for lhs
+    args = Tuple((1, Eq(x, 0)), (sin(x) + 1 + x, True))
+    ans = x + sin(x) + 1
+    f = Function('f')
+    assert Piecewise(*args).simplify() == ans
+    assert Piecewise(*args.subs(x, f(x))).simplify() == ans.subs(x, f(x))
+
+    # issue 18634
+    d = Symbol("d", integer=True)
+    n = Symbol("n", integer=True)
+    t = Symbol("t", positive=True)
+    expr = Piecewise((-d + 2*n, Eq(1/t, 1)), (t**(1 - 4*n)*t**(4*n - 1)*(-d + 2*n), True))
+    assert expr.simplify() == -d + 2*n
+
+    # issue 22747
+    p = Piecewise((0, (t < -2) & (t < -1) & (t < 0)), ((t/2 + 1)*(t +
+        1)*(t + 2), (t < -1) & (t < 0)), ((S.Half - t/2)*(1 - t)*(t + 1),
+        (t < -2) & (t < -1) & (t < 1)), ((t + 1)*(-t*(t/2 + 1) + (S.Half
+        - t/2)*(1 - t)), (t < -2) & (t < -1) & (t < 0) & (t < 1)), ((t +
+        1)*((S.Half - t/2)*(1 - t) + (t/2 + 1)*(t + 2)), (t < -1) & (t <
+        1)), ((t + 1)*(-t*(t/2 + 1) + (S.Half - t/2)*(1 - t)), (t < -1) &
+        (t < 0) & (t < 1)), (0, (t < -2) & (t < -1)), ((t/2 + 1)*(t +
+        1)*(t + 2), t < -1), ((t + 1)*(-t*(t/2 + 1) + (S.Half - t/2)*(t +
+        1)), (t < 0) & ((t < -2) | (t < 0))), ((S.Half - t/2)*(1 - t)*(t
+        + 1), (t < 1) & ((t < -2) | (t < 1))), (0, True)) + Piecewise((0,
+        (t < -1) & (t < 0) & (t < 1)), ((1 - t)*(t/2 + S.Half)*(t + 1),
+        (t < 0) & (t < 1)), ((1 - t)*(1 - t/2)*(2 - t), (t < -1) & (t <
+        0) & (t < 2)), ((1 - t)*((1 - t)*(t/2 + S.Half) + (1 - t/2)*(2 -
+        t)), (t < -1) & (t < 0) & (t < 1) & (t < 2)), ((1 - t)*((1 -
+        t/2)*(2 - t) + (t/2 + S.Half)*(t + 1)), (t < 0) & (t < 2)), ((1 -
+        t)*((1 - t)*(t/2 + S.Half) + (1 - t/2)*(2 - t)), (t < 0) & (t <
+        1) & (t < 2)), (0, (t < -1) & (t < 0)), ((1 - t)*(t/2 +
+        S.Half)*(t + 1), t < 0), ((1 - t)*(t*(1 - t/2) + (1 - t)*(t/2 +
+        S.Half)), (t < 1) & ((t < -1) | (t < 1))), ((1 - t)*(1 - t/2)*(2
+        - t), (t < 2) & ((t < -1) | (t < 2))), (0, True))
+    assert p.simplify() == Piecewise(
+        (0, t < -2), ((t + 1)*(t + 2)**2/2, t < -1), (-3*t**3/2
+        - 5*t**2/2 + 1, t < 0), (3*t**3/2 - 5*t**2/2 + 1, t < 1), ((1 -
+        t)*(t - 2)**2/2, t < 2), (0, True))
+
+    # coverage
+    nan = Undefined
+    assert Piecewise((1, x > 3), (2, x < 2), (3, x > 1)).simplify(
+        )  == Piecewise((1, x > 3), (2, x < 2), (3, True))
+    assert Piecewise((1, x < 2), (2, x < 1), (3, True)).simplify(
+        ) == Piecewise((1, x < 2), (3, True))
+    assert Piecewise((1, x > 2)).simplify() == Piecewise((1, x > 2),
+        (nan, True))
+    assert Piecewise((1, (x >= 2) & (x < oo))
+        ).simplify() == Piecewise((1, (x >= 2) & (x < oo)), (nan, True))
+    assert Piecewise((1, x < 2), (2, (x > 1) & (x < 3)), (3, True)
+        ). simplify() == Piecewise((1, x < 2), (2, x < 3), (3, True))
+    assert Piecewise((1, x < 2), (2, (x <= 3) & (x > 1)), (3, True)
+        ).simplify() == Piecewise((1, x < 2), (2, x <= 3), (3, True))
+    assert Piecewise((1, x < 2), (2, (x > 2) & (x < 3)), (3, True)
+        ).simplify() == Piecewise((1, x < 2), (2, (x > 2) & (x < 3)),
+        (3, True))
+    assert Piecewise((1, x < 2), (2, (x >= 1) & (x <= 3)), (3, True)
+        ).simplify() == Piecewise((1, x < 2), (2, x <= 3), (3, True))
+    assert Piecewise((1, x < 1), (2, (x >= 2) & (x <= 3)), (3, True)
+        ).simplify() == Piecewise((1, x < 1), (2, (x >= 2) & (x <= 3)),
+        (3, True))
+    # https://github.com/sympy/sympy/issues/25603
+    assert Piecewise((log(x), (x <= 5) & (x > 3)), (x, True)
+        ).simplify() == Piecewise((log(x), (x <= 5) & (x > 3)), (x, True))
+
+    assert Piecewise((1, (x >= 1) & (x < 3)), (2, (x > 2) & (x < 4))
+        ).simplify() == Piecewise((1, (x >= 1) & (x < 3)), (
+        2, (x >= 3) & (x < 4)), (nan, True))
+    assert Piecewise((1, (x >= 1) & (x <= 3)), (2, (x > 2) & (x < 4))
+        ).simplify() == Piecewise((1, (x >= 1) & (x <= 3)), (
+        2, (x > 3) & (x < 4)), (nan, True))
+
+    # involves a symbolic range so cset.inf fails
+    L = Symbol('L', nonnegative=True)
+    p = Piecewise((nan, x <= 0), (0, (x >= 0) & (L > x) & (L - x <= 0)),
+        (x - L/2, (L > x) & (L - x <= 0)),
+        (L/2 - x, (x >= 0) & (L > x)),
+        (0, L > x), (nan, True))
+    assert p.simplify() == Piecewise(
+        (nan, x <= 0), (L/2 - x, L > x), (nan, True))
+    assert p.subs(L, y).simplify() == Piecewise(
+        (nan, x <= 0), (-x + y/2, x < Max(0, y)), (0, x < y), (nan, True))
+
+
+def test_piecewise_solve():
+    abs2 = Piecewise((-x, x <= 0), (x, x > 0))
+    f = abs2.subs(x, x - 2)
+    assert solve(f, x) == [2]
+    assert solve(f - 1, x) == [1, 3]
+
+    f = Piecewise(((x - 2)**2, x >= 0), (1, True))
+    assert solve(f, x) == [2]
+
+    g = Piecewise(((x - 5)**5, x >= 4), (f, True))
+    assert solve(g, x) == [2, 5]
+
+    g = Piecewise(((x - 5)**5, x >= 4), (f, x < 4))
+    assert solve(g, x) == [2, 5]
+
+    g = Piecewise(((x - 5)**5, x >= 2), (f, x < 2))
+    assert solve(g, x) == [5]
+
+    g = Piecewise(((x - 5)**5, x >= 2), (f, True))
+    assert solve(g, x) == [5]
+
+    g = Piecewise(((x - 5)**5, x >= 2), (f, True), (10, False))
+    assert solve(g, x) == [5]
+
+    g = Piecewise(((x - 5)**5, x >= 2),
+                  (-x + 2, x - 2 <= 0), (x - 2, x - 2 > 0))
+    assert solve(g, x) == [5]
+
+    # if no symbol is given the piecewise detection must still work
+    assert solve(Piecewise((x - 2, x > 2), (2 - x, True)) - 3) == [-1, 5]
+
+    f = Piecewise(((x - 2)**2, x >= 0), (0, True))
+    raises(NotImplementedError, lambda: solve(f, x))
+
+    def nona(ans):
+        return list(filter(lambda x: x is not S.NaN, ans))
+    p = Piecewise((x**2 - 4, x < y), (x - 2, True))
+    ans = solve(p, x)
+    assert nona([i.subs(y, -2) for i in ans]) == [2]
+    assert nona([i.subs(y, 2) for i in ans]) == [-2, 2]
+    assert nona([i.subs(y, 3) for i in ans]) == [-2, 2]
+    assert ans == [
+        Piecewise((-2, y > -2), (S.NaN, True)),
+        Piecewise((2, y <= 2), (S.NaN, True)),
+        Piecewise((2, y > 2), (S.NaN, True))]
+
+    # issue 6060
+    absxm3 = Piecewise(
+        (x - 3, 0 <= x - 3),
+        (3 - x, 0 > x - 3)
+    )
+    assert solve(absxm3 - y, x) == [
+        Piecewise((-y + 3, -y < 0), (S.NaN, True)),
+        Piecewise((y + 3, y >= 0), (S.NaN, True))]
+    p = Symbol('p', positive=True)
+    assert solve(absxm3 - p, x) == [-p + 3, p + 3]
+
+    # issue 6989
+    f = Function('f')
+    assert solve(Eq(-f(x), Piecewise((1, x > 0), (0, True))), f(x)) == \
+        [Piecewise((-1, x > 0), (0, True))]
+
+    # issue 8587
+    f = Piecewise((2*x**2, And(0 < x, x < 1)), (2, True))
+    assert solve(f - 1) == [1/sqrt(2)]
+
+
+def test_piecewise_fold():
+    p = Piecewise((x, x < 1), (1, 1 <= x))
+
+    assert piecewise_fold(x*p) == Piecewise((x**2, x < 1), (x, 1 <= x))
+    assert piecewise_fold(p + p) == Piecewise((2*x, x < 1), (2, 1 <= x))
+    assert piecewise_fold(Piecewise((1, x < 0), (2, True))
+                          + Piecewise((10, x < 0), (-10, True))) == \
+        Piecewise((11, x < 0), (-8, True))
+
+    p1 = Piecewise((0, x < 0), (x, x <= 1), (0, True))
+    p2 = Piecewise((0, x < 0), (1 - x, x <= 1), (0, True))
+
+    p = 4*p1 + 2*p2
+    assert integrate(
+        piecewise_fold(p), (x, -oo, oo)) == integrate(2*x + 2, (x, 0, 1))
+
+    assert piecewise_fold(
+        Piecewise((1, y <= 0), (-Piecewise((2, y >= 0)), True)
+        )) == Piecewise((1, y <= 0), (-2, y >= 0))
+
+    assert piecewise_fold(Piecewise((x, ITE(x > 0, y < 1, y > 1)))
+        ) == Piecewise((x, ((x <= 0) | (y < 1)) & ((x > 0) | (y > 1))))
+
+    a, b = (Piecewise((2, Eq(x, 0)), (0, True)),
+        Piecewise((x, Eq(-x + y, 0)), (1, Eq(-x + y, 1)), (0, True)))
+    assert piecewise_fold(Mul(a, b, evaluate=False)
+        ) == piecewise_fold(Mul(b, a, evaluate=False))
+
+
+def test_piecewise_fold_piecewise_in_cond():
+    p1 = Piecewise((cos(x), x < 0), (0, True))
+    p2 = Piecewise((0, Eq(p1, 0)), (p1 / Abs(p1), True))
+    assert p2.subs(x, -pi/2) == 0
+    assert p2.subs(x, 1) == 0
+    assert p2.subs(x, -pi/4) == 1
+    p4 = Piecewise((0, Eq(p1, 0)), (1,True))
+    ans = piecewise_fold(p4)
+    for i in range(-1, 1):
+        assert ans.subs(x, i) == p4.subs(x, i)
+
+    r1 = 1 < Piecewise((1, x < 1), (3, True))
+    ans = piecewise_fold(r1)
+    for i in range(2):
+        assert ans.subs(x, i) == r1.subs(x, i)
+
+    p5 = Piecewise((1, x < 0), (3, True))
+    p6 = Piecewise((1, x < 1), (3, True))
+    p7 = Piecewise((1, p5 < p6), (0, True))
+    ans = piecewise_fold(p7)
+    for i in range(-1, 2):
+        assert ans.subs(x, i) == p7.subs(x, i)
+
+
+def test_piecewise_fold_piecewise_in_cond_2():
+    p1 = Piecewise((cos(x), x < 0), (0, True))
+    p2 = Piecewise((0, Eq(p1, 0)), (1 / p1, True))
+    p3 = Piecewise(
+        (0, (x >= 0) | Eq(cos(x), 0)),
+        (1/cos(x), x < 0),
+        (zoo, True))  # redundant b/c all x are already covered
+    assert(piecewise_fold(p2) == p3)
+
+
+def test_piecewise_fold_expand():
+    p1 = Piecewise((1, Interval(0, 1, False, True).contains(x)), (0, True))
+
+    p2 = piecewise_fold(expand((1 - x)*p1))
+    cond = ((x >= 0) & (x < 1))
+    assert piecewise_fold(expand((1 - x)*p1), evaluate=False
+        ) == Piecewise((1 - x, cond), (-x, cond), (1, cond), (0, True), evaluate=False)
+    assert piecewise_fold(expand((1 - x)*p1), evaluate=None
+        ) == Piecewise((1 - x, cond), (0, True))
+    assert p2 == Piecewise((1 - x, cond), (0, True))
+    assert p2 == expand(piecewise_fold((1 - x)*p1))
+
+
+def test_piecewise_duplicate():
+    p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x))
+    assert p == Piecewise(*p.args)
+
+
+def test_doit():
+    p1 = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
+    p2 = Piecewise((x, x < 1), (Integral(2 * x), -1 <= x), (x, 3 < x))
+    assert p2.doit() == p1
+    assert p2.doit(deep=False) == p2
+    # issue 17165
+    p1 = Sum(y**x, (x, -1, oo)).doit()
+    assert p1.doit() == p1
+
+
+def test_piecewise_interval():
+    p1 = Piecewise((x, Interval(0, 1).contains(x)), (0, True))
+    assert p1.subs(x, -0.5) == 0
+    assert p1.subs(x, 0.5) == 0.5
+    assert p1.diff(x) == Piecewise((1, Interval(0, 1).contains(x)), (0, True))
+    assert integrate(p1, x) == Piecewise(
+        (0, x <= 0),
+        (x**2/2, x <= 1),
+        (S.Half, True))
+
+
+def test_piecewise_exclusive():
+    p = Piecewise((0, x < 0), (S.Half, x <= 0), (1, True))
+    assert piecewise_exclusive(p) == Piecewise((0, x < 0), (S.Half, Eq(x, 0)),
+                                               (1, x > 0), evaluate=False)
+    assert piecewise_exclusive(p + 2) == Piecewise((0, x < 0), (S.Half, Eq(x, 0)),
+                                               (1, x > 0), evaluate=False) + 2
+    assert piecewise_exclusive(Piecewise((1, y <= 0),
+                                         (-Piecewise((2, y >= 0)), True))) == \
+        Piecewise((1, y <= 0),
+                  (-Piecewise((2, y >= 0),
+                              (S.NaN, y < 0), evaluate=False), y > 0), evaluate=False)
+    assert piecewise_exclusive(Piecewise((1, x > y))) == Piecewise((1, x > y),
+                                                                  (S.NaN, x <= y),
+                                                                  evaluate=False)
+    assert piecewise_exclusive(Piecewise((1, x > y)),
+                               skip_nan=True) == Piecewise((1, x > y))
+
+    xr, yr = symbols('xr, yr', real=True)
+
+    p1 = Piecewise((1, xr < 0), (2, True), evaluate=False)
+    p1x = Piecewise((1, xr < 0), (2, xr >= 0), evaluate=False)
+
+    p2 = Piecewise((p1, yr < 0), (3, True), evaluate=False)
+    p2x = Piecewise((p1, yr < 0), (3, yr >= 0), evaluate=False)
+    p2xx = Piecewise((p1x, yr < 0), (3, yr >= 0), evaluate=False)
+
+    assert piecewise_exclusive(p2) == p2xx
+    assert piecewise_exclusive(p2, deep=False) == p2x
+
+
+def test_piecewise_collapse():
+    assert Piecewise((x, True)) == x
+    a = x < 1
+    assert Piecewise((x, a), (x + 1, a)) == Piecewise((x, a))
+    assert Piecewise((x, a), (x + 1, a.reversed)) == Piecewise((x, a))
+    b = x < 5
+    def canonical(i):
+        if isinstance(i, Piecewise):
+            return Piecewise(*i.args)
+        return i
+    for args in [
+        ((1, a), (Piecewise((2, a), (3, b)), b)),
+        ((1, a), (Piecewise((2, a), (3, b.reversed)), b)),
+        ((1, a), (Piecewise((2, a), (3, b)), b), (4, True)),
+        ((1, a), (Piecewise((2, a), (3, b), (4, True)), b)),
+        ((1, a), (Piecewise((2, a), (3, b), (4, True)), b), (5, True))]:
+        for i in (0, 2, 10):
+            assert canonical(
+                Piecewise(*args, evaluate=False).subs(x, i)
+                ) == canonical(Piecewise(*args).subs(x, i))
+    r1, r2, r3, r4 = symbols('r1:5')
+    a = x < r1
+    b = x < r2
+    c = x < r3
+    d = x < r4
+    assert Piecewise((1, a), (Piecewise(
+        (2, a), (3, b), (4, c)), b), (5, c)
+        ) == Piecewise((1, a), (3, b), (5, c))
+    assert Piecewise((1, a), (Piecewise(
+        (2, a), (3, b), (4, c), (6, True)), c), (5, d)
+        ) == Piecewise((1, a), (Piecewise(
+        (3, b), (4, c)), c), (5, d))
+    assert Piecewise((1, Or(a, d)), (Piecewise(
+        (2, d), (3, b), (4, c)), b), (5, c)
+        ) == Piecewise((1, Or(a, d)), (Piecewise(
+        (2, d), (3, b)), b), (5, c))
+    assert Piecewise((1, c), (2, ~c), (3, S.true)
+        ) == Piecewise((1, c), (2, S.true))
+    assert Piecewise((1, c), (2, And(~c, b)), (3,True)
+        ) == Piecewise((1, c), (2, b), (3, True))
+    assert Piecewise((1, c), (2, Or(~c, b)), (3,True)
+        ).subs(dict(zip((r1, r2, r3, r4, x), (1, 2, 3, 4, 3.5))))  == 2
+    assert Piecewise((1, c), (2, ~c)) == Piecewise((1, c), (2, True))
+
+
+def test_piecewise_lambdify():
+    p = Piecewise(
+        (x**2, x < 0),
+        (x, Interval(0, 1, False, True).contains(x)),
+        (2 - x, x >= 1),
+        (0, True)
+    )
+
+    f = lambdify(x, p)
+    assert f(-2.0) == 4.0
+    assert f(0.0) == 0.0
+    assert f(0.5) == 0.5
+    assert f(2.0) == 0.0
+
+
+def test_piecewise_series():
+    from sympy.series.order import O
+    p1 = Piecewise((sin(x), x < 0), (cos(x), x > 0))
+    p2 = Piecewise((x + O(x**2), x < 0), (1 + O(x**2), x > 0))
+    assert p1.nseries(x, n=2) == p2
+
+
+def test_piecewise_as_leading_term():
+    p1 = Piecewise((1/x, x > 1), (0, True))
+    p2 = Piecewise((x, x > 1), (0, True))
+    p3 = Piecewise((1/x, x > 1), (x, True))
+    p4 = Piecewise((x, x > 1), (1/x, True))
+    p5 = Piecewise((1/x, x > 1), (x, True))
+    p6 = Piecewise((1/x, x < 1), (x, True))
+    p7 = Piecewise((x, x < 1), (1/x, True))
+    p8 = Piecewise((x, x > 1), (1/x, True))
+    assert p1.as_leading_term(x) == 0
+    assert p2.as_leading_term(x) == 0
+    assert p3.as_leading_term(x) == x
+    assert p4.as_leading_term(x) == 1/x
+    assert p5.as_leading_term(x) == x
+    assert p6.as_leading_term(x) == 1/x
+    assert p7.as_leading_term(x) == x
+    assert p8.as_leading_term(x) == 1/x
+
+
+def test_piecewise_complex():
+    p1 = Piecewise((2, x < 0), (1, 0 <= x))
+    p2 = Piecewise((2*I, x < 0), (I, 0 <= x))
+    p3 = Piecewise((I*x, x > 1), (1 + I, True))
+    p4 = Piecewise((-I*conjugate(x), x > 1), (1 - I, True))
+
+    assert conjugate(p1) == p1
+    assert conjugate(p2) == piecewise_fold(-p2)
+    assert conjugate(p3) == p4
+
+    assert p1.is_imaginary is False
+    assert p1.is_real is True
+    assert p2.is_imaginary is True
+    assert p2.is_real is False
+    assert p3.is_imaginary is None
+    assert p3.is_real is None
+
+    assert p1.as_real_imag() == (p1, 0)
+    assert p2.as_real_imag() == (0, -I*p2)
+
+
+def test_conjugate_transpose():
+    A, B = symbols("A B", commutative=False)
+    p = Piecewise((A*B**2, x > 0), (A**2*B, True))
+    assert p.adjoint() == \
+        Piecewise((adjoint(A*B**2), x > 0), (adjoint(A**2*B), True))
+    assert p.conjugate() == \
+        Piecewise((conjugate(A*B**2), x > 0), (conjugate(A**2*B), True))
+    assert p.transpose() == \
+        Piecewise((transpose(A*B**2), x > 0), (transpose(A**2*B), True))
+
+
+def test_piecewise_evaluate():
+    assert Piecewise((x, True)) == x
+    assert Piecewise((x, True), evaluate=True) == x
+    assert Piecewise((1, Eq(1, x))).args == ((1, Eq(x, 1)),)
+    assert Piecewise((1, Eq(1, x)), evaluate=False).args == (
+        (1, Eq(1, x)),)
+    # like the additive and multiplicative identities that
+    # cannot be kept in Add/Mul, we also do not keep a single True
+    p = Piecewise((x, True), evaluate=False)
+    assert p == x
+
+
+def test_as_expr_set_pairs():
+    assert Piecewise((x, x > 0), (-x, x <= 0)).as_expr_set_pairs() == \
+        [(x, Interval(0, oo, True, True)), (-x, Interval(-oo, 0))]
+
+    assert Piecewise(((x - 2)**2, x >= 0), (0, True)).as_expr_set_pairs() == \
+        [((x - 2)**2, Interval(0, oo)), (0, Interval(-oo, 0, True, True))]
+
+
+def test_S_srepr_is_identity():
+    p = Piecewise((10, Eq(x, 0)), (12, True))
+    q = S(srepr(p))
+    assert p == q
+
+
+def test_issue_12587():
+    # sort holes into intervals
+    p = Piecewise((1, x > 4), (2, Not((x <= 3) & (x > -1))), (3, True))
+    assert p.integrate((x, -5, 5)) == 23
+    p = Piecewise((1, x > 1), (2, x < y), (3, True))
+    lim = x, -3, 3
+    ans = p.integrate(lim)
+    for i in range(-1, 3):
+        assert ans.subs(y, i) == p.subs(y, i).integrate(lim)
+
+
+def test_issue_11045():
+    assert integrate(1/(x*sqrt(x**2 - 1)), (x, 1, 2)) == pi/3
+
+    # handle And with Or arguments
+    assert Piecewise((1, And(Or(x < 1, x > 3), x < 2)), (0, True)
+        ).integrate((x, 0, 3)) == 1
+
+    # hidden false
+    assert Piecewise((1, x > 1), (2, x > x + 1), (3, True)
+        ).integrate((x, 0, 3)) == 5
+    # targetcond is Eq
+    assert Piecewise((1, x > 1), (2, Eq(1, x)), (3, True)
+        ).integrate((x, 0, 4)) == 6
+    # And has Relational needing to be solved
+    assert Piecewise((1, And(2*x > x + 1, x < 2)), (0, True)
+        ).integrate((x, 0, 3)) == 1
+    # Or has Relational needing to be solved
+    assert Piecewise((1, Or(2*x > x + 2, x < 1)), (0, True)
+        ).integrate((x, 0, 3)) == 2
+    # ignore hidden false (handled in canonicalization)
+    assert Piecewise((1, x > 1), (2, x > x + 1), (3, True)
+        ).integrate((x, 0, 3)) == 5
+    # watch for hidden True Piecewise
+    assert Piecewise((2, Eq(1 - x, x*(1/x - 1))), (0, True)
+        ).integrate((x, 0, 3)) == 6
+
+    # overlapping conditions of targetcond are recognized and ignored;
+    # the condition x > 3 will be pre-empted by the first condition
+    assert Piecewise((1, Or(x < 1, x > 2)), (2, x > 3), (3, True)
+        ).integrate((x, 0, 4)) == 6
+
+    # convert Ne to Or
+    assert Piecewise((1, Ne(x, 0)), (2, True)
+        ).integrate((x, -1, 1)) == 2
+
+    # no default but well defined
+    assert Piecewise((x, (x > 1) & (x < 3)), (1, (x < 4))
+        ).integrate((x, 1, 4)) == 5
+
+    p = Piecewise((x, (x > 1) & (x < 3)), (1, (x < 4)))
+    nan = Undefined
+    i = p.integrate((x, 1, y))
+    assert i == Piecewise(
+        (y - 1, y < 1),
+        (Min(3, y)**2/2 - Min(3, y) + Min(4, y) - S.Half,
+            y <= Min(4, y)),
+        (nan, True))
+    assert p.integrate((x, 1, -1)) == i.subs(y, -1)
+    assert p.integrate((x, 1, 4)) == 5
+    assert p.integrate((x, 1, 5)) is nan
+
+    # handle Not
+    p = Piecewise((1, x > 1), (2, Not(And(x > 1, x< 3))), (3, True))
+    assert p.integrate((x, 0, 3)) == 4
+
+    # handle updating of int_expr when there is overlap
+    p = Piecewise(
+        (1, And(5 > x, x > 1)),
+        (2, Or(x < 3, x > 7)),
+        (4, x < 8))
+    assert p.integrate((x, 0, 10)) == 20
+
+    # And with Eq arg handling
+    assert Piecewise((1, x < 1), (2, And(Eq(x, 3), x > 1))
+        ).integrate((x, 0, 3)) is S.NaN
+    assert Piecewise((1, x < 1), (2, And(Eq(x, 3), x > 1)), (3, True)
+        ).integrate((x, 0, 3)) == 7
+    assert Piecewise((1, x < 0), (2, And(Eq(x, 3), x < 1)), (3, True)
+        ).integrate((x, -1, 1)) == 4
+    # middle condition doesn't matter: it's a zero width interval
+    assert Piecewise((1, x < 1), (2, Eq(x, 3) & (y < x)), (3, True)
+        ).integrate((x, 0, 3)) == 7
+
+
+def test_holes():
+    nan = Undefined
+    assert Piecewise((1, x < 2)).integrate(x) == Piecewise(
+        (x, x < 2), (nan, True))
+    assert Piecewise((1, And(x > 1, x < 2))).integrate(x) == Piecewise(
+        (nan, x < 1), (x, x < 2), (nan, True))
+    assert Piecewise((1, And(x > 1, x < 2))).integrate((x, 0, 3)) is nan
+    assert Piecewise((1, And(x > 0, x < 4))).integrate((x, 1, 3)) == 2
+
+    # this also tests that the integrate method is used on non-Piecwise
+    # arguments in _eval_integral
+    A, B = symbols("A B")
+    a, b = symbols('a b', real=True)
+    assert Piecewise((A, And(x < 0, a < 1)), (B, Or(x < 1, a > 2))
+        ).integrate(x) == Piecewise(
+        (B*x, (a > 2)),
+        (Piecewise((A*x, x < 0), (B*x, x < 1), (nan, True)), a < 1),
+        (Piecewise((B*x, x < 1), (nan, True)), True))
+
+
+def test_issue_11922():
+    def f(x):
+        return Piecewise((0, x < -1), (1 - x**2, x < 1), (0, True))
+    autocorr = lambda k: (
+        f(x) * f(x + k)).integrate((x, -1, 1))
+    assert autocorr(1.9) > 0
+    k = symbols('k')
+    good_autocorr = lambda k: (
+        (1 - x**2) * f(x + k)).integrate((x, -1, 1))
+    a = good_autocorr(k)
+    assert a.subs(k, 3) == 0
+    k = symbols('k', positive=True)
+    a = good_autocorr(k)
+    assert a.subs(k, 3) == 0
+    assert Piecewise((0, x < 1), (10, (x >= 1))
+        ).integrate() == Piecewise((0, x < 1), (10*x - 10, True))
+
+
+def test_issue_5227():
+    f = 0.0032513612725229*Piecewise((0, x < -80.8461538461539),
+        (-0.0160799238820171*x + 1.33215984776403, x < 2),
+        (Piecewise((0.3, x > 123), (0.7, True)) +
+        Piecewise((0.4, x > 2), (0.6, True)), x <=
+        123), (-0.00817409766454352*x + 2.10541401273885, x <
+        380.571428571429), (0, True))
+    i = integrate(f, (x, -oo, oo))
+    assert i == Integral(f, (x, -oo, oo)).doit()
+    assert str(i) == '1.00195081676351'
+    assert Piecewise((1, x - y < 0), (0, True)
+        ).integrate(y) == Piecewise((0, y <= x), (-x + y, True))
+
+
+def test_issue_10137():
+    a = Symbol('a', real=True)
+    b = Symbol('b', real=True)
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    p0 = Piecewise((0, Or(x < a, x > b)), (1, True))
+    p1 = Piecewise((0, Or(a > x, b < x)), (1, True))
+    assert integrate(p0, (x, y, oo)) == integrate(p1, (x, y, oo))
+    p3 = Piecewise((1, And(0 < x, x < a)), (0, True))
+    p4 = Piecewise((1, And(a > x, x > 0)), (0, True))
+    ip3 = integrate(p3, x)
+    assert ip3 == Piecewise(
+        (0, x <= 0),
+        (x, x <= Max(0, a)),
+        (Max(0, a), True))
+    ip4 = integrate(p4, x)
+    assert ip4 == ip3
+    assert p3.integrate((x, 2, 4)) == Min(4, Max(2, a)) - 2
+    assert p4.integrate((x, 2, 4)) == Min(4, Max(2, a)) - 2
+
+
+def test_stackoverflow_43852159():
+    f = lambda x: Piecewise((1, (x >= -1) & (x <= 1)), (0, True))
+    Conv = lambda x: integrate(f(x - y)*f(y), (y, -oo, +oo))
+    cx = Conv(x)
+    assert cx.subs(x, -1.5) == cx.subs(x, 1.5)
+    assert cx.subs(x, 3) == 0
+    assert piecewise_fold(f(x - y)*f(y)) == Piecewise(
+        (1, (y >= -1) & (y <= 1) & (x - y >= -1) & (x - y <= 1)),
+        (0, True))
+
+
+def test_issue_12557():
+    '''
+    # 3200 seconds to compute the fourier part of issue
+    import sympy as sym
+    x,y,z,t = sym.symbols('x y z t')
+    k = sym.symbols("k", integer=True)
+    fourier = sym.fourier_series(sym.cos(k*x)*sym.sqrt(x**2),
+                                 (x, -sym.pi, sym.pi))
+    assert fourier == FourierSeries(
+    sqrt(x**2)*cos(k*x), (x, -pi, pi), (Piecewise((pi**2,
+    Eq(k, 0)), (2*(-1)**k/k**2 - 2/k**2, True))/(2*pi),
+    SeqFormula(Piecewise((pi**2, (Eq(_n, 0) & Eq(k, 0)) | (Eq(_n, 0) &
+    Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) & Eq(k, 0) & Eq(_n, -k)) | (Eq(_n,
+    0) & Eq(_n, k) & Eq(k, 0) & Eq(_n, -k))), (pi**2/2, Eq(_n, k) | Eq(_n,
+    -k) | (Eq(_n, 0) & Eq(_n, k)) | (Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) &
+    Eq(_n, -k)) | (Eq(_n, k) & Eq(_n, -k)) | (Eq(k, 0) & Eq(_n, -k)) |
+    (Eq(_n, 0) & Eq(_n, k) & Eq(_n, -k)) | (Eq(_n, k) & Eq(k, 0) & Eq(_n,
+    -k))), ((-1)**k*pi**2*_n**3*sin(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
+    pi*k**4) - (-1)**k*pi**2*_n**3*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2
+    - pi*k**4) + (-1)**k*pi*_n**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
+    pi*k**4) - (-1)**k*pi*_n**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
+    pi*k**4) - (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(pi*_n**4 -
+    2*pi*_n**2*k**2 + pi*k**4) +
+    (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
+    pi*k**4) + (-1)**k*pi*k**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
+    pi*k**4) - (-1)**k*pi*k**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
+    pi*k**4) - (2*_n**2 + 2*k**2)/(_n**4 - 2*_n**2*k**2 + k**4),
+    True))*cos(_n*x)/pi, (_n, 1, oo)), SeqFormula(0, (_k, 1, oo))))
+    '''
+    x = symbols("x", real=True)
+    k = symbols('k', integer=True, finite=True)
+    abs2 = lambda x: Piecewise((-x, x <= 0), (x, x > 0))
+    assert integrate(abs2(x), (x, -pi, pi)) == pi**2
+    func = cos(k*x)*sqrt(x**2)
+    assert integrate(func, (x, -pi, pi)) == Piecewise(
+        (2*(-1)**k/k**2 - 2/k**2, Ne(k, 0)), (pi**2, True))
+
+def test_issue_6900():
+    from itertools import permutations
+    t0, t1, T, t = symbols('t0, t1 T t')
+    f = Piecewise((0, t < t0), (x, And(t0 <= t, t < t1)), (0, t >= t1))
+    g = f.integrate(t)
+    assert g == Piecewise(
+        (0, t <= t0),
+        (t*x - t0*x, t <= Max(t0, t1)),
+        (-t0*x + x*Max(t0, t1), True))
+    for i in permutations(range(2)):
+        reps = dict(zip((t0,t1), i))
+        for tt in range(-1,3):
+            assert (g.xreplace(reps).subs(t,tt) ==
+                f.xreplace(reps).integrate(t).subs(t,tt))
+    lim = Tuple(t, t0, T)
+    g = f.integrate(lim)
+    ans = Piecewise(
+        (-t0*x + x*Min(T, Max(t0, t1)), T > t0),
+        (0, True))
+    for i in permutations(range(3)):
+        reps = dict(zip((t0,t1,T), i))
+        tru = f.xreplace(reps).integrate(lim.xreplace(reps))
+        assert tru == ans.xreplace(reps)
+    assert g == ans
+
+
+def test_issue_10122():
+    assert solve(abs(x) + abs(x - 1) - 1 > 0, x
+        ) == Or(And(-oo < x, x < S.Zero), And(S.One < x, x < oo))
+
+
+def test_issue_4313():
+    u = Piecewise((0, x <= 0), (1, x >= a), (x/a, True))
+    e = (u - u.subs(x, y))**2/(x - y)**2
+    M = Max(0, a)
+    assert integrate(e,  x).expand() == Piecewise(
+        (Piecewise(
+            (0, x <= 0),
+            (-y**2/(a**2*x - a**2*y) + x/a**2 - 2*y*log(-y)/a**2 +
+                2*y*log(x - y)/a**2 - y/a**2, x <= M),
+            (-y**2/(-a**2*y + a**2*M) + 1/(-y + M) -
+                1/(x - y) - 2*y*log(-y)/a**2 + 2*y*log(-y +
+                M)/a**2 - y/a**2 + M/a**2, True)),
+        ((a <= y) & (y <= 0)) | ((y <= 0) & (y > -oo))),
+        (Piecewise(
+            (-1/(x - y), x <= 0),
+            (-a**2/(a**2*x - a**2*y) + 2*a*y/(a**2*x - a**2*y) -
+                y**2/(a**2*x - a**2*y) + 2*log(-y)/a - 2*log(x - y)/a +
+                2/a + x/a**2 - 2*y*log(-y)/a**2 + 2*y*log(x - y)/a**2 -
+                y/a**2, x <= M),
+            (-a**2/(-a**2*y + a**2*M) + 2*a*y/(-a**2*y +
+                a**2*M) - y**2/(-a**2*y + a**2*M) +
+                2*log(-y)/a - 2*log(-y + M)/a + 2/a -
+                2*y*log(-y)/a**2 + 2*y*log(-y + M)/a**2 -
+                y/a**2 + M/a**2, True)),
+        a <= y),
+        (Piecewise(
+            (-y**2/(a**2*x - a**2*y), x <= 0),
+            (x/a**2 + y/a**2, x <= M),
+            (a**2/(-a**2*y + a**2*M) -
+                a**2/(a**2*x - a**2*y) - 2*a*y/(-a**2*y + a**2*M) +
+                2*a*y/(a**2*x - a**2*y) + y**2/(-a**2*y + a**2*M) -
+                y**2/(a**2*x - a**2*y) + y/a**2 + M/a**2, True)),
+        True))
+
+
+def test__intervals():
+    assert Piecewise((x + 2, Eq(x, 3)))._intervals(x) == (True, [])
+    assert Piecewise(
+        (1, x > x + 1),
+        (Piecewise((1, x < x + 1)), 2*x < 2*x + 1),
+        (1, True))._intervals(x) == (True, [(-oo, oo, 1, 1)])
+    assert Piecewise((1, Ne(x, I)), (0, True))._intervals(x) == (True,
+        [(-oo, oo, 1, 0)])
+    assert Piecewise((-cos(x), sin(x) >= 0), (cos(x), True)
+        )._intervals(x) == (True,
+        [(0, pi, -cos(x), 0), (-oo, oo, cos(x), 1)])
+    # the following tests that duplicates are removed and that non-Eq
+    # generated zero-width intervals are removed
+    assert Piecewise((1, Abs(x**(-2)) > 1), (0, True)
+        )._intervals(x) == (True,
+        [(-1, 0, 1, 0), (0, 1, 1, 0), (-oo, oo, 0, 1)])
+
+
+def test_containment():
+    a, b, c, d, e = [1, 2, 3, 4, 5]
+    p = (Piecewise((d, x > 1), (e, True))*
+        Piecewise((a, Abs(x - 1) < 1), (b, Abs(x - 2) < 2), (c, True)))
+    assert p.integrate(x).diff(x) == Piecewise(
+        (c*e, x <= 0),
+        (a*e, x <= 1),
+        (a*d, x < 2),  # this is what we want to get right
+        (b*d, x < 4),
+        (c*d, True))
+
+
+def test_piecewise_with_DiracDelta():
+    d1 = DiracDelta(x - 1)
+    assert integrate(d1, (x, -oo, oo)) == 1
+    assert integrate(d1, (x, 0, 2)) == 1
+    assert Piecewise((d1, Eq(x, 2)), (0, True)).integrate(x) == 0
+    assert Piecewise((d1, x < 2), (0, True)).integrate(x) == Piecewise(
+        (Heaviside(x - 1), x < 2), (1, True))
+    # TODO raise error if function is discontinuous at limit of
+    # integration, e.g. integrate(d1, (x, -2, 1)) or Piecewise(
+    # (d1, Eq(x, 1)
+
+
+def test_issue_10258():
+    assert Piecewise((0, x < 1), (1, True)).is_zero is None
+    assert Piecewise((-1, x < 1), (1, True)).is_zero is False
+    a = Symbol('a', zero=True)
+    assert Piecewise((0, x < 1), (a, True)).is_zero
+    assert Piecewise((1, x < 1), (a, x < 3)).is_zero is None
+    a = Symbol('a')
+    assert Piecewise((0, x < 1), (a, True)).is_zero is None
+    assert Piecewise((0, x < 1), (1, True)).is_nonzero is None
+    assert Piecewise((1, x < 1), (2, True)).is_nonzero
+    assert Piecewise((0, x < 1), (oo, True)).is_finite is None
+    assert Piecewise((0, x < 1), (1, True)).is_finite
+    b = Basic()
+    assert Piecewise((b, x < 1)).is_finite is None
+
+    # 10258
+    c = Piecewise((1, x < 0), (2, True)) < 3
+    assert c != True
+    assert piecewise_fold(c) == True
+
+
+def test_issue_10087():
+    a, b = Piecewise((x, x > 1), (2, True)), Piecewise((x, x > 3), (3, True))
+    m = a*b
+    f = piecewise_fold(m)
+    for i in (0, 2, 4):
+        assert m.subs(x, i) == f.subs(x, i)
+    m = a + b
+    f = piecewise_fold(m)
+    for i in (0, 2, 4):
+        assert m.subs(x, i) == f.subs(x, i)
+
+
+def test_issue_8919():
+    c = symbols('c:5')
+    x = symbols("x")
+    f1 = Piecewise((c[1], x < 1), (c[2], True))
+    f2 = Piecewise((c[3], x < Rational(1, 3)), (c[4], True))
+    assert integrate(f1*f2, (x, 0, 2)
+        ) == c[1]*c[3]/3 + 2*c[1]*c[4]/3 + c[2]*c[4]
+    f1 = Piecewise((0, x < 1), (2, True))
+    f2 = Piecewise((3, x < 2), (0, True))
+    assert integrate(f1*f2, (x, 0, 3)) == 6
+
+    y = symbols("y", positive=True)
+    a, b, c, x, z = symbols("a,b,c,x,z", real=True)
+    I = Integral(Piecewise(
+        (0, (x >= y) | (x < 0) | (b > c)),
+        (a, True)), (x, 0, z))
+    ans = I.doit()
+    assert ans == Piecewise((0, b > c), (a*Min(y, z) - a*Min(0, z), True))
+    for cond in (True, False):
+        for yy in range(1, 3):
+            for zz in range(-yy, 0, yy):
+                reps = [(b > c, cond), (y, yy), (z, zz)]
+                assert ans.subs(reps) == I.subs(reps).doit()
+
+
+def test_unevaluated_integrals():
+    f = Function('f')
+    p = Piecewise((1, Eq(f(x) - 1, 0)), (2, x - 10 < 0), (0, True))
+    assert p.integrate(x) == Integral(p, x)
+    assert p.integrate((x, 0, 5)) == Integral(p, (x, 0, 5))
+    # test it by replacing f(x) with x%2 which will not
+    # affect the answer: the integrand is essentially 2 over
+    # the domain of integration
+    assert Integral(p, (x, 0, 5)).subs(f(x), x%2).n() == 10.0
+
+    # this is a test of using _solve_inequality when
+    # solve_univariate_inequality fails
+    assert p.integrate(y) == Piecewise(
+        (y, Eq(f(x), 1) | ((x < 10) & Eq(f(x), 1))),
+        (2*y, (x > -oo) & (x < 10)), (0, True))
+
+
+def test_conditions_as_alternate_booleans():
+    a, b, c = symbols('a:c')
+    assert Piecewise((x, Piecewise((y < 1, x > 0), (y > 1, True)))
+        ) == Piecewise((x, ITE(x > 0, y < 1, y > 1)))
+
+
+def test_Piecewise_rewrite_as_ITE():
+    a, b, c, d = symbols('a:d')
+
+    def _ITE(*args):
+        return Piecewise(*args).rewrite(ITE)
+
+    assert _ITE((a, x < 1), (b, x >= 1)) == ITE(x < 1, a, b)
+    assert _ITE((a, x < 1), (b, x < oo)) == ITE(x < 1, a, b)
+    assert _ITE((a, x < 1), (b, Or(y < 1, x < oo)), (c, y > 0)
+               ) == ITE(x < 1, a, b)
+    assert _ITE((a, x < 1), (b, True)) == ITE(x < 1, a, b)
+    assert _ITE((a, x < 1), (b, x < 2), (c, True)
+               ) == ITE(x < 1, a, ITE(x < 2, b, c))
+    assert _ITE((a, x < 1), (b, y < 2), (c, True)
+               ) == ITE(x < 1, a, ITE(y < 2, b, c))
+    assert _ITE((a, x < 1), (b, x < oo), (c, y < 1)
+               ) == ITE(x < 1, a, b)
+    assert _ITE((a, x < 1), (c, y < 1), (b, x < oo), (d, True)
+               ) == ITE(x < 1, a, ITE(y < 1, c, b))
+    assert _ITE((a, x < 0), (b, Or(x < oo, y < 1))
+               ) == ITE(x < 0, a, b)
+    raises(TypeError, lambda: _ITE((x + 1, x < 1), (x, True)))
+    # if `a` in the following were replaced with y then the coverage
+    # is complete but something other than as_set would need to be
+    # used to detect this
+    raises(NotImplementedError, lambda: _ITE((x, x < y), (y, x >= a)))
+    raises(ValueError, lambda: _ITE((a, x < 2), (b, x > 3)))
+
+
+def test_Piecewise_replace_relational_27538():
+    x, y = symbols('x, y')
+    p1 = Piecewise(
+        (0, Eq(x, True)),
+        (1, True),
+    )
+    p2 = p1.xreplace({x: y < 1})
+    assert p2.subs(y, 0) == 0
+    assert p2.subs(y, 1) == 1
+
+
+def test_issue_14052():
+    assert integrate(abs(sin(x)), (x, 0, 2*pi)) == 4
+
+
+def test_issue_14240():
+    assert piecewise_fold(
+        Piecewise((1, a), (2, b), (4, True)) +
+        Piecewise((8, a), (16, True))
+        ) == Piecewise((9, a), (18, b), (20, True))
+    assert piecewise_fold(
+        Piecewise((2, a), (3, b), (5, True)) *
+        Piecewise((7, a), (11, True))
+        ) == Piecewise((14, a), (33, b), (55, True))
+    # these will hang if naive folding is used
+    assert piecewise_fold(Add(*[
+        Piecewise((i, a), (0, True)) for i in range(40)])
+        ) == Piecewise((780, a), (0, True))
+    assert piecewise_fold(Mul(*[
+        Piecewise((i, a), (0, True)) for i in range(1, 41)])
+        ) == Piecewise((factorial(40), a), (0, True))
+
+
+def test_issue_14787():
+    x = Symbol('x')
+    f = Piecewise((x, x < 1), ((S(58) / 7), True))
+    assert str(f.evalf()) == "Piecewise((x, x < 1), (8.28571428571429, True))"
+
+def test_issue_21481():
+    b, e = symbols('b e')
+    C = Piecewise(
+        (2,
+        ((b > 1) & (e > 0)) |
+        ((b > 0) & (b < 1) & (e < 0)) |
+        ((e >= 2) & (b < -1) & Eq(Mod(e, 2), 0)) |
+        ((e <= -2) & (b > -1) & (b < 0) & Eq(Mod(e, 2), 0))),
+        (S.Half,
+        ((b > 1) & (e < 0)) |
+        ((b > 0) & (e > 0) & (b < 1)) |
+        ((e <= -2) & (b < -1) & Eq(Mod(e, 2), 0)) |
+        ((e >= 2) & (b > -1) & (b < 0) & Eq(Mod(e, 2), 0))),
+        (-S.Half,
+        Eq(Mod(e, 2), 1) &
+        (((e <= -1) & (b < -1)) | ((e >= 1) & (b > -1) & (b < 0)))),
+        (-2,
+        ((e >= 1) & (b < -1) & Eq(Mod(e, 2), 1)) |
+        ((e <= -1) & (b > -1) & (b < 0) & Eq(Mod(e, 2), 1)))
+    )
+    A = Piecewise(
+        (1, Eq(b, 1) | Eq(e, 0) | (Eq(b, -1) & Eq(Mod(e, 2), 0))),
+        (0, Eq(b, 0) & (e > 0)),
+        (-1, Eq(b, -1) & Eq(Mod(e, 2), 1)),
+        (C, Eq(im(b), 0) & Eq(im(e), 0))
+    )
+
+    B = piecewise_fold(A)
+    sa = A.simplify()
+    sb = B.simplify()
+    v = (-2, -1, -S.Half, 0, S.Half, 1, 2)
+    for i in v:
+        for j in v:
+            r = {b:i, e:j}
+            ok = [k.xreplace(r) for k in (A, B, sa, sb)]
+            assert len(set(ok)) == 1
+
+
+def test_issue_8458():
+    x, y = symbols('x y')
+    # Original issue
+    p1 = Piecewise((0, Eq(x, 0)), (sin(x), True))
+    assert p1.simplify() == sin(x)
+    # Slightly larger variant
+    p2 = Piecewise((x, Eq(x, 0)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
+    assert p2.simplify() == sin(x)
+    # Test for problem highlighted during review
+    p3 = Piecewise((x+1, Eq(x, -1)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
+    assert p3.simplify() == Piecewise((0, Eq(x, -1)), (sin(x), True))
+
+
+def test_issue_16417():
+    z = Symbol('z')
+    assert unchanged(Piecewise, (1, Or(Eq(im(z), 0), Gt(re(z), 0))), (2, True))
+
+    x = Symbol('x')
+    assert unchanged(Piecewise, (S.Pi, re(x) < 0),
+                 (0, Or(re(x) > 0, Ne(im(x), 0))),
+                 (S.NaN, True))
+    r = Symbol('r', real=True)
+    p = Piecewise((S.Pi, re(r) < 0),
+                 (0, Or(re(r) > 0, Ne(im(r), 0))),
+                 (S.NaN, True))
+    assert p == Piecewise((S.Pi, r < 0),
+                 (0, r > 0),
+                 (S.NaN, True), evaluate=False)
+    # Does not work since imaginary != 0...
+    #i = Symbol('i', imaginary=True)
+    #p = Piecewise((S.Pi, re(i) < 0),
+    #              (0, Or(re(i) > 0, Ne(im(i), 0))),
+    #              (S.NaN, True))
+    #assert p == Piecewise((0, Ne(im(i), 0)),
+    #                      (S.NaN, True), evaluate=False)
+    i = I*r
+    p = Piecewise((S.Pi, re(i) < 0),
+                  (0, Or(re(i) > 0, Ne(im(i), 0))),
+                  (S.NaN, True))
+    assert p == Piecewise((0, Ne(im(i), 0)),
+                          (S.NaN, True), evaluate=False)
+    assert p == Piecewise((0, Ne(r, 0)),
+                          (S.NaN, True), evaluate=False)
+
+
+def test_eval_rewrite_as_KroneckerDelta():
+    x, y, z, n, t, m = symbols('x y z n t m')
+    K = KroneckerDelta
+    f = lambda p: expand(p.rewrite(K))
+
+    p1 = Piecewise((0, Eq(x, y)), (1, True))
+    assert f(p1) == 1 - K(x, y)
+
+    p2 = Piecewise((x, Eq(y,0)), (z, Eq(t,0)), (n, True))
+    assert f(p2) == n*K(0, t)*K(0, y) - n*K(0, t) - n*K(0, y) + n + \
+           x*K(0, y) - z*K(0, t)*K(0, y) + z*K(0, t)
+
+    p3 = Piecewise((1, Ne(x, y)), (0, True))
+    assert f(p3) == 1 - K(x, y)
+
+    p4 = Piecewise((1, Eq(x, 3)), (4, True), (5, True))
+    assert f(p4) == 4 - 3*K(3, x)
+
+    p5 = Piecewise((3, Ne(x, 2)), (4, Eq(y, 2)), (5, True))
+    assert f(p5) == -K(2, x)*K(2, y) + 2*K(2, x) + 3
+
+    p6 = Piecewise((0, Ne(x, 1) & Ne(y, 4)), (1, True))
+    assert f(p6) == -K(1, x)*K(4, y) + K(1, x) + K(4, y)
+
+    p7 = Piecewise((2, Eq(y, 3) & Ne(x, 2)), (1, True))
+    assert f(p7) == -K(2, x)*K(3, y) + K(3, y) + 1
+
+    p8 = Piecewise((4, Eq(x, 3) & Ne(y, 2)), (1, True))
+    assert f(p8) == -3*K(2, y)*K(3, x) + 3*K(3, x) + 1
+
+    p9 = Piecewise((6, Eq(x, 4) & Eq(y, 1)), (1, True))
+    assert f(p9) == 5 * K(1, y) * K(4, x) + 1
+
+    p10 = Piecewise((4, Ne(x, -4) | Ne(y, 1)), (1, True))
+    assert f(p10) == -3 * K(-4, x) * K(1, y) + 4
+
+    p11 = Piecewise((1, Eq(y, 2) | Ne(x, -3)), (2, True))
+    assert f(p11) == -K(-3, x)*K(2, y) + K(-3, x) + 1
+
+    p12 = Piecewise((-1, Eq(x, 1) | Ne(y, 3)), (1, True))
+    assert f(p12) == -2*K(1, x)*K(3, y) + 2*K(3, y) - 1
+
+    p13 = Piecewise((3, Eq(x, 2) | Eq(y, 4)), (1, True))
+    assert f(p13) == -2*K(2, x)*K(4, y) + 2*K(2, x) + 2*K(4, y) + 1
+
+    p14 = Piecewise((1, Ne(x, 0) | Ne(y, 1)), (3, True))
+    assert f(p14) == 2 * K(0, x) * K(1, y) + 1
+
+    p15 = Piecewise((2, Eq(x, 3) | Ne(y, 2)), (3, Eq(x, 4) & Eq(y, 5)), (1, True))
+    assert f(p15) == -2*K(2, y)*K(3, x)*K(4, x)*K(5, y) + K(2, y)*K(3, x) + \
+           2*K(2, y)*K(4, x)*K(5, y) - K(2, y) + 2
+
+    p16 = Piecewise((0, Ne(m, n)), (1, True))*Piecewise((0, Ne(n, t)), (1, True))\
+          *Piecewise((0, Ne(n, x)), (1, True)) - Piecewise((0, Ne(t, x)), (1, True))
+    assert f(p16) == K(m, n)*K(n, t)*K(n, x) - K(t, x)
+
+    p17 = Piecewise((0, Ne(t, x) & (Ne(m, n) | Ne(n, t) | Ne(n, x))),
+                    (1, Ne(t, x)), (-1, Ne(m, n) | Ne(n, t) | Ne(n, x)), (0, True))
+    assert f(p17) == K(m, n)*K(n, t)*K(n, x) - K(t, x)
+
+    p18 = Piecewise((-4, Eq(y, 1) | (Eq(x, -5) & Eq(x, z))), (4, True))
+    assert f(p18) == 8*K(-5, x)*K(1, y)*K(x, z) - 8*K(-5, x)*K(x, z) - 8*K(1, y) + 4
+
+    p19 = Piecewise((0, x > 2), (1, True))
+    assert f(p19) == p19
+
+    p20 = Piecewise((0, And(x < 2, x > -5)), (1, True))
+    assert f(p20) == p20
+
+    p21 = Piecewise((0, Or(x > 1, x < 0)), (1, True))
+    assert f(p21) == p21
+
+    p22 = Piecewise((0, ~((Eq(y, -1) | Ne(x, 0)) & (Ne(x, 1) | Ne(y, -1)))), (1, True))
+    assert f(p22) == K(-1, y)*K(0, x) - K(-1, y)*K(1, x) - K(0, x) + 1
+
+
+@slow
+def test_identical_conds_issue():
+    from sympy.stats import Uniform, density
+    u1 = Uniform('u1', 0, 1)
+    u2 = Uniform('u2', 0, 1)
+    # Result is quite big, so not really important here (and should ideally be
+    # simpler). Should not give an exception though.
+    density(u1 + u2)
+
+
+def test_issue_7370():
+    f = Piecewise((1, x <= 2400))
+    v = integrate(f, (x, 0, Float("252.4", 30)))
+    assert str(v) == '252.400000000000000000000000000'
+
+
+def test_issue_14933():
+    x = Symbol('x')
+    y = Symbol('y')
+
+    inp = MatrixSymbol('inp', 1, 1)
+    rep_dict = {y: inp[0, 0], x: inp[0, 0]}
+
+    p = Piecewise((1, ITE(y > 0, x < 0, True)))
+    assert p.xreplace(rep_dict) == Piecewise((1, ITE(inp[0, 0] > 0, inp[0, 0] < 0, True)))
+
+
+def test_issue_16715():
+    raises(NotImplementedError, lambda: Piecewise((x, x<0), (0, y>1)).as_expr_set_pairs())
+
+
+def test_issue_20360():
+    t, tau = symbols("t tau", real=True)
+    n = symbols("n", integer=True)
+    lam = pi * (n - S.Half)
+    eq = integrate(exp(lam * tau), (tau, 0, t))
+    assert eq.simplify() == (2*exp(pi*t*(2*n - 1)/2) - 2)/(pi*(2*n - 1))
+
+
+def test_piecewise_eval():
+    # XXX these tests might need modification if this
+    # simplification is moved out of eval and into
+    # boolalg or Piecewise simplification functions
+    f = lambda x: x.args[0].cond
+    # unsimplified
+    assert f(Piecewise((x, (x > -oo) & (x < 3)))
+        ) == ((x > -oo) & (x < 3))
+    assert f(Piecewise((x, (x > -oo) & (x < oo)))
+        ) == ((x > -oo) & (x < oo))
+    assert f(Piecewise((x, (x > -3) & (x < 3)))
+        ) == ((x > -3) & (x < 3))
+    assert f(Piecewise((x, (x > -3) & (x < oo)))
+        ) == ((x > -3) & (x < oo))
+    assert f(Piecewise((x, (x <= 3) & (x > -oo)))
+        ) == ((x <= 3) & (x > -oo))
+    assert f(Piecewise((x, (x <= 3) & (x > -3)))
+        ) == ((x <= 3) & (x > -3))
+    assert f(Piecewise((x, (x >= -3) & (x < 3)))
+        ) == ((x >= -3) & (x < 3))
+    assert f(Piecewise((x, (x >= -3) & (x < oo)))
+        ) == ((x >= -3) & (x < oo))
+    assert f(Piecewise((x, (x >= -3) & (x <= 3)))
+        ) == ((x >= -3) & (x <= 3))
+    # could simplify by keeping only the first
+    # arg of result
+    assert f(Piecewise((x, (x <= oo) & (x > -oo)))
+        ) == (x > -oo) & (x <= oo)
+    assert f(Piecewise((x, (x <= oo) & (x > -3)))
+        ) == (x > -3) & (x <= oo)
+    assert f(Piecewise((x, (x >= -oo) & (x < 3)))
+        ) == (x < 3) & (x >= -oo)
+    assert f(Piecewise((x, (x >= -oo) & (x < oo)))
+        ) == (x < oo) & (x >= -oo)
+    assert f(Piecewise((x, (x >= -oo) & (x <= 3)))
+        ) == (x <= 3) & (x >= -oo)
+    assert f(Piecewise((x, (x >= -oo) & (x <= oo)))
+        ) == (x <= oo) & (x >= -oo)  # but cannot be True unless x is real
+    assert f(Piecewise((x, (x >= -3) & (x <= oo)))
+        ) == (x >= -3) & (x <= oo)
+    assert f(Piecewise((x, (Abs(arg(a)) <= 1) | (Abs(arg(a)) < 1)))
+        ) == (Abs(arg(a)) <= 1) | (Abs(arg(a)) < 1)
+
+
+def test_issue_22533():
+    x = Symbol('x', real=True)
+    f = Piecewise((-1 / x, x <= 0), (1 / x, True))
+    assert integrate(f, x) == Piecewise((-log(x), x <= 0), (log(x), True))
+
+
+def test_issue_24072():
+    assert Piecewise((1, x > 1), (2, x <= 1), (3, x <= 1)
+        ) == Piecewise((1, x > 1), (2, True))
+
+
+def test_piecewise__eval_is_meromorphic():
+    """ Issue 24127: Tests eval_is_meromorphic auxiliary method """
+    x = symbols('x', real=True)
+    f = Piecewise((1, x < 0), (sqrt(1 - x), True))
+    assert f.is_meromorphic(x, I) is None
+    assert f.is_meromorphic(x, -1) == True
+    assert f.is_meromorphic(x, 0) == None
+    assert f.is_meromorphic(x, 1) == False
+    assert f.is_meromorphic(x, 2) == True
+    assert f.is_meromorphic(x, Symbol('a')) == None
+    assert f.is_meromorphic(x, Symbol('a', real=True)) == None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_trigonometric.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_trigonometric.py
new file mode 100644
index 0000000000000000000000000000000000000000..815f424093aac72ee3a078d8ce62e5c195a625dc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/tests/test_trigonometric.py
@@ -0,0 +1,2236 @@
+from sympy.calculus.accumulationbounds import AccumBounds
+from sympy.core.add import Add
+from sympy.core.function import (Lambda, diff)
+from sympy.core.mod import Mod
+from sympy.core.mul import Mul
+from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi, zoo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (arg, conjugate, im, re)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (acoth, asinh, atanh, cosh, coth, sinh, tanh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, acot, acsc, asec, asin, atan, atan2,
+                                                      cos, cot, csc, sec, sin, sinc, tan)
+from sympy.functions.special.bessel import (besselj, jn)
+from sympy.functions.special.delta_functions import Heaviside
+from sympy.matrices.dense import Matrix
+from sympy.polys.polytools import (cancel, gcd)
+from sympy.series.limits import limit
+from sympy.series.order import O
+from sympy.series.series import series
+from sympy.sets.fancysets import ImageSet
+from sympy.sets.sets import (FiniteSet, Interval)
+from sympy.simplify.simplify import simplify
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError, PoleError
+from sympy.core.relational import Ne, Eq
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.sets.setexpr import SetExpr
+from sympy.testing.pytest import XFAIL, slow, raises
+
+
+x, y, z = symbols('x y z')
+r = Symbol('r', real=True)
+k, m = symbols('k m', integer=True)
+p = Symbol('p', positive=True)
+n = Symbol('n', negative=True)
+np = Symbol('p', nonpositive=True)
+nn = Symbol('n', nonnegative=True)
+nz = Symbol('nz', nonzero=True)
+ep = Symbol('ep', extended_positive=True)
+en = Symbol('en', extended_negative=True)
+enp = Symbol('ep', extended_nonpositive=True)
+enn = Symbol('en', extended_nonnegative=True)
+enz = Symbol('enz', extended_nonzero=True)
+a = Symbol('a', algebraic=True)
+na = Symbol('na', nonzero=True, algebraic=True)
+
+
+def test_sin():
+    x, y = symbols('x y')
+    z = symbols('z', imaginary=True)
+
+    assert sin.nargs == FiniteSet(1)
+    assert sin(nan) is nan
+    assert sin(zoo) is nan
+
+    assert sin(oo) == AccumBounds(-1, 1)
+    assert sin(oo) - sin(oo) == AccumBounds(-2, 2)
+    assert sin(oo*I) == oo*I
+    assert sin(-oo*I) == -oo*I
+    assert 0*sin(oo) is S.Zero
+    assert 0/sin(oo) is S.Zero
+    assert 0 + sin(oo) == AccumBounds(-1, 1)
+    assert 5 + sin(oo) == AccumBounds(4, 6)
+
+    assert sin(0) == 0
+
+    assert sin(z*I) == I*sinh(z)
+    assert sin(asin(x)) == x
+    assert sin(atan(x)) == x / sqrt(1 + x**2)
+    assert sin(acos(x)) == sqrt(1 - x**2)
+    assert sin(acot(x)) == 1 / (sqrt(1 + 1 / x**2) * x)
+    assert sin(acsc(x)) == 1 / x
+    assert sin(asec(x)) == sqrt(1 - 1 / x**2)
+    assert sin(atan2(y, x)) == y / sqrt(x**2 + y**2)
+
+    assert sin(pi*I) == sinh(pi)*I
+    assert sin(-pi*I) == -sinh(pi)*I
+    assert sin(-2*I) == -sinh(2)*I
+
+    assert sin(pi) == 0
+    assert sin(-pi) == 0
+    assert sin(2*pi) == 0
+    assert sin(-2*pi) == 0
+    assert sin(-3*10**73*pi) == 0
+    assert sin(7*10**103*pi) == 0
+
+    assert sin(pi/2) == 1
+    assert sin(-pi/2) == -1
+    assert sin(pi*Rational(5, 2)) == 1
+    assert sin(pi*Rational(7, 2)) == -1
+
+    ne = symbols('ne', integer=True, even=False)
+    e = symbols('e', even=True)
+    assert sin(pi*ne/2) == (-1)**(ne/2 - S.Half)
+    assert sin(pi*k/2).func == sin
+    assert sin(pi*e/2) == 0
+    assert sin(pi*k) == 0
+    assert sin(pi*k).subs(k, 3) == sin(pi*k/2).subs(k, 6)  # issue 8298
+
+    assert sin(pi/3) == S.Half*sqrt(3)
+    assert sin(pi*Rational(-2, 3)) == Rational(-1, 2)*sqrt(3)
+
+    assert sin(pi/4) == S.Half*sqrt(2)
+    assert sin(-pi/4) == Rational(-1, 2)*sqrt(2)
+    assert sin(pi*Rational(17, 4)) == S.Half*sqrt(2)
+    assert sin(pi*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2)
+
+    assert sin(pi/6) == S.Half
+    assert sin(-pi/6) == Rational(-1, 2)
+    assert sin(pi*Rational(7, 6)) == Rational(-1, 2)
+    assert sin(pi*Rational(-5, 6)) == Rational(-1, 2)
+
+    assert sin(pi*Rational(1, 5)) == sqrt((5 - sqrt(5)) / 8)
+    assert sin(pi*Rational(2, 5)) == sqrt((5 + sqrt(5)) / 8)
+    assert sin(pi*Rational(3, 5)) == sin(pi*Rational(2, 5))
+    assert sin(pi*Rational(4, 5)) == sin(pi*Rational(1, 5))
+    assert sin(pi*Rational(6, 5)) == -sin(pi*Rational(1, 5))
+    assert sin(pi*Rational(8, 5)) == -sin(pi*Rational(2, 5))
+
+    assert sin(pi*Rational(-1273, 5)) == -sin(pi*Rational(2, 5))
+
+    assert sin(pi/8) == sqrt((2 - sqrt(2))/4)
+
+    assert sin(pi/10) == Rational(-1, 4) + sqrt(5)/4
+
+    assert sin(pi/12) == -sqrt(2)/4 + sqrt(6)/4
+    assert sin(pi*Rational(5, 12)) == sqrt(2)/4 + sqrt(6)/4
+    assert sin(pi*Rational(-7, 12)) == -sqrt(2)/4 - sqrt(6)/4
+    assert sin(pi*Rational(-11, 12)) == sqrt(2)/4 - sqrt(6)/4
+
+    assert sin(pi*Rational(104, 105)) == sin(pi/105)
+    assert sin(pi*Rational(106, 105)) == -sin(pi/105)
+
+    assert sin(pi*Rational(-104, 105)) == -sin(pi/105)
+    assert sin(pi*Rational(-106, 105)) == sin(pi/105)
+
+    assert sin(x*I) == sinh(x)*I
+
+    assert sin(k*pi) == 0
+    assert sin(17*k*pi) == 0
+    assert sin(2*k*pi + 4) == sin(4)
+    assert sin(2*k*pi + m*pi + 1) == (-1)**(m + 2*k)*sin(1)
+
+    assert sin(k*pi*I) == sinh(k*pi)*I
+
+    assert sin(r).is_real is True
+
+    assert sin(0, evaluate=False).is_algebraic
+    assert sin(a).is_algebraic is None
+    assert sin(na).is_algebraic is False
+    q = Symbol('q', rational=True)
+    assert sin(pi*q).is_algebraic
+    qn = Symbol('qn', rational=True, nonzero=True)
+    assert sin(qn).is_rational is False
+    assert sin(q).is_rational is None  # issue 8653
+
+    assert isinstance(sin( re(x) - im(y)), sin) is True
+    assert isinstance(sin(-re(x) + im(y)), sin) is False
+
+    assert sin(SetExpr(Interval(0, 1))) == SetExpr(ImageSet(Lambda(x, sin(x)),
+                       Interval(0, 1)))
+
+    for d in list(range(1, 22)) + [60, 85]:
+        for n in range(d*2 + 1):
+            x = n*pi/d
+            e = abs( float(sin(x)) - sin(float(x)) )
+            assert e < 1e-12
+
+    assert sin(0, evaluate=False).is_zero is True
+    assert sin(k*pi, evaluate=False).is_zero is True
+
+    assert sin(Add(1, -1, evaluate=False), evaluate=False).is_zero is True
+
+
+def test_sin_cos():
+    for d in [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 24, 30, 40, 60, 120]:  # list is not exhaustive...
+        for n in range(-2*d, d*2):
+            x = n*pi/d
+            assert sin(x + pi/2) == cos(x), "fails for %d*pi/%d" % (n, d)
+            assert sin(x - pi/2) == -cos(x), "fails for %d*pi/%d" % (n, d)
+            assert sin(x) == cos(x - pi/2), "fails for %d*pi/%d" % (n, d)
+            assert -sin(x) == cos(x + pi/2), "fails for %d*pi/%d" % (n, d)
+
+
+def test_sin_series():
+    assert sin(x).series(x, 0, 9) == \
+        x - x**3/6 + x**5/120 - x**7/5040 + O(x**9)
+
+
+def test_sin_rewrite():
+    assert sin(x).rewrite(exp) == -I*(exp(I*x) - exp(-I*x))/2
+    assert sin(x).rewrite(tan) == 2*tan(x/2)/(1 + tan(x/2)**2)
+    assert sin(x).rewrite(cot) == \
+        Piecewise((0, Eq(im(x), 0) & Eq(Mod(x, pi), 0)),
+                  (2*cot(x/2)/(cot(x/2)**2 + 1), True))
+    assert sin(sinh(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, sinh(3)).n()
+    assert sin(cosh(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, cosh(3)).n()
+    assert sin(tanh(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, tanh(3)).n()
+    assert sin(coth(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, coth(3)).n()
+    assert sin(sin(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, sin(3)).n()
+    assert sin(cos(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, cos(3)).n()
+    assert sin(tan(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, tan(3)).n()
+    assert sin(cot(x)).rewrite(
+        exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, cot(3)).n()
+    assert sin(log(x)).rewrite(Pow) == I*x**-I / 2 - I*x**I /2
+    assert sin(x).rewrite(csc) == 1/csc(x)
+    assert sin(x).rewrite(cos) == cos(x - pi / 2, evaluate=False)
+    assert sin(x).rewrite(sec) == 1 / sec(x - pi / 2, evaluate=False)
+    assert sin(cos(x)).rewrite(Pow) == sin(cos(x))
+    assert sin(x).rewrite(besselj) == sqrt(pi*x/2)*besselj(S.Half, x)
+    assert sin(x).rewrite(besselj).subs(x, 0) == sin(0)
+
+
+def _test_extrig(f, i, e):
+    from sympy.core.function import expand_trig
+    assert unchanged(f, i)
+    assert expand_trig(f(i)) == f(i)
+    # testing directly instead of with .expand(trig=True)
+    # because the other expansions undo the unevaluated Mul
+    assert expand_trig(f(Mul(i, 1, evaluate=False))) == e
+    assert abs(f(i) - e).n() < 1e-10
+
+
+def test_sin_expansion():
+    # Note: these formulas are not unique.  The ones here come from the
+    # Chebyshev formulas.
+    assert sin(x + y).expand(trig=True) == sin(x)*cos(y) + cos(x)*sin(y)
+    assert sin(x - y).expand(trig=True) == sin(x)*cos(y) - cos(x)*sin(y)
+    assert sin(y - x).expand(trig=True) == cos(x)*sin(y) - sin(x)*cos(y)
+    assert sin(2*x).expand(trig=True) == 2*sin(x)*cos(x)
+    assert sin(3*x).expand(trig=True) == -4*sin(x)**3 + 3*sin(x)
+    assert sin(4*x).expand(trig=True) == -8*sin(x)**3*cos(x) + 4*sin(x)*cos(x)
+    assert sin(2*pi/17).expand(trig=True) == sin(2*pi/17, evaluate=False)
+    assert sin(x+pi/17).expand(trig=True) == sin(pi/17)*cos(x) + cos(pi/17)*sin(x)
+    _test_extrig(sin, 2, 2*sin(1)*cos(1))
+    _test_extrig(sin, 3, -4*sin(1)**3 + 3*sin(1))
+
+
+def test_sin_AccumBounds():
+    assert sin(AccumBounds(-oo, oo)) == AccumBounds(-1, 1)
+    assert sin(AccumBounds(0, oo)) == AccumBounds(-1, 1)
+    assert sin(AccumBounds(-oo, 0)) == AccumBounds(-1, 1)
+    assert sin(AccumBounds(0, 2*S.Pi)) == AccumBounds(-1, 1)
+    assert sin(AccumBounds(0, S.Pi*Rational(3, 4))) == AccumBounds(0, 1)
+    assert sin(AccumBounds(S.Pi*Rational(3, 4), S.Pi*Rational(7, 4))) == AccumBounds(-1, sin(S.Pi*Rational(3, 4)))
+    assert sin(AccumBounds(S.Pi/4, S.Pi/3)) == AccumBounds(sin(S.Pi/4), sin(S.Pi/3))
+    assert sin(AccumBounds(S.Pi*Rational(3, 4), S.Pi*Rational(5, 6))) == AccumBounds(sin(S.Pi*Rational(5, 6)), sin(S.Pi*Rational(3, 4)))
+
+
+def test_sin_fdiff():
+    assert sin(x).fdiff() == cos(x)
+    raises(ArgumentIndexError, lambda: sin(x).fdiff(2))
+
+
+def test_trig_symmetry():
+    assert sin(-x) == -sin(x)
+    assert cos(-x) == cos(x)
+    assert tan(-x) == -tan(x)
+    assert cot(-x) == -cot(x)
+    assert sin(x + pi) == -sin(x)
+    assert sin(x + 2*pi) == sin(x)
+    assert sin(x + 3*pi) == -sin(x)
+    assert sin(x + 4*pi) == sin(x)
+    assert sin(x - 5*pi) == -sin(x)
+    assert cos(x + pi) == -cos(x)
+    assert cos(x + 2*pi) == cos(x)
+    assert cos(x + 3*pi) == -cos(x)
+    assert cos(x + 4*pi) == cos(x)
+    assert cos(x - 5*pi) == -cos(x)
+    assert tan(x + pi) == tan(x)
+    assert tan(x - 3*pi) == tan(x)
+    assert cot(x + pi) == cot(x)
+    assert cot(x - 3*pi) == cot(x)
+    assert sin(pi/2 - x) == cos(x)
+    assert sin(pi*Rational(3, 2) - x) == -cos(x)
+    assert sin(pi*Rational(5, 2) - x) == cos(x)
+    assert cos(pi/2 - x) == sin(x)
+    assert cos(pi*Rational(3, 2) - x) == -sin(x)
+    assert cos(pi*Rational(5, 2) - x) == sin(x)
+    assert tan(pi/2 - x) == cot(x)
+    assert tan(pi*Rational(3, 2) - x) == cot(x)
+    assert tan(pi*Rational(5, 2) - x) == cot(x)
+    assert cot(pi/2 - x) == tan(x)
+    assert cot(pi*Rational(3, 2) - x) == tan(x)
+    assert cot(pi*Rational(5, 2) - x) == tan(x)
+    assert sin(pi/2 + x) == cos(x)
+    assert cos(pi/2 + x) == -sin(x)
+    assert tan(pi/2 + x) == -cot(x)
+    assert cot(pi/2 + x) == -tan(x)
+
+
+def test_cos():
+    x, y = symbols('x y')
+
+    assert cos.nargs == FiniteSet(1)
+    assert cos(nan) is nan
+
+    assert cos(oo) == AccumBounds(-1, 1)
+    assert cos(oo) - cos(oo) == AccumBounds(-2, 2)
+    assert cos(oo*I) is oo
+    assert cos(-oo*I) is oo
+    assert cos(zoo) is nan
+
+    assert cos(0) == 1
+
+    assert cos(acos(x)) == x
+    assert cos(atan(x)) == 1 / sqrt(1 + x**2)
+    assert cos(asin(x)) == sqrt(1 - x**2)
+    assert cos(acot(x)) == 1 / sqrt(1 + 1 / x**2)
+    assert cos(acsc(x)) == sqrt(1 - 1 / x**2)
+    assert cos(asec(x)) == 1 / x
+    assert cos(atan2(y, x)) == x / sqrt(x**2 + y**2)
+
+    assert cos(pi*I) == cosh(pi)
+    assert cos(-pi*I) == cosh(pi)
+    assert cos(-2*I) == cosh(2)
+
+    assert cos(pi/2) == 0
+    assert cos(-pi/2) == 0
+    assert cos(pi/2) == 0
+    assert cos(-pi/2) == 0
+    assert cos((-3*10**73 + 1)*pi/2) == 0
+    assert cos((7*10**103 + 1)*pi/2) == 0
+
+    n = symbols('n', integer=True, even=False)
+    e = symbols('e', even=True)
+    assert cos(pi*n/2) == 0
+    assert cos(pi*e/2) == (-1)**(e/2)
+
+    assert cos(pi) == -1
+    assert cos(-pi) == -1
+    assert cos(2*pi) == 1
+    assert cos(5*pi) == -1
+    assert cos(8*pi) == 1
+
+    assert cos(pi/3) == S.Half
+    assert cos(pi*Rational(-2, 3)) == Rational(-1, 2)
+
+    assert cos(pi/4) == S.Half*sqrt(2)
+    assert cos(-pi/4) == S.Half*sqrt(2)
+    assert cos(pi*Rational(11, 4)) == Rational(-1, 2)*sqrt(2)
+    assert cos(pi*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2)
+
+    assert cos(pi/6) == S.Half*sqrt(3)
+    assert cos(-pi/6) == S.Half*sqrt(3)
+    assert cos(pi*Rational(7, 6)) == Rational(-1, 2)*sqrt(3)
+    assert cos(pi*Rational(-5, 6)) == Rational(-1, 2)*sqrt(3)
+
+    assert cos(pi*Rational(1, 5)) == (sqrt(5) + 1)/4
+    assert cos(pi*Rational(2, 5)) == (sqrt(5) - 1)/4
+    assert cos(pi*Rational(3, 5)) == -cos(pi*Rational(2, 5))
+    assert cos(pi*Rational(4, 5)) == -cos(pi*Rational(1, 5))
+    assert cos(pi*Rational(6, 5)) == -cos(pi*Rational(1, 5))
+    assert cos(pi*Rational(8, 5)) == cos(pi*Rational(2, 5))
+
+    assert cos(pi*Rational(-1273, 5)) == -cos(pi*Rational(2, 5))
+
+    assert cos(pi/8) == sqrt((2 + sqrt(2))/4)
+
+    assert cos(pi/12) == sqrt(2)/4 + sqrt(6)/4
+    assert cos(pi*Rational(5, 12)) == -sqrt(2)/4 + sqrt(6)/4
+    assert cos(pi*Rational(7, 12)) == sqrt(2)/4 - sqrt(6)/4
+    assert cos(pi*Rational(11, 12)) == -sqrt(2)/4 - sqrt(6)/4
+
+    assert cos(pi*Rational(104, 105)) == -cos(pi/105)
+    assert cos(pi*Rational(106, 105)) == -cos(pi/105)
+
+    assert cos(pi*Rational(-104, 105)) == -cos(pi/105)
+    assert cos(pi*Rational(-106, 105)) == -cos(pi/105)
+
+    assert cos(x*I) == cosh(x)
+    assert cos(k*pi*I) == cosh(k*pi)
+
+    assert cos(r).is_real is True
+
+    assert cos(0, evaluate=False).is_algebraic
+    assert cos(a).is_algebraic is None
+    assert cos(na).is_algebraic is False
+    q = Symbol('q', rational=True)
+    assert cos(pi*q).is_algebraic
+    assert cos(pi*Rational(2, 7)).is_algebraic
+
+    assert cos(k*pi) == (-1)**k
+    assert cos(2*k*pi) == 1
+    assert cos(0, evaluate=False).is_zero is False
+    assert cos(Rational(1, 2)).is_zero is False
+    # The following test will return None as the result, but really it should
+    # be True even if it is not always possible to resolve an assumptions query.
+    assert cos(asin(-1, evaluate=False), evaluate=False).is_zero is None
+    for d in list(range(1, 22)) + [60, 85]:
+        for n in range(2*d + 1):
+            x = n*pi/d
+            e = abs( float(cos(x)) - cos(float(x)) )
+            assert e < 1e-12
+
+
+def test_issue_6190():
+    c = Float('123456789012345678901234567890.25', '')
+    for cls in [sin, cos, tan, cot]:
+        assert cls(c*pi) == cls(pi/4)
+        assert cls(4.125*pi) == cls(pi/8)
+        assert cls(4.7*pi) == cls((4.7 % 2)*pi)
+
+
+def test_cos_series():
+    assert cos(x).series(x, 0, 9) == \
+        1 - x**2/2 + x**4/24 - x**6/720 + x**8/40320 + O(x**9)
+
+
+def test_cos_rewrite():
+    assert cos(x).rewrite(exp) == exp(I*x)/2 + exp(-I*x)/2
+    assert cos(x).rewrite(tan) == (1 - tan(x/2)**2)/(1 + tan(x/2)**2)
+    assert cos(x).rewrite(cot) == \
+        Piecewise((1, Eq(im(x), 0) & Eq(Mod(x, 2*pi), 0)),
+                  ((cot(x/2)**2 - 1)/(cot(x/2)**2 + 1), True))
+    assert cos(sinh(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, sinh(3)).n()
+    assert cos(cosh(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, cosh(3)).n()
+    assert cos(tanh(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, tanh(3)).n()
+    assert cos(coth(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, coth(3)).n()
+    assert cos(sin(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, sin(3)).n()
+    assert cos(cos(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, cos(3)).n()
+    assert cos(tan(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, tan(3)).n()
+    assert cos(cot(x)).rewrite(
+        exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, cot(3)).n()
+    assert cos(log(x)).rewrite(Pow) == x**I/2 + x**-I/2
+    assert cos(x).rewrite(sec) == 1/sec(x)
+    assert cos(x).rewrite(sin) == sin(x + pi/2, evaluate=False)
+    assert cos(x).rewrite(csc) == 1/csc(-x + pi/2, evaluate=False)
+    assert cos(sin(x)).rewrite(Pow) == cos(sin(x))
+    assert cos(x).rewrite(besselj) == Piecewise(
+                (sqrt(pi*x/2)*besselj(-S.Half, x), Ne(x, 0)),
+                (1, True)
+            )
+    assert cos(x).rewrite(besselj).subs(x, 0) == cos(0)
+
+
+def test_cos_expansion():
+    assert cos(x + y).expand(trig=True) == cos(x)*cos(y) - sin(x)*sin(y)
+    assert cos(x - y).expand(trig=True) == cos(x)*cos(y) + sin(x)*sin(y)
+    assert cos(y - x).expand(trig=True) == cos(x)*cos(y) + sin(x)*sin(y)
+    assert cos(2*x).expand(trig=True) == 2*cos(x)**2 - 1
+    assert cos(3*x).expand(trig=True) == 4*cos(x)**3 - 3*cos(x)
+    assert cos(4*x).expand(trig=True) == 8*cos(x)**4 - 8*cos(x)**2 + 1
+    assert cos(2*pi/17).expand(trig=True) == cos(2*pi/17, evaluate=False)
+    assert cos(x+pi/17).expand(trig=True) == cos(pi/17)*cos(x) - sin(pi/17)*sin(x)
+    _test_extrig(cos, 2, 2*cos(1)**2 - 1)
+    _test_extrig(cos, 3, 4*cos(1)**3 - 3*cos(1))
+
+
+def test_cos_AccumBounds():
+    assert cos(AccumBounds(-oo, oo)) == AccumBounds(-1, 1)
+    assert cos(AccumBounds(0, oo)) == AccumBounds(-1, 1)
+    assert cos(AccumBounds(-oo, 0)) == AccumBounds(-1, 1)
+    assert cos(AccumBounds(0, 2*S.Pi)) == AccumBounds(-1, 1)
+    assert cos(AccumBounds(-S.Pi/3, S.Pi/4)) == AccumBounds(cos(-S.Pi/3), 1)
+    assert cos(AccumBounds(S.Pi*Rational(3, 4), S.Pi*Rational(5, 4))) == AccumBounds(-1, cos(S.Pi*Rational(3, 4)))
+    assert cos(AccumBounds(S.Pi*Rational(5, 4), S.Pi*Rational(4, 3))) == AccumBounds(cos(S.Pi*Rational(5, 4)), cos(S.Pi*Rational(4, 3)))
+    assert cos(AccumBounds(S.Pi/4, S.Pi/3)) == AccumBounds(cos(S.Pi/3), cos(S.Pi/4))
+
+
+def test_cos_fdiff():
+    assert cos(x).fdiff() == -sin(x)
+    raises(ArgumentIndexError, lambda: cos(x).fdiff(2))
+
+
+def test_tan():
+    assert tan(nan) is nan
+
+    assert tan(zoo) is nan
+    assert tan(oo) == AccumBounds(-oo, oo)
+    assert tan(oo) - tan(oo) == AccumBounds(-oo, oo)
+    assert tan.nargs == FiniteSet(1)
+    assert tan(oo*I) == I
+    assert tan(-oo*I) == -I
+
+    assert tan(0) == 0
+
+    assert tan(atan(x)) == x
+    assert tan(asin(x)) == x / sqrt(1 - x**2)
+    assert tan(acos(x)) == sqrt(1 - x**2) / x
+    assert tan(acot(x)) == 1 / x
+    assert tan(acsc(x)) == 1 / (sqrt(1 - 1 / x**2) * x)
+    assert tan(asec(x)) == sqrt(1 - 1 / x**2) * x
+    assert tan(atan2(y, x)) == y/x
+
+    assert tan(pi*I) == tanh(pi)*I
+    assert tan(-pi*I) == -tanh(pi)*I
+    assert tan(-2*I) == -tanh(2)*I
+
+    assert tan(pi) == 0
+    assert tan(-pi) == 0
+    assert tan(2*pi) == 0
+    assert tan(-2*pi) == 0
+    assert tan(-3*10**73*pi) == 0
+
+    assert tan(pi/2) is zoo
+    assert tan(pi*Rational(3, 2)) is zoo
+
+    assert tan(pi/3) == sqrt(3)
+    assert tan(pi*Rational(-2, 3)) == sqrt(3)
+
+    assert tan(pi/4) is S.One
+    assert tan(-pi/4) is S.NegativeOne
+    assert tan(pi*Rational(17, 4)) is S.One
+    assert tan(pi*Rational(-3, 4)) is S.One
+
+    assert tan(pi/5) == sqrt(5 - 2*sqrt(5))
+    assert tan(pi*Rational(2, 5)) == sqrt(5 + 2*sqrt(5))
+    assert tan(pi*Rational(18, 5)) == -sqrt(5 + 2*sqrt(5))
+    assert tan(pi*Rational(-16, 5)) == -sqrt(5 - 2*sqrt(5))
+
+    assert tan(pi/6) == 1/sqrt(3)
+    assert tan(-pi/6) == -1/sqrt(3)
+    assert tan(pi*Rational(7, 6)) == 1/sqrt(3)
+    assert tan(pi*Rational(-5, 6)) == 1/sqrt(3)
+
+    assert tan(pi/8) == -1 + sqrt(2)
+    assert tan(pi*Rational(3, 8)) == 1 + sqrt(2)  # issue 15959
+    assert tan(pi*Rational(5, 8)) == -1 - sqrt(2)
+    assert tan(pi*Rational(7, 8)) == 1 - sqrt(2)
+
+    assert tan(pi/10) == sqrt(1 - 2*sqrt(5)/5)
+    assert tan(pi*Rational(3, 10)) == sqrt(1 + 2*sqrt(5)/5)
+    assert tan(pi*Rational(17, 10)) == -sqrt(1 + 2*sqrt(5)/5)
+    assert tan(pi*Rational(-31, 10)) == -sqrt(1 - 2*sqrt(5)/5)
+
+    assert tan(pi/12) == -sqrt(3) + 2
+    assert tan(pi*Rational(5, 12)) == sqrt(3) + 2
+    assert tan(pi*Rational(7, 12)) == -sqrt(3) - 2
+    assert tan(pi*Rational(11, 12)) == sqrt(3) - 2
+
+    assert tan(pi/24).radsimp() == -2 - sqrt(3) + sqrt(2) + sqrt(6)
+    assert tan(pi*Rational(5, 24)).radsimp() == -2 + sqrt(3) - sqrt(2) + sqrt(6)
+    assert tan(pi*Rational(7, 24)).radsimp() == 2 - sqrt(3) - sqrt(2) + sqrt(6)
+    assert tan(pi*Rational(11, 24)).radsimp() == 2 + sqrt(3) + sqrt(2) + sqrt(6)
+    assert tan(pi*Rational(13, 24)).radsimp() == -2 - sqrt(3) - sqrt(2) - sqrt(6)
+    assert tan(pi*Rational(17, 24)).radsimp() == -2 + sqrt(3) + sqrt(2) - sqrt(6)
+    assert tan(pi*Rational(19, 24)).radsimp() == 2 - sqrt(3) + sqrt(2) - sqrt(6)
+    assert tan(pi*Rational(23, 24)).radsimp() == 2 + sqrt(3) - sqrt(2) - sqrt(6)
+
+    assert tan(x*I) == tanh(x)*I
+
+    assert tan(k*pi) == 0
+    assert tan(17*k*pi) == 0
+
+    assert tan(k*pi*I) == tanh(k*pi)*I
+
+    assert tan(r).is_real is None
+    assert tan(r).is_extended_real is True
+
+    assert tan(0, evaluate=False).is_algebraic
+    assert tan(a).is_algebraic is None
+    assert tan(na).is_algebraic is False
+
+    assert tan(pi*Rational(10, 7)) == tan(pi*Rational(3, 7))
+    assert tan(pi*Rational(11, 7)) == -tan(pi*Rational(3, 7))
+    assert tan(pi*Rational(-11, 7)) == tan(pi*Rational(3, 7))
+
+    assert tan(pi*Rational(15, 14)) == tan(pi/14)
+    assert tan(pi*Rational(-15, 14)) == -tan(pi/14)
+
+    assert tan(r).is_finite is None
+    assert tan(I*r).is_finite is True
+
+    # https://github.com/sympy/sympy/issues/21177
+    f = tan(pi*(x + S(3)/2))/(3*x)
+    assert f.as_leading_term(x) == -1/(3*pi*x**2)
+
+
+def test_tan_series():
+    assert tan(x).series(x, 0, 9) == \
+        x + x**3/3 + 2*x**5/15 + 17*x**7/315 + O(x**9)
+
+
+def test_tan_rewrite():
+    neg_exp, pos_exp = exp(-x*I), exp(x*I)
+    assert tan(x).rewrite(exp) == I*(neg_exp - pos_exp)/(neg_exp + pos_exp)
+    assert tan(x).rewrite(sin) == 2*sin(x)**2/sin(2*x)
+    assert tan(x).rewrite(cos) == cos(x - S.Pi/2, evaluate=False)/cos(x)
+    assert tan(x).rewrite(cot) == 1/cot(x)
+    assert tan(sinh(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, sinh(3)).n()
+    assert tan(cosh(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cosh(3)).n()
+    assert tan(tanh(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, tanh(3)).n()
+    assert tan(coth(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, coth(3)).n()
+    assert tan(sin(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, sin(3)).n()
+    assert tan(cos(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cos(3)).n()
+    assert tan(tan(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, tan(3)).n()
+    assert tan(cot(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cot(3)).n()
+    assert tan(log(x)).rewrite(Pow) == I*(x**-I - x**I)/(x**-I + x**I)
+    assert tan(x).rewrite(sec) == sec(x)/sec(x - pi/2, evaluate=False)
+    assert tan(x).rewrite(csc) == csc(-x + pi/2, evaluate=False)/csc(x)
+    assert tan(sin(x)).rewrite(Pow) == tan(sin(x))
+    assert tan(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == sqrt(sqrt(5)/8 +
+               Rational(5, 8))/(Rational(-1, 4) + sqrt(5)/4)
+    assert tan(x).rewrite(besselj) == besselj(S.Half, x)/besselj(-S.Half, x)
+    assert tan(x).rewrite(besselj).subs(x, 0) == tan(0)
+
+
+@slow
+def test_tan_rewrite_slow():
+    assert 0 == (cos(pi/34)*tan(pi/34) - sin(pi/34)).rewrite(pow)
+    assert 0 == (cos(pi/17)*tan(pi/17) - sin(pi/17)).rewrite(pow)
+    assert tan(pi/19).rewrite(pow) == tan(pi/19)
+    assert tan(pi*Rational(8, 19)).rewrite(sqrt) == tan(pi*Rational(8, 19))
+    assert tan(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == sqrt(sqrt(5)/8 +
+               Rational(5, 8))/(Rational(-1, 4) + sqrt(5)/4)
+
+
+def test_tan_subs():
+    assert tan(x).subs(tan(x), y) == y
+    assert tan(x).subs(x, y) == tan(y)
+    assert tan(x).subs(x, S.Pi/2) is zoo
+    assert tan(x).subs(x, S.Pi*Rational(3, 2)) is zoo
+
+
+def test_tan_expansion():
+    assert tan(x + y).expand(trig=True) == ((tan(x) + tan(y))/(1 - tan(x)*tan(y))).expand()
+    assert tan(x - y).expand(trig=True) == ((tan(x) - tan(y))/(1 + tan(x)*tan(y))).expand()
+    assert tan(x + y + z).expand(trig=True) == (
+        (tan(x) + tan(y) + tan(z) - tan(x)*tan(y)*tan(z))/
+        (1 - tan(x)*tan(y) - tan(x)*tan(z) - tan(y)*tan(z))).expand()
+    assert 0 == tan(2*x).expand(trig=True).rewrite(tan).subs([(tan(x), Rational(1, 7))])*24 - 7
+    assert 0 == tan(3*x).expand(trig=True).rewrite(tan).subs([(tan(x), Rational(1, 5))])*55 - 37
+    assert 0 == tan(4*x - pi/4).expand(trig=True).rewrite(tan).subs([(tan(x), Rational(1, 5))])*239 - 1
+    _test_extrig(tan, 2, 2*tan(1)/(1 - tan(1)**2))
+    _test_extrig(tan, 3, (-tan(1)**3 + 3*tan(1))/(1 - 3*tan(1)**2))
+
+
+def test_tan_AccumBounds():
+    assert tan(AccumBounds(-oo, oo)) == AccumBounds(-oo, oo)
+    assert tan(AccumBounds(S.Pi/3, S.Pi*Rational(2, 3))) == AccumBounds(-oo, oo)
+    assert tan(AccumBounds(S.Pi/6, S.Pi/3)) == AccumBounds(tan(S.Pi/6), tan(S.Pi/3))
+
+
+def test_tan_fdiff():
+    assert tan(x).fdiff() == tan(x)**2 + 1
+    raises(ArgumentIndexError, lambda: tan(x).fdiff(2))
+
+
+def test_cot():
+    assert cot(nan) is nan
+
+    assert cot.nargs == FiniteSet(1)
+    assert cot(oo*I) == -I
+    assert cot(-oo*I) == I
+    assert cot(zoo) is nan
+
+    assert cot(0) is zoo
+    assert cot(2*pi) is zoo
+
+    assert cot(acot(x)) == x
+    assert cot(atan(x)) == 1 / x
+    assert cot(asin(x)) == sqrt(1 - x**2) / x
+    assert cot(acos(x)) == x / sqrt(1 - x**2)
+    assert cot(acsc(x)) == sqrt(1 - 1 / x**2) * x
+    assert cot(asec(x)) == 1 / (sqrt(1 - 1 / x**2) * x)
+    assert cot(atan2(y, x)) == x/y
+
+    assert cot(pi*I) == -coth(pi)*I
+    assert cot(-pi*I) == coth(pi)*I
+    assert cot(-2*I) == coth(2)*I
+
+    assert cot(pi) == cot(2*pi) == cot(3*pi)
+    assert cot(-pi) == cot(-2*pi) == cot(-3*pi)
+
+    assert cot(pi/2) == 0
+    assert cot(-pi/2) == 0
+    assert cot(pi*Rational(5, 2)) == 0
+    assert cot(pi*Rational(7, 2)) == 0
+
+    assert cot(pi/3) == 1/sqrt(3)
+    assert cot(pi*Rational(-2, 3)) == 1/sqrt(3)
+
+    assert cot(pi/4) is S.One
+    assert cot(-pi/4) is S.NegativeOne
+    assert cot(pi*Rational(17, 4)) is S.One
+    assert cot(pi*Rational(-3, 4)) is S.One
+
+    assert cot(pi/6) == sqrt(3)
+    assert cot(-pi/6) == -sqrt(3)
+    assert cot(pi*Rational(7, 6)) == sqrt(3)
+    assert cot(pi*Rational(-5, 6)) == sqrt(3)
+
+    assert cot(pi/8) == 1 + sqrt(2)
+    assert cot(pi*Rational(3, 8)) == -1 + sqrt(2)
+    assert cot(pi*Rational(5, 8)) == 1 - sqrt(2)
+    assert cot(pi*Rational(7, 8)) == -1 - sqrt(2)
+
+    assert cot(pi/12) == sqrt(3) + 2
+    assert cot(pi*Rational(5, 12)) == -sqrt(3) + 2
+    assert cot(pi*Rational(7, 12)) == sqrt(3) - 2
+    assert cot(pi*Rational(11, 12)) == -sqrt(3) - 2
+
+    assert cot(pi/24).radsimp() == sqrt(2) + sqrt(3) + 2 + sqrt(6)
+    assert cot(pi*Rational(5, 24)).radsimp() == -sqrt(2) - sqrt(3) + 2 + sqrt(6)
+    assert cot(pi*Rational(7, 24)).radsimp() == -sqrt(2) + sqrt(3) - 2 + sqrt(6)
+    assert cot(pi*Rational(11, 24)).radsimp() == sqrt(2) - sqrt(3) - 2 + sqrt(6)
+    assert cot(pi*Rational(13, 24)).radsimp() == -sqrt(2) + sqrt(3) + 2 - sqrt(6)
+    assert cot(pi*Rational(17, 24)).radsimp() == sqrt(2) - sqrt(3) + 2 - sqrt(6)
+    assert cot(pi*Rational(19, 24)).radsimp() == sqrt(2) + sqrt(3) - 2 - sqrt(6)
+    assert cot(pi*Rational(23, 24)).radsimp() == -sqrt(2) - sqrt(3) - 2 - sqrt(6)
+
+    assert cot(x*I) == -coth(x)*I
+    assert cot(k*pi*I) == -coth(k*pi)*I
+
+    assert cot(r).is_real is None
+    assert cot(r).is_extended_real is True
+
+    assert cot(a).is_algebraic is None
+    assert cot(na).is_algebraic is False
+
+    assert cot(pi*Rational(10, 7)) == cot(pi*Rational(3, 7))
+    assert cot(pi*Rational(11, 7)) == -cot(pi*Rational(3, 7))
+    assert cot(pi*Rational(-11, 7)) == cot(pi*Rational(3, 7))
+
+    assert cot(pi*Rational(39, 34)) == cot(pi*Rational(5, 34))
+    assert cot(pi*Rational(-41, 34)) == -cot(pi*Rational(7, 34))
+
+    assert cot(x).is_finite is None
+    assert cot(r).is_finite is None
+    i = Symbol('i', imaginary=True)
+    assert cot(i).is_finite is True
+
+    assert cot(x).subs(x, 3*pi) is zoo
+
+    # https://github.com/sympy/sympy/issues/21177
+    f = cot(pi*(x + 4))/(3*x)
+    assert f.as_leading_term(x) == 1/(3*pi*x**2)
+
+
+def test_tan_cot_sin_cos_evalf():
+    assert abs((tan(pi*Rational(8, 15))*cos(pi*Rational(8, 15))/sin(pi*Rational(8, 15)) - 1).evalf()) < 1e-14
+    assert abs((cot(pi*Rational(4, 15))*sin(pi*Rational(4, 15))/cos(pi*Rational(4, 15)) - 1).evalf()) < 1e-14
+
+@XFAIL
+def test_tan_cot_sin_cos_ratsimp():
+    assert 1 == (tan(pi*Rational(8, 15))*cos(pi*Rational(8, 15))/sin(pi*Rational(8, 15))).ratsimp()
+    assert 1 == (cot(pi*Rational(4, 15))*sin(pi*Rational(4, 15))/cos(pi*Rational(4, 15))).ratsimp()
+
+
+def test_cot_series():
+    assert cot(x).series(x, 0, 9) == \
+        1/x - x/3 - x**3/45 - 2*x**5/945 - x**7/4725 + O(x**9)
+    # issue 6210
+    assert cot(x**4 + x**5).series(x, 0, 1) == \
+        x**(-4) - 1/x**3 + x**(-2) - 1/x + 1 + O(x)
+    assert cot(pi*(1-x)).series(x, 0, 3) == -1/(pi*x) + pi*x/3 + O(x**3)
+    assert cot(x).taylor_term(0, x) == 1/x
+    assert cot(x).taylor_term(2, x) is S.Zero
+    assert cot(x).taylor_term(3, x) == -x**3/45
+
+
+def test_cot_rewrite():
+    neg_exp, pos_exp = exp(-x*I), exp(x*I)
+    assert cot(x).rewrite(exp) == I*(pos_exp + neg_exp)/(pos_exp - neg_exp)
+    assert cot(x).rewrite(sin) == sin(2*x)/(2*(sin(x)**2))
+    assert cot(x).rewrite(cos) == cos(x)/cos(x - pi/2, evaluate=False)
+    assert cot(x).rewrite(tan) == 1/tan(x)
+    def check(func):
+        z = cot(func(x)).rewrite(exp) - cot(x).rewrite(exp).subs(x, func(x))
+        assert z.rewrite(exp).expand() == 0
+    check(sinh)
+    check(cosh)
+    check(tanh)
+    check(coth)
+    check(sin)
+    check(cos)
+    check(tan)
+    assert cot(log(x)).rewrite(Pow) == -I*(x**-I + x**I)/(x**-I - x**I)
+    assert cot(x).rewrite(sec) == sec(x - pi / 2, evaluate=False) / sec(x)
+    assert cot(x).rewrite(csc) == csc(x) / csc(- x + pi / 2, evaluate=False)
+    assert cot(sin(x)).rewrite(Pow) == cot(sin(x))
+    assert cot(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == (Rational(-1, 4) + sqrt(5)/4)/\
+                                                        sqrt(sqrt(5)/8 + Rational(5, 8))
+    assert cot(x).rewrite(besselj) == besselj(-S.Half, x)/besselj(S.Half, x)
+    assert cot(x).rewrite(besselj).subs(x, 0) == cot(0)
+
+
+@slow
+def test_cot_rewrite_slow():
+    assert cot(pi*Rational(4, 34)).rewrite(pow).ratsimp() == \
+        (cos(pi*Rational(4, 34))/sin(pi*Rational(4, 34))).rewrite(pow).ratsimp()
+    assert cot(pi*Rational(4, 17)).rewrite(pow) == \
+        (cos(pi*Rational(4, 17))/sin(pi*Rational(4, 17))).rewrite(pow)
+    assert cot(pi/19).rewrite(pow) == cot(pi/19)
+    assert cot(pi/19).rewrite(sqrt) == cot(pi/19)
+    assert cot(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == \
+        (Rational(-1, 4) + sqrt(5)/4) / sqrt(sqrt(5)/8 + Rational(5, 8))
+
+
+def test_cot_subs():
+    assert cot(x).subs(cot(x), y) == y
+    assert cot(x).subs(x, y) == cot(y)
+    assert cot(x).subs(x, 0) is zoo
+    assert cot(x).subs(x, S.Pi) is zoo
+
+
+def test_cot_expansion():
+    assert cot(x + y).expand(trig=True).together() == (
+        (cot(x)*cot(y) - 1)/(cot(x) + cot(y)))
+    assert cot(x - y).expand(trig=True).together() == (
+        cot(x)*cot(-y) - 1)/(cot(x) + cot(-y))
+    assert cot(x + y + z).expand(trig=True).together() == (
+        (cot(x)*cot(y)*cot(z) - cot(x) - cot(y) - cot(z))/
+        (-1 + cot(x)*cot(y) + cot(x)*cot(z) + cot(y)*cot(z)))
+    assert cot(3*x).expand(trig=True).together() == (
+        (cot(x)**2 - 3)*cot(x)/(3*cot(x)**2 - 1))
+    assert cot(2*x).expand(trig=True) == cot(x)/2 - 1/(2*cot(x))
+    assert cot(3*x).expand(trig=True).together() == (
+        cot(x)**2 - 3)*cot(x)/(3*cot(x)**2 - 1)
+    assert cot(4*x - pi/4).expand(trig=True).cancel() == (
+        -tan(x)**4 + 4*tan(x)**3 + 6*tan(x)**2 - 4*tan(x) - 1
+        )/(tan(x)**4 + 4*tan(x)**3 - 6*tan(x)**2 - 4*tan(x) + 1)
+    _test_extrig(cot, 2, (-1 + cot(1)**2)/(2*cot(1)))
+    _test_extrig(cot, 3, (-3*cot(1) + cot(1)**3)/(-1 + 3*cot(1)**2))
+
+
+def test_cot_AccumBounds():
+    assert cot(AccumBounds(-oo, oo)) == AccumBounds(-oo, oo)
+    assert cot(AccumBounds(-S.Pi/3, S.Pi/3)) == AccumBounds(-oo, oo)
+    assert cot(AccumBounds(S.Pi/6, S.Pi/3)) == AccumBounds(cot(S.Pi/3), cot(S.Pi/6))
+
+
+def test_cot_fdiff():
+    assert cot(x).fdiff() == -cot(x)**2 - 1
+    raises(ArgumentIndexError, lambda: cot(x).fdiff(2))
+
+
+def test_sinc():
+    assert isinstance(sinc(x), sinc)
+
+    s = Symbol('s', zero=True)
+    assert sinc(s) is S.One
+    assert sinc(S.Infinity) is S.Zero
+    assert sinc(S.NegativeInfinity) is S.Zero
+    assert sinc(S.NaN) is S.NaN
+    assert sinc(S.ComplexInfinity) is S.NaN
+
+    n = Symbol('n', integer=True, nonzero=True)
+    assert sinc(n*pi) is S.Zero
+    assert sinc(-n*pi) is S.Zero
+    assert sinc(pi/2) == 2 / pi
+    assert sinc(-pi/2) == 2 / pi
+    assert sinc(pi*Rational(5, 2)) == 2 / (5*pi)
+    assert sinc(pi*Rational(7, 2)) == -2 / (7*pi)
+
+    assert sinc(-x) == sinc(x)
+
+    assert sinc(x).diff(x) == cos(x)/x - sin(x)/x**2
+    assert sinc(x).diff(x) == (sin(x)/x).diff(x)
+    assert sinc(x).diff(x, x) == (-sin(x) - 2*cos(x)/x + 2*sin(x)/x**2)/x
+    assert sinc(x).diff(x, x) == (sin(x)/x).diff(x, x)
+    assert limit(sinc(x).diff(x), x, 0) == 0
+    assert limit(sinc(x).diff(x, x), x, 0) == -S(1)/3
+
+    # https://github.com/sympy/sympy/issues/11402
+    #
+    # assert sinc(x).diff(x) == Piecewise(((x*cos(x) - sin(x)) / x**2, Ne(x, 0)), (0, True))
+    #
+    # assert sinc(x).diff(x).equals(sinc(x).rewrite(sin).diff(x))
+    #
+    # assert sinc(x).diff(x).subs(x, 0) is S.Zero
+
+    assert sinc(x).series() == 1 - x**2/6 + x**4/120 + O(x**6)
+
+    assert sinc(x).rewrite(jn) == jn(0, x)
+    assert sinc(x).rewrite(sin) == Piecewise((sin(x)/x, Ne(x, 0)), (1, True))
+    assert sinc(pi, evaluate=False).is_zero is True
+    assert sinc(0, evaluate=False).is_zero is False
+    assert sinc(n*pi, evaluate=False).is_zero is True
+    assert sinc(x).is_zero is None
+    xr = Symbol('xr', real=True, nonzero=True)
+    assert sinc(x).is_real is None
+    assert sinc(xr).is_real is True
+    assert sinc(I*xr).is_real is True
+    assert sinc(I*100).is_real is True
+    assert sinc(x).is_finite is None
+    assert sinc(xr).is_finite is True
+
+
+def test_asin():
+    assert asin(nan) is nan
+
+    assert asin.nargs == FiniteSet(1)
+    assert asin(oo) == -I*oo
+    assert asin(-oo) == I*oo
+    assert asin(zoo) is zoo
+
+    # Note: asin(-x) = - asin(x)
+    assert asin(0) == 0
+    assert asin(1) == pi/2
+    assert asin(-1) == -pi/2
+    assert asin(sqrt(3)/2) == pi/3
+    assert asin(-sqrt(3)/2) == -pi/3
+    assert asin(sqrt(2)/2) == pi/4
+    assert asin(-sqrt(2)/2) == -pi/4
+    assert asin(sqrt((5 - sqrt(5))/8)) == pi/5
+    assert asin(-sqrt((5 - sqrt(5))/8)) == -pi/5
+    assert asin(S.Half) == pi/6
+    assert asin(Rational(-1, 2)) == -pi/6
+    assert asin((sqrt(2 - sqrt(2)))/2) == pi/8
+    assert asin(-(sqrt(2 - sqrt(2)))/2) == -pi/8
+    assert asin((sqrt(5) - 1)/4) == pi/10
+    assert asin(-(sqrt(5) - 1)/4) == -pi/10
+    assert asin((sqrt(3) - 1)/sqrt(2**3)) == pi/12
+    assert asin(-(sqrt(3) - 1)/sqrt(2**3)) == -pi/12
+
+    # check round-trip for exact values:
+    for d in [5, 6, 8, 10, 12]:
+        for n in range(-(d//2), d//2 + 1):
+            if gcd(n, d) == 1:
+                assert asin(sin(n*pi/d)) == n*pi/d
+
+    assert asin(x).diff(x) == 1/sqrt(1 - x**2)
+
+    assert asin(0.2, evaluate=False).is_real is True
+    assert asin(-2).is_real is False
+    assert asin(r).is_real is None
+
+    assert asin(-2*I) == -I*asinh(2)
+
+    assert asin(Rational(1, 7), evaluate=False).is_positive is True
+    assert asin(Rational(-1, 7), evaluate=False).is_positive is False
+    assert asin(p).is_positive is None
+    assert asin(sin(Rational(7, 2))) == Rational(-7, 2) + pi
+    assert asin(sin(Rational(-7, 4))) == Rational(7, 4) - pi
+    assert unchanged(asin, cos(x))
+
+
+def test_asin_series():
+    assert asin(x).series(x, 0, 9) == \
+        x + x**3/6 + 3*x**5/40 + 5*x**7/112 + O(x**9)
+    t5 = asin(x).taylor_term(5, x)
+    assert t5 == 3*x**5/40
+    assert asin(x).taylor_term(7, x, t5, 0) == 5*x**7/112
+
+
+def test_asin_leading_term():
+    assert asin(x).as_leading_term(x) == x
+    # Tests concerning branch points
+    assert asin(x + 1).as_leading_term(x) == pi/2
+    assert asin(x - 1).as_leading_term(x) == -pi/2
+    assert asin(1/x).as_leading_term(x, cdir=1) == I*log(x) + pi/2 - I*log(2)
+    assert asin(1/x).as_leading_term(x, cdir=-1) == -I*log(x) - 3*pi/2 + I*log(2)
+    # Tests concerning points lying on branch cuts
+    assert asin(I*x + 2).as_leading_term(x, cdir=1) == pi - asin(2)
+    assert asin(-I*x + 2).as_leading_term(x, cdir=1) == asin(2)
+    assert asin(I*x - 2).as_leading_term(x, cdir=1) == -asin(2)
+    assert asin(-I*x - 2).as_leading_term(x, cdir=1) == -pi + asin(2)
+    # Tests concerning im(ndir) == 0
+    assert asin(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == -pi/2 + I*log(2 - sqrt(3))
+    assert asin(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == -pi/2 + I*log(2 - sqrt(3))
+
+
+def test_asin_rewrite():
+    assert asin(x).rewrite(log) == -I*log(I*x + sqrt(1 - x**2))
+    assert asin(x).rewrite(atan) == 2*atan(x/(1 + sqrt(1 - x**2)))
+    assert asin(x).rewrite(acos) == S.Pi/2 - acos(x)
+    assert asin(x).rewrite(acot) == 2*acot((sqrt(-x**2 + 1) + 1)/x)
+    assert asin(x).rewrite(asec) == -asec(1/x) + pi/2
+    assert asin(x).rewrite(acsc) == acsc(1/x)
+
+
+def test_asin_fdiff():
+    assert asin(x).fdiff() == 1/sqrt(1 - x**2)
+    raises(ArgumentIndexError, lambda: asin(x).fdiff(2))
+
+
+def test_acos():
+    assert acos(nan) is nan
+    assert acos(zoo) is zoo
+
+    assert acos.nargs == FiniteSet(1)
+    assert acos(oo) == I*oo
+    assert acos(-oo) == -I*oo
+
+    # Note: acos(-x) = pi - acos(x)
+    assert acos(0) == pi/2
+    assert acos(S.Half) == pi/3
+    assert acos(Rational(-1, 2)) == pi*Rational(2, 3)
+    assert acos(1) == 0
+    assert acos(-1) == pi
+    assert acos(sqrt(2)/2) == pi/4
+    assert acos(-sqrt(2)/2) == pi*Rational(3, 4)
+
+    # check round-trip for exact values:
+    for d in range(5, 13):
+        for num in range(d):
+            if gcd(num, d) == 1:
+                assert acos(cos(num*pi/d)) == num*pi/d
+                assert acos(-cos(num*pi/d)) == pi - num*pi/d
+                assert acos(sin(num*pi/d)) == pi/2 - asin(sin(num*pi/d))
+                assert acos(-sin(num*pi/d)) == pi/2 - asin(-sin(num*pi/d))
+
+    assert acos(2*I) == pi/2 - asin(2*I)
+
+    assert acos(x).diff(x) == -1/sqrt(1 - x**2)
+
+    assert acos(0.2).is_real is True
+    assert acos(-2).is_real is False
+    assert acos(r).is_real is None
+
+    assert acos(Rational(1, 7), evaluate=False).is_positive is True
+    assert acos(Rational(-1, 7), evaluate=False).is_positive is True
+    assert acos(Rational(3, 2), evaluate=False).is_positive is False
+    assert acos(p).is_positive is None
+
+    assert acos(2 + p).conjugate() != acos(10 + p)
+    assert acos(-3 + n).conjugate() != acos(-3 + n)
+    assert acos(Rational(1, 3)).conjugate() == acos(Rational(1, 3))
+    assert acos(Rational(-1, 3)).conjugate() == acos(Rational(-1, 3))
+    assert acos(p + n*I).conjugate() == acos(p - n*I)
+    assert acos(z).conjugate() != acos(conjugate(z))
+
+
+def test_acos_leading_term():
+    assert acos(x).as_leading_term(x) == pi/2
+    # Tests concerning branch points
+    assert acos(x + 1).as_leading_term(x) == sqrt(2)*sqrt(-x)
+    assert acos(x - 1).as_leading_term(x) == pi
+    assert acos(1/x).as_leading_term(x, cdir=1) == -I*log(x) + I*log(2)
+    assert acos(1/x).as_leading_term(x, cdir=-1) == I*log(x) + 2*pi - I*log(2)
+    # Tests concerning points lying on branch cuts
+    assert acos(I*x + 2).as_leading_term(x, cdir=1) == -acos(2)
+    assert acos(-I*x + 2).as_leading_term(x, cdir=1) == acos(2)
+    assert acos(I*x - 2).as_leading_term(x, cdir=1) == acos(-2)
+    assert acos(-I*x - 2).as_leading_term(x, cdir=1) == 2*pi - acos(-2)
+    # Tests concerning im(ndir) == 0
+    assert acos(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == pi + I*log(sqrt(3) + 2)
+    assert acos(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == pi + I*log(sqrt(3) + 2)
+
+
+def test_acos_series():
+    assert acos(x).series(x, 0, 8) == \
+        pi/2 - x - x**3/6 - 3*x**5/40 - 5*x**7/112 + O(x**8)
+    assert acos(x).series(x, 0, 8) == pi/2 - asin(x).series(x, 0, 8)
+    t5 = acos(x).taylor_term(5, x)
+    assert t5 == -3*x**5/40
+    assert acos(x).taylor_term(7, x, t5, 0) == -5*x**7/112
+    assert acos(x).taylor_term(0, x) == pi/2
+    assert acos(x).taylor_term(2, x) is S.Zero
+
+
+def test_acos_rewrite():
+    assert acos(x).rewrite(log) == pi/2 + I*log(I*x + sqrt(1 - x**2))
+    assert acos(x).rewrite(atan) == pi*(-x*sqrt(x**(-2)) + 1)/2 + atan(sqrt(1 - x**2)/x)
+    assert acos(0).rewrite(atan) == S.Pi/2
+    assert acos(0.5).rewrite(atan) == acos(0.5).rewrite(log)
+    assert acos(x).rewrite(asin) == S.Pi/2 - asin(x)
+    assert acos(x).rewrite(acot) == -2*acot((sqrt(-x**2 + 1) + 1)/x) + pi/2
+    assert acos(x).rewrite(asec) == asec(1/x)
+    assert acos(x).rewrite(acsc) == -acsc(1/x) + pi/2
+
+
+def test_acos_fdiff():
+    assert acos(x).fdiff() == -1/sqrt(1 - x**2)
+    raises(ArgumentIndexError, lambda: acos(x).fdiff(2))
+
+
+def test_atan():
+    assert atan(nan) is nan
+
+    assert atan.nargs == FiniteSet(1)
+    assert atan(oo) == pi/2
+    assert atan(-oo) == -pi/2
+    assert atan(zoo) == AccumBounds(-pi/2, pi/2)
+
+    assert atan(0) == 0
+    assert atan(1) == pi/4
+    assert atan(sqrt(3)) == pi/3
+    assert atan(-(1 + sqrt(2))) == pi*Rational(-3, 8)
+    assert atan(sqrt(5 - 2 * sqrt(5))) == pi/5
+    assert atan(-sqrt(1 - 2 * sqrt(5)/ 5)) == -pi/10
+    assert atan(sqrt(1 + 2 * sqrt(5) / 5)) == pi*Rational(3, 10)
+    assert atan(-2 + sqrt(3)) == -pi/12
+    assert atan(2 + sqrt(3)) == pi*Rational(5, 12)
+    assert atan(-2 - sqrt(3)) == pi*Rational(-5, 12)
+
+    # check round-trip for exact values:
+    for d in [5, 6, 8, 10, 12]:
+        for num in range(-(d//2), d//2 + 1):
+            if gcd(num, d) == 1:
+                assert atan(tan(num*pi/d)) == num*pi/d
+
+    assert atan(oo) == pi/2
+    assert atan(x).diff(x) == 1/(1 + x**2)
+
+    assert atan(r).is_real is True
+
+    assert atan(-2*I) == -I*atanh(2)
+    assert unchanged(atan, cot(x))
+    assert atan(cot(Rational(1, 4))) == Rational(-1, 4) + pi/2
+    assert acot(Rational(1, 4)).is_rational is False
+
+    for s in (x, p, n, np, nn, nz, ep, en, enp, enn, enz):
+        if s.is_real or s.is_extended_real is None:
+            assert s.is_nonzero is atan(s).is_nonzero
+            assert s.is_positive is atan(s).is_positive
+            assert s.is_negative is atan(s).is_negative
+            assert s.is_nonpositive is atan(s).is_nonpositive
+            assert s.is_nonnegative is atan(s).is_nonnegative
+        else:
+            assert s.is_extended_nonzero is atan(s).is_nonzero
+            assert s.is_extended_positive is atan(s).is_positive
+            assert s.is_extended_negative is atan(s).is_negative
+            assert s.is_extended_nonpositive is atan(s).is_nonpositive
+            assert s.is_extended_nonnegative is atan(s).is_nonnegative
+        assert s.is_extended_nonzero is atan(s).is_extended_nonzero
+        assert s.is_extended_positive is atan(s).is_extended_positive
+        assert s.is_extended_negative is atan(s).is_extended_negative
+        assert s.is_extended_nonpositive is atan(s).is_extended_nonpositive
+        assert s.is_extended_nonnegative is atan(s).is_extended_nonnegative
+
+
+def test_atan_rewrite():
+    assert atan(x).rewrite(log) == I*(log(1 - I*x)-log(1 + I*x))/2
+    assert atan(x).rewrite(asin) == (-asin(1/sqrt(x**2 + 1)) + pi/2)*sqrt(x**2)/x
+    assert atan(x).rewrite(acos) == sqrt(x**2)*acos(1/sqrt(x**2 + 1))/x
+    assert atan(x).rewrite(acot) == acot(1/x)
+    assert atan(x).rewrite(asec) == sqrt(x**2)*asec(sqrt(x**2 + 1))/x
+    assert atan(x).rewrite(acsc) == (-acsc(sqrt(x**2 + 1)) + pi/2)*sqrt(x**2)/x
+
+    assert atan(-5*I).evalf() == atan(x).rewrite(log).evalf(subs={x:-5*I})
+    assert atan(5*I).evalf() == atan(x).rewrite(log).evalf(subs={x:5*I})
+
+
+def test_atan_fdiff():
+    assert atan(x).fdiff() == 1/(x**2 + 1)
+    raises(ArgumentIndexError, lambda: atan(x).fdiff(2))
+
+
+def test_atan_leading_term():
+    assert atan(x).as_leading_term(x) == x
+    assert atan(1/x).as_leading_term(x, cdir=1) == pi/2
+    assert atan(1/x).as_leading_term(x, cdir=-1) == -pi/2
+    # Tests concerning branch points
+    assert atan(x + I).as_leading_term(x, cdir=1) == -I*log(x)/2 + pi/4 + I*log(2)/2
+    assert atan(x + I).as_leading_term(x, cdir=-1) == -I*log(x)/2 - 3*pi/4 + I*log(2)/2
+    assert atan(x - I).as_leading_term(x, cdir=1) == I*log(x)/2 + pi/4 - I*log(2)/2
+    assert atan(x - I).as_leading_term(x, cdir=-1) == I*log(x)/2 + pi/4 - I*log(2)/2
+    # Tests concerning points lying on branch cuts
+    assert atan(x + 2*I).as_leading_term(x, cdir=1) == I*atanh(2)
+    assert atan(x + 2*I).as_leading_term(x, cdir=-1) == -pi + I*atanh(2)
+    assert atan(x - 2*I).as_leading_term(x, cdir=1) == pi - I*atanh(2)
+    assert atan(x - 2*I).as_leading_term(x, cdir=-1) == -I*atanh(2)
+    # Tests concerning re(ndir) == 0
+    assert atan(2*I - I*x - x**2).as_leading_term(x, cdir=1) == -pi/2 + I*log(3)/2
+    assert atan(2*I - I*x - x**2).as_leading_term(x, cdir=-1) == -pi/2 + I*log(3)/2
+
+
+def test_atan2():
+    assert atan2.nargs == FiniteSet(2)
+    assert atan2(0, 0) is S.NaN
+    assert atan2(0, 1) == 0
+    assert atan2(1, 1) == pi/4
+    assert atan2(1, 0) == pi/2
+    assert atan2(1, -1) == pi*Rational(3, 4)
+    assert atan2(0, -1) == pi
+    assert atan2(-1, -1) == pi*Rational(-3, 4)
+    assert atan2(-1, 0) == -pi/2
+    assert atan2(-1, 1) == -pi/4
+    i = symbols('i', imaginary=True)
+    r = symbols('r', real=True)
+    eq = atan2(r, i)
+    ans = -I*log((i + I*r)/sqrt(i**2 + r**2))
+    reps = ((r, 2), (i, I))
+    assert eq.subs(reps) == ans.subs(reps)
+
+    x = Symbol('x', negative=True)
+    y = Symbol('y', negative=True)
+    assert atan2(y, x) == atan(y/x) - pi
+    y = Symbol('y', nonnegative=True)
+    assert atan2(y, x) == atan(y/x) + pi
+    y = Symbol('y')
+    assert atan2(y, x) == atan2(y, x, evaluate=False)
+
+    u = Symbol("u", positive=True)
+    assert atan2(0, u) == 0
+    u = Symbol("u", negative=True)
+    assert atan2(0, u) == pi
+
+    assert atan2(y, oo) ==  0
+    assert atan2(y, -oo)==  2*pi*Heaviside(re(y), S.Half) - pi
+
+    assert atan2(y, x).rewrite(log) == -I*log((x + I*y)/sqrt(x**2 + y**2))
+    assert atan2(0, 0) is S.NaN
+
+    ex = atan2(y, x) - arg(x + I*y)
+    assert ex.subs({x:2, y:3}).rewrite(arg) == 0
+    assert ex.subs({x:2, y:3*I}).rewrite(arg) == -pi - I*log(sqrt(5)*I/5)
+    assert ex.subs({x:2*I, y:3}).rewrite(arg) == -pi/2 - I*log(sqrt(5)*I)
+    assert ex.subs({x:2*I, y:3*I}).rewrite(arg) == -pi + atan(Rational(2, 3)) + atan(Rational(3, 2))
+    i = symbols('i', imaginary=True)
+    r = symbols('r', real=True)
+    e = atan2(i, r)
+    rewrite = e.rewrite(arg)
+    reps = {i: I, r: -2}
+    assert rewrite == -I*log(abs(I*i + r)/sqrt(abs(i**2 + r**2))) + arg((I*i + r)/sqrt(i**2 + r**2))
+    assert (e - rewrite).subs(reps).equals(0)
+
+    assert atan2(0, x).rewrite(atan) == Piecewise((pi, re(x) < 0),
+                                            (0, Ne(x, 0)),
+                                            (nan, True))
+    assert atan2(0, r).rewrite(atan) == Piecewise((pi, r < 0), (0, Ne(r, 0)), (S.NaN, True))
+    assert atan2(0, i),rewrite(atan) == 0
+    assert atan2(0, r + i).rewrite(atan) == Piecewise((pi, r < 0), (0, True))
+
+    assert atan2(y, x).rewrite(atan) == Piecewise(
+            (2*atan(y/(x + sqrt(x**2 + y**2))), Ne(y, 0)),
+            (pi, re(x) < 0),
+            (0, (re(x) > 0) | Ne(im(x), 0)),
+            (nan, True))
+    assert conjugate(atan2(x, y)) == atan2(conjugate(x), conjugate(y))
+
+    assert diff(atan2(y, x), x) == -y/(x**2 + y**2)
+    assert diff(atan2(y, x), y) == x/(x**2 + y**2)
+
+    assert simplify(diff(atan2(y, x).rewrite(log), x)) == -y/(x**2 + y**2)
+    assert simplify(diff(atan2(y, x).rewrite(log), y)) ==  x/(x**2 + y**2)
+
+    assert str(atan2(1, 2).evalf(5)) == '0.46365'
+    raises(ArgumentIndexError, lambda: atan2(x, y).fdiff(3))
+
+def test_issue_17461():
+    class A(Symbol):
+        is_extended_real = True
+
+        def _eval_evalf(self, prec):
+            return Float(5.0)
+
+    x = A('X')
+    y = A('Y')
+    assert abs(atan2(x, y).evalf() - 0.785398163397448) <= 1e-10
+
+def test_acot():
+    assert acot(nan) is nan
+
+    assert acot.nargs == FiniteSet(1)
+    assert acot(-oo) == 0
+    assert acot(oo) == 0
+    assert acot(zoo) == 0
+    assert acot(1) == pi/4
+    assert acot(0) == pi/2
+    assert acot(sqrt(3)/3) == pi/3
+    assert acot(1/sqrt(3)) == pi/3
+    assert acot(-1/sqrt(3)) == -pi/3
+    assert acot(x).diff(x) == -1/(1 + x**2)
+
+    assert acot(r).is_extended_real is True
+
+    assert acot(I*pi) == -I*acoth(pi)
+    assert acot(-2*I) == I*acoth(2)
+    assert acot(x).is_positive is None
+    assert acot(n).is_positive is False
+    assert acot(p).is_positive is True
+    assert acot(I).is_positive is False
+    assert acot(Rational(1, 4)).is_rational is False
+    assert unchanged(acot, cot(x))
+    assert unchanged(acot, tan(x))
+    assert acot(cot(Rational(1, 4))) == Rational(1, 4)
+    assert acot(tan(Rational(-1, 4))) == Rational(1, 4) - pi/2
+
+
+def test_acot_rewrite():
+    assert acot(x).rewrite(log) == I*(log(1 - I/x)-log(1 + I/x))/2
+    assert acot(x).rewrite(asin) == x*(-asin(sqrt(-x**2)/sqrt(-x**2 - 1)) + pi/2)*sqrt(x**(-2))
+    assert acot(x).rewrite(acos) == x*sqrt(x**(-2))*acos(sqrt(-x**2)/sqrt(-x**2 - 1))
+    assert acot(x).rewrite(atan) == atan(1/x)
+    assert acot(x).rewrite(asec) == x*sqrt(x**(-2))*asec(sqrt((x**2 + 1)/x**2))
+    assert acot(x).rewrite(acsc) == x*(-acsc(sqrt((x**2 + 1)/x**2)) + pi/2)*sqrt(x**(-2))
+
+    assert acot(-I/5).evalf() == acot(x).rewrite(log).evalf(subs={x:-I/5})
+    assert acot(I/5).evalf() == acot(x).rewrite(log).evalf(subs={x:I/5})
+
+
+def test_acot_fdiff():
+    assert acot(x).fdiff() == -1/(x**2 + 1)
+    raises(ArgumentIndexError, lambda: acot(x).fdiff(2))
+
+def test_acot_leading_term():
+    assert acot(1/x).as_leading_term(x) == x
+    # Tests concerning branch points
+    assert acot(x + I).as_leading_term(x, cdir=1) == I*log(x)/2 + pi/4 - I*log(2)/2
+    assert acot(x + I).as_leading_term(x, cdir=-1) == I*log(x)/2 + pi/4 - I*log(2)/2
+    assert acot(x - I).as_leading_term(x, cdir=1) == -I*log(x)/2 + pi/4 + I*log(2)/2
+    assert acot(x - I).as_leading_term(x, cdir=-1) == -I*log(x)/2 - 3*pi/4 + I*log(2)/2
+    # Tests concerning points lying on branch cuts
+    assert acot(x).as_leading_term(x, cdir=1) == pi/2
+    assert acot(x).as_leading_term(x, cdir=-1) == -pi/2
+    assert acot(x + I/2).as_leading_term(x, cdir=1) == pi - I*acoth(S(1)/2)
+    assert acot(x + I/2).as_leading_term(x, cdir=-1) == -I*acoth(S(1)/2)
+    assert acot(x - I/2).as_leading_term(x, cdir=1) == I*acoth(S(1)/2)
+    assert acot(x - I/2).as_leading_term(x, cdir=-1) == -pi + I*acoth(S(1)/2)
+    # Tests concerning re(ndir) == 0
+    assert acot(I/2 - I*x - x**2).as_leading_term(x, cdir=1) == -pi/2 - I*log(3)/2
+    assert acot(I/2 - I*x - x**2).as_leading_term(x, cdir=-1) == -pi/2 - I*log(3)/2
+
+
+def test_attributes():
+    assert sin(x).args == (x,)
+
+
+def test_sincos_rewrite():
+    assert sin(pi/2 - x) == cos(x)
+    assert sin(pi - x) == sin(x)
+    assert cos(pi/2 - x) == sin(x)
+    assert cos(pi - x) == -cos(x)
+
+
+def _check_even_rewrite(func, arg):
+    """Checks that the expr has been rewritten using f(-x) -> f(x)
+    arg : -x
+    """
+    return func(arg).args[0] == -arg
+
+
+def _check_odd_rewrite(func, arg):
+    """Checks that the expr has been rewritten using f(-x) -> -f(x)
+    arg : -x
+    """
+    return func(arg).func.is_Mul
+
+
+def _check_no_rewrite(func, arg):
+    """Checks that the expr is not rewritten"""
+    return func(arg).args[0] == arg
+
+
+def test_evenodd_rewrite():
+    a = cos(2)  # negative
+    b = sin(1)  # positive
+    even = [cos]
+    odd = [sin, tan, cot, asin, atan, acot]
+    with_minus = [-1, -2**1024 * E, -pi/105, -x*y, -x - y]
+    for func in even:
+        for expr in with_minus:
+            assert _check_even_rewrite(func, expr)
+        assert _check_no_rewrite(func, a*b)
+        assert func(
+            x - y) == func(y - x)  # it doesn't matter which form is canonical
+    for func in odd:
+        for expr in with_minus:
+            assert _check_odd_rewrite(func, expr)
+        assert _check_no_rewrite(func, a*b)
+        assert func(
+            x - y) == -func(y - x)  # it doesn't matter which form is canonical
+
+
+def test_as_leading_term_issue_5272():
+    assert sin(x).as_leading_term(x) == x
+    assert cos(x).as_leading_term(x) == 1
+    assert tan(x).as_leading_term(x) == x
+    assert cot(x).as_leading_term(x) == 1/x
+
+
+def test_leading_terms():
+    assert sin(1/x).as_leading_term(x) == AccumBounds(-1, 1)
+    assert sin(S.Half).as_leading_term(x) == sin(S.Half)
+    assert cos(1/x).as_leading_term(x) == AccumBounds(-1, 1)
+    assert cos(S.Half).as_leading_term(x) == cos(S.Half)
+    assert sec(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity)
+    assert csc(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity)
+    assert tan(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity)
+    assert cot(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity)
+
+    # https://github.com/sympy/sympy/issues/21038
+    f = sin(pi*(x + 4))/(3*x)
+    assert f.as_leading_term(x) == pi/3
+
+
+def test_atan2_expansion():
+    assert cancel(atan2(x**2, x + 1).diff(x) - atan(x**2/(x + 1)).diff(x)) == 0
+    assert cancel(atan(y/x).series(y, 0, 5) - atan2(y, x).series(y, 0, 5)
+                  + atan2(0, x) - atan(0)) == O(y**5)
+    assert cancel(atan(y/x).series(x, 1, 4) - atan2(y, x).series(x, 1, 4)
+                  + atan2(y, 1) - atan(y)) == O((x - 1)**4, (x, 1))
+    assert cancel(atan((y + x)/x).series(x, 1, 3) - atan2(y + x, x).series(x, 1, 3)
+                  + atan2(1 + y, 1) - atan(1 + y)) == O((x - 1)**3, (x, 1))
+    assert Matrix([atan2(y, x)]).jacobian([y, x]) == \
+        Matrix([[x/(y**2 + x**2), -y/(y**2 + x**2)]])
+
+
+def test_aseries():
+    def t(n, v, d, e):
+        assert abs(
+            n(1/v).evalf() - n(1/x).series(x, dir=d).removeO().subs(x, v)) < e
+    t(atan, 0.1, '+', 1e-5)
+    t(atan, -0.1, '-', 1e-5)
+    t(acot, 0.1, '+', 1e-5)
+    t(acot, -0.1, '-', 1e-5)
+
+
+def test_issue_4420():
+    i = Symbol('i', integer=True)
+    e = Symbol('e', even=True)
+    o = Symbol('o', odd=True)
+
+    # unknown parity for variable
+    assert cos(4*i*pi) == 1
+    assert sin(4*i*pi) == 0
+    assert tan(4*i*pi) == 0
+    assert cot(4*i*pi) is zoo
+
+    assert cos(3*i*pi) == cos(pi*i)  # +/-1
+    assert sin(3*i*pi) == 0
+    assert tan(3*i*pi) == 0
+    assert cot(3*i*pi) is zoo
+
+    assert cos(4.0*i*pi) == 1
+    assert sin(4.0*i*pi) == 0
+    assert tan(4.0*i*pi) == 0
+    assert cot(4.0*i*pi) is zoo
+
+    assert cos(3.0*i*pi) == cos(pi*i)  # +/-1
+    assert sin(3.0*i*pi) == 0
+    assert tan(3.0*i*pi) == 0
+    assert cot(3.0*i*pi) is zoo
+
+    assert cos(4.5*i*pi) == cos(0.5*pi*i)
+    assert sin(4.5*i*pi) == sin(0.5*pi*i)
+    assert tan(4.5*i*pi) == tan(0.5*pi*i)
+    assert cot(4.5*i*pi) == cot(0.5*pi*i)
+
+    # parity of variable is known
+    assert cos(4*e*pi) == 1
+    assert sin(4*e*pi) == 0
+    assert tan(4*e*pi) == 0
+    assert cot(4*e*pi) is zoo
+
+    assert cos(3*e*pi) == 1
+    assert sin(3*e*pi) == 0
+    assert tan(3*e*pi) == 0
+    assert cot(3*e*pi) is zoo
+
+    assert cos(4.0*e*pi) == 1
+    assert sin(4.0*e*pi) == 0
+    assert tan(4.0*e*pi) == 0
+    assert cot(4.0*e*pi) is zoo
+
+    assert cos(3.0*e*pi) == 1
+    assert sin(3.0*e*pi) == 0
+    assert tan(3.0*e*pi) == 0
+    assert cot(3.0*e*pi) is zoo
+
+    assert cos(4.5*e*pi) == cos(0.5*pi*e)
+    assert sin(4.5*e*pi) == sin(0.5*pi*e)
+    assert tan(4.5*e*pi) == tan(0.5*pi*e)
+    assert cot(4.5*e*pi) == cot(0.5*pi*e)
+
+    assert cos(4*o*pi) == 1
+    assert sin(4*o*pi) == 0
+    assert tan(4*o*pi) == 0
+    assert cot(4*o*pi) is zoo
+
+    assert cos(3*o*pi) == -1
+    assert sin(3*o*pi) == 0
+    assert tan(3*o*pi) == 0
+    assert cot(3*o*pi) is zoo
+
+    assert cos(4.0*o*pi) == 1
+    assert sin(4.0*o*pi) == 0
+    assert tan(4.0*o*pi) == 0
+    assert cot(4.0*o*pi) is zoo
+
+    assert cos(3.0*o*pi) == -1
+    assert sin(3.0*o*pi) == 0
+    assert tan(3.0*o*pi) == 0
+    assert cot(3.0*o*pi) is zoo
+
+    assert cos(4.5*o*pi) == cos(0.5*pi*o)
+    assert sin(4.5*o*pi) == sin(0.5*pi*o)
+    assert tan(4.5*o*pi) == tan(0.5*pi*o)
+    assert cot(4.5*o*pi) == cot(0.5*pi*o)
+
+    # x could be imaginary
+    assert cos(4*x*pi) == cos(4*pi*x)
+    assert sin(4*x*pi) == sin(4*pi*x)
+    assert tan(4*x*pi) == tan(4*pi*x)
+    assert cot(4*x*pi) == cot(4*pi*x)
+
+    assert cos(3*x*pi) == cos(3*pi*x)
+    assert sin(3*x*pi) == sin(3*pi*x)
+    assert tan(3*x*pi) == tan(3*pi*x)
+    assert cot(3*x*pi) == cot(3*pi*x)
+
+    assert cos(4.0*x*pi) == cos(4.0*pi*x)
+    assert sin(4.0*x*pi) == sin(4.0*pi*x)
+    assert tan(4.0*x*pi) == tan(4.0*pi*x)
+    assert cot(4.0*x*pi) == cot(4.0*pi*x)
+
+    assert cos(3.0*x*pi) == cos(3.0*pi*x)
+    assert sin(3.0*x*pi) == sin(3.0*pi*x)
+    assert tan(3.0*x*pi) == tan(3.0*pi*x)
+    assert cot(3.0*x*pi) == cot(3.0*pi*x)
+
+    assert cos(4.5*x*pi) == cos(4.5*pi*x)
+    assert sin(4.5*x*pi) == sin(4.5*pi*x)
+    assert tan(4.5*x*pi) == tan(4.5*pi*x)
+    assert cot(4.5*x*pi) == cot(4.5*pi*x)
+
+
+def test_inverses():
+    raises(AttributeError, lambda: sin(x).inverse())
+    raises(AttributeError, lambda: cos(x).inverse())
+    assert tan(x).inverse() == atan
+    assert cot(x).inverse() == acot
+    raises(AttributeError, lambda: csc(x).inverse())
+    raises(AttributeError, lambda: sec(x).inverse())
+    assert asin(x).inverse() == sin
+    assert acos(x).inverse() == cos
+    assert atan(x).inverse() == tan
+    assert acot(x).inverse() == cot
+
+
+def test_real_imag():
+    a, b = symbols('a b', real=True)
+    z = a + b*I
+    for deep in [True, False]:
+        assert sin(
+            z).as_real_imag(deep=deep) == (sin(a)*cosh(b), cos(a)*sinh(b))
+        assert cos(
+            z).as_real_imag(deep=deep) == (cos(a)*cosh(b), -sin(a)*sinh(b))
+        assert tan(z).as_real_imag(deep=deep) == (sin(2*a)/(cos(2*a) +
+            cosh(2*b)), sinh(2*b)/(cos(2*a) + cosh(2*b)))
+        assert cot(z).as_real_imag(deep=deep) == (-sin(2*a)/(cos(2*a) -
+            cosh(2*b)), sinh(2*b)/(cos(2*a) - cosh(2*b)))
+        assert sin(a).as_real_imag(deep=deep) == (sin(a), 0)
+        assert cos(a).as_real_imag(deep=deep) == (cos(a), 0)
+        assert tan(a).as_real_imag(deep=deep) == (tan(a), 0)
+        assert cot(a).as_real_imag(deep=deep) == (cot(a), 0)
+
+
+@slow
+def test_sincos_rewrite_sqrt():
+    # equivalent to testing rewrite(pow)
+    for p in [1, 3, 5, 17]:
+        for t in [1, 8]:
+            n = t*p
+            # The vertices `exp(i*pi/n)` of a regular `n`-gon can
+            # be expressed by means of nested square roots if and
+            # only if `n` is a product of Fermat primes, `p`, and
+            # powers of 2, `t'. The code aims to check all vertices
+            # not belonging to an `m`-gon for `m < n`(`gcd(i, n) == 1`).
+            # For large `n` this makes the test too slow, therefore
+            # the vertices are limited to those of index `i < 10`.
+            for i in range(1, min((n + 1)//2 + 1, 10)):
+                if 1 == gcd(i, n):
+                    x = i*pi/n
+                    s1 = sin(x).rewrite(sqrt)
+                    c1 = cos(x).rewrite(sqrt)
+                    assert not s1.has(cos, sin), "fails for %d*pi/%d" % (i, n)
+                    assert not c1.has(cos, sin), "fails for %d*pi/%d" % (i, n)
+                    assert 1e-3 > abs(sin(x.evalf(5)) - s1.evalf(2)), "fails for %d*pi/%d" % (i, n)
+                    assert 1e-3 > abs(cos(x.evalf(5)) - c1.evalf(2)), "fails for %d*pi/%d" % (i, n)
+    assert cos(pi/14).rewrite(sqrt) == sqrt(cos(pi/7)/2 + S.Half)
+    assert cos(pi*Rational(-15, 2)/11, evaluate=False).rewrite(
+        sqrt) == -sqrt(-cos(pi*Rational(4, 11))/2 + S.Half)
+    assert cos(Mul(2, pi, S.Half, evaluate=False), evaluate=False).rewrite(
+        sqrt) == -1
+    e = cos(pi/3/17)  # don't use pi/15 since that is caught at instantiation
+    a = (
+        -3*sqrt(-sqrt(17) + 17)*sqrt(sqrt(17) + 17)/64 -
+        3*sqrt(34)*sqrt(sqrt(17) + 17)/128 - sqrt(sqrt(17) +
+        17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17)
+        + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 - sqrt(-sqrt(17)
+        + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/128 - Rational(1, 32) +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 +
+        3*sqrt(2)*sqrt(sqrt(17) + 17)/128 + sqrt(34)*sqrt(-sqrt(17) + 17)/128
+        + 13*sqrt(2)*sqrt(-sqrt(17) + 17)/128 + sqrt(17)*sqrt(-sqrt(17) +
+        17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17)
+        + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/128 + 5*sqrt(17)/32
+        + sqrt(3)*sqrt(-sqrt(2)*sqrt(sqrt(17) + 17)*sqrt(sqrt(17)/32 +
+        sqrt(2)*sqrt(-sqrt(17) + 17)/32 +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + Rational(15, 32))/8 -
+        5*sqrt(2)*sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + 17)/32 +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 +
+        Rational(15, 32))*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 -
+        3*sqrt(2)*sqrt(-sqrt(17) + 17)*sqrt(sqrt(17)/32 +
+        sqrt(2)*sqrt(-sqrt(17) + 17)/32 +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + Rational(15, 32))/32
+        + sqrt(34)*sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + 17)/32 +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 +
+        Rational(15, 32))*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 +
+        sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + 17)/32 +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + Rational(15, 32))/2 +
+        S.Half + sqrt(-sqrt(17) + 17)*sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) +
+        17)/32 + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) -
+        sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) +
+        6*sqrt(17) + 34)/32 + Rational(15, 32))*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) -
+        sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) +
+        6*sqrt(17) + 34)/32 + sqrt(34)*sqrt(-sqrt(17) + 17)*sqrt(sqrt(17)/32 +
+        sqrt(2)*sqrt(-sqrt(17) + 17)/32 +
+        sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) +
+        17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 +
+        Rational(15, 32))/32)/2)
+    assert e.rewrite(sqrt) == a
+    assert e.n() == a.n()
+    # coverage of fermatCoords: multiplicity > 1; the following could be
+    # different but that portion of the code should be tested in some way
+    assert cos(pi/9/17).rewrite(sqrt) == \
+        sin(pi/9)*sin(pi*Rational(2, 17)) + cos(pi/9)*cos(pi*Rational(2, 17))
+
+
+@slow
+def test_sincos_rewrite_sqrt_257():
+    assert cos(pi/257).rewrite(sqrt).evalf(64) == cos(pi/257).evalf(64)
+
+
+@slow
+def test_tancot_rewrite_sqrt():
+    # equivalent to testing rewrite(pow)
+    for p in [1, 3, 5, 17]:
+        for t in [1, 8]:
+            n = t*p
+            for i in range(1, min((n + 1)//2 + 1, 10)):
+                if 1 == gcd(i, n):
+                    x = i*pi/n
+                    if  2*i != n and 3*i != 2*n:
+                        t1 = tan(x).rewrite(sqrt)
+                        assert not t1.has(cot, tan), "fails for %d*pi/%d" % (i, n)
+                        assert 1e-3 > abs( tan(x.evalf(7)) - t1.evalf(4) ), "fails for %d*pi/%d" % (i, n)
+                    if  i != 0 and i != n:
+                        c1 = cot(x).rewrite(sqrt)
+                        assert not c1.has(cot, tan), "fails for %d*pi/%d" % (i, n)
+                        assert 1e-3 > abs( cot(x.evalf(7)) - c1.evalf(4) ), "fails for %d*pi/%d" % (i, n)
+
+
+def test_sec():
+    x = symbols('x', real=True)
+    z = symbols('z')
+
+    assert sec.nargs == FiniteSet(1)
+
+    assert sec(zoo) is nan
+    assert sec(0) == 1
+    assert sec(pi) == -1
+    assert sec(pi/2) is zoo
+    assert sec(-pi/2) is zoo
+    assert sec(pi/6) == 2*sqrt(3)/3
+    assert sec(pi/3) == 2
+    assert sec(pi*Rational(5, 2)) is zoo
+    assert sec(pi*Rational(9, 7)) == -sec(pi*Rational(2, 7))
+    assert sec(pi*Rational(3, 4)) == -sqrt(2)  # issue 8421
+    assert sec(I) == 1/cosh(1)
+    assert sec(x*I) == 1/cosh(x)
+    assert sec(-x) == sec(x)
+
+    assert sec(asec(x)) == x
+
+    assert sec(z).conjugate() == sec(conjugate(z))
+
+    assert (sec(z).as_real_imag() ==
+    (cos(re(z))*cosh(im(z))/(sin(re(z))**2*sinh(im(z))**2 +
+                             cos(re(z))**2*cosh(im(z))**2),
+     sin(re(z))*sinh(im(z))/(sin(re(z))**2*sinh(im(z))**2 +
+                             cos(re(z))**2*cosh(im(z))**2)))
+
+    assert sec(x).expand(trig=True) == 1/cos(x)
+    assert sec(2*x).expand(trig=True) == 1/(2*cos(x)**2 - 1)
+
+    assert sec(x).is_extended_real == True
+    assert sec(z).is_real == None
+
+    assert sec(a).is_algebraic is None
+    assert sec(na).is_algebraic is False
+
+    assert sec(x).as_leading_term() == sec(x)
+
+    assert sec(0, evaluate=False).is_finite == True
+    assert sec(x).is_finite == None
+    assert sec(pi/2, evaluate=False).is_finite == False
+
+    assert series(sec(x), x, x0=0, n=6) == 1 + x**2/2 + 5*x**4/24 + O(x**6)
+
+    # https://github.com/sympy/sympy/issues/7166
+    assert series(sqrt(sec(x))) == 1 + x**2/4 + 7*x**4/96 + O(x**6)
+
+    # https://github.com/sympy/sympy/issues/7167
+    assert (series(sqrt(sec(x)), x, x0=pi*3/2, n=4) ==
+            1/sqrt(x - pi*Rational(3, 2)) + (x - pi*Rational(3, 2))**Rational(3, 2)/12 +
+            (x - pi*Rational(3, 2))**Rational(7, 2)/160 + O((x - pi*Rational(3, 2))**4, (x, pi*Rational(3, 2))))
+
+    assert sec(x).diff(x) == tan(x)*sec(x)
+
+    # Taylor Term checks
+    assert sec(z).taylor_term(4, z) == 5*z**4/24
+    assert sec(z).taylor_term(6, z) == 61*z**6/720
+    assert sec(z).taylor_term(5, z) == 0
+
+
+def test_sec_rewrite():
+    assert sec(x).rewrite(exp) == 1/(exp(I*x)/2 + exp(-I*x)/2)
+    assert sec(x).rewrite(cos) == 1/cos(x)
+    assert sec(x).rewrite(tan) == (tan(x/2)**2 + 1)/(-tan(x/2)**2 + 1)
+    assert sec(x).rewrite(pow) == sec(x)
+    assert sec(x).rewrite(sqrt) == sec(x)
+    assert sec(z).rewrite(cot) == (cot(z/2)**2 + 1)/(cot(z/2)**2 - 1)
+    assert sec(x).rewrite(sin) == 1 / sin(x + pi / 2, evaluate=False)
+    assert sec(x).rewrite(tan) == (tan(x / 2)**2 + 1) / (-tan(x / 2)**2 + 1)
+    assert sec(x).rewrite(csc) == csc(-x + pi/2, evaluate=False)
+    assert sec(x).rewrite(besselj) == Piecewise(
+                (sqrt(2)/(sqrt(pi*x)*besselj(-S.Half, x)), Ne(x, 0)),
+                (1, True)
+            )
+    assert sec(x).rewrite(besselj).subs(x, 0) == sec(0)
+
+
+def test_sec_fdiff():
+    assert sec(x).fdiff() == tan(x)*sec(x)
+    raises(ArgumentIndexError, lambda: sec(x).fdiff(2))
+
+
+def test_csc():
+    x = symbols('x', real=True)
+    z = symbols('z')
+
+    # https://github.com/sympy/sympy/issues/6707
+    cosecant = csc('x')
+    alternate = 1/sin('x')
+    assert cosecant.equals(alternate) == True
+    assert alternate.equals(cosecant) == True
+
+    assert csc.nargs == FiniteSet(1)
+
+    assert csc(0) is zoo
+    assert csc(pi) is zoo
+    assert csc(zoo) is nan
+
+    assert csc(pi/2) == 1
+    assert csc(-pi/2) == -1
+    assert csc(pi/6) == 2
+    assert csc(pi/3) == 2*sqrt(3)/3
+    assert csc(pi*Rational(5, 2)) == 1
+    assert csc(pi*Rational(9, 7)) == -csc(pi*Rational(2, 7))
+    assert csc(pi*Rational(3, 4)) == sqrt(2)  # issue 8421
+    assert csc(I) == -I/sinh(1)
+    assert csc(x*I) == -I/sinh(x)
+    assert csc(-x) == -csc(x)
+
+    assert csc(acsc(x)) == x
+
+    assert csc(z).conjugate() == csc(conjugate(z))
+
+    assert (csc(z).as_real_imag() ==
+            (sin(re(z))*cosh(im(z))/(sin(re(z))**2*cosh(im(z))**2 +
+                                     cos(re(z))**2*sinh(im(z))**2),
+             -cos(re(z))*sinh(im(z))/(sin(re(z))**2*cosh(im(z))**2 +
+                          cos(re(z))**2*sinh(im(z))**2)))
+
+    assert csc(x).expand(trig=True) == 1/sin(x)
+    assert csc(2*x).expand(trig=True) == 1/(2*sin(x)*cos(x))
+
+    assert csc(x).is_extended_real == True
+    assert csc(z).is_real == None
+
+    assert csc(a).is_algebraic is None
+    assert csc(na).is_algebraic is False
+
+    assert csc(x).as_leading_term() == csc(x)
+
+    assert csc(0, evaluate=False).is_finite == False
+    assert csc(x).is_finite == None
+    assert csc(pi/2, evaluate=False).is_finite == True
+
+    assert series(csc(x), x, x0=pi/2, n=6) == \
+        1 + (x - pi/2)**2/2 + 5*(x - pi/2)**4/24 + O((x - pi/2)**6, (x, pi/2))
+    assert series(csc(x), x, x0=0, n=6) == \
+            1/x + x/6 + 7*x**3/360 + 31*x**5/15120 + O(x**6)
+
+    assert csc(x).diff(x) == -cot(x)*csc(x)
+
+    assert csc(x).taylor_term(2, x) == 0
+    assert csc(x).taylor_term(3, x) == 7*x**3/360
+    assert csc(x).taylor_term(5, x) == 31*x**5/15120
+    raises(ArgumentIndexError, lambda: csc(x).fdiff(2))
+
+
+def test_asec():
+    z = Symbol('z', zero=True)
+    assert asec(z) is zoo
+    assert asec(nan) is nan
+    assert asec(1) == 0
+    assert asec(-1) == pi
+    assert asec(oo) == pi/2
+    assert asec(-oo) == pi/2
+    assert asec(zoo) == pi/2
+
+    assert asec(sec(pi*Rational(13, 4))) == pi*Rational(3, 4)
+    assert asec(1 + sqrt(5)) == pi*Rational(2, 5)
+    assert asec(2/sqrt(3)) == pi/6
+    assert asec(sqrt(4 - 2*sqrt(2))) == pi/8
+    assert asec(-sqrt(4 + 2*sqrt(2))) == pi*Rational(5, 8)
+    assert asec(sqrt(2 + 2*sqrt(5)/5)) == pi*Rational(3, 10)
+    assert asec(-sqrt(2 + 2*sqrt(5)/5)) == pi*Rational(7, 10)
+    assert asec(sqrt(2) - sqrt(6)) == pi*Rational(11, 12)
+
+    for d in [3, 4, 6]:
+        for num in range(d):
+            if gcd(num, d) == 1:
+                assert asec(sec(num*pi/d)) == num*pi/d
+                assert asec(-sec(num*pi/d)) == pi - num*pi/d
+                assert asec(csc(num*pi/d)) == pi/2 - acsc(csc(num*pi/d))
+                assert asec(-csc(num*pi/d)) == pi/2 - acsc(-csc(num*pi/d))
+
+    assert asec(x).diff(x) == 1/(x**2*sqrt(1 - 1/x**2))
+
+    assert asec(x).rewrite(log) == I*log(sqrt(1 - 1/x**2) + I/x) + pi/2
+    assert asec(x).rewrite(asin) == -asin(1/x) + pi/2
+    assert asec(x).rewrite(acos) == acos(1/x)
+    assert asec(x).rewrite(atan) == \
+        pi*(1 - sqrt(x**2)/x)/2 + sqrt(x**2)*atan(sqrt(x**2 - 1))/x
+    assert asec(x).rewrite(acot) == \
+        pi*(1 - sqrt(x**2)/x)/2 + sqrt(x**2)*acot(1/sqrt(x**2 - 1))/x
+    assert asec(x).rewrite(acsc) == -acsc(x) + pi/2
+    raises(ArgumentIndexError, lambda: asec(x).fdiff(2))
+
+
+def test_asec_is_real():
+    assert asec(S.Half).is_real is False
+    n = Symbol('n', positive=True, integer=True)
+    assert asec(n).is_extended_real is True
+    assert asec(x).is_real is None
+    assert asec(r).is_real is None
+    t = Symbol('t', real=False, finite=True)
+    assert asec(t).is_real is False
+
+
+def test_asec_leading_term():
+    assert asec(1/x).as_leading_term(x) == pi/2
+    # Tests concerning branch points
+    assert asec(x + 1).as_leading_term(x) == sqrt(2)*sqrt(x)
+    assert asec(x - 1).as_leading_term(x) == pi
+    # Tests concerning points lying on branch cuts
+    assert asec(x).as_leading_term(x, cdir=1) == -I*log(x) + I*log(2)
+    assert asec(x).as_leading_term(x, cdir=-1) == I*log(x) + 2*pi - I*log(2)
+    assert asec(I*x + 1/2).as_leading_term(x, cdir=1) == asec(1/2)
+    assert asec(-I*x + 1/2).as_leading_term(x, cdir=1) == -asec(1/2)
+    assert asec(I*x - 1/2).as_leading_term(x, cdir=1) == 2*pi - asec(-1/2)
+    assert asec(-I*x - 1/2).as_leading_term(x, cdir=1) == asec(-1/2)
+    # Tests concerning im(ndir) == 0
+    assert asec(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=1) == pi + I*log(2 - sqrt(3))
+    assert asec(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=-1) == pi + I*log(2 - sqrt(3))
+
+
+def test_asec_series():
+    assert asec(x).series(x, 0, 9) == \
+        I*log(2) - I*log(x) - I*x**2/4 - 3*I*x**4/32 \
+        - 5*I*x**6/96 - 35*I*x**8/1024 + O(x**9)
+    t4 = asec(x).taylor_term(4, x)
+    assert t4 == -3*I*x**4/32
+    assert asec(x).taylor_term(6, x, t4, 0) == -5*I*x**6/96
+
+
+def test_acsc():
+    assert acsc(nan) is nan
+    assert acsc(1) == pi/2
+    assert acsc(-1) == -pi/2
+    assert acsc(oo) == 0
+    assert acsc(-oo) == 0
+    assert acsc(zoo) == 0
+    assert acsc(0) is zoo
+
+    assert acsc(csc(3)) == -3 + pi
+    assert acsc(csc(4)) == -4 + pi
+    assert acsc(csc(6)) == 6 - 2*pi
+    assert unchanged(acsc, csc(x))
+    assert unchanged(acsc, sec(x))
+
+    assert acsc(2/sqrt(3)) == pi/3
+    assert acsc(csc(pi*Rational(13, 4))) == -pi/4
+    assert acsc(sqrt(2 + 2*sqrt(5)/5)) == pi/5
+    assert acsc(-sqrt(2 + 2*sqrt(5)/5)) == -pi/5
+    assert acsc(-2) == -pi/6
+    assert acsc(-sqrt(4 + 2*sqrt(2))) == -pi/8
+    assert acsc(sqrt(4 - 2*sqrt(2))) == pi*Rational(3, 8)
+    assert acsc(1 + sqrt(5)) == pi/10
+    assert acsc(sqrt(2) - sqrt(6)) == pi*Rational(-5, 12)
+
+    assert acsc(x).diff(x) == -1/(x**2*sqrt(1 - 1/x**2))
+
+    assert acsc(x).rewrite(log) == -I*log(sqrt(1 - 1/x**2) + I/x)
+    assert acsc(x).rewrite(asin) == asin(1/x)
+    assert acsc(x).rewrite(acos) == -acos(1/x) + pi/2
+    assert acsc(x).rewrite(atan) == \
+        (-atan(sqrt(x**2 - 1)) + pi/2)*sqrt(x**2)/x
+    assert acsc(x).rewrite(acot) == (-acot(1/sqrt(x**2 - 1)) + pi/2)*sqrt(x**2)/x
+    assert acsc(x).rewrite(asec) == -asec(x) + pi/2
+    raises(ArgumentIndexError, lambda: acsc(x).fdiff(2))
+
+
+def test_csc_rewrite():
+    assert csc(x).rewrite(pow) == csc(x)
+    assert csc(x).rewrite(sqrt) == csc(x)
+
+    assert csc(x).rewrite(exp) == 2*I/(exp(I*x) - exp(-I*x))
+    assert csc(x).rewrite(sin) == 1/sin(x)
+    assert csc(x).rewrite(tan) == (tan(x/2)**2 + 1)/(2*tan(x/2))
+    assert csc(x).rewrite(cot) == (cot(x/2)**2 + 1)/(2*cot(x/2))
+    assert csc(x).rewrite(cos) == 1/cos(x - pi/2, evaluate=False)
+    assert csc(x).rewrite(sec) == sec(-x + pi/2, evaluate=False)
+
+    # issue 17349
+    assert csc(1 - exp(-besselj(I, I))).rewrite(cos) == \
+           -1/cos(-pi/2 - 1 + cos(I*besselj(I, I)) +
+                  I*cos(-pi/2 + I*besselj(I, I), evaluate=False), evaluate=False)
+    assert csc(x).rewrite(besselj) == sqrt(2)/(sqrt(pi*x)*besselj(S.Half, x))
+    assert csc(x).rewrite(besselj).subs(x, 0) == csc(0)
+
+
+def test_acsc_leading_term():
+    assert acsc(1/x).as_leading_term(x) == x
+    # Tests concerning branch points
+    assert acsc(x + 1).as_leading_term(x) == pi/2
+    assert acsc(x - 1).as_leading_term(x) == -pi/2
+    # Tests concerning points lying on branch cuts
+    assert acsc(x).as_leading_term(x, cdir=1) == I*log(x) + pi/2 - I*log(2)
+    assert acsc(x).as_leading_term(x, cdir=-1) == -I*log(x) - 3*pi/2 + I*log(2)
+    assert acsc(I*x + 1/2).as_leading_term(x, cdir=1) == acsc(1/2)
+    assert acsc(-I*x + 1/2).as_leading_term(x, cdir=1) == pi - acsc(1/2)
+    assert acsc(I*x - 1/2).as_leading_term(x, cdir=1) == -pi - acsc(-1/2)
+    assert acsc(-I*x - 1/2).as_leading_term(x, cdir=1) == -acsc(1/2)
+    # Tests concerning im(ndir) == 0
+    assert acsc(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=1) == -pi/2 + I*log(sqrt(3) + 2)
+    assert acsc(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=-1) == -pi/2 + I*log(sqrt(3) + 2)
+
+
+def test_acsc_series():
+    assert acsc(x).series(x, 0, 9) == \
+        -I*log(2) + pi/2 + I*log(x) + I*x**2/4 \
+        + 3*I*x**4/32 + 5*I*x**6/96 + 35*I*x**8/1024 + O(x**9)
+    t6 = acsc(x).taylor_term(6, x)
+    assert t6 == 5*I*x**6/96
+    assert acsc(x).taylor_term(8, x, t6, 0) == 35*I*x**8/1024
+
+
+def test_asin_nseries():
+    assert asin(x + 2)._eval_nseries(x, 4, None, I) == -asin(2) + pi + \
+    sqrt(3)*I*x/3 - sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    assert asin(x + 2)._eval_nseries(x, 4, None, -I) == asin(2) - \
+    sqrt(3)*I*x/3 + sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    assert asin(x - 2)._eval_nseries(x, 4, None, I) == -asin(2) - \
+    sqrt(3)*I*x/3 - sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    assert asin(x - 2)._eval_nseries(x, 4, None, -I) == asin(2) - pi + \
+    sqrt(3)*I*x/3 + sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    # testing nseries for asin at branch points
+    assert asin(1 + x)._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(-x) - \
+    sqrt(2)*(-x)**(S(3)/2)/12 - 3*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3)
+    assert asin(-1 + x)._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(x) + \
+    sqrt(2)*x**(S(3)/2)/12 + 3*sqrt(2)*x**(S(5)/2)/160 + O(x**3)
+    assert asin(exp(x))._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(-x) + \
+    sqrt(2)*(-x)**(S(3)/2)/6 - sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3)
+    assert asin(-exp(x))._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(-x) - \
+    sqrt(2)*(-x)**(S(3)/2)/6 + sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3)
+
+
+def test_acos_nseries():
+    assert acos(x + 2)._eval_nseries(x, 4, None, I) == -acos(2) - sqrt(3)*I*x/3 + \
+    sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    assert acos(x + 2)._eval_nseries(x, 4, None, -I) == acos(2) + sqrt(3)*I*x/3 - \
+    sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    assert acos(x - 2)._eval_nseries(x, 4, None, I) == acos(-2) + sqrt(3)*I*x/3 + \
+    sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4)
+    assert acos(x - 2)._eval_nseries(x, 4, None, -I) == -acos(-2) + 2*pi - \
+    sqrt(3)*I*x/3 - sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4)
+    # testing nseries for acos at branch points
+    assert acos(1 + x)._eval_nseries(x, 3, None) == sqrt(2)*sqrt(-x) + \
+    sqrt(2)*(-x)**(S(3)/2)/12 + 3*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3)
+    assert acos(-1 + x)._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(x) - \
+    sqrt(2)*x**(S(3)/2)/12 - 3*sqrt(2)*x**(S(5)/2)/160 + O(x**3)
+    assert acos(exp(x))._eval_nseries(x, 3, None) == sqrt(2)*sqrt(-x) - \
+    sqrt(2)*(-x)**(S(3)/2)/6 + sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3)
+    assert acos(-exp(x))._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(-x) + \
+    sqrt(2)*(-x)**(S(3)/2)/6 - sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3)
+
+
+def test_atan_nseries():
+    assert atan(x + 2*I)._eval_nseries(x, 4, None, 1) == I*atanh(2) - x/3 - \
+    2*I*x**2/9 + 13*x**3/81 + O(x**4)
+    assert atan(x + 2*I)._eval_nseries(x, 4, None, -1) == I*atanh(2) - pi - \
+    x/3 - 2*I*x**2/9 + 13*x**3/81 + O(x**4)
+    assert atan(x - 2*I)._eval_nseries(x, 4, None, 1) == -I*atanh(2) + pi - \
+    x/3 + 2*I*x**2/9 + 13*x**3/81 + O(x**4)
+    assert atan(x - 2*I)._eval_nseries(x, 4, None, -1) == -I*atanh(2) - x/3 + \
+    2*I*x**2/9 + 13*x**3/81 + O(x**4)
+    assert atan(1/x)._eval_nseries(x, 2, None, 1) == pi/2 - x + O(x**2)
+    assert atan(1/x)._eval_nseries(x, 2, None, -1) == -pi/2 - x + O(x**2)
+    # testing nseries for atan at branch points
+    assert atan(x + I)._eval_nseries(x, 4, None) == I*log(2)/2 + pi/4 - \
+    I*log(x)/2 + x/4 + I*x**2/16 - x**3/48 + O(x**4)
+    assert atan(x - I)._eval_nseries(x, 4, None) == -I*log(2)/2 + pi/4 + \
+    I*log(x)/2 + x/4 - I*x**2/16 - x**3/48 + O(x**4)
+
+
+def test_acot_nseries():
+    assert acot(x + S(1)/2*I)._eval_nseries(x, 4, None, 1) == -I*acoth(S(1)/2) + \
+    pi - 4*x/3 + 8*I*x**2/9 + 112*x**3/81 + O(x**4)
+    assert acot(x + S(1)/2*I)._eval_nseries(x, 4, None, -1) == -I*acoth(S(1)/2) - \
+    4*x/3 + 8*I*x**2/9 + 112*x**3/81 + O(x**4)
+    assert acot(x - S(1)/2*I)._eval_nseries(x, 4, None, 1) == I*acoth(S(1)/2) - \
+    4*x/3 - 8*I*x**2/9 + 112*x**3/81 + O(x**4)
+    assert acot(x - S(1)/2*I)._eval_nseries(x, 4, None, -1) == I*acoth(S(1)/2) - \
+    pi - 4*x/3 - 8*I*x**2/9 + 112*x**3/81 + O(x**4)
+    assert acot(x)._eval_nseries(x, 2, None, 1) == pi/2 - x + O(x**2)
+    assert acot(x)._eval_nseries(x, 2, None, -1) == -pi/2 - x + O(x**2)
+    # testing nseries for acot at branch points
+    assert acot(x + I)._eval_nseries(x, 4, None) == -I*log(2)/2 + pi/4 + \
+    I*log(x)/2 - x/4 - I*x**2/16 + x**3/48 + O(x**4)
+    assert acot(x - I)._eval_nseries(x, 4, None) == I*log(2)/2 + pi/4 - \
+    I*log(x)/2 - x/4 + I*x**2/16 + x**3/48 + O(x**4)
+
+
+def test_asec_nseries():
+    assert asec(x + S(1)/2)._eval_nseries(x, 4, None, I) == asec(S(1)/2) - \
+    4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert asec(x + S(1)/2)._eval_nseries(x, 4, None, -I) == -asec(S(1)/2) + \
+    4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert asec(x - S(1)/2)._eval_nseries(x, 4, None, I) == -asec(-S(1)/2) + \
+    2*pi + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert asec(x - S(1)/2)._eval_nseries(x, 4, None, -I) == asec(-S(1)/2) - \
+    4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4)
+    # testing nseries for asec at branch points
+    assert asec(1 + x)._eval_nseries(x, 3, None) == sqrt(2)*sqrt(x) - \
+    5*sqrt(2)*x**(S(3)/2)/12 + 43*sqrt(2)*x**(S(5)/2)/160 + O(x**3)
+    assert asec(-1 + x)._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(-x) + \
+    5*sqrt(2)*(-x)**(S(3)/2)/12 - 43*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3)
+    assert asec(exp(x))._eval_nseries(x, 3, None) == sqrt(2)*sqrt(x) - \
+    sqrt(2)*x**(S(3)/2)/6 + sqrt(2)*x**(S(5)/2)/120 + O(x**3)
+    assert asec(-exp(x))._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(x) + \
+    sqrt(2)*x**(S(3)/2)/6 - sqrt(2)*x**(S(5)/2)/120 + O(x**3)
+
+
+def test_acsc_nseries():
+    assert acsc(x + S(1)/2)._eval_nseries(x, 4, None, I) == acsc(S(1)/2) + \
+    4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert acsc(x + S(1)/2)._eval_nseries(x, 4, None, -I) == -acsc(S(1)/2) + \
+    pi - 4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert acsc(x - S(1)/2)._eval_nseries(x, 4, None, I) == acsc(S(1)/2) - pi -\
+    4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4)
+    assert acsc(x - S(1)/2)._eval_nseries(x, 4, None, -I) == -acsc(S(1)/2) + \
+    4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4)
+    # testing nseries for acsc at branch points
+    assert acsc(1 + x)._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(x) + \
+    5*sqrt(2)*x**(S(3)/2)/12 - 43*sqrt(2)*x**(S(5)/2)/160 + O(x**3)
+    assert acsc(-1 + x)._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(-x) - \
+    5*sqrt(2)*(-x)**(S(3)/2)/12 + 43*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3)
+    assert acsc(exp(x))._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(x) + \
+    sqrt(2)*x**(S(3)/2)/6 - sqrt(2)*x**(S(5)/2)/120 + O(x**3)
+    assert acsc(-exp(x))._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(x) - \
+    sqrt(2)*x**(S(3)/2)/6 + sqrt(2)*x**(S(5)/2)/120 + O(x**3)
+
+
+def test_issue_8653():
+    n = Symbol('n', integer=True)
+    assert sin(n).is_irrational is None
+    assert cos(n).is_irrational is None
+    assert tan(n).is_irrational is None
+
+
+def test_issue_9157():
+    n = Symbol('n', integer=True, positive=True)
+    assert atan(n - 1).is_nonnegative is True
+
+
+def test_trig_period():
+    x, y = symbols('x, y')
+
+    assert sin(x).period() == 2*pi
+    assert cos(x).period() == 2*pi
+    assert tan(x).period() == pi
+    assert cot(x).period() == pi
+    assert sec(x).period() == 2*pi
+    assert csc(x).period() == 2*pi
+    assert sin(2*x).period() == pi
+    assert cot(4*x - 6).period() == pi/4
+    assert cos((-3)*x).period() == pi*Rational(2, 3)
+    assert cos(x*y).period(x) == 2*pi/abs(y)
+    assert sin(3*x*y + 2*pi).period(y) == 2*pi/abs(3*x)
+    assert tan(3*x).period(y) is S.Zero
+    raises(NotImplementedError, lambda: sin(x**2).period(x))
+
+
+def test_issue_7171():
+    assert sin(x).rewrite(sqrt) == sin(x)
+    assert sin(x).rewrite(pow) == sin(x)
+
+
+def test_issue_11864():
+    w, k = symbols('w, k', real=True)
+    F = Piecewise((1, Eq(2*pi*k, 0)), (sin(pi*k)/(pi*k), True))
+    soln = Piecewise((1, Eq(2*pi*k, 0)), (sinc(pi*k), True))
+    assert F.rewrite(sinc) == soln
+
+def test_real_assumptions():
+    z = Symbol('z', real=False, finite=True)
+    assert sin(z).is_real is None
+    assert cos(z).is_real is None
+    assert tan(z).is_real is False
+    assert sec(z).is_real is None
+    assert csc(z).is_real is None
+    assert cot(z).is_real is False
+    assert asin(p).is_real is None
+    assert asin(n).is_real is None
+    assert asec(p).is_real is None
+    assert asec(n).is_real is None
+    assert acos(p).is_real is None
+    assert acos(n).is_real is None
+    assert acsc(p).is_real is None
+    assert acsc(n).is_real is None
+    assert atan(p).is_positive is True
+    assert atan(n).is_negative is True
+    assert acot(p).is_positive is True
+    assert acot(n).is_negative is True
+
+def test_issue_14320():
+    assert asin(sin(2)) == -2 + pi and (-pi/2 <= -2 + pi <= pi/2) and sin(2) == sin(-2 + pi)
+    assert asin(cos(2)) == -2 + pi/2 and (-pi/2 <= -2 + pi/2 <= pi/2) and cos(2) == sin(-2 + pi/2)
+    assert acos(sin(2)) == -pi/2 + 2 and (0 <= -pi/2 + 2 <= pi) and sin(2) == cos(-pi/2 + 2)
+    assert acos(cos(20)) == -6*pi + 20 and (0 <= -6*pi + 20 <= pi) and cos(20) == cos(-6*pi + 20)
+    assert acos(cos(30)) == -30 + 10*pi and (0 <= -30 + 10*pi <= pi) and cos(30) == cos(-30 + 10*pi)
+
+    assert atan(tan(17)) == -5*pi + 17 and (-pi/2 < -5*pi + 17 < pi/2) and tan(17) == tan(-5*pi + 17)
+    assert atan(tan(15)) == -5*pi + 15 and (-pi/2 < -5*pi + 15 < pi/2) and tan(15) == tan(-5*pi + 15)
+    assert atan(cot(12)) == -12 + pi*Rational(7, 2) and (-pi/2 < -12 + pi*Rational(7, 2) < pi/2) and cot(12) == tan(-12 + pi*Rational(7, 2))
+    assert acot(cot(15)) == -5*pi + 15 and (-pi/2 < -5*pi + 15 <= pi/2) and cot(15) == cot(-5*pi + 15)
+    assert acot(tan(19)) == -19 + pi*Rational(13, 2) and (-pi/2 < -19 + pi*Rational(13, 2) <= pi/2) and tan(19) == cot(-19 + pi*Rational(13, 2))
+
+    assert asec(sec(11)) == -11 + 4*pi and (0 <= -11 + 4*pi <= pi) and cos(11) == cos(-11 + 4*pi)
+    assert asec(csc(13)) == -13 + pi*Rational(9, 2) and (0 <= -13 + pi*Rational(9, 2) <= pi) and sin(13) == cos(-13 + pi*Rational(9, 2))
+    assert acsc(csc(14)) == -4*pi + 14 and (-pi/2 <= -4*pi + 14 <= pi/2) and sin(14) == sin(-4*pi + 14)
+    assert acsc(sec(10)) == pi*Rational(-7, 2) + 10 and (-pi/2 <= pi*Rational(-7, 2) + 10 <= pi/2) and cos(10) == sin(pi*Rational(-7, 2) + 10)
+
+def test_issue_14543():
+    assert sec(2*pi + 11) == sec(11)
+    assert sec(2*pi - 11) == sec(11)
+    assert sec(pi + 11) == -sec(11)
+    assert sec(pi - 11) == -sec(11)
+
+    assert csc(2*pi + 17) == csc(17)
+    assert csc(2*pi - 17) == -csc(17)
+    assert csc(pi + 17) == -csc(17)
+    assert csc(pi - 17) == csc(17)
+
+    x = Symbol('x')
+    assert csc(pi/2 + x) == sec(x)
+    assert csc(pi/2 - x) == sec(x)
+    assert csc(pi*Rational(3, 2) + x) == -sec(x)
+    assert csc(pi*Rational(3, 2) - x) == -sec(x)
+
+    assert sec(pi/2 - x) == csc(x)
+    assert sec(pi/2 + x) == -csc(x)
+    assert sec(pi*Rational(3, 2) + x) == csc(x)
+    assert sec(pi*Rational(3, 2) - x) == -csc(x)
+
+
+def test_as_real_imag():
+    # This is for https://github.com/sympy/sympy/issues/17142
+    # If it start failing again in irrelevant builds or in the master
+    # please open up the issue again.
+    expr = atan(I/(I + I*tan(1)))
+    assert expr.as_real_imag() == (expr, 0)
+
+
+def test_issue_18746():
+    e3 = cos(S.Pi*(x/4 + 1/4))
+    assert e3.period() == 8
+
+
+def test_issue_25833():
+    assert limit(atan(x**2), x, oo) == pi/2
+    assert limit(atan(x**2 - 1), x, oo) == pi/2
+    assert limit(atan(log(2**x)/log(2*x)), x, oo) == pi/2
+
+
+def test_issue_25847():
+    #atan
+    assert atan(sin(x)/x).as_leading_term(x) == pi/4
+    raises(PoleError, lambda: atan(exp(1/x)).as_leading_term(x))
+
+    #asin
+    assert asin(sin(x)/x).as_leading_term(x) == pi/2
+    raises(PoleError, lambda: asin(exp(1/x)).as_leading_term(x))
+
+    #acos
+    assert acos(sin(x)/x).as_leading_term(x) == 0
+    raises(PoleError, lambda: acos(exp(1/x)).as_leading_term(x))
+
+    #acot
+    assert acot(sin(x)/x).as_leading_term(x) == pi/4
+    raises(PoleError, lambda: acot(exp(1/x)).as_leading_term(x))
+
+    #asec
+    assert asec(sin(x)/x).as_leading_term(x) == 0
+    raises(PoleError, lambda: asec(exp(1/x)).as_leading_term(x))
+
+    #acsc
+    assert acsc(sin(x)/x).as_leading_term(x) == pi/2
+    raises(PoleError, lambda: acsc(exp(1/x)).as_leading_term(x))
+
+def test_issue_23843():
+    #atan
+    assert atan(x + I).series(x, oo) == -16/(5*x**5) - 2*I/x**4 + 4/(3*x**3) + I/x**2 - 1/x + pi/2 + O(x**(-6), (x, oo))
+    assert atan(x + I).series(x, -oo) == -16/(5*x**5) - 2*I/x**4 + 4/(3*x**3) + I/x**2 - 1/x - pi/2 + O(x**(-6), (x, -oo))
+    assert atan(x - I).series(x, oo) == -16/(5*x**5) + 2*I/x**4 + 4/(3*x**3) - I/x**2 - 1/x + pi/2 + O(x**(-6), (x, oo))
+    assert atan(x - I).series(x, -oo) == -16/(5*x**5) + 2*I/x**4 + 4/(3*x**3) - I/x**2 - 1/x - pi/2 + O(x**(-6), (x, -oo))
+
+    #acot
+    assert acot(x + I).series(x, oo) == 16/(5*x**5) + 2*I/x**4 - 4/(3*x**3) - I/x**2 + 1/x + O(x**(-6), (x, oo))
+    assert acot(x + I).series(x, -oo) == 16/(5*x**5) + 2*I/x**4 - 4/(3*x**3) - I/x**2 + 1/x + O(x**(-6), (x, -oo))
+    assert acot(x - I).series(x, oo) == 16/(5*x**5) - 2*I/x**4 - 4/(3*x**3) + I/x**2 + 1/x + O(x**(-6), (x, oo))
+    assert acot(x - I).series(x, -oo) == 16/(5*x**5) - 2*I/x**4 - 4/(3*x**3) + I/x**2 + 1/x + O(x**(-6), (x, -oo))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/trigonometric.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/trigonometric.py
new file mode 100644
index 0000000000000000000000000000000000000000..24e5db81f17a215f5b344291f0e9bf4752e5317d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/elementary/trigonometric.py
@@ -0,0 +1,3627 @@
+from __future__ import annotations
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.expr import Expr
+from sympy.core.function import DefinedFunction, ArgumentIndexError, PoleError, expand_mul
+from sympy.core.logic import fuzzy_not, fuzzy_or, FuzzyBool, fuzzy_and
+from sympy.core.mod import Mod
+from sympy.core.numbers import Rational, pi, Integer, Float, equal_valued
+from sympy.core.relational import Ne, Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol, Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial, RisingFactorial
+from sympy.functions.combinatorial.numbers import bernoulli, euler
+from sympy.functions.elementary.complexes import arg as arg_f, im, re
+from sympy.functions.elementary.exponential import log, exp
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import sqrt, Min, Max
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary._trigonometric_special import (
+    cos_table, ipartfrac, fermat_coords)
+from sympy.logic.boolalg import And
+from sympy.ntheory import factorint
+from sympy.polys.specialpolys import symmetric_poly
+from sympy.utilities.iterables import numbered_symbols
+
+
+###############################################################################
+########################## UTILITIES ##########################################
+###############################################################################
+
+
+def _imaginary_unit_as_coefficient(arg):
+    """ Helper to extract symbolic coefficient for imaginary unit """
+    if isinstance(arg, Float):
+        return None
+    else:
+        return arg.as_coefficient(S.ImaginaryUnit)
+
+###############################################################################
+########################## TRIGONOMETRIC FUNCTIONS ############################
+###############################################################################
+
+
+class TrigonometricFunction(DefinedFunction):
+    """Base class for trigonometric functions. """
+
+    unbranched = True
+    _singularities = (S.ComplexInfinity,)
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if s.args[0].is_rational and fuzzy_not(s.args[0].is_zero):
+                return False
+        else:
+            return s.is_rational
+
+    def _eval_is_algebraic(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if fuzzy_not(self.args[0].is_zero) and self.args[0].is_algebraic:
+                return False
+            pi_coeff = _pi_coeff(self.args[0])
+            if pi_coeff is not None and pi_coeff.is_rational:
+                return True
+        else:
+            return s.is_algebraic
+
+    def _eval_expand_complex(self, deep=True, **hints):
+        re_part, im_part = self.as_real_imag(deep=deep, **hints)
+        return re_part + im_part*S.ImaginaryUnit
+
+    def _as_real_imag(self, deep=True, **hints):
+        if self.args[0].is_extended_real:
+            if deep:
+                hints['complex'] = False
+                return (self.args[0].expand(deep, **hints), S.Zero)
+            else:
+                return (self.args[0], S.Zero)
+        if deep:
+            re, im = self.args[0].expand(deep, **hints).as_real_imag()
+        else:
+            re, im = self.args[0].as_real_imag()
+        return (re, im)
+
+    def _period(self, general_period, symbol=None):
+        f = expand_mul(self.args[0])
+        if symbol is None:
+            symbol = tuple(f.free_symbols)[0]
+
+        if not f.has(symbol):
+            return S.Zero
+
+        if f == symbol:
+            return general_period
+
+        if symbol in f.free_symbols:
+            if f.is_Mul:
+                g, h = f.as_independent(symbol)
+                if h == symbol:
+                    return general_period/abs(g)
+
+            if f.is_Add:
+                a, h = f.as_independent(symbol)
+                g, h = h.as_independent(symbol, as_Add=False)
+                if h == symbol:
+                    return general_period/abs(g)
+
+        raise NotImplementedError("Use the periodicity function instead.")
+
+
+@cacheit
+def _table2():
+    # If nested sqrt's are worse than un-evaluation
+    # you can require q to be in (1, 2, 3, 4, 6, 12)
+    # q <= 12, q=15, q=20, q=24, q=30, q=40, q=60, q=120 return
+    # expressions with 2 or fewer sqrt nestings.
+    return {
+        12: (3, 4),
+        20: (4, 5),
+        30: (5, 6),
+        15: (6, 10),
+        24: (6, 8),
+        40: (8, 10),
+        60: (20, 30),
+        120: (40, 60)
+    }
+
+
+def _peeloff_pi(arg):
+    r"""
+    Split ARG into two parts, a "rest" and a multiple of $\pi$.
+    This assumes ARG to be an Add.
+    The multiple of $\pi$ returned in the second position is always a Rational.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.elementary.trigonometric import _peeloff_pi
+    >>> from sympy import pi
+    >>> from sympy.abc import x, y
+    >>> _peeloff_pi(x + pi/2)
+    (x, 1/2)
+    >>> _peeloff_pi(x + 2*pi/3 + pi*y)
+    (x + pi*y + pi/6, 1/2)
+
+    """
+    pi_coeff = S.Zero
+    rest_terms = []
+    for a in Add.make_args(arg):
+        K = a.coeff(pi)
+        if K and K.is_rational:
+            pi_coeff += K
+        else:
+            rest_terms.append(a)
+
+    if pi_coeff is S.Zero:
+        return arg, S.Zero
+
+    m1 = (pi_coeff % S.Half)
+    m2 = pi_coeff - m1
+    if m2.is_integer or ((2*m2).is_integer and m2.is_even is False):
+        return Add(*(rest_terms + [m1*pi])), m2
+    return arg, S.Zero
+
+
+def _pi_coeff(arg: Expr, cycles: int = 1) -> Expr | None:
+    r"""
+    When arg is a Number times $\pi$ (e.g. $3\pi/2$) then return the Number
+    normalized to be in the range $[0, 2]$, else `None`.
+
+    When an even multiple of $\pi$ is encountered, if it is multiplying
+    something with known parity then the multiple is returned as 0 otherwise
+    as 2.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.elementary.trigonometric import _pi_coeff
+    >>> from sympy import pi, Dummy
+    >>> from sympy.abc import x
+    >>> _pi_coeff(3*x*pi)
+    3*x
+    >>> _pi_coeff(11*pi/7)
+    11/7
+    >>> _pi_coeff(-11*pi/7)
+    3/7
+    >>> _pi_coeff(4*pi)
+    0
+    >>> _pi_coeff(5*pi)
+    1
+    >>> _pi_coeff(5.0*pi)
+    1
+    >>> _pi_coeff(5.5*pi)
+    3/2
+    >>> _pi_coeff(2 + pi)
+
+    >>> _pi_coeff(2*Dummy(integer=True)*pi)
+    2
+    >>> _pi_coeff(2*Dummy(even=True)*pi)
+    0
+
+    """
+    if arg is pi:
+        return S.One
+    elif not arg:
+        return S.Zero
+    elif arg.is_Mul:
+        cx = arg.coeff(pi)
+        if cx:
+            c, x = cx.as_coeff_Mul()  # pi is not included as coeff
+            if c.is_Float:
+                # recast exact binary fractions to Rationals
+                f = abs(c) % 1
+                if f != 0:
+                    p = -int(round(log(f, 2).evalf()))
+                    m = 2**p
+                    cm = c*m
+                    i = int(cm)
+                    if equal_valued(i, cm):
+                        c = Rational(i, m)
+                        cx = c*x
+                else:
+                    c = Rational(int(c))
+                    cx = c*x
+            if x.is_integer:
+                c2 = c % 2
+                if c2 == 1:
+                    return x
+                elif not c2:
+                    if x.is_even is not None:  # known parity
+                        return S.Zero
+                    return Integer(2)
+                else:
+                    return c2*x
+            return cx
+    elif arg.is_zero:
+        return S.Zero
+    return None
+
+
+class sin(TrigonometricFunction):
+    r"""
+    The sine function.
+
+    Returns the sine of x (measured in radians).
+
+    Explanation
+    ===========
+
+    This function will evaluate automatically in the
+    case $x/\pi$ is some rational number [4]_.  For example,
+    if $x$ is a multiple of $\pi$, $\pi/2$, $\pi/3$, $\pi/4$, and $\pi/6$.
+
+    Examples
+    ========
+
+    >>> from sympy import sin, pi
+    >>> from sympy.abc import x
+    >>> sin(x**2).diff(x)
+    2*x*cos(x**2)
+    >>> sin(1).diff(x)
+    0
+    >>> sin(pi)
+    0
+    >>> sin(pi/2)
+    1
+    >>> sin(pi/6)
+    1/2
+    >>> sin(pi/12)
+    -sqrt(2)/4 + sqrt(6)/4
+
+
+    See Also
+    ========
+
+    csc, cos, sec, tan, cot
+    asin, acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.14
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/Sin
+    .. [4] https://mathworld.wolfram.com/TrigonometryAngles.html
+
+    """
+
+    def period(self, symbol=None):
+        return self._period(2*pi, symbol)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return cos(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.sets.setexpr import SetExpr
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg.is_zero:
+                return S.Zero
+            elif arg in (S.Infinity, S.NegativeInfinity):
+                return AccumBounds(-1, 1)
+
+        if arg is S.ComplexInfinity:
+            return S.NaN
+
+        if isinstance(arg, AccumBounds):
+            from sympy.sets.sets import FiniteSet
+            min, max = arg.min, arg.max
+            d = floor(min/(2*pi))
+            if min is not S.NegativeInfinity:
+                min = min - d*2*pi
+            if max is not S.Infinity:
+                max = max - d*2*pi
+            if AccumBounds(min, max).intersection(FiniteSet(pi/2, pi*Rational(5, 2))) \
+                    is not S.EmptySet and \
+                    AccumBounds(min, max).intersection(FiniteSet(pi*Rational(3, 2),
+                        pi*Rational(7, 2))) is not S.EmptySet:
+                return AccumBounds(-1, 1)
+            elif AccumBounds(min, max).intersection(FiniteSet(pi/2, pi*Rational(5, 2))) \
+                    is not S.EmptySet:
+                return AccumBounds(Min(sin(min), sin(max)), 1)
+            elif AccumBounds(min, max).intersection(FiniteSet(pi*Rational(3, 2), pi*Rational(8, 2))) \
+                        is not S.EmptySet:
+                return AccumBounds(-1, Max(sin(min), sin(max)))
+            else:
+                return AccumBounds(Min(sin(min), sin(max)),
+                                Max(sin(min), sin(max)))
+        elif isinstance(arg, SetExpr):
+            return arg._eval_func(cls)
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import sinh
+            return S.ImaginaryUnit*sinh(i_coeff)
+
+        pi_coeff = _pi_coeff(arg)
+        if pi_coeff is not None:
+            if pi_coeff.is_integer:
+                return S.Zero
+
+            if (2*pi_coeff).is_integer:
+                # is_even-case handled above as then pi_coeff.is_integer,
+                # so check if known to be not even
+                if pi_coeff.is_even is False:
+                    return S.NegativeOne**(pi_coeff - S.Half)
+
+            if not pi_coeff.is_Rational:
+                narg = pi_coeff*pi
+                if narg != arg:
+                    return cls(narg)
+                return None
+
+            # https://github.com/sympy/sympy/issues/6048
+            # transform a sine to a cosine, to avoid redundant code
+            if pi_coeff.is_Rational:
+                x = pi_coeff % 2
+                if x > 1:
+                    return -cls((x % 1)*pi)
+                if 2*x > 1:
+                    return cls((1 - x)*pi)
+                narg = ((pi_coeff + Rational(3, 2)) % 2)*pi
+                result = cos(narg)
+                if not isinstance(result, cos):
+                    return result
+                if pi_coeff*pi != arg:
+                    return cls(pi_coeff*pi)
+                return None
+
+        if arg.is_Add:
+            x, m = _peeloff_pi(arg)
+            if m:
+                m = m*pi
+                return sin(m)*cos(x) + cos(m)*sin(x)
+
+        if arg.is_zero:
+            return S.Zero
+
+        if isinstance(arg, asin):
+            return arg.args[0]
+
+        if isinstance(arg, atan):
+            x = arg.args[0]
+            return x/sqrt(1 + x**2)
+
+        if isinstance(arg, atan2):
+            y, x = arg.args
+            return y/sqrt(x**2 + y**2)
+
+        if isinstance(arg, acos):
+            x = arg.args[0]
+            return sqrt(1 - x**2)
+
+        if isinstance(arg, acot):
+            x = arg.args[0]
+            return 1/(sqrt(1 + 1/x**2)*x)
+
+        if isinstance(arg, acsc):
+            x = arg.args[0]
+            return 1/x
+
+        if isinstance(arg, asec):
+            x = arg.args[0]
+            return sqrt(1 - 1/x**2)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            if len(previous_terms) > 2:
+                p = previous_terms[-2]
+                return -p*x**2/(n*(n - 1))
+            else:
+                return S.NegativeOne**(n//2)*x**n/factorial(n)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.args[0]
+        if logx is not None:
+            arg = arg.subs(log(x), logx)
+        if arg.subs(x, 0).has(S.NaN, S.ComplexInfinity):
+            raise PoleError("Cannot expand %s around 0" % (self))
+        return super()._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        from sympy.functions.elementary.hyperbolic import HyperbolicFunction
+        I = S.ImaginaryUnit
+        if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)):
+            arg = arg.func(arg.args[0]).rewrite(exp)
+        return (exp(arg*I) - exp(-arg*I))/(2*I)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        if isinstance(arg, log):
+            I = S.ImaginaryUnit
+            x = arg.args[0]
+            return I*x**-I/2 - I*x**I /2
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        return cos(arg - pi/2, evaluate=False)
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        tan_half = tan(S.Half*arg)
+        return 2*tan_half/(1 + tan_half**2)
+
+    def _eval_rewrite_as_sincos(self, arg, **kwargs):
+        return sin(arg)*cos(arg)/cos(arg)
+
+    def _eval_rewrite_as_cot(self, arg, **kwargs):
+        cot_half = cot(S.Half*arg)
+        return Piecewise((0, And(Eq(im(arg), 0), Eq(Mod(arg, pi), 0))),
+                         (2*cot_half/(1 + cot_half**2), True))
+
+    def _eval_rewrite_as_pow(self, arg, **kwargs):
+        return self.rewrite(cos, **kwargs).rewrite(pow, **kwargs)
+
+    def _eval_rewrite_as_sqrt(self, arg, **kwargs):
+        return self.rewrite(cos, **kwargs).rewrite(sqrt, **kwargs)
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        return 1/csc(arg)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        return 1/sec(arg - pi/2, evaluate=False)
+
+    def _eval_rewrite_as_sinc(self, arg, **kwargs):
+        return arg*sinc(arg)
+
+    def _eval_rewrite_as_besselj(self, arg, **kwargs):
+        from sympy.functions.special.bessel import besselj
+        return sqrt(pi*arg/2)*besselj(S.Half, arg)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        from sympy.functions.elementary.hyperbolic import cosh, sinh
+        re, im = self._as_real_imag(deep=deep, **hints)
+        return (sin(re)*cosh(im), cos(re)*sinh(im))
+
+    def _eval_expand_trig(self, **hints):
+        from sympy.functions.special.polynomials import chebyshevt, chebyshevu
+        arg = self.args[0]
+        x = None
+        if arg.is_Add:  # TODO, implement more if deep stuff here
+            # TODO: Do this more efficiently for more than two terms
+            x, y = arg.as_two_terms()
+            sx = sin(x, evaluate=False)._eval_expand_trig()
+            sy = sin(y, evaluate=False)._eval_expand_trig()
+            cx = cos(x, evaluate=False)._eval_expand_trig()
+            cy = cos(y, evaluate=False)._eval_expand_trig()
+            return sx*cy + sy*cx
+        elif arg.is_Mul:
+            n, x = arg.as_coeff_Mul(rational=True)
+            if n.is_Integer:  # n will be positive because of .eval
+                # canonicalization
+
+                # See https://mathworld.wolfram.com/Multiple-AngleFormulas.html
+                if n.is_odd:
+                    return S.NegativeOne**((n - 1)/2)*chebyshevt(n, sin(x))
+                else:
+                    return expand_mul(S.NegativeOne**(n/2 - 1)*cos(x)*
+                                      chebyshevu(n - 1, sin(x)), deep=False)
+        return sin(arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        n = x0/pi
+        if n.is_integer:
+            lt = (arg - n*pi).as_leading_term(x)
+            return (S.NegativeOne**n)*lt
+        if x0 is S.ComplexInfinity:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if x0 in [S.Infinity, S.NegativeInfinity]:
+            return AccumBounds(-1, 1)
+        return self.func(x0) if x0.is_finite else self
+
+    def _eval_is_extended_real(self):
+        if self.args[0].is_extended_real:
+            return True
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+        if arg.is_extended_real:
+            return True
+
+    def _eval_is_zero(self):
+        rest, pi_mult = _peeloff_pi(self.args[0])
+        if rest.is_zero:
+            return pi_mult.is_integer
+
+    def _eval_is_complex(self):
+        if self.args[0].is_extended_real \
+                or self.args[0].is_complex:
+            return True
+
+
+class cos(TrigonometricFunction):
+    """
+    The cosine function.
+
+    Returns the cosine of x (measured in radians).
+
+    Explanation
+    ===========
+
+    See :func:`sin` for notes about automatic evaluation.
+
+    Examples
+    ========
+
+    >>> from sympy import cos, pi
+    >>> from sympy.abc import x
+    >>> cos(x**2).diff(x)
+    -2*x*sin(x**2)
+    >>> cos(1).diff(x)
+    0
+    >>> cos(pi)
+    -1
+    >>> cos(pi/2)
+    0
+    >>> cos(2*pi/3)
+    -1/2
+    >>> cos(pi/12)
+    sqrt(2)/4 + sqrt(6)/4
+
+    See Also
+    ========
+
+    sin, csc, sec, tan, cot
+    asin, acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.14
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/Cos
+
+    """
+
+    def period(self, symbol=None):
+        return self._period(2*pi, symbol)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -sin(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.functions.special.polynomials import chebyshevt
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.sets.setexpr import SetExpr
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg.is_zero:
+                return S.One
+            elif arg in (S.Infinity, S.NegativeInfinity):
+                # In this case it is better to return AccumBounds(-1, 1)
+                # rather than returning S.NaN, since AccumBounds(-1, 1)
+                # preserves the information that sin(oo) is between
+                # -1 and 1, where S.NaN does not do that.
+                return AccumBounds(-1, 1)
+
+        if arg is S.ComplexInfinity:
+            return S.NaN
+
+        if isinstance(arg, AccumBounds):
+            return sin(arg + pi/2)
+        elif isinstance(arg, SetExpr):
+            return arg._eval_func(cls)
+
+        if arg.is_extended_real and arg.is_finite is False:
+            return AccumBounds(-1, 1)
+
+        if arg.could_extract_minus_sign():
+            return cls(-arg)
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import cosh
+            return cosh(i_coeff)
+
+        pi_coeff = _pi_coeff(arg)
+        if pi_coeff is not None:
+            if pi_coeff.is_integer:
+                return (S.NegativeOne)**pi_coeff
+
+            if (2*pi_coeff).is_integer:
+                # is_even-case handled above as then pi_coeff.is_integer,
+                # so check if known to be not even
+                if pi_coeff.is_even is False:
+                    return S.Zero
+
+            if not pi_coeff.is_Rational:
+                narg = pi_coeff*pi
+                if narg != arg:
+                    return cls(narg)
+                return None
+
+            # cosine formula #####################
+            # https://github.com/sympy/sympy/issues/6048
+            # explicit calculations are performed for
+            # cos(k pi/n) for n = 8,10,12,15,20,24,30,40,60,120
+            # Some other exact values like cos(k pi/240) can be
+            # calculated using a partial-fraction decomposition
+            # by calling cos( X ).rewrite(sqrt)
+            if pi_coeff.is_Rational:
+                q = pi_coeff.q
+                p = pi_coeff.p % (2*q)
+                if p > q:
+                    narg = (pi_coeff - 1)*pi
+                    return -cls(narg)
+                if 2*p > q:
+                    narg = (1 - pi_coeff)*pi
+                    return -cls(narg)
+
+                # If nested sqrt's are worse than un-evaluation
+                # you can require q to be in (1, 2, 3, 4, 6, 12)
+                # q <= 12, q=15, q=20, q=24, q=30, q=40, q=60, q=120 return
+                # expressions with 2 or fewer sqrt nestings.
+                table2 = _table2()
+                if q in table2:
+                    a, b = table2[q]
+                    a, b = p*pi/a, p*pi/b
+                    nvala, nvalb = cls(a), cls(b)
+                    if None in (nvala, nvalb):
+                        return None
+                    return nvala*nvalb + cls(pi/2 - a)*cls(pi/2 - b)
+
+                if q > 12:
+                    return None
+
+                cst_table_some = {
+                    3: S.Half,
+                    5: (sqrt(5) + 1) / 4,
+                }
+                if q in cst_table_some:
+                    cts = cst_table_some[pi_coeff.q]
+                    return chebyshevt(pi_coeff.p, cts).expand()
+
+                if 0 == q % 2:
+                    narg = (pi_coeff*2)*pi
+                    nval = cls(narg)
+                    if None == nval:
+                        return None
+                    x = (2*pi_coeff + 1)/2
+                    sign_cos = (-1)**((-1 if x < 0 else 1)*int(abs(x)))
+                    return sign_cos*sqrt( (1 + nval)/2 )
+            return None
+
+        if arg.is_Add:
+            x, m = _peeloff_pi(arg)
+            if m:
+                m = m*pi
+                return cos(m)*cos(x) - sin(m)*sin(x)
+
+        if arg.is_zero:
+            return S.One
+
+        if isinstance(arg, acos):
+            return arg.args[0]
+
+        if isinstance(arg, atan):
+            x = arg.args[0]
+            return 1/sqrt(1 + x**2)
+
+        if isinstance(arg, atan2):
+            y, x = arg.args
+            return x/sqrt(x**2 + y**2)
+
+        if isinstance(arg, asin):
+            x = arg.args[0]
+            return sqrt(1 - x ** 2)
+
+        if isinstance(arg, acot):
+            x = arg.args[0]
+            return 1/sqrt(1 + 1/x**2)
+
+        if isinstance(arg, acsc):
+            x = arg.args[0]
+            return sqrt(1 - 1/x**2)
+
+        if isinstance(arg, asec):
+            x = arg.args[0]
+            return 1/x
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            if len(previous_terms) > 2:
+                p = previous_terms[-2]
+                return -p*x**2/(n*(n - 1))
+            else:
+                return S.NegativeOne**(n//2)*x**n/factorial(n)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.args[0]
+        if logx is not None:
+            arg = arg.subs(log(x), logx)
+        if arg.subs(x, 0).has(S.NaN, S.ComplexInfinity):
+            raise PoleError("Cannot expand %s around 0" % (self))
+        return super()._eval_nseries(x, n=n, logx=logx, cdir=cdir)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        I = S.ImaginaryUnit
+        from sympy.functions.elementary.hyperbolic import HyperbolicFunction
+        if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)):
+            arg = arg.func(arg.args[0]).rewrite(exp, **kwargs)
+        return (exp(arg*I) + exp(-arg*I))/2
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        if isinstance(arg, log):
+            I = S.ImaginaryUnit
+            x = arg.args[0]
+            return x**I/2 + x**-I/2
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return sin(arg + pi/2, evaluate=False)
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        tan_half = tan(S.Half*arg)**2
+        return (1 - tan_half)/(1 + tan_half)
+
+    def _eval_rewrite_as_sincos(self, arg, **kwargs):
+        return sin(arg)*cos(arg)/sin(arg)
+
+    def _eval_rewrite_as_cot(self, arg, **kwargs):
+        cot_half = cot(S.Half*arg)**2
+        return Piecewise((1, And(Eq(im(arg), 0), Eq(Mod(arg, 2*pi), 0))),
+                         ((cot_half - 1)/(cot_half + 1), True))
+
+    def _eval_rewrite_as_pow(self, arg, **kwargs):
+        return self._eval_rewrite_as_sqrt(arg, **kwargs)
+
+    def _eval_rewrite_as_sqrt(self, arg: Expr, **kwargs):
+        from sympy.functions.special.polynomials import chebyshevt
+
+        pi_coeff = _pi_coeff(arg)
+        if pi_coeff is None:
+            return None
+
+        if isinstance(pi_coeff, Integer):
+            return None
+
+        if not isinstance(pi_coeff, Rational):
+            return None
+
+        cst_table_some = cos_table()
+
+        if pi_coeff.q in cst_table_some:
+            rv = chebyshevt(pi_coeff.p, cst_table_some[pi_coeff.q]())
+            if pi_coeff.q < 257:
+                rv = rv.expand()
+            return rv
+
+        if not pi_coeff.q % 2:  # recursively remove factors of 2
+            pico2 = pi_coeff * 2
+            nval = cos(pico2 * pi).rewrite(sqrt, **kwargs)
+            x = (pico2 + 1) / 2
+            sign_cos = -1 if int(x) % 2 else 1
+            return sign_cos * sqrt((1 + nval) / 2)
+
+        FC = fermat_coords(pi_coeff.q)
+        if FC:
+            denoms = FC
+        else:
+            denoms = [b**e for b, e in factorint(pi_coeff.q).items()]
+
+        apart = ipartfrac(*denoms)
+        decomp = (pi_coeff.p * Rational(n, d) for n, d in zip(apart, denoms))
+        X = [(x[1], x[0]*pi) for x in zip(decomp, numbered_symbols('z'))]
+        pcls = cos(sum(x[0] for x in X))._eval_expand_trig().subs(X)
+
+        if not FC or len(FC) == 1:
+            return pcls
+        return pcls.rewrite(sqrt, **kwargs)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        return 1/sec(arg)
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        return 1/sec(arg).rewrite(csc, **kwargs)
+
+    def _eval_rewrite_as_besselj(self, arg, **kwargs):
+        from sympy.functions.special.bessel import besselj
+        return Piecewise(
+                (sqrt(pi*arg/2)*besselj(-S.Half, arg), Ne(arg, 0)),
+                (1, True)
+            )
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        from sympy.functions.elementary.hyperbolic import cosh, sinh
+        re, im = self._as_real_imag(deep=deep, **hints)
+        return (cos(re)*cosh(im), -sin(re)*sinh(im))
+
+    def _eval_expand_trig(self, **hints):
+        from sympy.functions.special.polynomials import chebyshevt
+        arg = self.args[0]
+        x = None
+        if arg.is_Add:  # TODO: Do this more efficiently for more than two terms
+            x, y = arg.as_two_terms()
+            sx = sin(x, evaluate=False)._eval_expand_trig()
+            sy = sin(y, evaluate=False)._eval_expand_trig()
+            cx = cos(x, evaluate=False)._eval_expand_trig()
+            cy = cos(y, evaluate=False)._eval_expand_trig()
+            return cx*cy - sx*sy
+        elif arg.is_Mul:
+            coeff, terms = arg.as_coeff_Mul(rational=True)
+            if coeff.is_Integer:
+                return chebyshevt(coeff, cos(terms))
+        return cos(arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        n = (x0 + pi/2)/pi
+        if n.is_integer:
+            lt = (arg - n*pi + pi/2).as_leading_term(x)
+            return (S.NegativeOne**n)*lt
+        if x0 is S.ComplexInfinity:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if x0 in [S.Infinity, S.NegativeInfinity]:
+            return AccumBounds(-1, 1)
+        return self.func(x0) if x0.is_finite else self
+
+    def _eval_is_extended_real(self):
+        if self.args[0].is_extended_real:
+            return True
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+
+        if arg.is_extended_real:
+            return True
+
+    def _eval_is_complex(self):
+        if self.args[0].is_extended_real \
+            or self.args[0].is_complex:
+            return True
+
+    def _eval_is_zero(self):
+        rest, pi_mult = _peeloff_pi(self.args[0])
+        if rest.is_zero and pi_mult:
+            return (pi_mult - S.Half).is_integer
+
+
+class tan(TrigonometricFunction):
+    """
+    The tangent function.
+
+    Returns the tangent of x (measured in radians).
+
+    Explanation
+    ===========
+
+    See :class:`sin` for notes about automatic evaluation.
+
+    Examples
+    ========
+
+    >>> from sympy import tan, pi
+    >>> from sympy.abc import x
+    >>> tan(x**2).diff(x)
+    2*x*(tan(x**2)**2 + 1)
+    >>> tan(1).diff(x)
+    0
+    >>> tan(pi/8).expand()
+    -1 + sqrt(2)
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, cot
+    asin, acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.14
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/Tan
+
+    """
+
+    def period(self, symbol=None):
+        return self._period(pi, symbol)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return S.One + self**2
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return atan
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg.is_zero:
+                return S.Zero
+            elif arg in (S.Infinity, S.NegativeInfinity):
+                return AccumBounds(S.NegativeInfinity, S.Infinity)
+
+        if arg is S.ComplexInfinity:
+            return S.NaN
+
+        if isinstance(arg, AccumBounds):
+            min, max = arg.min, arg.max
+            d = floor(min/pi)
+            if min is not S.NegativeInfinity:
+                min = min - d*pi
+            if max is not S.Infinity:
+                max = max - d*pi
+            from sympy.sets.sets import FiniteSet
+            if AccumBounds(min, max).intersection(FiniteSet(pi/2, pi*Rational(3, 2))):
+                return AccumBounds(S.NegativeInfinity, S.Infinity)
+            else:
+                return AccumBounds(tan(min), tan(max))
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import tanh
+            return S.ImaginaryUnit*tanh(i_coeff)
+
+        pi_coeff = _pi_coeff(arg, 2)
+        if pi_coeff is not None:
+            if pi_coeff.is_integer:
+                return S.Zero
+
+            if not pi_coeff.is_Rational:
+                narg = pi_coeff*pi
+                if narg != arg:
+                    return cls(narg)
+                return None
+
+            if pi_coeff.is_Rational:
+                q = pi_coeff.q
+                p = pi_coeff.p % q
+                # ensure simplified results are returned for n*pi/5, n*pi/10
+                table10 = {
+                    1: sqrt(1 - 2*sqrt(5)/5),
+                    2: sqrt(5 - 2*sqrt(5)),
+                    3: sqrt(1 + 2*sqrt(5)/5),
+                    4: sqrt(5 + 2*sqrt(5))
+                    }
+                if q in (5, 10):
+                    n = 10*p/q
+                    if n > 5:
+                        n = 10 - n
+                        return -table10[n]
+                    else:
+                        return table10[n]
+                if not pi_coeff.q % 2:
+                    narg = pi_coeff*pi*2
+                    cresult, sresult = cos(narg), cos(narg - pi/2)
+                    if not isinstance(cresult, cos) \
+                            and not isinstance(sresult, cos):
+                        if sresult == 0:
+                            return S.ComplexInfinity
+                        return 1/sresult - cresult/sresult
+
+                table2 = _table2()
+                if q in table2:
+                    a, b = table2[q]
+                    nvala, nvalb = cls(p*pi/a), cls(p*pi/b)
+                    if None in (nvala, nvalb):
+                        return None
+                    return (nvala - nvalb)/(1 + nvala*nvalb)
+                narg = ((pi_coeff + S.Half) % 1 - S.Half)*pi
+                # see cos() to specify which expressions should  be
+                # expanded automatically in terms of radicals
+                cresult, sresult = cos(narg), cos(narg - pi/2)
+                if not isinstance(cresult, cos) \
+                        and not isinstance(sresult, cos):
+                    if cresult == 0:
+                        return S.ComplexInfinity
+                    return (sresult/cresult)
+                if narg != arg:
+                    return cls(narg)
+
+        if arg.is_Add:
+            x, m = _peeloff_pi(arg)
+            if m:
+                tanm = tan(m*pi)
+                if tanm is S.ComplexInfinity:
+                    return -cot(x)
+                else: # tanm == 0
+                    return tan(x)
+
+        if arg.is_zero:
+            return S.Zero
+
+        if isinstance(arg, atan):
+            return arg.args[0]
+
+        if isinstance(arg, atan2):
+            y, x = arg.args
+            return y/x
+
+        if isinstance(arg, asin):
+            x = arg.args[0]
+            return x/sqrt(1 - x**2)
+
+        if isinstance(arg, acos):
+            x = arg.args[0]
+            return sqrt(1 - x**2)/x
+
+        if isinstance(arg, acot):
+            x = arg.args[0]
+            return 1/x
+
+        if isinstance(arg, acsc):
+            x = arg.args[0]
+            return 1/(sqrt(1 - 1/x**2)*x)
+
+        if isinstance(arg, asec):
+            x = arg.args[0]
+            return sqrt(1 - 1/x**2)*x
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            a, b = ((n - 1)//2), 2**(n + 1)
+
+            B = bernoulli(n + 1)
+            F = factorial(n + 1)
+
+            return S.NegativeOne**a*b*(b - 1)*B/F*x**n
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        i = self.args[0].limit(x, 0)*2/pi
+        if i and i.is_Integer:
+            return self.rewrite(cos)._eval_nseries(x, n=n, logx=logx)
+        return super()._eval_nseries(x, n=n, logx=logx)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        if isinstance(arg, log):
+            I = S.ImaginaryUnit
+            x = arg.args[0]
+            return I*(x**-I - x**I)/(x**-I + x**I)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        re, im = self._as_real_imag(deep=deep, **hints)
+        if im:
+            from sympy.functions.elementary.hyperbolic import cosh, sinh
+            denom = cos(2*re) + cosh(2*im)
+            return (sin(2*re)/denom, sinh(2*im)/denom)
+        else:
+            return (self.func(re), S.Zero)
+
+    def _eval_expand_trig(self, **hints):
+        arg = self.args[0]
+        x = None
+        if arg.is_Add:
+            n = len(arg.args)
+            TX = []
+            for x in arg.args:
+                tx = tan(x, evaluate=False)._eval_expand_trig()
+                TX.append(tx)
+
+            Yg = numbered_symbols('Y')
+            Y = [ next(Yg) for i in range(n) ]
+
+            p = [0, 0]
+            for i in range(n + 1):
+                p[1 - i % 2] += symmetric_poly(i, Y)*(-1)**((i % 4)//2)
+            return (p[0]/p[1]).subs(list(zip(Y, TX)))
+
+        elif arg.is_Mul:
+            coeff, terms = arg.as_coeff_Mul(rational=True)
+            if coeff.is_Integer and coeff > 1:
+                I = S.ImaginaryUnit
+                z = Symbol('dummy', real=True)
+                P = ((1 + I*z)**coeff).expand()
+                return (im(P)/re(P)).subs([(z, tan(terms))])
+        return tan(arg)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        I = S.ImaginaryUnit
+        from sympy.functions.elementary.hyperbolic import HyperbolicFunction
+        if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)):
+            arg = arg.func(arg.args[0]).rewrite(exp)
+        neg_exp, pos_exp = exp(-arg*I), exp(arg*I)
+        return I*(neg_exp - pos_exp)/(neg_exp + pos_exp)
+
+    def _eval_rewrite_as_sin(self, x, **kwargs):
+        return 2*sin(x)**2/sin(2*x)
+
+    def _eval_rewrite_as_cos(self, x, **kwargs):
+        return cos(x - pi/2, evaluate=False)/cos(x)
+
+    def _eval_rewrite_as_sincos(self, arg, **kwargs):
+        return sin(arg)/cos(arg)
+
+    def _eval_rewrite_as_cot(self, arg, **kwargs):
+        return 1/cot(arg)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        sin_in_sec_form = sin(arg).rewrite(sec, **kwargs)
+        cos_in_sec_form = cos(arg).rewrite(sec, **kwargs)
+        return sin_in_sec_form/cos_in_sec_form
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        sin_in_csc_form = sin(arg).rewrite(csc, **kwargs)
+        cos_in_csc_form = cos(arg).rewrite(csc, **kwargs)
+        return sin_in_csc_form/cos_in_csc_form
+
+    def _eval_rewrite_as_pow(self, arg, **kwargs):
+        y = self.rewrite(cos, **kwargs).rewrite(pow, **kwargs)
+        if y.has(cos):
+            return None
+        return y
+
+    def _eval_rewrite_as_sqrt(self, arg, **kwargs):
+        y = self.rewrite(cos, **kwargs).rewrite(sqrt, **kwargs)
+        if y.has(cos):
+            return None
+        return y
+
+    def _eval_rewrite_as_besselj(self, arg, **kwargs):
+        from sympy.functions.special.bessel import besselj
+        return besselj(S.Half, arg)/besselj(-S.Half, arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.functions.elementary.complexes import re
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        n = 2*x0/pi
+        if n.is_integer:
+            lt = (arg - n*pi/2).as_leading_term(x)
+            return lt if n.is_even else -1/lt
+        if x0 is S.ComplexInfinity:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if x0 in (S.Infinity, S.NegativeInfinity):
+            return AccumBounds(S.NegativeInfinity, S.Infinity)
+        return self.func(x0) if x0.is_finite else self
+
+    def _eval_is_extended_real(self):
+        # FIXME: currently tan(pi/2) return zoo
+        return self.args[0].is_extended_real
+
+    def _eval_is_real(self):
+        arg = self.args[0]
+        if arg.is_real and (arg/pi - S.Half).is_integer is False:
+            return True
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+
+        if arg.is_real and (arg/pi - S.Half).is_integer is False:
+            return True
+
+        if arg.is_imaginary:
+            return True
+
+    def _eval_is_zero(self):
+        rest, pi_mult = _peeloff_pi(self.args[0])
+        if rest.is_zero:
+            return pi_mult.is_integer
+
+    def _eval_is_complex(self):
+        arg = self.args[0]
+
+        if arg.is_real and (arg/pi - S.Half).is_integer is False:
+            return True
+
+
+class cot(TrigonometricFunction):
+    """
+    The cotangent function.
+
+    Returns the cotangent of x (measured in radians).
+
+    Explanation
+    ===========
+
+    See :class:`sin` for notes about automatic evaluation.
+
+    Examples
+    ========
+
+    >>> from sympy import cot, pi
+    >>> from sympy.abc import x
+    >>> cot(x**2).diff(x)
+    2*x*(-cot(x**2)**2 - 1)
+    >>> cot(1).diff(x)
+    0
+    >>> cot(pi/12)
+    sqrt(3) + 2
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan
+    asin, acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.14
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/Cot
+
+    """
+
+    def period(self, symbol=None):
+        return self._period(pi, symbol)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return S.NegativeOne - self**2
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return acot
+
+    @classmethod
+    def eval(cls, arg):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            if arg.is_zero:
+                return S.ComplexInfinity
+            elif arg in (S.Infinity, S.NegativeInfinity):
+                return AccumBounds(S.NegativeInfinity, S.Infinity)
+
+        if arg is S.ComplexInfinity:
+            return S.NaN
+
+        if isinstance(arg, AccumBounds):
+            return -tan(arg + pi/2)
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import coth
+            return -S.ImaginaryUnit*coth(i_coeff)
+
+        pi_coeff = _pi_coeff(arg, 2)
+        if pi_coeff is not None:
+            if pi_coeff.is_integer:
+                return S.ComplexInfinity
+
+            if not pi_coeff.is_Rational:
+                narg = pi_coeff*pi
+                if narg != arg:
+                    return cls(narg)
+                return None
+
+            if pi_coeff.is_Rational:
+                if pi_coeff.q in (5, 10):
+                    return tan(pi/2 - arg)
+                if pi_coeff.q > 2 and not pi_coeff.q % 2:
+                    narg = pi_coeff*pi*2
+                    cresult, sresult = cos(narg), cos(narg - pi/2)
+                    if not isinstance(cresult, cos) \
+                            and not isinstance(sresult, cos):
+                        return 1/sresult + cresult/sresult
+                q = pi_coeff.q
+                p = pi_coeff.p % q
+                table2 = _table2()
+                if q in table2:
+                    a, b = table2[q]
+                    nvala, nvalb = cls(p*pi/a), cls(p*pi/b)
+                    if None in (nvala, nvalb):
+                        return None
+                    return (1 + nvala*nvalb)/(nvalb - nvala)
+                narg = (((pi_coeff + S.Half) % 1) - S.Half)*pi
+                # see cos() to specify which expressions should be
+                # expanded automatically in terms of radicals
+                cresult, sresult = cos(narg), cos(narg - pi/2)
+                if not isinstance(cresult, cos) \
+                        and not isinstance(sresult, cos):
+                    if sresult == 0:
+                        return S.ComplexInfinity
+                    return cresult/sresult
+                if narg != arg:
+                    return cls(narg)
+
+        if arg.is_Add:
+            x, m = _peeloff_pi(arg)
+            if m:
+                cotm = cot(m*pi)
+                if cotm is S.ComplexInfinity:
+                    return cot(x)
+                else: # cotm == 0
+                    return -tan(x)
+
+        if arg.is_zero:
+            return S.ComplexInfinity
+
+        if isinstance(arg, acot):
+            return arg.args[0]
+
+        if isinstance(arg, atan):
+            x = arg.args[0]
+            return 1/x
+
+        if isinstance(arg, atan2):
+            y, x = arg.args
+            return x/y
+
+        if isinstance(arg, asin):
+            x = arg.args[0]
+            return sqrt(1 - x**2)/x
+
+        if isinstance(arg, acos):
+            x = arg.args[0]
+            return x/sqrt(1 - x**2)
+
+        if isinstance(arg, acsc):
+            x = arg.args[0]
+            return sqrt(1 - 1/x**2)*x
+
+        if isinstance(arg, asec):
+            x = arg.args[0]
+            return 1/(sqrt(1 - 1/x**2)*x)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return 1/sympify(x)
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+
+            B = bernoulli(n + 1)
+            F = factorial(n + 1)
+
+            return S.NegativeOne**((n + 1)//2)*2**(n + 1)*B/F*x**n
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        i = self.args[0].limit(x, 0)/pi
+        if i and i.is_Integer:
+            return self.rewrite(cos)._eval_nseries(x, n=n, logx=logx)
+        return self.rewrite(tan)._eval_nseries(x, n=n, logx=logx)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        re, im = self._as_real_imag(deep=deep, **hints)
+        if im:
+            from sympy.functions.elementary.hyperbolic import cosh, sinh
+            denom = cos(2*re) - cosh(2*im)
+            return (-sin(2*re)/denom, sinh(2*im)/denom)
+        else:
+            return (self.func(re), S.Zero)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        from sympy.functions.elementary.hyperbolic import HyperbolicFunction
+        I = S.ImaginaryUnit
+        if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)):
+            arg = arg.func(arg.args[0]).rewrite(exp, **kwargs)
+        neg_exp, pos_exp = exp(-arg*I), exp(arg*I)
+        return I*(pos_exp + neg_exp)/(pos_exp - neg_exp)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        if isinstance(arg, log):
+            I = S.ImaginaryUnit
+            x = arg.args[0]
+            return -I*(x**-I + x**I)/(x**-I - x**I)
+
+    def _eval_rewrite_as_sin(self, x, **kwargs):
+        return sin(2*x)/(2*(sin(x)**2))
+
+    def _eval_rewrite_as_cos(self, x, **kwargs):
+        return cos(x)/cos(x - pi/2, evaluate=False)
+
+    def _eval_rewrite_as_sincos(self, arg, **kwargs):
+        return cos(arg)/sin(arg)
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        return 1/tan(arg)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        cos_in_sec_form = cos(arg).rewrite(sec, **kwargs)
+        sin_in_sec_form = sin(arg).rewrite(sec, **kwargs)
+        return cos_in_sec_form/sin_in_sec_form
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        cos_in_csc_form = cos(arg).rewrite(csc, **kwargs)
+        sin_in_csc_form = sin(arg).rewrite(csc, **kwargs)
+        return cos_in_csc_form/sin_in_csc_form
+
+    def _eval_rewrite_as_pow(self, arg, **kwargs):
+        y = self.rewrite(cos, **kwargs).rewrite(pow, **kwargs)
+        if y.has(cos):
+            return None
+        return y
+
+    def _eval_rewrite_as_sqrt(self, arg, **kwargs):
+        y = self.rewrite(cos, **kwargs).rewrite(sqrt, **kwargs)
+        if y.has(cos):
+            return None
+        return y
+
+    def _eval_rewrite_as_besselj(self, arg, **kwargs):
+        from sympy.functions.special.bessel import besselj
+        return besselj(-S.Half, arg)/besselj(S.Half, arg)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.functions.elementary.complexes import re
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        n = 2*x0/pi
+        if n.is_integer:
+            lt = (arg - n*pi/2).as_leading_term(x)
+            return 1/lt if n.is_even else -lt
+        if x0 is S.ComplexInfinity:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if x0 in (S.Infinity, S.NegativeInfinity):
+            return AccumBounds(S.NegativeInfinity, S.Infinity)
+        return self.func(x0) if x0.is_finite else self
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    def _eval_expand_trig(self, **hints):
+        arg = self.args[0]
+        x = None
+        if arg.is_Add:
+            n = len(arg.args)
+            CX = []
+            for x in arg.args:
+                cx = cot(x, evaluate=False)._eval_expand_trig()
+                CX.append(cx)
+
+            Yg = numbered_symbols('Y')
+            Y = [ next(Yg) for i in range(n) ]
+
+            p = [0, 0]
+            for i in range(n, -1, -1):
+                p[(n - i) % 2] += symmetric_poly(i, Y)*(-1)**(((n - i) % 4)//2)
+            return (p[0]/p[1]).subs(list(zip(Y, CX)))
+        elif arg.is_Mul:
+            coeff, terms = arg.as_coeff_Mul(rational=True)
+            if coeff.is_Integer and coeff > 1:
+                I = S.ImaginaryUnit
+                z = Symbol('dummy', real=True)
+                P = ((z + I)**coeff).expand()
+                return (re(P)/im(P)).subs([(z, cot(terms))])
+        return cot(arg)  # XXX sec and csc return 1/cos and 1/sin
+
+    def _eval_is_finite(self):
+        arg = self.args[0]
+        if arg.is_real and (arg/pi).is_integer is False:
+            return True
+        if arg.is_imaginary:
+            return True
+
+    def _eval_is_real(self):
+        arg = self.args[0]
+        if arg.is_real and (arg/pi).is_integer is False:
+            return True
+
+    def _eval_is_complex(self):
+        arg = self.args[0]
+        if arg.is_real and (arg/pi).is_integer is False:
+            return True
+
+    def _eval_is_zero(self):
+        rest, pimult = _peeloff_pi(self.args[0])
+        if pimult and rest.is_zero:
+            return (pimult - S.Half).is_integer
+
+    def _eval_subs(self, old, new):
+        arg = self.args[0]
+        argnew = arg.subs(old, new)
+        if arg != argnew and (argnew/pi).is_integer:
+            return S.ComplexInfinity
+        return cot(argnew)
+
+
+class ReciprocalTrigonometricFunction(TrigonometricFunction):
+    """Base class for reciprocal functions of trigonometric functions. """
+
+    _reciprocal_of = None       # mandatory, to be defined in subclass
+    _singularities = (S.ComplexInfinity,)
+
+    # _is_even and _is_odd are used for correct evaluation of csc(-x), sec(-x)
+    # TODO refactor into TrigonometricFunction common parts of
+    # trigonometric functions eval() like even/odd, func(x+2*k*pi), etc.
+
+    # optional, to be defined in subclasses:
+    _is_even: FuzzyBool = None
+    _is_odd: FuzzyBool = None
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.could_extract_minus_sign():
+            if cls._is_even:
+                return cls(-arg)
+            if cls._is_odd:
+                return -cls(-arg)
+
+        pi_coeff = _pi_coeff(arg)
+        if (pi_coeff is not None
+            and not (2*pi_coeff).is_integer
+            and pi_coeff.is_Rational):
+                q = pi_coeff.q
+                p = pi_coeff.p % (2*q)
+                if p > q:
+                    narg = (pi_coeff - 1)*pi
+                    return -cls(narg)
+                if 2*p > q:
+                    narg = (1 - pi_coeff)*pi
+                    if cls._is_odd:
+                        return cls(narg)
+                    elif cls._is_even:
+                        return -cls(narg)
+
+        if hasattr(arg, 'inverse') and arg.inverse() == cls:
+            return arg.args[0]
+
+        t = cls._reciprocal_of.eval(arg)
+        if t is None:
+            return t
+        elif any(isinstance(i, cos) for i in (t, -t)):
+            return (1/t).rewrite(sec)
+        elif any(isinstance(i, sin) for i in (t, -t)):
+            return (1/t).rewrite(csc)
+        else:
+            return 1/t
+
+    def _call_reciprocal(self, method_name, *args, **kwargs):
+        # Calls method_name on _reciprocal_of
+        o = self._reciprocal_of(self.args[0])
+        return getattr(o, method_name)(*args, **kwargs)
+
+    def _calculate_reciprocal(self, method_name, *args, **kwargs):
+        # If calling method_name on _reciprocal_of returns a value != None
+        # then return the reciprocal of that value
+        t = self._call_reciprocal(method_name, *args, **kwargs)
+        return 1/t if t is not None else t
+
+    def _rewrite_reciprocal(self, method_name, arg):
+        # Special handling for rewrite functions. If reciprocal rewrite returns
+        # unmodified expression, then return None
+        t = self._call_reciprocal(method_name, arg)
+        if t is not None and t != self._reciprocal_of(arg):
+            return 1/t
+
+    def _period(self, symbol):
+        f = expand_mul(self.args[0])
+        return self._reciprocal_of(f).period(symbol)
+
+    def fdiff(self, argindex=1):
+        return -self._calculate_reciprocal("fdiff", argindex)/self**2
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_exp", arg)
+
+    def _eval_rewrite_as_Pow(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_Pow", arg)
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_sin", arg)
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_cos", arg)
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_tan", arg)
+
+    def _eval_rewrite_as_pow(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_pow", arg)
+
+    def _eval_rewrite_as_sqrt(self, arg, **kwargs):
+        return self._rewrite_reciprocal("_eval_rewrite_as_sqrt", arg)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def as_real_imag(self, deep=True, **hints):
+        return (1/self._reciprocal_of(self.args[0])).as_real_imag(deep,
+                                                                  **hints)
+
+    def _eval_expand_trig(self, **hints):
+        return self._calculate_reciprocal("_eval_expand_trig", **hints)
+
+    def _eval_is_extended_real(self):
+        return self._reciprocal_of(self.args[0])._eval_is_extended_real()
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        return (1/self._reciprocal_of(self.args[0]))._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_is_finite(self):
+        return (1/self._reciprocal_of(self.args[0])).is_finite
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        return (1/self._reciprocal_of(self.args[0]))._eval_nseries(x, n, logx)
+
+
+class sec(ReciprocalTrigonometricFunction):
+    """
+    The secant function.
+
+    Returns the secant of x (measured in radians).
+
+    Explanation
+    ===========
+
+    See :class:`sin` for notes about automatic evaluation.
+
+    Examples
+    ========
+
+    >>> from sympy import sec
+    >>> from sympy.abc import x
+    >>> sec(x**2).diff(x)
+    2*x*tan(x**2)*sec(x**2)
+    >>> sec(1).diff(x)
+    0
+
+    See Also
+    ========
+
+    sin, csc, cos, tan, cot
+    asin, acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.14
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/Sec
+
+    """
+
+    _reciprocal_of = cos
+    _is_even = True
+
+    def period(self, symbol=None):
+        return self._period(symbol)
+
+    def _eval_rewrite_as_cot(self, arg, **kwargs):
+        cot_half_sq = cot(arg/2)**2
+        return (cot_half_sq + 1)/(cot_half_sq - 1)
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        return (1/cos(arg))
+
+    def _eval_rewrite_as_sincos(self, arg, **kwargs):
+        return sin(arg)/(cos(arg)*sin(arg))
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return (1/cos(arg).rewrite(sin, **kwargs))
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        return (1/cos(arg).rewrite(tan, **kwargs))
+
+    def _eval_rewrite_as_csc(self, arg, **kwargs):
+        return csc(pi/2 - arg, evaluate=False)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return tan(self.args[0])*sec(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_besselj(self, arg, **kwargs):
+        from sympy.functions.special.bessel import besselj
+        return Piecewise(
+                (1/(sqrt(pi*arg)/(sqrt(2))*besselj(-S.Half, arg)), Ne(arg, 0)),
+                (1, True)
+            )
+
+    def _eval_is_complex(self):
+        arg = self.args[0]
+
+        if arg.is_complex and (arg/pi - S.Half).is_integer is False:
+            return True
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        # Reference Formula:
+        # https://functions.wolfram.com/ElementaryFunctions/Sec/06/01/02/01/
+        if n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+            k = n//2
+            return S.NegativeOne**k*euler(2*k)/factorial(2*k)*x**(2*k)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.functions.elementary.complexes import re
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        n = (x0 + pi/2)/pi
+        if n.is_integer:
+            lt = (arg - n*pi + pi/2).as_leading_term(x)
+            return (S.NegativeOne**n)/lt
+        if x0 is S.ComplexInfinity:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if x0 in (S.Infinity, S.NegativeInfinity):
+            return AccumBounds(S.NegativeInfinity, S.Infinity)
+        return self.func(x0) if x0.is_finite else self
+
+
+class csc(ReciprocalTrigonometricFunction):
+    """
+    The cosecant function.
+
+    Returns the cosecant of x (measured in radians).
+
+    Explanation
+    ===========
+
+    See :func:`sin` for notes about automatic evaluation.
+
+    Examples
+    ========
+
+    >>> from sympy import csc
+    >>> from sympy.abc import x
+    >>> csc(x**2).diff(x)
+    -2*x*cot(x**2)*csc(x**2)
+    >>> csc(1).diff(x)
+    0
+
+    See Also
+    ========
+
+    sin, cos, sec, tan, cot
+    asin, acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.14
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/Csc
+
+    """
+
+    _reciprocal_of = sin
+    _is_odd = True
+
+    def period(self, symbol=None):
+        return self._period(symbol)
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return (1/sin(arg))
+
+    def _eval_rewrite_as_sincos(self, arg, **kwargs):
+        return cos(arg)/(sin(arg)*cos(arg))
+
+    def _eval_rewrite_as_cot(self, arg, **kwargs):
+        cot_half = cot(arg/2)
+        return (1 + cot_half**2)/(2*cot_half)
+
+    def _eval_rewrite_as_cos(self, arg, **kwargs):
+        return 1/sin(arg).rewrite(cos, **kwargs)
+
+    def _eval_rewrite_as_sec(self, arg, **kwargs):
+        return sec(pi/2 - arg, evaluate=False)
+
+    def _eval_rewrite_as_tan(self, arg, **kwargs):
+        return (1/sin(arg).rewrite(tan, **kwargs))
+
+    def _eval_rewrite_as_besselj(self, arg, **kwargs):
+        from sympy.functions.special.bessel import besselj
+        return sqrt(2/pi)*(1/(sqrt(arg)*besselj(S.Half, arg)))
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -cot(self.args[0])*csc(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_complex(self):
+        arg = self.args[0]
+        if arg.is_real and (arg/pi).is_integer is False:
+            return True
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return 1/sympify(x)
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            k = n//2 + 1
+            return (S.NegativeOne**(k - 1)*2*(2**(2*k - 1) - 1)*
+                    bernoulli(2*k)*x**(2*k - 1)/factorial(2*k))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.calculus.accumulationbounds import AccumBounds
+        from sympy.functions.elementary.complexes import re
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        n = x0/pi
+        if n.is_integer:
+            lt = (arg - n*pi).as_leading_term(x)
+            return (S.NegativeOne**n)/lt
+        if x0 is S.ComplexInfinity:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if x0 in (S.Infinity, S.NegativeInfinity):
+            return AccumBounds(S.NegativeInfinity, S.Infinity)
+        return self.func(x0) if x0.is_finite else self
+
+
+class sinc(DefinedFunction):
+    r"""
+    Represents an unnormalized sinc function:
+
+    .. math::
+
+        \operatorname{sinc}(x) =
+        \begin{cases}
+          \frac{\sin x}{x} & \qquad x \neq 0 \\
+          1 & \qquad x = 0
+        \end{cases}
+
+    Examples
+    ========
+
+    >>> from sympy import sinc, oo, jn
+    >>> from sympy.abc import x
+    >>> sinc(x)
+    sinc(x)
+
+    * Automated Evaluation
+
+    >>> sinc(0)
+    1
+    >>> sinc(oo)
+    0
+
+    * Differentiation
+
+    >>> sinc(x).diff()
+    cos(x)/x - sin(x)/x**2
+
+    * Series Expansion
+
+    >>> sinc(x).series()
+    1 - x**2/6 + x**4/120 + O(x**6)
+
+    * As zero'th order spherical Bessel Function
+
+    >>> sinc(x).rewrite(jn)
+    jn(0, x)
+
+    See also
+    ========
+
+    sin
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Sinc_function
+
+    """
+    _singularities = (S.ComplexInfinity,)
+
+    def fdiff(self, argindex=1):
+        x = self.args[0]
+        if argindex == 1:
+            # We would like to return the Piecewise here, but Piecewise.diff
+            # currently can't handle removable singularities, meaning things
+            # like sinc(x).diff(x, 2) give the wrong answer at x = 0. See
+            # https://github.com/sympy/sympy/issues/11402.
+            #
+            # return Piecewise(((x*cos(x) - sin(x))/x**2, Ne(x, S.Zero)), (S.Zero, S.true))
+            return cos(x)/x - sin(x)/x**2
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_zero:
+            return S.One
+        if arg.is_Number:
+            if arg in [S.Infinity, S.NegativeInfinity]:
+                return S.Zero
+            elif arg is S.NaN:
+                return S.NaN
+
+        if arg is S.ComplexInfinity:
+            return S.NaN
+
+        if arg.could_extract_minus_sign():
+            return cls(-arg)
+
+        pi_coeff = _pi_coeff(arg)
+        if pi_coeff is not None:
+            if pi_coeff.is_integer:
+                if fuzzy_not(arg.is_zero):
+                    return S.Zero
+            elif (2*pi_coeff).is_integer:
+                return S.NegativeOne**(pi_coeff - S.Half)/arg
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        x = self.args[0]
+        return (sin(x)/x)._eval_nseries(x, n, logx)
+
+    def _eval_rewrite_as_jn(self, arg, **kwargs):
+        from sympy.functions.special.bessel import jn
+        return jn(0, arg)
+
+    def _eval_rewrite_as_sin(self, arg, **kwargs):
+        return Piecewise((sin(arg)/arg, Ne(arg, S.Zero)), (S.One, S.true))
+
+    def _eval_is_zero(self):
+        if self.args[0].is_infinite:
+            return True
+        rest, pi_mult = _peeloff_pi(self.args[0])
+        if rest.is_zero:
+            return fuzzy_and([pi_mult.is_integer, pi_mult.is_nonzero])
+        if rest.is_Number and pi_mult.is_integer:
+            return False
+
+    def _eval_is_real(self):
+        if self.args[0].is_extended_real or self.args[0].is_imaginary:
+            return True
+
+    _eval_is_finite = _eval_is_real
+
+
+###############################################################################
+########################### TRIGONOMETRIC INVERSES ############################
+###############################################################################
+
+
+class InverseTrigonometricFunction(DefinedFunction):
+    """Base class for inverse trigonometric functions."""
+    _singularities: tuple[Expr, ...] = (S.One, S.NegativeOne, S.Zero, S.ComplexInfinity)
+
+    @staticmethod
+    @cacheit
+    def _asin_table():
+        # Only keys with could_extract_minus_sign() == False
+        # are actually needed.
+        return {
+            sqrt(3)/2: pi/3,
+            sqrt(2)/2: pi/4,
+            1/sqrt(2): pi/4,
+            sqrt((5 - sqrt(5))/8): pi/5,
+            sqrt(2)*sqrt(5 - sqrt(5))/4: pi/5,
+            sqrt((5 + sqrt(5))/8): pi*Rational(2, 5),
+            sqrt(2)*sqrt(5 + sqrt(5))/4: pi*Rational(2, 5),
+            S.Half: pi/6,
+            sqrt(2 - sqrt(2))/2: pi/8,
+            sqrt(S.Half - sqrt(2)/4): pi/8,
+            sqrt(2 + sqrt(2))/2: pi*Rational(3, 8),
+            sqrt(S.Half + sqrt(2)/4): pi*Rational(3, 8),
+            (sqrt(5) - 1)/4: pi/10,
+            (1 - sqrt(5))/4: -pi/10,
+            (sqrt(5) + 1)/4: pi*Rational(3, 10),
+            sqrt(6)/4 - sqrt(2)/4: pi/12,
+            -sqrt(6)/4 + sqrt(2)/4: -pi/12,
+            (sqrt(3) - 1)/sqrt(8): pi/12,
+            (1 - sqrt(3))/sqrt(8): -pi/12,
+            sqrt(6)/4 + sqrt(2)/4: pi*Rational(5, 12),
+            (1 + sqrt(3))/sqrt(8): pi*Rational(5, 12)
+        }
+
+
+    @staticmethod
+    @cacheit
+    def _atan_table():
+        # Only keys with could_extract_minus_sign() == False
+        # are actually needed.
+        return {
+            sqrt(3)/3: pi/6,
+            1/sqrt(3): pi/6,
+            sqrt(3): pi/3,
+            sqrt(2) - 1: pi/8,
+            1 - sqrt(2): -pi/8,
+            1 + sqrt(2): pi*Rational(3, 8),
+            sqrt(5 - 2*sqrt(5)): pi/5,
+            sqrt(5 + 2*sqrt(5)): pi*Rational(2, 5),
+            sqrt(1 - 2*sqrt(5)/5): pi/10,
+            sqrt(1 + 2*sqrt(5)/5): pi*Rational(3, 10),
+            2 - sqrt(3): pi/12,
+            -2 + sqrt(3): -pi/12,
+            2 + sqrt(3): pi*Rational(5, 12)
+        }
+
+    @staticmethod
+    @cacheit
+    def _acsc_table():
+        # Keys for which could_extract_minus_sign()
+        # will obviously return True are omitted.
+        return {
+            2*sqrt(3)/3: pi/3,
+            sqrt(2): pi/4,
+            sqrt(2 + 2*sqrt(5)/5): pi/5,
+            1/sqrt(Rational(5, 8) - sqrt(5)/8): pi/5,
+            sqrt(2 - 2*sqrt(5)/5): pi*Rational(2, 5),
+            1/sqrt(Rational(5, 8) + sqrt(5)/8): pi*Rational(2, 5),
+            2: pi/6,
+            sqrt(4 + 2*sqrt(2)): pi/8,
+            2/sqrt(2 - sqrt(2)): pi/8,
+            sqrt(4 - 2*sqrt(2)): pi*Rational(3, 8),
+            2/sqrt(2 + sqrt(2)): pi*Rational(3, 8),
+            1 + sqrt(5): pi/10,
+            sqrt(5) - 1: pi*Rational(3, 10),
+            -(sqrt(5) - 1): pi*Rational(-3, 10),
+            sqrt(6) + sqrt(2): pi/12,
+            sqrt(6) - sqrt(2): pi*Rational(5, 12),
+            -(sqrt(6) - sqrt(2)): pi*Rational(-5, 12)
+        }
+
+
+class asin(InverseTrigonometricFunction):
+    r"""
+    The inverse sine function.
+
+    Returns the arcsine of x in radians.
+
+    Explanation
+    ===========
+
+    ``asin(x)`` will evaluate automatically in the cases
+    $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when the
+    result is a rational multiple of $\pi$ (see the ``eval`` class method).
+
+    A purely imaginary argument will lead to an asinh expression.
+
+    Examples
+    ========
+
+    >>> from sympy import asin, oo
+    >>> asin(1)
+    pi/2
+    >>> asin(-1)
+    -pi/2
+    >>> asin(-oo)
+    oo*I
+    >>> asin(oo)
+    -oo*I
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    acsc, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.23
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcSin
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 1/sqrt(1 - self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if s.args[0].is_rational:
+                return False
+        else:
+            return s.is_rational
+
+    def _eval_is_positive(self):
+        return self._eval_is_extended_real() and self.args[0].is_positive
+
+    def _eval_is_negative(self):
+        return self._eval_is_extended_real() and self.args[0].is_negative
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.NegativeInfinity*S.ImaginaryUnit
+            elif arg is S.NegativeInfinity:
+                return S.Infinity*S.ImaginaryUnit
+            elif arg.is_zero:
+                return S.Zero
+            elif arg is S.One:
+                return pi/2
+            elif arg is S.NegativeOne:
+                return -pi/2
+
+        if arg is S.ComplexInfinity:
+            return S.ComplexInfinity
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        if arg.is_number:
+            asin_table = cls._asin_table()
+            if arg in asin_table:
+                return asin_table[arg]
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import asinh
+            return S.ImaginaryUnit*asinh(i_coeff)
+
+        if arg.is_zero:
+            return S.Zero
+
+        if isinstance(arg, sin):
+            ang = arg.args[0]
+            if ang.is_comparable:
+                ang %= 2*pi # restrict to [0,2*pi)
+                if ang > pi: # restrict to (-pi,pi]
+                    ang = pi - ang
+
+                # restrict to [-pi/2,pi/2]
+                if ang > pi/2:
+                    ang = pi - ang
+                if ang < -pi/2:
+                    ang = -pi - ang
+
+                return ang
+
+        if isinstance(arg, cos): # acos(x) + asin(x) = pi/2
+            ang = arg.args[0]
+            if ang.is_comparable:
+                return pi/2 - acos(arg)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) >= 2 and n > 2:
+                p = previous_terms[-2]
+                return p*(n - 2)**2/(n*(n - 1))*x**2
+            else:
+                k = (n - 1) // 2
+                R = RisingFactorial(S.Half, k)
+                F = factorial(k)
+                return R/F*x**n/n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            return self.func(arg.as_leading_term(x))
+        if x0.is_zero:
+            return arg.as_leading_term(x)
+
+        # Handling branch points
+        if x0 in (-S.One, S.One, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        # Handling points lying on branch cuts (-oo, -1) U (1, oo)
+        if (1 - x0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if x0.is_negative:
+                    return -pi - self.func(x0)
+            elif im(ndir).is_positive:
+                if x0.is_positive:
+                    return pi - self.func(x0)
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # asin
+        from sympy.series.order import O
+        arg0 = self.args[0].subs(x, 0)
+        # Handling branch points
+        if arg0 is S.One:
+            t = Dummy('t', positive=True)
+            ser = asin(S.One - t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.One - self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else pi/2 + O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        if arg0 is S.NegativeOne:
+            t = Dummy('t', positive=True)
+            ser = asin(S.NegativeOne + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.One + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else -pi/2 + O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+        # Handling points lying on branch cuts (-oo, -1) U (1, oo)
+        if (1 - arg0**2).is_negative:
+            ndir = self.args[0].dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if arg0.is_negative:
+                    return -pi - res
+            elif im(ndir).is_positive:
+                if arg0.is_positive:
+                    return pi - res
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_acos(self, x, **kwargs):
+        return pi/2 - acos(x)
+
+    def _eval_rewrite_as_atan(self, x, **kwargs):
+        return 2*atan(x/(1 + sqrt(1 - x**2)))
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return -S.ImaginaryUnit*log(S.ImaginaryUnit*x + sqrt(1 - x**2))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_acot(self, arg, **kwargs):
+        return 2*acot((1 + sqrt(1 - arg**2))/arg)
+
+    def _eval_rewrite_as_asec(self, arg, **kwargs):
+        return pi/2 - asec(1/arg)
+
+    def _eval_rewrite_as_acsc(self, arg, **kwargs):
+        return acsc(1/arg)
+
+    def _eval_is_extended_real(self):
+        x = self.args[0]
+        return x.is_extended_real and (1 - abs(x)).is_nonnegative
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return sin
+
+
+class acos(InverseTrigonometricFunction):
+    r"""
+    The inverse cosine function.
+
+    Explanation
+    ===========
+
+    Returns the arc cosine of x (measured in radians).
+
+    ``acos(x)`` will evaluate automatically in the cases
+    $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when
+    the result is a rational multiple of $\pi$ (see the eval class method).
+
+    ``acos(zoo)`` evaluates to ``zoo``
+    (see note in :class:`sympy.functions.elementary.trigonometric.asec`)
+
+    A purely imaginary argument will be rewritten to asinh.
+
+    Examples
+    ========
+
+    >>> from sympy import acos, oo
+    >>> acos(1)
+    0
+    >>> acos(0)
+    pi/2
+    >>> acos(oo)
+    oo*I
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    asin, acsc, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.23
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcCos
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -1/sqrt(1 - self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if s.args[0].is_rational:
+                return False
+        else:
+            return s.is_rational
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity*S.ImaginaryUnit
+            elif arg is S.NegativeInfinity:
+                return S.NegativeInfinity*S.ImaginaryUnit
+            elif arg.is_zero:
+                return pi/2
+            elif arg is S.One:
+                return S.Zero
+            elif arg is S.NegativeOne:
+                return pi
+
+        if arg is S.ComplexInfinity:
+            return S.ComplexInfinity
+
+        if arg.is_number:
+            asin_table = cls._asin_table()
+            if arg in asin_table:
+                return pi/2 - asin_table[arg]
+            elif -arg in asin_table:
+                return pi/2 + asin_table[-arg]
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            return pi/2 - asin(arg)
+
+        if arg.is_Mul and len(arg.args) == 2 and arg.args[0] == -1:
+            narg = arg.args[1]
+            minus = True
+        else:
+            narg = arg
+            minus = False
+
+        if isinstance(narg, cos):
+            # acos(cos(x)) = x or acos(-cos(x)) = pi - x
+            ang = narg.args[0]
+            if ang.is_comparable:
+                if minus:
+                    ang = pi - ang
+                ang %= 2*pi # restrict to [0,2*pi)
+                if ang > pi: # restrict to [0,pi]
+                    ang = 2*pi - ang
+                return ang
+
+        if isinstance(narg, sin): # acos(x) + asin(x) = pi/2
+            ang = narg.args[0]
+            if ang.is_comparable:
+                if minus:
+                    return pi/2 + asin(narg)
+                return pi/2 - asin(narg)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return pi/2
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) >= 2 and n > 2:
+                p = previous_terms[-2]
+                return p*(n - 2)**2/(n*(n - 1))*x**2
+            else:
+                k = (n - 1) // 2
+                R = RisingFactorial(S.Half, k)
+                F = factorial(k)
+                return -R/F*x**n/n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            return self.func(arg.as_leading_term(x))
+        # Handling branch points
+        if x0 == 1:
+            return sqrt(2)*sqrt((S.One - arg).as_leading_term(x))
+        if x0 in (-S.One, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        # Handling points lying on branch cuts (-oo, -1) U (1, oo)
+        if (1 - x0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if x0.is_negative:
+                    return 2*pi - self.func(x0)
+            elif im(ndir).is_positive:
+                if x0.is_positive:
+                    return -self.func(x0)
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        return self.func(x0)
+
+    def _eval_is_extended_real(self):
+        x = self.args[0]
+        return x.is_extended_real and (1 - abs(x)).is_nonnegative
+
+    def _eval_is_nonnegative(self):
+        return self._eval_is_extended_real()
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # acos
+        from sympy.series.order import O
+        arg0 = self.args[0].subs(x, 0)
+        # Handling branch points
+        if arg0 is S.One:
+            t = Dummy('t', positive=True)
+            ser = acos(S.One - t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.One - self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        if arg0 is S.NegativeOne:
+            t = Dummy('t', positive=True)
+            ser = acos(S.NegativeOne + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.One + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            if not g.is_meromorphic(x, 0):   # cannot be expanded
+                return O(1) if n == 0 else pi + O(sqrt(x))
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+        # Handling points lying on branch cuts (-oo, -1) U (1, oo)
+        if (1 - arg0**2).is_negative:
+            ndir = self.args[0].dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if arg0.is_negative:
+                    return 2*pi - res
+            elif im(ndir).is_positive:
+                if arg0.is_positive:
+                    return -res
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return pi/2 + S.ImaginaryUnit*\
+            log(S.ImaginaryUnit*x + sqrt(1 - x**2))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_asin(self, x, **kwargs):
+        return pi/2 - asin(x)
+
+    def _eval_rewrite_as_atan(self, x, **kwargs):
+        return atan(sqrt(1 - x**2)/x) + (pi/2)*(1 - x*sqrt(1/x**2))
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return cos
+
+    def _eval_rewrite_as_acot(self, arg, **kwargs):
+        return pi/2 - 2*acot((1 + sqrt(1 - arg**2))/arg)
+
+    def _eval_rewrite_as_asec(self, arg, **kwargs):
+        return asec(1/arg)
+
+    def _eval_rewrite_as_acsc(self, arg, **kwargs):
+        return pi/2 - acsc(1/arg)
+
+    def _eval_conjugate(self):
+        z = self.args[0]
+        r = self.func(self.args[0].conjugate())
+        if z.is_extended_real is False:
+            return r
+        elif z.is_extended_real and (z + 1).is_nonnegative and (z - 1).is_nonpositive:
+            return r
+
+
+class atan(InverseTrigonometricFunction):
+    r"""
+    The inverse tangent function.
+
+    Returns the arc tangent of x (measured in radians).
+
+    Explanation
+    ===========
+
+    ``atan(x)`` will evaluate automatically in the cases
+    $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when the
+    result is a rational multiple of $\pi$ (see the eval class method).
+
+    Examples
+    ========
+
+    >>> from sympy import atan, oo
+    >>> atan(0)
+    0
+    >>> atan(1)
+    pi/4
+    >>> atan(oo)
+    pi/2
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    asin, acsc, acos, asec, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.23
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcTan
+
+    """
+
+    args: tuple[Expr]
+
+    _singularities = (S.ImaginaryUnit, -S.ImaginaryUnit)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 1/(1 + self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if s.args[0].is_rational:
+                return False
+        else:
+            return s.is_rational
+
+    def _eval_is_positive(self):
+        return self.args[0].is_extended_positive
+
+    def _eval_is_nonnegative(self):
+        return self.args[0].is_extended_nonnegative
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+    def _eval_is_real(self):
+        return self.args[0].is_extended_real
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return pi/2
+            elif arg is S.NegativeInfinity:
+                return -pi/2
+            elif arg.is_zero:
+                return S.Zero
+            elif arg is S.One:
+                return pi/4
+            elif arg is S.NegativeOne:
+                return -pi/4
+
+        if arg is S.ComplexInfinity:
+            from sympy.calculus.accumulationbounds import AccumBounds
+            return AccumBounds(-pi/2, pi/2)
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        if arg.is_number:
+            atan_table = cls._atan_table()
+            if arg in atan_table:
+                return atan_table[arg]
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import atanh
+            return S.ImaginaryUnit*atanh(i_coeff)
+
+        if arg.is_zero:
+            return S.Zero
+
+        if isinstance(arg, tan):
+            ang = arg.args[0]
+            if ang.is_comparable:
+                ang %= pi # restrict to [0,pi)
+                if ang > pi/2: # restrict to [-pi/2,pi/2]
+                    ang -= pi
+
+                return ang
+
+        if isinstance(arg, cot): # atan(x) + acot(x) = pi/2
+            ang = arg.args[0]
+            if ang.is_comparable:
+                ang = pi/2 - acot(arg)
+                if ang > pi/2: # restrict to [-pi/2,pi/2]
+                    ang -= pi
+                return ang
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            return S.NegativeOne**((n - 1)//2)*x**n/n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            return self.func(arg.as_leading_term(x))
+        if x0.is_zero:
+            return arg.as_leading_term(x)
+        # Handling branch points
+        if x0 in (-S.ImaginaryUnit, S.ImaginaryUnit, S.ComplexInfinity):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo)
+        if (1 + x0**2).is_negative:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if re(ndir).is_negative:
+                if im(x0).is_positive:
+                    return self.func(x0) - pi
+            elif re(ndir).is_positive:
+                if im(x0).is_negative:
+                    return self.func(x0) + pi
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # atan
+        arg0 = self.args[0].subs(x, 0)
+
+        # Handling branch points
+        if arg0 in (S.ImaginaryUnit, S.NegativeOne*S.ImaginaryUnit):
+            return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        ndir = self.args[0].dir(x, cdir if cdir else 1)
+        if arg0 is S.ComplexInfinity:
+            if re(ndir) > 0:
+                return res - pi
+            return res
+        # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo)
+        if (1 + arg0**2).is_negative:
+            if re(ndir).is_negative:
+                if im(arg0).is_positive:
+                    return res - pi
+            elif re(ndir).is_positive:
+                if im(arg0).is_negative:
+                    return res + pi
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return S.ImaginaryUnit/2*(log(S.One - S.ImaginaryUnit*x)
+            - log(S.One + S.ImaginaryUnit*x))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_aseries(self, n, args0, x, logx):
+        if args0[0] in [S.Infinity, S.NegativeInfinity]:
+            return (pi/2 - atan(1/self.args[0]))._eval_nseries(x, n, logx)
+        else:
+            return super()._eval_aseries(n, args0, x, logx)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return tan
+
+    def _eval_rewrite_as_asin(self, arg, **kwargs):
+        return sqrt(arg**2)/arg*(pi/2 - asin(1/sqrt(1 + arg**2)))
+
+    def _eval_rewrite_as_acos(self, arg, **kwargs):
+        return sqrt(arg**2)/arg*acos(1/sqrt(1 + arg**2))
+
+    def _eval_rewrite_as_acot(self, arg, **kwargs):
+        return acot(1/arg)
+
+    def _eval_rewrite_as_asec(self, arg, **kwargs):
+        return sqrt(arg**2)/arg*asec(sqrt(1 + arg**2))
+
+    def _eval_rewrite_as_acsc(self, arg, **kwargs):
+        return sqrt(arg**2)/arg*(pi/2 - acsc(sqrt(1 + arg**2)))
+
+
+class acot(InverseTrigonometricFunction):
+    r"""
+    The inverse cotangent function.
+
+    Returns the arc cotangent of x (measured in radians).
+
+    Explanation
+    ===========
+
+    ``acot(x)`` will evaluate automatically in the cases
+    $x \in \{\infty, -\infty, \tilde{\infty}, 0, 1, -1\}$
+    and for some instances when the result is a rational multiple of $\pi$
+    (see the eval class method).
+
+    A purely imaginary argument will lead to an ``acoth`` expression.
+
+    ``acot(x)`` has a branch cut along $(-i, i)$, hence it is discontinuous
+    at 0. Its range for real $x$ is $(-\frac{\pi}{2}, \frac{\pi}{2}]$.
+
+    Examples
+    ========
+
+    >>> from sympy import acot, sqrt
+    >>> acot(0)
+    pi/2
+    >>> acot(1)
+    pi/4
+    >>> acot(sqrt(3) - 2)
+    -5*pi/12
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    asin, acsc, acos, asec, atan, atan2
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/4.23
+    .. [2] https://functions.wolfram.com/ElementaryFunctions/ArcCot
+
+    """
+    _singularities = (S.ImaginaryUnit, -S.ImaginaryUnit)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -1/(1 + self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_rational(self):
+        s = self.func(*self.args)
+        if s.func == self.func:
+            if s.args[0].is_rational:
+                return False
+        else:
+            return s.is_rational
+
+    def _eval_is_positive(self):
+        return self.args[0].is_nonnegative
+
+    def _eval_is_negative(self):
+        return self.args[0].is_negative
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Zero
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+            elif arg.is_zero:
+                return pi/ 2
+            elif arg is S.One:
+                return pi/4
+            elif arg is S.NegativeOne:
+                return -pi/4
+
+        if arg is S.ComplexInfinity:
+            return S.Zero
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        if arg.is_number:
+            atan_table = cls._atan_table()
+            if arg in atan_table:
+                ang = pi/2 - atan_table[arg]
+                if ang > pi/2: # restrict to (-pi/2,pi/2]
+                    ang -= pi
+                return ang
+
+        i_coeff = _imaginary_unit_as_coefficient(arg)
+        if i_coeff is not None:
+            from sympy.functions.elementary.hyperbolic import acoth
+            return -S.ImaginaryUnit*acoth(i_coeff)
+
+        if arg.is_zero:
+            return pi*S.Half
+
+        if isinstance(arg, cot):
+            ang = arg.args[0]
+            if ang.is_comparable:
+                ang %= pi # restrict to [0,pi)
+                if ang > pi/2: # restrict to (-pi/2,pi/2]
+                    ang -= pi
+                return ang
+
+        if isinstance(arg, tan): # atan(x) + acot(x) = pi/2
+            ang = arg.args[0]
+            if ang.is_comparable:
+                ang = pi/2 - atan(arg)
+                if ang > pi/2: # restrict to (-pi/2,pi/2]
+                    ang -= pi
+                return ang
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return pi/2  # FIX THIS
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            return S.NegativeOne**((n + 1)//2)*x**n/n
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            return self.func(arg.as_leading_term(x))
+        if x0 is S.ComplexInfinity:
+            return (1/arg).as_leading_term(x)
+        # Handling branch points
+        if x0 in (-S.ImaginaryUnit, S.ImaginaryUnit, S.Zero):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        # Handling points lying on branch cuts [-I, I]
+        if x0.is_imaginary and (1 + x0**2).is_positive:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if re(ndir).is_positive:
+                if im(x0).is_positive:
+                    return self.func(x0) + pi
+            elif re(ndir).is_negative:
+                if im(x0).is_negative:
+                    return self.func(x0) - pi
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # acot
+        arg0 = self.args[0].subs(x, 0)
+
+        # Handling branch points
+        if arg0 in (S.ImaginaryUnit, S.NegativeOne*S.ImaginaryUnit):
+            return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+        ndir = self.args[0].dir(x, cdir if cdir else 1)
+        if arg0.is_zero:
+            if re(ndir) < 0:
+                return res - pi
+            return res
+        # Handling points lying on branch cuts [-I, I]
+        if arg0.is_imaginary and (1 + arg0**2).is_positive:
+            if re(ndir).is_positive:
+                if im(arg0).is_positive:
+                    return res + pi
+            elif re(ndir).is_negative:
+                if im(arg0).is_negative:
+                    return res - pi
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_aseries(self, n, args0, x, logx):
+        if args0[0] in [S.Infinity, S.NegativeInfinity]:
+            return atan(1/self.args[0])._eval_nseries(x, n, logx)
+        else:
+            return super()._eval_aseries(n, args0, x, logx)
+
+    def _eval_rewrite_as_log(self, x, **kwargs):
+        return S.ImaginaryUnit/2*(log(1 - S.ImaginaryUnit/x)
+            - log(1 + S.ImaginaryUnit/x))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return cot
+
+    def _eval_rewrite_as_asin(self, arg, **kwargs):
+        return (arg*sqrt(1/arg**2)*
+                (pi/2 - asin(sqrt(-arg**2)/sqrt(-arg**2 - 1))))
+
+    def _eval_rewrite_as_acos(self, arg, **kwargs):
+        return arg*sqrt(1/arg**2)*acos(sqrt(-arg**2)/sqrt(-arg**2 - 1))
+
+    def _eval_rewrite_as_atan(self, arg, **kwargs):
+        return atan(1/arg)
+
+    def _eval_rewrite_as_asec(self, arg, **kwargs):
+        return arg*sqrt(1/arg**2)*asec(sqrt((1 + arg**2)/arg**2))
+
+    def _eval_rewrite_as_acsc(self, arg, **kwargs):
+        return arg*sqrt(1/arg**2)*(pi/2 - acsc(sqrt((1 + arg**2)/arg**2)))
+
+
+class asec(InverseTrigonometricFunction):
+    r"""
+    The inverse secant function.
+
+    Returns the arc secant of x (measured in radians).
+
+    Explanation
+    ===========
+
+    ``asec(x)`` will evaluate automatically in the cases
+    $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when the
+    result is a rational multiple of $\pi$ (see the eval class method).
+
+    ``asec(x)`` has branch cut in the interval $[-1, 1]$. For complex arguments,
+    it can be defined [4]_ as
+
+    .. math::
+        \operatorname{sec^{-1}}(z) = -i\frac{\log\left(\sqrt{1 - z^2} + 1\right)}{z}
+
+    At ``x = 0``, for positive branch cut, the limit evaluates to ``zoo``. For
+    negative branch cut, the limit
+
+    .. math::
+        \lim_{z \to 0}-i\frac{\log\left(-\sqrt{1 - z^2} + 1\right)}{z}
+
+    simplifies to :math:`-i\log\left(z/2 + O\left(z^3\right)\right)` which
+    ultimately evaluates to ``zoo``.
+
+    As ``acos(x) = asec(1/x)``, a similar argument can be given for
+    ``acos(x)``.
+
+    Examples
+    ========
+
+    >>> from sympy import asec, oo
+    >>> asec(1)
+    0
+    >>> asec(-1)
+    pi
+    >>> asec(0)
+    zoo
+    >>> asec(-oo)
+    pi/2
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    asin, acsc, acos, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.23
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcSec
+    .. [4] https://reference.wolfram.com/language/ref/ArcSec.html
+
+    """
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_zero:
+            return S.ComplexInfinity
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.One:
+                return S.Zero
+            elif arg is S.NegativeOne:
+                return pi
+        if arg in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]:
+            return pi/2
+
+        if arg.is_number:
+            acsc_table = cls._acsc_table()
+            if arg in acsc_table:
+                return pi/2 - acsc_table[arg]
+            elif -arg in acsc_table:
+                return pi/2 + acsc_table[-arg]
+
+        if arg.is_infinite:
+            return pi/2
+
+        if arg.is_Mul and len(arg.args) == 2 and arg.args[0] == -1:
+            narg = arg.args[1]
+            minus = True
+        else:
+            narg = arg
+            minus = False
+
+        if isinstance(narg, sec):
+            # asec(sec(x)) = x or asec(-sec(x)) = pi - x
+            ang = narg.args[0]
+            if ang.is_comparable:
+                if minus:
+                    ang = pi - ang
+                ang %= 2*pi # restrict to [0,2*pi)
+                if ang > pi: # restrict to [0,pi]
+                    ang = 2*pi - ang
+                return ang
+
+        if isinstance(narg, csc): # asec(x) + acsc(x) = pi/2
+            ang = narg.args[0]
+            if ang.is_comparable:
+                if minus:
+                    pi/2 + acsc(narg)
+                return pi/2 - acsc(narg)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 1/(self.args[0]**2*sqrt(1 - 1/self.args[0]**2))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return sec
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return S.ImaginaryUnit*log(2 / x)
+        elif n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 2 and n > 2:
+                p = previous_terms[-2]
+                return p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2)
+            else:
+                k = n // 2
+                R = RisingFactorial(S.Half, k) *  n
+                F = factorial(k) * n // 2 * n // 2
+                return -S.ImaginaryUnit * R / F * x**n / 4
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            return self.func(arg.as_leading_term(x))
+        # Handling branch points
+        if x0 == 1:
+            return sqrt(2)*sqrt((arg - S.One).as_leading_term(x))
+        if x0 in (-S.One, S.Zero):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        # Handling points lying on branch cuts (-1, 1)
+        if x0.is_real and (1 - x0**2).is_positive:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if x0.is_positive:
+                    return -self.func(x0)
+            elif im(ndir).is_positive:
+                if x0.is_negative:
+                    return 2*pi - self.func(x0)
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # asec
+        from sympy.series.order import O
+        arg0 = self.args[0].subs(x, 0)
+        # Handling branch points
+        if arg0 is S.One:
+            t = Dummy('t', positive=True)
+            ser = asec(S.One + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.NegativeOne + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        if arg0 is S.NegativeOne:
+            t = Dummy('t', positive=True)
+            ser = asec(S.NegativeOne - t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.NegativeOne - self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+        # Handling points lying on branch cuts (-1, 1)
+        if arg0.is_real and (1 - arg0**2).is_positive:
+            ndir = self.args[0].dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if arg0.is_positive:
+                    return -res
+            elif im(ndir).is_positive:
+                if arg0.is_negative:
+                    return 2*pi - res
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_is_extended_real(self):
+        x = self.args[0]
+        if x.is_extended_real is False:
+            return False
+        return fuzzy_or(((x - 1).is_nonnegative, (-x - 1).is_nonnegative))
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return pi/2 + S.ImaginaryUnit*log(S.ImaginaryUnit/arg + sqrt(1 - 1/arg**2))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_asin(self, arg, **kwargs):
+        return pi/2 - asin(1/arg)
+
+    def _eval_rewrite_as_acos(self, arg, **kwargs):
+        return acos(1/arg)
+
+    def _eval_rewrite_as_atan(self, x, **kwargs):
+        sx2x = sqrt(x**2)/x
+        return pi/2*(1 - sx2x) + sx2x*atan(sqrt(x**2 - 1))
+
+    def _eval_rewrite_as_acot(self, x, **kwargs):
+        sx2x = sqrt(x**2)/x
+        return pi/2*(1 - sx2x) + sx2x*acot(1/sqrt(x**2 - 1))
+
+    def _eval_rewrite_as_acsc(self, arg, **kwargs):
+        return pi/2 - acsc(arg)
+
+
+class acsc(InverseTrigonometricFunction):
+    r"""
+    The inverse cosecant function.
+
+    Returns the arc cosecant of x (measured in radians).
+
+    Explanation
+    ===========
+
+    ``acsc(x)`` will evaluate automatically in the cases
+    $x \in \{\infty, -\infty, 0, 1, -1\}$` and for some instances when the
+    result is a rational multiple of $\pi$ (see the ``eval`` class method).
+
+    Examples
+    ========
+
+    >>> from sympy import acsc, oo
+    >>> acsc(1)
+    pi/2
+    >>> acsc(-1)
+    -pi/2
+    >>> acsc(oo)
+    0
+    >>> acsc(-oo) == acsc(oo)
+    True
+    >>> acsc(0)
+    zoo
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    asin, acos, asec, atan, acot, atan2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+    .. [2] https://dlmf.nist.gov/4.23
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcCsc
+
+    """
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_zero:
+            return S.ComplexInfinity
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.One:
+                return pi/2
+            elif arg is S.NegativeOne:
+                return -pi/2
+        if arg in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]:
+            return S.Zero
+
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+        if arg.is_infinite:
+            return S.Zero
+
+        if arg.is_number:
+            acsc_table = cls._acsc_table()
+            if arg in acsc_table:
+                return acsc_table[arg]
+
+        if isinstance(arg, csc):
+            ang = arg.args[0]
+            if ang.is_comparable:
+                ang %= 2*pi # restrict to [0,2*pi)
+                if ang > pi: # restrict to (-pi,pi]
+                    ang = pi - ang
+
+                # restrict to [-pi/2,pi/2]
+                if ang > pi/2:
+                    ang = pi - ang
+                if ang < -pi/2:
+                    ang = -pi - ang
+
+                return ang
+
+        if isinstance(arg, sec): # asec(x) + acsc(x) = pi/2
+            ang = arg.args[0]
+            if ang.is_comparable:
+                return pi/2 - asec(arg)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -1/(self.args[0]**2*sqrt(1 - 1/self.args[0]**2))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+        """
+        return csc
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return pi/2 - S.ImaginaryUnit*log(2) + S.ImaginaryUnit*log(x)
+        elif n < 0 or n % 2 == 1:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 2 and n > 2:
+                p = previous_terms[-2]
+                return p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2)
+            else:
+                k = n // 2
+                R = RisingFactorial(S.Half, k) *  n
+                F = factorial(k) * n // 2 * n // 2
+                return S.ImaginaryUnit * R / F * x**n / 4
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            return self.func(arg.as_leading_term(x))
+        # Handling branch points
+        if x0 in (-S.One, S.One, S.Zero):
+            return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        if x0 is S.ComplexInfinity:
+            return (1/arg).as_leading_term(x)
+        # Handling points lying on branch cuts (-1, 1)
+        if x0.is_real and (1 - x0**2).is_positive:
+            ndir = arg.dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if x0.is_positive:
+                    return pi - self.func(x0)
+            elif im(ndir).is_positive:
+                if x0.is_negative:
+                    return -pi - self.func(x0)
+            else:
+                return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand()
+        return self.func(x0)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):  # acsc
+        from sympy.series.order import O
+        arg0 = self.args[0].subs(x, 0)
+        # Handling branch points
+        if arg0 is S.One:
+            t = Dummy('t', positive=True)
+            ser = acsc(S.One + t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.NegativeOne + self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        if arg0 is S.NegativeOne:
+            t = Dummy('t', positive=True)
+            ser = acsc(S.NegativeOne - t**2).rewrite(log).nseries(t, 0, 2*n)
+            arg1 = S.NegativeOne - self.args[0]
+            f = arg1.as_leading_term(x)
+            g = (arg1 - f)/ f
+            res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx)
+            res = (res1.removeO()*sqrt(f)).expand()
+            return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x)
+
+        res = super()._eval_nseries(x, n=n, logx=logx)
+        if arg0 is S.ComplexInfinity:
+            return res
+        # Handling points lying on branch cuts (-1, 1)
+        if arg0.is_real and (1 - arg0**2).is_positive:
+            ndir = self.args[0].dir(x, cdir if cdir else 1)
+            if im(ndir).is_negative:
+                if arg0.is_positive:
+                    return pi - res
+            elif im(ndir).is_positive:
+                if arg0.is_negative:
+                    return -pi - res
+            else:
+                return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return res
+
+    def _eval_rewrite_as_log(self, arg, **kwargs):
+        return -S.ImaginaryUnit*log(S.ImaginaryUnit/arg + sqrt(1 - 1/arg**2))
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_log
+
+    def _eval_rewrite_as_asin(self, arg, **kwargs):
+        return asin(1/arg)
+
+    def _eval_rewrite_as_acos(self, arg, **kwargs):
+        return pi/2 - acos(1/arg)
+
+    def _eval_rewrite_as_atan(self, x, **kwargs):
+        return sqrt(x**2)/x*(pi/2 - atan(sqrt(x**2 - 1)))
+
+    def _eval_rewrite_as_acot(self, arg, **kwargs):
+        return sqrt(arg**2)/arg*(pi/2 - acot(1/sqrt(arg**2 - 1)))
+
+    def _eval_rewrite_as_asec(self, arg, **kwargs):
+        return pi/2 - asec(arg)
+
+
+class atan2(InverseTrigonometricFunction):
+    r"""
+    The function ``atan2(y, x)`` computes `\operatorname{atan}(y/x)` taking
+    two arguments `y` and `x`.  Signs of both `y` and `x` are considered to
+    determine the appropriate quadrant of `\operatorname{atan}(y/x)`.
+    The range is `(-\pi, \pi]`. The complete definition reads as follows:
+
+    .. math::
+
+        \operatorname{atan2}(y, x) =
+        \begin{cases}
+          \arctan\left(\frac y x\right) & \qquad x > 0 \\
+          \arctan\left(\frac y x\right) + \pi& \qquad y \ge 0, x < 0 \\
+          \arctan\left(\frac y x\right) - \pi& \qquad y < 0, x < 0 \\
+          +\frac{\pi}{2} & \qquad y > 0, x = 0 \\
+          -\frac{\pi}{2} & \qquad y < 0, x = 0 \\
+          \text{undefined} & \qquad y = 0, x = 0
+        \end{cases}
+
+    Attention: Note the role reversal of both arguments. The `y`-coordinate
+    is the first argument and the `x`-coordinate the second.
+
+    If either `x` or `y` is complex:
+
+    .. math::
+
+        \operatorname{atan2}(y, x) =
+            -i\log\left(\frac{x + iy}{\sqrt{x^2 + y^2}}\right)
+
+    Examples
+    ========
+
+    Going counter-clock wise around the origin we find the
+    following angles:
+
+    >>> from sympy import atan2
+    >>> atan2(0, 1)
+    0
+    >>> atan2(1, 1)
+    pi/4
+    >>> atan2(1, 0)
+    pi/2
+    >>> atan2(1, -1)
+    3*pi/4
+    >>> atan2(0, -1)
+    pi
+    >>> atan2(-1, -1)
+    -3*pi/4
+    >>> atan2(-1, 0)
+    -pi/2
+    >>> atan2(-1, 1)
+    -pi/4
+
+    which are all correct. Compare this to the results of the ordinary
+    `\operatorname{atan}` function for the point `(x, y) = (-1, 1)`
+
+    >>> from sympy import atan, S
+    >>> atan(S(1)/-1)
+    -pi/4
+    >>> atan2(1, -1)
+    3*pi/4
+
+    where only the `\operatorname{atan2}` function returns what we expect.
+    We can differentiate the function with respect to both arguments:
+
+    >>> from sympy import diff
+    >>> from sympy.abc import x, y
+    >>> diff(atan2(y, x), x)
+    -y/(x**2 + y**2)
+
+    >>> diff(atan2(y, x), y)
+    x/(x**2 + y**2)
+
+    We can express the `\operatorname{atan2}` function in terms of
+    complex logarithms:
+
+    >>> from sympy import log
+    >>> atan2(y, x).rewrite(log)
+    -I*log((x + I*y)/sqrt(x**2 + y**2))
+
+    and in terms of `\operatorname(atan)`:
+
+    >>> from sympy import atan
+    >>> atan2(y, x).rewrite(atan)
+    Piecewise((2*atan(y/(x + sqrt(x**2 + y**2))), Ne(y, 0)), (pi, re(x) < 0), (0, Ne(x, 0)), (nan, True))
+
+    but note that this form is undefined on the negative real axis.
+
+    See Also
+    ========
+
+    sin, csc, cos, sec, tan, cot
+    asin, acsc, acos, asec, atan, acot
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+    .. [2] https://en.wikipedia.org/wiki/Atan2
+    .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcTan2
+
+    """
+
+    @classmethod
+    def eval(cls, y, x):
+        from sympy.functions.special.delta_functions import Heaviside
+        if x is S.NegativeInfinity:
+            if y.is_zero:
+                # Special case y = 0 because we define Heaviside(0) = 1/2
+                return pi
+            return 2*pi*(Heaviside(re(y))) - pi
+        elif x is S.Infinity:
+            return S.Zero
+        elif x.is_imaginary and y.is_imaginary and x.is_number and y.is_number:
+            x = im(x)
+            y = im(y)
+
+        if x.is_extended_real and y.is_extended_real:
+            if x.is_positive:
+                return atan(y/x)
+            elif x.is_negative:
+                if y.is_negative:
+                    return atan(y/x) - pi
+                elif y.is_nonnegative:
+                    return atan(y/x) + pi
+            elif x.is_zero:
+                if y.is_positive:
+                    return pi/2
+                elif y.is_negative:
+                    return -pi/2
+                elif y.is_zero:
+                    return S.NaN
+        if y.is_zero:
+            if x.is_extended_nonzero:
+                return pi*(S.One - Heaviside(x))
+            if x.is_number:
+                return Piecewise((pi, re(x) < 0),
+                                 (0, Ne(x, 0)),
+                                 (S.NaN, True))
+        if x.is_number and y.is_number:
+            return -S.ImaginaryUnit*log(
+                (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
+
+    def _eval_rewrite_as_log(self, y, x, **kwargs):
+        return -S.ImaginaryUnit*log((x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
+
+    def _eval_rewrite_as_atan(self, y, x, **kwargs):
+        return Piecewise((2*atan(y/(x + sqrt(x**2 + y**2))), Ne(y, 0)),
+                         (pi, re(x) < 0),
+                         (0, Ne(x, 0)),
+                         (S.NaN, True))
+
+    def _eval_rewrite_as_arg(self, y, x, **kwargs):
+        if x.is_extended_real and y.is_extended_real:
+            return arg_f(x + y*S.ImaginaryUnit)
+        n = x + S.ImaginaryUnit*y
+        d = x**2 + y**2
+        return arg_f(n/sqrt(d)) - S.ImaginaryUnit*log(abs(n)/sqrt(abs(d)))
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real and self.args[1].is_extended_real
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate(), self.args[1].conjugate())
+
+    def fdiff(self, argindex):
+        y, x = self.args
+        if argindex == 1:
+            # Diff wrt y
+            return x/(x**2 + y**2)
+        elif argindex == 2:
+            # Diff wrt x
+            return -y/(x**2 + y**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_evalf(self, prec):
+        y, x = self.args
+        if x.is_extended_real and y.is_extended_real:
+            return super()._eval_evalf(prec)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..ab52ace36a8dfbe73179dbf4419a54f7fa1af5fa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/__init__.py
@@ -0,0 +1 @@
+# Stub __init__.py for the sympy.functions.special package
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/benchmarks/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/benchmarks/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/benchmarks/bench_special.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/benchmarks/bench_special.py
new file mode 100644
index 0000000000000000000000000000000000000000..25d7280c2cf31dcbff08065a78847ed03e0ebb05
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/benchmarks/bench_special.py
@@ -0,0 +1,8 @@
+from sympy.core.symbol import symbols
+from sympy.functions.special.spherical_harmonics import Ynm
+
+x, y = symbols('x,y')
+
+
+def timeit_Ynm_xy():
+    Ynm(1, 1, x, y)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/bessel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..a24e7dc442d2a5a9bf7047113fd81b36c6b6ba36
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/bessel.py
@@ -0,0 +1,2208 @@
+from functools import wraps
+
+from sympy.core import S
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.expr import Expr
+from sympy.core.function import DefinedFunction, ArgumentIndexError, _mexpand
+from sympy.core.logic import fuzzy_or, fuzzy_not
+from sympy.core.numbers import Rational, pi, I
+from sympy.core.power import Pow
+from sympy.core.symbol import Dummy, uniquely_named_symbol, Wild
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial, RisingFactorial
+from sympy.functions.elementary.trigonometric import sin, cos, csc, cot
+from sympy.functions.elementary.integers import ceiling
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.miscellaneous import cbrt, sqrt, root
+from sympy.functions.elementary.complexes import (Abs, re, im, polar_lift, unpolarify)
+from sympy.functions.special.gamma_functions import gamma, digamma, uppergamma
+from sympy.functions.special.hyper import hyper
+from sympy.polys.orthopolys import spherical_bessel_fn
+
+from mpmath import mp, workprec
+
+# TODO
+# o Scorer functions G1 and G2
+# o Asymptotic expansions
+#   These are possible, e.g. for fixed order, but since the bessel type
+#   functions are oscillatory they are not actually tractable at
+#   infinity, so this is not particularly useful right now.
+# o Nicer series expansions.
+# o More rewriting.
+# o Add solvers to ode.py (or rather add solvers for the hypergeometric equation).
+
+
+class BesselBase(DefinedFunction):
+    """
+    Abstract base class for Bessel-type functions.
+
+    This class is meant to reduce code duplication.
+    All Bessel-type functions can 1) be differentiated, with the derivatives
+    expressed in terms of similar functions, and 2) be rewritten in terms
+    of other Bessel-type functions.
+
+    Here, Bessel-type functions are assumed to have one complex parameter.
+
+    To use this base class, define class attributes ``_a`` and ``_b`` such that
+    ``2*F_n' = -_a*F_{n+1} + b*F_{n-1}``.
+
+    """
+
+    @property
+    def order(self):
+        """ The order of the Bessel-type function. """
+        return self.args[0]
+
+    @property
+    def argument(self):
+        """ The argument of the Bessel-type function. """
+        return self.args[1]
+
+    @classmethod
+    def eval(cls, nu, z):
+        return
+
+    def fdiff(self, argindex=2):
+        if argindex != 2:
+            raise ArgumentIndexError(self, argindex)
+        return (self._b/2 * self.__class__(self.order - 1, self.argument) -
+                self._a/2 * self.__class__(self.order + 1, self.argument))
+
+    def _eval_conjugate(self):
+        z = self.argument
+        if z.is_extended_negative is False:
+            return self.__class__(self.order.conjugate(), z.conjugate())
+
+    def _eval_is_meromorphic(self, x, a):
+        nu, z = self.order, self.argument
+
+        if nu.has(x):
+            return False
+        if not z._eval_is_meromorphic(x, a):
+            return None
+        z0 = z.subs(x, a)
+        if nu.is_integer:
+            if isinstance(self, (besselj, besseli, hn1, hn2, jn, yn)) or not nu.is_zero:
+                return fuzzy_not(z0.is_infinite)
+        return fuzzy_not(fuzzy_or([z0.is_zero, z0.is_infinite]))
+
+    def _eval_expand_func(self, **hints):
+        nu, z, f = self.order, self.argument, self.__class__
+        if nu.is_real:
+            if (nu - 1).is_positive:
+                return (-self._a*self._b*f(nu - 2, z)._eval_expand_func() +
+                        2*self._a*(nu - 1)*f(nu - 1, z)._eval_expand_func()/z)
+            elif (nu + 1).is_negative:
+                return (2*self._b*(nu + 1)*f(nu + 1, z)._eval_expand_func()/z -
+                        self._a*self._b*f(nu + 2, z)._eval_expand_func())
+        return self
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.simplify.simplify import besselsimp
+        return besselsimp(self)
+
+
+class besselj(BesselBase):
+    r"""
+    Bessel function of the first kind.
+
+    Explanation
+    ===========
+
+    The Bessel $J$ function of order $\nu$ is defined to be the function
+    satisfying Bessel's differential equation
+
+    .. math ::
+        z^2 \frac{\mathrm{d}^2 w}{\mathrm{d}z^2}
+        + z \frac{\mathrm{d}w}{\mathrm{d}z} + (z^2 - \nu^2) w = 0,
+
+    with Laurent expansion
+
+    .. math ::
+        J_\nu(z) = z^\nu \left(\frac{1}{\Gamma(\nu + 1) 2^\nu} + O(z^2) \right),
+
+    if $\nu$ is not a negative integer. If $\nu=-n \in \mathbb{Z}_{<0}$
+    *is* a negative integer, then the definition is
+
+    .. math ::
+        J_{-n}(z) = (-1)^n J_n(z).
+
+    Examples
+    ========
+
+    Create a Bessel function object:
+
+    >>> from sympy import besselj, jn
+    >>> from sympy.abc import z, n
+    >>> b = besselj(n, z)
+
+    Differentiate it:
+
+    >>> b.diff(z)
+    besselj(n - 1, z)/2 - besselj(n + 1, z)/2
+
+    Rewrite in terms of spherical Bessel functions:
+
+    >>> b.rewrite(jn)
+    sqrt(2)*sqrt(z)*jn(n - 1/2, z)/sqrt(pi)
+
+    Access the parameter and argument:
+
+    >>> b.order
+    n
+    >>> b.argument
+    z
+
+    See Also
+    ========
+
+    bessely, besseli, besselk
+
+    References
+    ==========
+
+    .. [1] Abramowitz, Milton; Stegun, Irene A., eds. (1965), "Chapter 9",
+           Handbook of Mathematical Functions with Formulas, Graphs, and
+           Mathematical Tables
+    .. [2] Luke, Y. L. (1969), The Special Functions and Their
+           Approximations, Volume 1
+    .. [3] https://en.wikipedia.org/wiki/Bessel_function
+    .. [4] https://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/
+
+    """
+
+    _a = S.One
+    _b = S.One
+
+    @classmethod
+    def eval(cls, nu, z):
+        if z.is_zero:
+            if nu.is_zero:
+                return S.One
+            elif (nu.is_integer and nu.is_zero is False) or re(nu).is_positive:
+                return S.Zero
+            elif re(nu).is_negative and not (nu.is_integer is True):
+                return S.ComplexInfinity
+            elif nu.is_imaginary:
+                return S.NaN
+        if z in (S.Infinity, S.NegativeInfinity):
+            return S.Zero
+
+        if z.could_extract_minus_sign():
+            return (z)**nu*(-z)**(-nu)*besselj(nu, -z)
+        if nu.is_integer:
+            if nu.could_extract_minus_sign():
+                return S.NegativeOne**(-nu)*besselj(-nu, z)
+            newz = z.extract_multiplicatively(I)
+            if newz:  # NOTE we don't want to change the function if z==0
+                return I**(nu)*besseli(nu, newz)
+
+        # branch handling:
+        if nu.is_integer:
+            newz = unpolarify(z)
+            if newz != z:
+                return besselj(nu, newz)
+        else:
+            newz, n = z.extract_branch_factor()
+            if n != 0:
+                return exp(2*n*pi*nu*I)*besselj(nu, newz)
+        nnu = unpolarify(nu)
+        if nu != nnu:
+            return besselj(nnu, z)
+
+    def _eval_rewrite_as_besseli(self, nu, z, **kwargs):
+        return exp(I*pi*nu/2)*besseli(nu, polar_lift(-I)*z)
+
+    def _eval_rewrite_as_bessely(self, nu, z, **kwargs):
+        if nu.is_integer is False:
+            return csc(pi*nu)*bessely(-nu, z) - cot(pi*nu)*bessely(nu, z)
+
+    def _eval_rewrite_as_jn(self, nu, z, **kwargs):
+        return sqrt(2*z/pi)*jn(nu - S.Half, self.argument)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        nu, z = self.args
+        try:
+            arg = z.as_leading_term(x)
+        except NotImplementedError:
+            return self
+        c, e = arg.as_coeff_exponent(x)
+
+        if e.is_positive:
+            return arg**nu/(2**nu*gamma(nu + 1))
+        elif e.is_negative:
+            cdir = 1 if cdir == 0 else cdir
+            sign = c*cdir**e
+            if not sign.is_negative:
+                # Refer Abramowitz and Stegun 1965, p. 364 for more information on
+                # asymptotic approximation of besselj function.
+                return sqrt(2)*cos(z - pi*(2*nu + 1)/4)/sqrt(pi*z)
+            return self
+
+        return super(besselj, self)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_is_extended_real(self):
+        nu, z = self.args
+        if nu.is_integer and z.is_extended_real:
+            return True
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/06/01/04/01/01/0003/
+        # for more information on nseries expansion of besselj function.
+        from sympy.series.order import Order
+        nu, z = self.args
+
+        # In case of powers less than 1, number of terms need to be computed
+        # separately to avoid repeated callings of _eval_nseries with wrong n
+        try:
+            _, exp = z.leadterm(x)
+        except (ValueError, NotImplementedError):
+            return self
+
+        if exp.is_positive:
+            newn = ceiling(n/exp)
+            o = Order(x**n, x)
+            r = (z/2)._eval_nseries(x, n, logx, cdir).removeO()
+            if r is S.Zero:
+                return o
+            t = (_mexpand(r**2) + o).removeO()
+
+            term = r**nu/gamma(nu + 1)
+            s = [term]
+            for k in range(1, (newn + 1)//2):
+                term *= -t/(k*(nu + k))
+                term = (_mexpand(term) + o).removeO()
+                s.append(term)
+            return Add(*s) + o
+
+        return super(besselj, self)._eval_nseries(x, n, logx, cdir)
+
+
+class bessely(BesselBase):
+    r"""
+    Bessel function of the second kind.
+
+    Explanation
+    ===========
+
+    The Bessel $Y$ function of order $\nu$ is defined as
+
+    .. math ::
+        Y_\nu(z) = \lim_{\mu \to \nu} \frac{J_\mu(z) \cos(\pi \mu)
+                                            - J_{-\mu}(z)}{\sin(\pi \mu)},
+
+    where $J_\mu(z)$ is the Bessel function of the first kind.
+
+    It is a solution to Bessel's equation, and linearly independent from
+    $J_\nu$.
+
+    Examples
+    ========
+
+    >>> from sympy import bessely, yn
+    >>> from sympy.abc import z, n
+    >>> b = bessely(n, z)
+    >>> b.diff(z)
+    bessely(n - 1, z)/2 - bessely(n + 1, z)/2
+    >>> b.rewrite(yn)
+    sqrt(2)*sqrt(z)*yn(n - 1/2, z)/sqrt(pi)
+
+    See Also
+    ========
+
+    besselj, besseli, besselk
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/BesselY/
+
+    """
+
+    _a = S.One
+    _b = S.One
+
+    @classmethod
+    def eval(cls, nu, z):
+        if z.is_zero:
+            if nu.is_zero:
+                return S.NegativeInfinity
+            elif re(nu).is_zero is False:
+                return S.ComplexInfinity
+            elif re(nu).is_zero:
+                return S.NaN
+        if z in (S.Infinity, S.NegativeInfinity):
+            return S.Zero
+        if z == I*S.Infinity:
+            return exp(I*pi*(nu + 1)/2) * S.Infinity
+        if z == I*S.NegativeInfinity:
+            return exp(-I*pi*(nu + 1)/2) * S.Infinity
+
+        if nu.is_integer:
+            if nu.could_extract_minus_sign():
+                return S.NegativeOne**(-nu)*bessely(-nu, z)
+
+    def _eval_rewrite_as_besselj(self, nu, z, **kwargs):
+        if nu.is_integer is False:
+            return csc(pi*nu)*(cos(pi*nu)*besselj(nu, z) - besselj(-nu, z))
+
+    def _eval_rewrite_as_besseli(self, nu, z, **kwargs):
+        aj = self._eval_rewrite_as_besselj(*self.args)
+        if aj:
+            return aj.rewrite(besseli)
+
+    def _eval_rewrite_as_yn(self, nu, z, **kwargs):
+        return sqrt(2*z/pi) * yn(nu - S.Half, self.argument)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        nu, z = self.args
+        try:
+            arg = z.as_leading_term(x)
+        except NotImplementedError:
+            return self
+        c, e = arg.as_coeff_exponent(x)
+
+        if e.is_positive:
+            term_one = ((2/pi)*log(z/2)*besselj(nu, z))
+            term_two = -(z/2)**(-nu)*factorial(nu - 1)/pi if (nu).is_positive else S.Zero
+            term_three = -(z/2)**nu/(pi*factorial(nu))*(digamma(nu + 1) - S.EulerGamma)
+            arg = Add(*[term_one, term_two, term_three]).as_leading_term(x, logx=logx)
+            return arg
+        elif e.is_negative:
+            cdir = 1 if cdir == 0 else cdir
+            sign = c*cdir**e
+            if not sign.is_negative:
+                # Refer Abramowitz and Stegun 1965, p. 364 for more information on
+                # asymptotic approximation of bessely function.
+                return sqrt(2)*(-sin(pi*nu/2 - z + pi/4) + 3*cos(pi*nu/2 - z + pi/4)/(8*z))*sqrt(1/z)/sqrt(pi)
+            return self
+
+        return super(bessely, self)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_is_extended_real(self):
+        nu, z = self.args
+        if nu.is_integer and z.is_positive:
+            return True
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselY/06/01/04/01/02/0008/
+        # for more information on nseries expansion of bessely function.
+        from sympy.series.order import Order
+        nu, z = self.args
+
+        # In case of powers less than 1, number of terms need to be computed
+        # separately to avoid repeated callings of _eval_nseries with wrong n
+        try:
+            _, exp = z.leadterm(x)
+        except (ValueError, NotImplementedError):
+            return self
+
+        if exp.is_positive and nu.is_integer:
+            newn = ceiling(n/exp)
+            bn = besselj(nu, z)
+            a = ((2/pi)*log(z/2)*bn)._eval_nseries(x, n, logx, cdir)
+
+            b, c = [], []
+            o = Order(x**n, x)
+            r = (z/2)._eval_nseries(x, n, logx, cdir).removeO()
+            if r is S.Zero:
+                return o
+            t = (_mexpand(r**2) + o).removeO()
+
+            if nu > S.Zero:
+                term = r**(-nu)*factorial(nu - 1)/pi
+                b.append(term)
+                for k in range(1, nu):
+                    denom = (nu - k)*k
+                    if denom == S.Zero:
+                        term *= t/k
+                    else:
+                        term *= t/denom
+                    term = (_mexpand(term) + o).removeO()
+                    b.append(term)
+
+            p = r**nu/(pi*factorial(nu))
+            term = p*(digamma(nu + 1) - S.EulerGamma)
+            c.append(term)
+            for k in range(1, (newn + 1)//2):
+                p *= -t/(k*(k + nu))
+                p = (_mexpand(p) + o).removeO()
+                term = p*(digamma(k + nu + 1) + digamma(k + 1))
+                c.append(term)
+            return a - Add(*b) - Add(*c) # Order term comes from a
+
+        return super(bessely, self)._eval_nseries(x, n, logx, cdir)
+
+
+class besseli(BesselBase):
+    r"""
+    Modified Bessel function of the first kind.
+
+    Explanation
+    ===========
+
+    The Bessel $I$ function is a solution to the modified Bessel equation
+
+    .. math ::
+        z^2 \frac{\mathrm{d}^2 w}{\mathrm{d}z^2}
+        + z \frac{\mathrm{d}w}{\mathrm{d}z} + (z^2 + \nu^2)^2 w = 0.
+
+    It can be defined as
+
+    .. math ::
+        I_\nu(z) = i^{-\nu} J_\nu(iz),
+
+    where $J_\nu(z)$ is the Bessel function of the first kind.
+
+    Examples
+    ========
+
+    >>> from sympy import besseli
+    >>> from sympy.abc import z, n
+    >>> besseli(n, z).diff(z)
+    besseli(n - 1, z)/2 + besseli(n + 1, z)/2
+
+    See Also
+    ========
+
+    besselj, bessely, besselk
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/BesselI/
+
+    """
+
+    _a = -S.One
+    _b = S.One
+
+    @classmethod
+    def eval(cls, nu, z):
+        if z.is_zero:
+            if nu.is_zero:
+                return S.One
+            elif (nu.is_integer and nu.is_zero is False) or re(nu).is_positive:
+                return S.Zero
+            elif re(nu).is_negative and not (nu.is_integer is True):
+                return S.ComplexInfinity
+            elif nu.is_imaginary:
+                return S.NaN
+        if im(z) in (S.Infinity, S.NegativeInfinity):
+            return S.Zero
+        if z is S.Infinity:
+            return S.Infinity
+        if z is S.NegativeInfinity:
+            return (-1)**nu*S.Infinity
+
+        if z.could_extract_minus_sign():
+            return (z)**nu*(-z)**(-nu)*besseli(nu, -z)
+        if nu.is_integer:
+            if nu.could_extract_minus_sign():
+                return besseli(-nu, z)
+            newz = z.extract_multiplicatively(I)
+            if newz:  # NOTE we don't want to change the function if z==0
+                return I**(-nu)*besselj(nu, -newz)
+
+        # branch handling:
+        if nu.is_integer:
+            newz = unpolarify(z)
+            if newz != z:
+                return besseli(nu, newz)
+        else:
+            newz, n = z.extract_branch_factor()
+            if n != 0:
+                return exp(2*n*pi*nu*I)*besseli(nu, newz)
+        nnu = unpolarify(nu)
+        if nu != nnu:
+            return besseli(nnu, z)
+
+    def _eval_rewrite_as_tractable(self, nu, z, limitvar=None, **kwargs):
+        if z.is_extended_real:
+            return exp(z)*_besseli(nu, z)
+
+    def _eval_rewrite_as_besselj(self, nu, z, **kwargs):
+        return exp(-I*pi*nu/2)*besselj(nu, polar_lift(I)*z)
+
+    def _eval_rewrite_as_bessely(self, nu, z, **kwargs):
+        aj = self._eval_rewrite_as_besselj(*self.args)
+        if aj:
+            return aj.rewrite(bessely)
+
+    def _eval_rewrite_as_jn(self, nu, z, **kwargs):
+        return self._eval_rewrite_as_besselj(*self.args).rewrite(jn)
+
+    def _eval_is_extended_real(self):
+        nu, z = self.args
+        if nu.is_integer and z.is_extended_real:
+            return True
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        nu, z = self.args
+        try:
+            arg = z.as_leading_term(x)
+        except NotImplementedError:
+            return self
+        c, e = arg.as_coeff_exponent(x)
+
+        if e.is_positive:
+            return arg**nu/(2**nu*gamma(nu + 1))
+        elif e.is_negative:
+            cdir = 1 if cdir == 0 else cdir
+            sign = c*cdir**e
+            if not sign.is_negative:
+                # Refer Abramowitz and Stegun 1965, p. 377 for more information on
+                # asymptotic approximation of besseli function.
+                return exp(z)/sqrt(2*pi*z)
+            return self
+
+        return super(besseli, self)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselI/06/01/04/01/01/0003/
+        # for more information on nseries expansion of besseli function.
+        from sympy.series.order import Order
+        nu, z = self.args
+
+        # In case of powers less than 1, number of terms need to be computed
+        # separately to avoid repeated callings of _eval_nseries with wrong n
+        try:
+            _, exp = z.leadterm(x)
+        except (ValueError, NotImplementedError):
+            return self
+
+        if exp.is_positive:
+            newn = ceiling(n/exp)
+            o = Order(x**n, x)
+            r = (z/2)._eval_nseries(x, n, logx, cdir).removeO()
+            if r is S.Zero:
+                return o
+            t = (_mexpand(r**2) + o).removeO()
+
+            term = r**nu/gamma(nu + 1)
+            s = [term]
+            for k in range(1, (newn + 1)//2):
+                term *= t/(k*(nu + k))
+                term = (_mexpand(term) + o).removeO()
+                s.append(term)
+            return Add(*s) + o
+
+        return super(besseli, self)._eval_nseries(x, n, logx, cdir)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.functions.combinatorial.factorials import RisingFactorial
+        from sympy.series.order import Order
+        point = args0[1]
+
+        if point in [S.Infinity, S.NegativeInfinity]:
+            nu, z = self.args
+            s = [(RisingFactorial(Rational(2*nu - 1, 2), k)*RisingFactorial(Rational(2*nu + 1, 2), k))/\
+            ((2)**(k)*z**(Rational(2*k + 1, 2))*factorial(k)) for k in range(n)] + [Order(1/z**(Rational(2*n + 1, 2)), x)]
+            return exp(z)/sqrt(2*pi) * (Add(*s))
+
+        return super()._eval_aseries(n, args0, x, logx)
+
+
+class besselk(BesselBase):
+    r"""
+    Modified Bessel function of the second kind.
+
+    Explanation
+    ===========
+
+    The Bessel $K$ function of order $\nu$ is defined as
+
+    .. math ::
+        K_\nu(z) = \lim_{\mu \to \nu} \frac{\pi}{2}
+                   \frac{I_{-\mu}(z) -I_\mu(z)}{\sin(\pi \mu)},
+
+    where $I_\mu(z)$ is the modified Bessel function of the first kind.
+
+    It is a solution of the modified Bessel equation, and linearly independent
+    from $Y_\nu$.
+
+    Examples
+    ========
+
+    >>> from sympy import besselk
+    >>> from sympy.abc import z, n
+    >>> besselk(n, z).diff(z)
+    -besselk(n - 1, z)/2 - besselk(n + 1, z)/2
+
+    See Also
+    ========
+
+    besselj, besseli, bessely
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/BesselK/
+
+    """
+
+    _a = S.One
+    _b = -S.One
+
+    @classmethod
+    def eval(cls, nu, z):
+        if z.is_zero:
+            if nu.is_zero:
+                return S.Infinity
+            elif re(nu).is_zero is False:
+                return S.ComplexInfinity
+            elif re(nu).is_zero:
+                return S.NaN
+        if z in (S.Infinity, I*S.Infinity, I*S.NegativeInfinity):
+            return S.Zero
+
+        if nu.is_integer:
+            if nu.could_extract_minus_sign():
+                return besselk(-nu, z)
+
+    def _eval_rewrite_as_besseli(self, nu, z, **kwargs):
+        if nu.is_integer is False:
+            return pi*csc(pi*nu)*(besseli(-nu, z) - besseli(nu, z))/2
+
+    def _eval_rewrite_as_besselj(self, nu, z, **kwargs):
+        ai = self._eval_rewrite_as_besseli(*self.args)
+        if ai:
+            return ai.rewrite(besselj)
+
+    def _eval_rewrite_as_bessely(self, nu, z, **kwargs):
+        aj = self._eval_rewrite_as_besselj(*self.args)
+        if aj:
+            return aj.rewrite(bessely)
+
+    def _eval_rewrite_as_yn(self, nu, z, **kwargs):
+        ay = self._eval_rewrite_as_bessely(*self.args)
+        if ay:
+            return ay.rewrite(yn)
+
+    def _eval_is_extended_real(self):
+        nu, z = self.args
+        if nu.is_integer and z.is_positive:
+            return True
+
+    def _eval_rewrite_as_tractable(self, nu, z, limitvar=None, **kwargs):
+        if z.is_extended_real:
+            return exp(-z)*_besselk(nu, z)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        nu, z = self.args
+        try:
+            arg = z.as_leading_term(x)
+        except NotImplementedError:
+            return self
+        _, e = arg.as_coeff_exponent(x)
+
+        if e.is_positive:
+            if nu.is_zero:
+                # Equation 9.6.8 of Abramowitz and Stegun (10th ed, 1972).
+                term = -log(z) - S.EulerGamma + log(2)
+            elif nu.is_nonzero:
+                # Equation 9.6.9 of Abramowitz and Stegun (10th ed, 1972).
+                term = gamma(Abs(nu))*(z/2)**(-Abs(nu))/2
+            else:
+                raise NotImplementedError(f"Cannot proceed without knowing if {nu} is zero or not.")
+
+            return term.as_leading_term(x, logx=logx)
+        elif e.is_negative:
+            # Equation 9.7.2 of Abramowitz and Stegun (10th ed, 1972).
+            return sqrt(pi)*exp(-arg)/sqrt(2*arg)
+        else:
+            return self.func(nu, arg)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.series.order import Order
+        nu, z = self.args
+
+        try:
+            _, exp = z.leadterm(x)
+        except (ValueError, NotImplementedError):
+            return self
+
+        # In case of powers less than 1, number of terms need to be computed
+        # separately to avoid repeated callings of _eval_nseries with wrong n
+        if exp.is_positive:
+            r = (z/2)._eval_nseries(x, n, logx, cdir).removeO()
+            if r is S.Zero:
+                return Order(z**(-nu) + z**nu, x)
+
+            o = Order(x**n, x)
+            if nu.is_integer:
+                # Reference: https://functions.wolfram.com/Bessel-TypeFunctions/BesselK/06/01/04/01/02/0008/ (only for integer order)
+                newn = ceiling(n/exp)
+                bn = besseli(nu, z)
+                a = ((-1)**(nu - 1)*log(z/2)*bn)._eval_nseries(x, n, logx, cdir)
+
+                b, c = [], []
+                t = _mexpand(r**2)
+
+                if nu > S.Zero:
+                    term = r**(-nu)*factorial(nu - 1)/2
+                    b.append(term)
+                    for k in range(1, nu):
+                        term *= t/((k - nu)*k)
+                        term = (_mexpand(term) + o).removeO()
+                        b.append(term)
+
+                p = r**nu*(-1)**nu/(2*factorial(nu))
+                term = p*(digamma(nu + 1) - S.EulerGamma)
+                c.append(term)
+                for k in range(1, (newn + 1)//2):
+                    p *= t/(k*(k + nu))
+                    p = (_mexpand(p) + o).removeO()
+                    term = p*(digamma(k + nu + 1) + digamma(k + 1))
+                    c.append(term)
+                return a + Add(*b) + Add(*c) + o
+            elif nu.is_noninteger:
+                # Reference: https://functions.wolfram.com/Bessel-TypeFunctions/BesselK/06/01/04/01/01/0003/
+                # (only for non-integer order).
+                # While the expression in the reference above seems correct
+                # for non-real order as well, it would need some manipulation
+                # (not implemented) to be written as a power series in x with
+                # real exponents [e.g. Dunster 1990. "Bessel functions
+                # of purely imaginary order, with an application to second-order
+                # linear differential equations having a large parameter".
+                # SIAM J. Math. Anal. Vol 21, No. 4, pp 995-1018.].
+                newn_a = ceiling((n+nu)/exp)
+                newn_b = ceiling((n-nu)/exp)
+
+                a, b = [], []
+                for k in range((newn_a+1)//2):
+                    term = gamma(nu)*r**(2*k-nu)/(2*RisingFactorial(1-nu, k)*factorial(k))
+                    a.append(_mexpand(term))
+                for k in range((newn_b+1)//2):
+                    term = gamma(-nu)*r**(2*k+nu)/(2*RisingFactorial(nu+1, k)*factorial(k))
+                    b.append(_mexpand(term))
+                return Add(*a) + Add(*b) + o
+            else:
+                raise NotImplementedError("besselk expansion is only implemented for real order")
+
+        return super(besselk, self)._eval_nseries(x, n, logx, cdir)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.functions.combinatorial.factorials import RisingFactorial
+        from sympy.series.order import Order
+        point = args0[1]
+
+        if point in [S.Infinity, S.NegativeInfinity]:
+            nu, z = self.args
+            s = [(RisingFactorial(Rational(2*nu - 1, 2), k)*RisingFactorial(Rational(2*nu + 1, 2), k))/\
+            ((-2)**(k)*z**(Rational(2*k + 1, 2))*factorial(k)) for k in range(n)] +[Order(1/z**(Rational(2*n + 1, 2)), x)]
+            return (exp(-z)*sqrt(pi/2))*Add(*s)
+
+        return super()._eval_aseries(n, args0, x, logx)
+
+
+class hankel1(BesselBase):
+    r"""
+    Hankel function of the first kind.
+
+    Explanation
+    ===========
+
+    This function is defined as
+
+    .. math ::
+        H_\nu^{(1)} = J_\nu(z) + iY_\nu(z),
+
+    where $J_\nu(z)$ is the Bessel function of the first kind, and
+    $Y_\nu(z)$ is the Bessel function of the second kind.
+
+    It is a solution to Bessel's equation.
+
+    Examples
+    ========
+
+    >>> from sympy import hankel1
+    >>> from sympy.abc import z, n
+    >>> hankel1(n, z).diff(z)
+    hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2
+
+    See Also
+    ========
+
+    hankel2, besselj, bessely
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/HankelH1/
+
+    """
+
+    _a = S.One
+    _b = S.One
+
+    def _eval_conjugate(self):
+        z = self.argument
+        if z.is_extended_negative is False:
+            return hankel2(self.order.conjugate(), z.conjugate())
+
+
+class hankel2(BesselBase):
+    r"""
+    Hankel function of the second kind.
+
+    Explanation
+    ===========
+
+    This function is defined as
+
+    .. math ::
+        H_\nu^{(2)} = J_\nu(z) - iY_\nu(z),
+
+    where $J_\nu(z)$ is the Bessel function of the first kind, and
+    $Y_\nu(z)$ is the Bessel function of the second kind.
+
+    It is a solution to Bessel's equation, and linearly independent from
+    $H_\nu^{(1)}$.
+
+    Examples
+    ========
+
+    >>> from sympy import hankel2
+    >>> from sympy.abc import z, n
+    >>> hankel2(n, z).diff(z)
+    hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2
+
+    See Also
+    ========
+
+    hankel1, besselj, bessely
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/HankelH2/
+
+    """
+
+    _a = S.One
+    _b = S.One
+
+    def _eval_conjugate(self):
+        z = self.argument
+        if z.is_extended_negative is False:
+            return hankel1(self.order.conjugate(), z.conjugate())
+
+
+def assume_integer_order(fn):
+    @wraps(fn)
+    def g(self, nu, z):
+        if nu.is_integer:
+            return fn(self, nu, z)
+    return g
+
+
+class SphericalBesselBase(BesselBase):
+    """
+    Base class for spherical Bessel functions.
+
+    These are thin wrappers around ordinary Bessel functions,
+    since spherical Bessel functions differ from the ordinary
+    ones just by a slight change in order.
+
+    To use this class, define the ``_eval_evalf()`` and ``_expand()`` methods.
+
+    """
+
+    def _expand(self, **hints):
+        """ Expand self into a polynomial. Nu is guaranteed to be Integer. """
+        raise NotImplementedError('expansion')
+
+    def _eval_expand_func(self, **hints):
+        if self.order.is_Integer:
+            return self._expand(**hints)
+        return self
+
+    def fdiff(self, argindex=2):
+        if argindex != 2:
+            raise ArgumentIndexError(self, argindex)
+        return self.__class__(self.order - 1, self.argument) - \
+            self * (self.order + 1)/self.argument
+
+
+def _jn(n, z):
+    return (spherical_bessel_fn(n, z)*sin(z) +
+            S.NegativeOne**(n + 1)*spherical_bessel_fn(-n - 1, z)*cos(z))
+
+
+def _yn(n, z):
+    # (-1)**(n + 1) * _jn(-n - 1, z)
+    return (S.NegativeOne**(n + 1) * spherical_bessel_fn(-n - 1, z)*sin(z) -
+            spherical_bessel_fn(n, z)*cos(z))
+
+
+class jn(SphericalBesselBase):
+    r"""
+    Spherical Bessel function of the first kind.
+
+    Explanation
+    ===========
+
+    This function is a solution to the spherical Bessel equation
+
+    .. math ::
+        z^2 \frac{\mathrm{d}^2 w}{\mathrm{d}z^2}
+          + 2z \frac{\mathrm{d}w}{\mathrm{d}z} + (z^2 - \nu(\nu + 1)) w = 0.
+
+    It can be defined as
+
+    .. math ::
+        j_\nu(z) = \sqrt{\frac{\pi}{2z}} J_{\nu + \frac{1}{2}}(z),
+
+    where $J_\nu(z)$ is the Bessel function of the first kind.
+
+    The spherical Bessel functions of integral order are
+    calculated using the formula:
+
+    .. math:: j_n(z) = f_n(z) \sin{z} + (-1)^{n+1} f_{-n-1}(z) \cos{z},
+
+    where the coefficients $f_n(z)$ are available as
+    :func:`sympy.polys.orthopolys.spherical_bessel_fn`.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, jn, sin, cos, expand_func, besselj, bessely
+    >>> z = Symbol("z")
+    >>> nu = Symbol("nu", integer=True)
+    >>> print(expand_func(jn(0, z)))
+    sin(z)/z
+    >>> expand_func(jn(1, z)) == sin(z)/z**2 - cos(z)/z
+    True
+    >>> expand_func(jn(3, z))
+    (-6/z**2 + 15/z**4)*sin(z) + (1/z - 15/z**3)*cos(z)
+    >>> jn(nu, z).rewrite(besselj)
+    sqrt(2)*sqrt(pi)*sqrt(1/z)*besselj(nu + 1/2, z)/2
+    >>> jn(nu, z).rewrite(bessely)
+    (-1)**nu*sqrt(2)*sqrt(pi)*sqrt(1/z)*bessely(-nu - 1/2, z)/2
+    >>> jn(2, 5.2+0.3j).evalf(20)
+    0.099419756723640344491 - 0.054525080242173562897*I
+
+    See Also
+    ========
+
+    besselj, bessely, besselk, yn
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/10.47
+
+    """
+    @classmethod
+    def eval(cls, nu, z):
+        if z.is_zero:
+            if nu.is_zero:
+                return S.One
+            elif nu.is_integer:
+                if nu.is_positive:
+                    return S.Zero
+                else:
+                    return S.ComplexInfinity
+        if z in (S.NegativeInfinity, S.Infinity):
+            return S.Zero
+
+    def _eval_rewrite_as_besselj(self, nu, z, **kwargs):
+        return sqrt(pi/(2*z)) * besselj(nu + S.Half, z)
+
+    def _eval_rewrite_as_bessely(self, nu, z, **kwargs):
+        return S.NegativeOne**nu * sqrt(pi/(2*z)) * bessely(-nu - S.Half, z)
+
+    def _eval_rewrite_as_yn(self, nu, z, **kwargs):
+        return S.NegativeOne**(nu) * yn(-nu - 1, z)
+
+    def _expand(self, **hints):
+        return _jn(self.order, self.argument)
+
+    def _eval_evalf(self, prec):
+        if self.order.is_Integer:
+            return self.rewrite(besselj)._eval_evalf(prec)
+
+
+class yn(SphericalBesselBase):
+    r"""
+    Spherical Bessel function of the second kind.
+
+    Explanation
+    ===========
+
+    This function is another solution to the spherical Bessel equation, and
+    linearly independent from $j_n$. It can be defined as
+
+    .. math ::
+        y_\nu(z) = \sqrt{\frac{\pi}{2z}} Y_{\nu + \frac{1}{2}}(z),
+
+    where $Y_\nu(z)$ is the Bessel function of the second kind.
+
+    For integral orders $n$, $y_n$ is calculated using the formula:
+
+    .. math:: y_n(z) = (-1)^{n+1} j_{-n-1}(z)
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, yn, sin, cos, expand_func, besselj, bessely
+    >>> z = Symbol("z")
+    >>> nu = Symbol("nu", integer=True)
+    >>> print(expand_func(yn(0, z)))
+    -cos(z)/z
+    >>> expand_func(yn(1, z)) == -cos(z)/z**2-sin(z)/z
+    True
+    >>> yn(nu, z).rewrite(besselj)
+    (-1)**(nu + 1)*sqrt(2)*sqrt(pi)*sqrt(1/z)*besselj(-nu - 1/2, z)/2
+    >>> yn(nu, z).rewrite(bessely)
+    sqrt(2)*sqrt(pi)*sqrt(1/z)*bessely(nu + 1/2, z)/2
+    >>> yn(2, 5.2+0.3j).evalf(20)
+    0.18525034196069722536 + 0.014895573969924817587*I
+
+    See Also
+    ========
+
+    besselj, bessely, besselk, jn
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/10.47
+
+    """
+    @assume_integer_order
+    def _eval_rewrite_as_besselj(self, nu, z, **kwargs):
+        return S.NegativeOne**(nu+1) * sqrt(pi/(2*z)) * besselj(-nu - S.Half, z)
+
+    @assume_integer_order
+    def _eval_rewrite_as_bessely(self, nu, z, **kwargs):
+        return sqrt(pi/(2*z)) * bessely(nu + S.Half, z)
+
+    def _eval_rewrite_as_jn(self, nu, z, **kwargs):
+        return S.NegativeOne**(nu + 1) * jn(-nu - 1, z)
+
+    def _expand(self, **hints):
+        return _yn(self.order, self.argument)
+
+    def _eval_evalf(self, prec):
+        if self.order.is_Integer:
+            return self.rewrite(bessely)._eval_evalf(prec)
+
+
+class SphericalHankelBase(SphericalBesselBase):
+
+    @assume_integer_order
+    def _eval_rewrite_as_besselj(self, nu, z, **kwargs):
+        # jn +- I*yn
+        # jn as beeselj: sqrt(pi/(2*z)) * besselj(nu + S.Half, z)
+        # yn as besselj: (-1)**(nu+1) * sqrt(pi/(2*z)) * besselj(-nu - S.Half, z)
+        hks = self._hankel_kind_sign
+        return sqrt(pi/(2*z))*(besselj(nu + S.Half, z) +
+                               hks*I*S.NegativeOne**(nu+1)*besselj(-nu - S.Half, z))
+
+    @assume_integer_order
+    def _eval_rewrite_as_bessely(self, nu, z, **kwargs):
+        # jn +- I*yn
+        # jn as bessely: (-1)**nu * sqrt(pi/(2*z)) * bessely(-nu - S.Half, z)
+        # yn as bessely: sqrt(pi/(2*z)) * bessely(nu + S.Half, z)
+        hks = self._hankel_kind_sign
+        return sqrt(pi/(2*z))*(S.NegativeOne**nu*bessely(-nu - S.Half, z) +
+                               hks*I*bessely(nu + S.Half, z))
+
+    def _eval_rewrite_as_yn(self, nu, z, **kwargs):
+        hks = self._hankel_kind_sign
+        return jn(nu, z).rewrite(yn) + hks*I*yn(nu, z)
+
+    def _eval_rewrite_as_jn(self, nu, z, **kwargs):
+        hks = self._hankel_kind_sign
+        return jn(nu, z) + hks*I*yn(nu, z).rewrite(jn)
+
+    def _eval_expand_func(self, **hints):
+        if self.order.is_Integer:
+            return self._expand(**hints)
+        else:
+            nu = self.order
+            z = self.argument
+            hks = self._hankel_kind_sign
+            return jn(nu, z) + hks*I*yn(nu, z)
+
+    def _expand(self, **hints):
+        n = self.order
+        z = self.argument
+        hks = self._hankel_kind_sign
+
+        # fully expanded version
+        # return ((fn(n, z) * sin(z) +
+        #          (-1)**(n + 1) * fn(-n - 1, z) * cos(z)) +  # jn
+        #         (hks * I * (-1)**(n + 1) *
+        #          (fn(-n - 1, z) * hk * I * sin(z) +
+        #           (-1)**(-n) * fn(n, z) * I * cos(z)))  # +-I*yn
+        #         )
+
+        return (_jn(n, z) + hks*I*_yn(n, z)).expand()
+
+    def _eval_evalf(self, prec):
+        if self.order.is_Integer:
+            return self.rewrite(besselj)._eval_evalf(prec)
+
+
+class hn1(SphericalHankelBase):
+    r"""
+    Spherical Hankel function of the first kind.
+
+    Explanation
+    ===========
+
+    This function is defined as
+
+    .. math:: h_\nu^(1)(z) = j_\nu(z) + i y_\nu(z),
+
+    where $j_\nu(z)$ and $y_\nu(z)$ are the spherical
+    Bessel function of the first and second kinds.
+
+    For integral orders $n$, $h_n^(1)$ is calculated using the formula:
+
+    .. math:: h_n^(1)(z) = j_{n}(z) + i (-1)^{n+1} j_{-n-1}(z)
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, hn1, hankel1, expand_func, yn, jn
+    >>> z = Symbol("z")
+    >>> nu = Symbol("nu", integer=True)
+    >>> print(expand_func(hn1(nu, z)))
+    jn(nu, z) + I*yn(nu, z)
+    >>> print(expand_func(hn1(0, z)))
+    sin(z)/z - I*cos(z)/z
+    >>> print(expand_func(hn1(1, z)))
+    -I*sin(z)/z - cos(z)/z + sin(z)/z**2 - I*cos(z)/z**2
+    >>> hn1(nu, z).rewrite(jn)
+    (-1)**(nu + 1)*I*jn(-nu - 1, z) + jn(nu, z)
+    >>> hn1(nu, z).rewrite(yn)
+    (-1)**nu*yn(-nu - 1, z) + I*yn(nu, z)
+    >>> hn1(nu, z).rewrite(hankel1)
+    sqrt(2)*sqrt(pi)*sqrt(1/z)*hankel1(nu, z)/2
+
+    See Also
+    ========
+
+    hn2, jn, yn, hankel1, hankel2
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/10.47
+
+    """
+
+    _hankel_kind_sign = S.One
+
+    @assume_integer_order
+    def _eval_rewrite_as_hankel1(self, nu, z, **kwargs):
+        return sqrt(pi/(2*z))*hankel1(nu, z)
+
+
+class hn2(SphericalHankelBase):
+    r"""
+    Spherical Hankel function of the second kind.
+
+    Explanation
+    ===========
+
+    This function is defined as
+
+    .. math:: h_\nu^(2)(z) = j_\nu(z) - i y_\nu(z),
+
+    where $j_\nu(z)$ and $y_\nu(z)$ are the spherical
+    Bessel function of the first and second kinds.
+
+    For integral orders $n$, $h_n^(2)$ is calculated using the formula:
+
+    .. math:: h_n^(2)(z) = j_{n} - i (-1)^{n+1} j_{-n-1}(z)
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, hn2, hankel2, expand_func, jn, yn
+    >>> z = Symbol("z")
+    >>> nu = Symbol("nu", integer=True)
+    >>> print(expand_func(hn2(nu, z)))
+    jn(nu, z) - I*yn(nu, z)
+    >>> print(expand_func(hn2(0, z)))
+    sin(z)/z + I*cos(z)/z
+    >>> print(expand_func(hn2(1, z)))
+    I*sin(z)/z - cos(z)/z + sin(z)/z**2 + I*cos(z)/z**2
+    >>> hn2(nu, z).rewrite(hankel2)
+    sqrt(2)*sqrt(pi)*sqrt(1/z)*hankel2(nu, z)/2
+    >>> hn2(nu, z).rewrite(jn)
+    -(-1)**(nu + 1)*I*jn(-nu - 1, z) + jn(nu, z)
+    >>> hn2(nu, z).rewrite(yn)
+    (-1)**nu*yn(-nu - 1, z) - I*yn(nu, z)
+
+    See Also
+    ========
+
+    hn1, jn, yn, hankel1, hankel2
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/10.47
+
+    """
+
+    _hankel_kind_sign = -S.One
+
+    @assume_integer_order
+    def _eval_rewrite_as_hankel2(self, nu, z, **kwargs):
+        return sqrt(pi/(2*z))*hankel2(nu, z)
+
+
+def jn_zeros(n, k, method="sympy", dps=15):
+    """
+    Zeros of the spherical Bessel function of the first kind.
+
+    Explanation
+    ===========
+
+    This returns an array of zeros of $jn$ up to the $k$-th zero.
+
+    * method = "sympy": uses `mpmath.besseljzero
+      `_
+    * method = "scipy": uses the
+      `SciPy's sph_jn `_
+      and
+      `newton `_
+      to find all
+      roots, which is faster than computing the zeros using a general
+      numerical solver, but it requires SciPy and only works with low
+      precision floating point numbers. (The function used with
+      method="sympy" is a recent addition to mpmath; before that a general
+      solver was used.)
+
+    Examples
+    ========
+
+    >>> from sympy import jn_zeros
+    >>> jn_zeros(2, 4, dps=5)
+    [5.7635, 9.095, 12.323, 15.515]
+
+    See Also
+    ========
+
+    jn, yn, besselj, besselk, bessely
+
+    Parameters
+    ==========
+
+    n : integer
+        order of Bessel function
+
+    k : integer
+        number of zeros to return
+
+
+    """
+    from math import pi as math_pi
+
+    if method == "sympy":
+        from mpmath import besseljzero
+        from mpmath.libmp.libmpf import dps_to_prec
+        prec = dps_to_prec(dps)
+        return [Expr._from_mpmath(besseljzero(S(n + 0.5)._to_mpmath(prec),
+                                              int(l)), prec)
+                for l in range(1, k + 1)]
+    elif method == "scipy":
+        from scipy.optimize import newton
+        try:
+            from scipy.special import spherical_jn
+            f = lambda x: spherical_jn(n, x)
+        except ImportError:
+            from scipy.special import sph_jn
+            f = lambda x: sph_jn(n, x)[0][-1]
+    else:
+        raise NotImplementedError("Unknown method.")
+
+    def solver(f, x):
+        if method == "scipy":
+            root = newton(f, x)
+        else:
+            raise NotImplementedError("Unknown method.")
+        return root
+
+    # we need to approximate the position of the first root:
+    root = n + math_pi
+    # determine the first root exactly:
+    root = solver(f, root)
+    roots = [root]
+    for i in range(k - 1):
+        # estimate the position of the next root using the last root + pi:
+        root = solver(f, root + math_pi)
+        roots.append(root)
+    return roots
+
+
+class AiryBase(DefinedFunction):
+    """
+    Abstract base class for Airy functions.
+
+    This class is meant to reduce code duplication.
+
+    """
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    def as_real_imag(self, deep=True, **hints):
+        z = self.args[0]
+        zc = z.conjugate()
+        f = self.func
+        u = (f(z)+f(zc))/2
+        v = I*(f(zc)-f(z))/2
+        return u, v
+
+    def _eval_expand_complex(self, deep=True, **hints):
+        re_part, im_part = self.as_real_imag(deep=deep, **hints)
+        return re_part + im_part*I
+
+
+class airyai(AiryBase):
+    r"""
+    The Airy function $\operatorname{Ai}$ of the first kind.
+
+    Explanation
+    ===========
+
+    The Airy function $\operatorname{Ai}(z)$ is defined to be the function
+    satisfying Airy's differential equation
+
+    .. math::
+        \frac{\mathrm{d}^2 w(z)}{\mathrm{d}z^2} - z w(z) = 0.
+
+    Equivalently, for real $z$
+
+    .. math::
+        \operatorname{Ai}(z) := \frac{1}{\pi}
+        \int_0^\infty \cos\left(\frac{t^3}{3} + z t\right) \mathrm{d}t.
+
+    Examples
+    ========
+
+    Create an Airy function object:
+
+    >>> from sympy import airyai
+    >>> from sympy.abc import z
+
+    >>> airyai(z)
+    airyai(z)
+
+    Several special values are known:
+
+    >>> airyai(0)
+    3**(1/3)/(3*gamma(2/3))
+    >>> from sympy import oo
+    >>> airyai(oo)
+    0
+    >>> airyai(-oo)
+    0
+
+    The Airy function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(airyai(z))
+    airyai(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(airyai(z), z)
+    airyaiprime(z)
+    >>> diff(airyai(z), z, 2)
+    z*airyai(z)
+
+    Series expansion is also supported:
+
+    >>> from sympy import series
+    >>> series(airyai(z), z, 0, 3)
+    3**(5/6)*gamma(1/3)/(6*pi) - 3**(1/6)*z*gamma(2/3)/(2*pi) + O(z**3)
+
+    We can numerically evaluate the Airy function to arbitrary precision
+    on the whole complex plane:
+
+    >>> airyai(-2).evalf(50)
+    0.22740742820168557599192443603787379946077222541710
+
+    Rewrite $\operatorname{Ai}(z)$ in terms of hypergeometric functions:
+
+    >>> from sympy import hyper
+    >>> airyai(z).rewrite(hyper)
+    -3**(2/3)*z*hyper((), (4/3,), z**3/9)/(3*gamma(1/3)) + 3**(1/3)*hyper((), (2/3,), z**3/9)/(3*gamma(2/3))
+
+    See Also
+    ========
+
+    airybi: Airy function of the second kind.
+    airyaiprime: Derivative of the Airy function of the first kind.
+    airybiprime: Derivative of the Airy function of the second kind.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Airy_function
+    .. [2] https://dlmf.nist.gov/9
+    .. [3] https://encyclopediaofmath.org/wiki/Airy_functions
+    .. [4] https://mathworld.wolfram.com/AiryFunctions.html
+
+    """
+
+    nargs = 1
+    unbranched = True
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Zero
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+            elif arg.is_zero:
+                return S.One / (3**Rational(2, 3) * gamma(Rational(2, 3)))
+        if arg.is_zero:
+            return S.One / (3**Rational(2, 3) * gamma(Rational(2, 3)))
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return airyaiprime(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 1:
+                p = previous_terms[-1]
+                return ((cbrt(3)*x)**(-n)*(cbrt(3)*x)**(n + 1)*sin(pi*(n*Rational(2, 3) + Rational(4, 3)))*factorial(n) *
+                        gamma(n/3 + Rational(2, 3))/(sin(pi*(n*Rational(2, 3) + Rational(2, 3)))*factorial(n + 1)*gamma(n/3 + Rational(1, 3))) * p)
+            else:
+                return (S.One/(3**Rational(2, 3)*pi) * gamma((n+S.One)/S(3)) * sin(Rational(2, 3)*pi*(n+S.One)) /
+                        factorial(n) * (cbrt(3)*x)**n)
+
+    def _eval_rewrite_as_besselj(self, z, **kwargs):
+        ot = Rational(1, 3)
+        tt = Rational(2, 3)
+        a = Pow(-z, Rational(3, 2))
+        if re(z).is_negative:
+            return ot*sqrt(-z) * (besselj(-ot, tt*a) + besselj(ot, tt*a))
+
+    def _eval_rewrite_as_besseli(self, z, **kwargs):
+        ot = Rational(1, 3)
+        tt = Rational(2, 3)
+        a = Pow(z, Rational(3, 2))
+        if re(z).is_positive:
+            return ot*sqrt(z) * (besseli(-ot, tt*a) - besseli(ot, tt*a))
+        else:
+            return ot*(Pow(a, ot)*besseli(-ot, tt*a) - z*Pow(a, -ot)*besseli(ot, tt*a))
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        pf1 = S.One / (3**Rational(2, 3)*gamma(Rational(2, 3)))
+        pf2 = z / (root(3, 3)*gamma(Rational(1, 3)))
+        return pf1 * hyper([], [Rational(2, 3)], z**3/9) - pf2 * hyper([], [Rational(4, 3)], z**3/9)
+
+    def _eval_expand_func(self, **hints):
+        arg = self.args[0]
+        symbs = arg.free_symbols
+
+        if len(symbs) == 1:
+            z = symbs.pop()
+            c = Wild("c", exclude=[z])
+            d = Wild("d", exclude=[z])
+            m = Wild("m", exclude=[z])
+            n = Wild("n", exclude=[z])
+            M = arg.match(c*(d*z**n)**m)
+            if M is not None:
+                m = M[m]
+                # The transformation is given by 03.05.16.0001.01
+                # https://functions.wolfram.com/Bessel-TypeFunctions/AiryAi/16/01/01/0001/
+                if (3*m).is_integer:
+                    c = M[c]
+                    d = M[d]
+                    n = M[n]
+                    pf = (d * z**n)**m / (d**m * z**(m*n))
+                    newarg = c * d**m * z**(m*n)
+                    return S.Half * ((pf + S.One)*airyai(newarg) - (pf - S.One)/sqrt(3)*airybi(newarg))
+
+
+class airybi(AiryBase):
+    r"""
+    The Airy function $\operatorname{Bi}$ of the second kind.
+
+    Explanation
+    ===========
+
+    The Airy function $\operatorname{Bi}(z)$ is defined to be the function
+    satisfying Airy's differential equation
+
+    .. math::
+        \frac{\mathrm{d}^2 w(z)}{\mathrm{d}z^2} - z w(z) = 0.
+
+    Equivalently, for real $z$
+
+    .. math::
+        \operatorname{Bi}(z) := \frac{1}{\pi}
+                 \int_0^\infty
+                   \exp\left(-\frac{t^3}{3} + z t\right)
+                   + \sin\left(\frac{t^3}{3} + z t\right) \mathrm{d}t.
+
+    Examples
+    ========
+
+    Create an Airy function object:
+
+    >>> from sympy import airybi
+    >>> from sympy.abc import z
+
+    >>> airybi(z)
+    airybi(z)
+
+    Several special values are known:
+
+    >>> airybi(0)
+    3**(5/6)/(3*gamma(2/3))
+    >>> from sympy import oo
+    >>> airybi(oo)
+    oo
+    >>> airybi(-oo)
+    0
+
+    The Airy function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(airybi(z))
+    airybi(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(airybi(z), z)
+    airybiprime(z)
+    >>> diff(airybi(z), z, 2)
+    z*airybi(z)
+
+    Series expansion is also supported:
+
+    >>> from sympy import series
+    >>> series(airybi(z), z, 0, 3)
+    3**(1/3)*gamma(1/3)/(2*pi) + 3**(2/3)*z*gamma(2/3)/(2*pi) + O(z**3)
+
+    We can numerically evaluate the Airy function to arbitrary precision
+    on the whole complex plane:
+
+    >>> airybi(-2).evalf(50)
+    -0.41230258795639848808323405461146104203453483447240
+
+    Rewrite $\operatorname{Bi}(z)$ in terms of hypergeometric functions:
+
+    >>> from sympy import hyper
+    >>> airybi(z).rewrite(hyper)
+    3**(1/6)*z*hyper((), (4/3,), z**3/9)/gamma(1/3) + 3**(5/6)*hyper((), (2/3,), z**3/9)/(3*gamma(2/3))
+
+    See Also
+    ========
+
+    airyai: Airy function of the first kind.
+    airyaiprime: Derivative of the Airy function of the first kind.
+    airybiprime: Derivative of the Airy function of the second kind.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Airy_function
+    .. [2] https://dlmf.nist.gov/9
+    .. [3] https://encyclopediaofmath.org/wiki/Airy_functions
+    .. [4] https://mathworld.wolfram.com/AiryFunctions.html
+
+    """
+
+    nargs = 1
+    unbranched = True
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+            elif arg.is_zero:
+                return S.One / (3**Rational(1, 6) * gamma(Rational(2, 3)))
+
+        if arg.is_zero:
+            return S.One / (3**Rational(1, 6) * gamma(Rational(2, 3)))
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return airybiprime(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 1:
+                p = previous_terms[-1]
+                return (cbrt(3)*x * Abs(sin(Rational(2, 3)*pi*(n + S.One))) * factorial((n - S.One)/S(3)) /
+                        ((n + S.One) * Abs(cos(Rational(2, 3)*pi*(n + S.Half))) * factorial((n - 2)/S(3))) * p)
+            else:
+                return (S.One/(root(3, 6)*pi) * gamma((n + S.One)/S(3)) * Abs(sin(Rational(2, 3)*pi*(n + S.One))) /
+                        factorial(n) * (cbrt(3)*x)**n)
+
+    def _eval_rewrite_as_besselj(self, z, **kwargs):
+        ot = Rational(1, 3)
+        tt = Rational(2, 3)
+        a = Pow(-z, Rational(3, 2))
+        if re(z).is_negative:
+            return sqrt(-z/3) * (besselj(-ot, tt*a) - besselj(ot, tt*a))
+
+    def _eval_rewrite_as_besseli(self, z, **kwargs):
+        ot = Rational(1, 3)
+        tt = Rational(2, 3)
+        a = Pow(z, Rational(3, 2))
+        if re(z).is_positive:
+            return sqrt(z)/sqrt(3) * (besseli(-ot, tt*a) + besseli(ot, tt*a))
+        else:
+            b = Pow(a, ot)
+            c = Pow(a, -ot)
+            return sqrt(ot)*(b*besseli(-ot, tt*a) + z*c*besseli(ot, tt*a))
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        pf1 = S.One / (root(3, 6)*gamma(Rational(2, 3)))
+        pf2 = z*root(3, 6) / gamma(Rational(1, 3))
+        return pf1 * hyper([], [Rational(2, 3)], z**3/9) + pf2 * hyper([], [Rational(4, 3)], z**3/9)
+
+    def _eval_expand_func(self, **hints):
+        arg = self.args[0]
+        symbs = arg.free_symbols
+
+        if len(symbs) == 1:
+            z = symbs.pop()
+            c = Wild("c", exclude=[z])
+            d = Wild("d", exclude=[z])
+            m = Wild("m", exclude=[z])
+            n = Wild("n", exclude=[z])
+            M = arg.match(c*(d*z**n)**m)
+            if M is not None:
+                m = M[m]
+                # The transformation is given by 03.06.16.0001.01
+                # https://functions.wolfram.com/Bessel-TypeFunctions/AiryBi/16/01/01/0001/
+                if (3*m).is_integer:
+                    c = M[c]
+                    d = M[d]
+                    n = M[n]
+                    pf = (d * z**n)**m / (d**m * z**(m*n))
+                    newarg = c * d**m * z**(m*n)
+                    return S.Half * (sqrt(3)*(S.One - pf)*airyai(newarg) + (S.One + pf)*airybi(newarg))
+
+
+class airyaiprime(AiryBase):
+    r"""
+    The derivative $\operatorname{Ai}^\prime$ of the Airy function of the first
+    kind.
+
+    Explanation
+    ===========
+
+    The Airy function $\operatorname{Ai}^\prime(z)$ is defined to be the
+    function
+
+    .. math::
+        \operatorname{Ai}^\prime(z) := \frac{\mathrm{d} \operatorname{Ai}(z)}{\mathrm{d} z}.
+
+    Examples
+    ========
+
+    Create an Airy function object:
+
+    >>> from sympy import airyaiprime
+    >>> from sympy.abc import z
+
+    >>> airyaiprime(z)
+    airyaiprime(z)
+
+    Several special values are known:
+
+    >>> airyaiprime(0)
+    -3**(2/3)/(3*gamma(1/3))
+    >>> from sympy import oo
+    >>> airyaiprime(oo)
+    0
+
+    The Airy function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(airyaiprime(z))
+    airyaiprime(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(airyaiprime(z), z)
+    z*airyai(z)
+    >>> diff(airyaiprime(z), z, 2)
+    z*airyaiprime(z) + airyai(z)
+
+    Series expansion is also supported:
+
+    >>> from sympy import series
+    >>> series(airyaiprime(z), z, 0, 3)
+    -3**(2/3)/(3*gamma(1/3)) + 3**(1/3)*z**2/(6*gamma(2/3)) + O(z**3)
+
+    We can numerically evaluate the Airy function to arbitrary precision
+    on the whole complex plane:
+
+    >>> airyaiprime(-2).evalf(50)
+    0.61825902074169104140626429133247528291577794512415
+
+    Rewrite $\operatorname{Ai}^\prime(z)$ in terms of hypergeometric functions:
+
+    >>> from sympy import hyper
+    >>> airyaiprime(z).rewrite(hyper)
+    3**(1/3)*z**2*hyper((), (5/3,), z**3/9)/(6*gamma(2/3)) - 3**(2/3)*hyper((), (1/3,), z**3/9)/(3*gamma(1/3))
+
+    See Also
+    ========
+
+    airyai: Airy function of the first kind.
+    airybi: Airy function of the second kind.
+    airybiprime: Derivative of the Airy function of the second kind.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Airy_function
+    .. [2] https://dlmf.nist.gov/9
+    .. [3] https://encyclopediaofmath.org/wiki/Airy_functions
+    .. [4] https://mathworld.wolfram.com/AiryFunctions.html
+
+    """
+
+    nargs = 1
+    unbranched = True
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Zero
+
+        if arg.is_zero:
+            return S.NegativeOne / (3**Rational(1, 3) * gamma(Rational(1, 3)))
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return self.args[0]*airyai(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_evalf(self, prec):
+        z = self.args[0]._to_mpmath(prec)
+        with workprec(prec):
+            res = mp.airyai(z, derivative=1)
+        return Expr._from_mpmath(res, prec)
+
+    def _eval_rewrite_as_besselj(self, z, **kwargs):
+        tt = Rational(2, 3)
+        a = Pow(-z, Rational(3, 2))
+        if re(z).is_negative:
+            return z/3 * (besselj(-tt, tt*a) - besselj(tt, tt*a))
+
+    def _eval_rewrite_as_besseli(self, z, **kwargs):
+        ot = Rational(1, 3)
+        tt = Rational(2, 3)
+        a = tt * Pow(z, Rational(3, 2))
+        if re(z).is_positive:
+            return z/3 * (besseli(tt, a) - besseli(-tt, a))
+        else:
+            a = Pow(z, Rational(3, 2))
+            b = Pow(a, tt)
+            c = Pow(a, -tt)
+            return ot * (z**2*c*besseli(tt, tt*a) - b*besseli(-ot, tt*a))
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        pf1 = z**2 / (2*3**Rational(2, 3)*gamma(Rational(2, 3)))
+        pf2 = 1 / (root(3, 3)*gamma(Rational(1, 3)))
+        return pf1 * hyper([], [Rational(5, 3)], z**3/9) - pf2 * hyper([], [Rational(1, 3)], z**3/9)
+
+    def _eval_expand_func(self, **hints):
+        arg = self.args[0]
+        symbs = arg.free_symbols
+
+        if len(symbs) == 1:
+            z = symbs.pop()
+            c = Wild("c", exclude=[z])
+            d = Wild("d", exclude=[z])
+            m = Wild("m", exclude=[z])
+            n = Wild("n", exclude=[z])
+            M = arg.match(c*(d*z**n)**m)
+            if M is not None:
+                m = M[m]
+                # The transformation is in principle
+                # given by 03.07.16.0001.01 but note
+                # that there is an error in this formula.
+                # https://functions.wolfram.com/Bessel-TypeFunctions/AiryAiPrime/16/01/01/0001/
+                if (3*m).is_integer:
+                    c = M[c]
+                    d = M[d]
+                    n = M[n]
+                    pf = (d**m * z**(n*m)) / (d * z**n)**m
+                    newarg = c * d**m * z**(n*m)
+                    return S.Half * ((pf + S.One)*airyaiprime(newarg) + (pf - S.One)/sqrt(3)*airybiprime(newarg))
+
+
+class airybiprime(AiryBase):
+    r"""
+    The derivative $\operatorname{Bi}^\prime$ of the Airy function of the first
+    kind.
+
+    Explanation
+    ===========
+
+    The Airy function $\operatorname{Bi}^\prime(z)$ is defined to be the
+    function
+
+    .. math::
+        \operatorname{Bi}^\prime(z) := \frac{\mathrm{d} \operatorname{Bi}(z)}{\mathrm{d} z}.
+
+    Examples
+    ========
+
+    Create an Airy function object:
+
+    >>> from sympy import airybiprime
+    >>> from sympy.abc import z
+
+    >>> airybiprime(z)
+    airybiprime(z)
+
+    Several special values are known:
+
+    >>> airybiprime(0)
+    3**(1/6)/gamma(1/3)
+    >>> from sympy import oo
+    >>> airybiprime(oo)
+    oo
+    >>> airybiprime(-oo)
+    0
+
+    The Airy function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(airybiprime(z))
+    airybiprime(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(airybiprime(z), z)
+    z*airybi(z)
+    >>> diff(airybiprime(z), z, 2)
+    z*airybiprime(z) + airybi(z)
+
+    Series expansion is also supported:
+
+    >>> from sympy import series
+    >>> series(airybiprime(z), z, 0, 3)
+    3**(1/6)/gamma(1/3) + 3**(5/6)*z**2/(6*gamma(2/3)) + O(z**3)
+
+    We can numerically evaluate the Airy function to arbitrary precision
+    on the whole complex plane:
+
+    >>> airybiprime(-2).evalf(50)
+    0.27879516692116952268509756941098324140300059345163
+
+    Rewrite $\operatorname{Bi}^\prime(z)$ in terms of hypergeometric functions:
+
+    >>> from sympy import hyper
+    >>> airybiprime(z).rewrite(hyper)
+    3**(5/6)*z**2*hyper((), (5/3,), z**3/9)/(6*gamma(2/3)) + 3**(1/6)*hyper((), (1/3,), z**3/9)/gamma(1/3)
+
+    See Also
+    ========
+
+    airyai: Airy function of the first kind.
+    airybi: Airy function of the second kind.
+    airyaiprime: Derivative of the Airy function of the first kind.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Airy_function
+    .. [2] https://dlmf.nist.gov/9
+    .. [3] https://encyclopediaofmath.org/wiki/Airy_functions
+    .. [4] https://mathworld.wolfram.com/AiryFunctions.html
+
+    """
+
+    nargs = 1
+    unbranched = True
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Infinity
+            elif arg is S.NegativeInfinity:
+                return S.Zero
+            elif arg.is_zero:
+                return 3**Rational(1, 6) / gamma(Rational(1, 3))
+
+        if arg.is_zero:
+            return 3**Rational(1, 6) / gamma(Rational(1, 3))
+
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return self.args[0]*airybi(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_evalf(self, prec):
+        z = self.args[0]._to_mpmath(prec)
+        with workprec(prec):
+            res = mp.airybi(z, derivative=1)
+        return Expr._from_mpmath(res, prec)
+
+    def _eval_rewrite_as_besselj(self, z, **kwargs):
+        tt = Rational(2, 3)
+        a = tt * Pow(-z, Rational(3, 2))
+        if re(z).is_negative:
+            return -z/sqrt(3) * (besselj(-tt, a) + besselj(tt, a))
+
+    def _eval_rewrite_as_besseli(self, z, **kwargs):
+        ot = Rational(1, 3)
+        tt = Rational(2, 3)
+        a = tt * Pow(z, Rational(3, 2))
+        if re(z).is_positive:
+            return z/sqrt(3) * (besseli(-tt, a) + besseli(tt, a))
+        else:
+            a = Pow(z, Rational(3, 2))
+            b = Pow(a, tt)
+            c = Pow(a, -tt)
+            return sqrt(ot) * (b*besseli(-tt, tt*a) + z**2*c*besseli(tt, tt*a))
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        pf1 = z**2 / (2*root(3, 6)*gamma(Rational(2, 3)))
+        pf2 = root(3, 6) / gamma(Rational(1, 3))
+        return pf1 * hyper([], [Rational(5, 3)], z**3/9) + pf2 * hyper([], [Rational(1, 3)], z**3/9)
+
+    def _eval_expand_func(self, **hints):
+        arg = self.args[0]
+        symbs = arg.free_symbols
+
+        if len(symbs) == 1:
+            z = symbs.pop()
+            c = Wild("c", exclude=[z])
+            d = Wild("d", exclude=[z])
+            m = Wild("m", exclude=[z])
+            n = Wild("n", exclude=[z])
+            M = arg.match(c*(d*z**n)**m)
+            if M is not None:
+                m = M[m]
+                # The transformation is in principle
+                # given by 03.08.16.0001.01 but note
+                # that there is an error in this formula.
+                # https://functions.wolfram.com/Bessel-TypeFunctions/AiryBiPrime/16/01/01/0001/
+                if (3*m).is_integer:
+                    c = M[c]
+                    d = M[d]
+                    n = M[n]
+                    pf = (d**m * z**(n*m)) / (d * z**n)**m
+                    newarg = c * d**m * z**(n*m)
+                    return S.Half * (sqrt(3)*(pf - S.One)*airyaiprime(newarg) + (pf + S.One)*airybiprime(newarg))
+
+
+class marcumq(DefinedFunction):
+    r"""
+    The Marcum Q-function.
+
+    Explanation
+    ===========
+
+    The Marcum Q-function is defined by the meromorphic continuation of
+
+    .. math::
+        Q_m(a, b) = a^{- m + 1} \int_{b}^{\infty} x^{m} e^{- \frac{a^{2}}{2} - \frac{x^{2}}{2}} I_{m - 1}\left(a x\right)\, dx
+
+    Examples
+    ========
+
+    >>> from sympy import marcumq
+    >>> from sympy.abc import m, a, b
+    >>> marcumq(m, a, b)
+    marcumq(m, a, b)
+
+    Special values:
+
+    >>> marcumq(m, 0, b)
+    uppergamma(m, b**2/2)/gamma(m)
+    >>> marcumq(0, 0, 0)
+    0
+    >>> marcumq(0, a, 0)
+    1 - exp(-a**2/2)
+    >>> marcumq(1, a, a)
+    1/2 + exp(-a**2)*besseli(0, a**2)/2
+    >>> marcumq(2, a, a)
+    1/2 + exp(-a**2)*besseli(0, a**2)/2 + exp(-a**2)*besseli(1, a**2)
+
+    Differentiation with respect to $a$ and $b$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(marcumq(m, a, b), a)
+    a*(-marcumq(m, a, b) + marcumq(m + 1, a, b))
+    >>> diff(marcumq(m, a, b), b)
+    -a**(1 - m)*b**m*exp(-a**2/2 - b**2/2)*besseli(m - 1, a*b)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Marcum_Q-function
+    .. [2] https://mathworld.wolfram.com/MarcumQ-Function.html
+
+    """
+
+    @classmethod
+    def eval(cls, m, a, b):
+        if a is S.Zero:
+            if m is S.Zero and b is S.Zero:
+                return S.Zero
+            return uppergamma(m, b**2 * S.Half) / gamma(m)
+
+        if m is S.Zero and b is S.Zero:
+            return 1 - 1 / exp(a**2 * S.Half)
+
+        if a == b:
+            if m is S.One:
+                return (1 + exp(-a**2) * besseli(0, a**2))*S.Half
+            if m == 2:
+                return S.Half + S.Half * exp(-a**2) * besseli(0, a**2) + exp(-a**2) * besseli(1, a**2)
+
+        if a.is_zero:
+            if m.is_zero and b.is_zero:
+                return S.Zero
+            return uppergamma(m, b**2*S.Half) / gamma(m)
+
+        if m.is_zero and b.is_zero:
+            return 1 - 1 / exp(a**2*S.Half)
+
+    def fdiff(self, argindex=2):
+        m, a, b = self.args
+        if argindex == 2:
+            return a * (-marcumq(m, a, b) + marcumq(1+m, a, b))
+        elif argindex == 3:
+            return (-b**m / a**(m-1)) * exp(-(a**2 + b**2)/2) * besseli(m-1, a*b)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Integral(self, m, a, b, **kwargs):
+        from sympy.integrals.integrals import Integral
+        x = kwargs.get('x', Dummy(uniquely_named_symbol('x').name))
+        return a ** (1 - m) * \
+               Integral(x**m * exp(-(x**2 + a**2)/2) * besseli(m-1, a*x), [x, b, S.Infinity])
+
+    def _eval_rewrite_as_Sum(self, m, a, b, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = kwargs.get('k', Dummy('k'))
+        return exp(-(a**2 + b**2) / 2) * Sum((a/b)**k * besseli(k, a*b), [k, 1-m, S.Infinity])
+
+    def _eval_rewrite_as_besseli(self, m, a, b, **kwargs):
+        if a == b:
+            if m == 1:
+                return (1 + exp(-a**2) * besseli(0, a**2)) / 2
+            if m.is_Integer and m >= 2:
+                s = sum(besseli(i, a**2) for i in range(1, m))
+                return S.Half + exp(-a**2) * besseli(0, a**2) / 2 + exp(-a**2) * s
+
+    def _eval_is_zero(self):
+        if all(arg.is_zero for arg in self.args):
+            return True
+
+class _besseli(DefinedFunction):
+    """
+    Helper function to make the $\\mathrm{besseli}(nu, z)$
+    function tractable for the Gruntz algorithm.
+
+    """
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.functions.combinatorial.factorials import RisingFactorial
+        from sympy.series.order import Order
+        point = args0[1]
+
+        if point in [S.Infinity, S.NegativeInfinity]:
+            nu, z = self.args
+            l = [((RisingFactorial(Rational(2*nu - 1, 2), k)*RisingFactorial(
+                    Rational(2*nu + 1, 2), k))/((2)**(k)*z**(Rational(2*k + 1, 2))*factorial(k))) for k in range(n)]
+            return sqrt(pi/(2))*(Add(*l)) + Order(1/z**(Rational(2*n + 1, 2)), x)
+
+        return super()._eval_aseries(n, args0, x, logx)
+
+    def _eval_rewrite_as_intractable(self, nu, z, **kwargs):
+        return exp(-z)*besseli(nu, z)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        x0 = self.args[0].limit(x, 0)
+        if x0.is_zero:
+            f = self._eval_rewrite_as_intractable(*self.args)
+            return f._eval_nseries(x, n, logx)
+        return super()._eval_nseries(x, n, logx)
+
+
+class _besselk(DefinedFunction):
+    """
+    Helper function to make the $\\mathrm{besselk}(nu, z)$
+    function tractable for the Gruntz algorithm.
+
+    """
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.functions.combinatorial.factorials import RisingFactorial
+        from sympy.series.order import Order
+        point = args0[1]
+
+        if point in [S.Infinity, S.NegativeInfinity]:
+            nu, z = self.args
+            l = [((RisingFactorial(Rational(2*nu - 1, 2), k)*RisingFactorial(
+                    Rational(2*nu + 1, 2), k))/((-2)**(k)*z**(Rational(2*k + 1, 2))*factorial(k))) for k in range(n)]
+            return sqrt(pi/(2))*(Add(*l)) + Order(1/z**(Rational(2*n + 1, 2)), x)
+
+        return super()._eval_aseries(n, args0, x, logx)
+
+    def _eval_rewrite_as_intractable(self,nu, z, **kwargs):
+        return exp(z)*besselk(nu, z)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        x0 = self.args[0].limit(x, 0)
+        if x0.is_zero:
+            f = self._eval_rewrite_as_intractable(*self.args)
+            return f._eval_nseries(x, n, logx)
+        return super()._eval_nseries(x, n, logx)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/beta_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/beta_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..337ae6c71fe5a38cc0fcd819e9d489ebbbd1946b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/beta_functions.py
@@ -0,0 +1,389 @@
+from sympy.core import S
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.symbol import Dummy, uniquely_named_symbol
+from sympy.functions.special.gamma_functions import gamma, digamma
+from sympy.functions.combinatorial.numbers import catalan
+from sympy.functions.elementary.complexes import conjugate
+
+# See mpmath #569 and SymPy #20569
+def betainc_mpmath_fix(a, b, x1, x2, reg=0):
+    from mpmath import betainc, mpf
+    if x1 == x2:
+        return mpf(0)
+    else:
+        return betainc(a, b, x1, x2, reg)
+
+###############################################################################
+############################ COMPLETE BETA  FUNCTION ##########################
+###############################################################################
+
+class beta(DefinedFunction):
+    r"""
+    The beta integral is called the Eulerian integral of the first kind by
+    Legendre:
+
+    .. math::
+        \mathrm{B}(x,y)  \int^{1}_{0} t^{x-1} (1-t)^{y-1} \mathrm{d}t.
+
+    Explanation
+    ===========
+
+    The Beta function or Euler's first integral is closely associated
+    with the gamma function. The Beta function is often used in probability
+    theory and mathematical statistics. It satisfies properties like:
+
+    .. math::
+        \mathrm{B}(a,1) = \frac{1}{a} \\
+        \mathrm{B}(a,b) = \mathrm{B}(b,a)  \\
+        \mathrm{B}(a,b) = \frac{\Gamma(a) \Gamma(b)}{\Gamma(a+b)}
+
+    Therefore for integral values of $a$ and $b$:
+
+    .. math::
+        \mathrm{B} = \frac{(a-1)! (b-1)!}{(a+b-1)!}
+
+    A special case of the Beta function when `x = y` is the
+    Central Beta function. It satisfies properties like:
+
+    .. math::
+        \mathrm{B}(x) = 2^{1 - 2x}\mathrm{B}(x, \frac{1}{2})
+        \mathrm{B}(x) = 2^{1 - 2x} cos(\pi x) \mathrm{B}(\frac{1}{2} - x, x)
+        \mathrm{B}(x) = \int_{0}^{1} \frac{t^x}{(1 + t)^{2x}} dt
+        \mathrm{B}(x) = \frac{2}{x} \prod_{n = 1}^{\infty} \frac{n(n + 2x)}{(n + x)^2}
+
+    Examples
+    ========
+
+    >>> from sympy import I, pi
+    >>> from sympy.abc import x, y
+
+    The Beta function obeys the mirror symmetry:
+
+    >>> from sympy import beta, conjugate
+    >>> conjugate(beta(x, y))
+    beta(conjugate(x), conjugate(y))
+
+    Differentiation with respect to both $x$ and $y$ is supported:
+
+    >>> from sympy import beta, diff
+    >>> diff(beta(x, y), x)
+    (polygamma(0, x) - polygamma(0, x + y))*beta(x, y)
+
+    >>> diff(beta(x, y), y)
+    (polygamma(0, y) - polygamma(0, x + y))*beta(x, y)
+
+    >>> diff(beta(x), x)
+    2*(polygamma(0, x) - polygamma(0, 2*x))*beta(x, x)
+
+    We can numerically evaluate the Beta function to
+    arbitrary precision for any complex numbers x and y:
+
+    >>> from sympy import beta
+    >>> beta(pi).evalf(40)
+    0.02671848900111377452242355235388489324562
+
+    >>> beta(1 + I).evalf(20)
+    -0.2112723729365330143 - 0.7655283165378005676*I
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    uppergamma: Upper incomplete gamma function.
+    lowergamma: Lower incomplete gamma function.
+    polygamma: Polygamma function.
+    loggamma: Log Gamma function.
+    digamma: Digamma function.
+    trigamma: Trigamma function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Beta_function
+    .. [2] https://mathworld.wolfram.com/BetaFunction.html
+    .. [3] https://dlmf.nist.gov/5.12
+
+    """
+    unbranched = True
+
+    def fdiff(self, argindex):
+        x, y = self.args
+        if argindex == 1:
+            # Diff wrt x
+            return beta(x, y)*(digamma(x) - digamma(x + y))
+        elif argindex == 2:
+            # Diff wrt y
+            return beta(x, y)*(digamma(y) - digamma(x + y))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, x, y=None):
+        if y is None:
+            return beta(x, x)
+        if x.is_Number and y.is_Number:
+            return beta(x, y, evaluate=False).doit()
+
+    def doit(self, **hints):
+        x = xold = self.args[0]
+        # Deal with unevaluated single argument beta
+        single_argument = len(self.args) == 1
+        y = yold = self.args[0] if single_argument else self.args[1]
+        if hints.get('deep', True):
+            x = x.doit(**hints)
+            y = y.doit(**hints)
+        if y.is_zero or x.is_zero:
+            return S.ComplexInfinity
+        if y is S.One:
+            return 1/x
+        if x is S.One:
+            return 1/y
+        if y == x + 1:
+            return 1/(x*y*catalan(x))
+        s = x + y
+        if (s.is_integer and s.is_negative and x.is_integer is False and
+            y.is_integer is False):
+            return S.Zero
+        if x == xold and y == yold and not single_argument:
+            return self
+        return beta(x, y)
+
+    def _eval_expand_func(self, **hints):
+        x, y = self.args
+        return gamma(x)*gamma(y) / gamma(x + y)
+
+    def _eval_is_real(self):
+        return self.args[0].is_real and self.args[1].is_real
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate(), self.args[1].conjugate())
+
+    def _eval_rewrite_as_gamma(self, x, y, piecewise=True, **kwargs):
+        return self._eval_expand_func(**kwargs)
+
+    def _eval_rewrite_as_Integral(self, x, y, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [x, y]).name)
+        return Integral(t**(x - 1)*(1 - t)**(y - 1), (t, 0, 1))
+
+###############################################################################
+########################## INCOMPLETE BETA FUNCTION ###########################
+###############################################################################
+
+class betainc(DefinedFunction):
+    r"""
+    The Generalized Incomplete Beta function is defined as
+
+    .. math::
+        \mathrm{B}_{(x_1, x_2)}(a, b) = \int_{x_1}^{x_2} t^{a - 1} (1 - t)^{b - 1} dt
+
+    The Incomplete Beta function is a special case
+    of the Generalized Incomplete Beta function :
+
+    .. math:: \mathrm{B}_z (a, b) = \mathrm{B}_{(0, z)}(a, b)
+
+    The Incomplete Beta function satisfies :
+
+    .. math:: \mathrm{B}_z (a, b) = (-1)^a \mathrm{B}_{\frac{z}{z - 1}} (a, 1 - a - b)
+
+    The Beta function is a special case of the Incomplete Beta function :
+
+    .. math:: \mathrm{B}(a, b) = \mathrm{B}_{1}(a, b)
+
+    Examples
+    ========
+
+    >>> from sympy import betainc, symbols, conjugate
+    >>> a, b, x, x1, x2 = symbols('a b x x1 x2')
+
+    The Generalized Incomplete Beta function is given by:
+
+    >>> betainc(a, b, x1, x2)
+    betainc(a, b, x1, x2)
+
+    The Incomplete Beta function can be obtained as follows:
+
+    >>> betainc(a, b, 0, x)
+    betainc(a, b, 0, x)
+
+    The Incomplete Beta function obeys the mirror symmetry:
+
+    >>> conjugate(betainc(a, b, x1, x2))
+    betainc(conjugate(a), conjugate(b), conjugate(x1), conjugate(x2))
+
+    We can numerically evaluate the Incomplete Beta function to
+    arbitrary precision for any complex numbers a, b, x1 and x2:
+
+    >>> from sympy import betainc, I
+    >>> betainc(2, 3, 4, 5).evalf(10)
+    56.08333333
+    >>> betainc(0.75, 1 - 4*I, 0, 2 + 3*I).evalf(25)
+    0.2241657956955709603655887 + 0.3619619242700451992411724*I
+
+    The Generalized Incomplete Beta function can be expressed
+    in terms of the Generalized Hypergeometric function.
+
+    >>> from sympy import hyper
+    >>> betainc(a, b, x1, x2).rewrite(hyper)
+    (-x1**a*hyper((a, 1 - b), (a + 1,), x1) + x2**a*hyper((a, 1 - b), (a + 1,), x2))/a
+
+    See Also
+    ========
+
+    beta: Beta function
+    hyper: Generalized Hypergeometric function
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function
+    .. [2] https://dlmf.nist.gov/8.17
+    .. [3] https://functions.wolfram.com/GammaBetaErf/Beta4/
+    .. [4] https://functions.wolfram.com/GammaBetaErf/BetaRegularized4/02/
+
+    """
+    nargs = 4
+    unbranched = True
+
+    def fdiff(self, argindex):
+        a, b, x1, x2 = self.args
+        if argindex == 3:
+            # Diff wrt x1
+            return -(1 - x1)**(b - 1)*x1**(a - 1)
+        elif argindex == 4:
+            # Diff wrt x2
+            return (1 - x2)**(b - 1)*x2**(a - 1)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_mpmath(self):
+        return betainc_mpmath_fix, self.args
+
+    def _eval_is_real(self):
+        if all(arg.is_real for arg in self.args):
+            return True
+
+    def _eval_conjugate(self):
+        return self.func(*map(conjugate, self.args))
+
+    def _eval_rewrite_as_Integral(self, a, b, x1, x2, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [a, b, x1, x2]).name)
+        return Integral(t**(a - 1)*(1 - t)**(b - 1), (t, x1, x2))
+
+    def _eval_rewrite_as_hyper(self, a, b, x1, x2, **kwargs):
+        from sympy.functions.special.hyper import hyper
+        return (x2**a * hyper((a, 1 - b), (a + 1,), x2) - x1**a * hyper((a, 1 - b), (a + 1,), x1)) / a
+
+###############################################################################
+#################### REGULARIZED INCOMPLETE BETA FUNCTION #####################
+###############################################################################
+
+class betainc_regularized(DefinedFunction):
+    r"""
+    The Generalized Regularized Incomplete Beta function is given by
+
+    .. math::
+        \mathrm{I}_{(x_1, x_2)}(a, b) = \frac{\mathrm{B}_{(x_1, x_2)}(a, b)}{\mathrm{B}(a, b)}
+
+    The Regularized Incomplete Beta function is a special case
+    of the Generalized Regularized Incomplete Beta function :
+
+    .. math:: \mathrm{I}_z (a, b) = \mathrm{I}_{(0, z)}(a, b)
+
+    The Regularized Incomplete Beta function is the cumulative distribution
+    function of the beta distribution.
+
+    Examples
+    ========
+
+    >>> from sympy import betainc_regularized, symbols, conjugate
+    >>> a, b, x, x1, x2 = symbols('a b x x1 x2')
+
+    The Generalized Regularized Incomplete Beta
+    function is given by:
+
+    >>> betainc_regularized(a, b, x1, x2)
+    betainc_regularized(a, b, x1, x2)
+
+    The Regularized Incomplete Beta function
+    can be obtained as follows:
+
+    >>> betainc_regularized(a, b, 0, x)
+    betainc_regularized(a, b, 0, x)
+
+    The Regularized Incomplete Beta function
+    obeys the mirror symmetry:
+
+    >>> conjugate(betainc_regularized(a, b, x1, x2))
+    betainc_regularized(conjugate(a), conjugate(b), conjugate(x1), conjugate(x2))
+
+    We can numerically evaluate the Regularized Incomplete Beta function
+    to arbitrary precision for any complex numbers a, b, x1 and x2:
+
+    >>> from sympy import betainc_regularized, pi, E
+    >>> betainc_regularized(1, 2, 0, 0.25).evalf(10)
+    0.4375000000
+    >>> betainc_regularized(pi, E, 0, 1).evalf(5)
+    1.00000
+
+    The Generalized Regularized Incomplete Beta function can be
+    expressed in terms of the Generalized Hypergeometric function.
+
+    >>> from sympy import hyper
+    >>> betainc_regularized(a, b, x1, x2).rewrite(hyper)
+    (-x1**a*hyper((a, 1 - b), (a + 1,), x1) + x2**a*hyper((a, 1 - b), (a + 1,), x2))/(a*beta(a, b))
+
+    See Also
+    ========
+
+    beta: Beta function
+    hyper: Generalized Hypergeometric function
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function
+    .. [2] https://dlmf.nist.gov/8.17
+    .. [3] https://functions.wolfram.com/GammaBetaErf/Beta4/
+    .. [4] https://functions.wolfram.com/GammaBetaErf/BetaRegularized4/02/
+
+    """
+    nargs = 4
+    unbranched = True
+
+    def __new__(cls, a, b, x1, x2):
+        return super().__new__(cls, a, b, x1, x2)
+
+    def _eval_mpmath(self):
+        return betainc_mpmath_fix, (*self.args, S(1))
+
+    def fdiff(self, argindex):
+        a, b, x1, x2 = self.args
+        if argindex == 3:
+            # Diff wrt x1
+            return -(1 - x1)**(b - 1)*x1**(a - 1) / beta(a, b)
+        elif argindex == 4:
+            # Diff wrt x2
+            return (1 - x2)**(b - 1)*x2**(a - 1) / beta(a, b)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_real(self):
+        if all(arg.is_real for arg in self.args):
+            return True
+
+    def _eval_conjugate(self):
+        return self.func(*map(conjugate, self.args))
+
+    def _eval_rewrite_as_Integral(self, a, b, x1, x2, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [a, b, x1, x2]).name)
+        integrand = t**(a - 1)*(1 - t)**(b - 1)
+        expr = Integral(integrand, (t, x1, x2))
+        return expr / Integral(integrand, (t, 0, 1))
+
+    def _eval_rewrite_as_hyper(self, a, b, x1, x2, **kwargs):
+        from sympy.functions.special.hyper import hyper
+        expr = (x2**a * hyper((a, 1 - b), (a + 1,), x2) - x1**a * hyper((a, 1 - b), (a + 1,), x1)) / a
+        return expr / beta(a, b)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/bsplines.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/bsplines.py
new file mode 100644
index 0000000000000000000000000000000000000000..50c9141e841288aa02457c466fc6573f9a20d09f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/bsplines.py
@@ -0,0 +1,348 @@
+from sympy.core import S, sympify
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.functions import Piecewise, piecewise_fold
+from sympy.logic.boolalg import And
+from sympy.sets.sets import Interval
+
+from functools import lru_cache
+
+
+def _ivl(cond, x):
+    """return the interval corresponding to the condition
+
+    Conditions in spline's Piecewise give the range over
+    which an expression is valid like (lo <= x) & (x <= hi).
+    This function returns (lo, hi).
+    """
+    if isinstance(cond, And) and len(cond.args) == 2:
+        a, b = cond.args
+        if a.lts == x:
+            a, b = b, a
+        return a.lts, b.gts
+    raise TypeError('unexpected cond type: %s' % cond)
+
+
+def _add_splines(c, b1, d, b2, x):
+    """Construct c*b1 + d*b2."""
+
+    if S.Zero in (b1, c):
+        rv = piecewise_fold(d * b2)
+    elif S.Zero in (b2, d):
+        rv = piecewise_fold(c * b1)
+    else:
+        new_args = []
+        # Just combining the Piecewise without any fancy optimization
+        p1 = piecewise_fold(c * b1)
+        p2 = piecewise_fold(d * b2)
+
+        # Search all Piecewise arguments except (0, True)
+        p2args = list(p2.args[:-1])
+
+        # This merging algorithm assumes the conditions in
+        # p1 and p2 are sorted
+        for arg in p1.args[:-1]:
+            expr = arg.expr
+            cond = arg.cond
+
+            lower = _ivl(cond, x)[0]
+
+            # Check p2 for matching conditions that can be merged
+            for i, arg2 in enumerate(p2args):
+                expr2 = arg2.expr
+                cond2 = arg2.cond
+
+                lower_2, upper_2 = _ivl(cond2, x)
+                if cond2 == cond:
+                    # Conditions match, join expressions
+                    expr += expr2
+                    # Remove matching element
+                    del p2args[i]
+                    # No need to check the rest
+                    break
+                elif lower_2 < lower and upper_2 <= lower:
+                    # Check if arg2 condition smaller than arg1,
+                    # add to new_args by itself (no match expected
+                    # in p1)
+                    new_args.append(arg2)
+                    del p2args[i]
+                    break
+
+            # Checked all, add expr and cond
+            new_args.append((expr, cond))
+
+        # Add remaining items from p2args
+        new_args.extend(p2args)
+
+        # Add final (0, True)
+        new_args.append((0, True))
+
+        rv = Piecewise(*new_args, evaluate=False)
+
+    return rv.expand()
+
+
+@lru_cache(maxsize=128)
+def bspline_basis(d, knots, n, x):
+    """
+    The $n$-th B-spline at $x$ of degree $d$ with knots.
+
+    Explanation
+    ===========
+
+    B-Splines are piecewise polynomials of degree $d$. They are defined on a
+    set of knots, which is a sequence of integers or floats.
+
+    Examples
+    ========
+
+    The 0th degree splines have a value of 1 on a single interval:
+
+        >>> from sympy import bspline_basis
+        >>> from sympy.abc import x
+        >>> d = 0
+        >>> knots = tuple(range(5))
+        >>> bspline_basis(d, knots, 0, x)
+        Piecewise((1, (x >= 0) & (x <= 1)), (0, True))
+
+    For a given ``(d, knots)`` there are ``len(knots)-d-1`` B-splines
+    defined, that are indexed by ``n`` (starting at 0).
+
+    Here is an example of a cubic B-spline:
+
+        >>> bspline_basis(3, tuple(range(5)), 0, x)
+        Piecewise((x**3/6, (x >= 0) & (x <= 1)),
+                  (-x**3/2 + 2*x**2 - 2*x + 2/3,
+                  (x >= 1) & (x <= 2)),
+                  (x**3/2 - 4*x**2 + 10*x - 22/3,
+                  (x >= 2) & (x <= 3)),
+                  (-x**3/6 + 2*x**2 - 8*x + 32/3,
+                  (x >= 3) & (x <= 4)),
+                  (0, True))
+
+    By repeating knot points, you can introduce discontinuities in the
+    B-splines and their derivatives:
+
+        >>> d = 1
+        >>> knots = (0, 0, 2, 3, 4)
+        >>> bspline_basis(d, knots, 0, x)
+        Piecewise((1 - x/2, (x >= 0) & (x <= 2)), (0, True))
+
+    It is quite time consuming to construct and evaluate B-splines. If
+    you need to evaluate a B-spline many times, it is best to lambdify them
+    first:
+
+        >>> from sympy import lambdify
+        >>> d = 3
+        >>> knots = tuple(range(10))
+        >>> b0 = bspline_basis(d, knots, 0, x)
+        >>> f = lambdify(x, b0)
+        >>> y = f(0.5)
+
+    Parameters
+    ==========
+
+    d : integer
+        degree of bspline
+
+    knots : list of integer values
+        list of knots points of bspline
+
+    n : integer
+        $n$-th B-spline
+
+    x : symbol
+
+    See Also
+    ========
+
+    bspline_basis_set
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/B-spline
+
+    """
+    # make sure x has no assumptions so conditions don't evaluate
+    xvar = x
+    x = Dummy()
+
+    knots = tuple(sympify(k) for k in knots)
+    d = int(d)
+    n = int(n)
+    n_knots = len(knots)
+    n_intervals = n_knots - 1
+    if n + d + 1 > n_intervals:
+        raise ValueError("n + d + 1 must not exceed len(knots) - 1")
+    if d == 0:
+        result = Piecewise(
+            (S.One, Interval(knots[n], knots[n + 1]).contains(x)), (0, True)
+        )
+    elif d > 0:
+        denom = knots[n + d + 1] - knots[n + 1]
+        if denom != S.Zero:
+            B = (knots[n + d + 1] - x) / denom
+            b2 = bspline_basis(d - 1, knots, n + 1, x)
+        else:
+            b2 = B = S.Zero
+
+        denom = knots[n + d] - knots[n]
+        if denom != S.Zero:
+            A = (x - knots[n]) / denom
+            b1 = bspline_basis(d - 1, knots, n, x)
+        else:
+            b1 = A = S.Zero
+
+        result = _add_splines(A, b1, B, b2, x)
+    else:
+        raise ValueError("degree must be non-negative: %r" % n)
+
+    # return result with user-given x
+    return result.xreplace({x: xvar})
+
+
+def bspline_basis_set(d, knots, x):
+    """
+    Return the ``len(knots)-d-1`` B-splines at *x* of degree *d*
+    with *knots*.
+
+    Explanation
+    ===========
+
+    This function returns a list of piecewise polynomials that are the
+    ``len(knots)-d-1`` B-splines of degree *d* for the given knots.
+    This function calls ``bspline_basis(d, knots, n, x)`` for different
+    values of *n*.
+
+    Examples
+    ========
+
+    >>> from sympy import bspline_basis_set
+    >>> from sympy.abc import x
+    >>> d = 2
+    >>> knots = range(5)
+    >>> splines = bspline_basis_set(d, knots, x)
+    >>> splines
+    [Piecewise((x**2/2, (x >= 0) & (x <= 1)),
+               (-x**2 + 3*x - 3/2, (x >= 1) & (x <= 2)),
+               (x**2/2 - 3*x + 9/2, (x >= 2) & (x <= 3)),
+               (0, True)),
+    Piecewise((x**2/2 - x + 1/2, (x >= 1) & (x <= 2)),
+              (-x**2 + 5*x - 11/2, (x >= 2) & (x <= 3)),
+              (x**2/2 - 4*x + 8, (x >= 3) & (x <= 4)),
+              (0, True))]
+
+    Parameters
+    ==========
+
+    d : integer
+        degree of bspline
+
+    knots : list of integers
+        list of knots points of bspline
+
+    x : symbol
+
+    See Also
+    ========
+
+    bspline_basis
+
+    """
+    n_splines = len(knots) - d - 1
+    return [bspline_basis(d, tuple(knots), i, x) for i in range(n_splines)]
+
+
+def interpolating_spline(d, x, X, Y):
+    """
+    Return spline of degree *d*, passing through the given *X*
+    and *Y* values.
+
+    Explanation
+    ===========
+
+    This function returns a piecewise function such that each part is
+    a polynomial of degree not greater than *d*. The value of *d*
+    must be 1 or greater and the values of *X* must be strictly
+    increasing.
+
+    Examples
+    ========
+
+    >>> from sympy import interpolating_spline
+    >>> from sympy.abc import x
+    >>> interpolating_spline(1, x, [1, 2, 4, 7], [3, 6, 5, 7])
+    Piecewise((3*x, (x >= 1) & (x <= 2)),
+            (7 - x/2, (x >= 2) & (x <= 4)),
+            (2*x/3 + 7/3, (x >= 4) & (x <= 7)))
+    >>> interpolating_spline(3, x, [-2, 0, 1, 3, 4], [4, 2, 1, 1, 3])
+    Piecewise((7*x**3/117 + 7*x**2/117 - 131*x/117 + 2, (x >= -2) & (x <= 1)),
+            (10*x**3/117 - 2*x**2/117 - 122*x/117 + 77/39, (x >= 1) & (x <= 4)))
+
+    Parameters
+    ==========
+
+    d : integer
+        Degree of Bspline strictly greater than equal to one
+
+    x : symbol
+
+    X : list of strictly increasing real values
+        list of X coordinates through which the spline passes
+
+    Y : list of real values
+        list of corresponding Y coordinates through which the spline passes
+
+    See Also
+    ========
+
+    bspline_basis_set, interpolating_poly
+
+    """
+    from sympy.solvers.solveset import linsolve
+    from sympy.matrices.dense import Matrix
+
+    # Input sanitization
+    d = sympify(d)
+    if not (d.is_Integer and d.is_positive):
+        raise ValueError("Spline degree must be a positive integer, not %s." % d)
+    if len(X) != len(Y):
+        raise ValueError("Number of X and Y coordinates must be the same.")
+    if len(X) < d + 1:
+        raise ValueError("Degree must be less than the number of control points.")
+    if not all(a < b for a, b in zip(X, X[1:])):
+        raise ValueError("The x-coordinates must be strictly increasing.")
+    X = [sympify(i) for i in X]
+
+    # Evaluating knots value
+    if d.is_odd:
+        j = (d + 1) // 2
+        interior_knots = X[j:-j]
+    else:
+        j = d // 2
+        interior_knots = [
+            (a + b)/2 for a, b in zip(X[j : -j - 1], X[j + 1 : -j])
+        ]
+
+    knots = [X[0]] * (d + 1) + list(interior_knots) + [X[-1]] * (d + 1)
+
+    basis = bspline_basis_set(d, knots, x)
+
+    A = [[b.subs(x, v) for b in basis] for v in X]
+
+    coeff = linsolve((Matrix(A), Matrix(Y)), symbols("c0:{}".format(len(X)), cls=Dummy))
+    coeff = list(coeff)[0]
+    intervals = {c for b in basis for (e, c) in b.args if c != True}
+
+    # Sorting the intervals
+    #  ival contains the end-points of each interval
+    intervals = sorted(intervals, key=lambda c: _ivl(c, x))
+
+    basis_dicts = [{c: e for (e, c) in b.args} for b in basis]
+    spline = []
+    for i in intervals:
+        piece = sum(
+            [c * d.get(i, S.Zero) for (c, d) in zip(coeff, basis_dicts)], S.Zero
+        )
+        spline.append((piece, i))
+    return Piecewise(*spline)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/delta_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/delta_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..698d8c0c3ba5e68c2f084e83e7a9ec070ce83307
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/delta_functions.py
@@ -0,0 +1,664 @@
+from sympy.core import S, diff
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.logic import fuzzy_not
+from sympy.core.relational import Eq, Ne
+from sympy.functions.elementary.complexes import im, sign
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.polys.polyerrors import PolynomialError
+from sympy.polys.polyroots import roots
+from sympy.utilities.misc import filldedent
+
+
+###############################################################################
+################################ DELTA FUNCTION ###############################
+###############################################################################
+
+
+class DiracDelta(DefinedFunction):
+    r"""
+    The DiracDelta function and its derivatives.
+
+    Explanation
+    ===========
+
+    DiracDelta is not an ordinary function. It can be rigorously defined either
+    as a distribution or as a measure.
+
+    DiracDelta only makes sense in definite integrals, and in particular,
+    integrals of the form ``Integral(f(x)*DiracDelta(x - x0), (x, a, b))``,
+    where it equals ``f(x0)`` if ``a <= x0 <= b`` and ``0`` otherwise. Formally,
+    DiracDelta acts in some ways like a function that is ``0`` everywhere except
+    at ``0``, but in many ways it also does not. It can often be useful to treat
+    DiracDelta in formal ways, building up and manipulating expressions with
+    delta functions (which may eventually be integrated), but care must be taken
+    to not treat it as a real function. SymPy's ``oo`` is similar. It only
+    truly makes sense formally in certain contexts (such as integration limits),
+    but SymPy allows its use everywhere, and it tries to be consistent with
+    operations on it (like ``1/oo``), but it is easy to get into trouble and get
+    wrong results if ``oo`` is treated too much like a number. Similarly, if
+    DiracDelta is treated too much like a function, it is easy to get wrong or
+    nonsensical results.
+
+    DiracDelta function has the following properties:
+
+    1) $\frac{d}{d x} \theta(x) = \delta(x)$
+    2) $\int_{-\infty}^\infty \delta(x - a)f(x)\, dx = f(a)$ and $\int_{a-
+       \epsilon}^{a+\epsilon} \delta(x - a)f(x)\, dx = f(a)$
+    3) $\delta(x) = 0$ for all $x \neq 0$
+    4) $\delta(g(x)) = \sum_i \frac{\delta(x - x_i)}{\|g'(x_i)\|}$ where $x_i$
+       are the roots of $g$
+    5) $\delta(-x) = \delta(x)$
+
+    Derivatives of ``k``-th order of DiracDelta have the following properties:
+
+    6) $\delta(x, k) = 0$ for all $x \neq 0$
+    7) $\delta(-x, k) = -\delta(x, k)$ for odd $k$
+    8) $\delta(-x, k) = \delta(x, k)$ for even $k$
+
+    Examples
+    ========
+
+    >>> from sympy import DiracDelta, diff, pi
+    >>> from sympy.abc import x, y
+
+    >>> DiracDelta(x)
+    DiracDelta(x)
+    >>> DiracDelta(1)
+    0
+    >>> DiracDelta(-1)
+    0
+    >>> DiracDelta(pi)
+    0
+    >>> DiracDelta(x - 4).subs(x, 4)
+    DiracDelta(0)
+    >>> diff(DiracDelta(x))
+    DiracDelta(x, 1)
+    >>> diff(DiracDelta(x - 1), x, 2)
+    DiracDelta(x - 1, 2)
+    >>> diff(DiracDelta(x**2 - 1), x, 2)
+    2*(2*x**2*DiracDelta(x**2 - 1, 2) + DiracDelta(x**2 - 1, 1))
+    >>> DiracDelta(3*x).is_simple(x)
+    True
+    >>> DiracDelta(x**2).is_simple(x)
+    False
+    >>> DiracDelta((x**2 - 1)*y).expand(diracdelta=True, wrt=x)
+    DiracDelta(x - 1)/(2*Abs(y)) + DiracDelta(x + 1)/(2*Abs(y))
+
+    See Also
+    ========
+
+    Heaviside
+    sympy.simplify.simplify.simplify, is_simple
+    sympy.functions.special.tensor_functions.KroneckerDelta
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/DeltaFunction.html
+
+    """
+
+    is_real = True
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of a DiracDelta Function.
+
+        Explanation
+        ===========
+
+        The difference between ``diff()`` and ``fdiff()`` is: ``diff()`` is the
+        user-level function and ``fdiff()`` is an object method. ``fdiff()`` is
+        a convenience method available in the ``Function`` class. It returns
+        the derivative of the function without considering the chain rule.
+        ``diff(function, x)`` calls ``Function._eval_derivative`` which in turn
+        calls ``fdiff()`` internally to compute the derivative of the function.
+
+        Examples
+        ========
+
+        >>> from sympy import DiracDelta, diff
+        >>> from sympy.abc import x
+
+        >>> DiracDelta(x).fdiff()
+        DiracDelta(x, 1)
+
+        >>> DiracDelta(x, 1).fdiff()
+        DiracDelta(x, 2)
+
+        >>> DiracDelta(x**2 - 1).fdiff()
+        DiracDelta(x**2 - 1, 1)
+
+        >>> diff(DiracDelta(x, 1)).fdiff()
+        DiracDelta(x, 3)
+
+        Parameters
+        ==========
+
+        argindex : integer
+            degree of derivative
+
+        """
+        if argindex == 1:
+            #I didn't know if there is a better way to handle default arguments
+            k = 0
+            if len(self.args) > 1:
+                k = self.args[1]
+            return self.func(self.args[0], k + 1)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg, k=S.Zero):
+        """
+        Returns a simplified form or a value of DiracDelta depending on the
+        argument passed by the DiracDelta object.
+
+        Explanation
+        ===========
+
+        The ``eval()`` method is automatically called when the ``DiracDelta``
+        class is about to be instantiated and it returns either some simplified
+        instance or the unevaluated instance depending on the argument passed.
+        In other words, ``eval()`` method is not needed to be called explicitly,
+        it is being called and evaluated once the object is called.
+
+        Examples
+        ========
+
+        >>> from sympy import DiracDelta, S
+        >>> from sympy.abc import x
+
+        >>> DiracDelta(x)
+        DiracDelta(x)
+
+        >>> DiracDelta(-x, 1)
+        -DiracDelta(x, 1)
+
+        >>> DiracDelta(1)
+        0
+
+        >>> DiracDelta(5, 1)
+        0
+
+        >>> DiracDelta(0)
+        DiracDelta(0)
+
+        >>> DiracDelta(-1)
+        0
+
+        >>> DiracDelta(S.NaN)
+        nan
+
+        >>> DiracDelta(x - 100).subs(x, 5)
+        0
+
+        >>> DiracDelta(x - 100).subs(x, 100)
+        DiracDelta(0)
+
+        Parameters
+        ==========
+
+        k : integer
+            order of derivative
+
+        arg : argument passed to DiracDelta
+
+        """
+        if not k.is_Integer or k.is_negative:
+            raise ValueError("Error: the second argument of DiracDelta must be \
+            a non-negative integer, %s given instead." % (k,))
+        if arg is S.NaN:
+            return S.NaN
+        if arg.is_nonzero:
+            return S.Zero
+        if fuzzy_not(im(arg).is_zero):
+            raise ValueError(filldedent('''
+                Function defined only for Real Values.
+                Complex part: %s  found in %s .''' % (
+                repr(im(arg)), repr(arg))))
+        c, nc = arg.args_cnc()
+        if c and c[0] is S.NegativeOne:
+            # keep this fast and simple instead of using
+            # could_extract_minus_sign
+            if k.is_odd:
+                return -cls(-arg, k)
+            elif k.is_even:
+                return cls(-arg, k) if k else cls(-arg)
+        elif k.is_zero:
+            return cls(arg, evaluate=False)
+
+    def _eval_expand_diracdelta(self, **hints):
+        """
+        Compute a simplified representation of the function using
+        property number 4. Pass ``wrt`` as a hint to expand the expression
+        with respect to a particular variable.
+
+        Explanation
+        ===========
+
+        ``wrt`` is:
+
+        - a variable with respect to which a DiracDelta expression will
+        get expanded.
+
+        Examples
+        ========
+
+        >>> from sympy import DiracDelta
+        >>> from sympy.abc import x, y
+
+        >>> DiracDelta(x*y).expand(diracdelta=True, wrt=x)
+        DiracDelta(x)/Abs(y)
+        >>> DiracDelta(x*y).expand(diracdelta=True, wrt=y)
+        DiracDelta(y)/Abs(x)
+
+        >>> DiracDelta(x**2 + x - 2).expand(diracdelta=True, wrt=x)
+        DiracDelta(x - 1)/3 + DiracDelta(x + 2)/3
+
+        See Also
+        ========
+
+        is_simple, Diracdelta
+
+        """
+        wrt = hints.get('wrt', None)
+        if wrt is None:
+            free = self.free_symbols
+            if len(free) == 1:
+                wrt = free.pop()
+            else:
+                raise TypeError(filldedent('''
+            When there is more than 1 free symbol or variable in the expression,
+            the 'wrt' keyword is required as a hint to expand when using the
+            DiracDelta hint.'''))
+
+        if not self.args[0].has(wrt) or (len(self.args) > 1 and self.args[1] != 0 ):
+            return self
+        try:
+            argroots = roots(self.args[0], wrt)
+            result = 0
+            valid = True
+            darg = abs(diff(self.args[0], wrt))
+            for r, m in argroots.items():
+                if r.is_real is not False and m == 1:
+                    result += self.func(wrt - r)/darg.subs(wrt, r)
+                else:
+                    # don't handle non-real and if m != 1 then
+                    # a polynomial will have a zero in the derivative (darg)
+                    # at r
+                    valid = False
+                    break
+            if valid:
+                return result
+        except PolynomialError:
+            pass
+        return self
+
+    def is_simple(self, x):
+        """
+        Tells whether the argument(args[0]) of DiracDelta is a linear
+        expression in *x*.
+
+        Examples
+        ========
+
+        >>> from sympy import DiracDelta, cos
+        >>> from sympy.abc import x, y
+
+        >>> DiracDelta(x*y).is_simple(x)
+        True
+        >>> DiracDelta(x*y).is_simple(y)
+        True
+
+        >>> DiracDelta(x**2 + x - 2).is_simple(x)
+        False
+
+        >>> DiracDelta(cos(x)).is_simple(x)
+        False
+
+        Parameters
+        ==========
+
+        x : can be a symbol
+
+        See Also
+        ========
+
+        sympy.simplify.simplify.simplify, DiracDelta
+
+        """
+        p = self.args[0].as_poly(x)
+        if p:
+            return p.degree() == 1
+        return False
+
+    def _eval_rewrite_as_Piecewise(self, *args, **kwargs):
+        """
+        Represents DiracDelta in a piecewise form.
+
+        Examples
+        ========
+
+        >>> from sympy import DiracDelta, Piecewise, Symbol
+        >>> x = Symbol('x')
+
+        >>> DiracDelta(x).rewrite(Piecewise)
+        Piecewise((DiracDelta(0), Eq(x, 0)), (0, True))
+
+        >>> DiracDelta(x - 5).rewrite(Piecewise)
+        Piecewise((DiracDelta(0), Eq(x, 5)), (0, True))
+
+        >>> DiracDelta(x**2 - 5).rewrite(Piecewise)
+           Piecewise((DiracDelta(0), Eq(x**2, 5)), (0, True))
+
+        >>> DiracDelta(x - 5, 4).rewrite(Piecewise)
+        DiracDelta(x - 5, 4)
+
+        """
+        if len(args) == 1:
+            return Piecewise((DiracDelta(0), Eq(args[0], 0)), (0, True))
+
+    def _eval_rewrite_as_SingularityFunction(self, *args, **kwargs):
+        """
+        Returns the DiracDelta expression written in the form of Singularity
+        Functions.
+
+        """
+        from sympy.solvers import solve
+        from sympy.functions.special.singularity_functions import SingularityFunction
+        if self == DiracDelta(0):
+            return SingularityFunction(0, 0, -1)
+        if self == DiracDelta(0, 1):
+            return SingularityFunction(0, 0, -2)
+        free = self.free_symbols
+        if len(free) == 1:
+            x = (free.pop())
+            if len(args) == 1:
+                return SingularityFunction(x, solve(args[0], x)[0], -1)
+            return SingularityFunction(x, solve(args[0], x)[0], -args[1] - 1)
+        else:
+            # I don't know how to handle the case for DiracDelta expressions
+            # having arguments with more than one variable.
+            raise TypeError(filldedent('''
+                rewrite(SingularityFunction) does not support
+                arguments with more that one variable.'''))
+
+
+###############################################################################
+############################## HEAVISIDE FUNCTION #############################
+###############################################################################
+
+
+class Heaviside(DefinedFunction):
+    r"""
+    Heaviside step function.
+
+    Explanation
+    ===========
+
+    The Heaviside step function has the following properties:
+
+    1) $\frac{d}{d x} \theta(x) = \delta(x)$
+    2) $\theta(x) = \begin{cases} 0 & \text{for}\: x < 0 \\ \frac{1}{2} &
+       \text{for}\: x = 0 \\1 & \text{for}\: x > 0 \end{cases}$
+    3) $\frac{d}{d x} \max(x, 0) = \theta(x)$
+
+    Heaviside(x) is printed as $\theta(x)$ with the SymPy LaTeX printer.
+
+    The value at 0 is set differently in different fields. SymPy uses 1/2,
+    which is a convention from electronics and signal processing, and is
+    consistent with solving improper integrals by Fourier transform and
+    convolution.
+
+    To specify a different value of Heaviside at ``x=0``, a second argument
+    can be given. Using ``Heaviside(x, nan)`` gives an expression that will
+    evaluate to nan for x=0.
+
+    .. versionchanged:: 1.9 ``Heaviside(0)`` now returns 1/2 (before: undefined)
+
+    Examples
+    ========
+
+    >>> from sympy import Heaviside, nan
+    >>> from sympy.abc import x
+    >>> Heaviside(9)
+    1
+    >>> Heaviside(-9)
+    0
+    >>> Heaviside(0)
+    1/2
+    >>> Heaviside(0, nan)
+    nan
+    >>> (Heaviside(x) + 1).replace(Heaviside(x), Heaviside(x, 1))
+    Heaviside(x, 1) + 1
+
+    See Also
+    ========
+
+    DiracDelta
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/HeavisideStepFunction.html
+    .. [2] https://dlmf.nist.gov/1.16#iv
+
+    """
+
+    is_real = True
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of a Heaviside Function.
+
+        Examples
+        ========
+
+        >>> from sympy import Heaviside, diff
+        >>> from sympy.abc import x
+
+        >>> Heaviside(x).fdiff()
+        DiracDelta(x)
+
+        >>> Heaviside(x**2 - 1).fdiff()
+        DiracDelta(x**2 - 1)
+
+        >>> diff(Heaviside(x)).fdiff()
+        DiracDelta(x, 1)
+
+        Parameters
+        ==========
+
+        argindex : integer
+            order of derivative
+
+        """
+        if argindex == 1:
+            return DiracDelta(self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def __new__(cls, arg, H0=S.Half, **options):
+        if isinstance(H0, Heaviside) and len(H0.args) == 1:
+            H0 = S.Half
+        return super(cls, cls).__new__(cls, arg, H0, **options)
+
+    @property
+    def pargs(self):
+        """Args without default S.Half"""
+        args = self.args
+        if args[1] is S.Half:
+            args = args[:1]
+        return args
+
+    @classmethod
+    def eval(cls, arg, H0=S.Half):
+        """
+        Returns a simplified form or a value of Heaviside depending on the
+        argument passed by the Heaviside object.
+
+        Explanation
+        ===========
+
+        The ``eval()`` method is automatically called when the ``Heaviside``
+        class is about to be instantiated and it returns either some simplified
+        instance or the unevaluated instance depending on the argument passed.
+        In other words, ``eval()`` method is not needed to be called explicitly,
+        it is being called and evaluated once the object is called.
+
+        Examples
+        ========
+
+        >>> from sympy import Heaviside, S
+        >>> from sympy.abc import x
+
+        >>> Heaviside(x)
+        Heaviside(x)
+
+        >>> Heaviside(19)
+        1
+
+        >>> Heaviside(0)
+        1/2
+
+        >>> Heaviside(0, 1)
+        1
+
+        >>> Heaviside(-5)
+        0
+
+        >>> Heaviside(S.NaN)
+        nan
+
+        >>> Heaviside(x - 100).subs(x, 5)
+        0
+
+        >>> Heaviside(x - 100).subs(x, 105)
+        1
+
+        Parameters
+        ==========
+
+        arg : argument passed by Heaviside object
+
+        H0 : value of Heaviside(0)
+
+        """
+        if arg.is_extended_negative:
+            return S.Zero
+        elif arg.is_extended_positive:
+            return S.One
+        elif arg.is_zero:
+            return H0
+        elif arg is S.NaN:
+            return S.NaN
+        elif fuzzy_not(im(arg).is_zero):
+            raise ValueError("Function defined only for Real Values. Complex part: %s  found in %s ." % (repr(im(arg)), repr(arg)) )
+
+    def _eval_rewrite_as_Piecewise(self, arg, H0=None, **kwargs):
+        """
+        Represents Heaviside in a Piecewise form.
+
+        Examples
+        ========
+
+        >>> from sympy import Heaviside, Piecewise, Symbol, nan
+        >>> x = Symbol('x')
+
+        >>> Heaviside(x).rewrite(Piecewise)
+        Piecewise((0, x < 0), (1/2, Eq(x, 0)), (1, True))
+
+        >>> Heaviside(x,nan).rewrite(Piecewise)
+        Piecewise((0, x < 0), (nan, Eq(x, 0)), (1, True))
+
+        >>> Heaviside(x - 5).rewrite(Piecewise)
+        Piecewise((0, x < 5), (1/2, Eq(x, 5)), (1, True))
+
+        >>> Heaviside(x**2 - 1).rewrite(Piecewise)
+        Piecewise((0, x**2 < 1), (1/2, Eq(x**2, 1)), (1, True))
+
+        """
+        if H0 == 0:
+            return Piecewise((0, arg <= 0), (1, True))
+        if H0 == 1:
+            return Piecewise((0, arg < 0), (1, True))
+        return Piecewise((0, arg < 0), (H0, Eq(arg, 0)), (1, True))
+
+    def _eval_rewrite_as_sign(self, arg, H0=S.Half, **kwargs):
+        """
+        Represents the Heaviside function in the form of sign function.
+
+        Explanation
+        ===========
+
+        The value of Heaviside(0) must be 1/2 for rewriting as sign to be
+        strictly equivalent. For easier usage, we also allow this rewriting
+        when Heaviside(0) is undefined.
+
+        Examples
+        ========
+
+        >>> from sympy import Heaviside, Symbol, sign, nan
+        >>> x = Symbol('x', real=True)
+        >>> y = Symbol('y')
+
+        >>> Heaviside(x).rewrite(sign)
+        sign(x)/2 + 1/2
+
+        >>> Heaviside(x, 0).rewrite(sign)
+        Piecewise((sign(x)/2 + 1/2, Ne(x, 0)), (0, True))
+
+        >>> Heaviside(x, nan).rewrite(sign)
+        Piecewise((sign(x)/2 + 1/2, Ne(x, 0)), (nan, True))
+
+        >>> Heaviside(x - 2).rewrite(sign)
+        sign(x - 2)/2 + 1/2
+
+        >>> Heaviside(x**2 - 2*x + 1).rewrite(sign)
+        sign(x**2 - 2*x + 1)/2 + 1/2
+
+        >>> Heaviside(y).rewrite(sign)
+        Heaviside(y)
+
+        >>> Heaviside(y**2 - 2*y + 1).rewrite(sign)
+        Heaviside(y**2 - 2*y + 1)
+
+        See Also
+        ========
+
+        sign
+
+        """
+        if arg.is_extended_real:
+            pw1 = Piecewise(
+                ((sign(arg) + 1)/2, Ne(arg, 0)),
+                (Heaviside(0, H0=H0), True))
+            pw2 = Piecewise(
+                ((sign(arg) + 1)/2, Eq(Heaviside(0, H0=H0), S.Half)),
+                (pw1, True))
+            return pw2
+
+    def _eval_rewrite_as_SingularityFunction(self, args, H0=S.Half, **kwargs):
+        """
+        Returns the Heaviside expression written in the form of Singularity
+        Functions.
+
+        """
+        from sympy.solvers import solve
+        from sympy.functions.special.singularity_functions import SingularityFunction
+        if self == Heaviside(0):
+            return SingularityFunction(0, 0, 0)
+        free = self.free_symbols
+        if len(free) == 1:
+            x = (free.pop())
+            return SingularityFunction(x, solve(args, x)[0], 0)
+            # TODO
+            # ((x - 5)**3*Heaviside(x - 5)).rewrite(SingularityFunction) should output
+            # SingularityFunction(x, 5, 0) instead of (x - 5)**3*SingularityFunction(x, 5, 0)
+        else:
+            # I don't know how to handle the case for Heaviside expressions
+            # having arguments with more than one variable.
+            raise TypeError(filldedent('''
+                rewrite(SingularityFunction) does not
+                support arguments with more that one variable.'''))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/elliptic_integrals.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/elliptic_integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..a94e343c0106891db44668ae05c33e84ecd05d0b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/elliptic_integrals.py
@@ -0,0 +1,445 @@
+""" Elliptic Integrals. """
+
+from sympy.core import S, pi, I, Rational
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.symbol import Dummy,uniquely_named_symbol
+from sympy.functions.elementary.complexes import sign
+from sympy.functions.elementary.hyperbolic import atanh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin, tan
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import hyper, meijerg
+
+class elliptic_k(DefinedFunction):
+    r"""
+    The complete elliptic integral of the first kind, defined by
+
+    .. math:: K(m) = F\left(\tfrac{\pi}{2}\middle| m\right)
+
+    where $F\left(z\middle| m\right)$ is the Legendre incomplete
+    elliptic integral of the first kind.
+
+    Explanation
+    ===========
+
+    The function $K(m)$ is a single-valued function on the complex
+    plane with branch cut along the interval $(1, \infty)$.
+
+    Note that our notation defines the incomplete elliptic integral
+    in terms of the parameter $m$ instead of the elliptic modulus
+    (eccentricity) $k$.
+    In this case, the parameter $m$ is defined as $m=k^2$.
+
+    Examples
+    ========
+
+    >>> from sympy import elliptic_k, I
+    >>> from sympy.abc import m
+    >>> elliptic_k(0)
+    pi/2
+    >>> elliptic_k(1.0 + I)
+    1.50923695405127 + 0.625146415202697*I
+    >>> elliptic_k(m).series(n=3)
+    pi/2 + pi*m/8 + 9*pi*m**2/128 + O(m**3)
+
+    See Also
+    ========
+
+    elliptic_f
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals
+    .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticK
+
+    """
+
+    @classmethod
+    def eval(cls, m):
+        if m.is_zero:
+            return pi*S.Half
+        elif m is S.Half:
+            return 8*pi**Rational(3, 2)/gamma(Rational(-1, 4))**2
+        elif m is S.One:
+            return S.ComplexInfinity
+        elif m is S.NegativeOne:
+            return gamma(Rational(1, 4))**2/(4*sqrt(2*pi))
+        elif m in (S.Infinity, S.NegativeInfinity, I*S.Infinity,
+                   I*S.NegativeInfinity, S.ComplexInfinity):
+            return S.Zero
+
+    def fdiff(self, argindex=1):
+        m = self.args[0]
+        return (elliptic_e(m) - (1 - m)*elliptic_k(m))/(2*m*(1 - m))
+
+    def _eval_conjugate(self):
+        m = self.args[0]
+        if (m.is_real and (m - 1).is_positive) is False:
+            return self.func(m.conjugate())
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.simplify import hyperexpand
+        return hyperexpand(self.rewrite(hyper)._eval_nseries(x, n=n, logx=logx))
+
+    def _eval_rewrite_as_hyper(self, m, **kwargs):
+        return pi*S.Half*hyper((S.Half, S.Half), (S.One,), m)
+
+    def _eval_rewrite_as_meijerg(self, m, **kwargs):
+        return meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -m)/2
+
+    def _eval_is_zero(self):
+        m = self.args[0]
+        if m.is_infinite:
+            return True
+
+    def _eval_rewrite_as_Integral(self, *args, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', args).name)
+        m = self.args[0]
+        return Integral(1/sqrt(1 - m*sin(t)**2), (t, 0, pi/2))
+
+
+class elliptic_f(DefinedFunction):
+    r"""
+    The Legendre incomplete elliptic integral of the first
+    kind, defined by
+
+    .. math:: F\left(z\middle| m\right) =
+              \int_0^z \frac{dt}{\sqrt{1 - m \sin^2 t}}
+
+    Explanation
+    ===========
+
+    This function reduces to a complete elliptic integral of
+    the first kind, $K(m)$, when $z = \pi/2$.
+
+    Note that our notation defines the incomplete elliptic integral
+    in terms of the parameter $m$ instead of the elliptic modulus
+    (eccentricity) $k$.
+    In this case, the parameter $m$ is defined as $m=k^2$.
+
+    Examples
+    ========
+
+    >>> from sympy import elliptic_f, I
+    >>> from sympy.abc import z, m
+    >>> elliptic_f(z, m).series(z)
+    z + z**5*(3*m**2/40 - m/30) + m*z**3/6 + O(z**6)
+    >>> elliptic_f(3.0 + I/2, 1.0 + I)
+    2.909449841483 + 1.74720545502474*I
+
+    See Also
+    ========
+
+    elliptic_k
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals
+    .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticF
+
+    """
+
+    @classmethod
+    def eval(cls, z, m):
+        if z.is_zero:
+            return S.Zero
+        if m.is_zero:
+            return z
+        k = 2*z/pi
+        if k.is_integer:
+            return k*elliptic_k(m)
+        elif m in (S.Infinity, S.NegativeInfinity):
+            return S.Zero
+        elif z.could_extract_minus_sign():
+            return -elliptic_f(-z, m)
+
+    def fdiff(self, argindex=1):
+        z, m = self.args
+        fm = sqrt(1 - m*sin(z)**2)
+        if argindex == 1:
+            return 1/fm
+        elif argindex == 2:
+            return (elliptic_e(z, m)/(2*m*(1 - m)) - elliptic_f(z, m)/(2*m) -
+                    sin(2*z)/(4*(1 - m)*fm))
+        raise ArgumentIndexError(self, argindex)
+
+    def _eval_conjugate(self):
+        z, m = self.args
+        if (m.is_real and (m - 1).is_positive) is False:
+            return self.func(z.conjugate(), m.conjugate())
+
+    def _eval_rewrite_as_Integral(self, *args, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', args).name)
+        z, m = self.args[0], self.args[1]
+        return Integral(1/(sqrt(1 - m*sin(t)**2)), (t, 0, z))
+
+    def _eval_is_zero(self):
+        z, m = self.args
+        if z.is_zero:
+            return True
+        if m.is_extended_real and m.is_infinite:
+            return True
+
+
+class elliptic_e(DefinedFunction):
+    r"""
+    Called with two arguments $z$ and $m$, evaluates the
+    incomplete elliptic integral of the second kind, defined by
+
+    .. math:: E\left(z\middle| m\right) = \int_0^z \sqrt{1 - m \sin^2 t} dt
+
+    Called with a single argument $m$, evaluates the Legendre complete
+    elliptic integral of the second kind
+
+    .. math:: E(m) = E\left(\tfrac{\pi}{2}\middle| m\right)
+
+    Explanation
+    ===========
+
+    The function $E(m)$ is a single-valued function on the complex
+    plane with branch cut along the interval $(1, \infty)$.
+
+    Note that our notation defines the incomplete elliptic integral
+    in terms of the parameter $m$ instead of the elliptic modulus
+    (eccentricity) $k$.
+    In this case, the parameter $m$ is defined as $m=k^2$.
+
+    Examples
+    ========
+
+    >>> from sympy import elliptic_e, I
+    >>> from sympy.abc import z, m
+    >>> elliptic_e(z, m).series(z)
+    z + z**5*(-m**2/40 + m/30) - m*z**3/6 + O(z**6)
+    >>> elliptic_e(m).series(n=4)
+    pi/2 - pi*m/8 - 3*pi*m**2/128 - 5*pi*m**3/512 + O(m**4)
+    >>> elliptic_e(1 + I, 2 - I/2).n()
+    1.55203744279187 + 0.290764986058437*I
+    >>> elliptic_e(0)
+    pi/2
+    >>> elliptic_e(2.0 - I)
+    0.991052601328069 + 0.81879421395609*I
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals
+    .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticE2
+    .. [3] https://functions.wolfram.com/EllipticIntegrals/EllipticE
+
+    """
+
+    @classmethod
+    def eval(cls, m, z=None):
+        if z is not None:
+            z, m = m, z
+            k = 2*z/pi
+            if m.is_zero:
+                return z
+            if z.is_zero:
+                return S.Zero
+            elif k.is_integer:
+                return k*elliptic_e(m)
+            elif m in (S.Infinity, S.NegativeInfinity):
+                return S.ComplexInfinity
+            elif z.could_extract_minus_sign():
+                return -elliptic_e(-z, m)
+        else:
+            if m.is_zero:
+                return pi/2
+            elif m is S.One:
+                return S.One
+            elif m is S.Infinity:
+                return I*S.Infinity
+            elif m is S.NegativeInfinity:
+                return S.Infinity
+            elif m is S.ComplexInfinity:
+                return S.ComplexInfinity
+
+    def fdiff(self, argindex=1):
+        if len(self.args) == 2:
+            z, m = self.args
+            if argindex == 1:
+                return sqrt(1 - m*sin(z)**2)
+            elif argindex == 2:
+                return (elliptic_e(z, m) - elliptic_f(z, m))/(2*m)
+        else:
+            m = self.args[0]
+            if argindex == 1:
+                return (elliptic_e(m) - elliptic_k(m))/(2*m)
+        raise ArgumentIndexError(self, argindex)
+
+    def _eval_conjugate(self):
+        if len(self.args) == 2:
+            z, m = self.args
+            if (m.is_real and (m - 1).is_positive) is False:
+                return self.func(z.conjugate(), m.conjugate())
+        else:
+            m = self.args[0]
+            if (m.is_real and (m - 1).is_positive) is False:
+                return self.func(m.conjugate())
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.simplify import hyperexpand
+        if len(self.args) == 1:
+            return hyperexpand(self.rewrite(hyper)._eval_nseries(x, n=n, logx=logx))
+        return super()._eval_nseries(x, n=n, logx=logx)
+
+    def _eval_rewrite_as_hyper(self, *args, **kwargs):
+        if len(args) == 1:
+            m = args[0]
+            return (pi/2)*hyper((Rational(-1, 2), S.Half), (S.One,), m)
+
+    def _eval_rewrite_as_meijerg(self, *args, **kwargs):
+        if len(args) == 1:
+            m = args[0]
+            return -meijerg(((S.Half, Rational(3, 2)), []), \
+                            ((S.Zero,), (S.Zero,)), -m)/4
+
+    def _eval_rewrite_as_Integral(self, *args, **kwargs):
+        from sympy.integrals.integrals import Integral
+        z, m = (pi/2, self.args[0]) if len(self.args) == 1 else self.args
+        t = Dummy(uniquely_named_symbol('t', args).name)
+        return Integral(sqrt(1 - m*sin(t)**2), (t, 0, z))
+
+
+class elliptic_pi(DefinedFunction):
+    r"""
+    Called with three arguments $n$, $z$ and $m$, evaluates the
+    Legendre incomplete elliptic integral of the third kind, defined by
+
+    .. math:: \Pi\left(n; z\middle| m\right) = \int_0^z \frac{dt}
+              {\left(1 - n \sin^2 t\right) \sqrt{1 - m \sin^2 t}}
+
+    Called with two arguments $n$ and $m$, evaluates the complete
+    elliptic integral of the third kind:
+
+    .. math:: \Pi\left(n\middle| m\right) =
+              \Pi\left(n; \tfrac{\pi}{2}\middle| m\right)
+
+    Explanation
+    ===========
+
+    Note that our notation defines the incomplete elliptic integral
+    in terms of the parameter $m$ instead of the elliptic modulus
+    (eccentricity) $k$.
+    In this case, the parameter $m$ is defined as $m=k^2$.
+
+    Examples
+    ========
+
+    >>> from sympy import elliptic_pi, I
+    >>> from sympy.abc import z, n, m
+    >>> elliptic_pi(n, z, m).series(z, n=4)
+    z + z**3*(m/6 + n/3) + O(z**4)
+    >>> elliptic_pi(0.5 + I, 1.0 - I, 1.2)
+    2.50232379629182 - 0.760939574180767*I
+    >>> elliptic_pi(0, 0)
+    pi/2
+    >>> elliptic_pi(1.0 - I/3, 2.0 + I)
+    3.29136443417283 + 0.32555634906645*I
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals
+    .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticPi3
+    .. [3] https://functions.wolfram.com/EllipticIntegrals/EllipticPi
+
+    """
+
+    @classmethod
+    def eval(cls, n, m, z=None):
+        if z is not None:
+            z, m = m, z
+            if n.is_zero:
+                return elliptic_f(z, m)
+            elif n is S.One:
+                return (elliptic_f(z, m) +
+                        (sqrt(1 - m*sin(z)**2)*tan(z) -
+                         elliptic_e(z, m))/(1 - m))
+            k = 2*z/pi
+            if k.is_integer:
+                return k*elliptic_pi(n, m)
+            elif m.is_zero:
+                return atanh(sqrt(n - 1)*tan(z))/sqrt(n - 1)
+            elif n == m:
+                return (elliptic_f(z, n) - elliptic_pi(1, z, n) +
+                        tan(z)/sqrt(1 - n*sin(z)**2))
+            elif n in (S.Infinity, S.NegativeInfinity):
+                return S.Zero
+            elif m in (S.Infinity, S.NegativeInfinity):
+                return S.Zero
+            elif z.could_extract_minus_sign():
+                return -elliptic_pi(n, -z, m)
+            if n.is_zero:
+                return elliptic_f(z, m)
+            if m.is_extended_real and m.is_infinite or \
+                    n.is_extended_real and n.is_infinite:
+                return S.Zero
+        else:
+            if n.is_zero:
+                return elliptic_k(m)
+            elif n is S.One:
+                return S.ComplexInfinity
+            elif m.is_zero:
+                return pi/(2*sqrt(1 - n))
+            elif m == S.One:
+                return S.NegativeInfinity/sign(n - 1)
+            elif n == m:
+                return elliptic_e(n)/(1 - n)
+            elif n in (S.Infinity, S.NegativeInfinity):
+                return S.Zero
+            elif m in (S.Infinity, S.NegativeInfinity):
+                return S.Zero
+            if n.is_zero:
+                return elliptic_k(m)
+            if m.is_extended_real and m.is_infinite or \
+                    n.is_extended_real and n.is_infinite:
+                return S.Zero
+
+    def _eval_conjugate(self):
+        if len(self.args) == 3:
+            n, z, m = self.args
+            if (n.is_real and (n - 1).is_positive) is False and \
+               (m.is_real and (m - 1).is_positive) is False:
+                return self.func(n.conjugate(), z.conjugate(), m.conjugate())
+        else:
+            n, m = self.args
+            return self.func(n.conjugate(), m.conjugate())
+
+    def fdiff(self, argindex=1):
+        if len(self.args) == 3:
+            n, z, m = self.args
+            fm, fn = sqrt(1 - m*sin(z)**2), 1 - n*sin(z)**2
+            if argindex == 1:
+                return (elliptic_e(z, m) + (m - n)*elliptic_f(z, m)/n +
+                        (n**2 - m)*elliptic_pi(n, z, m)/n -
+                        n*fm*sin(2*z)/(2*fn))/(2*(m - n)*(n - 1))
+            elif argindex == 2:
+                return 1/(fm*fn)
+            elif argindex == 3:
+                return (elliptic_e(z, m)/(m - 1) +
+                        elliptic_pi(n, z, m) -
+                        m*sin(2*z)/(2*(m - 1)*fm))/(2*(n - m))
+        else:
+            n, m = self.args
+            if argindex == 1:
+                return (elliptic_e(m) + (m - n)*elliptic_k(m)/n +
+                        (n**2 - m)*elliptic_pi(n, m)/n)/(2*(m - n)*(n - 1))
+            elif argindex == 2:
+                return (elliptic_e(m)/(m - 1) + elliptic_pi(n, m))/(2*(n - m))
+        raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Integral(self, *args, **kwargs):
+        from sympy.integrals.integrals import Integral
+        if len(self.args) == 2:
+            n, m, z = self.args[0], self.args[1], pi/2
+        else:
+            n, z, m = self.args
+        t = Dummy(uniquely_named_symbol('t', args).name)
+        return Integral(1/((1 - n*sin(t)**2)*sqrt(1 - m*sin(t)**2)), (t, 0, z))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/error_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/error_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..a778127d8b80583a892285fadbb8230f72de39f9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/error_functions.py
@@ -0,0 +1,2801 @@
+""" This module contains various functions that are special cases
+    of incomplete gamma functions. It should probably be renamed. """
+
+from sympy.core import EulerGamma # Must be imported from core, not core.numbers
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.function import DefinedFunction, ArgumentIndexError, expand_mul
+from sympy.core.logic import fuzzy_or
+from sympy.core.numbers import I, pi, Rational, Integer
+from sympy.core.relational import is_eq
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy, uniquely_named_symbol
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial, factorial2, RisingFactorial
+from sympy.functions.elementary.complexes import  polar_lift, re, unpolarify
+from sympy.functions.elementary.integers import ceiling, floor
+from sympy.functions.elementary.miscellaneous import sqrt, root
+from sympy.functions.elementary.exponential import exp, log, exp_polar
+from sympy.functions.elementary.hyperbolic import cosh, sinh
+from sympy.functions.elementary.trigonometric import cos, sin, sinc
+from sympy.functions.special.hyper import hyper, meijerg
+
+# TODO series expansions
+# TODO see the "Note:" in Ei
+
+# Helper function
+def real_to_real_as_real_imag(self, deep=True, **hints):
+    if self.args[0].is_extended_real:
+        if deep:
+            hints['complex'] = False
+            return (self.expand(deep, **hints), S.Zero)
+        else:
+            return (self, S.Zero)
+    if deep:
+        x, y = self.args[0].expand(deep, **hints).as_real_imag()
+    else:
+        x, y = self.args[0].as_real_imag()
+    re = (self.func(x + I*y) + self.func(x - I*y))/2
+    im = (self.func(x + I*y) - self.func(x - I*y))/(2*I)
+    return (re, im)
+
+
+###############################################################################
+################################ ERROR FUNCTION ###############################
+###############################################################################
+
+
+class erf(DefinedFunction):
+    r"""
+    The Gauss error function.
+
+    Explanation
+    ===========
+
+    This function is defined as:
+
+    .. math ::
+        \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \mathrm{d}t.
+
+    Examples
+    ========
+
+    >>> from sympy import I, oo, erf
+    >>> from sympy.abc import z
+
+    Several special values are known:
+
+    >>> erf(0)
+    0
+    >>> erf(oo)
+    1
+    >>> erf(-oo)
+    -1
+    >>> erf(I*oo)
+    oo*I
+    >>> erf(-I*oo)
+    -oo*I
+
+    In general one can pull out factors of -1 and $I$ from the argument:
+
+    >>> erf(-z)
+    -erf(z)
+
+    The error function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(erf(z))
+    erf(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erf(z), z)
+    2*exp(-z**2)/sqrt(pi)
+
+    We can numerically evaluate the error function to arbitrary precision
+    on the whole complex plane:
+
+    >>> erf(4).evalf(30)
+    0.999999984582742099719981147840
+
+    >>> erf(-4*I).evalf(30)
+    -1296959.73071763923152794095062*I
+
+    See Also
+    ========
+
+    erfc: Complementary error function.
+    erfi: Imaginary error function.
+    erf2: Two-argument error function.
+    erfinv: Inverse error function.
+    erfcinv: Inverse Complementary error function.
+    erf2inv: Inverse two-argument error function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Error_function
+    .. [2] https://dlmf.nist.gov/7
+    .. [3] https://mathworld.wolfram.com/Erf.html
+    .. [4] https://functions.wolfram.com/GammaBetaErf/Erf
+
+    """
+
+    unbranched = True
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 2*exp(-self.args[0]**2)/sqrt(pi)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+
+        """
+        return erfinv
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.One
+            elif arg is S.NegativeInfinity:
+                return S.NegativeOne
+            elif arg.is_zero:
+                return S.Zero
+
+        if isinstance(arg, erfinv):
+            return arg.args[0]
+
+        if isinstance(arg, erfcinv):
+            return S.One - arg.args[0]
+
+        if arg.is_zero:
+            return S.Zero
+
+        # Only happens with unevaluated erf2inv
+        if isinstance(arg, erf2inv) and arg.args[0].is_zero:
+            return arg.args[1]
+
+        # Try to pull out factors of I
+        t = arg.extract_multiplicatively(I)
+        if t in (S.Infinity, S.NegativeInfinity):
+            return arg
+
+        # Try to pull out factors of -1
+        if arg.could_extract_minus_sign():
+            return -cls(-arg)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            k = floor((n - 1)/S(2))
+            if len(previous_terms) > 2:
+                return -previous_terms[-2] * x**2 * (n - 2)/(n*k)
+            else:
+                return 2*S.NegativeOne**k * x**n/(n*factorial(k)*sqrt(pi))
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def _eval_is_real(self):
+        if self.args[0].is_extended_real is True:
+            return True
+        # There are cases where erf(z) becomes a real number
+        # even if z is a complex number
+
+    def _eval_is_imaginary(self):
+        if self.args[0].is_imaginary is True:
+            return True
+
+    def _eval_is_finite(self):
+        z = self.args[0]
+        return fuzzy_or([z.is_finite, z.is_extended_real])
+
+    def _eval_is_zero(self):
+        if self.args[0].is_extended_real is True:
+            return self.args[0].is_zero
+
+    def _eval_is_positive(self):
+        if self.args[0].is_extended_real is True:
+            return self.args[0].is_extended_positive
+
+    def _eval_is_negative(self):
+        if self.args[0].is_extended_real is True:
+            return self.args[0].is_extended_negative
+
+    def _eval_rewrite_as_uppergamma(self, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return sqrt(z**2)/z*(S.One - uppergamma(S.Half, z**2)/sqrt(pi))
+
+    def _eval_rewrite_as_fresnels(self, z, **kwargs):
+        arg = (S.One - I)*z/sqrt(pi)
+        return (S.One + I)*(fresnelc(arg) - I*fresnels(arg))
+
+    def _eval_rewrite_as_fresnelc(self, z, **kwargs):
+        arg = (S.One - I)*z/sqrt(pi)
+        return (S.One + I)*(fresnelc(arg) - I*fresnels(arg))
+
+    def _eval_rewrite_as_meijerg(self, z, **kwargs):
+        return z/sqrt(pi)*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2)
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        return 2*z/sqrt(pi)*hyper([S.Half], [3*S.Half], -z**2)
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        return sqrt(z**2)/z - z*expint(S.Half, z**2)/sqrt(pi)
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        from sympy.series.limits import limit
+        if limitvar:
+            lim = limit(z, limitvar, S.Infinity)
+            if lim is S.NegativeInfinity:
+                return S.NegativeOne + _erfs(-z)*exp(-z**2)
+        return S.One - _erfs(z)*exp(-z**2)
+
+    def _eval_rewrite_as_erfc(self, z, **kwargs):
+        return S.One - erfc(z)
+
+    def _eval_rewrite_as_erfi(self, z, **kwargs):
+        return -I*erfi(I*z)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.ComplexInfinity:
+            arg0 = arg.limit(x, 0, dir='-' if cdir == -1 else '+')
+        if x in arg.free_symbols and arg0.is_zero:
+            return 2*arg/sqrt(pi)
+        else:
+            return self.func(arg0)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        if point in [S.Infinity, S.NegativeInfinity]:
+            z = self.args[0]
+
+            try:
+                _, ex = z.leadterm(x)
+            except (ValueError, NotImplementedError):
+                return self
+
+            ex = -ex # as x->1/x for aseries
+            if ex.is_positive:
+                newn = ceiling(n/ex)
+                s = [S.NegativeOne**k * factorial2(2*k - 1) / (z**(2*k + 1) * 2**k)
+                     for k in range(newn)] + [Order(1/z**newn, x)]
+                return S.One - (exp(-z**2)/sqrt(pi)) * Add(*s)
+
+        return super(erf, self)._eval_aseries(n, args0, x, logx)
+
+    as_real_imag = real_to_real_as_real_imag
+
+
+class erfc(DefinedFunction):
+    r"""
+    Complementary Error Function.
+
+    Explanation
+    ===========
+
+    The function is defined as:
+
+    .. math ::
+        \mathrm{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} \mathrm{d}t
+
+    Examples
+    ========
+
+    >>> from sympy import I, oo, erfc
+    >>> from sympy.abc import z
+
+    Several special values are known:
+
+    >>> erfc(0)
+    1
+    >>> erfc(oo)
+    0
+    >>> erfc(-oo)
+    2
+    >>> erfc(I*oo)
+    -oo*I
+    >>> erfc(-I*oo)
+    oo*I
+
+    The error function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(erfc(z))
+    erfc(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erfc(z), z)
+    -2*exp(-z**2)/sqrt(pi)
+
+    It also follows
+
+    >>> erfc(-z)
+    2 - erfc(z)
+
+    We can numerically evaluate the complementary error function to arbitrary
+    precision on the whole complex plane:
+
+    >>> erfc(4).evalf(30)
+    0.0000000154172579002800188521596734869
+
+    >>> erfc(4*I).evalf(30)
+    1.0 - 1296959.73071763923152794095062*I
+
+    See Also
+    ========
+
+    erf: Gaussian error function.
+    erfi: Imaginary error function.
+    erf2: Two-argument error function.
+    erfinv: Inverse error function.
+    erfcinv: Inverse Complementary error function.
+    erf2inv: Inverse two-argument error function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Error_function
+    .. [2] https://dlmf.nist.gov/7
+    .. [3] https://mathworld.wolfram.com/Erfc.html
+    .. [4] https://functions.wolfram.com/GammaBetaErf/Erfc
+
+    """
+
+    unbranched = True
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return -2*exp(-self.args[0]**2)/sqrt(pi)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+
+        """
+        return erfcinv
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is S.Infinity:
+                return S.Zero
+            elif arg.is_zero:
+                return S.One
+
+        if isinstance(arg, erfinv):
+            return S.One - arg.args[0]
+
+        if isinstance(arg, erfcinv):
+            return arg.args[0]
+
+        if arg.is_zero:
+            return S.One
+
+        # Try to pull out factors of I
+        t = arg.extract_multiplicatively(I)
+        if t in (S.Infinity, S.NegativeInfinity):
+            return -arg
+
+        # Try to pull out factors of -1
+        if arg.could_extract_minus_sign():
+            return 2 - cls(-arg)
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n == 0:
+            return S.One
+        elif n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            k = floor((n - 1)/S(2))
+            if len(previous_terms) > 2:
+                return -previous_terms[-2] * x**2 * (n - 2)/(n*k)
+            else:
+                return -2*S.NegativeOne**k * x**n/(n*factorial(k)*sqrt(pi))
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def _eval_is_real(self):
+        if self.args[0].is_extended_real is True:
+            return True
+        if self.args[0].is_imaginary is True:
+            return False
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        return self.rewrite(erf).rewrite("tractable", deep=True, limitvar=limitvar)
+
+    def _eval_rewrite_as_erf(self, z, **kwargs):
+        return S.One - erf(z)
+
+    def _eval_rewrite_as_erfi(self, z, **kwargs):
+        return S.One + I*erfi(I*z)
+
+    def _eval_rewrite_as_fresnels(self, z, **kwargs):
+        arg = (S.One - I)*z/sqrt(pi)
+        return S.One - (S.One + I)*(fresnelc(arg) - I*fresnels(arg))
+
+    def _eval_rewrite_as_fresnelc(self, z, **kwargs):
+        arg = (S.One-I)*z/sqrt(pi)
+        return S.One - (S.One + I)*(fresnelc(arg) - I*fresnels(arg))
+
+    def _eval_rewrite_as_meijerg(self, z, **kwargs):
+        return S.One - z/sqrt(pi)*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2)
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        return S.One - 2*z/sqrt(pi)*hyper([S.Half], [3*S.Half], -z**2)
+
+    def _eval_rewrite_as_uppergamma(self, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return S.One - sqrt(z**2)/z*(S.One - uppergamma(S.Half, z**2)/sqrt(pi))
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        return S.One - sqrt(z**2)/z + z*expint(S.Half, z**2)/sqrt(pi)
+
+    def _eval_expand_func(self, **hints):
+        return self.rewrite(erf)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.ComplexInfinity:
+            arg0 = arg.limit(x, 0, dir='-' if cdir == -1 else '+')
+        if arg0.is_zero:
+            return S.One
+        else:
+            return self.func(arg0)
+
+    as_real_imag = real_to_real_as_real_imag
+
+    def _eval_aseries(self, n, args0, x, logx):
+        return S.One - erf(*self.args)._eval_aseries(n, args0, x, logx)
+
+
+class erfi(DefinedFunction):
+    r"""
+    Imaginary error function.
+
+    Explanation
+    ===========
+
+    The function erfi is defined as:
+
+    .. math ::
+        \mathrm{erfi}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{t^2} \mathrm{d}t
+
+    Examples
+    ========
+
+    >>> from sympy import I, oo, erfi
+    >>> from sympy.abc import z
+
+    Several special values are known:
+
+    >>> erfi(0)
+    0
+    >>> erfi(oo)
+    oo
+    >>> erfi(-oo)
+    -oo
+    >>> erfi(I*oo)
+    I
+    >>> erfi(-I*oo)
+    -I
+
+    In general one can pull out factors of -1 and $I$ from the argument:
+
+    >>> erfi(-z)
+    -erfi(z)
+
+    >>> from sympy import conjugate
+    >>> conjugate(erfi(z))
+    erfi(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erfi(z), z)
+    2*exp(z**2)/sqrt(pi)
+
+    We can numerically evaluate the imaginary error function to arbitrary
+    precision on the whole complex plane:
+
+    >>> erfi(2).evalf(30)
+    18.5648024145755525987042919132
+
+    >>> erfi(-2*I).evalf(30)
+    -0.995322265018952734162069256367*I
+
+    See Also
+    ========
+
+    erf: Gaussian error function.
+    erfc: Complementary error function.
+    erf2: Two-argument error function.
+    erfinv: Inverse error function.
+    erfcinv: Inverse Complementary error function.
+    erf2inv: Inverse two-argument error function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Error_function
+    .. [2] https://mathworld.wolfram.com/Erfi.html
+    .. [3] https://functions.wolfram.com/GammaBetaErf/Erfi
+
+    """
+
+    unbranched = True
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return 2*exp(self.args[0]**2)/sqrt(pi)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, z):
+        if z.is_Number:
+            if z is S.NaN:
+                return S.NaN
+            elif z.is_zero:
+                return S.Zero
+            elif z is S.Infinity:
+                return S.Infinity
+
+        if z.is_zero:
+            return S.Zero
+
+        # Try to pull out factors of -1
+        if z.could_extract_minus_sign():
+            return -cls(-z)
+
+        # Try to pull out factors of I
+        nz = z.extract_multiplicatively(I)
+        if nz is not None:
+            if nz is S.Infinity:
+                return I
+            if isinstance(nz, erfinv):
+                return I*nz.args[0]
+            if isinstance(nz, erfcinv):
+                return I*(S.One - nz.args[0])
+            # Only happens with unevaluated erf2inv
+            if isinstance(nz, erf2inv) and nz.args[0].is_zero:
+                return I*nz.args[1]
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0 or n % 2 == 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            k = floor((n - 1)/S(2))
+            if len(previous_terms) > 2:
+                return previous_terms[-2] * x**2 * (n - 2)/(n*k)
+            else:
+                return 2 * x**n/(n*factorial(k)*sqrt(pi))
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        return self.rewrite(erf).rewrite("tractable", deep=True, limitvar=limitvar)
+
+    def _eval_rewrite_as_erf(self, z, **kwargs):
+        return -I*erf(I*z)
+
+    def _eval_rewrite_as_erfc(self, z, **kwargs):
+        return I*erfc(I*z) - I
+
+    def _eval_rewrite_as_fresnels(self, z, **kwargs):
+        arg = (S.One + I)*z/sqrt(pi)
+        return (S.One - I)*(fresnelc(arg) - I*fresnels(arg))
+
+    def _eval_rewrite_as_fresnelc(self, z, **kwargs):
+        arg = (S.One + I)*z/sqrt(pi)
+        return (S.One - I)*(fresnelc(arg) - I*fresnels(arg))
+
+    def _eval_rewrite_as_meijerg(self, z, **kwargs):
+        return z/sqrt(pi)*meijerg([S.Half], [], [0], [Rational(-1, 2)], -z**2)
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        return 2*z/sqrt(pi)*hyper([S.Half], [3*S.Half], z**2)
+
+    def _eval_rewrite_as_uppergamma(self, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return sqrt(-z**2)/z*(uppergamma(S.Half, -z**2)/sqrt(pi) - S.One)
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        return sqrt(-z**2)/z - z*expint(S.Half, -z**2)/sqrt(pi)
+
+    def _eval_expand_func(self, **hints):
+        return self.rewrite(erf)
+
+    as_real_imag = real_to_real_as_real_imag
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if x in arg.free_symbols and arg0.is_zero:
+            return 2*arg/sqrt(pi)
+        elif arg0.is_finite:
+            return self.func(arg0)
+        return self.func(arg)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        if point is S.Infinity:
+            z = self.args[0]
+            s = [factorial2(2*k - 1) / (2**k * z**(2*k + 1))
+                    for k in range(n)] + [Order(1/z**n, x)]
+            return -I + (exp(z**2)/sqrt(pi)) * Add(*s)
+
+        return super(erfi, self)._eval_aseries(n, args0, x, logx)
+
+
+class erf2(DefinedFunction):
+    r"""
+    Two-argument error function.
+
+    Explanation
+    ===========
+
+    This function is defined as:
+
+    .. math ::
+        \mathrm{erf2}(x, y) = \frac{2}{\sqrt{\pi}} \int_x^y e^{-t^2} \mathrm{d}t
+
+    Examples
+    ========
+
+    >>> from sympy import oo, erf2
+    >>> from sympy.abc import x, y
+
+    Several special values are known:
+
+    >>> erf2(0, 0)
+    0
+    >>> erf2(x, x)
+    0
+    >>> erf2(x, oo)
+    1 - erf(x)
+    >>> erf2(x, -oo)
+    -erf(x) - 1
+    >>> erf2(oo, y)
+    erf(y) - 1
+    >>> erf2(-oo, y)
+    erf(y) + 1
+
+    In general one can pull out factors of -1:
+
+    >>> erf2(-x, -y)
+    -erf2(x, y)
+
+    The error function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(erf2(x, y))
+    erf2(conjugate(x), conjugate(y))
+
+    Differentiation with respect to $x$, $y$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erf2(x, y), x)
+    -2*exp(-x**2)/sqrt(pi)
+    >>> diff(erf2(x, y), y)
+    2*exp(-y**2)/sqrt(pi)
+
+    See Also
+    ========
+
+    erf: Gaussian error function.
+    erfc: Complementary error function.
+    erfi: Imaginary error function.
+    erfinv: Inverse error function.
+    erfcinv: Inverse Complementary error function.
+    erf2inv: Inverse two-argument error function.
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/GammaBetaErf/Erf2/
+
+    """
+
+
+    def fdiff(self, argindex):
+        x, y = self.args
+        if argindex == 1:
+            return -2*exp(-x**2)/sqrt(pi)
+        elif argindex == 2:
+            return 2*exp(-y**2)/sqrt(pi)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, x, y):
+        chk = (S.Infinity, S.NegativeInfinity, S.Zero)
+        if x is S.NaN or y is S.NaN:
+            return S.NaN
+        elif x == y:
+            return S.Zero
+        elif x in chk or y in chk:
+            return erf(y) - erf(x)
+
+        if isinstance(y, erf2inv) and y.args[0] == x:
+            return y.args[1]
+
+        if x.is_zero or y.is_zero or x.is_extended_real and x.is_infinite or \
+                y.is_extended_real and y.is_infinite:
+            return erf(y) - erf(x)
+
+        #Try to pull out -1 factor
+        sign_x = x.could_extract_minus_sign()
+        sign_y = y.could_extract_minus_sign()
+        if (sign_x and sign_y):
+            return -cls(-x, -y)
+        elif (sign_x or sign_y):
+            return erf(y)-erf(x)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate(), self.args[1].conjugate())
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real and self.args[1].is_extended_real
+
+    def _eval_rewrite_as_erf(self, x, y, **kwargs):
+        return erf(y) - erf(x)
+
+    def _eval_rewrite_as_erfc(self, x, y, **kwargs):
+        return erfc(x) - erfc(y)
+
+    def _eval_rewrite_as_erfi(self, x, y, **kwargs):
+        return I*(erfi(I*x)-erfi(I*y))
+
+    def _eval_rewrite_as_fresnels(self, x, y, **kwargs):
+        return erf(y).rewrite(fresnels) - erf(x).rewrite(fresnels)
+
+    def _eval_rewrite_as_fresnelc(self, x, y, **kwargs):
+        return erf(y).rewrite(fresnelc) - erf(x).rewrite(fresnelc)
+
+    def _eval_rewrite_as_meijerg(self, x, y, **kwargs):
+        return erf(y).rewrite(meijerg) - erf(x).rewrite(meijerg)
+
+    def _eval_rewrite_as_hyper(self, x, y, **kwargs):
+        return erf(y).rewrite(hyper) - erf(x).rewrite(hyper)
+
+    def _eval_rewrite_as_uppergamma(self, x, y, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return (sqrt(y**2)/y*(S.One - uppergamma(S.Half, y**2)/sqrt(pi)) -
+            sqrt(x**2)/x*(S.One - uppergamma(S.Half, x**2)/sqrt(pi)))
+
+    def _eval_rewrite_as_expint(self, x, y, **kwargs):
+        return erf(y).rewrite(expint) - erf(x).rewrite(expint)
+
+    def _eval_expand_func(self, **hints):
+        return self.rewrite(erf)
+
+    def _eval_is_zero(self):
+        return is_eq(*self.args)
+
+class erfinv(DefinedFunction):
+    r"""
+    Inverse Error Function. The erfinv function is defined as:
+
+    .. math ::
+        \mathrm{erf}(x) = y \quad \Rightarrow \quad \mathrm{erfinv}(y) = x
+
+    Examples
+    ========
+
+    >>> from sympy import erfinv
+    >>> from sympy.abc import x
+
+    Several special values are known:
+
+    >>> erfinv(0)
+    0
+    >>> erfinv(1)
+    oo
+
+    Differentiation with respect to $x$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erfinv(x), x)
+    sqrt(pi)*exp(erfinv(x)**2)/2
+
+    We can numerically evaluate the inverse error function to arbitrary
+    precision on [-1, 1]:
+
+    >>> erfinv(0.2).evalf(30)
+    0.179143454621291692285822705344
+
+    See Also
+    ========
+
+    erf: Gaussian error function.
+    erfc: Complementary error function.
+    erfi: Imaginary error function.
+    erf2: Two-argument error function.
+    erfcinv: Inverse Complementary error function.
+    erf2inv: Inverse two-argument error function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Error_function#Inverse_functions
+    .. [2] https://functions.wolfram.com/GammaBetaErf/InverseErf/
+
+    """
+
+
+    def fdiff(self, argindex =1):
+        if argindex == 1:
+            return sqrt(pi)*exp(self.func(self.args[0])**2)*S.Half
+        else :
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+
+        """
+        return erf
+
+    @classmethod
+    def eval(cls, z):
+        if z is S.NaN:
+            return S.NaN
+        elif z is S.NegativeOne:
+            return S.NegativeInfinity
+        elif z.is_zero:
+            return S.Zero
+        elif z is S.One:
+            return S.Infinity
+
+        if isinstance(z, erf) and z.args[0].is_extended_real:
+            return z.args[0]
+
+        if z.is_zero:
+            return S.Zero
+
+        # Try to pull out factors of -1
+        nz = z.extract_multiplicatively(-1)
+        if nz is not None and (isinstance(nz, erf) and (nz.args[0]).is_extended_real):
+            return -nz.args[0]
+
+    def _eval_rewrite_as_erfcinv(self, z, **kwargs):
+        return erfcinv(1-z)
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+
+class erfcinv (DefinedFunction):
+    r"""
+    Inverse Complementary Error Function. The erfcinv function is defined as:
+
+    .. math ::
+        \mathrm{erfc}(x) = y \quad \Rightarrow \quad \mathrm{erfcinv}(y) = x
+
+    Examples
+    ========
+
+    >>> from sympy import erfcinv
+    >>> from sympy.abc import x
+
+    Several special values are known:
+
+    >>> erfcinv(1)
+    0
+    >>> erfcinv(0)
+    oo
+
+    Differentiation with respect to $x$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erfcinv(x), x)
+    -sqrt(pi)*exp(erfcinv(x)**2)/2
+
+    See Also
+    ========
+
+    erf: Gaussian error function.
+    erfc: Complementary error function.
+    erfi: Imaginary error function.
+    erf2: Two-argument error function.
+    erfinv: Inverse error function.
+    erf2inv: Inverse two-argument error function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Error_function#Inverse_functions
+    .. [2] https://functions.wolfram.com/GammaBetaErf/InverseErfc/
+
+    """
+
+
+    def fdiff(self, argindex =1):
+        if argindex == 1:
+            return -sqrt(pi)*exp(self.func(self.args[0])**2)*S.Half
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """
+        Returns the inverse of this function.
+
+        """
+        return erfc
+
+    @classmethod
+    def eval(cls, z):
+        if z is S.NaN:
+            return S.NaN
+        elif z.is_zero:
+            return S.Infinity
+        elif z is S.One:
+            return S.Zero
+        elif z == 2:
+            return S.NegativeInfinity
+
+        if z.is_zero:
+            return S.Infinity
+
+    def _eval_rewrite_as_erfinv(self, z, **kwargs):
+        return erfinv(1-z)
+
+    def _eval_is_zero(self):
+        return (self.args[0] - 1).is_zero
+
+    def _eval_is_infinite(self):
+        z = self.args[0]
+        return fuzzy_or([z.is_zero, is_eq(z, Integer(2))])
+
+
+class erf2inv(DefinedFunction):
+    r"""
+    Two-argument Inverse error function. The erf2inv function is defined as:
+
+    .. math ::
+        \mathrm{erf2}(x, w) = y \quad \Rightarrow \quad \mathrm{erf2inv}(x, y) = w
+
+    Examples
+    ========
+
+    >>> from sympy import erf2inv, oo
+    >>> from sympy.abc import x, y
+
+    Several special values are known:
+
+    >>> erf2inv(0, 0)
+    0
+    >>> erf2inv(1, 0)
+    1
+    >>> erf2inv(0, 1)
+    oo
+    >>> erf2inv(0, y)
+    erfinv(y)
+    >>> erf2inv(oo, y)
+    erfcinv(-y)
+
+    Differentiation with respect to $x$ and $y$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(erf2inv(x, y), x)
+    exp(-x**2 + erf2inv(x, y)**2)
+    >>> diff(erf2inv(x, y), y)
+    sqrt(pi)*exp(erf2inv(x, y)**2)/2
+
+    See Also
+    ========
+
+    erf: Gaussian error function.
+    erfc: Complementary error function.
+    erfi: Imaginary error function.
+    erf2: Two-argument error function.
+    erfinv: Inverse error function.
+    erfcinv: Inverse complementary error function.
+
+    References
+    ==========
+
+    .. [1] https://functions.wolfram.com/GammaBetaErf/InverseErf2/
+
+    """
+
+
+    def fdiff(self, argindex):
+        x, y = self.args
+        if argindex == 1:
+            return exp(self.func(x,y)**2-x**2)
+        elif argindex == 2:
+            return sqrt(pi)*S.Half*exp(self.func(x,y)**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, x, y):
+        if x is S.NaN or y is S.NaN:
+            return S.NaN
+        elif x.is_zero and y.is_zero:
+            return S.Zero
+        elif x.is_zero and y is S.One:
+            return S.Infinity
+        elif x is S.One and y.is_zero:
+            return S.One
+        elif x.is_zero:
+            return erfinv(y)
+        elif x is S.Infinity:
+            return erfcinv(-y)
+        elif y.is_zero:
+            return x
+        elif y is S.Infinity:
+            return erfinv(x)
+
+        if x.is_zero:
+            if y.is_zero:
+                return S.Zero
+            else:
+                return erfinv(y)
+        if y.is_zero:
+            return x
+
+    def _eval_is_zero(self):
+        x, y = self.args
+        if x.is_zero and y.is_zero:
+            return True
+
+###############################################################################
+#################### EXPONENTIAL INTEGRALS ####################################
+###############################################################################
+
+class Ei(DefinedFunction):
+    r"""
+    The classical exponential integral.
+
+    Explanation
+    ===========
+
+    For use in SymPy, this function is defined as
+
+    .. math:: \operatorname{Ei}(x) = \sum_{n=1}^\infty \frac{x^n}{n\, n!}
+                                     + \log(x) + \gamma,
+
+    where $\gamma$ is the Euler-Mascheroni constant.
+
+    If $x$ is a polar number, this defines an analytic function on the
+    Riemann surface of the logarithm. Otherwise this defines an analytic
+    function in the cut plane $\mathbb{C} \setminus (-\infty, 0]$.
+
+    **Background**
+
+    The name exponential integral comes from the following statement:
+
+    .. math:: \operatorname{Ei}(x) = \int_{-\infty}^x \frac{e^t}{t} \mathrm{d}t
+
+    If the integral is interpreted as a Cauchy principal value, this statement
+    holds for $x > 0$ and $\operatorname{Ei}(x)$ as defined above.
+
+    Examples
+    ========
+
+    >>> from sympy import Ei, polar_lift, exp_polar, I, pi
+    >>> from sympy.abc import x
+
+    >>> Ei(-1)
+    Ei(-1)
+
+    This yields a real value:
+
+    >>> Ei(-1).n(chop=True)
+    -0.219383934395520
+
+    On the other hand the analytic continuation is not real:
+
+    >>> Ei(polar_lift(-1)).n(chop=True)
+    -0.21938393439552 + 3.14159265358979*I
+
+    The exponential integral has a logarithmic branch point at the origin:
+
+    >>> Ei(x*exp_polar(2*I*pi))
+    Ei(x) + 2*I*pi
+
+    Differentiation is supported:
+
+    >>> Ei(x).diff(x)
+    exp(x)/x
+
+    The exponential integral is related to many other special functions.
+    For example:
+
+    >>> from sympy import expint, Shi
+    >>> Ei(x).rewrite(expint)
+    -expint(1, x*exp_polar(I*pi)) - I*pi
+    >>> Ei(x).rewrite(Shi)
+    Chi(x) + Shi(x)
+
+    See Also
+    ========
+
+    expint: Generalised exponential integral.
+    E1: Special case of the generalised exponential integral.
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+    uppergamma: Upper incomplete gamma function.
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/6.6
+    .. [2] https://en.wikipedia.org/wiki/Exponential_integral
+    .. [3] Abramowitz & Stegun, section 5: https://web.archive.org/web/20201128173312/http://people.math.sfu.ca/~cbm/aands/page_228.htm
+
+    """
+
+
+    @classmethod
+    def eval(cls, z):
+        if z.is_zero:
+            return S.NegativeInfinity
+        elif z is S.Infinity:
+            return S.Infinity
+        elif z is S.NegativeInfinity:
+            return S.Zero
+
+        if z.is_zero:
+            return S.NegativeInfinity
+
+        nz, n = z.extract_branch_factor()
+        if n:
+            return Ei(nz) + 2*I*pi*n
+
+    def fdiff(self, argindex=1):
+        arg = unpolarify(self.args[0])
+        if argindex == 1:
+            return exp(arg)/arg
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_evalf(self, prec):
+        if (self.args[0]/polar_lift(-1)).is_positive:
+            return super()._eval_evalf(prec) + (I*pi)._eval_evalf(prec)
+        return super()._eval_evalf(prec)
+
+    def _eval_rewrite_as_uppergamma(self, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        # XXX this does not currently work usefully because uppergamma
+        #     immediately turns into expint
+        return -uppergamma(0, polar_lift(-1)*z) - I*pi
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        return -expint(1, polar_lift(-1)*z) - I*pi
+
+    def _eval_rewrite_as_li(self, z, **kwargs):
+        if isinstance(z, log):
+            return li(z.args[0])
+        # TODO:
+        # Actually it only holds that:
+        #  Ei(z) = li(exp(z))
+        # for -pi < imag(z) <= pi
+        return li(exp(z))
+
+    def _eval_rewrite_as_Si(self, z, **kwargs):
+        if z.is_negative:
+            return Shi(z) + Chi(z) - I*pi
+        else:
+            return Shi(z) + Chi(z)
+    _eval_rewrite_as_Ci = _eval_rewrite_as_Si
+    _eval_rewrite_as_Chi = _eval_rewrite_as_Si
+    _eval_rewrite_as_Shi = _eval_rewrite_as_Si
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        return exp(z) * _eis(z)
+
+    def _eval_rewrite_as_Integral(self, z, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [z]).name)
+        return Integral(S.Exp1**t/t, (t, S.NegativeInfinity, z))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy import re
+        x0 = self.args[0].limit(x, 0)
+        arg = self.args[0].as_leading_term(x, cdir=cdir)
+        cdir = arg.dir(x, cdir)
+        if x0.is_zero:
+            c, e = arg.as_coeff_exponent(x)
+            logx = log(x) if logx is None else logx
+            return log(c) + e*logx + EulerGamma - (
+                I*pi if re(cdir).is_negative else S.Zero)
+        return super()._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        x0 = self.args[0].limit(x, 0)
+        if x0.is_zero:
+            f = self._eval_rewrite_as_Si(*self.args)
+            return f._eval_nseries(x, n, logx)
+        return super()._eval_nseries(x, n, logx)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        if point in (S.Infinity, S.NegativeInfinity):
+            z = self.args[0]
+            s = [factorial(k) / (z)**k for k in range(n)] + \
+                    [Order(1/z**n, x)]
+            return (exp(z)/z) * Add(*s)
+
+        return super(Ei, self)._eval_aseries(n, args0, x, logx)
+
+
+class expint(DefinedFunction):
+    r"""
+    Generalized exponential integral.
+
+    Explanation
+    ===========
+
+    This function is defined as
+
+    .. math:: \operatorname{E}_\nu(z) = z^{\nu - 1} \Gamma(1 - \nu, z),
+
+    where $\Gamma(1 - \nu, z)$ is the upper incomplete gamma function
+    (``uppergamma``).
+
+    Hence for $z$ with positive real part we have
+
+    .. math:: \operatorname{E}_\nu(z)
+              =   \int_1^\infty \frac{e^{-zt}}{t^\nu} \mathrm{d}t,
+
+    which explains the name.
+
+    The representation as an incomplete gamma function provides an analytic
+    continuation for $\operatorname{E}_\nu(z)$. If $\nu$ is a
+    non-positive integer, the exponential integral is thus an unbranched
+    function of $z$, otherwise there is a branch point at the origin.
+    Refer to the incomplete gamma function documentation for details of the
+    branching behavior.
+
+    Examples
+    ========
+
+    >>> from sympy import expint, S
+    >>> from sympy.abc import nu, z
+
+    Differentiation is supported. Differentiation with respect to $z$ further
+    explains the name: for integral orders, the exponential integral is an
+    iterated integral of the exponential function.
+
+    >>> expint(nu, z).diff(z)
+    -expint(nu - 1, z)
+
+    Differentiation with respect to $\nu$ has no classical expression:
+
+    >>> expint(nu, z).diff(nu)
+    -z**(nu - 1)*meijerg(((), (1, 1)), ((0, 0, 1 - nu), ()), z)
+
+    At non-postive integer orders, the exponential integral reduces to the
+    exponential function:
+
+    >>> expint(0, z)
+    exp(-z)/z
+    >>> expint(-1, z)
+    exp(-z)/z + exp(-z)/z**2
+
+    At half-integers it reduces to error functions:
+
+    >>> expint(S(1)/2, z)
+    sqrt(pi)*erfc(sqrt(z))/sqrt(z)
+
+    At positive integer orders it can be rewritten in terms of exponentials
+    and ``expint(1, z)``. Use ``expand_func()`` to do this:
+
+    >>> from sympy import expand_func
+    >>> expand_func(expint(5, z))
+    z**4*expint(1, z)/24 + (-z**3 + z**2 - 2*z + 6)*exp(-z)/24
+
+    The generalised exponential integral is essentially equivalent to the
+    incomplete gamma function:
+
+    >>> from sympy import uppergamma
+    >>> expint(nu, z).rewrite(uppergamma)
+    z**(nu - 1)*uppergamma(1 - nu, z)
+
+    As such it is branched at the origin:
+
+    >>> from sympy import exp_polar, pi, I
+    >>> expint(4, z*exp_polar(2*pi*I))
+    I*pi*z**3/3 + expint(4, z)
+    >>> expint(nu, z*exp_polar(2*pi*I))
+    z**(nu - 1)*(exp(2*I*pi*nu) - 1)*gamma(1 - nu) + expint(nu, z)
+
+    See Also
+    ========
+
+    Ei: Another related function called exponential integral.
+    E1: The classical case, returns expint(1, z).
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+    uppergamma
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/8.19
+    .. [2] https://functions.wolfram.com/GammaBetaErf/ExpIntegralE/
+    .. [3] https://en.wikipedia.org/wiki/Exponential_integral
+
+    """
+
+
+    @classmethod
+    def eval(cls, nu, z):
+        from sympy.functions.special.gamma_functions import (gamma, uppergamma)
+        nu2 = unpolarify(nu)
+        if nu != nu2:
+            return expint(nu2, z)
+        if nu.is_Integer and nu <= 0 or (not nu.is_Integer and (2*nu).is_Integer):
+            return unpolarify(expand_mul(z**(nu - 1)*uppergamma(1 - nu, z)))
+
+        # Extract branching information. This can be deduced from what is
+        # explained in lowergamma.eval().
+        z, n = z.extract_branch_factor()
+        if n is S.Zero:
+            return
+        if nu.is_integer:
+            if not nu > 0:
+                return
+            return expint(nu, z) \
+                - 2*pi*I*n*S.NegativeOne**(nu - 1)/factorial(nu - 1)*unpolarify(z)**(nu - 1)
+        else:
+            return (exp(2*I*pi*nu*n) - 1)*z**(nu - 1)*gamma(1 - nu) + expint(nu, z)
+
+    def fdiff(self, argindex):
+        nu, z = self.args
+        if argindex == 1:
+            return -z**(nu - 1)*meijerg([], [1, 1], [0, 0, 1 - nu], [], z)
+        elif argindex == 2:
+            return -expint(nu - 1, z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_uppergamma(self, nu, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return z**(nu - 1)*uppergamma(1 - nu, z)
+
+    def _eval_rewrite_as_Ei(self, nu, z, **kwargs):
+        if nu == 1:
+            return -Ei(z*exp_polar(-I*pi)) - I*pi
+        elif nu.is_Integer and nu > 1:
+            # DLMF, 8.19.7
+            x = -unpolarify(z)
+            return x**(nu - 1)/factorial(nu - 1)*E1(z).rewrite(Ei) + \
+                exp(x)/factorial(nu - 1) * \
+                Add(*[factorial(nu - k - 2)*x**k for k in range(nu - 1)])
+        else:
+            return self
+
+    def _eval_expand_func(self, **hints):
+        return self.rewrite(Ei).rewrite(expint, **hints)
+
+    def _eval_rewrite_as_Si(self, nu, z, **kwargs):
+        if nu != 1:
+            return self
+        return Shi(z) - Chi(z)
+    _eval_rewrite_as_Ci = _eval_rewrite_as_Si
+    _eval_rewrite_as_Chi = _eval_rewrite_as_Si
+    _eval_rewrite_as_Shi = _eval_rewrite_as_Si
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        if not self.args[0].has(x):
+            nu = self.args[0]
+            if nu == 1:
+                f = self._eval_rewrite_as_Si(*self.args)
+                return f._eval_nseries(x, n, logx)
+            elif nu.is_Integer and nu > 1:
+                f = self._eval_rewrite_as_Ei(*self.args)
+                return f._eval_nseries(x, n, logx)
+        return super()._eval_nseries(x, n, logx)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[1]
+        nu = self.args[0]
+
+        if point is S.Infinity:
+            z = self.args[1]
+            s = [S.NegativeOne**k * RisingFactorial(nu, k) / z**k for k in range(n)] + [Order(1/z**n, x)]
+            return (exp(-z)/z) * Add(*s)
+
+        return super(expint, self)._eval_aseries(n, args0, x, logx)
+
+    def _eval_rewrite_as_Integral(self, *args, **kwargs):
+        from sympy.integrals.integrals import Integral
+        n, x = self.args
+        t = Dummy(uniquely_named_symbol('t', args).name)
+        return Integral(t**-n * exp(-t*x), (t, 1, S.Infinity))
+
+
+def E1(z):
+    """
+    Classical case of the generalized exponential integral.
+
+    Explanation
+    ===========
+
+    This is equivalent to ``expint(1, z)``.
+
+    Examples
+    ========
+
+    >>> from sympy import E1
+    >>> E1(0)
+    expint(1, 0)
+
+    >>> E1(5)
+    expint(1, 5)
+
+    See Also
+    ========
+
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+
+    """
+    return expint(1, z)
+
+
+class li(DefinedFunction):
+    r"""
+    The classical logarithmic integral.
+
+    Explanation
+    ===========
+
+    For use in SymPy, this function is defined as
+
+    .. math:: \operatorname{li}(x) = \int_0^x \frac{1}{\log(t)} \mathrm{d}t \,.
+
+    Examples
+    ========
+
+    >>> from sympy import I, oo, li
+    >>> from sympy.abc import z
+
+    Several special values are known:
+
+    >>> li(0)
+    0
+    >>> li(1)
+    -oo
+    >>> li(oo)
+    oo
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(li(z), z)
+    1/log(z)
+
+    Defining the ``li`` function via an integral:
+    >>> from sympy import integrate
+    >>> integrate(li(z))
+    z*li(z) - Ei(2*log(z))
+
+    >>> integrate(li(z),z)
+    z*li(z) - Ei(2*log(z))
+
+
+    The logarithmic integral can also be defined in terms of ``Ei``:
+
+    >>> from sympy import Ei
+    >>> li(z).rewrite(Ei)
+    Ei(log(z))
+    >>> diff(li(z).rewrite(Ei), z)
+    1/log(z)
+
+    We can numerically evaluate the logarithmic integral to arbitrary precision
+    on the whole complex plane (except the singular points):
+
+    >>> li(2).evalf(30)
+    1.04516378011749278484458888919
+
+    >>> li(2*I).evalf(30)
+    1.0652795784357498247001125598 + 3.08346052231061726610939702133*I
+
+    We can even compute Soldner's constant by the help of mpmath:
+
+    >>> from mpmath import findroot
+    >>> findroot(li, 2)
+    1.45136923488338
+
+    Further transformations include rewriting ``li`` in terms of
+    the trigonometric integrals ``Si``, ``Ci``, ``Shi`` and ``Chi``:
+
+    >>> from sympy import Si, Ci, Shi, Chi
+    >>> li(z).rewrite(Si)
+    -log(I*log(z)) - log(1/log(z))/2 + log(log(z))/2 + Ci(I*log(z)) + Shi(log(z))
+    >>> li(z).rewrite(Ci)
+    -log(I*log(z)) - log(1/log(z))/2 + log(log(z))/2 + Ci(I*log(z)) + Shi(log(z))
+    >>> li(z).rewrite(Shi)
+    -log(1/log(z))/2 + log(log(z))/2 + Chi(log(z)) - Shi(log(z))
+    >>> li(z).rewrite(Chi)
+    -log(1/log(z))/2 + log(log(z))/2 + Chi(log(z)) - Shi(log(z))
+
+    See Also
+    ========
+
+    Li: Offset logarithmic integral.
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    E1: Special case of the generalised exponential integral.
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Logarithmic_integral
+    .. [2] https://mathworld.wolfram.com/LogarithmicIntegral.html
+    .. [3] https://dlmf.nist.gov/6
+    .. [4] https://mathworld.wolfram.com/SoldnersConstant.html
+
+    """
+
+
+    @classmethod
+    def eval(cls, z):
+        if z.is_zero:
+            return S.Zero
+        elif z is S.One:
+            return S.NegativeInfinity
+        elif z is S.Infinity:
+            return S.Infinity
+        if z.is_zero:
+            return S.Zero
+
+    def fdiff(self, argindex=1):
+        arg = self.args[0]
+        if argindex == 1:
+            return S.One / log(arg)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_conjugate(self):
+        z = self.args[0]
+        # Exclude values on the branch cut (-oo, 0)
+        if not z.is_extended_negative:
+            return self.func(z.conjugate())
+
+    def _eval_rewrite_as_Li(self, z, **kwargs):
+        return Li(z) + li(2)
+
+    def _eval_rewrite_as_Ei(self, z, **kwargs):
+        return Ei(log(z))
+
+    def _eval_rewrite_as_uppergamma(self, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return (-uppergamma(0, -log(z)) +
+                S.Half*(log(log(z)) - log(S.One/log(z))) - log(-log(z)))
+
+    def _eval_rewrite_as_Si(self, z, **kwargs):
+        return (Ci(I*log(z)) - I*Si(I*log(z)) -
+                S.Half*(log(S.One/log(z)) - log(log(z))) - log(I*log(z)))
+
+    _eval_rewrite_as_Ci = _eval_rewrite_as_Si
+
+    def _eval_rewrite_as_Shi(self, z, **kwargs):
+        return (Chi(log(z)) - Shi(log(z)) - S.Half*(log(S.One/log(z)) - log(log(z))))
+
+    _eval_rewrite_as_Chi = _eval_rewrite_as_Shi
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        return (log(z)*hyper((1, 1), (2, 2), log(z)) +
+                S.Half*(log(log(z)) - log(S.One/log(z))) + EulerGamma)
+
+    def _eval_rewrite_as_meijerg(self, z, **kwargs):
+        return (-log(-log(z)) - S.Half*(log(S.One/log(z)) - log(log(z)))
+                - meijerg(((), (1,)), ((0, 0), ()), -log(z)))
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        return z * _eis(log(z))
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        z = self.args[0]
+        s = [(log(z))**k / (factorial(k) * k) for k in range(1, n)]
+        return EulerGamma + log(log(z)) + Add(*s)
+
+    def _eval_is_zero(self):
+        z = self.args[0]
+        if z.is_zero:
+            return True
+
+class Li(DefinedFunction):
+    r"""
+    The offset logarithmic integral.
+
+    Explanation
+    ===========
+
+    For use in SymPy, this function is defined as
+
+    .. math:: \operatorname{Li}(x) = \operatorname{li}(x) - \operatorname{li}(2)
+
+    Examples
+    ========
+
+    >>> from sympy import Li
+    >>> from sympy.abc import z
+
+    The following special value is known:
+
+    >>> Li(2)
+    0
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(Li(z), z)
+    1/log(z)
+
+    The shifted logarithmic integral can be written in terms of $li(z)$:
+
+    >>> from sympy import li
+    >>> Li(z).rewrite(li)
+    li(z) - li(2)
+
+    We can numerically evaluate the logarithmic integral to arbitrary precision
+    on the whole complex plane (except the singular points):
+
+    >>> Li(2).evalf(30)
+    0
+
+    >>> Li(4).evalf(30)
+    1.92242131492155809316615998938
+
+    See Also
+    ========
+
+    li: Logarithmic integral.
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    E1: Special case of the generalised exponential integral.
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Logarithmic_integral
+    .. [2] https://mathworld.wolfram.com/LogarithmicIntegral.html
+    .. [3] https://dlmf.nist.gov/6
+
+    """
+
+
+    @classmethod
+    def eval(cls, z):
+        if z is S.Infinity:
+            return S.Infinity
+        elif z == S(2):
+            return S.Zero
+
+    def fdiff(self, argindex=1):
+        arg = self.args[0]
+        if argindex == 1:
+            return S.One / log(arg)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_evalf(self, prec):
+        return self.rewrite(li).evalf(prec)
+
+    def _eval_rewrite_as_li(self, z, **kwargs):
+        return li(z) - li(2)
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        return self.rewrite(li).rewrite("tractable", deep=True)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        f = self._eval_rewrite_as_li(*self.args)
+        return f._eval_nseries(x, n, logx)
+
+###############################################################################
+#################### TRIGONOMETRIC INTEGRALS ##################################
+###############################################################################
+
+class TrigonometricIntegral(DefinedFunction):
+    """ Base class for trigonometric integrals. """
+
+
+    @classmethod
+    def eval(cls, z):
+        if z is S.Zero:
+            return cls._atzero
+        elif z is S.Infinity:
+            return cls._atinf()
+        elif z is S.NegativeInfinity:
+            return cls._atneginf()
+
+        if z.is_zero:
+            return cls._atzero
+
+        nz = z.extract_multiplicatively(polar_lift(I))
+        if nz is None and cls._trigfunc(0) == 0:
+            nz = z.extract_multiplicatively(I)
+        if nz is not None:
+            return cls._Ifactor(nz, 1)
+        nz = z.extract_multiplicatively(polar_lift(-I))
+        if nz is not None:
+            return cls._Ifactor(nz, -1)
+
+        nz = z.extract_multiplicatively(polar_lift(-1))
+        if nz is None and cls._trigfunc(0) == 0:
+            nz = z.extract_multiplicatively(-1)
+        if nz is not None:
+            return cls._minusfactor(nz)
+
+        nz, n = z.extract_branch_factor()
+        if n == 0 and nz == z:
+            return
+        return 2*pi*I*n*cls._trigfunc(0) + cls(nz)
+
+    def fdiff(self, argindex=1):
+        arg = unpolarify(self.args[0])
+        if argindex == 1:
+            return self._trigfunc(arg)/arg
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Ei(self, z, **kwargs):
+        return self._eval_rewrite_as_expint(z).rewrite(Ei)
+
+    def _eval_rewrite_as_uppergamma(self, z, **kwargs):
+        from sympy.functions.special.gamma_functions import uppergamma
+        return self._eval_rewrite_as_expint(z).rewrite(uppergamma)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        # NOTE this is fairly inefficient
+        if self.args[0].subs(x, 0) != 0:
+            return super()._eval_nseries(x, n, logx)
+        baseseries = self._trigfunc(x)._eval_nseries(x, n, logx)
+        if self._trigfunc(0) != 0:
+            baseseries -= 1
+        baseseries = baseseries.replace(Pow, lambda t, n: t**n/n, simultaneous=False)
+        if self._trigfunc(0) != 0:
+            baseseries += EulerGamma + log(x)
+        return baseseries.subs(x, self.args[0])._eval_nseries(x, n, logx)
+
+
+class Si(TrigonometricIntegral):
+    r"""
+    Sine integral.
+
+    Explanation
+    ===========
+
+    This function is defined by
+
+    .. math:: \operatorname{Si}(z) = \int_0^z \frac{\sin{t}}{t} \mathrm{d}t.
+
+    It is an entire function.
+
+    Examples
+    ========
+
+    >>> from sympy import Si
+    >>> from sympy.abc import z
+
+    The sine integral is an antiderivative of $sin(z)/z$:
+
+    >>> Si(z).diff(z)
+    sin(z)/z
+
+    It is unbranched:
+
+    >>> from sympy import exp_polar, I, pi
+    >>> Si(z*exp_polar(2*I*pi))
+    Si(z)
+
+    Sine integral behaves much like ordinary sine under multiplication by ``I``:
+
+    >>> Si(I*z)
+    I*Shi(z)
+    >>> Si(-z)
+    -Si(z)
+
+    It can also be expressed in terms of exponential integrals, but beware
+    that the latter is branched:
+
+    >>> from sympy import expint
+    >>> Si(z).rewrite(expint)
+    -I*(-expint(1, z*exp_polar(-I*pi/2))/2 +
+         expint(1, z*exp_polar(I*pi/2))/2) + pi/2
+
+    It can be rewritten in the form of sinc function (by definition):
+
+    >>> from sympy import sinc
+    >>> Si(z).rewrite(sinc)
+    Integral(sinc(_t), (_t, 0, z))
+
+    See Also
+    ========
+
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    sinc: unnormalized sinc function
+    E1: Special case of the generalised exponential integral.
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral
+
+    """
+
+    _trigfunc = sin
+    _atzero = S.Zero
+
+    @classmethod
+    def _atinf(cls):
+        return pi*S.Half
+
+    @classmethod
+    def _atneginf(cls):
+        return -pi*S.Half
+
+    @classmethod
+    def _minusfactor(cls, z):
+        return -Si(z)
+
+    @classmethod
+    def _Ifactor(cls, z, sign):
+        return I*Shi(z)*sign
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        # XXX should we polarify z?
+        return pi/2 + (E1(polar_lift(I)*z) - E1(polar_lift(-I)*z))/2/I
+
+    def _eval_rewrite_as_Integral(self, z, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [z]).name)
+        return Integral(sinc(t), (t, 0, z))
+
+    _eval_rewrite_as_sinc =  _eval_rewrite_as_Integral
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if arg0.is_zero:
+            return arg
+        elif not arg0.is_infinite:
+            return self.func(arg0)
+        else:
+            return self
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        # Expansion at oo
+        if point is S.Infinity:
+            z = self.args[0]
+            p = [S.NegativeOne**k * factorial(2*k) / z**(2*k + 1)
+                    for k in range(n//2 + 1)] + [Order(1/z**n, x)]
+            q = [S.NegativeOne**k * factorial(2*k + 1) / z**(2*(k + 1))
+                    for k in range(n//2)] + [Order(1/z**n, x)]
+            return pi/2 - cos(z)*Add(*p) - sin(z)*Add(*q)
+
+        # All other points are not handled
+        return super(Si, self)._eval_aseries(n, args0, x, logx)
+
+    def _eval_is_zero(self):
+        z = self.args[0]
+        if z.is_zero:
+            return True
+
+
+class Ci(TrigonometricIntegral):
+    r"""
+    Cosine integral.
+
+    Explanation
+    ===========
+
+    This function is defined for positive $x$ by
+
+    .. math:: \operatorname{Ci}(x) = \gamma + \log{x}
+                         + \int_0^x \frac{\cos{t} - 1}{t} \mathrm{d}t
+           = -\int_x^\infty \frac{\cos{t}}{t} \mathrm{d}t,
+
+    where $\gamma$ is the Euler-Mascheroni constant.
+
+    We have
+
+    .. math:: \operatorname{Ci}(z) =
+        -\frac{\operatorname{E}_1\left(e^{i\pi/2} z\right)
+               + \operatorname{E}_1\left(e^{-i \pi/2} z\right)}{2}
+
+    which holds for all polar $z$ and thus provides an analytic
+    continuation to the Riemann surface of the logarithm.
+
+    The formula also holds as stated
+    for $z \in \mathbb{C}$ with $\Re(z) > 0$.
+    By lifting to the principal branch, we obtain an analytic function on the
+    cut complex plane.
+
+    Examples
+    ========
+
+    >>> from sympy import Ci
+    >>> from sympy.abc import z
+
+    The cosine integral is a primitive of $\cos(z)/z$:
+
+    >>> Ci(z).diff(z)
+    cos(z)/z
+
+    It has a logarithmic branch point at the origin:
+
+    >>> from sympy import exp_polar, I, pi
+    >>> Ci(z*exp_polar(2*I*pi))
+    Ci(z) + 2*I*pi
+
+    The cosine integral behaves somewhat like ordinary $\cos$ under
+    multiplication by $i$:
+
+    >>> from sympy import polar_lift
+    >>> Ci(polar_lift(I)*z)
+    Chi(z) + I*pi/2
+    >>> Ci(polar_lift(-1)*z)
+    Ci(z) + I*pi
+
+    It can also be expressed in terms of exponential integrals:
+
+    >>> from sympy import expint
+    >>> Ci(z).rewrite(expint)
+    -expint(1, z*exp_polar(-I*pi/2))/2 - expint(1, z*exp_polar(I*pi/2))/2
+
+    See Also
+    ========
+
+    Si: Sine integral.
+    Shi: Hyperbolic sine integral.
+    Chi: Hyperbolic cosine integral.
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    E1: Special case of the generalised exponential integral.
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral
+
+    """
+
+    _trigfunc = cos
+    _atzero = S.ComplexInfinity
+
+    @classmethod
+    def _atinf(cls):
+        return S.Zero
+
+    @classmethod
+    def _atneginf(cls):
+        return I*pi
+
+    @classmethod
+    def _minusfactor(cls, z):
+        return Ci(z) + I*pi
+
+    @classmethod
+    def _Ifactor(cls, z, sign):
+        return Chi(z) + I*pi/2*sign
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        return -(E1(polar_lift(I)*z) + E1(polar_lift(-I)*z))/2
+
+    def _eval_rewrite_as_Integral(self, z, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [z]).name)
+        return S.EulerGamma + log(z) - Integral((1-cos(t))/t, (t, 0, z))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if arg0.is_zero:
+            c, e = arg.as_coeff_exponent(x)
+            logx = log(x) if logx is None else logx
+            return log(c) + e*logx + EulerGamma
+        elif arg0.is_finite:
+            return self.func(arg0)
+        else:
+            return self
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        if point in (S.Infinity, S.NegativeInfinity):
+            z = self.args[0]
+            p = [S.NegativeOne**k * factorial(2*k) / z**(2*k + 1)
+                    for k in range(n//2 + 1)] + [Order(1/z**n, x)]
+            q = [S.NegativeOne**k * factorial(2*k + 1) / z**(2*(k + 1))
+                    for k in range(n//2)] + [Order(1/z**n, x)]
+            result = sin(z)*(Add(*p)) - cos(z)*(Add(*q))
+
+            if point is S.NegativeInfinity:
+                result += I*pi
+            return result
+
+        return super(Ci, self)._eval_aseries(n, args0, x, logx)
+
+class Shi(TrigonometricIntegral):
+    r"""
+    Sinh integral.
+
+    Explanation
+    ===========
+
+    This function is defined by
+
+    .. math:: \operatorname{Shi}(z) = \int_0^z \frac{\sinh{t}}{t} \mathrm{d}t.
+
+    It is an entire function.
+
+    Examples
+    ========
+
+    >>> from sympy import Shi
+    >>> from sympy.abc import z
+
+    The Sinh integral is a primitive of $\sinh(z)/z$:
+
+    >>> Shi(z).diff(z)
+    sinh(z)/z
+
+    It is unbranched:
+
+    >>> from sympy import exp_polar, I, pi
+    >>> Shi(z*exp_polar(2*I*pi))
+    Shi(z)
+
+    The $\sinh$ integral behaves much like ordinary $\sinh$ under
+    multiplication by $i$:
+
+    >>> Shi(I*z)
+    I*Si(z)
+    >>> Shi(-z)
+    -Shi(z)
+
+    It can also be expressed in terms of exponential integrals, but beware
+    that the latter is branched:
+
+    >>> from sympy import expint
+    >>> Shi(z).rewrite(expint)
+    expint(1, z)/2 - expint(1, z*exp_polar(I*pi))/2 - I*pi/2
+
+    See Also
+    ========
+
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Chi: Hyperbolic cosine integral.
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    E1: Special case of the generalised exponential integral.
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral
+
+    """
+
+    _trigfunc = sinh
+    _atzero = S.Zero
+
+    @classmethod
+    def _atinf(cls):
+        return S.Infinity
+
+    @classmethod
+    def _atneginf(cls):
+        return S.NegativeInfinity
+
+    @classmethod
+    def _minusfactor(cls, z):
+        return -Shi(z)
+
+    @classmethod
+    def _Ifactor(cls, z, sign):
+        return I*Si(z)*sign
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        # XXX should we polarify z?
+        return (E1(z) - E1(exp_polar(I*pi)*z))/2 - I*pi/2
+
+    def _eval_is_zero(self):
+        z = self.args[0]
+        if z.is_zero:
+            return True
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if arg0.is_zero:
+            return arg
+        elif not arg0.is_infinite:
+            return self.func(arg0)
+        else:
+            return self
+
+
+class Chi(TrigonometricIntegral):
+    r"""
+    Cosh integral.
+
+    Explanation
+    ===========
+
+    This function is defined for positive $x$ by
+
+    .. math:: \operatorname{Chi}(x) = \gamma + \log{x}
+                         + \int_0^x \frac{\cosh{t} - 1}{t} \mathrm{d}t,
+
+    where $\gamma$ is the Euler-Mascheroni constant.
+
+    We have
+
+    .. math:: \operatorname{Chi}(z) = \operatorname{Ci}\left(e^{i \pi/2}z\right)
+                         - i\frac{\pi}{2},
+
+    which holds for all polar $z$ and thus provides an analytic
+    continuation to the Riemann surface of the logarithm.
+    By lifting to the principal branch we obtain an analytic function on the
+    cut complex plane.
+
+    Examples
+    ========
+
+    >>> from sympy import Chi
+    >>> from sympy.abc import z
+
+    The $\cosh$ integral is a primitive of $\cosh(z)/z$:
+
+    >>> Chi(z).diff(z)
+    cosh(z)/z
+
+    It has a logarithmic branch point at the origin:
+
+    >>> from sympy import exp_polar, I, pi
+    >>> Chi(z*exp_polar(2*I*pi))
+    Chi(z) + 2*I*pi
+
+    The $\cosh$ integral behaves somewhat like ordinary $\cosh$ under
+    multiplication by $i$:
+
+    >>> from sympy import polar_lift
+    >>> Chi(polar_lift(I)*z)
+    Ci(z) + I*pi/2
+    >>> Chi(polar_lift(-1)*z)
+    Chi(z) + I*pi
+
+    It can also be expressed in terms of exponential integrals:
+
+    >>> from sympy import expint
+    >>> Chi(z).rewrite(expint)
+    -expint(1, z)/2 - expint(1, z*exp_polar(I*pi))/2 - I*pi/2
+
+    See Also
+    ========
+
+    Si: Sine integral.
+    Ci: Cosine integral.
+    Shi: Hyperbolic sine integral.
+    Ei: Exponential integral.
+    expint: Generalised exponential integral.
+    E1: Special case of the generalised exponential integral.
+    li: Logarithmic integral.
+    Li: Offset logarithmic integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral
+
+    """
+
+    _trigfunc = cosh
+    _atzero = S.ComplexInfinity
+
+    @classmethod
+    def _atinf(cls):
+        return S.Infinity
+
+    @classmethod
+    def _atneginf(cls):
+        return S.Infinity
+
+    @classmethod
+    def _minusfactor(cls, z):
+        return Chi(z) + I*pi
+
+    @classmethod
+    def _Ifactor(cls, z, sign):
+        return Ci(z) + I*pi/2*sign
+
+    def _eval_rewrite_as_expint(self, z, **kwargs):
+        return -I*pi/2 - (E1(z) + E1(exp_polar(I*pi)*z))/2
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.NaN:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if arg0.is_zero:
+            c, e = arg.as_coeff_exponent(x)
+            logx = log(x) if logx is None else logx
+            return log(c) + e*logx + EulerGamma
+        elif arg0.is_finite:
+            return self.func(arg0)
+        else:
+            return self
+
+
+###############################################################################
+#################### FRESNEL INTEGRALS ########################################
+###############################################################################
+
+class FresnelIntegral(DefinedFunction):
+    """ Base class for the Fresnel integrals."""
+
+    unbranched = True
+
+    @classmethod
+    def eval(cls, z):
+        # Values at positive infinities signs
+        # if any were extracted automatically
+        if z is S.Infinity:
+            return S.Half
+
+        # Value at zero
+        if z.is_zero:
+            return S.Zero
+
+        # Try to pull out factors of -1 and I
+        prefact = S.One
+        newarg = z
+        changed = False
+
+        nz = newarg.extract_multiplicatively(-1)
+        if nz is not None:
+            prefact = -prefact
+            newarg = nz
+            changed = True
+
+        nz = newarg.extract_multiplicatively(I)
+        if nz is not None:
+            prefact = cls._sign*I*prefact
+            newarg = nz
+            changed = True
+
+        if changed:
+            return prefact*cls(newarg)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return self._trigfunc(S.Half*pi*self.args[0]**2)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_is_extended_real(self):
+        return self.args[0].is_extended_real
+
+    _eval_is_finite = _eval_is_extended_real
+
+    def _eval_is_zero(self):
+        return self.args[0].is_zero
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    as_real_imag = real_to_real_as_real_imag
+
+
+class fresnels(FresnelIntegral):
+    r"""
+    Fresnel integral S.
+
+    Explanation
+    ===========
+
+    This function is defined by
+
+    .. math:: \operatorname{S}(z) = \int_0^z \sin{\frac{\pi}{2} t^2} \mathrm{d}t.
+
+    It is an entire function.
+
+    Examples
+    ========
+
+    >>> from sympy import I, oo, fresnels
+    >>> from sympy.abc import z
+
+    Several special values are known:
+
+    >>> fresnels(0)
+    0
+    >>> fresnels(oo)
+    1/2
+    >>> fresnels(-oo)
+    -1/2
+    >>> fresnels(I*oo)
+    -I/2
+    >>> fresnels(-I*oo)
+    I/2
+
+    In general one can pull out factors of -1 and $i$ from the argument:
+
+    >>> fresnels(-z)
+    -fresnels(z)
+    >>> fresnels(I*z)
+    -I*fresnels(z)
+
+    The Fresnel S integral obeys the mirror symmetry
+    $\overline{S(z)} = S(\bar{z})$:
+
+    >>> from sympy import conjugate
+    >>> conjugate(fresnels(z))
+    fresnels(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(fresnels(z), z)
+    sin(pi*z**2/2)
+
+    Defining the Fresnel functions via an integral:
+
+    >>> from sympy import integrate, pi, sin, expand_func
+    >>> integrate(sin(pi*z**2/2), z)
+    3*fresnels(z)*gamma(3/4)/(4*gamma(7/4))
+    >>> expand_func(integrate(sin(pi*z**2/2), z))
+    fresnels(z)
+
+    We can numerically evaluate the Fresnel integral to arbitrary precision
+    on the whole complex plane:
+
+    >>> fresnels(2).evalf(30)
+    0.343415678363698242195300815958
+
+    >>> fresnels(-2*I).evalf(30)
+    0.343415678363698242195300815958*I
+
+    See Also
+    ========
+
+    fresnelc: Fresnel cosine integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fresnel_integral
+    .. [2] https://dlmf.nist.gov/7
+    .. [3] https://mathworld.wolfram.com/FresnelIntegrals.html
+    .. [4] https://functions.wolfram.com/GammaBetaErf/FresnelS
+    .. [5] The converging factors for the fresnel integrals
+            by John W. Wrench Jr. and Vicki Alley
+
+    """
+    _trigfunc = sin
+    _sign = -S.One
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 1:
+                p = previous_terms[-1]
+                return (-pi**2*x**4*(4*n - 1)/(8*n*(2*n + 1)*(4*n + 3))) * p
+            else:
+                return x**3 * (-x**4)**n * (S(2)**(-2*n - 1)*pi**(2*n + 1)) / ((4*n + 3)*factorial(2*n + 1))
+
+    def _eval_rewrite_as_erf(self, z, **kwargs):
+        return (S.One + I)/4 * (erf((S.One + I)/2*sqrt(pi)*z) - I*erf((S.One - I)/2*sqrt(pi)*z))
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        return pi*z**3/6 * hyper([Rational(3, 4)], [Rational(3, 2), Rational(7, 4)], -pi**2*z**4/16)
+
+    def _eval_rewrite_as_meijerg(self, z, **kwargs):
+        return (pi*z**Rational(9, 4) / (sqrt(2)*(z**2)**Rational(3, 4)*(-z)**Rational(3, 4))
+                * meijerg([], [1], [Rational(3, 4)], [Rational(1, 4), 0], -pi**2*z**4/16))
+
+    def _eval_rewrite_as_Integral(self, z, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [z]).name)
+        return Integral(sin(pi*t**2/2), (t, 0, z))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.series.order import Order
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.ComplexInfinity:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if arg0.is_zero:
+            return pi*arg**3/6
+        elif arg0 in [S.Infinity, S.NegativeInfinity]:
+            s = 1 if arg0 is S.Infinity else -1
+            return s*S.Half + Order(x, x)
+        else:
+            return self.func(arg0)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        # Expansion at oo and -oo
+        if point in [S.Infinity, -S.Infinity]:
+            z = self.args[0]
+
+            # expansion of S(x) = S1(x*sqrt(pi/2)), see reference[5] page 1-8
+            # as only real infinities are dealt with, sin and cos are O(1)
+            p = [S.NegativeOne**k * factorial(4*k + 1) /
+                 (2**(2*k + 2) * z**(4*k + 3) * 2**(2*k)*factorial(2*k))
+                 for k in range(0, n) if 4*k + 3 < n]
+            q = [1/(2*z)] + [S.NegativeOne**k * factorial(4*k - 1) /
+                 (2**(2*k + 1) * z**(4*k + 1) * 2**(2*k - 1)*factorial(2*k - 1))
+                 for k in range(1, n) if 4*k + 1 < n]
+
+            p = [-sqrt(2/pi)*t for t in p]
+            q = [-sqrt(2/pi)*t for t in q]
+            s = 1 if point is S.Infinity else -1
+            # The expansion at oo is 1/2 + some odd powers of z
+            # To get the expansion at -oo, replace z by -z and flip the sign
+            # The result -1/2 + the same odd powers of z as before.
+            return s*S.Half + (sin(z**2)*Add(*p) + cos(z**2)*Add(*q)
+                ).subs(x, sqrt(2/pi)*x) + Order(1/z**n, x)
+
+        # All other points are not handled
+        return super()._eval_aseries(n, args0, x, logx)
+
+
+class fresnelc(FresnelIntegral):
+    r"""
+    Fresnel integral C.
+
+    Explanation
+    ===========
+
+    This function is defined by
+
+    .. math:: \operatorname{C}(z) = \int_0^z \cos{\frac{\pi}{2} t^2} \mathrm{d}t.
+
+    It is an entire function.
+
+    Examples
+    ========
+
+    >>> from sympy import I, oo, fresnelc
+    >>> from sympy.abc import z
+
+    Several special values are known:
+
+    >>> fresnelc(0)
+    0
+    >>> fresnelc(oo)
+    1/2
+    >>> fresnelc(-oo)
+    -1/2
+    >>> fresnelc(I*oo)
+    I/2
+    >>> fresnelc(-I*oo)
+    -I/2
+
+    In general one can pull out factors of -1 and $i$ from the argument:
+
+    >>> fresnelc(-z)
+    -fresnelc(z)
+    >>> fresnelc(I*z)
+    I*fresnelc(z)
+
+    The Fresnel C integral obeys the mirror symmetry
+    $\overline{C(z)} = C(\bar{z})$:
+
+    >>> from sympy import conjugate
+    >>> conjugate(fresnelc(z))
+    fresnelc(conjugate(z))
+
+    Differentiation with respect to $z$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(fresnelc(z), z)
+    cos(pi*z**2/2)
+
+    Defining the Fresnel functions via an integral:
+
+    >>> from sympy import integrate, pi, cos, expand_func
+    >>> integrate(cos(pi*z**2/2), z)
+    fresnelc(z)*gamma(1/4)/(4*gamma(5/4))
+    >>> expand_func(integrate(cos(pi*z**2/2), z))
+    fresnelc(z)
+
+    We can numerically evaluate the Fresnel integral to arbitrary precision
+    on the whole complex plane:
+
+    >>> fresnelc(2).evalf(30)
+    0.488253406075340754500223503357
+
+    >>> fresnelc(-2*I).evalf(30)
+    -0.488253406075340754500223503357*I
+
+    See Also
+    ========
+
+    fresnels: Fresnel sine integral.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fresnel_integral
+    .. [2] https://dlmf.nist.gov/7
+    .. [3] https://mathworld.wolfram.com/FresnelIntegrals.html
+    .. [4] https://functions.wolfram.com/GammaBetaErf/FresnelC
+    .. [5] The converging factors for the fresnel integrals
+            by John W. Wrench Jr. and Vicki Alley
+
+    """
+    _trigfunc = cos
+    _sign = S.One
+
+    @staticmethod
+    @cacheit
+    def taylor_term(n, x, *previous_terms):
+        if n < 0:
+            return S.Zero
+        else:
+            x = sympify(x)
+            if len(previous_terms) > 1:
+                p = previous_terms[-1]
+                return (-pi**2*x**4*(4*n - 3)/(8*n*(2*n - 1)*(4*n + 1))) * p
+            else:
+                return x * (-x**4)**n * (S(2)**(-2*n)*pi**(2*n)) / ((4*n + 1)*factorial(2*n))
+
+    def _eval_rewrite_as_erf(self, z, **kwargs):
+        return (S.One - I)/4 * (erf((S.One + I)/2*sqrt(pi)*z) + I*erf((S.One - I)/2*sqrt(pi)*z))
+
+    def _eval_rewrite_as_hyper(self, z, **kwargs):
+        return z * hyper([Rational(1, 4)], [S.Half, Rational(5, 4)], -pi**2*z**4/16)
+
+    def _eval_rewrite_as_meijerg(self, z, **kwargs):
+        return (pi*z**Rational(3, 4) / (sqrt(2)*root(z**2, 4)*root(-z, 4))
+                * meijerg([], [1], [Rational(1, 4)], [Rational(3, 4), 0], -pi**2*z**4/16))
+
+    def _eval_rewrite_as_Integral(self, z, **kwargs):
+        from sympy.integrals.integrals import Integral
+        t = Dummy(uniquely_named_symbol('t', [z]).name)
+        return Integral(cos(pi*t**2/2), (t, 0, z))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.series.order import Order
+        arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir)
+        arg0 = arg.subs(x, 0)
+
+        if arg0 is S.ComplexInfinity:
+            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+        if arg0.is_zero:
+            return arg
+        elif arg0 in [S.Infinity, S.NegativeInfinity]:
+            s = 1 if arg0 is S.Infinity else -1
+            return s*S.Half + Order(x, x)
+        else:
+            return self.func(arg0)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        # Expansion at oo
+        if point in [S.Infinity, -S.Infinity]:
+            z = self.args[0]
+
+            # expansion of C(x) = C1(x*sqrt(pi/2)), see reference[5] page 1-8
+            # as only real infinities are dealt with, sin and cos are O(1)
+            p = [S.NegativeOne**k * factorial(4*k + 1) /
+                 (2**(2*k + 2) * z**(4*k + 3) * 2**(2*k)*factorial(2*k))
+                 for k in range(n) if 4*k + 3 < n]
+            q = [1/(2*z)] + [S.NegativeOne**k * factorial(4*k - 1) /
+                 (2**(2*k + 1) * z**(4*k + 1) * 2**(2*k - 1)*factorial(2*k - 1))
+                 for k in range(1, n) if 4*k + 1 < n]
+
+            p = [-sqrt(2/pi)*t for t in p]
+            q = [ sqrt(2/pi)*t for t in q]
+            s = 1 if point is S.Infinity else -1
+            # The expansion at oo is 1/2 + some odd powers of z
+            # To get the expansion at -oo, replace z by -z and flip the sign
+            # The result -1/2 + the same odd powers of z as before.
+            return s*S.Half + (cos(z**2)*Add(*p) + sin(z**2)*Add(*q)
+                ).subs(x, sqrt(2/pi)*x) + Order(1/z**n, x)
+
+        # All other points are not handled
+        return super()._eval_aseries(n, args0, x, logx)
+
+
+###############################################################################
+#################### HELPER FUNCTIONS #########################################
+###############################################################################
+
+
+class _erfs(DefinedFunction):
+    """
+    Helper function to make the $\\mathrm{erf}(z)$ function
+    tractable for the Gruntz algorithm.
+
+    """
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_zero:
+            return S.One
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        point = args0[0]
+
+        # Expansion at oo
+        if point is S.Infinity:
+            z = self.args[0]
+            l = [1/sqrt(pi) * factorial(2*k)*(-S(
+                 4))**(-k)/factorial(k) * (1/z)**(2*k + 1) for k in range(n)]
+            o = Order(1/z**(2*n + 1), x)
+            # It is very inefficient to first add the order and then do the nseries
+            return (Add(*l))._eval_nseries(x, n, logx) + o
+
+        # Expansion at I*oo
+        t = point.extract_multiplicatively(I)
+        if t is S.Infinity:
+            z = self.args[0]
+            # TODO: is the series really correct?
+            l = [1/sqrt(pi) * factorial(2*k)*(-S(
+                 4))**(-k)/factorial(k) * (1/z)**(2*k + 1) for k in range(n)]
+            o = Order(1/z**(2*n + 1), x)
+            # It is very inefficient to first add the order and then do the nseries
+            return (Add(*l))._eval_nseries(x, n, logx) + o
+
+        # All other points are not handled
+        return super()._eval_aseries(n, args0, x, logx)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            z = self.args[0]
+            return -2/sqrt(pi) + 2*z*_erfs(z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_intractable(self, z, **kwargs):
+        return (S.One - erf(z))*exp(z**2)
+
+
+class _eis(DefinedFunction):
+    """
+    Helper function to make the $\\mathrm{Ei}(z)$ and $\\mathrm{li}(z)$
+    functions tractable for the Gruntz algorithm.
+
+    """
+
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        if args0[0] not in (S.Infinity, S.NegativeInfinity):
+            return super()._eval_aseries(n, args0, x, logx)
+
+        z = self.args[0]
+        l = [factorial(k) * (1/z)**(k + 1) for k in range(n)]
+        o = Order(1/z**(n + 1), x)
+        # It is very inefficient to first add the order and then do the nseries
+        return (Add(*l))._eval_nseries(x, n, logx) + o
+
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            z = self.args[0]
+            return S.One / z - _eis(z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_intractable(self, z, **kwargs):
+        return exp(-z)*Ei(z)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        x0 = self.args[0].limit(x, 0)
+        if x0.is_zero:
+            f = self._eval_rewrite_as_intractable(*self.args)
+            return f._eval_as_leading_term(x, logx=logx, cdir=cdir)
+        return super()._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        x0 = self.args[0].limit(x, 0)
+        if x0.is_zero:
+            f = self._eval_rewrite_as_intractable(*self.args)
+            return f._eval_nseries(x, n, logx)
+        return super()._eval_nseries(x, n, logx)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/gamma_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/gamma_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..73a5a1585154c603e9c510b3c61144039e0e5502
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/gamma_functions.py
@@ -0,0 +1,1344 @@
+from math import prod
+
+from sympy.core import Add, S, Dummy, expand_func
+from sympy.core.expr import Expr
+from sympy.core.function import DefinedFunction, ArgumentIndexError, PoleError
+from sympy.core.logic import fuzzy_and, fuzzy_not
+from sympy.core.numbers import Rational, pi, oo, I
+from sympy.core.power import Pow
+from sympy.functions.special.zeta_functions import zeta
+from sympy.functions.special.error_functions import erf, erfc, Ei
+from sympy.functions.elementary.complexes import re, unpolarify
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.integers import ceiling, floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin, cos, cot
+from sympy.functions.combinatorial.numbers import bernoulli, harmonic
+from sympy.functions.combinatorial.factorials import factorial, rf, RisingFactorial
+from sympy.utilities.misc import as_int
+
+from mpmath import mp, workprec
+from mpmath.libmp.libmpf import prec_to_dps
+
+def intlike(n):
+    try:
+        as_int(n, strict=False)
+        return True
+    except ValueError:
+        return False
+
+###############################################################################
+############################ COMPLETE GAMMA FUNCTION ##########################
+###############################################################################
+
+class gamma(DefinedFunction):
+    r"""
+    The gamma function
+
+    .. math::
+        \Gamma(x) := \int^{\infty}_{0} t^{x-1} e^{-t} \mathrm{d}t.
+
+    Explanation
+    ===========
+
+    The ``gamma`` function implements the function which passes through the
+    values of the factorial function (i.e., $\Gamma(n) = (n - 1)!$ when n is
+    an integer). More generally, $\Gamma(z)$ is defined in the whole complex
+    plane except at the negative integers where there are simple poles.
+
+    Examples
+    ========
+
+    >>> from sympy import S, I, pi, gamma
+    >>> from sympy.abc import x
+
+    Several special values are known:
+
+    >>> gamma(1)
+    1
+    >>> gamma(4)
+    6
+    >>> gamma(S(3)/2)
+    sqrt(pi)/2
+
+    The ``gamma`` function obeys the mirror symmetry:
+
+    >>> from sympy import conjugate
+    >>> conjugate(gamma(x))
+    gamma(conjugate(x))
+
+    Differentiation with respect to $x$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(gamma(x), x)
+    gamma(x)*polygamma(0, x)
+
+    Series expansion is also supported:
+
+    >>> from sympy import series
+    >>> series(gamma(x), x, 0, 3)
+    1/x - EulerGamma + x*(EulerGamma**2/2 + pi**2/12) + x**2*(-EulerGamma*pi**2/12 - zeta(3)/3 - EulerGamma**3/6) + O(x**3)
+
+    We can numerically evaluate the ``gamma`` function to arbitrary precision
+    on the whole complex plane:
+
+    >>> gamma(pi).evalf(40)
+    2.288037795340032417959588909060233922890
+    >>> gamma(1+I).evalf(20)
+    0.49801566811835604271 - 0.15494982830181068512*I
+
+    See Also
+    ========
+
+    lowergamma: Lower incomplete gamma function.
+    uppergamma: Upper incomplete gamma function.
+    polygamma: Polygamma function.
+    loggamma: Log Gamma function.
+    digamma: Digamma function.
+    trigamma: Trigamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gamma_function
+    .. [2] https://dlmf.nist.gov/5
+    .. [3] https://mathworld.wolfram.com/GammaFunction.html
+    .. [4] https://functions.wolfram.com/GammaBetaErf/Gamma/
+
+    """
+
+    unbranched = True
+    _singularities = (S.ComplexInfinity,)
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return self.func(self.args[0])*polygamma(0, self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, arg):
+        if arg.is_Number:
+            if arg is S.NaN:
+                return S.NaN
+            elif arg is oo:
+                return oo
+            elif intlike(arg):
+                if arg.is_positive:
+                    return factorial(arg - 1)
+                else:
+                    return S.ComplexInfinity
+            elif arg.is_Rational:
+                if arg.q == 2:
+                    n = abs(arg.p) // arg.q
+
+                    if arg.is_positive:
+                        k, coeff = n, S.One
+                    else:
+                        n = k = n + 1
+
+                        if n & 1 == 0:
+                            coeff = S.One
+                        else:
+                            coeff = S.NegativeOne
+
+                    coeff *= prod(range(3, 2*k, 2))
+
+                    if arg.is_positive:
+                        return coeff*sqrt(pi) / 2**n
+                    else:
+                        return 2**n*sqrt(pi) / coeff
+
+    def _eval_expand_func(self, **hints):
+        arg = self.args[0]
+        if arg.is_Rational:
+            if abs(arg.p) > arg.q:
+                x = Dummy('x')
+                n = arg.p // arg.q
+                p = arg.p - n*arg.q
+                return self.func(x + n)._eval_expand_func().subs(x, Rational(p, arg.q))
+
+        if arg.is_Add:
+            coeff, tail = arg.as_coeff_add()
+            if coeff and coeff.q != 1:
+                intpart = floor(coeff)
+                tail = (coeff - intpart,) + tail
+                coeff = intpart
+            tail = arg._new_rawargs(*tail, reeval=False)
+            return self.func(tail)*RisingFactorial(tail, coeff)
+
+        return self.func(*self.args)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0].conjugate())
+
+    def _eval_is_real(self):
+        x = self.args[0]
+        if x.is_nonpositive and x.is_integer:
+            return False
+        if intlike(x) and x <= 0:
+            return False
+        if x.is_positive or x.is_noninteger:
+            return True
+
+    def _eval_is_positive(self):
+        x = self.args[0]
+        if x.is_positive:
+            return True
+        elif x.is_noninteger:
+            return floor(x).is_even
+
+    def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs):
+        return exp(loggamma(z))
+
+    def _eval_rewrite_as_factorial(self, z, **kwargs):
+        return factorial(z - 1)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        x0 = self.args[0].limit(x, 0)
+        if not (x0.is_Integer and x0 <= 0):
+            return super()._eval_nseries(x, n, logx)
+        t = self.args[0] - x0
+        return (self.func(t + 1)/rf(self.args[0], -x0 + 1))._eval_nseries(x, n, logx)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[0]
+        x0 = arg.subs(x, 0)
+
+        if x0.is_integer and x0.is_nonpositive:
+            n = -x0
+            res = S.NegativeOne**n/self.func(n + 1)
+            return res/(arg + n).as_leading_term(x)
+        elif not x0.is_infinite:
+            return self.func(x0)
+        raise PoleError()
+
+
+###############################################################################
+################## LOWER and UPPER INCOMPLETE GAMMA FUNCTIONS #################
+###############################################################################
+
+class lowergamma(DefinedFunction):
+    r"""
+    The lower incomplete gamma function.
+
+    Explanation
+    ===========
+
+    It can be defined as the meromorphic continuation of
+
+    .. math::
+        \gamma(s, x) := \int_0^x t^{s-1} e^{-t} \mathrm{d}t = \Gamma(s) - \Gamma(s, x).
+
+    This can be shown to be the same as
+
+    .. math::
+        \gamma(s, x) = \frac{x^s}{s} {}_1F_1\left({s \atop s+1} \middle| -x\right),
+
+    where ${}_1F_1$ is the (confluent) hypergeometric function.
+
+    Examples
+    ========
+
+    >>> from sympy import lowergamma, S
+    >>> from sympy.abc import s, x
+    >>> lowergamma(s, x)
+    lowergamma(s, x)
+    >>> lowergamma(3, x)
+    -2*(x**2/2 + x + 1)*exp(-x) + 2
+    >>> lowergamma(-S(1)/2, x)
+    -2*sqrt(pi)*erf(sqrt(x)) - 2*exp(-x)/sqrt(x)
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    uppergamma: Upper incomplete gamma function.
+    polygamma: Polygamma function.
+    loggamma: Log Gamma function.
+    digamma: Digamma function.
+    trigamma: Trigamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Incomplete_gamma_function#Lower_incomplete_gamma_function
+    .. [2] Abramowitz, Milton; Stegun, Irene A., eds. (1965), Chapter 6,
+           Section 5, Handbook of Mathematical Functions with Formulas, Graphs,
+           and Mathematical Tables
+    .. [3] https://dlmf.nist.gov/8
+    .. [4] https://functions.wolfram.com/GammaBetaErf/Gamma2/
+    .. [5] https://functions.wolfram.com/GammaBetaErf/Gamma3/
+
+    """
+
+
+    def fdiff(self, argindex=2):
+        from sympy.functions.special.hyper import meijerg
+        if argindex == 2:
+            a, z = self.args
+            return exp(-unpolarify(z))*z**(a - 1)
+        elif argindex == 1:
+            a, z = self.args
+            return gamma(a)*digamma(a) - log(z)*uppergamma(a, z) \
+                - meijerg([], [1, 1], [0, 0, a], [], z)
+
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, a, x):
+        # For lack of a better place, we use this one to extract branching
+        # information. The following can be
+        # found in the literature (c/f references given above), albeit scattered:
+        # 1) For fixed x != 0, lowergamma(s, x) is an entire function of s
+        # 2) For fixed positive integers s, lowergamma(s, x) is an entire
+        #    function of x.
+        # 3) For fixed non-positive integers s,
+        #    lowergamma(s, exp(I*2*pi*n)*x) =
+        #              2*pi*I*n*(-1)**(-s)/factorial(-s) + lowergamma(s, x)
+        #    (this follows from lowergamma(s, x).diff(x) = x**(s-1)*exp(-x)).
+        # 4) For fixed non-integral s,
+        #    lowergamma(s, x) = x**s*gamma(s)*lowergamma_unbranched(s, x),
+        #    where lowergamma_unbranched(s, x) is an entire function (in fact
+        #    of both s and x), i.e.
+        #    lowergamma(s, exp(2*I*pi*n)*x) = exp(2*pi*I*n*a)*lowergamma(a, x)
+        if x is S.Zero:
+            return S.Zero
+        nx, n = x.extract_branch_factor()
+        if a.is_integer and a.is_positive:
+            nx = unpolarify(x)
+            if nx != x:
+                return lowergamma(a, nx)
+        elif a.is_integer and a.is_nonpositive:
+            if n != 0:
+                return 2*pi*I*n*S.NegativeOne**(-a)/factorial(-a) + lowergamma(a, nx)
+        elif n != 0:
+            return exp(2*pi*I*n*a)*lowergamma(a, nx)
+
+        # Special values.
+        if a.is_Number:
+            if a is S.One:
+                return S.One - exp(-x)
+            elif a is S.Half:
+                return sqrt(pi)*erf(sqrt(x))
+            elif a.is_Integer or (2*a).is_Integer:
+                b = a - 1
+                if b.is_positive:
+                    if a.is_integer:
+                        return factorial(b) - exp(-x) * factorial(b) * Add(*[x ** k / factorial(k) for k in range(a)])
+                    else:
+                        return gamma(a)*(lowergamma(S.Half, x)/sqrt(pi) - exp(-x)*Add(*[x**(k - S.Half)/gamma(S.Half + k) for k in range(1, a + S.Half)]))
+
+                if not a.is_Integer:
+                    return S.NegativeOne**(S.Half - a)*pi*erf(sqrt(x))/gamma(1 - a) + exp(-x)*Add(*[x**(k + a - 1)*gamma(a)/gamma(a + k) for k in range(1, Rational(3, 2) - a)])
+
+        if x.is_zero:
+            return S.Zero
+
+    def _eval_evalf(self, prec):
+        if all(x.is_number for x in self.args):
+            a = self.args[0]._to_mpmath(prec)
+            z = self.args[1]._to_mpmath(prec)
+            with workprec(prec):
+                res = mp.gammainc(a, 0, z)
+            return Expr._from_mpmath(res, prec)
+        else:
+            return self
+
+    def _eval_conjugate(self):
+        x = self.args[1]
+        if x not in (S.Zero, S.NegativeInfinity):
+            return self.func(self.args[0].conjugate(), x.conjugate())
+
+    def _eval_is_meromorphic(self, x, a):
+        # By https://en.wikipedia.org/wiki/Incomplete_gamma_function#Holomorphic_extension,
+        #    lowergamma(s, z) = z**s*gamma(s)*gammastar(s, z),
+        # where gammastar(s, z) is holomorphic for all s and z.
+        # Hence the singularities of lowergamma are z = 0  (branch
+        # point) and nonpositive integer values of s (poles of gamma(s)).
+        s, z = self.args
+        args_merom = fuzzy_and([z._eval_is_meromorphic(x, a),
+            s._eval_is_meromorphic(x, a)])
+        if not args_merom:
+            return args_merom
+        z0 = z.subs(x, a)
+        if s.is_integer:
+            return fuzzy_and([s.is_positive, z0.is_finite])
+        s0 = s.subs(x, a)
+        return fuzzy_and([s0.is_finite, z0.is_finite, fuzzy_not(z0.is_zero)])
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import O
+        s, z = self.args
+        if args0[0] is oo and not z.has(x):
+            coeff = z**s*exp(-z)
+            sum_expr = sum(z**k/rf(s, k + 1) for k in range(n - 1))
+            o = O(z**s*s**(-n))
+            return coeff*sum_expr + o
+        return super()._eval_aseries(n, args0, x, logx)
+
+    def _eval_rewrite_as_uppergamma(self, s, x, **kwargs):
+        return gamma(s) - uppergamma(s, x)
+
+    def _eval_rewrite_as_expint(self, s, x, **kwargs):
+        from sympy.functions.special.error_functions import expint
+        if s.is_integer and s.is_nonpositive:
+            return self
+        return self.rewrite(uppergamma).rewrite(expint)
+
+    def _eval_is_zero(self):
+        x = self.args[1]
+        if x.is_zero:
+            return True
+
+
+class uppergamma(DefinedFunction):
+    r"""
+    The upper incomplete gamma function.
+
+    Explanation
+    ===========
+
+    It can be defined as the meromorphic continuation of
+
+    .. math::
+        \Gamma(s, x) := \int_x^\infty t^{s-1} e^{-t} \mathrm{d}t = \Gamma(s) - \gamma(s, x).
+
+    where $\gamma(s, x)$ is the lower incomplete gamma function,
+    :class:`lowergamma`. This can be shown to be the same as
+
+    .. math::
+        \Gamma(s, x) = \Gamma(s) - \frac{x^s}{s} {}_1F_1\left({s \atop s+1} \middle| -x\right),
+
+    where ${}_1F_1$ is the (confluent) hypergeometric function.
+
+    The upper incomplete gamma function is also essentially equivalent to the
+    generalized exponential integral:
+
+    .. math::
+        \operatorname{E}_{n}(x) = \int_{1}^{\infty}{\frac{e^{-xt}}{t^n} \, dt} = x^{n-1}\Gamma(1-n,x).
+
+    Examples
+    ========
+
+    >>> from sympy import uppergamma, S
+    >>> from sympy.abc import s, x
+    >>> uppergamma(s, x)
+    uppergamma(s, x)
+    >>> uppergamma(3, x)
+    2*(x**2/2 + x + 1)*exp(-x)
+    >>> uppergamma(-S(1)/2, x)
+    -2*sqrt(pi)*erfc(sqrt(x)) + 2*exp(-x)/sqrt(x)
+    >>> uppergamma(-2, x)
+    expint(3, x)/x**2
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    lowergamma: Lower incomplete gamma function.
+    polygamma: Polygamma function.
+    loggamma: Log Gamma function.
+    digamma: Digamma function.
+    trigamma: Trigamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Incomplete_gamma_function#Upper_incomplete_gamma_function
+    .. [2] Abramowitz, Milton; Stegun, Irene A., eds. (1965), Chapter 6,
+           Section 5, Handbook of Mathematical Functions with Formulas, Graphs,
+           and Mathematical Tables
+    .. [3] https://dlmf.nist.gov/8
+    .. [4] https://functions.wolfram.com/GammaBetaErf/Gamma2/
+    .. [5] https://functions.wolfram.com/GammaBetaErf/Gamma3/
+    .. [6] https://en.wikipedia.org/wiki/Exponential_integral#Relation_with_other_functions
+
+    """
+
+
+    def fdiff(self, argindex=2):
+        from sympy.functions.special.hyper import meijerg
+        if argindex == 2:
+            a, z = self.args
+            return -exp(-unpolarify(z))*z**(a - 1)
+        elif argindex == 1:
+            a, z = self.args
+            return uppergamma(a, z)*log(z) + meijerg([], [1, 1], [0, 0, a], [], z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_evalf(self, prec):
+        if all(x.is_number for x in self.args):
+            a = self.args[0]._to_mpmath(prec)
+            z = self.args[1]._to_mpmath(prec)
+            with workprec(prec):
+                res = mp.gammainc(a, z, mp.inf)
+            return Expr._from_mpmath(res, prec)
+        return self
+
+    @classmethod
+    def eval(cls, a, z):
+        from sympy.functions.special.error_functions import expint
+        if z.is_Number:
+            if z is S.NaN:
+                return S.NaN
+            elif z is oo:
+                return S.Zero
+            elif z.is_zero:
+                if re(a).is_positive:
+                    return gamma(a)
+
+        # We extract branching information here. C/f lowergamma.
+        nx, n = z.extract_branch_factor()
+        if a.is_integer and a.is_positive:
+            nx = unpolarify(z)
+            if z != nx:
+                return uppergamma(a, nx)
+        elif a.is_integer and a.is_nonpositive:
+            if n != 0:
+                return -2*pi*I*n*S.NegativeOne**(-a)/factorial(-a) + uppergamma(a, nx)
+        elif n != 0:
+            return gamma(a)*(1 - exp(2*pi*I*n*a)) + exp(2*pi*I*n*a)*uppergamma(a, nx)
+
+        # Special values.
+        if a.is_Number:
+            if a is S.Zero and z.is_positive:
+                return -Ei(-z)
+            elif a is S.One:
+                return exp(-z)
+            elif a is S.Half:
+                return sqrt(pi)*erfc(sqrt(z))
+            elif a.is_Integer or (2*a).is_Integer:
+                b = a - 1
+                if b.is_positive:
+                    if a.is_integer:
+                        return exp(-z) * factorial(b) * Add(*[z**k / factorial(k)
+                                                              for k in range(a)])
+                    else:
+                        return (gamma(a) * erfc(sqrt(z)) +
+                                S.NegativeOne**(a - S(3)/2) * exp(-z) * sqrt(z)
+                                * Add(*[gamma(-S.Half - k) * (-z)**k / gamma(1-a)
+                                        for k in range(a - S.Half)]))
+                elif b.is_Integer:
+                    return expint(-b, z)*unpolarify(z)**(b + 1)
+
+                if not a.is_Integer:
+                    return (S.NegativeOne**(S.Half - a) * pi*erfc(sqrt(z))/gamma(1-a)
+                            - z**a * exp(-z) * Add(*[z**k * gamma(a) / gamma(a+k+1)
+                                                     for k in range(S.Half - a)]))
+
+        if a.is_zero and z.is_positive:
+            return -Ei(-z)
+
+        if z.is_zero and re(a).is_positive:
+            return gamma(a)
+
+    def _eval_conjugate(self):
+        z = self.args[1]
+        if z not in (S.Zero, S.NegativeInfinity):
+            return self.func(self.args[0].conjugate(), z.conjugate())
+
+    def _eval_is_meromorphic(self, x, a):
+        return lowergamma._eval_is_meromorphic(self, x, a)
+
+    def _eval_rewrite_as_lowergamma(self, s, x, **kwargs):
+        return gamma(s) - lowergamma(s, x)
+
+    def _eval_rewrite_as_tractable(self, s, x, **kwargs):
+        return exp(loggamma(s)) - lowergamma(s, x)
+
+    def _eval_rewrite_as_expint(self, s, x, **kwargs):
+        from sympy.functions.special.error_functions import expint
+        return expint(1 - s, x)*x**s
+
+
+###############################################################################
+###################### POLYGAMMA and LOGGAMMA FUNCTIONS #######################
+###############################################################################
+
+class polygamma(DefinedFunction):
+    r"""
+    The function ``polygamma(n, z)`` returns ``log(gamma(z)).diff(n + 1)``.
+
+    Explanation
+    ===========
+
+    It is a meromorphic function on $\mathbb{C}$ and defined as the $(n+1)$-th
+    derivative of the logarithm of the gamma function:
+
+    .. math::
+        \psi^{(n)} (z) := \frac{\mathrm{d}^{n+1}}{\mathrm{d} z^{n+1}} \log\Gamma(z).
+
+    For `n` not a nonnegative integer the generalization by Espinosa and Moll [5]_
+    is used:
+
+    .. math:: \psi(s,z) = \frac{\zeta'(s+1, z) + (\gamma + \psi(-s)) \zeta(s+1, z)}
+        {\Gamma(-s)}
+
+    Examples
+    ========
+
+    Several special values are known:
+
+    >>> from sympy import S, polygamma
+    >>> polygamma(0, 1)
+    -EulerGamma
+    >>> polygamma(0, 1/S(2))
+    -2*log(2) - EulerGamma
+    >>> polygamma(0, 1/S(3))
+    -log(3) - sqrt(3)*pi/6 - EulerGamma - log(sqrt(3))
+    >>> polygamma(0, 1/S(4))
+    -pi/2 - log(4) - log(2) - EulerGamma
+    >>> polygamma(0, 2)
+    1 - EulerGamma
+    >>> polygamma(0, 23)
+    19093197/5173168 - EulerGamma
+
+    >>> from sympy import oo, I
+    >>> polygamma(0, oo)
+    oo
+    >>> polygamma(0, -oo)
+    oo
+    >>> polygamma(0, I*oo)
+    oo
+    >>> polygamma(0, -I*oo)
+    oo
+
+    Differentiation with respect to $x$ is supported:
+
+    >>> from sympy import Symbol, diff
+    >>> x = Symbol("x")
+    >>> diff(polygamma(0, x), x)
+    polygamma(1, x)
+    >>> diff(polygamma(0, x), x, 2)
+    polygamma(2, x)
+    >>> diff(polygamma(0, x), x, 3)
+    polygamma(3, x)
+    >>> diff(polygamma(1, x), x)
+    polygamma(2, x)
+    >>> diff(polygamma(1, x), x, 2)
+    polygamma(3, x)
+    >>> diff(polygamma(2, x), x)
+    polygamma(3, x)
+    >>> diff(polygamma(2, x), x, 2)
+    polygamma(4, x)
+
+    >>> n = Symbol("n")
+    >>> diff(polygamma(n, x), x)
+    polygamma(n + 1, x)
+    >>> diff(polygamma(n, x), x, 2)
+    polygamma(n + 2, x)
+
+    We can rewrite ``polygamma`` functions in terms of harmonic numbers:
+
+    >>> from sympy import harmonic
+    >>> polygamma(0, x).rewrite(harmonic)
+    harmonic(x - 1) - EulerGamma
+    >>> polygamma(2, x).rewrite(harmonic)
+    2*harmonic(x - 1, 3) - 2*zeta(3)
+    >>> ni = Symbol("n", integer=True)
+    >>> polygamma(ni, x).rewrite(harmonic)
+    (-1)**(n + 1)*(-harmonic(x - 1, n + 1) + zeta(n + 1))*factorial(n)
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    lowergamma: Lower incomplete gamma function.
+    uppergamma: Upper incomplete gamma function.
+    loggamma: Log Gamma function.
+    digamma: Digamma function.
+    trigamma: Trigamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Polygamma_function
+    .. [2] https://mathworld.wolfram.com/PolygammaFunction.html
+    .. [3] https://functions.wolfram.com/GammaBetaErf/PolyGamma/
+    .. [4] https://functions.wolfram.com/GammaBetaErf/PolyGamma2/
+    .. [5] O. Espinosa and V. Moll, "A generalized polygamma function",
+           *Integral Transforms and Special Functions* (2004), 101-115.
+
+    """
+
+    @classmethod
+    def eval(cls, n, z):
+        if n is S.NaN or z is S.NaN:
+            return S.NaN
+        elif z is oo:
+            return oo if n.is_zero else S.Zero
+        elif z.is_Integer and z.is_nonpositive:
+            return S.ComplexInfinity
+        elif n is S.NegativeOne:
+            return loggamma(z) - log(2*pi) / 2
+        elif n.is_zero:
+            if z is -oo or z.extract_multiplicatively(I) in (oo, -oo):
+                return oo
+            elif z.is_Integer:
+                return harmonic(z-1) - S.EulerGamma
+            elif z.is_Rational:
+                # TODO n == 1 also can do some rational z
+                p, q = z.as_numer_denom()
+                # only expand for small denominators to avoid creating long expressions
+                if q <= 6:
+                    return expand_func(polygamma(S.Zero, z, evaluate=False))
+        elif n.is_integer and n.is_nonnegative:
+            nz = unpolarify(z)
+            if z != nz:
+                return polygamma(n, nz)
+            if z.is_Integer:
+                return S.NegativeOne**(n+1) * factorial(n) * zeta(n+1, z)
+            elif z is S.Half:
+                return S.NegativeOne**(n+1) * factorial(n) * (2**(n+1)-1) * zeta(n+1)
+
+    def _eval_is_real(self):
+        if self.args[0].is_positive and self.args[1].is_positive:
+            return True
+
+    def _eval_is_complex(self):
+        z = self.args[1]
+        is_negative_integer = fuzzy_and([z.is_negative, z.is_integer])
+        return fuzzy_and([z.is_complex, fuzzy_not(is_negative_integer)])
+
+    def _eval_is_positive(self):
+        n, z = self.args
+        if n.is_positive:
+            if n.is_odd and z.is_real:
+                return True
+            if n.is_even and z.is_positive:
+                return False
+
+    def _eval_is_negative(self):
+        n, z = self.args
+        if n.is_positive:
+            if n.is_even and z.is_positive:
+                return True
+            if n.is_odd and z.is_real:
+                return False
+
+    def _eval_expand_func(self, **hints):
+        n, z = self.args
+
+        if n.is_Integer and n.is_nonnegative:
+            if z.is_Add:
+                coeff = z.args[0]
+                if coeff.is_Integer:
+                    e = -(n + 1)
+                    if coeff > 0:
+                        tail = Add(*[Pow(
+                            z - i, e) for i in range(1, int(coeff) + 1)])
+                    else:
+                        tail = -Add(*[Pow(
+                            z + i, e) for i in range(int(-coeff))])
+                    return polygamma(n, z - coeff) + S.NegativeOne**n*factorial(n)*tail
+
+            elif z.is_Mul:
+                coeff, z = z.as_two_terms()
+                if coeff.is_Integer and coeff.is_positive:
+                    tail = [polygamma(n, z + Rational(
+                        i, coeff)) for i in range(int(coeff))]
+                    if n == 0:
+                        return Add(*tail)/coeff + log(coeff)
+                    else:
+                        return Add(*tail)/coeff**(n + 1)
+                z *= coeff
+
+        if n == 0 and z.is_Rational:
+            p, q = z.as_numer_denom()
+
+            # Reference:
+            #   Values of the polygamma functions at rational arguments, J. Choi, 2007
+            part_1 = -S.EulerGamma - pi * cot(p * pi / q) / 2 - log(q) + Add(
+                *[cos(2 * k * pi * p / q) * log(2 * sin(k * pi / q)) for k in range(1, q)])
+
+            if z > 0:
+                n = floor(z)
+                z0 = z - n
+                return part_1 + Add(*[1 / (z0 + k) for k in range(n)])
+            elif z < 0:
+                n = floor(1 - z)
+                z0 = z + n
+                return part_1 - Add(*[1 / (z0 - 1 - k) for k in range(n)])
+
+        if n == -1:
+            return loggamma(z) - log(2*pi) / 2
+        if n.is_integer is False or n.is_nonnegative is False:
+            s = Dummy("s")
+            dzt = zeta(s, z).diff(s).subs(s, n+1)
+            return (dzt + (S.EulerGamma + digamma(-n)) * zeta(n+1, z)) / gamma(-n)
+
+        return polygamma(n, z)
+
+    def _eval_rewrite_as_zeta(self, n, z, **kwargs):
+        if n.is_integer and n.is_positive:
+            return S.NegativeOne**(n + 1)*factorial(n)*zeta(n + 1, z)
+
+    def _eval_rewrite_as_harmonic(self, n, z, **kwargs):
+        if n.is_integer:
+            if n.is_zero:
+                return harmonic(z - 1) - S.EulerGamma
+            else:
+                return S.NegativeOne**(n+1) * factorial(n) * (zeta(n+1) - harmonic(z-1, n+1))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.series.order import Order
+        n, z = [a.as_leading_term(x) for a in self.args]
+        o = Order(z, x)
+        if n == 0 and o.contains(1/x):
+            logx = log(x) if logx is None else logx
+            return o.getn() * logx
+        else:
+            return self.func(n, z)
+
+    def fdiff(self, argindex=2):
+        if argindex == 2:
+            n, z = self.args[:2]
+            return polygamma(n + 1, z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        if args0[1] != oo or not \
+                (self.args[0].is_Integer and self.args[0].is_nonnegative):
+            return super()._eval_aseries(n, args0, x, logx)
+        z = self.args[1]
+        N = self.args[0]
+
+        if N == 0:
+            # digamma function series
+            # Abramowitz & Stegun, p. 259, 6.3.18
+            r = log(z) - 1/(2*z)
+            o = None
+            if n < 2:
+                o = Order(1/z, x)
+            else:
+                m = ceiling((n + 1)//2)
+                l = [bernoulli(2*k) / (2*k*z**(2*k)) for k in range(1, m)]
+                r -= Add(*l)
+                o = Order(1/z**n, x)
+            return r._eval_nseries(x, n, logx) + o
+        else:
+            # proper polygamma function
+            # Abramowitz & Stegun, p. 260, 6.4.10
+            # We return terms to order higher than O(x**n) on purpose
+            # -- otherwise we would not be able to return any terms for
+            #    quite a long time!
+            fac = gamma(N)
+            e0 = fac + N*fac/(2*z)
+            m = ceiling((n + 1)//2)
+            for k in range(1, m):
+                fac = fac*(2*k + N - 1)*(2*k + N - 2) / ((2*k)*(2*k - 1))
+                e0 += bernoulli(2*k)*fac/z**(2*k)
+            o = Order(1/z**(2*m), x)
+            if n == 0:
+                o = Order(1/z, x)
+            elif n == 1:
+                o = Order(1/z**2, x)
+            r = e0._eval_nseries(z, n, logx) + o
+            return (-1 * (-1/z)**N * r)._eval_nseries(x, n, logx)
+
+    def _eval_evalf(self, prec):
+        if not all(i.is_number for i in self.args):
+            return
+        s = self.args[0]._to_mpmath(prec+12)
+        z = self.args[1]._to_mpmath(prec+12)
+        if mp.isint(z) and z <= 0:
+            return S.ComplexInfinity
+        with workprec(prec+12):
+            if mp.isint(s) and s >= 0:
+                res = mp.polygamma(s, z)
+            else:
+                zt = mp.zeta(s+1, z)
+                dzt = mp.zeta(s+1, z, 1)
+                res = (dzt + (mp.euler + mp.digamma(-s)) * zt) * mp.rgamma(-s)
+        return Expr._from_mpmath(res, prec)
+
+
+class loggamma(DefinedFunction):
+    r"""
+    The ``loggamma`` function implements the logarithm of the
+    gamma function (i.e., $\log\Gamma(x)$).
+
+    Examples
+    ========
+
+    Several special values are known. For numerical integral
+    arguments we have:
+
+    >>> from sympy import loggamma
+    >>> loggamma(-2)
+    oo
+    >>> loggamma(0)
+    oo
+    >>> loggamma(1)
+    0
+    >>> loggamma(2)
+    0
+    >>> loggamma(3)
+    log(2)
+
+    And for symbolic values:
+
+    >>> from sympy import Symbol
+    >>> n = Symbol("n", integer=True, positive=True)
+    >>> loggamma(n)
+    log(gamma(n))
+    >>> loggamma(-n)
+    oo
+
+    For half-integral values:
+
+    >>> from sympy import S
+    >>> loggamma(S(5)/2)
+    log(3*sqrt(pi)/4)
+    >>> loggamma(n/2)
+    log(2**(1 - n)*sqrt(pi)*gamma(n)/gamma(n/2 + 1/2))
+
+    And general rational arguments:
+
+    >>> from sympy import expand_func
+    >>> L = loggamma(S(16)/3)
+    >>> expand_func(L).doit()
+    -5*log(3) + loggamma(1/3) + log(4) + log(7) + log(10) + log(13)
+    >>> L = loggamma(S(19)/4)
+    >>> expand_func(L).doit()
+    -4*log(4) + loggamma(3/4) + log(3) + log(7) + log(11) + log(15)
+    >>> L = loggamma(S(23)/7)
+    >>> expand_func(L).doit()
+    -3*log(7) + log(2) + loggamma(2/7) + log(9) + log(16)
+
+    The ``loggamma`` function has the following limits towards infinity:
+
+    >>> from sympy import oo
+    >>> loggamma(oo)
+    oo
+    >>> loggamma(-oo)
+    zoo
+
+    The ``loggamma`` function obeys the mirror symmetry
+    if $x \in \mathbb{C} \setminus \{-\infty, 0\}$:
+
+    >>> from sympy.abc import x
+    >>> from sympy import conjugate
+    >>> conjugate(loggamma(x))
+    loggamma(conjugate(x))
+
+    Differentiation with respect to $x$ is supported:
+
+    >>> from sympy import diff
+    >>> diff(loggamma(x), x)
+    polygamma(0, x)
+
+    Series expansion is also supported:
+
+    >>> from sympy import series
+    >>> series(loggamma(x), x, 0, 4).cancel()
+    -log(x) - EulerGamma*x + pi**2*x**2/12 - x**3*zeta(3)/3 + O(x**4)
+
+    We can numerically evaluate the ``loggamma`` function
+    to arbitrary precision on the whole complex plane:
+
+    >>> from sympy import I
+    >>> loggamma(5).evalf(30)
+    3.17805383034794561964694160130
+    >>> loggamma(I).evalf(20)
+    -0.65092319930185633889 - 1.8724366472624298171*I
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    lowergamma: Lower incomplete gamma function.
+    uppergamma: Upper incomplete gamma function.
+    polygamma: Polygamma function.
+    digamma: Digamma function.
+    trigamma: Trigamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gamma_function
+    .. [2] https://dlmf.nist.gov/5
+    .. [3] https://mathworld.wolfram.com/LogGammaFunction.html
+    .. [4] https://functions.wolfram.com/GammaBetaErf/LogGamma/
+
+    """
+    @classmethod
+    def eval(cls, z):
+        if z.is_integer:
+            if z.is_nonpositive:
+                return oo
+            elif z.is_positive:
+                return log(gamma(z))
+        elif z.is_rational:
+            p, q = z.as_numer_denom()
+            # Half-integral values:
+            if p.is_positive and q == 2:
+                return log(sqrt(pi) * 2**(1 - p) * gamma(p) / gamma((p + 1)*S.Half))
+
+        if z is oo:
+            return oo
+        elif abs(z) is oo:
+            return S.ComplexInfinity
+        if z is S.NaN:
+            return S.NaN
+
+    def _eval_expand_func(self, **hints):
+        from sympy.concrete.summations import Sum
+        z = self.args[0]
+
+        if z.is_Rational:
+            p, q = z.as_numer_denom()
+            # General rational arguments (u + p/q)
+            # Split z as n + p/q with p < q
+            n = p // q
+            p = p - n*q
+            if p.is_positive and q.is_positive and p < q:
+                k = Dummy("k")
+                if n.is_positive:
+                    return loggamma(p / q) - n*log(q) + Sum(log((k - 1)*q + p), (k, 1, n))
+                elif n.is_negative:
+                    return loggamma(p / q) - n*log(q) + pi*I*n - Sum(log(k*q - p), (k, 1, -n))
+                elif n.is_zero:
+                    return loggamma(p / q)
+
+        return self
+
+    def _eval_nseries(self, x, n, logx=None, cdir=0):
+        x0 = self.args[0].limit(x, 0)
+        if x0.is_zero:
+            f = self._eval_rewrite_as_intractable(*self.args)
+            return f._eval_nseries(x, n, logx)
+        return super()._eval_nseries(x, n, logx)
+
+    def _eval_aseries(self, n, args0, x, logx):
+        from sympy.series.order import Order
+        if args0[0] != oo:
+            return super()._eval_aseries(n, args0, x, logx)
+        z = self.args[0]
+        r = log(z)*(z - S.Half) - z + log(2*pi)/2
+        l = [bernoulli(2*k) / (2*k*(2*k - 1)*z**(2*k - 1)) for k in range(1, n)]
+        o = None
+        if n == 0:
+            o = Order(1, x)
+        else:
+            o = Order(1/z**n, x)
+        # It is very inefficient to first add the order and then do the nseries
+        return (r + Add(*l))._eval_nseries(x, n, logx) + o
+
+    def _eval_rewrite_as_intractable(self, z, **kwargs):
+        return log(gamma(z))
+
+    def _eval_is_real(self):
+        z = self.args[0]
+        if z.is_positive:
+            return True
+        elif z.is_nonpositive:
+            return False
+
+    def _eval_conjugate(self):
+        z = self.args[0]
+        if z not in (S.Zero, S.NegativeInfinity):
+            return self.func(z.conjugate())
+
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return polygamma(0, self.args[0])
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+
+class digamma(DefinedFunction):
+    r"""
+    The ``digamma`` function is the first derivative of the ``loggamma``
+    function
+
+    .. math::
+        \psi(x) := \frac{\mathrm{d}}{\mathrm{d} z} \log\Gamma(z)
+                = \frac{\Gamma'(z)}{\Gamma(z) }.
+
+    In this case, ``digamma(z) = polygamma(0, z)``.
+
+    Examples
+    ========
+
+    >>> from sympy import digamma
+    >>> digamma(0)
+    zoo
+    >>> from sympy import Symbol
+    >>> z = Symbol('z')
+    >>> digamma(z)
+    polygamma(0, z)
+
+    To retain ``digamma`` as it is:
+
+    >>> digamma(0, evaluate=False)
+    digamma(0)
+    >>> digamma(z, evaluate=False)
+    digamma(z)
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    lowergamma: Lower incomplete gamma function.
+    uppergamma: Upper incomplete gamma function.
+    polygamma: Polygamma function.
+    loggamma: Log Gamma function.
+    trigamma: Trigamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Digamma_function
+    .. [2] https://mathworld.wolfram.com/DigammaFunction.html
+    .. [3] https://functions.wolfram.com/GammaBetaErf/PolyGamma2/
+
+    """
+    def _eval_evalf(self, prec):
+        z = self.args[0]
+        nprec = prec_to_dps(prec)
+        return polygamma(0, z).evalf(n=nprec)
+
+    def fdiff(self, argindex=1):
+        z = self.args[0]
+        return polygamma(0, z).fdiff()
+
+    def _eval_is_real(self):
+        z = self.args[0]
+        return polygamma(0, z).is_real
+
+    def _eval_is_positive(self):
+        z = self.args[0]
+        return polygamma(0, z).is_positive
+
+    def _eval_is_negative(self):
+        z = self.args[0]
+        return polygamma(0, z).is_negative
+
+    def _eval_aseries(self, n, args0, x, logx):
+        as_polygamma = self.rewrite(polygamma)
+        args0 = [S.Zero,] + args0
+        return as_polygamma._eval_aseries(n, args0, x, logx)
+
+    @classmethod
+    def eval(cls, z):
+        return polygamma(0, z)
+
+    def _eval_expand_func(self, **hints):
+        z = self.args[0]
+        return polygamma(0, z).expand(func=True)
+
+    def _eval_rewrite_as_harmonic(self, z, **kwargs):
+        return harmonic(z - 1) - S.EulerGamma
+
+    def _eval_rewrite_as_polygamma(self, z, **kwargs):
+        return polygamma(0, z)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        z = self.args[0]
+        return polygamma(0, z).as_leading_term(x)
+
+
+
+class trigamma(DefinedFunction):
+    r"""
+    The ``trigamma`` function is the second derivative of the ``loggamma``
+    function
+
+    .. math::
+        \psi^{(1)}(z) := \frac{\mathrm{d}^{2}}{\mathrm{d} z^{2}} \log\Gamma(z).
+
+    In this case, ``trigamma(z) = polygamma(1, z)``.
+
+    Examples
+    ========
+
+    >>> from sympy import trigamma
+    >>> trigamma(0)
+    zoo
+    >>> from sympy import Symbol
+    >>> z = Symbol('z')
+    >>> trigamma(z)
+    polygamma(1, z)
+
+    To retain ``trigamma`` as it is:
+
+    >>> trigamma(0, evaluate=False)
+    trigamma(0)
+    >>> trigamma(z, evaluate=False)
+    trigamma(z)
+
+
+    See Also
+    ========
+
+    gamma: Gamma function.
+    lowergamma: Lower incomplete gamma function.
+    uppergamma: Upper incomplete gamma function.
+    polygamma: Polygamma function.
+    loggamma: Log Gamma function.
+    digamma: Digamma function.
+    sympy.functions.special.beta_functions.beta: Euler Beta function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Trigamma_function
+    .. [2] https://mathworld.wolfram.com/TrigammaFunction.html
+    .. [3] https://functions.wolfram.com/GammaBetaErf/PolyGamma2/
+
+    """
+    def _eval_evalf(self, prec):
+        z = self.args[0]
+        nprec = prec_to_dps(prec)
+        return polygamma(1, z).evalf(n=nprec)
+
+    def fdiff(self, argindex=1):
+        z = self.args[0]
+        return polygamma(1, z).fdiff()
+
+    def _eval_is_real(self):
+        z = self.args[0]
+        return polygamma(1, z).is_real
+
+    def _eval_is_positive(self):
+        z = self.args[0]
+        return polygamma(1, z).is_positive
+
+    def _eval_is_negative(self):
+        z = self.args[0]
+        return polygamma(1, z).is_negative
+
+    def _eval_aseries(self, n, args0, x, logx):
+        as_polygamma = self.rewrite(polygamma)
+        args0 = [S.One,] + args0
+        return as_polygamma._eval_aseries(n, args0, x, logx)
+
+    @classmethod
+    def eval(cls, z):
+        return polygamma(1, z)
+
+    def _eval_expand_func(self, **hints):
+        z = self.args[0]
+        return polygamma(1, z).expand(func=True)
+
+    def _eval_rewrite_as_zeta(self, z, **kwargs):
+        return zeta(2, z)
+
+    def _eval_rewrite_as_polygamma(self, z, **kwargs):
+        return polygamma(1, z)
+
+    def _eval_rewrite_as_harmonic(self, z, **kwargs):
+        return -harmonic(z - 1, 2) + pi**2 / 6
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        z = self.args[0]
+        return polygamma(1, z).as_leading_term(x)
+
+
+###############################################################################
+##################### COMPLETE MULTIVARIATE GAMMA FUNCTION ####################
+###############################################################################
+
+
+class multigamma(DefinedFunction):
+    r"""
+    The multivariate gamma function is a generalization of the gamma function
+
+    .. math::
+        \Gamma_p(z) = \pi^{p(p-1)/4}\prod_{k=1}^p \Gamma[z + (1 - k)/2].
+
+    In a special case, ``multigamma(x, 1) = gamma(x)``.
+
+    Examples
+    ========
+
+    >>> from sympy import S, multigamma
+    >>> from sympy import Symbol
+    >>> x = Symbol('x')
+    >>> p = Symbol('p', positive=True, integer=True)
+
+    >>> multigamma(x, p)
+    pi**(p*(p - 1)/4)*Product(gamma(-_k/2 + x + 1/2), (_k, 1, p))
+
+    Several special values are known:
+
+    >>> multigamma(1, 1)
+    1
+    >>> multigamma(4, 1)
+    6
+    >>> multigamma(S(3)/2, 1)
+    sqrt(pi)/2
+
+    Writing ``multigamma`` in terms of the ``gamma`` function:
+
+    >>> multigamma(x, 1)
+    gamma(x)
+
+    >>> multigamma(x, 2)
+    sqrt(pi)*gamma(x)*gamma(x - 1/2)
+
+    >>> multigamma(x, 3)
+    pi**(3/2)*gamma(x)*gamma(x - 1)*gamma(x - 1/2)
+
+    Parameters
+    ==========
+
+    p : order or dimension of the multivariate gamma function
+
+    See Also
+    ========
+
+    gamma, lowergamma, uppergamma, polygamma, loggamma, digamma, trigamma,
+    sympy.functions.special.beta_functions.beta
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Multivariate_gamma_function
+
+    """
+    unbranched = True
+
+    def fdiff(self, argindex=2):
+        from sympy.concrete.summations import Sum
+        if argindex == 2:
+            x, p = self.args
+            k = Dummy("k")
+            return self.func(x, p)*Sum(polygamma(0, x + (1 - k)/2), (k, 1, p))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, x, p):
+        from sympy.concrete.products import Product
+        if p.is_positive is False or p.is_integer is False:
+            raise ValueError('Order parameter p must be positive integer.')
+        k = Dummy("k")
+        return (pi**(p*(p - 1)/4)*Product(gamma(x + (1 - k)/2),
+                                          (k, 1, p))).doit()
+
+    def _eval_conjugate(self):
+        x, p = self.args
+        return self.func(x.conjugate(), p)
+
+    def _eval_is_real(self):
+        x, p = self.args
+        y = 2*x
+        if y.is_integer and (y <= (p - 1)) is True:
+            return False
+        if intlike(y) and (y <= (p - 1)):
+            return False
+        if y > (p - 1) or y.is_noninteger:
+            return True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/hyper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/hyper.py
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--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/hyper.py
@@ -0,0 +1,1185 @@
+"""Hypergeometric and Meijer G-functions"""
+from collections import Counter
+
+from sympy.core import S, Mod
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.function import DefinedFunction, Derivative, ArgumentIndexError
+
+from sympy.core.containers import Tuple
+from sympy.core.mul import Mul
+from sympy.core.numbers import I, pi, oo, zoo
+from sympy.core.parameters import global_parameters
+from sympy.core.relational import Ne
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import Dummy
+
+from sympy.external.gmpy import lcm
+from sympy.functions import (sqrt, exp, log, sin, cos, asin, atan,
+        sinh, cosh, asinh, acosh, atanh, acoth)
+from sympy.functions import factorial, RisingFactorial
+from sympy.functions.elementary.complexes import Abs, re, unpolarify
+from sympy.functions.elementary.exponential import exp_polar
+from sympy.functions.elementary.integers import ceiling
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.logic.boolalg import (And, Or)
+from sympy import ordered
+
+
+class TupleArg(Tuple):
+
+    # This method is only needed because hyper._eval_as_leading_term falls back
+    # (via super()) on using Function._eval_as_leading_term, which in turn
+    # calls as_leading_term on the args of the hyper. Ideally hyper should just
+    # have an _eval_as_leading_term method that handles all cases and this
+    # method should be removed because leading terms of tuples don't make
+    # sense.
+    def as_leading_term(self, *x, logx=None, cdir=0):
+        return TupleArg(*[f.as_leading_term(*x, logx=logx, cdir=cdir) for f in self.args])
+
+    def limit(self, x, xlim, dir='+'):
+        """ Compute limit x->xlim.
+        """
+        from sympy.series.limits import limit
+        return TupleArg(*[limit(f, x, xlim, dir) for f in self.args])
+
+
+# TODO should __new__ accept **options?
+# TODO should constructors should check if parameters are sensible?
+
+
+def _prep_tuple(v):
+    """
+    Turn an iterable argument *v* into a tuple and unpolarify, since both
+    hypergeometric and meijer g-functions are unbranched in their parameters.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.special.hyper import _prep_tuple
+    >>> _prep_tuple([1, 2, 3])
+    (1, 2, 3)
+    >>> _prep_tuple((4, 5))
+    (4, 5)
+    >>> _prep_tuple((7, 8, 9))
+    (7, 8, 9)
+
+    """
+    return TupleArg(*[unpolarify(x) for x in v])
+
+
+class TupleParametersBase(DefinedFunction):
+    """ Base class that takes care of differentiation, when some of
+        the arguments are actually tuples. """
+    # This is not deduced automatically since there are Tuples as arguments.
+    is_commutative = True
+
+    def _eval_derivative(self, s):
+        try:
+            res = 0
+            if self.args[0].has(s) or self.args[1].has(s):
+                for i, p in enumerate(self._diffargs):
+                    m = self._diffargs[i].diff(s)
+                    if m != 0:
+                        res += self.fdiff((1, i))*m
+            return res + self.fdiff(3)*self.args[2].diff(s)
+        except (ArgumentIndexError, NotImplementedError):
+            return Derivative(self, s)
+
+
+class hyper(TupleParametersBase):
+    r"""
+    The generalized hypergeometric function is defined by a series where
+    the ratios of successive terms are a rational function of the summation
+    index. When convergent, it is continued analytically to the largest
+    possible domain.
+
+    Explanation
+    ===========
+
+    The hypergeometric function depends on two vectors of parameters, called
+    the numerator parameters $a_p$, and the denominator parameters
+    $b_q$. It also has an argument $z$. The series definition is
+
+    .. math ::
+        {}_pF_q\left(\begin{matrix} a_1, \cdots, a_p \\ b_1, \cdots, b_q \end{matrix}
+                     \middle| z \right)
+        = \sum_{n=0}^\infty \frac{(a_1)_n \cdots (a_p)_n}{(b_1)_n \cdots (b_q)_n}
+                            \frac{z^n}{n!},
+
+    where $(a)_n = (a)(a+1)\cdots(a+n-1)$ denotes the rising factorial.
+
+    If one of the $b_q$ is a non-positive integer then the series is
+    undefined unless one of the $a_p$ is a larger (i.e., smaller in
+    magnitude) non-positive integer. If none of the $b_q$ is a
+    non-positive integer and one of the $a_p$ is a non-positive
+    integer, then the series reduces to a polynomial. To simplify the
+    following discussion, we assume that none of the $a_p$ or
+    $b_q$ is a non-positive integer. For more details, see the
+    references.
+
+    The series converges for all $z$ if $p \le q$, and thus
+    defines an entire single-valued function in this case. If $p =
+    q+1$ the series converges for $|z| < 1$, and can be continued
+    analytically into a half-plane. If $p > q+1$ the series is
+    divergent for all $z$.
+
+    Please note the hypergeometric function constructor currently does *not*
+    check if the parameters actually yield a well-defined function.
+
+    Examples
+    ========
+
+    The parameters $a_p$ and $b_q$ can be passed as arbitrary
+    iterables, for example:
+
+    >>> from sympy import hyper
+    >>> from sympy.abc import x, n, a
+    >>> h = hyper((1, 2, 3), [3, 4], x); h
+    hyper((1, 2), (4,), x)
+    >>> hyper((3, 1, 2), [3, 4], x, evaluate=False)  # don't remove duplicates
+    hyper((1, 2, 3), (3, 4), x)
+
+    There is also pretty printing (it looks better using Unicode):
+
+    >>> from sympy import pprint
+    >>> pprint(h, use_unicode=False)
+      _
+     |_  /1, 2 |  \
+     |   |     | x|
+    2  1 \  4  |  /
+
+    The parameters must always be iterables, even if they are vectors of
+    length one or zero:
+
+    >>> hyper((1, ), [], x)
+    hyper((1,), (), x)
+
+    But of course they may be variables (but if they depend on $x$ then you
+    should not expect much implemented functionality):
+
+    >>> hyper((n, a), (n**2,), x)
+    hyper((a, n), (n**2,), x)
+
+    The hypergeometric function generalizes many named special functions.
+    The function ``hyperexpand()`` tries to express a hypergeometric function
+    using named special functions. For example:
+
+    >>> from sympy import hyperexpand
+    >>> hyperexpand(hyper([], [], x))
+    exp(x)
+
+    You can also use ``expand_func()``:
+
+    >>> from sympy import expand_func
+    >>> expand_func(x*hyper([1, 1], [2], -x))
+    log(x + 1)
+
+    More examples:
+
+    >>> from sympy import S
+    >>> hyperexpand(hyper([], [S(1)/2], -x**2/4))
+    cos(x)
+    >>> hyperexpand(x*hyper([S(1)/2, S(1)/2], [S(3)/2], x**2))
+    asin(x)
+
+    We can also sometimes ``hyperexpand()`` parametric functions:
+
+    >>> from sympy.abc import a
+    >>> hyperexpand(hyper([-a], [], x))
+    (1 - x)**a
+
+    See Also
+    ========
+
+    sympy.simplify.hyperexpand
+    gamma
+    meijerg
+
+    References
+    ==========
+
+    .. [1] Luke, Y. L. (1969), The Special Functions and Their Approximations,
+           Volume 1
+    .. [2] https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
+
+    """
+
+
+    def __new__(cls, ap, bq, z, **kwargs):
+        # TODO should we check convergence conditions?
+        if kwargs.pop('evaluate', global_parameters.evaluate):
+            ca = Counter(Tuple(*ap))
+            cb = Counter(Tuple(*bq))
+            common = ca & cb
+            arg = ap, bq = [], []
+            for i, c in enumerate((ca, cb)):
+                c -= common
+                for k in ordered(c):
+                    arg[i].extend([k]*c[k])
+        else:
+            ap = list(ordered(ap))
+            bq = list(ordered(bq))
+        return super().__new__(cls, _prep_tuple(ap), _prep_tuple(bq), z, **kwargs)
+
+    @classmethod
+    def eval(cls, ap, bq, z):
+        if len(ap) <= len(bq) or (len(ap) == len(bq) + 1 and (Abs(z) <= 1) == True):
+            nz = unpolarify(z)
+            if z != nz:
+                return hyper(ap, bq, nz)
+
+    def fdiff(self, argindex=3):
+        if argindex != 3:
+            raise ArgumentIndexError(self, argindex)
+        nap = Tuple(*[a + 1 for a in self.ap])
+        nbq = Tuple(*[b + 1 for b in self.bq])
+        fac = Mul(*self.ap)/Mul(*self.bq)
+        return fac*hyper(nap, nbq, self.argument)
+
+    def _eval_expand_func(self, **hints):
+        from sympy.functions.special.gamma_functions import gamma
+        from sympy.simplify.hyperexpand import hyperexpand
+        if len(self.ap) == 2 and len(self.bq) == 1 and self.argument == 1:
+            a, b = self.ap
+            c = self.bq[0]
+            return gamma(c)*gamma(c - a - b)/gamma(c - a)/gamma(c - b)
+        return hyperexpand(self)
+
+    def _eval_rewrite_as_Sum(self, ap, bq, z, **kwargs):
+        from sympy.concrete.summations import Sum
+        n = Dummy("n", integer=True)
+        rfap = [RisingFactorial(a, n) for a in ap]
+        rfbq = [RisingFactorial(b, n) for b in bq]
+        coeff = Mul(*rfap) / Mul(*rfbq)
+        return Piecewise((Sum(coeff * z**n / factorial(n), (n, 0, oo)),
+                         self.convergence_statement), (self, True))
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        arg = self.args[2]
+        x0 = arg.subs(x, 0)
+        if x0 is S.NaN:
+            x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+
+        if x0 is S.Zero:
+            return S.One
+        return super()._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+
+        from sympy.series.order import Order
+
+        arg = self.args[2]
+        x0 = arg.limit(x, 0)
+        ap = self.args[0]
+        bq = self.args[1]
+
+        if not (arg == x and x0 == 0):
+            # It would be better to do something with arg.nseries here, rather
+            # than falling back on Function._eval_nseries. The code below
+            # though is not sufficient if arg is something like x/(x+1).
+            from sympy.simplify.hyperexpand import hyperexpand
+            return hyperexpand(super()._eval_nseries(x, n, logx))
+
+        terms = []
+
+        for i in range(n):
+            num = Mul(*[RisingFactorial(a, i) for a in ap])
+            den = Mul(*[RisingFactorial(b, i) for b in bq])
+            terms.append(((num/den) * (arg**i)) / factorial(i))
+
+        return (Add(*terms) + Order(x**n,x))
+
+    @property
+    def argument(self):
+        """ Argument of the hypergeometric function. """
+        return self.args[2]
+
+    @property
+    def ap(self):
+        """ Numerator parameters of the hypergeometric function. """
+        return Tuple(*self.args[0])
+
+    @property
+    def bq(self):
+        """ Denominator parameters of the hypergeometric function. """
+        return Tuple(*self.args[1])
+
+    @property
+    def _diffargs(self):
+        return self.ap + self.bq
+
+    @property
+    def eta(self):
+        """ A quantity related to the convergence of the series. """
+        return sum(self.ap) - sum(self.bq)
+
+    @property
+    def radius_of_convergence(self):
+        """
+        Compute the radius of convergence of the defining series.
+
+        Explanation
+        ===========
+
+        Note that even if this is not ``oo``, the function may still be
+        evaluated outside of the radius of convergence by analytic
+        continuation. But if this is zero, then the function is not actually
+        defined anywhere else.
+
+        Examples
+        ========
+
+        >>> from sympy import hyper
+        >>> from sympy.abc import z
+        >>> hyper((1, 2), [3], z).radius_of_convergence
+        1
+        >>> hyper((1, 2, 3), [4], z).radius_of_convergence
+        0
+        >>> hyper((1, 2), (3, 4), z).radius_of_convergence
+        oo
+
+        """
+        if any(a.is_integer and (a <= 0) == True for a in self.ap + self.bq):
+            aints = [a for a in self.ap if a.is_Integer and (a <= 0) == True]
+            bints = [a for a in self.bq if a.is_Integer and (a <= 0) == True]
+            if len(aints) < len(bints):
+                return S.Zero
+            popped = False
+            for b in bints:
+                cancelled = False
+                while aints:
+                    a = aints.pop()
+                    if a >= b:
+                        cancelled = True
+                        break
+                    popped = True
+                if not cancelled:
+                    return S.Zero
+            if aints or popped:
+                # There are still non-positive numerator parameters.
+                # This is a polynomial.
+                return oo
+        if len(self.ap) == len(self.bq) + 1:
+            return S.One
+        elif len(self.ap) <= len(self.bq):
+            return oo
+        else:
+            return S.Zero
+
+    @property
+    def convergence_statement(self):
+        """ Return a condition on z under which the series converges. """
+        R = self.radius_of_convergence
+        if R == 0:
+            return False
+        if R == oo:
+            return True
+        # The special functions and their approximations, page 44
+        e = self.eta
+        z = self.argument
+        c1 = And(re(e) < 0, abs(z) <= 1)
+        c2 = And(0 <= re(e), re(e) < 1, abs(z) <= 1, Ne(z, 1))
+        c3 = And(re(e) >= 1, abs(z) < 1)
+        return Or(c1, c2, c3)
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.simplify.hyperexpand import hyperexpand
+        return hyperexpand(self)
+
+
+class meijerg(TupleParametersBase):
+    r"""
+    The Meijer G-function is defined by a Mellin-Barnes type integral that
+    resembles an inverse Mellin transform. It generalizes the hypergeometric
+    functions.
+
+    Explanation
+    ===========
+
+    The Meijer G-function depends on four sets of parameters. There are
+    "*numerator parameters*"
+    $a_1, \ldots, a_n$ and $a_{n+1}, \ldots, a_p$, and there are
+    "*denominator parameters*"
+    $b_1, \ldots, b_m$ and $b_{m+1}, \ldots, b_q$.
+    Confusingly, it is traditionally denoted as follows (note the position
+    of $m$, $n$, $p$, $q$, and how they relate to the lengths of the four
+    parameter vectors):
+
+    .. math ::
+        G_{p,q}^{m,n} \left(\begin{matrix}a_1, \cdots, a_n & a_{n+1}, \cdots, a_p \\
+                                        b_1, \cdots, b_m & b_{m+1}, \cdots, b_q
+                          \end{matrix} \middle| z \right).
+
+    However, in SymPy the four parameter vectors are always available
+    separately (see examples), so that there is no need to keep track of the
+    decorating sub- and super-scripts on the G symbol.
+
+    The G function is defined as the following integral:
+
+    .. math ::
+         \frac{1}{2 \pi i} \int_L \frac{\prod_{j=1}^m \Gamma(b_j - s)
+         \prod_{j=1}^n \Gamma(1 - a_j + s)}{\prod_{j=m+1}^q \Gamma(1- b_j +s)
+         \prod_{j=n+1}^p \Gamma(a_j - s)} z^s \mathrm{d}s,
+
+    where $\Gamma(z)$ is the gamma function. There are three possible
+    contours which we will not describe in detail here (see the references).
+    If the integral converges along more than one of them, the definitions
+    agree. The contours all separate the poles of $\Gamma(1-a_j+s)$
+    from the poles of $\Gamma(b_k-s)$, so in particular the G function
+    is undefined if $a_j - b_k \in \mathbb{Z}_{>0}$ for some
+    $j \le n$ and $k \le m$.
+
+    The conditions under which one of the contours yields a convergent integral
+    are complicated and we do not state them here, see the references.
+
+    Please note currently the Meijer G-function constructor does *not* check any
+    convergence conditions.
+
+    Examples
+    ========
+
+    You can pass the parameters either as four separate vectors:
+
+    >>> from sympy import meijerg, Tuple, pprint
+    >>> from sympy.abc import x, a
+    >>> pprint(meijerg((1, 2), (a, 4), (5,), [], x), use_unicode=False)
+     __1, 2 /1, 2  4, a |  \
+    /__     |           | x|
+    \_|4, 1 \ 5         |  /
+
+    Or as two nested vectors:
+
+    >>> pprint(meijerg([(1, 2), (3, 4)], ([5], Tuple()), x), use_unicode=False)
+     __1, 2 /1, 2  3, 4 |  \
+    /__     |           | x|
+    \_|4, 1 \ 5         |  /
+
+    As with the hypergeometric function, the parameters may be passed as
+    arbitrary iterables. Vectors of length zero and one also have to be
+    passed as iterables. The parameters need not be constants, but if they
+    depend on the argument then not much implemented functionality should be
+    expected.
+
+    All the subvectors of parameters are available:
+
+    >>> from sympy import pprint
+    >>> g = meijerg([1], [2], [3], [4], x)
+    >>> pprint(g, use_unicode=False)
+     __1, 1 /1  2 |  \
+    /__     |     | x|
+    \_|2, 2 \3  4 |  /
+    >>> g.an
+    (1,)
+    >>> g.ap
+    (1, 2)
+    >>> g.aother
+    (2,)
+    >>> g.bm
+    (3,)
+    >>> g.bq
+    (3, 4)
+    >>> g.bother
+    (4,)
+
+    The Meijer G-function generalizes the hypergeometric functions.
+    In some cases it can be expressed in terms of hypergeometric functions,
+    using Slater's theorem. For example:
+
+    >>> from sympy import hyperexpand
+    >>> from sympy.abc import a, b, c
+    >>> hyperexpand(meijerg([a], [], [c], [b], x), allow_hyper=True)
+    x**c*gamma(-a + c + 1)*hyper((-a + c + 1,),
+                                 (-b + c + 1,), -x)/gamma(-b + c + 1)
+
+    Thus the Meijer G-function also subsumes many named functions as special
+    cases. You can use ``expand_func()`` or ``hyperexpand()`` to (try to)
+    rewrite a Meijer G-function in terms of named special functions. For
+    example:
+
+    >>> from sympy import expand_func, S
+    >>> expand_func(meijerg([[],[]], [[0],[]], -x))
+    exp(x)
+    >>> hyperexpand(meijerg([[],[]], [[S(1)/2],[0]], (x/2)**2))
+    sin(x)/sqrt(pi)
+
+    See Also
+    ========
+
+    hyper
+    sympy.simplify.hyperexpand
+
+    References
+    ==========
+
+    .. [1] Luke, Y. L. (1969), The Special Functions and Their Approximations,
+           Volume 1
+    .. [2] https://en.wikipedia.org/wiki/Meijer_G-function
+
+    """
+
+
+    def __new__(cls, *args, **kwargs):
+        if len(args) == 5:
+            args = [(args[0], args[1]), (args[2], args[3]), args[4]]
+        if len(args) != 3:
+            raise TypeError("args must be either as, as', bs, bs', z or "
+                            "as, bs, z")
+
+        def tr(p):
+            if len(p) != 2:
+                raise TypeError("wrong argument")
+            p = [list(ordered(i)) for i in p]
+            return TupleArg(_prep_tuple(p[0]), _prep_tuple(p[1]))
+
+        arg0, arg1 = tr(args[0]), tr(args[1])
+        if Tuple(arg0, arg1).has(oo, zoo, -oo):
+            raise ValueError("G-function parameters must be finite")
+        if any((a - b).is_Integer and a - b > 0
+               for a in arg0[0] for b in arg1[0]):
+            raise ValueError("no parameter a1, ..., an may differ from "
+                         "any b1, ..., bm by a positive integer")
+
+        # TODO should we check convergence conditions?
+        return super().__new__(cls, arg0, arg1, args[2], **kwargs)
+
+    def fdiff(self, argindex=3):
+        if argindex != 3:
+            return self._diff_wrt_parameter(argindex[1])
+        if len(self.an) >= 1:
+            a = list(self.an)
+            a[0] -= 1
+            G = meijerg(a, self.aother, self.bm, self.bother, self.argument)
+            return 1/self.argument * ((self.an[0] - 1)*self + G)
+        elif len(self.bm) >= 1:
+            b = list(self.bm)
+            b[0] += 1
+            G = meijerg(self.an, self.aother, b, self.bother, self.argument)
+            return 1/self.argument * (self.bm[0]*self - G)
+        else:
+            return S.Zero
+
+    def _diff_wrt_parameter(self, idx):
+        # Differentiation wrt a parameter can only be done in very special
+        # cases. In particular, if we want to differentiate with respect to
+        # `a`, all other gamma factors have to reduce to rational functions.
+        #
+        # Let MT denote mellin transform. Suppose T(-s) is the gamma factor
+        # appearing in the definition of G. Then
+        #
+        #   MT(log(z)G(z)) = d/ds T(s) = d/da T(s) + ...
+        #
+        # Thus d/da G(z) = log(z)G(z) - ...
+        # The ... can be evaluated as a G function under the above conditions,
+        # the formula being most easily derived by using
+        #
+        # d  Gamma(s + n)    Gamma(s + n) / 1    1                1     \
+        # -- ------------ =  ------------ | - + ----  + ... + --------- |
+        # ds Gamma(s)        Gamma(s)     \ s   s + 1         s + n - 1 /
+        #
+        # which follows from the difference equation of the digamma function.
+        # (There is a similar equation for -n instead of +n).
+
+        # We first figure out how to pair the parameters.
+        an = list(self.an)
+        ap = list(self.aother)
+        bm = list(self.bm)
+        bq = list(self.bother)
+        if idx < len(an):
+            an.pop(idx)
+        else:
+            idx -= len(an)
+            if idx < len(ap):
+                ap.pop(idx)
+            else:
+                idx -= len(ap)
+                if idx < len(bm):
+                    bm.pop(idx)
+                else:
+                    bq.pop(idx - len(bm))
+        pairs1 = []
+        pairs2 = []
+        for l1, l2, pairs in [(an, bq, pairs1), (ap, bm, pairs2)]:
+            while l1:
+                x = l1.pop()
+                found = None
+                for i, y in enumerate(l2):
+                    if not Mod((x - y).simplify(), 1):
+                        found = i
+                        break
+                if found is None:
+                    raise NotImplementedError('Derivative not expressible '
+                                              'as G-function?')
+                y = l2[i]
+                l2.pop(i)
+                pairs.append((x, y))
+
+        # Now build the result.
+        res = log(self.argument)*self
+
+        for a, b in pairs1:
+            sign = 1
+            n = a - b
+            base = b
+            if n < 0:
+                sign = -1
+                n = b - a
+                base = a
+            for k in range(n):
+                res -= sign*meijerg(self.an + (base + k + 1,), self.aother,
+                                    self.bm, self.bother + (base + k + 0,),
+                                    self.argument)
+
+        for a, b in pairs2:
+            sign = 1
+            n = b - a
+            base = a
+            if n < 0:
+                sign = -1
+                n = a - b
+                base = b
+            for k in range(n):
+                res -= sign*meijerg(self.an, self.aother + (base + k + 1,),
+                                    self.bm + (base + k + 0,), self.bother,
+                                    self.argument)
+
+        return res
+
+    def get_period(self):
+        """
+        Return a number $P$ such that $G(x*exp(I*P)) == G(x)$.
+
+        Examples
+        ========
+
+        >>> from sympy import meijerg, pi, S
+        >>> from sympy.abc import z
+
+        >>> meijerg([1], [], [], [], z).get_period()
+        2*pi
+        >>> meijerg([pi], [], [], [], z).get_period()
+        oo
+        >>> meijerg([1, 2], [], [], [], z).get_period()
+        oo
+        >>> meijerg([1,1], [2], [1, S(1)/2, S(1)/3], [1], z).get_period()
+        12*pi
+
+        """
+        # This follows from slater's theorem.
+        def compute(l):
+            # first check that no two differ by an integer
+            for i, b in enumerate(l):
+                if not b.is_Rational:
+                    return oo
+                for j in range(i + 1, len(l)):
+                    if not Mod((b - l[j]).simplify(), 1):
+                        return oo
+            return lcm(*(x.q for x in l))
+        beta = compute(self.bm)
+        alpha = compute(self.an)
+        p, q = len(self.ap), len(self.bq)
+        if p == q:
+            if oo in (alpha, beta):
+                return oo
+            return 2*pi*lcm(alpha, beta)
+        elif p < q:
+            return 2*pi*beta
+        else:
+            return 2*pi*alpha
+
+    def _eval_expand_func(self, **hints):
+        from sympy.simplify.hyperexpand import hyperexpand
+        return hyperexpand(self)
+
+    def _eval_evalf(self, prec):
+        # The default code is insufficient for polar arguments.
+        # mpmath provides an optional argument "r", which evaluates
+        # G(z**(1/r)). I am not sure what its intended use is, but we hijack it
+        # here in the following way: to evaluate at a number z of |argument|
+        # less than (say) n*pi, we put r=1/n, compute z' = root(z, n)
+        # (carefully so as not to loose the branch information), and evaluate
+        # G(z'**(1/r)) = G(z'**n) = G(z).
+        import mpmath
+        znum = self.argument._eval_evalf(prec)
+        if znum.has(exp_polar):
+            znum, branch = znum.as_coeff_mul(exp_polar)
+            if len(branch) != 1:
+                return
+            branch = branch[0].args[0]/I
+        else:
+            branch = S.Zero
+        n = ceiling(abs(branch/pi)) + 1
+        znum = znum**(S.One/n)*exp(I*branch / n)
+
+        # Convert all args to mpf or mpc
+        try:
+            [z, r, ap, bq] = [arg._to_mpmath(prec)
+                    for arg in [znum, 1/n, self.args[0], self.args[1]]]
+        except ValueError:
+            return
+
+        with mpmath.workprec(prec):
+            v = mpmath.meijerg(ap, bq, z, r)
+
+        return Expr._from_mpmath(v, prec)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        from sympy.simplify.hyperexpand import hyperexpand
+        return hyperexpand(self).as_leading_term(x, logx=logx, cdir=cdir)
+
+    def integrand(self, s):
+        """ Get the defining integrand D(s). """
+        from sympy.functions.special.gamma_functions import gamma
+        return self.argument**s \
+            * Mul(*(gamma(b - s) for b in self.bm)) \
+            * Mul(*(gamma(1 - a + s) for a in self.an)) \
+            / Mul(*(gamma(1 - b + s) for b in self.bother)) \
+            / Mul(*(gamma(a - s) for a in self.aother))
+
+    @property
+    def argument(self):
+        """ Argument of the Meijer G-function. """
+        return self.args[2]
+
+    @property
+    def an(self):
+        """ First set of numerator parameters. """
+        return Tuple(*self.args[0][0])
+
+    @property
+    def ap(self):
+        """ Combined numerator parameters. """
+        return Tuple(*(self.args[0][0] + self.args[0][1]))
+
+    @property
+    def aother(self):
+        """ Second set of numerator parameters. """
+        return Tuple(*self.args[0][1])
+
+    @property
+    def bm(self):
+        """ First set of denominator parameters. """
+        return Tuple(*self.args[1][0])
+
+    @property
+    def bq(self):
+        """ Combined denominator parameters. """
+        return Tuple(*(self.args[1][0] + self.args[1][1]))
+
+    @property
+    def bother(self):
+        """ Second set of denominator parameters. """
+        return Tuple(*self.args[1][1])
+
+    @property
+    def _diffargs(self):
+        return self.ap + self.bq
+
+    @property
+    def nu(self):
+        """ A quantity related to the convergence region of the integral,
+            c.f. references. """
+        return sum(self.bq) - sum(self.ap)
+
+    @property
+    def delta(self):
+        """ A quantity related to the convergence region of the integral,
+            c.f. references. """
+        return len(self.bm) + len(self.an) - S(len(self.ap) + len(self.bq))/2
+
+    @property
+    def is_number(self):
+        """ Returns true if expression has numeric data only. """
+        return not self.free_symbols
+
+
+class HyperRep(DefinedFunction):
+    """
+    A base class for "hyper representation functions".
+
+    This is used exclusively in ``hyperexpand()``, but fits more logically here.
+
+    pFq is branched at 1 if p == q+1. For use with slater-expansion, we want
+    define an "analytic continuation" to all polar numbers, which is
+    continuous on circles and on the ray t*exp_polar(I*pi). Moreover, we want
+    a "nice" expression for the various cases.
+
+    This base class contains the core logic, concrete derived classes only
+    supply the actual functions.
+
+    """
+
+
+    @classmethod
+    def eval(cls, *args):
+        newargs = tuple(map(unpolarify, args[:-1])) + args[-1:]
+        if args != newargs:
+            return cls(*newargs)
+
+    @classmethod
+    def _expr_small(cls, x):
+        """ An expression for F(x) which holds for |x| < 1. """
+        raise NotImplementedError
+
+    @classmethod
+    def _expr_small_minus(cls, x):
+        """ An expression for F(-x) which holds for |x| < 1. """
+        raise NotImplementedError
+
+    @classmethod
+    def _expr_big(cls, x, n):
+        """ An expression for F(exp_polar(2*I*pi*n)*x), |x| > 1. """
+        raise NotImplementedError
+
+    @classmethod
+    def _expr_big_minus(cls, x, n):
+        """ An expression for F(exp_polar(2*I*pi*n + pi*I)*x), |x| > 1. """
+        raise NotImplementedError
+
+    def _eval_rewrite_as_nonrep(self, *args, **kwargs):
+        x, n = self.args[-1].extract_branch_factor(allow_half=True)
+        minus = False
+        newargs = self.args[:-1] + (x,)
+        if not n.is_Integer:
+            minus = True
+            n -= S.Half
+        newerargs = newargs + (n,)
+        if minus:
+            small = self._expr_small_minus(*newargs)
+            big = self._expr_big_minus(*newerargs)
+        else:
+            small = self._expr_small(*newargs)
+            big = self._expr_big(*newerargs)
+
+        if big == small:
+            return small
+        return Piecewise((big, abs(x) > 1), (small, True))
+
+    def _eval_rewrite_as_nonrepsmall(self, *args, **kwargs):
+        x, n = self.args[-1].extract_branch_factor(allow_half=True)
+        args = self.args[:-1] + (x,)
+        if not n.is_Integer:
+            return self._expr_small_minus(*args)
+        return self._expr_small(*args)
+
+
+class HyperRep_power1(HyperRep):
+    """ Return a representative for hyper([-a], [], z) == (1 - z)**a. """
+
+    @classmethod
+    def _expr_small(cls, a, x):
+        return (1 - x)**a
+
+    @classmethod
+    def _expr_small_minus(cls, a, x):
+        return (1 + x)**a
+
+    @classmethod
+    def _expr_big(cls, a, x, n):
+        if a.is_integer:
+            return cls._expr_small(a, x)
+        return (x - 1)**a*exp((2*n - 1)*pi*I*a)
+
+    @classmethod
+    def _expr_big_minus(cls, a, x, n):
+        if a.is_integer:
+            return cls._expr_small_minus(a, x)
+        return (1 + x)**a*exp(2*n*pi*I*a)
+
+
+class HyperRep_power2(HyperRep):
+    """ Return a representative for hyper([a, a - 1/2], [2*a], z). """
+
+    @classmethod
+    def _expr_small(cls, a, x):
+        return 2**(2*a - 1)*(1 + sqrt(1 - x))**(1 - 2*a)
+
+    @classmethod
+    def _expr_small_minus(cls, a, x):
+        return 2**(2*a - 1)*(1 + sqrt(1 + x))**(1 - 2*a)
+
+    @classmethod
+    def _expr_big(cls, a, x, n):
+        sgn = -1
+        if n.is_odd:
+            sgn = 1
+            n -= 1
+        return 2**(2*a - 1)*(1 + sgn*I*sqrt(x - 1))**(1 - 2*a) \
+            *exp(-2*n*pi*I*a)
+
+    @classmethod
+    def _expr_big_minus(cls, a, x, n):
+        sgn = 1
+        if n.is_odd:
+            sgn = -1
+        return sgn*2**(2*a - 1)*(sqrt(1 + x) + sgn)**(1 - 2*a)*exp(-2*pi*I*a*n)
+
+
+class HyperRep_log1(HyperRep):
+    """ Represent -z*hyper([1, 1], [2], z) == log(1 - z). """
+    @classmethod
+    def _expr_small(cls, x):
+        return log(1 - x)
+
+    @classmethod
+    def _expr_small_minus(cls, x):
+        return log(1 + x)
+
+    @classmethod
+    def _expr_big(cls, x, n):
+        return log(x - 1) + (2*n - 1)*pi*I
+
+    @classmethod
+    def _expr_big_minus(cls, x, n):
+        return log(1 + x) + 2*n*pi*I
+
+
+class HyperRep_atanh(HyperRep):
+    """ Represent hyper([1/2, 1], [3/2], z) == atanh(sqrt(z))/sqrt(z). """
+    @classmethod
+    def _expr_small(cls, x):
+        return atanh(sqrt(x))/sqrt(x)
+
+    def _expr_small_minus(cls, x):
+        return atan(sqrt(x))/sqrt(x)
+
+    def _expr_big(cls, x, n):
+        if n.is_even:
+            return (acoth(sqrt(x)) + I*pi/2)/sqrt(x)
+        else:
+            return (acoth(sqrt(x)) - I*pi/2)/sqrt(x)
+
+    def _expr_big_minus(cls, x, n):
+        if n.is_even:
+            return atan(sqrt(x))/sqrt(x)
+        else:
+            return (atan(sqrt(x)) - pi)/sqrt(x)
+
+
+class HyperRep_asin1(HyperRep):
+    """ Represent hyper([1/2, 1/2], [3/2], z) == asin(sqrt(z))/sqrt(z). """
+    @classmethod
+    def _expr_small(cls, z):
+        return asin(sqrt(z))/sqrt(z)
+
+    @classmethod
+    def _expr_small_minus(cls, z):
+        return asinh(sqrt(z))/sqrt(z)
+
+    @classmethod
+    def _expr_big(cls, z, n):
+        return S.NegativeOne**n*((S.Half - n)*pi/sqrt(z) + I*acosh(sqrt(z))/sqrt(z))
+
+    @classmethod
+    def _expr_big_minus(cls, z, n):
+        return S.NegativeOne**n*(asinh(sqrt(z))/sqrt(z) + n*pi*I/sqrt(z))
+
+
+class HyperRep_asin2(HyperRep):
+    """ Represent hyper([1, 1], [3/2], z) == asin(sqrt(z))/sqrt(z)/sqrt(1-z). """
+    # TODO this can be nicer
+    @classmethod
+    def _expr_small(cls, z):
+        return HyperRep_asin1._expr_small(z) \
+            /HyperRep_power1._expr_small(S.Half, z)
+
+    @classmethod
+    def _expr_small_minus(cls, z):
+        return HyperRep_asin1._expr_small_minus(z) \
+            /HyperRep_power1._expr_small_minus(S.Half, z)
+
+    @classmethod
+    def _expr_big(cls, z, n):
+        return HyperRep_asin1._expr_big(z, n) \
+            /HyperRep_power1._expr_big(S.Half, z, n)
+
+    @classmethod
+    def _expr_big_minus(cls, z, n):
+        return HyperRep_asin1._expr_big_minus(z, n) \
+            /HyperRep_power1._expr_big_minus(S.Half, z, n)
+
+
+class HyperRep_sqrts1(HyperRep):
+    """ Return a representative for hyper([-a, 1/2 - a], [1/2], z). """
+
+    @classmethod
+    def _expr_small(cls, a, z):
+        return ((1 - sqrt(z))**(2*a) + (1 + sqrt(z))**(2*a))/2
+
+    @classmethod
+    def _expr_small_minus(cls, a, z):
+        return (1 + z)**a*cos(2*a*atan(sqrt(z)))
+
+    @classmethod
+    def _expr_big(cls, a, z, n):
+        if n.is_even:
+            return ((sqrt(z) + 1)**(2*a)*exp(2*pi*I*n*a) +
+                    (sqrt(z) - 1)**(2*a)*exp(2*pi*I*(n - 1)*a))/2
+        else:
+            n -= 1
+            return ((sqrt(z) - 1)**(2*a)*exp(2*pi*I*a*(n + 1)) +
+                    (sqrt(z) + 1)**(2*a)*exp(2*pi*I*a*n))/2
+
+    @classmethod
+    def _expr_big_minus(cls, a, z, n):
+        if n.is_even:
+            return (1 + z)**a*exp(2*pi*I*n*a)*cos(2*a*atan(sqrt(z)))
+        else:
+            return (1 + z)**a*exp(2*pi*I*n*a)*cos(2*a*atan(sqrt(z)) - 2*pi*a)
+
+
+class HyperRep_sqrts2(HyperRep):
+    """ Return a representative for
+          sqrt(z)/2*[(1-sqrt(z))**2a - (1 + sqrt(z))**2a]
+          == -2*z/(2*a+1) d/dz hyper([-a - 1/2, -a], [1/2], z)"""
+
+    @classmethod
+    def _expr_small(cls, a, z):
+        return sqrt(z)*((1 - sqrt(z))**(2*a) - (1 + sqrt(z))**(2*a))/2
+
+    @classmethod
+    def _expr_small_minus(cls, a, z):
+        return sqrt(z)*(1 + z)**a*sin(2*a*atan(sqrt(z)))
+
+    @classmethod
+    def _expr_big(cls, a, z, n):
+        if n.is_even:
+            return sqrt(z)/2*((sqrt(z) - 1)**(2*a)*exp(2*pi*I*a*(n - 1)) -
+                              (sqrt(z) + 1)**(2*a)*exp(2*pi*I*a*n))
+        else:
+            n -= 1
+            return sqrt(z)/2*((sqrt(z) - 1)**(2*a)*exp(2*pi*I*a*(n + 1)) -
+                              (sqrt(z) + 1)**(2*a)*exp(2*pi*I*a*n))
+
+    def _expr_big_minus(cls, a, z, n):
+        if n.is_even:
+            return (1 + z)**a*exp(2*pi*I*n*a)*sqrt(z)*sin(2*a*atan(sqrt(z)))
+        else:
+            return (1 + z)**a*exp(2*pi*I*n*a)*sqrt(z) \
+                *sin(2*a*atan(sqrt(z)) - 2*pi*a)
+
+
+class HyperRep_log2(HyperRep):
+    """ Represent log(1/2 + sqrt(1 - z)/2) == -z/4*hyper([3/2, 1, 1], [2, 2], z) """
+
+    @classmethod
+    def _expr_small(cls, z):
+        return log(S.Half + sqrt(1 - z)/2)
+
+    @classmethod
+    def _expr_small_minus(cls, z):
+        return log(S.Half + sqrt(1 + z)/2)
+
+    @classmethod
+    def _expr_big(cls, z, n):
+        if n.is_even:
+            return (n - S.Half)*pi*I + log(sqrt(z)/2) + I*asin(1/sqrt(z))
+        else:
+            return (n - S.Half)*pi*I + log(sqrt(z)/2) - I*asin(1/sqrt(z))
+
+    def _expr_big_minus(cls, z, n):
+        if n.is_even:
+            return pi*I*n + log(S.Half + sqrt(1 + z)/2)
+        else:
+            return pi*I*n + log(sqrt(1 + z)/2 - S.Half)
+
+
+class HyperRep_cosasin(HyperRep):
+    """ Represent hyper([a, -a], [1/2], z) == cos(2*a*asin(sqrt(z))). """
+    # Note there are many alternative expressions, e.g. as powers of a sum of
+    # square roots.
+
+    @classmethod
+    def _expr_small(cls, a, z):
+        return cos(2*a*asin(sqrt(z)))
+
+    @classmethod
+    def _expr_small_minus(cls, a, z):
+        return cosh(2*a*asinh(sqrt(z)))
+
+    @classmethod
+    def _expr_big(cls, a, z, n):
+        return cosh(2*a*acosh(sqrt(z)) + a*pi*I*(2*n - 1))
+
+    @classmethod
+    def _expr_big_minus(cls, a, z, n):
+        return cosh(2*a*asinh(sqrt(z)) + 2*a*pi*I*n)
+
+
+class HyperRep_sinasin(HyperRep):
+    """ Represent 2*a*z*hyper([1 - a, 1 + a], [3/2], z)
+        == sqrt(z)/sqrt(1-z)*sin(2*a*asin(sqrt(z))) """
+
+    @classmethod
+    def _expr_small(cls, a, z):
+        return sqrt(z)/sqrt(1 - z)*sin(2*a*asin(sqrt(z)))
+
+    @classmethod
+    def _expr_small_minus(cls, a, z):
+        return -sqrt(z)/sqrt(1 + z)*sinh(2*a*asinh(sqrt(z)))
+
+    @classmethod
+    def _expr_big(cls, a, z, n):
+        return -1/sqrt(1 - 1/z)*sinh(2*a*acosh(sqrt(z)) + a*pi*I*(2*n - 1))
+
+    @classmethod
+    def _expr_big_minus(cls, a, z, n):
+        return -1/sqrt(1 + 1/z)*sinh(2*a*asinh(sqrt(z)) + 2*a*pi*I*n)
+
+class appellf1(DefinedFunction):
+    r"""
+    This is the Appell hypergeometric function of two variables as:
+
+    .. math ::
+        F_1(a,b_1,b_2,c,x,y) = \sum_{m=0}^{\infty} \sum_{n=0}^{\infty}
+        \frac{(a)_{m+n} (b_1)_m (b_2)_n}{(c)_{m+n}}
+        \frac{x^m y^n}{m! n!}.
+
+    Examples
+    ========
+
+    >>> from sympy import appellf1, symbols
+    >>> x, y, a, b1, b2, c = symbols('x y a b1 b2 c')
+    >>> appellf1(2., 1., 6., 4., 5., 6.)
+    0.0063339426292673
+    >>> appellf1(12., 12., 6., 4., 0.5, 0.12)
+    172870711.659936
+    >>> appellf1(40, 2, 6, 4, 15, 60)
+    appellf1(40, 2, 6, 4, 15, 60)
+    >>> appellf1(20., 12., 10., 3., 0.5, 0.12)
+    15605338197184.4
+    >>> appellf1(40, 2, 6, 4, x, y)
+    appellf1(40, 2, 6, 4, x, y)
+    >>> appellf1(a, b1, b2, c, x, y)
+    appellf1(a, b1, b2, c, x, y)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Appell_series
+    .. [2] https://functions.wolfram.com/HypergeometricFunctions/AppellF1/
+
+    """
+
+    @classmethod
+    def eval(cls, a, b1, b2, c, x, y):
+        if default_sort_key(b1) > default_sort_key(b2):
+            b1, b2 = b2, b1
+            x, y = y, x
+            return cls(a, b1, b2, c, x, y)
+        elif b1 == b2 and default_sort_key(x) > default_sort_key(y):
+            x, y = y, x
+            return cls(a, b1, b2, c, x, y)
+        if x == 0 and y == 0:
+            return S.One
+
+    def fdiff(self, argindex=5):
+        a, b1, b2, c, x, y = self.args
+        if argindex == 5:
+            return (a*b1/c)*appellf1(a + 1, b1 + 1, b2, c + 1, x, y)
+        elif argindex == 6:
+            return (a*b2/c)*appellf1(a + 1, b1, b2 + 1, c + 1, x, y)
+        elif argindex in (1, 2, 3, 4):
+            return Derivative(self, self.args[argindex-1])
+        else:
+            raise ArgumentIndexError(self, argindex)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/mathieu_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/mathieu_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..66bccd8d3e6dd357e1e0b93fb5cb5ad4c5f1367f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/mathieu_functions.py
@@ -0,0 +1,269 @@
+""" This module contains the Mathieu functions.
+"""
+
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin, cos
+
+
+class MathieuBase(DefinedFunction):
+    """
+    Abstract base class for Mathieu functions.
+
+    This class is meant to reduce code duplication.
+
+    """
+
+    unbranched = True
+
+    def _eval_conjugate(self):
+        a, q, z = self.args
+        return self.func(a.conjugate(), q.conjugate(), z.conjugate())
+
+
+class mathieus(MathieuBase):
+    r"""
+    The Mathieu Sine function $S(a,q,z)$.
+
+    Explanation
+    ===========
+
+    This function is one solution of the Mathieu differential equation:
+
+    .. math ::
+        y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0
+
+    The other solution is the Mathieu Cosine function.
+
+    Examples
+    ========
+
+    >>> from sympy import diff, mathieus
+    >>> from sympy.abc import a, q, z
+
+    >>> mathieus(a, q, z)
+    mathieus(a, q, z)
+
+    >>> mathieus(a, 0, z)
+    sin(sqrt(a)*z)
+
+    >>> diff(mathieus(a, q, z), z)
+    mathieusprime(a, q, z)
+
+    See Also
+    ========
+
+    mathieuc: Mathieu cosine function.
+    mathieusprime: Derivative of Mathieu sine function.
+    mathieucprime: Derivative of Mathieu cosine function.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Mathieu_function
+    .. [2] https://dlmf.nist.gov/28
+    .. [3] https://mathworld.wolfram.com/MathieuFunction.html
+    .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuS/
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 3:
+            a, q, z = self.args
+            return mathieusprime(a, q, z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, a, q, z):
+        if q.is_Number and q.is_zero:
+            return sin(sqrt(a)*z)
+        # Try to pull out factors of -1
+        if z.could_extract_minus_sign():
+            return -cls(a, q, -z)
+
+
+class mathieuc(MathieuBase):
+    r"""
+    The Mathieu Cosine function $C(a,q,z)$.
+
+    Explanation
+    ===========
+
+    This function is one solution of the Mathieu differential equation:
+
+    .. math ::
+        y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0
+
+    The other solution is the Mathieu Sine function.
+
+    Examples
+    ========
+
+    >>> from sympy import diff, mathieuc
+    >>> from sympy.abc import a, q, z
+
+    >>> mathieuc(a, q, z)
+    mathieuc(a, q, z)
+
+    >>> mathieuc(a, 0, z)
+    cos(sqrt(a)*z)
+
+    >>> diff(mathieuc(a, q, z), z)
+    mathieucprime(a, q, z)
+
+    See Also
+    ========
+
+    mathieus: Mathieu sine function
+    mathieusprime: Derivative of Mathieu sine function
+    mathieucprime: Derivative of Mathieu cosine function
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Mathieu_function
+    .. [2] https://dlmf.nist.gov/28
+    .. [3] https://mathworld.wolfram.com/MathieuFunction.html
+    .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuC/
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 3:
+            a, q, z = self.args
+            return mathieucprime(a, q, z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, a, q, z):
+        if q.is_Number and q.is_zero:
+            return cos(sqrt(a)*z)
+        # Try to pull out factors of -1
+        if z.could_extract_minus_sign():
+            return cls(a, q, -z)
+
+
+class mathieusprime(MathieuBase):
+    r"""
+    The derivative $S^{\prime}(a,q,z)$ of the Mathieu Sine function.
+
+    Explanation
+    ===========
+
+    This function is one solution of the Mathieu differential equation:
+
+    .. math ::
+        y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0
+
+    The other solution is the Mathieu Cosine function.
+
+    Examples
+    ========
+
+    >>> from sympy import diff, mathieusprime
+    >>> from sympy.abc import a, q, z
+
+    >>> mathieusprime(a, q, z)
+    mathieusprime(a, q, z)
+
+    >>> mathieusprime(a, 0, z)
+    sqrt(a)*cos(sqrt(a)*z)
+
+    >>> diff(mathieusprime(a, q, z), z)
+    (-a + 2*q*cos(2*z))*mathieus(a, q, z)
+
+    See Also
+    ========
+
+    mathieus: Mathieu sine function
+    mathieuc: Mathieu cosine function
+    mathieucprime: Derivative of Mathieu cosine function
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Mathieu_function
+    .. [2] https://dlmf.nist.gov/28
+    .. [3] https://mathworld.wolfram.com/MathieuFunction.html
+    .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuSPrime/
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 3:
+            a, q, z = self.args
+            return (2*q*cos(2*z) - a)*mathieus(a, q, z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, a, q, z):
+        if q.is_Number and q.is_zero:
+            return sqrt(a)*cos(sqrt(a)*z)
+        # Try to pull out factors of -1
+        if z.could_extract_minus_sign():
+            return cls(a, q, -z)
+
+
+class mathieucprime(MathieuBase):
+    r"""
+    The derivative $C^{\prime}(a,q,z)$ of the Mathieu Cosine function.
+
+    Explanation
+    ===========
+
+    This function is one solution of the Mathieu differential equation:
+
+    .. math ::
+        y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0
+
+    The other solution is the Mathieu Sine function.
+
+    Examples
+    ========
+
+    >>> from sympy import diff, mathieucprime
+    >>> from sympy.abc import a, q, z
+
+    >>> mathieucprime(a, q, z)
+    mathieucprime(a, q, z)
+
+    >>> mathieucprime(a, 0, z)
+    -sqrt(a)*sin(sqrt(a)*z)
+
+    >>> diff(mathieucprime(a, q, z), z)
+    (-a + 2*q*cos(2*z))*mathieuc(a, q, z)
+
+    See Also
+    ========
+
+    mathieus: Mathieu sine function
+    mathieuc: Mathieu cosine function
+    mathieusprime: Derivative of Mathieu sine function
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Mathieu_function
+    .. [2] https://dlmf.nist.gov/28
+    .. [3] https://mathworld.wolfram.com/MathieuFunction.html
+    .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuCPrime/
+
+    """
+
+    def fdiff(self, argindex=1):
+        if argindex == 3:
+            a, q, z = self.args
+            return (2*q*cos(2*z) - a)*mathieuc(a, q, z)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, a, q, z):
+        if q.is_Number and q.is_zero:
+            return -sqrt(a)*sin(sqrt(a)*z)
+        # Try to pull out factors of -1
+        if z.could_extract_minus_sign():
+            return -cls(a, q, -z)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/polynomials.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/polynomials.py
new file mode 100644
index 0000000000000000000000000000000000000000..5816baef600baf957c31a9dddaa5571da86d754a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/polynomials.py
@@ -0,0 +1,1447 @@
+"""
+This module mainly implements special orthogonal polynomials.
+
+See also functions.combinatorial.numbers which contains some
+combinatorial polynomials.
+
+"""
+
+from sympy.core import Rational
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy
+from sympy.functions.combinatorial.factorials import binomial, factorial, RisingFactorial
+from sympy.functions.elementary.complexes import re
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import cos, sec
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import hyper
+from sympy.polys.orthopolys import (chebyshevt_poly, chebyshevu_poly,
+                                    gegenbauer_poly, hermite_poly, hermite_prob_poly,
+                                    jacobi_poly, laguerre_poly, legendre_poly)
+
+_x = Dummy('x')
+
+
+class OrthogonalPolynomial(DefinedFunction):
+    """Base class for orthogonal polynomials.
+    """
+
+    @classmethod
+    def _eval_at_order(cls, n, x):
+        if n.is_integer and n >= 0:
+            return cls._ortho_poly(int(n), _x).subs(_x, x)
+
+    def _eval_conjugate(self):
+        return self.func(self.args[0], self.args[1].conjugate())
+
+#----------------------------------------------------------------------------
+# Jacobi polynomials
+#
+
+
+class jacobi(OrthogonalPolynomial):
+    r"""
+    Jacobi polynomial $P_n^{\left(\alpha, \beta\right)}(x)$.
+
+    Explanation
+    ===========
+
+    ``jacobi(n, alpha, beta, x)`` gives the $n$th Jacobi polynomial
+    in $x$, $P_n^{\left(\alpha, \beta\right)}(x)$.
+
+    The Jacobi polynomials are orthogonal on $[-1, 1]$ with respect
+    to the weight $\left(1-x\right)^\alpha \left(1+x\right)^\beta$.
+
+    Examples
+    ========
+
+    >>> from sympy import jacobi, S, conjugate, diff
+    >>> from sympy.abc import a, b, n, x
+
+    >>> jacobi(0, a, b, x)
+    1
+    >>> jacobi(1, a, b, x)
+    a/2 - b/2 + x*(a/2 + b/2 + 1)
+    >>> jacobi(2, a, b, x)
+    a**2/8 - a*b/4 - a/8 + b**2/8 - b/8 + x**2*(a**2/8 + a*b/4 + 7*a/8 + b**2/8 + 7*b/8 + 3/2) + x*(a**2/4 + 3*a/4 - b**2/4 - 3*b/4) - 1/2
+
+    >>> jacobi(n, a, b, x)
+    jacobi(n, a, b, x)
+
+    >>> jacobi(n, a, a, x)
+    RisingFactorial(a + 1, n)*gegenbauer(n,
+        a + 1/2, x)/RisingFactorial(2*a + 1, n)
+
+    >>> jacobi(n, 0, 0, x)
+    legendre(n, x)
+
+    >>> jacobi(n, S(1)/2, S(1)/2, x)
+    RisingFactorial(3/2, n)*chebyshevu(n, x)/factorial(n + 1)
+
+    >>> jacobi(n, -S(1)/2, -S(1)/2, x)
+    RisingFactorial(1/2, n)*chebyshevt(n, x)/factorial(n)
+
+    >>> jacobi(n, a, b, -x)
+    (-1)**n*jacobi(n, b, a, x)
+
+    >>> jacobi(n, a, b, 0)
+    gamma(a + n + 1)*hyper((-n, -b - n), (a + 1,), -1)/(2**n*factorial(n)*gamma(a + 1))
+    >>> jacobi(n, a, b, 1)
+    RisingFactorial(a + 1, n)/factorial(n)
+
+    >>> conjugate(jacobi(n, a, b, x))
+    jacobi(n, conjugate(a), conjugate(b), conjugate(x))
+
+    >>> diff(jacobi(n,a,b,x), x)
+    (a/2 + b/2 + n/2 + 1/2)*jacobi(n - 1, a + 1, b + 1, x)
+
+    See Also
+    ========
+
+    gegenbauer,
+    chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly,
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Jacobi_polynomials
+    .. [2] https://mathworld.wolfram.com/JacobiPolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/JacobiP/
+
+    """
+
+    @classmethod
+    def eval(cls, n, a, b, x):
+        # Simplify to other polynomials
+        # P^{a, a}_n(x)
+        if a == b:
+            if a == Rational(-1, 2):
+                return RisingFactorial(S.Half, n) / factorial(n) * chebyshevt(n, x)
+            elif a.is_zero:
+                return legendre(n, x)
+            elif a == S.Half:
+                return RisingFactorial(3*S.Half, n) / factorial(n + 1) * chebyshevu(n, x)
+            else:
+                return RisingFactorial(a + 1, n) / RisingFactorial(2*a + 1, n) * gegenbauer(n, a + S.Half, x)
+        elif b == -a:
+            # P^{a, -a}_n(x)
+            return gamma(n + a + 1) / gamma(n + 1) * (1 + x)**(a/2) / (1 - x)**(a/2) * assoc_legendre(n, -a, x)
+
+        if not n.is_Number:
+            # Symbolic result P^{a,b}_n(x)
+            # P^{a,b}_n(-x)  --->  (-1)**n * P^{b,a}_n(-x)
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * jacobi(n, b, a, -x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return (2**(-n) * gamma(a + n + 1) / (gamma(a + 1) * factorial(n)) *
+                        hyper([-b - n, -n], [a + 1], -1))
+            if x == S.One:
+                return RisingFactorial(a + 1, n) / factorial(n)
+            elif x is S.Infinity:
+                if n.is_positive:
+                    # Make sure a+b+2*n \notin Z
+                    if (a + b + 2*n).is_integer:
+                        raise ValueError("Error. a + b + 2*n should not be an integer.")
+                    return RisingFactorial(a + b + n + 1, n) * S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial
+            return jacobi_poly(n, a, b, x)
+
+    def fdiff(self, argindex=4):
+        from sympy.concrete.summations import Sum
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt a
+            n, a, b, x = self.args
+            k = Dummy("k")
+            f1 = 1 / (a + b + n + k + 1)
+            f2 = ((a + b + 2*k + 1) * RisingFactorial(b + k + 1, n - k) /
+                  ((n - k) * RisingFactorial(a + b + k + 1, n - k)))
+            return Sum(f1 * (jacobi(n, a, b, x) + f2*jacobi(k, a, b, x)), (k, 0, n - 1))
+        elif argindex == 3:
+            # Diff wrt b
+            n, a, b, x = self.args
+            k = Dummy("k")
+            f1 = 1 / (a + b + n + k + 1)
+            f2 = (-1)**(n - k) * ((a + b + 2*k + 1) * RisingFactorial(a + k + 1, n - k) /
+                  ((n - k) * RisingFactorial(a + b + k + 1, n - k)))
+            return Sum(f1 * (jacobi(n, a, b, x) + f2*jacobi(k, a, b, x)), (k, 0, n - 1))
+        elif argindex == 4:
+            # Diff wrt x
+            n, a, b, x = self.args
+            return S.Half * (a + b + n + 1) * jacobi(n - 1, a + 1, b + 1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, a, b, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        # Make sure n \in N
+        if n.is_negative or n.is_integer is False:
+            raise ValueError("Error: n should be a non-negative integer.")
+        k = Dummy("k")
+        kern = (RisingFactorial(-n, k) * RisingFactorial(a + b + n + 1, k) * RisingFactorial(a + k + 1, n - k) /
+                factorial(k) * ((1 - x)/2)**k)
+        return 1 / factorial(n) * Sum(kern, (k, 0, n))
+
+    def _eval_rewrite_as_polynomial(self, n, a, b, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, a, b, x, **kwargs)
+
+    def _eval_conjugate(self):
+        n, a, b, x = self.args
+        return self.func(n, a.conjugate(), b.conjugate(), x.conjugate())
+
+
+def jacobi_normalized(n, a, b, x):
+    r"""
+    Jacobi polynomial $P_n^{\left(\alpha, \beta\right)}(x)$.
+
+    Explanation
+    ===========
+
+    ``jacobi_normalized(n, alpha, beta, x)`` gives the $n$th
+    Jacobi polynomial in $x$, $P_n^{\left(\alpha, \beta\right)}(x)$.
+
+    The Jacobi polynomials are orthogonal on $[-1, 1]$ with respect
+    to the weight $\left(1-x\right)^\alpha \left(1+x\right)^\beta$.
+
+    This functions returns the polynomials normilzed:
+
+    .. math::
+
+        \int_{-1}^{1}
+          P_m^{\left(\alpha, \beta\right)}(x)
+          P_n^{\left(\alpha, \beta\right)}(x)
+          (1-x)^{\alpha} (1+x)^{\beta} \mathrm{d}x
+        = \delta_{m,n}
+
+    Examples
+    ========
+
+    >>> from sympy import jacobi_normalized
+    >>> from sympy.abc import n,a,b,x
+
+    >>> jacobi_normalized(n, a, b, x)
+    jacobi(n, a, b, x)/sqrt(2**(a + b + 1)*gamma(a + n + 1)*gamma(b + n + 1)/((a + b + 2*n + 1)*factorial(n)*gamma(a + b + n + 1)))
+
+    Parameters
+    ==========
+
+    n : integer degree of polynomial
+
+    a : alpha value
+
+    b : beta value
+
+    x : symbol
+
+    See Also
+    ========
+
+    gegenbauer,
+    chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly,
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Jacobi_polynomials
+    .. [2] https://mathworld.wolfram.com/JacobiPolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/JacobiP/
+
+    """
+    nfactor = (S(2)**(a + b + 1) * (gamma(n + a + 1) * gamma(n + b + 1))
+               / (2*n + a + b + 1) / (factorial(n) * gamma(n + a + b + 1)))
+
+    return jacobi(n, a, b, x) / sqrt(nfactor)
+
+
+#----------------------------------------------------------------------------
+# Gegenbauer polynomials
+#
+
+
+class gegenbauer(OrthogonalPolynomial):
+    r"""
+    Gegenbauer polynomial $C_n^{\left(\alpha\right)}(x)$.
+
+    Explanation
+    ===========
+
+    ``gegenbauer(n, alpha, x)`` gives the $n$th Gegenbauer polynomial
+    in $x$, $C_n^{\left(\alpha\right)}(x)$.
+
+    The Gegenbauer polynomials are orthogonal on $[-1, 1]$ with
+    respect to the weight $\left(1-x^2\right)^{\alpha-\frac{1}{2}}$.
+
+    Examples
+    ========
+
+    >>> from sympy import gegenbauer, conjugate, diff
+    >>> from sympy.abc import n,a,x
+    >>> gegenbauer(0, a, x)
+    1
+    >>> gegenbauer(1, a, x)
+    2*a*x
+    >>> gegenbauer(2, a, x)
+    -a + x**2*(2*a**2 + 2*a)
+    >>> gegenbauer(3, a, x)
+    x**3*(4*a**3/3 + 4*a**2 + 8*a/3) + x*(-2*a**2 - 2*a)
+
+    >>> gegenbauer(n, a, x)
+    gegenbauer(n, a, x)
+    >>> gegenbauer(n, a, -x)
+    (-1)**n*gegenbauer(n, a, x)
+
+    >>> gegenbauer(n, a, 0)
+    2**n*sqrt(pi)*gamma(a + n/2)/(gamma(a)*gamma(1/2 - n/2)*gamma(n + 1))
+    >>> gegenbauer(n, a, 1)
+    gamma(2*a + n)/(gamma(2*a)*gamma(n + 1))
+
+    >>> conjugate(gegenbauer(n, a, x))
+    gegenbauer(n, conjugate(a), conjugate(x))
+
+    >>> diff(gegenbauer(n, a, x), x)
+    2*a*gegenbauer(n - 1, a + 1, x)
+
+    See Also
+    ========
+
+    jacobi,
+    chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gegenbauer_polynomials
+    .. [2] https://mathworld.wolfram.com/GegenbauerPolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/GegenbauerC3/
+
+    """
+
+    @classmethod
+    def eval(cls, n, a, x):
+        # For negative n the polynomials vanish
+        # See https://functions.wolfram.com/Polynomials/GegenbauerC3/03/01/03/0012/
+        if n.is_negative:
+            return S.Zero
+
+        # Some special values for fixed a
+        if a == S.Half:
+            return legendre(n, x)
+        elif a == S.One:
+            return chebyshevu(n, x)
+        elif a == S.NegativeOne:
+            return S.Zero
+
+        if not n.is_Number:
+            # Handle this before the general sign extraction rule
+            if x == S.NegativeOne:
+                if (re(a) > S.Half) == True:
+                    return S.ComplexInfinity
+                else:
+                    return (cos(S.Pi*(a+n)) * sec(S.Pi*a) * gamma(2*a+n) /
+                                (gamma(2*a) * gamma(n+1)))
+
+            # Symbolic result C^a_n(x)
+            # C^a_n(-x)  --->  (-1)**n * C^a_n(x)
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * gegenbauer(n, a, -x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return (2**n * sqrt(S.Pi) * gamma(a + S.Half*n) /
+                        (gamma((1 - n)/2) * gamma(n + 1) * gamma(a)) )
+            if x == S.One:
+                return gamma(2*a + n) / (gamma(2*a) * gamma(n + 1))
+            elif x is S.Infinity:
+                if n.is_positive:
+                    return RisingFactorial(a, n) * S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial
+            return gegenbauer_poly(n, a, x)
+
+    def fdiff(self, argindex=3):
+        from sympy.concrete.summations import Sum
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt a
+            n, a, x = self.args
+            k = Dummy("k")
+            factor1 = 2 * (1 + (-1)**(n - k)) * (k + a) / ((k +
+                           n + 2*a) * (n - k))
+            factor2 = 2*(k + 1) / ((k + 2*a) * (2*k + 2*a + 1)) + \
+                2 / (k + n + 2*a)
+            kern = factor1*gegenbauer(k, a, x) + factor2*gegenbauer(n, a, x)
+            return Sum(kern, (k, 0, n - 1))
+        elif argindex == 3:
+            # Diff wrt x
+            n, a, x = self.args
+            return 2*a*gegenbauer(n - 1, a + 1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, a, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = ((-1)**k * RisingFactorial(a, n - k) * (2*x)**(n - 2*k) /
+                (factorial(k) * factorial(n - 2*k)))
+        return Sum(kern, (k, 0, floor(n/2)))
+
+    def _eval_rewrite_as_polynomial(self, n, a, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, a, x, **kwargs)
+
+    def _eval_conjugate(self):
+        n, a, x = self.args
+        return self.func(n, a.conjugate(), x.conjugate())
+
+#----------------------------------------------------------------------------
+# Chebyshev polynomials of first and second kind
+#
+
+
+class chebyshevt(OrthogonalPolynomial):
+    r"""
+    Chebyshev polynomial of the first kind, $T_n(x)$.
+
+    Explanation
+    ===========
+
+    ``chebyshevt(n, x)`` gives the $n$th Chebyshev polynomial (of the first
+    kind) in $x$, $T_n(x)$.
+
+    The Chebyshev polynomials of the first kind are orthogonal on
+    $[-1, 1]$ with respect to the weight $\frac{1}{\sqrt{1-x^2}}$.
+
+    Examples
+    ========
+
+    >>> from sympy import chebyshevt, diff
+    >>> from sympy.abc import n,x
+    >>> chebyshevt(0, x)
+    1
+    >>> chebyshevt(1, x)
+    x
+    >>> chebyshevt(2, x)
+    2*x**2 - 1
+
+    >>> chebyshevt(n, x)
+    chebyshevt(n, x)
+    >>> chebyshevt(n, -x)
+    (-1)**n*chebyshevt(n, x)
+    >>> chebyshevt(-n, x)
+    chebyshevt(n, x)
+
+    >>> chebyshevt(n, 0)
+    cos(pi*n/2)
+    >>> chebyshevt(n, -1)
+    (-1)**n
+
+    >>> diff(chebyshevt(n, x), x)
+    n*chebyshevu(n - 1, x)
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Chebyshev_polynomial
+    .. [2] https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html
+    .. [3] https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html
+    .. [4] https://functions.wolfram.com/Polynomials/ChebyshevT/
+    .. [5] https://functions.wolfram.com/Polynomials/ChebyshevU/
+
+    """
+
+    _ortho_poly = staticmethod(chebyshevt_poly)
+
+    @classmethod
+    def eval(cls, n, x):
+        if not n.is_Number:
+            # Symbolic result T_n(x)
+            # T_n(-x)  --->  (-1)**n * T_n(x)
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * chebyshevt(n, -x)
+            # T_{-n}(x)  --->  T_n(x)
+            if n.could_extract_minus_sign():
+                return chebyshevt(-n, x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return cos(S.Half * S.Pi * n)
+            if x == S.One:
+                return S.One
+            elif x is S.Infinity:
+                return S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial
+            if n.is_negative:
+                # T_{-n}(x) == T_n(x)
+                return cls._eval_at_order(-n, x)
+            else:
+                return cls._eval_at_order(n, x)
+
+    def fdiff(self, argindex=2):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt x
+            n, x = self.args
+            return n * chebyshevu(n - 1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = binomial(n, 2*k) * (x**2 - 1)**k * x**(n - 2*k)
+        return Sum(kern, (k, 0, floor(n/2)))
+
+    def _eval_rewrite_as_polynomial(self, n, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, x, **kwargs)
+
+
+class chebyshevu(OrthogonalPolynomial):
+    r"""
+    Chebyshev polynomial of the second kind, $U_n(x)$.
+
+    Explanation
+    ===========
+
+    ``chebyshevu(n, x)`` gives the $n$th Chebyshev polynomial of the second
+    kind in x, $U_n(x)$.
+
+    The Chebyshev polynomials of the second kind are orthogonal on
+    $[-1, 1]$ with respect to the weight $\sqrt{1-x^2}$.
+
+    Examples
+    ========
+
+    >>> from sympy import chebyshevu, diff
+    >>> from sympy.abc import n,x
+    >>> chebyshevu(0, x)
+    1
+    >>> chebyshevu(1, x)
+    2*x
+    >>> chebyshevu(2, x)
+    4*x**2 - 1
+
+    >>> chebyshevu(n, x)
+    chebyshevu(n, x)
+    >>> chebyshevu(n, -x)
+    (-1)**n*chebyshevu(n, x)
+    >>> chebyshevu(-n, x)
+    -chebyshevu(n - 2, x)
+
+    >>> chebyshevu(n, 0)
+    cos(pi*n/2)
+    >>> chebyshevu(n, 1)
+    n + 1
+
+    >>> diff(chebyshevu(n, x), x)
+    (-x*chebyshevu(n, x) + (n + 1)*chebyshevt(n + 1, x))/(x**2 - 1)
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Chebyshev_polynomial
+    .. [2] https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html
+    .. [3] https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html
+    .. [4] https://functions.wolfram.com/Polynomials/ChebyshevT/
+    .. [5] https://functions.wolfram.com/Polynomials/ChebyshevU/
+
+    """
+
+    _ortho_poly = staticmethod(chebyshevu_poly)
+
+    @classmethod
+    def eval(cls, n, x):
+        if not n.is_Number:
+            # Symbolic result U_n(x)
+            # U_n(-x)  --->  (-1)**n * U_n(x)
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * chebyshevu(n, -x)
+            # U_{-n}(x)  --->  -U_{n-2}(x)
+            if n.could_extract_minus_sign():
+                if n == S.NegativeOne:
+                    # n can not be -1 here
+                    return S.Zero
+                elif not (-n - 2).could_extract_minus_sign():
+                    return -chebyshevu(-n - 2, x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return cos(S.Half * S.Pi * n)
+            if x == S.One:
+                return S.One + n
+            elif x is S.Infinity:
+                return S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial
+            if n.is_negative:
+                # U_{-n}(x)  --->  -U_{n-2}(x)
+                if n == S.NegativeOne:
+                    return S.Zero
+                else:
+                    return -cls._eval_at_order(-n - 2, x)
+            else:
+                return cls._eval_at_order(n, x)
+
+    def fdiff(self, argindex=2):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt x
+            n, x = self.args
+            return ((n + 1) * chebyshevt(n + 1, x) - x * chebyshevu(n, x)) / (x**2 - 1)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = S.NegativeOne**k * factorial(
+            n - k) * (2*x)**(n - 2*k) / (factorial(k) * factorial(n - 2*k))
+        return Sum(kern, (k, 0, floor(n/2)))
+
+    def _eval_rewrite_as_polynomial(self, n, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, x, **kwargs)
+
+
+class chebyshevt_root(DefinedFunction):
+    r"""
+    ``chebyshev_root(n, k)`` returns the $k$th root (indexed from zero) of
+    the $n$th Chebyshev polynomial of the first kind; that is, if
+    $0 \le k < n$, ``chebyshevt(n, chebyshevt_root(n, k)) == 0``.
+
+    Examples
+    ========
+
+    >>> from sympy import chebyshevt, chebyshevt_root
+    >>> chebyshevt_root(3, 2)
+    -sqrt(3)/2
+    >>> chebyshevt(3, chebyshevt_root(3, 2))
+    0
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+    """
+
+    @classmethod
+    def eval(cls, n, k):
+        if not ((0 <= k) and (k < n)):
+            raise ValueError("must have 0 <= k < n, "
+                "got k = %s and n = %s" % (k, n))
+        return cos(S.Pi*(2*k + 1)/(2*n))
+
+
+class chebyshevu_root(DefinedFunction):
+    r"""
+    ``chebyshevu_root(n, k)`` returns the $k$th root (indexed from zero) of the
+    $n$th Chebyshev polynomial of the second kind; that is, if $0 \le k < n$,
+    ``chebyshevu(n, chebyshevu_root(n, k)) == 0``.
+
+    Examples
+    ========
+
+    >>> from sympy import chebyshevu, chebyshevu_root
+    >>> chebyshevu_root(3, 2)
+    -sqrt(2)/2
+    >>> chebyshevu(3, chebyshevu_root(3, 2))
+    0
+
+    See Also
+    ========
+
+    chebyshevt, chebyshevt_root, chebyshevu,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+    """
+
+
+    @classmethod
+    def eval(cls, n, k):
+        if not ((0 <= k) and (k < n)):
+            raise ValueError("must have 0 <= k < n, "
+                "got k = %s and n = %s" % (k, n))
+        return cos(S.Pi*(k + 1)/(n + 1))
+
+#----------------------------------------------------------------------------
+# Legendre polynomials and Associated Legendre polynomials
+#
+
+
+class legendre(OrthogonalPolynomial):
+    r"""
+    ``legendre(n, x)`` gives the $n$th Legendre polynomial of $x$, $P_n(x)$
+
+    Explanation
+    ===========
+
+    The Legendre polynomials are orthogonal on $[-1, 1]$ with respect to
+    the constant weight 1. They satisfy $P_n(1) = 1$ for all $n$; further,
+    $P_n$ is odd for odd $n$ and even for even $n$.
+
+    Examples
+    ========
+
+    >>> from sympy import legendre, diff
+    >>> from sympy.abc import x, n
+    >>> legendre(0, x)
+    1
+    >>> legendre(1, x)
+    x
+    >>> legendre(2, x)
+    3*x**2/2 - 1/2
+    >>> legendre(n, x)
+    legendre(n, x)
+    >>> diff(legendre(n,x), x)
+    n*(x*legendre(n, x) - legendre(n - 1, x))/(x**2 - 1)
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root,
+    assoc_legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Legendre_polynomial
+    .. [2] https://mathworld.wolfram.com/LegendrePolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/LegendreP/
+    .. [4] https://functions.wolfram.com/Polynomials/LegendreP2/
+
+    """
+
+    _ortho_poly = staticmethod(legendre_poly)
+
+    @classmethod
+    def eval(cls, n, x):
+        if not n.is_Number:
+            # Symbolic result L_n(x)
+            # L_n(-x)  --->  (-1)**n * L_n(x)
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * legendre(n, -x)
+            # L_{-n}(x)  --->  L_{n-1}(x)
+            if n.could_extract_minus_sign() and not(-n - 1).could_extract_minus_sign():
+                return legendre(-n - S.One, x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return sqrt(S.Pi)/(gamma(S.Half - n/2)*gamma(S.One + n/2))
+            elif x == S.One:
+                return S.One
+            elif x is S.Infinity:
+                return S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial;
+            # L_{-n}(x)  --->  L_{n-1}(x)
+            if n.is_negative:
+                n = -n - S.One
+            return cls._eval_at_order(n, x)
+
+    def fdiff(self, argindex=2):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt x
+            # Find better formula, this is unsuitable for x = +/-1
+            # https://www.autodiff.org/ad16/Oral/Buecker_Legendre.pdf says
+            # at x = 1:
+            #    n*(n + 1)/2            , m = 0
+            #    oo                     , m = 1
+            #    -(n-1)*n*(n+1)*(n+2)/4 , m = 2
+            #    0                      , m = 3, 4, ..., n
+            #
+            # at x = -1
+            #    (-1)**(n+1)*n*(n + 1)/2       , m = 0
+            #    (-1)**n*oo                    , m = 1
+            #    (-1)**n*(n-1)*n*(n+1)*(n+2)/4 , m = 2
+            #    0                             , m = 3, 4, ..., n
+            n, x = self.args
+            return n/(x**2 - 1)*(x*legendre(n, x) - legendre(n - 1, x))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = S.NegativeOne**k*binomial(n, k)**2*((1 + x)/2)**(n - k)*((1 - x)/2)**k
+        return Sum(kern, (k, 0, n))
+
+    def _eval_rewrite_as_polynomial(self, n, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, x, **kwargs)
+
+
+class assoc_legendre(DefinedFunction):
+    r"""
+    ``assoc_legendre(n, m, x)`` gives $P_n^m(x)$, where $n$ and $m$ are
+    the degree and order or an expression which is related to the nth
+    order Legendre polynomial, $P_n(x)$ in the following manner:
+
+    .. math::
+        P_n^m(x) = (-1)^m (1 - x^2)^{\frac{m}{2}}
+                   \frac{\mathrm{d}^m P_n(x)}{\mathrm{d} x^m}
+
+    Explanation
+    ===========
+
+    Associated Legendre polynomials are orthogonal on $[-1, 1]$ with:
+
+    - weight $= 1$            for the same $m$ and different $n$.
+    - weight $= \frac{1}{1-x^2}$   for the same $n$ and different $m$.
+
+    Examples
+    ========
+
+    >>> from sympy import assoc_legendre
+    >>> from sympy.abc import x, m, n
+    >>> assoc_legendre(0,0, x)
+    1
+    >>> assoc_legendre(1,0, x)
+    x
+    >>> assoc_legendre(1,1, x)
+    -sqrt(1 - x**2)
+    >>> assoc_legendre(n,m,x)
+    assoc_legendre(n, m, x)
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre,
+    hermite, hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
+    .. [2] https://mathworld.wolfram.com/LegendrePolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/LegendreP/
+    .. [4] https://functions.wolfram.com/Polynomials/LegendreP2/
+
+    """
+
+    @classmethod
+    def _eval_at_order(cls, n, m):
+        P = legendre_poly(n, _x, polys=True).diff((_x, m))
+        return S.NegativeOne**m * (1 - _x**2)**Rational(m, 2) * P.as_expr()
+
+    @classmethod
+    def eval(cls, n, m, x):
+        if m.could_extract_minus_sign():
+            # P^{-m}_n  --->  F * P^m_n
+            return S.NegativeOne**(-m) * (factorial(m + n)/factorial(n - m)) * assoc_legendre(n, -m, x)
+        if m == 0:
+            # P^0_n  --->  L_n
+            return legendre(n, x)
+        if x == 0:
+            return 2**m*sqrt(S.Pi) / (gamma((1 - m - n)/2)*gamma(1 - (m - n)/2))
+        if n.is_Number and m.is_Number and n.is_integer and m.is_integer:
+            if n.is_negative:
+                raise ValueError("%s : 1st index must be nonnegative integer (got %r)" % (cls, n))
+            if abs(m) > n:
+                raise ValueError("%s : abs('2nd index') must be <= '1st index' (got %r, %r)" % (cls, n, m))
+            return cls._eval_at_order(int(n), abs(int(m))).subs(_x, x)
+
+    def fdiff(self, argindex=3):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt m
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 3:
+            # Diff wrt x
+            # Find better formula, this is unsuitable for x = 1
+            n, m, x = self.args
+            return 1/(x**2 - 1)*(x*n*assoc_legendre(n, m, x) - (m + n)*assoc_legendre(n - 1, m, x))
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, m, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = factorial(2*n - 2*k)/(2**n*factorial(n - k)*factorial(
+            k)*factorial(n - 2*k - m))*S.NegativeOne**k*x**(n - m - 2*k)
+        return (1 - x**2)**(m/2) * Sum(kern, (k, 0, floor((n - m)*S.Half)))
+
+    def _eval_rewrite_as_polynomial(self, n, m, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, m, x, **kwargs)
+
+    def _eval_conjugate(self):
+        n, m, x = self.args
+        return self.func(n, m.conjugate(), x.conjugate())
+
+#----------------------------------------------------------------------------
+# Hermite polynomials
+#
+
+
+class hermite(OrthogonalPolynomial):
+    r"""
+    ``hermite(n, x)`` gives the $n$th Hermite polynomial in $x$, $H_n(x)$.
+
+    Explanation
+    ===========
+
+    The Hermite polynomials are orthogonal on $(-\infty, \infty)$
+    with respect to the weight $\exp\left(-x^2\right)$.
+
+    Examples
+    ========
+
+    >>> from sympy import hermite, diff
+    >>> from sympy.abc import x, n
+    >>> hermite(0, x)
+    1
+    >>> hermite(1, x)
+    2*x
+    >>> hermite(2, x)
+    4*x**2 - 2
+    >>> hermite(n, x)
+    hermite(n, x)
+    >>> diff(hermite(n,x), x)
+    2*n*hermite(n - 1, x)
+    >>> hermite(n, -x)
+    (-1)**n*hermite(n, x)
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite_prob,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hermite_polynomial
+    .. [2] https://mathworld.wolfram.com/HermitePolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/HermiteH/
+
+    """
+
+    _ortho_poly = staticmethod(hermite_poly)
+
+    @classmethod
+    def eval(cls, n, x):
+        if not n.is_Number:
+            # Symbolic result H_n(x)
+            # H_n(-x)  --->  (-1)**n * H_n(x)
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * hermite(n, -x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return 2**n * sqrt(S.Pi) / gamma((S.One - n)/2)
+            elif x is S.Infinity:
+                return S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial
+            if n.is_negative:
+                raise ValueError(
+                    "The index n must be nonnegative integer (got %r)" % n)
+            else:
+                return cls._eval_at_order(n, x)
+
+    def fdiff(self, argindex=2):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt x
+            n, x = self.args
+            return 2*n*hermite(n - 1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = S.NegativeOne**k / (factorial(k)*factorial(n - 2*k)) * (2*x)**(n - 2*k)
+        return factorial(n)*Sum(kern, (k, 0, floor(n/2)))
+
+    def _eval_rewrite_as_polynomial(self, n, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, x, **kwargs)
+
+    def _eval_rewrite_as_hermite_prob(self, n, x, **kwargs):
+        return sqrt(2)**n * hermite_prob(n, x*sqrt(2))
+
+
+class hermite_prob(OrthogonalPolynomial):
+    r"""
+    ``hermite_prob(n, x)`` gives the $n$th probabilist's Hermite polynomial
+    in $x$, $He_n(x)$.
+
+    Explanation
+    ===========
+
+    The probabilist's Hermite polynomials are orthogonal on $(-\infty, \infty)$
+    with respect to the weight $\exp\left(-\frac{x^2}{2}\right)$. They are monic
+    polynomials, related to the plain Hermite polynomials (:py:class:`~.hermite`) by
+
+    .. math :: He_n(x) = 2^{-n/2} H_n(x/\sqrt{2})
+
+    Examples
+    ========
+
+    >>> from sympy import hermite_prob, diff, I
+    >>> from sympy.abc import x, n
+    >>> hermite_prob(1, x)
+    x
+    >>> hermite_prob(5, x)
+    x**5 - 10*x**3 + 15*x
+    >>> diff(hermite_prob(n,x), x)
+    n*hermite_prob(n - 1, x)
+    >>> hermite_prob(n, -x)
+    (-1)**n*hermite_prob(n, x)
+
+    The sum of absolute values of coefficients of $He_n(x)$ is the number of
+    matchings in the complete graph $K_n$ or telephone number, A000085 in the OEIS:
+
+    >>> [hermite_prob(n,I) / I**n for n in range(11)]
+    [1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496]
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite,
+    laguerre, assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hermite_polynomial
+    .. [2] https://mathworld.wolfram.com/HermitePolynomial.html
+    """
+
+    _ortho_poly = staticmethod(hermite_prob_poly)
+
+    @classmethod
+    def eval(cls, n, x):
+        if not n.is_Number:
+            if x.could_extract_minus_sign():
+                return S.NegativeOne**n * hermite_prob(n, -x)
+            if x.is_zero:
+                return sqrt(S.Pi) / gamma((S.One-n) / 2)
+            elif x is S.Infinity:
+                return S.Infinity
+        else:
+            if n.is_negative:
+                ValueError("n must be a nonnegative integer, not %r" % n)
+            else:
+                return cls._eval_at_order(n, x)
+
+    def fdiff(self, argindex=2):
+        if argindex == 2:
+            n, x = self.args
+            return n*hermite_prob(n-1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        k = Dummy("k")
+        kern = (-S.Half)**k * x**(n-2*k) / (factorial(k) * factorial(n-2*k))
+        return factorial(n)*Sum(kern, (k, 0, floor(n/2)))
+
+    def _eval_rewrite_as_polynomial(self, n, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, x, **kwargs)
+
+    def _eval_rewrite_as_hermite(self, n, x, **kwargs):
+        return sqrt(2)**(-n) * hermite(n, x/sqrt(2))
+
+
+#----------------------------------------------------------------------------
+# Laguerre polynomials
+#
+
+
+class laguerre(OrthogonalPolynomial):
+    r"""
+    Returns the $n$th Laguerre polynomial in $x$, $L_n(x)$.
+
+    Examples
+    ========
+
+    >>> from sympy import laguerre, diff
+    >>> from sympy.abc import x, n
+    >>> laguerre(0, x)
+    1
+    >>> laguerre(1, x)
+    1 - x
+    >>> laguerre(2, x)
+    x**2/2 - 2*x + 1
+    >>> laguerre(3, x)
+    -x**3/6 + 3*x**2/2 - 3*x + 1
+
+    >>> laguerre(n, x)
+    laguerre(n, x)
+
+    >>> diff(laguerre(n, x), x)
+    -assoc_laguerre(n - 1, 1, x)
+
+    Parameters
+    ==========
+
+    n : int
+        Degree of Laguerre polynomial. Must be `n \ge 0`.
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    assoc_laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Laguerre_polynomial
+    .. [2] https://mathworld.wolfram.com/LaguerrePolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/LaguerreL/
+    .. [4] https://functions.wolfram.com/Polynomials/LaguerreL3/
+
+    """
+
+    _ortho_poly = staticmethod(laguerre_poly)
+
+    @classmethod
+    def eval(cls, n, x):
+        if n.is_integer is False:
+            raise ValueError("Error: n should be an integer.")
+        if not n.is_Number:
+            # Symbolic result L_n(x)
+            # L_{n}(-x)  --->  exp(-x) * L_{-n-1}(x)
+            # L_{-n}(x)  --->  exp(x) * L_{n-1}(-x)
+            if n.could_extract_minus_sign() and not(-n - 1).could_extract_minus_sign():
+                return exp(x)*laguerre(-n - 1, -x)
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return S.One
+            elif x is S.NegativeInfinity:
+                return S.Infinity
+            elif x is S.Infinity:
+                return S.NegativeOne**n * S.Infinity
+        else:
+            if n.is_negative:
+                return exp(x)*laguerre(-n - 1, -x)
+            else:
+                return cls._eval_at_order(n, x)
+
+    def fdiff(self, argindex=2):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt x
+            n, x = self.args
+            return -assoc_laguerre(n - 1, 1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        # Make sure n \in N_0
+        if n.is_negative:
+            return exp(x) * self._eval_rewrite_as_Sum(-n - 1, -x, **kwargs)
+        if n.is_integer is False:
+            raise ValueError("Error: n should be an integer.")
+        k = Dummy("k")
+        kern = RisingFactorial(-n, k) / factorial(k)**2 * x**k
+        return Sum(kern, (k, 0, n))
+
+    def _eval_rewrite_as_polynomial(self, n, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, x, **kwargs)
+
+
+class assoc_laguerre(OrthogonalPolynomial):
+    r"""
+    Returns the $n$th generalized Laguerre polynomial in $x$, $L_n(x)$.
+
+    Examples
+    ========
+
+    >>> from sympy import assoc_laguerre, diff
+    >>> from sympy.abc import x, n, a
+    >>> assoc_laguerre(0, a, x)
+    1
+    >>> assoc_laguerre(1, a, x)
+    a - x + 1
+    >>> assoc_laguerre(2, a, x)
+    a**2/2 + 3*a/2 + x**2/2 + x*(-a - 2) + 1
+    >>> assoc_laguerre(3, a, x)
+    a**3/6 + a**2 + 11*a/6 - x**3/6 + x**2*(a/2 + 3/2) +
+        x*(-a**2/2 - 5*a/2 - 3) + 1
+
+    >>> assoc_laguerre(n, a, 0)
+    binomial(a + n, a)
+
+    >>> assoc_laguerre(n, a, x)
+    assoc_laguerre(n, a, x)
+
+    >>> assoc_laguerre(n, 0, x)
+    laguerre(n, x)
+
+    >>> diff(assoc_laguerre(n, a, x), x)
+    -assoc_laguerre(n - 1, a + 1, x)
+
+    >>> diff(assoc_laguerre(n, a, x), a)
+    Sum(assoc_laguerre(_k, a, x)/(-a + n), (_k, 0, n - 1))
+
+    Parameters
+    ==========
+
+    n : int
+        Degree of Laguerre polynomial. Must be `n \ge 0`.
+
+    alpha : Expr
+        Arbitrary expression. For ``alpha=0`` regular Laguerre
+        polynomials will be generated.
+
+    See Also
+    ========
+
+    jacobi, gegenbauer,
+    chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root,
+    legendre, assoc_legendre,
+    hermite, hermite_prob,
+    laguerre,
+    sympy.polys.orthopolys.jacobi_poly
+    sympy.polys.orthopolys.gegenbauer_poly
+    sympy.polys.orthopolys.chebyshevt_poly
+    sympy.polys.orthopolys.chebyshevu_poly
+    sympy.polys.orthopolys.hermite_poly
+    sympy.polys.orthopolys.hermite_prob_poly
+    sympy.polys.orthopolys.legendre_poly
+    sympy.polys.orthopolys.laguerre_poly
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Laguerre_polynomial#Generalized_Laguerre_polynomials
+    .. [2] https://mathworld.wolfram.com/AssociatedLaguerrePolynomial.html
+    .. [3] https://functions.wolfram.com/Polynomials/LaguerreL/
+    .. [4] https://functions.wolfram.com/Polynomials/LaguerreL3/
+
+    """
+
+    @classmethod
+    def eval(cls, n, alpha, x):
+        # L_{n}^{0}(x)  --->  L_{n}(x)
+        if alpha.is_zero:
+            return laguerre(n, x)
+
+        if not n.is_Number:
+            # We can evaluate for some special values of x
+            if x.is_zero:
+                return binomial(n + alpha, alpha)
+            elif x is S.Infinity and n > 0:
+                return S.NegativeOne**n * S.Infinity
+            elif x is S.NegativeInfinity and n > 0:
+                return S.Infinity
+        else:
+            # n is a given fixed integer, evaluate into polynomial
+            if n.is_negative:
+                raise ValueError(
+                    "The index n must be nonnegative integer (got %r)" % n)
+            else:
+                return laguerre_poly(n, x, alpha)
+
+    def fdiff(self, argindex=3):
+        from sympy.concrete.summations import Sum
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt alpha
+            n, alpha, x = self.args
+            k = Dummy("k")
+            return Sum(assoc_laguerre(k, alpha, x) / (n - alpha), (k, 0, n - 1))
+        elif argindex == 3:
+            # Diff wrt x
+            n, alpha, x = self.args
+            return -assoc_laguerre(n - 1, alpha + 1, x)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_Sum(self, n, alpha, x, **kwargs):
+        from sympy.concrete.summations import Sum
+        # Make sure n \in N_0
+        if n.is_negative or n.is_integer is False:
+            raise ValueError("Error: n should be a non-negative integer.")
+        k = Dummy("k")
+        kern = RisingFactorial(
+            -n, k) / (gamma(k + alpha + 1) * factorial(k)) * x**k
+        return gamma(n + alpha + 1) / factorial(n) * Sum(kern, (k, 0, n))
+
+    def _eval_rewrite_as_polynomial(self, n, alpha, x, **kwargs):
+        # This function is just kept for backwards compatibility
+        # but should not be used
+        return self._eval_rewrite_as_Sum(n, alpha, x, **kwargs)
+
+    def _eval_conjugate(self):
+        n, alpha, x = self.args
+        return self.func(n, alpha.conjugate(), x.conjugate())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/singularity_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/singularity_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..a69026e6e657b1131880b47cb32202b6825b7158
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/singularity_functions.py
@@ -0,0 +1,235 @@
+from sympy.core import S, oo, diff
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.logic import fuzzy_not
+from sympy.core.relational import Eq
+from sympy.functions.elementary.complexes import im
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.special.delta_functions import Heaviside
+
+###############################################################################
+############################# SINGULARITY FUNCTION ############################
+###############################################################################
+
+
+class SingularityFunction(DefinedFunction):
+    r"""
+    Singularity functions are a class of discontinuous functions.
+
+    Explanation
+    ===========
+
+    Singularity functions take a variable, an offset, and an exponent as
+    arguments. These functions are represented using Macaulay brackets as:
+
+    SingularityFunction(x, a, n) := ^n
+
+    The singularity function will automatically evaluate to
+    ``Derivative(DiracDelta(x - a), x, -n - 1)`` if ``n < 0``
+    and ``(x - a)**n*Heaviside(x - a, 1)`` if ``n >= 0``.
+
+    Examples
+    ========
+
+    >>> from sympy import SingularityFunction, diff, Piecewise, DiracDelta, Heaviside, Symbol
+    >>> from sympy.abc import x, a, n
+    >>> SingularityFunction(x, a, n)
+    SingularityFunction(x, a, n)
+    >>> y = Symbol('y', positive=True)
+    >>> n = Symbol('n', nonnegative=True)
+    >>> SingularityFunction(y, -10, n)
+    (y + 10)**n
+    >>> y = Symbol('y', negative=True)
+    >>> SingularityFunction(y, 10, n)
+    0
+    >>> SingularityFunction(x, 4, -1).subs(x, 4)
+    oo
+    >>> SingularityFunction(x, 10, -2).subs(x, 10)
+    oo
+    >>> SingularityFunction(4, 1, 5)
+    243
+    >>> diff(SingularityFunction(x, 1, 5) + SingularityFunction(x, 1, 4), x)
+    4*SingularityFunction(x, 1, 3) + 5*SingularityFunction(x, 1, 4)
+    >>> diff(SingularityFunction(x, 4, 0), x, 2)
+    SingularityFunction(x, 4, -2)
+    >>> SingularityFunction(x, 4, 5).rewrite(Piecewise)
+    Piecewise(((x - 4)**5, x >= 4), (0, True))
+    >>> expr = SingularityFunction(x, a, n)
+    >>> y = Symbol('y', positive=True)
+    >>> n = Symbol('n', nonnegative=True)
+    >>> expr.subs({x: y, a: -10, n: n})
+    (y + 10)**n
+
+    The methods ``rewrite(DiracDelta)``, ``rewrite(Heaviside)``, and
+    ``rewrite('HeavisideDiracDelta')`` returns the same output. One can use any
+    of these methods according to their choice.
+
+    >>> expr = SingularityFunction(x, 4, 5) + SingularityFunction(x, -3, -1) - SingularityFunction(x, 0, -2)
+    >>> expr.rewrite(Heaviside)
+    (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1)
+    >>> expr.rewrite(DiracDelta)
+    (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1)
+    >>> expr.rewrite('HeavisideDiracDelta')
+    (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1)
+
+    See Also
+    ========
+
+    DiracDelta, Heaviside
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Singularity_function
+
+    """
+
+    is_real = True
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of a DiracDelta Function.
+
+        Explanation
+        ===========
+
+        The difference between ``diff()`` and ``fdiff()`` is: ``diff()`` is the
+        user-level function and ``fdiff()`` is an object method. ``fdiff()`` is
+        a convenience method available in the ``Function`` class. It returns
+        the derivative of the function without considering the chain rule.
+        ``diff(function, x)`` calls ``Function._eval_derivative`` which in turn
+        calls ``fdiff()`` internally to compute the derivative of the function.
+
+        """
+
+        if argindex == 1:
+            x, a, n = self.args
+            if n in (S.Zero, S.NegativeOne, S(-2), S(-3)):
+                return self.func(x, a, n-1)
+            elif n.is_positive:
+                return n*self.func(x, a, n-1)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    @classmethod
+    def eval(cls, variable, offset, exponent):
+        """
+        Returns a simplified form or a value of Singularity Function depending
+        on the argument passed by the object.
+
+        Explanation
+        ===========
+
+        The ``eval()`` method is automatically called when the
+        ``SingularityFunction`` class is about to be instantiated and it
+        returns either some simplified instance or the unevaluated instance
+        depending on the argument passed. In other words, ``eval()`` method is
+        not needed to be called explicitly, it is being called and evaluated
+        once the object is called.
+
+        Examples
+        ========
+
+        >>> from sympy import SingularityFunction, Symbol, nan
+        >>> from sympy.abc import x, a, n
+        >>> SingularityFunction(x, a, n)
+        SingularityFunction(x, a, n)
+        >>> SingularityFunction(5, 3, 2)
+        4
+        >>> SingularityFunction(x, a, nan)
+        nan
+        >>> SingularityFunction(x, 3, 0).subs(x, 3)
+        1
+        >>> SingularityFunction(4, 1, 5)
+        243
+        >>> x = Symbol('x', positive = True)
+        >>> a = Symbol('a', negative = True)
+        >>> n = Symbol('n', nonnegative = True)
+        >>> SingularityFunction(x, a, n)
+        (-a + x)**n
+        >>> x = Symbol('x', negative = True)
+        >>> a = Symbol('a', positive = True)
+        >>> SingularityFunction(x, a, n)
+        0
+
+        """
+
+        x = variable
+        a = offset
+        n = exponent
+        shift = (x - a)
+
+        if fuzzy_not(im(shift).is_zero):
+            raise ValueError("Singularity Functions are defined only for Real Numbers.")
+        if fuzzy_not(im(n).is_zero):
+            raise ValueError("Singularity Functions are not defined for imaginary exponents.")
+        if shift is S.NaN or n is S.NaN:
+            return S.NaN
+        if (n + 4).is_negative:
+            raise ValueError("Singularity Functions are not defined for exponents less than -4.")
+        if shift.is_extended_negative:
+            return S.Zero
+        if n.is_nonnegative:
+            if shift.is_zero:  # use literal 0 in case of Symbol('z', zero=True)
+                return S.Zero**n
+            if shift.is_extended_nonnegative:
+                return shift**n
+        if n in (S.NegativeOne, -2, -3, -4):
+            if shift.is_negative or shift.is_extended_positive:
+                return S.Zero
+            if shift.is_zero:
+                return oo
+
+    def _eval_rewrite_as_Piecewise(self, *args, **kwargs):
+        '''
+        Converts a Singularity Function expression into its Piecewise form.
+
+        '''
+        x, a, n = self.args
+
+        if n in (S.NegativeOne, S(-2), S(-3), S(-4)):
+            return Piecewise((oo, Eq(x - a, 0)), (0, True))
+        elif n.is_nonnegative:
+            return Piecewise(((x - a)**n, x - a >= 0), (0, True))
+
+    def _eval_rewrite_as_Heaviside(self, *args, **kwargs):
+        '''
+        Rewrites a Singularity Function expression using Heavisides and DiracDeltas.
+
+        '''
+        x, a, n = self.args
+
+        if n == -4:
+            return diff(Heaviside(x - a), x.free_symbols.pop(), 4)
+        if n == -3:
+            return diff(Heaviside(x - a), x.free_symbols.pop(), 3)
+        if n == -2:
+            return diff(Heaviside(x - a), x.free_symbols.pop(), 2)
+        if n == -1:
+            return diff(Heaviside(x - a), x.free_symbols.pop(), 1)
+        if n.is_nonnegative:
+            return (x - a)**n*Heaviside(x - a, 1)
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        z, a, n = self.args
+        shift = (z - a).subs(x, 0)
+        if n < 0:
+            return S.Zero
+        elif n.is_zero and shift.is_zero:
+            return S.Zero if cdir == -1 else S.One
+        elif shift.is_positive:
+            return shift**n
+        return S.Zero
+
+    def _eval_nseries(self, x, n, logx=None, cdir=0):
+        z, a, n = self.args
+        shift = (z - a).subs(x, 0)
+        if n < 0:
+            return S.Zero
+        elif n.is_zero and shift.is_zero:
+            return S.Zero if cdir == -1 else S.One
+        elif shift.is_positive:
+            return ((z - a)**n)._eval_nseries(x, n, logx=logx, cdir=cdir)
+        return S.Zero
+
+    _eval_rewrite_as_DiracDelta = _eval_rewrite_as_Heaviside
+    _eval_rewrite_as_HeavisideDiracDelta = _eval_rewrite_as_Heaviside
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/spherical_harmonics.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/spherical_harmonics.py
new file mode 100644
index 0000000000000000000000000000000000000000..541546b75e882b43c41814b5e92bb85ee41628d1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/spherical_harmonics.py
@@ -0,0 +1,334 @@
+from sympy.core.expr import Expr
+from sympy.core.function import DefinedFunction, ArgumentIndexError
+from sympy.core.numbers import I, pi
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy
+from sympy.functions import assoc_legendre
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import Abs, conjugate
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin, cos, cot
+
+_x = Dummy("x")
+
+class Ynm(DefinedFunction):
+    r"""
+    Spherical harmonics defined as
+
+    .. math::
+        Y_n^m(\theta, \varphi) := \sqrt{\frac{(2n+1)(n-m)!}{4\pi(n+m)!}}
+                                  \exp(i m \varphi)
+                                  \mathrm{P}_n^m\left(\cos(\theta)\right)
+
+    Explanation
+    ===========
+
+    ``Ynm()`` gives the spherical harmonic function of order $n$ and $m$
+    in $\theta$ and $\varphi$, $Y_n^m(\theta, \varphi)$. The four
+    parameters are as follows: $n \geq 0$ an integer and $m$ an integer
+    such that $-n \leq m \leq n$ holds. The two angles are real-valued
+    with $\theta \in [0, \pi]$ and $\varphi \in [0, 2\pi]$.
+
+    Examples
+    ========
+
+    >>> from sympy import Ynm, Symbol, simplify
+    >>> from sympy.abc import n,m
+    >>> theta = Symbol("theta")
+    >>> phi = Symbol("phi")
+
+    >>> Ynm(n, m, theta, phi)
+    Ynm(n, m, theta, phi)
+
+    Several symmetries are known, for the order:
+
+    >>> Ynm(n, -m, theta, phi)
+    (-1)**m*exp(-2*I*m*phi)*Ynm(n, m, theta, phi)
+
+    As well as for the angles:
+
+    >>> Ynm(n, m, -theta, phi)
+    Ynm(n, m, theta, phi)
+
+    >>> Ynm(n, m, theta, -phi)
+    exp(-2*I*m*phi)*Ynm(n, m, theta, phi)
+
+    For specific integers $n$ and $m$ we can evaluate the harmonics
+    to more useful expressions:
+
+    >>> simplify(Ynm(0, 0, theta, phi).expand(func=True))
+    1/(2*sqrt(pi))
+
+    >>> simplify(Ynm(1, -1, theta, phi).expand(func=True))
+    sqrt(6)*exp(-I*phi)*sin(theta)/(4*sqrt(pi))
+
+    >>> simplify(Ynm(1, 0, theta, phi).expand(func=True))
+    sqrt(3)*cos(theta)/(2*sqrt(pi))
+
+    >>> simplify(Ynm(1, 1, theta, phi).expand(func=True))
+    -sqrt(6)*exp(I*phi)*sin(theta)/(4*sqrt(pi))
+
+    >>> simplify(Ynm(2, -2, theta, phi).expand(func=True))
+    sqrt(30)*exp(-2*I*phi)*sin(theta)**2/(8*sqrt(pi))
+
+    >>> simplify(Ynm(2, -1, theta, phi).expand(func=True))
+    sqrt(30)*exp(-I*phi)*sin(2*theta)/(8*sqrt(pi))
+
+    >>> simplify(Ynm(2, 0, theta, phi).expand(func=True))
+    sqrt(5)*(3*cos(theta)**2 - 1)/(4*sqrt(pi))
+
+    >>> simplify(Ynm(2, 1, theta, phi).expand(func=True))
+    -sqrt(30)*exp(I*phi)*sin(2*theta)/(8*sqrt(pi))
+
+    >>> simplify(Ynm(2, 2, theta, phi).expand(func=True))
+    sqrt(30)*exp(2*I*phi)*sin(theta)**2/(8*sqrt(pi))
+
+    We can differentiate the functions with respect
+    to both angles:
+
+    >>> from sympy import Ynm, Symbol, diff
+    >>> from sympy.abc import n,m
+    >>> theta = Symbol("theta")
+    >>> phi = Symbol("phi")
+
+    >>> diff(Ynm(n, m, theta, phi), theta)
+    m*cot(theta)*Ynm(n, m, theta, phi) + sqrt((-m + n)*(m + n + 1))*exp(-I*phi)*Ynm(n, m + 1, theta, phi)
+
+    >>> diff(Ynm(n, m, theta, phi), phi)
+    I*m*Ynm(n, m, theta, phi)
+
+    Further we can compute the complex conjugation:
+
+    >>> from sympy import Ynm, Symbol, conjugate
+    >>> from sympy.abc import n,m
+    >>> theta = Symbol("theta")
+    >>> phi = Symbol("phi")
+
+    >>> conjugate(Ynm(n, m, theta, phi))
+    (-1)**(2*m)*exp(-2*I*m*phi)*Ynm(n, m, theta, phi)
+
+    To get back the well known expressions in spherical
+    coordinates, we use full expansion:
+
+    >>> from sympy import Ynm, Symbol, expand_func
+    >>> from sympy.abc import n,m
+    >>> theta = Symbol("theta")
+    >>> phi = Symbol("phi")
+
+    >>> expand_func(Ynm(n, m, theta, phi))
+    sqrt((2*n + 1)*factorial(-m + n)/factorial(m + n))*exp(I*m*phi)*assoc_legendre(n, m, cos(theta))/(2*sqrt(pi))
+
+    See Also
+    ========
+
+    Ynm_c, Znm
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Spherical_harmonics
+    .. [2] https://mathworld.wolfram.com/SphericalHarmonic.html
+    .. [3] https://functions.wolfram.com/Polynomials/SphericalHarmonicY/
+    .. [4] https://dlmf.nist.gov/14.30
+
+    """
+
+    @classmethod
+    def eval(cls, n, m, theta, phi):
+        # Handle negative index m and arguments theta, phi
+        if m.could_extract_minus_sign():
+            m = -m
+            return S.NegativeOne**m * exp(-2*I*m*phi) * Ynm(n, m, theta, phi)
+        if theta.could_extract_minus_sign():
+            theta = -theta
+            return Ynm(n, m, theta, phi)
+        if phi.could_extract_minus_sign():
+            phi = -phi
+            return exp(-2*I*m*phi) * Ynm(n, m, theta, phi)
+
+        # TODO Add more simplififcation here
+
+    def _eval_expand_func(self, **hints):
+        n, m, theta, phi = self.args
+        rv = (sqrt((2*n + 1)/(4*pi) * factorial(n - m)/factorial(n + m)) *
+                exp(I*m*phi) * assoc_legendre(n, m, cos(theta)))
+        # We can do this because of the range of theta
+        return rv.subs(sqrt(-cos(theta)**2 + 1), sin(theta))
+
+    def fdiff(self, argindex=4):
+        if argindex == 1:
+            # Diff wrt n
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 2:
+            # Diff wrt m
+            raise ArgumentIndexError(self, argindex)
+        elif argindex == 3:
+            # Diff wrt theta
+            n, m, theta, phi = self.args
+            return (m * cot(theta) * Ynm(n, m, theta, phi) +
+                    sqrt((n - m)*(n + m + 1)) * exp(-I*phi) * Ynm(n, m + 1, theta, phi))
+        elif argindex == 4:
+            # Diff wrt phi
+            n, m, theta, phi = self.args
+            return I * m * Ynm(n, m, theta, phi)
+        else:
+            raise ArgumentIndexError(self, argindex)
+
+    def _eval_rewrite_as_polynomial(self, n, m, theta, phi, **kwargs):
+        # TODO: Make sure n \in N
+        # TODO: Assert |m| <= n ortherwise we should return 0
+        return self.expand(func=True)
+
+    def _eval_rewrite_as_sin(self, n, m, theta, phi, **kwargs):
+        return self.rewrite(cos)
+
+    def _eval_rewrite_as_cos(self, n, m, theta, phi, **kwargs):
+        # This method can be expensive due to extensive use of simplification!
+        from sympy.simplify import simplify, trigsimp
+        # TODO: Make sure n \in N
+        # TODO: Assert |m| <= n ortherwise we should return 0
+        term = simplify(self.expand(func=True))
+        # We can do this because of the range of theta
+        term = term.xreplace({Abs(sin(theta)):sin(theta)})
+        return simplify(trigsimp(term))
+
+    def _eval_conjugate(self):
+        # TODO: Make sure theta \in R and phi \in R
+        n, m, theta, phi = self.args
+        return S.NegativeOne**m * self.func(n, -m, theta, phi)
+
+    def as_real_imag(self, deep=True, **hints):
+        # TODO: Handle deep and hints
+        n, m, theta, phi = self.args
+        re = (sqrt((2*n + 1)/(4*pi) * factorial(n - m)/factorial(n + m)) *
+              cos(m*phi) * assoc_legendre(n, m, cos(theta)))
+        im = (sqrt((2*n + 1)/(4*pi) * factorial(n - m)/factorial(n + m)) *
+              sin(m*phi) * assoc_legendre(n, m, cos(theta)))
+        return (re, im)
+
+    def _eval_evalf(self, prec):
+        # Note: works without this function by just calling
+        #       mpmath for Legendre polynomials. But using
+        #       the dedicated function directly is cleaner.
+        from mpmath import mp, workprec
+        n = self.args[0]._to_mpmath(prec)
+        m = self.args[1]._to_mpmath(prec)
+        theta = self.args[2]._to_mpmath(prec)
+        phi = self.args[3]._to_mpmath(prec)
+        with workprec(prec):
+            res = mp.spherharm(n, m, theta, phi)
+        return Expr._from_mpmath(res, prec)
+
+
+def Ynm_c(n, m, theta, phi):
+    r"""
+    Conjugate spherical harmonics defined as
+
+    .. math::
+        \overline{Y_n^m(\theta, \varphi)} := (-1)^m Y_n^{-m}(\theta, \varphi).
+
+    Examples
+    ========
+
+    >>> from sympy import Ynm_c, Symbol, simplify
+    >>> from sympy.abc import n,m
+    >>> theta = Symbol("theta")
+    >>> phi = Symbol("phi")
+    >>> Ynm_c(n, m, theta, phi)
+    (-1)**(2*m)*exp(-2*I*m*phi)*Ynm(n, m, theta, phi)
+    >>> Ynm_c(n, m, -theta, phi)
+    (-1)**(2*m)*exp(-2*I*m*phi)*Ynm(n, m, theta, phi)
+
+    For specific integers $n$ and $m$ we can evaluate the harmonics
+    to more useful expressions:
+
+    >>> simplify(Ynm_c(0, 0, theta, phi).expand(func=True))
+    1/(2*sqrt(pi))
+    >>> simplify(Ynm_c(1, -1, theta, phi).expand(func=True))
+    sqrt(6)*exp(I*(-phi + 2*conjugate(phi)))*sin(theta)/(4*sqrt(pi))
+
+    See Also
+    ========
+
+    Ynm, Znm
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Spherical_harmonics
+    .. [2] https://mathworld.wolfram.com/SphericalHarmonic.html
+    .. [3] https://functions.wolfram.com/Polynomials/SphericalHarmonicY/
+
+    """
+    return conjugate(Ynm(n, m, theta, phi))
+
+
+class Znm(DefinedFunction):
+    r"""
+    Real spherical harmonics defined as
+
+    .. math::
+
+        Z_n^m(\theta, \varphi) :=
+        \begin{cases}
+          \frac{Y_n^m(\theta, \varphi) + \overline{Y_n^m(\theta, \varphi)}}{\sqrt{2}} &\quad m > 0 \\
+          Y_n^m(\theta, \varphi) &\quad m = 0 \\
+          \frac{Y_n^m(\theta, \varphi) - \overline{Y_n^m(\theta, \varphi)}}{i \sqrt{2}} &\quad m < 0 \\
+        \end{cases}
+
+    which gives in simplified form
+
+    .. math::
+
+        Z_n^m(\theta, \varphi) =
+        \begin{cases}
+          \frac{Y_n^m(\theta, \varphi) + (-1)^m Y_n^{-m}(\theta, \varphi)}{\sqrt{2}} &\quad m > 0 \\
+          Y_n^m(\theta, \varphi) &\quad m = 0 \\
+          \frac{Y_n^m(\theta, \varphi) - (-1)^m Y_n^{-m}(\theta, \varphi)}{i \sqrt{2}} &\quad m < 0 \\
+        \end{cases}
+
+    Examples
+    ========
+
+    >>> from sympy import Znm, Symbol, simplify
+    >>> from sympy.abc import n, m
+    >>> theta = Symbol("theta")
+    >>> phi = Symbol("phi")
+    >>> Znm(n, m, theta, phi)
+    Znm(n, m, theta, phi)
+
+    For specific integers n and m we can evaluate the harmonics
+    to more useful expressions:
+
+    >>> simplify(Znm(0, 0, theta, phi).expand(func=True))
+    1/(2*sqrt(pi))
+    >>> simplify(Znm(1, 1, theta, phi).expand(func=True))
+    -sqrt(3)*sin(theta)*cos(phi)/(2*sqrt(pi))
+    >>> simplify(Znm(2, 1, theta, phi).expand(func=True))
+    -sqrt(15)*sin(2*theta)*cos(phi)/(4*sqrt(pi))
+
+    See Also
+    ========
+
+    Ynm, Ynm_c
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Spherical_harmonics
+    .. [2] https://mathworld.wolfram.com/SphericalHarmonic.html
+    .. [3] https://functions.wolfram.com/Polynomials/SphericalHarmonicY/
+
+    """
+
+    @classmethod
+    def eval(cls, n, m, theta, phi):
+        if m.is_positive:
+            zz = (Ynm(n, m, theta, phi) + Ynm_c(n, m, theta, phi)) / sqrt(2)
+            return zz
+        elif m.is_zero:
+            return Ynm(n, m, theta, phi)
+        elif m.is_negative:
+            zz = (Ynm(n, m, theta, phi) - Ynm_c(n, m, theta, phi)) / (sqrt(2)*I)
+            return zz
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tensor_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tensor_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..6d996a58cbc8320620c9a1f6e68529c3b5e99aef
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tensor_functions.py
@@ -0,0 +1,474 @@
+from math import prod
+
+from sympy.core import S, Integer
+from sympy.core.function import DefinedFunction
+from sympy.core.logic import fuzzy_not
+from sympy.core.relational import Ne
+from sympy.core.sorting import default_sort_key
+from sympy.external.gmpy import SYMPY_INTS
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.utilities.iterables import has_dups
+
+###############################################################################
+###################### Kronecker Delta, Levi-Civita etc. ######################
+###############################################################################
+
+
+def Eijk(*args, **kwargs):
+    """
+    Represent the Levi-Civita symbol.
+
+    This is a compatibility wrapper to ``LeviCivita()``.
+
+    See Also
+    ========
+
+    LeviCivita
+
+    """
+    return LeviCivita(*args, **kwargs)
+
+
+def eval_levicivita(*args):
+    """Evaluate Levi-Civita symbol."""
+    n = len(args)
+    return prod(
+        prod(args[j] - args[i] for j in range(i + 1, n))
+        / factorial(i) for i in range(n))
+    # converting factorial(i) to int is slightly faster
+
+
+class LeviCivita(DefinedFunction):
+    """
+    Represent the Levi-Civita symbol.
+
+    Explanation
+    ===========
+
+    For even permutations of indices it returns 1, for odd permutations -1, and
+    for everything else (a repeated index) it returns 0.
+
+    Thus it represents an alternating pseudotensor.
+
+    Examples
+    ========
+
+    >>> from sympy import LeviCivita
+    >>> from sympy.abc import i, j, k
+    >>> LeviCivita(1, 2, 3)
+    1
+    >>> LeviCivita(1, 3, 2)
+    -1
+    >>> LeviCivita(1, 2, 2)
+    0
+    >>> LeviCivita(i, j, k)
+    LeviCivita(i, j, k)
+    >>> LeviCivita(i, j, i)
+    0
+
+    See Also
+    ========
+
+    Eijk
+
+    """
+
+    is_integer = True
+
+    @classmethod
+    def eval(cls, *args):
+        if all(isinstance(a, (SYMPY_INTS, Integer)) for a in args):
+            return eval_levicivita(*args)
+        if has_dups(args):
+            return S.Zero
+
+    def doit(self, **hints):
+        return eval_levicivita(*self.args)
+
+
+class KroneckerDelta(DefinedFunction):
+    """
+    The discrete, or Kronecker, delta function.
+
+    Explanation
+    ===========
+
+    A function that takes in two integers $i$ and $j$. It returns $0$ if $i$
+    and $j$ are not equal, or it returns $1$ if $i$ and $j$ are equal.
+
+    Examples
+    ========
+
+    An example with integer indices:
+
+        >>> from sympy import KroneckerDelta
+        >>> KroneckerDelta(1, 2)
+        0
+        >>> KroneckerDelta(3, 3)
+        1
+
+    Symbolic indices:
+
+        >>> from sympy.abc import i, j, k
+        >>> KroneckerDelta(i, j)
+        KroneckerDelta(i, j)
+        >>> KroneckerDelta(i, i)
+        1
+        >>> KroneckerDelta(i, i + 1)
+        0
+        >>> KroneckerDelta(i, i + 1 + k)
+        KroneckerDelta(i, i + k + 1)
+
+    Parameters
+    ==========
+
+    i : Number, Symbol
+        The first index of the delta function.
+    j : Number, Symbol
+        The second index of the delta function.
+
+    See Also
+    ========
+
+    eval
+    DiracDelta
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Kronecker_delta
+
+    """
+
+    is_integer = True
+
+    @classmethod
+    def eval(cls, i, j, delta_range=None):
+        """
+        Evaluates the discrete delta function.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta
+        >>> from sympy.abc import i, j, k
+
+        >>> KroneckerDelta(i, j)
+        KroneckerDelta(i, j)
+        >>> KroneckerDelta(i, i)
+        1
+        >>> KroneckerDelta(i, i + 1)
+        0
+        >>> KroneckerDelta(i, i + 1 + k)
+        KroneckerDelta(i, i + k + 1)
+
+        # indirect doctest
+
+        """
+
+        if delta_range is not None:
+            dinf, dsup = delta_range
+            if (dinf - i > 0) == True:
+                return S.Zero
+            if (dinf - j > 0) == True:
+                return S.Zero
+            if (dsup - i < 0) == True:
+                return S.Zero
+            if (dsup - j < 0) == True:
+                return S.Zero
+
+        diff = i - j
+        if diff.is_zero:
+            return S.One
+        elif fuzzy_not(diff.is_zero):
+            return S.Zero
+
+        if i.assumptions0.get("below_fermi") and \
+                j.assumptions0.get("above_fermi"):
+            return S.Zero
+        if j.assumptions0.get("below_fermi") and \
+                i.assumptions0.get("above_fermi"):
+            return S.Zero
+        # to make KroneckerDelta canonical
+        # following lines will check if inputs are in order
+        # if not, will return KroneckerDelta with correct order
+        if default_sort_key(j) < default_sort_key(i):
+            if delta_range:
+                return cls(j, i, delta_range)
+            else:
+                return cls(j, i)
+
+    @property
+    def delta_range(self):
+        if len(self.args) > 2:
+            return self.args[2]
+
+    def _eval_power(self, expt):
+        if expt.is_positive:
+            return self
+        if expt.is_negative and expt is not S.NegativeOne:
+            return 1/self
+
+    @property
+    def is_above_fermi(self):
+        """
+        True if Delta can be non-zero above fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> q = Symbol('q')
+        >>> KroneckerDelta(p, a).is_above_fermi
+        True
+        >>> KroneckerDelta(p, i).is_above_fermi
+        False
+        >>> KroneckerDelta(p, q).is_above_fermi
+        True
+
+        See Also
+        ========
+
+        is_below_fermi, is_only_below_fermi, is_only_above_fermi
+
+        """
+        if self.args[0].assumptions0.get("below_fermi"):
+            return False
+        if self.args[1].assumptions0.get("below_fermi"):
+            return False
+        return True
+
+    @property
+    def is_below_fermi(self):
+        """
+        True if Delta can be non-zero below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> q = Symbol('q')
+        >>> KroneckerDelta(p, a).is_below_fermi
+        False
+        >>> KroneckerDelta(p, i).is_below_fermi
+        True
+        >>> KroneckerDelta(p, q).is_below_fermi
+        True
+
+        See Also
+        ========
+
+        is_above_fermi, is_only_above_fermi, is_only_below_fermi
+
+        """
+        if self.args[0].assumptions0.get("above_fermi"):
+            return False
+        if self.args[1].assumptions0.get("above_fermi"):
+            return False
+        return True
+
+    @property
+    def is_only_above_fermi(self):
+        """
+        True if Delta is restricted to above fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> q = Symbol('q')
+        >>> KroneckerDelta(p, a).is_only_above_fermi
+        True
+        >>> KroneckerDelta(p, q).is_only_above_fermi
+        False
+        >>> KroneckerDelta(p, i).is_only_above_fermi
+        False
+
+        See Also
+        ========
+
+        is_above_fermi, is_below_fermi, is_only_below_fermi
+
+        """
+        return ( self.args[0].assumptions0.get("above_fermi")
+                or
+                self.args[1].assumptions0.get("above_fermi")
+                ) or False
+
+    @property
+    def is_only_below_fermi(self):
+        """
+        True if Delta is restricted to below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> q = Symbol('q')
+        >>> KroneckerDelta(p, i).is_only_below_fermi
+        True
+        >>> KroneckerDelta(p, q).is_only_below_fermi
+        False
+        >>> KroneckerDelta(p, a).is_only_below_fermi
+        False
+
+        See Also
+        ========
+
+        is_above_fermi, is_below_fermi, is_only_above_fermi
+
+        """
+        return ( self.args[0].assumptions0.get("below_fermi")
+                or
+                self.args[1].assumptions0.get("below_fermi")
+                ) or False
+
+    @property
+    def indices_contain_equal_information(self):
+        """
+        Returns True if indices are either both above or below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> q = Symbol('q')
+        >>> KroneckerDelta(p, q).indices_contain_equal_information
+        True
+        >>> KroneckerDelta(p, q+1).indices_contain_equal_information
+        True
+        >>> KroneckerDelta(i, p).indices_contain_equal_information
+        False
+
+        """
+        if (self.args[0].assumptions0.get("below_fermi") and
+                self.args[1].assumptions0.get("below_fermi")):
+            return True
+        if (self.args[0].assumptions0.get("above_fermi")
+                and self.args[1].assumptions0.get("above_fermi")):
+            return True
+
+        # if both indices are general we are True, else false
+        return self.is_below_fermi and self.is_above_fermi
+
+    @property
+    def preferred_index(self):
+        """
+        Returns the index which is preferred to keep in the final expression.
+
+        Explanation
+        ===========
+
+        The preferred index is the index with more information regarding fermi
+        level. If indices contain the same information, 'a' is preferred before
+        'b'.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> j = Symbol('j', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> KroneckerDelta(p, i).preferred_index
+        i
+        >>> KroneckerDelta(p, a).preferred_index
+        a
+        >>> KroneckerDelta(i, j).preferred_index
+        i
+
+        See Also
+        ========
+
+        killable_index
+
+        """
+        if self._get_preferred_index():
+            return self.args[1]
+        else:
+            return self.args[0]
+
+    @property
+    def killable_index(self):
+        """
+        Returns the index which is preferred to substitute in the final
+        expression.
+
+        Explanation
+        ===========
+
+        The index to substitute is the index with less information regarding
+        fermi level. If indices contain the same information, 'a' is preferred
+        before 'b'.
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerDelta, Symbol
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> j = Symbol('j', below_fermi=True)
+        >>> p = Symbol('p')
+        >>> KroneckerDelta(p, i).killable_index
+        p
+        >>> KroneckerDelta(p, a).killable_index
+        p
+        >>> KroneckerDelta(i, j).killable_index
+        j
+
+        See Also
+        ========
+
+        preferred_index
+
+        """
+        if self._get_preferred_index():
+            return self.args[0]
+        else:
+            return self.args[1]
+
+    def _get_preferred_index(self):
+        """
+        Returns the index which is preferred to keep in the final expression.
+
+        The preferred index is the index with more information regarding fermi
+        level. If indices contain the same information, index 0 is returned.
+
+        """
+        if not self.is_above_fermi:
+            if self.args[0].assumptions0.get("below_fermi"):
+                return 0
+            else:
+                return 1
+        elif not self.is_below_fermi:
+            if self.args[0].assumptions0.get("above_fermi"):
+                return 0
+            else:
+                return 1
+        else:
+            return 0
+
+    @property
+    def indices(self):
+        return self.args[0:2]
+
+    def _eval_rewrite_as_Piecewise(self, *args, **kwargs):
+        i, j = args
+        return Piecewise((0, Ne(i, j)), (1, True))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_bessel.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..ccd1ce88ca9dea15f065e7c57d488498b8f79f4e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_bessel.py
@@ -0,0 +1,807 @@
+from itertools import product
+
+from sympy.concrete.summations import Sum
+from sympy.core.function import (diff, expand_func)
+from sympy.core.numbers import (I, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (conjugate, polar_lift)
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.hyperbolic import (cosh, sinh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.bessel import (besseli, besselj, besselk, bessely, hankel1, hankel2, hn1, hn2, jn, jn_zeros, yn)
+from sympy.functions.special.gamma_functions import (gamma, uppergamma)
+from sympy.functions.special.hyper import hyper
+from sympy.integrals.integrals import Integral
+from sympy.series.order import O
+from sympy.series.series import series
+from sympy.functions.special.bessel import (airyai, airybi,
+                                            airyaiprime, airybiprime, marcumq)
+from sympy.core.random import (random_complex_number as randcplx,
+                                      verify_numerically as tn,
+                                      test_derivative_numerically as td,
+                                      _randint)
+from sympy.simplify import besselsimp
+from sympy.testing.pytest import raises, slow
+
+from sympy.abc import z, n, k, x
+
+randint = _randint()
+
+
+def test_bessel_rand():
+    for f in [besselj, bessely, besseli, besselk, hankel1, hankel2]:
+        assert td(f(randcplx(), z), z)
+
+    for f in [jn, yn, hn1, hn2]:
+        assert td(f(randint(-10, 10), z), z)
+
+
+def test_bessel_twoinputs():
+    for f in [besselj, bessely, besseli, besselk, hankel1, hankel2, jn, yn]:
+        raises(TypeError, lambda: f(1))
+        raises(TypeError, lambda: f(1, 2, 3))
+
+
+def test_besselj_leading_term():
+    assert besselj(0, x).as_leading_term(x) == 1
+    assert besselj(1, sin(x)).as_leading_term(x) == x/2
+    assert besselj(1, 2*sqrt(x)).as_leading_term(x) == sqrt(x)
+
+    # https://github.com/sympy/sympy/issues/21701
+    assert (besselj(z, x)/x**z).as_leading_term(x) == 1/(2**z*gamma(z + 1))
+
+
+def test_bessely_leading_term():
+    assert bessely(0, x).as_leading_term(x) == (2*log(x) - 2*log(2) + 2*S.EulerGamma)/pi
+    assert bessely(1, sin(x)).as_leading_term(x) == -2/(pi*x)
+    assert bessely(1, 2*sqrt(x)).as_leading_term(x) == -1/(pi*sqrt(x))
+
+
+def test_besseli_leading_term():
+    assert besseli(0, x).as_leading_term(x) == 1
+    assert besseli(1, sin(x)).as_leading_term(x) == x/2
+    assert besseli(1, 2*sqrt(x)).as_leading_term(x) == sqrt(x)
+
+
+def test_besselk_leading_term():
+    assert besselk(0, x).as_leading_term(x) == -log(x) - S.EulerGamma + log(2)
+    assert besselk(1, sin(x)).as_leading_term(x) == 1/x
+    assert besselk(1, 2*sqrt(x)).as_leading_term(x) == 1/(2*sqrt(x))
+    assert besselk(S(5)/3, x).as_leading_term(x) == 2**(S(2)/3)*gamma(S(5)/3)/x**(S(5)/3)
+    assert besselk(S(2)/3, x).as_leading_term(x) == besselk(-S(2)/3, x).as_leading_term(x)
+    assert besselk(1,cos(x)).as_leading_term(x) == besselk(1,1)
+    assert besselk(3,1/x).as_leading_term(x) == sqrt(pi)*exp(-(1/x))/sqrt(2/x)
+    assert besselk(3,1/sin(x)).as_leading_term(x) == sqrt(pi)*exp(-(1/x))/sqrt(2/x)
+
+    nz = Symbol("nz", nonzero=True)
+    assert besselk(nz, x).as_leading_term(x).subs({nz:S(5)/7}) == besselk(S(5)/7, x).series(x).as_leading_term(x)
+    assert besselk(nz, x).as_leading_term(x).subs({nz:S(-15)/7}) == besselk(S(-15)/7, x).series(x).as_leading_term(x)
+    assert besselk(nz, x).as_leading_term(x).subs({nz:3}) == besselk(3, x).series(x).as_leading_term(x)
+    assert besselk(nz, x).as_leading_term(x).subs({nz:-2}) == besselk(-2, x).series(x).as_leading_term(x)
+
+
+def test_besselj_series():
+    assert besselj(0, x).series(x) == 1 - x**2/4 + x**4/64 + O(x**6)
+    assert besselj(0, x**(1.1)).series(x) == 1 + x**4.4/64 - x**2.2/4 + O(x**6)
+    assert besselj(0, x**2 + x).series(x) == 1 - x**2/4 - x**3/2\
+        - 15*x**4/64 + x**5/16 + O(x**6)
+    assert besselj(0, sqrt(x) + x).series(x, n=4) == 1 - x/4 - 15*x**2/64\
+        + 215*x**3/2304 - x**Rational(3, 2)/2 + x**Rational(5, 2)/16\
+        + 23*x**Rational(7, 2)/384 + O(x**4)
+    assert besselj(0, x/(1 - x)).series(x) == 1 - x**2/4 - x**3/2 - 47*x**4/64\
+        - 15*x**5/16 + O(x**6)
+    assert besselj(0, log(1 + x)).series(x) == 1 - x**2/4 + x**3/4\
+        - 41*x**4/192 + 17*x**5/96 + O(x**6)
+    assert besselj(1, sin(x)).series(x) == x/2 - 7*x**3/48 + 73*x**5/1920 + O(x**6)
+    assert besselj(1, 2*sqrt(x)).series(x) == sqrt(x) - x**Rational(3, 2)/2\
+        + x**Rational(5, 2)/12 - x**Rational(7, 2)/144 + x**Rational(9, 2)/2880\
+        - x**Rational(11, 2)/86400 + O(x**6)
+    assert besselj(-2, sin(x)).series(x, n=4) == besselj(2, sin(x)).series(x, n=4)
+
+
+def test_bessely_series():
+    const = 2*S.EulerGamma/pi - 2*log(2)/pi + 2*log(x)/pi
+    assert bessely(0, x).series(x, n=4) == const + x**2*(-log(x)/(2*pi)\
+        + (2 - 2*S.EulerGamma)/(4*pi) + log(2)/(2*pi)) + O(x**4*log(x))
+    assert bessely(1, x).series(x, n=4) == -2/(pi*x) + x*(log(x)/pi - log(2)/pi - \
+        (1 - 2*S.EulerGamma)/(2*pi)) + x**3*(-log(x)/(8*pi) + \
+        (S(5)/2 - 2*S.EulerGamma)/(16*pi) + log(2)/(8*pi)) + O(x**4*log(x))
+    assert bessely(2, x).series(x, n=4) == -4/(pi*x**2) - 1/pi + x**2*(log(x)/(4*pi) - \
+        log(2)/(4*pi) - (S(3)/2 - 2*S.EulerGamma)/(8*pi)) + O(x**4*log(x))
+    assert bessely(3, x).series(x, n=4) == -16/(pi*x**3) - 2/(pi*x) - \
+        x/(4*pi) + x**3*(log(x)/(24*pi) - log(2)/(24*pi) - \
+        (S(11)/6 - 2*S.EulerGamma)/(48*pi)) + O(x**4*log(x))
+    assert bessely(0, x**(1.1)).series(x, n=4) == 2*S.EulerGamma/pi\
+        - 2*log(2)/pi + 2.2*log(x)/pi + x**2.2*(-0.55*log(x)/pi\
+        + (2 - 2*S.EulerGamma)/(4*pi) + log(2)/(2*pi)) + O(x**4*log(x))
+    assert bessely(0, x**2 + x).series(x, n=4) == \
+        const - (2 - 2*S.EulerGamma)*(-x**3/(2*pi) - x**2/(4*pi)) + 2*x/pi\
+        + x**2*(-log(x)/(2*pi) - 1/pi + log(2)/(2*pi))\
+        + x**3*(-log(x)/pi + 1/(6*pi) + log(2)/pi) + O(x**4*log(x))
+    assert bessely(0, x/(1 - x)).series(x, n=3) == const\
+        + 2*x/pi + x**2*(-log(x)/(2*pi) + (2 - 2*S.EulerGamma)/(4*pi)\
+        + log(2)/(2*pi) + 1/pi) + O(x**3*log(x))
+    assert bessely(0, log(1 + x)).series(x, n=3) == const\
+        - x/pi + x**2*(-log(x)/(2*pi) + (2 - 2*S.EulerGamma)/(4*pi)\
+        + log(2)/(2*pi) + 5/(12*pi)) + O(x**3*log(x))
+    assert bessely(1, sin(x)).series(x, n=4) == -1/(pi*(-x**3/12 + x/2)) - \
+        (1 - 2*S.EulerGamma)*(-x**3/12 + x/2)/pi + x*(log(x)/pi - log(2)/pi) + \
+        x**3*(-7*log(x)/(24*pi) - 1/(6*pi) + (S(5)/2 - 2*S.EulerGamma)/(16*pi) +
+        7*log(2)/(24*pi)) + O(x**4*log(x))
+    assert bessely(1, 2*sqrt(x)).series(x, n=3) == -1/(pi*sqrt(x)) + \
+        sqrt(x)*(log(x)/pi - (1 - 2*S.EulerGamma)/pi) + x**(S(3)/2)*(-log(x)/(2*pi) + \
+        (S(5)/2 - 2*S.EulerGamma)/(2*pi)) + x**(S(5)/2)*(log(x)/(12*pi) - \
+        (S(10)/3 - 2*S.EulerGamma)/(12*pi)) + O(x**3*log(x))
+    assert bessely(-2, sin(x)).series(x, n=4) == bessely(2, sin(x)).series(x, n=4)
+
+
+def test_besseli_series():
+    assert besseli(0, x).series(x) == 1 + x**2/4 + x**4/64 + O(x**6)
+    assert besseli(0, x**(1.1)).series(x) == 1 + x**4.4/64 + x**2.2/4 + O(x**6)
+    assert besseli(0, x**2 + x).series(x) == 1 + x**2/4 + x**3/2 + 17*x**4/64 + \
+        x**5/16 + O(x**6)
+    assert besseli(0, sqrt(x) + x).series(x, n=4) == 1 + x/4 + 17*x**2/64 + \
+        217*x**3/2304 + x**(S(3)/2)/2 + x**(S(5)/2)/16 + 25*x**(S(7)/2)/384 + O(x**4)
+    assert besseli(0, x/(1 - x)).series(x) == 1 + x**2/4 + x**3/2 + 49*x**4/64 + \
+        17*x**5/16 + O(x**6)
+    assert besseli(0, log(1 + x)).series(x) == 1 + x**2/4 - x**3/4 + 47*x**4/192 - \
+        23*x**5/96 + O(x**6)
+    assert besseli(1, sin(x)).series(x) == x/2 - x**3/48 - 47*x**5/1920 + O(x**6)
+    assert besseli(1, 2*sqrt(x)).series(x) == sqrt(x) + x**(S(3)/2)/2 + x**(S(5)/2)/12 + \
+        x**(S(7)/2)/144 + x**(S(9)/2)/2880 + x**(S(11)/2)/86400 + O(x**6)
+    assert besseli(-2, sin(x)).series(x, n=4) == besseli(2, sin(x)).series(x, n=4)
+
+    #test for aseries
+    assert besseli(0,x).series(x, oo, n=4) == sqrt(2)*(sqrt(1/x) - (1/x)**(S(3)/2)/8 - \
+        3*(1/x)**(S(5)/2)/128 - 15*(1/x)**(S(7)/2)/1024 + O((1/x)**(S(9)/2), (x, oo)))*exp(x)/(2*sqrt(pi))
+    assert besseli(0,x).series(x,-oo, n=4) == sqrt(2)*(sqrt(-1/x) - (-1/x)**(S(3)/2)/8 - 3*(-1/x)**(S(5)/2)/128 - \
+        15*(-1/x)**(S(7)/2)/1024 + O((-1/x)**(S(9)/2), (x, -oo)))*exp(-x)/(2*sqrt(pi))
+
+
+def test_besselk_series():
+    const = log(2) - S.EulerGamma - log(x)
+    assert besselk(0, x).series(x, n=4) == const + \
+        x**2*(-log(x)/4 - S.EulerGamma/4 + log(2)/4 + S(1)/4) + O(x**4*log(x))
+    assert besselk(1, x).series(x, n=4) == 1/x + x*(log(x)/2 - log(2)/2 - \
+        S(1)/4 + S.EulerGamma/2) + x**3*(log(x)/16 - S(5)/64 - log(2)/16 + \
+        S.EulerGamma/16) + O(x**4*log(x))
+    assert besselk(2, x).series(x, n=4) == 2/x**2 - S(1)/2 + x**2*(-log(x)/8 - \
+        S.EulerGamma/8 + log(2)/8 + S(3)/32) + O(x**4*log(x))
+    assert besselk(2, x).series(x, n=1) == 2/x**2 - S(1)/2 + O(x) #edge case for series truncation
+    assert besselk(0, x**(1.1)).series(x, n=4) == log(2) - S.EulerGamma - \
+        1.1*log(x) + x**2.2*(-0.275*log(x) - S.EulerGamma/4 + \
+        log(2)/4 + S(1)/4) + O(x**4*log(x))
+    assert besselk(0, x**2 + x).series(x, n=4) == const + \
+        (2 - 2*S.EulerGamma)*(x**3/4 + x**2/8) - x + x**2*(-log(x)/4 + \
+        log(2)/4 + S(1)/2) + x**3*(-log(x)/2 - S(7)/12 + log(2)/2) + O(x**4*log(x))
+    assert besselk(0, x/(1 - x)).series(x, n=3) == const - x + x**2*(-log(x)/4 - \
+        S(1)/4 - S.EulerGamma/4 + log(2)/4) + O(x**3*log(x))
+    assert besselk(0, log(1 + x)).series(x, n=3) == const + x/2 + \
+        x**2*(-log(x)/4 - S.EulerGamma/4 + S(1)/24 + log(2)/4) + O(x**3*log(x))
+    assert besselk(1, 2*sqrt(x)).series(x, n=3) == 1/(2*sqrt(x)) + \
+        sqrt(x)*(log(x)/2 - S(1)/2 + S.EulerGamma) + x**(S(3)/2)*(log(x)/4 - S(5)/8 + \
+        S.EulerGamma/2) + x**(S(5)/2)*(log(x)/24 - S(5)/36 + S.EulerGamma/12) + O(x**3*log(x))
+    assert besselk(-2, sin(x)).series(x, n=4) == besselk(2, sin(x)).series(x, n=4)
+    assert besselk(2, x**2).series(x, n=2) == 2/x**4 - S(1)/2 + O(x**2) #edge case for series truncation
+    assert besselk(2, x**2).series(x, n=6) == 2/x**4 - S(1)/2 + x**4*(-log(x)/4 - S.EulerGamma/8 + log(2)/8 + S(3)/32) + O(x**6*log(x))
+    assert (x**2*besselk(2, x)).series(x, n=2) == 2 + O(x**2)
+
+    #test for aseries
+    assert besselk(0,x).series(x, oo, n=4) == sqrt(2)*sqrt(pi)*(sqrt(1/x) + (1/x)**(S(3)/2)/8 - \
+            3*(1/x)**(S(5)/2)/128 + 15*(1/x)**(S(7)/2)/1024 + O((1/x)**(S(9)/2), (x, oo)))*exp(-x)/2
+    assert besselk(0,x).series(x, -oo, n=4) == sqrt(2)*sqrt(pi)*(-I*sqrt(-1/x) + I*(-1/x)**(S(3)/2)/8 + \
+            3*I*(-1/x)**(S(5)/2)/128 + 15*I*(-1/x)**(S(7)/2)/1024 + O((-1/x)**(S(9)/2), (x, -oo)))*exp(-x)/2
+
+
+def test_besselk_frac_order_series():
+    assert besselk(S(5)/3, x).series(x, n=2) == 2**(S(2)/3)*gamma(S(5)/3)/x**(S(5)/3) - \
+        3*gamma(S(5)/3)*x**(S(1)/3)/(4*2**(S(1)/3)) + \
+            gamma(-S(5)/3)*x**(S(5)/3)/(4*2**(S(2)/3)) + O(x**2)
+    assert besselk(S(1)/2, x).series(x, n=2) == sqrt(pi/2)/sqrt(x) - \
+        sqrt(pi*x/2) + x**(S(3)/2)*sqrt(pi/2)/2 + O(x**2)
+    assert besselk(S(1)/2, sqrt(x)).series(x, n=2) == sqrt(pi/2)/x**(S(1)/4) - \
+        sqrt(pi/2)*x**(S(1)/4) + sqrt(pi/2)*x**(S(3)/4)/2 - \
+            sqrt(pi/2)*x**(S(5)/4)/6 + sqrt(pi/2)*x**(S(7)/4)/24 + O(x**2)
+    assert besselk(S(1)/2, x**2).series(x, n=2) == sqrt(pi/2)/x \
+        - sqrt(pi/2)*x + O(x**2)
+    assert besselk(-S(1)/2, x).series(x) == besselk(S(1)/2, x).series(x)
+    assert besselk(-S(7)/6, x).series(x) == besselk(S(7)/6, x).series(x)
+
+
+def test_diff():
+    assert besselj(n, z).diff(z) == besselj(n - 1, z)/2 - besselj(n + 1, z)/2
+    assert bessely(n, z).diff(z) == bessely(n - 1, z)/2 - bessely(n + 1, z)/2
+    assert besseli(n, z).diff(z) == besseli(n - 1, z)/2 + besseli(n + 1, z)/2
+    assert besselk(n, z).diff(z) == -besselk(n - 1, z)/2 - besselk(n + 1, z)/2
+    assert hankel1(n, z).diff(z) == hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2
+    assert hankel2(n, z).diff(z) == hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2
+
+
+def test_rewrite():
+    assert besselj(n, z).rewrite(jn) == sqrt(2*z/pi)*jn(n - S.Half, z)
+    assert bessely(n, z).rewrite(yn) == sqrt(2*z/pi)*yn(n - S.Half, z)
+    assert besseli(n, z).rewrite(besselj) == \
+        exp(-I*n*pi/2)*besselj(n, polar_lift(I)*z)
+    assert besselj(n, z).rewrite(besseli) == \
+        exp(I*n*pi/2)*besseli(n, polar_lift(-I)*z)
+
+    nu = randcplx()
+
+    assert tn(besselj(nu, z), besselj(nu, z).rewrite(besseli), z)
+    assert tn(besselj(nu, z), besselj(nu, z).rewrite(bessely), z)
+
+    assert tn(besseli(nu, z), besseli(nu, z).rewrite(besselj), z)
+    assert tn(besseli(nu, z), besseli(nu, z).rewrite(bessely), z)
+
+    assert tn(bessely(nu, z), bessely(nu, z).rewrite(besselj), z)
+    assert tn(bessely(nu, z), bessely(nu, z).rewrite(besseli), z)
+
+    assert tn(besselk(nu, z), besselk(nu, z).rewrite(besselj), z)
+    assert tn(besselk(nu, z), besselk(nu, z).rewrite(besseli), z)
+    assert tn(besselk(nu, z), besselk(nu, z).rewrite(bessely), z)
+
+    # check that a rewrite was triggered, when the order is set to a generic
+    # symbol 'nu'
+    assert yn(nu, z) != yn(nu, z).rewrite(jn)
+    assert hn1(nu, z) != hn1(nu, z).rewrite(jn)
+    assert hn2(nu, z) != hn2(nu, z).rewrite(jn)
+    assert jn(nu, z) != jn(nu, z).rewrite(yn)
+    assert hn1(nu, z) != hn1(nu, z).rewrite(yn)
+    assert hn2(nu, z) != hn2(nu, z).rewrite(yn)
+
+    # rewriting spherical bessel functions (SBFs) w.r.t. besselj, bessely is
+    # not allowed if a generic symbol 'nu' is used as the order of the SBFs
+    # to avoid inconsistencies (the order of bessel[jy] is allowed to be
+    # complex-valued, whereas SBFs are defined only for integer orders)
+    order = nu
+    for f in (besselj, bessely):
+        assert hn1(order, z) == hn1(order, z).rewrite(f)
+        assert hn2(order, z) == hn2(order, z).rewrite(f)
+
+    assert jn(order, z).rewrite(besselj) == sqrt(2)*sqrt(pi)*sqrt(1/z)*besselj(order + S.Half, z)/2
+    assert jn(order, z).rewrite(bessely) == (-1)**nu*sqrt(2)*sqrt(pi)*sqrt(1/z)*bessely(-order - S.Half, z)/2
+
+    # for integral orders rewriting SBFs w.r.t bessel[jy] is allowed
+    N = Symbol('n', integer=True)
+    ri = randint(-11, 10)
+    for order in (ri, N):
+        for f in (besselj, bessely):
+            assert yn(order, z) != yn(order, z).rewrite(f)
+            assert jn(order, z) != jn(order, z).rewrite(f)
+            assert hn1(order, z) != hn1(order, z).rewrite(f)
+            assert hn2(order, z) != hn2(order, z).rewrite(f)
+
+    for func, refunc in product((yn, jn, hn1, hn2),
+                                (jn, yn, besselj, bessely)):
+        assert tn(func(ri, z), func(ri, z).rewrite(refunc), z)
+
+
+def test_expand():
+    assert expand_func(besselj(S.Half, z).rewrite(jn)) == \
+        sqrt(2)*sin(z)/(sqrt(pi)*sqrt(z))
+    assert expand_func(bessely(S.Half, z).rewrite(yn)) == \
+        -sqrt(2)*cos(z)/(sqrt(pi)*sqrt(z))
+
+    # XXX: teach sin/cos to work around arguments like
+    # x*exp_polar(I*pi*n/2).  Then change besselsimp -> expand_func
+    assert besselsimp(besselj(S.Half, z)) == sqrt(2)*sin(z)/(sqrt(pi)*sqrt(z))
+    assert besselsimp(besselj(Rational(-1, 2), z)) == sqrt(2)*cos(z)/(sqrt(pi)*sqrt(z))
+    assert besselsimp(besselj(Rational(5, 2), z)) == \
+        -sqrt(2)*(z**2*sin(z) + 3*z*cos(z) - 3*sin(z))/(sqrt(pi)*z**Rational(5, 2))
+    assert besselsimp(besselj(Rational(-5, 2), z)) == \
+        -sqrt(2)*(z**2*cos(z) - 3*z*sin(z) - 3*cos(z))/(sqrt(pi)*z**Rational(5, 2))
+
+    assert besselsimp(bessely(S.Half, z)) == \
+        -(sqrt(2)*cos(z))/(sqrt(pi)*sqrt(z))
+    assert besselsimp(bessely(Rational(-1, 2), z)) == sqrt(2)*sin(z)/(sqrt(pi)*sqrt(z))
+    assert besselsimp(bessely(Rational(5, 2), z)) == \
+        sqrt(2)*(z**2*cos(z) - 3*z*sin(z) - 3*cos(z))/(sqrt(pi)*z**Rational(5, 2))
+    assert besselsimp(bessely(Rational(-5, 2), z)) == \
+        -sqrt(2)*(z**2*sin(z) + 3*z*cos(z) - 3*sin(z))/(sqrt(pi)*z**Rational(5, 2))
+
+    assert besselsimp(besseli(S.Half, z)) == sqrt(2)*sinh(z)/(sqrt(pi)*sqrt(z))
+    assert besselsimp(besseli(Rational(-1, 2), z)) == \
+        sqrt(2)*cosh(z)/(sqrt(pi)*sqrt(z))
+    assert besselsimp(besseli(Rational(5, 2), z)) == \
+        sqrt(2)*(z**2*sinh(z) - 3*z*cosh(z) + 3*sinh(z))/(sqrt(pi)*z**Rational(5, 2))
+    assert besselsimp(besseli(Rational(-5, 2), z)) == \
+        sqrt(2)*(z**2*cosh(z) - 3*z*sinh(z) + 3*cosh(z))/(sqrt(pi)*z**Rational(5, 2))
+
+    assert besselsimp(besselk(S.Half, z)) == \
+        besselsimp(besselk(Rational(-1, 2), z)) == sqrt(pi)*exp(-z)/(sqrt(2)*sqrt(z))
+    assert besselsimp(besselk(Rational(5, 2), z)) == \
+        besselsimp(besselk(Rational(-5, 2), z)) == \
+        sqrt(2)*sqrt(pi)*(z**2 + 3*z + 3)*exp(-z)/(2*z**Rational(5, 2))
+
+    n = Symbol('n', integer=True, positive=True)
+
+    assert expand_func(besseli(n + 2, z)) == \
+        besseli(n, z) + (-2*n - 2)*(-2*n*besseli(n, z)/z + besseli(n - 1, z))/z
+    assert expand_func(besselj(n + 2, z)) == \
+        -besselj(n, z) + (2*n + 2)*(2*n*besselj(n, z)/z - besselj(n - 1, z))/z
+    assert expand_func(besselk(n + 2, z)) == \
+        besselk(n, z) + (2*n + 2)*(2*n*besselk(n, z)/z + besselk(n - 1, z))/z
+    assert expand_func(bessely(n + 2, z)) == \
+        -bessely(n, z) + (2*n + 2)*(2*n*bessely(n, z)/z - bessely(n - 1, z))/z
+
+    assert expand_func(besseli(n + S.Half, z).rewrite(jn)) == \
+        (sqrt(2)*sqrt(z)*exp(-I*pi*(n + S.Half)/2) *
+         exp_polar(I*pi/4)*jn(n, z*exp_polar(I*pi/2))/sqrt(pi))
+    assert expand_func(besselj(n + S.Half, z).rewrite(jn)) == \
+        sqrt(2)*sqrt(z)*jn(n, z)/sqrt(pi)
+
+    r = Symbol('r', real=True)
+    p = Symbol('p', positive=True)
+    i = Symbol('i', integer=True)
+
+    for besselx in [besselj, bessely, besseli, besselk]:
+        assert besselx(i, p).is_extended_real is True
+        assert besselx(i, x).is_extended_real is None
+        assert besselx(x, z).is_extended_real is None
+
+    for besselx in [besselj, besseli]:
+        assert besselx(i, r).is_extended_real is True
+    for besselx in [bessely, besselk]:
+        assert besselx(i, r).is_extended_real is None
+
+    for besselx in [besselj, bessely, besseli, besselk]:
+        assert expand_func(besselx(oo, x)) == besselx(oo, x, evaluate=False)
+        assert expand_func(besselx(-oo, x)) == besselx(-oo, x, evaluate=False)
+
+
+# Quite varying time, but often really slow
+@slow
+def test_slow_expand():
+    def check(eq, ans):
+        return tn(eq, ans) and eq == ans
+
+    rn = randcplx(a=1, b=0, d=0, c=2)
+
+    for besselx in [besselj, bessely, besseli, besselk]:
+        ri = S(2*randint(-11, 10) + 1) / 2  # half integer in [-21/2, 21/2]
+        assert tn(besselsimp(besselx(ri, z)), besselx(ri, z))
+
+    assert check(expand_func(besseli(rn, x)),
+                 besseli(rn - 2, x) - 2*(rn - 1)*besseli(rn - 1, x)/x)
+    assert check(expand_func(besseli(-rn, x)),
+                 besseli(-rn + 2, x) + 2*(-rn + 1)*besseli(-rn + 1, x)/x)
+
+    assert check(expand_func(besselj(rn, x)),
+                 -besselj(rn - 2, x) + 2*(rn - 1)*besselj(rn - 1, x)/x)
+    assert check(expand_func(besselj(-rn, x)),
+                 -besselj(-rn + 2, x) + 2*(-rn + 1)*besselj(-rn + 1, x)/x)
+
+    assert check(expand_func(besselk(rn, x)),
+                 besselk(rn - 2, x) + 2*(rn - 1)*besselk(rn - 1, x)/x)
+    assert check(expand_func(besselk(-rn, x)),
+                 besselk(-rn + 2, x) - 2*(-rn + 1)*besselk(-rn + 1, x)/x)
+
+    assert check(expand_func(bessely(rn, x)),
+                 -bessely(rn - 2, x) + 2*(rn - 1)*bessely(rn - 1, x)/x)
+    assert check(expand_func(bessely(-rn, x)),
+                 -bessely(-rn + 2, x) + 2*(-rn + 1)*bessely(-rn + 1, x)/x)
+
+
+def mjn(n, z):
+    return expand_func(jn(n, z))
+
+
+def myn(n, z):
+    return expand_func(yn(n, z))
+
+
+def test_jn():
+    z = symbols("z")
+    assert jn(0, 0) == 1
+    assert jn(1, 0) == 0
+    assert jn(-1, 0) == S.ComplexInfinity
+    assert jn(z, 0) == jn(z, 0, evaluate=False)
+    assert jn(0, oo) == 0
+    assert jn(0, -oo) == 0
+
+    assert mjn(0, z) == sin(z)/z
+    assert mjn(1, z) == sin(z)/z**2 - cos(z)/z
+    assert mjn(2, z) == (3/z**3 - 1/z)*sin(z) - (3/z**2) * cos(z)
+    assert mjn(3, z) == (15/z**4 - 6/z**2)*sin(z) + (1/z - 15/z**3)*cos(z)
+    assert mjn(4, z) == (1/z + 105/z**5 - 45/z**3)*sin(z) + \
+        (-105/z**4 + 10/z**2)*cos(z)
+    assert mjn(5, z) == (945/z**6 - 420/z**4 + 15/z**2)*sin(z) + \
+        (-1/z - 945/z**5 + 105/z**3)*cos(z)
+    assert mjn(6, z) == (-1/z + 10395/z**7 - 4725/z**5 + 210/z**3)*sin(z) + \
+        (-10395/z**6 + 1260/z**4 - 21/z**2)*cos(z)
+
+    assert expand_func(jn(n, z)) == jn(n, z)
+
+    # SBFs not defined for complex-valued orders
+    assert jn(2+3j, 5.2+0.3j).evalf() == jn(2+3j, 5.2+0.3j)
+
+    assert eq([jn(2, 5.2+0.3j).evalf(10)],
+              [0.09941975672 - 0.05452508024*I])
+
+
+def test_yn():
+    z = symbols("z")
+    assert myn(0, z) == -cos(z)/z
+    assert myn(1, z) == -cos(z)/z**2 - sin(z)/z
+    assert myn(2, z) == -((3/z**3 - 1/z)*cos(z) + (3/z**2)*sin(z))
+    assert expand_func(yn(n, z)) == yn(n, z)
+
+    # SBFs not defined for complex-valued orders
+    assert yn(2+3j, 5.2+0.3j).evalf() == yn(2+3j, 5.2+0.3j)
+
+    assert eq([yn(2, 5.2+0.3j).evalf(10)],
+              [0.185250342 + 0.01489557397*I])
+
+
+def test_sympify_yn():
+    assert S(15) in myn(3, pi).atoms()
+    assert myn(3, pi) == 15/pi**4 - 6/pi**2
+
+
+def eq(a, b, tol=1e-6):
+    for u, v in zip(a, b):
+        if not (abs(u - v) < tol):
+            return False
+    return True
+
+
+def test_jn_zeros():
+    assert eq(jn_zeros(0, 4), [3.141592, 6.283185, 9.424777, 12.566370])
+    assert eq(jn_zeros(1, 4), [4.493409, 7.725251, 10.904121, 14.066193])
+    assert eq(jn_zeros(2, 4), [5.763459, 9.095011, 12.322940, 15.514603])
+    assert eq(jn_zeros(3, 4), [6.987932, 10.417118, 13.698023, 16.923621])
+    assert eq(jn_zeros(4, 4), [8.182561, 11.704907, 15.039664, 18.301255])
+
+
+def test_bessel_eval():
+    n, m, k = Symbol('n', integer=True), Symbol('m'), Symbol('k', integer=True, zero=False)
+
+    for f in [besselj, besseli]:
+        assert f(0, 0) is S.One
+        assert f(2.1, 0) is S.Zero
+        assert f(-3, 0) is S.Zero
+        assert f(-10.2, 0) is S.ComplexInfinity
+        assert f(1 + 3*I, 0) is S.Zero
+        assert f(-3 + I, 0) is S.ComplexInfinity
+        assert f(-2*I, 0) is S.NaN
+        assert f(n, 0) != S.One and f(n, 0) != S.Zero
+        assert f(m, 0) != S.One and f(m, 0) != S.Zero
+        assert f(k, 0) is S.Zero
+
+    assert bessely(0, 0) is S.NegativeInfinity
+    assert besselk(0, 0) is S.Infinity
+    for f in [bessely, besselk]:
+        assert f(1 + I, 0) is S.ComplexInfinity
+        assert f(I, 0) is S.NaN
+
+    for f in [besselj, bessely]:
+        assert f(m, S.Infinity) is S.Zero
+        assert f(m, S.NegativeInfinity) is S.Zero
+
+    for f in [besseli, besselk]:
+        assert f(m, I*S.Infinity) is S.Zero
+        assert f(m, I*S.NegativeInfinity) is S.Zero
+
+    for f in [besseli, besselk]:
+        assert f(-4, z) == f(4, z)
+        assert f(-3, z) == f(3, z)
+        assert f(-n, z) == f(n, z)
+        assert f(-m, z) != f(m, z)
+
+    for f in [besselj, bessely]:
+        assert f(-4, z) == f(4, z)
+        assert f(-3, z) == -f(3, z)
+        assert f(-n, z) == (-1)**n*f(n, z)
+        assert f(-m, z) != (-1)**m*f(m, z)
+
+    for f in [besselj, besseli]:
+        assert f(m, -z) == (-z)**m*z**(-m)*f(m, z)
+
+    assert besseli(2, -z) == besseli(2, z)
+    assert besseli(3, -z) == -besseli(3, z)
+
+    assert besselj(0, -z) == besselj(0, z)
+    assert besselj(1, -z) == -besselj(1, z)
+
+    assert besseli(0, I*z) == besselj(0, z)
+    assert besseli(1, I*z) == I*besselj(1, z)
+    assert besselj(3, I*z) == -I*besseli(3, z)
+
+
+def test_bessel_nan():
+    # FIXME: could have these return NaN; for now just fix infinite recursion
+    for f in [besselj, bessely, besseli, besselk, hankel1, hankel2, yn, jn]:
+        assert f(1, S.NaN) == f(1, S.NaN, evaluate=False)
+
+
+def test_meromorphic():
+    assert besselj(2, x).is_meromorphic(x, 1) == True
+    assert besselj(2, x).is_meromorphic(x, 0) == True
+    assert besselj(2, x).is_meromorphic(x, oo) == False
+    assert besselj(S(2)/3, x).is_meromorphic(x, 1) == True
+    assert besselj(S(2)/3, x).is_meromorphic(x, 0) == False
+    assert besselj(S(2)/3, x).is_meromorphic(x, oo) == False
+    assert besselj(x, 2*x).is_meromorphic(x, 2) == False
+    assert besselk(0, x).is_meromorphic(x, 1) == True
+    assert besselk(2, x).is_meromorphic(x, 0) == True
+    assert besseli(0, x).is_meromorphic(x, 1) == True
+    assert besseli(2, x).is_meromorphic(x, 0) == True
+    assert bessely(0, x).is_meromorphic(x, 1) == True
+    assert bessely(0, x).is_meromorphic(x, 0) == False
+    assert bessely(2, x).is_meromorphic(x, 0) == True
+    assert hankel1(3, x**2 + 2*x).is_meromorphic(x, 1) == True
+    assert hankel1(0, x).is_meromorphic(x, 0) == False
+    assert hankel2(11, 4).is_meromorphic(x, 5) == True
+    assert hn1(6, 7*x**3 + 4).is_meromorphic(x, 7) == True
+    assert hn2(3, 2*x).is_meromorphic(x, 9) == True
+    assert jn(5, 2*x + 7).is_meromorphic(x, 4) == True
+    assert yn(8, x**2 + 11).is_meromorphic(x, 6) == True
+
+
+def test_conjugate():
+    n = Symbol('n')
+    z = Symbol('z', extended_real=False)
+    x = Symbol('x', extended_real=True)
+    y = Symbol('y', positive=True)
+    t = Symbol('t', negative=True)
+
+    for f in [besseli, besselj, besselk, bessely, hankel1, hankel2]:
+        assert f(n, -1).conjugate() != f(conjugate(n), -1)
+        assert f(n, x).conjugate() != f(conjugate(n), x)
+        assert f(n, t).conjugate() != f(conjugate(n), t)
+
+    rz = randcplx(b=0.5)
+
+    for f in [besseli, besselj, besselk, bessely]:
+        assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
+        assert f(n, 0).conjugate() == f(conjugate(n), 0)
+        assert f(n, 1).conjugate() == f(conjugate(n), 1)
+        assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
+        assert f(n, y).conjugate() == f(conjugate(n), y)
+        assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))
+
+    assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
+    assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
+    assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
+    assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
+    assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
+    assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))
+
+    assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
+    assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
+    assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
+    assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
+    assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
+    assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))
+
+
+def test_branching():
+    assert besselj(polar_lift(k), x) == besselj(k, x)
+    assert besseli(polar_lift(k), x) == besseli(k, x)
+
+    n = Symbol('n', integer=True)
+    assert besselj(n, exp_polar(2*pi*I)*x) == besselj(n, x)
+    assert besselj(n, polar_lift(x)) == besselj(n, x)
+    assert besseli(n, exp_polar(2*pi*I)*x) == besseli(n, x)
+    assert besseli(n, polar_lift(x)) == besseli(n, x)
+
+    def tn(func, s):
+        from sympy.core.random import uniform
+        c = uniform(1, 5)
+        expr = func(s, c*exp_polar(I*pi)) - func(s, c*exp_polar(-I*pi))
+        eps = 1e-15
+        expr2 = func(s + eps, -c + eps*I) - func(s + eps, -c - eps*I)
+        return abs(expr.n() - expr2.n()).n() < 1e-10
+
+    nu = Symbol('nu')
+    assert besselj(nu, exp_polar(2*pi*I)*x) == exp(2*pi*I*nu)*besselj(nu, x)
+    assert besseli(nu, exp_polar(2*pi*I)*x) == exp(2*pi*I*nu)*besseli(nu, x)
+    assert tn(besselj, 2)
+    assert tn(besselj, pi)
+    assert tn(besselj, I)
+    assert tn(besseli, 2)
+    assert tn(besseli, pi)
+    assert tn(besseli, I)
+
+
+def test_airy_base():
+    z = Symbol('z')
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+
+    assert conjugate(airyai(z)) == airyai(conjugate(z))
+    assert airyai(x).is_extended_real
+
+    assert airyai(x+I*y).as_real_imag() == (
+            airyai(x - I*y)/2 + airyai(x + I*y)/2,
+            I*(airyai(x - I*y) - airyai(x + I*y))/2)
+
+
+def test_airyai():
+    z = Symbol('z', real=False)
+    t = Symbol('t', negative=True)
+    p = Symbol('p', positive=True)
+
+    assert isinstance(airyai(z), airyai)
+
+    assert airyai(0) == 3**Rational(1, 3)/(3*gamma(Rational(2, 3)))
+    assert airyai(oo) == 0
+    assert airyai(-oo) == 0
+
+    assert diff(airyai(z), z) == airyaiprime(z)
+
+    assert series(airyai(z), z, 0, 3) == (
+        3**Rational(5, 6)*gamma(Rational(1, 3))/(6*pi) - 3**Rational(1, 6)*z*gamma(Rational(2, 3))/(2*pi) + O(z**3))
+
+    assert airyai(z).rewrite(hyper) == (
+        -3**Rational(2, 3)*z*hyper((), (Rational(4, 3),), z**3/9)/(3*gamma(Rational(1, 3))) +
+         3**Rational(1, 3)*hyper((), (Rational(2, 3),), z**3/9)/(3*gamma(Rational(2, 3))))
+
+    assert isinstance(airyai(z).rewrite(besselj), airyai)
+    assert airyai(t).rewrite(besselj) == (
+        sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) +
+                  besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3)
+    assert airyai(z).rewrite(besseli) == (
+        -z*besseli(Rational(1, 3), 2*z**Rational(3, 2)/3)/(3*(z**Rational(3, 2))**Rational(1, 3)) +
+         (z**Rational(3, 2))**Rational(1, 3)*besseli(Rational(-1, 3), 2*z**Rational(3, 2)/3)/3)
+    assert airyai(p).rewrite(besseli) == (
+        sqrt(p)*(besseli(Rational(-1, 3), 2*p**Rational(3, 2)/3) -
+                 besseli(Rational(1, 3), 2*p**Rational(3, 2)/3))/3)
+
+    assert expand_func(airyai(2*(3*z**5)**Rational(1, 3))) == (
+        -sqrt(3)*(-1 + (z**5)**Rational(1, 3)/z**Rational(5, 3))*airybi(2*3**Rational(1, 3)*z**Rational(5, 3))/6 +
+         (1 + (z**5)**Rational(1, 3)/z**Rational(5, 3))*airyai(2*3**Rational(1, 3)*z**Rational(5, 3))/2)
+
+
+def test_airybi():
+    z = Symbol('z', real=False)
+    t = Symbol('t', negative=True)
+    p = Symbol('p', positive=True)
+
+    assert isinstance(airybi(z), airybi)
+
+    assert airybi(0) == 3**Rational(5, 6)/(3*gamma(Rational(2, 3)))
+    assert airybi(oo) is oo
+    assert airybi(-oo) == 0
+
+    assert diff(airybi(z), z) == airybiprime(z)
+
+    assert series(airybi(z), z, 0, 3) == (
+        3**Rational(1, 3)*gamma(Rational(1, 3))/(2*pi) + 3**Rational(2, 3)*z*gamma(Rational(2, 3))/(2*pi) + O(z**3))
+
+    assert airybi(z).rewrite(hyper) == (
+        3**Rational(1, 6)*z*hyper((), (Rational(4, 3),), z**3/9)/gamma(Rational(1, 3)) +
+        3**Rational(5, 6)*hyper((), (Rational(2, 3),), z**3/9)/(3*gamma(Rational(2, 3))))
+
+    assert isinstance(airybi(z).rewrite(besselj), airybi)
+    assert airyai(t).rewrite(besselj) == (
+        sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) +
+                  besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3)
+    assert airybi(z).rewrite(besseli) == (
+        sqrt(3)*(z*besseli(Rational(1, 3), 2*z**Rational(3, 2)/3)/(z**Rational(3, 2))**Rational(1, 3) +
+                 (z**Rational(3, 2))**Rational(1, 3)*besseli(Rational(-1, 3), 2*z**Rational(3, 2)/3))/3)
+    assert airybi(p).rewrite(besseli) == (
+        sqrt(3)*sqrt(p)*(besseli(Rational(-1, 3), 2*p**Rational(3, 2)/3) +
+                         besseli(Rational(1, 3), 2*p**Rational(3, 2)/3))/3)
+
+    assert expand_func(airybi(2*(3*z**5)**Rational(1, 3))) == (
+        sqrt(3)*(1 - (z**5)**Rational(1, 3)/z**Rational(5, 3))*airyai(2*3**Rational(1, 3)*z**Rational(5, 3))/2 +
+        (1 + (z**5)**Rational(1, 3)/z**Rational(5, 3))*airybi(2*3**Rational(1, 3)*z**Rational(5, 3))/2)
+
+
+def test_airyaiprime():
+    z = Symbol('z', real=False)
+    t = Symbol('t', negative=True)
+    p = Symbol('p', positive=True)
+
+    assert isinstance(airyaiprime(z), airyaiprime)
+
+    assert airyaiprime(0) == -3**Rational(2, 3)/(3*gamma(Rational(1, 3)))
+    assert airyaiprime(oo) == 0
+
+    assert diff(airyaiprime(z), z) == z*airyai(z)
+
+    assert series(airyaiprime(z), z, 0, 3) == (
+        -3**Rational(2, 3)/(3*gamma(Rational(1, 3))) + 3**Rational(1, 3)*z**2/(6*gamma(Rational(2, 3))) + O(z**3))
+
+    assert airyaiprime(z).rewrite(hyper) == (
+        3**Rational(1, 3)*z**2*hyper((), (Rational(5, 3),), z**3/9)/(6*gamma(Rational(2, 3))) -
+        3**Rational(2, 3)*hyper((), (Rational(1, 3),), z**3/9)/(3*gamma(Rational(1, 3))))
+
+    assert isinstance(airyaiprime(z).rewrite(besselj), airyaiprime)
+    assert airyai(t).rewrite(besselj) == (
+        sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) +
+                  besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3)
+    assert airyaiprime(z).rewrite(besseli) == (
+        z**2*besseli(Rational(2, 3), 2*z**Rational(3, 2)/3)/(3*(z**Rational(3, 2))**Rational(2, 3)) -
+        (z**Rational(3, 2))**Rational(2, 3)*besseli(Rational(-1, 3), 2*z**Rational(3, 2)/3)/3)
+    assert airyaiprime(p).rewrite(besseli) == (
+        p*(-besseli(Rational(-2, 3), 2*p**Rational(3, 2)/3) + besseli(Rational(2, 3), 2*p**Rational(3, 2)/3))/3)
+
+    assert expand_func(airyaiprime(2*(3*z**5)**Rational(1, 3))) == (
+        sqrt(3)*(z**Rational(5, 3)/(z**5)**Rational(1, 3) - 1)*airybiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/6 +
+        (z**Rational(5, 3)/(z**5)**Rational(1, 3) + 1)*airyaiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/2)
+
+
+def test_airybiprime():
+    z = Symbol('z', real=False)
+    t = Symbol('t', negative=True)
+    p = Symbol('p', positive=True)
+
+    assert isinstance(airybiprime(z), airybiprime)
+
+    assert airybiprime(0) == 3**Rational(1, 6)/gamma(Rational(1, 3))
+    assert airybiprime(oo) is oo
+    assert airybiprime(-oo) == 0
+
+    assert diff(airybiprime(z), z) == z*airybi(z)
+
+    assert series(airybiprime(z), z, 0, 3) == (
+        3**Rational(1, 6)/gamma(Rational(1, 3)) + 3**Rational(5, 6)*z**2/(6*gamma(Rational(2, 3))) + O(z**3))
+
+    assert airybiprime(z).rewrite(hyper) == (
+        3**Rational(5, 6)*z**2*hyper((), (Rational(5, 3),), z**3/9)/(6*gamma(Rational(2, 3))) +
+        3**Rational(1, 6)*hyper((), (Rational(1, 3),), z**3/9)/gamma(Rational(1, 3)))
+
+    assert isinstance(airybiprime(z).rewrite(besselj), airybiprime)
+    assert airyai(t).rewrite(besselj) == (
+        sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) +
+                  besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3)
+    assert airybiprime(z).rewrite(besseli) == (
+        sqrt(3)*(z**2*besseli(Rational(2, 3), 2*z**Rational(3, 2)/3)/(z**Rational(3, 2))**Rational(2, 3) +
+                 (z**Rational(3, 2))**Rational(2, 3)*besseli(Rational(-2, 3), 2*z**Rational(3, 2)/3))/3)
+    assert airybiprime(p).rewrite(besseli) == (
+        sqrt(3)*p*(besseli(Rational(-2, 3), 2*p**Rational(3, 2)/3) + besseli(Rational(2, 3), 2*p**Rational(3, 2)/3))/3)
+
+    assert expand_func(airybiprime(2*(3*z**5)**Rational(1, 3))) == (
+        sqrt(3)*(z**Rational(5, 3)/(z**5)**Rational(1, 3) - 1)*airyaiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/2 +
+        (z**Rational(5, 3)/(z**5)**Rational(1, 3) + 1)*airybiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/2)
+
+
+def test_marcumq():
+    m = Symbol('m')
+    a = Symbol('a')
+    b = Symbol('b')
+
+    assert marcumq(0, 0, 0) == 0
+    assert marcumq(m, 0, b) == uppergamma(m, b**2/2)/gamma(m)
+    assert marcumq(2, 0, 5) == 27*exp(Rational(-25, 2))/2
+    assert marcumq(0, a, 0) == 1 - exp(-a**2/2)
+    assert marcumq(0, pi, 0) == 1 - exp(-pi**2/2)
+    assert marcumq(1, a, a) == S.Half + exp(-a**2)*besseli(0, a**2)/2
+    assert marcumq(2, a, a) == S.Half + exp(-a**2)*besseli(0, a**2)/2 + exp(-a**2)*besseli(1, a**2)
+
+    assert diff(marcumq(1, a, 3), a) == a*(-marcumq(1, a, 3) + marcumq(2, a, 3))
+    assert diff(marcumq(2, 3, b), b) == -b**2*exp(-b**2/2 - Rational(9, 2))*besseli(1, 3*b)/3
+
+    x = Symbol('x')
+    assert marcumq(2, 3, 4).rewrite(Integral, x=x) == \
+           Integral(x**2*exp(-x**2/2 - Rational(9, 2))*besseli(1, 3*x), (x, 4, oo))/3
+    assert eq([marcumq(5, -2, 3).rewrite(Integral).evalf(10)],
+              [0.7905769565])
+
+    k = Symbol('k')
+    assert marcumq(-3, -5, -7).rewrite(Sum, k=k) == \
+           exp(-37)*Sum((Rational(5, 7))**k*besseli(k, 35), (k, 4, oo))
+    assert eq([marcumq(1, 3, 1).rewrite(Sum).evalf(10)],
+              [0.9891705502])
+
+    assert marcumq(1, a, a, evaluate=False).rewrite(besseli) == S.Half + exp(-a**2)*besseli(0, a**2)/2
+    assert marcumq(2, a, a, evaluate=False).rewrite(besseli) == S.Half + exp(-a**2)*besseli(0, a**2)/2 + \
+           exp(-a**2)*besseli(1, a**2)
+    assert marcumq(3, a, a).rewrite(besseli) == (besseli(1, a**2) + besseli(2, a**2))*exp(-a**2) + \
+           S.Half + exp(-a**2)*besseli(0, a**2)/2
+    assert marcumq(5, 8, 8).rewrite(besseli) == exp(-64)*besseli(0, 64)/2 + \
+           (besseli(4, 64) + besseli(3, 64) + besseli(2, 64) + besseli(1, 64))*exp(-64) + S.Half
+    assert marcumq(m, a, a).rewrite(besseli) == marcumq(m, a, a)
+
+    x = Symbol('x', integer=True)
+    assert marcumq(x, a, a).rewrite(besseli) == marcumq(x, a, a)
+
+
+def test_issue_26134():
+    x = Symbol('x')
+    assert marcumq(2, 3, 4).rewrite(Integral, x=x).dummy_eq(
+        Integral(x**2*exp(-x**2/2 - Rational(9, 2))*besseli(1, 3*x), (x, 4, oo))/3)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_beta_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_beta_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..b34cb2febf9e2746d869cd878525d2794535aea5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_beta_functions.py
@@ -0,0 +1,89 @@
+from sympy.core.function import (diff, expand_func)
+from sympy.core.numbers import I, Rational, pi
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.functions.combinatorial.numbers import catalan
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.beta_functions import (beta, betainc, betainc_regularized)
+from sympy.functions.special.gamma_functions import gamma, polygamma
+from sympy.functions.special.hyper import hyper
+from sympy.integrals.integrals import Integral
+from sympy.core.function import ArgumentIndexError
+from sympy.core.expr import unchanged
+from sympy.testing.pytest import raises
+
+
+def test_beta():
+    x, y = symbols('x y')
+    t = Dummy('t')
+
+    assert unchanged(beta, x, y)
+    assert unchanged(beta, x, x)
+
+    assert beta(5, -3).is_real == True
+    assert beta(3, y).is_real is None
+
+    assert expand_func(beta(x, y)) == gamma(x)*gamma(y)/gamma(x + y)
+    assert expand_func(beta(x, y) - beta(y, x)) == 0  # Symmetric
+    assert expand_func(beta(x, y)) == expand_func(beta(x, y + 1) + beta(x + 1, y)).simplify()
+
+    assert diff(beta(x, y), x) == beta(x, y)*(polygamma(0, x) - polygamma(0, x + y))
+    assert diff(beta(x, y), y) == beta(x, y)*(polygamma(0, y) - polygamma(0, x + y))
+
+    assert conjugate(beta(x, y)) == beta(conjugate(x), conjugate(y))
+
+    raises(ArgumentIndexError, lambda: beta(x, y).fdiff(3))
+
+    assert beta(x, y).rewrite(gamma) == gamma(x)*gamma(y)/gamma(x + y)
+    assert beta(x).rewrite(gamma) == gamma(x)**2/gamma(2*x)
+    assert beta(x, y).rewrite(Integral).dummy_eq(Integral(t**(x - 1) * (1 - t)**(y - 1), (t, 0, 1)))
+    assert beta(Rational(-19, 10), Rational(-1, 10)) == S.Zero
+    assert beta(Rational(-19, 10), Rational(-9, 10)) == \
+        800*2**(S(4)/5)*sqrt(pi)*gamma(S.One/10)/(171*gamma(-S(7)/5))
+    assert beta(Rational(19, 10), Rational(29, 10)) == 100/(551*catalan(Rational(19, 10)))
+    assert beta(1, 0) == S.ComplexInfinity
+    assert beta(0, 1) == S.ComplexInfinity
+    assert beta(2, 3) == S.One/12
+    assert unchanged(beta, x, x + 1)
+    assert unchanged(beta, x, 1)
+    assert unchanged(beta, 1, y)
+    assert beta(x, x + 1).doit() == 1/(x*(x+1)*catalan(x))
+    assert beta(1, y).doit() == 1/y
+    assert beta(x, 1).doit() == 1/x
+    assert beta(Rational(-19, 10), Rational(-1, 10), evaluate=False).doit() == S.Zero
+    assert beta(2) == beta(2, 2)
+    assert beta(x, evaluate=False) != beta(x, x)
+    assert beta(x, evaluate=False).doit() == beta(x, x)
+
+
+def test_betainc():
+    a, b, x1, x2 = symbols('a b x1 x2')
+
+    assert unchanged(betainc, a, b, x1, x2)
+    assert unchanged(betainc, a, b, 0, x1)
+
+    assert betainc(1, 2, 0, -5).is_real == True
+    assert betainc(1, 2, 0, x2).is_real is None
+    assert conjugate(betainc(I, 2, 3 - I, 1 + 4*I)) == betainc(-I, 2, 3 + I, 1 - 4*I)
+
+    assert betainc(a, b, 0, 1).rewrite(Integral).dummy_eq(beta(a, b).rewrite(Integral))
+    assert betainc(1, 2, 0, x2).rewrite(hyper) == x2*hyper((1, -1), (2,), x2)
+
+    assert betainc(1, 2, 3, 3).evalf() == 0
+
+
+def test_betainc_regularized():
+    a, b, x1, x2 = symbols('a b x1 x2')
+
+    assert unchanged(betainc_regularized, a, b, x1, x2)
+    assert unchanged(betainc_regularized, a, b, 0, x1)
+
+    assert betainc_regularized(3, 5, 0, -1).is_real == True
+    assert betainc_regularized(3, 5, 0, x2).is_real is None
+    assert conjugate(betainc_regularized(3*I, 1, 2 + I, 1 + 2*I)) == betainc_regularized(-3*I, 1, 2 - I, 1 - 2*I)
+
+    assert betainc_regularized(a, b, 0, 1).rewrite(Integral) == 1
+    assert betainc_regularized(1, 2, x1, x2).rewrite(hyper) == 2*x2*hyper((1, -1), (2,), x2) - 2*x1*hyper((1, -1), (2,), x1)
+
+    assert betainc_regularized(4, 1, 5, 5).evalf() == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_bsplines.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_bsplines.py
new file mode 100644
index 0000000000000000000000000000000000000000..136831b96ba16c95edba12ecd47b6f1566b68427
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_bsplines.py
@@ -0,0 +1,167 @@
+from sympy.functions import bspline_basis_set, interpolating_spline
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.logic.boolalg import And
+from sympy.sets.sets import Interval
+from sympy.testing.pytest import slow
+
+x, y = symbols('x,y')
+
+
+def test_basic_degree_0():
+    d = 0
+    knots = range(5)
+    splines = bspline_basis_set(d, knots, x)
+    for i in range(len(splines)):
+        assert splines[i] == Piecewise((1, Interval(i, i + 1).contains(x)),
+                                       (0, True))
+
+
+def test_basic_degree_1():
+    d = 1
+    knots = range(5)
+    splines = bspline_basis_set(d, knots, x)
+    assert splines[0] == Piecewise((x, Interval(0, 1).contains(x)),
+                                   (2 - x, Interval(1, 2).contains(x)),
+                                   (0, True))
+    assert splines[1] == Piecewise((-1 + x, Interval(1, 2).contains(x)),
+                                   (3 - x, Interval(2, 3).contains(x)),
+                                   (0, True))
+    assert splines[2] == Piecewise((-2 + x, Interval(2, 3).contains(x)),
+                                   (4 - x, Interval(3, 4).contains(x)),
+                                   (0, True))
+
+
+def test_basic_degree_2():
+    d = 2
+    knots = range(5)
+    splines = bspline_basis_set(d, knots, x)
+    b0 = Piecewise((x**2/2, Interval(0, 1).contains(x)),
+                   (Rational(-3, 2) + 3*x - x**2, Interval(1, 2).contains(x)),
+                   (Rational(9, 2) - 3*x + x**2/2, Interval(2, 3).contains(x)),
+                   (0, True))
+    b1 = Piecewise((S.Half - x + x**2/2, Interval(1, 2).contains(x)),
+                   (Rational(-11, 2) + 5*x - x**2, Interval(2, 3).contains(x)),
+                   (8 - 4*x + x**2/2, Interval(3, 4).contains(x)),
+                   (0, True))
+    assert splines[0] == b0
+    assert splines[1] == b1
+
+
+def test_basic_degree_3():
+    d = 3
+    knots = range(5)
+    splines = bspline_basis_set(d, knots, x)
+    b0 = Piecewise(
+        (x**3/6, Interval(0, 1).contains(x)),
+        (Rational(2, 3) - 2*x + 2*x**2 - x**3/2, Interval(1, 2).contains(x)),
+        (Rational(-22, 3) + 10*x - 4*x**2 + x**3/2, Interval(2, 3).contains(x)),
+        (Rational(32, 3) - 8*x + 2*x**2 - x**3/6, Interval(3, 4).contains(x)),
+        (0, True)
+    )
+    assert splines[0] == b0
+
+
+def test_repeated_degree_1():
+    d = 1
+    knots = [0, 0, 1, 2, 2, 3, 4, 4]
+    splines = bspline_basis_set(d, knots, x)
+    assert splines[0] == Piecewise((1 - x, Interval(0, 1).contains(x)),
+                                   (0, True))
+    assert splines[1] == Piecewise((x, Interval(0, 1).contains(x)),
+                                   (2 - x, Interval(1, 2).contains(x)),
+                                   (0, True))
+    assert splines[2] == Piecewise((-1 + x, Interval(1, 2).contains(x)),
+                                   (0, True))
+    assert splines[3] == Piecewise((3 - x, Interval(2, 3).contains(x)),
+                                   (0, True))
+    assert splines[4] == Piecewise((-2 + x, Interval(2, 3).contains(x)),
+                                   (4 - x, Interval(3, 4).contains(x)),
+                                   (0, True))
+    assert splines[5] == Piecewise((-3 + x, Interval(3, 4).contains(x)),
+                                   (0, True))
+
+
+def test_repeated_degree_2():
+    d = 2
+    knots = [0, 0, 1, 2, 2, 3, 4, 4]
+    splines = bspline_basis_set(d, knots, x)
+
+    assert splines[0] == Piecewise(((-3*x**2/2 + 2*x), And(x <= 1, x >= 0)),
+                                   (x**2/2 - 2*x + 2, And(x <= 2, x >= 1)),
+                                   (0, True))
+    assert splines[1] == Piecewise((x**2/2, And(x <= 1, x >= 0)),
+                                   (-3*x**2/2 + 4*x - 2, And(x <= 2, x >= 1)),
+                                   (0, True))
+    assert splines[2] == Piecewise((x**2 - 2*x + 1, And(x <= 2, x >= 1)),
+                                   (x**2 - 6*x + 9, And(x <= 3, x >= 2)),
+                                   (0, True))
+    assert splines[3] == Piecewise((-3*x**2/2 + 8*x - 10, And(x <= 3, x >= 2)),
+                                   (x**2/2 - 4*x + 8, And(x <= 4, x >= 3)),
+                                   (0, True))
+    assert splines[4] == Piecewise((x**2/2 - 2*x + 2, And(x <= 3, x >= 2)),
+                                   (-3*x**2/2 + 10*x - 16, And(x <= 4, x >= 3)),
+                                   (0, True))
+
+# Tests for interpolating_spline
+
+
+def test_10_points_degree_1():
+    d = 1
+    X = [-5, 2, 3, 4, 7, 9, 10, 30, 31, 34]
+    Y = [-10, -2, 2, 4, 7, 6, 20, 45, 19, 25]
+    spline = interpolating_spline(d, x, X, Y)
+
+    assert spline == Piecewise((x*Rational(8, 7) - Rational(30, 7), (x >= -5) & (x <= 2)), (4*x - 10, (x >= 2) & (x <= 3)),
+                               (2*x - 4, (x >= 3) & (x <= 4)), (x, (x >= 4) & (x <= 7)),
+                               (-x/2 + Rational(21, 2), (x >= 7) & (x <= 9)), (14*x - 120, (x >= 9) & (x <= 10)),
+                               (x*Rational(5, 4) + Rational(15, 2), (x >= 10) & (x <= 30)), (-26*x + 825, (x >= 30) & (x <= 31)),
+                               (2*x - 43, (x >= 31) & (x <= 34)))
+
+
+def test_3_points_degree_2():
+    d = 2
+    X = [-3, 10, 19]
+    Y = [3, -4, 30]
+    spline = interpolating_spline(d, x, X, Y)
+
+    assert spline == Piecewise((505*x**2/2574 - x*Rational(4921, 2574) - Rational(1931, 429), (x >= -3) & (x <= 19)))
+
+
+def test_5_points_degree_2():
+    d = 2
+    X = [-3, 2, 4, 5, 10]
+    Y = [-1, 2, 5, 10, 14]
+    spline = interpolating_spline(d, x, X, Y)
+
+    assert spline == Piecewise((4*x**2/329 + x*Rational(1007, 1645) + Rational(1196, 1645), (x >= -3) & (x <= 3)),
+                               (2701*x**2/1645 - x*Rational(15079, 1645) + Rational(5065, 329), (x >= 3) & (x <= Rational(9, 2))),
+                               (-1319*x**2/1645 + x*Rational(21101, 1645) - Rational(11216, 329), (x >= Rational(9, 2)) & (x <= 10)))
+
+
+@slow
+def test_6_points_degree_3():
+    d = 3
+    X = [-1, 0, 2, 3, 9, 12]
+    Y = [-4, 3, 3, 7, 9, 20]
+    spline = interpolating_spline(d, x, X, Y)
+
+    assert spline == Piecewise((6058*x**3/5301 - 18427*x**2/5301 + x*Rational(12622, 5301) + 3, (x >= -1) & (x <= 2)),
+                               (-8327*x**3/5301 + 67883*x**2/5301 - x*Rational(159998, 5301) + Rational(43661, 1767), (x >= 2) & (x <= 3)),
+                               (5414*x**3/47709 - 1386*x**2/589 + x*Rational(4267, 279) - Rational(12232, 589), (x >= 3) & (x <= 12)))
+
+
+def test_issue_19262():
+    Delta = symbols('Delta', positive=True)
+    knots = [i*Delta for i in range(4)]
+    basis = bspline_basis_set(1, knots, x)
+    y = symbols('y', nonnegative=True)
+    basis2 = bspline_basis_set(1, knots, y)
+    assert basis[0].subs(x, y) == basis2[0]
+    assert interpolating_spline(1, x,
+        [Delta*i for i in [1, 2, 4, 7]], [3, 6, 5, 7]
+        )  == Piecewise((3*x/Delta, (Delta <= x) & (x <= 2*Delta)),
+        (7 - x/(2*Delta), (x >= 2*Delta) & (x <= 4*Delta)),
+        (Rational(7, 3) + 2*x/(3*Delta), (x >= 4*Delta) & (x <= 7*Delta)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_delta_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_delta_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..d5a39d9e352143cf878cf69fa42f454f58be65c9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_delta_functions.py
@@ -0,0 +1,165 @@
+from sympy.core.numbers import (I, nan, oo, pi)
+from sympy.core.relational import (Eq, Ne)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import (adjoint, conjugate, sign, transpose)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.special.delta_functions import (DiracDelta, Heaviside)
+from sympy.functions.special.singularity_functions import SingularityFunction
+from sympy.simplify.simplify import signsimp
+
+
+from sympy.testing.pytest import raises
+
+from sympy.core.expr import unchanged
+
+from sympy.core.function import ArgumentIndexError
+
+
+x, y = symbols('x y')
+i = symbols('t', nonzero=True)
+j = symbols('j', positive=True)
+k = symbols('k', negative=True)
+
+def test_DiracDelta():
+    assert DiracDelta(1) == 0
+    assert DiracDelta(5.1) == 0
+    assert DiracDelta(-pi) == 0
+    assert DiracDelta(5, 7) == 0
+    assert DiracDelta(x, 0) == DiracDelta(x)
+    assert DiracDelta(i) == 0
+    assert DiracDelta(j) == 0
+    assert DiracDelta(k) == 0
+    assert DiracDelta(nan) is nan
+    assert DiracDelta(0).func is DiracDelta
+    assert DiracDelta(x).func is DiracDelta
+    # FIXME: this is generally undefined @ x=0
+    #         But then limit(Delta(c)*Heaviside(x),x,-oo)
+    #         need's to be implemented.
+    # assert 0*DiracDelta(x) == 0
+
+    assert adjoint(DiracDelta(x)) == DiracDelta(x)
+    assert adjoint(DiracDelta(x - y)) == DiracDelta(x - y)
+    assert conjugate(DiracDelta(x)) == DiracDelta(x)
+    assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y)
+    assert transpose(DiracDelta(x)) == DiracDelta(x)
+    assert transpose(DiracDelta(x - y)) == DiracDelta(x - y)
+
+    assert DiracDelta(x).diff(x) == DiracDelta(x, 1)
+    assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2)
+
+    assert DiracDelta(x).is_simple(x) is True
+    assert DiracDelta(3*x).is_simple(x) is True
+    assert DiracDelta(x**2).is_simple(x) is False
+    assert DiracDelta(sqrt(x)).is_simple(x) is False
+    assert DiracDelta(x).is_simple(y) is False
+
+    assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y)
+    assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x)
+    assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y)
+    assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y)
+    assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True, wrt=x) == (
+        DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
+
+    assert DiracDelta(2*x) != DiracDelta(x)  # scaling property
+    assert DiracDelta(x) == DiracDelta(-x)  # even function
+    assert DiracDelta(-x, 2) == DiracDelta(x, 2)
+    assert DiracDelta(-x, 1) == -DiracDelta(x, 1)  # odd deriv is odd
+    assert DiracDelta(-oo*x) == DiracDelta(oo*x)
+    assert DiracDelta(x - y) != DiracDelta(y - x)
+    assert signsimp(DiracDelta(x - y) - DiracDelta(y - x)) == 0
+
+    assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y)
+    assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x)
+    assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y)
+    assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y)
+    assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True) == (
+            DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
+
+    raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2))
+    raises(ValueError, lambda: DiracDelta(x, -1))
+    raises(ValueError, lambda: DiracDelta(I))
+    raises(ValueError, lambda: DiracDelta(2 + 3*I))
+
+
+def test_heaviside():
+    assert Heaviside(-5) == 0
+    assert Heaviside(1) == 1
+    assert Heaviside(0) == S.Half
+
+    assert Heaviside(0, x) == x
+    assert unchanged(Heaviside,x, nan)
+    assert Heaviside(0, nan) == nan
+
+    h0  = Heaviside(x, 0)
+    h12 = Heaviside(x, S.Half)
+    h1  = Heaviside(x, 1)
+
+    assert h0.args == h0.pargs == (x, 0)
+    assert h1.args == h1.pargs == (x, 1)
+    assert h12.args == (x, S.Half)
+    assert h12.pargs == (x,) # default 1/2 suppressed
+
+    assert adjoint(Heaviside(x)) == Heaviside(x)
+    assert adjoint(Heaviside(x - y)) == Heaviside(x - y)
+    assert conjugate(Heaviside(x)) == Heaviside(x)
+    assert conjugate(Heaviside(x - y)) == Heaviside(x - y)
+    assert transpose(Heaviside(x)) == Heaviside(x)
+    assert transpose(Heaviside(x - y)) == Heaviside(x - y)
+
+    assert Heaviside(x).diff(x) == DiracDelta(x)
+    assert Heaviside(x + I).is_Function is True
+    assert Heaviside(I*x).is_Function is True
+
+    raises(ArgumentIndexError, lambda: Heaviside(x).fdiff(2))
+    raises(ValueError, lambda: Heaviside(I))
+    raises(ValueError, lambda: Heaviside(2 + 3*I))
+
+
+def test_rewrite():
+    x, y = Symbol('x', real=True), Symbol('y')
+    assert Heaviside(x).rewrite(Piecewise) == (
+        Piecewise((0, x < 0), (Heaviside(0), Eq(x, 0)), (1, True)))
+    assert Heaviside(y).rewrite(Piecewise) == (
+        Piecewise((0, y < 0), (Heaviside(0), Eq(y, 0)), (1, True)))
+    assert Heaviside(x, y).rewrite(Piecewise) == (
+        Piecewise((0, x < 0), (y, Eq(x, 0)), (1, True)))
+    assert Heaviside(x, 0).rewrite(Piecewise) == (
+        Piecewise((0, x <= 0), (1, True)))
+    assert Heaviside(x, 1).rewrite(Piecewise) == (
+        Piecewise((0, x < 0), (1, True)))
+    assert Heaviside(x, nan).rewrite(Piecewise) == (
+        Piecewise((0, x < 0), (nan, Eq(x, 0)), (1, True)))
+
+    assert Heaviside(x).rewrite(sign) == \
+        Heaviside(x, H0=Heaviside(0)).rewrite(sign) == \
+        Piecewise(
+            (sign(x)/2 + S(1)/2, Eq(Heaviside(0), S(1)/2)),
+            (Piecewise(
+                (sign(x)/2 + S(1)/2, Ne(x, 0)), (Heaviside(0), True)), True)
+        )
+
+    assert Heaviside(y).rewrite(sign) == Heaviside(y)
+    assert Heaviside(x, S.Half).rewrite(sign) == (sign(x)+1)/2
+    assert Heaviside(x, y).rewrite(sign) == \
+        Piecewise(
+            (sign(x)/2 + S(1)/2, Eq(y, S(1)/2)),
+            (Piecewise(
+                (sign(x)/2 + S(1)/2, Ne(x, 0)), (y, True)), True)
+        )
+
+    assert DiracDelta(y).rewrite(Piecewise) == Piecewise((DiracDelta(0), Eq(y, 0)), (0, True))
+    assert DiracDelta(y, 1).rewrite(Piecewise) == DiracDelta(y, 1)
+    assert DiracDelta(x - 5).rewrite(Piecewise) == (
+        Piecewise((DiracDelta(0), Eq(x - 5, 0)), (0, True)))
+
+    assert (x*DiracDelta(x - 10)).rewrite(SingularityFunction) == x*SingularityFunction(x, 10, -1)
+    assert 5*x*y*DiracDelta(y, 1).rewrite(SingularityFunction) == 5*x*y*SingularityFunction(y, 0, -2)
+    assert DiracDelta(0).rewrite(SingularityFunction) == SingularityFunction(0, 0, -1)
+    assert DiracDelta(0, 1).rewrite(SingularityFunction) == SingularityFunction(0, 0, -2)
+
+    assert Heaviside(x).rewrite(SingularityFunction) == SingularityFunction(x, 0, 0)
+    assert 5*x*y*Heaviside(y + 1).rewrite(SingularityFunction) == 5*x*y*SingularityFunction(y, -1, 0)
+    assert ((x - 3)**3*Heaviside(x - 3)).rewrite(SingularityFunction) == (x - 3)**3*SingularityFunction(x, 3, 0)
+    assert Heaviside(0).rewrite(SingularityFunction) == S.Half
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_elliptic_integrals.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_elliptic_integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..a11e531af32301a00b6fc864064d02f9318929e1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_elliptic_integrals.py
@@ -0,0 +1,181 @@
+from sympy.core.numbers import (I, Rational, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.elementary.hyperbolic import atanh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (sin, tan)
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import (hyper, meijerg)
+from sympy.integrals.integrals import Integral
+from sympy.series.order import O
+from sympy.functions.special.elliptic_integrals import (elliptic_k as K,
+    elliptic_f as F, elliptic_e as E, elliptic_pi as P)
+from sympy.core.random import (test_derivative_numerically as td,
+                                      random_complex_number as randcplx,
+                                      verify_numerically as tn)
+from sympy.abc import z, m, n
+
+i = Symbol('i', integer=True)
+j = Symbol('k', integer=True, positive=True)
+t = Dummy('t')
+
+def test_K():
+    assert K(0) == pi/2
+    assert K(S.Half) == 8*pi**Rational(3, 2)/gamma(Rational(-1, 4))**2
+    assert K(1) is zoo
+    assert K(-1) == gamma(Rational(1, 4))**2/(4*sqrt(2*pi))
+    assert K(oo) == 0
+    assert K(-oo) == 0
+    assert K(I*oo) == 0
+    assert K(-I*oo) == 0
+    assert K(zoo) == 0
+
+    assert K(z).diff(z) == (E(z) - (1 - z)*K(z))/(2*z*(1 - z))
+    assert td(K(z), z)
+
+    zi = Symbol('z', real=False)
+    assert K(zi).conjugate() == K(zi.conjugate())
+    zr = Symbol('z', negative=True)
+    assert K(zr).conjugate() == K(zr)
+
+    assert K(z).rewrite(hyper) == \
+        (pi/2)*hyper((S.Half, S.Half), (S.One,), z)
+    assert tn(K(z), (pi/2)*hyper((S.Half, S.Half), (S.One,), z))
+    assert K(z).rewrite(meijerg) == \
+        meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z)/2
+    assert tn(K(z), meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z)/2)
+
+    assert K(z).series(z) == pi/2 + pi*z/8 + 9*pi*z**2/128 + \
+        25*pi*z**3/512 + 1225*pi*z**4/32768 + 3969*pi*z**5/131072 + O(z**6)
+
+    assert K(m).rewrite(Integral).dummy_eq(
+        Integral(1/sqrt(1 - m*sin(t)**2), (t, 0, pi/2)))
+
+def test_F():
+    assert F(z, 0) == z
+    assert F(0, m) == 0
+    assert F(pi*i/2, m) == i*K(m)
+    assert F(z, oo) == 0
+    assert F(z, -oo) == 0
+
+    assert F(-z, m) == -F(z, m)
+
+    assert F(z, m).diff(z) == 1/sqrt(1 - m*sin(z)**2)
+    assert F(z, m).diff(m) == E(z, m)/(2*m*(1 - m)) - F(z, m)/(2*m) - \
+        sin(2*z)/(4*(1 - m)*sqrt(1 - m*sin(z)**2))
+    r = randcplx()
+    assert td(F(z, r), z)
+    assert td(F(r, m), m)
+
+    mi = Symbol('m', real=False)
+    assert F(z, mi).conjugate() == F(z.conjugate(), mi.conjugate())
+    mr = Symbol('m', negative=True)
+    assert F(z, mr).conjugate() == F(z.conjugate(), mr)
+
+    assert F(z, m).series(z) == \
+        z + z**5*(3*m**2/40 - m/30) + m*z**3/6 + O(z**6)
+
+    assert F(z, m).rewrite(Integral).dummy_eq(
+        Integral(1/sqrt(1 - m*sin(t)**2), (t, 0, z)))
+
+def test_E():
+    assert E(z, 0) == z
+    assert E(0, m) == 0
+    assert E(i*pi/2, m) == i*E(m)
+    assert E(z, oo) is zoo
+    assert E(z, -oo) is zoo
+    assert E(0) == pi/2
+    assert E(1) == 1
+    assert E(oo) == I*oo
+    assert E(-oo) is oo
+    assert E(zoo) is zoo
+
+    assert E(-z, m) == -E(z, m)
+
+    assert E(z, m).diff(z) == sqrt(1 - m*sin(z)**2)
+    assert E(z, m).diff(m) == (E(z, m) - F(z, m))/(2*m)
+    assert E(z).diff(z) == (E(z) - K(z))/(2*z)
+    r = randcplx()
+    assert td(E(r, m), m)
+    assert td(E(z, r), z)
+    assert td(E(z), z)
+
+    mi = Symbol('m', real=False)
+    assert E(z, mi).conjugate() == E(z.conjugate(), mi.conjugate())
+    assert E(mi).conjugate() == E(mi.conjugate())
+    mr = Symbol('m', negative=True)
+    assert E(z, mr).conjugate() == E(z.conjugate(), mr)
+    assert E(mr).conjugate() == E(mr)
+
+    assert E(z).rewrite(hyper) == (pi/2)*hyper((Rational(-1, 2), S.Half), (S.One,), z)
+    assert tn(E(z), (pi/2)*hyper((Rational(-1, 2), S.Half), (S.One,), z))
+    assert E(z).rewrite(meijerg) == \
+        -meijerg(((S.Half, Rational(3, 2)), []), ((S.Zero,), (S.Zero,)), -z)/4
+    assert tn(E(z), -meijerg(((S.Half, Rational(3, 2)), []), ((S.Zero,), (S.Zero,)), -z)/4)
+
+    assert E(z, m).series(z) == \
+        z + z**5*(-m**2/40 + m/30) - m*z**3/6 + O(z**6)
+    assert E(z).series(z) == pi/2 - pi*z/8 - 3*pi*z**2/128 - \
+        5*pi*z**3/512 - 175*pi*z**4/32768 - 441*pi*z**5/131072 + O(z**6)
+    assert E(4*z/(z+1)).series(z) == \
+        pi/2 - pi*z/2 + pi*z**2/8 - 3*pi*z**3/8 - 15*pi*z**4/128 - 93*pi*z**5/128 + O(z**6)
+
+    assert E(z, m).rewrite(Integral).dummy_eq(
+        Integral(sqrt(1 - m*sin(t)**2), (t, 0, z)))
+    assert E(m).rewrite(Integral).dummy_eq(
+        Integral(sqrt(1 - m*sin(t)**2), (t, 0, pi/2)))
+
+def test_P():
+    assert P(0, z, m) == F(z, m)
+    assert P(1, z, m) == F(z, m) + \
+        (sqrt(1 - m*sin(z)**2)*tan(z) - E(z, m))/(1 - m)
+    assert P(n, i*pi/2, m) == i*P(n, m)
+    assert P(n, z, 0) == atanh(sqrt(n - 1)*tan(z))/sqrt(n - 1)
+    assert P(n, z, n) == F(z, n) - P(1, z, n) + tan(z)/sqrt(1 - n*sin(z)**2)
+    assert P(oo, z, m) == 0
+    assert P(-oo, z, m) == 0
+    assert P(n, z, oo) == 0
+    assert P(n, z, -oo) == 0
+    assert P(0, m) == K(m)
+    assert P(1, m) is zoo
+    assert P(n, 0) == pi/(2*sqrt(1 - n))
+    assert P(2, 1) is -oo
+    assert P(-1, 1) is oo
+    assert P(n, n) == E(n)/(1 - n)
+
+    assert P(n, -z, m) == -P(n, z, m)
+
+    ni, mi = Symbol('n', real=False), Symbol('m', real=False)
+    assert P(ni, z, mi).conjugate() == \
+        P(ni.conjugate(), z.conjugate(), mi.conjugate())
+    nr, mr = Symbol('n', negative=True), \
+        Symbol('m', negative=True)
+    assert P(nr, z, mr).conjugate() == P(nr, z.conjugate(), mr)
+    assert P(n, m).conjugate() == P(n.conjugate(), m.conjugate())
+
+    assert P(n, z, m).diff(n) == (E(z, m) + (m - n)*F(z, m)/n +
+        (n**2 - m)*P(n, z, m)/n - n*sqrt(1 -
+            m*sin(z)**2)*sin(2*z)/(2*(1 - n*sin(z)**2)))/(2*(m - n)*(n - 1))
+    assert P(n, z, m).diff(z) == 1/(sqrt(1 - m*sin(z)**2)*(1 - n*sin(z)**2))
+    assert P(n, z, m).diff(m) == (E(z, m)/(m - 1) + P(n, z, m) -
+        m*sin(2*z)/(2*(m - 1)*sqrt(1 - m*sin(z)**2)))/(2*(n - m))
+    assert P(n, m).diff(n) == (E(m) + (m - n)*K(m)/n +
+        (n**2 - m)*P(n, m)/n)/(2*(m - n)*(n - 1))
+    assert P(n, m).diff(m) == (E(m)/(m - 1) + P(n, m))/(2*(n - m))
+
+    # These tests fail due to
+    # https://github.com/fredrik-johansson/mpmath/issues/571#issuecomment-777201962
+    # https://github.com/sympy/sympy/issues/20933#issuecomment-777080385
+    #
+    # rx, ry = randcplx(), randcplx()
+    # assert td(P(n, rx, ry), n)
+    # assert td(P(rx, z, ry), z)
+    # assert td(P(rx, ry, m), m)
+
+    assert P(n, z, m).series(z) == z + z**3*(m/6 + n/3) + \
+        z**5*(3*m**2/40 + m*n/10 - m/30 + n**2/5 - n/15) + O(z**6)
+
+    assert P(n, z, m).rewrite(Integral).dummy_eq(
+        Integral(1/((1 - n*sin(t)**2)*sqrt(1 - m*sin(t)**2)), (t, 0, z)))
+    assert P(n, m).rewrite(Integral).dummy_eq(
+        Integral(1/((1 - n*sin(t)**2)*sqrt(1 - m*sin(t)**2)), (t, 0, pi/2)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_error_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_error_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..073371d3d584b97936729dc2e39c833ac347559b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_error_functions.py
@@ -0,0 +1,860 @@
+from sympy.core.function import (diff, expand, expand_func)
+from sympy.core import EulerGamma
+from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols, Dummy)
+from sympy.functions.elementary.complexes import (conjugate, im, polar_lift, re)
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.hyperbolic import (cosh, sinh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc)
+from sympy.functions.special.error_functions import (Chi, Ci, E1, Ei, Li, Shi, Si, erf, erf2, erf2inv, erfc, erfcinv, erfi, erfinv, expint, fresnelc, fresnels, li)
+from sympy.functions.special.gamma_functions import (gamma, uppergamma)
+from sympy.functions.special.hyper import (hyper, meijerg)
+from sympy.integrals.integrals import (Integral, integrate)
+from sympy.series.gruntz import gruntz
+from sympy.series.limits import limit
+from sympy.series.order import O
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.functions.special.error_functions import _erfs, _eis
+from sympy.testing.pytest import raises
+
+x, y, z = symbols('x,y,z')
+w = Symbol("w", real=True)
+n = Symbol("n", integer=True)
+t = Dummy('t')
+
+
+def test_erf():
+    assert erf(nan) is nan
+
+    assert erf(oo) == 1
+    assert erf(-oo) == -1
+
+    assert erf(0) is S.Zero
+
+    assert erf(I*oo) == oo*I
+    assert erf(-I*oo) == -oo*I
+
+    assert erf(-2) == -erf(2)
+    assert erf(-x*y) == -erf(x*y)
+    assert erf(-x - y) == -erf(x + y)
+
+    assert erf(erfinv(x)) == x
+    assert erf(erfcinv(x)) == 1 - x
+    assert erf(erf2inv(0, x)) == x
+    assert erf(erf2inv(0, x, evaluate=False)) == x # To cover code in erf
+    assert erf(erf2inv(0, erf(erfcinv(1 - erf(erfinv(x)))))) == x
+
+    alpha = symbols('alpha', extended_real=True)
+    assert erf(alpha).is_real is True
+    assert erf(alpha).is_finite is True
+    alpha = symbols('alpha', extended_real=False)
+    assert erf(alpha).is_real is None
+    assert erf(alpha).is_finite is None
+    assert erf(alpha).is_zero is None
+    assert erf(alpha).is_positive is None
+    assert erf(alpha).is_negative is None
+    alpha = symbols('alpha', extended_positive=True)
+    assert erf(alpha).is_positive is True
+    alpha = symbols('alpha', extended_negative=True)
+    assert erf(alpha).is_negative is True
+    assert erf(I).is_real is False
+    assert erf(0, evaluate=False).is_real
+    assert erf(0, evaluate=False).is_zero
+
+    assert conjugate(erf(z)) == erf(conjugate(z))
+
+    assert erf(x).as_leading_term(x) == 2*x/sqrt(pi)
+    assert erf(x*y).as_leading_term(y) == 2*x*y/sqrt(pi)
+    assert (erf(x*y)/erf(y)).as_leading_term(y) == x
+    assert erf(1/x).as_leading_term(x) == S.One
+
+    assert erf(z).rewrite('uppergamma') == sqrt(z**2)*(1 - erfc(sqrt(z**2)))/z
+    assert erf(z).rewrite('erfc') == S.One - erfc(z)
+    assert erf(z).rewrite('erfi') == -I*erfi(I*z)
+    assert erf(z).rewrite('fresnels') == (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
+        I*fresnels(z*(1 - I)/sqrt(pi)))
+    assert erf(z).rewrite('fresnelc') == (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
+        I*fresnels(z*(1 - I)/sqrt(pi)))
+    assert erf(z).rewrite('hyper') == 2*z*hyper([S.Half], [3*S.Half], -z**2)/sqrt(pi)
+    assert erf(z).rewrite('meijerg') == z*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2)/sqrt(pi)
+    assert erf(z).rewrite('expint') == sqrt(z**2)/z - z*expint(S.Half, z**2)/sqrt(S.Pi)
+
+    assert limit(exp(x)*exp(x**2)*(erf(x + 1/exp(x)) - erf(x)), x, oo) == \
+        2/sqrt(pi)
+    assert limit((1 - erf(z))*exp(z**2)*z, z, oo) == 1/sqrt(pi)
+    assert limit((1 - erf(x))*exp(x**2)*sqrt(pi)*x, x, oo) == 1
+    assert limit(((1 - erf(x))*exp(x**2)*sqrt(pi)*x - 1)*2*x**2, x, oo) == -1
+    assert limit(erf(x)/x, x, 0) == 2/sqrt(pi)
+    assert limit(x**(-4) - sqrt(pi)*erf(x**2) / (2*x**6), x, 0) == S(1)/3
+
+    assert erf(x).as_real_imag() == \
+        (erf(re(x) - I*im(x))/2 + erf(re(x) + I*im(x))/2,
+         -I*(-erf(re(x) - I*im(x)) + erf(re(x) + I*im(x)))/2)
+
+    assert erf(x).as_real_imag(deep=False) == \
+        (erf(re(x) - I*im(x))/2 + erf(re(x) + I*im(x))/2,
+         -I*(-erf(re(x) - I*im(x)) + erf(re(x) + I*im(x)))/2)
+
+    assert erf(w).as_real_imag() == (erf(w), 0)
+    assert erf(w).as_real_imag(deep=False) == (erf(w), 0)
+    # issue 13575
+    assert erf(I).as_real_imag() == (0, -I*erf(I))
+
+    raises(ArgumentIndexError, lambda: erf(x).fdiff(2))
+
+    assert erf(x).inverse() == erfinv
+
+
+def test_erf_series():
+    assert erf(x).series(x, 0, 7) == 2*x/sqrt(pi) - \
+        2*x**3/3/sqrt(pi) + x**5/5/sqrt(pi) + O(x**7)
+
+    assert erf(x).series(x, oo) == \
+        -exp(-x**2)*(3/(4*x**5) - 1/(2*x**3) + 1/x + O(x**(-6), (x, oo)))/sqrt(pi) + 1
+    assert erf(x**2).series(x, oo, n=8) == \
+        (-1/(2*x**6) + x**(-2) + O(x**(-8), (x, oo)))*exp(-x**4)/sqrt(pi)*-1 + 1
+    assert erf(sqrt(x)).series(x, oo, n=3) == (sqrt(1/x) - (1/x)**(S(3)/2)/2\
+        + 3*(1/x)**(S(5)/2)/4 + O(x**(-3), (x, oo)))*exp(-x)/sqrt(pi)*-1 + 1
+
+
+def test_erf_evalf():
+    assert abs( erf(Float(2.0)) - 0.995322265 ) < 1E-8 # XXX
+
+
+def test__erfs():
+    assert _erfs(z).diff(z) == -2/sqrt(S.Pi) + 2*z*_erfs(z)
+
+    assert _erfs(1/z).series(z) == \
+        z/sqrt(pi) - z**3/(2*sqrt(pi)) + 3*z**5/(4*sqrt(pi)) + O(z**6)
+
+    assert expand(erf(z).rewrite('tractable').diff(z).rewrite('intractable')) \
+        == erf(z).diff(z)
+    assert _erfs(z).rewrite("intractable") == (-erf(z) + 1)*exp(z**2)
+    raises(ArgumentIndexError, lambda: _erfs(z).fdiff(2))
+
+
+def test_erfc():
+    assert erfc(nan) is nan
+
+    assert erfc(oo) is S.Zero
+    assert erfc(-oo) == 2
+
+    assert erfc(0) == 1
+
+    assert erfc(I*oo) == -oo*I
+    assert erfc(-I*oo) == oo*I
+
+    assert erfc(-x) == S(2) - erfc(x)
+    assert erfc(erfcinv(x)) == x
+
+    alpha = symbols('alpha', extended_real=True)
+    assert erfc(alpha).is_real is True
+    alpha = symbols('alpha', extended_real=False)
+    assert erfc(alpha).is_real is None
+    assert erfc(I).is_real is False
+    assert erfc(0, evaluate=False).is_real
+    assert erfc(0, evaluate=False).is_zero is False
+
+    assert erfc(erfinv(x)) == 1 - x
+
+    assert conjugate(erfc(z)) == erfc(conjugate(z))
+
+    assert erfc(x).as_leading_term(x) is S.One
+    assert erfc(1/x).as_leading_term(x) == S.Zero
+
+    assert erfc(z).rewrite('erf') == 1 - erf(z)
+    assert erfc(z).rewrite('erfi') == 1 + I*erfi(I*z)
+    assert erfc(z).rewrite('fresnels') == 1 - (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
+        I*fresnels(z*(1 - I)/sqrt(pi)))
+    assert erfc(z).rewrite('fresnelc') == 1 - (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
+        I*fresnels(z*(1 - I)/sqrt(pi)))
+    assert erfc(z).rewrite('hyper') == 1 - 2*z*hyper([S.Half], [3*S.Half], -z**2)/sqrt(pi)
+    assert erfc(z).rewrite('meijerg') == 1 - z*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2)/sqrt(pi)
+    assert erfc(z).rewrite('uppergamma') == 1 - sqrt(z**2)*(1 - erfc(sqrt(z**2)))/z
+    assert erfc(z).rewrite('expint') == S.One - sqrt(z**2)/z + z*expint(S.Half, z**2)/sqrt(S.Pi)
+    assert erfc(z).rewrite('tractable') == _erfs(z)*exp(-z**2)
+    assert expand_func(erf(x) + erfc(x)) is S.One
+
+    assert erfc(x).as_real_imag() == \
+        (erfc(re(x) - I*im(x))/2 + erfc(re(x) + I*im(x))/2,
+         -I*(-erfc(re(x) - I*im(x)) + erfc(re(x) + I*im(x)))/2)
+
+    assert erfc(x).as_real_imag(deep=False) == \
+        (erfc(re(x) - I*im(x))/2 + erfc(re(x) + I*im(x))/2,
+         -I*(-erfc(re(x) - I*im(x)) + erfc(re(x) + I*im(x)))/2)
+
+    assert erfc(w).as_real_imag() == (erfc(w), 0)
+    assert erfc(w).as_real_imag(deep=False) == (erfc(w), 0)
+    raises(ArgumentIndexError, lambda: erfc(x).fdiff(2))
+
+    assert erfc(x).inverse() == erfcinv
+
+
+def test_erfc_series():
+    assert erfc(x).series(x, 0, 7) == 1 - 2*x/sqrt(pi) + \
+        2*x**3/3/sqrt(pi) - x**5/5/sqrt(pi) + O(x**7)
+
+    assert erfc(x).series(x, oo) == \
+            (3/(4*x**5) - 1/(2*x**3) + 1/x + O(x**(-6), (x, oo)))*exp(-x**2)/sqrt(pi)
+
+
+def test_erfc_evalf():
+    assert abs( erfc(Float(2.0)) - 0.00467773 ) < 1E-8 # XXX
+
+
+def test_erfi():
+    assert erfi(nan) is nan
+
+    assert erfi(oo) is S.Infinity
+    assert erfi(-oo) is S.NegativeInfinity
+
+    assert erfi(0) is S.Zero
+
+    assert erfi(I*oo) == I
+    assert erfi(-I*oo) == -I
+
+    assert erfi(-x) == -erfi(x)
+
+    assert erfi(I*erfinv(x)) == I*x
+    assert erfi(I*erfcinv(x)) == I*(1 - x)
+    assert erfi(I*erf2inv(0, x)) == I*x
+    assert erfi(I*erf2inv(0, x, evaluate=False)) == I*x # To cover code in erfi
+
+    assert erfi(I).is_real is False
+    assert erfi(0, evaluate=False).is_real
+    assert erfi(0, evaluate=False).is_zero
+
+    assert conjugate(erfi(z)) == erfi(conjugate(z))
+
+    assert erfi(x).as_leading_term(x) == 2*x/sqrt(pi)
+    assert erfi(x*y).as_leading_term(y) == 2*x*y/sqrt(pi)
+    assert (erfi(x*y)/erfi(y)).as_leading_term(y) == x
+    assert erfi(1/x).as_leading_term(x) == erfi(1/x)
+
+    assert erfi(z).rewrite('erf') == -I*erf(I*z)
+    assert erfi(z).rewrite('erfc') == I*erfc(I*z) - I
+    assert erfi(z).rewrite('fresnels') == (1 - I)*(fresnelc(z*(1 + I)/sqrt(pi)) -
+        I*fresnels(z*(1 + I)/sqrt(pi)))
+    assert erfi(z).rewrite('fresnelc') == (1 - I)*(fresnelc(z*(1 + I)/sqrt(pi)) -
+        I*fresnels(z*(1 + I)/sqrt(pi)))
+    assert erfi(z).rewrite('hyper') == 2*z*hyper([S.Half], [3*S.Half], z**2)/sqrt(pi)
+    assert erfi(z).rewrite('meijerg') == z*meijerg([S.Half], [], [0], [Rational(-1, 2)], -z**2)/sqrt(pi)
+    assert erfi(z).rewrite('uppergamma') == (sqrt(-z**2)/z*(uppergamma(S.Half,
+        -z**2)/sqrt(S.Pi) - S.One))
+    assert erfi(z).rewrite('expint') == sqrt(-z**2)/z - z*expint(S.Half, -z**2)/sqrt(S.Pi)
+    assert erfi(z).rewrite('tractable') == -I*(-_erfs(I*z)*exp(z**2) + 1)
+    assert expand_func(erfi(I*z)) == I*erf(z)
+
+    assert erfi(x).as_real_imag() == \
+        (erfi(re(x) - I*im(x))/2 + erfi(re(x) + I*im(x))/2,
+         -I*(-erfi(re(x) - I*im(x)) + erfi(re(x) + I*im(x)))/2)
+    assert erfi(x).as_real_imag(deep=False) == \
+        (erfi(re(x) - I*im(x))/2 + erfi(re(x) + I*im(x))/2,
+         -I*(-erfi(re(x) - I*im(x)) + erfi(re(x) + I*im(x)))/2)
+
+    assert erfi(w).as_real_imag() == (erfi(w), 0)
+    assert erfi(w).as_real_imag(deep=False) == (erfi(w), 0)
+
+    raises(ArgumentIndexError, lambda: erfi(x).fdiff(2))
+
+
+def test_erfi_series():
+    assert erfi(x).series(x, 0, 7) == 2*x/sqrt(pi) + \
+        2*x**3/3/sqrt(pi) + x**5/5/sqrt(pi) + O(x**7)
+
+    assert erfi(x).series(x, oo) == \
+        (3/(4*x**5) + 1/(2*x**3) + 1/x + O(x**(-6), (x, oo)))*exp(x**2)/sqrt(pi) - I
+
+
+def test_erfi_evalf():
+    assert abs( erfi(Float(2.0)) - 18.5648024145756 ) < 1E-13  # XXX
+
+
+def test_erf2():
+
+    assert erf2(0, 0) is S.Zero
+    assert erf2(x, x) is S.Zero
+    assert erf2(nan, 0) is nan
+
+    assert erf2(-oo,  y) ==  erf(y) + 1
+    assert erf2( oo,  y) ==  erf(y) - 1
+    assert erf2(  x, oo) ==  1 - erf(x)
+    assert erf2(  x,-oo) == -1 - erf(x)
+    assert erf2(x, erf2inv(x, y)) == y
+
+    assert erf2(-x, -y) == -erf2(x,y)
+    assert erf2(-x,  y) == erf(y) + erf(x)
+    assert erf2( x, -y) == -erf(y) - erf(x)
+    assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels)
+    assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc)
+    assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper)
+    assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg)
+    assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
+    assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint)
+
+    assert erf2(I, 0).is_real is False
+    assert erf2(0, 0, evaluate=False).is_real
+    assert erf2(0, 0, evaluate=False).is_zero
+    assert erf2(x, x, evaluate=False).is_zero
+    assert erf2(x, y).is_zero is None
+
+    assert expand_func(erf(x) + erf2(x, y)) == erf(y)
+
+    assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))
+
+    assert erf2(x, y).rewrite('erf')  == erf(y) - erf(x)
+    assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y)
+    assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y))
+
+    assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1)
+    assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2)
+    assert erf2(x, y).diff(x) == -2*exp(-x**2)/sqrt(pi)
+    assert erf2(x, y).diff(y) == 2*exp(-y**2)/sqrt(pi)
+    raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3))
+
+    assert erf2(x, y).is_extended_real is None
+    xr, yr = symbols('xr yr', extended_real=True)
+    assert erf2(xr, yr).is_extended_real is True
+
+
+def test_erfinv():
+    assert erfinv(0) is S.Zero
+    assert erfinv(1) is S.Infinity
+    assert erfinv(nan) is S.NaN
+    assert erfinv(-1) is S.NegativeInfinity
+
+    assert erfinv(erf(w)) == w
+    assert erfinv(erf(-w)) == -w
+
+    assert erfinv(x).diff() == sqrt(pi)*exp(erfinv(x)**2)/2
+    raises(ArgumentIndexError, lambda: erfinv(x).fdiff(2))
+
+    assert erfinv(z).rewrite('erfcinv') == erfcinv(1-z)
+    assert erfinv(z).inverse() == erf
+
+
+def test_erfinv_evalf():
+    assert abs( erfinv(Float(0.2)) - 0.179143454621292 ) < 1E-13
+
+
+def test_erfcinv():
+    assert erfcinv(1) is S.Zero
+    assert erfcinv(0) is S.Infinity
+    assert erfcinv(0, evaluate=False).is_infinite is True
+    assert erfcinv(2, evaluate=False).is_infinite is True
+    assert erfcinv(nan) is S.NaN
+
+    assert erfcinv(x).diff() == -sqrt(pi)*exp(erfcinv(x)**2)/2
+    raises(ArgumentIndexError, lambda: erfcinv(x).fdiff(2))
+
+    assert erfcinv(z).rewrite('erfinv') == erfinv(1-z)
+    assert erfcinv(z).inverse() == erfc
+
+
+def test_erf2inv():
+    assert erf2inv(0, 0) is S.Zero
+    assert erf2inv(0, 1) is S.Infinity
+    assert erf2inv(1, 0) is S.One
+    assert erf2inv(0, y) == erfinv(y)
+    assert erf2inv(oo, y) == erfcinv(-y)
+    assert erf2inv(x, 0) == x
+    assert erf2inv(x, oo) == erfinv(x)
+    assert erf2inv(nan, 0) is nan
+    assert erf2inv(0, nan) is nan
+
+    assert erf2inv(x, y).diff(x) == exp(-x**2 + erf2inv(x, y)**2)
+    assert erf2inv(x, y).diff(y) == sqrt(pi)*exp(erf2inv(x, y)**2)/2
+    raises(ArgumentIndexError, lambda: erf2inv(x, y).fdiff(3))
+
+
+# NOTE we multiply by exp_polar(I*pi) and need this to be on the principal
+# branch, hence take x in the lower half plane (d=0).
+
+
+def mytn(expr1, expr2, expr3, x, d=0):
+    from sympy.core.random import verify_numerically, random_complex_number
+    subs = {}
+    for a in expr1.free_symbols:
+        if a != x:
+            subs[a] = random_complex_number()
+    return expr2 == expr3 and verify_numerically(expr1.subs(subs),
+                                               expr2.subs(subs), x, d=d)
+
+
+def mytd(expr1, expr2, x):
+    from sympy.core.random import test_derivative_numerically, \
+        random_complex_number
+    subs = {}
+    for a in expr1.free_symbols:
+        if a != x:
+            subs[a] = random_complex_number()
+    return expr1.diff(x) == expr2 and test_derivative_numerically(expr1.subs(subs), x)
+
+
+def tn_branch(func, s=None):
+    from sympy.core.random import uniform
+
+    def fn(x):
+        if s is None:
+            return func(x)
+        return func(s, x)
+    c = uniform(1, 5)
+    expr = fn(c*exp_polar(I*pi)) - fn(c*exp_polar(-I*pi))
+    eps = 1e-15
+    expr2 = fn(-c + eps*I) - fn(-c - eps*I)
+    return abs(expr.n() - expr2.n()).n() < 1e-10
+
+
+def test_ei():
+    assert Ei(0) is S.NegativeInfinity
+    assert Ei(oo) is S.Infinity
+    assert Ei(-oo) is S.Zero
+
+    assert tn_branch(Ei)
+    assert mytd(Ei(x), exp(x)/x, x)
+    assert mytn(Ei(x), Ei(x).rewrite(uppergamma),
+                -uppergamma(0, x*polar_lift(-1)) - I*pi, x)
+    assert mytn(Ei(x), Ei(x).rewrite(expint),
+                -expint(1, x*polar_lift(-1)) - I*pi, x)
+    assert Ei(x).rewrite(expint).rewrite(Ei) == Ei(x)
+    assert Ei(x*exp_polar(2*I*pi)) == Ei(x) + 2*I*pi
+    assert Ei(x*exp_polar(-2*I*pi)) == Ei(x) - 2*I*pi
+
+    assert mytn(Ei(x), Ei(x).rewrite(Shi), Chi(x) + Shi(x), x)
+    assert mytn(Ei(x*polar_lift(I)), Ei(x*polar_lift(I)).rewrite(Si),
+                Ci(x) + I*Si(x) + I*pi/2, x)
+
+    assert Ei(log(x)).rewrite(li) == li(x)
+    assert Ei(2*log(x)).rewrite(li) == li(x**2)
+
+    assert gruntz(Ei(x+exp(-x))*exp(-x)*x, x, oo) == 1
+
+    assert Ei(x).series(x) == EulerGamma + log(x) + x + x**2/4 + \
+        x**3/18 + x**4/96 + x**5/600 + O(x**6)
+    assert Ei(x).series(x, 1, 3) == Ei(1) + E*(x - 1) + O((x - 1)**3, (x, 1))
+    assert Ei(x).series(x, oo) == \
+        (120/x**5 + 24/x**4 + 6/x**3 + 2/x**2 + 1/x + 1 + O(x**(-6), (x, oo)))*exp(x)/x
+    assert Ei(x).series(x, -oo) == \
+        (120/x**5 + 24/x**4 + 6/x**3 + 2/x**2 + 1/x + 1 + O(x**(-6), (x, -oo)))*exp(x)/x
+    assert Ei(-x).series(x, oo) == \
+        -((-120/x**5 + 24/x**4 - 6/x**3 + 2/x**2 - 1/x + 1 + O(x**(-6), (x, oo)))*exp(-x)/x)
+
+    assert str(Ei(cos(2)).evalf(n=10)) == '-0.6760647401'
+    raises(ArgumentIndexError, lambda: Ei(x).fdiff(2))
+
+
+def test_expint():
+    assert mytn(expint(x, y), expint(x, y).rewrite(uppergamma),
+                y**(x - 1)*uppergamma(1 - x, y), x)
+    assert mytd(
+        expint(x, y), -y**(x - 1)*meijerg([], [1, 1], [0, 0, 1 - x], [], y), x)
+    assert mytd(expint(x, y), -expint(x - 1, y), y)
+    assert mytn(expint(1, x), expint(1, x).rewrite(Ei),
+                -Ei(x*polar_lift(-1)) + I*pi, x)
+
+    assert expint(-4, x) == exp(-x)/x + 4*exp(-x)/x**2 + 12*exp(-x)/x**3 \
+        + 24*exp(-x)/x**4 + 24*exp(-x)/x**5
+    assert expint(Rational(-3, 2), x) == \
+        exp(-x)/x + 3*exp(-x)/(2*x**2) + 3*sqrt(pi)*erfc(sqrt(x))/(4*x**S('5/2'))
+
+    assert tn_branch(expint, 1)
+    assert tn_branch(expint, 2)
+    assert tn_branch(expint, 3)
+    assert tn_branch(expint, 1.7)
+    assert tn_branch(expint, pi)
+
+    assert expint(y, x*exp_polar(2*I*pi)) == \
+        x**(y - 1)*(exp(2*I*pi*y) - 1)*gamma(-y + 1) + expint(y, x)
+    assert expint(y, x*exp_polar(-2*I*pi)) == \
+        x**(y - 1)*(exp(-2*I*pi*y) - 1)*gamma(-y + 1) + expint(y, x)
+    assert expint(2, x*exp_polar(2*I*pi)) == 2*I*pi*x + expint(2, x)
+    assert expint(2, x*exp_polar(-2*I*pi)) == -2*I*pi*x + expint(2, x)
+    assert expint(1, x).rewrite(Ei).rewrite(expint) == expint(1, x)
+    assert expint(x, y).rewrite(Ei) == expint(x, y)
+    assert expint(x, y).rewrite(Ci) == expint(x, y)
+
+    assert mytn(E1(x), E1(x).rewrite(Shi), Shi(x) - Chi(x), x)
+    assert mytn(E1(polar_lift(I)*x), E1(polar_lift(I)*x).rewrite(Si),
+                -Ci(x) + I*Si(x) - I*pi/2, x)
+
+    assert mytn(expint(2, x), expint(2, x).rewrite(Ei).rewrite(expint),
+                -x*E1(x) + exp(-x), x)
+    assert mytn(expint(3, x), expint(3, x).rewrite(Ei).rewrite(expint),
+                x**2*E1(x)/2 + (1 - x)*exp(-x)/2, x)
+
+    assert expint(Rational(3, 2), z).nseries(z) == \
+        2 + 2*z - z**2/3 + z**3/15 - z**4/84 + z**5/540 - \
+        2*sqrt(pi)*sqrt(z) + O(z**6)
+
+    assert E1(z).series(z) == -EulerGamma - log(z) + z - \
+        z**2/4 + z**3/18 - z**4/96 + z**5/600 + O(z**6)
+
+    assert expint(4, z).series(z) == Rational(1, 3) - z/2 + z**2/2 + \
+        z**3*(log(z)/6 - Rational(11, 36) + EulerGamma/6 - I*pi/6) - z**4/24 + \
+        z**5/240 + O(z**6)
+
+    assert expint(n, x).series(x, oo, n=3) == \
+        (n*(n + 1)/x**2 - n/x + 1 + O(x**(-3), (x, oo)))*exp(-x)/x
+
+    assert expint(z, y).series(z, 0, 2) == exp(-y)/y - z*meijerg(((), (1, 1)),
+                                  ((0, 0, 1), ()), y)/y + O(z**2)
+    raises(ArgumentIndexError, lambda: expint(x, y).fdiff(3))
+
+    neg = Symbol('neg', negative=True)
+    assert Ei(neg).rewrite(Si) == Shi(neg) + Chi(neg) - I*pi
+
+
+def test__eis():
+    assert _eis(z).diff(z) == -_eis(z) + 1/z
+
+    assert _eis(1/z).series(z) == \
+        z + z**2 + 2*z**3 + 6*z**4 + 24*z**5 + O(z**6)
+
+    assert Ei(z).rewrite('tractable') == exp(z)*_eis(z)
+    assert li(z).rewrite('tractable') == z*_eis(log(z))
+
+    assert _eis(z).rewrite('intractable') == exp(-z)*Ei(z)
+
+    assert expand(li(z).rewrite('tractable').diff(z).rewrite('intractable')) \
+        == li(z).diff(z)
+
+    assert expand(Ei(z).rewrite('tractable').diff(z).rewrite('intractable')) \
+        == Ei(z).diff(z)
+
+    assert _eis(z).series(z, n=3) == EulerGamma + log(z) + z*(-log(z) - \
+        EulerGamma + 1) + z**2*(log(z)/2 - Rational(3, 4) + EulerGamma/2)\
+        + O(z**3*log(z))
+    raises(ArgumentIndexError, lambda: _eis(z).fdiff(2))
+
+
+def tn_arg(func):
+    def test(arg, e1, e2):
+        from sympy.core.random import uniform
+        v = uniform(1, 5)
+        v1 = func(arg*x).subs(x, v).n()
+        v2 = func(e1*v + e2*1e-15).n()
+        return abs(v1 - v2).n() < 1e-10
+    return test(exp_polar(I*pi/2), I, 1) and \
+        test(exp_polar(-I*pi/2), -I, 1) and \
+        test(exp_polar(I*pi), -1, I) and \
+        test(exp_polar(-I*pi), -1, -I)
+
+
+def test_li():
+    z = Symbol("z")
+    zr = Symbol("z", real=True)
+    zp = Symbol("z", positive=True)
+    zn = Symbol("z", negative=True)
+
+    assert li(0) is S.Zero
+    assert li(1) is -oo
+    assert li(oo) is oo
+
+    assert isinstance(li(z), li)
+    assert unchanged(li, -zp)
+    assert unchanged(li, zn)
+
+    assert diff(li(z), z) == 1/log(z)
+
+    assert conjugate(li(z)) == li(conjugate(z))
+    assert conjugate(li(-zr)) == li(-zr)
+    assert unchanged(conjugate, li(-zp))
+    assert unchanged(conjugate, li(zn))
+
+    assert li(z).rewrite(Li) == Li(z) + li(2)
+    assert li(z).rewrite(Ei) == Ei(log(z))
+    assert li(z).rewrite(uppergamma) == (-log(1/log(z))/2 - log(-log(z)) +
+                                         log(log(z))/2 - expint(1, -log(z)))
+    assert li(z).rewrite(Si) == (-log(I*log(z)) - log(1/log(z))/2 +
+                                 log(log(z))/2 + Ci(I*log(z)) + Shi(log(z)))
+    assert li(z).rewrite(Ci) == (-log(I*log(z)) - log(1/log(z))/2 +
+                                 log(log(z))/2 + Ci(I*log(z)) + Shi(log(z)))
+    assert li(z).rewrite(Shi) == (-log(1/log(z))/2 + log(log(z))/2 +
+                                  Chi(log(z)) - Shi(log(z)))
+    assert li(z).rewrite(Chi) == (-log(1/log(z))/2 + log(log(z))/2 +
+                                  Chi(log(z)) - Shi(log(z)))
+    assert li(z).rewrite(hyper) ==(log(z)*hyper((1, 1), (2, 2), log(z)) -
+                                   log(1/log(z))/2 + log(log(z))/2 + EulerGamma)
+    assert li(z).rewrite(meijerg) == (-log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 -
+                                      meijerg(((), (1,)), ((0, 0), ()), -log(z)))
+
+    assert gruntz(1/li(z), z, oo) is S.Zero
+    assert li(z).series(z) == log(z)**5/600 + log(z)**4/96 + log(z)**3/18 + log(z)**2/4 + \
+            log(z) + log(log(z)) + EulerGamma
+    raises(ArgumentIndexError, lambda: li(z).fdiff(2))
+
+
+def test_Li():
+    assert Li(2) is S.Zero
+    assert Li(oo) is oo
+
+    assert isinstance(Li(z), Li)
+
+    assert diff(Li(z), z) == 1/log(z)
+
+    assert gruntz(1/Li(z), z, oo) is S.Zero
+    assert Li(z).rewrite(li) == li(z) - li(2)
+    assert Li(z).series(z) == \
+        log(z)**5/600 + log(z)**4/96 + log(z)**3/18 + log(z)**2/4 + log(z) + log(log(z)) - li(2) + EulerGamma
+    raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
+
+
+def test_si():
+    assert Si(I*x) == I*Shi(x)
+    assert Shi(I*x) == I*Si(x)
+    assert Si(-I*x) == -I*Shi(x)
+    assert Shi(-I*x) == -I*Si(x)
+    assert Si(-x) == -Si(x)
+    assert Shi(-x) == -Shi(x)
+    assert Si(exp_polar(2*pi*I)*x) == Si(x)
+    assert Si(exp_polar(-2*pi*I)*x) == Si(x)
+    assert Shi(exp_polar(2*pi*I)*x) == Shi(x)
+    assert Shi(exp_polar(-2*pi*I)*x) == Shi(x)
+
+    assert Si(oo) == pi/2
+    assert Si(-oo) == -pi/2
+    assert Shi(oo) is oo
+    assert Shi(-oo) is -oo
+
+    assert mytd(Si(x), sin(x)/x, x)
+    assert mytd(Shi(x), sinh(x)/x, x)
+
+    assert mytn(Si(x), Si(x).rewrite(Ei),
+                -I*(-Ei(x*exp_polar(-I*pi/2))/2
+               + Ei(x*exp_polar(I*pi/2))/2 - I*pi) + pi/2, x)
+    assert mytn(Si(x), Si(x).rewrite(expint),
+                -I*(-expint(1, x*exp_polar(-I*pi/2))/2 +
+                    expint(1, x*exp_polar(I*pi/2))/2) + pi/2, x)
+    assert mytn(Shi(x), Shi(x).rewrite(Ei),
+                Ei(x)/2 - Ei(x*exp_polar(I*pi))/2 + I*pi/2, x)
+    assert mytn(Shi(x), Shi(x).rewrite(expint),
+                expint(1, x)/2 - expint(1, x*exp_polar(I*pi))/2 - I*pi/2, x)
+
+    assert tn_arg(Si)
+    assert tn_arg(Shi)
+
+    assert Si(x)._eval_as_leading_term(x, None, 1) == x
+    assert Si(2*x)._eval_as_leading_term(x, None, 1) == 2*x
+    assert Si(sin(x))._eval_as_leading_term(x, None, 1) == x
+    assert Si(x + 1)._eval_as_leading_term(x, None, 1) == Si(1)
+    assert Si(1/x)._eval_as_leading_term(x, None, 1) == \
+        Si(1/x)._eval_as_leading_term(x, None, -1) == Si(1/x)
+
+    assert Si(x).nseries(x, n=8) == \
+        x - x**3/18 + x**5/600 - x**7/35280 + O(x**8)
+    assert Shi(x).nseries(x, n=8) == \
+        x + x**3/18 + x**5/600 + x**7/35280 + O(x**8)
+    assert Si(sin(x)).nseries(x, n=5) == x - 2*x**3/9 + O(x**5)
+    assert Si(x).nseries(x, 1, n=3) == \
+        Si(1) + (x - 1)*sin(1) + (x - 1)**2*(-sin(1)/2 + cos(1)/2) + O((x - 1)**3, (x, 1))
+
+    assert Si(x).series(x, oo) == -sin(x)*(-6/x**4 + x**(-2) + O(x**(-6), (x, oo))) - \
+        cos(x)*(24/x**5 - 2/x**3 + 1/x + O(x**(-6), (x, oo))) + pi/2
+
+    t = Symbol('t', Dummy=True)
+    assert Si(x).rewrite(sinc).dummy_eq(Integral(sinc(t), (t, 0, x)))
+
+    assert limit(Shi(x), x, S.Infinity) == S.Infinity
+    assert limit(Shi(x), x, S.NegativeInfinity) == S.NegativeInfinity
+
+
+def test_ci():
+    m1 = exp_polar(I*pi)
+    m1_ = exp_polar(-I*pi)
+    pI = exp_polar(I*pi/2)
+    mI = exp_polar(-I*pi/2)
+
+    assert Ci(m1*x) == Ci(x) + I*pi
+    assert Ci(m1_*x) == Ci(x) - I*pi
+    assert Ci(pI*x) == Chi(x) + I*pi/2
+    assert Ci(mI*x) == Chi(x) - I*pi/2
+    assert Chi(m1*x) == Chi(x) + I*pi
+    assert Chi(m1_*x) == Chi(x) - I*pi
+    assert Chi(pI*x) == Ci(x) + I*pi/2
+    assert Chi(mI*x) == Ci(x) - I*pi/2
+    assert Ci(exp_polar(2*I*pi)*x) == Ci(x) + 2*I*pi
+    assert Chi(exp_polar(-2*I*pi)*x) == Chi(x) - 2*I*pi
+    assert Chi(exp_polar(2*I*pi)*x) == Chi(x) + 2*I*pi
+    assert Ci(exp_polar(-2*I*pi)*x) == Ci(x) - 2*I*pi
+
+    assert Ci(oo) is S.Zero
+    assert Ci(-oo) == I*pi
+    assert Chi(oo) is oo
+    assert Chi(-oo) is oo
+
+    assert mytd(Ci(x), cos(x)/x, x)
+    assert mytd(Chi(x), cosh(x)/x, x)
+
+    assert mytn(Ci(x), Ci(x).rewrite(Ei),
+                Ei(x*exp_polar(-I*pi/2))/2 + Ei(x*exp_polar(I*pi/2))/2, x)
+    assert mytn(Chi(x), Chi(x).rewrite(Ei),
+                Ei(x)/2 + Ei(x*exp_polar(I*pi))/2 - I*pi/2, x)
+
+    assert tn_arg(Ci)
+    assert tn_arg(Chi)
+
+    assert Ci(x).nseries(x, n=4) == \
+        EulerGamma + log(x) - x**2/4 + O(x**4)
+    assert Chi(x).nseries(x, n=4) == \
+        EulerGamma + log(x) + x**2/4 + O(x**4)
+
+    assert Ci(x).series(x, oo) == -cos(x)*(-6/x**4 + x**(-2) + O(x**(-6), (x, oo))) + \
+        sin(x)*(24/x**5 - 2/x**3 + 1/x + O(x**(-6), (x, oo)))
+
+    assert Ci(x).series(x, -oo) == -cos(x)*(-6/x**4 + x**(-2) + O(x**(-6), (x, -oo))) + \
+        sin(x)*(24/x**5 - 2/x**3 + 1/x + O(x**(-6), (x, -oo))) + I*pi
+
+    assert limit(log(x) - Ci(2*x), x, 0) == -log(2) - EulerGamma
+    assert Ci(x).rewrite(uppergamma) == -expint(1, x*exp_polar(-I*pi/2))/2 -\
+                                        expint(1, x*exp_polar(I*pi/2))/2
+    assert Ci(x).rewrite(expint) == -expint(1, x*exp_polar(-I*pi/2))/2 -\
+                                        expint(1, x*exp_polar(I*pi/2))/2
+    raises(ArgumentIndexError, lambda: Ci(x).fdiff(2))
+
+
+def test_fresnel():
+    assert fresnels(0) is S.Zero
+    assert fresnels(oo) is S.Half
+    assert fresnels(-oo) == Rational(-1, 2)
+    assert fresnels(I*oo) == -I*S.Half
+
+    assert unchanged(fresnels, z)
+    assert fresnels(-z) == -fresnels(z)
+    assert fresnels(I*z) == -I*fresnels(z)
+    assert fresnels(-I*z) == I*fresnels(z)
+
+    assert conjugate(fresnels(z)) == fresnels(conjugate(z))
+
+    assert fresnels(z).diff(z) == sin(pi*z**2/2)
+
+    assert fresnels(z).rewrite(erf) == (S.One + I)/4 * (
+        erf((S.One + I)/2*sqrt(pi)*z) - I*erf((S.One - I)/2*sqrt(pi)*z))
+
+    assert fresnels(z).rewrite(hyper) == \
+        pi*z**3/6 * hyper([Rational(3, 4)], [Rational(3, 2), Rational(7, 4)], -pi**2*z**4/16)
+
+    assert fresnels(z).series(z, n=15) == \
+        pi*z**3/6 - pi**3*z**7/336 + pi**5*z**11/42240 + O(z**15)
+
+    assert fresnels(w).is_extended_real is True
+    assert fresnels(w).is_finite is True
+
+    assert fresnels(z).is_extended_real is None
+    assert fresnels(z).is_finite is None
+
+    assert fresnels(z).as_real_imag() == (fresnels(re(z) - I*im(z))/2 +
+                    fresnels(re(z) + I*im(z))/2,
+                    -I*(-fresnels(re(z) - I*im(z)) + fresnels(re(z) + I*im(z)))/2)
+
+    assert fresnels(z).as_real_imag(deep=False) == (fresnels(re(z) - I*im(z))/2 +
+                    fresnels(re(z) + I*im(z))/2,
+                    -I*(-fresnels(re(z) - I*im(z)) + fresnels(re(z) + I*im(z)))/2)
+
+    assert fresnels(w).as_real_imag() == (fresnels(w), 0)
+    assert fresnels(w).as_real_imag(deep=True) == (fresnels(w), 0)
+
+    assert fresnels(2 + 3*I).as_real_imag() == (
+            fresnels(2 + 3*I)/2 + fresnels(2 - 3*I)/2,
+            -I*(fresnels(2 + 3*I) - fresnels(2 - 3*I))/2
+            )
+
+    assert expand_func(integrate(fresnels(z), z)) == \
+        z*fresnels(z) + cos(pi*z**2/2)/pi
+
+    assert fresnels(z).rewrite(meijerg) == sqrt(2)*pi*z**Rational(9, 4) * \
+        meijerg(((), (1,)), ((Rational(3, 4),),
+        (Rational(1, 4), 0)), -pi**2*z**4/16)/(2*(-z)**Rational(3, 4)*(z**2)**Rational(3, 4))
+
+    assert fresnelc(0) is S.Zero
+    assert fresnelc(oo) == S.Half
+    assert fresnelc(-oo) == Rational(-1, 2)
+    assert fresnelc(I*oo) == I*S.Half
+
+    assert unchanged(fresnelc, z)
+    assert fresnelc(-z) == -fresnelc(z)
+    assert fresnelc(I*z) == I*fresnelc(z)
+    assert fresnelc(-I*z) == -I*fresnelc(z)
+
+    assert conjugate(fresnelc(z)) == fresnelc(conjugate(z))
+
+    assert fresnelc(z).diff(z) == cos(pi*z**2/2)
+
+    assert fresnelc(z).rewrite(erf) == (S.One - I)/4 * (
+        erf((S.One + I)/2*sqrt(pi)*z) + I*erf((S.One - I)/2*sqrt(pi)*z))
+
+    assert fresnelc(z).rewrite(hyper) == \
+        z * hyper([Rational(1, 4)], [S.Half, Rational(5, 4)], -pi**2*z**4/16)
+
+    assert fresnelc(w).is_extended_real is True
+
+    assert fresnelc(z).as_real_imag() == \
+        (fresnelc(re(z) - I*im(z))/2 + fresnelc(re(z) + I*im(z))/2,
+         -I*(-fresnelc(re(z) - I*im(z)) + fresnelc(re(z) + I*im(z)))/2)
+
+    assert fresnelc(z).as_real_imag(deep=False) == \
+        (fresnelc(re(z) - I*im(z))/2 + fresnelc(re(z) + I*im(z))/2,
+         -I*(-fresnelc(re(z) - I*im(z)) + fresnelc(re(z) + I*im(z)))/2)
+
+    assert fresnelc(2 + 3*I).as_real_imag() == (
+        fresnelc(2 - 3*I)/2 + fresnelc(2 + 3*I)/2,
+         -I*(fresnelc(2 + 3*I) - fresnelc(2 - 3*I))/2
+    )
+
+    assert expand_func(integrate(fresnelc(z), z)) == \
+        z*fresnelc(z) - sin(pi*z**2/2)/pi
+
+    assert fresnelc(z).rewrite(meijerg) == sqrt(2)*pi*z**Rational(3, 4) * \
+        meijerg(((), (1,)), ((Rational(1, 4),),
+        (Rational(3, 4), 0)), -pi**2*z**4/16)/(2*(-z)**Rational(1, 4)*(z**2)**Rational(1, 4))
+
+    from sympy.core.random import verify_numerically
+
+    verify_numerically(re(fresnels(z)), fresnels(z).as_real_imag()[0], z)
+    verify_numerically(im(fresnels(z)), fresnels(z).as_real_imag()[1], z)
+    verify_numerically(fresnels(z), fresnels(z).rewrite(hyper), z)
+    verify_numerically(fresnels(z), fresnels(z).rewrite(meijerg), z)
+
+    verify_numerically(re(fresnelc(z)), fresnelc(z).as_real_imag()[0], z)
+    verify_numerically(im(fresnelc(z)), fresnelc(z).as_real_imag()[1], z)
+    verify_numerically(fresnelc(z), fresnelc(z).rewrite(hyper), z)
+    verify_numerically(fresnelc(z), fresnelc(z).rewrite(meijerg), z)
+
+    raises(ArgumentIndexError, lambda: fresnels(z).fdiff(2))
+    raises(ArgumentIndexError, lambda: fresnelc(z).fdiff(2))
+
+    assert fresnels(x).taylor_term(-1, x) is S.Zero
+    assert fresnelc(x).taylor_term(-1, x) is S.Zero
+    assert fresnelc(x).taylor_term(1, x) == -pi**2*x**5/40
+
+
+def test_fresnel_series():
+    assert fresnelc(z).series(z, n=15) == \
+        z - pi**2*z**5/40 + pi**4*z**9/3456 - pi**6*z**13/599040 + O(z**15)
+
+    # issues 6510, 10102
+    fs = (S.Half - sin(pi*z**2/2)/(pi**2*z**3)
+        + (-1/(pi*z) + 3/(pi**3*z**5))*cos(pi*z**2/2))
+    fc = (S.Half - cos(pi*z**2/2)/(pi**2*z**3)
+        + (1/(pi*z) - 3/(pi**3*z**5))*sin(pi*z**2/2))
+    assert fresnels(z).series(z, oo) == fs + O(z**(-6), (z, oo))
+    assert fresnelc(z).series(z, oo) == fc + O(z**(-6), (z, oo))
+    assert (fresnels(z).series(z, -oo) + fs.subs(z, -z)).expand().is_Order
+    assert (fresnelc(z).series(z, -oo) + fc.subs(z, -z)).expand().is_Order
+    assert (fresnels(1/z).series(z) - fs.subs(z, 1/z)).expand().is_Order
+    assert (fresnelc(1/z).series(z) - fc.subs(z, 1/z)).expand().is_Order
+    assert ((2*fresnels(3*z)).series(z, oo) - 2*fs.subs(z, 3*z)).expand().is_Order
+    assert ((3*fresnelc(2*z)).series(z, oo) - 3*fc.subs(z, 2*z)).expand().is_Order
+
+
+def test_integral_rewrites(): #issues 26134, 26144, 26306
+    assert expint(n, x).rewrite(Integral).dummy_eq(Integral(t**-n * exp(-t*x), (t, 1, oo)))
+    assert Si(x).rewrite(Integral).dummy_eq(Integral(sinc(t), (t, 0, x)))
+    assert Ci(x).rewrite(Integral).dummy_eq(log(x) - Integral((1 - cos(t))/t, (t, 0, x)) + EulerGamma)
+    assert fresnels(x).rewrite(Integral).dummy_eq(Integral(sin(pi*t**2/2), (t, 0, x)))
+    assert fresnelc(x).rewrite(Integral).dummy_eq(Integral(cos(pi*t**2/2), (t, 0, x)))
+    assert Ei(x).rewrite(Integral).dummy_eq(Integral(exp(t)/t, (t, -oo, x)))
+    assert fresnels(x).diff(x) == fresnels(x).rewrite(Integral).diff(x)
+    assert fresnelc(x).diff(x) == fresnelc(x).rewrite(Integral).diff(x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_gamma_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_gamma_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..14c57a31ce2edaa60fd5efc8bcbc95668961fd41
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_gamma_functions.py
@@ -0,0 +1,741 @@
+from sympy.core.function import expand_func, Subs
+from sympy.core import EulerGamma
+from sympy.core.numbers import (I, Rational, nan, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.combinatorial.numbers import harmonic
+from sympy.functions.elementary.complexes import (Abs, conjugate, im, re)
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.hyperbolic import tanh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin, atan)
+from sympy.functions.special.error_functions import (Ei, erf, erfc)
+from sympy.functions.special.gamma_functions import (digamma, gamma, loggamma, lowergamma, multigamma, polygamma, trigamma, uppergamma)
+from sympy.functions.special.zeta_functions import zeta
+from sympy.series.order import O
+
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.testing.pytest import raises
+from sympy.core.random import (test_derivative_numerically as td,
+                                      random_complex_number as randcplx,
+                                      verify_numerically as tn)
+
+x = Symbol('x')
+y = Symbol('y')
+n = Symbol('n', integer=True)
+w = Symbol('w', real=True)
+
+def test_gamma():
+    assert gamma(nan) is nan
+    assert gamma(oo) is oo
+
+    assert gamma(-100) is zoo
+    assert gamma(0) is zoo
+    assert gamma(-100.0) is zoo
+
+    assert gamma(1) == 1
+    assert gamma(2) == 1
+    assert gamma(3) == 2
+
+    assert gamma(102) == factorial(101)
+
+    assert gamma(S.Half) == sqrt(pi)
+
+    assert gamma(Rational(3, 2)) == sqrt(pi)*S.Half
+    assert gamma(Rational(5, 2)) == sqrt(pi)*Rational(3, 4)
+    assert gamma(Rational(7, 2)) == sqrt(pi)*Rational(15, 8)
+
+    assert gamma(Rational(-1, 2)) == -2*sqrt(pi)
+    assert gamma(Rational(-3, 2)) == sqrt(pi)*Rational(4, 3)
+    assert gamma(Rational(-5, 2)) == sqrt(pi)*Rational(-8, 15)
+
+    assert gamma(Rational(-15, 2)) == sqrt(pi)*Rational(256, 2027025)
+
+    assert gamma(Rational(
+        -11, 8)).expand(func=True) == Rational(64, 33)*gamma(Rational(5, 8))
+    assert gamma(Rational(
+        -10, 3)).expand(func=True) == Rational(81, 280)*gamma(Rational(2, 3))
+    assert gamma(Rational(
+        14, 3)).expand(func=True) == Rational(880, 81)*gamma(Rational(2, 3))
+    assert gamma(Rational(
+        17, 7)).expand(func=True) == Rational(30, 49)*gamma(Rational(3, 7))
+    assert gamma(Rational(
+        19, 8)).expand(func=True) == Rational(33, 64)*gamma(Rational(3, 8))
+
+    assert gamma(x).diff(x) == gamma(x)*polygamma(0, x)
+
+    assert gamma(x - 1).expand(func=True) == gamma(x)/(x - 1)
+    assert gamma(x + 2).expand(func=True, mul=False) == x*(x + 1)*gamma(x)
+
+    assert conjugate(gamma(x)) == gamma(conjugate(x))
+
+    assert expand_func(gamma(x + Rational(3, 2))) == \
+        (x + S.Half)*gamma(x + S.Half)
+
+    assert expand_func(gamma(x - S.Half)) == \
+        gamma(S.Half + x)/(x - S.Half)
+
+    # Test a bug:
+    assert expand_func(gamma(x + Rational(3, 4))) == gamma(x + Rational(3, 4))
+
+    # XXX: Not sure about these tests. I can fix them by defining e.g.
+    # exp_polar.is_integer but I'm not sure if that makes sense.
+    assert gamma(3*exp_polar(I*pi)/4).is_nonnegative is False
+    assert gamma(3*exp_polar(I*pi)/4).is_extended_nonpositive is True
+
+    y = Symbol('y', nonpositive=True, integer=True)
+    assert gamma(y).is_real == False
+    y = Symbol('y', positive=True, noninteger=True)
+    assert gamma(y).is_real == True
+
+    assert gamma(-1.0, evaluate=False).is_real == False
+    assert gamma(0, evaluate=False).is_real == False
+    assert gamma(-2, evaluate=False).is_real == False
+
+
+def test_gamma_rewrite():
+    assert gamma(n).rewrite(factorial) == factorial(n - 1)
+
+
+def test_gamma_series():
+    assert gamma(x + 1).series(x, 0, 3) == \
+        1 - EulerGamma*x + x**2*(EulerGamma**2/2 + pi**2/12) + O(x**3)
+    assert gamma(x).series(x, -1, 3) == \
+        -1/(x + 1) + EulerGamma - 1 + (x + 1)*(-1 - pi**2/12 - EulerGamma**2/2 + \
+       EulerGamma) + (x + 1)**2*(-1 - pi**2/12 - EulerGamma**2/2 + EulerGamma**3/6 - \
+       polygamma(2, 1)/6 + EulerGamma*pi**2/12 + EulerGamma) + O((x + 1)**3, (x, -1))
+
+
+def tn_branch(s, func):
+    from sympy.core.random import uniform
+    c = uniform(1, 5)
+    expr = func(s, c*exp_polar(I*pi)) - func(s, c*exp_polar(-I*pi))
+    eps = 1e-15
+    expr2 = func(s + eps, -c + eps*I) - func(s + eps, -c - eps*I)
+    return abs(expr.n() - expr2.n()).n() < 1e-10
+
+
+def test_lowergamma():
+    from sympy.functions.special.error_functions import expint
+    from sympy.functions.special.hyper import meijerg
+    assert lowergamma(x, 0) == 0
+    assert lowergamma(x, y).diff(y) == y**(x - 1)*exp(-y)
+    assert td(lowergamma(randcplx(), y), y)
+    assert td(lowergamma(x, randcplx()), x)
+    assert lowergamma(x, y).diff(x) == \
+        gamma(x)*digamma(x) - uppergamma(x, y)*log(y) \
+        - meijerg([], [1, 1], [0, 0, x], [], y)
+
+    assert lowergamma(S.Half, x) == sqrt(pi)*erf(sqrt(x))
+    assert not lowergamma(S.Half - 3, x).has(lowergamma)
+    assert not lowergamma(S.Half + 3, x).has(lowergamma)
+    assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
+    assert tn(lowergamma(S.Half + 3, x, evaluate=False),
+              lowergamma(S.Half + 3, x), x)
+    assert tn(lowergamma(S.Half - 3, x, evaluate=False),
+              lowergamma(S.Half - 3, x), x)
+
+    assert tn_branch(-3, lowergamma)
+    assert tn_branch(-4, lowergamma)
+    assert tn_branch(Rational(1, 3), lowergamma)
+    assert tn_branch(pi, lowergamma)
+    assert lowergamma(3, exp_polar(4*pi*I)*x) == lowergamma(3, x)
+    assert lowergamma(y, exp_polar(5*pi*I)*x) == \
+        exp(4*I*pi*y)*lowergamma(y, x*exp_polar(pi*I))
+    assert lowergamma(-2, exp_polar(5*pi*I)*x) == \
+        lowergamma(-2, x*exp_polar(I*pi)) + 2*pi*I
+
+    assert conjugate(lowergamma(x, y)) == lowergamma(conjugate(x), conjugate(y))
+    assert conjugate(lowergamma(x, 0)) == 0
+    assert unchanged(conjugate, lowergamma(x, -oo))
+
+    assert lowergamma(0, x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(S(1)/3, x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(1, x, evaluate=False)._eval_is_meromorphic(x, 0) == True
+    assert lowergamma(x, x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(x + 1, x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(1/x, x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(0, x + 1)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(S(1)/3, x + 1)._eval_is_meromorphic(x, 0) == True
+    assert lowergamma(1, x + 1, evaluate=False)._eval_is_meromorphic(x, 0) == True
+    assert lowergamma(x, x + 1)._eval_is_meromorphic(x, 0) == True
+    assert lowergamma(x + 1, x + 1)._eval_is_meromorphic(x, 0) == True
+    assert lowergamma(1/x, x + 1)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(0, 1/x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(S(1)/3, 1/x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(1, 1/x, evaluate=False)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(x, 1/x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(x + 1, 1/x)._eval_is_meromorphic(x, 0) == False
+    assert lowergamma(1/x, 1/x)._eval_is_meromorphic(x, 0) == False
+
+    assert lowergamma(x, 2).series(x, oo, 3) == \
+        2**x*(1 + 2/(x + 1))*exp(-2)/x + O(exp(x*log(2))/x**3, (x, oo))
+
+    assert lowergamma(
+        x, y).rewrite(expint) == -y**x*expint(-x + 1, y) + gamma(x)
+    k = Symbol('k', integer=True)
+    assert lowergamma(
+        k, y).rewrite(expint) == -y**k*expint(-k + 1, y) + gamma(k)
+    k = Symbol('k', integer=True, positive=False)
+    assert lowergamma(k, y).rewrite(expint) == lowergamma(k, y)
+    assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y)
+
+    assert lowergamma(70, 6) == factorial(69) - 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320 * exp(-6)
+    assert (lowergamma(S(77) / 2, 6) - lowergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
+    assert (lowergamma(-S(77) / 2, 6) - lowergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
+
+
+def test_uppergamma():
+    from sympy.functions.special.error_functions import expint
+    from sympy.functions.special.hyper import meijerg
+    assert uppergamma(4, 0) == 6
+    assert uppergamma(x, y).diff(y) == -y**(x - 1)*exp(-y)
+    assert td(uppergamma(randcplx(), y), y)
+    assert uppergamma(x, y).diff(x) == \
+        uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
+    assert td(uppergamma(x, randcplx()), x)
+
+    p = Symbol('p', positive=True)
+    assert uppergamma(0, p) == -Ei(-p)
+    assert uppergamma(p, 0) == gamma(p)
+    assert uppergamma(S.Half, x) == sqrt(pi)*erfc(sqrt(x))
+    assert not uppergamma(S.Half - 3, x).has(uppergamma)
+    assert not uppergamma(S.Half + 3, x).has(uppergamma)
+    assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
+    assert tn(uppergamma(S.Half + 3, x, evaluate=False),
+              uppergamma(S.Half + 3, x), x)
+    assert tn(uppergamma(S.Half - 3, x, evaluate=False),
+              uppergamma(S.Half - 3, x), x)
+
+    assert unchanged(uppergamma, x, -oo)
+    assert unchanged(uppergamma, x, 0)
+
+    assert tn_branch(-3, uppergamma)
+    assert tn_branch(-4, uppergamma)
+    assert tn_branch(Rational(1, 3), uppergamma)
+    assert tn_branch(pi, uppergamma)
+    assert uppergamma(3, exp_polar(4*pi*I)*x) == uppergamma(3, x)
+    assert uppergamma(y, exp_polar(5*pi*I)*x) == \
+        exp(4*I*pi*y)*uppergamma(y, x*exp_polar(pi*I)) + \
+        gamma(y)*(1 - exp(4*pi*I*y))
+    assert uppergamma(-2, exp_polar(5*pi*I)*x) == \
+        uppergamma(-2, x*exp_polar(I*pi)) - 2*pi*I
+
+    assert uppergamma(-2, x) == expint(3, x)/x**2
+
+    assert conjugate(uppergamma(x, y)) == uppergamma(conjugate(x), conjugate(y))
+    assert unchanged(conjugate, uppergamma(x, -oo))
+
+    assert uppergamma(x, y).rewrite(expint) == y**x*expint(-x + 1, y)
+    assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y)
+
+    assert uppergamma(70, 6) == 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320*exp(-6)
+    assert (uppergamma(S(77) / 2, 6) - uppergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
+    assert (uppergamma(-S(77) / 2, 6) - uppergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
+
+
+def test_polygamma():
+    assert polygamma(n, nan) is nan
+
+    assert polygamma(0, oo) is oo
+    assert polygamma(0, -oo) is oo
+    assert polygamma(0, I*oo) is oo
+    assert polygamma(0, -I*oo) is oo
+    assert polygamma(1, oo) == 0
+    assert polygamma(5, oo) == 0
+
+    assert polygamma(0, -9) is zoo
+
+    assert polygamma(0, -9) is zoo
+    assert polygamma(0, -1) is zoo
+    assert polygamma(Rational(3, 2), -1) is zoo
+
+    assert polygamma(0, 0) is zoo
+
+    assert polygamma(0, 1) == -EulerGamma
+    assert polygamma(0, 7) == Rational(49, 20) - EulerGamma
+
+    assert polygamma(1, 1) == pi**2/6
+    assert polygamma(1, 2) == pi**2/6 - 1
+    assert polygamma(1, 3) == pi**2/6 - Rational(5, 4)
+    assert polygamma(3, 1) == pi**4 / 15
+    assert polygamma(3, 5) == 6*(Rational(-22369, 20736) + pi**4/90)
+    assert polygamma(5, 1) == 8 * pi**6 / 63
+
+    assert polygamma(1, S.Half) == pi**2 / 2
+    assert polygamma(2, S.Half) == -14*zeta(3)
+    assert polygamma(11, S.Half) == 176896*pi**12
+
+    def t(m, n):
+        x = S(m)/n
+        r = polygamma(0, x)
+        if r.has(polygamma):
+            return False
+        return abs(polygamma(0, x.n()).n() - r.n()).n() < 1e-10
+    assert t(1, 2)
+    assert t(3, 2)
+    assert t(-1, 2)
+    assert t(1, 4)
+    assert t(-3, 4)
+    assert t(1, 3)
+    assert t(4, 3)
+    assert t(3, 4)
+    assert t(2, 3)
+    assert t(123, 5)
+
+    assert polygamma(0, x).rewrite(zeta) == polygamma(0, x)
+    assert polygamma(1, x).rewrite(zeta) == zeta(2, x)
+    assert polygamma(2, x).rewrite(zeta) == -2*zeta(3, x)
+    assert polygamma(I, 2).rewrite(zeta) == polygamma(I, 2)
+    n1 = Symbol('n1')
+    n2 = Symbol('n2', real=True)
+    n3 = Symbol('n3', integer=True)
+    n4 = Symbol('n4', positive=True)
+    n5 = Symbol('n5', positive=True, integer=True)
+    assert polygamma(n1, x).rewrite(zeta) == polygamma(n1, x)
+    assert polygamma(n2, x).rewrite(zeta) == polygamma(n2, x)
+    assert polygamma(n3, x).rewrite(zeta) == polygamma(n3, x)
+    assert polygamma(n4, x).rewrite(zeta) == polygamma(n4, x)
+    assert polygamma(n5, x).rewrite(zeta) == (-1)**(n5 + 1) * factorial(n5) * zeta(n5 + 1, x)
+
+    assert polygamma(3, 7*x).diff(x) == 7*polygamma(4, 7*x)
+
+    assert polygamma(0, x).rewrite(harmonic) == harmonic(x - 1) - EulerGamma
+    assert polygamma(2, x).rewrite(harmonic) == 2*harmonic(x - 1, 3) - 2*zeta(3)
+    ni = Symbol("n", integer=True)
+    assert polygamma(ni, x).rewrite(harmonic) == (-1)**(ni + 1)*(-harmonic(x - 1, ni + 1)
+                                                                 + zeta(ni + 1))*factorial(ni)
+
+    # Polygamma of non-negative integer order is unbranched:
+    k = Symbol('n', integer=True, nonnegative=True)
+    assert polygamma(k, exp_polar(2*I*pi)*x) == polygamma(k, x)
+
+    # but negative integers are branched!
+    k = Symbol('n', integer=True)
+    assert polygamma(k, exp_polar(2*I*pi)*x).args == (k, exp_polar(2*I*pi)*x)
+
+    # Polygamma of order -1 is loggamma:
+    assert polygamma(-1, x) == loggamma(x) - log(2*pi) / 2
+
+    # But smaller orders are iterated integrals and don't have a special name
+    assert polygamma(-2, x).func is polygamma
+
+    # Test a bug
+    assert polygamma(0, -x).expand(func=True) == polygamma(0, -x)
+
+    assert polygamma(2, 2.5).is_positive == False
+    assert polygamma(2, -2.5).is_positive == False
+    assert polygamma(3, 2.5).is_positive == True
+    assert polygamma(3, -2.5).is_positive is True
+    assert polygamma(-2, -2.5).is_positive is None
+    assert polygamma(-3, -2.5).is_positive is None
+
+    assert polygamma(2, 2.5).is_negative == True
+    assert polygamma(3, 2.5).is_negative == False
+    assert polygamma(3, -2.5).is_negative == False
+    assert polygamma(2, -2.5).is_negative is True
+    assert polygamma(-2, -2.5).is_negative is None
+    assert polygamma(-3, -2.5).is_negative is None
+
+    assert polygamma(I, 2).is_positive is None
+    assert polygamma(I, 3).is_negative is None
+
+    # issue 17350
+    assert (I*polygamma(I, pi)).as_real_imag() == \
+           (-im(polygamma(I, pi)), re(polygamma(I, pi)))
+    assert (tanh(polygamma(I, 1))).rewrite(exp) == \
+           (exp(polygamma(I, 1)) - exp(-polygamma(I, 1)))/(exp(polygamma(I, 1)) + exp(-polygamma(I, 1)))
+    assert (I / polygamma(I, 4)).rewrite(exp) == \
+           I*exp(-I*atan(im(polygamma(I, 4))/re(polygamma(I, 4))))/Abs(polygamma(I, 4))
+
+    # issue 12569
+    assert unchanged(im, polygamma(0, I))
+    assert polygamma(Symbol('a', positive=True), Symbol('b', positive=True)).is_real is True
+    assert polygamma(0, I).is_real is None
+
+    assert str(polygamma(pi, 3).evalf(n=10)) == "0.1169314564"
+    assert str(polygamma(2.3, 1.0).evalf(n=10)) == "-3.003302909"
+    assert str(polygamma(-1, 1).evalf(n=10)) == "-0.9189385332" # not zero
+    assert str(polygamma(I, 1).evalf(n=10)) == "-3.109856569 + 1.89089016*I"
+    assert str(polygamma(1, I).evalf(n=10)) == "-0.5369999034 - 0.7942335428*I"
+    assert str(polygamma(I, I).evalf(n=10)) == "6.332362889 + 45.92828268*I"
+
+
+def test_polygamma_expand_func():
+    assert polygamma(0, x).expand(func=True) == polygamma(0, x)
+    assert polygamma(0, 2*x).expand(func=True) == \
+        polygamma(0, x)/2 + polygamma(0, S.Half + x)/2 + log(2)
+    assert polygamma(1, 2*x).expand(func=True) == \
+        polygamma(1, x)/4 + polygamma(1, S.Half + x)/4
+    assert polygamma(2, x).expand(func=True) == \
+        polygamma(2, x)
+    assert polygamma(0, -1 + x).expand(func=True) == \
+        polygamma(0, x) - 1/(x - 1)
+    assert polygamma(0, 1 + x).expand(func=True) == \
+        1/x + polygamma(0, x )
+    assert polygamma(0, 2 + x).expand(func=True) == \
+        1/x + 1/(1 + x) + polygamma(0, x)
+    assert polygamma(0, 3 + x).expand(func=True) == \
+        polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x)
+    assert polygamma(0, 4 + x).expand(func=True) == \
+        polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x) + 1/(3 + x)
+    assert polygamma(1, 1 + x).expand(func=True) == \
+        polygamma(1, x) - 1/x**2
+    assert polygamma(1, 2 + x).expand(func=True, multinomial=False) == \
+        polygamma(1, x) - 1/x**2 - 1/(1 + x)**2
+    assert polygamma(1, 3 + x).expand(func=True, multinomial=False) == \
+        polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - 1/(2 + x)**2
+    assert polygamma(1, 4 + x).expand(func=True, multinomial=False) == \
+        polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - \
+        1/(2 + x)**2 - 1/(3 + x)**2
+    assert polygamma(0, x + y).expand(func=True) == \
+        polygamma(0, x + y)
+    assert polygamma(1, x + y).expand(func=True) == \
+        polygamma(1, x + y)
+    assert polygamma(1, 3 + 4*x + y).expand(func=True, multinomial=False) == \
+        polygamma(1, y + 4*x) - 1/(y + 4*x)**2 - \
+        1/(1 + y + 4*x)**2 - 1/(2 + y + 4*x)**2
+    assert polygamma(3, 3 + 4*x + y).expand(func=True, multinomial=False) == \
+        polygamma(3, y + 4*x) - 6/(y + 4*x)**4 - \
+        6/(1 + y + 4*x)**4 - 6/(2 + y + 4*x)**4
+    assert polygamma(3, 4*x + y + 1).expand(func=True, multinomial=False) == \
+        polygamma(3, y + 4*x) - 6/(y + 4*x)**4
+    e = polygamma(3, 4*x + y + Rational(3, 2))
+    assert e.expand(func=True) == e
+    e = polygamma(3, x + y + Rational(3, 4))
+    assert e.expand(func=True, basic=False) == e
+
+    assert polygamma(-1, x, evaluate=False).expand(func=True) == \
+        loggamma(x) - log(pi)/2 - log(2)/2
+    p2 = polygamma(-2, x).expand(func=True) + x**2/2 - x/2 + S(1)/12
+    assert isinstance(p2, Subs)
+    assert p2.point == (-1,)
+
+
+def test_digamma():
+    assert digamma(nan) == nan
+
+    assert digamma(oo) == oo
+    assert digamma(-oo) == oo
+    assert digamma(I*oo) == oo
+    assert digamma(-I*oo) == oo
+
+    assert digamma(-9) == zoo
+
+    assert digamma(-9) == zoo
+    assert digamma(-1) == zoo
+
+    assert digamma(0) == zoo
+
+    assert digamma(1) == -EulerGamma
+    assert digamma(7) == Rational(49, 20) - EulerGamma
+
+    def t(m, n):
+        x = S(m)/n
+        r = digamma(x)
+        if r.has(digamma):
+            return False
+        return abs(digamma(x.n()).n() - r.n()).n() < 1e-10
+    assert t(1, 2)
+    assert t(3, 2)
+    assert t(-1, 2)
+    assert t(1, 4)
+    assert t(-3, 4)
+    assert t(1, 3)
+    assert t(4, 3)
+    assert t(3, 4)
+    assert t(2, 3)
+    assert t(123, 5)
+
+    assert digamma(x).rewrite(zeta) == polygamma(0, x)
+
+    assert digamma(x).rewrite(harmonic) == harmonic(x - 1) - EulerGamma
+
+    assert digamma(I).is_real is None
+
+    assert digamma(x,evaluate=False).fdiff() == polygamma(1, x)
+
+    assert digamma(x,evaluate=False).is_real is None
+
+    assert digamma(x,evaluate=False).is_positive is None
+
+    assert digamma(x,evaluate=False).is_negative is None
+
+    assert digamma(x,evaluate=False).rewrite(polygamma) == polygamma(0, x)
+
+
+def test_digamma_expand_func():
+    assert digamma(x).expand(func=True) == polygamma(0, x)
+    assert digamma(2*x).expand(func=True) == \
+        polygamma(0, x)/2 + polygamma(0, Rational(1, 2) + x)/2 + log(2)
+    assert digamma(-1 + x).expand(func=True) == \
+        polygamma(0, x) - 1/(x - 1)
+    assert digamma(1 + x).expand(func=True) == \
+        1/x + polygamma(0, x )
+    assert digamma(2 + x).expand(func=True) == \
+        1/x + 1/(1 + x) + polygamma(0, x)
+    assert digamma(3 + x).expand(func=True) == \
+        polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x)
+    assert digamma(4 + x).expand(func=True) == \
+        polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x) + 1/(3 + x)
+    assert digamma(x + y).expand(func=True) == \
+        polygamma(0, x + y)
+
+def test_trigamma():
+    assert trigamma(nan) == nan
+
+    assert trigamma(oo) == 0
+
+    assert trigamma(1) == pi**2/6
+    assert trigamma(2) == pi**2/6 - 1
+    assert trigamma(3) == pi**2/6 - Rational(5, 4)
+
+    assert trigamma(x, evaluate=False).rewrite(zeta) == zeta(2, x)
+    assert trigamma(x, evaluate=False).rewrite(harmonic) == \
+        trigamma(x).rewrite(polygamma).rewrite(harmonic)
+
+    assert trigamma(x,evaluate=False).fdiff() == polygamma(2, x)
+
+    assert trigamma(x,evaluate=False).is_real is None
+
+    assert trigamma(x,evaluate=False).is_positive is None
+
+    assert trigamma(x,evaluate=False).is_negative is None
+
+    assert trigamma(x,evaluate=False).rewrite(polygamma) == polygamma(1, x)
+
+def test_trigamma_expand_func():
+    assert trigamma(2*x).expand(func=True) == \
+        polygamma(1, x)/4 + polygamma(1, Rational(1, 2) + x)/4
+    assert trigamma(1 + x).expand(func=True) == \
+        polygamma(1, x) - 1/x**2
+    assert trigamma(2 + x).expand(func=True, multinomial=False) == \
+        polygamma(1, x) - 1/x**2 - 1/(1 + x)**2
+    assert trigamma(3 + x).expand(func=True, multinomial=False) == \
+        polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - 1/(2 + x)**2
+    assert trigamma(4 + x).expand(func=True, multinomial=False) == \
+        polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - \
+        1/(2 + x)**2 - 1/(3 + x)**2
+    assert trigamma(x + y).expand(func=True) == \
+        polygamma(1, x + y)
+    assert trigamma(3 + 4*x + y).expand(func=True, multinomial=False) == \
+        polygamma(1, y + 4*x) - 1/(y + 4*x)**2 - \
+        1/(1 + y + 4*x)**2 - 1/(2 + y + 4*x)**2
+
+def test_loggamma():
+    raises(TypeError, lambda: loggamma(2, 3))
+    raises(ArgumentIndexError, lambda: loggamma(x).fdiff(2))
+
+    assert loggamma(-1) is oo
+    assert loggamma(-2) is oo
+    assert loggamma(0) is oo
+    assert loggamma(1) == 0
+    assert loggamma(2) == 0
+    assert loggamma(3) == log(2)
+    assert loggamma(4) == log(6)
+
+    n = Symbol("n", integer=True, positive=True)
+    assert loggamma(n) == log(gamma(n))
+    assert loggamma(-n) is oo
+    assert loggamma(n/2) == log(2**(-n + 1)*sqrt(pi)*gamma(n)/gamma(n/2 + S.Half))
+
+    assert loggamma(oo) is oo
+    assert loggamma(-oo) is zoo
+    assert loggamma(I*oo) is zoo
+    assert loggamma(-I*oo) is zoo
+    assert loggamma(zoo) is zoo
+    assert loggamma(nan) is nan
+
+    L = loggamma(Rational(16, 3))
+    E = -5*log(3) + loggamma(Rational(1, 3)) + log(4) + log(7) + log(10) + log(13)
+    assert expand_func(L).doit() == E
+    assert L.n() == E.n()
+
+    L = loggamma(Rational(19, 4))
+    E = -4*log(4) + loggamma(Rational(3, 4)) + log(3) + log(7) + log(11) + log(15)
+    assert expand_func(L).doit() == E
+    assert L.n() == E.n()
+
+    L = loggamma(Rational(23, 7))
+    E = -3*log(7) + log(2) + loggamma(Rational(2, 7)) + log(9) + log(16)
+    assert expand_func(L).doit() == E
+    assert L.n() == E.n()
+
+    L = loggamma(Rational(19, 4) - 7)
+    E = -log(9) - log(5) + loggamma(Rational(3, 4)) + 3*log(4) - 3*I*pi
+    assert expand_func(L).doit() == E
+    assert L.n() == E.n()
+
+    L = loggamma(Rational(23, 7) - 6)
+    E = -log(19) - log(12) - log(5) + loggamma(Rational(2, 7)) + 3*log(7) - 3*I*pi
+    assert expand_func(L).doit() == E
+    assert L.n() == E.n()
+
+    assert loggamma(x).diff(x) == polygamma(0, x)
+    s1 = loggamma(1/(x + sin(x)) + cos(x)).nseries(x, n=4)
+    s2 = (-log(2*x) - 1)/(2*x) - log(x/pi)/2 + (4 - log(2*x))*x/24 + O(x**2) + \
+        log(x)*x**2/2
+    assert (s1 - s2).expand(force=True).removeO() == 0
+    s1 = loggamma(1/x).series(x)
+    s2 = (1/x - S.Half)*log(1/x) - 1/x + log(2*pi)/2 + \
+        x/12 - x**3/360 + x**5/1260 + O(x**7)
+    assert ((s1 - s2).expand(force=True)).removeO() == 0
+
+    assert loggamma(x).rewrite('intractable') == log(gamma(x))
+
+    s1 = loggamma(x).series(x).cancel()
+    assert s1 == -log(x) - EulerGamma*x + pi**2*x**2/12 + x**3*polygamma(2, 1)/6 + \
+        pi**4*x**4/360 + x**5*polygamma(4, 1)/120 + O(x**6)
+    assert s1 == loggamma(x).rewrite('intractable').series(x).cancel()
+
+    assert conjugate(loggamma(x)) == loggamma(conjugate(x))
+    assert conjugate(loggamma(0)) is oo
+    assert conjugate(loggamma(1)) == loggamma(conjugate(1))
+    assert conjugate(loggamma(-oo)) == conjugate(zoo)
+
+    assert loggamma(Symbol('v', positive=True)).is_real is True
+    assert loggamma(Symbol('v', zero=True)).is_real is False
+    assert loggamma(Symbol('v', negative=True)).is_real is False
+    assert loggamma(Symbol('v', nonpositive=True)).is_real is False
+    assert loggamma(Symbol('v', nonnegative=True)).is_real is None
+    assert loggamma(Symbol('v', imaginary=True)).is_real is None
+    assert loggamma(Symbol('v', real=True)).is_real is None
+    assert loggamma(Symbol('v')).is_real is None
+
+    assert loggamma(S.Half).is_real is True
+    assert loggamma(0).is_real is False
+    assert loggamma(Rational(-1, 2)).is_real is False
+    assert loggamma(I).is_real is None
+    assert loggamma(2 + 3*I).is_real is None
+
+    def tN(N, M):
+        assert loggamma(1/x)._eval_nseries(x, n=N).getn() == M
+    tN(0, 0)
+    tN(1, 1)
+    tN(2, 2)
+    tN(3, 3)
+    tN(4, 4)
+    tN(5, 5)
+
+
+def test_polygamma_expansion():
+    # A. & S., pa. 259 and 260
+    assert polygamma(0, 1/x).nseries(x, n=3) == \
+        -log(x) - x/2 - x**2/12 + O(x**3)
+    assert polygamma(1, 1/x).series(x, n=5) == \
+        x + x**2/2 + x**3/6 + O(x**5)
+    assert polygamma(3, 1/x).nseries(x, n=11) == \
+        2*x**3 + 3*x**4 + 2*x**5 - x**7 + 4*x**9/3 + O(x**11)
+
+
+def test_polygamma_leading_term():
+    expr = -log(1/x) + polygamma(0, 1 + 1/x) + S.EulerGamma
+    assert expr.as_leading_term(x, logx=-y) == S.EulerGamma
+
+
+def test_issue_8657():
+    n = Symbol('n', negative=True, integer=True)
+    m = Symbol('m', integer=True)
+    o = Symbol('o', positive=True)
+    p = Symbol('p', negative=True, integer=False)
+    assert gamma(n).is_real is False
+    assert gamma(m).is_real is None
+    assert gamma(o).is_real is True
+    assert gamma(p).is_real is True
+    assert gamma(w).is_real is None
+
+
+def test_issue_8524():
+    x = Symbol('x', positive=True)
+    y = Symbol('y', negative=True)
+    z = Symbol('z', positive=False)
+    p = Symbol('p', negative=False)
+    q = Symbol('q', integer=True)
+    r = Symbol('r', integer=False)
+    e = Symbol('e', even=True, negative=True)
+    assert gamma(x).is_positive is True
+    assert gamma(y).is_positive is None
+    assert gamma(z).is_positive is None
+    assert gamma(p).is_positive is None
+    assert gamma(q).is_positive is None
+    assert gamma(r).is_positive is None
+    assert gamma(e + S.Half).is_positive is True
+    assert gamma(e - S.Half).is_positive is False
+
+def test_issue_14450():
+    assert uppergamma(Rational(3, 8), x).evalf() == uppergamma(Rational(3, 8), x)
+    assert lowergamma(x, Rational(3, 8)).evalf() == lowergamma(x, Rational(3, 8))
+    # some values from Wolfram Alpha for comparison
+    assert abs(uppergamma(Rational(3, 8), 2).evalf() - 0.07105675881) < 1e-9
+    assert abs(lowergamma(Rational(3, 8), 2).evalf() - 2.2993794256) < 1e-9
+
+def test_issue_14528():
+    k = Symbol('k', integer=True, nonpositive=True)
+    assert isinstance(gamma(k), gamma)
+
+def test_multigamma():
+    from sympy.concrete.products import Product
+    p = Symbol('p')
+    _k = Dummy('_k')
+
+    assert multigamma(x, p).dummy_eq(pi**(p*(p - 1)/4)*\
+        Product(gamma(x + (1 - _k)/2), (_k, 1, p)))
+
+    assert conjugate(multigamma(x, p)).dummy_eq(pi**((conjugate(p) - 1)*\
+        conjugate(p)/4)*Product(gamma(conjugate(x) + (1-conjugate(_k))/2), (_k, 1, p)))
+    assert conjugate(multigamma(x, 1)) == gamma(conjugate(x))
+
+    p = Symbol('p', positive=True)
+    assert conjugate(multigamma(x, p)).dummy_eq(pi**((p - 1)*p/4)*\
+        Product(gamma(conjugate(x) + (1-conjugate(_k))/2), (_k, 1, p)))
+
+    assert multigamma(nan, 1) is nan
+    assert multigamma(oo, 1).doit() is oo
+
+    assert multigamma(1, 1) == 1
+    assert multigamma(2, 1) == 1
+    assert multigamma(3, 1) == 2
+
+    assert multigamma(102, 1) == factorial(101)
+    assert multigamma(S.Half, 1) == sqrt(pi)
+
+    assert multigamma(1, 2) == pi
+    assert multigamma(2, 2) == pi/2
+
+    assert multigamma(1, 3) is zoo
+    assert multigamma(2, 3) == pi**2/2
+    assert multigamma(3, 3) == 3*pi**2/2
+
+    assert multigamma(x, 1).diff(x) == gamma(x)*polygamma(0, x)
+    assert multigamma(x, 2).diff(x) == sqrt(pi)*gamma(x)*gamma(x - S.Half)*\
+        polygamma(0, x) + sqrt(pi)*gamma(x)*gamma(x - S.Half)*polygamma(0, x - S.Half)
+
+    assert multigamma(x - 1, 1).expand(func=True) == gamma(x)/(x - 1)
+    assert multigamma(x + 2, 1).expand(func=True, mul=False) == x*(x + 1)*\
+        gamma(x)
+    assert multigamma(x - 1, 2).expand(func=True) == sqrt(pi)*gamma(x)*\
+        gamma(x + S.Half)/(x**3 - 3*x**2 + x*Rational(11, 4) - Rational(3, 4))
+    assert multigamma(x - 1, 3).expand(func=True) == pi**Rational(3, 2)*gamma(x)**2*\
+        gamma(x + S.Half)/(x**5 - 6*x**4 + 55*x**3/4 - 15*x**2 + x*Rational(31, 4) - Rational(3, 2))
+
+    assert multigamma(n, 1).rewrite(factorial) == factorial(n - 1)
+    assert multigamma(n, 2).rewrite(factorial) == sqrt(pi)*\
+        factorial(n - Rational(3, 2))*factorial(n - 1)
+    assert multigamma(n, 3).rewrite(factorial) == pi**Rational(3, 2)*\
+        factorial(n - 2)*factorial(n - Rational(3, 2))*factorial(n - 1)
+
+    assert multigamma(Rational(-1, 2), 3, evaluate=False).is_real == False
+    assert multigamma(S.Half, 3, evaluate=False).is_real == False
+    assert multigamma(0, 1, evaluate=False).is_real == False
+    assert multigamma(1, 3, evaluate=False).is_real == False
+    assert multigamma(-1.0, 3, evaluate=False).is_real == False
+    assert multigamma(0.7, 3, evaluate=False).is_real == True
+    assert multigamma(3, 3, evaluate=False).is_real == True
+
+def test_gamma_as_leading_term():
+    assert gamma(x).as_leading_term(x) == 1/x
+    assert gamma(2 + x).as_leading_term(x) == S(1)
+    assert gamma(cos(x)).as_leading_term(x) == S(1)
+    assert gamma(sin(x)).as_leading_term(x) == 1/x
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_hyper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_hyper.py
new file mode 100644
index 0000000000000000000000000000000000000000..f1be5b5f0db158ff76173e180ed8d88bd59461b9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_hyper.py
@@ -0,0 +1,403 @@
+from sympy.core.containers import Tuple
+from sympy.core.function import Derivative
+from sympy.core.numbers import (I, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import cos
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import (appellf1, hyper, meijerg)
+from sympy.series.order import O
+from sympy.abc import x, z, k
+from sympy.series.limits import limit
+from sympy.testing.pytest import raises, slow
+from sympy.core.random import (
+    random_complex_number as randcplx,
+    verify_numerically as tn,
+    test_derivative_numerically as td)
+
+
+def test_TupleParametersBase():
+    # test that our implementation of the chain rule works
+    p = hyper((), (), z**2)
+    assert p.diff(z) == p*2*z
+
+
+def test_hyper():
+    raises(TypeError, lambda: hyper(1, 2, z))
+
+    assert hyper((2, 1), (1,), z) == hyper(Tuple(1, 2), Tuple(1), z)
+    assert hyper((2, 1, 2), (1, 2, 1, 3), z) == hyper((2,), (1, 3), z)
+    u = hyper((2, 1, 2), (1, 2, 1, 3), z, evaluate=False)
+    assert u.ap == Tuple(1, 2, 2)
+    assert u.bq == Tuple(1, 1, 2, 3)
+
+    h = hyper((1, 2), (3, 4, 5), z)
+    assert h.ap == Tuple(1, 2)
+    assert h.bq == Tuple(3, 4, 5)
+    assert h.argument == z
+    assert h.is_commutative is True
+    h = hyper((2, 1), (4, 3, 5), z)
+    assert h.ap == Tuple(1, 2)
+    assert h.bq == Tuple(3, 4, 5)
+    assert h.argument == z
+    assert h.is_commutative is True
+
+    # just a few checks to make sure that all arguments go where they should
+    assert tn(hyper(Tuple(), Tuple(), z), exp(z), z)
+    assert tn(z*hyper((1, 1), Tuple(2), -z), log(1 + z), z)
+
+    # differentiation
+    h = hyper(
+        (randcplx(), randcplx(), randcplx()), (randcplx(), randcplx()), z)
+    assert td(h, z)
+
+    a1, a2, b1, b2, b3 = symbols('a1:3, b1:4')
+    assert hyper((a1, a2), (b1, b2, b3), z).diff(z) == \
+        a1*a2/(b1*b2*b3) * hyper((a1 + 1, a2 + 1), (b1 + 1, b2 + 1, b3 + 1), z)
+
+    # differentiation wrt parameters is not supported
+    assert hyper([z], [], z).diff(z) == Derivative(hyper([z], [], z), z)
+
+    # hyper is unbranched wrt parameters
+    from sympy.functions.elementary.complexes import polar_lift
+    assert hyper([polar_lift(z)], [polar_lift(k)], polar_lift(x)) == \
+        hyper([z], [k], polar_lift(x))
+
+    # hyper does not automatically evaluate anyway, but the test is to make
+    # sure that the evaluate keyword is accepted
+    assert hyper((1, 2), (1,), z, evaluate=False).func is hyper
+
+
+def test_expand_func():
+    # evaluation at 1 of Gauss' hypergeometric function:
+    from sympy.abc import a, b, c
+    from sympy.core.function import expand_func
+    a1, b1, c1 = randcplx(), randcplx(), randcplx() + 5
+    assert expand_func(hyper([a, b], [c], 1)) == \
+        gamma(c)*gamma(-a - b + c)/(gamma(-a + c)*gamma(-b + c))
+    assert abs(expand_func(hyper([a1, b1], [c1], 1)).n()
+               - hyper([a1, b1], [c1], 1).n()) < 1e-10
+
+    # hyperexpand wrapper for hyper:
+    assert expand_func(hyper([], [], z)) == exp(z)
+    assert expand_func(hyper([1, 2, 3], [], z)) == hyper([1, 2, 3], [], z)
+    assert expand_func(meijerg([[1, 1], []], [[1], [0]], z)) == log(z + 1)
+    assert expand_func(meijerg([[1, 1], []], [[], []], z)) == \
+        meijerg([[1, 1], []], [[], []], z)
+
+
+def replace_dummy(expr, sym):
+    from sympy.core.symbol import Dummy
+    dum = expr.atoms(Dummy)
+    if not dum:
+        return expr
+    assert len(dum) == 1
+    return expr.xreplace({dum.pop(): sym})
+
+
+def test_hyper_rewrite_sum():
+    from sympy.concrete.summations import Sum
+    from sympy.core.symbol import Dummy
+    from sympy.functions.combinatorial.factorials import (RisingFactorial, factorial)
+    _k = Dummy("k")
+    assert replace_dummy(hyper((1, 2), (1, 3), x).rewrite(Sum), _k) == \
+        Sum(x**_k / factorial(_k) * RisingFactorial(2, _k) /
+            RisingFactorial(3, _k), (_k, 0, oo))
+
+    assert hyper((1, 2, 3), (-1, 3), z).rewrite(Sum) == \
+        hyper((1, 2, 3), (-1, 3), z)
+
+
+def test_radius_of_convergence():
+    assert hyper((1, 2), [3], z).radius_of_convergence == 1
+    assert hyper((1, 2), [3, 4], z).radius_of_convergence is oo
+    assert hyper((1, 2, 3), [4], z).radius_of_convergence == 0
+    assert hyper((0, 1, 2), [4], z).radius_of_convergence is oo
+    assert hyper((-1, 1, 2), [-4], z).radius_of_convergence == 0
+    assert hyper((-1, -2, 2), [-1], z).radius_of_convergence is oo
+    assert hyper((-1, 2), [-1, -2], z).radius_of_convergence == 0
+    assert hyper([-1, 1, 3], [-2, 2], z).radius_of_convergence == 1
+    assert hyper([-1, 1], [-2, 2], z).radius_of_convergence is oo
+    assert hyper([-1, 1, 3], [-2], z).radius_of_convergence == 0
+    assert hyper((-1, 2, 3, 4), [], z).radius_of_convergence is oo
+
+    assert hyper([1, 1], [3], 1).convergence_statement == True
+    assert hyper([1, 1], [2], 1).convergence_statement == False
+    assert hyper([1, 1], [2], -1).convergence_statement == True
+    assert hyper([1, 1], [1], -1).convergence_statement == False
+
+
+def test_meijer():
+    raises(TypeError, lambda: meijerg(1, z))
+    raises(TypeError, lambda: meijerg(((1,), (2,)), (3,), (4,), z))
+
+    assert meijerg(((1, 2), (3,)), ((4,), (5,)), z) == \
+        meijerg(Tuple(1, 2), Tuple(3), Tuple(4), Tuple(5), z)
+
+    g = meijerg((1, 2), (3, 4, 5), (6, 7, 8, 9), (10, 11, 12, 13, 14), z)
+    assert g.an == Tuple(1, 2)
+    assert g.ap == Tuple(1, 2, 3, 4, 5)
+    assert g.aother == Tuple(3, 4, 5)
+    assert g.bm == Tuple(6, 7, 8, 9)
+    assert g.bq == Tuple(6, 7, 8, 9, 10, 11, 12, 13, 14)
+    assert g.bother == Tuple(10, 11, 12, 13, 14)
+    assert g.argument == z
+    assert g.nu == 75
+    assert g.delta == -1
+    assert g.is_commutative is True
+    assert g.is_number is False
+    #issue 13071
+    assert meijerg([[],[]], [[S.Half],[0]], 1).is_number is True
+
+    assert meijerg([1, 2], [3], [4], [5], z).delta == S.Half
+
+    # just a few checks to make sure that all arguments go where they should
+    assert tn(meijerg(Tuple(), Tuple(), Tuple(0), Tuple(), -z), exp(z), z)
+    assert tn(sqrt(pi)*meijerg(Tuple(), Tuple(),
+                               Tuple(0), Tuple(S.Half), z**2/4), cos(z), z)
+    assert tn(meijerg(Tuple(1, 1), Tuple(), Tuple(1), Tuple(0), z),
+              log(1 + z), z)
+
+    # test exceptions
+    raises(ValueError, lambda: meijerg(((3, 1), (2,)), ((oo,), (2, 0)), x))
+    raises(ValueError, lambda: meijerg(((3, 1), (2,)), ((1,), (2, 0)), x))
+
+    # differentiation
+    g = meijerg((randcplx(),), (randcplx() + 2*I,), Tuple(),
+                (randcplx(), randcplx()), z)
+    assert td(g, z)
+
+    g = meijerg(Tuple(), (randcplx(),), Tuple(),
+                (randcplx(), randcplx()), z)
+    assert td(g, z)
+
+    g = meijerg(Tuple(), Tuple(), Tuple(randcplx()),
+                Tuple(randcplx(), randcplx()), z)
+    assert td(g, z)
+
+    a1, a2, b1, b2, c1, c2, d1, d2 = symbols('a1:3, b1:3, c1:3, d1:3')
+    assert meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z).diff(z) == \
+        (meijerg((a1 - 1, a2), (b1, b2), (c1, c2), (d1, d2), z)
+         + (a1 - 1)*meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z))/z
+
+    assert meijerg([z, z], [], [], [], z).diff(z) == \
+        Derivative(meijerg([z, z], [], [], [], z), z)
+
+    # meijerg is unbranched wrt parameters
+    from sympy.functions.elementary.complexes import polar_lift as pl
+    assert meijerg([pl(a1)], [pl(a2)], [pl(b1)], [pl(b2)], pl(z)) == \
+        meijerg([a1], [a2], [b1], [b2], pl(z))
+
+    # integrand
+    from sympy.abc import a, b, c, d, s
+    assert meijerg([a], [b], [c], [d], z).integrand(s) == \
+        z**s*gamma(c - s)*gamma(-a + s + 1)/(gamma(b - s)*gamma(-d + s + 1))
+
+
+def test_meijerg_derivative():
+    assert meijerg([], [1, 1], [0, 0, x], [], z).diff(x) == \
+        log(z)*meijerg([], [1, 1], [0, 0, x], [], z) \
+        + 2*meijerg([], [1, 1, 1], [0, 0, x, 0], [], z)
+
+    y = randcplx()
+    a = 5  # mpmath chokes with non-real numbers, and Mod1 with floats
+    assert td(meijerg([x], [], [], [], y), x)
+    assert td(meijerg([x**2], [], [], [], y), x)
+    assert td(meijerg([], [x], [], [], y), x)
+    assert td(meijerg([], [], [x], [], y), x)
+    assert td(meijerg([], [], [], [x], y), x)
+    assert td(meijerg([x], [a], [a + 1], [], y), x)
+    assert td(meijerg([x], [a + 1], [a], [], y), x)
+    assert td(meijerg([x, a], [], [], [a + 1], y), x)
+    assert td(meijerg([x, a + 1], [], [], [a], y), x)
+    b = Rational(3, 2)
+    assert td(meijerg([a + 2], [b], [b - 3, x], [a], y), x)
+
+
+def test_meijerg_period():
+    assert meijerg([], [1], [0], [], x).get_period() == 2*pi
+    assert meijerg([1], [], [], [0], x).get_period() == 2*pi
+    assert meijerg([], [], [0], [], x).get_period() == 2*pi  # exp(x)
+    assert meijerg(
+        [], [], [0], [S.Half], x).get_period() == 2*pi  # cos(sqrt(x))
+    assert meijerg(
+        [], [], [S.Half], [0], x).get_period() == 4*pi  # sin(sqrt(x))
+    assert meijerg([1, 1], [], [1], [0], x).get_period() is oo  # log(1 + x)
+
+
+def test_hyper_unpolarify():
+    from sympy.functions.elementary.exponential import exp_polar
+    a = exp_polar(2*pi*I)*x
+    b = x
+    assert hyper([], [], a).argument == b
+    assert hyper([0], [], a).argument == a
+    assert hyper([0], [0], a).argument == b
+    assert hyper([0, 1], [0], a).argument == a
+    assert hyper([0, 1], [0], exp_polar(2*pi*I)).argument == 1
+
+
+@slow
+def test_hyperrep():
+    from sympy.functions.special.hyper import (HyperRep, HyperRep_atanh,
+        HyperRep_power1, HyperRep_power2, HyperRep_log1, HyperRep_asin1,
+        HyperRep_asin2, HyperRep_sqrts1, HyperRep_sqrts2, HyperRep_log2,
+        HyperRep_cosasin, HyperRep_sinasin)
+    # First test the base class works.
+    from sympy.functions.elementary.exponential import exp_polar
+    from sympy.functions.elementary.piecewise import Piecewise
+    a, b, c, d, z = symbols('a b c d z')
+
+    class myrep(HyperRep):
+        @classmethod
+        def _expr_small(cls, x):
+            return a
+
+        @classmethod
+        def _expr_small_minus(cls, x):
+            return b
+
+        @classmethod
+        def _expr_big(cls, x, n):
+            return c*n
+
+        @classmethod
+        def _expr_big_minus(cls, x, n):
+            return d*n
+    assert myrep(z).rewrite('nonrep') == Piecewise((0, abs(z) > 1), (a, True))
+    assert myrep(exp_polar(I*pi)*z).rewrite('nonrep') == \
+        Piecewise((0, abs(z) > 1), (b, True))
+    assert myrep(exp_polar(2*I*pi)*z).rewrite('nonrep') == \
+        Piecewise((c, abs(z) > 1), (a, True))
+    assert myrep(exp_polar(3*I*pi)*z).rewrite('nonrep') == \
+        Piecewise((d, abs(z) > 1), (b, True))
+    assert myrep(exp_polar(4*I*pi)*z).rewrite('nonrep') == \
+        Piecewise((2*c, abs(z) > 1), (a, True))
+    assert myrep(exp_polar(5*I*pi)*z).rewrite('nonrep') == \
+        Piecewise((2*d, abs(z) > 1), (b, True))
+    assert myrep(z).rewrite('nonrepsmall') == a
+    assert myrep(exp_polar(I*pi)*z).rewrite('nonrepsmall') == b
+
+    def t(func, hyp, z):
+        """ Test that func is a valid representation of hyp. """
+        # First test that func agrees with hyp for small z
+        if not tn(func.rewrite('nonrepsmall'), hyp, z,
+                  a=Rational(-1, 2), b=Rational(-1, 2), c=S.Half, d=S.Half):
+            return False
+        # Next check that the two small representations agree.
+        if not tn(
+            func.rewrite('nonrepsmall').subs(
+                z, exp_polar(I*pi)*z).replace(exp_polar, exp),
+            func.subs(z, exp_polar(I*pi)*z).rewrite('nonrepsmall'),
+                z, a=Rational(-1, 2), b=Rational(-1, 2), c=S.Half, d=S.Half):
+            return False
+        # Next check continuity along exp_polar(I*pi)*t
+        expr = func.subs(z, exp_polar(I*pi)*z).rewrite('nonrep')
+        if abs(expr.subs(z, 1 + 1e-15).n() - expr.subs(z, 1 - 1e-15).n()) > 1e-10:
+            return False
+        # Finally check continuity of the big reps.
+
+        def dosubs(func, a, b):
+            rv = func.subs(z, exp_polar(a)*z).rewrite('nonrep')
+            return rv.subs(z, exp_polar(b)*z).replace(exp_polar, exp)
+        for n in [0, 1, 2, 3, 4, -1, -2, -3, -4]:
+            expr1 = dosubs(func, 2*I*pi*n, I*pi/2)
+            expr2 = dosubs(func, 2*I*pi*n + I*pi, -I*pi/2)
+            if not tn(expr1, expr2, z):
+                return False
+            expr1 = dosubs(func, 2*I*pi*(n + 1), -I*pi/2)
+            expr2 = dosubs(func, 2*I*pi*n + I*pi, I*pi/2)
+            if not tn(expr1, expr2, z):
+                return False
+        return True
+
+    # Now test the various representatives.
+    a = Rational(1, 3)
+    assert t(HyperRep_atanh(z), hyper([S.Half, 1], [Rational(3, 2)], z), z)
+    assert t(HyperRep_power1(a, z), hyper([-a], [], z), z)
+    assert t(HyperRep_power2(a, z), hyper([a, a - S.Half], [2*a], z), z)
+    assert t(HyperRep_log1(z), -z*hyper([1, 1], [2], z), z)
+    assert t(HyperRep_asin1(z), hyper([S.Half, S.Half], [Rational(3, 2)], z), z)
+    assert t(HyperRep_asin2(z), hyper([1, 1], [Rational(3, 2)], z), z)
+    assert t(HyperRep_sqrts1(a, z), hyper([-a, S.Half - a], [S.Half], z), z)
+    assert t(HyperRep_sqrts2(a, z),
+             -2*z/(2*a + 1)*hyper([-a - S.Half, -a], [S.Half], z).diff(z), z)
+    assert t(HyperRep_log2(z), -z/4*hyper([Rational(3, 2), 1, 1], [2, 2], z), z)
+    assert t(HyperRep_cosasin(a, z), hyper([-a, a], [S.Half], z), z)
+    assert t(HyperRep_sinasin(a, z), 2*a*z*hyper([1 - a, 1 + a], [Rational(3, 2)], z), z)
+
+
+@slow
+def test_meijerg_eval():
+    from sympy.functions.elementary.exponential import exp_polar
+    from sympy.functions.special.bessel import besseli
+    from sympy.abc import l
+    a = randcplx()
+    arg = x*exp_polar(k*pi*I)
+    expr1 = pi*meijerg([[], [(a + 1)/2]], [[a/2], [-a/2, (a + 1)/2]], arg**2/4)
+    expr2 = besseli(a, arg)
+
+    # Test that the two expressions agree for all arguments.
+    for x_ in [0.5, 1.5]:
+        for k_ in [0.0, 0.1, 0.3, 0.5, 0.8, 1, 5.751, 15.3]:
+            assert abs((expr1 - expr2).n(subs={x: x_, k: k_})) < 1e-10
+            assert abs((expr1 - expr2).n(subs={x: x_, k: -k_})) < 1e-10
+
+    # Test continuity independently
+    eps = 1e-13
+    expr2 = expr1.subs(k, l)
+    for x_ in [0.5, 1.5]:
+        for k_ in [0.5, Rational(1, 3), 0.25, 0.75, Rational(2, 3), 1.0, 1.5]:
+            assert abs((expr1 - expr2).n(
+                       subs={x: x_, k: k_ + eps, l: k_ - eps})) < 1e-10
+            assert abs((expr1 - expr2).n(
+                       subs={x: x_, k: -k_ + eps, l: -k_ - eps})) < 1e-10
+
+    expr = (meijerg(((0.5,), ()), ((0.5, 0, 0.5), ()), exp_polar(-I*pi)/4)
+            + meijerg(((0.5,), ()), ((0.5, 0, 0.5), ()), exp_polar(I*pi)/4)) \
+        /(2*sqrt(pi))
+    assert (expr - pi/exp(1)).n(chop=True) == 0
+
+
+def test_limits():
+    k, x = symbols('k, x')
+    assert hyper((1,), (Rational(4, 3), Rational(5, 3)), k**2).series(k) == \
+           1 + 9*k**2/20 + 81*k**4/1120 + O(k**6) # issue 6350
+
+    # https://github.com/sympy/sympy/issues/11465
+    assert limit(1/hyper((1, ), (1, ), x), x, 0) == 1
+
+
+def test_appellf1():
+    a, b1, b2, c, x, y = symbols('a b1 b2 c x y')
+    assert appellf1(a, b2, b1, c, y, x) == appellf1(a, b1, b2, c, x, y)
+    assert appellf1(a, b1, b1, c, y, x) == appellf1(a, b1, b1, c, x, y)
+    assert appellf1(a, b1, b2, c, S.Zero, S.Zero) is S.One
+
+    f = appellf1(a, b1, b2, c, S.Zero, S.Zero, evaluate=False)
+    assert f.func is appellf1
+    assert f.doit() is S.One
+
+
+def test_derivative_appellf1():
+    from sympy.core.function import diff
+    a, b1, b2, c, x, y, z = symbols('a b1 b2 c x y z')
+    assert diff(appellf1(a, b1, b2, c, x, y), x) == a*b1*appellf1(a + 1, b2, b1 + 1, c + 1, y, x)/c
+    assert diff(appellf1(a, b1, b2, c, x, y), y) == a*b2*appellf1(a + 1, b1, b2 + 1, c + 1, x, y)/c
+    assert diff(appellf1(a, b1, b2, c, x, y), z) == 0
+    assert diff(appellf1(a, b1, b2, c, x, y), a) ==  Derivative(appellf1(a, b1, b2, c, x, y), a)
+
+
+def test_eval_nseries():
+    a1, b1, a2, b2 = symbols('a1 b1 a2 b2')
+    assert hyper((1,2), (1,2,3), x**2)._eval_nseries(x, 7, None) == \
+        1 + x**2/3 + x**4/24 + x**6/360 + O(x**7)
+    assert exp(x)._eval_nseries(x,7,None) == \
+        hyper((a1, b1), (a1, b1), x)._eval_nseries(x, 7, None)
+    assert hyper((a1, a2), (b1, b2), x)._eval_nseries(z, 7, None) ==\
+        hyper((a1, a2), (b1, b2), x) + O(z**7)
+    assert hyper((-S(1)/2, S(1)/2), (1,), 4*x/(x + 1)).nseries(x) == \
+        1 - x + x**2/4 - 3*x**3/4 - 15*x**4/64 - 93*x**5/64 + O(x**6)
+    assert (pi/2*hyper((-S(1)/2, S(1)/2), (1,), 4*x/(x + 1))).nseries(x) == \
+        pi/2 - pi*x/2 + pi*x**2/8 - 3*pi*x**3/8 - 15*pi*x**4/128 - 93*pi*x**5/128 + O(x**6)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_mathieu.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_mathieu.py
new file mode 100644
index 0000000000000000000000000000000000000000..b9296f0657d920c8d297f820fb3ab8b6a53129ab
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_mathieu.py
@@ -0,0 +1,29 @@
+from sympy.core.function import diff
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.mathieu_functions import (mathieuc, mathieucprime, mathieus, mathieusprime)
+
+from sympy.abc import a, q, z
+
+
+def test_mathieus():
+    assert isinstance(mathieus(a, q, z), mathieus)
+    assert mathieus(a, 0, z) == sin(sqrt(a)*z)
+    assert conjugate(mathieus(a, q, z)) == mathieus(conjugate(a), conjugate(q), conjugate(z))
+    assert diff(mathieus(a, q, z), z) == mathieusprime(a, q, z)
+
+def test_mathieuc():
+    assert isinstance(mathieuc(a, q, z), mathieuc)
+    assert mathieuc(a, 0, z) == cos(sqrt(a)*z)
+    assert diff(mathieuc(a, q, z), z) == mathieucprime(a, q, z)
+
+def test_mathieusprime():
+    assert isinstance(mathieusprime(a, q, z), mathieusprime)
+    assert mathieusprime(a, 0, z) == sqrt(a)*cos(sqrt(a)*z)
+    assert diff(mathieusprime(a, q, z), z) == (-a + 2*q*cos(2*z))*mathieus(a, q, z)
+
+def test_mathieucprime():
+    assert isinstance(mathieucprime(a, q, z), mathieucprime)
+    assert mathieucprime(a, 0, z) == -sqrt(a)*sin(sqrt(a)*z)
+    assert diff(mathieucprime(a, q, z), z) == (-a + 2*q*cos(2*z))*mathieuc(a, q, z)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_singularity_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_singularity_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..dbd85cb0c7e5524d4fe1441615879b9776ad1693
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_singularity_functions.py
@@ -0,0 +1,129 @@
+from sympy.core.function import (Derivative, diff)
+from sympy.core.numbers import (Float, I, nan, oo, pi)
+from sympy.core.relational import Eq
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.special.delta_functions import (DiracDelta, Heaviside)
+from sympy.functions.special.singularity_functions import SingularityFunction
+from sympy.series.order import O
+
+
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.testing.pytest import raises
+
+x, y, a, n = symbols('x y a n')
+
+
+def test_fdiff():
+    assert SingularityFunction(x, 4, 5).fdiff() == 5*SingularityFunction(x, 4, 4)
+    assert SingularityFunction(x, 4, -1).fdiff() == SingularityFunction(x, 4, -2)
+    assert SingularityFunction(x, 4, -2).fdiff() == SingularityFunction(x, 4, -3)
+    assert SingularityFunction(x, 4, -3).fdiff() == SingularityFunction(x, 4, -4)
+    assert SingularityFunction(x, 4, 0).fdiff() == SingularityFunction(x, 4, -1)
+
+    assert SingularityFunction(y, 6, 2).diff(y) == 2*SingularityFunction(y, 6, 1)
+    assert SingularityFunction(y, -4, -1).diff(y) == SingularityFunction(y, -4, -2)
+    assert SingularityFunction(y, 4, 0).diff(y) == SingularityFunction(y, 4, -1)
+    assert SingularityFunction(y, 4, 0).diff(y, 2) == SingularityFunction(y, 4, -2)
+
+    n = Symbol('n', positive=True)
+    assert SingularityFunction(x, a, n).fdiff() == n*SingularityFunction(x, a, n - 1)
+    assert SingularityFunction(y, a, n).diff(y) == n*SingularityFunction(y, a, n - 1)
+
+    expr_in = 4*SingularityFunction(x, a, n) + 3*SingularityFunction(x, a, -1) + -10*SingularityFunction(x, a, 0)
+    expr_out = n*4*SingularityFunction(x, a, n - 1) + 3*SingularityFunction(x, a, -2) - 10*SingularityFunction(x, a, -1)
+    assert diff(expr_in, x) == expr_out
+
+    assert SingularityFunction(x, -10, 5).diff(evaluate=False) == (
+        Derivative(SingularityFunction(x, -10, 5), x))
+
+    raises(ArgumentIndexError, lambda: SingularityFunction(x, 4, 5).fdiff(2))
+
+
+def test_eval():
+    assert SingularityFunction(x, a, n).func == SingularityFunction
+    assert unchanged(SingularityFunction, x, 5, n)
+    assert SingularityFunction(5, 3, 2) == 4
+    assert SingularityFunction(3, 5, 1) == 0
+    assert SingularityFunction(3, 3, 0) == 1
+    assert SingularityFunction(3, 3, 1) == 0
+    assert SingularityFunction(Symbol('z', zero=True), 0, 1) == 0  # like sin(z) == 0
+    assert SingularityFunction(4, 4, -1) is oo
+    assert SingularityFunction(4, 2, -1) == 0
+    assert SingularityFunction(4, 7, -1) == 0
+    assert SingularityFunction(5, 6, -2) == 0
+    assert SingularityFunction(4, 2, -2) == 0
+    assert SingularityFunction(4, 4, -2) is oo
+    assert SingularityFunction(4, 2, -3) == 0
+    assert SingularityFunction(8, 8, -3) is oo
+    assert SingularityFunction(4, 2, -4) == 0
+    assert SingularityFunction(8, 8, -4) is oo
+    assert (SingularityFunction(6.1, 4, 5)).evalf(5) == Float('40.841', '5')
+    assert SingularityFunction(6.1, pi, 2) == (-pi + 6.1)**2
+    assert SingularityFunction(x, a, nan) is nan
+    assert SingularityFunction(x, nan, 1) is nan
+    assert SingularityFunction(nan, a, n) is nan
+
+    raises(ValueError, lambda: SingularityFunction(x, a, I))
+    raises(ValueError, lambda: SingularityFunction(2*I, I, n))
+    raises(ValueError, lambda: SingularityFunction(x, a, -5))
+
+
+def test_leading_term():
+    l = Symbol('l', positive=True)
+    assert SingularityFunction(x, 3, 2).as_leading_term(x) == 0
+    assert SingularityFunction(x, -2, 1).as_leading_term(x) == 2
+    assert SingularityFunction(x, 0, 0).as_leading_term(x) == 1
+    assert SingularityFunction(x, 0, 0).as_leading_term(x, cdir=-1) == 0
+    assert SingularityFunction(x, 0, -1).as_leading_term(x) == 0
+    assert SingularityFunction(x, 0, -2).as_leading_term(x) == 0
+    assert SingularityFunction(x, 0, -3).as_leading_term(x) == 0
+    assert SingularityFunction(x, 0, -4).as_leading_term(x) == 0
+    assert (SingularityFunction(x + l, 0, 1)/2\
+        - SingularityFunction(x + l, l/2, 1)\
+        + SingularityFunction(x + l, l, 1)/2).as_leading_term(x) == -x/2
+
+
+def test_series():
+    l = Symbol('l', positive=True)
+    assert SingularityFunction(x, -3, 2).series(x) == x**2 + 6*x + 9
+    assert SingularityFunction(x, -2, 1).series(x) == x + 2
+    assert SingularityFunction(x, 0, 0).series(x) == 1
+    assert SingularityFunction(x, 0, 0).series(x, dir='-') == 0
+    assert SingularityFunction(x, 0, -1).series(x) == 0
+    assert SingularityFunction(x, 0, -2).series(x) == 0
+    assert SingularityFunction(x, 0, -3).series(x) == 0
+    assert SingularityFunction(x, 0, -4).series(x) == 0
+    assert (SingularityFunction(x + l, 0, 1)/2\
+        - SingularityFunction(x + l, l/2, 1)\
+        + SingularityFunction(x + l, l, 1)/2).nseries(x) == -x/2 + O(x**6)
+
+
+def test_rewrite():
+    assert SingularityFunction(x, 4, 5).rewrite(Piecewise) == (
+        Piecewise(((x - 4)**5, x - 4 >= 0), (0, True)))
+    assert SingularityFunction(x, -10, 0).rewrite(Piecewise) == (
+        Piecewise((1, x + 10 >= 0), (0, True)))
+    assert SingularityFunction(x, 2, -1).rewrite(Piecewise) == (
+        Piecewise((oo, Eq(x - 2, 0)), (0, True)))
+    assert SingularityFunction(x, 0, -2).rewrite(Piecewise) == (
+        Piecewise((oo, Eq(x, 0)), (0, True)))
+
+    n = Symbol('n', nonnegative=True)
+    p = SingularityFunction(x, a, n).rewrite(Piecewise)
+    assert p == (
+        Piecewise(((x - a)**n, x - a >= 0), (0, True)))
+    assert p.subs(x, a).subs(n, 0) == 1
+
+    expr_in = SingularityFunction(x, 4, 5) + SingularityFunction(x, -3, -1) - SingularityFunction(x, 0, -2)
+    expr_out = (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1)
+    assert expr_in.rewrite(Heaviside) == expr_out
+    assert expr_in.rewrite(DiracDelta) == expr_out
+    assert expr_in.rewrite('HeavisideDiracDelta') == expr_out
+
+    expr_in = SingularityFunction(x, a, n) + SingularityFunction(x, a, -1) - SingularityFunction(x, a, -2)
+    expr_out = (x - a)**n*Heaviside(x - a, 1) + DiracDelta(x - a) + DiracDelta(a - x, 1)
+    assert expr_in.rewrite(Heaviside) == expr_out
+    assert expr_in.rewrite(DiracDelta) == expr_out
+    assert expr_in.rewrite('HeavisideDiracDelta') == expr_out
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_spec_polynomials.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_spec_polynomials.py
new file mode 100644
index 0000000000000000000000000000000000000000..584ad3cf97df8b9d92da9fc7805ab4296f40671c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_spec_polynomials.py
@@ -0,0 +1,475 @@
+from sympy.concrete.summations import Sum
+from sympy.core.function import (Derivative, diff)
+from sympy.core.numbers import (Rational, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.combinatorial.factorials import (RisingFactorial, binomial, factorial)
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import cos
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import hyper
+from sympy.functions.special.polynomials import (assoc_laguerre, assoc_legendre, chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, gegenbauer, hermite, hermite_prob, jacobi, jacobi_normalized, laguerre, legendre)
+from sympy.polys.orthopolys import laguerre_poly
+from sympy.polys.polyroots import roots
+
+from sympy.core.expr import unchanged
+from sympy.core.function import ArgumentIndexError
+from sympy.testing.pytest import raises
+
+
+x = Symbol('x')
+
+
+def test_jacobi():
+    n = Symbol("n")
+    a = Symbol("a")
+    b = Symbol("b")
+
+    assert jacobi(0, a, b, x) == 1
+    assert jacobi(1, a, b, x) == a/2 - b/2 + x*(a/2 + b/2 + 1)
+
+    assert jacobi(n, a, a, x) == RisingFactorial(
+        a + 1, n)*gegenbauer(n, a + S.Half, x)/RisingFactorial(2*a + 1, n)
+    assert jacobi(n, a, -a, x) == ((-1)**a*(-x + 1)**(-a/2)*(x + 1)**(a/2)*assoc_legendre(n, a, x)*
+                                   factorial(-a + n)*gamma(a + n + 1)/(factorial(a + n)*gamma(n + 1)))
+    assert jacobi(n, -b, b, x) == ((-x + 1)**(b/2)*(x + 1)**(-b/2)*assoc_legendre(n, b, x)*
+                                   gamma(-b + n + 1)/gamma(n + 1))
+    assert jacobi(n, 0, 0, x) == legendre(n, x)
+    assert jacobi(n, S.Half, S.Half, x) == RisingFactorial(
+        Rational(3, 2), n)*chebyshevu(n, x)/factorial(n + 1)
+    assert jacobi(n, Rational(-1, 2), Rational(-1, 2), x) == RisingFactorial(
+        S.Half, n)*chebyshevt(n, x)/factorial(n)
+
+    X = jacobi(n, a, b, x)
+    assert isinstance(X, jacobi)
+
+    assert jacobi(n, a, b, -x) == (-1)**n*jacobi(n, b, a, x)
+    assert jacobi(n, a, b, 0) == 2**(-n)*gamma(a + n + 1)*hyper(
+        (-b - n, -n), (a + 1,), -1)/(factorial(n)*gamma(a + 1))
+    assert jacobi(n, a, b, 1) == RisingFactorial(a + 1, n)/factorial(n)
+
+    m = Symbol("m", positive=True)
+    assert jacobi(m, a, b, oo) == oo*RisingFactorial(a + b + m + 1, m)
+    assert unchanged(jacobi, n, a, b, oo)
+
+    assert conjugate(jacobi(m, a, b, x)) == \
+        jacobi(m, conjugate(a), conjugate(b), conjugate(x))
+
+    _k = Dummy('k')
+    assert diff(jacobi(n, a, b, x), n) == Derivative(jacobi(n, a, b, x), n)
+    assert diff(jacobi(n, a, b, x), a).dummy_eq(Sum((jacobi(n, a, b, x) +
+        (2*_k + a + b + 1)*RisingFactorial(_k + b + 1, -_k + n)*jacobi(_k, a,
+        b, x)/((-_k + n)*RisingFactorial(_k + a + b + 1, -_k + n)))/(_k + a
+        + b + n + 1), (_k, 0, n - 1)))
+    assert diff(jacobi(n, a, b, x), b).dummy_eq(Sum(((-1)**(-_k + n)*(2*_k +
+        a + b + 1)*RisingFactorial(_k + a + 1, -_k + n)*jacobi(_k, a, b, x)/
+        ((-_k + n)*RisingFactorial(_k + a + b + 1, -_k + n)) + jacobi(n, a,
+        b, x))/(_k + a + b + n + 1), (_k, 0, n - 1)))
+    assert diff(jacobi(n, a, b, x), x) == \
+        (a/2 + b/2 + n/2 + S.Half)*jacobi(n - 1, a + 1, b + 1, x)
+
+    assert jacobi_normalized(n, a, b, x) == \
+           (jacobi(n, a, b, x)/sqrt(2**(a + b + 1)*gamma(a + n + 1)*gamma(b + n + 1)
+                                    /((a + b + 2*n + 1)*factorial(n)*gamma(a + b + n + 1))))
+
+    raises(ValueError, lambda: jacobi(-2.1, a, b, x))
+    raises(ValueError, lambda: jacobi(Dummy(positive=True, integer=True), 1, 2, oo))
+
+    assert jacobi(n, a, b, x).rewrite(Sum).dummy_eq(Sum((S.Half - x/2)
+        **_k*RisingFactorial(-n, _k)*RisingFactorial(_k + a + 1, -_k + n)*
+        RisingFactorial(a + b + n + 1, _k)/factorial(_k), (_k, 0, n))/factorial(n))
+    assert jacobi(n, a, b, x).rewrite("polynomial").dummy_eq(Sum((S.Half - x/2)
+        **_k*RisingFactorial(-n, _k)*RisingFactorial(_k + a + 1, -_k + n)*
+        RisingFactorial(a + b + n + 1, _k)/factorial(_k), (_k, 0, n))/factorial(n))
+    raises(ArgumentIndexError, lambda: jacobi(n, a, b, x).fdiff(5))
+
+
+def test_gegenbauer():
+    n = Symbol("n")
+    a = Symbol("a")
+
+    assert gegenbauer(0, a, x) == 1
+    assert gegenbauer(1, a, x) == 2*a*x
+    assert gegenbauer(2, a, x) == -a + x**2*(2*a**2 + 2*a)
+    assert gegenbauer(3, a, x) == \
+        x**3*(4*a**3/3 + 4*a**2 + a*Rational(8, 3)) + x*(-2*a**2 - 2*a)
+
+    assert gegenbauer(-1, a, x) == 0
+    assert gegenbauer(n, S.Half, x) == legendre(n, x)
+    assert gegenbauer(n, 1, x) == chebyshevu(n, x)
+    assert gegenbauer(n, -1, x) == 0
+
+    X = gegenbauer(n, a, x)
+    assert isinstance(X, gegenbauer)
+
+    assert gegenbauer(n, a, -x) == (-1)**n*gegenbauer(n, a, x)
+    assert gegenbauer(n, a, 0) == 2**n*sqrt(pi) * \
+        gamma(a + n/2)/(gamma(a)*gamma(-n/2 + S.Half)*gamma(n + 1))
+    assert gegenbauer(n, a, 1) == gamma(2*a + n)/(gamma(2*a)*gamma(n + 1))
+
+    assert gegenbauer(n, Rational(3, 4), -1) is zoo
+    assert gegenbauer(n, Rational(1, 4), -1) == (sqrt(2)*cos(pi*(n + S.One/4))*
+                      gamma(n + S.Half)/(sqrt(pi)*gamma(n + 1)))
+
+    m = Symbol("m", positive=True)
+    assert gegenbauer(m, a, oo) == oo*RisingFactorial(a, m)
+    assert unchanged(gegenbauer, n, a, oo)
+
+    assert conjugate(gegenbauer(n, a, x)) == gegenbauer(n, conjugate(a), conjugate(x))
+
+    _k = Dummy('k')
+
+    assert diff(gegenbauer(n, a, x), n) == Derivative(gegenbauer(n, a, x), n)
+    assert diff(gegenbauer(n, a, x), a).dummy_eq(Sum((2*(-1)**(-_k + n) + 2)*
+        (_k + a)*gegenbauer(_k, a, x)/((-_k + n)*(_k + 2*a + n)) + ((2*_k +
+        2)/((_k + 2*a)*(2*_k + 2*a + 1)) + 2/(_k + 2*a + n))*gegenbauer(n, a
+        , x), (_k, 0, n - 1)))
+    assert diff(gegenbauer(n, a, x), x) == 2*a*gegenbauer(n - 1, a + 1, x)
+
+    assert gegenbauer(n, a, x).rewrite(Sum).dummy_eq(
+        Sum((-1)**_k*(2*x)**(-2*_k + n)*RisingFactorial(a, -_k + n)
+        /(factorial(_k)*factorial(-2*_k + n)), (_k, 0, floor(n/2))))
+    assert gegenbauer(n, a, x).rewrite("polynomial").dummy_eq(
+        Sum((-1)**_k*(2*x)**(-2*_k + n)*RisingFactorial(a, -_k + n)
+        /(factorial(_k)*factorial(-2*_k + n)), (_k, 0, floor(n/2))))
+
+    raises(ArgumentIndexError, lambda: gegenbauer(n, a, x).fdiff(4))
+
+
+def test_legendre():
+    assert legendre(0, x) == 1
+    assert legendre(1, x) == x
+    assert legendre(2, x) == ((3*x**2 - 1)/2).expand()
+    assert legendre(3, x) == ((5*x**3 - 3*x)/2).expand()
+    assert legendre(4, x) == ((35*x**4 - 30*x**2 + 3)/8).expand()
+    assert legendre(5, x) == ((63*x**5 - 70*x**3 + 15*x)/8).expand()
+    assert legendre(6, x) == ((231*x**6 - 315*x**4 + 105*x**2 - 5)/16).expand()
+
+    assert legendre(10, -1) == 1
+    assert legendre(11, -1) == -1
+    assert legendre(10, 1) == 1
+    assert legendre(11, 1) == 1
+    assert legendre(10, 0) != 0
+    assert legendre(11, 0) == 0
+
+    assert legendre(-1, x) == 1
+    k = Symbol('k')
+    assert legendre(5 - k, x).subs(k, 2) == ((5*x**3 - 3*x)/2).expand()
+
+    assert roots(legendre(4, x), x) == {
+        sqrt(Rational(3, 7) - Rational(2, 35)*sqrt(30)): 1,
+        -sqrt(Rational(3, 7) - Rational(2, 35)*sqrt(30)): 1,
+        sqrt(Rational(3, 7) + Rational(2, 35)*sqrt(30)): 1,
+        -sqrt(Rational(3, 7) + Rational(2, 35)*sqrt(30)): 1,
+    }
+
+    n = Symbol("n")
+
+    X = legendre(n, x)
+    assert isinstance(X, legendre)
+    assert unchanged(legendre, n, x)
+
+    assert legendre(n, 0) == sqrt(pi)/(gamma(S.Half - n/2)*gamma(n/2 + 1))
+    assert legendre(n, 1) == 1
+    assert legendre(n, oo) is oo
+    assert legendre(-n, x) == legendre(n - 1, x)
+    assert legendre(n, -x) == (-1)**n*legendre(n, x)
+    assert unchanged(legendre, -n + k, x)
+
+    assert conjugate(legendre(n, x)) == legendre(n, conjugate(x))
+
+    assert diff(legendre(n, x), x) == \
+        n*(x*legendre(n, x) - legendre(n - 1, x))/(x**2 - 1)
+    assert diff(legendre(n, x), n) == Derivative(legendre(n, x), n)
+
+    _k = Dummy('k')
+    assert legendre(n, x).rewrite(Sum).dummy_eq(Sum((-1)**_k*(S.Half -
+            x/2)**_k*(x/2 + S.Half)**(-_k + n)*binomial(n, _k)**2, (_k, 0, n)))
+    assert legendre(n, x).rewrite("polynomial").dummy_eq(Sum((-1)**_k*(S.Half -
+            x/2)**_k*(x/2 + S.Half)**(-_k + n)*binomial(n, _k)**2, (_k, 0, n)))
+    raises(ArgumentIndexError, lambda: legendre(n, x).fdiff(1))
+    raises(ArgumentIndexError, lambda: legendre(n, x).fdiff(3))
+
+
+def test_assoc_legendre():
+    Plm = assoc_legendre
+    Q = sqrt(1 - x**2)
+
+    assert Plm(0, 0, x) == 1
+    assert Plm(1, 0, x) == x
+    assert Plm(1, 1, x) == -Q
+    assert Plm(2, 0, x) == (3*x**2 - 1)/2
+    assert Plm(2, 1, x) == -3*x*Q
+    assert Plm(2, 2, x) == 3*Q**2
+    assert Plm(3, 0, x) == (5*x**3 - 3*x)/2
+    assert Plm(3, 1, x).expand() == (( 3*(1 - 5*x**2)/2 ).expand() * Q).expand()
+    assert Plm(3, 2, x) == 15*x * Q**2
+    assert Plm(3, 3, x) == -15 * Q**3
+
+    # negative m
+    assert Plm(1, -1, x) == -Plm(1, 1, x)/2
+    assert Plm(2, -2, x) == Plm(2, 2, x)/24
+    assert Plm(2, -1, x) == -Plm(2, 1, x)/6
+    assert Plm(3, -3, x) == -Plm(3, 3, x)/720
+    assert Plm(3, -2, x) == Plm(3, 2, x)/120
+    assert Plm(3, -1, x) == -Plm(3, 1, x)/12
+
+    n = Symbol("n")
+    m = Symbol("m")
+    X = Plm(n, m, x)
+    assert isinstance(X, assoc_legendre)
+
+    assert Plm(n, 0, x) == legendre(n, x)
+    assert Plm(n, m, 0) == 2**m*sqrt(pi)/(gamma(-m/2 - n/2 +
+                           S.Half)*gamma(-m/2 + n/2 + 1))
+
+    assert diff(Plm(m, n, x), x) == (m*x*assoc_legendre(m, n, x) -
+                (m + n)*assoc_legendre(m - 1, n, x))/(x**2 - 1)
+
+    _k = Dummy('k')
+    assert Plm(m, n, x).rewrite(Sum).dummy_eq(
+            (1 - x**2)**(n/2)*Sum((-1)**_k*2**(-m)*x**(-2*_k + m - n)*factorial
+             (-2*_k + 2*m)/(factorial(_k)*factorial(-_k + m)*factorial(-2*_k + m
+              - n)), (_k, 0, floor(m/2 - n/2))))
+    assert Plm(m, n, x).rewrite("polynomial").dummy_eq(
+            (1 - x**2)**(n/2)*Sum((-1)**_k*2**(-m)*x**(-2*_k + m - n)*factorial
+             (-2*_k + 2*m)/(factorial(_k)*factorial(-_k + m)*factorial(-2*_k + m
+              - n)), (_k, 0, floor(m/2 - n/2))))
+    assert conjugate(assoc_legendre(n, m, x)) == \
+        assoc_legendre(n, conjugate(m), conjugate(x))
+    raises(ValueError, lambda: Plm(0, 1, x))
+    raises(ValueError, lambda: Plm(-1, 1, x))
+    raises(ArgumentIndexError, lambda: Plm(n, m, x).fdiff(1))
+    raises(ArgumentIndexError, lambda: Plm(n, m, x).fdiff(2))
+    raises(ArgumentIndexError, lambda: Plm(n, m, x).fdiff(4))
+
+
+def test_chebyshev():
+    assert chebyshevt(0, x) == 1
+    assert chebyshevt(1, x) == x
+    assert chebyshevt(2, x) == 2*x**2 - 1
+    assert chebyshevt(3, x) == 4*x**3 - 3*x
+
+    for n in range(1, 4):
+        for k in range(n):
+            z = chebyshevt_root(n, k)
+            assert chebyshevt(n, z) == 0
+        raises(ValueError, lambda: chebyshevt_root(n, n))
+
+    for n in range(1, 4):
+        for k in range(n):
+            z = chebyshevu_root(n, k)
+            assert chebyshevu(n, z) == 0
+        raises(ValueError, lambda: chebyshevu_root(n, n))
+
+    n = Symbol("n")
+    X = chebyshevt(n, x)
+    assert isinstance(X, chebyshevt)
+    assert unchanged(chebyshevt, n, x)
+    assert chebyshevt(n, -x) == (-1)**n*chebyshevt(n, x)
+    assert chebyshevt(-n, x) == chebyshevt(n, x)
+
+    assert chebyshevt(n, 0) == cos(pi*n/2)
+    assert chebyshevt(n, 1) == 1
+    assert chebyshevt(n, oo) is oo
+
+    assert conjugate(chebyshevt(n, x)) == chebyshevt(n, conjugate(x))
+
+    assert diff(chebyshevt(n, x), x) == n*chebyshevu(n - 1, x)
+
+    X = chebyshevu(n, x)
+    assert isinstance(X, chebyshevu)
+
+    y = Symbol('y')
+    assert chebyshevu(n, -x) == (-1)**n*chebyshevu(n, x)
+    assert chebyshevu(-n, x) == -chebyshevu(n - 2, x)
+    assert unchanged(chebyshevu, -n + y, x)
+
+    assert chebyshevu(n, 0) == cos(pi*n/2)
+    assert chebyshevu(n, 1) == n + 1
+    assert chebyshevu(n, oo) is oo
+
+    assert conjugate(chebyshevu(n, x)) == chebyshevu(n, conjugate(x))
+
+    assert diff(chebyshevu(n, x), x) == \
+        (-x*chebyshevu(n, x) + (n + 1)*chebyshevt(n + 1, x))/(x**2 - 1)
+
+    _k = Dummy('k')
+    assert chebyshevt(n, x).rewrite(Sum).dummy_eq(Sum(x**(-2*_k + n)
+                    *(x**2 - 1)**_k*binomial(n, 2*_k), (_k, 0, floor(n/2))))
+    assert chebyshevt(n, x).rewrite("polynomial").dummy_eq(Sum(x**(-2*_k + n)
+                    *(x**2 - 1)**_k*binomial(n, 2*_k), (_k, 0, floor(n/2))))
+    assert chebyshevu(n, x).rewrite(Sum).dummy_eq(Sum((-1)**_k*(2*x)
+                    **(-2*_k + n)*factorial(-_k + n)/(factorial(_k)*
+                       factorial(-2*_k + n)), (_k, 0, floor(n/2))))
+    assert chebyshevu(n, x).rewrite("polynomial").dummy_eq(Sum((-1)**_k*(2*x)
+                    **(-2*_k + n)*factorial(-_k + n)/(factorial(_k)*
+                       factorial(-2*_k + n)), (_k, 0, floor(n/2))))
+    raises(ArgumentIndexError, lambda: chebyshevt(n, x).fdiff(1))
+    raises(ArgumentIndexError, lambda: chebyshevt(n, x).fdiff(3))
+    raises(ArgumentIndexError, lambda: chebyshevu(n, x).fdiff(1))
+    raises(ArgumentIndexError, lambda: chebyshevu(n, x).fdiff(3))
+
+
+def test_hermite():
+    assert hermite(0, x) == 1
+    assert hermite(1, x) == 2*x
+    assert hermite(2, x) == 4*x**2 - 2
+    assert hermite(3, x) == 8*x**3 - 12*x
+    assert hermite(4, x) == 16*x**4 - 48*x**2 + 12
+    assert hermite(6, x) == 64*x**6 - 480*x**4 + 720*x**2 - 120
+
+    n = Symbol("n")
+    assert unchanged(hermite, n, x)
+    assert hermite(n, -x) == (-1)**n*hermite(n, x)
+    assert unchanged(hermite, -n, x)
+
+    assert hermite(n, 0) == 2**n*sqrt(pi)/gamma(S.Half - n/2)
+    assert hermite(n, oo) is oo
+
+    assert conjugate(hermite(n, x)) == hermite(n, conjugate(x))
+
+    _k = Dummy('k')
+    assert hermite(n, x).rewrite(Sum).dummy_eq(factorial(n)*Sum((-1)
+        **_k*(2*x)**(-2*_k + n)/(factorial(_k)*factorial(-2*_k + n)), (_k,
+        0, floor(n/2))))
+    assert hermite(n, x).rewrite("polynomial").dummy_eq(factorial(n)*Sum((-1)
+        **_k*(2*x)**(-2*_k + n)/(factorial(_k)*factorial(-2*_k + n)), (_k,
+        0, floor(n/2))))
+
+    assert diff(hermite(n, x), x) == 2*n*hermite(n - 1, x)
+    assert diff(hermite(n, x), n) == Derivative(hermite(n, x), n)
+    raises(ArgumentIndexError, lambda: hermite(n, x).fdiff(3))
+
+    assert hermite(n, x).rewrite(hermite_prob) == \
+            sqrt(2)**n * hermite_prob(n, x*sqrt(2))
+
+
+def test_hermite_prob():
+    assert hermite_prob(0, x) == 1
+    assert hermite_prob(1, x) == x
+    assert hermite_prob(2, x) == x**2 - 1
+    assert hermite_prob(3, x) == x**3 - 3*x
+    assert hermite_prob(4, x) == x**4 - 6*x**2 + 3
+    assert hermite_prob(6, x) == x**6 - 15*x**4 + 45*x**2 - 15
+
+    n = Symbol("n")
+    assert unchanged(hermite_prob, n, x)
+    assert hermite_prob(n, -x) == (-1)**n*hermite_prob(n, x)
+    assert unchanged(hermite_prob, -n, x)
+
+    assert hermite_prob(n, 0) == sqrt(pi)/gamma(S.Half - n/2)
+    assert hermite_prob(n, oo) is oo
+
+    assert conjugate(hermite_prob(n, x)) == hermite_prob(n, conjugate(x))
+
+    _k = Dummy('k')
+    assert hermite_prob(n, x).rewrite(Sum).dummy_eq(factorial(n) *
+        Sum((-S.Half)**_k * x**(n-2*_k) / (factorial(_k) * factorial(n-2*_k)),
+        (_k, 0, floor(n/2))))
+    assert hermite_prob(n, x).rewrite("polynomial").dummy_eq(factorial(n) *
+        Sum((-S.Half)**_k * x**(n-2*_k) / (factorial(_k) * factorial(n-2*_k)),
+        (_k, 0, floor(n/2))))
+
+    assert diff(hermite_prob(n, x), x) == n*hermite_prob(n-1, x)
+    assert diff(hermite_prob(n, x), n) == Derivative(hermite_prob(n, x), n)
+    raises(ArgumentIndexError, lambda: hermite_prob(n, x).fdiff(3))
+
+    assert hermite_prob(n, x).rewrite(hermite) == \
+            sqrt(2)**(-n) * hermite(n, x/sqrt(2))
+
+
+def test_laguerre():
+    n = Symbol("n")
+    m = Symbol("m", negative=True)
+
+    # Laguerre polynomials:
+    assert laguerre(0, x) == 1
+    assert laguerre(1, x) == -x + 1
+    assert laguerre(2, x) == x**2/2 - 2*x + 1
+    assert laguerre(3, x) == -x**3/6 + 3*x**2/2 - 3*x + 1
+    assert laguerre(-2, x) == (x + 1)*exp(x)
+
+    X = laguerre(n, x)
+    assert isinstance(X, laguerre)
+
+    assert laguerre(n, 0) == 1
+    assert laguerre(n, oo) == (-1)**n*oo
+    assert laguerre(n, -oo) is oo
+
+    assert conjugate(laguerre(n, x)) == laguerre(n, conjugate(x))
+
+    _k = Dummy('k')
+
+    assert laguerre(n, x).rewrite(Sum).dummy_eq(
+        Sum(x**_k*RisingFactorial(-n, _k)/factorial(_k)**2, (_k, 0, n)))
+    assert laguerre(n, x).rewrite("polynomial").dummy_eq(
+        Sum(x**_k*RisingFactorial(-n, _k)/factorial(_k)**2, (_k, 0, n)))
+    assert laguerre(m, x).rewrite(Sum).dummy_eq(
+        exp(x)*Sum((-x)**_k*RisingFactorial(m + 1, _k)/factorial(_k)**2,
+            (_k, 0, -m - 1)))
+    assert laguerre(m, x).rewrite("polynomial").dummy_eq(
+        exp(x)*Sum((-x)**_k*RisingFactorial(m + 1, _k)/factorial(_k)**2,
+            (_k, 0, -m - 1)))
+
+    assert diff(laguerre(n, x), x) == -assoc_laguerre(n - 1, 1, x)
+
+    k = Symbol('k')
+    assert laguerre(-n, x) == exp(x)*laguerre(n - 1, -x)
+    assert laguerre(-3, x) == exp(x)*laguerre(2, -x)
+    assert unchanged(laguerre, -n + k, x)
+
+    raises(ValueError, lambda: laguerre(-2.1, x))
+    raises(ValueError, lambda: laguerre(Rational(5, 2), x))
+    raises(ArgumentIndexError, lambda: laguerre(n, x).fdiff(1))
+    raises(ArgumentIndexError, lambda: laguerre(n, x).fdiff(3))
+
+
+def test_assoc_laguerre():
+    n = Symbol("n")
+    m = Symbol("m")
+    alpha = Symbol("alpha")
+
+    # generalized Laguerre polynomials:
+    assert assoc_laguerre(0, alpha, x) == 1
+    assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
+    assert assoc_laguerre(2, alpha, x).expand() == \
+        (x**2/2 - (alpha + 2)*x + (alpha + 2)*(alpha + 1)/2).expand()
+    assert assoc_laguerre(3, alpha, x).expand() == \
+        (-x**3/6 + (alpha + 3)*x**2/2 - (alpha + 2)*(alpha + 3)*x/2 +
+        (alpha + 1)*(alpha + 2)*(alpha + 3)/6).expand()
+
+    # Test the lowest 10 polynomials with laguerre_poly, to make sure it works:
+    for i in range(10):
+        assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)
+
+    X = assoc_laguerre(n, m, x)
+    assert isinstance(X, assoc_laguerre)
+
+    assert assoc_laguerre(n, 0, x) == laguerre(n, x)
+    assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)
+    p = Symbol("p", positive=True)
+    assert assoc_laguerre(p, alpha, oo) == (-1)**p*oo
+    assert assoc_laguerre(p, alpha, -oo) is oo
+
+    assert diff(assoc_laguerre(n, alpha, x), x) == \
+        -assoc_laguerre(n - 1, alpha + 1, x)
+    _k = Dummy('k')
+    assert diff(assoc_laguerre(n, alpha, x), alpha).dummy_eq(
+        Sum(assoc_laguerre(_k, alpha, x)/(-alpha + n), (_k, 0, n - 1)))
+
+    assert conjugate(assoc_laguerre(n, alpha, x)) == \
+        assoc_laguerre(n, conjugate(alpha), conjugate(x))
+
+    assert assoc_laguerre(n, alpha, x).rewrite(Sum).dummy_eq(
+            gamma(alpha + n + 1)*Sum(x**_k*RisingFactorial(-n, _k)/
+            (factorial(_k)*gamma(_k + alpha + 1)), (_k, 0, n))/factorial(n))
+    assert assoc_laguerre(n, alpha, x).rewrite("polynomial").dummy_eq(
+            gamma(alpha + n + 1)*Sum(x**_k*RisingFactorial(-n, _k)/
+            (factorial(_k)*gamma(_k + alpha + 1)), (_k, 0, n))/factorial(n))
+    raises(ValueError, lambda: assoc_laguerre(-2.1, alpha, x))
+    raises(ArgumentIndexError, lambda: assoc_laguerre(n, alpha, x).fdiff(1))
+    raises(ArgumentIndexError, lambda: assoc_laguerre(n, alpha, x).fdiff(4))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_spherical_harmonics.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_spherical_harmonics.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e0d4ffebabb62c13d3fc2996e8ba23866467720
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_spherical_harmonics.py
@@ -0,0 +1,66 @@
+from sympy.core.function import diff
+from sympy.core.numbers import (I, pi)
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, cot, sin)
+from sympy.functions.special.spherical_harmonics import Ynm, Znm, Ynm_c
+
+
+def test_Ynm():
+    # https://en.wikipedia.org/wiki/Spherical_harmonics
+    th, ph = Symbol("theta", real=True), Symbol("phi", real=True)
+    from sympy.abc import n,m
+
+    assert Ynm(0, 0, th, ph).expand(func=True) == 1/(2*sqrt(pi))
+    assert Ynm(1, -1, th, ph) == -exp(-2*I*ph)*Ynm(1, 1, th, ph)
+    assert Ynm(1, -1, th, ph).expand(func=True) == sqrt(6)*sin(th)*exp(-I*ph)/(4*sqrt(pi))
+    assert Ynm(1, 0, th, ph).expand(func=True) == sqrt(3)*cos(th)/(2*sqrt(pi))
+    assert Ynm(1, 1, th, ph).expand(func=True) == -sqrt(6)*sin(th)*exp(I*ph)/(4*sqrt(pi))
+    assert Ynm(2, 0, th, ph).expand(func=True) == 3*sqrt(5)*cos(th)**2/(4*sqrt(pi)) - sqrt(5)/(4*sqrt(pi))
+    assert Ynm(2, 1, th, ph).expand(func=True) == -sqrt(30)*sin(th)*exp(I*ph)*cos(th)/(4*sqrt(pi))
+    assert Ynm(2, -2, th, ph).expand(func=True) == (-sqrt(30)*exp(-2*I*ph)*cos(th)**2/(8*sqrt(pi))
+                                                    + sqrt(30)*exp(-2*I*ph)/(8*sqrt(pi)))
+    assert Ynm(2, 2, th, ph).expand(func=True) == (-sqrt(30)*exp(2*I*ph)*cos(th)**2/(8*sqrt(pi))
+                                                   + sqrt(30)*exp(2*I*ph)/(8*sqrt(pi)))
+
+    assert diff(Ynm(n, m, th, ph), th) == (m*cot(th)*Ynm(n, m, th, ph)
+                                           + sqrt((-m + n)*(m + n + 1))*exp(-I*ph)*Ynm(n, m + 1, th, ph))
+    assert diff(Ynm(n, m, th, ph), ph) == I*m*Ynm(n, m, th, ph)
+
+    assert conjugate(Ynm(n, m, th, ph)) == (-1)**(2*m)*exp(-2*I*m*ph)*Ynm(n, m, th, ph)
+
+    assert Ynm(n, m, -th, ph) == Ynm(n, m, th, ph)
+    assert Ynm(n, m, th, -ph) == exp(-2*I*m*ph)*Ynm(n, m, th, ph)
+    assert Ynm(n, -m, th, ph) == (-1)**m*exp(-2*I*m*ph)*Ynm(n, m, th, ph)
+
+
+def test_Ynm_c():
+    th, ph = Symbol("theta", real=True), Symbol("phi", real=True)
+    from sympy.abc import n,m
+
+    assert Ynm_c(n, m, th, ph) == (-1)**(2*m)*exp(-2*I*m*ph)*Ynm(n, m, th, ph)
+
+
+def test_Znm():
+    # https://en.wikipedia.org/wiki/Solid_harmonics#List_of_lowest_functions
+    th, ph = Symbol("theta", real=True), Symbol("phi", real=True)
+
+    assert Znm(0, 0, th, ph) == Ynm(0, 0, th, ph)
+    assert Znm(1, -1, th, ph) == (-sqrt(2)*I*(Ynm(1, 1, th, ph)
+                                  - exp(-2*I*ph)*Ynm(1, 1, th, ph))/2)
+    assert Znm(1, 0, th, ph) == Ynm(1, 0, th, ph)
+    assert Znm(1, 1, th, ph) == (sqrt(2)*(Ynm(1, 1, th, ph)
+                                 + exp(-2*I*ph)*Ynm(1, 1, th, ph))/2)
+    assert Znm(0, 0, th, ph).expand(func=True) == 1/(2*sqrt(pi))
+    assert Znm(1, -1, th, ph).expand(func=True) == (sqrt(3)*I*sin(th)*exp(I*ph)/(4*sqrt(pi))
+                                                    - sqrt(3)*I*sin(th)*exp(-I*ph)/(4*sqrt(pi)))
+    assert Znm(1, 0, th, ph).expand(func=True) == sqrt(3)*cos(th)/(2*sqrt(pi))
+    assert Znm(1, 1, th, ph).expand(func=True) == (-sqrt(3)*sin(th)*exp(I*ph)/(4*sqrt(pi))
+                                                   - sqrt(3)*sin(th)*exp(-I*ph)/(4*sqrt(pi)))
+    assert Znm(2, -1, th, ph).expand(func=True) == (sqrt(15)*I*sin(th)*exp(I*ph)*cos(th)/(4*sqrt(pi))
+                                                    - sqrt(15)*I*sin(th)*exp(-I*ph)*cos(th)/(4*sqrt(pi)))
+    assert Znm(2, 0, th, ph).expand(func=True) == 3*sqrt(5)*cos(th)**2/(4*sqrt(pi)) - sqrt(5)/(4*sqrt(pi))
+    assert Znm(2, 1, th, ph).expand(func=True) == (-sqrt(15)*sin(th)*exp(I*ph)*cos(th)/(4*sqrt(pi))
+                                                   - sqrt(15)*sin(th)*exp(-I*ph)*cos(th)/(4*sqrt(pi)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_tensor_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_tensor_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..7d4f31c45ae0a60a6f72dc5551794b2110f5ab99
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_tensor_functions.py
@@ -0,0 +1,145 @@
+from sympy.core.relational import Ne
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.elementary.complexes import (adjoint, conjugate, transpose)
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.special.tensor_functions import (Eijk, KroneckerDelta, LeviCivita)
+
+from sympy.physics.secondquant import evaluate_deltas, F
+
+x, y = symbols('x y')
+
+
+def test_levicivita():
+    assert Eijk(1, 2, 3) == LeviCivita(1, 2, 3)
+    assert LeviCivita(1, 2, 3) == 1
+    assert LeviCivita(int(1), int(2), int(3)) == 1
+    assert LeviCivita(1, 3, 2) == -1
+    assert LeviCivita(1, 2, 2) == 0
+    i, j, k = symbols('i j k')
+    assert LeviCivita(i, j, k) == LeviCivita(i, j, k, evaluate=False)
+    assert LeviCivita(i, j, i) == 0
+    assert LeviCivita(1, i, i) == 0
+    assert LeviCivita(i, j, k).doit() == (j - i)*(k - i)*(k - j)/2
+    assert LeviCivita(1, 2, 3, 1) == 0
+    assert LeviCivita(4, 5, 1, 2, 3) == 1
+    assert LeviCivita(4, 5, 2, 1, 3) == -1
+
+    assert LeviCivita(i, j, k).is_integer is True
+
+    assert adjoint(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
+    assert conjugate(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
+    assert transpose(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
+
+
+def test_kronecker_delta():
+    i, j = symbols('i j')
+    k = Symbol('k', nonzero=True)
+    assert KroneckerDelta(1, 1) == 1
+    assert KroneckerDelta(1, 2) == 0
+    assert KroneckerDelta(k, 0) == 0
+    assert KroneckerDelta(x, x) == 1
+    assert KroneckerDelta(x**2 - y**2, x**2 - y**2) == 1
+    assert KroneckerDelta(i, i) == 1
+    assert KroneckerDelta(i, i + 1) == 0
+    assert KroneckerDelta(0, 0) == 1
+    assert KroneckerDelta(0, 1) == 0
+    assert KroneckerDelta(i + k, i) == 0
+    assert KroneckerDelta(i + k, i + k) == 1
+    assert KroneckerDelta(i + k, i + 1 + k) == 0
+    assert KroneckerDelta(i, j).subs({"i": 1, "j": 0}) == 0
+    assert KroneckerDelta(i, j).subs({"i": 3, "j": 3}) == 1
+
+    assert KroneckerDelta(i, j)**0 == 1
+    for n in range(1, 10):
+        assert KroneckerDelta(i, j)**n == KroneckerDelta(i, j)
+        assert KroneckerDelta(i, j)**-n == 1/KroneckerDelta(i, j)
+
+    assert KroneckerDelta(i, j).is_integer is True
+
+    assert adjoint(KroneckerDelta(i, j)) == KroneckerDelta(i, j)
+    assert conjugate(KroneckerDelta(i, j)) == KroneckerDelta(i, j)
+    assert transpose(KroneckerDelta(i, j)) == KroneckerDelta(i, j)
+    # to test if canonical
+    assert (KroneckerDelta(i, j) == KroneckerDelta(j, i)) == True
+
+    assert KroneckerDelta(i, j).rewrite(Piecewise) == Piecewise((0, Ne(i, j)), (1, True))
+
+    # Tests with range:
+    assert KroneckerDelta(i, j, (0, i)).args == (i, j, (0, i))
+    assert KroneckerDelta(i, j, (-j, i)).delta_range == (-j, i)
+
+    # If index is out of range, return zero:
+    assert KroneckerDelta(i, j, (0, i-1)) == 0
+    assert KroneckerDelta(-1, j, (0, i-1)) == 0
+    assert KroneckerDelta(j, -1, (0, i-1)) == 0
+    assert KroneckerDelta(j, i, (0, i-1)) == 0
+
+
+def test_kronecker_delta_secondquant():
+    """secondquant-specific methods"""
+    D = KroneckerDelta
+    i, j, v, w = symbols('i j v w', below_fermi=True, cls=Dummy)
+    a, b, t, u = symbols('a b t u', above_fermi=True, cls=Dummy)
+    p, q, r, s = symbols('p q r s', cls=Dummy)
+
+    assert D(i, a) == 0
+    assert D(i, t) == 0
+
+    assert D(i, j).is_above_fermi is False
+    assert D(a, b).is_above_fermi is True
+    assert D(p, q).is_above_fermi is True
+    assert D(i, q).is_above_fermi is False
+    assert D(q, i).is_above_fermi is False
+    assert D(q, v).is_above_fermi is False
+    assert D(a, q).is_above_fermi is True
+
+    assert D(i, j).is_below_fermi is True
+    assert D(a, b).is_below_fermi is False
+    assert D(p, q).is_below_fermi is True
+    assert D(p, j).is_below_fermi is True
+    assert D(q, b).is_below_fermi is False
+
+    assert D(i, j).is_only_above_fermi is False
+    assert D(a, b).is_only_above_fermi is True
+    assert D(p, q).is_only_above_fermi is False
+    assert D(i, q).is_only_above_fermi is False
+    assert D(q, i).is_only_above_fermi is False
+    assert D(a, q).is_only_above_fermi is True
+
+    assert D(i, j).is_only_below_fermi is True
+    assert D(a, b).is_only_below_fermi is False
+    assert D(p, q).is_only_below_fermi is False
+    assert D(p, j).is_only_below_fermi is True
+    assert D(q, b).is_only_below_fermi is False
+
+    assert not D(i, q).indices_contain_equal_information
+    assert not D(a, q).indices_contain_equal_information
+    assert D(p, q).indices_contain_equal_information
+    assert D(a, b).indices_contain_equal_information
+    assert D(i, j).indices_contain_equal_information
+
+    assert D(q, b).preferred_index == b
+    assert D(q, b).killable_index == q
+    assert D(q, t).preferred_index == t
+    assert D(q, t).killable_index == q
+    assert D(q, i).preferred_index == i
+    assert D(q, i).killable_index == q
+    assert D(q, v).preferred_index == v
+    assert D(q, v).killable_index == q
+    assert D(q, p).preferred_index == p
+    assert D(q, p).killable_index == q
+
+    EV = evaluate_deltas
+    assert EV(D(a, q)*F(q)) == F(a)
+    assert EV(D(i, q)*F(q)) == F(i)
+    assert EV(D(a, q)*F(a)) == D(a, q)*F(a)
+    assert EV(D(i, q)*F(i)) == D(i, q)*F(i)
+    assert EV(D(a, b)*F(a)) == F(b)
+    assert EV(D(a, b)*F(b)) == F(a)
+    assert EV(D(i, j)*F(i)) == F(j)
+    assert EV(D(i, j)*F(j)) == F(i)
+    assert EV(D(p, q)*F(q)) == F(p)
+    assert EV(D(p, q)*F(p)) == F(q)
+    assert EV(D(p, j)*D(p, i)*F(i)) == F(j)
+    assert EV(D(p, j)*D(p, i)*F(j)) == F(i)
+    assert EV(D(p, q)*D(p, i))*F(i) == D(q, i)*F(i)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_zeta_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_zeta_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..c2083b0b6e8cb38fde17fb1ede2a34be6338b1dc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/tests/test_zeta_functions.py
@@ -0,0 +1,286 @@
+from sympy.concrete.summations import Sum
+from sympy.core.function import expand_func
+from sympy.core.numbers import (Float, I, Rational, nan, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import (Abs, polar_lift)
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.zeta_functions import (dirichlet_eta, lerchphi, polylog, riemann_xi, stieltjes, zeta)
+from sympy.series.order import O
+from sympy.core.function import ArgumentIndexError
+from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic
+from sympy.testing.pytest import raises
+from sympy.core.random import (test_derivative_numerically as td,
+                      random_complex_number as randcplx, verify_numerically)
+
+x = Symbol('x')
+a = Symbol('a')
+b = Symbol('b', negative=True)
+z = Symbol('z')
+s = Symbol('s')
+
+
+def test_zeta_eval():
+
+    assert zeta(nan) is nan
+    assert zeta(x, nan) is nan
+
+    assert zeta(0) == Rational(-1, 2)
+    assert zeta(0, x) == S.Half - x
+    assert zeta(0, b) == S.Half - b
+
+    assert zeta(1) is zoo
+    assert zeta(1, 2) is zoo
+    assert zeta(1, -7) is zoo
+    assert zeta(1, x) is zoo
+
+    assert zeta(2, 1) == pi**2/6
+    assert zeta(3, 1) == zeta(3)
+
+    assert zeta(2) == pi**2/6
+    assert zeta(4) == pi**4/90
+    assert zeta(6) == pi**6/945
+
+    assert zeta(4, 3) == pi**4/90 - Rational(17, 16)
+    assert zeta(7, 4) == zeta(7) - Rational(282251, 279936)
+    assert zeta(S.Half, 2).func == zeta
+    assert expand_func(zeta(S.Half, 2)) == zeta(S.Half) - 1
+    assert zeta(x, 3).func == zeta
+    assert expand_func(zeta(x, 3)) == zeta(x) - 1 - 1/2**x
+
+    assert zeta(2, 0) is nan
+    assert zeta(3, -1) is nan
+    assert zeta(4, -2) is nan
+
+    assert zeta(oo) == 1
+
+    assert zeta(-1) == Rational(-1, 12)
+    assert zeta(-2) == 0
+    assert zeta(-3) == Rational(1, 120)
+    assert zeta(-4) == 0
+    assert zeta(-5) == Rational(-1, 252)
+
+    assert zeta(-1, 3) == Rational(-37, 12)
+    assert zeta(-1, 7) == Rational(-253, 12)
+    assert zeta(-1, -4) == Rational(-121, 12)
+    assert zeta(-1, -9) == Rational(-541, 12)
+
+    assert zeta(-4, 3) == -17
+    assert zeta(-4, -8) == 8772
+
+    assert zeta(0, 1) == Rational(-1, 2)
+    assert zeta(0, -1) == Rational(3, 2)
+
+    assert zeta(0, 2) == Rational(-3, 2)
+    assert zeta(0, -2) == Rational(5, 2)
+
+    assert zeta(
+        3).evalf(20).epsilon_eq(Float("1.2020569031595942854", 20), 1e-19)
+
+
+def test_zeta_series():
+    assert zeta(x, a).series(a, z, 2) == \
+        zeta(x, z) - x*(a-z)*zeta(x+1, z) + O((a-z)**2, (a, z))
+
+
+def test_dirichlet_eta_eval():
+    assert dirichlet_eta(0) == S.Half
+    assert dirichlet_eta(-1) == Rational(1, 4)
+    assert dirichlet_eta(1) == log(2)
+    assert dirichlet_eta(1, S.Half).simplify() == pi/2
+    assert dirichlet_eta(1, 2) == 1 - log(2)
+    assert dirichlet_eta(2) == pi**2/12
+    assert dirichlet_eta(4) == pi**4*Rational(7, 720)
+    assert str(dirichlet_eta(I).evalf(n=10)) == '0.5325931818 + 0.2293848577*I'
+    assert str(dirichlet_eta(I, I).evalf(n=10)) == '3.462349253 + 0.220285771*I'
+
+
+def test_riemann_xi_eval():
+    assert riemann_xi(2) == pi/6
+    assert riemann_xi(0) == Rational(1, 2)
+    assert riemann_xi(1) == Rational(1, 2)
+    assert riemann_xi(3).rewrite(zeta) == 3*zeta(3)/(2*pi)
+    assert riemann_xi(4) == pi**2/15
+
+
+def test_rewriting():
+    from sympy.functions.elementary.piecewise import Piecewise
+    assert isinstance(dirichlet_eta(x).rewrite(zeta), Piecewise)
+    assert isinstance(dirichlet_eta(x).rewrite(genocchi), Piecewise)
+    assert zeta(x).rewrite(dirichlet_eta) == dirichlet_eta(x)/(1 - 2**(1 - x))
+    assert zeta(x).rewrite(dirichlet_eta, a=2) == zeta(x)
+    assert verify_numerically(dirichlet_eta(x), dirichlet_eta(x).rewrite(zeta), x)
+    assert verify_numerically(dirichlet_eta(x), dirichlet_eta(x).rewrite(genocchi), x)
+    assert verify_numerically(zeta(x), zeta(x).rewrite(dirichlet_eta), x)
+
+    assert zeta(x, a).rewrite(lerchphi) == lerchphi(1, x, a)
+    assert polylog(s, z).rewrite(lerchphi) == lerchphi(z, s, 1)*z
+
+    assert lerchphi(1, x, a).rewrite(zeta) == zeta(x, a)
+    assert z*lerchphi(z, s, 1).rewrite(polylog) == polylog(s, z)
+
+
+def test_derivatives():
+    from sympy.core.function import Derivative
+    assert zeta(x, a).diff(x) == Derivative(zeta(x, a), x)
+    assert zeta(x, a).diff(a) == -x*zeta(x + 1, a)
+    assert lerchphi(
+        z, s, a).diff(z) == (lerchphi(z, s - 1, a) - a*lerchphi(z, s, a))/z
+    assert lerchphi(z, s, a).diff(a) == -s*lerchphi(z, s + 1, a)
+    assert polylog(s, z).diff(z) == polylog(s - 1, z)/z
+
+    b = randcplx()
+    c = randcplx()
+    assert td(zeta(b, x), x)
+    assert td(polylog(b, z), z)
+    assert td(lerchphi(c, b, x), x)
+    assert td(lerchphi(x, b, c), x)
+    raises(ArgumentIndexError, lambda: lerchphi(c, b, x).fdiff(2))
+    raises(ArgumentIndexError, lambda: lerchphi(c, b, x).fdiff(4))
+    raises(ArgumentIndexError, lambda: polylog(b, z).fdiff(1))
+    raises(ArgumentIndexError, lambda: polylog(b, z).fdiff(3))
+
+
+def myexpand(func, target):
+    expanded = expand_func(func)
+    if target is not None:
+        return expanded == target
+    if expanded == func:  # it didn't expand
+        return False
+
+    # check to see that the expanded and original evaluate to the same value
+    subs = {}
+    for a in func.free_symbols:
+        subs[a] = randcplx()
+    return abs(func.subs(subs).n()
+               - expanded.replace(exp_polar, exp).subs(subs).n()) < 1e-10
+
+
+def test_polylog_expansion():
+    assert polylog(s, 0) == 0
+    assert polylog(s, 1) == zeta(s)
+    assert polylog(s, -1) == -dirichlet_eta(s)
+    assert polylog(s, exp_polar(I*pi*Rational(4, 3))) == polylog(s, exp(I*pi*Rational(4, 3)))
+    assert polylog(s, exp_polar(I*pi)/3) == polylog(s, exp(I*pi)/3)
+
+    assert myexpand(polylog(1, z), -log(1 - z))
+    assert myexpand(polylog(0, z), z/(1 - z))
+    assert myexpand(polylog(-1, z), z/(1 - z)**2)
+    assert ((1-z)**3 * expand_func(polylog(-2, z))).simplify() == z*(1 + z)
+    assert myexpand(polylog(-5, z), None)
+
+
+def test_polylog_series():
+    assert polylog(1, z).series(z, n=5) == z + z**2/2 + z**3/3 + z**4/4 + O(z**5)
+    assert polylog(1, sqrt(z)).series(z, n=3) == z/2 + z**2/4 + sqrt(z)\
+        + z**(S(3)/2)/3 + z**(S(5)/2)/5 + O(z**3)
+
+    # https://github.com/sympy/sympy/issues/9497
+    assert polylog(S(3)/2, -z).series(z, 0, 5) == -z + sqrt(2)*z**2/4\
+        - sqrt(3)*z**3/9 + z**4/8 + O(z**5)
+
+
+def test_issue_8404():
+    i = Symbol('i', integer=True)
+    assert Abs(Sum(1/(3*i + 1)**2, (i, 0, S.Infinity)).doit().n(4)
+        - 1.122) < 0.001
+
+
+def test_polylog_values():
+    assert polylog(2, 2) == pi**2/4 - I*pi*log(2)
+    assert polylog(2, S.Half) == pi**2/12 - log(2)**2/2
+    for z in [S.Half, 2, (sqrt(5)-1)/2, -(sqrt(5)-1)/2, -(sqrt(5)+1)/2, (3-sqrt(5))/2]:
+        assert Abs(polylog(2, z).evalf() - polylog(2, z, evaluate=False).evalf()) < 1e-15
+    z = Symbol("z")
+    for s in [-1, 0]:
+        for _ in range(10):
+            assert verify_numerically(polylog(s, z), polylog(s, z, evaluate=False),
+                                      z, a=-3, b=-2, c=S.Half, d=2)
+            assert verify_numerically(polylog(s, z), polylog(s, z, evaluate=False),
+                                      z, a=2, b=-2, c=5, d=2)
+
+    from sympy.integrals.integrals import Integral
+    assert polylog(0, Integral(1, (x, 0, 1))) == -S.Half
+
+
+def test_lerchphi_expansion():
+    assert myexpand(lerchphi(1, s, a), zeta(s, a))
+    assert myexpand(lerchphi(z, s, 1), polylog(s, z)/z)
+
+    # direct summation
+    assert myexpand(lerchphi(z, -1, a), a/(1 - z) + z/(1 - z)**2)
+    assert myexpand(lerchphi(z, -3, a), None)
+    # polylog reduction
+    assert myexpand(lerchphi(z, s, S.Half),
+                    2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z)
+                              - polylog(s, polar_lift(-1)*sqrt(z))/sqrt(z)))
+    assert myexpand(lerchphi(z, s, 2), -1/z + polylog(s, z)/z**2)
+    assert myexpand(lerchphi(z, s, Rational(3, 2)), None)
+    assert myexpand(lerchphi(z, s, Rational(7, 3)), None)
+    assert myexpand(lerchphi(z, s, Rational(-1, 3)), None)
+    assert myexpand(lerchphi(z, s, Rational(-5, 2)), None)
+
+    # hurwitz zeta reduction
+    assert myexpand(lerchphi(-1, s, a),
+                    2**(-s)*zeta(s, a/2) - 2**(-s)*zeta(s, (a + 1)/2))
+    assert myexpand(lerchphi(I, s, a), None)
+    assert myexpand(lerchphi(-I, s, a), None)
+    assert myexpand(lerchphi(exp(I*pi*Rational(2, 5)), s, a), None)
+
+
+def test_stieltjes():
+    assert isinstance(stieltjes(x), stieltjes)
+    assert isinstance(stieltjes(x, a), stieltjes)
+
+    # Zero'th constant EulerGamma
+    assert stieltjes(0) == S.EulerGamma
+    assert stieltjes(0, 1) == S.EulerGamma
+
+    # Not defined
+    assert stieltjes(nan) is nan
+    assert stieltjes(0, nan) is nan
+    assert stieltjes(-1) is S.ComplexInfinity
+    assert stieltjes(1.5) is S.ComplexInfinity
+    assert stieltjes(z, 0) is S.ComplexInfinity
+    assert stieltjes(z, -1) is S.ComplexInfinity
+
+
+def test_stieltjes_evalf():
+    assert abs(stieltjes(0).evalf() - 0.577215664) < 1E-9
+    assert abs(stieltjes(0, 0.5).evalf() - 1.963510026) < 1E-9
+    assert abs(stieltjes(1, 2).evalf() + 0.072815845) < 1E-9
+
+
+def test_issue_10475():
+    a = Symbol('a', extended_real=True)
+    b = Symbol('b', extended_positive=True)
+    s = Symbol('s', zero=False)
+
+    assert zeta(2 + I).is_finite
+    assert zeta(1).is_finite is False
+    assert zeta(x).is_finite is None
+    assert zeta(x + I).is_finite is None
+    assert zeta(a).is_finite is None
+    assert zeta(b).is_finite is None
+    assert zeta(-b).is_finite is True
+    assert zeta(b**2 - 2*b + 1).is_finite is None
+    assert zeta(a + I).is_finite is True
+    assert zeta(b + 1).is_finite is True
+    assert zeta(s + 1).is_finite is True
+
+
+def test_issue_14177():
+    n = Symbol('n', nonnegative=True, integer=True)
+
+    assert zeta(-n).rewrite(bernoulli) == bernoulli(n+1) / (-n-1)
+    assert zeta(-n, a).rewrite(bernoulli) == bernoulli(n+1, a) / (-n-1)
+    z2n = -(2*I*pi)**(2*n)*bernoulli(2*n) / (2*factorial(2*n))
+    assert zeta(2*n).rewrite(bernoulli) == z2n
+    assert expand_func(zeta(s, n+1)) == zeta(s) - harmonic(n, s)
+    assert expand_func(zeta(-b, -n)) is nan
+    assert expand_func(zeta(-b, n)) == zeta(-b, n)
+
+    n = Symbol('n')
+
+    assert zeta(2*n) == zeta(2*n) # As sign of z (= 2*n) is not determined
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/zeta_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/zeta_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..8f410f0f1086de91490c714cd3becf11df9ab189
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/functions/special/zeta_functions.py
@@ -0,0 +1,786 @@
+""" Riemann zeta and related function. """
+
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.function import ArgumentIndexError, expand_mul, DefinedFunction
+from sympy.core.logic import fuzzy_not
+from sympy.core.numbers import pi, I, Integer
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic
+from sympy.functions.elementary.complexes import re, unpolarify, Abs, polar_lift
+from sympy.functions.elementary.exponential import log, exp_polar, exp
+from sympy.functions.elementary.integers import ceiling, floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.polys.polytools import Poly
+
+###############################################################################
+###################### LERCH TRANSCENDENT #####################################
+###############################################################################
+
+
+class lerchphi(DefinedFunction):
+    r"""
+    Lerch transcendent (Lerch phi function).
+
+    Explanation
+    ===========
+
+    For $\operatorname{Re}(a) > 0$, $|z| < 1$ and $s \in \mathbb{C}$, the
+    Lerch transcendent is defined as
+
+    .. math :: \Phi(z, s, a) = \sum_{n=0}^\infty \frac{z^n}{(n + a)^s},
+
+    where the standard branch of the argument is used for $n + a$,
+    and by analytic continuation for other values of the parameters.
+
+    A commonly used related function is the Lerch zeta function, defined by
+
+    .. math:: L(q, s, a) = \Phi(e^{2\pi i q}, s, a).
+
+    **Analytic Continuation and Branching Behavior**
+
+    It can be shown that
+
+    .. math:: \Phi(z, s, a) = z\Phi(z, s, a+1) + a^{-s}.
+
+    This provides the analytic continuation to $\operatorname{Re}(a) \le 0$.
+
+    Assume now $\operatorname{Re}(a) > 0$. The integral representation
+
+    .. math:: \Phi_0(z, s, a) = \int_0^\infty \frac{t^{s-1} e^{-at}}{1 - ze^{-t}}
+                                \frac{\mathrm{d}t}{\Gamma(s)}
+
+    provides an analytic continuation to $\mathbb{C} - [1, \infty)$.
+    Finally, for $x \in (1, \infty)$ we find
+
+    .. math:: \lim_{\epsilon \to 0^+} \Phi_0(x + i\epsilon, s, a)
+             -\lim_{\epsilon \to 0^+} \Phi_0(x - i\epsilon, s, a)
+             = \frac{2\pi i \log^{s-1}{x}}{x^a \Gamma(s)},
+
+    using the standard branch for both $\log{x}$ and
+    $\log{\log{x}}$ (a branch of $\log{\log{x}}$ is needed to
+    evaluate $\log{x}^{s-1}$).
+    This concludes the analytic continuation. The Lerch transcendent is thus
+    branched at $z \in \{0, 1, \infty\}$ and
+    $a \in \mathbb{Z}_{\le 0}$. For fixed $z, a$ outside these
+    branch points, it is an entire function of $s$.
+
+    Examples
+    ========
+
+    The Lerch transcendent is a fairly general function, for this reason it does
+    not automatically evaluate to simpler functions. Use ``expand_func()`` to
+    achieve this.
+
+    If $z=1$, the Lerch transcendent reduces to the Hurwitz zeta function:
+
+    >>> from sympy import lerchphi, expand_func
+    >>> from sympy.abc import z, s, a
+    >>> expand_func(lerchphi(1, s, a))
+    zeta(s, a)
+
+    More generally, if $z$ is a root of unity, the Lerch transcendent
+    reduces to a sum of Hurwitz zeta functions:
+
+    >>> expand_func(lerchphi(-1, s, a))
+    zeta(s, a/2)/2**s - zeta(s, a/2 + 1/2)/2**s
+
+    If $a=1$, the Lerch transcendent reduces to the polylogarithm:
+
+    >>> expand_func(lerchphi(z, s, 1))
+    polylog(s, z)/z
+
+    More generally, if $a$ is rational, the Lerch transcendent reduces
+    to a sum of polylogarithms:
+
+    >>> from sympy import S
+    >>> expand_func(lerchphi(z, s, S(1)/2))
+    2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z) -
+                polylog(s, sqrt(z)*exp_polar(I*pi))/sqrt(z))
+    >>> expand_func(lerchphi(z, s, S(3)/2))
+    -2**s/z + 2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z) -
+                          polylog(s, sqrt(z)*exp_polar(I*pi))/sqrt(z))/z
+
+    The derivatives with respect to $z$ and $a$ can be computed in
+    closed form:
+
+    >>> lerchphi(z, s, a).diff(z)
+    (-a*lerchphi(z, s, a) + lerchphi(z, s - 1, a))/z
+    >>> lerchphi(z, s, a).diff(a)
+    -s*lerchphi(z, s + 1, a)
+
+    See Also
+    ========
+
+    polylog, zeta
+
+    References
+    ==========
+
+    .. [1] Bateman, H.; Erdelyi, A. (1953), Higher Transcendental Functions,
+           Vol. I, New York: McGraw-Hill. Section 1.11.
+    .. [2] https://dlmf.nist.gov/25.14
+    .. [3] https://en.wikipedia.org/wiki/Lerch_transcendent
+
+    """
+
+    def _eval_expand_func(self, **hints):
+        z, s, a = self.args
+        if z == 1:
+            return zeta(s, a)
+        if s.is_Integer and s <= 0:
+            t = Dummy('t')
+            p = Poly((t + a)**(-s), t)
+            start = 1/(1 - t)
+            res = S.Zero
+            for c in reversed(p.all_coeffs()):
+                res += c*start
+                start = t*start.diff(t)
+            return res.subs(t, z)
+
+        if a.is_Rational:
+            # See section 18 of
+            #   Kelly B. Roach.  Hypergeometric Function Representations.
+            #   In: Proceedings of the 1997 International Symposium on Symbolic and
+            #   Algebraic Computation, pages 205-211, New York, 1997. ACM.
+            # TODO should something be polarified here?
+            add = S.Zero
+            mul = S.One
+            # First reduce a to the interaval (0, 1]
+            if a > 1:
+                n = floor(a)
+                if n == a:
+                    n -= 1
+                a -= n
+                mul = z**(-n)
+                add = Add(*[-z**(k - n)/(a + k)**s for k in range(n)])
+            elif a <= 0:
+                n = floor(-a) + 1
+                a += n
+                mul = z**n
+                add = Add(*[z**(n - 1 - k)/(a - k - 1)**s for k in range(n)])
+
+            m, n = S([a.p, a.q])
+            zet = exp_polar(2*pi*I/n)
+            root = z**(1/n)
+            up_zet = unpolarify(zet)
+            addargs = []
+            for k in range(n):
+                p = polylog(s, zet**k*root)
+                if isinstance(p, polylog):
+                    p = p._eval_expand_func(**hints)
+                addargs.append(p/(up_zet**k*root)**m)
+            return add + mul*n**(s - 1)*Add(*addargs)
+
+        # TODO use minpoly instead of ad-hoc methods when issue 5888 is fixed
+        if isinstance(z, exp) and (z.args[0]/(pi*I)).is_Rational or z in [-1, I, -I]:
+            # TODO reference?
+            if z == -1:
+                p, q = S([1, 2])
+            elif z == I:
+                p, q = S([1, 4])
+            elif z == -I:
+                p, q = S([-1, 4])
+            else:
+                arg = z.args[0]/(2*pi*I)
+                p, q = S([arg.p, arg.q])
+            return Add(*[exp(2*pi*I*k*p/q)/q**s*zeta(s, (k + a)/q)
+                         for k in range(q)])
+
+        return lerchphi(z, s, a)
+
+    def fdiff(self, argindex=1):
+        z, s, a = self.args
+        if argindex == 3:
+            return -s*lerchphi(z, s + 1, a)
+        elif argindex == 1:
+            return (lerchphi(z, s - 1, a) - a*lerchphi(z, s, a))/z
+        else:
+            raise ArgumentIndexError
+
+    def _eval_rewrite_helper(self, target):
+        res = self._eval_expand_func()
+        if res.has(target):
+            return res
+        else:
+            return self
+
+    def _eval_rewrite_as_zeta(self, z, s, a, **kwargs):
+        return self._eval_rewrite_helper(zeta)
+
+    def _eval_rewrite_as_polylog(self, z, s, a, **kwargs):
+        return self._eval_rewrite_helper(polylog)
+
+###############################################################################
+###################### POLYLOGARITHM ##########################################
+###############################################################################
+
+
+class polylog(DefinedFunction):
+    r"""
+    Polylogarithm function.
+
+    Explanation
+    ===========
+
+    For $|z| < 1$ and $s \in \mathbb{C}$, the polylogarithm is
+    defined by
+
+    .. math:: \operatorname{Li}_s(z) = \sum_{n=1}^\infty \frac{z^n}{n^s},
+
+    where the standard branch of the argument is used for $n$. It admits
+    an analytic continuation which is branched at $z=1$ (notably not on the
+    sheet of initial definition), $z=0$ and $z=\infty$.
+
+    The name polylogarithm comes from the fact that for $s=1$, the
+    polylogarithm is related to the ordinary logarithm (see examples), and that
+
+    .. math:: \operatorname{Li}_{s+1}(z) =
+                    \int_0^z \frac{\operatorname{Li}_s(t)}{t} \mathrm{d}t.
+
+    The polylogarithm is a special case of the Lerch transcendent:
+
+    .. math:: \operatorname{Li}_{s}(z) = z \Phi(z, s, 1).
+
+    Examples
+    ========
+
+    For $z \in \{0, 1, -1\}$, the polylogarithm is automatically expressed
+    using other functions:
+
+    >>> from sympy import polylog
+    >>> from sympy.abc import s
+    >>> polylog(s, 0)
+    0
+    >>> polylog(s, 1)
+    zeta(s)
+    >>> polylog(s, -1)
+    -dirichlet_eta(s)
+
+    If $s$ is a negative integer, $0$ or $1$, the polylogarithm can be
+    expressed using elementary functions. This can be done using
+    ``expand_func()``:
+
+    >>> from sympy import expand_func
+    >>> from sympy.abc import z
+    >>> expand_func(polylog(1, z))
+    -log(1 - z)
+    >>> expand_func(polylog(0, z))
+    z/(1 - z)
+
+    The derivative with respect to $z$ can be computed in closed form:
+
+    >>> polylog(s, z).diff(z)
+    polylog(s - 1, z)/z
+
+    The polylogarithm can be expressed in terms of the lerch transcendent:
+
+    >>> from sympy import lerchphi
+    >>> polylog(s, z).rewrite(lerchphi)
+    z*lerchphi(z, s, 1)
+
+    See Also
+    ========
+
+    zeta, lerchphi
+
+    """
+
+    @classmethod
+    def eval(cls, s, z):
+        if z.is_number:
+            if z is S.One:
+                return zeta(s)
+            elif z is S.NegativeOne:
+                return -dirichlet_eta(s)
+            elif z is S.Zero:
+                return S.Zero
+            elif s == 2:
+                dilogtable = _dilogtable()
+                if z in dilogtable:
+                    return dilogtable[z]
+
+        if z.is_zero:
+            return S.Zero
+
+        # Make an effort to determine if z is 1 to avoid replacing into
+        # expression with singularity
+        zone = z.equals(S.One)
+
+        if zone:
+            return zeta(s)
+        elif zone is False:
+            # For s = 0 or -1 use explicit formulas to evaluate, but
+            # automatically expanding polylog(1, z) to -log(1-z) seems
+            # undesirable for summation methods based on hypergeometric
+            # functions
+            if s is S.Zero:
+                return z/(1 - z)
+            elif s is S.NegativeOne:
+                return z/(1 - z)**2
+            if s.is_zero:
+                return z/(1 - z)
+
+        # polylog is branched, but not over the unit disk
+        if z.has(exp_polar, polar_lift) and (zone or (Abs(z) <= S.One) == True):
+            return cls(s, unpolarify(z))
+
+    def fdiff(self, argindex=1):
+        s, z = self.args
+        if argindex == 2:
+            return polylog(s - 1, z)/z
+        raise ArgumentIndexError
+
+    def _eval_rewrite_as_lerchphi(self, s, z, **kwargs):
+        return z*lerchphi(z, s, 1)
+
+    def _eval_expand_func(self, **hints):
+        s, z = self.args
+        if s == 1:
+            return -log(1 - z)
+        if s.is_Integer and s <= 0:
+            u = Dummy('u')
+            start = u/(1 - u)
+            for _ in range(-s):
+                start = u*start.diff(u)
+            return expand_mul(start).subs(u, z)
+        return polylog(s, z)
+
+    def _eval_is_zero(self):
+        z = self.args[1]
+        if z.is_zero:
+            return True
+
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        from sympy.series.order import Order
+        nu, z = self.args
+
+        z0 = z.subs(x, 0)
+        if z0 is S.NaN:
+            z0 = z.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
+
+        if z0.is_zero:
+            # In case of powers less than 1, number of terms need to be computed
+            # separately to avoid repeated callings of _eval_nseries with wrong n
+            try:
+                _, exp = z.leadterm(x)
+            except (ValueError, NotImplementedError):
+                return self
+
+            if exp.is_positive:
+                newn = ceiling(n/exp)
+                o = Order(x**n, x)
+                r = z._eval_nseries(x, n, logx, cdir).removeO()
+                if r is S.Zero:
+                    return o
+
+                term = r
+                s = [term]
+                for k in range(2, newn):
+                    term *= r
+                    s.append(term/k**nu)
+                return Add(*s) + o
+
+        return super(polylog, self)._eval_nseries(x, n, logx, cdir)
+
+###############################################################################
+###################### HURWITZ GENERALIZED ZETA FUNCTION ######################
+###############################################################################
+
+
+class zeta(DefinedFunction):
+    r"""
+    Hurwitz zeta function (or Riemann zeta function).
+
+    Explanation
+    ===========
+
+    For $\operatorname{Re}(a) > 0$ and $\operatorname{Re}(s) > 1$, this
+    function is defined as
+
+    .. math:: \zeta(s, a) = \sum_{n=0}^\infty \frac{1}{(n + a)^s},
+
+    where the standard choice of argument for $n + a$ is used. For fixed
+    $a$ not a nonpositive integer the Hurwitz zeta function admits a
+    meromorphic continuation to all of $\mathbb{C}$; it is an unbranched
+    function with a simple pole at $s = 1$.
+
+    The Hurwitz zeta function is a special case of the Lerch transcendent:
+
+    .. math:: \zeta(s, a) = \Phi(1, s, a).
+
+    This formula defines an analytic continuation for all possible values of
+    $s$ and $a$ (also $\operatorname{Re}(a) < 0$), see the documentation of
+    :class:`lerchphi` for a description of the branching behavior.
+
+    If no value is passed for $a$ a default value of $a = 1$ is assumed,
+    yielding the Riemann zeta function.
+
+    Examples
+    ========
+
+    For $a = 1$ the Hurwitz zeta function reduces to the famous Riemann
+    zeta function:
+
+    .. math:: \zeta(s, 1) = \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}.
+
+    >>> from sympy import zeta
+    >>> from sympy.abc import s
+    >>> zeta(s, 1)
+    zeta(s)
+    >>> zeta(s)
+    zeta(s)
+
+    The Riemann zeta function can also be expressed using the Dirichlet eta
+    function:
+
+    >>> from sympy import dirichlet_eta
+    >>> zeta(s).rewrite(dirichlet_eta)
+    dirichlet_eta(s)/(1 - 2**(1 - s))
+
+    The Riemann zeta function at nonnegative even and negative integer
+    values is related to the Bernoulli numbers and polynomials:
+
+    >>> zeta(2)
+    pi**2/6
+    >>> zeta(4)
+    pi**4/90
+    >>> zeta(0)
+    -1/2
+    >>> zeta(-1)
+    -1/12
+    >>> zeta(-4)
+    0
+
+    The specific formulae are:
+
+    .. math:: \zeta(2n) = -\frac{(2\pi i)^{2n} B_{2n}}{2(2n)!}
+    .. math:: \zeta(-n,a) = -\frac{B_{n+1}(a)}{n+1}
+
+    No closed-form expressions are known at positive odd integers, but
+    numerical evaluation is possible:
+
+    >>> zeta(3).n()
+    1.20205690315959
+
+    The derivative of $\zeta(s, a)$ with respect to $a$ can be computed:
+
+    >>> from sympy.abc import a
+    >>> zeta(s, a).diff(a)
+    -s*zeta(s + 1, a)
+
+    However the derivative with respect to $s$ has no useful closed form
+    expression:
+
+    >>> zeta(s, a).diff(s)
+    Derivative(zeta(s, a), s)
+
+    The Hurwitz zeta function can be expressed in terms of the Lerch
+    transcendent, :class:`~.lerchphi`:
+
+    >>> from sympy import lerchphi
+    >>> zeta(s, a).rewrite(lerchphi)
+    lerchphi(1, s, a)
+
+    See Also
+    ========
+
+    dirichlet_eta, lerchphi, polylog
+
+    References
+    ==========
+
+    .. [1] https://dlmf.nist.gov/25.11
+    .. [2] https://en.wikipedia.org/wiki/Hurwitz_zeta_function
+
+    """
+
+    @classmethod
+    def eval(cls, s, a=None):
+        if a is S.One:
+            return cls(s)
+        elif s is S.NaN or a is S.NaN:
+            return S.NaN
+        elif s is S.One:
+            return S.ComplexInfinity
+        elif s is S.Infinity:
+            return S.One
+        elif a is S.Infinity:
+            return S.Zero
+
+        sint = s.is_Integer
+        if a is None:
+            a = S.One
+        if sint and s.is_nonpositive:
+            return bernoulli(1-s, a) / (s-1)
+        elif a is S.One:
+            if sint and s.is_even:
+                return -(2*pi*I)**s * bernoulli(s) / (2*factorial(s))
+        elif sint and a.is_Integer and a.is_positive:
+            return cls(s) - harmonic(a-1, s)
+        elif a.is_Integer and a.is_nonpositive and \
+                (s.is_integer is False or s.is_nonpositive is False):
+            return S.NaN
+
+    def _eval_rewrite_as_bernoulli(self, s, a=1, **kwargs):
+        if a == 1 and s.is_integer and s.is_nonnegative and s.is_even:
+            return -(2*pi*I)**s * bernoulli(s) / (2*factorial(s))
+        return bernoulli(1-s, a) / (s-1)
+
+    def _eval_rewrite_as_dirichlet_eta(self, s, a=1, **kwargs):
+        if a != 1:
+            return self
+        s = self.args[0]
+        return dirichlet_eta(s)/(1 - 2**(1 - s))
+
+    def _eval_rewrite_as_lerchphi(self, s, a=1, **kwargs):
+        return lerchphi(1, s, a)
+
+    def _eval_is_finite(self):
+        return fuzzy_not((self.args[0] - 1).is_zero)
+
+    def _eval_expand_func(self, **hints):
+        s = self.args[0]
+        a = self.args[1] if len(self.args) > 1 else S.One
+        if a.is_integer:
+            if a.is_positive:
+                return zeta(s) - harmonic(a-1, s)
+            if a.is_nonpositive and (s.is_integer is False or
+                    s.is_nonpositive is False):
+                return S.NaN
+        return self
+
+    def fdiff(self, argindex=1):
+        if len(self.args) == 2:
+            s, a = self.args
+        else:
+            s, a = self.args + (1,)
+        if argindex == 2:
+            return -s*zeta(s + 1, a)
+        else:
+            raise ArgumentIndexError
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        if len(self.args) == 2:
+            s, a = self.args
+        else:
+            s, a = self.args + (S.One,)
+
+        try:
+            c, e = a.leadterm(x)
+        except NotImplementedError:
+            return self
+
+        if e.is_negative and not s.is_positive:
+            raise NotImplementedError
+
+        return super(zeta, self)._eval_as_leading_term(x, logx=logx, cdir=cdir)
+
+
+class dirichlet_eta(DefinedFunction):
+    r"""
+    Dirichlet eta function.
+
+    Explanation
+    ===========
+
+    For $\operatorname{Re}(s) > 0$ and $0 < x \le 1$, this function is defined as
+
+    .. math:: \eta(s, a) = \sum_{n=0}^\infty \frac{(-1)^n}{(n+a)^s}.
+
+    It admits a unique analytic continuation to all of $\mathbb{C}$ for any
+    fixed $a$ not a nonpositive integer. It is an entire, unbranched function.
+
+    It can be expressed using the Hurwitz zeta function as
+
+    .. math:: \eta(s, a) = \zeta(s,a) - 2^{1-s} \zeta\left(s, \frac{a+1}{2}\right)
+
+    and using the generalized Genocchi function as
+
+    .. math:: \eta(s, a) = \frac{G(1-s, a)}{2(s-1)}.
+
+    In both cases the limiting value of $\log2 - \psi(a) + \psi\left(\frac{a+1}{2}\right)$
+    is used when $s = 1$.
+
+    Examples
+    ========
+
+    >>> from sympy import dirichlet_eta, zeta
+    >>> from sympy.abc import s
+    >>> dirichlet_eta(s).rewrite(zeta)
+    Piecewise((log(2), Eq(s, 1)), ((1 - 2**(1 - s))*zeta(s), True))
+
+    See Also
+    ========
+
+    zeta
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Dirichlet_eta_function
+    .. [2] Peter Luschny, "An introduction to the Bernoulli function",
+           https://arxiv.org/abs/2009.06743
+
+    """
+
+    @classmethod
+    def eval(cls, s, a=None):
+        if a is S.One:
+            return cls(s)
+        if a is None:
+            if s == 1:
+                return log(2)
+            z = zeta(s)
+            if not z.has(zeta):
+                return (1 - 2**(1-s)) * z
+            return
+        elif s == 1:
+            from sympy.functions.special.gamma_functions import digamma
+            return log(2) - digamma(a) + digamma((a+1)/2)
+        z1 = zeta(s, a)
+        z2 = zeta(s, (a+1)/2)
+        if not z1.has(zeta) and not z2.has(zeta):
+            return z1 - 2**(1-s) * z2
+
+    def _eval_rewrite_as_zeta(self, s, a=1, **kwargs):
+        from sympy.functions.special.gamma_functions import digamma
+        if a == 1:
+            return Piecewise((log(2), Eq(s, 1)), ((1 - 2**(1-s)) * zeta(s), True))
+        return Piecewise((log(2) - digamma(a) + digamma((a+1)/2), Eq(s, 1)),
+                (zeta(s, a) - 2**(1-s) * zeta(s, (a+1)/2), True))
+
+    def _eval_rewrite_as_genocchi(self, s, a=S.One, **kwargs):
+        from sympy.functions.special.gamma_functions import digamma
+        return Piecewise((log(2) - digamma(a) + digamma((a+1)/2), Eq(s, 1)),
+                (genocchi(1-s, a) / (2 * (s-1)), True))
+
+    def _eval_evalf(self, prec):
+        if all(i.is_number for i in self.args):
+            return self.rewrite(zeta)._eval_evalf(prec)
+
+
+class riemann_xi(DefinedFunction):
+    r"""
+    Riemann Xi function.
+
+    Examples
+    ========
+
+    The Riemann Xi function is closely related to the Riemann zeta function.
+    The zeros of Riemann Xi function are precisely the non-trivial zeros
+    of the zeta function.
+
+    >>> from sympy import riemann_xi, zeta
+    >>> from sympy.abc import s
+    >>> riemann_xi(s).rewrite(zeta)
+    s*(s - 1)*gamma(s/2)*zeta(s)/(2*pi**(s/2))
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Riemann_Xi_function
+
+    """
+
+
+    @classmethod
+    def eval(cls, s):
+        from sympy.functions.special.gamma_functions import gamma
+        z = zeta(s)
+        if s in (S.Zero, S.One):
+            return S.Half
+
+        if not isinstance(z, zeta):
+            return s*(s - 1)*gamma(s/2)*z/(2*pi**(s/2))
+
+    def _eval_rewrite_as_zeta(self, s, **kwargs):
+        from sympy.functions.special.gamma_functions import gamma
+        return s*(s - 1)*gamma(s/2)*zeta(s)/(2*pi**(s/2))
+
+
+class stieltjes(DefinedFunction):
+    r"""
+    Represents Stieltjes constants, $\gamma_{k}$ that occur in
+    Laurent Series expansion of the Riemann zeta function.
+
+    Examples
+    ========
+
+    >>> from sympy import stieltjes
+    >>> from sympy.abc import n, m
+    >>> stieltjes(n)
+    stieltjes(n)
+
+    The zero'th stieltjes constant:
+
+    >>> stieltjes(0)
+    EulerGamma
+    >>> stieltjes(0, 1)
+    EulerGamma
+
+    For generalized stieltjes constants:
+
+    >>> stieltjes(n, m)
+    stieltjes(n, m)
+
+    Constants are only defined for integers >= 0:
+
+    >>> stieltjes(-1)
+    zoo
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Stieltjes_constants
+
+    """
+
+    @classmethod
+    def eval(cls, n, a=None):
+        if a is not None:
+            a = sympify(a)
+            if a is S.NaN:
+                return S.NaN
+            if a.is_Integer and a.is_nonpositive:
+                return S.ComplexInfinity
+
+        if n.is_Number:
+            if n is S.NaN:
+                return S.NaN
+            elif n < 0:
+                return S.ComplexInfinity
+            elif not n.is_Integer:
+                return S.ComplexInfinity
+            elif n is S.Zero and a in [None, 1]:
+                return S.EulerGamma
+
+        if n.is_extended_negative:
+            return S.ComplexInfinity
+
+        if n.is_zero and a in [None, 1]:
+            return S.EulerGamma
+
+        if n.is_integer == False:
+            return S.ComplexInfinity
+
+
+@cacheit
+def _dilogtable():
+    return {
+        S.Half: pi**2/12 - log(2)**2/2,
+        Integer(2) : pi**2/4 - I*pi*log(2),
+        -(sqrt(5) - 1)/2 : -pi**2/15 + log((sqrt(5)-1)/2)**2/2,
+        -(sqrt(5) + 1)/2 : -pi**2/10 - log((sqrt(5)+1)/2)**2,
+        (3 - sqrt(5))/2 : pi**2/15 - log((sqrt(5)-1)/2)**2,
+        (sqrt(5) - 1)/2 : pi**2/10 - log((sqrt(5)-1)/2)**2,
+        I : I*S.Catalan - pi**2/48,
+        -I : -I*S.Catalan - pi**2/48,
+        1 - I : pi**2/16 - I*S.Catalan - pi*I/4*log(2),
+        1 + I : pi**2/16 + I*S.Catalan + pi*I/4*log(2),
+        (1 - I)/2 : -log(2)**2/8 + pi*I*log(2)/8 + 5*pi**2/96 - I*S.Catalan
+    }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/galgebra.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/galgebra.py
new file mode 100644
index 0000000000000000000000000000000000000000..be812bfcbcece834c86d7b55eb846286acd0ac08
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/galgebra.py
@@ -0,0 +1 @@
+raise ImportError("""As of SymPy 1.0 the galgebra module is maintained separately at https://github.com/pygae/galgebra""")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..bb85d4ff5d53eb44a039a95cfc2fff687322cc76
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/__init__.py
@@ -0,0 +1,45 @@
+"""
+A geometry module for the SymPy library. This module contains all of the
+entities and functions needed to construct basic geometrical data and to
+perform simple informational queries.
+
+Usage:
+======
+
+Examples
+========
+
+"""
+from sympy.geometry.point import Point, Point2D, Point3D
+from sympy.geometry.line import Line, Ray, Segment, Line2D, Segment2D, Ray2D, \
+    Line3D, Segment3D, Ray3D
+from sympy.geometry.plane import Plane
+from sympy.geometry.ellipse import Ellipse, Circle
+from sympy.geometry.polygon import Polygon, RegularPolygon, Triangle, rad, deg
+from sympy.geometry.util import are_similar, centroid, convex_hull, idiff, \
+    intersection, closest_points, farthest_points
+from sympy.geometry.exceptions import GeometryError
+from sympy.geometry.curve import Curve
+from sympy.geometry.parabola import Parabola
+
+__all__ = [
+    'Point', 'Point2D', 'Point3D',
+
+    'Line', 'Ray', 'Segment', 'Line2D', 'Segment2D', 'Ray2D', 'Line3D',
+    'Segment3D', 'Ray3D',
+
+    'Plane',
+
+    'Ellipse', 'Circle',
+
+    'Polygon', 'RegularPolygon', 'Triangle', 'rad', 'deg',
+
+    'are_similar', 'centroid', 'convex_hull', 'idiff', 'intersection',
+    'closest_points', 'farthest_points',
+
+    'GeometryError',
+
+    'Curve',
+
+    'Parabola',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/curve.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/curve.py
new file mode 100644
index 0000000000000000000000000000000000000000..c074f22cad79b1261ad44be4ccface972cdd3b82
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/curve.py
@@ -0,0 +1,424 @@
+"""Curves in 2-dimensional Euclidean space.
+
+Contains
+========
+Curve
+
+"""
+
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.core import diff
+from sympy.core.containers import Tuple
+from sympy.core.symbol import _symbol
+from sympy.geometry.entity import GeometryEntity, GeometrySet
+from sympy.geometry.point import Point
+from sympy.integrals import integrate
+from sympy.matrices import Matrix, rot_axis3
+from sympy.utilities.iterables import is_sequence
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+
+class Curve(GeometrySet):
+    """A curve in space.
+
+    A curve is defined by parametric functions for the coordinates, a
+    parameter and the lower and upper bounds for the parameter value.
+
+    Parameters
+    ==========
+
+    function : list of functions
+    limits : 3-tuple
+        Function parameter and lower and upper bounds.
+
+    Attributes
+    ==========
+
+    functions
+    parameter
+    limits
+
+    Raises
+    ======
+
+    ValueError
+        When `functions` are specified incorrectly.
+        When `limits` are specified incorrectly.
+
+    Examples
+    ========
+
+    >>> from sympy import Curve, sin, cos, interpolate
+    >>> from sympy.abc import t, a
+    >>> C = Curve((sin(t), cos(t)), (t, 0, 2))
+    >>> C.functions
+    (sin(t), cos(t))
+    >>> C.limits
+    (t, 0, 2)
+    >>> C.parameter
+    t
+    >>> C = Curve((t, interpolate([1, 4, 9, 16], t)), (t, 0, 1)); C
+    Curve((t, t**2), (t, 0, 1))
+    >>> C.subs(t, 4)
+    Point2D(4, 16)
+    >>> C.arbitrary_point(a)
+    Point2D(a, a**2)
+
+    See Also
+    ========
+
+    sympy.core.function.Function
+    sympy.polys.polyfuncs.interpolate
+
+    """
+
+    def __new__(cls, function, limits):
+        if not is_sequence(function) or len(function) != 2:
+            raise ValueError("Function argument should be (x(t), y(t)) "
+                "but got %s" % str(function))
+        if not is_sequence(limits) or len(limits) != 3:
+            raise ValueError("Limit argument should be (t, tmin, tmax) "
+                "but got %s" % str(limits))
+
+        return GeometryEntity.__new__(cls, Tuple(*function), Tuple(*limits))
+
+    def __call__(self, f):
+        return self.subs(self.parameter, f)
+
+    def _eval_subs(self, old, new):
+        if old == self.parameter:
+            return Point(*[f.subs(old, new) for f in self.functions])
+
+    def _eval_evalf(self, prec=15, **options):
+        f, (t, a, b) = self.args
+        dps = prec_to_dps(prec)
+        f = tuple([i.evalf(n=dps, **options) for i in f])
+        a, b = [i.evalf(n=dps, **options) for i in (a, b)]
+        return self.func(f, (t, a, b))
+
+    def arbitrary_point(self, parameter='t'):
+        """A parameterized point on the curve.
+
+        Parameters
+        ==========
+
+        parameter : str or Symbol, optional
+            Default value is 't'.
+            The Curve's parameter is selected with None or self.parameter
+            otherwise the provided symbol is used.
+
+        Returns
+        =======
+
+        Point :
+            Returns a point in parametric form.
+
+        Raises
+        ======
+
+        ValueError
+            When `parameter` already appears in the functions.
+
+        Examples
+        ========
+
+        >>> from sympy import Curve, Symbol
+        >>> from sympy.abc import s
+        >>> C = Curve([2*s, s**2], (s, 0, 2))
+        >>> C.arbitrary_point()
+        Point2D(2*t, t**2)
+        >>> C.arbitrary_point(C.parameter)
+        Point2D(2*s, s**2)
+        >>> C.arbitrary_point(None)
+        Point2D(2*s, s**2)
+        >>> C.arbitrary_point(Symbol('a'))
+        Point2D(2*a, a**2)
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        """
+        if parameter is None:
+            return Point(*self.functions)
+
+        tnew = _symbol(parameter, self.parameter, real=True)
+        t = self.parameter
+        if (tnew.name != t.name and
+                tnew.name in (f.name for f in self.free_symbols)):
+            raise ValueError('Symbol %s already appears in object '
+                'and cannot be used as a parameter.' % tnew.name)
+        return Point(*[w.subs(t, tnew) for w in self.functions])
+
+    @property
+    def free_symbols(self):
+        """Return a set of symbols other than the bound symbols used to
+        parametrically define the Curve.
+
+        Returns
+        =======
+
+        set :
+            Set of all non-parameterized symbols.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import t, a
+        >>> from sympy import Curve
+        >>> Curve((t, t**2), (t, 0, 2)).free_symbols
+        set()
+        >>> Curve((t, t**2), (t, a, 2)).free_symbols
+        {a}
+
+        """
+        free = set()
+        for a in self.functions + self.limits[1:]:
+            free |= a.free_symbols
+        free = free.difference({self.parameter})
+        return free
+
+    @property
+    def ambient_dimension(self):
+        """The dimension of the curve.
+
+        Returns
+        =======
+
+        int :
+            the dimension of curve.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import t
+        >>> from sympy import Curve
+        >>> C = Curve((t, t**2), (t, 0, 2))
+        >>> C.ambient_dimension
+        2
+
+        """
+
+        return len(self.args[0])
+
+    @property
+    def functions(self):
+        """The functions specifying the curve.
+
+        Returns
+        =======
+
+        functions :
+            list of parameterized coordinate functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import t
+        >>> from sympy import Curve
+        >>> C = Curve((t, t**2), (t, 0, 2))
+        >>> C.functions
+        (t, t**2)
+
+        See Also
+        ========
+
+        parameter
+
+        """
+        return self.args[0]
+
+    @property
+    def limits(self):
+        """The limits for the curve.
+
+        Returns
+        =======
+
+        limits : tuple
+            Contains parameter and lower and upper limits.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import t
+        >>> from sympy import Curve
+        >>> C = Curve([t, t**3], (t, -2, 2))
+        >>> C.limits
+        (t, -2, 2)
+
+        See Also
+        ========
+
+        plot_interval
+
+        """
+        return self.args[1]
+
+    @property
+    def parameter(self):
+        """The curve function variable.
+
+        Returns
+        =======
+
+        Symbol :
+            returns a bound symbol.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import t
+        >>> from sympy import Curve
+        >>> C = Curve([t, t**2], (t, 0, 2))
+        >>> C.parameter
+        t
+
+        See Also
+        ========
+
+        functions
+
+        """
+        return self.args[1][0]
+
+    @property
+    def length(self):
+        """The curve length.
+
+        Examples
+        ========
+
+        >>> from sympy import Curve
+        >>> from sympy.abc import t
+        >>> Curve((t, t), (t, 0, 1)).length
+        sqrt(2)
+
+        """
+        integrand = sqrt(sum(diff(func, self.limits[0])**2 for func in self.functions))
+        return integrate(integrand, self.limits)
+
+    def plot_interval(self, parameter='t'):
+        """The plot interval for the default geometric plot of the curve.
+
+        Parameters
+        ==========
+
+        parameter : str or Symbol, optional
+            Default value is 't';
+            otherwise the provided symbol is used.
+
+        Returns
+        =======
+
+        List :
+            the plot interval as below:
+                [parameter, lower_bound, upper_bound]
+
+        Examples
+        ========
+
+        >>> from sympy import Curve, sin
+        >>> from sympy.abc import x, s
+        >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval()
+        [t, 1, 2]
+        >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval(s)
+        [s, 1, 2]
+
+        See Also
+        ========
+
+        limits : Returns limits of the parameter interval
+
+        """
+        t = _symbol(parameter, self.parameter, real=True)
+        return [t] + list(self.limits[1:])
+
+    def rotate(self, angle=0, pt=None):
+        """This function is used to rotate a curve along given point ``pt`` at given angle(in radian).
+
+        Parameters
+        ==========
+
+        angle :
+            the angle at which the curve will be rotated(in radian) in counterclockwise direction.
+            default value of angle is 0.
+
+        pt : Point
+            the point along which the curve will be rotated.
+            If no point given, the curve will be rotated around origin.
+
+        Returns
+        =======
+
+        Curve :
+            returns a curve rotated at given angle along given point.
+
+        Examples
+        ========
+
+        >>> from sympy import Curve, pi
+        >>> from sympy.abc import x
+        >>> Curve((x, x), (x, 0, 1)).rotate(pi/2)
+        Curve((-x, x), (x, 0, 1))
+
+        """
+        if pt:
+            pt = -Point(pt, dim=2)
+        else:
+            pt = Point(0,0)
+        rv = self.translate(*pt.args)
+        f = list(rv.functions)
+        f.append(0)
+        f = Matrix(1, 3, f)
+        f *= rot_axis3(angle)
+        rv = self.func(f[0, :2].tolist()[0], self.limits)
+        pt = -pt
+        return rv.translate(*pt.args)
+
+    def scale(self, x=1, y=1, pt=None):
+        """Override GeometryEntity.scale since Curve is not made up of Points.
+
+        Returns
+        =======
+
+        Curve :
+            returns scaled curve.
+
+        Examples
+        ========
+
+        >>> from sympy import Curve
+        >>> from sympy.abc import x
+        >>> Curve((x, x), (x, 0, 1)).scale(2)
+        Curve((2*x, x), (x, 0, 1))
+
+        """
+        if pt:
+            pt = Point(pt, dim=2)
+            return self.translate(*(-pt).args).scale(x, y).translate(*pt.args)
+        fx, fy = self.functions
+        return self.func((fx*x, fy*y), self.limits)
+
+    def translate(self, x=0, y=0):
+        """Translate the Curve by (x, y).
+
+        Returns
+        =======
+
+        Curve :
+            returns a translated curve.
+
+        Examples
+        ========
+
+        >>> from sympy import Curve
+        >>> from sympy.abc import x
+        >>> Curve((x, x), (x, 0, 1)).translate(1, 2)
+        Curve((x + 1, x + 2), (x, 0, 1))
+
+        """
+        fx, fy = self.functions
+        return self.func((fx + x, fy + y), self.limits)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/ellipse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/ellipse.py
new file mode 100644
index 0000000000000000000000000000000000000000..199db25fde9b019893a275d69959154990e8a4a7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/ellipse.py
@@ -0,0 +1,1768 @@
+"""Elliptical geometrical entities.
+
+Contains
+* Ellipse
+* Circle
+
+"""
+
+from sympy.core.expr import Expr
+from sympy.core.relational import Eq
+from sympy.core import S, pi, sympify
+from sympy.core.evalf import N
+from sympy.core.parameters import global_parameters
+from sympy.core.logic import fuzzy_bool
+from sympy.core.numbers import Rational, oo
+from sympy.core.sorting import ordered
+from sympy.core.symbol import Dummy, uniquely_named_symbol, _symbol
+from sympy.simplify.simplify import simplify
+from sympy.simplify.trigsimp import trigsimp
+from sympy.functions.elementary.miscellaneous import sqrt, Max
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.functions.special.elliptic_integrals import elliptic_e
+from .entity import GeometryEntity, GeometrySet
+from .exceptions import GeometryError
+from .line import Line, Segment, Ray2D, Segment2D, Line2D, LinearEntity3D
+from .point import Point, Point2D, Point3D
+from .util import idiff, find
+from sympy.polys import DomainError, Poly, PolynomialError
+from sympy.polys.polyutils import _not_a_coeff, _nsort
+from sympy.solvers import solve
+from sympy.solvers.solveset import linear_coeffs
+from sympy.utilities.misc import filldedent, func_name
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+import random
+
+x, y = [Dummy('ellipse_dummy', real=True) for i in range(2)]
+
+
+class Ellipse(GeometrySet):
+    """An elliptical GeometryEntity.
+
+    Parameters
+    ==========
+
+    center : Point, optional
+        Default value is Point(0, 0)
+    hradius : number or SymPy expression, optional
+    vradius : number or SymPy expression, optional
+    eccentricity : number or SymPy expression, optional
+        Two of `hradius`, `vradius` and `eccentricity` must be supplied to
+        create an Ellipse. The third is derived from the two supplied.
+
+    Attributes
+    ==========
+
+    center
+    hradius
+    vradius
+    area
+    circumference
+    eccentricity
+    periapsis
+    apoapsis
+    focus_distance
+    foci
+
+    Raises
+    ======
+
+    GeometryError
+        When `hradius`, `vradius` and `eccentricity` are incorrectly supplied
+        as parameters.
+    TypeError
+        When `center` is not a Point.
+
+    See Also
+    ========
+
+    Circle
+
+    Notes
+    -----
+    Constructed from a center and two radii, the first being the horizontal
+    radius (along the x-axis) and the second being the vertical radius (along
+    the y-axis).
+
+    When symbolic value for hradius and vradius are used, any calculation that
+    refers to the foci or the major or minor axis will assume that the ellipse
+    has its major radius on the x-axis. If this is not true then a manual
+    rotation is necessary.
+
+    Examples
+    ========
+
+    >>> from sympy import Ellipse, Point, Rational
+    >>> e1 = Ellipse(Point(0, 0), 5, 1)
+    >>> e1.hradius, e1.vradius
+    (5, 1)
+    >>> e2 = Ellipse(Point(3, 1), hradius=3, eccentricity=Rational(4, 5))
+    >>> e2
+    Ellipse(Point2D(3, 1), 3, 9/5)
+
+    """
+
+    def __contains__(self, o):
+        if isinstance(o, Point):
+            res = self.equation(x, y).subs({x: o.x, y: o.y})
+            return trigsimp(simplify(res)) is S.Zero
+        elif isinstance(o, Ellipse):
+            return self == o
+        return False
+
+    def __eq__(self, o):
+        """Is the other GeometryEntity the same as this ellipse?"""
+        return isinstance(o, Ellipse) and (self.center == o.center and
+                                           self.hradius == o.hradius and
+                                           self.vradius == o.vradius)
+
+    def __hash__(self):
+        return super().__hash__()
+
+    def __new__(
+        cls, center=None, hradius=None, vradius=None, eccentricity=None, **kwargs):
+
+        hradius = sympify(hradius)
+        vradius = sympify(vradius)
+
+        if center is None:
+            center = Point(0, 0)
+        else:
+            if len(center) != 2:
+                raise ValueError('The center of "{}" must be a two dimensional point'.format(cls))
+            center = Point(center, dim=2)
+
+        if len(list(filter(lambda x: x is not None, (hradius, vradius, eccentricity)))) != 2:
+            raise ValueError(filldedent('''
+                Exactly two arguments of "hradius", "vradius", and
+                "eccentricity" must not be None.'''))
+
+        if eccentricity is not None:
+            eccentricity = sympify(eccentricity)
+            if eccentricity.is_negative:
+                raise GeometryError("Eccentricity of ellipse/circle should lie between [0, 1)")
+            elif hradius is None:
+                hradius = vradius / sqrt(1 - eccentricity**2)
+            elif vradius is None:
+                vradius = hradius * sqrt(1 - eccentricity**2)
+
+        if hradius == vradius:
+            return Circle(center, hradius, **kwargs)
+
+        if S.Zero in (hradius, vradius):
+            return Segment(Point(center[0] - hradius, center[1] - vradius), Point(center[0] + hradius, center[1] + vradius))
+
+        if hradius.is_real is False or vradius.is_real is False:
+            raise GeometryError("Invalid value encountered when computing hradius / vradius.")
+
+        return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
+
+    def _svg(self, scale_factor=1., fill_color="#66cc99"):
+        """Returns SVG ellipse element for the Ellipse.
+
+        Parameters
+        ==========
+
+        scale_factor : float
+            Multiplication factor for the SVG stroke-width.  Default is 1.
+        fill_color : str, optional
+            Hex string for fill color. Default is "#66cc99".
+        """
+
+        c = N(self.center)
+        h, v = N(self.hradius), N(self.vradius)
+        return (
+            ''
+        ).format(2. * scale_factor, fill_color, c.x, c.y, h, v)
+
+    @property
+    def ambient_dimension(self):
+        return 2
+
+    @property
+    def apoapsis(self):
+        """The apoapsis of the ellipse.
+
+        The greatest distance between the focus and the contour.
+
+        Returns
+        =======
+
+        apoapsis : number
+
+        See Also
+        ========
+
+        periapsis : Returns shortest distance between foci and contour
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.apoapsis
+        2*sqrt(2) + 3
+
+        """
+        return self.major * (1 + self.eccentricity)
+
+    def arbitrary_point(self, parameter='t'):
+        """A parameterized point on the ellipse.
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        arbitrary_point : Point
+
+        Raises
+        ======
+
+        ValueError
+            When `parameter` already appears in the functions.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> e1 = Ellipse(Point(0, 0), 3, 2)
+        >>> e1.arbitrary_point()
+        Point2D(3*cos(t), 2*sin(t))
+
+        """
+        t = _symbol(parameter, real=True)
+        if t.name in (f.name for f in self.free_symbols):
+            raise ValueError(filldedent('Symbol %s already appears in object '
+                                        'and cannot be used as a parameter.' % t.name))
+        return Point(self.center.x + self.hradius*cos(t),
+                     self.center.y + self.vradius*sin(t))
+
+    @property
+    def area(self):
+        """The area of the ellipse.
+
+        Returns
+        =======
+
+        area : number
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.area
+        3*pi
+
+        """
+        return simplify(S.Pi * self.hradius * self.vradius)
+
+    @property
+    def bounds(self):
+        """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
+        rectangle for the geometric figure.
+
+        """
+
+        h, v = self.hradius, self.vradius
+        return (self.center.x - h, self.center.y - v, self.center.x + h, self.center.y + v)
+
+    @property
+    def center(self):
+        """The center of the ellipse.
+
+        Returns
+        =======
+
+        center : number
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.center
+        Point2D(0, 0)
+
+        """
+        return self.args[0]
+
+    @property
+    def circumference(self):
+        """The circumference of the ellipse.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.circumference
+        12*elliptic_e(8/9)
+
+        """
+        if self.eccentricity == 1:
+            # degenerate
+            return 4*self.major
+        elif self.eccentricity == 0:
+            # circle
+            return 2*pi*self.hradius
+        else:
+            return 4*self.major*elliptic_e(self.eccentricity**2)
+
+    @property
+    def eccentricity(self):
+        """The eccentricity of the ellipse.
+
+        Returns
+        =======
+
+        eccentricity : number
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse, sqrt
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, sqrt(2))
+        >>> e1.eccentricity
+        sqrt(7)/3
+
+        """
+        return self.focus_distance / self.major
+
+    def encloses_point(self, p):
+        """
+        Return True if p is enclosed by (is inside of) self.
+
+        Notes
+        -----
+        Being on the border of self is considered False.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        encloses_point : True, False or None
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Ellipse, S
+        >>> from sympy.abc import t
+        >>> e = Ellipse((0, 0), 3, 2)
+        >>> e.encloses_point((0, 0))
+        True
+        >>> e.encloses_point(e.arbitrary_point(t).subs(t, S.Half))
+        False
+        >>> e.encloses_point((4, 0))
+        False
+
+        """
+        p = Point(p, dim=2)
+        if p in self:
+            return False
+
+        if len(self.foci) == 2:
+            # if the combined distance from the foci to p (h1 + h2) is less
+            # than the combined distance from the foci to the minor axis
+            # (which is the same as the major axis length) then p is inside
+            # the ellipse
+            h1, h2 = [f.distance(p) for f in self.foci]
+            test = 2*self.major - (h1 + h2)
+        else:
+            test = self.radius - self.center.distance(p)
+
+        return fuzzy_bool(test.is_positive)
+
+    def equation(self, x='x', y='y', _slope=None):
+        """
+        Returns the equation of an ellipse aligned with the x and y axes;
+        when slope is given, the equation returned corresponds to an ellipse
+        with a major axis having that slope.
+
+        Parameters
+        ==========
+
+        x : str, optional
+            Label for the x-axis. Default value is 'x'.
+        y : str, optional
+            Label for the y-axis. Default value is 'y'.
+        _slope : Expr, optional
+                The slope of the major axis. Ignored when 'None'.
+
+        Returns
+        =======
+
+        equation : SymPy expression
+
+        See Also
+        ========
+
+        arbitrary_point : Returns parameterized point on ellipse
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse, pi
+        >>> from sympy.abc import x, y
+        >>> e1 = Ellipse(Point(1, 0), 3, 2)
+        >>> eq1 = e1.equation(x, y); eq1
+        y**2/4 + (x/3 - 1/3)**2 - 1
+        >>> eq2 = e1.equation(x, y, _slope=1); eq2
+        (-x + y + 1)**2/8 + (x + y - 1)**2/18 - 1
+
+        A point on e1 satisfies eq1. Let's use one on the x-axis:
+
+        >>> p1 = e1.center + Point(e1.major, 0)
+        >>> assert eq1.subs(x, p1.x).subs(y, p1.y) == 0
+
+        When rotated the same as the rotated ellipse, about the center
+        point of the ellipse, it will satisfy the rotated ellipse's
+        equation, too:
+
+        >>> r1 = p1.rotate(pi/4, e1.center)
+        >>> assert eq2.subs(x, r1.x).subs(y, r1.y) == 0
+
+        References
+        ==========
+
+        .. [1] https://math.stackexchange.com/questions/108270/what-is-the-equation-of-an-ellipse-that-is-not-aligned-with-the-axis
+        .. [2] https://en.wikipedia.org/wiki/Ellipse#Shifted_ellipse
+
+        """
+
+        x = _symbol(x, real=True)
+        y = _symbol(y, real=True)
+
+        dx = x - self.center.x
+        dy = y - self.center.y
+
+        if _slope is not None:
+            L = (dy - _slope*dx)**2
+            l = (_slope*dy + dx)**2
+            h = 1 + _slope**2
+            b = h*self.major**2
+            a = h*self.minor**2
+            return l/b + L/a - 1
+
+        else:
+            t1 = (dx/self.hradius)**2
+            t2 = (dy/self.vradius)**2
+            return t1 + t2 - 1
+
+    def evolute(self, x='x', y='y'):
+        """The equation of evolute of the ellipse.
+
+        Parameters
+        ==========
+
+        x : str, optional
+            Label for the x-axis. Default value is 'x'.
+        y : str, optional
+            Label for the y-axis. Default value is 'y'.
+
+        Returns
+        =======
+
+        equation : SymPy expression
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> e1 = Ellipse(Point(1, 0), 3, 2)
+        >>> e1.evolute()
+        2**(2/3)*y**(2/3) + (3*x - 3)**(2/3) - 5**(2/3)
+        """
+        if len(self.args) != 3:
+            raise NotImplementedError('Evolute of arbitrary Ellipse is not supported.')
+        x = _symbol(x, real=True)
+        y = _symbol(y, real=True)
+        t1 = (self.hradius*(x - self.center.x))**Rational(2, 3)
+        t2 = (self.vradius*(y - self.center.y))**Rational(2, 3)
+        return t1 + t2 - (self.hradius**2 - self.vradius**2)**Rational(2, 3)
+
+    @property
+    def foci(self):
+        """The foci of the ellipse.
+
+        Notes
+        -----
+        The foci can only be calculated if the major/minor axes are known.
+
+        Raises
+        ======
+
+        ValueError
+            When the major and minor axis cannot be determined.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+        focus_distance : Returns the distance between focus and center
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.foci
+        (Point2D(-2*sqrt(2), 0), Point2D(2*sqrt(2), 0))
+
+        """
+        c = self.center
+        hr, vr = self.hradius, self.vradius
+        if hr == vr:
+            return (c, c)
+
+        # calculate focus distance manually, since focus_distance calls this
+        # routine
+        fd = sqrt(self.major**2 - self.minor**2)
+        if hr == self.minor:
+            # foci on the y-axis
+            return (c + Point(0, -fd), c + Point(0, fd))
+        elif hr == self.major:
+            # foci on the x-axis
+            return (c + Point(-fd, 0), c + Point(fd, 0))
+
+    @property
+    def focus_distance(self):
+        """The focal distance of the ellipse.
+
+        The distance between the center and one focus.
+
+        Returns
+        =======
+
+        focus_distance : number
+
+        See Also
+        ========
+
+        foci
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.focus_distance
+        2*sqrt(2)
+
+        """
+        return Point.distance(self.center, self.foci[0])
+
+    @property
+    def hradius(self):
+        """The horizontal radius of the ellipse.
+
+        Returns
+        =======
+
+        hradius : number
+
+        See Also
+        ========
+
+        vradius, major, minor
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.hradius
+        3
+
+        """
+        return self.args[1]
+
+    def intersection(self, o):
+        """The intersection of this ellipse and another geometrical entity
+        `o`.
+
+        Parameters
+        ==========
+
+        o : GeometryEntity
+
+        Returns
+        =======
+
+        intersection : list of GeometryEntity objects
+
+        Notes
+        -----
+        Currently supports intersections with Point, Line, Segment, Ray,
+        Circle and Ellipse types.
+
+        See Also
+        ========
+
+        sympy.geometry.entity.GeometryEntity
+
+        Examples
+        ========
+
+        >>> from sympy import Ellipse, Point, Line
+        >>> e = Ellipse(Point(0, 0), 5, 7)
+        >>> e.intersection(Point(0, 0))
+        []
+        >>> e.intersection(Point(5, 0))
+        [Point2D(5, 0)]
+        >>> e.intersection(Line(Point(0,0), Point(0, 1)))
+        [Point2D(0, -7), Point2D(0, 7)]
+        >>> e.intersection(Line(Point(5,0), Point(5, 1)))
+        [Point2D(5, 0)]
+        >>> e.intersection(Line(Point(6,0), Point(6, 1)))
+        []
+        >>> e = Ellipse(Point(-1, 0), 4, 3)
+        >>> e.intersection(Ellipse(Point(1, 0), 4, 3))
+        [Point2D(0, -3*sqrt(15)/4), Point2D(0, 3*sqrt(15)/4)]
+        >>> e.intersection(Ellipse(Point(5, 0), 4, 3))
+        [Point2D(2, -3*sqrt(7)/4), Point2D(2, 3*sqrt(7)/4)]
+        >>> e.intersection(Ellipse(Point(100500, 0), 4, 3))
+        []
+        >>> e.intersection(Ellipse(Point(0, 0), 3, 4))
+        [Point2D(3, 0), Point2D(-363/175, -48*sqrt(111)/175), Point2D(-363/175, 48*sqrt(111)/175)]
+        >>> e.intersection(Ellipse(Point(-1, 0), 3, 4))
+        [Point2D(-17/5, -12/5), Point2D(-17/5, 12/5), Point2D(7/5, -12/5), Point2D(7/5, 12/5)]
+        """
+        # TODO: Replace solve with nonlinsolve, when nonlinsolve will be able to solve in real domain
+
+        if isinstance(o, Point):
+            if o in self:
+                return [o]
+            else:
+                return []
+
+        elif isinstance(o, (Segment2D, Ray2D)):
+            ellipse_equation = self.equation(x, y)
+            result = solve([ellipse_equation, Line(
+                o.points[0], o.points[1]).equation(x, y)], [x, y],
+                set=True)[1]
+            return list(ordered([Point(i) for i in result if i in o]))
+
+        elif isinstance(o, Polygon):
+            return o.intersection(self)
+
+        elif isinstance(o, (Ellipse, Line2D)):
+            if o == self:
+                return self
+            else:
+                ellipse_equation = self.equation(x, y)
+                return list(ordered([Point(i) for i in solve(
+                    [ellipse_equation, o.equation(x, y)], [x, y],
+                    set=True)[1]]))
+        elif isinstance(o, LinearEntity3D):
+            raise TypeError('Entity must be two dimensional, not three dimensional')
+        else:
+            raise TypeError('Intersection not handled for %s' % func_name(o))
+
+    def is_tangent(self, o):
+        """Is `o` tangent to the ellipse?
+
+        Parameters
+        ==========
+
+        o : GeometryEntity
+            An Ellipse, LinearEntity or Polygon
+
+        Raises
+        ======
+
+        NotImplementedError
+            When the wrong type of argument is supplied.
+
+        Returns
+        =======
+
+        is_tangent: boolean
+            True if o is tangent to the ellipse, False otherwise.
+
+        See Also
+        ========
+
+        tangent_lines
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse, Line
+        >>> p0, p1, p2 = Point(0, 0), Point(3, 0), Point(3, 3)
+        >>> e1 = Ellipse(p0, 3, 2)
+        >>> l1 = Line(p1, p2)
+        >>> e1.is_tangent(l1)
+        True
+
+        """
+        if isinstance(o, Point2D):
+            return False
+        elif isinstance(o, Ellipse):
+            intersect = self.intersection(o)
+            if isinstance(intersect, Ellipse):
+                return True
+            elif intersect:
+                return all((self.tangent_lines(i)[0]).equals(o.tangent_lines(i)[0]) for i in intersect)
+            else:
+                return False
+        elif isinstance(o, Line2D):
+            hit = self.intersection(o)
+            if not hit:
+                return False
+            if len(hit) == 1:
+                return True
+            # might return None if it can't decide
+            return hit[0].equals(hit[1])
+        elif isinstance(o, (Segment2D, Ray2D)):
+            intersect = self.intersection(o)
+            if len(intersect) == 1:
+                return o in self.tangent_lines(intersect[0])[0]
+            else:
+                return False
+        elif isinstance(o, Polygon):
+            return all(self.is_tangent(s) for s in o.sides)
+        elif isinstance(o, (LinearEntity3D, Point3D)):
+            raise TypeError('Entity must be two dimensional, not three dimensional')
+        else:
+            raise TypeError('Is_tangent not handled for %s' % func_name(o))
+
+    @property
+    def major(self):
+        """Longer axis of the ellipse (if it can be determined) else hradius.
+
+        Returns
+        =======
+
+        major : number or expression
+
+        See Also
+        ========
+
+        hradius, vradius, minor
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse, Symbol
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.major
+        3
+
+        >>> a = Symbol('a')
+        >>> b = Symbol('b')
+        >>> Ellipse(p1, a, b).major
+        a
+        >>> Ellipse(p1, b, a).major
+        b
+
+        >>> m = Symbol('m')
+        >>> M = m + 1
+        >>> Ellipse(p1, m, M).major
+        m + 1
+
+        """
+        ab = self.args[1:3]
+        if len(ab) == 1:
+            return ab[0]
+        a, b = ab
+        o = b - a < 0
+        if o == True:
+            return a
+        elif o == False:
+            return b
+        return self.hradius
+
+    @property
+    def minor(self):
+        """Shorter axis of the ellipse (if it can be determined) else vradius.
+
+        Returns
+        =======
+
+        minor : number or expression
+
+        See Also
+        ========
+
+        hradius, vradius, major
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse, Symbol
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.minor
+        1
+
+        >>> a = Symbol('a')
+        >>> b = Symbol('b')
+        >>> Ellipse(p1, a, b).minor
+        b
+        >>> Ellipse(p1, b, a).minor
+        a
+
+        >>> m = Symbol('m')
+        >>> M = m + 1
+        >>> Ellipse(p1, m, M).minor
+        m
+
+        """
+        ab = self.args[1:3]
+        if len(ab) == 1:
+            return ab[0]
+        a, b = ab
+        o = a - b < 0
+        if o == True:
+            return a
+        elif o == False:
+            return b
+        return self.vradius
+
+    def normal_lines(self, p, prec=None):
+        """Normal lines between `p` and the ellipse.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        normal_lines : list with 1, 2 or 4 Lines
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> e = Ellipse((0, 0), 2, 3)
+        >>> c = e.center
+        >>> e.normal_lines(c + Point(1, 0))
+        [Line2D(Point2D(0, 0), Point2D(1, 0))]
+        >>> e.normal_lines(c)
+        [Line2D(Point2D(0, 0), Point2D(0, 1)), Line2D(Point2D(0, 0), Point2D(1, 0))]
+
+        Off-axis points require the solution of a quartic equation. This
+        often leads to very large expressions that may be of little practical
+        use. An approximate solution of `prec` digits can be obtained by
+        passing in the desired value:
+
+        >>> e.normal_lines((3, 3), prec=2)
+        [Line2D(Point2D(-0.81, -2.7), Point2D(0.19, -1.2)),
+        Line2D(Point2D(1.5, -2.0), Point2D(2.5, -2.7))]
+
+        Whereas the above solution has an operation count of 12, the exact
+        solution has an operation count of 2020.
+        """
+        p = Point(p, dim=2)
+
+        # XXX change True to something like self.angle == 0 if the arbitrarily
+        # rotated ellipse is introduced.
+        # https://github.com/sympy/sympy/issues/2815)
+        if True:
+            rv = []
+            if p.x == self.center.x:
+                rv.append(Line(self.center, slope=oo))
+            if p.y == self.center.y:
+                rv.append(Line(self.center, slope=0))
+            if rv:
+                # at these special orientations of p either 1 or 2 normals
+                # exist and we are done
+                return rv
+
+        # find the 4 normal points and construct lines through them with
+        # the corresponding slope
+        eq = self.equation(x, y)
+        dydx = idiff(eq, y, x)
+        norm = -1/dydx
+        slope = Line(p, (x, y)).slope
+        seq = slope - norm
+
+        # TODO: Replace solve with solveset, when this line is tested
+        yis = solve(seq, y)[0]
+        xeq = eq.subs(y, yis).as_numer_denom()[0].expand()
+        if len(xeq.free_symbols) == 1:
+            try:
+                # this is so much faster, it's worth a try
+                xsol = Poly(xeq, x).real_roots()
+            except (DomainError, PolynomialError, NotImplementedError):
+                # TODO: Replace solve with solveset, when these lines are tested
+                xsol = _nsort(solve(xeq, x), separated=True)[0]
+            points = [Point(i, solve(eq.subs(x, i), y)[0]) for i in xsol]
+        else:
+            raise NotImplementedError(
+                'intersections for the general ellipse are not supported')
+        slopes = [norm.subs(zip((x, y), pt.args)) for pt in points]
+        if prec is not None:
+            points = [pt.n(prec) for pt in points]
+            slopes = [i if _not_a_coeff(i) else i.n(prec) for i in slopes]
+        return [Line(pt, slope=s) for pt, s in zip(points, slopes)]
+
+    @property
+    def periapsis(self):
+        """The periapsis of the ellipse.
+
+        The shortest distance between the focus and the contour.
+
+        Returns
+        =======
+
+        periapsis : number
+
+        See Also
+        ========
+
+        apoapsis : Returns greatest distance between focus and contour
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.periapsis
+        3 - 2*sqrt(2)
+
+        """
+        return self.major * (1 - self.eccentricity)
+
+    @property
+    def semilatus_rectum(self):
+        """
+        Calculates the semi-latus rectum of the Ellipse.
+
+        Semi-latus rectum is defined as one half of the chord through a
+        focus parallel to the conic section directrix of a conic section.
+
+        Returns
+        =======
+
+        semilatus_rectum : number
+
+        See Also
+        ========
+
+        apoapsis : Returns greatest distance between focus and contour
+
+        periapsis : The shortest distance between the focus and the contour
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.semilatus_rectum
+        1/3
+
+        References
+        ==========
+
+        .. [1] https://mathworld.wolfram.com/SemilatusRectum.html
+        .. [2] https://en.wikipedia.org/wiki/Ellipse#Semi-latus_rectum
+
+        """
+        return self.major * (1 - self.eccentricity ** 2)
+
+    def auxiliary_circle(self):
+        """Returns a Circle whose diameter is the major axis of the ellipse.
+
+        Examples
+        ========
+
+        >>> from sympy import Ellipse, Point, symbols
+        >>> c = Point(1, 2)
+        >>> Ellipse(c, 8, 7).auxiliary_circle()
+        Circle(Point2D(1, 2), 8)
+        >>> a, b = symbols('a b')
+        >>> Ellipse(c, a, b).auxiliary_circle()
+        Circle(Point2D(1, 2), Max(a, b))
+        """
+        return Circle(self.center, Max(self.hradius, self.vradius))
+
+    def director_circle(self):
+        """
+        Returns a Circle consisting of all points where two perpendicular
+        tangent lines to the ellipse cross each other.
+
+        Returns
+        =======
+
+        Circle
+            A director circle returned as a geometric object.
+
+        Examples
+        ========
+
+        >>> from sympy import Ellipse, Point, symbols
+        >>> c = Point(3,8)
+        >>> Ellipse(c, 7, 9).director_circle()
+        Circle(Point2D(3, 8), sqrt(130))
+        >>> a, b = symbols('a b')
+        >>> Ellipse(c, a, b).director_circle()
+        Circle(Point2D(3, 8), sqrt(a**2 + b**2))
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Director_circle
+
+        """
+        return Circle(self.center, sqrt(self.hradius**2 + self.vradius**2))
+
+    def plot_interval(self, parameter='t'):
+        """The plot interval for the default geometric plot of the Ellipse.
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        plot_interval : list
+            [parameter, lower_bound, upper_bound]
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> e1 = Ellipse(Point(0, 0), 3, 2)
+        >>> e1.plot_interval()
+        [t, -pi, pi]
+
+        """
+        t = _symbol(parameter, real=True)
+        return [t, -S.Pi, S.Pi]
+
+    def random_point(self, seed=None):
+        """A random point on the ellipse.
+
+        Returns
+        =======
+
+        point : Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> e1 = Ellipse(Point(0, 0), 3, 2)
+        >>> e1.random_point() # gives some random point
+        Point2D(...)
+        >>> p1 = e1.random_point(seed=0); p1.n(2)
+        Point2D(2.1, 1.4)
+
+        Notes
+        =====
+
+        When creating a random point, one may simply replace the
+        parameter with a random number. When doing so, however, the
+        random number should be made a Rational or else the point
+        may not test as being in the ellipse:
+
+        >>> from sympy.abc import t
+        >>> from sympy import Rational
+        >>> arb = e1.arbitrary_point(t); arb
+        Point2D(3*cos(t), 2*sin(t))
+        >>> arb.subs(t, .1) in e1
+        False
+        >>> arb.subs(t, Rational(.1)) in e1
+        True
+        >>> arb.subs(t, Rational('.1')) in e1
+        True
+
+        See Also
+        ========
+        sympy.geometry.point.Point
+        arbitrary_point : Returns parameterized point on ellipse
+        """
+        t = _symbol('t', real=True)
+        x, y = self.arbitrary_point(t).args
+        # get a random value in [-1, 1) corresponding to cos(t)
+        # and confirm that it will test as being in the ellipse
+        if seed is not None:
+            rng = random.Random(seed)
+        else:
+            rng = random
+        # simplify this now or else the Float will turn s into a Float
+        r = Rational(rng.random())
+        c = 2*r - 1
+        s = sqrt(1 - c**2)
+        return Point(x.subs(cos(t), c), y.subs(sin(t), s))
+
+    def reflect(self, line):
+        """Override GeometryEntity.reflect since the radius
+        is not a GeometryEntity.
+
+        Examples
+        ========
+
+        >>> from sympy import Circle, Line
+        >>> Circle((0, 1), 1).reflect(Line((0, 0), (1, 1)))
+        Circle(Point2D(1, 0), -1)
+        >>> from sympy import Ellipse, Line, Point
+        >>> Ellipse(Point(3, 4), 1, 3).reflect(Line(Point(0, -4), Point(5, 0)))
+        Traceback (most recent call last):
+        ...
+        NotImplementedError:
+        General Ellipse is not supported but the equation of the reflected
+        Ellipse is given by the zeros of: f(x, y) = (9*x/41 + 40*y/41 +
+        37/41)**2 + (40*x/123 - 3*y/41 - 364/123)**2 - 1
+
+        Notes
+        =====
+
+        Until the general ellipse (with no axis parallel to the x-axis) is
+        supported a NotImplemented error is raised and the equation whose
+        zeros define the rotated ellipse is given.
+
+        """
+
+        if line.slope in (0, oo):
+            c = self.center
+            c = c.reflect(line)
+            return self.func(c, -self.hradius, self.vradius)
+        else:
+            x, y = [uniquely_named_symbol(
+                name, (self, line), modify=lambda s: '_' + s, real=True)
+                for name in 'xy']
+            expr = self.equation(x, y)
+            p = Point(x, y).reflect(line)
+            result = expr.subs(zip((x, y), p.args
+                                   ), simultaneous=True)
+            raise NotImplementedError(filldedent(
+                'General Ellipse is not supported but the equation '
+                'of the reflected Ellipse is given by the zeros of: ' +
+                "f(%s, %s) = %s" % (str(x), str(y), str(result))))
+
+    def rotate(self, angle=0, pt=None):
+        """Rotate ``angle`` radians counterclockwise about Point ``pt``.
+
+        Note: since the general ellipse is not supported, only rotations that
+        are integer multiples of pi/2 are allowed.
+
+        Examples
+        ========
+
+        >>> from sympy import Ellipse, pi
+        >>> Ellipse((1, 0), 2, 1).rotate(pi/2)
+        Ellipse(Point2D(0, 1), 1, 2)
+        >>> Ellipse((1, 0), 2, 1).rotate(pi)
+        Ellipse(Point2D(-1, 0), 2, 1)
+        """
+        if self.hradius == self.vradius:
+            return self.func(self.center.rotate(angle, pt), self.hradius)
+        if (angle/S.Pi).is_integer:
+            return super().rotate(angle, pt)
+        if (2*angle/S.Pi).is_integer:
+            return self.func(self.center.rotate(angle, pt), self.vradius, self.hradius)
+        # XXX see https://github.com/sympy/sympy/issues/2815 for general ellipes
+        raise NotImplementedError('Only rotations of pi/2 are currently supported for Ellipse.')
+
+    def scale(self, x=1, y=1, pt=None):
+        """Override GeometryEntity.scale since it is the major and minor
+        axes which must be scaled and they are not GeometryEntities.
+
+        Examples
+        ========
+
+        >>> from sympy import Ellipse
+        >>> Ellipse((0, 0), 2, 1).scale(2, 4)
+        Circle(Point2D(0, 0), 4)
+        >>> Ellipse((0, 0), 2, 1).scale(2)
+        Ellipse(Point2D(0, 0), 4, 1)
+        """
+        c = self.center
+        if pt:
+            pt = Point(pt, dim=2)
+            return self.translate(*(-pt).args).scale(x, y).translate(*pt.args)
+        h = self.hradius
+        v = self.vradius
+        return self.func(c.scale(x, y), hradius=h*x, vradius=v*y)
+
+    def tangent_lines(self, p):
+        """Tangent lines between `p` and the ellipse.
+
+        If `p` is on the ellipse, returns the tangent line through point `p`.
+        Otherwise, returns the tangent line(s) from `p` to the ellipse, or
+        None if no tangent line is possible (e.g., `p` inside ellipse).
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        tangent_lines : list with 1 or 2 Lines
+
+        Raises
+        ======
+
+        NotImplementedError
+            Can only find tangent lines for a point, `p`, on the ellipse.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.line.Line
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> e1 = Ellipse(Point(0, 0), 3, 2)
+        >>> e1.tangent_lines(Point(3, 0))
+        [Line2D(Point2D(3, 0), Point2D(3, -12))]
+
+        """
+        p = Point(p, dim=2)
+        if self.encloses_point(p):
+            return []
+
+        if p in self:
+            delta = self.center - p
+            rise = (self.vradius**2)*delta.x
+            run = -(self.hradius**2)*delta.y
+            p2 = Point(simplify(p.x + run),
+                       simplify(p.y + rise))
+            return [Line(p, p2)]
+        else:
+            if len(self.foci) == 2:
+                f1, f2 = self.foci
+                maj = self.hradius
+                test = (2*maj -
+                        Point.distance(f1, p) -
+                        Point.distance(f2, p))
+            else:
+                test = self.radius - Point.distance(self.center, p)
+            if test.is_number and test.is_positive:
+                return []
+            # else p is outside the ellipse or we can't tell. In case of the
+            # latter, the solutions returned will only be valid if
+            # the point is not inside the ellipse; if it is, nan will result.
+            eq = self.equation(x, y)
+            dydx = idiff(eq, y, x)
+            slope = Line(p, Point(x, y)).slope
+
+            # TODO: Replace solve with solveset, when this line is tested
+            tangent_points = solve([slope - dydx, eq], [x, y])
+
+            # handle horizontal and vertical tangent lines
+            if len(tangent_points) == 1:
+                if tangent_points[0][
+                           0] == p.x or tangent_points[0][1] == p.y:
+                    return [Line(p, p + Point(1, 0)), Line(p, p + Point(0, 1))]
+                else:
+                    return [Line(p, p + Point(0, 1)), Line(p, tangent_points[0])]
+
+            # others
+            return [Line(p, tangent_points[0]), Line(p, tangent_points[1])]
+
+    @property
+    def vradius(self):
+        """The vertical radius of the ellipse.
+
+        Returns
+        =======
+
+        vradius : number
+
+        See Also
+        ========
+
+        hradius, major, minor
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.vradius
+        1
+
+        """
+        return self.args[2]
+
+
+    def second_moment_of_area(self, point=None):
+        """Returns the second moment and product moment area of an ellipse.
+
+        Parameters
+        ==========
+
+        point : Point, two-tuple of sympifiable objects, or None(default=None)
+            point is the point about which second moment of area is to be found.
+            If "point=None" it will be calculated about the axis passing through the
+            centroid of the ellipse.
+
+        Returns
+        =======
+
+        I_xx, I_yy, I_xy : number or SymPy expression
+            I_xx, I_yy are second moment of area of an ellise.
+            I_xy is product moment of area of an ellipse.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ellipse
+        >>> p1 = Point(0, 0)
+        >>> e1 = Ellipse(p1, 3, 1)
+        >>> e1.second_moment_of_area()
+        (3*pi/4, 27*pi/4, 0)
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/List_of_second_moments_of_area
+
+        """
+
+        I_xx = (S.Pi*(self.hradius)*(self.vradius**3))/4
+        I_yy = (S.Pi*(self.hradius**3)*(self.vradius))/4
+        I_xy = 0
+
+        if point is None:
+            return I_xx, I_yy, I_xy
+
+        # parallel axis theorem
+        I_xx = I_xx + self.area*((point[1] - self.center.y)**2)
+        I_yy = I_yy + self.area*((point[0] - self.center.x)**2)
+        I_xy = I_xy + self.area*(point[0] - self.center.x)*(point[1] - self.center.y)
+
+        return I_xx, I_yy, I_xy
+
+
+    def polar_second_moment_of_area(self):
+        """Returns the polar second moment of area of an Ellipse
+
+        It is a constituent of the second moment of area, linked through
+        the perpendicular axis theorem. While the planar second moment of
+        area describes an object's resistance to deflection (bending) when
+        subjected to a force applied to a plane parallel to the central
+        axis, the polar second moment of area describes an object's
+        resistance to deflection when subjected to a moment applied in a
+        plane perpendicular to the object's central axis (i.e. parallel to
+        the cross-section)
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Circle, Ellipse
+        >>> c = Circle((5, 5), 4)
+        >>> c.polar_second_moment_of_area()
+        128*pi
+        >>> a, b = symbols('a, b')
+        >>> e = Ellipse((0, 0), a, b)
+        >>> e.polar_second_moment_of_area()
+        pi*a**3*b/4 + pi*a*b**3/4
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Polar_moment_of_inertia
+
+        """
+        second_moment = self.second_moment_of_area()
+        return second_moment[0] + second_moment[1]
+
+
+    def section_modulus(self, point=None):
+        """Returns a tuple with the section modulus of an ellipse
+
+        Section modulus is a geometric property of an ellipse defined as the
+        ratio of second moment of area to the distance of the extreme end of
+        the ellipse from the centroidal axis.
+
+        Parameters
+        ==========
+
+        point : Point, two-tuple of sympifyable objects, or None(default=None)
+            point is the point at which section modulus is to be found.
+            If "point=None" section modulus will be calculated for the
+            point farthest from the centroidal axis of the ellipse.
+
+        Returns
+        =======
+
+        S_x, S_y: numbers or SymPy expressions
+                  S_x is the section modulus with respect to the x-axis
+                  S_y is the section modulus with respect to the y-axis
+                  A negative sign indicates that the section modulus is
+                  determined for a point below the centroidal axis.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Ellipse, Circle, Point2D
+        >>> d = Symbol('d', positive=True)
+        >>> c = Circle((0, 0), d/2)
+        >>> c.section_modulus()
+        (pi*d**3/32, pi*d**3/32)
+        >>> e = Ellipse(Point2D(0, 0), 2, 4)
+        >>> e.section_modulus()
+        (8*pi, 4*pi)
+        >>> e.section_modulus((2, 2))
+        (16*pi, 4*pi)
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Section_modulus
+
+        """
+        x_c, y_c = self.center
+        if point is None:
+            # taking x and y as maximum distances from centroid
+            x_min, y_min, x_max, y_max = self.bounds
+            y = max(y_c - y_min, y_max - y_c)
+            x = max(x_c - x_min, x_max - x_c)
+        else:
+            # taking x and y as distances of the given point from the center
+            point = Point2D(point)
+            y = point.y - y_c
+            x = point.x - x_c
+
+        second_moment = self.second_moment_of_area()
+        S_x = second_moment[0]/y
+        S_y = second_moment[1]/x
+
+        return S_x, S_y
+
+
+class Circle(Ellipse):
+    r"""A circle in space.
+
+    Constructed simply from a center and a radius, from three
+    non-collinear points, or the equation of a circle.
+
+    Parameters
+    ==========
+
+    center : Point
+    radius : number or SymPy expression
+    points : sequence of three Points
+    equation : equation of a circle
+
+    Attributes
+    ==========
+
+    radius (synonymous with hradius, vradius, major and minor)
+    circumference
+    equation
+
+    Raises
+    ======
+
+    GeometryError
+        When the given equation is not that of a circle.
+        When trying to construct circle from incorrect parameters.
+
+    See Also
+    ========
+
+    Ellipse, sympy.geometry.point.Point
+
+    Examples
+    ========
+
+    >>> from sympy import Point, Circle, Eq
+    >>> from sympy.abc import x, y, a, b
+
+    A circle constructed from a center and radius:
+
+    >>> c1 = Circle(Point(0, 0), 5)
+    >>> c1.hradius, c1.vradius, c1.radius
+    (5, 5, 5)
+
+    A circle constructed from three points:
+
+    >>> c2 = Circle(Point(0, 0), Point(1, 1), Point(1, 0))
+    >>> c2.hradius, c2.vradius, c2.radius, c2.center
+    (sqrt(2)/2, sqrt(2)/2, sqrt(2)/2, Point2D(1/2, 1/2))
+
+    A circle can be constructed from an equation in the form
+    `ax^2 + by^2 + gx + hy + c = 0`, too:
+
+    >>> Circle(x**2 + y**2 - 25)
+    Circle(Point2D(0, 0), 5)
+
+    If the variables corresponding to x and y are named something
+    else, their name or symbol can be supplied:
+
+    >>> Circle(Eq(a**2 + b**2, 25), x='a', y=b)
+    Circle(Point2D(0, 0), 5)
+    """
+
+    def __new__(cls, *args, **kwargs):
+        evaluate = kwargs.get('evaluate', global_parameters.evaluate)
+        if len(args) == 1 and isinstance(args[0], (Expr, Eq)):
+            x = kwargs.get('x', 'x')
+            y = kwargs.get('y', 'y')
+            equation = args[0].expand()
+            if isinstance(equation, Eq):
+                equation = equation.lhs - equation.rhs
+            x = find(x, equation)
+            y = find(y, equation)
+
+            try:
+                a, b, c, d, e = linear_coeffs(equation, x**2, y**2, x, y)
+            except ValueError:
+                raise GeometryError("The given equation is not that of a circle.")
+
+            if S.Zero in (a, b) or a != b:
+                raise GeometryError("The given equation is not that of a circle.")
+
+            center_x = -c/a/2
+            center_y = -d/b/2
+            r2 = (center_x**2) + (center_y**2) - e/a
+
+            return Circle((center_x, center_y), sqrt(r2), evaluate=evaluate)
+
+        else:
+            c, r = None, None
+            if len(args) == 3:
+                args = [Point(a, dim=2, evaluate=evaluate) for a in args]
+                t = Triangle(*args)
+                if not isinstance(t, Triangle):
+                    return t
+                c = t.circumcenter
+                r = t.circumradius
+            elif len(args) == 2:
+                # Assume (center, radius) pair
+                c = Point(args[0], dim=2, evaluate=evaluate)
+                r = args[1]
+                # this will prohibit imaginary radius
+                try:
+                    r = Point(r, 0, evaluate=evaluate).x
+                except ValueError:
+                    raise GeometryError("Circle with imaginary radius is not permitted")
+
+            if not (c is None or r is None):
+                if r == 0:
+                    return c
+                return GeometryEntity.__new__(cls, c, r, **kwargs)
+
+            raise GeometryError("Circle.__new__ received unknown arguments")
+
+    def _eval_evalf(self, prec=15, **options):
+        pt, r = self.args
+        dps = prec_to_dps(prec)
+        pt = pt.evalf(n=dps, **options)
+        r = r.evalf(n=dps, **options)
+        return self.func(pt, r, evaluate=False)
+
+    @property
+    def circumference(self):
+        """The circumference of the circle.
+
+        Returns
+        =======
+
+        circumference : number or SymPy expression
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Circle
+        >>> c1 = Circle(Point(3, 4), 6)
+        >>> c1.circumference
+        12*pi
+
+        """
+        return 2 * S.Pi * self.radius
+
+    def equation(self, x='x', y='y'):
+        """The equation of the circle.
+
+        Parameters
+        ==========
+
+        x : str or Symbol, optional
+            Default value is 'x'.
+        y : str or Symbol, optional
+            Default value is 'y'.
+
+        Returns
+        =======
+
+        equation : SymPy expression
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Circle
+        >>> c1 = Circle(Point(0, 0), 5)
+        >>> c1.equation()
+        x**2 + y**2 - 25
+
+        """
+        x = _symbol(x, real=True)
+        y = _symbol(y, real=True)
+        t1 = (x - self.center.x)**2
+        t2 = (y - self.center.y)**2
+        return t1 + t2 - self.major**2
+
+    def intersection(self, o):
+        """The intersection of this circle with another geometrical entity.
+
+        Parameters
+        ==========
+
+        o : GeometryEntity
+
+        Returns
+        =======
+
+        intersection : list of GeometryEntities
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Circle, Line, Ray
+        >>> p1, p2, p3 = Point(0, 0), Point(5, 5), Point(6, 0)
+        >>> p4 = Point(5, 0)
+        >>> c1 = Circle(p1, 5)
+        >>> c1.intersection(p2)
+        []
+        >>> c1.intersection(p4)
+        [Point2D(5, 0)]
+        >>> c1.intersection(Ray(p1, p2))
+        [Point2D(5*sqrt(2)/2, 5*sqrt(2)/2)]
+        >>> c1.intersection(Line(p2, p3))
+        []
+
+        """
+        return Ellipse.intersection(self, o)
+
+    @property
+    def radius(self):
+        """The radius of the circle.
+
+        Returns
+        =======
+
+        radius : number or SymPy expression
+
+        See Also
+        ========
+
+        Ellipse.major, Ellipse.minor, Ellipse.hradius, Ellipse.vradius
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Circle
+        >>> c1 = Circle(Point(3, 4), 6)
+        >>> c1.radius
+        6
+
+        """
+        return self.args[1]
+
+    def reflect(self, line):
+        """Override GeometryEntity.reflect since the radius
+        is not a GeometryEntity.
+
+        Examples
+        ========
+
+        >>> from sympy import Circle, Line
+        >>> Circle((0, 1), 1).reflect(Line((0, 0), (1, 1)))
+        Circle(Point2D(1, 0), -1)
+        """
+        c = self.center
+        c = c.reflect(line)
+        return self.func(c, -self.radius)
+
+    def scale(self, x=1, y=1, pt=None):
+        """Override GeometryEntity.scale since the radius
+        is not a GeometryEntity.
+
+        Examples
+        ========
+
+        >>> from sympy import Circle
+        >>> Circle((0, 0), 1).scale(2, 2)
+        Circle(Point2D(0, 0), 2)
+        >>> Circle((0, 0), 1).scale(2, 4)
+        Ellipse(Point2D(0, 0), 2, 4)
+        """
+        c = self.center
+        if pt:
+            pt = Point(pt, dim=2)
+            return self.translate(*(-pt).args).scale(x, y).translate(*pt.args)
+        c = c.scale(x, y)
+        x, y = [abs(i) for i in (x, y)]
+        if x == y:
+            return self.func(c, x*self.radius)
+        h = v = self.radius
+        return Ellipse(c, hradius=h*x, vradius=v*y)
+
+    @property
+    def vradius(self):
+        """
+        This Ellipse property is an alias for the Circle's radius.
+
+        Whereas hradius, major and minor can use Ellipse's conventions,
+        the vradius does not exist for a circle. It is always a positive
+        value in order that the Circle, like Polygons, will have an
+        area that can be positive or negative as determined by the sign
+        of the hradius.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Circle
+        >>> c1 = Circle(Point(3, 4), 6)
+        >>> c1.vradius
+        6
+        """
+        return abs(self.radius)
+
+
+from .polygon import Polygon, Triangle
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/entity.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/entity.py
new file mode 100644
index 0000000000000000000000000000000000000000..5ea1e807542c43eb955c2d778cec0f101d78bdce
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/entity.py
@@ -0,0 +1,641 @@
+"""The definition of the base geometrical entity with attributes common to
+all derived geometrical entities.
+
+Contains
+========
+
+GeometryEntity
+GeometricSet
+
+Notes
+=====
+
+A GeometryEntity is any object that has special geometric properties.
+A GeometrySet is a superclass of any GeometryEntity that can also
+be viewed as a sympy.sets.Set.  In particular, points are the only
+GeometryEntity not considered a Set.
+
+Rn is a GeometrySet representing n-dimensional Euclidean space. R2 and
+R3 are currently the only ambient spaces implemented.
+
+"""
+from __future__ import annotations
+
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.evalf import EvalfMixin, N
+from sympy.core.numbers import oo
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.trigonometric import cos, sin, atan
+from sympy.matrices import eye
+from sympy.multipledispatch import dispatch
+from sympy.printing import sstr
+from sympy.sets import Set, Union, FiniteSet
+from sympy.sets.handlers.intersection import intersection_sets
+from sympy.sets.handlers.union import union_sets
+from sympy.solvers.solvers import solve
+from sympy.utilities.misc import func_name
+from sympy.utilities.iterables import is_sequence
+
+
+# How entities are ordered; used by __cmp__ in GeometryEntity
+ordering_of_classes = [
+    "Point2D",
+    "Point3D",
+    "Point",
+    "Segment2D",
+    "Ray2D",
+    "Line2D",
+    "Segment3D",
+    "Line3D",
+    "Ray3D",
+    "Segment",
+    "Ray",
+    "Line",
+    "Plane",
+    "Triangle",
+    "RegularPolygon",
+    "Polygon",
+    "Circle",
+    "Ellipse",
+    "Curve",
+    "Parabola"
+]
+
+
+x, y = [Dummy('entity_dummy') for i in range(2)]
+T = Dummy('entity_dummy', real=True)
+
+
+class GeometryEntity(Basic, EvalfMixin):
+    """The base class for all geometrical entities.
+
+    This class does not represent any particular geometric entity, it only
+    provides the implementation of some methods common to all subclasses.
+
+    """
+
+    __slots__: tuple[str, ...] = ()
+
+    def __cmp__(self, other):
+        """Comparison of two GeometryEntities."""
+        n1 = self.__class__.__name__
+        n2 = other.__class__.__name__
+        c = (n1 > n2) - (n1 < n2)
+        if not c:
+            return 0
+
+        i1 = -1
+        for cls in self.__class__.__mro__:
+            try:
+                i1 = ordering_of_classes.index(cls.__name__)
+                break
+            except ValueError:
+                i1 = -1
+        if i1 == -1:
+            return c
+
+        i2 = -1
+        for cls in other.__class__.__mro__:
+            try:
+                i2 = ordering_of_classes.index(cls.__name__)
+                break
+            except ValueError:
+                i2 = -1
+        if i2 == -1:
+            return c
+
+        return (i1 > i2) - (i1 < i2)
+
+    def __contains__(self, other):
+        """Subclasses should implement this method for anything more complex than equality."""
+        if type(self) is type(other):
+            return self == other
+        raise NotImplementedError()
+
+    def __getnewargs__(self):
+        """Returns a tuple that will be passed to __new__ on unpickling."""
+        return tuple(self.args)
+
+    def __ne__(self, o):
+        """Test inequality of two geometrical entities."""
+        return not self == o
+
+    def __new__(cls, *args, **kwargs):
+        # Points are sequences, but they should not
+        # be converted to Tuples, so use this detection function instead.
+        def is_seq_and_not_point(a):
+            # we cannot use isinstance(a, Point) since we cannot import Point
+            if hasattr(a, 'is_Point') and a.is_Point:
+                return False
+            return is_sequence(a)
+
+        args = [Tuple(*a) if is_seq_and_not_point(a) else sympify(a) for a in args]
+        return Basic.__new__(cls, *args)
+
+    def __radd__(self, a):
+        """Implementation of reverse add method."""
+        return a.__add__(self)
+
+    def __rtruediv__(self, a):
+        """Implementation of reverse division method."""
+        return a.__truediv__(self)
+
+    def __repr__(self):
+        """String representation of a GeometryEntity that can be evaluated
+        by sympy."""
+        return type(self).__name__ + repr(self.args)
+
+    def __rmul__(self, a):
+        """Implementation of reverse multiplication method."""
+        return a.__mul__(self)
+
+    def __rsub__(self, a):
+        """Implementation of reverse subtraction method."""
+        return a.__sub__(self)
+
+    def __str__(self):
+        """String representation of a GeometryEntity."""
+        return type(self).__name__ + sstr(self.args)
+
+    def _eval_subs(self, old, new):
+        from sympy.geometry.point import Point, Point3D
+        if is_sequence(old) or is_sequence(new):
+            if isinstance(self, Point3D):
+                old = Point3D(old)
+                new = Point3D(new)
+            else:
+                old = Point(old)
+                new = Point(new)
+            return  self._subs(old, new)
+
+    def _repr_svg_(self):
+        """SVG representation of a GeometryEntity suitable for IPython"""
+
+        try:
+            bounds = self.bounds
+        except (NotImplementedError, TypeError):
+            # if we have no SVG representation, return None so IPython
+            # will fall back to the next representation
+            return None
+
+        if not all(x.is_number and x.is_finite for x in bounds):
+            return None
+
+        svg_top = '''
+            
+                
+                    
+                
+                
+                    
+                
+                
+                    
+                
+            '''
+
+        # Establish SVG canvas that will fit all the data + small space
+        xmin, ymin, xmax, ymax = map(N, bounds)
+        if xmin == xmax and ymin == ymax:
+            # This is a point; buffer using an arbitrary size
+            xmin, ymin, xmax, ymax = xmin - .5, ymin -.5, xmax + .5, ymax + .5
+        else:
+            # Expand bounds by a fraction of the data ranges
+            expand = 0.1  # or 10%; this keeps arrowheads in view (R plots use 4%)
+            widest_part = max([xmax - xmin, ymax - ymin])
+            expand_amount = widest_part * expand
+            xmin -= expand_amount
+            ymin -= expand_amount
+            xmax += expand_amount
+            ymax += expand_amount
+        dx = xmax - xmin
+        dy = ymax - ymin
+        width = min([max([100., dx]), 300])
+        height = min([max([100., dy]), 300])
+
+        scale_factor = 1. if max(width, height) == 0 else max(dx, dy) / max(width, height)
+        try:
+            svg = self._svg(scale_factor)
+        except (NotImplementedError, TypeError):
+            # if we have no SVG representation, return None so IPython
+            # will fall back to the next representation
+            return None
+
+        view_box = "{} {} {} {}".format(xmin, ymin, dx, dy)
+        transform = "matrix(1,0,0,-1,0,{})".format(ymax + ymin)
+        svg_top = svg_top.format(view_box, width, height)
+
+        return svg_top + (
+            '{}'
+            ).format(transform, svg)
+
+    def _svg(self, scale_factor=1., fill_color="#66cc99"):
+        """Returns SVG path element for the GeometryEntity.
+
+        Parameters
+        ==========
+
+        scale_factor : float
+            Multiplication factor for the SVG stroke-width.  Default is 1.
+        fill_color : str, optional
+            Hex string for fill color. Default is "#66cc99".
+        """
+        raise NotImplementedError()
+
+    def _sympy_(self):
+        return self
+
+    @property
+    def ambient_dimension(self):
+        """What is the dimension of the space that the object is contained in?"""
+        raise NotImplementedError()
+
+    @property
+    def bounds(self):
+        """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
+        rectangle for the geometric figure.
+
+        """
+
+        raise NotImplementedError()
+
+    def encloses(self, o):
+        """
+        Return True if o is inside (not on or outside) the boundaries of self.
+
+        The object will be decomposed into Points and individual Entities need
+        only define an encloses_point method for their class.
+
+        See Also
+        ========
+
+        sympy.geometry.ellipse.Ellipse.encloses_point
+        sympy.geometry.polygon.Polygon.encloses_point
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point, Polygon
+        >>> t  = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
+        >>> t2 = Polygon(*RegularPolygon(Point(0, 0), 2, 3).vertices)
+        >>> t2.encloses(t)
+        True
+        >>> t.encloses(t2)
+        False
+
+        """
+
+        from sympy.geometry.point import Point
+        from sympy.geometry.line import Segment, Ray, Line
+        from sympy.geometry.ellipse import Ellipse
+        from sympy.geometry.polygon import Polygon, RegularPolygon
+
+        if isinstance(o, Point):
+            return self.encloses_point(o)
+        elif isinstance(o, Segment):
+            return all(self.encloses_point(x) for x in o.points)
+        elif isinstance(o, (Ray, Line)):
+            return False
+        elif isinstance(o, Ellipse):
+            return self.encloses_point(o.center) and \
+                self.encloses_point(
+                Point(o.center.x + o.hradius, o.center.y)) and \
+                not self.intersection(o)
+        elif isinstance(o, Polygon):
+            if isinstance(o, RegularPolygon):
+                if not self.encloses_point(o.center):
+                    return False
+            return all(self.encloses_point(v) for v in o.vertices)
+        raise NotImplementedError()
+
+    def equals(self, o):
+        return self == o
+
+    def intersection(self, o):
+        """
+        Returns a list of all of the intersections of self with o.
+
+        Notes
+        =====
+
+        An entity is not required to implement this method.
+
+        If two different types of entities can intersect, the item with
+        higher index in ordering_of_classes should implement
+        intersections with anything having a lower index.
+
+        See Also
+        ========
+
+        sympy.geometry.util.intersection
+
+        """
+        raise NotImplementedError()
+
+    def is_similar(self, other):
+        """Is this geometrical entity similar to another geometrical entity?
+
+        Two entities are similar if a uniform scaling (enlarging or
+        shrinking) of one of the entities will allow one to obtain the other.
+
+        Notes
+        =====
+
+        This method is not intended to be used directly but rather
+        through the `are_similar` function found in util.py.
+        An entity is not required to implement this method.
+        If two different types of entities can be similar, it is only
+        required that one of them be able to determine this.
+
+        See Also
+        ========
+
+        scale
+
+        """
+        raise NotImplementedError()
+
+    def reflect(self, line):
+        """
+        Reflects an object across a line.
+
+        Parameters
+        ==========
+
+        line: Line
+
+        Examples
+        ========
+
+        >>> from sympy import pi, sqrt, Line, RegularPolygon
+        >>> l = Line((0, pi), slope=sqrt(2))
+        >>> pent = RegularPolygon((1, 2), 1, 5)
+        >>> rpent = pent.reflect(l)
+        >>> rpent
+        RegularPolygon(Point2D(-2*sqrt(2)*pi/3 - 1/3 + 4*sqrt(2)/3, 2/3 + 2*sqrt(2)/3 + 2*pi/3), -1, 5, -atan(2*sqrt(2)) + 3*pi/5)
+
+        >>> from sympy import pi, Line, Circle, Point
+        >>> l = Line((0, pi), slope=1)
+        >>> circ = Circle(Point(0, 0), 5)
+        >>> rcirc = circ.reflect(l)
+        >>> rcirc
+        Circle(Point2D(-pi, pi), -5)
+
+        """
+        from sympy.geometry.point import Point
+
+        g = self
+        l = line
+        o = Point(0, 0)
+        if l.slope.is_zero:
+            v = l.args[0].y
+            if not v:  # x-axis
+                return g.scale(y=-1)
+            reps = [(p, p.translate(y=2*(v - p.y))) for p in g.atoms(Point)]
+        elif l.slope is oo:
+            v = l.args[0].x
+            if not v:  # y-axis
+                return g.scale(x=-1)
+            reps = [(p, p.translate(x=2*(v - p.x))) for p in g.atoms(Point)]
+        else:
+            if not hasattr(g, 'reflect') and not all(
+                    isinstance(arg, Point) for arg in g.args):
+                raise NotImplementedError(
+                    'reflect undefined or non-Point args in %s' % g)
+            a = atan(l.slope)
+            c = l.coefficients
+            d = -c[-1]/c[1]  # y-intercept
+            # apply the transform to a single point
+            xf = Point(x, y)
+            xf = xf.translate(y=-d).rotate(-a, o).scale(y=-1
+                ).rotate(a, o).translate(y=d)
+            # replace every point using that transform
+            reps = [(p, xf.xreplace({x: p.x, y: p.y})) for p in g.atoms(Point)]
+        return g.xreplace(dict(reps))
+
+    def rotate(self, angle, pt=None):
+        """Rotate ``angle`` radians counterclockwise about Point ``pt``.
+
+        The default pt is the origin, Point(0, 0)
+
+        See Also
+        ========
+
+        scale, translate
+
+        Examples
+        ========
+
+        >>> from sympy import Point, RegularPolygon, Polygon, pi
+        >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
+        >>> t # vertex on x axis
+        Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2))
+        >>> t.rotate(pi/2) # vertex on y axis now
+        Triangle(Point2D(0, 1), Point2D(-sqrt(3)/2, -1/2), Point2D(sqrt(3)/2, -1/2))
+
+        """
+        newargs = []
+        for a in self.args:
+            if isinstance(a, GeometryEntity):
+                newargs.append(a.rotate(angle, pt))
+            else:
+                newargs.append(a)
+        return type(self)(*newargs)
+
+    def scale(self, x=1, y=1, pt=None):
+        """Scale the object by multiplying the x,y-coordinates by x and y.
+
+        If pt is given, the scaling is done relative to that point; the
+        object is shifted by -pt, scaled, and shifted by pt.
+
+        See Also
+        ========
+
+        rotate, translate
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point, Polygon
+        >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
+        >>> t
+        Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2))
+        >>> t.scale(2)
+        Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)/2), Point2D(-1, -sqrt(3)/2))
+        >>> t.scale(2, 2)
+        Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)), Point2D(-1, -sqrt(3)))
+
+        """
+        from sympy.geometry.point import Point
+        if pt:
+            pt = Point(pt, dim=2)
+            return self.translate(*(-pt).args).scale(x, y).translate(*pt.args)
+        return type(self)(*[a.scale(x, y) for a in self.args])  # if this fails, override this class
+
+    def translate(self, x=0, y=0):
+        """Shift the object by adding to the x,y-coordinates the values x and y.
+
+        See Also
+        ========
+
+        rotate, scale
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point, Polygon
+        >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
+        >>> t
+        Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2))
+        >>> t.translate(2)
+        Triangle(Point2D(3, 0), Point2D(3/2, sqrt(3)/2), Point2D(3/2, -sqrt(3)/2))
+        >>> t.translate(2, 2)
+        Triangle(Point2D(3, 2), Point2D(3/2, sqrt(3)/2 + 2), Point2D(3/2, 2 - sqrt(3)/2))
+
+        """
+        newargs = []
+        for a in self.args:
+            if isinstance(a, GeometryEntity):
+                newargs.append(a.translate(x, y))
+            else:
+                newargs.append(a)
+        return self.func(*newargs)
+
+    def parameter_value(self, other, t):
+        """Return the parameter corresponding to the given point.
+        Evaluating an arbitrary point of the entity at this parameter
+        value will return the given point.
+
+        Examples
+        ========
+
+        >>> from sympy import Line, Point
+        >>> from sympy.abc import t
+        >>> a = Point(0, 0)
+        >>> b = Point(2, 2)
+        >>> Line(a, b).parameter_value((1, 1), t)
+        {t: 1/2}
+        >>> Line(a, b).arbitrary_point(t).subs(_)
+        Point2D(1, 1)
+        """
+        from sympy.geometry.point import Point
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if not isinstance(other, Point):
+            raise ValueError("other must be a point")
+        sol = solve(self.arbitrary_point(T) - other, T, dict=True)
+        if not sol:
+            raise ValueError("Given point is not on %s" % func_name(self))
+        return {t: sol[0][T]}
+
+
+class GeometrySet(GeometryEntity, Set):
+    """Parent class of all GeometryEntity that are also Sets
+    (compatible with sympy.sets)
+    """
+    __slots__ = ()
+
+    def _contains(self, other):
+        """sympy.sets uses the _contains method, so include it for compatibility."""
+
+        if isinstance(other, Set) and other.is_FiniteSet:
+            return all(self.__contains__(i) for i in other)
+
+        return self.__contains__(other)
+
+@dispatch(GeometrySet, Set)  # type:ignore # noqa:F811
+def union_sets(self, o): # noqa:F811
+    """ Returns the union of self and o
+    for use with sympy.sets.Set, if possible. """
+
+
+    # if its a FiniteSet, merge any points
+    # we contain and return a union with the rest
+    if o.is_FiniteSet:
+        other_points = [p for p in o if not self._contains(p)]
+        if len(other_points) == len(o):
+            return None
+        return Union(self, FiniteSet(*other_points))
+    if self._contains(o):
+        return self
+    return None
+
+
+@dispatch(GeometrySet, Set)  # type: ignore # noqa:F811
+def intersection_sets(self, o): # noqa:F811
+    """ Returns a sympy.sets.Set of intersection objects,
+    if possible. """
+
+    from sympy.geometry.point import Point
+
+    try:
+        # if o is a FiniteSet, find the intersection directly
+        # to avoid infinite recursion
+        if o.is_FiniteSet:
+            inter = FiniteSet(*(p for p in o if self.contains(p)))
+        else:
+            inter = self.intersection(o)
+    except NotImplementedError:
+        # sympy.sets.Set.reduce expects None if an object
+        # doesn't know how to simplify
+        return None
+
+    # put the points in a FiniteSet
+    points = FiniteSet(*[p for p in inter if isinstance(p, Point)])
+    non_points = [p for p in inter if not isinstance(p, Point)]
+
+    return Union(*(non_points + [points]))
+
+def translate(x, y):
+    """Return the matrix to translate a 2-D point by x and y."""
+    rv = eye(3)
+    rv[2, 0] = x
+    rv[2, 1] = y
+    return rv
+
+
+def scale(x, y, pt=None):
+    """Return the matrix to multiply a 2-D point's coordinates by x and y.
+
+    If pt is given, the scaling is done relative to that point."""
+    rv = eye(3)
+    rv[0, 0] = x
+    rv[1, 1] = y
+    if pt:
+        from sympy.geometry.point import Point
+        pt = Point(pt, dim=2)
+        tr1 = translate(*(-pt).args)
+        tr2 = translate(*pt.args)
+        return tr1*rv*tr2
+    return rv
+
+
+def rotate(th):
+    """Return the matrix to rotate a 2-D point about the origin by ``angle``.
+
+    The angle is measured in radians. To Point a point about a point other
+    then the origin, translate the Point, do the rotation, and
+    translate it back:
+
+    >>> from sympy.geometry.entity import rotate, translate
+    >>> from sympy import Point, pi
+    >>> rot_about_11 = translate(-1, -1)*rotate(pi/2)*translate(1, 1)
+    >>> Point(1, 1).transform(rot_about_11)
+    Point2D(1, 1)
+    >>> Point(0, 0).transform(rot_about_11)
+    Point2D(2, 0)
+    """
+    s = sin(th)
+    rv = eye(3)*cos(th)
+    rv[0, 1] = s
+    rv[1, 0] = -s
+    rv[2, 2] = 1
+    return rv
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/exceptions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/exceptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..41d97af718de2cebad3accefcd60e43ccf74a3f6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/exceptions.py
@@ -0,0 +1,5 @@
+"""Geometry Errors."""
+
+class GeometryError(ValueError):
+    """An exception raised by classes in the geometry module."""
+    pass
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/line.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/line.py
new file mode 100644
index 0000000000000000000000000000000000000000..ed73d43d0c9581f9d51f299cf4425acb11958e57
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/line.py
@@ -0,0 +1,2877 @@
+"""Line-like geometrical entities.
+
+Contains
+========
+LinearEntity
+Line
+Ray
+Segment
+LinearEntity2D
+Line2D
+Ray2D
+Segment2D
+LinearEntity3D
+Line3D
+Ray3D
+Segment3D
+
+"""
+
+from sympy.core.containers import Tuple
+from sympy.core.evalf import N
+from sympy.core.expr import Expr
+from sympy.core.numbers import Rational, oo, Float
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.sorting import ordered
+from sympy.core.symbol import _symbol, Dummy, uniquely_named_symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (_pi_coeff, acos, tan, atan2)
+from .entity import GeometryEntity, GeometrySet
+from .exceptions import GeometryError
+from .point import Point, Point3D
+from .util import find, intersection
+from sympy.logic.boolalg import And
+from sympy.matrices import Matrix
+from sympy.sets.sets import Intersection
+from sympy.simplify.simplify import simplify
+from sympy.solvers.solvers import solve
+from sympy.solvers.solveset import linear_coeffs
+from sympy.utilities.misc import Undecidable, filldedent
+
+
+import random
+
+
+t, u = [Dummy('line_dummy') for i in range(2)]
+
+
+class LinearEntity(GeometrySet):
+    """A base class for all linear entities (Line, Ray and Segment)
+    in n-dimensional Euclidean space.
+
+    Attributes
+    ==========
+
+    ambient_dimension
+    direction
+    length
+    p1
+    p2
+    points
+
+    Notes
+    =====
+
+    This is an abstract class and is not meant to be instantiated.
+
+    See Also
+    ========
+
+    sympy.geometry.entity.GeometryEntity
+
+    """
+    def __new__(cls, p1, p2=None, **kwargs):
+        p1, p2 = Point._normalize_dimension(p1, p2)
+        if p1 == p2:
+            # sometimes we return a single point if we are not given two unique
+            # points. This is done in the specific subclass
+            raise ValueError(
+                "%s.__new__ requires two unique Points." % cls.__name__)
+        if len(p1) != len(p2):
+            raise ValueError(
+                "%s.__new__ requires two Points of equal dimension." % cls.__name__)
+
+        return GeometryEntity.__new__(cls, p1, p2, **kwargs)
+
+    def __contains__(self, other):
+        """Return a definitive answer or else raise an error if it cannot
+        be determined that other is on the boundaries of self."""
+        result = self.contains(other)
+
+        if result is not None:
+            return result
+        else:
+            raise Undecidable(
+                "Cannot decide whether '%s' contains '%s'" % (self, other))
+
+    def _span_test(self, other):
+        """Test whether the point `other` lies in the positive span of `self`.
+        A point x is 'in front' of a point y if x.dot(y) >= 0.  Return
+        -1 if `other` is behind `self.p1`, 0 if `other` is `self.p1` and
+        and 1 if `other` is in front of `self.p1`."""
+        if self.p1 == other:
+            return 0
+
+        rel_pos = other - self.p1
+        d = self.direction
+        if d.dot(rel_pos) > 0:
+            return 1
+        return -1
+
+    @property
+    def ambient_dimension(self):
+        """A property method that returns the dimension of LinearEntity
+        object.
+
+        Parameters
+        ==========
+
+        p1 : LinearEntity
+
+        Returns
+        =======
+
+        dimension : integer
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(1, 1)
+        >>> l1 = Line(p1, p2)
+        >>> l1.ambient_dimension
+        2
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0, 0), Point(1, 1, 1)
+        >>> l1 = Line(p1, p2)
+        >>> l1.ambient_dimension
+        3
+
+        """
+        return len(self.p1)
+
+    def angle_between(l1, l2):
+        """Return the non-reflex angle formed by rays emanating from
+        the origin with directions the same as the direction vectors
+        of the linear entities.
+
+        Parameters
+        ==========
+
+        l1 : LinearEntity
+        l2 : LinearEntity
+
+        Returns
+        =======
+
+        angle : angle in radians
+
+        Notes
+        =====
+
+        From the dot product of vectors v1 and v2 it is known that:
+
+            ``dot(v1, v2) = |v1|*|v2|*cos(A)``
+
+        where A is the angle formed between the two vectors. We can
+        get the directional vectors of the two lines and readily
+        find the angle between the two using the above formula.
+
+        See Also
+        ========
+
+        is_perpendicular, Ray2D.closing_angle
+
+        Examples
+        ========
+
+        >>> from sympy import Line
+        >>> e = Line((0, 0), (1, 0))
+        >>> ne = Line((0, 0), (1, 1))
+        >>> sw = Line((1, 1), (0, 0))
+        >>> ne.angle_between(e)
+        pi/4
+        >>> sw.angle_between(e)
+        3*pi/4
+
+        To obtain the non-obtuse angle at the intersection of lines, use
+        the ``smallest_angle_between`` method:
+
+        >>> sw.smallest_angle_between(e)
+        pi/4
+
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(-1, 2, 0)
+        >>> l1, l2 = Line3D(p1, p2), Line3D(p2, p3)
+        >>> l1.angle_between(l2)
+        acos(-sqrt(2)/3)
+        >>> l1.smallest_angle_between(l2)
+        acos(sqrt(2)/3)
+        """
+        if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity):
+            raise TypeError('Must pass only LinearEntity objects')
+
+        v1, v2 = l1.direction, l2.direction
+        return acos(v1.dot(v2)/(abs(v1)*abs(v2)))
+
+    def smallest_angle_between(l1, l2):
+        """Return the smallest angle formed at the intersection of the
+        lines containing the linear entities.
+
+        Parameters
+        ==========
+
+        l1 : LinearEntity
+        l2 : LinearEntity
+
+        Returns
+        =======
+
+        angle : angle in radians
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2, p3 = Point(0, 0), Point(0, 4), Point(2, -2)
+        >>> l1, l2 = Line(p1, p2), Line(p1, p3)
+        >>> l1.smallest_angle_between(l2)
+        pi/4
+
+        See Also
+        ========
+
+        angle_between, is_perpendicular, Ray2D.closing_angle
+        """
+        if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity):
+            raise TypeError('Must pass only LinearEntity objects')
+
+        v1, v2 = l1.direction, l2.direction
+        return acos(abs(v1.dot(v2))/(abs(v1)*abs(v2)))
+
+    def arbitrary_point(self, parameter='t'):
+        """A parameterized point on the Line.
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            The name of the parameter which will be used for the parametric
+            point. The default value is 't'. When this parameter is 0, the
+            first point used to define the line will be returned, and when
+            it is 1 the second point will be returned.
+
+        Returns
+        =======
+
+        point : Point
+
+        Raises
+        ======
+
+        ValueError
+            When ``parameter`` already appears in the Line's definition.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(1, 0), Point(5, 3)
+        >>> l1 = Line(p1, p2)
+        >>> l1.arbitrary_point()
+        Point2D(4*t + 1, 3*t)
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2 = Point3D(1, 0, 0), Point3D(5, 3, 1)
+        >>> l1 = Line3D(p1, p2)
+        >>> l1.arbitrary_point()
+        Point3D(4*t + 1, 3*t, t)
+
+        """
+        t = _symbol(parameter, real=True)
+        if t.name in (f.name for f in self.free_symbols):
+            raise ValueError(filldedent('''
+                Symbol %s already appears in object
+                and cannot be used as a parameter.
+                ''' % t.name))
+        # multiply on the right so the variable gets
+        # combined with the coordinates of the point
+        return self.p1 + (self.p2 - self.p1)*t
+
+    @staticmethod
+    def are_concurrent(*lines):
+        """Is a sequence of linear entities concurrent?
+
+        Two or more linear entities are concurrent if they all
+        intersect at a single point.
+
+        Parameters
+        ==========
+
+        lines
+            A sequence of linear entities.
+
+        Returns
+        =======
+
+        True : if the set of linear entities intersect in one point
+        False : otherwise.
+
+        See Also
+        ========
+
+        sympy.geometry.util.intersection
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(3, 5)
+        >>> p3, p4 = Point(-2, -2), Point(0, 2)
+        >>> l1, l2, l3 = Line(p1, p2), Line(p1, p3), Line(p1, p4)
+        >>> Line.are_concurrent(l1, l2, l3)
+        True
+        >>> l4 = Line(p2, p3)
+        >>> Line.are_concurrent(l2, l3, l4)
+        False
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(3, 5, 2)
+        >>> p3, p4 = Point3D(-2, -2, -2), Point3D(0, 2, 1)
+        >>> l1, l2, l3 = Line3D(p1, p2), Line3D(p1, p3), Line3D(p1, p4)
+        >>> Line3D.are_concurrent(l1, l2, l3)
+        True
+        >>> l4 = Line3D(p2, p3)
+        >>> Line3D.are_concurrent(l2, l3, l4)
+        False
+
+        """
+        common_points = Intersection(*lines)
+        if common_points.is_FiniteSet and len(common_points) == 1:
+            return True
+        return False
+
+    def contains(self, other):
+        """Subclasses should implement this method and should return
+            True if other is on the boundaries of self;
+            False if not on the boundaries of self;
+            None if a determination cannot be made."""
+        raise NotImplementedError()
+
+    @property
+    def direction(self):
+        """The direction vector of the LinearEntity.
+
+        Returns
+        =======
+
+        p : a Point; the ray from the origin to this point is the
+            direction of `self`
+
+        Examples
+        ========
+
+        >>> from sympy import Line
+        >>> a, b = (1, 1), (1, 3)
+        >>> Line(a, b).direction
+        Point2D(0, 2)
+        >>> Line(b, a).direction
+        Point2D(0, -2)
+
+        This can be reported so the distance from the origin is 1:
+
+        >>> Line(b, a).direction.unit
+        Point2D(0, -1)
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.unit
+
+        """
+        return self.p2 - self.p1
+
+    def intersection(self, other):
+        """The intersection with another geometrical entity.
+
+        Parameters
+        ==========
+
+        o : Point or LinearEntity
+
+        Returns
+        =======
+
+        intersection : list of geometrical entities
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line, Segment
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(7, 7)
+        >>> l1 = Line(p1, p2)
+        >>> l1.intersection(p3)
+        [Point2D(7, 7)]
+        >>> p4, p5 = Point(5, 0), Point(0, 3)
+        >>> l2 = Line(p4, p5)
+        >>> l1.intersection(l2)
+        [Point2D(15/8, 15/8)]
+        >>> p6, p7 = Point(0, 5), Point(2, 6)
+        >>> s1 = Segment(p6, p7)
+        >>> l1.intersection(s1)
+        []
+        >>> from sympy import Point3D, Line3D, Segment3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(7, 7, 7)
+        >>> l1 = Line3D(p1, p2)
+        >>> l1.intersection(p3)
+        [Point3D(7, 7, 7)]
+        >>> l1 = Line3D(Point3D(4,19,12), Point3D(5,25,17))
+        >>> l2 = Line3D(Point3D(-3, -15, -19), direction_ratio=[2,8,8])
+        >>> l1.intersection(l2)
+        [Point3D(1, 1, -3)]
+        >>> p6, p7 = Point3D(0, 5, 2), Point3D(2, 6, 3)
+        >>> s1 = Segment3D(p6, p7)
+        >>> l1.intersection(s1)
+        []
+
+        """
+        def intersect_parallel_rays(ray1, ray2):
+            if ray1.direction.dot(ray2.direction) > 0:
+                # rays point in the same direction
+                # so return the one that is "in front"
+                return [ray2] if ray1._span_test(ray2.p1) >= 0 else [ray1]
+            else:
+                # rays point in opposite directions
+                st = ray1._span_test(ray2.p1)
+                if st < 0:
+                    return []
+                elif st == 0:
+                    return [ray2.p1]
+                return [Segment(ray1.p1, ray2.p1)]
+
+        def intersect_parallel_ray_and_segment(ray, seg):
+            st1, st2 = ray._span_test(seg.p1), ray._span_test(seg.p2)
+            if st1 < 0 and st2 < 0:
+                return []
+            elif st1 >= 0 and st2 >= 0:
+                return [seg]
+            elif st1 >= 0:  # st2 < 0:
+                return [Segment(ray.p1, seg.p1)]
+            else:  # st1 < 0 and st2 >= 0:
+                return [Segment(ray.p1, seg.p2)]
+
+        def intersect_parallel_segments(seg1, seg2):
+            if seg1.contains(seg2):
+                return [seg2]
+            if seg2.contains(seg1):
+                return [seg1]
+
+            # direct the segments so they're oriented the same way
+            if seg1.direction.dot(seg2.direction) < 0:
+                seg2 = Segment(seg2.p2, seg2.p1)
+            # order the segments so seg1 is "behind" seg2
+            if seg1._span_test(seg2.p1) < 0:
+                seg1, seg2 = seg2, seg1
+            if seg2._span_test(seg1.p2) < 0:
+                return []
+            return [Segment(seg2.p1, seg1.p2)]
+
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if other.is_Point:
+            if self.contains(other):
+                return [other]
+            else:
+                return []
+        elif isinstance(other, LinearEntity):
+            # break into cases based on whether
+            # the lines are parallel, non-parallel intersecting, or skew
+            pts = Point._normalize_dimension(self.p1, self.p2, other.p1, other.p2)
+            rank = Point.affine_rank(*pts)
+
+            if rank == 1:
+                # we're collinear
+                if isinstance(self, Line):
+                    return [other]
+                if isinstance(other, Line):
+                    return [self]
+
+                if isinstance(self, Ray) and isinstance(other, Ray):
+                    return intersect_parallel_rays(self, other)
+                if isinstance(self, Ray) and isinstance(other, Segment):
+                    return intersect_parallel_ray_and_segment(self, other)
+                if isinstance(self, Segment) and isinstance(other, Ray):
+                    return intersect_parallel_ray_and_segment(other, self)
+                if isinstance(self, Segment) and isinstance(other, Segment):
+                    return intersect_parallel_segments(self, other)
+            elif rank == 2:
+                # we're in the same plane
+                l1 = Line(*pts[:2])
+                l2 = Line(*pts[2:])
+
+                # check to see if we're parallel.  If we are, we can't
+                # be intersecting, since the collinear case was already
+                # handled
+                if l1.direction.is_scalar_multiple(l2.direction):
+                    return []
+
+                # find the intersection as if everything were lines
+                # by solving the equation t*d + p1 == s*d' + p1'
+                m = Matrix([l1.direction, -l2.direction]).transpose()
+                v = Matrix([l2.p1 - l1.p1]).transpose()
+
+                # we cannot use m.solve(v) because that only works for square matrices
+                m_rref, pivots = m.col_insert(2, v).rref(simplify=True)
+                # rank == 2 ensures we have 2 pivots, but let's check anyway
+                if len(pivots) != 2:
+                    raise GeometryError("Failed when solving Mx=b when M={} and b={}".format(m, v))
+                coeff = m_rref[0, 2]
+                line_intersection = l1.direction*coeff + self.p1
+
+                # if both are lines, skip a containment check
+                if isinstance(self, Line) and isinstance(other, Line):
+                    return [line_intersection]
+
+                if ((isinstance(self, Line) or
+                     self.contains(line_intersection)) and
+                        other.contains(line_intersection)):
+                    return [line_intersection]
+                if not self.atoms(Float) and not other.atoms(Float):
+                    # if it can fail when there are no Floats then
+                    # maybe the following parametric check should be
+                    # done
+                    return []
+                # floats may fail exact containment so check that the
+                # arbitrary points, when  equal, both give a
+                # non-negative parameter when the arbitrary point
+                # coordinates are equated
+                tu = solve(self.arbitrary_point(t) - other.arbitrary_point(u),
+                    t, u, dict=True)[0]
+                def ok(p, l):
+                    if isinstance(l, Line):
+                        # p > -oo
+                        return True
+                    if isinstance(l, Ray):
+                        # p >= 0
+                        return p.is_nonnegative
+                    if isinstance(l, Segment):
+                        # 0 <= p <= 1
+                        return p.is_nonnegative and (1 - p).is_nonnegative
+                    raise ValueError("unexpected line type")
+                if ok(tu[t], self) and ok(tu[u], other):
+                    return [line_intersection]
+                return []
+            else:
+                # we're skew
+                return []
+
+        return other.intersection(self)
+
+    def is_parallel(l1, l2):
+        """Are two linear entities parallel?
+
+        Parameters
+        ==========
+
+        l1 : LinearEntity
+        l2 : LinearEntity
+
+        Returns
+        =======
+
+        True : if l1 and l2 are parallel,
+        False : otherwise.
+
+        See Also
+        ========
+
+        coefficients
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(1, 1)
+        >>> p3, p4 = Point(3, 4), Point(6, 7)
+        >>> l1, l2 = Line(p1, p2), Line(p3, p4)
+        >>> Line.is_parallel(l1, l2)
+        True
+        >>> p5 = Point(6, 6)
+        >>> l3 = Line(p3, p5)
+        >>> Line.is_parallel(l1, l3)
+        False
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(3, 4, 5)
+        >>> p3, p4 = Point3D(2, 1, 1), Point3D(8, 9, 11)
+        >>> l1, l2 = Line3D(p1, p2), Line3D(p3, p4)
+        >>> Line3D.is_parallel(l1, l2)
+        True
+        >>> p5 = Point3D(6, 6, 6)
+        >>> l3 = Line3D(p3, p5)
+        >>> Line3D.is_parallel(l1, l3)
+        False
+
+        """
+        if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity):
+            raise TypeError('Must pass only LinearEntity objects')
+
+        return l1.direction.is_scalar_multiple(l2.direction)
+
+    def is_perpendicular(l1, l2):
+        """Are two linear entities perpendicular?
+
+        Parameters
+        ==========
+
+        l1 : LinearEntity
+        l2 : LinearEntity
+
+        Returns
+        =======
+
+        True : if l1 and l2 are perpendicular,
+        False : otherwise.
+
+        See Also
+        ========
+
+        coefficients
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(-1, 1)
+        >>> l1, l2 = Line(p1, p2), Line(p1, p3)
+        >>> l1.is_perpendicular(l2)
+        True
+        >>> p4 = Point(5, 3)
+        >>> l3 = Line(p1, p4)
+        >>> l1.is_perpendicular(l3)
+        False
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(-1, 2, 0)
+        >>> l1, l2 = Line3D(p1, p2), Line3D(p2, p3)
+        >>> l1.is_perpendicular(l2)
+        False
+        >>> p4 = Point3D(5, 3, 7)
+        >>> l3 = Line3D(p1, p4)
+        >>> l1.is_perpendicular(l3)
+        False
+
+        """
+        if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity):
+            raise TypeError('Must pass only LinearEntity objects')
+
+        return S.Zero.equals(l1.direction.dot(l2.direction))
+
+    def is_similar(self, other):
+        """
+        Return True if self and other are contained in the same line.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2, p3 = Point(0, 1), Point(3, 4), Point(2, 3)
+        >>> l1 = Line(p1, p2)
+        >>> l2 = Line(p1, p3)
+        >>> l1.is_similar(l2)
+        True
+        """
+        l = Line(self.p1, self.p2)
+        return l.contains(other)
+
+    @property
+    def length(self):
+        """
+        The length of the line.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(3, 5)
+        >>> l1 = Line(p1, p2)
+        >>> l1.length
+        oo
+        """
+        return S.Infinity
+
+    @property
+    def p1(self):
+        """The first defining point of a linear entity.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(5, 3)
+        >>> l = Line(p1, p2)
+        >>> l.p1
+        Point2D(0, 0)
+
+        """
+        return self.args[0]
+
+    @property
+    def p2(self):
+        """The second defining point of a linear entity.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(5, 3)
+        >>> l = Line(p1, p2)
+        >>> l.p2
+        Point2D(5, 3)
+
+        """
+        return self.args[1]
+
+    def parallel_line(self, p):
+        """Create a new Line parallel to this linear entity which passes
+        through the point `p`.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        line : Line
+
+        See Also
+        ========
+
+        is_parallel
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2, p3 = Point(0, 0), Point(2, 3), Point(-2, 2)
+        >>> l1 = Line(p1, p2)
+        >>> l2 = l1.parallel_line(p3)
+        >>> p3 in l2
+        True
+        >>> l1.is_parallel(l2)
+        True
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(2, 3, 4), Point3D(-2, 2, 0)
+        >>> l1 = Line3D(p1, p2)
+        >>> l2 = l1.parallel_line(p3)
+        >>> p3 in l2
+        True
+        >>> l1.is_parallel(l2)
+        True
+
+        """
+        p = Point(p, dim=self.ambient_dimension)
+        return Line(p, p + self.direction)
+
+    def perpendicular_line(self, p):
+        """Create a new Line perpendicular to this linear entity which passes
+        through the point `p`.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        line : Line
+
+        See Also
+        ========
+
+        sympy.geometry.line.LinearEntity.is_perpendicular, perpendicular_segment
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(2, 3, 4), Point3D(-2, 2, 0)
+        >>> L = Line3D(p1, p2)
+        >>> P = L.perpendicular_line(p3); P
+        Line3D(Point3D(-2, 2, 0), Point3D(4/29, 6/29, 8/29))
+        >>> L.is_perpendicular(P)
+        True
+
+        In 3D the, the first point used to define the line is the point
+        through which the perpendicular was required to pass; the
+        second point is (arbitrarily) contained in the given line:
+
+        >>> P.p2 in L
+        True
+        """
+        p = Point(p, dim=self.ambient_dimension)
+        if p in self:
+            p = p + self.direction.orthogonal_direction
+        return Line(p, self.projection(p))
+
+    def perpendicular_segment(self, p):
+        """Create a perpendicular line segment from `p` to this line.
+
+        The endpoints of the segment are ``p`` and the closest point in
+        the line containing self. (If self is not a line, the point might
+        not be in self.)
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        segment : Segment
+
+        Notes
+        =====
+
+        Returns `p` itself if `p` is on this linear entity.
+
+        See Also
+        ========
+
+        perpendicular_line
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, 2)
+        >>> l1 = Line(p1, p2)
+        >>> s1 = l1.perpendicular_segment(p3)
+        >>> l1.is_perpendicular(s1)
+        True
+        >>> p3 in s1
+        True
+        >>> l1.perpendicular_segment(Point(4, 0))
+        Segment2D(Point2D(4, 0), Point2D(2, 2))
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, 2, 0)
+        >>> l1 = Line3D(p1, p2)
+        >>> s1 = l1.perpendicular_segment(p3)
+        >>> l1.is_perpendicular(s1)
+        True
+        >>> p3 in s1
+        True
+        >>> l1.perpendicular_segment(Point3D(4, 0, 0))
+        Segment3D(Point3D(4, 0, 0), Point3D(4/3, 4/3, 4/3))
+
+        """
+        p = Point(p, dim=self.ambient_dimension)
+        if p in self:
+            return p
+        l = self.perpendicular_line(p)
+        # The intersection should be unique, so unpack the singleton
+        p2, = Intersection(Line(self.p1, self.p2), l)
+
+        return Segment(p, p2)
+
+    @property
+    def points(self):
+        """The two points used to define this linear entity.
+
+        Returns
+        =======
+
+        points : tuple of Points
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(5, 11)
+        >>> l1 = Line(p1, p2)
+        >>> l1.points
+        (Point2D(0, 0), Point2D(5, 11))
+
+        """
+        return (self.p1, self.p2)
+
+    def projection(self, other):
+        """Project a point, line, ray, or segment onto this linear entity.
+
+        Parameters
+        ==========
+
+        other : Point or LinearEntity (Line, Ray, Segment)
+
+        Returns
+        =======
+
+        projection : Point or LinearEntity (Line, Ray, Segment)
+            The return type matches the type of the parameter ``other``.
+
+        Raises
+        ======
+
+        GeometryError
+            When method is unable to perform projection.
+
+        Notes
+        =====
+
+        A projection involves taking the two points that define
+        the linear entity and projecting those points onto a
+        Line and then reforming the linear entity using these
+        projections.
+        A point P is projected onto a line L by finding the point
+        on L that is closest to P. This point is the intersection
+        of L and the line perpendicular to L that passes through P.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, perpendicular_line
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line, Segment, Rational
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(Rational(1, 2), 0)
+        >>> l1 = Line(p1, p2)
+        >>> l1.projection(p3)
+        Point2D(1/4, 1/4)
+        >>> p4, p5 = Point(10, 0), Point(12, 1)
+        >>> s1 = Segment(p4, p5)
+        >>> l1.projection(s1)
+        Segment2D(Point2D(5, 5), Point2D(13/2, 13/2))
+        >>> p1, p2, p3 = Point(0, 0, 1), Point(1, 1, 2), Point(2, 0, 1)
+        >>> l1 = Line(p1, p2)
+        >>> l1.projection(p3)
+        Point3D(2/3, 2/3, 5/3)
+        >>> p4, p5 = Point(10, 0, 1), Point(12, 1, 3)
+        >>> s1 = Segment(p4, p5)
+        >>> l1.projection(s1)
+        Segment3D(Point3D(10/3, 10/3, 13/3), Point3D(5, 5, 6))
+
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+
+        def proj_point(p):
+            return Point.project(p - self.p1, self.direction) + self.p1
+
+        if isinstance(other, Point):
+            return proj_point(other)
+        elif isinstance(other, LinearEntity):
+            p1, p2 = proj_point(other.p1), proj_point(other.p2)
+            # test to see if we're degenerate
+            if p1 == p2:
+                return p1
+            projected = other.__class__(p1, p2)
+            projected = Intersection(self, projected)
+            if projected.is_empty:
+                return projected
+            # if we happen to have intersected in only a point, return that
+            if projected.is_FiniteSet and len(projected) == 1:
+                # projected is a set of size 1, so unpack it in `a`
+                a, = projected
+                return a
+            # order args so projection is in the same direction as self
+            if self.direction.dot(projected.direction) < 0:
+                p1, p2 = projected.args
+                projected = projected.func(p2, p1)
+            return projected
+
+        raise GeometryError(
+            "Do not know how to project %s onto %s" % (other, self))
+
+    def random_point(self, seed=None):
+        """A random point on a LinearEntity.
+
+        Returns
+        =======
+
+        point : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line, Ray, Segment
+        >>> p1, p2 = Point(0, 0), Point(5, 3)
+        >>> line = Line(p1, p2)
+        >>> r = line.random_point(seed=42)  # seed value is optional
+        >>> r.n(3)
+        Point2D(-0.72, -0.432)
+        >>> r in line
+        True
+        >>> Ray(p1, p2).random_point(seed=42).n(3)
+        Point2D(0.72, 0.432)
+        >>> Segment(p1, p2).random_point(seed=42).n(3)
+        Point2D(3.2, 1.92)
+
+        """
+        if seed is not None:
+            rng = random.Random(seed)
+        else:
+            rng = random
+        pt = self.arbitrary_point(t)
+        if isinstance(self, Ray):
+            v = abs(rng.gauss(0, 1))
+        elif isinstance(self, Segment):
+            v = rng.random()
+        elif isinstance(self, Line):
+            v = rng.gauss(0, 1)
+        else:
+            raise NotImplementedError('unhandled line type')
+        return pt.subs(t, Rational(v))
+
+    def bisectors(self, other):
+        """Returns the perpendicular lines which pass through the intersections
+        of self and other that are in the same plane.
+
+        Parameters
+        ==========
+
+        line : Line3D
+
+        Returns
+        =======
+
+        list: two Line instances
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D
+        >>> r1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))
+        >>> r2 = Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))
+        >>> r1.bisectors(r2)
+        [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 0)), Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))]
+
+        """
+        if not isinstance(other, LinearEntity):
+            raise GeometryError("Expecting LinearEntity, not %s" % other)
+
+        l1, l2 = self, other
+
+        # make sure dimensions match or else a warning will rise from
+        # intersection calculation
+        if l1.p1.ambient_dimension != l2.p1.ambient_dimension:
+            if isinstance(l1, Line2D):
+                l1, l2 = l2, l1
+            _, p1 = Point._normalize_dimension(l1.p1, l2.p1, on_morph='ignore')
+            _, p2 = Point._normalize_dimension(l1.p2, l2.p2, on_morph='ignore')
+            l2 = Line(p1, p2)
+
+        point = intersection(l1, l2)
+
+        # Three cases: Lines may intersect in a point, may be equal or may not intersect.
+        if not point:
+            raise GeometryError("The lines do not intersect")
+        else:
+            pt = point[0]
+            if isinstance(pt, Line):
+                # Intersection is a line because both lines are coincident
+                return [self]
+
+
+        d1 = l1.direction.unit
+        d2 = l2.direction.unit
+
+        bis1 = Line(pt, pt + d1 + d2)
+        bis2 = Line(pt, pt + d1 - d2)
+
+        return [bis1, bis2]
+
+
+class Line(LinearEntity):
+    """An infinite line in space.
+
+    A 2D line is declared with two distinct points, point and slope, or
+    an equation. A 3D line may be defined with a point and a direction ratio.
+
+    Parameters
+    ==========
+
+    p1 : Point
+    p2 : Point
+    slope : SymPy expression
+    direction_ratio : list
+    equation : equation of a line
+
+    Notes
+    =====
+
+    `Line` will automatically subclass to `Line2D` or `Line3D` based
+    on the dimension of `p1`.  The `slope` argument is only relevant
+    for `Line2D` and the `direction_ratio` argument is only relevant
+    for `Line3D`.
+
+    The order of the points will define the direction of the line
+    which is used when calculating the angle between lines.
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point
+    sympy.geometry.line.Line2D
+    sympy.geometry.line.Line3D
+
+    Examples
+    ========
+
+    >>> from sympy import Line, Segment, Point, Eq
+    >>> from sympy.abc import x, y, a, b
+
+    >>> L = Line(Point(2,3), Point(3,5))
+    >>> L
+    Line2D(Point2D(2, 3), Point2D(3, 5))
+    >>> L.points
+    (Point2D(2, 3), Point2D(3, 5))
+    >>> L.equation()
+    -2*x + y + 1
+    >>> L.coefficients
+    (-2, 1, 1)
+
+    Instantiate with keyword ``slope``:
+
+    >>> Line(Point(0, 0), slope=0)
+    Line2D(Point2D(0, 0), Point2D(1, 0))
+
+    Instantiate with another linear object
+
+    >>> s = Segment((0, 0), (0, 1))
+    >>> Line(s).equation()
+    x
+
+    The line corresponding to an equation in the for `ax + by + c = 0`,
+    can be entered:
+
+    >>> Line(3*x + y + 18)
+    Line2D(Point2D(0, -18), Point2D(1, -21))
+
+    If `x` or `y` has a different name, then they can be specified, too,
+    as a string (to match the name) or symbol:
+
+    >>> Line(Eq(3*a + b, -18), x='a', y=b)
+    Line2D(Point2D(0, -18), Point2D(1, -21))
+    """
+    def __new__(cls, *args, **kwargs):
+        if len(args) == 1 and isinstance(args[0], (Expr, Eq)):
+            missing = uniquely_named_symbol('?', args)
+            if not kwargs:
+                x = 'x'
+                y = 'y'
+            else:
+                x = kwargs.pop('x', missing)
+                y = kwargs.pop('y', missing)
+            if kwargs:
+                raise ValueError('expecting only x and y as keywords')
+
+            equation = args[0]
+            if isinstance(equation, Eq):
+                equation = equation.lhs - equation.rhs
+
+            def find_or_missing(x):
+                try:
+                    return find(x, equation)
+                except ValueError:
+                    return missing
+            x = find_or_missing(x)
+            y = find_or_missing(y)
+
+            a, b, c = linear_coeffs(equation, x, y)
+
+            if b:
+                return Line((0, -c/b), slope=-a/b)
+            if a:
+                return Line((-c/a, 0), slope=oo)
+
+            raise ValueError('not found in equation: %s' % (set('xy') - {x, y}))
+
+        else:
+            if len(args) > 0:
+                p1 = args[0]
+                if len(args) > 1:
+                    p2 = args[1]
+                else:
+                    p2 = None
+
+                if isinstance(p1, LinearEntity):
+                    if p2:
+                        raise ValueError('If p1 is a LinearEntity, p2 must be None.')
+                    dim = len(p1.p1)
+                else:
+                    p1 = Point(p1)
+                    dim = len(p1)
+                    if p2 is not None or isinstance(p2, Point) and p2.ambient_dimension != dim:
+                        p2 = Point(p2)
+
+                if dim == 2:
+                    return Line2D(p1, p2, **kwargs)
+                elif dim == 3:
+                    return Line3D(p1, p2, **kwargs)
+                return LinearEntity.__new__(cls, p1, p2, **kwargs)
+
+    def contains(self, other):
+        """
+        Return True if `other` is on this Line, or False otherwise.
+
+        Examples
+        ========
+
+        >>> from sympy import Line,Point
+        >>> p1, p2 = Point(0, 1), Point(3, 4)
+        >>> l = Line(p1, p2)
+        >>> l.contains(p1)
+        True
+        >>> l.contains((0, 1))
+        True
+        >>> l.contains((0, 0))
+        False
+        >>> a = (0, 0, 0)
+        >>> b = (1, 1, 1)
+        >>> c = (2, 2, 2)
+        >>> l1 = Line(a, b)
+        >>> l2 = Line(b, a)
+        >>> l1 == l2
+        False
+        >>> l1 in l2
+        True
+
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if isinstance(other, Point):
+            return Point.is_collinear(other, self.p1, self.p2)
+        if isinstance(other, LinearEntity):
+            return Point.is_collinear(self.p1, self.p2, other.p1, other.p2)
+        return False
+
+    def distance(self, other):
+        """
+        Finds the shortest distance between a line and a point.
+
+        Raises
+        ======
+
+        NotImplementedError is raised if `other` is not a Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(1, 1)
+        >>> s = Line(p1, p2)
+        >>> s.distance(Point(-1, 1))
+        sqrt(2)
+        >>> s.distance((-1, 2))
+        3*sqrt(2)/2
+        >>> p1, p2 = Point(0, 0, 0), Point(1, 1, 1)
+        >>> s = Line(p1, p2)
+        >>> s.distance(Point(-1, 1, 1))
+        2*sqrt(6)/3
+        >>> s.distance((-1, 1, 1))
+        2*sqrt(6)/3
+
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if self.contains(other):
+            return S.Zero
+        return self.perpendicular_segment(other).length
+
+    def equals(self, other):
+        """Returns True if self and other are the same mathematical entities"""
+        if not isinstance(other, Line):
+            return False
+        return Point.is_collinear(self.p1, other.p1, self.p2, other.p2)
+
+    def plot_interval(self, parameter='t'):
+        """The plot interval for the default geometric plot of line. Gives
+        values that will produce a line that is +/- 5 units long (where a
+        unit is the distance between the two points that define the line).
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        plot_interval : list (plot interval)
+            [parameter, lower_bound, upper_bound]
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(5, 3)
+        >>> l1 = Line(p1, p2)
+        >>> l1.plot_interval()
+        [t, -5, 5]
+
+        """
+        t = _symbol(parameter, real=True)
+        return [t, -5, 5]
+
+
+class Ray(LinearEntity):
+    """A Ray is a semi-line in the space with a source point and a direction.
+
+    Parameters
+    ==========
+
+    p1 : Point
+        The source of the Ray
+    p2 : Point or radian value
+        This point determines the direction in which the Ray propagates.
+        If given as an angle it is interpreted in radians with the positive
+        direction being ccw.
+
+    Attributes
+    ==========
+
+    source
+
+    See Also
+    ========
+
+    sympy.geometry.line.Ray2D
+    sympy.geometry.line.Ray3D
+    sympy.geometry.point.Point
+    sympy.geometry.line.Line
+
+    Notes
+    =====
+
+    `Ray` will automatically subclass to `Ray2D` or `Ray3D` based on the
+    dimension of `p1`.
+
+    Examples
+    ========
+
+    >>> from sympy import Ray, Point, pi
+    >>> r = Ray(Point(2, 3), Point(3, 5))
+    >>> r
+    Ray2D(Point2D(2, 3), Point2D(3, 5))
+    >>> r.points
+    (Point2D(2, 3), Point2D(3, 5))
+    >>> r.source
+    Point2D(2, 3)
+    >>> r.xdirection
+    oo
+    >>> r.ydirection
+    oo
+    >>> r.slope
+    2
+    >>> Ray(Point(0, 0), angle=pi/4).slope
+    1
+
+    """
+    def __new__(cls, p1, p2=None, **kwargs):
+        p1 = Point(p1)
+        if p2 is not None:
+            p1, p2 = Point._normalize_dimension(p1, Point(p2))
+        dim = len(p1)
+
+        if dim == 2:
+            return Ray2D(p1, p2, **kwargs)
+        elif dim == 3:
+            return Ray3D(p1, p2, **kwargs)
+        return LinearEntity.__new__(cls, p1, p2, **kwargs)
+
+    def _svg(self, scale_factor=1., fill_color="#66cc99"):
+        """Returns SVG path element for the LinearEntity.
+
+        Parameters
+        ==========
+
+        scale_factor : float
+            Multiplication factor for the SVG stroke-width.  Default is 1.
+        fill_color : str, optional
+            Hex string for fill color. Default is "#66cc99".
+        """
+        verts = (N(self.p1), N(self.p2))
+        coords = ["{},{}".format(p.x, p.y) for p in verts]
+        path = "M {} L {}".format(coords[0], " L ".join(coords[1:]))
+
+        return (
+            ''
+        ).format(2.*scale_factor, path, fill_color)
+
+    def contains(self, other):
+        """
+        Is other GeometryEntity contained in this Ray?
+
+        Examples
+        ========
+
+        >>> from sympy import Ray,Point,Segment
+        >>> p1, p2 = Point(0, 0), Point(4, 4)
+        >>> r = Ray(p1, p2)
+        >>> r.contains(p1)
+        True
+        >>> r.contains((1, 1))
+        True
+        >>> r.contains((1, 3))
+        False
+        >>> s = Segment((1, 1), (2, 2))
+        >>> r.contains(s)
+        True
+        >>> s = Segment((1, 2), (2, 5))
+        >>> r.contains(s)
+        False
+        >>> r1 = Ray((2, 2), (3, 3))
+        >>> r.contains(r1)
+        True
+        >>> r1 = Ray((2, 2), (3, 5))
+        >>> r.contains(r1)
+        False
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if isinstance(other, Point):
+            if Point.is_collinear(self.p1, self.p2, other):
+                # if we're in the direction of the ray, our
+                # direction vector dot the ray's direction vector
+                # should be non-negative
+                return bool((self.p2 - self.p1).dot(other - self.p1) >= S.Zero)
+            return False
+        elif isinstance(other, Ray):
+            if Point.is_collinear(self.p1, self.p2, other.p1, other.p2):
+                return bool((self.p2 - self.p1).dot(other.p2 - other.p1) > S.Zero)
+            return False
+        elif isinstance(other, Segment):
+            return other.p1 in self and other.p2 in self
+
+        # No other known entity can be contained in a Ray
+        return False
+
+    def distance(self, other):
+        """
+        Finds the shortest distance between the ray and a point.
+
+        Raises
+        ======
+
+        NotImplementedError is raised if `other` is not a Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ray
+        >>> p1, p2 = Point(0, 0), Point(1, 1)
+        >>> s = Ray(p1, p2)
+        >>> s.distance(Point(-1, -1))
+        sqrt(2)
+        >>> s.distance((-1, 2))
+        3*sqrt(2)/2
+        >>> p1, p2 = Point(0, 0, 0), Point(1, 1, 2)
+        >>> s = Ray(p1, p2)
+        >>> s
+        Ray3D(Point3D(0, 0, 0), Point3D(1, 1, 2))
+        >>> s.distance(Point(-1, -1, 2))
+        4*sqrt(3)/3
+        >>> s.distance((-1, -1, 2))
+        4*sqrt(3)/3
+
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if self.contains(other):
+            return S.Zero
+
+        proj = Line(self.p1, self.p2).projection(other)
+        if self.contains(proj):
+            return abs(other - proj)
+        else:
+            return abs(other - self.source)
+
+    def equals(self, other):
+        """Returns True if self and other are the same mathematical entities"""
+        if not isinstance(other, Ray):
+            return False
+        return self.source == other.source and other.p2 in self
+
+    def plot_interval(self, parameter='t'):
+        """The plot interval for the default geometric plot of the Ray. Gives
+        values that will produce a ray that is 10 units long (where a unit is
+        the distance between the two points that define the ray).
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        plot_interval : list
+            [parameter, lower_bound, upper_bound]
+
+        Examples
+        ========
+
+        >>> from sympy import Ray, pi
+        >>> r = Ray((0, 0), angle=pi/4)
+        >>> r.plot_interval()
+        [t, 0, 10]
+
+        """
+        t = _symbol(parameter, real=True)
+        return [t, 0, 10]
+
+    @property
+    def source(self):
+        """The point from which the ray emanates.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ray
+        >>> p1, p2 = Point(0, 0), Point(4, 1)
+        >>> r1 = Ray(p1, p2)
+        >>> r1.source
+        Point2D(0, 0)
+        >>> p1, p2 = Point(0, 0, 0), Point(4, 1, 5)
+        >>> r1 = Ray(p2, p1)
+        >>> r1.source
+        Point3D(4, 1, 5)
+
+        """
+        return self.p1
+
+
+class Segment(LinearEntity):
+    """A line segment in space.
+
+    Parameters
+    ==========
+
+    p1 : Point
+    p2 : Point
+
+    Attributes
+    ==========
+
+    length : number or SymPy expression
+    midpoint : Point
+
+    See Also
+    ========
+
+    sympy.geometry.line.Segment2D
+    sympy.geometry.line.Segment3D
+    sympy.geometry.point.Point
+    sympy.geometry.line.Line
+
+    Notes
+    =====
+
+    If 2D or 3D points are used to define `Segment`, it will
+    be automatically subclassed to `Segment2D` or `Segment3D`.
+
+    Examples
+    ========
+
+    >>> from sympy import Point, Segment
+    >>> Segment((1, 0), (1, 1)) # tuples are interpreted as pts
+    Segment2D(Point2D(1, 0), Point2D(1, 1))
+    >>> s = Segment(Point(4, 3), Point(1, 1))
+    >>> s.points
+    (Point2D(4, 3), Point2D(1, 1))
+    >>> s.slope
+    2/3
+    >>> s.length
+    sqrt(13)
+    >>> s.midpoint
+    Point2D(5/2, 2)
+    >>> Segment((1, 0, 0), (1, 1, 1)) # tuples are interpreted as pts
+    Segment3D(Point3D(1, 0, 0), Point3D(1, 1, 1))
+    >>> s = Segment(Point(4, 3, 9), Point(1, 1, 7)); s
+    Segment3D(Point3D(4, 3, 9), Point3D(1, 1, 7))
+    >>> s.points
+    (Point3D(4, 3, 9), Point3D(1, 1, 7))
+    >>> s.length
+    sqrt(17)
+    >>> s.midpoint
+    Point3D(5/2, 2, 8)
+
+    """
+    def __new__(cls, p1, p2, **kwargs):
+        p1, p2 = Point._normalize_dimension(Point(p1), Point(p2))
+        dim = len(p1)
+
+        if dim == 2:
+            return Segment2D(p1, p2, **kwargs)
+        elif dim == 3:
+            return Segment3D(p1, p2, **kwargs)
+        return LinearEntity.__new__(cls, p1, p2, **kwargs)
+
+    def contains(self, other):
+        """
+        Is the other GeometryEntity contained within this Segment?
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Segment
+        >>> p1, p2 = Point(0, 1), Point(3, 4)
+        >>> s = Segment(p1, p2)
+        >>> s2 = Segment(p2, p1)
+        >>> s.contains(s2)
+        True
+        >>> from sympy import Point3D, Segment3D
+        >>> p1, p2 = Point3D(0, 1, 1), Point3D(3, 4, 5)
+        >>> s = Segment3D(p1, p2)
+        >>> s2 = Segment3D(p2, p1)
+        >>> s.contains(s2)
+        True
+        >>> s.contains((p1 + p2)/2)
+        True
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if isinstance(other, Point):
+            if Point.is_collinear(other, self.p1, self.p2):
+                if isinstance(self, Segment2D):
+                    # if it is collinear and is in the bounding box of the
+                    # segment then it must be on the segment
+                    vert = (1/self.slope).equals(0)
+                    if vert is False:
+                        isin = (self.p1.x - other.x)*(self.p2.x - other.x) <= 0
+                        if isin in (True, False):
+                            return isin
+                    if vert is True:
+                        isin = (self.p1.y - other.y)*(self.p2.y - other.y) <= 0
+                        if isin in (True, False):
+                            return isin
+                # use the triangle inequality
+                d1, d2 = other - self.p1, other - self.p2
+                d = self.p2 - self.p1
+                # without the call to simplify, SymPy cannot tell that an expression
+                # like (a+b)*(a/2+b/2) is always non-negative.  If it cannot be
+                # determined, raise an Undecidable error
+                try:
+                    # the triangle inequality says that |d1|+|d2| >= |d| and is strict
+                    # only if other lies in the line segment
+                    return bool(simplify(Eq(abs(d1) + abs(d2) - abs(d), 0)))
+                except TypeError:
+                    raise Undecidable("Cannot determine if {} is in {}".format(other, self))
+        if isinstance(other, Segment):
+            return other.p1 in self and other.p2 in self
+
+        return False
+
+    def equals(self, other):
+        """Returns True if self and other are the same mathematical entities"""
+        return isinstance(other, self.func) and list(
+            ordered(self.args)) == list(ordered(other.args))
+
+    def distance(self, other):
+        """
+        Finds the shortest distance between a line segment and a point.
+
+        Raises
+        ======
+
+        NotImplementedError is raised if `other` is not a Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Segment
+        >>> p1, p2 = Point(0, 1), Point(3, 4)
+        >>> s = Segment(p1, p2)
+        >>> s.distance(Point(10, 15))
+        sqrt(170)
+        >>> s.distance((0, 12))
+        sqrt(73)
+        >>> from sympy import Point3D, Segment3D
+        >>> p1, p2 = Point3D(0, 0, 3), Point3D(1, 1, 4)
+        >>> s = Segment3D(p1, p2)
+        >>> s.distance(Point3D(10, 15, 12))
+        sqrt(341)
+        >>> s.distance((10, 15, 12))
+        sqrt(341)
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if isinstance(other, Point):
+            vp1 = other - self.p1
+            vp2 = other - self.p2
+
+            dot_prod_sign_1 = self.direction.dot(vp1) >= 0
+            dot_prod_sign_2 = self.direction.dot(vp2) <= 0
+            if dot_prod_sign_1 and dot_prod_sign_2:
+                return Line(self.p1, self.p2).distance(other)
+            if dot_prod_sign_1 and not dot_prod_sign_2:
+                return abs(vp2)
+            if not dot_prod_sign_1 and dot_prod_sign_2:
+                return abs(vp1)
+        raise NotImplementedError()
+
+    @property
+    def length(self):
+        """The length of the line segment.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.distance
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Segment
+        >>> p1, p2 = Point(0, 0), Point(4, 3)
+        >>> s1 = Segment(p1, p2)
+        >>> s1.length
+        5
+        >>> from sympy import Point3D, Segment3D
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(4, 3, 3)
+        >>> s1 = Segment3D(p1, p2)
+        >>> s1.length
+        sqrt(34)
+
+        """
+        return Point.distance(self.p1, self.p2)
+
+    @property
+    def midpoint(self):
+        """The midpoint of the line segment.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.midpoint
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Segment
+        >>> p1, p2 = Point(0, 0), Point(4, 3)
+        >>> s1 = Segment(p1, p2)
+        >>> s1.midpoint
+        Point2D(2, 3/2)
+        >>> from sympy import Point3D, Segment3D
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(4, 3, 3)
+        >>> s1 = Segment3D(p1, p2)
+        >>> s1.midpoint
+        Point3D(2, 3/2, 3/2)
+
+        """
+        return Point.midpoint(self.p1, self.p2)
+
+    def perpendicular_bisector(self, p=None):
+        """The perpendicular bisector of this segment.
+
+        If no point is specified or the point specified is not on the
+        bisector then the bisector is returned as a Line. Otherwise a
+        Segment is returned that joins the point specified and the
+        intersection of the bisector and the segment.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        bisector : Line or Segment
+
+        See Also
+        ========
+
+        LinearEntity.perpendicular_segment
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Segment
+        >>> p1, p2, p3 = Point(0, 0), Point(6, 6), Point(5, 1)
+        >>> s1 = Segment(p1, p2)
+        >>> s1.perpendicular_bisector()
+        Line2D(Point2D(3, 3), Point2D(-3, 9))
+
+        >>> s1.perpendicular_bisector(p3)
+        Segment2D(Point2D(5, 1), Point2D(3, 3))
+
+        """
+        l = self.perpendicular_line(self.midpoint)
+        if p is not None:
+            p2 = Point(p, dim=self.ambient_dimension)
+            if p2 in l:
+                return Segment(p2, self.midpoint)
+        return l
+
+    def plot_interval(self, parameter='t'):
+        """The plot interval for the default geometric plot of the Segment gives
+        values that will produce the full segment in a plot.
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        plot_interval : list
+            [parameter, lower_bound, upper_bound]
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Segment
+        >>> p1, p2 = Point(0, 0), Point(5, 3)
+        >>> s1 = Segment(p1, p2)
+        >>> s1.plot_interval()
+        [t, 0, 1]
+
+        """
+        t = _symbol(parameter, real=True)
+        return [t, 0, 1]
+
+
+class LinearEntity2D(LinearEntity):
+    """A base class for all linear entities (line, ray and segment)
+    in a 2-dimensional Euclidean space.
+
+    Attributes
+    ==========
+
+    p1
+    p2
+    coefficients
+    slope
+    points
+
+    Notes
+    =====
+
+    This is an abstract class and is not meant to be instantiated.
+
+    See Also
+    ========
+
+    sympy.geometry.entity.GeometryEntity
+
+    """
+    @property
+    def bounds(self):
+        """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
+        rectangle for the geometric figure.
+
+        """
+        verts = self.points
+        xs = [p.x for p in verts]
+        ys = [p.y for p in verts]
+        return (min(xs), min(ys), max(xs), max(ys))
+
+    def perpendicular_line(self, p):
+        """Create a new Line perpendicular to this linear entity which passes
+        through the point `p`.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        line : Line
+
+        See Also
+        ========
+
+        sympy.geometry.line.LinearEntity.is_perpendicular, perpendicular_segment
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2, p3 = Point(0, 0), Point(2, 3), Point(-2, 2)
+        >>> L = Line(p1, p2)
+        >>> P = L.perpendicular_line(p3); P
+        Line2D(Point2D(-2, 2), Point2D(-5, 4))
+        >>> L.is_perpendicular(P)
+        True
+
+        In 2D, the first point of the perpendicular line is the
+        point through which was required to pass; the second
+        point is arbitrarily chosen. To get a line that explicitly
+        uses a point in the line, create a line from the perpendicular
+        segment from the line to the point:
+
+        >>> Line(L.perpendicular_segment(p3))
+        Line2D(Point2D(-2, 2), Point2D(4/13, 6/13))
+        """
+        p = Point(p, dim=self.ambient_dimension)
+        # any two lines in R^2 intersect, so blindly making
+        # a line through p in an orthogonal direction will work
+        # and is faster than finding the projection point as in 3D
+        return Line(p, p + self.direction.orthogonal_direction)
+
+    @property
+    def slope(self):
+        """The slope of this linear entity, or infinity if vertical.
+
+        Returns
+        =======
+
+        slope : number or SymPy expression
+
+        See Also
+        ========
+
+        coefficients
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(0, 0), Point(3, 5)
+        >>> l1 = Line(p1, p2)
+        >>> l1.slope
+        5/3
+
+        >>> p3 = Point(0, 4)
+        >>> l2 = Line(p1, p3)
+        >>> l2.slope
+        oo
+
+        """
+        d1, d2 = (self.p1 - self.p2).args
+        if d1 == 0:
+            return S.Infinity
+        return simplify(d2/d1)
+
+
+class Line2D(LinearEntity2D, Line):
+    """An infinite line in space 2D.
+
+    A line is declared with two distinct points or a point and slope
+    as defined using keyword `slope`.
+
+    Parameters
+    ==========
+
+    p1 : Point
+    pt : Point
+    slope : SymPy expression
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point
+
+    Examples
+    ========
+
+    >>> from sympy import Line, Segment, Point
+    >>> L = Line(Point(2,3), Point(3,5))
+    >>> L
+    Line2D(Point2D(2, 3), Point2D(3, 5))
+    >>> L.points
+    (Point2D(2, 3), Point2D(3, 5))
+    >>> L.equation()
+    -2*x + y + 1
+    >>> L.coefficients
+    (-2, 1, 1)
+
+    Instantiate with keyword ``slope``:
+
+    >>> Line(Point(0, 0), slope=0)
+    Line2D(Point2D(0, 0), Point2D(1, 0))
+
+    Instantiate with another linear object
+
+    >>> s = Segment((0, 0), (0, 1))
+    >>> Line(s).equation()
+    x
+    """
+    def __new__(cls, p1, pt=None, slope=None, **kwargs):
+        if isinstance(p1, LinearEntity):
+            if pt is not None:
+                raise ValueError('When p1 is a LinearEntity, pt should be None')
+            p1, pt = Point._normalize_dimension(*p1.args, dim=2)
+        else:
+            p1 = Point(p1, dim=2)
+        if pt is not None and slope is None:
+            try:
+                p2 = Point(pt, dim=2)
+            except (NotImplementedError, TypeError, ValueError):
+                raise ValueError(filldedent('''
+                    The 2nd argument was not a valid Point.
+                    If it was a slope, enter it with keyword "slope".
+                    '''))
+        elif slope is not None and pt is None:
+            slope = sympify(slope)
+            if slope.is_finite is False:
+                # when infinite slope, don't change x
+                dx = 0
+                dy = 1
+            else:
+                # go over 1 up slope
+                dx = 1
+                dy = slope
+            # XXX avoiding simplification by adding to coords directly
+            p2 = Point(p1.x + dx, p1.y + dy, evaluate=False)
+        else:
+            raise ValueError('A 2nd Point or keyword "slope" must be used.')
+        return LinearEntity2D.__new__(cls, p1, p2, **kwargs)
+
+    def _svg(self, scale_factor=1., fill_color="#66cc99"):
+        """Returns SVG path element for the LinearEntity.
+
+        Parameters
+        ==========
+
+        scale_factor : float
+            Multiplication factor for the SVG stroke-width.  Default is 1.
+        fill_color : str, optional
+            Hex string for fill color. Default is "#66cc99".
+        """
+        verts = (N(self.p1), N(self.p2))
+        coords = ["{},{}".format(p.x, p.y) for p in verts]
+        path = "M {} L {}".format(coords[0], " L ".join(coords[1:]))
+
+        return (
+            ''
+        ).format(2.*scale_factor, path, fill_color)
+
+    @property
+    def coefficients(self):
+        """The coefficients (`a`, `b`, `c`) for `ax + by + c = 0`.
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line2D.equation
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> from sympy.abc import x, y
+        >>> p1, p2 = Point(0, 0), Point(5, 3)
+        >>> l = Line(p1, p2)
+        >>> l.coefficients
+        (-3, 5, 0)
+
+        >>> p3 = Point(x, y)
+        >>> l2 = Line(p1, p3)
+        >>> l2.coefficients
+        (-y, x, 0)
+
+        """
+        p1, p2 = self.points
+        if p1.x == p2.x:
+            return (S.One, S.Zero, -p1.x)
+        elif p1.y == p2.y:
+            return (S.Zero, S.One, -p1.y)
+        return tuple([simplify(i) for i in
+                      (self.p1.y - self.p2.y,
+                       self.p2.x - self.p1.x,
+                       self.p1.x*self.p2.y - self.p1.y*self.p2.x)])
+
+    def equation(self, x='x', y='y'):
+        """The equation of the line: ax + by + c.
+
+        Parameters
+        ==========
+
+        x : str, optional
+            The name to use for the x-axis, default value is 'x'.
+        y : str, optional
+            The name to use for the y-axis, default value is 'y'.
+
+        Returns
+        =======
+
+        equation : SymPy expression
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line2D.coefficients
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(1, 0), Point(5, 3)
+        >>> l1 = Line(p1, p2)
+        >>> l1.equation()
+        -3*x + 4*y + 3
+
+        """
+        x = _symbol(x, real=True)
+        y = _symbol(y, real=True)
+        p1, p2 = self.points
+        if p1.x == p2.x:
+            return x - p1.x
+        elif p1.y == p2.y:
+            return y - p1.y
+
+        a, b, c = self.coefficients
+        return a*x + b*y + c
+
+
+class Ray2D(LinearEntity2D, Ray):
+    """
+    A Ray is a semi-line in the space with a source point and a direction.
+
+    Parameters
+    ==========
+
+    p1 : Point
+        The source of the Ray
+    p2 : Point or radian value
+        This point determines the direction in which the Ray propagates.
+        If given as an angle it is interpreted in radians with the positive
+        direction being ccw.
+
+    Attributes
+    ==========
+
+    source
+    xdirection
+    ydirection
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, Line
+
+    Examples
+    ========
+
+    >>> from sympy import Point, pi, Ray
+    >>> r = Ray(Point(2, 3), Point(3, 5))
+    >>> r
+    Ray2D(Point2D(2, 3), Point2D(3, 5))
+    >>> r.points
+    (Point2D(2, 3), Point2D(3, 5))
+    >>> r.source
+    Point2D(2, 3)
+    >>> r.xdirection
+    oo
+    >>> r.ydirection
+    oo
+    >>> r.slope
+    2
+    >>> Ray(Point(0, 0), angle=pi/4).slope
+    1
+
+    """
+    def __new__(cls, p1, pt=None, angle=None, **kwargs):
+        p1 = Point(p1, dim=2)
+        if pt is not None and angle is None:
+            try:
+                p2 = Point(pt, dim=2)
+            except (NotImplementedError, TypeError, ValueError):
+                raise ValueError(filldedent('''
+                    The 2nd argument was not a valid Point; if
+                    it was meant to be an angle it should be
+                    given with keyword "angle".'''))
+            if p1 == p2:
+                raise ValueError('A Ray requires two distinct points.')
+        elif angle is not None and pt is None:
+            # we need to know if the angle is an odd multiple of pi/2
+            angle = sympify(angle)
+            c = _pi_coeff(angle)
+            p2 = None
+            if c is not None:
+                if c.is_Rational:
+                    if c.q == 2:
+                        if c.p == 1:
+                            p2 = p1 + Point(0, 1)
+                        elif c.p == 3:
+                            p2 = p1 + Point(0, -1)
+                    elif c.q == 1:
+                        if c.p == 0:
+                            p2 = p1 + Point(1, 0)
+                        elif c.p == 1:
+                            p2 = p1 + Point(-1, 0)
+                if p2 is None:
+                    c *= S.Pi
+            else:
+                c = angle % (2*S.Pi)
+            if not p2:
+                m = 2*c/S.Pi
+                left = And(1 < m, m < 3)  # is it in quadrant 2 or 3?
+                x = Piecewise((-1, left), (Piecewise((0, Eq(m % 1, 0)), (1, True)), True))
+                y = Piecewise((-tan(c), left), (Piecewise((1, Eq(m, 1)), (-1, Eq(m, 3)), (tan(c), True)), True))
+                p2 = p1 + Point(x, y)
+        else:
+            raise ValueError('A 2nd point or keyword "angle" must be used.')
+
+        return LinearEntity2D.__new__(cls, p1, p2, **kwargs)
+
+    @property
+    def xdirection(self):
+        """The x direction of the ray.
+
+        Positive infinity if the ray points in the positive x direction,
+        negative infinity if the ray points in the negative x direction,
+        or 0 if the ray is vertical.
+
+        See Also
+        ========
+
+        ydirection
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ray
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, -1)
+        >>> r1, r2 = Ray(p1, p2), Ray(p1, p3)
+        >>> r1.xdirection
+        oo
+        >>> r2.xdirection
+        0
+
+        """
+        if self.p1.x < self.p2.x:
+            return S.Infinity
+        elif self.p1.x == self.p2.x:
+            return S.Zero
+        else:
+            return S.NegativeInfinity
+
+    @property
+    def ydirection(self):
+        """The y direction of the ray.
+
+        Positive infinity if the ray points in the positive y direction,
+        negative infinity if the ray points in the negative y direction,
+        or 0 if the ray is horizontal.
+
+        See Also
+        ========
+
+        xdirection
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Ray
+        >>> p1, p2, p3 = Point(0, 0), Point(-1, -1), Point(-1, 0)
+        >>> r1, r2 = Ray(p1, p2), Ray(p1, p3)
+        >>> r1.ydirection
+        -oo
+        >>> r2.ydirection
+        0
+
+        """
+        if self.p1.y < self.p2.y:
+            return S.Infinity
+        elif self.p1.y == self.p2.y:
+            return S.Zero
+        else:
+            return S.NegativeInfinity
+
+    def closing_angle(r1, r2):
+        """Return the angle by which r2 must be rotated so it faces the same
+        direction as r1.
+
+        Parameters
+        ==========
+
+        r1 : Ray2D
+        r2 : Ray2D
+
+        Returns
+        =======
+
+        angle : angle in radians (ccw angle is positive)
+
+        See Also
+        ========
+
+        LinearEntity.angle_between
+
+        Examples
+        ========
+
+        >>> from sympy import Ray, pi
+        >>> r1 = Ray((0, 0), (1, 0))
+        >>> r2 = r1.rotate(-pi/2)
+        >>> angle = r1.closing_angle(r2); angle
+        pi/2
+        >>> r2.rotate(angle).direction.unit == r1.direction.unit
+        True
+        >>> r2.closing_angle(r1)
+        -pi/2
+        """
+        if not all(isinstance(r, Ray2D) for r in (r1, r2)):
+            # although the direction property is defined for
+            # all linear entities, only the Ray is truly a
+            # directed object
+            raise TypeError('Both arguments must be Ray2D objects.')
+
+        a1 = atan2(*list(reversed(r1.direction.args)))
+        a2 = atan2(*list(reversed(r2.direction.args)))
+        if a1*a2 < 0:
+            a1 = 2*S.Pi + a1 if a1 < 0 else a1
+            a2 = 2*S.Pi + a2 if a2 < 0 else a2
+        return a1 - a2
+
+
+class Segment2D(LinearEntity2D, Segment):
+    """A line segment in 2D space.
+
+    Parameters
+    ==========
+
+    p1 : Point
+    p2 : Point
+
+    Attributes
+    ==========
+
+    length : number or SymPy expression
+    midpoint : Point
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, Line
+
+    Examples
+    ========
+
+    >>> from sympy import Point, Segment
+    >>> Segment((1, 0), (1, 1)) # tuples are interpreted as pts
+    Segment2D(Point2D(1, 0), Point2D(1, 1))
+    >>> s = Segment(Point(4, 3), Point(1, 1)); s
+    Segment2D(Point2D(4, 3), Point2D(1, 1))
+    >>> s.points
+    (Point2D(4, 3), Point2D(1, 1))
+    >>> s.slope
+    2/3
+    >>> s.length
+    sqrt(13)
+    >>> s.midpoint
+    Point2D(5/2, 2)
+
+    """
+    def __new__(cls, p1, p2, **kwargs):
+        p1 = Point(p1, dim=2)
+        p2 = Point(p2, dim=2)
+
+        if p1 == p2:
+            return p1
+
+        return LinearEntity2D.__new__(cls, p1, p2, **kwargs)
+
+    def _svg(self, scale_factor=1., fill_color="#66cc99"):
+        """Returns SVG path element for the LinearEntity.
+
+        Parameters
+        ==========
+
+        scale_factor : float
+            Multiplication factor for the SVG stroke-width.  Default is 1.
+        fill_color : str, optional
+            Hex string for fill color. Default is "#66cc99".
+        """
+        verts = (N(self.p1), N(self.p2))
+        coords = ["{},{}".format(p.x, p.y) for p in verts]
+        path = "M {} L {}".format(coords[0], " L ".join(coords[1:]))
+        return (
+            ''
+        ).format(2.*scale_factor, path, fill_color)
+
+
+class LinearEntity3D(LinearEntity):
+    """An base class for all linear entities (line, ray and segment)
+    in a 3-dimensional Euclidean space.
+
+    Attributes
+    ==========
+
+    p1
+    p2
+    direction_ratio
+    direction_cosine
+    points
+
+    Notes
+    =====
+
+    This is a base class and is not meant to be instantiated.
+    """
+    def __new__(cls, p1, p2, **kwargs):
+        p1 = Point3D(p1, dim=3)
+        p2 = Point3D(p2, dim=3)
+        if p1 == p2:
+            # if it makes sense to return a Point, handle in subclass
+            raise ValueError(
+                "%s.__new__ requires two unique Points." % cls.__name__)
+
+        return GeometryEntity.__new__(cls, p1, p2, **kwargs)
+
+    ambient_dimension = 3
+
+    @property
+    def direction_ratio(self):
+        """The direction ratio of a given line in 3D.
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line3D.equation
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(5, 3, 1)
+        >>> l = Line3D(p1, p2)
+        >>> l.direction_ratio
+        [5, 3, 1]
+        """
+        p1, p2 = self.points
+        return p1.direction_ratio(p2)
+
+    @property
+    def direction_cosine(self):
+        """The normalized direction ratio of a given line in 3D.
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line3D.equation
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(5, 3, 1)
+        >>> l = Line3D(p1, p2)
+        >>> l.direction_cosine
+        [sqrt(35)/7, 3*sqrt(35)/35, sqrt(35)/35]
+        >>> sum(i**2 for i in _)
+        1
+        """
+        p1, p2 = self.points
+        return p1.direction_cosine(p2)
+
+
+class Line3D(LinearEntity3D, Line):
+    """An infinite 3D line in space.
+
+    A line is declared with two distinct points or a point and direction_ratio
+    as defined using keyword `direction_ratio`.
+
+    Parameters
+    ==========
+
+    p1 : Point3D
+    pt : Point3D
+    direction_ratio : list
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point3D
+    sympy.geometry.line.Line
+    sympy.geometry.line.Line2D
+
+    Examples
+    ========
+
+    >>> from sympy import Line3D, Point3D
+    >>> L = Line3D(Point3D(2, 3, 4), Point3D(3, 5, 1))
+    >>> L
+    Line3D(Point3D(2, 3, 4), Point3D(3, 5, 1))
+    >>> L.points
+    (Point3D(2, 3, 4), Point3D(3, 5, 1))
+    """
+    def __new__(cls, p1, pt=None, direction_ratio=(), **kwargs):
+        if isinstance(p1, LinearEntity3D):
+            if pt is not None:
+                raise ValueError('if p1 is a LinearEntity, pt must be None.')
+            p1, pt = p1.args
+        else:
+            p1 = Point(p1, dim=3)
+        if pt is not None and len(direction_ratio) == 0:
+            pt = Point(pt, dim=3)
+        elif len(direction_ratio) == 3 and pt is None:
+            pt = Point3D(p1.x + direction_ratio[0], p1.y + direction_ratio[1],
+                         p1.z + direction_ratio[2])
+        else:
+            raise ValueError('A 2nd Point or keyword "direction_ratio" must '
+                             'be used.')
+
+        return LinearEntity3D.__new__(cls, p1, pt, **kwargs)
+
+    def equation(self, x='x', y='y', z='z'):
+        """Return the equations that define the line in 3D.
+
+        Parameters
+        ==========
+
+        x : str, optional
+            The name to use for the x-axis, default value is 'x'.
+        y : str, optional
+            The name to use for the y-axis, default value is 'y'.
+        z : str, optional
+            The name to use for the z-axis, default value is 'z'.
+
+        Returns
+        =======
+
+        equation : Tuple of simultaneous equations
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D, solve
+        >>> from sympy.abc import x, y, z
+        >>> p1, p2 = Point3D(1, 0, 0), Point3D(5, 3, 0)
+        >>> l1 = Line3D(p1, p2)
+        >>> eq = l1.equation(x, y, z); eq
+        (-3*x + 4*y + 3, z)
+        >>> solve(eq.subs(z, 0), (x, y, z))
+        {x: 4*y/3 + 1}
+        """
+        x, y, z, k = [_symbol(i, real=True) for i in (x, y, z, 'k')]
+        p1, p2 = self.points
+        d1, d2, d3 = p1.direction_ratio(p2)
+        x1, y1, z1 = p1
+        eqs = [-d1*k + x - x1, -d2*k + y - y1, -d3*k + z - z1]
+        # eliminate k from equations by solving first eq with k for k
+        for i, e in enumerate(eqs):
+            if e.has(k):
+                kk = solve(e, k)[0]
+                eqs.pop(i)
+                break
+        return Tuple(*[i.subs(k, kk).as_numer_denom()[0] for i in eqs])
+
+    def distance(self, other):
+        """
+        Finds the shortest distance between a line and another object.
+
+        Parameters
+        ==========
+
+        Point3D, Line3D, Plane, tuple, list
+
+        Returns
+        =======
+
+        distance
+
+        Notes
+        =====
+
+        This method accepts only 3D entities as it's parameter
+
+        Tuples and lists are converted to Point3D and therefore must be of
+        length 3, 2 or 1.
+
+        NotImplementedError is raised if `other` is not an instance of one
+        of the specified classes: Point3D, Line3D, or Plane.
+
+        Examples
+        ========
+
+        >>> from sympy.geometry import Line3D
+        >>> l1 = Line3D((0, 0, 0), (0, 0, 1))
+        >>> l2 = Line3D((0, 1, 0), (1, 1, 1))
+        >>> l1.distance(l2)
+        1
+
+        The computed distance may be symbolic, too:
+
+        >>> from sympy.abc import x, y
+        >>> l1 = Line3D((0, 0, 0), (0, 0, 1))
+        >>> l2 = Line3D((0, x, 0), (y, x, 1))
+        >>> l1.distance(l2)
+        Abs(x*y)/Abs(sqrt(y**2))
+
+        """
+
+        from .plane import Plane  # Avoid circular import
+
+        if isinstance(other, (tuple, list)):
+            try:
+                other = Point3D(other)
+            except ValueError:
+                pass
+
+        if isinstance(other, Point3D):
+            return super().distance(other)
+
+        if isinstance(other, Line3D):
+            if self == other:
+                return S.Zero
+            if self.is_parallel(other):
+                return super().distance(other.p1)
+
+            # Skew lines
+            self_direction = Matrix(self.direction_ratio)
+            other_direction = Matrix(other.direction_ratio)
+            normal = self_direction.cross(other_direction)
+            plane_through_self = Plane(p1=self.p1, normal_vector=normal)
+            return other.p1.distance(plane_through_self)
+
+        if isinstance(other, Plane):
+            return other.distance(self)
+
+        msg = f"{other} has type {type(other)}, which is unsupported"
+        raise NotImplementedError(msg)
+
+
+class Ray3D(LinearEntity3D, Ray):
+    """
+    A Ray is a semi-line in the space with a source point and a direction.
+
+    Parameters
+    ==========
+
+    p1 : Point3D
+        The source of the Ray
+    p2 : Point or a direction vector
+    direction_ratio: Determines the direction in which the Ray propagates.
+
+
+    Attributes
+    ==========
+
+    source
+    xdirection
+    ydirection
+    zdirection
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point3D, Line3D
+
+
+    Examples
+    ========
+
+    >>> from sympy import Point3D, Ray3D
+    >>> r = Ray3D(Point3D(2, 3, 4), Point3D(3, 5, 0))
+    >>> r
+    Ray3D(Point3D(2, 3, 4), Point3D(3, 5, 0))
+    >>> r.points
+    (Point3D(2, 3, 4), Point3D(3, 5, 0))
+    >>> r.source
+    Point3D(2, 3, 4)
+    >>> r.xdirection
+    oo
+    >>> r.ydirection
+    oo
+    >>> r.direction_ratio
+    [1, 2, -4]
+
+    """
+    def __new__(cls, p1, pt=None, direction_ratio=(), **kwargs):
+        if isinstance(p1, LinearEntity3D):
+            if pt is not None:
+                raise ValueError('If p1 is a LinearEntity, pt must be None')
+            p1, pt = p1.args
+        else:
+            p1 = Point(p1, dim=3)
+        if pt is not None and len(direction_ratio) == 0:
+            pt = Point(pt, dim=3)
+        elif len(direction_ratio) == 3 and pt is None:
+            pt = Point3D(p1.x + direction_ratio[0], p1.y + direction_ratio[1],
+                         p1.z + direction_ratio[2])
+        else:
+            raise ValueError(filldedent('''
+                A 2nd Point or keyword "direction_ratio" must be used.
+            '''))
+
+        return LinearEntity3D.__new__(cls, p1, pt, **kwargs)
+
+    @property
+    def xdirection(self):
+        """The x direction of the ray.
+
+        Positive infinity if the ray points in the positive x direction,
+        negative infinity if the ray points in the negative x direction,
+        or 0 if the ray is vertical.
+
+        See Also
+        ========
+
+        ydirection
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Ray3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, -1, 0)
+        >>> r1, r2 = Ray3D(p1, p2), Ray3D(p1, p3)
+        >>> r1.xdirection
+        oo
+        >>> r2.xdirection
+        0
+
+        """
+        if self.p1.x < self.p2.x:
+            return S.Infinity
+        elif self.p1.x == self.p2.x:
+            return S.Zero
+        else:
+            return S.NegativeInfinity
+
+    @property
+    def ydirection(self):
+        """The y direction of the ray.
+
+        Positive infinity if the ray points in the positive y direction,
+        negative infinity if the ray points in the negative y direction,
+        or 0 if the ray is horizontal.
+
+        See Also
+        ========
+
+        xdirection
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Ray3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(-1, -1, -1), Point3D(-1, 0, 0)
+        >>> r1, r2 = Ray3D(p1, p2), Ray3D(p1, p3)
+        >>> r1.ydirection
+        -oo
+        >>> r2.ydirection
+        0
+
+        """
+        if self.p1.y < self.p2.y:
+            return S.Infinity
+        elif self.p1.y == self.p2.y:
+            return S.Zero
+        else:
+            return S.NegativeInfinity
+
+    @property
+    def zdirection(self):
+        """The z direction of the ray.
+
+        Positive infinity if the ray points in the positive z direction,
+        negative infinity if the ray points in the negative z direction,
+        or 0 if the ray is horizontal.
+
+        See Also
+        ========
+
+        xdirection
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Ray3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(-1, -1, -1), Point3D(-1, 0, 0)
+        >>> r1, r2 = Ray3D(p1, p2), Ray3D(p1, p3)
+        >>> r1.ydirection
+        -oo
+        >>> r2.ydirection
+        0
+        >>> r2.zdirection
+        0
+
+        """
+        if self.p1.z < self.p2.z:
+            return S.Infinity
+        elif self.p1.z == self.p2.z:
+            return S.Zero
+        else:
+            return S.NegativeInfinity
+
+
+class Segment3D(LinearEntity3D, Segment):
+    """A line segment in a 3D space.
+
+    Parameters
+    ==========
+
+    p1 : Point3D
+    p2 : Point3D
+
+    Attributes
+    ==========
+
+    length : number or SymPy expression
+    midpoint : Point3D
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point3D, Line3D
+
+    Examples
+    ========
+
+    >>> from sympy import Point3D, Segment3D
+    >>> Segment3D((1, 0, 0), (1, 1, 1)) # tuples are interpreted as pts
+    Segment3D(Point3D(1, 0, 0), Point3D(1, 1, 1))
+    >>> s = Segment3D(Point3D(4, 3, 9), Point3D(1, 1, 7)); s
+    Segment3D(Point3D(4, 3, 9), Point3D(1, 1, 7))
+    >>> s.points
+    (Point3D(4, 3, 9), Point3D(1, 1, 7))
+    >>> s.length
+    sqrt(17)
+    >>> s.midpoint
+    Point3D(5/2, 2, 8)
+
+    """
+    def __new__(cls, p1, p2, **kwargs):
+        p1 = Point(p1, dim=3)
+        p2 = Point(p2, dim=3)
+
+        if p1 == p2:
+            return p1
+
+        return LinearEntity3D.__new__(cls, p1, p2, **kwargs)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/parabola.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/parabola.py
new file mode 100644
index 0000000000000000000000000000000000000000..183c593785bb610e6f451a0c87abb2aa34d22494
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/parabola.py
@@ -0,0 +1,422 @@
+"""Parabolic geometrical entity.
+
+Contains
+* Parabola
+
+"""
+
+from sympy.core import S
+from sympy.core.sorting import ordered
+from sympy.core.symbol import _symbol, symbols
+from sympy.geometry.entity import GeometryEntity, GeometrySet
+from sympy.geometry.point import Point, Point2D
+from sympy.geometry.line import Line, Line2D, Ray2D, Segment2D, LinearEntity3D
+from sympy.geometry.ellipse import Ellipse
+from sympy.functions import sign
+from sympy.simplify.simplify import simplify
+from sympy.solvers.solvers import solve
+
+
+class Parabola(GeometrySet):
+    """A parabolic GeometryEntity.
+
+    A parabola is declared with a point, that is called 'focus', and
+    a line, that is called 'directrix'.
+    Only vertical or horizontal parabolas are currently supported.
+
+    Parameters
+    ==========
+
+    focus : Point
+        Default value is Point(0, 0)
+    directrix : Line
+
+    Attributes
+    ==========
+
+    focus
+    directrix
+    axis of symmetry
+    focal length
+    p parameter
+    vertex
+    eccentricity
+
+    Raises
+    ======
+    ValueError
+        When `focus` is not a two dimensional point.
+        When `focus` is a point of directrix.
+    NotImplementedError
+        When `directrix` is neither horizontal nor vertical.
+
+    Examples
+    ========
+
+    >>> from sympy import Parabola, Point, Line
+    >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7,8)))
+    >>> p1.focus
+    Point2D(0, 0)
+    >>> p1.directrix
+    Line2D(Point2D(5, 8), Point2D(7, 8))
+
+    """
+
+    def __new__(cls, focus=None, directrix=None, **kwargs):
+
+        if focus:
+            focus = Point(focus, dim=2)
+        else:
+            focus = Point(0, 0)
+
+        directrix = Line(directrix)
+
+        if directrix.contains(focus):
+            raise ValueError('The focus must not be a point of directrix')
+
+        return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
+
+    @property
+    def ambient_dimension(self):
+        """Returns the ambient dimension of parabola.
+
+        Returns
+        =======
+
+        ambient_dimension : integer
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> f1 = Point(0, 0)
+        >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8)))
+        >>> p1.ambient_dimension
+        2
+
+        """
+        return 2
+
+    @property
+    def axis_of_symmetry(self):
+        """Return the axis of symmetry of the parabola: a line
+        perpendicular to the directrix passing through the focus.
+
+        Returns
+        =======
+
+        axis_of_symmetry : Line
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8)))
+        >>> p1.axis_of_symmetry
+        Line2D(Point2D(0, 0), Point2D(0, 1))
+
+        """
+        return self.directrix.perpendicular_line(self.focus)
+
+    @property
+    def directrix(self):
+        """The directrix of the parabola.
+
+        Returns
+        =======
+
+        directrix : Line
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> l1 = Line(Point(5, 8), Point(7, 8))
+        >>> p1 = Parabola(Point(0, 0), l1)
+        >>> p1.directrix
+        Line2D(Point2D(5, 8), Point2D(7, 8))
+
+        """
+        return self.args[1]
+
+    @property
+    def eccentricity(self):
+        """The eccentricity of the parabola.
+
+        Returns
+        =======
+
+        eccentricity : number
+
+        A parabola may also be characterized as a conic section with an
+        eccentricity of 1. As a consequence of this, all parabolas are
+        similar, meaning that while they can be different sizes,
+        they are all the same shape.
+
+        See Also
+        ========
+
+        https://en.wikipedia.org/wiki/Parabola
+
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8)))
+        >>> p1.eccentricity
+        1
+
+        Notes
+        -----
+        The eccentricity for every Parabola is 1 by definition.
+
+        """
+        return S.One
+
+    def equation(self, x='x', y='y'):
+        """The equation of the parabola.
+
+        Parameters
+        ==========
+        x : str, optional
+            Label for the x-axis. Default value is 'x'.
+        y : str, optional
+            Label for the y-axis. Default value is 'y'.
+
+        Returns
+        =======
+        equation : SymPy expression
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8)))
+        >>> p1.equation()
+        -x**2 - 16*y + 64
+        >>> p1.equation('f')
+        -f**2 - 16*y + 64
+        >>> p1.equation(y='z')
+        -x**2 - 16*z + 64
+
+        """
+        x = _symbol(x, real=True)
+        y = _symbol(y, real=True)
+
+        m = self.directrix.slope
+        if m is S.Infinity:
+            t1 = 4 * (self.p_parameter) * (x - self.vertex.x)
+            t2 = (y - self.vertex.y)**2
+        elif m == 0:
+            t1 = 4 * (self.p_parameter) * (y - self.vertex.y)
+            t2 = (x - self.vertex.x)**2
+        else:
+            a, b = self.focus
+            c, d = self.directrix.coefficients[:2]
+            t1 = (x - a)**2 + (y - b)**2
+            t2 = self.directrix.equation(x, y)**2/(c**2 + d**2)
+        return t1 - t2
+
+    @property
+    def focal_length(self):
+        """The focal length of the parabola.
+
+        Returns
+        =======
+
+        focal_lenght : number or symbolic expression
+
+        Notes
+        =====
+
+        The distance between the vertex and the focus
+        (or the vertex and directrix), measured along the axis
+        of symmetry, is the "focal length".
+
+        See Also
+        ========
+
+        https://en.wikipedia.org/wiki/Parabola
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8)))
+        >>> p1.focal_length
+        4
+
+        """
+        distance = self.directrix.distance(self.focus)
+        focal_length = distance/2
+
+        return focal_length
+
+    @property
+    def focus(self):
+        """The focus of the parabola.
+
+        Returns
+        =======
+
+        focus : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> f1 = Point(0, 0)
+        >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8)))
+        >>> p1.focus
+        Point2D(0, 0)
+
+        """
+        return self.args[0]
+
+    def intersection(self, o):
+        """The intersection of the parabola and another geometrical entity `o`.
+
+        Parameters
+        ==========
+
+        o : GeometryEntity, LinearEntity
+
+        Returns
+        =======
+
+        intersection : list of GeometryEntity objects
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Ellipse, Line, Segment
+        >>> p1 = Point(0,0)
+        >>> l1 = Line(Point(1, -2), Point(-1,-2))
+        >>> parabola1 = Parabola(p1, l1)
+        >>> parabola1.intersection(Ellipse(Point(0, 0), 2, 5))
+        [Point2D(-2, 0), Point2D(2, 0)]
+        >>> parabola1.intersection(Line(Point(-7, 3), Point(12, 3)))
+        [Point2D(-4, 3), Point2D(4, 3)]
+        >>> parabola1.intersection(Segment((-12, -65), (14, -68)))
+        []
+
+        """
+        x, y = symbols('x y', real=True)
+        parabola_eq = self.equation()
+        if isinstance(o, Parabola):
+            if o in self:
+                return [o]
+            else:
+                return list(ordered([Point(i) for i in solve(
+                    [parabola_eq, o.equation()], [x, y], set=True)[1]]))
+        elif isinstance(o, Point2D):
+            if simplify(parabola_eq.subs([(x, o._args[0]), (y, o._args[1])])) == 0:
+                return [o]
+            else:
+                return []
+        elif isinstance(o, (Segment2D, Ray2D)):
+            result = solve([parabola_eq,
+                Line2D(o.points[0], o.points[1]).equation()],
+                [x, y], set=True)[1]
+            return list(ordered([Point2D(i) for i in result if i in o]))
+        elif isinstance(o, (Line2D, Ellipse)):
+            return list(ordered([Point2D(i) for i in solve(
+                [parabola_eq, o.equation()], [x, y], set=True)[1]]))
+        elif isinstance(o, LinearEntity3D):
+            raise TypeError('Entity must be two dimensional, not three dimensional')
+        else:
+            raise TypeError('Wrong type of argument were put')
+
+    @property
+    def p_parameter(self):
+        """P is a parameter of parabola.
+
+        Returns
+        =======
+
+        p : number or symbolic expression
+
+        Notes
+        =====
+
+        The absolute value of p is the focal length. The sign on p tells
+        which way the parabola faces. Vertical parabolas that open up
+        and horizontal that open right, give a positive value for p.
+        Vertical parabolas that open down and horizontal that open left,
+        give a negative value for p.
+
+
+        See Also
+        ========
+
+        https://www.sparknotes.com/math/precalc/conicsections/section2/
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8)))
+        >>> p1.p_parameter
+        -4
+
+        """
+        m = self.directrix.slope
+        if m is S.Infinity:
+            x = self.directrix.coefficients[2]
+            p = sign(self.focus.args[0] + x)
+        elif m == 0:
+            y = self.directrix.coefficients[2]
+            p = sign(self.focus.args[1] + y)
+        else:
+            d = self.directrix.projection(self.focus)
+            p = sign(self.focus.x - d.x)
+        return p * self.focal_length
+
+    @property
+    def vertex(self):
+        """The vertex of the parabola.
+
+        Returns
+        =======
+
+        vertex : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Parabola, Point, Line
+        >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8)))
+        >>> p1.vertex
+        Point2D(0, 4)
+
+        """
+        focus = self.focus
+        m = self.directrix.slope
+        if m is S.Infinity:
+            vertex = Point(focus.args[0] - self.p_parameter, focus.args[1])
+        elif m == 0:
+            vertex = Point(focus.args[0], focus.args[1] - self.p_parameter)
+        else:
+            vertex = self.axis_of_symmetry.intersection(self)[0]
+        return vertex
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/plane.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/plane.py
new file mode 100644
index 0000000000000000000000000000000000000000..509dc4be5dc41c5df7c33561fdbe5bb0b6620352
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/plane.py
@@ -0,0 +1,878 @@
+"""Geometrical Planes.
+
+Contains
+========
+Plane
+
+"""
+
+from sympy.core import Dummy, Rational, S, Symbol
+from sympy.core.symbol import _symbol
+from sympy.functions.elementary.trigonometric import cos, sin, acos, asin, sqrt
+from .entity import GeometryEntity
+from .line import (Line, Ray, Segment, Line3D, LinearEntity, LinearEntity3D,
+                   Ray3D, Segment3D)
+from .point import Point, Point3D
+from sympy.matrices import Matrix
+from sympy.polys.polytools import cancel
+from sympy.solvers import solve, linsolve
+from sympy.utilities.iterables import uniq, is_sequence
+from sympy.utilities.misc import filldedent, func_name, Undecidable
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+import random
+
+
+x, y, z, t = [Dummy('plane_dummy') for i in range(4)]
+
+
+class Plane(GeometryEntity):
+    """
+    A plane is a flat, two-dimensional surface. A plane is the two-dimensional
+    analogue of a point (zero-dimensions), a line (one-dimension) and a solid
+    (three-dimensions). A plane can generally be constructed by two types of
+    inputs. They are:
+    - three non-collinear points
+    - a point and the plane's normal vector
+
+    Attributes
+    ==========
+
+    p1
+    normal_vector
+
+    Examples
+    ========
+
+    >>> from sympy import Plane, Point3D
+    >>> Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))
+    Plane(Point3D(1, 1, 1), (-1, 2, -1))
+    >>> Plane((1, 1, 1), (2, 3, 4), (2, 2, 2))
+    Plane(Point3D(1, 1, 1), (-1, 2, -1))
+    >>> Plane(Point3D(1, 1, 1), normal_vector=(1,4,7))
+    Plane(Point3D(1, 1, 1), (1, 4, 7))
+
+    """
+    def __new__(cls, p1, a=None, b=None, **kwargs):
+        p1 = Point3D(p1, dim=3)
+        if a and b:
+            p2 = Point(a, dim=3)
+            p3 = Point(b, dim=3)
+            if Point3D.are_collinear(p1, p2, p3):
+                raise ValueError('Enter three non-collinear points')
+            a = p1.direction_ratio(p2)
+            b = p1.direction_ratio(p3)
+            normal_vector = tuple(Matrix(a).cross(Matrix(b)))
+        else:
+            a = kwargs.pop('normal_vector', a)
+            evaluate = kwargs.get('evaluate', True)
+            if is_sequence(a) and len(a) == 3:
+                normal_vector = Point3D(a).args if evaluate else a
+            else:
+                raise ValueError(filldedent('''
+                    Either provide 3 3D points or a point with a
+                    normal vector expressed as a sequence of length 3'''))
+            if all(coord.is_zero for coord in normal_vector):
+                raise ValueError('Normal vector cannot be zero vector')
+        return GeometryEntity.__new__(cls, p1, normal_vector, **kwargs)
+
+    def __contains__(self, o):
+        k = self.equation(x, y, z)
+        if isinstance(o, (LinearEntity, LinearEntity3D)):
+            d = Point3D(o.arbitrary_point(t))
+            e = k.subs([(x, d.x), (y, d.y), (z, d.z)])
+            return e.equals(0)
+        try:
+            o = Point(o, dim=3, strict=True)
+            d = k.xreplace(dict(zip((x, y, z), o.args)))
+            return d.equals(0)
+        except TypeError:
+            return False
+
+    def _eval_evalf(self, prec=15, **options):
+        pt, tup = self.args
+        dps = prec_to_dps(prec)
+        pt = pt.evalf(n=dps, **options)
+        tup = tuple([i.evalf(n=dps, **options) for i in tup])
+        return self.func(pt, normal_vector=tup, evaluate=False)
+
+    def angle_between(self, o):
+        """Angle between the plane and other geometric entity.
+
+        Parameters
+        ==========
+
+        LinearEntity3D, Plane.
+
+        Returns
+        =======
+
+        angle : angle in radians
+
+        Notes
+        =====
+
+        This method accepts only 3D entities as it's parameter, but if you want
+        to calculate the angle between a 2D entity and a plane you should
+        first convert to a 3D entity by projecting onto a desired plane and
+        then proceed to calculate the angle.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D, Plane
+        >>> a = Plane(Point3D(1, 2, 2), normal_vector=(1, 2, 3))
+        >>> b = Line3D(Point3D(1, 3, 4), Point3D(2, 2, 2))
+        >>> a.angle_between(b)
+        -asin(sqrt(21)/6)
+
+        """
+        if isinstance(o, LinearEntity3D):
+            a = Matrix(self.normal_vector)
+            b = Matrix(o.direction_ratio)
+            c = a.dot(b)
+            d = sqrt(sum(i**2 for i in self.normal_vector))
+            e = sqrt(sum(i**2 for i in o.direction_ratio))
+            return asin(c/(d*e))
+        if isinstance(o, Plane):
+            a = Matrix(self.normal_vector)
+            b = Matrix(o.normal_vector)
+            c = a.dot(b)
+            d = sqrt(sum(i**2 for i in self.normal_vector))
+            e = sqrt(sum(i**2 for i in o.normal_vector))
+            return acos(c/(d*e))
+
+
+    def arbitrary_point(self, u=None, v=None):
+        """ Returns an arbitrary point on the Plane. If given two
+        parameters, the point ranges over the entire plane. If given 1
+        or no parameters, returns a point with one parameter which,
+        when varying from 0 to 2*pi, moves the point in a circle of
+        radius 1 about p1 of the Plane.
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Ray
+        >>> from sympy.abc import u, v, t, r
+        >>> p = Plane((1, 1, 1), normal_vector=(1, 0, 0))
+        >>> p.arbitrary_point(u, v)
+        Point3D(1, u + 1, v + 1)
+        >>> p.arbitrary_point(t)
+        Point3D(1, cos(t) + 1, sin(t) + 1)
+
+        While arbitrary values of u and v can move the point anywhere in
+        the plane, the single-parameter point can be used to construct a
+        ray whose arbitrary point can be located at angle t and radius
+        r from p.p1:
+
+        >>> Ray(p.p1, _).arbitrary_point(r)
+        Point3D(1, r*cos(t) + 1, r*sin(t) + 1)
+
+        Returns
+        =======
+
+        Point3D
+
+        """
+        circle = v is None
+        if circle:
+            u = _symbol(u or 't', real=True)
+        else:
+            u = _symbol(u or 'u', real=True)
+            v = _symbol(v or 'v', real=True)
+        x, y, z = self.normal_vector
+        a, b, c = self.p1.args
+        # x1, y1, z1 is a nonzero vector parallel to the plane
+        if x.is_zero and y.is_zero:
+            x1, y1, z1 = S.One, S.Zero, S.Zero
+        else:
+            x1, y1, z1 = -y, x, S.Zero
+        # x2, y2, z2 is also parallel to the plane, and orthogonal to x1, y1, z1
+        x2, y2, z2 = tuple(Matrix((x, y, z)).cross(Matrix((x1, y1, z1))))
+        if circle:
+            x1, y1, z1 = (w/sqrt(x1**2 + y1**2 + z1**2) for w in (x1, y1, z1))
+            x2, y2, z2 = (w/sqrt(x2**2 + y2**2 + z2**2) for w in (x2, y2, z2))
+            p = Point3D(a + x1*cos(u) + x2*sin(u), \
+                        b + y1*cos(u) + y2*sin(u), \
+                        c + z1*cos(u) + z2*sin(u))
+        else:
+            p = Point3D(a + x1*u + x2*v, b + y1*u + y2*v, c + z1*u + z2*v)
+        return p
+
+
+    @staticmethod
+    def are_concurrent(*planes):
+        """Is a sequence of Planes concurrent?
+
+        Two or more Planes are concurrent if their intersections
+        are a common line.
+
+        Parameters
+        ==========
+
+        planes: list
+
+        Returns
+        =======
+
+        Boolean
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a = Plane(Point3D(5, 0, 0), normal_vector=(1, -1, 1))
+        >>> b = Plane(Point3D(0, -2, 0), normal_vector=(3, 1, 1))
+        >>> c = Plane(Point3D(0, -1, 0), normal_vector=(5, -1, 9))
+        >>> Plane.are_concurrent(a, b)
+        True
+        >>> Plane.are_concurrent(a, b, c)
+        False
+
+        """
+        planes = list(uniq(planes))
+        for i in planes:
+            if not isinstance(i, Plane):
+                raise ValueError('All objects should be Planes but got %s' % i.func)
+        if len(planes) < 2:
+            return False
+        planes = list(planes)
+        first = planes.pop(0)
+        sol = first.intersection(planes[0])
+        if sol == []:
+            return False
+        else:
+            line = sol[0]
+            for i in planes[1:]:
+                l = first.intersection(i)
+                if not l or l[0] not in line:
+                    return False
+            return True
+
+
+    def distance(self, o):
+        """Distance between the plane and another geometric entity.
+
+        Parameters
+        ==========
+
+        Point3D, LinearEntity3D, Plane.
+
+        Returns
+        =======
+
+        distance
+
+        Notes
+        =====
+
+        This method accepts only 3D entities as it's parameter, but if you want
+        to calculate the distance between a 2D entity and a plane you should
+        first convert to a 3D entity by projecting onto a desired plane and
+        then proceed to calculate the distance.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D, Plane
+        >>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 1, 1))
+        >>> b = Point3D(1, 2, 3)
+        >>> a.distance(b)
+        sqrt(3)
+        >>> c = Line3D(Point3D(2, 3, 1), Point3D(1, 2, 2))
+        >>> a.distance(c)
+        0
+
+        """
+        if self.intersection(o) != []:
+            return S.Zero
+
+        if isinstance(o, (Segment3D, Ray3D)):
+            a, b = o.p1, o.p2
+            pi, = self.intersection(Line3D(a, b))
+            if pi in o:
+                return self.distance(pi)
+            elif a in Segment3D(pi, b):
+                return self.distance(a)
+            else:
+                assert isinstance(o, Segment3D) is True
+                return self.distance(b)
+
+        # following code handles `Point3D`, `LinearEntity3D`, `Plane`
+        a = o if isinstance(o, Point3D) else o.p1
+        n = Point3D(self.normal_vector).unit
+        d = (a - self.p1).dot(n)
+        return abs(d)
+
+
+    def equals(self, o):
+        """
+        Returns True if self and o are the same mathematical entities.
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a = Plane(Point3D(1, 2, 3), normal_vector=(1, 1, 1))
+        >>> b = Plane(Point3D(1, 2, 3), normal_vector=(2, 2, 2))
+        >>> c = Plane(Point3D(1, 2, 3), normal_vector=(-1, 4, 6))
+        >>> a.equals(a)
+        True
+        >>> a.equals(b)
+        True
+        >>> a.equals(c)
+        False
+        """
+        if isinstance(o, Plane):
+            a = self.equation()
+            b = o.equation()
+            return cancel(a/b).is_constant()
+        else:
+            return False
+
+
+    def equation(self, x=None, y=None, z=None):
+        """The equation of the Plane.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Plane
+        >>> a = Plane(Point3D(1, 1, 2), Point3D(2, 4, 7), Point3D(3, 5, 1))
+        >>> a.equation()
+        -23*x + 11*y - 2*z + 16
+        >>> a = Plane(Point3D(1, 4, 2), normal_vector=(6, 6, 6))
+        >>> a.equation()
+        6*x + 6*y + 6*z - 42
+
+        """
+        x, y, z = [i if i else Symbol(j, real=True) for i, j in zip((x, y, z), 'xyz')]
+        a = Point3D(x, y, z)
+        b = self.p1.direction_ratio(a)
+        c = self.normal_vector
+        return (sum(i*j for i, j in zip(b, c)))
+
+
+    def intersection(self, o):
+        """ The intersection with other geometrical entity.
+
+        Parameters
+        ==========
+
+        Point, Point3D, LinearEntity, LinearEntity3D, Plane
+
+        Returns
+        =======
+
+        List
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Line3D, Plane
+        >>> a = Plane(Point3D(1, 2, 3), normal_vector=(1, 1, 1))
+        >>> b = Point3D(1, 2, 3)
+        >>> a.intersection(b)
+        [Point3D(1, 2, 3)]
+        >>> c = Line3D(Point3D(1, 4, 7), Point3D(2, 2, 2))
+        >>> a.intersection(c)
+        [Point3D(2, 2, 2)]
+        >>> d = Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3))
+        >>> e = Plane(Point3D(2, 0, 0), normal_vector=(3, 4, -3))
+        >>> d.intersection(e)
+        [Line3D(Point3D(78/23, -24/23, 0), Point3D(147/23, 321/23, 23))]
+
+        """
+        if not isinstance(o, GeometryEntity):
+            o = Point(o, dim=3)
+        if isinstance(o, Point):
+            if o in self:
+                return [o]
+            else:
+                return []
+        if isinstance(o, (LinearEntity, LinearEntity3D)):
+            # recast to 3D
+            p1, p2 = o.p1, o.p2
+            if isinstance(o, Segment):
+                o = Segment3D(p1, p2)
+            elif isinstance(o, Ray):
+                o = Ray3D(p1, p2)
+            elif isinstance(o, Line):
+                o = Line3D(p1, p2)
+            else:
+                raise ValueError('unhandled linear entity: %s' % o.func)
+            if o in self:
+                return [o]
+            else:
+                a = Point3D(o.arbitrary_point(t))
+                p1, n = self.p1, Point3D(self.normal_vector)
+
+                # TODO: Replace solve with solveset, when this line is tested
+                c = solve((a - p1).dot(n), t)
+                if not c:
+                    return []
+                else:
+                    c = [i for i in c if i.is_real is not False]
+                    if len(c) > 1:
+                        c = [i for i in c if i.is_real]
+                    if len(c) != 1:
+                        raise Undecidable("not sure which point is real")
+                    p = a.subs(t, c[0])
+                    if p not in o:
+                        return []  # e.g. a segment might not intersect a plane
+                    return [p]
+        if isinstance(o, Plane):
+            if self.equals(o):
+                return [self]
+            if self.is_parallel(o):
+                return []
+            else:
+                x, y, z = map(Dummy, 'xyz')
+                a, b = Matrix([self.normal_vector]), Matrix([o.normal_vector])
+                c = list(a.cross(b))
+                d = self.equation(x, y, z)
+                e = o.equation(x, y, z)
+                result = list(linsolve([d, e], x, y, z))[0]
+                for i in (x, y, z): result = result.subs(i, 0)
+                return [Line3D(Point3D(result), direction_ratio=c)]
+
+
+    def is_coplanar(self, o):
+        """ Returns True if `o` is coplanar with self, else False.
+
+        Examples
+        ========
+
+        >>> from sympy import Plane
+        >>> o = (0, 0, 0)
+        >>> p = Plane(o, (1, 1, 1))
+        >>> p2 = Plane(o, (2, 2, 2))
+        >>> p == p2
+        False
+        >>> p.is_coplanar(p2)
+        True
+        """
+        if isinstance(o, Plane):
+            return not cancel(self.equation(x, y, z)/o.equation(x, y, z)).has(x, y, z)
+        if isinstance(o, Point3D):
+            return o in self
+        elif isinstance(o, LinearEntity3D):
+            return all(i in self for i in self)
+        elif isinstance(o, GeometryEntity):  # XXX should only be handling 2D objects now
+            return all(i == 0 for i in self.normal_vector[:2])
+
+
+    def is_parallel(self, l):
+        """Is the given geometric entity parallel to the plane?
+
+        Parameters
+        ==========
+
+        LinearEntity3D or Plane
+
+        Returns
+        =======
+
+        Boolean
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6))
+        >>> b = Plane(Point3D(3,1,3), normal_vector=(4, 8, 12))
+        >>> a.is_parallel(b)
+        True
+
+        """
+        if isinstance(l, LinearEntity3D):
+            a = l.direction_ratio
+            b = self.normal_vector
+            return sum(i*j for i, j in zip(a, b)) == 0
+        if isinstance(l, Plane):
+            a = Matrix(l.normal_vector)
+            b = Matrix(self.normal_vector)
+            return bool(a.cross(b).is_zero_matrix)
+
+
+    def is_perpendicular(self, l):
+        """Is the given geometric entity perpendicualar to the given plane?
+
+        Parameters
+        ==========
+
+        LinearEntity3D or Plane
+
+        Returns
+        =======
+
+        Boolean
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6))
+        >>> b = Plane(Point3D(2, 2, 2), normal_vector=(-1, 2, -1))
+        >>> a.is_perpendicular(b)
+        True
+
+        """
+        if isinstance(l, LinearEntity3D):
+            a = Matrix(l.direction_ratio)
+            b = Matrix(self.normal_vector)
+            if a.cross(b).is_zero_matrix:
+                return True
+            else:
+                return False
+        elif isinstance(l, Plane):
+            a = Matrix(l.normal_vector)
+            b = Matrix(self.normal_vector)
+            if a.dot(b) == 0:
+                return True
+            else:
+                return False
+        else:
+            return False
+
+    @property
+    def normal_vector(self):
+        """Normal vector of the given plane.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Plane
+        >>> a = Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))
+        >>> a.normal_vector
+        (-1, 2, -1)
+        >>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 4, 7))
+        >>> a.normal_vector
+        (1, 4, 7)
+
+        """
+        return self.args[1]
+
+    @property
+    def p1(self):
+        """The only defining point of the plane. Others can be obtained from the
+        arbitrary_point method.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point3D
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D, Plane
+        >>> a = Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))
+        >>> a.p1
+        Point3D(1, 1, 1)
+
+        """
+        return self.args[0]
+
+    def parallel_plane(self, pt):
+        """
+        Plane parallel to the given plane and passing through the point pt.
+
+        Parameters
+        ==========
+
+        pt: Point3D
+
+        Returns
+        =======
+
+        Plane
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a = Plane(Point3D(1, 4, 6), normal_vector=(2, 4, 6))
+        >>> a.parallel_plane(Point3D(2, 3, 5))
+        Plane(Point3D(2, 3, 5), (2, 4, 6))
+
+        """
+        a = self.normal_vector
+        return Plane(pt, normal_vector=a)
+
+    def perpendicular_line(self, pt):
+        """A line perpendicular to the given plane.
+
+        Parameters
+        ==========
+
+        pt: Point3D
+
+        Returns
+        =======
+
+        Line3D
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6))
+        >>> a.perpendicular_line(Point3D(9, 8, 7))
+        Line3D(Point3D(9, 8, 7), Point3D(11, 12, 13))
+
+        """
+        a = self.normal_vector
+        return Line3D(pt, direction_ratio=a)
+
+    def perpendicular_plane(self, *pts):
+        """
+        Return a perpendicular passing through the given points. If the
+        direction ratio between the points is the same as the Plane's normal
+        vector then, to select from the infinite number of possible planes,
+        a third point will be chosen on the z-axis (or the y-axis
+        if the normal vector is already parallel to the z-axis). If less than
+        two points are given they will be supplied as follows: if no point is
+        given then pt1 will be self.p1; if a second point is not given it will
+        be a point through pt1 on a line parallel to the z-axis (if the normal
+        is not already the z-axis, otherwise on the line parallel to the
+        y-axis).
+
+        Parameters
+        ==========
+
+        pts: 0, 1 or 2 Point3D
+
+        Returns
+        =======
+
+        Plane
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> a, b = Point3D(0, 0, 0), Point3D(0, 1, 0)
+        >>> Z = (0, 0, 1)
+        >>> p = Plane(a, normal_vector=Z)
+        >>> p.perpendicular_plane(a, b)
+        Plane(Point3D(0, 0, 0), (1, 0, 0))
+        """
+        if len(pts) > 2:
+            raise ValueError('No more than 2 pts should be provided.')
+
+        pts = list(pts)
+        if len(pts) == 0:
+            pts.append(self.p1)
+        if len(pts) == 1:
+            x, y, z = self.normal_vector
+            if x == y == 0:
+                dir = (0, 1, 0)
+            else:
+                dir = (0, 0, 1)
+            pts.append(pts[0] + Point3D(*dir))
+
+        p1, p2 = [Point(i, dim=3) for i in pts]
+        l = Line3D(p1, p2)
+        n = Line3D(p1, direction_ratio=self.normal_vector)
+        if l in n:  # XXX should an error be raised instead?
+            # there are infinitely many perpendicular planes;
+            x, y, z = self.normal_vector
+            if x == y == 0:
+                # the z axis is the normal so pick a pt on the y-axis
+                p3 = Point3D(0, 1, 0)  # case 1
+            else:
+                # else pick a pt on the z axis
+                p3 = Point3D(0, 0, 1)  # case 2
+            # in case that point is already given, move it a bit
+            if p3 in l:
+                p3 *= 2  # case 3
+        else:
+            p3 = p1 + Point3D(*self.normal_vector)  # case 4
+        return Plane(p1, p2, p3)
+
+    def projection_line(self, line):
+        """Project the given line onto the plane through the normal plane
+        containing the line.
+
+        Parameters
+        ==========
+
+        LinearEntity or LinearEntity3D
+
+        Returns
+        =======
+
+        Point3D, Line3D, Ray3D or Segment3D
+
+        Notes
+        =====
+
+        For the interaction between 2D and 3D lines(segments, rays), you should
+        convert the line to 3D by using this method. For example for finding the
+        intersection between a 2D and a 3D line, convert the 2D line to a 3D line
+        by projecting it on a required plane and then proceed to find the
+        intersection between those lines.
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Line, Line3D, Point3D
+        >>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 1, 1))
+        >>> b = Line(Point3D(1, 1), Point3D(2, 2))
+        >>> a.projection_line(b)
+        Line3D(Point3D(4/3, 4/3, 1/3), Point3D(5/3, 5/3, -1/3))
+        >>> c = Line3D(Point3D(1, 1, 1), Point3D(2, 2, 2))
+        >>> a.projection_line(c)
+        Point3D(1, 1, 1)
+
+        """
+        if not isinstance(line, (LinearEntity, LinearEntity3D)):
+            raise NotImplementedError('Enter a linear entity only')
+        a, b = self.projection(line.p1), self.projection(line.p2)
+        if a == b:
+            # projection does not imply intersection so for
+            # this case (line parallel to plane's normal) we
+            # return the projection point
+            return a
+        if isinstance(line, (Line, Line3D)):
+            return Line3D(a, b)
+        if isinstance(line, (Ray, Ray3D)):
+            return Ray3D(a, b)
+        if isinstance(line, (Segment, Segment3D)):
+            return Segment3D(a, b)
+
+    def projection(self, pt):
+        """Project the given point onto the plane along the plane normal.
+
+        Parameters
+        ==========
+
+        Point or Point3D
+
+        Returns
+        =======
+
+        Point3D
+
+        Examples
+        ========
+
+        >>> from sympy import Plane, Point3D
+        >>> A = Plane(Point3D(1, 1, 2), normal_vector=(1, 1, 1))
+
+        The projection is along the normal vector direction, not the z
+        axis, so (1, 1) does not project to (1, 1, 2) on the plane A:
+
+        >>> b = Point3D(1, 1)
+        >>> A.projection(b)
+        Point3D(5/3, 5/3, 2/3)
+        >>> _ in A
+        True
+
+        But the point (1, 1, 2) projects to (1, 1) on the XY-plane:
+
+        >>> XY = Plane((0, 0, 0), (0, 0, 1))
+        >>> XY.projection((1, 1, 2))
+        Point3D(1, 1, 0)
+        """
+        rv = Point(pt, dim=3)
+        if rv in self:
+            return rv
+        return self.intersection(Line3D(rv, rv + Point3D(self.normal_vector)))[0]
+
+    def random_point(self, seed=None):
+        """ Returns a random point on the Plane.
+
+        Returns
+        =======
+
+        Point3D
+
+        Examples
+        ========
+
+        >>> from sympy import Plane
+        >>> p = Plane((1, 0, 0), normal_vector=(0, 1, 0))
+        >>> r = p.random_point(seed=42)  # seed value is optional
+        >>> r.n(3)
+        Point3D(2.29, 0, -1.35)
+
+        The random point can be moved to lie on the circle of radius
+        1 centered on p1:
+
+        >>> c = p.p1 + (r - p.p1).unit
+        >>> c.distance(p.p1).equals(1)
+        True
+        """
+        if seed is not None:
+            rng = random.Random(seed)
+        else:
+            rng = random
+        params = {
+            x: 2*Rational(rng.gauss(0, 1)) - 1,
+            y: 2*Rational(rng.gauss(0, 1)) - 1}
+        return self.arbitrary_point(x, y).subs(params)
+
+    def parameter_value(self, other, u, v=None):
+        """Return the parameter(s) corresponding to the given point.
+
+        Examples
+        ========
+
+        >>> from sympy import pi, Plane
+        >>> from sympy.abc import t, u, v
+        >>> p = Plane((2, 0, 0), (0, 0, 1), (0, 1, 0))
+
+        By default, the parameter value returned defines a point
+        that is a distance of 1 from the Plane's p1 value and
+        in line with the given point:
+
+        >>> on_circle = p.arbitrary_point(t).subs(t, pi/4)
+        >>> on_circle.distance(p.p1)
+        1
+        >>> p.parameter_value(on_circle, t)
+        {t: pi/4}
+
+        Moving the point twice as far from p1 does not change
+        the parameter value:
+
+        >>> off_circle = p.p1 + (on_circle - p.p1)*2
+        >>> off_circle.distance(p.p1)
+        2
+        >>> p.parameter_value(off_circle, t)
+        {t: pi/4}
+
+        If the 2-value parameter is desired, supply the two
+        parameter symbols and a replacement dictionary will
+        be returned:
+
+        >>> p.parameter_value(on_circle, u, v)
+        {u: sqrt(10)/10, v: sqrt(10)/30}
+        >>> p.parameter_value(off_circle, u, v)
+        {u: sqrt(10)/5, v: sqrt(10)/15}
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if not isinstance(other, Point):
+            raise ValueError("other must be a point")
+        if other == self.p1:
+            return other
+        if isinstance(u, Symbol) and v is None:
+            delta = self.arbitrary_point(u) - self.p1
+            eq = delta - (other - self.p1).unit
+            sol = solve(eq, u, dict=True)
+        elif isinstance(u, Symbol) and isinstance(v, Symbol):
+            pt = self.arbitrary_point(u, v)
+            sol = solve(pt - other, (u, v), dict=True)
+        else:
+            raise ValueError('expecting 1 or 2 symbols')
+        if not sol:
+            raise ValueError("Given point is not on %s" % func_name(self))
+        return sol[0]  # {t: tval} or {u: uval, v: vval}
+
+    @property
+    def ambient_dimension(self):
+        return self.p1.ambient_dimension
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/point.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/point.py
new file mode 100644
index 0000000000000000000000000000000000000000..19e6c566f06de4df086912470dc35d0f4af3bd38
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/point.py
@@ -0,0 +1,1378 @@
+"""Geometrical Points.
+
+Contains
+========
+Point
+Point2D
+Point3D
+
+When methods of Point require 1 or more points as arguments, they
+can be passed as a sequence of coordinates or Points:
+
+>>> from sympy import Point
+>>> Point(1, 1).is_collinear((2, 2), (3, 4))
+False
+>>> Point(1, 1).is_collinear(Point(2, 2), Point(3, 4))
+False
+
+"""
+
+import warnings
+
+from sympy.core import S, sympify, Expr
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.numbers import Float
+from sympy.core.parameters import global_parameters
+from sympy.simplify.simplify import nsimplify, simplify
+from sympy.geometry.exceptions import GeometryError
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.complexes import im
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.matrices import Matrix
+from sympy.matrices.expressions import Transpose
+from sympy.utilities.iterables import uniq, is_sequence
+from sympy.utilities.misc import filldedent, func_name, Undecidable
+
+from .entity import GeometryEntity
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+
+class Point(GeometryEntity):
+    """A point in a n-dimensional Euclidean space.
+
+    Parameters
+    ==========
+
+    coords : sequence of n-coordinate values. In the special
+        case where n=2 or 3, a Point2D or Point3D will be created
+        as appropriate.
+    evaluate : if `True` (default), all floats are turn into
+        exact types.
+    dim : number of coordinates the point should have.  If coordinates
+        are unspecified, they are padded with zeros.
+    on_morph : indicates what should happen when the number of
+        coordinates of a point need to be changed by adding or
+        removing zeros.  Possible values are `'warn'`, `'error'`, or
+        `ignore` (default).  No warning or error is given when `*args`
+        is empty and `dim` is given. An error is always raised when
+        trying to remove nonzero coordinates.
+
+
+    Attributes
+    ==========
+
+    length
+    origin: A `Point` representing the origin of the
+        appropriately-dimensioned space.
+
+    Raises
+    ======
+
+    TypeError : When instantiating with anything but a Point or sequence
+    ValueError : when instantiating with a sequence with length < 2 or
+        when trying to reduce dimensions if keyword `on_morph='error'` is
+        set.
+
+    See Also
+    ========
+
+    sympy.geometry.line.Segment : Connects two Points
+
+    Examples
+    ========
+
+    >>> from sympy import Point
+    >>> from sympy.abc import x
+    >>> Point(1, 2, 3)
+    Point3D(1, 2, 3)
+    >>> Point([1, 2])
+    Point2D(1, 2)
+    >>> Point(0, x)
+    Point2D(0, x)
+    >>> Point(dim=4)
+    Point(0, 0, 0, 0)
+
+    Floats are automatically converted to Rational unless the
+    evaluate flag is False:
+
+    >>> Point(0.5, 0.25)
+    Point2D(1/2, 1/4)
+    >>> Point(0.5, 0.25, evaluate=False)
+    Point2D(0.5, 0.25)
+
+    """
+
+    is_Point = True
+
+    def __new__(cls, *args, **kwargs):
+        evaluate = kwargs.get('evaluate', global_parameters.evaluate)
+        on_morph = kwargs.get('on_morph', 'ignore')
+
+        # unpack into coords
+        coords = args[0] if len(args) == 1 else args
+
+        # check args and handle quickly handle Point instances
+        if isinstance(coords, Point):
+            # even if we're mutating the dimension of a point, we
+            # don't reevaluate its coordinates
+            evaluate = False
+            if len(coords) == kwargs.get('dim', len(coords)):
+                return coords
+
+        if not is_sequence(coords):
+            raise TypeError(filldedent('''
+                Expecting sequence of coordinates, not `{}`'''
+                                       .format(func_name(coords))))
+        # A point where only `dim` is specified is initialized
+        # to zeros.
+        if len(coords) == 0 and kwargs.get('dim', None):
+            coords = (S.Zero,)*kwargs.get('dim')
+
+        coords = Tuple(*coords)
+        dim = kwargs.get('dim', len(coords))
+
+        if len(coords) < 2:
+            raise ValueError(filldedent('''
+                Point requires 2 or more coordinates or
+                keyword `dim` > 1.'''))
+        if len(coords) != dim:
+            message = ("Dimension of {} needs to be changed "
+                       "from {} to {}.").format(coords, len(coords), dim)
+            if on_morph == 'ignore':
+                pass
+            elif on_morph == "error":
+                raise ValueError(message)
+            elif on_morph == 'warn':
+                warnings.warn(message, stacklevel=2)
+            else:
+                raise ValueError(filldedent('''
+                        on_morph value should be 'error',
+                        'warn' or 'ignore'.'''))
+        if any(coords[dim:]):
+            raise ValueError('Nonzero coordinates cannot be removed.')
+        if any(a.is_number and im(a).is_zero is False for a in coords):
+            raise ValueError('Imaginary coordinates are not permitted.')
+        if not all(isinstance(a, Expr) for a in coords):
+            raise TypeError('Coordinates must be valid SymPy expressions.')
+
+        # pad with zeros appropriately
+        coords = coords[:dim] + (S.Zero,)*(dim - len(coords))
+
+        # Turn any Floats into rationals and simplify
+        # any expressions before we instantiate
+        if evaluate:
+            coords = coords.xreplace({
+                f: simplify(nsimplify(f, rational=True))
+                 for f in coords.atoms(Float)})
+
+        # return 2D or 3D instances
+        if len(coords) == 2:
+            kwargs['_nocheck'] = True
+            return Point2D(*coords, **kwargs)
+        elif len(coords) == 3:
+            kwargs['_nocheck'] = True
+            return Point3D(*coords, **kwargs)
+
+        # the general Point
+        return GeometryEntity.__new__(cls, *coords)
+
+    def __abs__(self):
+        """Returns the distance between this point and the origin."""
+        origin = Point([0]*len(self))
+        return Point.distance(origin, self)
+
+    def __add__(self, other):
+        """Add other to self by incrementing self's coordinates by
+        those of other.
+
+        Notes
+        =====
+
+        >>> from sympy import Point
+
+        When sequences of coordinates are passed to Point methods, they
+        are converted to a Point internally. This __add__ method does
+        not do that so if floating point values are used, a floating
+        point result (in terms of SymPy Floats) will be returned.
+
+        >>> Point(1, 2) + (.1, .2)
+        Point2D(1.1, 2.2)
+
+        If this is not desired, the `translate` method can be used or
+        another Point can be added:
+
+        >>> Point(1, 2).translate(.1, .2)
+        Point2D(11/10, 11/5)
+        >>> Point(1, 2) + Point(.1, .2)
+        Point2D(11/10, 11/5)
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.translate
+
+        """
+        try:
+            s, o = Point._normalize_dimension(self, Point(other, evaluate=False))
+        except TypeError:
+            raise GeometryError("Don't know how to add {} and a Point object".format(other))
+
+        coords = [simplify(a + b) for a, b in zip(s, o)]
+        return Point(coords, evaluate=False)
+
+    def __contains__(self, item):
+        return item in self.args
+
+    def __truediv__(self, divisor):
+        """Divide point's coordinates by a factor."""
+        divisor = sympify(divisor)
+        coords = [simplify(x/divisor) for x in self.args]
+        return Point(coords, evaluate=False)
+
+    def __eq__(self, other):
+        if not isinstance(other, Point) or len(self.args) != len(other.args):
+            return False
+        return self.args == other.args
+
+    def __getitem__(self, key):
+        return self.args[key]
+
+    def __hash__(self):
+        return hash(self.args)
+
+    def __iter__(self):
+        return self.args.__iter__()
+
+    def __len__(self):
+        return len(self.args)
+
+    def __mul__(self, factor):
+        """Multiply point's coordinates by a factor.
+
+        Notes
+        =====
+
+        >>> from sympy import Point
+
+        When multiplying a Point by a floating point number,
+        the coordinates of the Point will be changed to Floats:
+
+        >>> Point(1, 2)*0.1
+        Point2D(0.1, 0.2)
+
+        If this is not desired, the `scale` method can be used or
+        else only multiply or divide by integers:
+
+        >>> Point(1, 2).scale(1.1, 1.1)
+        Point2D(11/10, 11/5)
+        >>> Point(1, 2)*11/10
+        Point2D(11/10, 11/5)
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.scale
+        """
+        factor = sympify(factor)
+        coords = [simplify(x*factor) for x in self.args]
+        return Point(coords, evaluate=False)
+
+    def __rmul__(self, factor):
+        """Multiply a factor by point's coordinates."""
+        return self.__mul__(factor)
+
+    def __neg__(self):
+        """Negate the point."""
+        coords = [-x for x in self.args]
+        return Point(coords, evaluate=False)
+
+    def __sub__(self, other):
+        """Subtract two points, or subtract a factor from this point's
+        coordinates."""
+        return self + [-x for x in other]
+
+    @classmethod
+    def _normalize_dimension(cls, *points, **kwargs):
+        """Ensure that points have the same dimension.
+        By default `on_morph='warn'` is passed to the
+        `Point` constructor."""
+        # if we have a built-in ambient dimension, use it
+        dim = getattr(cls, '_ambient_dimension', None)
+        # override if we specified it
+        dim = kwargs.get('dim', dim)
+        # if no dim was given, use the highest dimensional point
+        if dim is None:
+            dim = max(i.ambient_dimension for i in points)
+        if all(i.ambient_dimension == dim for i in points):
+            return list(points)
+        kwargs['dim'] = dim
+        kwargs['on_morph'] = kwargs.get('on_morph', 'warn')
+        return [Point(i, **kwargs) for i in points]
+
+    @staticmethod
+    def affine_rank(*args):
+        """The affine rank of a set of points is the dimension
+        of the smallest affine space containing all the points.
+        For example, if the points lie on a line (and are not all
+        the same) their affine rank is 1.  If the points lie on a plane
+        but not a line, their affine rank is 2.  By convention, the empty
+        set has affine rank -1."""
+
+        if len(args) == 0:
+            return -1
+        # make sure we're genuinely points
+        # and translate every point to the origin
+        points = Point._normalize_dimension(*[Point(i) for i in args])
+        origin = points[0]
+        points = [i - origin for i in points[1:]]
+
+        m = Matrix([i.args for i in points])
+        # XXX fragile -- what is a better way?
+        return m.rank(iszerofunc = lambda x:
+            abs(x.n(2)) < 1e-12 if x.is_number else x.is_zero)
+
+    @property
+    def ambient_dimension(self):
+        """Number of components this point has."""
+        return getattr(self, '_ambient_dimension', len(self))
+
+    @classmethod
+    def are_coplanar(cls, *points):
+        """Return True if there exists a plane in which all the points
+        lie.  A trivial True value is returned if `len(points) < 3` or
+        all Points are 2-dimensional.
+
+        Parameters
+        ==========
+
+        A set of points
+
+        Raises
+        ======
+
+        ValueError : if less than 3 unique points are given
+
+        Returns
+        =======
+
+        boolean
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p1 = Point3D(1, 2, 2)
+        >>> p2 = Point3D(2, 7, 2)
+        >>> p3 = Point3D(0, 0, 2)
+        >>> p4 = Point3D(1, 1, 2)
+        >>> Point3D.are_coplanar(p1, p2, p3, p4)
+        True
+        >>> p5 = Point3D(0, 1, 3)
+        >>> Point3D.are_coplanar(p1, p2, p3, p5)
+        False
+
+        """
+        if len(points) <= 1:
+            return True
+
+        points = cls._normalize_dimension(*[Point(i) for i in points])
+        # quick exit if we are in 2D
+        if points[0].ambient_dimension == 2:
+            return True
+        points = list(uniq(points))
+        return Point.affine_rank(*points) <= 2
+
+    def distance(self, other):
+        """The Euclidean distance between self and another GeometricEntity.
+
+        Returns
+        =======
+
+        distance : number or symbolic expression.
+
+        Raises
+        ======
+
+        TypeError : if other is not recognized as a GeometricEntity or is a
+                    GeometricEntity for which distance is not defined.
+
+        See Also
+        ========
+
+        sympy.geometry.line.Segment.length
+        sympy.geometry.point.Point.taxicab_distance
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Line
+        >>> p1, p2 = Point(1, 1), Point(4, 5)
+        >>> l = Line((3, 1), (2, 2))
+        >>> p1.distance(p2)
+        5
+        >>> p1.distance(l)
+        sqrt(2)
+
+        The computed distance may be symbolic, too:
+
+        >>> from sympy.abc import x, y
+        >>> p3 = Point(x, y)
+        >>> p3.distance((0, 0))
+        sqrt(x**2 + y**2)
+
+        """
+        if not isinstance(other, GeometryEntity):
+            try:
+                other = Point(other, dim=self.ambient_dimension)
+            except TypeError:
+                raise TypeError("not recognized as a GeometricEntity: %s" % type(other))
+        if isinstance(other, Point):
+            s, p = Point._normalize_dimension(self, Point(other))
+            return sqrt(Add(*((a - b)**2 for a, b in zip(s, p))))
+        distance = getattr(other, 'distance', None)
+        if distance is None:
+            raise TypeError("distance between Point and %s is not defined" % type(other))
+        return distance(self)
+
+    def dot(self, p):
+        """Return dot product of self with another Point."""
+        if not is_sequence(p):
+            p = Point(p)  # raise the error via Point
+        return Add(*(a*b for a, b in zip(self, p)))
+
+    def equals(self, other):
+        """Returns whether the coordinates of self and other agree."""
+        # a point is equal to another point if all its components are equal
+        if not isinstance(other, Point) or len(self) != len(other):
+            return False
+        return all(a.equals(b) for a, b in zip(self, other))
+
+    def _eval_evalf(self, prec=15, **options):
+        """Evaluate the coordinates of the point.
+
+        This method will, where possible, create and return a new Point
+        where the coordinates are evaluated as floating point numbers to
+        the precision indicated (default=15).
+
+        Parameters
+        ==========
+
+        prec : int
+
+        Returns
+        =======
+
+        point : Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Rational
+        >>> p1 = Point(Rational(1, 2), Rational(3, 2))
+        >>> p1
+        Point2D(1/2, 3/2)
+        >>> p1.evalf()
+        Point2D(0.5, 1.5)
+
+        """
+        dps = prec_to_dps(prec)
+        coords = [x.evalf(n=dps, **options) for x in self.args]
+        return Point(*coords, evaluate=False)
+
+    def intersection(self, other):
+        """The intersection between this point and another GeometryEntity.
+
+        Parameters
+        ==========
+
+        other : GeometryEntity or sequence of coordinates
+
+        Returns
+        =======
+
+        intersection : list of Points
+
+        Notes
+        =====
+
+        The return value will either be an empty list if there is no
+        intersection, otherwise it will contain this point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, 0)
+        >>> p1.intersection(p2)
+        []
+        >>> p1.intersection(p3)
+        [Point2D(0, 0)]
+
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other)
+        if isinstance(other, Point):
+            if self == other:
+                return [self]
+            p1, p2 = Point._normalize_dimension(self, other)
+            if p1 == self and p1 == p2:
+                return [self]
+            return []
+        return other.intersection(self)
+
+    def is_collinear(self, *args):
+        """Returns `True` if there exists a line
+        that contains `self` and `points`.  Returns `False` otherwise.
+        A trivially True value is returned if no points are given.
+
+        Parameters
+        ==========
+
+        args : sequence of Points
+
+        Returns
+        =======
+
+        is_collinear : boolean
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+        >>> from sympy.abc import x
+        >>> p1, p2 = Point(0, 0), Point(1, 1)
+        >>> p3, p4, p5 = Point(2, 2), Point(x, x), Point(1, 2)
+        >>> Point.is_collinear(p1, p2, p3, p4)
+        True
+        >>> Point.is_collinear(p1, p2, p3, p5)
+        False
+
+        """
+        points = (self,) + args
+        points = Point._normalize_dimension(*[Point(i) for i in points])
+        points = list(uniq(points))
+        return Point.affine_rank(*points) <= 1
+
+    def is_concyclic(self, *args):
+        """Do `self` and the given sequence of points lie in a circle?
+
+        Returns True if the set of points are concyclic and
+        False otherwise. A trivial value of True is returned
+        if there are fewer than 2 other points.
+
+        Parameters
+        ==========
+
+        args : sequence of Points
+
+        Returns
+        =======
+
+        is_concyclic : boolean
+
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+
+        Define 4 points that are on the unit circle:
+
+        >>> p1, p2, p3, p4 = Point(1, 0), (0, 1), (-1, 0), (0, -1)
+
+        >>> p1.is_concyclic() == p1.is_concyclic(p2, p3, p4) == True
+        True
+
+        Define a point not on that circle:
+
+        >>> p = Point(1, 1)
+
+        >>> p.is_concyclic(p1, p2, p3)
+        False
+
+        """
+        points = (self,) + args
+        points = Point._normalize_dimension(*[Point(i) for i in points])
+        points = list(uniq(points))
+        if not Point.affine_rank(*points) <= 2:
+            return False
+        origin = points[0]
+        points = [p - origin for p in points]
+        # points are concyclic if they are coplanar and
+        # there is a point c so that ||p_i-c|| == ||p_j-c|| for all
+        # i and j.  Rearranging this equation gives us the following
+        # condition: the matrix `mat` must not a pivot in the last
+        # column.
+        mat = Matrix([list(i) + [i.dot(i)] for i in points])
+        rref, pivots = mat.rref()
+        if len(origin) not in pivots:
+            return True
+        return False
+
+    @property
+    def is_nonzero(self):
+        """True if any coordinate is nonzero, False if every coordinate is zero,
+        and None if it cannot be determined."""
+        is_zero = self.is_zero
+        if is_zero is None:
+            return None
+        return not is_zero
+
+    def is_scalar_multiple(self, p):
+        """Returns whether each coordinate of `self` is a scalar
+        multiple of the corresponding coordinate in point p.
+        """
+        s, o = Point._normalize_dimension(self, Point(p))
+        # 2d points happen a lot, so optimize this function call
+        if s.ambient_dimension == 2:
+            (x1, y1), (x2, y2) = s.args, o.args
+            rv = (x1*y2 - x2*y1).equals(0)
+            if rv is None:
+                raise Undecidable(filldedent(
+                    '''Cannot determine if %s is a scalar multiple of
+                    %s''' % (s, o)))
+
+        # if the vectors p1 and p2 are linearly dependent, then they must
+        # be scalar multiples of each other
+        m = Matrix([s.args, o.args])
+        return m.rank() < 2
+
+    @property
+    def is_zero(self):
+        """True if every coordinate is zero, False if any coordinate is not zero,
+        and None if it cannot be determined."""
+        nonzero = [x.is_nonzero for x in self.args]
+        if any(nonzero):
+            return False
+        if any(x is None for x in nonzero):
+            return None
+        return True
+
+    @property
+    def length(self):
+        """
+        Treating a Point as a Line, this returns 0 for the length of a Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+        >>> p = Point(0, 1)
+        >>> p.length
+        0
+        """
+        return S.Zero
+
+    def midpoint(self, p):
+        """The midpoint between self and point p.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        midpoint : Point
+
+        See Also
+        ========
+
+        sympy.geometry.line.Segment.midpoint
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+        >>> p1, p2 = Point(1, 1), Point(13, 5)
+        >>> p1.midpoint(p2)
+        Point2D(7, 3)
+
+        """
+        s, p = Point._normalize_dimension(self, Point(p))
+        return Point([simplify((a + b)*S.Half) for a, b in zip(s, p)])
+
+    @property
+    def origin(self):
+        """A point of all zeros of the same ambient dimension
+        as the current point"""
+        return Point([0]*len(self), evaluate=False)
+
+    @property
+    def orthogonal_direction(self):
+        """Returns a non-zero point that is orthogonal to the
+        line containing `self` and the origin.
+
+        Examples
+        ========
+
+        >>> from sympy import Line, Point
+        >>> a = Point(1, 2, 3)
+        >>> a.orthogonal_direction
+        Point3D(-2, 1, 0)
+        >>> b = _
+        >>> Line(b, b.origin).is_perpendicular(Line(a, a.origin))
+        True
+        """
+        dim = self.ambient_dimension
+        # if a coordinate is zero, we can put a 1 there and zeros elsewhere
+        if self[0].is_zero:
+            return Point([1] + (dim - 1)*[0])
+        if self[1].is_zero:
+            return Point([0,1] + (dim - 2)*[0])
+        # if the first two coordinates aren't zero, we can create a non-zero
+        # orthogonal vector by swapping them, negating one, and padding with zeros
+        return Point([-self[1], self[0]] + (dim - 2)*[0])
+
+    @staticmethod
+    def project(a, b):
+        """Project the point `a` onto the line between the origin
+        and point `b` along the normal direction.
+
+        Parameters
+        ==========
+
+        a : Point
+        b : Point
+
+        Returns
+        =======
+
+        p : Point
+
+        See Also
+        ========
+
+        sympy.geometry.line.LinearEntity.projection
+
+        Examples
+        ========
+
+        >>> from sympy import Line, Point
+        >>> a = Point(1, 2)
+        >>> b = Point(2, 5)
+        >>> z = a.origin
+        >>> p = Point.project(a, b)
+        >>> Line(p, a).is_perpendicular(Line(p, b))
+        True
+        >>> Point.is_collinear(z, p, b)
+        True
+        """
+        a, b = Point._normalize_dimension(Point(a), Point(b))
+        if b.is_zero:
+            raise ValueError("Cannot project to the zero vector.")
+        return b*(a.dot(b) / b.dot(b))
+
+    def taxicab_distance(self, p):
+        """The Taxicab Distance from self to point p.
+
+        Returns the sum of the horizontal and vertical distances to point p.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        taxicab_distance : The sum of the horizontal
+        and vertical distances to point p.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.distance
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+        >>> p1, p2 = Point(1, 1), Point(4, 5)
+        >>> p1.taxicab_distance(p2)
+        7
+
+        """
+        s, p = Point._normalize_dimension(self, Point(p))
+        return Add(*(abs(a - b) for a, b in zip(s, p)))
+
+    def canberra_distance(self, p):
+        """The Canberra Distance from self to point p.
+
+        Returns the weighted sum of horizontal and vertical distances to
+        point p.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        canberra_distance : The weighted sum of horizontal and vertical
+        distances to point p. The weight used is the sum of absolute values
+        of the coordinates.
+
+        Examples
+        ========
+
+        >>> from sympy import Point
+        >>> p1, p2 = Point(1, 1), Point(3, 3)
+        >>> p1.canberra_distance(p2)
+        1
+        >>> p1, p2 = Point(0, 0), Point(3, 3)
+        >>> p1.canberra_distance(p2)
+        2
+
+        Raises
+        ======
+
+        ValueError when both vectors are zero.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.distance
+
+        """
+
+        s, p = Point._normalize_dimension(self, Point(p))
+        if self.is_zero and p.is_zero:
+            raise ValueError("Cannot project to the zero vector.")
+        return Add(*((abs(a - b)/(abs(a) + abs(b))) for a, b in zip(s, p)))
+
+    @property
+    def unit(self):
+        """Return the Point that is in the same direction as `self`
+        and a distance of 1 from the origin"""
+        return self / abs(self)
+
+
+class Point2D(Point):
+    """A point in a 2-dimensional Euclidean space.
+
+    Parameters
+    ==========
+
+    coords
+        A sequence of 2 coordinate values.
+
+    Attributes
+    ==========
+
+    x
+    y
+    length
+
+    Raises
+    ======
+
+    TypeError
+        When trying to add or subtract points with different dimensions.
+        When trying to create a point with more than two dimensions.
+        When `intersection` is called with object other than a Point.
+
+    See Also
+    ========
+
+    sympy.geometry.line.Segment : Connects two Points
+
+    Examples
+    ========
+
+    >>> from sympy import Point2D
+    >>> from sympy.abc import x
+    >>> Point2D(1, 2)
+    Point2D(1, 2)
+    >>> Point2D([1, 2])
+    Point2D(1, 2)
+    >>> Point2D(0, x)
+    Point2D(0, x)
+
+    Floats are automatically converted to Rational unless the
+    evaluate flag is False:
+
+    >>> Point2D(0.5, 0.25)
+    Point2D(1/2, 1/4)
+    >>> Point2D(0.5, 0.25, evaluate=False)
+    Point2D(0.5, 0.25)
+
+    """
+
+    _ambient_dimension = 2
+
+    def __new__(cls, *args, _nocheck=False, **kwargs):
+        if not _nocheck:
+            kwargs['dim'] = 2
+            args = Point(*args, **kwargs)
+        return GeometryEntity.__new__(cls, *args)
+
+    def __contains__(self, item):
+        return item == self
+
+    @property
+    def bounds(self):
+        """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
+        rectangle for the geometric figure.
+
+        """
+
+        return (self.x, self.y, self.x, self.y)
+
+    def rotate(self, angle, pt=None):
+        """Rotate ``angle`` radians counterclockwise about Point ``pt``.
+
+        See Also
+        ========
+
+        translate, scale
+
+        Examples
+        ========
+
+        >>> from sympy import Point2D, pi
+        >>> t = Point2D(1, 0)
+        >>> t.rotate(pi/2)
+        Point2D(0, 1)
+        >>> t.rotate(pi/2, (2, 0))
+        Point2D(2, -1)
+
+        """
+        c = cos(angle)
+        s = sin(angle)
+
+        rv = self
+        if pt is not None:
+            pt = Point(pt, dim=2)
+            rv -= pt
+        x, y = rv.args
+        rv = Point(c*x - s*y, s*x + c*y)
+        if pt is not None:
+            rv += pt
+        return rv
+
+    def scale(self, x=1, y=1, pt=None):
+        """Scale the coordinates of the Point by multiplying by
+        ``x`` and ``y`` after subtracting ``pt`` -- default is (0, 0) --
+        and then adding ``pt`` back again (i.e. ``pt`` is the point of
+        reference for the scaling).
+
+        See Also
+        ========
+
+        rotate, translate
+
+        Examples
+        ========
+
+        >>> from sympy import Point2D
+        >>> t = Point2D(1, 1)
+        >>> t.scale(2)
+        Point2D(2, 1)
+        >>> t.scale(2, 2)
+        Point2D(2, 2)
+
+        """
+        if pt:
+            pt = Point(pt, dim=2)
+            return self.translate(*(-pt).args).scale(x, y).translate(*pt.args)
+        return Point(self.x*x, self.y*y)
+
+    def transform(self, matrix):
+        """Return the point after applying the transformation described
+        by the 3x3 Matrix, ``matrix``.
+
+        See Also
+        ========
+        sympy.geometry.point.Point2D.rotate
+        sympy.geometry.point.Point2D.scale
+        sympy.geometry.point.Point2D.translate
+        """
+        if not (matrix.is_Matrix and matrix.shape == (3, 3)):
+            raise ValueError("matrix must be a 3x3 matrix")
+        x, y = self.args
+        return Point(*(Matrix(1, 3, [x, y, 1])*matrix).tolist()[0][:2])
+
+    def translate(self, x=0, y=0):
+        """Shift the Point by adding x and y to the coordinates of the Point.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point2D.rotate, scale
+
+        Examples
+        ========
+
+        >>> from sympy import Point2D
+        >>> t = Point2D(0, 1)
+        >>> t.translate(2)
+        Point2D(2, 1)
+        >>> t.translate(2, 2)
+        Point2D(2, 3)
+        >>> t + Point2D(2, 2)
+        Point2D(2, 3)
+
+        """
+        return Point(self.x + x, self.y + y)
+
+    @property
+    def coordinates(self):
+        """
+        Returns the two coordinates of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point2D
+        >>> p = Point2D(0, 1)
+        >>> p.coordinates
+        (0, 1)
+        """
+        return self.args
+
+    @property
+    def x(self):
+        """
+        Returns the X coordinate of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point2D
+        >>> p = Point2D(0, 1)
+        >>> p.x
+        0
+        """
+        return self.args[0]
+
+    @property
+    def y(self):
+        """
+        Returns the Y coordinate of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point2D
+        >>> p = Point2D(0, 1)
+        >>> p.y
+        1
+        """
+        return self.args[1]
+
+class Point3D(Point):
+    """A point in a 3-dimensional Euclidean space.
+
+    Parameters
+    ==========
+
+    coords
+        A sequence of 3 coordinate values.
+
+    Attributes
+    ==========
+
+    x
+    y
+    z
+    length
+
+    Raises
+    ======
+
+    TypeError
+        When trying to add or subtract points with different dimensions.
+        When `intersection` is called with object other than a Point.
+
+    Examples
+    ========
+
+    >>> from sympy import Point3D
+    >>> from sympy.abc import x
+    >>> Point3D(1, 2, 3)
+    Point3D(1, 2, 3)
+    >>> Point3D([1, 2, 3])
+    Point3D(1, 2, 3)
+    >>> Point3D(0, x, 3)
+    Point3D(0, x, 3)
+
+    Floats are automatically converted to Rational unless the
+    evaluate flag is False:
+
+    >>> Point3D(0.5, 0.25, 2)
+    Point3D(1/2, 1/4, 2)
+    >>> Point3D(0.5, 0.25, 3, evaluate=False)
+    Point3D(0.5, 0.25, 3)
+
+    """
+
+    _ambient_dimension = 3
+
+    def __new__(cls, *args, _nocheck=False, **kwargs):
+        if not _nocheck:
+            kwargs['dim'] = 3
+            args = Point(*args, **kwargs)
+        return GeometryEntity.__new__(cls, *args)
+
+    def __contains__(self, item):
+        return item == self
+
+    @staticmethod
+    def are_collinear(*points):
+        """Is a sequence of points collinear?
+
+        Test whether or not a set of points are collinear. Returns True if
+        the set of points are collinear, or False otherwise.
+
+        Parameters
+        ==========
+
+        points : sequence of Point
+
+        Returns
+        =======
+
+        are_collinear : boolean
+
+        See Also
+        ========
+
+        sympy.geometry.line.Line3D
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> from sympy.abc import x
+        >>> p1, p2 = Point3D(0, 0, 0), Point3D(1, 1, 1)
+        >>> p3, p4, p5 = Point3D(2, 2, 2), Point3D(x, x, x), Point3D(1, 2, 6)
+        >>> Point3D.are_collinear(p1, p2, p3, p4)
+        True
+        >>> Point3D.are_collinear(p1, p2, p3, p5)
+        False
+        """
+        return Point.is_collinear(*points)
+
+    def direction_cosine(self, point):
+        """
+        Gives the direction cosine between 2 points
+
+        Parameters
+        ==========
+
+        p : Point3D
+
+        Returns
+        =======
+
+        list
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p1 = Point3D(1, 2, 3)
+        >>> p1.direction_cosine(Point3D(2, 3, 5))
+        [sqrt(6)/6, sqrt(6)/6, sqrt(6)/3]
+        """
+        a = self.direction_ratio(point)
+        b = sqrt(Add(*(i**2 for i in a)))
+        return [(point.x - self.x) / b,(point.y - self.y) / b,
+                (point.z - self.z) / b]
+
+    def direction_ratio(self, point):
+        """
+        Gives the direction ratio between 2 points
+
+        Parameters
+        ==========
+
+        p : Point3D
+
+        Returns
+        =======
+
+        list
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p1 = Point3D(1, 2, 3)
+        >>> p1.direction_ratio(Point3D(2, 3, 5))
+        [1, 1, 2]
+        """
+        return [(point.x - self.x),(point.y - self.y),(point.z - self.z)]
+
+    def intersection(self, other):
+        """The intersection between this point and another GeometryEntity.
+
+        Parameters
+        ==========
+
+        other : GeometryEntity or sequence of coordinates
+
+        Returns
+        =======
+
+        intersection : list of Points
+
+        Notes
+        =====
+
+        The return value will either be an empty list if there is no
+        intersection, otherwise it will contain this point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, 0, 0)
+        >>> p1.intersection(p2)
+        []
+        >>> p1.intersection(p3)
+        [Point3D(0, 0, 0)]
+
+        """
+        if not isinstance(other, GeometryEntity):
+            other = Point(other, dim=3)
+        if isinstance(other, Point3D):
+            if self == other:
+                return [self]
+            return []
+        return other.intersection(self)
+
+    def scale(self, x=1, y=1, z=1, pt=None):
+        """Scale the coordinates of the Point by multiplying by
+        ``x`` and ``y`` after subtracting ``pt`` -- default is (0, 0) --
+        and then adding ``pt`` back again (i.e. ``pt`` is the point of
+        reference for the scaling).
+
+        See Also
+        ========
+
+        translate
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> t = Point3D(1, 1, 1)
+        >>> t.scale(2)
+        Point3D(2, 1, 1)
+        >>> t.scale(2, 2)
+        Point3D(2, 2, 1)
+
+        """
+        if pt:
+            pt = Point3D(pt)
+            return self.translate(*(-pt).args).scale(x, y, z).translate(*pt.args)
+        return Point3D(self.x*x, self.y*y, self.z*z)
+
+    def transform(self, matrix):
+        """Return the point after applying the transformation described
+        by the 4x4 Matrix, ``matrix``.
+
+        See Also
+        ========
+        sympy.geometry.point.Point3D.scale
+        sympy.geometry.point.Point3D.translate
+        """
+        if not (matrix.is_Matrix and matrix.shape == (4, 4)):
+            raise ValueError("matrix must be a 4x4 matrix")
+        x, y, z = self.args
+        m = Transpose(matrix)
+        return Point3D(*(Matrix(1, 4, [x, y, z, 1])*m).tolist()[0][:3])
+
+    def translate(self, x=0, y=0, z=0):
+        """Shift the Point by adding x and y to the coordinates of the Point.
+
+        See Also
+        ========
+
+        scale
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> t = Point3D(0, 1, 1)
+        >>> t.translate(2)
+        Point3D(2, 1, 1)
+        >>> t.translate(2, 2)
+        Point3D(2, 3, 1)
+        >>> t + Point3D(2, 2, 2)
+        Point3D(2, 3, 3)
+
+        """
+        return Point3D(self.x + x, self.y + y, self.z + z)
+
+    @property
+    def coordinates(self):
+        """
+        Returns the three coordinates of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p = Point3D(0, 1, 2)
+        >>> p.coordinates
+        (0, 1, 2)
+        """
+        return self.args
+
+    @property
+    def x(self):
+        """
+        Returns the X coordinate of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p = Point3D(0, 1, 3)
+        >>> p.x
+        0
+        """
+        return self.args[0]
+
+    @property
+    def y(self):
+        """
+        Returns the Y coordinate of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p = Point3D(0, 1, 2)
+        >>> p.y
+        1
+        """
+        return self.args[1]
+
+    @property
+    def z(self):
+        """
+        Returns the Z coordinate of the Point.
+
+        Examples
+        ========
+
+        >>> from sympy import Point3D
+        >>> p = Point3D(0, 1, 1)
+        >>> p.z
+        1
+        """
+        return self.args[2]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/polygon.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/polygon.py
new file mode 100644
index 0000000000000000000000000000000000000000..63031183438e2d228f881fd82e1b0ecca04ec534
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/polygon.py
@@ -0,0 +1,2891 @@
+from sympy.core import Expr, S, oo, pi, sympify
+from sympy.core.evalf import N
+from sympy.core.sorting import default_sort_key, ordered
+from sympy.core.symbol import _symbol, Dummy, Symbol
+from sympy.functions.elementary.complexes import sign
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import cos, sin, tan
+from .ellipse import Circle
+from .entity import GeometryEntity, GeometrySet
+from .exceptions import GeometryError
+from .line import Line, Segment, Ray
+from .point import Point
+from sympy.logic import And
+from sympy.matrices import Matrix
+from sympy.simplify.simplify import simplify
+from sympy.solvers.solvers import solve
+from sympy.utilities.iterables import has_dups, has_variety, uniq, rotate_left, least_rotation
+from sympy.utilities.misc import as_int, func_name
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+import warnings
+
+
+x, y, T = [Dummy('polygon_dummy', real=True) for i in range(3)]
+
+
+class Polygon(GeometrySet):
+    """A two-dimensional polygon.
+
+    A simple polygon in space. Can be constructed from a sequence of points
+    or from a center, radius, number of sides and rotation angle.
+
+    Parameters
+    ==========
+
+    vertices
+        A sequence of points.
+
+    n : int, optional
+        If $> 0$, an n-sided RegularPolygon is created.
+        Default value is $0$.
+
+    Attributes
+    ==========
+
+    area
+    angles
+    perimeter
+    vertices
+    centroid
+    sides
+
+    Raises
+    ======
+
+    GeometryError
+        If all parameters are not Points.
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, sympy.geometry.line.Segment, Triangle
+
+    Notes
+    =====
+
+    Polygons are treated as closed paths rather than 2D areas so
+    some calculations can be be negative or positive (e.g., area)
+    based on the orientation of the points.
+
+    Any consecutive identical points are reduced to a single point
+    and any points collinear and between two points will be removed
+    unless they are needed to define an explicit intersection (see examples).
+
+    A Triangle, Segment or Point will be returned when there are 3 or
+    fewer points provided.
+
+    Examples
+    ========
+
+    >>> from sympy import Polygon, pi
+    >>> p1, p2, p3, p4, p5 = [(0, 0), (1, 0), (5, 1), (0, 1), (3, 0)]
+    >>> Polygon(p1, p2, p3, p4)
+    Polygon(Point2D(0, 0), Point2D(1, 0), Point2D(5, 1), Point2D(0, 1))
+    >>> Polygon(p1, p2)
+    Segment2D(Point2D(0, 0), Point2D(1, 0))
+    >>> Polygon(p1, p2, p5)
+    Segment2D(Point2D(0, 0), Point2D(3, 0))
+
+    The area of a polygon is calculated as positive when vertices are
+    traversed in a ccw direction. When the sides of a polygon cross the
+    area will have positive and negative contributions. The following
+    defines a Z shape where the bottom right connects back to the top
+    left.
+
+    >>> Polygon((0, 2), (2, 2), (0, 0), (2, 0)).area
+    0
+
+    When the keyword `n` is used to define the number of sides of the
+    Polygon then a RegularPolygon is created and the other arguments are
+    interpreted as center, radius and rotation. The unrotated RegularPolygon
+    will always have a vertex at Point(r, 0) where `r` is the radius of the
+    circle that circumscribes the RegularPolygon. Its method `spin` can be
+    used to increment that angle.
+
+    >>> p = Polygon((0,0), 1, n=3)
+    >>> p
+    RegularPolygon(Point2D(0, 0), 1, 3, 0)
+    >>> p.vertices[0]
+    Point2D(1, 0)
+    >>> p.args[0]
+    Point2D(0, 0)
+    >>> p.spin(pi/2)
+    >>> p.vertices[0]
+    Point2D(0, 1)
+
+    """
+
+    __slots__ = ()
+
+    def __new__(cls, *args, n = 0, **kwargs):
+        if n:
+            args = list(args)
+            # return a virtual polygon with n sides
+            if len(args) == 2:  # center, radius
+                args.append(n)
+            elif len(args) == 3:  # center, radius, rotation
+                args.insert(2, n)
+            return RegularPolygon(*args, **kwargs)
+
+        vertices = [Point(a, dim=2, **kwargs) for a in args]
+
+        # remove consecutive duplicates
+        nodup = []
+        for p in vertices:
+            if nodup and p == nodup[-1]:
+                continue
+            nodup.append(p)
+        if len(nodup) > 1 and nodup[-1] == nodup[0]:
+            nodup.pop()  # last point was same as first
+
+        # remove collinear points
+        i = -3
+        while i < len(nodup) - 3 and len(nodup) > 2:
+            a, b, c = nodup[i], nodup[i + 1], nodup[i + 2]
+            if Point.is_collinear(a, b, c):
+                nodup.pop(i + 1)
+                if a == c:
+                    nodup.pop(i)
+            else:
+                i += 1
+
+        vertices = list(nodup)
+
+        if len(vertices) > 3:
+            return GeometryEntity.__new__(cls, *vertices, **kwargs)
+        elif len(vertices) == 3:
+            return Triangle(*vertices, **kwargs)
+        elif len(vertices) == 2:
+            return Segment(*vertices, **kwargs)
+        else:
+            return Point(*vertices, **kwargs)
+
+    @property
+    def area(self):
+        """
+        The area of the polygon.
+
+        Notes
+        =====
+
+        The area calculation can be positive or negative based on the
+        orientation of the points. If any side of the polygon crosses
+        any other side, there will be areas having opposite signs.
+
+        See Also
+        ========
+
+        sympy.geometry.ellipse.Ellipse.area
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.area
+        3
+
+        In the Z shaped polygon (with the lower right connecting back
+        to the upper left) the areas cancel out:
+
+        >>> Z = Polygon((0, 1), (1, 1), (0, 0), (1, 0))
+        >>> Z.area
+        0
+
+        In the M shaped polygon, areas do not cancel because no side
+        crosses any other (though there is a point of contact).
+
+        >>> M = Polygon((0, 0), (0, 1), (2, 0), (3, 1), (3, 0))
+        >>> M.area
+        -3/2
+
+        """
+        area = 0
+        args = self.args
+        for i in range(len(args)):
+            x1, y1 = args[i - 1].args
+            x2, y2 = args[i].args
+            area += x1*y2 - x2*y1
+        return simplify(area) / 2
+
+    @staticmethod
+    def _is_clockwise(a, b, c):
+        """Return True/False for cw/ccw orientation.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> a, b, c = [Point(i) for i in [(0, 0), (1, 1), (1, 0)]]
+        >>> Polygon._is_clockwise(a, b, c)
+        True
+        >>> Polygon._is_clockwise(a, c, b)
+        False
+        """
+        ba = b - a
+        ca = c - a
+        t_area = simplify(ba.x*ca.y - ca.x*ba.y)
+        res = t_area.is_nonpositive
+        if res is None:
+            raise ValueError("Can't determine orientation")
+        return res
+
+    @property
+    def angles(self):
+        """The internal angle at each vertex.
+
+        Returns
+        =======
+
+        angles : dict
+            A dictionary where each key is a vertex and each value is the
+            internal angle at that vertex. The vertices are represented as
+            Points.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.line.LinearEntity.angle_between
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.angles[p1]
+        pi/2
+        >>> poly.angles[p2]
+        acos(-4*sqrt(17)/17)
+
+        """
+
+        args = self.vertices
+        n = len(args)
+        ret = {}
+        for i in range(n):
+            a, b, c = args[i - 2], args[i - 1], args[i]
+            reflex_ang = Ray(b, a).angle_between(Ray(b, c))
+            if self._is_clockwise(a, b, c):
+                ret[b] = 2*S.Pi - reflex_ang
+            else:
+                ret[b] = reflex_ang
+
+        # internal sum should be pi*(n - 2), not pi*(n+2)
+        # so if ratio is (n+2)/(n-2) > 1 it is wrong
+        wrong = ((sum(ret.values())/S.Pi-1)/(n - 2) - 1).is_positive
+        if wrong:
+            two_pi = 2*S.Pi
+            for b in ret:
+                ret[b] = two_pi - ret[b]
+        elif wrong is None:
+            raise ValueError("could not determine Polygon orientation.")
+        return ret
+
+    @property
+    def ambient_dimension(self):
+        return self.vertices[0].ambient_dimension
+
+    @property
+    def perimeter(self):
+        """The perimeter of the polygon.
+
+        Returns
+        =======
+
+        perimeter : number or Basic instance
+
+        See Also
+        ========
+
+        sympy.geometry.line.Segment.length
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.perimeter
+        sqrt(17) + 7
+        """
+        p = 0
+        args = self.vertices
+        for i in range(len(args)):
+            p += args[i - 1].distance(args[i])
+        return simplify(p)
+
+    @property
+    def vertices(self):
+        """The vertices of the polygon.
+
+        Returns
+        =======
+
+        vertices : list of Points
+
+        Notes
+        =====
+
+        When iterating over the vertices, it is more efficient to index self
+        rather than to request the vertices and index them. Only use the
+        vertices when you want to process all of them at once. This is even
+        more important with RegularPolygons that calculate each vertex.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.vertices
+        [Point2D(0, 0), Point2D(1, 0), Point2D(5, 1), Point2D(0, 1)]
+        >>> poly.vertices[0]
+        Point2D(0, 0)
+
+        """
+        return list(self.args)
+
+    @property
+    def centroid(self):
+        """The centroid of the polygon.
+
+        Returns
+        =======
+
+        centroid : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.util.centroid
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.centroid
+        Point2D(31/18, 11/18)
+
+        """
+        A = 1/(6*self.area)
+        cx, cy = 0, 0
+        args = self.args
+        for i in range(len(args)):
+            x1, y1 = args[i - 1].args
+            x2, y2 = args[i].args
+            v = x1*y2 - x2*y1
+            cx += v*(x1 + x2)
+            cy += v*(y1 + y2)
+        return Point(simplify(A*cx), simplify(A*cy))
+
+
+    def second_moment_of_area(self, point=None):
+        """Returns the second moment and product moment of area of a two dimensional polygon.
+
+        Parameters
+        ==========
+
+        point : Point, two-tuple of sympifyable objects, or None(default=None)
+            point is the point about which second moment of area is to be found.
+            If "point=None" it will be calculated about the axis passing through the
+            centroid of the polygon.
+
+        Returns
+        =======
+
+        I_xx, I_yy, I_xy : number or SymPy expression
+                           I_xx, I_yy are second moment of area of a two dimensional polygon.
+                           I_xy is product moment of area of a two dimensional polygon.
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon, symbols
+        >>> a, b = symbols('a, b')
+        >>> p1, p2, p3, p4, p5 = [(0, 0), (a, 0), (a, b), (0, b), (a/3, b/3)]
+        >>> rectangle = Polygon(p1, p2, p3, p4)
+        >>> rectangle.second_moment_of_area()
+        (a*b**3/12, a**3*b/12, 0)
+        >>> rectangle.second_moment_of_area(p5)
+        (a*b**3/9, a**3*b/9, a**2*b**2/36)
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Second_moment_of_area
+
+        """
+
+        I_xx, I_yy, I_xy = 0, 0, 0
+        args = self.vertices
+        for i in range(len(args)):
+            x1, y1 = args[i-1].args
+            x2, y2 = args[i].args
+            v = x1*y2 - x2*y1
+            I_xx += (y1**2 + y1*y2 + y2**2)*v
+            I_yy += (x1**2 + x1*x2 + x2**2)*v
+            I_xy += (x1*y2 + 2*x1*y1 + 2*x2*y2 + x2*y1)*v
+        A = self.area
+        c_x = self.centroid[0]
+        c_y = self.centroid[1]
+        # parallel axis theorem
+        I_xx_c = (I_xx/12) - (A*(c_y**2))
+        I_yy_c = (I_yy/12) - (A*(c_x**2))
+        I_xy_c = (I_xy/24) - (A*(c_x*c_y))
+        if point is None:
+            return I_xx_c, I_yy_c, I_xy_c
+
+        I_xx = (I_xx_c + A*((point[1]-c_y)**2))
+        I_yy = (I_yy_c + A*((point[0]-c_x)**2))
+        I_xy = (I_xy_c + A*((point[0]-c_x)*(point[1]-c_y)))
+
+        return I_xx, I_yy, I_xy
+
+
+    def first_moment_of_area(self, point=None):
+        """
+        Returns the first moment of area of a two-dimensional polygon with
+        respect to a certain point of interest.
+
+        First moment of area is a measure of the distribution of the area
+        of a polygon in relation to an axis. The first moment of area of
+        the entire polygon about its own centroid is always zero. Therefore,
+        here it is calculated for an area, above or below a certain point
+        of interest, that makes up a smaller portion of the polygon. This
+        area is bounded by the point of interest and the extreme end
+        (top or bottom) of the polygon. The first moment for this area is
+        is then determined about the centroidal axis of the initial polygon.
+
+        References
+        ==========
+
+        .. [1] https://skyciv.com/docs/tutorials/section-tutorials/calculating-the-statical-or-first-moment-of-area-of-beam-sections/?cc=BMD
+        .. [2] https://mechanicalc.com/reference/cross-sections
+
+        Parameters
+        ==========
+
+        point: Point, two-tuple of sympifyable objects, or None (default=None)
+            point is the point above or below which the area of interest lies
+            If ``point=None`` then the centroid acts as the point of interest.
+
+        Returns
+        =======
+
+        Q_x, Q_y: number or SymPy expressions
+            Q_x is the first moment of area about the x-axis
+            Q_y is the first moment of area about the y-axis
+            A negative sign indicates that the section modulus is
+            determined for a section below (or left of) the centroidal axis
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> a, b = 50, 10
+        >>> p1, p2, p3, p4 = [(0, b), (0, 0), (a, 0), (a, b)]
+        >>> p = Polygon(p1, p2, p3, p4)
+        >>> p.first_moment_of_area()
+        (625, 3125)
+        >>> p.first_moment_of_area(point=Point(30, 7))
+        (525, 3000)
+        """
+        if point:
+            xc, yc = self.centroid
+        else:
+            point = self.centroid
+            xc, yc = point
+
+        h_line = Line(point, slope=0)
+        v_line = Line(point, slope=S.Infinity)
+
+        h_poly = self.cut_section(h_line)
+        v_poly = self.cut_section(v_line)
+
+        poly_1 = h_poly[0] if h_poly[0].area <= h_poly[1].area else h_poly[1]
+        poly_2 = v_poly[0] if v_poly[0].area <= v_poly[1].area else v_poly[1]
+
+        Q_x = (poly_1.centroid.y - yc)*poly_1.area
+        Q_y = (poly_2.centroid.x - xc)*poly_2.area
+
+        return Q_x, Q_y
+
+
+    def polar_second_moment_of_area(self):
+        """Returns the polar modulus of a two-dimensional polygon
+
+        It is a constituent of the second moment of area, linked through
+        the perpendicular axis theorem. While the planar second moment of
+        area describes an object's resistance to deflection (bending) when
+        subjected to a force applied to a plane parallel to the central
+        axis, the polar second moment of area describes an object's
+        resistance to deflection when subjected to a moment applied in a
+        plane perpendicular to the object's central axis (i.e. parallel to
+        the cross-section)
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon, symbols
+        >>> a, b = symbols('a, b')
+        >>> rectangle = Polygon((0, 0), (a, 0), (a, b), (0, b))
+        >>> rectangle.polar_second_moment_of_area()
+        a**3*b/12 + a*b**3/12
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Polar_moment_of_inertia
+
+        """
+        second_moment = self.second_moment_of_area()
+        return second_moment[0] + second_moment[1]
+
+
+    def section_modulus(self, point=None):
+        """Returns a tuple with the section modulus of a two-dimensional
+        polygon.
+
+        Section modulus is a geometric property of a polygon defined as the
+        ratio of second moment of area to the distance of the extreme end of
+        the polygon from the centroidal axis.
+
+        Parameters
+        ==========
+
+        point : Point, two-tuple of sympifyable objects, or None(default=None)
+            point is the point at which section modulus is to be found.
+            If "point=None" it will be calculated for the point farthest from the
+            centroidal axis of the polygon.
+
+        Returns
+        =======
+
+        S_x, S_y: numbers or SymPy expressions
+                  S_x is the section modulus with respect to the x-axis
+                  S_y is the section modulus with respect to the y-axis
+                  A negative sign indicates that the section modulus is
+                  determined for a point below the centroidal axis
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Polygon, Point
+        >>> a, b = symbols('a, b', positive=True)
+        >>> rectangle = Polygon((0, 0), (a, 0), (a, b), (0, b))
+        >>> rectangle.section_modulus()
+        (a*b**2/6, a**2*b/6)
+        >>> rectangle.section_modulus(Point(a/4, b/4))
+        (-a*b**2/3, -a**2*b/3)
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Section_modulus
+
+        """
+        x_c, y_c = self.centroid
+        if point is None:
+            # taking x and y as maximum distances from centroid
+            x_min, y_min, x_max, y_max = self.bounds
+            y = max(y_c - y_min, y_max - y_c)
+            x = max(x_c - x_min, x_max - x_c)
+        else:
+            # taking x and y as distances of the given point from the centroid
+            y = point.y - y_c
+            x = point.x - x_c
+
+        second_moment= self.second_moment_of_area()
+        S_x = second_moment[0]/y
+        S_y = second_moment[1]/x
+
+        return S_x, S_y
+
+
+    @property
+    def sides(self):
+        """The directed line segments that form the sides of the polygon.
+
+        Returns
+        =======
+
+        sides : list of sides
+            Each side is a directed Segment.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.line.Segment
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.sides
+        [Segment2D(Point2D(0, 0), Point2D(1, 0)),
+        Segment2D(Point2D(1, 0), Point2D(5, 1)),
+        Segment2D(Point2D(5, 1), Point2D(0, 1)), Segment2D(Point2D(0, 1), Point2D(0, 0))]
+
+        """
+        res = []
+        args = self.vertices
+        for i in range(-len(args), 0):
+            res.append(Segment(args[i], args[i + 1]))
+        return res
+
+    @property
+    def bounds(self):
+        """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
+        rectangle for the geometric figure.
+
+        """
+
+        verts = self.vertices
+        xs = [p.x for p in verts]
+        ys = [p.y for p in verts]
+        return (min(xs), min(ys), max(xs), max(ys))
+
+    def is_convex(self):
+        """Is the polygon convex?
+
+        A polygon is convex if all its interior angles are less than 180
+        degrees and there are no intersections between sides.
+
+        Returns
+        =======
+
+        is_convex : boolean
+            True if this polygon is convex, False otherwise.
+
+        See Also
+        ========
+
+        sympy.geometry.util.convex_hull
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly = Polygon(p1, p2, p3, p4)
+        >>> poly.is_convex()
+        True
+
+        """
+        # Determine orientation of points
+        args = self.vertices
+        cw = self._is_clockwise(args[-2], args[-1], args[0])
+        for i in range(1, len(args)):
+            if cw ^ self._is_clockwise(args[i - 2], args[i - 1], args[i]):
+                return False
+        # check for intersecting sides
+        sides = self.sides
+        for i, si in enumerate(sides):
+            pts = si.args
+            # exclude the sides connected to si
+            for j in range(1 if i == len(sides) - 1 else 0, i - 1):
+                sj = sides[j]
+                if sj.p1 not in pts and sj.p2 not in pts:
+                    hit = si.intersection(sj)
+                    if hit:
+                        return False
+        return True
+
+    def encloses_point(self, p):
+        """
+        Return True if p is enclosed by (is inside of) self.
+
+        Notes
+        =====
+
+        Being on the border of self is considered False.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        encloses_point : True, False or None
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.ellipse.Ellipse.encloses_point
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon, Point
+        >>> p = Polygon((0, 0), (4, 0), (4, 4))
+        >>> p.encloses_point(Point(2, 1))
+        True
+        >>> p.encloses_point(Point(2, 2))
+        False
+        >>> p.encloses_point(Point(5, 5))
+        False
+
+        References
+        ==========
+
+        .. [1] https://paulbourke.net/geometry/polygonmesh/#insidepoly
+
+        """
+        p = Point(p, dim=2)
+        if p in self.vertices or any(p in s for s in self.sides):
+            return False
+
+        # move to p, checking that the result is numeric
+        lit = []
+        for v in self.vertices:
+            lit.append(v - p)  # the difference is simplified
+            if lit[-1].free_symbols:
+                return None
+
+        poly = Polygon(*lit)
+
+        # polygon closure is assumed in the following test but Polygon removes duplicate pts so
+        # the last point has to be added so all sides are computed. Using Polygon.sides is
+        # not good since Segments are unordered.
+        args = poly.args
+        indices = list(range(-len(args), 1))
+
+        if poly.is_convex():
+            orientation = None
+            for i in indices:
+                a = args[i]
+                b = args[i + 1]
+                test = ((-a.y)*(b.x - a.x) - (-a.x)*(b.y - a.y)).is_negative
+                if orientation is None:
+                    orientation = test
+                elif test is not orientation:
+                    return False
+            return True
+
+        hit_odd = False
+        p1x, p1y = args[0].args
+        for i in indices[1:]:
+            p2x, p2y = args[i].args
+            if 0 > min(p1y, p2y):
+                if 0 <= max(p1y, p2y):
+                    if 0 <= max(p1x, p2x):
+                        if p1y != p2y:
+                            xinters = (-p1y)*(p2x - p1x)/(p2y - p1y) + p1x
+                            if p1x == p2x or 0 <= xinters:
+                                hit_odd = not hit_odd
+            p1x, p1y = p2x, p2y
+        return hit_odd
+
+    def arbitrary_point(self, parameter='t'):
+        """A parameterized point on the polygon.
+
+        The parameter, varying from 0 to 1, assigns points to the position on
+        the perimeter that is that fraction of the total perimeter. So the
+        point evaluated at t=1/2 would return the point from the first vertex
+        that is 1/2 way around the polygon.
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        arbitrary_point : Point
+
+        Raises
+        ======
+
+        ValueError
+            When `parameter` already appears in the Polygon's definition.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon, Symbol
+        >>> t = Symbol('t', real=True)
+        >>> tri = Polygon((0, 0), (1, 0), (1, 1))
+        >>> p = tri.arbitrary_point('t')
+        >>> perimeter = tri.perimeter
+        >>> s1, s2 = [s.length for s in tri.sides[:2]]
+        >>> p.subs(t, (s1 + s2/2)/perimeter)
+        Point2D(1, 1/2)
+
+        """
+        t = _symbol(parameter, real=True)
+        if t.name in (f.name for f in self.free_symbols):
+            raise ValueError('Symbol %s already appears in object and cannot be used as a parameter.' % t.name)
+        sides = []
+        perimeter = self.perimeter
+        perim_fraction_start = 0
+        for s in self.sides:
+            side_perim_fraction = s.length/perimeter
+            perim_fraction_end = perim_fraction_start + side_perim_fraction
+            pt = s.arbitrary_point(parameter).subs(
+                t, (t - perim_fraction_start)/side_perim_fraction)
+            sides.append(
+                (pt, (And(perim_fraction_start <= t, t < perim_fraction_end))))
+            perim_fraction_start = perim_fraction_end
+        return Piecewise(*sides)
+
+    def parameter_value(self, other, t):
+        if not isinstance(other,GeometryEntity):
+            other = Point(other, dim=self.ambient_dimension)
+        if not isinstance(other,Point):
+            raise ValueError("other must be a point")
+        if other.free_symbols:
+            raise NotImplementedError('non-numeric coordinates')
+        unknown = False
+        p = self.arbitrary_point(T)
+        for pt, cond in p.args:
+            sol = solve(pt - other, T, dict=True)
+            if not sol:
+                continue
+            value = sol[0][T]
+            if simplify(cond.subs(T, value)) == True:
+                return {t: value}
+            unknown = True
+        if unknown:
+            raise ValueError("Given point may not be on %s" % func_name(self))
+        raise ValueError("Given point is not on %s" % func_name(self))
+
+    def plot_interval(self, parameter='t'):
+        """The plot interval for the default geometric plot of the polygon.
+
+        Parameters
+        ==========
+
+        parameter : str, optional
+            Default value is 't'.
+
+        Returns
+        =======
+
+        plot_interval : list (plot interval)
+            [parameter, lower_bound, upper_bound]
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon
+        >>> p = Polygon((0, 0), (1, 0), (1, 1))
+        >>> p.plot_interval()
+        [t, 0, 1]
+
+        """
+        t = Symbol(parameter, real=True)
+        return [t, 0, 1]
+
+    def intersection(self, o):
+        """The intersection of polygon and geometry entity.
+
+        The intersection may be empty and can contain individual Points and
+        complete Line Segments.
+
+        Parameters
+        ==========
+
+        other: GeometryEntity
+
+        Returns
+        =======
+
+        intersection : list
+            The list of Segments and Points
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.line.Segment
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon, Line
+        >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+        >>> poly1 = Polygon(p1, p2, p3, p4)
+        >>> p5, p6, p7 = map(Point, [(3, 2), (1, -1), (0, 2)])
+        >>> poly2 = Polygon(p5, p6, p7)
+        >>> poly1.intersection(poly2)
+        [Point2D(1/3, 1), Point2D(2/3, 0), Point2D(9/5, 1/5), Point2D(7/3, 1)]
+        >>> poly1.intersection(Line(p1, p2))
+        [Segment2D(Point2D(0, 0), Point2D(1, 0))]
+        >>> poly1.intersection(p1)
+        [Point2D(0, 0)]
+        """
+        intersection_result = []
+        k = o.sides if isinstance(o, Polygon) else [o]
+        for side in self.sides:
+            for side1 in k:
+                intersection_result.extend(side.intersection(side1))
+
+        intersection_result = list(uniq(intersection_result))
+        points = [entity for entity in intersection_result if isinstance(entity, Point)]
+        segments = [entity for entity in intersection_result if isinstance(entity, Segment)]
+
+        if points and segments:
+            points_in_segments = list(uniq([point for point in points for segment in segments if point in segment]))
+            if points_in_segments:
+                for i in points_in_segments:
+                    points.remove(i)
+            return list(ordered(segments + points))
+        else:
+            return list(ordered(intersection_result))
+
+
+    def cut_section(self, line):
+        """
+        Returns a tuple of two polygon segments that lie above and below
+        the intersecting line respectively.
+
+        Parameters
+        ==========
+
+        line: Line object of geometry module
+            line which cuts the Polygon. The part of the Polygon that lies
+            above and below this line is returned.
+
+        Returns
+        =======
+
+        upper_polygon, lower_polygon: Polygon objects or None
+            upper_polygon is the polygon that lies above the given line.
+            lower_polygon is the polygon that lies below the given line.
+            upper_polygon and lower polygon are ``None`` when no polygon
+            exists above the line or below the line.
+
+        Raises
+        ======
+
+        ValueError: When the line does not intersect the polygon
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon, Line
+        >>> a, b = 20, 10
+        >>> p1, p2, p3, p4 = [(0, b), (0, 0), (a, 0), (a, b)]
+        >>> rectangle = Polygon(p1, p2, p3, p4)
+        >>> t = rectangle.cut_section(Line((0, 5), slope=0))
+        >>> t
+        (Polygon(Point2D(0, 10), Point2D(0, 5), Point2D(20, 5), Point2D(20, 10)),
+        Polygon(Point2D(0, 5), Point2D(0, 0), Point2D(20, 0), Point2D(20, 5)))
+        >>> upper_segment, lower_segment = t
+        >>> upper_segment.area
+        100
+        >>> upper_segment.centroid
+        Point2D(10, 15/2)
+        >>> lower_segment.centroid
+        Point2D(10, 5/2)
+
+        References
+        ==========
+
+        .. [1] https://github.com/sympy/sympy/wiki/A-method-to-return-a-cut-section-of-any-polygon-geometry
+
+        """
+        intersection_points = self.intersection(line)
+        if not intersection_points:
+            raise ValueError("This line does not intersect the polygon")
+
+        points = list(self.vertices)
+        points.append(points[0])
+
+        eq = line.equation(x, y)
+
+        # considering equation of line to be `ax +by + c`
+        a = eq.coeff(x)
+        b = eq.coeff(y)
+
+        upper_vertices = []
+        lower_vertices = []
+        # prev is true when previous point is above the line
+        prev = True
+        prev_point = None
+        for point in points:
+            # when coefficient of y is 0, right side of the line is
+            # considered
+            compare = eq.subs({x: point.x, y: point.y})/b if b \
+                    else eq.subs(x, point.x)/a
+
+            # if point lies above line
+            if compare > 0:
+                if not prev:
+                    # if previous point lies below the line, the intersection
+                    # point of the polygon edge and the line has to be included
+                    edge = Line(point, prev_point)
+                    new_point = edge.intersection(line)
+                    upper_vertices.append(new_point[0])
+                    lower_vertices.append(new_point[0])
+
+                upper_vertices.append(point)
+                prev = True
+            else:
+                if prev and prev_point:
+                    edge = Line(point, prev_point)
+                    new_point = edge.intersection(line)
+                    upper_vertices.append(new_point[0])
+                    lower_vertices.append(new_point[0])
+                lower_vertices.append(point)
+                prev = False
+            prev_point = point
+
+        upper_polygon, lower_polygon = None, None
+        if upper_vertices and isinstance(Polygon(*upper_vertices), Polygon):
+            upper_polygon = Polygon(*upper_vertices)
+        if lower_vertices and isinstance(Polygon(*lower_vertices), Polygon):
+            lower_polygon = Polygon(*lower_vertices)
+
+        return upper_polygon, lower_polygon
+
+
+    def distance(self, o):
+        """
+        Returns the shortest distance between self and o.
+
+        If o is a point, then self does not need to be convex.
+        If o is another polygon self and o must be convex.
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon, RegularPolygon
+        >>> p1, p2 = map(Point, [(0, 0), (7, 5)])
+        >>> poly = Polygon(*RegularPolygon(p1, 1, 3).vertices)
+        >>> poly.distance(p2)
+        sqrt(61)
+        """
+        if isinstance(o, Point):
+            dist = oo
+            for side in self.sides:
+                current = side.distance(o)
+                if current == 0:
+                    return S.Zero
+                elif current < dist:
+                    dist = current
+            return dist
+        elif isinstance(o, Polygon) and self.is_convex() and o.is_convex():
+            return self._do_poly_distance(o)
+        raise NotImplementedError()
+
+    def _do_poly_distance(self, e2):
+        """
+        Calculates the least distance between the exteriors of two
+        convex polygons e1 and e2. Does not check for the convexity
+        of the polygons as this is checked by Polygon.distance.
+
+        Notes
+        =====
+
+            - Prints a warning if the two polygons possibly intersect as the return
+              value will not be valid in such a case. For a more through test of
+              intersection use intersection().
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.distance
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Polygon
+        >>> square = Polygon(Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0))
+        >>> triangle = Polygon(Point(1, 2), Point(2, 2), Point(2, 1))
+        >>> square._do_poly_distance(triangle)
+        sqrt(2)/2
+
+        Description of method used
+        ==========================
+
+        Method:
+        [1] https://web.archive.org/web/20150509035744/http://cgm.cs.mcgill.ca/~orm/mind2p.html
+        Uses rotating calipers:
+        [2] https://en.wikipedia.org/wiki/Rotating_calipers
+        and antipodal points:
+        [3] https://en.wikipedia.org/wiki/Antipodal_point
+        """
+        e1 = self
+
+        '''Tests for a possible intersection between the polygons and outputs a warning'''
+        e1_center = e1.centroid
+        e2_center = e2.centroid
+        e1_max_radius = S.Zero
+        e2_max_radius = S.Zero
+        for vertex in e1.vertices:
+            r = Point.distance(e1_center, vertex)
+            if e1_max_radius < r:
+                e1_max_radius = r
+        for vertex in e2.vertices:
+            r = Point.distance(e2_center, vertex)
+            if e2_max_radius < r:
+                e2_max_radius = r
+        center_dist = Point.distance(e1_center, e2_center)
+        if center_dist <= e1_max_radius + e2_max_radius:
+            warnings.warn("Polygons may intersect producing erroneous output",
+                          stacklevel=3)
+
+        '''
+        Find the upper rightmost vertex of e1 and the lowest leftmost vertex of e2
+        '''
+        e1_ymax = Point(0, -oo)
+        e2_ymin = Point(0, oo)
+
+        for vertex in e1.vertices:
+            if vertex.y > e1_ymax.y or (vertex.y == e1_ymax.y and vertex.x > e1_ymax.x):
+                e1_ymax = vertex
+        for vertex in e2.vertices:
+            if vertex.y < e2_ymin.y or (vertex.y == e2_ymin.y and vertex.x < e2_ymin.x):
+                e2_ymin = vertex
+        min_dist = Point.distance(e1_ymax, e2_ymin)
+
+        '''
+        Produce a dictionary with vertices of e1 as the keys and, for each vertex, the points
+        to which the vertex is connected as its value. The same is then done for e2.
+        '''
+        e1_connections = {}
+        e2_connections = {}
+
+        for side in e1.sides:
+            if side.p1 in e1_connections:
+                e1_connections[side.p1].append(side.p2)
+            else:
+                e1_connections[side.p1] = [side.p2]
+
+            if side.p2 in e1_connections:
+                e1_connections[side.p2].append(side.p1)
+            else:
+                e1_connections[side.p2] = [side.p1]
+
+        for side in e2.sides:
+            if side.p1 in e2_connections:
+                e2_connections[side.p1].append(side.p2)
+            else:
+                e2_connections[side.p1] = [side.p2]
+
+            if side.p2 in e2_connections:
+                e2_connections[side.p2].append(side.p1)
+            else:
+                e2_connections[side.p2] = [side.p1]
+
+        e1_current = e1_ymax
+        e2_current = e2_ymin
+        support_line = Line(Point(S.Zero, S.Zero), Point(S.One, S.Zero))
+
+        '''
+        Determine which point in e1 and e2 will be selected after e2_ymin and e1_ymax,
+        this information combined with the above produced dictionaries determines the
+        path that will be taken around the polygons
+        '''
+        point1 = e1_connections[e1_ymax][0]
+        point2 = e1_connections[e1_ymax][1]
+        angle1 = support_line.angle_between(Line(e1_ymax, point1))
+        angle2 = support_line.angle_between(Line(e1_ymax, point2))
+        if angle1 < angle2:
+            e1_next = point1
+        elif angle2 < angle1:
+            e1_next = point2
+        elif Point.distance(e1_ymax, point1) > Point.distance(e1_ymax, point2):
+            e1_next = point2
+        else:
+            e1_next = point1
+
+        point1 = e2_connections[e2_ymin][0]
+        point2 = e2_connections[e2_ymin][1]
+        angle1 = support_line.angle_between(Line(e2_ymin, point1))
+        angle2 = support_line.angle_between(Line(e2_ymin, point2))
+        if angle1 > angle2:
+            e2_next = point1
+        elif angle2 > angle1:
+            e2_next = point2
+        elif Point.distance(e2_ymin, point1) > Point.distance(e2_ymin, point2):
+            e2_next = point2
+        else:
+            e2_next = point1
+
+        '''
+        Loop which determines the distance between anti-podal pairs and updates the
+        minimum distance accordingly. It repeats until it reaches the starting position.
+        '''
+        while True:
+            e1_angle = support_line.angle_between(Line(e1_current, e1_next))
+            e2_angle = pi - support_line.angle_between(Line(
+                e2_current, e2_next))
+
+            if (e1_angle < e2_angle) is True:
+                support_line = Line(e1_current, e1_next)
+                e1_segment = Segment(e1_current, e1_next)
+                min_dist_current = e1_segment.distance(e2_current)
+
+                if min_dist_current.evalf() < min_dist.evalf():
+                    min_dist = min_dist_current
+
+                if e1_connections[e1_next][0] != e1_current:
+                    e1_current = e1_next
+                    e1_next = e1_connections[e1_next][0]
+                else:
+                    e1_current = e1_next
+                    e1_next = e1_connections[e1_next][1]
+            elif (e1_angle > e2_angle) is True:
+                support_line = Line(e2_next, e2_current)
+                e2_segment = Segment(e2_current, e2_next)
+                min_dist_current = e2_segment.distance(e1_current)
+
+                if min_dist_current.evalf() < min_dist.evalf():
+                    min_dist = min_dist_current
+
+                if e2_connections[e2_next][0] != e2_current:
+                    e2_current = e2_next
+                    e2_next = e2_connections[e2_next][0]
+                else:
+                    e2_current = e2_next
+                    e2_next = e2_connections[e2_next][1]
+            else:
+                support_line = Line(e1_current, e1_next)
+                e1_segment = Segment(e1_current, e1_next)
+                e2_segment = Segment(e2_current, e2_next)
+                min1 = e1_segment.distance(e2_next)
+                min2 = e2_segment.distance(e1_next)
+
+                min_dist_current = min(min1, min2)
+                if min_dist_current.evalf() < min_dist.evalf():
+                    min_dist = min_dist_current
+
+                if e1_connections[e1_next][0] != e1_current:
+                    e1_current = e1_next
+                    e1_next = e1_connections[e1_next][0]
+                else:
+                    e1_current = e1_next
+                    e1_next = e1_connections[e1_next][1]
+
+                if e2_connections[e2_next][0] != e2_current:
+                    e2_current = e2_next
+                    e2_next = e2_connections[e2_next][0]
+                else:
+                    e2_current = e2_next
+                    e2_next = e2_connections[e2_next][1]
+            if e1_current == e1_ymax and e2_current == e2_ymin:
+                break
+        return min_dist
+
+    def _svg(self, scale_factor=1., fill_color="#66cc99"):
+        """Returns SVG path element for the Polygon.
+
+        Parameters
+        ==========
+
+        scale_factor : float
+            Multiplication factor for the SVG stroke-width.  Default is 1.
+        fill_color : str, optional
+            Hex string for fill color. Default is "#66cc99".
+        """
+        verts = map(N, self.vertices)
+        coords = ["{},{}".format(p.x, p.y) for p in verts]
+        path = "M {} L {} z".format(coords[0], " L ".join(coords[1:]))
+        return (
+            ''
+            ).format(2. * scale_factor, path, fill_color)
+
+    def _hashable_content(self):
+
+        D = {}
+        def ref_list(point_list):
+            kee = {}
+            for i, p in enumerate(ordered(set(point_list))):
+                kee[p] = i
+                D[i] = p
+            return [kee[p] for p in point_list]
+
+        S1 = ref_list(self.args)
+        r_nor = rotate_left(S1, least_rotation(S1))
+        S2 = ref_list(list(reversed(self.args)))
+        r_rev = rotate_left(S2, least_rotation(S2))
+        if r_nor < r_rev:
+            r = r_nor
+        else:
+            r = r_rev
+        canonical_args = [ D[order] for order in r ]
+        return tuple(canonical_args)
+
+    def __contains__(self, o):
+        """
+        Return True if o is contained within the boundary lines of self.altitudes
+
+        Parameters
+        ==========
+
+        other : GeometryEntity
+
+        Returns
+        =======
+
+        contained in : bool
+            The points (and sides, if applicable) are contained in self.
+
+        See Also
+        ========
+
+        sympy.geometry.entity.GeometryEntity.encloses
+
+        Examples
+        ========
+
+        >>> from sympy import Line, Segment, Point
+        >>> p = Point(0, 0)
+        >>> q = Point(1, 1)
+        >>> s = Segment(p, q*2)
+        >>> l = Line(p, q)
+        >>> p in q
+        False
+        >>> p in s
+        True
+        >>> q*3 in s
+        False
+        >>> s in l
+        True
+
+        """
+
+        if isinstance(o, Polygon):
+            return self == o
+        elif isinstance(o, Segment):
+            return any(o in s for s in self.sides)
+        elif isinstance(o, Point):
+            if o in self.vertices:
+                return True
+            for side in self.sides:
+                if o in side:
+                    return True
+
+        return False
+
+    def bisectors(p, prec=None):
+        """Returns angle bisectors of a polygon. If prec is given
+        then approximate the point defining the ray to that precision.
+
+        The distance between the points defining the bisector ray is 1.
+
+        Examples
+        ========
+
+        >>> from sympy import Polygon, Point
+        >>> p = Polygon(Point(0, 0), Point(2, 0), Point(1, 1), Point(0, 3))
+        >>> p.bisectors(2)
+        {Point2D(0, 0): Ray2D(Point2D(0, 0), Point2D(0.71, 0.71)),
+         Point2D(0, 3): Ray2D(Point2D(0, 3), Point2D(0.23, 2.0)),
+         Point2D(1, 1): Ray2D(Point2D(1, 1), Point2D(0.19, 0.42)),
+         Point2D(2, 0): Ray2D(Point2D(2, 0), Point2D(1.1, 0.38))}
+        """
+        b = {}
+        pts = list(p.args)
+        pts.append(pts[0])  # close it
+        cw = Polygon._is_clockwise(*pts[:3])
+        if cw:
+            pts = list(reversed(pts))
+        for v, a in p.angles.items():
+            i = pts.index(v)
+            p1, p2 = Point._normalize_dimension(pts[i], pts[i + 1])
+            ray = Ray(p1, p2).rotate(a/2, v)
+            dir = ray.direction
+            ray = Ray(ray.p1, ray.p1 + dir/dir.distance((0, 0)))
+            if prec is not None:
+                ray = Ray(ray.p1, ray.p2.n(prec))
+            b[v] = ray
+        return b
+
+
+class RegularPolygon(Polygon):
+    """
+    A regular polygon.
+
+    Such a polygon has all internal angles equal and all sides the same length.
+
+    Parameters
+    ==========
+
+    center : Point
+    radius : number or Basic instance
+        The distance from the center to a vertex
+    n : int
+        The number of sides
+
+    Attributes
+    ==========
+
+    vertices
+    center
+    radius
+    rotation
+    apothem
+    interior_angle
+    exterior_angle
+    circumcircle
+    incircle
+    angles
+
+    Raises
+    ======
+
+    GeometryError
+        If the `center` is not a Point, or the `radius` is not a number or Basic
+        instance, or the number of sides, `n`, is less than three.
+
+    Notes
+    =====
+
+    A RegularPolygon can be instantiated with Polygon with the kwarg n.
+
+    Regular polygons are instantiated with a center, radius, number of sides
+    and a rotation angle. Whereas the arguments of a Polygon are vertices, the
+    vertices of the RegularPolygon must be obtained with the vertices method.
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, Polygon
+
+    Examples
+    ========
+
+    >>> from sympy import RegularPolygon, Point
+    >>> r = RegularPolygon(Point(0, 0), 5, 3)
+    >>> r
+    RegularPolygon(Point2D(0, 0), 5, 3, 0)
+    >>> r.vertices[0]
+    Point2D(5, 0)
+
+    """
+
+    __slots__ = ('_n', '_center', '_radius', '_rot')
+
+    def __new__(self, c, r, n, rot=0, **kwargs):
+        r, n, rot = map(sympify, (r, n, rot))
+        c = Point(c, dim=2, **kwargs)
+        if not isinstance(r, Expr):
+            raise GeometryError("r must be an Expr object, not %s" % r)
+        if n.is_Number:
+            as_int(n)  # let an error raise if necessary
+            if n < 3:
+                raise GeometryError("n must be a >= 3, not %s" % n)
+
+        obj = GeometryEntity.__new__(self, c, r, n, **kwargs)
+        obj._n = n
+        obj._center = c
+        obj._radius = r
+        obj._rot = rot % (2*S.Pi/n) if rot.is_number else rot
+        return obj
+
+    def _eval_evalf(self, prec=15, **options):
+        c, r, n, a = self.args
+        dps = prec_to_dps(prec)
+        c, r, a = [i.evalf(n=dps, **options) for i in (c, r, a)]
+        return self.func(c, r, n, a)
+
+    @property
+    def args(self):
+        """
+        Returns the center point, the radius,
+        the number of sides, and the orientation angle.
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> r = RegularPolygon(Point(0, 0), 5, 3)
+        >>> r.args
+        (Point2D(0, 0), 5, 3, 0)
+        """
+        return self._center, self._radius, self._n, self._rot
+
+    def __str__(self):
+        return 'RegularPolygon(%s, %s, %s, %s)' % tuple(self.args)
+
+    def __repr__(self):
+        return 'RegularPolygon(%s, %s, %s, %s)' % tuple(self.args)
+
+    @property
+    def area(self):
+        """Returns the area.
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon
+        >>> square = RegularPolygon((0, 0), 1, 4)
+        >>> square.area
+        2
+        >>> _ == square.length**2
+        True
+        """
+        c, r, n, rot = self.args
+        return sign(r)*n*self.length**2/(4*tan(pi/n))
+
+    @property
+    def length(self):
+        """Returns the length of the sides.
+
+        The half-length of the side and the apothem form two legs
+        of a right triangle whose hypotenuse is the radius of the
+        regular polygon.
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon
+        >>> from sympy import sqrt
+        >>> s = square_in_unit_circle = RegularPolygon((0, 0), 1, 4)
+        >>> s.length
+        sqrt(2)
+        >>> sqrt((_/2)**2 + s.apothem**2) == s.radius
+        True
+
+        """
+        return self.radius*2*sin(pi/self._n)
+
+    @property
+    def center(self):
+        """The center of the RegularPolygon
+
+        This is also the center of the circumscribing circle.
+
+        Returns
+        =======
+
+        center : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.ellipse.Ellipse.center
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 5, 4)
+        >>> rp.center
+        Point2D(0, 0)
+        """
+        return self._center
+
+    centroid = center
+
+    @property
+    def circumcenter(self):
+        """
+        Alias for center.
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 5, 4)
+        >>> rp.circumcenter
+        Point2D(0, 0)
+        """
+        return self.center
+
+    @property
+    def radius(self):
+        """Radius of the RegularPolygon
+
+        This is also the radius of the circumscribing circle.
+
+        Returns
+        =======
+
+        radius : number or instance of Basic
+
+        See Also
+        ========
+
+        sympy.geometry.line.Segment.length, sympy.geometry.ellipse.Circle.radius
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy import RegularPolygon, Point
+        >>> radius = Symbol('r')
+        >>> rp = RegularPolygon(Point(0, 0), radius, 4)
+        >>> rp.radius
+        r
+
+        """
+        return self._radius
+
+    @property
+    def circumradius(self):
+        """
+        Alias for radius.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy import RegularPolygon, Point
+        >>> radius = Symbol('r')
+        >>> rp = RegularPolygon(Point(0, 0), radius, 4)
+        >>> rp.circumradius
+        r
+        """
+        return self.radius
+
+    @property
+    def rotation(self):
+        """CCW angle by which the RegularPolygon is rotated
+
+        Returns
+        =======
+
+        rotation : number or instance of Basic
+
+        Examples
+        ========
+
+        >>> from sympy import pi
+        >>> from sympy.abc import a
+        >>> from sympy import RegularPolygon, Point
+        >>> RegularPolygon(Point(0, 0), 3, 4, pi/4).rotation
+        pi/4
+
+        Numerical rotation angles are made canonical:
+
+        >>> RegularPolygon(Point(0, 0), 3, 4, a).rotation
+        a
+        >>> RegularPolygon(Point(0, 0), 3, 4, pi).rotation
+        0
+
+        """
+        return self._rot
+
+    @property
+    def apothem(self):
+        """The inradius of the RegularPolygon.
+
+        The apothem/inradius is the radius of the inscribed circle.
+
+        Returns
+        =======
+
+        apothem : number or instance of Basic
+
+        See Also
+        ========
+
+        sympy.geometry.line.Segment.length, sympy.geometry.ellipse.Circle.radius
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy import RegularPolygon, Point
+        >>> radius = Symbol('r')
+        >>> rp = RegularPolygon(Point(0, 0), radius, 4)
+        >>> rp.apothem
+        sqrt(2)*r/2
+
+        """
+        return self.radius * cos(S.Pi/self._n)
+
+    @property
+    def inradius(self):
+        """
+        Alias for apothem.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy import RegularPolygon, Point
+        >>> radius = Symbol('r')
+        >>> rp = RegularPolygon(Point(0, 0), radius, 4)
+        >>> rp.inradius
+        sqrt(2)*r/2
+        """
+        return self.apothem
+
+    @property
+    def interior_angle(self):
+        """Measure of the interior angles.
+
+        Returns
+        =======
+
+        interior_angle : number
+
+        See Also
+        ========
+
+        sympy.geometry.line.LinearEntity.angle_between
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 4, 8)
+        >>> rp.interior_angle
+        3*pi/4
+
+        """
+        return (self._n - 2)*S.Pi/self._n
+
+    @property
+    def exterior_angle(self):
+        """Measure of the exterior angles.
+
+        Returns
+        =======
+
+        exterior_angle : number
+
+        See Also
+        ========
+
+        sympy.geometry.line.LinearEntity.angle_between
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 4, 8)
+        >>> rp.exterior_angle
+        pi/4
+
+        """
+        return 2*S.Pi/self._n
+
+    @property
+    def circumcircle(self):
+        """The circumcircle of the RegularPolygon.
+
+        Returns
+        =======
+
+        circumcircle : Circle
+
+        See Also
+        ========
+
+        circumcenter, sympy.geometry.ellipse.Circle
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 4, 8)
+        >>> rp.circumcircle
+        Circle(Point2D(0, 0), 4)
+
+        """
+        return Circle(self.center, self.radius)
+
+    @property
+    def incircle(self):
+        """The incircle of the RegularPolygon.
+
+        Returns
+        =======
+
+        incircle : Circle
+
+        See Also
+        ========
+
+        inradius, sympy.geometry.ellipse.Circle
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 4, 7)
+        >>> rp.incircle
+        Circle(Point2D(0, 0), 4*cos(pi/7))
+
+        """
+        return Circle(self.center, self.apothem)
+
+    @property
+    def angles(self):
+        """
+        Returns a dictionary with keys, the vertices of the Polygon,
+        and values, the interior angle at each vertex.
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> r = RegularPolygon(Point(0, 0), 5, 3)
+        >>> r.angles
+        {Point2D(-5/2, -5*sqrt(3)/2): pi/3,
+         Point2D(-5/2, 5*sqrt(3)/2): pi/3,
+         Point2D(5, 0): pi/3}
+        """
+        ret = {}
+        ang = self.interior_angle
+        for v in self.vertices:
+            ret[v] = ang
+        return ret
+
+    def encloses_point(self, p):
+        """
+        Return True if p is enclosed by (is inside of) self.
+
+        Notes
+        =====
+
+        Being on the border of self is considered False.
+
+        The general Polygon.encloses_point method is called only if
+        a point is not within or beyond the incircle or circumcircle,
+        respectively.
+
+        Parameters
+        ==========
+
+        p : Point
+
+        Returns
+        =======
+
+        encloses_point : True, False or None
+
+        See Also
+        ========
+
+        sympy.geometry.ellipse.Ellipse.encloses_point
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, S, Point, Symbol
+        >>> p = RegularPolygon((0, 0), 3, 4)
+        >>> p.encloses_point(Point(0, 0))
+        True
+        >>> r, R = p.inradius, p.circumradius
+        >>> p.encloses_point(Point((r + R)/2, 0))
+        True
+        >>> p.encloses_point(Point(R/2, R/2 + (R - r)/10))
+        False
+        >>> t = Symbol('t', real=True)
+        >>> p.encloses_point(p.arbitrary_point().subs(t, S.Half))
+        False
+        >>> p.encloses_point(Point(5, 5))
+        False
+
+        """
+
+        c = self.center
+        d = Segment(c, p).length
+        if d >= self.radius:
+            return False
+        elif d < self.inradius:
+            return True
+        else:
+            # now enumerate the RegularPolygon like a general polygon.
+            return Polygon.encloses_point(self, p)
+
+    def spin(self, angle):
+        """Increment *in place* the virtual Polygon's rotation by ccw angle.
+
+        See also: rotate method which moves the center.
+
+        >>> from sympy import Polygon, Point, pi
+        >>> r = Polygon(Point(0,0), 1, n=3)
+        >>> r.vertices[0]
+        Point2D(1, 0)
+        >>> r.spin(pi/6)
+        >>> r.vertices[0]
+        Point2D(sqrt(3)/2, 1/2)
+
+        See Also
+        ========
+
+        rotation
+        rotate : Creates a copy of the RegularPolygon rotated about a Point
+
+        """
+        self._rot += angle
+
+    def rotate(self, angle, pt=None):
+        """Override GeometryEntity.rotate to first rotate the RegularPolygon
+        about its center.
+
+        >>> from sympy import Point, RegularPolygon, pi
+        >>> t = RegularPolygon(Point(1, 0), 1, 3)
+        >>> t.vertices[0] # vertex on x-axis
+        Point2D(2, 0)
+        >>> t.rotate(pi/2).vertices[0] # vertex on y axis now
+        Point2D(0, 2)
+
+        See Also
+        ========
+
+        rotation
+        spin : Rotates a RegularPolygon in place
+
+        """
+
+        r = type(self)(*self.args)  # need a copy or else changes are in-place
+        r._rot += angle
+        return GeometryEntity.rotate(r, angle, pt)
+
+    def scale(self, x=1, y=1, pt=None):
+        """Override GeometryEntity.scale since it is the radius that must be
+        scaled (if x == y) or else a new Polygon must be returned.
+
+        >>> from sympy import RegularPolygon
+
+        Symmetric scaling returns a RegularPolygon:
+
+        >>> RegularPolygon((0, 0), 1, 4).scale(2, 2)
+        RegularPolygon(Point2D(0, 0), 2, 4, 0)
+
+        Asymmetric scaling returns a kite as a Polygon:
+
+        >>> RegularPolygon((0, 0), 1, 4).scale(2, 1)
+        Polygon(Point2D(2, 0), Point2D(0, 1), Point2D(-2, 0), Point2D(0, -1))
+
+        """
+        if pt:
+            pt = Point(pt, dim=2)
+            return self.translate(*(-pt).args).scale(x, y).translate(*pt.args)
+        if x != y:
+            return Polygon(*self.vertices).scale(x, y)
+        c, r, n, rot = self.args
+        r *= x
+        return self.func(c, r, n, rot)
+
+    def reflect(self, line):
+        """Override GeometryEntity.reflect since this is not made of only
+        points.
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Line
+
+        >>> RegularPolygon((0, 0), 1, 4).reflect(Line((0, 1), slope=-2))
+        RegularPolygon(Point2D(4/5, 2/5), -1, 4, atan(4/3))
+
+        """
+        c, r, n, rot = self.args
+        v = self.vertices[0]
+        d = v - c
+        cc = c.reflect(line)
+        vv = v.reflect(line)
+        dd = vv - cc
+        # calculate rotation about the new center
+        # which will align the vertices
+        l1 = Ray((0, 0), dd)
+        l2 = Ray((0, 0), d)
+        ang = l1.closing_angle(l2)
+        rot += ang
+        # change sign of radius as point traversal is reversed
+        return self.func(cc, -r, n, rot)
+
+    @property
+    def vertices(self):
+        """The vertices of the RegularPolygon.
+
+        Returns
+        =======
+
+        vertices : list
+            Each vertex is a Point.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import RegularPolygon, Point
+        >>> rp = RegularPolygon(Point(0, 0), 5, 4)
+        >>> rp.vertices
+        [Point2D(5, 0), Point2D(0, 5), Point2D(-5, 0), Point2D(0, -5)]
+
+        """
+        c = self._center
+        r = abs(self._radius)
+        rot = self._rot
+        v = 2*S.Pi/self._n
+
+        return [Point(c.x + r*cos(k*v + rot), c.y + r*sin(k*v + rot))
+                for k in range(self._n)]
+
+    def __eq__(self, o):
+        if not isinstance(o, Polygon):
+            return False
+        elif not isinstance(o, RegularPolygon):
+            return Polygon.__eq__(o, self)
+        return self.args == o.args
+
+    def __hash__(self):
+        return super().__hash__()
+
+
+class Triangle(Polygon):
+    """
+    A polygon with three vertices and three sides.
+
+    Parameters
+    ==========
+
+    points : sequence of Points
+    keyword: asa, sas, or sss to specify sides/angles of the triangle
+
+    Attributes
+    ==========
+
+    vertices
+    altitudes
+    orthocenter
+    circumcenter
+    circumradius
+    circumcircle
+    inradius
+    incircle
+    exradii
+    medians
+    medial
+    nine_point_circle
+
+    Raises
+    ======
+
+    GeometryError
+        If the number of vertices is not equal to three, or one of the vertices
+        is not a Point, or a valid keyword is not given.
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, Polygon
+
+    Examples
+    ========
+
+    >>> from sympy import Triangle, Point
+    >>> Triangle(Point(0, 0), Point(4, 0), Point(4, 3))
+    Triangle(Point2D(0, 0), Point2D(4, 0), Point2D(4, 3))
+
+    Keywords sss, sas, or asa can be used to give the desired
+    side lengths (in order) and interior angles (in degrees) that
+    define the triangle:
+
+    >>> Triangle(sss=(3, 4, 5))
+    Triangle(Point2D(0, 0), Point2D(3, 0), Point2D(3, 4))
+    >>> Triangle(asa=(30, 1, 30))
+    Triangle(Point2D(0, 0), Point2D(1, 0), Point2D(1/2, sqrt(3)/6))
+    >>> Triangle(sas=(1, 45, 2))
+    Triangle(Point2D(0, 0), Point2D(2, 0), Point2D(sqrt(2)/2, sqrt(2)/2))
+
+    """
+
+    def __new__(cls, *args, **kwargs):
+        if len(args) != 3:
+            if 'sss' in kwargs:
+                return _sss(*[simplify(a) for a in kwargs['sss']])
+            if 'asa' in kwargs:
+                return _asa(*[simplify(a) for a in kwargs['asa']])
+            if 'sas' in kwargs:
+                return _sas(*[simplify(a) for a in kwargs['sas']])
+            msg = "Triangle instantiates with three points or a valid keyword."
+            raise GeometryError(msg)
+
+        vertices = [Point(a, dim=2, **kwargs) for a in args]
+
+        # remove consecutive duplicates
+        nodup = []
+        for p in vertices:
+            if nodup and p == nodup[-1]:
+                continue
+            nodup.append(p)
+        if len(nodup) > 1 and nodup[-1] == nodup[0]:
+            nodup.pop()  # last point was same as first
+
+        # remove collinear points
+        i = -3
+        while i < len(nodup) - 3 and len(nodup) > 2:
+            a, b, c = sorted(
+                [nodup[i], nodup[i + 1], nodup[i + 2]], key=default_sort_key)
+            if Point.is_collinear(a, b, c):
+                nodup[i] = a
+                nodup[i + 1] = None
+                nodup.pop(i + 1)
+            i += 1
+
+        vertices = list(filter(lambda x: x is not None, nodup))
+
+        if len(vertices) == 3:
+            return GeometryEntity.__new__(cls, *vertices, **kwargs)
+        elif len(vertices) == 2:
+            return Segment(*vertices, **kwargs)
+        else:
+            return Point(*vertices, **kwargs)
+
+    @property
+    def vertices(self):
+        """The triangle's vertices
+
+        Returns
+        =======
+
+        vertices : tuple
+            Each element in the tuple is a Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Triangle, Point
+        >>> t = Triangle(Point(0, 0), Point(4, 0), Point(4, 3))
+        >>> t.vertices
+        (Point2D(0, 0), Point2D(4, 0), Point2D(4, 3))
+
+        """
+        return self.args
+
+    def is_similar(t1, t2):
+        """Is another triangle similar to this one.
+
+        Two triangles are similar if one can be uniformly scaled to the other.
+
+        Parameters
+        ==========
+
+        other: Triangle
+
+        Returns
+        =======
+
+        is_similar : boolean
+
+        See Also
+        ========
+
+        sympy.geometry.entity.GeometryEntity.is_similar
+
+        Examples
+        ========
+
+        >>> from sympy import Triangle, Point
+        >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(4, 3))
+        >>> t2 = Triangle(Point(0, 0), Point(-4, 0), Point(-4, -3))
+        >>> t1.is_similar(t2)
+        True
+
+        >>> t2 = Triangle(Point(0, 0), Point(-4, 0), Point(-4, -4))
+        >>> t1.is_similar(t2)
+        False
+
+        """
+        if not isinstance(t2, Polygon):
+            return False
+
+        s1_1, s1_2, s1_3 = [side.length for side in t1.sides]
+        s2 = [side.length for side in t2.sides]
+
+        def _are_similar(u1, u2, u3, v1, v2, v3):
+            e1 = simplify(u1/v1)
+            e2 = simplify(u2/v2)
+            e3 = simplify(u3/v3)
+            return bool(e1 == e2) and bool(e2 == e3)
+
+        # There's only 6 permutations, so write them out
+        return _are_similar(s1_1, s1_2, s1_3, *s2) or \
+            _are_similar(s1_1, s1_3, s1_2, *s2) or \
+            _are_similar(s1_2, s1_1, s1_3, *s2) or \
+            _are_similar(s1_2, s1_3, s1_1, *s2) or \
+            _are_similar(s1_3, s1_1, s1_2, *s2) or \
+            _are_similar(s1_3, s1_2, s1_1, *s2)
+
+    def is_equilateral(self):
+        """Are all the sides the same length?
+
+        Returns
+        =======
+
+        is_equilateral : boolean
+
+        See Also
+        ========
+
+        sympy.geometry.entity.GeometryEntity.is_similar, RegularPolygon
+        is_isosceles, is_right, is_scalene
+
+        Examples
+        ========
+
+        >>> from sympy import Triangle, Point
+        >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(4, 3))
+        >>> t1.is_equilateral()
+        False
+
+        >>> from sympy import sqrt
+        >>> t2 = Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3)))
+        >>> t2.is_equilateral()
+        True
+
+        """
+        return not has_variety(s.length for s in self.sides)
+
+    def is_isosceles(self):
+        """Are two or more of the sides the same length?
+
+        Returns
+        =======
+
+        is_isosceles : boolean
+
+        See Also
+        ========
+
+        is_equilateral, is_right, is_scalene
+
+        Examples
+        ========
+
+        >>> from sympy import Triangle, Point
+        >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(2, 4))
+        >>> t1.is_isosceles()
+        True
+
+        """
+        return has_dups(s.length for s in self.sides)
+
+    def is_scalene(self):
+        """Are all the sides of the triangle of different lengths?
+
+        Returns
+        =======
+
+        is_scalene : boolean
+
+        See Also
+        ========
+
+        is_equilateral, is_isosceles, is_right
+
+        Examples
+        ========
+
+        >>> from sympy import Triangle, Point
+        >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(1, 4))
+        >>> t1.is_scalene()
+        True
+
+        """
+        return not has_dups(s.length for s in self.sides)
+
+    def is_right(self):
+        """Is the triangle right-angled.
+
+        Returns
+        =======
+
+        is_right : boolean
+
+        See Also
+        ========
+
+        sympy.geometry.line.LinearEntity.is_perpendicular
+        is_equilateral, is_isosceles, is_scalene
+
+        Examples
+        ========
+
+        >>> from sympy import Triangle, Point
+        >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(4, 3))
+        >>> t1.is_right()
+        True
+
+        """
+        s = self.sides
+        return Segment.is_perpendicular(s[0], s[1]) or \
+            Segment.is_perpendicular(s[1], s[2]) or \
+            Segment.is_perpendicular(s[0], s[2])
+
+    @property
+    def altitudes(self):
+        """The altitudes of the triangle.
+
+        An altitude of a triangle is a segment through a vertex,
+        perpendicular to the opposite side, with length being the
+        height of the vertex measured from the line containing the side.
+
+        Returns
+        =======
+
+        altitudes : dict
+            The dictionary consists of keys which are vertices and values
+            which are Segments.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.line.Segment.length
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.altitudes[p1]
+        Segment2D(Point2D(0, 0), Point2D(1/2, 1/2))
+
+        """
+        s = self.sides
+        v = self.vertices
+        return {v[0]: s[1].perpendicular_segment(v[0]),
+                v[1]: s[2].perpendicular_segment(v[1]),
+                v[2]: s[0].perpendicular_segment(v[2])}
+
+    @property
+    def orthocenter(self):
+        """The orthocenter of the triangle.
+
+        The orthocenter is the intersection of the altitudes of a triangle.
+        It may lie inside, outside or on the triangle.
+
+        Returns
+        =======
+
+        orthocenter : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.orthocenter
+        Point2D(0, 0)
+
+        """
+        a = self.altitudes
+        v = self.vertices
+        return Line(a[v[0]]).intersection(Line(a[v[1]]))[0]
+
+    @property
+    def circumcenter(self):
+        """The circumcenter of the triangle
+
+        The circumcenter is the center of the circumcircle.
+
+        Returns
+        =======
+
+        circumcenter : Point
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.circumcenter
+        Point2D(1/2, 1/2)
+        """
+        a, b, c = [x.perpendicular_bisector() for x in self.sides]
+        return a.intersection(b)[0]
+
+    @property
+    def circumradius(self):
+        """The radius of the circumcircle of the triangle.
+
+        Returns
+        =======
+
+        circumradius : number of Basic instance
+
+        See Also
+        ========
+
+        sympy.geometry.ellipse.Circle.radius
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy import Point, Triangle
+        >>> a = Symbol('a')
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, a)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.circumradius
+        sqrt(a**2/4 + 1/4)
+        """
+        return Point.distance(self.circumcenter, self.vertices[0])
+
+    @property
+    def circumcircle(self):
+        """The circle which passes through the three vertices of the triangle.
+
+        Returns
+        =======
+
+        circumcircle : Circle
+
+        See Also
+        ========
+
+        sympy.geometry.ellipse.Circle
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.circumcircle
+        Circle(Point2D(1/2, 1/2), sqrt(2)/2)
+
+        """
+        return Circle(self.circumcenter, self.circumradius)
+
+    def bisectors(self):
+        """The angle bisectors of the triangle.
+
+        An angle bisector of a triangle is a straight line through a vertex
+        which cuts the corresponding angle in half.
+
+        Returns
+        =======
+
+        bisectors : dict
+            Each key is a vertex (Point) and each value is the corresponding
+            bisector (Segment).
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point, sympy.geometry.line.Segment
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle, Segment
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> from sympy import sqrt
+        >>> t.bisectors()[p2] == Segment(Point(1, 0), Point(0, sqrt(2) - 1))
+        True
+
+        """
+        # use lines containing sides so containment check during
+        # intersection calculation can be avoided, thus reducing
+        # the processing time for calculating the bisectors
+        s = [Line(l) for l in self.sides]
+        v = self.vertices
+        c = self.incenter
+        l1 = Segment(v[0], Line(v[0], c).intersection(s[1])[0])
+        l2 = Segment(v[1], Line(v[1], c).intersection(s[2])[0])
+        l3 = Segment(v[2], Line(v[2], c).intersection(s[0])[0])
+        return {v[0]: l1, v[1]: l2, v[2]: l3}
+
+    @property
+    def incenter(self):
+        """The center of the incircle.
+
+        The incircle is the circle which lies inside the triangle and touches
+        all three sides.
+
+        Returns
+        =======
+
+        incenter : Point
+
+        See Also
+        ========
+
+        incircle, sympy.geometry.point.Point
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.incenter
+        Point2D(1 - sqrt(2)/2, 1 - sqrt(2)/2)
+
+        """
+        s = self.sides
+        l = Matrix([s[i].length for i in [1, 2, 0]])
+        p = sum(l)
+        v = self.vertices
+        x = simplify(l.dot(Matrix([vi.x for vi in v]))/p)
+        y = simplify(l.dot(Matrix([vi.y for vi in v]))/p)
+        return Point(x, y)
+
+    @property
+    def inradius(self):
+        """The radius of the incircle.
+
+        Returns
+        =======
+
+        inradius : number of Basic instance
+
+        See Also
+        ========
+
+        incircle, sympy.geometry.ellipse.Circle.radius
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(4, 0), Point(0, 3)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.inradius
+        1
+
+        """
+        return simplify(2 * self.area / self.perimeter)
+
+    @property
+    def incircle(self):
+        """The incircle of the triangle.
+
+        The incircle is the circle which lies inside the triangle and touches
+        all three sides.
+
+        Returns
+        =======
+
+        incircle : Circle
+
+        See Also
+        ========
+
+        sympy.geometry.ellipse.Circle
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(2, 0), Point(0, 2)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.incircle
+        Circle(Point2D(2 - sqrt(2), 2 - sqrt(2)), 2 - sqrt(2))
+
+        """
+        return Circle(self.incenter, self.inradius)
+
+    @property
+    def exradii(self):
+        """The radius of excircles of a triangle.
+
+        An excircle of the triangle is a circle lying outside the triangle,
+        tangent to one of its sides and tangent to the extensions of the
+        other two.
+
+        Returns
+        =======
+
+        exradii : dict
+
+        See Also
+        ========
+
+        sympy.geometry.polygon.Triangle.inradius
+
+        Examples
+        ========
+
+        The exradius touches the side of the triangle to which it is keyed, e.g.
+        the exradius touching side 2 is:
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(6, 0), Point(0, 2)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.exradii[t.sides[2]]
+        -2 + sqrt(10)
+
+        References
+        ==========
+
+        .. [1] https://mathworld.wolfram.com/Exradius.html
+        .. [2] https://mathworld.wolfram.com/Excircles.html
+
+        """
+
+        side = self.sides
+        a = side[0].length
+        b = side[1].length
+        c = side[2].length
+        s = (a+b+c)/2
+        area = self.area
+        exradii = {self.sides[0]: simplify(area/(s-a)),
+                   self.sides[1]: simplify(area/(s-b)),
+                   self.sides[2]: simplify(area/(s-c))}
+
+        return exradii
+
+    @property
+    def excenters(self):
+        """Excenters of the triangle.
+
+        An excenter is the center of a circle that is tangent to a side of the
+        triangle and the extensions of the other two sides.
+
+        Returns
+        =======
+
+        excenters : dict
+
+
+        Examples
+        ========
+
+        The excenters are keyed to the side of the triangle to which their corresponding
+        excircle is tangent: The center is keyed, e.g. the excenter of a circle touching
+        side 0 is:
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(6, 0), Point(0, 2)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.excenters[t.sides[0]]
+        Point2D(12*sqrt(10), 2/3 + sqrt(10)/3)
+
+        See Also
+        ========
+
+        sympy.geometry.polygon.Triangle.exradii
+
+        References
+        ==========
+
+        .. [1] https://mathworld.wolfram.com/Excircles.html
+
+        """
+
+        s = self.sides
+        v = self.vertices
+        a = s[0].length
+        b = s[1].length
+        c = s[2].length
+        x = [v[0].x, v[1].x, v[2].x]
+        y = [v[0].y, v[1].y, v[2].y]
+
+        exc_coords = {
+            "x1": simplify(-a*x[0]+b*x[1]+c*x[2]/(-a+b+c)),
+            "x2": simplify(a*x[0]-b*x[1]+c*x[2]/(a-b+c)),
+            "x3": simplify(a*x[0]+b*x[1]-c*x[2]/(a+b-c)),
+            "y1": simplify(-a*y[0]+b*y[1]+c*y[2]/(-a+b+c)),
+            "y2": simplify(a*y[0]-b*y[1]+c*y[2]/(a-b+c)),
+            "y3": simplify(a*y[0]+b*y[1]-c*y[2]/(a+b-c))
+        }
+
+        excenters = {
+            s[0]: Point(exc_coords["x1"], exc_coords["y1"]),
+            s[1]: Point(exc_coords["x2"], exc_coords["y2"]),
+            s[2]: Point(exc_coords["x3"], exc_coords["y3"])
+        }
+
+        return excenters
+
+    @property
+    def medians(self):
+        """The medians of the triangle.
+
+        A median of a triangle is a straight line through a vertex and the
+        midpoint of the opposite side, and divides the triangle into two
+        equal areas.
+
+        Returns
+        =======
+
+        medians : dict
+            Each key is a vertex (Point) and each value is the median (Segment)
+            at that point.
+
+        See Also
+        ========
+
+        sympy.geometry.point.Point.midpoint, sympy.geometry.line.Segment.midpoint
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.medians[p1]
+        Segment2D(Point2D(0, 0), Point2D(1/2, 1/2))
+
+        """
+        s = self.sides
+        v = self.vertices
+        return {v[0]: Segment(v[0], s[1].midpoint),
+                v[1]: Segment(v[1], s[2].midpoint),
+                v[2]: Segment(v[2], s[0].midpoint)}
+
+    @property
+    def medial(self):
+        """The medial triangle of the triangle.
+
+        The triangle which is formed from the midpoints of the three sides.
+
+        Returns
+        =======
+
+        medial : Triangle
+
+        See Also
+        ========
+
+        sympy.geometry.line.Segment.midpoint
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.medial
+        Triangle(Point2D(1/2, 0), Point2D(1/2, 1/2), Point2D(0, 1/2))
+
+        """
+        s = self.sides
+        return Triangle(s[0].midpoint, s[1].midpoint, s[2].midpoint)
+
+    @property
+    def nine_point_circle(self):
+        """The nine-point circle of the triangle.
+
+        Nine-point circle is the circumcircle of the medial triangle, which
+        passes through the feet of altitudes and the middle points of segments
+        connecting the vertices and the orthocenter.
+
+        Returns
+        =======
+
+        nine_point_circle : Circle
+
+        See also
+        ========
+
+        sympy.geometry.line.Segment.midpoint
+        sympy.geometry.polygon.Triangle.medial
+        sympy.geometry.polygon.Triangle.orthocenter
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.nine_point_circle
+        Circle(Point2D(1/4, 1/4), sqrt(2)/4)
+
+        """
+        return Circle(*self.medial.vertices)
+
+    @property
+    def eulerline(self):
+        """The Euler line of the triangle.
+
+        The line which passes through circumcenter, centroid and orthocenter.
+
+        Returns
+        =======
+
+        eulerline : Line (or Point for equilateral triangles in which case all
+                    centers coincide)
+
+        Examples
+        ========
+
+        >>> from sympy import Point, Triangle
+        >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        >>> t = Triangle(p1, p2, p3)
+        >>> t.eulerline
+        Line2D(Point2D(0, 0), Point2D(1/2, 1/2))
+
+        """
+        if self.is_equilateral():
+            return self.orthocenter
+        return Line(self.orthocenter, self.circumcenter)
+
+def rad(d):
+    """Return the radian value for the given degrees (pi = 180 degrees)."""
+    return d*pi/180
+
+
+def deg(r):
+    """Return the degree value for the given radians (pi = 180 degrees)."""
+    return r/pi*180
+
+
+def _slope(d):
+    rv = tan(rad(d))
+    return rv
+
+
+def _asa(d1, l, d2):
+    """Return triangle having side with length l on the x-axis."""
+    xy = Line((0, 0), slope=_slope(d1)).intersection(
+        Line((l, 0), slope=_slope(180 - d2)))[0]
+    return Triangle((0, 0), (l, 0), xy)
+
+
+def _sss(l1, l2, l3):
+    """Return triangle having side of length l1 on the x-axis."""
+    c1 = Circle((0, 0), l3)
+    c2 = Circle((l1, 0), l2)
+    inter = [a for a in c1.intersection(c2) if a.y.is_nonnegative]
+    if not inter:
+        return None
+    pt = inter[0]
+    return Triangle((0, 0), (l1, 0), pt)
+
+
+def _sas(l1, d, l2):
+    """Return triangle having side with length l2 on the x-axis."""
+    p1 = Point(0, 0)
+    p2 = Point(l2, 0)
+    p3 = Point(cos(rad(d))*l1, sin(rad(d))*l1)
+    return Triangle(p1, p2, p3)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/__init__.py
new file mode 100644
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diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_curve.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_curve.py
new file mode 100644
index 0000000000000000000000000000000000000000..50aa80273a1d8eb9e414a8d591571f3127352dad
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_curve.py
@@ -0,0 +1,120 @@
+from sympy.core.containers import Tuple
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.hyperbolic import asinh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.geometry import Curve, Line, Point, Ellipse, Ray, Segment, Circle, Polygon, RegularPolygon
+from sympy.testing.pytest import raises, slow
+
+
+def test_curve():
+    x = Symbol('x', real=True)
+    s = Symbol('s')
+    z = Symbol('z')
+
+    # this curve is independent of the indicated parameter
+    c = Curve([2*s, s**2], (z, 0, 2))
+
+    assert c.parameter == z
+    assert c.functions == (2*s, s**2)
+    assert c.arbitrary_point() == Point(2*s, s**2)
+    assert c.arbitrary_point(z) == Point(2*s, s**2)
+
+    # this is how it is normally used
+    c = Curve([2*s, s**2], (s, 0, 2))
+
+    assert c.parameter == s
+    assert c.functions == (2*s, s**2)
+    t = Symbol('t')
+    # the t returned as assumptions
+    assert c.arbitrary_point() != Point(2*t, t**2)
+    t = Symbol('t', real=True)
+    # now t has the same assumptions so the test passes
+    assert c.arbitrary_point() == Point(2*t, t**2)
+    assert c.arbitrary_point(z) == Point(2*z, z**2)
+    assert c.arbitrary_point(c.parameter) == Point(2*s, s**2)
+    assert c.arbitrary_point(None) == Point(2*s, s**2)
+    assert c.plot_interval() == [t, 0, 2]
+    assert c.plot_interval(z) == [z, 0, 2]
+
+    assert Curve([x, x], (x, 0, 1)).rotate(pi/2) == Curve([-x, x], (x, 0, 1))
+    assert Curve([x, x], (x, 0, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate(
+        1, 3).arbitrary_point(s) == \
+        Line((0, 0), (1, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate(
+            1, 3).arbitrary_point(s) == \
+        Point(-2*s + 7, 3*s + 6)
+
+    raises(ValueError, lambda: Curve((s), (s, 1, 2)))
+    raises(ValueError, lambda: Curve((x, x * 2), (1, x)))
+
+    raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point())
+    raises(ValueError, lambda: Curve((s, s + t), (t, 1, 2)).arbitrary_point(s))
+
+
+@slow
+def test_free_symbols():
+    a, b, c, d, e, f, s = symbols('a:f,s')
+    assert Point(a, b).free_symbols == {a, b}
+    assert Line((a, b), (c, d)).free_symbols == {a, b, c, d}
+    assert Ray((a, b), (c, d)).free_symbols == {a, b, c, d}
+    assert Ray((a, b), angle=c).free_symbols == {a, b, c}
+    assert Segment((a, b), (c, d)).free_symbols == {a, b, c, d}
+    assert Line((a, b), slope=c).free_symbols == {a, b, c}
+    assert Curve((a*s, b*s), (s, c, d)).free_symbols == {a, b, c, d}
+    assert Ellipse((a, b), c, d).free_symbols == {a, b, c, d}
+    assert Ellipse((a, b), c, eccentricity=d).free_symbols == \
+        {a, b, c, d}
+    assert Ellipse((a, b), vradius=c, eccentricity=d).free_symbols == \
+        {a, b, c, d}
+    assert Circle((a, b), c).free_symbols == {a, b, c}
+    assert Circle((a, b), (c, d), (e, f)).free_symbols == \
+        {e, d, c, b, f, a}
+    assert Polygon((a, b), (c, d), (e, f)).free_symbols == \
+        {e, b, d, f, a, c}
+    assert RegularPolygon((a, b), c, d, e).free_symbols == {e, a, b, c, d}
+
+
+def test_transform():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    c = Curve((x, x**2), (x, 0, 1))
+    cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1))
+    pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)]
+    pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)]
+
+    assert c.scale(2, 3, (4, 5)) == cout
+    assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts
+    assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out
+    assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \
+        Curve((x + S.Half, 3*x), (x, 0, 1))
+    assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \
+        Curve((x + 4, 3*x + 5), (x, 0, 1))
+
+
+def test_length():
+    t = Symbol('t', real=True)
+
+    c1 = Curve((t, 0), (t, 0, 1))
+    assert c1.length == 1
+
+    c2 = Curve((t, t), (t, 0, 1))
+    assert c2.length == sqrt(2)
+
+    c3 = Curve((t ** 2, t), (t, 2, 5))
+    assert c3.length == -sqrt(17) - asinh(4) / 4 + asinh(10) / 4 + 5 * sqrt(101) / 2
+
+
+def test_parameter_value():
+    t = Symbol('t')
+    C = Curve([2*t, t**2], (t, 0, 2))
+    assert C.parameter_value((2, 1), t) == {t: 1}
+    raises(ValueError, lambda: C.parameter_value((2, 0), t))
+
+
+def test_issue_17997():
+    t, s = symbols('t s')
+    c = Curve((t, t**2), (t, 0, 10))
+    p = Curve([2*s, s**2], (s, 0, 2))
+    assert c(2) == Point(2, 4)
+    assert p(1) == Point(2, 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_ellipse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_ellipse.py
new file mode 100644
index 0000000000000000000000000000000000000000..a79eba8c35771bda9f0980aca68d937f8e625c0a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_ellipse.py
@@ -0,0 +1,613 @@
+from sympy.core import expand
+from sympy.core.numbers import (Rational, oo, pi)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sec
+from sympy.geometry.line import Segment2D
+from sympy.geometry.point import Point2D
+from sympy.geometry import (Circle, Ellipse, GeometryError, Line, Point,
+                            Polygon, Ray, RegularPolygon, Segment,
+                            Triangle, intersection)
+from sympy.testing.pytest import raises, slow
+from sympy.integrals.integrals import integrate
+from sympy.functions.special.elliptic_integrals import elliptic_e
+from sympy.functions.elementary.miscellaneous import Max
+
+
+def test_ellipse_equation_using_slope():
+    from sympy.abc import x, y
+
+    e1 = Ellipse(Point(1, 0), 3, 2)
+    assert str(e1.equation(_slope=1)) == str((-x + y + 1)**2/8 + (x + y - 1)**2/18 - 1)
+
+    e2 = Ellipse(Point(0, 0), 4, 1)
+    assert str(e2.equation(_slope=1)) == str((-x + y)**2/2 + (x + y)**2/32 - 1)
+
+    e3 = Ellipse(Point(1, 5), 6, 2)
+    assert str(e3.equation(_slope=2)) == str((-2*x + y - 3)**2/20 + (x + 2*y - 11)**2/180 - 1)
+
+
+def test_object_from_equation():
+    from sympy.abc import x, y, a, b, c, d, e
+    assert Circle(x**2 + y**2 + 3*x + 4*y - 8) == Circle(Point2D(S(-3) / 2, -2), sqrt(57) / 2)
+    assert Circle(x**2 + y**2 + 6*x + 8*y + 25) == Circle(Point2D(-3, -4), 0)
+    assert Circle(a**2 + b**2 + 6*a + 8*b + 25, x='a', y='b') == Circle(Point2D(-3, -4), 0)
+    assert Circle(x**2 + y**2 - 25) == Circle(Point2D(0, 0), 5)
+    assert Circle(x**2 + y**2) == Circle(Point2D(0, 0), 0)
+    assert Circle(a**2 + b**2, x='a', y='b') == Circle(Point2D(0, 0), 0)
+    assert Circle(x**2 + y**2 + 6*x + 8) == Circle(Point2D(-3, 0), 1)
+    assert Circle(x**2 + y**2 + 6*y + 8) == Circle(Point2D(0, -3), 1)
+    assert Circle((x - 1)**2 + y**2 - 9) == Circle(Point2D(1, 0), 3)
+    assert Circle(6*(x**2) + 6*(y**2) + 6*x + 8*y - 25) == Circle(Point2D(Rational(-1, 2), Rational(-2, 3)), 5*sqrt(7)/6)
+    assert Circle(Eq(a**2 + b**2, 25), x='a', y=b) == Circle(Point2D(0, 0), 5)
+    raises(GeometryError, lambda: Circle(x**2 + y**2 + 3*x + 4*y + 26))
+    raises(GeometryError, lambda: Circle(x**2 + y**2 + 25))
+    raises(GeometryError, lambda: Circle(a**2 + b**2 + 25, x='a', y='b'))
+    raises(GeometryError, lambda: Circle(x**2 + 6*y + 8))
+    raises(GeometryError, lambda: Circle(6*(x ** 2) + 4*(y**2) + 6*x + 8*y + 25))
+    raises(ValueError, lambda: Circle(a**2 + b**2 + 3*a + 4*b - 8))
+    # .equation() adds 'real=True' assumption; '==' would fail if assumptions differed
+    x, y = symbols('x y', real=True)
+    eq = a*x**2 + a*y**2 + c*x + d*y + e
+    assert expand(Circle(eq).equation()*a) == eq
+
+
+@slow
+def test_ellipse_geom():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    t = Symbol('t', real=True)
+    y1 = Symbol('y1', real=True)
+    half = S.Half
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+    p4 = Point(0, 1)
+
+    e1 = Ellipse(p1, 1, 1)
+    e2 = Ellipse(p2, half, 1)
+    e3 = Ellipse(p1, y1, y1)
+    c1 = Circle(p1, 1)
+    c2 = Circle(p2, 1)
+    c3 = Circle(Point(sqrt(2), sqrt(2)), 1)
+    l1 = Line(p1, p2)
+
+    # Test creation with three points
+    cen, rad = Point(3*half, 2), 5*half
+    assert Circle(Point(0, 0), Point(3, 0), Point(0, 4)) == Circle(cen, rad)
+    assert Circle(Point(0, 0), Point(1, 1), Point(2, 2)) == Segment2D(Point2D(0, 0), Point2D(2, 2))
+
+    raises(ValueError, lambda: Ellipse(None, None, None, 1))
+    raises(ValueError, lambda: Ellipse())
+    raises(GeometryError, lambda: Circle(Point(0, 0)))
+    raises(GeometryError, lambda: Circle(Symbol('x')*Symbol('y')))
+
+    # Basic Stuff
+    assert Ellipse(None, 1, 1).center == Point(0, 0)
+    assert e1 == c1
+    assert e1 != e2
+    assert e1 != l1
+    assert p4 in e1
+    assert e1 in e1
+    assert e2 in e2
+    assert 1 not in e2
+    assert p2 not in e2
+    assert e1.area == pi
+    assert e2.area == pi/2
+    assert e3.area == pi*y1*abs(y1)
+    assert c1.area == e1.area
+    assert c1.circumference == e1.circumference
+    assert e3.circumference == 2*pi*y1
+    assert e1.plot_interval() == e2.plot_interval() == [t, -pi, pi]
+    assert e1.plot_interval(x) == e2.plot_interval(x) == [x, -pi, pi]
+
+    assert c1.minor == 1
+    assert c1.major == 1
+    assert c1.hradius == 1
+    assert c1.vradius == 1
+
+    assert Ellipse((1, 1), 0, 0) == Point(1, 1)
+    assert Ellipse((1, 1), 1, 0) == Segment(Point(0, 1), Point(2, 1))
+    assert Ellipse((1, 1), 0, 1) == Segment(Point(1, 0), Point(1, 2))
+
+    # Private Functions
+    assert hash(c1) == hash(Circle(Point(1, 0), Point(0, 1), Point(0, -1)))
+    assert c1 in e1
+    assert (Line(p1, p2) in e1) is False
+    assert e1.__cmp__(e1) == 0
+    assert e1.__cmp__(Point(0, 0)) > 0
+
+    # Encloses
+    assert e1.encloses(Segment(Point(-0.5, -0.5), Point(0.5, 0.5))) is True
+    assert e1.encloses(Line(p1, p2)) is False
+    assert e1.encloses(Ray(p1, p2)) is False
+    assert e1.encloses(e1) is False
+    assert e1.encloses(
+        Polygon(Point(-0.5, -0.5), Point(-0.5, 0.5), Point(0.5, 0.5))) is True
+    assert e1.encloses(RegularPolygon(p1, 0.5, 3)) is True
+    assert e1.encloses(RegularPolygon(p1, 5, 3)) is False
+    assert e1.encloses(RegularPolygon(p2, 5, 3)) is False
+
+    assert e2.arbitrary_point() in e2
+    raises(ValueError, lambda: Ellipse(Point(x, y), 1, 1).arbitrary_point(parameter='x'))
+
+    # Foci
+    f1, f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
+    ef = Ellipse(Point(0, 0), 4, 2)
+    assert ef.foci in [(f1, f2), (f2, f1)]
+
+    # Tangents
+    v = sqrt(2) / 2
+    p1_1 = Point(v, v)
+    p1_2 = p2 + Point(half, 0)
+    p1_3 = p2 + Point(0, 1)
+    assert e1.tangent_lines(p4) == c1.tangent_lines(p4)
+    assert e2.tangent_lines(p1_2) == [Line(Point(Rational(3, 2), 1), Point(Rational(3, 2), S.Half))]
+    assert e2.tangent_lines(p1_3) == [Line(Point(1, 2), Point(Rational(5, 4), 2))]
+    assert c1.tangent_lines(p1_1) != [Line(p1_1, Point(0, sqrt(2)))]
+    assert c1.tangent_lines(p1) == []
+    assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
+    assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
+    assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
+    assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) is False
+    assert c1.is_tangent(e1) is True
+    assert c1.is_tangent(Ellipse(Point(2, 0), 1, 1)) is True
+    assert c1.is_tangent(
+        Polygon(Point(1, 1), Point(1, -1), Point(2, 0))) is False
+    assert c1.is_tangent(
+        Polygon(Point(1, 1), Point(1, 0), Point(2, 0))) is False
+    assert Circle(Point(5, 5), 3).is_tangent(Circle(Point(0, 5), 1)) is False
+
+    assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(0, 0)) == \
+        [Line(Point(0, 0), Point(Rational(77, 25), Rational(132, 25))),
+     Line(Point(0, 0), Point(Rational(33, 5), Rational(22, 5)))]
+    assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(3, 4)) == \
+        [Line(Point(3, 4), Point(4, 4)), Line(Point(3, 4), Point(3, 5))]
+    assert Circle(Point(5, 5), 2).tangent_lines(Point(3, 3)) == \
+        [Line(Point(3, 3), Point(4, 3)), Line(Point(3, 3), Point(3, 4))]
+    assert Circle(Point(5, 5), 2).tangent_lines(Point(5 - 2*sqrt(2), 5)) == \
+        [Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 - sqrt(2))),
+     Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 + sqrt(2))), ]
+    assert Circle(Point(5, 5), 5).tangent_lines(Point(4, 0)) == \
+        [Line(Point(4, 0), Point(Rational(40, 13), Rational(5, 13))),
+     Line(Point(4, 0), Point(5, 0))]
+    assert Circle(Point(5, 5), 5).tangent_lines(Point(0, 6)) == \
+        [Line(Point(0, 6), Point(0, 7)),
+        Line(Point(0, 6), Point(Rational(5, 13), Rational(90, 13)))]
+
+    # for numerical calculations, we shouldn't demand exact equality,
+    # so only test up to the desired precision
+    def lines_close(l1, l2, prec):
+        """ tests whether l1 and 12 are within 10**(-prec)
+        of each other """
+        return abs(l1.p1 - l2.p1) < 10**(-prec) and abs(l1.p2 - l2.p2) < 10**(-prec)
+    def line_list_close(ll1, ll2, prec):
+        return all(lines_close(l1, l2, prec) for l1, l2 in zip(ll1, ll2))
+
+    e = Ellipse(Point(0, 0), 2, 1)
+    assert e.normal_lines(Point(0, 0)) == \
+        [Line(Point(0, 0), Point(0, 1)), Line(Point(0, 0), Point(1, 0))]
+    assert e.normal_lines(Point(1, 0)) == \
+        [Line(Point(0, 0), Point(1, 0))]
+    assert e.normal_lines((0, 1)) == \
+        [Line(Point(0, 0), Point(0, 1))]
+    assert line_list_close(e.normal_lines(Point(1, 1), 2), [
+        Line(Point(Rational(-51, 26), Rational(-1, 5)), Point(Rational(-25, 26), Rational(17, 83))),
+        Line(Point(Rational(28, 29), Rational(-7, 8)), Point(Rational(57, 29), Rational(-9, 2)))], 2)
+    # test the failure of Poly.intervals and checks a point on the boundary
+    p = Point(sqrt(3), S.Half)
+    assert p in e
+    assert line_list_close(e.normal_lines(p, 2), [
+        Line(Point(Rational(-341, 171), Rational(-1, 13)), Point(Rational(-170, 171), Rational(5, 64))),
+        Line(Point(Rational(26, 15), Rational(-1, 2)), Point(Rational(41, 15), Rational(-43, 26)))], 2)
+    # be sure to use the slope that isn't undefined on boundary
+    e = Ellipse((0, 0), 2, 2*sqrt(3)/3)
+    assert line_list_close(e.normal_lines((1, 1), 2), [
+        Line(Point(Rational(-64, 33), Rational(-20, 71)), Point(Rational(-31, 33), Rational(2, 13))),
+        Line(Point(1, -1), Point(2, -4))], 2)
+    # general ellipse fails except under certain conditions
+    e = Ellipse((0, 0), x, 1)
+    assert e.normal_lines((x + 1, 0)) == [Line(Point(0, 0), Point(1, 0))]
+    raises(NotImplementedError, lambda: e.normal_lines((x + 1, 1)))
+    # Properties
+    major = 3
+    minor = 1
+    e4 = Ellipse(p2, minor, major)
+    assert e4.focus_distance == sqrt(major**2 - minor**2)
+    ecc = e4.focus_distance / major
+    assert e4.eccentricity == ecc
+    assert e4.periapsis == major*(1 - ecc)
+    assert e4.apoapsis == major*(1 + ecc)
+    assert e4.semilatus_rectum == major*(1 - ecc ** 2)
+    # independent of orientation
+    e4 = Ellipse(p2, major, minor)
+    assert e4.focus_distance == sqrt(major**2 - minor**2)
+    ecc = e4.focus_distance / major
+    assert e4.eccentricity == ecc
+    assert e4.periapsis == major*(1 - ecc)
+    assert e4.apoapsis == major*(1 + ecc)
+
+    # Intersection
+    l1 = Line(Point(1, -5), Point(1, 5))
+    l2 = Line(Point(-5, -1), Point(5, -1))
+    l3 = Line(Point(-1, -1), Point(1, 1))
+    l4 = Line(Point(-10, 0), Point(0, 10))
+    pts_c1_l3 = [Point(sqrt(2)/2, sqrt(2)/2), Point(-sqrt(2)/2, -sqrt(2)/2)]
+
+    assert intersection(e2, l4) == []
+    assert intersection(c1, Point(1, 0)) == [Point(1, 0)]
+    assert intersection(c1, l1) == [Point(1, 0)]
+    assert intersection(c1, l2) == [Point(0, -1)]
+    assert intersection(c1, l3) in [pts_c1_l3, [pts_c1_l3[1], pts_c1_l3[0]]]
+    assert intersection(c1, c2) == [Point(0, 1), Point(1, 0)]
+    assert intersection(c1, c3) == [Point(sqrt(2)/2, sqrt(2)/2)]
+    assert e1.intersection(l1) == [Point(1, 0)]
+    assert e2.intersection(l4) == []
+    assert e1.intersection(Circle(Point(0, 2), 1)) == [Point(0, 1)]
+    assert e1.intersection(Circle(Point(5, 0), 1)) == []
+    assert e1.intersection(Ellipse(Point(2, 0), 1, 1)) == [Point(1, 0)]
+    assert e1.intersection(Ellipse(Point(5, 0), 1, 1)) == []
+    assert e1.intersection(Point(2, 0)) == []
+    assert e1.intersection(e1) == e1
+    assert intersection(Ellipse(Point(0, 0), 2, 1), Ellipse(Point(3, 0), 1, 2)) == [Point(2, 0)]
+    assert intersection(Circle(Point(0, 0), 2), Circle(Point(3, 0), 1)) == [Point(2, 0)]
+    assert intersection(Circle(Point(0, 0), 2), Circle(Point(7, 0), 1)) == []
+    assert intersection(Ellipse(Point(0, 0), 5, 17), Ellipse(Point(4, 0), 1, 0.2)
+        ) == [Point(5.0, 0, evaluate=False)]
+    assert intersection(Ellipse(Point(0, 0), 5, 17), Ellipse(Point(4, 0), 0.999, 0.2)) == []
+    assert Circle((0, 0), S.Half).intersection(
+        Triangle((-1, 0), (1, 0), (0, 1))) == [
+        Point(Rational(-1, 2), 0), Point(S.Half, 0)]
+    raises(TypeError, lambda: intersection(e2, Line((0, 0, 0), (0, 0, 1))))
+    raises(TypeError, lambda: intersection(e2, Rational(12)))
+    raises(TypeError, lambda: Ellipse.intersection(e2, 1))
+    # some special case intersections
+    csmall = Circle(p1, 3)
+    cbig = Circle(p1, 5)
+    cout = Circle(Point(5, 5), 1)
+    # one circle inside of another
+    assert csmall.intersection(cbig) == []
+    # separate circles
+    assert csmall.intersection(cout) == []
+    # coincident circles
+    assert csmall.intersection(csmall) == csmall
+
+    v = sqrt(2)
+    t1 = Triangle(Point(0, v), Point(0, -v), Point(v, 0))
+    points = intersection(t1, c1)
+    assert len(points) == 4
+    assert Point(0, 1) in points
+    assert Point(0, -1) in points
+    assert Point(v/2, v/2) in points
+    assert Point(v/2, -v/2) in points
+
+    circ = Circle(Point(0, 0), 5)
+    elip = Ellipse(Point(0, 0), 5, 20)
+    assert intersection(circ, elip) in \
+        [[Point(5, 0), Point(-5, 0)], [Point(-5, 0), Point(5, 0)]]
+    assert elip.tangent_lines(Point(0, 0)) == []
+    elip = Ellipse(Point(0, 0), 3, 2)
+    assert elip.tangent_lines(Point(3, 0)) == \
+        [Line(Point(3, 0), Point(3, -12))]
+
+    e1 = Ellipse(Point(0, 0), 5, 10)
+    e2 = Ellipse(Point(2, 1), 4, 8)
+    a = Rational(53, 17)
+    c = 2*sqrt(3991)/17
+    ans = [Point(a - c/8, a/2 + c), Point(a + c/8, a/2 - c)]
+    assert e1.intersection(e2) == ans
+    e2 = Ellipse(Point(x, y), 4, 8)
+    c = sqrt(3991)
+    ans = [Point(-c/68 + a, c*Rational(2, 17) + a/2), Point(c/68 + a, c*Rational(-2, 17) + a/2)]
+    assert [p.subs({x: 2, y:1}) for p in e1.intersection(e2)] == ans
+
+    # Combinations of above
+    assert e3.is_tangent(e3.tangent_lines(p1 + Point(y1, 0))[0])
+
+    e = Ellipse((1, 2), 3, 2)
+    assert e.tangent_lines(Point(10, 0)) == \
+        [Line(Point(10, 0), Point(1, 0)),
+        Line(Point(10, 0), Point(Rational(14, 5), Rational(18, 5)))]
+
+    # encloses_point
+    e = Ellipse((0, 0), 1, 2)
+    assert e.encloses_point(e.center)
+    assert e.encloses_point(e.center + Point(0, e.vradius - Rational(1, 10)))
+    assert e.encloses_point(e.center + Point(e.hradius - Rational(1, 10), 0))
+    assert e.encloses_point(e.center + Point(e.hradius, 0)) is False
+    assert e.encloses_point(
+        e.center + Point(e.hradius + Rational(1, 10), 0)) is False
+    e = Ellipse((0, 0), 2, 1)
+    assert e.encloses_point(e.center)
+    assert e.encloses_point(e.center + Point(0, e.vradius - Rational(1, 10)))
+    assert e.encloses_point(e.center + Point(e.hradius - Rational(1, 10), 0))
+    assert e.encloses_point(e.center + Point(e.hradius, 0)) is False
+    assert e.encloses_point(
+        e.center + Point(e.hradius + Rational(1, 10), 0)) is False
+    assert c1.encloses_point(Point(1, 0)) is False
+    assert c1.encloses_point(Point(0.3, 0.4)) is True
+
+    assert e.scale(2, 3) == Ellipse((0, 0), 4, 3)
+    assert e.scale(3, 6) == Ellipse((0, 0), 6, 6)
+    assert e.rotate(pi) == e
+    assert e.rotate(pi, (1, 2)) == Ellipse(Point(2, 4), 2, 1)
+    raises(NotImplementedError, lambda: e.rotate(pi/3))
+
+    # Circle rotation tests (Issue #11743)
+    # Link - https://github.com/sympy/sympy/issues/11743
+    cir = Circle(Point(1, 0), 1)
+    assert cir.rotate(pi/2) == Circle(Point(0, 1), 1)
+    assert cir.rotate(pi/3) == Circle(Point(S.Half, sqrt(3)/2), 1)
+    assert cir.rotate(pi/3, Point(1, 0)) == Circle(Point(1, 0), 1)
+    assert cir.rotate(pi/3, Point(0, 1)) == Circle(Point(S.Half + sqrt(3)/2, S.Half + sqrt(3)/2), 1)
+
+
+def test_construction():
+    e1 = Ellipse(hradius=2, vradius=1, eccentricity=None)
+    assert e1.eccentricity == sqrt(3)/2
+
+    e2 = Ellipse(hradius=2, vradius=None, eccentricity=sqrt(3)/2)
+    assert e2.vradius == 1
+
+    e3 = Ellipse(hradius=None, vradius=1, eccentricity=sqrt(3)/2)
+    assert e3.hradius == 2
+
+    # filter(None, iterator) filters out anything falsey, including 0
+    # eccentricity would be filtered out in this case and the constructor would throw an error
+    e4 = Ellipse(Point(0, 0), hradius=1, eccentricity=0)
+    assert e4.vradius == 1
+
+    #tests for eccentricity > 1
+    raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity = S(3)/2))
+    raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity=sec(5)))
+    raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity=S.Pi-S(2)))
+
+    #tests for eccentricity = 1
+    #if vradius is not defined
+    assert Ellipse(None, 1, None, 1).length == 2
+    #if hradius is not defined
+    raises(GeometryError, lambda: Ellipse(None, None, 1, eccentricity = 1))
+
+    #tests for eccentricity < 0
+    raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity = -3))
+    raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity = -0.5))
+
+def test_ellipse_random_point():
+    y1 = Symbol('y1', real=True)
+    e3 = Ellipse(Point(0, 0), y1, y1)
+    rx, ry = Symbol('rx'), Symbol('ry')
+    for ind in range(0, 5):
+        r = e3.random_point()
+        # substitution should give zero*y1**2
+        assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)).equals(0)
+    # test for the case with seed
+    r = e3.random_point(seed=1)
+    assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)).equals(0)
+
+
+def test_repr():
+    assert repr(Circle((0, 1), 2)) == 'Circle(Point2D(0, 1), 2)'
+
+
+def test_transform():
+    c = Circle((1, 1), 2)
+    assert c.scale(-1) == Circle((-1, 1), 2)
+    assert c.scale(y=-1) == Circle((1, -1), 2)
+    assert c.scale(2) == Ellipse((2, 1), 4, 2)
+
+    assert Ellipse((0, 0), 2, 3).scale(2, 3, (4, 5)) == \
+        Ellipse(Point(-4, -10), 4, 9)
+    assert Circle((0, 0), 2).scale(2, 3, (4, 5)) == \
+        Ellipse(Point(-4, -10), 4, 6)
+    assert Ellipse((0, 0), 2, 3).scale(3, 3, (4, 5)) == \
+        Ellipse(Point(-8, -10), 6, 9)
+    assert Circle((0, 0), 2).scale(3, 3, (4, 5)) == \
+        Circle(Point(-8, -10), 6)
+    assert Circle(Point(-8, -10), 6).scale(Rational(1, 3), Rational(1, 3), (4, 5)) == \
+        Circle((0, 0), 2)
+    assert Circle((0, 0), 2).translate(4, 5) == \
+        Circle((4, 5), 2)
+    assert Circle((0, 0), 2).scale(3, 3) == \
+        Circle((0, 0), 6)
+
+
+def test_bounds():
+    e1 = Ellipse(Point(0, 0), 3, 5)
+    e2 = Ellipse(Point(2, -2), 7, 7)
+    c1 = Circle(Point(2, -2), 7)
+    c2 = Circle(Point(-2, 0), Point(0, 2), Point(2, 0))
+    assert e1.bounds == (-3, -5, 3, 5)
+    assert e2.bounds == (-5, -9, 9, 5)
+    assert c1.bounds == (-5, -9, 9, 5)
+    assert c2.bounds == (-2, -2, 2, 2)
+
+
+def test_reflect():
+    b = Symbol('b')
+    m = Symbol('m')
+    l = Line((0, b), slope=m)
+    t1 = Triangle((0, 0), (1, 0), (2, 3))
+    assert t1.area == -t1.reflect(l).area
+    e = Ellipse((1, 0), 1, 2)
+    assert e.area == -e.reflect(Line((1, 0), slope=0)).area
+    assert e.area == -e.reflect(Line((1, 0), slope=oo)).area
+    raises(NotImplementedError, lambda: e.reflect(Line((1, 0), slope=m)))
+    assert Circle((0, 1), 1).reflect(Line((0, 0), (1, 1))) == Circle(Point2D(1, 0), -1)
+
+
+def test_is_tangent():
+    e1 = Ellipse(Point(0, 0), 3, 5)
+    c1 = Circle(Point(2, -2), 7)
+    assert e1.is_tangent(Point(0, 0)) is False
+    assert e1.is_tangent(Point(3, 0)) is False
+    assert e1.is_tangent(e1) is True
+    assert e1.is_tangent(Ellipse((0, 0), 1, 2)) is False
+    assert e1.is_tangent(Ellipse((0, 0), 3, 2)) is True
+    assert c1.is_tangent(Ellipse((2, -2), 7, 1)) is True
+    assert c1.is_tangent(Circle((11, -2), 2)) is True
+    assert c1.is_tangent(Circle((7, -2), 2)) is True
+    assert c1.is_tangent(Ray((-5, -2), (-15, -20))) is False
+    assert c1.is_tangent(Ray((-3, -2), (-15, -20))) is False
+    assert c1.is_tangent(Ray((-3, -22), (15, 20))) is False
+    assert c1.is_tangent(Ray((9, 20), (9, -20))) is True
+    assert c1.is_tangent(Ray((2, 5), (9, 5))) is True
+    assert c1.is_tangent(Segment((2, 5), (9, 5))) is True
+    assert e1.is_tangent(Segment((2, 2), (-7, 7))) is False
+    assert e1.is_tangent(Segment((0, 0), (1, 2))) is False
+    assert c1.is_tangent(Segment((0, 0), (-5, -2))) is False
+    assert e1.is_tangent(Segment((3, 0), (12, 12))) is False
+    assert e1.is_tangent(Segment((12, 12), (3, 0))) is False
+    assert e1.is_tangent(Segment((-3, 0), (3, 0))) is False
+    assert e1.is_tangent(Segment((-3, 5), (3, 5))) is True
+    assert e1.is_tangent(Line((10, 0), (10, 10))) is False
+    assert e1.is_tangent(Line((0, 0), (1, 1))) is False
+    assert e1.is_tangent(Line((-3, 0), (-2.99, -0.001))) is False
+    assert e1.is_tangent(Line((-3, 0), (-3, 1))) is True
+    assert e1.is_tangent(Polygon((0, 0), (5, 5), (5, -5))) is False
+    assert e1.is_tangent(Polygon((-100, -50), (-40, -334), (-70, -52))) is False
+    assert e1.is_tangent(Polygon((-3, 0), (3, 0), (0, 1))) is False
+    assert e1.is_tangent(Polygon((-3, 0), (3, 0), (0, 5))) is False
+    assert e1.is_tangent(Polygon((-3, 0), (0, -5), (3, 0), (0, 5))) is False
+    assert e1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is True
+    assert c1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is False
+    assert e1.is_tangent(Polygon((0, 0), (3, 0), (7, 7), (0, 5))) is False
+    assert e1.is_tangent(Polygon((3, 12), (3, -12), (6, 5))) is False
+    assert e1.is_tangent(Polygon((3, 12), (3, -12), (0, -5), (0, 5))) is False
+    assert e1.is_tangent(Polygon((3, 0), (5, 7), (6, -5))) is False
+    assert c1.is_tangent(Segment((0, 0), (-5, -2))) is False
+    assert e1.is_tangent(Segment((-3, 0), (3, 0))) is False
+    assert e1.is_tangent(Segment((-3, 5), (3, 5))) is True
+    assert e1.is_tangent(Polygon((0, 0), (5, 5), (5, -5))) is False
+    assert e1.is_tangent(Polygon((-100, -50), (-40, -334), (-70, -52))) is False
+    assert e1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is True
+    assert c1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is False
+    assert e1.is_tangent(Polygon((3, 12), (3, -12), (0, -5), (0, 5))) is False
+    assert e1.is_tangent(Polygon((3, 0), (5, 7), (6, -5))) is False
+    raises(TypeError, lambda: e1.is_tangent(Point(0, 0, 0)))
+    raises(TypeError, lambda: e1.is_tangent(Rational(5)))
+
+
+def test_parameter_value():
+    t = Symbol('t')
+    e = Ellipse(Point(0, 0), 3, 5)
+    assert e.parameter_value((3, 0), t) == {t: 0}
+    raises(ValueError, lambda: e.parameter_value((4, 0), t))
+
+
+@slow
+def test_second_moment_of_area():
+    x, y = symbols('x, y')
+    e = Ellipse(Point(0, 0), 5, 4)
+    I_yy = 2*4*integrate(sqrt(25 - x**2)*x**2, (x, -5, 5))/5
+    I_xx = 2*5*integrate(sqrt(16 - y**2)*y**2, (y, -4, 4))/4
+    Y = 3*sqrt(1 - x**2/5**2)
+    I_xy = integrate(integrate(y, (y, -Y, Y))*x, (x, -5, 5))
+    assert I_yy == e.second_moment_of_area()[1]
+    assert I_xx == e.second_moment_of_area()[0]
+    assert I_xy == e.second_moment_of_area()[2]
+    #checking for other point
+    t1 = e.second_moment_of_area(Point(6,5))
+    t2 = (580*pi, 845*pi, 600*pi)
+    assert t1==t2
+
+
+def test_section_modulus_and_polar_second_moment_of_area():
+    d = Symbol('d', positive=True)
+    c = Circle((3, 7), 8)
+    assert c.polar_second_moment_of_area() == 2048*pi
+    assert c.section_modulus() == (128*pi, 128*pi)
+    c = Circle((2, 9), d/2)
+    assert c.polar_second_moment_of_area() == pi*d**3*Abs(d)/64 + pi*d*Abs(d)**3/64
+    assert c.section_modulus() == (pi*d**3/S(32), pi*d**3/S(32))
+
+    a, b = symbols('a, b', positive=True)
+    e = Ellipse((4, 6), a, b)
+    assert e.section_modulus() == (pi*a*b**2/S(4), pi*a**2*b/S(4))
+    assert e.polar_second_moment_of_area() == pi*a**3*b/S(4) + pi*a*b**3/S(4)
+    e = e.rotate(pi/2) # no change in polar and section modulus
+    assert e.section_modulus() == (pi*a**2*b/S(4), pi*a*b**2/S(4))
+    assert e.polar_second_moment_of_area() == pi*a**3*b/S(4) + pi*a*b**3/S(4)
+
+    e = Ellipse((a, b), 2, 6)
+    assert e.section_modulus() == (18*pi, 6*pi)
+    assert e.polar_second_moment_of_area() == 120*pi
+
+    e = Ellipse(Point(0, 0), 2, 2)
+    assert e.section_modulus() == (2*pi, 2*pi)
+    assert e.section_modulus(Point(2, 2)) == (2*pi, 2*pi)
+    assert e.section_modulus((2, 2)) == (2*pi, 2*pi)
+
+
+def test_circumference():
+    M = Symbol('M')
+    m = Symbol('m')
+    assert Ellipse(Point(0, 0), M, m).circumference == 4 * M * elliptic_e((M ** 2 - m ** 2) / M**2)
+
+    assert Ellipse(Point(0, 0), 5, 4).circumference == 20 * elliptic_e(S(9) / 25)
+
+    # circle
+    assert Ellipse(None, 1, None, 0).circumference == 2*pi
+
+    # test numerically
+    assert abs(Ellipse(None, hradius=5, vradius=3).circumference.evalf(16) - 25.52699886339813) < 1e-10
+
+
+def test_issue_15259():
+    assert Circle((1, 2), 0) == Point(1, 2)
+
+
+def test_issue_15797_equals():
+    Ri = 0.024127189424130748
+    Ci = (0.0864931002830291, 0.0819863295239654)
+    A = Point(0, 0.0578591400998346)
+    c = Circle(Ci, Ri)  # evaluated
+    assert c.is_tangent(c.tangent_lines(A)[0]) == True
+    assert c.center.x.is_Rational
+    assert c.center.y.is_Rational
+    assert c.radius.is_Rational
+    u = Circle(Ci, Ri, evaluate=False)  # unevaluated
+    assert u.center.x.is_Float
+    assert u.center.y.is_Float
+    assert u.radius.is_Float
+
+
+def test_auxiliary_circle():
+    x, y, a, b = symbols('x y a b')
+    e = Ellipse((x, y), a, b)
+    # the general result
+    assert e.auxiliary_circle() == Circle((x, y), Max(a, b))
+    # a special case where Ellipse is a Circle
+    assert Circle((3, 4), 8).auxiliary_circle() == Circle((3, 4), 8)
+
+
+def test_director_circle():
+    x, y, a, b = symbols('x y a b')
+    e = Ellipse((x, y), a, b)
+    # the general result
+    assert e.director_circle() == Circle((x, y), sqrt(a**2 + b**2))
+    # a special case where Ellipse is a Circle
+    assert Circle((3, 4), 8).director_circle() == Circle((3, 4), 8*sqrt(2))
+
+
+def test_evolute():
+    #ellipse centered at h,k
+    x, y, h, k = symbols('x y h k',real = True)
+    a, b = symbols('a b')
+    e = Ellipse(Point(h, k), a, b)
+    t1 = (e.hradius*(x - e.center.x))**Rational(2, 3)
+    t2 = (e.vradius*(y - e.center.y))**Rational(2, 3)
+    E = t1 + t2 - (e.hradius**2 - e.vradius**2)**Rational(2, 3)
+    assert e.evolute() == E
+    #Numerical Example
+    e = Ellipse(Point(1, 1), 6, 3)
+    t1 = (6*(x - 1))**Rational(2, 3)
+    t2 = (3*(y - 1))**Rational(2, 3)
+    E = t1 + t2 - (27)**Rational(2, 3)
+    assert e.evolute() == E
+
+
+def test_svg():
+    e1 = Ellipse(Point(1, 0), 3, 2)
+    assert e1._svg(2, "#FFAAFF") == ''
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_entity.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_entity.py
new file mode 100644
index 0000000000000000000000000000000000000000..0d440fd5dbd193c7c490b45a706fab2703e247ec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_entity.py
@@ -0,0 +1,120 @@
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.geometry import (Circle, Ellipse, Point, Line, Parabola,
+    Polygon, Ray, RegularPolygon, Segment, Triangle, Plane, Curve)
+from sympy.geometry.entity import scale, GeometryEntity
+from sympy.testing.pytest import raises
+
+
+def test_entity():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+
+    assert GeometryEntity(x, y) in GeometryEntity(x, y)
+    raises(NotImplementedError, lambda: Point(0, 0) in GeometryEntity(x, y))
+
+    assert GeometryEntity(x, y) == GeometryEntity(x, y)
+    assert GeometryEntity(x, y).equals(GeometryEntity(x, y))
+
+    c = Circle((0, 0), 5)
+    assert GeometryEntity.encloses(c, Point(0, 0))
+    assert GeometryEntity.encloses(c, Segment((0, 0), (1, 1)))
+    assert GeometryEntity.encloses(c, Line((0, 0), (1, 1))) is False
+    assert GeometryEntity.encloses(c, Circle((0, 0), 4))
+    assert GeometryEntity.encloses(c, Polygon(Point(0, 0), Point(1, 0), Point(0, 1)))
+    assert GeometryEntity.encloses(c, RegularPolygon(Point(8, 8), 1, 3)) is False
+
+
+def test_svg():
+    a = Symbol('a')
+    b = Symbol('b')
+    d = Symbol('d')
+
+    entity = Circle(Point(a, b), d)
+    assert entity._repr_svg_() is None
+
+    entity = Circle(Point(0, 0), S.Infinity)
+    assert entity._repr_svg_() is None
+
+
+def test_subs():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    p = Point(x, 2)
+    q = Point(1, 1)
+    r = Point(3, 4)
+    for o in [p,
+              Segment(p, q),
+              Ray(p, q),
+              Line(p, q),
+              Triangle(p, q, r),
+              RegularPolygon(p, 3, 6),
+              Polygon(p, q, r, Point(5, 4)),
+              Circle(p, 3),
+              Ellipse(p, 3, 4)]:
+        assert 'y' in str(o.subs(x, y))
+    assert p.subs({x: 1}) == Point(1, 2)
+    assert Point(1, 2).subs(Point(1, 2), Point(3, 4)) == Point(3, 4)
+    assert Point(1, 2).subs((1, 2), Point(3, 4)) == Point(3, 4)
+    assert Point(1, 2).subs(Point(1, 2), Point(3, 4)) == Point(3, 4)
+    assert Point(1, 2).subs({(1, 2)}) == Point(2, 2)
+    raises(ValueError, lambda: Point(1, 2).subs(1))
+    raises(TypeError, lambda: Point(1, 1).subs((Point(1, 1), Point(1,
+           2)), 1, 2))
+
+
+def test_transform():
+    assert scale(1, 2, (3, 4)).tolist() == \
+        [[1, 0, 0], [0, 2, 0], [0, -4, 1]]
+
+
+def test_reflect_entity_overrides():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    b = Symbol('b')
+    m = Symbol('m')
+    l = Line((0, b), slope=m)
+    p = Point(x, y)
+    r = p.reflect(l)
+    c = Circle((x, y), 3)
+    cr = c.reflect(l)
+    assert cr == Circle(r, -3)
+    assert c.area == -cr.area
+
+    pent = RegularPolygon((1, 2), 1, 5)
+    slope = S.ComplexInfinity
+    while slope is S.ComplexInfinity:
+        slope = Rational(*(x._random()/2).as_real_imag())
+    l = Line(pent.vertices[1], slope=slope)
+    rpent = pent.reflect(l)
+    assert rpent.center == pent.center.reflect(l)
+    rvert = [i.reflect(l) for i in pent.vertices]
+    for v in rpent.vertices:
+        for i in range(len(rvert)):
+            ri = rvert[i]
+            if ri.equals(v):
+                rvert.remove(ri)
+                break
+    assert not rvert
+    assert pent.area.equals(-rpent.area)
+
+
+def test_geometry_EvalfMixin():
+    x = pi
+    t = Symbol('t')
+    for g in [
+            Point(x, x),
+            Plane(Point(0, x, 0), (0, 0, x)),
+            Curve((x*t, x), (t, 0, x)),
+            Ellipse((x, x), x, -x),
+            Circle((x, x), x),
+            Line((0, x), (x, 0)),
+            Segment((0, x), (x, 0)),
+            Ray((0, x), (x, 0)),
+            Parabola((0, x), Line((-x, 0), (x, 0))),
+            Polygon((0, 0), (0, x), (x, 0), (x, x)),
+            RegularPolygon((0, x), x, 4, x),
+            Triangle((0, 0), (x, 0), (x, x)),
+            ]:
+        assert str(g).replace('pi', '3.1') == str(g.n(2))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_geometrysets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_geometrysets.py
new file mode 100644
index 0000000000000000000000000000000000000000..c52898b3c9ba4e9db80c244db3aebf88db2cc8b4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_geometrysets.py
@@ -0,0 +1,38 @@
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.geometry import Circle, Line, Point, Polygon, Segment
+from sympy.sets import FiniteSet, Union, Intersection, EmptySet
+
+
+def test_booleans():
+    """ test basic unions and intersections """
+    half = S.Half
+
+    p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
+    p5, p6, p7 = map(Point, [(3, 2), (1, -1), (0, 2)])
+    l1 = Line(Point(0,0), Point(1,1))
+    l2 = Line(Point(half, half), Point(5,5))
+    l3 = Line(p2, p3)
+    l4 = Line(p3, p4)
+    poly1 = Polygon(p1, p2, p3, p4)
+    poly2 = Polygon(p5, p6, p7)
+    poly3 = Polygon(p1, p2, p5)
+    assert Union(l1, l2).equals(l1)
+    assert Intersection(l1, l2).equals(l1)
+    assert Intersection(l1, l4) == FiniteSet(Point(1,1))
+    assert Intersection(Union(l1, l4), l3) == FiniteSet(Point(Rational(-1, 3), Rational(-1, 3)), Point(5, 1))
+    assert Intersection(l1, FiniteSet(Point(7,-7))) == EmptySet
+    assert Intersection(Circle(Point(0,0), 3), Line(p1,p2)) == FiniteSet(Point(-3,0), Point(3,0))
+    assert Intersection(l1, FiniteSet(p1)) == FiniteSet(p1)
+    assert Union(l1, FiniteSet(p1)) == l1
+
+    fs = FiniteSet(Point(Rational(1, 3), 1), Point(Rational(2, 3), 0), Point(Rational(9, 5), Rational(1, 5)), Point(Rational(7, 3), 1))
+    # test the intersection of polygons
+    assert Intersection(poly1, poly2) == fs
+    # make sure if we union polygons with subsets, the subsets go away
+    assert Union(poly1, poly2, fs) == Union(poly1, poly2)
+    # make sure that if we union with a FiniteSet that isn't a subset,
+    # that the points in the intersection stop being listed
+    assert Union(poly1, FiniteSet(Point(0,0), Point(3,5))) == Union(poly1, FiniteSet(Point(3,5)))
+    # intersect two polygons that share an edge
+    assert Intersection(poly1, poly3) == Union(FiniteSet(Point(Rational(3, 2), 1), Point(2, 1)), Segment(Point(0, 0), Point(1, 0)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_line.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_line.py
new file mode 100644
index 0000000000000000000000000000000000000000..5158ec05ab414020fbbe2681a2658454dd15b6eb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_line.py
@@ -0,0 +1,861 @@
+from sympy.core.numbers import (Float, Rational, oo, pi)
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, cos, sin)
+from sympy.sets import EmptySet
+from sympy.simplify.simplify import simplify
+from sympy.functions.elementary.trigonometric import tan
+from sympy.geometry import (Circle, GeometryError, Line, Point, Ray,
+    Segment, Triangle, intersection, Point3D, Line3D, Ray3D, Segment3D,
+    Point2D, Line2D, Plane)
+from sympy.geometry.line import Undecidable
+from sympy.geometry.polygon import _asa as asa
+from sympy.utilities.iterables import cartes
+from sympy.testing.pytest import raises, warns
+
+
+x = Symbol('x', real=True)
+y = Symbol('y', real=True)
+z = Symbol('z', real=True)
+k = Symbol('k', real=True)
+x1 = Symbol('x1', real=True)
+y1 = Symbol('y1', real=True)
+t = Symbol('t', real=True)
+a, b = symbols('a,b', real=True)
+m = symbols('m', real=True)
+
+
+def test_object_from_equation():
+    from sympy.abc import x, y, a, b
+    assert Line(3*x + y + 18) == Line2D(Point2D(0, -18), Point2D(1, -21))
+    assert Line(3*x + 5 * y + 1) == Line2D(
+        Point2D(0, Rational(-1, 5)), Point2D(1, Rational(-4, 5)))
+    assert Line(3*a + b + 18, x="a", y="b") == Line2D(
+        Point2D(0, -18), Point2D(1, -21))
+    assert Line(3*x + y) == Line2D(Point2D(0, 0), Point2D(1, -3))
+    assert Line(x + y) == Line2D(Point2D(0, 0), Point2D(1, -1))
+    assert Line(Eq(3*a + b, -18), x="a", y=b) == Line2D(
+        Point2D(0, -18), Point2D(1, -21))
+    # issue 22361
+    assert Line(x - 1) == Line2D(Point2D(1, 0), Point2D(1, 1))
+    assert Line(2*x - 2, y=x) == Line2D(Point2D(0, 1), Point2D(1, 1))
+    assert Line(y) == Line2D(Point2D(0, 0), Point2D(1, 0))
+    assert Line(2*y, x=y) == Line2D(Point2D(0, 0), Point2D(0, 1))
+    assert Line(y, x=y) == Line2D(Point2D(0, 0), Point2D(0, 1))
+    raises(ValueError, lambda: Line(x / y))
+    raises(ValueError, lambda: Line(a / b, x='a', y='b'))
+    raises(ValueError, lambda: Line(y / x))
+    raises(ValueError, lambda: Line(b / a, x='a', y='b'))
+    raises(ValueError, lambda: Line((x + 1)**2 + y))
+
+
+def feq(a, b):
+    """Test if two floating point values are 'equal'."""
+    t_float = Float("1.0E-10")
+    return -t_float < a - b < t_float
+
+
+def test_angle_between():
+    a = Point(1, 2, 3, 4)
+    b = a.orthogonal_direction
+    o = a.origin
+    assert feq(Line.angle_between(Line(Point(0, 0), Point(1, 1)),
+                                  Line(Point(0, 0), Point(5, 0))).evalf(), pi.evalf() / 4)
+    assert Line(a, o).angle_between(Line(b, o)) == pi / 2
+    z = Point3D(0, 0, 0)
+    assert Line3D.angle_between(Line3D(z, Point3D(1, 1, 1)),
+                                Line3D(z, Point3D(5, 0, 0))) == acos(sqrt(3) / 3)
+    # direction of points is used to determine angle
+    assert Line3D.angle_between(Line3D(z, Point3D(1, 1, 1)),
+                                Line3D(Point3D(5, 0, 0), z)) == acos(-sqrt(3) / 3)
+
+
+def test_closing_angle():
+    a = Ray((0, 0), angle=0)
+    b = Ray((1, 2), angle=pi/2)
+    assert a.closing_angle(b) == -pi/2
+    assert b.closing_angle(a) == pi/2
+    assert a.closing_angle(a) == 0
+
+
+def test_smallest_angle():
+    a = Line(Point(1, 1), Point(1, 2))
+    b = Line(Point(1, 1),Point(2, 3))
+    assert a.smallest_angle_between(b) == acos(2*sqrt(5)/5)
+
+
+def test_svg():
+    a = Line(Point(1, 1),Point(1, 2))
+    assert a._svg() == ''
+    a = Segment(Point(1, 0),Point(1, 1))
+    assert a._svg() == ''
+    a = Ray(Point(2, 3), Point(3, 5))
+    assert a._svg() == ''
+
+
+def test_arbitrary_point():
+    l1 = Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1))
+    l2 = Line(Point(x1, x1), Point(y1, y1))
+    assert l2.arbitrary_point() in l2
+    assert Ray((1, 1), angle=pi / 4).arbitrary_point() == \
+           Point(t + 1, t + 1)
+    assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2 * t)
+    assert l1.perpendicular_segment(l1.arbitrary_point()) == l1.arbitrary_point()
+    assert Ray3D((1, 1, 1), direction_ratio=[1, 2, 3]).arbitrary_point() == \
+           Point3D(t + 1, 2 * t + 1, 3 * t + 1)
+    assert Segment3D(Point3D(0, 0, 0), Point3D(1, 1, 1)).midpoint == \
+           Point3D(S.Half, S.Half, S.Half)
+    assert Segment3D(Point3D(x1, x1, x1), Point3D(y1, y1, y1)).length == sqrt(3) * sqrt((x1 - y1) ** 2)
+    assert Segment3D((1, 1, 1), (2, 3, 4)).arbitrary_point() == \
+           Point3D(t + 1, 2 * t + 1, 3 * t + 1)
+    raises(ValueError, (lambda: Line((x, 1), (2, 3)).arbitrary_point(x)))
+
+
+def test_are_concurrent_2d():
+    l1 = Line(Point(0, 0), Point(1, 1))
+    l2 = Line(Point(x1, x1), Point(x1, 1 + x1))
+    assert Line.are_concurrent(l1) is False
+    assert Line.are_concurrent(l1, l2)
+    assert Line.are_concurrent(l1, l1, l1, l2)
+    assert Line.are_concurrent(l1, l2, Line(Point(5, x1), Point(Rational(-3, 5), x1)))
+    assert Line.are_concurrent(l1, Line(Point(0, 0), Point(-x1, x1)), l2) is False
+
+
+def test_are_concurrent_3d():
+    p1 = Point3D(0, 0, 0)
+    l1 = Line(p1, Point3D(1, 1, 1))
+    parallel_1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))
+    parallel_2 = Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0))
+    assert Line3D.are_concurrent(l1) is False
+    assert Line3D.are_concurrent(l1, Line(Point3D(x1, x1, x1), Point3D(y1, y1, y1))) is False
+    assert Line3D.are_concurrent(l1, Line3D(p1, Point3D(x1, x1, x1)),
+                                 Line(Point3D(x1, x1, x1), Point3D(x1, 1 + x1, 1))) is True
+    assert Line3D.are_concurrent(parallel_1, parallel_2) is False
+
+
+def test_arguments():
+    """Functions accepting `Point` objects in `geometry`
+    should also accept tuples, lists, and generators and
+    automatically convert them to points."""
+    from sympy.utilities.iterables import subsets
+
+    singles2d = ((1, 2), [1, 3], Point(1, 5))
+    doubles2d = subsets(singles2d, 2)
+    l2d = Line(Point2D(1, 2), Point2D(2, 3))
+    singles3d = ((1, 2, 3), [1, 2, 4], Point(1, 2, 6))
+    doubles3d = subsets(singles3d, 2)
+    l3d = Line(Point3D(1, 2, 3), Point3D(1, 1, 2))
+    singles4d = ((1, 2, 3, 4), [1, 2, 3, 5], Point(1, 2, 3, 7))
+    doubles4d = subsets(singles4d, 2)
+    l4d = Line(Point(1, 2, 3, 4), Point(2, 2, 2, 2))
+    # test 2D
+    test_single = ['contains', 'distance', 'equals', 'parallel_line', 'perpendicular_line', 'perpendicular_segment',
+                   'projection', 'intersection']
+    for p in doubles2d:
+        Line2D(*p)
+    for func in test_single:
+        for p in singles2d:
+            getattr(l2d, func)(p)
+    # test 3D
+    for p in doubles3d:
+        Line3D(*p)
+    for func in test_single:
+        for p in singles3d:
+            getattr(l3d, func)(p)
+    # test 4D
+    for p in doubles4d:
+        Line(*p)
+    for func in test_single:
+        for p in singles4d:
+            getattr(l4d, func)(p)
+
+
+def test_basic_properties_2d():
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+    p10 = Point(2000, 2000)
+    p_r3 = Ray(p1, p2).random_point()
+    p_r4 = Ray(p2, p1).random_point()
+
+    l1 = Line(p1, p2)
+    l3 = Line(Point(x1, x1), Point(x1, 1 + x1))
+    l4 = Line(p1, Point(1, 0))
+
+    r1 = Ray(p1, Point(0, 1))
+    r2 = Ray(Point(0, 1), p1)
+
+    s1 = Segment(p1, p10)
+    p_s1 = s1.random_point()
+
+    assert Line((1, 1), slope=1) == Line((1, 1), (2, 2))
+    assert Line((1, 1), slope=oo) == Line((1, 1), (1, 2))
+    assert Line((1, 1), slope=oo).bounds == (1, 1, 1, 2)
+    assert Line((1, 1), slope=-oo) == Line((1, 1), (1, 2))
+    assert Line(p1, p2).scale(2, 1) == Line(p1, Point(2, 1))
+    assert Line(p1, p2) == Line(p1, p2)
+    assert Line(p1, p2) != Line(p2, p1)
+    assert l1 != Line(Point(x1, x1), Point(y1, y1))
+    assert l1 != l3
+    assert Line(p1, p10) != Line(p10, p1)
+    assert Line(p1, p10) != p1
+    assert p1 in l1  # is p1 on the line l1?
+    assert p1 not in l3
+    assert s1 in Line(p1, p10)
+    assert Ray(Point(0, 0), Point(0, 1)) in Ray(Point(0, 0), Point(0, 2))
+    assert Ray(Point(0, 0), Point(0, 2)) in Ray(Point(0, 0), Point(0, 1))
+    assert Ray(Point(0, 0), Point(0, 2)).xdirection == S.Zero
+    assert Ray(Point(0, 0), Point(1, 2)).xdirection == S.Infinity
+    assert Ray(Point(0, 0), Point(-1, 2)).xdirection == S.NegativeInfinity
+    assert Ray(Point(0, 0), Point(2, 0)).ydirection == S.Zero
+    assert Ray(Point(0, 0), Point(2, 2)).ydirection == S.Infinity
+    assert Ray(Point(0, 0), Point(2, -2)).ydirection == S.NegativeInfinity
+    assert (r1 in s1) is False
+    assert Segment(p1, p2) in s1
+    assert Ray(Point(x1, x1), Point(x1, 1 + x1)) != Ray(p1, Point(-1, 5))
+    assert Segment(p1, p2).midpoint == Point(S.Half, S.Half)
+    assert Segment(p1, Point(-x1, x1)).length == sqrt(2 * (x1 ** 2))
+
+    assert l1.slope == 1
+    assert l3.slope is oo
+    assert l4.slope == 0
+    assert Line(p1, Point(0, 1)).slope is oo
+    assert Line(r1.source, r1.random_point()).slope == r1.slope
+    assert Line(r2.source, r2.random_point()).slope == r2.slope
+    assert Segment(Point(0, -1), Segment(p1, Point(0, 1)).random_point()).slope == Segment(p1, Point(0, 1)).slope
+
+    assert l4.coefficients == (0, 1, 0)
+    assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0)
+    assert Line(p1, Point(0, 1)).coefficients == (1, 0, 0)
+    # issue 7963
+    r = Ray((0, 0), angle=x)
+    assert r.subs(x, 3 * pi / 4) == Ray((0, 0), (-1, 1))
+    assert r.subs(x, 5 * pi / 4) == Ray((0, 0), (-1, -1))
+    assert r.subs(x, -pi / 4) == Ray((0, 0), (1, -1))
+    assert r.subs(x, pi / 2) == Ray((0, 0), (0, 1))
+    assert r.subs(x, -pi / 2) == Ray((0, 0), (0, -1))
+
+    for ind in range(0, 5):
+        assert l3.random_point() in l3
+
+    assert p_r3.x >= p1.x and p_r3.y >= p1.y
+    assert p_r4.x <= p2.x and p_r4.y <= p2.y
+    assert p1.x <= p_s1.x <= p10.x and p1.y <= p_s1.y <= p10.y
+    assert hash(s1) != hash(Segment(p10, p1))
+
+    assert s1.plot_interval() == [t, 0, 1]
+    assert Line(p1, p10).plot_interval() == [t, -5, 5]
+    assert Ray((0, 0), angle=pi / 4).plot_interval() == [t, 0, 10]
+
+
+def test_basic_properties_3d():
+    p1 = Point3D(0, 0, 0)
+    p2 = Point3D(1, 1, 1)
+    p3 = Point3D(x1, x1, x1)
+    p5 = Point3D(x1, 1 + x1, 1)
+
+    l1 = Line3D(p1, p2)
+    l3 = Line3D(p3, p5)
+
+    r1 = Ray3D(p1, Point3D(-1, 5, 0))
+    r3 = Ray3D(p1, p2)
+
+    s1 = Segment3D(p1, p2)
+
+    assert Line3D((1, 1, 1), direction_ratio=[2, 3, 4]) == Line3D(Point3D(1, 1, 1), Point3D(3, 4, 5))
+    assert Line3D((1, 1, 1), direction_ratio=[1, 5, 7]) == Line3D(Point3D(1, 1, 1), Point3D(2, 6, 8))
+    assert Line3D((1, 1, 1), direction_ratio=[1, 2, 3]) == Line3D(Point3D(1, 1, 1), Point3D(2, 3, 4))
+    assert Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).direction_cosine == [1, 0, 0]
+    assert Line3D(Line3D(p1, Point3D(0, 1, 0))) == Line3D(p1, Point3D(0, 1, 0))
+    assert Ray3D(Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))) == Ray3D(p1, Point3D(1, 0, 0))
+    assert Line3D(p1, p2) != Line3D(p2, p1)
+    assert l1 != l3
+    assert l1 != Line3D(p3, Point3D(y1, y1, y1))
+    assert r3 != r1
+    assert Ray3D(Point3D(0, 0, 0), Point3D(1, 1, 1)) in Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2))
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)) in Ray3D(Point3D(0, 0, 0), Point3D(1, 1, 1))
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)).xdirection == S.Infinity
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)).ydirection == S.Infinity
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)).zdirection == S.Infinity
+    assert Ray3D(Point3D(0, 0, 0), Point3D(-2, 2, 2)).xdirection == S.NegativeInfinity
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, -2, 2)).ydirection == S.NegativeInfinity
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, -2)).zdirection == S.NegativeInfinity
+    assert Ray3D(Point3D(0, 0, 0), Point3D(0, 2, 2)).xdirection == S.Zero
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 0, 2)).ydirection == S.Zero
+    assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 0)).zdirection == S.Zero
+    assert p1 in l1
+    assert p1 not in l3
+
+    assert l1.direction_ratio == [1, 1, 1]
+
+    assert s1.midpoint == Point3D(S.Half, S.Half, S.Half)
+    # Test zdirection
+    assert Ray3D(p1, Point3D(0, 0, -1)).zdirection is S.NegativeInfinity
+
+
+def test_contains():
+    p1 = Point(0, 0)
+
+    r = Ray(p1, Point(4, 4))
+    r1 = Ray3D(p1, Point3D(0, 0, -1))
+    r2 = Ray3D(p1, Point3D(0, 1, 0))
+    r3 = Ray3D(p1, Point3D(0, 0, 1))
+
+    l = Line(Point(0, 1), Point(3, 4))
+    # Segment contains
+    assert Point(0, (a + b) / 2) in Segment((0, a), (0, b))
+    assert Point((a + b) / 2, 0) in Segment((a, 0), (b, 0))
+    assert Point3D(0, 1, 0) in Segment3D((0, 1, 0), (0, 1, 0))
+    assert Point3D(1, 0, 0) in Segment3D((1, 0, 0), (1, 0, 0))
+    assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains([]) is True
+    assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains(
+        Segment3D(Point3D(2, 2, 2), Point3D(3, 2, 2))) is False
+    # Line contains
+    assert l.contains(Point(0, 1)) is True
+    assert l.contains((0, 1)) is True
+    assert l.contains((0, 0)) is False
+    # Ray contains
+    assert r.contains(p1) is True
+    assert r.contains((1, 1)) is True
+    assert r.contains((1, 3)) is False
+    assert r.contains(Segment((1, 1), (2, 2))) is True
+    assert r.contains(Segment((1, 2), (2, 5))) is False
+    assert r.contains(Ray((2, 2), (3, 3))) is True
+    assert r.contains(Ray((2, 2), (3, 5))) is False
+    assert r1.contains(Segment3D(p1, Point3D(0, 0, -10))) is True
+    assert r1.contains(Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))) is False
+    assert r2.contains(Point3D(0, 0, 0)) is True
+    assert r3.contains(Point3D(0, 0, 0)) is True
+    assert Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0)).contains([]) is False
+    assert Line3D((0, 0, 0), (x, y, z)).contains((2 * x, 2 * y, 2 * z))
+    with warns(UserWarning, test_stacklevel=False):
+        assert Line3D(p1, Point3D(0, 1, 0)).contains(Point(1.0, 1.0)) is False
+
+    with warns(UserWarning, test_stacklevel=False):
+        assert r3.contains(Point(1.0, 1.0)) is False
+
+
+def test_contains_nonreal_symbols():
+    u, v, w, z = symbols('u, v, w, z')
+    l = Segment(Point(u, w), Point(v, z))
+    p = Point(u*Rational(2, 3) + v/3, w*Rational(2, 3) + z/3)
+    assert l.contains(p)
+
+
+def test_distance_2d():
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+    half = S.Half
+
+    s1 = Segment(Point(0, 0), Point(1, 1))
+    s2 = Segment(Point(half, half), Point(1, 0))
+
+    r = Ray(p1, p2)
+
+    assert s1.distance(Point(0, 0)) == 0
+    assert s1.distance((0, 0)) == 0
+    assert s2.distance(Point(0, 0)) == 2 ** half / 2
+    assert s2.distance(Point(Rational(3) / 2, Rational(3) / 2)) == 2 ** half
+    assert Line(p1, p2).distance(Point(-1, 1)) == sqrt(2)
+    assert Line(p1, p2).distance(Point(1, -1)) == sqrt(2)
+    assert Line(p1, p2).distance(Point(2, 2)) == 0
+    assert Line(p1, p2).distance((-1, 1)) == sqrt(2)
+    assert Line((0, 0), (0, 1)).distance(p1) == 0
+    assert Line((0, 0), (0, 1)).distance(p2) == 1
+    assert Line((0, 0), (1, 0)).distance(p1) == 0
+    assert Line((0, 0), (1, 0)).distance(p2) == 1
+    assert r.distance(Point(-1, -1)) == sqrt(2)
+    assert r.distance(Point(1, 1)) == 0
+    assert r.distance(Point(-1, 1)) == sqrt(2)
+    assert Ray((1, 1), (2, 2)).distance(Point(1.5, 3)) == 3 * sqrt(2) / 4
+    assert r.distance((1, 1)) == 0
+
+
+def test_dimension_normalization():
+    with warns(UserWarning, test_stacklevel=False):
+        assert Ray((1, 1), (2, 1, 2)) == Ray((1, 1, 0), (2, 1, 2))
+
+
+def test_distance_3d():
+    p1, p2 = Point3D(0, 0, 0), Point3D(1, 1, 1)
+    p3 = Point3D(Rational(3) / 2, Rational(3) / 2, Rational(3) / 2)
+
+    s1 = Segment3D(Point3D(0, 0, 0), Point3D(1, 1, 1))
+    s2 = Segment3D(Point3D(S.Half, S.Half, S.Half), Point3D(1, 0, 1))
+
+    r = Ray3D(p1, p2)
+
+    assert s1.distance(p1) == 0
+    assert s2.distance(p1) == sqrt(3) / 2
+    assert s2.distance(p3) == 2 * sqrt(6) / 3
+    assert s1.distance((0, 0, 0)) == 0
+    assert s2.distance((0, 0, 0)) == sqrt(3) / 2
+    assert s1.distance(p1) == 0
+    assert s2.distance(p1) == sqrt(3) / 2
+    assert s2.distance(p3) == 2 * sqrt(6) / 3
+    assert s1.distance((0, 0, 0)) == 0
+    assert s2.distance((0, 0, 0)) == sqrt(3) / 2
+    # Line to point
+    assert Line3D(p1, p2).distance(Point3D(-1, 1, 1)) == 2 * sqrt(6) / 3
+    assert Line3D(p1, p2).distance(Point3D(1, -1, 1)) == 2 * sqrt(6) / 3
+    assert Line3D(p1, p2).distance(Point3D(2, 2, 2)) == 0
+    assert Line3D(p1, p2).distance((2, 2, 2)) == 0
+    assert Line3D(p1, p2).distance((1, -1, 1)) == 2 * sqrt(6) / 3
+    assert Line3D((0, 0, 0), (0, 1, 0)).distance(p1) == 0
+    assert Line3D((0, 0, 0), (0, 1, 0)).distance(p2) == sqrt(2)
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(p1) == 0
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(p2) == sqrt(2)
+    # Line to line
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((0, 0, 0), (0, 1, 2))) == 0
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((0, 0, 0), (1, 0, 0))) == 0
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((10, 0, 0), (10, 1, 2))) == 0
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((0, 1, 0), (0, 1, 1))) == 1
+    # Line to plane
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Plane((2, 0, 0), (0, 0, 1))) == 0
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Plane((0, 1, 0), (0, 1, 0))) == 1
+    assert Line3D((0, 0, 0), (1, 0, 0)).distance(Plane((1, 1, 3), (1, 0, 0))) == 0
+    # Ray to point
+    assert r.distance(Point3D(-1, -1, -1)) == sqrt(3)
+    assert r.distance(Point3D(1, 1, 1)) == 0
+    assert r.distance((-1, -1, -1)) == sqrt(3)
+    assert r.distance((1, 1, 1)) == 0
+    assert Ray3D((0, 0, 0), (1, 1, 2)).distance((-1, -1, 2)) == 4 * sqrt(3) / 3
+    assert Ray3D((1, 1, 1), (2, 2, 2)).distance(Point3D(1.5, -3, -1)) == Rational(9) / 2
+    assert Ray3D((1, 1, 1), (2, 2, 2)).distance(Point3D(1.5, 3, 1)) == sqrt(78) / 6
+
+
+def test_equals():
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+
+    l1 = Line(p1, p2)
+    l2 = Line((0, 5), slope=m)
+    l3 = Line(Point(x1, x1), Point(x1, 1 + x1))
+
+    assert l1.perpendicular_line(p1.args).equals(Line(Point(0, 0), Point(1, -1)))
+    assert l1.perpendicular_line(p1).equals(Line(Point(0, 0), Point(1, -1)))
+    assert Line(Point(x1, x1), Point(y1, y1)).parallel_line(Point(-x1, x1)). \
+        equals(Line(Point(-x1, x1), Point(-y1, 2 * x1 - y1)))
+    assert l3.parallel_line(p1.args).equals(Line(Point(0, 0), Point(0, -1)))
+    assert l3.parallel_line(p1).equals(Line(Point(0, 0), Point(0, -1)))
+    assert (l2.distance(Point(2, 3)) - 2 * abs(m + 1) / sqrt(m ** 2 + 1)).equals(0)
+    assert Line3D(p1, Point3D(0, 1, 0)).equals(Point(1.0, 1.0)) is False
+    assert Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).equals(Line3D(Point3D(-5, 0, 0), Point3D(-1, 0, 0))) is True
+    assert Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).equals(Line3D(p1, Point3D(0, 1, 0))) is False
+    assert Ray3D(p1, Point3D(0, 0, -1)).equals(Point(1.0, 1.0)) is False
+    assert Ray3D(p1, Point3D(0, 0, -1)).equals(Ray3D(p1, Point3D(0, 0, -1))) is True
+    assert Line3D((0, 0), (t, t)).perpendicular_line(Point(0, 1, 0)).equals(
+        Line3D(Point3D(0, 1, 0), Point3D(S.Half, S.Half, 0)))
+    assert Line3D((0, 0), (t, t)).perpendicular_segment(Point(0, 1, 0)).equals(Segment3D((0, 1), (S.Half, S.Half)))
+    assert Line3D(p1, Point3D(0, 1, 0)).equals(Point(1.0, 1.0)) is False
+
+
+def test_equation():
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+    l1 = Line(p1, p2)
+    l3 = Line(Point(x1, x1), Point(x1, 1 + x1))
+
+    assert simplify(l1.equation()) in (x - y, y - x)
+    assert simplify(l3.equation()) in (x - x1, x1 - x)
+    assert simplify(l1.equation()) in (x - y, y - x)
+    assert simplify(l3.equation()) in (x - x1, x1 - x)
+
+    assert Line(p1, Point(1, 0)).equation(x=x, y=y) == y
+    assert Line(p1, Point(0, 1)).equation() == x
+    assert Line(Point(2, 0), Point(2, 1)).equation() == x - 2
+    assert Line(p2, Point(2, 1)).equation() == y - 1
+
+    assert Line3D(Point(x1, x1, x1), Point(y1, y1, y1)
+        ).equation() == (-x + y, -x + z)
+    assert Line3D(Point(1, 2, 3), Point(2, 3, 4)
+        ).equation() == (-x + y - 1, -x + z - 2)
+    assert Line3D(Point(1, 2, 3), Point(1, 3, 4)
+        ).equation() == (x - 1, -y + z - 1)
+    assert Line3D(Point(1, 2, 3), Point(2, 2, 4)
+        ).equation() == (y - 2, -x + z - 2)
+    assert Line3D(Point(1, 2, 3), Point(2, 3, 3)
+        ).equation() == (-x + y - 1, z - 3)
+    assert Line3D(Point(1, 2, 3), Point(1, 2, 4)
+        ).equation() == (x - 1, y - 2)
+    assert Line3D(Point(1, 2, 3), Point(1, 3, 3)
+        ).equation() == (x - 1, z - 3)
+    assert Line3D(Point(1, 2, 3), Point(2, 2, 3)
+        ).equation() == (y - 2, z - 3)
+
+
+def test_intersection_2d():
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+    p3 = Point(x1, x1)
+    p4 = Point(y1, y1)
+
+    l1 = Line(p1, p2)
+    l3 = Line(Point(0, 0), Point(3, 4))
+
+    r1 = Ray(Point(1, 1), Point(2, 2))
+    r2 = Ray(Point(0, 0), Point(3, 4))
+    r4 = Ray(p1, p2)
+    r6 = Ray(Point(0, 1), Point(1, 2))
+    r7 = Ray(Point(0.5, 0.5), Point(1, 1))
+
+    s1 = Segment(p1, p2)
+    s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5))
+    s3 = Segment(Point(0, 0), Point(3, 4))
+
+    assert intersection(l1, p1) == [p1]
+    assert intersection(l1, Point(x1, 1 + x1)) == []
+    assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]]
+    assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == []
+    assert intersection(l3, l3) == [l3]
+    assert intersection(l3, r2) == [r2]
+    assert intersection(l3, s3) == [s3]
+    assert intersection(s3, l3) == [s3]
+    assert intersection(Segment(Point(-10, 10), Point(10, 10)), Segment(Point(-5, -5), Point(-5, 5))) == []
+    assert intersection(r2, l3) == [r2]
+    assert intersection(r1, Ray(Point(2, 2), Point(0, 0))) == [Segment(Point(1, 1), Point(2, 2))]
+    assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)]
+    assert intersection(r1, Segment(Point(0, 0), Point(2, 2))) == [Segment(Point(1, 1), Point(2, 2))]
+
+    assert r4.intersection(s2) == [s2]
+    assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == []
+    assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
+    assert r4.intersection(Ray(p2, p1)) == [s1]
+    assert Ray(p2, p1).intersection(r6) == []
+    assert r4.intersection(r7) == r7.intersection(r4) == [r7]
+    assert Ray3D((0, 0), (3, 0)).intersection(Ray3D((1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
+    assert Ray3D((1, 0), (3, 0)).intersection(Ray3D((0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
+    assert Ray(Point(0, 0), Point(0, 4)).intersection(Ray(Point(0, 1), Point(0, -1))) == \
+           [Segment(Point(0, 0), Point(0, 1))]
+
+    assert Segment3D((0, 0), (3, 0)).intersection(
+        Segment3D((1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))]
+    assert Segment3D((1, 0), (2, 0)).intersection(
+        Segment3D((0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))]
+    assert Segment3D((0, 0), (3, 0)).intersection(
+        Segment3D((3, 0), (4, 0))) == [Point3D((3, 0))]
+    assert Segment3D((0, 0), (3, 0)).intersection(
+        Segment3D((2, 0), (5, 0))) == [Segment3D((2, 0), (3, 0))]
+    assert Segment3D((0, 0), (3, 0)).intersection(
+        Segment3D((-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))]
+    assert Segment3D((0, 0), (3, 0)).intersection(
+        Segment3D((-2, 0), (0, 0))) == [Point3D(0, 0)]
+    assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)]
+    assert s1.intersection(Segment(Point(0.5, 0.5), Point(1.5, 1.5))) == [Segment(Point(0.5, 0.5), p2)]
+    assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == []
+    assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1]
+    assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
+    assert s1.intersection(Line(Point(1, 0), Point(2, 1))) == []
+    assert s1.intersection(s2) == [s2]
+    assert s2.intersection(s1) == [s2]
+
+    assert asa(120, 8, 52) == \
+           Triangle(
+               Point(0, 0),
+               Point(8, 0),
+               Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45),
+                     4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45)))
+    assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
+    assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
+    assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
+    assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
+    assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
+    assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
+    assert s1.intersection(Ray((1, 1), (4, 4))) == [Point(1, 1)]
+
+    # This test is disabled because it hangs after rref changes which simplify
+    # intermediate results and return a different representation from when the
+    # test was written.
+    # # 16628 - this should be fast
+    # p0 = Point2D(Rational(249, 5), Rational(497999, 10000))
+    # p1 = Point2D((-58977084786*sqrt(405639795226) + 2030690077184193 +
+    #     20112207807*sqrt(630547164901) + 99600*sqrt(255775022850776494562626))
+    #     /(2000*sqrt(255775022850776494562626) + 1991998000*sqrt(405639795226)
+    #     + 1991998000*sqrt(630547164901) + 1622561172902000),
+    #     (-498000*sqrt(255775022850776494562626) - 995999*sqrt(630547164901) +
+    #     90004251917891999 +
+    #     496005510002*sqrt(405639795226))/(10000*sqrt(255775022850776494562626)
+    #     + 9959990000*sqrt(405639795226) + 9959990000*sqrt(630547164901) +
+    #     8112805864510000))
+    # p2 = Point2D(Rational(497, 10), Rational(-497, 10))
+    # p3 = Point2D(Rational(-497, 10), Rational(-497, 10))
+    # l = Line(p0, p1)
+    # s = Segment(p2, p3)
+    # n = (-52673223862*sqrt(405639795226) - 15764156209307469 -
+    #     9803028531*sqrt(630547164901) +
+    #     33200*sqrt(255775022850776494562626))
+    # d = sqrt(405639795226) + 315274080450 + 498000*sqrt(
+    #     630547164901) + sqrt(255775022850776494562626)
+    # assert intersection(l, s) == [
+    #     Point2D(n/d*Rational(3, 2000), Rational(-497, 10))]
+
+
+def test_line_intersection():
+    # see also test_issue_11238 in test_matrices.py
+    x0 = tan(pi*Rational(13, 45))
+    x1 = sqrt(3)
+    x2 = x0**2
+    x, y = [8*x0/(x0 + x1), (24*x0 - 8*x1*x2)/(x2 - 3)]
+    assert Line(Point(0, 0), Point(1, -sqrt(3))).contains(Point(x, y)) is True
+
+
+def test_intersection_3d():
+    p1 = Point3D(0, 0, 0)
+    p2 = Point3D(1, 1, 1)
+
+    l1 = Line3D(p1, p2)
+    l2 = Line3D(Point3D(0, 0, 0), Point3D(3, 4, 0))
+
+    r1 = Ray3D(Point3D(1, 1, 1), Point3D(2, 2, 2))
+    r2 = Ray3D(Point3D(0, 0, 0), Point3D(3, 4, 0))
+
+    s1 = Segment3D(Point3D(0, 0, 0), Point3D(3, 4, 0))
+
+    assert intersection(l1, p1) == [p1]
+    assert intersection(l1, Point3D(x1, 1 + x1, 1)) == []
+    assert intersection(l1, l1.parallel_line(p1)) == [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1))]
+    assert intersection(l2, r2) == [r2]
+    assert intersection(l2, s1) == [s1]
+    assert intersection(r2, l2) == [r2]
+    assert intersection(r1, Ray3D(Point3D(1, 1, 1), Point3D(-1, -1, -1))) == [Point3D(1, 1, 1)]
+    assert intersection(r1, Segment3D(Point3D(0, 0, 0), Point3D(2, 2, 2))) == [
+        Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))]
+    assert intersection(Ray3D(Point3D(1, 0, 0), Point3D(-1, 0, 0)), Ray3D(Point3D(0, 1, 0), Point3D(0, -1, 0))) \
+           == [Point3D(0, 0, 0)]
+    assert intersection(r1, Ray3D(Point3D(2, 2, 2), Point3D(0, 0, 0))) == \
+           [Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))]
+    assert intersection(s1, r2) == [s1]
+
+    assert Line3D(Point3D(4, 0, 1), Point3D(0, 4, 1)).intersection(Line3D(Point3D(0, 0, 1), Point3D(4, 4, 1))) == \
+           [Point3D(2, 2, 1)]
+    assert Line3D((0, 1, 2), (0, 2, 3)).intersection(Line3D((0, 1, 2), (0, 1, 1))) == [Point3D(0, 1, 2)]
+    assert Line3D((0, 0), (t, t)).intersection(Line3D((0, 1), (t, t))) == \
+           [Point3D(t, t)]
+
+    assert Ray3D(Point3D(0, 0, 0), Point3D(0, 4, 0)).intersection(Ray3D(Point3D(0, 1, 1), Point3D(0, -1, 1))) == []
+
+
+def test_is_parallel():
+    p1 = Point3D(0, 0, 0)
+    p2 = Point3D(1, 1, 1)
+    p3 = Point3D(x1, x1, x1)
+
+    l2 = Line(Point(x1, x1), Point(y1, y1))
+    l2_1 = Line(Point(x1, x1), Point(x1, 1 + x1))
+
+    assert Line.is_parallel(Line(Point(0, 0), Point(1, 1)), l2)
+    assert Line.is_parallel(l2, Line(Point(x1, x1), Point(x1, 1 + x1))) is False
+    assert Line.is_parallel(l2, l2.parallel_line(Point(-x1, x1)))
+    assert Line.is_parallel(l2_1, l2_1.parallel_line(Point(0, 0)))
+    assert Line3D(p1, p2).is_parallel(Line3D(p1, p2))  # same as in 2D
+    assert Line3D(Point3D(4, 0, 1), Point3D(0, 4, 1)).is_parallel(Line3D(Point3D(0, 0, 1), Point3D(4, 4, 1))) is False
+    assert Line3D(p1, p2).parallel_line(p3) == Line3D(Point3D(x1, x1, x1),
+                                                      Point3D(x1 + 1, x1 + 1, x1 + 1))
+    assert Line3D(p1, p2).parallel_line(p3.args) == \
+           Line3D(Point3D(x1, x1, x1), Point3D(x1 + 1, x1 + 1, x1 + 1))
+    assert Line3D(Point3D(4, 0, 1), Point3D(0, 4, 1)).is_parallel(Line3D(Point3D(0, 0, 1), Point3D(4, 4, 1))) is False
+
+
+def test_is_perpendicular():
+    p1 = Point(0, 0)
+    p2 = Point(1, 1)
+
+    l1 = Line(p1, p2)
+    l2 = Line(Point(x1, x1), Point(y1, y1))
+    l1_1 = Line(p1, Point(-x1, x1))
+    # 2D
+    assert Line.is_perpendicular(l1, l1_1)
+    assert Line.is_perpendicular(l1, l2) is False
+    p = l1.random_point()
+    assert l1.perpendicular_segment(p) == p
+    # 3D
+    assert Line3D.is_perpendicular(Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)),
+                                   Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))) is True
+    assert Line3D.is_perpendicular(Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)),
+                                   Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0))) is False
+    assert Line3D.is_perpendicular(Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1)),
+                                   Line3D(Point3D(x1, x1, x1), Point3D(y1, y1, y1))) is False
+
+
+def test_is_similar():
+    p1 = Point(2000, 2000)
+    p2 = p1.scale(2, 2)
+
+    r1 = Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0))
+    r2 = Ray(Point(0, 0), Point(0, 1))
+
+    s1 = Segment(Point(0, 0), p1)
+
+    assert s1.is_similar(Segment(p1, p2))
+    assert s1.is_similar(r2) is False
+    assert r1.is_similar(Line3D(Point3D(1, 1, 1), Point3D(1, 0, 0))) is True
+    assert r1.is_similar(Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))) is False
+
+
+def test_length():
+    s2 = Segment3D(Point3D(x1, x1, x1), Point3D(y1, y1, y1))
+    assert Line(Point(0, 0), Point(1, 1)).length is oo
+    assert s2.length == sqrt(3) * sqrt((x1 - y1) ** 2)
+    assert Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1)).length is oo
+
+
+def test_projection():
+    p1 = Point(0, 0)
+    p2 = Point3D(0, 0, 0)
+    p3 = Point(-x1, x1)
+
+    l1 = Line(p1, Point(1, 1))
+    l2 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))
+    l3 = Line3D(p2, Point3D(1, 1, 1))
+
+    r1 = Ray(Point(1, 1), Point(2, 2))
+
+    s1 = Segment(Point2D(0, 0), Point2D(0, 1))
+    s2 = Segment(Point2D(1, 0), Point2D(2, 1/2))
+
+    assert Line(Point(x1, x1), Point(y1, y1)).projection(Point(y1, y1)) == Point(y1, y1)
+    assert Line(Point(x1, x1), Point(x1, 1 + x1)).projection(Point(1, 1)) == Point(x1, 1)
+    assert Segment(Point(-2, 2), Point(0, 4)).projection(r1) == Segment(Point(-1, 3), Point(0, 4))
+    assert Segment(Point(0, 4), Point(-2, 2)).projection(r1) == Segment(Point(0, 4), Point(-1, 3))
+    assert s2.projection(s1) == EmptySet
+    assert l1.projection(p3) == p1
+    assert l1.projection(Ray(p1, Point(-1, 5))) == Ray(Point(0, 0), Point(2, 2))
+    assert l1.projection(Ray(p1, Point(-1, 1))) == p1
+    assert r1.projection(Ray(Point(1, 1), Point(-1, -1))) == Point(1, 1)
+    assert r1.projection(Ray(Point(0, 4), Point(-1, -5))) == Segment(Point(1, 1), Point(2, 2))
+    assert r1.projection(Segment(Point(-1, 5), Point(-5, -10))) == Segment(Point(1, 1), Point(2, 2))
+    assert r1.projection(Ray(Point(1, 1), Point(-1, -1))) == Point(1, 1)
+    assert r1.projection(Ray(Point(0, 4), Point(-1, -5))) == Segment(Point(1, 1), Point(2, 2))
+    assert r1.projection(Segment(Point(-1, 5), Point(-5, -10))) == Segment(Point(1, 1), Point(2, 2))
+
+    assert l3.projection(Ray3D(p2, Point3D(-1, 5, 0))) == Ray3D(Point3D(0, 0, 0), Point3D(Rational(4, 3), Rational(4, 3), Rational(4, 3)))
+    assert l3.projection(Ray3D(p2, Point3D(-1, 1, 1))) == Ray3D(Point3D(0, 0, 0), Point3D(Rational(1, 3), Rational(1, 3), Rational(1, 3)))
+    assert l2.projection(Point3D(5, 5, 0)) == Point3D(5, 0)
+    assert l2.projection(Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0))).equals(l2)
+
+
+def test_perpendicular_line():
+    # 3d - requires a particular orthogonal to be selected
+    p1, p2, p3 = Point(0, 0, 0), Point(2, 3, 4), Point(-2, 2, 0)
+    l = Line(p1, p2)
+    p = l.perpendicular_line(p3)
+    assert p.p1 == p3
+    assert p.p2 in l
+    # 2d - does not require special selection
+    p1, p2, p3 = Point(0, 0), Point(2, 3), Point(-2, 2)
+    l = Line(p1, p2)
+    p = l.perpendicular_line(p3)
+    assert p.p1 == p3
+    # p is directed from l to p3
+    assert p.direction.unit == (p3 - l.projection(p3)).unit
+
+
+def test_perpendicular_bisector():
+    s1 = Segment(Point(0, 0), Point(1, 1))
+    aline = Line(Point(S.Half, S.Half), Point(Rational(3, 2), Rational(-1, 2)))
+    on_line = Segment(Point(S.Half, S.Half), Point(Rational(3, 2), Rational(-1, 2))).midpoint
+
+    assert s1.perpendicular_bisector().equals(aline)
+    assert s1.perpendicular_bisector(on_line).equals(Segment(s1.midpoint, on_line))
+    assert s1.perpendicular_bisector(on_line + (1, 0)).equals(aline)
+
+
+def test_raises():
+    d, e = symbols('a,b', real=True)
+    s = Segment((d, 0), (e, 0))
+
+    raises(TypeError, lambda: Line((1, 1), 1))
+    raises(ValueError, lambda: Line(Point(0, 0), Point(0, 0)))
+    raises(Undecidable, lambda: Point(2 * d, 0) in s)
+    raises(ValueError, lambda: Ray3D(Point(1.0, 1.0)))
+    raises(ValueError, lambda: Line3D(Point3D(0, 0, 0), Point3D(0, 0, 0)))
+    raises(TypeError, lambda: Line3D((1, 1), 1))
+    raises(ValueError, lambda: Line3D(Point3D(0, 0, 0)))
+    raises(TypeError, lambda: Ray((1, 1), 1))
+    raises(GeometryError, lambda: Line(Point(0, 0), Point(1, 0))
+           .projection(Circle(Point(0, 0), 1)))
+
+
+def test_ray_generation():
+    assert Ray((1, 1), angle=pi / 4) == Ray((1, 1), (2, 2))
+    assert Ray((1, 1), angle=pi / 2) == Ray((1, 1), (1, 2))
+    assert Ray((1, 1), angle=-pi / 2) == Ray((1, 1), (1, 0))
+    assert Ray((1, 1), angle=-3 * pi / 2) == Ray((1, 1), (1, 2))
+    assert Ray((1, 1), angle=5 * pi / 2) == Ray((1, 1), (1, 2))
+    assert Ray((1, 1), angle=5.0 * pi / 2) == Ray((1, 1), (1, 2))
+    assert Ray((1, 1), angle=pi) == Ray((1, 1), (0, 1))
+    assert Ray((1, 1), angle=3.0 * pi) == Ray((1, 1), (0, 1))
+    assert Ray((1, 1), angle=4.0 * pi) == Ray((1, 1), (2, 1))
+    assert Ray((1, 1), angle=0) == Ray((1, 1), (2, 1))
+    assert Ray((1, 1), angle=4.05 * pi) == Ray(Point(1, 1),
+                                               Point(2, -sqrt(5) * sqrt(2 * sqrt(5) + 10) / 4 - sqrt(
+                                                   2 * sqrt(5) + 10) / 4 + 2 + sqrt(5)))
+    assert Ray((1, 1), angle=4.02 * pi) == Ray(Point(1, 1),
+                                               Point(2, 1 + tan(4.02 * pi)))
+    assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + tan(5)))
+
+    assert Ray3D((1, 1, 1), direction_ratio=[4, 4, 4]) == Ray3D(Point3D(1, 1, 1), Point3D(5, 5, 5))
+    assert Ray3D((1, 1, 1), direction_ratio=[1, 2, 3]) == Ray3D(Point3D(1, 1, 1), Point3D(2, 3, 4))
+    assert Ray3D((1, 1, 1), direction_ratio=[1, 1, 1]) == Ray3D(Point3D(1, 1, 1), Point3D(2, 2, 2))
+
+
+def test_issue_7814():
+    circle = Circle(Point(x, 0), y)
+    line = Line(Point(k, z), slope=0)
+    _s = sqrt((y - z)*(y + z))
+    assert line.intersection(circle) == [Point2D(x + _s, z), Point2D(x - _s, z)]
+
+
+def test_issue_2941():
+    def _check():
+        for f, g in cartes(*[(Line, Ray, Segment)] * 2):
+            l1 = f(a, b)
+            l2 = g(c, d)
+            assert l1.intersection(l2) == l2.intersection(l1)
+    # intersect at end point
+    c, d = (-2, -2), (-2, 0)
+    a, b = (0, 0), (1, 1)
+    _check()
+    # midline intersection
+    c, d = (-2, -3), (-2, 0)
+    _check()
+
+
+def test_parameter_value():
+    t = Symbol('t')
+    p1, p2 = Point(0, 1), Point(5, 6)
+    l = Line(p1, p2)
+    assert l.parameter_value((5, 6), t) == {t: 1}
+    raises(ValueError, lambda: l.parameter_value((0, 0), t))
+
+
+def test_bisectors():
+    r1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))
+    r2 = Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))
+    bisections = r1.bisectors(r2)
+    assert bisections == [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 0)),
+        Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))]
+    ans = [Line3D(Point3D(0, 0, 0), Point3D(1, 0, 1)),
+        Line3D(Point3D(0, 0, 0), Point3D(-1, 0, 1))]
+    l1 = (0, 0, 0), (0, 0, 1)
+    l2 = (0, 0), (1, 0)
+    for a, b in cartes((Line, Segment, Ray), repeat=2):
+        assert a(*l1).bisectors(b(*l2)) == ans
+
+
+def test_issue_8615():
+    a = Line3D(Point3D(6, 5, 0), Point3D(6, -6, 0))
+    b = Line3D(Point3D(6, -1, 19/10), Point3D(6, -1, 0))
+    assert a.intersection(b) == [Point3D(6, -1, 0)]
+
+
+def test_issue_12598():
+    r1 = Ray(Point(0, 1), Point(0.98, 0.79).n(2))
+    r2 = Ray(Point(0, 0), Point(0.71, 0.71).n(2))
+    assert str(r1.intersection(r2)[0]) == 'Point2D(0.82, 0.82)'
+    l1 = Line((0, 0), (1, 1))
+    l2 = Segment((-1, 1), (0, -1)).n(2)
+    assert str(l1.intersection(l2)[0]) == 'Point2D(-0.33, -0.33)'
+    l2 = Segment((-1, 1), (-1/2, 1/2)).n(2)
+    assert not l1.intersection(l2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_parabola.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_parabola.py
new file mode 100644
index 0000000000000000000000000000000000000000..2a683f26619952d93475aca9ebd3d47cfb3657a6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_parabola.py
@@ -0,0 +1,143 @@
+from sympy.core.numbers import (Rational, oo)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.complexes import sign
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.geometry.ellipse import (Circle, Ellipse)
+from sympy.geometry.line import (Line, Ray2D, Segment2D)
+from sympy.geometry.parabola import Parabola
+from sympy.geometry.point import (Point, Point2D)
+from sympy.testing.pytest import raises
+
+from sympy.abc import x, y
+
+def test_parabola_geom():
+    a, b = symbols('a b')
+    p1 = Point(0, 0)
+    p2 = Point(3, 7)
+    p3 = Point(0, 4)
+    p4 = Point(6, 0)
+    p5 = Point(a, a)
+    d1 = Line(Point(4, 0), Point(4, 9))
+    d2 = Line(Point(7, 6), Point(3, 6))
+    d3 = Line(Point(4, 0), slope=oo)
+    d4 = Line(Point(7, 6), slope=0)
+    d5 = Line(Point(b, a), slope=oo)
+    d6 = Line(Point(a, b), slope=0)
+
+    half = S.Half
+
+    pa1 = Parabola(None, d2)
+    pa2 = Parabola(directrix=d1)
+    pa3 = Parabola(p1, d1)
+    pa4 = Parabola(p2, d2)
+    pa5 = Parabola(p2, d4)
+    pa6 = Parabola(p3, d2)
+    pa7 = Parabola(p2, d1)
+    pa8 = Parabola(p4, d1)
+    pa9 = Parabola(p4, d3)
+    pa10 = Parabola(p5, d5)
+    pa11 = Parabola(p5, d6)
+    d = Line(Point(3, 7), Point(2, 9))
+    pa12 = Parabola(Point(7, 8), d)
+    pa12r = Parabola(Point(7, 8).reflect(d), d)
+
+    raises(ValueError, lambda:
+           Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7))))
+    raises(ValueError, lambda:
+           Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2))))
+    raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8)))
+
+    # Basic Stuff
+    assert pa1.focus == Point(0, 0)
+    assert pa1.ambient_dimension == S(2)
+    assert pa2 == pa3
+    assert pa4 != pa7
+    assert pa6 != pa7
+    assert pa6.focus == Point2D(0, 4)
+    assert pa6.focal_length == 1
+    assert pa6.p_parameter == -1
+    assert pa6.vertex == Point2D(0, 5)
+    assert pa6.eccentricity == 1
+    assert pa7.focus == Point2D(3, 7)
+    assert pa7.focal_length == half
+    assert pa7.p_parameter == -half
+    assert pa7.vertex == Point2D(7*half, 7)
+    assert pa4.focal_length == half
+    assert pa4.p_parameter == half
+    assert pa4.vertex == Point2D(3, 13*half)
+    assert pa8.focal_length == 1
+    assert pa8.p_parameter == 1
+    assert pa8.vertex == Point2D(5, 0)
+    assert pa4.focal_length == pa5.focal_length
+    assert pa4.p_parameter == pa5.p_parameter
+    assert pa4.vertex == pa5.vertex
+    assert pa4.equation() == pa5.equation()
+    assert pa8.focal_length == pa9.focal_length
+    assert pa8.p_parameter == pa9.p_parameter
+    assert pa8.vertex == pa9.vertex
+    assert pa8.equation() == pa9.equation()
+    assert pa10.focal_length == pa11.focal_length == sqrt((a - b) ** 2) / 2 # if a, b real == abs(a - b)/2
+    assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point(a,
+                            a - sqrt((a - b)**2)*sign(a - b)/2) # change axis x->y, y->x on pa10
+    aos = pa12.axis_of_symmetry
+    assert aos == Line(Point(7, 8), Point(5, 7))
+    assert pa12.directrix == Line(Point(3, 7), Point(2, 9))
+    assert pa12.directrix.angle_between(aos) == S.Pi/2
+    assert pa12.eccentricity == 1
+    assert pa12.equation(x, y) == (x - 7)**2 + (y - 8)**2 - (-2*x - y + 13)**2/5
+    assert pa12.focal_length == 9*sqrt(5)/10
+    assert pa12.focus == Point(7, 8)
+    assert pa12.p_parameter == 9*sqrt(5)/10
+    assert pa12.vertex == Point2D(S(26)/5, S(71)/10)
+    assert pa12r.focal_length == 9*sqrt(5)/10
+    assert pa12r.focus == Point(-S(1)/5, S(22)/5)
+    assert pa12r.p_parameter == -9*sqrt(5)/10
+    assert pa12r.vertex == Point(S(8)/5, S(53)/10)
+
+
+def test_parabola_intersection():
+    l1 = Line(Point(1, -2), Point(-1,-2))
+    l2 = Line(Point(1, 2), Point(-1,2))
+    l3 = Line(Point(1, 0), Point(-1,0))
+
+    p1 = Point(0,0)
+    p2 = Point(0, -2)
+    p3 = Point(120, -12)
+    parabola1 = Parabola(p1, l1)
+
+    # parabola with parabola
+    assert parabola1.intersection(parabola1) == [parabola1]
+    assert parabola1.intersection(Parabola(p1, l2)) == [Point2D(-2, 0), Point2D(2, 0)]
+    assert parabola1.intersection(Parabola(p2, l3)) == [Point2D(0, -1)]
+    assert parabola1.intersection(Parabola(Point(16, 0), l1)) == [Point2D(8, 15)]
+    assert parabola1.intersection(Parabola(Point(0, 16), l1)) == [Point2D(-6, 8), Point2D(6, 8)]
+    assert parabola1.intersection(Parabola(p3, l3)) == []
+    # parabola with point
+    assert parabola1.intersection(p1) == []
+    assert parabola1.intersection(Point2D(0, -1)) == [Point2D(0, -1)]
+    assert parabola1.intersection(Point2D(4, 3)) == [Point2D(4, 3)]
+    # parabola with line
+    assert parabola1.intersection(Line(Point2D(-7, 3), Point(12, 3))) == [Point2D(-4, 3), Point2D(4, 3)]
+    assert parabola1.intersection(Line(Point(-4, -1), Point(4, -1))) == [Point(0, -1)]
+    assert parabola1.intersection(Line(Point(2, 0), Point(0, -2))) == [Point2D(2, 0)]
+    raises(TypeError, lambda: parabola1.intersection(Line(Point(0, 0, 0), Point(1, 1, 1))))
+    # parabola with segment
+    assert parabola1.intersection(Segment2D((-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)]
+    assert parabola1.intersection(Segment2D((0, -5), (0, 6))) == [Point2D(0, -1)]
+    assert parabola1.intersection(Segment2D((-12, -65), (14, -68))) == []
+    # parabola with ray
+    assert parabola1.intersection(Ray2D((-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)]
+    assert parabola1.intersection(Ray2D((0, 7), (1, 14))) == [Point2D(14 + 2*sqrt(57), 105 + 14*sqrt(57))]
+    assert parabola1.intersection(Ray2D((0, 7), (0, 14))) == []
+    # parabola with ellipse/circle
+    assert parabola1.intersection(Circle(p1, 2)) == [Point2D(-2, 0), Point2D(2, 0)]
+    assert parabola1.intersection(Circle(p2, 1)) == [Point2D(0, -1)]
+    assert parabola1.intersection(Ellipse(p2, 2, 1)) == [Point2D(0, -1)]
+    assert parabola1.intersection(Ellipse(Point(0, 19), 5, 7)) == []
+    assert parabola1.intersection(Ellipse((0, 3), 12, 4)) == [
+           Point2D(0, -1),
+           Point2D(-4*sqrt(17)/3, Rational(59, 9)),
+           Point2D(4*sqrt(17)/3, Rational(59, 9))]
+    # parabola with unsupported type
+    raises(TypeError, lambda: parabola1.intersection(2))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_plane.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_plane.py
new file mode 100644
index 0000000000000000000000000000000000000000..1010fce5c3bc68348eacee13f29c1d7588f17e39
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_plane.py
@@ -0,0 +1,268 @@
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (asin, cos, sin)
+from sympy.geometry import Line, Point, Ray, Segment, Point3D, Line3D, Ray3D, Segment3D, Plane, Circle
+from sympy.geometry.util import are_coplanar
+from sympy.testing.pytest import raises
+
+
+def test_plane():
+    x, y, z, u, v = symbols('x y z u v', real=True)
+    p1 = Point3D(0, 0, 0)
+    p2 = Point3D(1, 1, 1)
+    p3 = Point3D(1, 2, 3)
+    pl3 = Plane(p1, p2, p3)
+    pl4 = Plane(p1, normal_vector=(1, 1, 1))
+    pl4b = Plane(p1, p2)
+    pl5 = Plane(p3, normal_vector=(1, 2, 3))
+    pl6 = Plane(Point3D(2, 3, 7), normal_vector=(2, 2, 2))
+    pl7 = Plane(Point3D(1, -5, -6), normal_vector=(1, -2, 1))
+    pl8 = Plane(p1, normal_vector=(0, 0, 1))
+    pl9 = Plane(p1, normal_vector=(0, 12, 0))
+    pl10 = Plane(p1, normal_vector=(-2, 0, 0))
+    pl11 = Plane(p2, normal_vector=(0, 0, 1))
+    l1 = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
+    l2 = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
+    l3 = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))
+
+    raises(ValueError, lambda: Plane(p1, p1, p1))
+
+    assert Plane(p1, p2, p3) != Plane(p1, p3, p2)
+    assert Plane(p1, p2, p3).is_coplanar(Plane(p1, p3, p2))
+    assert Plane(p1, p2, p3).is_coplanar(p1)
+    assert Plane(p1, p2, p3).is_coplanar(Circle(p1, 1)) is False
+    assert Plane(p1, normal_vector=(0, 0, 1)).is_coplanar(Circle(p1, 1))
+
+    assert pl3 == Plane(Point3D(0, 0, 0), normal_vector=(1, -2, 1))
+    assert pl3 != pl4
+    assert pl4 == pl4b
+    assert pl5 == Plane(Point3D(1, 2, 3), normal_vector=(1, 2, 3))
+
+    assert pl5.equation(x, y, z) == x + 2*y + 3*z - 14
+    assert pl3.equation(x, y, z) == x - 2*y + z
+
+    assert pl3.p1 == p1
+    assert pl4.p1 == p1
+    assert pl5.p1 == p3
+
+    assert pl4.normal_vector == (1, 1, 1)
+    assert pl5.normal_vector == (1, 2, 3)
+
+    assert p1 in pl3
+    assert p1 in pl4
+    assert p3 in pl5
+
+    assert pl3.projection(Point(0, 0)) == p1
+    p = pl3.projection(Point3D(1, 1, 0))
+    assert p == Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6))
+    assert p in pl3
+
+    l = pl3.projection_line(Line(Point(0, 0), Point(1, 1)))
+    assert l == Line3D(Point3D(0, 0, 0), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6)))
+    assert l in pl3
+    # get a segment that does not intersect the plane which is also
+    # parallel to pl3's normal veector
+    t = Dummy()
+    r = pl3.random_point()
+    a = pl3.perpendicular_line(r).arbitrary_point(t)
+    s = Segment3D(a.subs(t, 1), a.subs(t, 2))
+    assert s.p1 not in pl3 and s.p2 not in pl3
+    assert pl3.projection_line(s).equals(r)
+    assert pl3.projection_line(Segment(Point(1, 0), Point(1, 1))) == \
+               Segment3D(Point3D(Rational(5, 6), Rational(1, 3), Rational(-1, 6)), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6)))
+    assert pl6.projection_line(Ray(Point(1, 0), Point(1, 1))) == \
+               Ray3D(Point3D(Rational(14, 3), Rational(11, 3), Rational(11, 3)), Point3D(Rational(13, 3), Rational(13, 3), Rational(10, 3)))
+    assert pl3.perpendicular_line(r.args) == pl3.perpendicular_line(r)
+
+    assert pl3.is_parallel(pl6) is False
+    assert pl4.is_parallel(pl6)
+    assert pl3.is_parallel(Line(p1, p2))
+    assert pl6.is_parallel(l1) is False
+
+    assert pl3.is_perpendicular(pl6)
+    assert pl4.is_perpendicular(pl7)
+    assert pl6.is_perpendicular(pl7)
+    assert pl6.is_perpendicular(pl4) is False
+    assert pl6.is_perpendicular(l1) is False
+    assert pl6.is_perpendicular(Line((0, 0, 0), (1, 1, 1)))
+    assert pl6.is_perpendicular((1, 1)) is False
+
+    assert pl6.distance(pl6.arbitrary_point(u, v)) == 0
+    assert pl7.distance(pl7.arbitrary_point(u, v)) == 0
+    assert pl6.distance(pl6.arbitrary_point(t)) == 0
+    assert pl7.distance(pl7.arbitrary_point(t)) == 0
+    assert pl6.p1.distance(pl6.arbitrary_point(t)).simplify() == 1
+    assert pl7.p1.distance(pl7.arbitrary_point(t)).simplify() == 1
+    assert pl3.arbitrary_point(t) == Point3D(-sqrt(30)*sin(t)/30 + \
+        2*sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/15 + sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/6)
+    assert pl3.arbitrary_point(u, v) == Point3D(2*u - v, u + 2*v, 5*v)
+
+    assert pl7.distance(Point3D(1, 3, 5)) == 5*sqrt(6)/6
+    assert pl6.distance(Point3D(0, 0, 0)) == 4*sqrt(3)
+    assert pl6.distance(pl6.p1) == 0
+    assert pl7.distance(pl6) == 0
+    assert pl7.distance(l1) == 0
+    assert pl6.distance(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == \
+        pl6.distance(Point3D(1, 3, 4)) == 4*sqrt(3)/3
+    assert pl6.distance(Segment3D(Point3D(1, 3, 4), Point3D(0, 3, 7))) == \
+        pl6.distance(Point3D(0, 3, 7)) == 2*sqrt(3)/3
+    assert pl6.distance(Segment3D(Point3D(0, 3, 7), Point3D(-1, 3, 10))) == 0
+    assert pl6.distance(Segment3D(Point3D(-1, 3, 10), Point3D(-2, 3, 13))) == 0
+    assert pl6.distance(Segment3D(Point3D(-2, 3, 13), Point3D(-3, 3, 16))) == \
+        pl6.distance(Point3D(-2, 3, 13)) == 2*sqrt(3)/3
+    assert pl6.distance(Plane(Point3D(5, 5, 5), normal_vector=(8, 8, 8))) == sqrt(3)
+    assert pl6.distance(Ray3D(Point3D(1, 3, 4), direction_ratio=[1, 0, -3])) == 4*sqrt(3)/3
+    assert pl6.distance(Ray3D(Point3D(2, 3, 1), direction_ratio=[-1, 0, 3])) == 0
+
+
+    assert pl6.angle_between(pl3) == pi/2
+    assert pl6.angle_between(pl6) == 0
+    assert pl6.angle_between(pl4) == 0
+    assert pl7.angle_between(Line3D(Point3D(2, 3, 5), Point3D(2, 4, 6))) == \
+        -asin(sqrt(3)/6)
+    assert pl6.angle_between(Ray3D(Point3D(2, 4, 1), Point3D(6, 5, 3))) == \
+        asin(sqrt(7)/3)
+    assert pl7.angle_between(Segment3D(Point3D(5, 6, 1), Point3D(1, 2, 4))) == \
+        asin(7*sqrt(246)/246)
+
+    assert are_coplanar(l1, l2, l3) is False
+    assert are_coplanar(l1) is False
+    assert are_coplanar(Point3D(2, 7, 2), Point3D(0, 0, 2),
+        Point3D(1, 1, 2), Point3D(1, 2, 2))
+    assert are_coplanar(Plane(p1, p2, p3), Plane(p1, p3, p2))
+    assert Plane.are_concurrent(pl3, pl4, pl5) is False
+    assert Plane.are_concurrent(pl6) is False
+    raises(ValueError, lambda: Plane.are_concurrent(Point3D(0, 0, 0)))
+    raises(ValueError, lambda: Plane((1, 2, 3), normal_vector=(0, 0, 0)))
+
+    assert pl3.parallel_plane(Point3D(1, 2, 5)) == Plane(Point3D(1, 2, 5), \
+                                                      normal_vector=(1, -2, 1))
+
+    # perpendicular_plane
+    p = Plane((0, 0, 0), (1, 0, 0))
+    # default
+    assert p.perpendicular_plane() == Plane(Point3D(0, 0, 0), (0, 1, 0))
+    # 1 pt
+    assert p.perpendicular_plane(Point3D(1, 0, 1)) == \
+        Plane(Point3D(1, 0, 1), (0, 1, 0))
+    # pts as tuples
+    assert p.perpendicular_plane((1, 0, 1), (1, 1, 1)) == \
+        Plane(Point3D(1, 0, 1), (0, 0, -1))
+    # more than two planes
+    raises(ValueError, lambda: p.perpendicular_plane((1, 0, 1), (1, 1, 1), (1, 1, 0)))
+
+    a, b = Point3D(0, 0, 0), Point3D(0, 1, 0)
+    Z = (0, 0, 1)
+    p = Plane(a, normal_vector=Z)
+    # case 4
+    assert p.perpendicular_plane(a, b) == Plane(a, (1, 0, 0))
+    n = Point3D(*Z)
+    # case 1
+    assert p.perpendicular_plane(a, n) == Plane(a, (-1, 0, 0))
+    # case 2
+    assert Plane(a, normal_vector=b.args).perpendicular_plane(a, a + b) == \
+        Plane(Point3D(0, 0, 0), (1, 0, 0))
+    # case 1&3
+    assert Plane(b, normal_vector=Z).perpendicular_plane(b, b + n) == \
+        Plane(Point3D(0, 1, 0), (-1, 0, 0))
+    # case 2&3
+    assert Plane(b, normal_vector=b.args).perpendicular_plane(n, n + b) == \
+        Plane(Point3D(0, 0, 1), (1, 0, 0))
+
+    p = Plane(a, normal_vector=(0, 0, 1))
+    assert p.perpendicular_plane() == Plane(a, normal_vector=(1, 0, 0))
+
+    assert pl6.intersection(pl6) == [pl6]
+    assert pl4.intersection(pl4.p1) == [pl4.p1]
+    assert pl3.intersection(pl6) == [
+        Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6))]
+    assert pl3.intersection(Line3D(Point3D(1,2,4), Point3D(4,4,2))) == [
+        Point3D(2, Rational(8, 3), Rational(10, 3))]
+    assert pl3.intersection(Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3))
+        ) == [Line3D(Point3D(-24, -12, 0), Point3D(-25, -13, -1))]
+    assert pl6.intersection(Ray3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == [
+        Point3D(-1, 3, 10)]
+    assert pl6.intersection(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == []
+    assert pl7.intersection(Line(Point(2, 3), Point(4, 2))) == [
+        Point3D(Rational(13, 2), Rational(3, 4), 0)]
+    r = Ray(Point(2, 3), Point(4, 2))
+    assert Plane((1,2,0), normal_vector=(0,0,1)).intersection(r) == [
+        Ray3D(Point(2, 3), Point(4, 2))]
+    assert pl9.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, 0))]
+    assert pl10.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(0, 2, 1))]
+    assert pl4.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))]
+    assert pl11.intersection(pl8) == []
+    assert pl9.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(12, 0, 1))]
+    assert pl9.intersection(pl4) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, -12))]
+    assert pl3.random_point() in pl3
+    assert pl3.random_point(seed=1) in pl3
+
+    # test geometrical entity using equals
+    assert pl4.intersection(pl4.p1)[0].equals(pl4.p1)
+    assert pl3.intersection(pl6)[0].equals(Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6)))
+    pl8 = Plane((1, 2, 0), normal_vector=(0, 0, 1))
+    assert pl8.intersection(Line3D(p1, (1, 12, 0)))[0].equals(Line((0, 0, 0), (0.1, 1.2, 0)))
+    assert pl8.intersection(Ray3D(p1, (1, 12, 0)))[0].equals(Ray((0, 0, 0), (1, 12, 0)))
+    assert pl8.intersection(Segment3D(p1, (21, 1, 0)))[0].equals(Segment3D(p1, (21, 1, 0)))
+    assert pl8.intersection(Plane(p1, normal_vector=(0, 0, 112)))[0].equals(pl8)
+    assert pl8.intersection(Plane(p1, normal_vector=(0, 12, 0)))[0].equals(
+        Line3D(p1, direction_ratio=(112 * pi, 0, 0)))
+    assert pl8.intersection(Plane(p1, normal_vector=(11, 0, 1)))[0].equals(
+        Line3D(p1, direction_ratio=(0, -11, 0)))
+    assert pl8.intersection(Plane(p1, normal_vector=(1, 0, 11)))[0].equals(
+        Line3D(p1, direction_ratio=(0, 11, 0)))
+    assert pl8.intersection(Plane(p1, normal_vector=(-1, -1, -11)))[0].equals(
+        Line3D(p1, direction_ratio=(1, -1, 0)))
+    assert pl3.random_point() in pl3
+    assert len(pl8.intersection(Ray3D(Point3D(0, 2, 3), Point3D(1, 0, 3)))) == 0
+    # check if two plane are equals
+    assert pl6.intersection(pl6)[0].equals(pl6)
+    assert pl8.equals(Plane(p1, normal_vector=(0, 12, 0))) is False
+    assert pl8.equals(pl8)
+    assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12)))
+    assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12*sqrt(3))))
+    assert pl8.equals(p1) is False
+
+    # issue 8570
+    l2 = Line3D(Point3D(Rational(50000004459633, 5000000000000),
+                        Rational(-891926590718643, 1000000000000000),
+                        Rational(231800966893633, 100000000000000)),
+                Point3D(Rational(50000004459633, 50000000000000),
+                        Rational(-222981647679771, 250000000000000),
+                        Rational(231800966893633, 100000000000000)))
+
+    p2 = Plane(Point3D(Rational(402775636372767, 100000000000000),
+                       Rational(-97224357654973, 100000000000000),
+                       Rational(216793600814789, 100000000000000)),
+               (-S('9.00000087501922'), -S('4.81170658872543e-13'),
+                S('0.0')))
+
+    assert str([i.n(2) for i in p2.intersection(l2)]) == \
+           '[Point3D(4.0, -0.89, 2.3)]'
+
+
+def test_dimension_normalization():
+    A = Plane(Point3D(1, 1, 2), normal_vector=(1, 1, 1))
+    b = Point(1, 1)
+    assert A.projection(b) == Point(Rational(5, 3), Rational(5, 3), Rational(2, 3))
+
+    a, b = Point(0, 0), Point3D(0, 1)
+    Z = (0, 0, 1)
+    p = Plane(a, normal_vector=Z)
+    assert p.perpendicular_plane(a, b) == Plane(Point3D(0, 0, 0), (1, 0, 0))
+    assert Plane((1, 2, 1), (2, 1, 0), (3, 1, 2)
+        ).intersection((2, 1)) == [Point(2, 1, 0)]
+
+
+def test_parameter_value():
+    t, u, v = symbols("t, u v")
+    p1, p2, p3 = Point(0, 0, 0), Point(0, 0, 1), Point(0, 1, 0)
+    p = Plane(p1, p2, p3)
+    assert p.parameter_value((0, -3, 2), t) == {t: asin(2*sqrt(13)/13)}
+    assert p.parameter_value((0, -3, 2), u, v) == {u: 3, v: 2}
+    assert p.parameter_value(p1, t) == p1
+    raises(ValueError, lambda: p.parameter_value((1, 0, 0), t))
+    raises(ValueError, lambda: p.parameter_value(Line(Point(0, 0), Point(1, 1)), t))
+    raises(ValueError, lambda: p.parameter_value((0, -3, 2), t, 1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_point.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_point.py
new file mode 100644
index 0000000000000000000000000000000000000000..1f2b2768eb3fba2009f702351de1aac3ed6e71d4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_point.py
@@ -0,0 +1,481 @@
+from sympy.core.basic import Basic
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.parameters import evaluate
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.geometry import Line, Point, Point2D, Point3D, Line3D, Plane
+from sympy.geometry.entity import rotate, scale, translate, GeometryEntity
+from sympy.matrices import Matrix
+from sympy.utilities.iterables import subsets, permutations, cartes
+from sympy.utilities.misc import Undecidable
+from sympy.testing.pytest import raises, warns
+
+
+def test_point():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    x1 = Symbol('x1', real=True)
+    x2 = Symbol('x2', real=True)
+    y1 = Symbol('y1', real=True)
+    y2 = Symbol('y2', real=True)
+    half = S.Half
+    p1 = Point(x1, x2)
+    p2 = Point(y1, y2)
+    p3 = Point(0, 0)
+    p4 = Point(1, 1)
+    p5 = Point(0, 1)
+    line = Line(Point(1, 0), slope=1)
+
+    assert p1 in p1
+    assert p1 not in p2
+    assert p2.y == y2
+    assert (p3 + p4) == p4
+    assert (p2 - p1) == Point(y1 - x1, y2 - x2)
+    assert -p2 == Point(-y1, -y2)
+    raises(TypeError, lambda: Point(1))
+    raises(ValueError, lambda: Point([1]))
+    raises(ValueError, lambda: Point(3, I))
+    raises(ValueError, lambda: Point(2*I, I))
+    raises(ValueError, lambda: Point(3 + I, I))
+
+    assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
+    assert Point.midpoint(p3, p4) == Point(half, half)
+    assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2)
+    assert Point.midpoint(p2, p2) == p2
+    assert p2.midpoint(p2) == p2
+    assert p1.origin == Point(0, 0)
+
+    assert Point.distance(p3, p4) == sqrt(2)
+    assert Point.distance(p1, p1) == 0
+    assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
+    raises(TypeError, lambda: Point.distance(p1, 0))
+    raises(TypeError, lambda: Point.distance(p1, GeometryEntity()))
+
+    # distance should be symmetric
+    assert p1.distance(line) == line.distance(p1)
+    assert p4.distance(line) == line.distance(p4)
+
+    assert Point.taxicab_distance(p4, p3) == 2
+
+    assert Point.canberra_distance(p4, p5) == 1
+    raises(ValueError, lambda: Point.canberra_distance(p3, p3))
+
+    p1_1 = Point(x1, x1)
+    p1_2 = Point(y2, y2)
+    p1_3 = Point(x1 + 1, x1)
+    assert Point.is_collinear(p3)
+
+    with warns(UserWarning, test_stacklevel=False):
+        assert Point.is_collinear(p3, Point(p3, dim=4))
+    assert p3.is_collinear()
+    assert Point.is_collinear(p3, p4)
+    assert Point.is_collinear(p3, p4, p1_1, p1_2)
+    assert Point.is_collinear(p3, p4, p1_1, p1_3) is False
+    assert Point.is_collinear(p3, p3, p4, p5) is False
+
+    raises(TypeError, lambda: Point.is_collinear(line))
+    raises(TypeError, lambda: p1_1.is_collinear(line))
+
+    assert p3.intersection(Point(0, 0)) == [p3]
+    assert p3.intersection(p4) == []
+    assert p3.intersection(line) == []
+    with warns(UserWarning, test_stacklevel=False):
+        assert Point.intersection(Point(0, 0, 0), Point(0, 0)) == [Point(0, 0, 0)]
+
+    x_pos = Symbol('x', positive=True)
+    p2_1 = Point(x_pos, 0)
+    p2_2 = Point(0, x_pos)
+    p2_3 = Point(-x_pos, 0)
+    p2_4 = Point(0, -x_pos)
+    p2_5 = Point(x_pos, 5)
+    assert Point.is_concyclic(p2_1)
+    assert Point.is_concyclic(p2_1, p2_2)
+    assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
+    for pts in permutations((p2_1, p2_2, p2_3, p2_5)):
+        assert Point.is_concyclic(*pts) is False
+    assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False
+    assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) is False
+    assert Point.is_concyclic(Point(0, 0, 0, 0), Point(1, 0, 0, 0), Point(1, 1, 0, 0), Point(1, 1, 1, 0)) is False
+
+    assert p1.is_scalar_multiple(p1)
+    assert p1.is_scalar_multiple(2*p1)
+    assert not p1.is_scalar_multiple(p2)
+    assert Point.is_scalar_multiple(Point(1, 1), (-1, -1))
+    assert Point.is_scalar_multiple(Point(0, 0), (0, -1))
+    # test when is_scalar_multiple can't be determined
+    raises(Undecidable, lambda: Point.is_scalar_multiple(Point(sympify("x1%y1"), sympify("x2%y2")), Point(0, 1)))
+
+    assert Point(0, 1).orthogonal_direction == Point(1, 0)
+    assert Point(1, 0).orthogonal_direction == Point(0, 1)
+
+    assert p1.is_zero is None
+    assert p3.is_zero
+    assert p4.is_zero is False
+    assert p1.is_nonzero is None
+    assert p3.is_nonzero is False
+    assert p4.is_nonzero
+
+    assert p4.scale(2, 3) == Point(2, 3)
+    assert p3.scale(2, 3) == p3
+
+    assert p4.rotate(pi, Point(0.5, 0.5)) == p3
+    assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
+    assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
+
+    assert p4 * 5 == Point(5, 5)
+    assert p4 / 5 == Point(0.2, 0.2)
+    assert 5 * p4 == Point(5, 5)
+
+    raises(ValueError, lambda: Point(0, 0) + 10)
+
+    # Point differences should be simplified
+    assert Point(x*(x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1)
+
+    a, b = S.Half, Rational(1, 3)
+    assert Point(a, b).evalf(2) == \
+        Point(a.n(2), b.n(2), evaluate=False)
+    raises(ValueError, lambda: Point(1, 2) + 1)
+
+    # test project
+    assert Point.project((0, 1), (1, 0)) == Point(0, 0)
+    assert Point.project((1, 1), (1, 0)) == Point(1, 0)
+    raises(ValueError, lambda: Point.project(p1, Point(0, 0)))
+
+    # test transformations
+    p = Point(1, 0)
+    assert p.rotate(pi/2) == Point(0, 1)
+    assert p.rotate(pi/2, p) == p
+    p = Point(1, 1)
+    assert p.scale(2, 3) == Point(2, 3)
+    assert p.translate(1, 2) == Point(2, 3)
+    assert p.translate(1) == Point(2, 1)
+    assert p.translate(y=1) == Point(1, 2)
+    assert p.translate(*p.args) == Point(2, 2)
+
+    # Check invalid input for transform
+    raises(ValueError, lambda: p3.transform(p3))
+    raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
+
+    # test __contains__
+    assert 0 in Point(0, 0, 0, 0)
+    assert 1 not in Point(0, 0, 0, 0)
+
+    # test affine_rank
+    assert Point.affine_rank() == -1
+
+
+def test_point3D():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    x1 = Symbol('x1', real=True)
+    x2 = Symbol('x2', real=True)
+    x3 = Symbol('x3', real=True)
+    y1 = Symbol('y1', real=True)
+    y2 = Symbol('y2', real=True)
+    y3 = Symbol('y3', real=True)
+    half = S.Half
+    p1 = Point3D(x1, x2, x3)
+    p2 = Point3D(y1, y2, y3)
+    p3 = Point3D(0, 0, 0)
+    p4 = Point3D(1, 1, 1)
+    p5 = Point3D(0, 1, 2)
+
+    assert p1 in p1
+    assert p1 not in p2
+    assert p2.y == y2
+    assert (p3 + p4) == p4
+    assert (p2 - p1) == Point3D(y1 - x1, y2 - x2, y3 - x3)
+    assert -p2 == Point3D(-y1, -y2, -y3)
+
+    assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
+    assert Point3D.midpoint(p3, p4) == Point3D(half, half, half)
+    assert Point3D.midpoint(p1, p4) == Point3D(half + half*x1, half + half*x2,
+                                         half + half*x3)
+    assert Point3D.midpoint(p2, p2) == p2
+    assert p2.midpoint(p2) == p2
+
+    assert Point3D.distance(p3, p4) == sqrt(3)
+    assert Point3D.distance(p1, p1) == 0
+    assert Point3D.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2 + p2.z**2)
+
+    p1_1 = Point3D(x1, x1, x1)
+    p1_2 = Point3D(y2, y2, y2)
+    p1_3 = Point3D(x1 + 1, x1, x1)
+    Point3D.are_collinear(p3)
+    assert Point3D.are_collinear(p3, p4)
+    assert Point3D.are_collinear(p3, p4, p1_1, p1_2)
+    assert Point3D.are_collinear(p3, p4, p1_1, p1_3) is False
+    assert Point3D.are_collinear(p3, p3, p4, p5) is False
+
+    assert p3.intersection(Point3D(0, 0, 0)) == [p3]
+    assert p3.intersection(p4) == []
+
+
+    assert p4 * 5 == Point3D(5, 5, 5)
+    assert p4 / 5 == Point3D(0.2, 0.2, 0.2)
+    assert 5 * p4 == Point3D(5, 5, 5)
+
+    raises(ValueError, lambda: Point3D(0, 0, 0) + 10)
+
+    # Test coordinate properties
+    assert p1.coordinates == (x1, x2, x3)
+    assert p2.coordinates == (y1, y2, y3)
+    assert p3.coordinates == (0, 0, 0)
+    assert p4.coordinates == (1, 1, 1)
+    assert p5.coordinates == (0, 1, 2)
+    assert p5.x == 0
+    assert p5.y == 1
+    assert p5.z == 2
+
+    # Point differences should be simplified
+    assert Point3D(x*(x - 1), y, 2) - Point3D(x**2 - x, y + 1, 1) == \
+        Point3D(0, -1, 1)
+
+    a, b, c = S.Half, Rational(1, 3), Rational(1, 4)
+    assert Point3D(a, b, c).evalf(2) == \
+        Point(a.n(2), b.n(2), c.n(2), evaluate=False)
+    raises(ValueError, lambda: Point3D(1, 2, 3) + 1)
+
+    # test transformations
+    p = Point3D(1, 1, 1)
+    assert p.scale(2, 3) == Point3D(2, 3, 1)
+    assert p.translate(1, 2) == Point3D(2, 3, 1)
+    assert p.translate(1) == Point3D(2, 1, 1)
+    assert p.translate(z=1) == Point3D(1, 1, 2)
+    assert p.translate(*p.args) == Point3D(2, 2, 2)
+
+    # Test __new__
+    assert Point3D(0.1, 0.2, evaluate=False, on_morph='ignore').args[0].is_Float
+
+    # Test length property returns correctly
+    assert p.length == 0
+    assert p1_1.length == 0
+    assert p1_2.length == 0
+
+    # Test are_colinear type error
+    raises(TypeError, lambda: Point3D.are_collinear(p, x))
+
+    # Test are_coplanar
+    assert Point.are_coplanar()
+    assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0))
+    assert Point.are_coplanar((1, 2, 0), (1, 2, 3))
+    with warns(UserWarning, test_stacklevel=False):
+        raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3)))
+    assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3))
+    assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1), (1, 2, 1)) is False
+    planar2 = Point3D(1, -1, 1)
+    planar3 = Point3D(-1, 1, 1)
+    assert Point3D.are_coplanar(p, planar2, planar3) == True
+    assert Point3D.are_coplanar(p, planar2, planar3, p3) == False
+    assert Point.are_coplanar(p, planar2)
+    planar2 = Point3D(1, 1, 2)
+    planar3 = Point3D(1, 1, 3)
+    assert Point3D.are_coplanar(p, planar2, planar3)  # line, not plane
+    plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2))
+    assert Point.are_coplanar(*[plane.projection(((-1)**i, i)) for i in range(4)])
+
+    # all 2D points are coplanar
+    assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point(y, x + 2)) is True
+
+    # Test Intersection
+    assert planar2.intersection(Line3D(p, planar3)) == [Point3D(1, 1, 2)]
+
+    # Test Scale
+    assert planar2.scale(1, 1, 1) == planar2
+    assert planar2.scale(2, 2, 2, planar3) == Point3D(1, 1, 1)
+    assert planar2.scale(1, 1, 1, p3) == planar2
+
+    # Test Transform
+    identity = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
+    assert p.transform(identity) == p
+    trans = Matrix([[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 1], [0, 0, 0, 1]])
+    assert p.transform(trans) == Point3D(2, 2, 2)
+    raises(ValueError, lambda: p.transform(p))
+    raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
+
+    # Test Equals
+    assert p.equals(x1) == False
+
+    # Test __sub__
+    p_4d = Point(0, 0, 0, 1)
+    with warns(UserWarning, test_stacklevel=False):
+        assert p - p_4d == Point(1, 1, 1, -1)
+    p_4d3d = Point(0, 0, 1, 0)
+    with warns(UserWarning, test_stacklevel=False):
+        assert p - p_4d3d == Point(1, 1, 0, 0)
+
+
+def test_Point2D():
+
+    # Test Distance
+    p1 = Point2D(1, 5)
+    p2 = Point2D(4, 2.5)
+    p3 = (6, 3)
+    assert p1.distance(p2) == sqrt(61)/2
+    assert p2.distance(p3) == sqrt(17)/2
+
+    # Test coordinates
+    assert p1.x == 1
+    assert p1.y == 5
+    assert p2.x == 4
+    assert p2.y == S(5)/2
+    assert p1.coordinates == (1, 5)
+    assert p2.coordinates == (4, S(5)/2)
+
+    # test bounds
+    assert p1.bounds == (1, 5, 1, 5)
+
+def test_issue_9214():
+    p1 = Point3D(4, -2, 6)
+    p2 = Point3D(1, 2, 3)
+    p3 = Point3D(7, 2, 3)
+
+    assert Point3D.are_collinear(p1, p2, p3) is False
+
+
+def test_issue_11617():
+    p1 = Point3D(1,0,2)
+    p2 = Point2D(2,0)
+
+    with warns(UserWarning, test_stacklevel=False):
+        assert p1.distance(p2) == sqrt(5)
+
+
+def test_transform():
+    p = Point(1, 1)
+    assert p.transform(rotate(pi/2)) == Point(-1, 1)
+    assert p.transform(scale(3, 2)) == Point(3, 2)
+    assert p.transform(translate(1, 2)) == Point(2, 3)
+    assert Point(1, 1).scale(2, 3, (4, 5)) == \
+        Point(-2, -7)
+    assert Point(1, 1).translate(4, 5) == \
+        Point(5, 6)
+
+
+def test_concyclic_doctest_bug():
+    p1, p2 = Point(-1, 0), Point(1, 0)
+    p3, p4 = Point(0, 1), Point(-1, 2)
+    assert Point.is_concyclic(p1, p2, p3)
+    assert not Point.is_concyclic(p1, p2, p3, p4)
+
+
+def test_arguments():
+    """Functions accepting `Point` objects in `geometry`
+    should also accept tuples and lists and
+    automatically convert them to points."""
+
+    singles2d = ((1,2), [1,2], Point(1,2))
+    singles2d2 = ((1,3), [1,3], Point(1,3))
+    doubles2d = cartes(singles2d, singles2d2)
+    p2d = Point2D(1,2)
+    singles3d = ((1,2,3), [1,2,3], Point(1,2,3))
+    doubles3d = subsets(singles3d, 2)
+    p3d = Point3D(1,2,3)
+    singles4d = ((1,2,3,4), [1,2,3,4], Point(1,2,3,4))
+    doubles4d = subsets(singles4d, 2)
+    p4d = Point(1,2,3,4)
+
+    # test 2D
+    test_single = ['distance', 'is_scalar_multiple', 'taxicab_distance', 'midpoint', 'intersection', 'dot', 'equals', '__add__', '__sub__']
+    test_double = ['is_concyclic', 'is_collinear']
+    for p in singles2d:
+        Point2D(p)
+    for func in test_single:
+        for p in singles2d:
+            getattr(p2d, func)(p)
+    for func in test_double:
+        for p in doubles2d:
+            getattr(p2d, func)(*p)
+
+    # test 3D
+    test_double = ['is_collinear']
+    for p in singles3d:
+        Point3D(p)
+    for func in test_single:
+        for p in singles3d:
+            getattr(p3d, func)(p)
+    for func in test_double:
+        for p in doubles3d:
+            getattr(p3d, func)(*p)
+
+    # test 4D
+    test_double = ['is_collinear']
+    for p in singles4d:
+        Point(p)
+    for func in test_single:
+        for p in singles4d:
+            getattr(p4d, func)(p)
+    for func in test_double:
+        for p in doubles4d:
+            getattr(p4d, func)(*p)
+
+    # test evaluate=False for ops
+    x = Symbol('x')
+    a = Point(0, 1)
+    assert a + (0.1, x) == Point(0.1, 1 + x, evaluate=False)
+    a = Point(0, 1)
+    assert a/10.0 == Point(0, 0.1, evaluate=False)
+    a = Point(0, 1)
+    assert a*10.0 == Point(0, 10.0, evaluate=False)
+
+    # test evaluate=False when changing dimensions
+    u = Point(.1, .2, evaluate=False)
+    u4 = Point(u, dim=4, on_morph='ignore')
+    assert u4.args == (.1, .2, 0, 0)
+    assert all(i.is_Float for i in u4.args[:2])
+    # and even when *not* changing dimensions
+    assert all(i.is_Float for i in Point(u).args)
+
+    # never raise error if creating an origin
+    assert Point(dim=3, on_morph='error')
+
+    # raise error with unmatched dimension
+    raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='error'))
+    # test unknown on_morph
+    raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='unknown'))
+    # test invalid expressions
+    raises(TypeError, lambda: Point(Basic(), Basic()))
+
+def test_unit():
+    assert Point(1, 1).unit == Point(sqrt(2)/2, sqrt(2)/2)
+
+
+def test_dot():
+    raises(TypeError, lambda: Point(1, 2).dot(Line((0, 0), (1, 1))))
+
+
+def test__normalize_dimension():
+    assert Point._normalize_dimension(Point(1, 2), Point(3, 4)) == [
+        Point(1, 2), Point(3, 4)]
+    assert Point._normalize_dimension(
+        Point(1, 2), Point(3, 4, 0), on_morph='ignore') == [
+        Point(1, 2, 0), Point(3, 4, 0)]
+
+
+def test_issue_22684():
+    # Used to give an error
+    with evaluate(False):
+        Point(1, 2)
+
+
+def test_direction_cosine():
+    p1 = Point3D(0, 0, 0)
+    p2 = Point3D(1, 1, 1)
+
+    assert p1.direction_cosine(Point3D(1, 0, 0)) == [1, 0, 0]
+    assert p1.direction_cosine(Point3D(0, 1, 0)) == [0, 1, 0]
+    assert p1.direction_cosine(Point3D(0, 0, pi)) == [0, 0, 1]
+
+    assert p1.direction_cosine(Point3D(5, 0, 0)) == [1, 0, 0]
+    assert p1.direction_cosine(Point3D(0, sqrt(3), 0)) == [0, 1, 0]
+    assert p1.direction_cosine(Point3D(0, 0, 5)) == [0, 0, 1]
+
+    assert p1.direction_cosine(Point3D(2.4, 2.4, 0)) == [sqrt(2)/2, sqrt(2)/2, 0]
+    assert p1.direction_cosine(Point3D(1, 1, 1)) == [sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3]
+    assert p1.direction_cosine(Point3D(-12, 0 -15)) == [-4*sqrt(41)/41, -5*sqrt(41)/41, 0]
+
+    assert p2.direction_cosine(Point3D(0, 0, 0)) == [-sqrt(3) / 3, -sqrt(3) / 3, -sqrt(3) / 3]
+    assert p2.direction_cosine(Point3D(1, 1, 12)) == [0, 0, 1]
+    assert p2.direction_cosine(Point3D(12, 1, 12)) == [sqrt(2) / 2, 0, sqrt(2) / 2]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_polygon.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_polygon.py
new file mode 100644
index 0000000000000000000000000000000000000000..520023349f363bdb12146465305c2a5650c80934
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_polygon.py
@@ -0,0 +1,676 @@
+from sympy.core.numbers import (Float, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, cos, sin)
+from sympy.functions.elementary.trigonometric import tan
+from sympy.geometry import (Circle, Ellipse, GeometryError, Point, Point2D,
+                            Polygon, Ray, RegularPolygon, Segment, Triangle,
+                            are_similar, convex_hull, intersection, Line, Ray2D)
+from sympy.testing.pytest import raises, slow, warns
+from sympy.core.random import verify_numerically
+from sympy.geometry.polygon import rad, deg
+from sympy.integrals.integrals import integrate
+from sympy.utilities.iterables import rotate_left
+
+
+def feq(a, b):
+    """Test if two floating point values are 'equal'."""
+    t_float = Float("1.0E-10")
+    return -t_float < a - b < t_float
+
+@slow
+def test_polygon():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    q = Symbol('q', real=True)
+    u = Symbol('u', real=True)
+    v = Symbol('v', real=True)
+    w = Symbol('w', real=True)
+    x1 = Symbol('x1', real=True)
+    half = S.Half
+    a, b, c = Point(0, 0), Point(2, 0), Point(3, 3)
+    t = Triangle(a, b, c)
+    assert Polygon(Point(0, 0)) == Point(0, 0)
+    assert Polygon(a, Point(1, 0), b, c) == t
+    assert Polygon(Point(1, 0), b, c, a) == t
+    assert Polygon(b, c, a, Point(1, 0)) == t
+    # 2 "remove folded" tests
+    assert Polygon(a, Point(3, 0), b, c) == t
+    assert Polygon(a, b, Point(3, -1), b, c) == t
+    # remove multiple collinear points
+    assert Polygon(Point(-4, 15), Point(-11, 15), Point(-15, 15),
+        Point(-15, 33/5), Point(-15, -87/10), Point(-15, -15),
+        Point(-42/5, -15), Point(-2, -15), Point(7, -15), Point(15, -15),
+        Point(15, -3), Point(15, 10), Point(15, 15)) == \
+        Polygon(Point(-15, -15), Point(15, -15), Point(15, 15), Point(-15, 15))
+
+    p1 = Polygon(
+        Point(0, 0), Point(3, -1),
+        Point(6, 0), Point(4, 5),
+        Point(2, 3), Point(0, 3))
+    p2 = Polygon(
+        Point(6, 0), Point(3, -1),
+        Point(0, 0), Point(0, 3),
+        Point(2, 3), Point(4, 5))
+    p3 = Polygon(
+        Point(0, 0), Point(3, 0),
+        Point(5, 2), Point(4, 4))
+    p4 = Polygon(
+        Point(0, 0), Point(4, 4),
+        Point(5, 2), Point(3, 0))
+    p5 = Polygon(
+        Point(0, 0), Point(4, 4),
+        Point(0, 4))
+    p6 = Polygon(
+        Point(-11, 1), Point(-9, 6.6),
+        Point(-4, -3), Point(-8.4, -8.7))
+    p7 = Polygon(
+        Point(x, y), Point(q, u),
+        Point(v, w))
+    p8 = Polygon(
+        Point(x, y), Point(v, w),
+        Point(q, u))
+    p9 = Polygon(
+        Point(0, 0), Point(4, 4),
+        Point(3, 0), Point(5, 2))
+    p10 = Polygon(
+        Point(0, 2), Point(2, 2),
+        Point(0, 0), Point(2, 0))
+    p11 = Polygon(Point(0, 0), 1, n=3)
+    p12 = Polygon(Point(0, 0), 1, 0, n=3)
+    p13 = Polygon(
+        Point(0, 0),Point(8, 8),
+        Point(23, 20),Point(0, 20))
+    p14 = Polygon(*rotate_left(p13.args, 1))
+
+
+    r = Ray(Point(-9, 6.6), Point(-9, 5.5))
+    #
+    # General polygon
+    #
+    assert p1 == p2
+    assert len(p1.args) == 6
+    assert len(p1.sides) == 6
+    assert p1.perimeter == 5 + 2*sqrt(10) + sqrt(29) + sqrt(8)
+    assert p1.area == 22
+    assert not p1.is_convex()
+    assert Polygon((-1, 1), (2, -1), (2, 1), (-1, -1), (3, 0)
+        ).is_convex() is False
+    # ensure convex for both CW and CCW point specification
+    assert p3.is_convex()
+    assert p4.is_convex()
+    dict5 = p5.angles
+    assert dict5[Point(0, 0)] == pi / 4
+    assert dict5[Point(0, 4)] == pi / 2
+    assert p5.encloses_point(Point(x, y)) is None
+    assert p5.encloses_point(Point(1, 3))
+    assert p5.encloses_point(Point(0, 0)) is False
+    assert p5.encloses_point(Point(4, 0)) is False
+    assert p1.encloses(Circle(Point(2.5, 2.5), 5)) is False
+    assert p1.encloses(Ellipse(Point(2.5, 2), 5, 6)) is False
+    assert p5.plot_interval('x') == [x, 0, 1]
+    assert p5.distance(
+        Polygon(Point(10, 10), Point(14, 14), Point(10, 14))) == 6 * sqrt(2)
+    assert p5.distance(
+        Polygon(Point(1, 8), Point(5, 8), Point(8, 12), Point(1, 12))) == 4
+    with warns(UserWarning, \
+               match="Polygons may intersect producing erroneous output"):
+        Polygon(Point(0, 0), Point(1, 0), Point(1, 1)).distance(
+                Polygon(Point(0, 0), Point(0, 1), Point(1, 1)))
+    assert hash(p5) == hash(Polygon(Point(0, 0), Point(4, 4), Point(0, 4)))
+    assert hash(p1) == hash(p2)
+    assert hash(p7) == hash(p8)
+    assert hash(p3) != hash(p9)
+    assert p5 == Polygon(Point(4, 4), Point(0, 4), Point(0, 0))
+    assert Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) in p5
+    assert p5 != Point(0, 4)
+    assert Point(0, 1) in p5
+    assert p5.arbitrary_point('t').subs(Symbol('t', real=True), 0) == \
+        Point(0, 0)
+    raises(ValueError, lambda: Polygon(
+        Point(x, 0), Point(0, y), Point(x, y)).arbitrary_point('x'))
+    assert p6.intersection(r) == [Point(-9, Rational(-84, 13)), Point(-9, Rational(33, 5))]
+    assert p10.area == 0
+    assert p11 == RegularPolygon(Point(0, 0), 1, 3, 0)
+    assert p11 == p12
+    assert p11.vertices[0] == Point(1, 0)
+    assert p11.args[0] == Point(0, 0)
+    p11.spin(pi/2)
+    assert p11.vertices[0] == Point(0, 1)
+    #
+    # Regular polygon
+    #
+    p1 = RegularPolygon(Point(0, 0), 10, 5)
+    p2 = RegularPolygon(Point(0, 0), 5, 5)
+    raises(GeometryError, lambda: RegularPolygon(Point(0, 0), Point(0,
+           1), Point(1, 1)))
+    raises(GeometryError, lambda: RegularPolygon(Point(0, 0), 1, 2))
+    raises(ValueError, lambda: RegularPolygon(Point(0, 0), 1, 2.5))
+
+    assert p1 != p2
+    assert p1.interior_angle == pi*Rational(3, 5)
+    assert p1.exterior_angle == pi*Rational(2, 5)
+    assert p2.apothem == 5*cos(pi/5)
+    assert p2.circumcenter == p1.circumcenter == Point(0, 0)
+    assert p1.circumradius == p1.radius == 10
+    assert p2.circumcircle == Circle(Point(0, 0), 5)
+    assert p2.incircle == Circle(Point(0, 0), p2.apothem)
+    assert p2.inradius == p2.apothem == (5 * (1 + sqrt(5)) / 4)
+    p2.spin(pi / 10)
+    dict1 = p2.angles
+    assert dict1[Point(0, 5)] == 3 * pi / 5
+    assert p1.is_convex()
+    assert p1.rotation == 0
+    assert p1.encloses_point(Point(0, 0))
+    assert p1.encloses_point(Point(11, 0)) is False
+    assert p2.encloses_point(Point(0, 4.9))
+    p1.spin(pi/3)
+    assert p1.rotation == pi/3
+    assert p1.vertices[0] == Point(5, 5*sqrt(3))
+    for var in p1.args:
+        if isinstance(var, Point):
+            assert var == Point(0, 0)
+        else:
+            assert var in (5, 10, pi / 3)
+    assert p1 != Point(0, 0)
+    assert p1 != p5
+
+    # while spin works in place (notice that rotation is 2pi/3 below)
+    # rotate returns a new object
+    p1_old = p1
+    assert p1.rotate(pi/3) == RegularPolygon(Point(0, 0), 10, 5, pi*Rational(2, 3))
+    assert p1 == p1_old
+
+    assert p1.area == (-250*sqrt(5) + 1250)/(4*tan(pi/5))
+    assert p1.length == 20*sqrt(-sqrt(5)/8 + Rational(5, 8))
+    assert p1.scale(2, 2) == \
+        RegularPolygon(p1.center, p1.radius*2, p1._n, p1.rotation)
+    assert RegularPolygon((0, 0), 1, 4).scale(2, 3) == \
+        Polygon(Point(2, 0), Point(0, 3), Point(-2, 0), Point(0, -3))
+
+    assert repr(p1) == str(p1)
+
+    #
+    # Angles
+    #
+    angles = p4.angles
+    assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483"))
+    assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544"))
+    assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388"))
+    assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449"))
+
+    angles = p3.angles
+    assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483"))
+    assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544"))
+    assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388"))
+    assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449"))
+
+    # https://github.com/sympy/sympy/issues/24885
+    interior_angles_sum = sum(p13.angles.values())
+    assert feq(interior_angles_sum, (len(p13.angles) - 2)*pi )
+    interior_angles_sum = sum(p14.angles.values())
+    assert feq(interior_angles_sum, (len(p14.angles) - 2)*pi )
+
+    #
+    # Triangle
+    #
+    p1 = Point(0, 0)
+    p2 = Point(5, 0)
+    p3 = Point(0, 5)
+    t1 = Triangle(p1, p2, p3)
+    t2 = Triangle(p1, p2, Point(Rational(5, 2), sqrt(Rational(75, 4))))
+    t3 = Triangle(p1, Point(x1, 0), Point(0, x1))
+    s1 = t1.sides
+    assert Triangle(p1, p2, p1) == Polygon(p1, p2, p1) == Segment(p1, p2)
+    raises(GeometryError, lambda: Triangle(Point(0, 0)))
+
+    # Basic stuff
+    assert Triangle(p1, p1, p1) == p1
+    assert Triangle(p2, p2*2, p2*3) == Segment(p2, p2*3)
+    assert t1.area == Rational(25, 2)
+    assert t1.is_right()
+    assert t2.is_right() is False
+    assert t3.is_right()
+    assert p1 in t1
+    assert t1.sides[0] in t1
+    assert Segment((0, 0), (1, 0)) in t1
+    assert Point(5, 5) not in t2
+    assert t1.is_convex()
+    assert feq(t1.angles[p1].evalf(), pi.evalf()/2)
+
+    assert t1.is_equilateral() is False
+    assert t2.is_equilateral()
+    assert t3.is_equilateral() is False
+    assert are_similar(t1, t2) is False
+    assert are_similar(t1, t3)
+    assert are_similar(t2, t3) is False
+    assert t1.is_similar(Point(0, 0)) is False
+    assert t1.is_similar(t2) is False
+
+    # Bisectors
+    bisectors = t1.bisectors()
+    assert bisectors[p1] == Segment(
+        p1, Point(Rational(5, 2), Rational(5, 2)))
+    assert t2.bisectors()[p2] == Segment(
+        Point(5, 0), Point(Rational(5, 4), 5*sqrt(3)/4))
+    p4 = Point(0, x1)
+    assert t3.bisectors()[p4] == Segment(p4, Point(x1*(sqrt(2) - 1), 0))
+    ic = (250 - 125*sqrt(2))/50
+    assert t1.incenter == Point(ic, ic)
+
+    # Inradius
+    assert t1.inradius == t1.incircle.radius == 5 - 5*sqrt(2)/2
+    assert t2.inradius == t2.incircle.radius == 5*sqrt(3)/6
+    assert t3.inradius == t3.incircle.radius == x1**2/((2 + sqrt(2))*Abs(x1))
+
+    # Exradius
+    assert t1.exradii[t1.sides[2]] == 5*sqrt(2)/2
+
+    # Excenters
+    assert t1.excenters[t1.sides[2]] == Point2D(25*sqrt(2), -5*sqrt(2)/2)
+
+    # Circumcircle
+    assert t1.circumcircle.center == Point(2.5, 2.5)
+
+    # Medians + Centroid
+    m = t1.medians
+    assert t1.centroid == Point(Rational(5, 3), Rational(5, 3))
+    assert m[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2)))
+    assert t3.medians[p1] == Segment(p1, Point(x1/2, x1/2))
+    assert intersection(m[p1], m[p2], m[p3]) == [t1.centroid]
+    assert t1.medial == Triangle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5))
+
+    # Nine-point circle
+    assert t1.nine_point_circle == Circle(Point(2.5, 0),
+                                          Point(0, 2.5), Point(2.5, 2.5))
+    assert t1.nine_point_circle == Circle(Point(0, 0),
+                                          Point(0, 2.5), Point(2.5, 2.5))
+
+    # Perpendicular
+    altitudes = t1.altitudes
+    assert altitudes[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2)))
+    assert altitudes[p2].equals(s1[0])
+    assert altitudes[p3] == s1[2]
+    assert t1.orthocenter == p1
+    t = S('''Triangle(
+    Point(100080156402737/5000000000000, 79782624633431/500000000000),
+    Point(39223884078253/2000000000000, 156345163124289/1000000000000),
+    Point(31241359188437/1250000000000, 338338270939941/1000000000000000))''')
+    assert t.orthocenter == S('''Point(-780660869050599840216997'''
+    '''79471538701955848721853/80368430960602242240789074233100000000000000,'''
+    '''20151573611150265741278060334545897615974257/16073686192120448448157'''
+    '''8148466200000000000)''')
+
+    # Ensure
+    assert len(intersection(*bisectors.values())) == 1
+    assert len(intersection(*altitudes.values())) == 1
+    assert len(intersection(*m.values())) == 1
+
+    # Distance
+    p1 = Polygon(
+        Point(0, 0), Point(1, 0),
+        Point(1, 1), Point(0, 1))
+    p2 = Polygon(
+        Point(0, Rational(5)/4), Point(1, Rational(5)/4),
+        Point(1, Rational(9)/4), Point(0, Rational(9)/4))
+    p3 = Polygon(
+        Point(1, 2), Point(2, 2),
+        Point(2, 1))
+    p4 = Polygon(
+        Point(1, 1), Point(Rational(6)/5, 1),
+        Point(1, Rational(6)/5))
+    pt1 = Point(half, half)
+    pt2 = Point(1, 1)
+
+    '''Polygon to Point'''
+    assert p1.distance(pt1) == half
+    assert p1.distance(pt2) == 0
+    assert p2.distance(pt1) == Rational(3)/4
+    assert p3.distance(pt2) == sqrt(2)/2
+
+    '''Polygon to Polygon'''
+    # p1.distance(p2) emits a warning
+    with warns(UserWarning, \
+               match="Polygons may intersect producing erroneous output"):
+        assert p1.distance(p2) == half/2
+
+    assert p1.distance(p3) == sqrt(2)/2
+
+    # p3.distance(p4) emits a warning
+    with warns(UserWarning, \
+               match="Polygons may intersect producing erroneous output"):
+        assert p3.distance(p4) == (sqrt(2)/2 - sqrt(Rational(2)/25)/2)
+
+
+def test_convex_hull():
+    p = [Point(-5, -1), Point(-2, 1), Point(-2, -1), Point(-1, -3), \
+         Point(0, 0), Point(1, 1), Point(2, 2), Point(2, -1), Point(3, 1), \
+         Point(4, -1), Point(6, 2)]
+    ch = Polygon(p[0], p[3], p[9], p[10], p[6], p[1])
+    #test handling of duplicate points
+    p.append(p[3])
+
+    #more than 3 collinear points
+    another_p = [Point(-45, -85), Point(-45, 85), Point(-45, 26), \
+                 Point(-45, -24)]
+    ch2 = Segment(another_p[0], another_p[1])
+
+    assert convex_hull(*another_p) == ch2
+    assert convex_hull(*p) == ch
+    assert convex_hull(p[0]) == p[0]
+    assert convex_hull(p[0], p[1]) == Segment(p[0], p[1])
+
+    # no unique points
+    assert convex_hull(*[p[-1]]*3) == p[-1]
+
+    # collection of items
+    assert convex_hull(*[Point(0, 0), \
+                        Segment(Point(1, 0), Point(1, 1)), \
+                        RegularPolygon(Point(2, 0), 2, 4)]) == \
+        Polygon(Point(0, 0), Point(2, -2), Point(4, 0), Point(2, 2))
+
+
+def test_encloses():
+    # square with a dimpled left side
+    s = Polygon(Point(0, 0), Point(1, 0), Point(1, 1), Point(0, 1), \
+        Point(S.Half, S.Half))
+    # the following is True if the polygon isn't treated as closing on itself
+    assert s.encloses(Point(0, S.Half)) is False
+    assert s.encloses(Point(S.Half, S.Half)) is False  # it's a vertex
+    assert s.encloses(Point(Rational(3, 4), S.Half)) is True
+
+
+def test_triangle_kwargs():
+    assert Triangle(sss=(3, 4, 5)) == \
+        Triangle(Point(0, 0), Point(3, 0), Point(3, 4))
+    assert Triangle(asa=(30, 2, 30)) == \
+        Triangle(Point(0, 0), Point(2, 0), Point(1, sqrt(3)/3))
+    assert Triangle(sas=(1, 45, 2)) == \
+        Triangle(Point(0, 0), Point(2, 0), Point(sqrt(2)/2, sqrt(2)/2))
+    assert Triangle(sss=(1, 2, 5)) is None
+    assert deg(rad(180)) == 180
+
+
+def test_transform():
+    pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)]
+    pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)]
+    assert Triangle(*pts).scale(2, 3, (4, 5)) == Triangle(*pts_out)
+    assert RegularPolygon((0, 0), 1, 4).scale(2, 3, (4, 5)) == \
+        Polygon(Point(-2, -10), Point(-4, -7), Point(-6, -10), Point(-4, -13))
+    # Checks for symmetric scaling
+    assert RegularPolygon((0, 0), 1, 4).scale(2, 2) == \
+        RegularPolygon(Point2D(0, 0), 2, 4, 0)
+
+def test_reflect():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    b = Symbol('b')
+    m = Symbol('m')
+    l = Line((0, b), slope=m)
+    p = Point(x, y)
+    r = p.reflect(l)
+    dp = l.perpendicular_segment(p).length
+    dr = l.perpendicular_segment(r).length
+
+    assert verify_numerically(dp, dr)
+
+    assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((3, 0), slope=oo)) \
+        == Triangle(Point(5, 0), Point(4, 0), Point(4, 2))
+    assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((0, 3), slope=oo)) \
+        == Triangle(Point(-1, 0), Point(-2, 0), Point(-2, 2))
+    assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((0, 3), slope=0)) \
+        == Triangle(Point(1, 6), Point(2, 6), Point(2, 4))
+    assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((3, 0), slope=0)) \
+        == Triangle(Point(1, 0), Point(2, 0), Point(2, -2))
+
+def test_bisectors():
+    p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+    p = Polygon(Point(0, 0), Point(2, 0), Point(1, 1), Point(0, 3))
+    q = Polygon(Point(1, 0), Point(2, 0), Point(3, 3), Point(-1, 5))
+    poly = Polygon(Point(3, 4), Point(0, 0), Point(8, 7), Point(-1, 1), Point(19, -19))
+    t = Triangle(p1, p2, p3)
+    assert t.bisectors()[p2] == Segment(Point(1, 0), Point(0, sqrt(2) - 1))
+    assert p.bisectors()[Point2D(0, 3)] == Ray2D(Point2D(0, 3), \
+        Point2D(sin(acos(2*sqrt(5)/5)/2), 3 - cos(acos(2*sqrt(5)/5)/2)))
+    assert q.bisectors()[Point2D(-1, 5)] == \
+        Ray2D(Point2D(-1, 5), Point2D(-1 + sqrt(29)*(5*sin(acos(9*sqrt(145)/145)/2) + \
+        2*cos(acos(9*sqrt(145)/145)/2))/29, sqrt(29)*(-5*cos(acos(9*sqrt(145)/145)/2) + \
+        2*sin(acos(9*sqrt(145)/145)/2))/29 + 5))
+    assert poly.bisectors()[Point2D(-1, 1)] == Ray2D(Point2D(-1, 1), \
+        Point2D(-1 + sin(acos(sqrt(26)/26)/2 + pi/4), 1 - sin(-acos(sqrt(26)/26)/2 + pi/4)))
+
+def test_incenter():
+    assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).incenter \
+        == Point(1 - sqrt(2)/2, 1 - sqrt(2)/2)
+
+def test_inradius():
+    assert Triangle(Point(0, 0), Point(4, 0), Point(0, 3)).inradius == 1
+
+def test_incircle():
+    assert Triangle(Point(0, 0), Point(2, 0), Point(0, 2)).incircle \
+        == Circle(Point(2 - sqrt(2), 2 - sqrt(2)), 2 - sqrt(2))
+
+def test_exradii():
+    t = Triangle(Point(0, 0), Point(6, 0), Point(0, 2))
+    assert t.exradii[t.sides[2]] == (-2 + sqrt(10))
+
+def test_medians():
+    t = Triangle(Point(0, 0), Point(1, 0), Point(0, 1))
+    assert t.medians[Point(0, 0)] == Segment(Point(0, 0), Point(S.Half, S.Half))
+
+def test_medial():
+    assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).medial \
+        == Triangle(Point(S.Half, 0), Point(S.Half, S.Half), Point(0, S.Half))
+
+def test_nine_point_circle():
+    assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).nine_point_circle \
+        == Circle(Point2D(Rational(1, 4), Rational(1, 4)), sqrt(2)/4)
+
+def test_eulerline():
+    assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).eulerline \
+        == Line(Point2D(0, 0), Point2D(S.Half, S.Half))
+    assert Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3))).eulerline \
+        == Point2D(5, 5*sqrt(3)/3)
+    assert Triangle(Point(4, -6), Point(4, -1), Point(-3, 3)).eulerline \
+        == Line(Point2D(Rational(64, 7), 3), Point2D(Rational(-29, 14), Rational(-7, 2)))
+
+def test_intersection():
+    poly1 = Triangle(Point(0, 0), Point(1, 0), Point(0, 1))
+    poly2 = Polygon(Point(0, 1), Point(-5, 0),
+                    Point(0, -4), Point(0, Rational(1, 5)),
+                    Point(S.Half, -0.1), Point(1, 0), Point(0, 1))
+
+    assert poly1.intersection(poly2) == [Point2D(Rational(1, 3), 0),
+        Segment(Point(0, Rational(1, 5)), Point(0, 0)),
+        Segment(Point(1, 0), Point(0, 1))]
+    assert poly2.intersection(poly1) == [Point(Rational(1, 3), 0),
+        Segment(Point(0, 0), Point(0, Rational(1, 5))),
+        Segment(Point(1, 0), Point(0, 1))]
+    assert poly1.intersection(Point(0, 0)) == [Point(0, 0)]
+    assert poly1.intersection(Point(-12,  -43)) == []
+    assert poly2.intersection(Line((-12, 0), (12, 0))) == [Point(-5, 0),
+        Point(0, 0), Point(Rational(1, 3), 0), Point(1, 0)]
+    assert poly2.intersection(Line((-12, 12), (12, 12))) == []
+    assert poly2.intersection(Ray((-3, 4), (1, 0))) == [Segment(Point(1, 0),
+        Point(0, 1))]
+    assert poly2.intersection(Circle((0, -1), 1)) == [Point(0, -2),
+        Point(0, 0)]
+    assert poly1.intersection(poly1) == [Segment(Point(0, 0), Point(1, 0)),
+        Segment(Point(0, 1), Point(0, 0)), Segment(Point(1, 0), Point(0, 1))]
+    assert poly2.intersection(poly2) == [Segment(Point(-5, 0), Point(0, -4)),
+        Segment(Point(0, -4), Point(0, Rational(1, 5))),
+        Segment(Point(0, Rational(1, 5)), Point(S.Half, Rational(-1, 10))),
+        Segment(Point(0, 1), Point(-5, 0)),
+        Segment(Point(S.Half, Rational(-1, 10)), Point(1, 0)),
+        Segment(Point(1, 0), Point(0, 1))]
+    assert poly2.intersection(Triangle(Point(0, 1), Point(1, 0), Point(-1, 1))) \
+        == [Point(Rational(-5, 7), Rational(6, 7)), Segment(Point2D(0, 1), Point(1, 0))]
+    assert poly1.intersection(RegularPolygon((-12, -15), 3, 3)) == []
+
+
+def test_parameter_value():
+    t = Symbol('t')
+    sq = Polygon((0, 0), (0, 1), (1, 1), (1, 0))
+    assert sq.parameter_value((0.5, 1), t) == {t: Rational(3, 8)}
+    q = Polygon((0, 0), (2, 1), (2, 4), (4, 0))
+    assert q.parameter_value((4, 0), t) == {t: -6 + 3*sqrt(5)} # ~= 0.708
+
+    raises(ValueError, lambda: sq.parameter_value((5, 6), t))
+    raises(ValueError, lambda: sq.parameter_value(Circle(Point(0, 0), 1), t))
+
+
+def test_issue_12966():
+    poly = Polygon(Point(0, 0), Point(0, 10), Point(5, 10), Point(5, 5),
+        Point(10, 5), Point(10, 0))
+    t = Symbol('t')
+    pt = poly.arbitrary_point(t)
+    DELTA = 5/poly.perimeter
+    assert [pt.subs(t, DELTA*i) for i in range(int(1/DELTA))] == [
+        Point(0, 0), Point(0, 5), Point(0, 10), Point(5, 10),
+        Point(5, 5), Point(10, 5), Point(10, 0), Point(5, 0)]
+
+
+def test_second_moment_of_area():
+    x, y = symbols('x, y')
+    # triangle
+    p1, p2, p3 = [(0, 0), (4, 0), (0, 2)]
+    p = (0, 0)
+    # equation of hypotenuse
+    eq_y = (1-x/4)*2
+    I_yy = integrate((x**2) * (integrate(1, (y, 0, eq_y))), (x, 0, 4))
+    I_xx = integrate(1 * (integrate(y**2, (y, 0, eq_y))), (x, 0, 4))
+    I_xy = integrate(x * (integrate(y, (y, 0, eq_y))), (x, 0, 4))
+
+    triangle = Polygon(p1, p2, p3)
+
+    assert (I_xx - triangle.second_moment_of_area(p)[0]) == 0
+    assert (I_yy - triangle.second_moment_of_area(p)[1]) == 0
+    assert (I_xy - triangle.second_moment_of_area(p)[2]) == 0
+
+    # rectangle
+    p1, p2, p3, p4=[(0, 0), (4, 0), (4, 2), (0, 2)]
+    I_yy = integrate((x**2) * integrate(1, (y, 0, 2)), (x, 0, 4))
+    I_xx = integrate(1 * integrate(y**2, (y, 0, 2)), (x, 0, 4))
+    I_xy = integrate(x * integrate(y, (y, 0, 2)), (x, 0, 4))
+
+    rectangle = Polygon(p1, p2, p3, p4)
+
+    assert (I_xx - rectangle.second_moment_of_area(p)[0]) == 0
+    assert (I_yy - rectangle.second_moment_of_area(p)[1]) == 0
+    assert (I_xy - rectangle.second_moment_of_area(p)[2]) == 0
+
+
+    r = RegularPolygon(Point(0, 0), 5, 3)
+    assert r.second_moment_of_area() == (1875*sqrt(3)/S(32), 1875*sqrt(3)/S(32), 0)
+
+
+def test_first_moment():
+    a, b  = symbols('a, b', positive=True)
+    # rectangle
+    p1 = Polygon((0, 0), (a, 0), (a, b), (0, b))
+    assert p1.first_moment_of_area() == (a*b**2/8, a**2*b/8)
+    assert p1.first_moment_of_area((a/3, b/4)) == (-3*a*b**2/32, -a**2*b/9)
+
+    p1 = Polygon((0, 0), (40, 0), (40, 30), (0, 30))
+    assert p1.first_moment_of_area() == (4500, 6000)
+
+    # triangle
+    p2 = Polygon((0, 0), (a, 0), (a/2, b))
+    assert p2.first_moment_of_area() == (4*a*b**2/81, a**2*b/24)
+    assert p2.first_moment_of_area((a/8, b/6)) == (-25*a*b**2/648, -5*a**2*b/768)
+
+    p2 = Polygon((0, 0), (12, 0), (12, 30))
+    assert p2.first_moment_of_area() == (S(1600)/3, -S(640)/3)
+
+
+def test_section_modulus_and_polar_second_moment_of_area():
+    a, b = symbols('a, b', positive=True)
+    x, y = symbols('x, y')
+    rectangle = Polygon((0, b), (0, 0), (a, 0), (a, b))
+    assert rectangle.section_modulus(Point(x, y)) == (a*b**3/12/(-b/2 + y), a**3*b/12/(-a/2 + x))
+    assert rectangle.polar_second_moment_of_area() == a**3*b/12 + a*b**3/12
+
+    convex = RegularPolygon((0, 0), 1, 6)
+    assert convex.section_modulus() == (Rational(5, 8), sqrt(3)*Rational(5, 16))
+    assert convex.polar_second_moment_of_area() == 5*sqrt(3)/S(8)
+
+    concave = Polygon((0, 0), (1, 8), (3, 4), (4, 6), (7, 1))
+    assert concave.section_modulus() == (Rational(-6371, 429), Rational(-9778, 519))
+    assert concave.polar_second_moment_of_area() == Rational(-38669, 252)
+
+
+def test_cut_section():
+    # concave polygon
+    p = Polygon((-1, -1), (1, Rational(5, 2)), (2, 1), (3, Rational(5, 2)), (4, 2), (5, 3), (-1, 3))
+    l = Line((0, 0), (Rational(9, 2), 3))
+    p1 = p.cut_section(l)[0]
+    p2 = p.cut_section(l)[1]
+    assert p1 == Polygon(
+        Point2D(Rational(-9, 13), Rational(-6, 13)), Point2D(1, Rational(5, 2)), Point2D(Rational(24, 13), Rational(16, 13)),
+        Point2D(Rational(12, 5), Rational(8, 5)), Point2D(3, Rational(5, 2)), Point2D(Rational(24, 7), Rational(16, 7)),
+        Point2D(Rational(9, 2), 3), Point2D(-1, 3), Point2D(-1, Rational(-2, 3)))
+    assert p2 == Polygon(Point2D(-1, -1), Point2D(Rational(-9, 13), Rational(-6, 13)), Point2D(Rational(24, 13), Rational(16, 13)),
+        Point2D(2, 1), Point2D(Rational(12, 5), Rational(8, 5)), Point2D(Rational(24, 7), Rational(16, 7)), Point2D(4, 2), Point2D(5, 3),
+        Point2D(Rational(9, 2), 3), Point2D(-1, Rational(-2, 3)))
+
+    # convex polygon
+    p = RegularPolygon(Point2D(0, 0), 6, 6)
+    s = p.cut_section(Line((0, 0), slope=1))
+    assert s[0] == Polygon(Point2D(-3*sqrt(3) + 9, -3*sqrt(3) + 9), Point2D(3, 3*sqrt(3)),
+        Point2D(-3, 3*sqrt(3)), Point2D(-6, 0), Point2D(-9 + 3*sqrt(3), -9 + 3*sqrt(3)))
+    assert s[1] == Polygon(Point2D(6, 0), Point2D(-3*sqrt(3) + 9, -3*sqrt(3) + 9),
+        Point2D(-9 + 3*sqrt(3), -9 + 3*sqrt(3)), Point2D(-3, -3*sqrt(3)), Point2D(3, -3*sqrt(3)))
+
+    # case where line does not intersects but coincides with the edge of polygon
+    a, b = 20, 10
+    t1, t2, t3, t4 = [(0, b), (0, 0), (a, 0), (a, b)]
+    p = Polygon(t1, t2, t3, t4)
+    p1, p2 = p.cut_section(Line((0, b), slope=0))
+    assert p1 == None
+    assert p2 == Polygon(Point2D(0, 10), Point2D(0, 0), Point2D(20, 0), Point2D(20, 10))
+
+    p3, p4 = p.cut_section(Line((0, 0), slope=0))
+    assert p3 == Polygon(Point2D(0, 10), Point2D(0, 0), Point2D(20, 0), Point2D(20, 10))
+    assert p4 == None
+
+    # case where the line does not intersect with a polygon at all
+    raises(ValueError, lambda: p.cut_section(Line((0, a), slope=0)))
+
+def test_type_of_triangle():
+    # Isoceles triangle
+    p1 = Polygon(Point(0, 0), Point(5, 0), Point(2, 4))
+    assert p1.is_isosceles() == True
+    assert p1.is_scalene() == False
+    assert p1.is_equilateral() == False
+
+    # Scalene triangle
+    p2 = Polygon (Point(0, 0), Point(0, 2), Point(4, 0))
+    assert p2.is_isosceles() == False
+    assert p2.is_scalene() == True
+    assert p2.is_equilateral() == False
+
+    # Equilateral triangle
+    p3 = Polygon(Point(0, 0), Point(6, 0), Point(3, sqrt(27)))
+    assert p3.is_isosceles() == True
+    assert p3.is_scalene() == False
+    assert p3.is_equilateral() == True
+
+def test_do_poly_distance():
+    # Non-intersecting polygons
+    square1 = Polygon (Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0))
+    triangle1 = Polygon(Point(1, 2), Point(2, 2), Point(2, 1))
+    assert square1._do_poly_distance(triangle1) == sqrt(2)/2
+
+    # Polygons which sides intersect
+    square2 = Polygon(Point(1, 0), Point(2, 0), Point(2, 1), Point(1, 1))
+    with warns(UserWarning, \
+               match="Polygons may intersect producing erroneous output", test_stacklevel=False):
+        assert square1._do_poly_distance(square2) == 0
+
+    # Polygons which bodies intersect
+    triangle2 = Polygon(Point(0, -1), Point(2, -1), Point(S.Half, S.Half))
+    with warns(UserWarning, \
+               match="Polygons may intersect producing erroneous output", test_stacklevel=False):
+        assert triangle2._do_poly_distance(square1) == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..da52a795a9383c6438ca06303e8ae6506dccdc65
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/tests/test_util.py
@@ -0,0 +1,170 @@
+import pytest
+from sympy.core.numbers import Float
+from sympy.core.function import (Derivative, Function)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions import exp, cos, sin, tan, cosh, sinh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.geometry import Point, Point2D, Line, Polygon, Segment, convex_hull,\
+    intersection, centroid, Point3D, Line3D, Ray, Ellipse
+from sympy.geometry.util import idiff, closest_points, farthest_points, _ordered_points, are_coplanar
+from sympy.solvers.solvers import solve
+from sympy.testing.pytest import raises
+
+
+def test_idiff():
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    t = Symbol('t', real=True)
+    f = Function('f')
+    g = Function('g')
+    # the use of idiff in ellipse also provides coverage
+    circ = x**2 + y**2 - 4
+    ans = -3*x*(x**2/y**2 + 1)/y**3
+    assert ans == idiff(circ, y, x, 3), idiff(circ, y, x, 3)
+    assert ans == idiff(circ, [y], x, 3)
+    assert idiff(circ, y, x, 3) == ans
+    explicit  = 12*x/sqrt(-x**2 + 4)**5
+    assert ans.subs(y, solve(circ, y)[0]).equals(explicit)
+    assert True in [sol.diff(x, 3).equals(explicit) for sol in solve(circ, y)]
+    assert idiff(x + t + y, [y, t], x) == -Derivative(t, x) - 1
+    assert idiff(f(x) * exp(f(x)) - x * exp(x), f(x), x) == (x + 1)*exp(x)*exp(-f(x))/(f(x) + 1)
+    assert idiff(f(x) - y * exp(x), [f(x), y], x) == (y + Derivative(y, x))*exp(x)
+    assert idiff(f(x) - y * exp(x), [y, f(x)], x) == -y + Derivative(f(x), x)*exp(-x)
+    assert idiff(f(x) - g(x), [f(x), g(x)], x) == Derivative(g(x), x)
+    # this should be fast
+    fxy = y - (-10*(-sin(x) + 1/x)**2 + tan(x)**2 + 2*cosh(x/10))
+    assert idiff(fxy, y, x) == -20*sin(x)*cos(x) + 2*tan(x)**3 + \
+        2*tan(x) + sinh(x/10)/5 + 20*cos(x)/x - 20*sin(x)/x**2 + 20/x**3
+
+
+def test_intersection():
+    assert intersection(Point(0, 0)) == []
+    raises(TypeError, lambda: intersection(Point(0, 0), 3))
+    assert intersection(
+            Segment((0, 0), (2, 0)),
+            Segment((-1, 0), (1, 0)),
+            Line((0, 0), (0, 1)), pairwise=True) == [
+        Point(0, 0), Segment((0, 0), (1, 0))]
+    assert intersection(
+            Line((0, 0), (0, 1)),
+            Segment((0, 0), (2, 0)),
+            Segment((-1, 0), (1, 0)), pairwise=True) == [
+        Point(0, 0), Segment((0, 0), (1, 0))]
+    assert intersection(
+            Line((0, 0), (0, 1)),
+            Segment((0, 0), (2, 0)),
+            Segment((-1, 0), (1, 0)),
+            Line((0, 0), slope=1), pairwise=True) == [
+        Point(0, 0), Segment((0, 0), (1, 0))]
+    R = 4.0
+    c = intersection(
+            Ray(Point2D(0.001, -1),
+            Point2D(0.0008, -1.7)),
+            Ellipse(center=Point2D(0, 0), hradius=R, vradius=2.0), pairwise=True)[0].coordinates
+    assert c == pytest.approx(
+            Point2D(0.000714285723396502, -1.99999996811224, evaluate=False).coordinates)
+    # check this is responds to a lower precision parameter
+    R = Float(4, 5)
+    c2 = intersection(
+            Ray(Point2D(0.001, -1),
+            Point2D(0.0008, -1.7)),
+            Ellipse(center=Point2D(0, 0), hradius=R, vradius=2.0), pairwise=True)[0].coordinates
+    assert c2 == pytest.approx(
+            Point2D(0.000714285723396502, -1.99999996811224, evaluate=False).coordinates)
+    assert c[0]._prec == 53
+    assert c2[0]._prec == 20
+
+
+def test_convex_hull():
+    raises(TypeError, lambda: convex_hull(Point(0, 0), 3))
+    points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)]
+    assert convex_hull(*points, **{"polygon": False}) == (
+        [Point2D(-5, -2), Point2D(1, -1), Point2D(3, -1), Point2D(15, -4)],
+        [Point2D(-5, -2), Point2D(15, -4)])
+
+
+def test_centroid():
+    p = Polygon((0, 0), (10, 0), (10, 10))
+    q = p.translate(0, 20)
+    assert centroid(p, q) == Point(20, 40)/3
+    p = Segment((0, 0), (2, 0))
+    q = Segment((0, 0), (2, 2))
+    assert centroid(p, q) == Point(1, -sqrt(2) + 2)
+    assert centroid(Point(0, 0), Point(2, 0)) == Point(2, 0)/2
+    assert centroid(Point(0, 0), Point(0, 0), Point(2, 0)) == Point(2, 0)/3
+
+
+def test_farthest_points_closest_points():
+    from sympy.core.random import randint
+    from sympy.utilities.iterables import subsets
+
+    for how in (min, max):
+        if how == min:
+            func = closest_points
+        else:
+            func = farthest_points
+
+        raises(ValueError, lambda: func(Point2D(0, 0), Point2D(0, 0)))
+
+        # 3rd pt dx is close and pt is closer to 1st pt
+        p1 = [Point2D(0, 0), Point2D(3, 0), Point2D(1, 1)]
+        # 3rd pt dx is close and pt is closer to 2nd pt
+        p2 = [Point2D(0, 0), Point2D(3, 0), Point2D(2, 1)]
+        # 3rd pt dx is close and but pt is not closer
+        p3 = [Point2D(0, 0), Point2D(3, 0), Point2D(1, 10)]
+        # 3rd pt dx is not closer and it's closer to 2nd pt
+        p4 = [Point2D(0, 0), Point2D(3, 0), Point2D(4, 0)]
+        # 3rd pt dx is not closer and it's closer to 1st pt
+        p5 = [Point2D(0, 0), Point2D(3, 0), Point2D(-1, 0)]
+        # duplicate point doesn't affect outcome
+        dup = [Point2D(0, 0), Point2D(3, 0), Point2D(3, 0), Point2D(-1, 0)]
+        # symbolic
+        x = Symbol('x', positive=True)
+        s = [Point2D(a) for a in ((x, 1), (x + 3, 2), (x + 2, 2))]
+
+        for points in (p1, p2, p3, p4, p5, dup, s):
+            d = how(i.distance(j) for i, j in subsets(set(points), 2))
+            ans = a, b = list(func(*points))[0]
+            assert a.distance(b) == d
+            assert ans == _ordered_points(ans)
+
+        # if the following ever fails, the above tests were not sufficient
+        # and the logical error in the routine should be fixed
+        points = set()
+        while len(points) != 7:
+            points.add(Point2D(randint(1, 100), randint(1, 100)))
+        points = list(points)
+        d = how(i.distance(j) for i, j in subsets(points, 2))
+        ans = a, b = list(func(*points))[0]
+        assert a.distance(b) == d
+        assert ans == _ordered_points(ans)
+
+    # equidistant points
+    a, b, c = (
+        Point2D(0, 0), Point2D(1, 0), Point2D(S.Half, sqrt(3)/2))
+    ans = {_ordered_points((i, j))
+        for i, j in subsets((a, b, c), 2)}
+    assert closest_points(b, c, a) == ans
+    assert farthest_points(b, c, a) == ans
+
+    # unique to farthest
+    points = [(1, 1), (1, 2), (3, 1), (-5, 2), (15, 4)]
+    assert farthest_points(*points) == {
+        (Point2D(-5, 2), Point2D(15, 4))}
+    points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)]
+    assert farthest_points(*points) == {
+        (Point2D(-5, -2), Point2D(15, -4))}
+    assert farthest_points((1, 1), (0, 0)) == {
+        (Point2D(0, 0), Point2D(1, 1))}
+    raises(ValueError, lambda: farthest_points((1, 1)))
+
+
+def test_are_coplanar():
+    a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
+    b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
+    c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))
+    d = Line(Point2D(0, 3), Point2D(1, 5))
+
+    assert are_coplanar(a, b, c) == False
+    assert are_coplanar(a, d) == False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/util.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/util.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d8fb77550f2faea8185ff0c373b5f1680e623ec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/geometry/util.py
@@ -0,0 +1,731 @@
+"""Utility functions for geometrical entities.
+
+Contains
+========
+intersection
+convex_hull
+closest_points
+farthest_points
+are_coplanar
+are_similar
+
+"""
+
+from collections import deque
+from math import sqrt as _sqrt
+
+from sympy import nsimplify
+from .entity import GeometryEntity
+from .exceptions import GeometryError
+from .point import Point, Point2D, Point3D
+from sympy.core.containers import OrderedSet
+from sympy.core.exprtools import factor_terms
+from sympy.core.function import Function, expand_mul
+from sympy.core.numbers import Float
+from sympy.core.sorting import ordered
+from sympy.core.symbol import Symbol
+from sympy.core.singleton import S
+from sympy.polys.polytools import cancel
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.utilities.iterables import is_sequence
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+
+def find(x, equation):
+    """
+    Checks whether a Symbol matching ``x`` is present in ``equation``
+    or not. If present, the matching symbol is returned, else a
+    ValueError is raised. If ``x`` is a string the matching symbol
+    will have the same name; if ``x`` is a Symbol then it will be
+    returned if found.
+
+    Examples
+    ========
+
+    >>> from sympy.geometry.util import find
+    >>> from sympy import Dummy
+    >>> from sympy.abc import x
+    >>> find('x', x)
+    x
+    >>> find('x', Dummy('x'))
+    _x
+
+    The dummy symbol is returned since it has a matching name:
+
+    >>> _.name == 'x'
+    True
+    >>> find(x, Dummy('x'))
+    Traceback (most recent call last):
+    ...
+    ValueError: could not find x
+    """
+
+    free = equation.free_symbols
+    xs = [i for i in free if (i.name if isinstance(x, str) else i) == x]
+    if not xs:
+        raise ValueError('could not find %s' % x)
+    if len(xs) != 1:
+        raise ValueError('ambiguous %s' % x)
+    return xs[0]
+
+
+def _ordered_points(p):
+    """Return the tuple of points sorted numerically according to args"""
+    return tuple(sorted(p, key=lambda x: x.args))
+
+
+def are_coplanar(*e):
+    """ Returns True if the given entities are coplanar otherwise False
+
+    Parameters
+    ==========
+
+    e: entities to be checked for being coplanar
+
+    Returns
+    =======
+
+    Boolean
+
+    Examples
+    ========
+
+    >>> from sympy import Point3D, Line3D
+    >>> from sympy.geometry.util import are_coplanar
+    >>> a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
+    >>> b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
+    >>> c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))
+    >>> are_coplanar(a, b, c)
+    False
+
+    """
+    from .line import LinearEntity3D
+    from .plane import Plane
+    # XXX update tests for coverage
+
+    e = set(e)
+    # first work with a Plane if present
+    for i in list(e):
+        if isinstance(i, Plane):
+            e.remove(i)
+            return all(p.is_coplanar(i) for p in e)
+
+    if all(isinstance(i, Point3D) for i in e):
+        if len(e) < 3:
+            return False
+
+        # remove pts that are collinear with 2 pts
+        a, b = e.pop(), e.pop()
+        for i in list(e):
+            if Point3D.are_collinear(a, b, i):
+                e.remove(i)
+
+        if not e:
+            return False
+        else:
+            # define a plane
+            p = Plane(a, b, e.pop())
+            for i in e:
+                if i not in p:
+                    return False
+            return True
+    else:
+        pt3d = []
+        for i in e:
+            if isinstance(i, Point3D):
+                pt3d.append(i)
+            elif isinstance(i, LinearEntity3D):
+                pt3d.extend(i.args)
+            elif isinstance(i, GeometryEntity):  # XXX we should have a GeometryEntity3D class so we can tell the difference between 2D and 3D -- here we just want to deal with 2D objects; if new 3D objects are encountered that we didn't handle above, an error should be raised
+                # all 2D objects have some Point that defines them; so convert those points to 3D pts by making z=0
+                for p in i.args:
+                    if isinstance(p, Point):
+                        pt3d.append(Point3D(*(p.args + (0,))))
+        return are_coplanar(*pt3d)
+
+
+def are_similar(e1, e2):
+    """Are two geometrical entities similar.
+
+    Can one geometrical entity be uniformly scaled to the other?
+
+    Parameters
+    ==========
+
+    e1 : GeometryEntity
+    e2 : GeometryEntity
+
+    Returns
+    =======
+
+    are_similar : boolean
+
+    Raises
+    ======
+
+    GeometryError
+        When `e1` and `e2` cannot be compared.
+
+    Notes
+    =====
+
+    If the two objects are equal then they are similar.
+
+    See Also
+    ========
+
+    sympy.geometry.entity.GeometryEntity.is_similar
+
+    Examples
+    ========
+
+    >>> from sympy import Point, Circle, Triangle, are_similar
+    >>> c1, c2 = Circle(Point(0, 0), 4), Circle(Point(1, 4), 3)
+    >>> t1 = Triangle(Point(0, 0), Point(1, 0), Point(0, 1))
+    >>> t2 = Triangle(Point(0, 0), Point(2, 0), Point(0, 2))
+    >>> t3 = Triangle(Point(0, 0), Point(3, 0), Point(0, 1))
+    >>> are_similar(t1, t2)
+    True
+    >>> are_similar(t1, t3)
+    False
+
+    """
+    if e1 == e2:
+        return True
+    is_similar1 = getattr(e1, 'is_similar', None)
+    if is_similar1:
+        return is_similar1(e2)
+    is_similar2 = getattr(e2, 'is_similar', None)
+    if is_similar2:
+        return is_similar2(e1)
+    n1 = e1.__class__.__name__
+    n2 = e2.__class__.__name__
+    raise GeometryError(
+        "Cannot test similarity between %s and %s" % (n1, n2))
+
+
+def centroid(*args):
+    """Find the centroid (center of mass) of the collection containing only Points,
+    Segments or Polygons. The centroid is the weighted average of the individual centroid
+    where the weights are the lengths (of segments) or areas (of polygons).
+    Overlapping regions will add to the weight of that region.
+
+    If there are no objects (or a mixture of objects) then None is returned.
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, sympy.geometry.line.Segment,
+    sympy.geometry.polygon.Polygon
+
+    Examples
+    ========
+
+    >>> from sympy import Point, Segment, Polygon
+    >>> from sympy.geometry.util import centroid
+    >>> p = Polygon((0, 0), (10, 0), (10, 10))
+    >>> q = p.translate(0, 20)
+    >>> p.centroid, q.centroid
+    (Point2D(20/3, 10/3), Point2D(20/3, 70/3))
+    >>> centroid(p, q)
+    Point2D(20/3, 40/3)
+    >>> p, q = Segment((0, 0), (2, 0)), Segment((0, 0), (2, 2))
+    >>> centroid(p, q)
+    Point2D(1, 2 - sqrt(2))
+    >>> centroid(Point(0, 0), Point(2, 0))
+    Point2D(1, 0)
+
+    Stacking 3 polygons on top of each other effectively triples the
+    weight of that polygon:
+
+    >>> p = Polygon((0, 0), (1, 0), (1, 1), (0, 1))
+    >>> q = Polygon((1, 0), (3, 0), (3, 1), (1, 1))
+    >>> centroid(p, q)
+    Point2D(3/2, 1/2)
+    >>> centroid(p, p, p, q) # centroid x-coord shifts left
+    Point2D(11/10, 1/2)
+
+    Stacking the squares vertically above and below p has the same
+    effect:
+
+    >>> centroid(p, p.translate(0, 1), p.translate(0, -1), q)
+    Point2D(11/10, 1/2)
+
+    """
+    from .line import Segment
+    from .polygon import Polygon
+    if args:
+        if all(isinstance(g, Point) for g in args):
+            c = Point(0, 0)
+            for g in args:
+                c += g
+            den = len(args)
+        elif all(isinstance(g, Segment) for g in args):
+            c = Point(0, 0)
+            L = 0
+            for g in args:
+                l = g.length
+                c += g.midpoint*l
+                L += l
+            den = L
+        elif all(isinstance(g, Polygon) for g in args):
+            c = Point(0, 0)
+            A = 0
+            for g in args:
+                a = g.area
+                c += g.centroid*a
+                A += a
+            den = A
+        c /= den
+        return c.func(*[i.simplify() for i in c.args])
+
+
+def closest_points(*args):
+    """Return the subset of points from a set of points that were
+    the closest to each other in the 2D plane.
+
+    Parameters
+    ==========
+
+    args
+        A collection of Points on 2D plane.
+
+    Notes
+    =====
+
+    This can only be performed on a set of points whose coordinates can
+    be ordered on the number line. If there are no ties then a single
+    pair of Points will be in the set.
+
+    Examples
+    ========
+
+    >>> from sympy import closest_points, Triangle
+    >>> Triangle(sss=(3, 4, 5)).args
+    (Point2D(0, 0), Point2D(3, 0), Point2D(3, 4))
+    >>> closest_points(*_)
+    {(Point2D(0, 0), Point2D(3, 0))}
+
+    References
+    ==========
+
+    .. [1] https://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairPS.html
+
+    .. [2] Sweep line algorithm
+        https://en.wikipedia.org/wiki/Sweep_line_algorithm
+
+    """
+    p = [Point2D(i) for i in set(args)]
+    if len(p) < 2:
+        raise ValueError('At least 2 distinct points must be given.')
+
+    try:
+        p.sort(key=lambda x: x.args)
+    except TypeError:
+        raise ValueError("The points could not be sorted.")
+
+    if not all(i.is_Rational for j in p for i in j.args):
+        def hypot(x, y):
+            arg = x*x + y*y
+            if arg.is_Rational:
+                return _sqrt(arg)
+            return sqrt(arg)
+    else:
+        from math import hypot
+
+    rv = [(0, 1)]
+    best_dist = hypot(p[1].x - p[0].x, p[1].y - p[0].y)
+    left = 0
+    box = deque([0, 1])
+    for i in range(2, len(p)):
+        while left < i and p[i][0] - p[left][0] > best_dist:
+            box.popleft()
+            left += 1
+
+        for j in box:
+            d = hypot(p[i].x - p[j].x, p[i].y - p[j].y)
+            if d < best_dist:
+                rv = [(j, i)]
+            elif d == best_dist:
+                rv.append((j, i))
+            else:
+                continue
+            best_dist = d
+        box.append(i)
+
+    return {tuple([p[i] for i in pair]) for pair in rv}
+
+
+def convex_hull(*args, polygon=True):
+    """The convex hull surrounding the Points contained in the list of entities.
+
+    Parameters
+    ==========
+
+    args : a collection of Points, Segments and/or Polygons
+
+    Optional parameters
+    ===================
+
+    polygon : Boolean. If True, returns a Polygon, if false a tuple, see below.
+              Default is True.
+
+    Returns
+    =======
+
+    convex_hull : Polygon if ``polygon`` is True else as a tuple `(U, L)` where
+                  ``L`` and ``U`` are the lower and upper hulls, respectively.
+
+    Notes
+    =====
+
+    This can only be performed on a set of points whose coordinates can
+    be ordered on the number line.
+
+    See Also
+    ========
+
+    sympy.geometry.point.Point, sympy.geometry.polygon.Polygon
+
+    Examples
+    ========
+
+    >>> from sympy import convex_hull
+    >>> points = [(1, 1), (1, 2), (3, 1), (-5, 2), (15, 4)]
+    >>> convex_hull(*points)
+    Polygon(Point2D(-5, 2), Point2D(1, 1), Point2D(3, 1), Point2D(15, 4))
+    >>> convex_hull(*points, **dict(polygon=False))
+    ([Point2D(-5, 2), Point2D(15, 4)],
+     [Point2D(-5, 2), Point2D(1, 1), Point2D(3, 1), Point2D(15, 4)])
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Graham_scan
+
+    .. [2] Andrew's Monotone Chain Algorithm
+      (A.M. Andrew,
+      "Another Efficient Algorithm for Convex Hulls in Two Dimensions", 1979)
+      https://web.archive.org/web/20210511015444/http://geomalgorithms.com/a10-_hull-1.html
+
+    """
+    from .line import Segment
+    from .polygon import Polygon
+    p = OrderedSet()
+    for e in args:
+        if not isinstance(e, GeometryEntity):
+            try:
+                e = Point(e)
+            except NotImplementedError:
+                raise ValueError('%s is not a GeometryEntity and cannot be made into Point' % str(e))
+        if isinstance(e, Point):
+            p.add(e)
+        elif isinstance(e, Segment):
+            p.update(e.points)
+        elif isinstance(e, Polygon):
+            p.update(e.vertices)
+        else:
+            raise NotImplementedError(
+                'Convex hull for %s not implemented.' % type(e))
+
+    # make sure all our points are of the same dimension
+    if any(len(x) != 2 for x in p):
+        raise ValueError('Can only compute the convex hull in two dimensions')
+
+    p = list(p)
+    if len(p) == 1:
+        return p[0] if polygon else (p[0], None)
+    elif len(p) == 2:
+        s = Segment(p[0], p[1])
+        return s if polygon else (s, None)
+
+    def _orientation(p, q, r):
+        '''Return positive if p-q-r are clockwise, neg if ccw, zero if
+        collinear.'''
+        return (q.y - p.y)*(r.x - p.x) - (q.x - p.x)*(r.y - p.y)
+
+    # scan to find upper and lower convex hulls of a set of 2d points.
+    U = []
+    L = []
+    try:
+        p.sort(key=lambda x: x.args)
+    except TypeError:
+        raise ValueError("The points could not be sorted.")
+    for p_i in p:
+        while len(U) > 1 and _orientation(U[-2], U[-1], p_i) <= 0:
+            U.pop()
+        while len(L) > 1 and _orientation(L[-2], L[-1], p_i) >= 0:
+            L.pop()
+        U.append(p_i)
+        L.append(p_i)
+    U.reverse()
+    convexHull = tuple(L + U[1:-1])
+
+    if len(convexHull) == 2:
+        s = Segment(convexHull[0], convexHull[1])
+        return s if polygon else (s, None)
+    if polygon:
+        return Polygon(*convexHull)
+    else:
+        U.reverse()
+        return (U, L)
+
+def farthest_points(*args):
+    """Return the subset of points from a set of points that were
+    the furthest apart from each other in the 2D plane.
+
+    Parameters
+    ==========
+
+    args
+        A collection of Points on 2D plane.
+
+    Notes
+    =====
+
+    This can only be performed on a set of points whose coordinates can
+    be ordered on the number line. If there are no ties then a single
+    pair of Points will be in the set.
+
+    Examples
+    ========
+
+    >>> from sympy.geometry import farthest_points, Triangle
+    >>> Triangle(sss=(3, 4, 5)).args
+    (Point2D(0, 0), Point2D(3, 0), Point2D(3, 4))
+    >>> farthest_points(*_)
+    {(Point2D(0, 0), Point2D(3, 4))}
+
+    References
+    ==========
+
+    .. [1] https://code.activestate.com/recipes/117225-convex-hull-and-diameter-of-2d-point-sets/
+
+    .. [2] Rotating Callipers Technique
+        https://en.wikipedia.org/wiki/Rotating_calipers
+
+    """
+
+    def rotatingCalipers(Points):
+        U, L = convex_hull(*Points, **{"polygon": False})
+
+        if L is None:
+            if isinstance(U, Point):
+                raise ValueError('At least two distinct points must be given.')
+            yield U.args
+        else:
+            i = 0
+            j = len(L) - 1
+            while i < len(U) - 1 or j > 0:
+                yield U[i], L[j]
+                # if all the way through one side of hull, advance the other side
+                if i == len(U) - 1:
+                    j -= 1
+                elif j == 0:
+                    i += 1
+                # still points left on both lists, compare slopes of next hull edges
+                # being careful to avoid divide-by-zero in slope calculation
+                elif (U[i+1].y - U[i].y) * (L[j].x - L[j-1].x) > \
+                        (L[j].y - L[j-1].y) * (U[i+1].x - U[i].x):
+                    i += 1
+                else:
+                    j -= 1
+
+    p = [Point2D(i) for i in set(args)]
+
+    if not all(i.is_Rational for j in p for i in j.args):
+        def hypot(x, y):
+            arg = x*x + y*y
+            if arg.is_Rational:
+                return _sqrt(arg)
+            return sqrt(arg)
+    else:
+        from math import hypot
+
+    rv = []
+    diam = 0
+    for pair in rotatingCalipers(args):
+        h, q = _ordered_points(pair)
+        d = hypot(h.x - q.x, h.y - q.y)
+        if d > diam:
+            rv = [(h, q)]
+        elif d == diam:
+            rv.append((h, q))
+        else:
+            continue
+        diam = d
+
+    return set(rv)
+
+
+def idiff(eq, y, x, n=1):
+    """Return ``dy/dx`` assuming that ``eq == 0``.
+
+    Parameters
+    ==========
+
+    y : the dependent variable or a list of dependent variables (with y first)
+    x : the variable that the derivative is being taken with respect to
+    n : the order of the derivative (default is 1)
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y, a
+    >>> from sympy.geometry.util import idiff
+
+    >>> circ = x**2 + y**2 - 4
+    >>> idiff(circ, y, x)
+    -x/y
+    >>> idiff(circ, y, x, 2).simplify()
+    (-x**2 - y**2)/y**3
+
+    Here, ``a`` is assumed to be independent of ``x``:
+
+    >>> idiff(x + a + y, y, x)
+    -1
+
+    Now the x-dependence of ``a`` is made explicit by listing ``a`` after
+    ``y`` in a list.
+
+    >>> idiff(x + a + y, [y, a], x)
+    -Derivative(a, x) - 1
+
+    See Also
+    ========
+
+    sympy.core.function.Derivative: represents unevaluated derivatives
+    sympy.core.function.diff: explicitly differentiates wrt symbols
+
+    """
+    if is_sequence(y):
+        dep = set(y)
+        y = y[0]
+    elif isinstance(y, Symbol):
+        dep = {y}
+    elif isinstance(y, Function):
+        pass
+    else:
+        raise ValueError("expecting x-dependent symbol(s) or function(s) but got: %s" % y)
+
+    f = {s: Function(s.name)(x) for s in eq.free_symbols
+        if s != x and s in dep}
+
+    if isinstance(y, Symbol):
+        dydx = Function(y.name)(x).diff(x)
+    else:
+        dydx = y.diff(x)
+
+    eq = eq.subs(f)
+    derivs = {}
+    for i in range(n):
+        # equation will be linear in dydx, a*dydx + b, so dydx = -b/a
+        deq = eq.diff(x)
+        b = deq.xreplace({dydx: S.Zero})
+        a = (deq - b).xreplace({dydx: S.One})
+        yp = factor_terms(expand_mul(cancel((-b/a).subs(derivs)), deep=False))
+        if i == n - 1:
+            return yp.subs([(v, k) for k, v in f.items()])
+        derivs[dydx] = yp
+        eq = dydx - yp
+        dydx = dydx.diff(x)
+
+
+def intersection(*entities, pairwise=False, **kwargs):
+    """The intersection of a collection of GeometryEntity instances.
+
+    Parameters
+    ==========
+    entities : sequence of GeometryEntity
+    pairwise (keyword argument) : Can be either True or False
+
+    Returns
+    =======
+    intersection : list of GeometryEntity
+
+    Raises
+    ======
+    NotImplementedError
+        When unable to calculate intersection.
+
+    Notes
+    =====
+    The intersection of any geometrical entity with itself should return
+    a list with one item: the entity in question.
+    An intersection requires two or more entities. If only a single
+    entity is given then the function will return an empty list.
+    It is possible for `intersection` to miss intersections that one
+    knows exists because the required quantities were not fully
+    simplified internally.
+    Reals should be converted to Rationals, e.g. Rational(str(real_num))
+    or else failures due to floating point issues may result.
+
+    Case 1: When the keyword argument 'pairwise' is False (default value):
+    In this case, the function returns a list of intersections common to
+    all entities.
+
+    Case 2: When the keyword argument 'pairwise' is True:
+    In this case, the functions returns a list intersections that occur
+    between any pair of entities.
+
+    See Also
+    ========
+
+    sympy.geometry.entity.GeometryEntity.intersection
+
+    Examples
+    ========
+
+    >>> from sympy import Ray, Circle, intersection
+    >>> c = Circle((0, 1), 1)
+    >>> intersection(c, c.center)
+    []
+    >>> right = Ray((0, 0), (1, 0))
+    >>> up = Ray((0, 0), (0, 1))
+    >>> intersection(c, right, up)
+    [Point2D(0, 0)]
+    >>> intersection(c, right, up, pairwise=True)
+    [Point2D(0, 0), Point2D(0, 2)]
+    >>> left = Ray((1, 0), (0, 0))
+    >>> intersection(right, left)
+    [Segment2D(Point2D(0, 0), Point2D(1, 0))]
+
+    """
+    if len(entities) <= 1:
+        return []
+
+    entities = list(entities)
+    prec = None
+    for i, e in enumerate(entities):
+        if not isinstance(e, GeometryEntity):
+            # entities may be an immutable tuple
+            e = Point(e)
+        # convert to exact Rationals
+        d = {}
+        for f in e.atoms(Float):
+            prec = f._prec if prec is None else min(f._prec, prec)
+            d.setdefault(f, nsimplify(f, rational=True))
+        entities[i] = e.xreplace(d)
+
+    if not pairwise:
+        # find the intersection common to all objects
+        res = entities[0].intersection(entities[1])
+        for entity in entities[2:]:
+            newres = []
+            for x in res:
+                newres.extend(x.intersection(entity))
+            res = newres
+    else:
+        # find all pairwise intersections
+        ans = []
+        for j in range(len(entities)):
+            for k in range(j + 1, len(entities)):
+                ans.extend(intersection(entities[j], entities[k]))
+        res = list(ordered(set(ans)))
+
+    # convert back to Floats
+    if prec is not None:
+        p = prec_to_dps(prec)
+        res = [i.n(p) for i in res]
+    return res
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..45412acad0ab9e5c7424b1888648a638ef208142
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/__init__.py
@@ -0,0 +1,18 @@
+r"""
+The :py:mod:`~sympy.holonomic` module is intended to deal with holonomic functions along
+with various operations on them like addition, multiplication, composition,
+integration and differentiation. The module also implements various kinds of
+conversions such as converting holonomic functions to a different form and the
+other way around.
+"""
+
+from .holonomic import (DifferentialOperator, HolonomicFunction, DifferentialOperators,
+    from_hyper, from_meijerg, expr_to_holonomic)
+from .recurrence import RecurrenceOperators, RecurrenceOperator, HolonomicSequence
+
+__all__ = [
+    'DifferentialOperator', 'HolonomicFunction', 'DifferentialOperators',
+    'from_hyper', 'from_meijerg', 'expr_to_holonomic',
+
+    'RecurrenceOperators', 'RecurrenceOperator', 'HolonomicSequence',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/holonomic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/holonomic.py
new file mode 100644
index 0000000000000000000000000000000000000000..e31c4d4511d4c07aa4049a62253cdb060758cf3d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/holonomic.py
@@ -0,0 +1,2765 @@
+"""
+This module implements Holonomic Functions and
+various operations on them.
+"""
+
+from sympy.core import Add, Mul, Pow
+from sympy.core.numbers import (NaN, Infinity, NegativeInfinity, Float, I, pi,
+        equal_valued, int_valued)
+from sympy.core.singleton import S
+from sympy.core.sorting import ordered
+from sympy.core.symbol import Dummy, Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import binomial, factorial, rf
+from sympy.functions.elementary.exponential import exp_polar, exp, log
+from sympy.functions.elementary.hyperbolic import (cosh, sinh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc)
+from sympy.functions.special.error_functions import (Ci, Shi, Si, erf, erfc, erfi)
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import hyper, meijerg
+from sympy.integrals import meijerint
+from sympy.matrices import Matrix
+from sympy.polys.rings import PolyElement
+from sympy.polys.fields import FracElement
+from sympy.polys.domains import QQ, RR
+from sympy.polys.polyclasses import DMF
+from sympy.polys.polyroots import roots
+from sympy.polys.polytools import Poly
+from sympy.polys.matrices import DomainMatrix
+from sympy.printing import sstr
+from sympy.series.limits import limit
+from sympy.series.order import Order
+from sympy.simplify.hyperexpand import hyperexpand
+from sympy.simplify.simplify import nsimplify
+from sympy.solvers.solvers import solve
+
+from .recurrence import HolonomicSequence, RecurrenceOperator, RecurrenceOperators
+from .holonomicerrors import (NotPowerSeriesError, NotHyperSeriesError,
+    SingularityError, NotHolonomicError)
+
+
+def _find_nonzero_solution(r, homosys):
+    ones = lambda shape: DomainMatrix.ones(shape, r.domain)
+    particular, nullspace = r._solve(homosys)
+    nullity = nullspace.shape[0]
+    nullpart = ones((1, nullity)) * nullspace
+    sol = (particular + nullpart).transpose()
+    return sol
+
+
+
+def DifferentialOperators(base, generator):
+    r"""
+    This function is used to create annihilators using ``Dx``.
+
+    Explanation
+    ===========
+
+    Returns an Algebra of Differential Operators also called Weyl Algebra
+    and the operator for differentiation i.e. the ``Dx`` operator.
+
+    Parameters
+    ==========
+
+    base:
+        Base polynomial ring for the algebra.
+        The base polynomial ring is the ring of polynomials in :math:`x` that
+        will appear as coefficients in the operators.
+    generator:
+        Generator of the algebra which can
+        be either a noncommutative ``Symbol`` or a string. e.g. "Dx" or "D".
+
+    Examples
+    ========
+
+    >>> from sympy import ZZ
+    >>> from sympy.abc import x
+    >>> from sympy.holonomic.holonomic import DifferentialOperators
+    >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    >>> R
+    Univariate Differential Operator Algebra in intermediate Dx over the base ring ZZ[x]
+    >>> Dx*x
+    (1) + (x)*Dx
+    """
+
+    ring = DifferentialOperatorAlgebra(base, generator)
+    return (ring, ring.derivative_operator)
+
+
+class DifferentialOperatorAlgebra:
+    r"""
+    An Ore Algebra is a set of noncommutative polynomials in the
+    intermediate ``Dx`` and coefficients in a base polynomial ring :math:`A`.
+    It follows the commutation rule:
+
+    .. math ::
+       Dxa = \sigma(a)Dx + \delta(a)
+
+    for :math:`a \subset A`.
+
+    Where :math:`\sigma: A \Rightarrow A` is an endomorphism and :math:`\delta: A \rightarrow A`
+    is a skew-derivation i.e. :math:`\delta(ab) = \delta(a) b + \sigma(a) \delta(b)`.
+
+    If one takes the sigma as identity map and delta as the standard derivation
+    then it becomes the algebra of Differential Operators also called
+    a Weyl Algebra i.e. an algebra whose elements are Differential Operators.
+
+    This class represents a Weyl Algebra and serves as the parent ring for
+    Differential Operators.
+
+    Examples
+    ========
+
+    >>> from sympy import ZZ
+    >>> from sympy import symbols
+    >>> from sympy.holonomic.holonomic import DifferentialOperators
+    >>> x = symbols('x')
+    >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    >>> R
+    Univariate Differential Operator Algebra in intermediate Dx over the base ring
+    ZZ[x]
+
+    See Also
+    ========
+
+    DifferentialOperator
+    """
+
+    def __init__(self, base, generator):
+        # the base polynomial ring for the algebra
+        self.base = base
+        # the operator representing differentiation i.e. `Dx`
+        self.derivative_operator = DifferentialOperator(
+            [base.zero, base.one], self)
+
+        if generator is None:
+            self.gen_symbol = Symbol('Dx', commutative=False)
+        else:
+            if isinstance(generator, str):
+                self.gen_symbol = Symbol(generator, commutative=False)
+            elif isinstance(generator, Symbol):
+                self.gen_symbol = generator
+
+    def __str__(self):
+        string = 'Univariate Differential Operator Algebra in intermediate '\
+            + sstr(self.gen_symbol) + ' over the base ring ' + \
+            (self.base).__str__()
+
+        return string
+
+    __repr__ = __str__
+
+    def __eq__(self, other):
+        return self.base == other.base and \
+               self.gen_symbol == other.gen_symbol
+
+
+class DifferentialOperator:
+    """
+    Differential Operators are elements of Weyl Algebra. The Operators
+    are defined by a list of polynomials in the base ring and the
+    parent ring of the Operator i.e. the algebra it belongs to.
+
+    Explanation
+    ===========
+
+    Takes a list of polynomials for each power of ``Dx`` and the
+    parent ring which must be an instance of DifferentialOperatorAlgebra.
+
+    A Differential Operator can be created easily using
+    the operator ``Dx``. See examples below.
+
+    Examples
+    ========
+
+    >>> from sympy.holonomic.holonomic import DifferentialOperator, DifferentialOperators
+    >>> from sympy import ZZ
+    >>> from sympy import symbols
+    >>> x = symbols('x')
+    >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx')
+
+    >>> DifferentialOperator([0, 1, x**2], R)
+    (1)*Dx + (x**2)*Dx**2
+
+    >>> (x*Dx*x + 1 - Dx**2)**2
+    (2*x**2 + 2*x + 1) + (4*x**3 + 2*x**2 - 4)*Dx + (x**4 - 6*x - 2)*Dx**2 + (-2*x**2)*Dx**3 + (1)*Dx**4
+
+    See Also
+    ========
+
+    DifferentialOperatorAlgebra
+    """
+
+    _op_priority = 20
+
+    def __init__(self, list_of_poly, parent):
+        """
+        Parameters
+        ==========
+
+        list_of_poly:
+            List of polynomials belonging to the base ring of the algebra.
+        parent:
+            Parent algebra of the operator.
+        """
+
+        # the parent ring for this operator
+        # must be an DifferentialOperatorAlgebra object
+        self.parent = parent
+        base = self.parent.base
+        self.x = base.gens[0] if isinstance(base.gens[0], Symbol) else base.gens[0][0]
+        # sequence of polynomials in x for each power of Dx
+        # the list should not have trailing zeroes
+        # represents the operator
+        # convert the expressions into ring elements using from_sympy
+        for i, j in enumerate(list_of_poly):
+            if not isinstance(j, base.dtype):
+                list_of_poly[i] = base.from_sympy(sympify(j))
+            else:
+                list_of_poly[i] = base.from_sympy(base.to_sympy(j))
+
+        self.listofpoly = list_of_poly
+        # highest power of `Dx`
+        self.order = len(self.listofpoly) - 1
+
+    def __mul__(self, other):
+        """
+        Multiplies two DifferentialOperator and returns another
+        DifferentialOperator instance using the commutation rule
+        Dx*a = a*Dx + a'
+        """
+
+        listofself = self.listofpoly
+        if isinstance(other, DifferentialOperator):
+            listofother = other.listofpoly
+        elif isinstance(other, self.parent.base.dtype):
+            listofother = [other]
+        else:
+            listofother = [self.parent.base.from_sympy(sympify(other))]
+
+        # multiplies a polynomial `b` with a list of polynomials
+        def _mul_dmp_diffop(b, listofother):
+            if isinstance(listofother, list):
+                return [i * b for i in listofother]
+            return [b * listofother]
+
+        sol = _mul_dmp_diffop(listofself[0], listofother)
+
+        # compute Dx^i * b
+        def _mul_Dxi_b(b):
+            sol1 = [self.parent.base.zero]
+            sol2 = []
+
+            if isinstance(b, list):
+                for i in b:
+                    sol1.append(i)
+                    sol2.append(i.diff())
+            else:
+                sol1.append(self.parent.base.from_sympy(b))
+                sol2.append(self.parent.base.from_sympy(b).diff())
+
+            return _add_lists(sol1, sol2)
+
+        for i in range(1, len(listofself)):
+            # find Dx^i * b in ith iteration
+            listofother = _mul_Dxi_b(listofother)
+            # solution = solution + listofself[i] * (Dx^i * b)
+            sol = _add_lists(sol, _mul_dmp_diffop(listofself[i], listofother))
+
+        return DifferentialOperator(sol, self.parent)
+
+    def __rmul__(self, other):
+        if not isinstance(other, DifferentialOperator):
+
+            if not isinstance(other, self.parent.base.dtype):
+                other = (self.parent.base).from_sympy(sympify(other))
+
+            sol = [other * j for j in self.listofpoly]
+            return DifferentialOperator(sol, self.parent)
+
+    def __add__(self, other):
+        if isinstance(other, DifferentialOperator):
+
+            sol = _add_lists(self.listofpoly, other.listofpoly)
+            return DifferentialOperator(sol, self.parent)
+
+        list_self = self.listofpoly
+        if not isinstance(other, self.parent.base.dtype):
+            list_other = [((self.parent).base).from_sympy(sympify(other))]
+        else:
+            list_other = [other]
+        sol = [list_self[0] + list_other[0]] + list_self[1:]
+        return DifferentialOperator(sol, self.parent)
+
+    __radd__ = __add__
+
+    def __sub__(self, other):
+        return self + (-1) * other
+
+    def __rsub__(self, other):
+        return (-1) * self + other
+
+    def __neg__(self):
+        return -1 * self
+
+    def __truediv__(self, other):
+        return self * (S.One / other)
+
+    def __pow__(self, n):
+        if n == 1:
+            return self
+        result = DifferentialOperator([self.parent.base.one], self.parent)
+        if n == 0:
+            return result
+        # if self is `Dx`
+        if self.listofpoly == self.parent.derivative_operator.listofpoly:
+            sol = [self.parent.base.zero]*n + [self.parent.base.one]
+            return DifferentialOperator(sol, self.parent)
+        x = self
+        while True:
+            if n % 2:
+                result *= x
+            n >>= 1
+            if not n:
+                break
+            x *= x
+        return result
+
+    def __str__(self):
+        listofpoly = self.listofpoly
+        print_str = ''
+
+        for i, j in enumerate(listofpoly):
+            if j == self.parent.base.zero:
+                continue
+
+            j = self.parent.base.to_sympy(j)
+
+            if i == 0:
+                print_str += '(' + sstr(j) + ')'
+                continue
+
+            if print_str:
+                print_str += ' + '
+
+            if i == 1:
+                print_str += '(' + sstr(j) + ')*%s' %(self.parent.gen_symbol)
+                continue
+
+            print_str += '(' + sstr(j) + ')' + '*%s**' %(self.parent.gen_symbol) + sstr(i)
+
+        return print_str
+
+    __repr__ = __str__
+
+    def __eq__(self, other):
+        if isinstance(other, DifferentialOperator):
+            return self.listofpoly == other.listofpoly and \
+                   self.parent == other.parent
+        return self.listofpoly[0] == other and \
+            all(i is self.parent.base.zero for i in self.listofpoly[1:])
+
+    def is_singular(self, x0):
+        """
+        Checks if the differential equation is singular at x0.
+        """
+
+        base = self.parent.base
+        return x0 in roots(base.to_sympy(self.listofpoly[-1]), self.x)
+
+
+class HolonomicFunction:
+    r"""
+    A Holonomic Function is a solution to a linear homogeneous ordinary
+    differential equation with polynomial coefficients. This differential
+    equation can also be represented by an annihilator i.e. a Differential
+    Operator ``L`` such that :math:`L.f = 0`. For uniqueness of these functions,
+    initial conditions can also be provided along with the annihilator.
+
+    Explanation
+    ===========
+
+    Holonomic functions have closure properties and thus forms a ring.
+    Given two Holonomic Functions f and g, their sum, product,
+    integral and derivative is also a Holonomic Function.
+
+    For ordinary points initial condition should be a vector of values of
+    the derivatives i.e. :math:`[y(x_0), y'(x_0), y''(x_0) ... ]`.
+
+    For regular singular points initial conditions can also be provided in this
+    format:
+    :math:`{s0: [C_0, C_1, ...], s1: [C^1_0, C^1_1, ...], ...}`
+    where s0, s1, ... are the roots of indicial equation and vectors
+    :math:`[C_0, C_1, ...], [C^0_0, C^0_1, ...], ...` are the corresponding initial
+    terms of the associated power series. See Examples below.
+
+    Examples
+    ========
+
+    >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+    >>> from sympy import QQ
+    >>> from sympy import symbols, S
+    >>> x = symbols('x')
+    >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')
+
+    >>> p = HolonomicFunction(Dx - 1, x, 0, [1])  # e^x
+    >>> q = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])  # sin(x)
+
+    >>> p + q  # annihilator of e^x + sin(x)
+    HolonomicFunction((-1) + (1)*Dx + (-1)*Dx**2 + (1)*Dx**3, x, 0, [1, 2, 1])
+
+    >>> p * q  # annihilator of e^x * sin(x)
+    HolonomicFunction((2) + (-2)*Dx + (1)*Dx**2, x, 0, [0, 1])
+
+    An example of initial conditions for regular singular points,
+    the indicial equation has only one root `1/2`.
+
+    >>> HolonomicFunction(-S(1)/2 + x*Dx, x, 0, {S(1)/2: [1]})
+    HolonomicFunction((-1/2) + (x)*Dx, x, 0, {1/2: [1]})
+
+    >>> HolonomicFunction(-S(1)/2 + x*Dx, x, 0, {S(1)/2: [1]}).to_expr()
+    sqrt(x)
+
+    To plot a Holonomic Function, one can use `.evalf()` for numerical
+    computation. Here's an example on `sin(x)**2/x` using numpy and matplotlib.
+
+    >>> import sympy.holonomic # doctest: +SKIP
+    >>> from sympy import var, sin # doctest: +SKIP
+    >>> import matplotlib.pyplot as plt # doctest: +SKIP
+    >>> import numpy as np # doctest: +SKIP
+    >>> var("x") # doctest: +SKIP
+    >>> r = np.linspace(1, 5, 100) # doctest: +SKIP
+    >>> y = sympy.holonomic.expr_to_holonomic(sin(x)**2/x, x0=1).evalf(r) # doctest: +SKIP
+    >>> plt.plot(r, y, label="holonomic function") # doctest: +SKIP
+    >>> plt.show() # doctest: +SKIP
+
+    """
+
+    _op_priority = 20
+
+    def __init__(self, annihilator, x, x0=0, y0=None):
+        """
+
+        Parameters
+        ==========
+
+        annihilator:
+            Annihilator of the Holonomic Function, represented by a
+            `DifferentialOperator` object.
+        x:
+            Variable of the function.
+        x0:
+            The point at which initial conditions are stored.
+            Generally an integer.
+        y0:
+            The initial condition. The proper format for the initial condition
+            is described in class docstring. To make the function unique,
+            length of the vector `y0` should be equal to or greater than the
+            order of differential equation.
+        """
+
+        # initial condition
+        self.y0 = y0
+        # the point for initial conditions, default is zero.
+        self.x0 = x0
+        # differential operator L such that L.f = 0
+        self.annihilator = annihilator
+        self.x = x
+
+    def __str__(self):
+        if self._have_init_cond():
+            str_sol = 'HolonomicFunction(%s, %s, %s, %s)' % (str(self.annihilator),\
+                sstr(self.x), sstr(self.x0), sstr(self.y0))
+        else:
+            str_sol = 'HolonomicFunction(%s, %s)' % (str(self.annihilator),\
+                sstr(self.x))
+
+        return str_sol
+
+    __repr__ = __str__
+
+    def unify(self, other):
+        """
+        Unifies the base polynomial ring of a given two Holonomic
+        Functions.
+        """
+
+        R1 = self.annihilator.parent.base
+        R2 = other.annihilator.parent.base
+
+        dom1 = R1.dom
+        dom2 = R2.dom
+
+        if R1 == R2:
+            return (self, other)
+
+        R = (dom1.unify(dom2)).old_poly_ring(self.x)
+
+        newparent, _ = DifferentialOperators(R, str(self.annihilator.parent.gen_symbol))
+
+        sol1 = [R1.to_sympy(i) for i in self.annihilator.listofpoly]
+        sol2 = [R2.to_sympy(i) for i in other.annihilator.listofpoly]
+
+        sol1 = DifferentialOperator(sol1, newparent)
+        sol2 = DifferentialOperator(sol2, newparent)
+
+        sol1 = HolonomicFunction(sol1, self.x, self.x0, self.y0)
+        sol2 = HolonomicFunction(sol2, other.x, other.x0, other.y0)
+
+        return (sol1, sol2)
+
+    def is_singularics(self):
+        """
+        Returns True if the function have singular initial condition
+        in the dictionary format.
+
+        Returns False if the function have ordinary initial condition
+        in the list format.
+
+        Returns None for all other cases.
+        """
+
+        if isinstance(self.y0, dict):
+            return True
+        elif isinstance(self.y0, list):
+            return False
+
+    def _have_init_cond(self):
+        """
+        Checks if the function have initial condition.
+        """
+        return bool(self.y0)
+
+    def _singularics_to_ord(self):
+        """
+        Converts a singular initial condition to ordinary if possible.
+        """
+        a = list(self.y0)[0]
+        b = self.y0[a]
+
+        if len(self.y0) == 1 and a == int(a) and a > 0:
+            a = int(a)
+            y0 = [S.Zero] * a
+            y0 += [j * factorial(a + i) for i, j in enumerate(b)]
+
+            return HolonomicFunction(self.annihilator, self.x, self.x0, y0)
+
+    def __add__(self, other):
+        # if the ground domains are different
+        if self.annihilator.parent.base != other.annihilator.parent.base:
+            a, b = self.unify(other)
+            return a + b
+
+        deg1 = self.annihilator.order
+        deg2 = other.annihilator.order
+        dim = max(deg1, deg2)
+        R = self.annihilator.parent.base
+        K = R.get_field()
+
+        rowsself = [self.annihilator]
+        rowsother = [other.annihilator]
+        gen = self.annihilator.parent.derivative_operator
+
+        # constructing annihilators up to order dim
+        for i in range(dim - deg1):
+            diff1 = (gen * rowsself[-1])
+            rowsself.append(diff1)
+
+        for i in range(dim - deg2):
+            diff2 = (gen * rowsother[-1])
+            rowsother.append(diff2)
+
+        row = rowsself + rowsother
+
+        # constructing the matrix of the ansatz
+        r = []
+
+        for expr in row:
+            p = []
+            for i in range(dim + 1):
+                if i >= len(expr.listofpoly):
+                    p.append(K.zero)
+                else:
+                    p.append(K.new(expr.listofpoly[i].to_list()))
+            r.append(p)
+
+        # solving the linear system using gauss jordan solver
+        r = DomainMatrix(r, (len(row), dim+1), K).transpose()
+        homosys = DomainMatrix.zeros((dim+1, 1), K)
+        sol = _find_nonzero_solution(r, homosys)
+
+        # if a solution is not obtained then increasing the order by 1 in each
+        # iteration
+        while sol.is_zero_matrix:
+            dim += 1
+
+            diff1 = (gen * rowsself[-1])
+            rowsself.append(diff1)
+
+            diff2 = (gen * rowsother[-1])
+            rowsother.append(diff2)
+
+            row = rowsself + rowsother
+            r = []
+
+            for expr in row:
+                p = []
+                for i in range(dim + 1):
+                    if i >= len(expr.listofpoly):
+                        p.append(K.zero)
+                    else:
+                        p.append(K.new(expr.listofpoly[i].to_list()))
+                r.append(p)
+
+            # solving the linear system using gauss jordan solver
+            r = DomainMatrix(r, (len(row), dim+1), K).transpose()
+            homosys = DomainMatrix.zeros((dim+1, 1), K)
+            sol = _find_nonzero_solution(r, homosys)
+
+        # taking only the coefficients needed to multiply with `self`
+        # can be also be done the other way by taking R.H.S and multiplying with
+        # `other`
+        sol = sol.flat()[:dim + 1 - deg1]
+        sol1 = _normalize(sol, self.annihilator.parent)
+        # annihilator of the solution
+        sol = sol1 * (self.annihilator)
+        sol = _normalize(sol.listofpoly, self.annihilator.parent, negative=False)
+
+        if not (self._have_init_cond() and other._have_init_cond()):
+            return HolonomicFunction(sol, self.x)
+
+        # both the functions have ordinary initial conditions
+        if self.is_singularics() == False and other.is_singularics() == False:
+
+            # directly add the corresponding value
+            if self.x0 == other.x0:
+                # try to extended the initial conditions
+                # using the annihilator
+                y1 = _extend_y0(self, sol.order)
+                y2 = _extend_y0(other, sol.order)
+                y0 = [a + b for a, b in zip(y1, y2)]
+                return HolonomicFunction(sol, self.x, self.x0, y0)
+
+            # change the initial conditions to a same point
+            selfat0 = self.annihilator.is_singular(0)
+            otherat0 = other.annihilator.is_singular(0)
+            if self.x0 == 0 and not selfat0 and not otherat0:
+                return self + other.change_ics(0)
+            if other.x0 == 0 and not selfat0 and not otherat0:
+                return self.change_ics(0) + other
+
+            selfatx0 = self.annihilator.is_singular(self.x0)
+            otheratx0 = other.annihilator.is_singular(self.x0)
+            if not selfatx0 and not otheratx0:
+                return self + other.change_ics(self.x0)
+            return self.change_ics(other.x0) + other
+
+        if self.x0 != other.x0:
+            return HolonomicFunction(sol, self.x)
+
+        # if the functions have singular_ics
+        y1 = None
+        y2 = None
+
+        if self.is_singularics() == False and other.is_singularics() == True:
+            # convert the ordinary initial condition to singular.
+            _y0 = [j / factorial(i) for i, j in enumerate(self.y0)]
+            y1 = {S.Zero: _y0}
+            y2 = other.y0
+        elif self.is_singularics() == True and other.is_singularics() == False:
+            _y0 = [j / factorial(i) for i, j in enumerate(other.y0)]
+            y1 = self.y0
+            y2 = {S.Zero: _y0}
+        elif self.is_singularics() == True and other.is_singularics() == True:
+            y1 = self.y0
+            y2 = other.y0
+
+        # computing singular initial condition for the result
+        # taking union of the series terms of both functions
+        y0 = {}
+        for i in y1:
+            # add corresponding initial terms if the power
+            # on `x` is same
+            if i in y2:
+                y0[i] = [a + b for a, b in zip(y1[i], y2[i])]
+            else:
+                y0[i] = y1[i]
+        for i in y2:
+            if i not in y1:
+                y0[i] = y2[i]
+        return HolonomicFunction(sol, self.x, self.x0, y0)
+
+    def integrate(self, limits, initcond=False):
+        """
+        Integrates the given holonomic function.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import QQ
+        >>> from sympy import symbols
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')
+        >>> HolonomicFunction(Dx - 1, x, 0, [1]).integrate((x, 0, x))  # e^x - 1
+        HolonomicFunction((-1)*Dx + (1)*Dx**2, x, 0, [0, 1])
+        >>> HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]).integrate((x, 0, x))
+        HolonomicFunction((1)*Dx + (1)*Dx**3, x, 0, [0, 1, 0])
+        """
+
+        # to get the annihilator, just multiply by Dx from right
+        D = self.annihilator.parent.derivative_operator
+
+        # if the function have initial conditions of the series format
+        if self.is_singularics() == True:
+
+            r = self._singularics_to_ord()
+            if r:
+                return r.integrate(limits, initcond=initcond)
+
+            # computing singular initial condition for the function
+            # produced after integration.
+            y0 = {}
+            for i in self.y0:
+                c = self.y0[i]
+                c2 = []
+                for j, cj in enumerate(c):
+                    if cj == 0:
+                        c2.append(S.Zero)
+
+                    # if power on `x` is -1, the integration becomes log(x)
+                    # TODO: Implement this case
+                    elif i + j + 1 == 0:
+                        raise NotImplementedError("logarithmic terms in the series are not supported")
+                    else:
+                        c2.append(cj / S(i + j + 1))
+                y0[i + 1] = c2
+
+            if hasattr(limits, "__iter__"):
+                raise NotImplementedError("Definite integration for singular initial conditions")
+
+            return HolonomicFunction(self.annihilator * D, self.x, self.x0, y0)
+
+        # if no initial conditions are available for the function
+        if not self._have_init_cond():
+            if initcond:
+                return HolonomicFunction(self.annihilator * D, self.x, self.x0, [S.Zero])
+            return HolonomicFunction(self.annihilator * D, self.x)
+
+        # definite integral
+        # initial conditions for the answer will be stored at point `a`,
+        # where `a` is the lower limit of the integrand
+        if hasattr(limits, "__iter__"):
+
+            if len(limits) == 3 and limits[0] == self.x:
+                x0 = self.x0
+                a = limits[1]
+                b = limits[2]
+                definite = True
+
+        else:
+            definite = False
+
+        y0 = [S.Zero]
+        y0 += self.y0
+
+        indefinite_integral = HolonomicFunction(self.annihilator * D, self.x, self.x0, y0)
+
+        if not definite:
+            return indefinite_integral
+
+        # use evalf to get the values at `a`
+        if x0 != a:
+            try:
+                indefinite_expr = indefinite_integral.to_expr()
+            except (NotHyperSeriesError, NotPowerSeriesError):
+                indefinite_expr = None
+
+            if indefinite_expr:
+                lower = indefinite_expr.subs(self.x, a)
+                if isinstance(lower, NaN):
+                    lower = indefinite_expr.limit(self.x, a)
+            else:
+                lower = indefinite_integral.evalf(a)
+
+            if b == self.x:
+                y0[0] = y0[0] - lower
+                return HolonomicFunction(self.annihilator * D, self.x, x0, y0)
+
+            elif S(b).is_Number:
+                if indefinite_expr:
+                    upper = indefinite_expr.subs(self.x, b)
+                    if isinstance(upper, NaN):
+                        upper = indefinite_expr.limit(self.x, b)
+                else:
+                    upper = indefinite_integral.evalf(b)
+
+                return upper - lower
+
+
+        # if the upper limit is `x`, the answer will be a function
+        if b == self.x:
+            return HolonomicFunction(self.annihilator * D, self.x, a, y0)
+
+        # if the upper limits is a Number, a numerical value will be returned
+        elif S(b).is_Number:
+            try:
+                s = HolonomicFunction(self.annihilator * D, self.x, a,\
+                    y0).to_expr()
+                indefinite = s.subs(self.x, b)
+                if not isinstance(indefinite, NaN):
+                    return indefinite
+                else:
+                    return s.limit(self.x, b)
+            except (NotHyperSeriesError, NotPowerSeriesError):
+                return HolonomicFunction(self.annihilator * D, self.x, a, y0).evalf(b)
+
+        return HolonomicFunction(self.annihilator * D, self.x)
+
+    def diff(self, *args, **kwargs):
+        r"""
+        Differentiation of the given Holonomic function.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import ZZ
+        >>> from sympy import symbols
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx')
+        >>> HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).diff().to_expr()
+        cos(x)
+        >>> HolonomicFunction(Dx - 2, x, 0, [1]).diff().to_expr()
+        2*exp(2*x)
+
+        See Also
+        ========
+
+        integrate
+        """
+        kwargs.setdefault('evaluate', True)
+        if args:
+            if args[0] != self.x:
+                return S.Zero
+            elif len(args) == 2:
+                sol = self
+                for i in range(args[1]):
+                    sol = sol.diff(args[0])
+                return sol
+
+        ann = self.annihilator
+
+        # if the function is constant.
+        if ann.listofpoly[0] == ann.parent.base.zero and ann.order == 1:
+            return S.Zero
+
+        # if the coefficient of y in the differential equation is zero.
+        # a shifting is done to compute the answer in this case.
+        elif ann.listofpoly[0] == ann.parent.base.zero:
+
+            sol = DifferentialOperator(ann.listofpoly[1:], ann.parent)
+
+            if self._have_init_cond():
+                # if ordinary initial condition
+                if self.is_singularics() == False:
+                    return HolonomicFunction(sol, self.x, self.x0, self.y0[1:])
+                # TODO: support for singular initial condition
+                return HolonomicFunction(sol, self.x)
+            else:
+                return HolonomicFunction(sol, self.x)
+
+        # the general algorithm
+        R = ann.parent.base
+        K = R.get_field()
+
+        seq_dmf = [K.new(i.to_list()) for i in ann.listofpoly]
+
+        # -y = a1*y'/a0 + a2*y''/a0 ... + an*y^n/a0
+        rhs = [i / seq_dmf[0] for i in seq_dmf[1:]]
+        rhs.insert(0, K.zero)
+
+        # differentiate both lhs and rhs
+        sol = _derivate_diff_eq(rhs, K)
+
+        # add the term y' in lhs to rhs
+        sol = _add_lists(sol, [K.zero, K.one])
+
+        sol = _normalize(sol[1:], self.annihilator.parent, negative=False)
+
+        if not self._have_init_cond() or self.is_singularics() == True:
+            return HolonomicFunction(sol, self.x)
+
+        y0 = _extend_y0(self, sol.order + 1)[1:]
+        return HolonomicFunction(sol, self.x, self.x0, y0)
+
+    def __eq__(self, other):
+        if self.annihilator != other.annihilator or self.x != other.x:
+            return False
+        if self._have_init_cond() and other._have_init_cond():
+            return self.x0 == other.x0 and self.y0 == other.y0
+        return True
+
+    def __mul__(self, other):
+        ann_self = self.annihilator
+
+        if not isinstance(other, HolonomicFunction):
+            other = sympify(other)
+
+            if other.has(self.x):
+                raise NotImplementedError(" Can't multiply a HolonomicFunction and expressions/functions.")
+
+            if not self._have_init_cond():
+                return self
+            y0 = _extend_y0(self, ann_self.order)
+            y1 = [(Poly.new(j, self.x) * other).rep for j in y0]
+            return HolonomicFunction(ann_self, self.x, self.x0, y1)
+
+        if self.annihilator.parent.base != other.annihilator.parent.base:
+            a, b = self.unify(other)
+            return a * b
+
+        ann_other = other.annihilator
+
+        a = ann_self.order
+        b = ann_other.order
+
+        R = ann_self.parent.base
+        K = R.get_field()
+
+        list_self = [K.new(j.to_list()) for j in ann_self.listofpoly]
+        list_other = [K.new(j.to_list()) for j in ann_other.listofpoly]
+
+        # will be used to reduce the degree
+        self_red = [-list_self[i] / list_self[a] for i in range(a)]
+
+        other_red = [-list_other[i] / list_other[b] for i in range(b)]
+
+        # coeff_mull[i][j] is the coefficient of Dx^i(f).Dx^j(g)
+        coeff_mul = [[K.zero for i in range(b + 1)] for j in range(a + 1)]
+        coeff_mul[0][0] = K.one
+
+        # making the ansatz
+        lin_sys_elements = [[coeff_mul[i][j] for i in range(a) for j in range(b)]]
+        lin_sys = DomainMatrix(lin_sys_elements, (1, a*b), K).transpose()
+
+        homo_sys = DomainMatrix.zeros((a*b, 1), K)
+
+        sol = _find_nonzero_solution(lin_sys, homo_sys)
+
+        # until a non trivial solution is found
+        while sol.is_zero_matrix:
+
+            # updating the coefficients Dx^i(f).Dx^j(g) for next degree
+            for i in range(a - 1, -1, -1):
+                for j in range(b - 1, -1, -1):
+                    coeff_mul[i][j + 1] += coeff_mul[i][j]
+                    coeff_mul[i + 1][j] += coeff_mul[i][j]
+                    if isinstance(coeff_mul[i][j], K.dtype):
+                        coeff_mul[i][j] = DMFdiff(coeff_mul[i][j], K)
+                    else:
+                        coeff_mul[i][j] = coeff_mul[i][j].diff(self.x)
+
+            # reduce the terms to lower power using annihilators of f, g
+            for i in range(a + 1):
+                if coeff_mul[i][b].is_zero:
+                    continue
+                for j in range(b):
+                    coeff_mul[i][j] += other_red[j] * coeff_mul[i][b]
+                coeff_mul[i][b] = K.zero
+
+            # not d2 + 1, as that is already covered in previous loop
+            for j in range(b):
+                if coeff_mul[a][j] == 0:
+                    continue
+                for i in range(a):
+                    coeff_mul[i][j] += self_red[i] * coeff_mul[a][j]
+                coeff_mul[a][j] = K.zero
+
+            lin_sys_elements.append([coeff_mul[i][j] for i in range(a) for j in range(b)])
+            lin_sys = DomainMatrix(lin_sys_elements, (len(lin_sys_elements), a*b), K).transpose()
+
+            sol = _find_nonzero_solution(lin_sys, homo_sys)
+
+        sol_ann = _normalize(sol.flat(), self.annihilator.parent, negative=False)
+
+        if not (self._have_init_cond() and other._have_init_cond()):
+            return HolonomicFunction(sol_ann, self.x)
+
+        if self.is_singularics() == False and other.is_singularics() == False:
+
+            # if both the conditions are at same point
+            if self.x0 == other.x0:
+
+                # try to find more initial conditions
+                y0_self = _extend_y0(self, sol_ann.order)
+                y0_other = _extend_y0(other, sol_ann.order)
+                # h(x0) = f(x0) * g(x0)
+                y0 = [y0_self[0] * y0_other[0]]
+
+                # coefficient of Dx^j(f)*Dx^i(g) in Dx^i(fg)
+                for i in range(1, min(len(y0_self), len(y0_other))):
+                    coeff = [[0 for i in range(i + 1)] for j in range(i + 1)]
+                    for j in range(i + 1):
+                        for k in range(i + 1):
+                            if j + k == i:
+                                coeff[j][k] = binomial(i, j)
+
+                    sol = 0
+                    for j in range(i + 1):
+                        for k in range(i + 1):
+                            sol += coeff[j][k]* y0_self[j] * y0_other[k]
+
+                    y0.append(sol)
+
+                return HolonomicFunction(sol_ann, self.x, self.x0, y0)
+
+            # if the points are different, consider one
+            selfat0 = self.annihilator.is_singular(0)
+            otherat0 = other.annihilator.is_singular(0)
+
+            if self.x0 == 0 and not selfat0 and not otherat0:
+                return self * other.change_ics(0)
+            if other.x0 == 0 and not selfat0 and not otherat0:
+                return self.change_ics(0) * other
+
+            selfatx0 = self.annihilator.is_singular(self.x0)
+            otheratx0 = other.annihilator.is_singular(self.x0)
+            if not selfatx0 and not otheratx0:
+                return self * other.change_ics(self.x0)
+            return self.change_ics(other.x0) * other
+
+        if self.x0 != other.x0:
+            return HolonomicFunction(sol_ann, self.x)
+
+        # if the functions have singular_ics
+        y1 = None
+        y2 = None
+
+        if self.is_singularics() == False and other.is_singularics() == True:
+            _y0 = [j / factorial(i) for i, j in enumerate(self.y0)]
+            y1 = {S.Zero: _y0}
+            y2 = other.y0
+        elif self.is_singularics() == True and other.is_singularics() == False:
+            _y0 = [j / factorial(i) for i, j in enumerate(other.y0)]
+            y1 = self.y0
+            y2 = {S.Zero: _y0}
+        elif self.is_singularics() == True and other.is_singularics() == True:
+            y1 = self.y0
+            y2 = other.y0
+
+        y0 = {}
+        # multiply every possible pair of the series terms
+        for i in y1:
+            for j in y2:
+                k = min(len(y1[i]), len(y2[j]))
+                c = [sum((y1[i][b] * y2[j][a - b] for b in range(a + 1)),
+                         start=S.Zero) for a in range(k)]
+                if not i + j in y0:
+                    y0[i + j] = c
+                else:
+                    y0[i + j] = [a + b for a, b in zip(c, y0[i + j])]
+        return HolonomicFunction(sol_ann, self.x, self.x0, y0)
+
+    __rmul__ = __mul__
+
+    def __sub__(self, other):
+        return self + other * -1
+
+    def __rsub__(self, other):
+        return self * -1 + other
+
+    def __neg__(self):
+        return -1 * self
+
+    def __truediv__(self, other):
+        return self * (S.One / other)
+
+    def __pow__(self, n):
+        if self.annihilator.order <= 1:
+            ann = self.annihilator
+            parent = ann.parent
+
+            if self.y0 is None:
+                y0 = None
+            else:
+                y0 = [list(self.y0)[0] ** n]
+
+            p0 = ann.listofpoly[0]
+            p1 = ann.listofpoly[1]
+
+            p0 = (Poly.new(p0, self.x) * n).rep
+
+            sol = [parent.base.to_sympy(i) for i in [p0, p1]]
+            dd = DifferentialOperator(sol, parent)
+            return HolonomicFunction(dd, self.x, self.x0, y0)
+        if n < 0:
+            raise NotHolonomicError("Negative Power on a Holonomic Function")
+        Dx = self.annihilator.parent.derivative_operator
+        result = HolonomicFunction(Dx, self.x, S.Zero, [S.One])
+        if n == 0:
+            return result
+        x = self
+        while True:
+            if n % 2:
+                result *= x
+            n >>= 1
+            if not n:
+                break
+            x *= x
+        return result
+
+    def degree(self):
+        """
+        Returns the highest power of `x` in the annihilator.
+        """
+        return max(i.degree() for i in self.annihilator.listofpoly)
+
+    def composition(self, expr, *args, **kwargs):
+        """
+        Returns function after composition of a holonomic
+        function with an algebraic function. The method cannot compute
+        initial conditions for the result by itself, so they can be also be
+        provided.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import QQ
+        >>> from sympy import symbols
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')
+        >>> HolonomicFunction(Dx - 1, x).composition(x**2, 0, [1])  # e^(x**2)
+        HolonomicFunction((-2*x) + (1)*Dx, x, 0, [1])
+        >>> HolonomicFunction(Dx**2 + 1, x).composition(x**2 - 1, 1, [1, 0])
+        HolonomicFunction((4*x**3) + (-1)*Dx + (x)*Dx**2, x, 1, [1, 0])
+
+        See Also
+        ========
+
+        from_hyper
+        """
+
+        R = self.annihilator.parent
+        a = self.annihilator.order
+        diff = expr.diff(self.x)
+        listofpoly = self.annihilator.listofpoly
+
+        for i, j in enumerate(listofpoly):
+            if isinstance(j, self.annihilator.parent.base.dtype):
+                listofpoly[i] = self.annihilator.parent.base.to_sympy(j)
+
+        r = listofpoly[a].subs({self.x:expr})
+        subs = [-listofpoly[i].subs({self.x:expr}) / r for i in range (a)]
+        coeffs = [S.Zero for i in range(a)]  # coeffs[i] == coeff of (D^i f)(a) in D^k (f(a))
+        coeffs[0] = S.One
+        system = [coeffs]
+        homogeneous = Matrix([[S.Zero for i in range(a)]]).transpose()
+        while True:
+            coeffs_next = [p.diff(self.x) for p in coeffs]
+            for i in range(a - 1):
+                coeffs_next[i + 1] += (coeffs[i] * diff)
+            for i in range(a):
+                coeffs_next[i] += (coeffs[-1] * subs[i] * diff)
+            coeffs = coeffs_next
+            # check for linear relations
+            system.append(coeffs)
+            sol, taus = (Matrix(system).transpose()
+                ).gauss_jordan_solve(homogeneous)
+            if sol.is_zero_matrix is not True:
+                break
+
+        tau = list(taus)[0]
+        sol = sol.subs(tau, 1)
+        sol = _normalize(sol[0:], R, negative=False)
+
+        # if initial conditions are given for the resulting function
+        if args:
+            return HolonomicFunction(sol, self.x, args[0], args[1])
+        return HolonomicFunction(sol, self.x)
+
+    def to_sequence(self, lb=True):
+        r"""
+        Finds recurrence relation for the coefficients in the series expansion
+        of the function about :math:`x_0`, where :math:`x_0` is the point at
+        which the initial condition is stored.
+
+        Explanation
+        ===========
+
+        If the point :math:`x_0` is ordinary, solution of the form :math:`[(R, n_0)]`
+        is returned. Where :math:`R` is the recurrence relation and :math:`n_0` is the
+        smallest ``n`` for which the recurrence holds true.
+
+        If the point :math:`x_0` is regular singular, a list of solutions in
+        the format :math:`(R, p, n_0)` is returned, i.e. `[(R, p, n_0), ... ]`.
+        Each tuple in this vector represents a recurrence relation :math:`R`
+        associated with a root of the indicial equation ``p``. Conditions of
+        a different format can also be provided in this case, see the
+        docstring of HolonomicFunction class.
+
+        If it's not possible to numerically compute a initial condition,
+        it is returned as a symbol :math:`C_j`, denoting the coefficient of
+        :math:`(x - x_0)^j` in the power series about :math:`x_0`.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import QQ
+        >>> from sympy import symbols, S
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')
+        >>> HolonomicFunction(Dx - 1, x, 0, [1]).to_sequence()
+        [(HolonomicSequence((-1) + (n + 1)Sn, n), u(0) = 1, 0)]
+        >>> HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]).to_sequence()
+        [(HolonomicSequence((n**2) + (n**2 + n)Sn, n), u(0) = 0, u(1) = 1, u(2) = -1/2, 2)]
+        >>> HolonomicFunction(-S(1)/2 + x*Dx, x, 0, {S(1)/2: [1]}).to_sequence()
+        [(HolonomicSequence((n), n), u(0) = 1, 1/2, 1)]
+
+        See Also
+        ========
+
+        HolonomicFunction.series
+
+        References
+        ==========
+
+        .. [1] https://hal.inria.fr/inria-00070025/document
+        .. [2] https://www3.risc.jku.at/publications/download/risc_2244/DIPLFORM.pdf
+
+        """
+
+        if self.x0 != 0:
+            return self.shift_x(self.x0).to_sequence()
+
+        # check whether a power series exists if the point is singular
+        if self.annihilator.is_singular(self.x0):
+            return self._frobenius(lb=lb)
+
+        dict1 = {}
+        n = Symbol('n', integer=True)
+        dom = self.annihilator.parent.base.dom
+        R, _ = RecurrenceOperators(dom.old_poly_ring(n), 'Sn')
+
+        # substituting each term of the form `x^k Dx^j` in the
+        # annihilator, according to the formula below:
+        # x^k Dx^j = Sum(rf(n + 1 - k, j) * a(n + j - k) * x^n, (n, k, oo))
+        # for explanation see [2].
+        for i, j in enumerate(self.annihilator.listofpoly):
+
+            listofdmp = j.all_coeffs()
+            degree = len(listofdmp) - 1
+
+            for k in range(degree + 1):
+                coeff = listofdmp[degree - k]
+
+                if coeff == 0:
+                    continue
+
+                if (i - k, k) in dict1:
+                    dict1[(i - k, k)] += (dom.to_sympy(coeff) * rf(n - k + 1, i))
+                else:
+                    dict1[(i - k, k)] = (dom.to_sympy(coeff) * rf(n - k + 1, i))
+
+
+        sol = []
+        keylist = [i[0] for i in dict1]
+        lower = min(keylist)
+        upper = max(keylist)
+        degree = self.degree()
+
+        # the recurrence relation holds for all values of
+        # n greater than smallest_n, i.e. n >= smallest_n
+        smallest_n = lower + degree
+        dummys = {}
+        eqs = []
+        unknowns = []
+
+        # an appropriate shift of the recurrence
+        for j in range(lower, upper + 1):
+            if j in keylist:
+                temp = sum((v.subs(n, n - lower)
+                           for k, v in dict1.items() if k[0] == j),
+                           start=S.Zero)
+                sol.append(temp)
+            else:
+                sol.append(S.Zero)
+
+        # the recurrence relation
+        sol = RecurrenceOperator(sol, R)
+
+        # computing the initial conditions for recurrence
+        order = sol.order
+        all_roots = roots(R.base.to_sympy(sol.listofpoly[-1]), n, filter='Z')
+        all_roots = all_roots.keys()
+
+        if all_roots:
+            max_root = max(all_roots) + 1
+            smallest_n = max(max_root, smallest_n)
+        order += smallest_n
+
+        y0 = _extend_y0(self, order)
+        # u(n) = y^n(0)/factorial(n)
+        u0 = [j / factorial(i) for i, j in enumerate(y0)]
+
+        # if sufficient conditions can't be computed then
+        # try to use the series method i.e.
+        # equate the coefficients of x^k in the equation formed by
+        # substituting the series in differential equation, to zero.
+        if len(u0) < order:
+
+            for i in range(degree):
+                eq = S.Zero
+
+                for j in dict1:
+
+                    if i + j[0] < 0:
+                        dummys[i + j[0]] = S.Zero
+
+                    elif i + j[0] < len(u0):
+                        dummys[i + j[0]] = u0[i + j[0]]
+
+                    elif not i + j[0] in dummys:
+                        dummys[i + j[0]] = Symbol('C_%s' %(i + j[0]))
+                        unknowns.append(dummys[i + j[0]])
+
+                    if j[1] <= i:
+                        eq += dict1[j].subs(n, i) * dummys[i + j[0]]
+
+                eqs.append(eq)
+
+            # solve the system of equations formed
+            soleqs = solve(eqs, *unknowns)
+
+            if isinstance(soleqs, dict):
+
+                for i in range(len(u0), order):
+
+                    if i not in dummys:
+                        dummys[i] = Symbol('C_%s' %i)
+
+                    if dummys[i] in soleqs:
+                        u0.append(soleqs[dummys[i]])
+
+                    else:
+                        u0.append(dummys[i])
+
+                if lb:
+                    return [(HolonomicSequence(sol, u0), smallest_n)]
+                return [HolonomicSequence(sol, u0)]
+
+            for i in range(len(u0), order):
+
+                if i not in dummys:
+                    dummys[i] = Symbol('C_%s' %i)
+
+                s = False
+                for j in soleqs:
+                    if dummys[i] in j:
+                        u0.append(j[dummys[i]])
+                        s = True
+                if not s:
+                    u0.append(dummys[i])
+
+        if lb:
+            return [(HolonomicSequence(sol, u0), smallest_n)]
+
+        return [HolonomicSequence(sol, u0)]
+
+    def _frobenius(self, lb=True):
+        # compute the roots of indicial equation
+        indicialroots = self._indicial()
+
+        reals = []
+        compl = []
+        for i in ordered(indicialroots.keys()):
+            if i.is_real:
+                reals.extend([i] * indicialroots[i])
+            else:
+                a, b = i.as_real_imag()
+                compl.extend([(i, a, b)] * indicialroots[i])
+
+        # sort the roots for a fixed ordering of solution
+        compl.sort(key=lambda x : x[1])
+        compl.sort(key=lambda x : x[2])
+        reals.sort()
+
+        # grouping the roots, roots differ by an integer are put in the same group.
+        grp = []
+
+        for i in reals:
+            if len(grp) == 0:
+                grp.append([i])
+                continue
+            for j in grp:
+                if int_valued(j[0] - i):
+                    j.append(i)
+                    break
+            else:
+                grp.append([i])
+
+        # True if none of the roots differ by an integer i.e.
+        # each element in group have only one member
+        independent = all(len(i) == 1 for i in grp)
+
+        allpos = all(i >= 0 for i in reals)
+        allint = all(int_valued(i) for i in reals)
+
+        # if initial conditions are provided
+        # then use them.
+        if self.is_singularics() == True:
+            rootstoconsider = []
+            for i in ordered(self.y0.keys()):
+                for j in ordered(indicialroots.keys()):
+                    if equal_valued(j, i):
+                        rootstoconsider.append(i)
+
+        elif allpos and allint:
+            rootstoconsider = [min(reals)]
+
+        elif independent:
+            rootstoconsider = [i[0] for i in grp] + [j[0] for j in compl]
+
+        elif not allint:
+            rootstoconsider = [i for i in reals if not int(i) == i]
+
+        elif not allpos:
+
+            if not self._have_init_cond() or S(self.y0[0]).is_finite ==  False:
+                rootstoconsider = [min(reals)]
+
+            else:
+                posroots = [i for i in reals if i >= 0]
+                rootstoconsider = [min(posroots)]
+
+        n = Symbol('n', integer=True)
+        dom = self.annihilator.parent.base.dom
+        R, _ = RecurrenceOperators(dom.old_poly_ring(n), 'Sn')
+
+        finalsol = []
+        char = ord('C')
+
+        for p in rootstoconsider:
+            dict1 = {}
+
+            for i, j in enumerate(self.annihilator.listofpoly):
+
+                listofdmp = j.all_coeffs()
+                degree = len(listofdmp) - 1
+
+                for k in range(degree + 1):
+                    coeff = listofdmp[degree - k]
+
+                    if coeff == 0:
+                        continue
+
+                    if (i - k, k - i) in dict1:
+                        dict1[(i - k, k - i)] += (dom.to_sympy(coeff) * rf(n - k + 1 + p, i))
+                    else:
+                        dict1[(i - k, k - i)] = (dom.to_sympy(coeff) * rf(n - k + 1 + p, i))
+
+            sol = []
+            keylist = [i[0] for i in dict1]
+            lower = min(keylist)
+            upper = max(keylist)
+            degree = max(i[1] for i in dict1)
+            degree2 = min(i[1] for i in dict1)
+
+            smallest_n = lower + degree
+            dummys = {}
+            eqs = []
+            unknowns = []
+
+            for j in range(lower, upper + 1):
+                if j in keylist:
+                    temp = sum((v.subs(n, n - lower)
+                               for k, v in dict1.items() if k[0] == j),
+                               start=S.Zero)
+                    sol.append(temp)
+                else:
+                    sol.append(S.Zero)
+
+            # the recurrence relation
+            sol = RecurrenceOperator(sol, R)
+
+            # computing the initial conditions for recurrence
+            order = sol.order
+            all_roots = roots(R.base.to_sympy(sol.listofpoly[-1]), n, filter='Z')
+            all_roots = all_roots.keys()
+
+            if all_roots:
+                max_root = max(all_roots) + 1
+                smallest_n = max(max_root, smallest_n)
+            order += smallest_n
+
+            u0 = []
+
+            if self.is_singularics() == True:
+                u0 = self.y0[p]
+
+            elif self.is_singularics() == False and p >= 0 and int(p) == p and len(rootstoconsider) == 1:
+                y0 = _extend_y0(self, order + int(p))
+                # u(n) = y^n(0)/factorial(n)
+                if len(y0) > int(p):
+                    u0 = [y0[i] / factorial(i) for i in range(int(p), len(y0))]
+
+            if len(u0) < order:
+
+                for i in range(degree2, degree):
+                    eq = S.Zero
+
+                    for j in dict1:
+                        if i + j[0] < 0:
+                            dummys[i + j[0]] = S.Zero
+
+                        elif i + j[0] < len(u0):
+                            dummys[i + j[0]] = u0[i + j[0]]
+
+                        elif not i + j[0] in dummys:
+                            letter = chr(char) + '_%s' %(i + j[0])
+                            dummys[i + j[0]] = Symbol(letter)
+                            unknowns.append(dummys[i + j[0]])
+
+                        if j[1] <= i:
+                            eq += dict1[j].subs(n, i) * dummys[i + j[0]]
+
+                    eqs.append(eq)
+
+                # solve the system of equations formed
+                soleqs = solve(eqs, *unknowns)
+
+                if isinstance(soleqs, dict):
+
+                    for i in range(len(u0), order):
+
+                        if i not in dummys:
+                            letter = chr(char) + '_%s' %i
+                            dummys[i] = Symbol(letter)
+
+                        if dummys[i] in soleqs:
+                            u0.append(soleqs[dummys[i]])
+
+                        else:
+                            u0.append(dummys[i])
+
+                    if lb:
+                        finalsol.append((HolonomicSequence(sol, u0), p, smallest_n))
+                        continue
+                    else:
+                        finalsol.append((HolonomicSequence(sol, u0), p))
+                        continue
+
+                for i in range(len(u0), order):
+
+                    if i not in dummys:
+                        letter = chr(char) + '_%s' %i
+                        dummys[i] = Symbol(letter)
+
+                    s = False
+                    for j in soleqs:
+                        if dummys[i] in j:
+                            u0.append(j[dummys[i]])
+                            s = True
+                    if not s:
+                        u0.append(dummys[i])
+            if lb:
+                finalsol.append((HolonomicSequence(sol, u0), p, smallest_n))
+
+            else:
+                finalsol.append((HolonomicSequence(sol, u0), p))
+            char += 1
+        return finalsol
+
+    def series(self, n=6, coefficient=False, order=True, _recur=None):
+        r"""
+        Finds the power series expansion of given holonomic function about :math:`x_0`.
+
+        Explanation
+        ===========
+
+        A list of series might be returned if :math:`x_0` is a regular point with
+        multiple roots of the indicial equation.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import QQ
+        >>> from sympy import symbols
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')
+        >>> HolonomicFunction(Dx - 1, x, 0, [1]).series()  # e^x
+        1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120 + O(x**6)
+        >>> HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).series(n=8)  # sin(x)
+        x - x**3/6 + x**5/120 - x**7/5040 + O(x**8)
+
+        See Also
+        ========
+
+        HolonomicFunction.to_sequence
+        """
+
+        if _recur is None:
+            recurrence = self.to_sequence()
+        else:
+            recurrence = _recur
+
+        if isinstance(recurrence, tuple) and len(recurrence) == 2:
+            recurrence = recurrence[0]
+            constantpower = 0
+        elif isinstance(recurrence, tuple) and len(recurrence) == 3:
+            constantpower = recurrence[1]
+            recurrence = recurrence[0]
+
+        elif len(recurrence) == 1 and len(recurrence[0]) == 2:
+            recurrence = recurrence[0][0]
+            constantpower = 0
+        elif len(recurrence) == 1 and len(recurrence[0]) == 3:
+            constantpower = recurrence[0][1]
+            recurrence = recurrence[0][0]
+        else:
+            return [self.series(_recur=i) for i in recurrence]
+
+        n = n - int(constantpower)
+        l = len(recurrence.u0) - 1
+        k = recurrence.recurrence.order
+        x = self.x
+        x0 = self.x0
+        seq_dmp = recurrence.recurrence.listofpoly
+        R = recurrence.recurrence.parent.base
+        K = R.get_field()
+        seq = [K.new(j.to_list()) for j in seq_dmp]
+        sub = [-seq[i] / seq[k] for i in range(k)]
+        sol = list(recurrence.u0)
+
+        if l + 1 < n:
+            # use the initial conditions to find the next term
+            for i in range(l + 1 - k, n - k):
+                coeff = sum((DMFsubs(sub[j], i) * sol[i + j]
+                            for j in range(k) if i + j >= 0), start=S.Zero)
+                sol.append(coeff)
+
+        if coefficient:
+            return sol
+
+        ser = sum((x**(i + constantpower) * j for i, j in enumerate(sol)),
+                  start=S.Zero)
+        if order:
+            ser += Order(x**(n + int(constantpower)), x)
+        if x0 != 0:
+            return ser.subs(x, x - x0)
+        return ser
+
+    def _indicial(self):
+        """
+        Computes roots of the Indicial equation.
+        """
+
+        if self.x0 != 0:
+            return self.shift_x(self.x0)._indicial()
+
+        list_coeff = self.annihilator.listofpoly
+        R = self.annihilator.parent.base
+        x = self.x
+        s = R.zero
+        y = R.one
+
+        def _pole_degree(poly):
+            root_all = roots(R.to_sympy(poly), x, filter='Z')
+            if 0 in root_all.keys():
+                return root_all[0]
+            else:
+                return 0
+
+        degree = max(j.degree() for j in list_coeff)
+        inf = 10 * (max(1, degree) + max(1, self.annihilator.order))
+
+        deg = lambda q: inf if q.is_zero else _pole_degree(q)
+        b = min(deg(q) - j for j, q in enumerate(list_coeff))
+
+        for i, j in enumerate(list_coeff):
+            listofdmp = j.all_coeffs()
+            degree = len(listofdmp) - 1
+            if 0 <= i + b <= degree:
+                s = s + listofdmp[degree - i - b] * y
+            y *= R.from_sympy(x - i)
+
+        return roots(R.to_sympy(s), x)
+
+    def evalf(self, points, method='RK4', h=0.05, derivatives=False):
+        r"""
+        Finds numerical value of a holonomic function using numerical methods.
+        (RK4 by default). A set of points (real or complex) must be provided
+        which will be the path for the numerical integration.
+
+        Explanation
+        ===========
+
+        The path should be given as a list :math:`[x_1, x_2, \dots x_n]`. The numerical
+        values will be computed at each point in this order
+        :math:`x_1 \rightarrow x_2 \rightarrow x_3 \dots \rightarrow x_n`.
+
+        Returns values of the function at :math:`x_1, x_2, \dots x_n` in a list.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import QQ
+        >>> from sympy import symbols
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')
+
+        A straight line on the real axis from (0 to 1)
+
+        >>> r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]
+
+        Runge-Kutta 4th order on e^x from 0.1 to 1.
+        Exact solution at 1 is 2.71828182845905
+
+        >>> HolonomicFunction(Dx - 1, x, 0, [1]).evalf(r)
+        [1.10517083333333, 1.22140257085069, 1.34985849706254, 1.49182424008069,
+        1.64872063859684, 1.82211796209193, 2.01375162659678, 2.22553956329232,
+        2.45960141378007, 2.71827974413517]
+
+        Euler's method for the same
+
+        >>> HolonomicFunction(Dx - 1, x, 0, [1]).evalf(r, method='Euler')
+        [1.1, 1.21, 1.331, 1.4641, 1.61051, 1.771561, 1.9487171, 2.14358881,
+        2.357947691, 2.5937424601]
+
+        One can also observe that the value obtained using Runge-Kutta 4th order
+        is much more accurate than Euler's method.
+        """
+
+        from sympy.holonomic.numerical import _evalf
+        lp = False
+
+        # if a point `b` is given instead of a mesh
+        if not hasattr(points, "__iter__"):
+            lp = True
+            b = S(points)
+            if self.x0 == b:
+                return _evalf(self, [b], method=method, derivatives=derivatives)[-1]
+
+            if not b.is_Number:
+                raise NotImplementedError
+
+            a = self.x0
+            if a > b:
+                h = -h
+            n = int((b - a) / h)
+            points = [a + h]
+            for i in range(n - 1):
+                points.append(points[-1] + h)
+
+        for i in roots(self.annihilator.parent.base.to_sympy(self.annihilator.listofpoly[-1]), self.x):
+            if i == self.x0 or i in points:
+                raise SingularityError(self, i)
+
+        if lp:
+            return _evalf(self, points, method=method, derivatives=derivatives)[-1]
+        return _evalf(self, points, method=method, derivatives=derivatives)
+
+    def change_x(self, z):
+        """
+        Changes only the variable of Holonomic Function, for internal
+        purposes. For composition use HolonomicFunction.composition()
+        """
+
+        dom = self.annihilator.parent.base.dom
+        R = dom.old_poly_ring(z)
+        parent, _ = DifferentialOperators(R, 'Dx')
+        sol = [R(j.to_list()) for j in self.annihilator.listofpoly]
+        sol =  DifferentialOperator(sol, parent)
+        return HolonomicFunction(sol, z, self.x0, self.y0)
+
+    def shift_x(self, a):
+        """
+        Substitute `x + a` for `x`.
+        """
+
+        x = self.x
+        listaftershift = self.annihilator.listofpoly
+        base = self.annihilator.parent.base
+
+        sol = [base.from_sympy(base.to_sympy(i).subs(x, x + a)) for i in listaftershift]
+        sol = DifferentialOperator(sol, self.annihilator.parent)
+        x0 = self.x0 - a
+        if not self._have_init_cond():
+            return HolonomicFunction(sol, x)
+        return HolonomicFunction(sol, x, x0, self.y0)
+
+    def to_hyper(self, as_list=False, _recur=None):
+        r"""
+        Returns a hypergeometric function (or linear combination of them)
+        representing the given holonomic function.
+
+        Explanation
+        ===========
+
+        Returns an answer of the form:
+        `a_1 \cdot x^{b_1} \cdot{hyper()} + a_2 \cdot x^{b_2} \cdot{hyper()} \dots`
+
+        This is very useful as one can now use ``hyperexpand`` to find the
+        symbolic expressions/functions.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import ZZ
+        >>> from sympy import symbols
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx')
+        >>> # sin(x)
+        >>> HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).to_hyper()
+        x*hyper((), (3/2,), -x**2/4)
+        >>> # exp(x)
+        >>> HolonomicFunction(Dx - 1, x, 0, [1]).to_hyper()
+        hyper((), (), x)
+
+        See Also
+        ========
+
+        from_hyper, from_meijerg
+        """
+
+        if _recur is None:
+            recurrence = self.to_sequence()
+        else:
+            recurrence = _recur
+
+        if isinstance(recurrence, tuple) and len(recurrence) == 2:
+            smallest_n = recurrence[1]
+            recurrence = recurrence[0]
+            constantpower = 0
+        elif isinstance(recurrence, tuple) and len(recurrence) == 3:
+            smallest_n = recurrence[2]
+            constantpower = recurrence[1]
+            recurrence = recurrence[0]
+        elif len(recurrence) == 1 and len(recurrence[0]) == 2:
+            smallest_n = recurrence[0][1]
+            recurrence = recurrence[0][0]
+            constantpower = 0
+        elif len(recurrence) == 1 and len(recurrence[0]) == 3:
+            smallest_n = recurrence[0][2]
+            constantpower = recurrence[0][1]
+            recurrence = recurrence[0][0]
+        else:
+            sol = self.to_hyper(as_list=as_list, _recur=recurrence[0])
+            for i in recurrence[1:]:
+                sol += self.to_hyper(as_list=as_list, _recur=i)
+            return sol
+
+        u0 = recurrence.u0
+        r = recurrence.recurrence
+        x = self.x
+        x0 = self.x0
+
+        # order of the recurrence relation
+        m = r.order
+
+        # when no recurrence exists, and the power series have finite terms
+        if m == 0:
+            nonzeroterms = roots(r.parent.base.to_sympy(r.listofpoly[0]), recurrence.n, filter='R')
+
+            sol = S.Zero
+            for j, i in enumerate(nonzeroterms):
+
+                if i < 0 or not int_valued(i):
+                    continue
+
+                i = int(i)
+                if i < len(u0):
+                    if isinstance(u0[i], (PolyElement, FracElement)):
+                        u0[i] = u0[i].as_expr()
+                    sol += u0[i] * x**i
+
+                else:
+                    sol += Symbol('C_%s' %j) * x**i
+
+            if isinstance(sol, (PolyElement, FracElement)):
+                sol = sol.as_expr() * x**constantpower
+            else:
+                sol = sol * x**constantpower
+            if as_list:
+                if x0 != 0:
+                    return [(sol.subs(x, x - x0), )]
+                return [(sol, )]
+            if x0 != 0:
+                return sol.subs(x, x - x0)
+            return sol
+
+        if smallest_n + m > len(u0):
+            raise NotImplementedError("Can't compute sufficient Initial Conditions")
+
+        # check if the recurrence represents a hypergeometric series
+        if any(i != r.parent.base.zero for i in r.listofpoly[1:-1]):
+            raise NotHyperSeriesError(self, self.x0)
+
+        a = r.listofpoly[0]
+        b = r.listofpoly[-1]
+
+        # the constant multiple of argument of hypergeometric function
+        if isinstance(a.LC(), (PolyElement, FracElement)):
+            c = - (S(a.LC().as_expr()) * m**(a.degree())) / (S(b.LC().as_expr()) * m**(b.degree()))
+        else:
+            c = - (S(a.LC()) * m**(a.degree())) / (S(b.LC()) * m**(b.degree()))
+
+        sol = 0
+
+        arg1 = roots(r.parent.base.to_sympy(a), recurrence.n)
+        arg2 = roots(r.parent.base.to_sympy(b), recurrence.n)
+
+        # iterate through the initial conditions to find
+        # the hypergeometric representation of the given
+        # function.
+        # The answer will be a linear combination
+        # of different hypergeometric series which satisfies
+        # the recurrence.
+        if as_list:
+            listofsol = []
+        for i in range(smallest_n + m):
+
+            # if the recurrence relation doesn't hold for `n = i`,
+            # then a Hypergeometric representation doesn't exist.
+            # add the algebraic term a * x**i to the solution,
+            # where a is u0[i]
+            if i < smallest_n:
+                if as_list:
+                    listofsol.append(((S(u0[i]) * x**(i+constantpower)).subs(x, x-x0), ))
+                else:
+                    sol += S(u0[i]) * x**i
+                continue
+
+            # if the coefficient u0[i] is zero, then the
+            # independent hypergeomtric series starting with
+            # x**i is not a part of the answer.
+            if S(u0[i]) == 0:
+                continue
+
+            ap = []
+            bq = []
+
+            # substitute m * n + i for n
+            for k in ordered(arg1.keys()):
+                ap.extend([nsimplify((i - k) / m)] * arg1[k])
+
+            for k in ordered(arg2.keys()):
+                bq.extend([nsimplify((i - k) / m)] * arg2[k])
+
+            # convention of (k + 1) in the denominator
+            if 1 in bq:
+                bq.remove(1)
+            else:
+                ap.append(1)
+            if as_list:
+                listofsol.append(((S(u0[i])*x**(i+constantpower)).subs(x, x-x0), (hyper(ap, bq, c*x**m)).subs(x, x-x0)))
+            else:
+                sol += S(u0[i]) * hyper(ap, bq, c * x**m) * x**i
+        if as_list:
+            return listofsol
+        sol = sol * x**constantpower
+        if x0 != 0:
+            return sol.subs(x, x - x0)
+
+        return sol
+
+    def to_expr(self):
+        """
+        Converts a Holonomic Function back to elementary functions.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
+        >>> from sympy import ZZ
+        >>> from sympy import symbols, S
+        >>> x = symbols('x')
+        >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx')
+        >>> HolonomicFunction(x**2*Dx**2 + x*Dx + (x**2 - 1), x, 0, [0, S(1)/2]).to_expr()
+        besselj(1, x)
+        >>> HolonomicFunction((1 + x)*Dx**3 + Dx**2, x, 0, [1, 1, 1]).to_expr()
+        x*log(x + 1) + log(x + 1) + 1
+
+        """
+
+        return hyperexpand(self.to_hyper()).simplify()
+
+    def change_ics(self, b, lenics=None):
+        """
+        Changes the point `x0` to ``b`` for initial conditions.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic import expr_to_holonomic
+        >>> from sympy import symbols, sin, exp
+        >>> x = symbols('x')
+
+        >>> expr_to_holonomic(sin(x)).change_ics(1)
+        HolonomicFunction((1) + (1)*Dx**2, x, 1, [sin(1), cos(1)])
+
+        >>> expr_to_holonomic(exp(x)).change_ics(2)
+        HolonomicFunction((-1) + (1)*Dx, x, 2, [exp(2)])
+        """
+
+        symbolic = True
+
+        if lenics is None and len(self.y0) > self.annihilator.order:
+            lenics = len(self.y0)
+        dom = self.annihilator.parent.base.domain
+
+        try:
+            sol = expr_to_holonomic(self.to_expr(), x=self.x, x0=b, lenics=lenics, domain=dom)
+        except (NotPowerSeriesError, NotHyperSeriesError):
+            symbolic = False
+
+        if symbolic and sol.x0 == b:
+            return sol
+
+        y0 = self.evalf(b, derivatives=True)
+        return HolonomicFunction(self.annihilator, self.x, b, y0)
+
+    def to_meijerg(self):
+        """
+        Returns a linear combination of Meijer G-functions.
+
+        Examples
+        ========
+
+        >>> from sympy.holonomic import expr_to_holonomic
+        >>> from sympy import sin, cos, hyperexpand, log, symbols
+        >>> x = symbols('x')
+        >>> hyperexpand(expr_to_holonomic(cos(x) + sin(x)).to_meijerg())
+        sin(x) + cos(x)
+        >>> hyperexpand(expr_to_holonomic(log(x)).to_meijerg()).simplify()
+        log(x)
+
+        See Also
+        ========
+
+        to_hyper
+        """
+
+        # convert to hypergeometric first
+        rep = self.to_hyper(as_list=True)
+        sol = S.Zero
+
+        for i in rep:
+            if len(i) == 1:
+                sol += i[0]
+
+            elif len(i) == 2:
+                sol += i[0] * _hyper_to_meijerg(i[1])
+
+        return sol
+
+
+def from_hyper(func, x0=0, evalf=False):
+    r"""
+    Converts a hypergeometric function to holonomic.
+    ``func`` is the Hypergeometric Function and ``x0`` is the point at
+    which initial conditions are required.
+
+    Examples
+    ========
+
+    >>> from sympy.holonomic.holonomic import from_hyper
+    >>> from sympy import symbols, hyper, S
+    >>> x = symbols('x')
+    >>> from_hyper(hyper([], [S(3)/2], x**2/4))
+    HolonomicFunction((-x) + (2)*Dx + (x)*Dx**2, x, 1, [sinh(1), -sinh(1) + cosh(1)])
+    """
+
+    a = func.ap
+    b = func.bq
+    z = func.args[2]
+    x = z.atoms(Symbol).pop()
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+
+    # generalized hypergeometric differential equation
+    xDx = x*Dx
+    r1 = 1
+    for ai in a:  # XXX gives sympify error if Mul is used with list of all factors
+        r1 *= xDx + ai
+    xDx_1 = xDx - 1
+    # r2 = Mul(*([Dx] + [xDx_1 + bi for bi in b]))  # XXX gives sympify error
+    r2 = Dx
+    for bi in b:
+        r2 *= xDx_1 + bi
+    sol = r1 - r2
+
+    simp = hyperexpand(func)
+
+    if simp in (Infinity, NegativeInfinity):
+        return HolonomicFunction(sol, x).composition(z)
+
+    # if the function is known symbolically
+    if not isinstance(simp, hyper):
+        y0 = _find_conditions(simp, x, x0, sol.order, use_limit=False)
+        while not y0:
+            # if values don't exist at 0, then try to find initial
+            # conditions at 1. If it doesn't exist at 1 too then
+            # try 2 and so on.
+            x0 += 1
+            y0 = _find_conditions(simp, x, x0, sol.order, use_limit=False)
+
+        return HolonomicFunction(sol, x).composition(z, x0, y0)
+
+    if isinstance(simp, hyper):
+        x0 = 1
+        # use evalf if the function can't be simplified
+        y0 = _find_conditions(simp, x, x0, sol.order, evalf, use_limit=False)
+        while not y0:
+            x0 += 1
+            y0 = _find_conditions(simp, x, x0, sol.order, evalf, use_limit=False)
+        return HolonomicFunction(sol, x).composition(z, x0, y0)
+
+    return HolonomicFunction(sol, x).composition(z)
+
+
+def from_meijerg(func, x0=0, evalf=False, initcond=True, domain=QQ):
+    """
+    Converts a Meijer G-function to Holonomic.
+    ``func`` is the G-Function and ``x0`` is the point at
+    which initial conditions are required.
+
+    Examples
+    ========
+
+    >>> from sympy.holonomic.holonomic import from_meijerg
+    >>> from sympy import symbols, meijerg, S
+    >>> x = symbols('x')
+    >>> from_meijerg(meijerg(([], []), ([S(1)/2], [0]), x**2/4))
+    HolonomicFunction((1) + (1)*Dx**2, x, 0, [0, 1/sqrt(pi)])
+    """
+
+    a = func.ap
+    b = func.bq
+    n = len(func.an)
+    m = len(func.bm)
+    p = len(a)
+    z = func.args[2]
+    x = z.atoms(Symbol).pop()
+    R, Dx = DifferentialOperators(domain.old_poly_ring(x), 'Dx')
+
+    # compute the differential equation satisfied by the
+    # Meijer G-function.
+    xDx = x*Dx
+    xDx1 = xDx + 1
+    r1 = x*(-1)**(m + n - p)
+    for ai in a:  # XXX gives sympify error if args given in list
+        r1 *= xDx1 - ai
+    # r2 = Mul(*[xDx - bi for bi in b])  # gives sympify error
+    r2 = 1
+    for bi in b:
+        r2 *= xDx - bi
+    sol = r1 - r2
+
+    if not initcond:
+        return HolonomicFunction(sol, x).composition(z)
+
+    simp = hyperexpand(func)
+
+    if simp in (Infinity, NegativeInfinity):
+        return HolonomicFunction(sol, x).composition(z)
+
+    # computing initial conditions
+    if not isinstance(simp, meijerg):
+        y0 = _find_conditions(simp, x, x0, sol.order, use_limit=False)
+        while not y0:
+            x0 += 1
+            y0 = _find_conditions(simp, x, x0, sol.order, use_limit=False)
+
+        return HolonomicFunction(sol, x).composition(z, x0, y0)
+
+    if isinstance(simp, meijerg):
+        x0 = 1
+        y0 = _find_conditions(simp, x, x0, sol.order, evalf, use_limit=False)
+        while not y0:
+            x0 += 1
+            y0 = _find_conditions(simp, x, x0, sol.order, evalf, use_limit=False)
+
+        return HolonomicFunction(sol, x).composition(z, x0, y0)
+
+    return HolonomicFunction(sol, x).composition(z)
+
+
+x_1 = Dummy('x_1')
+_lookup_table = None
+domain_for_table = None
+from sympy.integrals.meijerint import _mytype
+
+
+def expr_to_holonomic(func, x=None, x0=0, y0=None, lenics=None, domain=None, initcond=True):
+    """
+    Converts a function or an expression to a holonomic function.
+
+    Parameters
+    ==========
+
+    func:
+        The expression to be converted.
+    x:
+        variable for the function.
+    x0:
+        point at which initial condition must be computed.
+    y0:
+        One can optionally provide initial condition if the method
+        is not able to do it automatically.
+    lenics:
+        Number of terms in the initial condition. By default it is
+        equal to the order of the annihilator.
+    domain:
+        Ground domain for the polynomials in ``x`` appearing as coefficients
+        in the annihilator.
+    initcond:
+        Set it false if you do not want the initial conditions to be computed.
+
+    Examples
+    ========
+
+    >>> from sympy.holonomic.holonomic import expr_to_holonomic
+    >>> from sympy import sin, exp, symbols
+    >>> x = symbols('x')
+    >>> expr_to_holonomic(sin(x))
+    HolonomicFunction((1) + (1)*Dx**2, x, 0, [0, 1])
+    >>> expr_to_holonomic(exp(x))
+    HolonomicFunction((-1) + (1)*Dx, x, 0, [1])
+
+    See Also
+    ========
+
+    sympy.integrals.meijerint._rewrite1, _convert_poly_rat_alg, _create_table
+    """
+    func = sympify(func)
+    syms = func.free_symbols
+
+    if not x:
+        if len(syms) == 1:
+            x= syms.pop()
+        else:
+            raise ValueError("Specify the variable for the function")
+    elif x in syms:
+        syms.remove(x)
+
+    extra_syms = list(syms)
+
+    if domain is None:
+        if func.has(Float):
+            domain = RR
+        else:
+            domain = QQ
+        if len(extra_syms) != 0:
+            domain = domain[extra_syms].get_field()
+
+    # try to convert if the function is polynomial or rational
+    solpoly = _convert_poly_rat_alg(func, x, x0=x0, y0=y0, lenics=lenics, domain=domain, initcond=initcond)
+    if solpoly:
+        return solpoly
+
+    # create the lookup table
+    global _lookup_table, domain_for_table
+    if not _lookup_table:
+        domain_for_table = domain
+        _lookup_table = {}
+        _create_table(_lookup_table, domain=domain)
+    elif domain != domain_for_table:
+        domain_for_table = domain
+        _lookup_table = {}
+        _create_table(_lookup_table, domain=domain)
+
+    # use the table directly to convert to Holonomic
+    if func.is_Function:
+        f = func.subs(x, x_1)
+        t = _mytype(f, x_1)
+        if t in _lookup_table:
+            l = _lookup_table[t]
+            sol = l[0][1].change_x(x)
+        else:
+            sol = _convert_meijerint(func, x, initcond=False, domain=domain)
+            if not sol:
+                raise NotImplementedError
+            if y0:
+                sol.y0 = y0
+            if y0 or not initcond:
+                sol.x0 = x0
+                return sol
+            if not lenics:
+                lenics = sol.annihilator.order
+            _y0 = _find_conditions(func, x, x0, lenics)
+            while not _y0:
+                x0 += 1
+                _y0 = _find_conditions(func, x, x0, lenics)
+            return HolonomicFunction(sol.annihilator, x, x0, _y0)
+
+        if y0 or not initcond:
+            sol = sol.composition(func.args[0])
+            if y0:
+                sol.y0 = y0
+            sol.x0 = x0
+            return sol
+        if not lenics:
+            lenics = sol.annihilator.order
+
+        _y0 = _find_conditions(func, x, x0, lenics)
+        while not _y0:
+            x0 += 1
+            _y0 = _find_conditions(func, x, x0, lenics)
+        return sol.composition(func.args[0], x0, _y0)
+
+    # iterate through the expression recursively
+    args = func.args
+    f = func.func
+    sol = expr_to_holonomic(args[0], x=x, initcond=False, domain=domain)
+
+    if f is Add:
+        for i in range(1, len(args)):
+            sol += expr_to_holonomic(args[i], x=x, initcond=False, domain=domain)
+
+    elif f is Mul:
+        for i in range(1, len(args)):
+            sol *= expr_to_holonomic(args[i], x=x, initcond=False, domain=domain)
+
+    elif f is Pow:
+        sol = sol**args[1]
+    sol.x0 = x0
+    if not sol:
+        raise NotImplementedError
+    if y0:
+        sol.y0 = y0
+    if y0 or not initcond:
+        return sol
+    if sol.y0:
+        return sol
+    if not lenics:
+        lenics = sol.annihilator.order
+    if sol.annihilator.is_singular(x0):
+        r = sol._indicial()
+        l = list(r)
+        if len(r) == 1 and r[l[0]] == S.One:
+            r = l[0]
+            g = func / (x - x0)**r
+            singular_ics = _find_conditions(g, x, x0, lenics)
+            singular_ics = [j / factorial(i) for i, j in enumerate(singular_ics)]
+            y0 = {r:singular_ics}
+            return HolonomicFunction(sol.annihilator, x, x0, y0)
+
+    _y0 = _find_conditions(func, x, x0, lenics)
+    while not _y0:
+        x0 += 1
+        _y0 = _find_conditions(func, x, x0, lenics)
+
+    return HolonomicFunction(sol.annihilator, x, x0, _y0)
+
+
+## Some helper functions ##
+
+def _normalize(list_of, parent, negative=True):
+    """
+    Normalize a given annihilator
+    """
+
+    num = []
+    denom = []
+    base = parent.base
+    K = base.get_field()
+    lcm_denom = base.from_sympy(S.One)
+    list_of_coeff = []
+
+    # convert polynomials to the elements of associated
+    # fraction field
+    for i, j in enumerate(list_of):
+        if isinstance(j, base.dtype):
+            list_of_coeff.append(K.new(j.to_list()))
+        elif not isinstance(j, K.dtype):
+            list_of_coeff.append(K.from_sympy(sympify(j)))
+        else:
+            list_of_coeff.append(j)
+
+        # corresponding numerators of the sequence of polynomials
+        num.append(list_of_coeff[i].numer())
+
+        # corresponding denominators
+        denom.append(list_of_coeff[i].denom())
+
+    # lcm of denominators in the coefficients
+    for i in denom:
+        lcm_denom = i.lcm(lcm_denom)
+
+    if negative:
+        lcm_denom = -lcm_denom
+
+    lcm_denom = K.new(lcm_denom.to_list())
+
+    # multiply the coefficients with lcm
+    for i, j in enumerate(list_of_coeff):
+        list_of_coeff[i] = j * lcm_denom
+
+    gcd_numer = base((list_of_coeff[-1].numer() / list_of_coeff[-1].denom()).to_list())
+
+    # gcd of numerators in the coefficients
+    for i in num:
+        gcd_numer = i.gcd(gcd_numer)
+
+    gcd_numer = K.new(gcd_numer.to_list())
+
+    # divide all the coefficients by the gcd
+    for i, j in enumerate(list_of_coeff):
+        frac_ans = j / gcd_numer
+        list_of_coeff[i] = base((frac_ans.numer() / frac_ans.denom()).to_list())
+
+    return DifferentialOperator(list_of_coeff, parent)
+
+
+def _derivate_diff_eq(listofpoly, K):
+    """
+    Let a differential equation a0(x)y(x) + a1(x)y'(x) + ... = 0
+    where a0, a1,... are polynomials or rational functions. The function
+    returns b0, b1, b2... such that the differential equation
+    b0(x)y(x) + b1(x)y'(x) +... = 0 is formed after differentiating the
+    former equation.
+    """
+
+    sol = []
+    a = len(listofpoly) - 1
+    sol.append(DMFdiff(listofpoly[0], K))
+
+    for i, j in enumerate(listofpoly[1:]):
+        sol.append(DMFdiff(j, K) + listofpoly[i])
+
+    sol.append(listofpoly[a])
+    return sol
+
+
+def _hyper_to_meijerg(func):
+    """
+    Converts a `hyper` to meijerg.
+    """
+    ap = func.ap
+    bq = func.bq
+
+    if any(i <= 0 and int(i) == i for i in ap):
+        return hyperexpand(func)
+
+    z = func.args[2]
+
+    # parameters of the `meijerg` function.
+    an = (1 - i for i in ap)
+    anp = ()
+    bm = (S.Zero, )
+    bmq = (1 - i for i in bq)
+
+    k = S.One
+
+    for i in bq:
+        k = k * gamma(i)
+
+    for i in ap:
+        k = k / gamma(i)
+
+    return k * meijerg(an, anp, bm, bmq, -z)
+
+
+def _add_lists(list1, list2):
+    """Takes polynomial sequences of two annihilators a and b and returns
+    the list of polynomials of sum of a and b.
+    """
+    if len(list1) <= len(list2):
+        sol = [a + b for a, b in zip(list1, list2)] + list2[len(list1):]
+    else:
+        sol = [a + b for a, b in zip(list1, list2)] + list1[len(list2):]
+    return sol
+
+
+def _extend_y0(Holonomic, n):
+    """
+    Tries to find more initial conditions by substituting the initial
+    value point in the differential equation.
+    """
+
+    if Holonomic.annihilator.is_singular(Holonomic.x0) or Holonomic.is_singularics() == True:
+        return Holonomic.y0
+
+    annihilator = Holonomic.annihilator
+    a = annihilator.order
+
+    listofpoly = []
+
+    y0 = Holonomic.y0
+    R = annihilator.parent.base
+    K = R.get_field()
+
+    for j in annihilator.listofpoly:
+        if isinstance(j, annihilator.parent.base.dtype):
+            listofpoly.append(K.new(j.to_list()))
+
+    if len(y0) < a or n <= len(y0):
+        return y0
+    list_red = [-listofpoly[i] / listofpoly[a]
+                for i in range(a)]
+    y1 = y0[:min(len(y0), a)]
+    for _ in range(n - a):
+        sol = 0
+        for a, b in zip(y1, list_red):
+            r = DMFsubs(b, Holonomic.x0)
+            if not getattr(r, 'is_finite', True):
+                return y0
+            if isinstance(r, (PolyElement, FracElement)):
+                r = r.as_expr()
+            sol += a * r
+        y1.append(sol)
+        list_red = _derivate_diff_eq(list_red, K)
+    return y0 + y1[len(y0):]
+
+
+def DMFdiff(frac, K):
+    # differentiate a DMF object represented as p/q
+    if not isinstance(frac, DMF):
+        return frac.diff()
+
+    p = K.numer(frac)
+    q = K.denom(frac)
+    sol_num = - p * q.diff() + q * p.diff()
+    sol_denom = q**2
+    return K((sol_num.to_list(), sol_denom.to_list()))
+
+
+def DMFsubs(frac, x0, mpm=False):
+    # substitute the point x0 in DMF object of the form p/q
+    if not isinstance(frac, DMF):
+        return frac
+
+    p = frac.num
+    q = frac.den
+    sol_p = S.Zero
+    sol_q = S.Zero
+
+    if mpm:
+        from mpmath import mp
+
+    for i, j in enumerate(reversed(p)):
+        if mpm:
+            j = sympify(j)._to_mpmath(mp.prec)
+        sol_p += j * x0**i
+
+    for i, j in enumerate(reversed(q)):
+        if mpm:
+            j = sympify(j)._to_mpmath(mp.prec)
+        sol_q += j * x0**i
+
+    if isinstance(sol_p, (PolyElement, FracElement)):
+        sol_p = sol_p.as_expr()
+    if isinstance(sol_q, (PolyElement, FracElement)):
+        sol_q = sol_q.as_expr()
+
+    return sol_p / sol_q
+
+
+def _convert_poly_rat_alg(func, x, x0=0, y0=None, lenics=None, domain=QQ, initcond=True):
+    """
+    Converts polynomials, rationals and algebraic functions to holonomic.
+    """
+
+    ispoly = func.is_polynomial()
+    if not ispoly:
+        israt = func.is_rational_function()
+    else:
+        israt = True
+
+    if not (ispoly or israt):
+        basepoly, ratexp = func.as_base_exp()
+        if basepoly.is_polynomial() and ratexp.is_Number:
+            if isinstance(ratexp, Float):
+                ratexp = nsimplify(ratexp)
+            m, n = ratexp.p, ratexp.q
+            is_alg = True
+        else:
+            is_alg = False
+    else:
+        is_alg = True
+
+    if not (ispoly or israt or is_alg):
+        return None
+
+    R = domain.old_poly_ring(x)
+    _, Dx = DifferentialOperators(R, 'Dx')
+
+    # if the function is constant
+    if not func.has(x):
+        return HolonomicFunction(Dx, x, 0, [func])
+
+    if ispoly:
+        # differential equation satisfied by polynomial
+        sol = func * Dx - func.diff(x)
+        sol = _normalize(sol.listofpoly, sol.parent, negative=False)
+        is_singular = sol.is_singular(x0)
+
+        # try to compute the conditions for singular points
+        if y0 is None and x0 == 0 and is_singular:
+            rep = R.from_sympy(func).to_list()
+            for i, j in enumerate(reversed(rep)):
+                if j == 0:
+                    continue
+                coeff = list(reversed(rep))[i:]
+                indicial = i
+                break
+            for i, j in enumerate(coeff):
+                if isinstance(j, (PolyElement, FracElement)):
+                    coeff[i] = j.as_expr()
+            y0 = {indicial: S(coeff)}
+
+    elif israt:
+        p, q = func.as_numer_denom()
+        # differential equation satisfied by rational
+        sol = p * q * Dx + p * q.diff(x) - q * p.diff(x)
+        sol = _normalize(sol.listofpoly, sol.parent, negative=False)
+
+    elif is_alg:
+        sol = n * (x / m) * Dx - 1
+        sol = HolonomicFunction(sol, x).composition(basepoly).annihilator
+        is_singular = sol.is_singular(x0)
+
+        # try to compute the conditions for singular points
+        if y0 is None and x0 == 0 and is_singular and \
+            (lenics is None or lenics <= 1):
+            rep = R.from_sympy(basepoly).to_list()
+            for i, j in enumerate(reversed(rep)):
+                if j == 0:
+                    continue
+                if isinstance(j, (PolyElement, FracElement)):
+                    j = j.as_expr()
+
+                coeff = S(j)**ratexp
+                indicial = S(i) * ratexp
+                break
+            if isinstance(coeff, (PolyElement, FracElement)):
+                coeff = coeff.as_expr()
+            y0 = {indicial: S([coeff])}
+
+    if y0 or not initcond:
+        return HolonomicFunction(sol, x, x0, y0)
+
+    if not lenics:
+        lenics = sol.order
+
+    if sol.is_singular(x0):
+        r = HolonomicFunction(sol, x, x0)._indicial()
+        l = list(r)
+        if len(r) == 1 and r[l[0]] == S.One:
+            r = l[0]
+            g = func / (x - x0)**r
+            singular_ics = _find_conditions(g, x, x0, lenics)
+            singular_ics = [j / factorial(i) for i, j in enumerate(singular_ics)]
+            y0 = {r:singular_ics}
+            return HolonomicFunction(sol, x, x0, y0)
+
+    y0 = _find_conditions(func, x, x0, lenics)
+    while not y0:
+        x0 += 1
+        y0 = _find_conditions(func, x, x0, lenics)
+
+    return HolonomicFunction(sol, x, x0, y0)
+
+
+def _convert_meijerint(func, x, initcond=True, domain=QQ):
+    args = meijerint._rewrite1(func, x)
+
+    if args:
+        fac, po, g, _ = args
+    else:
+        return None
+
+    # lists for sum of meijerg functions
+    fac_list = [fac * i[0] for i in g]
+    t = po.as_base_exp()
+    s = t[1] if t[0] == x else S.Zero
+    po_list = [s + i[1] for i in g]
+    G_list = [i[2] for i in g]
+
+    # finds meijerg representation of x**s * meijerg(a1 ... ap, b1 ... bq, z)
+    def _shift(func, s):
+        z = func.args[-1]
+        if z.has(I):
+            z = z.subs(exp_polar, exp)
+
+        d = z.collect(x, evaluate=False)
+        b = list(d)[0]
+        a = d[b]
+
+        t = b.as_base_exp()
+        b = t[1] if t[0] == x else S.Zero
+        r = s / b
+        an = (i + r for i in func.args[0][0])
+        ap = (i + r for i in func.args[0][1])
+        bm = (i + r for i in func.args[1][0])
+        bq = (i + r for i in func.args[1][1])
+
+        return a**-r, meijerg((an, ap), (bm, bq), z)
+
+    coeff, m = _shift(G_list[0], po_list[0])
+    sol = fac_list[0] * coeff * from_meijerg(m, initcond=initcond, domain=domain)
+
+    # add all the meijerg functions after converting to holonomic
+    for i in range(1, len(G_list)):
+        coeff, m = _shift(G_list[i], po_list[i])
+        sol += fac_list[i] * coeff * from_meijerg(m, initcond=initcond, domain=domain)
+
+    return sol
+
+
+def _create_table(table, domain=QQ):
+    """
+    Creates the look-up table. For a similar implementation
+    see meijerint._create_lookup_table.
+    """
+
+    def add(formula, annihilator, arg, x0=0, y0=()):
+        """
+        Adds a formula in the dictionary
+        """
+        table.setdefault(_mytype(formula, x_1), []).append((formula,
+            HolonomicFunction(annihilator, arg, x0, y0)))
+
+    R = domain.old_poly_ring(x_1)
+    _, Dx = DifferentialOperators(R, 'Dx')
+
+    # add some basic functions
+    add(sin(x_1), Dx**2 + 1, x_1, 0, [0, 1])
+    add(cos(x_1), Dx**2 + 1, x_1, 0, [1, 0])
+    add(exp(x_1), Dx - 1, x_1, 0, 1)
+    add(log(x_1), Dx + x_1*Dx**2, x_1, 1, [0, 1])
+
+    add(erf(x_1), 2*x_1*Dx + Dx**2, x_1, 0, [0, 2/sqrt(pi)])
+    add(erfc(x_1), 2*x_1*Dx + Dx**2, x_1, 0, [1, -2/sqrt(pi)])
+    add(erfi(x_1), -2*x_1*Dx + Dx**2, x_1, 0, [0, 2/sqrt(pi)])
+
+    add(sinh(x_1), Dx**2 - 1, x_1, 0, [0, 1])
+    add(cosh(x_1), Dx**2 - 1, x_1, 0, [1, 0])
+
+    add(sinc(x_1), x_1 + 2*Dx + x_1*Dx**2, x_1)
+
+    add(Si(x_1), x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1)
+    add(Ci(x_1), x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1)
+
+    add(Shi(x_1), -x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1)
+
+
+def _find_conditions(func, x, x0, order, evalf=False, use_limit=True):
+    y0 = []
+    for _ in range(order):
+        val = func.subs(x, x0)
+        if evalf:
+            val = val.evalf()
+        if use_limit and isinstance(val, NaN):
+            val = limit(func, x, x0)
+        if val.is_finite is False or isinstance(val, NaN):
+            return None
+        y0.append(val)
+        func = func.diff(x)
+    return y0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/holonomicerrors.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/holonomicerrors.py
new file mode 100644
index 0000000000000000000000000000000000000000..459a94eb25b186e30b9577d972ebc62a36801f6f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/holonomicerrors.py
@@ -0,0 +1,49 @@
+""" Common Exceptions for `holonomic` module. """
+
+class BaseHolonomicError(Exception):
+
+    def new(self, *args):
+        raise NotImplementedError("abstract base class")
+
+class NotPowerSeriesError(BaseHolonomicError):
+
+    def __init__(self, holonomic, x0):
+        self.holonomic = holonomic
+        self.x0 = x0
+
+    def __str__(self):
+        s = 'A Power Series does not exists for '
+        s += str(self.holonomic)
+        s += ' about %s.' %self.x0
+        return s
+
+class NotHolonomicError(BaseHolonomicError):
+
+    def __init__(self, m):
+        self.m = m
+
+    def __str__(self):
+        return self.m
+
+class SingularityError(BaseHolonomicError):
+
+    def __init__(self, holonomic, x0):
+        self.holonomic = holonomic
+        self.x0 = x0
+
+    def __str__(self):
+        s = str(self.holonomic)
+        s += ' has a singularity at %s.' %self.x0
+        return s
+
+class NotHyperSeriesError(BaseHolonomicError):
+
+    def __init__(self, holonomic, x0):
+        self.holonomic = holonomic
+        self.x0 = x0
+
+    def __str__(self):
+        s = 'Power series expansion of '
+        s += str(self.holonomic)
+        s += ' about %s is not hypergeometric' %self.x0
+        return s
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/numerical.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/numerical.py
new file mode 100644
index 0000000000000000000000000000000000000000..418b7c627e2e3d74dcded080a9b6d351cdaa9f3f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/numerical.py
@@ -0,0 +1,98 @@
+"""Numerical Methods for Holonomic Functions"""
+
+from sympy.core.sympify import sympify
+from sympy.holonomic.holonomic import DMFsubs
+
+from mpmath import mp
+
+
+def _evalf(func, points, derivatives=False, method='RK4'):
+    """
+    Numerical methods for numerical integration along a given set of
+    points in the complex plane.
+    """
+
+    ann = func.annihilator
+    a = ann.order
+    R = ann.parent.base
+    K = R.get_field()
+
+    if method == 'Euler':
+        meth = _euler
+    else:
+        meth = _rk4
+
+    dmf = [K.new(j.to_list()) for j in ann.listofpoly]
+    red = [-dmf[i] / dmf[a] for i in range(a)]
+
+    y0 = func.y0
+    if len(y0) < a:
+        raise TypeError("Not Enough Initial Conditions")
+    x0 = func.x0
+    sol = [meth(red, x0, points[0], y0, a)]
+
+    for i, j in enumerate(points[1:]):
+        sol.append(meth(red, points[i], j, sol[-1], a))
+
+    if not derivatives:
+        return [sympify(i[0]) for i in sol]
+    else:
+        return sympify(sol)
+
+
+def _euler(red, x0, x1, y0, a):
+    """
+    Euler's method for numerical integration.
+    From x0 to x1 with initial values given at x0 as vector y0.
+    """
+
+    A = sympify(x0)._to_mpmath(mp.prec)
+    B = sympify(x1)._to_mpmath(mp.prec)
+    y_0 = [sympify(i)._to_mpmath(mp.prec) for i in y0]
+    h = B - A
+    f_0 = y_0[1:]
+    f_0_n = 0
+
+    for i in range(a):
+        f_0_n += sympify(DMFsubs(red[i], A, mpm=True))._to_mpmath(mp.prec) * y_0[i]
+    f_0.append(f_0_n)
+
+    return [y_0[i] + h * f_0[i] for i in range(a)]
+
+
+def _rk4(red, x0, x1, y0, a):
+    """
+    Runge-Kutta 4th order numerical method.
+    """
+
+    A = sympify(x0)._to_mpmath(mp.prec)
+    B = sympify(x1)._to_mpmath(mp.prec)
+    y_0 = [sympify(i)._to_mpmath(mp.prec) for i in y0]
+    h = B - A
+
+    f_0_n = 0
+    f_1_n = 0
+    f_2_n = 0
+    f_3_n = 0
+
+    f_0 = y_0[1:]
+    for i in range(a):
+        f_0_n += sympify(DMFsubs(red[i], A, mpm=True))._to_mpmath(mp.prec) * y_0[i]
+    f_0.append(f_0_n)
+
+    f_1 = [y_0[i] + f_0[i]*h/2 for i in range(1, a)]
+    for i in range(a):
+        f_1_n += sympify(DMFsubs(red[i], A + h/2, mpm=True))._to_mpmath(mp.prec) * (y_0[i] + f_0[i]*h/2)
+    f_1.append(f_1_n)
+
+    f_2 = [y_0[i] + f_1[i]*h/2 for i in range(1, a)]
+    for i in range(a):
+        f_2_n += sympify(DMFsubs(red[i], A + h/2, mpm=True))._to_mpmath(mp.prec) * (y_0[i] + f_1[i]*h/2)
+    f_2.append(f_2_n)
+
+    f_3 = [y_0[i] + f_2[i]*h for i in range(1, a)]
+    for i in range(a):
+        f_3_n += sympify(DMFsubs(red[i], A + h, mpm=True))._to_mpmath(mp.prec) * (y_0[i] + f_2[i]*h)
+    f_3.append(f_3_n)
+
+    return [y_0[i] + h*(f_0[i]+2*f_1[i]+2*f_2[i]+f_3[i])/6 for i in range(a)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/recurrence.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/recurrence.py
new file mode 100644
index 0000000000000000000000000000000000000000..8c2c17ceda2d042c12778977cadd5ce9ee3b7479
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/recurrence.py
@@ -0,0 +1,342 @@
+"""Recurrence Operators"""
+
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.printing import sstr
+from sympy.core.sympify import sympify
+
+
+def RecurrenceOperators(base, generator):
+    """
+    Returns an Algebra of Recurrence Operators and the operator for
+    shifting i.e. the `Sn` operator.
+    The first argument needs to be the base polynomial ring for the algebra
+    and the second argument must be a generator which can be either a
+    noncommutative Symbol or a string.
+
+    Examples
+    ========
+
+    >>> from sympy import ZZ
+    >>> from sympy import symbols
+    >>> from sympy.holonomic.recurrence import RecurrenceOperators
+    >>> n = symbols('n', integer=True)
+    >>> R, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn')
+    """
+
+    ring = RecurrenceOperatorAlgebra(base, generator)
+    return (ring, ring.shift_operator)
+
+
+class RecurrenceOperatorAlgebra:
+    """
+    A Recurrence Operator Algebra is a set of noncommutative polynomials
+    in intermediate `Sn` and coefficients in a base ring A. It follows the
+    commutation rule:
+    Sn * a(n) = a(n + 1) * Sn
+
+    This class represents a Recurrence Operator Algebra and serves as the parent ring
+    for Recurrence Operators.
+
+    Examples
+    ========
+
+    >>> from sympy import ZZ
+    >>> from sympy import symbols
+    >>> from sympy.holonomic.recurrence import RecurrenceOperators
+    >>> n = symbols('n', integer=True)
+    >>> R, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn')
+    >>> R
+    Univariate Recurrence Operator Algebra in intermediate Sn over the base ring
+    ZZ[n]
+
+    See Also
+    ========
+
+    RecurrenceOperator
+    """
+
+    def __init__(self, base, generator):
+        # the base ring for the algebra
+        self.base = base
+        # the operator representing shift i.e. `Sn`
+        self.shift_operator = RecurrenceOperator(
+            [base.zero, base.one], self)
+
+        if generator is None:
+            self.gen_symbol = symbols('Sn', commutative=False)
+        else:
+            if isinstance(generator, str):
+                self.gen_symbol = symbols(generator, commutative=False)
+            elif isinstance(generator, Symbol):
+                self.gen_symbol = generator
+
+    def __str__(self):
+        string = 'Univariate Recurrence Operator Algebra in intermediate '\
+            + sstr(self.gen_symbol) + ' over the base ring ' + \
+            (self.base).__str__()
+
+        return string
+
+    __repr__ = __str__
+
+    def __eq__(self, other):
+        if self.base == other.base and self.gen_symbol == other.gen_symbol:
+            return True
+        else:
+            return False
+
+
+def _add_lists(list1, list2):
+    if len(list1) <= len(list2):
+        sol = [a + b for a, b in zip(list1, list2)] + list2[len(list1):]
+    else:
+        sol = [a + b for a, b in zip(list1, list2)] + list1[len(list2):]
+    return sol
+
+
+class RecurrenceOperator:
+    """
+    The Recurrence Operators are defined by a list of polynomials
+    in the base ring and the parent ring of the Operator.
+
+    Explanation
+    ===========
+
+    Takes a list of polynomials for each power of Sn and the
+    parent ring which must be an instance of RecurrenceOperatorAlgebra.
+
+    A Recurrence Operator can be created easily using
+    the operator `Sn`. See examples below.
+
+    Examples
+    ========
+
+    >>> from sympy.holonomic.recurrence import RecurrenceOperator, RecurrenceOperators
+    >>> from sympy import ZZ
+    >>> from sympy import symbols
+    >>> n = symbols('n', integer=True)
+    >>> R, Sn = RecurrenceOperators(ZZ.old_poly_ring(n),'Sn')
+
+    >>> RecurrenceOperator([0, 1, n**2], R)
+    (1)Sn + (n**2)Sn**2
+
+    >>> Sn*n
+    (n + 1)Sn
+
+    >>> n*Sn*n + 1 - Sn**2*n
+    (1) + (n**2 + n)Sn + (-n - 2)Sn**2
+
+    See Also
+    ========
+
+    DifferentialOperatorAlgebra
+    """
+
+    _op_priority = 20
+
+    def __init__(self, list_of_poly, parent):
+        # the parent ring for this operator
+        # must be an RecurrenceOperatorAlgebra object
+        self.parent = parent
+        # sequence of polynomials in n for each power of Sn
+        # represents the operator
+        # convert the expressions into ring elements using from_sympy
+        if isinstance(list_of_poly, list):
+            for i, j in enumerate(list_of_poly):
+                if isinstance(j, int):
+                    list_of_poly[i] = self.parent.base.from_sympy(S(j))
+                elif not isinstance(j, self.parent.base.dtype):
+                    list_of_poly[i] = self.parent.base.from_sympy(j)
+
+            self.listofpoly = list_of_poly
+        self.order = len(self.listofpoly) - 1
+
+    def __mul__(self, other):
+        """
+        Multiplies two Operators and returns another
+        RecurrenceOperator instance using the commutation rule
+        Sn * a(n) = a(n + 1) * Sn
+        """
+
+        listofself = self.listofpoly
+        base = self.parent.base
+
+        if not isinstance(other, RecurrenceOperator):
+            if not isinstance(other, self.parent.base.dtype):
+                listofother = [self.parent.base.from_sympy(sympify(other))]
+
+            else:
+                listofother = [other]
+        else:
+            listofother = other.listofpoly
+        # multiply a polynomial `b` with a list of polynomials
+
+        def _mul_dmp_diffop(b, listofother):
+            if isinstance(listofother, list):
+                return [i * b for i in listofother]
+            return [b * listofother]
+
+        sol = _mul_dmp_diffop(listofself[0], listofother)
+
+        # compute Sn^i * b
+        def _mul_Sni_b(b):
+            sol = [base.zero]
+
+            if isinstance(b, list):
+                for i in b:
+                    j = base.to_sympy(i).subs(base.gens[0], base.gens[0] + S.One)
+                    sol.append(base.from_sympy(j))
+
+            else:
+                j = b.subs(base.gens[0], base.gens[0] + S.One)
+                sol.append(base.from_sympy(j))
+
+            return sol
+
+        for i in range(1, len(listofself)):
+            # find Sn^i * b in ith iteration
+            listofother = _mul_Sni_b(listofother)
+            # solution = solution + listofself[i] * (Sn^i * b)
+            sol = _add_lists(sol, _mul_dmp_diffop(listofself[i], listofother))
+
+        return RecurrenceOperator(sol, self.parent)
+
+    def __rmul__(self, other):
+        if not isinstance(other, RecurrenceOperator):
+
+            if isinstance(other, int):
+                other = S(other)
+
+            if not isinstance(other, self.parent.base.dtype):
+                other = (self.parent.base).from_sympy(other)
+
+            sol = [other * j for j in self.listofpoly]
+            return RecurrenceOperator(sol, self.parent)
+
+    def __add__(self, other):
+        if isinstance(other, RecurrenceOperator):
+
+            sol = _add_lists(self.listofpoly, other.listofpoly)
+            return RecurrenceOperator(sol, self.parent)
+
+        else:
+
+            if isinstance(other, int):
+                other = S(other)
+            list_self = self.listofpoly
+            if not isinstance(other, self.parent.base.dtype):
+                list_other = [((self.parent).base).from_sympy(other)]
+            else:
+                list_other = [other]
+            sol = [list_self[0] + list_other[0]] + list_self[1:]
+
+            return RecurrenceOperator(sol, self.parent)
+
+    __radd__ = __add__
+
+    def __sub__(self, other):
+        return self + (-1) * other
+
+    def __rsub__(self, other):
+        return (-1) * self + other
+
+    def __pow__(self, n):
+        if n == 1:
+            return self
+        result = RecurrenceOperator([self.parent.base.one], self.parent)
+        if n == 0:
+            return result
+        # if self is `Sn`
+        if self.listofpoly == self.parent.shift_operator.listofpoly:
+            sol = [self.parent.base.zero] * n + [self.parent.base.one]
+            return RecurrenceOperator(sol, self.parent)
+        x = self
+        while True:
+            if n % 2:
+                result *= x
+            n >>= 1
+            if not n:
+                break
+            x *= x
+        return result
+
+    def __str__(self):
+        listofpoly = self.listofpoly
+        print_str = ''
+
+        for i, j in enumerate(listofpoly):
+            if j == self.parent.base.zero:
+                continue
+
+            j = self.parent.base.to_sympy(j)
+
+            if i == 0:
+                print_str += '(' + sstr(j) + ')'
+                continue
+
+            if print_str:
+                print_str += ' + '
+
+            if i == 1:
+                print_str += '(' + sstr(j) + ')Sn'
+                continue
+
+            print_str += '(' + sstr(j) + ')' + 'Sn**' + sstr(i)
+
+        return print_str
+
+    __repr__ = __str__
+
+    def __eq__(self, other):
+        if isinstance(other, RecurrenceOperator):
+            if self.listofpoly == other.listofpoly and self.parent == other.parent:
+                return True
+            else:
+                return False
+        return self.listofpoly[0] == other and \
+            all(i is self.parent.base.zero for i in self.listofpoly[1:])
+
+
+class HolonomicSequence:
+    """
+    A Holonomic Sequence is a type of sequence satisfying a linear homogeneous
+    recurrence relation with Polynomial coefficients. Alternatively, A sequence
+    is Holonomic if and only if its generating function is a Holonomic Function.
+    """
+
+    def __init__(self, recurrence, u0=[]):
+        self.recurrence = recurrence
+        if not isinstance(u0, list):
+            self.u0 = [u0]
+        else:
+            self.u0 = u0
+
+        if len(self.u0) == 0:
+            self._have_init_cond = False
+        else:
+            self._have_init_cond = True
+        self.n = recurrence.parent.base.gens[0]
+
+    def __repr__(self):
+        str_sol = 'HolonomicSequence(%s, %s)' % ((self.recurrence).__repr__(), sstr(self.n))
+        if not self._have_init_cond:
+            return str_sol
+        else:
+            cond_str = ''
+            seq_str = 0
+            for i in self.u0:
+                cond_str += ', u(%s) = %s' % (sstr(seq_str), sstr(i))
+                seq_str += 1
+
+            sol = str_sol + cond_str
+            return sol
+
+    __str__ = __repr__
+
+    def __eq__(self, other):
+        if self.recurrence != other.recurrence or self.n != other.n:
+            return False
+        if self._have_init_cond and other._have_init_cond:
+            return self.u0 == other.u0
+        return True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/test_holonomic.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/test_holonomic.py
new file mode 100644
index 0000000000000000000000000000000000000000..49956419e917b3bc81a163d29862c539f33f6284
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/test_holonomic.py
@@ -0,0 +1,851 @@
+from sympy.holonomic import (DifferentialOperator, HolonomicFunction,
+                             DifferentialOperators, from_hyper,
+                             from_meijerg, expr_to_holonomic)
+from sympy.holonomic.recurrence import RecurrenceOperators, HolonomicSequence
+from sympy.core import EulerGamma
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (asinh, cosh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.bessel import besselj
+from sympy.functions.special.beta_functions import beta
+from sympy.functions.special.error_functions import (Ci, Si, erf, erfc)
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import (hyper, meijerg)
+from sympy.printing.str import sstr
+from sympy.series.order import O
+from sympy.simplify.hyperexpand import hyperexpand
+from sympy.polys.domains.integerring import ZZ
+from sympy.polys.domains.rationalfield import QQ
+from sympy.polys.domains.realfield import RR
+
+
+def test_DifferentialOperator():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    assert Dx == R.derivative_operator
+    assert Dx == DifferentialOperator([R.base.zero, R.base.one], R)
+    assert x * Dx + x**2 * Dx**2 == DifferentialOperator([0, x, x**2], R)
+    assert (x**2 + 1) + Dx + x * \
+        Dx**5 == DifferentialOperator([x**2 + 1, 1, 0, 0, 0, x], R)
+    assert (x * Dx + x**2 + 1 - Dx * (x**3 + x))**3 == (-48 * x**6) + \
+        (-57 * x**7) * Dx + (-15 * x**8) * Dx**2 + (-x**9) * Dx**3
+    p = (x * Dx**2 + (x**2 + 3) * Dx**5) * (Dx + x**2)
+    q = (2 * x) + (4 * x**2) * Dx + (x**3) * Dx**2 + \
+        (20 * x**2 + x + 60) * Dx**3 + (10 * x**3 + 30 * x) * Dx**4 + \
+        (x**4 + 3 * x**2) * Dx**5 + (x**2 + 3) * Dx**6
+    assert p == q
+
+
+def test_HolonomicFunction_addition():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx**2 * x, x)
+    q = HolonomicFunction((2) * Dx + (x) * Dx**2, x)
+    assert p == q
+    p = HolonomicFunction(x * Dx + 1, x)
+    q = HolonomicFunction(Dx + 1, x)
+    r = HolonomicFunction((x - 2) + (x**2 - 2) * Dx + (x**2 - x) * Dx**2, x)
+    assert p + q == r
+    p = HolonomicFunction(x * Dx + Dx**2 * (x**2 + 2), x)
+    q = HolonomicFunction(Dx - 3, x)
+    r = HolonomicFunction((-54 * x**2 - 126 * x - 150) + (-135 * x**3 - 252 * x**2 - 270 * x + 140) * Dx +\
+                 (-27 * x**4 - 24 * x**2 + 14 * x - 150) * Dx**2 + \
+                 (9 * x**4 + 15 * x**3 + 38 * x**2 + 30 * x +40) * Dx**3, x)
+    assert p + q == r
+    p = HolonomicFunction(Dx**5 - 1, x)
+    q = HolonomicFunction(x**3 + Dx, x)
+    r = HolonomicFunction((-x**18 + 45*x**14 - 525*x**10 + 1575*x**6 - x**3 - 630*x**2) + \
+        (-x**15 + 30*x**11 - 195*x**7 + 210*x**3 - 1)*Dx + (x**18 - 45*x**14 + 525*x**10 - \
+        1575*x**6 + x**3 + 630*x**2)*Dx**5 + (x**15 - 30*x**11 + 195*x**7 - 210*x**3 + \
+        1)*Dx**6, x)
+    assert p+q == r
+
+    p = x**2 + 3*x + 8
+    q = x**3 - 7*x + 5
+    p = p*Dx - p.diff()
+    q = q*Dx - q.diff()
+    r = HolonomicFunction(p, x) + HolonomicFunction(q, x)
+    s = HolonomicFunction((6*x**2 + 18*x + 14) + (-4*x**3 - 18*x**2 - 62*x + 10)*Dx +\
+        (x**4 + 6*x**3 + 31*x**2 - 10*x - 71)*Dx**2, x)
+    assert r == s
+
+
+def test_HolonomicFunction_multiplication():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx+x+x*Dx**2, x)
+    q = HolonomicFunction(x*Dx+Dx*x+Dx**2, x)
+    r = HolonomicFunction((8*x**6 + 4*x**4 + 6*x**2 + 3) + (24*x**5 - 4*x**3 + 24*x)*Dx + \
+        (8*x**6 + 20*x**4 + 12*x**2 + 2)*Dx**2 + (8*x**5 + 4*x**3 + 4*x)*Dx**3 + \
+        (2*x**4 + x**2)*Dx**4, x)
+    assert p*q == r
+    p = HolonomicFunction(Dx**2+1, x)
+    q = HolonomicFunction(Dx-1, x)
+    r = HolonomicFunction((2) + (-2)*Dx + (1)*Dx**2, x)
+    assert p*q == r
+    p = HolonomicFunction(Dx**2+1+x+Dx, x)
+    q = HolonomicFunction((Dx*x-1)**2, x)
+    r = HolonomicFunction((4*x**7 + 11*x**6 + 16*x**5 + 4*x**4 - 6*x**3 - 7*x**2 - 8*x - 2) + \
+        (8*x**6 + 26*x**5 + 24*x**4 - 3*x**3 - 11*x**2 - 6*x - 2)*Dx + \
+        (8*x**6 + 18*x**5 + 15*x**4 - 3*x**3 - 6*x**2 - 6*x - 2)*Dx**2 + (8*x**5 + \
+            10*x**4 + 6*x**3 - 2*x**2 - 4*x)*Dx**3 + (4*x**5 + 3*x**4 - x**2)*Dx**4, x)
+    assert p*q == r
+    p = HolonomicFunction(x*Dx**2-1, x)
+    q = HolonomicFunction(Dx*x-x, x)
+    r = HolonomicFunction((x - 3) + (-2*x + 2)*Dx + (x)*Dx**2, x)
+    assert p*q == r
+
+
+def test_HolonomicFunction_power():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx+x+x*Dx**2, x)
+    a = HolonomicFunction(Dx, x)
+    for n in range(10):
+        assert a == p**n
+        a *= p
+
+
+def test_addition_initial_condition():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx-1, x, 0, [3])
+    q = HolonomicFunction(Dx**2+1, x, 0, [1, 0])
+    r = HolonomicFunction(-1 + Dx - Dx**2 + Dx**3, x, 0, [4, 3, 2])
+    assert p + q == r
+    p = HolonomicFunction(Dx - x + Dx**2, x, 0, [1, 2])
+    q = HolonomicFunction(Dx**2 + x, x, 0, [1, 0])
+    r = HolonomicFunction((-x**4 - x**3/4 - x**2 + Rational(1, 4)) + (x**3 + x**2/4 + x*Rational(3, 4) + 1)*Dx + \
+        (x*Rational(-3, 2) + Rational(7, 4))*Dx**2 + (x**2 - x*Rational(7, 4) + Rational(1, 4))*Dx**3 + (x**2 + x/4 + S.Half)*Dx**4, x, 0, [2, 2, -2, 2])
+    assert p + q == r
+    p = HolonomicFunction(Dx**2 + 4*x*Dx + x**2, x, 0, [3, 4])
+    q = HolonomicFunction(Dx**2 + 1, x, 0, [1, 1])
+    r = HolonomicFunction((x**6 + 2*x**4 - 5*x**2 - 6) + (4*x**5 + 36*x**3 - 32*x)*Dx + \
+         (x**6 + 3*x**4 + 5*x**2 - 9)*Dx**2 + (4*x**5 + 36*x**3 - 32*x)*Dx**3 + (x**4 + \
+            10*x**2 - 3)*Dx**4, x, 0, [4, 5, -1, -17])
+    assert p + q == r
+    q = HolonomicFunction(Dx**3 + x, x, 2, [3, 0, 1])
+    p = HolonomicFunction(Dx - 1, x, 2, [1])
+    r = HolonomicFunction((-x**2 - x + 1) + (x**2 + x)*Dx + (-x - 2)*Dx**3 + \
+        (x + 1)*Dx**4, x, 2, [4, 1, 2, -5 ])
+    assert p + q == r
+    p = expr_to_holonomic(sin(x))
+    q = expr_to_holonomic(1/x, x0=1)
+    r = HolonomicFunction((x**2 + 6) + (x**3 + 2*x)*Dx + (x**2 + 6)*Dx**2 + (x**3 + 2*x)*Dx**3, \
+        x, 1, [sin(1) + 1, -1 + cos(1), -sin(1) + 2])
+    assert p + q == r
+    C_1 = symbols('C_1')
+    p = expr_to_holonomic(sqrt(x))
+    q = expr_to_holonomic(sqrt(x**2-x))
+    r = (p + q).to_expr().subs(C_1, -I/2).expand()
+    assert r == I*sqrt(x)*sqrt(-x + 1) + sqrt(x)
+
+
+def test_multiplication_initial_condition():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx**2 + x*Dx - 1, x, 0, [3, 1])
+    q = HolonomicFunction(Dx**2 + 1, x, 0, [1, 1])
+    r = HolonomicFunction((x**4 + 14*x**2 + 60) + 4*x*Dx + (x**4 + 9*x**2 + 20)*Dx**2 + \
+        (2*x**3 + 18*x)*Dx**3 + (x**2 + 10)*Dx**4, x, 0, [3, 4, 2, 3])
+    assert p * q == r
+    p = HolonomicFunction(Dx**2 + x, x, 0, [1, 0])
+    q = HolonomicFunction(Dx**3 - x**2, x, 0, [3, 3, 3])
+    r = HolonomicFunction((x**8 - 37*x**7/27 - 10*x**6/27 - 164*x**5/9 - 184*x**4/9 + \
+        160*x**3/27 + 404*x**2/9 + 8*x + Rational(40, 3)) + (6*x**7 - 128*x**6/9 - 98*x**5/9 - 28*x**4/9 + \
+        8*x**3/9 + 28*x**2 + x*Rational(40, 9) - 40)*Dx + (3*x**6 - 82*x**5/9 + 76*x**4/9 + 4*x**3/3 + \
+        220*x**2/9 - x*Rational(80, 3))*Dx**2 + (-2*x**6 + 128*x**5/27 - 2*x**4/3 -80*x**2/9 + Rational(200, 9))*Dx**3 + \
+        (3*x**5 - 64*x**4/9 - 28*x**3/9 + 6*x**2 - x*Rational(20, 9) - Rational(20, 3))*Dx**4 + (-4*x**3 + 64*x**2/9 + \
+            x*Rational(8, 3))*Dx**5 + (x**4 - 64*x**3/27 - 4*x**2/3 + Rational(20, 9))*Dx**6, x, 0, [3, 3, 3, -3, -12, -24])
+    assert p * q == r
+    p = HolonomicFunction(Dx - 1, x, 0, [2])
+    q = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])
+    r = HolonomicFunction(2 -2*Dx + Dx**2, x, 0, [0, 2])
+    assert p * q == r
+    q = HolonomicFunction(x*Dx**2 + 1 + 2*Dx, x, 0,[0, 1])
+    r = HolonomicFunction((x - 1) + (-2*x + 2)*Dx + x*Dx**2, x, 0, [0, 2])
+    assert p * q == r
+    p = HolonomicFunction(Dx**2 - 1, x, 0, [1, 3])
+    q = HolonomicFunction(Dx**3 + 1, x, 0, [1, 2, 1])
+    r = HolonomicFunction(6*Dx + 3*Dx**2 + 2*Dx**3 - 3*Dx**4 + Dx**6, x, 0, [1, 5, 14, 17, 17, 2])
+    assert p * q == r
+    p = expr_to_holonomic(sin(x))
+    q = expr_to_holonomic(1/x, x0=1)
+    r = HolonomicFunction(x + 2*Dx + x*Dx**2, x, 1, [sin(1), -sin(1) + cos(1)])
+    assert p * q == r
+    p = expr_to_holonomic(sqrt(x))
+    q = expr_to_holonomic(sqrt(x**2-x))
+    r = (p * q).to_expr()
+    assert r == I*x*sqrt(-x + 1)
+
+
+def test_HolonomicFunction_composition():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx-1, x).composition(x**2+x)
+    r = HolonomicFunction((-2*x - 1) + Dx, x)
+    assert p == r
+    p = HolonomicFunction(Dx**2+1, x).composition(x**5+x**2+1)
+    r = HolonomicFunction((125*x**12 + 150*x**9 + 60*x**6 + 8*x**3) + (-20*x**3 - 2)*Dx + \
+        (5*x**4 + 2*x)*Dx**2, x)
+    assert p == r
+    p = HolonomicFunction(Dx**2*x+x, x).composition(2*x**3+x**2+1)
+    r = HolonomicFunction((216*x**9 + 324*x**8 + 180*x**7 + 152*x**6 + 112*x**5 + \
+        36*x**4 + 4*x**3) + (24*x**4 + 16*x**3 + 3*x**2 - 6*x - 1)*Dx + (6*x**5 + 5*x**4 + \
+        x**3 + 3*x**2 + x)*Dx**2, x)
+    assert p == r
+    p = HolonomicFunction(Dx**2+1, x).composition(1-x**2)
+    r = HolonomicFunction((4*x**3) - Dx + x*Dx**2, x)
+    assert p == r
+    p = HolonomicFunction(Dx**2+1, x).composition(x - 2/(x**2 + 1))
+    r = HolonomicFunction((x**12 + 6*x**10 + 12*x**9 + 15*x**8 + 48*x**7 + 68*x**6 + \
+        72*x**5 + 111*x**4 + 112*x**3 + 54*x**2 + 12*x + 1) + (12*x**8 + 32*x**6 + \
+        24*x**4 - 4)*Dx + (x**12 + 6*x**10 + 4*x**9 + 15*x**8 + 16*x**7 + 20*x**6 + 24*x**5+ \
+        15*x**4 + 16*x**3 + 6*x**2 + 4*x + 1)*Dx**2, x)
+    assert p == r
+
+
+def test_from_hyper():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    p = hyper([1, 1], [Rational(3, 2)], x**2/4)
+    q = HolonomicFunction((4*x) + (5*x**2 - 8)*Dx + (x**3 - 4*x)*Dx**2, x, 1, [2*sqrt(3)*pi/9, -4*sqrt(3)*pi/27 + Rational(4, 3)])
+    r = from_hyper(p)
+    assert r == q
+    p = from_hyper(hyper([1], [Rational(3, 2)], x**2/4))
+    q = HolonomicFunction(-x + (-x**2/2 + 2)*Dx + x*Dx**2, x)
+    # x0 = 1
+    y0 = '[sqrt(pi)*exp(1/4)*erf(1/2), -sqrt(pi)*exp(1/4)*erf(1/2)/2 + 1]'
+    assert sstr(p.y0) == y0
+    assert q.annihilator == p.annihilator
+
+
+def test_from_meijerg():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    p = from_meijerg(meijerg(([], [Rational(3, 2)]), ([S.Half], [S.Half, 1]), x))
+    q = HolonomicFunction(x/2 - Rational(1, 4) + (-x**2 + x/4)*Dx + x**2*Dx**2 + x**3*Dx**3, x, 1, \
+        [1/sqrt(pi), 1/(2*sqrt(pi)), -1/(4*sqrt(pi))])
+    assert p == q
+    p = from_meijerg(meijerg(([], []), ([0], []), x))
+    q = HolonomicFunction(1 + Dx, x, 0, [1])
+    assert p == q
+    p = from_meijerg(meijerg(([1], []), ([S.Half], [0]), x))
+    q = HolonomicFunction((x + S.Half)*Dx + x*Dx**2, x, 1, [sqrt(pi)*erf(1), exp(-1)])
+    assert p == q
+    p = from_meijerg(meijerg(([0], [1]), ([0], []), 2*x**2))
+    q = HolonomicFunction((3*x**2 - 1)*Dx + x**3*Dx**2, x, 1, [-exp(Rational(-1, 2)) + 1, -exp(Rational(-1, 2))])
+    assert p == q
+
+
+def test_to_Sequence():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    n = symbols('n', integer=True)
+    _, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn')
+    p = HolonomicFunction(x**2*Dx**4 + x + Dx, x).to_sequence()
+    q = [(HolonomicSequence(1 + (n + 2)*Sn**2 + (n**4 + 6*n**3 + 11*n**2 + 6*n)*Sn**3), 0, 1)]
+    assert p == q
+    p = HolonomicFunction(x**2*Dx**4 + x**3 + Dx**2, x).to_sequence()
+    q = [(HolonomicSequence(1 + (n**4 + 14*n**3 + 72*n**2 + 163*n + 140)*Sn**5), 0, 0)]
+    assert p == q
+    p = HolonomicFunction(x**3*Dx**4 + 1 + Dx**2, x).to_sequence()
+    q = [(HolonomicSequence(1 + (n**4 - 2*n**3 - n**2 + 2*n)*Sn + (n**2 + 3*n + 2)*Sn**2), 0, 0)]
+    assert p == q
+    p = HolonomicFunction(3*x**3*Dx**4 + 2*x*Dx + x*Dx**3, x).to_sequence()
+    q = [(HolonomicSequence(2*n + (3*n**4 - 6*n**3 - 3*n**2 + 6*n)*Sn + (n**3 + 3*n**2 + 2*n)*Sn**2), 0, 1)]
+    assert p == q
+
+
+def test_to_Sequence_Initial_Coniditons():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    n = symbols('n', integer=True)
+    _, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn')
+    p = HolonomicFunction(Dx - 1, x, 0, [1]).to_sequence()
+    q = [(HolonomicSequence(-1 + (n + 1)*Sn, 1), 0)]
+    assert p == q
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).to_sequence()
+    q = [(HolonomicSequence(1 + (n**2 + 3*n + 2)*Sn**2, [0, 1]), 0)]
+    assert p == q
+    p = HolonomicFunction(Dx**2 + 1 + x**3*Dx, x, 0, [2, 3]).to_sequence()
+    q = [(HolonomicSequence(n + Sn**2 + (n**2 + 7*n + 12)*Sn**4, [2, 3, -1, Rational(-1, 2), Rational(1, 12)]), 1)]
+    assert p == q
+    p = HolonomicFunction(x**3*Dx**5 + 1 + Dx, x).to_sequence()
+    q = [(HolonomicSequence(1 + (n + 1)*Sn + (n**5 - 5*n**3 + 4*n)*Sn**2), 0, 3)]
+    assert p == q
+    C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3')
+    p = expr_to_holonomic(log(1+x**2))
+    q = [(HolonomicSequence(n**2 + (n**2 + 2*n)*Sn**2, [0, 0, C_2]), 0, 1)]
+    assert p.to_sequence() == q
+    p = p.diff()
+    q = [(HolonomicSequence((n + 2) + (n + 2)*Sn**2, [C_0, 0]), 1, 0)]
+    assert p.to_sequence() == q
+    p = expr_to_holonomic(erf(x) + x).to_sequence()
+    q = [(HolonomicSequence((2*n**2 - 2*n) + (n**3 + 2*n**2 - n - 2)*Sn**2, [0, 1 + 2/sqrt(pi), 0, C_3]), 0, 2)]
+    assert p == q
+
+def test_series():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx**2 + 2*x*Dx, x, 0, [0, 1]).series(n=10)
+    q = x - x**3/3 + x**5/10 - x**7/42 + x**9/216 + O(x**10)
+    assert p == q
+    p = HolonomicFunction(Dx - 1, x).composition(x**2, 0, [1])  # e^(x**2)
+    q = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0])  # cos(x)
+    r = (p * q).series(n=10)  # expansion of cos(x) * exp(x**2)
+    s = 1 + x**2/2 + x**4/24 - 31*x**6/720 - 179*x**8/8064 + O(x**10)
+    assert r == s
+    t = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1])  # log(1 + x)
+    r = (p * t + q).series(n=10)
+    s = 1 + x - x**2 + 4*x**3/3 - 17*x**4/24 + 31*x**5/30 - 481*x**6/720 +\
+     71*x**7/105 - 20159*x**8/40320 + 379*x**9/840 + O(x**10)
+    assert r == s
+    p = HolonomicFunction((6+6*x-3*x**2) - (10*x-3*x**2-3*x**3)*Dx + \
+        (4-6*x**3+2*x**4)*Dx**2, x, 0, [0, 1]).series(n=7)
+    q = x + x**3/6 - 3*x**4/16 + x**5/20 - 23*x**6/960 + O(x**7)
+    assert p == q
+    p = HolonomicFunction((6+6*x-3*x**2) - (10*x-3*x**2-3*x**3)*Dx + \
+        (4-6*x**3+2*x**4)*Dx**2, x, 0, [1, 0]).series(n=7)
+    q = 1 - 3*x**2/4 - x**3/4 - 5*x**4/32 - 3*x**5/40 - 17*x**6/384 + O(x**7)
+    assert p == q
+    p = expr_to_holonomic(erf(x) + x).series(n=10)
+    C_3 = symbols('C_3')
+    q = (erf(x) + x).series(n=10)
+    assert p.subs(C_3, -2/(3*sqrt(pi))) == q
+    assert expr_to_holonomic(sqrt(x**3 + x)).series(n=10) == sqrt(x**3 + x).series(n=10)
+    assert expr_to_holonomic((2*x - 3*x**2)**Rational(1, 3)).series() == ((2*x - 3*x**2)**Rational(1, 3)).series()
+    assert  expr_to_holonomic(sqrt(x**2-x)).series() == (sqrt(x**2-x)).series()
+    assert expr_to_holonomic(cos(x)**2/x**2, y0={-2: [1, 0, -1]}).series(n=10) == (cos(x)**2/x**2).series(n=10)
+    assert expr_to_holonomic(cos(x)**2/x**2, x0=1).series(n=10).together() == (cos(x)**2/x**2).series(n=10, x0=1).together()
+    assert expr_to_holonomic(cos(x-1)**2/(x-1)**2, x0=1, y0={-2: [1, 0, -1]}).series(n=10) \
+        == (cos(x-1)**2/(x-1)**2).series(x0=1, n=10)
+
+def test_evalf_euler():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+
+    # log(1+x)
+    p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1])
+
+    # path taken is a straight line from 0 to 1, on the real axis
+    r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]
+    s = '0.699525841805253'  # approx. equal to log(2) i.e. 0.693147180559945
+    assert sstr(p.evalf(r, method='Euler')[-1]) == s
+
+    # path taken is a triangle 0-->1+i-->2
+    r = [0.1 + 0.1*I]
+    for i in range(9):
+        r.append(r[-1]+0.1+0.1*I)
+    for i in range(10):
+        r.append(r[-1]+0.1-0.1*I)
+
+    # close to the exact solution 1.09861228866811
+    # imaginary part also close to zero
+    s = '1.07530466271334 - 0.0251200594793912*I'
+    assert sstr(p.evalf(r, method='Euler')[-1]) == s
+
+    # sin(x)
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])
+    s = '0.905546532085401 - 6.93889390390723e-18*I'
+    assert sstr(p.evalf(r, method='Euler')[-1]) == s
+
+    # computing sin(pi/2) using this method
+    # using a linear path from 0 to pi/2
+    r = [0.1]
+    for i in range(14):
+        r.append(r[-1] + 0.1)
+    r.append(pi/2)
+    s = '1.08016557252834' # close to 1.0 (exact solution)
+    assert sstr(p.evalf(r, method='Euler')[-1]) == s
+
+    # trying different path, a rectangle (0-->i-->pi/2 + i-->pi/2)
+    # computing the same value sin(pi/2) using different path
+    r = [0.1*I]
+    for i in range(9):
+        r.append(r[-1]+0.1*I)
+    for i in range(15):
+        r.append(r[-1]+0.1)
+    r.append(pi/2+I)
+    for i in range(10):
+        r.append(r[-1]-0.1*I)
+
+    # close to 1.0
+    s = '0.976882381836257 - 1.65557671738537e-16*I'
+    assert sstr(p.evalf(r, method='Euler')[-1]) == s
+
+    # cos(x)
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0])
+    # compute cos(pi) along 0-->pi
+    r = [0.05]
+    for i in range(61):
+        r.append(r[-1]+0.05)
+    r.append(pi)
+    # close to -1 (exact answer)
+    s = '-1.08140824719196'
+    assert sstr(p.evalf(r, method='Euler')[-1]) == s
+
+    # a rectangular path (0 -> i -> 2+i -> 2)
+    r = [0.1*I]
+    for i in range(9):
+        r.append(r[-1]+0.1*I)
+    for i in range(20):
+        r.append(r[-1]+0.1)
+    for i in range(10):
+        r.append(r[-1]-0.1*I)
+
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r, method='Euler')
+    s = '0.501421652861245 - 3.88578058618805e-16*I'
+    assert sstr(p[-1]) == s
+
+def test_evalf_rk4():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+
+    # log(1+x)
+    p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1])
+
+    # path taken is a straight line from 0 to 1, on the real axis
+    r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]
+    s = '0.693146363174626'  # approx. equal to log(2) i.e. 0.693147180559945
+    assert sstr(p.evalf(r)[-1]) == s
+
+    # path taken is a triangle 0-->1+i-->2
+    r = [0.1 + 0.1*I]
+    for i in range(9):
+        r.append(r[-1]+0.1+0.1*I)
+    for i in range(10):
+        r.append(r[-1]+0.1-0.1*I)
+
+    # close to the exact solution 1.09861228866811
+    # imaginary part also close to zero
+    s = '1.098616 + 1.36083e-7*I'
+    assert sstr(p.evalf(r)[-1].n(7)) == s
+
+    # sin(x)
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])
+    s = '0.90929463522785 + 1.52655665885959e-16*I'
+    assert sstr(p.evalf(r)[-1]) == s
+
+    # computing sin(pi/2) using this method
+    # using a linear path from 0 to pi/2
+    r = [0.1]
+    for i in range(14):
+        r.append(r[-1] + 0.1)
+    r.append(pi/2)
+    s = '0.999999895088917' # close to 1.0 (exact solution)
+    assert sstr(p.evalf(r)[-1]) == s
+
+    # trying different path, a rectangle (0-->i-->pi/2 + i-->pi/2)
+    # computing the same value sin(pi/2) using different path
+    r = [0.1*I]
+    for i in range(9):
+        r.append(r[-1]+0.1*I)
+    for i in range(15):
+        r.append(r[-1]+0.1)
+    r.append(pi/2+I)
+    for i in range(10):
+        r.append(r[-1]-0.1*I)
+
+    # close to 1.0
+    s = '1.00000003415141 + 6.11940487991086e-16*I'
+    assert sstr(p.evalf(r)[-1]) == s
+
+    # cos(x)
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0])
+    # compute cos(pi) along 0-->pi
+    r = [0.05]
+    for i in range(61):
+        r.append(r[-1]+0.05)
+    r.append(pi)
+    # close to -1 (exact answer)
+    s = '-0.999999993238714'
+    assert sstr(p.evalf(r)[-1]) == s
+
+    # a rectangular path (0 -> i -> 2+i -> 2)
+    r = [0.1*I]
+    for i in range(9):
+        r.append(r[-1]+0.1*I)
+    for i in range(20):
+        r.append(r[-1]+0.1)
+    for i in range(10):
+        r.append(r[-1]-0.1*I)
+
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r)
+    s = '0.493152791638442 - 1.41553435639707e-15*I'
+    assert sstr(p[-1]) == s
+
+
+def test_expr_to_holonomic():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    p = expr_to_holonomic((sin(x)/x)**2)
+    q = HolonomicFunction(8*x + (4*x**2 + 6)*Dx + 6*x*Dx**2 + x**2*Dx**3, x, 0, \
+        [1, 0, Rational(-2, 3)])
+    assert p == q
+    p = expr_to_holonomic(1/(1+x**2)**2)
+    q = HolonomicFunction(4*x + (x**2 + 1)*Dx, x, 0, [1])
+    assert p == q
+    p = expr_to_holonomic(exp(x)*sin(x)+x*log(1+x))
+    q = HolonomicFunction((2*x**3 + 10*x**2 + 20*x + 18) + (-2*x**4 - 10*x**3 - 20*x**2 \
+        - 18*x)*Dx + (2*x**5 + 6*x**4 + 7*x**3 + 8*x**2 + 10*x - 4)*Dx**2 + \
+        (-2*x**5 - 5*x**4 - 2*x**3 + 2*x**2 - x + 4)*Dx**3 + (x**5 + 2*x**4 - x**3 - \
+        7*x**2/2 + x + Rational(5, 2))*Dx**4, x, 0, [0, 1, 4, -1])
+    assert p == q
+    p = expr_to_holonomic(x*exp(x)+cos(x)+1)
+    q = HolonomicFunction((-x - 3)*Dx + (x + 2)*Dx**2 + (-x - 3)*Dx**3 + (x + 2)*Dx**4, x, \
+        0, [2, 1, 1, 3])
+    assert p == q
+    assert (x*exp(x)+cos(x)+1).series(n=10) == p.series(n=10)
+    p = expr_to_holonomic(log(1 + x)**2 + 1)
+    q = HolonomicFunction(Dx + (3*x + 3)*Dx**2 + (x**2 + 2*x + 1)*Dx**3, x, 0, [1, 0, 2])
+    assert p == q
+    p = expr_to_holonomic(erf(x)**2 + x)
+    q = HolonomicFunction((8*x**4 - 2*x**2 + 2)*Dx**2 + (6*x**3 - x/2)*Dx**3 + \
+        (x**2+ Rational(1, 4))*Dx**4, x, 0, [0, 1, 8/pi, 0])
+    assert p == q
+    p = expr_to_holonomic(cosh(x)*x)
+    q = HolonomicFunction((-x**2 + 2) -2*x*Dx + x**2*Dx**2, x, 0, [0, 1])
+    assert p == q
+    p = expr_to_holonomic(besselj(2, x))
+    q = HolonomicFunction((x**2 - 4) + x*Dx + x**2*Dx**2, x, 0, [0, 0])
+    assert p == q
+    p = expr_to_holonomic(besselj(0, x) + exp(x))
+    q = HolonomicFunction((-x**2 - x/2 + S.Half) + (x**2 - x/2 - Rational(3, 2))*Dx + (-x**2 + x/2 + 1)*Dx**2 +\
+        (x**2 + x/2)*Dx**3, x, 0, [2, 1, S.Half])
+    assert p == q
+    p = expr_to_holonomic(sin(x)**2/x)
+    q = HolonomicFunction(4 + 4*x*Dx + 3*Dx**2 + x*Dx**3, x, 0, [0, 1, 0])
+    assert p == q
+    p = expr_to_holonomic(sin(x)**2/x, x0=2)
+    q = HolonomicFunction((4) + (4*x)*Dx + (3)*Dx**2 + (x)*Dx**3, x, 2, [sin(2)**2/2,
+        sin(2)*cos(2) - sin(2)**2/4, -3*sin(2)**2/4 + cos(2)**2 - sin(2)*cos(2)])
+    assert p == q
+    p = expr_to_holonomic(log(x)/2 - Ci(2*x)/2 + Ci(2)/2)
+    q = HolonomicFunction(4*Dx + 4*x*Dx**2 + 3*Dx**3 + x*Dx**4, x, 0, \
+        [-log(2)/2 - EulerGamma/2 + Ci(2)/2, 0, 1, 0])
+    assert p == q
+    p = p.to_expr()
+    q = log(x)/2 - Ci(2*x)/2 + Ci(2)/2
+    assert p == q
+    p = expr_to_holonomic(x**S.Half, x0=1)
+    q = HolonomicFunction(x*Dx - S.Half, x, 1, [1])
+    assert p == q
+    p = expr_to_holonomic(sqrt(1 + x**2))
+    q = HolonomicFunction((-x) + (x**2 + 1)*Dx, x, 0, [1])
+    assert p == q
+    assert (expr_to_holonomic(sqrt(x) + sqrt(2*x)).to_expr()-\
+        (sqrt(x) + sqrt(2*x))).simplify() == 0
+    assert expr_to_holonomic(3*x+2*sqrt(x)).to_expr() == 3*x+2*sqrt(x)
+    p = expr_to_holonomic((x**4+x**3+5*x**2+3*x+2)/x**2, lenics=3)
+    q = HolonomicFunction((-2*x**4 - x**3 + 3*x + 4) + (x**5 + x**4 + 5*x**3 + 3*x**2 + \
+        2*x)*Dx, x, 0, {-2: [2, 3, 5]})
+    assert p == q
+    p = expr_to_holonomic(1/(x-1)**2, lenics=3, x0=1)
+    q = HolonomicFunction((2) + (x - 1)*Dx, x, 1, {-2: [1, 0, 0]})
+    assert p == q
+    a = symbols("a")
+    p = expr_to_holonomic(sqrt(a*x), x=x)
+    assert p.to_expr() == sqrt(a)*sqrt(x)
+
+def test_to_hyper():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx - 2, x, 0, [3]).to_hyper()
+    q = 3 * hyper([], [], 2*x)
+    assert p == q
+    p = hyperexpand(HolonomicFunction((1 + x) * Dx - 3, x, 0, [2]).to_hyper()).expand()
+    q = 2*x**3 + 6*x**2 + 6*x + 2
+    assert p == q
+    p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]).to_hyper()
+    q = -x**2*hyper((2, 2, 1), (3, 2), -x)/2 + x
+    assert p == q
+    p = HolonomicFunction(2*x*Dx + Dx**2, x, 0, [0, 2/sqrt(pi)]).to_hyper()
+    q = 2*x*hyper((S.Half,), (Rational(3, 2),), -x**2)/sqrt(pi)
+    assert p == q
+    p = hyperexpand(HolonomicFunction(2*x*Dx + Dx**2, x, 0, [1, -2/sqrt(pi)]).to_hyper())
+    q = erfc(x)
+    assert p.rewrite(erfc) == q
+    p =  hyperexpand(HolonomicFunction((x**2 - 1) + x*Dx + x**2*Dx**2,
+        x, 0, [0, S.Half]).to_hyper())
+    q = besselj(1, x)
+    assert p == q
+    p = hyperexpand(HolonomicFunction(x*Dx**2 + Dx + x, x, 0, [1, 0]).to_hyper())
+    q = besselj(0, x)
+    assert p == q
+
+def test_to_expr():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(Dx - 1, x, 0, [1]).to_expr()
+    q = exp(x)
+    assert p == q
+    p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]).to_expr()
+    q = cos(x)
+    assert p == q
+    p = HolonomicFunction(Dx**2 - 1, x, 0, [1, 0]).to_expr()
+    q = cosh(x)
+    assert p == q
+    p = HolonomicFunction(2 + (4*x - 1)*Dx + \
+        (x**2 - x)*Dx**2, x, 0, [1, 2]).to_expr().expand()
+    q = 1/(x**2 - 2*x + 1)
+    assert p == q
+    p = expr_to_holonomic(sin(x)**2/x).integrate((x, 0, x)).to_expr()
+    q = (sin(x)**2/x).integrate((x, 0, x))
+    assert p == q
+    C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3')
+    p = expr_to_holonomic(log(1+x**2)).to_expr()
+    q = C_2*log(x**2 + 1)
+    assert p == q
+    p = expr_to_holonomic(log(1+x**2)).diff().to_expr()
+    q = C_0*x/(x**2 + 1)
+    assert p == q
+    p = expr_to_holonomic(erf(x) + x).to_expr()
+    q = 3*C_3*x - 3*sqrt(pi)*C_3*erf(x)/2 + x + 2*x/sqrt(pi)
+    assert p == q
+    p = expr_to_holonomic(sqrt(x), x0=1).to_expr()
+    assert p == sqrt(x)
+    assert expr_to_holonomic(sqrt(x)).to_expr() == sqrt(x)
+    p = expr_to_holonomic(sqrt(1 + x**2)).to_expr()
+    assert p == sqrt(1+x**2)
+    p = expr_to_holonomic((2*x**2 + 1)**Rational(2, 3)).to_expr()
+    assert p == (2*x**2 + 1)**Rational(2, 3)
+    p = expr_to_holonomic(sqrt(-x**2+2*x)).to_expr()
+    assert p == sqrt(x)*sqrt(-x + 2)
+    p = expr_to_holonomic((-2*x**3+7*x)**Rational(2, 3)).to_expr()
+    q = x**Rational(2, 3)*(-2*x**2 + 7)**Rational(2, 3)
+    assert p == q
+    p = from_hyper(hyper((-2, -3), (S.Half, ), x))
+    s = hyperexpand(hyper((-2, -3), (S.Half, ), x))
+    D_0 = Symbol('D_0')
+    C_0 = Symbol('C_0')
+    assert (p.to_expr().subs({C_0:1, D_0:0}) - s).simplify() == 0
+    p.y0 = {0: [1], S.Half: [0]}
+    assert p.to_expr() == s
+    assert expr_to_holonomic(x**5).to_expr() == x**5
+    assert expr_to_holonomic(2*x**3-3*x**2).to_expr().expand() == \
+        2*x**3-3*x**2
+    a = symbols("a")
+    p = (expr_to_holonomic(1.4*x)*expr_to_holonomic(a*x, x)).to_expr()
+    q = 1.4*a*x**2
+    assert p == q
+    p = (expr_to_holonomic(1.4*x)+expr_to_holonomic(a*x, x)).to_expr()
+    q = x*(a + 1.4)
+    assert p == q
+    p = (expr_to_holonomic(1.4*x)+expr_to_holonomic(x)).to_expr()
+    assert p == 2.4*x
+
+
+def test_integrate():
+    x = symbols('x')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 2, 3))
+    q = '0.166270406994788'
+    assert sstr(p) == q
+    p = expr_to_holonomic(sin(x)).integrate((x, 0, x)).to_expr()
+    q = 1 - cos(x)
+    assert p == q
+    p = expr_to_holonomic(sin(x)).integrate((x, 0, 3))
+    q = 1 - cos(3)
+    assert p == q
+    p = expr_to_holonomic(sin(x)/x, x0=1).integrate((x, 1, 2))
+    q = '0.659329913368450'
+    assert sstr(p) == q
+    p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 1, 0))
+    q = '-0.423690480850035'
+    assert sstr(p) == q
+    p = expr_to_holonomic(sin(x)/x)
+    assert p.integrate(x).to_expr() == Si(x)
+    assert p.integrate((x, 0, 2)) == Si(2)
+    p = expr_to_holonomic(sin(x)**2/x)
+    q = p.to_expr()
+    assert p.integrate(x).to_expr() == q.integrate((x, 0, x))
+    assert p.integrate((x, 0, 1)) == q.integrate((x, 0, 1))
+    assert expr_to_holonomic(1/x, x0=1).integrate(x).to_expr() == log(x)
+    p = expr_to_holonomic((x + 1)**3*exp(-x), x0=-1).integrate(x).to_expr()
+    q = (-x**3 - 6*x**2 - 15*x + 6*exp(x + 1) - 16)*exp(-x)
+    assert p == q
+    p = expr_to_holonomic(cos(x)**2/x**2, y0={-2: [1, 0, -1]}).integrate(x).to_expr()
+    q = -Si(2*x) - cos(x)**2/x
+    assert p == q
+    p = expr_to_holonomic(sqrt(x**2+x)).integrate(x).to_expr()
+    q = (x**Rational(3, 2)*(2*x**2 + 3*x + 1) - x*sqrt(x + 1)*asinh(sqrt(x)))/(4*x*sqrt(x + 1))
+    assert p == q
+    p = expr_to_holonomic(sqrt(x**2+1)).integrate(x).to_expr()
+    q = (sqrt(x**2+1)).integrate(x)
+    assert (p-q).simplify() == 0
+    p = expr_to_holonomic(1/x**2, y0={-2:[1, 0, 0]})
+    r = expr_to_holonomic(1/x**2, lenics=3)
+    assert p == r
+    q = expr_to_holonomic(cos(x)**2)
+    assert (r*q).integrate(x).to_expr() == -Si(2*x) - cos(x)**2/x
+
+
+def test_diff():
+    x, y = symbols('x, y')
+    R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
+    p = HolonomicFunction(x*Dx**2 + 1, x, 0, [0, 1])
+    assert p.diff().to_expr() == p.to_expr().diff().simplify()
+    p = HolonomicFunction(Dx**2 - 1, x, 0, [1, 0])
+    assert p.diff(x, 2).to_expr() == p.to_expr()
+    p = expr_to_holonomic(Si(x))
+    assert p.diff().to_expr() == sin(x)/x
+    assert p.diff(y) == 0
+    C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3')
+    q = Si(x)
+    assert p.diff(x).to_expr() == q.diff()
+    assert p.diff(x, 2).to_expr().subs(C_0, Rational(-1, 3)).cancel() == q.diff(x, 2).cancel()
+    assert p.diff(x, 3).series().subs({C_3: Rational(-1, 3), C_0: 0}) == q.diff(x, 3).series()
+
+
+def test_extended_domain_in_expr_to_holonomic():
+    x = symbols('x')
+    p = expr_to_holonomic(1.2*cos(3.1*x))
+    assert p.to_expr() == 1.2*cos(3.1*x)
+    assert sstr(p.integrate(x).to_expr()) == '0.387096774193548*sin(3.1*x)'
+    _, Dx = DifferentialOperators(RR.old_poly_ring(x), 'Dx')
+    p = expr_to_holonomic(1.1329138213*x)
+    q = HolonomicFunction((-1.1329138213) + (1.1329138213*x)*Dx, x, 0, {1: [1.1329138213]})
+    assert p == q
+    assert p.to_expr() == 1.1329138213*x
+    assert sstr(p.integrate((x, 1, 2))) == sstr((1.1329138213*x).integrate((x, 1, 2)))
+    y, z = symbols('y, z')
+    p = expr_to_holonomic(sin(x*y*z), x=x)
+    assert p.to_expr() == sin(x*y*z)
+    assert p.integrate(x).to_expr() == (-cos(x*y*z) + 1)/(y*z)
+    p = expr_to_holonomic(sin(x*y + z), x=x).integrate(x).to_expr()
+    q = (cos(z) - cos(x*y + z))/y
+    assert p == q
+    a = symbols('a')
+    p = expr_to_holonomic(a*x, x)
+    assert p.to_expr() == a*x
+    assert p.integrate(x).to_expr() == a*x**2/2
+    D_2, C_1 = symbols("D_2, C_1")
+    p = expr_to_holonomic(x) + expr_to_holonomic(1.2*cos(x))
+    p = p.to_expr().subs(D_2, 0)
+    assert p - x - 1.2*cos(1.0*x) == 0
+    p = expr_to_holonomic(x) * expr_to_holonomic(1.2*cos(x))
+    p = p.to_expr().subs(C_1, 0)
+    assert p - 1.2*x*cos(1.0*x) == 0
+
+
+def test_to_meijerg():
+    x = symbols('x')
+    assert hyperexpand(expr_to_holonomic(sin(x)).to_meijerg()) == sin(x)
+    assert hyperexpand(expr_to_holonomic(cos(x)).to_meijerg()) == cos(x)
+    assert hyperexpand(expr_to_holonomic(exp(x)).to_meijerg()) == exp(x)
+    assert hyperexpand(expr_to_holonomic(log(x)).to_meijerg()).simplify() == log(x)
+    assert expr_to_holonomic(4*x**2/3 + 7).to_meijerg() == 4*x**2/3 + 7
+    assert hyperexpand(expr_to_holonomic(besselj(2, x), lenics=3).to_meijerg()) == besselj(2, x)
+    p = hyper((Rational(-1, 2), -3), (), x)
+    assert from_hyper(p).to_meijerg() == hyperexpand(p)
+    p = hyper((S.One, S(3)), (S(2), ), x)
+    assert (hyperexpand(from_hyper(p).to_meijerg()) - hyperexpand(p)).expand() == 0
+    p = from_hyper(hyper((-2, -3), (S.Half, ), x))
+    s = hyperexpand(hyper((-2, -3), (S.Half, ), x))
+    C_0 = Symbol('C_0')
+    C_1 = Symbol('C_1')
+    D_0 = Symbol('D_0')
+    assert (hyperexpand(p.to_meijerg()).subs({C_0:1, D_0:0}) - s).simplify() == 0
+    p.y0 = {0: [1], S.Half: [0]}
+    assert (hyperexpand(p.to_meijerg()) - s).simplify() == 0
+    p = expr_to_holonomic(besselj(S.Half, x), initcond=False)
+    assert (p.to_expr() - (D_0*sin(x) + C_0*cos(x) + C_1*sin(x))/sqrt(x)).simplify() == 0
+    p = expr_to_holonomic(besselj(S.Half, x), y0={Rational(-1, 2): [sqrt(2)/sqrt(pi), sqrt(2)/sqrt(pi)]})
+    assert (p.to_expr() - besselj(S.Half, x) - besselj(Rational(-1, 2), x)).simplify() == 0
+
+
+def test_gaussian():
+    mu, x = symbols("mu x")
+    sd = symbols("sd", positive=True)
+    Q = QQ[mu, sd].get_field()
+    e = sqrt(2)*exp(-(-mu + x)**2/(2*sd**2))/(2*sqrt(pi)*sd)
+    h1 = expr_to_holonomic(e, x, domain=Q)
+
+    _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx')
+    h2 = HolonomicFunction((-mu/sd**2 + x/sd**2) + (1)*Dx, x)
+
+    assert h1 == h2
+
+
+def test_beta():
+    a, b, x = symbols("a b x", positive=True)
+    e = x**(a - 1)*(-x + 1)**(b - 1)/beta(a, b)
+    Q = QQ[a, b].get_field()
+    h1 = expr_to_holonomic(e, x, domain=Q)
+
+    _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx')
+    h2 = HolonomicFunction((a + x*(-a - b + 2) - 1) + (x**2 - x)*Dx, x)
+
+    assert h1 == h2
+
+
+def test_gamma():
+    a, b, x = symbols("a b x", positive=True)
+    e = b**(-a)*x**(a - 1)*exp(-x/b)/gamma(a)
+    Q = QQ[a, b].get_field()
+    h1 = expr_to_holonomic(e, x, domain=Q)
+
+    _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx')
+    h2 = HolonomicFunction((-a + 1 + x/b) + (x)*Dx, x)
+
+    assert h1 == h2
+
+
+def test_symbolic_power():
+    x, n = symbols("x n")
+    Q = QQ[n].get_field()
+    _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx')
+    h1 = HolonomicFunction((-1) + (x)*Dx, x) ** -n
+    h2 = HolonomicFunction((n) + (x)*Dx, x)
+
+    assert h1 == h2
+
+
+def test_negative_power():
+    x = symbols("x")
+    _, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    h1 = HolonomicFunction((-1) + (x)*Dx, x) ** -2
+    h2 = HolonomicFunction((2) + (x)*Dx, x)
+
+    assert h1 == h2
+
+
+def test_expr_in_power():
+    x, n = symbols("x n")
+    Q = QQ[n].get_field()
+    _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx')
+    h1 = HolonomicFunction((-1) + (x)*Dx, x) ** (n - 3)
+    h2 = HolonomicFunction((-n + 3) + (x)*Dx, x)
+
+    assert h1 == h2
+
+
+def test_DifferentialOperatorEqPoly():
+    x = symbols('x', integer=True)
+    R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    do = DifferentialOperator([x**2, R.base.zero, R.base.zero], R)
+    do2 = DifferentialOperator([x**2, 1, x], R)
+    assert not do == do2
+
+    # polynomial comparison issue, see https://github.com/sympy/sympy/pull/15799
+    # should work once that is solved
+    # p = do.listofpoly[0]
+    # assert do == p
+
+    p2 = do2.listofpoly[0]
+    assert not do2 == p2
+
+
+def test_DifferentialOperatorPow():
+    x = symbols('x', integer=True)
+    R, _ = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
+    do = DifferentialOperator([x**2, R.base.zero, R.base.zero], R)
+    a = DifferentialOperator([R.base.one], R)
+    for n in range(10):
+        assert a == do**n
+        a *= do
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/test_recurrence.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/test_recurrence.py
new file mode 100644
index 0000000000000000000000000000000000000000..526595e91c5fc507877275e3e53e78c6f3716095
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/holonomic/tests/test_recurrence.py
@@ -0,0 +1,41 @@
+from sympy.holonomic.recurrence import RecurrenceOperators, RecurrenceOperator
+from sympy.core.symbol import symbols
+from sympy.polys.domains.rationalfield import QQ
+
+
+def test_RecurrenceOperator():
+    n = symbols('n', integer=True)
+    R, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn')
+    assert Sn*n == (n + 1)*Sn
+    assert Sn*n**2 == (n**2+1+2*n)*Sn
+    assert Sn**2*n**2 == (n**2 + 4*n + 4)*Sn**2
+    p = (Sn**3*n**2 + Sn*n)**2
+    q = (n**2 + 3*n + 2)*Sn**2 + (2*n**3 + 19*n**2 + 57*n + 52)*Sn**4 + (n**4 + 18*n**3 + \
+        117*n**2 + 324*n + 324)*Sn**6
+    assert p == q
+
+
+def test_RecurrenceOperatorEqPoly():
+    n = symbols('n', integer=True)
+    R, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn')
+    rr = RecurrenceOperator([n**2, 0, 0], R)
+    rr2 = RecurrenceOperator([n**2, 1, n], R)
+    assert not rr == rr2
+
+    # polynomial comparison issue, see https://github.com/sympy/sympy/pull/15799
+    # should work once that is solved
+    # d = rr.listofpoly[0]
+    # assert rr == d
+
+    d2 = rr2.listofpoly[0]
+    assert not rr2 == d2
+
+
+def test_RecurrenceOperatorPow():
+    n = symbols('n', integer=True)
+    R, _ = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn')
+    rr = RecurrenceOperator([n**2, 0, 0], R)
+    a = RecurrenceOperator([R.base.one], R)
+    for m in range(10):
+        assert a == rr**m
+        a *= rr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e78fe96f84d68e9b119571eb22dedb7033811b23
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/__init__.py
@@ -0,0 +1,45 @@
+"""Integration functions that integrate a SymPy expression.
+
+    Examples
+    ========
+
+    >>> from sympy import integrate, sin
+    >>> from sympy.abc import x
+    >>> integrate(1/x,x)
+    log(x)
+    >>> integrate(sin(x),x)
+    -cos(x)
+"""
+from .integrals import integrate, Integral, line_integrate
+from .transforms import (mellin_transform, inverse_mellin_transform,
+                        MellinTransform, InverseMellinTransform,
+                        laplace_transform, inverse_laplace_transform,
+                        laplace_correspondence, laplace_initial_conds,
+                        LaplaceTransform, InverseLaplaceTransform,
+                        fourier_transform, inverse_fourier_transform,
+                        FourierTransform, InverseFourierTransform,
+                        sine_transform, inverse_sine_transform,
+                        SineTransform, InverseSineTransform,
+                        cosine_transform, inverse_cosine_transform,
+                        CosineTransform, InverseCosineTransform,
+                        hankel_transform, inverse_hankel_transform,
+                        HankelTransform, InverseHankelTransform)
+from .singularityfunctions import singularityintegrate
+
+__all__ = [
+    'integrate', 'Integral', 'line_integrate',
+
+    'mellin_transform', 'inverse_mellin_transform', 'MellinTransform',
+    'InverseMellinTransform', 'laplace_transform',
+    'inverse_laplace_transform', 'LaplaceTransform',
+    'laplace_correspondence', 'laplace_initial_conds',
+    'InverseLaplaceTransform', 'fourier_transform',
+    'inverse_fourier_transform', 'FourierTransform',
+    'InverseFourierTransform', 'sine_transform', 'inverse_sine_transform',
+    'SineTransform', 'InverseSineTransform', 'cosine_transform',
+    'inverse_cosine_transform', 'CosineTransform', 'InverseCosineTransform',
+    'hankel_transform', 'inverse_hankel_transform', 'HankelTransform',
+    'InverseHankelTransform',
+
+    'singularityintegrate',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/bench_integrate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/bench_integrate.py
new file mode 100644
index 0000000000000000000000000000000000000000..833bc57403b34df1e75c798084ffc4d8afe9eae6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/bench_integrate.py
@@ -0,0 +1,21 @@
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.trigonometric import sin
+from sympy.integrals.integrals import integrate
+
+x = Symbol('x')
+
+
+def bench_integrate_sin():
+    integrate(sin(x), x)
+
+
+def bench_integrate_x1sin():
+    integrate(x**1*sin(x), x)
+
+
+def bench_integrate_x2sin():
+    integrate(x**2*sin(x), x)
+
+
+def bench_integrate_x3sin():
+    integrate(x**3*sin(x), x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/bench_trigintegrate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/bench_trigintegrate.py
new file mode 100644
index 0000000000000000000000000000000000000000..403c5471b8048ff2aa97bf2f837b9ea05f0fd904
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/benchmarks/bench_trigintegrate.py
@@ -0,0 +1,13 @@
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.trigonometric import sin
+from sympy.integrals.trigonometry import trigintegrate
+
+x = Symbol('x')
+
+
+def timeit_trigintegrate_sin3x():
+    trigintegrate(sin(x)**3, x)
+
+
+def timeit_trigintegrate_x2():
+    trigintegrate(x**2, x)  # -> None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/deltafunctions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/deltafunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae9fef0b0010a313e0866a54d978024dd475f882
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/deltafunctions.py
@@ -0,0 +1,201 @@
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.functions import DiracDelta, Heaviside
+from .integrals import Integral, integrate
+
+
+def change_mul(node, x):
+    """change_mul(node, x)
+
+       Rearranges the operands of a product, bringing to front any simple
+       DiracDelta expression.
+
+       Explanation
+       ===========
+
+       If no simple DiracDelta expression was found, then all the DiracDelta
+       expressions are simplified (using DiracDelta.expand(diracdelta=True, wrt=x)).
+
+       Return: (dirac, new node)
+       Where:
+         o dirac is either a simple DiracDelta expression or None (if no simple
+           expression was found);
+         o new node is either a simplified DiracDelta expressions or None (if it
+           could not be simplified).
+
+       Examples
+       ========
+
+       >>> from sympy import DiracDelta, cos
+       >>> from sympy.integrals.deltafunctions import change_mul
+       >>> from sympy.abc import x, y
+       >>> change_mul(x*y*DiracDelta(x)*cos(x), x)
+       (DiracDelta(x), x*y*cos(x))
+       >>> change_mul(x*y*DiracDelta(x**2 - 1)*cos(x), x)
+       (None, x*y*cos(x)*DiracDelta(x - 1)/2 + x*y*cos(x)*DiracDelta(x + 1)/2)
+       >>> change_mul(x*y*DiracDelta(cos(x))*cos(x), x)
+       (None, None)
+
+       See Also
+       ========
+
+       sympy.functions.special.delta_functions.DiracDelta
+       deltaintegrate
+    """
+
+    new_args = []
+    dirac = None
+
+    #Sorting is needed so that we consistently collapse the same delta;
+    #However, we must preserve the ordering of non-commutative terms
+    c, nc = node.args_cnc()
+    sorted_args = sorted(c, key=default_sort_key)
+    sorted_args.extend(nc)
+
+    for arg in sorted_args:
+        if arg.is_Pow and isinstance(arg.base, DiracDelta):
+            new_args.append(arg.func(arg.base, arg.exp - 1))
+            arg = arg.base
+        if dirac is None and (isinstance(arg, DiracDelta) and arg.is_simple(x)):
+            dirac = arg
+        else:
+            new_args.append(arg)
+    if not dirac:  # there was no simple dirac
+        new_args = []
+        for arg in sorted_args:
+            if isinstance(arg, DiracDelta):
+                new_args.append(arg.expand(diracdelta=True, wrt=x))
+            elif arg.is_Pow and isinstance(arg.base, DiracDelta):
+                new_args.append(arg.func(arg.base.expand(diracdelta=True, wrt=x), arg.exp))
+            else:
+                new_args.append(arg)
+        if new_args != sorted_args:
+            nnode = Mul(*new_args).expand()
+        else:  # if the node didn't change there is nothing to do
+            nnode = None
+        return (None, nnode)
+    return (dirac, Mul(*new_args))
+
+
+def deltaintegrate(f, x):
+    """
+    deltaintegrate(f, x)
+
+    Explanation
+    ===========
+
+    The idea for integration is the following:
+
+    - If we are dealing with a DiracDelta expression, i.e. DiracDelta(g(x)),
+      we try to simplify it.
+
+      If we could simplify it, then we integrate the resulting expression.
+      We already know we can integrate a simplified expression, because only
+      simple DiracDelta expressions are involved.
+
+      If we couldn't simplify it, there are two cases:
+
+      1) The expression is a simple expression: we return the integral,
+         taking care if we are dealing with a Derivative or with a proper
+         DiracDelta.
+
+      2) The expression is not simple (i.e. DiracDelta(cos(x))): we can do
+         nothing at all.
+
+    - If the node is a multiplication node having a DiracDelta term:
+
+      First we expand it.
+
+      If the expansion did work, then we try to integrate the expansion.
+
+      If not, we try to extract a simple DiracDelta term, then we have two
+      cases:
+
+      1) We have a simple DiracDelta term, so we return the integral.
+
+      2) We didn't have a simple term, but we do have an expression with
+         simplified DiracDelta terms, so we integrate this expression.
+
+    Examples
+    ========
+
+        >>> from sympy.abc import x, y, z
+        >>> from sympy.integrals.deltafunctions import deltaintegrate
+        >>> from sympy import sin, cos, DiracDelta
+        >>> deltaintegrate(x*sin(x)*cos(x)*DiracDelta(x - 1), x)
+        sin(1)*cos(1)*Heaviside(x - 1)
+        >>> deltaintegrate(y**2*DiracDelta(x - z)*DiracDelta(y - z), y)
+        z**2*DiracDelta(x - z)*Heaviside(y - z)
+
+    See Also
+    ========
+
+    sympy.functions.special.delta_functions.DiracDelta
+    sympy.integrals.integrals.Integral
+    """
+    if not f.has(DiracDelta):
+        return None
+
+    # g(x) = DiracDelta(h(x))
+    if f.func == DiracDelta:
+        h = f.expand(diracdelta=True, wrt=x)
+        if h == f:  # can't simplify the expression
+            #FIXME: the second term tells whether is DeltaDirac or Derivative
+            #For integrating derivatives of DiracDelta we need the chain rule
+            if f.is_simple(x):
+                if (len(f.args) <= 1 or f.args[1] == 0):
+                    return Heaviside(f.args[0])
+                else:
+                    return (DiracDelta(f.args[0], f.args[1] - 1) /
+                        f.args[0].as_poly().LC())
+        else:  # let's try to integrate the simplified expression
+            fh = integrate(h, x)
+            return fh
+    elif f.is_Mul or f.is_Pow:  # g(x) = a*b*c*f(DiracDelta(h(x)))*d*e
+        g = f.expand()
+        if f != g:  # the expansion worked
+            fh = integrate(g, x)
+            if fh is not None and not isinstance(fh, Integral):
+                return fh
+        else:
+            # no expansion performed, try to extract a simple DiracDelta term
+            deltaterm, rest_mult = change_mul(f, x)
+
+            if not deltaterm:
+                if rest_mult:
+                    fh = integrate(rest_mult, x)
+                    return fh
+            else:
+                from sympy.solvers import solve
+                deltaterm = deltaterm.expand(diracdelta=True, wrt=x)
+                if deltaterm.is_Mul:  # Take out any extracted factors
+                    deltaterm, rest_mult_2 = change_mul(deltaterm, x)
+                    rest_mult = rest_mult*rest_mult_2
+                point = solve(deltaterm.args[0], x)[0]
+
+                # Return the largest hyperreal term left after
+                # repeated integration by parts.  For example,
+                #
+                #   integrate(y*DiracDelta(x, 1),x) == y*DiracDelta(x,0),  not 0
+                #
+                # This is so Integral(y*DiracDelta(x).diff(x),x).doit()
+                # will return y*DiracDelta(x) instead of 0 or DiracDelta(x),
+                # both of which are correct everywhere the value is defined
+                # but give wrong answers for nested integration.
+                n = (0 if len(deltaterm.args)==1 else deltaterm.args[1])
+                m = 0
+                while n >= 0:
+                    r = S.NegativeOne**n*rest_mult.diff(x, n).subs(x, point)
+                    if r.is_zero:
+                        n -= 1
+                        m += 1
+                    else:
+                        if m == 0:
+                            return r*Heaviside(x - point)
+                        else:
+                            return r*DiracDelta(x,m-1)
+                # In some very weak sense, x=0 is still a singularity,
+                # but we hope will not be of any practical consequence.
+                return S.Zero
+    return None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/heurisch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/heurisch.py
new file mode 100644
index 0000000000000000000000000000000000000000..a27e2700afd08db16c7a86020eabe5feeb6e1c85
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/heurisch.py
@@ -0,0 +1,781 @@
+from __future__ import annotations
+
+from collections import defaultdict
+from functools import reduce
+from itertools import permutations
+
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.mul import Mul
+from sympy.core.symbol import Wild, Dummy, Symbol
+from sympy.core.basic import sympify
+from sympy.core.numbers import Rational, pi, I
+from sympy.core.relational import Eq, Ne
+from sympy.core.singleton import S
+from sympy.core.sorting import ordered
+from sympy.core.traversal import iterfreeargs
+
+from sympy.functions import exp, sin, cos, tan, cot, asin, atan
+from sympy.functions import log, sinh, cosh, tanh, coth, asinh
+from sympy.functions import sqrt, erf, erfi, li, Ei
+from sympy.functions import besselj, bessely, besseli, besselk
+from sympy.functions import hankel1, hankel2, jn, yn
+from sympy.functions.elementary.complexes import Abs, re, im, sign, arg
+from sympy.functions.elementary.exponential import LambertW
+from sympy.functions.elementary.integers import floor, ceiling
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.special.delta_functions import Heaviside, DiracDelta
+
+from sympy.simplify.radsimp import collect
+
+from sympy.logic.boolalg import And, Or
+from sympy.utilities.iterables import uniq
+
+from sympy.polys import quo, gcd, lcm, factor_list, cancel, PolynomialError
+from sympy.polys.monomials import itermonomials
+from sympy.polys.polyroots import root_factors
+
+from sympy.polys.rings import PolyRing
+from sympy.polys.solvers import solve_lin_sys
+from sympy.polys.constructor import construct_domain
+
+from sympy.integrals.integrals import integrate
+
+
+def components(f, x):
+    """
+    Returns a set of all functional components of the given expression
+    which includes symbols, function applications and compositions and
+    non-integer powers. Fractional powers are collected with
+    minimal, positive exponents.
+
+    Examples
+    ========
+
+    >>> from sympy import cos, sin
+    >>> from sympy.abc import x
+    >>> from sympy.integrals.heurisch import components
+
+    >>> components(sin(x)*cos(x)**2, x)
+    {x, sin(x), cos(x)}
+
+    See Also
+    ========
+
+    heurisch
+    """
+    result = set()
+
+    if f.has_free(x):
+        if f.is_symbol and f.is_commutative:
+            result.add(f)
+        elif f.is_Function or f.is_Derivative:
+            for g in f.args:
+                result |= components(g, x)
+
+            result.add(f)
+        elif f.is_Pow:
+            result |= components(f.base, x)
+
+            if not f.exp.is_Integer:
+                if f.exp.is_Rational:
+                    result.add(f.base**Rational(1, f.exp.q))
+                else:
+                    result |= components(f.exp, x) | {f}
+        else:
+            for g in f.args:
+                result |= components(g, x)
+
+    return result
+
+# name -> [] of symbols
+_symbols_cache: dict[str, list[Dummy]] = {}
+
+
+# NB @cacheit is not convenient here
+def _symbols(name, n):
+    """get vector of symbols local to this module"""
+    try:
+        lsyms = _symbols_cache[name]
+    except KeyError:
+        lsyms = []
+        _symbols_cache[name] = lsyms
+
+    while len(lsyms) < n:
+        lsyms.append( Dummy('%s%i' % (name, len(lsyms))) )
+
+    return lsyms[:n]
+
+
+def heurisch_wrapper(f, x, rewrite=False, hints=None, mappings=None, retries=3,
+                     degree_offset=0, unnecessary_permutations=None,
+                     _try_heurisch=None):
+    """
+    A wrapper around the heurisch integration algorithm.
+
+    Explanation
+    ===========
+
+    This method takes the result from heurisch and checks for poles in the
+    denominator. For each of these poles, the integral is reevaluated, and
+    the final integration result is given in terms of a Piecewise.
+
+    Examples
+    ========
+
+    >>> from sympy import cos, symbols
+    >>> from sympy.integrals.heurisch import heurisch, heurisch_wrapper
+    >>> n, x = symbols('n x')
+    >>> heurisch(cos(n*x), x)
+    sin(n*x)/n
+    >>> heurisch_wrapper(cos(n*x), x)
+    Piecewise((sin(n*x)/n, Ne(n, 0)), (x, True))
+
+    See Also
+    ========
+
+    heurisch
+    """
+    from sympy.solvers.solvers import solve, denoms
+    f = sympify(f)
+    if not f.has_free(x):
+        return f*x
+
+    res = heurisch(f, x, rewrite, hints, mappings, retries, degree_offset,
+                   unnecessary_permutations, _try_heurisch)
+    if not isinstance(res, Basic):
+        return res
+
+    # We consider each denominator in the expression, and try to find
+    # cases where one or more symbolic denominator might be zero. The
+    # conditions for these cases are stored in the list slns.
+    #
+    # Since denoms returns a set we use ordered. This is important because the
+    # ordering of slns determines the order of the resulting Piecewise so we
+    # need a deterministic order here to make the output deterministic.
+    slns = []
+    for d in ordered(denoms(res)):
+        try:
+            slns += solve([d], dict=True, exclude=(x,))
+        except NotImplementedError:
+            pass
+    if not slns:
+        return res
+    slns = list(uniq(slns))
+    # Remove the solutions corresponding to poles in the original expression.
+    slns0 = []
+    for d in denoms(f):
+        try:
+            slns0 += solve([d], dict=True, exclude=(x,))
+        except NotImplementedError:
+            pass
+    slns = [s for s in slns if s not in slns0]
+    if not slns:
+        return res
+    if len(slns) > 1:
+        eqs = []
+        for sub_dict in slns:
+            eqs.extend([Eq(key, value) for key, value in sub_dict.items()])
+        slns = solve(eqs, dict=True, exclude=(x,)) + slns
+    # For each case listed in the list slns, we reevaluate the integral.
+    pairs = []
+    for sub_dict in slns:
+        expr = heurisch(f.subs(sub_dict), x, rewrite, hints, mappings, retries,
+                        degree_offset, unnecessary_permutations,
+                        _try_heurisch)
+        cond = And(*[Eq(key, value) for key, value in sub_dict.items()])
+        generic = Or(*[Ne(key, value) for key, value in sub_dict.items()])
+        if expr is None:
+            expr = integrate(f.subs(sub_dict),x)
+        pairs.append((expr, cond))
+    # If there is one condition, put the generic case first. Otherwise,
+    # doing so may lead to longer Piecewise formulas
+    if len(pairs) == 1:
+        pairs = [(heurisch(f, x, rewrite, hints, mappings, retries,
+                              degree_offset, unnecessary_permutations,
+                              _try_heurisch),
+                              generic),
+                 (pairs[0][0], True)]
+    else:
+        pairs.append((heurisch(f, x, rewrite, hints, mappings, retries,
+                              degree_offset, unnecessary_permutations,
+                              _try_heurisch),
+                              True))
+    return Piecewise(*pairs)
+
+class BesselTable:
+    """
+    Derivatives of Bessel functions of orders n and n-1
+    in terms of each other.
+
+    See the docstring of DiffCache.
+    """
+
+    def __init__(self):
+        self.table = {}
+        self.n = Dummy('n')
+        self.z = Dummy('z')
+        self._create_table()
+
+    def _create_table(t):
+        table, n, z = t.table, t.n, t.z
+        for f in (besselj, bessely, hankel1, hankel2):
+            table[f] = (f(n-1, z) - n*f(n, z)/z,
+                        (n-1)*f(n-1, z)/z - f(n, z))
+
+        f = besseli
+        table[f] = (f(n-1, z) - n*f(n, z)/z,
+                    (n-1)*f(n-1, z)/z + f(n, z))
+        f = besselk
+        table[f] = (-f(n-1, z) - n*f(n, z)/z,
+                    (n-1)*f(n-1, z)/z - f(n, z))
+
+        for f in (jn, yn):
+            table[f] = (f(n-1, z) - (n+1)*f(n, z)/z,
+                        (n-1)*f(n-1, z)/z - f(n, z))
+
+    def diffs(t, f, n, z):
+        if f in t.table:
+            diff0, diff1 = t.table[f]
+            repl = [(t.n, n), (t.z, z)]
+            return (diff0.subs(repl), diff1.subs(repl))
+
+    def has(t, f):
+        return f in t.table
+
+_bessel_table = None
+
+class DiffCache:
+    """
+    Store for derivatives of expressions.
+
+    Explanation
+    ===========
+
+    The standard form of the derivative of a Bessel function of order n
+    contains two Bessel functions of orders n-1 and n+1, respectively.
+    Such forms cannot be used in parallel Risch algorithm, because
+    there is a linear recurrence relation between the three functions
+    while the algorithm expects that functions and derivatives are
+    represented in terms of algebraically independent transcendentals.
+
+    The solution is to take two of the functions, e.g., those of orders
+    n and n-1, and to express the derivatives in terms of the pair.
+    To guarantee that the proper form is used the two derivatives are
+    cached as soon as one is encountered.
+
+    Derivatives of other functions are also cached at no extra cost.
+    All derivatives are with respect to the same variable `x`.
+    """
+
+    def __init__(self, x):
+        self.cache = {}
+        self.x = x
+
+        global _bessel_table
+        if not _bessel_table:
+            _bessel_table = BesselTable()
+
+    def get_diff(self, f):
+        cache = self.cache
+
+        if f in cache:
+            pass
+        elif (not hasattr(f, 'func') or
+            not _bessel_table.has(f.func)):
+            cache[f] = cancel(f.diff(self.x))
+        else:
+            n, z = f.args
+            d0, d1 = _bessel_table.diffs(f.func, n, z)
+            dz = self.get_diff(z)
+            cache[f] = d0*dz
+            cache[f.func(n-1, z)] = d1*dz
+
+        return cache[f]
+
+def heurisch(f, x, rewrite=False, hints=None, mappings=None, retries=3,
+             degree_offset=0, unnecessary_permutations=None,
+             _try_heurisch=None):
+    """
+    Compute indefinite integral using heuristic Risch algorithm.
+
+    Explanation
+    ===========
+
+    This is a heuristic approach to indefinite integration in finite
+    terms using the extended heuristic (parallel) Risch algorithm, based
+    on Manuel Bronstein's "Poor Man's Integrator".
+
+    The algorithm supports various classes of functions including
+    transcendental elementary or special functions like Airy,
+    Bessel, Whittaker and Lambert.
+
+    Note that this algorithm is not a decision procedure. If it isn't
+    able to compute the antiderivative for a given function, then this is
+    not a proof that such a functions does not exist.  One should use
+    recursive Risch algorithm in such case.  It's an open question if
+    this algorithm can be made a full decision procedure.
+
+    This is an internal integrator procedure. You should use top level
+    'integrate' function in most cases, as this procedure needs some
+    preprocessing steps and otherwise may fail.
+
+    Specification
+    =============
+
+     heurisch(f, x, rewrite=False, hints=None)
+
+       where
+         f : expression
+         x : symbol
+
+         rewrite -> force rewrite 'f' in terms of 'tan' and 'tanh'
+         hints   -> a list of functions that may appear in anti-derivate
+
+          - hints = None          --> no suggestions at all
+          - hints = [ ]           --> try to figure out
+          - hints = [f1, ..., fn] --> we know better
+
+    Examples
+    ========
+
+    >>> from sympy import tan
+    >>> from sympy.integrals.heurisch import heurisch
+    >>> from sympy.abc import x, y
+
+    >>> heurisch(y*tan(x), x)
+    y*log(tan(x)**2 + 1)/2
+
+    See Manuel Bronstein's "Poor Man's Integrator":
+
+    References
+    ==========
+
+    .. [1] https://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/index.html
+
+    For more information on the implemented algorithm refer to:
+
+    .. [2] K. Geddes, L. Stefanus, On the Risch-Norman Integration
+       Method and its Implementation in Maple, Proceedings of
+       ISSAC'89, ACM Press, 212-217.
+
+    .. [3] J. H. Davenport, On the Parallel Risch Algorithm (I),
+       Proceedings of EUROCAM'82, LNCS 144, Springer, 144-157.
+
+    .. [4] J. H. Davenport, On the Parallel Risch Algorithm (III):
+       Use of Tangents, SIGSAM Bulletin 16 (1982), 3-6.
+
+    .. [5] J. H. Davenport, B. M. Trager, On the Parallel Risch
+       Algorithm (II), ACM Transactions on Mathematical
+       Software 11 (1985), 356-362.
+
+    See Also
+    ========
+
+    sympy.integrals.integrals.Integral.doit
+    sympy.integrals.integrals.Integral
+    sympy.integrals.heurisch.components
+    """
+    f = sympify(f)
+
+    # There are some functions that Heurisch cannot currently handle,
+    # so do not even try.
+    # Set _try_heurisch=True to skip this check
+    if _try_heurisch is not True:
+        if f.has(Abs, re, im, sign, Heaviside, DiracDelta, floor, ceiling, arg):
+            return
+
+    if not f.has_free(x):
+        return f*x
+
+    if not f.is_Add:
+        indep, f = f.as_independent(x)
+    else:
+        indep = S.One
+
+    rewritables = {
+        (sin, cos, cot): tan,
+        (sinh, cosh, coth): tanh,
+    }
+
+    if rewrite:
+        for candidates, rule in rewritables.items():
+            f = f.rewrite(candidates, rule)
+    else:
+        for candidates in rewritables.keys():
+            if f.has(*candidates):
+                break
+        else:
+            rewrite = True
+
+    terms = components(f, x)
+    dcache = DiffCache(x)
+
+    if hints is not None:
+        if not hints:
+            a = Wild('a', exclude=[x])
+            b = Wild('b', exclude=[x])
+            c = Wild('c', exclude=[x])
+
+            for g in set(terms):  # using copy of terms
+                if g.is_Function:
+                    if isinstance(g, li):
+                        M = g.args[0].match(a*x**b)
+
+                        if M is not None:
+                            terms.add( x*(li(M[a]*x**M[b]) - (M[a]*x**M[b])**(-1/M[b])*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) )
+                            #terms.add( x*(li(M[a]*x**M[b]) - (x**M[b])**(-1/M[b])*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) )
+                            #terms.add( x*(li(M[a]*x**M[b]) - x*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) )
+                            #terms.add( li(M[a]*x**M[b]) - Ei((M[b]+1)*log(M[a]*x**M[b])/M[b]) )
+
+                    elif isinstance(g, exp):
+                        M = g.args[0].match(a*x**2)
+
+                        if M is not None:
+                            if M[a].is_positive:
+                                terms.add(erfi(sqrt(M[a])*x))
+                            else: # M[a].is_negative or unknown
+                                terms.add(erf(sqrt(-M[a])*x))
+
+                        M = g.args[0].match(a*x**2 + b*x + c)
+
+                        if M is not None:
+                            if M[a].is_positive:
+                                terms.add(sqrt(pi/4*(-M[a]))*exp(M[c] - M[b]**2/(4*M[a]))*
+                                          erfi(sqrt(M[a])*x + M[b]/(2*sqrt(M[a]))))
+                            elif M[a].is_negative:
+                                terms.add(sqrt(pi/4*(-M[a]))*exp(M[c] - M[b]**2/(4*M[a]))*
+                                          erf(sqrt(-M[a])*x - M[b]/(2*sqrt(-M[a]))))
+
+                        M = g.args[0].match(a*log(x)**2)
+
+                        if M is not None:
+                            if M[a].is_positive:
+                                terms.add(erfi(sqrt(M[a])*log(x) + 1/(2*sqrt(M[a]))))
+                            if M[a].is_negative:
+                                terms.add(erf(sqrt(-M[a])*log(x) - 1/(2*sqrt(-M[a]))))
+
+                elif g.is_Pow:
+                    if g.exp.is_Rational and g.exp.q == 2:
+                        M = g.base.match(a*x**2 + b)
+
+                        if M is not None and M[b].is_positive:
+                            if M[a].is_positive:
+                                terms.add(asinh(sqrt(M[a]/M[b])*x))
+                            elif M[a].is_negative:
+                                terms.add(asin(sqrt(-M[a]/M[b])*x))
+
+                        M = g.base.match(a*x**2 - b)
+
+                        if M is not None and M[b].is_positive:
+                            if M[a].is_positive:
+                                dF = 1/sqrt(M[a]*x**2 - M[b])
+                                F = log(2*sqrt(M[a])*sqrt(M[a]*x**2 - M[b]) + 2*M[a]*x)/sqrt(M[a])
+                                dcache.cache[F] = dF  # hack: F.diff(x) doesn't automatically simplify to f
+                                terms.add(F)
+                            elif M[a].is_negative:
+                                terms.add(-M[b]/2*sqrt(-M[a])*
+                                           atan(sqrt(-M[a])*x/sqrt(M[a]*x**2 - M[b])))
+
+        else:
+            terms |= set(hints)
+
+    for g in set(terms):  # using copy of terms
+        terms |= components(dcache.get_diff(g), x)
+
+    # XXX: The commented line below makes heurisch more deterministic wrt
+    # PYTHONHASHSEED and the iteration order of sets. There are other places
+    # where sets are iterated over but this one is possibly the most important.
+    # Theoretically the order here should not matter but different orderings
+    # can expose potential bugs in the different code paths so potentially it
+    # is better to keep the non-determinism.
+    #
+    # terms = list(ordered(terms))
+
+    # TODO: caching is significant factor for why permutations work at all. Change this.
+    V = _symbols('x', len(terms))
+
+
+    # sort mapping expressions from largest to smallest (last is always x).
+    mapping = list(reversed(list(zip(*ordered(                          #
+        [(a[0].as_independent(x)[1], a) for a in zip(terms, V)])))[1])) #
+    rev_mapping = {v: k for k, v in mapping}                            #
+    if mappings is None:                                                #
+        # optimizing the number of permutations of mapping              #
+        assert mapping[-1][0] == x # if not, find it and correct this comment
+        unnecessary_permutations = [mapping.pop(-1)]
+        # permute types of objects
+        types = defaultdict(list)
+        for i in mapping:
+            e, _ = i
+            types[type(e)].append(i)
+        mapping = [types[i] for i in types]
+        def _iter_mappings():
+            for i in permutations(mapping):
+                # make the expression of a given type be ordered
+                yield [j for i in i for j in ordered(i)]
+        mappings = _iter_mappings()
+    else:
+        unnecessary_permutations = unnecessary_permutations or []
+
+    def _substitute(expr):
+        return expr.subs(mapping)
+
+    for mapping in mappings:
+        mapping = list(mapping)
+        mapping = mapping + unnecessary_permutations
+        diffs = [ _substitute(dcache.get_diff(g)) for g in terms ]
+        denoms = [ g.as_numer_denom()[1] for g in diffs ]
+        if all(h.is_polynomial(*V) for h in denoms) and _substitute(f).is_rational_function(*V):
+            denom = reduce(lambda p, q: lcm(p, q, *V), denoms)
+            break
+    else:
+        if not rewrite:
+            result = heurisch(f, x, rewrite=True, hints=hints,
+                unnecessary_permutations=unnecessary_permutations)
+
+            if result is not None:
+                return indep*result
+        return None
+
+    numers = [ cancel(denom*g) for g in diffs ]
+    def _derivation(h):
+        return Add(*[ d * h.diff(v) for d, v in zip(numers, V) ])
+
+    def _deflation(p):
+        for y in V:
+            if not p.has(y):
+                continue
+
+            if _derivation(p) is not S.Zero:
+                c, q = p.as_poly(y).primitive()
+                return _deflation(c)*gcd(q, q.diff(y)).as_expr()
+
+        return p
+
+    def _splitter(p):
+        for y in V:
+            if not p.has(y):
+                continue
+
+            if _derivation(y) is not S.Zero:
+                c, q = p.as_poly(y).primitive()
+
+                q = q.as_expr()
+
+                h = gcd(q, _derivation(q), y)
+                s = quo(h, gcd(q, q.diff(y), y), y)
+
+                c_split = _splitter(c)
+
+                if s.as_poly(y).degree() == 0:
+                    return (c_split[0], q * c_split[1])
+
+                q_split = _splitter(cancel(q / s))
+
+                return (c_split[0]*q_split[0]*s, c_split[1]*q_split[1])
+
+        return (S.One, p)
+
+    special = {}
+
+    for term in terms:
+        if term.is_Function:
+            if isinstance(term, tan):
+                special[1 + _substitute(term)**2] = False
+            elif isinstance(term, tanh):
+                special[1 + _substitute(term)] = False
+                special[1 - _substitute(term)] = False
+            elif isinstance(term, LambertW):
+                special[_substitute(term)] = True
+
+    F = _substitute(f)
+
+    P, Q = F.as_numer_denom()
+
+    u_split = _splitter(denom)
+    v_split = _splitter(Q)
+
+    polys = set(list(v_split) + [ u_split[0] ] + list(special.keys()))
+
+    s = u_split[0] * Mul(*[ k for k, v in special.items() if v ])
+    polified = [ p.as_poly(*V) for p in [s, P, Q] ]
+
+    if None in polified:
+        return None
+
+    #--- definitions for _integrate
+    a, b, c = [ p.total_degree() for p in polified ]
+
+    poly_denom = (s * v_split[0] * _deflation(v_split[1])).as_expr()
+
+    def _exponent(g):
+        if g.is_Pow:
+            if g.exp.is_Rational and g.exp.q != 1:
+                if g.exp.p > 0:
+                    return g.exp.p + g.exp.q - 1
+                else:
+                    return abs(g.exp.p + g.exp.q)
+            else:
+                return 1
+        elif not g.is_Atom and g.args:
+            return max(_exponent(h) for h in g.args)
+        else:
+            return 1
+
+    A, B = _exponent(f), a + max(b, c)
+
+    if A > 1 and B > 1:
+        monoms = tuple(ordered(itermonomials(V, A + B - 1 + degree_offset)))
+    else:
+        monoms = tuple(ordered(itermonomials(V, A + B + degree_offset)))
+
+    poly_coeffs = _symbols('A', len(monoms))
+
+    poly_part = Add(*[ poly_coeffs[i]*monomial
+        for i, monomial in enumerate(monoms) ])
+
+    reducibles = set()
+
+    for poly in ordered(polys):
+        coeff, factors = factor_list(poly, *V)
+        reducibles.add(coeff)
+        reducibles.update(fact for fact, mul in factors)
+
+    def _integrate(field=None):
+        atans = set()
+        pairs = set()
+
+        if field == 'Q':
+            irreducibles = set(reducibles)
+        else:
+            setV = set(V)
+            irreducibles = set()
+            for poly in ordered(reducibles):
+                zV = setV & set(iterfreeargs(poly))
+                for z in ordered(zV):
+                    s = set(root_factors(poly, z, filter=field))
+                    irreducibles |= s
+                    break
+
+        log_part, atan_part = [], []
+
+        for poly in ordered(irreducibles):
+            m = collect(poly, I, evaluate=False)
+            y = m.get(I, S.Zero)
+            if y:
+                x = m.get(S.One, S.Zero)
+                if x.has(I) or y.has(I):
+                    continue  # nontrivial x + I*y
+                pairs.add((x, y))
+                irreducibles.remove(poly)
+
+        while pairs:
+            x, y = pairs.pop()
+            if (x, -y) in pairs:
+                pairs.remove((x, -y))
+                # Choosing b with no minus sign
+                if y.could_extract_minus_sign():
+                    y = -y
+                irreducibles.add(x*x + y*y)
+                atans.add(atan(x/y))
+            else:
+                irreducibles.add(x + I*y)
+
+
+        B = _symbols('B', len(irreducibles))
+        C = _symbols('C', len(atans))
+
+        # Note: the ordering matters here
+        for poly, b in reversed(list(zip(ordered(irreducibles), B))):
+            if poly.has(*V):
+                poly_coeffs.append(b)
+                log_part.append(b * log(poly))
+
+        for poly, c in reversed(list(zip(ordered(atans), C))):
+            if poly.has(*V):
+                poly_coeffs.append(c)
+                atan_part.append(c * poly)
+
+        # TODO: Currently it's better to use symbolic expressions here instead
+        # of rational functions, because it's simpler and FracElement doesn't
+        # give big speed improvement yet. This is because cancellation is slow
+        # due to slow polynomial GCD algorithms. If this gets improved then
+        # revise this code.
+        candidate = poly_part/poly_denom + Add(*log_part) + Add(*atan_part)
+        h = F - _derivation(candidate) / denom
+        raw_numer = h.as_numer_denom()[0]
+
+        # Rewrite raw_numer as a polynomial in K[coeffs][V] where K is a field
+        # that we have to determine. We can't use simply atoms() because log(3),
+        # sqrt(y) and similar expressions can appear, leading to non-trivial
+        # domains.
+        syms = set(poly_coeffs) | set(V)
+        non_syms = set()
+
+        def find_non_syms(expr):
+            if expr.is_Integer or expr.is_Rational:
+                pass # ignore trivial numbers
+            elif expr in syms:
+                pass # ignore variables
+            elif not expr.has_free(*syms):
+                non_syms.add(expr)
+            elif expr.is_Add or expr.is_Mul or expr.is_Pow:
+                list(map(find_non_syms, expr.args))
+            else:
+                # TODO: Non-polynomial expression. This should have been
+                # filtered out at an earlier stage.
+                raise PolynomialError
+
+        try:
+            find_non_syms(raw_numer)
+        except PolynomialError:
+            return None
+        else:
+            ground, _ = construct_domain(non_syms, field=True)
+
+        coeff_ring = PolyRing(poly_coeffs, ground)
+        ring = PolyRing(V, coeff_ring)
+        try:
+            numer = ring.from_expr(raw_numer)
+        except ValueError:
+            raise PolynomialError
+        solution = solve_lin_sys(numer.coeffs(), coeff_ring, _raw=False)
+
+        if solution is None:
+            return None
+        else:
+            return candidate.xreplace(solution).xreplace(
+                dict(zip(poly_coeffs, [S.Zero]*len(poly_coeffs))))
+
+    if all(isinstance(_, Symbol) for _ in V):
+        more_free = F.free_symbols - set(V)
+    else:
+        Fd = F.as_dummy()
+        more_free = Fd.xreplace(dict(zip(V, (Dummy() for _ in V)))
+            ).free_symbols & Fd.free_symbols
+    if not more_free:
+        # all free generators are identified in V
+        solution = _integrate('Q')
+
+        if solution is None:
+            solution = _integrate()
+    else:
+        solution = _integrate()
+
+    if solution is not None:
+        antideriv = solution.subs(rev_mapping)
+        antideriv = cancel(antideriv).expand()
+
+        if antideriv.is_Add:
+            antideriv = antideriv.as_independent(x)[1]
+
+        return indep*antideriv
+    else:
+        if retries >= 0:
+            result = heurisch(f, x, mappings=mappings, rewrite=rewrite, hints=hints, retries=retries - 1, unnecessary_permutations=unnecessary_permutations)
+
+            if result is not None:
+                return indep*result
+
+        return None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/integrals.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..b9ed4a22802acc455f5162e109fc575223c97338
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/integrals.py
@@ -0,0 +1,1640 @@
+from __future__ import annotations
+
+from sympy.concrete.expr_with_limits import AddWithLimits
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.exprtools import factor_terms
+from sympy.core.function import diff
+from sympy.core.logic import fuzzy_bool
+from sympy.core.mul import Mul
+from sympy.core.numbers import oo, pi
+from sympy.core.relational import Ne
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, Wild)
+from sympy.core.sympify import sympify
+from sympy.functions import Piecewise, sqrt, piecewise_fold, tan, cot, atan
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.complexes import Abs, sign
+from sympy.functions.elementary.miscellaneous import Min, Max
+from sympy.functions.special.singularity_functions import Heaviside
+from .rationaltools import ratint
+from sympy.matrices import MatrixBase
+from sympy.polys import Poly, PolynomialError
+from sympy.series.formal import FormalPowerSeries
+from sympy.series.limits import limit
+from sympy.series.order import Order
+from sympy.tensor.functions import shape
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.misc import filldedent
+
+
+class Integral(AddWithLimits):
+    """Represents unevaluated integral."""
+
+    __slots__ = ()
+
+    args: tuple[Expr, Tuple] # type: ignore
+
+    def __new__(cls, function, *symbols, **assumptions) -> Integral:
+        """Create an unevaluated integral.
+
+        Explanation
+        ===========
+
+        Arguments are an integrand followed by one or more limits.
+
+        If no limits are given and there is only one free symbol in the
+        expression, that symbol will be used, otherwise an error will be
+        raised.
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x, y
+        >>> Integral(x)
+        Integral(x, x)
+        >>> Integral(y)
+        Integral(y, y)
+
+        When limits are provided, they are interpreted as follows (using
+        ``x`` as though it were the variable of integration):
+
+            (x,) or x - indefinite integral
+            (x, a) - "evaluate at" integral is an abstract antiderivative
+            (x, a, b) - definite integral
+
+        The ``as_dummy`` method can be used to see which symbols cannot be
+        targeted by subs: those with a prepended underscore cannot be
+        changed with ``subs``. (Also, the integration variables themselves --
+        the first element of a limit -- can never be changed by subs.)
+
+        >>> i = Integral(x, x)
+        >>> at = Integral(x, (x, x))
+        >>> i.as_dummy()
+        Integral(x, x)
+        >>> at.as_dummy()
+        Integral(_0, (_0, x))
+
+        """
+
+        #This will help other classes define their own definitions
+        #of behaviour with Integral.
+        if hasattr(function, '_eval_Integral'):
+            return function._eval_Integral(*symbols, **assumptions)
+
+        if isinstance(function, Poly):
+            sympy_deprecation_warning(
+                """
+                integrate(Poly) and Integral(Poly) are deprecated. Instead,
+                use the Poly.integrate() method, or convert the Poly to an
+                Expr first with the Poly.as_expr() method.
+                """,
+                deprecated_since_version="1.6",
+                active_deprecations_target="deprecated-integrate-poly")
+
+        obj = AddWithLimits.__new__(cls, function, *symbols, **assumptions)
+        return obj
+
+    def __getnewargs__(self):
+        return (self.function,) + tuple([tuple(xab) for xab in self.limits])
+
+    @property
+    def free_symbols(self):
+        """
+        This method returns the symbols that will exist when the
+        integral is evaluated. This is useful if one is trying to
+        determine whether an integral depends on a certain
+        symbol or not.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x, y
+        >>> Integral(x, (x, y, 1)).free_symbols
+        {y}
+
+        See Also
+        ========
+
+        sympy.concrete.expr_with_limits.ExprWithLimits.function
+        sympy.concrete.expr_with_limits.ExprWithLimits.limits
+        sympy.concrete.expr_with_limits.ExprWithLimits.variables
+        """
+        return super().free_symbols
+
+    def _eval_is_zero(self):
+        # This is a very naive and quick test, not intended to do the integral to
+        # answer whether it is zero or not, e.g. Integral(sin(x), (x, 0, 2*pi))
+        # is zero but this routine should return None for that case. But, like
+        # Mul, there are trivial situations for which the integral will be
+        # zero so we check for those.
+        if self.function.is_zero:
+            return True
+        got_none = False
+        for l in self.limits:
+            if len(l) == 3:
+                z = (l[1] == l[2]) or (l[1] - l[2]).is_zero
+                if z:
+                    return True
+                elif z is None:
+                    got_none = True
+        free = self.function.free_symbols
+        for xab in self.limits:
+            if len(xab) == 1:
+                free.add(xab[0])
+                continue
+            if len(xab) == 2 and xab[0] not in free:
+                if xab[1].is_zero:
+                    return True
+                elif xab[1].is_zero is None:
+                    got_none = True
+            # take integration symbol out of free since it will be replaced
+            # with the free symbols in the limits
+            free.discard(xab[0])
+            # add in the new symbols
+            for i in xab[1:]:
+                free.update(i.free_symbols)
+        if self.function.is_zero is False and got_none is False:
+            return False
+
+    def transform(self, x, u):
+        r"""
+        Performs a change of variables from `x` to `u` using the relationship
+        given by `x` and `u` which will define the transformations `f` and `F`
+        (which are inverses of each other) as follows:
+
+        1) If `x` is a Symbol (which is a variable of integration) then `u`
+           will be interpreted as some function, f(u), with inverse F(u).
+           This, in effect, just makes the substitution of x with f(x).
+
+        2) If `u` is a Symbol then `x` will be interpreted as some function,
+           F(x), with inverse f(u). This is commonly referred to as
+           u-substitution.
+
+        Once f and F have been identified, the transformation is made as
+        follows:
+
+        .. math:: \int_a^b x \mathrm{d}x \rightarrow \int_{F(a)}^{F(b)} f(x)
+                  \frac{\mathrm{d}}{\mathrm{d}x}
+
+        where `F(x)` is the inverse of `f(x)` and the limits and integrand have
+        been corrected so as to retain the same value after integration.
+
+        Notes
+        =====
+
+        The mappings, F(x) or f(u), must lead to a unique integral. Linear
+        or rational linear expression, ``2*x``, ``1/x`` and ``sqrt(x)``, will
+        always work; quadratic expressions like ``x**2 - 1`` are acceptable
+        as long as the resulting integrand does not depend on the sign of
+        the solutions (see examples).
+
+        The integral will be returned unchanged if ``x`` is not a variable of
+        integration.
+
+        ``x`` must be (or contain) only one of of the integration variables. If
+        ``u`` has more than one free symbol then it should be sent as a tuple
+        (``u``, ``uvar``) where ``uvar`` identifies which variable is replacing
+        the integration variable.
+        XXX can it contain another integration variable?
+
+        Examples
+        ========
+
+        >>> from sympy.abc import a, x, u
+        >>> from sympy import Integral, cos, sqrt
+
+        >>> i = Integral(x*cos(x**2 - 1), (x, 0, 1))
+
+        transform can change the variable of integration
+
+        >>> i.transform(x, u)
+        Integral(u*cos(u**2 - 1), (u, 0, 1))
+
+        transform can perform u-substitution as long as a unique
+        integrand is obtained:
+
+        >>> ui = i.transform(x**2 - 1, u)
+        >>> ui
+        Integral(cos(u)/2, (u, -1, 0))
+
+        This attempt fails because x = +/-sqrt(u + 1) and the
+        sign does not cancel out of the integrand:
+
+        >>> Integral(cos(x**2 - 1), (x, 0, 1)).transform(x**2 - 1, u)
+        Traceback (most recent call last):
+        ...
+        ValueError:
+        The mapping between F(x) and f(u) did not give a unique integrand.
+
+        transform can do a substitution. Here, the previous
+        result is transformed back into the original expression
+        using "u-substitution":
+
+        >>> ui.transform(sqrt(u + 1), x) == i
+        True
+
+        We can accomplish the same with a regular substitution:
+
+        >>> ui.transform(u, x**2 - 1) == i
+        True
+
+        If the `x` does not contain a symbol of integration then
+        the integral will be returned unchanged. Integral `i` does
+        not have an integration variable `a` so no change is made:
+
+        >>> i.transform(a, x) == i
+        True
+
+        When `u` has more than one free symbol the symbol that is
+        replacing `x` must be identified by passing `u` as a tuple:
+
+        >>> Integral(x, (x, 0, 1)).transform(x, (u + a, u))
+        Integral(a + u, (u, -a, 1 - a))
+        >>> Integral(x, (x, 0, 1)).transform(x, (u + a, a))
+        Integral(a + u, (a, -u, 1 - u))
+
+        See Also
+        ========
+
+        sympy.concrete.expr_with_limits.ExprWithLimits.variables : Lists the integration variables
+        as_dummy : Replace integration variables with dummy ones
+        """
+        d = Dummy('d')
+
+        xfree = x.free_symbols.intersection(self.variables)
+        if len(xfree) > 1:
+            raise ValueError(
+                'F(x) can only contain one of: %s' % self.variables)
+        xvar = xfree.pop() if xfree else d
+
+        if xvar not in self.variables:
+            return self
+
+        u = sympify(u)
+        if isinstance(u, Expr):
+            ufree = u.free_symbols
+            if len(ufree) == 0:
+                raise ValueError(filldedent('''
+                f(u) cannot be a constant'''))
+            if len(ufree) > 1:
+                raise ValueError(filldedent('''
+                When f(u) has more than one free symbol, the one replacing x
+                must be identified: pass f(u) as (f(u), u)'''))
+            uvar = ufree.pop()
+        else:
+            u, uvar = u
+            if uvar not in u.free_symbols:
+                raise ValueError(filldedent('''
+                Expecting a tuple (expr, symbol) where symbol identified
+                a free symbol in expr, but symbol is not in expr's free
+                symbols.'''))
+            if not isinstance(uvar, Symbol):
+                # This probably never evaluates to True
+                raise ValueError(filldedent('''
+                Expecting a tuple (expr, symbol) but didn't get
+                a symbol; got %s''' % uvar))
+
+        if x.is_Symbol and u.is_Symbol:
+            return self.xreplace({x: u})
+
+        if not x.is_Symbol and not u.is_Symbol:
+            raise ValueError('either x or u must be a symbol')
+
+        if uvar == xvar:
+            return self.transform(x, (u.subs(uvar, d), d)).xreplace({d: uvar})
+
+        if uvar in self.limits:
+            raise ValueError(filldedent('''
+            u must contain the same variable as in x
+            or a variable that is not already an integration variable'''))
+
+        from sympy.solvers.solvers import solve
+        if not x.is_Symbol:
+            F = [x.subs(xvar, d)]
+            soln = solve(u - x, xvar, check=False)
+            if not soln:
+                raise ValueError('no solution for solve(F(x) - f(u), x)')
+            f = [fi.subs(uvar, d) for fi in soln]
+        else:
+            f = [u.subs(uvar, d)]
+            from sympy.simplify.simplify import posify
+            pdiff, reps = posify(u - x)
+            puvar = uvar.subs([(v, k) for k, v in reps.items()])
+            soln = [s.subs(reps) for s in solve(pdiff, puvar)]
+            if not soln:
+                raise ValueError('no solution for solve(F(x) - f(u), u)')
+            F = [fi.subs(xvar, d) for fi in soln]
+
+        newfuncs = {(self.function.subs(xvar, fi)*fi.diff(d)
+                        ).subs(d, uvar) for fi in f}
+        if len(newfuncs) > 1:
+            raise ValueError(filldedent('''
+            The mapping between F(x) and f(u) did not give
+            a unique integrand.'''))
+        newfunc = newfuncs.pop()
+
+        def _calc_limit_1(F, a, b):
+            """
+            replace d with a, using subs if possible, otherwise limit
+            where sign of b is considered
+            """
+            wok = F.subs(d, a)
+            if wok is S.NaN or wok.is_finite is False and a.is_finite:
+                return limit(sign(b)*F, d, a)
+            return wok
+
+        def _calc_limit(a, b):
+            """
+            replace d with a, using subs if possible, otherwise limit
+            where sign of b is considered
+            """
+            avals = list({_calc_limit_1(Fi, a, b) for Fi in F})
+            if len(avals) > 1:
+                raise ValueError(filldedent('''
+                The mapping between F(x) and f(u) did not
+                give a unique limit.'''))
+            return avals[0]
+
+        newlimits = []
+        for xab in self.limits:
+            sym = xab[0]
+            if sym == xvar:
+                if len(xab) == 3:
+                    a, b = xab[1:]
+                    a, b = _calc_limit(a, b), _calc_limit(b, a)
+                    if fuzzy_bool(a - b > 0):
+                        a, b = b, a
+                        newfunc = -newfunc
+                    newlimits.append((uvar, a, b))
+                elif len(xab) == 2:
+                    a = _calc_limit(xab[1], 1)
+                    newlimits.append((uvar, a))
+                else:
+                    newlimits.append(uvar)
+            else:
+                newlimits.append(xab)
+
+        return self.func(newfunc, *newlimits)
+
+    def doit(self, **hints):
+        """
+        Perform the integration using any hints given.
+
+        Examples
+        ========
+
+        >>> from sympy import Piecewise, S
+        >>> from sympy.abc import x, t
+        >>> p = x**2 + Piecewise((0, x/t < 0), (1, True))
+        >>> p.integrate((t, S(4)/5, 1), (x, -1, 1))
+        1/3
+
+        See Also
+        ========
+
+        sympy.integrals.trigonometry.trigintegrate
+        sympy.integrals.heurisch.heurisch
+        sympy.integrals.rationaltools.ratint
+        as_sum : Approximate the integral using a sum
+        """
+        if not hints.get('integrals', True):
+            return self
+
+        deep = hints.get('deep', True)
+        meijerg = hints.get('meijerg', None)
+        conds = hints.get('conds', 'piecewise')
+        risch = hints.get('risch', None)
+        heurisch = hints.get('heurisch', None)
+        manual = hints.get('manual', None)
+        if len(list(filter(None, (manual, meijerg, risch, heurisch)))) > 1:
+            raise ValueError("At most one of manual, meijerg, risch, heurisch can be True")
+        elif manual:
+            meijerg = risch = heurisch = False
+        elif meijerg:
+            manual = risch = heurisch = False
+        elif risch:
+            manual = meijerg = heurisch = False
+        elif heurisch:
+            manual = meijerg = risch = False
+        eval_kwargs = {"meijerg": meijerg, "risch": risch, "manual": manual, "heurisch": heurisch,
+            "conds": conds}
+
+        if conds not in ('separate', 'piecewise', 'none'):
+            raise ValueError('conds must be one of "separate", "piecewise", '
+                             '"none", got: %s' % conds)
+
+        if risch and any(len(xab) > 1 for xab in self.limits):
+            raise ValueError('risch=True is only allowed for indefinite integrals.')
+
+        # check for the trivial zero
+        if self.is_zero:
+            return S.Zero
+
+        # hacks to handle integrals of
+        # nested summations
+        from sympy.concrete.summations import Sum
+        if isinstance(self.function, Sum):
+            if any(v in self.function.limits[0] for v in self.variables):
+                raise ValueError('Limit of the sum cannot be an integration variable.')
+            if any(l.is_infinite for l in self.function.limits[0][1:]):
+                return self
+            _i = self
+            _sum = self.function
+            return _sum.func(_i.func(_sum.function, *_i.limits).doit(), *_sum.limits).doit()
+
+        # now compute and check the function
+        function = self.function
+
+        # hack to use a consistent Heaviside(x, 1/2)
+        function = function.replace(
+            lambda x: isinstance(x, Heaviside) and x.args[1]*2 != 1,
+            lambda x: Heaviside(x.args[0]))
+
+        if deep:
+            function = function.doit(**hints)
+        if function.is_zero:
+            return S.Zero
+
+        # hacks to handle special cases
+        if isinstance(function, MatrixBase):
+            return function.applyfunc(
+                lambda f: self.func(f, *self.limits).doit(**hints))
+
+        if isinstance(function, FormalPowerSeries):
+            if len(self.limits) > 1:
+                raise NotImplementedError
+            xab = self.limits[0]
+            if len(xab) > 1:
+                return function.integrate(xab, **eval_kwargs)
+            else:
+                return function.integrate(xab[0], **eval_kwargs)
+
+        # There is no trivial answer and special handling
+        # is done so continue
+
+        # first make sure any definite limits have integration
+        # variables with matching assumptions
+        reps = {}
+        for xab in self.limits:
+            if len(xab) != 3:
+                # it makes sense to just make
+                # all x real but in practice with the
+                # current state of integration...this
+                # doesn't work out well
+                # x = xab[0]
+                # if x not in reps and not x.is_real:
+                #     reps[x] = Dummy(real=True)
+                continue
+            x, a, b = xab
+            l = (a, b)
+            if all(i.is_nonnegative for i in l) and not x.is_nonnegative:
+                d = Dummy(positive=True)
+            elif all(i.is_nonpositive for i in l) and not x.is_nonpositive:
+                d = Dummy(negative=True)
+            elif all(i.is_real for i in l) and not x.is_real:
+                d = Dummy(real=True)
+            else:
+                d = None
+            if d:
+                reps[x] = d
+        if reps:
+            undo = {v: k for k, v in reps.items()}
+            did = self.xreplace(reps).doit(**hints)
+            if isinstance(did, tuple):  # when separate=True
+                did = tuple([i.xreplace(undo) for i in did])
+            else:
+                did = did.xreplace(undo)
+            return did
+
+        # continue with existing assumptions
+        undone_limits = []
+        # ulj = free symbols of any undone limits' upper and lower limits
+        ulj = set()
+        for xab in self.limits:
+            # compute uli, the free symbols in the
+            # Upper and Lower limits of limit I
+            if len(xab) == 1:
+                uli = set(xab[:1])
+            elif len(xab) == 2:
+                uli = xab[1].free_symbols
+            elif len(xab) == 3:
+                uli = xab[1].free_symbols.union(xab[2].free_symbols)
+            # this integral can be done as long as there is no blocking
+            # limit that has been undone. An undone limit is blocking if
+            # it contains an integration variable that is in this limit's
+            # upper or lower free symbols or vice versa
+            if xab[0] in ulj or any(v[0] in uli for v in undone_limits):
+                undone_limits.append(xab)
+                ulj.update(uli)
+                function = self.func(*([function] + [xab]))
+                factored_function = function.factor()
+                if not isinstance(factored_function, Integral):
+                    function = factored_function
+                continue
+
+            if function.has(Abs, sign) and (
+                (len(xab) < 3 and all(x.is_extended_real for x in xab)) or
+                (len(xab) == 3 and all(x.is_extended_real and not x.is_infinite for
+                 x in xab[1:]))):
+                    # some improper integrals are better off with Abs
+                    xr = Dummy("xr", real=True)
+                    function = (function.xreplace({xab[0]: xr})
+                        .rewrite(Piecewise).xreplace({xr: xab[0]}))
+            elif function.has(Min, Max):
+                function = function.rewrite(Piecewise)
+            if (function.has(Piecewise) and
+                not isinstance(function, Piecewise)):
+                    function = piecewise_fold(function)
+            if isinstance(function, Piecewise):
+                if len(xab) == 1:
+                    antideriv = function._eval_integral(xab[0],
+                        **eval_kwargs)
+                else:
+                    antideriv = self._eval_integral(
+                        function, xab[0], **eval_kwargs)
+            else:
+                # There are a number of tradeoffs in using the
+                # Meijer G method. It can sometimes be a lot faster
+                # than other methods, and sometimes slower. And
+                # there are certain types of integrals for which it
+                # is more likely to work than others. These
+                # heuristics are incorporated in deciding what
+                # integration methods to try, in what order. See the
+                # integrate() docstring for details.
+                def try_meijerg(function, xab):
+                    ret = None
+                    if len(xab) == 3 and meijerg is not False:
+                        x, a, b = xab
+                        try:
+                            res = meijerint_definite(function, x, a, b)
+                        except NotImplementedError:
+                            _debug('NotImplementedError '
+                                'from meijerint_definite')
+                            res = None
+                        if res is not None:
+                            f, cond = res
+                            if conds == 'piecewise':
+                                u = self.func(function, (x, a, b))
+                                # if Piecewise modifies cond too
+                                # much it may not be recognized by
+                                # _condsimp pattern matching so just
+                                # turn off all evaluation
+                                return Piecewise((f, cond), (u, True),
+                                    evaluate=False)
+                            elif conds == 'separate':
+                                if len(self.limits) != 1:
+                                    raise ValueError(filldedent('''
+                                        conds=separate not supported in
+                                        multiple integrals'''))
+                                ret = f, cond
+                            else:
+                                ret = f
+                    return ret
+
+                meijerg1 = meijerg
+                if (meijerg is not False and
+                        len(xab) == 3 and xab[1].is_extended_real and xab[2].is_extended_real
+                        and not function.is_Poly and
+                        (xab[1].has(oo, -oo) or xab[2].has(oo, -oo))):
+                    ret = try_meijerg(function, xab)
+                    if ret is not None:
+                        function = ret
+                        continue
+                    meijerg1 = False
+                # If the special meijerg code did not succeed in
+                # finding a definite integral, then the code using
+                # meijerint_indefinite will not either (it might
+                # find an antiderivative, but the answer is likely
+                # to be nonsensical). Thus if we are requested to
+                # only use Meijer G-function methods, we give up at
+                # this stage. Otherwise we just disable G-function
+                # methods.
+                if meijerg1 is False and meijerg is True:
+                    antideriv = None
+                else:
+                    antideriv = self._eval_integral(
+                        function, xab[0], **eval_kwargs)
+                    if antideriv is None and meijerg is True:
+                        ret = try_meijerg(function, xab)
+                        if ret is not None:
+                            function = ret
+                            continue
+
+            final = hints.get('final', True)
+            # dotit may be iterated but floor terms making atan and acot
+            # continuous should only be added in the final round
+            if (final and not isinstance(antideriv, Integral) and
+                antideriv is not None):
+                for atan_term in antideriv.atoms(atan):
+                    atan_arg = atan_term.args[0]
+                    # Checking `atan_arg` to be linear combination of `tan` or `cot`
+                    for tan_part in atan_arg.atoms(tan):
+                        x1 = Dummy('x1')
+                        tan_exp1 = atan_arg.subs(tan_part, x1)
+                        # The coefficient of `tan` should be constant
+                        coeff = tan_exp1.diff(x1)
+                        if x1 not in coeff.free_symbols:
+                            a = tan_part.args[0]
+                            antideriv = antideriv.subs(atan_term, Add(atan_term,
+                                sign(coeff)*pi*floor((a-pi/2)/pi)))
+                    for cot_part in atan_arg.atoms(cot):
+                        x1 = Dummy('x1')
+                        cot_exp1 = atan_arg.subs(cot_part, x1)
+                        # The coefficient of `cot` should be constant
+                        coeff = cot_exp1.diff(x1)
+                        if x1 not in coeff.free_symbols:
+                            a = cot_part.args[0]
+                            antideriv = antideriv.subs(atan_term, Add(atan_term,
+                                sign(coeff)*pi*floor((a)/pi)))
+
+            if antideriv is None:
+                undone_limits.append(xab)
+                function = self.func(*([function] + [xab])).factor()
+                factored_function = function.factor()
+                if not isinstance(factored_function, Integral):
+                    function = factored_function
+                continue
+            else:
+                if len(xab) == 1:
+                    function = antideriv
+                else:
+                    if len(xab) == 3:
+                        x, a, b = xab
+                    elif len(xab) == 2:
+                        x, b = xab
+                        a = None
+                    else:
+                        raise NotImplementedError
+
+                    if deep:
+                        if isinstance(a, Basic):
+                            a = a.doit(**hints)
+                        if isinstance(b, Basic):
+                            b = b.doit(**hints)
+
+                    if antideriv.is_Poly:
+                        gens = list(antideriv.gens)
+                        gens.remove(x)
+
+                        antideriv = antideriv.as_expr()
+
+                        function = antideriv._eval_interval(x, a, b)
+                        function = Poly(function, *gens)
+                    else:
+                        def is_indef_int(g, x):
+                            return (isinstance(g, Integral) and
+                                    any(i == (x,) for i in g.limits))
+
+                        def eval_factored(f, x, a, b):
+                            # _eval_interval for integrals with
+                            # (constant) factors
+                            # a single indefinite integral is assumed
+                            args = []
+                            for g in Mul.make_args(f):
+                                if is_indef_int(g, x):
+                                    args.append(g._eval_interval(x, a, b))
+                                else:
+                                    args.append(g)
+                            return Mul(*args)
+
+                        integrals, others, piecewises = [], [], []
+                        for f in Add.make_args(antideriv):
+                            if any(is_indef_int(g, x)
+                                   for g in Mul.make_args(f)):
+                                integrals.append(f)
+                            elif any(isinstance(g, Piecewise)
+                                     for g in Mul.make_args(f)):
+                                piecewises.append(piecewise_fold(f))
+                            else:
+                                others.append(f)
+                        uneval = Add(*[eval_factored(f, x, a, b)
+                                       for f in integrals])
+                        try:
+                            evalued = Add(*others)._eval_interval(x, a, b)
+                            evalued_pw = piecewise_fold(Add(*piecewises))._eval_interval(x, a, b)
+                            function = uneval + evalued + evalued_pw
+                        except NotImplementedError:
+                            # This can happen if _eval_interval depends in a
+                            # complicated way on limits that cannot be computed
+                            undone_limits.append(xab)
+                            function = self.func(*([function] + [xab]))
+                            factored_function = function.factor()
+                            if not isinstance(factored_function, Integral):
+                                function = factored_function
+        return function
+
+    def _eval_derivative(self, sym):
+        """Evaluate the derivative of the current Integral object by
+        differentiating under the integral sign [1], using the Fundamental
+        Theorem of Calculus [2] when possible.
+
+        Explanation
+        ===========
+
+        Whenever an Integral is encountered that is equivalent to zero or
+        has an integrand that is independent of the variable of integration
+        those integrals are performed. All others are returned as Integral
+        instances which can be resolved with doit() (provided they are integrable).
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign
+        .. [2] https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus
+
+        Examples
+        ========
+
+        >>> from sympy import Integral
+        >>> from sympy.abc import x, y
+        >>> i = Integral(x + y, y, (y, 1, x))
+        >>> i.diff(x)
+        Integral(x + y, (y, x)) + Integral(1, y, (y, 1, x))
+        >>> i.doit().diff(x) == i.diff(x).doit()
+        True
+        >>> i.diff(y)
+        0
+
+        The previous must be true since there is no y in the evaluated integral:
+
+        >>> i.free_symbols
+        {x}
+        >>> i.doit()
+        2*x**3/3 - x/2 - 1/6
+
+        """
+
+        # differentiate under the integral sign; we do not
+        # check for regularity conditions (TODO), see issue 4215
+
+        # get limits and the function
+        f, limits = self.function, list(self.limits)
+
+        # the order matters if variables of integration appear in the limits
+        # so work our way in from the outside to the inside.
+        limit = limits.pop(-1)
+        if len(limit) == 3:
+            x, a, b = limit
+        elif len(limit) == 2:
+            x, b = limit
+            a = None
+        else:
+            a = b = None
+            x = limit[0]
+
+        if limits:  # f is the argument to an integral
+            f = self.func(f, *tuple(limits))
+
+        # assemble the pieces
+        def _do(f, ab):
+            dab_dsym = diff(ab, sym)
+            if not dab_dsym:
+                return S.Zero
+            if isinstance(f, Integral):
+                limits = [(x, x) if (len(l) == 1 and l[0] == x) else l
+                          for l in f.limits]
+                f = self.func(f.function, *limits)
+            return f.subs(x, ab)*dab_dsym
+
+        rv = S.Zero
+        if b is not None:
+            rv += _do(f, b)
+        if a is not None:
+            rv -= _do(f, a)
+        if len(limit) == 1 and sym == x:
+            # the dummy variable *is* also the real-world variable
+            arg = f
+            rv += arg
+        else:
+            # the dummy variable might match sym but it's
+            # only a dummy and the actual variable is determined
+            # by the limits, so mask off the variable of integration
+            # while differentiating
+            u = Dummy('u')
+            arg = f.subs(x, u).diff(sym).subs(u, x)
+            if arg:
+                rv += self.func(arg, (x, a, b))
+        return rv
+
+    def _eval_integral(self, f, x, meijerg=None, risch=None, manual=None,
+                       heurisch=None, conds='piecewise',final=None):
+        """
+        Calculate the anti-derivative to the function f(x).
+
+        Explanation
+        ===========
+
+        The following algorithms are applied (roughly in this order):
+
+        1. Simple heuristics (based on pattern matching and integral table):
+
+           - most frequently used functions (e.g. polynomials, products of
+             trig functions)
+
+        2. Integration of rational functions:
+
+           - A complete algorithm for integrating rational functions is
+             implemented (the Lazard-Rioboo-Trager algorithm).  The algorithm
+             also uses the partial fraction decomposition algorithm
+             implemented in apart() as a preprocessor to make this process
+             faster.  Note that the integral of a rational function is always
+             elementary, but in general, it may include a RootSum.
+
+        3. Full Risch algorithm:
+
+           - The Risch algorithm is a complete decision
+             procedure for integrating elementary functions, which means that
+             given any elementary function, it will either compute an
+             elementary antiderivative, or else prove that none exists.
+             Currently, part of transcendental case is implemented, meaning
+             elementary integrals containing exponentials, logarithms, and
+             (soon!) trigonometric functions can be computed.  The algebraic
+             case, e.g., functions containing roots, is much more difficult
+             and is not implemented yet.
+
+           - If the routine fails (because the integrand is not elementary, or
+             because a case is not implemented yet), it continues on to the
+             next algorithms below.  If the routine proves that the integrals
+             is nonelementary, it still moves on to the algorithms below,
+             because we might be able to find a closed-form solution in terms
+             of special functions.  If risch=True, however, it will stop here.
+
+        4. The Meijer G-Function algorithm:
+
+           - This algorithm works by first rewriting the integrand in terms of
+             very general Meijer G-Function (meijerg in SymPy), integrating
+             it, and then rewriting the result back, if possible.  This
+             algorithm is particularly powerful for definite integrals (which
+             is actually part of a different method of Integral), since it can
+             compute closed-form solutions of definite integrals even when no
+             closed-form indefinite integral exists.  But it also is capable
+             of computing many indefinite integrals as well.
+
+           - Another advantage of this method is that it can use some results
+             about the Meijer G-Function to give a result in terms of a
+             Piecewise expression, which allows to express conditionally
+             convergent integrals.
+
+           - Setting meijerg=True will cause integrate() to use only this
+             method.
+
+        5. The "manual integration" algorithm:
+
+           - This algorithm tries to mimic how a person would find an
+             antiderivative by hand, for example by looking for a
+             substitution or applying integration by parts. This algorithm
+             does not handle as many integrands but can return results in a
+             more familiar form.
+
+           - Sometimes this algorithm can evaluate parts of an integral; in
+             this case integrate() will try to evaluate the rest of the
+             integrand using the other methods here.
+
+           - Setting manual=True will cause integrate() to use only this
+             method.
+
+        6. The Heuristic Risch algorithm:
+
+           - This is a heuristic version of the Risch algorithm, meaning that
+             it is not deterministic.  This is tried as a last resort because
+             it can be very slow.  It is still used because not enough of the
+             full Risch algorithm is implemented, so that there are still some
+             integrals that can only be computed using this method.  The goal
+             is to implement enough of the Risch and Meijer G-function methods
+             so that this can be deleted.
+
+             Setting heurisch=True will cause integrate() to use only this
+             method. Set heurisch=False to not use it.
+
+        """
+
+        from sympy.integrals.risch import risch_integrate, NonElementaryIntegral
+        from sympy.integrals.manualintegrate import manualintegrate
+
+        if risch:
+            try:
+                return risch_integrate(f, x, conds=conds)
+            except NotImplementedError:
+                return None
+
+        if manual:
+            try:
+                result = manualintegrate(f, x)
+                if result is not None and result.func != Integral:
+                    return result
+            except (ValueError, PolynomialError):
+                pass
+
+        eval_kwargs = {"meijerg": meijerg, "risch": risch, "manual": manual,
+            "heurisch": heurisch, "conds": conds}
+
+        # if it is a poly(x) then let the polynomial integrate itself (fast)
+        #
+        # It is important to make this check first, otherwise the other code
+        # will return a SymPy expression instead of a Polynomial.
+        #
+        # see Polynomial for details.
+        if isinstance(f, Poly) and not (manual or meijerg or risch):
+            # Note: this is deprecated, but the deprecation warning is already
+            # issued in the Integral constructor.
+            return f.integrate(x)
+
+        # Piecewise antiderivatives need to call special integrate.
+        if isinstance(f, Piecewise):
+            return f.piecewise_integrate(x, **eval_kwargs)
+
+        # let's cut it short if `f` does not depend on `x`; if
+        # x is only a dummy, that will be handled below
+        if not f.has(x):
+            return f*x
+
+        # try to convert to poly(x) and then integrate if successful (fast)
+        poly = f.as_poly(x)
+        if poly is not None and not (manual or meijerg or risch):
+            return poly.integrate().as_expr()
+
+        if risch is not False:
+            try:
+                result, i = risch_integrate(f, x, separate_integral=True,
+                    conds=conds)
+            except NotImplementedError:
+                pass
+            else:
+                if i:
+                    # There was a nonelementary integral. Try integrating it.
+
+                    # if no part of the NonElementaryIntegral is integrated by
+                    # the Risch algorithm, then use the original function to
+                    # integrate, instead of re-written one
+                    if result == 0:
+                        return NonElementaryIntegral(f, x).doit(risch=False)
+                    else:
+                        return result + i.doit(risch=False)
+                else:
+                    return result
+
+        # since Integral(f=g1+g2+...) == Integral(g1) + Integral(g2) + ...
+        # we are going to handle Add terms separately,
+        # if `f` is not Add -- we only have one term
+
+        # Note that in general, this is a bad idea, because Integral(g1) +
+        # Integral(g2) might not be computable, even if Integral(g1 + g2) is.
+        # For example, Integral(x**x + x**x*log(x)).  But many heuristics only
+        # work term-wise.  So we compute this step last, after trying
+        # risch_integrate.  We also try risch_integrate again in this loop,
+        # because maybe the integral is a sum of an elementary part and a
+        # nonelementary part (like erf(x) + exp(x)).  risch_integrate() is
+        # quite fast, so this is acceptable.
+        from sympy.simplify.fu import sincos_to_sum
+        parts = []
+        args = Add.make_args(f)
+        for g in args:
+            coeff, g = g.as_independent(x)
+
+            # g(x) = const
+            if g is S.One and not meijerg:
+                parts.append(coeff*x)
+                continue
+
+            # g(x) = expr + O(x**n)
+            order_term = g.getO()
+
+            if order_term is not None:
+                h = self._eval_integral(g.removeO(), x, **eval_kwargs)
+
+                if h is not None:
+                    h_order_expr = self._eval_integral(order_term.expr, x, **eval_kwargs)
+
+                    if h_order_expr is not None:
+                        h_order_term = order_term.func(
+                            h_order_expr, *order_term.variables)
+                        parts.append(coeff*(h + h_order_term))
+                        continue
+
+                # NOTE: if there is O(x**n) and we fail to integrate then
+                # there is no point in trying other methods because they
+                # will fail, too.
+                return None
+
+            #               c
+            # g(x) = (a*x+b)
+            if g.is_Pow and not g.exp.has(x) and not meijerg:
+                a = Wild('a', exclude=[x])
+                b = Wild('b', exclude=[x])
+
+                M = g.base.match(a*x + b)
+
+                if M is not None:
+                    if g.exp == -1:
+                        h = log(g.base)
+                    elif conds != 'piecewise':
+                        h = g.base**(g.exp + 1) / (g.exp + 1)
+                    else:
+                        h1 = log(g.base)
+                        h2 = g.base**(g.exp + 1) / (g.exp + 1)
+                        h = Piecewise((h2, Ne(g.exp, -1)), (h1, True))
+
+                    parts.append(coeff * h / M[a])
+                    continue
+
+            #        poly(x)
+            # g(x) = -------
+            #        poly(x)
+            if g.is_rational_function(x) and not (manual or meijerg or risch):
+                parts.append(coeff * ratint(g, x))
+                continue
+
+            if not (manual or meijerg or risch):
+                # g(x) = Mul(trig)
+                h = trigintegrate(g, x, conds=conds)
+                if h is not None:
+                    parts.append(coeff * h)
+                    continue
+
+                # g(x) has at least a DiracDelta term
+                h = deltaintegrate(g, x)
+                if h is not None:
+                    parts.append(coeff * h)
+                    continue
+
+                from .singularityfunctions import singularityintegrate
+                # g(x) has at least a Singularity Function term
+                h = singularityintegrate(g, x)
+                if h is not None:
+                    parts.append(coeff * h)
+                    continue
+
+                # Try risch again.
+                if risch is not False:
+                    try:
+                        h, i = risch_integrate(g, x,
+                            separate_integral=True, conds=conds)
+                    except NotImplementedError:
+                        h = None
+                    else:
+                        if i:
+                            h = h + i.doit(risch=False)
+
+                        parts.append(coeff*h)
+                        continue
+
+                # fall back to heurisch
+                if heurisch is not False:
+                    from sympy.integrals.heurisch import (heurisch as heurisch_,
+                                                          heurisch_wrapper)
+                    try:
+                        if conds == 'piecewise':
+                            h = heurisch_wrapper(g, x, hints=[])
+                        else:
+                            h = heurisch_(g, x, hints=[])
+                    except PolynomialError:
+                        # XXX: this exception means there is a bug in the
+                        # implementation of heuristic Risch integration
+                        # algorithm.
+                        h = None
+            else:
+                h = None
+
+            if meijerg is not False and h is None:
+                # rewrite using G functions
+                try:
+                    h = meijerint_indefinite(g, x)
+                except NotImplementedError:
+                    _debug('NotImplementedError from meijerint_definite')
+                if h is not None:
+                    parts.append(coeff * h)
+                    continue
+
+            if h is None and manual is not False:
+                try:
+                    result = manualintegrate(g, x)
+                    if result is not None and not isinstance(result, Integral):
+                        if result.has(Integral) and not manual:
+                            # Try to have other algorithms do the integrals
+                            # manualintegrate can't handle,
+                            # unless we were asked to use manual only.
+                            # Keep the rest of eval_kwargs in case another
+                            # method was set to False already
+                            new_eval_kwargs = eval_kwargs
+                            new_eval_kwargs["manual"] = False
+                            new_eval_kwargs["final"] = False
+                            result = result.func(*[
+                                arg.doit(**new_eval_kwargs) if
+                                arg.has(Integral) else arg
+                                for arg in result.args
+                            ]).expand(multinomial=False,
+                                      log=False,
+                                      power_exp=False,
+                                      power_base=False)
+                        if not result.has(Integral):
+                            parts.append(coeff * result)
+                            continue
+                except (ValueError, PolynomialError):
+                    # can't handle some SymPy expressions
+                    pass
+
+            # if we failed maybe it was because we had
+            # a product that could have been expanded,
+            # so let's try an expansion of the whole
+            # thing before giving up; we don't try this
+            # at the outset because there are things
+            # that cannot be solved unless they are
+            # NOT expanded e.g., x**x*(1+log(x)). There
+            # should probably be a checker somewhere in this
+            # routine to look for such cases and try to do
+            # collection on the expressions if they are already
+            # in an expanded form
+            if not h and len(args) == 1:
+                f = sincos_to_sum(f).expand(mul=True, deep=False)
+                if f.is_Add:
+                    # Note: risch will be identical on the expanded
+                    # expression, but maybe it will be able to pick out parts,
+                    # like x*(exp(x) + erf(x)).
+                    return self._eval_integral(f, x, **eval_kwargs)
+
+            if h is not None:
+                parts.append(coeff * h)
+            else:
+                return None
+
+        return Add(*parts)
+
+    def _eval_lseries(self, x, logx=None, cdir=0):
+        expr = self.as_dummy()
+        symb = x
+        for l in expr.limits:
+            if x in l[1:]:
+                symb = l[0]
+                break
+        for term in expr.function.lseries(symb, logx):
+            yield integrate(term, *expr.limits)
+
+    def _eval_nseries(self, x, n, logx=None, cdir=0):
+        symb = x
+        for l in self.limits:
+            if x in l[1:]:
+                symb = l[0]
+                break
+        terms, order = self.function.nseries(
+            x=symb, n=n, logx=logx).as_coeff_add(Order)
+        order = [o.subs(symb, x) for o in order]
+        return integrate(terms, *self.limits) + Add(*order)*x
+
+    def _eval_as_leading_term(self, x, logx, cdir):
+        series_gen = self.args[0].lseries(x)
+        for leading_term in series_gen:
+            if leading_term != 0:
+                break
+        return integrate(leading_term, *self.args[1:])
+
+    def _eval_simplify(self, **kwargs):
+        expr = factor_terms(self)
+        if isinstance(expr, Integral):
+            from sympy.simplify.simplify import simplify
+            return expr.func(*[simplify(i, **kwargs) for i in expr.args])
+        return expr.simplify(**kwargs)
+
+    def as_sum(self, n=None, method="midpoint", evaluate=True):
+        """
+        Approximates a definite integral by a sum.
+
+        Parameters
+        ==========
+
+        n :
+            The number of subintervals to use, optional.
+        method :
+            One of: 'left', 'right', 'midpoint', 'trapezoid'.
+        evaluate : bool
+            If False, returns an unevaluated Sum expression. The default
+            is True, evaluate the sum.
+
+        Notes
+        =====
+
+        These methods of approximate integration are described in [1].
+
+        Examples
+        ========
+
+        >>> from sympy import Integral, sin, sqrt
+        >>> from sympy.abc import x, n
+        >>> e = Integral(sin(x), (x, 3, 7))
+        >>> e
+        Integral(sin(x), (x, 3, 7))
+
+        For demonstration purposes, this interval will only be split into 2
+        regions, bounded by [3, 5] and [5, 7].
+
+        The left-hand rule uses function evaluations at the left of each
+        interval:
+
+        >>> e.as_sum(2, 'left')
+        2*sin(5) + 2*sin(3)
+
+        The midpoint rule uses evaluations at the center of each interval:
+
+        >>> e.as_sum(2, 'midpoint')
+        2*sin(4) + 2*sin(6)
+
+        The right-hand rule uses function evaluations at the right of each
+        interval:
+
+        >>> e.as_sum(2, 'right')
+        2*sin(5) + 2*sin(7)
+
+        The trapezoid rule uses function evaluations on both sides of the
+        intervals. This is equivalent to taking the average of the left and
+        right hand rule results:
+
+        >>> s = e.as_sum(2, 'trapezoid')
+        >>> s
+        2*sin(5) + sin(3) + sin(7)
+        >>> (e.as_sum(2, 'left') + e.as_sum(2, 'right'))/2 == s
+        True
+
+        Here, the discontinuity at x = 0 can be avoided by using the
+        midpoint or right-hand method:
+
+        >>> e = Integral(1/sqrt(x), (x, 0, 1))
+        >>> e.as_sum(5).n(4)
+        1.730
+        >>> e.as_sum(10).n(4)
+        1.809
+        >>> e.doit().n(4)  # the actual value is 2
+        2.000
+
+        The left- or trapezoid method will encounter the discontinuity and
+        return infinity:
+
+        >>> e.as_sum(5, 'left')
+        zoo
+
+        The number of intervals can be symbolic. If omitted, a dummy symbol
+        will be used for it.
+
+        >>> e = Integral(x**2, (x, 0, 2))
+        >>> e.as_sum(n, 'right').expand()
+        8/3 + 4/n + 4/(3*n**2)
+
+        This shows that the midpoint rule is more accurate, as its error
+        term decays as the square of n:
+
+        >>> e.as_sum(method='midpoint').expand()
+        8/3 - 2/(3*_n**2)
+
+        A symbolic sum is returned with evaluate=False:
+
+        >>> e.as_sum(n, 'midpoint', evaluate=False)
+        2*Sum((2*_k/n - 1/n)**2, (_k, 1, n))/n
+
+        See Also
+        ========
+
+        Integral.doit : Perform the integration using any hints
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Riemann_sum#Riemann_summation_methods
+        """
+
+        from sympy.concrete.summations import Sum
+        limits = self.limits
+        if len(limits) > 1:
+            raise NotImplementedError(
+                "Multidimensional midpoint rule not implemented yet")
+        else:
+            limit = limits[0]
+            if (len(limit) != 3 or limit[1].is_finite is False or
+                limit[2].is_finite is False):
+                raise ValueError("Expecting a definite integral over "
+                                  "a finite interval.")
+        if n is None:
+            n = Dummy('n', integer=True, positive=True)
+        else:
+            n = sympify(n)
+        if (n.is_positive is False or n.is_integer is False or
+            n.is_finite is False):
+            raise ValueError("n must be a positive integer, got %s" % n)
+        x, a, b = limit
+        dx = (b - a)/n
+        k = Dummy('k', integer=True, positive=True)
+        f = self.function
+
+        if method == "left":
+            result = dx*Sum(f.subs(x, a + (k-1)*dx), (k, 1, n))
+        elif method == "right":
+            result = dx*Sum(f.subs(x, a + k*dx), (k, 1, n))
+        elif method == "midpoint":
+            result = dx*Sum(f.subs(x, a + k*dx - dx/2), (k, 1, n))
+        elif method == "trapezoid":
+            result = dx*((f.subs(x, a) + f.subs(x, b))/2 +
+                Sum(f.subs(x, a + k*dx), (k, 1, n - 1)))
+        else:
+            raise ValueError("Unknown method %s" % method)
+        return result.doit() if evaluate else result
+
+    def principal_value(self, **kwargs):
+        """
+        Compute the Cauchy Principal Value of the definite integral of a real function in the given interval
+        on the real axis.
+
+        Explanation
+        ===========
+
+        In mathematics, the Cauchy principal value, is a method for assigning values to certain improper
+        integrals which would otherwise be undefined.
+
+        Examples
+        ========
+
+        >>> from sympy import Integral, oo
+        >>> from sympy.abc import x
+        >>> Integral(x+1, (x, -oo, oo)).principal_value()
+        oo
+        >>> f = 1 / (x**3)
+        >>> Integral(f, (x, -oo, oo)).principal_value()
+        0
+        >>> Integral(f, (x, -10, 10)).principal_value()
+        0
+        >>> Integral(f, (x, -10, oo)).principal_value() + Integral(f, (x, -oo, 10)).principal_value()
+        0
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Cauchy_principal_value
+        .. [2] https://mathworld.wolfram.com/CauchyPrincipalValue.html
+        """
+        if len(self.limits) != 1 or len(list(self.limits[0])) != 3:
+            raise ValueError("You need to insert a variable, lower_limit, and upper_limit correctly to calculate "
+                             "cauchy's principal value")
+        x, a, b = self.limits[0]
+        if not (a.is_comparable and b.is_comparable and a <= b):
+            raise ValueError("The lower_limit must be smaller than or equal to the upper_limit to calculate "
+                             "cauchy's principal value. Also, a and b need to be comparable.")
+        if a == b:
+            return S.Zero
+
+        from sympy.calculus.singularities import singularities
+
+        r = Dummy('r')
+        f = self.function
+        singularities_list = [s for s in singularities(f, x) if s.is_comparable and a <= s <= b]
+        for i in singularities_list:
+            if i in (a, b):
+                raise ValueError(
+                    'The principal value is not defined in the given interval due to singularity at %d.' % (i))
+        F = integrate(f, x, **kwargs)
+        if F.has(Integral):
+            return self
+        if a is -oo and b is oo:
+            I = limit(F - F.subs(x, -x), x, oo)
+        else:
+            I = limit(F, x, b, '-') - limit(F, x, a, '+')
+        for s in singularities_list:
+            I += limit(((F.subs(x, s - r)) - F.subs(x, s + r)), r, 0, '+')
+        return I
+
+
+
+def integrate(*args, meijerg=None, conds='piecewise', risch=None, heurisch=None, manual=None, **kwargs):
+    """integrate(f, var, ...)
+
+    .. deprecated:: 1.6
+
+       Using ``integrate()`` with :class:`~.Poly` is deprecated. Use
+       :meth:`.Poly.integrate` instead. See :ref:`deprecated-integrate-poly`.
+
+    Explanation
+    ===========
+
+    Compute definite or indefinite integral of one or more variables
+    using Risch-Norman algorithm and table lookup. This procedure is
+    able to handle elementary algebraic and transcendental functions
+    and also a huge class of special functions, including Airy,
+    Bessel, Whittaker and Lambert.
+
+    var can be:
+
+    - a symbol                   -- indefinite integration
+    - a tuple (symbol, a)        -- indefinite integration with result
+                                    given with ``a`` replacing ``symbol``
+    - a tuple (symbol, a, b)     -- definite integration
+
+    Several variables can be specified, in which case the result is
+    multiple integration. (If var is omitted and the integrand is
+    univariate, the indefinite integral in that variable will be performed.)
+
+    Indefinite integrals are returned without terms that are independent
+    of the integration variables. (see examples)
+
+    Definite improper integrals often entail delicate convergence
+    conditions. Pass conds='piecewise', 'separate' or 'none' to have
+    these returned, respectively, as a Piecewise function, as a separate
+    result (i.e. result will be a tuple), or not at all (default is
+    'piecewise').
+
+    **Strategy**
+
+    SymPy uses various approaches to definite integration. One method is to
+    find an antiderivative for the integrand, and then use the fundamental
+    theorem of calculus. Various functions are implemented to integrate
+    polynomial, rational and trigonometric functions, and integrands
+    containing DiracDelta terms.
+
+    SymPy also implements the part of the Risch algorithm, which is a decision
+    procedure for integrating elementary functions, i.e., the algorithm can
+    either find an elementary antiderivative, or prove that one does not
+    exist.  There is also a (very successful, albeit somewhat slow) general
+    implementation of the heuristic Risch algorithm.  This algorithm will
+    eventually be phased out as more of the full Risch algorithm is
+    implemented. See the docstring of Integral._eval_integral() for more
+    details on computing the antiderivative using algebraic methods.
+
+    The option risch=True can be used to use only the (full) Risch algorithm.
+    This is useful if you want to know if an elementary function has an
+    elementary antiderivative.  If the indefinite Integral returned by this
+    function is an instance of NonElementaryIntegral, that means that the
+    Risch algorithm has proven that integral to be non-elementary.  Note that
+    by default, additional methods (such as the Meijer G method outlined
+    below) are tried on these integrals, as they may be expressible in terms
+    of special functions, so if you only care about elementary answers, use
+    risch=True.  Also note that an unevaluated Integral returned by this
+    function is not necessarily a NonElementaryIntegral, even with risch=True,
+    as it may just be an indication that the particular part of the Risch
+    algorithm needed to integrate that function is not yet implemented.
+
+    Another family of strategies comes from re-writing the integrand in
+    terms of so-called Meijer G-functions. Indefinite integrals of a
+    single G-function can always be computed, and the definite integral
+    of a product of two G-functions can be computed from zero to
+    infinity. Various strategies are implemented to rewrite integrands
+    as G-functions, and use this information to compute integrals (see
+    the ``meijerint`` module).
+
+    The option manual=True can be used to use only an algorithm that tries
+    to mimic integration by hand. This algorithm does not handle as many
+    integrands as the other algorithms implemented but may return results in
+    a more familiar form. The ``manualintegrate`` module has functions that
+    return the steps used (see the module docstring for more information).
+
+    In general, the algebraic methods work best for computing
+    antiderivatives of (possibly complicated) combinations of elementary
+    functions. The G-function methods work best for computing definite
+    integrals from zero to infinity of moderately complicated
+    combinations of special functions, or indefinite integrals of very
+    simple combinations of special functions.
+
+    The strategy employed by the integration code is as follows:
+
+    - If computing a definite integral, and both limits are real,
+      and at least one limit is +- oo, try the G-function method of
+      definite integration first.
+
+    - Try to find an antiderivative, using all available methods, ordered
+      by performance (that is try fastest method first, slowest last; in
+      particular polynomial integration is tried first, Meijer
+      G-functions second to last, and heuristic Risch last).
+
+    - If still not successful, try G-functions irrespective of the
+      limits.
+
+    The option meijerg=True, False, None can be used to, respectively:
+    always use G-function methods and no others, never use G-function
+    methods, or use all available methods (in order as described above).
+    It defaults to None.
+
+    Examples
+    ========
+
+    >>> from sympy import integrate, log, exp, oo
+    >>> from sympy.abc import a, x, y
+
+    >>> integrate(x*y, x)
+    x**2*y/2
+
+    >>> integrate(log(x), x)
+    x*log(x) - x
+
+    >>> integrate(log(x), (x, 1, a))
+    a*log(a) - a + 1
+
+    >>> integrate(x)
+    x**2/2
+
+    Terms that are independent of x are dropped by indefinite integration:
+
+    >>> from sympy import sqrt
+    >>> integrate(sqrt(1 + x), (x, 0, x))
+    2*(x + 1)**(3/2)/3 - 2/3
+    >>> integrate(sqrt(1 + x), x)
+    2*(x + 1)**(3/2)/3
+
+    >>> integrate(x*y)
+    Traceback (most recent call last):
+    ...
+    ValueError: specify integration variables to integrate x*y
+
+    Note that ``integrate(x)`` syntax is meant only for convenience
+    in interactive sessions and should be avoided in library code.
+
+    >>> integrate(x**a*exp(-x), (x, 0, oo)) # same as conds='piecewise'
+    Piecewise((gamma(a + 1), re(a) > -1),
+        (Integral(x**a*exp(-x), (x, 0, oo)), True))
+
+    >>> integrate(x**a*exp(-x), (x, 0, oo), conds='none')
+    gamma(a + 1)
+
+    >>> integrate(x**a*exp(-x), (x, 0, oo), conds='separate')
+    (gamma(a + 1), re(a) > -1)
+
+    See Also
+    ========
+
+    Integral, Integral.doit
+
+    """
+    doit_flags = {
+        'deep': False,
+        'meijerg': meijerg,
+        'conds': conds,
+        'risch': risch,
+        'heurisch': heurisch,
+        'manual': manual
+        }
+
+    integral = Integral(*args, **kwargs)
+
+    if isinstance(integral, Integral):
+        return integral.doit(**doit_flags)
+    else:
+        new_args = [a.doit(**doit_flags) if isinstance(a, Integral) else a
+            for a in integral.args]
+        return integral.func(*new_args)
+
+def line_integrate(field, curve, vars):
+    """line_integrate(field, Curve, variables)
+
+    Compute the line integral.
+
+    Examples
+    ========
+
+    >>> from sympy import Curve, line_integrate, E, ln
+    >>> from sympy.abc import x, y, t
+    >>> C = Curve([E**t + 1, E**t - 1], (t, 0, ln(2)))
+    >>> line_integrate(x + y, C, [x, y])
+    3*sqrt(2)
+
+    See Also
+    ========
+
+    sympy.integrals.integrals.integrate, Integral
+    """
+    from sympy.geometry import Curve
+    F = sympify(field)
+    if not F:
+        raise ValueError(
+            "Expecting function specifying field as first argument.")
+    if not isinstance(curve, Curve):
+        raise ValueError("Expecting Curve entity as second argument.")
+    if not is_sequence(vars):
+        raise ValueError("Expecting ordered iterable for variables.")
+    if len(curve.functions) != len(vars):
+        raise ValueError("Field variable size does not match curve dimension.")
+
+    if curve.parameter in vars:
+        raise ValueError("Curve parameter clashes with field parameters.")
+
+    # Calculate derivatives for line parameter functions
+    # F(r) -> F(r(t)) and finally F(r(t)*r'(t))
+    Ft = F
+    dldt = 0
+    for i, var in enumerate(vars):
+        _f = curve.functions[i]
+        _dn = diff(_f, curve.parameter)
+        # ...arc length
+        dldt = dldt + (_dn * _dn)
+        Ft = Ft.subs(var, _f)
+    Ft = Ft * sqrt(dldt)
+
+    integral = Integral(Ft, curve.limits).doit(deep=False)
+    return integral
+
+
+### Property function dispatching ###
+
+@shape.register(Integral)
+def _(expr):
+    return shape(expr.function)
+
+# Delayed imports
+from .deltafunctions import deltaintegrate
+from .meijerint import meijerint_definite, meijerint_indefinite, _debug
+from .trigonometry import trigintegrate
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/intpoly.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/intpoly.py
new file mode 100644
index 0000000000000000000000000000000000000000..38fd071183fb2192f4c1443d04c8f0ecfb6cc4ea
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/intpoly.py
@@ -0,0 +1,1302 @@
+"""
+Module to implement integration of uni/bivariate polynomials over
+2D Polytopes and uni/bi/trivariate polynomials over 3D Polytopes.
+
+Uses evaluation techniques as described in Chin et al. (2015) [1].
+
+
+References
+===========
+
+.. [1] Chin, Eric B., Jean B. Lasserre, and N. Sukumar. "Numerical integration
+of homogeneous functions on convex and nonconvex polygons and polyhedra."
+Computational Mechanics 56.6 (2015): 967-981
+
+PDF link : http://dilbert.engr.ucdavis.edu/~suku/quadrature/cls-integration.pdf
+"""
+
+from functools import cmp_to_key
+
+from sympy.abc import x, y, z
+from sympy.core import S, diff, Expr, Symbol
+from sympy.core.sympify import _sympify
+from sympy.geometry import Segment2D, Polygon, Point, Point2D
+from sympy.polys.polytools import LC, gcd_list, degree_list, Poly
+from sympy.simplify.simplify import nsimplify
+
+
+def polytope_integrate(poly, expr=None, *, clockwise=False, max_degree=None):
+    """Integrates polynomials over 2/3-Polytopes.
+
+    Explanation
+    ===========
+
+    This function accepts the polytope in ``poly`` and the function in ``expr``
+    (uni/bi/trivariate polynomials are implemented) and returns
+    the exact integral of ``expr`` over ``poly``.
+
+    Parameters
+    ==========
+
+    poly : The input Polygon.
+
+    expr : The input polynomial.
+
+    clockwise : Binary value to sort input points of 2-Polytope clockwise.(Optional)
+
+    max_degree : The maximum degree of any monomial of the input polynomial.(Optional)
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy import Point, Polygon
+    >>> from sympy.integrals.intpoly import polytope_integrate
+    >>> polygon = Polygon(Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0))
+    >>> polys = [1, x, y, x*y, x**2*y, x*y**2]
+    >>> expr = x*y
+    >>> polytope_integrate(polygon, expr)
+    1/4
+    >>> polytope_integrate(polygon, polys, max_degree=3)
+    {1: 1, x: 1/2, y: 1/2, x*y: 1/4, x*y**2: 1/6, x**2*y: 1/6}
+    """
+    if clockwise:
+        if isinstance(poly, Polygon):
+            poly = Polygon(*point_sort(poly.vertices), evaluate=False)
+        else:
+            raise TypeError("clockwise=True works for only 2-Polytope"
+                            "V-representation input")
+
+    if isinstance(poly, Polygon):
+        # For Vertex Representation(2D case)
+        hp_params = hyperplane_parameters(poly)
+        facets = poly.sides
+    elif len(poly[0]) == 2:
+        # For Hyperplane Representation(2D case)
+        plen = len(poly)
+        if len(poly[0][0]) == 2:
+            intersections = [intersection(poly[(i - 1) % plen], poly[i],
+                                          "plane2D")
+                             for i in range(0, plen)]
+            hp_params = poly
+            lints = len(intersections)
+            facets = [Segment2D(intersections[i],
+                                intersections[(i + 1) % lints])
+                      for i in range(lints)]
+        else:
+            raise NotImplementedError("Integration for H-representation 3D"
+                                      "case not implemented yet.")
+    else:
+        # For Vertex Representation(3D case)
+        vertices = poly[0]
+        facets = poly[1:]
+        hp_params = hyperplane_parameters(facets, vertices)
+
+        if max_degree is None:
+            if expr is None:
+                raise TypeError('Input expression must be a valid SymPy expression')
+            return main_integrate3d(expr, facets, vertices, hp_params)
+
+    if max_degree is not None:
+        result = {}
+        if expr is not None:
+            f_expr = []
+            for e in expr:
+                _ = decompose(e)
+                if len(_) == 1 and not _.popitem()[0]:
+                    f_expr.append(e)
+                elif Poly(e).total_degree() <= max_degree:
+                    f_expr.append(e)
+            expr = f_expr
+
+        if not isinstance(expr, list) and expr is not None:
+            raise TypeError('Input polynomials must be list of expressions')
+
+        if len(hp_params[0][0]) == 3:
+            result_dict = main_integrate3d(0, facets, vertices, hp_params,
+                                           max_degree)
+        else:
+            result_dict = main_integrate(0, facets, hp_params, max_degree)
+
+        if expr is None:
+            return result_dict
+
+        for poly in expr:
+            poly = _sympify(poly)
+            if poly not in result:
+                if poly.is_zero:
+                    result[S.Zero] = S.Zero
+                    continue
+                integral_value = S.Zero
+                monoms = decompose(poly, separate=True)
+                for monom in monoms:
+                    monom = nsimplify(monom)
+                    coeff, m = strip(monom)
+                    integral_value += result_dict[m] * coeff
+                result[poly] = integral_value
+        return result
+
+    if expr is None:
+        raise TypeError('Input expression must be a valid SymPy expression')
+
+    return main_integrate(expr, facets, hp_params)
+
+
+def strip(monom):
+    if monom.is_zero:
+        return S.Zero, S.Zero
+    elif monom.is_number:
+        return monom, S.One
+    else:
+        coeff = LC(monom)
+        return coeff, monom / coeff
+
+def _polynomial_integrate(polynomials, facets, hp_params):
+    dims = (x, y)
+    dim_length = len(dims)
+    integral_value = S.Zero
+    for deg in polynomials:
+        poly_contribute = S.Zero
+        facet_count = 0
+        for hp in hp_params:
+            value_over_boundary = integration_reduction(facets,
+                                                        facet_count,
+                                                        hp[0], hp[1],
+                                                        polynomials[deg],
+                                                        dims, deg)
+            poly_contribute += value_over_boundary * (hp[1] / norm(hp[0]))
+            facet_count += 1
+        poly_contribute /= (dim_length + deg)
+        integral_value += poly_contribute
+
+    return integral_value
+
+
+def main_integrate3d(expr, facets, vertices, hp_params, max_degree=None):
+    """Function to translate the problem of integrating uni/bi/tri-variate
+    polynomials over a 3-Polytope to integrating over its faces.
+    This is done using Generalized Stokes' Theorem and Euler's Theorem.
+
+    Parameters
+    ==========
+
+    expr :
+        The input polynomial.
+    facets :
+        Faces of the 3-Polytope(expressed as indices of `vertices`).
+    vertices :
+        Vertices that constitute the Polytope.
+    hp_params :
+        Hyperplane Parameters of the facets.
+    max_degree : optional
+        Max degree of constituent monomial in given list of polynomial.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import main_integrate3d, \
+    hyperplane_parameters
+    >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
+                (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
+                [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
+                [3, 1, 0, 2], [0, 4, 6, 2]]
+    >>> vertices = cube[0]
+    >>> faces = cube[1:]
+    >>> hp_params = hyperplane_parameters(faces, vertices)
+    >>> main_integrate3d(1, faces, vertices, hp_params)
+    -125
+    """
+    result = {}
+    dims = (x, y, z)
+    dim_length = len(dims)
+    if max_degree:
+        grad_terms = gradient_terms(max_degree, 3)
+        flat_list = [term for z_terms in grad_terms
+                     for x_term in z_terms
+                     for term in x_term]
+
+        for term in flat_list:
+            result[term[0]] = 0
+
+        for facet_count, hp in enumerate(hp_params):
+            a, b = hp[0], hp[1]
+            x0 = vertices[facets[facet_count][0]]
+
+            for i, monom in enumerate(flat_list):
+                #  Every monomial is a tuple :
+                #  (term, x_degree, y_degree, z_degree, value over boundary)
+                expr, x_d, y_d, z_d, z_index, y_index, x_index, _ = monom
+                degree = x_d + y_d + z_d
+                if b.is_zero:
+                    value_over_face = S.Zero
+                else:
+                    value_over_face = \
+                        integration_reduction_dynamic(facets, facet_count, a,
+                                                      b, expr, degree, dims,
+                                                      x_index, y_index,
+                                                      z_index, x0, grad_terms,
+                                                      i, vertices, hp)
+                monom[7] = value_over_face
+                result[expr] += value_over_face * \
+                    (b / norm(a)) / (dim_length + x_d + y_d + z_d)
+        return result
+    else:
+        integral_value = S.Zero
+        polynomials = decompose(expr)
+        for deg in polynomials:
+            poly_contribute = S.Zero
+            facet_count = 0
+            for i, facet in enumerate(facets):
+                hp = hp_params[i]
+                if hp[1].is_zero:
+                    continue
+                pi = polygon_integrate(facet, hp, i, facets, vertices, expr, deg)
+                poly_contribute += pi *\
+                    (hp[1] / norm(tuple(hp[0])))
+                facet_count += 1
+            poly_contribute /= (dim_length + deg)
+            integral_value += poly_contribute
+    return integral_value
+
+
+def main_integrate(expr, facets, hp_params, max_degree=None):
+    """Function to translate the problem of integrating univariate/bivariate
+    polynomials over a 2-Polytope to integrating over its boundary facets.
+    This is done using Generalized Stokes's Theorem and Euler's Theorem.
+
+    Parameters
+    ==========
+
+    expr :
+        The input polynomial.
+    facets :
+        Facets(Line Segments) of the 2-Polytope.
+    hp_params :
+        Hyperplane Parameters of the facets.
+    max_degree : optional
+        The maximum degree of any monomial of the input polynomial.
+
+    >>> from sympy.abc import x, y
+    >>> from sympy.integrals.intpoly import main_integrate,\
+    hyperplane_parameters
+    >>> from sympy import Point, Polygon
+    >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    >>> facets = triangle.sides
+    >>> hp_params = hyperplane_parameters(triangle)
+    >>> main_integrate(x**2 + y**2, facets, hp_params)
+    325/6
+    """
+    dims = (x, y)
+    dim_length = len(dims)
+    result = {}
+
+    if max_degree:
+        grad_terms = [[0, 0, 0, 0]] + gradient_terms(max_degree)
+
+        for facet_count, hp in enumerate(hp_params):
+            a, b = hp[0], hp[1]
+            x0 = facets[facet_count].points[0]
+
+            for i, monom in enumerate(grad_terms):
+                #  Every monomial is a tuple :
+                #  (term, x_degree, y_degree, value over boundary)
+                m, x_d, y_d, _ = monom
+                value = result.get(m, None)
+                degree = S.Zero
+                if b.is_zero:
+                    value_over_boundary = S.Zero
+                else:
+                    degree = x_d + y_d
+                    value_over_boundary = \
+                        integration_reduction_dynamic(facets, facet_count, a,
+                                                      b, m, degree, dims, x_d,
+                                                      y_d, max_degree, x0,
+                                                      grad_terms, i)
+                monom[3] = value_over_boundary
+                if value is not None:
+                    result[m] += value_over_boundary * \
+                                        (b / norm(a)) / (dim_length + degree)
+                else:
+                    result[m] = value_over_boundary * \
+                                (b / norm(a)) / (dim_length + degree)
+        return result
+    else:
+        if not isinstance(expr, list):
+            polynomials = decompose(expr)
+            return _polynomial_integrate(polynomials, facets, hp_params)
+        else:
+            return {e: _polynomial_integrate(decompose(e), facets, hp_params) for e in expr}
+
+
+def polygon_integrate(facet, hp_param, index, facets, vertices, expr, degree):
+    """Helper function to integrate the input uni/bi/trivariate polynomial
+    over a certain face of the 3-Polytope.
+
+    Parameters
+    ==========
+
+    facet :
+        Particular face of the 3-Polytope over which ``expr`` is integrated.
+    index :
+        The index of ``facet`` in ``facets``.
+    facets :
+        Faces of the 3-Polytope(expressed as indices of `vertices`).
+    vertices :
+        Vertices that constitute the facet.
+    expr :
+        The input polynomial.
+    degree :
+        Degree of ``expr``.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import polygon_integrate
+    >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
+                 (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
+                 [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
+                 [3, 1, 0, 2], [0, 4, 6, 2]]
+    >>> facet = cube[1]
+    >>> facets = cube[1:]
+    >>> vertices = cube[0]
+    >>> polygon_integrate(facet, [(0, 1, 0), 5], 0, facets, vertices, 1, 0)
+    -25
+    """
+    expr = S(expr)
+    if expr.is_zero:
+        return S.Zero
+    result = S.Zero
+    x0 = vertices[facet[0]]
+    facet_len = len(facet)
+    for i, fac in enumerate(facet):
+        side = (vertices[fac], vertices[facet[(i + 1) % facet_len]])
+        result += distance_to_side(x0, side, hp_param[0]) *\
+            lineseg_integrate(facet, i, side, expr, degree)
+    if not expr.is_number:
+        expr = diff(expr, x) * x0[0] + diff(expr, y) * x0[1] +\
+            diff(expr, z) * x0[2]
+        result += polygon_integrate(facet, hp_param, index, facets, vertices,
+                                    expr, degree - 1)
+    result /= (degree + 2)
+    return result
+
+
+def distance_to_side(point, line_seg, A):
+    """Helper function to compute the signed distance between given 3D point
+    and a line segment.
+
+    Parameters
+    ==========
+
+    point : 3D Point
+    line_seg : Line Segment
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import distance_to_side
+    >>> point = (0, 0, 0)
+    >>> distance_to_side(point, [(0, 0, 1), (0, 1, 0)], (1, 0, 0))
+    -sqrt(2)/2
+    """
+    x1, x2 = line_seg
+    rev_normal = [-1 * S(i)/norm(A) for i in A]
+    vector = [x2[i] - x1[i] for i in range(0, 3)]
+    vector = [vector[i]/norm(vector) for i in range(0, 3)]
+
+    n_side = cross_product((0, 0, 0), rev_normal, vector)
+    vectorx0 = [line_seg[0][i] - point[i] for i in range(0, 3)]
+    dot_product = sum(vectorx0[i] * n_side[i] for i in range(0, 3))
+
+    return dot_product
+
+
+def lineseg_integrate(polygon, index, line_seg, expr, degree):
+    """Helper function to compute the line integral of ``expr`` over ``line_seg``.
+
+    Parameters
+    ===========
+
+    polygon :
+        Face of a 3-Polytope.
+    index :
+        Index of line_seg in polygon.
+    line_seg :
+        Line Segment.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import lineseg_integrate
+    >>> polygon = [(0, 5, 0), (5, 5, 0), (5, 5, 5), (0, 5, 5)]
+    >>> line_seg = [(0, 5, 0), (5, 5, 0)]
+    >>> lineseg_integrate(polygon, 0, line_seg, 1, 0)
+    5
+    """
+    expr = _sympify(expr)
+    if expr.is_zero:
+        return S.Zero
+    result = S.Zero
+    x0 = line_seg[0]
+    distance = norm(tuple([line_seg[1][i] - line_seg[0][i] for i in
+                           range(3)]))
+    if isinstance(expr, Expr):
+        expr_dict = {x: line_seg[1][0],
+                     y: line_seg[1][1],
+                     z: line_seg[1][2]}
+        result += distance * expr.subs(expr_dict)
+    else:
+        result += distance * expr
+
+    expr = diff(expr, x) * x0[0] + diff(expr, y) * x0[1] +\
+        diff(expr, z) * x0[2]
+
+    result += lineseg_integrate(polygon, index, line_seg, expr, degree - 1)
+    result /= (degree + 1)
+    return result
+
+
+def integration_reduction(facets, index, a, b, expr, dims, degree):
+    """Helper method for main_integrate. Returns the value of the input
+    expression evaluated over the polytope facet referenced by a given index.
+
+    Parameters
+    ===========
+
+    facets :
+        List of facets of the polytope.
+    index :
+        Index referencing the facet to integrate the expression over.
+    a :
+        Hyperplane parameter denoting direction.
+    b :
+        Hyperplane parameter denoting distance.
+    expr :
+        The expression to integrate over the facet.
+    dims :
+        List of symbols denoting axes.
+    degree :
+        Degree of the homogeneous polynomial.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy.integrals.intpoly import integration_reduction,\
+    hyperplane_parameters
+    >>> from sympy import Point, Polygon
+    >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    >>> facets = triangle.sides
+    >>> a, b = hyperplane_parameters(triangle)[0]
+    >>> integration_reduction(facets, 0, a, b, 1, (x, y), 0)
+    5
+    """
+    expr = _sympify(expr)
+    if expr.is_zero:
+        return expr
+
+    value = S.Zero
+    x0 = facets[index].points[0]
+    m = len(facets)
+    gens = (x, y)
+
+    inner_product = diff(expr, gens[0]) * x0[0] + diff(expr, gens[1]) * x0[1]
+
+    if inner_product != 0:
+        value += integration_reduction(facets, index, a, b,
+                                       inner_product, dims, degree - 1)
+
+    value += left_integral2D(m, index, facets, x0, expr, gens)
+
+    return value/(len(dims) + degree - 1)
+
+
+def left_integral2D(m, index, facets, x0, expr, gens):
+    """Computes the left integral of Eq 10 in Chin et al.
+    For the 2D case, the integral is just an evaluation of the polynomial
+    at the intersection of two facets which is multiplied by the distance
+    between the first point of facet and that intersection.
+
+    Parameters
+    ==========
+
+    m :
+        No. of hyperplanes.
+    index :
+        Index of facet to find intersections with.
+    facets :
+        List of facets(Line Segments in 2D case).
+    x0 :
+        First point on facet referenced by index.
+    expr :
+        Input polynomial
+    gens :
+        Generators which generate the polynomial
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy.integrals.intpoly import left_integral2D
+    >>> from sympy import Point, Polygon
+    >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    >>> facets = triangle.sides
+    >>> left_integral2D(3, 0, facets, facets[0].points[0], 1, (x, y))
+    5
+    """
+    value = S.Zero
+    for j in range(m):
+        intersect = ()
+        if j in ((index - 1) % m, (index + 1) % m):
+            intersect = intersection(facets[index], facets[j], "segment2D")
+        if intersect:
+            distance_origin = norm(tuple(map(lambda x, y: x - y,
+                                             intersect, x0)))
+            if is_vertex(intersect):
+                if isinstance(expr, Expr):
+                    if len(gens) == 3:
+                        expr_dict = {gens[0]: intersect[0],
+                                     gens[1]: intersect[1],
+                                     gens[2]: intersect[2]}
+                    else:
+                        expr_dict = {gens[0]: intersect[0],
+                                     gens[1]: intersect[1]}
+                    value += distance_origin * expr.subs(expr_dict)
+                else:
+                    value += distance_origin * expr
+    return value
+
+
+def integration_reduction_dynamic(facets, index, a, b, expr, degree, dims,
+                                  x_index, y_index, max_index, x0,
+                                  monomial_values, monom_index, vertices=None,
+                                  hp_param=None):
+    """The same integration_reduction function which uses a dynamic
+    programming approach to compute terms by using the values of the integral
+    of previously computed terms.
+
+    Parameters
+    ==========
+
+    facets :
+        Facets of the Polytope.
+    index :
+        Index of facet to find intersections with.(Used in left_integral()).
+    a, b :
+        Hyperplane parameters.
+    expr :
+        Input monomial.
+    degree :
+        Total degree of ``expr``.
+    dims :
+        Tuple denoting axes variables.
+    x_index :
+        Exponent of 'x' in ``expr``.
+    y_index :
+        Exponent of 'y' in ``expr``.
+    max_index :
+        Maximum exponent of any monomial in ``monomial_values``.
+    x0 :
+        First point on ``facets[index]``.
+    monomial_values :
+        List of monomial values constituting the polynomial.
+    monom_index :
+        Index of monomial whose integration is being found.
+    vertices : optional
+        Coordinates of vertices constituting the 3-Polytope.
+    hp_param : optional
+        Hyperplane Parameter of the face of the facets[index].
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy.integrals.intpoly import (integration_reduction_dynamic, \
+            hyperplane_parameters)
+    >>> from sympy import Point, Polygon
+    >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    >>> facets = triangle.sides
+    >>> a, b = hyperplane_parameters(triangle)[0]
+    >>> x0 = facets[0].points[0]
+    >>> monomial_values = [[0, 0, 0, 0], [1, 0, 0, 5],\
+                           [y, 0, 1, 15], [x, 1, 0, None]]
+    >>> integration_reduction_dynamic(facets, 0, a, b, x, 1, (x, y), 1, 0, 1,\
+                                      x0, monomial_values, 3)
+    25/2
+    """
+    value = S.Zero
+    m = len(facets)
+
+    if expr == S.Zero:
+        return expr
+
+    if len(dims) == 2:
+        if not expr.is_number:
+            _, x_degree, y_degree, _ = monomial_values[monom_index]
+            x_index = monom_index - max_index + \
+                x_index - 2 if x_degree > 0 else 0
+            y_index = monom_index - 1 if y_degree > 0 else 0
+            x_value, y_value =\
+                monomial_values[x_index][3], monomial_values[y_index][3]
+
+            value += x_degree * x_value * x0[0] + y_degree * y_value * x0[1]
+
+        value += left_integral2D(m, index, facets, x0, expr, dims)
+    else:
+        # For 3D use case the max_index contains the z_degree of the term
+        z_index = max_index
+        if not expr.is_number:
+            x_degree, y_degree, z_degree = y_index,\
+                                           z_index - x_index - y_index, x_index
+            x_value = monomial_values[z_index - 1][y_index - 1][x_index][7]\
+                if x_degree > 0 else 0
+            y_value = monomial_values[z_index - 1][y_index][x_index][7]\
+                if y_degree > 0 else 0
+            z_value = monomial_values[z_index - 1][y_index][x_index - 1][7]\
+                if z_degree > 0 else 0
+
+            value += x_degree * x_value * x0[0] + y_degree * y_value * x0[1] \
+                + z_degree * z_value * x0[2]
+
+        value += left_integral3D(facets, index, expr,
+                                 vertices, hp_param, degree)
+    return value / (len(dims) + degree - 1)
+
+
+def left_integral3D(facets, index, expr, vertices, hp_param, degree):
+    """Computes the left integral of Eq 10 in Chin et al.
+
+    Explanation
+    ===========
+
+    For the 3D case, this is the sum of the integral values over constituting
+    line segments of the face (which is accessed by facets[index]) multiplied
+    by the distance between the first point of facet and that line segment.
+
+    Parameters
+    ==========
+
+    facets :
+        List of faces of the 3-Polytope.
+    index :
+        Index of face over which integral is to be calculated.
+    expr :
+        Input polynomial.
+    vertices :
+        List of vertices that constitute the 3-Polytope.
+    hp_param :
+        The hyperplane parameters of the face.
+    degree :
+        Degree of the ``expr``.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import left_integral3D
+    >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
+                 (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
+                 [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
+                 [3, 1, 0, 2], [0, 4, 6, 2]]
+    >>> facets = cube[1:]
+    >>> vertices = cube[0]
+    >>> left_integral3D(facets, 3, 1, vertices, ([0, -1, 0], -5), 0)
+    -50
+    """
+    value = S.Zero
+    facet = facets[index]
+    x0 = vertices[facet[0]]
+    facet_len = len(facet)
+    for i, fac in enumerate(facet):
+        side = (vertices[fac], vertices[facet[(i + 1) % facet_len]])
+        value += distance_to_side(x0, side, hp_param[0]) * \
+            lineseg_integrate(facet, i, side, expr, degree)
+    return value
+
+
+def gradient_terms(binomial_power=0, no_of_gens=2):
+    """Returns a list of all the possible monomials between
+    0 and y**binomial_power for 2D case and z**binomial_power
+    for 3D case.
+
+    Parameters
+    ==========
+
+    binomial_power :
+        Power upto which terms are generated.
+    no_of_gens :
+        Denotes whether terms are being generated for 2D or 3D case.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import gradient_terms
+    >>> gradient_terms(2)
+    [[1, 0, 0, 0], [y, 0, 1, 0], [y**2, 0, 2, 0], [x, 1, 0, 0],
+    [x*y, 1, 1, 0], [x**2, 2, 0, 0]]
+    >>> gradient_terms(2, 3)
+    [[[[1, 0, 0, 0, 0, 0, 0, 0]]], [[[y, 0, 1, 0, 1, 0, 0, 0],
+    [z, 0, 0, 1, 1, 0, 1, 0]], [[x, 1, 0, 0, 1, 1, 0, 0]]],
+    [[[y**2, 0, 2, 0, 2, 0, 0, 0], [y*z, 0, 1, 1, 2, 0, 1, 0],
+    [z**2, 0, 0, 2, 2, 0, 2, 0]], [[x*y, 1, 1, 0, 2, 1, 0, 0],
+    [x*z, 1, 0, 1, 2, 1, 1, 0]], [[x**2, 2, 0, 0, 2, 2, 0, 0]]]]
+    """
+    if no_of_gens == 2:
+        count = 0
+        terms = [None] * int((binomial_power ** 2 + 3 * binomial_power + 2) / 2)
+        for x_count in range(0, binomial_power + 1):
+            for y_count in range(0, binomial_power - x_count + 1):
+                terms[count] = [x**x_count*y**y_count,
+                                x_count, y_count, 0]
+                count += 1
+    else:
+        terms = [[[[x ** x_count * y ** y_count *
+                    z ** (z_count - y_count - x_count),
+                    x_count, y_count, z_count - y_count - x_count,
+                    z_count, x_count, z_count - y_count - x_count, 0]
+                 for y_count in range(z_count - x_count, -1, -1)]
+                 for x_count in range(0, z_count + 1)]
+                 for z_count in range(0, binomial_power + 1)]
+    return terms
+
+
+def hyperplane_parameters(poly, vertices=None):
+    """A helper function to return the hyperplane parameters
+    of which the facets of the polytope are a part of.
+
+    Parameters
+    ==========
+
+    poly :
+        The input 2/3-Polytope.
+    vertices :
+        Vertex indices of 3-Polytope.
+
+    Examples
+    ========
+
+    >>> from sympy import Point, Polygon
+    >>> from sympy.integrals.intpoly import hyperplane_parameters
+    >>> hyperplane_parameters(Polygon(Point(0, 3), Point(5, 3), Point(1, 1)))
+    [((0, 1), 3), ((1, -2), -1), ((-2, -1), -3)]
+    >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
+                (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
+                [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
+                [3, 1, 0, 2], [0, 4, 6, 2]]
+    >>> hyperplane_parameters(cube[1:], cube[0])
+    [([0, -1, 0], -5), ([0, 0, -1], -5), ([-1, 0, 0], -5),
+    ([0, 1, 0], 0), ([1, 0, 0], 0), ([0, 0, 1], 0)]
+    """
+    if isinstance(poly, Polygon):
+        vertices = list(poly.vertices) + [poly.vertices[0]]  # Close the polygon
+        params = [None] * (len(vertices) - 1)
+
+        for i in range(len(vertices) - 1):
+            v1 = vertices[i]
+            v2 = vertices[i + 1]
+
+            a1 = v1[1] - v2[1]
+            a2 = v2[0] - v1[0]
+            b = v2[0] * v1[1] - v2[1] * v1[0]
+
+            factor = gcd_list([a1, a2, b])
+
+            b = S(b) / factor
+            a = (S(a1) / factor, S(a2) / factor)
+            params[i] = (a, b)
+    else:
+        params = [None] * len(poly)
+        for i, polygon in enumerate(poly):
+            v1, v2, v3 = [vertices[vertex] for vertex in polygon[:3]]
+            normal = cross_product(v1, v2, v3)
+            b = sum(normal[j] * v1[j] for j in range(0, 3))
+            fac = gcd_list(normal)
+            if fac.is_zero:
+                fac = 1
+            normal = [j / fac for j in normal]
+            b = b / fac
+            params[i] = (normal, b)
+    return params
+
+
+def cross_product(v1, v2, v3):
+    """Returns the cross-product of vectors (v2 - v1) and (v3 - v1)
+    That is : (v2 - v1) X (v3 - v1)
+    """
+    v2 = [v2[j] - v1[j] for j in range(0, 3)]
+    v3 = [v3[j] - v1[j] for j in range(0, 3)]
+    return [v3[2] * v2[1] - v3[1] * v2[2],
+            v3[0] * v2[2] - v3[2] * v2[0],
+            v3[1] * v2[0] - v3[0] * v2[1]]
+
+
+def best_origin(a, b, lineseg, expr):
+    """Helper method for polytope_integrate. Currently not used in the main
+    algorithm.
+
+    Explanation
+    ===========
+
+    Returns a point on the lineseg whose vector inner product with the
+    divergence of `expr` yields an expression with the least maximum
+    total power.
+
+    Parameters
+    ==========
+
+    a :
+        Hyperplane parameter denoting direction.
+    b :
+        Hyperplane parameter denoting distance.
+    lineseg :
+        Line segment on which to find the origin.
+    expr :
+        The expression which determines the best point.
+
+    Algorithm(currently works only for 2D use case)
+    ===============================================
+
+    1 > Firstly, check for edge cases. Here that would refer to vertical
+        or horizontal lines.
+
+    2 > If input expression is a polynomial containing more than one generator
+        then find out the total power of each of the generators.
+
+        x**2 + 3 + x*y + x**4*y**5 ---> {x: 7, y: 6}
+
+        If expression is a constant value then pick the first boundary point
+        of the line segment.
+
+    3 > First check if a point exists on the line segment where the value of
+        the highest power generator becomes 0. If not check if the value of
+        the next highest becomes 0. If none becomes 0 within line segment
+        constraints then pick the first boundary point of the line segment.
+        Actually, any point lying on the segment can be picked as best origin
+        in the last case.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import best_origin
+    >>> from sympy.abc import x, y
+    >>> from sympy import Point, Segment2D
+    >>> l = Segment2D(Point(0, 3), Point(1, 1))
+    >>> expr = x**3*y**7
+    >>> best_origin((2, 1), 3, l, expr)
+    (0, 3.0)
+    """
+    a1, b1 = lineseg.points[0]
+
+    def x_axis_cut(ls):
+        """Returns the point where the input line segment
+        intersects the x-axis.
+
+        Parameters
+        ==========
+
+        ls :
+            Line segment
+        """
+        p, q = ls.points
+        if p.y.is_zero:
+            return tuple(p)
+        elif q.y.is_zero:
+            return tuple(q)
+        elif p.y/q.y < S.Zero:
+            return p.y * (p.x - q.x)/(q.y - p.y) + p.x, S.Zero
+        else:
+            return ()
+
+    def y_axis_cut(ls):
+        """Returns the point where the input line segment
+        intersects the y-axis.
+
+        Parameters
+        ==========
+
+        ls :
+            Line segment
+        """
+        p, q = ls.points
+        if p.x.is_zero:
+            return tuple(p)
+        elif q.x.is_zero:
+            return tuple(q)
+        elif p.x/q.x < S.Zero:
+            return S.Zero, p.x * (p.y - q.y)/(q.x - p.x) + p.y
+        else:
+            return ()
+
+    gens = (x, y)
+    power_gens = {}
+
+    for i in gens:
+        power_gens[i] = S.Zero
+
+    if len(gens) > 1:
+        # Special case for vertical and horizontal lines
+        if len(gens) == 2:
+            if a[0] == 0:
+                if y_axis_cut(lineseg):
+                    return S.Zero, b/a[1]
+                else:
+                    return a1, b1
+            elif a[1] == 0:
+                if x_axis_cut(lineseg):
+                    return b/a[0], S.Zero
+                else:
+                    return a1, b1
+
+        if isinstance(expr, Expr):  # Find the sum total of power of each
+            if expr.is_Add:         # generator and store in a dictionary.
+                for monomial in expr.args:
+                    if monomial.is_Pow:
+                        if monomial.args[0] in gens:
+                            power_gens[monomial.args[0]] += monomial.args[1]
+                    else:
+                        for univariate in monomial.args:
+                            term_type = len(univariate.args)
+                            if term_type == 0 and univariate in gens:
+                                power_gens[univariate] += 1
+                            elif term_type == 2 and univariate.args[0] in gens:
+                                power_gens[univariate.args[0]] +=\
+                                           univariate.args[1]
+            elif expr.is_Mul:
+                for term in expr.args:
+                    term_type = len(term.args)
+                    if term_type == 0 and term in gens:
+                        power_gens[term] += 1
+                    elif term_type == 2 and term.args[0] in gens:
+                        power_gens[term.args[0]] += term.args[1]
+            elif expr.is_Pow:
+                power_gens[expr.args[0]] = expr.args[1]
+            elif expr.is_Symbol:
+                power_gens[expr] += 1
+        else:  # If `expr` is a constant take first vertex of the line segment.
+            return a1, b1
+
+        #  TODO : This part is quite hacky. Should be made more robust with
+        #  TODO : respect to symbol names and scalable w.r.t higher dimensions.
+        power_gens = sorted(power_gens.items(), key=lambda k: str(k[0]))
+        if power_gens[0][1] >= power_gens[1][1]:
+            if y_axis_cut(lineseg):
+                x0 = (S.Zero, b / a[1])
+            elif x_axis_cut(lineseg):
+                x0 = (b / a[0], S.Zero)
+            else:
+                x0 = (a1, b1)
+        else:
+            if x_axis_cut(lineseg):
+                x0 = (b/a[0], S.Zero)
+            elif y_axis_cut(lineseg):
+                x0 = (S.Zero, b/a[1])
+            else:
+                x0 = (a1, b1)
+    else:
+        x0 = (b/a[0])
+    return x0
+
+
+def decompose(expr, separate=False):
+    """Decomposes an input polynomial into homogeneous ones of
+    smaller or equal degree.
+
+    Explanation
+    ===========
+
+    Returns a dictionary with keys as the degree of the smaller
+    constituting polynomials. Values are the constituting polynomials.
+
+    Parameters
+    ==========
+
+    expr : Expr
+        Polynomial(SymPy expression).
+    separate : bool
+        If True then simply return a list of the constituent monomials
+        If not then break up the polynomial into constituent homogeneous
+        polynomials.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy.integrals.intpoly import decompose
+    >>> decompose(x**2 + x*y + x + y + x**3*y**2 + y**5)
+    {1: x + y, 2: x**2 + x*y, 5: x**3*y**2 + y**5}
+    >>> decompose(x**2 + x*y + x + y + x**3*y**2 + y**5, True)
+    {x, x**2, y, y**5, x*y, x**3*y**2}
+    """
+    poly_dict = {}
+
+    if isinstance(expr, Expr) and not expr.is_number:
+        if expr.is_Symbol:
+            poly_dict[1] = expr
+        elif expr.is_Add:
+            symbols = expr.atoms(Symbol)
+            degrees = [(sum(degree_list(monom, *symbols)), monom)
+                       for monom in expr.args]
+            if separate:
+                return {monom[1] for monom in degrees}
+            else:
+                for monom in degrees:
+                    degree, term = monom
+                    if poly_dict.get(degree):
+                        poly_dict[degree] += term
+                    else:
+                        poly_dict[degree] = term
+        elif expr.is_Pow:
+            _, degree = expr.args
+            poly_dict[degree] = expr
+        else:  # Now expr can only be of `Mul` type
+            degree = 0
+            for term in expr.args:
+                term_type = len(term.args)
+                if term_type == 0 and term.is_Symbol:
+                    degree += 1
+                elif term_type == 2:
+                    degree += term.args[1]
+            poly_dict[degree] = expr
+    else:
+        poly_dict[0] = expr
+
+    if separate:
+        return set(poly_dict.values())
+    return poly_dict
+
+
+def point_sort(poly, normal=None, clockwise=True):
+    """Returns the same polygon with points sorted in clockwise or
+    anti-clockwise order.
+
+    Note that it's necessary for input points to be sorted in some order
+    (clockwise or anti-clockwise) for the integration algorithm to work.
+    As a convention algorithm has been implemented keeping clockwise
+    orientation in mind.
+
+    Parameters
+    ==========
+
+    poly:
+        2D or 3D Polygon.
+    normal : optional
+        The normal of the plane which the 3-Polytope is a part of.
+    clockwise : bool, optional
+        Returns points sorted in clockwise order if True and
+        anti-clockwise if False.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import point_sort
+    >>> from sympy import Point
+    >>> point_sort([Point(0, 0), Point(1, 0), Point(1, 1)])
+    [Point2D(1, 1), Point2D(1, 0), Point2D(0, 0)]
+    """
+    pts = poly.vertices if isinstance(poly, Polygon) else poly
+    n = len(pts)
+    if n < 2:
+        return list(pts)
+
+    order = S.One if clockwise else S.NegativeOne
+    dim = len(pts[0])
+    if dim == 2:
+        center = Point(sum((vertex.x for vertex in pts)) / n,
+                        sum((vertex.y for vertex in pts)) / n)
+    else:
+        center = Point(sum((vertex.x for vertex in pts)) / n,
+                        sum((vertex.y for vertex in pts)) / n,
+                        sum((vertex.z for vertex in pts)) / n)
+
+    def compare(a, b):
+        if a.x - center.x >= S.Zero and b.x - center.x < S.Zero:
+            return -order
+        elif a.x - center.x < 0 and b.x - center.x >= 0:
+            return order
+        elif a.x - center.x == 0 and b.x - center.x == 0:
+            if a.y - center.y >= 0 or b.y - center.y >= 0:
+                return -order if a.y > b.y else order
+            return -order if b.y > a.y else order
+
+        det = (a.x - center.x) * (b.y - center.y) -\
+              (b.x - center.x) * (a.y - center.y)
+        if det < 0:
+            return -order
+        elif det > 0:
+            return order
+
+        first = (a.x - center.x) * (a.x - center.x) +\
+                (a.y - center.y) * (a.y - center.y)
+        second = (b.x - center.x) * (b.x - center.x) +\
+                 (b.y - center.y) * (b.y - center.y)
+        return -order if first > second else order
+
+    def compare3d(a, b):
+        det = cross_product(center, a, b)
+        dot_product = sum(det[i] * normal[i] for i in range(0, 3))
+        if dot_product < 0:
+            return -order
+        elif dot_product > 0:
+            return order
+
+    return sorted(pts, key=cmp_to_key(compare if dim==2 else compare3d))
+
+
+def norm(point):
+    """Returns the Euclidean norm of a point from origin.
+
+    Parameters
+    ==========
+
+    point:
+        This denotes a point in the dimension_al spac_e.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import norm
+    >>> from sympy import Point
+    >>> norm(Point(2, 7))
+    sqrt(53)
+    """
+    half = S.Half
+    if isinstance(point, (list, tuple)):
+        return sum(coord ** 2 for coord in point) ** half
+    elif isinstance(point, Point):
+        if isinstance(point, Point2D):
+            return (point.x ** 2 + point.y ** 2) ** half
+        else:
+            return (point.x ** 2 + point.y ** 2 + point.z) ** half
+    elif isinstance(point, dict):
+        return sum(i**2 for i in point.values()) ** half
+
+
+def intersection(geom_1, geom_2, intersection_type):
+    """Returns intersection between geometric objects.
+
+    Explanation
+    ===========
+
+    Note that this function is meant for use in integration_reduction and
+    at that point in the calling function the lines denoted by the segments
+    surely intersect within segment boundaries. Coincident lines are taken
+    to be non-intersecting. Also, the hyperplane intersection for 2D case is
+    also implemented.
+
+    Parameters
+    ==========
+
+    geom_1, geom_2:
+        The input line segments.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.intpoly import intersection
+    >>> from sympy import Point, Segment2D
+    >>> l1 = Segment2D(Point(1, 1), Point(3, 5))
+    >>> l2 = Segment2D(Point(2, 0), Point(2, 5))
+    >>> intersection(l1, l2, "segment2D")
+    (2, 3)
+    >>> p1 = ((-1, 0), 0)
+    >>> p2 = ((0, 1), 1)
+    >>> intersection(p1, p2, "plane2D")
+    (0, 1)
+    """
+    if intersection_type[:-2] == "segment":
+        if intersection_type == "segment2D":
+            x1, y1 = geom_1.points[0]
+            x2, y2 = geom_1.points[1]
+            x3, y3 = geom_2.points[0]
+            x4, y4 = geom_2.points[1]
+        elif intersection_type == "segment3D":
+            x1, y1, z1 = geom_1.points[0]
+            x2, y2, z2 = geom_1.points[1]
+            x3, y3, z3 = geom_2.points[0]
+            x4, y4, z4 = geom_2.points[1]
+
+        denom = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
+        if denom:
+            t1 = x1 * y2 - y1 * x2
+            t2 = x3 * y4 - x4 * y3
+            return (S(t1 * (x3 - x4) - t2 * (x1 - x2)) / denom,
+                    S(t1 * (y3 - y4) - t2 * (y1 - y2)) / denom)
+    if intersection_type[:-2] == "plane":
+        if intersection_type == "plane2D":  # Intersection of hyperplanes
+            a1x, a1y = geom_1[0]
+            a2x, a2y = geom_2[0]
+            b1, b2 = geom_1[1], geom_2[1]
+
+            denom = a1x * a2y - a2x * a1y
+            if denom:
+                return (S(b1 * a2y - b2 * a1y) / denom,
+                        S(b2 * a1x - b1 * a2x) / denom)
+
+
+def is_vertex(ent):
+    """If the input entity is a vertex return True.
+
+    Parameter
+    =========
+
+    ent :
+        Denotes a geometric entity representing a point.
+
+    Examples
+    ========
+
+    >>> from sympy import Point
+    >>> from sympy.integrals.intpoly import is_vertex
+    >>> is_vertex((2, 3))
+    True
+    >>> is_vertex((2, 3, 6))
+    True
+    >>> is_vertex(Point(2, 3))
+    True
+    """
+    if isinstance(ent, tuple):
+        if len(ent) in [2, 3]:
+            return True
+    elif isinstance(ent, Point):
+        return True
+    return False
+
+
+def plot_polytope(poly):
+    """Plots the 2D polytope using the functions written in plotting
+    module which in turn uses matplotlib backend.
+
+    Parameter
+    =========
+
+    poly:
+        Denotes a 2-Polytope.
+    """
+    from sympy.plotting.plot import Plot, List2DSeries
+
+    xl = [vertex.x for vertex in poly.vertices]
+    yl = [vertex.y for vertex in poly.vertices]
+
+    xl.append(poly.vertices[0].x)  # Closing the polygon
+    yl.append(poly.vertices[0].y)
+
+    l2ds = List2DSeries(xl, yl)
+    p = Plot(l2ds, axes='label_axes=True')
+    p.show()
+
+
+def plot_polynomial(expr):
+    """Plots the polynomial using the functions written in
+    plotting module which in turn uses matplotlib backend.
+
+    Parameter
+    =========
+
+    expr:
+        Denotes a polynomial(SymPy expression).
+    """
+    from sympy.plotting.plot import plot3d, plot
+    gens = expr.free_symbols
+    if len(gens) == 2:
+        plot3d(expr)
+    else:
+        plot(expr)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/laplace.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/laplace.py
new file mode 100644
index 0000000000000000000000000000000000000000..604c4a2711440f13c62f0d778e382e4daaf33148
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/laplace.py
@@ -0,0 +1,2377 @@
+"""Laplace Transforms"""
+import sys
+import sympy
+from sympy.core import S, pi, I
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.expr import Expr
+from sympy.core.function import (
+    AppliedUndef, Derivative, expand, expand_complex, expand_mul, expand_trig,
+    Lambda, WildFunction, diff, Subs)
+from sympy.core.mul import Mul, prod
+from sympy.core.relational import (
+    _canonical, Ge, Gt, Lt, Unequality, Eq, Ne, Relational)
+from sympy.core.sorting import ordered
+from sympy.core.symbol import Dummy, symbols, Wild
+from sympy.functions.elementary.complexes import (
+    re, im, arg, Abs, polar_lift, periodic_argument)
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.hyperbolic import cosh, coth, sinh, asinh
+from sympy.functions.elementary.miscellaneous import Max, Min, sqrt
+from sympy.functions.elementary.piecewise import (
+    Piecewise, piecewise_exclusive)
+from sympy.functions.elementary.trigonometric import cos, sin, atan, sinc
+from sympy.functions.special.bessel import besseli, besselj, besselk, bessely
+from sympy.functions.special.delta_functions import DiracDelta, Heaviside
+from sympy.functions.special.error_functions import erf, erfc, Ei
+from sympy.functions.special.gamma_functions import (
+    digamma, gamma, lowergamma, uppergamma)
+from sympy.functions.special.singularity_functions import SingularityFunction
+from sympy.integrals import integrate, Integral
+from sympy.integrals.transforms import (
+    _simplify, IntegralTransform, IntegralTransformError)
+from sympy.logic.boolalg import to_cnf, conjuncts, disjuncts, Or, And
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.polys.matrices.linsolve import _lin_eq2dict
+from sympy.polys.polyerrors import PolynomialError
+from sympy.polys.polyroots import roots
+from sympy.polys.polytools import Poly
+from sympy.polys.rationaltools import together
+from sympy.polys.rootoftools import RootSum
+from sympy.utilities.exceptions import (
+    sympy_deprecation_warning, SymPyDeprecationWarning, ignore_warnings)
+from sympy.utilities.misc import debugf
+
+_LT_level = 0
+
+
+def DEBUG_WRAP(func):
+    def wrap(*args, **kwargs):
+        from sympy import SYMPY_DEBUG
+        global _LT_level
+
+        if not SYMPY_DEBUG:
+            return func(*args, **kwargs)
+
+        if _LT_level == 0:
+            print('\n' + '-'*78, file=sys.stderr)
+        print('-LT- %s%s%s' % ('  '*_LT_level, func.__name__, args),
+              file=sys.stderr)
+        _LT_level += 1
+        if (
+                func.__name__ == '_laplace_transform_integration' or
+                func.__name__ == '_inverse_laplace_transform_integration'):
+            sympy.SYMPY_DEBUG = False
+            print('**** %sIntegrating ...' % ('  '*_LT_level), file=sys.stderr)
+            result = func(*args, **kwargs)
+            sympy.SYMPY_DEBUG = True
+        else:
+            result = func(*args, **kwargs)
+        _LT_level -= 1
+        print('-LT- %s---> %s' % ('  '*_LT_level, result), file=sys.stderr)
+        if _LT_level == 0:
+            print('-'*78 + '\n', file=sys.stderr)
+        return result
+    return wrap
+
+
+def _debug(text):
+    from sympy import SYMPY_DEBUG
+
+    if SYMPY_DEBUG:
+        print('-LT- %s%s' % ('  '*_LT_level, text), file=sys.stderr)
+
+
+def _simplifyconds(expr, s, a):
+    r"""
+    Naively simplify some conditions occurring in ``expr``,
+    given that `\operatorname{Re}(s) > a`.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.laplace import _simplifyconds
+    >>> from sympy.abc import x
+    >>> from sympy import sympify as S
+    >>> _simplifyconds(abs(x**2) < 1, x, 1)
+    False
+    >>> _simplifyconds(abs(x**2) < 1, x, 2)
+    False
+    >>> _simplifyconds(abs(x**2) < 1, x, 0)
+    Abs(x**2) < 1
+    >>> _simplifyconds(abs(1/x**2) < 1, x, 1)
+    True
+    >>> _simplifyconds(S(1) < abs(x), x, 1)
+    True
+    >>> _simplifyconds(S(1) < abs(1/x), x, 1)
+    False
+
+    >>> from sympy import Ne
+    >>> _simplifyconds(Ne(1, x**3), x, 1)
+    True
+    >>> _simplifyconds(Ne(1, x**3), x, 2)
+    True
+    >>> _simplifyconds(Ne(1, x**3), x, 0)
+    Ne(1, x**3)
+    """
+
+    def power(ex):
+        if ex == s:
+            return 1
+        if ex.is_Pow and ex.base == s:
+            return ex.exp
+        return None
+
+    def bigger(ex1, ex2):
+        """ Return True only if |ex1| > |ex2|, False only if |ex1| < |ex2|.
+            Else return None. """
+        if ex1.has(s) and ex2.has(s):
+            return None
+        if isinstance(ex1, Abs):
+            ex1 = ex1.args[0]
+        if isinstance(ex2, Abs):
+            ex2 = ex2.args[0]
+        if ex1.has(s):
+            return bigger(1/ex2, 1/ex1)
+        n = power(ex2)
+        if n is None:
+            return None
+        try:
+            if n > 0 and (Abs(ex1) <= Abs(a)**n) == S.true:
+                return False
+            if n < 0 and (Abs(ex1) >= Abs(a)**n) == S.true:
+                return True
+        except TypeError:
+            return None
+
+    def replie(x, y):
+        """ simplify x < y """
+        if (not (x.is_positive or isinstance(x, Abs))
+                or not (y.is_positive or isinstance(y, Abs))):
+            return (x < y)
+        r = bigger(x, y)
+        if r is not None:
+            return not r
+        return (x < y)
+
+    def replue(x, y):
+        b = bigger(x, y)
+        if b in (True, False):
+            return True
+        return Unequality(x, y)
+
+    def repl(ex, *args):
+        if ex in (True, False):
+            return bool(ex)
+        return ex.replace(*args)
+
+    from sympy.simplify.radsimp import collect_abs
+    expr = collect_abs(expr)
+    expr = repl(expr, Lt, replie)
+    expr = repl(expr, Gt, lambda x, y: replie(y, x))
+    expr = repl(expr, Unequality, replue)
+    return S(expr)
+
+
+@DEBUG_WRAP
+def expand_dirac_delta(expr):
+    """
+    Expand an expression involving DiractDelta to get it as a linear
+    combination of DiracDelta functions.
+    """
+    return _lin_eq2dict(expr, expr.atoms(DiracDelta))
+
+
+@DEBUG_WRAP
+def _laplace_transform_integration(f, t, s_, *, simplify):
+    """ The backend function for doing Laplace transforms by integration.
+
+    This backend assumes that the frontend has already split sums
+    such that `f` is to an addition anymore.
+    """
+    s = Dummy('s')
+
+    if f.has(DiracDelta):
+        return None
+
+    F = integrate(f*exp(-s*t), (t, S.Zero, S.Infinity))
+
+    if not F.has(Integral):
+        return _simplify(F.subs(s, s_), simplify), S.NegativeInfinity, S.true
+
+    if not F.is_Piecewise:
+        return None
+
+    F, cond = F.args[0]
+    if F.has(Integral):
+        return None
+
+    def process_conds(conds):
+        """ Turn ``conds`` into a strip and auxiliary conditions. """
+        from sympy.solvers.inequalities import _solve_inequality
+        a = S.NegativeInfinity
+        aux = S.true
+        conds = conjuncts(to_cnf(conds))
+        p, q, w1, w2, w3, w4, w5 = symbols(
+            'p q w1 w2 w3 w4 w5', cls=Wild, exclude=[s])
+        patterns = (
+            p*Abs(arg((s + w3)*q)) < w2,
+            p*Abs(arg((s + w3)*q)) <= w2,
+            Abs(periodic_argument((s + w3)**p*q, w1)) < w2,
+            Abs(periodic_argument((s + w3)**p*q, w1)) <= w2,
+            Abs(periodic_argument((polar_lift(s + w3))**p*q, w1)) < w2,
+            Abs(periodic_argument((polar_lift(s + w3))**p*q, w1)) <= w2)
+        for c in conds:
+            a_ = S.Infinity
+            aux_ = []
+            for d in disjuncts(c):
+                if d.is_Relational and s in d.rhs.free_symbols:
+                    d = d.reversed
+                if d.is_Relational and isinstance(d, (Ge, Gt)):
+                    d = d.reversedsign
+                for pat in patterns:
+                    m = d.match(pat)
+                    if m:
+                        break
+                if m and m[q].is_positive and m[w2]/m[p] == pi/2:
+                    d = -re(s + m[w3]) < 0
+                m = d.match(p - cos(w1*Abs(arg(s*w5))*w2)*Abs(s**w3)**w4 < 0)
+                if not m:
+                    m = d.match(
+                        cos(p - Abs(periodic_argument(s**w1*w5, q))*w2) *
+                        Abs(s**w3)**w4 < 0)
+                if not m:
+                    m = d.match(
+                        p - cos(
+                            Abs(periodic_argument(polar_lift(s)**w1*w5, q))*w2
+                            )*Abs(s**w3)**w4 < 0)
+                if m and all(m[wild].is_positive for wild in [
+                        w1, w2, w3, w4, w5]):
+                    d = re(s) > m[p]
+                d_ = d.replace(
+                    re, lambda x: x.expand().as_real_imag()[0]).subs(re(s), t)
+                if (
+                        not d.is_Relational or d.rel_op in ('==', '!=')
+                        or d_.has(s) or not d_.has(t)):
+                    aux_ += [d]
+                    continue
+                soln = _solve_inequality(d_, t)
+                if not soln.is_Relational or soln.rel_op in ('==', '!='):
+                    aux_ += [d]
+                    continue
+                if soln.lts == t:
+                    return None
+                else:
+                    a_ = Min(soln.lts, a_)
+            if a_ is not S.Infinity:
+                a = Max(a_, a)
+            else:
+                aux = And(aux, Or(*aux_))
+        return a, aux.canonical if aux.is_Relational else aux
+
+    conds = [process_conds(c) for c in disjuncts(cond)]
+    conds2 = [x for x in conds if x[1] !=
+              S.false and x[0] is not S.NegativeInfinity]
+    if not conds2:
+        conds2 = [x for x in conds if x[1] != S.false]
+    conds = list(ordered(conds2))
+
+    def cnt(expr):
+        if expr in (True, False):
+            return 0
+        return expr.count_ops()
+    conds.sort(key=lambda x: (-x[0], cnt(x[1])))
+
+    if not conds:
+        return None
+    a, aux = conds[0]  # XXX is [0] always the right one?
+
+    def sbs(expr):
+        return expr.subs(s, s_)
+    if simplify:
+        F = _simplifyconds(F, s, a)
+        aux = _simplifyconds(aux, s, a)
+    return _simplify(F.subs(s, s_), simplify), sbs(a), _canonical(sbs(aux))
+
+
+@DEBUG_WRAP
+def _laplace_deep_collect(f, t):
+    """
+    This is an internal helper function that traverses through the expression
+    tree of `f(t)` and collects arguments. The purpose of it is that
+    anything like `f(w*t-1*t-c)` will be written as `f((w-1)*t-c)` such that
+    it can match `f(a*t+b)`.
+    """
+    if not isinstance(f, Expr):
+        return f
+    if (p := f.as_poly(t)) is not None:
+        return p.as_expr()
+    func = f.func
+    args = [_laplace_deep_collect(arg, t) for arg in f.args]
+    return func(*args)
+
+
+@cacheit
+def _laplace_build_rules():
+    """
+    This is an internal helper function that returns the table of Laplace
+    transform rules in terms of the time variable `t` and the frequency
+    variable `s`.  It is used by ``_laplace_apply_rules``.  Each entry is a
+    tuple containing:
+
+        (time domain pattern,
+         frequency-domain replacement,
+         condition for the rule to be applied,
+         convergence plane,
+         preparation function)
+
+    The preparation function is a function with one argument that is applied
+    to the expression before matching. For most rules it should be
+    ``_laplace_deep_collect``.
+    """
+    t = Dummy('t')
+    s = Dummy('s')
+    a = Wild('a', exclude=[t])
+    b = Wild('b', exclude=[t])
+    n = Wild('n', exclude=[t])
+    tau = Wild('tau', exclude=[t])
+    omega = Wild('omega', exclude=[t])
+    def dco(f): return _laplace_deep_collect(f, t)
+    _debug('_laplace_build_rules is building rules')
+
+    laplace_transform_rules = [
+        (a, a/s,
+         S.true, S.Zero, dco),  # 4.2.1
+        (DiracDelta(a*t-b), exp(-s*b/a)/Abs(a),
+         Or(And(a > 0, b >= 0), And(a < 0, b <= 0)),
+         S.NegativeInfinity, dco),  # Not in Bateman54
+        (DiracDelta(a*t-b), S(0),
+         Or(And(a < 0, b >= 0), And(a > 0, b <= 0)),
+         S.NegativeInfinity, dco),  # Not in Bateman54
+        (Heaviside(a*t-b), exp(-s*b/a)/s,
+         And(a > 0, b > 0), S.Zero, dco),  # 4.4.1
+        (Heaviside(a*t-b), (1-exp(-s*b/a))/s,
+         And(a < 0, b < 0), S.Zero, dco),  # 4.4.1
+        (Heaviside(a*t-b), 1/s,
+         And(a > 0, b <= 0), S.Zero, dco),  # 4.4.1
+        (Heaviside(a*t-b), 0,
+         And(a < 0, b > 0), S.Zero, dco),  # 4.4.1
+        (t, 1/s**2,
+         S.true, S.Zero, dco),  # 4.2.3
+        (1/(a*t+b), -exp(-b/a*s)*Ei(-b/a*s)/a,
+         Abs(arg(b/a)) < pi, S.Zero, dco),  # 4.2.6
+        (1/sqrt(a*t+b), sqrt(a*pi/s)*exp(b/a*s)*erfc(sqrt(b/a*s))/a,
+         Abs(arg(b/a)) < pi, S.Zero, dco),  # 4.2.18
+        ((a*t+b)**(-S(3)/2),
+         2*b**(-S(1)/2)-2*(pi*s/a)**(S(1)/2)*exp(b/a*s) * erfc(sqrt(b/a*s))/a,
+         Abs(arg(b/a)) < pi, S.Zero, dco),  # 4.2.20
+        (sqrt(t)/(t+b), sqrt(pi/s)-pi*sqrt(b)*exp(b*s)*erfc(sqrt(b*s)),
+         Abs(arg(b)) < pi, S.Zero, dco),  # 4.2.22
+        (1/(a*sqrt(t) + t**(3/2)), pi*a**(S(1)/2)*exp(a*s)*erfc(sqrt(a*s)),
+         S.true, S.Zero, dco),  # Not in Bateman54
+        (t**n, gamma(n+1)/s**(n+1),
+         n > -1, S.Zero, dco),  # 4.3.1
+        ((a*t+b)**n, uppergamma(n+1, b/a*s)*exp(-b/a*s)/s**(n+1)/a,
+         And(n > -1, Abs(arg(b/a)) < pi), S.Zero, dco),  # 4.3.4
+        (t**n/(t+a), a**n*gamma(n+1)*uppergamma(-n, a*s),
+         And(n > -1, Abs(arg(a)) < pi), S.Zero, dco),  # 4.3.7
+        (exp(a*t-tau), exp(-tau)/(s-a),
+         S.true, re(a), dco),  # 4.5.1
+        (t*exp(a*t-tau), exp(-tau)/(s-a)**2,
+         S.true, re(a), dco),  # 4.5.2
+        (t**n*exp(a*t), gamma(n+1)/(s-a)**(n+1),
+         re(n) > -1, re(a), dco),  # 4.5.3
+        (exp(-a*t**2), sqrt(pi/4/a)*exp(s**2/4/a)*erfc(s/sqrt(4*a)),
+         re(a) > 0, S.Zero, dco),  # 4.5.21
+        (t*exp(-a*t**2),
+         1/(2*a)-2/sqrt(pi)/(4*a)**(S(3)/2)*s*erfc(s/sqrt(4*a)),
+         re(a) > 0, S.Zero, dco),  # 4.5.22
+        (exp(-a/t), 2*sqrt(a/s)*besselk(1, 2*sqrt(a*s)),
+         re(a) >= 0, S.Zero, dco),  # 4.5.25
+        (sqrt(t)*exp(-a/t),
+         S(1)/2*sqrt(pi/s**3)*(1+2*sqrt(a*s))*exp(-2*sqrt(a*s)),
+         re(a) >= 0, S.Zero, dco),  # 4.5.26
+        (exp(-a/t)/sqrt(t), sqrt(pi/s)*exp(-2*sqrt(a*s)),
+         re(a) >= 0, S.Zero, dco),  # 4.5.27
+        (exp(-a/t)/(t*sqrt(t)), sqrt(pi/a)*exp(-2*sqrt(a*s)),
+         re(a) > 0, S.Zero, dco),  # 4.5.28
+        (t**n*exp(-a/t), 2*(a/s)**((n+1)/2)*besselk(n+1, 2*sqrt(a*s)),
+         re(a) > 0, S.Zero, dco),  # 4.5.29
+        # TODO: rules with sqrt(a*t) and sqrt(a/t) have stopped working after
+        #       changes to as_base_exp
+        # (exp(-2*sqrt(a*t)),
+        #  s**(-1)-sqrt(pi*a)*s**(-S(3)/2)*exp(a/s) * erfc(sqrt(a/s)),
+        #  Abs(arg(a)) < pi, S.Zero, dco),  # 4.5.31
+        # (exp(-2*sqrt(a*t))/sqrt(t), (pi/s)**(S(1)/2)*exp(a/s)*erfc(sqrt(a/s)),
+        #  Abs(arg(a)) < pi, S.Zero, dco),  # 4.5.33
+        (exp(-a*exp(-t)), a**(-s)*lowergamma(s, a),
+         S.true, S.Zero, dco),  # 4.5.36
+        (exp(-a*exp(t)), a**s*uppergamma(-s, a),
+         re(a) > 0, S.Zero, dco),  # 4.5.37
+        (log(a*t), -log(exp(S.EulerGamma)*s/a)/s,
+         a > 0, S.Zero, dco),  # 4.6.1
+        (log(1+a*t), -exp(s/a)/s*Ei(-s/a),
+         Abs(arg(a)) < pi, S.Zero, dco),  # 4.6.4
+        (log(a*t+b), (log(b)-exp(s/b/a)/s*a*Ei(-s/b))/s*a,
+         And(a > 0, Abs(arg(b)) < pi), S.Zero, dco),  # 4.6.5
+        (log(t)/sqrt(t), -sqrt(pi/s)*log(4*s*exp(S.EulerGamma)),
+         S.true, S.Zero, dco),  # 4.6.9
+        (t**n*log(t), gamma(n+1)*s**(-n-1)*(digamma(n+1)-log(s)),
+         re(n) > -1, S.Zero, dco),  # 4.6.11
+        (log(a*t)**2, (log(exp(S.EulerGamma)*s/a)**2+pi**2/6)/s,
+         a > 0, S.Zero, dco),  # 4.6.13
+        (sin(omega*t), omega/(s**2+omega**2),
+         S.true, Abs(im(omega)), dco),  # 4,7,1
+        (Abs(sin(omega*t)), omega/(s**2+omega**2)*coth(pi*s/2/omega),
+         omega > 0, S.Zero, dco),  # 4.7.2
+        (sin(omega*t)/t, atan(omega/s),
+         S.true, Abs(im(omega)), dco),  # 4.7.16
+        (sin(omega*t)**2/t, log(1+4*omega**2/s**2)/4,
+         S.true, 2*Abs(im(omega)), dco),  # 4.7.17
+        (sin(omega*t)**2/t**2,
+         omega*atan(2*omega/s)-s*log(1+4*omega**2/s**2)/4,
+         S.true, 2*Abs(im(omega)), dco),  # 4.7.20
+        # (sin(2*sqrt(a*t)), sqrt(pi*a)/s/sqrt(s)*exp(-a/s),
+        #  S.true, S.Zero, dco),  # 4.7.32
+        # (sin(2*sqrt(a*t))/t, pi*erf(sqrt(a/s)),
+        #  S.true, S.Zero, dco),  # 4.7.34
+        (cos(omega*t), s/(s**2+omega**2),
+         S.true, Abs(im(omega)), dco),  # 4.7.43
+        (cos(omega*t)**2, (s**2+2*omega**2)/(s**2+4*omega**2)/s,
+         S.true, 2*Abs(im(omega)), dco),  # 4.7.45
+        # (sqrt(t)*cos(2*sqrt(a*t)), sqrt(pi)/2*s**(-S(5)/2)*(s-2*a)*exp(-a/s),
+        #  S.true, S.Zero, dco),  # 4.7.66
+        # (cos(2*sqrt(a*t))/sqrt(t), sqrt(pi/s)*exp(-a/s),
+        #  S.true, S.Zero, dco),  # 4.7.67
+        (sin(a*t)*sin(b*t), 2*a*b*s/(s**2+(a+b)**2)/(s**2+(a-b)**2),
+         S.true, Abs(im(a))+Abs(im(b)), dco),  # 4.7.78
+        (cos(a*t)*sin(b*t), b*(s**2-a**2+b**2)/(s**2+(a+b)**2)/(s**2+(a-b)**2),
+         S.true, Abs(im(a))+Abs(im(b)), dco),  # 4.7.79
+        (cos(a*t)*cos(b*t), s*(s**2+a**2+b**2)/(s**2+(a+b)**2)/(s**2+(a-b)**2),
+         S.true, Abs(im(a))+Abs(im(b)), dco),  # 4.7.80
+        (sinh(a*t), a/(s**2-a**2),
+         S.true, Abs(re(a)), dco),  # 4.9.1
+        (cosh(a*t), s/(s**2-a**2),
+         S.true, Abs(re(a)), dco),  # 4.9.2
+        (sinh(a*t)**2, 2*a**2/(s**3-4*a**2*s),
+         S.true, 2*Abs(re(a)), dco),  # 4.9.3
+        (cosh(a*t)**2, (s**2-2*a**2)/(s**3-4*a**2*s),
+         S.true, 2*Abs(re(a)), dco),  # 4.9.4
+        (sinh(a*t)/t, log((s+a)/(s-a))/2,
+         S.true, Abs(re(a)), dco),  # 4.9.12
+        (t**n*sinh(a*t), gamma(n+1)/2*((s-a)**(-n-1)-(s+a)**(-n-1)),
+         n > -2, Abs(a), dco),  # 4.9.18
+        (t**n*cosh(a*t), gamma(n+1)/2*((s-a)**(-n-1)+(s+a)**(-n-1)),
+         n > -1, Abs(a), dco),  # 4.9.19
+        # TODO
+        # (sinh(2*sqrt(a*t)), sqrt(pi*a)/s/sqrt(s)*exp(a/s),
+        #  S.true, S.Zero, dco),  # 4.9.34
+        # (cosh(2*sqrt(a*t)), 1/s+sqrt(pi*a)/s/sqrt(s)*exp(a/s)*erf(sqrt(a/s)),
+        #  S.true, S.Zero, dco),  # 4.9.35
+        # (
+        #     sqrt(t)*sinh(2*sqrt(a*t)),
+        #     pi**(S(1)/2)*s**(-S(5)/2)*(s/2+a) *
+        #     exp(a/s)*erf(sqrt(a/s))-a**(S(1)/2)*s**(-2),
+        #     S.true, S.Zero, dco),  # 4.9.36
+        # (sqrt(t)*cosh(2*sqrt(a*t)), pi**(S(1)/2)*s**(-S(5)/2)*(s/2+a)*exp(a/s),
+        #   S.true, S.Zero, dco),  # 4.9.37
+        # (sinh(2*sqrt(a*t))/sqrt(t),
+        #  pi**(S(1)/2)*s**(-S(1)/2)*exp(a/s) * erf(sqrt(a/s)),
+        #     S.true, S.Zero, dco),  # 4.9.38
+        # (cosh(2*sqrt(a*t))/sqrt(t), pi**(S(1)/2)*s**(-S(1)/2)*exp(a/s),
+        #  S.true, S.Zero, dco),  # 4.9.39
+        # (sinh(sqrt(a*t))**2/sqrt(t), pi**(S(1)/2)/2*s**(-S(1)/2)*(exp(a/s)-1),
+        #  S.true, S.Zero, dco),  # 4.9.40
+        # (cosh(sqrt(a*t))**2/sqrt(t), pi**(S(1)/2)/2*s**(-S(1)/2)*(exp(a/s)+1),
+        #  S.true, S.Zero, dco),  # 4.9.41
+        (erf(a*t), exp(s**2/(2*a)**2)*erfc(s/(2*a))/s,
+         4*Abs(arg(a)) < pi, S.Zero, dco),  # 4.12.2
+        # (erf(sqrt(a*t)), sqrt(a)/sqrt(s+a)/s,
+        #  S.true, Max(S.Zero, -re(a)), dco),  # 4.12.4
+        # (exp(a*t)*erf(sqrt(a*t)), sqrt(a)/sqrt(s)/(s-a),
+        #  S.true, Max(S.Zero, re(a)), dco),  # 4.12.5
+        # (erf(sqrt(a/t)/2), (1-exp(-sqrt(a*s)))/s,
+        #  re(a) > 0, S.Zero, dco),  # 4.12.6
+        # (erfc(sqrt(a*t)), (sqrt(s+a)-sqrt(a))/sqrt(s+a)/s,
+        #  S.true, -re(a), dco),  # 4.12.9
+        # (exp(a*t)*erfc(sqrt(a*t)), 1/(s+sqrt(a*s)),
+        #  S.true, S.Zero, dco),  # 4.12.10
+        # (erfc(sqrt(a/t)/2), exp(-sqrt(a*s))/s,
+        #  re(a) > 0, S.Zero, dco),  # 4.2.11
+        (besselj(n, a*t), a**n/(sqrt(s**2+a**2)*(s+sqrt(s**2+a**2))**n),
+         re(n) > -1, Abs(im(a)), dco),  # 4.14.1
+        (t**b*besselj(n, a*t),
+         2**n/sqrt(pi)*gamma(n+S.Half)*a**n*(s**2+a**2)**(-n-S.Half),
+         And(re(n) > -S.Half, Eq(b, n)), Abs(im(a)), dco),  # 4.14.7
+        (t**b*besselj(n, a*t),
+         2**(n+1)/sqrt(pi)*gamma(n+S(3)/2)*a**n*s*(s**2+a**2)**(-n-S(3)/2),
+         And(re(n) > -1, Eq(b, n+1)), Abs(im(a)), dco),  # 4.14.8
+        # (besselj(0, 2*sqrt(a*t)), exp(-a/s)/s,
+        #  S.true, S.Zero, dco),  # 4.14.25
+        # (t**(b)*besselj(n, 2*sqrt(a*t)), a**(n/2)*s**(-n-1)*exp(-a/s),
+        #  And(re(n) > -1, Eq(b, n*S.Half)), S.Zero, dco),  # 4.14.30
+        (besselj(0, a*sqrt(t**2+b*t)),
+         exp(b*s-b*sqrt(s**2+a**2))/sqrt(s**2+a**2),
+         Abs(arg(b)) < pi, Abs(im(a)), dco),  # 4.15.19
+        (besseli(n, a*t), a**n/(sqrt(s**2-a**2)*(s+sqrt(s**2-a**2))**n),
+         re(n) > -1, Abs(re(a)), dco),  # 4.16.1
+        (t**b*besseli(n, a*t),
+         2**n/sqrt(pi)*gamma(n+S.Half)*a**n*(s**2-a**2)**(-n-S.Half),
+         And(re(n) > -S.Half, Eq(b, n)), Abs(re(a)), dco),  # 4.16.6
+        (t**b*besseli(n, a*t),
+         2**(n+1)/sqrt(pi)*gamma(n+S(3)/2)*a**n*s*(s**2-a**2)**(-n-S(3)/2),
+         And(re(n) > -1, Eq(b, n+1)), Abs(re(a)), dco),  # 4.16.7
+        # (t**(b)*besseli(n, 2*sqrt(a*t)), a**(n/2)*s**(-n-1)*exp(a/s),
+        #  And(re(n) > -1, Eq(b, n*S.Half)), S.Zero, dco),  # 4.16.18
+        (bessely(0, a*t), -2/pi*asinh(s/a)/sqrt(s**2+a**2),
+         S.true, Abs(im(a)), dco),  # 4.15.44
+        (besselk(0, a*t), log((s + sqrt(s**2-a**2))/a)/(sqrt(s**2-a**2)),
+         S.true, -re(a), dco)  # 4.16.23
+    ]
+    return laplace_transform_rules, t, s
+
+
+@DEBUG_WRAP
+def _laplace_rule_timescale(f, t, s):
+    """
+    This function applies the time-scaling rule of the Laplace transform in
+    a straight-forward way. For example, if it gets ``(f(a*t), t, s)``, it will
+    compute ``LaplaceTransform(f(t)/a, t, s/a)`` if ``a>0``.
+    """
+
+    a = Wild('a', exclude=[t])
+    g = WildFunction('g', nargs=1)
+    ma1 = f.match(g)
+    if ma1:
+        arg = ma1[g].args[0].collect(t)
+        ma2 = arg.match(a*t)
+        if ma2 and ma2[a].is_positive and ma2[a] != 1:
+            _debug('     rule: time scaling (4.1.4)')
+            r, pr, cr = _laplace_transform(
+                1/ma2[a]*ma1[g].func(t), t, s/ma2[a], simplify=False)
+            return (r, pr, cr)
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_rule_heaviside(f, t, s):
+    """
+    This function deals with time-shifted Heaviside step functions. If the time
+    shift is positive, it applies the time-shift rule of the Laplace transform.
+    For example, if it gets ``(Heaviside(t-a)*f(t), t, s)``, it will compute
+    ``exp(-a*s)*LaplaceTransform(f(t+a), t, s)``.
+
+    If the time shift is negative, the Heaviside function is simply removed
+    as it means nothing to the Laplace transform.
+
+    The function does not remove a factor ``Heaviside(t)``; this is done by
+    the simple rules.
+    """
+
+    a = Wild('a', exclude=[t])
+    y = Wild('y')
+    g = Wild('g')
+    if ma1 := f.match(Heaviside(y) * g):
+        if ma2 := ma1[y].match(t - a):
+            if ma2[a].is_positive:
+                _debug('     rule: time shift (4.1.4)')
+                r, pr, cr = _laplace_transform(
+                    ma1[g].subs(t, t + ma2[a]), t, s, simplify=False)
+                return (exp(-ma2[a] * s) * r, pr, cr)
+            if ma2[a].is_negative:
+                _debug(
+                    '     rule: Heaviside factor; negative time shift (4.1.4)')
+                r, pr, cr = _laplace_transform(ma1[g], t, s, simplify=False)
+                return (r, pr, cr)
+        if ma2 := ma1[y].match(a - t):
+            if ma2[a].is_positive:
+                _debug('     rule: Heaviside window open')
+                r, pr, cr = _laplace_transform(
+                    (1 - Heaviside(t - ma2[a])) * ma1[g], t, s, simplify=False)
+                return (r, pr, cr)
+            if ma2[a].is_negative:
+                _debug('     rule: Heaviside window closed')
+                return (0, 0, S.true)
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_rule_exp(f, t, s):
+    """
+    If this function finds a factor ``exp(a*t)``, it applies the
+    frequency-shift rule of the Laplace transform and adjusts the convergence
+    plane accordingly.  For example, if it gets ``(exp(-a*t)*f(t), t, s)``, it
+    will compute ``LaplaceTransform(f(t), t, s+a)``.
+    """
+
+    a = Wild('a', exclude=[t])
+    y = Wild('y')
+    z = Wild('z')
+    ma1 = f.match(exp(y)*z)
+    if ma1:
+        ma2 = ma1[y].collect(t).match(a*t)
+        if ma2:
+            _debug('     rule: multiply with exp (4.1.5)')
+            r, pr, cr = _laplace_transform(ma1[z], t, s-ma2[a],
+                                           simplify=False)
+            return (r, pr+re(ma2[a]), cr)
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_rule_delta(f, t, s):
+    """
+    If this function finds a factor ``DiracDelta(b*t-a)``, it applies the
+    masking property of the delta distribution. For example, if it gets
+    ``(DiracDelta(t-a)*f(t), t, s)``, it will return
+    ``(f(a)*exp(-a*s), -a, True)``.
+    """
+    # This rule is not in Bateman54
+
+    a = Wild('a', exclude=[t])
+    b = Wild('b', exclude=[t])
+
+    y = Wild('y')
+    z = Wild('z')
+    ma1 = f.match(DiracDelta(y)*z)
+    if ma1 and not ma1[z].has(DiracDelta):
+        ma2 = ma1[y].collect(t).match(b*t-a)
+        if ma2:
+            _debug('     rule: multiply with DiracDelta')
+            loc = ma2[a]/ma2[b]
+            if re(loc) >= 0 and im(loc) == 0:
+                fn = exp(-ma2[a]/ma2[b]*s)*ma1[z]
+                if fn.has(sin, cos):
+                    # Then it may be possible that a sinc() is present in the
+                    # term; let's try this:
+                    fn = fn.rewrite(sinc).ratsimp()
+                n, d = [x.subs(t, ma2[a]/ma2[b]) for x in fn.as_numer_denom()]
+                if d != 0:
+                    return (n/d/ma2[b], S.NegativeInfinity, S.true)
+                else:
+                    return None
+            else:
+                return (0, S.NegativeInfinity, S.true)
+        if ma1[y].is_polynomial(t):
+            ro = roots(ma1[y], t)
+            if ro != {} and set(ro.values()) == {1}:
+                slope = diff(ma1[y], t)
+                r = Add(
+                    *[exp(-x*s)*ma1[z].subs(t, s)/slope.subs(t, x)
+                      for x in list(ro.keys()) if im(x) == 0 and re(x) >= 0])
+                return (r, S.NegativeInfinity, S.true)
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_trig_split(fn):
+    """
+    Helper function for `_laplace_rule_trig`.  This function returns two terms
+    `f` and `g`.  `f` contains all product terms with sin, cos, sinh, cosh in
+    them; `g` contains everything else.
+    """
+    trigs = [S.One]
+    other = [S.One]
+    for term in Mul.make_args(fn):
+        if term.has(sin, cos, sinh, cosh, exp):
+            trigs.append(term)
+        else:
+            other.append(term)
+    f = Mul(*trigs)
+    g = Mul(*other)
+    return f, g
+
+
+@DEBUG_WRAP
+def _laplace_trig_expsum(f, t):
+    """
+    Helper function for `_laplace_rule_trig`.  This function expects the `f`
+    from `_laplace_trig_split`.  It returns two lists `xm` and `xn`.  `xm` is
+    a list of dictionaries with keys `k` and `a` representing a function
+    `k*exp(a*t)`.  `xn` is a list of all terms that cannot be brought into
+    that form, which may happen, e.g., when a trigonometric function has
+    another function in its argument.
+    """
+    c1 = Wild('c1', exclude=[t])
+    c0 = Wild('c0', exclude=[t])
+    p = Wild('p', exclude=[t])
+    xm = []
+    xn = []
+
+    x1 = f.rewrite(exp).expand()
+
+    for term in Add.make_args(x1):
+        if not term.has(t):
+            xm.append({'k': term, 'a': 0, re: 0, im: 0})
+            continue
+        term = _laplace_deep_collect(term.powsimp(combine='exp'), t)
+
+        if (r := term.match(p*exp(c1*t+c0))) is not None:
+            xm.append({
+                'k': r[p]*exp(r[c0]), 'a': r[c1],
+                re: re(r[c1]), im: im(r[c1])})
+        else:
+            xn.append(term)
+    return xm, xn
+
+
+@DEBUG_WRAP
+def _laplace_trig_ltex(xm, t, s):
+    """
+    Helper function for `_laplace_rule_trig`.  This function takes the list of
+    exponentials `xm` from `_laplace_trig_expsum` and simplifies complex
+    conjugate and real symmetric poles.  It returns the result as a sum and
+    the convergence plane.
+    """
+    results = []
+    planes = []
+
+    def _simpc(coeffs):
+        nc = coeffs.copy()
+        for k in range(len(nc)):
+            ri = nc[k].as_real_imag()
+            if ri[0].has(im):
+                nc[k] = nc[k].rewrite(cos)
+            else:
+                nc[k] = (ri[0] + I*ri[1]).rewrite(cos)
+        return nc
+
+    def _quadpole(t1, k1, k2, k3, s):
+        a, k0, a_r, a_i = t1['a'], t1['k'], t1[re], t1[im]
+        nc = [
+            k0 + k1 + k2 + k3,
+            a*(k0 + k1 - k2 - k3) - 2*I*a_i*k1 + 2*I*a_i*k2,
+            (
+                a**2*(-k0 - k1 - k2 - k3) +
+                a*(4*I*a_i*k0 + 4*I*a_i*k3) +
+                4*a_i**2*k0 + 4*a_i**2*k3),
+            (
+                a**3*(-k0 - k1 + k2 + k3) +
+                a**2*(4*I*a_i*k0 + 2*I*a_i*k1 - 2*I*a_i*k2 - 4*I*a_i*k3) +
+                a*(4*a_i**2*k0 - 4*a_i**2*k3))
+        ]
+        dc = [
+            S.One, S.Zero, 2*a_i**2 - 2*a_r**2,
+            S.Zero, a_i**4 + 2*a_i**2*a_r**2 + a_r**4]
+        n = Add(
+            *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])])
+        d = Add(
+            *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])])
+        return n/d
+
+    def _ccpole(t1, k1, s):
+        a, k0, a_r, a_i = t1['a'], t1['k'], t1[re], t1[im]
+        nc = [k0 + k1, -a*k0 - a*k1 + 2*I*a_i*k0]
+        dc = [S.One, -2*a_r, a_i**2 + a_r**2]
+        n = Add(
+            *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])])
+        d = Add(
+            *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])])
+        return n/d
+
+    def _rspole(t1, k2, s):
+        a, k0, a_r, a_i = t1['a'], t1['k'], t1[re], t1[im]
+        nc = [k0 + k2, a*k0 - a*k2 - 2*I*a_i*k0]
+        dc = [S.One, -2*I*a_i, -a_i**2 - a_r**2]
+        n = Add(
+            *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])])
+        d = Add(
+            *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])])
+        return n/d
+
+    def _sypole(t1, k3, s):
+        a, k0 = t1['a'], t1['k']
+        nc = [k0 + k3, a*(k0 - k3)]
+        dc = [S.One, S.Zero, -a**2]
+        n = Add(
+            *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])])
+        d = Add(
+            *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])])
+        return n/d
+
+    def _simplepole(t1, s):
+        a, k0 = t1['a'], t1['k']
+        n = k0
+        d = s - a
+        return n/d
+
+    while len(xm) > 0:
+        t1 = xm.pop()
+        i_imagsym = None
+        i_realsym = None
+        i_pointsym = None
+        # The following code checks all remaining poles. If t1 is a pole at
+        # a+b*I, then we check for a-b*I, -a+b*I, and -a-b*I, and
+        # assign the respective indices to i_imagsym, i_realsym, i_pointsym.
+        # -a-b*I / i_pointsym only applies if both a and b are != 0.
+        for i in range(len(xm)):
+            real_eq = t1[re] == xm[i][re]
+            realsym = t1[re] == -xm[i][re]
+            imag_eq = t1[im] == xm[i][im]
+            imagsym = t1[im] == -xm[i][im]
+            if realsym and imagsym and t1[re] != 0 and t1[im] != 0:
+                i_pointsym = i
+            elif realsym and imag_eq and t1[re] != 0:
+                i_realsym = i
+            elif real_eq and imagsym and t1[im] != 0:
+                i_imagsym = i
+
+        # The next part looks for four possible pole constellations:
+        # quad:   a+b*I, a-b*I, -a+b*I, -a-b*I
+        # cc:     a+b*I, a-b*I (a may be zero)
+        # quad:   a+b*I, -a+b*I (b may be zero)
+        # point:  a+b*I, -a-b*I (a!=0 and b!=0 is needed, but that has been
+        #                        asserted when finding i_pointsym above.)
+        # If none apply, then t1 is a simple pole.
+        if (
+                i_imagsym is not None and i_realsym is not None
+                and i_pointsym is not None):
+            results.append(
+                _quadpole(t1,
+                          xm[i_imagsym]['k'], xm[i_realsym]['k'],
+                          xm[i_pointsym]['k'], s))
+            planes.append(Abs(re(t1['a'])))
+            # The three additional poles have now been used; to pop them
+            # easily we have to do it from the back.
+            indices_to_pop = [i_imagsym, i_realsym, i_pointsym]
+            indices_to_pop.sort(reverse=True)
+            for i in indices_to_pop:
+                xm.pop(i)
+        elif i_imagsym is not None:
+            results.append(_ccpole(t1, xm[i_imagsym]['k'], s))
+            planes.append(t1[re])
+            xm.pop(i_imagsym)
+        elif i_realsym is not None:
+            results.append(_rspole(t1, xm[i_realsym]['k'], s))
+            planes.append(Abs(t1[re]))
+            xm.pop(i_realsym)
+        elif i_pointsym is not None:
+            results.append(_sypole(t1, xm[i_pointsym]['k'], s))
+            planes.append(Abs(t1[re]))
+            xm.pop(i_pointsym)
+        else:
+            results.append(_simplepole(t1, s))
+            planes.append(t1[re])
+
+    return Add(*results), Max(*planes)
+
+
+@DEBUG_WRAP
+def _laplace_rule_trig(fn, t_, s):
+    """
+    This rule covers trigonometric factors by splitting everything into a
+    sum of exponential functions and collecting complex conjugate poles and
+    real symmetric poles.
+    """
+    t = Dummy('t', real=True)
+
+    if not fn.has(sin, cos, sinh, cosh):
+        return None
+
+    f, g = _laplace_trig_split(fn.subs(t_, t))
+    xm, xn = _laplace_trig_expsum(f, t)
+
+    if len(xn) > 0:
+        # TODO not implemented yet, but also not important
+        return None
+
+    if not g.has(t):
+        r, p = _laplace_trig_ltex(xm, t, s)
+        return g*r, p, S.true
+    else:
+        # Just transform `g` and make frequency-shifted copies
+        planes = []
+        results = []
+        G, G_plane, G_cond = _laplace_transform(g, t, s, simplify=False)
+        for x1 in xm:
+            results.append(x1['k']*G.subs(s, s-x1['a']))
+            planes.append(G_plane+re(x1['a']))
+    return Add(*results).subs(t, t_), Max(*planes), G_cond
+
+
+@DEBUG_WRAP
+def _laplace_rule_diff(f, t, s):
+    """
+    This function looks for derivatives in the time domain and replaces it
+    by factors of `s` and initial conditions in the frequency domain. For
+    example, if it gets ``(diff(f(t), t), t, s)``, it will compute
+    ``s*LaplaceTransform(f(t), t, s) - f(0)``.
+    """
+
+    a = Wild('a', exclude=[t])
+    n = Wild('n', exclude=[t])
+    g = WildFunction('g')
+    ma1 = f.match(a*Derivative(g, (t, n)))
+    if ma1 and ma1[n].is_integer:
+        m = [z.has(t) for z in ma1[g].args]
+        if sum(m) == 1:
+            _debug('     rule: time derivative (4.1.8)')
+            d = []
+            for k in range(ma1[n]):
+                if k == 0:
+                    y = ma1[g].subs(t, 0)
+                else:
+                    y = Derivative(ma1[g], (t, k)).subs(t, 0)
+                d.append(s**(ma1[n]-k-1)*y)
+            r, pr, cr = _laplace_transform(ma1[g], t, s, simplify=False)
+            return (ma1[a]*(s**ma1[n]*r - Add(*d)),  pr, cr)
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_rule_sdiff(f, t, s):
+    """
+    This function looks for multiplications with polynoimials in `t` as they
+    correspond to differentiation in the frequency domain. For example, if it
+    gets ``(t*f(t), t, s)``, it will compute
+    ``-Derivative(LaplaceTransform(f(t), t, s), s)``.
+    """
+
+    if f.is_Mul:
+        pfac = [1]
+        ofac = [1]
+        for fac in Mul.make_args(f):
+            if fac.is_polynomial(t):
+                pfac.append(fac)
+            else:
+                ofac.append(fac)
+        if len(pfac) > 1:
+            pex = prod(pfac)
+            pc = Poly(pex, t).all_coeffs()
+            N = len(pc)
+            if N > 1:
+                oex = prod(ofac)
+                r_, p_, c_ = _laplace_transform(oex, t, s, simplify=False)
+                deri = [r_]
+                d1 = False
+                try:
+                    d1 = -diff(deri[-1], s)
+                except ValueError:
+                    d1 = False
+                if r_.has(LaplaceTransform):
+                    for k in range(N-1):
+                        deri.append((-1)**(k+1)*Derivative(r_, s, k+1))
+                elif d1:
+                    deri.append(d1)
+                    for k in range(N-2):
+                        deri.append(-diff(deri[-1], s))
+                if d1:
+                    r = Add(*[pc[N-n-1]*deri[n] for n in range(N)])
+                    return (r, p_, c_)
+    # We still have to cover the possibility that there is a symbolic positive
+    # integer exponent.
+    n = Wild('n', exclude=[t])
+    g = Wild('g')
+    if ma1 := f.match(t**n*g):
+        if ma1[n].is_integer and ma1[n].is_positive:
+            r_, p_, c_ = _laplace_transform(ma1[g], t, s, simplify=False)
+            return (-1)**ma1[n]*diff(r_, (s, ma1[n])), p_, c_
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_expand(f, t, s):
+    """
+    This function tries to expand its argument with successively stronger
+    methods: first it will expand on the top level, then it will expand any
+    multiplications in depth, then it will try all available expansion methods,
+    and finally it will try to expand trigonometric functions.
+
+    If it can expand, it will then compute the Laplace transform of the
+    expanded term.
+    """
+
+    r = expand(f, deep=False)
+    if r.is_Add:
+        return _laplace_transform(r, t, s, simplify=False)
+    r = expand_mul(f)
+    if r.is_Add:
+        return _laplace_transform(r, t, s, simplify=False)
+    r = expand(f)
+    if r.is_Add:
+        return _laplace_transform(r, t, s, simplify=False)
+    if r != f:
+        return _laplace_transform(r, t, s, simplify=False)
+    r = expand(expand_trig(f))
+    if r.is_Add:
+        return _laplace_transform(r, t, s, simplify=False)
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_apply_prog_rules(f, t, s):
+    """
+    This function applies all program rules and returns the result if one
+    of them gives a result.
+    """
+
+    prog_rules = [_laplace_rule_heaviside, _laplace_rule_delta,
+                  _laplace_rule_timescale, _laplace_rule_exp,
+                  _laplace_rule_trig,
+                  _laplace_rule_diff, _laplace_rule_sdiff]
+
+    for p_rule in prog_rules:
+        if (L := p_rule(f, t, s)) is not None:
+            return L
+    return None
+
+
+@DEBUG_WRAP
+def _laplace_apply_simple_rules(f, t, s):
+    """
+    This function applies all simple rules and returns the result if one
+    of them gives a result.
+    """
+    simple_rules, t_, s_ = _laplace_build_rules()
+    prep_old = ''
+    prep_f = ''
+    for t_dom, s_dom, check, plane, prep in simple_rules:
+        if prep_old != prep:
+            prep_f = prep(f.subs({t: t_}))
+            prep_old = prep
+        ma = prep_f.match(t_dom)
+        if ma:
+            try:
+                c = check.xreplace(ma)
+            except TypeError:
+                # This may happen if the time function has imaginary
+                # numbers in it. Then we give up.
+                continue
+            if c == S.true:
+                return (s_dom.xreplace(ma).subs({s_: s}),
+                        plane.xreplace(ma), S.true)
+    return None
+
+
+@DEBUG_WRAP
+def _piecewise_to_heaviside(f, t):
+    """
+    This function converts a Piecewise expression to an expression written
+    with Heaviside. It is not exact, but valid in the context of the Laplace
+    transform.
+    """
+    if not t.is_real:
+        r = Dummy('r', real=True)
+        return _piecewise_to_heaviside(f.xreplace({t: r}), r).xreplace({r: t})
+    x = piecewise_exclusive(f)
+    r = []
+    for fn, cond in x.args:
+        # Here we do not need to do many checks because piecewise_exclusive
+        # has a clearly predictable output. However, if any of the conditions
+        # is not relative to t, this function just returns the input argument.
+        if isinstance(cond, Relational) and t in cond.args:
+            if isinstance(cond, (Eq, Ne)):
+                # We do not cover this case; these would be single-point
+                # exceptions that do not play a role in Laplace practice,
+                # except if they contain Dirac impulses, and then we can
+                # expect users to not try to use Piecewise for writing it.
+                return f
+            else:
+                r.append(Heaviside(cond.gts - cond.lts)*fn)
+        elif isinstance(cond, Or) and len(cond.args) == 2:
+            # Or(t<2, t>4), Or(t>4, t<=2), ... in any order with any <= >=
+            for c2 in cond.args:
+                if c2.lhs == t:
+                    r.append(Heaviside(c2.gts - c2.lts)*fn)
+                else:
+                    return f
+        elif isinstance(cond, And) and len(cond.args) == 2:
+            # And(t>2, t<4), And(t>4, t<=2), ...  in any order with any <= >=
+            c0, c1 = cond.args
+            if c0.lhs == t and c1.lhs == t:
+                if '>' in c0.rel_op:
+                    c0, c1 = c1, c0
+                r.append(
+                    (Heaviside(c1.gts - c1.lts) -
+                     Heaviside(c0.lts - c0.gts))*fn)
+            else:
+                return f
+        else:
+            return f
+    return Add(*r)
+
+
+def laplace_correspondence(f, fdict, /):
+    """
+    This helper function takes a function `f` that is the result of a
+    ``laplace_transform`` or an ``inverse_laplace_transform``.  It replaces all
+    unevaluated ``LaplaceTransform(y(t), t, s)`` by `Y(s)` for any `s` and
+    all ``InverseLaplaceTransform(Y(s), s, t)`` by `y(t)` for any `t` if
+    ``fdict`` contains a correspondence ``{y: Y}``.
+
+    Parameters
+    ==========
+
+    f : sympy expression
+        Expression containing unevaluated ``LaplaceTransform`` or
+        ``LaplaceTransform`` objects.
+    fdict : dictionary
+        Dictionary containing one or more function correspondences,
+        e.g., ``{x: X, y: Y}`` meaning that ``X`` and ``Y`` are the
+        Laplace transforms of ``x`` and ``y``, respectively.
+
+    Examples
+    ========
+
+    >>> from sympy import laplace_transform, diff, Function
+    >>> from sympy import laplace_correspondence, inverse_laplace_transform
+    >>> from sympy.abc import t, s
+    >>> y = Function("y")
+    >>> Y = Function("Y")
+    >>> z = Function("z")
+    >>> Z = Function("Z")
+    >>> f = laplace_transform(diff(y(t), t, 1) + z(t), t, s, noconds=True)
+    >>> laplace_correspondence(f, {y: Y, z: Z})
+    s*Y(s) + Z(s) - y(0)
+    >>> f = inverse_laplace_transform(Y(s), s, t)
+    >>> laplace_correspondence(f, {y: Y})
+    y(t)
+    """
+    p = Wild('p')
+    s = Wild('s')
+    t = Wild('t')
+    a = Wild('a')
+    if (
+            not isinstance(f, Expr)
+            or (not f.has(LaplaceTransform)
+                and not f.has(InverseLaplaceTransform))):
+        return f
+    for y, Y in fdict.items():
+        if (
+                (m := f.match(LaplaceTransform(y(a), t, s))) is not None
+                and m[a] == m[t]):
+            return Y(m[s])
+        if (
+                (m := f.match(InverseLaplaceTransform(Y(a), s, t, p)))
+                is not None
+                and m[a] == m[s]):
+            return y(m[t])
+    func = f.func
+    args = [laplace_correspondence(arg, fdict) for arg in f.args]
+    return func(*args)
+
+
+def laplace_initial_conds(f, t, fdict, /):
+    """
+    This helper function takes a function `f` that is the result of a
+    ``laplace_transform``.  It takes an fdict of the form ``{y: [1, 4, 2]}``,
+    where the values in the list are the initial value, the initial slope, the
+    initial second derivative, etc., of the function `y(t)`, and replaces all
+    unevaluated initial conditions.
+
+    Parameters
+    ==========
+
+    f : sympy expression
+        Expression containing initial conditions of unevaluated functions.
+    t : sympy expression
+        Variable for which the initial conditions are to be applied.
+    fdict : dictionary
+        Dictionary containing a list of initial conditions for every
+        function, e.g., ``{y: [0, 1, 2], x: [3, 4, 5]}``. The order
+        of derivatives is ascending, so `0`, `1`, `2` are `y(0)`, `y'(0)`,
+        and `y''(0)`, respectively.
+
+    Examples
+    ========
+
+    >>> from sympy import laplace_transform, diff, Function
+    >>> from sympy import laplace_correspondence, laplace_initial_conds
+    >>> from sympy.abc import t, s
+    >>> y = Function("y")
+    >>> Y = Function("Y")
+    >>> f = laplace_transform(diff(y(t), t, 3), t, s, noconds=True)
+    >>> g = laplace_correspondence(f, {y: Y})
+    >>> laplace_initial_conds(g, t, {y: [2, 4, 8, 16, 32]})
+    s**3*Y(s) - 2*s**2 - 4*s - 8
+    """
+    for y, ic in fdict.items():
+        for k in range(len(ic)):
+            if k == 0:
+                f = f.replace(y(0), ic[0])
+            elif k == 1:
+                f = f.replace(Subs(Derivative(y(t), t), t, 0), ic[1])
+            else:
+                f = f.replace(Subs(Derivative(y(t), (t, k)), t, 0), ic[k])
+    return f
+
+
+@DEBUG_WRAP
+def _laplace_transform(fn, t_, s_, *, simplify):
+    """
+    Front-end function of the Laplace transform. It tries to apply all known
+    rules recursively, and if everything else fails, it tries to integrate.
+    """
+
+    terms_t = Add.make_args(fn)
+    terms_s = []
+    terms = []
+    planes = []
+    conditions = []
+
+    for ff in terms_t:
+        k, ft = ff.as_independent(t_, as_Add=False)
+        if ft.has(SingularityFunction):
+            _terms = Add.make_args(ft.rewrite(Heaviside))
+            for _term in _terms:
+                k1, f1 = _term.as_independent(t_, as_Add=False)
+                terms.append((k*k1, f1))
+        elif ft.func == Piecewise and not ft.has(DiracDelta(t_)):
+            _terms = Add.make_args(_piecewise_to_heaviside(ft, t_))
+            for _term in _terms:
+                k1, f1 = _term.as_independent(t_, as_Add=False)
+                terms.append((k*k1, f1))
+        else:
+            terms.append((k, ft))
+
+    for k, ft in terms:
+        if ft.has(SingularityFunction):
+            r = (LaplaceTransform(ft, t_, s_), S.NegativeInfinity, True)
+        else:
+            if ft.has(Heaviside(t_)) and not ft.has(DiracDelta(t_)):
+                # For t>=0, Heaviside(t)=1 can be used, except if there is also
+                # a DiracDelta(t) present, in which case removing Heaviside(t)
+                # is unnecessary because _laplace_rule_delta can deal with it.
+                ft = ft.subs(Heaviside(t_), 1)
+            if (
+                    (r := _laplace_apply_simple_rules(ft, t_, s_))
+                    is not None or
+                    (r := _laplace_apply_prog_rules(ft, t_, s_))
+                    is not None or
+                    (r := _laplace_expand(ft, t_, s_)) is not None):
+                pass
+            elif any(undef.has(t_) for undef in ft.atoms(AppliedUndef)):
+                # If there are undefined functions f(t) then integration is
+                # unlikely to do anything useful so we skip it and given an
+                # unevaluated LaplaceTransform.
+                r = (LaplaceTransform(ft, t_, s_), S.NegativeInfinity, True)
+            elif (r := _laplace_transform_integration(
+                    ft, t_, s_, simplify=simplify)) is not None:
+                pass
+            else:
+                r = (LaplaceTransform(ft, t_, s_), S.NegativeInfinity, True)
+        (ri_, pi_, ci_) = r
+        terms_s.append(k*ri_)
+        planes.append(pi_)
+        conditions.append(ci_)
+
+    result = Add(*terms_s)
+    if simplify:
+        result = result.simplify(doit=False)
+    plane = Max(*planes)
+    condition = And(*conditions)
+
+    return result, plane, condition
+
+
+class LaplaceTransform(IntegralTransform):
+    """
+    Class representing unevaluated Laplace transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute Laplace transforms, see the :func:`laplace_transform`
+    docstring.
+
+    If this is called with ``.doit()``, it returns the Laplace transform as an
+    expression. If it is called with ``.doit(noconds=False)``, it returns a
+    tuple containing the same expression, a convergence plane, and conditions.
+    """
+
+    _name = 'Laplace'
+
+    def _compute_transform(self, f, t, s, **hints):
+        _simplify = hints.get('simplify', False)
+        LT = _laplace_transform_integration(f, t, s, simplify=_simplify)
+        return LT
+
+    def _as_integral(self, f, t, s):
+        return Integral(f*exp(-s*t), (t, S.Zero, S.Infinity))
+
+    def doit(self, **hints):
+        """
+        Try to evaluate the transform in closed form.
+
+        Explanation
+        ===========
+
+        Standard hints are the following:
+        - ``noconds``:  if True, do not return convergence conditions. The
+        default setting is `True`.
+        - ``simplify``: if True, it simplifies the final result. The
+        default setting is `False`.
+        """
+        _noconds = hints.get('noconds', True)
+        _simplify = hints.get('simplify', False)
+
+        debugf('[LT doit] (%s, %s, %s)', (self.function,
+                                          self.function_variable,
+                                          self.transform_variable))
+
+        t_ = self.function_variable
+        s_ = self.transform_variable
+        fn = self.function
+
+        r = _laplace_transform(fn, t_, s_, simplify=_simplify)
+
+        if _noconds:
+            return r[0]
+        else:
+            return r
+
+
+def laplace_transform(f, t, s, legacy_matrix=True, **hints):
+    r"""
+    Compute the Laplace Transform `F(s)` of `f(t)`,
+
+    .. math :: F(s) = \int_{0^{-}}^\infty e^{-st} f(t) \mathrm{d}t.
+
+    Explanation
+    ===========
+
+    For all sensible functions, this converges absolutely in a
+    half-plane
+
+    .. math :: a < \operatorname{Re}(s)
+
+    This function returns ``(F, a, cond)`` where ``F`` is the Laplace
+    transform of ``f``, `a` is the half-plane of convergence, and `cond` are
+    auxiliary convergence conditions.
+
+    The implementation is rule-based, and if you are interested in which
+    rules are applied, and whether integration is attempted, you can switch
+    debug information on by setting ``sympy.SYMPY_DEBUG=True``. The numbers
+    of the rules in the debug information (and the code) refer to Bateman's
+    Tables of Integral Transforms [1].
+
+    The lower bound is `0-`, meaning that this bound should be approached
+    from the lower side. This is only necessary if distributions are involved.
+    At present, it is only done if `f(t)` contains ``DiracDelta``, in which
+    case the Laplace transform is computed implicitly as
+
+    .. math ::
+        F(s) = \lim_{\tau\to 0^{-}} \int_{\tau}^\infty e^{-st}
+        f(t) \mathrm{d}t
+
+    by applying rules.
+
+    If the Laplace transform cannot be fully computed in closed form, this
+    function returns expressions containing unevaluated
+    :class:`LaplaceTransform` objects.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`. If
+    ``noconds=True``, only `F` will be returned (i.e. not ``cond``, and also
+    not the plane ``a``).
+
+    .. deprecated:: 1.9
+        Legacy behavior for matrices where ``laplace_transform`` with
+        ``noconds=False`` (the default) returns a Matrix whose elements are
+        tuples. The behavior of ``laplace_transform`` for matrices will change
+        in a future release of SymPy to return a tuple of the transformed
+        Matrix and the convergence conditions for the matrix as a whole. Use
+        ``legacy_matrix=False`` to enable the new behavior.
+
+    Examples
+    ========
+
+    >>> from sympy import DiracDelta, exp, laplace_transform
+    >>> from sympy.abc import t, s, a
+    >>> laplace_transform(t**4, t, s)
+    (24/s**5, 0, True)
+    >>> laplace_transform(t**a, t, s)
+    (gamma(a + 1)/(s*s**a), 0, re(a) > -1)
+    >>> laplace_transform(DiracDelta(t)-a*exp(-a*t), t, s, simplify=True)
+    (s/(a + s), -re(a), True)
+
+    There are also helper functions that make it easy to solve differential
+    equations by Laplace transform. For example, to solve
+
+    .. math :: m x''(t) + d x'(t) + k x(t) = 0
+
+    with initial value `0` and initial derivative `v`:
+
+    >>> from sympy import Function, laplace_correspondence, diff, solve
+    >>> from sympy import laplace_initial_conds, inverse_laplace_transform
+    >>> from sympy.abc import d, k, m, v
+    >>> x = Function('x')
+    >>> X = Function('X')
+    >>> f = m*diff(x(t), t, 2) + d*diff(x(t), t) + k*x(t)
+    >>> F = laplace_transform(f, t, s, noconds=True)
+    >>> F = laplace_correspondence(F, {x: X})
+    >>> F = laplace_initial_conds(F, t, {x: [0, v]})
+    >>> F
+    d*s*X(s) + k*X(s) + m*(s**2*X(s) - v)
+    >>> Xs = solve(F, X(s))[0]
+    >>> Xs
+    m*v/(d*s + k + m*s**2)
+    >>> inverse_laplace_transform(Xs, s, t)
+    2*v*exp(-d*t/(2*m))*sin(t*sqrt((-d**2 + 4*k*m)/m**2)/2)*Heaviside(t)/sqrt((-d**2 + 4*k*m)/m**2)
+
+    References
+    ==========
+
+    .. [1] Erdelyi, A. (ed.), Tables of Integral Transforms, Volume 1,
+           Bateman Manuscript Prooject, McGraw-Hill (1954), available:
+           https://resolver.caltech.edu/CaltechAUTHORS:20140123-101456353
+
+    See Also
+    ========
+
+    inverse_laplace_transform, mellin_transform, fourier_transform
+    hankel_transform, inverse_hankel_transform
+
+    """
+
+    _noconds = hints.get('noconds', False)
+    _simplify = hints.get('simplify', False)
+
+    if isinstance(f, MatrixBase) and hasattr(f, 'applyfunc'):
+
+        conds = not hints.get('noconds', False)
+
+        if conds and legacy_matrix:
+            adt = 'deprecated-laplace-transform-matrix'
+            sympy_deprecation_warning(
+                """
+Calling laplace_transform() on a Matrix with noconds=False (the default) is
+deprecated. Either noconds=True or use legacy_matrix=False to get the new
+behavior.
+                """,
+                deprecated_since_version='1.9',
+                active_deprecations_target=adt,
+            )
+            # Temporarily disable the deprecation warning for non-Expr objects
+            # in Matrix
+            with ignore_warnings(SymPyDeprecationWarning):
+                return f.applyfunc(
+                    lambda fij: laplace_transform(fij, t, s, **hints))
+        else:
+            elements_trans = [laplace_transform(
+                fij, t, s, **hints) for fij in f]
+            if conds:
+                elements, avals, conditions = zip(*elements_trans)
+                f_laplace = type(f)(*f.shape, elements)
+                return f_laplace, Max(*avals), And(*conditions)
+            else:
+                return type(f)(*f.shape, elements_trans)
+
+    LT, p, c = LaplaceTransform(f, t, s).doit(noconds=False,
+                                              simplify=_simplify)
+
+    if not _noconds:
+        return LT, p, c
+    else:
+        return LT
+
+
+@DEBUG_WRAP
+def _inverse_laplace_transform_integration(F, s, t_, plane, *, simplify):
+    """ The backend function for inverse Laplace transforms. """
+    from sympy.integrals.meijerint import meijerint_inversion, _get_coeff_exp
+    from sympy.integrals.transforms import inverse_mellin_transform
+
+    # There are two strategies we can try:
+    # 1) Use inverse mellin transform, related by a simple change of variables.
+    # 2) Use the inversion integral.
+
+    t = Dummy('t', real=True)
+
+    def pw_simp(*args):
+        """ Simplify a piecewise expression from hyperexpand. """
+        if len(args) != 3:
+            return Piecewise(*args)
+        arg = args[2].args[0].argument
+        coeff, exponent = _get_coeff_exp(arg, t)
+        e1 = args[0].args[0]
+        e2 = args[1].args[0]
+        return (
+            Heaviside(1/Abs(coeff) - t**exponent)*e1 +
+            Heaviside(t**exponent - 1/Abs(coeff))*e2)
+
+    if F.is_rational_function(s):
+        F = F.apart(s)
+
+    if F.is_Add:
+        f = Add(
+            *[_inverse_laplace_transform_integration(X, s, t, plane, simplify)
+              for X in F.args])
+        return _simplify(f.subs(t, t_), simplify), True
+
+    try:
+        f, cond = inverse_mellin_transform(F, s, exp(-t), (None, S.Infinity),
+                                           needeval=True, noconds=False)
+    except IntegralTransformError:
+        f = None
+
+    if f is None:
+        f = meijerint_inversion(F, s, t)
+        if f is None:
+            return None
+        if f.is_Piecewise:
+            f, cond = f.args[0]
+            if f.has(Integral):
+                return None
+        else:
+            cond = S.true
+        f = f.replace(Piecewise, pw_simp)
+
+    if f.is_Piecewise:
+        # many of the functions called below can't work with piecewise
+        # (b/c it has a bool in args)
+        return f.subs(t, t_), cond
+
+    u = Dummy('u')
+
+    def simp_heaviside(arg, H0=S.Half):
+        a = arg.subs(exp(-t), u)
+        if a.has(t):
+            return Heaviside(arg, H0)
+        from sympy.solvers.inequalities import _solve_inequality
+        rel = _solve_inequality(a > 0, u)
+        if rel.lts == u:
+            k = log(rel.gts)
+            return Heaviside(t + k, H0)
+        else:
+            k = log(rel.lts)
+            return Heaviside(-(t + k), H0)
+
+    f = f.replace(Heaviside, simp_heaviside)
+
+    def simp_exp(arg):
+        return expand_complex(exp(arg))
+
+    f = f.replace(exp, simp_exp)
+
+    return _simplify(f.subs(t, t_), simplify), cond
+
+
+@DEBUG_WRAP
+def _complete_the_square_in_denom(f, s):
+    from sympy.simplify.radsimp import fraction
+    [n, d] = fraction(f)
+    if d.is_polynomial(s):
+        cf = d.as_poly(s).all_coeffs()
+        if len(cf) == 3:
+            a, b, c = cf
+            d = a*((s+b/(2*a))**2+c/a-(b/(2*a))**2)
+    return n/d
+
+
+@cacheit
+def _inverse_laplace_build_rules():
+    """
+    This is an internal helper function that returns the table of inverse
+    Laplace transform rules in terms of the time variable `t` and the
+    frequency variable `s`.  It is used by `_inverse_laplace_apply_rules`.
+    """
+    s = Dummy('s')
+    t = Dummy('t')
+    a = Wild('a', exclude=[s])
+    b = Wild('b', exclude=[s])
+    c = Wild('c', exclude=[s])
+
+    _debug('_inverse_laplace_build_rules is building rules')
+
+    def _frac(f, s):
+        try:
+            return f.factor(s)
+        except PolynomialError:
+            return f
+
+    def same(f): return f
+    # This list is sorted according to the prep function needed.
+    _ILT_rules = [
+        (a/s, a, S.true, same, 1),
+        (
+            b*(s+a)**(-c), t**(c-1)*exp(-a*t)/gamma(c),
+            S.true, same, 1),
+        (1/(s**2+a**2)**2, (sin(a*t) - a*t*cos(a*t))/(2*a**3),
+         S.true, same, 1),
+        # The next two rules must be there in that order. For the second
+        # one, the condition would be a != 0 or, respectively, to take the
+        # limit a -> 0 after the transform if a == 0. It is much simpler if
+        # the case a == 0 has its own rule.
+        (1/(s**b), t**(b - 1)/gamma(b), S.true, same, 1),
+        (1/(s*(s+a)**b), lowergamma(b, a*t)/(a**b*gamma(b)),
+         S.true, same, 1)
+    ]
+    return _ILT_rules, s, t
+
+
+@DEBUG_WRAP
+def _inverse_laplace_apply_simple_rules(f, s, t):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    if f == 1:
+        _debug('     rule: 1 o---o DiracDelta()')
+        return DiracDelta(t), S.true
+
+    _ILT_rules, s_, t_ = _inverse_laplace_build_rules()
+    _prep = ''
+    fsubs = f.subs({s: s_})
+
+    for s_dom, t_dom, check, prep, fac in _ILT_rules:
+        if _prep != (prep, fac):
+            _F = prep(fsubs*fac)
+            _prep = (prep, fac)
+        ma = _F.match(s_dom)
+        if ma:
+            c = check
+            if c is not S.true:
+                args = [x.xreplace(ma) for x in c[0]]
+                c = c[1](*args)
+            if c == S.true:
+                return Heaviside(t)*t_dom.xreplace(ma).subs({t_: t}), S.true
+
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_diff(f, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    a = Wild('a', exclude=[s])
+    n = Wild('n', exclude=[s])
+    g = Wild('g')
+    ma = f.match(a*Derivative(g, (s, n)))
+    if ma and ma[n].is_integer:
+        _debug('     rule: t**n*f(t) o---o (-1)**n*diff(F(s), s, n)')
+        r, c = _inverse_laplace_transform(
+            ma[g], s, t, plane, simplify=False, dorational=False)
+        return (-t)**ma[n]*r, c
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_time_shift(F, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    a = Wild('a', exclude=[s])
+    g = Wild('g')
+
+    if not F.has(s):
+        return F*DiracDelta(t), S.true
+    if not F.has(exp):
+        return None
+
+    ma1 = F.match(exp(a*s))
+    if ma1:
+        if ma1[a].is_negative:
+            _debug('     rule: exp(-a*s) o---o DiracDelta(t-a)')
+            return DiracDelta(t+ma1[a]), S.true
+        else:
+            return InverseLaplaceTransform(F, s, t, plane), S.true
+
+    ma1 = F.match(exp(a*s)*g)
+    if ma1:
+        if ma1[a].is_negative:
+            _debug('     rule: exp(-a*s)*F(s) o---o Heaviside(t-a)*f(t-a)')
+            return _inverse_laplace_transform(
+                ma1[g], s, t+ma1[a], plane, simplify=False, dorational=True)
+        else:
+            return InverseLaplaceTransform(F, s, t, plane), S.true
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_freq_shift(F, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    if not F.has(s):
+        return F*DiracDelta(t), S.true
+    if len(args := F.args) == 1:
+        a = Wild('a', exclude=[s])
+        if (ma := args[0].match(s-a)) and re(ma[a]).is_positive:
+            _debug('     rule: F(s-a) o---o exp(-a*t)*f(t)')
+            return (
+                exp(-ma[a]*t) *
+                InverseLaplaceTransform(F.func(s), s, t, plane), S.true)
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_time_diff(F, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    n = Wild('n', exclude=[s])
+    g = Wild('g')
+
+    ma1 = F.match(s**n*g)
+    if ma1 and ma1[n].is_integer and ma1[n].is_positive:
+        _debug('     rule: s**n*F(s) o---o diff(f(t), t, n)')
+        r, c = _inverse_laplace_transform(
+            ma1[g], s, t, plane, simplify=False, dorational=True)
+        r = r.replace(Heaviside(t), 1)
+        if r.has(InverseLaplaceTransform):
+            return diff(r, t, ma1[n]), c
+        else:
+            return Heaviside(t)*diff(r, t, ma1[n]), c
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_irrational(fn, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+
+    a = Wild('a', exclude=[s])
+    b = Wild('b', exclude=[s])
+    m = Wild('m', exclude=[s])
+    n = Wild('n', exclude=[s])
+
+    result = None
+    condition = S.true
+
+    fa = fn.as_ordered_factors()
+
+    ma = [x.match((a*s**m+b)**n) for x in fa]
+
+    if None in ma:
+        return None
+
+    constants = S.One
+    zeros = []
+    poles = []
+    rest = []
+
+    for term in ma:
+        if term[a] == 0:
+            constants = constants*term
+        elif term[n].is_positive:
+            zeros.append(term)
+        elif term[n].is_negative:
+            poles.append(term)
+        else:
+            rest.append(term)
+
+    # The code below assumes that the poles are sorted in a specific way:
+    poles = sorted(poles, key=lambda x: (x[n], x[b] != 0, x[b]))
+    zeros = sorted(zeros, key=lambda x: (x[n], x[b] != 0, x[b]))
+
+    if len(rest) != 0:
+        return None
+
+    if len(poles) == 1 and len(zeros) == 0:
+        if poles[0][n] == -1 and poles[0][m] == S.Half:
+            # 1/(a0*sqrt(s)+b0) == 1/a0 * 1/(sqrt(s)+b0/a0)
+            a_ = poles[0][b]/poles[0][a]
+            k_ = 1/poles[0][a]*constants
+            if a_.is_positive:
+                result = (
+                    k_/sqrt(pi)/sqrt(t) -
+                    k_*a_*exp(a_**2*t)*erfc(a_*sqrt(t)))
+                _debug('     rule 5.3.4')
+        elif poles[0][n] == -2 and poles[0][m] == S.Half:
+            # 1/(a0*sqrt(s)+b0)**2 == 1/a0**2 * 1/(sqrt(s)+b0/a0)**2
+            a_sq = poles[0][b]/poles[0][a]
+            a_ = a_sq**2
+            k_ = 1/poles[0][a]**2*constants
+            if a_sq.is_positive:
+                result = (
+                    k_*(1 - 2/sqrt(pi)*sqrt(a_)*sqrt(t) +
+                        (1-2*a_*t)*exp(a_*t)*(erf(sqrt(a_)*sqrt(t))-1)))
+                _debug('     rule 5.3.10')
+        elif poles[0][n] == -3 and poles[0][m] == S.Half:
+            # 1/(a0*sqrt(s)+b0)**3 == 1/a0**3 * 1/(sqrt(s)+b0/a0)**3
+            a_ = poles[0][b]/poles[0][a]
+            k_ = 1/poles[0][a]**3*constants
+            if a_.is_positive:
+                result = (
+                    k_*(2/sqrt(pi)*(a_**2*t+1)*sqrt(t) -
+                        a_*t*exp(a_**2*t)*(2*a_**2*t+3)*erfc(a_*sqrt(t))))
+                _debug('     rule 5.3.13')
+        elif poles[0][n] == -4 and poles[0][m] == S.Half:
+            # 1/(a0*sqrt(s)+b0)**4 == 1/a0**4 * 1/(sqrt(s)+b0/a0)**4
+            a_ = poles[0][b]/poles[0][a]
+            k_ = 1/poles[0][a]**4*constants/3
+            if a_.is_positive:
+                result = (
+                    k_*(t*(4*a_**4*t**2+12*a_**2*t+3)*exp(a_**2*t) *
+                        erfc(a_*sqrt(t)) -
+                        2/sqrt(pi)*a_**3*t**(S(5)/2)*(2*a_**2*t+5)))
+                _debug('     rule 5.3.16')
+        elif poles[0][n] == -S.Half and poles[0][m] == 2:
+            # 1/sqrt(a0*s**2+b0) == 1/sqrt(a0) * 1/sqrt(s**2+b0/a0)
+            a_ = sqrt(poles[0][b]/poles[0][a])
+            k_ = 1/sqrt(poles[0][a])*constants
+            result = (k_*(besselj(0, a_*t)))
+            _debug('     rule 5.3.35/44')
+
+    elif len(poles) == 1 and len(zeros) == 1:
+        if (
+                poles[0][n] == -3 and poles[0][m] == S.Half and
+                zeros[0][n] == S.Half and zeros[0][b] == 0):
+            # sqrt(az*s)/(ap*sqrt(s+bp)**3)
+            # == sqrt(az)/ap * sqrt(s)/(sqrt(s+bp)**3)
+            a_ = poles[0][b]
+            k_ = sqrt(zeros[0][a])/poles[0][a]*constants
+            result = (
+                k_*(2*a_**4*t**2+5*a_**2*t+1)*exp(a_**2*t) *
+                erfc(a_*sqrt(t)) - 2/sqrt(pi)*a_*(a_**2*t+2)*sqrt(t))
+            _debug('     rule 5.3.14')
+        if (
+                poles[0][n] == -1 and poles[0][m] == 1 and
+                zeros[0][n] == S.Half and zeros[0][m] == 1):
+            # sqrt(az*s+bz)/(ap*s+bp)
+            # == sqrt(az)/ap * (sqrt(s+bz/az)/(s+bp/ap))
+            a_ = zeros[0][b]/zeros[0][a]
+            b_ = poles[0][b]/poles[0][a]
+            k_ = sqrt(zeros[0][a])/poles[0][a]*constants
+            result = (
+                k_*(exp(-a_*t)/sqrt(t)/sqrt(pi)+sqrt(a_-b_) *
+                    exp(-b_*t)*erf(sqrt(a_-b_)*sqrt(t))))
+            _debug('     rule 5.3.22')
+
+    elif len(poles) == 2 and len(zeros) == 0:
+        if (
+                poles[0][n] == -1 and poles[0][m] == 1 and
+                poles[1][n] == -S.Half and poles[1][m] == 1 and
+                poles[1][b] == 0):
+            # 1/((a0*s+b0)*sqrt(a1*s))
+            # == 1/(a0*sqrt(a1)) * 1/((s+b0/a0)*sqrt(s))
+            a_ = -poles[0][b]/poles[0][a]
+            k_ = 1/sqrt(poles[1][a])/poles[0][a]*constants
+            if a_.is_positive:
+                result = (k_/sqrt(a_)*exp(a_*t)*erf(sqrt(a_)*sqrt(t)))
+                _debug('     rule 5.3.1')
+        elif (
+                poles[0][n] == -1 and poles[0][m] == 1 and poles[0][b] == 0 and
+                poles[1][n] == -1 and poles[1][m] == S.Half):
+            # 1/(a0*s*(a1*sqrt(s)+b1))
+            # == 1/(a0*a1) * 1/(s*(sqrt(s)+b1/a1))
+            a_ = poles[1][b]/poles[1][a]
+            k_ = 1/poles[0][a]/poles[1][a]/a_*constants
+            if a_.is_positive:
+                result = k_*(1-exp(a_**2*t)*erfc(a_*sqrt(t)))
+                _debug('     rule 5.3.5')
+        elif (
+                poles[0][n] == -1 and poles[0][m] == S.Half and
+                poles[1][n] == -S.Half and poles[1][m] == 1 and
+                poles[1][b] == 0):
+            # 1/((a0*sqrt(s)+b0)*(sqrt(a1*s))
+            # == 1/(a0*sqrt(a1)) * 1/((sqrt(s)+b0/a0)"sqrt(s))
+            a_ = poles[0][b]/poles[0][a]
+            k_ = 1/(poles[0][a]*sqrt(poles[1][a]))*constants
+            if a_.is_positive:
+                result = k_*exp(a_**2*t)*erfc(a_*sqrt(t))
+                _debug('     rule 5.3.7')
+        elif (
+                poles[0][n] == -S(3)/2 and poles[0][m] == 1 and
+                poles[0][b] == 0 and poles[1][n] == -1 and
+                poles[1][m] == S.Half):
+            # 1/((a0**(3/2)*s**(3/2))*(a1*sqrt(s)+b1))
+            # == 1/(a0**(3/2)*a1)  1/((s**(3/2))*(sqrt(s)+b1/a1))
+            # Note that Bateman54 5.3 (8) is incorrect; there (sqrt(p)+a)
+            # should be (sqrt(p)+a)**(-1).
+            a_ = poles[1][b]/poles[1][a]
+            k_ = 1/(poles[0][a]**(S(3)/2)*poles[1][a])/a_**2*constants
+            if a_.is_positive:
+                result = (
+                    k_*(2/sqrt(pi)*a_*sqrt(t)+exp(a_**2*t)*erfc(a_*sqrt(t))-1))
+                _debug('     rule 5.3.8')
+        elif (
+                poles[0][n] == -2 and poles[0][m] == S.Half and
+                poles[1][n] == -1 and poles[1][m] == 1 and
+                poles[1][b] == 0):
+            # 1/((a0*sqrt(s)+b0)**2*a1*s)
+            # == 1/a0**2/a1 * 1/(sqrt(s)+b0/a0)**2/s
+            a_sq = poles[0][b]/poles[0][a]
+            a_ = a_sq**2
+            k_ = 1/poles[0][a]**2/poles[1][a]*constants
+            if a_sq.is_positive:
+                result = (
+                    k_*(1/a_ + (2*t-1/a_)*exp(a_*t)*erfc(sqrt(a_)*sqrt(t)) -
+                        2/sqrt(pi)/sqrt(a_)*sqrt(t)))
+                _debug('     rule 5.3.11')
+        elif (
+                poles[0][n] == -2 and poles[0][m] == S.Half and
+                poles[1][n] == -S.Half and poles[1][m] == 1 and
+                poles[1][b] == 0):
+            # 1/((a0*sqrt(s)+b0)**2*sqrt(a1*s))
+            # == 1/a0**2/sqrt(a1) * 1/(sqrt(s)+b0/a0)**2/sqrt(s)
+            a_ = poles[0][b]/poles[0][a]
+            k_ = 1/poles[0][a]**2/sqrt(poles[1][a])*constants
+            if a_.is_positive:
+                result = (
+                    k_*(2/sqrt(pi)*sqrt(t) -
+                        2*a_*t*exp(a_**2*t)*erfc(a_*sqrt(t))))
+                _debug('     rule 5.3.12')
+        elif (
+                poles[0][n] == -3 and poles[0][m] == S.Half and
+                poles[1][n] == -S.Half and poles[1][m] == 1 and
+                poles[1][b] == 0):
+            # 1 / (sqrt(a1*s)*(a0*sqrt(s+b0)**3))
+            # == 1/(sqrt(a1)*a0) * 1/(sqrt(s)*(sqrt(s+b0)**3))
+            a_ = poles[0][b]
+            k_ = constants/sqrt(poles[1][a])/poles[0][a]
+            result = k_*(
+                (2*a_**2*t+1)*t*exp(a_**2*t)*erfc(a_*sqrt(t)) -
+                2/sqrt(pi)*a_*t**(S(3)/2))
+            _debug('     rule 5.3.15')
+        elif (
+                poles[0][n] == -1 and poles[0][m] == 1 and
+                poles[1][n] == -S.Half and poles[1][m] == 1):
+            # 1 / ( (a0*s+b0)* sqrt(a1*s+b1) )
+            # == 1/(sqrt(a1)*a0) * 1 / ( (s+b0/a0)* sqrt(s+b1/a1) )
+            a_ = poles[0][b]/poles[0][a]
+            b_ = poles[1][b]/poles[1][a]
+            k_ = constants/sqrt(poles[1][a])/poles[0][a]
+            result = k_*(
+                1/sqrt(b_-a_)*exp(-a_*t)*erf(sqrt(b_-a_)*sqrt(t)))
+            _debug('     rule 5.3.23')
+
+    elif len(poles) == 2 and len(zeros) == 1:
+        if (
+                poles[0][n] == -1 and poles[0][m] == 1 and
+                poles[1][n] == -1 and poles[1][m] == S.Half and
+                zeros[0][n] == S.Half and zeros[0][m] == 1 and
+                zeros[0][b] == 0):
+            # sqrt(za0*s)/((a0*s+b0)*(a1*sqrt(s)+b1))
+            # == sqrt(za0)/(a0*a1) * s/((s+b0/a0)*(sqrt(s)+b1/a1))
+            a_sq = poles[1][b]/poles[1][a]
+            a_ = a_sq**2
+            b_ = -poles[0][b]/poles[0][a]
+            k_ = sqrt(zeros[0][a])/poles[0][a]/poles[1][a]/(a_-b_)*constants
+            if a_sq.is_positive and b_.is_positive:
+                result = k_*(
+                    a_*exp(a_*t)*erfc(sqrt(a_)*sqrt(t)) +
+                    sqrt(a_)*sqrt(b_)*exp(b_*t)*erfc(sqrt(b_)*sqrt(t)) -
+                    b_*exp(b_*t))
+                _debug('     rule 5.3.6')
+        elif (
+                poles[0][n] == -1 and poles[0][m] == 1 and
+                poles[0][b] == 0 and poles[1][n] == -1 and
+                poles[1][m] == S.Half and zeros[0][n] == 1 and
+                zeros[0][m] == S.Half):
+            # (az*sqrt(s)+bz)/(a0*s*(a1*sqrt(s)+b1))
+            # == az/a0/a1 * (sqrt(z)+bz/az)/(s*(sqrt(s)+b1/a1))
+            a_num = zeros[0][b]/zeros[0][a]
+            a_ = poles[1][b]/poles[1][a]
+            if a_+a_num == 0:
+                k_ = zeros[0][a]/poles[0][a]/poles[1][a]*constants
+                result = k_*(
+                    2*exp(a_**2*t)*erfc(a_*sqrt(t))-1)
+                _debug('     rule 5.3.17')
+        elif (
+                poles[1][n] == -1 and poles[1][m] == 1 and
+                poles[1][b] == 0 and poles[0][n] == -2 and
+                poles[0][m] == S.Half and zeros[0][n] == 2 and
+                zeros[0][m] == S.Half):
+            # (az*sqrt(s)+bz)**2/(a1*s*(a0*sqrt(s)+b0)**2)
+            # == az**2/a1/a0**2 * (sqrt(z)+bz/az)**2/(s*(sqrt(s)+b0/a0)**2)
+            a_num = zeros[0][b]/zeros[0][a]
+            a_ = poles[0][b]/poles[0][a]
+            if a_+a_num == 0:
+                k_ = zeros[0][a]**2/poles[1][a]/poles[0][a]**2*constants
+                result = k_*(
+                    1 + 8*a_**2*t*exp(a_**2*t)*erfc(a_*sqrt(t)) -
+                    8/sqrt(pi)*a_*sqrt(t))
+                _debug('     rule 5.3.18')
+        elif (
+                poles[1][n] == -1 and poles[1][m] == 1 and
+                poles[1][b] == 0 and poles[0][n] == -3 and
+                poles[0][m] == S.Half and zeros[0][n] == 3 and
+                zeros[0][m] == S.Half):
+            # (az*sqrt(s)+bz)**3/(a1*s*(a0*sqrt(s)+b0)**3)
+            # == az**3/a1/a0**3 * (sqrt(z)+bz/az)**3/(s*(sqrt(s)+b0/a0)**3)
+            a_num = zeros[0][b]/zeros[0][a]
+            a_ = poles[0][b]/poles[0][a]
+            if a_+a_num == 0:
+                k_ = zeros[0][a]**3/poles[1][a]/poles[0][a]**3*constants
+                result = k_*(
+                    2*(8*a_**4*t**2+8*a_**2*t+1)*exp(a_**2*t) *
+                    erfc(a_*sqrt(t))-8/sqrt(pi)*a_*sqrt(t)*(2*a_**2*t+1)-1)
+                _debug('     rule 5.3.19')
+
+    elif len(poles) == 3 and len(zeros) == 0:
+        if (
+                poles[0][n] == -1 and poles[0][b] == 0 and poles[0][m] == 1 and
+                poles[1][n] == -1 and poles[1][m] == 1 and
+                poles[2][n] == -S.Half and poles[2][m] == 1):
+            # 1/((a0*s)*(a1*s+b1)*sqrt(a2*s))
+            # == 1/(a0*a1*sqrt(a2)) * 1/((s)*(s+b1/a1)*sqrt(s))
+            a_ = -poles[1][b]/poles[1][a]
+            k_ = 1/poles[0][a]/poles[1][a]/sqrt(poles[2][a])*constants
+            if a_.is_positive:
+                result = k_ * (
+                    a_**(-S(3)/2) * exp(a_*t) * erf(sqrt(a_)*sqrt(t)) -
+                    2/a_/sqrt(pi)*sqrt(t))
+                _debug('     rule 5.3.2')
+        elif (
+                poles[0][n] == -1 and poles[0][m] == 1 and
+                poles[1][n] == -1 and poles[1][m] == S.Half and
+                poles[2][n] == -S.Half and poles[2][m] == 1 and
+                poles[2][b] == 0):
+            # 1/((a0*s+b0)*(a1*sqrt(s)+b1)*(sqrt(a2)*sqrt(s)))
+            # == 1/(a0*a1*sqrt(a2)) * 1/((s+b0/a0)*(sqrt(s)+b1/a1)*sqrt(s))
+            a_sq = poles[1][b]/poles[1][a]
+            a_ = a_sq**2
+            b_ = -poles[0][b]/poles[0][a]
+            k_ = (
+                1/poles[0][a]/poles[1][a]/sqrt(poles[2][a]) /
+                (sqrt(b_)*(a_-b_)))
+            if a_sq.is_positive and b_.is_positive:
+                result = k_ * (
+                    sqrt(b_)*exp(a_*t)*erfc(sqrt(a_)*sqrt(t)) +
+                    sqrt(a_)*exp(b_*t)*erf(sqrt(b_)*sqrt(t)) -
+                    sqrt(b_)*exp(b_*t))
+                _debug('     rule 5.3.9')
+
+    if result is None:
+        return None
+    else:
+        return Heaviside(t)*result, condition
+
+
+@DEBUG_WRAP
+def _inverse_laplace_early_prog_rules(F, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    prog_rules = [_inverse_laplace_irrational]
+
+    for p_rule in prog_rules:
+        if (r := p_rule(F, s, t, plane)) is not None:
+            return r
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_apply_prog_rules(F, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    prog_rules = [_inverse_laplace_time_shift, _inverse_laplace_freq_shift,
+                  _inverse_laplace_time_diff, _inverse_laplace_diff,
+                  _inverse_laplace_irrational]
+
+    for p_rule in prog_rules:
+        if (r := p_rule(F, s, t, plane)) is not None:
+            return r
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_expand(fn, s, t, plane):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    if fn.is_Add:
+        return None
+    r = expand(fn, deep=False)
+    if r.is_Add:
+        return _inverse_laplace_transform(
+            r, s, t, plane, simplify=False, dorational=True)
+    r = expand_mul(fn)
+    if r.is_Add:
+        return _inverse_laplace_transform(
+            r, s, t, plane, simplify=False, dorational=True)
+    r = expand(fn)
+    if r.is_Add:
+        return _inverse_laplace_transform(
+            r, s, t, plane, simplify=False, dorational=True)
+    if fn.is_rational_function(s):
+        r = fn.apart(s).doit()
+    if r.is_Add:
+        return _inverse_laplace_transform(
+            r, s, t, plane, simplify=False, dorational=True)
+    return None
+
+
+@DEBUG_WRAP
+def _inverse_laplace_rational(fn, s, t, plane, *, simplify):
+    """
+    Helper function for the class InverseLaplaceTransform.
+    """
+    x_ = symbols('x_')
+    f = fn.apart(s)
+    terms = Add.make_args(f)
+    terms_t = []
+    conditions = [S.true]
+    for term in terms:
+        [n, d] = term.as_numer_denom()
+        dc = d.as_poly(s).all_coeffs()
+        dc_lead = dc[0]
+        dc = [x/dc_lead for x in dc]
+        nc = [x/dc_lead for x in n.as_poly(s).all_coeffs()]
+        if len(dc) == 1:
+            N = len(nc)-1
+            for c in enumerate(nc):
+                r = c[1]*DiracDelta(t, N-c[0])
+                terms_t.append(r)
+        elif len(dc) == 2:
+            r = nc[0]*exp(-dc[1]*t)
+            terms_t.append(Heaviside(t)*r)
+        elif len(dc) == 3:
+            a = dc[1]/2
+            b = (dc[2]-a**2).factor()
+            if len(nc) == 1:
+                nc = [S.Zero] + nc
+            l, m = tuple(nc)
+            if b == 0:
+                r = (m*t+l*(1-a*t))*exp(-a*t)
+            else:
+                hyp = False
+                if b.is_negative:
+                    b = -b
+                    hyp = True
+                b2 = list(roots(x_**2-b, x_).keys())[0]
+                bs = sqrt(b).simplify()
+                if hyp:
+                    r = (
+                        l*exp(-a*t)*cosh(b2*t) + (m-a*l) /
+                        bs*exp(-a*t)*sinh(bs*t))
+                else:
+                    r = l*exp(-a*t)*cos(b2*t) + (m-a*l)/bs*exp(-a*t)*sin(bs*t)
+            terms_t.append(Heaviside(t)*r)
+        else:
+            ft, cond = _inverse_laplace_transform(
+                term, s, t, plane, simplify=simplify, dorational=False)
+            terms_t.append(ft)
+            conditions.append(cond)
+
+    result = Add(*terms_t)
+    if simplify:
+        result = result.simplify(doit=False)
+    return result, And(*conditions)
+
+
+@DEBUG_WRAP
+def _inverse_laplace_transform(fn, s_, t_, plane, *, simplify, dorational):
+    """
+    Front-end function of the inverse Laplace transform. It tries to apply all
+    known rules recursively.  If everything else fails, it tries to integrate.
+    """
+    terms = Add.make_args(fn)
+    terms_t = []
+    conditions = []
+
+    for term in terms:
+        if term.has(exp):
+            # Simplify expressions with exp() such that time-shifted
+            # expressions have negative exponents in the numerator instead of
+            # positive exponents in the numerator and denominator; this is a
+            # (necessary) trick. It will, for example, convert
+            # (s**2*exp(2*s) + 4*exp(s) - 4)*exp(-2*s)/(s*(s**2 + 1)) into
+            # (s**2 + 4*exp(-s) - 4*exp(-2*s))/(s*(s**2 + 1))
+            term = term.subs(s_, -s_).together().subs(s_, -s_)
+        k, f = term.as_independent(s_, as_Add=False)
+        if (
+                dorational and term.is_rational_function(s_) and
+                (r := _inverse_laplace_rational(
+                    f, s_, t_, plane, simplify=simplify))
+                is not None or
+                (r := _inverse_laplace_apply_simple_rules(f, s_, t_))
+                is not None or
+                (r := _inverse_laplace_early_prog_rules(f, s_, t_, plane))
+                is not None or
+                (r := _inverse_laplace_expand(f, s_, t_, plane))
+                is not None or
+                (r := _inverse_laplace_apply_prog_rules(f, s_, t_, plane))
+                is not None):
+            pass
+        elif any(undef.has(s_) for undef in f.atoms(AppliedUndef)):
+            # If there are undefined functions f(t) then integration is
+            # unlikely to do anything useful so we skip it and given an
+            # unevaluated LaplaceTransform.
+            r = (InverseLaplaceTransform(f, s_, t_, plane), S.true)
+        elif (
+                r := _inverse_laplace_transform_integration(
+                    f, s_, t_, plane, simplify=simplify)) is not None:
+            pass
+        else:
+            r = (InverseLaplaceTransform(f, s_, t_, plane), S.true)
+        (ri_, ci_) = r
+        terms_t.append(k*ri_)
+        conditions.append(ci_)
+
+    result = Add(*terms_t)
+    if simplify:
+        result = result.simplify(doit=False)
+    condition = And(*conditions)
+
+    return result, condition
+
+
+class InverseLaplaceTransform(IntegralTransform):
+    """
+    Class representing unevaluated inverse Laplace transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute inverse Laplace transforms, see the
+    :func:`inverse_laplace_transform` docstring.
+    """
+
+    _name = 'Inverse Laplace'
+    _none_sentinel = Dummy('None')
+    _c = Dummy('c')
+
+    def __new__(cls, F, s, x, plane, **opts):
+        if plane is None:
+            plane = InverseLaplaceTransform._none_sentinel
+        return IntegralTransform.__new__(cls, F, s, x, plane, **opts)
+
+    @property
+    def fundamental_plane(self):
+        plane = self.args[3]
+        if plane is InverseLaplaceTransform._none_sentinel:
+            plane = None
+        return plane
+
+    def _compute_transform(self, F, s, t, **hints):
+        return _inverse_laplace_transform_integration(
+            F, s, t, self.fundamental_plane, **hints)
+
+    def _as_integral(self, F, s, t):
+        c = self.__class__._c
+        return (
+            Integral(exp(s*t)*F, (s, c - S.ImaginaryUnit*S.Infinity,
+                                  c + S.ImaginaryUnit*S.Infinity)) /
+            (2*S.Pi*S.ImaginaryUnit))
+
+    def doit(self, **hints):
+        """
+        Try to evaluate the transform in closed form.
+
+        Explanation
+        ===========
+
+        Standard hints are the following:
+        - ``noconds``:  if True, do not return convergence conditions. The
+        default setting is `True`.
+        - ``simplify``: if True, it simplifies the final result. The
+        default setting is `False`.
+        """
+        _noconds = hints.get('noconds', True)
+        _simplify = hints.get('simplify', False)
+
+        debugf('[ILT doit] (%s, %s, %s)', (self.function,
+                                           self.function_variable,
+                                           self.transform_variable))
+
+        s_ = self.function_variable
+        t_ = self.transform_variable
+        fn = self.function
+        plane = self.fundamental_plane
+
+        r = _inverse_laplace_transform(
+            fn, s_, t_, plane, simplify=_simplify, dorational=True)
+
+        if _noconds:
+            return r[0]
+        else:
+            return r
+
+
+def inverse_laplace_transform(F, s, t, plane=None, **hints):
+    r"""
+    Compute the inverse Laplace transform of `F(s)`, defined as
+
+    .. math ::
+        f(t) = \frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty} e^{st}
+        F(s) \mathrm{d}s,
+
+    for `c` so large that `F(s)` has no singularites in the
+    half-plane `\operatorname{Re}(s) > c-\epsilon`.
+
+    Explanation
+    ===========
+
+    The plane can be specified by
+    argument ``plane``, but will be inferred if passed as None.
+
+    Under certain regularity conditions, this recovers `f(t)` from its
+    Laplace Transform `F(s)`, for non-negative `t`, and vice
+    versa.
+
+    If the integral cannot be computed in closed form, this function returns
+    an unevaluated :class:`InverseLaplaceTransform` object.
+
+    Note that this function will always assume `t` to be real,
+    regardless of the SymPy assumption on `t`.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+
+    Examples
+    ========
+
+    >>> from sympy import inverse_laplace_transform, exp, Symbol
+    >>> from sympy.abc import s, t
+    >>> a = Symbol('a', positive=True)
+    >>> inverse_laplace_transform(exp(-a*s)/s, s, t)
+    Heaviside(-a + t)
+
+    See Also
+    ========
+
+    laplace_transform
+    hankel_transform, inverse_hankel_transform
+    """
+    _noconds = hints.get('noconds', True)
+    _simplify = hints.get('simplify', False)
+
+    if isinstance(F, MatrixBase) and hasattr(F, 'applyfunc'):
+        return F.applyfunc(
+            lambda Fij: inverse_laplace_transform(Fij, s, t, plane, **hints))
+
+    r, c = InverseLaplaceTransform(F, s, t, plane).doit(
+        noconds=False, simplify=_simplify)
+
+    if _noconds:
+        return r
+    else:
+        return r, c
+
+
+def _fast_inverse_laplace(e, s, t):
+    """Fast inverse Laplace transform of rational function including RootSum"""
+    a, b, n = symbols('a, b, n', cls=Wild, exclude=[s])
+
+    def _ilt(e):
+        if not e.has(s):
+            return e
+        elif e.is_Add:
+            return _ilt_add(e)
+        elif e.is_Mul:
+            return _ilt_mul(e)
+        elif e.is_Pow:
+            return _ilt_pow(e)
+        elif isinstance(e, RootSum):
+            return _ilt_rootsum(e)
+        else:
+            raise NotImplementedError
+
+    def _ilt_add(e):
+        return e.func(*map(_ilt, e.args))
+
+    def _ilt_mul(e):
+        coeff, expr = e.as_independent(s)
+        if expr.is_Mul:
+            raise NotImplementedError
+        return coeff * _ilt(expr)
+
+    def _ilt_pow(e):
+        match = e.match((a*s + b)**n)
+        if match is not None:
+            nm, am, bm = match[n], match[a], match[b]
+            if nm.is_Integer and nm < 0:
+                return t**(-nm-1)*exp(-(bm/am)*t)/(am**-nm*gamma(-nm))
+            if nm == 1:
+                return exp(-(bm/am)*t) / am
+        raise NotImplementedError
+
+    def _ilt_rootsum(e):
+        expr = e.fun.expr
+        [variable] = e.fun.variables
+        return RootSum(e.poly, Lambda(variable, together(_ilt(expr))))
+
+    return _ilt(e)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/manualintegrate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/manualintegrate.py
new file mode 100644
index 0000000000000000000000000000000000000000..2908fb33003ba9c22da47e550edcfea2b41a26a0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/manualintegrate.py
@@ -0,0 +1,2174 @@
+"""Integration method that emulates by-hand techniques.
+
+This module also provides functionality to get the steps used to evaluate a
+particular integral, in the ``integral_steps`` function. This will return
+nested ``Rule`` s representing the integration rules used.
+
+Each ``Rule`` class represents a (maybe parametrized) integration rule, e.g.
+``SinRule`` for integrating ``sin(x)`` and ``ReciprocalSqrtQuadraticRule``
+for integrating ``1/sqrt(a+b*x+c*x**2)``. The ``eval`` method returns the
+integration result.
+
+The ``manualintegrate`` function computes the integral by calling ``eval``
+on the rule returned by ``integral_steps``.
+
+The integrator can be extended with new heuristics and evaluation
+techniques. To do so, extend the ``Rule`` class, implement ``eval`` method,
+then write a function that accepts an ``IntegralInfo`` object and returns
+either a ``Rule`` instance or ``None``. If the new technique requires a new
+match, add the key and call to the antiderivative function to integral_steps.
+To enable simple substitutions, add the match to find_substitutions.
+
+"""
+
+from __future__ import annotations
+from typing import NamedTuple, Type, Callable, Sequence
+from abc import ABC, abstractmethod
+from dataclasses import dataclass
+from collections import defaultdict
+from collections.abc import Mapping
+
+from sympy.core.add import Add
+from sympy.core.cache import cacheit
+from sympy.core.containers import Dict
+from sympy.core.expr import Expr
+from sympy.core.function import Derivative
+from sympy.core.logic import fuzzy_not
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer, Number, E
+from sympy.core.power import Pow
+from sympy.core.relational import Eq, Ne, Boolean
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy, Symbol, Wild
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.hyperbolic import (HyperbolicFunction, csch,
+    cosh, coth, sech, sinh, tanh, asinh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (TrigonometricFunction,
+    cos, sin, tan, cot, csc, sec, acos, asin, atan, acot, acsc, asec)
+from sympy.functions.special.delta_functions import Heaviside, DiracDelta
+from sympy.functions.special.error_functions import (erf, erfi, fresnelc,
+    fresnels, Ci, Chi, Si, Shi, Ei, li)
+from sympy.functions.special.gamma_functions import uppergamma
+from sympy.functions.special.elliptic_integrals import elliptic_e, elliptic_f
+from sympy.functions.special.polynomials import (chebyshevt, chebyshevu,
+    legendre, hermite, laguerre, assoc_laguerre, gegenbauer, jacobi,
+    OrthogonalPolynomial)
+from sympy.functions.special.zeta_functions import polylog
+from .integrals import Integral
+from sympy.logic.boolalg import And
+from sympy.ntheory.factor_ import primefactors
+from sympy.polys.polytools import degree, lcm_list, gcd_list, Poly
+from sympy.simplify.radsimp import fraction
+from sympy.simplify.simplify import simplify
+from sympy.solvers.solvers import solve
+from sympy.strategies.core import switch, do_one, null_safe, condition
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import debug
+
+
+@dataclass
+class Rule(ABC):
+    integrand: Expr
+    variable: Symbol
+
+    @abstractmethod
+    def eval(self) -> Expr:
+        pass
+
+    @abstractmethod
+    def contains_dont_know(self) -> bool:
+        pass
+
+
+@dataclass
+class AtomicRule(Rule, ABC):
+    """A simple rule that does not depend on other rules"""
+    def contains_dont_know(self) -> bool:
+        return False
+
+
+@dataclass
+class ConstantRule(AtomicRule):
+    """integrate(a, x)  ->  a*x"""
+    def eval(self) -> Expr:
+        return self.integrand * self.variable
+
+
+@dataclass
+class ConstantTimesRule(Rule):
+    """integrate(a*f(x), x)  ->  a*integrate(f(x), x)"""
+    constant: Expr
+    other: Expr
+    substep: Rule
+
+    def eval(self) -> Expr:
+        return self.constant * self.substep.eval()
+
+    def contains_dont_know(self) -> bool:
+        return self.substep.contains_dont_know()
+
+
+@dataclass
+class PowerRule(AtomicRule):
+    """integrate(x**a, x)"""
+    base: Expr
+    exp: Expr
+
+    def eval(self) -> Expr:
+        return Piecewise(
+            ((self.base**(self.exp + 1))/(self.exp + 1), Ne(self.exp, -1)),
+            (log(self.base), True),
+        )
+
+
+@dataclass
+class NestedPowRule(AtomicRule):
+    """integrate((x**a)**b, x)"""
+    base: Expr
+    exp: Expr
+
+    def eval(self) -> Expr:
+        m = self.base * self.integrand
+        return Piecewise((m / (self.exp + 1), Ne(self.exp, -1)),
+                         (m * log(self.base), True))
+
+
+@dataclass
+class AddRule(Rule):
+    """integrate(f(x) + g(x), x) -> integrate(f(x), x) + integrate(g(x), x)"""
+    substeps: list[Rule]
+
+    def eval(self) -> Expr:
+        return Add(*(substep.eval() for substep in self.substeps))
+
+    def contains_dont_know(self) -> bool:
+        return any(substep.contains_dont_know() for substep in self.substeps)
+
+
+@dataclass
+class URule(Rule):
+    """integrate(f(g(x))*g'(x), x) -> integrate(f(u), u), u = g(x)"""
+    u_var: Symbol
+    u_func: Expr
+    substep: Rule
+
+    def eval(self) -> Expr:
+        result = self.substep.eval()
+        if self.u_func.is_Pow:
+            base, exp_ = self.u_func.as_base_exp()
+            if exp_ == -1:
+                # avoid needless -log(1/x) from substitution
+                result = result.subs(log(self.u_var), -log(base))
+        return result.subs(self.u_var, self.u_func)
+
+    def contains_dont_know(self) -> bool:
+        return self.substep.contains_dont_know()
+
+
+@dataclass
+class PartsRule(Rule):
+    """integrate(u(x)*v'(x), x) -> u(x)*v(x) - integrate(u'(x)*v(x), x)"""
+    u: Symbol
+    dv: Expr
+    v_step: Rule
+    second_step: Rule | None  # None when is a substep of CyclicPartsRule
+
+    def eval(self) -> Expr:
+        assert self.second_step is not None
+        v = self.v_step.eval()
+        return self.u * v - self.second_step.eval()
+
+    def contains_dont_know(self) -> bool:
+        return self.v_step.contains_dont_know() or (
+            self.second_step is not None and self.second_step.contains_dont_know())
+
+
+@dataclass
+class CyclicPartsRule(Rule):
+    """Apply PartsRule multiple times to integrate exp(x)*sin(x)"""
+    parts_rules: list[PartsRule]
+    coefficient: Expr
+
+    def eval(self) -> Expr:
+        result = []
+        sign = 1
+        for rule in self.parts_rules:
+            result.append(sign * rule.u * rule.v_step.eval())
+            sign *= -1
+        return Add(*result) / (1 - self.coefficient)
+
+    def contains_dont_know(self) -> bool:
+        return any(substep.contains_dont_know() for substep in self.parts_rules)
+
+
+@dataclass
+class TrigRule(AtomicRule, ABC):
+    pass
+
+
+@dataclass
+class SinRule(TrigRule):
+    """integrate(sin(x), x) -> -cos(x)"""
+    def eval(self) -> Expr:
+        return -cos(self.variable)
+
+
+@dataclass
+class CosRule(TrigRule):
+    """integrate(cos(x), x) -> sin(x)"""
+    def eval(self) -> Expr:
+        return sin(self.variable)
+
+
+@dataclass
+class SecTanRule(TrigRule):
+    """integrate(sec(x)*tan(x), x) -> sec(x)"""
+    def eval(self) -> Expr:
+        return sec(self.variable)
+
+
+@dataclass
+class CscCotRule(TrigRule):
+    """integrate(csc(x)*cot(x), x) -> -csc(x)"""
+    def eval(self) -> Expr:
+        return -csc(self.variable)
+
+
+@dataclass
+class Sec2Rule(TrigRule):
+    """integrate(sec(x)**2, x) -> tan(x)"""
+    def eval(self) -> Expr:
+        return tan(self.variable)
+
+
+@dataclass
+class Csc2Rule(TrigRule):
+    """integrate(csc(x)**2, x) -> -cot(x)"""
+    def eval(self) -> Expr:
+        return -cot(self.variable)
+
+
+@dataclass
+class HyperbolicRule(AtomicRule, ABC):
+    pass
+
+
+@dataclass
+class SinhRule(HyperbolicRule):
+    """integrate(sinh(x), x) -> cosh(x)"""
+    def eval(self) -> Expr:
+        return cosh(self.variable)
+
+
+@dataclass
+class CoshRule(HyperbolicRule):
+    """integrate(cosh(x), x) -> sinh(x)"""
+    def eval(self):
+        return sinh(self.variable)
+
+
+@dataclass
+class ExpRule(AtomicRule):
+    """integrate(a**x, x) -> a**x/ln(a)"""
+    base: Expr
+    exp: Expr
+
+    def eval(self) -> Expr:
+        return self.integrand / log(self.base)
+
+
+@dataclass
+class ReciprocalRule(AtomicRule):
+    """integrate(1/x, x) -> ln(x)"""
+    base: Expr
+
+    def eval(self) -> Expr:
+        return log(self.base)
+
+
+@dataclass
+class ArcsinRule(AtomicRule):
+    """integrate(1/sqrt(1-x**2), x) -> asin(x)"""
+    def eval(self) -> Expr:
+        return asin(self.variable)
+
+
+@dataclass
+class ArcsinhRule(AtomicRule):
+    """integrate(1/sqrt(1+x**2), x) -> asin(x)"""
+    def eval(self) -> Expr:
+        return asinh(self.variable)
+
+
+@dataclass
+class ReciprocalSqrtQuadraticRule(AtomicRule):
+    """integrate(1/sqrt(a+b*x+c*x**2), x) -> log(2*sqrt(c)*sqrt(a+b*x+c*x**2)+b+2*c*x)/sqrt(c)"""
+    a: Expr
+    b: Expr
+    c: Expr
+
+    def eval(self) -> Expr:
+        a, b, c, x = self.a, self.b, self.c, self.variable
+        return log(2*sqrt(c)*sqrt(a+b*x+c*x**2)+b+2*c*x)/sqrt(c)
+
+
+@dataclass
+class SqrtQuadraticDenomRule(AtomicRule):
+    """integrate(poly(x)/sqrt(a+b*x+c*x**2), x)"""
+    a: Expr
+    b: Expr
+    c: Expr
+    coeffs: list[Expr]
+
+    def eval(self) -> Expr:
+        a, b, c, coeffs, x = self.a, self.b, self.c, self.coeffs.copy(), self.variable
+        # Integrate poly/sqrt(a+b*x+c*x**2) using recursion.
+        # coeffs are coefficients of the polynomial.
+        # Let I_n = x**n/sqrt(a+b*x+c*x**2), then
+        # I_n = A * x**(n-1)*sqrt(a+b*x+c*x**2) - B * I_{n-1} - C * I_{n-2}
+        # where A = 1/(n*c), B = (2*n-1)*b/(2*n*c), C = (n-1)*a/(n*c)
+        # See https://github.com/sympy/sympy/pull/23608 for proof.
+        result_coeffs = []
+        coeffs = coeffs.copy()
+        for i in range(len(coeffs)-2):
+            n = len(coeffs)-1-i
+            coeff = coeffs[i]/(c*n)
+            result_coeffs.append(coeff)
+            coeffs[i+1] -= (2*n-1)*b/2*coeff
+            coeffs[i+2] -= (n-1)*a*coeff
+        d, e = coeffs[-1], coeffs[-2]
+        s = sqrt(a+b*x+c*x**2)
+        constant = d-b*e/(2*c)
+        if constant == 0:
+            I0 = 0
+        else:
+            step = inverse_trig_rule(IntegralInfo(1/s, x), degenerate=False)
+            I0 = constant*step.eval()
+        return Add(*(result_coeffs[i]*x**(len(coeffs)-2-i)
+                     for i in range(len(result_coeffs))), e/c)*s + I0
+
+
+@dataclass
+class SqrtQuadraticRule(AtomicRule):
+    """integrate(sqrt(a+b*x+c*x**2), x)"""
+    a: Expr
+    b: Expr
+    c: Expr
+
+    def eval(self) -> Expr:
+        step = sqrt_quadratic_rule(IntegralInfo(self.integrand, self.variable), degenerate=False)
+        return step.eval()
+
+
+@dataclass
+class AlternativeRule(Rule):
+    """Multiple ways to do integration."""
+    alternatives: list[Rule]
+
+    def eval(self) -> Expr:
+        return self.alternatives[0].eval()
+
+    def contains_dont_know(self) -> bool:
+        return any(substep.contains_dont_know() for substep in self.alternatives)
+
+
+@dataclass
+class DontKnowRule(Rule):
+    """Leave the integral as is."""
+    def eval(self) -> Expr:
+        return Integral(self.integrand, self.variable)
+
+    def contains_dont_know(self) -> bool:
+        return True
+
+
+@dataclass
+class DerivativeRule(AtomicRule):
+    """integrate(f'(x), x) -> f(x)"""
+    def eval(self) -> Expr:
+        assert isinstance(self.integrand, Derivative)
+        variable_count = list(self.integrand.variable_count)
+        for i, (var, count) in enumerate(variable_count):
+            if var == self.variable:
+                variable_count[i] = (var, count - 1)
+                break
+        return Derivative(self.integrand.expr, *variable_count)
+
+
+@dataclass
+class RewriteRule(Rule):
+    """Rewrite integrand to another form that is easier to handle."""
+    rewritten: Expr
+    substep: Rule
+
+    def eval(self) -> Expr:
+        return self.substep.eval()
+
+    def contains_dont_know(self) -> bool:
+        return self.substep.contains_dont_know()
+
+
+@dataclass
+class CompleteSquareRule(RewriteRule):
+    """Rewrite a+b*x+c*x**2 to a-b**2/(4*c) + c*(x+b/(2*c))**2"""
+    pass
+
+
+@dataclass
+class PiecewiseRule(Rule):
+    subfunctions: Sequence[tuple[Rule, bool | Boolean]]
+
+    def eval(self) -> Expr:
+        return Piecewise(*[(substep.eval(), cond)
+                           for substep, cond in self.subfunctions])
+
+    def contains_dont_know(self) -> bool:
+        return any(substep.contains_dont_know() for substep, _ in self.subfunctions)
+
+
+@dataclass
+class HeavisideRule(Rule):
+    harg: Expr
+    ibnd: Expr
+    substep: Rule
+
+    def eval(self) -> Expr:
+        # If we are integrating over x and the integrand has the form
+        #       Heaviside(m*x+b)*g(x) == Heaviside(harg)*g(symbol)
+        # then there needs to be continuity at -b/m == ibnd,
+        # so we subtract the appropriate term.
+        result = self.substep.eval()
+        return Heaviside(self.harg) * (result - result.subs(self.variable, self.ibnd))
+
+    def contains_dont_know(self) -> bool:
+        return self.substep.contains_dont_know()
+
+
+@dataclass
+class DiracDeltaRule(AtomicRule):
+    n: Expr
+    a: Expr
+    b: Expr
+
+    def eval(self) -> Expr:
+        n, a, b, x = self.n, self.a, self.b, self.variable
+        if n == 0:
+            return Heaviside(a+b*x)/b
+        return DiracDelta(a+b*x, n-1)/b
+
+
+@dataclass
+class TrigSubstitutionRule(Rule):
+    theta: Expr
+    func: Expr
+    rewritten: Expr
+    substep: Rule
+    restriction: bool | Boolean
+
+    def eval(self) -> Expr:
+        theta, func, x = self.theta, self.func, self.variable
+        func = func.subs(sec(theta), 1/cos(theta))
+        func = func.subs(csc(theta), 1/sin(theta))
+        func = func.subs(cot(theta), 1/tan(theta))
+
+        trig_function = list(func.find(TrigonometricFunction))
+        assert len(trig_function) == 1
+        trig_function = trig_function[0]
+        relation = solve(x - func, trig_function)
+        assert len(relation) == 1
+        numer, denom = fraction(relation[0])
+
+        if isinstance(trig_function, sin):
+            opposite = numer
+            hypotenuse = denom
+            adjacent = sqrt(denom**2 - numer**2)
+            inverse = asin(relation[0])
+        elif isinstance(trig_function, cos):
+            adjacent = numer
+            hypotenuse = denom
+            opposite = sqrt(denom**2 - numer**2)
+            inverse = acos(relation[0])
+        else:  # tan
+            opposite = numer
+            adjacent = denom
+            hypotenuse = sqrt(denom**2 + numer**2)
+            inverse = atan(relation[0])
+
+        substitution = [
+            (sin(theta), opposite/hypotenuse),
+            (cos(theta), adjacent/hypotenuse),
+            (tan(theta), opposite/adjacent),
+            (theta, inverse)
+        ]
+        return Piecewise(
+                (self.substep.eval().subs(substitution).trigsimp(), self.restriction) # type: ignore
+        )
+
+    def contains_dont_know(self) -> bool:
+        return self.substep.contains_dont_know()
+
+
+@dataclass
+class ArctanRule(AtomicRule):
+    """integrate(a/(b*x**2+c), x) -> a/b / sqrt(c/b) * atan(x/sqrt(c/b))"""
+    a: Expr
+    b: Expr
+    c: Expr
+
+    def eval(self) -> Expr:
+        a, b, c, x = self.a, self.b, self.c, self.variable
+        return a/b / sqrt(c/b) * atan(x/sqrt(c/b))
+
+
+@dataclass
+class OrthogonalPolyRule(AtomicRule, ABC):
+    n: Expr
+
+
+@dataclass
+class JacobiRule(OrthogonalPolyRule):
+    a: Expr
+    b: Expr
+
+    def eval(self) -> Expr:
+        n, a, b, x = self.n, self.a, self.b, self.variable
+        return Piecewise(
+            (2*jacobi(n + 1, a - 1, b - 1, x)/(n + a + b), Ne(n + a + b, 0)),
+            (x, Eq(n, 0)),
+            ((a + b + 2)*x**2/4 + (a - b)*x/2, Eq(n, 1)))
+
+
+@dataclass
+class GegenbauerRule(OrthogonalPolyRule):
+    a: Expr
+
+    def eval(self) -> Expr:
+        n, a, x = self.n, self.a, self.variable
+        return Piecewise(
+            (gegenbauer(n + 1, a - 1, x)/(2*(a - 1)), Ne(a, 1)),
+            (chebyshevt(n + 1, x)/(n + 1), Ne(n, -1)),
+            (S.Zero, True))
+
+
+@dataclass
+class ChebyshevTRule(OrthogonalPolyRule):
+    def eval(self) -> Expr:
+        n, x = self.n, self.variable
+        return Piecewise(
+            ((chebyshevt(n + 1, x)/(n + 1) -
+              chebyshevt(n - 1, x)/(n - 1))/2, Ne(Abs(n), 1)),
+            (x**2/2, True))
+
+
+@dataclass
+class ChebyshevURule(OrthogonalPolyRule):
+    def eval(self) -> Expr:
+        n, x = self.n, self.variable
+        return Piecewise(
+            (chebyshevt(n + 1, x)/(n + 1), Ne(n, -1)),
+            (S.Zero, True))
+
+
+@dataclass
+class LegendreRule(OrthogonalPolyRule):
+    def eval(self) -> Expr:
+        n, x = self.n, self.variable
+        return(legendre(n + 1, x) - legendre(n - 1, x))/(2*n + 1)
+
+
+@dataclass
+class HermiteRule(OrthogonalPolyRule):
+    def eval(self) -> Expr:
+        n, x = self.n, self.variable
+        return hermite(n + 1, x)/(2*(n + 1))
+
+
+@dataclass
+class LaguerreRule(OrthogonalPolyRule):
+    def eval(self) -> Expr:
+        n, x = self.n, self.variable
+        return laguerre(n, x) - laguerre(n + 1, x)
+
+
+@dataclass
+class AssocLaguerreRule(OrthogonalPolyRule):
+    a: Expr
+
+    def eval(self) -> Expr:
+        return -assoc_laguerre(self.n + 1, self.a - 1, self.variable)
+
+
+@dataclass
+class IRule(AtomicRule, ABC):
+    a: Expr
+    b: Expr
+
+
+@dataclass
+class CiRule(IRule):
+    def eval(self) -> Expr:
+        a, b, x = self.a, self.b, self.variable
+        return cos(b)*Ci(a*x) - sin(b)*Si(a*x)
+
+
+@dataclass
+class ChiRule(IRule):
+    def eval(self) -> Expr:
+        a, b, x = self.a, self.b, self.variable
+        return cosh(b)*Chi(a*x) + sinh(b)*Shi(a*x)
+
+
+@dataclass
+class EiRule(IRule):
+    def eval(self) -> Expr:
+        a, b, x = self.a, self.b, self.variable
+        return exp(b)*Ei(a*x)
+
+
+@dataclass
+class SiRule(IRule):
+    def eval(self) -> Expr:
+        a, b, x = self.a, self.b, self.variable
+        return sin(b)*Ci(a*x) + cos(b)*Si(a*x)
+
+
+@dataclass
+class ShiRule(IRule):
+    def eval(self) -> Expr:
+        a, b, x = self.a, self.b, self.variable
+        return sinh(b)*Chi(a*x) + cosh(b)*Shi(a*x)
+
+
+@dataclass
+class LiRule(IRule):
+    def eval(self) -> Expr:
+        a, b, x = self.a, self.b, self.variable
+        return li(a*x + b)/a
+
+
+@dataclass
+class ErfRule(AtomicRule):
+    a: Expr
+    b: Expr
+    c: Expr
+
+    def eval(self) -> Expr:
+        a, b, c, x = self.a, self.b, self.c, self.variable
+        if a.is_extended_real:
+            return Piecewise(
+                (sqrt(S.Pi)/sqrt(-a)/2 * exp(c - b**2/(4*a)) *
+                    erf((-2*a*x - b)/(2*sqrt(-a))), a < 0),
+                (sqrt(S.Pi)/sqrt(a)/2 * exp(c - b**2/(4*a)) *
+                    erfi((2*a*x + b)/(2*sqrt(a))), True))
+        return sqrt(S.Pi)/sqrt(a)/2 * exp(c - b**2/(4*a)) * \
+                erfi((2*a*x + b)/(2*sqrt(a)))
+
+
+@dataclass
+class FresnelCRule(AtomicRule):
+    a: Expr
+    b: Expr
+    c: Expr
+
+    def eval(self) -> Expr:
+        a, b, c, x = self.a, self.b, self.c, self.variable
+        return sqrt(S.Pi)/sqrt(2*a) * (
+            cos(b**2/(4*a) - c)*fresnelc((2*a*x + b)/sqrt(2*a*S.Pi)) +
+            sin(b**2/(4*a) - c)*fresnels((2*a*x + b)/sqrt(2*a*S.Pi)))
+
+
+@dataclass
+class FresnelSRule(AtomicRule):
+    a: Expr
+    b: Expr
+    c: Expr
+
+    def eval(self) -> Expr:
+        a, b, c, x = self.a, self.b, self.c, self.variable
+        return sqrt(S.Pi)/sqrt(2*a) * (
+            cos(b**2/(4*a) - c)*fresnels((2*a*x + b)/sqrt(2*a*S.Pi)) -
+            sin(b**2/(4*a) - c)*fresnelc((2*a*x + b)/sqrt(2*a*S.Pi)))
+
+
+@dataclass
+class PolylogRule(AtomicRule):
+    a: Expr
+    b: Expr
+
+    def eval(self) -> Expr:
+        return polylog(self.b + 1, self.a * self.variable)
+
+
+@dataclass
+class UpperGammaRule(AtomicRule):
+    a: Expr
+    e: Expr
+
+    def eval(self) -> Expr:
+        a, e, x = self.a, self.e, self.variable
+        return x**e * (-a*x)**(-e) * uppergamma(e + 1, -a*x)/a
+
+
+@dataclass
+class EllipticFRule(AtomicRule):
+    a: Expr
+    d: Expr
+
+    def eval(self) -> Expr:
+        return elliptic_f(self.variable, self.d/self.a)/sqrt(self.a)
+
+
+@dataclass
+class EllipticERule(AtomicRule):
+    a: Expr
+    d: Expr
+
+    def eval(self) -> Expr:
+        return elliptic_e(self.variable, self.d/self.a)*sqrt(self.a)
+
+
+class IntegralInfo(NamedTuple):
+    integrand: Expr
+    symbol: Symbol
+
+
+def manual_diff(f, symbol):
+    """Derivative of f in form expected by find_substitutions
+
+    SymPy's derivatives for some trig functions (like cot) are not in a form
+    that works well with finding substitutions; this replaces the
+    derivatives for those particular forms with something that works better.
+
+    """
+    if f.args:
+        arg = f.args[0]
+        if isinstance(f, tan):
+            return arg.diff(symbol) * sec(arg)**2
+        elif isinstance(f, cot):
+            return -arg.diff(symbol) * csc(arg)**2
+        elif isinstance(f, sec):
+            return arg.diff(symbol) * sec(arg) * tan(arg)
+        elif isinstance(f, csc):
+            return -arg.diff(symbol) * csc(arg) * cot(arg)
+        elif isinstance(f, Add):
+            return sum(manual_diff(arg, symbol) for arg in f.args)
+        elif isinstance(f, Mul):
+            if len(f.args) == 2 and isinstance(f.args[0], Number):
+                return f.args[0] * manual_diff(f.args[1], symbol)
+    return f.diff(symbol)
+
+def manual_subs(expr, *args):
+    """
+    A wrapper for `expr.subs(*args)` with additional logic for substitution
+    of invertible functions.
+    """
+    if len(args) == 1:
+        sequence = args[0]
+        if isinstance(sequence, (Dict, Mapping)):
+            sequence = sequence.items()
+        elif not iterable(sequence):
+            raise ValueError("Expected an iterable of (old, new) pairs")
+    elif len(args) == 2:
+        sequence = [args]
+    else:
+        raise ValueError("subs accepts either 1 or 2 arguments")
+
+    new_subs = []
+    for old, new in sequence:
+        if isinstance(old, log):
+            # If log(x) = y, then exp(a*log(x)) = exp(a*y)
+            # that is, x**a = exp(a*y). Replace nontrivial powers of x
+            # before subs turns them into `exp(y)**a`, but
+            # do not replace x itself yet, to avoid `log(exp(y))`.
+            x0 = old.args[0]
+            expr = expr.replace(lambda x: x.is_Pow and x.base == x0,
+                lambda x: exp(x.exp*new))
+            new_subs.append((x0, exp(new)))
+
+    return expr.subs(list(sequence) + new_subs)
+
+# Method based on that on SIN, described in "Symbolic Integration: The
+# Stormy Decade"
+
+inverse_trig_functions = (atan, asin, acos, acot, acsc, asec)
+
+
+def find_substitutions(integrand, symbol, u_var):
+    results = []
+
+    def test_subterm(u, u_diff):
+        if u_diff == 0:
+            return False
+        substituted = integrand / u_diff
+        debug("substituted: {}, u: {}, u_var: {}".format(substituted, u, u_var))
+        substituted = manual_subs(substituted, u, u_var).cancel()
+
+        if substituted.has_free(symbol):
+            return False
+        # avoid increasing the degree of a rational function
+        if integrand.is_rational_function(symbol) and substituted.is_rational_function(u_var):
+            deg_before = max(degree(t, symbol) for t in integrand.as_numer_denom())
+            deg_after = max(degree(t, u_var) for t in substituted.as_numer_denom())
+            if deg_after > deg_before:
+                return False
+        return substituted.as_independent(u_var, as_Add=False)
+
+    def exp_subterms(term: Expr):
+        linear_coeffs = []
+        terms = []
+        n = Wild('n', properties=[lambda n: n.is_Integer])
+        for exp_ in term.find(exp):
+            arg = exp_.args[0]
+            if symbol not in arg.free_symbols:
+                continue
+            match = arg.match(n*symbol)
+            if match:
+                linear_coeffs.append(match[n])
+            else:
+                terms.append(exp_)
+        if linear_coeffs:
+            terms.append(exp(gcd_list(linear_coeffs)*symbol))
+        return terms
+
+    def possible_subterms(term):
+        if isinstance(term, (TrigonometricFunction, HyperbolicFunction,
+                             *inverse_trig_functions,
+                             exp, log, Heaviside)):
+            return [term.args[0]]
+        elif isinstance(term, (chebyshevt, chebyshevu,
+                        legendre, hermite, laguerre)):
+            return [term.args[1]]
+        elif isinstance(term, (gegenbauer, assoc_laguerre)):
+            return [term.args[2]]
+        elif isinstance(term, jacobi):
+            return [term.args[3]]
+        elif isinstance(term, Mul):
+            r = []
+            for u in term.args:
+                r.append(u)
+                r.extend(possible_subterms(u))
+            return r
+        elif isinstance(term, Pow):
+            r = [arg for arg in term.args if arg.has(symbol)]
+            if term.exp.is_Integer:
+                r.extend([term.base**d for d in primefactors(term.exp)
+                    if 1 < d < abs(term.args[1])])
+                if term.base.is_Add:
+                    r.extend([t for t in possible_subterms(term.base)
+                        if t.is_Pow])
+            return r
+        elif isinstance(term, Add):
+            r = []
+            for arg in term.args:
+                r.append(arg)
+                r.extend(possible_subterms(arg))
+            return r
+        return []
+
+    for u in list(dict.fromkeys(possible_subterms(integrand) + exp_subterms(integrand))):
+        if u == symbol:
+            continue
+        u_diff = manual_diff(u, symbol)
+        new_integrand = test_subterm(u, u_diff)
+        if new_integrand is not False:
+            constant, new_integrand = new_integrand
+            if new_integrand == integrand.subs(symbol, u_var):
+                continue
+            substitution = (u, constant, new_integrand)
+            if substitution not in results:
+                results.append(substitution)
+
+    return results
+
+def rewriter(condition, rewrite):
+    """Strategy that rewrites an integrand."""
+    def _rewriter(integral):
+        integrand, symbol = integral
+        debug("Integral: {} is rewritten with {} on symbol: {}".format(integrand, rewrite, symbol))
+        if condition(*integral):
+            rewritten = rewrite(*integral)
+            if rewritten != integrand:
+                substep = integral_steps(rewritten, symbol)
+                if not isinstance(substep, DontKnowRule) and substep:
+                    return RewriteRule(integrand, symbol, rewritten, substep)
+    return _rewriter
+
+def proxy_rewriter(condition, rewrite):
+    """Strategy that rewrites an integrand based on some other criteria."""
+    def _proxy_rewriter(criteria):
+        criteria, integral = criteria
+        integrand, symbol = integral
+        debug("Integral: {} is rewritten with {} on symbol: {} and criteria: {}".format(integrand, rewrite, symbol, criteria))
+        args = criteria + list(integral)
+        if condition(*args):
+            rewritten = rewrite(*args)
+            if rewritten != integrand:
+                return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol))
+    return _proxy_rewriter
+
+def multiplexer(conditions):
+    """Apply the rule that matches the condition, else None"""
+    def multiplexer_rl(expr):
+        for key, rule in conditions.items():
+            if key(expr):
+                return rule(expr)
+    return multiplexer_rl
+
+def alternatives(*rules):
+    """Strategy that makes an AlternativeRule out of multiple possible results."""
+    def _alternatives(integral):
+        alts = []
+        count = 0
+        debug("List of Alternative Rules")
+        for rule in rules:
+            count = count + 1
+            debug("Rule {}: {}".format(count, rule))
+
+            result = rule(integral)
+            if (result and not isinstance(result, DontKnowRule) and
+                result != integral and result not in alts):
+                alts.append(result)
+        if len(alts) == 1:
+            return alts[0]
+        elif alts:
+            doable = [rule for rule in alts if not rule.contains_dont_know()]
+            if doable:
+                return AlternativeRule(*integral, doable)
+            else:
+                return AlternativeRule(*integral, alts)
+    return _alternatives
+
+def constant_rule(integral):
+    return ConstantRule(*integral)
+
+def power_rule(integral):
+    integrand, symbol = integral
+    base, expt = integrand.as_base_exp()
+
+    if symbol not in expt.free_symbols and isinstance(base, Symbol):
+        if simplify(expt + 1) == 0:
+            return ReciprocalRule(integrand, symbol, base)
+        return PowerRule(integrand, symbol, base, expt)
+    elif symbol not in base.free_symbols and isinstance(expt, Symbol):
+        rule = ExpRule(integrand, symbol, base, expt)
+
+        if fuzzy_not(log(base).is_zero):
+            return rule
+        elif log(base).is_zero:
+            return ConstantRule(1, symbol)
+
+        return PiecewiseRule(integrand, symbol, [
+            (rule, Ne(log(base), 0)),
+            (ConstantRule(1, symbol), True)
+        ])
+
+def exp_rule(integral):
+    integrand, symbol = integral
+    if isinstance(integrand.args[0], Symbol):
+        return ExpRule(integrand, symbol, E, integrand.args[0])
+
+
+def orthogonal_poly_rule(integral):
+    orthogonal_poly_classes = {
+        jacobi: JacobiRule,
+        gegenbauer: GegenbauerRule,
+        chebyshevt: ChebyshevTRule,
+        chebyshevu: ChebyshevURule,
+        legendre: LegendreRule,
+        hermite: HermiteRule,
+        laguerre: LaguerreRule,
+        assoc_laguerre: AssocLaguerreRule
+        }
+    orthogonal_poly_var_index = {
+        jacobi: 3,
+        gegenbauer: 2,
+        assoc_laguerre: 2
+        }
+    integrand, symbol = integral
+    for klass in orthogonal_poly_classes:
+        if isinstance(integrand, klass):
+            var_index = orthogonal_poly_var_index.get(klass, 1)
+            if (integrand.args[var_index] is symbol and not
+                any(v.has(symbol) for v in integrand.args[:var_index])):
+                    return orthogonal_poly_classes[klass](integrand, symbol, *integrand.args[:var_index])
+
+
+_special_function_patterns: list[tuple[Type, Expr, Callable | None, tuple]] = []
+_wilds = []
+_symbol = Dummy('x')
+
+
+def special_function_rule(integral):
+    integrand, symbol = integral
+    if not _special_function_patterns:
+        a = Wild('a', exclude=[_symbol], properties=[lambda x: not x.is_zero])
+        b = Wild('b', exclude=[_symbol])
+        c = Wild('c', exclude=[_symbol])
+        d = Wild('d', exclude=[_symbol], properties=[lambda x: not x.is_zero])
+        e = Wild('e', exclude=[_symbol], properties=[
+            lambda x: not (x.is_nonnegative and x.is_integer)])
+        _wilds.extend((a, b, c, d, e))
+        # patterns consist of a SymPy class, a wildcard expr, an optional
+        # condition coded as a lambda (when Wild properties are not enough),
+        # followed by an applicable rule
+        linear_pattern = a*_symbol + b
+        quadratic_pattern = a*_symbol**2 + b*_symbol + c
+        _special_function_patterns.extend((
+            (Mul, exp(linear_pattern, evaluate=False)/_symbol, None, EiRule),
+            (Mul, cos(linear_pattern, evaluate=False)/_symbol, None, CiRule),
+            (Mul, cosh(linear_pattern, evaluate=False)/_symbol, None, ChiRule),
+            (Mul, sin(linear_pattern, evaluate=False)/_symbol, None, SiRule),
+            (Mul, sinh(linear_pattern, evaluate=False)/_symbol, None, ShiRule),
+            (Pow, 1/log(linear_pattern, evaluate=False), None, LiRule),
+            (exp, exp(quadratic_pattern, evaluate=False), None, ErfRule),
+            (sin, sin(quadratic_pattern, evaluate=False), None, FresnelSRule),
+            (cos, cos(quadratic_pattern, evaluate=False), None, FresnelCRule),
+            (Mul, _symbol**e*exp(a*_symbol, evaluate=False), None, UpperGammaRule),
+            (Mul, polylog(b, a*_symbol, evaluate=False)/_symbol, None, PolylogRule),
+            (Pow, 1/sqrt(a - d*sin(_symbol, evaluate=False)**2),
+                lambda a, d: a != d, EllipticFRule),
+            (Pow, sqrt(a - d*sin(_symbol, evaluate=False)**2),
+                lambda a, d: a != d, EllipticERule),
+        ))
+    _integrand = integrand.subs(symbol, _symbol)
+    for type_, pattern, constraint, rule in _special_function_patterns:
+        if isinstance(_integrand, type_):
+            match = _integrand.match(pattern)
+            if match:
+                wild_vals = tuple(match.get(w) for w in _wilds
+                                  if match.get(w) is not None)
+                if constraint is None or constraint(*wild_vals):
+                    return rule(integrand, symbol, *wild_vals)
+
+
+def _add_degenerate_step(generic_cond, generic_step: Rule, degenerate_step: Rule | None) -> Rule:
+    if degenerate_step is None:
+        return generic_step
+    if isinstance(generic_step, PiecewiseRule):
+        subfunctions = [(substep, (cond & generic_cond).simplify())
+                        for substep, cond in generic_step.subfunctions]
+    else:
+        subfunctions = [(generic_step, generic_cond)]
+    if isinstance(degenerate_step, PiecewiseRule):
+        subfunctions += degenerate_step.subfunctions
+    else:
+        subfunctions.append((degenerate_step, S.true))
+    return PiecewiseRule(generic_step.integrand, generic_step.variable, subfunctions)
+
+
+def nested_pow_rule(integral: IntegralInfo):
+    # nested (c*(a+b*x)**d)**e
+    integrand, x = integral
+
+    a_ = Wild('a', exclude=[x])
+    b_ = Wild('b', exclude=[x, 0])
+    pattern = a_+b_*x
+    generic_cond = S.true
+
+    class NoMatch(Exception):
+        pass
+
+    def _get_base_exp(expr: Expr) -> tuple[Expr, Expr]:
+        if not expr.has_free(x):
+            return S.One, S.Zero
+        if expr.is_Mul:
+            _, terms = expr.as_coeff_mul()
+            if not terms:
+                return S.One, S.Zero
+            results = [_get_base_exp(term) for term in terms]
+            bases = {b for b, _ in results}
+            bases.discard(S.One)
+            if len(bases) == 1:
+                return bases.pop(), Add(*(e for _, e in results))
+            raise NoMatch
+        if expr.is_Pow:
+            b, e = expr.base, expr.exp  # type: ignore
+            if e.has_free(x):
+                raise NoMatch
+            base_, sub_exp = _get_base_exp(b)
+            return base_, sub_exp * e
+        match = expr.match(pattern)
+        if match:
+            a, b = match[a_], match[b_]
+            base_ = x + a/b
+            nonlocal generic_cond
+            generic_cond = Ne(b, 0)
+            return base_, S.One
+        raise NoMatch
+
+    try:
+        base, exp_ = _get_base_exp(integrand)
+    except NoMatch:
+        return
+    if generic_cond is S.true:
+        degenerate_step = None
+    else:
+        # equivalent with subs(b, 0) but no need to find b
+        degenerate_step = ConstantRule(integrand.subs(x, 0), x)
+    generic_step = NestedPowRule(integrand, x, base, exp_)
+    return _add_degenerate_step(generic_cond, generic_step, degenerate_step)
+
+
+def inverse_trig_rule(integral: IntegralInfo, degenerate=True):
+    """
+    Set degenerate=False on recursive call where coefficient of quadratic term
+    is assumed non-zero.
+    """
+    integrand, symbol = integral
+    base, exp = integrand.as_base_exp()
+    a = Wild('a', exclude=[symbol])
+    b = Wild('b', exclude=[symbol])
+    c = Wild('c', exclude=[symbol, 0])
+    match = base.match(a + b*symbol + c*symbol**2)
+
+    if not match:
+        return
+
+    def make_inverse_trig(RuleClass, a, sign_a, c, sign_c, h) -> Rule:
+        u_var = Dummy("u")
+        rewritten = 1/sqrt(sign_a*a + sign_c*c*(symbol-h)**2)  # a>0, c>0
+        quadratic_base = sqrt(c/a)*(symbol-h)
+        constant = 1/sqrt(c)
+        u_func = None
+        if quadratic_base is not symbol:
+            u_func = quadratic_base
+            quadratic_base = u_var
+        standard_form = 1/sqrt(sign_a + sign_c*quadratic_base**2)
+        substep = RuleClass(standard_form, quadratic_base)
+        if constant != 1:
+            substep = ConstantTimesRule(constant*standard_form, symbol, constant, standard_form, substep)
+        if u_func is not None:
+            substep = URule(rewritten, symbol, u_var, u_func, substep)
+        if h != 0:
+            substep = CompleteSquareRule(integrand, symbol, rewritten, substep)
+        return substep
+
+    a, b, c = [match.get(i, S.Zero) for i in (a, b, c)]
+    generic_cond = Ne(c, 0)
+    if not degenerate or generic_cond is S.true:
+        degenerate_step = None
+    elif b.is_zero:
+        degenerate_step = ConstantRule(a ** exp, symbol)
+    else:
+        degenerate_step = sqrt_linear_rule(IntegralInfo((a + b * symbol) ** exp, symbol))
+
+    if simplify(2*exp + 1) == 0:
+        h, k = -b/(2*c), a - b**2/(4*c)  # rewrite base to k + c*(symbol-h)**2
+        non_square_cond = Ne(k, 0)
+        square_step = None
+        if non_square_cond is not S.true:
+            square_step = NestedPowRule(1/sqrt(c*(symbol-h)**2), symbol, symbol-h, S.NegativeOne)
+        if non_square_cond is S.false:
+            return square_step
+        generic_step = ReciprocalSqrtQuadraticRule(integrand, symbol, a, b, c)
+        step = _add_degenerate_step(non_square_cond, generic_step, square_step)
+        if k.is_real and c.is_real:
+            # list of ((rule, base_exp, a, sign_a, b, sign_b), condition)
+            rules = []
+            for args, cond in (  # don't apply ArccoshRule to x**2-1
+                ((ArcsinRule, k, 1, -c, -1, h), And(k > 0, c < 0)),  # 1-x**2
+                ((ArcsinhRule, k, 1, c, 1, h), And(k > 0, c > 0)),  # 1+x**2
+            ):
+                if cond is S.true:
+                    return make_inverse_trig(*args)
+                if cond is not S.false:
+                    rules.append((make_inverse_trig(*args), cond))
+            if rules:
+                if not k.is_positive:  # conditions are not thorough, need fall back rule
+                    rules.append((generic_step, S.true))
+                step = PiecewiseRule(integrand, symbol, rules)
+            else:
+                step = generic_step
+        return _add_degenerate_step(generic_cond, step, degenerate_step)
+    if exp == S.Half:
+        step = SqrtQuadraticRule(integrand, symbol, a, b, c)
+        return _add_degenerate_step(generic_cond, step, degenerate_step)
+
+
+def add_rule(integral):
+    integrand, symbol = integral
+    results = [integral_steps(g, symbol)
+              for g in integrand.as_ordered_terms()]
+    return None if None in results else AddRule(integrand, symbol, results)
+
+
+def mul_rule(integral: IntegralInfo):
+    integrand, symbol = integral
+
+    # Constant times function case
+    coeff, f = integrand.as_independent(symbol)
+    if coeff != 1:
+        next_step = integral_steps(f, symbol)
+        if next_step is not None:
+            return ConstantTimesRule(integrand, symbol, coeff, f, next_step)
+
+
+def _parts_rule(integrand, symbol) -> tuple[Expr, Expr, Expr, Expr, Rule] | None:
+    # LIATE rule:
+    # log, inverse trig, algebraic, trigonometric, exponential
+    def pull_out_algebraic(integrand):
+        integrand = integrand.cancel().together()
+        # iterating over Piecewise args would not work here
+        algebraic = ([] if isinstance(integrand, Piecewise) or not integrand.is_Mul
+            else [arg for arg in integrand.args if arg.is_algebraic_expr(symbol)])
+        if algebraic:
+            u = Mul(*algebraic)
+            dv = (integrand / u).cancel()
+            return u, dv
+
+    def pull_out_u(*functions) -> Callable[[Expr], tuple[Expr, Expr] | None]:
+        def pull_out_u_rl(integrand: Expr) -> tuple[Expr, Expr] | None:
+            if any(integrand.has(f) for f in functions):
+                args = [arg for arg in integrand.args
+                        if any(isinstance(arg, cls) for cls in functions)]
+                if args:
+                    u = Mul(*args) # type: ignore
+                    dv = integrand / u
+                    return u, dv
+            return None
+
+        return pull_out_u_rl
+
+    liate_rules = [pull_out_u(log), pull_out_u(*inverse_trig_functions),
+                   pull_out_algebraic, pull_out_u(sin, cos),
+                   pull_out_u(exp)]
+
+
+    dummy = Dummy("temporary")
+    # we can integrate log(x) and atan(x) by setting dv = 1
+    if isinstance(integrand, (log, *inverse_trig_functions)):
+        integrand = dummy * integrand
+
+    for index, rule in enumerate(liate_rules):
+        result = rule(integrand)
+
+        if result:
+            u, dv = result
+
+            # Don't pick u to be a constant if possible
+            if symbol not in u.free_symbols and not u.has(dummy):
+                return None
+
+            u = u.subs(dummy, 1)
+            dv = dv.subs(dummy, 1)
+
+            # Don't pick a non-polynomial algebraic to be differentiated
+            if rule == pull_out_algebraic and not u.is_polynomial(symbol):
+                return None
+            # Don't trade one logarithm for another
+            if isinstance(u, log):
+                rec_dv = 1/dv
+                if (rec_dv.is_polynomial(symbol) and
+                    degree(rec_dv, symbol) == 1):
+                    return None
+
+            # Can integrate a polynomial times OrthogonalPolynomial
+            if rule == pull_out_algebraic:
+                if dv.is_Derivative or dv.has(TrigonometricFunction) or \
+                        isinstance(dv, OrthogonalPolynomial):
+                    v_step = integral_steps(dv, symbol)
+                    if v_step.contains_dont_know():
+                        return None
+                    else:
+                        du = u.diff(symbol)
+                        v = v_step.eval()
+                        return u, dv, v, du, v_step
+
+            # make sure dv is amenable to integration
+            accept = False
+            if index < 2:  # log and inverse trig are usually worth trying
+                accept = True
+            elif (rule == pull_out_algebraic and dv.args and
+                all(isinstance(a, (sin, cos, exp))
+                for a in dv.args)):
+                    accept = True
+            else:
+                for lrule in liate_rules[index + 1:]:
+                    r = lrule(integrand)
+                    if r and r[0].subs(dummy, 1).equals(dv):
+                        accept = True
+                        break
+
+            if accept:
+                du = u.diff(symbol)
+                v_step = integral_steps(simplify(dv), symbol)
+                if not v_step.contains_dont_know():
+                    v = v_step.eval()
+                    return u, dv, v, du, v_step
+    return None
+
+
+def parts_rule(integral):
+    integrand, symbol = integral
+    constant, integrand = integrand.as_coeff_Mul()
+
+    result = _parts_rule(integrand, symbol)
+
+    steps = []
+    if result:
+        u, dv, v, du, v_step = result
+        debug("u : {}, dv : {}, v : {}, du : {}, v_step: {}".format(u, dv, v, du, v_step))
+        steps.append(result)
+
+        if isinstance(v, Integral):
+            return
+
+        # Set a limit on the number of times u can be used
+        if isinstance(u, (sin, cos, exp, sinh, cosh)):
+            cachekey = u.xreplace({symbol: _cache_dummy})
+            if _parts_u_cache[cachekey] > 2:
+                return
+            _parts_u_cache[cachekey] += 1
+
+        # Try cyclic integration by parts a few times
+        for _ in range(4):
+            debug("Cyclic integration {} with v: {}, du: {}, integrand: {}".format(_, v, du, integrand))
+            coefficient = ((v * du) / integrand).cancel()
+            if coefficient == 1:
+                break
+            if symbol not in coefficient.free_symbols:
+                rule = CyclicPartsRule(integrand, symbol,
+                    [PartsRule(None, None, u, dv, v_step, None)
+                     for (u, dv, v, du, v_step) in steps],
+                    (-1) ** len(steps) * coefficient)
+                if (constant != 1) and rule:
+                    rule = ConstantTimesRule(constant * integrand, symbol, constant, integrand, rule)
+                return rule
+
+            # _parts_rule is sensitive to constants, factor it out
+            next_constant, next_integrand = (v * du).as_coeff_Mul()
+            result = _parts_rule(next_integrand, symbol)
+
+            if result:
+                u, dv, v, du, v_step = result
+                u *= next_constant
+                du *= next_constant
+                steps.append((u, dv, v, du, v_step))
+            else:
+                break
+
+    def make_second_step(steps, integrand):
+        if steps:
+            u, dv, v, du, v_step = steps[0]
+            return PartsRule(integrand, symbol, u, dv, v_step, make_second_step(steps[1:], v * du))
+        return integral_steps(integrand, symbol)
+
+    if steps:
+        u, dv, v, du, v_step = steps[0]
+        rule = PartsRule(integrand, symbol, u, dv, v_step, make_second_step(steps[1:], v * du))
+        if (constant != 1) and rule:
+            rule = ConstantTimesRule(constant * integrand, symbol, constant, integrand, rule)
+        return rule
+
+
+def trig_rule(integral):
+    integrand, symbol = integral
+    if integrand == sin(symbol):
+        return SinRule(integrand, symbol)
+    if integrand == cos(symbol):
+        return CosRule(integrand, symbol)
+    if integrand == sec(symbol)**2:
+        return Sec2Rule(integrand, symbol)
+    if integrand == csc(symbol)**2:
+        return Csc2Rule(integrand, symbol)
+
+    if isinstance(integrand, tan):
+        rewritten = sin(*integrand.args) / cos(*integrand.args)
+    elif isinstance(integrand, cot):
+        rewritten = cos(*integrand.args) / sin(*integrand.args)
+    elif isinstance(integrand, sec):
+        arg = integrand.args[0]
+        rewritten = ((sec(arg)**2 + tan(arg) * sec(arg)) /
+                     (sec(arg) + tan(arg)))
+    elif isinstance(integrand, csc):
+        arg = integrand.args[0]
+        rewritten = ((csc(arg)**2 + cot(arg) * csc(arg)) /
+                     (csc(arg) + cot(arg)))
+    else:
+        return
+
+    return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol))
+
+def trig_product_rule(integral: IntegralInfo):
+    integrand, symbol = integral
+    if integrand == sec(symbol) * tan(symbol):
+        return SecTanRule(integrand, symbol)
+    if integrand == csc(symbol) * cot(symbol):
+        return CscCotRule(integrand, symbol)
+
+
+def quadratic_denom_rule(integral):
+    integrand, symbol = integral
+    a = Wild('a', exclude=[symbol])
+    b = Wild('b', exclude=[symbol])
+    c = Wild('c', exclude=[symbol])
+
+    match = integrand.match(a / (b * symbol ** 2 + c))
+
+    if match:
+        a, b, c = match[a], match[b], match[c]
+        general_rule = ArctanRule(integrand, symbol, a, b, c)
+        if b.is_extended_real and c.is_extended_real:
+            positive_cond = c/b > 0
+            if positive_cond is S.true:
+                return general_rule
+            coeff = a/(2*sqrt(-c)*sqrt(b))
+            constant = sqrt(-c/b)
+            r1 = 1/(symbol-constant)
+            r2 = 1/(symbol+constant)
+            log_steps = [ReciprocalRule(r1, symbol, symbol-constant),
+                         ConstantTimesRule(-r2, symbol, -1, r2, ReciprocalRule(r2, symbol, symbol+constant))]
+            rewritten = sub = r1 - r2
+            negative_step = AddRule(sub, symbol, log_steps)
+            if coeff != 1:
+                rewritten = Mul(coeff, sub, evaluate=False)
+                negative_step = ConstantTimesRule(rewritten, symbol, coeff, sub, negative_step)
+            negative_step = RewriteRule(integrand, symbol, rewritten, negative_step)
+            if positive_cond is S.false:
+                return negative_step
+            return PiecewiseRule(integrand, symbol, [(general_rule, positive_cond), (negative_step, S.true)])
+
+        power = PowerRule(integrand, symbol, symbol, -2)
+        if b != 1:
+            power = ConstantTimesRule(integrand, symbol, 1/b, symbol**-2, power)
+
+        return PiecewiseRule(integrand, symbol, [(general_rule, Ne(c, 0)), (power, True)])
+
+    d = Wild('d', exclude=[symbol])
+    match2 = integrand.match(a / (b * symbol ** 2 + c * symbol + d))
+    if match2:
+        b, c =  match2[b], match2[c]
+        if b.is_zero:
+            return
+        u = Dummy('u')
+        u_func = symbol + c/(2*b)
+        integrand2 = integrand.subs(symbol, u - c / (2*b))
+        next_step = integral_steps(integrand2, u)
+        if next_step:
+            return URule(integrand2, symbol, u, u_func, next_step)
+        else:
+            return
+    e = Wild('e', exclude=[symbol])
+    match3 = integrand.match((a* symbol + b) / (c * symbol ** 2 + d * symbol + e))
+    if match3:
+        a, b, c, d, e = match3[a], match3[b], match3[c], match3[d], match3[e]
+        if c.is_zero:
+            return
+        denominator = c * symbol**2 + d * symbol + e
+        const =  a/(2*c)
+        numer1 =  (2*c*symbol+d)
+        numer2 = - const*d + b
+        u = Dummy('u')
+        step1 = URule(integrand, symbol,
+                      u, denominator, integral_steps(u**(-1), u))
+        if const != 1:
+            step1 = ConstantTimesRule(const*numer1/denominator, symbol,
+                                      const, numer1/denominator, step1)
+        if numer2.is_zero:
+            return step1
+        step2 = integral_steps(numer2/denominator, symbol)
+        substeps = AddRule(integrand, symbol, [step1, step2])
+        rewriten = const*numer1/denominator+numer2/denominator
+        return RewriteRule(integrand, symbol, rewriten, substeps)
+
+    return
+
+
+def sqrt_linear_rule(integral: IntegralInfo):
+    """
+    Substitute common (a+b*x)**(1/n)
+    """
+    integrand, x = integral
+    a = Wild('a', exclude=[x])
+    b = Wild('b', exclude=[x, 0])
+    a0 = b0 = 0
+    bases, qs, bs = [], [], []
+    for pow_ in integrand.find(Pow):  # collect all (a+b*x)**(p/q)
+        base, exp_ = pow_.base, pow_.exp
+        if exp_.is_Integer or x not in base.free_symbols:  # skip 1/x and sqrt(2)
+            continue
+        if not exp_.is_Rational:  # exclude x**pi
+            return
+        match = base.match(a+b*x)
+        if not match:  # skip non-linear
+            continue  # for sqrt(x+sqrt(x)), although base is non-linear, we can still substitute sqrt(x)
+        a1, b1 = match[a], match[b]
+        if a0*b1 != a1*b0 or not (b0/b1).is_nonnegative:  # cannot transform sqrt(x) to sqrt(x+1) or sqrt(-x)
+            return
+        if b0 == 0 or (b0/b1 > 1) is S.true:  # choose the latter of sqrt(2*x) and sqrt(x) as representative
+            a0, b0 = a1, b1
+        bases.append(base)
+        bs.append(b1)
+        qs.append(exp_.q)
+    if b0 == 0:  # no such pattern found
+        return
+    q0: Integer = lcm_list(qs)
+    u_x = (a0 + b0*x)**(1/q0)
+    u = Dummy("u")
+    substituted = integrand.subs({base**(S.One/q): (b/b0)**(S.One/q)*u**(q0/q)
+                                  for base, b, q in zip(bases, bs, qs)}).subs(x, (u**q0-a0)/b0)
+    substep = integral_steps(substituted*u**(q0-1)*q0/b0, u)
+    if not substep.contains_dont_know():
+        step: Rule = URule(integrand, x, u, u_x, substep)
+        generic_cond = Ne(b0, 0)
+        if generic_cond is not S.true:  # possible degenerate case
+            simplified = integrand.subs(dict.fromkeys(bs, 0))
+            degenerate_step = integral_steps(simplified, x)
+            step = PiecewiseRule(integrand, x, [(step, generic_cond), (degenerate_step, S.true)])
+        return step
+
+
+def sqrt_quadratic_rule(integral: IntegralInfo, degenerate=True):
+    integrand, x = integral
+    a = Wild('a', exclude=[x])
+    b = Wild('b', exclude=[x])
+    c = Wild('c', exclude=[x, 0])
+    f = Wild('f')
+    n = Wild('n', properties=[lambda n: n.is_Integer and n.is_odd])
+    match = integrand.match(f*sqrt(a+b*x+c*x**2)**n)
+    if not match:
+        return
+    a, b, c, f, n = match[a], match[b], match[c], match[f], match[n]
+    f_poly = f.as_poly(x)
+    if f_poly is None:
+        return
+
+    generic_cond = Ne(c, 0)
+    if not degenerate or generic_cond is S.true:
+        degenerate_step = None
+    elif b.is_zero:
+        degenerate_step = integral_steps(f*sqrt(a)**n, x)
+    else:
+        degenerate_step = sqrt_linear_rule(IntegralInfo(f*sqrt(a+b*x)**n, x))
+
+    def sqrt_quadratic_denom_rule(numer_poly: Poly, integrand: Expr):
+        denom = sqrt(a+b*x+c*x**2)
+        deg = numer_poly.degree()
+        if deg <= 1:
+            # integrand == (d+e*x)/sqrt(a+b*x+c*x**2)
+            e, d = numer_poly.all_coeffs() if deg == 1 else (S.Zero, numer_poly.as_expr())
+            # rewrite numerator to A*(2*c*x+b) + B
+            A = e/(2*c)
+            B = d-A*b
+            pre_substitute = (2*c*x+b)/denom
+            constant_step: Rule | None = None
+            linear_step: Rule | None = None
+            if A != 0:
+                u = Dummy("u")
+                pow_rule = PowerRule(1/sqrt(u), u, u, -S.Half)
+                linear_step = URule(pre_substitute, x, u, a+b*x+c*x**2, pow_rule)
+                if A != 1:
+                    linear_step = ConstantTimesRule(A*pre_substitute, x, A, pre_substitute, linear_step)
+            if B != 0:
+                constant_step = inverse_trig_rule(IntegralInfo(1/denom, x), degenerate=False)
+                if B != 1:
+                    constant_step = ConstantTimesRule(B/denom, x, B, 1/denom, constant_step)  # type: ignore
+            if linear_step and constant_step:
+                add = Add(A*pre_substitute, B/denom, evaluate=False)
+                step: Rule | None = RewriteRule(integrand, x, add, AddRule(add, x, [linear_step, constant_step]))
+            else:
+                step = linear_step or constant_step
+        else:
+            coeffs = numer_poly.all_coeffs()
+            step = SqrtQuadraticDenomRule(integrand, x, a, b, c, coeffs)
+        return step
+
+    if n > 0:  # rewrite poly * sqrt(s)**(2*k-1) to poly*s**k / sqrt(s)
+        numer_poly = f_poly * (a+b*x+c*x**2)**((n+1)/2)
+        rewritten = numer_poly.as_expr()/sqrt(a+b*x+c*x**2)
+        substep = sqrt_quadratic_denom_rule(numer_poly, rewritten)
+        generic_step = RewriteRule(integrand, x, rewritten, substep)
+    elif n == -1:
+        generic_step = sqrt_quadratic_denom_rule(f_poly, integrand)
+    else:
+        return  # todo: handle n < -1 case
+    return _add_degenerate_step(generic_cond, generic_step, degenerate_step)
+
+
+def hyperbolic_rule(integral: tuple[Expr, Symbol]):
+    integrand, symbol = integral
+    if isinstance(integrand, HyperbolicFunction) and integrand.args[0] == symbol:
+        if integrand.func == sinh:
+            return SinhRule(integrand, symbol)
+        if integrand.func == cosh:
+            return CoshRule(integrand, symbol)
+        u = Dummy('u')
+        if integrand.func == tanh:
+            rewritten = sinh(symbol)/cosh(symbol)
+            return RewriteRule(integrand, symbol, rewritten,
+                   URule(rewritten, symbol, u, cosh(symbol), ReciprocalRule(1/u, u, u)))
+        if integrand.func == coth:
+            rewritten = cosh(symbol)/sinh(symbol)
+            return RewriteRule(integrand, symbol, rewritten,
+                   URule(rewritten, symbol, u, sinh(symbol), ReciprocalRule(1/u, u, u)))
+        else:
+            rewritten = integrand.rewrite(tanh)
+            if integrand.func == sech:
+                return RewriteRule(integrand, symbol, rewritten,
+                       URule(rewritten, symbol, u, tanh(symbol/2),
+                       ArctanRule(2/(u**2 + 1), u, S(2), S.One, S.One)))
+            if integrand.func == csch:
+                return RewriteRule(integrand, symbol, rewritten,
+                       URule(rewritten, symbol, u, tanh(symbol/2),
+                       ReciprocalRule(1/u, u, u)))
+
+@cacheit
+def make_wilds(symbol):
+    a = Wild('a', exclude=[symbol])
+    b = Wild('b', exclude=[symbol])
+    m = Wild('m', exclude=[symbol], properties=[lambda n: isinstance(n, Integer)])
+    n = Wild('n', exclude=[symbol], properties=[lambda n: isinstance(n, Integer)])
+
+    return a, b, m, n
+
+@cacheit
+def sincos_pattern(symbol):
+    a, b, m, n = make_wilds(symbol)
+    pattern = sin(a*symbol)**m * cos(b*symbol)**n
+
+    return pattern, a, b, m, n
+
+@cacheit
+def tansec_pattern(symbol):
+    a, b, m, n = make_wilds(symbol)
+    pattern = tan(a*symbol)**m * sec(b*symbol)**n
+
+    return pattern, a, b, m, n
+
+@cacheit
+def cotcsc_pattern(symbol):
+    a, b, m, n = make_wilds(symbol)
+    pattern = cot(a*symbol)**m * csc(b*symbol)**n
+
+    return pattern, a, b, m, n
+
+@cacheit
+def heaviside_pattern(symbol):
+    m = Wild('m', exclude=[symbol])
+    b = Wild('b', exclude=[symbol])
+    g = Wild('g')
+    pattern = Heaviside(m*symbol + b) * g
+
+    return pattern, m, b, g
+
+def uncurry(func):
+    def uncurry_rl(args):
+        return func(*args)
+    return uncurry_rl
+
+def trig_rewriter(rewrite):
+    def trig_rewriter_rl(args):
+        a, b, m, n, integrand, symbol = args
+        rewritten = rewrite(a, b, m, n, integrand, symbol)
+        if rewritten != integrand:
+            return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol))
+    return trig_rewriter_rl
+
+sincos_botheven_condition = uncurry(
+    lambda a, b, m, n, i, s: m.is_even and n.is_even and
+    m.is_nonnegative and n.is_nonnegative)
+
+sincos_botheven = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (((1 - cos(2*a*symbol)) / 2) ** (m / 2)) *
+                                    (((1 + cos(2*b*symbol)) / 2) ** (n / 2)) ))
+
+sincos_sinodd_condition = uncurry(lambda a, b, m, n, i, s: m.is_odd and m >= 3)
+
+sincos_sinodd = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (1 - cos(a*symbol)**2)**((m - 1) / 2) *
+                                    sin(a*symbol) *
+                                    cos(b*symbol) ** n))
+
+sincos_cosodd_condition = uncurry(lambda a, b, m, n, i, s: n.is_odd and n >= 3)
+
+sincos_cosodd = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (1 - sin(b*symbol)**2)**((n - 1) / 2) *
+                                    cos(b*symbol) *
+                                    sin(a*symbol) ** m))
+
+tansec_seceven_condition = uncurry(lambda a, b, m, n, i, s: n.is_even and n >= 4)
+tansec_seceven = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (1 + tan(b*symbol)**2) ** (n/2 - 1) *
+                                    sec(b*symbol)**2 *
+                                    tan(a*symbol) ** m ))
+
+tansec_tanodd_condition = uncurry(lambda a, b, m, n, i, s: m.is_odd)
+tansec_tanodd = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (sec(a*symbol)**2 - 1) ** ((m - 1) / 2) *
+                                     tan(a*symbol) *
+                                     sec(b*symbol) ** n ))
+
+tan_tansquared_condition = uncurry(lambda a, b, m, n, i, s: m == 2 and n == 0)
+tan_tansquared = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( sec(a*symbol)**2 - 1))
+
+cotcsc_csceven_condition = uncurry(lambda a, b, m, n, i, s: n.is_even and n >= 4)
+cotcsc_csceven = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (1 + cot(b*symbol)**2) ** (n/2 - 1) *
+                                    csc(b*symbol)**2 *
+                                    cot(a*symbol) ** m ))
+
+cotcsc_cotodd_condition = uncurry(lambda a, b, m, n, i, s: m.is_odd)
+cotcsc_cotodd = trig_rewriter(
+    lambda a, b, m, n, i, symbol: ( (csc(a*symbol)**2 - 1) ** ((m - 1) / 2) *
+                                    cot(a*symbol) *
+                                    csc(b*symbol) ** n ))
+
+def trig_sincos_rule(integral):
+    integrand, symbol = integral
+
+    if any(integrand.has(f) for f in (sin, cos)):
+        pattern, a, b, m, n = sincos_pattern(symbol)
+        match = integrand.match(pattern)
+        if not match:
+            return
+
+        return multiplexer({
+            sincos_botheven_condition: sincos_botheven,
+            sincos_sinodd_condition: sincos_sinodd,
+            sincos_cosodd_condition: sincos_cosodd
+        })(tuple(
+            [match.get(i, S.Zero) for i in (a, b, m, n)] +
+            [integrand, symbol]))
+
+def trig_tansec_rule(integral):
+    integrand, symbol = integral
+
+    integrand = integrand.subs({
+        1 / cos(symbol): sec(symbol)
+    })
+
+    if any(integrand.has(f) for f in (tan, sec)):
+        pattern, a, b, m, n = tansec_pattern(symbol)
+        match = integrand.match(pattern)
+        if not match:
+            return
+
+        return multiplexer({
+            tansec_tanodd_condition: tansec_tanodd,
+            tansec_seceven_condition: tansec_seceven,
+            tan_tansquared_condition: tan_tansquared
+        })(tuple(
+            [match.get(i, S.Zero) for i in (a, b, m, n)] +
+            [integrand, symbol]))
+
+def trig_cotcsc_rule(integral):
+    integrand, symbol = integral
+    integrand = integrand.subs({
+        1 / sin(symbol): csc(symbol),
+        1 / tan(symbol): cot(symbol),
+        cos(symbol) / tan(symbol): cot(symbol)
+    })
+
+    if any(integrand.has(f) for f in (cot, csc)):
+        pattern, a, b, m, n = cotcsc_pattern(symbol)
+        match = integrand.match(pattern)
+        if not match:
+            return
+
+        return multiplexer({
+            cotcsc_cotodd_condition: cotcsc_cotodd,
+            cotcsc_csceven_condition: cotcsc_csceven
+        })(tuple(
+            [match.get(i, S.Zero) for i in (a, b, m, n)] +
+            [integrand, symbol]))
+
+def trig_sindouble_rule(integral):
+    integrand, symbol = integral
+    a = Wild('a', exclude=[sin(2*symbol)])
+    match = integrand.match(sin(2*symbol)*a)
+    if match:
+        sin_double = 2*sin(symbol)*cos(symbol)/sin(2*symbol)
+        return integral_steps(integrand * sin_double, symbol)
+
+def trig_powers_products_rule(integral):
+    return do_one(null_safe(trig_sincos_rule),
+                  null_safe(trig_tansec_rule),
+                  null_safe(trig_cotcsc_rule),
+                  null_safe(trig_sindouble_rule))(integral)
+
+def trig_substitution_rule(integral):
+    integrand, symbol = integral
+    A = Wild('a', exclude=[0, symbol])
+    B = Wild('b', exclude=[0, symbol])
+    theta = Dummy("theta")
+    target_pattern = A + B*symbol**2
+
+    matches = integrand.find(target_pattern)
+    for expr in matches:
+        match = expr.match(target_pattern)
+        a = match.get(A, S.Zero)
+        b = match.get(B, S.Zero)
+
+        a_positive = ((a.is_number and a > 0) or a.is_positive)
+        b_positive = ((b.is_number and b > 0) or b.is_positive)
+        a_negative = ((a.is_number and a < 0) or a.is_negative)
+        b_negative = ((b.is_number and b < 0) or b.is_negative)
+        x_func = None
+        if a_positive and b_positive:
+            # a**2 + b*x**2. Assume sec(theta) > 0, -pi/2 < theta < pi/2
+            x_func = (sqrt(a)/sqrt(b)) * tan(theta)
+            # Do not restrict the domain: tan(theta) takes on any real
+            # value on the interval -pi/2 < theta < pi/2 so x takes on
+            # any value
+            restriction = True
+        elif a_positive and b_negative:
+            # a**2 - b*x**2. Assume cos(theta) > 0, -pi/2 < theta < pi/2
+            constant = sqrt(a)/sqrt(-b)
+            x_func = constant * sin(theta)
+            restriction = And(symbol > -constant, symbol < constant)
+        elif a_negative and b_positive:
+            # b*x**2 - a**2. Assume sin(theta) > 0, 0 < theta < pi
+            constant = sqrt(-a)/sqrt(b)
+            x_func = constant * sec(theta)
+            restriction = And(symbol > -constant, symbol < constant)
+        if x_func:
+            # Manually simplify sqrt(trig(theta)**2) to trig(theta)
+            # Valid due to assumed domain restriction
+            substitutions = {}
+            for f in [sin, cos, tan,
+                      sec, csc, cot]:
+                substitutions[sqrt(f(theta)**2)] = f(theta)
+                substitutions[sqrt(f(theta)**(-2))] = 1/f(theta)
+
+            replaced = integrand.subs(symbol, x_func).trigsimp()
+            replaced = manual_subs(replaced, substitutions)
+            if not replaced.has(symbol):
+                replaced *= manual_diff(x_func, theta)
+                replaced = replaced.trigsimp()
+                secants = replaced.find(1/cos(theta))
+                if secants:
+                    replaced = replaced.xreplace({
+                        1/cos(theta): sec(theta)
+                    })
+
+                substep = integral_steps(replaced, theta)
+                if not substep.contains_dont_know():
+                    return TrigSubstitutionRule(integrand, symbol,
+                        theta, x_func, replaced, substep, restriction)
+
+def heaviside_rule(integral):
+    integrand, symbol = integral
+    pattern, m, b, g = heaviside_pattern(symbol)
+    match = integrand.match(pattern)
+    if match and 0 != match[g]:
+        # f = Heaviside(m*x + b)*g
+        substep = integral_steps(match[g], symbol)
+        m, b = match[m], match[b]
+        return HeavisideRule(integrand, symbol, m*symbol + b, -b/m, substep)
+
+
+def dirac_delta_rule(integral: IntegralInfo):
+    integrand, x = integral
+    if len(integrand.args) == 1:
+        n = S.Zero
+    else:
+        n = integrand.args[1] # type: ignore
+    if not n.is_Integer or n < 0:
+        return
+    a, b = Wild('a', exclude=[x]), Wild('b', exclude=[x, 0])
+    match = integrand.args[0].match(a+b*x)
+    if not match:
+        return
+    a, b = match[a], match[b]
+    generic_cond = Ne(b, 0)
+    if generic_cond is S.true:
+        degenerate_step = None
+    else:
+        degenerate_step = ConstantRule(DiracDelta(a, n), x)
+    generic_step = DiracDeltaRule(integrand, x, n, a, b)
+    return _add_degenerate_step(generic_cond, generic_step, degenerate_step)
+
+
+def substitution_rule(integral):
+    integrand, symbol = integral
+
+    u_var = Dummy("u")
+    substitutions = find_substitutions(integrand, symbol, u_var)
+    count = 0
+    if substitutions:
+        debug("List of Substitution Rules")
+        ways = []
+        for u_func, c, substituted in substitutions:
+            subrule = integral_steps(substituted, u_var)
+            count = count + 1
+            debug("Rule {}: {}".format(count, subrule))
+
+            if subrule.contains_dont_know():
+                continue
+
+            if simplify(c - 1) != 0:
+                _, denom = c.as_numer_denom()
+                if subrule:
+                    subrule = ConstantTimesRule(c * substituted, u_var, c, substituted, subrule)
+
+                if denom.free_symbols:
+                    piecewise = []
+                    could_be_zero = []
+
+                    if isinstance(denom, Mul):
+                        could_be_zero = denom.args
+                    else:
+                        could_be_zero.append(denom)
+
+                    for expr in could_be_zero:
+                        if not fuzzy_not(expr.is_zero):
+                            substep = integral_steps(manual_subs(integrand, expr, 0), symbol)
+
+                            if substep:
+                                piecewise.append((
+                                    substep,
+                                    Eq(expr, 0)
+                                ))
+                    piecewise.append((subrule, True))
+                    subrule = PiecewiseRule(substituted, symbol, piecewise)
+
+            ways.append(URule(integrand, symbol, u_var, u_func, subrule))
+
+        if len(ways) > 1:
+            return AlternativeRule(integrand, symbol, ways)
+        elif ways:
+            return ways[0]
+
+
+partial_fractions_rule = rewriter(
+    lambda integrand, symbol: integrand.is_rational_function(),
+    lambda integrand, symbol: integrand.apart(symbol))
+
+cancel_rule = rewriter(
+    # lambda integrand, symbol: integrand.is_algebraic_expr(),
+    # lambda integrand, symbol: isinstance(integrand, Mul),
+    lambda integrand, symbol: True,
+    lambda integrand, symbol: integrand.cancel())
+
+distribute_expand_rule = rewriter(
+    lambda integrand, symbol: (
+        isinstance(integrand, (Pow, Mul)) or all(arg.is_Pow or arg.is_polynomial(symbol) for arg in integrand.args)),
+    lambda integrand, symbol: integrand.expand())
+
+trig_expand_rule = rewriter(
+    # If there are trig functions with different arguments, expand them
+    lambda integrand, symbol: (
+        len({a.args[0] for a in integrand.atoms(TrigonometricFunction)}) > 1),
+    lambda integrand, symbol: integrand.expand(trig=True))
+
+def derivative_rule(integral):
+    integrand = integral[0]
+    diff_variables = integrand.variables
+    undifferentiated_function = integrand.expr
+    integrand_variables = undifferentiated_function.free_symbols
+
+    if integral.symbol in integrand_variables:
+        if integral.symbol in diff_variables:
+            return DerivativeRule(*integral)
+        else:
+            return DontKnowRule(integrand, integral.symbol)
+    else:
+        return ConstantRule(*integral)
+
+def rewrites_rule(integral):
+    integrand, symbol = integral
+
+    if integrand.match(1/cos(symbol)):
+        rewritten = integrand.subs(1/cos(symbol), sec(symbol))
+        return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol))
+
+def fallback_rule(integral):
+    return DontKnowRule(*integral)
+
+# Cache is used to break cyclic integrals.
+# Need to use the same dummy variable in cached expressions for them to match.
+# Also record "u" of integration by parts, to avoid infinite repetition.
+_integral_cache: dict[Expr, Expr | None] = {}
+_parts_u_cache: dict[Expr, int] = defaultdict(int)
+_cache_dummy = Dummy("z")
+
+def integral_steps(integrand, symbol, **options):
+    """Returns the steps needed to compute an integral.
+
+    Explanation
+    ===========
+
+    This function attempts to mirror what a student would do by hand as
+    closely as possible.
+
+    SymPy Gamma uses this to provide a step-by-step explanation of an
+    integral. The code it uses to format the results of this function can be
+    found at
+    https://github.com/sympy/sympy_gamma/blob/master/app/logic/intsteps.py.
+
+    Examples
+    ========
+
+    >>> from sympy import exp, sin
+    >>> from sympy.integrals.manualintegrate import integral_steps
+    >>> from sympy.abc import x
+    >>> print(repr(integral_steps(exp(x) / (1 + exp(2 * x)), x))) \
+    # doctest: +NORMALIZE_WHITESPACE
+    URule(integrand=exp(x)/(exp(2*x) + 1), variable=x, u_var=_u, u_func=exp(x),
+    substep=ArctanRule(integrand=1/(_u**2 + 1), variable=_u, a=1, b=1, c=1))
+    >>> print(repr(integral_steps(sin(x), x))) \
+    # doctest: +NORMALIZE_WHITESPACE
+    SinRule(integrand=sin(x), variable=x)
+    >>> print(repr(integral_steps((x**2 + 3)**2, x))) \
+    # doctest: +NORMALIZE_WHITESPACE
+    RewriteRule(integrand=(x**2 + 3)**2, variable=x, rewritten=x**4 + 6*x**2 + 9,
+    substep=AddRule(integrand=x**4 + 6*x**2 + 9, variable=x,
+    substeps=[PowerRule(integrand=x**4, variable=x, base=x, exp=4),
+    ConstantTimesRule(integrand=6*x**2, variable=x, constant=6, other=x**2,
+    substep=PowerRule(integrand=x**2, variable=x, base=x, exp=2)),
+    ConstantRule(integrand=9, variable=x)]))
+
+    Returns
+    =======
+
+    rule : Rule
+        The first step; most rules have substeps that must also be
+        considered. These substeps can be evaluated using ``manualintegrate``
+        to obtain a result.
+
+    """
+    cachekey = integrand.xreplace({symbol: _cache_dummy})
+    if cachekey in _integral_cache:
+        if _integral_cache[cachekey] is None:
+            # Stop this attempt, because it leads around in a loop
+            return DontKnowRule(integrand, symbol)
+        else:
+            # TODO: This is for future development, as currently
+            # _integral_cache gets no values other than None
+            return (_integral_cache[cachekey].xreplace(_cache_dummy, symbol),
+                symbol)
+    else:
+        _integral_cache[cachekey] = None
+
+    integral = IntegralInfo(integrand, symbol)
+
+    def key(integral):
+        integrand = integral.integrand
+
+        if symbol not in integrand.free_symbols:
+            return Number
+        for cls in (Symbol, TrigonometricFunction, OrthogonalPolynomial):
+            if isinstance(integrand, cls):
+                return cls
+        return type(integrand)
+
+    def integral_is_subclass(*klasses):
+        def _integral_is_subclass(integral):
+            k = key(integral)
+            return k and issubclass(k, klasses)
+        return _integral_is_subclass
+
+    result = do_one(
+        null_safe(special_function_rule),
+        null_safe(switch(key, {
+            Pow: do_one(null_safe(power_rule), null_safe(inverse_trig_rule),
+                        null_safe(sqrt_linear_rule),
+                        null_safe(quadratic_denom_rule)),
+            Symbol: power_rule,
+            exp: exp_rule,
+            Add: add_rule,
+            Mul: do_one(null_safe(mul_rule), null_safe(trig_product_rule),
+                        null_safe(heaviside_rule), null_safe(quadratic_denom_rule),
+                        null_safe(sqrt_linear_rule),
+                        null_safe(sqrt_quadratic_rule)),
+            Derivative: derivative_rule,
+            TrigonometricFunction: trig_rule,
+            Heaviside: heaviside_rule,
+            DiracDelta: dirac_delta_rule,
+            OrthogonalPolynomial: orthogonal_poly_rule,
+            Number: constant_rule
+        })),
+        do_one(
+            null_safe(trig_rule),
+            null_safe(hyperbolic_rule),
+            null_safe(alternatives(
+                rewrites_rule,
+                substitution_rule,
+                condition(
+                    integral_is_subclass(Mul, Pow),
+                    partial_fractions_rule),
+                condition(
+                    integral_is_subclass(Mul, Pow),
+                    cancel_rule),
+                condition(
+                    integral_is_subclass(Mul, log,
+                    *inverse_trig_functions),
+                    parts_rule),
+                condition(
+                    integral_is_subclass(Mul, Pow),
+                    distribute_expand_rule),
+                trig_powers_products_rule,
+                trig_expand_rule
+            )),
+            null_safe(condition(integral_is_subclass(Mul, Pow), nested_pow_rule)),
+            null_safe(trig_substitution_rule)
+        ),
+        fallback_rule)(integral)
+    del _integral_cache[cachekey]
+    return result
+
+
+def manualintegrate(f, var):
+    """manualintegrate(f, var)
+
+    Explanation
+    ===========
+
+    Compute indefinite integral of a single variable using an algorithm that
+    resembles what a student would do by hand.
+
+    Unlike :func:`~.integrate`, var can only be a single symbol.
+
+    Examples
+    ========
+
+    >>> from sympy import sin, cos, tan, exp, log, integrate
+    >>> from sympy.integrals.manualintegrate import manualintegrate
+    >>> from sympy.abc import x
+    >>> manualintegrate(1 / x, x)
+    log(x)
+    >>> integrate(1/x)
+    log(x)
+    >>> manualintegrate(log(x), x)
+    x*log(x) - x
+    >>> integrate(log(x))
+    x*log(x) - x
+    >>> manualintegrate(exp(x) / (1 + exp(2 * x)), x)
+    atan(exp(x))
+    >>> integrate(exp(x) / (1 + exp(2 * x)))
+    RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x))))
+    >>> manualintegrate(cos(x)**4 * sin(x), x)
+    -cos(x)**5/5
+    >>> integrate(cos(x)**4 * sin(x), x)
+    -cos(x)**5/5
+    >>> manualintegrate(cos(x)**4 * sin(x)**3, x)
+    cos(x)**7/7 - cos(x)**5/5
+    >>> integrate(cos(x)**4 * sin(x)**3, x)
+    cos(x)**7/7 - cos(x)**5/5
+    >>> manualintegrate(tan(x), x)
+    -log(cos(x))
+    >>> integrate(tan(x), x)
+    -log(cos(x))
+
+    See Also
+    ========
+
+    sympy.integrals.integrals.integrate
+    sympy.integrals.integrals.Integral.doit
+    sympy.integrals.integrals.Integral
+    """
+    result = integral_steps(f, var).eval()
+    # Clear the cache of u-parts
+    _parts_u_cache.clear()
+    # If we got Piecewise with two parts, put generic first
+    if isinstance(result, Piecewise) and len(result.args) == 2:
+        cond = result.args[0][1]
+        if isinstance(cond, Eq) and result.args[1][1] == True:
+            result = result.func(
+                (result.args[1][0], Ne(*cond.args)),
+                (result.args[0][0], True))
+    return result
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/meijerint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/meijerint.py
new file mode 100644
index 0000000000000000000000000000000000000000..89d8401c7eee0147df2e824dc1dc50b59ca7f0be
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/meijerint.py
@@ -0,0 +1,2191 @@
+"""
+Integrate functions by rewriting them as Meijer G-functions.
+
+There are three user-visible functions that can be used by other parts of the
+sympy library to solve various integration problems:
+
+- meijerint_indefinite
+- meijerint_definite
+- meijerint_inversion
+
+They can be used to compute, respectively, indefinite integrals, definite
+integrals over intervals of the real line, and inverse laplace-type integrals
+(from c-I*oo to c+I*oo). See the respective docstrings for details.
+
+The main references for this are:
+
+[L] Luke, Y. L. (1969), The Special Functions and Their Approximations,
+    Volume 1
+
+[R] Kelly B. Roach.  Meijer G Function Representations.
+    In: Proceedings of the 1997 International Symposium on Symbolic and
+    Algebraic Computation, pages 205-211, New York, 1997. ACM.
+
+[P] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev (1990).
+    Integrals and Series: More Special Functions, Vol. 3,.
+    Gordon and Breach Science Publisher
+"""
+
+from __future__ import annotations
+import itertools
+
+from sympy import SYMPY_DEBUG
+from sympy.core import S, Expr
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.cache import cacheit
+from sympy.core.containers import Tuple
+from sympy.core.exprtools import factor_terms
+from sympy.core.function import (expand, expand_mul, expand_power_base,
+                                 expand_trig, Function)
+from sympy.core.mul import Mul
+from sympy.core.intfunc import ilcm
+from sympy.core.numbers import Rational, pi
+from sympy.core.relational import Eq, Ne, _canonical_coeff
+from sympy.core.sorting import default_sort_key, ordered
+from sympy.core.symbol import Dummy, symbols, Wild, Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import (re, im, arg, Abs, sign,
+        unpolarify, polarify, polar_lift, principal_branch, unbranched_argument,
+        periodic_argument)
+from sympy.functions.elementary.exponential import exp, exp_polar, log
+from sympy.functions.elementary.integers import ceiling
+from sympy.functions.elementary.hyperbolic import (cosh, sinh,
+        _rewrite_hyperbolics_as_exp, HyperbolicFunction)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc,
+        TrigonometricFunction)
+from sympy.functions.special.bessel import besselj, bessely, besseli, besselk
+from sympy.functions.special.delta_functions import DiracDelta, Heaviside
+from sympy.functions.special.elliptic_integrals import elliptic_k, elliptic_e
+from sympy.functions.special.error_functions import (erf, erfc, erfi, Ei,
+        expint, Si, Ci, Shi, Chi, fresnels, fresnelc)
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import hyper, meijerg
+from sympy.functions.special.singularity_functions import SingularityFunction
+from .integrals import Integral
+from sympy.logic.boolalg import And, Or, BooleanAtom, Not, BooleanFunction
+from sympy.polys import cancel, factor
+from sympy.utilities.iterables import multiset_partitions
+from sympy.utilities.misc import debug as _debug
+from sympy.utilities.misc import debugf as _debugf
+
+# keep this at top for easy reference
+z = Dummy('z')
+
+
+def _has(res, *f):
+    # return True if res has f; in the case of Piecewise
+    # only return True if *all* pieces have f
+    res = piecewise_fold(res)
+    if getattr(res, 'is_Piecewise', False):
+        return all(_has(i, *f) for i in res.args)
+    return res.has(*f)
+
+
+def _create_lookup_table(table):
+    """ Add formulae for the function -> meijerg lookup table. """
+    def wild(n):
+        return Wild(n, exclude=[z])
+    p, q, a, b, c = list(map(wild, 'pqabc'))
+    n = Wild('n', properties=[lambda x: x.is_Integer and x > 0])
+    t = p*z**q
+
+    def add(formula, an, ap, bm, bq, arg=t, fac=S.One, cond=True, hint=True):
+        table.setdefault(_mytype(formula, z), []).append((formula,
+                                     [(fac, meijerg(an, ap, bm, bq, arg))], cond, hint))
+
+    def addi(formula, inst, cond, hint=True):
+        table.setdefault(
+            _mytype(formula, z), []).append((formula, inst, cond, hint))
+
+    def constant(a):
+        return [(a, meijerg([1], [], [], [0], z)),
+                (a, meijerg([], [1], [0], [], z))]
+    table[()] = [(a, constant(a), True, True)]
+
+    # [P], Section 8.
+    class IsNonPositiveInteger(Function):
+
+        @classmethod
+        def eval(cls, arg):
+            arg = unpolarify(arg)
+            if arg.is_Integer is True:
+                return arg <= 0
+
+    # Section 8.4.2
+    # TODO this needs more polar_lift (c/f entry for exp)
+    add(Heaviside(t - b)*(t - b)**(a - 1), [a], [], [], [0], t/b,
+        gamma(a)*b**(a - 1), And(b > 0))
+    add(Heaviside(b - t)*(b - t)**(a - 1), [], [a], [0], [], t/b,
+        gamma(a)*b**(a - 1), And(b > 0))
+    add(Heaviside(z - (b/p)**(1/q))*(t - b)**(a - 1), [a], [], [], [0], t/b,
+        gamma(a)*b**(a - 1), And(b > 0))
+    add(Heaviside((b/p)**(1/q) - z)*(b - t)**(a - 1), [], [a], [0], [], t/b,
+        gamma(a)*b**(a - 1), And(b > 0))
+    add((b + t)**(-a), [1 - a], [], [0], [], t/b, b**(-a)/gamma(a),
+        hint=Not(IsNonPositiveInteger(a)))
+    add(Abs(b - t)**(-a), [1 - a], [(1 - a)/2], [0], [(1 - a)/2], t/b,
+        2*sin(pi*a/2)*gamma(1 - a)*Abs(b)**(-a), re(a) < 1)
+    add((t**a - b**a)/(t - b), [0, a], [], [0, a], [], t/b,
+        b**(a - 1)*sin(a*pi)/pi)
+
+    # 12
+    def A1(r, sign, nu):
+        return pi**Rational(-1, 2)*(-sign*nu/2)**(1 - 2*r)
+
+    def tmpadd(r, sgn):
+        # XXX the a**2 is bad for matching
+        add((sqrt(a**2 + t) + sgn*a)**b/(a**2 + t)**r,
+            [(1 + b)/2, 1 - 2*r + b/2], [],
+            [(b - sgn*b)/2], [(b + sgn*b)/2], t/a**2,
+            a**(b - 2*r)*A1(r, sgn, b))
+    tmpadd(0, 1)
+    tmpadd(0, -1)
+    tmpadd(S.Half, 1)
+    tmpadd(S.Half, -1)
+
+    # 13
+    def tmpadd(r, sgn):
+        add((sqrt(a + p*z**q) + sgn*sqrt(p)*z**(q/2))**b/(a + p*z**q)**r,
+            [1 - r + sgn*b/2], [1 - r - sgn*b/2], [0, S.Half], [],
+            p*z**q/a, a**(b/2 - r)*A1(r, sgn, b))
+    tmpadd(0, 1)
+    tmpadd(0, -1)
+    tmpadd(S.Half, 1)
+    tmpadd(S.Half, -1)
+    # (those after look obscure)
+
+    # Section 8.4.3
+    add(exp(polar_lift(-1)*t), [], [], [0], [])
+
+    # TODO can do sin^n, sinh^n by expansion ... where?
+    # 8.4.4 (hyperbolic functions)
+    add(sinh(t), [], [1], [S.Half], [1, 0], t**2/4, pi**Rational(3, 2))
+    add(cosh(t), [], [S.Half], [0], [S.Half, S.Half], t**2/4, pi**Rational(3, 2))
+
+    # Section 8.4.5
+    # TODO can do t + a. but can also do by expansion... (XXX not really)
+    add(sin(t), [], [], [S.Half], [0], t**2/4, sqrt(pi))
+    add(cos(t), [], [], [0], [S.Half], t**2/4, sqrt(pi))
+
+    # Section 8.4.6 (sinc function)
+    add(sinc(t), [], [], [0], [Rational(-1, 2)], t**2/4, sqrt(pi)/2)
+
+    # Section 8.5.5
+    def make_log1(subs):
+        N = subs[n]
+        return [(S.NegativeOne**N*factorial(N),
+                 meijerg([], [1]*(N + 1), [0]*(N + 1), [], t))]
+
+    def make_log2(subs):
+        N = subs[n]
+        return [(factorial(N),
+                 meijerg([1]*(N + 1), [], [], [0]*(N + 1), t))]
+    # TODO these only hold for positive p, and can be made more general
+    #      but who uses log(x)*Heaviside(a-x) anyway ...
+    # TODO also it would be nice to derive them recursively ...
+    addi(log(t)**n*Heaviside(1 - t), make_log1, True)
+    addi(log(t)**n*Heaviside(t - 1), make_log2, True)
+
+    def make_log3(subs):
+        return make_log1(subs) + make_log2(subs)
+    addi(log(t)**n, make_log3, True)
+    addi(log(t + a),
+         constant(log(a)) + [(S.One, meijerg([1, 1], [], [1], [0], t/a))],
+         True)
+    addi(log(Abs(t - a)), constant(log(Abs(a))) +
+         [(pi, meijerg([1, 1], [S.Half], [1], [0, S.Half], t/a))],
+         True)
+    # TODO log(x)/(x+a) and log(x)/(x-1) can also be done. should they
+    #      be derivable?
+    # TODO further formulae in this section seem obscure
+
+    # Sections 8.4.9-10
+    # TODO
+
+    # Section 8.4.11
+    addi(Ei(t),
+         constant(-S.ImaginaryUnit*pi) + [(S.NegativeOne, meijerg([], [1], [0, 0], [],
+                  t*polar_lift(-1)))],
+         True)
+
+    # Section 8.4.12
+    add(Si(t), [1], [], [S.Half], [0, 0], t**2/4, sqrt(pi)/2)
+    add(Ci(t), [], [1], [0, 0], [S.Half], t**2/4, -sqrt(pi)/2)
+
+    # Section 8.4.13
+    add(Shi(t), [S.Half], [], [0], [Rational(-1, 2), Rational(-1, 2)], polar_lift(-1)*t**2/4,
+        t*sqrt(pi)/4)
+    add(Chi(t), [], [S.Half, 1], [0, 0], [S.Half, S.Half], t**2/4, -
+        pi**S('3/2')/2)
+
+    # generalized exponential integral
+    add(expint(a, t), [], [a], [a - 1, 0], [], t)
+
+    # Section 8.4.14
+    add(erf(t), [1], [], [S.Half], [0], t**2, 1/sqrt(pi))
+    # TODO exp(-x)*erf(I*x) does not work
+    add(erfc(t), [], [1], [0, S.Half], [], t**2, 1/sqrt(pi))
+    # This formula for erfi(z) yields a wrong(?) minus sign
+    #add(erfi(t), [1], [], [S.Half], [0], -t**2, I/sqrt(pi))
+    add(erfi(t), [S.Half], [], [0], [Rational(-1, 2)], -t**2, t/sqrt(pi))
+
+    # Fresnel Integrals
+    add(fresnels(t), [1], [], [Rational(3, 4)], [0, Rational(1, 4)], pi**2*t**4/16, S.Half)
+    add(fresnelc(t), [1], [], [Rational(1, 4)], [0, Rational(3, 4)], pi**2*t**4/16, S.Half)
+
+    ##### bessel-type functions #####
+    # Section 8.4.19
+    add(besselj(a, t), [], [], [a/2], [-a/2], t**2/4)
+
+    # all of the following are derivable
+    #add(sin(t)*besselj(a, t), [Rational(1, 4), Rational(3, 4)], [], [(1+a)/2],
+    #    [-a/2, a/2, (1-a)/2], t**2, 1/sqrt(2))
+    #add(cos(t)*besselj(a, t), [Rational(1, 4), Rational(3, 4)], [], [a/2],
+    #    [-a/2, (1+a)/2, (1-a)/2], t**2, 1/sqrt(2))
+    #add(besselj(a, t)**2, [S.Half], [], [a], [-a, 0], t**2, 1/sqrt(pi))
+    #add(besselj(a, t)*besselj(b, t), [0, S.Half], [], [(a + b)/2],
+    #    [-(a+b)/2, (a - b)/2, (b - a)/2], t**2, 1/sqrt(pi))
+
+    # Section 8.4.20
+    add(bessely(a, t), [], [-(a + 1)/2], [a/2, -a/2], [-(a + 1)/2], t**2/4)
+
+    # TODO all of the following should be derivable
+    #add(sin(t)*bessely(a, t), [Rational(1, 4), Rational(3, 4)], [(1 - a - 1)/2],
+    #    [(1 + a)/2, (1 - a)/2], [(1 - a - 1)/2, (1 - 1 - a)/2, (1 - 1 + a)/2],
+    #    t**2, 1/sqrt(2))
+    #add(cos(t)*bessely(a, t), [Rational(1, 4), Rational(3, 4)], [(0 - a - 1)/2],
+    #    [(0 + a)/2, (0 - a)/2], [(0 - a - 1)/2, (1 - 0 - a)/2, (1 - 0 + a)/2],
+    #    t**2, 1/sqrt(2))
+    #add(besselj(a, t)*bessely(b, t), [0, S.Half], [(a - b - 1)/2],
+    #    [(a + b)/2, (a - b)/2], [(a - b - 1)/2, -(a + b)/2, (b - a)/2],
+    #    t**2, 1/sqrt(pi))
+    #addi(bessely(a, t)**2,
+    #     [(2/sqrt(pi), meijerg([], [S.Half, S.Half - a], [0, a, -a],
+    #                           [S.Half - a], t**2)),
+    #      (1/sqrt(pi), meijerg([S.Half], [], [a], [-a, 0], t**2))],
+    #     True)
+    #addi(bessely(a, t)*bessely(b, t),
+    #     [(2/sqrt(pi), meijerg([], [0, S.Half, (1 - a - b)/2],
+    #                           [(a + b)/2, (a - b)/2, (b - a)/2, -(a + b)/2],
+    #                           [(1 - a - b)/2], t**2)),
+    #      (1/sqrt(pi), meijerg([0, S.Half], [], [(a + b)/2],
+    #                           [-(a + b)/2, (a - b)/2, (b - a)/2], t**2))],
+    #     True)
+
+    # Section 8.4.21 ?
+    # Section 8.4.22
+    add(besseli(a, t), [], [(1 + a)/2], [a/2], [-a/2, (1 + a)/2], t**2/4, pi)
+    # TODO many more formulas. should all be derivable
+
+    # Section 8.4.23
+    add(besselk(a, t), [], [], [a/2, -a/2], [], t**2/4, S.Half)
+    # TODO many more formulas. should all be derivable
+
+    # Complete elliptic integrals K(z) and E(z)
+    add(elliptic_k(t), [S.Half, S.Half], [], [0], [0], -t, S.Half)
+    add(elliptic_e(t), [S.Half, 3*S.Half], [], [0], [0], -t, Rational(-1, 2)/2)
+
+
+####################################################################
+# First some helper functions.
+####################################################################
+
+from sympy.utilities.timeutils import timethis
+timeit = timethis('meijerg')
+
+
+def _mytype(f: Basic, x: Symbol) -> tuple[type[Basic], ...]:
+    """ Create a hashable entity describing the type of f. """
+    def key(x: type[Basic]) -> tuple[int, int, str]:
+        return x.class_key()
+
+    if x not in f.free_symbols:
+        return ()
+    elif f.is_Function:
+        return type(f),
+    return tuple(sorted((t for a in f.args for t in _mytype(a, x)), key=key))
+
+
+class _CoeffExpValueError(ValueError):
+    """
+    Exception raised by _get_coeff_exp, for internal use only.
+    """
+    pass
+
+
+def _get_coeff_exp(expr, x):
+    """
+    When expr is known to be of the form c*x**b, with c and/or b possibly 1,
+    return c, b.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, a, b
+    >>> from sympy.integrals.meijerint import _get_coeff_exp
+    >>> _get_coeff_exp(a*x**b, x)
+    (a, b)
+    >>> _get_coeff_exp(x, x)
+    (1, 1)
+    >>> _get_coeff_exp(2*x, x)
+    (2, 1)
+    >>> _get_coeff_exp(x**3, x)
+    (1, 3)
+    """
+    from sympy.simplify import powsimp
+    (c, m) = expand_power_base(powsimp(expr)).as_coeff_mul(x)
+    if not m:
+        return c, S.Zero
+    [m] = m
+    if m.is_Pow:
+        if m.base != x:
+            raise _CoeffExpValueError('expr not of form a*x**b')
+        return c, m.exp
+    elif m == x:
+        return c, S.One
+    else:
+        raise _CoeffExpValueError('expr not of form a*x**b: %s' % expr)
+
+
+def _exponents(expr, x):
+    """
+    Find the exponents of ``x`` (not including zero) in ``expr``.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _exponents
+    >>> from sympy.abc import x, y
+    >>> from sympy import sin
+    >>> _exponents(x, x)
+    {1}
+    >>> _exponents(x**2, x)
+    {2}
+    >>> _exponents(x**2 + x, x)
+    {1, 2}
+    >>> _exponents(x**3*sin(x + x**y) + 1/x, x)
+    {-1, 1, 3, y}
+    """
+    def _exponents_(expr, x, res):
+        if expr == x:
+            res.update([1])
+            return
+        if expr.is_Pow and expr.base == x:
+            res.update([expr.exp])
+            return
+        for argument in expr.args:
+            _exponents_(argument, x, res)
+    res = set()
+    _exponents_(expr, x, res)
+    return res
+
+
+def _functions(expr, x):
+    """ Find the types of functions in expr, to estimate the complexity. """
+    return {e.func for e in expr.atoms(Function) if x in e.free_symbols}
+
+
+def _find_splitting_points(expr, x):
+    """
+    Find numbers a such that a linear substitution x -> x + a would
+    (hopefully) simplify expr.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _find_splitting_points as fsp
+    >>> from sympy import sin
+    >>> from sympy.abc import x
+    >>> fsp(x, x)
+    {0}
+    >>> fsp((x-1)**3, x)
+    {1}
+    >>> fsp(sin(x+3)*x, x)
+    {-3, 0}
+    """
+    p, q = [Wild(n, exclude=[x]) for n in 'pq']
+
+    def compute_innermost(expr, res):
+        if not isinstance(expr, Expr):
+            return
+        m = expr.match(p*x + q)
+        if m and m[p] != 0:
+            res.add(-m[q]/m[p])
+            return
+        if expr.is_Atom:
+            return
+        for argument in expr.args:
+            compute_innermost(argument, res)
+    innermost = set()
+    compute_innermost(expr, innermost)
+    return innermost
+
+
+def _split_mul(f, x):
+    """
+    Split expression ``f`` into fac, po, g, where fac is a constant factor,
+    po = x**s for some s independent of s, and g is "the rest".
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _split_mul
+    >>> from sympy import sin
+    >>> from sympy.abc import s, x
+    >>> _split_mul((3*x)**s*sin(x**2)*x, x)
+    (3**s, x*x**s, sin(x**2))
+    """
+    fac = S.One
+    po = S.One
+    g = S.One
+    f = expand_power_base(f)
+
+    args = Mul.make_args(f)
+    for a in args:
+        if a == x:
+            po *= x
+        elif x not in a.free_symbols:
+            fac *= a
+        else:
+            if a.is_Pow and x not in a.exp.free_symbols:
+                c, t = a.base.as_coeff_mul(x)
+                if t != (x,):
+                    c, t = expand_mul(a.base).as_coeff_mul(x)
+                if t == (x,):
+                    po *= x**a.exp
+                    fac *= unpolarify(polarify(c**a.exp, subs=False))
+                    continue
+            g *= a
+
+    return fac, po, g
+
+
+def _mul_args(f):
+    """
+    Return a list ``L`` such that ``Mul(*L) == f``.
+
+    If ``f`` is not a ``Mul`` or ``Pow``, ``L=[f]``.
+    If ``f=g**n`` for an integer ``n``, ``L=[g]*n``.
+    If ``f`` is a ``Mul``, ``L`` comes from applying ``_mul_args`` to all factors of ``f``.
+    """
+    args = Mul.make_args(f)
+    gs = []
+    for g in args:
+        if g.is_Pow and g.exp.is_Integer:
+            n = g.exp
+            base = g.base
+            if n < 0:
+                n = -n
+                base = 1/base
+            gs += [base]*n
+        else:
+            gs.append(g)
+    return gs
+
+
+def _mul_as_two_parts(f):
+    """
+    Find all the ways to split ``f`` into a product of two terms.
+    Return None on failure.
+
+    Explanation
+    ===========
+
+    Although the order is canonical from multiset_partitions, this is
+    not necessarily the best order to process the terms. For example,
+    if the case of len(gs) == 2 is removed and multiset is allowed to
+    sort the terms, some tests fail.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _mul_as_two_parts
+    >>> from sympy import sin, exp, ordered
+    >>> from sympy.abc import x
+    >>> list(ordered(_mul_as_two_parts(x*sin(x)*exp(x))))
+    [(x, exp(x)*sin(x)), (x*exp(x), sin(x)), (x*sin(x), exp(x))]
+    """
+
+    gs = _mul_args(f)
+    if len(gs) < 2:
+        return None
+    if len(gs) == 2:
+        return [tuple(gs)]
+    return [(Mul(*x), Mul(*y)) for (x, y) in multiset_partitions(gs, 2)]
+
+
+def _inflate_g(g, n):
+    """ Return C, h such that h is a G function of argument z**n and
+        g = C*h. """
+    # TODO should this be a method of meijerg?
+    # See: [L, page 150, equation (5)]
+    def inflate(params, n):
+        """ (a1, .., ak) -> (a1/n, (a1+1)/n, ..., (ak + n-1)/n) """
+        return [(a + i)/n for a, i in itertools.product(params, range(n))]
+    v = S(len(g.ap) - len(g.bq))
+    C = n**(1 + g.nu + v/2)
+    C /= (2*pi)**((n - 1)*g.delta)
+    return C, meijerg(inflate(g.an, n), inflate(g.aother, n),
+                      inflate(g.bm, n), inflate(g.bother, n),
+                      g.argument**n * n**(n*v))
+
+
+def _flip_g(g):
+    """ Turn the G function into one of inverse argument
+        (i.e. G(1/x) -> G'(x)) """
+    # See [L], section 5.2
+    def tr(l):
+        return [1 - a for a in l]
+    return meijerg(tr(g.bm), tr(g.bother), tr(g.an), tr(g.aother), 1/g.argument)
+
+
+def _inflate_fox_h(g, a):
+    r"""
+    Let d denote the integrand in the definition of the G function ``g``.
+    Consider the function H which is defined in the same way, but with
+    integrand d/Gamma(a*s) (contour conventions as usual).
+
+    If ``a`` is rational, the function H can be written as C*G, for a constant C
+    and a G-function G.
+
+    This function returns C, G.
+    """
+    if a < 0:
+        return _inflate_fox_h(_flip_g(g), -a)
+    p = S(a.p)
+    q = S(a.q)
+    # We use the substitution s->qs, i.e. inflate g by q. We are left with an
+    # extra factor of Gamma(p*s), for which we use Gauss' multiplication
+    # theorem.
+    D, g = _inflate_g(g, q)
+    z = g.argument
+    D /= (2*pi)**((1 - p)/2)*p**Rational(-1, 2)
+    z /= p**p
+    bs = [(n + 1)/p for n in range(p)]
+    return D, meijerg(g.an, g.aother, g.bm, list(g.bother) + bs, z)
+
+
+_dummies: dict[tuple[str, str], Dummy]  = {}
+
+
+def _dummy(name, token, expr, **kwargs):
+    """
+    Return a dummy. This will return the same dummy if the same token+name is
+    requested more than once, and it is not already in expr.
+    This is for being cache-friendly.
+    """
+    d = _dummy_(name, token, **kwargs)
+    if d in expr.free_symbols:
+        return Dummy(name, **kwargs)
+    return d
+
+
+def _dummy_(name, token, **kwargs):
+    """
+    Return a dummy associated to name and token. Same effect as declaring
+    it globally.
+    """
+    if not (name, token) in _dummies:
+        _dummies[(name, token)] = Dummy(name, **kwargs)
+    return _dummies[(name, token)]
+
+
+def _is_analytic(f, x):
+    """ Check if f(x), when expressed using G functions on the positive reals,
+        will in fact agree with the G functions almost everywhere """
+    return not any(x in expr.free_symbols for expr in f.atoms(Heaviside, Abs))
+
+
+def _condsimp(cond, first=True):
+    """
+    Do naive simplifications on ``cond``.
+
+    Explanation
+    ===========
+
+    Note that this routine is completely ad-hoc, simplification rules being
+    added as need arises rather than following any logical pattern.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _condsimp as simp
+    >>> from sympy import Or, Eq
+    >>> from sympy.abc import x, y
+    >>> simp(Or(x < y, Eq(x, y)))
+    x <= y
+    """
+    if first:
+        cond = cond.replace(lambda _: _.is_Relational, _canonical_coeff)
+        first = False
+    if not isinstance(cond, BooleanFunction):
+        return cond
+    p, q, r = symbols('p q r', cls=Wild)
+    # transforms tests use 0, 4, 5 and 11-14
+    # meijer tests use 0, 2, 11, 14
+    # joint_rv uses 6, 7
+    rules = [
+        (Or(p < q, Eq(p, q)), p <= q),  # 0
+        # The next two obviously are instances of a general pattern, but it is
+        # easier to spell out the few cases we care about.
+        (And(Abs(arg(p)) <= pi, Abs(arg(p) - 2*pi) <= pi),
+         Eq(arg(p) - pi, 0)),  # 1
+        (And(Abs(2*arg(p) + pi) <= pi, Abs(2*arg(p) - pi) <= pi),
+         Eq(arg(p), 0)), # 2
+        (And(Abs(2*arg(p) + pi) < pi, Abs(2*arg(p) - pi) <= pi),
+         S.false),  # 3
+        (And(Abs(arg(p) - pi/2) <= pi/2, Abs(arg(p) + pi/2) <= pi/2),
+         Eq(arg(p), 0)),  # 4
+        (And(Abs(arg(p) - pi/2) <= pi/2, Abs(arg(p) + pi/2) < pi/2),
+         S.false),  # 5
+        (And(Abs(arg(p**2/2 + 1)) < pi, Ne(Abs(arg(p**2/2 + 1)), pi)),
+         S.true),  # 6
+        (Or(Abs(arg(p**2/2 + 1)) < pi, Ne(1/(p**2/2 + 1), 0)),
+         S.true),  # 7
+        (And(Abs(unbranched_argument(p)) <= pi,
+           Abs(unbranched_argument(exp_polar(-2*pi*S.ImaginaryUnit)*p)) <= pi),
+         Eq(unbranched_argument(exp_polar(-S.ImaginaryUnit*pi)*p), 0)),  # 8
+        (And(Abs(unbranched_argument(p)) <= pi/2,
+           Abs(unbranched_argument(exp_polar(-pi*S.ImaginaryUnit)*p)) <= pi/2),
+         Eq(unbranched_argument(exp_polar(-S.ImaginaryUnit*pi/2)*p), 0)),  # 9
+        (Or(p <= q, And(p < q, r)), p <= q),  # 10
+        (Ne(p**2, 1) & (p**2 > 1), p**2 > 1),  # 11
+        (Ne(1/p, 1) & (cos(Abs(arg(p)))*Abs(p) > 1), Abs(p) > 1),  # 12
+        (Ne(p, 2) & (cos(Abs(arg(p)))*Abs(p) > 2), Abs(p) > 2),  # 13
+        ((Abs(arg(p)) < pi/2) & (cos(Abs(arg(p)))*sqrt(Abs(p**2)) > 1), p**2 > 1),  # 14
+    ]
+    cond = cond.func(*[_condsimp(_, first) for _ in cond.args])
+    change = True
+    while change:
+        change = False
+        for irule, (fro, to) in enumerate(rules):
+            if fro.func != cond.func:
+                continue
+            for n, arg1 in enumerate(cond.args):
+                if r in fro.args[0].free_symbols:
+                    m = arg1.match(fro.args[1])
+                    num = 1
+                else:
+                    num = 0
+                    m = arg1.match(fro.args[0])
+                if not m:
+                    continue
+                otherargs = [x.subs(m) for x in fro.args[:num] + fro.args[num + 1:]]
+                otherlist = [n]
+                for arg2 in otherargs:
+                    for k, arg3 in enumerate(cond.args):
+                        if k in otherlist:
+                            continue
+                        if arg2 == arg3:
+                            otherlist += [k]
+                            break
+                        if isinstance(arg3, And) and arg2.args[1] == r and \
+                                isinstance(arg2, And) and arg2.args[0] in arg3.args:
+                            otherlist += [k]
+                            break
+                        if isinstance(arg3, And) and arg2.args[0] == r and \
+                                isinstance(arg2, And) and arg2.args[1] in arg3.args:
+                            otherlist += [k]
+                            break
+                if len(otherlist) != len(otherargs) + 1:
+                    continue
+                newargs = [arg_ for (k, arg_) in enumerate(cond.args)
+                           if k not in otherlist] + [to.subs(m)]
+                if SYMPY_DEBUG:
+                    if irule not in (0, 2, 4, 5, 6, 7, 11, 12, 13, 14):
+                        print('used new rule:', irule)
+                cond = cond.func(*newargs)
+                change = True
+                break
+
+    # final tweak
+    def rel_touchup(rel):
+        if rel.rel_op != '==' or rel.rhs != 0:
+            return rel
+
+        # handle Eq(*, 0)
+        LHS = rel.lhs
+        m = LHS.match(arg(p)**q)
+        if not m:
+            m = LHS.match(unbranched_argument(polar_lift(p)**q))
+        if not m:
+            if isinstance(LHS, periodic_argument) and not LHS.args[0].is_polar \
+                    and LHS.args[1] is S.Infinity:
+                return (LHS.args[0] > 0)
+            return rel
+        return (m[p] > 0)
+    cond = cond.replace(lambda _: _.is_Relational, rel_touchup)
+    if SYMPY_DEBUG:
+        print('_condsimp: ', cond)
+    return cond
+
+def _eval_cond(cond):
+    """ Re-evaluate the conditions. """
+    if isinstance(cond, bool):
+        return cond
+    return _condsimp(cond.doit())
+
+####################################################################
+# Now the "backbone" functions to do actual integration.
+####################################################################
+
+
+def _my_principal_branch(expr, period, full_pb=False):
+    """ Bring expr nearer to its principal branch by removing superfluous
+        factors.
+        This function does *not* guarantee to yield the principal branch,
+        to avoid introducing opaque principal_branch() objects,
+        unless full_pb=True. """
+    res = principal_branch(expr, period)
+    if not full_pb:
+        res = res.replace(principal_branch, lambda x, y: x)
+    return res
+
+
+def _rewrite_saxena_1(fac, po, g, x):
+    """
+    Rewrite the integral fac*po*g dx, from zero to infinity, as
+    integral fac*G, where G has argument a*x. Note po=x**s.
+    Return fac, G.
+    """
+    _, s = _get_coeff_exp(po, x)
+    a, b = _get_coeff_exp(g.argument, x)
+    period = g.get_period()
+    a = _my_principal_branch(a, period)
+
+    # We substitute t = x**b.
+    C = fac/(Abs(b)*a**((s + 1)/b - 1))
+    # Absorb a factor of (at)**((1 + s)/b - 1).
+
+    def tr(l):
+        return [a + (1 + s)/b - 1 for a in l]
+    return C, meijerg(tr(g.an), tr(g.aother), tr(g.bm), tr(g.bother),
+                      a*x)
+
+
+def _check_antecedents_1(g, x, helper=False):
+    r"""
+    Return a condition under which the mellin transform of g exists.
+    Any power of x has already been absorbed into the G function,
+    so this is just $\int_0^\infty g\, dx$.
+
+    See [L, section 5.6.1]. (Note that s=1.)
+
+    If ``helper`` is True, only check if the MT exists at infinity, i.e. if
+    $\int_1^\infty g\, dx$ exists.
+    """
+    # NOTE if you update these conditions, please update the documentation as well
+    delta = g.delta
+    eta, _ = _get_coeff_exp(g.argument, x)
+    m, n, p, q = S([len(g.bm), len(g.an), len(g.ap), len(g.bq)])
+
+    if p > q:
+        def tr(l):
+            return [1 - x for x in l]
+        return _check_antecedents_1(meijerg(tr(g.bm), tr(g.bother),
+                                            tr(g.an), tr(g.aother), x/eta),
+                                    x)
+
+    tmp = [-re(b) < 1 for b in g.bm] + [1 < 1 - re(a) for a in g.an]
+    cond_3 = And(*tmp)
+
+    tmp += [-re(b) < 1 for b in g.bother]
+    tmp += [1 < 1 - re(a) for a in g.aother]
+    cond_3_star = And(*tmp)
+
+    cond_4 = (-re(g.nu) + (q + 1 - p)/2 > q - p)
+
+    def debug(*msg):
+        _debug(*msg)
+
+    def debugf(string, arg):
+        _debugf(string, arg)
+
+    debug('Checking antecedents for 1 function:')
+    debugf('  delta=%s, eta=%s, m=%s, n=%s, p=%s, q=%s',
+           (delta, eta, m, n, p, q))
+    debugf('  ap = %s, %s', (list(g.an), list(g.aother)))
+    debugf('  bq = %s, %s', (list(g.bm), list(g.bother)))
+    debugf('  cond_3=%s, cond_3*=%s, cond_4=%s', (cond_3, cond_3_star, cond_4))
+
+    conds = []
+
+    # case 1
+    case1 = []
+    tmp1 = [1 <= n, p < q, 1 <= m]
+    tmp2 = [1 <= p, 1 <= m, Eq(q, p + 1), Not(And(Eq(n, 0), Eq(m, p + 1)))]
+    tmp3 = [1 <= p, Eq(q, p)]
+    for k in range(ceiling(delta/2) + 1):
+        tmp3 += [Ne(Abs(unbranched_argument(eta)), (delta - 2*k)*pi)]
+    tmp = [delta > 0, Abs(unbranched_argument(eta)) < delta*pi]
+    extra = [Ne(eta, 0), cond_3]
+    if helper:
+        extra = []
+    for t in [tmp1, tmp2, tmp3]:
+        case1 += [And(*(t + tmp + extra))]
+    conds += case1
+    debug('  case 1:', case1)
+
+    # case 2
+    extra = [cond_3]
+    if helper:
+        extra = []
+    case2 = [And(Eq(n, 0), p + 1 <= m, m <= q,
+                 Abs(unbranched_argument(eta)) < delta*pi, *extra)]
+    conds += case2
+    debug('  case 2:', case2)
+
+    # case 3
+    extra = [cond_3, cond_4]
+    if helper:
+        extra = []
+    case3 = [And(p < q, 1 <= m, delta > 0, Eq(Abs(unbranched_argument(eta)), delta*pi),
+                 *extra)]
+    case3 += [And(p <= q - 2, Eq(delta, 0), Eq(Abs(unbranched_argument(eta)), 0), *extra)]
+    conds += case3
+    debug('  case 3:', case3)
+
+    # TODO altered cases 4-7
+
+    # extra case from wofram functions site:
+    # (reproduced verbatim from Prudnikov, section 2.24.2)
+    # https://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/01/
+    case_extra = []
+    case_extra += [Eq(p, q), Eq(delta, 0), Eq(unbranched_argument(eta), 0), Ne(eta, 0)]
+    if not helper:
+        case_extra += [cond_3]
+    s = []
+    for a, b in zip(g.ap, g.bq):
+        s += [b - a]
+    case_extra += [re(Add(*s)) < 0]
+    case_extra = And(*case_extra)
+    conds += [case_extra]
+    debug('  extra case:', [case_extra])
+
+    case_extra_2 = [And(delta > 0, Abs(unbranched_argument(eta)) < delta*pi)]
+    if not helper:
+        case_extra_2 += [cond_3]
+    case_extra_2 = And(*case_extra_2)
+    conds += [case_extra_2]
+    debug('  second extra case:', [case_extra_2])
+
+    # TODO This leaves only one case from the three listed by Prudnikov.
+    #      Investigate if these indeed cover everything; if so, remove the rest.
+
+    return Or(*conds)
+
+
+def _int0oo_1(g, x):
+    r"""
+    Evaluate $\int_0^\infty g\, dx$ using G functions,
+    assuming the necessary conditions are fulfilled.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import a, b, c, d, x, y
+    >>> from sympy import meijerg
+    >>> from sympy.integrals.meijerint import _int0oo_1
+    >>> _int0oo_1(meijerg([a], [b], [c], [d], x*y), x)
+    gamma(-a)*gamma(c + 1)/(y*gamma(-d)*gamma(b + 1))
+    """
+    from sympy.simplify import gammasimp
+    # See [L, section 5.6.1]. Note that s=1.
+    eta, _ = _get_coeff_exp(g.argument, x)
+    res = 1/eta
+    # XXX TODO we should reduce order first
+    for b in g.bm:
+        res *= gamma(b + 1)
+    for a in g.an:
+        res *= gamma(1 - a - 1)
+    for b in g.bother:
+        res /= gamma(1 - b - 1)
+    for a in g.aother:
+        res /= gamma(a + 1)
+    return gammasimp(unpolarify(res))
+
+
+def _rewrite_saxena(fac, po, g1, g2, x, full_pb=False):
+    """
+    Rewrite the integral ``fac*po*g1*g2`` from 0 to oo in terms of G
+    functions with argument ``c*x``.
+
+    Explanation
+    ===========
+
+    Return C, f1, f2 such that integral C f1 f2 from 0 to infinity equals
+    integral fac ``po``, ``g1``, ``g2`` from 0 to infinity.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _rewrite_saxena
+    >>> from sympy.abc import s, t, m
+    >>> from sympy import meijerg
+    >>> g1 = meijerg([], [], [0], [], s*t)
+    >>> g2 = meijerg([], [], [m/2], [-m/2], t**2/4)
+    >>> r = _rewrite_saxena(1, t**0, g1, g2, t)
+    >>> r[0]
+    s/(4*sqrt(pi))
+    >>> r[1]
+    meijerg(((), ()), ((-1/2, 0), ()), s**2*t/4)
+    >>> r[2]
+    meijerg(((), ()), ((m/2,), (-m/2,)), t/4)
+    """
+    def pb(g):
+        a, b = _get_coeff_exp(g.argument, x)
+        per = g.get_period()
+        return meijerg(g.an, g.aother, g.bm, g.bother,
+                       _my_principal_branch(a, per, full_pb)*x**b)
+
+    _, s = _get_coeff_exp(po, x)
+    _, b1 = _get_coeff_exp(g1.argument, x)
+    _, b2 = _get_coeff_exp(g2.argument, x)
+    if (b1 < 0) == True:
+        b1 = -b1
+        g1 = _flip_g(g1)
+    if (b2 < 0) == True:
+        b2 = -b2
+        g2 = _flip_g(g2)
+    if not b1.is_Rational or not b2.is_Rational:
+        return
+    m1, n1 = b1.p, b1.q
+    m2, n2 = b2.p, b2.q
+    tau = ilcm(m1*n2, m2*n1)
+    r1 = tau//(m1*n2)
+    r2 = tau//(m2*n1)
+
+    C1, g1 = _inflate_g(g1, r1)
+    C2, g2 = _inflate_g(g2, r2)
+    g1 = pb(g1)
+    g2 = pb(g2)
+
+    fac *= C1*C2
+    a1, b = _get_coeff_exp(g1.argument, x)
+    a2, _ = _get_coeff_exp(g2.argument, x)
+
+    # arbitrarily tack on the x**s part to g1
+    # TODO should we try both?
+    exp = (s + 1)/b - 1
+    fac = fac/(Abs(b) * a1**exp)
+
+    def tr(l):
+        return [a + exp for a in l]
+    g1 = meijerg(tr(g1.an), tr(g1.aother), tr(g1.bm), tr(g1.bother), a1*x)
+    g2 = meijerg(g2.an, g2.aother, g2.bm, g2.bother, a2*x)
+
+    from sympy.simplify import powdenest
+    return powdenest(fac, polar=True), g1, g2
+
+
+def _check_antecedents(g1, g2, x):
+    """ Return a condition under which the integral theorem applies. """
+    #  Yes, this is madness.
+    # XXX TODO this is a testing *nightmare*
+    # NOTE if you update these conditions, please update the documentation as well
+
+    # The following conditions are found in
+    # [P], Section 2.24.1
+    #
+    # They are also reproduced (verbatim!) at
+    # https://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/03/
+    #
+    # Note: k=l=r=alpha=1
+    sigma, _ = _get_coeff_exp(g1.argument, x)
+    omega, _ = _get_coeff_exp(g2.argument, x)
+    s, t, u, v = S([len(g1.bm), len(g1.an), len(g1.ap), len(g1.bq)])
+    m, n, p, q = S([len(g2.bm), len(g2.an), len(g2.ap), len(g2.bq)])
+    bstar = s + t - (u + v)/2
+    cstar = m + n - (p + q)/2
+    rho = g1.nu + (u - v)/2 + 1
+    mu = g2.nu + (p - q)/2 + 1
+    phi = q - p - (v - u)
+    eta = 1 - (v - u) - mu - rho
+    psi = (pi*(q - m - n) + Abs(unbranched_argument(omega)))/(q - p)
+    theta = (pi*(v - s - t) + Abs(unbranched_argument(sigma)))/(v - u)
+
+    _debug('Checking antecedents:')
+    _debugf('  sigma=%s, s=%s, t=%s, u=%s, v=%s, b*=%s, rho=%s',
+            (sigma, s, t, u, v, bstar, rho))
+    _debugf('  omega=%s, m=%s, n=%s, p=%s, q=%s, c*=%s, mu=%s,',
+            (omega, m, n, p, q, cstar, mu))
+    _debugf('  phi=%s, eta=%s, psi=%s, theta=%s', (phi, eta, psi, theta))
+
+    def _c1():
+        for g in [g1, g2]:
+            for i, j in itertools.product(g.an, g.bm):
+                diff = i - j
+                if diff.is_integer and diff.is_positive:
+                    return False
+        return True
+    c1 = _c1()
+    c2 = And(*[re(1 + i + j) > 0 for i in g1.bm for j in g2.bm])
+    c3 = And(*[re(1 + i + j) < 1 + 1 for i in g1.an for j in g2.an])
+    c4 = And(*[(p - q)*re(1 + i - 1) - re(mu) > Rational(-3, 2) for i in g1.an])
+    c5 = And(*[(p - q)*re(1 + i) - re(mu) > Rational(-3, 2) for i in g1.bm])
+    c6 = And(*[(u - v)*re(1 + i - 1) - re(rho) > Rational(-3, 2) for i in g2.an])
+    c7 = And(*[(u - v)*re(1 + i) - re(rho) > Rational(-3, 2) for i in g2.bm])
+    c8 = (Abs(phi) + 2*re((rho - 1)*(q - p) + (v - u)*(q - p) + (mu -
+          1)*(v - u)) > 0)
+    c9 = (Abs(phi) - 2*re((rho - 1)*(q - p) + (v - u)*(q - p) + (mu -
+          1)*(v - u)) > 0)
+    c10 = (Abs(unbranched_argument(sigma)) < bstar*pi)
+    c11 = Eq(Abs(unbranched_argument(sigma)), bstar*pi)
+    c12 = (Abs(unbranched_argument(omega)) < cstar*pi)
+    c13 = Eq(Abs(unbranched_argument(omega)), cstar*pi)
+
+    # The following condition is *not* implemented as stated on the wolfram
+    # function site. In the book of Prudnikov there is an additional part
+    # (the And involving re()). However, I only have this book in russian, and
+    # I don't read any russian. The following condition is what other people
+    # have told me it means.
+    # Worryingly, it is different from the condition implemented in REDUCE.
+    # The REDUCE implementation:
+    #   https://reduce-algebra.svn.sourceforge.net/svnroot/reduce-algebra/trunk/packages/defint/definta.red
+    #   (search for tst14)
+    # The Wolfram alpha version:
+    #   https://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/03/03/0014/
+    z0 = exp(-(bstar + cstar)*pi*S.ImaginaryUnit)
+    zos = unpolarify(z0*omega/sigma)
+    zso = unpolarify(z0*sigma/omega)
+    if zos == 1/zso:
+        c14 = And(Eq(phi, 0), bstar + cstar <= 1,
+                  Or(Ne(zos, 1), re(mu + rho + v - u) < 1,
+                     re(mu + rho + q - p) < 1))
+    else:
+        def _cond(z):
+            '''Returns True if abs(arg(1-z)) < pi, avoiding arg(0).
+
+            Explanation
+            ===========
+
+            If ``z`` is 1 then arg is NaN. This raises a
+            TypeError on `NaN < pi`. Previously this gave `False` so
+            this behavior has been hardcoded here but someone should
+            check if this NaN is more serious! This NaN is triggered by
+            test_meijerint() in test_meijerint.py:
+            `meijerint_definite(exp(x), x, 0, I)`
+            '''
+            return z != 1 and Abs(arg(1 - z)) < pi
+
+        c14 = And(Eq(phi, 0), bstar - 1 + cstar <= 0,
+                  Or(And(Ne(zos, 1), _cond(zos)),
+                     And(re(mu + rho + v - u) < 1, Eq(zos, 1))))
+
+        c14_alt = And(Eq(phi, 0), cstar - 1 + bstar <= 0,
+                  Or(And(Ne(zso, 1), _cond(zso)),
+                     And(re(mu + rho + q - p) < 1, Eq(zso, 1))))
+
+        # Since r=k=l=1, in our case there is c14_alt which is the same as calling
+        # us with (g1, g2) = (g2, g1). The conditions below enumerate all cases
+        # (i.e. we don't have to try arguments reversed by hand), and indeed try
+        # all symmetric cases. (i.e. whenever there is a condition involving c14,
+        # there is also a dual condition which is exactly what we would get when g1,
+        # g2 were interchanged, *but c14 was unaltered*).
+        # Hence the following seems correct:
+        c14 = Or(c14, c14_alt)
+
+    '''
+    When `c15` is NaN (e.g. from `psi` being NaN as happens during
+    'test_issue_4992' and/or `theta` is NaN as in 'test_issue_6253',
+    both in `test_integrals.py`) the comparison to 0 formerly gave False
+    whereas now an error is raised. To keep the old behavior, the value
+    of NaN is replaced with False but perhaps a closer look at this condition
+    should be made: XXX how should conditions leading to c15=NaN be handled?
+    '''
+    try:
+        lambda_c = (q - p)*Abs(omega)**(1/(q - p))*cos(psi) \
+            + (v - u)*Abs(sigma)**(1/(v - u))*cos(theta)
+        # the TypeError might be raised here, e.g. if lambda_c is NaN
+        if _eval_cond(lambda_c > 0) != False:
+            c15 = (lambda_c > 0)
+        else:
+            def lambda_s0(c1, c2):
+                return c1*(q - p)*Abs(omega)**(1/(q - p))*sin(psi) \
+                    + c2*(v - u)*Abs(sigma)**(1/(v - u))*sin(theta)
+            lambda_s = Piecewise(
+                ((lambda_s0(+1, +1)*lambda_s0(-1, -1)),
+                 And(Eq(unbranched_argument(sigma), 0), Eq(unbranched_argument(omega), 0))),
+                (lambda_s0(sign(unbranched_argument(omega)), +1)*lambda_s0(sign(unbranched_argument(omega)), -1),
+                 And(Eq(unbranched_argument(sigma), 0), Ne(unbranched_argument(omega), 0))),
+                (lambda_s0(+1, sign(unbranched_argument(sigma)))*lambda_s0(-1, sign(unbranched_argument(sigma))),
+                 And(Ne(unbranched_argument(sigma), 0), Eq(unbranched_argument(omega), 0))),
+                (lambda_s0(sign(unbranched_argument(omega)), sign(unbranched_argument(sigma))), True))
+            tmp = [lambda_c > 0,
+                   And(Eq(lambda_c, 0), Ne(lambda_s, 0), re(eta) > -1),
+                   And(Eq(lambda_c, 0), Eq(lambda_s, 0), re(eta) > 0)]
+            c15 = Or(*tmp)
+    except TypeError:
+        c15 = False
+    for cond, i in [(c1, 1), (c2, 2), (c3, 3), (c4, 4), (c5, 5), (c6, 6),
+                    (c7, 7), (c8, 8), (c9, 9), (c10, 10), (c11, 11),
+                    (c12, 12), (c13, 13), (c14, 14), (c15, 15)]:
+        _debugf('  c%s: %s', (i, cond))
+
+    # We will return Or(*conds)
+    conds = []
+
+    def pr(count):
+        _debugf('  case %s: %s', (count, conds[-1]))
+    conds += [And(m*n*s*t != 0, bstar.is_positive is True, cstar.is_positive is True, c1, c2, c3, c10,
+                  c12)]  # 1
+    pr(1)
+    conds += [And(Eq(u, v), Eq(bstar, 0), cstar.is_positive is True, sigma.is_positive is True, re(rho) < 1,
+                  c1, c2, c3, c12)]  # 2
+    pr(2)
+    conds += [And(Eq(p, q), Eq(cstar, 0), bstar.is_positive is True, omega.is_positive is True, re(mu) < 1,
+                  c1, c2, c3, c10)]  # 3
+    pr(3)
+    conds += [And(Eq(p, q), Eq(u, v), Eq(bstar, 0), Eq(cstar, 0),
+                  sigma.is_positive is True, omega.is_positive is True, re(mu) < 1, re(rho) < 1,
+                  Ne(sigma, omega), c1, c2, c3)]  # 4
+    pr(4)
+    conds += [And(Eq(p, q), Eq(u, v), Eq(bstar, 0), Eq(cstar, 0),
+                  sigma.is_positive is True, omega.is_positive is True, re(mu + rho) < 1,
+                  Ne(omega, sigma), c1, c2, c3)]  # 5
+    pr(5)
+    conds += [And(p > q, s.is_positive is True, bstar.is_positive is True, cstar >= 0,
+                  c1, c2, c3, c5, c10, c13)]  # 6
+    pr(6)
+    conds += [And(p < q, t.is_positive is True, bstar.is_positive is True, cstar >= 0,
+                  c1, c2, c3, c4, c10, c13)]  # 7
+    pr(7)
+    conds += [And(u > v, m.is_positive is True, cstar.is_positive is True, bstar >= 0,
+                  c1, c2, c3, c7, c11, c12)]  # 8
+    pr(8)
+    conds += [And(u < v, n.is_positive is True, cstar.is_positive is True, bstar >= 0,
+                  c1, c2, c3, c6, c11, c12)]  # 9
+    pr(9)
+    conds += [And(p > q, Eq(u, v), Eq(bstar, 0), cstar >= 0, sigma.is_positive is True,
+                  re(rho) < 1, c1, c2, c3, c5, c13)]  # 10
+    pr(10)
+    conds += [And(p < q, Eq(u, v), Eq(bstar, 0), cstar >= 0, sigma.is_positive is True,
+                  re(rho) < 1, c1, c2, c3, c4, c13)]  # 11
+    pr(11)
+    conds += [And(Eq(p, q), u > v, bstar >= 0, Eq(cstar, 0), omega.is_positive is True,
+                  re(mu) < 1, c1, c2, c3, c7, c11)]  # 12
+    pr(12)
+    conds += [And(Eq(p, q), u < v, bstar >= 0, Eq(cstar, 0), omega.is_positive is True,
+                  re(mu) < 1, c1, c2, c3, c6, c11)]  # 13
+    pr(13)
+    conds += [And(p < q, u > v, bstar >= 0, cstar >= 0,
+                  c1, c2, c3, c4, c7, c11, c13)]  # 14
+    pr(14)
+    conds += [And(p > q, u < v, bstar >= 0, cstar >= 0,
+                  c1, c2, c3, c5, c6, c11, c13)]  # 15
+    pr(15)
+    conds += [And(p > q, u > v, bstar >= 0, cstar >= 0,
+                  c1, c2, c3, c5, c7, c8, c11, c13, c14)]  # 16
+    pr(16)
+    conds += [And(p < q, u < v, bstar >= 0, cstar >= 0,
+                  c1, c2, c3, c4, c6, c9, c11, c13, c14)]  # 17
+    pr(17)
+    conds += [And(Eq(t, 0), s.is_positive is True, bstar.is_positive is True, phi.is_positive is True, c1, c2, c10)]  # 18
+    pr(18)
+    conds += [And(Eq(s, 0), t.is_positive is True, bstar.is_positive is True, phi.is_negative is True, c1, c3, c10)]  # 19
+    pr(19)
+    conds += [And(Eq(n, 0), m.is_positive is True, cstar.is_positive is True, phi.is_negative is True, c1, c2, c12)]  # 20
+    pr(20)
+    conds += [And(Eq(m, 0), n.is_positive is True, cstar.is_positive is True, phi.is_positive is True, c1, c3, c12)]  # 21
+    pr(21)
+    conds += [And(Eq(s*t, 0), bstar.is_positive is True, cstar.is_positive is True,
+                  c1, c2, c3, c10, c12)]  # 22
+    pr(22)
+    conds += [And(Eq(m*n, 0), bstar.is_positive is True, cstar.is_positive is True,
+                  c1, c2, c3, c10, c12)]  # 23
+    pr(23)
+
+    # The following case is from [Luke1969]. As far as I can tell, it is *not*
+    # covered by Prudnikov's.
+    # Let G1 and G2 be the two G-functions. Suppose the integral exists from
+    # 0 to a > 0 (this is easy the easy part), that G1 is exponential decay at
+    # infinity, and that the mellin transform of G2 exists.
+    # Then the integral exists.
+    mt1_exists = _check_antecedents_1(g1, x, helper=True)
+    mt2_exists = _check_antecedents_1(g2, x, helper=True)
+    conds += [And(mt2_exists, Eq(t, 0), u < s, bstar.is_positive is True, c10, c1, c2, c3)]
+    pr('E1')
+    conds += [And(mt2_exists, Eq(s, 0), v < t, bstar.is_positive is True, c10, c1, c2, c3)]
+    pr('E2')
+    conds += [And(mt1_exists, Eq(n, 0), p < m, cstar.is_positive is True, c12, c1, c2, c3)]
+    pr('E3')
+    conds += [And(mt1_exists, Eq(m, 0), q < n, cstar.is_positive is True, c12, c1, c2, c3)]
+    pr('E4')
+
+    # Let's short-circuit if this worked ...
+    # the rest is corner-cases and terrible to read.
+    r = Or(*conds)
+    if _eval_cond(r) != False:
+        return r
+
+    conds += [And(m + n > p, Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True, cstar.is_negative is True,
+                  Abs(unbranched_argument(omega)) < (m + n - p + 1)*pi,
+                  c1, c2, c10, c14, c15)]  # 24
+    pr(24)
+    conds += [And(m + n > q, Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, cstar.is_negative is True,
+                  Abs(unbranched_argument(omega)) < (m + n - q + 1)*pi,
+                  c1, c3, c10, c14, c15)]  # 25
+    pr(25)
+    conds += [And(Eq(p, q - 1), Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True,
+                  cstar >= 0, cstar*pi < Abs(unbranched_argument(omega)),
+                  c1, c2, c10, c14, c15)]  # 26
+    pr(26)
+    conds += [And(Eq(p, q + 1), Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True,
+                  cstar >= 0, cstar*pi < Abs(unbranched_argument(omega)),
+                  c1, c3, c10, c14, c15)]  # 27
+    pr(27)
+    conds += [And(p < q - 1, Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True,
+                  cstar >= 0, cstar*pi < Abs(unbranched_argument(omega)),
+                  Abs(unbranched_argument(omega)) < (m + n - p + 1)*pi,
+                  c1, c2, c10, c14, c15)]  # 28
+    pr(28)
+    conds += [And(
+        p > q + 1, Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, cstar >= 0,
+                  cstar*pi < Abs(unbranched_argument(omega)),
+                  Abs(unbranched_argument(omega)) < (m + n - q + 1)*pi,
+                  c1, c3, c10, c14, c15)]  # 29
+    pr(29)
+    conds += [And(Eq(n, 0), Eq(phi, 0), s + t > 0, m.is_positive is True, cstar.is_positive is True, bstar.is_negative is True,
+                  Abs(unbranched_argument(sigma)) < (s + t - u + 1)*pi,
+                  c1, c2, c12, c14, c15)]  # 30
+    pr(30)
+    conds += [And(Eq(m, 0), Eq(phi, 0), s + t > v, n.is_positive is True, cstar.is_positive is True, bstar.is_negative is True,
+                  Abs(unbranched_argument(sigma)) < (s + t - v + 1)*pi,
+                  c1, c3, c12, c14, c15)]  # 31
+    pr(31)
+    conds += [And(Eq(n, 0), Eq(phi, 0), Eq(u, v - 1), m.is_positive is True, cstar.is_positive is True,
+                  bstar >= 0, bstar*pi < Abs(unbranched_argument(sigma)),
+                  Abs(unbranched_argument(sigma)) < (bstar + 1)*pi,
+                  c1, c2, c12, c14, c15)]  # 32
+    pr(32)
+    conds += [And(Eq(m, 0), Eq(phi, 0), Eq(u, v + 1), n.is_positive is True, cstar.is_positive is True,
+                  bstar >= 0, bstar*pi < Abs(unbranched_argument(sigma)),
+                  Abs(unbranched_argument(sigma)) < (bstar + 1)*pi,
+                  c1, c3, c12, c14, c15)]  # 33
+    pr(33)
+    conds += [And(
+        Eq(n, 0), Eq(phi, 0), u < v - 1, m.is_positive is True, cstar.is_positive is True, bstar >= 0,
+        bstar*pi < Abs(unbranched_argument(sigma)),
+        Abs(unbranched_argument(sigma)) < (s + t - u + 1)*pi,
+        c1, c2, c12, c14, c15)]  # 34
+    pr(34)
+    conds += [And(
+        Eq(m, 0), Eq(phi, 0), u > v + 1, n.is_positive is True, cstar.is_positive is True, bstar >= 0,
+        bstar*pi < Abs(unbranched_argument(sigma)),
+        Abs(unbranched_argument(sigma)) < (s + t - v + 1)*pi,
+        c1, c3, c12, c14, c15)]  # 35
+    pr(35)
+
+    return Or(*conds)
+
+    # NOTE An alternative, but as far as I can tell weaker, set of conditions
+    #      can be found in [L, section 5.6.2].
+
+
+def _int0oo(g1, g2, x):
+    """
+    Express integral from zero to infinity g1*g2 using a G function,
+    assuming the necessary conditions are fulfilled.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import _int0oo
+    >>> from sympy.abc import s, t, m
+    >>> from sympy import meijerg, S
+    >>> g1 = meijerg([], [], [-S(1)/2, 0], [], s**2*t/4)
+    >>> g2 = meijerg([], [], [m/2], [-m/2], t/4)
+    >>> _int0oo(g1, g2, t)
+    4*meijerg(((0, 1/2), ()), ((m/2,), (-m/2,)), s**(-2))/s**2
+    """
+    # See: [L, section 5.6.2, equation (1)]
+    eta, _ = _get_coeff_exp(g1.argument, x)
+    omega, _ = _get_coeff_exp(g2.argument, x)
+
+    def neg(l):
+        return [-x for x in l]
+    a1 = neg(g1.bm) + list(g2.an)
+    a2 = list(g2.aother) + neg(g1.bother)
+    b1 = neg(g1.an) + list(g2.bm)
+    b2 = list(g2.bother) + neg(g1.aother)
+    return meijerg(a1, a2, b1, b2, omega/eta)/eta
+
+
+def _rewrite_inversion(fac, po, g, x):
+    """ Absorb ``po`` == x**s into g. """
+    _, s = _get_coeff_exp(po, x)
+    a, b = _get_coeff_exp(g.argument, x)
+
+    def tr(l):
+        return [t + s/b for t in l]
+    from sympy.simplify import powdenest
+    return (powdenest(fac/a**(s/b), polar=True),
+            meijerg(tr(g.an), tr(g.aother), tr(g.bm), tr(g.bother), g.argument))
+
+
+def _check_antecedents_inversion(g, x):
+    """ Check antecedents for the laplace inversion integral. """
+    _debug('Checking antecedents for inversion:')
+    z = g.argument
+    _, e = _get_coeff_exp(z, x)
+    if e < 0:
+        _debug('  Flipping G.')
+        # We want to assume that argument gets large as |x| -> oo
+        return _check_antecedents_inversion(_flip_g(g), x)
+
+    def statement_half(a, b, c, z, plus):
+        coeff, exponent = _get_coeff_exp(z, x)
+        a *= exponent
+        b *= coeff**c
+        c *= exponent
+        conds = []
+        wp = b*exp(S.ImaginaryUnit*re(c)*pi/2)
+        wm = b*exp(-S.ImaginaryUnit*re(c)*pi/2)
+        if plus:
+            w = wp
+        else:
+            w = wm
+        conds += [And(Or(Eq(b, 0), re(c) <= 0), re(a) <= -1)]
+        conds += [And(Ne(b, 0), Eq(im(c), 0), re(c) > 0, re(w) < 0)]
+        conds += [And(Ne(b, 0), Eq(im(c), 0), re(c) > 0, re(w) <= 0,
+                      re(a) <= -1)]
+        return Or(*conds)
+
+    def statement(a, b, c, z):
+        """ Provide a convergence statement for z**a * exp(b*z**c),
+             c/f sphinx docs. """
+        return And(statement_half(a, b, c, z, True),
+                   statement_half(a, b, c, z, False))
+
+    # Notations from [L], section 5.7-10
+    m, n, p, q = S([len(g.bm), len(g.an), len(g.ap), len(g.bq)])
+    tau = m + n - p
+    nu = q - m - n
+    rho = (tau - nu)/2
+    sigma = q - p
+    if sigma == 1:
+        epsilon = S.Half
+    elif sigma > 1:
+        epsilon = 1
+    else:
+        epsilon = S.NaN
+    theta = ((1 - sigma)/2 + Add(*g.bq) - Add(*g.ap))/sigma
+    delta = g.delta
+    _debugf('  m=%s, n=%s, p=%s, q=%s, tau=%s, nu=%s, rho=%s, sigma=%s',
+            (m, n, p, q, tau, nu, rho, sigma))
+    _debugf('  epsilon=%s, theta=%s, delta=%s', (epsilon, theta, delta))
+
+    # First check if the computation is valid.
+    if not (g.delta >= e/2 or (p >= 1 and p >= q)):
+        _debug('  Computation not valid for these parameters.')
+        return False
+
+    # Now check if the inversion integral exists.
+
+    # Test "condition A"
+    for a, b in itertools.product(g.an, g.bm):
+        if (a - b).is_integer and a > b:
+            _debug('  Not a valid G function.')
+            return False
+
+    # There are two cases. If p >= q, we can directly use a slater expansion
+    # like [L], 5.2 (11). Note in particular that the asymptotics of such an
+    # expansion even hold when some of the parameters differ by integers, i.e.
+    # the formula itself would not be valid! (b/c G functions are cts. in their
+    # parameters)
+    # When p < q, we need to use the theorems of [L], 5.10.
+
+    if p >= q:
+        _debug('  Using asymptotic Slater expansion.')
+        return And(*[statement(a - 1, 0, 0, z) for a in g.an])
+
+    def E(z):
+        return And(*[statement(a - 1, 0, 0, z) for a in g.an])
+
+    def H(z):
+        return statement(theta, -sigma, 1/sigma, z)
+
+    def Hp(z):
+        return statement_half(theta, -sigma, 1/sigma, z, True)
+
+    def Hm(z):
+        return statement_half(theta, -sigma, 1/sigma, z, False)
+
+    # [L], section 5.10
+    conds = []
+    # Theorem 1 -- p < q from test above
+    conds += [And(1 <= n, 1 <= m, rho*pi - delta >= pi/2, delta > 0,
+                  E(z*exp(S.ImaginaryUnit*pi*(nu + 1))))]
+    # Theorem 2, statements (2) and (3)
+    conds += [And(p + 1 <= m, m + 1 <= q, delta > 0, delta < pi/2, n == 0,
+                  (m - p + 1)*pi - delta >= pi/2,
+                  Hp(z*exp(S.ImaginaryUnit*pi*(q - m))),
+                  Hm(z*exp(-S.ImaginaryUnit*pi*(q - m))))]
+    # Theorem 2, statement (5)  -- p < q from test above
+    conds += [And(m == q, n == 0, delta > 0,
+                  (sigma + epsilon)*pi - delta >= pi/2, H(z))]
+    # Theorem 3, statements (6) and (7)
+    conds += [And(Or(And(p <= q - 2, 1 <= tau, tau <= sigma/2),
+                     And(p + 1 <= m + n, m + n <= (p + q)/2)),
+                  delta > 0, delta < pi/2, (tau + 1)*pi - delta >= pi/2,
+                  Hp(z*exp(S.ImaginaryUnit*pi*nu)),
+                  Hm(z*exp(-S.ImaginaryUnit*pi*nu)))]
+    # Theorem 4, statements (10) and (11)  -- p < q from test above
+    conds += [And(1 <= m, rho > 0, delta > 0, delta + rho*pi < pi/2,
+                  (tau + epsilon)*pi - delta >= pi/2,
+                  Hp(z*exp(S.ImaginaryUnit*pi*nu)),
+                  Hm(z*exp(-S.ImaginaryUnit*pi*nu)))]
+    # Trivial case
+    conds += [m == 0]
+
+    # TODO
+    # Theorem 5 is quite general
+    # Theorem 6 contains special cases for q=p+1
+
+    return Or(*conds)
+
+
+def _int_inversion(g, x, t):
+    """
+    Compute the laplace inversion integral, assuming the formula applies.
+    """
+    b, a = _get_coeff_exp(g.argument, x)
+    C, g = _inflate_fox_h(meijerg(g.an, g.aother, g.bm, g.bother, b/t**a), -a)
+    return C/t*g
+
+
+####################################################################
+# Finally, the real meat.
+####################################################################
+
+_lookup_table = None
+
+
+@cacheit
+@timeit
+def _rewrite_single(f, x, recursive=True):
+    """
+    Try to rewrite f as a sum of single G functions of the form
+    C*x**s*G(a*x**b), where b is a rational number and C is independent of x.
+    We guarantee that result.argument.as_coeff_mul(x) returns (a, (x**b,))
+    or (a, ()).
+    Returns a list of tuples (C, s, G) and a condition cond.
+    Returns None on failure.
+    """
+    from .transforms import (mellin_transform, inverse_mellin_transform,
+        IntegralTransformError, MellinTransformStripError)
+
+    global _lookup_table
+    if not _lookup_table:
+        _lookup_table = {}
+        _create_lookup_table(_lookup_table)
+
+    if isinstance(f, meijerg):
+        coeff, m = factor(f.argument, x).as_coeff_mul(x)
+        if len(m) > 1:
+            return None
+        m = m[0]
+        if m.is_Pow:
+            if m.base != x or not m.exp.is_Rational:
+                return None
+        elif m != x:
+            return None
+        return [(1, 0, meijerg(f.an, f.aother, f.bm, f.bother, coeff*m))], True
+
+    f_ = f
+    f = f.subs(x, z)
+    t = _mytype(f, z)
+    if t in _lookup_table:
+        l = _lookup_table[t]
+        for formula, terms, cond, hint in l:
+            subs = f.match(formula, old=True)
+            if subs:
+                subs_ = {}
+                for fro, to in subs.items():
+                    subs_[fro] = unpolarify(polarify(to, lift=True),
+                                            exponents_only=True)
+                subs = subs_
+                if not isinstance(hint, bool):
+                    hint = hint.subs(subs)
+                if hint == False:
+                    continue
+                if not isinstance(cond, (bool, BooleanAtom)):
+                    cond = unpolarify(cond.subs(subs))
+                if _eval_cond(cond) == False:
+                    continue
+                if not isinstance(terms, list):
+                    terms = terms(subs)
+                res = []
+                for fac, g in terms:
+                    r1 = _get_coeff_exp(unpolarify(fac.subs(subs).subs(z, x),
+                                                   exponents_only=True), x)
+                    try:
+                        g = g.subs(subs).subs(z, x)
+                    except ValueError:
+                        continue
+                    # NOTE these substitutions can in principle introduce oo,
+                    #      zoo and other absurdities. It shouldn't matter,
+                    #      but better be safe.
+                    if Tuple(*(r1 + (g,))).has(S.Infinity, S.ComplexInfinity, S.NegativeInfinity):
+                        continue
+                    g = meijerg(g.an, g.aother, g.bm, g.bother,
+                                unpolarify(g.argument, exponents_only=True))
+                    res.append(r1 + (g,))
+                if res:
+                    return res, cond
+
+    # try recursive mellin transform
+    if not recursive:
+        return None
+    _debug('Trying recursive Mellin transform method.')
+
+    def my_imt(F, s, x, strip):
+        """ Calling simplify() all the time is slow and not helpful, since
+            most of the time it only factors things in a way that has to be
+            un-done anyway. But sometimes it can remove apparent poles. """
+        # XXX should this be in inverse_mellin_transform?
+        try:
+            return inverse_mellin_transform(F, s, x, strip,
+                                            as_meijerg=True, needeval=True)
+        except MellinTransformStripError:
+            from sympy.simplify import simplify
+            return inverse_mellin_transform(
+                simplify(cancel(expand(F))), s, x, strip,
+                as_meijerg=True, needeval=True)
+    f = f_
+    s = _dummy('s', 'rewrite-single', f)
+    # to avoid infinite recursion, we have to force the two g functions case
+
+    def my_integrator(f, x):
+        r = _meijerint_definite_4(f, x, only_double=True)
+        if r is not None:
+            from sympy.simplify import hyperexpand
+            res, cond = r
+            res = _my_unpolarify(hyperexpand(res, rewrite='nonrepsmall'))
+            return Piecewise((res, cond),
+                             (Integral(f, (x, S.Zero, S.Infinity)), True))
+        return Integral(f, (x, S.Zero, S.Infinity))
+    try:
+        F, strip, _ = mellin_transform(f, x, s, integrator=my_integrator,
+                                       simplify=False, needeval=True)
+        g = my_imt(F, s, x, strip)
+    except IntegralTransformError:
+        g = None
+    if g is None:
+        # We try to find an expression by analytic continuation.
+        # (also if the dummy is already in the expression, there is no point in
+        #  putting in another one)
+        a = _dummy_('a', 'rewrite-single')
+        if a not in f.free_symbols and _is_analytic(f, x):
+            try:
+                F, strip, _ = mellin_transform(f.subs(x, a*x), x, s,
+                                               integrator=my_integrator,
+                                               needeval=True, simplify=False)
+                g = my_imt(F, s, x, strip).subs(a, 1)
+            except IntegralTransformError:
+                g = None
+    if g is None or g.has(S.Infinity, S.NaN, S.ComplexInfinity):
+        _debug('Recursive Mellin transform failed.')
+        return None
+    args = Add.make_args(g)
+    res = []
+    for f in args:
+        c, m = f.as_coeff_mul(x)
+        if len(m) > 1:
+            raise NotImplementedError('Unexpected form...')
+        g = m[0]
+        a, b = _get_coeff_exp(g.argument, x)
+        res += [(c, 0, meijerg(g.an, g.aother, g.bm, g.bother,
+                               unpolarify(polarify(
+                                   a, lift=True), exponents_only=True)
+                               *x**b))]
+    _debug('Recursive Mellin transform worked:', g)
+    return res, True
+
+
+def _rewrite1(f, x, recursive=True):
+    """
+    Try to rewrite ``f`` using a (sum of) single G functions with argument a*x**b.
+    Return fac, po, g such that f = fac*po*g, fac is independent of ``x``.
+    and po = x**s.
+    Here g is a result from _rewrite_single.
+    Return None on failure.
+    """
+    fac, po, g = _split_mul(f, x)
+    g = _rewrite_single(g, x, recursive)
+    if g:
+        return fac, po, g[0], g[1]
+
+
+def _rewrite2(f, x):
+    """
+    Try to rewrite ``f`` as a product of two G functions of arguments a*x**b.
+    Return fac, po, g1, g2 such that f = fac*po*g1*g2, where fac is
+    independent of x and po is x**s.
+    Here g1 and g2 are results of _rewrite_single.
+    Returns None on failure.
+    """
+    fac, po, g = _split_mul(f, x)
+    if any(_rewrite_single(expr, x, False) is None for expr in _mul_args(g)):
+        return None
+    l = _mul_as_two_parts(g)
+    if not l:
+        return None
+    l = list(ordered(l, [
+        lambda p: max(len(_exponents(p[0], x)), len(_exponents(p[1], x))),
+        lambda p: max(len(_functions(p[0], x)), len(_functions(p[1], x))),
+        lambda p: max(len(_find_splitting_points(p[0], x)),
+                      len(_find_splitting_points(p[1], x)))]))
+
+    for recursive, (fac1, fac2) in itertools.product((False, True), l):
+        g1 = _rewrite_single(fac1, x, recursive)
+        g2 = _rewrite_single(fac2, x, recursive)
+        if g1 and g2:
+            cond = And(g1[1], g2[1])
+            if cond != False:
+                return fac, po, g1[0], g2[0], cond
+
+
+def meijerint_indefinite(f, x):
+    """
+    Compute an indefinite integral of ``f`` by rewriting it as a G function.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import meijerint_indefinite
+    >>> from sympy import sin
+    >>> from sympy.abc import x
+    >>> meijerint_indefinite(sin(x), x)
+    -cos(x)
+    """
+    f = sympify(f)
+    results = []
+    for a in sorted(_find_splitting_points(f, x) | {S.Zero}, key=default_sort_key):
+        res = _meijerint_indefinite_1(f.subs(x, x + a), x)
+        if not res:
+            continue
+        res = res.subs(x, x - a)
+        if _has(res, hyper, meijerg):
+            results.append(res)
+        else:
+            return res
+    if f.has(HyperbolicFunction):
+        _debug('Try rewriting hyperbolics in terms of exp.')
+        rv = meijerint_indefinite(
+            _rewrite_hyperbolics_as_exp(f), x)
+        if rv:
+            if not isinstance(rv, list):
+                from sympy.simplify.radsimp import collect
+                return collect(factor_terms(rv), rv.atoms(exp))
+            results.extend(rv)
+    if results:
+        return next(ordered(results))
+
+
+def _meijerint_indefinite_1(f, x):
+    """ Helper that does not attempt any substitution. """
+    _debug('Trying to compute the indefinite integral of', f, 'wrt', x)
+    from sympy.simplify import hyperexpand, powdenest
+
+    gs = _rewrite1(f, x)
+    if gs is None:
+        # Note: the code that calls us will do expand() and try again
+        return None
+
+    fac, po, gl, cond = gs
+    _debug(' could rewrite:', gs)
+    res = S.Zero
+    for C, s, g in gl:
+        a, b = _get_coeff_exp(g.argument, x)
+        _, c = _get_coeff_exp(po, x)
+        c += s
+
+        # we do a substitution t=a*x**b, get integrand fac*t**rho*g
+        fac_ = fac * C * x**(1 + c) / b
+        rho = (c + 1)/b
+
+        # we now use t**rho*G(params, t) = G(params + rho, t)
+        # [L, page 150, equation (4)]
+        # and integral G(params, t) dt = G(1, params+1, 0, t)
+        #   (or a similar expression with 1 and 0 exchanged ... pick the one
+        #    which yields a well-defined function)
+        # [R, section 5]
+        # (Note that this dummy will immediately go away again, so we
+        #  can safely pass S.One for ``expr``.)
+        t = _dummy('t', 'meijerint-indefinite', S.One)
+
+        def tr(p):
+            return [a + rho for a in p]
+        if any(b.is_integer and (b <= 0) == True for b in tr(g.bm)):
+            r = -meijerg(
+                list(g.an), list(g.aother) + [1-rho], list(g.bm) + [-rho], list(g.bother), t)
+        else:
+            r = meijerg(
+                list(g.an) + [1-rho], list(g.aother), list(g.bm), list(g.bother) + [-rho], t)
+        # The antiderivative is most often expected to be defined
+        # in the neighborhood of  x = 0.
+        if b.is_extended_nonnegative and not f.subs(x, 0).has(S.NaN, S.ComplexInfinity):
+            place = 0  # Assume we can expand at zero
+        else:
+            place = None
+        r = hyperexpand(r.subs(t, a*x**b), place=place)
+
+        # now substitute back
+        # Note: we really do want the powers of x to combine.
+        res += powdenest(fac_*r, polar=True)
+
+    def _clean(res):
+        """This multiplies out superfluous powers of x we created, and chops off
+        constants:
+
+            >> _clean(x*(exp(x)/x - 1/x) + 3)
+            exp(x)
+
+        cancel is used before mul_expand since it is possible for an
+        expression to have an additive constant that does not become isolated
+        with simple expansion. Such a situation was identified in issue 6369:
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt, cancel
+        >>> from sympy.abc import x
+        >>> a = sqrt(2*x + 1)
+        >>> bad = (3*x*a**5 + 2*x - a**5 + 1)/a**2
+        >>> bad.expand().as_independent(x)[0]
+        0
+        >>> cancel(bad).expand().as_independent(x)[0]
+        1
+        """
+        res = expand_mul(cancel(res), deep=False)
+        return Add._from_args(res.as_coeff_add(x)[1])
+
+    res = piecewise_fold(res, evaluate=None)
+    if res.is_Piecewise:
+        newargs = []
+        for e, c in res.args:
+            e = _my_unpolarify(_clean(e))
+            newargs += [(e, c)]
+        res = Piecewise(*newargs, evaluate=False)
+    else:
+        res = _my_unpolarify(_clean(res))
+    return Piecewise((res, _my_unpolarify(cond)), (Integral(f, x), True))
+
+
+@timeit
+def meijerint_definite(f, x, a, b):
+    """
+    Integrate ``f`` over the interval [``a``, ``b``], by rewriting it as a product
+    of two G functions, or as a single G function.
+
+    Return res, cond, where cond are convergence conditions.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.meijerint import meijerint_definite
+    >>> from sympy import exp, oo
+    >>> from sympy.abc import x
+    >>> meijerint_definite(exp(-x**2), x, -oo, oo)
+    (sqrt(pi), True)
+
+    This function is implemented as a succession of functions
+    meijerint_definite, _meijerint_definite_2, _meijerint_definite_3,
+    _meijerint_definite_4. Each function in the list calls the next one
+    (presumably) several times. This means that calling meijerint_definite
+    can be very costly.
+    """
+    # This consists of three steps:
+    # 1) Change the integration limits to 0, oo
+    # 2) Rewrite in terms of G functions
+    # 3) Evaluate the integral
+    #
+    # There are usually several ways of doing this, and we want to try all.
+    # This function does (1), calls _meijerint_definite_2 for step (2).
+    _debugf('Integrating %s wrt %s from %s to %s.', (f, x, a, b))
+    f = sympify(f)
+    if f.has(DiracDelta):
+        _debug('Integrand has DiracDelta terms - giving up.')
+        return None
+
+    if f.has(SingularityFunction):
+        _debug('Integrand has Singularity Function terms - giving up.')
+        return None
+
+    f_, x_, a_, b_ = f, x, a, b
+
+    # Let's use a dummy in case any of the boundaries has x.
+    d = Dummy('x')
+    f = f.subs(x, d)
+    x = d
+
+    if a == b:
+        return (S.Zero, True)
+
+    results = []
+    if a is S.NegativeInfinity and b is not S.Infinity:
+        return meijerint_definite(f.subs(x, -x), x, -b, -a)
+
+    elif a is S.NegativeInfinity:
+        # Integrating -oo to oo. We need to find a place to split the integral.
+        _debug('  Integrating -oo to +oo.')
+        innermost = _find_splitting_points(f, x)
+        _debug('  Sensible splitting points:', innermost)
+        for c in sorted(innermost, key=default_sort_key, reverse=True) + [S.Zero]:
+            _debug('  Trying to split at', c)
+            if not c.is_extended_real:
+                _debug('  Non-real splitting point.')
+                continue
+            res1 = _meijerint_definite_2(f.subs(x, x + c), x)
+            if res1 is None:
+                _debug('  But could not compute first integral.')
+                continue
+            res2 = _meijerint_definite_2(f.subs(x, c - x), x)
+            if res2 is None:
+                _debug('  But could not compute second integral.')
+                continue
+            res1, cond1 = res1
+            res2, cond2 = res2
+            cond = _condsimp(And(cond1, cond2))
+            if cond == False:
+                _debug('  But combined condition is always false.')
+                continue
+            res = res1 + res2
+            return res, cond
+
+    elif a is S.Infinity:
+        res = meijerint_definite(f, x, b, S.Infinity)
+        return -res[0], res[1]
+
+    elif (a, b) == (S.Zero, S.Infinity):
+        # This is a common case - try it directly first.
+        res = _meijerint_definite_2(f, x)
+        if res:
+            if _has(res[0], meijerg):
+                results.append(res)
+            else:
+                return res
+
+    else:
+        if b is S.Infinity:
+            for split in _find_splitting_points(f, x):
+                if (a - split >= 0) == True:
+                    _debugf('Trying x -> x + %s', split)
+                    res = _meijerint_definite_2(f.subs(x, x + split)
+                                                *Heaviside(x + split - a), x)
+                    if res:
+                        if _has(res[0], meijerg):
+                            results.append(res)
+                        else:
+                            return res
+
+        f = f.subs(x, x + a)
+        b = b - a
+        a = 0
+        if b is not S.Infinity:
+            phi = exp(S.ImaginaryUnit*arg(b))
+            b = Abs(b)
+            f = f.subs(x, phi*x)
+            f *= Heaviside(b - x)*phi
+            b = S.Infinity
+
+        _debug('Changed limits to', a, b)
+        _debug('Changed function to', f)
+        res = _meijerint_definite_2(f, x)
+        if res:
+            if _has(res[0], meijerg):
+                results.append(res)
+            else:
+                return res
+    if f_.has(HyperbolicFunction):
+        _debug('Try rewriting hyperbolics in terms of exp.')
+        rv = meijerint_definite(
+            _rewrite_hyperbolics_as_exp(f_), x_, a_, b_)
+        if rv:
+            if not isinstance(rv, list):
+                from sympy.simplify.radsimp import collect
+                rv = (collect(factor_terms(rv[0]), rv[0].atoms(exp)),) + rv[1:]
+                return rv
+            results.extend(rv)
+    if results:
+        return next(ordered(results))
+
+
+def _guess_expansion(f, x):
+    """ Try to guess sensible rewritings for integrand f(x). """
+    res = [(f, 'original integrand')]
+
+    orig = res[-1][0]
+    saw = {orig}
+    expanded = expand_mul(orig)
+    if expanded not in saw:
+        res += [(expanded, 'expand_mul')]
+        saw.add(expanded)
+
+    expanded = expand(orig)
+    if expanded not in saw:
+        res += [(expanded, 'expand')]
+        saw.add(expanded)
+
+    if orig.has(TrigonometricFunction, HyperbolicFunction):
+        expanded = expand_mul(expand_trig(orig))
+        if expanded not in saw:
+            res += [(expanded, 'expand_trig, expand_mul')]
+            saw.add(expanded)
+
+    if orig.has(cos, sin):
+        from sympy.simplify.fu import sincos_to_sum
+        reduced = sincos_to_sum(orig)
+        if reduced not in saw:
+            res += [(reduced, 'trig power reduction')]
+            saw.add(reduced)
+
+    return res
+
+
+def _meijerint_definite_2(f, x):
+    """
+    Try to integrate f dx from zero to infinity.
+
+    The body of this function computes various 'simplifications'
+    f1, f2, ... of f (e.g. by calling expand_mul(), trigexpand()
+    - see _guess_expansion) and calls _meijerint_definite_3 with each of
+    these in succession.
+    If _meijerint_definite_3 succeeds with any of the simplified functions,
+    returns this result.
+    """
+    # This function does preparation for (2), calls
+    # _meijerint_definite_3 for (2) and (3) combined.
+
+    # use a positive dummy - we integrate from 0 to oo
+    # XXX if a nonnegative symbol is used there will be test failures
+    dummy = _dummy('x', 'meijerint-definite2', f, positive=True)
+    f = f.subs(x, dummy)
+    x = dummy
+
+    if f == 0:
+        return S.Zero, True
+
+    for g, explanation in _guess_expansion(f, x):
+        _debug('Trying', explanation)
+        res = _meijerint_definite_3(g, x)
+        if res:
+            return res
+
+
+def _meijerint_definite_3(f, x):
+    """
+    Try to integrate f dx from zero to infinity.
+
+    This function calls _meijerint_definite_4 to try to compute the
+    integral. If this fails, it tries using linearity.
+    """
+    res = _meijerint_definite_4(f, x)
+    if res and res[1] != False:
+        return res
+    if f.is_Add:
+        _debug('Expanding and evaluating all terms.')
+        ress = [_meijerint_definite_4(g, x) for g in f.args]
+        if all(r is not None for r in ress):
+            conds = []
+            res = S.Zero
+            for r, c in ress:
+                res += r
+                conds += [c]
+            c = And(*conds)
+            if c != False:
+                return res, c
+
+
+def _my_unpolarify(f):
+    return _eval_cond(unpolarify(f))
+
+
+@timeit
+def _meijerint_definite_4(f, x, only_double=False):
+    """
+    Try to integrate f dx from zero to infinity.
+
+    Explanation
+    ===========
+
+    This function tries to apply the integration theorems found in literature,
+    i.e. it tries to rewrite f as either one or a product of two G-functions.
+
+    The parameter ``only_double`` is used internally in the recursive algorithm
+    to disable trying to rewrite f as a single G-function.
+    """
+    from sympy.simplify import hyperexpand
+    # This function does (2) and (3)
+    _debug('Integrating', f)
+    # Try single G function.
+    if not only_double:
+        gs = _rewrite1(f, x, recursive=False)
+        if gs is not None:
+            fac, po, g, cond = gs
+            _debug('Could rewrite as single G function:', fac, po, g)
+            res = S.Zero
+            for C, s, f in g:
+                if C == 0:
+                    continue
+                C, f = _rewrite_saxena_1(fac*C, po*x**s, f, x)
+                res += C*_int0oo_1(f, x)
+                cond = And(cond, _check_antecedents_1(f, x))
+                if cond == False:
+                    break
+            cond = _my_unpolarify(cond)
+            if cond == False:
+                _debug('But cond is always False.')
+            else:
+                _debug('Result before branch substitutions is:', res)
+                return _my_unpolarify(hyperexpand(res)), cond
+
+    # Try two G functions.
+    gs = _rewrite2(f, x)
+    if gs is not None:
+        for full_pb in [False, True]:
+            fac, po, g1, g2, cond = gs
+            _debug('Could rewrite as two G functions:', fac, po, g1, g2)
+            res = S.Zero
+            for C1, s1, f1 in g1:
+                for C2, s2, f2 in g2:
+                    r = _rewrite_saxena(fac*C1*C2, po*x**(s1 + s2),
+                                        f1, f2, x, full_pb)
+                    if r is None:
+                        _debug('Non-rational exponents.')
+                        return
+                    C, f1_, f2_ = r
+                    _debug('Saxena subst for yielded:', C, f1_, f2_)
+                    cond = And(cond, _check_antecedents(f1_, f2_, x))
+                    if cond == False:
+                        break
+                    res += C*_int0oo(f1_, f2_, x)
+                else:
+                    continue
+                break
+            cond = _my_unpolarify(cond)
+            if cond == False:
+                _debugf('But cond is always False (full_pb=%s).', full_pb)
+            else:
+                _debugf('Result before branch substitutions is: %s', (res, ))
+                if only_double:
+                    return res, cond
+                return _my_unpolarify(hyperexpand(res)), cond
+
+
+def meijerint_inversion(f, x, t):
+    r"""
+    Compute the inverse laplace transform
+    $\int_{c+i\infty}^{c-i\infty} f(x) e^{tx}\, dx$,
+    for real c larger than the real part of all singularities of ``f``.
+
+    Note that ``t`` is always assumed real and positive.
+
+    Return None if the integral does not exist or could not be evaluated.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, t
+    >>> from sympy.integrals.meijerint import meijerint_inversion
+    >>> meijerint_inversion(1/x, x, t)
+    Heaviside(t)
+    """
+    f_ = f
+    t_ = t
+    t = Dummy('t', polar=True)  # We don't want sqrt(t**2) = abs(t) etc
+    f = f.subs(t_, t)
+    _debug('Laplace-inverting', f)
+    if not _is_analytic(f, x):
+        _debug('But expression is not analytic.')
+        return None
+    # Exponentials correspond to shifts; we filter them out and then
+    # shift the result later.  If we are given an Add this will not
+    # work, but the calling code will take care of that.
+    shift = S.Zero
+
+    if f.is_Mul:
+        args = list(f.args)
+    elif isinstance(f, exp):
+        args = [f]
+    else:
+        args = None
+
+    if args:
+        newargs = []
+        exponentials = []
+        while args:
+            arg = args.pop()
+            if isinstance(arg, exp):
+                arg2 = expand(arg)
+                if arg2.is_Mul:
+                    args += arg2.args
+                    continue
+                try:
+                    a, b = _get_coeff_exp(arg.args[0], x)
+                except _CoeffExpValueError:
+                    b = 0
+                if b == 1:
+                    exponentials.append(a)
+                else:
+                    newargs.append(arg)
+            elif arg.is_Pow:
+                arg2 = expand(arg)
+                if arg2.is_Mul:
+                    args += arg2.args
+                    continue
+                if x not in arg.base.free_symbols:
+                    try:
+                        a, b = _get_coeff_exp(arg.exp, x)
+                    except _CoeffExpValueError:
+                        b = 0
+                    if b == 1:
+                        exponentials.append(a*log(arg.base))
+                newargs.append(arg)
+            else:
+                newargs.append(arg)
+        shift = Add(*exponentials)
+        f = Mul(*newargs)
+
+    if x not in f.free_symbols:
+        _debug('Expression consists of constant and exp shift:', f, shift)
+        cond = Eq(im(shift), 0)
+        if cond == False:
+            _debug('but shift is nonreal, cannot be a Laplace transform')
+            return None
+        res = f*DiracDelta(t + shift)
+        _debug('Result is a delta function, possibly conditional:', res, cond)
+        # cond is True or Eq
+        return Piecewise((res.subs(t, t_), cond))
+
+    gs = _rewrite1(f, x)
+    if gs is not None:
+        fac, po, g, cond = gs
+        _debug('Could rewrite as single G function:', fac, po, g)
+        res = S.Zero
+        for C, s, f in g:
+            C, f = _rewrite_inversion(fac*C, po*x**s, f, x)
+            res += C*_int_inversion(f, x, t)
+            cond = And(cond, _check_antecedents_inversion(f, x))
+            if cond == False:
+                break
+        cond = _my_unpolarify(cond)
+        if cond == False:
+            _debug('But cond is always False.')
+        else:
+            _debug('Result before branch substitution:', res)
+            from sympy.simplify import hyperexpand
+            res = _my_unpolarify(hyperexpand(res))
+            if not res.has(Heaviside):
+                res *= Heaviside(t)
+            res = res.subs(t, t + shift)
+            if not isinstance(cond, bool):
+                cond = cond.subs(t, t + shift)
+            from .transforms import InverseLaplaceTransform
+            return Piecewise((res.subs(t, t_), cond),
+                             (InverseLaplaceTransform(f_.subs(t, t_), x, t_, None), True))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/meijerint_doc.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/meijerint_doc.py
new file mode 100644
index 0000000000000000000000000000000000000000..1df385db6b6fe6d46d4a14217aa53d1fdd9670b5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/meijerint_doc.py
@@ -0,0 +1,38 @@
+""" This module cooks up a docstring when imported. Its only purpose is to
+    be displayed in the sphinx documentation. """
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.integrals.meijerint import _create_lookup_table
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.relational import Eq
+from sympy.core.symbol import Symbol
+from sympy.printing.latex import latex
+
+t: dict[tuple[type[Basic], ...], list[Any]] = {}
+_create_lookup_table(t)
+
+
+doc = ""
+for about, category in t.items():
+    if about == ():
+        doc += 'Elementary functions:\n\n'
+    else:
+        doc += 'Functions involving ' + ', '.join('`%s`' % latex(
+            list(category[0][0].atoms(func))[0]) for func in about) + ':\n\n'
+    for formula, gs, cond, hint in category:
+        if not isinstance(gs, list):
+            g: Expr = Symbol('\\text{generated}')
+        else:
+            g = Add(*[fac*f for (fac, f) in gs])
+        obj = Eq(formula, g)
+        if cond is True:
+            cond = ""
+        else:
+            cond = ',\\text{ if } %s' % latex(cond)
+        doc += ".. math::\n  %s%s\n\n" % (latex(obj), cond)
+
+__doc__ = doc
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/prde.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/prde.py
new file mode 100644
index 0000000000000000000000000000000000000000..28e91ea0ff3a82cbeca24c6ed4267503ceb758b5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/prde.py
@@ -0,0 +1,1333 @@
+"""
+Algorithms for solving Parametric Risch Differential Equations.
+
+The methods used for solving Parametric Risch Differential Equations parallel
+those for solving Risch Differential Equations.  See the outline in the
+docstring of rde.py for more information.
+
+The Parametric Risch Differential Equation problem is, given f, g1, ..., gm in
+K(t), to determine if there exist y in K(t) and c1, ..., cm in Const(K) such
+that Dy + f*y == Sum(ci*gi, (i, 1, m)), and to find such y and ci if they exist.
+
+For the algorithms here G is a list of tuples of factions of the terms on the
+right hand side of the equation (i.e., gi in k(t)), and Q is a list of terms on
+the right hand side of the equation (i.e., qi in k[t]).  See the docstring of
+each function for more information.
+"""
+import itertools
+from functools import reduce
+
+from sympy.core.intfunc import ilcm
+from sympy.core import Dummy, Add, Mul, Pow, S
+from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
+    bound_degree)
+from sympy.integrals.risch import (gcdex_diophantine, frac_in, derivation,
+    residue_reduce, splitfactor, residue_reduce_derivation, DecrementLevel,
+    recognize_log_derivative)
+from sympy.polys import Poly, lcm, cancel, sqf_list
+from sympy.polys.polymatrix import PolyMatrix as Matrix
+from sympy.solvers import solve
+
+zeros = Matrix.zeros
+eye = Matrix.eye
+
+
+def prde_normal_denom(fa, fd, G, DE):
+    """
+    Parametric Risch Differential Equation - Normal part of the denominator.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and f, g1, ..., gm in k(t) with f weakly
+    normalized with respect to t, return the tuple (a, b, G, h) such that
+    a, h in k[t], b in k, G = [g1, ..., gm] in k(t)^m, and for any solution
+    c1, ..., cm in Const(k) and y in k(t) of Dy + f*y == Sum(ci*gi, (i, 1, m)),
+    q == y*h in k satisfies a*Dq + b*q == Sum(ci*Gi, (i, 1, m)).
+    """
+    dn, ds = splitfactor(fd, DE)
+    Gas, Gds = list(zip(*G))
+    gd = reduce(lambda i, j: i.lcm(j), Gds, Poly(1, DE.t))
+    en, es = splitfactor(gd, DE)
+
+    p = dn.gcd(en)
+    h = en.gcd(en.diff(DE.t)).quo(p.gcd(p.diff(DE.t)))
+
+    a = dn*h
+    c = a*h
+
+    ba = a*fa - dn*derivation(h, DE)*fd
+    ba, bd = ba.cancel(fd, include=True)
+
+    G = [(c*A).cancel(D, include=True) for A, D in G]
+
+    return (a, (ba, bd), G, h)
+
+def real_imag(ba, bd, gen):
+    """
+    Helper function, to get the real and imaginary part of a rational function
+    evaluated at sqrt(-1) without actually evaluating it at sqrt(-1).
+
+    Explanation
+    ===========
+
+    Separates the even and odd power terms by checking the degree of terms wrt
+    mod 4. Returns a tuple (ba[0], ba[1], bd) where ba[0] is real part
+    of the numerator ba[1] is the imaginary part and bd is the denominator
+    of the rational function.
+    """
+    bd = bd.as_poly(gen).as_dict()
+    ba = ba.as_poly(gen).as_dict()
+    denom_real = [value if key[0] % 4 == 0 else -value if key[0] % 4 == 2 else 0 for key, value in bd.items()]
+    denom_imag = [value if key[0] % 4 == 1 else -value if key[0] % 4 == 3 else 0 for key, value in bd.items()]
+    bd_real = sum(r for r in denom_real)
+    bd_imag = sum(r for r in denom_imag)
+    num_real = [value if key[0] % 4 == 0 else -value if key[0] % 4 == 2 else 0 for key, value in ba.items()]
+    num_imag = [value if key[0] % 4 == 1 else -value if key[0] % 4 == 3 else 0 for key, value in ba.items()]
+    ba_real = sum(r for r in num_real)
+    ba_imag = sum(r for r in num_imag)
+    ba = ((ba_real*bd_real + ba_imag*bd_imag).as_poly(gen), (ba_imag*bd_real - ba_real*bd_imag).as_poly(gen))
+    bd = (bd_real*bd_real + bd_imag*bd_imag).as_poly(gen)
+    return (ba[0], ba[1], bd)
+
+
+def prde_special_denom(a, ba, bd, G, DE, case='auto'):
+    """
+    Parametric Risch Differential Equation - Special part of the denominator.
+
+    Explanation
+    ===========
+
+    Case is one of {'exp', 'tan', 'primitive'} for the hyperexponential,
+    hypertangent, and primitive cases, respectively.  For the hyperexponential
+    (resp. hypertangent) case, given a derivation D on k[t] and a in k[t],
+    b in k, and g1, ..., gm in k(t) with Dt/t in k (resp. Dt/(t**2 + 1) in
+    k, sqrt(-1) not in k), a != 0, and gcd(a, t) == 1 (resp.
+    gcd(a, t**2 + 1) == 1), return the tuple (A, B, GG, h) such that A, B, h in
+    k[t], GG = [gg1, ..., ggm] in k(t)^m, and for any solution c1, ..., cm in
+    Const(k) and q in k of a*Dq + b*q == Sum(ci*gi, (i, 1, m)), r == q*h in
+    k[t] satisfies A*Dr + B*r == Sum(ci*ggi, (i, 1, m)).
+
+    For case == 'primitive', k == k[t], so it returns (a, b, G, 1) in this
+    case.
+    """
+    # TODO: Merge this with the very similar special_denom() in rde.py
+    if case == 'auto':
+        case = DE.case
+
+    if case == 'exp':
+        p = Poly(DE.t, DE.t)
+    elif case == 'tan':
+        p = Poly(DE.t**2 + 1, DE.t)
+    elif case in ('primitive', 'base'):
+        B = ba.quo(bd)
+        return (a, B, G, Poly(1, DE.t))
+    else:
+        raise ValueError("case must be one of {'exp', 'tan', 'primitive', "
+            "'base'}, not %s." % case)
+
+    nb = order_at(ba, p, DE.t) - order_at(bd, p, DE.t)
+    nc = min(order_at(Ga, p, DE.t) - order_at(Gd, p, DE.t) for Ga, Gd in G)
+    n = min(0, nc - min(0, nb))
+    if not nb:
+        # Possible cancellation.
+        if case == 'exp':
+            dcoeff = DE.d.quo(Poly(DE.t, DE.t))
+            with DecrementLevel(DE):  # We are guaranteed to not have problems,
+                                      # because case != 'base'.
+                alphaa, alphad = frac_in(-ba.eval(0)/bd.eval(0)/a.eval(0), DE.t)
+                etaa, etad = frac_in(dcoeff, DE.t)
+                A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE)
+                if A is not None:
+                    Q, m, z = A
+                    if Q == 1:
+                        n = min(n, m)
+
+        elif case == 'tan':
+            dcoeff = DE.d.quo(Poly(DE.t**2 + 1, DE.t))
+            with DecrementLevel(DE):  # We are guaranteed to not have problems,
+                                      # because case != 'base'.
+                betaa, alphaa, alphad =  real_imag(ba, bd*a, DE.t)
+                betad = alphad
+                etaa, etad = frac_in(dcoeff, DE.t)
+                if recognize_log_derivative(Poly(2, DE.t)*betaa, betad, DE):
+                    A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE)
+                    B = parametric_log_deriv(betaa, betad, etaa, etad, DE)
+                    if A is not None and B is not None:
+                        Q, s, z = A
+                        # TODO: Add test
+                        if Q == 1:
+                            n = min(n, s/2)
+
+    N = max(0, -nb)
+    pN = p**N
+    pn = p**-n  # This is 1/h
+
+    A = a*pN
+    B = ba*pN.quo(bd) + Poly(n, DE.t)*a*derivation(p, DE).quo(p)*pN
+    G = [(Ga*pN*pn).cancel(Gd, include=True) for Ga, Gd in G]
+    h = pn
+
+    # (a*p**N, (b + n*a*Dp/p)*p**N, g1*p**(N - n), ..., gm*p**(N - n), p**-n)
+    return (A, B, G, h)
+
+
+def prde_linear_constraints(a, b, G, DE):
+    """
+    Parametric Risch Differential Equation - Generate linear constraints on the constants.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], a, b, in k[t] with gcd(a, b) == 1, and
+    G = [g1, ..., gm] in k(t)^m, return Q = [q1, ..., qm] in k[t]^m and a
+    matrix M with entries in k(t) such that for any solution c1, ..., cm in
+    Const(k) and p in k[t] of a*Dp + b*p == Sum(ci*gi, (i, 1, m)),
+    (c1, ..., cm) is a solution of Mx == 0, and p and the ci satisfy
+    a*Dp + b*p == Sum(ci*qi, (i, 1, m)).
+
+    Because M has entries in k(t), and because Matrix does not play well with
+    Poly, M will be a Matrix of Basic expressions.
+    """
+    m = len(G)
+
+    Gns, Gds = list(zip(*G))
+    d = reduce(lambda i, j: i.lcm(j), Gds)
+    d = Poly(d, field=True)
+    Q = [(ga*(d).quo(gd)).div(d) for ga, gd in G]
+
+    if not all(ri.is_zero for _, ri in Q):
+        N = max(ri.degree(DE.t) for _, ri in Q)
+        M = Matrix(N + 1, m, lambda i, j: Q[j][1].nth(i), DE.t)
+    else:
+        M = Matrix(0, m, [], DE.t)  # No constraints, return the empty matrix.
+
+    qs, _ = list(zip(*Q))
+    return (qs, M)
+
+def poly_linear_constraints(p, d):
+    """
+    Given p = [p1, ..., pm] in k[t]^m and d in k[t], return
+    q = [q1, ..., qm] in k[t]^m and a matrix M with entries in k such
+    that Sum(ci*pi, (i, 1, m)), for c1, ..., cm in k, is divisible
+    by d if and only if (c1, ..., cm) is a solution of Mx = 0, in
+    which case the quotient is Sum(ci*qi, (i, 1, m)).
+    """
+    m = len(p)
+    q, r = zip(*[pi.div(d) for pi in p])
+
+    if not all(ri.is_zero for ri in r):
+        n = max(ri.degree() for ri in r)
+        M = Matrix(n + 1, m, lambda i, j: r[j].nth(i), d.gens)
+    else:
+        M = Matrix(0, m, [], d.gens)  # No constraints.
+
+    return q, M
+
+def constant_system(A, u, DE):
+    """
+    Generate a system for the constant solutions.
+
+    Explanation
+    ===========
+
+    Given a differential field (K, D) with constant field C = Const(K), a Matrix
+    A, and a vector (Matrix) u with coefficients in K, returns the tuple
+    (B, v, s), where B is a Matrix with coefficients in C and v is a vector
+    (Matrix) such that either v has coefficients in C, in which case s is True
+    and the solutions in C of Ax == u are exactly all the solutions of Bx == v,
+    or v has a non-constant coefficient, in which case s is False Ax == u has no
+    constant solution.
+
+    This algorithm is used both in solving parametric problems and in
+    determining if an element a of K is a derivative of an element of K or the
+    logarithmic derivative of a K-radical using the structure theorem approach.
+
+    Because Poly does not play well with Matrix yet, this algorithm assumes that
+    all matrix entries are Basic expressions.
+    """
+    if not A:
+        return A, u
+    Au = A.row_join(u)
+    Au, _ = Au.rref()
+    # Warning: This will NOT return correct results if cancel() cannot reduce
+    # an identically zero expression to 0.  The danger is that we might
+    # incorrectly prove that an integral is nonelementary (such as
+    # risch_integrate(exp((sin(x)**2 + cos(x)**2 - 1)*x**2), x).
+    # But this is a limitation in computer algebra in general, and implicit
+    # in the correctness of the Risch Algorithm is the computability of the
+    # constant field (actually, this same correctness problem exists in any
+    # algorithm that uses rref()).
+    #
+    # We therefore limit ourselves to constant fields that are computable
+    # via the cancel() function, in order to prevent a speed bottleneck from
+    # calling some more complex simplification function (rational function
+    # coefficients will fall into this class).  Furthermore, (I believe) this
+    # problem will only crop up if the integral explicitly contains an
+    # expression in the constant field that is identically zero, but cannot
+    # be reduced to such by cancel().  Therefore, a careful user can avoid this
+    # problem entirely by being careful with the sorts of expressions that
+    # appear in his integrand in the variables other than the integration
+    # variable (the structure theorems should be able to completely decide these
+    # problems in the integration variable).
+
+    A, u = Au[:, :-1], Au[:, -1]
+
+    D = lambda x: derivation(x, DE, basic=True)
+
+    for j, i in itertools.product(range(A.cols), range(A.rows)):
+        if A[i, j].expr.has(*DE.T):
+            # This assumes that const(F(t0, ..., tn) == const(K) == F
+            Ri = A[i, :]
+            # Rm+1; m = A.rows
+            DAij = D(A[i, j])
+            Rm1 = Ri.applyfunc(lambda x: D(x) / DAij)
+            um1 = D(u[i]) / DAij
+
+            Aj = A[:, j]
+            A = A - Aj * Rm1
+            u = u - Aj * um1
+
+            A = A.col_join(Rm1)
+            u = u.col_join(Matrix([um1], u.gens))
+
+    return (A, u)
+
+
+def prde_spde(a, b, Q, n, DE):
+    """
+    Special Polynomial Differential Equation algorithm: Parametric Version.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], an integer n, and a, b, q1, ..., qm in k[t]
+    with deg(a) > 0 and gcd(a, b) == 1, return (A, B, Q, R, n1), with
+    Qq = [q1, ..., qm] and R = [r1, ..., rm], such that for any solution
+    c1, ..., cm in Const(k) and q in k[t] of degree at most n of
+    a*Dq + b*q == Sum(ci*gi, (i, 1, m)), p = (q - Sum(ci*ri, (i, 1, m)))/a has
+    degree at most n1 and satisfies A*Dp + B*p == Sum(ci*qi, (i, 1, m))
+    """
+    R, Z = list(zip(*[gcdex_diophantine(b, a, qi) for qi in Q]))
+
+    A = a
+    B = b + derivation(a, DE)
+    Qq = [zi - derivation(ri, DE) for ri, zi in zip(R, Z)]
+    R = list(R)
+    n1 = n - a.degree(DE.t)
+
+    return (A, B, Qq, R, n1)
+
+
+def prde_no_cancel_b_large(b, Q, n, DE):
+    """
+    Parametric Poly Risch Differential Equation - No cancellation: deg(b) large enough.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], n in ZZ, and b, q1, ..., qm in k[t] with
+    b != 0 and either D == d/dt or deg(b) > max(0, deg(D) - 1), returns
+    h1, ..., hr in k[t] and a matrix A with coefficients in Const(k) such that
+    if c1, ..., cm in Const(k) and q in k[t] satisfy deg(q) <= n and
+    Dq + b*q == Sum(ci*qi, (i, 1, m)), then q = Sum(dj*hj, (j, 1, r)), where
+    d1, ..., dr in Const(k) and A*Matrix([[c1, ..., cm, d1, ..., dr]]).T == 0.
+    """
+    db = b.degree(DE.t)
+    m = len(Q)
+    H = [Poly(0, DE.t)]*m
+
+    for N, i in itertools.product(range(n, -1, -1), range(m)):  # [n, ..., 0]
+        si = Q[i].nth(N + db)/b.LC()
+        sitn = Poly(si*DE.t**N, DE.t)
+        H[i] = H[i] + sitn
+        Q[i] = Q[i] - derivation(sitn, DE) - b*sitn
+
+    if all(qi.is_zero for qi in Q):
+        dc = -1
+    else:
+        dc = max(qi.degree(DE.t) for qi in Q)
+    M = Matrix(dc + 1, m, lambda i, j: Q[j].nth(i), DE.t)
+    A, u = constant_system(M, zeros(dc + 1, 1, DE.t), DE)
+    c = eye(m, DE.t)
+    A = A.row_join(zeros(A.rows, m, DE.t)).col_join(c.row_join(-c))
+
+    return (H, A)
+
+
+def prde_no_cancel_b_small(b, Q, n, DE):
+    """
+    Parametric Poly Risch Differential Equation - No cancellation: deg(b) small enough.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], n in ZZ, and b, q1, ..., qm in k[t] with
+    deg(b) < deg(D) - 1 and either D == d/dt or deg(D) >= 2, returns
+    h1, ..., hr in k[t] and a matrix A with coefficients in Const(k) such that
+    if c1, ..., cm in Const(k) and q in k[t] satisfy deg(q) <= n and
+    Dq + b*q == Sum(ci*qi, (i, 1, m)) then q = Sum(dj*hj, (j, 1, r)) where
+    d1, ..., dr in Const(k) and A*Matrix([[c1, ..., cm, d1, ..., dr]]).T == 0.
+    """
+    m = len(Q)
+    H = [Poly(0, DE.t)]*m
+
+    for N, i in itertools.product(range(n, 0, -1), range(m)):  # [n, ..., 1]
+        si = Q[i].nth(N + DE.d.degree(DE.t) - 1)/(N*DE.d.LC())
+        sitn = Poly(si*DE.t**N, DE.t)
+        H[i] = H[i] + sitn
+        Q[i] = Q[i] - derivation(sitn, DE) - b*sitn
+
+    if b.degree(DE.t) > 0:
+        for i in range(m):
+            si = Poly(Q[i].nth(b.degree(DE.t))/b.LC(), DE.t)
+            H[i] = H[i] + si
+            Q[i] = Q[i] - derivation(si, DE) - b*si
+        if all(qi.is_zero for qi in Q):
+            dc = -1
+        else:
+            dc = max(qi.degree(DE.t) for qi in Q)
+        M = Matrix(dc + 1, m, lambda i, j: Q[j].nth(i), DE.t)
+        A, u = constant_system(M, zeros(dc + 1, 1, DE.t), DE)
+        c = eye(m, DE.t)
+        A = A.row_join(zeros(A.rows, m, DE.t)).col_join(c.row_join(-c))
+        return (H, A)
+
+    # else: b is in k, deg(qi) < deg(Dt)
+
+    t = DE.t
+    if DE.case != 'base':
+        with DecrementLevel(DE):
+            t0 = DE.t  # k = k0(t0)
+            ba, bd = frac_in(b, t0, field=True)
+            Q0 = [frac_in(qi.TC(), t0, field=True) for qi in Q]
+            f, B = param_rischDE(ba, bd, Q0, DE)
+
+            # f = [f1, ..., fr] in k^r and B is a matrix with
+            # m + r columns and entries in Const(k) = Const(k0)
+            # such that Dy0 + b*y0 = Sum(ci*qi, (i, 1, m)) has
+            # a solution y0 in k with c1, ..., cm in Const(k)
+            # if and only y0 = Sum(dj*fj, (j, 1, r)) where
+            # d1, ..., dr ar in Const(k) and
+            # B*Matrix([c1, ..., cm, d1, ..., dr]) == 0.
+
+        # Transform fractions (fa, fd) in f into constant
+        # polynomials fa/fd in k[t].
+        # (Is there a better way?)
+        f = [Poly(fa.as_expr()/fd.as_expr(), t, field=True)
+             for fa, fd in f]
+        B = Matrix.from_Matrix(B.to_Matrix(), t)
+    else:
+        # Base case. Dy == 0 for all y in k and b == 0.
+        # Dy + b*y = Sum(ci*qi) is solvable if and only if
+        # Sum(ci*qi) == 0 in which case the solutions are
+        # y = d1*f1 for f1 = 1 and any d1 in Const(k) = k.
+
+        f = [Poly(1, t, field=True)]  # r = 1
+        B = Matrix([[qi.TC() for qi in Q] + [S.Zero]], DE.t)
+        # The condition for solvability is
+        # B*Matrix([c1, ..., cm, d1]) == 0
+        # There are no constraints on d1.
+
+    # Coefficients of t^j (j > 0) in Sum(ci*qi) must be zero.
+    d = max(qi.degree(DE.t) for qi in Q)
+    if d > 0:
+        M = Matrix(d, m, lambda i, j: Q[j].nth(i + 1), DE.t)
+        A, _ = constant_system(M, zeros(d, 1, DE.t), DE)
+    else:
+        # No constraints on the hj.
+        A = Matrix(0, m, [], DE.t)
+
+    # Solutions of the original equation are
+    #    y = Sum(dj*fj, (j, 1, r) + Sum(ei*hi, (i, 1, m)),
+    # where  ei == ci  (i = 1, ..., m),  when
+    # A*Matrix([c1, ..., cm]) == 0 and
+    # B*Matrix([c1, ..., cm, d1, ..., dr]) == 0
+
+    # Build combined constraint matrix with m + r + m columns.
+
+    r = len(f)
+    I = eye(m, DE.t)
+    A = A.row_join(zeros(A.rows, r + m, DE.t))
+    B = B.row_join(zeros(B.rows, m, DE.t))
+    C = I.row_join(zeros(m, r, DE.t)).row_join(-I)
+
+    return f + H, A.col_join(B).col_join(C)
+
+
+def prde_cancel_liouvillian(b, Q, n, DE):
+    """
+    Pg, 237.
+    """
+    H = []
+
+    # Why use DecrementLevel? Below line answers that:
+    # Assuming that we can solve such problems over 'k' (not k[t])
+    if DE.case == 'primitive':
+        with DecrementLevel(DE):
+            ba, bd = frac_in(b, DE.t, field=True)
+
+    for i in range(n, -1, -1):
+        if DE.case == 'exp': # this re-checking can be avoided
+            with DecrementLevel(DE):
+                ba, bd = frac_in(b + (i*(derivation(DE.t, DE)/DE.t)).as_poly(b.gens),
+                                DE.t, field=True)
+        with DecrementLevel(DE):
+            Qy = [frac_in(q.nth(i), DE.t, field=True) for q in Q]
+            fi, Ai = param_rischDE(ba, bd, Qy, DE)
+        fi = [Poly(fa.as_expr()/fd.as_expr(), DE.t, field=True)
+                for fa, fd in fi]
+        Ai = Ai.set_gens(DE.t)
+
+        ri = len(fi)
+
+        if i == n:
+            M = Ai
+        else:
+            M = Ai.col_join(M.row_join(zeros(M.rows, ri, DE.t)))
+
+        Fi, hi = [None]*ri, [None]*ri
+
+        # from eq. on top of p.238 (unnumbered)
+        for j in range(ri):
+            hji = fi[j] * (DE.t**i).as_poly(fi[j].gens)
+            hi[j] = hji
+            # building up Sum(djn*(D(fjn*t^n) - b*fjnt^n))
+            Fi[j] = -(derivation(hji, DE) - b*hji)
+
+        H += hi
+        # in the next loop instead of Q it has
+        # to be Q + Fi taking its place
+        Q = Q + Fi
+
+    return (H, M)
+
+
+def param_poly_rischDE(a, b, q, n, DE):
+    """Polynomial solutions of a parametric Risch differential equation.
+
+    Explanation
+    ===========
+
+    Given a derivation D in k[t], a, b in k[t] relatively prime, and q
+    = [q1, ..., qm] in k[t]^m, return h = [h1, ..., hr] in k[t]^r and
+    a matrix A with m + r columns and entries in Const(k) such that
+    a*Dp + b*p = Sum(ci*qi, (i, 1, m)) has a solution p of degree <= n
+    in k[t] with c1, ..., cm in Const(k) if and only if p = Sum(dj*hj,
+    (j, 1, r)) where d1, ..., dr are in Const(k) and (c1, ..., cm,
+    d1, ..., dr) is a solution of Ax == 0.
+    """
+    m = len(q)
+    if n < 0:
+        # Only the trivial zero solution is possible.
+        # Find relations between the qi.
+        if all(qi.is_zero for qi in q):
+            return [], zeros(1, m, DE.t)  # No constraints.
+
+        N = max(qi.degree(DE.t) for qi in q)
+        M = Matrix(N + 1, m, lambda i, j: q[j].nth(i), DE.t)
+        A, _ = constant_system(M, zeros(M.rows, 1, DE.t), DE)
+
+        return [], A
+
+    if a.is_ground:
+        # Normalization: a = 1.
+        a = a.LC()
+        b, q = b.to_field().exquo_ground(a), [qi.to_field().exquo_ground(a) for qi in q]
+
+        if not b.is_zero and (DE.case == 'base' or
+                b.degree() > max(0, DE.d.degree() - 1)):
+            return prde_no_cancel_b_large(b, q, n, DE)
+
+        elif ((b.is_zero or b.degree() < DE.d.degree() - 1)
+                and (DE.case == 'base' or DE.d.degree() >= 2)):
+            return prde_no_cancel_b_small(b, q, n, DE)
+
+        elif (DE.d.degree() >= 2 and
+              b.degree() == DE.d.degree() - 1 and
+              n > -b.as_poly().LC()/DE.d.as_poly().LC()):
+            raise NotImplementedError("prde_no_cancel_b_equal() is "
+                "not yet implemented.")
+
+        else:
+            # Liouvillian cases
+            if DE.case in ('primitive', 'exp'):
+                return prde_cancel_liouvillian(b, q, n, DE)
+            else:
+                raise NotImplementedError("non-linear and hypertangent "
+                        "cases have not yet been implemented")
+
+    # else: deg(a) > 0
+
+    # Iterate SPDE as long as possible cumulating coefficient
+    # and terms for the recovery of original solutions.
+    alpha, beta = a.one, [a.zero]*m
+    while n >= 0:  # and a, b relatively prime
+        a, b, q, r, n = prde_spde(a, b, q, n, DE)
+        beta = [betai + alpha*ri for betai, ri in zip(beta, r)]
+        alpha *= a
+        # Solutions p of a*Dp + b*p = Sum(ci*qi) correspond to
+        # solutions alpha*p + Sum(ci*betai) of the initial equation.
+        d = a.gcd(b)
+        if not d.is_ground:
+            break
+
+    # a*Dp + b*p = Sum(ci*qi) may have a polynomial solution
+    # only if the sum is divisible by d.
+
+    qq, M = poly_linear_constraints(q, d)
+    # qq = [qq1, ..., qqm] where qqi = qi.quo(d).
+    # M is a matrix with m columns an entries in k.
+    # Sum(fi*qi, (i, 1, m)), where f1, ..., fm are elements of k, is
+    # divisible by d if and only if M*Matrix([f1, ..., fm]) == 0,
+    # in which case the quotient is Sum(fi*qqi).
+
+    A, _ = constant_system(M, zeros(M.rows, 1, DE.t), DE)
+    # A is a matrix with m columns and entries in Const(k).
+    # Sum(ci*qqi) is Sum(ci*qi).quo(d), and the remainder is zero
+    # for c1, ..., cm in Const(k) if and only if
+    # A*Matrix([c1, ...,cm]) == 0.
+
+    V = A.nullspace()
+    # V = [v1, ..., vu] where each vj is a column matrix with
+    # entries aj1, ..., ajm in Const(k).
+    # Sum(aji*qi) is divisible by d with exact quotient Sum(aji*qqi).
+    # Sum(ci*qi) is divisible by d if and only if ci = Sum(dj*aji)
+    # (i = 1, ..., m) for some d1, ..., du in Const(k).
+    # In that case, solutions of
+    #     a*Dp + b*p = Sum(ci*qi) = Sum(dj*Sum(aji*qi))
+    # are the same as those of
+    #     (a/d)*Dp + (b/d)*p = Sum(dj*rj)
+    # where rj = Sum(aji*qqi).
+
+    if not V:  # No non-trivial solution.
+        return [], eye(m, DE.t)  # Could return A, but this has
+                                 # the minimum number of rows.
+
+    Mqq = Matrix([qq])  # A single row.
+    r = [(Mqq*vj)[0] for vj in V]  # [r1, ..., ru]
+
+    # Solutions of (a/d)*Dp + (b/d)*p = Sum(dj*rj) correspond to
+    # solutions alpha*p + Sum(Sum(dj*aji)*betai) of the initial
+    # equation. These are equal to alpha*p + Sum(dj*fj) where
+    # fj = Sum(aji*betai).
+    Mbeta = Matrix([beta])
+    f = [(Mbeta*vj)[0] for vj in V]  # [f1, ..., fu]
+
+    #
+    # Solve the reduced equation recursively.
+    #
+    g, B = param_poly_rischDE(a.quo(d), b.quo(d), r, n, DE)
+
+    # g = [g1, ..., gv] in k[t]^v and and B is a matrix with u + v
+    # columns and entries in Const(k) such that
+    # (a/d)*Dp + (b/d)*p = Sum(dj*rj) has a solution p of degree <= n
+    # in k[t] if and only if p = Sum(ek*gk) where e1, ..., ev are in
+    # Const(k) and B*Matrix([d1, ..., du, e1, ..., ev]) == 0.
+    # The solutions of the original equation are then
+    # Sum(dj*fj, (j, 1, u)) + alpha*Sum(ek*gk, (k, 1, v)).
+
+    # Collect solution components.
+    h = f + [alpha*gk for gk in g]
+
+    # Build combined relation matrix.
+    A = -eye(m, DE.t)
+    for vj in V:
+        A = A.row_join(vj)
+    A = A.row_join(zeros(m, len(g), DE.t))
+    A = A.col_join(zeros(B.rows, m, DE.t).row_join(B))
+
+    return h, A
+
+
+def param_rischDE(fa, fd, G, DE):
+    """
+    Solve a Parametric Risch Differential Equation: Dy + f*y == Sum(ci*Gi, (i, 1, m)).
+
+    Explanation
+    ===========
+
+    Given a derivation D in k(t), f in k(t), and G
+    = [G1, ..., Gm] in k(t)^m, return h = [h1, ..., hr] in k(t)^r and
+    a matrix A with m + r columns and entries in Const(k) such that
+    Dy + f*y = Sum(ci*Gi, (i, 1, m)) has a solution y
+    in k(t) with c1, ..., cm in Const(k) if and only if y = Sum(dj*hj,
+    (j, 1, r)) where d1, ..., dr are in Const(k) and (c1, ..., cm,
+    d1, ..., dr) is a solution of Ax == 0.
+
+    Elements of k(t) are tuples (a, d) with a and d in k[t].
+    """
+    m = len(G)
+    q, (fa, fd) = weak_normalizer(fa, fd, DE)
+    # Solutions of the weakly normalized equation Dz + f*z = q*Sum(ci*Gi)
+    # correspond to solutions y = z/q of the original equation.
+    gamma = q
+    G = [(q*ga).cancel(gd, include=True) for ga, gd in G]
+
+    a, (ba, bd), G, hn = prde_normal_denom(fa, fd, G, DE)
+    # Solutions q in k of  a*Dq + b*q = Sum(ci*Gi) correspond
+    # to solutions z = q/hn of the weakly normalized equation.
+    gamma *= hn
+
+    A, B, G, hs = prde_special_denom(a, ba, bd, G, DE)
+    # Solutions p in k[t] of  A*Dp + B*p = Sum(ci*Gi) correspond
+    # to solutions q = p/hs of the previous equation.
+    gamma *= hs
+
+    g = A.gcd(B)
+    a, b, g = A.quo(g), B.quo(g), [gia.cancel(gid*g, include=True) for
+        gia, gid in G]
+
+    # a*Dp + b*p = Sum(ci*gi)  may have a polynomial solution
+    # only if the sum is in k[t].
+
+    q, M = prde_linear_constraints(a, b, g, DE)
+
+    # q = [q1, ..., qm] where qi in k[t] is the polynomial component
+    # of the partial fraction expansion of gi.
+    # M is a matrix with m columns and entries in k.
+    # Sum(fi*gi, (i, 1, m)), where f1, ..., fm are elements of k,
+    # is a polynomial if and only if M*Matrix([f1, ..., fm]) == 0,
+    # in which case the sum is equal to Sum(fi*qi).
+
+    M, _ = constant_system(M, zeros(M.rows, 1, DE.t), DE)
+    # M is a matrix with m columns and entries in Const(k).
+    # Sum(ci*gi) is in k[t] for c1, ..., cm in Const(k)
+    # if and only if M*Matrix([c1, ..., cm]) == 0,
+    # in which case the sum is Sum(ci*qi).
+
+    ## Reduce number of constants at this point
+
+    V = M.nullspace()
+    # V = [v1, ..., vu] where each vj is a column matrix with
+    # entries aj1, ..., ajm in Const(k).
+    # Sum(aji*gi) is in k[t] and equal to Sum(aji*qi) (j = 1, ..., u).
+    # Sum(ci*gi) is in k[t] if and only is ci = Sum(dj*aji)
+    # (i = 1, ..., m) for some d1, ..., du in Const(k).
+    # In that case,
+    #     Sum(ci*gi) = Sum(ci*qi) = Sum(dj*Sum(aji*qi)) = Sum(dj*rj)
+    # where rj = Sum(aji*qi) (j = 1, ..., u) in k[t].
+
+    if not V:  # No non-trivial solution
+        return [], eye(m, DE.t)
+
+    Mq = Matrix([q])  # A single row.
+    r = [(Mq*vj)[0] for vj in V]  # [r1, ..., ru]
+
+    # Solutions of a*Dp + b*p = Sum(dj*rj) correspond to solutions
+    # y = p/gamma of the initial equation with ci = Sum(dj*aji).
+
+    try:
+        # We try n=5. At least for prde_spde, it will always
+        # terminate no matter what n is.
+        n = bound_degree(a, b, r, DE, parametric=True)
+    except NotImplementedError:
+        # A temporary bound is set. Eventually, it will be removed.
+        # the currently added test case takes large time
+        # even with n=5, and much longer with large n's.
+        n = 5
+
+    h, B = param_poly_rischDE(a, b, r, n, DE)
+
+    # h = [h1, ..., hv] in k[t]^v and and B is a matrix with u + v
+    # columns and entries in Const(k) such that
+    # a*Dp + b*p = Sum(dj*rj) has a solution p of degree <= n
+    # in k[t] if and only if p = Sum(ek*hk) where e1, ..., ev are in
+    # Const(k) and B*Matrix([d1, ..., du, e1, ..., ev]) == 0.
+    # The solutions of the original equation for ci = Sum(dj*aji)
+    # (i = 1, ..., m) are then y = Sum(ek*hk, (k, 1, v))/gamma.
+
+    ## Build combined relation matrix with m + u + v columns.
+
+    A = -eye(m, DE.t)
+    for vj in V:
+        A = A.row_join(vj)
+    A = A.row_join(zeros(m, len(h), DE.t))
+    A = A.col_join(zeros(B.rows, m, DE.t).row_join(B))
+
+    ## Eliminate d1, ..., du.
+
+    W = A.nullspace()
+
+    # W = [w1, ..., wt] where each wl is a column matrix with
+    # entries blk (k = 1, ..., m + u + v) in Const(k).
+    # The vectors (bl1, ..., blm) generate the space of those
+    # constant families (c1, ..., cm) for which a solution of
+    # the equation Dy + f*y == Sum(ci*Gi) exists. They generate
+    # the space and form a basis except possibly when Dy + f*y == 0
+    # is solvable in k(t}. The corresponding solutions are
+    # y = Sum(blk'*hk, (k, 1, v))/gamma, where k' = k + m + u.
+
+    v = len(h)
+    shape = (len(W), m+v)
+    elements = [wl[:m] + wl[-v:] for wl in W] # excise dj's.
+    items = [e for row in elements for e in row]
+
+    # Need to set the shape in case W is empty
+    M = Matrix(*shape, items, DE.t)
+    N = M.nullspace()
+
+    # N = [n1, ..., ns] where the ni in Const(k)^(m + v) are column
+    # vectors generating the space of linear relations between
+    # c1, ..., cm, e1, ..., ev.
+
+    C = Matrix([ni[:] for ni in N], DE.t)  # rows n1, ..., ns.
+
+    return [hk.cancel(gamma, include=True) for hk in h], C
+
+
+def limited_integrate_reduce(fa, fd, G, DE):
+    """
+    Simpler version of step 1 & 2 for the limited integration problem.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k(t) and f, g1, ..., gn in k(t), return
+    (a, b, h, N, g, V) such that a, b, h in k[t], N is a non-negative integer,
+    g in k(t), V == [v1, ..., vm] in k(t)^m, and for any solution v in k(t),
+    c1, ..., cm in C of f == Dv + Sum(ci*wi, (i, 1, m)), p = v*h is in k, and
+    p and the ci satisfy a*Dp + b*p == g + Sum(ci*vi, (i, 1, m)).  Furthermore,
+    if S1irr == Sirr, then p is in k[t], and if t is nonlinear or Liouvillian
+    over k, then deg(p) <= N.
+
+    So that the special part is always computed, this function calls the more
+    general prde_special_denom() automatically if it cannot determine that
+    S1irr == Sirr.  Furthermore, it will automatically call bound_degree() when
+    t is linear and non-Liouvillian, which for the transcendental case, implies
+    that Dt == a*t + b with for some a, b in k*.
+    """
+    dn, ds = splitfactor(fd, DE)
+    E = [splitfactor(gd, DE) for _, gd in G]
+    En, Es = list(zip(*E))
+    c = reduce(lambda i, j: i.lcm(j), (dn,) + En)  # lcm(dn, en1, ..., enm)
+    hn = c.gcd(c.diff(DE.t))
+    a = hn
+    b = -derivation(hn, DE)
+    N = 0
+
+    # These are the cases where we know that S1irr = Sirr, but there could be
+    # others, and this algorithm will need to be extended to handle them.
+    if DE.case in ('base', 'primitive', 'exp', 'tan'):
+        hs = reduce(lambda i, j: i.lcm(j), (ds,) + Es)  # lcm(ds, es1, ..., esm)
+        a = hn*hs
+        b -= (hn*derivation(hs, DE)).quo(hs)
+        mu = min(order_at_oo(fa, fd, DE.t), min(order_at_oo(ga, gd, DE.t) for
+            ga, gd in G))
+        # So far, all the above are also nonlinear or Liouvillian, but if this
+        # changes, then this will need to be updated to call bound_degree()
+        # as per the docstring of this function (DE.case == 'other_linear').
+        N = hn.degree(DE.t) + hs.degree(DE.t) + max(0, 1 - DE.d.degree(DE.t) - mu)
+    else:
+        # TODO: implement this
+        raise NotImplementedError
+
+    V = [(-a*hn*ga).cancel(gd, include=True) for ga, gd in G]
+    return (a, b, a, N, (a*hn*fa).cancel(fd, include=True), V)
+
+
+def limited_integrate(fa, fd, G, DE):
+    """
+    Solves the limited integration problem:  f = Dv + Sum(ci*wi, (i, 1, n))
+    """
+    fa, fd = fa*Poly(1/fd.LC(), DE.t), fd.monic()
+    # interpreting limited integration problem as a
+    # parametric Risch DE problem
+    Fa = Poly(0, DE.t)
+    Fd = Poly(1, DE.t)
+    G = [(fa, fd)] + G
+    h, A = param_rischDE(Fa, Fd, G, DE)
+    V = A.nullspace()
+    V = [v for v in V if v[0] != 0]
+    if not V:
+        return None
+    else:
+        # we can take any vector from V, we take V[0]
+        c0 = V[0][0]
+        # v = [-1, c1, ..., cm, d1, ..., dr]
+        v = V[0]/(-c0)
+        r = len(h)
+        m = len(v) - r - 1
+        C = list(v[1: m + 1])
+        y = -sum(v[m + 1 + i]*h[i][0].as_expr()/h[i][1].as_expr() \
+                for i in range(r))
+        y_num, y_den = y.as_numer_denom()
+        Ya, Yd = Poly(y_num, DE.t), Poly(y_den, DE.t)
+        Y = Ya*Poly(1/Yd.LC(), DE.t), Yd.monic()
+        return Y, C
+
+
+def parametric_log_deriv_heu(fa, fd, wa, wd, DE, c1=None):
+    """
+    Parametric logarithmic derivative heuristic.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], f in k(t), and a hyperexponential monomial
+    theta over k(t), raises either NotImplementedError, in which case the
+    heuristic failed, or returns None, in which case it has proven that no
+    solution exists, or returns a solution (n, m, v) of the equation
+    n*f == Dv/v + m*Dtheta/theta, with v in k(t)* and n, m in ZZ with n != 0.
+
+    If this heuristic fails, the structure theorem approach will need to be
+    used.
+
+    The argument w == Dtheta/theta
+    """
+    # TODO: finish writing this and write tests
+    c1 = c1 or Dummy('c1')
+
+    p, a = fa.div(fd)
+    q, b = wa.div(wd)
+
+    B = max(0, derivation(DE.t, DE).degree(DE.t) - 1)
+    C = max(p.degree(DE.t), q.degree(DE.t))
+
+    if q.degree(DE.t) > B:
+        eqs = [p.nth(i) - c1*q.nth(i) for i in range(B + 1, C + 1)]
+        s = solve(eqs, c1)
+        if not s or not s[c1].is_Rational:
+            # deg(q) > B, no solution for c.
+            return None
+
+        M, N = s[c1].as_numer_denom()
+        M_poly = M.as_poly(q.gens)
+        N_poly = N.as_poly(q.gens)
+
+        nfmwa = N_poly*fa*wd - M_poly*wa*fd
+        nfmwd = fd*wd
+        Qv = is_log_deriv_k_t_radical_in_field(nfmwa, nfmwd, DE, 'auto')
+        if Qv is None:
+            # (N*f - M*w) is not the logarithmic derivative of a k(t)-radical.
+            return None
+
+        Q, v = Qv
+
+        if Q.is_zero or v.is_zero:
+            return None
+
+        return (Q*N, Q*M, v)
+
+    if p.degree(DE.t) > B:
+        return None
+
+    c = lcm(fd.as_poly(DE.t).LC(), wd.as_poly(DE.t).LC())
+    l = fd.monic().lcm(wd.monic())*Poly(c, DE.t)
+    ln, ls = splitfactor(l, DE)
+    z = ls*ln.gcd(ln.diff(DE.t))
+
+    if not z.has(DE.t):
+        # TODO: We treat this as 'no solution', until the structure
+        # theorem version of parametric_log_deriv is implemented.
+        return None
+
+    u1, r1 = (fa*l.quo(fd)).div(z)  # (l*f).div(z)
+    u2, r2 = (wa*l.quo(wd)).div(z)  # (l*w).div(z)
+
+    eqs = [r1.nth(i) - c1*r2.nth(i) for i in range(z.degree(DE.t))]
+    s = solve(eqs, c1)
+    if not s or not s[c1].is_Rational:
+        # deg(q) <= B, no solution for c.
+        return None
+
+    M, N = s[c1].as_numer_denom()
+
+    nfmwa = N.as_poly(DE.t)*fa*wd - M.as_poly(DE.t)*wa*fd
+    nfmwd = fd*wd
+    Qv = is_log_deriv_k_t_radical_in_field(nfmwa, nfmwd, DE)
+    if Qv is None:
+        # (N*f - M*w) is not the logarithmic derivative of a k(t)-radical.
+        return None
+
+    Q, v = Qv
+
+    if Q.is_zero or v.is_zero:
+        return None
+
+    return (Q*N, Q*M, v)
+
+
+def parametric_log_deriv(fa, fd, wa, wd, DE):
+    # TODO: Write the full algorithm using the structure theorems.
+#    try:
+    A = parametric_log_deriv_heu(fa, fd, wa, wd, DE)
+#    except NotImplementedError:
+        # Heuristic failed, we have to use the full method.
+        # TODO: This could be implemented more efficiently.
+        # It isn't too worrisome, because the heuristic handles most difficult
+        # cases.
+    return A
+
+
+def is_deriv_k(fa, fd, DE):
+    r"""
+    Checks if Df/f is the derivative of an element of k(t).
+
+    Explanation
+    ===========
+
+    a in k(t) is the derivative of an element of k(t) if there exists b in k(t)
+    such that a = Db.  Either returns (ans, u), such that Df/f == Du, or None,
+    which means that Df/f is not the derivative of an element of k(t).  ans is
+    a list of tuples such that Add(*[i*j for i, j in ans]) == u.  This is useful
+    for seeing exactly which elements of k(t) produce u.
+
+    This function uses the structure theorem approach, which says that for any
+    f in K, Df/f is the derivative of a element of K if and only if there are ri
+    in QQ such that::
+
+            ---               ---       Dt
+            \    r  * Dt   +  \    r  *   i      Df
+            /     i     i     /     i   ---   =  --.
+            ---               ---        t        f
+         i in L            i in E         i
+               K/C(x)            K/C(x)
+
+
+    Where C = Const(K), L_K/C(x) = { i in {1, ..., n} such that t_i is
+    transcendental over C(x)(t_1, ..., t_i-1) and Dt_i = Da_i/a_i, for some a_i
+    in C(x)(t_1, ..., t_i-1)* } (i.e., the set of all indices of logarithmic
+    monomials of K over C(x)), and E_K/C(x) = { i in {1, ..., n} such that t_i
+    is transcendental over C(x)(t_1, ..., t_i-1) and Dt_i/t_i = Da_i, for some
+    a_i in C(x)(t_1, ..., t_i-1) } (i.e., the set of all indices of
+    hyperexponential monomials of K over C(x)).  If K is an elementary extension
+    over C(x), then the cardinality of L_K/C(x) U E_K/C(x) is exactly the
+    transcendence degree of K over C(x).  Furthermore, because Const_D(K) ==
+    Const_D(C(x)) == C, deg(Dt_i) == 1 when t_i is in E_K/C(x) and
+    deg(Dt_i) == 0 when t_i is in L_K/C(x), implying in particular that E_K/C(x)
+    and L_K/C(x) are disjoint.
+
+    The sets L_K/C(x) and E_K/C(x) must, by their nature, be computed
+    recursively using this same function.  Therefore, it is required to pass
+    them as indices to D (or T).  E_args are the arguments of the
+    hyperexponentials indexed by E_K (i.e., if i is in E_K, then T[i] ==
+    exp(E_args[i])).  This is needed to compute the final answer u such that
+    Df/f == Du.
+
+    log(f) will be the same as u up to a additive constant.  This is because
+    they will both behave the same as monomials. For example, both log(x) and
+    log(2*x) == log(x) + log(2) satisfy Dt == 1/x, because log(2) is constant.
+    Therefore, the term const is returned.  const is such that
+    log(const) + f == u.  This is calculated by dividing the arguments of one
+    logarithm from the other.  Therefore, it is necessary to pass the arguments
+    of the logarithmic terms in L_args.
+
+    To handle the case where we are given Df/f, not f, use is_deriv_k_in_field().
+
+    See also
+    ========
+    is_log_deriv_k_t_radical_in_field, is_log_deriv_k_t_radical
+
+    """
+    # Compute Df/f
+    dfa, dfd = (fd*derivation(fa, DE) - fa*derivation(fd, DE)), fd*fa
+    dfa, dfd = dfa.cancel(dfd, include=True)
+
+    # Our assumption here is that each monomial is recursively transcendental
+    if len(DE.exts) != len(DE.D):
+        if [i for i in DE.cases if i == 'tan'] or \
+                ({i for i in DE.cases if i == 'primitive'} -
+                        set(DE.indices('log'))):
+            raise NotImplementedError("Real version of the structure "
+                "theorems with hypertangent support is not yet implemented.")
+
+        # TODO: What should really be done in this case?
+        raise NotImplementedError("Nonelementary extensions not supported "
+            "in the structure theorems.")
+
+    E_part = [DE.D[i].quo(Poly(DE.T[i], DE.T[i])).as_expr() for i in DE.indices('exp')]
+    L_part = [DE.D[i].as_expr() for i in DE.indices('log')]
+
+    # The expression dfa/dfd might not be polynomial in any of its symbols so we
+    # use a Dummy as the generator for PolyMatrix.
+    dum = Dummy()
+    lhs = Matrix([E_part + L_part], dum)
+    rhs = Matrix([dfa.as_expr()/dfd.as_expr()], dum)
+
+    A, u = constant_system(lhs, rhs, DE)
+
+    u = u.to_Matrix()  # Poly to Expr
+
+    if not A or not all(derivation(i, DE, basic=True).is_zero for i in u):
+        # If the elements of u are not all constant
+        # Note: See comment in constant_system
+
+        # Also note: derivation(basic=True) calls cancel()
+        return None
+    else:
+        if not all(i.is_Rational for i in u):
+            raise NotImplementedError("Cannot work with non-rational "
+                "coefficients in this case.")
+        else:
+            terms = ([DE.extargs[i] for i in DE.indices('exp')] +
+                    [DE.T[i] for i in DE.indices('log')])
+            ans = list(zip(terms, u))
+            result = Add(*[Mul(i, j) for i, j in ans])
+            argterms = ([DE.T[i] for i in DE.indices('exp')] +
+                    [DE.extargs[i] for i in DE.indices('log')])
+            l = []
+            ld = []
+            for i, j in zip(argterms, u):
+                # We need to get around things like sqrt(x**2) != x
+                # and also sqrt(x**2 + 2*x + 1) != x + 1
+                # Issue 10798: i need not be a polynomial
+                i, d = i.as_numer_denom()
+                icoeff, iterms = sqf_list(i)
+                l.append(Mul(*([Pow(icoeff, j)] + [Pow(b, e*j) for b, e in iterms])))
+                dcoeff, dterms = sqf_list(d)
+                ld.append(Mul(*([Pow(dcoeff, j)] + [Pow(b, e*j) for b, e in dterms])))
+            const = cancel(fa.as_expr()/fd.as_expr()/Mul(*l)*Mul(*ld))
+
+            return (ans, result, const)
+
+
+def is_log_deriv_k_t_radical(fa, fd, DE, Df=True):
+    r"""
+    Checks if Df is the logarithmic derivative of a k(t)-radical.
+
+    Explanation
+    ===========
+
+    b in k(t) can be written as the logarithmic derivative of a k(t) radical if
+    there exist n in ZZ and u in k(t) with n, u != 0 such that n*b == Du/u.
+    Either returns (ans, u, n, const) or None, which means that Df cannot be
+    written as the logarithmic derivative of a k(t)-radical.  ans is a list of
+    tuples such that Mul(*[i**j for i, j in ans]) == u.  This is useful for
+    seeing exactly what elements of k(t) produce u.
+
+    This function uses the structure theorem approach, which says that for any
+    f in K, Df is the logarithmic derivative of a K-radical if and only if there
+    are ri in QQ such that::
+
+            ---               ---       Dt
+            \    r  * Dt   +  \    r  *   i
+            /     i     i     /     i   ---   =  Df.
+            ---               ---        t
+         i in L            i in E         i
+               K/C(x)            K/C(x)
+
+
+    Where C = Const(K), L_K/C(x) = { i in {1, ..., n} such that t_i is
+    transcendental over C(x)(t_1, ..., t_i-1) and Dt_i = Da_i/a_i, for some a_i
+    in C(x)(t_1, ..., t_i-1)* } (i.e., the set of all indices of logarithmic
+    monomials of K over C(x)), and E_K/C(x) = { i in {1, ..., n} such that t_i
+    is transcendental over C(x)(t_1, ..., t_i-1) and Dt_i/t_i = Da_i, for some
+    a_i in C(x)(t_1, ..., t_i-1) } (i.e., the set of all indices of
+    hyperexponential monomials of K over C(x)).  If K is an elementary extension
+    over C(x), then the cardinality of L_K/C(x) U E_K/C(x) is exactly the
+    transcendence degree of K over C(x).  Furthermore, because Const_D(K) ==
+    Const_D(C(x)) == C, deg(Dt_i) == 1 when t_i is in E_K/C(x) and
+    deg(Dt_i) == 0 when t_i is in L_K/C(x), implying in particular that E_K/C(x)
+    and L_K/C(x) are disjoint.
+
+    The sets L_K/C(x) and E_K/C(x) must, by their nature, be computed
+    recursively using this same function.  Therefore, it is required to pass
+    them as indices to D (or T).  L_args are the arguments of the logarithms
+    indexed by L_K (i.e., if i is in L_K, then T[i] == log(L_args[i])).  This is
+    needed to compute the final answer u such that n*f == Du/u.
+
+    exp(f) will be the same as u up to a multiplicative constant.  This is
+    because they will both behave the same as monomials.  For example, both
+    exp(x) and exp(x + 1) == E*exp(x) satisfy Dt == t. Therefore, the term const
+    is returned.  const is such that exp(const)*f == u.  This is calculated by
+    subtracting the arguments of one exponential from the other.  Therefore, it
+    is necessary to pass the arguments of the exponential terms in E_args.
+
+    To handle the case where we are given Df, not f, use
+    is_log_deriv_k_t_radical_in_field().
+
+    See also
+    ========
+
+    is_log_deriv_k_t_radical_in_field, is_deriv_k
+
+    """
+    if Df:
+        dfa, dfd = (fd*derivation(fa, DE) - fa*derivation(fd, DE)).cancel(fd**2,
+            include=True)
+    else:
+        dfa, dfd = fa, fd
+
+    # Our assumption here is that each monomial is recursively transcendental
+    if len(DE.exts) != len(DE.D):
+        if [i for i in DE.cases if i == 'tan'] or \
+                ({i for i in DE.cases if i == 'primitive'} -
+                        set(DE.indices('log'))):
+            raise NotImplementedError("Real version of the structure "
+                "theorems with hypertangent support is not yet implemented.")
+
+        # TODO: What should really be done in this case?
+        raise NotImplementedError("Nonelementary extensions not supported "
+            "in the structure theorems.")
+
+    E_part = [DE.D[i].quo(Poly(DE.T[i], DE.T[i])).as_expr() for i in DE.indices('exp')]
+    L_part = [DE.D[i].as_expr() for i in DE.indices('log')]
+
+    # The expression dfa/dfd might not be polynomial in any of its symbols so we
+    # use a Dummy as the generator for PolyMatrix.
+    dum = Dummy()
+    lhs = Matrix([E_part + L_part], dum)
+    rhs = Matrix([dfa.as_expr()/dfd.as_expr()], dum)
+
+    A, u = constant_system(lhs, rhs, DE)
+
+    u = u.to_Matrix()  # Poly to Expr
+
+    if not A or not all(derivation(i, DE, basic=True).is_zero for i in u):
+        # If the elements of u are not all constant
+        # Note: See comment in constant_system
+
+        # Also note: derivation(basic=True) calls cancel()
+        return None
+    else:
+        if not all(i.is_Rational for i in u):
+            # TODO: But maybe we can tell if they're not rational, like
+            # log(2)/log(3). Also, there should be an option to continue
+            # anyway, even if the result might potentially be wrong.
+            raise NotImplementedError("Cannot work with non-rational "
+                "coefficients in this case.")
+        else:
+            n = S.One*reduce(ilcm, [i.as_numer_denom()[1] for i in u])
+            u *= n
+            terms = ([DE.T[i] for i in DE.indices('exp')] +
+                    [DE.extargs[i] for i in DE.indices('log')])
+            ans = list(zip(terms, u))
+            result = Mul(*[Pow(i, j) for i, j in ans])
+
+            # exp(f) will be the same as result up to a multiplicative
+            # constant.  We now find the log of that constant.
+            argterms = ([DE.extargs[i] for i in DE.indices('exp')] +
+                    [DE.T[i] for i in DE.indices('log')])
+            const = cancel(fa.as_expr()/fd.as_expr() -
+                Add(*[Mul(i, j/n) for i, j in zip(argterms, u)]))
+
+            return (ans, result, n, const)
+
+
+def is_log_deriv_k_t_radical_in_field(fa, fd, DE, case='auto', z=None):
+    """
+    Checks if f can be written as the logarithmic derivative of a k(t)-radical.
+
+    Explanation
+    ===========
+
+    It differs from is_log_deriv_k_t_radical(fa, fd, DE, Df=False)
+    for any given fa, fd, DE in that it finds the solution in the
+    given field not in some (possibly unspecified extension) and
+    "in_field" with the function name is used to indicate that.
+
+    f in k(t) can be written as the logarithmic derivative of a k(t) radical if
+    there exist n in ZZ and u in k(t) with n, u != 0 such that n*f == Du/u.
+    Either returns (n, u) or None, which means that f cannot be written as the
+    logarithmic derivative of a k(t)-radical.
+
+    case is one of {'primitive', 'exp', 'tan', 'auto'} for the primitive,
+    hyperexponential, and hypertangent cases, respectively.  If case is 'auto',
+    it will attempt to determine the type of the derivation automatically.
+
+    See also
+    ========
+    is_log_deriv_k_t_radical, is_deriv_k
+
+    """
+    fa, fd = fa.cancel(fd, include=True)
+
+    # f must be simple
+    n, s = splitfactor(fd, DE)
+    if not s.is_one:
+        pass
+
+    z = z or Dummy('z')
+    H, b = residue_reduce(fa, fd, DE, z=z)
+    if not b:
+        # I will have to verify, but I believe that the answer should be
+        # None in this case. This should never happen for the
+        # functions given when solving the parametric logarithmic
+        # derivative problem when integration elementary functions (see
+        # Bronstein's book, page 255), so most likely this indicates a bug.
+        return None
+
+    roots = [(i, i.real_roots()) for i, _ in H]
+    if not all(len(j) == i.degree() and all(k.is_Rational for k in j) for
+               i, j in roots):
+        # If f is the logarithmic derivative of a k(t)-radical, then all the
+        # roots of the resultant must be rational numbers.
+        return None
+
+    # [(a, i), ...], where i*log(a) is a term in the log-part of the integral
+    # of f
+    respolys, residues = list(zip(*roots)) or [[], []]
+    # Note: this might be empty, but everything below should work find in that
+    # case (it should be the same as if it were [[1, 1]])
+    residueterms = [(H[j][1].subs(z, i), i) for j in range(len(H)) for
+        i in residues[j]]
+
+    # TODO: finish writing this and write tests
+
+    p = cancel(fa.as_expr()/fd.as_expr() - residue_reduce_derivation(H, DE, z))
+
+    p = p.as_poly(DE.t)
+    if p is None:
+        # f - Dg will be in k[t] if f is the logarithmic derivative of a k(t)-radical
+        return None
+
+    if p.degree(DE.t) >= max(1, DE.d.degree(DE.t)):
+        return None
+
+    if case == 'auto':
+        case = DE.case
+
+    if case == 'exp':
+        wa, wd = derivation(DE.t, DE).cancel(Poly(DE.t, DE.t), include=True)
+        with DecrementLevel(DE):
+            pa, pd = frac_in(p, DE.t, cancel=True)
+            wa, wd = frac_in((wa, wd), DE.t)
+            A = parametric_log_deriv(pa, pd, wa, wd, DE)
+        if A is None:
+            return None
+        n, e, u = A
+        u *= DE.t**e
+
+    elif case == 'primitive':
+        with DecrementLevel(DE):
+            pa, pd = frac_in(p, DE.t)
+            A = is_log_deriv_k_t_radical_in_field(pa, pd, DE, case='auto')
+        if A is None:
+            return None
+        n, u = A
+
+    elif case == 'base':
+        # TODO: we can use more efficient residue reduction from ratint()
+        if not fd.is_sqf or fa.degree() >= fd.degree():
+            # f is the logarithmic derivative in the base case if and only if
+            # f = fa/fd, fd is square-free, deg(fa) < deg(fd), and
+            # gcd(fa, fd) == 1.  The last condition is handled by cancel() above.
+            return None
+        # Note: if residueterms = [], returns (1, 1)
+        # f had better be 0 in that case.
+        n = S.One*reduce(ilcm, [i.as_numer_denom()[1] for _, i in residueterms], 1)
+        u = Mul(*[Pow(i, j*n) for i, j in residueterms])
+        return (n, u)
+
+    elif case == 'tan':
+        raise NotImplementedError("The hypertangent case is "
+        "not yet implemented for is_log_deriv_k_t_radical_in_field()")
+
+    elif case in ('other_linear', 'other_nonlinear'):
+        # XXX: If these are supported by the structure theorems, change to NotImplementedError.
+        raise ValueError("The %s case is not supported in this function." % case)
+
+    else:
+        raise ValueError("case must be one of {'primitive', 'exp', 'tan', "
+        "'base', 'auto'}, not %s" % case)
+
+    common_denom = S.One*reduce(ilcm, [i.as_numer_denom()[1] for i in [j for _, j in
+        residueterms]] + [n], 1)
+    residueterms = [(i, j*common_denom) for i, j in residueterms]
+    m = common_denom//n
+    if common_denom != n*m:  # Verify exact division
+        raise ValueError("Inexact division")
+    u = cancel(u**m*Mul(*[Pow(i, j) for i, j in residueterms]))
+
+    return (common_denom, u)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/quadrature.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/quadrature.py
new file mode 100644
index 0000000000000000000000000000000000000000..b518bd427dc9980d6a941d2e1ef4d139c5f0f5f9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/quadrature.py
@@ -0,0 +1,617 @@
+from sympy.core import S, Dummy, pi
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.trigonometric import sin, cos
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.gamma_functions import gamma
+from sympy.polys.orthopolys import (legendre_poly, laguerre_poly,
+                                    hermite_poly, jacobi_poly)
+from sympy.polys.rootoftools import RootOf
+
+
+def gauss_legendre(n, n_digits):
+    r"""
+    Computes the Gauss-Legendre quadrature [1]_ points and weights.
+
+    Explanation
+    ===========
+
+    The Gauss-Legendre quadrature approximates the integral:
+
+    .. math::
+        \int_{-1}^1 f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of `P_n`
+    and the weights `w_i` are given by:
+
+    .. math::
+        w_i = \frac{2}{\left(1-x_i^2\right) \left(P'_n(x_i)\right)^2}
+
+    Parameters
+    ==========
+
+    n :
+        The order of quadrature.
+    n_digits :
+        Number of significant digits of the points and weights to return.
+
+    Returns
+    =======
+
+    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.quadrature import gauss_legendre
+    >>> x, w = gauss_legendre(3, 5)
+    >>> x
+    [-0.7746, 0, 0.7746]
+    >>> w
+    [0.55556, 0.88889, 0.55556]
+    >>> x, w = gauss_legendre(4, 5)
+    >>> x
+    [-0.86114, -0.33998, 0.33998, 0.86114]
+    >>> w
+    [0.34785, 0.65215, 0.65215, 0.34785]
+
+    See Also
+    ========
+
+    gauss_laguerre, gauss_gen_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gaussian_quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/legendre_rule/legendre_rule.html
+    """
+    x = Dummy("x")
+    p = legendre_poly(n, x, polys=True)
+    pd = p.diff(x)
+    xi = []
+    w = []
+    for r in p.real_roots():
+        if isinstance(r, RootOf):
+            r = r.eval_rational(S.One/10**(n_digits+2))
+        xi.append(r.n(n_digits))
+        w.append((2/((1-r**2) * pd.subs(x, r)**2)).n(n_digits))
+    return xi, w
+
+
+def gauss_laguerre(n, n_digits):
+    r"""
+    Computes the Gauss-Laguerre quadrature [1]_ points and weights.
+
+    Explanation
+    ===========
+
+    The Gauss-Laguerre quadrature approximates the integral:
+
+    .. math::
+        \int_0^{\infty} e^{-x} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)
+
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of `L_n`
+    and the weights `w_i` are given by:
+
+    .. math::
+        w_i = \frac{x_i}{(n+1)^2 \left(L_{n+1}(x_i)\right)^2}
+
+    Parameters
+    ==========
+
+    n :
+        The order of quadrature.
+    n_digits :
+        Number of significant digits of the points and weights to return.
+
+    Returns
+    =======
+
+    (x, w) : The ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.quadrature import gauss_laguerre
+    >>> x, w = gauss_laguerre(3, 5)
+    >>> x
+    [0.41577, 2.2943, 6.2899]
+    >>> w
+    [0.71109, 0.27852, 0.010389]
+    >>> x, w = gauss_laguerre(6, 5)
+    >>> x
+    [0.22285, 1.1889, 2.9927, 5.7751, 9.8375, 15.983]
+    >>> w
+    [0.45896, 0.417, 0.11337, 0.010399, 0.00026102, 8.9855e-7]
+
+    See Also
+    ========
+
+    gauss_legendre, gauss_gen_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gauss%E2%80%93Laguerre_quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/laguerre_rule/laguerre_rule.html
+    """
+    x = Dummy("x")
+    p = laguerre_poly(n, x, polys=True)
+    p1 = laguerre_poly(n+1, x, polys=True)
+    xi = []
+    w = []
+    for r in p.real_roots():
+        if isinstance(r, RootOf):
+            r = r.eval_rational(S.One/10**(n_digits+2))
+        xi.append(r.n(n_digits))
+        w.append((r/((n+1)**2 * p1.subs(x, r)**2)).n(n_digits))
+    return xi, w
+
+
+def gauss_hermite(n, n_digits):
+    r"""
+    Computes the Gauss-Hermite quadrature [1]_ points and weights.
+
+    Explanation
+    ===========
+
+    The Gauss-Hermite quadrature approximates the integral:
+
+    .. math::
+        \int_{-\infty}^{\infty} e^{-x^2} f(x)\,dx \approx
+            \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of `H_n`
+    and the weights `w_i` are given by:
+
+    .. math::
+        w_i = \frac{2^{n-1} n! \sqrt{\pi}}{n^2 \left(H_{n-1}(x_i)\right)^2}
+
+    Parameters
+    ==========
+
+    n :
+        The order of quadrature.
+    n_digits :
+        Number of significant digits of the points and weights to return.
+
+    Returns
+    =======
+
+    (x, w) : The ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.quadrature import gauss_hermite
+    >>> x, w = gauss_hermite(3, 5)
+    >>> x
+    [-1.2247, 0, 1.2247]
+    >>> w
+    [0.29541, 1.1816, 0.29541]
+
+    >>> x, w = gauss_hermite(6, 5)
+    >>> x
+    [-2.3506, -1.3358, -0.43608, 0.43608, 1.3358, 2.3506]
+    >>> w
+    [0.00453, 0.15707, 0.72463, 0.72463, 0.15707, 0.00453]
+
+    See Also
+    ========
+
+    gauss_legendre, gauss_laguerre, gauss_gen_laguerre, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gauss-Hermite_Quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/hermite_rule/hermite_rule.html
+    .. [3] https://people.sc.fsu.edu/~jburkardt/cpp_src/gen_hermite_rule/gen_hermite_rule.html
+    """
+    x = Dummy("x")
+    p = hermite_poly(n, x, polys=True)
+    p1 = hermite_poly(n-1, x, polys=True)
+    xi = []
+    w = []
+    for r in p.real_roots():
+        if isinstance(r, RootOf):
+            r = r.eval_rational(S.One/10**(n_digits+2))
+        xi.append(r.n(n_digits))
+        w.append(((2**(n-1) * factorial(n) * sqrt(pi)) /
+                 (n**2 * p1.subs(x, r)**2)).n(n_digits))
+    return xi, w
+
+
+def gauss_gen_laguerre(n, alpha, n_digits):
+    r"""
+    Computes the generalized Gauss-Laguerre quadrature [1]_ points and weights.
+
+    Explanation
+    ===========
+
+    The generalized Gauss-Laguerre quadrature approximates the integral:
+
+    .. math::
+        \int_{0}^\infty x^{\alpha} e^{-x} f(x)\,dx \approx
+            \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of
+    `L^{\alpha}_n` and the weights `w_i` are given by:
+
+    .. math::
+        w_i = \frac{\Gamma(\alpha+n)}
+                {n \Gamma(n) L^{\alpha}_{n-1}(x_i) L^{\alpha+1}_{n-1}(x_i)}
+
+    Parameters
+    ==========
+
+    n :
+        The order of quadrature.
+
+    alpha :
+        The exponent of the singularity, `\alpha > -1`.
+
+    n_digits :
+        Number of significant digits of the points and weights to return.
+
+    Returns
+    =======
+
+    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> from sympy.integrals.quadrature import gauss_gen_laguerre
+    >>> x, w = gauss_gen_laguerre(3, -S.Half, 5)
+    >>> x
+    [0.19016, 1.7845, 5.5253]
+    >>> w
+    [1.4493, 0.31413, 0.00906]
+
+    >>> x, w = gauss_gen_laguerre(4, 3*S.Half, 5)
+    >>> x
+    [0.97851, 2.9904, 6.3193, 11.712]
+    >>> w
+    [0.53087, 0.67721, 0.11895, 0.0023152]
+
+    See Also
+    ========
+
+    gauss_legendre, gauss_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gauss%E2%80%93Laguerre_quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/gen_laguerre_rule/gen_laguerre_rule.html
+    """
+    x = Dummy("x")
+    p = laguerre_poly(n, x, alpha=alpha, polys=True)
+    p1 = laguerre_poly(n-1, x, alpha=alpha, polys=True)
+    p2 = laguerre_poly(n-1, x, alpha=alpha+1, polys=True)
+    xi = []
+    w = []
+    for r in p.real_roots():
+        if isinstance(r, RootOf):
+            r = r.eval_rational(S.One/10**(n_digits+2))
+        xi.append(r.n(n_digits))
+        w.append((gamma(alpha+n) /
+                 (n*gamma(n)*p1.subs(x, r)*p2.subs(x, r))).n(n_digits))
+    return xi, w
+
+
+def gauss_chebyshev_t(n, n_digits):
+    r"""
+    Computes the Gauss-Chebyshev quadrature [1]_ points and weights of
+    the first kind.
+
+    Explanation
+    ===========
+
+    The Gauss-Chebyshev quadrature of the first kind approximates the integral:
+
+    .. math::
+        \int_{-1}^{1} \frac{1}{\sqrt{1-x^2}} f(x)\,dx \approx
+            \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of `T_n`
+    and the weights `w_i` are given by:
+
+    .. math::
+        w_i = \frac{\pi}{n}
+
+    Parameters
+    ==========
+
+    n :
+        The order of quadrature.
+
+    n_digits :
+        Number of significant digits of the points and weights to return.
+
+    Returns
+    =======
+
+    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.quadrature import gauss_chebyshev_t
+    >>> x, w = gauss_chebyshev_t(3, 5)
+    >>> x
+    [0.86602, 0, -0.86602]
+    >>> w
+    [1.0472, 1.0472, 1.0472]
+
+    >>> x, w = gauss_chebyshev_t(6, 5)
+    >>> x
+    [0.96593, 0.70711, 0.25882, -0.25882, -0.70711, -0.96593]
+    >>> w
+    [0.5236, 0.5236, 0.5236, 0.5236, 0.5236, 0.5236]
+
+    See Also
+    ========
+
+    gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Chebyshev%E2%80%93Gauss_quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/chebyshev1_rule/chebyshev1_rule.html
+    """
+    xi = []
+    w = []
+    for i in range(1, n+1):
+        xi.append((cos((2*i-S.One)/(2*n)*S.Pi)).n(n_digits))
+        w.append((S.Pi/n).n(n_digits))
+    return xi, w
+
+
+def gauss_chebyshev_u(n, n_digits):
+    r"""
+    Computes the Gauss-Chebyshev quadrature [1]_ points and weights of
+    the second kind.
+
+    Explanation
+    ===========
+
+    The Gauss-Chebyshev quadrature of the second kind approximates the
+    integral:
+
+    .. math::
+        \int_{-1}^{1} \sqrt{1-x^2} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of `U_n`
+    and the weights `w_i` are given by:
+
+    .. math::
+        w_i = \frac{\pi}{n+1} \sin^2 \left(\frac{i}{n+1}\pi\right)
+
+    Parameters
+    ==========
+
+    n : the order of quadrature
+
+    n_digits : number of significant digits of the points and weights to return
+
+    Returns
+    =======
+
+    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.quadrature import gauss_chebyshev_u
+    >>> x, w = gauss_chebyshev_u(3, 5)
+    >>> x
+    [0.70711, 0, -0.70711]
+    >>> w
+    [0.3927, 0.7854, 0.3927]
+
+    >>> x, w = gauss_chebyshev_u(6, 5)
+    >>> x
+    [0.90097, 0.62349, 0.22252, -0.22252, -0.62349, -0.90097]
+    >>> w
+    [0.084489, 0.27433, 0.42658, 0.42658, 0.27433, 0.084489]
+
+    See Also
+    ========
+
+    gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, gauss_chebyshev_t, gauss_jacobi, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Chebyshev%E2%80%93Gauss_quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/chebyshev2_rule/chebyshev2_rule.html
+    """
+    xi = []
+    w = []
+    for i in range(1, n+1):
+        xi.append((cos(i/(n+S.One)*S.Pi)).n(n_digits))
+        w.append((S.Pi/(n+S.One)*sin(i*S.Pi/(n+S.One))**2).n(n_digits))
+    return xi, w
+
+
+def gauss_jacobi(n, alpha, beta, n_digits):
+    r"""
+    Computes the Gauss-Jacobi quadrature [1]_ points and weights.
+
+    Explanation
+    ===========
+
+    The Gauss-Jacobi quadrature of the first kind approximates the integral:
+
+    .. math::
+        \int_{-1}^1 (1-x)^\alpha (1+x)^\beta f(x)\,dx \approx
+            \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of
+    `P^{(\alpha,\beta)}_n` and the weights `w_i` are given by:
+
+    .. math::
+        w_i = -\frac{2n+\alpha+\beta+2}{n+\alpha+\beta+1}
+              \frac{\Gamma(n+\alpha+1)\Gamma(n+\beta+1)}
+              {\Gamma(n+\alpha+\beta+1)(n+1)!}
+              \frac{2^{\alpha+\beta}}{P'_n(x_i)
+              P^{(\alpha,\beta)}_{n+1}(x_i)}
+
+    Parameters
+    ==========
+
+    n : the order of quadrature
+
+    alpha : the first parameter of the Jacobi Polynomial, `\alpha > -1`
+
+    beta : the second parameter of the Jacobi Polynomial, `\beta > -1`
+
+    n_digits : number of significant digits of the points and weights to return
+
+    Returns
+    =======
+
+    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> from sympy.integrals.quadrature import gauss_jacobi
+    >>> x, w = gauss_jacobi(3, S.Half, -S.Half, 5)
+    >>> x
+    [-0.90097, -0.22252, 0.62349]
+    >>> w
+    [1.7063, 1.0973, 0.33795]
+
+    >>> x, w = gauss_jacobi(6, 1, 1, 5)
+    >>> x
+    [-0.87174, -0.5917, -0.2093, 0.2093, 0.5917, 0.87174]
+    >>> w
+    [0.050584, 0.22169, 0.39439, 0.39439, 0.22169, 0.050584]
+
+    See Also
+    ========
+
+    gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre,
+    gauss_chebyshev_t, gauss_chebyshev_u, gauss_lobatto
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gauss%E2%80%93Jacobi_quadrature
+    .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/jacobi_rule/jacobi_rule.html
+    .. [3] https://people.sc.fsu.edu/~jburkardt/cpp_src/gegenbauer_rule/gegenbauer_rule.html
+    """
+    x = Dummy("x")
+    p = jacobi_poly(n, alpha, beta, x, polys=True)
+    pd = p.diff(x)
+    pn = jacobi_poly(n+1, alpha, beta, x, polys=True)
+    xi = []
+    w = []
+    for r in p.real_roots():
+        if isinstance(r, RootOf):
+            r = r.eval_rational(S.One/10**(n_digits+2))
+        xi.append(r.n(n_digits))
+        w.append((
+            - (2*n+alpha+beta+2) / (n+alpha+beta+S.One) *
+            (gamma(n+alpha+1)*gamma(n+beta+1)) /
+            (gamma(n+alpha+beta+S.One)*gamma(n+2)) *
+            2**(alpha+beta) / (pd.subs(x, r) * pn.subs(x, r))).n(n_digits))
+    return xi, w
+
+
+def gauss_lobatto(n, n_digits):
+    r"""
+    Computes the Gauss-Lobatto quadrature [1]_ points and weights.
+
+    Explanation
+    ===========
+
+    The Gauss-Lobatto quadrature approximates the integral:
+
+    .. math::
+        \int_{-1}^1 f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)
+
+    The nodes `x_i` of an order `n` quadrature rule are the roots of `P'_(n-1)`
+    and the weights `w_i` are given by:
+
+    .. math::
+        &w_i = \frac{2}{n(n-1) \left[P_{n-1}(x_i)\right]^2},\quad x\neq\pm 1\\
+        &w_i = \frac{2}{n(n-1)},\quad x=\pm 1
+
+    Parameters
+    ==========
+
+    n : the order of quadrature
+
+    n_digits : number of significant digits of the points and weights to return
+
+    Returns
+    =======
+
+    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
+             The points `x_i` and weights `w_i` are returned as ``(x, w)``
+             tuple of lists.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.quadrature import gauss_lobatto
+    >>> x, w = gauss_lobatto(3, 5)
+    >>> x
+    [-1, 0, 1]
+    >>> w
+    [0.33333, 1.3333, 0.33333]
+    >>> x, w = gauss_lobatto(4, 5)
+    >>> x
+    [-1, -0.44721, 0.44721, 1]
+    >>> w
+    [0.16667, 0.83333, 0.83333, 0.16667]
+
+    See Also
+    ========
+
+    gauss_legendre,gauss_laguerre, gauss_gen_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gaussian_quadrature#Gauss.E2.80.93Lobatto_rules
+    .. [2] https://web.archive.org/web/20200118141346/http://people.math.sfu.ca/~cbm/aands/page_888.htm
+    """
+    x = Dummy("x")
+    p = legendre_poly(n-1, x, polys=True)
+    pd = p.diff(x)
+    xi = []
+    w = []
+    for r in pd.real_roots():
+        if isinstance(r, RootOf):
+            r = r.eval_rational(S.One/10**(n_digits+2))
+        xi.append(r.n(n_digits))
+        w.append((2/(n*(n-1) * p.subs(x, r)**2)).n(n_digits))
+
+    xi.insert(0, -1)
+    xi.append(1)
+    w.insert(0, (S(2)/(n*(n-1))).n(n_digits))
+    w.append((S(2)/(n*(n-1))).n(n_digits))
+    return xi, w
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/rationaltools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/rationaltools.py
new file mode 100644
index 0000000000000000000000000000000000000000..e95ff5da2e9d1be6f07d8fe6e9c572f692e92efb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/rationaltools.py
@@ -0,0 +1,445 @@
+"""This module implements tools for integrating rational functions. """
+
+from sympy.core.function import Lambda
+from sympy.core.numbers import I
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.trigonometric import atan
+from sympy.polys.polyerrors import DomainError
+from sympy.polys.polyroots import roots
+from sympy.polys.polytools import cancel
+from sympy.polys.rootoftools import RootSum
+from sympy.polys import Poly, resultant, ZZ
+
+
+def ratint(f, x, **flags):
+    """
+    Performs indefinite integration of rational functions.
+
+    Explanation
+    ===========
+
+    Given a field :math:`K` and a rational function :math:`f = p/q`,
+    where :math:`p` and :math:`q` are polynomials in :math:`K[x]`,
+    returns a function :math:`g` such that :math:`f = g'`.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.rationaltools import ratint
+    >>> from sympy.abc import x
+
+    >>> ratint(36/(x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2), x)
+    (12*x + 6)/(x**2 - 1) + 4*log(x - 2) - 4*log(x + 1)
+
+    References
+    ==========
+
+    .. [1] M. Bronstein, Symbolic Integration I: Transcendental
+       Functions, Second Edition, Springer-Verlag, 2005, pp. 35-70
+
+    See Also
+    ========
+
+    sympy.integrals.integrals.Integral.doit
+    sympy.integrals.rationaltools.ratint_logpart
+    sympy.integrals.rationaltools.ratint_ratpart
+
+    """
+    if isinstance(f, tuple):
+        p, q = f
+    else:
+        p, q = f.as_numer_denom()
+
+    p, q = Poly(p, x, composite=False, field=True), Poly(q, x, composite=False, field=True)
+
+    coeff, p, q = p.cancel(q)
+    poly, p = p.div(q)
+
+    result = poly.integrate(x).as_expr()
+
+    if p.is_zero:
+        return coeff*result
+
+    g, h = ratint_ratpart(p, q, x)
+
+    P, Q = h.as_numer_denom()
+
+    P = Poly(P, x)
+    Q = Poly(Q, x)
+
+    q, r = P.div(Q)
+
+    result += g + q.integrate(x).as_expr()
+
+    if not r.is_zero:
+        symbol = flags.get('symbol', 't')
+
+        if not isinstance(symbol, Symbol):
+            t = Dummy(symbol)
+        else:
+            t = symbol.as_dummy()
+
+        L = ratint_logpart(r, Q, x, t)
+
+        real = flags.get('real')
+
+        if real is None:
+            if isinstance(f, tuple):
+                p, q = f
+                atoms = p.atoms() | q.atoms()
+            else:
+                atoms = f.atoms()
+
+            for elt in atoms - {x}:
+                if not elt.is_extended_real:
+                    real = False
+                    break
+            else:
+                real = True
+
+        eps = S.Zero
+
+        if not real:
+            for h, q in L:
+                _, h = h.primitive()
+                eps += RootSum(
+                    q, Lambda(t, t*log(h.as_expr())), quadratic=True)
+        else:
+            for h, q in L:
+                _, h = h.primitive()
+                R = log_to_real(h, q, x, t)
+
+                if R is not None:
+                    eps += R
+                else:
+                    eps += RootSum(
+                        q, Lambda(t, t*log(h.as_expr())), quadratic=True)
+
+        result += eps
+
+    return coeff*result
+
+
+def ratint_ratpart(f, g, x):
+    """
+    Horowitz-Ostrogradsky algorithm.
+
+    Explanation
+    ===========
+
+    Given a field K and polynomials f and g in K[x], such that f and g
+    are coprime and deg(f) < deg(g), returns fractions A and B in K(x),
+    such that f/g = A' + B and B has square-free denominator.
+
+    Examples
+    ========
+
+        >>> from sympy.integrals.rationaltools import ratint_ratpart
+        >>> from sympy.abc import x, y
+        >>> from sympy import Poly
+        >>> ratint_ratpart(Poly(1, x, domain='ZZ'),
+        ... Poly(x + 1, x, domain='ZZ'), x)
+        (0, 1/(x + 1))
+        >>> ratint_ratpart(Poly(1, x, domain='EX'),
+        ... Poly(x**2 + y**2, x, domain='EX'), x)
+        (0, 1/(x**2 + y**2))
+        >>> ratint_ratpart(Poly(36, x, domain='ZZ'),
+        ... Poly(x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2, x, domain='ZZ'), x)
+        ((12*x + 6)/(x**2 - 1), 12/(x**2 - x - 2))
+
+    See Also
+    ========
+
+    ratint, ratint_logpart
+    """
+    from sympy.solvers.solvers import solve
+
+    f = Poly(f, x)
+    g = Poly(g, x)
+
+    u, v, _ = g.cofactors(g.diff())
+
+    n = u.degree()
+    m = v.degree()
+
+    A_coeffs = [ Dummy('a' + str(n - i)) for i in range(0, n) ]
+    B_coeffs = [ Dummy('b' + str(m - i)) for i in range(0, m) ]
+
+    C_coeffs = A_coeffs + B_coeffs
+
+    A = Poly(A_coeffs, x, domain=ZZ[C_coeffs])
+    B = Poly(B_coeffs, x, domain=ZZ[C_coeffs])
+
+    H = f - A.diff()*v + A*(u.diff()*v).quo(u) - B*u
+
+    result = solve(H.coeffs(), C_coeffs)
+
+    A = A.as_expr().subs(result)
+    B = B.as_expr().subs(result)
+
+    rat_part = cancel(A/u.as_expr(), x)
+    log_part = cancel(B/v.as_expr(), x)
+
+    return rat_part, log_part
+
+
+def ratint_logpart(f, g, x, t=None):
+    r"""
+    Lazard-Rioboo-Trager algorithm.
+
+    Explanation
+    ===========
+
+    Given a field K and polynomials f and g in K[x], such that f and g
+    are coprime, deg(f) < deg(g) and g is square-free, returns a list
+    of tuples (s_i, q_i) of polynomials, for i = 1..n, such that s_i
+    in K[t, x] and q_i in K[t], and::
+
+                           ___    ___
+                 d  f   d  \  `   \  `
+                 -- - = --  )      )   a log(s_i(a, x))
+                 dx g   dx /__,   /__,
+                          i=1..n a | q_i(a) = 0
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.rationaltools import ratint_logpart
+    >>> from sympy.abc import x
+    >>> from sympy import Poly
+    >>> ratint_logpart(Poly(1, x, domain='ZZ'),
+    ... Poly(x**2 + x + 1, x, domain='ZZ'), x)
+    [(Poly(x + 3*_t/2 + 1/2, x, domain='QQ[_t]'),
+    ...Poly(3*_t**2 + 1, _t, domain='ZZ'))]
+    >>> ratint_logpart(Poly(12, x, domain='ZZ'),
+    ... Poly(x**2 - x - 2, x, domain='ZZ'), x)
+    [(Poly(x - 3*_t/8 - 1/2, x, domain='QQ[_t]'),
+    ...Poly(-_t**2 + 16, _t, domain='ZZ'))]
+
+    See Also
+    ========
+
+    ratint, ratint_ratpart
+    """
+    f, g = Poly(f, x), Poly(g, x)
+
+    t = t or Dummy('t')
+    a, b = g, f - g.diff()*Poly(t, x)
+
+    res, R = resultant(a, b, includePRS=True)
+    res = Poly(res, t, composite=False)
+
+    assert res, "BUG: resultant(%s, %s) cannot be zero" % (a, b)
+
+    R_map, H = {}, []
+
+    for r in R:
+        R_map[r.degree()] = r
+
+    def _include_sign(c, sqf):
+        if c.is_extended_real and (c < 0) == True:
+            h, k = sqf[0]
+            c_poly = c.as_poly(h.gens)
+            sqf[0] = h*c_poly, k
+
+    C, res_sqf = res.sqf_list()
+    _include_sign(C, res_sqf)
+
+    for q, i in res_sqf:
+        _, q = q.primitive()
+
+        if g.degree() == i:
+            H.append((g, q))
+        else:
+            h = R_map[i]
+            h_lc = Poly(h.LC(), t, field=True)
+
+            c, h_lc_sqf = h_lc.sqf_list(all=True)
+            _include_sign(c, h_lc_sqf)
+
+            for a, j in h_lc_sqf:
+                h = h.quo(Poly(a.gcd(q)**j, x))
+
+            inv, coeffs = h_lc.invert(q), [S.One]
+
+            for coeff in h.coeffs()[1:]:
+                coeff = coeff.as_poly(inv.gens)
+                T = (inv*coeff).rem(q)
+                coeffs.append(T.as_expr())
+
+            h = Poly(dict(list(zip(h.monoms(), coeffs))), x)
+
+            H.append((h, q))
+
+    return H
+
+
+def log_to_atan(f, g):
+    """
+    Convert complex logarithms to real arctangents.
+
+    Explanation
+    ===========
+
+    Given a real field K and polynomials f and g in K[x], with g != 0,
+    returns a sum h of arctangents of polynomials in K[x], such that:
+
+                   dh   d         f + I g
+                   -- = -- I log( ------- )
+                   dx   dx        f - I g
+
+    Examples
+    ========
+
+        >>> from sympy.integrals.rationaltools import log_to_atan
+        >>> from sympy.abc import x
+        >>> from sympy import Poly, sqrt, S
+        >>> log_to_atan(Poly(x, x, domain='ZZ'), Poly(1, x, domain='ZZ'))
+        2*atan(x)
+        >>> log_to_atan(Poly(x + S(1)/2, x, domain='QQ'),
+        ... Poly(sqrt(3)/2, x, domain='EX'))
+        2*atan(2*sqrt(3)*x/3 + sqrt(3)/3)
+
+    See Also
+    ========
+
+    log_to_real
+    """
+    if f.degree() < g.degree():
+        f, g = -g, f
+
+    f = f.to_field()
+    g = g.to_field()
+
+    p, q = f.div(g)
+
+    if q.is_zero:
+        return 2*atan(p.as_expr())
+    else:
+        s, t, h = g.gcdex(-f)
+        u = (f*s + g*t).quo(h)
+        A = 2*atan(u.as_expr())
+
+        return A + log_to_atan(s, t)
+
+
+def _get_real_roots(f, x):
+    """get real roots of f if possible"""
+    rs = roots(f, filter='R')
+
+    try:
+        num_roots = f.count_roots()
+    except DomainError:
+        return rs
+    else:
+        if len(rs) == num_roots:
+            return rs
+        else:
+            return None
+
+
+def log_to_real(h, q, x, t):
+    r"""
+    Convert complex logarithms to real functions.
+
+    Explanation
+    ===========
+
+    Given real field K and polynomials h in K[t,x] and q in K[t],
+    returns real function f such that:
+                          ___
+                  df   d  \  `
+                  -- = --  )  a log(h(a, x))
+                  dx   dx /__,
+                         a | q(a) = 0
+
+    Examples
+    ========
+
+        >>> from sympy.integrals.rationaltools import log_to_real
+        >>> from sympy.abc import x, y
+        >>> from sympy import Poly, S
+        >>> log_to_real(Poly(x + 3*y/2 + S(1)/2, x, domain='QQ[y]'),
+        ... Poly(3*y**2 + 1, y, domain='ZZ'), x, y)
+        2*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3
+        >>> log_to_real(Poly(x**2 - 1, x, domain='ZZ'),
+        ... Poly(-2*y + 1, y, domain='ZZ'), x, y)
+        log(x**2 - 1)/2
+
+    See Also
+    ========
+
+    log_to_atan
+    """
+    from sympy.simplify.radsimp import collect
+    u, v = symbols('u,v', cls=Dummy)
+
+    H = h.as_expr().xreplace({t: u + I*v}).expand()
+    Q = q.as_expr().xreplace({t: u + I*v}).expand()
+
+    H_map = collect(H, I, evaluate=False)
+    Q_map = collect(Q, I, evaluate=False)
+
+    a, b = H_map.get(S.One, S.Zero), H_map.get(I, S.Zero)
+    c, d = Q_map.get(S.One, S.Zero), Q_map.get(I, S.Zero)
+
+    R = Poly(resultant(c, d, v), u)
+
+    R_u = _get_real_roots(R, u)
+
+    if R_u is None:
+        return None
+
+    result = S.Zero
+
+    for r_u in R_u.keys():
+        C = Poly(c.xreplace({u: r_u}), v)
+        if not C:
+            # t was split into real and imaginary parts
+            # and denom Q(u, v) = c + I*d. We just found
+            # that c(r_u) is 0 so the roots are in d
+            C = Poly(d.xreplace({u: r_u}), v)
+            # we were going to reject roots from C that
+            # did not set d to zero, but since we are now
+            # using C = d and c is already 0, there is
+            # nothing to check
+            d = S.Zero
+
+        R_v = _get_real_roots(C, v)
+
+        if R_v is None:
+            return None
+
+        R_v_paired = [] # take one from each pair of conjugate roots
+        for r_v in R_v:
+            if r_v not in R_v_paired and -r_v not in R_v_paired:
+                if r_v.is_negative or r_v.could_extract_minus_sign():
+                    R_v_paired.append(-r_v)
+                elif not r_v.is_zero:
+                    R_v_paired.append(r_v)
+
+        for r_v in R_v_paired:
+
+            D = d.xreplace({u: r_u, v: r_v})
+
+            if D.evalf(chop=True) != 0:
+                continue
+
+            A = Poly(a.xreplace({u: r_u, v: r_v}), x)
+            B = Poly(b.xreplace({u: r_u, v: r_v}), x)
+
+            AB = (A**2 + B**2).as_expr()
+
+            result += r_u*log(AB) + r_v*log_to_atan(A, B)
+
+    R_q = _get_real_roots(q, t)
+
+    if R_q is None:
+        return None
+
+    for r in R_q.keys():
+        result += r*log(h.as_expr().subs(t, r))
+
+    return result
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/rde.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/rde.py
new file mode 100644
index 0000000000000000000000000000000000000000..9fb14a1d14b743b1e0885bf25a0d4b409e8a610d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/rde.py
@@ -0,0 +1,800 @@
+"""
+Algorithms for solving the Risch differential equation.
+
+Given a differential field K of characteristic 0 that is a simple
+monomial extension of a base field k and f, g in K, the Risch
+Differential Equation problem is to decide if there exist y in K such
+that Dy + f*y == g and to find one if there are some.  If t is a
+monomial over k and the coefficients of f and g are in k(t), then y is
+in k(t), and the outline of the algorithm here is given as:
+
+1. Compute the normal part n of the denominator of y.  The problem is
+then reduced to finding y' in k, where y == y'/n.
+2. Compute the special part s of the denominator of y.   The problem is
+then reduced to finding y'' in k[t], where y == y''/(n*s)
+3. Bound the degree of y''.
+4. Reduce the equation Dy + f*y == g to a similar equation with f, g in
+k[t].
+5. Find the solutions in k[t] of bounded degree of the reduced equation.
+
+See Chapter 6 of "Symbolic Integration I: Transcendental Functions" by
+Manuel Bronstein.  See also the docstring of risch.py.
+"""
+
+from operator import mul
+from functools import reduce
+
+from sympy.core import oo
+from sympy.core.symbol import Dummy
+
+from sympy.polys import Poly, gcd, ZZ, cancel
+
+from sympy.functions.elementary.complexes import (im, re)
+from sympy.functions.elementary.miscellaneous import sqrt
+
+from sympy.integrals.risch import (gcdex_diophantine, frac_in, derivation,
+    splitfactor, NonElementaryIntegralException, DecrementLevel, recognize_log_derivative)
+
+# TODO: Add messages to NonElementaryIntegralException errors
+
+
+def order_at(a, p, t):
+    """
+    Computes the order of a at p, with respect to t.
+
+    Explanation
+    ===========
+
+    For a, p in k[t], the order of a at p is defined as nu_p(a) = max({n
+    in Z+ such that p**n|a}), where a != 0.  If a == 0, nu_p(a) = +oo.
+
+    To compute the order at a rational function, a/b, use the fact that
+    nu_p(a/b) == nu_p(a) - nu_p(b).
+    """
+    if a.is_zero:
+        return oo
+    if p == Poly(t, t):
+        return a.as_poly(t).ET()[0][0]
+
+    # Uses binary search for calculating the power. power_list collects the tuples
+    # (p^k,k) where each k is some power of 2. After deciding the largest k
+    # such that k is power of 2 and p^k|a the loop iteratively calculates
+    # the actual power.
+    power_list = []
+    p1 = p
+    r = a.rem(p1)
+    tracks_power = 1
+    while r.is_zero:
+        power_list.append((p1,tracks_power))
+        p1 = p1*p1
+        tracks_power *= 2
+        r = a.rem(p1)
+    n = 0
+    product = Poly(1, t)
+    while len(power_list) != 0:
+        final = power_list.pop()
+        productf = product*final[0]
+        r = a.rem(productf)
+        if r.is_zero:
+            n += final[1]
+            product = productf
+    return n
+
+
+def order_at_oo(a, d, t):
+    """
+    Computes the order of a/d at oo (infinity), with respect to t.
+
+    For f in k(t), the order or f at oo is defined as deg(d) - deg(a), where
+    f == a/d.
+    """
+    if a.is_zero:
+        return oo
+    return d.degree(t) - a.degree(t)
+
+
+def weak_normalizer(a, d, DE, z=None):
+    """
+    Weak normalization.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and f == a/d in k(t), return q in k[t]
+    such that f - Dq/q is weakly normalized with respect to t.
+
+    f in k(t) is said to be "weakly normalized" with respect to t if
+    residue_p(f) is not a positive integer for any normal irreducible p
+    in k[t] such that f is in R_p (Definition 6.1.1).  If f has an
+    elementary integral, this is equivalent to no logarithm of
+    integral(f) whose argument depends on t has a positive integer
+    coefficient, where the arguments of the logarithms not in k(t) are
+    in k[t].
+
+    Returns (q, f - Dq/q)
+    """
+    z = z or Dummy('z')
+    dn, ds = splitfactor(d, DE)
+
+    # Compute d1, where dn == d1*d2**2*...*dn**n is a square-free
+    # factorization of d.
+    g = gcd(dn, dn.diff(DE.t))
+    d_sqf_part = dn.quo(g)
+    d1 = d_sqf_part.quo(gcd(d_sqf_part, g))
+
+    a1, b = gcdex_diophantine(d.quo(d1).as_poly(DE.t), d1.as_poly(DE.t),
+        a.as_poly(DE.t))
+    r = (a - Poly(z, DE.t)*derivation(d1, DE)).as_poly(DE.t).resultant(
+        d1.as_poly(DE.t))
+    r = Poly(r, z)
+
+    if not r.expr.has(z):
+        return (Poly(1, DE.t), (a, d))
+
+    N = [i for i in r.real_roots() if i in ZZ and i > 0]
+
+    q = reduce(mul, [gcd(a - Poly(n, DE.t)*derivation(d1, DE), d1) for n in N],
+        Poly(1, DE.t))
+
+    dq = derivation(q, DE)
+    sn = q*a - d*dq
+    sd = q*d
+    sn, sd = sn.cancel(sd, include=True)
+
+    return (q, (sn, sd))
+
+
+def normal_denom(fa, fd, ga, gd, DE):
+    """
+    Normal part of the denominator.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and f, g in k(t) with f weakly
+    normalized with respect to t, either raise NonElementaryIntegralException,
+    in which case the equation Dy + f*y == g has no solution in k(t), or the
+    quadruplet (a, b, c, h) such that a, h in k[t], b, c in k, and for any
+    solution y in k(t) of Dy + f*y == g, q = y*h in k satisfies
+    a*Dq + b*q == c.
+
+    This constitutes step 1 in the outline given in the rde.py docstring.
+    """
+    dn, ds = splitfactor(fd, DE)
+    en, es = splitfactor(gd, DE)
+
+    p = dn.gcd(en)
+    h = en.gcd(en.diff(DE.t)).quo(p.gcd(p.diff(DE.t)))
+
+    a = dn*h
+    c = a*h
+    if c.div(en)[1]:
+        # en does not divide dn*h**2
+        raise NonElementaryIntegralException
+    ca = c*ga
+    ca, cd = ca.cancel(gd, include=True)
+
+    ba = a*fa - dn*derivation(h, DE)*fd
+    ba, bd = ba.cancel(fd, include=True)
+
+    # (dn*h, dn*h*f - dn*Dh, dn*h**2*g, h)
+    return (a, (ba, bd), (ca, cd), h)
+
+
+def special_denom(a, ba, bd, ca, cd, DE, case='auto'):
+    """
+    Special part of the denominator.
+
+    Explanation
+    ===========
+
+    case is one of {'exp', 'tan', 'primitive'} for the hyperexponential,
+    hypertangent, and primitive cases, respectively.  For the
+    hyperexponential (resp. hypertangent) case, given a derivation D on
+    k[t] and a in k[t], b, c, in k with Dt/t in k (resp. Dt/(t**2 + 1) in
+    k, sqrt(-1) not in k), a != 0, and gcd(a, t) == 1 (resp.
+    gcd(a, t**2 + 1) == 1), return the quadruplet (A, B, C, 1/h) such that
+    A, B, C, h in k[t] and for any solution q in k of a*Dq + b*q == c,
+    r = qh in k[t] satisfies A*Dr + B*r == C.
+
+    For ``case == 'primitive'``, k == k[t], so it returns (a, b, c, 1) in
+    this case.
+
+    This constitutes step 2 of the outline given in the rde.py docstring.
+    """
+    # TODO: finish writing this and write tests
+
+    if case == 'auto':
+        case = DE.case
+
+    if case == 'exp':
+        p = Poly(DE.t, DE.t)
+    elif case == 'tan':
+        p = Poly(DE.t**2 + 1, DE.t)
+    elif case in ('primitive', 'base'):
+        B = ba.to_field().quo(bd)
+        C = ca.to_field().quo(cd)
+        return (a, B, C, Poly(1, DE.t))
+    else:
+        raise ValueError("case must be one of {'exp', 'tan', 'primitive', "
+            "'base'}, not %s." % case)
+
+    nb = order_at(ba, p, DE.t) - order_at(bd, p, DE.t)
+    nc = order_at(ca, p, DE.t) - order_at(cd, p, DE.t)
+
+    n = min(0, nc - min(0, nb))
+    if not nb:
+        # Possible cancellation.
+        from .prde import parametric_log_deriv
+        if case == 'exp':
+            dcoeff = DE.d.quo(Poly(DE.t, DE.t))
+            with DecrementLevel(DE):  # We are guaranteed to not have problems,
+                                      # because case != 'base'.
+                alphaa, alphad = frac_in(-ba.eval(0)/bd.eval(0)/a.eval(0), DE.t)
+                etaa, etad = frac_in(dcoeff, DE.t)
+                A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE)
+                if A is not None:
+                    Q, m, z = A
+                    if Q == 1:
+                        n = min(n, m)
+
+        elif case == 'tan':
+            dcoeff = DE.d.quo(Poly(DE.t**2+1, DE.t))
+            with DecrementLevel(DE):  # We are guaranteed to not have problems,
+                                      # because case != 'base'.
+                alphaa, alphad = frac_in(im(-ba.eval(sqrt(-1))/bd.eval(sqrt(-1))/a.eval(sqrt(-1))), DE.t)
+                betaa, betad = frac_in(re(-ba.eval(sqrt(-1))/bd.eval(sqrt(-1))/a.eval(sqrt(-1))), DE.t)
+                etaa, etad = frac_in(dcoeff, DE.t)
+
+                if recognize_log_derivative(Poly(2, DE.t)*betaa, betad, DE):
+                    A = parametric_log_deriv(alphaa*Poly(sqrt(-1), DE.t)*betad+alphad*betaa, alphad*betad, etaa, etad, DE)
+                    if A is not None:
+                        Q, m, z = A
+                        if Q == 1:
+                            n = min(n, m)
+    N = max(0, -nb, n - nc)
+    pN = p**N
+    pn = p**-n
+
+    A = a*pN
+    B = ba*pN.quo(bd) + Poly(n, DE.t)*a*derivation(p, DE).quo(p)*pN
+    C = (ca*pN*pn).quo(cd)
+    h = pn
+
+    # (a*p**N, (b + n*a*Dp/p)*p**N, c*p**(N - n), p**-n)
+    return (A, B, C, h)
+
+
+def bound_degree(a, b, cQ, DE, case='auto', parametric=False):
+    """
+    Bound on polynomial solutions.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and ``a``, ``b``, ``c`` in k[t] with ``a != 0``, return
+    n in ZZ such that deg(q) <= n for any solution q in k[t] of
+    a*Dq + b*q == c, when parametric=False, or deg(q) <= n for any solution
+    c1, ..., cm in Const(k) and q in k[t] of a*Dq + b*q == Sum(ci*gi, (i, 1, m))
+    when parametric=True.
+
+    For ``parametric=False``, ``cQ`` is ``c``, a ``Poly``; for ``parametric=True``, ``cQ`` is Q ==
+    [q1, ..., qm], a list of Polys.
+
+    This constitutes step 3 of the outline given in the rde.py docstring.
+    """
+    # TODO: finish writing this and write tests
+
+    if case == 'auto':
+        case = DE.case
+
+    da = a.degree(DE.t)
+    db = b.degree(DE.t)
+
+    # The parametric and regular cases are identical, except for this part
+    if parametric:
+        dc = max(i.degree(DE.t) for i in cQ)
+    else:
+        dc = cQ.degree(DE.t)
+
+    alpha = cancel(-b.as_poly(DE.t).LC().as_expr()/
+        a.as_poly(DE.t).LC().as_expr())
+
+    if case == 'base':
+        n = max(0, dc - max(db, da - 1))
+        if db == da - 1 and alpha.is_Integer:
+            n = max(0, alpha, dc - db)
+
+    elif case == 'primitive':
+        if db > da:
+            n = max(0, dc - db)
+        else:
+            n = max(0, dc - da + 1)
+
+        etaa, etad = frac_in(DE.d, DE.T[DE.level - 1])
+
+        t1 = DE.t
+        with DecrementLevel(DE):
+            alphaa, alphad = frac_in(alpha, DE.t)
+            if db == da - 1:
+                from .prde import limited_integrate
+                # if alpha == m*Dt + Dz for z in k and m in ZZ:
+                try:
+                    (za, zd), m = limited_integrate(alphaa, alphad, [(etaa, etad)],
+                        DE)
+                except NonElementaryIntegralException:
+                    pass
+                else:
+                    if len(m) != 1:
+                        raise ValueError("Length of m should be 1")
+                    n = max(n, m[0])
+
+            elif db == da:
+                # if alpha == Dz/z for z in k*:
+                    # beta = -lc(a*Dz + b*z)/(z*lc(a))
+                    # if beta == m*Dt + Dw for w in k and m in ZZ:
+                        # n = max(n, m)
+                from .prde import is_log_deriv_k_t_radical_in_field
+                A = is_log_deriv_k_t_radical_in_field(alphaa, alphad, DE)
+                if A is not None:
+                    aa, z = A
+                    if aa == 1:
+                        beta = -(a*derivation(z, DE).as_poly(t1) +
+                            b*z.as_poly(t1)).LC()/(z.as_expr()*a.LC())
+                        betaa, betad = frac_in(beta, DE.t)
+                        from .prde import limited_integrate
+                        try:
+                            (za, zd), m = limited_integrate(betaa, betad,
+                                [(etaa, etad)], DE)
+                        except NonElementaryIntegralException:
+                            pass
+                        else:
+                            if len(m) != 1:
+                                raise ValueError("Length of m should be 1")
+                            n = max(n, m[0].as_expr())
+
+    elif case == 'exp':
+        from .prde import parametric_log_deriv
+
+        n = max(0, dc - max(db, da))
+        if da == db:
+            etaa, etad = frac_in(DE.d.quo(Poly(DE.t, DE.t)), DE.T[DE.level - 1])
+            with DecrementLevel(DE):
+                alphaa, alphad = frac_in(alpha, DE.t)
+                A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE)
+                if A is not None:
+                    # if alpha == m*Dt/t + Dz/z for z in k* and m in ZZ:
+                        # n = max(n, m)
+                    a, m, z = A
+                    if a == 1:
+                        n = max(n, m)
+
+    elif case in ('tan', 'other_nonlinear'):
+        delta = DE.d.degree(DE.t)
+        lam = DE.d.LC()
+        alpha = cancel(alpha/lam)
+        n = max(0, dc - max(da + delta - 1, db))
+        if db == da + delta - 1 and alpha.is_Integer:
+            n = max(0, alpha, dc - db)
+
+    else:
+        raise ValueError("case must be one of {'exp', 'tan', 'primitive', "
+            "'other_nonlinear', 'base'}, not %s." % case)
+
+    return n
+
+
+def spde(a, b, c, n, DE):
+    """
+    Rothstein's Special Polynomial Differential Equation algorithm.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], an integer n and ``a``,``b``,``c`` in k[t] with
+    ``a != 0``, either raise NonElementaryIntegralException, in which case the
+    equation a*Dq + b*q == c has no solution of degree at most ``n`` in
+    k[t], or return the tuple (B, C, m, alpha, beta) such that B, C,
+    alpha, beta in k[t], m in ZZ, and any solution q in k[t] of degree
+    at most n of a*Dq + b*q == c must be of the form
+    q == alpha*h + beta, where h in k[t], deg(h) <= m, and Dh + B*h == C.
+
+    This constitutes step 4 of the outline given in the rde.py docstring.
+    """
+    zero = Poly(0, DE.t)
+
+    alpha = Poly(1, DE.t)
+    beta = Poly(0, DE.t)
+
+    while True:
+        if c.is_zero:
+            return (zero, zero, 0, zero, beta)  # -1 is more to the point
+        if (n < 0) is True:
+            raise NonElementaryIntegralException
+
+        g = a.gcd(b)
+        if not c.rem(g).is_zero:  # g does not divide c
+            raise NonElementaryIntegralException
+
+        a, b, c = a.quo(g), b.quo(g), c.quo(g)
+
+        if a.degree(DE.t) == 0:
+            b = b.to_field().quo(a)
+            c = c.to_field().quo(a)
+            return (b, c, n, alpha, beta)
+
+        r, z = gcdex_diophantine(b, a, c)
+        b += derivation(a, DE)
+        c = z - derivation(r, DE)
+        n -= a.degree(DE.t)
+
+        beta += alpha * r
+        alpha *= a
+
+def no_cancel_b_large(b, c, n, DE):
+    """
+    Poly Risch Differential Equation - No cancellation: deg(b) large enough.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], ``n`` either an integer or +oo, and ``b``,``c``
+    in k[t] with ``b != 0`` and either D == d/dt or
+    deg(b) > max(0, deg(D) - 1), either raise NonElementaryIntegralException, in
+    which case the equation ``Dq + b*q == c`` has no solution of degree at
+    most n in k[t], or a solution q in k[t] of this equation with
+    ``deg(q) < n``.
+    """
+    q = Poly(0, DE.t)
+
+    while not c.is_zero:
+        m = c.degree(DE.t) - b.degree(DE.t)
+        if not 0 <= m <= n:  # n < 0 or m < 0 or m > n
+            raise NonElementaryIntegralException
+
+        p = Poly(c.as_poly(DE.t).LC()/b.as_poly(DE.t).LC()*DE.t**m, DE.t,
+            expand=False)
+        q = q + p
+        n = m - 1
+        c = c - derivation(p, DE) - b*p
+
+    return q
+
+
+def no_cancel_b_small(b, c, n, DE):
+    """
+    Poly Risch Differential Equation - No cancellation: deg(b) small enough.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], ``n`` either an integer or +oo, and ``b``,``c``
+    in k[t] with deg(b) < deg(D) - 1 and either D == d/dt or
+    deg(D) >= 2, either raise NonElementaryIntegralException, in which case the
+    equation Dq + b*q == c has no solution of degree at most n in k[t],
+    or a solution q in k[t] of this equation with deg(q) <= n, or the
+    tuple (h, b0, c0) such that h in k[t], b0, c0, in k, and for any
+    solution q in k[t] of degree at most n of Dq + bq == c, y == q - h
+    is a solution in k of Dy + b0*y == c0.
+    """
+    q = Poly(0, DE.t)
+
+    while not c.is_zero:
+        if n == 0:
+            m = 0
+        else:
+            m = c.degree(DE.t) - DE.d.degree(DE.t) + 1
+
+        if not 0 <= m <= n:  # n < 0 or m < 0 or m > n
+            raise NonElementaryIntegralException
+
+        if m > 0:
+            p = Poly(c.as_poly(DE.t).LC()/(m*DE.d.as_poly(DE.t).LC())*DE.t**m,
+                DE.t, expand=False)
+        else:
+            if b.degree(DE.t) != c.degree(DE.t):
+                raise NonElementaryIntegralException
+            if b.degree(DE.t) == 0:
+                return (q, b.as_poly(DE.T[DE.level - 1]),
+                    c.as_poly(DE.T[DE.level - 1]))
+            p = Poly(c.as_poly(DE.t).LC()/b.as_poly(DE.t).LC(), DE.t,
+                expand=False)
+
+        q = q + p
+        n = m - 1
+        c = c - derivation(p, DE) - b*p
+
+    return q
+
+
+# TODO: better name for this function
+def no_cancel_equal(b, c, n, DE):
+    """
+    Poly Risch Differential Equation - No cancellation: deg(b) == deg(D) - 1
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] with deg(D) >= 2, n either an integer
+    or +oo, and b, c in k[t] with deg(b) == deg(D) - 1, either raise
+    NonElementaryIntegralException, in which case the equation Dq + b*q == c has
+    no solution of degree at most n in k[t], or a solution q in k[t] of
+    this equation with deg(q) <= n, or the tuple (h, m, C) such that h
+    in k[t], m in ZZ, and C in k[t], and for any solution q in k[t] of
+    degree at most n of Dq + b*q == c, y == q - h is a solution in k[t]
+    of degree at most m of Dy + b*y == C.
+    """
+    q = Poly(0, DE.t)
+    lc = cancel(-b.as_poly(DE.t).LC()/DE.d.as_poly(DE.t).LC())
+    if lc.is_Integer and lc.is_positive:
+        M = lc
+    else:
+        M = -1
+
+    while not c.is_zero:
+        m = max(M, c.degree(DE.t) - DE.d.degree(DE.t) + 1)
+
+        if not 0 <= m <= n:  # n < 0 or m < 0 or m > n
+            raise NonElementaryIntegralException
+
+        u = cancel(m*DE.d.as_poly(DE.t).LC() + b.as_poly(DE.t).LC())
+        if u.is_zero:
+            return (q, m, c)
+        if m > 0:
+            p = Poly(c.as_poly(DE.t).LC()/u*DE.t**m, DE.t, expand=False)
+        else:
+            if c.degree(DE.t) != DE.d.degree(DE.t) - 1:
+                raise NonElementaryIntegralException
+            else:
+                p = c.as_poly(DE.t).LC()/b.as_poly(DE.t).LC()
+
+        q = q + p
+        n = m - 1
+        c = c - derivation(p, DE) - b*p
+
+    return q
+
+
+def cancel_primitive(b, c, n, DE):
+    """
+    Poly Risch Differential Equation - Cancellation: Primitive case.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], n either an integer or +oo, ``b`` in k, and
+    ``c`` in k[t] with Dt in k and ``b != 0``, either raise
+    NonElementaryIntegralException, in which case the equation Dq + b*q == c
+    has no solution of degree at most n in k[t], or a solution q in k[t] of
+    this equation with deg(q) <= n.
+    """
+    # Delayed imports
+    from .prde import is_log_deriv_k_t_radical_in_field
+    with DecrementLevel(DE):
+        ba, bd = frac_in(b, DE.t)
+        A = is_log_deriv_k_t_radical_in_field(ba, bd, DE)
+        if A is not None:
+            n, z = A
+            if n == 1:  # b == Dz/z
+                raise NotImplementedError("is_deriv_in_field() is required to "
+                    " solve this problem.")
+                # if z*c == Dp for p in k[t] and deg(p) <= n:
+                #     return p/z
+                # else:
+                #     raise NonElementaryIntegralException
+
+    if c.is_zero:
+        return c  # return 0
+
+    if n < c.degree(DE.t):
+        raise NonElementaryIntegralException
+
+    q = Poly(0, DE.t)
+    while not c.is_zero:
+        m = c.degree(DE.t)
+        if n < m:
+            raise NonElementaryIntegralException
+        with DecrementLevel(DE):
+            a2a, a2d = frac_in(c.LC(), DE.t)
+            sa, sd = rischDE(ba, bd, a2a, a2d, DE)
+        stm = Poly(sa.as_expr()/sd.as_expr()*DE.t**m, DE.t, expand=False)
+        q += stm
+        n = m - 1
+        c -= b*stm + derivation(stm, DE)
+
+    return q
+
+
+def cancel_exp(b, c, n, DE):
+    """
+    Poly Risch Differential Equation - Cancellation: Hyperexponential case.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t], n either an integer or +oo, ``b`` in k, and
+    ``c`` in k[t] with Dt/t in k and ``b != 0``, either raise
+    NonElementaryIntegralException, in which case the equation Dq + b*q == c
+    has no solution of degree at most n in k[t], or a solution q in k[t] of
+    this equation with deg(q) <= n.
+    """
+    from .prde import parametric_log_deriv
+    eta = DE.d.quo(Poly(DE.t, DE.t)).as_expr()
+
+    with DecrementLevel(DE):
+        etaa, etad = frac_in(eta, DE.t)
+        ba, bd = frac_in(b, DE.t)
+        A = parametric_log_deriv(ba, bd, etaa, etad, DE)
+        if A is not None:
+            a, m, z = A
+            if a == 1:
+                raise NotImplementedError("is_deriv_in_field() is required to "
+                    "solve this problem.")
+                # if c*z*t**m == Dp for p in k and q = p/(z*t**m) in k[t] and
+                # deg(q) <= n:
+                #     return q
+                # else:
+                #     raise NonElementaryIntegralException
+
+    if c.is_zero:
+        return c  # return 0
+
+    if n < c.degree(DE.t):
+        raise NonElementaryIntegralException
+
+    q = Poly(0, DE.t)
+    while not c.is_zero:
+        m = c.degree(DE.t)
+        if n < m:
+            raise NonElementaryIntegralException
+        # a1 = b + m*Dt/t
+        a1 = b.as_expr()
+        with DecrementLevel(DE):
+            # TODO: Write a dummy function that does this idiom
+            a1a, a1d = frac_in(a1, DE.t)
+            a1a = a1a*etad + etaa*a1d*Poly(m, DE.t)
+            a1d = a1d*etad
+
+            a2a, a2d = frac_in(c.LC(), DE.t)
+
+            sa, sd = rischDE(a1a, a1d, a2a, a2d, DE)
+        stm = Poly(sa.as_expr()/sd.as_expr()*DE.t**m, DE.t, expand=False)
+        q += stm
+        n = m - 1
+        c -= b*stm + derivation(stm, DE)  # deg(c) becomes smaller
+    return q
+
+
+def solve_poly_rde(b, cQ, n, DE, parametric=False):
+    """
+    Solve a Polynomial Risch Differential Equation with degree bound ``n``.
+
+    This constitutes step 4 of the outline given in the rde.py docstring.
+
+    For parametric=False, cQ is c, a Poly; for parametric=True, cQ is Q ==
+    [q1, ..., qm], a list of Polys.
+    """
+    # No cancellation
+    if not b.is_zero and (DE.case == 'base' or
+            b.degree(DE.t) > max(0, DE.d.degree(DE.t) - 1)):
+
+        if parametric:
+            # Delayed imports
+            from .prde import prde_no_cancel_b_large
+            return prde_no_cancel_b_large(b, cQ, n, DE)
+        return no_cancel_b_large(b, cQ, n, DE)
+
+    elif (b.is_zero or b.degree(DE.t) < DE.d.degree(DE.t) - 1) and \
+            (DE.case == 'base' or DE.d.degree(DE.t) >= 2):
+
+        if parametric:
+            from .prde import prde_no_cancel_b_small
+            return prde_no_cancel_b_small(b, cQ, n, DE)
+
+        R = no_cancel_b_small(b, cQ, n, DE)
+
+        if isinstance(R, Poly):
+            return R
+        else:
+            # XXX: Might k be a field? (pg. 209)
+            h, b0, c0 = R
+            with DecrementLevel(DE):
+                b0, c0 = b0.as_poly(DE.t), c0.as_poly(DE.t)
+                if b0 is None:  # See above comment
+                    raise ValueError("b0 should be a non-Null value")
+                if c0 is  None:
+                    raise ValueError("c0 should be a non-Null value")
+                y = solve_poly_rde(b0, c0, n, DE).as_poly(DE.t)
+            return h + y
+
+    elif DE.d.degree(DE.t) >= 2 and b.degree(DE.t) == DE.d.degree(DE.t) - 1 and \
+            n > -b.as_poly(DE.t).LC()/DE.d.as_poly(DE.t).LC():
+
+        # TODO: Is this check necessary, and if so, what should it do if it fails?
+        # b comes from the first element returned from spde()
+        if not b.as_poly(DE.t).LC().is_number:
+            raise TypeError("Result should be a number")
+
+        if parametric:
+            raise NotImplementedError("prde_no_cancel_b_equal() is not yet "
+                "implemented.")
+
+        R = no_cancel_equal(b, cQ, n, DE)
+
+        if isinstance(R, Poly):
+            return R
+        else:
+            h, m, C = R
+            # XXX: Or should it be rischDE()?
+            y = solve_poly_rde(b, C, m, DE)
+            return h + y
+
+    else:
+        # Cancellation
+        if b.is_zero:
+            raise NotImplementedError("Remaining cases for Poly (P)RDE are "
+            "not yet implemented (is_deriv_in_field() required).")
+        else:
+            if DE.case == 'exp':
+                if parametric:
+                    raise NotImplementedError("Parametric RDE cancellation "
+                        "hyperexponential case is not yet implemented.")
+                return cancel_exp(b, cQ, n, DE)
+
+            elif DE.case == 'primitive':
+                if parametric:
+                    raise NotImplementedError("Parametric RDE cancellation "
+                        "primitive case is not yet implemented.")
+                return cancel_primitive(b, cQ, n, DE)
+
+            else:
+                raise NotImplementedError("Other Poly (P)RDE cancellation "
+                    "cases are not yet implemented (%s)." % DE.case)
+
+        if parametric:
+            raise NotImplementedError("Remaining cases for Poly PRDE not yet "
+                "implemented.")
+        raise NotImplementedError("Remaining cases for Poly RDE not yet "
+            "implemented.")
+
+
+def rischDE(fa, fd, ga, gd, DE):
+    """
+    Solve a Risch Differential Equation: Dy + f*y == g.
+
+    Explanation
+    ===========
+
+    See the outline in the docstring of rde.py for more information
+    about the procedure used.  Either raise NonElementaryIntegralException, in
+    which case there is no solution y in the given differential field,
+    or return y in k(t) satisfying Dy + f*y == g, or raise
+    NotImplementedError, in which case, the algorithms necessary to
+    solve the given Risch Differential Equation have not yet been
+    implemented.
+    """
+    _, (fa, fd) = weak_normalizer(fa, fd, DE)
+    a, (ba, bd), (ca, cd), hn = normal_denom(fa, fd, ga, gd, DE)
+    A, B, C, hs = special_denom(a, ba, bd, ca, cd, DE)
+    try:
+        # Until this is fully implemented, use oo.  Note that this will almost
+        # certainly cause non-termination in spde() (unless A == 1), and
+        # *might* lead to non-termination in the next step for a nonelementary
+        # integral (I don't know for certain yet).  Fortunately, spde() is
+        # currently written recursively, so this will just give
+        # RuntimeError: maximum recursion depth exceeded.
+        n = bound_degree(A, B, C, DE)
+    except NotImplementedError:
+        # Useful for debugging:
+        # import warnings
+        # warnings.warn("rischDE: Proceeding with n = oo; may cause "
+        #     "non-termination.")
+        n = oo
+
+    B, C, m, alpha, beta = spde(A, B, C, n, DE)
+    if C.is_zero:
+        y = C
+    else:
+        y = solve_poly_rde(B, C, m, DE)
+
+    return (alpha*y + beta, hn*hs)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/risch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/risch.py
new file mode 100644
index 0000000000000000000000000000000000000000..89e5f10bbb1d011d98a5884ce74ab25b615e1c51
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/risch.py
@@ -0,0 +1,1851 @@
+"""
+The Risch Algorithm for transcendental function integration.
+
+The core algorithms for the Risch algorithm are here.  The subproblem
+algorithms are in the rde.py and prde.py files for the Risch
+Differential Equation solver and the parametric problems solvers,
+respectively.  All important information concerning the differential extension
+for an integrand is stored in a DifferentialExtension object, which in the code
+is usually called DE.  Throughout the code and Inside the DifferentialExtension
+object, the conventions/attribute names are that the base domain is QQ and each
+differential extension is x, t0, t1, ..., tn-1 = DE.t. DE.x is the variable of
+integration (Dx == 1), DE.D is a list of the derivatives of
+x, t1, t2, ..., tn-1 = t, DE.T is the list [x, t1, t2, ..., tn-1], DE.t is the
+outer-most variable of the differential extension at the given level (the level
+can be adjusted using DE.increment_level() and DE.decrement_level()),
+k is the field C(x, t0, ..., tn-2), where C is the constant field.  The
+numerator of a fraction is denoted by a and the denominator by
+d.  If the fraction is named f, fa == numer(f) and fd == denom(f).
+Fractions are returned as tuples (fa, fd).  DE.d and DE.t are used to
+represent the topmost derivation and extension variable, respectively.
+The docstring of a function signifies whether an argument is in k[t], in
+which case it will just return a Poly in t, or in k(t), in which case it
+will return the fraction (fa, fd). Other variable names probably come
+from the names used in Bronstein's book.
+"""
+from types import GeneratorType
+from functools import reduce
+
+from sympy.core.function import Lambda
+from sympy.core.mul import Mul
+from sympy.core.intfunc import ilcm
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.core.relational import Ne
+from sympy.core.singleton import S
+from sympy.core.sorting import ordered, default_sort_key
+from sympy.core.symbol import Dummy, Symbol
+from sympy.functions.elementary.exponential import log, exp
+from sympy.functions.elementary.hyperbolic import (cosh, coth, sinh,
+    tanh)
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (atan, sin, cos,
+    tan, acot, cot, asin, acos)
+from .integrals import integrate, Integral
+from .heurisch import _symbols
+from sympy.polys.polyerrors import PolynomialError
+from sympy.polys.polytools import (real_roots, cancel, Poly, gcd,
+    reduced)
+from sympy.polys.rootoftools import RootSum
+from sympy.utilities.iterables import numbered_symbols
+
+
+def integer_powers(exprs):
+    """
+    Rewrites a list of expressions as integer multiples of each other.
+
+    Explanation
+    ===========
+
+    For example, if you have [x, x/2, x**2 + 1, 2*x/3], then you can rewrite
+    this as [(x/6) * 6, (x/6) * 3, (x**2 + 1) * 1, (x/6) * 4]. This is useful
+    in the Risch integration algorithm, where we must write exp(x) + exp(x/2)
+    as (exp(x/2))**2 + exp(x/2), but not as exp(x) + sqrt(exp(x)) (this is
+    because only the transcendental case is implemented and we therefore cannot
+    integrate algebraic extensions). The integer multiples returned by this
+    function for each term are the smallest possible (their content equals 1).
+
+    Returns a list of tuples where the first element is the base term and the
+    second element is a list of `(item, factor)` terms, where `factor` is the
+    integer multiplicative factor that must multiply the base term to obtain
+    the original item.
+
+    The easiest way to understand this is to look at an example:
+
+    >>> from sympy.abc import x
+    >>> from sympy.integrals.risch import integer_powers
+    >>> integer_powers([x, x/2, x**2 + 1, 2*x/3])
+    [(x/6, [(x, 6), (x/2, 3), (2*x/3, 4)]), (x**2 + 1, [(x**2 + 1, 1)])]
+
+    We can see how this relates to the example at the beginning of the
+    docstring.  It chose x/6 as the first base term.  Then, x can be written as
+    (x/2) * 2, so we get (0, 2), and so on. Now only element (x**2 + 1)
+    remains, and there are no other terms that can be written as a rational
+    multiple of that, so we get that it can be written as (x**2 + 1) * 1.
+
+    """
+    # Here is the strategy:
+
+    # First, go through each term and determine if it can be rewritten as a
+    # rational multiple of any of the terms gathered so far.
+    # cancel(a/b).is_Rational is sufficient for this.  If it is a multiple, we
+    # add its multiple to the dictionary.
+
+    terms = {}
+    for term in exprs:
+        for trm, trm_list in terms.items():
+            a = cancel(term/trm)
+            if a.is_Rational:
+                trm_list.append((term, a))
+                break
+        else:
+            terms[term] = [(term, S.One)]
+
+    # After we have done this, we have all the like terms together, so we just
+    # need to find a common denominator so that we can get the base term and
+    # integer multiples such that each term can be written as an integer
+    # multiple of the base term, and the content of the integers is 1.
+
+    newterms = {}
+    for term, term_list in terms.items():
+        common_denom = reduce(ilcm, [i.as_numer_denom()[1] for _, i in
+            term_list])
+        newterm = term/common_denom
+        newmults = [(i, j*common_denom) for i, j in term_list]
+        newterms[newterm] = newmults
+
+    return sorted(iter(newterms.items()), key=lambda item: item[0].sort_key())
+
+
+class DifferentialExtension:
+    """
+    A container for all the information relating to a differential extension.
+
+    Explanation
+    ===========
+
+    The attributes of this object are (see also the docstring of __init__):
+
+    - f: The original (Expr) integrand.
+    - x: The variable of integration.
+    - T: List of variables in the extension.
+    - D: List of derivations in the extension; corresponds to the elements of T.
+    - fa: Poly of the numerator of the integrand.
+    - fd: Poly of the denominator of the integrand.
+    - Tfuncs: Lambda() representations of each element of T (except for x).
+      For back-substitution after integration.
+    - backsubs: A (possibly empty) list of further substitutions to be made on
+      the final integral to make it look more like the integrand.
+    - exts:
+    - extargs:
+    - cases: List of string representations of the cases of T.
+    - t: The top level extension variable, as defined by the current level
+      (see level below).
+    - d: The top level extension derivation, as defined by the current
+      derivation (see level below).
+    - case: The string representation of the case of self.d.
+    (Note that self.T and self.D will always contain the complete extension,
+    regardless of the level.  Therefore, you should ALWAYS use DE.t and DE.d
+    instead of DE.T[-1] and DE.D[-1].  If you want to have a list of the
+    derivations or variables only up to the current level, use
+    DE.D[:len(DE.D) + DE.level + 1] and DE.T[:len(DE.T) + DE.level + 1].  Note
+    that, in particular, the derivation() function does this.)
+
+    The following are also attributes, but will probably not be useful other
+    than in internal use:
+    - newf: Expr form of fa/fd.
+    - level: The number (between -1 and -len(self.T)) such that
+      self.T[self.level] == self.t and self.D[self.level] == self.d.
+      Use the methods self.increment_level() and self.decrement_level() to change
+      the current level.
+    """
+    # __slots__ is defined mainly so we can iterate over all the attributes
+    # of the class easily (the memory use doesn't matter too much, since we
+    # only create one DifferentialExtension per integration).  Also, it's nice
+    # to have a safeguard when debugging.
+    __slots__ = ('f', 'x', 'T', 'D', 'fa', 'fd', 'Tfuncs', 'backsubs',
+        'exts', 'extargs', 'cases', 'case', 't', 'd', 'newf', 'level',
+        'ts', 'dummy')
+
+    def __init__(self, f=None, x=None, handle_first='log', dummy=False, extension=None, rewrite_complex=None):
+        """
+        Tries to build a transcendental extension tower from ``f`` with respect to ``x``.
+
+        Explanation
+        ===========
+
+        If it is successful, creates a DifferentialExtension object with, among
+        others, the attributes fa, fd, D, T, Tfuncs, and backsubs such that
+        fa and fd are Polys in T[-1] with rational coefficients in T[:-1],
+        fa/fd == f, and D[i] is a Poly in T[i] with rational coefficients in
+        T[:i] representing the derivative of T[i] for each i from 1 to len(T).
+        Tfuncs is a list of Lambda objects for back replacing the functions
+        after integrating.  Lambda() is only used (instead of lambda) to make
+        them easier to test and debug. Note that Tfuncs corresponds to the
+        elements of T, except for T[0] == x, but they should be back-substituted
+        in reverse order.  backsubs is a (possibly empty) back-substitution list
+        that should be applied on the completed integral to make it look more
+        like the original integrand.
+
+        If it is unsuccessful, it raises NotImplementedError.
+
+        You can also create an object by manually setting the attributes as a
+        dictionary to the extension keyword argument.  You must include at least
+        D.  Warning, any attribute that is not given will be set to None. The
+        attributes T, t, d, cases, case, x, and level are set automatically and
+        do not need to be given.  The functions in the Risch Algorithm will NOT
+        check to see if an attribute is None before using it.  This also does not
+        check to see if the extension is valid (non-algebraic) or even if it is
+        self-consistent.  Therefore, this should only be used for
+        testing/debugging purposes.
+        """
+        # XXX: If you need to debug this function, set the break point here
+
+        if extension:
+            if 'D' not in extension:
+                raise ValueError("At least the key D must be included with "
+                    "the extension flag to DifferentialExtension.")
+            for attr in extension:
+                setattr(self, attr, extension[attr])
+
+            self._auto_attrs()
+
+            return
+        elif f is None or x is None:
+            raise ValueError("Either both f and x or a manual extension must "
+            "be given.")
+
+        if handle_first not in ('log', 'exp'):
+            raise ValueError("handle_first must be 'log' or 'exp', not %s." %
+                str(handle_first))
+
+        # f will be the original function, self.f might change if we reset
+        # (e.g., we pull out a constant from an exponential)
+        self.f = f
+        self.x = x
+        # setting the default value 'dummy'
+        self.dummy = dummy
+        self.reset()
+        exp_new_extension, log_new_extension = True, True
+
+        # case of 'automatic' choosing
+        if rewrite_complex is None:
+            rewrite_complex = I in self.f.atoms()
+
+        if rewrite_complex:
+            rewritables = {
+                (sin, cos, cot, tan, sinh, cosh, coth, tanh): exp,
+                (asin, acos, acot, atan): log,
+            }
+            # rewrite the trigonometric components
+            for candidates, rule in rewritables.items():
+                self.newf = self.newf.rewrite(candidates, rule)
+            self.newf = cancel(self.newf)
+        else:
+            if any(i.has(x) for i in self.f.atoms(sin, cos, tan, atan, asin, acos)):
+                raise NotImplementedError("Trigonometric extensions are not "
+                "supported (yet!)")
+
+        exps = set()
+        pows = set()
+        numpows = set()
+        sympows = set()
+        logs = set()
+        symlogs = set()
+
+        while True:
+            if self.newf.is_rational_function(*self.T):
+                break
+
+            if not exp_new_extension and not log_new_extension:
+                # We couldn't find a new extension on the last pass, so I guess
+                # we can't do it.
+                raise NotImplementedError("Couldn't find an elementary "
+                    "transcendental extension for %s.  Try using a " % str(f) +
+                    "manual extension with the extension flag.")
+
+            exps, pows, numpows, sympows, log_new_extension = \
+                    self._rewrite_exps_pows(exps, pows, numpows, sympows, log_new_extension)
+
+            logs, symlogs = self._rewrite_logs(logs, symlogs)
+
+            if handle_first == 'exp' or not log_new_extension:
+                exp_new_extension = self._exp_part(exps)
+                if exp_new_extension is None:
+                    # reset and restart
+                    self.f = self.newf
+                    self.reset()
+                    exp_new_extension = True
+                    continue
+
+            if handle_first == 'log' or not exp_new_extension:
+                log_new_extension = self._log_part(logs)
+
+        self.fa, self.fd = frac_in(self.newf, self.t)
+        self._auto_attrs()
+
+        return
+
+    def __getattr__(self, attr):
+        # Avoid AttributeErrors when debugging
+        if attr not in self.__slots__:
+            raise AttributeError("%s has no attribute %s" % (repr(self), repr(attr)))
+        return None
+
+    def _rewrite_exps_pows(self, exps, pows, numpows,
+            sympows, log_new_extension):
+        """
+        Rewrite exps/pows for better processing.
+        """
+        from .prde import is_deriv_k
+
+        # Pre-preparsing.
+        #################
+        # Get all exp arguments, so we can avoid ahead of time doing
+        # something like t1 = exp(x), t2 = exp(x/2) == sqrt(t1).
+
+        # Things like sqrt(exp(x)) do not automatically simplify to
+        # exp(x/2), so they will be viewed as algebraic.  The easiest way
+        # to handle this is to convert all instances of exp(a)**Rational
+        # to exp(Rational*a) before doing anything else.  Note that the
+        # _exp_part code can generate terms of this form, so we do need to
+        # do this at each pass (or else modify it to not do that).
+
+        ratpows = [i for i in self.newf.atoms(Pow)
+                   if (isinstance(i.base, exp) and i.exp.is_Rational)]
+
+        ratpows_repl = [
+            (i, i.base.base**(i.exp*i.base.exp)) for i in ratpows]
+        self.backsubs += [(j, i) for i, j in ratpows_repl]
+        self.newf = self.newf.xreplace(dict(ratpows_repl))
+
+        # To make the process deterministic, the args are sorted
+        # so that functions with smaller op-counts are processed first.
+        # Ties are broken with the default_sort_key.
+
+        # XXX Although the method is deterministic no additional work
+        # has been done to guarantee that the simplest solution is
+        # returned and that it would be affected be using different
+        # variables. Though it is possible that this is the case
+        # one should know that it has not been done intentionally, so
+        # further improvements may be possible.
+
+        # TODO: This probably doesn't need to be completely recomputed at
+        # each pass.
+        exps = update_sets(exps, self.newf.atoms(exp),
+            lambda i: i.exp.is_rational_function(*self.T) and
+            i.exp.has(*self.T))
+        pows = update_sets(pows, self.newf.atoms(Pow),
+            lambda i: i.exp.is_rational_function(*self.T) and
+            i.exp.has(*self.T))
+        numpows = update_sets(numpows, set(pows),
+            lambda i: not i.base.has(*self.T))
+        sympows = update_sets(sympows, set(pows) - set(numpows),
+            lambda i: i.base.is_rational_function(*self.T) and
+            not i.exp.is_Integer)
+
+        # The easiest way to deal with non-base E powers is to convert them
+        # into base E, integrate, and then convert back.
+        for i in ordered(pows):
+            old = i
+            new = exp(i.exp*log(i.base))
+            # If exp is ever changed to automatically reduce exp(x*log(2))
+            # to 2**x, then this will break.  The solution is to not change
+            # exp to do that :)
+            if i in sympows:
+                if i.exp.is_Rational:
+                    raise NotImplementedError("Algebraic extensions are "
+                        "not supported (%s)." % str(i))
+                # We can add a**b only if log(a) in the extension, because
+                # a**b == exp(b*log(a)).
+                basea, based = frac_in(i.base, self.t)
+                A = is_deriv_k(basea, based, self)
+                if A is None:
+                    # Nonelementary monomial (so far)
+
+                    # TODO: Would there ever be any benefit from just
+                    # adding log(base) as a new monomial?
+                    # ANSWER: Yes, otherwise we can't integrate x**x (or
+                    # rather prove that it has no elementary integral)
+                    # without first manually rewriting it as exp(x*log(x))
+                    self.newf = self.newf.xreplace({old: new})
+                    self.backsubs += [(new, old)]
+                    log_new_extension = self._log_part([log(i.base)])
+                    exps = update_sets(exps, self.newf.atoms(exp), lambda i:
+                        i.exp.is_rational_function(*self.T) and i.exp.has(*self.T))
+                    continue
+                ans, u, const = A
+                newterm = exp(i.exp*(log(const) + u))
+                # Under the current implementation, exp kills terms
+                # only if they are of the form a*log(x), where a is a
+                # Number.  This case should have already been killed by the
+                # above tests.  Again, if this changes to kill more than
+                # that, this will break, which maybe is a sign that you
+                # shouldn't be changing that.  Actually, if anything, this
+                # auto-simplification should be removed.  See
+                # https://groups.google.com/group/sympy/browse_thread/thread/a61d48235f16867f
+
+                self.newf = self.newf.xreplace({i: newterm})
+
+            elif i not in numpows:
+                continue
+            else:
+                # i in numpows
+                newterm = new
+            # TODO: Just put it in self.Tfuncs
+            self.backsubs.append((new, old))
+            self.newf = self.newf.xreplace({old: newterm})
+            exps.append(newterm)
+
+        return exps, pows, numpows, sympows, log_new_extension
+
+    def _rewrite_logs(self, logs, symlogs):
+        """
+        Rewrite logs for better processing.
+        """
+        atoms = self.newf.atoms(log)
+        logs = update_sets(logs, atoms,
+            lambda i: i.args[0].is_rational_function(*self.T) and
+            i.args[0].has(*self.T))
+        symlogs = update_sets(symlogs, atoms,
+            lambda i: i.has(*self.T) and i.args[0].is_Pow and
+            i.args[0].base.is_rational_function(*self.T) and
+            not i.args[0].exp.is_Integer)
+
+        # We can handle things like log(x**y) by converting it to y*log(x)
+        # This will fix not only symbolic exponents of the argument, but any
+        # non-Integer exponent, like log(sqrt(x)).  The exponent can also
+        # depend on x, like log(x**x).
+        for i in ordered(symlogs):
+            # Unlike in the exponential case above, we do not ever
+            # potentially add new monomials (above we had to add log(a)).
+            # Therefore, there is no need to run any is_deriv functions
+            # here.  Just convert log(a**b) to b*log(a) and let
+            # log_new_extension() handle it from there.
+            lbase = log(i.args[0].base)
+            logs.append(lbase)
+            new = i.args[0].exp*lbase
+            self.newf = self.newf.xreplace({i: new})
+            self.backsubs.append((new, i))
+
+        # remove any duplicates
+        logs = sorted(set(logs), key=default_sort_key)
+
+        return logs, symlogs
+
+    def _auto_attrs(self):
+        """
+        Set attributes that are generated automatically.
+        """
+        if not self.T:
+            # i.e., when using the extension flag and T isn't given
+            self.T = [i.gen for i in self.D]
+        if not self.x:
+            self.x = self.T[0]
+        self.cases = [get_case(d, t) for d, t in zip(self.D, self.T)]
+        self.level = -1
+        self.t = self.T[self.level]
+        self.d = self.D[self.level]
+        self.case = self.cases[self.level]
+
+    def _exp_part(self, exps):
+        """
+        Try to build an exponential extension.
+
+        Returns
+        =======
+
+        Returns True if there was a new extension, False if there was no new
+        extension but it was able to rewrite the given exponentials in terms
+        of the existing extension, and None if the entire extension building
+        process should be restarted.  If the process fails because there is no
+        way around an algebraic extension (e.g., exp(log(x)/2)), it will raise
+        NotImplementedError.
+        """
+        from .prde import is_log_deriv_k_t_radical
+        new_extension = False
+        restart = False
+        expargs = [i.exp for i in exps]
+        ip = integer_powers(expargs)
+        for arg, others in ip:
+            # Minimize potential problems with algebraic substitution
+            others.sort(key=lambda i: i[1])
+
+            arga, argd = frac_in(arg, self.t)
+            A = is_log_deriv_k_t_radical(arga, argd, self)
+
+            if A is not None:
+                ans, u, n, const = A
+                # if n is 1 or -1, it's algebraic, but we can handle it
+                if n == -1:
+                    # This probably will never happen, because
+                    # Rational.as_numer_denom() returns the negative term in
+                    # the numerator.  But in case that changes, reduce it to
+                    # n == 1.
+                    n = 1
+                    u **= -1
+                    const *= -1
+                    ans = [(i, -j) for i, j in ans]
+
+                if n == 1:
+                    # Example: exp(x + x**2) over QQ(x, exp(x), exp(x**2))
+                    self.newf = self.newf.xreplace({exp(arg): exp(const)*Mul(*[
+                        u**power for u, power in ans])})
+                    self.newf = self.newf.xreplace({exp(p*exparg):
+                        exp(const*p) * Mul(*[u**power for u, power in ans])
+                        for exparg, p in others})
+                    # TODO: Add something to backsubs to put exp(const*p)
+                    # back together.
+
+                    continue
+
+                else:
+                    # Bad news: we have an algebraic radical.  But maybe we
+                    # could still avoid it by choosing a different extension.
+                    # For example, integer_powers() won't handle exp(x/2 + 1)
+                    # over QQ(x, exp(x)), but if we pull out the exp(1), it
+                    # will.  Or maybe we have exp(x + x**2/2), over
+                    # QQ(x, exp(x), exp(x**2)), which is exp(x)*sqrt(exp(x**2)),
+                    # but if we use QQ(x, exp(x), exp(x**2/2)), then they will
+                    # all work.
+                    #
+                    # So here is what we do: If there is a non-zero const, pull
+                    # it out and retry.  Also, if len(ans) > 1, then rewrite
+                    # exp(arg) as the product of exponentials from ans, and
+                    # retry that.  If const == 0 and len(ans) == 1, then we
+                    # assume that it would have been handled by either
+                    # integer_powers() or n == 1 above if it could be handled,
+                    # so we give up at that point.  For example, you can never
+                    # handle exp(log(x)/2) because it equals sqrt(x).
+
+                    if const or len(ans) > 1:
+                        rad = Mul(*[term**(power/n) for term, power in ans])
+                        self.newf = self.newf.xreplace({exp(p*exparg):
+                            exp(const*p)*rad for exparg, p in others})
+                        self.newf = self.newf.xreplace(dict(list(zip(reversed(self.T),
+                            reversed([f(self.x) for f in self.Tfuncs])))))
+                        restart = True
+                        break
+                    else:
+                        # TODO: give algebraic dependence in error string
+                        raise NotImplementedError("Cannot integrate over "
+                            "algebraic extensions.")
+
+            else:
+                arga, argd = frac_in(arg, self.t)
+                darga = (argd*derivation(Poly(arga, self.t), self) -
+                    arga*derivation(Poly(argd, self.t), self))
+                dargd = argd**2
+                darga, dargd = darga.cancel(dargd, include=True)
+                darg = darga.as_expr()/dargd.as_expr()
+                self.t = next(self.ts)
+                self.T.append(self.t)
+                self.extargs.append(arg)
+                self.exts.append('exp')
+                self.D.append(darg.as_poly(self.t, expand=False)*Poly(self.t,
+                    self.t, expand=False))
+                if self.dummy:
+                    i = Dummy("i")
+                else:
+                    i = Symbol('i')
+                self.Tfuncs += [Lambda(i, exp(arg.subs(self.x, i)))]
+                self.newf = self.newf.xreplace(
+                        {exp(exparg): self.t**p for exparg, p in others})
+                new_extension = True
+
+        if restart:
+            return None
+        return new_extension
+
+    def _log_part(self, logs):
+        """
+        Try to build a logarithmic extension.
+
+        Returns
+        =======
+
+        Returns True if there was a new extension and False if there was no new
+        extension but it was able to rewrite the given logarithms in terms
+        of the existing extension.  Unlike with exponential extensions, there
+        is no way that a logarithm is not transcendental over and cannot be
+        rewritten in terms of an already existing extension in a non-algebraic
+        way, so this function does not ever return None or raise
+        NotImplementedError.
+        """
+        from .prde import is_deriv_k
+        new_extension = False
+        logargs = [i.args[0] for i in logs]
+        for arg in ordered(logargs):
+            # The log case is easier, because whenever a logarithm is algebraic
+            # over the base field, it is of the form a1*t1 + ... an*tn + c,
+            # which is a polynomial, so we can just replace it with that.
+            # In other words, we don't have to worry about radicals.
+            arga, argd = frac_in(arg, self.t)
+            A = is_deriv_k(arga, argd, self)
+            if A is not None:
+                ans, u, const = A
+                newterm = log(const) + u
+                self.newf = self.newf.xreplace({log(arg): newterm})
+                continue
+
+            else:
+                arga, argd = frac_in(arg, self.t)
+                darga = (argd*derivation(Poly(arga, self.t), self) -
+                    arga*derivation(Poly(argd, self.t), self))
+                dargd = argd**2
+                darg = darga.as_expr()/dargd.as_expr()
+                self.t = next(self.ts)
+                self.T.append(self.t)
+                self.extargs.append(arg)
+                self.exts.append('log')
+                self.D.append(cancel(darg.as_expr()/arg).as_poly(self.t,
+                    expand=False))
+                if self.dummy:
+                    i = Dummy("i")
+                else:
+                    i = Symbol('i')
+                self.Tfuncs += [Lambda(i, log(arg.subs(self.x, i)))]
+                self.newf = self.newf.xreplace({log(arg): self.t})
+                new_extension = True
+
+        return new_extension
+
+    @property
+    def _important_attrs(self):
+        """
+        Returns some of the more important attributes of self.
+
+        Explanation
+        ===========
+
+        Used for testing and debugging purposes.
+
+        The attributes are (fa, fd, D, T, Tfuncs, backsubs,
+        exts, extargs).
+        """
+        return (self.fa, self.fd, self.D, self.T, self.Tfuncs,
+            self.backsubs, self.exts, self.extargs)
+
+    # NOTE: this printing doesn't follow the Python's standard
+    # eval(repr(DE)) == DE, where DE is the DifferentialExtension object,
+    # also this printing is supposed to contain all the important
+    # attributes of a DifferentialExtension object
+    def __repr__(self):
+        # no need to have GeneratorType object printed in it
+        r = [(attr, getattr(self, attr)) for attr in self.__slots__
+                if not isinstance(getattr(self, attr), GeneratorType)]
+        return self.__class__.__name__ + '(dict(%r))' % (r)
+
+    # fancy printing of DifferentialExtension object
+    def __str__(self):
+        return (self.__class__.__name__ + '({fa=%s, fd=%s, D=%s})' %
+                (self.fa, self.fd, self.D))
+
+    # should only be used for debugging purposes, internally
+    # f1 = f2 = log(x) at different places in code execution
+    # may return D1 != D2 as True, since 'level' or other attribute
+    # may differ
+    def __eq__(self, other):
+        for attr in self.__class__.__slots__:
+            d1, d2 = getattr(self, attr), getattr(other, attr)
+            if not (isinstance(d1, GeneratorType) or d1 == d2):
+                return False
+        return True
+
+    def reset(self):
+        """
+        Reset self to an initial state.  Used by __init__.
+        """
+        self.t = self.x
+        self.T = [self.x]
+        self.D = [Poly(1, self.x)]
+        self.level = -1
+        self.exts = [None]
+        self.extargs = [None]
+        if self.dummy:
+            self.ts = numbered_symbols('t', cls=Dummy)
+        else:
+            # For testing
+            self.ts = numbered_symbols('t')
+        # For various things that we change to make things work that we need to
+        # change back when we are done.
+        self.backsubs = []
+        self.Tfuncs = []
+        self.newf = self.f
+
+    def indices(self, extension):
+        """
+        Parameters
+        ==========
+
+        extension : str
+            Represents a valid extension type.
+
+        Returns
+        =======
+
+        list: A list of indices of 'exts' where extension of
+            type 'extension' is present.
+
+        Examples
+        ========
+
+        >>> from sympy.integrals.risch import DifferentialExtension
+        >>> from sympy import log, exp
+        >>> from sympy.abc import x
+        >>> DE = DifferentialExtension(log(x) + exp(x), x, handle_first='exp')
+        >>> DE.indices('log')
+        [2]
+        >>> DE.indices('exp')
+        [1]
+
+        """
+        return [i for i, ext in enumerate(self.exts) if ext == extension]
+
+    def increment_level(self):
+        """
+        Increment the level of self.
+
+        Explanation
+        ===========
+
+        This makes the working differential extension larger.  self.level is
+        given relative to the end of the list (-1, -2, etc.), so we do not need
+        do worry about it when building the extension.
+        """
+        if self.level >= -1:
+            raise ValueError("The level of the differential extension cannot "
+                "be incremented any further.")
+
+        self.level += 1
+        self.t = self.T[self.level]
+        self.d = self.D[self.level]
+        self.case = self.cases[self.level]
+        return None
+
+    def decrement_level(self):
+        """
+        Decrease the level of self.
+
+        Explanation
+        ===========
+
+        This makes the working differential extension smaller.  self.level is
+        given relative to the end of the list (-1, -2, etc.), so we do not need
+        do worry about it when building the extension.
+        """
+        if self.level <= -len(self.T):
+            raise ValueError("The level of the differential extension cannot "
+                "be decremented any further.")
+
+        self.level -= 1
+        self.t = self.T[self.level]
+        self.d = self.D[self.level]
+        self.case = self.cases[self.level]
+        return None
+
+
+def update_sets(seq, atoms, func):
+    s = set(seq)
+    s = atoms.intersection(s)
+    new = atoms - s
+    s.update(list(filter(func, new)))
+    return list(s)
+
+
+class DecrementLevel:
+    """
+    A context manager for decrementing the level of a DifferentialExtension.
+    """
+    __slots__ = ('DE',)
+
+    def __init__(self, DE):
+        self.DE = DE
+        return
+
+    def __enter__(self):
+        self.DE.decrement_level()
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        self.DE.increment_level()
+
+
+class NonElementaryIntegralException(Exception):
+    """
+    Exception used by subroutines within the Risch algorithm to indicate to one
+    another that the function being integrated does not have an elementary
+    integral in the given differential field.
+    """
+    # TODO: Rewrite algorithms below to use this (?)
+
+    # TODO: Pass through information about why the integral was nonelementary,
+    # and store that in the resulting NonElementaryIntegral somehow.
+    pass
+
+
+def gcdex_diophantine(a, b, c):
+    """
+    Extended Euclidean Algorithm, Diophantine version.
+
+    Explanation
+    ===========
+
+    Given ``a``, ``b`` in K[x] and ``c`` in (a, b), the ideal generated by ``a`` and
+    ``b``, return (s, t) such that s*a + t*b == c and either s == 0 or s.degree()
+    < b.degree().
+    """
+    # Extended Euclidean Algorithm (Diophantine Version) pg. 13
+    # TODO: This should go in densetools.py.
+    # XXX: Better name?
+
+    s, g = a.half_gcdex(b)
+    s *= c.exquo(g)  # Inexact division means c is not in (a, b)
+    if s and s.degree() >= b.degree():
+        _, s = s.div(b)
+    t = (c - s*a).exquo(b)
+    return (s, t)
+
+
+def frac_in(f, t, *, cancel=False, **kwargs):
+    """
+    Returns the tuple (fa, fd), where fa and fd are Polys in t.
+
+    Explanation
+    ===========
+
+    This is a common idiom in the Risch Algorithm functions, so we abstract
+    it out here. ``f`` should be a basic expression, a Poly, or a tuple (fa, fd),
+    where fa and fd are either basic expressions or Polys, and f == fa/fd.
+    **kwargs are applied to Poly.
+    """
+    if isinstance(f, tuple):
+        fa, fd = f
+        f = fa.as_expr()/fd.as_expr()
+    fa, fd = f.as_expr().as_numer_denom()
+    fa, fd = fa.as_poly(t, **kwargs), fd.as_poly(t, **kwargs)
+    if cancel:
+        fa, fd = fa.cancel(fd, include=True)
+    if fa is None or fd is None:
+        raise ValueError("Could not turn %s into a fraction in %s." % (f, t))
+    return (fa, fd)
+
+
+def as_poly_1t(p, t, z):
+    """
+    (Hackish) way to convert an element ``p`` of K[t, 1/t] to K[t, z].
+
+    In other words, ``z == 1/t`` will be a dummy variable that Poly can handle
+    better.
+
+    See issue 5131.
+
+    Examples
+    ========
+
+    >>> from sympy import random_poly
+    >>> from sympy.integrals.risch import as_poly_1t
+    >>> from sympy.abc import x, z
+
+    >>> p1 = random_poly(x, 10, -10, 10)
+    >>> p2 = random_poly(x, 10, -10, 10)
+    >>> p = p1 + p2.subs(x, 1/x)
+    >>> as_poly_1t(p, x, z).as_expr().subs(z, 1/x) == p
+    True
+    """
+    # TODO: Use this on the final result.  That way, we can avoid answers like
+    # (...)*exp(-x).
+    pa, pd = frac_in(p, t, cancel=True)
+    if not pd.is_monomial:
+        # XXX: Is there a better Poly exception that we could raise here?
+        # Either way, if you see this (from the Risch Algorithm) it indicates
+        # a bug.
+        raise PolynomialError("%s is not an element of K[%s, 1/%s]." % (p, t, t))
+
+    t_part, remainder = pa.div(pd)
+
+    ans = t_part.as_poly(t, z, expand=False)
+
+    if remainder:
+        one = remainder.one
+        tp = t*one
+        r = pd.degree() - remainder.degree()
+        z_part = remainder.transform(one, tp) * tp**r
+        z_part = z_part.replace(t, z).to_field().quo_ground(pd.LC())
+        ans += z_part.as_poly(t, z, expand=False)
+
+    return ans
+
+
+def derivation(p, DE, coefficientD=False, basic=False):
+    """
+    Computes Dp.
+
+    Explanation
+    ===========
+
+    Given the derivation D with D = d/dx and p is a polynomial in t over
+    K(x), return Dp.
+
+    If coefficientD is True, it computes the derivation kD
+    (kappaD), which is defined as kD(sum(ai*Xi**i, (i, 0, n))) ==
+    sum(Dai*Xi**i, (i, 1, n)) (Definition 3.2.2, page 80).  X in this case is
+    T[-1], so coefficientD computes the derivative just with respect to T[:-1],
+    with T[-1] treated as a constant.
+
+    If ``basic=True``, the returns a Basic expression.  Elements of D can still be
+    instances of Poly.
+    """
+    if basic:
+        r = 0
+    else:
+        r = Poly(0, DE.t)
+
+    t = DE.t
+    if coefficientD:
+        if DE.level <= -len(DE.T):
+            # 'base' case, the answer is 0.
+            return r
+        DE.decrement_level()
+
+    D = DE.D[:len(DE.D) + DE.level + 1]
+    T = DE.T[:len(DE.T) + DE.level + 1]
+
+    for d, v in zip(D, T):
+        pv = p.as_poly(v)
+        if pv is None or basic:
+            pv = p.as_expr()
+
+        if basic:
+            r += d.as_expr()*pv.diff(v)
+        else:
+            r += (d.as_expr()*pv.diff(v).as_expr()).as_poly(t)
+
+    if basic:
+        r = cancel(r)
+    if coefficientD:
+        DE.increment_level()
+
+    return r
+
+
+def get_case(d, t):
+    """
+    Returns the type of the derivation d.
+
+    Returns one of {'exp', 'tan', 'base', 'primitive', 'other_linear',
+    'other_nonlinear'}.
+    """
+    if not d.expr.has(t):
+        if d.is_one:
+            return 'base'
+        return 'primitive'
+    if d.rem(Poly(t, t)).is_zero:
+        return 'exp'
+    if d.rem(Poly(1 + t**2, t)).is_zero:
+        return 'tan'
+    if d.degree(t) > 1:
+        return 'other_nonlinear'
+    return 'other_linear'
+
+
+def splitfactor(p, DE, coefficientD=False, z=None):
+    """
+    Splitting factorization.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and ``p`` in k[t], return (p_n, p_s) in
+    k[t] x k[t] such that p = p_n*p_s, p_s is special, and each square
+    factor of p_n is normal.
+
+    Page. 100
+    """
+    kinv = [1/x for x in DE.T[:DE.level]]
+    if z:
+        kinv.append(z)
+
+    One = Poly(1, DE.t, domain=p.get_domain())
+    Dp = derivation(p, DE, coefficientD=coefficientD)
+    # XXX: Is this right?
+    if p.is_zero:
+        return (p, One)
+
+    if not p.expr.has(DE.t):
+        s = p.as_poly(*kinv).gcd(Dp.as_poly(*kinv)).as_poly(DE.t)
+        n = p.exquo(s)
+        return (n, s)
+
+    if not Dp.is_zero:
+        h = p.gcd(Dp).to_field()
+        g = p.gcd(p.diff(DE.t)).to_field()
+        s = h.exquo(g)
+
+        if s.degree(DE.t) == 0:
+            return (p, One)
+
+        q_split = splitfactor(p.exquo(s), DE, coefficientD=coefficientD)
+
+        return (q_split[0], q_split[1]*s)
+    else:
+        return (p, One)
+
+
+def splitfactor_sqf(p, DE, coefficientD=False, z=None, basic=False):
+    """
+    Splitting Square-free Factorization.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and ``p`` in k[t], returns (N1, ..., Nm)
+    and (S1, ..., Sm) in k[t]^m such that p =
+    (N1*N2**2*...*Nm**m)*(S1*S2**2*...*Sm**m) is a splitting
+    factorization of ``p`` and the Ni and Si are square-free and coprime.
+    """
+    # TODO: This algorithm appears to be faster in every case
+    # TODO: Verify this and splitfactor() for multiple extensions
+    kkinv = [1/x for x in DE.T[:DE.level]] + DE.T[:DE.level]
+    if z:
+        kkinv = [z]
+
+    S = []
+    N = []
+    p_sqf = p.sqf_list_include()
+    if p.is_zero:
+        return (((p, 1),), ())
+
+    for pi, i in p_sqf:
+        Si = pi.as_poly(*kkinv).gcd(derivation(pi, DE,
+            coefficientD=coefficientD,basic=basic).as_poly(*kkinv)).as_poly(DE.t)
+        pi = Poly(pi, DE.t)
+        Si = Poly(Si, DE.t)
+        Ni = pi.exquo(Si)
+        if not Si.is_one:
+            S.append((Si, i))
+        if not Ni.is_one:
+            N.append((Ni, i))
+
+    return (tuple(N), tuple(S))
+
+
+def canonical_representation(a, d, DE):
+    """
+    Canonical Representation.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k[t] and f = a/d in k(t), return (f_p, f_s,
+    f_n) in k[t] x k(t) x k(t) such that f = f_p + f_s + f_n is the
+    canonical representation of f (f_p is a polynomial, f_s is reduced
+    (has a special denominator), and f_n is simple (has a normal
+    denominator).
+    """
+    # Make d monic
+    l = Poly(1/d.LC(), DE.t)
+    a, d = a.mul(l), d.mul(l)
+
+    q, r = a.div(d)
+    dn, ds = splitfactor(d, DE)
+
+    b, c = gcdex_diophantine(dn.as_poly(DE.t), ds.as_poly(DE.t), r.as_poly(DE.t))
+    b, c = b.as_poly(DE.t), c.as_poly(DE.t)
+
+    return (q, (b, ds), (c, dn))
+
+
+def hermite_reduce(a, d, DE):
+    """
+    Hermite Reduction - Mack's Linear Version.
+
+    Given a derivation D on k(t) and f = a/d in k(t), returns g, h, r in
+    k(t) such that f = Dg + h + r, h is simple, and r is reduced.
+
+    """
+    # Make d monic
+    l = Poly(1/d.LC(), DE.t)
+    a, d = a.mul(l), d.mul(l)
+
+    fp, fs, fn = canonical_representation(a, d, DE)
+    a, d = fn
+    l = Poly(1/d.LC(), DE.t)
+    a, d = a.mul(l), d.mul(l)
+
+    ga = Poly(0, DE.t)
+    gd = Poly(1, DE.t)
+
+    dd = derivation(d, DE)
+    dm = gcd(d.to_field(), dd.to_field()).as_poly(DE.t)
+    ds, _ = d.div(dm)
+
+    while dm.degree(DE.t) > 0:
+
+        ddm = derivation(dm, DE)
+        dm2 = gcd(dm.to_field(), ddm.to_field())
+        dms, _ = dm.div(dm2)
+        ds_ddm = ds.mul(ddm)
+        ds_ddm_dm, _ = ds_ddm.div(dm)
+
+        b, c = gcdex_diophantine(-ds_ddm_dm.as_poly(DE.t),
+            dms.as_poly(DE.t), a.as_poly(DE.t))
+        b, c = b.as_poly(DE.t), c.as_poly(DE.t)
+
+        db = derivation(b, DE).as_poly(DE.t)
+        ds_dms, _ = ds.div(dms)
+        a = c.as_poly(DE.t) - db.mul(ds_dms).as_poly(DE.t)
+
+        ga = ga*dm + b*gd
+        gd = gd*dm
+        ga, gd = ga.cancel(gd, include=True)
+        dm = dm2
+
+    q, r = a.div(ds)
+    ga, gd = ga.cancel(gd, include=True)
+
+    r, d = r.cancel(ds, include=True)
+    rra = q*fs[1] + fp*fs[1] + fs[0]
+    rrd = fs[1]
+    rra, rrd = rra.cancel(rrd, include=True)
+
+    return ((ga, gd), (r, d), (rra, rrd))
+
+
+def polynomial_reduce(p, DE):
+    """
+    Polynomial Reduction.
+
+    Explanation
+    ===========
+
+    Given a derivation D on k(t) and p in k[t] where t is a nonlinear
+    monomial over k, return q, r in k[t] such that p = Dq  + r, and
+    deg(r) < deg_t(Dt).
+    """
+    q = Poly(0, DE.t)
+    while p.degree(DE.t) >= DE.d.degree(DE.t):
+        m = p.degree(DE.t) - DE.d.degree(DE.t) + 1
+        q0 = Poly(DE.t**m, DE.t).mul(Poly(p.as_poly(DE.t).LC()/
+            (m*DE.d.LC()), DE.t))
+        q += q0
+        p = p - derivation(q0, DE)
+
+    return (q, p)
+
+
+def laurent_series(a, d, F, n, DE):
+    """
+    Contribution of ``F`` to the full partial fraction decomposition of A/D.
+
+    Explanation
+    ===========
+
+    Given a field K of characteristic 0 and ``A``,``D``,``F`` in K[x] with D monic,
+    nonzero, coprime with A, and ``F`` the factor of multiplicity n in the square-
+    free factorization of D, return the principal parts of the Laurent series of
+    A/D at all the zeros of ``F``.
+    """
+    if F.degree()==0:
+        return 0
+    Z = _symbols('z', n)
+    z = Symbol('z')
+    Z.insert(0, z)
+    delta_a = Poly(0, DE.t)
+    delta_d = Poly(1, DE.t)
+
+    E = d.quo(F**n)
+    ha, hd = (a, E*Poly(z**n, DE.t))
+    dF = derivation(F,DE)
+    B, _ = gcdex_diophantine(E, F, Poly(1,DE.t))
+    C, _ = gcdex_diophantine(dF, F, Poly(1,DE.t))
+
+    # initialization
+    F_store = F
+    V, DE_D_list, H_list= [], [], []
+
+    for j in range(0, n):
+    # jth derivative of z would be substituted with dfnth/(j+1) where dfnth =(d^n)f/(dx)^n
+        F_store = derivation(F_store, DE)
+        v = (F_store.as_expr())/(j + 1)
+        V.append(v)
+        DE_D_list.append(Poly(Z[j + 1],Z[j]))
+
+    DE_new = DifferentialExtension(extension = {'D': DE_D_list}) #a differential indeterminate
+    for j in range(0, n):
+        zEha = Poly(z**(n + j), DE.t)*E**(j + 1)*ha
+        zEhd = hd
+        Pa, Pd = cancel((zEha, zEhd))[1], cancel((zEha, zEhd))[2]
+        Q = Pa.quo(Pd)
+        for i in range(0, j + 1):
+            Q = Q.subs(Z[i], V[i])
+        Dha = (hd*derivation(ha, DE, basic=True).as_poly(DE.t)
+             + ha*derivation(hd, DE, basic=True).as_poly(DE.t)
+             + hd*derivation(ha, DE_new, basic=True).as_poly(DE.t)
+             + ha*derivation(hd, DE_new, basic=True).as_poly(DE.t))
+        Dhd = Poly(j + 1, DE.t)*hd**2
+        ha, hd = Dha, Dhd
+
+        Ff, _ = F.div(gcd(F, Q))
+        F_stara, F_stard = frac_in(Ff, DE.t)
+        if F_stara.degree(DE.t) - F_stard.degree(DE.t) > 0:
+            QBC = Poly(Q, DE.t)*B**(1 + j)*C**(n + j)
+            H = QBC
+            H_list.append(H)
+            H = (QBC*F_stard).rem(F_stara)
+            alphas = real_roots(F_stara)
+            for alpha in list(alphas):
+                delta_a = delta_a*Poly((DE.t - alpha)**(n - j), DE.t) + Poly(H.eval(alpha), DE.t)
+                delta_d = delta_d*Poly((DE.t - alpha)**(n - j), DE.t)
+    return (delta_a, delta_d, H_list)
+
+
+def recognize_derivative(a, d, DE, z=None):
+    """
+    Compute the squarefree factorization of the denominator of f
+    and for each Di the polynomial H in K[x] (see Theorem 2.7.1), using the
+    LaurentSeries algorithm. Write Di = GiEi where Gj = gcd(Hn, Di) and
+    gcd(Ei,Hn) = 1. Since the residues of f at the roots of Gj are all 0, and
+    the residue of f at a root alpha of Ei is Hi(a) != 0, f is the derivative of a
+    rational function if and only if Ei = 1 for each i, which is equivalent to
+    Di | H[-1] for each i.
+    """
+    flag =True
+    a, d = a.cancel(d, include=True)
+    _, r = a.div(d)
+    Np, Sp = splitfactor_sqf(d, DE, coefficientD=True, z=z)
+
+    j = 1
+    for s, _ in Sp:
+        delta_a, delta_d, H = laurent_series(r, d, s, j, DE)
+        g = gcd(d, H[-1]).as_poly()
+        if g is not d:
+            flag = False
+            break
+        j = j + 1
+    return flag
+
+
+def recognize_log_derivative(a, d, DE, z=None):
+    """
+    There exists a v in K(x)* such that f = dv/v
+    where f a rational function if and only if f can be written as f = A/D
+    where D is squarefree,deg(A) < deg(D), gcd(A, D) = 1,
+    and all the roots of the Rothstein-Trager resultant are integers. In that case,
+    any of the Rothstein-Trager, Lazard-Rioboo-Trager or Czichowski algorithm
+    produces u in K(x) such that du/dx = uf.
+    """
+
+    z = z or Dummy('z')
+    a, d = a.cancel(d, include=True)
+    _, a = a.div(d)
+
+    pz = Poly(z, DE.t)
+    Dd = derivation(d, DE)
+    q = a - pz*Dd
+    r, _ = d.resultant(q, includePRS=True)
+    r = Poly(r, z)
+    Np, Sp = splitfactor_sqf(r, DE, coefficientD=True, z=z)
+
+    for s, _ in Sp:
+        # TODO also consider the complex roots which should
+        # turn the flag false
+        a = real_roots(s.as_poly(z))
+
+        if not all(j.is_Integer for j in a):
+            return False
+    return True
+
+def residue_reduce(a, d, DE, z=None, invert=True):
+    """
+    Lazard-Rioboo-Rothstein-Trager resultant reduction.
+
+    Explanation
+    ===========
+
+    Given a derivation ``D`` on k(t) and f in k(t) simple, return g
+    elementary over k(t) and a Boolean b in {True, False} such that f -
+    Dg in k[t] if b == True or f + h and f + h - Dg do not have an
+    elementary integral over k(t) for any h in k (reduced) if b ==
+    False.
+
+    Returns (G, b), where G is a tuple of tuples of the form (s_i, S_i),
+    such that g = Add(*[RootSum(s_i, lambda z: z*log(S_i(z, t))) for
+    S_i, s_i in G]). f - Dg is the remaining integral, which is elementary
+    only if b == True, and hence the integral of f is elementary only if
+    b == True.
+
+    f - Dg is not calculated in this function because that would require
+    explicitly calculating the RootSum.  Use residue_reduce_derivation().
+    """
+    # TODO: Use log_to_atan() from rationaltools.py
+    # If r = residue_reduce(...), then the logarithmic part is given by:
+    # sum([RootSum(a[0].as_poly(z), lambda i: i*log(a[1].as_expr()).subs(z,
+    # i)).subs(t, log(x)) for a in r[0]])
+
+    z = z or Dummy('z')
+    a, d = a.cancel(d, include=True)
+    a, d = a.to_field().mul_ground(1/d.LC()), d.to_field().mul_ground(1/d.LC())
+    kkinv = [1/x for x in DE.T[:DE.level]] + DE.T[:DE.level]
+
+    if a.is_zero:
+        return ([], True)
+    _, a = a.div(d)
+
+    pz = Poly(z, DE.t)
+
+    Dd = derivation(d, DE)
+    q = a - pz*Dd
+
+    if Dd.degree(DE.t) <= d.degree(DE.t):
+        r, R = d.resultant(q, includePRS=True)
+    else:
+        r, R = q.resultant(d, includePRS=True)
+
+    R_map, H = {}, []
+    for i in R:
+        R_map[i.degree()] = i
+
+    r = Poly(r, z)
+    Np, Sp = splitfactor_sqf(r, DE, coefficientD=True, z=z)
+
+    for s, i in Sp:
+        if i == d.degree(DE.t):
+            s = Poly(s, z).monic()
+            H.append((s, d))
+        else:
+            h = R_map.get(i)
+            if h is None:
+                continue
+            h_lc = Poly(h.as_poly(DE.t).LC(), DE.t, field=True)
+
+            h_lc_sqf = h_lc.sqf_list_include(all=True)
+
+            for a, j in h_lc_sqf:
+                h = Poly(h, DE.t, field=True).exquo(Poly(gcd(a, s**j, *kkinv),
+                    DE.t))
+
+            s = Poly(s, z).monic()
+
+            if invert:
+                h_lc = Poly(h.as_poly(DE.t).LC(), DE.t, field=True, expand=False)
+                inv, coeffs = h_lc.as_poly(z, field=True).invert(s), [S.One]
+
+                for coeff in h.coeffs()[1:]:
+                    L = reduced(inv*coeff.as_poly(inv.gens), [s])[1]
+                    coeffs.append(L.as_expr())
+
+                h = Poly(dict(list(zip(h.monoms(), coeffs))), DE.t)
+
+            H.append((s, h))
+
+    b = not any(cancel(i.as_expr()).has(DE.t, z) for i, _ in Np)
+
+    return (H, b)
+
+
+def residue_reduce_to_basic(H, DE, z):
+    """
+    Converts the tuple returned by residue_reduce() into a Basic expression.
+    """
+    # TODO: check what Lambda does with RootOf
+    i = Dummy('i')
+    s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs])))
+
+    return sum(RootSum(a[0].as_poly(z), Lambda(i, i*log(a[1].as_expr()).subs(
+        {z: i}).subs(s))) for a in H)
+
+
+def residue_reduce_derivation(H, DE, z):
+    """
+    Computes the derivation of an expression returned by residue_reduce().
+
+    In general, this is a rational function in t, so this returns an
+    as_expr() result.
+    """
+    # TODO: verify that this is correct for multiple extensions
+    i = Dummy('i')
+    return S(sum(RootSum(a[0].as_poly(z), Lambda(i, i*derivation(a[1],
+        DE).as_expr().subs(z, i)/a[1].as_expr().subs(z, i))) for a in H))
+
+
+def integrate_primitive_polynomial(p, DE):
+    """
+    Integration of primitive polynomials.
+
+    Explanation
+    ===========
+
+    Given a primitive monomial t over k, and ``p`` in k[t], return q in k[t],
+    r in k, and a bool b in {True, False} such that r = p - Dq is in k if b is
+    True, or r = p - Dq does not have an elementary integral over k(t) if b is
+    False.
+    """
+    Zero = Poly(0, DE.t)
+    q = Poly(0, DE.t)
+
+    if not p.expr.has(DE.t):
+        return (Zero, p, True)
+
+    from .prde import limited_integrate
+    while True:
+        if not p.expr.has(DE.t):
+            return (q, p, True)
+
+        Dta, Dtb = frac_in(DE.d, DE.T[DE.level - 1])
+
+        with DecrementLevel(DE):  # We had better be integrating the lowest extension (x)
+                                  # with ratint().
+            a = p.LC()
+            aa, ad = frac_in(a, DE.t)
+
+            try:
+                rv = limited_integrate(aa, ad, [(Dta, Dtb)], DE)
+                if rv is None:
+                    raise NonElementaryIntegralException
+                (ba, bd), c = rv
+            except NonElementaryIntegralException:
+                return (q, p, False)
+
+        m = p.degree(DE.t)
+        q0 = c[0].as_poly(DE.t)*Poly(DE.t**(m + 1)/(m + 1), DE.t) + \
+            (ba.as_expr()/bd.as_expr()).as_poly(DE.t)*Poly(DE.t**m, DE.t)
+
+        p = p - derivation(q0, DE)
+        q = q + q0
+
+
+def integrate_primitive(a, d, DE, z=None):
+    """
+    Integration of primitive functions.
+
+    Explanation
+    ===========
+
+    Given a primitive monomial t over k and f in k(t), return g elementary over
+    k(t), i in k(t), and b in {True, False} such that i = f - Dg is in k if b
+    is True or i = f - Dg does not have an elementary integral over k(t) if b
+    is False.
+
+    This function returns a Basic expression for the first argument.  If b is
+    True, the second argument is Basic expression in k to recursively integrate.
+    If b is False, the second argument is an unevaluated Integral, which has
+    been proven to be nonelementary.
+    """
+    # XXX: a and d must be canceled, or this might return incorrect results
+    z = z or Dummy("z")
+    s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs])))
+
+    g1, h, r = hermite_reduce(a, d, DE)
+    g2, b = residue_reduce(h[0], h[1], DE, z=z)
+    if not b:
+        i = cancel(a.as_expr()/d.as_expr() - (g1[1]*derivation(g1[0], DE) -
+            g1[0]*derivation(g1[1], DE)).as_expr()/(g1[1]**2).as_expr() -
+            residue_reduce_derivation(g2, DE, z))
+        i = NonElementaryIntegral(cancel(i).subs(s), DE.x)
+        return ((g1[0].as_expr()/g1[1].as_expr()).subs(s) +
+            residue_reduce_to_basic(g2, DE, z), i, b)
+
+    # h - Dg2 + r
+    p = cancel(h[0].as_expr()/h[1].as_expr() - residue_reduce_derivation(g2,
+        DE, z) + r[0].as_expr()/r[1].as_expr())
+    p = p.as_poly(DE.t)
+
+    q, i, b = integrate_primitive_polynomial(p, DE)
+
+    ret = ((g1[0].as_expr()/g1[1].as_expr() + q.as_expr()).subs(s) +
+        residue_reduce_to_basic(g2, DE, z))
+    if not b:
+        # TODO: This does not do the right thing when b is False
+        i = NonElementaryIntegral(cancel(i.as_expr()).subs(s), DE.x)
+    else:
+        i = cancel(i.as_expr())
+
+    return (ret, i, b)
+
+
+def integrate_hyperexponential_polynomial(p, DE, z):
+    """
+    Integration of hyperexponential polynomials.
+
+    Explanation
+    ===========
+
+    Given a hyperexponential monomial t over k and ``p`` in k[t, 1/t], return q in
+    k[t, 1/t] and a bool b in {True, False} such that p - Dq in k if b is True,
+    or p - Dq does not have an elementary integral over k(t) if b is False.
+    """
+    t1 = DE.t
+    dtt = DE.d.exquo(Poly(DE.t, DE.t))
+    qa = Poly(0, DE.t)
+    qd = Poly(1, DE.t)
+    b = True
+
+    if p.is_zero:
+        return(qa, qd, b)
+
+    from sympy.integrals.rde import rischDE
+
+    with DecrementLevel(DE):
+        for i in range(-p.degree(z), p.degree(t1) + 1):
+            if not i:
+                continue
+            elif i < 0:
+                # If you get AttributeError: 'NoneType' object has no attribute 'nth'
+                # then this should really not have expand=False
+                # But it shouldn't happen because p is already a Poly in t and z
+                a = p.as_poly(z, expand=False).nth(-i)
+            else:
+                # If you get AttributeError: 'NoneType' object has no attribute 'nth'
+                # then this should really not have expand=False
+                a = p.as_poly(t1, expand=False).nth(i)
+
+            aa, ad = frac_in(a, DE.t, field=True)
+            aa, ad = aa.cancel(ad, include=True)
+            iDt = Poly(i, t1)*dtt
+            iDta, iDtd = frac_in(iDt, DE.t, field=True)
+            try:
+                va, vd = rischDE(iDta, iDtd, Poly(aa, DE.t), Poly(ad, DE.t), DE)
+                va, vd = frac_in((va, vd), t1, cancel=True)
+            except NonElementaryIntegralException:
+                b = False
+            else:
+                qa = qa*vd + va*Poly(t1**i)*qd
+                qd *= vd
+
+    return (qa, qd, b)
+
+
+def integrate_hyperexponential(a, d, DE, z=None, conds='piecewise'):
+    """
+    Integration of hyperexponential functions.
+
+    Explanation
+    ===========
+
+    Given a hyperexponential monomial t over k and f in k(t), return g
+    elementary over k(t), i in k(t), and a bool b in {True, False} such that
+    i = f - Dg is in k if b is True or i = f - Dg does not have an elementary
+    integral over k(t) if b is False.
+
+    This function returns a Basic expression for the first argument.  If b is
+    True, the second argument is Basic expression in k to recursively integrate.
+    If b is False, the second argument is an unevaluated Integral, which has
+    been proven to be nonelementary.
+    """
+    # XXX: a and d must be canceled, or this might return incorrect results
+    z = z or Dummy("z")
+    s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs])))
+
+    g1, h, r = hermite_reduce(a, d, DE)
+    g2, b = residue_reduce(h[0], h[1], DE, z=z)
+    if not b:
+        i = cancel(a.as_expr()/d.as_expr() - (g1[1]*derivation(g1[0], DE) -
+            g1[0]*derivation(g1[1], DE)).as_expr()/(g1[1]**2).as_expr() -
+            residue_reduce_derivation(g2, DE, z))
+        i = NonElementaryIntegral(cancel(i.subs(s)), DE.x)
+        return ((g1[0].as_expr()/g1[1].as_expr()).subs(s) +
+            residue_reduce_to_basic(g2, DE, z), i, b)
+
+    # p should be a polynomial in t and 1/t, because Sirr == k[t, 1/t]
+    # h - Dg2 + r
+    p = cancel(h[0].as_expr()/h[1].as_expr() - residue_reduce_derivation(g2,
+        DE, z) + r[0].as_expr()/r[1].as_expr())
+    pp = as_poly_1t(p, DE.t, z)
+
+    qa, qd, b = integrate_hyperexponential_polynomial(pp, DE, z)
+
+    i = pp.nth(0, 0)
+
+    ret = ((g1[0].as_expr()/g1[1].as_expr()).subs(s) \
+        + residue_reduce_to_basic(g2, DE, z))
+
+    qas = qa.as_expr().subs(s)
+    qds = qd.as_expr().subs(s)
+    if conds == 'piecewise' and DE.x not in qds.free_symbols:
+        # We have to be careful if the exponent is S.Zero!
+
+        # XXX: Does qd = 0 always necessarily correspond to the exponential
+        # equaling 1?
+        ret += Piecewise(
+                (qas/qds, Ne(qds, 0)),
+                (integrate((p - i).subs(DE.t, 1).subs(s), DE.x), True)
+            )
+    else:
+        ret += qas/qds
+
+    if not b:
+        i = p - (qd*derivation(qa, DE) - qa*derivation(qd, DE)).as_expr()/\
+            (qd**2).as_expr()
+        i = NonElementaryIntegral(cancel(i).subs(s), DE.x)
+    return (ret, i, b)
+
+
+def integrate_hypertangent_polynomial(p, DE):
+    """
+    Integration of hypertangent polynomials.
+
+    Explanation
+    ===========
+
+    Given a differential field k such that sqrt(-1) is not in k, a
+    hypertangent monomial t over k, and p in k[t], return q in k[t] and
+    c in k such that p - Dq - c*D(t**2 + 1)/(t**1 + 1) is in k and p -
+    Dq does not have an elementary integral over k(t) if Dc != 0.
+    """
+    # XXX: Make sure that sqrt(-1) is not in k.
+    q, r = polynomial_reduce(p, DE)
+    a = DE.d.exquo(Poly(DE.t**2 + 1, DE.t))
+    c = Poly(r.nth(1)/(2*a.as_expr()), DE.t)
+    return (q, c)
+
+
+def integrate_nonlinear_no_specials(a, d, DE, z=None):
+    """
+    Integration of nonlinear monomials with no specials.
+
+    Explanation
+    ===========
+
+    Given a nonlinear monomial t over k such that Sirr ({p in k[t] | p is
+    special, monic, and irreducible}) is empty, and f in k(t), returns g
+    elementary over k(t) and a Boolean b in {True, False} such that f - Dg is
+    in k if b == True, or f - Dg does not have an elementary integral over k(t)
+    if b == False.
+
+    This function is applicable to all nonlinear extensions, but in the case
+    where it returns b == False, it will only have proven that the integral of
+    f - Dg is nonelementary if Sirr is empty.
+
+    This function returns a Basic expression.
+    """
+    # TODO: Integral from k?
+    # TODO: split out nonelementary integral
+    # XXX: a and d must be canceled, or this might not return correct results
+    z = z or Dummy("z")
+    s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs])))
+
+    g1, h, r = hermite_reduce(a, d, DE)
+    g2, b = residue_reduce(h[0], h[1], DE, z=z)
+    if not b:
+        return ((g1[0].as_expr()/g1[1].as_expr()).subs(s) +
+            residue_reduce_to_basic(g2, DE, z), b)
+
+    # Because f has no specials, this should be a polynomial in t, or else
+    # there is a bug.
+    p = cancel(h[0].as_expr()/h[1].as_expr() - residue_reduce_derivation(g2,
+        DE, z).as_expr() + r[0].as_expr()/r[1].as_expr()).as_poly(DE.t)
+    q1, q2 = polynomial_reduce(p, DE)
+
+    if q2.expr.has(DE.t):
+        b = False
+    else:
+        b = True
+
+    ret = (cancel(g1[0].as_expr()/g1[1].as_expr() + q1.as_expr()).subs(s) +
+        residue_reduce_to_basic(g2, DE, z))
+    return (ret, b)
+
+
+class NonElementaryIntegral(Integral):
+    """
+    Represents a nonelementary Integral.
+
+    Explanation
+    ===========
+
+    If the result of integrate() is an instance of this class, it is
+    guaranteed to be nonelementary.  Note that integrate() by default will try
+    to find any closed-form solution, even in terms of special functions which
+    may themselves not be elementary.  To make integrate() only give
+    elementary solutions, or, in the cases where it can prove the integral to
+    be nonelementary, instances of this class, use integrate(risch=True).
+    In this case, integrate() may raise NotImplementedError if it cannot make
+    such a determination.
+
+    integrate() uses the deterministic Risch algorithm to integrate elementary
+    functions or prove that they have no elementary integral.  In some cases,
+    this algorithm can split an integral into an elementary and nonelementary
+    part, so that the result of integrate will be the sum of an elementary
+    expression and a NonElementaryIntegral.
+
+    Examples
+    ========
+
+    >>> from sympy import integrate, exp, log, Integral
+    >>> from sympy.abc import x
+
+    >>> a = integrate(exp(-x**2), x, risch=True)
+    >>> print(a)
+    Integral(exp(-x**2), x)
+    >>> type(a)
+    
+
+    >>> expr = (2*log(x)**2 - log(x) - x**2)/(log(x)**3 - x**2*log(x))
+    >>> b = integrate(expr, x, risch=True)
+    >>> print(b)
+    -log(-x + log(x))/2 + log(x + log(x))/2 + Integral(1/log(x), x)
+    >>> type(b.atoms(Integral).pop())
+    
+
+    """
+    # TODO: This is useful in and of itself, because isinstance(result,
+    # NonElementaryIntegral) will tell if the integral has been proven to be
+    # elementary. But should we do more?  Perhaps a no-op .doit() if
+    # elementary=True?  Or maybe some information on why the integral is
+    # nonelementary.
+    pass
+
+
+def risch_integrate(f, x, extension=None, handle_first='log',
+                    separate_integral=False, rewrite_complex=None,
+                    conds='piecewise'):
+    r"""
+    The Risch Integration Algorithm.
+
+    Explanation
+    ===========
+
+    Only transcendental functions are supported.  Currently, only exponentials
+    and logarithms are supported, but support for trigonometric functions is
+    forthcoming.
+
+    If this function returns an unevaluated Integral in the result, it means
+    that it has proven that integral to be nonelementary.  Any errors will
+    result in raising NotImplementedError.  The unevaluated Integral will be
+    an instance of NonElementaryIntegral, a subclass of Integral.
+
+    handle_first may be either 'exp' or 'log'.  This changes the order in
+    which the extension is built, and may result in a different (but
+    equivalent) solution (for an example of this, see issue 5109).  It is also
+    possible that the integral may be computed with one but not the other,
+    because not all cases have been implemented yet.  It defaults to 'log' so
+    that the outer extension is exponential when possible, because more of the
+    exponential case has been implemented.
+
+    If ``separate_integral`` is ``True``, the result is returned as a tuple (ans, i),
+    where the integral is ans + i, ans is elementary, and i is either a
+    NonElementaryIntegral or 0.  This useful if you want to try further
+    integrating the NonElementaryIntegral part using other algorithms to
+    possibly get a solution in terms of special functions.  It is False by
+    default.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.risch import risch_integrate
+    >>> from sympy import exp, log, pprint
+    >>> from sympy.abc import x
+
+    First, we try integrating exp(-x**2). Except for a constant factor of
+    2/sqrt(pi), this is the famous error function.
+
+    >>> pprint(risch_integrate(exp(-x**2), x))
+      /
+     |
+     |    2
+     |  -x
+     | e    dx
+     |
+    /
+
+    The unevaluated Integral in the result means that risch_integrate() has
+    proven that exp(-x**2) does not have an elementary anti-derivative.
+
+    In many cases, risch_integrate() can split out the elementary
+    anti-derivative part from the nonelementary anti-derivative part.
+    For example,
+
+    >>> pprint(risch_integrate((2*log(x)**2 - log(x) - x**2)/(log(x)**3 -
+    ... x**2*log(x)), x))
+                                             /
+                                            |
+      log(-x + log(x))   log(x + log(x))    |   1
+    - ---------------- + --------------- +  | ------ dx
+             2                  2           | log(x)
+                                            |
+                                           /
+
+    This means that it has proven that the integral of 1/log(x) is
+    nonelementary.  This function is also known as the logarithmic integral,
+    and is often denoted as Li(x).
+
+    risch_integrate() currently only accepts purely transcendental functions
+    with exponentials and logarithms, though note that this can include
+    nested exponentials and logarithms, as well as exponentials with bases
+    other than E.
+
+    >>> pprint(risch_integrate(exp(x)*exp(exp(x)), x))
+     / x\
+     \e /
+    e
+    >>> pprint(risch_integrate(exp(exp(x)), x))
+      /
+     |
+     |  / x\
+     |  \e /
+     | e     dx
+     |
+    /
+
+    >>> pprint(risch_integrate(x*x**x*log(x) + x**x + x*x**x, x))
+       x
+    x*x
+    >>> pprint(risch_integrate(x**x, x))
+      /
+     |
+     |  x
+     | x  dx
+     |
+    /
+
+    >>> pprint(risch_integrate(-1/(x*log(x)*log(log(x))**2), x))
+         1
+    -----------
+    log(log(x))
+
+    """
+    f = S(f)
+
+    DE = extension or DifferentialExtension(f, x, handle_first=handle_first,
+            dummy=True, rewrite_complex=rewrite_complex)
+    fa, fd = DE.fa, DE.fd
+
+    result = S.Zero
+    for case in reversed(DE.cases):
+        if not fa.expr.has(DE.t) and not fd.expr.has(DE.t) and not case == 'base':
+            DE.decrement_level()
+            fa, fd = frac_in((fa, fd), DE.t)
+            continue
+
+        fa, fd = fa.cancel(fd, include=True)
+        if case == 'exp':
+            ans, i, b = integrate_hyperexponential(fa, fd, DE, conds=conds)
+        elif case == 'primitive':
+            ans, i, b = integrate_primitive(fa, fd, DE)
+        elif case == 'base':
+            # XXX: We can't call ratint() directly here because it doesn't
+            # handle polynomials correctly.
+            ans = integrate(fa.as_expr()/fd.as_expr(), DE.x, risch=False)
+            b = False
+            i = S.Zero
+        else:
+            raise NotImplementedError("Only exponential and logarithmic "
+            "extensions are currently supported.")
+
+        result += ans
+        if b:
+            DE.decrement_level()
+            fa, fd = frac_in(i, DE.t)
+        else:
+            result = result.subs(DE.backsubs)
+            if not i.is_zero:
+                i = NonElementaryIntegral(i.function.subs(DE.backsubs),i.limits)
+            if not separate_integral:
+                result += i
+                return result
+            else:
+
+                if isinstance(i, NonElementaryIntegral):
+                    return (result, i)
+                else:
+                    return (result, 0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/singularityfunctions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/singularityfunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e33d0542c45b67b193f17e00c25837f3a82109a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/singularityfunctions.py
@@ -0,0 +1,63 @@
+from sympy.functions import SingularityFunction, DiracDelta
+from sympy.integrals import integrate
+
+
+def singularityintegrate(f, x):
+    """
+    This function handles the indefinite integrations of Singularity functions.
+    The ``integrate`` function calls this function internally whenever an
+    instance of SingularityFunction is passed as argument.
+
+    Explanation
+    ===========
+
+    The idea for integration is the following:
+
+    - If we are dealing with a SingularityFunction expression,
+      i.e. ``SingularityFunction(x, a, n)``, we just return
+      ``SingularityFunction(x, a, n + 1)/(n + 1)`` if ``n >= 0`` and
+      ``SingularityFunction(x, a, n + 1)`` if ``n < 0``.
+
+    - If the node is a multiplication or power node having a
+      SingularityFunction term we rewrite the whole expression in terms of
+      Heaviside and DiracDelta and then integrate the output. Lastly, we
+      rewrite the output of integration back in terms of SingularityFunction.
+
+    - If none of the above case arises, we return None.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.singularityfunctions import singularityintegrate
+    >>> from sympy import SingularityFunction, symbols, Function
+    >>> x, a, n, y = symbols('x a n y')
+    >>> f = Function('f')
+    >>> singularityintegrate(SingularityFunction(x, a, 3), x)
+    SingularityFunction(x, a, 4)/4
+    >>> singularityintegrate(5*SingularityFunction(x, 5, -2), x)
+    5*SingularityFunction(x, 5, -1)
+    >>> singularityintegrate(6*SingularityFunction(x, 5, -1), x)
+    6*SingularityFunction(x, 5, 0)
+    >>> singularityintegrate(x*SingularityFunction(x, 0, -1), x)
+    0
+    >>> singularityintegrate(SingularityFunction(x, 1, -1) * f(x), x)
+    f(1)*SingularityFunction(x, 1, 0)
+
+    """
+
+    if not f.has(SingularityFunction):
+        return None
+
+    if isinstance(f, SingularityFunction):
+        x, a, n = f.args
+        if n.is_positive or n.is_zero:
+            return SingularityFunction(x, a, n + 1)/(n + 1)
+        elif n in (-1, -2, -3, -4):
+            return SingularityFunction(x, a, n + 1)
+
+    if f.is_Mul or f.is_Pow:
+
+        expr = f.rewrite(DiracDelta)
+        expr = integrate(expr, x)
+        return expr.rewrite(SingularityFunction)
+    return None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_deltafunctions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_deltafunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..d4fd567349b50f795e08d583fd08db67b1596577
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_deltafunctions.py
@@ -0,0 +1,79 @@
+from sympy.core.function import Function
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.delta_functions import (DiracDelta, Heaviside)
+from sympy.integrals.deltafunctions import change_mul, deltaintegrate
+
+f = Function("f")
+x_1, x_2, x, y, z = symbols("x_1 x_2 x y z")
+
+
+def test_change_mul():
+    assert change_mul(x, x) == (None, None)
+    assert change_mul(x*y, x) == (None, None)
+    assert change_mul(x*y*DiracDelta(x), x) == (DiracDelta(x), x*y)
+    assert change_mul(x*y*DiracDelta(x)*DiracDelta(y), x) == \
+        (DiracDelta(x), x*y*DiracDelta(y))
+    assert change_mul(DiracDelta(x)**2, x) == \
+        (DiracDelta(x), DiracDelta(x))
+    assert change_mul(y*DiracDelta(x)**2, x) == \
+        (DiracDelta(x), y*DiracDelta(x))
+
+
+def test_deltaintegrate():
+    assert deltaintegrate(x, x) is None
+    assert deltaintegrate(x + DiracDelta(x), x) is None
+    assert deltaintegrate(DiracDelta(x, 0), x) == Heaviside(x)
+    for n in range(10):
+        assert deltaintegrate(DiracDelta(x, n + 1), x) == DiracDelta(x, n)
+    assert deltaintegrate(DiracDelta(x), x) == Heaviside(x)
+    assert deltaintegrate(DiracDelta(-x), x) == Heaviside(x)
+    assert deltaintegrate(DiracDelta(x - y), x) == Heaviside(x - y)
+    assert deltaintegrate(DiracDelta(y - x), x) == Heaviside(x - y)
+
+    assert deltaintegrate(x*DiracDelta(x), x) == 0
+    assert deltaintegrate((x - y)*DiracDelta(x - y), x) == 0
+
+    assert deltaintegrate(DiracDelta(x)**2, x) == DiracDelta(0)*Heaviside(x)
+    assert deltaintegrate(y*DiracDelta(x)**2, x) == \
+        y*DiracDelta(0)*Heaviside(x)
+    assert deltaintegrate(DiracDelta(x, 1), x) == DiracDelta(x, 0)
+    assert deltaintegrate(y*DiracDelta(x, 1), x) == y*DiracDelta(x, 0)
+    assert deltaintegrate(DiracDelta(x, 1)**2, x) == -DiracDelta(0, 2)*Heaviside(x)
+    assert deltaintegrate(y*DiracDelta(x, 1)**2, x) == -y*DiracDelta(0, 2)*Heaviside(x)
+
+
+    assert deltaintegrate(DiracDelta(x) * f(x), x) == f(0) * Heaviside(x)
+    assert deltaintegrate(DiracDelta(-x) * f(x), x) == f(0) * Heaviside(x)
+    assert deltaintegrate(DiracDelta(x - 1) * f(x), x) == f(1) * Heaviside(x - 1)
+    assert deltaintegrate(DiracDelta(1 - x) * f(x), x) == f(1) * Heaviside(x - 1)
+    assert deltaintegrate(DiracDelta(x**2 + x - 2), x) == \
+        Heaviside(x - 1)/3 + Heaviside(x + 2)/3
+
+    p = cos(x)*(DiracDelta(x) + DiracDelta(x**2 - 1))*sin(x)*(x - pi)
+    assert deltaintegrate(p, x) - (-pi*(cos(1)*Heaviside(-1 + x)*sin(1)/2 - \
+        cos(1)*Heaviside(1 + x)*sin(1)/2) + \
+        cos(1)*Heaviside(1 + x)*sin(1)/2 + \
+        cos(1)*Heaviside(-1 + x)*sin(1)/2) == 0
+
+    p = x_2*DiracDelta(x - x_2)*DiracDelta(x_2 - x_1)
+    assert deltaintegrate(p, x_2) == x*DiracDelta(x - x_1)*Heaviside(x_2 - x)
+
+    p = x*y**2*z*DiracDelta(y - x)*DiracDelta(y - z)*DiracDelta(x - z)
+    assert deltaintegrate(p, y) == x**3*z*DiracDelta(x - z)**2*Heaviside(y - x)
+    assert deltaintegrate((x + 1)*DiracDelta(2*x), x) == S.Half * Heaviside(x)
+    assert deltaintegrate((x + 1)*DiracDelta(x*Rational(2, 3) + Rational(4, 9)), x) == \
+        S.Half * Heaviside(x + Rational(2, 3))
+
+    a, b, c = symbols('a b c', commutative=False)
+    assert deltaintegrate(DiracDelta(x - y)*f(x - b)*f(x - a), x) == \
+        f(y - b)*f(y - a)*Heaviside(x - y)
+
+    p = f(x - a)*DiracDelta(x - y)*f(x - c)*f(x - b)
+    assert deltaintegrate(p, x) == f(y - a)*f(y - c)*f(y - b)*Heaviside(x - y)
+
+    p = DiracDelta(x - z)*f(x - b)*f(x - a)*DiracDelta(x - y)
+    assert deltaintegrate(p, x) == DiracDelta(y - z)*f(y - b)*f(y - a) * \
+        Heaviside(x - y)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_failing_integrals.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_failing_integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..9bb434cf0009cd96ad2b7882d109b7fbe23193c2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_failing_integrals.py
@@ -0,0 +1,277 @@
+# A collection of failing integrals from the issues.
+
+from sympy.core.numbers import (I, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.complexes import sign
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (sech, sinh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (acos, atan, cos, sin, tan)
+from sympy.functions.special.delta_functions import DiracDelta
+from sympy.functions.special.gamma_functions import gamma
+from sympy.integrals.integrals import (Integral, integrate)
+from sympy.simplify.fu import fu
+
+
+from sympy.testing.pytest import XFAIL, slow, tooslow
+
+from sympy.abc import x, k, c, y, b, h, a, m, z, n, t
+
+
+@tooslow
+@XFAIL
+def test_issue_3880():
+    # integrate_hyperexponential(Poly(t*2*(1 - t0**2)*t0*(x**3 + x**2), t), Poly((1 + t0**2)**2*2*(x**2 + x + 1), t), [Poly(1, x), Poly(1 + t0**2, t0), Poly(t, t)], [x, t0, t], [exp, tan])
+    assert not integrate(exp(x)*cos(2*x)*sin(2*x) * (x**3 + x**2)/(2*(x**2 + x + 1)), x).has(Integral)
+
+
+def test_issue_4212_real():
+    xr = symbols('xr', real=True)
+    negabsx = Piecewise((-xr, xr < 0), (xr, True))
+    assert integrate(sign(xr), xr) == negabsx
+
+
+@XFAIL
+def test_issue_4212():
+    # XXX: Maybe this should be expected to fail without real assumptions on x.
+    # As a complex function sign(x) is not analytic and so there is no complex
+    # function whose complex derivative is sign(x). With real assumptions this
+    # works (see test_issue_4212_real above).
+    assert not integrate(sign(x), x).has(Integral)
+
+
+def test_issue_4511():
+    # This works, but gives a slightly over-complicated answer.
+    f = integrate(cos(x)**2 / (1 - sin(x)), x)
+    assert fu(f) == x - cos(x) - 1
+    assert f == ((x*tan(x/2)**2 + x - 2)/(tan(x/2)**2 + 1)).expand()
+
+
+def test_integrate_DiracDelta_no_meijerg():
+    assert integrate(integrate(integrate(
+        DiracDelta(x - y - z), (z, 0, oo)), (y, 0, 1), meijerg=False), (x, 0, 1)) == S.Half
+
+
+@XFAIL
+def test_integrate_DiracDelta_fails():
+    # issue 6427
+    # works without meijerg. See test_integrate_DiracDelta_no_meijerg above.
+    assert integrate(integrate(integrate(
+        DiracDelta(x - y - z), (z, 0, oo)), (y, 0, 1)), (x, 0, 1)) == S.Half
+
+
+@XFAIL
+@slow
+def test_issue_4525():
+    # Warning: takes a long time
+    assert not integrate((x**m * (1 - x)**n * (a + b*x + c*x**2))/(1 + x**2), (x, 0, 1)).has(Integral)
+
+
+@XFAIL
+@tooslow
+def test_issue_4540():
+    # Note, this integral is probably nonelementary
+    assert not integrate(
+        (sin(1/x) - x*exp(x)) /
+        ((-sin(1/x) + x*exp(x))*x + x*sin(1/x)), x).has(Integral)
+
+
+@XFAIL
+@slow
+def test_issue_4891():
+    # Requires the hypergeometric function.
+    assert not integrate(cos(x)**y, x).has(Integral)
+
+
+@XFAIL
+@slow
+def test_issue_1796a():
+    assert not integrate(exp(2*b*x)*exp(-a*x**2), x).has(Integral)
+
+
+@XFAIL
+def test_issue_4895b():
+    assert not integrate(exp(2*b*x)*exp(-a*x**2), (x, -oo, 0)).has(Integral)
+
+
+@XFAIL
+def test_issue_4895c():
+    assert not integrate(exp(2*b*x)*exp(-a*x**2), (x, -oo, oo)).has(Integral)
+
+
+@XFAIL
+def test_issue_4895d():
+    assert not integrate(exp(2*b*x)*exp(-a*x**2), (x, 0, oo)).has(Integral)
+
+
+@XFAIL
+@slow
+def test_issue_4941():
+    assert not integrate(sqrt(1 + sinh(x/20)**2), (x, -25, 25)).has(Integral)
+
+
+@XFAIL
+def test_issue_4992():
+    # Nonelementary integral.  Requires hypergeometric/Meijer-G handling.
+    assert not integrate(log(x) * x**(k - 1) * exp(-x) / gamma(k), (x, 0, oo)).has(Integral)
+
+
+@XFAIL
+def test_issue_16396a():
+    i = integrate(1/(1+sqrt(tan(x))), (x, pi/3, pi/6))
+    assert not i.has(Integral)
+
+
+@XFAIL
+def test_issue_16396b():
+    i = integrate(x*sin(x)/(1+cos(x)**2), (x, 0, pi))
+    assert not i.has(Integral)
+
+
+@XFAIL
+def test_issue_16046():
+    assert integrate(exp(exp(I*x)), [x, 0, 2*pi]) == 2*pi
+
+
+@XFAIL
+def test_issue_15925a():
+    assert not integrate(sqrt((1+sin(x))**2+(cos(x))**2), (x, -pi/2, pi/2)).has(Integral)
+
+
+def test_issue_15925b():
+    f = sqrt((-12*cos(x)**2*sin(x))**2+(12*cos(x)*sin(x)**2)**2)
+    assert integrate(f, (x, 0, pi/6)) == Rational(3, 2)
+
+
+@XFAIL
+def test_issue_15925b_manual():
+    assert not integrate(sqrt((-12*cos(x)**2*sin(x))**2+(12*cos(x)*sin(x)**2)**2),
+                         (x, 0, pi/6), manual=True).has(Integral)
+
+
+@XFAIL
+@tooslow
+def test_issue_15227():
+    i = integrate(log(1-x)*log((1+x)**2)/x, (x, 0, 1))
+    assert not i.has(Integral)
+    # assert i == -5*zeta(3)/4
+
+
+@XFAIL
+@slow
+def test_issue_14716():
+    i = integrate(log(x + 5)*cos(pi*x),(x, S.Half, 1))
+    assert not i.has(Integral)
+    # Mathematica can not solve it either, but
+    # integrate(log(x + 5)*cos(pi*x),(x, S.Half, 1)).transform(x, y - 5).doit()
+    # works
+    # assert i == -log(Rational(11, 2))/pi - Si(pi*Rational(11, 2))/pi + Si(6*pi)/pi
+
+
+@XFAIL
+def test_issue_14709a():
+    i = integrate(x*acos(1 - 2*x/h), (x, 0, h))
+    assert not i.has(Integral)
+    # assert i == 5*h**2*pi/16
+
+
+@slow
+@XFAIL
+def test_issue_14398():
+    assert not integrate(exp(x**2)*cos(x), x).has(Integral)
+
+
+@XFAIL
+def test_issue_14074():
+    i = integrate(log(sin(x)), (x, 0, pi/2))
+    assert not i.has(Integral)
+    # assert i == -pi*log(2)/2
+
+
+@XFAIL
+@slow
+def test_issue_14078b():
+    i = integrate((atan(4*x)-atan(2*x))/x, (x, 0, oo))
+    assert not i.has(Integral)
+    # assert i == pi*log(2)/2
+
+
+@XFAIL
+def test_issue_13792():
+    i =  integrate(log(1/x) / (1 - x), (x, 0, 1))
+    assert not i.has(Integral)
+    # assert i in [polylog(2, -exp_polar(I*pi)), pi**2/6]
+
+
+@XFAIL
+def test_issue_11845a():
+    assert not integrate(exp(y - x**3), (x, 0, 1)).has(Integral)
+
+
+@XFAIL
+def test_issue_11845b():
+    assert not integrate(exp(-y - x**3), (x, 0, 1)).has(Integral)
+
+
+@XFAIL
+def test_issue_11813():
+    assert not integrate((a - x)**Rational(-1, 2)*x, (x, 0, a)).has(Integral)
+
+
+@XFAIL
+def test_issue_11254c():
+    assert not integrate(sech(x)**2, (x, 0, 1)).has(Integral)
+
+
+@XFAIL
+def test_issue_10584():
+    assert not integrate(sqrt(x**2 + 1/x**2), x).has(Integral)
+
+
+@XFAIL
+def test_issue_9101():
+    assert not integrate(log(x + sqrt(x**2 + y**2 + z**2)), z).has(Integral)
+
+
+@XFAIL
+def test_issue_7147():
+    assert not integrate(x/sqrt(a*x**2 + b*x + c)**3, x).has(Integral)
+
+
+@XFAIL
+def test_issue_7109():
+    assert not integrate(sqrt(a**2/(a**2 - x**2)), x).has(Integral)
+
+
+@XFAIL
+def test_integrate_Piecewise_rational_over_reals():
+    f = Piecewise(
+        (0,                                              t - 478.515625*pi <  0),
+        (13.2075145209219*pi/(0.000871222*t + 0.995)**2, t - 478.515625*pi >= 0))
+
+    assert abs((integrate(f, (t, 0, oo)) - 15235.9375*pi).evalf()) <= 1e-7
+
+
+@XFAIL
+def test_issue_4311_slow():
+    # Not slow when bypassing heurish
+    assert not integrate(x*abs(9-x**2), x).has(Integral)
+
+@XFAIL
+def test_issue_20370():
+    a = symbols('a', positive=True)
+    assert integrate((1 + a * cos(x))**-1, (x, 0, 2 * pi)) == (2 * pi / sqrt(1 - a**2))
+
+
+@XFAIL
+def test_polylog():
+    # log(1/x)*log(x+1)-polylog(2, -x)
+    assert not integrate(log(1/x)/(x + 1), x).has(Integral)
+
+
+@XFAIL
+def test_polylog_manual():
+    # Make sure _parts_rule does not go into an infinite loop here
+    assert not integrate(log(1/x)/(x + 1), x, manual=True).has(Integral)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_heurisch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_heurisch.py
new file mode 100644
index 0000000000000000000000000000000000000000..f02556dedd597721529cab47bf53609110e0ce2a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_heurisch.py
@@ -0,0 +1,417 @@
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.relational import Eq, Ne
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.exponential import (LambertW, exp, log)
+from sympy.functions.elementary.hyperbolic import (asinh, cosh, sinh, tanh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (acos, asin, atan, cos, sin, tan)
+from sympy.functions.special.bessel import (besselj, besselk, bessely, jn)
+from sympy.functions.special.error_functions import erf
+from sympy.integrals.integrals import Integral
+from sympy.logic.boolalg import And
+from sympy.matrices import Matrix
+from sympy.simplify.ratsimp import ratsimp
+from sympy.simplify.simplify import simplify
+from sympy.integrals.heurisch import components, heurisch, heurisch_wrapper
+from sympy.testing.pytest import XFAIL, slow
+from sympy.integrals.integrals import integrate
+from sympy import S
+
+x, y, z, nu = symbols('x,y,z,nu')
+f = Function('f')
+
+
+def test_components():
+    assert components(x*y, x) == {x}
+    assert components(1/(x + y), x) == {x}
+    assert components(sin(x), x) == {sin(x), x}
+    assert components(sin(x)*sqrt(log(x)), x) == \
+        {log(x), sin(x), sqrt(log(x)), x}
+    assert components(x*sin(exp(x)*y), x) == \
+        {sin(y*exp(x)), x, exp(x)}
+    assert components(x**Rational(17, 54)/sqrt(sin(x)), x) == \
+        {sin(x), x**Rational(1, 54), sqrt(sin(x)), x}
+
+    assert components(f(x), x) == \
+        {x, f(x)}
+    assert components(Derivative(f(x), x), x) == \
+        {x, f(x), Derivative(f(x), x)}
+    assert components(f(x)*diff(f(x), x), x) == \
+        {x, f(x), Derivative(f(x), x), Derivative(f(x), x)}
+
+
+def test_issue_10680():
+    assert isinstance(integrate(x**log(x**log(x**log(x))),x), Integral)
+
+
+def test_issue_21166():
+    assert integrate(sin(x/sqrt(abs(x))), (x, -1, 1)) == 0
+
+
+def test_heurisch_polynomials():
+    assert heurisch(1, x) == x
+    assert heurisch(x, x) == x**2/2
+    assert heurisch(x**17, x) == x**18/18
+    # For coverage
+    assert heurisch_wrapper(y, x) == y*x
+
+
+def test_heurisch_fractions():
+    assert heurisch(1/x, x) == log(x)
+    assert heurisch(1/(2 + x), x) == log(x + 2)
+    assert heurisch(1/(x + sin(y)), x) == log(x + sin(y))
+
+    # Up to a constant, where C = pi*I*Rational(5, 12), Mathematica gives identical
+    # result in the first case. The difference is because SymPy changes
+    # signs of expressions without any care.
+    # XXX ^ ^ ^ is this still correct?
+    assert heurisch(5*x**5/(
+        2*x**6 - 5), x) in [5*log(2*x**6 - 5) / 12, 5*log(-2*x**6 + 5) / 12]
+    assert heurisch(5*x**5/(2*x**6 + 5), x) == 5*log(2*x**6 + 5) / 12
+
+    assert heurisch(1/x**2, x) == -1/x
+    assert heurisch(-1/x**5, x) == 1/(4*x**4)
+
+
+def test_heurisch_log():
+    assert heurisch(log(x), x) == x*log(x) - x
+    assert heurisch(log(3*x), x) == -x + x*log(3) + x*log(x)
+    assert heurisch(log(x**2), x) in [x*log(x**2) - 2*x, 2*x*log(x) - 2*x]
+
+
+def test_heurisch_exp():
+    assert heurisch(exp(x), x) == exp(x)
+    assert heurisch(exp(-x), x) == -exp(-x)
+    assert heurisch(exp(17*x), x) == exp(17*x) / 17
+    assert heurisch(x*exp(x), x) == x*exp(x) - exp(x)
+    assert heurisch(x*exp(x**2), x) == exp(x**2) / 2
+
+    assert heurisch(exp(-x**2), x) is None
+
+    assert heurisch(2**x, x) == 2**x/log(2)
+    assert heurisch(x*2**x, x) == x*2**x/log(2) - 2**x*log(2)**(-2)
+
+    assert heurisch(Integral(x**z*y, (y, 1, 2), (z, 2, 3)).function, x) == (x*x**z*y)/(z+1)
+    assert heurisch(Sum(x**z, (z, 1, 2)).function, z) == x**z/log(x)
+
+    # https://github.com/sympy/sympy/issues/23707
+    anti = -exp(z)/(sqrt(x - y)*exp(z*sqrt(x - y)) - exp(z*sqrt(x - y)))
+    assert heurisch(exp(z)*exp(-z*sqrt(x - y)), z) == anti
+
+
+def test_heurisch_trigonometric():
+    assert heurisch(sin(x), x) == -cos(x)
+    assert heurisch(pi*sin(x) + 1, x) == x - pi*cos(x)
+
+    assert heurisch(cos(x), x) == sin(x)
+    assert heurisch(tan(x), x) in [
+        log(1 + tan(x)**2)/2,
+        log(tan(x) + I) + I*x,
+        log(tan(x) - I) - I*x,
+    ]
+
+    assert heurisch(sin(x)*sin(y), x) == -cos(x)*sin(y)
+    assert heurisch(sin(x)*sin(y), y) == -cos(y)*sin(x)
+
+    # gives sin(x) in answer when run via setup.py and cos(x) when run via py.test
+    assert heurisch(sin(x)*cos(x), x) in [sin(x)**2 / 2, -cos(x)**2 / 2]
+    assert heurisch(cos(x)/sin(x), x) == log(sin(x))
+
+    assert heurisch(x*sin(7*x), x) == sin(7*x) / 49 - x*cos(7*x) / 7
+    assert heurisch(1/pi/4 * x**2*cos(x), x) == 1/pi/4*(x**2*sin(x) -
+                    2*sin(x) + 2*x*cos(x))
+
+    assert heurisch(acos(x/4) * asin(x/4), x) == 2*x - (sqrt(16 - x**2))*asin(x/4) \
+        + (sqrt(16 - x**2))*acos(x/4) + x*asin(x/4)*acos(x/4)
+
+    assert heurisch(sin(x)/(cos(x)**2+1), x) == -atan(cos(x)) #fixes issue 13723
+    assert heurisch(1/(cos(x)+2), x) == 2*sqrt(3)*atan(sqrt(3)*tan(x/2)/3)/3
+    assert heurisch(2*sin(x)*cos(x)/(sin(x)**4 + 1), x) == atan(sqrt(2)*sin(x)
+        - 1) - atan(sqrt(2)*sin(x) + 1)
+
+    assert heurisch(1/cosh(x), x) == 2*atan(tanh(x/2))
+
+
+def test_heurisch_hyperbolic():
+    assert heurisch(sinh(x), x) == cosh(x)
+    assert heurisch(cosh(x), x) == sinh(x)
+
+    assert heurisch(x*sinh(x), x) == x*cosh(x) - sinh(x)
+    assert heurisch(x*cosh(x), x) == x*sinh(x) - cosh(x)
+
+    assert heurisch(
+        x*asinh(x/2), x) == x**2*asinh(x/2)/2 + asinh(x/2) - x*sqrt(4 + x**2)/4
+
+
+def test_heurisch_mixed():
+    assert heurisch(sin(x)*exp(x), x) == exp(x)*sin(x)/2 - exp(x)*cos(x)/2
+    assert heurisch(sin(x/sqrt(-x)), x) == 2*x*cos(x/sqrt(-x))/sqrt(-x) - 2*sin(x/sqrt(-x))
+
+
+def test_heurisch_radicals():
+    assert heurisch(1/sqrt(x), x) == 2*sqrt(x)
+    assert heurisch(1/sqrt(x)**3, x) == -2/sqrt(x)
+    assert heurisch(sqrt(x)**3, x) == 2*sqrt(x)**5/5
+
+    assert heurisch(sin(x)*sqrt(cos(x)), x) == -2*sqrt(cos(x))**3/3
+    y = Symbol('y')
+    assert heurisch(sin(y*sqrt(x)), x) == 2/y**2*sin(y*sqrt(x)) - \
+        2*sqrt(x)*cos(y*sqrt(x))/y
+    assert heurisch_wrapper(sin(y*sqrt(x)), x) == Piecewise(
+        (-2*sqrt(x)*cos(sqrt(x)*y)/y + 2*sin(sqrt(x)*y)/y**2, Ne(y, 0)),
+        (0, True))
+    y = Symbol('y', positive=True)
+    assert heurisch_wrapper(sin(y*sqrt(x)), x) == 2/y**2*sin(y*sqrt(x)) - \
+        2*sqrt(x)*cos(y*sqrt(x))/y
+
+
+def test_heurisch_special():
+    assert heurisch(erf(x), x) == x*erf(x) + exp(-x**2)/sqrt(pi)
+    assert heurisch(exp(-x**2)*erf(x), x) == sqrt(pi)*erf(x)**2 / 4
+
+
+def test_heurisch_symbolic_coeffs():
+    assert heurisch(1/(x + y), x) == log(x + y)
+    assert heurisch(1/(x + sqrt(2)), x) == log(x + sqrt(2))
+    assert simplify(diff(heurisch(log(x + y + z), y), y)) == log(x + y + z)
+
+
+def test_heurisch_symbolic_coeffs_1130():
+    y = Symbol('y')
+    assert heurisch_wrapper(1/(x**2 + y), x) == Piecewise(
+    (log(x - sqrt(-y))/(2*sqrt(-y)) - log(x + sqrt(-y))/(2*sqrt(-y)),
+    Ne(y, 0)), (-1/x, True))
+    y = Symbol('y', positive=True)
+    assert heurisch_wrapper(1/(x**2 + y), x) == (atan(x/sqrt(y))/sqrt(y))
+
+
+def test_heurisch_hacking():
+    assert heurisch(sqrt(1 + 7*x**2), x, hints=[]) == \
+        x*sqrt(1 + 7*x**2)/2 + sqrt(7)*asinh(sqrt(7)*x)/14
+    assert heurisch(sqrt(1 - 7*x**2), x, hints=[]) == \
+        x*sqrt(1 - 7*x**2)/2 + sqrt(7)*asin(sqrt(7)*x)/14
+
+    assert heurisch(1/sqrt(1 + 7*x**2), x, hints=[]) == \
+        sqrt(7)*asinh(sqrt(7)*x)/7
+    assert heurisch(1/sqrt(1 - 7*x**2), x, hints=[]) == \
+        sqrt(7)*asin(sqrt(7)*x)/7
+
+    assert heurisch(exp(-7*x**2), x, hints=[]) == \
+        sqrt(7*pi)*erf(sqrt(7)*x)/14
+
+    assert heurisch(1/sqrt(9 - 4*x**2), x, hints=[]) == \
+        asin(x*Rational(2, 3))/2
+
+    assert heurisch(1/sqrt(9 + 4*x**2), x, hints=[]) == \
+        asinh(x*Rational(2, 3))/2
+
+    assert heurisch(1/sqrt(3*x**2-4), x, hints=[]) == \
+           sqrt(3)*log(3*x + sqrt(3)*sqrt(3*x**2 - 4))/3
+
+
+def test_heurisch_function():
+    assert heurisch(f(x), x) is None
+
+@XFAIL
+def test_heurisch_function_derivative():
+    # TODO: it looks like this used to work just by coincindence and
+    # thanks to sloppy implementation. Investigate why this used to
+    # work at all and if support for this can be restored.
+
+    df = diff(f(x), x)
+
+    assert heurisch(f(x)*df, x) == f(x)**2/2
+    assert heurisch(f(x)**2*df, x) == f(x)**3/3
+    assert heurisch(df/f(x), x) == log(f(x))
+
+
+def test_heurisch_wrapper():
+    f = 1/(y + x)
+    assert heurisch_wrapper(f, x) == log(x + y)
+    f = 1/(y - x)
+    assert heurisch_wrapper(f, x) == -log(x - y)
+    f = 1/((y - x)*(y + x))
+    assert heurisch_wrapper(f, x) == Piecewise(
+        (-log(x - y)/(2*y) + log(x + y)/(2*y), Ne(y, 0)), (1/x, True))
+    # issue 6926
+    f = sqrt(x**2/((y - x)*(y + x)))
+    assert heurisch_wrapper(f, x) == x*sqrt(-x**2/(x**2 - y**2)) \
+    - y**2*sqrt(-x**2/(x**2 - y**2))/x
+
+
+def test_issue_3609():
+    assert heurisch(1/(x * (1 + log(x)**2)), x) == atan(log(x))
+
+### These are examples from the Poor Man's Integrator
+### http://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/examples/
+
+
+def test_pmint_rat():
+    # TODO: heurisch() is off by a constant: -3/4. Possibly different permutation
+    # would give the optimal result?
+
+    def drop_const(expr, x):
+        if expr.is_Add:
+            return Add(*[ arg for arg in expr.args if arg.has(x) ])
+        else:
+            return expr
+
+    f = (x**7 - 24*x**4 - 4*x**2 + 8*x - 8)/(x**8 + 6*x**6 + 12*x**4 + 8*x**2)
+    g = (4 + 8*x**2 + 6*x + 3*x**3)/(x**5 + 4*x**3 + 4*x) + log(x)
+
+    assert drop_const(ratsimp(heurisch(f, x)), x) == g
+
+
+def test_pmint_trig():
+    f = (x - tan(x)) / tan(x)**2 + tan(x)
+    g = -x**2/2 - x/tan(x) + log(tan(x)**2 + 1)/2
+
+    assert heurisch(f, x) == g
+
+
+def test_pmint_logexp():
+    f = (1 + x + x*exp(x))*(x + log(x) + exp(x) - 1)/(x + log(x) + exp(x))**2/x
+    g = log(x + exp(x) + log(x)) + 1/(x + exp(x) + log(x))
+
+    assert ratsimp(heurisch(f, x)) == g
+
+
+def test_pmint_erf():
+    f = exp(-x**2)*erf(x)/(erf(x)**3 - erf(x)**2 - erf(x) + 1)
+    g = sqrt(pi)*log(erf(x) - 1)/8 - sqrt(pi)*log(erf(x) + 1)/8 - sqrt(pi)/(4*erf(x) - 4)
+
+    assert ratsimp(heurisch(f, x)) == g
+
+
+def test_pmint_LambertW():
+    f = LambertW(x)
+    g = x*LambertW(x) - x + x/LambertW(x)
+
+    assert heurisch(f, x) == g
+
+
+def test_pmint_besselj():
+    f = besselj(nu + 1, x)/besselj(nu, x)
+    g = nu*log(x) - log(besselj(nu, x))
+
+    assert heurisch(f, x) == g
+
+    f = (nu*besselj(nu, x) - x*besselj(nu + 1, x))/x
+    g = besselj(nu, x)
+
+    assert heurisch(f, x) == g
+
+    f = jn(nu + 1, x)/jn(nu, x)
+    g = nu*log(x) - log(jn(nu, x))
+
+    assert heurisch(f, x) == g
+
+
+@slow
+def test_pmint_bessel_products():
+    f = x*besselj(nu, x)*bessely(nu, 2*x)
+    g = -2*x*besselj(nu, x)*bessely(nu - 1, 2*x)/3 + x*besselj(nu - 1, x)*bessely(nu, 2*x)/3
+
+    assert heurisch(f, x) == g
+
+    f = x*besselj(nu, x)*besselk(nu, 2*x)
+    g = -2*x*besselj(nu, x)*besselk(nu - 1, 2*x)/5 - x*besselj(nu - 1, x)*besselk(nu, 2*x)/5
+
+    assert heurisch(f, x) == g
+
+
+def test_pmint_WrightOmega():
+    def omega(x):
+        return LambertW(exp(x))
+
+    f = (1 + omega(x) * (2 + cos(omega(x)) * (x + omega(x))))/(1 + omega(x))/(x + omega(x))
+    g = log(x + LambertW(exp(x))) + sin(LambertW(exp(x)))
+
+    assert heurisch(f, x) == g
+
+
+def test_RR():
+    # Make sure the algorithm does the right thing if the ring is RR. See
+    # issue 8685.
+    assert heurisch(sqrt(1 + 0.25*x**2), x, hints=[]) == \
+        0.5*x*sqrt(0.25*x**2 + 1) + 1.0*asinh(0.5*x)
+
+# TODO: convert the rest of PMINT tests:
+# Airy functions
+# f = (x - AiryAi(x)*AiryAi(1, x)) / (x**2 - AiryAi(x)**2)
+# g = Rational(1,2)*ln(x + AiryAi(x)) + Rational(1,2)*ln(x - AiryAi(x))
+# f = x**2 * AiryAi(x)
+# g = -AiryAi(x) + AiryAi(1, x)*x
+# Whittaker functions
+# f = WhittakerW(mu + 1, nu, x) / (WhittakerW(mu, nu, x) * x)
+# g = x/2 - mu*ln(x) - ln(WhittakerW(mu, nu, x))
+
+
+def test_issue_22527():
+    t, R = symbols(r't R')
+    z = Function('z')(t)
+    def f(x):
+        return x/sqrt(R**2 - x**2)
+    Uz = integrate(f(z), z)
+    Ut = integrate(f(t), t)
+    assert Ut == Uz.subs(z, t)
+
+
+def test_heurisch_complex_erf_issue_26338():
+    r = symbols('r', real=True)
+    a = sqrt(pi)*erf((1 + I)/2)/2
+    assert integrate(exp(-I*r**2/2), (r, 0, 1)) == a - I*a
+
+    a = exp(-x**2/(2*(2 - I)**2))
+    assert heurisch(a, x, hints=[]) is None  # None, not a wrong soln
+    a = exp(-r**2/(2*(2 - I)**2))
+    assert heurisch(a, r, hints=[]) is None
+    a = sqrt(pi)*erf((1 + I)/2)/2
+    assert integrate(exp(-I*x**2/2), (x, 0, 1)) == a - I*a
+
+
+def test_issue_15498():
+    Z0 = Function('Z0')
+    k01, k10, t, s= symbols('k01 k10 t s', real=True, positive=True)
+    m = Matrix([[exp(-k10*t)]])
+    _83 = Rational(83, 100)  # 0.83 works, too
+    [a, b, c, d, e, f, g] = [100, 0.5, _83, 50, 0.6, 2, 120]
+    AIF_btf = a*(d*e*(1 - exp(-(t - b)/e)) + f*g*(1 - exp(-(t - b)/g)))
+    AIF_atf = a*(d*e*exp(-(t - b)/e)*(exp((c - b)/e) - 1
+        ) + f*g*exp(-(t - b)/g)*(exp((c - b)/g) - 1))
+    AIF_sym = Piecewise((0, t < b), (AIF_btf, And(b <= t, t < c)), (AIF_atf, c <= t))
+    aif_eq = Eq(Z0(t), AIF_sym)
+    f_vec = Matrix([[k01*Z0(t)]])
+    integrand = m*m.subs(t, s)**-1*f_vec.subs(aif_eq.lhs, aif_eq.rhs).subs(t, s)
+    solution = integrate(integrand[0], (s, 0, t))
+    assert solution is not None  # does not hang and takes less than 10 s
+
+
+@slow
+def test_heurisch_issue_26930():
+    integrand = x**Rational(4, 3)*log(x)
+    anti = 3*x**(S(7)/3)*log(x)/7 - 9*x**(S(7)/3)/49
+    assert heurisch(integrand, x) == anti
+    assert integrate(integrand, x) == anti
+    assert integrate(integrand, (x, 0, 1)) == -S(9)/49
+
+
+def test_heurisch_issue_26922():
+
+    a, b, x = symbols("a, b, x", real=True, positive=True)
+    C = symbols("C", real=True)
+    i1 = -C*x*exp(-a*x**2 - sqrt(b)*x)
+    i2 = C*x*exp(-a*x**2 + sqrt(b)*x)
+    i = Integral(i1, x) + Integral(i2, x)
+    res = (
+        -C*exp(-a*x**2)*exp(sqrt(b)*x)/(2*a)
+        + C*exp(-a*x**2)*exp(-sqrt(b)*x)/(2*a)
+        + sqrt(pi)*C*sqrt(b)*exp(b/(4*a))*erf(sqrt(a)*x - sqrt(b)/(2*sqrt(a)))/(4*a**(S(3)/2))
+        + sqrt(pi)*C*sqrt(b)*exp(b/(4*a))*erf(sqrt(a)*x + sqrt(b)/(2*sqrt(a)))/(4*a**(S(3)/2))
+    )
+
+    assert i.doit(heurisch=False).expand() == res
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_integrals.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..41e1ef3aa36334189f14cf734ac2ad26d001b506
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_integrals.py
@@ -0,0 +1,2187 @@
+import math
+from sympy.concrete.summations import (Sum, summation)
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import (Derivative, Function, Lambda, diff)
+from sympy.core import EulerGamma
+from sympy.core.numbers import (E, I, Rational, nan, oo, pi, zoo, all_close)
+from sympy.core.relational import (Eq, Ne)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.complexes import (Abs, im, polar_lift, re, sign)
+from sympy.functions.elementary.exponential import (LambertW, exp, exp_polar, log)
+from sympy.functions.elementary.hyperbolic import (acosh, asinh, cosh, coth, csch, sinh, tanh, sech)
+from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt)
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (acos, asin, atan, cos, sin, sinc, tan, sec)
+from sympy.functions.special.delta_functions import DiracDelta, Heaviside
+from sympy.functions.special.error_functions import (Ci, Ei, Si, erf, erfc, erfi, fresnelc, li)
+from sympy.functions.special.gamma_functions import (gamma, polygamma)
+from sympy.functions.special.hyper import (hyper, meijerg)
+from sympy.functions.special.singularity_functions import SingularityFunction
+from sympy.functions.special.zeta_functions import lerchphi
+from sympy.integrals.integrals import integrate
+from sympy.logic.boolalg import And
+from sympy.matrices.dense import Matrix
+from sympy.polys.polytools import (Poly, factor)
+from sympy.printing.str import sstr
+from sympy.series.order import O
+from sympy.sets.sets import Interval
+from sympy.simplify.gammasimp import gammasimp
+from sympy.simplify.simplify import simplify
+from sympy.simplify.trigsimp import trigsimp
+from sympy.tensor.indexed import (Idx, IndexedBase)
+from sympy.core.expr import unchanged
+from sympy.functions.elementary.integers import floor
+from sympy.integrals.integrals import Integral
+from sympy.integrals.risch import NonElementaryIntegral
+from sympy.physics import units
+from sympy.testing.pytest import raises, slow, warns_deprecated_sympy, warns
+from sympy.utilities.exceptions import SymPyDeprecationWarning
+from sympy.core.random import verify_numerically
+
+
+x, y, z, a, b, c, d, e, s, t, x_1, x_2 = symbols('x y z a b c d e s t x_1 x_2')
+n = Symbol('n', integer=True)
+f = Function('f')
+
+
+def NS(e, n=15, **options):
+    return sstr(sympify(e).evalf(n, **options), full_prec=True)
+
+
+def test_poly_deprecated():
+    p = Poly(2*x, x)
+    assert p.integrate(x) == Poly(x**2, x, domain='QQ')
+    # The stacklevel is based on Integral(Poly)
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        integrate(p, x)
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        Integral(p, (x,))
+
+
+@slow
+def test_principal_value():
+    g = 1 / x
+    assert Integral(g, (x, -oo, oo)).principal_value() == 0
+    assert Integral(g, (y, -oo, oo)).principal_value() == oo * sign(1 / x)
+    raises(ValueError, lambda: Integral(g, (x)).principal_value())
+    raises(ValueError, lambda: Integral(g).principal_value())
+
+    l = 1 / ((x ** 3) - 1)
+    assert Integral(l, (x, -oo, oo)).principal_value().together() == -sqrt(3)*pi/3
+    raises(ValueError, lambda: Integral(l, (x, -oo, 1)).principal_value())
+
+    d = 1 / (x ** 2 - 1)
+    assert Integral(d, (x, -oo, oo)).principal_value() == 0
+    assert Integral(d, (x, -2, 2)).principal_value() == -log(3)
+
+    v = x / (x ** 2 - 1)
+    assert Integral(v, (x, -oo, oo)).principal_value() == 0
+    assert Integral(v, (x, -2, 2)).principal_value() == 0
+
+    s = x ** 2 / (x ** 2 - 1)
+    assert Integral(s, (x, -oo, oo)).principal_value() is oo
+    assert Integral(s, (x, -2, 2)).principal_value() == -log(3) + 4
+
+    f = 1 / ((x ** 2 - 1) * (1 + x ** 2))
+    assert Integral(f, (x, -oo, oo)).principal_value() == -pi / 2
+    assert Integral(f, (x, -2, 2)).principal_value() == -atan(2) - log(3) / 2
+
+
+def diff_test(i):
+    """Return the set of symbols, s, which were used in testing that
+    i.diff(s) agrees with i.doit().diff(s). If there is an error then
+    the assertion will fail, causing the test to fail."""
+    syms = i.free_symbols
+    for s in syms:
+        assert (i.diff(s).doit() - i.doit().diff(s)).expand() == 0
+    return syms
+
+
+def test_improper_integral():
+    assert integrate(log(x), (x, 0, 1)) == -1
+    assert integrate(x**(-2), (x, 1, oo)) == 1
+    assert integrate(1/(1 + exp(x)), (x, 0, oo)) == log(2)
+
+
+def test_constructor():
+    # this is shared by Sum, so testing Integral's constructor
+    # is equivalent to testing Sum's
+    s1 = Integral(n, n)
+    assert s1.limits == (Tuple(n),)
+    s2 = Integral(n, (n,))
+    assert s2.limits == (Tuple(n),)
+    s3 = Integral(Sum(x, (x, 1, y)))
+    assert s3.limits == (Tuple(y),)
+    s4 = Integral(n, Tuple(n,))
+    assert s4.limits == (Tuple(n),)
+
+    s5 = Integral(n, (n, Interval(1, 2)))
+    assert s5.limits == (Tuple(n, 1, 2),)
+
+    # Testing constructor with inequalities:
+    s6 = Integral(n, n > 10)
+    assert s6.limits == (Tuple(n, 10, oo),)
+    s7 = Integral(n, (n > 2) & (n < 5))
+    assert s7.limits == (Tuple(n, 2, 5),)
+
+
+def test_basics():
+
+    assert Integral(0, x) != 0
+    assert Integral(x, (x, 1, 1)) != 0
+    assert Integral(oo, x) != oo
+    assert Integral(S.NaN, x) is S.NaN
+
+    assert diff(Integral(y, y), x) == 0
+    assert diff(Integral(x, (x, 0, 1)), x) == 0
+    assert diff(Integral(x, x), x) == x
+    assert diff(Integral(t, (t, 0, x)), x) == x
+
+    e = (t + 1)**2
+    assert diff(integrate(e, (t, 0, x)), x) == \
+        diff(Integral(e, (t, 0, x)), x).doit().expand() == \
+        ((1 + x)**2).expand()
+    assert diff(integrate(e, (t, 0, x)), t) == \
+        diff(Integral(e, (t, 0, x)), t) == 0
+    assert diff(integrate(e, (t, 0, x)), a) == \
+        diff(Integral(e, (t, 0, x)), a) == 0
+    assert diff(integrate(e, t), a) == diff(Integral(e, t), a) == 0
+
+    assert integrate(e, (t, a, x)).diff(x) == \
+        Integral(e, (t, a, x)).diff(x).doit().expand()
+    assert Integral(e, (t, a, x)).diff(x).doit() == ((1 + x)**2)
+    assert integrate(e, (t, x, a)).diff(x).doit() == (-(1 + x)**2).expand()
+
+    assert integrate(t**2, (t, x, 2*x)).diff(x) == 7*x**2
+
+    assert Integral(x, x).atoms() == {x}
+    assert Integral(f(x), (x, 0, 1)).atoms() == {S.Zero, S.One, x}
+
+    assert diff_test(Integral(x, (x, 3*y))) == {y}
+    assert diff_test(Integral(x, (a, 3*y))) == {x, y}
+
+    assert integrate(x, (x, oo, oo)) == 0 #issue 8171
+    assert integrate(x, (x, -oo, -oo)) == 0
+
+    # sum integral of terms
+    assert integrate(y + x + exp(x), x) == x*y + x**2/2 + exp(x)
+
+    assert Integral(x).is_commutative
+    n = Symbol('n', commutative=False)
+    assert Integral(n + x, x).is_commutative is False
+
+
+def test_diff_wrt():
+    class Test(Expr):
+        _diff_wrt = True
+        is_commutative = True
+
+    t = Test()
+    assert integrate(t + 1, t) == t**2/2 + t
+    assert integrate(t + 1, (t, 0, 1)) == Rational(3, 2)
+
+    raises(ValueError, lambda: integrate(x + 1, x + 1))
+    raises(ValueError, lambda: integrate(x + 1, (x + 1, 0, 1)))
+
+
+def test_basics_multiple():
+    assert diff_test(Integral(x, (x, 3*x, 5*y), (y, x, 2*x))) == {x}
+    assert diff_test(Integral(x, (x, 5*y), (y, x, 2*x))) == {x}
+    assert diff_test(Integral(x, (x, 5*y), (y, y, 2*x))) == {x, y}
+    assert diff_test(Integral(y, y, x)) == {x, y}
+    assert diff_test(Integral(y*x, x, y)) == {x, y}
+    assert diff_test(Integral(x + y, y, (y, 1, x))) == {x}
+    assert diff_test(Integral(x + y, (x, x, y), (y, y, x))) == {x, y}
+
+
+def test_conjugate_transpose():
+    A, B = symbols("A B", commutative=False)
+
+    x = Symbol("x", complex=True)
+    p = Integral(A*B, (x,))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+    x = Symbol("x", real=True)
+    p = Integral(A*B, (x,))
+    assert p.adjoint().doit() == p.doit().adjoint()
+    assert p.conjugate().doit() == p.doit().conjugate()
+    assert p.transpose().doit() == p.doit().transpose()
+
+
+def test_integration():
+    assert integrate(0, (t, 0, x)) == 0
+    assert integrate(3, (t, 0, x)) == 3*x
+    assert integrate(t, (t, 0, x)) == x**2/2
+    assert integrate(3*t, (t, 0, x)) == 3*x**2/2
+    assert integrate(3*t**2, (t, 0, x)) == x**3
+    assert integrate(1/t, (t, 1, x)) == log(x)
+    assert integrate(-1/t**2, (t, 1, x)) == 1/x - 1
+    assert integrate(t**2 + 5*t - 8, (t, 0, x)) == x**3/3 + 5*x**2/2 - 8*x
+    assert integrate(x**2, x) == x**3/3
+    assert integrate((3*t*x)**5, x) == (3*t)**5 * x**6 / 6
+
+    b = Symbol("b")
+    c = Symbol("c")
+    assert integrate(a*t, (t, 0, x)) == a*x**2/2
+    assert integrate(a*t**4, (t, 0, x)) == a*x**5/5
+    assert integrate(a*t**2 + b*t + c, (t, 0, x)) == a*x**3/3 + b*x**2/2 + c*x
+
+
+def test_multiple_integration():
+    assert integrate((x**2)*(y**2), (x, 0, 1), (y, -1, 2)) == Rational(1)
+    assert integrate((y**2)*(x**2), x, y) == Rational(1, 9)*(x**3)*(y**3)
+    assert integrate(1/(x + 3)/(1 + x)**3, x) == \
+        log(3 + x)*Rational(-1, 8) + log(1 + x)*Rational(1, 8) + x/(4 + 8*x + 4*x**2)
+    assert integrate(sin(x*y)*y, (x, 0, 1), (y, 0, 1)) == -sin(1) + 1
+
+
+def test_issue_3532():
+    assert integrate(exp(-x), (x, 0, oo)) == 1
+
+
+def test_issue_3560():
+    assert integrate(sqrt(x)**3, x) == 2*sqrt(x)**5/5
+    assert integrate(sqrt(x), x) == 2*sqrt(x)**3/3
+    assert integrate(1/sqrt(x)**3, x) == -2/sqrt(x)
+
+
+def test_issue_18038():
+    raises(AttributeError, lambda: integrate((x, x)))
+
+
+def test_integrate_poly():
+    p = Poly(x + x**2*y + y**3, x, y)
+
+    # The stacklevel is based on Integral(Poly)
+    with warns_deprecated_sympy():
+        qx = Integral(p, x)
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        qx = integrate(p, x)
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        qy = integrate(p, y)
+
+    assert isinstance(qx, Poly) is True
+    assert isinstance(qy, Poly) is True
+
+    assert qx.gens == (x, y)
+    assert qy.gens == (x, y)
+
+    assert qx.as_expr() == x**2/2 + x**3*y/3 + x*y**3
+    assert qy.as_expr() == x*y + x**2*y**2/2 + y**4/4
+
+
+def test_integrate_poly_definite():
+    p = Poly(x + x**2*y + y**3, x, y)
+
+    with warns_deprecated_sympy():
+        Qx = Integral(p, (x, 0, 1))
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        Qx = integrate(p, (x, 0, 1))
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        Qy = integrate(p, (y, 0, pi))
+
+    assert isinstance(Qx, Poly) is True
+    assert isinstance(Qy, Poly) is True
+
+    assert Qx.gens == (y,)
+    assert Qy.gens == (x,)
+
+    assert Qx.as_expr() == S.Half + y/3 + y**3
+    assert Qy.as_expr() == pi**4/4 + pi*x + pi**2*x**2/2
+
+
+def test_integrate_omit_var():
+    y = Symbol('y')
+
+    assert integrate(x) == x**2/2
+
+    raises(ValueError, lambda: integrate(2))
+    raises(ValueError, lambda: integrate(x*y))
+
+
+def test_integrate_poly_accurately():
+    y = Symbol('y')
+    assert integrate(x*sin(y), x) == x**2*sin(y)/2
+
+    # when passed to risch_norman, this will be a CPU hog, so this really
+    # checks, that integrated function is recognized as polynomial
+    assert integrate(x**1000*sin(y), x) == x**1001*sin(y)/1001
+
+
+def test_issue_3635():
+    y = Symbol('y')
+    assert integrate(x**2, y) == x**2*y
+    assert integrate(x**2, (y, -1, 1)) == 2*x**2
+
+# works in SymPy and py.test but hangs in `setup.py test`
+
+
+def test_integrate_linearterm_pow():
+    # check integrate((a*x+b)^c, x)  --  issue 3499
+    y = Symbol('y', positive=True)
+    # TODO: Remove conds='none' below, let the assumption take care of it.
+    assert integrate(x**y, x, conds='none') == x**(y + 1)/(y + 1)
+    assert integrate((exp(y)*x + 1/y)**(1 + sin(y)), x, conds='none') == \
+        exp(-y)*(exp(y)*x + 1/y)**(2 + sin(y)) / (2 + sin(y))
+
+
+def test_issue_3618():
+    assert integrate(pi*sqrt(x), x) == 2*pi*sqrt(x)**3/3
+    assert integrate(pi*sqrt(x) + E*sqrt(x)**3, x) == \
+        2*pi*sqrt(x)**3/3 + 2*E *sqrt(x)**5/5
+
+
+def test_issue_3623():
+    assert integrate(cos((n + 1)*x), x) == Piecewise(
+        (sin(x*(n + 1))/(n + 1), Ne(n + 1, 0)), (x, True))
+    assert integrate(cos((n - 1)*x), x) == Piecewise(
+        (sin(x*(n - 1))/(n - 1), Ne(n - 1, 0)), (x, True))
+    assert integrate(cos((n + 1)*x) + cos((n - 1)*x), x) == \
+        Piecewise((sin(x*(n - 1))/(n - 1), Ne(n - 1, 0)), (x, True)) + \
+        Piecewise((sin(x*(n + 1))/(n + 1), Ne(n + 1, 0)), (x, True))
+
+
+def test_issue_3664():
+    n = Symbol('n', integer=True, nonzero=True)
+    assert integrate(-1./2 * x * sin(n * pi * x/2), [x, -2, 0]) == \
+        2.0*cos(pi*n)/(pi*n)
+    assert integrate(x * sin(n * pi * x/2) * Rational(-1, 2), [x, -2, 0]) == \
+        2*cos(pi*n)/(pi*n)
+
+
+def test_issue_3679():
+    # definite integration of rational functions gives wrong answers
+    assert NS(Integral(1/(x**2 - 8*x + 17), (x, 2, 4))) == '1.10714871779409'
+
+
+def test_issue_3686():  # remove this when fresnel integrals are implemented
+    from sympy.core.function import expand_func
+    from sympy.functions.special.error_functions import fresnels
+    assert expand_func(integrate(sin(x**2), x)) == \
+        sqrt(2)*sqrt(pi)*fresnels(sqrt(2)*x/sqrt(pi))/2
+
+
+def test_integrate_units():
+    m = units.m
+    s = units.s
+    assert integrate(x * m/s, (x, 1*s, 5*s)) == 12*m*s
+
+
+def test_transcendental_functions():
+    assert integrate(LambertW(2*x), x) == \
+        -x + x*LambertW(2*x) + x/LambertW(2*x)
+
+
+def test_log_polylog():
+    assert integrate(log(1 - x)/x, (x, 0, 1)) == -pi**2/6
+    assert integrate(log(x)*(1 - x)**(-1), (x, 0, 1)) == -pi**2/6
+
+
+def test_issue_3740():
+    f = 4*log(x) - 2*log(x)**2
+    fid = diff(integrate(f, x), x)
+    assert abs(f.subs(x, 42).evalf() - fid.subs(x, 42).evalf()) < 1e-10
+
+
+def test_issue_3788():
+    assert integrate(1/(1 + x**2), x) == atan(x)
+
+
+def test_issue_3952():
+    f = sin(x)
+    assert integrate(f, x) == -cos(x)
+    raises(ValueError, lambda: integrate(f, 2*x))
+
+
+def test_issue_4516():
+    assert integrate(2**x - 2*x, x) == 2**x/log(2) - x**2
+
+
+def test_issue_7450():
+    ans = integrate(exp(-(1 + I)*x), (x, 0, oo))
+    assert re(ans) == S.Half and im(ans) == Rational(-1, 2)
+
+
+def test_issue_8623():
+    assert integrate((1 + cos(2*x)) / (3 - 2*cos(2*x)), (x, 0, pi)) == -pi/2 + sqrt(5)*pi/2
+    assert integrate((1 + cos(2*x))/(3 - 2*cos(2*x))) == -x/2 + sqrt(5)*(atan(sqrt(5)*tan(x)) + \
+        pi*floor((x - pi/2)/pi))/2
+
+
+def test_issue_9569():
+    assert integrate(1 / (2 - cos(x)), (x, 0, pi)) == pi/sqrt(3)
+    assert integrate(1/(2 - cos(x))) == 2*sqrt(3)*(atan(sqrt(3)*tan(x/2)) + pi*floor((x/2 - pi/2)/pi))/3
+
+
+def test_issue_13733():
+    s = Symbol('s', positive=True)
+    pz = exp(-(z - y)**2/(2*s*s))/sqrt(2*pi*s*s)
+    pzgx = integrate(pz, (z, x, oo))
+    assert integrate(pzgx, (x, 0, oo)) == sqrt(2)*s*exp(-y**2/(2*s**2))/(2*sqrt(pi)) + \
+        y*erf(sqrt(2)*y/(2*s))/2 + y/2
+
+
+def test_issue_13749():
+    assert integrate(1 / (2 + cos(x)), (x, 0, pi)) == pi/sqrt(3)
+    assert integrate(1/(2 + cos(x))) == 2*sqrt(3)*(atan(sqrt(3)*tan(x/2)/3) + pi*floor((x/2 - pi/2)/pi))/3
+
+
+def test_issue_18133():
+    assert integrate(exp(x)/(1 + x)**2, x) == NonElementaryIntegral(exp(x)/(x + 1)**2, x)
+
+
+def test_issue_21741():
+    a = 4e6
+    b = 2.5e-7
+    r = Piecewise((b*I*exp(-a*I*pi*t*y)*exp(-a*I*pi*x*z)/(pi*x), Ne(x, 0)),
+                  (z*exp(-a*I*pi*t*y), True))
+    fun = E**((-2*I*pi*(z*x+t*y))/(500*10**(-9)))
+    assert all_close(integrate(fun, z), r)
+
+
+def test_matrices():
+    M = Matrix(2, 2, lambda i, j: (i + j + 1)*sin((i + j + 1)*x))
+
+    assert integrate(M, x) == Matrix([
+        [-cos(x), -cos(2*x)],
+        [-cos(2*x), -cos(3*x)],
+    ])
+
+
+def test_integrate_functions():
+    # issue 4111
+    assert integrate(f(x), x) == Integral(f(x), x)
+    assert integrate(f(x), (x, 0, 1)) == Integral(f(x), (x, 0, 1))
+    assert integrate(f(x)*diff(f(x), x), x) == f(x)**2/2
+    assert integrate(diff(f(x), x) / f(x), x) == log(f(x))
+
+
+def test_integrate_derivatives():
+    assert integrate(Derivative(f(x), x), x) == f(x)
+    assert integrate(Derivative(f(y), y), x) == x*Derivative(f(y), y)
+    assert integrate(Derivative(f(x), x)**2, x) == \
+        Integral(Derivative(f(x), x)**2, x)
+
+
+def test_transform():
+    a = Integral(x**2 + 1, (x, -1, 2))
+    fx = x
+    fy = 3*y + 1
+    assert a.doit() == a.transform(fx, fy).doit()
+    assert a.transform(fx, fy).transform(fy, fx) == a
+    fx = 3*x + 1
+    fy = y
+    assert a.transform(fx, fy).transform(fy, fx) == a
+    a = Integral(sin(1/x), (x, 0, 1))
+    assert a.transform(x, 1/y) == Integral(sin(y)/y**2, (y, 1, oo))
+    assert a.transform(x, 1/y).transform(y, 1/x) == a
+    a = Integral(exp(-x**2), (x, -oo, oo))
+    assert a.transform(x, 2*y) == Integral(2*exp(-4*y**2), (y, -oo, oo))
+    # < 3 arg limit handled properly
+    assert Integral(x, x).transform(x, a*y).doit() == \
+        Integral(y*a**2, y).doit()
+    _3 = S(3)
+    assert Integral(x, (x, 0, -_3)).transform(x, 1/y).doit() == \
+        Integral(-1/x**3, (x, -oo, -1/_3)).doit()
+    assert Integral(x, (x, 0, _3)).transform(x, 1/y) == \
+        Integral(y**(-3), (y, 1/_3, oo))
+    # issue 8400
+    i = Integral(x + y, (x, 1, 2), (y, 1, 2))
+    assert i.transform(x, (x + 2*y, x)).doit() == \
+        i.transform(x, (x + 2*z, x)).doit() == 3
+
+    i = Integral(x, (x, a, b))
+    assert i.transform(x, 2*s) == Integral(4*s, (s, a/2, b/2))
+    raises(ValueError, lambda: i.transform(x, 1))
+    raises(ValueError, lambda: i.transform(x, s*t))
+    raises(ValueError, lambda: i.transform(x, -s))
+    raises(ValueError, lambda: i.transform(x, (s, t)))
+    raises(ValueError, lambda: i.transform(2*x, 2*s))
+
+    i = Integral(x**2, (x, 1, 2))
+    raises(ValueError, lambda: i.transform(x**2, s))
+
+    am = Symbol('a', negative=True)
+    bp = Symbol('b', positive=True)
+    i = Integral(x, (x, bp, am))
+    i.transform(x, 2*s)
+    assert i.transform(x, 2*s) == Integral(-4*s, (s, am/2, bp/2))
+
+    i = Integral(x, (x, a))
+    assert i.transform(x, 2*s) == Integral(4*s, (s, a/2))
+
+
+def test_issue_4052():
+    f = S.Half*asin(x) + x*sqrt(1 - x**2)/2
+
+    assert integrate(cos(asin(x)), x) == f
+    assert integrate(sin(acos(x)), x) == f
+
+
+@slow
+def test_evalf_integrals():
+    assert NS(Integral(x, (x, 2, 5)), 15) == '10.5000000000000'
+    gauss = Integral(exp(-x**2), (x, -oo, oo))
+    assert NS(gauss, 15) == '1.77245385090552'
+    assert NS(gauss**2 - pi + E*Rational(
+        1, 10**20), 15) in ('2.71828182845904e-20', '2.71828182845905e-20')
+    # A monster of an integral from http://mathworld.wolfram.com/DefiniteIntegral.html
+    t = Symbol('t')
+    a = 8*sqrt(3)/(1 + 3*t**2)
+    b = 16*sqrt(2)*(3*t + 1)*sqrt(4*t**2 + t + 1)**3
+    c = (3*t**2 + 1)*(11*t**2 + 2*t + 3)**2
+    d = sqrt(2)*(249*t**2 + 54*t + 65)/(11*t**2 + 2*t + 3)**2
+    f = a - b/c - d
+    assert NS(Integral(f, (t, 0, 1)), 50) == \
+        NS((3*sqrt(2) - 49*pi + 162*atan(sqrt(2)))/12, 50)
+    # http://mathworld.wolfram.com/VardisIntegral.html
+    assert NS(Integral(log(log(1/x))/(1 + x + x**2), (x, 0, 1)), 15) == \
+        NS('pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))', 15)
+    # http://mathworld.wolfram.com/AhmedsIntegral.html
+    assert NS(Integral(atan(sqrt(x**2 + 2))/(sqrt(x**2 + 2)*(x**2 + 1)), (x,
+              0, 1)), 15) == NS(5*pi**2/96, 15)
+    # http://mathworld.wolfram.com/AbelsIntegral.html
+    assert NS(Integral(x/((exp(pi*x) - exp(
+        -pi*x))*(x**2 + 1)), (x, 0, oo)), 15) == NS('log(2)/2-1/4', 15)
+    # Complex part trimming
+    # http://mathworld.wolfram.com/VardisIntegral.html
+    assert NS(Integral(log(log(sin(x)/cos(x))), (x, pi/4, pi/2)), 15, chop=True) == \
+        NS('pi/4*log(4*pi**3/gamma(1/4)**4)', 15)
+    #
+    # Endpoints causing trouble (rounding error in integration points -> complex log)
+    assert NS(
+        2 + Integral(log(2*cos(x/2)), (x, -pi, pi)), 17, chop=True) == NS(2, 17)
+    assert NS(
+        2 + Integral(log(2*cos(x/2)), (x, -pi, pi)), 20, chop=True) == NS(2, 20)
+    assert NS(
+        2 + Integral(log(2*cos(x/2)), (x, -pi, pi)), 22, chop=True) == NS(2, 22)
+    # Needs zero handling
+    assert NS(pi - 4*Integral(
+        'sqrt(1-x**2)', (x, 0, 1)), 15, maxn=30, chop=True) in ('0.0', '0')
+    # Oscillatory quadrature
+    a = Integral(sin(x)/x**2, (x, 1, oo)).evalf(maxn=15)
+    assert 0.49 < a < 0.51
+    assert NS(
+        Integral(sin(x)/x**2, (x, 1, oo)), quad='osc') == '0.504067061906928'
+    assert NS(Integral(
+        cos(pi*x + 1)/x, (x, -oo, -1)), quad='osc') == '0.276374705640365'
+    # indefinite integrals aren't evaluated
+    assert NS(Integral(x, x)) == 'Integral(x, x)'
+    assert NS(Integral(x, (x, y))) == 'Integral(x, (x, y))'
+
+
+def test_evalf_issue_939():
+    # https://github.com/sympy/sympy/issues/4038
+
+    # The output form of an integral may differ by a step function between
+    # revisions, making this test a bit useless. This can't be said about
+    # other two tests. For now, all values of this evaluation are used here,
+    # but in future this should be reconsidered.
+    assert NS(integrate(1/(x**5 + 1), x).subs(x, 4), chop=True) in \
+        ['-0.000976138910649103', '0.965906660135753', '1.93278945918216']
+
+    assert NS(Integral(1/(x**5 + 1), (x, 2, 4))) == '0.0144361088886740'
+    assert NS(
+        integrate(1/(x**5 + 1), (x, 2, 4)), chop=True) == '0.0144361088886740'
+
+
+def test_double_previously_failing_integrals():
+    # Double integrals not implemented <- Sure it is!
+    res = integrate(sqrt(x) + x*y, (x, 1, 2), (y, -1, 1))
+    # Old numerical test
+    assert NS(res, 15) == '2.43790283299492'
+    # Symbolic test
+    assert res == Rational(-4, 3) + 8*sqrt(2)/3
+    # double integral + zero detection
+    assert integrate(sin(x + x*y), (x, -1, 1), (y, -1, 1)) is S.Zero
+
+
+def test_integrate_SingularityFunction():
+    in_1 = SingularityFunction(x, a, 3) + SingularityFunction(x, 5, -1)
+    out_1 = SingularityFunction(x, a, 4)/4 + SingularityFunction(x, 5, 0)
+    assert integrate(in_1, x) == out_1
+
+    in_2 = 10*SingularityFunction(x, 4, 0) - 5*SingularityFunction(x, -6, -2)
+    out_2 = 10*SingularityFunction(x, 4, 1) - 5*SingularityFunction(x, -6, -1)
+    assert integrate(in_2, x) == out_2
+
+    in_3 = 2*x**2*y -10*SingularityFunction(x, -4, 7) - 2*SingularityFunction(y, 10, -2)
+    out_3_1 = 2*x**3*y/3 - 2*x*SingularityFunction(y, 10, -2) - 5*SingularityFunction(x, -4, 8)/4
+    out_3_2 = x**2*y**2 - 10*y*SingularityFunction(x, -4, 7) - 2*SingularityFunction(y, 10, -1)
+    assert integrate(in_3, x) == out_3_1
+    assert integrate(in_3, y) == out_3_2
+
+    assert unchanged(Integral, in_3, (x,))
+    assert Integral(in_3, x) == Integral(in_3, (x,))
+    assert Integral(in_3, x).doit() == out_3_1
+
+    in_4 = 10*SingularityFunction(x, -4, 7) - 2*SingularityFunction(x, 10, -2)
+    out_4 = 5*SingularityFunction(x, -4, 8)/4 - 2*SingularityFunction(x, 10, -1)
+    assert integrate(in_4, (x, -oo, x)) == out_4
+
+    assert integrate(SingularityFunction(x, 5, -1), x) == SingularityFunction(x, 5, 0)
+    assert integrate(SingularityFunction(x, 0, -1), (x, -oo, oo)) == 1
+    assert integrate(5*SingularityFunction(x, 5, -1), (x, -oo, oo)) == 5
+    assert integrate(SingularityFunction(x, 5, -1) * f(x), (x, -oo, oo)) == f(5)
+
+
+def test_integrate_DiracDelta():
+    # This is here to check that deltaintegrate is being called, but also
+    # to test definite integrals. More tests are in test_deltafunctions.py
+    assert integrate(DiracDelta(x) * f(x), (x, -oo, oo)) == f(0)
+    assert integrate(DiracDelta(x)**2, (x, -oo, oo)) == DiracDelta(0)
+    # issue 4522
+    assert integrate(integrate((4 - 4*x + x*y - 4*y) * \
+        DiracDelta(x)*DiracDelta(y - 1), (x, 0, 1)), (y, 0, 1)) == 0
+    # issue 5729
+    p = exp(-(x**2 + y**2))/pi
+    assert integrate(p*DiracDelta(x - 10*y), (x, -oo, oo), (y, -oo, oo)) == \
+        integrate(p*DiracDelta(x - 10*y), (y, -oo, oo), (x, -oo, oo)) == \
+        integrate(p*DiracDelta(10*x - y), (x, -oo, oo), (y, -oo, oo)) == \
+        integrate(p*DiracDelta(10*x - y), (y, -oo, oo), (x, -oo, oo)) == \
+        1/sqrt(101*pi)
+
+
+def test_integrate_returns_piecewise():
+    assert integrate(x**y, x) == Piecewise(
+        (x**(y + 1)/(y + 1), Ne(y, -1)), (log(x), True))
+    assert integrate(x**y, y) == Piecewise(
+        (x**y/log(x), Ne(log(x), 0)), (y, True))
+    assert integrate(exp(n*x), x) == Piecewise(
+        (exp(n*x)/n, Ne(n, 0)), (x, True))
+    assert integrate(x*exp(n*x), x) == Piecewise(
+        ((n*x - 1)*exp(n*x)/n**2, Ne(n**2, 0)), (x**2/2, True))
+    assert integrate(x**(n*y), x) == Piecewise(
+        (x**(n*y + 1)/(n*y + 1), Ne(n*y, -1)), (log(x), True))
+    assert integrate(x**(n*y), y) == Piecewise(
+        (x**(n*y)/(n*log(x)), Ne(n*log(x), 0)), (y, True))
+    assert integrate(cos(n*x), x) == Piecewise(
+        (sin(n*x)/n, Ne(n, 0)), (x, True))
+    assert integrate(cos(n*x)**2, x) == Piecewise(
+        ((n*x/2 + sin(n*x)*cos(n*x)/2)/n, Ne(n, 0)), (x, True))
+    assert integrate(x*cos(n*x), x) == Piecewise(
+        (x*sin(n*x)/n + cos(n*x)/n**2, Ne(n, 0)), (x**2/2, True))
+    assert integrate(sin(n*x), x) == Piecewise(
+        (-cos(n*x)/n, Ne(n, 0)), (0, True))
+    assert integrate(sin(n*x)**2, x) == Piecewise(
+        ((n*x/2 - sin(n*x)*cos(n*x)/2)/n, Ne(n, 0)), (0, True))
+    assert integrate(x*sin(n*x), x) == Piecewise(
+        (-x*cos(n*x)/n + sin(n*x)/n**2, Ne(n, 0)), (0, True))
+    assert integrate(exp(x*y), (x, 0, z)) == Piecewise(
+        (exp(y*z)/y - 1/y, (y > -oo) & (y < oo) & Ne(y, 0)), (z, True))
+    # https://github.com/sympy/sympy/issues/23707
+    assert integrate(exp(t)*exp(-t*sqrt(x - y)), t) == Piecewise(
+        (-exp(t)/(sqrt(x - y)*exp(t*sqrt(x - y)) - exp(t*sqrt(x - y))),
+        Ne(x, y + 1)), (t, True))
+
+
+def test_integrate_max_min():
+    x = symbols('x', real=True)
+    assert integrate(Min(x, 2), (x, 0, 3)) == 4
+    assert integrate(Max(x**2, x**3), (x, 0, 2)) == Rational(49, 12)
+    assert integrate(Min(exp(x), exp(-x))**2, x) == Piecewise( \
+        (exp(2*x)/2, x <= 0), (1 - exp(-2*x)/2, True))
+    # issue 7907
+    c = symbols('c', extended_real=True)
+    int1 = integrate(Max(c, x)*exp(-x**2), (x, -oo, oo))
+    int2 = integrate(c*exp(-x**2), (x, -oo, c))
+    int3 = integrate(x*exp(-x**2), (x, c, oo))
+    assert int1 == int2 + int3 == sqrt(pi)*c*erf(c)/2 + \
+        sqrt(pi)*c/2 + exp(-c**2)/2
+
+
+def test_integrate_Abs_sign():
+    assert integrate(Abs(x), (x, -2, 1)) == Rational(5, 2)
+    assert integrate(Abs(x), (x, 0, 1)) == S.Half
+    assert integrate(Abs(x + 1), (x, 0, 1)) == Rational(3, 2)
+    assert integrate(Abs(x**2 - 1), (x, -2, 2)) == 4
+    assert integrate(Abs(x**2 - 3*x), (x, -15, 15)) == 2259
+    assert integrate(sign(x), (x, -1, 2)) == 1
+    assert integrate(sign(x)*sin(x), (x, -pi, pi)) == 4
+    assert integrate(sign(x - 2) * x**2, (x, 0, 3)) == Rational(11, 3)
+
+    t, s = symbols('t s', real=True)
+    assert integrate(Abs(t), t) == Piecewise(
+        (-t**2/2, t <= 0), (t**2/2, True))
+    assert integrate(Abs(2*t - 6), t) == Piecewise(
+        (-t**2 + 6*t, t <= 3), (t**2 - 6*t + 18, True))
+    assert (integrate(abs(t - s**2), (t, 0, 2)) ==
+        2*s**2*Min(2, s**2) - 2*s**2 - Min(2, s**2)**2 + 2)
+    assert integrate(exp(-Abs(t)), t) == Piecewise(
+        (exp(t), t <= 0), (2 - exp(-t), True))
+    assert integrate(sign(2*t - 6), t) == Piecewise(
+        (-t, t < 3), (t - 6, True))
+    assert integrate(2*t*sign(t**2 - 1), t) == Piecewise(
+        (t**2, t < -1), (-t**2 + 2, t < 1), (t**2, True))
+    assert integrate(sign(t), (t, s + 1)) == Piecewise(
+        (s + 1, s + 1 > 0), (-s - 1, s + 1 < 0), (0, True))
+
+
+def test_subs1():
+    e = Integral(exp(x - y), x)
+    assert e.subs(y, 3) == Integral(exp(x - 3), x)
+    e = Integral(exp(x - y), (x, 0, 1))
+    assert e.subs(y, 3) == Integral(exp(x - 3), (x, 0, 1))
+    f = Lambda(x, exp(-x**2))
+    conv = Integral(f(x - y)*f(y), (y, -oo, oo))
+    assert conv.subs({x: 0}) == Integral(exp(-2*y**2), (y, -oo, oo))
+
+
+def test_subs2():
+    e = Integral(exp(x - y), x, t)
+    assert e.subs(y, 3) == Integral(exp(x - 3), x, t)
+    e = Integral(exp(x - y), (x, 0, 1), (t, 0, 1))
+    assert e.subs(y, 3) == Integral(exp(x - 3), (x, 0, 1), (t, 0, 1))
+    f = Lambda(x, exp(-x**2))
+    conv = Integral(f(x - y)*f(y), (y, -oo, oo), (t, 0, 1))
+    assert conv.subs({x: 0}) == Integral(exp(-2*y**2), (y, -oo, oo), (t, 0, 1))
+
+
+def test_subs3():
+    e = Integral(exp(x - y), (x, 0, y), (t, y, 1))
+    assert e.subs(y, 3) == Integral(exp(x - 3), (x, 0, 3), (t, 3, 1))
+    f = Lambda(x, exp(-x**2))
+    conv = Integral(f(x - y)*f(y), (y, -oo, oo), (t, x, 1))
+    assert conv.subs({x: 0}) == Integral(exp(-2*y**2), (y, -oo, oo), (t, 0, 1))
+
+
+def test_subs4():
+    e = Integral(exp(x), (x, 0, y), (t, y, 1))
+    assert e.subs(y, 3) == Integral(exp(x), (x, 0, 3), (t, 3, 1))
+    f = Lambda(x, exp(-x**2))
+    conv = Integral(f(y)*f(y), (y, -oo, oo), (t, x, 1))
+    assert conv.subs({x: 0}) == Integral(exp(-2*y**2), (y, -oo, oo), (t, 0, 1))
+
+
+def test_subs5():
+    e = Integral(exp(-x**2), (x, -oo, oo))
+    assert e.subs(x, 5) == e
+    e = Integral(exp(-x**2 + y), x)
+    assert e.subs(y, 5) == Integral(exp(-x**2 + 5), x)
+    e = Integral(exp(-x**2 + y), (x, x))
+    assert e.subs(x, 5) == Integral(exp(y - x**2), (x, 5))
+    assert e.subs(y, 5) == Integral(exp(-x**2 + 5), x)
+    e = Integral(exp(-x**2 + y), (y, -oo, oo), (x, -oo, oo))
+    assert e.subs(x, 5) == e
+    assert e.subs(y, 5) == e
+    # Test evaluation of antiderivatives
+    e = Integral(exp(-x**2), (x, x))
+    assert e.subs(x, 5) == Integral(exp(-x**2), (x, 5))
+    e = Integral(exp(x), x)
+    assert (e.subs(x,1) - e.subs(x,0) - Integral(exp(x), (x, 0, 1))
+        ).doit().is_zero
+
+
+def test_subs6():
+    a, b = symbols('a b')
+    e = Integral(x*y, (x, f(x), f(y)))
+    assert e.subs(x, 1) == Integral(x*y, (x, f(1), f(y)))
+    assert e.subs(y, 1) == Integral(x, (x, f(x), f(1)))
+    e = Integral(x*y, (x, f(x), f(y)), (y, f(x), f(y)))
+    assert e.subs(x, 1) == Integral(x*y, (x, f(1), f(y)), (y, f(1), f(y)))
+    assert e.subs(y, 1) == Integral(x*y, (x, f(x), f(y)), (y, f(x), f(1)))
+    e = Integral(x*y, (x, f(x), f(a)), (y, f(x), f(a)))
+    assert e.subs(a, 1) == Integral(x*y, (x, f(x), f(1)), (y, f(x), f(1)))
+
+
+def test_subs7():
+    e = Integral(x, (x, 1, y), (y, 1, 2))
+    assert e.subs({x: 1, y: 2}) == e
+    e = Integral(sin(x) + sin(y), (x, sin(x), sin(y)),
+                                  (y, 1, 2))
+    assert e.subs(sin(y), 1) == e
+    assert e.subs(sin(x), 1) == Integral(sin(x) + sin(y), (x, 1, sin(y)),
+                                         (y, 1, 2))
+
+def test_expand():
+    e = Integral(f(x)+f(x**2), (x, 1, y))
+    assert e.expand() == Integral(f(x), (x, 1, y)) + Integral(f(x**2), (x, 1, y))
+    e = Integral(f(x)+f(x**2), (x, 1, oo))
+    assert e.expand() == e
+    assert e.expand(force=True) == Integral(f(x), (x, 1, oo)) + \
+           Integral(f(x**2), (x, 1, oo))
+
+
+def test_integration_variable():
+    raises(ValueError, lambda: Integral(exp(-x**2), 3))
+    raises(ValueError, lambda: Integral(exp(-x**2), (3, -oo, oo)))
+
+
+def test_expand_integral():
+    assert Integral(cos(x**2)*(sin(x**2) + 1), (x, 0, 1)).expand() == \
+        Integral(cos(x**2)*sin(x**2), (x, 0, 1)) + \
+        Integral(cos(x**2), (x, 0, 1))
+    assert Integral(cos(x**2)*(sin(x**2) + 1), x).expand() == \
+        Integral(cos(x**2)*sin(x**2), x) + \
+        Integral(cos(x**2), x)
+
+
+def test_as_sum_midpoint1():
+    e = Integral(sqrt(x**3 + 1), (x, 2, 10))
+    assert e.as_sum(1, method="midpoint") == 8*sqrt(217)
+    assert e.as_sum(2, method="midpoint") == 4*sqrt(65) + 12*sqrt(57)
+    assert e.as_sum(3, method="midpoint") == 8*sqrt(217)/3 + \
+        8*sqrt(3081)/27 + 8*sqrt(52809)/27
+    assert e.as_sum(4, method="midpoint") == 2*sqrt(730) + \
+        4*sqrt(7) + 4*sqrt(86) + 6*sqrt(14)
+    assert abs(e.as_sum(4, method="midpoint").n() - e.n()) < 0.5
+
+    e = Integral(sqrt(x**3 + y**3), (x, 2, 10), (y, 0, 10))
+    raises(NotImplementedError, lambda: e.as_sum(4))
+
+
+def test_as_sum_midpoint2():
+    e = Integral((x + y)**2, (x, 0, 1))
+    n = Symbol('n', positive=True, integer=True)
+    assert e.as_sum(1, method="midpoint").expand() == Rational(1, 4) + y + y**2
+    assert e.as_sum(2, method="midpoint").expand() == Rational(5, 16) + y + y**2
+    assert e.as_sum(3, method="midpoint").expand() == Rational(35, 108) + y + y**2
+    assert e.as_sum(4, method="midpoint").expand() == Rational(21, 64) + y + y**2
+    assert e.as_sum(n, method="midpoint").expand() == \
+        y**2 + y + Rational(1, 3) - 1/(12*n**2)
+
+
+def test_as_sum_left():
+    e = Integral((x + y)**2, (x, 0, 1))
+    assert e.as_sum(1, method="left").expand() == y**2
+    assert e.as_sum(2, method="left").expand() == Rational(1, 8) + y/2 + y**2
+    assert e.as_sum(3, method="left").expand() == Rational(5, 27) + y*Rational(2, 3) + y**2
+    assert e.as_sum(4, method="left").expand() == Rational(7, 32) + y*Rational(3, 4) + y**2
+    assert e.as_sum(n, method="left").expand() == \
+        y**2 + y + Rational(1, 3) - y/n - 1/(2*n) + 1/(6*n**2)
+    assert e.as_sum(10, method="left", evaluate=False).has(Sum)
+
+
+def test_as_sum_right():
+    e = Integral((x + y)**2, (x, 0, 1))
+    assert e.as_sum(1, method="right").expand() == 1 + 2*y + y**2
+    assert e.as_sum(2, method="right").expand() == Rational(5, 8) + y*Rational(3, 2) + y**2
+    assert e.as_sum(3, method="right").expand() == Rational(14, 27) + y*Rational(4, 3) + y**2
+    assert e.as_sum(4, method="right").expand() == Rational(15, 32) + y*Rational(5, 4) + y**2
+    assert e.as_sum(n, method="right").expand() == \
+        y**2 + y + Rational(1, 3) + y/n + 1/(2*n) + 1/(6*n**2)
+
+
+def test_as_sum_trapezoid():
+    e = Integral((x + y)**2, (x, 0, 1))
+    assert e.as_sum(1, method="trapezoid").expand() == y**2 + y + S.Half
+    assert e.as_sum(2, method="trapezoid").expand() == y**2 + y + Rational(3, 8)
+    assert e.as_sum(3, method="trapezoid").expand() == y**2 + y + Rational(19, 54)
+    assert e.as_sum(4, method="trapezoid").expand() == y**2 + y + Rational(11, 32)
+    assert e.as_sum(n, method="trapezoid").expand() == \
+        y**2 + y + Rational(1, 3) + 1/(6*n**2)
+    assert Integral(sign(x), (x, 0, 1)).as_sum(1, 'trapezoid') == S.Half
+
+
+def test_as_sum_raises():
+    e = Integral((x + y)**2, (x, 0, 1))
+    raises(ValueError, lambda: e.as_sum(-1))
+    raises(ValueError, lambda: e.as_sum(0))
+    raises(ValueError, lambda: Integral(x).as_sum(3))
+    raises(ValueError, lambda: e.as_sum(oo))
+    raises(ValueError, lambda: e.as_sum(3, method='xxxx2'))
+
+
+def test_nested_doit():
+    e = Integral(Integral(x, x), x)
+    f = Integral(x, x, x)
+    assert e.doit() == f.doit()
+
+
+def test_issue_4665():
+    # Allow only upper or lower limit evaluation
+    e = Integral(x**2, (x, None, 1))
+    f = Integral(x**2, (x, 1, None))
+    assert e.doit() == Rational(1, 3)
+    assert f.doit() == Rational(-1, 3)
+    assert Integral(x*y, (x, None, y)).subs(y, t) == Integral(x*t, (x, None, t))
+    assert Integral(x*y, (x, y, None)).subs(y, t) == Integral(x*t, (x, t, None))
+    assert integrate(x**2, (x, None, 1)) == Rational(1, 3)
+    assert integrate(x**2, (x, 1, None)) == Rational(-1, 3)
+    assert integrate("x**2", ("x", "1", None)) == Rational(-1, 3)
+
+
+def test_integral_reconstruct():
+    e = Integral(x**2, (x, -1, 1))
+    assert e == Integral(*e.args)
+
+
+def test_doit_integrals():
+    e = Integral(Integral(2*x), (x, 0, 1))
+    assert e.doit() == Rational(1, 3)
+    assert e.doit(deep=False) == Rational(1, 3)
+    f = Function('f')
+    # doesn't matter if the integral can't be performed
+    assert Integral(f(x), (x, 1, 1)).doit() == 0
+    # doesn't matter if the limits can't be evaluated
+    assert Integral(0, (x, 1, Integral(f(x), x))).doit() == 0
+    assert Integral(x, (a, 0)).doit() == 0
+    limits = ((a, 1, exp(x)), (x, 0))
+    assert Integral(a, *limits).doit() == Rational(1, 4)
+    assert Integral(a, *list(reversed(limits))).doit() == 0
+
+
+def test_issue_4884():
+    assert integrate(sqrt(x)*(1 + x)) == \
+        Piecewise(
+            (2*sqrt(x)*(x + 1)**2/5 - 2*sqrt(x)*(x + 1)/15 - 4*sqrt(x)/15,
+            Abs(x + 1) > 1),
+            (2*I*sqrt(-x)*(x + 1)**2/5 - 2*I*sqrt(-x)*(x + 1)/15 -
+            4*I*sqrt(-x)/15, True))
+    assert integrate(x**x*(1 + log(x))) == x**x
+
+def test_issue_18153():
+    assert integrate(x**n*log(x),x) == \
+    Piecewise(
+        (n*x*x**n*log(x)/(n**2 + 2*n + 1) +
+    x*x**n*log(x)/(n**2 + 2*n + 1) - x*x**n/(n**2 + 2*n + 1)
+    , Ne(n, -1)), (log(x)**2/2, True)
+    )
+
+
+def test_is_number():
+    from sympy.abc import x, y, z
+    assert Integral(x).is_number is False
+    assert Integral(1, x).is_number is False
+    assert Integral(1, (x, 1)).is_number is True
+    assert Integral(1, (x, 1, 2)).is_number is True
+    assert Integral(1, (x, 1, y)).is_number is False
+    assert Integral(1, (x, y)).is_number is False
+    assert Integral(x, y).is_number is False
+    assert Integral(x, (y, 1, x)).is_number is False
+    assert Integral(x, (y, 1, 2)).is_number is False
+    assert Integral(x, (x, 1, 2)).is_number is True
+    # `foo.is_number` should always be equivalent to `not foo.free_symbols`
+    # in each of these cases, there are pseudo-free symbols
+    i = Integral(x, (y, 1, 1))
+    assert i.is_number is False and i.n() == 0
+    i = Integral(x, (y, z, z))
+    assert i.is_number is False and i.n() == 0
+    i = Integral(1, (y, z, z + 2))
+    assert i.is_number is False and i.n() == 2.0
+
+    assert Integral(x*y, (x, 1, 2), (y, 1, 3)).is_number is True
+    assert Integral(x*y, (x, 1, 2), (y, 1, z)).is_number is False
+    assert Integral(x, (x, 1)).is_number is True
+    assert Integral(x, (x, 1, Integral(y, (y, 1, 2)))).is_number is True
+    assert Integral(Sum(z, (z, 1, 2)), (x, 1, 2)).is_number is True
+    # it is possible to get a false negative if the integrand is
+    # actually an unsimplified zero, but this is true of is_number in general.
+    assert Integral(sin(x)**2 + cos(x)**2 - 1, x).is_number is False
+    assert Integral(f(x), (x, 0, 1)).is_number is True
+
+
+def test_free_symbols():
+    from sympy.abc import x, y, z
+    assert Integral(0, x).free_symbols == {x}
+    assert Integral(x).free_symbols == {x}
+    assert Integral(x, (x, None, y)).free_symbols == {y}
+    assert Integral(x, (x, y, None)).free_symbols == {y}
+    assert Integral(x, (x, 1, y)).free_symbols == {y}
+    assert Integral(x, (x, y, 1)).free_symbols == {y}
+    assert Integral(x, (x, x, y)).free_symbols == {x, y}
+    assert Integral(x, x, y).free_symbols == {x, y}
+    assert Integral(x, (x, 1, 2)).free_symbols == set()
+    assert Integral(x, (y, 1, 2)).free_symbols == {x}
+    # pseudo-free in this case
+    assert Integral(x, (y, z, z)).free_symbols == {x, z}
+    assert Integral(x, (y, 1, 2), (y, None, None)
+        ).free_symbols == {x, y}
+    assert Integral(x, (y, 1, 2), (x, 1, y)
+        ).free_symbols == {y}
+    assert Integral(2, (y, 1, 2), (y, 1, x), (x, 1, 2)
+        ).free_symbols == set()
+    assert Integral(2, (y, x, 2), (y, 1, x), (x, 1, 2)
+        ).free_symbols == set()
+    assert Integral(2, (x, 1, 2), (y, x, 2), (y, 1, 2)
+        ).free_symbols == {x}
+    assert Integral(f(x), (f(x), 1, y)).free_symbols == {y}
+    assert Integral(f(x), (f(x), 1, x)).free_symbols == {x}
+
+
+def test_is_zero():
+    from sympy.abc import x, m
+    assert Integral(0, (x, 1, x)).is_zero
+    assert Integral(1, (x, 1, 1)).is_zero
+    assert Integral(1, (x, 1, 2), (y, 2)).is_zero is False
+    assert Integral(x, (m, 0)).is_zero
+    assert Integral(x + m, (m, 0)).is_zero is None
+    i = Integral(m, (m, 1, exp(x)), (x, 0))
+    assert i.is_zero is None
+    assert Integral(m, (x, 0), (m, 1, exp(x))).is_zero is True
+
+    assert Integral(x, (x, oo, oo)).is_zero # issue 8171
+    assert Integral(x, (x, -oo, -oo)).is_zero
+
+    # this is zero but is beyond the scope of what is_zero
+    # should be doing
+    assert Integral(sin(x), (x, 0, 2*pi)).is_zero is None
+
+
+def test_series():
+    from sympy.abc import x
+    i = Integral(cos(x), (x, x))
+    e = i.lseries(x)
+    assert i.nseries(x, n=8).removeO() == Add(*[next(e) for j in range(4)])
+
+
+def test_trig_nonelementary_integrals():
+    x = Symbol('x')
+    assert integrate((1 + sin(x))/x, x) == log(x) + Si(x)
+    # next one comes out as log(x) + log(x**2)/2 + Ci(x)
+    # so not hardcoding this log ugliness
+    assert integrate((cos(x) + 2)/x, x).has(Ci)
+
+
+def test_issue_4403():
+    x = Symbol('x')
+    y = Symbol('y')
+    z = Symbol('z', positive=True)
+    assert integrate(sqrt(x**2 + z**2), x) == \
+        z**2*asinh(x/z)/2 + x*sqrt(x**2 + z**2)/2
+    assert integrate(sqrt(x**2 - z**2), x) == \
+        x*sqrt(x**2 - z**2)/2 - z**2*log(x + sqrt(x**2 - z**2))/2
+
+    x = Symbol('x', real=True)
+    y = Symbol('y', positive=True)
+    assert integrate(1/(x**2 + y**2)**S('3/2'), x) == \
+        x/(y**2*sqrt(x**2 + y**2))
+    # If y is real and nonzero, we get x*Abs(y)/(y**3*sqrt(x**2 + y**2)),
+    # which results from sqrt(1 + x**2/y**2) = sqrt(x**2 + y**2)/|y|.
+
+
+def test_issue_4403_2():
+    assert integrate(sqrt(-x**2 - 4), x) == \
+        -2*atan(x/sqrt(-4 - x**2)) + x*sqrt(-4 - x**2)/2
+
+
+def test_issue_4100():
+    R = Symbol('R', positive=True)
+    assert integrate(sqrt(R**2 - x**2), (x, 0, R)) == pi*R**2/4
+
+
+def test_issue_5167():
+    from sympy.abc import w, x, y, z
+    f = Function('f')
+    assert Integral(Integral(f(x), x), x) == Integral(f(x), x, x)
+    assert Integral(f(x)).args == (f(x), Tuple(x))
+    assert Integral(Integral(f(x))).args == (f(x), Tuple(x), Tuple(x))
+    assert Integral(Integral(f(x)), y).args == (f(x), Tuple(x), Tuple(y))
+    assert Integral(Integral(f(x), z), y).args == (f(x), Tuple(z), Tuple(y))
+    assert Integral(Integral(Integral(f(x), x), y), z).args == \
+        (f(x), Tuple(x), Tuple(y), Tuple(z))
+    assert integrate(Integral(f(x), x), x) == Integral(f(x), x, x)
+    assert integrate(Integral(f(x), y), x) == y*Integral(f(x), x)
+    assert integrate(Integral(f(x), x), y) in [Integral(y*f(x), x), y*Integral(f(x), x)]
+    assert integrate(Integral(2, x), x) == x**2
+    assert integrate(Integral(2, x), y) == 2*x*y
+    # don't re-order given limits
+    assert Integral(1, x, y).args != Integral(1, y, x).args
+    # do as many as possible
+    assert Integral(f(x), y, x, y, x).doit() == y**2*Integral(f(x), x, x)/2
+    assert Integral(f(x), (x, 1, 2), (w, 1, x), (z, 1, y)).doit() == \
+        y*(x - 1)*Integral(f(x), (x, 1, 2)) - (x - 1)*Integral(f(x), (x, 1, 2))
+
+
+def test_issue_4890():
+    z = Symbol('z', positive=True)
+    assert integrate(exp(-log(x)**2), x) == \
+        sqrt(pi)*exp(Rational(1, 4))*erf(log(x) - S.Half)/2
+    assert integrate(exp(log(x)**2), x) == \
+        sqrt(pi)*exp(Rational(-1, 4))*erfi(log(x)+S.Half)/2
+    assert integrate(exp(-z*log(x)**2), x) == \
+        sqrt(pi)*exp(1/(4*z))*erf(sqrt(z)*log(x) - 1/(2*sqrt(z)))/(2*sqrt(z))
+
+
+def test_issue_4551():
+    assert not integrate(1/(x*sqrt(1 - x**2)), x).has(Integral)
+
+
+def test_issue_4376():
+    n = Symbol('n', integer=True, positive=True)
+    assert simplify(integrate(n*(x**(1/n) - 1), (x, 0, S.Half)) -
+                (n**2 - 2**(1/n)*n**2 - n*2**(1/n))/(2**(1 + 1/n) + n*2**(1 + 1/n))) == 0
+
+
+def test_issue_4517():
+    assert integrate((sqrt(x) - x**3)/x**Rational(1, 3), x) == \
+        6*x**Rational(7, 6)/7 - 3*x**Rational(11, 3)/11
+
+
+def test_issue_4527():
+    k, m = symbols('k m', integer=True)
+    assert integrate(sin(k*x)*sin(m*x), (x, 0, pi)).simplify() == \
+        Piecewise((0, Eq(k, 0) | Eq(m, 0)),
+                  (-pi/2, Eq(k, -m) | (Eq(k, 0) & Eq(m, 0))),
+                  (pi/2, Eq(k, m) | (Eq(k, 0) & Eq(m, 0))),
+                  (0, True))
+    # Should be possible to further simplify to:
+    # Piecewise(
+    #    (0, Eq(k, 0) | Eq(m, 0)),
+    #    (-pi/2, Eq(k, -m)),
+    #    (pi/2, Eq(k, m)),
+    #    (0, True))
+    assert integrate(sin(k*x)*sin(m*x), (x,)) == Piecewise(
+        (0, And(Eq(k, 0), Eq(m, 0))),
+        (-x*sin(m*x)**2/2 - x*cos(m*x)**2/2 + sin(m*x)*cos(m*x)/(2*m), Eq(k, -m)),
+        (x*sin(m*x)**2/2 + x*cos(m*x)**2/2 - sin(m*x)*cos(m*x)/(2*m), Eq(k, m)),
+        (m*sin(k*x)*cos(m*x)/(k**2 - m**2) -
+         k*sin(m*x)*cos(k*x)/(k**2 - m**2), True))
+
+
+def test_issue_4199():
+    ypos = Symbol('y', positive=True)
+    # TODO: Remove conds='none' below, let the assumption take care of it.
+    assert integrate(exp(-I*2*pi*ypos*x)*x, (x, -oo, oo), conds='none') == \
+        Integral(exp(-I*2*pi*ypos*x)*x, (x, -oo, oo))
+
+
+def test_issue_3940():
+    a, b, c, d = symbols('a:d', positive=True)
+    assert integrate(exp(-x**2 + I*c*x), x) == \
+        -sqrt(pi)*exp(-c**2/4)*erf(I*c/2 - x)/2
+    assert integrate(exp(a*x**2 + b*x + c), x).equals(
+        sqrt(pi)*exp(c - b**2/(4*a))*erfi((2*a*x + b)/(2*sqrt(a)))/(2*sqrt(a)))
+
+    from sympy.core.function import expand_mul
+    from sympy.abc import k
+    assert expand_mul(integrate(exp(-x**2)*exp(I*k*x), (x, -oo, oo))) == \
+        sqrt(pi)*exp(-k**2/4)
+    a, d = symbols('a d', positive=True)
+    assert expand_mul(integrate(exp(-a*x**2 + 2*d*x), (x, -oo, oo))) == \
+        sqrt(pi)*exp(d**2/a)/sqrt(a)
+
+
+def test_issue_5413():
+    # Note that this is not the same as testing ratint() because integrate()
+    # pulls out the coefficient.
+    assert integrate(-a/(a**2 + x**2), x) == I*log(-I*a + x)/2 - I*log(I*a + x)/2
+
+
+def test_issue_4892a():
+    A, z = symbols('A z')
+    c = Symbol('c', nonzero=True)
+    P1 = -A*exp(-z)
+    P2 = -A/(c*t)*(sin(x)**2 + cos(y)**2)
+
+    h1 = -sin(x)**2 - cos(y)**2
+    h2 = -sin(x)**2 + sin(y)**2 - 1
+
+    # there is still some non-deterministic behavior in integrate
+    # or trigsimp which permits one of the following
+    assert integrate(c*(P2 - P1), t) in [
+        c*(-A*(-h1)*log(c*t)/c + A*t*exp(-z)),
+        c*(-A*(-h2)*log(c*t)/c + A*t*exp(-z)),
+        c*( A* h1 *log(c*t)/c + A*t*exp(-z)),
+        c*( A* h2 *log(c*t)/c + A*t*exp(-z)),
+        (A*c*t - A*(-h1)*log(t)*exp(z))*exp(-z),
+        (A*c*t - A*(-h2)*log(t)*exp(z))*exp(-z),
+    ]
+
+
+def test_issue_4892b():
+    # Issues relating to issue 4596 are making the actual result of this hard
+    # to test.  The answer should be something like
+    #
+    # (-sin(y) + sqrt(-72 + 48*cos(y) - 8*cos(y)**2)/2)*log(x + sqrt(-72 +
+    # 48*cos(y) - 8*cos(y)**2)/(2*(3 - cos(y)))) + (-sin(y) - sqrt(-72 +
+    # 48*cos(y) - 8*cos(y)**2)/2)*log(x - sqrt(-72 + 48*cos(y) -
+    # 8*cos(y)**2)/(2*(3 - cos(y)))) + x**2*sin(y)/2 + 2*x*cos(y)
+
+    expr = (sin(y)*x**3 + 2*cos(y)*x**2 + 12)/(x**2 + 2)
+    assert trigsimp(factor(integrate(expr, x).diff(x) - expr)) == 0
+
+
+def test_issue_5178():
+    assert integrate(sin(x)*f(y, z), (x, 0, pi), (y, 0, pi), (z, 0, pi)) == \
+        2*Integral(f(y, z), (y, 0, pi), (z, 0, pi))
+
+
+def test_integrate_series():
+    f = sin(x).series(x, 0, 10)
+    g = x**2/2 - x**4/24 + x**6/720 - x**8/40320 + x**10/3628800 + O(x**11)
+
+    assert integrate(f, x) == g
+    assert diff(integrate(f, x), x) == f
+
+    assert integrate(O(x**5), x) == O(x**6)
+
+
+def test_atom_bug():
+    from sympy.integrals.heurisch import heurisch
+    assert heurisch(meijerg([], [], [1], [], x), x) is None
+
+
+def test_limit_bug():
+    z = Symbol('z', zero=False)
+    assert integrate(sin(x*y*z), (x, 0, pi), (y, 0, pi)).together() == \
+        (log(z) - Ci(pi**2*z) + EulerGamma + 2*log(pi))/z
+
+
+def test_issue_4703():
+    g = Function('g')
+    assert integrate(exp(x)*g(x), x).has(Integral)
+
+
+def test_issue_1888():
+    f = Function('f')
+    assert integrate(f(x).diff(x)**2, x).has(Integral)
+
+# The following tests work using meijerint.
+
+
+def test_issue_3558():
+    assert integrate(cos(x*y), (x, -pi/2, pi/2), (y, 0, pi)) == 2*Si(pi**2/2)
+
+
+def test_issue_4422():
+    assert integrate(1/sqrt(16 + 4*x**2), x) == asinh(x/2) / 2
+
+
+def test_issue_4493():
+    assert simplify(integrate(x*sqrt(1 + 2*x), x)) == \
+        sqrt(2*x + 1)*(6*x**2 + x - 1)/15
+
+
+def test_issue_4737():
+    assert integrate(sin(x)/x, (x, -oo, oo)) == pi
+    assert integrate(sin(x)/x, (x, 0, oo)) == pi/2
+    assert integrate(sin(x)/x, x) == Si(x)
+
+
+def test_issue_4992():
+    # Note: psi in _check_antecedents becomes NaN.
+    from sympy.core.function import expand_func
+    a = Symbol('a', positive=True)
+    assert simplify(expand_func(integrate(exp(-x)*log(x)*x**a, (x, 0, oo)))) == \
+        (a*polygamma(0, a) + 1)*gamma(a)
+
+
+def test_issue_4487():
+    from sympy.functions.special.gamma_functions import lowergamma
+    assert simplify(integrate(exp(-x)*x**y, x)) == lowergamma(y + 1, x)
+
+
+def test_issue_4215():
+    x = Symbol("x")
+    assert integrate(1/(x**2), (x, -1, 1)) is oo
+
+
+def test_issue_4400():
+    n = Symbol('n', integer=True, positive=True)
+    assert integrate((x**n)*log(x), x) == \
+        n*x*x**n*log(x)/(n**2 + 2*n + 1) + x*x**n*log(x)/(n**2 + 2*n + 1) - \
+        x*x**n/(n**2 + 2*n + 1)
+
+
+def test_issue_6253():
+    # Note: this used to raise NotImplementedError
+    # Note: psi in _check_antecedents becomes NaN.
+    assert integrate((sqrt(1 - x) + sqrt(1 + x))**2/x, x, meijerg=True) == \
+        Integral((sqrt(-x + 1) + sqrt(x + 1))**2/x, x)
+
+
+def test_issue_4153():
+    assert integrate(1/(1 + x + y + z), (x, 0, 1), (y, 0, 1), (z, 0, 1)) in [
+        -12*log(3) - 3*log(6)/2 + 3*log(8)/2 + 5*log(2) + 7*log(4),
+        6*log(2) + 8*log(4) - 27*log(3)/2, 22*log(2) - 27*log(3)/2,
+        -12*log(3) - 3*log(6)/2 + 47*log(2)/2]
+
+
+def test_issue_4326():
+    R, b, h = symbols('R b h')
+    # It doesn't matter if we can do the integral.  Just make sure the result
+    # doesn't contain nan.  This is really a test against _eval_interval.
+    e = integrate(((h*(x - R + b))/b)*sqrt(R**2 - x**2), (x, R - b, R))
+    assert not e.has(nan)
+    # See that it evaluates
+    assert not e.has(Integral)
+
+
+def test_powers():
+    assert integrate(2**x + 3**x, x) == 2**x/log(2) + 3**x/log(3)
+
+
+def test_manual_option():
+    raises(ValueError, lambda: integrate(1/x, x, manual=True, meijerg=True))
+    # an example of a function that manual integration cannot handle
+    assert integrate(log(1+x)/x, (x, 0, 1), manual=True).has(Integral)
+
+
+def test_meijerg_option():
+    raises(ValueError, lambda: integrate(1/x, x, meijerg=True, risch=True))
+    # an example of a function that meijerg integration cannot handle
+    assert integrate(tan(x), x, meijerg=True) == Integral(tan(x), x)
+
+
+def test_risch_option():
+    # risch=True only allowed on indefinite integrals
+    raises(ValueError, lambda: integrate(1/log(x), (x, 0, oo), risch=True))
+    assert integrate(exp(-x**2), x, risch=True) == NonElementaryIntegral(exp(-x**2), x)
+    assert integrate(log(1/x)*y, x, y, risch=True) == y**2*(x*log(1/x)/2 + x/2)
+    assert integrate(erf(x), x, risch=True) == Integral(erf(x), x)
+    # TODO: How to test risch=False?
+
+
+@slow
+def test_heurisch_option():
+    raises(ValueError, lambda: integrate(1/x, x, risch=True, heurisch=True))
+    # an integral that heurisch can handle
+    assert integrate(exp(x**2), x, heurisch=True) == sqrt(pi)*erfi(x)/2
+    # an integral that heurisch currently cannot handle
+    assert integrate(exp(x)/x, x, heurisch=True) == Integral(exp(x)/x, x)
+    # an integral where heurisch currently hangs, issue 15471
+    assert integrate(log(x)*cos(log(x))/x**Rational(3, 4), x, heurisch=False) == (
+        -128*x**Rational(1, 4)*sin(log(x))/289 + 240*x**Rational(1, 4)*cos(log(x))/289 +
+        (16*x**Rational(1, 4)*sin(log(x))/17 + 4*x**Rational(1, 4)*cos(log(x))/17)*log(x))
+
+
+def test_issue_6828():
+    f = 1/(1.08*x**2 - 4.3)
+    g = integrate(f, x).diff(x)
+    assert verify_numerically(f, g, tol=1e-12)
+
+
+def test_issue_4803():
+    x_max = Symbol("x_max")
+    assert integrate(y/pi*exp(-(x_max - x)/cos(a)), x) == \
+        y*exp((x - x_max)/cos(a))*cos(a)/pi
+
+
+def test_issue_4234():
+    assert integrate(1/sqrt(1 + tan(x)**2)) == tan(x)/sqrt(1 + tan(x)**2)
+
+
+def test_issue_4492():
+    assert simplify(integrate(x**2 * sqrt(5 - x**2), x)).factor(
+        deep=True) == Piecewise(
+        (I*(2*x**5 - 15*x**3 + 25*x - 25*sqrt(x**2 - 5)*acosh(sqrt(5)*x/5)) /
+            (8*sqrt(x**2 - 5)), (x > sqrt(5)) | (x < -sqrt(5))),
+        ((2*x**5 - 15*x**3 + 25*x - 25*sqrt(5 - x**2)*asin(sqrt(5)*x/5)) /
+            (-8*sqrt(-x**2 + 5)), True))
+
+
+def test_issue_2708():
+    # This test needs to use an integration function that can
+    # not be evaluated in closed form.  Update as needed.
+    f = 1/(a + z + log(z))
+    integral_f = NonElementaryIntegral(f, (z, 2, 3))
+    assert Integral(f, (z, 2, 3)).doit() == integral_f
+    assert integrate(f + exp(z), (z, 2, 3)) == integral_f - exp(2) + exp(3)
+    assert integrate(2*f + exp(z), (z, 2, 3)) == \
+        2*integral_f - exp(2) + exp(3)
+    assert integrate(exp(1.2*n*s*z*(-t + z)/t), (z, 0, x)) == \
+        NonElementaryIntegral(exp(-1.2*n*s*z)*exp(1.2*n*s*z**2/t),
+                                  (z, 0, x))
+
+
+def test_issue_2884():
+    f = (4.000002016020*x + 4.000002016020*y + 4.000006024032)*exp(10.0*x)
+    e = integrate(f, (x, 0.1, 0.2))
+    assert str(e) == '1.86831064982608*y + 2.16387491480008'
+
+
+def test_issue_8368i():
+    from sympy.functions.elementary.complexes import arg, Abs
+    assert integrate(exp(-s*x)*cosh(x), (x, 0, oo)) == \
+        Piecewise(
+            (   pi*Piecewise(
+                    (   -s/(pi*(-s**2 + 1)),
+                        Abs(s**2) < 1),
+                    (   1/(pi*s*(1 - 1/s**2)),
+                        Abs(s**(-2)) < 1),
+                    (   meijerg(
+                            ((S.Half,), (0, 0)),
+                            ((0, S.Half), (0,)),
+                            polar_lift(s)**2),
+                        True)
+                ),
+                s**2 > 1
+            ),
+            (
+                Integral(exp(-s*x)*cosh(x), (x, 0, oo)),
+                True))
+    assert integrate(exp(-s*x)*sinh(x), (x, 0, oo)) == \
+        Piecewise(
+            (   -1/(s + 1)/2 - 1/(-s + 1)/2,
+                And(
+                    Abs(s) > 1,
+                    Abs(arg(s)) < pi/2,
+                    Abs(arg(s)) <= pi/2
+                    )),
+            (   Integral(exp(-s*x)*sinh(x), (x, 0, oo)),
+                True))
+
+
+def test_issue_8901():
+    assert integrate(sinh(1.0*x)) == 1.0*cosh(1.0*x)
+    assert integrate(tanh(1.0*x)) == 1.0*x - 1.0*log(tanh(1.0*x) + 1)
+    assert integrate(tanh(x)) == x - log(tanh(x) + 1)
+
+
+@slow
+def test_issue_8945():
+    assert integrate(sin(x)**3/x, (x, 0, 1)) == -Si(3)/4 + 3*Si(1)/4
+    assert integrate(sin(x)**3/x, (x, 0, oo)) == pi/4
+    assert integrate(cos(x)**2/x**2, x) == -Si(2*x) - cos(2*x)/(2*x) - 1/(2*x)
+
+
+@slow
+def test_issue_7130():
+    i, L, a, b = symbols('i L a b')
+    integrand = (cos(pi*i*x/L)**2 / (a + b*x)).rewrite(exp)
+    assert x not in integrate(integrand, (x, 0, L)).free_symbols
+
+
+def test_issue_10567():
+    a, b, c, t = symbols('a b c t')
+    vt = Matrix([a*t, b, c])
+    assert integrate(vt, t) == Integral(vt, t).doit()
+    assert integrate(vt, t) == Matrix([[a*t**2/2], [b*t], [c*t]])
+
+
+def test_issue_11742():
+    assert integrate(sqrt(-x**2 + 8*x + 48), (x, 4, 12)) == 16*pi
+
+
+def test_issue_11856():
+    t = symbols('t')
+    assert integrate(sinc(pi*t), t) == Si(pi*t)/pi
+
+
+@slow
+def test_issue_11876():
+    assert integrate(sqrt(log(1/x)), (x, 0, 1)) == sqrt(pi)/2
+
+
+def test_issue_4950():
+    assert integrate((-60*exp(x) - 19.2*exp(4*x))*exp(4*x), x) ==\
+        -2.4*exp(8*x) - 12.0*exp(5*x)
+
+
+def test_issue_4968():
+    assert integrate(sin(log(x**2))) == x*sin(log(x**2))/5 - 2*x*cos(log(x**2))/5
+
+
+def test_singularities():
+    assert integrate(1/x**2, (x, -oo, oo)) is oo
+    assert integrate(1/x**2, (x, -1, 1)) is oo
+    assert integrate(1/(x - 1)**2, (x, -2, 2)) is oo
+
+    assert integrate(1/x**2, (x, 1, -1)) is -oo
+    assert integrate(1/(x - 1)**2, (x, 2, -2)) is -oo
+
+
+def test_issue_12645():
+    x, y = symbols('x y', real=True)
+    assert (integrate(sin(x*x*x + y*y),
+                      (x, -sqrt(pi - y*y), sqrt(pi - y*y)),
+                      (y, -sqrt(pi), sqrt(pi)))
+                == Integral(sin(x**3 + y**2),
+                            (x, -sqrt(-y**2 + pi), sqrt(-y**2 + pi)),
+                            (y, -sqrt(pi), sqrt(pi))))
+
+
+def test_issue_12677():
+    assert integrate(sin(x) / (cos(x)**3), (x, 0, pi/6)) == Rational(1, 6)
+
+
+def test_issue_14078():
+    assert integrate((cos(3*x)-cos(x))/x, (x, 0, oo)) == -log(3)
+
+
+def test_issue_14064():
+    assert integrate(1/cosh(x), (x, 0, oo)) == pi/2
+
+
+def test_issue_14027():
+    assert integrate(1/(1 + exp(x - S.Half)/(1 + exp(x))), x) == \
+        x - exp(S.Half)*log(exp(x) + exp(S.Half)/(1 + exp(S.Half)))/(exp(S.Half) + E)
+
+
+def test_issue_8170():
+    assert integrate(tan(x), (x, 0, pi/2)) is S.Infinity
+
+
+def test_issue_8440_14040():
+    assert integrate(1/x, (x, -1, 1)) is S.NaN
+    assert integrate(1/(x + 1), (x, -2, 3)) is S.NaN
+
+
+def test_issue_14096():
+    assert integrate(1/(x + y)**2, (x, 0, 1)) == -1/(y + 1) + 1/y
+    assert integrate(1/(1 + x + y + z)**2, (x, 0, 1), (y, 0, 1), (z, 0, 1)) == \
+        -4*log(4) - 6*log(2) + 9*log(3)
+
+
+def test_issue_14144():
+    assert Abs(integrate(1/sqrt(1 - x**3), (x, 0, 1)).n() - 1.402182) < 1e-6
+    assert Abs(integrate(sqrt(1 - x**3), (x, 0, 1)).n() - 0.841309) < 1e-6
+
+
+def test_issue_14375():
+    # This raised a TypeError. The antiderivative has exp_polar, which
+    # may be possible to unpolarify, so the exact output is not asserted here.
+    assert integrate(exp(I*x)*log(x), x).has(Ei)
+
+
+def test_issue_14437():
+    f = Function('f')(x, y, z)
+    assert integrate(f, (x, 0, 1), (y, 0, 2), (z, 0, 3)) == \
+                Integral(f, (x, 0, 1), (y, 0, 2), (z, 0, 3))
+
+
+def test_issue_14470():
+    assert integrate(1/sqrt(exp(x) + 1), x) == log(sqrt(exp(x) + 1) - 1) - log(sqrt(exp(x) + 1) + 1)
+
+
+def test_issue_14877():
+    f = exp(1 - exp(x**2)*x + 2*x**2)*(2*x**3 + x)/(1 - exp(x**2)*x)**2
+    assert integrate(f, x) == \
+        -exp(2*x**2 - x*exp(x**2) + 1)/(x*exp(3*x**2) - exp(2*x**2))
+
+
+def test_issue_14782():
+    f = sqrt(-x**2 + 1)*(-x**2 + x)
+    assert integrate(f, [x, -1, 1]) == - pi / 8
+
+
+@slow
+def test_issue_14782_slow():
+    f = sqrt(-x**2 + 1)*(-x**2 + x)
+    assert integrate(f, [x, 0, 1]) == S.One / 3 - pi / 16
+
+
+def test_issue_12081():
+    f = x**(Rational(-3, 2))*exp(-x)
+    assert integrate(f, [x, 0, oo]) is oo
+
+
+def test_issue_15285():
+    y = 1/x - 1
+    f = 4*y*exp(-2*y)/x**2
+    assert integrate(f, [x, 0, 1]) == 1
+
+
+def test_issue_15432():
+    assert integrate(x**n * exp(-x) * log(x), (x, 0, oo)).gammasimp() == Piecewise(
+        (gamma(n + 1)*polygamma(0, n) + gamma(n + 1)/n, re(n) + 1 > 0),
+        (Integral(x**n*exp(-x)*log(x), (x, 0, oo)), True))
+
+
+def test_issue_15124():
+    omega = IndexedBase('omega')
+    m, p = symbols('m p', cls=Idx)
+    assert integrate(exp(x*I*(omega[m] + omega[p])), x, conds='none') == \
+        -I*exp(I*x*omega[m])*exp(I*x*omega[p])/(omega[m] + omega[p])
+
+
+def test_issue_15218():
+    with warns_deprecated_sympy():
+        Integral(Eq(x, y))
+    with warns_deprecated_sympy():
+        assert Integral(Eq(x, y), x) == Eq(Integral(x, x), Integral(y, x))
+    with warns_deprecated_sympy():
+        assert Integral(Eq(x, y), x).doit() == Eq(x**2/2, x*y)
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        # The warning is made in the ExprWithLimits superclass. The stacklevel
+        # is correct for integrate(Eq) but not Eq.integrate
+        assert Eq(x, y).integrate(x) == Eq(x**2/2, x*y)
+
+    # These are not deprecated because they are definite integrals
+    assert integrate(Eq(x, y), (x, 0, 1)) == Eq(S.Half, y)
+    assert Eq(x, y).integrate((x, 0, 1)) == Eq(S.Half, y)
+
+
+def test_issue_15292():
+    res = integrate(exp(-x**2*cos(2*t)) * cos(x**2*sin(2*t)), (x, 0, oo))
+    assert isinstance(res, Piecewise)
+    assert gammasimp((res - sqrt(pi)/2 * cos(t)).subs(t, pi/6)) == 0
+
+
+def test_issue_4514():
+    assert integrate(sin(2*x)/sin(x), x) == 2*sin(x)
+
+
+def test_issue_15457():
+    x, a, b = symbols('x a b', real=True)
+    definite = integrate(exp(Abs(x-2)), (x, a, b))
+    indefinite = integrate(exp(Abs(x-2)), x)
+    assert definite.subs({a: 1, b: 3}) == -2 + 2*E
+    assert indefinite.subs(x, 3) - indefinite.subs(x, 1) == -2 + 2*E
+    assert definite.subs({a: -3, b: -1}) == -exp(3) + exp(5)
+    assert indefinite.subs(x, -1) - indefinite.subs(x, -3) == -exp(3) + exp(5)
+
+
+def test_issue_15431():
+    assert integrate(x*exp(x)*log(x), x) == \
+        (x*exp(x) - exp(x))*log(x) - exp(x) + Ei(x)
+
+
+def test_issue_15640_log_substitutions():
+    f = x/log(x)
+    F = Ei(2*log(x))
+    assert integrate(f, x) == F and F.diff(x) == f
+    f = x**3/log(x)**2
+    F = -x**4/log(x) + 4*Ei(4*log(x))
+    assert integrate(f, x) == F and F.diff(x) == f
+    f = sqrt(log(x))/x**2
+    F = -sqrt(pi)*erfc(sqrt(log(x)))/2 - sqrt(log(x))/x
+    assert integrate(f, x) == F and F.diff(x) == f
+
+
+def test_issue_15509():
+    from sympy.vector import CoordSys3D
+    N = CoordSys3D('N')
+    x = N.x
+    assert integrate(cos(a*x + b), (x, x_1, x_2), heurisch=True) == Piecewise(
+        (-sin(a*x_1 + b)/a + sin(a*x_2 + b)/a, (a > -oo) & (a < oo) & Ne(a, 0)), \
+            (-x_1*cos(b) + x_2*cos(b), True))
+
+
+def test_issue_4311_fast():
+    x = symbols('x', real=True)
+    assert integrate(x*abs(9-x**2), x) == Piecewise(
+        (x**4/4 - 9*x**2/2, x <= -3),
+        (-x**4/4 + 9*x**2/2 - Rational(81, 2), x <= 3),
+        (x**4/4 - 9*x**2/2, True))
+
+
+def test_integrate_with_complex_constants():
+    K = Symbol('K', positive=True)
+    x = Symbol('x', real=True)
+    m = Symbol('m', real=True)
+    t = Symbol('t', real=True)
+    assert integrate(exp(-I*K*x**2+m*x), x) == sqrt(pi)*exp(-I*m**2
+                    /(4*K))*erfi((-2*I*K*x + m)/(2*sqrt(K)*sqrt(-I)))/(2*sqrt(K)*sqrt(-I))
+    assert integrate(1/(1 + I*x**2), x) == (-I*(sqrt(-I)*log(x - I*sqrt(-I))/2
+            - sqrt(-I)*log(x + I*sqrt(-I))/2))
+    assert integrate(exp(-I*x**2), x) == sqrt(pi)*erf(sqrt(I)*x)/(2*sqrt(I))
+
+    assert integrate((1/(exp(I*t)-2)), t) == -t/2 - I*log(exp(I*t) - 2)/2
+    assert integrate((1/(exp(I*t)-2)), (t, 0, 2*pi)) == -pi
+
+
+def test_issue_14241():
+    x = Symbol('x')
+    n = Symbol('n', positive=True, integer=True)
+    assert integrate(n * x ** (n - 1) / (x + 1), x) == \
+           n**2*x**n*lerchphi(x*exp_polar(I*pi), 1, n)*gamma(n)/gamma(n + 1)
+
+
+def test_issue_13112():
+    assert integrate(sin(t)**2 / (5 - 4*cos(t)), [t, 0, 2*pi]) == pi / 4
+
+
+def test_issue_14709b():
+    h = Symbol('h', positive=True)
+    i = integrate(x*acos(1 - 2*x/h), (x, 0, h))
+    assert i == 5*h**2*pi/16
+
+
+def test_issue_8614():
+    x = Symbol('x')
+    t = Symbol('t')
+    assert integrate(exp(t)/t, (t, -oo, x)) == Ei(x)
+    assert integrate((exp(-x) - exp(-2*x))/x, (x, 0, oo)) == log(2)
+
+
+@slow
+def test_issue_15494():
+    s = symbols('s', positive=True)
+
+    integrand = (exp(s/2) - 2*exp(1.6*s) + exp(s))*exp(s)
+    solution = integrate(integrand, s)
+    assert solution != S.NaN
+    # Not sure how to test this properly as it is a symbolic expression with floats
+    # assert str(solution) == '0.666666666666667*exp(1.5*s) + 0.5*exp(2.0*s) - 0.769230769230769*exp(2.6*s)'
+    # Maybe
+    assert abs(solution.subs(s, 1) - (-3.67440080236188)) <= 1e-8
+
+    integrand = (exp(s/2) - 2*exp(S(8)/5*s) + exp(s))*exp(s)
+    assert integrate(integrand, s) == -10*exp(13*s/5)/13 + 2*exp(3*s/2)/3 + exp(2*s)/2
+
+
+def test_li_integral():
+    y = Symbol('y')
+    assert Integral(li(y*x**2), x).doit() == Piecewise((x*li(x**2*y) - \
+        x*Ei(3*log(x**2*y)/2)/sqrt(x**2*y),
+        Ne(y, 0)), (0, True))
+
+
+def test_issue_17473():
+    x = Symbol('x')
+    n = Symbol('n')
+    h = S.Half
+    ans = x**(n + 1)*gamma(h + h/n)*hyper((h + h/n,),
+        (3*h, 3*h + h/n), -x**(2*n)/4)/(2*n*gamma(3*h + h/n))
+    got = integrate(sin(x**n), x)
+    assert got == ans
+    _x = Symbol('x', zero=False)
+    reps = {x: _x}
+    assert integrate(sin(_x**n), _x) == ans.xreplace(reps).expand()
+
+
+def test_issue_17671():
+    assert integrate(log(log(x)) / x**2, [x, 1, oo]) == -EulerGamma
+    assert integrate(log(log(x)) / x**3, [x, 1, oo]) == -log(2)/2 - EulerGamma/2
+    assert integrate(log(log(x)) / x**10, [x, 1, oo]) == -log(9)/9 - EulerGamma/9
+
+
+def test_issue_2975():
+    w = Symbol('w')
+    C = Symbol('C')
+    y = Symbol('y')
+    assert integrate(1/(y**2+C)**(S(3)/2), (y, -w/2, w/2)) == w/(C**(S(3)/2)*sqrt(1 + w**2/(4*C)))
+
+
+def test_issue_7827():
+    x, n, M = symbols('x n M')
+    N = Symbol('N', integer=True)
+    assert integrate(summation(x*n, (n, 1, N)), x) == x**2*(N**2/4 + N/4)
+    assert integrate(summation(x*sin(n), (n,1,N)), x) == \
+        Sum(x**2*sin(n)/2, (n, 1, N))
+    assert integrate(summation(sin(n*x), (n,1,N)), x) == \
+        Sum(Piecewise((-cos(n*x)/n, Ne(n, 0)), (0, True)), (n, 1, N))
+    assert integrate(integrate(summation(sin(n*x), (n,1,N)), x), x) == \
+        Piecewise((Sum(Piecewise((-sin(n*x)/n**2, Ne(n, 0)), (-x/n, True)),
+        (n, 1, N)), (n > -oo) & (n < oo) & Ne(n, 0)), (0, True))
+    assert integrate(Sum(x, (n, 1, M)), x) == M*x**2/2
+    raises(ValueError, lambda: integrate(Sum(x, (x, y, n)), y))
+    raises(ValueError, lambda: integrate(Sum(x, (x, 1, n)), n))
+    raises(ValueError, lambda: integrate(Sum(x, (x, 1, y)), x))
+
+
+def test_issue_4231():
+    f = (1 + 2*x + sqrt(x + log(x))*(1 + 3*x) + x**2)/(x*(x + sqrt(x + log(x)))*sqrt(x + log(x)))
+    assert integrate(f, x) == 2*sqrt(x + log(x)) + 2*log(x + sqrt(x + log(x)))
+
+
+def test_issue_17841():
+    f = diff(1/(x**2+x+I), x)
+    assert integrate(f, x) == 1/(x**2 + x + I)
+
+
+def test_issue_21034():
+    x = Symbol('x', real=True, nonzero=True)
+    f1 = x*(-x**4/asin(5)**4 - x*sinh(x + log(asin(5))) + 5)
+    f2 = (x + cosh(cos(4)))/(x*(x + 1/(12*x)))
+
+    assert integrate(f1, x) == \
+        -x**6/(6*asin(5)**4) - x**2*cosh(x + log(asin(5))) + 5*x**2/2 + 2*x*sinh(x + log(asin(5))) - 2*cosh(x + log(asin(5)))
+
+    assert integrate(f2, x) == \
+        log(x**2 + S(1)/12)/2 + 2*sqrt(3)*cosh(cos(4))*atan(2*sqrt(3)*x)
+
+
+def test_issue_4187():
+    assert integrate(log(x)*exp(-x), x) == Ei(-x) - exp(-x)*log(x)
+    assert integrate(log(x)*exp(-x), (x, 0, oo)) == -EulerGamma
+
+
+def test_issue_5547():
+    L = Symbol('L')
+    z = Symbol('z')
+    r0 = Symbol('r0')
+    R0 = Symbol('R0')
+
+    assert integrate(r0**2*cos(z)**2, (z, -L/2, L/2)) == -r0**2*(-L/4 -
+                    sin(L/2)*cos(L/2)/2) + r0**2*(L/4 + sin(L/2)*cos(L/2)/2)
+
+    assert integrate(r0**2*cos(R0*z)**2, (z, -L/2, L/2)) == Piecewise(
+        (-r0**2*(-L*R0/4 - sin(L*R0/2)*cos(L*R0/2)/2)/R0 +
+         r0**2*(L*R0/4 + sin(L*R0/2)*cos(L*R0/2)/2)/R0, (R0 > -oo) & (R0 < oo) & Ne(R0, 0)),
+        (L*r0**2, True))
+
+    w = 2*pi*z/L
+
+    sol = sqrt(2)*sqrt(L)*r0**2*fresnelc(sqrt(2)*sqrt(L))*gamma(S.One/4)/(16*gamma(S(5)/4)) + L*r0**2/2
+
+    assert integrate(r0**2*cos(w*z)**2, (z, -L/2, L/2)) == sol
+
+
+def test_issue_15810():
+    assert integrate(1/(2**(2*x/3) + 1), (x, 0, oo)) == Rational(3, 2)
+
+
+def test_issue_21024():
+    x = Symbol('x', real=True, nonzero=True)
+    f = log(x)*log(4*x) + log(3*x + exp(2))
+    F = x*log(x)**2 + x*log(3*x + exp(2)) + x*(1 - 2*log(2)) + \
+        (-2*x + 2*x*log(2))*log(x) + exp(2)*log(3*x + exp(2))/3
+    assert F == integrate(f, x)
+
+    f = (x + exp(3))/x**2
+    F = log(x) - exp(3)/x
+    assert F == integrate(f, x)
+
+    f = (x**2 + exp(5))/x
+    F = x**2/2 + exp(5)*log(x)
+    assert F == integrate(f, x)
+
+    f = x/(2*x + tanh(1))
+    F = x/2 - log(2*x + tanh(1))*tanh(1)/4
+    assert F == integrate(f, x)
+
+    f = x - sinh(4)/x
+    F = x**2/2 - log(x)*sinh(4)
+    assert F == integrate(f, x)
+
+    f = log(x + exp(5)/x)
+    F = x*log(x + exp(5)/x) - x + 2*exp(Rational(5, 2))*atan(x*exp(Rational(-5, 2)))
+    assert F == integrate(f, x)
+
+    f = x**5/(x + E)
+    F = x**5/5 - E*x**4/4 + x**3*exp(2)/3 - x**2*exp(3)/2 + x*exp(4) - exp(5)*log(x + E)
+    assert F == integrate(f, x)
+
+    f = 4*x/(x + sinh(5))
+    F = 4*x - 4*log(x + sinh(5))*sinh(5)
+    assert F == integrate(f, x)
+
+    f = x**2/(2*x + sinh(2))
+    F = x**2/4 - x*sinh(2)/4 + log(2*x + sinh(2))*sinh(2)**2/8
+    assert F == integrate(f, x)
+
+    f = -x**2/(x + E)
+    F = -x**2/2 + E*x - exp(2)*log(x + E)
+    assert F == integrate(f, x)
+
+    f = (2*x + 3)*exp(5)/x
+    F = 2*x*exp(5) + 3*exp(5)*log(x)
+    assert F == integrate(f, x)
+
+    f = x + 2 + cosh(3)/x
+    F = x**2/2 + 2*x + log(x)*cosh(3)
+    assert F == integrate(f, x)
+
+    f = x - tanh(1)/x**3
+    F = x**2/2 + tanh(1)/(2*x**2)
+    assert F == integrate(f, x)
+
+    f = (3*x - exp(6))/x
+    F = 3*x - exp(6)*log(x)
+    assert F == integrate(f, x)
+
+    f = x**4/(x + exp(5))**2 + x
+    F = x**3/3 + x**2*(Rational(1, 2) - exp(5)) + 3*x*exp(10) - 4*exp(15)*log(x + exp(5)) - exp(20)/(x + exp(5))
+    assert F == integrate(f, x)
+
+    f = x*(x + exp(10)/x**2) + x
+    F = x**3/3 + x**2/2 + exp(10)*log(x)
+    assert F == integrate(f, x)
+
+    f = x + x/(5*x + sinh(3))
+    F = x**2/2 + x/5 - log(5*x + sinh(3))*sinh(3)/25
+    assert F == integrate(f, x)
+
+    f = (x + exp(3))/(2*x**2 + 2*x)
+    F = exp(3)*log(x)/2 - exp(3)*log(x + 1)/2 + log(x + 1)/2
+    assert F == integrate(f, x).expand()
+
+    f = log(x + 4*sinh(4))
+    F = x*log(x + 4*sinh(4)) - x + 4*log(x + 4*sinh(4))*sinh(4)
+    assert F == integrate(f, x)
+
+    f = -x + 20*(exp(-5) - atan(4)/x)**3*sin(4)/x
+    F = (-x**2*exp(15)/2 + 20*log(x)*sin(4) - (-180*x**2*exp(5)*sin(4)*atan(4) + 90*x*exp(10)*sin(4)*atan(4)**2 - \
+        20*exp(15)*sin(4)*atan(4)**3)/(3*x**3))*exp(-15)
+    assert F == integrate(f, x)
+
+    f = 2*x**2*exp(-4) + 6/x
+    F_true = (2*x**3/3 + 6*exp(4)*log(x))*exp(-4)
+    assert F_true == integrate(f, x)
+
+
+def test_issue_21721():
+    a = Symbol('a')
+    assert integrate(1/(pi*(1+(x-a)**2)),(x,-oo,oo)).expand() == \
+    -Heaviside(im(a) - 1, 0) + Heaviside(im(a) + 1, 0)
+
+
+def test_issue_21831():
+    theta = symbols('theta')
+    assert integrate(cos(3*theta)/(5-4*cos(theta)), (theta, 0, 2*pi)) == pi/12
+    integrand = cos(2*theta)/(5 - 4*cos(theta))
+    assert integrate(integrand, (theta, 0, 2*pi)) == pi/6
+
+
+@slow
+def test_issue_22033_integral():
+    assert integrate((x**2 - Rational(1, 4))**2 * sqrt(1 - x**2), (x, -1, 1)) == pi/32
+
+
+@slow
+def test_issue_21671():
+    assert integrate(1,(z,x**2+y**2,2-x**2-y**2),(y,-sqrt(1-x**2),sqrt(1-x**2)),(x,-1,1)) == pi
+    assert integrate(-4*(1 - x**2)**(S(3)/2)/3 + 2*sqrt(1 - x**2)*(2 - 2*x**2), (x, -1, 1)) == pi
+
+
+def test_issue_18527():
+    # The manual integrator can not currently solve this. Assert that it does
+    # not give an incorrect result involving Abs when x has real assumptions.
+    xr = symbols('xr', real=True)
+    expr = (cos(x)/(4+(sin(x))**2))
+    res_real = integrate(expr.subs(x, xr), xr, manual=True).subs(xr, x)
+    assert integrate(expr, x, manual=True) == res_real == Integral(expr, x)
+
+
+def test_issue_23718():
+    f = 1/(b*cos(x) + a*sin(x))
+    Fpos = (-log(-a/b + tan(x/2) - sqrt(a**2 + b**2)/b)/sqrt(a**2 + b**2)
+            +log(-a/b + tan(x/2) + sqrt(a**2 + b**2)/b)/sqrt(a**2 + b**2))
+    F = Piecewise(
+        # XXX: The zoo case here is for a=b=0 so it should just be zoo or maybe
+        # it doesn't really need to be included at all given that the original
+        # integrand is really undefined in that case anyway.
+        (zoo*(-log(tan(x/2) - 1) + log(tan(x/2) + 1)),  Eq(a, 0) & Eq(b, 0)),
+        (log(tan(x/2))/a,                               Eq(b, 0)),
+        (-I/(-I*b*sin(x) + b*cos(x)),                   Eq(a, -I*b)),
+        (I/(I*b*sin(x) + b*cos(x)),                     Eq(a,  I*b)),
+        (Fpos,                                          True),
+    )
+    assert integrate(f, x) == F
+
+    ap, bp = symbols('a, b', positive=True)
+    rep = {a: ap, b: bp}
+    assert integrate(f.subs(rep), x) == Fpos.subs(rep)
+
+
+def test_issue_23566():
+    i = integrate(1/sqrt(x**2-1), (x, -2, -1))
+    assert i == -log(2 - sqrt(3))
+    assert math.isclose(i.n(), 1.31695789692482)
+
+
+def test_pr_23583():
+    # This result from meijerg is wrong. Check whether new result is correct when this test fail.
+    assert integrate(1/sqrt((x - I)**2-1)) == Piecewise((acosh(x - I), Abs((x - I)**2) > 1), (-I*asin(x - I), True))
+
+
+def test_issue_7264():
+    assert integrate(exp(x)*sqrt(1 + exp(2*x))) == sqrt(exp(2*x) + 1)*exp(x)/2 + asinh(exp(x))/2
+
+
+def test_issue_11254a():
+    assert integrate(sech(x), (x, 0, 1)) == 2*atan(tanh(S.Half))
+
+
+def test_issue_11254b():
+    assert integrate(csch(x), x) == log(tanh(x/2))
+    assert integrate(csch(x), (x, 0, 1)) == oo
+
+
+def test_issue_11254d():
+    # (sech(x)**2).rewrite(sinh)
+    assert integrate(-1/sinh(x + I*pi/2, evaluate=False)**2, x) == -2/(exp(2*x) + 1)
+    assert integrate(cosh(x)**(-2), x) == 2*tanh(x/2)/(tanh(x/2)**2 + 1)
+
+
+def test_issue_22863():
+    i = integrate((3*x**3-x**2+2*x-4)/sqrt(x**2-3*x+2), (x, 0, 1))
+    assert i == -101*sqrt(2)/8 - 135*log(3 - 2*sqrt(2))/16
+    assert math.isclose(i.n(), -2.98126694400554)
+
+
+def test_issue_9723():
+    assert integrate(sqrt(x + sqrt(x))) == \
+        2*sqrt(sqrt(x) + x)*(sqrt(x)/12 + x/3 - S(1)/8) + log(2*sqrt(x) + 2*sqrt(sqrt(x) + x) + 1)/8
+    assert integrate(sqrt(2*x+3+sqrt(4*x+5))**3) == \
+        sqrt(2*x + sqrt(4*x + 5) + 3) * \
+           (9*x/10 + 11*(4*x + 5)**(S(3)/2)/40 + sqrt(4*x + 5)/40 + (4*x + 5)**2/10 + S(11)/10)/2
+
+
+def test_issue_23704():
+    # XXX: This is testing that an exception is not raised in risch Ideally
+    # manualintegrate (manual=True) would be able to compute this but
+    # manualintegrate is very slow for this example so we don't test that here.
+    assert (integrate(log(x)/x**2/(c*x**2+b*x+a),x, risch=True)
+        == NonElementaryIntegral(log(x)/(a*x**2 + b*x**3 + c*x**4), x))
+
+
+def test_exp_substitution():
+    assert integrate(1/sqrt(1-exp(2*x))) == log(sqrt(1 - exp(2*x)) - 1)/2 - log(sqrt(1 - exp(2*x)) + 1)/2
+
+
+def test_hyperbolic():
+    assert integrate(coth(x)) == x - log(tanh(x) + 1) + log(tanh(x))
+    assert integrate(sech(x)) == 2*atan(tanh(x/2))
+    assert integrate(csch(x)) == log(tanh(x/2))
+
+
+def test_nested_pow():
+    assert integrate(sqrt(x**2)) == x*sqrt(x**2)/2
+    assert integrate(sqrt(x**(S(5)/3))) == 6*x*sqrt(x**(S(5)/3))/11
+    assert integrate(1/sqrt(x**2)) == x*log(x)/sqrt(x**2)
+    assert integrate(x*sqrt(x**(-4))) == x**2*sqrt(x**-4)*log(x)
+
+
+def test_sqrt_quadratic():
+    assert integrate(1/sqrt(3*x**2+4*x+5)) == sqrt(3)*asinh(3*sqrt(11)*(x + S(2)/3)/11)/3
+    assert integrate(1/sqrt(-3*x**2+4*x+5)) == sqrt(3)*asin(3*sqrt(19)*(x - S(2)/3)/19)/3
+    assert integrate(1/sqrt(3*x**2+4*x-5)) == sqrt(3)*log(6*x + 2*sqrt(3)*sqrt(3*x**2 + 4*x - 5) + 4)/3
+    assert integrate(1/sqrt(4*x**2-4*x+1)) == (x - S.Half)*log(x - S.Half)/(2*sqrt((x - S.Half)**2))
+    assert integrate(1/sqrt(a+b*x+c*x**2), x) == \
+        Piecewise((log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/sqrt(c), Ne(c, 0) & Ne(a - b**2/(4*c), 0)),
+                  ((b/(2*c) + x)*log(b/(2*c) + x)/sqrt(c*(b/(2*c) + x)**2), Ne(c, 0)),
+                  (2*sqrt(a + b*x)/b, Ne(b, 0)), (x/sqrt(a), True))
+
+    assert integrate((7*x+6)/sqrt(3*x**2+4*x+5)) == \
+           7*sqrt(3*x**2 + 4*x + 5)/3 + 4*sqrt(3)*asinh(3*sqrt(11)*(x + S(2)/3)/11)/9
+    assert integrate((7*x+6)/sqrt(-3*x**2+4*x+5)) == \
+           -7*sqrt(-3*x**2 + 4*x + 5)/3 + 32*sqrt(3)*asin(3*sqrt(19)*(x - S(2)/3)/19)/9
+    assert integrate((7*x+6)/sqrt(3*x**2+4*x-5)) == \
+           7*sqrt(3*x**2 + 4*x - 5)/3 + 4*sqrt(3)*log(6*x + 2*sqrt(3)*sqrt(3*x**2 + 4*x - 5) + 4)/9
+    assert integrate((d+e*x)/sqrt(a+b*x+c*x**2), x) == \
+        Piecewise(((-b*e/(2*c) + d) *
+                   Piecewise((log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/sqrt(c), Ne(a - b**2/(4*c), 0)),
+                             ((b/(2*c) + x)*log(b/(2*c) + x)/sqrt(c*(b/(2*c) + x)**2), True)) +
+                   e*sqrt(a + b*x + c*x**2)/c, Ne(c, 0)),
+                  ((2*d*sqrt(a + b*x) + 2*e*(-a*sqrt(a + b*x) + (a + b*x)**(S(3)/2)/3)/b)/b, Ne(b, 0)),
+                  ((d*x + e*x**2/2)/sqrt(a), True))
+
+    assert integrate((3*x**3-x**2+2*x-4)/sqrt(x**2-3*x+2)) == \
+           sqrt(x**2 - 3*x + 2)*(x**2 + 13*x/4 + S(101)/8) + 135*log(2*x + 2*sqrt(x**2 - 3*x + 2) - 3)/16
+
+    assert integrate(sqrt(53225*x**2-66732*x+23013)) == \
+           (x/2 - S(16683)/53225)*sqrt(53225*x**2 - 66732*x + 23013) + \
+           111576969*sqrt(2129)*asinh(53225*x/10563 - S(11122)/3521)/1133160250
+    assert integrate(sqrt(a+b*x+c*x**2), x) == \
+        Piecewise(((a/2 - b**2/(8*c)) *
+                   Piecewise((log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/sqrt(c), Ne(a - b**2/(4*c), 0)),
+                             ((b/(2*c) + x)*log(b/(2*c) + x)/sqrt(c*(b/(2*c) + x)**2), True)) +
+                   (b/(4*c) + x/2)*sqrt(a + b*x + c*x**2), Ne(c, 0)),
+                  (2*(a + b*x)**(S(3)/2)/(3*b), Ne(b, 0)),
+                  (sqrt(a)*x, True))
+
+    assert integrate(x*sqrt(x**2+2*x+4)) == \
+        (x**2/3 + x/6 + S(5)/6)*sqrt(x**2 + 2*x + 4) - 3*asinh(sqrt(3)*(x + 1)/3)/2
+
+
+def test_mul_pow_derivative():
+    assert integrate(x*sec(x)*tan(x)) == x*sec(x) - log(tan(x) + sec(x))
+    assert integrate(x*sec(x)**2, x) == x*tan(x) + log(cos(x))
+    assert integrate(x**3*Derivative(f(x), (x, 4))) == \
+           x**3*Derivative(f(x), (x, 3)) - 3*x**2*Derivative(f(x), (x, 2)) + 6*x*Derivative(f(x), x) - 6*f(x)
+
+
+def test_issue_20782():
+    fun1 = Piecewise((0, x < 0.0), (1, True))
+    fun2 = -Piecewise((0, x < 1.0), (1, True))
+    fun_sum = fun1 + fun2
+    L = (x, -float('Inf'), 1)
+
+    assert integrate(fun1, L) == 1
+    assert integrate(fun2, L) == 0
+    assert integrate(-fun1, L) == -1
+    assert integrate(-fun2, L) == 0
+    assert integrate(fun_sum, L) == 1.
+    assert integrate(-fun_sum, L) == -1.
+
+
+def test_issue_20781():
+    P = lambda a: Piecewise((0, x < a), (1, x >= a))
+    f = lambda a: P(int(a)) + P(float(a))
+    L = (x, -float('Inf'), x)
+    f1 = integrate(f(1), L)
+    assert f1 == 2*x - Min(1.0, x) - Min(x, Max(1.0, 1, evaluate=False))
+    # XXX is_zero is True for S(0) and Float(0) and this is baked into
+    # the code more deeply than the issue of Float(0) != S(0)
+    assert integrate(f(0), (x, -float('Inf'), x)
+        ) == 2*x - 2*Min(0, x)
+
+
+@slow
+def test_issue_19427():
+    # 
+    x = Symbol("x")
+
+    # Have always been okay:
+    assert integrate((x ** 4) * sqrt(1 - x ** 2), (x, -1, 1)) == pi / 16
+    assert integrate((-2 * x ** 2) * sqrt(1 - x ** 2), (x, -1, 1)) == -pi / 4
+    assert integrate((1) * sqrt(1 - x ** 2), (x, -1, 1)) == pi / 2
+
+    # Sum of the above, used to incorrectly return 0 for a while:
+    assert integrate((x ** 4 - 2 * x ** 2 + 1) * sqrt(1 - x ** 2), (x, -1, 1)) == 5 * pi / 16
+
+
+def test_issue_23942():
+    I1 = Integral(1/sqrt(a*(1 + x)**3 + (1 + x)**2), (x, 0, z))
+    assert I1.series(a, 1, n=1) == Integral(1/sqrt(x**3 + 4*x**2 + 5*x + 2), (x, 0, z)) + O(a - 1, (a, 1))
+    I2 = Integral(1/sqrt(a*(4 - x)**4 + (5 + x)**2), (x, 0, z))
+    assert I2.series(a, 2, n=1) == Integral(1/sqrt(2*x**4 - 32*x**3 + 193*x**2 - 502*x + 537), (x, 0, z)) + O(a - 2, (a, 2))
+
+
+def test_issue_25886():
+    # https://github.com/sympy/sympy/issues/25886
+    f = (1-x)*exp(0.937098661j*x)
+    F_exp = (1.0*(-1.0671234968289*I*y
+             + 1.13875255748434
+             + 1.0671234968289*I)*exp(0.937098661*I*y)
+            - 1.13875255748434*exp(0.937098661*I))
+    F = integrate(f, (x, y, 1.0))
+    assert F.is_same(F_exp, math.isclose)
+
+
+def test_old_issues():
+    # https://github.com/sympy/sympy/issues/5212
+    I1 = integrate(cos(log(x**2))/x)
+    assert I1 == sin(log(x**2))/2
+    # https://github.com/sympy/sympy/issues/5462
+    I2 = integrate(1/(x**2+y**2)**(Rational(3,2)),x)
+    assert I2 == x/(y**3*sqrt(x**2/y**2 + 1))
+    # https://github.com/sympy/sympy/issues/6278
+    I3 = integrate(1/(cos(x)+2),(x,0,2*pi))
+    assert I3 == 2*sqrt(3)*pi/3
+
+
+def test_integral_issue_26566():
+    # Define the symbols
+    x = symbols('x', real=True)
+    a = symbols('a', real=True, positive=True)
+
+    # Define the integral expression
+    integral_expr = sin(a * (x + pi))**2
+    symbolic_result = integrate(integral_expr, (x, -pi, -pi/2))
+
+    # Known correct result
+    correct_result = pi / 4
+
+    # Substitute a specific value for 'a' to evaluate both results
+    a_value = 1
+    numeric_symbolic_result = symbolic_result.subs(a, a_value).evalf()
+    numeric_correct_result = correct_result.evalf()
+
+    # Assert that the symbolic result matches the correct value
+    assert simplify(numeric_symbolic_result - numeric_correct_result) == 0
+
+
+def test_definite_integral_with_floats_issue_27231():
+    # Define the symbol and the integral expression
+    x = symbols('x', real=True)
+    integral_expr = sqrt(1 - 0.5625 * (x + 0.333333333333333) ** 2)
+
+    # Perform the definite integral with the known limits
+    result_symbolic = integrate(integral_expr, (x, -1, 1))
+    result_numeric = result_symbolic.evalf()
+
+    # Expected result with higher precision
+    expected_result = sqrt(3) / 6 + 4 * pi / 9
+
+    # Verify that the result is approximately equal within a larger tolerance
+    assert abs(result_numeric - expected_result.evalf()) < 1e-8
+
+
+def test_issue_27374():
+    #https://github.com/sympy/sympy/issues/27374
+    r = sqrt(x**2 + z**2)
+    u = erf(a*r/sqrt(2))/r
+    Ec = diff(u, z, z).subs([(x, sqrt(b*b-z*z))])
+    expected_result = -2*sqrt(2)*b*a**3*exp(-b**2*a**2/2)/(3*sqrt(pi))
+    assert simplify(integrate(Ec, (z, -b, b))) == expected_result
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_intpoly.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_intpoly.py
new file mode 100644
index 0000000000000000000000000000000000000000..ddbaad1fbdeca53ccab8e8b22758a6ad2d89836e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_intpoly.py
@@ -0,0 +1,627 @@
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.miscellaneous import sqrt
+
+from sympy.core import S, Rational
+
+from sympy.integrals.intpoly import (decompose, best_origin, distance_to_side,
+                                     polytope_integrate, point_sort,
+                                     hyperplane_parameters, main_integrate3d,
+                                     main_integrate, polygon_integrate,
+                                     lineseg_integrate, integration_reduction,
+                                     integration_reduction_dynamic, is_vertex)
+
+from sympy.geometry.line import Segment2D
+from sympy.geometry.polygon import Polygon
+from sympy.geometry.point import Point, Point2D
+from sympy.abc import x, y, z
+
+from sympy.testing.pytest import slow
+
+
+def test_decompose():
+    assert decompose(x) == {1: x}
+    assert decompose(x**2) == {2: x**2}
+    assert decompose(x*y) == {2: x*y}
+    assert decompose(x + y) == {1: x + y}
+    assert decompose(x**2 + y) == {1: y, 2: x**2}
+    assert decompose(8*x**2 + 4*y + 7) == {0: 7, 1: 4*y, 2: 8*x**2}
+    assert decompose(x**2 + 3*y*x) == {2: x**2 + 3*x*y}
+    assert decompose(9*x**2 + y + 4*x + x**3 + y**2*x + 3) ==\
+        {0: 3, 1: 4*x + y, 2: 9*x**2, 3: x**3 + x*y**2}
+
+    assert decompose(x, True) == {x}
+    assert decompose(x ** 2, True) == {x**2}
+    assert decompose(x * y, True) == {x * y}
+    assert decompose(x + y, True) == {x, y}
+    assert decompose(x ** 2 + y, True) == {y, x ** 2}
+    assert decompose(8 * x ** 2 + 4 * y + 7, True) == {7, 4*y, 8*x**2}
+    assert decompose(x ** 2 + 3 * y * x, True) == {x ** 2, 3 * x * y}
+    assert decompose(9 * x ** 2 + y + 4 * x + x ** 3 + y ** 2 * x + 3, True) == \
+           {3, y, 4*x, 9*x**2, x*y**2, x**3}
+
+
+def test_best_origin():
+    expr1 = y ** 2 * x ** 5 + y ** 5 * x ** 7 + 7 * x + x ** 12 + y ** 7 * x
+
+    l1 = Segment2D(Point(0, 3), Point(1, 1))
+    l2 = Segment2D(Point(S(3) / 2, 0), Point(S(3) / 2, 3))
+    l3 = Segment2D(Point(0, S(3) / 2), Point(3, S(3) / 2))
+    l4 = Segment2D(Point(0, 2), Point(2, 0))
+    l5 = Segment2D(Point(0, 2), Point(1, 1))
+    l6 = Segment2D(Point(2, 0), Point(1, 1))
+
+    assert best_origin((2, 1), 3, l1, expr1) == (0, 3)
+    # XXX: Should these return exact Rational output? Maybe best_origin should
+    #      sympify its arguments...
+    assert best_origin((2, 0), 3, l2, x ** 7) == (1.5, 0)
+    assert best_origin((0, 2), 3, l3, x ** 7) == (0, 1.5)
+    assert best_origin((1, 1), 2, l4, x ** 7 * y ** 3) == (0, 2)
+    assert best_origin((1, 1), 2, l4, x ** 3 * y ** 7) == (2, 0)
+    assert best_origin((1, 1), 2, l5, x ** 2 * y ** 9) == (0, 2)
+    assert best_origin((1, 1), 2, l6, x ** 9 * y ** 2) == (2, 0)
+
+
+@slow
+def test_polytope_integrate():
+    #  Convex 2-Polytopes
+    #  Vertex representation
+    assert polytope_integrate(Polygon(Point(0, 0), Point(0, 2),
+                                      Point(4, 0)), 1) == 4
+    assert polytope_integrate(Polygon(Point(0, 0), Point(0, 1),
+                                      Point(1, 1), Point(1, 0)), x * y) ==\
+                                      Rational(1, 4)
+    assert polytope_integrate(Polygon(Point(0, 3), Point(5, 3), Point(1, 1)),
+                              6*x**2 - 40*y) == Rational(-935, 3)
+
+    assert polytope_integrate(Polygon(Point(0, 0), Point(0, sqrt(3)),
+                                      Point(sqrt(3), sqrt(3)),
+                                      Point(sqrt(3), 0)), 1) == 3
+
+    hexagon = Polygon(Point(0, 0), Point(-sqrt(3) / 2, S.Half),
+                      Point(-sqrt(3) / 2, S(3) / 2), Point(0, 2),
+                      Point(sqrt(3) / 2, S(3) / 2), Point(sqrt(3) / 2, S.Half))
+
+    assert polytope_integrate(hexagon, 1) == S(3*sqrt(3)) / 2
+
+    #  Hyperplane representation
+    assert polytope_integrate([((-1, 0), 0), ((1, 2), 4),
+                               ((0, -1), 0)], 1) == 4
+    assert polytope_integrate([((-1, 0), 0), ((0, 1), 1),
+                               ((1, 0), 1), ((0, -1), 0)], x * y) == Rational(1, 4)
+    assert polytope_integrate([((0, 1), 3), ((1, -2), -1),
+                               ((-2, -1), -3)], 6*x**2 - 40*y) == Rational(-935, 3)
+    assert polytope_integrate([((-1, 0), 0), ((0, sqrt(3)), 3),
+                               ((sqrt(3), 0), 3), ((0, -1), 0)], 1) == 3
+
+    hexagon = [((Rational(-1, 2), -sqrt(3) / 2), 0),
+               ((-1, 0), sqrt(3) / 2),
+               ((Rational(-1, 2), sqrt(3) / 2), sqrt(3)),
+               ((S.Half, sqrt(3) / 2), sqrt(3)),
+               ((1, 0), sqrt(3) / 2),
+               ((S.Half, -sqrt(3) / 2), 0)]
+    assert polytope_integrate(hexagon, 1) == S(3*sqrt(3)) / 2
+
+    #  Non-convex polytopes
+    #  Vertex representation
+    assert polytope_integrate(Polygon(Point(-1, -1), Point(-1, 1),
+                                      Point(1, 1), Point(0, 0),
+                                      Point(1, -1)), 1) == 3
+    assert polytope_integrate(Polygon(Point(-1, -1), Point(-1, 1),
+                                      Point(0, 0), Point(1, 1),
+                                      Point(1, -1), Point(0, 0)), 1) == 2
+    #  Hyperplane representation
+    assert polytope_integrate([((-1, 0), 1), ((0, 1), 1), ((1, -1), 0),
+                               ((1, 1), 0), ((0, -1), 1)], 1) == 3
+    assert polytope_integrate([((-1, 0), 1), ((1, 1), 0), ((-1, 1), 0),
+                               ((1, 0), 1), ((-1, -1), 0),
+                               ((1, -1), 0)], 1) == 2
+
+    #  Tests for 2D polytopes mentioned in Chin et al(Page 10):
+    #  http://dilbert.engr.ucdavis.edu/~suku/quadrature/cls-integration.pdf
+    fig1 = Polygon(Point(1.220, -0.827), Point(-1.490, -4.503),
+                   Point(-3.766, -1.622), Point(-4.240, -0.091),
+                   Point(-3.160, 4), Point(-0.981, 4.447),
+                   Point(0.132, 4.027))
+    assert polytope_integrate(fig1, x**2 + x*y + y**2) ==\
+        S(2031627344735367)/(8*10**12)
+
+    fig2 = Polygon(Point(4.561, 2.317), Point(1.491, -1.315),
+                   Point(-3.310, -3.164), Point(-4.845, -3.110),
+                   Point(-4.569, 1.867))
+    assert polytope_integrate(fig2, x**2 + x*y + y**2) ==\
+        S(517091313866043)/(16*10**11)
+
+    fig3 = Polygon(Point(-2.740, -1.888), Point(-3.292, 4.233),
+                   Point(-2.723, -0.697), Point(-0.643, -3.151))
+    assert polytope_integrate(fig3, x**2 + x*y + y**2) ==\
+        S(147449361647041)/(8*10**12)
+
+    fig4 = Polygon(Point(0.211, -4.622), Point(-2.684, 3.851),
+                   Point(0.468, 4.879), Point(4.630, -1.325),
+                   Point(-0.411, -1.044))
+    assert polytope_integrate(fig4, x**2 + x*y + y**2) ==\
+        S(180742845225803)/(10**12)
+
+    #  Tests for many polynomials with maximum degree given(2D case).
+    tri = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    polys = []
+    expr1 = x**9*y + x**7*y**3 + 2*x**2*y**8
+    expr2 = x**6*y**4 + x**5*y**5 + 2*y**10
+    expr3 = x**10 + x**9*y + x**8*y**2 + x**5*y**5
+    polys.extend((expr1, expr2, expr3))
+    result_dict = polytope_integrate(tri, polys, max_degree=10)
+    assert result_dict[expr1] == Rational(615780107, 594)
+    assert result_dict[expr2] == Rational(13062161, 27)
+    assert result_dict[expr3] == Rational(1946257153, 924)
+
+    tri = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    expr1 = x**7*y**1 + 2*x**2*y**6
+    expr2 = x**6*y**4 + x**5*y**5 + 2*y**10
+    expr3 = x**10 + x**9*y + x**8*y**2 + x**5*y**5
+    polys.extend((expr1, expr2, expr3))
+    assert polytope_integrate(tri, polys, max_degree=9) == \
+        {x**7*y + 2*x**2*y**6: Rational(489262, 9)}
+
+    #  Tests when all integral of all monomials up to a max_degree is to be
+    #  calculated.
+    assert polytope_integrate(Polygon(Point(0, 0), Point(0, 1),
+                                      Point(1, 1), Point(1, 0)),
+                              max_degree=4) == {0: 0, 1: 1, x: S.Half,
+                                                x ** 2 * y ** 2: S.One / 9,
+                                                x ** 4: S.One / 5,
+                                                y ** 4: S.One / 5,
+                                                y: S.Half,
+                                                x * y ** 2: S.One / 6,
+                                                y ** 2: S.One / 3,
+                                                x ** 3: S.One / 4,
+                                                x ** 2 * y: S.One / 6,
+                                                x ** 3 * y: S.One / 8,
+                                                x * y: S.One / 4,
+                                                y ** 3: S.One / 4,
+                                                x ** 2: S.One / 3,
+                                                x * y ** 3: S.One / 8}
+
+    #  Tests for 3D polytopes
+    cube1 = [[(0, 0, 0), (0, 6, 6), (6, 6, 6), (3, 6, 0),
+              (0, 6, 0), (6, 0, 6), (3, 0, 0), (0, 0, 6)],
+             [1, 2, 3, 4], [3, 2, 5, 6], [1, 7, 5, 2], [0, 6, 5, 7],
+             [1, 4, 0, 7], [0, 4, 3, 6]]
+    assert polytope_integrate(cube1, 1) == S(162)
+
+    #  3D Test cases in Chin et al(2015)
+    cube2 = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),
+             (5, 0, 5), (5, 5, 0), (5, 5, 5)],
+             [3, 7, 6, 2], [1, 5, 7, 3], [5, 4, 6, 7], [0, 4, 5, 1],
+             [2, 0, 1, 3], [2, 6, 4, 0]]
+
+    cube3 = [[(0, 0, 0), (5, 0, 0), (5, 4, 0), (3, 2, 0), (3, 5, 0),
+              (0, 5, 0), (0, 0, 5), (5, 0, 5), (5, 4, 5), (3, 2, 5),
+              (3, 5, 5), (0, 5, 5)],
+             [6, 11, 5, 0], [1, 7, 6, 0], [5, 4, 3, 2, 1, 0], [11, 10, 4, 5],
+             [10, 9, 3, 4], [9, 8, 2, 3], [8, 7, 1, 2], [7, 8, 9, 10, 11, 6]]
+
+    cube4 = [[(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1),
+              (S.One / 4, S.One / 4, S.One / 4)],
+             [0, 2, 1], [1, 3, 0], [4, 2, 3], [4, 3, 1],
+             [0, 1, 2], [2, 4, 1], [0, 3, 2]]
+
+    assert polytope_integrate(cube2, x ** 2 + y ** 2 + x * y + z ** 2) ==\
+           Rational(15625, 4)
+    assert polytope_integrate(cube3, x ** 2 + y ** 2 + x * y + z ** 2) ==\
+           S(33835) / 12
+    assert polytope_integrate(cube4, x ** 2 + y ** 2 + x * y + z ** 2) ==\
+           S(37) / 960
+
+    #  Test cases from Mathematica's PolyhedronData library
+    octahedron = [[(S.NegativeOne / sqrt(2), 0, 0), (0, S.One / sqrt(2), 0),
+                   (0, 0, S.NegativeOne / sqrt(2)), (0, 0, S.One / sqrt(2)),
+                   (0, S.NegativeOne / sqrt(2), 0), (S.One / sqrt(2), 0, 0)],
+                  [3, 4, 5], [3, 5, 1], [3, 1, 0], [3, 0, 4], [4, 0, 2],
+                  [4, 2, 5], [2, 0, 1], [5, 2, 1]]
+
+    assert polytope_integrate(octahedron, 1) == sqrt(2) / 3
+
+    great_stellated_dodecahedron =\
+        [[(-0.32491969623290634095, 0, 0.42532540417601993887),
+          (0.32491969623290634095, 0, -0.42532540417601993887),
+          (-0.52573111211913359231, 0, 0.10040570794311363956),
+          (0.52573111211913359231, 0, -0.10040570794311363956),
+          (-0.10040570794311363956, -0.3090169943749474241, 0.42532540417601993887),
+          (-0.10040570794311363956, 0.30901699437494742410, 0.42532540417601993887),
+          (0.10040570794311363956, -0.3090169943749474241, -0.42532540417601993887),
+          (0.10040570794311363956, 0.30901699437494742410, -0.42532540417601993887),
+          (-0.16245984811645317047, -0.5, 0.10040570794311363956),
+          (-0.16245984811645317047,  0.5, 0.10040570794311363956),
+          (0.16245984811645317047,  -0.5, -0.10040570794311363956),
+          (0.16245984811645317047,   0.5, -0.10040570794311363956),
+          (-0.42532540417601993887, -0.3090169943749474241, -0.10040570794311363956),
+          (-0.42532540417601993887, 0.30901699437494742410, -0.10040570794311363956),
+          (-0.26286555605956679615, 0.1909830056250525759, -0.42532540417601993887),
+          (-0.26286555605956679615, -0.1909830056250525759, -0.42532540417601993887),
+          (0.26286555605956679615, 0.1909830056250525759, 0.42532540417601993887),
+          (0.26286555605956679615, -0.1909830056250525759, 0.42532540417601993887),
+          (0.42532540417601993887, -0.3090169943749474241, 0.10040570794311363956),
+          (0.42532540417601993887, 0.30901699437494742410, 0.10040570794311363956)],
+         [12, 3, 0, 6, 16], [17, 7, 0, 3, 13],
+         [9, 6, 0, 7, 8], [18, 2, 1, 4, 14],
+         [15, 5, 1, 2, 19], [11, 4, 1, 5, 10],
+         [8, 19, 2, 18, 9], [10, 13, 3, 12, 11],
+         [16, 14, 4, 11, 12], [13, 10, 5, 15, 17],
+         [14, 16, 6, 9, 18], [19, 8, 7, 17, 15]]
+    #  Actual volume is : 0.163118960624632
+    assert Abs(polytope_integrate(great_stellated_dodecahedron, 1) -\
+        0.163118960624632) < 1e-12
+
+    expr = x **2 + y ** 2 + z ** 2
+    octahedron_five_compound = [[(0, -0.7071067811865475244, 0),
+                                 (0, 0.70710678118654752440, 0),
+                                 (0.1148764602736805918,
+                                  -0.35355339059327376220, -0.60150095500754567366),
+                                 (0.1148764602736805918, 0.35355339059327376220,
+                                     -0.60150095500754567366),
+                                 (0.18587401723009224507,
+                                  -0.57206140281768429760, 0.37174803446018449013),
+                                 (0.18587401723009224507,  0.57206140281768429760,
+                                  0.37174803446018449013),
+                                 (0.30075047750377283683, -0.21850801222441053540,
+                                  0.60150095500754567366),
+                                 (0.30075047750377283683, 0.21850801222441053540,
+                                  0.60150095500754567366),
+                                 (0.48662449473386508189, -0.35355339059327376220,
+                                  -0.37174803446018449013),
+                                 (0.48662449473386508189, 0.35355339059327376220,
+                                  -0.37174803446018449013),
+                                 (-0.60150095500754567366, 0, -0.37174803446018449013),
+                                 (-0.30075047750377283683, -0.21850801222441053540,
+                                  -0.60150095500754567366),
+                                 (-0.30075047750377283683, 0.21850801222441053540,
+                                  -0.60150095500754567366),
+                                 (0.60150095500754567366, 0, 0.37174803446018449013),
+                                 (0.4156269377774534286, -0.57206140281768429760, 0),
+                                 (0.4156269377774534286, 0.57206140281768429760, 0),
+                                 (0.37174803446018449013, 0, -0.60150095500754567366),
+                                 (-0.4156269377774534286, -0.57206140281768429760, 0),
+                                 (-0.4156269377774534286, 0.57206140281768429760, 0),
+                                 (-0.67249851196395732696, -0.21850801222441053540, 0),
+                                 (-0.67249851196395732696, 0.21850801222441053540, 0),
+                                 (0.67249851196395732696, -0.21850801222441053540, 0),
+                                 (0.67249851196395732696, 0.21850801222441053540, 0),
+                                 (-0.37174803446018449013, 0, 0.60150095500754567366),
+                                 (-0.48662449473386508189, -0.35355339059327376220,
+                                 0.37174803446018449013),
+                                 (-0.48662449473386508189, 0.35355339059327376220,
+                                  0.37174803446018449013),
+                                 (-0.18587401723009224507, -0.57206140281768429760,
+                                  -0.37174803446018449013),
+                                 (-0.18587401723009224507, 0.57206140281768429760,
+                                  -0.37174803446018449013),
+                                 (-0.11487646027368059176, -0.35355339059327376220,
+                                  0.60150095500754567366),
+                                 (-0.11487646027368059176, 0.35355339059327376220,
+                                 0.60150095500754567366)],
+                                 [0, 10, 16], [23, 10, 0], [16, 13, 0],
+                                 [0, 13, 23], [16, 10, 1], [1, 10, 23],
+                                 [1, 13, 16], [23, 13, 1], [2, 4, 19],
+                                 [22, 4, 2], [2, 19, 27], [27, 22, 2],
+                                 [20, 5, 3], [3, 5, 21], [26, 20, 3],
+                                 [3, 21, 26], [29, 19, 4], [4, 22, 29],
+                                 [5, 20, 28], [28, 21, 5], [6, 8, 15],
+                                 [17, 8, 6], [6, 15, 25], [25, 17, 6],
+                                 [14, 9, 7], [7, 9, 18], [24, 14, 7],
+                                 [7, 18, 24], [8, 12, 15], [17, 12, 8],
+                                 [14, 11, 9], [9, 11, 18], [11, 14, 24],
+                                 [24, 18, 11], [25, 15, 12], [12, 17, 25],
+                                 [29, 27, 19], [20, 26, 28], [28, 26, 21],
+                                 [22, 27, 29]]
+    assert Abs(polytope_integrate(octahedron_five_compound, expr)) - 0.353553\
+        < 1e-6
+
+    cube_five_compound = [[(-0.1624598481164531631, -0.5, -0.6881909602355867691),
+                           (-0.1624598481164531631, 0.5, -0.6881909602355867691),
+                           (0.1624598481164531631, -0.5, 0.68819096023558676910),
+                           (0.1624598481164531631, 0.5, 0.68819096023558676910),
+                          (-0.52573111211913359231, 0, -0.6881909602355867691),
+                          (0.52573111211913359231, 0, 0.68819096023558676910),
+                          (-0.26286555605956679615, -0.8090169943749474241,
+                           -0.1624598481164531631),
+                          (-0.26286555605956679615, 0.8090169943749474241,
+                           -0.1624598481164531631),
+                          (0.26286555605956680301, -0.8090169943749474241,
+                           0.1624598481164531631),
+                          (0.26286555605956680301, 0.8090169943749474241,
+                           0.1624598481164531631),
+                          (-0.42532540417601993887, -0.3090169943749474241,
+                           0.68819096023558676910),
+                          (-0.42532540417601993887, 0.30901699437494742410,
+                           0.68819096023558676910),
+                          (0.42532540417601996609, -0.3090169943749474241,
+                           -0.6881909602355867691),
+                          (0.42532540417601996609, 0.30901699437494742410,
+                           -0.6881909602355867691),
+                          (-0.6881909602355867691, -0.5, 0.1624598481164531631),
+                          (-0.6881909602355867691, 0.5,  0.1624598481164531631),
+                          (0.68819096023558676910, -0.5, -0.1624598481164531631),
+                          (0.68819096023558676910, 0.5, -0.1624598481164531631),
+                          (-0.85065080835203998877, 0, -0.1624598481164531631),
+                          (0.85065080835203993218, 0, 0.1624598481164531631)],
+                          [18, 10, 3, 7], [13, 19, 8, 0], [18, 0, 8, 10],
+                          [3, 19, 13, 7], [18, 7, 13, 0], [8, 19, 3, 10],
+                          [6, 2, 11, 18], [1, 9, 19, 12], [11, 9, 1, 18],
+                          [6, 12, 19, 2], [1, 12, 6, 18], [11, 2, 19, 9],
+                          [4, 14, 11, 7], [17, 5, 8, 12], [4, 12, 8, 14],
+                          [11, 5, 17, 7], [4, 7, 17, 12], [8, 5, 11, 14],
+                          [6, 10, 15, 4], [13, 9, 5, 16], [15, 9, 13, 4],
+                          [6, 16, 5, 10], [13, 16, 6, 4], [15, 10, 5, 9],
+                          [14, 15, 1, 0], [16, 17, 3, 2], [14, 2, 3, 15],
+                          [1, 17, 16, 0], [14, 0, 16, 2], [3, 17, 1, 15]]
+    assert Abs(polytope_integrate(cube_five_compound, expr) - 1.25) < 1e-12
+
+    echidnahedron = [[(0, 0, -2.4898982848827801995),
+                      (0, 0, 2.4898982848827802734),
+                      (0, -4.2360679774997896964, -2.4898982848827801995),
+                      (0, -4.2360679774997896964, 2.4898982848827802734),
+                      (0, 4.2360679774997896964, -2.4898982848827801995),
+                      (0, 4.2360679774997896964, 2.4898982848827802734),
+                      (-4.0287400534704067567, -1.3090169943749474241, -2.4898982848827801995),
+                      (-4.0287400534704067567, -1.3090169943749474241, 2.4898982848827802734),
+                      (-4.0287400534704067567, 1.3090169943749474241, -2.4898982848827801995),
+                      (-4.0287400534704067567, 1.3090169943749474241, 2.4898982848827802734),
+                      (4.0287400534704069747, -1.3090169943749474241, -2.4898982848827801995),
+                      (4.0287400534704069747, -1.3090169943749474241, 2.4898982848827802734),
+                      (4.0287400534704069747, 1.3090169943749474241, -2.4898982848827801995),
+                      (4.0287400534704069747, 1.3090169943749474241, 2.4898982848827802734),
+                      (-2.4898982848827801995, -3.4270509831248422723, -2.4898982848827801995),
+                      (-2.4898982848827801995, -3.4270509831248422723, 2.4898982848827802734),
+                      (-2.4898982848827801995, 3.4270509831248422723, -2.4898982848827801995),
+                      (-2.4898982848827801995, 3.4270509831248422723, 2.4898982848827802734),
+                      (2.4898982848827802734, -3.4270509831248422723, -2.4898982848827801995),
+                      (2.4898982848827802734, -3.4270509831248422723, 2.4898982848827802734),
+                      (2.4898982848827802734, 3.4270509831248422723, -2.4898982848827801995),
+                      (2.4898982848827802734, 3.4270509831248422723, 2.4898982848827802734),
+                      (-4.7169310137059934362, -0.8090169943749474241, -1.1135163644116066184),
+                      (-4.7169310137059934362, 0.8090169943749474241, -1.1135163644116066184),
+                      (4.7169310137059937438, -0.8090169943749474241, 1.11351636441160673519),
+                      (4.7169310137059937438, 0.8090169943749474241, 1.11351636441160673519),
+                      (-4.2916056095299737777, -2.1180339887498948482, 1.11351636441160673519),
+                      (-4.2916056095299737777, 2.1180339887498948482, 1.11351636441160673519),
+                      (4.2916056095299737777, -2.1180339887498948482, -1.1135163644116066184),
+                      (4.2916056095299737777, 2.1180339887498948482, -1.1135163644116066184),
+                      (-3.6034146492943870399, 0, -3.3405490932348205213),
+                      (3.6034146492943870399, 0, 3.3405490932348202056),
+                      (-3.3405490932348205213, -3.4270509831248422723, 1.11351636441160673519),
+                      (-3.3405490932348205213, 3.4270509831248422723, 1.11351636441160673519),
+                      (3.3405490932348202056, -3.4270509831248422723, -1.1135163644116066184),
+                      (3.3405490932348202056, 3.4270509831248422723, -1.1135163644116066184),
+                      (-2.9152236890588002395, -2.1180339887498948482, 3.3405490932348202056),
+                      (-2.9152236890588002395, 2.1180339887498948482, 3.3405490932348202056),
+                      (2.9152236890588002395, -2.1180339887498948482, -3.3405490932348205213),
+                      (2.9152236890588002395, 2.1180339887498948482, -3.3405490932348205213),
+                      (-2.2270327288232132368, 0, -1.1135163644116066184),
+                      (-2.2270327288232132368, -4.2360679774997896964, -1.1135163644116066184),
+                      (-2.2270327288232132368, 4.2360679774997896964, -1.1135163644116066184),
+                      (2.2270327288232134704, 0, 1.11351636441160673519),
+                      (2.2270327288232134704, -4.2360679774997896964, 1.11351636441160673519),
+                      (2.2270327288232134704, 4.2360679774997896964, 1.11351636441160673519),
+                      (-1.8017073246471935200, -1.3090169943749474241, 1.11351636441160673519),
+                      (-1.8017073246471935200, 1.3090169943749474241, 1.11351636441160673519),
+                      (1.8017073246471935043, -1.3090169943749474241, -1.1135163644116066184),
+                      (1.8017073246471935043, 1.3090169943749474241, -1.1135163644116066184),
+                      (-1.3763819204711735382, 0, -4.7169310137059934362),
+                      (-1.3763819204711735382, 0, 0.26286555605956679615),
+                      (1.37638192047117353821, 0, 4.7169310137059937438),
+                      (1.37638192047117353821, 0, -0.26286555605956679615),
+                      (-1.1135163644116066184, -3.4270509831248422723, -3.3405490932348205213),
+                      (-1.1135163644116066184, -0.8090169943749474241, 4.7169310137059937438),
+                      (-1.1135163644116066184, -0.8090169943749474241, -0.26286555605956679615),
+                      (-1.1135163644116066184, 0.8090169943749474241, 4.7169310137059937438),
+                      (-1.1135163644116066184, 0.8090169943749474241, -0.26286555605956679615),
+                      (-1.1135163644116066184, 3.4270509831248422723, -3.3405490932348205213),
+                      (1.11351636441160673519, -3.4270509831248422723, 3.3405490932348202056),
+                      (1.11351636441160673519, -0.8090169943749474241, -4.7169310137059934362),
+                      (1.11351636441160673519, -0.8090169943749474241, 0.26286555605956679615),
+                      (1.11351636441160673519, 0.8090169943749474241, -4.7169310137059934362),
+                      (1.11351636441160673519, 0.8090169943749474241, 0.26286555605956679615),
+                      (1.11351636441160673519, 3.4270509831248422723, 3.3405490932348202056),
+                      (-0.85065080835203998877, 0, 1.11351636441160673519),
+                      (0.85065080835203993218, 0, -1.1135163644116066184),
+                      (-0.6881909602355867691, -0.5, -1.1135163644116066184),
+                      (-0.6881909602355867691, 0.5, -1.1135163644116066184),
+                      (-0.6881909602355867691, -4.7360679774997896964, -1.1135163644116066184),
+                      (-0.6881909602355867691, -2.1180339887498948482, -1.1135163644116066184),
+                      (-0.6881909602355867691, 2.1180339887498948482, -1.1135163644116066184),
+                      (-0.6881909602355867691, 4.7360679774997896964, -1.1135163644116066184),
+                      (0.68819096023558676910, -0.5, 1.11351636441160673519),
+                      (0.68819096023558676910, 0.5, 1.11351636441160673519),
+                      (0.68819096023558676910, -4.7360679774997896964, 1.11351636441160673519),
+                      (0.68819096023558676910, -2.1180339887498948482, 1.11351636441160673519),
+                      (0.68819096023558676910, 2.1180339887498948482, 1.11351636441160673519),
+                      (0.68819096023558676910, 4.7360679774997896964, 1.11351636441160673519),
+                      (-0.42532540417601993887, -1.3090169943749474241, -4.7169310137059934362),
+                      (-0.42532540417601993887, -1.3090169943749474241, 0.26286555605956679615),
+                      (-0.42532540417601993887, 1.3090169943749474241, -4.7169310137059934362),
+                      (-0.42532540417601993887, 1.3090169943749474241, 0.26286555605956679615),
+                      (-0.26286555605956679615, -0.8090169943749474241, 1.11351636441160673519),
+                      (-0.26286555605956679615, 0.8090169943749474241, 1.11351636441160673519),
+                      (0.26286555605956679615, -0.8090169943749474241, -1.1135163644116066184),
+                      (0.26286555605956679615, 0.8090169943749474241, -1.1135163644116066184),
+                      (0.42532540417601996609, -1.3090169943749474241, 4.7169310137059937438),
+                      (0.42532540417601996609, -1.3090169943749474241, -0.26286555605956679615),
+                      (0.42532540417601996609, 1.3090169943749474241, 4.7169310137059937438),
+                      (0.42532540417601996609, 1.3090169943749474241, -0.26286555605956679615)],
+                      [9, 66, 47], [44, 62, 77], [20, 91, 49], [33, 47, 83],
+                      [3, 77, 84], [12, 49, 53], [36, 84, 66], [28, 53, 62],
+                      [73, 83, 91], [15, 84, 46], [25, 64, 43], [16, 58, 72],
+                      [26, 46, 51], [11, 43, 74], [4, 72, 91], [60, 74, 84],
+                      [35, 91, 64], [23, 51, 58], [19, 74, 77], [79, 83, 78],
+                      [6, 56, 40], [76, 77, 81], [21, 78, 75], [8, 40, 58],
+                      [31, 75, 74], [42, 58, 83], [41, 81, 56], [13, 75, 43],
+                      [27, 51, 47], [2, 89, 71], [24, 43, 62], [17, 47, 85],
+                      [14, 71, 56], [65, 85, 75], [22, 56, 51], [34, 62, 89],
+                      [5, 85, 78], [32, 81, 46], [10, 53, 48], [45, 78, 64],
+                      [7, 46, 66], [18, 48, 89], [37, 66, 85], [70, 89, 81],
+                      [29, 64, 53], [88, 74, 1], [38, 67, 48], [42, 83, 72],
+                      [57, 1, 85], [34, 48, 62], [59, 72, 87], [19, 62, 74],
+                      [63, 87, 67], [17, 85, 83], [52, 75, 1], [39, 87, 49],
+                      [22, 51, 40], [55, 1, 66], [29, 49, 64], [30, 40, 69],
+                      [13, 64, 75], [82, 69, 87], [7, 66, 51], [90, 85, 1],
+                      [59, 69, 72], [70, 81, 71], [88, 1, 84], [73, 72, 83],
+                      [54, 71, 68], [5, 83, 85], [50, 68, 69], [3, 84, 81],
+                      [57, 66, 1], [30, 68, 40], [28, 62, 48], [52, 1, 74],
+                      [23, 40, 51], [38, 48, 86], [9, 51, 66], [80, 86, 68],
+                      [11, 74, 62], [55, 84, 1], [54, 86, 71], [35, 64, 49],
+                      [90, 1, 75], [41, 71, 81], [39, 49, 67], [15, 81, 84],
+                      [61, 67, 86], [21, 75, 64], [24, 53, 43], [50, 69, 0],
+                      [37, 85, 47], [31, 43, 75], [61, 0, 67], [27, 47, 58],
+                      [10, 67, 53], [8, 58, 69], [90, 75, 85], [45, 91, 78],
+                      [80, 68, 0], [36, 66, 46], [65, 78, 85], [63, 0, 87],
+                      [32, 46, 56], [20, 87, 91], [14, 56, 68], [57, 85, 66],
+                      [33, 58, 47], [61, 86, 0], [60, 84, 77], [37, 47, 66],
+                      [82, 0, 69], [44, 77, 89], [16, 69, 58], [18, 89, 86],
+                      [55, 66, 84], [26, 56, 46], [63, 67, 0], [31, 74, 43],
+                      [36, 46, 84], [50, 0, 68], [25, 43, 53], [6, 68, 56],
+                      [12, 53, 67], [88, 84, 74], [76, 89, 77], [82, 87, 0],
+                      [65, 75, 78], [60, 77, 74], [80, 0, 86], [79, 78, 91],
+                      [2, 86, 89], [4, 91, 87], [52, 74, 75], [21, 64, 78],
+                      [18, 86, 48], [23, 58, 40], [5, 78, 83], [28, 48, 53],
+                      [6, 40, 68], [25, 53, 64], [54, 68, 86], [33, 83, 58],
+                      [17, 83, 47], [12, 67, 49], [41, 56, 71], [9, 47, 51],
+                      [35, 49, 91], [2, 71, 86], [79, 91, 83], [38, 86, 67],
+                      [26, 51, 56], [7, 51, 46], [4, 87, 72], [34, 89, 48],
+                      [15, 46, 81], [42, 72, 58], [10, 48, 67], [27, 58, 51],
+                      [39, 67, 87], [76, 81, 89], [3, 81, 77], [8, 69, 40],
+                      [29, 53, 49], [19, 77, 62], [22, 40, 56], [20, 49, 87],
+                      [32, 56, 81], [59, 87, 69], [24, 62, 53], [11, 62, 43],
+                      [14, 68, 71], [73, 91, 72], [13, 43, 64], [70, 71, 89],
+                      [16, 72, 69], [44, 89, 62], [30, 69, 68], [45, 64, 91]]
+    #  Actual volume is : 51.405764746872634
+    assert Abs(polytope_integrate(echidnahedron, 1) - 51.4057647468726) < 1e-12
+    assert Abs(polytope_integrate(echidnahedron, expr) - 253.569603474519) <\
+    1e-12
+
+    #  Tests for many polynomials with maximum degree given(2D case).
+    assert polytope_integrate(cube2, [x**2, y*z], max_degree=2) == \
+        {y * z: 3125 / S(4), x ** 2: 3125 / S(3)}
+
+    assert polytope_integrate(cube2, max_degree=2) == \
+        {1: 125, x: 625 / S(2), x * z: 3125 / S(4), y: 625 / S(2),
+         y * z: 3125 / S(4), z ** 2: 3125 / S(3), y ** 2: 3125 / S(3),
+         z: 625 / S(2), x * y: 3125 / S(4), x ** 2: 3125 / S(3)}
+
+def test_point_sort():
+    assert point_sort([Point(0, 0), Point(1, 0), Point(1, 1)]) == \
+        [Point2D(1, 1), Point2D(1, 0), Point2D(0, 0)]
+
+    fig6 = Polygon((0, 0), (1, 0), (1, 1))
+    assert polytope_integrate(fig6, x*y) == Rational(-1, 8)
+    assert polytope_integrate(fig6, x*y, clockwise = True) == Rational(1, 8)
+
+
+def test_polytopes_intersecting_sides():
+    fig5 = Polygon(Point(-4.165, -0.832), Point(-3.668, 1.568),
+                   Point(-3.266, 1.279), Point(-1.090, -2.080),
+                   Point(3.313, -0.683), Point(3.033, -4.845),
+                   Point(-4.395, 4.840), Point(-1.007, -3.328))
+    assert polytope_integrate(fig5, x**2 + x*y + y**2) ==\
+        S(1633405224899363)/(24*10**12)
+
+    fig6 = Polygon(Point(-3.018, -4.473), Point(-0.103, 2.378),
+                   Point(-1.605, -2.308), Point(4.516, -0.771),
+                   Point(4.203, 0.478))
+    assert polytope_integrate(fig6, x**2 + x*y + y**2) ==\
+        S(88161333955921)/(3*10**12)
+
+
+def test_max_degree():
+    polygon = Polygon((0, 0), (0, 1), (1, 1), (1, 0))
+    polys = [1, x, y, x*y, x**2*y, x*y**2]
+    assert polytope_integrate(polygon, polys, max_degree=3) == \
+        {1: 1, x: S.Half, y: S.Half, x*y: Rational(1, 4), x**2*y: Rational(1, 6), x*y**2: Rational(1, 6)}
+    assert polytope_integrate(polygon, polys, max_degree=2) == \
+        {1: 1, x: S.Half, y: S.Half, x*y: Rational(1, 4)}
+    assert polytope_integrate(polygon, polys, max_degree=1) == \
+        {1: 1, x: S.Half, y: S.Half}
+
+
+def test_main_integrate3d():
+    cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
+             (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
+            [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
+            [3, 1, 0, 2], [0, 4, 6, 2]]
+    vertices = cube[0]
+    faces = cube[1:]
+    hp_params = hyperplane_parameters(faces, vertices)
+    assert main_integrate3d(1, faces, vertices, hp_params) == -125
+    assert main_integrate3d(1, faces, vertices, hp_params, max_degree=1) == \
+        {1: -125, y: Rational(-625, 2), z: Rational(-625, 2), x: Rational(-625, 2)}
+
+
+def test_main_integrate():
+    triangle = Polygon((0, 3), (5, 3), (1, 1))
+    facets = triangle.sides
+    hp_params = hyperplane_parameters(triangle)
+    assert main_integrate(x**2 + y**2, facets, hp_params) == Rational(325, 6)
+    assert main_integrate(x**2 + y**2, facets, hp_params, max_degree=1) == \
+        {0: 0, 1: 5, y: Rational(35, 3), x: 10}
+
+
+def test_polygon_integrate():
+    cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
+             (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
+            [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
+            [3, 1, 0, 2], [0, 4, 6, 2]]
+    facet = cube[1]
+    facets = cube[1:]
+    vertices = cube[0]
+    assert polygon_integrate(facet, [(0, 1, 0), 5], 0, facets, vertices, 1, 0) == -25
+
+
+def test_distance_to_side():
+    point = (0, 0, 0)
+    assert distance_to_side(point, [(0, 0, 1), (0, 1, 0)], (1, 0, 0)) == -sqrt(2)/2
+
+
+def test_lineseg_integrate():
+    polygon = [(0, 5, 0), (5, 5, 0), (5, 5, 5), (0, 5, 5)]
+    line_seg = [(0, 5, 0), (5, 5, 0)]
+    assert lineseg_integrate(polygon, 0, line_seg, 1, 0) == 5
+    assert lineseg_integrate(polygon, 0, line_seg, 0, 0) == 0
+
+
+def test_integration_reduction():
+    triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    facets = triangle.sides
+    a, b = hyperplane_parameters(triangle)[0]
+    assert integration_reduction(facets, 0, a, b, 1, (x, y), 0) == 5
+    assert integration_reduction(facets, 0, a, b, 0, (x, y), 0) == 0
+
+
+def test_integration_reduction_dynamic():
+    triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
+    facets = triangle.sides
+    a, b = hyperplane_parameters(triangle)[0]
+    x0 = facets[0].points[0]
+    monomial_values = [[0, 0, 0, 0], [1, 0, 0, 5],\
+                       [y, 0, 1, 15], [x, 1, 0, None]]
+
+    assert integration_reduction_dynamic(facets, 0, a, b, x, 1, (x, y), 1,\
+                                         0, 1, x0, monomial_values, 3) == Rational(25, 2)
+    assert integration_reduction_dynamic(facets, 0, a, b, 0, 1, (x, y), 1,\
+                                         0, 1, x0, monomial_values, 3) == 0
+
+
+def test_is_vertex():
+    assert is_vertex(2) is False
+    assert is_vertex((2, 3)) is True
+    assert is_vertex(Point(2, 3)) is True
+    assert is_vertex((2, 3, 4)) is True
+    assert is_vertex((2, 3, 4, 5)) is False
+
+
+def test_issue_19234():
+    polygon = Polygon(Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0))
+    polys =  [ 1, x, y, x*y, x**2*y, x*y**2]
+    assert polytope_integrate(polygon, polys) == \
+        {1: 1, x: S.Half, y: S.Half, x*y: Rational(1, 4), x**2*y: Rational(1, 6), x*y**2: Rational(1, 6)}
+    polys =  [ 1, x, y, x*y, 3 + x**2*y, x + x*y**2]
+    assert polytope_integrate(polygon, polys) == \
+        {1: 1, x: S.Half, y: S.Half, x*y: Rational(1, 4), x**2*y + 3: Rational(19, 6), x*y**2 + x: Rational(2, 3)}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_laplace.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_laplace.py
new file mode 100644
index 0000000000000000000000000000000000000000..cb7222d01e3dcb3e14e8d0564610ab553e637155
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_laplace.py
@@ -0,0 +1,774 @@
+from sympy.integrals.laplace import (
+    laplace_transform, inverse_laplace_transform,
+    LaplaceTransform, InverseLaplaceTransform,
+    _laplace_deep_collect, laplace_correspondence,
+    laplace_initial_conds)
+from sympy.core.function import Function, expand_mul
+from sympy.core import EulerGamma, Subs, Derivative, diff
+from sympy.core.exprtools import factor_terms
+from sympy.core.numbers import I, oo, pi
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol, symbols
+from sympy.simplify.simplify import simplify
+from sympy.functions.elementary.complexes import Abs, re
+from sympy.functions.elementary.exponential import exp, log, exp_polar
+from sympy.functions.elementary.hyperbolic import cosh, sinh, coth, asinh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import atan, cos, sin
+from sympy.logic.boolalg import And
+from sympy.functions.special.gamma_functions import (
+    lowergamma, gamma, uppergamma)
+from sympy.functions.special.delta_functions import DiracDelta, Heaviside
+from sympy.functions.special.singularity_functions import SingularityFunction
+from sympy.functions.special.zeta_functions import lerchphi
+from sympy.functions.special.error_functions import (
+    fresnelc, fresnels, erf, erfc, Ei, Ci, expint, E1)
+from sympy.functions.special.bessel import besseli, besselj, besselk, bessely
+from sympy.testing.pytest import slow, warns_deprecated_sympy
+from sympy.matrices import Matrix, eye
+from sympy.abc import s
+
+
+@slow
+def test_laplace_transform():
+    LT = laplace_transform
+    ILT = inverse_laplace_transform
+    a, b, c = symbols('a, b, c', positive=True)
+    np = symbols('np', integer=True, positive=True)
+    t, w, x = symbols('t, w, x')
+    f = Function('f')
+    F = Function('F')
+    g = Function('g')
+    y = Function('y')
+    Y = Function('Y')
+
+    # Test helper functions
+    assert (
+        _laplace_deep_collect(exp((t+a)*(t+b)) +
+                              besselj(2, exp((t+a)*(t+b)-t**2)), t) ==
+        exp(a*b + t**2 + t*(a + b)) + besselj(2, exp(a*b + t*(a + b))))
+    L = laplace_transform(diff(y(t), t, 3), t, s, noconds=True)
+    L = laplace_correspondence(L, {y: Y})
+    L = laplace_initial_conds(L, t, {y: [2, 4, 8, 16, 32]})
+    assert L == s**3*Y(s) - 2*s**2 - 4*s - 8
+    # Test whether `noconds=True` in `doit`:
+    assert (2*LaplaceTransform(exp(t), t, s) - 1).doit() == -1 + 2/(s - 1)
+    assert (LT(a*t+t**2+t**(S(5)/2), t, s) ==
+            (a/s**2 + 2/s**3 + 15*sqrt(pi)/(8*s**(S(7)/2)), 0, True))
+    assert LT(b/(t+a), t, s) == (-b*exp(-a*s)*Ei(-a*s), 0, True)
+    assert (LT(1/sqrt(t+a), t, s) ==
+            (sqrt(pi)*sqrt(1/s)*exp(a*s)*erfc(sqrt(a)*sqrt(s)), 0, True))
+    assert (LT(sqrt(t)/(t+a), t, s) ==
+            (-pi*sqrt(a)*exp(a*s)*erfc(sqrt(a)*sqrt(s)) + sqrt(pi)*sqrt(1/s),
+             0, True))
+    assert (LT((t+a)**(-S(3)/2), t, s) ==
+            (-2*sqrt(pi)*sqrt(s)*exp(a*s)*erfc(sqrt(a)*sqrt(s)) + 2/sqrt(a),
+             0, True))
+    assert (LT(t**(S(1)/2)*(t+a)**(-1), t, s) ==
+            (-pi*sqrt(a)*exp(a*s)*erfc(sqrt(a)*sqrt(s)) + sqrt(pi)*sqrt(1/s),
+             0, True))
+    assert (LT(1/(a*sqrt(t) + t**(3/2)), t, s) ==
+            (pi*sqrt(a)*exp(a*s)*erfc(sqrt(a)*sqrt(s)), 0, True))
+    assert (LT((t+a)**b, t, s) ==
+            (s**(-b - 1)*exp(-a*s)*uppergamma(b + 1, a*s), 0, True))
+    assert LT(t**5/(t+a), t, s) == (120*a**5*uppergamma(-5, a*s), 0, True)
+    assert LT(exp(t), t, s) == (1/(s - 1), 1, True)
+    assert LT(exp(2*t), t, s) == (1/(s - 2), 2, True)
+    assert LT(exp(a*t), t, s) == (1/(s - a), a, True)
+    assert LT(exp(a*(t-b)), t, s) == (exp(-a*b)/(-a + s), a, True)
+    assert LT(t*exp(-a*(t)), t, s) == ((a + s)**(-2), -a, True)
+    assert LT(t*exp(-a*(t-b)), t, s) == (exp(a*b)/(a + s)**2, -a, True)
+    assert LT(b*t*exp(-a*t), t, s) == (b/(a + s)**2, -a, True)
+    assert LT(exp(-a*exp(-t)), t, s) == (lowergamma(s, a)/a**s, 0, True)
+    assert LT(exp(-a*exp(t)), t, s) == (a**s*uppergamma(-s, a), 0, True)
+    assert (LT(t**(S(7)/4)*exp(-8*t)/gamma(S(11)/4), t, s) ==
+            ((s + 8)**(-S(11)/4), -8, True))
+    assert (LT(t**(S(3)/2)*exp(-8*t), t, s) ==
+            (3*sqrt(pi)/(4*(s + 8)**(S(5)/2)), -8, True))
+    assert LT(t**a*exp(-a*t), t, s) == ((a+s)**(-a-1)*gamma(a+1), -a, True)
+    assert (LT(b*exp(-a*t**2), t, s) ==
+            (sqrt(pi)*b*exp(s**2/(4*a))*erfc(s/(2*sqrt(a)))/(2*sqrt(a)),
+             0, True))
+    assert (LT(exp(-2*t**2), t, s) ==
+            (sqrt(2)*sqrt(pi)*exp(s**2/8)*erfc(sqrt(2)*s/4)/4, 0, True))
+    assert (LT(b*exp(2*t**2), t, s) ==
+            (b*LaplaceTransform(exp(2*t**2), t, s), -oo, True))
+    assert (LT(t*exp(-a*t**2), t, s) ==
+            (1/(2*a) - s*erfc(s/(2*sqrt(a)))/(4*sqrt(pi)*a**(S(3)/2)),
+             0, True))
+    assert (LT(exp(-a/t), t, s) ==
+            (2*sqrt(a)*sqrt(1/s)*besselk(1, 2*sqrt(a)*sqrt(s)), 0, True))
+    assert LT(sqrt(t)*exp(-a/t), t, s, simplify=True) == (
+        sqrt(pi)*(sqrt(a)*sqrt(s) + 1/S(2))*sqrt(s**(-3)) *
+        exp(-2*sqrt(a)*sqrt(s)), 0, True)
+    assert (LT(exp(-a/t)/sqrt(t), t, s) ==
+            (sqrt(pi)*sqrt(1/s)*exp(-2*sqrt(a)*sqrt(s)), 0, True))
+    assert (LT(exp(-a/t)/(t*sqrt(t)), t, s) ==
+            (sqrt(pi)*sqrt(1/a)*exp(-2*sqrt(a)*sqrt(s)), 0, True))
+    # TODO: rules with sqrt(a*t) and sqrt(a/t) have stopped working after
+    #       changes to as_base_exp
+    # assert (
+    #     LT(exp(-2*sqrt(a*t)), t, s) ==
+    #     (1/s - sqrt(pi)*sqrt(a) * exp(a/s)*erfc(sqrt(a)*sqrt(1/s)) /
+    #      s**(S(3)/2), 0, True))
+    # assert LT(exp(-2*sqrt(a*t))/sqrt(t), t, s) == (
+    #     exp(a/s)*erfc(sqrt(a) * sqrt(1/s))*(sqrt(pi)*sqrt(1/s)), 0, True)
+    assert (LT(t**4*exp(-2/t), t, s) ==
+            (8*sqrt(2)*(1/s)**(S(5)/2)*besselk(5, 2*sqrt(2)*sqrt(s)),
+             0, True))
+    assert LT(sinh(a*t), t, s) == (a/(-a**2 + s**2), a, True)
+    assert (LT(b*sinh(a*t)**2, t, s) ==
+            (2*a**2*b/(-4*a**2*s + s**3), 2*a, True))
+    assert (LT(b*sinh(a*t)**2, t, s, simplify=True) ==
+            (2*a**2*b/(s*(-4*a**2 + s**2)), 2*a, True))
+    # The following line confirms that issue #21202 is solved
+    assert LT(cosh(2*t), t, s) == (s/(-4 + s**2), 2, True)
+    assert LT(cosh(a*t), t, s) == (s/(-a**2 + s**2), a, True)
+    assert (LT(cosh(a*t)**2, t, s, simplify=True) ==
+            ((2*a**2 - s**2)/(s*(4*a**2 - s**2)), 2*a, True))
+    assert (LT(sinh(x+3), x, s, simplify=True) ==
+            ((s*sinh(3) + cosh(3))/(s**2 - 1), 1, True))
+    L, _, _ = LT(42*sin(w*t+x)**2, t, s)
+    assert (
+        L -
+        21*(s**2 + s*(-s*cos(2*x) + 2*w*sin(2*x)) +
+            4*w**2)/(s*(s**2 + 4*w**2))).simplify() == 0
+    # The following line replaces the old test test_issue_7173()
+    assert LT(sinh(a*t)*cosh(a*t), t, s, simplify=True) == (a/(-4*a**2 + s**2),
+                                                            2*a, True)
+    assert LT(sinh(a*t)/t, t, s) == (log((a + s)/(-a + s))/2, a, True)
+    assert (LT(t**(-S(3)/2)*sinh(a*t), t, s) ==
+            (-sqrt(pi)*(sqrt(-a + s) - sqrt(a + s)), a, True))
+    # assert (LT(sinh(2*sqrt(a*t)), t, s) ==
+    #         (sqrt(pi)*sqrt(a)*exp(a/s)/s**(S(3)/2), 0, True))
+    # assert (LT(sqrt(t)*sinh(2*sqrt(a*t)), t, s, simplify=True) ==
+    #         ((-sqrt(a)*s**(S(5)/2) + sqrt(pi)*s**2*(2*a + s)*exp(a/s) *
+    #           erf(sqrt(a)*sqrt(1/s))/2)/s**(S(9)/2), 0, True))
+    # assert (LT(sinh(2*sqrt(a*t))/sqrt(t), t, s) ==
+    #         (sqrt(pi)*exp(a/s)*erf(sqrt(a)*sqrt(1/s))/sqrt(s), 0, True))
+    # assert (LT(sinh(sqrt(a*t))**2/sqrt(t), t, s) ==
+    #         (sqrt(pi)*(exp(a/s) - 1)/(2*sqrt(s)), 0, True))
+    assert (LT(t**(S(3)/7)*cosh(a*t), t, s) ==
+            (((a + s)**(-S(10)/7) + (-a+s)**(-S(10)/7))*gamma(S(10)/7)/2,
+             a, True))
+    # assert (LT(cosh(2*sqrt(a*t)), t, s) ==
+    #         (sqrt(pi)*sqrt(a)*exp(a/s)*erf(sqrt(a)*sqrt(1/s))/s**(S(3)/2) +
+    #          1/s, 0, True))
+    # assert (LT(sqrt(t)*cosh(2*sqrt(a*t)), t, s) ==
+    #         (sqrt(pi)*(a + s/2)*exp(a/s)/s**(S(5)/2), 0, True))
+    # assert (LT(cosh(2*sqrt(a*t))/sqrt(t), t, s) ==
+    #         (sqrt(pi)*exp(a/s)/sqrt(s), 0, True))
+    # assert (LT(cosh(sqrt(a*t))**2/sqrt(t), t, s) ==
+    #         (sqrt(pi)*(exp(a/s) + 1)/(2*sqrt(s)), 0, True))
+    assert LT(log(t), t, s, simplify=True) == (
+        (-log(s) - EulerGamma)/s, 0, True)
+    assert (LT(-log(t/a), t, s, simplify=True) ==
+            ((log(a) + log(s) + EulerGamma)/s, 0, True))
+    assert LT(log(1+a*t), t, s) == (-exp(s/a)*Ei(-s/a)/s, 0, True)
+    assert (LT(log(t+a), t, s, simplify=True) ==
+            ((s*log(a) - exp(s/a)*Ei(-s/a))/s**2, 0, True))
+    assert (LT(log(t)/sqrt(t), t, s, simplify=True) ==
+            (sqrt(pi)*(-log(s) - log(4) - EulerGamma)/sqrt(s), 0, True))
+    assert (LT(t**(S(5)/2)*log(t), t, s, simplify=True) ==
+            (sqrt(pi)*(-15*log(s) - log(1073741824) - 15*EulerGamma + 46) /
+             (8*s**(S(7)/2)), 0, True))
+    assert (LT(t**3*log(t), t, s, noconds=True, simplify=True) -
+            6*(-log(s) - S.EulerGamma + S(11)/6)/s**4).simplify() == S.Zero
+    assert (LT(log(t)**2, t, s, simplify=True) ==
+            (((log(s) + EulerGamma)**2 + pi**2/6)/s, 0, True))
+    assert (LT(exp(-a*t)*log(t), t, s, simplify=True) ==
+            ((-log(a + s) - EulerGamma)/(a + s), -a, True))
+    assert LT(sin(a*t), t, s) == (a/(a**2 + s**2), 0, True)
+    assert (LT(Abs(sin(a*t)), t, s) ==
+            (a*coth(pi*s/(2*a))/(a**2 + s**2), 0, True))
+    assert LT(sin(a*t)/t, t, s) == (atan(a/s), 0, True)
+    assert LT(sin(a*t)**2/t, t, s) == (log(4*a**2/s**2 + 1)/4, 0, True)
+    assert (LT(sin(a*t)**2/t**2, t, s) ==
+            (a*atan(2*a/s) - s*log(4*a**2/s**2 + 1)/4, 0, True))
+    # assert (LT(sin(2*sqrt(a*t)), t, s) ==
+    #         (sqrt(pi)*sqrt(a)*exp(-a/s)/s**(S(3)/2), 0, True))
+    # assert LT(sin(2*sqrt(a*t))/t, t, s) == (pi*erf(sqrt(a)*sqrt(1/s)), 0, True)
+    assert LT(cos(a*t), t, s) == (s/(a**2 + s**2), 0, True)
+    assert (LT(cos(a*t)**2, t, s) ==
+            ((2*a**2 + s**2)/(s*(4*a**2 + s**2)), 0, True))
+    # assert (LT(sqrt(t)*cos(2*sqrt(a*t)), t, s, simplify=True) ==
+    #         (sqrt(pi)*(-a + s/2)*exp(-a/s)/s**(S(5)/2), 0, True))
+    # assert (LT(cos(2*sqrt(a*t))/sqrt(t), t, s) ==
+    #         (sqrt(pi)*sqrt(1/s)*exp(-a/s), 0, True))
+    assert (LT(sin(a*t)*sin(b*t), t, s) ==
+            (2*a*b*s/((s**2 + (a - b)**2)*(s**2 + (a + b)**2)), 0, True))
+    assert (LT(cos(a*t)*sin(b*t), t, s) ==
+            (b*(-a**2 + b**2 + s**2)/((s**2 + (a - b)**2)*(s**2 + (a + b)**2)),
+             0, True))
+    assert (LT(cos(a*t)*cos(b*t), t, s) ==
+            (s*(a**2 + b**2 + s**2)/((s**2 + (a - b)**2)*(s**2 + (a + b)**2)),
+             0, True))
+    assert (LT(-a*t*cos(a*t) + sin(a*t), t, s, simplify=True) ==
+            (2*a**3/(a**4 + 2*a**2*s**2 + s**4), 0, True))
+    assert LT(c*exp(-b*t)*sin(a*t), t, s) == (a *
+                                              c/(a**2 + (b + s)**2), -b, True)
+    assert LT(c*exp(-b*t)*cos(a*t), t, s) == (c*(b + s)/(a**2 + (b + s)**2),
+                                              -b, True)
+    L, plane, cond = LT(cos(x + 3), x, s, simplify=True)
+    assert plane == 0
+    assert L - (s*cos(3) - sin(3))/(s**2 + 1) == 0
+    # Error functions (laplace7.pdf)
+    assert LT(erf(a*t), t, s) == (exp(s**2/(4*a**2))*erfc(s/(2*a))/s, 0, True)
+    # assert LT(erf(sqrt(a*t)), t, s) == (sqrt(a)/(s*sqrt(a + s)), 0, True)
+    # assert (LT(exp(a*t)*erf(sqrt(a*t)), t, s, simplify=True) ==
+    #         (-sqrt(a)/(sqrt(s)*(a - s)), a, True))
+    # assert (LT(erf(sqrt(a/t)/2), t, s, simplify=True) ==
+    #         (1/s - exp(-sqrt(a)*sqrt(s))/s, 0, True))
+    # assert (LT(erfc(sqrt(a*t)), t, s, simplify=True) ==
+    #         (-sqrt(a)/(s*sqrt(a + s)) + 1/s, -a, True))
+    # assert (LT(exp(a*t)*erfc(sqrt(a*t)), t, s) ==
+    #         (1/(sqrt(a)*sqrt(s) + s), 0, True))
+    # assert LT(erfc(sqrt(a/t)/2), t, s) == (exp(-sqrt(a)*sqrt(s))/s, 0, True)
+    # Bessel functions (laplace8.pdf)
+    assert LT(besselj(0, a*t), t, s) == (1/sqrt(a**2 + s**2), 0, True)
+    assert (LT(besselj(1, a*t), t, s, simplify=True) ==
+            (a/(a**2 + s**2 + s*sqrt(a**2 + s**2)), 0, True))
+    assert (LT(besselj(2, a*t), t, s, simplify=True) ==
+            (a**2/(sqrt(a**2 + s**2)*(s + sqrt(a**2 + s**2))**2), 0, True))
+    assert (LT(t*besselj(0, a*t), t, s) ==
+            (s/(a**2 + s**2)**(S(3)/2), 0, True))
+    assert (LT(t*besselj(1, a*t), t, s) ==
+            (a/(a**2 + s**2)**(S(3)/2), 0, True))
+    assert (LT(t**2*besselj(2, a*t), t, s) ==
+            (3*a**2/(a**2 + s**2)**(S(5)/2), 0, True))
+    # assert LT(besselj(0, 2*sqrt(a*t)), t, s) == (exp(-a/s)/s, 0, True)
+    # assert (LT(t**(S(3)/2)*besselj(3, 2*sqrt(a*t)), t, s) ==
+    #         (a**(S(3)/2)*exp(-a/s)/s**4, 0, True))
+    assert (LT(besselj(0, a*sqrt(t**2+b*t)), t, s, simplify=True) ==
+            (exp(b*(s - sqrt(a**2 + s**2)))/sqrt(a**2 + s**2), 0, True))
+    assert LT(besseli(0, a*t), t, s) == (1/sqrt(-a**2 + s**2), a, True)
+    assert (LT(besseli(1, a*t), t, s, simplify=True) ==
+            (a/(-a**2 + s**2 + s*sqrt(-a**2 + s**2)), a, True))
+    assert (LT(besseli(2, a*t), t, s, simplify=True) ==
+            (a**2/(sqrt(-a**2 + s**2)*(s + sqrt(-a**2 + s**2))**2), a, True))
+    assert LT(t*besseli(0, a*t), t, s) == (s/(-a**2 + s**2)**(S(3)/2), a, True)
+    assert LT(t*besseli(1, a*t), t, s) == (a/(-a**2 + s**2)**(S(3)/2), a, True)
+    assert (LT(t**2*besseli(2, a*t), t, s) ==
+            (3*a**2/(-a**2 + s**2)**(S(5)/2), a, True))
+    # assert (LT(t**(S(3)/2)*besseli(3, 2*sqrt(a*t)), t, s) ==
+    #         (a**(S(3)/2)*exp(a/s)/s**4, 0, True))
+    assert (LT(bessely(0, a*t), t, s) ==
+            (-2*asinh(s/a)/(pi*sqrt(a**2 + s**2)), 0, True))
+    assert (LT(besselk(0, a*t), t, s) ==
+            (log((s + sqrt(-a**2 + s**2))/a)/sqrt(-a**2 + s**2), -a, True))
+    assert (LT(sin(a*t)**4, t, s, simplify=True) ==
+            (24*a**4/(s*(64*a**4 + 20*a**2*s**2 + s**4)), 0, True))
+    # Test general rules and unevaluated forms
+    # These all also test whether issue #7219 is solved.
+    assert LT(Heaviside(t-1)*cos(t-1), t, s) == (s*exp(-s)/(s**2 + 1), 0, True)
+    assert LT(a*f(t), t, w) == (a*LaplaceTransform(f(t), t, w), -oo, True)
+    assert (LT(a*Heaviside(t+1)*f(t+1), t, s) ==
+            (a*LaplaceTransform(f(t + 1), t, s), -oo, True))
+    assert (LT(a*Heaviside(t-1)*f(t-1), t, s) ==
+            (a*LaplaceTransform(f(t), t, s)*exp(-s), -oo, True))
+    assert (LT(b*f(t/a), t, s) ==
+            (a*b*LaplaceTransform(f(t), t, a*s), -oo, True))
+    assert LT(exp(-f(x)*t), t, s) == (1/(s + f(x)), -re(f(x)), True)
+    assert (LT(exp(-a*t)*f(t), t, s) ==
+            (LaplaceTransform(f(t), t, a + s), -oo, True))
+    # assert (LT(exp(-a*t)*erfc(sqrt(b/t)/2), t, s) ==
+    #         (exp(-sqrt(b)*sqrt(a + s))/(a + s), -a, True))
+    assert (LT(sinh(a*t)*f(t), t, s) ==
+            (LaplaceTransform(f(t), t, -a + s)/2 -
+             LaplaceTransform(f(t), t, a + s)/2, -oo, True))
+    assert (LT(sinh(a*t)*t, t, s, simplify=True) ==
+            (2*a*s/(a**4 - 2*a**2*s**2 + s**4), a, True))
+    assert (LT(cosh(a*t)*f(t), t, s) ==
+            (LaplaceTransform(f(t), t, -a + s)/2 +
+             LaplaceTransform(f(t), t, a + s)/2, -oo, True))
+    assert (LT(cosh(a*t)*t, t, s, simplify=True) ==
+            (1/(2*(a + s)**2) + 1/(2*(a - s)**2), a, True))
+    assert (LT(sin(a*t)*f(t), t, s, simplify=True) ==
+            (I*(-LaplaceTransform(f(t), t, -I*a + s) +
+                LaplaceTransform(f(t), t, I*a + s))/2, -oo, True))
+    assert (LT(sin(f(t)), t, s) ==
+            (LaplaceTransform(sin(f(t)), t, s), -oo, True))
+    assert (LT(sin(a*t)*t, t, s, simplify=True) ==
+            (2*a*s/(a**4 + 2*a**2*s**2 + s**4), 0, True))
+    assert (LT(cos(a*t)*f(t), t, s) ==
+            (LaplaceTransform(f(t), t, -I*a + s)/2 +
+             LaplaceTransform(f(t), t, I*a + s)/2, -oo, True))
+    assert (LT(cos(a*t)*t, t, s, simplify=True) ==
+            ((-a**2 + s**2)/(a**4 + 2*a**2*s**2 + s**4), 0, True))
+    L, plane, _ = LT(sin(a*t+b)**2*f(t), t, s)
+    assert plane == -oo
+    assert (
+        -L + (
+            LaplaceTransform(f(t), t, s)/2 -
+            LaplaceTransform(f(t), t, -2*I*a + s)*exp(2*I*b)/4 -
+            LaplaceTransform(f(t), t, 2*I*a + s)*exp(-2*I*b)/4)) == 0
+    L = LT(sin(a*t+b)**2*f(t), t, s, noconds=True)
+    assert (
+        laplace_correspondence(L, {f: F}) ==
+        F(s)/2 - F(-2*I*a + s)*exp(2*I*b)/4 -
+        F(2*I*a + s)*exp(-2*I*b)/4)
+    L, plane, _ = LT(sin(a*t)**3*cosh(b*t), t, s)
+    assert plane == b
+    assert (
+        -L - 3*a/(8*(9*a**2 + b**2 + 2*b*s + s**2)) -
+        3*a/(8*(9*a**2 + b**2 - 2*b*s + s**2)) +
+        3*a/(8*(a**2 + b**2 + 2*b*s + s**2)) +
+        3*a/(8*(a**2 + b**2 - 2*b*s + s**2))).simplify() == 0
+    assert (LT(t**2*exp(-t**2), t, s) ==
+            (sqrt(pi)*s**2*exp(s**2/4)*erfc(s/2)/8 - s/4 +
+             sqrt(pi)*exp(s**2/4)*erfc(s/2)/4, 0, True))
+    assert (LT((a*t**2 + b*t + c)*f(t), t, s) ==
+            (a*Derivative(LaplaceTransform(f(t), t, s), (s, 2)) -
+             b*Derivative(LaplaceTransform(f(t), t, s), s) +
+            c*LaplaceTransform(f(t), t, s), -oo, True))
+    assert (LT(t**np*g(t), t, s) ==
+            ((-1)**np*Derivative(LaplaceTransform(g(t), t, s), (s, np)),
+             -oo, True))
+    # The following tests check whether _piecewise_to_heaviside works:
+    x1 = Piecewise((0, t <= 0), (1, t <= 1), (0, True))
+    X1 = LT(x1, t, s)[0]
+    assert X1 == 1/s - exp(-s)/s
+    y1 = ILT(X1, s, t)
+    assert y1 == Heaviside(t) - Heaviside(t - 1)
+    x1 = Piecewise((0, t <= 0), (t, t <= 1), (2-t, t <= 2), (0, True))
+    X1 = LT(x1, t, s)[0].simplify()
+    assert X1 == (exp(2*s) - 2*exp(s) + 1)*exp(-2*s)/s**2
+    y1 = ILT(X1, s, t)
+    assert (
+        -y1 + t*Heaviside(t) + (t - 2)*Heaviside(t - 2) -
+        2*(t - 1)*Heaviside(t - 1)).simplify() == 0
+    x1 = Piecewise((exp(t), t <= 0), (1, t <= 1), (exp(-(t)), True))
+    X1 = LT(x1, t, s)[0]
+    assert X1 == exp(-1)*exp(-s)/(s + 1) + 1/s - exp(-s)/s
+    y1 = ILT(X1, s, t)
+    assert y1 == (
+        exp(-1)*exp(1 - t)*Heaviside(t - 1) + Heaviside(t) - Heaviside(t - 1))
+    x1 = Piecewise((0, x <= 0), (1, x <= 1), (0, True))
+    X1 = LT(x1, t, s)[0]
+    assert X1 == Piecewise((0, x <= 0), (1, x <= 1), (0, True))/s
+    x1 = [
+        a*Piecewise((1, And(t > 1, t <= 3)), (2, True)),
+        a*Piecewise((1, And(t >= 1, t <= 3)), (2, True)),
+        a*Piecewise((1, And(t >= 1, t < 3)), (2, True)),
+        a*Piecewise((1, And(t > 1, t < 3)), (2, True))]
+    for x2 in x1:
+        assert LT(x2, t, s)[0].expand() == 2*a/s - a*exp(-s)/s + a*exp(-3*s)/s
+    assert (
+        LT(Piecewise((1, Eq(t, 1)), (2, True)), t, s)[0] ==
+        LaplaceTransform(Piecewise((1, Eq(t, 1)), (2, True)), t, s))
+    # The following lines test whether _laplace_transform successfully
+    # removes Heaviside(1) before processing espressions. It fails if
+    # Heaviside(t) remains because then meijerg functions will appear.
+    X1 = 1/sqrt(a*s**2-b)
+    x1 = ILT(X1, s, t)
+    Y1 = LT(x1, t, s)[0]
+    Z1 = (Y1**2/X1**2).simplify()
+    assert Z1 == 1
+    # The following two lines test whether issues #5813 and #7176 are solved.
+    assert (LT(diff(f(t), (t, 1)), t, s, noconds=True) ==
+            s*LaplaceTransform(f(t), t, s) - f(0))
+    assert (LT(diff(f(t), (t, 3)), t, s, noconds=True) ==
+            s**3*LaplaceTransform(f(t), t, s) - s**2*f(0) -
+            s*Subs(Derivative(f(t), t), t, 0) -
+            Subs(Derivative(f(t), (t, 2)), t, 0))
+    # Issue #7219
+    assert (LT(diff(f(x, t, w), t, 2), t, s) ==
+            (s**2*LaplaceTransform(f(x, t, w), t, s) - s*f(x, 0, w) -
+             Subs(Derivative(f(x, t, w), t), t, 0), -oo, True))
+    # Issue #23307
+    assert (LT(10*diff(f(t), (t, 1)), t, s, noconds=True) ==
+            10*s*LaplaceTransform(f(t), t, s) - 10*f(0))
+    assert (LT(a*f(b*t)+g(c*t), t, s, noconds=True) ==
+            a*LaplaceTransform(f(t), t, s/b)/b +
+            LaplaceTransform(g(t), t, s/c)/c)
+    assert inverse_laplace_transform(
+        f(w), w, t, plane=0) == InverseLaplaceTransform(f(w), w, t, 0)
+    assert (LT(f(t)*g(t), t, s, noconds=True) ==
+            LaplaceTransform(f(t)*g(t), t, s))
+    # Issue #24294
+    assert (LT(b*f(a*t), t, s, noconds=True) ==
+            b*LaplaceTransform(f(t), t, s/a)/a)
+    assert LT(3*exp(t)*Heaviside(t), t, s) == (3/(s - 1), 1, True)
+    assert (LT(2*sin(t)*Heaviside(t), t, s, simplify=True) ==
+            (2/(s**2 + 1), 0, True))
+    # Issue #25293
+    assert (
+        LT((1/(t-1))*sin(4*pi*(t-1))*DiracDelta(t-1) *
+           (Heaviside(t-1/4) - Heaviside(t-2)), t, s)[0] == 4*pi*exp(-s))
+    # additional basic tests from wikipedia
+    assert (LT((t - a)**b*exp(-c*(t - a))*Heaviside(t - a), t, s) ==
+            ((c + s)**(-b - 1)*exp(-a*s)*gamma(b + 1), -c, True))
+    assert (
+        LT((exp(2*t)-1)*exp(-b-t)*Heaviside(t)/2, t, s, noconds=True,
+           simplify=True) ==
+        exp(-b)/(s**2 - 1))
+    # DiracDelta function: standard cases
+    assert LT(DiracDelta(t), t, s) == (1, -oo, True)
+    assert LT(DiracDelta(a*t), t, s) == (1/a, -oo, True)
+    assert LT(DiracDelta(t/42), t, s) == (42, -oo, True)
+    assert LT(DiracDelta(t+42), t, s) == (0, -oo, True)
+    assert (LT(DiracDelta(t)+DiracDelta(t-42), t, s) ==
+            (1 + exp(-42*s), -oo, True))
+    assert (LT(DiracDelta(t)-a*exp(-a*t), t, s, simplify=True) ==
+            (s/(a + s), -a, True))
+    assert (
+        LT(exp(-t)*(DiracDelta(t)+DiracDelta(t-42)), t, s, simplify=True) ==
+        (exp(-42*s - 42) + 1, -oo, True))
+    assert LT(f(t)*DiracDelta(t-42), t, s) == (f(42)*exp(-42*s), -oo, True)
+    assert LT(f(t)*DiracDelta(b*t-a), t, s) == (f(a/b)*exp(-a*s/b)/b,
+                                                -oo, True)
+    assert LT(f(t)*DiracDelta(b*t+a), t, s) == (0, -oo, True)
+    # SingularityFunction
+    assert LT(SingularityFunction(t, a, -1), t, s)[0] == exp(-a*s)
+    assert LT(SingularityFunction(t, a, 1), t, s)[0] == exp(-a*s)/s**2
+    assert LT(SingularityFunction(t, a, x), t, s)[0] == (
+        LaplaceTransform(SingularityFunction(t, a, x), t, s))
+    # Collection of cases that cannot be fully evaluated and/or would catch
+    # some common implementation errors
+    assert (LT(DiracDelta(t**2), t, s, noconds=True) ==
+            LaplaceTransform(DiracDelta(t**2), t, s))
+    assert LT(DiracDelta(t**2 - 1), t, s) == (exp(-s)/2, -oo, True)
+    assert LT(DiracDelta(t*(1 - t)), t, s) == (1 - exp(-s), -oo, True)
+    assert (LT((DiracDelta(t) + 1)*(DiracDelta(t - 1) + 1), t, s) ==
+            (LaplaceTransform(DiracDelta(t)*DiracDelta(t - 1), t, s) +
+             1 + exp(-s) + 1/s, 0, True))
+    assert LT(DiracDelta(2*t-2*exp(a)), t, s) == (exp(-s*exp(a))/2, -oo, True)
+    assert LT(DiracDelta(-2*t+2*exp(a)), t, s) == (exp(-s*exp(a))/2, -oo, True)
+    # Heaviside tests
+    assert LT(Heaviside(t), t, s) == (1/s, 0, True)
+    assert LT(Heaviside(t - a), t, s) == (exp(-a*s)/s, 0, True)
+    assert LT(Heaviside(t-1), t, s) == (exp(-s)/s, 0, True)
+    assert LT(Heaviside(2*t-4), t, s) == (exp(-2*s)/s, 0, True)
+    assert LT(Heaviside(2*t+4), t, s) == (1/s, 0, True)
+    assert (LT(Heaviside(-2*t+4), t, s, simplify=True) ==
+            (1/s - exp(-2*s)/s, 0, True))
+    assert (LT(g(t)*Heaviside(t - w), t, s) ==
+            (LaplaceTransform(g(t)*Heaviside(t - w), t, s), -oo, True))
+    assert (
+        LT(Heaviside(t-a)*g(t), t, s) ==
+        (LaplaceTransform(g(a + t), t, s)*exp(-a*s), -oo, True))
+    assert (
+        LT(Heaviside(t+a)*g(t), t, s) ==
+        (LaplaceTransform(g(t), t, s), -oo, True))
+    assert (
+        LT(Heaviside(-t+a)*g(t), t, s) ==
+        (LaplaceTransform(g(t), t, s) -
+         LaplaceTransform(g(a + t), t, s)*exp(-a*s), -oo, True))
+    assert (
+        LT(Heaviside(-t-a)*g(t), t, s) == (0, 0, True))
+    # Fresnel functions
+    assert (laplace_transform(fresnels(t), t, s, simplify=True) ==
+            ((-sin(s**2/(2*pi))*fresnels(s/pi) +
+              sqrt(2)*sin(s**2/(2*pi) + pi/4)/2 -
+              cos(s**2/(2*pi))*fresnelc(s/pi))/s, 0, True))
+    assert (laplace_transform(fresnelc(t), t, s, simplify=True) ==
+            ((sin(s**2/(2*pi))*fresnelc(s/pi) -
+              cos(s**2/(2*pi))*fresnels(s/pi) +
+              sqrt(2)*cos(s**2/(2*pi) + pi/4)/2)/s, 0, True))
+    # Matrix tests
+    Mt = Matrix([[exp(t), t*exp(-t)], [t*exp(-t), exp(t)]])
+    Ms = Matrix([[1/(s - 1), (s + 1)**(-2)],
+                 [(s + 1)**(-2),     1/(s - 1)]])
+    # The default behaviour for Laplace transform of a Matrix returns a Matrix
+    # of Tuples and is deprecated:
+    with warns_deprecated_sympy():
+        Ms_conds = Matrix(
+            [[(1/(s - 1), 1, True), ((s + 1)**(-2), -1, True)],
+             [((s + 1)**(-2), -1, True), (1/(s - 1), 1, True)]])
+    with warns_deprecated_sympy():
+        assert LT(Mt, t, s) == Ms_conds
+    # The new behavior is to return a tuple of a Matrix and the convergence
+    # conditions for the matrix as a whole:
+    assert LT(Mt, t, s, legacy_matrix=False) == (Ms, 1, True)
+    # With noconds=True the transformed matrix is returned without conditions
+    # either way:
+    assert LT(Mt, t, s, noconds=True) == Ms
+    assert LT(Mt, t, s, legacy_matrix=False, noconds=True) == Ms
+
+
+@slow
+def test_inverse_laplace_transform():
+    s = symbols('s')
+    k, n, t = symbols('k, n, t', real=True)
+    a, b, c, d = symbols('a, b, c, d', positive=True)
+    f = Function('f')
+    F = Function('F')
+
+    def ILT(g):
+        return inverse_laplace_transform(g, s, t)
+
+    def ILTS(g):
+        return inverse_laplace_transform(g, s, t, simplify=True)
+
+    def ILTF(g):
+        return laplace_correspondence(
+            inverse_laplace_transform(g, s, t), {f: F})
+
+    # Tests for the rules in Bateman54.
+
+    # Section 4.1: Some of the Laplace transform rules can also be used well
+    #     in the inverse transform.
+    assert ILTF(exp(-a*s)*F(s)) == f(-a + t)
+    assert ILTF(k*F(s-a)) == k*f(t)*exp(-a*t)
+    assert ILTF(diff(F(s), s, 3)) == -t**3*f(t)
+    assert ILTF(diff(F(s), s, 4)) == t**4*f(t)
+
+    # Section 5.1: Most rules are impractical for a computer algebra system.
+
+    # Section 5.2: Rational functions
+    assert ILT(2) == 2*DiracDelta(t)
+    assert ILT(1/s) == Heaviside(t)
+    assert ILT(1/s**2) == t*Heaviside(t)
+    assert ILT(1/s**5) == t**4*Heaviside(t)/24
+    assert ILT(1/s**n) == t**(n - 1)*Heaviside(t)/gamma(n)
+    assert ILT(a/(a + s)) == a*exp(-a*t)*Heaviside(t)
+    assert ILT(s/(a + s)) == -a*exp(-a*t)*Heaviside(t) + DiracDelta(t)
+    assert (ILT(b*s/(s+a)**2) ==
+            b*(-a*t*exp(-a*t)*Heaviside(t) + exp(-a*t)*Heaviside(t)))
+    assert (ILTS(c/((s+a)*(s+b))) ==
+            c*(exp(a*t) - exp(b*t))*exp(-t*(a + b))*Heaviside(t)/(a - b))
+    assert (ILTS(c*s/((s+a)*(s+b))) ==
+            c*(a*exp(b*t) - b*exp(a*t))*exp(-t*(a + b))*Heaviside(t)/(a - b))
+    assert ILTS(s/(a + s)**3) == t*(-a*t + 2)*exp(-a*t)*Heaviside(t)/2
+    assert ILTS(1/(s*(a + s)**3)) == (
+        -a**2*t**2 - 2*a*t + 2*exp(a*t) - 2)*exp(-a*t)*Heaviside(t)/(2*a**3)
+    assert ILT(1/(s*(a + s)**n)) == (
+        Heaviside(t)*lowergamma(n, a*t)/(a**n*gamma(n)))
+    assert ILT((s-a)**(-b)) == t**(b - 1)*exp(a*t)*Heaviside(t)/gamma(b)
+    assert ILT((a + s)**(-2)) == t*exp(-a*t)*Heaviside(t)
+    assert ILT((a + s)**(-5)) == t**4*exp(-a*t)*Heaviside(t)/24
+    assert ILT(s**2/(s**2 + 1)) == -sin(t)*Heaviside(t) + DiracDelta(t)
+    assert ILT(1 - 1/(s**2 + 1)) == -sin(t)*Heaviside(t) + DiracDelta(t)
+    assert ILT(a/(a**2 + s**2)) == sin(a*t)*Heaviside(t)
+    assert ILT(s/(s**2 + a**2)) == cos(a*t)*Heaviside(t)
+    assert ILT(b/(b**2 + (a + s)**2)) == exp(-a*t)*sin(b*t)*Heaviside(t)
+    assert (ILT(b*s/(b**2 + (a + s)**2)) ==
+            b*(-a*exp(-a*t)*sin(b*t)/b + exp(-a*t)*cos(b*t))*Heaviside(t))
+    assert ILT(1/(s**2*(s**2 + 1))) == t*Heaviside(t) - sin(t)*Heaviside(t)
+    assert (ILTS(c*s/(d**2*(s+a)**2+b**2)) ==
+            c*(-a*d*sin(b*t/d) + b*cos(b*t/d))*exp(-a*t)*Heaviside(t)/(b*d**2))
+    assert ILTS((b*s**2 + d)/(a**2 + s**2)**2) == (
+        2*a**2*b*sin(a*t) + (a**2*b - d)*(a*t*cos(a*t) -
+                                          sin(a*t)))*Heaviside(t)/(2*a**3)
+    assert ILTS(b/(s**2-a**2)) == b*sinh(a*t)*Heaviside(t)/a
+    assert (ILT(b/(s**2-a**2)) ==
+            b*(exp(a*t)*Heaviside(t)/(2*a) - exp(-a*t)*Heaviside(t)/(2*a)))
+    assert ILTS(b*s/(s**2-a**2)) == b*cosh(a*t)*Heaviside(t)
+    assert (ILT(b/(s*(s+a))) ==
+            b*(Heaviside(t)/a - exp(-a*t)*Heaviside(t)/a))
+    # Issue #24424
+    assert (ILTS((s + 8)/((s + 2)*(s**2 + 2*s + 10))) ==
+            ((8*sin(3*t) - 9*cos(3*t))*exp(t) + 9)*exp(-2*t)*Heaviside(t)/15)
+    # Issue #8514; this is not important anymore, since this function
+    # is not solved by integration anymore
+    assert (ILT(1/(a*s**2+b*s+c)) ==
+            2*exp(-b*t/(2*a))*sin(t*sqrt(4*a*c - b**2)/(2*a)) *
+            Heaviside(t)/sqrt(4*a*c - b**2))
+
+    # Section 5.3: Irrational algebraic functions
+    assert (  # (1)
+        ILT(1/sqrt(s)/(b*s-a)) ==
+        exp(a*t/b)*Heaviside(t)*erf(sqrt(a)*sqrt(t)/sqrt(b))/(sqrt(a)*sqrt(b)))
+    assert (  # (2)
+        ILT(1/sqrt(k*s)/(c*s-a)/s) ==
+        (-2*c*sqrt(t)/(sqrt(pi)*a) +
+         c**(S(3)/2)*exp(a*t/c)*erf(sqrt(a)*sqrt(t)/sqrt(c))/a**(S(3)/2)) *
+        Heaviside(t)/(c*sqrt(k)))
+    assert (  # (4)
+        ILT(1/(sqrt(c*s)+a)) == (-a*exp(a**2*t/c)*erfc(a*sqrt(t)/sqrt(c))/c +
+                                 1/(sqrt(pi)*sqrt(c)*sqrt(t)))*Heaviside(t))
+    assert (  # (5)
+        ILT(a/s/(b*sqrt(s)+a)) ==
+        (-exp(a**2*t/b**2)*erfc(a*sqrt(t)/b) + 1)*Heaviside(t))
+    assert (  # (6)
+            ILT((a-b)*sqrt(s)/(sqrt(s)+sqrt(a))/(s-b)) ==
+            (sqrt(a)*sqrt(b)*exp(b*t)*erfc(sqrt(b)*sqrt(t)) +
+             a*exp(a*t)*erfc(sqrt(a)*sqrt(t)) - b*exp(b*t))*Heaviside(t))
+    assert (  # (7)
+            ILT(1/sqrt(s)/(sqrt(b*s)+a)) ==
+            exp(a**2*t/b)*Heaviside(t)*erfc(a*sqrt(t)/sqrt(b))/sqrt(b))
+    assert (  # (8)
+            ILT(a**2/(sqrt(s)+a)/s**(S(3)/2)) ==
+            (2*a*sqrt(t)/sqrt(pi) + exp(a**2*t)*erfc(a*sqrt(t)) - 1) *
+            Heaviside(t))
+    assert (  # (9)
+            ILT((a-b)*sqrt(b)/(s-b)/sqrt(s)/(sqrt(s)+sqrt(a))) ==
+            (sqrt(a)*exp(b*t)*erf(sqrt(b)*sqrt(t)) +
+             sqrt(b)*exp(a*t)*erfc(sqrt(a)*sqrt(t)) -
+             sqrt(b)*exp(b*t))*Heaviside(t))
+    assert (  # (10)
+            ILT(1/(sqrt(s)+sqrt(a))**2) ==
+            (-2*sqrt(a)*sqrt(t)/sqrt(pi) +
+             (-2*a*t + 1)*(erf(sqrt(a)*sqrt(t)) -
+                           1)*exp(a*t) + 1)*Heaviside(t))
+    assert (  # (11)
+            ILT(1/(sqrt(s)+sqrt(a))**2/s) ==
+            ((2*t - 1/a)*exp(a*t)*erfc(sqrt(a)*sqrt(t)) + 1/a -
+             2*sqrt(t)/(sqrt(pi)*sqrt(a)))*Heaviside(t))
+    assert (  # (12)
+            ILT(1/(sqrt(s)+a)**2/sqrt(s)) ==
+            (-2*a*t*exp(a**2*t)*erfc(a*sqrt(t)) +
+             2*sqrt(t)/sqrt(pi))*Heaviside(t))
+    assert (  # (13)
+            ILT(1/(sqrt(s)+a)**3) ==
+            (-a*t*(2*a**2*t + 3)*exp(a**2*t)*erfc(a*sqrt(t)) +
+             2*sqrt(t)*(a**2*t + 1)/sqrt(pi))*Heaviside(t))
+    x = (
+        - ILT(sqrt(s)/(sqrt(s)+a)**3) +
+        2*(sqrt(pi)*a**2*t*(-2*sqrt(pi)*erfc(a*sqrt(t)) +
+                            2*exp(-a**2*t)/(a*sqrt(t))) *
+           (-a**4*t**2 - 5*a**2*t/2 - S.Half) * exp(a**2*t)/2 +
+           sqrt(pi)*a*sqrt(t)*(a**2*t + 1)/2) *
+        Heaviside(t)/(pi*a**2*t)).simplify()
+    assert (  # (14)
+            x == 0)
+    x = (
+        - ILT(1/sqrt(s)/(sqrt(s)+a)**3) +
+        Heaviside(t)*(sqrt(t)*((2*a**2*t + 1) *
+                               (sqrt(pi)*a*sqrt(t)*exp(a**2*t) *
+                                erfc(a*sqrt(t)) - 1) + 1) /
+                      (sqrt(pi)*a))).simplify()
+    assert (  # (15)
+            x == 0)
+    assert (  # (16)
+            factor_terms(ILT(3/(sqrt(s)+a)**4)) ==
+            3*(-2*a**3*t**(S(5)/2)*(2*a**2*t + 5)/(3*sqrt(pi)) +
+               t*(4*a**4*t**2 + 12*a**2*t + 3)*exp(a**2*t) *
+               erfc(a*sqrt(t))/3)*Heaviside(t))
+    assert (  # (17)
+            ILT((sqrt(s)-a)/(s*(sqrt(s)+a))) ==
+            (2*exp(a**2*t)*erfc(a*sqrt(t))-1)*Heaviside(t))
+    assert (  # (18)
+            ILT((sqrt(s)-a)**2/(s*(sqrt(s)+a)**2)) == (
+                1 + 8*a**2*t*exp(a**2*t)*erfc(a*sqrt(t)) -
+                8/sqrt(pi)*a*sqrt(t))*Heaviside(t))
+    assert (  # (19)
+            ILT((sqrt(s)-a)**3/(s*(sqrt(s)+a)**3)) == Heaviside(t)*(
+                2*(8*a**4*t**2+8*a**2*t+1)*exp(a**2*t) *
+                erfc(a*sqrt(t))-8/sqrt(pi)*a*sqrt(t)*(2*a**2*t+1)-1))
+    assert (  # (22)
+            ILT(sqrt(s+a)/(s+b)) == Heaviside(t)*(
+                exp(-a*t)/sqrt(t)/sqrt(pi) +
+                sqrt(a-b)*exp(-b*t)*erf(sqrt(a-b)*sqrt(t))))
+    assert (  # (23)
+            ILT(1/sqrt(s+b)/(s+a)) == Heaviside(t)*(
+                1/sqrt(b-a)*exp(-a*t)*erf(sqrt(b-a)*sqrt(t))))
+    assert (  # (35)
+            ILT(1/sqrt(s**2+a**2)) == Heaviside(t)*(
+                besselj(0, a*t)))
+    assert (  # (44)
+            ILT(1/sqrt(s**2-a**2)) == Heaviside(t)*(
+                besseli(0, a*t)))
+
+    # Miscellaneous tests
+    # Can _inverse_laplace_time_shift deal with positive exponents?
+    assert (
+        - ILT((s**2*exp(2*s) + 4*exp(s) - 4)*exp(-2*s)/(s*(s**2 + 1))) +
+        cos(t)*Heaviside(t) + 4*cos(t - 2)*Heaviside(t - 2) -
+        4*cos(t - 1)*Heaviside(t - 1) - 4*Heaviside(t - 2) +
+        4*Heaviside(t - 1)).simplify() == 0
+
+
+@slow
+def test_inverse_laplace_transform_old():
+    from sympy.functions.special.delta_functions import DiracDelta
+    ILT = inverse_laplace_transform
+    a, b, c, d = symbols('a b c d', positive=True)
+    n, r = symbols('n, r', real=True)
+    t, z = symbols('t z')
+    f = Function('f')
+    F = Function('F')
+
+    def simp_hyp(expr):
+        return factor_terms(expand_mul(expr)).rewrite(sin)
+
+    L = ILT(F(s), s, t)
+    assert laplace_correspondence(L, {f: F}) == f(t)
+    assert ILT(exp(-a*s)/s, s, t) == Heaviside(-a + t)
+    assert ILT(exp(-a*s)/(b + s), s, t) == exp(-b*(-a + t))*Heaviside(-a + t)
+    assert (ILT((b + s)/(a**2 + (b + s)**2), s, t) ==
+            exp(-b*t)*cos(a*t)*Heaviside(t))
+    assert (ILT(exp(-a*s)/s**b, s, t) ==
+            (-a + t)**(b - 1)*Heaviside(-a + t)/gamma(b))
+    assert (ILT(exp(-a*s)/sqrt(s**2 + 1), s, t) ==
+            Heaviside(-a + t)*besselj(0, a - t))
+    assert ILT(1/(s*sqrt(s + 1)), s, t) == Heaviside(t)*erf(sqrt(t))
+    # TODO sinh/cosh shifted come out a mess. also delayed trig is a mess
+    # TODO should this simplify further?
+    assert (ILT(exp(-a*s)/s**b, s, t) ==
+            (t - a)**(b - 1)*Heaviside(t - a)/gamma(b))
+    assert (ILT(exp(-a*s)/sqrt(1 + s**2), s, t) ==
+            Heaviside(t - a)*besselj(0, a - t))  # note: besselj(0, x) is even
+    # XXX ILT turns these branch factor into trig functions ...
+    assert (
+        simplify(ILT(a**b*(s + sqrt(s**2 - a**2))**(-b)/sqrt(s**2 - a**2),
+                     s, t).rewrite(exp)) ==
+        Heaviside(t)*besseli(b, a*t))
+    assert (
+        ILT(a**b*(s + sqrt(s**2 + a**2))**(-b)/sqrt(s**2 + a**2),
+            s, t, simplify=True).rewrite(exp) ==
+        Heaviside(t)*besselj(b, a*t))
+    assert ILT(1/(s*sqrt(s + 1)), s, t) == Heaviside(t)*erf(sqrt(t))
+    # TODO can we make erf(t) work?
+    assert (ILT((s * eye(2) - Matrix([[1, 0], [0, 2]])).inv(), s, t) ==
+            Matrix([[exp(t)*Heaviside(t), 0], [0, exp(2*t)*Heaviside(t)]]))
+    # Test time_diff rule
+    assert (ILT(s**42*f(s), s, t) ==
+            Derivative(InverseLaplaceTransform(f(s), s, t, None), (t, 42)))
+    assert ILT(cos(s), s, t) == InverseLaplaceTransform(cos(s), s, t, None)
+    # Rules for testing different DiracDelta cases
+    assert (
+        ILT(1 + 2*s + 3*s**2 + 5*s**3, s, t) == DiracDelta(t) +
+        2*DiracDelta(t, 1) + 3*DiracDelta(t, 2) + 5*DiracDelta(t, 3))
+    assert (ILT(2*exp(3*s) - 5*exp(-7*s), s, t) ==
+            2*InverseLaplaceTransform(exp(3*s), s, t, None) -
+            5*DiracDelta(t - 7))
+    a = cos(sin(7)/2)
+    assert ILT(a*exp(-3*s), s, t) == a*DiracDelta(t - 3)
+    assert ILT(exp(2*s), s, t) == InverseLaplaceTransform(exp(2*s), s, t, None)
+    r = Symbol('r', real=True)
+    assert ILT(exp(r*s), s, t) == InverseLaplaceTransform(exp(r*s), s, t, None)
+    # Rules for testing whether Heaviside(t) is treated properly in diff rule
+    assert ILT(s**2/(a**2 + s**2), s, t) == (
+        -a*sin(a*t)*Heaviside(t) + DiracDelta(t))
+    assert ILT(s**2*(f(s) + 1/(a**2 + s**2)), s, t) == (
+        -a*sin(a*t)*Heaviside(t) + DiracDelta(t) +
+        Derivative(InverseLaplaceTransform(f(s), s, t, None), (t, 2)))
+    # Rules from the previous test_inverse_laplace_transform_delta_cond():
+    assert (ILT(exp(r*s), s, t, noconds=False) ==
+            (InverseLaplaceTransform(exp(r*s), s, t, None), True))
+    # inversion does not exist: verify it doesn't evaluate to DiracDelta
+    for z in (Symbol('z', extended_real=False),
+              Symbol('z', imaginary=True, zero=False)):
+        f = ILT(exp(z*s), s, t, noconds=False)
+        f = f[0] if isinstance(f, tuple) else f
+        assert f.func != DiracDelta
+
+
+@slow
+def test_expint():
+    x = Symbol('x')
+    a = Symbol('a')
+    u = Symbol('u', polar=True)
+
+    # TODO LT of Si, Shi, Chi is a mess ...
+    assert laplace_transform(Ci(x), x, s) == (-log(1 + s**2)/2/s, 0, True)
+    assert (laplace_transform(expint(a, x), x, s, simplify=True) ==
+            (lerchphi(s*exp_polar(I*pi), 1, a), 0, re(a) > S.Zero))
+    assert (laplace_transform(expint(1, x), x, s, simplify=True) ==
+            (log(s + 1)/s, 0, True))
+    assert (laplace_transform(expint(2, x), x, s, simplify=True) ==
+            ((s - log(s + 1))/s**2, 0, True))
+    assert (inverse_laplace_transform(-log(1 + s**2)/2/s, s, u).expand() ==
+            Heaviside(u)*Ci(u))
+    assert (
+        inverse_laplace_transform(log(s + 1)/s, s, x,
+                                  simplify=True).rewrite(expint) ==
+        Heaviside(x)*E1(x))
+    assert (
+        inverse_laplace_transform(
+            (s - log(s + 1))/s**2, s, x,
+            simplify=True).rewrite(expint).expand() ==
+        (expint(2, x)*Heaviside(x)).rewrite(Ei).rewrite(expint).expand())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_lineintegrals.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_lineintegrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..d0af146b52406a153d033286f3fcfa79334d2a73
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_lineintegrals.py
@@ -0,0 +1,13 @@
+from sympy.core.numbers import E
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.geometry.curve import Curve
+from sympy.integrals.integrals import line_integrate
+
+s, t, x, y, z = symbols('s,t,x,y,z')
+
+
+def test_lineintegral():
+    c = Curve([E**t + 1, E**t - 1], (t, 0, log(2)))
+    assert line_integrate(x + y, c, [x, y]) == 3*sqrt(2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_manual.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_manual.py
new file mode 100644
index 0000000000000000000000000000000000000000..74cae4521ec97608a21553e0203be60c210387b3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_manual.py
@@ -0,0 +1,714 @@
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.function import (Derivative, Function, diff, expand)
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.relational import Ne
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol, symbols)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.hyperbolic import (asinh, csch, cosh, coth, sech, sinh, tanh)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold
+from sympy.functions.elementary.trigonometric import (acos, acot, acsc, asec, asin, atan, cos, cot, csc, sec, sin, tan)
+from sympy.functions.special.delta_functions import Heaviside, DiracDelta
+from sympy.functions.special.elliptic_integrals import (elliptic_e, elliptic_f)
+from sympy.functions.special.error_functions import (Chi, Ci, Ei, Shi, Si, erf, erfi, fresnelc, fresnels, li)
+from sympy.functions.special.gamma_functions import uppergamma
+from sympy.functions.special.polynomials import (assoc_laguerre, chebyshevt, chebyshevu, gegenbauer, hermite, jacobi, laguerre, legendre)
+from sympy.functions.special.zeta_functions import polylog
+from sympy.integrals.integrals import (Integral, integrate)
+from sympy.logic.boolalg import And
+from sympy.integrals.manualintegrate import (manualintegrate, find_substitutions,
+    _parts_rule, integral_steps, manual_subs)
+from sympy.testing.pytest import raises, slow
+
+x, y, z, u, n, a, b, c, d, e = symbols('x y z u n a b c d e')
+f = Function('f')
+
+
+def assert_is_integral_of(f: Expr, F: Expr):
+    assert manualintegrate(f, x) == F
+    assert F.diff(x).equals(f)
+
+
+def test_find_substitutions():
+    assert find_substitutions((cot(x)**2 + 1)**2*csc(x)**2*cot(x)**2, x, u) == \
+        [(cot(x), 1, -u**6 - 2*u**4 - u**2)]
+    assert find_substitutions((sec(x)**2 + tan(x) * sec(x)) / (sec(x) + tan(x)),
+                              x, u) == [(sec(x) + tan(x), 1, 1/u)]
+    assert (-x**2, Rational(-1, 2), exp(u)) in find_substitutions(x * exp(-x**2), x, u)
+    assert not find_substitutions(Derivative(f(x), x)**2, x, u)
+
+
+def test_manualintegrate_polynomials():
+    assert manualintegrate(y, x) == x*y
+    assert manualintegrate(exp(2), x) == x * exp(2)
+    assert manualintegrate(x**2, x) == x**3 / 3
+    assert manualintegrate(3 * x**2 + 4 * x**3, x) == x**3 + x**4
+
+    assert manualintegrate((x + 2)**3, x) == (x + 2)**4 / 4
+    assert manualintegrate((3*x + 4)**2, x) == (3*x + 4)**3 / 9
+
+    assert manualintegrate((u + 2)**3, u) == (u + 2)**4 / 4
+    assert manualintegrate((3*u + 4)**2, u) == (3*u + 4)**3 / 9
+
+
+def test_manualintegrate_exponentials():
+    assert manualintegrate(exp(2*x), x) == exp(2*x) / 2
+    assert manualintegrate(2**x, x) == (2 ** x) / log(2)
+    assert_is_integral_of(1/sqrt(1-exp(2*x)),
+                          log(sqrt(1 - exp(2*x)) - 1)/2 - log(sqrt(1 - exp(2*x)) + 1)/2)
+
+    assert manualintegrate(1 / x, x) == log(x)
+    assert manualintegrate(1 / (2*x + 3), x) == log(2*x + 3) / 2
+    assert manualintegrate(log(x)**2 / x, x) == log(x)**3 / 3
+
+    assert_is_integral_of(x**x*(log(x)+1), x**x)
+
+
+def test_manualintegrate_parts():
+    assert manualintegrate(exp(x) * sin(x), x) == \
+        (exp(x) * sin(x)) / 2 - (exp(x) * cos(x)) / 2
+    assert manualintegrate(2*x*cos(x), x) == 2*x*sin(x) + 2*cos(x)
+    assert manualintegrate(x * log(x), x) == x**2*log(x)/2 - x**2/4
+    assert manualintegrate(log(x), x) == x * log(x) - x
+    assert manualintegrate((3*x**2 + 5) * exp(x), x) == \
+        3*x**2*exp(x) - 6*x*exp(x) + 11*exp(x)
+    assert manualintegrate(atan(x), x) == x*atan(x) - log(x**2 + 1)/2
+
+    # Make sure _parts_rule doesn't pick u = constant but can pick dv =
+    # constant if necessary, e.g. for integrate(atan(x))
+    assert _parts_rule(cos(x), x) == None
+    assert _parts_rule(exp(x), x) == None
+    assert _parts_rule(x**2, x) == None
+    result = _parts_rule(atan(x), x)
+    assert result[0] == atan(x) and result[1] == 1
+
+
+def test_manualintegrate_trigonometry():
+    assert manualintegrate(sin(x), x) == -cos(x)
+    assert manualintegrate(tan(x), x) == -log(cos(x))
+
+    assert manualintegrate(sec(x), x) == log(sec(x) + tan(x))
+    assert manualintegrate(csc(x), x) == -log(csc(x) + cot(x))
+
+    assert manualintegrate(sin(x) * cos(x), x) in [sin(x) ** 2 / 2, -cos(x)**2 / 2]
+    assert manualintegrate(-sec(x) * tan(x), x) == -sec(x)
+    assert manualintegrate(csc(x) * cot(x), x) == -csc(x)
+    assert manualintegrate(sec(x)**2, x) == tan(x)
+    assert manualintegrate(csc(x)**2, x) == -cot(x)
+
+    assert manualintegrate(x * sec(x**2), x) == log(tan(x**2) + sec(x**2))/2
+    assert manualintegrate(cos(x)*csc(sin(x)), x) == -log(cot(sin(x)) + csc(sin(x)))
+    assert manualintegrate(cos(3*x)*sec(x), x) == -x + sin(2*x)
+    assert manualintegrate(sin(3*x)*sec(x), x) == \
+        -3*log(cos(x)) + 2*log(cos(x)**2) - 2*cos(x)**2
+
+    assert_is_integral_of(sinh(2*x), cosh(2*x)/2)
+    assert_is_integral_of(x*cosh(x**2), sinh(x**2)/2)
+    assert_is_integral_of(tanh(x), log(cosh(x)))
+    assert_is_integral_of(coth(x), log(sinh(x)))
+    f, F = sech(x), 2*atan(tanh(x/2))
+    assert manualintegrate(f, x) == F
+    assert (F.diff(x) - f).rewrite(exp).simplify() == 0  # todo: equals returns None
+    f, F = csch(x), log(tanh(x/2))
+    assert manualintegrate(f, x) == F
+    assert (F.diff(x) - f).rewrite(exp).simplify() == 0
+
+
+@slow
+def test_manualintegrate_trigpowers():
+    assert manualintegrate(sin(x)**2 * cos(x), x) == sin(x)**3 / 3
+    assert manualintegrate(sin(x)**2 * cos(x) **2, x) == \
+        x / 8 - sin(4*x) / 32
+    assert manualintegrate(sin(x) * cos(x)**3, x) == -cos(x)**4 / 4
+    assert manualintegrate(sin(x)**3 * cos(x)**2, x) == \
+        cos(x)**5 / 5 - cos(x)**3 / 3
+
+    assert manualintegrate(tan(x)**3 * sec(x), x) == sec(x)**3/3 - sec(x)
+    assert manualintegrate(tan(x) * sec(x) **2, x) == sec(x)**2/2
+
+    assert manualintegrate(cot(x)**5 * csc(x), x) == \
+        -csc(x)**5/5 + 2*csc(x)**3/3 - csc(x)
+    assert manualintegrate(cot(x)**2 * csc(x)**6, x) == \
+        -cot(x)**7/7 - 2*cot(x)**5/5 - cot(x)**3/3
+
+
+@slow
+def test_manualintegrate_inversetrig():
+    # atan
+    assert manualintegrate(exp(x) / (1 + exp(2*x)), x) == atan(exp(x))
+    assert manualintegrate(1 / (4 + 9 * x**2), x) == atan(3 * x/2) / 6
+    assert manualintegrate(1 / (16 + 16 * x**2), x) == atan(x) / 16
+    assert manualintegrate(1 / (4 + x**2), x) == atan(x / 2) / 2
+    assert manualintegrate(1 / (1 + 4 * x**2), x) == atan(2*x) / 2
+    ra = Symbol('a', real=True)
+    rb = Symbol('b', real=True)
+    assert manualintegrate(1/(ra + rb*x**2), x) == \
+        Piecewise((atan(x/sqrt(ra/rb))/(rb*sqrt(ra/rb)), ra/rb > 0),
+                  ((log(x - sqrt(-ra/rb)) - log(x + sqrt(-ra/rb)))/(2*sqrt(rb)*sqrt(-ra)), True))
+    assert manualintegrate(1/(4 + rb*x**2), x) == \
+        Piecewise((atan(x/(2*sqrt(1/rb)))/(2*rb*sqrt(1/rb)), 1/rb > 0),
+                  (-I*(log(x - 2*sqrt(-1/rb)) - log(x + 2*sqrt(-1/rb)))/(4*sqrt(rb)), True))
+    assert manualintegrate(1/(ra + 4*x**2), x) == \
+        Piecewise((atan(2*x/sqrt(ra))/(2*sqrt(ra)), ra > 0),
+                  ((log(x - sqrt(-ra)/2) - log(x + sqrt(-ra)/2))/(4*sqrt(-ra)), True))
+    assert manualintegrate(1/(4 + 4*x**2), x) == atan(x) / 4
+
+    assert manualintegrate(1/(a + b*x**2), x) == Piecewise((atan(x/sqrt(a/b))/(b*sqrt(a/b)), Ne(a, 0)),
+                                                           (-1/(b*x), True))
+
+    # asin
+    assert manualintegrate(1/sqrt(1-x**2), x) == asin(x)
+    assert manualintegrate(1/sqrt(4-4*x**2), x) == asin(x)/2
+    assert manualintegrate(3/sqrt(1-9*x**2), x) == asin(3*x)
+    assert manualintegrate(1/sqrt(4-9*x**2), x) == asin(x*Rational(3, 2))/3
+
+    # asinh
+    assert manualintegrate(1/sqrt(x**2 + 1), x) == \
+        asinh(x)
+    assert manualintegrate(1/sqrt(x**2 + 4), x) == \
+        asinh(x/2)
+    assert manualintegrate(1/sqrt(4*x**2 + 4), x) == \
+        asinh(x)/2
+    assert manualintegrate(1/sqrt(4*x**2 + 1), x) == \
+        asinh(2*x)/2
+    assert manualintegrate(1/sqrt(ra*x**2 + 1), x) == \
+        Piecewise((asin(x*sqrt(-ra))/sqrt(-ra), ra < 0), (asinh(sqrt(ra)*x)/sqrt(ra), ra > 0), (x, True))
+    assert manualintegrate(1/sqrt(ra + x**2), x) == \
+        Piecewise((asinh(x*sqrt(1/ra)), ra > 0), (log(2*x + 2*sqrt(ra + x**2)), True))
+
+    # log
+    assert manualintegrate(1/sqrt(x**2 - 1), x) == log(2*x + 2*sqrt(x**2 - 1))
+    assert manualintegrate(1/sqrt(x**2 - 4), x) == log(2*x + 2*sqrt(x**2 - 4))
+    assert manualintegrate(1/sqrt(4*x**2 - 4), x) == log(8*x + 4*sqrt(4*x**2 - 4))/2
+    assert manualintegrate(1/sqrt(9*x**2 - 1), x) == log(18*x + 6*sqrt(9*x**2 - 1))/3
+    assert manualintegrate(1/sqrt(ra*x**2 - 4), x) == \
+           Piecewise((log(2*sqrt(ra)*sqrt(ra*x**2 - 4) + 2*ra*x)/sqrt(ra), Ne(ra, 0)), (-I*x/2, True))
+    assert manualintegrate(1/sqrt(-ra + 4*x**2), x) == \
+        Piecewise((asinh(2*x*sqrt(-1/ra))/2, ra < 0), (log(8*x + 4*sqrt(-ra + 4*x**2))/2, True))
+
+    # From https://www.wikiwand.com/en/List_of_integrals_of_inverse_trigonometric_functions
+    # asin
+    assert manualintegrate(asin(x), x) == x*asin(x) + sqrt(1 - x**2)
+    assert manualintegrate(asin(a*x), x) == Piecewise(((a*x*asin(a*x) + sqrt(-a**2*x**2 + 1))/a, Ne(a, 0)), (0, True))
+    assert manualintegrate(x*asin(a*x), x) == \
+           -a*Piecewise((-x*sqrt(-a**2*x**2 + 1)/(2*a**2) +
+                         log(-2*a**2*x + 2*sqrt(-a**2)*sqrt(-a**2*x**2 + 1))/(2*a**2*sqrt(-a**2)), Ne(a**2, 0)),
+                        (x**3/3, True))/2 + x**2*asin(a*x)/2
+    # acos
+    assert manualintegrate(acos(x), x) == x*acos(x) - sqrt(1 - x**2)
+    assert manualintegrate(acos(a*x), x) == Piecewise(((a*x*acos(a*x) - sqrt(-a**2*x**2 + 1))/a, Ne(a, 0)), (pi*x/2, True))
+    assert manualintegrate(x*acos(a*x), x) == \
+           a*Piecewise((-x*sqrt(-a**2*x**2 + 1)/(2*a**2) +
+                        log(-2*a**2*x + 2*sqrt(-a**2)*sqrt(-a**2*x**2 + 1))/(2*a**2*sqrt(-a**2)), Ne(a**2, 0)),
+                       (x**3/3, True))/2 + x**2*acos(a*x)/2
+    # atan
+    assert manualintegrate(atan(x), x) == x*atan(x) - log(x**2 + 1)/2
+    assert manualintegrate(atan(a*x), x) == Piecewise(((a*x*atan(a*x) - log(a**2*x**2 + 1)/2)/a, Ne(a, 0)), (0, True))
+    assert manualintegrate(x*atan(a*x), x) == -a*(x/a**2 - atan(x/sqrt(a**(-2)))/(a**4*sqrt(a**(-2))))/2 + x**2*atan(a*x)/2
+    # acsc
+    assert manualintegrate(acsc(x), x) == x*acsc(x) + Integral(1/(x*sqrt(1 - 1/x**2)), x)
+    assert manualintegrate(acsc(a*x), x) == x*acsc(a*x) + Integral(1/(x*sqrt(1 - 1/(a**2*x**2))), x)/a
+    assert manualintegrate(x*acsc(a*x), x) == x**2*acsc(a*x)/2 + Integral(1/sqrt(1 - 1/(a**2*x**2)), x)/(2*a)
+    # asec
+    assert manualintegrate(asec(x), x) == x*asec(x) - Integral(1/(x*sqrt(1 - 1/x**2)), x)
+    assert manualintegrate(asec(a*x), x) == x*asec(a*x) - Integral(1/(x*sqrt(1 - 1/(a**2*x**2))), x)/a
+    assert manualintegrate(x*asec(a*x), x) == x**2*asec(a*x)/2 - Integral(1/sqrt(1 - 1/(a**2*x**2)), x)/(2*a)
+    # acot
+    assert manualintegrate(acot(x), x) == x*acot(x) + log(x**2 + 1)/2
+    assert manualintegrate(acot(a*x), x) == Piecewise(((a*x*acot(a*x) + log(a**2*x**2 + 1)/2)/a, Ne(a, 0)), (pi*x/2, True))
+    assert manualintegrate(x*acot(a*x), x) == a*(x/a**2 - atan(x/sqrt(a**(-2)))/(a**4*sqrt(a**(-2))))/2 + x**2*acot(a*x)/2
+
+    # piecewise
+    assert manualintegrate(1/sqrt(ra-rb*x**2), x) == \
+        Piecewise((asin(x*sqrt(rb/ra))/sqrt(rb), And(-rb < 0, ra > 0)),
+                  (asinh(x*sqrt(-rb/ra))/sqrt(-rb), And(-rb > 0, ra > 0)),
+                  (log(-2*rb*x + 2*sqrt(-rb)*sqrt(ra - rb*x**2))/sqrt(-rb), Ne(rb, 0)),
+                  (x/sqrt(ra), True))
+    assert manualintegrate(1/sqrt(ra + rb*x**2), x) == \
+        Piecewise((asin(x*sqrt(-rb/ra))/sqrt(-rb), And(ra > 0, rb < 0)),
+                  (asinh(x*sqrt(rb/ra))/sqrt(rb), And(ra > 0, rb > 0)),
+                  (log(2*sqrt(rb)*sqrt(ra + rb*x**2) + 2*rb*x)/sqrt(rb), Ne(rb, 0)),
+                  (x/sqrt(ra), True))
+
+
+def test_manualintegrate_trig_substitution():
+    assert manualintegrate(sqrt(16*x**2 - 9)/x, x) == \
+        Piecewise((sqrt(16*x**2 - 9) - 3*acos(3/(4*x)),
+                   And(x < Rational(3, 4), x > Rational(-3, 4))))
+    assert manualintegrate(1/(x**4 * sqrt(25-x**2)), x) == \
+        Piecewise((-sqrt(-x**2/25 + 1)/(125*x) -
+                   (-x**2/25 + 1)**(3*S.Half)/(15*x**3), And(x < 5, x > -5)))
+    assert manualintegrate(x**7/(49*x**2 + 1)**(3 * S.Half), x) == \
+        ((49*x**2 + 1)**(5*S.Half)/28824005 -
+         (49*x**2 + 1)**(3*S.Half)/5764801 +
+         3*sqrt(49*x**2 + 1)/5764801 + 1/(5764801*sqrt(49*x**2 + 1)))
+
+def test_manualintegrate_trivial_substitution():
+    assert manualintegrate((exp(x) - exp(-x))/x, x) == -Ei(-x) + Ei(x)
+    f = Function('f')
+    assert manualintegrate((f(x) - f(-x))/x, x) == \
+        -Integral(f(-x)/x, x) + Integral(f(x)/x, x)
+
+
+def test_manualintegrate_rational():
+    assert manualintegrate(1/(4 - x**2), x) == -log(x - 2)/4 + log(x + 2)/4
+    assert manualintegrate(1/(-1 + x**2), x) == log(x - 1)/2 - log(x + 1)/2
+
+
+def test_manualintegrate_special():
+    f, F = 4*exp(-x**2/3), 2*sqrt(3)*sqrt(pi)*erf(sqrt(3)*x/3)
+    assert_is_integral_of(f, F)
+    f, F = 3*exp(4*x**2), 3*sqrt(pi)*erfi(2*x)/4
+    assert_is_integral_of(f, F)
+    f, F = x**Rational(1, 3)*exp(-x/8), -16*uppergamma(Rational(4, 3), x/8)
+    assert_is_integral_of(f, F)
+    f, F = exp(2*x)/x, Ei(2*x)
+    assert_is_integral_of(f, F)
+    f, F = exp(1 + 2*x - x**2), sqrt(pi)*exp(2)*erf(x - 1)/2
+    assert_is_integral_of(f, F)
+    f = sin(x**2 + 4*x + 1)
+    F = (sqrt(2)*sqrt(pi)*(-sin(3)*fresnelc(sqrt(2)*(2*x + 4)/(2*sqrt(pi))) +
+        cos(3)*fresnels(sqrt(2)*(2*x + 4)/(2*sqrt(pi))))/2)
+    assert_is_integral_of(f, F)
+    f, F = cos(4*x**2), sqrt(2)*sqrt(pi)*fresnelc(2*sqrt(2)*x/sqrt(pi))/4
+    assert_is_integral_of(f, F)
+    f, F = sin(3*x + 2)/x, sin(2)*Ci(3*x) + cos(2)*Si(3*x)
+    assert_is_integral_of(f, F)
+    f, F = sinh(3*x - 2)/x, -sinh(2)*Chi(3*x) + cosh(2)*Shi(3*x)
+    assert_is_integral_of(f, F)
+    f, F = 5*cos(2*x - 3)/x, 5*cos(3)*Ci(2*x) + 5*sin(3)*Si(2*x)
+    assert_is_integral_of(f, F)
+    f, F = cosh(x/2)/x, Chi(x/2)
+    assert_is_integral_of(f, F)
+    f, F = cos(x**2)/x, Ci(x**2)/2
+    assert_is_integral_of(f, F)
+    f, F = 1/log(2*x + 1), li(2*x + 1)/2
+    assert_is_integral_of(f, F)
+    f, F = polylog(2, 5*x)/x, polylog(3, 5*x)
+    assert_is_integral_of(f, F)
+    f, F = 5/sqrt(3 - 2*sin(x)**2), 5*sqrt(3)*elliptic_f(x, Rational(2, 3))/3
+    assert_is_integral_of(f, F)
+    f, F = sqrt(4 + 9*sin(x)**2), 2*elliptic_e(x, Rational(-9, 4))
+    assert_is_integral_of(f, F)
+
+
+def test_manualintegrate_derivative():
+    assert manualintegrate(pi * Derivative(x**2 + 2*x + 3), x) == \
+        pi * (x**2 + 2*x + 3)
+    assert manualintegrate(Derivative(x**2 + 2*x + 3, y), x) == \
+        Integral(Derivative(x**2 + 2*x + 3, y))
+    assert manualintegrate(Derivative(sin(x), x, x, x, y), x) == \
+        Derivative(sin(x), x, x, y)
+
+
+def test_manualintegrate_Heaviside():
+    assert_is_integral_of(DiracDelta(3*x+2), Heaviside(3*x+2)/3)
+    assert_is_integral_of(DiracDelta(3*x, 0), Heaviside(3*x)/3)
+    assert manualintegrate(DiracDelta(a+b*x, 1), x) == \
+        Piecewise((DiracDelta(a + b*x)/b, Ne(b, 0)), (x*DiracDelta(a, 1), True))
+    assert_is_integral_of(DiracDelta(x/3-1, 2), 3*DiracDelta(x/3-1, 1))
+    assert manualintegrate(Heaviside(x), x) == x*Heaviside(x)
+    assert manualintegrate(x*Heaviside(2), x) == x**2/2
+    assert manualintegrate(x*Heaviside(-2), x) == 0
+    assert manualintegrate(x*Heaviside( x), x) == x**2*Heaviside( x)/2
+    assert manualintegrate(x*Heaviside(-x), x) == x**2*Heaviside(-x)/2
+    assert manualintegrate(Heaviside(2*x + 4), x) == (x+2)*Heaviside(2*x + 4)
+    assert manualintegrate(x*Heaviside(x), x) == x**2*Heaviside(x)/2
+    assert manualintegrate(Heaviside(x + 1)*Heaviside(1 - x)*x**2, x) == \
+        ((x**3/3 + Rational(1, 3))*Heaviside(x + 1) - Rational(2, 3))*Heaviside(-x + 1)
+
+    y = Symbol('y')
+    assert manualintegrate(sin(7 + x)*Heaviside(3*x - 7), x) == \
+            (- cos(x + 7) + cos(Rational(28, 3)))*Heaviside(3*x - S(7))
+
+    assert manualintegrate(sin(y + x)*Heaviside(3*x - y), x) == \
+            (cos(y*Rational(4, 3)) - cos(x + y))*Heaviside(3*x - y)
+
+
+def test_manualintegrate_orthogonal_poly():
+    n = symbols('n')
+    a, b = 7, Rational(5, 3)
+    polys = [jacobi(n, a, b, x), gegenbauer(n, a, x), chebyshevt(n, x),
+        chebyshevu(n, x), legendre(n, x), hermite(n, x), laguerre(n, x),
+        assoc_laguerre(n, a, x)]
+    for p in polys:
+        integral = manualintegrate(p, x)
+        for deg in [-2, -1, 0, 1, 3, 5, 8]:
+            # some accept negative "degree", some do not
+            try:
+                p_subbed = p.subs(n, deg)
+            except ValueError:
+                continue
+            assert (integral.subs(n, deg).diff(x) - p_subbed).expand() == 0
+
+        # can also integrate simple expressions with these polynomials
+        q = x*p.subs(x, 2*x + 1)
+        integral = manualintegrate(q, x)
+        for deg in [2, 4, 7]:
+            assert (integral.subs(n, deg).diff(x) - q.subs(n, deg)).expand() == 0
+
+        # cannot integrate with respect to any other parameter
+        t = symbols('t')
+        for i in range(len(p.args) - 1):
+            new_args = list(p.args)
+            new_args[i] = t
+            assert isinstance(manualintegrate(p.func(*new_args), t), Integral)
+
+
+@slow
+def test_issue_6799():
+    r, x, phi = map(Symbol, 'r x phi'.split())
+    n = Symbol('n', integer=True, positive=True)
+
+    integrand = (cos(n*(x-phi))*cos(n*x))
+    limits = (x, -pi, pi)
+    assert manualintegrate(integrand, x) == \
+        ((n*x/2 + sin(2*n*x)/4)*cos(n*phi) - sin(n*phi)*cos(n*x)**2/2)/n
+    assert r * integrate(integrand, limits).trigsimp() / pi == r * cos(n * phi)
+    assert not integrate(integrand, limits).has(Dummy)
+
+
+def test_issue_12251():
+    assert manualintegrate(x**y, x) == Piecewise(
+        (x**(y + 1)/(y + 1), Ne(y, -1)), (log(x), True))
+
+
+def test_issue_3796():
+    assert manualintegrate(diff(exp(x + x**2)), x) == exp(x + x**2)
+    assert integrate(x * exp(x**4), x, risch=False) == -I*sqrt(pi)*erf(I*x**2)/4
+
+
+def test_manual_true():
+    assert integrate(exp(x) * sin(x), x, manual=True) == \
+        (exp(x) * sin(x)) / 2 - (exp(x) * cos(x)) / 2
+    assert integrate(sin(x) * cos(x), x, manual=True) in \
+        [sin(x) ** 2 / 2, -cos(x)**2 / 2]
+
+
+def test_issue_6746():
+    y = Symbol('y')
+    n = Symbol('n')
+    assert manualintegrate(y**x, x) == Piecewise(
+        (y**x/log(y), Ne(log(y), 0)), (x, True))
+    assert manualintegrate(y**(n*x), x) == Piecewise(
+        (Piecewise(
+            (y**(n*x)/log(y), Ne(log(y), 0)),
+            (n*x, True)
+        )/n, Ne(n, 0)),
+        (x, True))
+    assert manualintegrate(exp(n*x), x) == Piecewise(
+        (exp(n*x)/n, Ne(n, 0)), (x, True))
+
+    y = Symbol('y', positive=True)
+    assert manualintegrate((y + 1)**x, x) == (y + 1)**x/log(y + 1)
+    y = Symbol('y', zero=True)
+    assert manualintegrate((y + 1)**x, x) == x
+    y = Symbol('y')
+    n = Symbol('n', nonzero=True)
+    assert manualintegrate(y**(n*x), x) == Piecewise(
+        (y**(n*x)/log(y), Ne(log(y), 0)), (n*x, True))/n
+    y = Symbol('y', positive=True)
+    assert manualintegrate((y + 1)**(n*x), x) == \
+        (y + 1)**(n*x)/(n*log(y + 1))
+    a = Symbol('a', negative=True)
+    b = Symbol('b')
+    assert manualintegrate(1/(a + b*x**2), x) == atan(x/sqrt(a/b))/(b*sqrt(a/b))
+    b = Symbol('b', negative=True)
+    assert manualintegrate(1/(a + b*x**2), x) == \
+        atan(x/(sqrt(-a)*sqrt(-1/b)))/(b*sqrt(-a)*sqrt(-1/b))
+    assert manualintegrate(1/((x**a + y**b + 4)*sqrt(a*x**2 + 1)), x) == \
+        y**(-b)*Integral(x**(-a)/(y**(-b)*sqrt(a*x**2 + 1) +
+        x**(-a)*sqrt(a*x**2 + 1) + 4*x**(-a)*y**(-b)*sqrt(a*x**2 + 1)), x)
+    assert manualintegrate(1/((x**2 + 4)*sqrt(4*x**2 + 1)), x) == \
+        Integral(1/((x**2 + 4)*sqrt(4*x**2 + 1)), x)
+    assert manualintegrate(1/(x - a**x + x*b**2), x) == \
+        Integral(1/(-a**x + b**2*x + x), x)
+
+
+@slow
+def test_issue_2850():
+    assert manualintegrate(asin(x)*log(x), x) == -x*asin(x) - sqrt(-x**2 + 1) \
+            + (x*asin(x) + sqrt(-x**2 + 1))*log(x) - Integral(sqrt(-x**2 + 1)/x, x)
+    assert manualintegrate(acos(x)*log(x), x) == -x*acos(x) + sqrt(-x**2 + 1) + \
+        (x*acos(x) - sqrt(-x**2 + 1))*log(x) + Integral(sqrt(-x**2 + 1)/x, x)
+    assert manualintegrate(atan(x)*log(x), x) == -x*atan(x) + (x*atan(x) - \
+            log(x**2 + 1)/2)*log(x) + log(x**2 + 1)/2 + Integral(log(x**2 + 1)/x, x)/2
+
+
+def test_issue_9462():
+    assert manualintegrate(sin(2*x)*exp(x), x) == exp(x)*sin(2*x)/5 - 2*exp(x)*cos(2*x)/5
+    assert not integral_steps(sin(2*x)*exp(x), x).contains_dont_know()
+    assert manualintegrate((x - 3) / (x**2 - 2*x + 2)**2, x) == \
+                           Integral(x/(x**4 - 4*x**3 + 8*x**2 - 8*x + 4), x) \
+                           - 3*Integral(1/(x**4 - 4*x**3 + 8*x**2 - 8*x + 4), x)
+
+
+def test_cyclic_parts():
+    f = cos(x)*exp(x/4)
+    F = 16*exp(x/4)*sin(x)/17 + 4*exp(x/4)*cos(x)/17
+    assert manualintegrate(f, x) == F and F.diff(x) == f
+    f = x*cos(x)*exp(x/4)
+    F = (x*(16*exp(x/4)*sin(x)/17 + 4*exp(x/4)*cos(x)/17) -
+        128*exp(x/4)*sin(x)/289 + 240*exp(x/4)*cos(x)/289)
+    assert manualintegrate(f, x) == F and F.diff(x) == f
+
+
+@slow
+def test_issue_10847_slow():
+    assert manualintegrate((4*x**4 + 4*x**3 + 16*x**2 + 12*x + 8)
+                           / (x**6 + 2*x**5 + 3*x**4 + 4*x**3 + 3*x**2 + 2*x + 1), x) == \
+                           2*x/(x**2 + 1) + 3*atan(x) - 1/(x**2 + 1) - 3/(x + 1)
+
+
+@slow
+def test_issue_10847():
+
+    assert manualintegrate(x**2 / (x**2 - c), x) == \
+        c*Piecewise((atan(x/sqrt(-c))/sqrt(-c), Ne(c, 0)), (-1/x, True)) + x
+
+    rc = Symbol('c', real=True)
+    assert manualintegrate(x**2 / (x**2 - rc), x) == \
+        rc*Piecewise((atan(x/sqrt(-rc))/sqrt(-rc), rc < 0),
+                     ((log(-sqrt(rc) + x) - log(sqrt(rc) + x))/(2*sqrt(rc)), True)) + x
+
+    assert manualintegrate(sqrt(x - y) * log(z / x), x) == \
+        4*y**2*Piecewise((atan(sqrt(x - y)/sqrt(y))/sqrt(y), Ne(y, 0)),
+                         (-1/sqrt(x - y), True))/3 - 4*y*sqrt(x - y)/3 + \
+        2*(x - y)**Rational(3, 2)*log(z/x)/3 + 4*(x - y)**Rational(3, 2)/9
+    ry = Symbol('y', real=True)
+    rz = Symbol('z', real=True)
+    assert manualintegrate(sqrt(x - ry) * log(rz / x), x) == \
+        4*ry**2*Piecewise((atan(sqrt(x - ry)/sqrt(ry))/sqrt(ry), ry > 0),
+                         ((log(-sqrt(-ry) + sqrt(x - ry)) - log(sqrt(-ry) + sqrt(x - ry)))/(2*sqrt(-ry)), True))/3 \
+                         - 4*ry*sqrt(x - ry)/3 + 2*(x - ry)**Rational(3, 2)*log(rz/x)/3 \
+                         + 4*(x - ry)**Rational(3, 2)/9
+
+    assert manualintegrate(sqrt(x) * log(x), x) == 2*x**Rational(3, 2)*log(x)/3 - 4*x**Rational(3, 2)/9
+
+    result = manualintegrate(sqrt(a*x + b) / x, x)
+    assert result == Piecewise((-2*b*Piecewise(
+        (-atan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b), Ne(b, 0)),
+        (1/sqrt(a*x + b), True)) + 2*sqrt(a*x + b), Ne(a, 0)),
+        (sqrt(b)*log(x), True))
+    assert piecewise_fold(result) == Piecewise(
+        (2*b*atan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + 2*sqrt(a*x + b), Ne(a, 0) & Ne(b, 0)),
+        (-2*b/sqrt(a*x + b) + 2*sqrt(a*x + b), Ne(a, 0)),
+        (sqrt(b)*log(x), True))
+
+    ra = Symbol('a', real=True)
+    rb = Symbol('b', real=True)
+    assert manualintegrate(sqrt(ra*x + rb) / x, x) == \
+        Piecewise(
+            (-2*rb*Piecewise(
+                (-atan(sqrt(ra*x + rb)/sqrt(-rb))/sqrt(-rb), rb < 0),
+                (-I*(log(-sqrt(rb) + sqrt(ra*x + rb)) - log(sqrt(rb) + sqrt(ra*x + rb)))/(2*sqrt(-rb)), True)) +
+             2*sqrt(ra*x + rb), Ne(ra, 0)),
+            (sqrt(rb)*log(x), True))
+
+    assert expand(manualintegrate(sqrt(ra*x + rb) / (x + rc), x)) == \
+           Piecewise((-2*ra*rc*Piecewise((atan(sqrt(ra*x + rb)/sqrt(ra*rc - rb))/sqrt(ra*rc - rb), ra*rc - rb > 0),
+                                       (log(-sqrt(-ra*rc + rb) + sqrt(ra*x + rb))/(2*sqrt(-ra*rc + rb)) -
+                                        log(sqrt(-ra*rc + rb) + sqrt(ra*x + rb))/(2*sqrt(-ra*rc + rb)), True)) +
+                      2*rb*Piecewise((atan(sqrt(ra*x + rb)/sqrt(ra*rc - rb))/sqrt(ra*rc - rb), ra*rc - rb > 0),
+                                    (log(-sqrt(-ra*rc + rb) + sqrt(ra*x + rb))/(2*sqrt(-ra*rc + rb)) -
+                                     log(sqrt(-ra*rc + rb) + sqrt(ra*x + rb))/(2*sqrt(-ra*rc + rb)), True)) +
+                      2*sqrt(ra*x + rb), Ne(ra, 0)), (sqrt(rb)*log(rc + x), True))
+
+    assert manualintegrate(sqrt(2*x + 3) / (x + 1), x) == 2*sqrt(2*x + 3) - log(sqrt(2*x + 3) + 1) + log(sqrt(2*x + 3) - 1)
+    assert manualintegrate(sqrt(2*x + 3) / 2 * x, x) == (2*x + 3)**Rational(5, 2)/20 - (2*x + 3)**Rational(3, 2)/4
+    assert manualintegrate(x**Rational(3,2) * log(x), x) == 2*x**Rational(5,2)*log(x)/5 - 4*x**Rational(5,2)/25
+    assert manualintegrate(x**(-3) * log(x), x) == -log(x)/(2*x**2) - 1/(4*x**2)
+    assert manualintegrate(log(y)/(y**2*(1 - 1/y)), y) == \
+        log(y)*log(-1 + 1/y) - Integral(log(-1 + 1/y)/y, y)
+
+
+def test_issue_12899():
+    assert manualintegrate(f(x,y).diff(x),y) == Integral(Derivative(f(x,y),x),y)
+    assert manualintegrate(f(x,y).diff(y).diff(x),y) == Derivative(f(x,y),x)
+
+
+def test_constant_independent_of_symbol():
+    assert manualintegrate(Integral(y, (x, 1, 2)), x) == \
+        x*Integral(y, (x, 1, 2))
+
+
+def test_issue_12641():
+    assert manualintegrate(sin(2*x), x) == -cos(2*x)/2
+    assert manualintegrate(cos(x)*sin(2*x), x) == -2*cos(x)**3/3
+    assert manualintegrate((sin(2*x)*cos(x))/(1 + cos(x)), x) == \
+        -2*log(cos(x) + 1) - cos(x)**2 + 2*cos(x)
+
+
+@slow
+def test_issue_13297():
+    assert manualintegrate(sin(x) * cos(x)**5, x) == -cos(x)**6 / 6
+
+
+def test_issue_14470():
+    assert_is_integral_of(1/(x*sqrt(x + 1)), log(sqrt(x + 1) - 1) - log(sqrt(x + 1) + 1))
+
+
+@slow
+def test_issue_9858():
+    assert manualintegrate(exp(x)*cos(exp(x)), x) == sin(exp(x))
+    assert manualintegrate(exp(2*x)*cos(exp(x)), x) == \
+        exp(x)*sin(exp(x)) + cos(exp(x))
+    res = manualintegrate(exp(10*x)*sin(exp(x)), x)
+    assert not res.has(Integral)
+    assert res.diff(x) == exp(10*x)*sin(exp(x))
+    # an example with many similar integrations by parts
+    assert manualintegrate(sum(x*exp(k*x) for k in range(1, 8)), x) == (
+        x*exp(7*x)/7 + x*exp(6*x)/6 + x*exp(5*x)/5 + x*exp(4*x)/4 +
+        x*exp(3*x)/3 + x*exp(2*x)/2 + x*exp(x) - exp(7*x)/49 -exp(6*x)/36 -
+        exp(5*x)/25 - exp(4*x)/16 - exp(3*x)/9 - exp(2*x)/4 - exp(x))
+
+
+def test_issue_8520():
+    assert manualintegrate(x/(x**4 + 1), x) == atan(x**2)/2
+    assert manualintegrate(x**2/(x**6 + 25), x) == atan(x**3/5)/15
+    f = x/(9*x**4 + 4)**2
+    assert manualintegrate(f, x).diff(x).factor() == f
+
+
+def test_manual_subs():
+    x, y = symbols('x y')
+    expr = log(x) + exp(x)
+    # if log(x) is y, then exp(y) is x
+    assert manual_subs(expr, log(x), y) == y + exp(exp(y))
+    # if exp(x) is y, then log(y) need not be x
+    assert manual_subs(expr, exp(x), y) == log(x) + y
+
+    raises(ValueError, lambda: manual_subs(expr, x))
+    raises(ValueError, lambda: manual_subs(expr, exp(x), x, y))
+
+
+@slow
+def test_issue_15471():
+    f = log(x)*cos(log(x))/x**Rational(3, 4)
+    F = -128*x**Rational(1, 4)*sin(log(x))/289 + 240*x**Rational(1, 4)*cos(log(x))/289 + (16*x**Rational(1, 4)*sin(log(x))/17 + 4*x**Rational(1, 4)*cos(log(x))/17)*log(x)
+    assert_is_integral_of(f, F)
+
+
+def test_quadratic_denom():
+    f = (5*x + 2)/(3*x**2 - 2*x + 8)
+    assert manualintegrate(f, x) == 5*log(3*x**2 - 2*x + 8)/6 + 11*sqrt(23)*atan(3*sqrt(23)*(x - Rational(1, 3))/23)/69
+    g = 3/(2*x**2 + 3*x + 1)
+    assert manualintegrate(g, x) == 3*log(4*x + 2) - 3*log(4*x + 4)
+
+def test_issue_22757():
+    assert manualintegrate(sin(x), y) == y * sin(x)
+
+
+def test_issue_23348():
+    steps = integral_steps(tan(x), x)
+    constant_times_step = steps.substep.substep
+    assert constant_times_step.integrand == constant_times_step.constant * constant_times_step.other
+
+
+def test_issue_23566():
+    i = Integral(1/sqrt(x**2 - 1), (x, -2, -1)).doit(manual=True)
+    assert i == -log(4 - 2*sqrt(3)) + log(2)
+    assert str(i.n()) == '1.31695789692482'
+
+
+def test_issue_25093():
+    ap = Symbol('ap', positive=True)
+    an = Symbol('an', negative=True)
+    assert manualintegrate(exp(a*x**2 + b), x) == sqrt(pi)*exp(b)*erfi(sqrt(a)*x)/(2*sqrt(a))
+    assert manualintegrate(exp(ap*x**2 + b), x) == sqrt(pi)*exp(b)*erfi(sqrt(ap)*x)/(2*sqrt(ap))
+    assert manualintegrate(exp(an*x**2 + b), x) == -sqrt(pi)*exp(b)*erf(an*x/sqrt(-an))/(2*sqrt(-an))
+    assert manualintegrate(sin(a*x**2 + b), x) == (
+        sqrt(2)*sqrt(pi)*(sin(b)*fresnelc(sqrt(2)*sqrt(a)*x/sqrt(pi))
+        + cos(b)*fresnels(sqrt(2)*sqrt(a)*x/sqrt(pi)))/(2*sqrt(a)))
+    assert manualintegrate(cos(a*x**2 + b), x) == (
+        sqrt(2)*sqrt(pi)*(-sin(b)*fresnels(sqrt(2)*sqrt(a)*x/sqrt(pi))
+        + cos(b)*fresnelc(sqrt(2)*sqrt(a)*x/sqrt(pi)))/(2*sqrt(a)))
+
+
+def test_nested_pow():
+    assert_is_integral_of(sqrt(x**2), x*sqrt(x**2)/2)
+    assert_is_integral_of(sqrt(x**(S(5)/3)), 6*x*sqrt(x**(S(5)/3))/11)
+    assert_is_integral_of(1/sqrt(x**2), x*log(x)/sqrt(x**2))
+    assert_is_integral_of(x*sqrt(x**(-4)), x**2*sqrt(x**-4)*log(x))
+    f = (c*(a+b*x)**d)**e
+    F1 = (c*(a + b*x)**d)**e*(a/b + x)/(d*e + 1)
+    F2 = (c*(a + b*x)**d)**e*(a/b + x)*log(a/b + x)
+    assert manualintegrate(f, x) == \
+        Piecewise((Piecewise((F1, Ne(d*e, -1)), (F2, True)), Ne(b, 0)), (x*(a**d*c)**e, True))
+    assert F1.diff(x).equals(f)
+    assert F2.diff(x).subs(d*e, -1).equals(f)
+
+
+def test_manualintegrate_sqrt_linear():
+    assert_is_integral_of((5*x**3+4)/sqrt(2+3*x),
+                          10*(3*x + 2)**(S(7)/2)/567 - 4*(3*x + 2)**(S(5)/2)/27 +
+                          40*(3*x + 2)**(S(3)/2)/81 + 136*sqrt(3*x + 2)/81)
+    assert manualintegrate(x/sqrt(a+b*x)**3, x) == \
+        Piecewise((Mul(2, b**-2, a/sqrt(a + b*x) + sqrt(a + b*x)), Ne(b, 0)), (x**2/(2*a**(S(3)/2)), True))
+    assert_is_integral_of((sqrt(3*x+3)+1)/((2*x+2)**(1/S(3))+1),
+                          3*sqrt(6)*(2*x + 2)**(S(7)/6)/14 - 3*sqrt(6)*(2*x + 2)**(S(5)/6)/10 -
+                          3*sqrt(6)*(2*x + 2)**(S.One/6)/2 + 3*(2*x + 2)**(S(2)/3)/4 - 3*(2*x + 2)**(S.One/3)/2 +
+                          sqrt(6)*sqrt(2*x + 2)/2 + 3*log((2*x + 2)**(S.One/3) + 1)/2 +
+                          3*sqrt(6)*atan((2*x + 2)**(S.One/6))/2)
+    assert_is_integral_of(sqrt(x+sqrt(x)),
+                          2*sqrt(sqrt(x) + x)*(sqrt(x)/12 + x/3 - S(1)/8) + log(2*sqrt(x) + 2*sqrt(sqrt(x) + x) + 1)/8)
+    assert_is_integral_of(sqrt(2*x+3+sqrt(4*x+5))**3,
+                          sqrt(2*x + sqrt(4*x + 5) + 3) *
+                          (9*x/10 + 11*(4*x + 5)**(S(3)/2)/40 + sqrt(4*x + 5)/40 + (4*x + 5)**2/10 + S(11)/10)/2)
+
+
+def test_manualintegrate_sqrt_quadratic():
+    assert_is_integral_of(1/sqrt((x - I)**2-1), log(2*x + 2*sqrt(x**2 - 2*I*x - 2) - 2*I))
+    assert_is_integral_of(1/sqrt(3*x**2+4*x+5), sqrt(3)*asinh(3*sqrt(11)*(x + S(2)/3)/11)/3)
+    assert_is_integral_of(1/sqrt(-3*x**2+4*x+5), sqrt(3)*asin(3*sqrt(19)*(x - S(2)/3)/19)/3)
+    assert_is_integral_of(1/sqrt(3*x**2+4*x-5), sqrt(3)*log(6*x + 2*sqrt(3)*sqrt(3*x**2 + 4*x - 5) + 4)/3)
+    assert_is_integral_of(1/sqrt(4*x**2-4*x+1), (x - S.Half)*log(x - S.Half)/(2*sqrt((x - S.Half)**2)))
+    assert manualintegrate(1/sqrt(a+b*x+c*x**2), x) == \
+        Piecewise((log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/sqrt(c), Ne(c, 0) & Ne(a - b**2/(4*c), 0)),
+                  ((b/(2*c) + x)*log(b/(2*c) + x)/sqrt(c*(b/(2*c) + x)**2), Ne(c, 0)),
+                  (2*sqrt(a + b*x)/b, Ne(b, 0)), (x/sqrt(a), True))
+
+    assert_is_integral_of((7*x+6)/sqrt(3*x**2+4*x+5),
+                          7*sqrt(3*x**2 + 4*x + 5)/3 + 4*sqrt(3)*asinh(3*sqrt(11)*(x + S(2)/3)/11)/9)
+    assert_is_integral_of((7*x+6)/sqrt(-3*x**2+4*x+5),
+                          -7*sqrt(-3*x**2 + 4*x + 5)/3 + 32*sqrt(3)*asin(3*sqrt(19)*(x - S(2)/3)/19)/9)
+    assert_is_integral_of((7*x+6)/sqrt(3*x**2+4*x-5),
+                          7*sqrt(3*x**2 + 4*x - 5)/3 + 4*sqrt(3)*log(6*x + 2*sqrt(3)*sqrt(3*x**2 + 4*x - 5) + 4)/9)
+    assert manualintegrate((d+e*x)/sqrt(a+b*x+c*x**2), x) == \
+        Piecewise(((-b*e/(2*c) + d) *
+                   Piecewise((log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/sqrt(c), Ne(a - b**2/(4*c), 0)),
+                             ((b/(2*c) + x)*log(b/(2*c) + x)/sqrt(c*(b/(2*c) + x)**2), True)) +
+                   e*sqrt(a + b*x + c*x**2)/c, Ne(c, 0)),
+                  ((2*d*sqrt(a + b*x) + 2*e*(-a*sqrt(a + b*x) + (a + b*x)**(S(3)/2)/3)/b)/b, Ne(b, 0)),
+                  ((d*x + e*x**2/2)/sqrt(a), True))
+
+    assert manualintegrate((3*x**3-x**2+2*x-4)/sqrt(x**2-3*x+2), x) == \
+        sqrt(x**2 - 3*x + 2)*(x**2 + 13*x/4 + S(101)/8) + 135*log(2*x + 2*sqrt(x**2 - 3*x + 2) - 3)/16
+
+    assert_is_integral_of(sqrt(53225*x**2-66732*x+23013),
+                          (x/2 - S(16683)/53225)*sqrt(53225*x**2 - 66732*x + 23013) +
+                          111576969*sqrt(2129)*asinh(53225*x/10563 - S(11122)/3521)/1133160250)
+    assert manualintegrate(sqrt(a+c*x**2), x) == \
+        Piecewise((a*Piecewise((log(2*sqrt(c)*sqrt(a + c*x**2) + 2*c*x)/sqrt(c), Ne(a, 0)),
+                               (x*log(x)/sqrt(c*x**2), True))/2 + x*sqrt(a + c*x**2)/2, Ne(c, 0)),
+                  (sqrt(a)*x, True))
+    assert manualintegrate(sqrt(a+b*x+c*x**2), x) == \
+        Piecewise(((a/2 - b**2/(8*c)) *
+                   Piecewise((log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/sqrt(c), Ne(a - b**2/(4*c), 0)),
+                             ((b/(2*c) + x)*log(b/(2*c) + x)/sqrt(c*(b/(2*c) + x)**2), True)) +
+                   (b/(4*c) + x/2)*sqrt(a + b*x + c*x**2), Ne(c, 0)),
+                  (2*(a + b*x)**(S(3)/2)/(3*b), Ne(b, 0)),
+                  (sqrt(a)*x, True))
+
+    assert_is_integral_of(x*sqrt(x**2+2*x+4),
+                          (x**2/3 + x/6 + S(5)/6)*sqrt(x**2 + 2*x + 4) - 3*asinh(sqrt(3)*(x + 1)/3)/2)
+
+
+def test_mul_pow_derivative():
+    assert_is_integral_of(x*sec(x)*tan(x), x*sec(x) - log(tan(x) + sec(x)))
+    assert_is_integral_of(x*sec(x)**2, x*tan(x) + log(cos(x)))
+    assert_is_integral_of(x**3*Derivative(f(x), (x, 4)),
+                          x**3*Derivative(f(x), (x, 3)) - 3*x**2*Derivative(f(x), (x, 2)) +
+                          6*x*Derivative(f(x), x) - 6*f(x))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_meijerint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_meijerint.py
new file mode 100644
index 0000000000000000000000000000000000000000..899bc96e63d6dd5bccd52856f15d3085e87d5807
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_meijerint.py
@@ -0,0 +1,774 @@
+from sympy.core.function import expand_func
+from sympy.core.numbers import (I, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.functions.elementary.complexes import Abs, arg, re, unpolarify
+from sympy.functions.elementary.exponential import (exp, exp_polar, log)
+from sympy.functions.elementary.hyperbolic import cosh, acosh, sinh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc, asin)
+from sympy.functions.special.error_functions import (erf, erfc)
+from sympy.functions.special.gamma_functions import (gamma, polygamma)
+from sympy.functions.special.hyper import (hyper, meijerg)
+from sympy.integrals.integrals import (Integral, integrate)
+from sympy.simplify.hyperexpand import hyperexpand
+from sympy.simplify.simplify import simplify
+from sympy.integrals.meijerint import (_rewrite_single, _rewrite1,
+    meijerint_indefinite, _inflate_g, _create_lookup_table,
+    meijerint_definite, meijerint_inversion)
+from sympy.testing.pytest import slow
+from sympy.core.random import (verify_numerically,
+        random_complex_number as randcplx)
+from sympy.abc import x, y, a, b, c, d, s, t, z
+
+
+def test_rewrite_single():
+    def t(expr, c, m):
+        e = _rewrite_single(meijerg([a], [b], [c], [d], expr), x)
+        assert e is not None
+        assert isinstance(e[0][0][2], meijerg)
+        assert e[0][0][2].argument.as_coeff_mul(x) == (c, (m,))
+
+    def tn(expr):
+        assert _rewrite_single(meijerg([a], [b], [c], [d], expr), x) is None
+
+    t(x, 1, x)
+    t(x**2, 1, x**2)
+    t(x**2 + y*x**2, y + 1, x**2)
+    tn(x**2 + x)
+    tn(x**y)
+
+    def u(expr, x):
+        from sympy.core.add import Add
+        r = _rewrite_single(expr, x)
+        e = Add(*[res[0]*res[2] for res in r[0]]).replace(
+            exp_polar, exp)  # XXX Hack?
+        assert verify_numerically(e, expr, x)
+
+    u(exp(-x)*sin(x), x)
+
+    # The following has stopped working because hyperexpand changed slightly.
+    # It is probably not worth fixing
+    #u(exp(-x)*sin(x)*cos(x), x)
+
+    # This one cannot be done numerically, since it comes out as a g-function
+    # of argument 4*pi
+    # NOTE This also tests a bug in inverse mellin transform (which used to
+    #      turn exp(4*pi*I*t) into a factor of exp(4*pi*I)**t instead of
+    #      exp_polar).
+    #u(exp(x)*sin(x), x)
+    assert _rewrite_single(exp(x)*sin(x), x) == \
+        ([(-sqrt(2)/(2*sqrt(pi)), 0,
+           meijerg(((Rational(-1, 2), 0, Rational(1, 4), S.Half, Rational(3, 4)), (1,)),
+                   ((), (Rational(-1, 2), 0)), 64*exp_polar(-4*I*pi)/x**4))], True)
+
+
+def test_rewrite1():
+    assert _rewrite1(x**3*meijerg([a], [b], [c], [d], x**2 + y*x**2)*5, x) == \
+        (5, x**3, [(1, 0, meijerg([a], [b], [c], [d], x**2*(y + 1)))], True)
+
+
+def test_meijerint_indefinite_numerically():
+    def t(fac, arg):
+        g = meijerg([a], [b], [c], [d], arg)*fac
+        subs = {a: randcplx()/10, b: randcplx()/10 + I,
+                c: randcplx(), d: randcplx()}
+        integral = meijerint_indefinite(g, x)
+        assert integral is not None
+        assert verify_numerically(g.subs(subs), integral.diff(x).subs(subs), x)
+    t(1, x)
+    t(2, x)
+    t(1, 2*x)
+    t(1, x**2)
+    t(5, x**S('3/2'))
+    t(x**3, x)
+    t(3*x**S('3/2'), 4*x**S('7/3'))
+
+
+def test_meijerint_definite():
+    v, b = meijerint_definite(x, x, 0, 0)
+    assert v.is_zero and b is True
+    v, b = meijerint_definite(x, x, oo, oo)
+    assert v.is_zero and b is True
+
+
+def test_inflate():
+    subs = {a: randcplx()/10, b: randcplx()/10 + I, c: randcplx(),
+            d: randcplx(), y: randcplx()/10}
+
+    def t(a, b, arg, n):
+        from sympy.core.mul import Mul
+        m1 = meijerg(a, b, arg)
+        m2 = Mul(*_inflate_g(m1, n))
+        # NOTE: (the random number)**9 must still be on the principal sheet.
+        # Thus make b&d small to create random numbers of small imaginary part.
+        return verify_numerically(m1.subs(subs), m2.subs(subs), x, b=0.1, d=-0.1)
+    assert t([[a], [b]], [[c], [d]], x, 3)
+    assert t([[a, y], [b]], [[c], [d]], x, 3)
+    assert t([[a], [b]], [[c, y], [d]], 2*x**3, 3)
+
+
+def test_recursive():
+    from sympy.core.symbol import symbols
+    a, b, c = symbols('a b c', positive=True)
+    r = exp(-(x - a)**2)*exp(-(x - b)**2)
+    e = integrate(r, (x, 0, oo), meijerg=True)
+    assert simplify(e.expand()) == (
+        sqrt(2)*sqrt(pi)*(
+        (erf(sqrt(2)*(a + b)/2) + 1)*exp(-a**2/2 + a*b - b**2/2))/4)
+    e = integrate(exp(-(x - a)**2)*exp(-(x - b)**2)*exp(c*x), (x, 0, oo), meijerg=True)
+    assert simplify(e) == (
+        sqrt(2)*sqrt(pi)*(erf(sqrt(2)*(2*a + 2*b + c)/4) + 1)*exp(-a**2 - b**2
+        + (2*a + 2*b + c)**2/8)/4)
+    assert simplify(integrate(exp(-(x - a - b - c)**2), (x, 0, oo), meijerg=True)) == \
+        sqrt(pi)/2*(1 + erf(a + b + c))
+    assert simplify(integrate(exp(-(x + a + b + c)**2), (x, 0, oo), meijerg=True)) == \
+        sqrt(pi)/2*(1 - erf(a + b + c))
+
+
+@slow
+def test_meijerint():
+    from sympy.core.function import expand
+    from sympy.core.symbol import symbols
+    s, t, mu = symbols('s t mu', real=True)
+    assert integrate(meijerg([], [], [0], [], s*t)
+                     *meijerg([], [], [mu/2], [-mu/2], t**2/4),
+                     (t, 0, oo)).is_Piecewise
+    s = symbols('s', positive=True)
+    assert integrate(x**s*meijerg([[], []], [[0], []], x), (x, 0, oo)) == \
+        gamma(s + 1)
+    assert integrate(x**s*meijerg([[], []], [[0], []], x), (x, 0, oo),
+                     meijerg=True) == gamma(s + 1)
+    assert isinstance(integrate(x**s*meijerg([[], []], [[0], []], x),
+                                (x, 0, oo), meijerg=False),
+                      Integral)
+
+    assert meijerint_indefinite(exp(x), x) == exp(x)
+
+    # TODO what simplifications should be done automatically?
+    # This tests "extra case" for antecedents_1.
+    a, b = symbols('a b', positive=True)
+    assert simplify(meijerint_definite(x**a, x, 0, b)[0]) == \
+        b**(a + 1)/(a + 1)
+
+    # This tests various conditions and expansions:
+    assert meijerint_definite((x + 1)**3*exp(-x), x, 0, oo) == (16, True)
+
+    # Again, how about simplifications?
+    sigma, mu = symbols('sigma mu', positive=True)
+    i, c = meijerint_definite(exp(-((x - mu)/(2*sigma))**2), x, 0, oo)
+    assert simplify(i) == sqrt(pi)*sigma*(2 - erfc(mu/(2*sigma)))
+    assert c == True
+
+    i, _ = meijerint_definite(exp(-mu*x)*exp(sigma*x), x, 0, oo)
+    # TODO it would be nice to test the condition
+    assert simplify(i) == 1/(mu - sigma)
+
+    # Test substitutions to change limits
+    assert meijerint_definite(exp(x), x, -oo, 2) == (exp(2), True)
+    # Note: causes a NaN in _check_antecedents
+    assert expand(meijerint_definite(exp(x), x, 0, I)[0]) == exp(I) - 1
+    assert expand(meijerint_definite(exp(-x), x, 0, x)[0]) == \
+        1 - exp(-exp(I*arg(x))*abs(x))
+
+    # Test -oo to oo
+    assert meijerint_definite(exp(-x**2), x, -oo, oo) == (sqrt(pi), True)
+    assert meijerint_definite(exp(-abs(x)), x, -oo, oo) == (2, True)
+    assert meijerint_definite(exp(-(2*x - 3)**2), x, -oo, oo) == \
+        (sqrt(pi)/2, True)
+    assert meijerint_definite(exp(-abs(2*x - 3)), x, -oo, oo) == (1, True)
+    assert meijerint_definite(exp(-((x - mu)/sigma)**2/2)/sqrt(2*pi*sigma**2),
+                              x, -oo, oo) == (1, True)
+    assert meijerint_definite(sinc(x)**2, x, -oo, oo) == (pi, True)
+
+    # Test one of the extra conditions for 2 g-functinos
+    assert meijerint_definite(exp(-x)*sin(x), x, 0, oo) == (S.Half, True)
+
+    # Test a bug
+    def res(n):
+        return (1/(1 + x**2)).diff(x, n).subs(x, 1)*(-1)**n
+    for n in range(6):
+        assert integrate(exp(-x)*sin(x)*x**n, (x, 0, oo), meijerg=True) == \
+            res(n)
+
+    # This used to test trigexpand... now it is done by linear substitution
+    assert simplify(integrate(exp(-x)*sin(x + a), (x, 0, oo), meijerg=True)
+                    ) == sqrt(2)*sin(a + pi/4)/2
+
+    # Test the condition 14 from prudnikov.
+    # (This is besselj*besselj in disguise, to stop the product from being
+    #  recognised in the tables.)
+    a, b, s = symbols('a b s')
+    assert meijerint_definite(meijerg([], [], [a/2], [-a/2], x/4)
+                  *meijerg([], [], [b/2], [-b/2], x/4)*x**(s - 1), x, 0, oo
+        ) == (
+        (4*2**(2*s - 2)*gamma(-2*s + 1)*gamma(a/2 + b/2 + s)
+         /(gamma(-a/2 + b/2 - s + 1)*gamma(a/2 - b/2 - s + 1)
+           *gamma(a/2 + b/2 - s + 1)),
+            (re(s) < 1) & (re(s) < S(1)/2) & (re(a)/2 + re(b)/2 + re(s) > 0)))
+
+    # test a bug
+    assert integrate(sin(x**a)*sin(x**b), (x, 0, oo), meijerg=True) == \
+        Integral(sin(x**a)*sin(x**b), (x, 0, oo))
+
+    # test better hyperexpand
+    assert integrate(exp(-x**2)*log(x), (x, 0, oo), meijerg=True) == \
+        (sqrt(pi)*polygamma(0, S.Half)/4).expand()
+
+    # Test hyperexpand bug.
+    from sympy.functions.special.gamma_functions import lowergamma
+    n = symbols('n', integer=True)
+    assert simplify(integrate(exp(-x)*x**n, x, meijerg=True)) == \
+        lowergamma(n + 1, x)
+
+    # Test a bug with argument 1/x
+    alpha = symbols('alpha', positive=True)
+    assert meijerint_definite((2 - x)**alpha*sin(alpha/x), x, 0, 2) == \
+        (sqrt(pi)*alpha*gamma(alpha + 1)*meijerg(((), (alpha/2 + S.Half,
+        alpha/2 + 1)), ((0, 0, S.Half), (Rational(-1, 2),)), alpha**2/16)/4, True)
+
+    # test a bug related to 3016
+    a, s = symbols('a s', positive=True)
+    assert simplify(integrate(x**s*exp(-a*x**2), (x, -oo, oo))) == \
+        a**(-s/2 - S.Half)*((-1)**s + 1)*gamma(s/2 + S.Half)/2
+
+
+def test_bessel():
+    from sympy.functions.special.bessel import (besseli, besselj)
+    assert simplify(integrate(besselj(a, z)*besselj(b, z)/z, (z, 0, oo),
+                     meijerg=True, conds='none')) == \
+        2*sin(pi*(a/2 - b/2))/(pi*(a - b)*(a + b))
+    assert simplify(integrate(besselj(a, z)*besselj(a, z)/z, (z, 0, oo),
+                     meijerg=True, conds='none')) == 1/(2*a)
+
+    # TODO more orthogonality integrals
+
+    assert simplify(integrate(sin(z*x)*(x**2 - 1)**(-(y + S.Half)),
+                              (x, 1, oo), meijerg=True, conds='none')
+                    *2/((z/2)**y*sqrt(pi)*gamma(S.Half - y))) == \
+        besselj(y, z)
+
+    # Werner Rosenheinrich
+    # SOME INDEFINITE INTEGRALS OF BESSEL FUNCTIONS
+
+    assert integrate(x*besselj(0, x), x, meijerg=True) == x*besselj(1, x)
+    assert integrate(x*besseli(0, x), x, meijerg=True) == x*besseli(1, x)
+    # TODO can do higher powers, but come out as high order ... should they be
+    #      reduced to order 0, 1?
+    assert integrate(besselj(1, x), x, meijerg=True) == -besselj(0, x)
+    assert integrate(besselj(1, x)**2/x, x, meijerg=True) == \
+        -(besselj(0, x)**2 + besselj(1, x)**2)/2
+    # TODO more besseli when tables are extended or recursive mellin works
+    assert integrate(besselj(0, x)**2/x**2, x, meijerg=True) == \
+        -2*x*besselj(0, x)**2 - 2*x*besselj(1, x)**2 \
+        + 2*besselj(0, x)*besselj(1, x) - besselj(0, x)**2/x
+    assert integrate(besselj(0, x)*besselj(1, x), x, meijerg=True) == \
+        -besselj(0, x)**2/2
+    assert integrate(x**2*besselj(0, x)*besselj(1, x), x, meijerg=True) == \
+        x**2*besselj(1, x)**2/2
+    assert integrate(besselj(0, x)*besselj(1, x)/x, x, meijerg=True) == \
+        (x*besselj(0, x)**2 + x*besselj(1, x)**2 -
+            besselj(0, x)*besselj(1, x))
+    # TODO how does besselj(0, a*x)*besselj(0, b*x) work?
+    # TODO how does besselj(0, x)**2*besselj(1, x)**2 work?
+    # TODO sin(x)*besselj(0, x) etc come out a mess
+    # TODO can x*log(x)*besselj(0, x) be done?
+    # TODO how does besselj(1, x)*besselj(0, x+a) work?
+    # TODO more indefinite integrals when struve functions etc are implemented
+
+    # test a substitution
+    assert integrate(besselj(1, x**2)*x, x, meijerg=True) == \
+        -besselj(0, x**2)/2
+
+
+def test_inversion():
+    from sympy.functions.special.bessel import besselj
+    from sympy.functions.special.delta_functions import Heaviside
+
+    def inv(f):
+        return piecewise_fold(meijerint_inversion(f, s, t))
+    assert inv(1/(s**2 + 1)) == sin(t)*Heaviside(t)
+    assert inv(s/(s**2 + 1)) == cos(t)*Heaviside(t)
+    assert inv(exp(-s)/s) == Heaviside(t - 1)
+    assert inv(1/sqrt(1 + s**2)) == besselj(0, t)*Heaviside(t)
+
+    # Test some antcedents checking.
+    assert meijerint_inversion(sqrt(s)/sqrt(1 + s**2), s, t) is None
+    assert inv(exp(s**2)) is None
+    assert meijerint_inversion(exp(-s**2), s, t) is None
+
+
+def test_inversion_conditional_output():
+    from sympy.core.symbol import Symbol
+    from sympy.integrals.transforms import InverseLaplaceTransform
+
+    a = Symbol('a', positive=True)
+    F = sqrt(pi/a)*exp(-2*sqrt(a)*sqrt(s))
+    f = meijerint_inversion(F, s, t)
+    assert not f.is_Piecewise
+
+    b = Symbol('b', real=True)
+    F = F.subs(a, b)
+    f2 = meijerint_inversion(F, s, t)
+    assert f2.is_Piecewise
+    # first piece is same as f
+    assert f2.args[0][0] == f.subs(a, b)
+    # last piece is an unevaluated transform
+    assert f2.args[-1][1]
+    ILT = InverseLaplaceTransform(F, s, t, None)
+    assert f2.args[-1][0] == ILT or f2.args[-1][0] == ILT.as_integral
+
+
+def test_inversion_exp_real_nonreal_shift():
+    from sympy.core.symbol import Symbol
+    from sympy.functions.special.delta_functions import DiracDelta
+    r = Symbol('r', real=True)
+    c = Symbol('c', extended_real=False)
+    a = 1 + 2*I
+    z = Symbol('z')
+    assert not meijerint_inversion(exp(r*s), s, t).is_Piecewise
+    assert meijerint_inversion(exp(a*s), s, t) is None
+    assert meijerint_inversion(exp(c*s), s, t) is None
+    f = meijerint_inversion(exp(z*s), s, t)
+    assert f.is_Piecewise
+    assert isinstance(f.args[0][0], DiracDelta)
+
+
+@slow
+def test_lookup_table():
+    from sympy.core.random import uniform, randrange
+    from sympy.core.add import Add
+    from sympy.integrals.meijerint import z as z_dummy
+    table = {}
+    _create_lookup_table(table)
+    for l in table.values():
+        for formula, terms, cond, hint in sorted(l, key=default_sort_key):
+            subs = {}
+            for ai in list(formula.free_symbols) + [z_dummy]:
+                if hasattr(ai, 'properties') and ai.properties:
+                    # these Wilds match positive integers
+                    subs[ai] = randrange(1, 10)
+                else:
+                    subs[ai] = uniform(1.5, 2.0)
+            if not isinstance(terms, list):
+                terms = terms(subs)
+
+            # First test that hyperexpand can do this.
+            expanded = [hyperexpand(g) for (_, g) in terms]
+            assert all(x.is_Piecewise or not x.has(meijerg) for x in expanded)
+
+            # Now test that the meijer g-function is indeed as advertised.
+            expanded = Add(*[f*x for (f, x) in terms])
+            a, b = formula.n(subs=subs), expanded.n(subs=subs)
+            r = min(abs(a), abs(b))
+            if r < 1:
+                assert abs(a - b).n() <= 1e-10
+            else:
+                assert (abs(a - b)/r).n() <= 1e-10
+
+
+def test_branch_bug():
+    from sympy.functions.special.gamma_functions import lowergamma
+    from sympy.simplify.powsimp import powdenest
+    # TODO gammasimp cannot prove that the factor is unity
+    assert powdenest(integrate(erf(x**3), x, meijerg=True).diff(x),
+           polar=True) == 2*erf(x**3)*gamma(Rational(2, 3))/3/gamma(Rational(5, 3))
+    assert integrate(erf(x**3), x, meijerg=True) == \
+        2*x*erf(x**3)*gamma(Rational(2, 3))/(3*gamma(Rational(5, 3))) \
+        - 2*gamma(Rational(2, 3))*lowergamma(Rational(2, 3), x**6)/(3*sqrt(pi)*gamma(Rational(5, 3)))
+
+
+def test_linear_subs():
+    from sympy.functions.special.bessel import besselj
+    assert integrate(sin(x - 1), x, meijerg=True) == -cos(1 - x)
+    assert integrate(besselj(1, x - 1), x, meijerg=True) == -besselj(0, 1 - x)
+
+
+@slow
+def test_probability():
+    # various integrals from probability theory
+    from sympy.core.function import expand_mul
+    from sympy.core.symbol import (Symbol, symbols)
+    from sympy.simplify.gammasimp import gammasimp
+    from sympy.simplify.powsimp import powsimp
+    mu1, mu2 = symbols('mu1 mu2', nonzero=True)
+    sigma1, sigma2 = symbols('sigma1 sigma2', positive=True)
+    rate = Symbol('lambda', positive=True)
+
+    def normal(x, mu, sigma):
+        return 1/sqrt(2*pi*sigma**2)*exp(-(x - mu)**2/2/sigma**2)
+
+    def exponential(x, rate):
+        return rate*exp(-rate*x)
+
+    assert integrate(normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True) == 1
+    assert integrate(x*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True) == \
+        mu1
+    assert integrate(x**2*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True) \
+        == mu1**2 + sigma1**2
+    assert integrate(x**3*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True) \
+        == mu1**3 + 3*mu1*sigma1**2
+    assert integrate(normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == 1
+    assert integrate(x*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == mu1
+    assert integrate(y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == mu2
+    assert integrate(x*y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == mu1*mu2
+    assert integrate((x + y + 1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == 1 + mu1 + mu2
+    assert integrate((x + y - 1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == \
+        -1 + mu1 + mu2
+
+    i = integrate(x**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                  (x, -oo, oo), (y, -oo, oo), meijerg=True)
+    assert not i.has(Abs)
+    assert simplify(i) == mu1**2 + sigma1**2
+    assert integrate(y**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),
+                     (x, -oo, oo), (y, -oo, oo), meijerg=True) == \
+        sigma2**2 + mu2**2
+
+    assert integrate(exponential(x, rate), (x, 0, oo), meijerg=True) == 1
+    assert integrate(x*exponential(x, rate), (x, 0, oo), meijerg=True) == \
+        1/rate
+    assert integrate(x**2*exponential(x, rate), (x, 0, oo), meijerg=True) == \
+        2/rate**2
+
+    def E(expr):
+        res1 = integrate(expr*exponential(x, rate)*normal(y, mu1, sigma1),
+                         (x, 0, oo), (y, -oo, oo), meijerg=True)
+        res2 = integrate(expr*exponential(x, rate)*normal(y, mu1, sigma1),
+                        (y, -oo, oo), (x, 0, oo), meijerg=True)
+        assert expand_mul(res1) == expand_mul(res2)
+        return res1
+
+    assert E(1) == 1
+    assert E(x*y) == mu1/rate
+    assert E(x*y**2) == mu1**2/rate + sigma1**2/rate
+    ans = sigma1**2 + 1/rate**2
+    assert simplify(E((x + y + 1)**2) - E(x + y + 1)**2) == ans
+    assert simplify(E((x + y - 1)**2) - E(x + y - 1)**2) == ans
+    assert simplify(E((x + y)**2) - E(x + y)**2) == ans
+
+    # Beta' distribution
+    alpha, beta = symbols('alpha beta', positive=True)
+    betadist = x**(alpha - 1)*(1 + x)**(-alpha - beta)*gamma(alpha + beta) \
+        /gamma(alpha)/gamma(beta)
+    assert integrate(betadist, (x, 0, oo), meijerg=True) == 1
+    i = integrate(x*betadist, (x, 0, oo), meijerg=True, conds='separate')
+    assert (gammasimp(i[0]), i[1]) == (alpha/(beta - 1), 1 < beta)
+    j = integrate(x**2*betadist, (x, 0, oo), meijerg=True, conds='separate')
+    assert j[1] == (beta > 2)
+    assert gammasimp(j[0] - i[0]**2) == (alpha + beta - 1)*alpha \
+        /(beta - 2)/(beta - 1)**2
+
+    # Beta distribution
+    # NOTE: this is evaluated using antiderivatives. It also tests that
+    #       meijerint_indefinite returns the simplest possible answer.
+    a, b = symbols('a b', positive=True)
+    betadist = x**(a - 1)*(-x + 1)**(b - 1)*gamma(a + b)/(gamma(a)*gamma(b))
+    assert simplify(integrate(betadist, (x, 0, 1), meijerg=True)) == 1
+    assert simplify(integrate(x*betadist, (x, 0, 1), meijerg=True)) == \
+        a/(a + b)
+    assert simplify(integrate(x**2*betadist, (x, 0, 1), meijerg=True)) == \
+        a*(a + 1)/(a + b)/(a + b + 1)
+    assert simplify(integrate(x**y*betadist, (x, 0, 1), meijerg=True)) == \
+        gamma(a + b)*gamma(a + y)/gamma(a)/gamma(a + b + y)
+
+    # Chi distribution
+    k = Symbol('k', integer=True, positive=True)
+    chi = 2**(1 - k/2)*x**(k - 1)*exp(-x**2/2)/gamma(k/2)
+    assert powsimp(integrate(chi, (x, 0, oo), meijerg=True)) == 1
+    assert simplify(integrate(x*chi, (x, 0, oo), meijerg=True)) == \
+        sqrt(2)*gamma((k + 1)/2)/gamma(k/2)
+    assert simplify(integrate(x**2*chi, (x, 0, oo), meijerg=True)) == k
+
+    # Chi^2 distribution
+    chisquared = 2**(-k/2)/gamma(k/2)*x**(k/2 - 1)*exp(-x/2)
+    assert powsimp(integrate(chisquared, (x, 0, oo), meijerg=True)) == 1
+    assert simplify(integrate(x*chisquared, (x, 0, oo), meijerg=True)) == k
+    assert simplify(integrate(x**2*chisquared, (x, 0, oo), meijerg=True)) == \
+        k*(k + 2)
+    assert gammasimp(integrate(((x - k)/sqrt(2*k))**3*chisquared, (x, 0, oo),
+                    meijerg=True)) == 2*sqrt(2)/sqrt(k)
+
+    # Dagum distribution
+    a, b, p = symbols('a b p', positive=True)
+    # XXX (x/b)**a does not work
+    dagum = a*p/x*(x/b)**(a*p)/(1 + x**a/b**a)**(p + 1)
+    assert simplify(integrate(dagum, (x, 0, oo), meijerg=True)) == 1
+    # XXX conditions are a mess
+    arg = x*dagum
+    assert simplify(integrate(arg, (x, 0, oo), meijerg=True, conds='none')
+                    ) == a*b*gamma(1 - 1/a)*gamma(p + 1 + 1/a)/(
+                    (a*p + 1)*gamma(p))
+    assert simplify(integrate(x*arg, (x, 0, oo), meijerg=True, conds='none')
+                    ) == a*b**2*gamma(1 - 2/a)*gamma(p + 1 + 2/a)/(
+                    (a*p + 2)*gamma(p))
+
+    # F-distribution
+    d1, d2 = symbols('d1 d2', positive=True)
+    f = sqrt(((d1*x)**d1 * d2**d2)/(d1*x + d2)**(d1 + d2))/x \
+        /gamma(d1/2)/gamma(d2/2)*gamma((d1 + d2)/2)
+    assert simplify(integrate(f, (x, 0, oo), meijerg=True)) == 1
+    # TODO conditions are a mess
+    assert simplify(integrate(x*f, (x, 0, oo), meijerg=True, conds='none')
+                    ) == d2/(d2 - 2)
+    assert simplify(integrate(x**2*f, (x, 0, oo), meijerg=True, conds='none')
+                    ) == d2**2*(d1 + 2)/d1/(d2 - 4)/(d2 - 2)
+
+    # TODO gamma, rayleigh
+
+    # inverse gaussian
+    lamda, mu = symbols('lamda mu', positive=True)
+    dist = sqrt(lamda/2/pi)*x**(Rational(-3, 2))*exp(-lamda*(x - mu)**2/x/2/mu**2)
+    mysimp = lambda expr: simplify(expr.rewrite(exp))
+    assert mysimp(integrate(dist, (x, 0, oo))) == 1
+    assert mysimp(integrate(x*dist, (x, 0, oo))) == mu
+    assert mysimp(integrate((x - mu)**2*dist, (x, 0, oo))) == mu**3/lamda
+    assert mysimp(integrate((x - mu)**3*dist, (x, 0, oo))) == 3*mu**5/lamda**2
+
+    # Levi
+    c = Symbol('c', positive=True)
+    assert integrate(sqrt(c/2/pi)*exp(-c/2/(x - mu))/(x - mu)**S('3/2'),
+                    (x, mu, oo)) == 1
+    # higher moments oo
+
+    # log-logistic
+    alpha, beta = symbols('alpha beta', positive=True)
+    distn = (beta/alpha)*x**(beta - 1)/alpha**(beta - 1)/ \
+        (1 + x**beta/alpha**beta)**2
+    # FIXME: If alpha, beta are not declared as finite the line below hangs
+    # after the changes in:
+    #    https://github.com/sympy/sympy/pull/16603
+    assert simplify(integrate(distn, (x, 0, oo))) == 1
+    # NOTE the conditions are a mess, but correctly state beta > 1
+    assert simplify(integrate(x*distn, (x, 0, oo), conds='none')) == \
+        pi*alpha/beta/sin(pi/beta)
+    # (similar comment for conditions applies)
+    assert simplify(integrate(x**y*distn, (x, 0, oo), conds='none')) == \
+        pi*alpha**y*y/beta/sin(pi*y/beta)
+
+    # weibull
+    k = Symbol('k', positive=True)
+    n = Symbol('n', positive=True)
+    distn = k/lamda*(x/lamda)**(k - 1)*exp(-(x/lamda)**k)
+    assert simplify(integrate(distn, (x, 0, oo))) == 1
+    assert simplify(integrate(x**n*distn, (x, 0, oo))) == \
+        lamda**n*gamma(1 + n/k)
+
+    # rice distribution
+    from sympy.functions.special.bessel import besseli
+    nu, sigma = symbols('nu sigma', positive=True)
+    rice = x/sigma**2*exp(-(x**2 + nu**2)/2/sigma**2)*besseli(0, x*nu/sigma**2)
+    assert integrate(rice, (x, 0, oo), meijerg=True) == 1
+    # can someone verify higher moments?
+
+    # Laplace distribution
+    mu = Symbol('mu', real=True)
+    b = Symbol('b', positive=True)
+    laplace = exp(-abs(x - mu)/b)/2/b
+    assert integrate(laplace, (x, -oo, oo), meijerg=True) == 1
+    assert integrate(x*laplace, (x, -oo, oo), meijerg=True) == mu
+    assert integrate(x**2*laplace, (x, -oo, oo), meijerg=True) == \
+        2*b**2 + mu**2
+
+    # TODO are there other distributions supported on (-oo, oo) that we can do?
+
+    # misc tests
+    k = Symbol('k', positive=True)
+    assert gammasimp(expand_mul(integrate(log(x)*x**(k - 1)*exp(-x)/gamma(k),
+                              (x, 0, oo)))) == polygamma(0, k)
+
+
+@slow
+def test_expint():
+    """ Test various exponential integrals. """
+    from sympy.core.symbol import Symbol
+    from sympy.functions.elementary.hyperbolic import sinh
+    from sympy.functions.special.error_functions import (Chi, Ci, Ei, Shi, Si, expint)
+    assert simplify(unpolarify(integrate(exp(-z*x)/x**y, (x, 1, oo),
+                meijerg=True, conds='none'
+                ).rewrite(expint).expand(func=True))) == expint(y, z)
+
+    assert integrate(exp(-z*x)/x, (x, 1, oo), meijerg=True,
+                     conds='none').rewrite(expint).expand() == \
+        expint(1, z)
+    assert integrate(exp(-z*x)/x**2, (x, 1, oo), meijerg=True,
+                     conds='none').rewrite(expint).expand() == \
+        expint(2, z).rewrite(Ei).rewrite(expint)
+    assert integrate(exp(-z*x)/x**3, (x, 1, oo), meijerg=True,
+                     conds='none').rewrite(expint).expand() == \
+        expint(3, z).rewrite(Ei).rewrite(expint).expand()
+
+    t = Symbol('t', positive=True)
+    assert integrate(-cos(x)/x, (x, t, oo), meijerg=True).expand() == Ci(t)
+    assert integrate(-sin(x)/x, (x, t, oo), meijerg=True).expand() == \
+        Si(t) - pi/2
+    assert integrate(sin(x)/x, (x, 0, z), meijerg=True) == Si(z)
+    assert integrate(sinh(x)/x, (x, 0, z), meijerg=True) == Shi(z)
+    assert integrate(exp(-x)/x, x, meijerg=True).expand().rewrite(expint) == \
+        I*pi - expint(1, x)
+    assert integrate(exp(-x)/x**2, x, meijerg=True).rewrite(expint).expand() \
+        == expint(1, x) - exp(-x)/x - I*pi
+
+    u = Symbol('u', polar=True)
+    assert integrate(cos(u)/u, u, meijerg=True).expand().as_independent(u)[1] \
+        == Ci(u)
+    assert integrate(cosh(u)/u, u, meijerg=True).expand().as_independent(u)[1] \
+        == Chi(u)
+
+    assert integrate(expint(1, x), x, meijerg=True
+            ).rewrite(expint).expand() == x*expint(1, x) - exp(-x)
+    assert integrate(expint(2, x), x, meijerg=True
+            ).rewrite(expint).expand() == \
+        -x**2*expint(1, x)/2 + x*exp(-x)/2 - exp(-x)/2
+    assert simplify(unpolarify(integrate(expint(y, x), x,
+                 meijerg=True).rewrite(expint).expand(func=True))) == \
+        -expint(y + 1, x)
+
+    assert integrate(Si(x), x, meijerg=True) == x*Si(x) + cos(x)
+    assert integrate(Ci(u), u, meijerg=True).expand() == u*Ci(u) - sin(u)
+    assert integrate(Shi(x), x, meijerg=True) == x*Shi(x) - cosh(x)
+    assert integrate(Chi(u), u, meijerg=True).expand() == u*Chi(u) - sinh(u)
+
+    assert integrate(Si(x)*exp(-x), (x, 0, oo), meijerg=True) == pi/4
+    assert integrate(expint(1, x)*sin(x), (x, 0, oo), meijerg=True) == log(2)/2
+
+
+def test_messy():
+    from sympy.functions.elementary.hyperbolic import (acosh, acoth)
+    from sympy.functions.elementary.trigonometric import (asin, atan)
+    from sympy.functions.special.bessel import besselj
+    from sympy.functions.special.error_functions import (Chi, E1, Shi, Si)
+    from sympy.integrals.transforms import (fourier_transform, laplace_transform)
+    assert (laplace_transform(Si(x), x, s, simplify=True) ==
+            ((-atan(s) + pi/2)/s, 0, True))
+
+    assert laplace_transform(Shi(x), x, s, simplify=True) == (
+        acoth(s)/s, -oo, s**2 > 1)
+
+    # where should the logs be simplified?
+    assert laplace_transform(Chi(x), x, s, simplify=True) == (
+        (log(s**(-2)) - log(1 - 1/s**2))/(2*s), -oo, s**2 > 1)
+
+    # TODO maybe simplify the inequalities? when the simplification
+    # allows for generators instead of symbols this will work
+    assert laplace_transform(besselj(a, x), x, s)[1:] == \
+        (0, (re(a) > -2) & (re(a) > -1))
+
+    # NOTE s < 0 can be done, but argument reduction is not good enough yet
+    ans = fourier_transform(besselj(1, x)/x, x, s, noconds=False)
+    assert (ans[0].factor(deep=True).expand(), ans[1]) == \
+        (Piecewise((0, (s > 1/(2*pi)) | (s < -1/(2*pi))),
+                   (2*sqrt(-4*pi**2*s**2 + 1), True)), s > 0)
+    # TODO FT(besselj(0,x)) - conditions are messy (but for acceptable reasons)
+    #                       - folding could be better
+
+    assert integrate(E1(x)*besselj(0, x), (x, 0, oo), meijerg=True) == \
+        log(1 + sqrt(2))
+    assert integrate(E1(x)*besselj(1, x), (x, 0, oo), meijerg=True) == \
+        log(S.Half + sqrt(2)/2)
+
+    assert integrate(1/x/sqrt(1 - x**2), x, meijerg=True) == \
+        Piecewise((-acosh(1/x), abs(x**(-2)) > 1), (I*asin(1/x), True))
+
+
+def test_issue_6122():
+    assert integrate(exp(-I*x**2), (x, -oo, oo), meijerg=True) == \
+        -I*sqrt(pi)*exp(I*pi/4)
+
+
+def test_issue_6252():
+    expr = 1/x/(a + b*x)**Rational(1, 3)
+    anti = integrate(expr, x, meijerg=True)
+    assert not anti.has(hyper)
+    # XXX the expression is a mess, but actually upon differentiation and
+    # putting in numerical values seems to work...
+
+
+def test_issue_6348():
+    assert integrate(exp(I*x)/(1 + x**2), (x, -oo, oo)).simplify().rewrite(exp) \
+        == pi*exp(-1)
+
+
+def test_fresnel():
+    from sympy.functions.special.error_functions import (fresnelc, fresnels)
+
+    assert expand_func(integrate(sin(pi*x**2/2), x)) == fresnels(x)
+    assert expand_func(integrate(cos(pi*x**2/2), x)) == fresnelc(x)
+
+
+def test_issue_6860():
+    assert meijerint_indefinite(x**x**x, x) is None
+
+
+def test_issue_7337():
+    f = meijerint_indefinite(x*sqrt(2*x + 3), x).together()
+    assert f == sqrt(2*x + 3)*(2*x**2 + x - 3)/5
+    assert f._eval_interval(x, S.NegativeOne, S.One) == Rational(2, 5)
+
+
+def test_issue_8368():
+    assert meijerint_indefinite(cosh(x)*exp(-x*t), x) == (
+        (-t - 1)*exp(x) + (-t + 1)*exp(-x))*exp(-t*x)/2/(t**2 - 1)
+
+
+def test_issue_10211():
+    from sympy.abc import h, w
+    assert integrate((1/sqrt((y-x)**2 + h**2)**3), (x,0,w), (y,0,w)) == \
+        2*sqrt(1 + w**2/h**2)/h - 2/h
+
+
+def test_issue_11806():
+    from sympy.core.symbol import symbols
+    y, L = symbols('y L', positive=True)
+    assert integrate(1/sqrt(x**2 + y**2)**3, (x, -L, L)) == \
+        2*L/(y**2*sqrt(L**2 + y**2))
+
+def test_issue_10681():
+    from sympy.polys.domains.realfield import RR
+    from sympy.abc import R, r
+    f = integrate(r**2*(R**2-r**2)**0.5, r, meijerg=True)
+    g = (1.0/3)*R**1.0*r**3*hyper((-0.5, Rational(3, 2)), (Rational(5, 2),),
+                                  r**2*exp_polar(2*I*pi)/R**2)
+    assert RR.almosteq((f/g).n(), 1.0, 1e-12)
+
+def test_issue_13536():
+    from sympy.core.symbol import Symbol
+    a = Symbol('a', positive=True)
+    assert integrate(1/x**2, (x, oo, a)) == -1/a
+
+
+def test_issue_6462():
+    from sympy.core.symbol import Symbol
+    x = Symbol('x')
+    n = Symbol('n')
+    # Not the actual issue, still wrong answer for n = 1, but that there is no
+    # exception
+    assert integrate(cos(x**n)/x**n, x, meijerg=True).subs(n, 2).equals(
+            integrate(cos(x**2)/x**2, x, meijerg=True))
+
+
+def test_indefinite_1_bug():
+    assert integrate((b + t)**(-a), t, meijerg=True) == -b*(1 + t/b)**(1 - a)/(a*b**a - b**a)
+
+
+def test_pr_23583():
+    # This result is wrong. Check whether new result is correct when this test fail.
+    assert integrate(1/sqrt((x - I)**2-1), meijerg=True) == \
+           Piecewise((acosh(x - I), Abs((x - I)**2) > 1), (-I*asin(x - I), True))
+
+
+# 25786
+def test_integrate_function_of_square_over_negatives():
+    assert integrate(exp(-x**2), (x,-5,0), meijerg=True) == sqrt(pi)/2 * erf(5)
+
+
+def test_issue_25949():
+    from sympy.core.symbol import symbols
+    y = symbols("y", nonzero=True)
+    assert integrate(cosh(y*(x + 1)), (x, -1, -0.25), meijerg=True) == sinh(0.75*y)/y
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_prde.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_prde.py
new file mode 100644
index 0000000000000000000000000000000000000000..a7429ea8634c742eb77cdb26f99b2cb15853cd42
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_prde.py
@@ -0,0 +1,322 @@
+"""Most of these tests come from the examples in Bronstein's book."""
+from sympy.integrals.risch import DifferentialExtension, derivation
+from sympy.integrals.prde import (prde_normal_denom, prde_special_denom,
+    prde_linear_constraints, constant_system, prde_spde, prde_no_cancel_b_large,
+    prde_no_cancel_b_small, limited_integrate_reduce, limited_integrate,
+    is_deriv_k, is_log_deriv_k_t_radical, parametric_log_deriv_heu,
+    is_log_deriv_k_t_radical_in_field, param_poly_rischDE, param_rischDE,
+    prde_cancel_liouvillian)
+
+from sympy.polys.polymatrix import PolyMatrix as Matrix
+
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.polys.domains.rationalfield import QQ
+from sympy.polys.polytools import Poly
+from sympy.abc import x, t, n
+
+t0, t1, t2, t3, k = symbols('t:4 k')
+
+
+def test_prde_normal_denom():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
+    fa = Poly(1, t)
+    fd = Poly(x, t)
+    G = [(Poly(t, t), Poly(1 + t**2, t)), (Poly(1, t), Poly(x + x*t**2, t))]
+    assert prde_normal_denom(fa, fd, G, DE) == \
+        (Poly(x, t, domain='ZZ(x)'), (Poly(1, t, domain='ZZ(x)'), Poly(1, t,
+            domain='ZZ(x)')), [(Poly(x*t, t, domain='ZZ(x)'),
+         Poly(t**2 + 1, t, domain='ZZ(x)')), (Poly(1, t, domain='ZZ(x)'),
+             Poly(t**2 + 1, t, domain='ZZ(x)'))], Poly(1, t, domain='ZZ(x)'))
+    G = [(Poly(t, t), Poly(t**2 + 2*t + 1, t)), (Poly(x*t, t),
+        Poly(t**2 + 2*t + 1, t)), (Poly(x*t**2, t), Poly(t**2 + 2*t + 1, t))]
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert prde_normal_denom(Poly(x, t), Poly(1, t), G, DE) == \
+        (Poly(t + 1, t), (Poly((-1 + x)*t + x, t), Poly(1, t, domain='ZZ[x]')), [(Poly(t, t),
+        Poly(1, t)), (Poly(x*t, t), Poly(1, t, domain='ZZ[x]')), (Poly(x*t**2, t),
+        Poly(1, t, domain='ZZ[x]'))], Poly(t + 1, t))
+
+
+def test_prde_special_denom():
+    a = Poly(t + 1, t)
+    ba = Poly(t**2, t)
+    bd = Poly(1, t)
+    G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))]
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert prde_special_denom(a, ba, bd, G, DE) == \
+        (Poly(t + 1, t), Poly(t**2, t), [(Poly(t, t), Poly(1, t)),
+        (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))], Poly(1, t))
+    G = [(Poly(t, t), Poly(1, t)), (Poly(1, t), Poly(t, t))]
+    assert prde_special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), G, DE) == \
+        (Poly(1, t), Poly(t**2 - 1, t), [(Poly(t**2, t), Poly(1, t)),
+        (Poly(1, t), Poly(1, t))], Poly(t, t))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-2*x*t0, t0)]})
+    DE.decrement_level()
+    G = [(Poly(t, t), Poly(t**2, t)), (Poly(2*t, t), Poly(t, t))]
+    assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3 + 2, t), G, DE) == \
+        (Poly(5*x*t + 1, t), Poly(0, t, domain='ZZ[x]'), [(Poly(t, t), Poly(t**2, t)),
+        (Poly(2*t, t), Poly(t, t))], Poly(1, x))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly((t**2 + 1)*2*x, t)]})
+    G = [(Poly(t + x, t), Poly(t*x, t)), (Poly(2*t, t), Poly(x**2, x))]
+    assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3, t), G, DE) == \
+        (Poly(5*x*t + 1, t), Poly(0, t, domain='ZZ[x]'), [(Poly(t + x, t), Poly(x*t, t)),
+        (Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t))
+    assert prde_special_denom(Poly(t + 1, t), Poly(t**2, t), Poly(t**3, t), G, DE) == \
+        (Poly(t + 1, t), Poly(0, t, domain='ZZ[x]'), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x),
+        Poly(x**2, t, x))], Poly(1, t))
+
+
+def test_prde_linear_constraints():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    G = [(Poly(2*x**3 + 3*x + 1, x), Poly(x**2 - 1, x)), (Poly(1, x), Poly(x - 1, x)),
+        (Poly(1, x), Poly(x + 1, x))]
+    assert prde_linear_constraints(Poly(1, x), Poly(0, x), G, DE) == \
+        ((Poly(2*x, x, domain='QQ'), Poly(0, x, domain='QQ'), Poly(0, x, domain='QQ')),
+            Matrix([[1, 1, -1], [5, 1, 1]], x))
+    G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))]
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert prde_linear_constraints(Poly(t + 1, t), Poly(t**2, t), G, DE) == \
+        ((Poly(t, t, domain='QQ'), Poly(t**2, t, domain='QQ'), Poly(t**3, t, domain='QQ')),
+            Matrix(0, 3, [], t))
+    G = [(Poly(2*x, t), Poly(t, t)), (Poly(-x, t), Poly(t, t))]
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    assert prde_linear_constraints(Poly(1, t), Poly(0, t), G, DE) == \
+        ((Poly(0, t, domain='QQ[x]'), Poly(0, t, domain='QQ[x]')), Matrix([[2*x, -x]], t))
+
+
+def test_constant_system():
+    A = Matrix([[-(x + 3)/(x - 1), (x + 1)/(x - 1), 1],
+                [-x - 3, x + 1, x - 1],
+                [2*(x + 3)/(x - 1), 0, 0]], t)
+    u = Matrix([[(x + 1)/(x - 1)], [x + 1], [0]], t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    R = QQ.frac_field(x)[t]
+    assert constant_system(A, u, DE) == \
+        (Matrix([[1, 0, 0],
+                 [0, 1, 0],
+                 [0, 0, 0],
+                 [0, 0, 1]], ring=R), Matrix([0, 1, 0, 0], ring=R))
+
+
+def test_prde_spde():
+    D = [Poly(x, t), Poly(-x*t, t)]
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    # TODO: when bound_degree() can handle this, test degree bound from that too
+    assert prde_spde(Poly(t, t), Poly(-1/x, t), D, n, DE) == \
+        (Poly(t, t), Poly(0, t, domain='ZZ(x)'),
+        [Poly(2*x, t, domain='ZZ(x)'), Poly(-x, t, domain='ZZ(x)')],
+        [Poly(-x**2, t, domain='ZZ(x)'), Poly(0, t, domain='ZZ(x)')], n - 1)
+
+
+def test_prde_no_cancel():
+    # b large
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert prde_no_cancel_b_large(Poly(1, x), [Poly(x**2, x), Poly(1, x)], 2, DE) == \
+        ([Poly(x**2 - 2*x + 2, x), Poly(1, x)], Matrix([[1, 0, -1, 0],
+                                                        [0, 1, 0, -1]], x))
+    assert prde_no_cancel_b_large(Poly(1, x), [Poly(x**3, x), Poly(1, x)], 3, DE) == \
+        ([Poly(x**3 - 3*x**2 + 6*x - 6, x), Poly(1, x)], Matrix([[1, 0, -1, 0],
+                                                                 [0, 1, 0, -1]], x))
+    assert prde_no_cancel_b_large(Poly(x, x), [Poly(x**2, x), Poly(1, x)], 1, DE) == \
+        ([Poly(x, x, domain='ZZ'), Poly(0, x, domain='ZZ')], Matrix([[1, -1,  0,  0],
+                                                                    [1,  0, -1,  0],
+                                                                    [0,  1,  0, -1]], x))
+    # b small
+    # XXX: Is there a better example of a monomial with D.degree() > 2?
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**3 + 1, t)]})
+
+    # My original q was t**4 + t + 1, but this solution implies q == t**4
+    # (c1 = 4), with some of the ci for the original q equal to 0.
+    G = [Poly(t**6, t), Poly(x*t**5, t), Poly(t**3, t), Poly(x*t**2, t), Poly(1 + x, t)]
+    R = QQ.frac_field(x)[t]
+    assert prde_no_cancel_b_small(Poly(x*t, t), G, 4, DE) == \
+        ([Poly(t**4/4 - x/12*t**3 + x**2/24*t**2 + (Rational(-11, 12) - x**3/24)*t + x/24, t),
+        Poly(x/3*t**3 - x**2/6*t**2 + (Rational(-1, 3) + x**3/6)*t - x/6, t), Poly(t, t),
+        Poly(0, t), Poly(0, t)], Matrix([[1, 0,              -1, 0, 0,  0,  0,  0,  0,  0],
+                                         [0, 1, Rational(-1, 4), 0, 0,  0,  0,  0,  0,  0],
+                                         [0, 0,               0, 0, 0,  0,  0,  0,  0,  0],
+                                         [0, 0,               0, 1, 0,  0,  0,  0,  0,  0],
+                                         [0, 0,               0, 0, 1,  0,  0,  0,  0,  0],
+                                         [1, 0,               0, 0, 0, -1,  0,  0,  0,  0],
+                                         [0, 1,               0, 0, 0,  0, -1,  0,  0,  0],
+                                         [0, 0,               1, 0, 0,  0,  0, -1,  0,  0],
+                                         [0, 0,               0, 1, 0,  0,  0,  0, -1,  0],
+                                         [0, 0,               0, 0, 1,  0,  0,  0,  0, -1]], ring=R))
+
+    # TODO: Add test for deg(b) <= 0 with b small
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
+    b = Poly(-1/x**2, t, field=True)  # deg(b) == 0
+    q = [Poly(x**i*t**j, t, field=True) for i in range(2) for j in range(3)]
+    h, A = prde_no_cancel_b_small(b, q, 3, DE)
+    V = A.nullspace()
+    R = QQ.frac_field(x)[t]
+    assert len(V) == 1
+    assert V[0] == Matrix([Rational(-1, 2), 0, 0, 1, 0, 0]*3, ring=R)
+    assert (Matrix([h])*V[0][6:, :])[0] == Poly(x**2/2, t, domain='QQ(x)')
+    assert (Matrix([q])*V[0][:6, :])[0] == Poly(x - S.Half, t, domain='QQ(x)')
+
+
+def test_prde_cancel_liouvillian():
+    ### 1. case == 'primitive'
+    # used when integrating f = log(x) - log(x - 1)
+    # Not taken from 'the' book
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    p0 = Poly(0, t, field=True)
+    p1 = Poly((x - 1)*t, t, domain='ZZ(x)')
+    p2 = Poly(x - 1, t, domain='ZZ(x)')
+    p3 = Poly(-x**2 + x, t, domain='ZZ(x)')
+    h, A = prde_cancel_liouvillian(Poly(-1/(x - 1), t), [Poly(-x + 1, t), Poly(1, t)], 1, DE)
+    V = A.nullspace()
+    assert h == [p0, p0, p1, p0, p0, p0, p0, p0, p0, p0, p2, p3, p0, p0, p0, p0]
+    assert A.rank() == 16
+    assert (Matrix([h])*V[0][:16, :]) == Matrix([[Poly(0, t, domain='QQ(x)')]])
+
+    ### 2. case == 'exp'
+    # used when integrating log(x/exp(x) + 1)
+    # Not taken from book
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t, t)]})
+    assert prde_cancel_liouvillian(Poly(0, t, domain='QQ[x]'), [Poly(1, t, domain='QQ(x)')], 0, DE) == \
+            ([Poly(1, t, domain='QQ'), Poly(x, t, domain='ZZ(x)')], Matrix([[-1, 0, 1]], DE.t))
+
+
+def test_param_poly_rischDE():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    a = Poly(x**2 - x, x, field=True)
+    b = Poly(1, x, field=True)
+    q = [Poly(x, x, field=True), Poly(x**2, x, field=True)]
+    h, A = param_poly_rischDE(a, b, q, 3, DE)
+
+    assert A.nullspace() == [Matrix([0, 1, 1, 1], DE.t)]  # c1, c2, d1, d2
+    # Solution of a*Dp + b*p = c1*q1 + c2*q2 = q2 = x**2
+    # is d1*h1 + d2*h2 = h1 + h2 = x.
+    assert h[0] + h[1] == Poly(x, x, domain='QQ')
+    # a*Dp + b*p = q1 = x has no solution.
+
+    a = Poly(x**2 - x, x, field=True)
+    b = Poly(x**2 - 5*x + 3, x, field=True)
+    q = [Poly(1, x, field=True), Poly(x, x, field=True),
+         Poly(x**2, x, field=True)]
+    h, A = param_poly_rischDE(a, b, q, 3, DE)
+
+    assert A.nullspace() == [Matrix([3, -5, 1, -5, 1, 1], DE.t)]
+    p = -Poly(5, DE.t)*h[0] + h[1] + h[2]  # Poly(1, x)
+    assert a*derivation(p, DE) + b*p == Poly(x**2 - 5*x + 3, x, domain='QQ')
+
+
+def test_param_rischDE():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    p1, px = Poly(1, x, field=True), Poly(x, x, field=True)
+    G = [(p1, px), (p1, p1), (px, p1)]  # [1/x, 1, x]
+    h, A = param_rischDE(-p1, Poly(x**2, x, field=True), G, DE)
+    assert len(h) == 3
+    p = [hi[0].as_expr()/hi[1].as_expr() for hi in h]
+    V = A.nullspace()
+    assert len(V) == 2
+    assert V[0] == Matrix([-1, 1, 0, -1, 1, 0], DE.t)
+    y = -p[0] + p[1] + 0*p[2]  # x
+    assert y.diff(x) - y/x**2 == 1 - 1/x  # Dy + f*y == -G0 + G1 + 0*G2
+
+    # the below test computation takes place while computing the integral
+    # of 'f = log(log(x + exp(x)))'
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    G = [(Poly(t + x, t, domain='ZZ(x)'), Poly(1, t, domain='QQ')), (Poly(0, t, domain='QQ'), Poly(1, t, domain='QQ'))]
+    h, A = param_rischDE(Poly(-t - 1, t, field=True), Poly(t + x, t, field=True), G, DE)
+    assert len(h) == 5
+    p = [hi[0].as_expr()/hi[1].as_expr() for hi in h]
+    V = A.nullspace()
+    assert len(V) == 3
+    assert V[0] == Matrix([0, 0, 0, 0, 1, 0, 0], DE.t)
+    y = 0*p[0] + 0*p[1] + 1*p[2] + 0*p[3] + 0*p[4]
+    assert y.diff(t) - y/(t + x) == 0   # Dy + f*y = 0*G0 + 0*G1
+
+
+def test_limited_integrate_reduce():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    assert limited_integrate_reduce(Poly(x, t), Poly(t**2, t), [(Poly(x, t),
+    Poly(t, t))], DE) == \
+        (Poly(t, t), Poly(-1/x, t), Poly(t, t), 1, (Poly(x, t), Poly(1, t, domain='ZZ[x]')),
+        [(Poly(-x*t, t), Poly(1, t, domain='ZZ[x]'))])
+
+
+def test_limited_integrate():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    G = [(Poly(x, x), Poly(x + 1, x))]
+    assert limited_integrate(Poly(-(1 + x + 5*x**2 - 3*x**3), x),
+    Poly(1 - x - x**2 + x**3, x), G, DE) == \
+        ((Poly(x**2 - x + 2, x), Poly(x - 1, x, domain='QQ')), [2])
+    G = [(Poly(1, x), Poly(x, x))]
+    assert limited_integrate(Poly(5*x**2, x), Poly(3, x), G, DE) == \
+        ((Poly(5*x**3/9, x), Poly(1, x, domain='QQ')), [0])
+
+
+def test_is_log_deriv_k_t_radical():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)], 'exts': [None],
+        'extargs': [None]})
+    assert is_log_deriv_k_t_radical(Poly(2*x, x), Poly(1, x), DE) is None
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2*t1, t1), Poly(1/x, t2)],
+        'exts': [None, 'exp', 'log'], 'extargs': [None, 2*x, x]})
+    assert is_log_deriv_k_t_radical(Poly(x + t2/2, t2), Poly(1, t2), DE) == \
+        ([(t1, 1), (x, 1)], t1*x, 2, 0)
+    # TODO: Add more tests
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0, t0), Poly(1/x, t)],
+        'exts': [None, 'exp', 'log'], 'extargs': [None, x, x]})
+    assert is_log_deriv_k_t_radical(Poly(x + t/2 + 3, t), Poly(1, t), DE) == \
+        ([(t0, 2), (x, 1)], x*t0**2, 2, 3)
+
+
+def test_is_deriv_k():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
+        'exts': [None, 'log', 'log'], 'extargs': [None, x, x + 1]})
+    assert is_deriv_k(Poly(2*x**2 + 2*x, t2), Poly(1, t2), DE) == \
+        ([(t1, 1), (t2, 1)], t1 + t2, 2)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(t2, t2)],
+        'exts': [None, 'log', 'exp'], 'extargs': [None, x, x]})
+    assert is_deriv_k(Poly(x**2*t2**3, t2), Poly(1, t2), DE) == \
+        ([(x, 3), (t1, 2)], 2*t1 + 3*x, 1)
+    # TODO: Add more tests, including ones with exponentials
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/x, t1)],
+        'exts': [None, 'log'], 'extargs': [None, x**2]})
+    assert is_deriv_k(Poly(x, t1), Poly(1, t1), DE) == \
+        ([(t1, S.Half)], t1/2, 1)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/(1 + x), t0)],
+        'exts': [None, 'log'], 'extargs': [None, x**2 + 2*x + 1]})
+    assert is_deriv_k(Poly(1 + x, t0), Poly(1, t0), DE) == \
+        ([(t0, S.Half)], t0/2, 1)
+
+    # Issue 10798
+    # DE = DifferentialExtension(log(1/x), x)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-1/x, t)],
+        'exts': [None, 'log'], 'extargs': [None, 1/x]})
+    assert is_deriv_k(Poly(1, t), Poly(x, t), DE) == ([(t, 1)], t, 1)
+
+
+def test_is_log_deriv_k_t_radical_in_field():
+    # NOTE: any potential constant factor in the second element of the result
+    # doesn't matter, because it cancels in Da/a.
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    assert is_log_deriv_k_t_radical_in_field(Poly(5*t + 1, t), Poly(2*t*x, t), DE) == \
+        (2, t*x**5)
+    assert is_log_deriv_k_t_radical_in_field(Poly(2 + 3*t, t), Poly(5*x*t, t), DE) == \
+        (5, x**3*t**2)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t/x**2, t)]})
+    assert is_log_deriv_k_t_radical_in_field(Poly(-(1 + 2*t), t),
+    Poly(2*x**2 + 2*x**2*t, t), DE) == \
+        (2, t + t**2)
+    assert is_log_deriv_k_t_radical_in_field(Poly(-1, t), Poly(x**2, t), DE) == \
+        (1, t)
+    assert is_log_deriv_k_t_radical_in_field(Poly(1, t), Poly(2*x**2, t), DE) == \
+        (2, 1/t)
+
+
+def test_parametric_log_deriv():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    assert parametric_log_deriv_heu(Poly(5*t**2 + t - 6, t), Poly(2*x*t**2, t),
+    Poly(-1, t), Poly(x*t**2, t), DE) == \
+        (2, 6, t*x**5)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_quadrature.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_quadrature.py
new file mode 100644
index 0000000000000000000000000000000000000000..97471dbdbc13fda0bce7a8823ff2cefac4ab8802
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_quadrature.py
@@ -0,0 +1,601 @@
+from sympy.core import S, Rational
+from sympy.integrals.quadrature import (gauss_legendre, gauss_laguerre,
+                                        gauss_hermite, gauss_gen_laguerre,
+                                        gauss_chebyshev_t, gauss_chebyshev_u,
+                                        gauss_jacobi, gauss_lobatto)
+
+
+def test_legendre():
+    x, w = gauss_legendre(1, 17)
+    assert [str(r) for r in x] == ['0']
+    assert [str(r) for r in w] == ['2.0000000000000000']
+
+    x, w = gauss_legendre(2, 17)
+    assert [str(r) for r in x] == [
+            '-0.57735026918962576',
+            '0.57735026918962576']
+    assert [str(r) for r in w] == [
+            '1.0000000000000000',
+            '1.0000000000000000']
+
+    x, w = gauss_legendre(3, 17)
+    assert [str(r) for r in x] == [
+            '-0.77459666924148338',
+            '0',
+            '0.77459666924148338']
+    assert [str(r) for r in w] == [
+            '0.55555555555555556',
+            '0.88888888888888889',
+            '0.55555555555555556']
+
+    x, w = gauss_legendre(4, 17)
+    assert [str(r) for r in x] == [
+            '-0.86113631159405258',
+            '-0.33998104358485626',
+            '0.33998104358485626',
+            '0.86113631159405258']
+    assert [str(r) for r in w] == [
+            '0.34785484513745386',
+            '0.65214515486254614',
+            '0.65214515486254614',
+            '0.34785484513745386']
+
+
+def test_legendre_precise():
+    x, w = gauss_legendre(3, 40)
+    assert [str(r) for r in x] == [
+            '-0.7745966692414833770358530799564799221666',
+            '0',
+            '0.7745966692414833770358530799564799221666']
+    assert [str(r) for r in w] == [
+            '0.5555555555555555555555555555555555555556',
+            '0.8888888888888888888888888888888888888889',
+            '0.5555555555555555555555555555555555555556']
+
+
+def test_laguerre():
+    x, w = gauss_laguerre(1, 17)
+    assert [str(r) for r in x] == ['1.0000000000000000']
+    assert [str(r) for r in w] == ['1.0000000000000000']
+
+    x, w = gauss_laguerre(2, 17)
+    assert [str(r) for r in x] == [
+            '0.58578643762690495',
+            '3.4142135623730950']
+    assert [str(r) for r in w] == [
+            '0.85355339059327376',
+            '0.14644660940672624']
+
+    x, w = gauss_laguerre(3, 17)
+    assert [str(r) for r in x] == [
+            '0.41577455678347908',
+            '2.2942803602790417',
+            '6.2899450829374792',
+            ]
+    assert [str(r) for r in w] == [
+            '0.71109300992917302',
+            '0.27851773356924085',
+            '0.010389256501586136',
+            ]
+
+    x, w = gauss_laguerre(4, 17)
+    assert [str(r) for r in x] == [
+            '0.32254768961939231',
+            '1.7457611011583466',
+            '4.5366202969211280',
+            '9.3950709123011331']
+    assert [str(r) for r in w] == [
+            '0.60315410434163360',
+            '0.35741869243779969',
+            '0.038887908515005384',
+            '0.00053929470556132745']
+
+    x, w = gauss_laguerre(5, 17)
+    assert [str(r) for r in x] == [
+            '0.26356031971814091',
+            '1.4134030591065168',
+            '3.5964257710407221',
+            '7.0858100058588376',
+            '12.640800844275783']
+    assert [str(r) for r in w] == [
+            '0.52175561058280865',
+            '0.39866681108317593',
+            '0.075942449681707595',
+            '0.0036117586799220485',
+            '2.3369972385776228e-5']
+
+
+def test_laguerre_precise():
+    x, w = gauss_laguerre(3, 40)
+    assert [str(r) for r in x] == [
+            '0.4157745567834790833115338731282744735466',
+            '2.294280360279041719822050361359593868960',
+            '6.289945082937479196866415765512131657493']
+    assert [str(r) for r in w] == [
+            '0.7110930099291730154495901911425944313094',
+            '0.2785177335692408488014448884567264810349',
+            '0.01038925650158613574896492040067908765572']
+
+
+def test_hermite():
+    x, w = gauss_hermite(1, 17)
+    assert [str(r) for r in x] == ['0']
+    assert [str(r) for r in w] == ['1.7724538509055160']
+
+    x, w = gauss_hermite(2, 17)
+    assert [str(r) for r in x] == [
+            '-0.70710678118654752',
+            '0.70710678118654752']
+    assert [str(r) for r in w] == [
+            '0.88622692545275801',
+            '0.88622692545275801']
+
+    x, w = gauss_hermite(3, 17)
+    assert [str(r) for r in x] == [
+            '-1.2247448713915890',
+            '0',
+            '1.2247448713915890']
+    assert [str(r) for r in w] == [
+            '0.29540897515091934',
+            '1.1816359006036774',
+            '0.29540897515091934']
+
+    x, w = gauss_hermite(4, 17)
+    assert [str(r) for r in x] == [
+            '-1.6506801238857846',
+            '-0.52464762327529032',
+            '0.52464762327529032',
+            '1.6506801238857846']
+    assert [str(r) for r in w] == [
+            '0.081312835447245177',
+            '0.80491409000551284',
+            '0.80491409000551284',
+            '0.081312835447245177']
+
+    x, w = gauss_hermite(5, 17)
+    assert [str(r) for r in x] == [
+            '-2.0201828704560856',
+            '-0.95857246461381851',
+            '0',
+            '0.95857246461381851',
+            '2.0201828704560856']
+    assert [str(r) for r in w] == [
+            '0.019953242059045913',
+            '0.39361932315224116',
+            '0.94530872048294188',
+            '0.39361932315224116',
+            '0.019953242059045913']
+
+
+def test_hermite_precise():
+    x, w = gauss_hermite(3, 40)
+    assert [str(r) for r in x] == [
+        '-1.224744871391589049098642037352945695983',
+        '0',
+        '1.224744871391589049098642037352945695983']
+    assert [str(r) for r in w] == [
+        '0.2954089751509193378830279138901908637996',
+        '1.181635900603677351532111655560763455198',
+        '0.2954089751509193378830279138901908637996']
+
+
+def test_gen_laguerre():
+    x, w = gauss_gen_laguerre(1, Rational(-1, 2), 17)
+    assert [str(r) for r in x] == ['0.50000000000000000']
+    assert [str(r) for r in w] == ['1.7724538509055160']
+
+    x, w = gauss_gen_laguerre(2, Rational(-1, 2), 17)
+    assert [str(r) for r in x] == [
+            '0.27525512860841095',
+            '2.7247448713915890']
+    assert [str(r) for r in w] == [
+            '1.6098281800110257',
+            '0.16262567089449035']
+
+    x, w = gauss_gen_laguerre(3, Rational(-1, 2), 17)
+    assert [str(r) for r in x] == [
+            '0.19016350919348813',
+            '1.7844927485432516',
+            '5.5253437422632603']
+    assert [str(r) for r in w] == [
+            '1.4492591904487850',
+            '0.31413464064571329',
+            '0.0090600198110176913']
+
+    x, w = gauss_gen_laguerre(4, Rational(-1, 2), 17)
+    assert [str(r) for r in x] == [
+            '0.14530352150331709',
+            '1.3390972881263614',
+            '3.9269635013582872',
+            '8.5886356890120343']
+    assert [str(r) for r in w] == [
+            '1.3222940251164826',
+            '0.41560465162978376',
+            '0.034155966014826951',
+            '0.00039920814442273524']
+
+    x, w = gauss_gen_laguerre(5, Rational(-1, 2), 17)
+    assert [str(r) for r in x] == [
+            '0.11758132021177814',
+            '1.0745620124369040',
+            '3.0859374437175500',
+            '6.4147297336620305',
+            '11.807189489971737']
+    assert [str(r) for r in w] == [
+            '1.2217252674706516',
+            '0.48027722216462937',
+            '0.067748788910962126',
+            '0.0026872914935624654',
+            '1.5280865710465241e-5']
+
+    x, w = gauss_gen_laguerre(1, 2, 17)
+    assert [str(r) for r in x] == ['3.0000000000000000']
+    assert [str(r) for r in w] == ['2.0000000000000000']
+
+    x, w = gauss_gen_laguerre(2, 2, 17)
+    assert [str(r) for r in x] == [
+            '2.0000000000000000',
+            '6.0000000000000000']
+    assert [str(r) for r in w] == [
+            '1.5000000000000000',
+            '0.50000000000000000']
+
+    x, w = gauss_gen_laguerre(3, 2, 17)
+    assert [str(r) for r in x] == [
+            '1.5173870806774125',
+            '4.3115831337195203',
+            '9.1710297856030672']
+    assert [str(r) for r in w] == [
+            '1.0374949614904253',
+            '0.90575000470306537',
+            '0.056755033806509347']
+
+    x, w = gauss_gen_laguerre(4, 2, 17)
+    assert [str(r) for r in x] == [
+            '1.2267632635003021',
+            '3.4125073586969460',
+            '6.9026926058516134',
+            '12.458036771951139']
+    assert [str(r) for r in w] == [
+            '0.72552499769865438',
+            '1.0634242919791946',
+            '0.20669613102835355',
+            '0.0043545792937974889']
+
+    x, w = gauss_gen_laguerre(5, 2, 17)
+    assert [str(r) for r in x] == [
+            '1.0311091440933816',
+            '2.8372128239538217',
+            '5.6202942725987079',
+            '9.6829098376640271',
+            '15.828473921690062']
+    assert [str(r) for r in w] == [
+            '0.52091739683509184',
+            '1.0667059331592211',
+            '0.38354972366693113',
+            '0.028564233532974658',
+            '0.00026271280578124935']
+
+
+def test_gen_laguerre_precise():
+    x, w = gauss_gen_laguerre(3, Rational(-1, 2), 40)
+    assert [str(r) for r in x] == [
+            '0.1901635091934881328718554276203028970878',
+            '1.784492748543251591186722461957367638500',
+            '5.525343742263260275941422110422329464413']
+    assert [str(r) for r in w] == [
+            '1.449259190448785048183829411195134343108',
+            '0.3141346406457132878326231270167565378246',
+            '0.009060019811017691281714945129254301865020']
+
+    x, w = gauss_gen_laguerre(3, 2, 40)
+    assert [str(r) for r in x] == [
+            '1.517387080677412495020323111016672547482',
+            '4.311583133719520302881184669723530562299',
+            '9.171029785603067202098492219259796890218']
+    assert [str(r) for r in w] == [
+            '1.037494961490425285817554606541269153041',
+            '0.9057500047030653669269785048806009945254',
+            '0.05675503380650934725546688857812985243312']
+
+
+def test_chebyshev_t():
+    x, w = gauss_chebyshev_t(1, 17)
+    assert [str(r) for r in x] == ['0']
+    assert [str(r) for r in w] == ['3.1415926535897932']
+
+    x, w = gauss_chebyshev_t(2, 17)
+    assert [str(r) for r in x] == [
+            '0.70710678118654752',
+            '-0.70710678118654752']
+    assert [str(r) for r in w] == [
+            '1.5707963267948966',
+            '1.5707963267948966']
+
+    x, w = gauss_chebyshev_t(3, 17)
+    assert [str(r) for r in x] == [
+            '0.86602540378443865',
+            '0',
+            '-0.86602540378443865']
+    assert [str(r) for r in w] == [
+            '1.0471975511965977',
+            '1.0471975511965977',
+            '1.0471975511965977']
+
+    x, w = gauss_chebyshev_t(4, 17)
+    assert [str(r) for r in x] == [
+            '0.92387953251128676',
+            '0.38268343236508977',
+            '-0.38268343236508977',
+            '-0.92387953251128676']
+    assert [str(r) for r in w] == [
+            '0.78539816339744831',
+            '0.78539816339744831',
+            '0.78539816339744831',
+            '0.78539816339744831']
+
+    x, w = gauss_chebyshev_t(5, 17)
+    assert [str(r) for r in x] == [
+            '0.95105651629515357',
+            '0.58778525229247313',
+            '0',
+            '-0.58778525229247313',
+            '-0.95105651629515357']
+    assert [str(r) for r in w] == [
+            '0.62831853071795865',
+            '0.62831853071795865',
+            '0.62831853071795865',
+            '0.62831853071795865',
+            '0.62831853071795865']
+
+
+def test_chebyshev_t_precise():
+    x, w = gauss_chebyshev_t(3, 40)
+    assert [str(r) for r in x] == [
+            '0.8660254037844386467637231707529361834714',
+            '0',
+            '-0.8660254037844386467637231707529361834714']
+    assert [str(r) for r in w] == [
+            '1.047197551196597746154214461093167628066',
+            '1.047197551196597746154214461093167628066',
+            '1.047197551196597746154214461093167628066']
+
+
+def test_chebyshev_u():
+    x, w = gauss_chebyshev_u(1, 17)
+    assert [str(r) for r in x] == ['0']
+    assert [str(r) for r in w] == ['1.5707963267948966']
+
+    x, w = gauss_chebyshev_u(2, 17)
+    assert [str(r) for r in x] == [
+            '0.50000000000000000',
+            '-0.50000000000000000']
+    assert [str(r) for r in w] == [
+            '0.78539816339744831',
+            '0.78539816339744831']
+
+    x, w = gauss_chebyshev_u(3, 17)
+    assert [str(r) for r in x] == [
+            '0.70710678118654752',
+            '0',
+            '-0.70710678118654752']
+    assert [str(r) for r in w] == [
+            '0.39269908169872415',
+            '0.78539816339744831',
+            '0.39269908169872415']
+
+    x, w = gauss_chebyshev_u(4, 17)
+    assert [str(r) for r in x] == [
+            '0.80901699437494742',
+            '0.30901699437494742',
+            '-0.30901699437494742',
+            '-0.80901699437494742']
+    assert [str(r) for r in w] == [
+            '0.21707871342270599',
+            '0.56831944997474231',
+            '0.56831944997474231',
+            '0.21707871342270599']
+
+    x, w = gauss_chebyshev_u(5, 17)
+    assert [str(r) for r in x] == [
+            '0.86602540378443865',
+            '0.50000000000000000',
+            '0',
+            '-0.50000000000000000',
+            '-0.86602540378443865']
+    assert [str(r) for r in w] == [
+            '0.13089969389957472',
+            '0.39269908169872415',
+            '0.52359877559829887',
+            '0.39269908169872415',
+            '0.13089969389957472']
+
+
+def test_chebyshev_u_precise():
+    x, w = gauss_chebyshev_u(3, 40)
+    assert [str(r) for r in x] == [
+            '0.7071067811865475244008443621048490392848',
+            '0',
+            '-0.7071067811865475244008443621048490392848']
+    assert [str(r) for r in w] == [
+            '0.3926990816987241548078304229099378605246',
+            '0.7853981633974483096156608458198757210493',
+            '0.3926990816987241548078304229099378605246']
+
+
+def test_jacobi():
+    x, w = gauss_jacobi(1, Rational(-1, 2), S.Half, 17)
+    assert [str(r) for r in x] == ['0.50000000000000000']
+    assert [str(r) for r in w] == ['3.1415926535897932']
+
+    x, w = gauss_jacobi(2, Rational(-1, 2), S.Half, 17)
+    assert [str(r) for r in x] == [
+            '-0.30901699437494742',
+            '0.80901699437494742']
+    assert [str(r) for r in w] == [
+            '0.86831485369082398',
+            '2.2732777998989693']
+
+    x, w = gauss_jacobi(3, Rational(-1, 2), S.Half, 17)
+    assert [str(r) for r in x] == [
+            '-0.62348980185873353',
+            '0.22252093395631440',
+            '0.90096886790241913']
+    assert [str(r) for r in w] == [
+            '0.33795476356635433',
+            '1.0973322242791115',
+            '1.7063056657443274']
+
+    x, w = gauss_jacobi(4, Rational(-1, 2), S.Half, 17)
+    assert [str(r) for r in x] == [
+            '-0.76604444311897804',
+            '-0.17364817766693035',
+            '0.50000000000000000',
+            '0.93969262078590838']
+    assert [str(r) for r in w] == [
+            '0.16333179083642836',
+            '0.57690240318269103',
+            '1.0471975511965977',
+            '1.3541609083740761']
+
+    x, w = gauss_jacobi(5, Rational(-1, 2), S.Half, 17)
+    assert [str(r) for r in x] == [
+            '-0.84125353283118117',
+            '-0.41541501300188643',
+            '0.14231483827328514',
+            '0.65486073394528506',
+            '0.95949297361449739']
+    assert [str(r) for r in w] == [
+            '0.090675770007435372',
+            '0.33391416373675607',
+            '0.65248870981926643',
+            '0.94525424081394926',
+            '1.1192597692123861']
+
+    x, w = gauss_jacobi(1, 2, 3, 17)
+    assert [str(r) for r in x] == ['0.14285714285714286']
+    assert [str(r) for r in w] == ['1.0666666666666667']
+
+    x, w = gauss_jacobi(2, 2, 3, 17)
+    assert [str(r) for r in x] == [
+            '-0.24025307335204215',
+            '0.46247529557426437']
+    assert [str(r) for r in w] == [
+            '0.48514624517838660',
+            '0.58152042148828007']
+
+    x, w = gauss_jacobi(3, 2, 3, 17)
+    assert [str(r) for r in x] == [
+            '-0.46115870378089762',
+            '0.10438533038323902',
+            '0.62950064612493132']
+    assert [str(r) for r in w] == [
+            '0.17937613502213266',
+            '0.61595640991147154',
+            '0.27133412173306246']
+
+    x, w = gauss_jacobi(4, 2, 3, 17)
+    assert [str(r) for r in x] == [
+            '-0.59903470850824782',
+            '-0.14761105199952565',
+            '0.32554377081188859',
+            '0.72879429738819258']
+    assert [str(r) for r in w] == [
+            '0.067809641836772187',
+            '0.38956404952032481',
+            '0.47995970868024150',
+            '0.12933326662932816']
+
+    x, w = gauss_jacobi(5, 2, 3, 17)
+    assert [str(r) for r in x] == [
+            '-0.69045775012676106',
+            '-0.32651993134900065',
+            '0.082337849552034905',
+            '0.47517887061283164',
+            '0.79279429464422850']
+    assert [str(r) for r in w] == [
+            '0.027410178066337099',
+            '0.21291786060364828',
+            '0.43908437944395081',
+            '0.32220656547221822',
+            '0.065047683080512268']
+
+
+def test_jacobi_precise():
+    x, w = gauss_jacobi(3, Rational(-1, 2), S.Half, 40)
+    assert [str(r) for r in x] == [
+            '-0.6234898018587335305250048840042398106323',
+            '0.2225209339563144042889025644967947594664',
+            '0.9009688679024191262361023195074450511659']
+    assert [str(r) for r in w] == [
+            '0.3379547635663543330553835737094171534907',
+            '1.097332224279111467485302294320899710461',
+            '1.706305665744327437921957515249186020246']
+
+    x, w = gauss_jacobi(3, 2, 3, 40)
+    assert [str(r) for r in x] == [
+            '-0.4611587037808976179121958105554375981274',
+            '0.1043853303832390210914918407615869143233',
+            '0.6295006461249313240934312425211234110769']
+    assert [str(r) for r in w] == [
+            '0.1793761350221326596137764371503859752628',
+            '0.6159564099114715430909548532229749439714',
+            '0.2713341217330624639619353762933057474325']
+
+
+def test_lobatto():
+    x, w = gauss_lobatto(2, 17)
+    assert [str(r) for r in x] == [
+            '-1',
+            '1']
+    assert [str(r) for r in w] == [
+            '1.0000000000000000',
+            '1.0000000000000000']
+
+    x, w = gauss_lobatto(3, 17)
+    assert [str(r) for r in x] == [
+            '-1',
+            '0',
+            '1']
+    assert [str(r) for r in w] == [
+            '0.33333333333333333',
+            '1.3333333333333333',
+            '0.33333333333333333']
+
+    x, w = gauss_lobatto(4, 17)
+    assert [str(r) for r in x] == [
+            '-1',
+            '-0.44721359549995794',
+            '0.44721359549995794',
+            '1']
+    assert [str(r) for r in w] == [
+            '0.16666666666666667',
+            '0.83333333333333333',
+            '0.83333333333333333',
+            '0.16666666666666667']
+
+    x, w = gauss_lobatto(5, 17)
+    assert [str(r) for r in x] == [
+            '-1',
+            '-0.65465367070797714',
+            '0',
+            '0.65465367070797714',
+            '1']
+    assert [str(r) for r in w] == [
+            '0.10000000000000000',
+            '0.54444444444444444',
+            '0.71111111111111111',
+            '0.54444444444444444',
+            '0.10000000000000000']
+
+
+def test_lobatto_precise():
+    x, w = gauss_lobatto(3, 40)
+    assert [str(r) for r in x] == [
+            '-1',
+            '0',
+            '1']
+    assert [str(r) for r in w] == [
+            '0.3333333333333333333333333333333333333333',
+            '1.333333333333333333333333333333333333333',
+            '0.3333333333333333333333333333333333333333']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_rationaltools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_rationaltools.py
new file mode 100644
index 0000000000000000000000000000000000000000..809bf30c1c35f80e2a0b15c1e639603eab28a250
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_rationaltools.py
@@ -0,0 +1,183 @@
+from sympy.core.numbers import (I, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import atan
+from sympy.integrals.integrals import integrate
+from sympy.polys.polytools import Poly
+from sympy.simplify.simplify import simplify
+
+from sympy.integrals.rationaltools import ratint, ratint_logpart, log_to_atan
+
+from sympy.abc import a, b, x, t
+
+half = S.Half
+
+
+def test_ratint():
+    assert ratint(S.Zero, x) == 0
+    assert ratint(S(7), x) == 7*x
+
+    assert ratint(x, x) == x**2/2
+    assert ratint(2*x, x) == x**2
+    assert ratint(-2*x, x) == -x**2
+
+    assert ratint(8*x**7 + 2*x + 1, x) == x**8 + x**2 + x
+
+    f = S.One
+    g = x + 1
+
+    assert ratint(f / g, x) == log(x + 1)
+    assert ratint((f, g), x) == log(x + 1)
+
+    f = x**3 - x
+    g = x - 1
+
+    assert ratint(f/g, x) == x**3/3 + x**2/2
+
+    f = x
+    g = (x - a)*(x + a)
+
+    assert ratint(f/g, x) == log(x**2 - a**2)/2
+
+    f = S.One
+    g = x**2 + 1
+
+    assert ratint(f/g, x, real=None) == atan(x)
+    assert ratint(f/g, x, real=True) == atan(x)
+
+    assert ratint(f/g, x, real=False) == I*log(x + I)/2 - I*log(x - I)/2
+
+    f = S(36)
+    g = x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2
+
+    assert ratint(f/g, x) == \
+        -4*log(x + 1) + 4*log(x - 2) + (12*x + 6)/(x**2 - 1)
+
+    f = x**4 - 3*x**2 + 6
+    g = x**6 - 5*x**4 + 5*x**2 + 4
+
+    assert ratint(f/g, x) == \
+        atan(x) + atan(x**3) + atan(x/2 - Rational(3, 2)*x**3 + S.Half*x**5)
+
+    f = x**7 - 24*x**4 - 4*x**2 + 8*x - 8
+    g = x**8 + 6*x**6 + 12*x**4 + 8*x**2
+
+    assert ratint(f/g, x) == \
+        (4 + 6*x + 8*x**2 + 3*x**3)/(4*x + 4*x**3 + x**5) + log(x)
+
+    assert ratint((x**3*f)/(x*g), x) == \
+        -(12 - 16*x + 6*x**2 - 14*x**3)/(4 + 4*x**2 + x**4) - \
+        5*sqrt(2)*atan(x*sqrt(2)/2) + S.Half*x**2 - 3*log(2 + x**2)
+
+    f = x**5 - x**4 + 4*x**3 + x**2 - x + 5
+    g = x**4 - 2*x**3 + 5*x**2 - 4*x + 4
+
+    assert ratint(f/g, x) == \
+        x + S.Half*x**2 + S.Half*log(2 - x + x**2) + (9 - 4*x)/(7*x**2 - 7*x + 14) + \
+        13*sqrt(7)*atan(Rational(-1, 7)*sqrt(7) + 2*x*sqrt(7)/7)/49
+
+    assert ratint(1/(x**2 + x + 1), x) == \
+        2*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3)/3
+
+    assert ratint(1/(x**3 + 1), x) == \
+        -log(1 - x + x**2)/6 + log(1 + x)/3 + sqrt(3)*atan(-sqrt(3)
+             /3 + 2*x*sqrt(3)/3)/3
+
+    assert ratint(1/(x**2 + x + 1), x, real=False) == \
+        -I*3**half*log(half + x - half*I*3**half)/3 + \
+        I*3**half*log(half + x + half*I*3**half)/3
+
+    assert ratint(1/(x**3 + 1), x, real=False) == log(1 + x)/3 + \
+        (Rational(-1, 6) + I*3**half/6)*log(-half + x + I*3**half/2) + \
+        (Rational(-1, 6) - I*3**half/6)*log(-half + x - I*3**half/2)
+
+    # issue 4991
+    assert ratint(1/(x*(a + b*x)**3), x) == \
+        (3*a + 2*b*x)/(2*a**4 + 4*a**3*b*x + 2*a**2*b**2*x**2) + (
+            log(x) - log(a/b + x))/a**3
+
+    assert ratint(x/(1 - x**2), x) == -log(x**2 - 1)/2
+    assert ratint(-x/(1 - x**2), x) == log(x**2 - 1)/2
+
+    assert ratint((x/4 - 4/(1 - x)).diff(x), x) == x/4 + 4/(x - 1)
+
+    ans = atan(x)
+    assert ratint(1/(x**2 + 1), x, symbol=x) == ans
+    assert ratint(1/(x**2 + 1), x, symbol='x') == ans
+    assert ratint(1/(x**2 + 1), x, symbol=a) == ans
+    # this asserts that as_dummy must return a unique symbol
+    # even if the symbol is already a Dummy
+    d = Dummy()
+    assert ratint(1/(d**2 + 1), d, symbol=d) == atan(d)
+
+
+def test_ratint_logpart():
+    assert ratint_logpart(x, x**2 - 9, x, t) == \
+        [(Poly(x**2 - 9, x), Poly(-2*t + 1, t))]
+    assert ratint_logpart(x**2, x**3 - 5, x, t) == \
+        [(Poly(x**3 - 5, x), Poly(-3*t + 1, t))]
+
+
+def test_issue_5414():
+    assert ratint(1/(x**2 + 16), x) == atan(x/4)/4
+
+
+def test_issue_5249():
+    assert ratint(
+        1/(x**2 + a**2), x) == (-I*log(-I*a + x)/2 + I*log(I*a + x)/2)/a
+
+
+def test_issue_5817():
+    a, b, c = symbols('a,b,c', positive=True)
+
+    assert simplify(ratint(a/(b*c*x**2 + a**2 + b*a), x)) == \
+        sqrt(a)*atan(sqrt(
+            b)*sqrt(c)*x/(sqrt(a)*sqrt(a + b)))/(sqrt(b)*sqrt(c)*sqrt(a + b))
+
+
+def test_issue_5981():
+    u = symbols('u')
+    assert integrate(1/(u**2 + 1)) == atan(u)
+
+def test_issue_10488():
+    a,b,c,x = symbols('a b c x', positive=True)
+    assert integrate(x/(a*x+b),x) == x/a - b*log(a*x + b)/a**2
+
+
+def test_issues_8246_12050_13501_14080():
+    a = symbols('a', nonzero=True)
+    assert integrate(a/(x**2 + a**2), x) == atan(x/a)
+    assert integrate(1/(x**2 + a**2), x) == atan(x/a)/a
+    assert integrate(1/(1 + a**2*x**2), x) == atan(a*x)/a
+
+
+def test_issue_6308():
+    k, a0 = symbols('k a0', real=True)
+    assert integrate((x**2 + 1 - k**2)/(x**2 + 1 + a0**2), x) == \
+        x - (a0**2 + k**2)*atan(x/sqrt(a0**2 + 1))/sqrt(a0**2 + 1)
+
+
+def test_issue_5907():
+    a = symbols('a', nonzero=True)
+    assert integrate(1/(x**2 + a**2)**2, x) == \
+         x/(2*a**4 + 2*a**2*x**2) + atan(x/a)/(2*a**3)
+
+
+def test_log_to_atan():
+    f, g = (Poly(x + S.Half, x, domain='QQ'), Poly(sqrt(3)/2, x, domain='EX'))
+    fg_ans = 2*atan(2*sqrt(3)*x/3 + sqrt(3)/3)
+    assert log_to_atan(f, g) == fg_ans
+    assert log_to_atan(g, f) == -fg_ans
+
+
+def test_issue_25896():
+    # for both tests, C = 0 in log_to_real
+    # but this only has a log result
+    e = (2*x + 1)/(x**2 + x + 1) + 1/x
+    assert ratint(e, x) == log(x**3 + x**2 + x)
+    # while this has more
+    assert ratint((4*x + 7)/(x**2 + 4*x + 6) + 2/x, x) == (
+        2*log(x) + 2*log(x**2 + 4*x + 6) - sqrt(2)*atan(
+        sqrt(2)*x/2 + sqrt(2))/2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_rde.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_rde.py
new file mode 100644
index 0000000000000000000000000000000000000000..3c7df5ce05846dc270756cd878870bbff78ff976
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_rde.py
@@ -0,0 +1,202 @@
+"""Most of these tests come from the examples in Bronstein's book."""
+from sympy.core.numbers import (I, Rational, oo)
+from sympy.core.symbol import symbols
+from sympy.polys.polytools import Poly
+from sympy.integrals.risch import (DifferentialExtension,
+    NonElementaryIntegralException)
+from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
+    normal_denom, special_denom, bound_degree, spde, solve_poly_rde,
+    no_cancel_equal, cancel_primitive, cancel_exp, rischDE)
+
+from sympy.testing.pytest import raises
+from sympy.abc import x, t, z, n
+
+t0, t1, t2, k = symbols('t:3 k')
+
+
+def test_order_at():
+    a = Poly(t**4, t)
+    b = Poly((t**2 + 1)**3*t, t)
+    c = Poly((t**2 + 1)**6*t, t)
+    d = Poly((t**2 + 1)**10*t**10, t)
+    e = Poly((t**2 + 1)**100*t**37, t)
+    p1 = Poly(t, t)
+    p2 = Poly(1 + t**2, t)
+    assert order_at(a, p1, t) == 4
+    assert order_at(b, p1, t) == 1
+    assert order_at(c, p1, t) == 1
+    assert order_at(d, p1, t) == 10
+    assert order_at(e, p1, t) == 37
+    assert order_at(a, p2, t) == 0
+    assert order_at(b, p2, t) == 3
+    assert order_at(c, p2, t) == 6
+    assert order_at(d, p1, t) == 10
+    assert order_at(e, p2, t) == 100
+    assert order_at(Poly(0, t), Poly(t, t), t) is oo
+    assert order_at_oo(Poly(t**2 - 1, t), Poly(t + 1), t) == \
+        order_at_oo(Poly(t - 1, t), Poly(1, t), t) == -1
+    assert order_at_oo(Poly(0, t), Poly(1, t), t) is oo
+
+def test_weak_normalizer():
+    a = Poly((1 + x)*t**5 + 4*t**4 + (-1 - 3*x)*t**3 - 4*t**2 + (-2 + 2*x)*t, t)
+    d = Poly(t**4 - 3*t**2 + 2, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    r = weak_normalizer(a, d, DE, z)
+    assert r == (Poly(t**5 - t**4 - 4*t**3 + 4*t**2 + 4*t - 4, t, domain='ZZ[x]'),
+        (Poly((1 + x)*t**2 + x*t, t, domain='ZZ[x]'),
+         Poly(t + 1, t, domain='ZZ[x]')))
+    assert weak_normalizer(r[1][0], r[1][1], DE) == (Poly(1, t), r[1])
+    r = weak_normalizer(Poly(1 + t**2), Poly(t**2 - 1, t), DE, z)
+    assert r == (Poly(t**4 - 2*t**2 + 1, t), (Poly(-3*t**2 + 1, t), Poly(t**2 - 1, t)))
+    assert weak_normalizer(r[1][0], r[1][1], DE, z) == (Poly(1, t), r[1])
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2)]})
+    r = weak_normalizer(Poly(1 + t**2), Poly(t, t), DE, z)
+    assert r == (Poly(t, t), (Poly(0, t), Poly(1, t)))
+    assert weak_normalizer(r[1][0], r[1][1], DE, z) == (Poly(1, t), r[1])
+
+
+def test_normal_denom():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    raises(NonElementaryIntegralException, lambda: normal_denom(Poly(1, x), Poly(1, x),
+    Poly(1, x), Poly(x, x), DE))
+    fa, fd = Poly(t**2 + 1, t), Poly(1, t)
+    ga, gd = Poly(1, t), Poly(t**2, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert normal_denom(fa, fd, ga, gd, DE) == \
+        (Poly(t, t), (Poly(t**3 - t**2 + t - 1, t), Poly(1, t)), (Poly(1, t),
+        Poly(1, t)), Poly(t, t))
+
+
+def test_special_denom():
+    # TODO: add more tests here
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
+    Poly(t, t), DE) == \
+        (Poly(1, t), Poly(t**2 - 1, t), Poly(t**2 - 1, t), Poly(t, t))
+#    assert special_denom(Poly(1, t), Poly(2*x, t), Poly((1 + 2*x)*t, t), DE) == 1
+
+    # issue 3940
+    # Note, this isn't a very good test, because the denominator is just 1,
+    # but at least it tests the exp cancellation case
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-2*x*t0, t0),
+        Poly(I*k*t1, t1)]})
+    DE.decrement_level()
+    assert special_denom(Poly(1, t0), Poly(I*k, t0), Poly(1, t0), Poly(t0, t0),
+    Poly(1, t0), DE) == \
+        (Poly(1, t0, domain='ZZ'), Poly(I*k, t0, domain='ZZ_I[k,x]'),
+                Poly(t0, t0, domain='ZZ'), Poly(1, t0, domain='ZZ'))
+
+
+    assert special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
+    Poly(t, t), DE, case='tan') == \
+           (Poly(1, t, t0, domain='ZZ'), Poly(t**2, t0, t, domain='ZZ[x]'),
+            Poly(t, t, t0, domain='ZZ'), Poly(1, t0, domain='ZZ'))
+
+    raises(ValueError, lambda: special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
+    Poly(t, t), DE, case='unrecognized_case'))
+
+
+def test_bound_degree_fail():
+    # Primitive
+    DE = DifferentialExtension(extension={'D': [Poly(1, x),
+        Poly(t0/x**2, t0), Poly(1/x, t)]})
+    assert bound_degree(Poly(t**2, t), Poly(-(1/x**2*t**2 + 1/x), t),
+        Poly((2*x - 1)*t**4 + (t0 + x)/x*t**3 - (t0 + 4*x**2)/2*x*t**2 + x*t,
+        t), DE) == 3
+
+
+def test_bound_degree():
+    # Base
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert bound_degree(Poly(1, x), Poly(-2*x, x), Poly(1, x), DE) == 0
+
+    # Primitive (see above test_bound_degree_fail)
+    # TODO: Add test for when the degree bound becomes larger after limited_integrate
+    # TODO: Add test for db == da - 1 case
+
+    # Exp
+    # TODO: Add tests
+    # TODO: Add test for when the degree becomes larger after parametric_log_deriv()
+
+    # Nonlinear
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert bound_degree(Poly(t, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), DE) == 0
+
+
+def test_spde():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    raises(NonElementaryIntegralException, lambda: spde(Poly(t, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), 0, DE))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert spde(Poly(t**2 + x*t*2 + x**2, t), Poly(t**2/x**2 + (2/x - 1)*t, t),
+        Poly(t**2/x**2 + (2/x - 1)*t, t), 0, DE) == \
+        (Poly(0, t), Poly(0, t), 0, Poly(0, t), Poly(1, t, domain='ZZ(x)'))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0/x**2, t0), Poly(1/x, t)]})
+    assert spde(Poly(t**2, t), Poly(-t**2/x**2 - 1/x, t),
+    Poly((2*x - 1)*t**4 + (t0 + x)/x*t**3 - (t0 + 4*x**2)/(2*x)*t**2 + x*t, t), 3, DE) == \
+        (Poly(0, t), Poly(0, t), 0, Poly(0, t),
+        Poly(t0*t**2/2 + x**2*t**2 - x**2*t, t, domain='ZZ(x,t0)'))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert spde(Poly(x**2 + x + 1, x), Poly(-2*x - 1, x), Poly(x**5/2 +
+    3*x**4/4 + x**3 - x**2 + 1, x), 4, DE) == \
+        (Poly(0, x, domain='QQ'), Poly(x/2 - Rational(1, 4), x), 2, Poly(x**2 + x + 1, x), Poly(x*Rational(5, 4), x))
+    assert spde(Poly(x**2 + x + 1, x), Poly(-2*x - 1, x), Poly(x**5/2 +
+    3*x**4/4 + x**3 - x**2 + 1, x), n, DE) == \
+        (Poly(0, x, domain='QQ'), Poly(x/2 - Rational(1, 4), x), -2 + n, Poly(x**2 + x + 1, x), Poly(x*Rational(5, 4), x))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1, t)]})
+    raises(NonElementaryIntegralException, lambda: spde(Poly((t - 1)*(t**2 + 1)**2, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), 0, DE))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert spde(Poly(x**2 - x, x), Poly(1, x), Poly(9*x**4 - 10*x**3 + 2*x**2, x), 4, DE) == \
+        (Poly(0, x, domain='ZZ'), Poly(0, x), 0, Poly(0, x), Poly(3*x**3 - 2*x**2, x, domain='QQ'))
+    assert spde(Poly(x**2 - x, x), Poly(x**2 - 5*x + 3, x), Poly(x**7 - x**6 - 2*x**4 + 3*x**3 - x**2, x), 5, DE) == \
+        (Poly(1, x, domain='QQ'), Poly(x + 1, x, domain='QQ'), 1, Poly(x**4 - x**3, x), Poly(x**3 - x**2, x, domain='QQ'))
+
+def test_solve_poly_rde_no_cancel():
+    # deg(b) large
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
+    assert solve_poly_rde(Poly(t**2 + 1, t), Poly(t**3 + (x + 1)*t**2 + t + x + 2, t),
+    oo, DE) == Poly(t + x, t)
+    # deg(b) small
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert solve_poly_rde(Poly(0, x), Poly(x/2 - Rational(1, 4), x), oo, DE) == \
+        Poly(x**2/4 - x/4, x)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert solve_poly_rde(Poly(2, t), Poly(t**2 + 2*t + 3, t), 1, DE) == \
+        Poly(t + 1, t, x)
+    # deg(b) == deg(D) - 1
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert no_cancel_equal(Poly(1 - t, t),
+    Poly(t**3 + t**2 - 2*x*t - 2*x, t), oo, DE) == \
+        (Poly(t**2, t), 1, Poly((-2 - 2*x)*t - 2*x, t))
+
+
+def test_solve_poly_rde_cancel():
+    # exp
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert cancel_exp(Poly(2*x, t), Poly(2*x, t), 0, DE) == \
+        Poly(1, t)
+    assert cancel_exp(Poly(2*x, t), Poly((1 + 2*x)*t, t), 1, DE) == \
+        Poly(t, t)
+    # TODO: Add more exp tests, including tests that require is_deriv_in_field()
+
+    # primitive
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+
+    # If the DecrementLevel context manager is working correctly, this shouldn't
+    # cause any problems with the further tests.
+    raises(NonElementaryIntegralException, lambda: cancel_primitive(Poly(1, t), Poly(t, t), oo, DE))
+
+    assert cancel_primitive(Poly(1, t), Poly(t + 1/x, t), 2, DE) == \
+        Poly(t, t)
+    assert cancel_primitive(Poly(4*x, t), Poly(4*x*t**2 + 2*t/x, t), 3, DE) == \
+        Poly(t**2, t)
+
+    # TODO: Add more primitive tests, including tests that require is_deriv_in_field()
+
+
+def test_rischDE():
+    # TODO: Add more tests for rischDE, including ones from the text
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    DE.decrement_level()
+    assert rischDE(Poly(-2*x, x), Poly(1, x), Poly(1 - 2*x - 2*x**2, x),
+    Poly(1, x), DE) == \
+        (Poly(x + 1, x), Poly(1, x))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_risch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_risch.py
new file mode 100644
index 0000000000000000000000000000000000000000..68be260e1f3d42fb14c790afe6bda1768e777666
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_risch.py
@@ -0,0 +1,763 @@
+"""Most of these tests come from the examples in Bronstein's book."""
+from sympy.core.function import (Function, Lambda, diff, expand_log)
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.relational import Ne
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import (atan, sin, tan)
+from sympy.polys.polytools import (Poly, cancel, factor)
+from sympy.integrals.risch import (gcdex_diophantine, frac_in, as_poly_1t,
+    derivation, splitfactor, splitfactor_sqf, canonical_representation,
+    hermite_reduce, polynomial_reduce, residue_reduce, residue_reduce_to_basic,
+    integrate_primitive, integrate_hyperexponential_polynomial,
+    integrate_hyperexponential, integrate_hypertangent_polynomial,
+    integrate_nonlinear_no_specials, integer_powers, DifferentialExtension,
+    risch_integrate, DecrementLevel, NonElementaryIntegral, recognize_log_derivative,
+    recognize_derivative, laurent_series)
+from sympy.testing.pytest import raises
+
+from sympy.abc import x, t, nu, z, a, y
+t0, t1, t2 = symbols('t:3')
+i = Symbol('i')
+
+def test_gcdex_diophantine():
+    assert gcdex_diophantine(Poly(x**4 - 2*x**3 - 6*x**2 + 12*x + 15),
+    Poly(x**3 + x**2 - 4*x - 4), Poly(x**2 - 1)) == \
+        (Poly((-x**2 + 4*x - 3)/5), Poly((x**3 - 7*x**2 + 16*x - 10)/5))
+    assert gcdex_diophantine(Poly(x**3 + 6*x + 7), Poly(x**2 + 3*x + 2), Poly(x + 1)) == \
+        (Poly(1/13, x, domain='QQ'), Poly(-1/13*x + 3/13, x, domain='QQ'))
+
+
+def test_frac_in():
+    assert frac_in(Poly((x + 1)/x*t, t), x) == \
+        (Poly(t*x + t, x), Poly(x, x))
+    assert frac_in((x + 1)/x*t, x) == \
+        (Poly(t*x + t, x), Poly(x, x))
+    assert frac_in((Poly((x + 1)/x*t, t), Poly(t + 1, t)), x) == \
+        (Poly(t*x + t, x), Poly((1 + t)*x, x))
+    raises(ValueError, lambda: frac_in((x + 1)/log(x)*t, x))
+    assert frac_in(Poly((2 + 2*x + x*(1 + x))/(1 + x)**2, t), x, cancel=True) == \
+        (Poly(x + 2, x), Poly(x + 1, x))
+
+
+def test_as_poly_1t():
+    assert as_poly_1t(2/t + t, t, z) in [
+        Poly(t + 2*z, t, z), Poly(t + 2*z, z, t)]
+    assert as_poly_1t(2/t + 3/t**2, t, z) in [
+        Poly(2*z + 3*z**2, t, z), Poly(2*z + 3*z**2, z, t)]
+    assert as_poly_1t(2/((exp(2) + 1)*t), t, z) in [
+        Poly(2/(exp(2) + 1)*z, t, z), Poly(2/(exp(2) + 1)*z, z, t)]
+    assert as_poly_1t(2/((exp(2) + 1)*t) + t, t, z) in [
+        Poly(t + 2/(exp(2) + 1)*z, t, z), Poly(t + 2/(exp(2) + 1)*z, z, t)]
+    assert as_poly_1t(S.Zero, t, z) == Poly(0, t, z)
+
+
+def test_derivation():
+    p = Poly(4*x**4*t**5 + (-4*x**3 - 4*x**4)*t**4 + (-3*x**2 + 2*x**3)*t**3 +
+        (2*x + 7*x**2 + 2*x**3)*t**2 + (1 - 4*x - 4*x**2)*t - 1 + 2*x, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - 3/(2*x)*t + 1/(2*x), t)]})
+    assert derivation(p, DE) == Poly(-20*x**4*t**6 + (2*x**3 + 16*x**4)*t**5 +
+        (21*x**2 + 12*x**3)*t**4 + (x*Rational(7, 2) - 25*x**2 - 12*x**3)*t**3 +
+        (-5 - x*Rational(15, 2) + 7*x**2)*t**2 - (3 - 8*x - 10*x**2 - 4*x**3)/(2*x)*t +
+        (1 - 4*x**2)/(2*x), t)
+    assert derivation(Poly(1, t), DE) == Poly(0, t)
+    assert derivation(Poly(t, t), DE) == DE.d
+    assert derivation(Poly(t**2 + 1/x*t + (1 - 2*x)/(4*x**2), t), DE) == \
+        Poly(-2*t**3 - 4/x*t**2 - (5 - 2*x)/(2*x**2)*t - (1 - 2*x)/(2*x**3), t, domain='ZZ(x)')
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(t, t)]})
+    assert derivation(Poly(x*t*t1, t), DE) == Poly(t*t1 + x*t*t1 + t, t)
+    assert derivation(Poly(x*t*t1, t), DE, coefficientD=True) == \
+        Poly((1 + t1)*t, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert derivation(Poly(x, x), DE) == Poly(1, x)
+    # Test basic option
+    assert derivation((x + 1)/(x - 1), DE, basic=True) == -2/(1 - 2*x + x**2)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert derivation((t + 1)/(t - 1), DE, basic=True) == -2*t/(1 - 2*t + t**2)
+    assert derivation(t + 1, DE, basic=True) == t
+
+
+def test_splitfactor():
+    p = Poly(4*x**4*t**5 + (-4*x**3 - 4*x**4)*t**4 + (-3*x**2 + 2*x**3)*t**3 +
+        (2*x + 7*x**2 + 2*x**3)*t**2 + (1 - 4*x - 4*x**2)*t - 1 + 2*x, t, field=True)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - 3/(2*x)*t + 1/(2*x), t)]})
+    assert splitfactor(p, DE) == (Poly(4*x**4*t**3 + (-8*x**3 - 4*x**4)*t**2 +
+        (4*x**2 + 8*x**3)*t - 4*x**2, t, domain='ZZ(x)'),
+        Poly(t**2 + 1/x*t + (1 - 2*x)/(4*x**2), t, domain='ZZ(x)'))
+    assert splitfactor(Poly(x, t), DE) == (Poly(x, t), Poly(1, t))
+    r = Poly(-4*x**4*z**2 + 4*x**6*z**2 - z*x**3 - 4*x**5*z**3 + 4*x**3*z**3 + x**4 + z*x**5 - x**6, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    assert splitfactor(r, DE, coefficientD=True) == \
+        (Poly(x*z - x**2 - z*x**3 + x**4, t), Poly(-x**2 + 4*x**2*z**2, t))
+    assert splitfactor_sqf(r, DE, coefficientD=True) == \
+        (((Poly(x*z - x**2 - z*x**3 + x**4, t), 1),), ((Poly(-x**2 + 4*x**2*z**2, t), 1),))
+    assert splitfactor(Poly(0, t), DE) == (Poly(0, t), Poly(1, t))
+    assert splitfactor_sqf(Poly(0, t), DE) == (((Poly(0, t), 1),), ())
+
+
+def test_canonical_representation():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
+    assert canonical_representation(Poly(x - t, t), Poly(t**2, t), DE) == \
+        (Poly(0, t, domain='ZZ[x]'), (Poly(0, t, domain='QQ[x]'),
+        Poly(1, t, domain='ZZ')), (Poly(-t + x, t, domain='QQ[x]'),
+        Poly(t**2, t)))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert canonical_representation(Poly(t**5 + t**3 + x**2*t + 1, t),
+    Poly((t**2 + 1)**3, t), DE) == \
+        (Poly(0, t, domain='ZZ[x]'), (Poly(t**5 + t**3 + x**2*t + 1, t, domain='QQ[x]'),
+         Poly(t**6 + 3*t**4 + 3*t**2 + 1, t, domain='QQ')),
+        (Poly(0, t, domain='QQ[x]'), Poly(1, t, domain='QQ')))
+
+
+def test_hermite_reduce():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+
+    assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
+        ((Poly(-x, t, domain='QQ[x]'), Poly(t, t, domain='QQ[x]')),
+         (Poly(0, t, domain='QQ[x]'), Poly(1, t, domain='QQ[x]')),
+         (Poly(-x, t, domain='QQ[x]'), Poly(1, t, domain='QQ[x]')))
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})
+
+    assert hermite_reduce(
+            Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 - (x**2 - nu**2)*t - x**5/4, t),
+            Poly(x**2*t**4 + x**2*(x**2 + 2)*t**2 + x**2 + x**4 + x**6/4, t), DE) == \
+        ((Poly(-x**2 - 4, t, domain='ZZ(x,nu)'), Poly(4*t**2 + 2*x**2 + 4, t, domain='ZZ(x,nu)')),
+         (Poly((-2*nu**2 - x**4)*t - (2*x**3 + 2*x), t, domain='ZZ(x,nu)'),
+          Poly(2*x**2*t**2 + x**4 + 2*x**2, t, domain='ZZ(x,nu)')),
+         (Poly(x*t + 1, t, domain='ZZ(x,nu)'), Poly(x, t, domain='ZZ(x,nu)')))
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+
+    a = Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 + (-4*x + 2*x**2)*t + x**2, t)
+    d = Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t)
+
+    assert hermite_reduce(a, d, DE) == \
+        ((Poly(3*t**2 + t + 3*x, t, domain='ZZ(x)'),
+          Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t, domain='ZZ(x)')),
+         (Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
+         (Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')))
+
+    assert hermite_reduce(
+            Poly(-t**2 + 2*t + 2, t, domain='ZZ(x)'),
+            Poly(-x*t**2 + 2*x*t - x, t, domain='ZZ(x)'), DE) == \
+        ((Poly(3, t, domain='ZZ(x)'), Poly(t - 1, t, domain='ZZ(x)')),
+         (Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
+         (Poly(1, t, domain='ZZ(x)'), Poly(x, t, domain='ZZ(x)')))
+
+    assert hermite_reduce(
+            Poly(-x**2*t**6 + (-1 - 2*x**3 + x**4)*t**3 + (-3 - 3*x**4)*t**2 -
+                2*x*t - x - 3*x**2, t, domain='ZZ(x)'),
+            Poly(x**4*t**6 - 2*x**2*t**3 + 1, t, domain='ZZ(x)'), DE) == \
+        ((Poly(x**3*t + x**4 + 1, t, domain='ZZ(x)'), Poly(x**3*t**3 - x, t, domain='ZZ(x)')),
+         (Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
+         (Poly(-1, t, domain='ZZ(x)'), Poly(x**2, t, domain='ZZ(x)')))
+
+    assert hermite_reduce(
+            Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 + (-4*x + 2*x**2)*t + x**2, t),
+            Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t), DE) == \
+        ((Poly(3*t**2 + t + 3*x, t, domain='ZZ(x)'),
+          Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t, domain='ZZ(x)')),
+         (Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
+         (Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')))
+
+
+def test_polynomial_reduce():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
+    assert polynomial_reduce(Poly(1 + x*t + t**2, t), DE) == \
+        (Poly(t, t), Poly(x*t, t))
+    assert polynomial_reduce(Poly(0, t), DE) == \
+        (Poly(0, t), Poly(0, t))
+
+
+def test_laurent_series():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1, t)]})
+    a = Poly(36, t)
+    d = Poly((t - 2)*(t**2 - 1)**2, t)
+    F = Poly(t**2 - 1, t)
+    n = 2
+    assert laurent_series(a, d, F, n, DE) == \
+        (Poly(-3*t**3 + 3*t**2 - 6*t - 8, t), Poly(t**5 + t**4 - 2*t**3 - 2*t**2 + t + 1, t),
+        [Poly(-3*t**3 - 6*t**2, t, domain='QQ'), Poly(2*t**6 + 6*t**5 - 8*t**3, t, domain='QQ')])
+
+
+def test_recognize_derivative():
+    DE = DifferentialExtension(extension={'D': [Poly(1, t)]})
+    a = Poly(36, t)
+    d = Poly((t - 2)*(t**2 - 1)**2, t)
+    assert recognize_derivative(a, d, DE) == False
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    a = Poly(2, t)
+    d = Poly(t**2 - 1, t)
+    assert recognize_derivative(a, d, DE) == False
+    assert recognize_derivative(Poly(x*t, t), Poly(1, t), DE) == True
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert recognize_derivative(Poly(t, t), Poly(1, t), DE) == True
+
+
+def test_recognize_log_derivative():
+
+    a = Poly(2*x**2 + 4*x*t - 2*t - x**2*t, t)
+    d = Poly((2*x + t)*(t + x**2), t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert recognize_log_derivative(a, d, DE, z) == True
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
+    assert recognize_log_derivative(Poly(t + 1, t), Poly(t + x, t), DE) == True
+    assert recognize_log_derivative(Poly(2, t), Poly(t**2 - 1, t), DE) == True
+    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
+    assert recognize_log_derivative(Poly(1, x), Poly(x**2 - 2, x), DE) == False
+    assert recognize_log_derivative(Poly(1, x), Poly(x**2 + x, x), DE) == True
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert recognize_log_derivative(Poly(1, t), Poly(t**2 - 2, t), DE) == False
+    assert recognize_log_derivative(Poly(1, t), Poly(t**2 + t, t), DE) == False
+
+
+def test_residue_reduce():
+    a = Poly(2*t**2 - t - x**2, t)
+    d = Poly(t**3 - x**2*t, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)], 'Tfuncs': [log]})
+    assert residue_reduce(a, d, DE, z, invert=False) == \
+        ([(Poly(z**2 - Rational(1, 4), z, domain='ZZ(x)'),
+          Poly((1 + 3*x*z - 6*z**2 - 2*x**2 + 4*x**2*z**2)*t - x*z + x**2 +
+              2*x**2*z**2 - 2*z*x**3, t, domain='ZZ(z, x)'))], False)
+    assert residue_reduce(a, d, DE, z, invert=True) == \
+        ([(Poly(z**2 - Rational(1, 4), z, domain='ZZ(x)'), Poly(t + 2*x*z, t))], False)
+    assert residue_reduce(Poly(-2/x, t), Poly(t**2 - 1, t,), DE, z, invert=False) == \
+        ([(Poly(z**2 - 1, z, domain='QQ'), Poly(-2*z*t/x - 2/x, t, domain='ZZ(z,x)'))], True)
+    ans = residue_reduce(Poly(-2/x, t), Poly(t**2 - 1, t), DE, z, invert=True)
+    assert ans == ([(Poly(z**2 - 1, z, domain='QQ'), Poly(t + z, t))], True)
+    assert residue_reduce_to_basic(ans[0], DE, z) == -log(-1 + log(x)) + log(1 + log(x))
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})
+    # TODO: Skip or make faster
+    assert residue_reduce(Poly((-2*nu**2 - x**4)/(2*x**2)*t - (1 + x**2)/x, t),
+    Poly(t**2 + 1 + x**2/2, t), DE, z) == \
+        ([(Poly(z + S.Half, z, domain='QQ'), Poly(t**2 + 1 + x**2/2, t,
+            domain='ZZ(x,nu)'))], True)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
+    assert residue_reduce(Poly(-2*x*t + 1 - x**2, t),
+    Poly(t**2 + 2*x*t + 1 + x**2, t), DE, z) == \
+        ([(Poly(z**2 + Rational(1, 4), z), Poly(t + x + 2*z, t))], True)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert residue_reduce(Poly(t, t), Poly(t + sqrt(2), t), DE, z) == \
+        ([(Poly(z - 1, z, domain='QQ'), Poly(t + sqrt(2), t))], True)
+
+
+def test_integrate_hyperexponential():
+    # TODO: Add tests for integrate_hyperexponential() from the book
+    a = Poly((1 + 2*t1 + t1**2 + 2*t1**3)*t**2 + (1 + t1**2)*t + 1 + t1**2, t)
+    d = Poly(1, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t1**2, t1),
+        Poly(t*(1 + t1**2), t)], 'Tfuncs': [tan, Lambda(i, exp(tan(i)))]})
+    assert integrate_hyperexponential(a, d, DE) == \
+        (exp(2*tan(x))*tan(x) + exp(tan(x)), 1 + t1**2, True)
+    a = Poly((t1**3 + (x + 1)*t1**2 + t1 + x + 2)*t, t)
+    assert integrate_hyperexponential(a, d, DE) == \
+        ((x + tan(x))*exp(tan(x)), 0, True)
+
+    a = Poly(t, t)
+    d = Poly(1, t)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2*x*t, t)],
+        'Tfuncs': [Lambda(i, exp(x**2))]})
+
+    assert integrate_hyperexponential(a, d, DE) == \
+        (0, NonElementaryIntegral(exp(x**2), x), False)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)], 'Tfuncs': [exp]})
+    assert integrate_hyperexponential(a, d, DE) == (exp(x), 0, True)
+
+    a = Poly(25*t**6 - 10*t**5 + 7*t**4 - 8*t**3 + 13*t**2 + 2*t - 1, t)
+    d = Poly(25*t**6 + 35*t**4 + 11*t**2 + 1, t)
+    assert integrate_hyperexponential(a, d, DE) == \
+        (-(11 - 10*exp(x))/(5 + 25*exp(2*x)) + log(1 + exp(2*x)), -1, True)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0, t0), Poly(t0*t, t)],
+        'Tfuncs': [exp, Lambda(i, exp(exp(i)))]})
+    assert integrate_hyperexponential(Poly(2*t0*t**2, t), Poly(1, t), DE) == (exp(2*exp(x)), 0, True)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0, t0), Poly(-t0*t, t)],
+        'Tfuncs': [exp, Lambda(i, exp(-exp(i)))]})
+    assert integrate_hyperexponential(Poly(-27*exp(9) - 162*t0*exp(9) +
+    27*x*t0*exp(9), t), Poly((36*exp(18) + x**2*exp(18) - 12*x*exp(18))*t, t), DE) == \
+        (27*exp(exp(x))/(-6*exp(9) + x*exp(9)), 0, True)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)], 'Tfuncs': [exp]})
+    assert integrate_hyperexponential(Poly(x**2/2*t, t), Poly(1, t), DE) == \
+        ((2 - 2*x + x**2)*exp(x)/2, 0, True)
+    assert integrate_hyperexponential(Poly(1 + t, t), Poly(t, t), DE) == \
+        (-exp(-x), 1, True)  # x - exp(-x)
+    assert integrate_hyperexponential(Poly(x, t), Poly(t + 1, t), DE) == \
+        (0, NonElementaryIntegral(x/(1 + exp(x)), x), False)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t0), Poly(2*x*t1, t1)],
+        'Tfuncs': [log, Lambda(i, exp(i**2))]})
+
+    elem, nonelem, b = integrate_hyperexponential(Poly((8*x**7 - 12*x**5 + 6*x**3 - x)*t1**4 +
+        (8*t0*x**7 - 8*t0*x**6 - 4*t0*x**5 + 2*t0*x**3 + 2*t0*x**2 - t0*x +
+        24*x**8 - 36*x**6 - 4*x**5 + 22*x**4 + 4*x**3 - 7*x**2 - x + 1)*t1**3
+        + (8*t0*x**8 - 4*t0*x**6 - 16*t0*x**5 - 2*t0*x**4 + 12*t0*x**3 +
+        t0*x**2 - 2*t0*x + 24*x**9 - 36*x**7 - 8*x**6 + 22*x**5 + 12*x**4 -
+        7*x**3 - 6*x**2 + x + 1)*t1**2 + (8*t0*x**8 - 8*t0*x**6 - 16*t0*x**5 +
+        6*t0*x**4 + 10*t0*x**3 - 2*t0*x**2 - t0*x + 8*x**10 - 12*x**8 - 4*x**7
+        + 2*x**6 + 12*x**5 + 3*x**4 - 9*x**3 - x**2 + 2*x)*t1 + 8*t0*x**7 -
+        12*t0*x**6 - 4*t0*x**5 + 8*t0*x**4 - t0*x**2 - 4*x**7 + 4*x**6 +
+        4*x**5 - 4*x**4 - x**3 + x**2, t1), Poly((8*x**7 - 12*x**5 + 6*x**3 -
+        x)*t1**4 + (24*x**8 + 8*x**7 - 36*x**6 - 12*x**5 + 18*x**4 + 6*x**3 -
+        3*x**2 - x)*t1**3 + (24*x**9 + 24*x**8 - 36*x**7 - 36*x**6 + 18*x**5 +
+        18*x**4 - 3*x**3 - 3*x**2)*t1**2 + (8*x**10 + 24*x**9 - 12*x**8 -
+        36*x**7 + 6*x**6 + 18*x**5 - x**4 - 3*x**3)*t1 + 8*x**10 - 12*x**8 +
+        6*x**6 - x**4, t1), DE)
+
+    assert factor(elem) == -((x - 1)*log(x)/((x + exp(x**2))*(2*x**2 - 1)))
+    assert (nonelem, b) == (NonElementaryIntegral(exp(x**2)/(exp(x**2) + 1), x), False)
+
+def test_integrate_hyperexponential_polynomial():
+    # Without proper cancellation within integrate_hyperexponential_polynomial(),
+    # this will take a long time to complete, and will return a complicated
+    # expression
+    p = Poly((-28*x**11*t0 - 6*x**8*t0 + 6*x**9*t0 - 15*x**8*t0**2 +
+        15*x**7*t0**2 + 84*x**10*t0**2 - 140*x**9*t0**3 - 20*x**6*t0**3 +
+        20*x**7*t0**3 - 15*x**6*t0**4 + 15*x**5*t0**4 + 140*x**8*t0**4 -
+        84*x**7*t0**5 - 6*x**4*t0**5 + 6*x**5*t0**5 + x**3*t0**6 - x**4*t0**6 +
+        28*x**6*t0**6 - 4*x**5*t0**7 + x**9 - x**10 + 4*x**12)/(-8*x**11*t0 +
+        28*x**10*t0**2 - 56*x**9*t0**3 + 70*x**8*t0**4 - 56*x**7*t0**5 +
+        28*x**6*t0**6 - 8*x**5*t0**7 + x**4*t0**8 + x**12)*t1**2 +
+        (-28*x**11*t0 - 12*x**8*t0 + 12*x**9*t0 - 30*x**8*t0**2 +
+        30*x**7*t0**2 + 84*x**10*t0**2 - 140*x**9*t0**3 - 40*x**6*t0**3 +
+        40*x**7*t0**3 - 30*x**6*t0**4 + 30*x**5*t0**4 + 140*x**8*t0**4 -
+        84*x**7*t0**5 - 12*x**4*t0**5 + 12*x**5*t0**5 - 2*x**4*t0**6 +
+        2*x**3*t0**6 + 28*x**6*t0**6 - 4*x**5*t0**7 + 2*x**9 - 2*x**10 +
+        4*x**12)/(-8*x**11*t0 + 28*x**10*t0**2 - 56*x**9*t0**3 +
+        70*x**8*t0**4 - 56*x**7*t0**5 + 28*x**6*t0**6 - 8*x**5*t0**7 +
+        x**4*t0**8 + x**12)*t1 + (-2*x**2*t0 + 2*x**3*t0 + x*t0**2 -
+        x**2*t0**2 + x**3 - x**4)/(-4*x**5*t0 + 6*x**4*t0**2 - 4*x**3*t0**3 +
+        x**2*t0**4 + x**6), t1, z, expand=False)
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t0), Poly(2*x*t1, t1)]})
+    assert integrate_hyperexponential_polynomial(p, DE, z) == (
+        Poly((x - t0)*t1**2 + (-2*t0 + 2*x)*t1, t1), Poly(-2*x*t0 + x**2 +
+        t0**2, t1), True)
+
+    DE = DifferentialExtension(extension={'D':[Poly(1, x), Poly(t0, t0)]})
+    assert integrate_hyperexponential_polynomial(Poly(0, t0), DE, z) == (
+        Poly(0, t0), Poly(1, t0), True)
+
+
+def test_integrate_hyperexponential_returns_piecewise():
+    a, b = symbols('a b')
+    DE = DifferentialExtension(a**x, x)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        (exp(x*log(a))/log(a), Ne(log(a), 0)), (x, True)), 0, True)
+    DE = DifferentialExtension(a**(b*x), x)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        (exp(b*x*log(a))/(b*log(a)), Ne(b*log(a), 0)), (x, True)), 0, True)
+    DE = DifferentialExtension(exp(a*x), x)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        (exp(a*x)/a, Ne(a, 0)), (x, True)), 0, True)
+    DE = DifferentialExtension(x*exp(a*x), x)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        ((a*x - 1)*exp(a*x)/a**2, Ne(a**2, 0)), (x**2/2, True)), 0, True)
+    DE = DifferentialExtension(x**2*exp(a*x), x)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        ((x**2*a**2 - 2*a*x + 2)*exp(a*x)/a**3, Ne(a**3, 0)),
+        (x**3/3, True)), 0, True)
+    DE = DifferentialExtension(x**y + z, y)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        (exp(log(x)*y)/log(x), Ne(log(x), 0)), (y, True)), z, True)
+    DE = DifferentialExtension(x**y + z + x**(2*y), y)
+    assert integrate_hyperexponential(DE.fa, DE.fd, DE) == (Piecewise(
+        ((exp(2*log(x)*y)*log(x) +
+            2*exp(log(x)*y)*log(x))/(2*log(x)**2), Ne(2*log(x)**2, 0)),
+            (2*y, True),
+        ), z, True)
+    # TODO: Add a test where two different parts of the extension use a
+    # Piecewise, like y**x + z**x.
+
+
+def test_issue_13947():
+    a, t, s = symbols('a t s')
+    assert risch_integrate(2**(-pi)/(2**t + 1), t) == \
+        2**(-pi)*t - 2**(-pi)*log(2**t + 1)/log(2)
+    assert risch_integrate(a**(t - s)/(a**t + 1), t) == \
+        exp(-s*log(a))*log(a**t + 1)/log(a)
+
+
+def test_integrate_primitive():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)],
+        'Tfuncs': [log]})
+    assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x*log(x), -1, True)
+    assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (0, NonElementaryIntegral(x/log(x), x), False)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
+        'Tfuncs': [log, Lambda(i, log(i + 1))]})
+    assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == \
+        (0, NonElementaryIntegral(log(x)/log(1 + x), x), False)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x*t1), t2)],
+        'Tfuncs': [log, Lambda(i, log(log(i)))]})
+    assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == \
+        (0, NonElementaryIntegral(log(log(x))/log(x), x), False)
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t0)],
+        'Tfuncs': [log]})
+    assert integrate_primitive(Poly(x**2*t0**3 + (3*x**2 + x)*t0**2 + (3*x**2
+    + 2*x)*t0 + x**2 + x, t0), Poly(x**2*t0**4 + 4*x**2*t0**3 + 6*x**2*t0**2 +
+    4*x**2*t0 + x**2, t0), DE) == \
+        (-1/(log(x) + 1), NonElementaryIntegral(1/(log(x) + 1), x), False)
+
+def test_integrate_hypertangent_polynomial():
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
+    assert integrate_hypertangent_polynomial(Poly(t**2 + x*t + 1, t), DE) == \
+        (Poly(t, t), Poly(x/2, t))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(a*(t**2 + 1), t)]})
+    assert integrate_hypertangent_polynomial(Poly(t**5, t), DE) == \
+        (Poly(1/(4*a)*t**4 - 1/(2*a)*t**2, t), Poly(1/(2*a), t))
+
+
+def test_integrate_nonlinear_no_specials():
+    a, d, = Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 - (x**2 -
+    nu**2)*t - x**5/4, t), Poly(x**2*t**4 + x**2*(x**2 + 2)*t**2 + x**2 + x**4 + x**6/4, t)
+    # f(x) == phi_nu(x), the logarithmic derivative of J_v, the Bessel function,
+    # which has no specials (see Chapter 5, note 4 of Bronstein's book).
+    f = Function('phi_nu')
+    DE = DifferentialExtension(extension={'D': [Poly(1, x),
+        Poly(-t**2 - t/x - (1 - nu**2/x**2), t)], 'Tfuncs': [f]})
+    assert integrate_nonlinear_no_specials(a, d, DE) == \
+        (-log(1 + f(x)**2 + x**2/2)/2 + (- 4 - x**2)/(4 + 2*x**2 + 4*f(x)**2), True)
+    assert integrate_nonlinear_no_specials(Poly(t, t), Poly(1, t), DE) == \
+        (0, False)
+
+
+def test_integer_powers():
+    assert integer_powers([x, x/2, x**2 + 1, x*Rational(2, 3)]) == [
+            (x/6, [(x, 6), (x/2, 3), (x*Rational(2, 3), 4)]),
+            (1 + x**2, [(1 + x**2, 1)])]
+
+
+def test_DifferentialExtension_exp():
+    assert DifferentialExtension(exp(x) + exp(x**2), x)._important_attrs == \
+        (Poly(t1 + t0, t1), Poly(1, t1), [Poly(1, x,), Poly(t0, t0),
+        Poly(2*x*t1, t1)], [x, t0, t1], [Lambda(i, exp(i)),
+        Lambda(i, exp(i**2))], [], [None, 'exp', 'exp'], [None, x, x**2])
+    assert DifferentialExtension(exp(x) + exp(2*x), x)._important_attrs == \
+        (Poly(t0**2 + t0, t0), Poly(1, t0), [Poly(1, x), Poly(t0, t0)], [x, t0],
+        [Lambda(i, exp(i))], [], [None, 'exp'], [None, x])
+    assert DifferentialExtension(exp(x) + exp(x/2), x)._important_attrs == \
+        (Poly(t0**2 + t0, t0), Poly(1, t0), [Poly(1, x), Poly(t0/2, t0)],
+        [x, t0], [Lambda(i, exp(i/2))], [], [None, 'exp'], [None, x/2])
+    assert DifferentialExtension(exp(x) + exp(x**2) + exp(x + x**2), x)._important_attrs == \
+        (Poly((1 + t0)*t1 + t0, t1), Poly(1, t1), [Poly(1, x), Poly(t0, t0),
+        Poly(2*x*t1, t1)], [x, t0, t1], [Lambda(i, exp(i)),
+        Lambda(i, exp(i**2))], [], [None, 'exp', 'exp'], [None, x, x**2])
+    assert DifferentialExtension(exp(x) + exp(x**2) + exp(x + x**2 + 1), x)._important_attrs == \
+        (Poly((1 + S.Exp1*t0)*t1 + t0, t1), Poly(1, t1), [Poly(1, x),
+        Poly(t0, t0), Poly(2*x*t1, t1)], [x, t0, t1], [Lambda(i, exp(i)),
+        Lambda(i, exp(i**2))], [], [None, 'exp', 'exp'], [None, x, x**2])
+    assert DifferentialExtension(exp(x) + exp(x**2) + exp(x/2 + x**2), x)._important_attrs == \
+        (Poly((t0 + 1)*t1 + t0**2, t1), Poly(1, t1), [Poly(1, x),
+        Poly(t0/2, t0), Poly(2*x*t1, t1)], [x, t0, t1],
+        [Lambda(i, exp(i/2)), Lambda(i, exp(i**2))],
+        [(exp(x/2), sqrt(exp(x)))], [None, 'exp', 'exp'], [None, x/2, x**2])
+    assert DifferentialExtension(exp(x) + exp(x**2) + exp(x/2 + x**2 + 3), x)._important_attrs == \
+        (Poly((t0*exp(3) + 1)*t1 + t0**2, t1), Poly(1, t1), [Poly(1, x),
+        Poly(t0/2, t0), Poly(2*x*t1, t1)], [x, t0, t1], [Lambda(i, exp(i/2)),
+        Lambda(i, exp(i**2))], [(exp(x/2), sqrt(exp(x)))], [None, 'exp', 'exp'],
+        [None, x/2, x**2])
+    assert DifferentialExtension(sqrt(exp(x)), x)._important_attrs == \
+        (Poly(t0, t0), Poly(1, t0), [Poly(1, x), Poly(t0/2, t0)], [x, t0],
+        [Lambda(i, exp(i/2))], [(exp(x/2), sqrt(exp(x)))], [None, 'exp'], [None, x/2])
+
+    assert DifferentialExtension(exp(x/2), x)._important_attrs == \
+        (Poly(t0, t0), Poly(1, t0), [Poly(1, x), Poly(t0/2, t0)], [x, t0],
+        [Lambda(i, exp(i/2))], [], [None, 'exp'], [None, x/2])
+
+
+def test_DifferentialExtension_log():
+    assert DifferentialExtension(log(x)*log(x + 1)*log(2*x**2 + 2*x), x)._important_attrs == \
+        (Poly(t0*t1**2 + (t0*log(2) + t0**2)*t1, t1), Poly(1, t1),
+        [Poly(1, x), Poly(1/x, t0),
+        Poly(1/(x + 1), t1, expand=False)], [x, t0, t1],
+        [Lambda(i, log(i)), Lambda(i, log(i + 1))], [], [None, 'log', 'log'],
+        [None, x, x + 1])
+    assert DifferentialExtension(x**x*log(x), x)._important_attrs == \
+        (Poly(t0*t1, t1), Poly(1, t1), [Poly(1, x), Poly(1/x, t0),
+        Poly((1 + t0)*t1, t1)], [x, t0, t1], [Lambda(i, log(i)),
+        Lambda(i, exp(t0*i))], [(exp(x*log(x)), x**x)], [None, 'log', 'exp'],
+        [None, x, t0*x])
+
+
+def test_DifferentialExtension_symlog():
+    # See comment on test_risch_integrate below
+    assert DifferentialExtension(log(x**x), x)._important_attrs == \
+        (Poly(t0*x, t1), Poly(1, t1), [Poly(1, x), Poly(1/x, t0), Poly((t0 +
+            1)*t1, t1)], [x, t0, t1], [Lambda(i, log(i)), Lambda(i, exp(i*t0))],
+            [(exp(x*log(x)), x**x)], [None, 'log', 'exp'], [None, x, t0*x])
+    assert DifferentialExtension(log(x**y), x)._important_attrs == \
+        (Poly(y*t0, t0), Poly(1, t0), [Poly(1, x), Poly(1/x, t0)], [x, t0],
+        [Lambda(i, log(i))], [(y*log(x), log(x**y))], [None, 'log'],
+        [None, x])
+    assert DifferentialExtension(log(sqrt(x)), x)._important_attrs == \
+        (Poly(t0, t0), Poly(2, t0), [Poly(1, x), Poly(1/x, t0)], [x, t0],
+        [Lambda(i, log(i))], [(log(x)/2, log(sqrt(x)))], [None, 'log'],
+        [None, x])
+
+
+def test_DifferentialExtension_handle_first():
+    assert DifferentialExtension(exp(x)*log(x), x, handle_first='log')._important_attrs == \
+        (Poly(t0*t1, t1), Poly(1, t1), [Poly(1, x), Poly(1/x, t0),
+        Poly(t1, t1)], [x, t0, t1], [Lambda(i, log(i)), Lambda(i, exp(i))],
+        [], [None, 'log', 'exp'], [None, x, x])
+    assert DifferentialExtension(exp(x)*log(x), x, handle_first='exp')._important_attrs == \
+        (Poly(t0*t1, t1), Poly(1, t1), [Poly(1, x), Poly(t0, t0),
+        Poly(1/x, t1)], [x, t0, t1], [Lambda(i, exp(i)), Lambda(i, log(i))],
+        [], [None, 'exp', 'log'], [None, x, x])
+
+    # This one must have the log first, regardless of what we set it to
+    # (because the log is inside of the exponential: x**x == exp(x*log(x)))
+    assert DifferentialExtension(-x**x*log(x)**2 + x**x - x**x/x, x,
+    handle_first='exp')._important_attrs == \
+        DifferentialExtension(-x**x*log(x)**2 + x**x - x**x/x, x,
+        handle_first='log')._important_attrs == \
+        (Poly((-1 + x - x*t0**2)*t1, t1), Poly(x, t1),
+            [Poly(1, x), Poly(1/x, t0), Poly((1 + t0)*t1, t1)], [x, t0, t1],
+            [Lambda(i, log(i)), Lambda(i, exp(t0*i))], [(exp(x*log(x)), x**x)],
+            [None, 'log', 'exp'], [None, x, t0*x])
+
+
+def test_DifferentialExtension_all_attrs():
+    # Test 'unimportant' attributes
+    DE = DifferentialExtension(exp(x)*log(x), x, handle_first='exp')
+    assert DE.f == exp(x)*log(x)
+    assert DE.newf == t0*t1
+    assert DE.x == x
+    assert DE.cases == ['base', 'exp', 'primitive']
+    assert DE.case == 'primitive'
+
+    assert DE.level == -1
+    assert DE.t == t1 == DE.T[DE.level]
+    assert DE.d == Poly(1/x, t1) == DE.D[DE.level]
+    raises(ValueError, lambda: DE.increment_level())
+    DE.decrement_level()
+    assert DE.level == -2
+    assert DE.t == t0 == DE.T[DE.level]
+    assert DE.d == Poly(t0, t0) == DE.D[DE.level]
+    assert DE.case == 'exp'
+    DE.decrement_level()
+    assert DE.level == -3
+    assert DE.t == x == DE.T[DE.level] == DE.x
+    assert DE.d == Poly(1, x) == DE.D[DE.level]
+    assert DE.case == 'base'
+    raises(ValueError, lambda: DE.decrement_level())
+    DE.increment_level()
+    DE.increment_level()
+    assert DE.level == -1
+    assert DE.t == t1 == DE.T[DE.level]
+    assert DE.d == Poly(1/x, t1) == DE.D[DE.level]
+    assert DE.case == 'primitive'
+
+    # Test methods
+    assert DE.indices('log') == [2]
+    assert DE.indices('exp') == [1]
+
+
+def test_DifferentialExtension_extension_flag():
+    raises(ValueError, lambda: DifferentialExtension(extension={'T': [x, t]}))
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
+    assert DE._important_attrs == (None, None, [Poly(1, x), Poly(t, t)], [x, t],
+        None, None, None, None)
+    assert DE.d == Poly(t, t)
+    assert DE.t == t
+    assert DE.level == -1
+    assert DE.cases == ['base', 'exp']
+    assert DE.x == x
+    assert DE.case == 'exp'
+
+    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)],
+        'exts': [None, 'exp'], 'extargs': [None, x]})
+    assert DE._important_attrs == (None, None, [Poly(1, x), Poly(t, t)], [x, t],
+        None, None, [None, 'exp'], [None, x])
+    raises(ValueError, lambda: DifferentialExtension())
+
+
+def test_DifferentialExtension_misc():
+    # Odd ends
+    assert DifferentialExtension(sin(y)*exp(x), x)._important_attrs == \
+        (Poly(sin(y)*t0, t0, domain='ZZ[sin(y)]'), Poly(1, t0, domain='ZZ'),
+        [Poly(1, x, domain='ZZ'), Poly(t0, t0, domain='ZZ')], [x, t0],
+        [Lambda(i, exp(i))], [], [None, 'exp'], [None, x])
+    raises(NotImplementedError, lambda: DifferentialExtension(sin(x), x))
+    assert DifferentialExtension(10**x, x)._important_attrs == \
+        (Poly(t0, t0), Poly(1, t0), [Poly(1, x), Poly(log(10)*t0, t0)], [x, t0],
+        [Lambda(i, exp(i*log(10)))], [(exp(x*log(10)), 10**x)], [None, 'exp'],
+        [None, x*log(10)])
+    assert DifferentialExtension(log(x) + log(x**2), x)._important_attrs in [
+        (Poly(3*t0, t0), Poly(2, t0), [Poly(1, x), Poly(2/x, t0)], [x, t0],
+        [Lambda(i, log(i**2))], [], [None, ], [], [1], [x**2]),
+        (Poly(3*t0, t0), Poly(1, t0), [Poly(1, x), Poly(1/x, t0)], [x, t0],
+        [Lambda(i, log(i))], [], [None, 'log'], [None, x])]
+    assert DifferentialExtension(S.Zero, x)._important_attrs == \
+        (Poly(0, x), Poly(1, x), [Poly(1, x)], [x], [], [], [None], [None])
+    assert DifferentialExtension(tan(atan(x).rewrite(log)), x)._important_attrs == \
+        (Poly(x, x), Poly(1, x), [Poly(1, x)], [x], [], [], [None], [None])
+
+
+def test_DifferentialExtension_Rothstein():
+    # Rothstein's integral
+    f = (2581284541*exp(x) + 1757211400)/(39916800*exp(3*x) +
+    119750400*exp(x)**2 + 119750400*exp(x) + 39916800)*exp(1/(exp(x) + 1) - 10*x)
+    assert DifferentialExtension(f, x)._important_attrs == \
+        (Poly((1757211400 + 2581284541*t0)*t1, t1), Poly(39916800 +
+        119750400*t0 + 119750400*t0**2 + 39916800*t0**3, t1),
+        [Poly(1, x), Poly(t0, t0), Poly(-(10 + 21*t0 + 10*t0**2)/(1 + 2*t0 +
+        t0**2)*t1, t1, domain='ZZ(t0)')], [x, t0, t1],
+        [Lambda(i, exp(i)), Lambda(i, exp(1/(t0 + 1) - 10*i))], [],
+        [None, 'exp', 'exp'], [None, x, 1/(t0 + 1) - 10*x])
+
+
+class _TestingException(Exception):
+    """Dummy Exception class for testing."""
+    pass
+
+
+def test_DecrementLevel():
+    DE = DifferentialExtension(x*log(exp(x) + 1), x)
+    assert DE.level == -1
+    assert DE.t == t1
+    assert DE.d == Poly(t0/(t0 + 1), t1)
+    assert DE.case == 'primitive'
+
+    with DecrementLevel(DE):
+        assert DE.level == -2
+        assert DE.t == t0
+        assert DE.d == Poly(t0, t0)
+        assert DE.case == 'exp'
+
+        with DecrementLevel(DE):
+            assert DE.level == -3
+            assert DE.t == x
+            assert DE.d == Poly(1, x)
+            assert DE.case == 'base'
+
+        assert DE.level == -2
+        assert DE.t == t0
+        assert DE.d == Poly(t0, t0)
+        assert DE.case == 'exp'
+
+    assert DE.level == -1
+    assert DE.t == t1
+    assert DE.d == Poly(t0/(t0 + 1), t1)
+    assert DE.case == 'primitive'
+
+    # Test that __exit__ is called after an exception correctly
+    try:
+        with DecrementLevel(DE):
+            raise _TestingException
+    except _TestingException:
+        pass
+    else:
+        raise AssertionError("Did not raise.")
+
+    assert DE.level == -1
+    assert DE.t == t1
+    assert DE.d == Poly(t0/(t0 + 1), t1)
+    assert DE.case == 'primitive'
+
+
+def test_risch_integrate():
+    assert risch_integrate(t0*exp(x), x) == t0*exp(x)
+    assert risch_integrate(sin(x), x, rewrite_complex=True) == -exp(I*x)/2 - exp(-I*x)/2
+
+    # From my GSoC writeup
+    assert risch_integrate((1 + 2*x**2 + x**4 + 2*x**3*exp(2*x**2))/
+    (x**4*exp(x**2) + 2*x**2*exp(x**2) + exp(x**2)), x) == \
+        NonElementaryIntegral(exp(-x**2), x) + exp(x**2)/(1 + x**2)
+
+
+    assert risch_integrate(0, x) == 0
+
+    # also tests prde_cancel()
+    e1 = log(x/exp(x) + 1)
+    ans1 = risch_integrate(e1, x)
+    assert ans1 == (x*log(x*exp(-x) + 1) + NonElementaryIntegral((x**2 - x)/(x + exp(x)), x))
+    assert cancel(diff(ans1, x) - e1) == 0
+
+    # also tests issue #10798
+    e2 = (log(-1/y)/2 - log(1/y)/2)/y - (log(1 - 1/y)/2 - log(1 + 1/y)/2)/y
+    ans2 = risch_integrate(e2, y)
+    assert ans2 == log(1/y)*log(1 - 1/y)/2 - log(1/y)*log(1 + 1/y)/2 + \
+            NonElementaryIntegral((I*pi*y**2 - 2*y*log(1/y) - I*pi)/(2*y**3 - 2*y), y)
+    assert expand_log(cancel(diff(ans2, y) - e2), force=True) == 0
+
+    # These are tested here in addition to in test_DifferentialExtension above
+    # (symlogs) to test that backsubs works correctly.  The integrals should be
+    # written in terms of the original logarithms in the integrands.
+
+    # XXX: Unfortunately, making backsubs work on this one is a little
+    # trickier, because x**x is converted to exp(x*log(x)), and so log(x**x)
+    # is converted to x*log(x). (x**2*log(x)).subs(x*log(x), log(x**x)) is
+    # smart enough, the issue is that these splits happen at different places
+    # in the algorithm.  Maybe a heuristic is in order
+    assert risch_integrate(log(x**x), x) == x**2*log(x)/2 - x**2/4
+
+    assert risch_integrate(log(x**y), x) == x*log(x**y) - x*y
+    assert risch_integrate(log(sqrt(x)), x) == x*log(sqrt(x)) - x/2
+
+
+def test_risch_integrate_float():
+    assert risch_integrate((-60*exp(x) - 19.2*exp(4*x))*exp(4*x), x) == -2.4*exp(8*x) - 12.0*exp(5*x)
+
+
+def test_NonElementaryIntegral():
+    assert isinstance(risch_integrate(exp(x**2), x), NonElementaryIntegral)
+    assert isinstance(risch_integrate(x**x*log(x), x), NonElementaryIntegral)
+    # Make sure methods of Integral still give back a NonElementaryIntegral
+    assert isinstance(NonElementaryIntegral(x**x*t0, x).subs(t0, log(x)), NonElementaryIntegral)
+
+
+def test_xtothex():
+    a = risch_integrate(x**x, x)
+    assert a == NonElementaryIntegral(x**x, x)
+    assert isinstance(a, NonElementaryIntegral)
+
+
+def test_DifferentialExtension_equality():
+    DE1 = DE2 = DifferentialExtension(log(x), x)
+    assert DE1 == DE2
+
+
+def test_DifferentialExtension_printing():
+    DE = DifferentialExtension(exp(2*x**2) + log(exp(x**2) + 1), x)
+    assert repr(DE) == ("DifferentialExtension(dict([('f', exp(2*x**2) + log(exp(x**2) + 1)), "
+        "('x', x), ('T', [x, t0, t1]), ('D', [Poly(1, x, domain='ZZ'), Poly(2*x*t0, t0, domain='ZZ[x]'), "
+        "Poly(2*t0*x/(t0 + 1), t1, domain='ZZ(x,t0)')]), ('fa', Poly(t1 + t0**2, t1, domain='ZZ[t0]')), "
+        "('fd', Poly(1, t1, domain='ZZ')), ('Tfuncs', [Lambda(i, exp(i**2)), Lambda(i, log(t0 + 1))]), "
+        "('backsubs', []), ('exts', [None, 'exp', 'log']), ('extargs', [None, x**2, t0 + 1]), "
+        "('cases', ['base', 'exp', 'primitive']), ('case', 'primitive'), ('t', t1), "
+        "('d', Poly(2*t0*x/(t0 + 1), t1, domain='ZZ(x,t0)')), ('newf', t0**2 + t1), ('level', -1), "
+        "('dummy', False)]))")
+
+    assert str(DE) == ("DifferentialExtension({fa=Poly(t1 + t0**2, t1, domain='ZZ[t0]'), "
+        "fd=Poly(1, t1, domain='ZZ'), D=[Poly(1, x, domain='ZZ'), Poly(2*x*t0, t0, domain='ZZ[x]'), "
+        "Poly(2*t0*x/(t0 + 1), t1, domain='ZZ(x,t0)')]})")
+
+
+def test_issue_23948():
+    f = (
+        ( (-2*x**5 + 28*x**4 - 144*x**3 + 324*x**2 - 270*x)*log(x)**2
+         +(-4*x**6 + 56*x**5 - 288*x**4 + 648*x**3 - 540*x**2)*log(x)
+         +(2*x**5 - 28*x**4 + 144*x**3 - 324*x**2 + 270*x)*exp(x)
+         +(2*x**5 - 28*x**4 + 144*x**3 - 324*x**2 + 270*x)*log(5)
+         -2*x**7 + 26*x**6 - 116*x**5 + 180*x**4 + 54*x**3 - 270*x**2
+        )*log(-log(x)**2 - 2*x*log(x) + exp(x) + log(5) - x**2 - x)**2
+       +( (4*x**5 - 44*x**4 + 168*x**3 - 216*x**2 - 108*x + 324)*log(x)
+         +(-2*x**5 + 24*x**4 - 108*x**3 + 216*x**2 - 162*x)*exp(x)
+         +4*x**6 - 42*x**5 + 144*x**4 - 108*x**3 - 324*x**2 + 486*x
+        )*log(-log(x)**2 - 2*x*log(x) + exp(x) + log(5) - x**2 - x)
+    )/(x*exp(x)**2*log(x)**2 + 2*x**2*exp(x)**2*log(x) - x*exp(x)**3
+       +(-x*log(5) + x**3 + x**2)*exp(x)**2)
+
+    F = ((x**4 - 12*x**3 + 54*x**2 - 108*x + 81)*exp(-2*x)
+        *log(-x**2 - 2*x*log(x) - x + exp(x) - log(x)**2 + log(5))**2)
+
+    assert risch_integrate(f, x) == F
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_singularityfunctions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_singularityfunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..587e5f104cbf095f851ec538601ca146377b51ae
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_singularityfunctions.py
@@ -0,0 +1,22 @@
+from sympy.integrals.singularityfunctions import singularityintegrate
+from sympy.core.function import Function
+from sympy.core.symbol import symbols
+from sympy.functions.special.singularity_functions import SingularityFunction
+
+x, a, n, y = symbols('x a n y')
+f = Function('f')
+
+
+def test_singularityintegrate():
+    assert singularityintegrate(x, x) is None
+    assert singularityintegrate(x + SingularityFunction(x, 9, 1), x) is None
+
+    assert 4*singularityintegrate(SingularityFunction(x, a, 3), x) == 4*SingularityFunction(x, a, 4)/4
+    assert singularityintegrate(5*SingularityFunction(x, 5, -2), x) == 5*SingularityFunction(x, 5, -1)
+    assert singularityintegrate(6*SingularityFunction(x, 5, -1), x) == 6*SingularityFunction(x, 5, 0)
+    assert singularityintegrate(x*SingularityFunction(x, 0, -1), x) == 0
+    assert singularityintegrate((x - 5)*SingularityFunction(x, 5, -1), x) == 0
+    assert singularityintegrate(SingularityFunction(x, 0, -1) * f(x), x) == f(0) * SingularityFunction(x, 0, 0)
+    assert singularityintegrate(SingularityFunction(x, 1, -1) * f(x), x) == f(1) * SingularityFunction(x, 1, 0)
+    assert singularityintegrate(y*SingularityFunction(x, 0, -1)**2, x) == \
+        y*SingularityFunction(0, 0, -1)*SingularityFunction(x, 0, 0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_transforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..fdf7192594bad532c93ffb31e5b2f05cfd8970f1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_transforms.py
@@ -0,0 +1,637 @@
+from sympy.integrals.transforms import (
+    mellin_transform, inverse_mellin_transform,
+    fourier_transform, inverse_fourier_transform,
+    sine_transform, inverse_sine_transform,
+    cosine_transform, inverse_cosine_transform,
+    hankel_transform, inverse_hankel_transform,
+    FourierTransform, SineTransform, CosineTransform, InverseFourierTransform,
+    InverseSineTransform, InverseCosineTransform, IntegralTransformError)
+from sympy.integrals.laplace import (
+    laplace_transform, inverse_laplace_transform)
+from sympy.core.function import Function, expand_mul
+from sympy.core import EulerGamma
+from sympy.core.numbers import I, Rational, oo, pi
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import re, unpolarify
+from sympy.functions.elementary.exponential import exp, exp_polar, log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import atan, cos, sin, tan
+from sympy.functions.special.bessel import besseli, besselj, besselk, bessely
+from sympy.functions.special.delta_functions import Heaviside
+from sympy.functions.special.error_functions import erf, expint
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import meijerg
+from sympy.simplify.gammasimp import gammasimp
+from sympy.simplify.hyperexpand import hyperexpand
+from sympy.simplify.trigsimp import trigsimp
+from sympy.testing.pytest import XFAIL, slow, skip, raises
+from sympy.abc import x, s, a, b, c, d
+
+
+nu, beta, rho = symbols('nu beta rho')
+
+
+def test_undefined_function():
+    from sympy.integrals.transforms import MellinTransform
+    f = Function('f')
+    assert mellin_transform(f(x), x, s) == MellinTransform(f(x), x, s)
+    assert mellin_transform(f(x) + exp(-x), x, s) == \
+        (MellinTransform(f(x), x, s) + gamma(s + 1)/s, (0, oo), True)
+
+
+def test_free_symbols():
+    f = Function('f')
+    assert mellin_transform(f(x), x, s).free_symbols == {s}
+    assert mellin_transform(f(x)*a, x, s).free_symbols == {s, a}
+
+
+def test_as_integral():
+    from sympy.integrals.integrals import Integral
+    f = Function('f')
+    assert mellin_transform(f(x), x, s).rewrite('Integral') == \
+        Integral(x**(s - 1)*f(x), (x, 0, oo))
+    assert fourier_transform(f(x), x, s).rewrite('Integral') == \
+        Integral(f(x)*exp(-2*I*pi*s*x), (x, -oo, oo))
+    assert laplace_transform(f(x), x, s, noconds=True).rewrite('Integral') == \
+        Integral(f(x)*exp(-s*x), (x, 0, oo))
+    assert str(2*pi*I*inverse_mellin_transform(f(s), s, x, (a, b)).rewrite('Integral')) \
+        == "Integral(f(s)/x**s, (s, _c - oo*I, _c + oo*I))"
+    assert str(2*pi*I*inverse_laplace_transform(f(s), s, x).rewrite('Integral')) == \
+        "Integral(f(s)*exp(s*x), (s, _c - oo*I, _c + oo*I))"
+    assert inverse_fourier_transform(f(s), s, x).rewrite('Integral') == \
+        Integral(f(s)*exp(2*I*pi*s*x), (s, -oo, oo))
+
+# NOTE this is stuck in risch because meijerint cannot handle it
+
+
+@slow
+@XFAIL
+def test_mellin_transform_fail():
+    skip("Risch takes forever.")
+
+    MT = mellin_transform
+
+    bpos = symbols('b', positive=True)
+    # bneg = symbols('b', negative=True)
+
+    expr = (sqrt(x + b**2) + b)**a/sqrt(x + b**2)
+    # TODO does not work with bneg, argument wrong. Needs changes to matching.
+    assert MT(expr.subs(b, -bpos), x, s) == \
+        ((-1)**(a + 1)*2**(a + 2*s)*bpos**(a + 2*s - 1)*gamma(a + s)
+         *gamma(1 - a - 2*s)/gamma(1 - s),
+            (-re(a), -re(a)/2 + S.Half), True)
+
+    expr = (sqrt(x + b**2) + b)**a
+    assert MT(expr.subs(b, -bpos), x, s) == \
+        (
+            2**(a + 2*s)*a*bpos**(a + 2*s)*gamma(-a - 2*
+                   s)*gamma(a + s)/gamma(-s + 1),
+            (-re(a), -re(a)/2), True)
+
+    # Test exponent 1:
+    assert MT(expr.subs({b: -bpos, a: 1}), x, s) == \
+        (-bpos**(2*s + 1)*gamma(s)*gamma(-s - S.Half)/(2*sqrt(pi)),
+            (-1, Rational(-1, 2)), True)
+
+
+def test_mellin_transform():
+    from sympy.functions.elementary.miscellaneous import (Max, Min)
+    MT = mellin_transform
+
+    bpos = symbols('b', positive=True)
+
+    # 8.4.2
+    assert MT(x**nu*Heaviside(x - 1), x, s) == \
+        (-1/(nu + s), (-oo, -re(nu)), True)
+    assert MT(x**nu*Heaviside(1 - x), x, s) == \
+        (1/(nu + s), (-re(nu), oo), True)
+
+    assert MT((1 - x)**(beta - 1)*Heaviside(1 - x), x, s) == \
+        (gamma(beta)*gamma(s)/gamma(beta + s), (0, oo), re(beta) > 0)
+    assert MT((x - 1)**(beta - 1)*Heaviside(x - 1), x, s) == \
+        (gamma(beta)*gamma(1 - beta - s)/gamma(1 - s),
+            (-oo, 1 - re(beta)), re(beta) > 0)
+
+    assert MT((1 + x)**(-rho), x, s) == \
+        (gamma(s)*gamma(rho - s)/gamma(rho), (0, re(rho)), True)
+
+    assert MT(abs(1 - x)**(-rho), x, s) == (
+        2*sin(pi*rho/2)*gamma(1 - rho)*
+        cos(pi*(s - rho/2))*gamma(s)*gamma(rho-s)/pi,
+        (0, re(rho)), re(rho) < 1)
+    mt = MT((1 - x)**(beta - 1)*Heaviside(1 - x)
+            + a*(x - 1)**(beta - 1)*Heaviside(x - 1), x, s)
+    assert mt[1], mt[2] == ((0, -re(beta) + 1), re(beta) > 0)
+
+    assert MT((x**a - b**a)/(x - b), x, s)[0] == \
+        pi*b**(a + s - 1)*sin(pi*a)/(sin(pi*s)*sin(pi*(a + s)))
+    assert MT((x**a - bpos**a)/(x - bpos), x, s) == \
+        (pi*bpos**(a + s - 1)*sin(pi*a)/(sin(pi*s)*sin(pi*(a + s))),
+            (Max(0, -re(a)), Min(1, 1 - re(a))), True)
+
+    expr = (sqrt(x + b**2) + b)**a
+    assert MT(expr.subs(b, bpos), x, s) == \
+        (-a*(2*bpos)**(a + 2*s)*gamma(s)*gamma(-a - 2*s)/gamma(-a - s + 1),
+            (0, -re(a)/2), True)
+
+    expr = (sqrt(x + b**2) + b)**a/sqrt(x + b**2)
+    assert MT(expr.subs(b, bpos), x, s) == \
+        (2**(a + 2*s)*bpos**(a + 2*s - 1)*gamma(s)
+                                         *gamma(1 - a - 2*s)/gamma(1 - a - s),
+            (0, -re(a)/2 + S.Half), True)
+
+    # 8.4.2
+    assert MT(exp(-x), x, s) == (gamma(s), (0, oo), True)
+    assert MT(exp(-1/x), x, s) == (gamma(-s), (-oo, 0), True)
+
+    # 8.4.5
+    assert MT(log(x)**4*Heaviside(1 - x), x, s) == (24/s**5, (0, oo), True)
+    assert MT(log(x)**3*Heaviside(x - 1), x, s) == (6/s**4, (-oo, 0), True)
+    assert MT(log(x + 1), x, s) == (pi/(s*sin(pi*s)), (-1, 0), True)
+    assert MT(log(1/x + 1), x, s) == (pi/(s*sin(pi*s)), (0, 1), True)
+    assert MT(log(abs(1 - x)), x, s) == (pi/(s*tan(pi*s)), (-1, 0), True)
+    assert MT(log(abs(1 - 1/x)), x, s) == (pi/(s*tan(pi*s)), (0, 1), True)
+
+    # 8.4.14
+    assert MT(erf(sqrt(x)), x, s) == \
+        (-gamma(s + S.Half)/(sqrt(pi)*s), (Rational(-1, 2), 0), True)
+
+
+def test_mellin_transform2():
+    MT = mellin_transform
+    # TODO we cannot currently do these (needs summation of 3F2(-1))
+    #      this also implies that they cannot be written as a single g-function
+    #      (although this is possible)
+    mt = MT(log(x)/(x + 1), x, s)
+    assert mt[1:] == ((0, 1), True)
+    assert not hyperexpand(mt[0], allow_hyper=True).has(meijerg)
+    mt = MT(log(x)**2/(x + 1), x, s)
+    assert mt[1:] == ((0, 1), True)
+    assert not hyperexpand(mt[0], allow_hyper=True).has(meijerg)
+    mt = MT(log(x)/(x + 1)**2, x, s)
+    assert mt[1:] == ((0, 2), True)
+    assert not hyperexpand(mt[0], allow_hyper=True).has(meijerg)
+
+
+@slow
+def test_mellin_transform_bessel():
+    from sympy.functions.elementary.miscellaneous import Max
+    MT = mellin_transform
+
+    # 8.4.19
+    assert MT(besselj(a, 2*sqrt(x)), x, s) == \
+        (gamma(a/2 + s)/gamma(a/2 - s + 1), (-re(a)/2, Rational(3, 4)), True)
+    assert MT(sin(sqrt(x))*besselj(a, sqrt(x)), x, s) == \
+        (2**a*gamma(-2*s + S.Half)*gamma(a/2 + s + S.Half)/(
+        gamma(-a/2 - s + 1)*gamma(a - 2*s + 1)), (
+        -re(a)/2 - S.Half, Rational(1, 4)), True)
+    assert MT(cos(sqrt(x))*besselj(a, sqrt(x)), x, s) == \
+        (2**a*gamma(a/2 + s)*gamma(-2*s + S.Half)/(
+        gamma(-a/2 - s + S.Half)*gamma(a - 2*s + 1)), (
+        -re(a)/2, Rational(1, 4)), True)
+    assert MT(besselj(a, sqrt(x))**2, x, s) == \
+        (gamma(a + s)*gamma(S.Half - s)
+         / (sqrt(pi)*gamma(1 - s)*gamma(1 + a - s)),
+            (-re(a), S.Half), True)
+    assert MT(besselj(a, sqrt(x))*besselj(-a, sqrt(x)), x, s) == \
+        (gamma(s)*gamma(S.Half - s)
+         / (sqrt(pi)*gamma(1 - a - s)*gamma(1 + a - s)),
+            (0, S.Half), True)
+    # NOTE: prudnikov gives the strip below as (1/2 - re(a), 1). As far as
+    #       I can see this is wrong (since besselj(z) ~ 1/sqrt(z) for z large)
+    assert MT(besselj(a - 1, sqrt(x))*besselj(a, sqrt(x)), x, s) == \
+        (gamma(1 - s)*gamma(a + s - S.Half)
+         / (sqrt(pi)*gamma(Rational(3, 2) - s)*gamma(a - s + S.Half)),
+            (S.Half - re(a), S.Half), True)
+    assert MT(besselj(a, sqrt(x))*besselj(b, sqrt(x)), x, s) == \
+        (4**s*gamma(1 - 2*s)*gamma((a + b)/2 + s)
+         / (gamma(1 - s + (b - a)/2)*gamma(1 - s + (a - b)/2)
+            *gamma( 1 - s + (a + b)/2)),
+            (-(re(a) + re(b))/2, S.Half), True)
+    assert MT(besselj(a, sqrt(x))**2 + besselj(-a, sqrt(x))**2, x, s)[1:] == \
+        ((Max(re(a), -re(a)), S.Half), True)
+
+    # Section 8.4.20
+    assert MT(bessely(a, 2*sqrt(x)), x, s) == \
+        (-cos(pi*(a/2 - s))*gamma(s - a/2)*gamma(s + a/2)/pi,
+            (Max(-re(a)/2, re(a)/2), Rational(3, 4)), True)
+    assert MT(sin(sqrt(x))*bessely(a, sqrt(x)), x, s) == \
+        (-4**s*sin(pi*(a/2 - s))*gamma(S.Half - 2*s)
+         * gamma((1 - a)/2 + s)*gamma((1 + a)/2 + s)
+         / (sqrt(pi)*gamma(1 - s - a/2)*gamma(1 - s + a/2)),
+            (Max(-(re(a) + 1)/2, (re(a) - 1)/2), Rational(1, 4)), True)
+    assert MT(cos(sqrt(x))*bessely(a, sqrt(x)), x, s) == \
+        (-4**s*cos(pi*(a/2 - s))*gamma(s - a/2)*gamma(s + a/2)*gamma(S.Half - 2*s)
+         / (sqrt(pi)*gamma(S.Half - s - a/2)*gamma(S.Half - s + a/2)),
+            (Max(-re(a)/2, re(a)/2), Rational(1, 4)), True)
+    assert MT(besselj(a, sqrt(x))*bessely(a, sqrt(x)), x, s) == \
+        (-cos(pi*s)*gamma(s)*gamma(a + s)*gamma(S.Half - s)
+         / (pi**S('3/2')*gamma(1 + a - s)),
+            (Max(-re(a), 0), S.Half), True)
+    assert MT(besselj(a, sqrt(x))*bessely(b, sqrt(x)), x, s) == \
+        (-4**s*cos(pi*(a/2 - b/2 + s))*gamma(1 - 2*s)
+         * gamma(a/2 - b/2 + s)*gamma(a/2 + b/2 + s)
+         / (pi*gamma(a/2 - b/2 - s + 1)*gamma(a/2 + b/2 - s + 1)),
+            (Max((-re(a) + re(b))/2, (-re(a) - re(b))/2), S.Half), True)
+    # NOTE bessely(a, sqrt(x))**2 and bessely(a, sqrt(x))*bessely(b, sqrt(x))
+    # are a mess (no matter what way you look at it ...)
+    assert MT(bessely(a, sqrt(x))**2, x, s)[1:] == \
+             ((Max(-re(a), 0, re(a)), S.Half), True)
+
+    # Section 8.4.22
+    # TODO we can't do any of these (delicate cancellation)
+
+    # Section 8.4.23
+    assert MT(besselk(a, 2*sqrt(x)), x, s) == \
+        (gamma(
+         s - a/2)*gamma(s + a/2)/2, (Max(-re(a)/2, re(a)/2), oo), True)
+    assert MT(besselj(a, 2*sqrt(2*sqrt(x)))*besselk(
+        a, 2*sqrt(2*sqrt(x))), x, s) == (4**(-s)*gamma(2*s)*
+        gamma(a/2 + s)/(2*gamma(a/2 - s + 1)), (Max(0, -re(a)/2), oo), True)
+    # TODO bessely(a, x)*besselk(a, x) is a mess
+    assert MT(besseli(a, sqrt(x))*besselk(a, sqrt(x)), x, s) == \
+        (gamma(s)*gamma(
+        a + s)*gamma(-s + S.Half)/(2*sqrt(pi)*gamma(a - s + 1)),
+        (Max(-re(a), 0), S.Half), True)
+    assert MT(besseli(b, sqrt(x))*besselk(a, sqrt(x)), x, s) == \
+        (2**(2*s - 1)*gamma(-2*s + 1)*gamma(-a/2 + b/2 + s)* \
+        gamma(a/2 + b/2 + s)/(gamma(-a/2 + b/2 - s + 1)* \
+        gamma(a/2 + b/2 - s + 1)), (Max(-re(a)/2 - re(b)/2, \
+        re(a)/2 - re(b)/2), S.Half), True)
+
+    # TODO products of besselk are a mess
+
+    mt = MT(exp(-x/2)*besselk(a, x/2), x, s)
+    mt0 = gammasimp(trigsimp(gammasimp(mt[0].expand(func=True))))
+    assert mt0 == 2*pi**Rational(3, 2)*cos(pi*s)*gamma(S.Half - s)/(
+        (cos(2*pi*a) - cos(2*pi*s))*gamma(-a - s + 1)*gamma(a - s + 1))
+    assert mt[1:] == ((Max(-re(a), re(a)), oo), True)
+    # TODO exp(x/2)*besselk(a, x/2) [etc] cannot currently be done
+    # TODO various strange products of special orders
+
+
+@slow
+def test_expint():
+    from sympy.functions.elementary.miscellaneous import Max
+    from sympy.functions.special.error_functions import Ci, E1, Si
+    from sympy.simplify.simplify import simplify
+
+    aneg = Symbol('a', negative=True)
+    u = Symbol('u', polar=True)
+
+    assert mellin_transform(E1(x), x, s) == (gamma(s)/s, (0, oo), True)
+    assert inverse_mellin_transform(gamma(s)/s, s, x,
+              (0, oo)).rewrite(expint).expand() == E1(x)
+    assert mellin_transform(expint(a, x), x, s) == \
+        (gamma(s)/(a + s - 1), (Max(1 - re(a), 0), oo), True)
+    # XXX IMT has hickups with complicated strips ...
+    assert simplify(unpolarify(
+                    inverse_mellin_transform(gamma(s)/(aneg + s - 1), s, x,
+                  (1 - aneg, oo)).rewrite(expint).expand(func=True))) == \
+        expint(aneg, x)
+
+    assert mellin_transform(Si(x), x, s) == \
+        (-2**s*sqrt(pi)*gamma(s/2 + S.Half)/(
+        2*s*gamma(-s/2 + 1)), (-1, 0), True)
+    assert inverse_mellin_transform(-2**s*sqrt(pi)*gamma((s + 1)/2)
+                                    /(2*s*gamma(-s/2 + 1)), s, x, (-1, 0)) \
+        == Si(x)
+
+    assert mellin_transform(Ci(sqrt(x)), x, s) == \
+        (-2**(2*s - 1)*sqrt(pi)*gamma(s)/(s*gamma(-s + S.Half)), (0, 1), True)
+    assert inverse_mellin_transform(
+        -4**s*sqrt(pi)*gamma(s)/(2*s*gamma(-s + S.Half)),
+        s, u, (0, 1)).expand() == Ci(sqrt(u))
+
+
+@slow
+def test_inverse_mellin_transform():
+    from sympy.core.function import expand
+    from sympy.functions.elementary.miscellaneous import (Max, Min)
+    from sympy.functions.elementary.trigonometric import cot
+    from sympy.simplify.powsimp import powsimp
+    from sympy.simplify.simplify import simplify
+    IMT = inverse_mellin_transform
+
+    assert IMT(gamma(s), s, x, (0, oo)) == exp(-x)
+    assert IMT(gamma(-s), s, x, (-oo, 0)) == exp(-1/x)
+    assert simplify(IMT(s/(2*s**2 - 2), s, x, (2, oo))) == \
+        (x**2 + 1)*Heaviside(1 - x)/(4*x)
+
+    # test passing "None"
+    assert IMT(1/(s**2 - 1), s, x, (-1, None)) == \
+        -x*Heaviside(-x + 1)/2 - Heaviside(x - 1)/(2*x)
+    assert IMT(1/(s**2 - 1), s, x, (None, 1)) == \
+        -x*Heaviside(-x + 1)/2 - Heaviside(x - 1)/(2*x)
+
+    # test expansion of sums
+    assert IMT(gamma(s) + gamma(s - 1), s, x, (1, oo)) == (x + 1)*exp(-x)/x
+
+    # test factorisation of polys
+    r = symbols('r', real=True)
+    assert IMT(1/(s**2 + 1), s, exp(-x), (None, oo)
+              ).subs(x, r).rewrite(sin).simplify() \
+        == sin(r)*Heaviside(1 - exp(-r))
+
+    # test multiplicative substitution
+    _a, _b = symbols('a b', positive=True)
+    assert IMT(_b**(-s/_a)*factorial(s/_a)/s, s, x, (0, oo)) == exp(-_b*x**_a)
+    assert IMT(factorial(_a/_b + s/_b)/(_a + s), s, x, (-_a, oo)) == x**_a*exp(-x**_b)
+
+    def simp_pows(expr):
+        return simplify(powsimp(expand_mul(expr, deep=False), force=True)).replace(exp_polar, exp)
+
+    # Now test the inverses of all direct transforms tested above
+
+    # Section 8.4.2
+    nu = symbols('nu', real=True)
+    assert IMT(-1/(nu + s), s, x, (-oo, None)) == x**nu*Heaviside(x - 1)
+    assert IMT(1/(nu + s), s, x, (None, oo)) == x**nu*Heaviside(1 - x)
+    assert simp_pows(IMT(gamma(beta)*gamma(s)/gamma(s + beta), s, x, (0, oo))) \
+        == (1 - x)**(beta - 1)*Heaviside(1 - x)
+    assert simp_pows(IMT(gamma(beta)*gamma(1 - beta - s)/gamma(1 - s),
+                         s, x, (-oo, None))) \
+        == (x - 1)**(beta - 1)*Heaviside(x - 1)
+    assert simp_pows(IMT(gamma(s)*gamma(rho - s)/gamma(rho), s, x, (0, None))) \
+        == (1/(x + 1))**rho
+    expr = IMT(d**c*d**(s - 1)*sin(pi*c)
+                         *gamma(s)*gamma(s + c)*gamma(1 - s)*gamma(1 - s - c)/pi,
+                         s, x, (Max(-re(c), 0), Min(1 - re(c), 1)))
+    assert powsimp(expand_mul(expr, deep=False)).replace(exp_polar, exp).simplify() \
+        == (-d**c + x**c)/(-d + x)
+
+    assert simplify(IMT(1/sqrt(pi)*(-c/2)*gamma(s)*gamma((1 - c)/2 - s)
+                        *gamma(-c/2 - s)/gamma(1 - c - s),
+                        s, x, (0, -re(c)/2))) == \
+        (1 + sqrt(x + 1))**c
+    assert simplify(IMT(2**(a + 2*s)*b**(a + 2*s - 1)*gamma(s)*gamma(1 - a - 2*s)
+                        /gamma(1 - a - s), s, x, (0, (-re(a) + 1)/2))) == \
+        b**(a - 1)*(b**2*(sqrt(1 + x/b**2) + 1)**a + x*(sqrt(1 + x/b**2) + 1
+        )**(a - 1))/(b**2 + x)
+    assert simplify(IMT(-2**(c + 2*s)*c*b**(c + 2*s)*gamma(s)*gamma(-c - 2*s)
+                        / gamma(-c - s + 1), s, x, (0, -re(c)/2))) == \
+        b**c*(sqrt(1 + x/b**2) + 1)**c
+
+    # Section 8.4.5
+    assert IMT(24/s**5, s, x, (0, oo)) == log(x)**4*Heaviside(1 - x)
+    assert expand(IMT(6/s**4, s, x, (-oo, 0)), force=True) == \
+        log(x)**3*Heaviside(x - 1)
+    assert IMT(pi/(s*sin(pi*s)), s, x, (-1, 0)) == log(x + 1)
+    assert IMT(pi/(s*sin(pi*s/2)), s, x, (-2, 0)) == log(x**2 + 1)
+    assert IMT(pi/(s*sin(2*pi*s)), s, x, (Rational(-1, 2), 0)) == log(sqrt(x) + 1)
+    assert IMT(pi/(s*sin(pi*s)), s, x, (0, 1)) == log(1 + 1/x)
+
+    # TODO
+    def mysimp(expr):
+        from sympy.core.function import expand
+        from sympy.simplify.powsimp import powsimp
+        from sympy.simplify.simplify import logcombine
+        return expand(
+            powsimp(logcombine(expr, force=True), force=True, deep=True),
+            force=True).replace(exp_polar, exp)
+
+    assert mysimp(mysimp(IMT(pi/(s*tan(pi*s)), s, x, (-1, 0)))) in [
+        log(1 - x)*Heaviside(1 - x) + log(x - 1)*Heaviside(x - 1),
+        log(x)*Heaviside(x - 1) + log(1 - 1/x)*Heaviside(x - 1) + log(-x +
+        1)*Heaviside(-x + 1)]
+    # test passing cot
+    assert mysimp(IMT(pi*cot(pi*s)/s, s, x, (0, 1))) in [
+        log(1/x - 1)*Heaviside(1 - x) + log(1 - 1/x)*Heaviside(x - 1),
+        -log(x)*Heaviside(-x + 1) + log(1 - 1/x)*Heaviside(x - 1) + log(-x +
+        1)*Heaviside(-x + 1), ]
+
+    # 8.4.14
+    assert IMT(-gamma(s + S.Half)/(sqrt(pi)*s), s, x, (Rational(-1, 2), 0)) == \
+        erf(sqrt(x))
+
+    # 8.4.19
+    assert simplify(IMT(gamma(a/2 + s)/gamma(a/2 - s + 1), s, x, (-re(a)/2, Rational(3, 4)))) \
+        == besselj(a, 2*sqrt(x))
+    assert simplify(IMT(2**a*gamma(S.Half - 2*s)*gamma(s + (a + 1)/2)
+                      / (gamma(1 - s - a/2)*gamma(1 - 2*s + a)),
+                      s, x, (-(re(a) + 1)/2, Rational(1, 4)))) == \
+        sin(sqrt(x))*besselj(a, sqrt(x))
+    assert simplify(IMT(2**a*gamma(a/2 + s)*gamma(S.Half - 2*s)
+                      / (gamma(S.Half - s - a/2)*gamma(1 - 2*s + a)),
+                      s, x, (-re(a)/2, Rational(1, 4)))) == \
+        cos(sqrt(x))*besselj(a, sqrt(x))
+    # TODO this comes out as an amazing mess, but simplifies nicely
+    assert simplify(IMT(gamma(a + s)*gamma(S.Half - s)
+                      / (sqrt(pi)*gamma(1 - s)*gamma(1 + a - s)),
+                      s, x, (-re(a), S.Half))) == \
+        besselj(a, sqrt(x))**2
+    assert simplify(IMT(gamma(s)*gamma(S.Half - s)
+                      / (sqrt(pi)*gamma(1 - s - a)*gamma(1 + a - s)),
+                      s, x, (0, S.Half))) == \
+        besselj(-a, sqrt(x))*besselj(a, sqrt(x))
+    assert simplify(IMT(4**s*gamma(-2*s + 1)*gamma(a/2 + b/2 + s)
+                      / (gamma(-a/2 + b/2 - s + 1)*gamma(a/2 - b/2 - s + 1)
+                         *gamma(a/2 + b/2 - s + 1)),
+                      s, x, (-(re(a) + re(b))/2, S.Half))) == \
+        besselj(a, sqrt(x))*besselj(b, sqrt(x))
+
+    # Section 8.4.20
+    # TODO this can be further simplified!
+    assert simplify(IMT(-2**(2*s)*cos(pi*a/2 - pi*b/2 + pi*s)*gamma(-2*s + 1) *
+                    gamma(a/2 - b/2 + s)*gamma(a/2 + b/2 + s) /
+                    (pi*gamma(a/2 - b/2 - s + 1)*gamma(a/2 + b/2 - s + 1)),
+                    s, x,
+                    (Max(-re(a)/2 - re(b)/2, -re(a)/2 + re(b)/2), S.Half))) == \
+                    besselj(a, sqrt(x))*-(besselj(-b, sqrt(x)) -
+                    besselj(b, sqrt(x))*cos(pi*b))/sin(pi*b)
+    # TODO more
+
+    # for coverage
+
+    assert IMT(pi/cos(pi*s), s, x, (0, S.Half)) == sqrt(x)/(x + 1)
+
+
+def test_fourier_transform():
+    from sympy.core.function import (expand, expand_complex, expand_trig)
+    from sympy.polys.polytools import factor
+    from sympy.simplify.simplify import simplify
+    FT = fourier_transform
+    IFT = inverse_fourier_transform
+
+    def simp(x):
+        return simplify(expand_trig(expand_complex(expand(x))))
+
+    def sinc(x):
+        return sin(pi*x)/(pi*x)
+    k = symbols('k', real=True)
+    f = Function("f")
+
+    # TODO for this to work with real a, need to expand abs(a*x) to abs(a)*abs(x)
+    a = symbols('a', positive=True)
+    b = symbols('b', positive=True)
+
+    posk = symbols('posk', positive=True)
+
+    # Test unevaluated form
+    assert fourier_transform(f(x), x, k) == FourierTransform(f(x), x, k)
+    assert inverse_fourier_transform(
+        f(k), k, x) == InverseFourierTransform(f(k), k, x)
+
+    # basic examples from wikipedia
+    assert simp(FT(Heaviside(1 - abs(2*a*x)), x, k)) == sinc(k/a)/a
+    # TODO IFT is a *mess*
+    assert simp(FT(Heaviside(1 - abs(a*x))*(1 - abs(a*x)), x, k)) == sinc(k/a)**2/a
+    # TODO IFT
+
+    assert factor(FT(exp(-a*x)*Heaviside(x), x, k), extension=I) == \
+        1/(a + 2*pi*I*k)
+    # NOTE: the ift comes out in pieces
+    assert IFT(1/(a + 2*pi*I*x), x, posk,
+            noconds=False) == (exp(-a*posk), True)
+    assert IFT(1/(a + 2*pi*I*x), x, -posk,
+            noconds=False) == (0, True)
+    assert IFT(1/(a + 2*pi*I*x), x, symbols('k', negative=True),
+            noconds=False) == (0, True)
+    # TODO IFT without factoring comes out as meijer g
+
+    assert factor(FT(x*exp(-a*x)*Heaviside(x), x, k), extension=I) == \
+        1/(a + 2*pi*I*k)**2
+    assert FT(exp(-a*x)*sin(b*x)*Heaviside(x), x, k) == \
+        b/(b**2 + (a + 2*I*pi*k)**2)
+
+    assert FT(exp(-a*x**2), x, k) == sqrt(pi)*exp(-pi**2*k**2/a)/sqrt(a)
+    assert IFT(sqrt(pi/a)*exp(-(pi*k)**2/a), k, x) == exp(-a*x**2)
+    assert FT(exp(-a*abs(x)), x, k) == 2*a/(a**2 + 4*pi**2*k**2)
+    # TODO IFT (comes out as meijer G)
+
+    # TODO besselj(n, x), n an integer > 0 actually can be done...
+
+    # TODO are there other common transforms (no distributions!)?
+
+
+def test_sine_transform():
+    t = symbols("t")
+    w = symbols("w")
+    a = symbols("a")
+    f = Function("f")
+
+    # Test unevaluated form
+    assert sine_transform(f(t), t, w) == SineTransform(f(t), t, w)
+    assert inverse_sine_transform(
+        f(w), w, t) == InverseSineTransform(f(w), w, t)
+
+    assert sine_transform(1/sqrt(t), t, w) == 1/sqrt(w)
+    assert inverse_sine_transform(1/sqrt(w), w, t) == 1/sqrt(t)
+
+    assert sine_transform((1/sqrt(t))**3, t, w) == 2*sqrt(w)
+
+    assert sine_transform(t**(-a), t, w) == 2**(
+        -a + S.Half)*w**(a - 1)*gamma(-a/2 + 1)/gamma((a + 1)/2)
+    assert inverse_sine_transform(2**(-a + S(
+        1)/2)*w**(a - 1)*gamma(-a/2 + 1)/gamma(a/2 + S.Half), w, t) == t**(-a)
+
+    assert sine_transform(
+        exp(-a*t), t, w) == sqrt(2)*w/(sqrt(pi)*(a**2 + w**2))
+    assert inverse_sine_transform(
+        sqrt(2)*w/(sqrt(pi)*(a**2 + w**2)), w, t) == exp(-a*t)
+
+    assert sine_transform(
+        log(t)/t, t, w) == sqrt(2)*sqrt(pi)*-(log(w**2) + 2*EulerGamma)/4
+
+    assert sine_transform(
+        t*exp(-a*t**2), t, w) == sqrt(2)*w*exp(-w**2/(4*a))/(4*a**Rational(3, 2))
+    assert inverse_sine_transform(
+        sqrt(2)*w*exp(-w**2/(4*a))/(4*a**Rational(3, 2)), w, t) == t*exp(-a*t**2)
+
+
+def test_cosine_transform():
+    from sympy.functions.special.error_functions import (Ci, Si)
+
+    t = symbols("t")
+    w = symbols("w")
+    a = symbols("a")
+    f = Function("f")
+
+    # Test unevaluated form
+    assert cosine_transform(f(t), t, w) == CosineTransform(f(t), t, w)
+    assert inverse_cosine_transform(
+        f(w), w, t) == InverseCosineTransform(f(w), w, t)
+
+    assert cosine_transform(1/sqrt(t), t, w) == 1/sqrt(w)
+    assert inverse_cosine_transform(1/sqrt(w), w, t) == 1/sqrt(t)
+
+    assert cosine_transform(1/(
+        a**2 + t**2), t, w) == sqrt(2)*sqrt(pi)*exp(-a*w)/(2*a)
+
+    assert cosine_transform(t**(
+        -a), t, w) == 2**(-a + S.Half)*w**(a - 1)*gamma((-a + 1)/2)/gamma(a/2)
+    assert inverse_cosine_transform(2**(-a + S(
+        1)/2)*w**(a - 1)*gamma(-a/2 + S.Half)/gamma(a/2), w, t) == t**(-a)
+
+    assert cosine_transform(
+        exp(-a*t), t, w) == sqrt(2)*a/(sqrt(pi)*(a**2 + w**2))
+    assert inverse_cosine_transform(
+        sqrt(2)*a/(sqrt(pi)*(a**2 + w**2)), w, t) == exp(-a*t)
+
+    assert cosine_transform(exp(-a*sqrt(t))*cos(a*sqrt(
+        t)), t, w) == a*exp(-a**2/(2*w))/(2*w**Rational(3, 2))
+
+    assert cosine_transform(1/(a + t), t, w) == sqrt(2)*(
+        (-2*Si(a*w) + pi)*sin(a*w)/2 - cos(a*w)*Ci(a*w))/sqrt(pi)
+    assert inverse_cosine_transform(sqrt(2)*meijerg(((S.Half, 0), ()), (
+        (S.Half, 0, 0), (S.Half,)), a**2*w**2/4)/(2*pi), w, t) == 1/(a + t)
+
+    assert cosine_transform(1/sqrt(a**2 + t**2), t, w) == sqrt(2)*meijerg(
+        ((S.Half,), ()), ((0, 0), (S.Half,)), a**2*w**2/4)/(2*sqrt(pi))
+    assert inverse_cosine_transform(sqrt(2)*meijerg(((S.Half,), ()), ((0, 0), (S.Half,)), a**2*w**2/4)/(2*sqrt(pi)), w, t) == 1/(t*sqrt(a**2/t**2 + 1))
+
+
+def test_hankel_transform():
+    r = Symbol("r")
+    k = Symbol("k")
+    nu = Symbol("nu")
+    m = Symbol("m")
+    a = symbols("a")
+
+    assert hankel_transform(1/r, r, k, 0) == 1/k
+    assert inverse_hankel_transform(1/k, k, r, 0) == 1/r
+
+    assert hankel_transform(
+        1/r**m, r, k, 0) == 2**(-m + 1)*k**(m - 2)*gamma(-m/2 + 1)/gamma(m/2)
+    assert inverse_hankel_transform(
+        2**(-m + 1)*k**(m - 2)*gamma(-m/2 + 1)/gamma(m/2), k, r, 0) == r**(-m)
+
+    assert hankel_transform(1/r**m, r, k, nu) == (
+        2*2**(-m)*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2))
+    assert inverse_hankel_transform(2**(-m + 1)*k**(
+        m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2), k, r, nu) == r**(-m)
+
+    assert hankel_transform(r**nu*exp(-a*r), r, k, nu) == \
+        2**(nu + 1)*a*k**(-nu - 3)*(a**2/k**2 + 1)**(-nu - S(
+                                                     3)/2)*gamma(nu + Rational(3, 2))/sqrt(pi)
+    assert inverse_hankel_transform(
+        2**(nu + 1)*a*k**(-nu - 3)*(a**2/k**2 + 1)**(-nu - Rational(3, 2))*gamma(
+        nu + Rational(3, 2))/sqrt(pi), k, r, nu) == r**nu*exp(-a*r)
+
+
+def test_issue_7181():
+    assert mellin_transform(1/(1 - x), x, s) != None
+
+
+def test_issue_8882():
+    # This is the original test.
+    # from sympy import diff, Integral, integrate
+    # r = Symbol('r')
+    # psi = 1/r*sin(r)*exp(-(a0*r))
+    # h = -1/2*diff(psi, r, r) - 1/r*psi
+    # f = 4*pi*psi*h*r**2
+    # assert integrate(f, (r, -oo, 3), meijerg=True).has(Integral) == True
+
+    # To save time, only the critical part is included.
+    F = -a**(-s + 1)*(4 + 1/a**2)**(-s/2)*sqrt(1/a**2)*exp(-s*I*pi)* \
+        sin(s*atan(sqrt(1/a**2)/2))*gamma(s)
+    raises(IntegralTransformError, lambda:
+        inverse_mellin_transform(F, s, x, (-1, oo),
+        **{'as_meijerg': True, 'needeval': True}))
+
+
+def test_issue_12591():
+    x, y = symbols("x y", real=True)
+    assert fourier_transform(exp(x), x, y) == FourierTransform(exp(x), x, y)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_trigonometry.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_trigonometry.py
new file mode 100644
index 0000000000000000000000000000000000000000..857c8503c5aa690d66e9cdab49730b4ea655a52c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/tests/test_trigonometry.py
@@ -0,0 +1,98 @@
+from sympy.core import Ne, Rational, Symbol
+from sympy.functions import sin, cos, tan, csc, sec, cot, log, Piecewise
+from sympy.integrals.trigonometry import trigintegrate
+
+x = Symbol('x')
+
+
+def test_trigintegrate_odd():
+    assert trigintegrate(Rational(1), x) == x
+    assert trigintegrate(x, x) is None
+    assert trigintegrate(x**2, x) is None
+
+    assert trigintegrate(sin(x), x) == -cos(x)
+    assert trigintegrate(cos(x), x) == sin(x)
+
+    assert trigintegrate(sin(3*x), x) == -cos(3*x)/3
+    assert trigintegrate(cos(3*x), x) == sin(3*x)/3
+
+    y = Symbol('y')
+    assert trigintegrate(sin(y*x), x) == Piecewise(
+        (-cos(y*x)/y, Ne(y, 0)), (0, True))
+    assert trigintegrate(cos(y*x), x) == Piecewise(
+        (sin(y*x)/y, Ne(y, 0)), (x, True))
+    assert trigintegrate(sin(y*x)**2, x) == Piecewise(
+        ((x*y/2 - sin(x*y)*cos(x*y)/2)/y, Ne(y, 0)), (0, True))
+    assert trigintegrate(sin(y*x)*cos(y*x), x) == Piecewise(
+        (sin(x*y)**2/(2*y), Ne(y, 0)), (0, True))
+    assert trigintegrate(cos(y*x)**2, x) == Piecewise(
+        ((x*y/2 + sin(x*y)*cos(x*y)/2)/y, Ne(y, 0)), (x, True))
+
+    y = Symbol('y', positive=True)
+    # TODO: remove conds='none' below. For this to work we would have to rule
+    #       out (e.g. by trying solve) the condition y = 0, incompatible with
+    #       y.is_positive being True.
+    assert trigintegrate(sin(y*x), x, conds='none') == -cos(y*x)/y
+    assert trigintegrate(cos(y*x), x, conds='none') == sin(y*x)/y
+
+    assert trigintegrate(sin(x)*cos(x), x) == sin(x)**2/2
+    assert trigintegrate(sin(x)*cos(x)**2, x) == -cos(x)**3/3
+    assert trigintegrate(sin(x)**2*cos(x), x) == sin(x)**3/3
+
+    # check if it selects right function to substitute,
+    # so the result is kept simple
+    assert trigintegrate(sin(x)**7 * cos(x), x) == sin(x)**8/8
+    assert trigintegrate(sin(x) * cos(x)**7, x) == -cos(x)**8/8
+
+    assert trigintegrate(sin(x)**7 * cos(x)**3, x) == \
+        -sin(x)**10/10 + sin(x)**8/8
+    assert trigintegrate(sin(x)**3 * cos(x)**7, x) == \
+        cos(x)**10/10 - cos(x)**8/8
+
+    # both n, m are odd and -ve, and not necessarily equal
+    assert trigintegrate(sin(x)**-1*cos(x)**-1, x) == \
+        -log(sin(x)**2 - 1)/2 + log(sin(x))
+
+
+def test_trigintegrate_even():
+    assert trigintegrate(sin(x)**2, x) == x/2 - cos(x)*sin(x)/2
+    assert trigintegrate(cos(x)**2, x) == x/2 + cos(x)*sin(x)/2
+
+    assert trigintegrate(sin(3*x)**2, x) == x/2 - cos(3*x)*sin(3*x)/6
+    assert trigintegrate(cos(3*x)**2, x) == x/2 + cos(3*x)*sin(3*x)/6
+    assert trigintegrate(sin(x)**2 * cos(x)**2, x) == \
+        x/8 - sin(2*x)*cos(2*x)/16
+
+    assert trigintegrate(sin(x)**4 * cos(x)**2, x) == \
+        x/16 - sin(x) *cos(x)/16 - sin(x)**3*cos(x)/24 + \
+        sin(x)**5*cos(x)/6
+
+    assert trigintegrate(sin(x)**2 * cos(x)**4, x) == \
+        x/16 + cos(x) *sin(x)/16 + cos(x)**3*sin(x)/24 - \
+        cos(x)**5*sin(x)/6
+
+    assert trigintegrate(sin(x)**(-4), x) == -2*cos(x)/(3*sin(x)) \
+        - cos(x)/(3*sin(x)**3)
+
+    assert trigintegrate(cos(x)**(-6), x) == sin(x)/(5*cos(x)**5) \
+        + 4*sin(x)/(15*cos(x)**3) + 8*sin(x)/(15*cos(x))
+
+
+def test_trigintegrate_mixed():
+    assert trigintegrate(sin(x)*sec(x), x) == -log(cos(x))
+    assert trigintegrate(sin(x)*csc(x), x) == x
+    assert trigintegrate(sin(x)*cot(x), x) == sin(x)
+
+    assert trigintegrate(cos(x)*sec(x), x) == x
+    assert trigintegrate(cos(x)*csc(x), x) == log(sin(x))
+    assert trigintegrate(cos(x)*tan(x), x) == -cos(x)
+    assert trigintegrate(cos(x)*cot(x), x) == log(cos(x) - 1)/2 \
+        - log(cos(x) + 1)/2 + cos(x)
+    assert trigintegrate(cot(x)*cos(x)**2, x) == log(sin(x)) - sin(x)**2/2
+
+
+def test_trigintegrate_symbolic():
+    n = Symbol('n', integer=True)
+    assert trigintegrate(cos(x)**n, x) is None
+    assert trigintegrate(sin(x)**n, x) is None
+    assert trigintegrate(cot(x)**n, x) is None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/transforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..19dbd990e4f0320e76707a1a2a8b1601fcd8a3df
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/transforms.py
@@ -0,0 +1,1590 @@
+""" Integral Transforms """
+from functools import reduce, wraps
+from itertools import repeat
+from sympy.core import S, pi
+from sympy.core.add import Add
+from sympy.core.function import (
+    AppliedUndef, count_ops, expand, expand_mul, Function)
+from sympy.core.mul import Mul
+from sympy.core.intfunc import igcd, ilcm
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import Dummy
+from sympy.core.traversal import postorder_traversal
+from sympy.functions.combinatorial.factorials import factorial, rf
+from sympy.functions.elementary.complexes import re, arg, Abs
+from sympy.functions.elementary.exponential import exp, exp_polar
+from sympy.functions.elementary.hyperbolic import cosh, coth, sinh, tanh
+from sympy.functions.elementary.integers import ceiling
+from sympy.functions.elementary.miscellaneous import Max, Min, sqrt
+from sympy.functions.elementary.piecewise import piecewise_fold
+from sympy.functions.elementary.trigonometric import cos, cot, sin, tan
+from sympy.functions.special.bessel import besselj
+from sympy.functions.special.delta_functions import Heaviside
+from sympy.functions.special.gamma_functions import gamma
+from sympy.functions.special.hyper import meijerg
+from sympy.integrals import integrate, Integral
+from sympy.integrals.meijerint import _dummy
+from sympy.logic.boolalg import to_cnf, conjuncts, disjuncts, Or, And
+from sympy.polys.polyroots import roots
+from sympy.polys.polytools import factor, Poly
+from sympy.polys.rootoftools import CRootOf
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import debug
+
+
+##########################################################################
+# Helpers / Utilities
+##########################################################################
+
+
+class IntegralTransformError(NotImplementedError):
+    """
+    Exception raised in relation to problems computing transforms.
+
+    Explanation
+    ===========
+
+    This class is mostly used internally; if integrals cannot be computed
+    objects representing unevaluated transforms are usually returned.
+
+    The hint ``needeval=True`` can be used to disable returning transform
+    objects, and instead raise this exception if an integral cannot be
+    computed.
+    """
+    def __init__(self, transform, function, msg):
+        super().__init__(
+            "%s Transform could not be computed: %s." % (transform, msg))
+        self.function = function
+
+
+class IntegralTransform(Function):
+    """
+    Base class for integral transforms.
+
+    Explanation
+    ===========
+
+    This class represents unevaluated transforms.
+
+    To implement a concrete transform, derive from this class and implement
+    the ``_compute_transform(f, x, s, **hints)`` and ``_as_integral(f, x, s)``
+    functions. If the transform cannot be computed, raise :obj:`IntegralTransformError`.
+
+    Also set ``cls._name``. For instance,
+
+    >>> from sympy import LaplaceTransform
+    >>> LaplaceTransform._name
+    'Laplace'
+
+    Implement ``self._collapse_extra`` if your function returns more than just a
+    number and possibly a convergence condition.
+    """
+
+    @property
+    def function(self):
+        """ The function to be transformed. """
+        return self.args[0]
+
+    @property
+    def function_variable(self):
+        """ The dependent variable of the function to be transformed. """
+        return self.args[1]
+
+    @property
+    def transform_variable(self):
+        """ The independent transform variable. """
+        return self.args[2]
+
+    @property
+    def free_symbols(self):
+        """
+        This method returns the symbols that will exist when the transform
+        is evaluated.
+        """
+        return self.function.free_symbols.union({self.transform_variable}) \
+            - {self.function_variable}
+
+    def _compute_transform(self, f, x, s, **hints):
+        raise NotImplementedError
+
+    def _as_integral(self, f, x, s):
+        raise NotImplementedError
+
+    def _collapse_extra(self, extra):
+        cond = And(*extra)
+        if cond == False:
+            raise IntegralTransformError(self.__class__.name, None, '')
+        return cond
+
+    def _try_directly(self, **hints):
+        T = None
+        try_directly = not any(func.has(self.function_variable)
+                               for func in self.function.atoms(AppliedUndef))
+        if try_directly:
+            try:
+                T = self._compute_transform(self.function,
+                    self.function_variable, self.transform_variable, **hints)
+            except IntegralTransformError:
+                debug('[IT _try ] Caught IntegralTransformError, returns None')
+                T = None
+
+        fn = self.function
+        if not fn.is_Add:
+            fn = expand_mul(fn)
+        return fn, T
+
+    def doit(self, **hints):
+        """
+        Try to evaluate the transform in closed form.
+
+        Explanation
+        ===========
+
+        This general function handles linearity, but apart from that leaves
+        pretty much everything to _compute_transform.
+
+        Standard hints are the following:
+
+        - ``simplify``: whether or not to simplify the result
+        - ``noconds``: if True, do not return convergence conditions
+        - ``needeval``: if True, raise IntegralTransformError instead of
+                        returning IntegralTransform objects
+
+        The default values of these hints depend on the concrete transform,
+        usually the default is
+        ``(simplify, noconds, needeval) = (True, False, False)``.
+        """
+        needeval = hints.pop('needeval', False)
+        simplify = hints.pop('simplify', True)
+        hints['simplify'] = simplify
+
+        fn, T = self._try_directly(**hints)
+
+        if T is not None:
+            return T
+
+        if fn.is_Add:
+            hints['needeval'] = needeval
+            res = [self.__class__(*([x] + list(self.args[1:]))).doit(**hints)
+                   for x in fn.args]
+            extra = []
+            ress = []
+            for x in res:
+                if not isinstance(x, tuple):
+                    x = [x]
+                ress.append(x[0])
+                if len(x) == 2:
+                    # only a condition
+                    extra.append(x[1])
+                elif len(x) > 2:
+                    # some region parameters and a condition (Mellin, Laplace)
+                    extra += [x[1:]]
+            if simplify==True:
+                res = Add(*ress).simplify()
+            else:
+                res = Add(*ress)
+            if not extra:
+                return res
+            try:
+                extra = self._collapse_extra(extra)
+                if iterable(extra):
+                    return (res,) + tuple(extra)
+                else:
+                    return (res, extra)
+            except IntegralTransformError:
+                pass
+
+        if needeval:
+            raise IntegralTransformError(
+                self.__class__._name, self.function, 'needeval')
+
+        # TODO handle derivatives etc
+
+        # pull out constant coefficients
+        coeff, rest = fn.as_coeff_mul(self.function_variable)
+        return coeff*self.__class__(*([Mul(*rest)] + list(self.args[1:])))
+
+    @property
+    def as_integral(self):
+        return self._as_integral(self.function, self.function_variable,
+                                 self.transform_variable)
+
+    def _eval_rewrite_as_Integral(self, *args, **kwargs):
+        return self.as_integral
+
+
+def _simplify(expr, doit):
+    if doit:
+        from sympy.simplify import simplify
+        from sympy.simplify.powsimp import powdenest
+        return simplify(powdenest(piecewise_fold(expr), polar=True))
+    return expr
+
+
+def _noconds_(default):
+    """
+    This is a decorator generator for dropping convergence conditions.
+
+    Explanation
+    ===========
+
+    Suppose you define a function ``transform(*args)`` which returns a tuple of
+    the form ``(result, cond1, cond2, ...)``.
+
+    Decorating it ``@_noconds_(default)`` will add a new keyword argument
+    ``noconds`` to it. If ``noconds=True``, the return value will be altered to
+    be only ``result``, whereas if ``noconds=False`` the return value will not
+    be altered.
+
+    The default value of the ``noconds`` keyword will be ``default`` (i.e. the
+    argument of this function).
+    """
+    def make_wrapper(func):
+        @wraps(func)
+        def wrapper(*args, noconds=default, **kwargs):
+            res = func(*args, **kwargs)
+            if noconds:
+                return res[0]
+            return res
+        return wrapper
+    return make_wrapper
+_noconds = _noconds_(False)
+
+
+##########################################################################
+# Mellin Transform
+##########################################################################
+
+def _default_integrator(f, x):
+    return integrate(f, (x, S.Zero, S.Infinity))
+
+
+@_noconds
+def _mellin_transform(f, x, s_, integrator=_default_integrator, simplify=True):
+    """ Backend function to compute Mellin transforms. """
+    # We use a fresh dummy, because assumptions on s might drop conditions on
+    # convergence of the integral.
+    s = _dummy('s', 'mellin-transform', f)
+    F = integrator(x**(s - 1) * f, x)
+
+    if not F.has(Integral):
+        return _simplify(F.subs(s, s_), simplify), (S.NegativeInfinity, S.Infinity), S.true
+
+    if not F.is_Piecewise:  # XXX can this work if integration gives continuous result now?
+        raise IntegralTransformError('Mellin', f, 'could not compute integral')
+
+    F, cond = F.args[0]
+    if F.has(Integral):
+        raise IntegralTransformError(
+            'Mellin', f, 'integral in unexpected form')
+
+    def process_conds(cond):
+        """
+        Turn ``cond`` into a strip (a, b), and auxiliary conditions.
+        """
+        from sympy.solvers.inequalities import _solve_inequality
+        a = S.NegativeInfinity
+        b = S.Infinity
+        aux = S.true
+        conds = conjuncts(to_cnf(cond))
+        t = Dummy('t', real=True)
+        for c in conds:
+            a_ = S.Infinity
+            b_ = S.NegativeInfinity
+            aux_ = []
+            for d in disjuncts(c):
+                d_ = d.replace(
+                    re, lambda x: x.as_real_imag()[0]).subs(re(s), t)
+                if not d.is_Relational or \
+                    d.rel_op in ('==', '!=') \
+                        or d_.has(s) or not d_.has(t):
+                    aux_ += [d]
+                    continue
+                soln = _solve_inequality(d_, t)
+                if not soln.is_Relational or \
+                        soln.rel_op in ('==', '!='):
+                    aux_ += [d]
+                    continue
+                if soln.lts == t:
+                    b_ = Max(soln.gts, b_)
+                else:
+                    a_ = Min(soln.lts, a_)
+            if a_ is not S.Infinity and a_ != b:
+                a = Max(a_, a)
+            elif b_ is not S.NegativeInfinity and b_ != a:
+                b = Min(b_, b)
+            else:
+                aux = And(aux, Or(*aux_))
+        return a, b, aux
+
+    conds = [process_conds(c) for c in disjuncts(cond)]
+    conds = [x for x in conds if x[2] != False]
+    conds.sort(key=lambda x: (x[0] - x[1], count_ops(x[2])))
+
+    if not conds:
+        raise IntegralTransformError('Mellin', f, 'no convergence found')
+
+    a, b, aux = conds[0]
+    return _simplify(F.subs(s, s_), simplify), (a, b), aux
+
+
+class MellinTransform(IntegralTransform):
+    """
+    Class representing unevaluated Mellin transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute Mellin transforms, see the :func:`mellin_transform`
+    docstring.
+    """
+
+    _name = 'Mellin'
+
+    def _compute_transform(self, f, x, s, **hints):
+        return _mellin_transform(f, x, s, **hints)
+
+    def _as_integral(self, f, x, s):
+        return Integral(f*x**(s - 1), (x, S.Zero, S.Infinity))
+
+    def _collapse_extra(self, extra):
+        a = []
+        b = []
+        cond = []
+        for (sa, sb), c in extra:
+            a += [sa]
+            b += [sb]
+            cond += [c]
+        res = (Max(*a), Min(*b)), And(*cond)
+        if (res[0][0] >= res[0][1]) == True or res[1] == False:
+            raise IntegralTransformError(
+                'Mellin', None, 'no combined convergence.')
+        return res
+
+
+def mellin_transform(f, x, s, **hints):
+    r"""
+    Compute the Mellin transform `F(s)` of `f(x)`,
+
+    .. math :: F(s) = \int_0^\infty x^{s-1} f(x) \mathrm{d}x.
+
+    For all "sensible" functions, this converges absolutely in a strip
+      `a < \operatorname{Re}(s) < b`.
+
+    Explanation
+    ===========
+
+    The Mellin transform is related via change of variables to the Fourier
+    transform, and also to the (bilateral) Laplace transform.
+
+    This function returns ``(F, (a, b), cond)``
+    where ``F`` is the Mellin transform of ``f``, ``(a, b)`` is the fundamental strip
+    (as above), and ``cond`` are auxiliary convergence conditions.
+
+    If the integral cannot be computed in closed form, this function returns
+    an unevaluated :class:`MellinTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`. If ``noconds=False``,
+    then only `F` will be returned (i.e. not ``cond``, and also not the strip
+    ``(a, b)``).
+
+    Examples
+    ========
+
+    >>> from sympy import mellin_transform, exp
+    >>> from sympy.abc import x, s
+    >>> mellin_transform(exp(-x), x, s)
+    (gamma(s), (0, oo), True)
+
+    See Also
+    ========
+
+    inverse_mellin_transform, laplace_transform, fourier_transform
+    hankel_transform, inverse_hankel_transform
+    """
+    return MellinTransform(f, x, s).doit(**hints)
+
+
+def _rewrite_sin(m_n, s, a, b):
+    """
+    Re-write the sine function ``sin(m*s + n)`` as gamma functions, compatible
+    with the strip (a, b).
+
+    Return ``(gamma1, gamma2, fac)`` so that ``f == fac/(gamma1 * gamma2)``.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.transforms import _rewrite_sin
+    >>> from sympy import pi, S
+    >>> from sympy.abc import s
+    >>> _rewrite_sin((pi, 0), s, 0, 1)
+    (gamma(s), gamma(1 - s), pi)
+    >>> _rewrite_sin((pi, 0), s, 1, 0)
+    (gamma(s - 1), gamma(2 - s), -pi)
+    >>> _rewrite_sin((pi, 0), s, -1, 0)
+    (gamma(s + 1), gamma(-s), -pi)
+    >>> _rewrite_sin((pi, pi/2), s, S(1)/2, S(3)/2)
+    (gamma(s - 1/2), gamma(3/2 - s), -pi)
+    >>> _rewrite_sin((pi, pi), s, 0, 1)
+    (gamma(s), gamma(1 - s), -pi)
+    >>> _rewrite_sin((2*pi, 0), s, 0, S(1)/2)
+    (gamma(2*s), gamma(1 - 2*s), pi)
+    >>> _rewrite_sin((2*pi, 0), s, S(1)/2, 1)
+    (gamma(2*s - 1), gamma(2 - 2*s), -pi)
+    """
+    # (This is a separate function because it is moderately complicated,
+    #  and I want to doctest it.)
+    # We want to use pi/sin(pi*x) = gamma(x)*gamma(1-x).
+    # But there is one complication: the gamma functions determine the
+    # integration contour in the definition of the G-function. Usually
+    # it would not matter if this is slightly shifted, unless this way
+    # we create an undefined function!
+    # So we try to write this in such a way that the gammas are
+    # eminently on the right side of the strip.
+    m, n = m_n
+
+    m = expand_mul(m/pi)
+    n = expand_mul(n/pi)
+    r = ceiling(-m*a - n.as_real_imag()[0])  # Don't use re(n), does not expand
+    return gamma(m*s + n + r), gamma(1 - n - r - m*s), (-1)**r*pi
+
+
+class MellinTransformStripError(ValueError):
+    """
+    Exception raised by _rewrite_gamma. Mainly for internal use.
+    """
+    pass
+
+
+def _rewrite_gamma(f, s, a, b):
+    """
+    Try to rewrite the product f(s) as a product of gamma functions,
+    so that the inverse Mellin transform of f can be expressed as a meijer
+    G function.
+
+    Explanation
+    ===========
+
+    Return (an, ap), (bm, bq), arg, exp, fac such that
+    G((an, ap), (bm, bq), arg/z**exp)*fac is the inverse Mellin transform of f(s).
+
+    Raises IntegralTransformError or MellinTransformStripError on failure.
+
+    It is asserted that f has no poles in the fundamental strip designated by
+    (a, b). One of a and b is allowed to be None. The fundamental strip is
+    important, because it determines the inversion contour.
+
+    This function can handle exponentials, linear factors, trigonometric
+    functions.
+
+    This is a helper function for inverse_mellin_transform that will not
+    attempt any transformations on f.
+
+    Examples
+    ========
+
+    >>> from sympy.integrals.transforms import _rewrite_gamma
+    >>> from sympy.abc import s
+    >>> from sympy import oo
+    >>> _rewrite_gamma(s*(s+3)*(s-1), s, -oo, oo)
+    (([], [-3, 0, 1]), ([-2, 1, 2], []), 1, 1, -1)
+    >>> _rewrite_gamma((s-1)**2, s, -oo, oo)
+    (([], [1, 1]), ([2, 2], []), 1, 1, 1)
+
+    Importance of the fundamental strip:
+
+    >>> _rewrite_gamma(1/s, s, 0, oo)
+    (([1], []), ([], [0]), 1, 1, 1)
+    >>> _rewrite_gamma(1/s, s, None, oo)
+    (([1], []), ([], [0]), 1, 1, 1)
+    >>> _rewrite_gamma(1/s, s, 0, None)
+    (([1], []), ([], [0]), 1, 1, 1)
+    >>> _rewrite_gamma(1/s, s, -oo, 0)
+    (([], [1]), ([0], []), 1, 1, -1)
+    >>> _rewrite_gamma(1/s, s, None, 0)
+    (([], [1]), ([0], []), 1, 1, -1)
+    >>> _rewrite_gamma(1/s, s, -oo, None)
+    (([], [1]), ([0], []), 1, 1, -1)
+
+    >>> _rewrite_gamma(2**(-s+3), s, -oo, oo)
+    (([], []), ([], []), 1/2, 1, 8)
+    """
+    # Our strategy will be as follows:
+    # 1) Guess a constant c such that the inversion integral should be
+    #    performed wrt s'=c*s (instead of plain s). Write s for s'.
+    # 2) Process all factors, rewrite them independently as gamma functions in
+    #    argument s, or exponentials of s.
+    # 3) Try to transform all gamma functions s.t. they have argument
+    #    a+s or a-s.
+    # 4) Check that the resulting G function parameters are valid.
+    # 5) Combine all the exponentials.
+
+    a_, b_ = S([a, b])
+
+    def left(c, is_numer):
+        """
+        Decide whether pole at c lies to the left of the fundamental strip.
+        """
+        # heuristically, this is the best chance for us to solve the inequalities
+        c = expand(re(c))
+        if a_ is None and b_ is S.Infinity:
+            return True
+        if a_ is None:
+            return c < b_
+        if b_ is None:
+            return c <= a_
+        if (c >= b_) == True:
+            return False
+        if (c <= a_) == True:
+            return True
+        if is_numer:
+            return None
+        if a_.free_symbols or b_.free_symbols or c.free_symbols:
+            return None  # XXX
+            #raise IntegralTransformError('Inverse Mellin', f,
+            #                     'Could not determine position of singularity %s'
+            #                     ' relative to fundamental strip' % c)
+        raise MellinTransformStripError('Pole inside critical strip?')
+
+    # 1)
+    s_multipliers = []
+    for g in f.atoms(gamma):
+        if not g.has(s):
+            continue
+        arg = g.args[0]
+        if arg.is_Add:
+            arg = arg.as_independent(s)[1]
+        coeff, _ = arg.as_coeff_mul(s)
+        s_multipliers += [coeff]
+    for g in f.atoms(sin, cos, tan, cot):
+        if not g.has(s):
+            continue
+        arg = g.args[0]
+        if arg.is_Add:
+            arg = arg.as_independent(s)[1]
+        coeff, _ = arg.as_coeff_mul(s)
+        s_multipliers += [coeff/pi]
+    s_multipliers = [Abs(x) if x.is_extended_real else x for x in s_multipliers]
+    common_coefficient = S.One
+    for x in s_multipliers:
+        if not x.is_Rational:
+            common_coefficient = x
+            break
+    s_multipliers = [x/common_coefficient for x in s_multipliers]
+    if not (all(x.is_Rational for x in s_multipliers) and
+            common_coefficient.is_extended_real):
+        raise IntegralTransformError("Gamma", None, "Nonrational multiplier")
+    s_multiplier = common_coefficient/reduce(ilcm, [S(x.q)
+                                             for x in s_multipliers], S.One)
+    if s_multiplier == common_coefficient:
+        if len(s_multipliers) == 0:
+            s_multiplier = common_coefficient
+        else:
+            s_multiplier = common_coefficient \
+                *reduce(igcd, [S(x.p) for x in s_multipliers])
+
+    f = f.subs(s, s/s_multiplier)
+    fac = S.One/s_multiplier
+    exponent = S.One/s_multiplier
+    if a_ is not None:
+        a_ *= s_multiplier
+    if b_ is not None:
+        b_ *= s_multiplier
+
+    # 2)
+    numer, denom = f.as_numer_denom()
+    numer = Mul.make_args(numer)
+    denom = Mul.make_args(denom)
+    args = list(zip(numer, repeat(True))) + list(zip(denom, repeat(False)))
+
+    facs = []
+    dfacs = []
+    # *_gammas will contain pairs (a, c) representing Gamma(a*s + c)
+    numer_gammas = []
+    denom_gammas = []
+    # exponentials will contain bases for exponentials of s
+    exponentials = []
+
+    def exception(fact):
+        return IntegralTransformError("Inverse Mellin", f, "Unrecognised form '%s'." % fact)
+    while args:
+        fact, is_numer = args.pop()
+        if is_numer:
+            ugammas, lgammas = numer_gammas, denom_gammas
+            ufacs = facs
+        else:
+            ugammas, lgammas = denom_gammas, numer_gammas
+            ufacs = dfacs
+
+        def linear_arg(arg):
+            """ Test if arg is of form a*s+b, raise exception if not. """
+            if not arg.is_polynomial(s):
+                raise exception(fact)
+            p = Poly(arg, s)
+            if p.degree() != 1:
+                raise exception(fact)
+            return p.all_coeffs()
+
+        # constants
+        if not fact.has(s):
+            ufacs += [fact]
+        # exponentials
+        elif fact.is_Pow or isinstance(fact, exp):
+            if fact.is_Pow:
+                base = fact.base
+                exp_ = fact.exp
+            else:
+                base = exp_polar(1)
+                exp_ = fact.exp
+            if exp_.is_Integer:
+                cond = is_numer
+                if exp_ < 0:
+                    cond = not cond
+                args += [(base, cond)]*Abs(exp_)
+                continue
+            elif not base.has(s):
+                a, b = linear_arg(exp_)
+                if not is_numer:
+                    base = 1/base
+                exponentials += [base**a]
+                facs += [base**b]
+            else:
+                raise exception(fact)
+        # linear factors
+        elif fact.is_polynomial(s):
+            p = Poly(fact, s)
+            if p.degree() != 1:
+                # We completely factor the poly. For this we need the roots.
+                # Now roots() only works in some cases (low degree), and CRootOf
+                # only works without parameters. So try both...
+                coeff = p.LT()[1]
+                rs = roots(p, s)
+                if len(rs) != p.degree():
+                    rs = CRootOf.all_roots(p)
+                ufacs += [coeff]
+                args += [(s - c, is_numer) for c in rs]
+                continue
+            a, c = p.all_coeffs()
+            ufacs += [a]
+            c /= -a
+            # Now need to convert s - c
+            if left(c, is_numer):
+                ugammas += [(S.One, -c + 1)]
+                lgammas += [(S.One, -c)]
+            else:
+                ufacs += [-1]
+                ugammas += [(S.NegativeOne, c + 1)]
+                lgammas += [(S.NegativeOne, c)]
+        elif isinstance(fact, gamma):
+            a, b = linear_arg(fact.args[0])
+            if is_numer:
+                if (a > 0 and (left(-b/a, is_numer) == False)) or \
+                   (a < 0 and (left(-b/a, is_numer) == True)):
+                    raise NotImplementedError(
+                        'Gammas partially over the strip.')
+            ugammas += [(a, b)]
+        elif isinstance(fact, sin):
+            # We try to re-write all trigs as gammas. This is not in
+            # general the best strategy, since sometimes this is impossible,
+            # but rewriting as exponentials would work. However trig functions
+            # in inverse mellin transforms usually all come from simplifying
+            # gamma terms, so this should work.
+            a = fact.args[0]
+            if is_numer:
+                # No problem with the poles.
+                gamma1, gamma2, fac_ = gamma(a/pi), gamma(1 - a/pi), pi
+            else:
+                gamma1, gamma2, fac_ = _rewrite_sin(linear_arg(a), s, a_, b_)
+            args += [(gamma1, not is_numer), (gamma2, not is_numer)]
+            ufacs += [fac_]
+        elif isinstance(fact, tan):
+            a = fact.args[0]
+            args += [(sin(a, evaluate=False), is_numer),
+                     (sin(pi/2 - a, evaluate=False), not is_numer)]
+        elif isinstance(fact, cos):
+            a = fact.args[0]
+            args += [(sin(pi/2 - a, evaluate=False), is_numer)]
+        elif isinstance(fact, cot):
+            a = fact.args[0]
+            args += [(sin(pi/2 - a, evaluate=False), is_numer),
+                     (sin(a, evaluate=False), not is_numer)]
+        else:
+            raise exception(fact)
+
+    fac *= Mul(*facs)/Mul(*dfacs)
+
+    # 3)
+    an, ap, bm, bq = [], [], [], []
+    for gammas, plus, minus, is_numer in [(numer_gammas, an, bm, True),
+                                          (denom_gammas, bq, ap, False)]:
+        while gammas:
+            a, c = gammas.pop()
+            if a != -1 and a != +1:
+                # We use the gamma function multiplication theorem.
+                p = Abs(S(a))
+                newa = a/p
+                newc = c/p
+                if not a.is_Integer:
+                    raise TypeError("a is not an integer")
+                for k in range(p):
+                    gammas += [(newa, newc + k/p)]
+                if is_numer:
+                    fac *= (2*pi)**((1 - p)/2) * p**(c - S.Half)
+                    exponentials += [p**a]
+                else:
+                    fac /= (2*pi)**((1 - p)/2) * p**(c - S.Half)
+                    exponentials += [p**(-a)]
+                continue
+            if a == +1:
+                plus.append(1 - c)
+            else:
+                minus.append(c)
+
+    # 4)
+    # TODO
+
+    # 5)
+    arg = Mul(*exponentials)
+
+    # for testability, sort the arguments
+    an.sort(key=default_sort_key)
+    ap.sort(key=default_sort_key)
+    bm.sort(key=default_sort_key)
+    bq.sort(key=default_sort_key)
+
+    return (an, ap), (bm, bq), arg, exponent, fac
+
+
+@_noconds_(True)
+def _inverse_mellin_transform(F, s, x_, strip, as_meijerg=False):
+    """ A helper for the real inverse_mellin_transform function, this one here
+        assumes x to be real and positive. """
+    x = _dummy('t', 'inverse-mellin-transform', F, positive=True)
+    # Actually, we won't try integration at all. Instead we use the definition
+    # of the Meijer G function as a fairly general inverse mellin transform.
+    F = F.rewrite(gamma)
+    for g in [factor(F), expand_mul(F), expand(F)]:
+        if g.is_Add:
+            # do all terms separately
+            ress = [_inverse_mellin_transform(G, s, x, strip, as_meijerg,
+                                              noconds=False)
+                    for G in g.args]
+            conds = [p[1] for p in ress]
+            ress = [p[0] for p in ress]
+            res = Add(*ress)
+            if not as_meijerg:
+                res = factor(res, gens=res.atoms(Heaviside))
+            return res.subs(x, x_), And(*conds)
+
+        try:
+            a, b, C, e, fac = _rewrite_gamma(g, s, strip[0], strip[1])
+        except IntegralTransformError:
+            continue
+        try:
+            G = meijerg(a, b, C/x**e)
+        except ValueError:
+            continue
+        if as_meijerg:
+            h = G
+        else:
+            try:
+                from sympy.simplify import hyperexpand
+                h = hyperexpand(G)
+            except NotImplementedError:
+                raise IntegralTransformError(
+                    'Inverse Mellin', F, 'Could not calculate integral')
+
+            if h.is_Piecewise and len(h.args) == 3:
+                # XXX we break modularity here!
+                h = Heaviside(x - Abs(C))*h.args[0].args[0] \
+                    + Heaviside(Abs(C) - x)*h.args[1].args[0]
+        # We must ensure that the integral along the line we want converges,
+        # and return that value.
+        # See [L], 5.2
+        cond = [Abs(arg(G.argument)) < G.delta*pi]
+        # Note: we allow ">=" here, this corresponds to convergence if we let
+        # limits go to oo symmetrically. ">" corresponds to absolute convergence.
+        cond += [And(Or(len(G.ap) != len(G.bq), 0 >= re(G.nu) + 1),
+                     Abs(arg(G.argument)) == G.delta*pi)]
+        cond = Or(*cond)
+        if cond == False:
+            raise IntegralTransformError(
+                'Inverse Mellin', F, 'does not converge')
+        return (h*fac).subs(x, x_), cond
+
+    raise IntegralTransformError('Inverse Mellin', F, '')
+
+_allowed = None
+
+
+class InverseMellinTransform(IntegralTransform):
+    """
+    Class representing unevaluated inverse Mellin transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute inverse Mellin transforms, see the
+    :func:`inverse_mellin_transform` docstring.
+    """
+
+    _name = 'Inverse Mellin'
+    _none_sentinel = Dummy('None')
+    _c = Dummy('c')
+
+    def __new__(cls, F, s, x, a, b, **opts):
+        if a is None:
+            a = InverseMellinTransform._none_sentinel
+        if b is None:
+            b = InverseMellinTransform._none_sentinel
+        return IntegralTransform.__new__(cls, F, s, x, a, b, **opts)
+
+    @property
+    def fundamental_strip(self):
+        a, b = self.args[3], self.args[4]
+        if a is InverseMellinTransform._none_sentinel:
+            a = None
+        if b is InverseMellinTransform._none_sentinel:
+            b = None
+        return a, b
+
+    def _compute_transform(self, F, s, x, **hints):
+        # IntegralTransform's doit will cause this hint to exist, but
+        # InverseMellinTransform should ignore it
+        hints.pop('simplify', True)
+        global _allowed
+        if _allowed is None:
+            _allowed = {
+                exp, gamma, sin, cos, tan, cot, cosh, sinh, tanh, coth,
+                factorial, rf}
+        for f in postorder_traversal(F):
+            if f.is_Function and f.has(s) and f.func not in _allowed:
+                raise IntegralTransformError('Inverse Mellin', F,
+                                     'Component %s not recognised.' % f)
+        strip = self.fundamental_strip
+        return _inverse_mellin_transform(F, s, x, strip, **hints)
+
+    def _as_integral(self, F, s, x):
+        c = self.__class__._c
+        return Integral(F*x**(-s), (s, c - S.ImaginaryUnit*S.Infinity, c +
+                                    S.ImaginaryUnit*S.Infinity))/(2*S.Pi*S.ImaginaryUnit)
+
+
+def inverse_mellin_transform(F, s, x, strip, **hints):
+    r"""
+    Compute the inverse Mellin transform of `F(s)` over the fundamental
+    strip given by ``strip=(a, b)``.
+
+    Explanation
+    ===========
+
+    This can be defined as
+
+    .. math:: f(x) = \frac{1}{2\pi i} \int_{c - i\infty}^{c + i\infty} x^{-s} F(s) \mathrm{d}s,
+
+    for any `c` in the fundamental strip. Under certain regularity
+    conditions on `F` and/or `f`,
+    this recovers `f` from its Mellin transform `F`
+    (and vice versa), for positive real `x`.
+
+    One of `a` or `b` may be passed as ``None``; a suitable `c` will be
+    inferred.
+
+    If the integral cannot be computed in closed form, this function returns
+    an unevaluated :class:`InverseMellinTransform` object.
+
+    Note that this function will assume x to be positive and real, regardless
+    of the SymPy assumptions!
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+
+    Examples
+    ========
+
+    >>> from sympy import inverse_mellin_transform, oo, gamma
+    >>> from sympy.abc import x, s
+    >>> inverse_mellin_transform(gamma(s), s, x, (0, oo))
+    exp(-x)
+
+    The fundamental strip matters:
+
+    >>> f = 1/(s**2 - 1)
+    >>> inverse_mellin_transform(f, s, x, (-oo, -1))
+    x*(1 - 1/x**2)*Heaviside(x - 1)/2
+    >>> inverse_mellin_transform(f, s, x, (-1, 1))
+    -x*Heaviside(1 - x)/2 - Heaviside(x - 1)/(2*x)
+    >>> inverse_mellin_transform(f, s, x, (1, oo))
+    (1/2 - x**2/2)*Heaviside(1 - x)/x
+
+    See Also
+    ========
+
+    mellin_transform
+    hankel_transform, inverse_hankel_transform
+    """
+    return InverseMellinTransform(F, s, x, strip[0], strip[1]).doit(**hints)
+
+
+##########################################################################
+# Fourier Transform
+##########################################################################
+
+@_noconds_(True)
+def _fourier_transform(f, x, k, a, b, name, simplify=True):
+    r"""
+    Compute a general Fourier-type transform
+
+    .. math::
+
+        F(k) = a \int_{-\infty}^{\infty} e^{bixk} f(x)\, dx.
+
+    For suitable choice of *a* and *b*, this reduces to the standard Fourier
+    and inverse Fourier transforms.
+    """
+    F = integrate(a*f*exp(b*S.ImaginaryUnit*x*k), (x, S.NegativeInfinity, S.Infinity))
+
+    if not F.has(Integral):
+        return _simplify(F, simplify), S.true
+
+    integral_f = integrate(f, (x, S.NegativeInfinity, S.Infinity))
+    if integral_f in (S.NegativeInfinity, S.Infinity, S.NaN) or integral_f.has(Integral):
+        raise IntegralTransformError(name, f, 'function not integrable on real axis')
+
+    if not F.is_Piecewise:
+        raise IntegralTransformError(name, f, 'could not compute integral')
+
+    F, cond = F.args[0]
+    if F.has(Integral):
+        raise IntegralTransformError(name, f, 'integral in unexpected form')
+
+    return _simplify(F, simplify), cond
+
+
+class FourierTypeTransform(IntegralTransform):
+    """ Base class for Fourier transforms."""
+
+    def a(self):
+        raise NotImplementedError(
+            "Class %s must implement a(self) but does not" % self.__class__)
+
+    def b(self):
+        raise NotImplementedError(
+            "Class %s must implement b(self) but does not" % self.__class__)
+
+    def _compute_transform(self, f, x, k, **hints):
+        return _fourier_transform(f, x, k,
+                                  self.a(), self.b(),
+                                  self.__class__._name, **hints)
+
+    def _as_integral(self, f, x, k):
+        a = self.a()
+        b = self.b()
+        return Integral(a*f*exp(b*S.ImaginaryUnit*x*k), (x, S.NegativeInfinity, S.Infinity))
+
+
+class FourierTransform(FourierTypeTransform):
+    """
+    Class representing unevaluated Fourier transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute Fourier transforms, see the :func:`fourier_transform`
+    docstring.
+    """
+
+    _name = 'Fourier'
+
+    def a(self):
+        return 1
+
+    def b(self):
+        return -2*S.Pi
+
+
+def fourier_transform(f, x, k, **hints):
+    r"""
+    Compute the unitary, ordinary-frequency Fourier transform of ``f``, defined
+    as
+
+    .. math:: F(k) = \int_{-\infty}^\infty f(x) e^{-2\pi i x k} \mathrm{d} x.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`FourierTransform` object.
+
+    For other Fourier transform conventions, see the function
+    :func:`sympy.integrals.transforms._fourier_transform`.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import fourier_transform, exp
+    >>> from sympy.abc import x, k
+    >>> fourier_transform(exp(-x**2), x, k)
+    sqrt(pi)*exp(-pi**2*k**2)
+    >>> fourier_transform(exp(-x**2), x, k, noconds=False)
+    (sqrt(pi)*exp(-pi**2*k**2), True)
+
+    See Also
+    ========
+
+    inverse_fourier_transform
+    sine_transform, inverse_sine_transform
+    cosine_transform, inverse_cosine_transform
+    hankel_transform, inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return FourierTransform(f, x, k).doit(**hints)
+
+
+class InverseFourierTransform(FourierTypeTransform):
+    """
+    Class representing unevaluated inverse Fourier transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute inverse Fourier transforms, see the
+    :func:`inverse_fourier_transform` docstring.
+    """
+
+    _name = 'Inverse Fourier'
+
+    def a(self):
+        return 1
+
+    def b(self):
+        return 2*S.Pi
+
+
+def inverse_fourier_transform(F, k, x, **hints):
+    r"""
+    Compute the unitary, ordinary-frequency inverse Fourier transform of `F`,
+    defined as
+
+    .. math:: f(x) = \int_{-\infty}^\infty F(k) e^{2\pi i x k} \mathrm{d} k.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`InverseFourierTransform` object.
+
+    For other Fourier transform conventions, see the function
+    :func:`sympy.integrals.transforms._fourier_transform`.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import inverse_fourier_transform, exp, sqrt, pi
+    >>> from sympy.abc import x, k
+    >>> inverse_fourier_transform(sqrt(pi)*exp(-(pi*k)**2), k, x)
+    exp(-x**2)
+    >>> inverse_fourier_transform(sqrt(pi)*exp(-(pi*k)**2), k, x, noconds=False)
+    (exp(-x**2), True)
+
+    See Also
+    ========
+
+    fourier_transform
+    sine_transform, inverse_sine_transform
+    cosine_transform, inverse_cosine_transform
+    hankel_transform, inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return InverseFourierTransform(F, k, x).doit(**hints)
+
+
+##########################################################################
+# Fourier Sine and Cosine Transform
+##########################################################################
+
+@_noconds_(True)
+def _sine_cosine_transform(f, x, k, a, b, K, name, simplify=True):
+    """
+    Compute a general sine or cosine-type transform
+        F(k) = a int_0^oo b*sin(x*k) f(x) dx.
+        F(k) = a int_0^oo b*cos(x*k) f(x) dx.
+
+    For suitable choice of a and b, this reduces to the standard sine/cosine
+    and inverse sine/cosine transforms.
+    """
+    F = integrate(a*f*K(b*x*k), (x, S.Zero, S.Infinity))
+
+    if not F.has(Integral):
+        return _simplify(F, simplify), S.true
+
+    if not F.is_Piecewise:
+        raise IntegralTransformError(name, f, 'could not compute integral')
+
+    F, cond = F.args[0]
+    if F.has(Integral):
+        raise IntegralTransformError(name, f, 'integral in unexpected form')
+
+    return _simplify(F, simplify), cond
+
+
+class SineCosineTypeTransform(IntegralTransform):
+    """
+    Base class for sine and cosine transforms.
+    Specify cls._kern.
+    """
+
+    def a(self):
+        raise NotImplementedError(
+            "Class %s must implement a(self) but does not" % self.__class__)
+
+    def b(self):
+        raise NotImplementedError(
+            "Class %s must implement b(self) but does not" % self.__class__)
+
+
+    def _compute_transform(self, f, x, k, **hints):
+        return _sine_cosine_transform(f, x, k,
+                                      self.a(), self.b(),
+                                      self.__class__._kern,
+                                      self.__class__._name, **hints)
+
+    def _as_integral(self, f, x, k):
+        a = self.a()
+        b = self.b()
+        K = self.__class__._kern
+        return Integral(a*f*K(b*x*k), (x, S.Zero, S.Infinity))
+
+
+class SineTransform(SineCosineTypeTransform):
+    """
+    Class representing unevaluated sine transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute sine transforms, see the :func:`sine_transform`
+    docstring.
+    """
+
+    _name = 'Sine'
+    _kern = sin
+
+    def a(self):
+        return sqrt(2)/sqrt(pi)
+
+    def b(self):
+        return S.One
+
+
+def sine_transform(f, x, k, **hints):
+    r"""
+    Compute the unitary, ordinary-frequency sine transform of `f`, defined
+    as
+
+    .. math:: F(k) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty f(x) \sin(2\pi x k) \mathrm{d} x.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`SineTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import sine_transform, exp
+    >>> from sympy.abc import x, k, a
+    >>> sine_transform(x*exp(-a*x**2), x, k)
+    sqrt(2)*k*exp(-k**2/(4*a))/(4*a**(3/2))
+    >>> sine_transform(x**(-a), x, k)
+    2**(1/2 - a)*k**(a - 1)*gamma(1 - a/2)/gamma(a/2 + 1/2)
+
+    See Also
+    ========
+
+    fourier_transform, inverse_fourier_transform
+    inverse_sine_transform
+    cosine_transform, inverse_cosine_transform
+    hankel_transform, inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return SineTransform(f, x, k).doit(**hints)
+
+
+class InverseSineTransform(SineCosineTypeTransform):
+    """
+    Class representing unevaluated inverse sine transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute inverse sine transforms, see the
+    :func:`inverse_sine_transform` docstring.
+    """
+
+    _name = 'Inverse Sine'
+    _kern = sin
+
+    def a(self):
+        return sqrt(2)/sqrt(pi)
+
+    def b(self):
+        return S.One
+
+
+def inverse_sine_transform(F, k, x, **hints):
+    r"""
+    Compute the unitary, ordinary-frequency inverse sine transform of `F`,
+    defined as
+
+    .. math:: f(x) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty F(k) \sin(2\pi x k) \mathrm{d} k.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`InverseSineTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import inverse_sine_transform, exp, sqrt, gamma
+    >>> from sympy.abc import x, k, a
+    >>> inverse_sine_transform(2**((1-2*a)/2)*k**(a - 1)*
+    ...     gamma(-a/2 + 1)/gamma((a+1)/2), k, x)
+    x**(-a)
+    >>> inverse_sine_transform(sqrt(2)*k*exp(-k**2/(4*a))/(4*sqrt(a)**3), k, x)
+    x*exp(-a*x**2)
+
+    See Also
+    ========
+
+    fourier_transform, inverse_fourier_transform
+    sine_transform
+    cosine_transform, inverse_cosine_transform
+    hankel_transform, inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return InverseSineTransform(F, k, x).doit(**hints)
+
+
+class CosineTransform(SineCosineTypeTransform):
+    """
+    Class representing unevaluated cosine transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute cosine transforms, see the :func:`cosine_transform`
+    docstring.
+    """
+
+    _name = 'Cosine'
+    _kern = cos
+
+    def a(self):
+        return sqrt(2)/sqrt(pi)
+
+    def b(self):
+        return S.One
+
+
+def cosine_transform(f, x, k, **hints):
+    r"""
+    Compute the unitary, ordinary-frequency cosine transform of `f`, defined
+    as
+
+    .. math:: F(k) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty f(x) \cos(2\pi x k) \mathrm{d} x.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`CosineTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import cosine_transform, exp, sqrt, cos
+    >>> from sympy.abc import x, k, a
+    >>> cosine_transform(exp(-a*x), x, k)
+    sqrt(2)*a/(sqrt(pi)*(a**2 + k**2))
+    >>> cosine_transform(exp(-a*sqrt(x))*cos(a*sqrt(x)), x, k)
+    a*exp(-a**2/(2*k))/(2*k**(3/2))
+
+    See Also
+    ========
+
+    fourier_transform, inverse_fourier_transform,
+    sine_transform, inverse_sine_transform
+    inverse_cosine_transform
+    hankel_transform, inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return CosineTransform(f, x, k).doit(**hints)
+
+
+class InverseCosineTransform(SineCosineTypeTransform):
+    """
+    Class representing unevaluated inverse cosine transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute inverse cosine transforms, see the
+    :func:`inverse_cosine_transform` docstring.
+    """
+
+    _name = 'Inverse Cosine'
+    _kern = cos
+
+    def a(self):
+        return sqrt(2)/sqrt(pi)
+
+    def b(self):
+        return S.One
+
+
+def inverse_cosine_transform(F, k, x, **hints):
+    r"""
+    Compute the unitary, ordinary-frequency inverse cosine transform of `F`,
+    defined as
+
+    .. math:: f(x) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty F(k) \cos(2\pi x k) \mathrm{d} k.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`InverseCosineTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import inverse_cosine_transform, sqrt, pi
+    >>> from sympy.abc import x, k, a
+    >>> inverse_cosine_transform(sqrt(2)*a/(sqrt(pi)*(a**2 + k**2)), k, x)
+    exp(-a*x)
+    >>> inverse_cosine_transform(1/sqrt(k), k, x)
+    1/sqrt(x)
+
+    See Also
+    ========
+
+    fourier_transform, inverse_fourier_transform,
+    sine_transform, inverse_sine_transform
+    cosine_transform
+    hankel_transform, inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return InverseCosineTransform(F, k, x).doit(**hints)
+
+
+##########################################################################
+# Hankel Transform
+##########################################################################
+
+@_noconds_(True)
+def _hankel_transform(f, r, k, nu, name, simplify=True):
+    r"""
+    Compute a general Hankel transform
+
+    .. math:: F_\nu(k) = \int_{0}^\infty f(r) J_\nu(k r) r \mathrm{d} r.
+    """
+    F = integrate(f*besselj(nu, k*r)*r, (r, S.Zero, S.Infinity))
+
+    if not F.has(Integral):
+        return _simplify(F, simplify), S.true
+
+    if not F.is_Piecewise:
+        raise IntegralTransformError(name, f, 'could not compute integral')
+
+    F, cond = F.args[0]
+    if F.has(Integral):
+        raise IntegralTransformError(name, f, 'integral in unexpected form')
+
+    return _simplify(F, simplify), cond
+
+
+class HankelTypeTransform(IntegralTransform):
+    """
+    Base class for Hankel transforms.
+    """
+
+    def doit(self, **hints):
+        return self._compute_transform(self.function,
+                                       self.function_variable,
+                                       self.transform_variable,
+                                       self.args[3],
+                                       **hints)
+
+    def _compute_transform(self, f, r, k, nu, **hints):
+        return _hankel_transform(f, r, k, nu, self._name, **hints)
+
+    def _as_integral(self, f, r, k, nu):
+        return Integral(f*besselj(nu, k*r)*r, (r, S.Zero, S.Infinity))
+
+    @property
+    def as_integral(self):
+        return self._as_integral(self.function,
+                                 self.function_variable,
+                                 self.transform_variable,
+                                 self.args[3])
+
+
+class HankelTransform(HankelTypeTransform):
+    """
+    Class representing unevaluated Hankel transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute Hankel transforms, see the :func:`hankel_transform`
+    docstring.
+    """
+
+    _name = 'Hankel'
+
+
+def hankel_transform(f, r, k, nu, **hints):
+    r"""
+    Compute the Hankel transform of `f`, defined as
+
+    .. math:: F_\nu(k) = \int_{0}^\infty f(r) J_\nu(k r) r \mathrm{d} r.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`HankelTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import hankel_transform, inverse_hankel_transform
+    >>> from sympy import exp
+    >>> from sympy.abc import r, k, m, nu, a
+
+    >>> ht = hankel_transform(1/r**m, r, k, nu)
+    >>> ht
+    2*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/(2**m*gamma(m/2 + nu/2))
+
+    >>> inverse_hankel_transform(ht, k, r, nu)
+    r**(-m)
+
+    >>> ht = hankel_transform(exp(-a*r), r, k, 0)
+    >>> ht
+    a/(k**3*(a**2/k**2 + 1)**(3/2))
+
+    >>> inverse_hankel_transform(ht, k, r, 0)
+    exp(-a*r)
+
+    See Also
+    ========
+
+    fourier_transform, inverse_fourier_transform
+    sine_transform, inverse_sine_transform
+    cosine_transform, inverse_cosine_transform
+    inverse_hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return HankelTransform(f, r, k, nu).doit(**hints)
+
+
+class InverseHankelTransform(HankelTypeTransform):
+    """
+    Class representing unevaluated inverse Hankel transforms.
+
+    For usage of this class, see the :class:`IntegralTransform` docstring.
+
+    For how to compute inverse Hankel transforms, see the
+    :func:`inverse_hankel_transform` docstring.
+    """
+
+    _name = 'Inverse Hankel'
+
+
+def inverse_hankel_transform(F, k, r, nu, **hints):
+    r"""
+    Compute the inverse Hankel transform of `F` defined as
+
+    .. math:: f(r) = \int_{0}^\infty F_\nu(k) J_\nu(k r) k \mathrm{d} k.
+
+    Explanation
+    ===========
+
+    If the transform cannot be computed in closed form, this
+    function returns an unevaluated :class:`InverseHankelTransform` object.
+
+    For a description of possible hints, refer to the docstring of
+    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
+    Note that for this transform, by default ``noconds=True``.
+
+    Examples
+    ========
+
+    >>> from sympy import hankel_transform, inverse_hankel_transform
+    >>> from sympy import exp
+    >>> from sympy.abc import r, k, m, nu, a
+
+    >>> ht = hankel_transform(1/r**m, r, k, nu)
+    >>> ht
+    2*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/(2**m*gamma(m/2 + nu/2))
+
+    >>> inverse_hankel_transform(ht, k, r, nu)
+    r**(-m)
+
+    >>> ht = hankel_transform(exp(-a*r), r, k, 0)
+    >>> ht
+    a/(k**3*(a**2/k**2 + 1)**(3/2))
+
+    >>> inverse_hankel_transform(ht, k, r, 0)
+    exp(-a*r)
+
+    See Also
+    ========
+
+    fourier_transform, inverse_fourier_transform
+    sine_transform, inverse_sine_transform
+    cosine_transform, inverse_cosine_transform
+    hankel_transform
+    mellin_transform, laplace_transform
+    """
+    return InverseHankelTransform(F, k, r, nu).doit(**hints)
+
+
+##########################################################################
+# Laplace Transform
+##########################################################################
+
+# Stub classes and functions that used to be here
+import sympy.integrals.laplace as _laplace
+
+LaplaceTransform = _laplace.LaplaceTransform
+laplace_transform = _laplace.laplace_transform
+laplace_correspondence = _laplace.laplace_correspondence
+laplace_initial_conds = _laplace.laplace_initial_conds
+InverseLaplaceTransform = _laplace.InverseLaplaceTransform
+inverse_laplace_transform = _laplace.inverse_laplace_transform
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/trigonometry.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/trigonometry.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd6389bcc79f28ed6c255546685da1a0e061c327
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/integrals/trigonometry.py
@@ -0,0 +1,335 @@
+from sympy.core import cacheit, Dummy, Ne, Integer, Rational, S, Wild
+from sympy.functions import binomial, sin, cos, Piecewise, Abs
+from .integrals import integrate
+
+# TODO sin(a*x)*cos(b*x) -> sin((a+b)x) + sin((a-b)x) ?
+
+# creating, each time, Wild's and sin/cos/Mul is expensive. Also, our match &
+# subs are very slow when not cached, and if we create Wild each time, we
+# effectively block caching.
+#
+# so we cache the pattern
+
+# need to use a function instead of lamda since hash of lambda changes on
+# each call to _pat_sincos
+def _integer_instance(n):
+    return isinstance(n, Integer)
+
+@cacheit
+def _pat_sincos(x):
+    a = Wild('a', exclude=[x])
+    n, m = [Wild(s, exclude=[x], properties=[_integer_instance])
+                for s in 'nm']
+    pat = sin(a*x)**n * cos(a*x)**m
+    return pat, a, n, m
+
+_u = Dummy('u')
+
+
+def trigintegrate(f, x, conds='piecewise'):
+    """
+    Integrate f = Mul(trig) over x.
+
+    Examples
+    ========
+
+    >>> from sympy import sin, cos, tan, sec
+    >>> from sympy.integrals.trigonometry import trigintegrate
+    >>> from sympy.abc import x
+
+    >>> trigintegrate(sin(x)*cos(x), x)
+    sin(x)**2/2
+
+    >>> trigintegrate(sin(x)**2, x)
+    x/2 - sin(x)*cos(x)/2
+
+    >>> trigintegrate(tan(x)*sec(x), x)
+    1/cos(x)
+
+    >>> trigintegrate(sin(x)*tan(x), x)
+    -log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - sin(x)
+
+    References
+    ==========
+
+    .. [1] https://en.wikibooks.org/wiki/Calculus/Integration_techniques
+
+    See Also
+    ========
+
+    sympy.integrals.integrals.Integral.doit
+    sympy.integrals.integrals.Integral
+    """
+    pat, a, n, m = _pat_sincos(x)
+
+    f = f.rewrite('sincos')
+    M = f.match(pat)
+
+    if M is None:
+        return
+
+    n, m = M[n], M[m]
+    if n.is_zero and m.is_zero:
+        return x
+    zz = x if n.is_zero else S.Zero
+
+    a = M[a]
+
+    if n.is_odd or m.is_odd:
+        u = _u
+        n_, m_ = n.is_odd, m.is_odd
+
+        # take smallest n or m -- to choose simplest substitution
+        if n_ and m_:
+
+            # Make sure to choose the positive one
+            # otherwise an incorrect integral can occur.
+            if n < 0 and m > 0:
+                m_ = True
+                n_ = False
+            elif m < 0 and n > 0:
+                n_ = True
+                m_ = False
+            # Both are negative so choose the smallest n or m
+            # in absolute value for simplest substitution.
+            elif (n < 0 and m < 0):
+                n_ = n > m
+                m_ = not (n > m)
+
+            # Both n and m are odd and positive
+            else:
+                n_ = (n < m)      # NB: careful here, one of the
+                m_ = not (n < m)  # conditions *must* be true
+
+        #  n      m       u=C        (n-1)/2    m
+        # S(x) * C(x) dx  --> -(1-u^2)       * u  du
+        if n_:
+            ff = -(1 - u**2)**((n - 1)/2) * u**m
+            uu = cos(a*x)
+
+        #  n      m       u=S   n         (m-1)/2
+        # S(x) * C(x) dx  -->  u  * (1-u^2)       du
+        elif m_:
+            ff = u**n * (1 - u**2)**((m - 1)/2)
+            uu = sin(a*x)
+
+        fi = integrate(ff, u)  # XXX cyclic deps
+        fx = fi.subs(u, uu)
+        if conds == 'piecewise':
+            return Piecewise((fx / a, Ne(a, 0)), (zz, True))
+        return fx / a
+
+    # n & m are both even
+    #
+    #               2k      2m                         2l       2l
+    # we transform S (x) * C (x) into terms with only S (x) or C (x)
+    #
+    # example:
+    #  100     4       100        2    2    100          4         2
+    # S (x) * C (x) = S (x) * (1-S (x))  = S (x) * (1 + S (x) - 2*S (x))
+    #
+    #                  104       102     100
+    #               = S (x) - 2*S (x) + S (x)
+    #       2k
+    # then S   is integrated with recursive formula
+
+    # take largest n or m -- to choose simplest substitution
+    n_ = (Abs(n) > Abs(m))
+    m_ = (Abs(m) > Abs(n))
+    res = S.Zero
+
+    if n_:
+        #  2k         2 k             i             2i
+        # C   = (1 - S )  = sum(i, (-) * B(k, i) * S  )
+        if m > 0:
+            for i in range(0, m//2 + 1):
+                res += (S.NegativeOne**i * binomial(m//2, i) *
+                        _sin_pow_integrate(n + 2*i, x))
+
+        elif m == 0:
+            res = _sin_pow_integrate(n, x)
+        else:
+
+            # m < 0 , |n| > |m|
+            #  /
+            # |
+            # |    m       n
+            # | cos (x) sin (x) dx =
+            # |
+            # |
+            #/
+            #                                      /
+            #                                     |
+            #   -1        m+1     n-1     n - 1   |     m+2     n-2
+            # ________ cos (x) sin (x) + _______  |  cos (x) sin (x) dx
+            #                                     |
+            #   m + 1                     m + 1   |
+            #                                    /
+
+            res = (Rational(-1, m + 1) * cos(x)**(m + 1) * sin(x)**(n - 1) +
+                   Rational(n - 1, m + 1) *
+                   trigintegrate(cos(x)**(m + 2)*sin(x)**(n - 2), x))
+
+    elif m_:
+        #  2k         2 k            i             2i
+        # S   = (1 - C ) = sum(i, (-) * B(k, i) * C  )
+        if n > 0:
+
+            #      /                            /
+            #     |                            |
+            #     |    m       n               |    -m         n
+            #     | cos (x)*sin (x) dx  or     | cos (x) * sin (x) dx
+            #     |                            |
+            #    /                            /
+            #
+            #    |m| > |n| ; m, n >0 ; m, n belong to Z - {0}
+            #       n                                         2
+            #    sin (x) term is expanded here in terms of cos (x),
+            #    and then integrated.
+            #
+
+            for i in range(0, n//2 + 1):
+                res += (S.NegativeOne**i * binomial(n//2, i) *
+                        _cos_pow_integrate(m + 2*i, x))
+
+        elif n == 0:
+
+            #   /
+            #  |
+            #  |  1
+            #  | _ _ _
+            #  |    m
+            #  | cos (x)
+            # /
+            #
+
+            res = _cos_pow_integrate(m, x)
+        else:
+
+            # n < 0 , |m| > |n|
+            #  /
+            # |
+            # |    m       n
+            # | cos (x) sin (x) dx =
+            # |
+            # |
+            #/
+            #                                      /
+            #                                     |
+            #    1        m-1     n+1     m - 1   |     m-2     n+2
+            #  _______ cos (x) sin (x) + _______  |  cos (x) sin (x) dx
+            #                                     |
+            #   n + 1                     n + 1   |
+            #                                    /
+
+            res = (Rational(1, n + 1) * cos(x)**(m - 1)*sin(x)**(n + 1) +
+                   Rational(m - 1, n + 1) *
+                   trigintegrate(cos(x)**(m - 2)*sin(x)**(n + 2), x))
+
+    else:
+        if m == n:
+            ##Substitute sin(2x)/2 for sin(x)cos(x) and then Integrate.
+            res = integrate((sin(2*x)*S.Half)**m, x)
+        elif (m == -n):
+            if n < 0:
+                # Same as the scheme described above.
+                # the function argument to integrate in the end will
+                # be 1, this cannot be integrated by trigintegrate.
+                # Hence use sympy.integrals.integrate.
+                res = (Rational(1, n + 1) * cos(x)**(m - 1) * sin(x)**(n + 1) +
+                       Rational(m - 1, n + 1) *
+                       integrate(cos(x)**(m - 2) * sin(x)**(n + 2), x))
+            else:
+                res = (Rational(-1, m + 1) * cos(x)**(m + 1) * sin(x)**(n - 1) +
+                       Rational(n - 1, m + 1) *
+                       integrate(cos(x)**(m + 2)*sin(x)**(n - 2), x))
+    if conds == 'piecewise':
+        return Piecewise((res.subs(x, a*x) / a, Ne(a, 0)), (zz, True))
+    return res.subs(x, a*x) / a
+
+
+def _sin_pow_integrate(n, x):
+    if n > 0:
+        if n == 1:
+            #Recursion break
+            return -cos(x)
+
+        # n > 0
+        #  /                                                 /
+        # |                                                 |
+        # |    n           -1               n-1     n - 1   |     n-2
+        # | sin (x) dx =  ______ cos (x) sin (x) + _______  |  sin (x) dx
+        # |                                                 |
+        # |                 n                         n     |
+        #/                                                 /
+        #
+        #
+
+        return (Rational(-1, n) * cos(x) * sin(x)**(n - 1) +
+                Rational(n - 1, n) * _sin_pow_integrate(n - 2, x))
+
+    if n < 0:
+        if n == -1:
+            ##Make sure this does not come back here again.
+            ##Recursion breaks here or at n==0.
+            return trigintegrate(1/sin(x), x)
+
+        # n < 0
+        #  /                                                 /
+        # |                                                 |
+        # |    n            1               n+1     n + 2   |     n+2
+        # | sin (x) dx = _______ cos (x) sin (x) + _______  |  sin (x) dx
+        # |                                                 |
+        # |               n + 1                     n + 1   |
+        #/                                                 /
+        #
+
+        return (Rational(1, n + 1) * cos(x) * sin(x)**(n + 1) +
+                Rational(n + 2, n + 1) * _sin_pow_integrate(n + 2, x))
+
+    else:
+        #n == 0
+        #Recursion break.
+        return x
+
+
+def _cos_pow_integrate(n, x):
+    if n > 0:
+        if n == 1:
+            #Recursion break.
+            return sin(x)
+
+        # n > 0
+        #  /                                                 /
+        # |                                                 |
+        # |    n            1               n-1     n - 1   |     n-2
+        # | sin (x) dx =  ______ sin (x) cos (x) + _______  |  cos (x) dx
+        # |                                                 |
+        # |                 n                         n     |
+        #/                                                 /
+        #
+
+        return (Rational(1, n) * sin(x) * cos(x)**(n - 1) +
+                Rational(n - 1, n) * _cos_pow_integrate(n - 2, x))
+
+    if n < 0:
+        if n == -1:
+            ##Recursion break
+            return trigintegrate(1/cos(x), x)
+
+        # n < 0
+        #  /                                                 /
+        # |                                                 |
+        # |    n            -1              n+1     n + 2   |     n+2
+        # | cos (x) dx = _______ sin (x) cos (x) + _______  |  cos (x) dx
+        # |                                                 |
+        # |               n + 1                     n + 1   |
+        #/                                                 /
+        #
+
+        return (Rational(-1, n + 1) * sin(x) * cos(x)**(n + 1) +
+                Rational(n + 2, n + 1) * _cos_pow_integrate(n + 2, x))
+    else:
+        # n == 0
+        #Recursion Break.
+        return x
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..1b3f043ada6222d79dd52fd28b035e2ea45c5683
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/__init__.py
@@ -0,0 +1,8 @@
+"""Helper module for setting up interactive SymPy sessions. """
+
+from .printing import init_printing
+from .session import init_session
+from .traversal import interactive_traversal
+
+
+__all__ = ['init_printing', 'init_session', 'interactive_traversal']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/printing.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/printing.py
new file mode 100644
index 0000000000000000000000000000000000000000..2fcc73e3e96a5b7e25f7fc7ebf54a5781c3b15b9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/printing.py
@@ -0,0 +1,532 @@
+"""Tools for setting up printing in interactive sessions. """
+
+from io import BytesIO
+
+from sympy.printing.latex import latex as default_latex
+from sympy.printing.preview import preview
+from sympy.utilities.misc import debug
+from sympy.printing.defaults import Printable
+from sympy.external import import_module
+
+
+def _init_python_printing(stringify_func, **settings):
+    """Setup printing in Python interactive session. """
+    import sys
+    import builtins
+
+    def _displayhook(arg):
+        """Python's pretty-printer display hook.
+
+           This function was adapted from:
+
+            https://www.python.org/dev/peps/pep-0217/
+
+        """
+        if arg is not None:
+            builtins._ = None
+            print(stringify_func(arg, **settings))
+            builtins._ = arg
+
+    sys.displayhook = _displayhook
+
+
+def _init_ipython_printing(ip, stringify_func, use_latex, euler, forecolor,
+                           backcolor, fontsize, latex_mode, print_builtin,
+                           latex_printer, scale, **settings):
+    """Setup printing in IPython interactive session. """
+    IPython = import_module("IPython", min_module_version="1.0")
+    try:
+        from IPython.lib.latextools import latex_to_png
+    except ImportError:
+        pass
+
+    # Guess best font color if none was given based on the ip.colors string.
+    # From the IPython documentation:
+    #   It has four case-insensitive values: 'nocolor', 'neutral', 'linux',
+    #   'lightbg'. The default is neutral, which should be legible on either
+    #   dark or light terminal backgrounds. linux is optimised for dark
+    #   backgrounds and lightbg for light ones.
+    if forecolor is None:
+        color = ip.colors.lower()
+        if color == 'lightbg':
+            forecolor = 'Black'
+        elif color == 'linux':
+            forecolor = 'White'
+        else:
+            # No idea, go with gray.
+            forecolor = 'Gray'
+        debug("init_printing: Automatic foreground color:", forecolor)
+
+    if use_latex == "svg":
+        extra_preamble = "\n\\special{color %s}" % forecolor
+    else:
+        extra_preamble = ""
+
+    imagesize = 'tight'
+    offset = "0cm,0cm"
+    resolution = round(150*scale)
+    dvi = r"-T %s -D %d -bg %s -fg %s -O %s" % (
+        imagesize, resolution, backcolor, forecolor, offset)
+    dvioptions = dvi.split()
+
+    svg_scale = 150/72*scale
+    dvioptions_svg = ["--no-fonts", "--scale={}".format(svg_scale)]
+
+    debug("init_printing: DVIOPTIONS:", dvioptions)
+    debug("init_printing: DVIOPTIONS_SVG:", dvioptions_svg)
+
+    latex = latex_printer or default_latex
+
+    def _print_plain(arg, p, cycle):
+        """caller for pretty, for use in IPython 0.11"""
+        if _can_print(arg):
+            p.text(stringify_func(arg))
+        else:
+            p.text(IPython.lib.pretty.pretty(arg))
+
+    def _preview_wrapper(o):
+        exprbuffer = BytesIO()
+        try:
+            preview(o, output='png', viewer='BytesIO', euler=euler,
+                    outputbuffer=exprbuffer, extra_preamble=extra_preamble,
+                    dvioptions=dvioptions, fontsize=fontsize)
+        except Exception as e:
+            # IPython swallows exceptions
+            debug("png printing:", "_preview_wrapper exception raised:",
+                  repr(e))
+            raise
+        return exprbuffer.getvalue()
+
+    def _svg_wrapper(o):
+        exprbuffer = BytesIO()
+        try:
+            preview(o, output='svg', viewer='BytesIO', euler=euler,
+                    outputbuffer=exprbuffer, extra_preamble=extra_preamble,
+                    dvioptions=dvioptions_svg, fontsize=fontsize)
+        except Exception as e:
+            # IPython swallows exceptions
+            debug("svg printing:", "_preview_wrapper exception raised:",
+                  repr(e))
+            raise
+        return exprbuffer.getvalue().decode('utf-8')
+
+    def _matplotlib_wrapper(o):
+        # mathtext can't render some LaTeX commands. For example, it can't
+        # render any LaTeX environments such as array or matrix. So here we
+        # ensure that if mathtext fails to render, we return None.
+        try:
+            try:
+                return latex_to_png(o, color=forecolor, scale=scale)
+            except TypeError: #  Old IPython version without color and scale
+                return latex_to_png(o)
+        except ValueError as e:
+            debug('matplotlib exception caught:', repr(e))
+            return None
+
+
+    # Hook methods for builtin SymPy printers
+    printing_hooks = ('_latex', '_sympystr', '_pretty', '_sympyrepr')
+
+
+    def _can_print(o):
+        """Return True if type o can be printed with one of the SymPy printers.
+
+        If o is a container type, this is True if and only if every element of
+        o can be printed in this way.
+        """
+
+        try:
+            # If you're adding another type, make sure you add it to printable_types
+            # later in this file as well
+
+            builtin_types = (list, tuple, set, frozenset)
+            if isinstance(o, builtin_types):
+                # If the object is a custom subclass with a custom str or
+                # repr, use that instead.
+                if (type(o).__str__ not in (i.__str__ for i in builtin_types) or
+                    type(o).__repr__ not in (i.__repr__ for i in builtin_types)):
+                    return False
+                return all(_can_print(i) for i in o)
+            elif isinstance(o, dict):
+                return all(_can_print(i) and _can_print(o[i]) for i in o)
+            elif isinstance(o, bool):
+                return False
+            elif isinstance(o, Printable):
+                # types known to SymPy
+                return True
+            elif any(hasattr(o, hook) for hook in printing_hooks):
+                # types which add support themselves
+                return True
+            elif isinstance(o, (float, int)) and print_builtin:
+                return True
+            return False
+        except RuntimeError:
+            return False
+            # This is in case maximum recursion depth is reached.
+            # Since RecursionError is for versions of Python 3.5+
+            # so this is to guard against RecursionError for older versions.
+
+    def _print_latex_png(o):
+        """
+        A function that returns a png rendered by an external latex
+        distribution, falling back to matplotlib rendering
+        """
+        if _can_print(o):
+            s = latex(o, mode=latex_mode, **settings)
+            if latex_mode == 'plain':
+                s = '$\\displaystyle %s$' % s
+            try:
+                return _preview_wrapper(s)
+            except RuntimeError as e:
+                debug('preview failed with:', repr(e),
+                      ' Falling back to matplotlib backend')
+                if latex_mode != 'inline':
+                    s = latex(o, mode='inline', **settings)
+                return _matplotlib_wrapper(s)
+
+    def _print_latex_svg(o):
+        """
+        A function that returns a svg rendered by an external latex
+        distribution, no fallback available.
+        """
+        if _can_print(o):
+            s = latex(o, mode=latex_mode, **settings)
+            if latex_mode == 'plain':
+                s = '$\\displaystyle %s$' % s
+            try:
+                return _svg_wrapper(s)
+            except RuntimeError as e:
+                debug('preview failed with:', repr(e),
+                      ' No fallback available.')
+
+    def _print_latex_matplotlib(o):
+        """
+        A function that returns a png rendered by mathtext
+        """
+        if _can_print(o):
+            s = latex(o, mode='inline', **settings)
+            return _matplotlib_wrapper(s)
+
+    def _print_latex_text(o):
+        """
+        A function to generate the latex representation of SymPy expressions.
+        """
+        if _can_print(o):
+            s = latex(o, mode=latex_mode, **settings)
+            if latex_mode == 'plain':
+                return '$\\displaystyle %s$' % s
+            return s
+
+    # Printable is our own type, so we handle it with methods instead of
+    # the approach required by builtin types. This allows downstream
+    # packages to override the methods in their own subclasses of Printable,
+    # which avoids the effects of gh-16002.
+    printable_types = [float, tuple, list, set, frozenset, dict, int]
+
+    plaintext_formatter = ip.display_formatter.formatters['text/plain']
+
+    # Exception to the rule above: IPython has better dispatching rules
+    # for plaintext printing (xref ipython/ipython#8938), and we can't
+    # use `_repr_pretty_` without hitting a recursion error in _print_plain.
+    for cls in printable_types + [Printable]:
+        plaintext_formatter.for_type(cls, _print_plain)
+
+    svg_formatter = ip.display_formatter.formatters['image/svg+xml']
+    if use_latex in ('svg', ):
+        debug("init_printing: using svg formatter")
+        for cls in printable_types:
+            svg_formatter.for_type(cls, _print_latex_svg)
+        Printable._repr_svg_ = _print_latex_svg
+    else:
+        debug("init_printing: not using any svg formatter")
+        for cls in printable_types:
+            # Better way to set this, but currently does not work in IPython
+            #png_formatter.for_type(cls, None)
+            if cls in svg_formatter.type_printers:
+                svg_formatter.type_printers.pop(cls)
+        Printable._repr_svg_ = Printable._repr_disabled
+
+    png_formatter = ip.display_formatter.formatters['image/png']
+    if use_latex in (True, 'png'):
+        debug("init_printing: using png formatter")
+        for cls in printable_types:
+            png_formatter.for_type(cls, _print_latex_png)
+        Printable._repr_png_ = _print_latex_png
+    elif use_latex == 'matplotlib':
+        debug("init_printing: using matplotlib formatter")
+        for cls in printable_types:
+            png_formatter.for_type(cls, _print_latex_matplotlib)
+        Printable._repr_png_ = _print_latex_matplotlib
+    else:
+        debug("init_printing: not using any png formatter")
+        for cls in printable_types:
+            # Better way to set this, but currently does not work in IPython
+            #png_formatter.for_type(cls, None)
+            if cls in png_formatter.type_printers:
+                png_formatter.type_printers.pop(cls)
+        Printable._repr_png_ = Printable._repr_disabled
+
+    latex_formatter = ip.display_formatter.formatters['text/latex']
+    if use_latex in (True, 'mathjax'):
+        debug("init_printing: using mathjax formatter")
+        for cls in printable_types:
+            latex_formatter.for_type(cls, _print_latex_text)
+        Printable._repr_latex_ = _print_latex_text
+    else:
+        debug("init_printing: not using text/latex formatter")
+        for cls in printable_types:
+            # Better way to set this, but currently does not work in IPython
+            #latex_formatter.for_type(cls, None)
+            if cls in latex_formatter.type_printers:
+                latex_formatter.type_printers.pop(cls)
+        Printable._repr_latex_ = Printable._repr_disabled
+
+def _is_ipython(shell):
+    """Is a shell instance an IPython shell?"""
+    # shortcut, so we don't import IPython if we don't have to
+    from sys import modules
+    if 'IPython' not in modules:
+        return False
+    try:
+        from IPython.core.interactiveshell import InteractiveShell
+    except ImportError:
+        # IPython < 0.11
+        try:
+            from IPython.iplib import InteractiveShell
+        except ImportError:
+            # Reaching this points means IPython has changed in a backward-incompatible way
+            # that we don't know about. Warn?
+            return False
+    return isinstance(shell, InteractiveShell)
+
+# Used by the doctester to override the default for no_global
+NO_GLOBAL = False
+
+def init_printing(pretty_print=True, order=None, use_unicode=None,
+                  use_latex=None, wrap_line=None, num_columns=None,
+                  no_global=False, ip=None, euler=False, forecolor=None,
+                  backcolor='Transparent', fontsize='10pt',
+                  latex_mode='plain', print_builtin=True,
+                  str_printer=None, pretty_printer=None,
+                  latex_printer=None, scale=1.0, **settings):
+    r"""
+    Initializes pretty-printer depending on the environment.
+
+    Parameters
+    ==========
+
+    pretty_print : bool, default=True
+        If ``True``, use :func:`~.pretty_print` to stringify or the provided pretty
+        printer; if ``False``, use :func:`~.sstrrepr` to stringify or the provided string
+        printer.
+    order : string or None, default='lex'
+        There are a few different settings for this parameter:
+        ``'lex'`` (default), which is lexographic order;
+        ``'grlex'``, which is graded lexographic order;
+        ``'grevlex'``, which is reversed graded lexographic order;
+        ``'old'``, which is used for compatibility reasons and for long expressions;
+        ``None``, which sets it to lex.
+    use_unicode : bool or None, default=None
+        If ``True``, use unicode characters;
+        if ``False``, do not use unicode characters;
+        if ``None``, make a guess based on the environment.
+    use_latex : string, bool, or None, default=None
+        If ``True``, use default LaTeX rendering in GUI interfaces (png and
+        mathjax);
+        if ``False``, do not use LaTeX rendering;
+        if ``None``, make a guess based on the environment;
+        if ``'png'``, enable LaTeX rendering with an external LaTeX compiler,
+        falling back to matplotlib if external compilation fails;
+        if ``'matplotlib'``, enable LaTeX rendering with matplotlib;
+        if ``'mathjax'``, enable LaTeX text generation, for example MathJax
+        rendering in IPython notebook or text rendering in LaTeX documents;
+        if ``'svg'``, enable LaTeX rendering with an external latex compiler,
+        no fallback
+    wrap_line : bool
+        If True, lines will wrap at the end; if False, they will not wrap
+        but continue as one line. This is only relevant if ``pretty_print`` is
+        True.
+    num_columns : int or None, default=None
+        If ``int``, number of columns before wrapping is set to num_columns; if
+        ``None``, number of columns before wrapping is set to terminal width.
+        This is only relevant if ``pretty_print`` is ``True``.
+    no_global : bool, default=False
+        If ``True``, the settings become system wide;
+        if ``False``, use just for this console/session.
+    ip : An interactive console
+        This can either be an instance of IPython,
+        or a class that derives from code.InteractiveConsole.
+    euler : bool, optional, default=False
+        Loads the euler package in the LaTeX preamble for handwritten style
+        fonts (https://www.ctan.org/pkg/euler).
+    forecolor : string or None, optional, default=None
+        DVI setting for foreground color. ``None`` means that either ``'Black'``,
+        ``'White'``, or ``'Gray'`` will be selected based on a guess of the IPython
+        terminal color setting. See notes.
+    backcolor : string, optional, default='Transparent'
+        DVI setting for background color. See notes.
+    fontsize : string or int, optional, default='10pt'
+        A font size to pass to the LaTeX documentclass function in the
+        preamble. Note that the options are limited by the documentclass.
+        Consider using scale instead.
+    latex_mode : string, optional, default='plain'
+        The mode used in the LaTeX printer. Can be one of:
+        ``{'inline'|'plain'|'equation'|'equation*'}``.
+    print_builtin : boolean, optional, default=True
+        If ``True`` then floats and integers will be printed. If ``False`` the
+        printer will only print SymPy types.
+    str_printer : function, optional, default=None
+        A custom string printer function. This should mimic
+        :func:`~.sstrrepr`.
+    pretty_printer : function, optional, default=None
+        A custom pretty printer. This should mimic :func:`~.pretty`.
+    latex_printer : function, optional, default=None
+        A custom LaTeX printer. This should mimic :func:`~.latex`.
+    scale : float, optional, default=1.0
+        Scale the LaTeX output when using the ``'png'`` or ``'svg'`` backends.
+        Useful for high dpi screens.
+    settings :
+        Any additional settings for the ``latex`` and ``pretty`` commands can
+        be used to fine-tune the output.
+
+    Examples
+    ========
+
+    >>> from sympy.interactive import init_printing
+    >>> from sympy import Symbol, sqrt
+    >>> from sympy.abc import x, y
+    >>> sqrt(5)
+    sqrt(5)
+    >>> init_printing(pretty_print=True) # doctest: +SKIP
+    >>> sqrt(5) # doctest: +SKIP
+      ___
+    \/ 5
+    >>> theta = Symbol('theta') # doctest: +SKIP
+    >>> init_printing(use_unicode=True) # doctest: +SKIP
+    >>> theta # doctest: +SKIP
+    \u03b8
+    >>> init_printing(use_unicode=False) # doctest: +SKIP
+    >>> theta # doctest: +SKIP
+    theta
+    >>> init_printing(order='lex') # doctest: +SKIP
+    >>> str(y + x + y**2 + x**2) # doctest: +SKIP
+    x**2 + x + y**2 + y
+    >>> init_printing(order='grlex') # doctest: +SKIP
+    >>> str(y + x + y**2 + x**2) # doctest: +SKIP
+    x**2 + x + y**2 + y
+    >>> init_printing(order='grevlex') # doctest: +SKIP
+    >>> str(y * x**2 + x * y**2) # doctest: +SKIP
+    x**2*y + x*y**2
+    >>> init_printing(order='old') # doctest: +SKIP
+    >>> str(x**2 + y**2 + x + y) # doctest: +SKIP
+    x**2 + x + y**2 + y
+    >>> init_printing(num_columns=10) # doctest: +SKIP
+    >>> x**2 + x + y**2 + y # doctest: +SKIP
+    x + y +
+    x**2 + y**2
+
+    Notes
+    =====
+
+    The foreground and background colors can be selected when using ``'png'`` or
+    ``'svg'`` LaTeX rendering. Note that before the ``init_printing`` command is
+    executed, the LaTeX rendering is handled by the IPython console and not SymPy.
+
+    The colors can be selected among the 68 standard colors known to ``dvips``,
+    for a list see [1]_. In addition, the background color can be
+    set to  ``'Transparent'`` (which is the default value).
+
+    When using the ``'Auto'`` foreground color, the guess is based on the
+    ``colors`` variable in the IPython console, see [2]_. Hence, if
+    that variable is set correctly in your IPython console, there is a high
+    chance that the output will be readable, although manual settings may be
+    needed.
+
+
+    References
+    ==========
+
+    .. [1] https://en.wikibooks.org/wiki/LaTeX/Colors#The_68_standard_colors_known_to_dvips
+
+    .. [2] https://ipython.readthedocs.io/en/stable/config/details.html#terminal-colors
+
+    See Also
+    ========
+
+    sympy.printing.latex
+    sympy.printing.pretty
+
+    """
+    import sys
+    from sympy.printing.printer import Printer
+
+    if pretty_print:
+        if pretty_printer is not None:
+            stringify_func = pretty_printer
+        else:
+            from sympy.printing import pretty as stringify_func
+    else:
+        if str_printer is not None:
+            stringify_func = str_printer
+        else:
+            from sympy.printing import sstrrepr as stringify_func
+
+    # Even if ip is not passed, double check that not in IPython shell
+    in_ipython = False
+    if ip is None:
+        try:
+            ip = get_ipython()
+        except NameError:
+            pass
+        else:
+            in_ipython = (ip is not None)
+
+    if ip and not in_ipython:
+        in_ipython = _is_ipython(ip)
+
+    if in_ipython and pretty_print:
+        try:
+            from IPython.terminal.interactiveshell import TerminalInteractiveShell
+            from code import InteractiveConsole
+        except ImportError:
+            pass
+        else:
+            # This will be True if we are in the qtconsole or notebook
+            if not isinstance(ip, (InteractiveConsole, TerminalInteractiveShell)) \
+                    and 'ipython-console' not in ''.join(sys.argv):
+                if use_unicode is None:
+                    debug("init_printing: Setting use_unicode to True")
+                    use_unicode = True
+                if use_latex is None:
+                    debug("init_printing: Setting use_latex to True")
+                    use_latex = True
+
+    if not NO_GLOBAL and not no_global:
+        Printer.set_global_settings(order=order, use_unicode=use_unicode,
+                                    wrap_line=wrap_line, num_columns=num_columns)
+    else:
+        _stringify_func = stringify_func
+
+        if pretty_print:
+            stringify_func = lambda expr, **settings: \
+                             _stringify_func(expr, order=order,
+                                             use_unicode=use_unicode,
+                                             wrap_line=wrap_line,
+                                             num_columns=num_columns,
+                                             **settings)
+        else:
+            stringify_func = \
+                lambda expr, **settings: _stringify_func(
+                    expr, order=order, **settings)
+
+    if in_ipython:
+        mode_in_settings = settings.pop("mode", None)
+        if mode_in_settings:
+            debug("init_printing: Mode is not able to be set due to internals"
+                  "of IPython printing")
+        _init_ipython_printing(ip, stringify_func, use_latex, euler,
+                               forecolor, backcolor, fontsize, latex_mode,
+                               print_builtin, latex_printer, scale,
+                               **settings)
+    else:
+        _init_python_printing(stringify_func, **settings)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/session.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/session.py
new file mode 100644
index 0000000000000000000000000000000000000000..348b0938d69e5e7ffa9510f7d9ac759eb6683b8f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/session.py
@@ -0,0 +1,463 @@
+"""Tools for setting up interactive sessions. """
+
+from sympy.external.gmpy import GROUND_TYPES
+from sympy.external.importtools import version_tuple
+
+from sympy.interactive.printing import init_printing
+
+from sympy.utilities.misc import ARCH
+
+preexec_source = """\
+from sympy import *
+x, y, z, t = symbols('x y z t')
+k, m, n = symbols('k m n', integer=True)
+f, g, h = symbols('f g h', cls=Function)
+init_printing()
+"""
+
+verbose_message = """\
+These commands were executed:
+%(source)s
+Documentation can be found at https://docs.sympy.org/%(version)s
+"""
+
+no_ipython = """\
+Could not locate IPython. Having IPython installed is greatly recommended.
+See http://ipython.scipy.org for more details. If you use Debian/Ubuntu,
+just install the 'ipython' package and start isympy again.
+"""
+
+
+def _make_message(ipython=True, quiet=False, source=None):
+    """Create a banner for an interactive session. """
+    from sympy import __version__ as sympy_version
+    from sympy import SYMPY_DEBUG
+
+    import sys
+    import os
+
+    if quiet:
+        return ""
+
+    python_version = "%d.%d.%d" % sys.version_info[:3]
+
+    if ipython:
+        shell_name = "IPython"
+    else:
+        shell_name = "Python"
+
+    info = ['ground types: %s' % GROUND_TYPES]
+
+    cache = os.getenv('SYMPY_USE_CACHE')
+
+    if cache is not None and cache.lower() == 'no':
+        info.append('cache: off')
+
+    if SYMPY_DEBUG:
+        info.append('debugging: on')
+
+    args = shell_name, sympy_version, python_version, ARCH, ', '.join(info)
+    message = "%s console for SymPy %s (Python %s-%s) (%s)\n" % args
+
+    if source is None:
+        source = preexec_source
+
+    _source = ""
+
+    for line in source.split('\n')[:-1]:
+        if not line:
+            _source += '\n'
+        else:
+            _source += '>>> ' + line + '\n'
+
+    doc_version = sympy_version
+    if 'dev' in doc_version:
+        doc_version = "dev"
+    else:
+        doc_version = "%s/" % doc_version
+
+    message += '\n' + verbose_message % {'source': _source,
+                                         'version': doc_version}
+
+    return message
+
+
+def int_to_Integer(s):
+    """
+    Wrap integer literals with Integer.
+
+    This is based on the decistmt example from
+    https://docs.python.org/3/library/tokenize.html.
+
+    Only integer literals are converted.  Float literals are left alone.
+
+    Examples
+    ========
+
+    >>> from sympy import Integer # noqa: F401
+    >>> from sympy.interactive.session import int_to_Integer
+    >>> s = '1.2 + 1/2 - 0x12 + a1'
+    >>> int_to_Integer(s)
+    '1.2 +Integer (1 )/Integer (2 )-Integer (0x12 )+a1 '
+    >>> s = 'print (1/2)'
+    >>> int_to_Integer(s)
+    'print (Integer (1 )/Integer (2 ))'
+    >>> exec(s)
+    0.5
+    >>> exec(int_to_Integer(s))
+    1/2
+    """
+    from tokenize import generate_tokens, untokenize, NUMBER, NAME, OP
+    from io import StringIO
+
+    def _is_int(num):
+        """
+        Returns true if string value num (with token NUMBER) represents an integer.
+        """
+        # XXX: Is there something in the standard library that will do this?
+        if '.' in num or 'j' in num.lower() or 'e' in num.lower():
+            return False
+        return True
+
+    result = []
+    g = generate_tokens(StringIO(s).readline)  # tokenize the string
+    for toknum, tokval, _, _, _ in g:
+        if toknum == NUMBER and _is_int(tokval):  # replace NUMBER tokens
+            result.extend([
+                (NAME, 'Integer'),
+                (OP, '('),
+                (NUMBER, tokval),
+                (OP, ')')
+            ])
+        else:
+            result.append((toknum, tokval))
+    return untokenize(result)
+
+
+def enable_automatic_int_sympification(shell):
+    """
+    Allow IPython to automatically convert integer literals to Integer.
+    """
+    import ast
+    old_run_cell = shell.run_cell
+
+    def my_run_cell(cell, *args, **kwargs):
+        try:
+            # Check the cell for syntax errors.  This way, the syntax error
+            # will show the original input, not the transformed input.  The
+            # downside here is that IPython magic like %timeit will not work
+            # with transformed input (but on the other hand, IPython magic
+            # that doesn't expect transformed input will continue to work).
+            ast.parse(cell)
+        except SyntaxError:
+            pass
+        else:
+            cell = int_to_Integer(cell)
+        return old_run_cell(cell, *args, **kwargs)
+
+    shell.run_cell = my_run_cell
+
+
+def enable_automatic_symbols(shell):
+    """Allow IPython to automatically create symbols (``isympy -a``). """
+    # XXX: This should perhaps use tokenize, like int_to_Integer() above.
+    # This would avoid re-executing the code, which can lead to subtle
+    # issues.  For example:
+    #
+    # In [1]: a = 1
+    #
+    # In [2]: for i in range(10):
+    #    ...:     a += 1
+    #    ...:
+    #
+    # In [3]: a
+    # Out[3]: 11
+    #
+    # In [4]: a = 1
+    #
+    # In [5]: for i in range(10):
+    #    ...:     a += 1
+    #    ...:     print b
+    #    ...:
+    # b
+    # b
+    # b
+    # b
+    # b
+    # b
+    # b
+    # b
+    # b
+    # b
+    #
+    # In [6]: a
+    # Out[6]: 12
+    #
+    # Note how the for loop is executed again because `b` was not defined, but `a`
+    # was already incremented once, so the result is that it is incremented
+    # multiple times.
+
+    import re
+    re_nameerror = re.compile(
+        "name '(?P[A-Za-z_][A-Za-z0-9_]*)' is not defined")
+
+    def _handler(self, etype, value, tb, tb_offset=None):
+        """Handle :exc:`NameError` exception and allow injection of missing symbols. """
+        if etype is NameError and tb.tb_next and not tb.tb_next.tb_next:
+            match = re_nameerror.match(str(value))
+
+            if match is not None:
+                # XXX: Make sure Symbol is in scope. Otherwise you'll get infinite recursion.
+                self.run_cell("%(symbol)s = Symbol('%(symbol)s')" %
+                              {'symbol': match.group("symbol")}, store_history=False)
+
+                try:
+                    code = self.user_ns['In'][-1]
+                except (KeyError, IndexError):
+                    pass
+                else:
+                    self.run_cell(code, store_history=False)
+                    return None
+                finally:
+                    self.run_cell("del %s" % match.group("symbol"),
+                                  store_history=False)
+
+        stb = self.InteractiveTB.structured_traceback(
+            etype, value, tb, tb_offset=tb_offset)
+        self._showtraceback(etype, value, stb)
+
+    shell.set_custom_exc((NameError,), _handler)
+
+
+def init_ipython_session(shell=None, argv=[], auto_symbols=False, auto_int_to_Integer=False):
+    """Construct new IPython session. """
+    import IPython
+
+    if version_tuple(IPython.__version__) >= version_tuple('0.11'):
+        if not shell:
+            # use an app to parse the command line, and init config
+            # IPython 1.0 deprecates the frontend module, so we import directly
+            # from the terminal module to prevent a deprecation message from being
+            # shown.
+            if version_tuple(IPython.__version__) >= version_tuple('1.0'):
+                from IPython.terminal import ipapp
+            else:
+                from IPython.frontend.terminal import ipapp
+            app = ipapp.TerminalIPythonApp()
+
+            # don't draw IPython banner during initialization:
+            app.display_banner = False
+            app.initialize(argv)
+
+            shell = app.shell
+
+        if auto_symbols:
+            enable_automatic_symbols(shell)
+        if auto_int_to_Integer:
+            enable_automatic_int_sympification(shell)
+
+        return shell
+    else:
+        from IPython.Shell import make_IPython
+        return make_IPython(argv)
+
+
+def init_python_session():
+    """Construct new Python session. """
+    from code import InteractiveConsole
+
+    class SymPyConsole(InteractiveConsole):
+        """An interactive console with readline support. """
+
+        def __init__(self):
+            ns_locals = {}
+            InteractiveConsole.__init__(self, locals=ns_locals)
+            try:
+                import rlcompleter
+                import readline
+            except ImportError:
+                pass
+            else:
+                import os
+                import atexit
+
+                readline.set_completer(rlcompleter.Completer(ns_locals).complete)
+                readline.parse_and_bind('tab: complete')
+
+                if hasattr(readline, 'read_history_file'):
+                    history = os.path.expanduser('~/.sympy-history')
+
+                    try:
+                        readline.read_history_file(history)
+                    except OSError:
+                        pass
+
+                    atexit.register(readline.write_history_file, history)
+
+    return SymPyConsole()
+
+
+def init_session(ipython=None, pretty_print=True, order=None,
+                 use_unicode=None, use_latex=None, quiet=False, auto_symbols=False,
+                 auto_int_to_Integer=False, str_printer=None, pretty_printer=None,
+                 latex_printer=None, argv=[]):
+    """
+    Initialize an embedded IPython or Python session. The IPython session is
+    initiated with the --pylab option, without the numpy imports, so that
+    matplotlib plotting can be interactive.
+
+    Parameters
+    ==========
+
+    pretty_print: boolean
+        If True, use pretty_print to stringify;
+        if False, use sstrrepr to stringify.
+    order: string or None
+        There are a few different settings for this parameter:
+        lex (default), which is lexographic order;
+        grlex, which is graded lexographic order;
+        grevlex, which is reversed graded lexographic order;
+        old, which is used for compatibility reasons and for long expressions;
+        None, which sets it to lex.
+    use_unicode: boolean or None
+        If True, use unicode characters;
+        if False, do not use unicode characters.
+    use_latex: boolean or None
+        If True, use latex rendering if IPython GUI's;
+        if False, do not use latex rendering.
+    quiet: boolean
+        If True, init_session will not print messages regarding its status;
+        if False, init_session will print messages regarding its status.
+    auto_symbols: boolean
+        If True, IPython will automatically create symbols for you.
+        If False, it will not.
+        The default is False.
+    auto_int_to_Integer: boolean
+        If True, IPython will automatically wrap int literals with Integer, so
+        that things like 1/2 give Rational(1, 2).
+        If False, it will not.
+        The default is False.
+    ipython: boolean or None
+        If True, printing will initialize for an IPython console;
+        if False, printing will initialize for a normal console;
+        The default is None, which automatically determines whether we are in
+        an ipython instance or not.
+    str_printer: function, optional, default=None
+        A custom string printer function. This should mimic
+        sympy.printing.sstrrepr().
+    pretty_printer: function, optional, default=None
+        A custom pretty printer. This should mimic sympy.printing.pretty().
+    latex_printer: function, optional, default=None
+        A custom LaTeX printer. This should mimic sympy.printing.latex()
+        This should mimic sympy.printing.latex().
+    argv: list of arguments for IPython
+        See sympy.bin.isympy for options that can be used to initialize IPython.
+
+    See Also
+    ========
+
+    sympy.interactive.printing.init_printing: for examples and the rest of the parameters.
+
+
+    Examples
+    ========
+
+    >>> from sympy import init_session, Symbol, sin, sqrt
+    >>> sin(x) #doctest: +SKIP
+    NameError: name 'x' is not defined
+    >>> init_session() #doctest: +SKIP
+    >>> sin(x) #doctest: +SKIP
+    sin(x)
+    >>> sqrt(5) #doctest: +SKIP
+      ___
+    \\/ 5
+    >>> init_session(pretty_print=False) #doctest: +SKIP
+    >>> sqrt(5) #doctest: +SKIP
+    sqrt(5)
+    >>> y + x + y**2 + x**2 #doctest: +SKIP
+    x**2 + x + y**2 + y
+    >>> init_session(order='grlex') #doctest: +SKIP
+    >>> y + x + y**2 + x**2 #doctest: +SKIP
+    x**2 + y**2 + x + y
+    >>> init_session(order='grevlex') #doctest: +SKIP
+    >>> y * x**2 + x * y**2 #doctest: +SKIP
+    x**2*y + x*y**2
+    >>> init_session(order='old') #doctest: +SKIP
+    >>> x**2 + y**2 + x + y #doctest: +SKIP
+    x + y + x**2 + y**2
+    >>> theta = Symbol('theta') #doctest: +SKIP
+    >>> theta #doctest: +SKIP
+    theta
+    >>> init_session(use_unicode=True) #doctest: +SKIP
+    >>> theta # doctest: +SKIP
+    \u03b8
+    """
+    import sys
+
+    in_ipython = False
+
+    if ipython is not False:
+        try:
+            import IPython
+        except ImportError:
+            if ipython is True:
+                raise RuntimeError("IPython is not available on this system")
+            ip = None
+        else:
+            try:
+                from IPython import get_ipython
+                ip = get_ipython()
+            except ImportError:
+                ip = None
+        in_ipython = bool(ip)
+        if ipython is None:
+            ipython = in_ipython
+
+    if ipython is False:
+        ip = init_python_session()
+        mainloop = ip.interact
+    else:
+        ip = init_ipython_session(ip, argv=argv, auto_symbols=auto_symbols,
+                                  auto_int_to_Integer=auto_int_to_Integer)
+
+        if version_tuple(IPython.__version__) >= version_tuple('0.11'):
+            # runsource is gone, use run_cell instead, which doesn't
+            # take a symbol arg.  The second arg is `store_history`,
+            # and False means don't add the line to IPython's history.
+            ip.runsource = lambda src, symbol='exec': ip.run_cell(src, False)
+
+            # Enable interactive plotting using pylab.
+            try:
+                ip.enable_pylab(import_all=False)
+            except Exception:
+                # Causes an import error if matplotlib is not installed.
+                # Causes other errors (depending on the backend) if there
+                # is no display, or if there is some problem in the
+                # backend, so we have a bare "except Exception" here
+                pass
+        if not in_ipython:
+            mainloop = ip.mainloop
+
+    if auto_symbols and (not ipython or version_tuple(IPython.__version__) < version_tuple('0.11')):
+        raise RuntimeError("automatic construction of symbols is possible only in IPython 0.11 or above")
+    if auto_int_to_Integer and (not ipython or version_tuple(IPython.__version__) < version_tuple('0.11')):
+        raise RuntimeError("automatic int to Integer transformation is possible only in IPython 0.11 or above")
+
+    _preexec_source = preexec_source
+
+    ip.runsource(_preexec_source, symbol='exec')
+    init_printing(pretty_print=pretty_print, order=order,
+                  use_unicode=use_unicode, use_latex=use_latex, ip=ip,
+                  str_printer=str_printer, pretty_printer=pretty_printer,
+                  latex_printer=latex_printer)
+
+    message = _make_message(ipython, quiet, _preexec_source)
+
+    if not in_ipython:
+        print(message)
+        mainloop()
+        sys.exit('Exiting ...')
+    else:
+        print(message)
+        import atexit
+        atexit.register(lambda: print("Exiting ...\n"))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/test_interactive.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/test_interactive.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e088c42fd872c13849e593b04734158f5d1e5bc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/test_interactive.py
@@ -0,0 +1,10 @@
+from sympy.interactive.session import int_to_Integer
+
+
+def test_int_to_Integer():
+    assert int_to_Integer("1 + 2.2 + 0x3 + 40") == \
+        'Integer (1 )+2.2 +Integer (0x3 )+Integer (40 )'
+    assert int_to_Integer("0b101") == 'Integer (0b101 )'
+    assert int_to_Integer("ab1 + 1 + '1 + 2'") == "ab1 +Integer (1 )+'1 + 2'"
+    assert int_to_Integer("(2 + \n3)") == '(Integer (2 )+\nInteger (3 ))'
+    assert int_to_Integer("2 + 2.0 + 2j + 2e-10") == 'Integer (2 )+2.0 +2j +2e-10 '
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/test_ipython.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/test_ipython.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac4734406d2f1197732a9dcbdd94b2b34e9fe170
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/tests/test_ipython.py
@@ -0,0 +1,278 @@
+"""Tests of tools for setting up interactive IPython sessions. """
+
+from sympy.interactive.session import (init_ipython_session,
+    enable_automatic_symbols, enable_automatic_int_sympification)
+
+from sympy.core import Symbol, Rational, Integer
+from sympy.external import import_module
+from sympy.testing.pytest import raises
+
+# TODO: The code below could be made more granular with something like:
+#
+# @requires('IPython', version=">=1.0")
+# def test_automatic_symbols(ipython):
+
+ipython = import_module("IPython", min_module_version="1.0")
+
+if not ipython:
+    #bin/test will not execute any tests now
+    disabled = True
+
+# WARNING: These tests will modify the existing IPython environment. IPython
+# uses a single instance for its interpreter, so there is no way to isolate
+# the test from another IPython session. It also means that if this test is
+# run twice in the same Python session it will fail. This isn't usually a
+# problem because the test suite is run in a subprocess by default, but if the
+# tests are run with subprocess=False it can pollute the current IPython
+# session. See the discussion in issue #15149.
+
+def test_automatic_symbols():
+    # NOTE: Because of the way the hook works, you have to use run_cell(code,
+    # True).  This means that the code must have no Out, or it will be printed
+    # during the tests.
+    app = init_ipython_session()
+    app.run_cell("from sympy import *")
+
+    enable_automatic_symbols(app)
+
+    symbol = "verylongsymbolname"
+    assert symbol not in app.user_ns
+    app.run_cell("a = %s" % symbol, True)
+    assert symbol not in app.user_ns
+    app.run_cell("a = type(%s)" % symbol, True)
+    assert app.user_ns['a'] == Symbol
+    app.run_cell("%s = Symbol('%s')" % (symbol, symbol), True)
+    assert symbol in app.user_ns
+
+    # Check that built-in names aren't overridden
+    app.run_cell("a = all == __builtin__.all", True)
+    assert "all" not in app.user_ns
+    assert app.user_ns['a'] is True
+
+    # Check that SymPy names aren't overridden
+    app.run_cell("import sympy")
+    app.run_cell("a = factorial == sympy.factorial", True)
+    assert app.user_ns['a'] is True
+
+
+def test_int_to_Integer():
+    # XXX: Warning, don't test with == here.  0.5 == Rational(1, 2) is True!
+    app = init_ipython_session()
+    app.run_cell("from sympy import Integer")
+    app.run_cell("a = 1")
+    assert isinstance(app.user_ns['a'], int)
+
+    enable_automatic_int_sympification(app)
+    app.run_cell("a = 1/2")
+    assert isinstance(app.user_ns['a'], Rational)
+    app.run_cell("a = 1")
+    assert isinstance(app.user_ns['a'], Integer)
+    app.run_cell("a = int(1)")
+    assert isinstance(app.user_ns['a'], int)
+    app.run_cell("a = (1/\n2)")
+    assert app.user_ns['a'] == Rational(1, 2)
+    # TODO: How can we test that the output of a SyntaxError is the original
+    # input, not the transformed input?
+
+
+def test_ipythonprinting():
+    # Initialize and setup IPython session
+    app = init_ipython_session()
+    app.run_cell("ip = get_ipython()")
+    app.run_cell("inst = ip.instance()")
+    app.run_cell("format = inst.display_formatter.format")
+    app.run_cell("from sympy import Symbol")
+
+    # Printing without printing extension
+    app.run_cell("a = format(Symbol('pi'))")
+    app.run_cell("a2 = format(Symbol('pi')**2)")
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        assert app.user_ns['a']['text/plain'] == "pi"
+        assert app.user_ns['a2']['text/plain'] == "pi**2"
+    else:
+        assert app.user_ns['a'][0]['text/plain'] == "pi"
+        assert app.user_ns['a2'][0]['text/plain'] == "pi**2"
+
+    # Load printing extension
+    app.run_cell("from sympy import init_printing")
+    app.run_cell("init_printing()")
+    # Printing with printing extension
+    app.run_cell("a = format(Symbol('pi'))")
+    app.run_cell("a2 = format(Symbol('pi')**2)")
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        assert app.user_ns['a']['text/plain'] in ('\N{GREEK SMALL LETTER PI}', 'pi')
+        assert app.user_ns['a2']['text/plain'] in (' 2\n\N{GREEK SMALL LETTER PI} ', '  2\npi ')
+    else:
+        assert app.user_ns['a'][0]['text/plain'] in ('\N{GREEK SMALL LETTER PI}', 'pi')
+        assert app.user_ns['a2'][0]['text/plain'] in (' 2\n\N{GREEK SMALL LETTER PI} ', '  2\npi ')
+
+
+def test_print_builtin_option():
+    # Initialize and setup IPython session
+    app = init_ipython_session()
+    app.run_cell("ip = get_ipython()")
+    app.run_cell("inst = ip.instance()")
+    app.run_cell("format = inst.display_formatter.format")
+    app.run_cell("from sympy import Symbol")
+    app.run_cell("from sympy import init_printing")
+
+    app.run_cell("a = format({Symbol('pi'): 3.14, Symbol('n_i'): 3})")
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        text = app.user_ns['a']['text/plain']
+        raises(KeyError, lambda: app.user_ns['a']['text/latex'])
+    else:
+        text = app.user_ns['a'][0]['text/plain']
+        raises(KeyError, lambda: app.user_ns['a'][0]['text/latex'])
+    # XXX: How can we make this ignore the terminal width? This test fails if
+    # the terminal is too narrow.
+    assert text in ("{pi: 3.14, n_i: 3}",
+                    '{n\N{LATIN SUBSCRIPT SMALL LETTER I}: 3, \N{GREEK SMALL LETTER PI}: 3.14}',
+                    "{n_i: 3, pi: 3.14}",
+                    '{\N{GREEK SMALL LETTER PI}: 3.14, n\N{LATIN SUBSCRIPT SMALL LETTER I}: 3}')
+
+    # If we enable the default printing, then the dictionary's should render
+    # as a LaTeX version of the whole dict: ${\pi: 3.14, n_i: 3}$
+    app.run_cell("inst.display_formatter.formatters['text/latex'].enabled = True")
+    app.run_cell("init_printing(use_latex=True)")
+    app.run_cell("a = format({Symbol('pi'): 3.14, Symbol('n_i'): 3})")
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        text = app.user_ns['a']['text/plain']
+        latex = app.user_ns['a']['text/latex']
+    else:
+        text = app.user_ns['a'][0]['text/plain']
+        latex = app.user_ns['a'][0]['text/latex']
+    assert text in ("{pi: 3.14, n_i: 3}",
+                    '{n\N{LATIN SUBSCRIPT SMALL LETTER I}: 3, \N{GREEK SMALL LETTER PI}: 3.14}',
+                    "{n_i: 3, pi: 3.14}",
+                    '{\N{GREEK SMALL LETTER PI}: 3.14, n\N{LATIN SUBSCRIPT SMALL LETTER I}: 3}')
+    assert latex == r'$\displaystyle \left\{ n_{i} : 3, \  \pi : 3.14\right\}$'
+
+    # Objects with an _latex overload should also be handled by our tuple
+    # printer.
+    app.run_cell("""\
+    class WithOverload:
+        def _latex(self, printer):
+            return r"\\LaTeX"
+    """)
+    app.run_cell("a = format((WithOverload(),))")
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        latex = app.user_ns['a']['text/latex']
+    else:
+        latex = app.user_ns['a'][0]['text/latex']
+    assert latex == r'$\displaystyle \left( \LaTeX,\right)$'
+
+    app.run_cell("inst.display_formatter.formatters['text/latex'].enabled = True")
+    app.run_cell("init_printing(use_latex=True, print_builtin=False)")
+    app.run_cell("a = format({Symbol('pi'): 3.14, Symbol('n_i'): 3})")
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        text = app.user_ns['a']['text/plain']
+        raises(KeyError, lambda: app.user_ns['a']['text/latex'])
+    else:
+        text = app.user_ns['a'][0]['text/plain']
+        raises(KeyError, lambda: app.user_ns['a'][0]['text/latex'])
+    # Note : In Python 3 we have one text type: str which holds Unicode data
+    # and two byte types bytes and bytearray.
+    # Python 3.3.3 + IPython 0.13.2 gives: '{n_i: 3, pi: 3.14}'
+    # Python 3.3.3 + IPython 1.1.0 gives: '{n_i: 3, pi: 3.14}'
+    assert text in ("{pi: 3.14, n_i: 3}", "{n_i: 3, pi: 3.14}")
+
+
+def test_builtin_containers():
+    # Initialize and setup IPython session
+    app = init_ipython_session()
+    app.run_cell("ip = get_ipython()")
+    app.run_cell("inst = ip.instance()")
+    app.run_cell("format = inst.display_formatter.format")
+    app.run_cell("inst.display_formatter.formatters['text/latex'].enabled = True")
+    app.run_cell("from sympy import init_printing, Matrix")
+    app.run_cell('init_printing(use_latex=True, use_unicode=False)')
+
+    # Make sure containers that shouldn't pretty print don't.
+    app.run_cell('a = format((True, False))')
+    app.run_cell('import sys')
+    app.run_cell('b = format(sys.flags)')
+    app.run_cell('c = format((Matrix([1, 2]),))')
+    # Deal with API change starting at IPython 1.0
+    if int(ipython.__version__.split(".")[0]) < 1:
+        assert app.user_ns['a']['text/plain'] ==  '(True, False)'
+        assert 'text/latex' not in app.user_ns['a']
+        assert app.user_ns['b']['text/plain'][:10] == 'sys.flags('
+        assert 'text/latex' not in app.user_ns['b']
+        assert app.user_ns['c']['text/plain'] == \
+"""\
+ [1]  \n\
+([ ],)
+ [2]  \
+"""
+        assert app.user_ns['c']['text/latex'] == '$\\displaystyle \\left( \\left[\\begin{matrix}1\\\\2\\end{matrix}\\right],\\right)$'
+    else:
+        assert app.user_ns['a'][0]['text/plain'] ==  '(True, False)'
+        assert 'text/latex' not in app.user_ns['a'][0]
+        assert app.user_ns['b'][0]['text/plain'][:10] == 'sys.flags('
+        assert 'text/latex' not in app.user_ns['b'][0]
+        assert app.user_ns['c'][0]['text/plain'] == \
+"""\
+ [1]  \n\
+([ ],)
+ [2]  \
+"""
+        assert app.user_ns['c'][0]['text/latex'] == '$\\displaystyle \\left( \\left[\\begin{matrix}1\\\\2\\end{matrix}\\right],\\right)$'
+
+def test_matplotlib_bad_latex():
+    # Initialize and setup IPython session
+    app = init_ipython_session()
+    app.run_cell("import IPython")
+    app.run_cell("ip = get_ipython()")
+    app.run_cell("inst = ip.instance()")
+    app.run_cell("format = inst.display_formatter.format")
+    app.run_cell("from sympy import init_printing, Matrix")
+    app.run_cell("init_printing(use_latex='matplotlib')")
+
+    # The png formatter is not enabled by default in this context
+    app.run_cell("inst.display_formatter.formatters['image/png'].enabled = True")
+
+    # Make sure no warnings are raised by IPython
+    app.run_cell("import warnings")
+    # IPython.core.formatters.FormatterWarning was introduced in IPython 2.0
+    if int(ipython.__version__.split(".")[0]) < 2:
+        app.run_cell("warnings.simplefilter('error')")
+    else:
+        app.run_cell("warnings.simplefilter('error', IPython.core.formatters.FormatterWarning)")
+
+    # This should not raise an exception
+    app.run_cell("a = format(Matrix([1, 2, 3]))")
+
+    # issue 9799
+    app.run_cell("from sympy import Piecewise, Symbol, Eq")
+    app.run_cell("x = Symbol('x'); pw = format(Piecewise((1, Eq(x, 0)), (0, True)))")
+
+
+def test_override_repr_latex():
+    # Initialize and setup IPython session
+    app = init_ipython_session()
+    app.run_cell("import IPython")
+    app.run_cell("ip = get_ipython()")
+    app.run_cell("inst = ip.instance()")
+    app.run_cell("format = inst.display_formatter.format")
+    app.run_cell("inst.display_formatter.formatters['text/latex'].enabled = True")
+    app.run_cell("from sympy import init_printing")
+    app.run_cell("from sympy import Symbol")
+    app.run_cell("init_printing(use_latex=True)")
+    app.run_cell("""\
+    class SymbolWithOverload(Symbol):
+        def _repr_latex_(self):
+            return r"Hello " + super()._repr_latex_() + " world"
+    """)
+    app.run_cell("a = format(SymbolWithOverload('s'))")
+
+    if int(ipython.__version__.split(".")[0]) < 1:
+        latex = app.user_ns['a']['text/latex']
+    else:
+        latex = app.user_ns['a'][0]['text/latex']
+    assert latex == r'Hello $\displaystyle s$ world'
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/traversal.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/traversal.py
new file mode 100644
index 0000000000000000000000000000000000000000..1315ec4ef7868b666bb6b978b3d8b20442d100b0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/interactive/traversal.py
@@ -0,0 +1,95 @@
+from sympy.core.basic import Basic
+from sympy.printing import pprint
+
+import random
+
+def interactive_traversal(expr):
+    """Traverse a tree asking a user which branch to choose. """
+
+    RED, BRED = '\033[0;31m', '\033[1;31m'
+    GREEN, BGREEN = '\033[0;32m', '\033[1;32m'
+    YELLOW, BYELLOW = '\033[0;33m', '\033[1;33m'  # noqa
+    BLUE, BBLUE = '\033[0;34m', '\033[1;34m'      # noqa
+    MAGENTA, BMAGENTA = '\033[0;35m', '\033[1;35m'# noqa
+    CYAN, BCYAN = '\033[0;36m', '\033[1;36m'      # noqa
+    END = '\033[0m'
+
+    def cprint(*args):
+        print("".join(map(str, args)) + END)
+
+    def _interactive_traversal(expr, stage):
+        if stage > 0:
+            print()
+
+        cprint("Current expression (stage ", BYELLOW, stage, END, "):")
+        print(BCYAN)
+        pprint(expr)
+        print(END)
+
+        if isinstance(expr, Basic):
+            if expr.is_Add:
+                args = expr.as_ordered_terms()
+            elif expr.is_Mul:
+                args = expr.as_ordered_factors()
+            else:
+                args = expr.args
+        elif hasattr(expr, "__iter__"):
+            args = list(expr)
+        else:
+            return expr
+
+        n_args = len(args)
+
+        if not n_args:
+            return expr
+
+        for i, arg in enumerate(args):
+            cprint(GREEN, "[", BGREEN, i, GREEN, "] ", BLUE, type(arg), END)
+            pprint(arg)
+            print()
+
+        if n_args == 1:
+            choices = '0'
+        else:
+            choices = '0-%d' % (n_args - 1)
+
+        try:
+            choice = input("Your choice [%s,f,l,r,d,?]: " % choices)
+        except EOFError:
+            result = expr
+            print()
+        else:
+            if choice == '?':
+                cprint(RED, "%s - select subexpression with the given index" %
+                       choices)
+                cprint(RED, "f - select the first subexpression")
+                cprint(RED, "l - select the last subexpression")
+                cprint(RED, "r - select a random subexpression")
+                cprint(RED, "d - done\n")
+
+                result = _interactive_traversal(expr, stage)
+            elif choice in ('d', ''):
+                result = expr
+            elif choice == 'f':
+                result = _interactive_traversal(args[0], stage + 1)
+            elif choice == 'l':
+                result = _interactive_traversal(args[-1], stage + 1)
+            elif choice == 'r':
+                result = _interactive_traversal(random.choice(args), stage + 1)
+            else:
+                try:
+                    choice = int(choice)
+                except ValueError:
+                    cprint(BRED,
+                           "Choice must be a number in %s range\n" % choices)
+                    result = _interactive_traversal(expr, stage)
+                else:
+                    if choice < 0 or choice >= n_args:
+                        cprint(BRED, "Choice must be in %s range\n" % choices)
+                        result = _interactive_traversal(expr, stage)
+                    else:
+                        result = _interactive_traversal(args[choice], stage + 1)
+
+        return result
+
+    return _interactive_traversal(expr, 0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..d023d86f2c6f0c64d7ac460c50eedc355e78b21f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/__init__.py
@@ -0,0 +1,3 @@
+from sympy.liealgebras.cartan_type import CartanType
+
+__all__ = ['CartanType']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/cartan_matrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/cartan_matrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d29b37bc9a1a26790ee88b5902951afe4fc4560
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/cartan_matrix.py
@@ -0,0 +1,25 @@
+from .cartan_type import CartanType
+
+def CartanMatrix(ct):
+    """Access the Cartan matrix of a specific Lie algebra
+
+    Examples
+    ========
+
+    >>> from sympy.liealgebras.cartan_matrix import CartanMatrix
+    >>> CartanMatrix("A2")
+    Matrix([
+    [ 2, -1],
+    [-1,  2]])
+
+    >>> CartanMatrix(['C', 3])
+    Matrix([
+    [ 2, -1,  0],
+    [-1,  2, -1],
+    [ 0, -2,  2]])
+
+    This method works by returning the Cartan matrix
+    which corresponds to Cartan type t.
+    """
+
+    return CartanType(ct).cartan_matrix()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/cartan_type.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/cartan_type.py
new file mode 100644
index 0000000000000000000000000000000000000000..16bb152469238ea912a30c2d0f8210d6f729bdb1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/cartan_type.py
@@ -0,0 +1,73 @@
+from sympy.core import Atom, Basic
+
+
+class CartanType_generator():
+    """
+    Constructor for actually creating things
+    """
+    def __call__(self, *args):
+        c = args[0]
+        if isinstance(c, list):
+            letter, n = c[0], int(c[1])
+        elif isinstance(c, str):
+            letter, n = c[0], int(c[1:])
+        else:
+            raise TypeError("Argument must be a string (e.g. 'A3') or a list (e.g. ['A', 3])")
+
+        if n < 0:
+            raise ValueError("Lie algebra rank cannot be negative")
+        if letter == "A":
+            from . import type_a
+            return type_a.TypeA(n)
+        if letter == "B":
+            from . import type_b
+            return type_b.TypeB(n)
+
+        if letter == "C":
+            from . import type_c
+            return type_c.TypeC(n)
+
+        if letter == "D":
+            from . import type_d
+            return type_d.TypeD(n)
+
+        if letter == "E":
+            if n >= 6 and n <= 8:
+                from . import type_e
+                return type_e.TypeE(n)
+
+        if letter == "F":
+            if n == 4:
+                from . import type_f
+                return type_f.TypeF(n)
+
+        if letter == "G":
+            if n == 2:
+                from . import type_g
+                return type_g.TypeG(n)
+
+CartanType = CartanType_generator()
+
+
+class Standard_Cartan(Atom):
+    """
+    Concrete base class for Cartan types such as A4, etc
+    """
+
+    def __new__(cls, series, n):
+        obj = Basic.__new__(cls)
+        obj.n = n
+        obj.series = series
+        return obj
+
+    def rank(self):
+        """
+        Returns the rank of the Lie algebra
+        """
+        return self.n
+
+    def series(self):
+        """
+        Returns the type of the Lie algebra
+        """
+        return self.series
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/dynkin_diagram.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/dynkin_diagram.py
new file mode 100644
index 0000000000000000000000000000000000000000..cc9e2dac4d54490b803eeaf9637cb9b66b01f058
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/dynkin_diagram.py
@@ -0,0 +1,24 @@
+from .cartan_type import CartanType
+
+
+def DynkinDiagram(t):
+    """Display the Dynkin diagram of a given Lie algebra
+
+    Works by generating the CartanType for the input, t, and then returning the
+    Dynkin diagram method from the individual classes.
+
+    Examples
+    ========
+
+    >>> from sympy.liealgebras.dynkin_diagram import DynkinDiagram
+    >>> print(DynkinDiagram("A3"))
+    0---0---0
+    1   2   3
+
+    >>> print(DynkinDiagram("B4"))
+    0---0---0=>=0
+    1   2   3   4
+
+    """
+
+    return CartanType(t).dynkin_diagram()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/root_system.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/root_system.py
new file mode 100644
index 0000000000000000000000000000000000000000..36eb24605e78bbdc669736910d89be5606df1389
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/root_system.py
@@ -0,0 +1,196 @@
+from .cartan_type import CartanType
+from sympy.core.basic import Atom
+
+class RootSystem(Atom):
+    """Represent the root system of a simple Lie algebra
+
+    Every simple Lie algebra has a unique root system.  To find the root
+    system, we first consider the Cartan subalgebra of g, which is the maximal
+    abelian subalgebra, and consider the adjoint action of g on this
+    subalgebra.  There is a root system associated with this action. Now, a
+    root system over a vector space V is a set of finite vectors Phi (called
+    roots), which satisfy:
+
+    1.  The roots span V
+    2.  The only scalar multiples of x in Phi are x and -x
+    3.  For every x in Phi, the set Phi is closed under reflection
+        through the hyperplane perpendicular to x.
+    4.  If x and y are roots in Phi, then the projection of y onto
+        the line through x is a half-integral multiple of x.
+
+    Now, there is a subset of Phi, which we will call Delta, such that:
+    1.  Delta is a basis of V
+    2.  Each root x in Phi can be written x = sum k_y y for y in Delta
+
+    The elements of Delta are called the simple roots.
+    Therefore, we see that the simple roots span the root space of a given
+    simple Lie algebra.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Root_system
+    .. [2] Lie Algebras and Representation Theory - Humphreys
+
+    """
+
+    def __new__(cls, cartantype):
+        """Create a new RootSystem object
+
+        This method assigns an attribute called cartan_type to each instance of
+        a RootSystem object.  When an instance of RootSystem is called, it
+        needs an argument, which should be an instance of a simple Lie algebra.
+        We then take the CartanType of this argument and set it as the
+        cartan_type attribute of the RootSystem instance.
+
+        """
+        obj = Atom.__new__(cls)
+        obj.cartan_type = CartanType(cartantype)
+        return obj
+
+    def simple_roots(self):
+        """Generate the simple roots of the Lie algebra
+
+        The rank of the Lie algebra determines the number of simple roots that
+        it has.  This method obtains the rank of the Lie algebra, and then uses
+        the simple_root method from the Lie algebra classes to generate all the
+        simple roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.root_system import RootSystem
+        >>> c = RootSystem("A3")
+        >>> roots = c.simple_roots()
+        >>> roots
+        {1: [1, -1, 0, 0], 2: [0, 1, -1, 0], 3: [0, 0, 1, -1]}
+
+        """
+        n = self.cartan_type.rank()
+        roots = {i: self.cartan_type.simple_root(i) for i in range(1, n+1)}
+        return roots
+
+
+    def all_roots(self):
+        """Generate all the roots of a given root system
+
+        The result is a dictionary where the keys are integer numbers.  It
+        generates the roots by getting the dictionary of all positive roots
+        from the bases classes, and then taking each root, and multiplying it
+        by -1 and adding it to the dictionary.  In this way all the negative
+        roots are generated.
+
+        """
+        alpha = self.cartan_type.positive_roots()
+        keys = list(alpha.keys())
+        k = max(keys)
+        for val in keys:
+            k += 1
+            root = alpha[val]
+            newroot = [-x for x in root]
+            alpha[k] = newroot
+        return alpha
+
+    def root_space(self):
+        """Return the span of the simple roots
+
+        The root space is the vector space spanned by the simple roots, i.e. it
+        is a vector space with a distinguished basis, the simple roots.  This
+        method returns a string that represents the root space as the span of
+        the simple roots, alpha[1],...., alpha[n].
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.root_system import RootSystem
+        >>> c = RootSystem("A3")
+        >>> c.root_space()
+        'alpha[1] + alpha[2] + alpha[3]'
+
+        """
+        n = self.cartan_type.rank()
+        rs = " + ".join("alpha["+str(i) +"]" for i in range(1, n+1))
+        return rs
+
+    def add_simple_roots(self, root1, root2):
+        """Add two simple roots together
+
+        The function takes as input two integers, root1 and root2.  It then
+        uses these integers as keys in the dictionary of simple roots, and gets
+        the corresponding simple roots, and then adds them together.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.root_system import RootSystem
+        >>> c = RootSystem("A3")
+        >>> newroot = c.add_simple_roots(1, 2)
+        >>> newroot
+        [1, 0, -1, 0]
+
+        """
+
+        alpha = self.simple_roots()
+        if root1 > len(alpha) or root2 > len(alpha):
+            raise ValueError("You've used a root that doesn't exist!")
+        a1 = alpha[root1]
+        a2 = alpha[root2]
+        newroot = [_a1 + _a2 for _a1, _a2 in zip(a1, a2)]
+        return newroot
+
+    def add_as_roots(self, root1, root2):
+        """Add two roots together if and only if their sum is also a root
+
+        It takes as input two vectors which should be roots.  It then computes
+        their sum and checks if it is in the list of all possible roots.  If it
+        is, it returns the sum.  Otherwise it returns a string saying that the
+        sum is not a root.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.root_system import RootSystem
+        >>> c = RootSystem("A3")
+        >>> c.add_as_roots([1, 0, -1, 0], [0, 0, 1, -1])
+        [1, 0, 0, -1]
+        >>> c.add_as_roots([1, -1, 0, 0], [0, 0, -1, 1])
+        'The sum of these two roots is not a root'
+
+        """
+        alpha = self.all_roots()
+        newroot = [r1 + r2 for r1, r2 in zip(root1, root2)]
+        if newroot in alpha.values():
+            return newroot
+        else:
+            return "The sum of these two roots is not a root"
+
+
+    def cartan_matrix(self):
+        """Cartan matrix of Lie algebra associated with this root system
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.root_system import RootSystem
+        >>> c = RootSystem("A3")
+        >>> c.cartan_matrix()
+        Matrix([
+            [ 2, -1,  0],
+            [-1,  2, -1],
+            [ 0, -1,  2]])
+        """
+        return self.cartan_type.cartan_matrix()
+
+    def dynkin_diagram(self):
+        """Dynkin diagram of the Lie algebra associated with this root system
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.root_system import RootSystem
+        >>> c = RootSystem("A3")
+        >>> print(c.dynkin_diagram())
+        0---0---0
+        1   2   3
+        """
+        return self.cartan_type.dynkin_diagram()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_cartan_matrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_cartan_matrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..98b1793dee63e0e87c610768554a8388dfd641a1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_cartan_matrix.py
@@ -0,0 +1,10 @@
+from sympy.liealgebras.cartan_matrix import CartanMatrix
+from sympy.matrices import Matrix
+
+def test_CartanMatrix():
+    c = CartanMatrix("A3")
+    m = Matrix(3, 3, [2, -1, 0, -1, 2, -1, 0, -1, 2])
+    assert c == m
+    a = CartanMatrix(["G",2])
+    mt = Matrix(2, 2, [2, -1, -3, 2])
+    assert a == mt
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_cartan_type.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_cartan_type.py
new file mode 100644
index 0000000000000000000000000000000000000000..257eeca41d0f5f2eb240cc270f76d452848ed405
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_cartan_type.py
@@ -0,0 +1,12 @@
+from sympy.liealgebras.cartan_type import CartanType, Standard_Cartan
+
+def test_Standard_Cartan():
+    c = CartanType("A4")
+    assert c.rank() == 4
+    assert c.series == "A"
+    m = Standard_Cartan("A", 2)
+    assert m.rank() == 2
+    assert m.series == "A"
+    b = CartanType("B12")
+    assert b.rank() == 12
+    assert b.series == "B"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_dynkin_diagram.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_dynkin_diagram.py
new file mode 100644
index 0000000000000000000000000000000000000000..ad2ee4c162945c437ecf83d75c7fef9455c9464a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_dynkin_diagram.py
@@ -0,0 +1,9 @@
+from sympy.liealgebras.dynkin_diagram import DynkinDiagram
+
+def test_DynkinDiagram():
+    c = DynkinDiagram("A3")
+    diag = "0---0---0\n1   2   3"
+    assert c == diag
+    ct = DynkinDiagram(["B", 3])
+    diag2 = "0---0=>=0\n1   2   3"
+    assert ct == diag2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_root_system.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_root_system.py
new file mode 100644
index 0000000000000000000000000000000000000000..42110da5a1c59a7e6b2e537ee13746bfce361579
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_root_system.py
@@ -0,0 +1,18 @@
+from sympy.liealgebras.root_system import RootSystem
+from sympy.liealgebras.type_a import TypeA
+from sympy.matrices import Matrix
+
+def test_root_system():
+    c = RootSystem("A3")
+    assert c.cartan_type == TypeA(3)
+    assert c.simple_roots() ==  {1: [1, -1, 0, 0], 2: [0, 1, -1, 0], 3: [0, 0, 1, -1]}
+    assert c.root_space() == "alpha[1] + alpha[2] + alpha[3]"
+    assert c.cartan_matrix() == Matrix([[ 2, -1,  0], [-1,  2, -1], [ 0, -1,  2]])
+    assert c.dynkin_diagram() == "0---0---0\n1   2   3"
+    assert c.add_simple_roots(1, 2) == [1, 0, -1, 0]
+    assert c.all_roots() == {1: [1, -1, 0, 0], 2: [1, 0, -1, 0],
+            3: [1, 0, 0, -1], 4: [0, 1, -1, 0], 5: [0, 1, 0, -1],
+            6: [0, 0, 1, -1], 7: [-1, 1, 0, 0], 8: [-1, 0, 1, 0],
+            9: [-1, 0, 0, 1], 10: [0, -1, 1, 0],
+            11: [0, -1, 0, 1], 12: [0, 0, -1, 1]}
+    assert c.add_as_roots([1, 0, -1, 0], [0, 0, 1, -1]) == [1, 0, 0, -1]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_A.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_A.py
new file mode 100644
index 0000000000000000000000000000000000000000..85d6f451ee167cf6db17ab20e59efab86ac0b691
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_A.py
@@ -0,0 +1,17 @@
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+
+def test_type_A():
+    c = CartanType("A3")
+    m = Matrix(3, 3, [2, -1, 0, -1, 2, -1, 0, -1, 2])
+    assert m == c.cartan_matrix()
+    assert c.basis() == 8
+    assert c.roots() == 12
+    assert c.dimension() == 4
+    assert c.simple_root(1) == [1, -1, 0, 0]
+    assert c.highest_root() == [1, 0, 0, -1]
+    assert c.lie_algebra() == "su(4)"
+    diag = "0---0---0\n1   2   3"
+    assert c.dynkin_diagram() == diag
+    assert c.positive_roots() == {1: [1, -1, 0, 0], 2: [1, 0, -1, 0],
+            3: [1, 0, 0, -1], 4: [0, 1, -1, 0], 5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_B.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_B.py
new file mode 100644
index 0000000000000000000000000000000000000000..8f2a9011f96bc647e48d39e16cf10703a99d86b3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_B.py
@@ -0,0 +1,17 @@
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+
+def test_type_B():
+    c = CartanType("B3")
+    m = Matrix(3, 3, [2, -1, 0, -1, 2, -2, 0, -1, 2])
+    assert m == c.cartan_matrix()
+    assert c.dimension() == 3
+    assert c.roots() == 18
+    assert c.simple_root(3) == [0, 0, 1]
+    assert c.basis() == 3
+    assert c.lie_algebra() == "so(6)"
+    diag = "0---0=>=0\n1   2   3"
+    assert c.dynkin_diagram() == diag
+    assert c.positive_roots() ==  {1: [1, -1, 0], 2: [1, 1, 0], 3: [1, 0, -1],
+            4: [1, 0, 1], 5: [0, 1, -1], 6: [0, 1, 1], 7: [1, 0, 0],
+            8: [0, 1, 0], 9: [0, 0, 1]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_C.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_C.py
new file mode 100644
index 0000000000000000000000000000000000000000..8154c201e6c50adb7c74458b240ed98b9a0dd123
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_C.py
@@ -0,0 +1,22 @@
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+
+def test_type_C():
+    c = CartanType("C4")
+    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -2, 2])
+    assert c.cartan_matrix() == m
+    assert c.dimension() == 4
+    assert c.simple_root(4) == [0, 0, 0, 2]
+    assert c.roots() == 32
+    assert c.basis() == 36
+    assert c.lie_algebra() == "sp(8)"
+    t = CartanType(['C', 3])
+    assert t.dimension() == 3
+    diag = "0---0---0=<=0\n1   2   3   4"
+    assert c.dynkin_diagram() == diag
+    assert c.positive_roots() == {1: [1, -1, 0, 0], 2: [1, 1, 0, 0],
+            3: [1, 0, -1, 0], 4: [1, 0, 1, 0], 5: [1, 0, 0, -1],
+            6: [1, 0, 0, 1], 7: [0, 1, -1, 0], 8: [0, 1, 1, 0],
+            9: [0, 1, 0, -1], 10: [0, 1, 0, 1], 11: [0, 0, 1, -1],
+            12: [0, 0, 1, 1], 13: [2, 0, 0, 0], 14: [0, 2, 0, 0], 15: [0, 0, 2, 0],
+            16: [0, 0, 0, 2]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_D.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_D.py
new file mode 100644
index 0000000000000000000000000000000000000000..ddf6a34cb5be475cc30042e95bf8eae2376a2223
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_D.py
@@ -0,0 +1,19 @@
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+
+
+
+def test_type_D():
+    c = CartanType("D4")
+    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, -1, 0, -1, 2, 0, 0, -1, 0, 2])
+    assert c.cartan_matrix() == m
+    assert c.basis() == 6
+    assert c.lie_algebra() == "so(8)"
+    assert c.roots() == 24
+    assert c.simple_root(3) == [0, 0, 1, -1]
+    diag = "    3\n    0\n    |\n    |\n0---0---0\n1   2   4"
+    assert diag == c.dynkin_diagram()
+    assert c.positive_roots() == {1: [1, -1, 0, 0], 2: [1, 1, 0, 0],
+            3: [1, 0, -1, 0], 4: [1, 0, 1, 0], 5: [1, 0, 0, -1], 6: [1, 0, 0, 1],
+            7: [0, 1, -1, 0], 8: [0, 1, 1, 0], 9: [0, 1, 0, -1], 10: [0, 1, 0, 1],
+            11: [0, 0, 1, -1], 12: [0, 0, 1, 1]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_E.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_E.py
new file mode 100644
index 0000000000000000000000000000000000000000..bdb08342f41ede3390f34e9b297864eda16bedc7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_E.py
@@ -0,0 +1,22 @@
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+from sympy.core.backend import Rational
+
+def test_type_E():
+    c = CartanType("E6")
+    m = Matrix(6, 6, [2, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0,
+        -1, 0, 2, -1, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0,
+        -1, 2, -1, 0, 0, 0, 0, -1, 2])
+    assert c.cartan_matrix() == m
+    assert c.dimension() == 8
+    assert c.simple_root(6) == [0, 0, 0, -1, 1, 0, 0, 0]
+    assert c.roots() == 72
+    assert c.basis() == 78
+    diag = " "*8 + "2\n" + " "*8 + "0\n" + " "*8 + "|\n" + " "*8 + "|\n"
+    diag += "---".join("0" for i in range(1, 6))+"\n"
+    diag += "1   " + "   ".join(str(i) for i in range(3, 7))
+    assert c.dynkin_diagram() == diag
+    posroots = c.positive_roots()
+    assert posroots[8] == [1, 0, 0, 0, 1, 0, 0, 0]
+    assert posroots[21] == [Rational(1,2),Rational(1,2),Rational(1,2),Rational(1,2),
+                            Rational(1,2),Rational(-1,2),Rational(-1,2),Rational(1,2)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_F.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_F.py
new file mode 100644
index 0000000000000000000000000000000000000000..fbb58223d0b5886e6044108c9c5cc3bbf371dd14
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_F.py
@@ -0,0 +1,24 @@
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+from sympy.core.backend import S
+
+def test_type_F():
+    c = CartanType("F4")
+    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0, -1, 2, -1, 0, 0, -1, 2])
+    assert c.cartan_matrix() == m
+    assert c.dimension() == 4
+    assert c.simple_root(1) == [1, -1, 0, 0]
+    assert c.simple_root(2) == [0, 1, -1, 0]
+    assert c.simple_root(3) == [0, 0, 0, 1]
+    assert c.simple_root(4) == [-S.Half, -S.Half, -S.Half, -S.Half]
+    assert c.roots() == 48
+    assert c.basis() == 52
+    diag = "0---0=>=0---0\n" + "   ".join(str(i) for i in range(1, 5))
+    assert c.dynkin_diagram() == diag
+    assert c.positive_roots() == {1: [1, -1, 0, 0], 2: [1, 1, 0, 0], 3: [1, 0, -1, 0],
+            4: [1, 0, 1, 0], 5: [1, 0, 0, -1], 6: [1, 0, 0, 1], 7: [0, 1, -1, 0],
+            8: [0, 1, 1, 0], 9: [0, 1, 0, -1], 10: [0, 1, 0, 1], 11: [0, 0, 1, -1],
+            12: [0, 0, 1, 1], 13: [1, 0, 0, 0], 14: [0, 1, 0, 0], 15: [0, 0, 1, 0],
+            16: [0, 0, 0, 1], 17: [S.Half, S.Half, S.Half, S.Half], 18: [S.Half, -S.Half, S.Half, S.Half],
+            19: [S.Half, S.Half, -S.Half, S.Half], 20: [S.Half, S.Half, S.Half, -S.Half], 21: [S.Half, S.Half, -S.Half, -S.Half],
+            22: [S.Half, -S.Half, S.Half, -S.Half], 23: [S.Half, -S.Half, -S.Half, S.Half], 24: [S.Half, -S.Half, -S.Half, -S.Half]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_G.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_G.py
new file mode 100644
index 0000000000000000000000000000000000000000..c427eeb85bad8fc77d17a1563a7b796d4e0f217f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_type_G.py
@@ -0,0 +1,16 @@
+# coding=utf-8
+from sympy.liealgebras.cartan_type import CartanType
+from sympy.matrices import Matrix
+
+def test_type_G():
+    c = CartanType("G2")
+    m = Matrix(2, 2, [2, -1, -3, 2])
+    assert c.cartan_matrix() == m
+    assert c.simple_root(2) == [1, -2, 1]
+    assert c.basis() == 14
+    assert c.roots() == 12
+    assert c.dimension() == 3
+    diag = "0≡<≡0\n1   2"
+    assert diag == c.dynkin_diagram()
+    assert c.positive_roots() == {1: [0, 1, -1], 2: [1, -2, 1], 3: [1, -1, 0],
+            4: [1, 0, 1], 5: [1, 1, -2], 6: [2, -1, -1]}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_weyl_group.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_weyl_group.py
new file mode 100644
index 0000000000000000000000000000000000000000..e4e57246fdcb5a431d8bbd65f1f60e0254a9cdf0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/tests/test_weyl_group.py
@@ -0,0 +1,35 @@
+from sympy.liealgebras.weyl_group import WeylGroup
+from sympy.matrices import Matrix
+
+def test_weyl_group():
+    c = WeylGroup("A3")
+    assert c.matrix_form('r1*r2') == Matrix([[0, 0, 1, 0], [1, 0, 0, 0],
+        [0, 1, 0, 0], [0, 0, 0, 1]])
+    assert c.generators() == ['r1', 'r2', 'r3']
+    assert c.group_order() == 24.0
+    assert c.group_name() == "S4: the symmetric group acting on 4 elements."
+    assert c.coxeter_diagram() == "0---0---0\n1   2   3"
+    assert c.element_order('r1*r2*r3') == 4
+    assert c.element_order('r1*r3*r2*r3') == 3
+    d = WeylGroup("B5")
+    assert d.group_order() == 3840
+    assert d.element_order('r1*r2*r4*r5') == 12
+    assert d.matrix_form('r2*r3') ==  Matrix([[0, 0, 1, 0, 0], [1, 0, 0, 0, 0],
+        [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]])
+    assert d.element_order('r1*r2*r1*r3*r5') == 6
+    e = WeylGroup("D5")
+    assert e.element_order('r2*r3*r5') == 4
+    assert e.matrix_form('r2*r3*r5') == Matrix([[1, 0, 0, 0, 0], [0, 0, 0, 0, -1],
+        [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 0]])
+    f = WeylGroup("G2")
+    assert f.element_order('r1*r2*r1*r2') == 3
+    assert f.element_order('r2*r1*r1*r2') == 1
+
+    assert f.matrix_form('r1*r2*r1*r2') == Matrix([[0, 1, 0], [0, 0, 1], [1, 0, 0]])
+    g = WeylGroup("F4")
+    assert g.matrix_form('r2*r3') == Matrix([[1, 0, 0, 0], [0, 1, 0, 0],
+        [0, 0, 0, -1], [0, 0, 1, 0]])
+
+    assert g.element_order('r2*r3') == 4
+    h = WeylGroup("E6")
+    assert h.group_order() == 51840
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_a.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_a.py
new file mode 100644
index 0000000000000000000000000000000000000000..96dc615366ae20d668d651620ac088f15751c50e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_a.py
@@ -0,0 +1,164 @@
+from sympy.liealgebras.cartan_type import Standard_Cartan
+from sympy.core.backend import eye
+
+
+class TypeA(Standard_Cartan):
+    """
+    This class contains the information about
+    the A series of simple Lie algebras.
+    ====
+    """
+
+    def __new__(cls, n):
+        if n < 1:
+            raise ValueError("n cannot be less than 1")
+        return Standard_Cartan.__new__(cls, "A", n)
+
+
+    def dimension(self):
+        """Dimension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A4")
+        >>> c.dimension()
+        5
+        """
+        return self.n+1
+
+
+    def basic_root(self, i, j):
+        """
+        This is a method just to generate roots
+        with a 1 iin the ith position and a -1
+        in the jth position.
+
+        """
+
+        n = self.n
+        root = [0]*(n+1)
+        root[i] = 1
+        root[j] = -1
+        return root
+
+    def simple_root(self, i):
+        """
+        Every lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        In A_n the ith simple root is the root which has a 1
+        in the ith position, a -1 in the (i+1)th position,
+        and zeroes elsewhere.
+
+        This method returns the ith simple root for the A series.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A4")
+        >>> c.simple_root(1)
+        [1, -1, 0, 0, 0]
+
+        """
+
+        return self.basic_root(i-1, i)
+
+    def positive_roots(self):
+        """
+        This method generates all the positive roots of
+        A_n.  This is half of all of the roots of A_n;
+        by multiplying all the positive roots by -1 we
+        get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+        """
+
+        n = self.n
+        posroots = {}
+        k = 0
+        for i in range(0, n):
+            for j in range(i+1, n+1):
+                k += 1
+                posroots[k] = self.basic_root(i, j)
+        return posroots
+
+    def highest_root(self):
+        """
+        Returns the highest weight root for A_n
+        """
+
+        return self.basic_root(0, self.n)
+
+    def roots(self):
+        """
+        Returns the total number of roots for A_n
+        """
+        n = self.n
+        return n*(n+1)
+
+    def cartan_matrix(self):
+        """
+        Returns the Cartan matrix for A_n.
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType('A4')
+        >>> c.cartan_matrix()
+        Matrix([
+        [ 2, -1,  0,  0],
+        [-1,  2, -1,  0],
+        [ 0, -1,  2, -1],
+        [ 0,  0, -1,  2]])
+
+        """
+
+        n = self.n
+        m = 2 * eye(n)
+        for i in range(1, n - 1):
+            m[i, i+1] = -1
+            m[i, i-1] = -1
+        m[0,1] = -1
+        m[n-1, n-2] = -1
+        return m
+
+    def basis(self):
+        """
+        Returns the number of independent generators of A_n
+        """
+        n = self.n
+        return n**2 - 1
+
+    def lie_algebra(self):
+        """
+        Returns the Lie algebra associated with A_n
+        """
+        n = self.n
+        return "su(" + str(n + 1) + ")"
+
+    def dynkin_diagram(self):
+        n = self.n
+        diag = "---".join("0" for i in range(1, n+1)) + "\n"
+        diag += "   ".join(str(i) for i in range(1, n+1))
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_b.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_b.py
new file mode 100644
index 0000000000000000000000000000000000000000..c6ee85502261f4702769067c64021521a2bc1725
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_b.py
@@ -0,0 +1,170 @@
+from .cartan_type import Standard_Cartan
+from sympy.core.backend import eye
+
+class TypeB(Standard_Cartan):
+
+    def __new__(cls, n):
+        if n < 2:
+            raise ValueError("n cannot be less than 2")
+        return Standard_Cartan.__new__(cls, "B", n)
+
+    def dimension(self):
+        """Dimension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("B3")
+        >>> c.dimension()
+        3
+        """
+
+        return self.n
+
+    def basic_root(self, i, j):
+        """
+        This is a method just to generate roots
+        with a 1 iin the ith position and a -1
+        in the jth position.
+
+        """
+        root = [0]*self.n
+        root[i] = 1
+        root[j] = -1
+        return root
+
+    def simple_root(self, i):
+        """
+        Every lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        In B_n the first n-1 simple roots are the same as the
+        roots in A_(n-1) (a 1 in the ith position, a -1 in
+        the (i+1)th position, and zeroes elsewhere).  The n-th
+        simple root is the root with a 1 in the nth position
+        and zeroes elsewhere.
+
+        This method returns the ith simple root for the B series.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("B3")
+        >>> c.simple_root(2)
+        [0, 1, -1]
+
+        """
+        n = self.n
+        if i < n:
+            return self.basic_root(i-1, i)
+        else:
+            root = [0]*self.n
+            root[n-1] = 1
+            return root
+
+    def positive_roots(self):
+        """
+        This method generates all the positive roots of
+        A_n.  This is half of all of the roots of B_n;
+        by multiplying all the positive roots by -1 we
+        get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+        """
+
+        n = self.n
+        posroots = {}
+        k = 0
+        for i in range(0, n-1):
+            for j in range(i+1, n):
+                k += 1
+                posroots[k] = self.basic_root(i, j)
+                k += 1
+                root = self.basic_root(i, j)
+                root[j] = 1
+                posroots[k] = root
+
+        for i in range(0, n):
+            k += 1
+            root = [0]*n
+            root[i] = 1
+            posroots[k] = root
+
+        return posroots
+
+    def roots(self):
+        """
+        Returns the total number of roots for B_n"
+        """
+
+        n = self.n
+        return 2*(n**2)
+
+    def cartan_matrix(self):
+        """
+        Returns the Cartan matrix for B_n.
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType('B4')
+        >>> c.cartan_matrix()
+        Matrix([
+        [ 2, -1,  0,  0],
+        [-1,  2, -1,  0],
+        [ 0, -1,  2, -2],
+        [ 0,  0, -1,  2]])
+
+        """
+
+        n = self.n
+        m = 2* eye(n)
+        for i in range(1, n - 1):
+            m[i, i+1] = -1
+            m[i, i-1] = -1
+        m[0, 1] = -1
+        m[n-2, n-1] = -2
+        m[n-1, n-2] = -1
+        return m
+
+    def basis(self):
+        """
+        Returns the number of independent generators of B_n
+        """
+
+        n = self.n
+        return (n**2 - n)/2
+
+    def lie_algebra(self):
+        """
+        Returns the Lie algebra associated with B_n
+        """
+
+        n = self.n
+        return "so(" + str(2*n) + ")"
+
+    def dynkin_diagram(self):
+        n = self.n
+        diag = "---".join("0" for i in range(1, n)) + "=>=0\n"
+        diag += "   ".join(str(i) for i in range(1, n+1))
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_c.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_c.py
new file mode 100644
index 0000000000000000000000000000000000000000..615bb900b5ba9613fd02e43f476d34eef0d5d35c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_c.py
@@ -0,0 +1,169 @@
+from .cartan_type import Standard_Cartan
+from sympy.core.backend import eye
+
+class TypeC(Standard_Cartan):
+
+    def __new__(cls, n):
+        if n < 3:
+            raise ValueError("n cannot be less than 3")
+        return Standard_Cartan.__new__(cls, "C", n)
+
+
+    def dimension(self):
+        """Dimension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("C3")
+        >>> c.dimension()
+        3
+        """
+        n = self.n
+        return n
+
+    def basic_root(self, i, j):
+        """Generate roots with 1 in ith position and a -1 in jth position
+        """
+        n = self.n
+        root = [0]*n
+        root[i] = 1
+        root[j] = -1
+        return root
+
+    def simple_root(self, i):
+        """The ith simple root for the C series
+
+        Every lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        In C_n, the first n-1 simple roots are the same as
+        the roots in A_(n-1) (a 1 in the ith position, a -1
+        in the (i+1)th position, and zeroes elsewhere).  The
+        nth simple root is the root in which there is a 2 in
+        the nth position and zeroes elsewhere.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("C3")
+        >>> c.simple_root(2)
+        [0, 1, -1]
+
+        """
+
+        n = self.n
+        if i < n:
+            return self.basic_root(i-1,i)
+        else:
+            root = [0]*self.n
+            root[n-1] = 2
+            return root
+
+
+    def positive_roots(self):
+        """Generates all the positive roots of A_n
+
+        This is half of all of the roots of C_n; by multiplying all the
+        positive roots by -1 we get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+
+        """
+
+        n = self.n
+        posroots = {}
+        k = 0
+        for i in range(0, n-1):
+            for j in range(i+1, n):
+                k += 1
+                posroots[k] = self.basic_root(i, j)
+                k += 1
+                root = self.basic_root(i, j)
+                root[j] = 1
+                posroots[k] = root
+
+        for i in range(0, n):
+            k += 1
+            root = [0]*n
+            root[i] = 2
+            posroots[k] = root
+
+        return posroots
+
+    def roots(self):
+        """
+        Returns the total number of roots for C_n"
+        """
+
+        n = self.n
+        return 2*(n**2)
+
+    def cartan_matrix(self):
+        """The Cartan matrix for C_n
+
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType('C4')
+        >>> c.cartan_matrix()
+        Matrix([
+        [ 2, -1,  0,  0],
+        [-1,  2, -1,  0],
+        [ 0, -1,  2, -1],
+        [ 0,  0, -2,  2]])
+
+        """
+
+        n = self.n
+        m = 2 * eye(n)
+        for i in range(1, n - 1):
+            m[i, i+1] = -1
+            m[i, i-1] = -1
+        m[0,1] = -1
+        m[n-1, n-2] = -2
+        return m
+
+
+    def basis(self):
+        """
+        Returns the number of independent generators of C_n
+        """
+
+        n = self.n
+        return n*(2*n + 1)
+
+    def lie_algebra(self):
+        """
+        Returns the Lie algebra associated with C_n"
+        """
+
+        n = self.n
+        return "sp(" + str(2*n) + ")"
+
+    def dynkin_diagram(self):
+        n = self.n
+        diag = "---".join("0" for i in range(1, n)) + "=<=0\n"
+        diag += "   ".join(str(i) for i in range(1, n+1))
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_d.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_d.py
new file mode 100644
index 0000000000000000000000000000000000000000..9450d76e906c79e23db0ce223ed0de03d71c1199
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_d.py
@@ -0,0 +1,173 @@
+from .cartan_type import Standard_Cartan
+from sympy.core.backend import eye
+
+class TypeD(Standard_Cartan):
+
+    def __new__(cls, n):
+        if n < 3:
+            raise ValueError("n cannot be less than 3")
+        return Standard_Cartan.__new__(cls, "D", n)
+
+
+    def dimension(self):
+        """Dmension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("D4")
+        >>> c.dimension()
+        4
+        """
+
+        return self.n
+
+    def basic_root(self, i, j):
+        """
+        This is a method just to generate roots
+        with a 1 iin the ith position and a -1
+        in the jth position.
+
+        """
+
+        n = self.n
+        root = [0]*n
+        root[i] = 1
+        root[j] = -1
+        return root
+
+    def simple_root(self, i):
+        """
+        Every lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        In D_n, the first n-1 simple roots are the same as
+        the roots in A_(n-1) (a 1 in the ith position, a -1
+        in the (i+1)th position, and zeroes elsewhere).
+        The nth simple root is the root in which there 1s in
+        the nth and (n-1)th positions, and zeroes elsewhere.
+
+        This method returns the ith simple root for the D series.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("D4")
+        >>> c.simple_root(2)
+        [0, 1, -1, 0]
+
+        """
+
+        n = self.n
+        if i < n:
+            return self.basic_root(i-1, i)
+        else:
+            root = [0]*n
+            root[n-2] = 1
+            root[n-1] = 1
+            return root
+
+
+    def positive_roots(self):
+        """
+        This method generates all the positive roots of
+        A_n.  This is half of all of the roots of D_n
+        by multiplying all the positive roots by -1 we
+        get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+        """
+
+        n = self.n
+        posroots = {}
+        k = 0
+        for i in range(0, n-1):
+            for j in range(i+1, n):
+                k += 1
+                posroots[k] = self.basic_root(i, j)
+                k += 1
+                root = self.basic_root(i, j)
+                root[j] = 1
+                posroots[k] = root
+        return posroots
+
+    def roots(self):
+        """
+        Returns the total number of roots for D_n"
+        """
+
+        n = self.n
+        return 2*n*(n-1)
+
+    def cartan_matrix(self):
+        """
+        Returns the Cartan matrix for D_n.
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType('D4')
+        >>> c.cartan_matrix()
+            Matrix([
+            [ 2, -1,  0,  0],
+            [-1,  2, -1, -1],
+            [ 0, -1,  2,  0],
+            [ 0, -1,  0,  2]])
+
+        """
+
+        n = self.n
+        m = 2*eye(n)
+        for i in range(1, n - 2):
+            m[i,i+1] = -1
+            m[i,i-1] = -1
+        m[n-2, n-3] = -1
+        m[n-3, n-1] = -1
+        m[n-1, n-3] = -1
+        m[0, 1] = -1
+        return m
+
+    def basis(self):
+        """
+        Returns the number of independent generators of D_n
+        """
+        n = self.n
+        return n*(n-1)/2
+
+    def lie_algebra(self):
+        """
+        Returns the Lie algebra associated with D_n"
+        """
+
+        n = self.n
+        return "so(" + str(2*n) + ")"
+
+    def dynkin_diagram(self):
+        n = self.n
+        diag = " "*4*(n-3) + str(n-1) + "\n"
+        diag += " "*4*(n-3) + "0\n"
+        diag += " "*4*(n-3) +"|\n"
+        diag += " "*4*(n-3) + "|\n"
+        diag += "---".join("0" for i in range(1,n)) + "\n"
+        diag += "   ".join(str(i) for i in range(1, n-1)) + "   "+str(n)
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_e.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_e.py
new file mode 100644
index 0000000000000000000000000000000000000000..3db9a820d31bff31acc58ba1592a1b10f8be53db
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_e.py
@@ -0,0 +1,275 @@
+import itertools
+
+from .cartan_type import Standard_Cartan
+from sympy.core.backend import eye, Rational
+from sympy.core.singleton import S
+
+class TypeE(Standard_Cartan):
+
+    def __new__(cls, n):
+        if n < 6 or n > 8:
+            raise ValueError("Invalid value of n")
+        return Standard_Cartan.__new__(cls, "E", n)
+
+    def dimension(self):
+        """Dimension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("E6")
+        >>> c.dimension()
+        8
+        """
+
+        return 8
+
+    def basic_root(self, i, j):
+        """
+        This is a method just to generate roots
+        with a -1 in the ith position and a 1
+        in the jth position.
+
+        """
+
+        root = [0]*8
+        root[i] = -1
+        root[j] = 1
+        return root
+
+    def simple_root(self, i):
+        """
+        Every Lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        This method returns the ith simple root for E_n.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("E6")
+        >>> c.simple_root(2)
+        [1, 1, 0, 0, 0, 0, 0, 0]
+        """
+        n = self.n
+        if i == 1:
+            root = [-0.5]*8
+            root[0] = 0.5
+            root[7] = 0.5
+            return root
+        elif i == 2:
+            root = [0]*8
+            root[1] = 1
+            root[0] = 1
+            return root
+        else:
+            if i in (7, 8) and n == 6:
+                raise ValueError("E6 only has six simple roots!")
+            if i == 8 and n == 7:
+                raise ValueError("E7 only has seven simple roots!")
+
+            return self.basic_root(i - 3, i - 2)
+
+    def positive_roots(self):
+        """
+        This method generates all the positive roots of
+        A_n.  This is half of all of the roots of E_n;
+        by multiplying all the positive roots by -1 we
+        get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+        """
+        n = self.n
+        neghalf = Rational(-1, 2)
+        poshalf = S.Half
+        if n == 6:
+            posroots = {}
+            k = 0
+            for i in range(n-1):
+                for j in range(i+1, n-1):
+                    k += 1
+                    root = self.basic_root(i, j)
+                    posroots[k] = root
+                    k += 1
+                    root = self.basic_root(i, j)
+                    root[i] = 1
+                    posroots[k] = root
+
+            root = [poshalf, poshalf, poshalf, poshalf, poshalf,
+                    neghalf, neghalf, poshalf]
+            for a, b, c, d, e in itertools.product(
+                    range(2), range(2), range(2), range(2), range(2)):
+                if (a + b + c + d + e)%2 == 0:
+                    k += 1
+                    if a == 1:
+                        root[0] = neghalf
+                    if b == 1:
+                        root[1] = neghalf
+                    if c == 1:
+                        root[2] = neghalf
+                    if d == 1:
+                        root[3] = neghalf
+                    if e == 1:
+                        root[4] = neghalf
+                    posroots[k] = root[:]
+            return posroots
+        if n == 7:
+            posroots = {}
+            k = 0
+            for i in range(n-1):
+                for j in range(i+1, n-1):
+                    k += 1
+                    root = self.basic_root(i, j)
+                    posroots[k] = root
+                    k += 1
+                    root = self.basic_root(i, j)
+                    root[i] = 1
+                    posroots[k] = root
+
+            k += 1
+            posroots[k] = [0, 0, 0, 0, 0, 1, 1, 0]
+            root = [poshalf, poshalf, poshalf, poshalf, poshalf,
+                    neghalf, neghalf, poshalf]
+            for a, b, c, d, e, f in itertools.product(
+                    range(2), range(2), range(2), range(2), range(2), range(2)):
+                if (a + b + c + d + e + f)%2 == 0:
+                    k += 1
+                    if a == 1:
+                        root[0] = neghalf
+                    if b == 1:
+                        root[1] = neghalf
+                    if c == 1:
+                        root[2] = neghalf
+                    if d == 1:
+                        root[3] = neghalf
+                    if e == 1:
+                        root[4] = neghalf
+                    if f == 1:
+                        root[5] = poshalf
+                    posroots[k] = root[:]
+            return posroots
+        if n == 8:
+            posroots = {}
+            k = 0
+            for i in range(n):
+                for j in range(i+1, n):
+                    k += 1
+                    root = self.basic_root(i, j)
+                    posroots[k] = root
+                    k += 1
+                    root = self.basic_root(i, j)
+                    root[i] = 1
+                    posroots[k] = root
+
+            root = [poshalf, poshalf, poshalf, poshalf, poshalf,
+                    neghalf, neghalf, poshalf]
+            for a, b, c, d, e, f, g in itertools.product(
+                    range(2), range(2), range(2), range(2), range(2),
+                    range(2), range(2)):
+                if (a + b + c + d + e + f + g)%2 == 0:
+                    k += 1
+                    if a == 1:
+                        root[0] = neghalf
+                    if b == 1:
+                        root[1] = neghalf
+                    if c == 1:
+                        root[2] = neghalf
+                    if d == 1:
+                        root[3] = neghalf
+                    if e == 1:
+                        root[4] = neghalf
+                    if f == 1:
+                        root[5] = poshalf
+                    if g == 1:
+                        root[6] = poshalf
+                    posroots[k] = root[:]
+            return posroots
+
+
+
+    def roots(self):
+        """
+        Returns the total number of roots of E_n
+        """
+
+        n = self.n
+        if n == 6:
+            return 72
+        if n == 7:
+            return 126
+        if n == 8:
+            return 240
+
+
+    def cartan_matrix(self):
+        """
+        Returns the Cartan matrix for G_2
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType('A4')
+        >>> c.cartan_matrix()
+        Matrix([
+        [ 2, -1,  0,  0],
+        [-1,  2, -1,  0],
+        [ 0, -1,  2, -1],
+        [ 0,  0, -1,  2]])
+
+
+        """
+
+        n = self.n
+        m = 2*eye(n)
+        for i in range(3, n - 1):
+            m[i, i+1] = -1
+            m[i, i-1] = -1
+        m[0, 2] = m[2, 0] = -1
+        m[1, 3] = m[3, 1] = -1
+        m[2, 3] = -1
+        m[n-1, n-2] = -1
+        return m
+
+
+    def basis(self):
+        """
+        Returns the number of independent generators of E_n
+        """
+
+        n = self.n
+        if n == 6:
+            return 78
+        if n == 7:
+            return 133
+        if n == 8:
+            return 248
+
+    def dynkin_diagram(self):
+        n = self.n
+        diag = " "*8 + str(2) + "\n"
+        diag += " "*8 + "0\n"
+        diag += " "*8 + "|\n"
+        diag += " "*8 + "|\n"
+        diag += "---".join("0" for i in range(1, n)) + "\n"
+        diag += "1   " + "   ".join(str(i) for i in range(3, n+1))
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_f.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_f.py
new file mode 100644
index 0000000000000000000000000000000000000000..f04da557870f2cd21818cf69c454ef598e2ab65a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_f.py
@@ -0,0 +1,162 @@
+from .cartan_type import Standard_Cartan
+from sympy.core.backend import Matrix, Rational
+
+
+class TypeF(Standard_Cartan):
+
+    def __new__(cls, n):
+        if n != 4:
+            raise ValueError("n should be 4")
+        return Standard_Cartan.__new__(cls, "F", 4)
+
+    def dimension(self):
+        """Dimension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("F4")
+        >>> c.dimension()
+        4
+        """
+
+        return 4
+
+
+    def basic_root(self, i, j):
+        """Generate roots with 1 in ith position and -1 in jth position
+
+        """
+
+        n = self.n
+        root = [0]*n
+        root[i] = 1
+        root[j] = -1
+        return root
+
+    def simple_root(self, i):
+        """The ith simple root of F_4
+
+        Every lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("F4")
+        >>> c.simple_root(3)
+        [0, 0, 0, 1]
+
+        """
+
+        if i < 3:
+            return self.basic_root(i-1, i)
+        if i == 3:
+            root = [0]*4
+            root[3] = 1
+            return root
+        if i == 4:
+            root = [Rational(-1, 2)]*4
+            return root
+
+    def positive_roots(self):
+        """Generate all the positive roots of A_n
+
+        This is half of all of the roots of F_4; by multiplying all the
+        positive roots by -1 we get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+
+        """
+
+        n = self.n
+        posroots = {}
+        k = 0
+        for i in range(0, n-1):
+            for j in range(i+1, n):
+                k += 1
+                posroots[k] = self.basic_root(i, j)
+                k += 1
+                root = self.basic_root(i, j)
+                root[j] = 1
+                posroots[k] = root
+
+        for i in range(0, n):
+            k += 1
+            root = [0]*n
+            root[i] = 1
+            posroots[k] = root
+
+        k += 1
+        root = [Rational(1, 2)]*n
+        posroots[k] = root
+        for i in range(1, 4):
+            k += 1
+            root = [Rational(1, 2)]*n
+            root[i] = Rational(-1, 2)
+            posroots[k] = root
+
+        posroots[k+1] = [Rational(1, 2), Rational(1, 2), Rational(-1, 2), Rational(-1, 2)]
+        posroots[k+2] = [Rational(1, 2), Rational(-1, 2), Rational(1, 2), Rational(-1, 2)]
+        posroots[k+3] = [Rational(1, 2), Rational(-1, 2), Rational(-1, 2), Rational(1, 2)]
+        posroots[k+4] = [Rational(1, 2), Rational(-1, 2), Rational(-1, 2), Rational(-1, 2)]
+
+        return posroots
+
+
+    def roots(self):
+        """
+        Returns the total number of roots for F_4
+        """
+        return 48
+
+    def cartan_matrix(self):
+        """The Cartan matrix for F_4
+
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType('A4')
+        >>> c.cartan_matrix()
+        Matrix([
+        [ 2, -1,  0,  0],
+        [-1,  2, -1,  0],
+        [ 0, -1,  2, -1],
+        [ 0,  0, -1,  2]])
+        """
+
+        m = Matrix( 4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0,
+            -1, 2, -1, 0, 0, -1, 2])
+        return m
+
+    def basis(self):
+        """
+        Returns the number of independent generators of F_4
+        """
+        return 52
+
+    def dynkin_diagram(self):
+        diag = "0---0=>=0---0\n"
+        diag += "   ".join(str(i) for i in range(1, 5))
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_g.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_g.py
new file mode 100644
index 0000000000000000000000000000000000000000..014409cf5ed966b53c596b14e0073e89ceee05b6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/type_g.py
@@ -0,0 +1,111 @@
+# -*- coding: utf-8 -*-
+
+from .cartan_type import Standard_Cartan
+from sympy.core.backend import Matrix
+
+class TypeG(Standard_Cartan):
+
+    def __new__(cls, n):
+        if n != 2:
+            raise ValueError("n should be 2")
+        return Standard_Cartan.__new__(cls, "G", 2)
+
+
+    def dimension(self):
+        """Dimension of the vector space V underlying the Lie algebra
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("G2")
+        >>> c.dimension()
+        3
+        """
+        return 3
+
+    def simple_root(self, i):
+        """The ith simple root of G_2
+
+        Every lie algebra has a unique root system.
+        Given a root system Q, there is a subset of the
+        roots such that an element of Q is called a
+        simple root if it cannot be written as the sum
+        of two elements in Q.  If we let D denote the
+        set of simple roots, then it is clear that every
+        element of Q can be written as a linear combination
+        of elements of D with all coefficients non-negative.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("G2")
+        >>> c.simple_root(1)
+        [0, 1, -1]
+
+        """
+        if i == 1:
+            return [0, 1, -1]
+        else:
+            return [1, -2, 1]
+
+    def positive_roots(self):
+        """Generate all the positive roots of A_n
+
+        This is half of all of the roots of A_n; by multiplying all the
+        positive roots by -1 we get the negative roots.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("A3")
+        >>> c.positive_roots()
+        {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
+                5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
+
+        """
+
+        roots = {1: [0, 1, -1], 2: [1, -2, 1], 3: [1, -1, 0], 4: [1, 0, 1],
+                5: [1, 1, -2], 6: [2, -1, -1]}
+        return roots
+
+    def roots(self):
+        """
+        Returns the total number of roots of G_2"
+        """
+        return 12
+
+    def cartan_matrix(self):
+        """The Cartan matrix for G_2
+
+        The Cartan matrix matrix for a Lie algebra is
+        generated by assigning an ordering to the simple
+        roots, (alpha[1], ...., alpha[l]).  Then the ijth
+        entry of the Cartan matrix is ().
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.cartan_type import CartanType
+        >>> c = CartanType("G2")
+        >>> c.cartan_matrix()
+        Matrix([
+            [ 2, -1],
+            [-3,  2]])
+
+        """
+
+        m = Matrix( 2, 2, [2, -1, -3, 2])
+        return m
+
+    def basis(self):
+        """
+        Returns the number of independent generators of G_2
+        """
+        return 14
+
+    def dynkin_diagram(self):
+        diag = "0≡<≡0\n1   2"
+        return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/weyl_group.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/weyl_group.py
new file mode 100644
index 0000000000000000000000000000000000000000..15ff70b6f1fc4649268a38ee13e1f717a1c9f5fa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/liealgebras/weyl_group.py
@@ -0,0 +1,403 @@
+# -*- coding: utf-8 -*-
+
+from .cartan_type import CartanType
+from mpmath import fac
+from sympy.core.backend import Matrix, eye, Rational, igcd
+from sympy.core.basic import Atom
+
+class WeylGroup(Atom):
+
+    """
+    For each semisimple Lie group, we have a Weyl group.  It is a subgroup of
+    the isometry group of the root system.  Specifically, it's the subgroup
+    that is generated by reflections through the hyperplanes orthogonal to
+    the roots.  Therefore, Weyl groups are reflection groups, and so a Weyl
+    group is a finite Coxeter group.
+
+    """
+
+    def __new__(cls, cartantype):
+        obj = Atom.__new__(cls)
+        obj.cartan_type = CartanType(cartantype)
+        return obj
+
+    def generators(self):
+        """
+        This method creates the generating reflections of the Weyl group for
+        a given Lie algebra.  For a Lie algebra of rank n, there are n
+        different generating reflections.  This function returns them as
+        a list.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.weyl_group import WeylGroup
+        >>> c = WeylGroup("F4")
+        >>> c.generators()
+        ['r1', 'r2', 'r3', 'r4']
+        """
+        n = self.cartan_type.rank()
+        generators = []
+        for i in range(1, n+1):
+            reflection = "r"+str(i)
+            generators.append(reflection)
+        return generators
+
+    def group_order(self):
+        """
+        This method returns the order of the Weyl group.
+        For types A, B, C, D, and E the order depends on
+        the rank of the Lie algebra.  For types F and G,
+        the order is fixed.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.weyl_group import WeylGroup
+        >>> c = WeylGroup("D4")
+        >>> c.group_order()
+        192.0
+        """
+        n = self.cartan_type.rank()
+        if self.cartan_type.series == "A":
+            return fac(n+1)
+
+        if self.cartan_type.series in ("B", "C"):
+            return fac(n)*(2**n)
+
+        if self.cartan_type.series == "D":
+            return fac(n)*(2**(n-1))
+
+        if self.cartan_type.series == "E":
+            if n == 6:
+                return 51840
+            if n == 7:
+                return 2903040
+            if n == 8:
+                return 696729600
+        if self.cartan_type.series == "F":
+            return 1152
+
+        if self.cartan_type.series == "G":
+            return 12
+
+    def group_name(self):
+        """
+        This method returns some general information about the Weyl group for
+        a given Lie algebra.  It returns the name of the group and the elements
+        it acts on, if relevant.
+        """
+        n = self.cartan_type.rank()
+        if self.cartan_type.series == "A":
+            return "S"+str(n+1) + ": the symmetric group acting on " + str(n+1) + " elements."
+
+        if self.cartan_type.series in ("B", "C"):
+            return "The hyperoctahedral group acting on " + str(2*n) + " elements."
+
+        if self.cartan_type.series == "D":
+            return "The symmetry group of the " + str(n) + "-dimensional demihypercube."
+
+        if self.cartan_type.series == "E":
+            if n == 6:
+                return "The symmetry group of the 6-polytope."
+
+            if n == 7:
+                return "The symmetry group of the 7-polytope."
+
+            if n == 8:
+                return "The symmetry group of the 8-polytope."
+
+        if self.cartan_type.series == "F":
+            return "The symmetry group of the 24-cell, or icositetrachoron."
+
+        if self.cartan_type.series == "G":
+            return "D6, the dihedral group of order 12, and symmetry group of the hexagon."
+
+    def element_order(self, weylelt):
+        """
+        This method returns the order of a given Weyl group element, which should
+        be specified by the user in the form of products of the generating
+        reflections, i.e. of the form r1*r2 etc.
+
+        For types A-F, this method current works by taking the matrix form of
+        the specified element, and then finding what power of the matrix is the
+        identity.  It then returns this power.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.weyl_group import WeylGroup
+        >>> b = WeylGroup("B4")
+        >>> b.element_order('r1*r4*r2')
+        4
+        """
+        n = self.cartan_type.rank()
+        if self.cartan_type.series == "A":
+            a = self.matrix_form(weylelt)
+            order = 1
+            while a != eye(n+1):
+                a *= self.matrix_form(weylelt)
+                order += 1
+            return order
+
+        if self.cartan_type.series == "D":
+            a = self.matrix_form(weylelt)
+            order = 1
+            while a != eye(n):
+                a *= self.matrix_form(weylelt)
+                order += 1
+            return order
+
+        if self.cartan_type.series == "E":
+            a = self.matrix_form(weylelt)
+            order = 1
+            while a != eye(8):
+                a *= self.matrix_form(weylelt)
+                order += 1
+            return order
+
+        if self.cartan_type.series == "G":
+            elts = list(weylelt)
+            reflections = elts[1::3]
+            m = self.delete_doubles(reflections)
+            while self.delete_doubles(m) != m:
+                m = self.delete_doubles(m)
+                reflections = m
+            if len(reflections) % 2 == 1:
+                return 2
+
+            elif len(reflections) == 0:
+                return 1
+
+            else:
+                if len(reflections) == 1:
+                    return 2
+                else:
+                    m = len(reflections) // 2
+                    lcm = (6 * m)/ igcd(m, 6)
+                order = lcm / m
+                return order
+
+
+        if self.cartan_type.series == 'F':
+            a = self.matrix_form(weylelt)
+            order = 1
+            while a != eye(4):
+                a *= self.matrix_form(weylelt)
+                order += 1
+            return order
+
+
+        if self.cartan_type.series in ("B", "C"):
+            a = self.matrix_form(weylelt)
+            order = 1
+            while a != eye(n):
+                a *= self.matrix_form(weylelt)
+                order += 1
+            return order
+
+    def delete_doubles(self, reflections):
+        """
+        This is a helper method for determining the order of an element in the
+        Weyl group of G2.  It takes a Weyl element and if repeated simple reflections
+        in it, it deletes them.
+        """
+        counter = 0
+        copy = list(reflections)
+        for elt in copy:
+            if counter < len(copy)-1:
+                if copy[counter + 1] == elt:
+                    del copy[counter]
+                    del copy[counter]
+            counter += 1
+
+
+        return copy
+
+
+    def matrix_form(self, weylelt):
+        """
+        This method takes input from the user in the form of products of the
+        generating reflections, and returns the matrix corresponding to the
+        element of the Weyl group.  Since each element of the Weyl group is
+        a reflection of some type, there is a corresponding matrix representation.
+        This method uses the standard representation for all the generating
+        reflections.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.weyl_group import WeylGroup
+        >>> f = WeylGroup("F4")
+        >>> f.matrix_form('r2*r3')
+        Matrix([
+        [1, 0, 0,  0],
+        [0, 1, 0,  0],
+        [0, 0, 0, -1],
+        [0, 0, 1,  0]])
+
+        """
+        elts = list(weylelt)
+        reflections = elts[1::3]
+        n = self.cartan_type.rank()
+        if self.cartan_type.series == 'A':
+            matrixform = eye(n+1)
+            for elt in reflections:
+                a = int(elt)
+                mat = eye(n+1)
+                mat[a-1, a-1] = 0
+                mat[a-1, a] = 1
+                mat[a, a-1] = 1
+                mat[a, a] = 0
+                matrixform *= mat
+            return matrixform
+
+        if self.cartan_type.series == 'D':
+            matrixform = eye(n)
+            for elt in reflections:
+                a = int(elt)
+                mat = eye(n)
+                if a < n:
+                    mat[a-1, a-1] = 0
+                    mat[a-1, a] = 1
+                    mat[a, a-1] = 1
+                    mat[a, a] = 0
+                    matrixform *= mat
+                else:
+                    mat[n-2, n-1] = -1
+                    mat[n-2, n-2] = 0
+                    mat[n-1, n-2] = -1
+                    mat[n-1, n-1] = 0
+                    matrixform *= mat
+            return matrixform
+
+        if self.cartan_type.series == 'G':
+            matrixform = eye(3)
+            for elt in reflections:
+                a = int(elt)
+                if a == 1:
+                    gen1 = Matrix([[1, 0, 0], [0, 0, 1], [0, 1, 0]])
+                    matrixform *= gen1
+                else:
+                    gen2 = Matrix([[Rational(2, 3), Rational(2, 3), Rational(-1, 3)],
+                                   [Rational(2, 3), Rational(-1, 3), Rational(2, 3)],
+                                   [Rational(-1, 3), Rational(2, 3), Rational(2, 3)]])
+                    matrixform *= gen2
+            return matrixform
+
+        if self.cartan_type.series == 'F':
+            matrixform = eye(4)
+            for elt in reflections:
+                a = int(elt)
+                if a == 1:
+                    mat = Matrix([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
+                    matrixform *= mat
+                elif a == 2:
+                    mat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
+                    matrixform *= mat
+                elif a == 3:
+                    mat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]])
+                    matrixform *= mat
+                else:
+
+                    mat = Matrix([[Rational(1, 2), Rational(1, 2), Rational(1, 2), Rational(1, 2)],
+                        [Rational(1, 2), Rational(1, 2), Rational(-1, 2), Rational(-1, 2)],
+                        [Rational(1, 2), Rational(-1, 2), Rational(1, 2), Rational(-1, 2)],
+                        [Rational(1, 2), Rational(-1, 2), Rational(-1, 2), Rational(1, 2)]])
+                    matrixform *= mat
+            return matrixform
+
+        if self.cartan_type.series == 'E':
+            matrixform = eye(8)
+            for elt in reflections:
+                a = int(elt)
+                if a == 1:
+                    mat = Matrix([[Rational(3, 4), Rational(1, 4), Rational(1, 4), Rational(1, 4),
+                        Rational(1, 4), Rational(1, 4), Rational(1, 4), Rational(-1, 4)],
+                        [Rational(1, 4), Rational(3, 4), Rational(-1, 4), Rational(-1, 4),
+                            Rational(-1, 4), Rational(-1, 4), Rational(1, 4), Rational(-1, 4)],
+                        [Rational(1, 4), Rational(-1, 4), Rational(3, 4), Rational(-1, 4),
+                        Rational(-1, 4), Rational(-1, 4), Rational(-1, 4), Rational(1, 4)],
+                        [Rational(1, 4), Rational(-1, 4), Rational(-1, 4), Rational(3, 4),
+                        Rational(-1, 4), Rational(-1, 4), Rational(-1, 4), Rational(1, 4)],
+                        [Rational(1, 4), Rational(-1, 4), Rational(-1, 4), Rational(-1, 4),
+                        Rational(3, 4), Rational(-1, 4), Rational(-1, 4), Rational(1, 4)],
+                        [Rational(1, 4), Rational(-1, 4), Rational(-1, 4), Rational(-1, 4),
+                        Rational(-1, 4), Rational(3, 4), Rational(-1, 4), Rational(1, 4)],
+                        [Rational(1, 4), Rational(-1, 4), Rational(-1, 4), Rational(-1, 4),
+                        Rational(-1, 4), Rational(-1, 4), Rational(-3, 4), Rational(1, 4)],
+                        [Rational(1, 4), Rational(-1, 4), Rational(-1, 4), Rational(-1, 4),
+                        Rational(-1, 4), Rational(-1, 4), Rational(-1, 4), Rational(3, 4)]])
+                    matrixform *= mat
+                elif a == 2:
+                    mat = eye(8)
+                    mat[0, 0] = 0
+                    mat[0, 1] = -1
+                    mat[1, 0] = -1
+                    mat[1, 1] = 0
+                    matrixform *= mat
+                else:
+                    mat = eye(8)
+                    mat[a-3, a-3] = 0
+                    mat[a-3, a-2] = 1
+                    mat[a-2, a-3] = 1
+                    mat[a-2, a-2] = 0
+                    matrixform *= mat
+            return matrixform
+
+
+        if self.cartan_type.series in ("B", "C"):
+            matrixform = eye(n)
+            for elt in reflections:
+                a = int(elt)
+                mat = eye(n)
+                if a == 1:
+                    mat[0, 0] = -1
+                    matrixform *= mat
+                else:
+                    mat[a - 2, a - 2] = 0
+                    mat[a-2, a-1] = 1
+                    mat[a - 1, a - 2] = 1
+                    mat[a -1, a - 1] = 0
+                    matrixform *= mat
+            return matrixform
+
+
+
+    def coxeter_diagram(self):
+        """
+        This method returns the Coxeter diagram corresponding to a Weyl group.
+        The Coxeter diagram can be obtained from a Lie algebra's Dynkin diagram
+        by deleting all arrows; the Coxeter diagram is the undirected graph.
+        The vertices of the Coxeter diagram represent the generating reflections
+        of the Weyl group, $s_i$.  An edge is drawn between $s_i$ and $s_j$ if the order
+        $m(i, j)$ of $s_is_j$ is greater than two.  If there is one edge, the order
+        $m(i, j)$ is 3.  If there are two edges, the order $m(i, j)$ is 4, and if there
+        are three edges, the order $m(i, j)$ is 6.
+
+        Examples
+        ========
+
+        >>> from sympy.liealgebras.weyl_group import WeylGroup
+        >>> c = WeylGroup("B3")
+        >>> print(c.coxeter_diagram())
+        0---0===0
+        1   2   3
+        """
+        n = self.cartan_type.rank()
+        if self.cartan_type.series in ("A", "D", "E"):
+            return self.cartan_type.dynkin_diagram()
+
+        if self.cartan_type.series in ("B", "C"):
+            diag = "---".join("0" for i in range(1, n)) + "===0\n"
+            diag += "   ".join(str(i) for i in range(1, n+1))
+            return diag
+
+        if self.cartan_type.series == "F":
+            diag = "0---0===0---0\n"
+            diag += "   ".join(str(i) for i in range(1, 5))
+            return diag
+
+        if self.cartan_type.series == "G":
+            diag = "0≡≡≡0\n1   2"
+            return diag
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..cb26903a384e9df3a0f02a92c488c5442cee1486
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/__init__.py
@@ -0,0 +1,12 @@
+from .boolalg import (to_cnf, to_dnf, to_nnf, And, Or, Not, Xor, Nand, Nor, Implies,
+    Equivalent, ITE, POSform, SOPform, simplify_logic, bool_map, true, false,
+    gateinputcount)
+from .inference import satisfiable
+
+__all__ = [
+    'to_cnf', 'to_dnf', 'to_nnf', 'And', 'Or', 'Not', 'Xor', 'Nand', 'Nor',
+    'Implies', 'Equivalent', 'ITE', 'POSform', 'SOPform', 'simplify_logic',
+    'bool_map', 'true', 'false', 'gateinputcount',
+
+    'satisfiable',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/dpll.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/dpll.py
new file mode 100644
index 0000000000000000000000000000000000000000..40e6802f7626c982a9a6cd7146baea3ac6b8b6e0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/dpll.py
@@ -0,0 +1,308 @@
+"""Implementation of DPLL algorithm
+
+Further improvements: eliminate calls to pl_true, implement branching rules,
+efficient unit propagation.
+
+References:
+  - https://en.wikipedia.org/wiki/DPLL_algorithm
+  - https://www.researchgate.net/publication/242384772_Implementations_of_the_DPLL_Algorithm
+"""
+
+from sympy.core.sorting import default_sort_key
+from sympy.logic.boolalg import Or, Not, conjuncts, disjuncts, to_cnf, \
+    to_int_repr, _find_predicates
+from sympy.assumptions.cnf import CNF
+from sympy.logic.inference import pl_true, literal_symbol
+
+
+def dpll_satisfiable(expr):
+    """
+    Check satisfiability of a propositional sentence.
+    It returns a model rather than True when it succeeds
+
+    >>> from sympy.abc import A, B
+    >>> from sympy.logic.algorithms.dpll import dpll_satisfiable
+    >>> dpll_satisfiable(A & ~B)
+    {A: True, B: False}
+    >>> dpll_satisfiable(A & ~A)
+    False
+
+    """
+    if not isinstance(expr, CNF):
+        clauses = conjuncts(to_cnf(expr))
+    else:
+        clauses = expr.clauses
+    if False in clauses:
+        return False
+    symbols = sorted(_find_predicates(expr), key=default_sort_key)
+    symbols_int_repr = set(range(1, len(symbols) + 1))
+    clauses_int_repr = to_int_repr(clauses, symbols)
+    result = dpll_int_repr(clauses_int_repr, symbols_int_repr, {})
+    if not result:
+        return result
+    output = {}
+    for key in result:
+        output.update({symbols[key - 1]: result[key]})
+    return output
+
+
+def dpll(clauses, symbols, model):
+    """
+    Compute satisfiability in a partial model.
+    Clauses is an array of conjuncts.
+
+    >>> from sympy.abc import A, B, D
+    >>> from sympy.logic.algorithms.dpll import dpll
+    >>> dpll([A, B, D], [A, B], {D: False})
+    False
+
+    """
+    # compute DP kernel
+    P, value = find_unit_clause(clauses, model)
+    while P:
+        model.update({P: value})
+        symbols.remove(P)
+        if not value:
+            P = ~P
+        clauses = unit_propagate(clauses, P)
+        P, value = find_unit_clause(clauses, model)
+    P, value = find_pure_symbol(symbols, clauses)
+    while P:
+        model.update({P: value})
+        symbols.remove(P)
+        if not value:
+            P = ~P
+        clauses = unit_propagate(clauses, P)
+        P, value = find_pure_symbol(symbols, clauses)
+    # end DP kernel
+    unknown_clauses = []
+    for c in clauses:
+        val = pl_true(c, model)
+        if val is False:
+            return False
+        if val is not True:
+            unknown_clauses.append(c)
+    if not unknown_clauses:
+        return model
+    if not clauses:
+        return model
+    P = symbols.pop()
+    model_copy = model.copy()
+    model.update({P: True})
+    model_copy.update({P: False})
+    symbols_copy = symbols[:]
+    return (dpll(unit_propagate(unknown_clauses, P), symbols, model) or
+            dpll(unit_propagate(unknown_clauses, Not(P)), symbols_copy, model_copy))
+
+
+def dpll_int_repr(clauses, symbols, model):
+    """
+    Compute satisfiability in a partial model.
+    Arguments are expected to be in integer representation
+
+    >>> from sympy.logic.algorithms.dpll import dpll_int_repr
+    >>> dpll_int_repr([{1}, {2}, {3}], {1, 2}, {3: False})
+    False
+
+    """
+    # compute DP kernel
+    P, value = find_unit_clause_int_repr(clauses, model)
+    while P:
+        model.update({P: value})
+        symbols.remove(P)
+        if not value:
+            P = -P
+        clauses = unit_propagate_int_repr(clauses, P)
+        P, value = find_unit_clause_int_repr(clauses, model)
+    P, value = find_pure_symbol_int_repr(symbols, clauses)
+    while P:
+        model.update({P: value})
+        symbols.remove(P)
+        if not value:
+            P = -P
+        clauses = unit_propagate_int_repr(clauses, P)
+        P, value = find_pure_symbol_int_repr(symbols, clauses)
+    # end DP kernel
+    unknown_clauses = []
+    for c in clauses:
+        val = pl_true_int_repr(c, model)
+        if val is False:
+            return False
+        if val is not True:
+            unknown_clauses.append(c)
+    if not unknown_clauses:
+        return model
+    P = symbols.pop()
+    model_copy = model.copy()
+    model.update({P: True})
+    model_copy.update({P: False})
+    symbols_copy = symbols.copy()
+    return (dpll_int_repr(unit_propagate_int_repr(unknown_clauses, P), symbols, model) or
+            dpll_int_repr(unit_propagate_int_repr(unknown_clauses, -P), symbols_copy, model_copy))
+
+### helper methods for DPLL
+
+
+def pl_true_int_repr(clause, model={}):
+    """
+    Lightweight version of pl_true.
+    Argument clause represents the set of args of an Or clause. This is used
+    inside dpll_int_repr, it is not meant to be used directly.
+
+    >>> from sympy.logic.algorithms.dpll import pl_true_int_repr
+    >>> pl_true_int_repr({1, 2}, {1: False})
+    >>> pl_true_int_repr({1, 2}, {1: False, 2: False})
+    False
+
+    """
+    result = False
+    for lit in clause:
+        if lit < 0:
+            p = model.get(-lit)
+            if p is not None:
+                p = not p
+        else:
+            p = model.get(lit)
+        if p is True:
+            return True
+        elif p is None:
+            result = None
+    return result
+
+
+def unit_propagate(clauses, symbol):
+    """
+    Returns an equivalent set of clauses
+    If a set of clauses contains the unit clause l, the other clauses are
+    simplified by the application of the two following rules:
+
+      1. every clause containing l is removed
+      2. in every clause that contains ~l this literal is deleted
+
+    Arguments are expected to be in CNF.
+
+    >>> from sympy.abc import A, B, D
+    >>> from sympy.logic.algorithms.dpll import unit_propagate
+    >>> unit_propagate([A | B, D | ~B, B], B)
+    [D, B]
+
+    """
+    output = []
+    for c in clauses:
+        if c.func != Or:
+            output.append(c)
+            continue
+        for arg in c.args:
+            if arg == ~symbol:
+                output.append(Or(*[x for x in c.args if x != ~symbol]))
+                break
+            if arg == symbol:
+                break
+        else:
+            output.append(c)
+    return output
+
+
+def unit_propagate_int_repr(clauses, s):
+    """
+    Same as unit_propagate, but arguments are expected to be in integer
+    representation
+
+    >>> from sympy.logic.algorithms.dpll import unit_propagate_int_repr
+    >>> unit_propagate_int_repr([{1, 2}, {3, -2}, {2}], 2)
+    [{3}]
+
+    """
+    negated = {-s}
+    return [clause - negated for clause in clauses if s not in clause]
+
+
+def find_pure_symbol(symbols, unknown_clauses):
+    """
+    Find a symbol and its value if it appears only as a positive literal
+    (or only as a negative) in clauses.
+
+    >>> from sympy.abc import A, B, D
+    >>> from sympy.logic.algorithms.dpll import find_pure_symbol
+    >>> find_pure_symbol([A, B, D], [A|~B,~B|~D,D|A])
+    (A, True)
+
+    """
+    for sym in symbols:
+        found_pos, found_neg = False, False
+        for c in unknown_clauses:
+            if not found_pos and sym in disjuncts(c):
+                found_pos = True
+            if not found_neg and Not(sym) in disjuncts(c):
+                found_neg = True
+        if found_pos != found_neg:
+            return sym, found_pos
+    return None, None
+
+
+def find_pure_symbol_int_repr(symbols, unknown_clauses):
+    """
+    Same as find_pure_symbol, but arguments are expected
+    to be in integer representation
+
+    >>> from sympy.logic.algorithms.dpll import find_pure_symbol_int_repr
+    >>> find_pure_symbol_int_repr({1,2,3},
+    ...     [{1, -2}, {-2, -3}, {3, 1}])
+    (1, True)
+
+    """
+    all_symbols = set().union(*unknown_clauses)
+    found_pos = all_symbols.intersection(symbols)
+    found_neg = all_symbols.intersection([-s for s in symbols])
+    for p in found_pos:
+        if -p not in found_neg:
+            return p, True
+    for p in found_neg:
+        if -p not in found_pos:
+            return -p, False
+    return None, None
+
+
+def find_unit_clause(clauses, model):
+    """
+    A unit clause has only 1 variable that is not bound in the model.
+
+    >>> from sympy.abc import A, B, D
+    >>> from sympy.logic.algorithms.dpll import find_unit_clause
+    >>> find_unit_clause([A | B | D, B | ~D, A | ~B], {A:True})
+    (B, False)
+
+    """
+    for clause in clauses:
+        num_not_in_model = 0
+        for literal in disjuncts(clause):
+            sym = literal_symbol(literal)
+            if sym not in model:
+                num_not_in_model += 1
+                P, value = sym, not isinstance(literal, Not)
+        if num_not_in_model == 1:
+            return P, value
+    return None, None
+
+
+def find_unit_clause_int_repr(clauses, model):
+    """
+    Same as find_unit_clause, but arguments are expected to be in
+    integer representation.
+
+    >>> from sympy.logic.algorithms.dpll import find_unit_clause_int_repr
+    >>> find_unit_clause_int_repr([{1, 2, 3},
+    ...     {2, -3}, {1, -2}], {1: True})
+    (2, False)
+
+    """
+    bound = set(model) | {-sym for sym in model}
+    for clause in clauses:
+        unbound = clause - bound
+        if len(unbound) == 1:
+            p = unbound.pop()
+            if p < 0:
+                return -p, False
+            else:
+                return p, True
+    return None, None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/dpll2.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/dpll2.py
new file mode 100644
index 0000000000000000000000000000000000000000..4f18c81189d6be565dc9b7caa3f0bf48e978bb56
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/dpll2.py
@@ -0,0 +1,688 @@
+"""Implementation of DPLL algorithm
+
+Features:
+  - Clause learning
+  - Watch literal scheme
+  - VSIDS heuristic
+
+References:
+  - https://en.wikipedia.org/wiki/DPLL_algorithm
+"""
+
+from collections import defaultdict
+from heapq import heappush, heappop
+
+from sympy.core.sorting import ordered
+from sympy.assumptions.cnf import EncodedCNF
+
+from sympy.logic.algorithms.lra_theory import LRASolver
+
+
+def dpll_satisfiable(expr, all_models=False, use_lra_theory=False):
+    """
+    Check satisfiability of a propositional sentence.
+    It returns a model rather than True when it succeeds.
+    Returns a generator of all models if all_models is True.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B
+    >>> from sympy.logic.algorithms.dpll2 import dpll_satisfiable
+    >>> dpll_satisfiable(A & ~B)
+    {A: True, B: False}
+    >>> dpll_satisfiable(A & ~A)
+    False
+
+    """
+    if not isinstance(expr, EncodedCNF):
+        exprs = EncodedCNF()
+        exprs.add_prop(expr)
+        expr = exprs
+
+    # Return UNSAT when False (encoded as 0) is present in the CNF
+    if {0} in expr.data:
+        if all_models:
+            return (f for f in [False])
+        return False
+
+    if use_lra_theory:
+        lra, immediate_conflicts = LRASolver.from_encoded_cnf(expr)
+    else:
+        lra = None
+        immediate_conflicts = []
+    solver = SATSolver(expr.data + immediate_conflicts, expr.variables, set(), expr.symbols, lra_theory=lra)
+    models = solver._find_model()
+
+    if all_models:
+        return _all_models(models)
+
+    try:
+        return next(models)
+    except StopIteration:
+        return False
+
+    # Uncomment to confirm the solution is valid (hitting set for the clauses)
+    #else:
+        #for cls in clauses_int_repr:
+            #assert solver.var_settings.intersection(cls)
+
+
+def _all_models(models):
+    satisfiable = False
+    try:
+        while True:
+            yield next(models)
+            satisfiable = True
+    except StopIteration:
+        if not satisfiable:
+            yield False
+
+
+class SATSolver:
+    """
+    Class for representing a SAT solver capable of
+     finding a model to a boolean theory in conjunctive
+     normal form.
+    """
+
+    def __init__(self, clauses, variables, var_settings, symbols=None,
+                heuristic='vsids', clause_learning='none', INTERVAL=500,
+                 lra_theory = None):
+
+        self.var_settings = var_settings
+        self.heuristic = heuristic
+        self.is_unsatisfied = False
+        self._unit_prop_queue = []
+        self.update_functions = []
+        self.INTERVAL = INTERVAL
+
+        if symbols is None:
+            self.symbols = list(ordered(variables))
+        else:
+            self.symbols = symbols
+
+        self._initialize_variables(variables)
+        self._initialize_clauses(clauses)
+
+        if 'vsids' == heuristic:
+            self._vsids_init()
+            self.heur_calculate = self._vsids_calculate
+            self.heur_lit_assigned = self._vsids_lit_assigned
+            self.heur_lit_unset = self._vsids_lit_unset
+            self.heur_clause_added = self._vsids_clause_added
+
+            # Note: Uncomment this if/when clause learning is enabled
+            #self.update_functions.append(self._vsids_decay)
+
+        else:
+            raise NotImplementedError
+
+        if 'simple' == clause_learning:
+            self.add_learned_clause = self._simple_add_learned_clause
+            self.compute_conflict = self._simple_compute_conflict
+            self.update_functions.append(self._simple_clean_clauses)
+        elif 'none' == clause_learning:
+            self.add_learned_clause = lambda x: None
+            self.compute_conflict = lambda: None
+        else:
+            raise NotImplementedError
+
+        # Create the base level
+        self.levels = [Level(0)]
+        self._current_level.varsettings = var_settings
+
+        # Keep stats
+        self.num_decisions = 0
+        self.num_learned_clauses = 0
+        self.original_num_clauses = len(self.clauses)
+
+        self.lra = lra_theory
+
+    def _initialize_variables(self, variables):
+        """Set up the variable data structures needed."""
+        self.sentinels = defaultdict(set)
+        self.occurrence_count = defaultdict(int)
+        self.variable_set = [False] * (len(variables) + 1)
+
+    def _initialize_clauses(self, clauses):
+        """Set up the clause data structures needed.
+
+        For each clause, the following changes are made:
+        - Unit clauses are queued for propagation right away.
+        - Non-unit clauses have their first and last literals set as sentinels.
+        - The number of clauses a literal appears in is computed.
+        """
+        self.clauses = [list(clause) for clause in clauses]
+
+        for i, clause in enumerate(self.clauses):
+
+            # Handle the unit clauses
+            if 1 == len(clause):
+                self._unit_prop_queue.append(clause[0])
+                continue
+
+            self.sentinels[clause[0]].add(i)
+            self.sentinels[clause[-1]].add(i)
+
+            for lit in clause:
+                self.occurrence_count[lit] += 1
+
+    def _find_model(self):
+        """
+        Main DPLL loop. Returns a generator of models.
+
+        Variables are chosen successively, and assigned to be either
+        True or False. If a solution is not found with this setting,
+        the opposite is chosen and the search continues. The solver
+        halts when every variable has a setting.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> list(l._find_model())
+        [{1: True, 2: False, 3: False}, {1: True, 2: True, 3: True}]
+
+        >>> from sympy.abc import A, B, C
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set(), [A, B, C])
+        >>> list(l._find_model())
+        [{A: True, B: False, C: False}, {A: True, B: True, C: True}]
+
+        """
+
+        # We use this variable to keep track of if we should flip a
+        #  variable setting in successive rounds
+        flip_var = False
+
+        # Check if unit prop says the theory is unsat right off the bat
+        self._simplify()
+        if self.is_unsatisfied:
+            return
+
+        # While the theory still has clauses remaining
+        while True:
+            # Perform cleanup / fixup at regular intervals
+            if self.num_decisions % self.INTERVAL == 0:
+                for func in self.update_functions:
+                    func()
+
+            if flip_var:
+                # We have just backtracked and we are trying to opposite literal
+                flip_var = False
+                lit = self._current_level.decision
+
+            else:
+                # Pick a literal to set
+                lit = self.heur_calculate()
+                self.num_decisions += 1
+
+                # Stopping condition for a satisfying theory
+                if 0 == lit:
+
+                    # check if assignment satisfies lra theory
+                    if self.lra:
+                        for enc_var in self.var_settings:
+                            res = self.lra.assert_lit(enc_var)
+                            if res is not None:
+                                break
+                        res = self.lra.check()
+                        self.lra.reset_bounds()
+                    else:
+                        res = None
+                    if res is None or res[0]:
+                        yield {self.symbols[abs(lit) - 1]:
+                                    lit > 0 for lit in self.var_settings}
+                    else:
+                        self._simple_add_learned_clause(res[1])
+
+                        # backtrack until we unassign one of the literals causing the conflict
+                        while not any(-lit in res[1] for lit in self._current_level.var_settings):
+                            self._undo()
+
+                    while self._current_level.flipped:
+                        self._undo()
+                    if len(self.levels) == 1:
+                        return
+                    flip_lit = -self._current_level.decision
+                    self._undo()
+                    self.levels.append(Level(flip_lit, flipped=True))
+                    flip_var = True
+                    continue
+
+                # Start the new decision level
+                self.levels.append(Level(lit))
+
+            # Assign the literal, updating the clauses it satisfies
+            self._assign_literal(lit)
+
+            # _simplify the theory
+            self._simplify()
+
+            # Check if we've made the theory unsat
+            if self.is_unsatisfied:
+
+                self.is_unsatisfied = False
+
+                # We unroll all of the decisions until we can flip a literal
+                while self._current_level.flipped:
+                    self._undo()
+
+                    # If we've unrolled all the way, the theory is unsat
+                    if 1 == len(self.levels):
+                        return
+
+                # Detect and add a learned clause
+                self.add_learned_clause(self.compute_conflict())
+
+                # Try the opposite setting of the most recent decision
+                flip_lit = -self._current_level.decision
+                self._undo()
+                self.levels.append(Level(flip_lit, flipped=True))
+                flip_var = True
+
+    ########################
+    #    Helper Methods    #
+    ########################
+    @property
+    def _current_level(self):
+        """The current decision level data structure
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{1}, {2}], {1, 2}, set())
+        >>> next(l._find_model())
+        {1: True, 2: True}
+        >>> l._current_level.decision
+        0
+        >>> l._current_level.flipped
+        False
+        >>> l._current_level.var_settings
+        {1, 2}
+
+        """
+        return self.levels[-1]
+
+    def _clause_sat(self, cls):
+        """Check if a clause is satisfied by the current variable setting.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{1}, {-1}], {1}, set())
+        >>> try:
+        ...     next(l._find_model())
+        ... except StopIteration:
+        ...     pass
+        >>> l._clause_sat(0)
+        False
+        >>> l._clause_sat(1)
+        True
+
+        """
+        for lit in self.clauses[cls]:
+            if lit in self.var_settings:
+                return True
+        return False
+
+    def _is_sentinel(self, lit, cls):
+        """Check if a literal is a sentinel of a given clause.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> next(l._find_model())
+        {1: True, 2: False, 3: False}
+        >>> l._is_sentinel(2, 3)
+        True
+        >>> l._is_sentinel(-3, 1)
+        False
+
+        """
+        return cls in self.sentinels[lit]
+
+    def _assign_literal(self, lit):
+        """Make a literal assignment.
+
+        The literal assignment must be recorded as part of the current
+        decision level. Additionally, if the literal is marked as a
+        sentinel of any clause, then a new sentinel must be chosen. If
+        this is not possible, then unit propagation is triggered and
+        another literal is added to the queue to be set in the future.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> next(l._find_model())
+        {1: True, 2: False, 3: False}
+        >>> l.var_settings
+        {-3, -2, 1}
+
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> l._assign_literal(-1)
+        >>> try:
+        ...     next(l._find_model())
+        ... except StopIteration:
+        ...     pass
+        >>> l.var_settings
+        {-1}
+
+        """
+        self.var_settings.add(lit)
+        self._current_level.var_settings.add(lit)
+        self.variable_set[abs(lit)] = True
+        self.heur_lit_assigned(lit)
+
+        sentinel_list = list(self.sentinels[-lit])
+
+        for cls in sentinel_list:
+            if not self._clause_sat(cls):
+                other_sentinel = None
+                for newlit in self.clauses[cls]:
+                    if newlit != -lit:
+                        if self._is_sentinel(newlit, cls):
+                            other_sentinel = newlit
+                        elif not self.variable_set[abs(newlit)]:
+                            self.sentinels[-lit].remove(cls)
+                            self.sentinels[newlit].add(cls)
+                            other_sentinel = None
+                            break
+
+                # Check if no sentinel update exists
+                if other_sentinel:
+                    self._unit_prop_queue.append(other_sentinel)
+
+    def _undo(self):
+        """
+        _undo the changes of the most recent decision level.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> next(l._find_model())
+        {1: True, 2: False, 3: False}
+        >>> level = l._current_level
+        >>> level.decision, level.var_settings, level.flipped
+        (-3, {-3, -2}, False)
+        >>> l._undo()
+        >>> level = l._current_level
+        >>> level.decision, level.var_settings, level.flipped
+        (0, {1}, False)
+
+        """
+        # Undo the variable settings
+        for lit in self._current_level.var_settings:
+            self.var_settings.remove(lit)
+            self.heur_lit_unset(lit)
+            self.variable_set[abs(lit)] = False
+
+        # Pop the level off the stack
+        self.levels.pop()
+
+    #########################
+    #      Propagation      #
+    #########################
+    """
+    Propagation methods should attempt to soundly simplify the boolean
+      theory, and return True if any simplification occurred and False
+      otherwise.
+    """
+    def _simplify(self):
+        """Iterate over the various forms of propagation to simplify the theory.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> l.variable_set
+        [False, False, False, False]
+        >>> l.sentinels
+        {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}}
+
+        >>> l._simplify()
+
+        >>> l.variable_set
+        [False, True, False, False]
+        >>> l.sentinels
+        {-3: {0, 2}, -2: {3, 4}, -1: set(), 2: {0, 3},
+        ...3: {2, 4}}
+
+        """
+        changed = True
+        while changed:
+            changed = False
+            changed |= self._unit_prop()
+            changed |= self._pure_literal()
+
+    def _unit_prop(self):
+        """Perform unit propagation on the current theory."""
+        result = len(self._unit_prop_queue) > 0
+        while self._unit_prop_queue:
+            next_lit = self._unit_prop_queue.pop()
+            if -next_lit in self.var_settings:
+                self.is_unsatisfied = True
+                self._unit_prop_queue = []
+                return False
+            else:
+                self._assign_literal(next_lit)
+
+        return result
+
+    def _pure_literal(self):
+        """Look for pure literals and assign them when found."""
+        return False
+
+    #########################
+    #      Heuristics       #
+    #########################
+    def _vsids_init(self):
+        """Initialize the data structures needed for the VSIDS heuristic."""
+        self.lit_heap = []
+        self.lit_scores = {}
+
+        for var in range(1, len(self.variable_set)):
+            self.lit_scores[var] = float(-self.occurrence_count[var])
+            self.lit_scores[-var] = float(-self.occurrence_count[-var])
+            heappush(self.lit_heap, (self.lit_scores[var], var))
+            heappush(self.lit_heap, (self.lit_scores[-var], -var))
+
+    def _vsids_decay(self):
+        """Decay the VSIDS scores for every literal.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+
+        >>> l.lit_scores
+        {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0}
+
+        >>> l._vsids_decay()
+
+        >>> l.lit_scores
+        {-3: -1.0, -2: -1.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -1.0}
+
+        """
+        # We divide every literal score by 2 for a decay factor
+        #  Note: This doesn't change the heap property
+        for lit in self.lit_scores.keys():
+            self.lit_scores[lit] /= 2.0
+
+    def _vsids_calculate(self):
+        """
+            VSIDS Heuristic Calculation
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+
+        >>> l.lit_heap
+        [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)]
+
+        >>> l._vsids_calculate()
+        -3
+
+        >>> l.lit_heap
+        [(-2.0, -2), (-2.0, 2), (0.0, -1), (0.0, 1), (-2.0, 3)]
+
+        """
+        if len(self.lit_heap) == 0:
+            return 0
+
+        # Clean out the front of the heap as long the variables are set
+        while self.variable_set[abs(self.lit_heap[0][1])]:
+            heappop(self.lit_heap)
+            if len(self.lit_heap) == 0:
+                return 0
+
+        return heappop(self.lit_heap)[1]
+
+    def _vsids_lit_assigned(self, lit):
+        """Handle the assignment of a literal for the VSIDS heuristic."""
+        pass
+
+    def _vsids_lit_unset(self, lit):
+        """Handle the unsetting of a literal for the VSIDS heuristic.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> l.lit_heap
+        [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)]
+
+        >>> l._vsids_lit_unset(2)
+
+        >>> l.lit_heap
+        [(-2.0, -3), (-2.0, -2), (-2.0, -2), (-2.0, 2), (-2.0, 3), (0.0, -1),
+        ...(-2.0, 2), (0.0, 1)]
+
+        """
+        var = abs(lit)
+        heappush(self.lit_heap, (self.lit_scores[var], var))
+        heappush(self.lit_heap, (self.lit_scores[-var], -var))
+
+    def _vsids_clause_added(self, cls):
+        """Handle the addition of a new clause for the VSIDS heuristic.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+
+        >>> l.num_learned_clauses
+        0
+        >>> l.lit_scores
+        {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0}
+
+        >>> l._vsids_clause_added({2, -3})
+
+        >>> l.num_learned_clauses
+        1
+        >>> l.lit_scores
+        {-3: -1.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -2.0}
+
+        """
+        self.num_learned_clauses += 1
+        for lit in cls:
+            self.lit_scores[lit] += 1
+
+    ########################
+    #   Clause Learning    #
+    ########################
+    def _simple_add_learned_clause(self, cls):
+        """Add a new clause to the theory.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+
+        >>> l.num_learned_clauses
+        0
+        >>> l.clauses
+        [[2, -3], [1], [3, -3], [2, -2], [3, -2]]
+        >>> l.sentinels
+        {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}}
+
+        >>> l._simple_add_learned_clause([3])
+
+        >>> l.clauses
+        [[2, -3], [1], [3, -3], [2, -2], [3, -2], [3]]
+        >>> l.sentinels
+        {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4, 5}}
+
+        """
+        cls_num = len(self.clauses)
+        self.clauses.append(cls)
+
+        for lit in cls:
+            self.occurrence_count[lit] += 1
+
+        self.sentinels[cls[0]].add(cls_num)
+        self.sentinels[cls[-1]].add(cls_num)
+
+        self.heur_clause_added(cls)
+
+    def _simple_compute_conflict(self):
+        """ Build a clause representing the fact that at least one decision made
+        so far is wrong.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.algorithms.dpll2 import SATSolver
+        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
+        ... {3, -2}], {1, 2, 3}, set())
+        >>> next(l._find_model())
+        {1: True, 2: False, 3: False}
+        >>> l._simple_compute_conflict()
+        [3]
+
+        """
+        return [-(level.decision) for level in self.levels[1:]]
+
+    def _simple_clean_clauses(self):
+        """Clean up learned clauses."""
+        pass
+
+
+class Level:
+    """
+    Represents a single level in the DPLL algorithm, and contains
+    enough information for a sound backtracking procedure.
+    """
+
+    def __init__(self, decision, flipped=False):
+        self.decision = decision
+        self.var_settings = set()
+        self.flipped = flipped
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/lra_theory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/lra_theory.py
new file mode 100644
index 0000000000000000000000000000000000000000..1690760d36003aed6866f593120c05a5b8f92c83
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/lra_theory.py
@@ -0,0 +1,912 @@
+"""Implements "A Fast Linear-Arithmetic Solver for DPLL(T)"
+
+The LRASolver class defined in this file can be used
+in conjunction with a SAT solver to check the
+satisfiability of formulas involving inequalities.
+
+Here's an example of how that would work:
+
+    Suppose you want to check the satisfiability of
+    the following formula:
+
+    >>> from sympy.core.relational import Eq
+    >>> from sympy.abc import x, y
+    >>> f = ((x > 0) | (x < 0)) & (Eq(x, 0) | Eq(y, 1)) & (~Eq(y, 1) | Eq(1, 2))
+
+    First a preprocessing step should be done on f. During preprocessing,
+    f should be checked for any predicates such as `Q.prime` that can't be
+    handled. Also unequality like `~Eq(y, 1)` should be split.
+
+    I should mention that the paper says to split both equalities and
+    unequality, but this implementation only requires that unequality
+    be split.
+
+    >>> f = ((x > 0) | (x < 0)) & (Eq(x, 0) | Eq(y, 1)) & ((y < 1) | (y > 1) | Eq(1, 2))
+
+    Then an LRASolver instance needs to be initialized with this formula.
+
+    >>> from sympy.assumptions.cnf import CNF, EncodedCNF
+    >>> from sympy.assumptions.ask import Q
+    >>> from sympy.logic.algorithms.lra_theory import LRASolver
+    >>> cnf = CNF.from_prop(f)
+    >>> enc = EncodedCNF()
+    >>> enc.add_from_cnf(cnf)
+    >>> lra, conflicts = LRASolver.from_encoded_cnf(enc)
+
+    Any immediate one-lital conflicts clauses will be detected here.
+    In this example, `~Eq(1, 2)` is one such conflict clause. We'll
+    want to add it to `f` so that the SAT solver is forced to
+    assign Eq(1, 2) to False.
+
+    >>> f = f & ~Eq(1, 2)
+
+    Now that the one-literal conflict clauses have been added
+    and an lra object has been initialized, we can pass `f`
+    to a SAT solver. The SAT solver will give us a satisfying
+    assignment such as:
+
+    (1 = 2): False
+    (y = 1): True
+    (y < 1): True
+    (y > 1): True
+    (x = 0): True
+    (x < 0): True
+    (x > 0): True
+
+    Next you would pass this assignment to the LRASolver
+    which will be able to determine that this particular
+    assignment is satisfiable or not.
+
+    Note that since EncodedCNF is inherently non-deterministic,
+    the int each predicate is encoded as is not consistent. As a
+    result, the code below likely does not reflect the assignment
+    given above.
+
+    >>> lra.assert_lit(-1) #doctest: +SKIP
+    >>> lra.assert_lit(2) #doctest: +SKIP
+    >>> lra.assert_lit(3) #doctest: +SKIP
+    >>> lra.assert_lit(4) #doctest: +SKIP
+    >>> lra.assert_lit(5) #doctest: +SKIP
+    >>> lra.assert_lit(6) #doctest: +SKIP
+    >>> lra.assert_lit(7) #doctest: +SKIP
+    >>> is_sat, conflict_or_assignment = lra.check()
+
+    As the particular assignment suggested is not satisfiable,
+    the LRASolver will return unsat and a conflict clause when
+    given that assignment. The conflict clause will always be
+    minimal, but there can be multiple minimal conflict clauses.
+    One possible conflict clause could be `~(x < 0) | ~(x > 0)`.
+
+    We would then add whatever conflict clause is given to
+    `f` to prevent the SAT solver from coming up with an
+    assignment with the same conflicting literals. In this case,
+    the conflict clause `~(x < 0) | ~(x > 0)` would prevent
+    any assignment where both (x < 0) and (x > 0) were both
+    true.
+
+    The SAT solver would then find another assignment
+    and we would check that assignment with the LRASolver
+    and so on. Eventually either a satisfying assignment
+    that the SAT solver and LRASolver agreed on would be found
+    or enough conflict clauses would be added so that the
+    boolean formula was unsatisfiable.
+
+
+This implementation is based on [1]_, which includes a
+detailed explanation of the algorithm and pseudocode
+for the most important functions.
+
+[1]_ also explains how backtracking and theory propagation
+could be implemented to speed up the current implementation,
+but these are not currently implemented.
+
+TODO:
+ - Handle non-rational real numbers
+ - Handle positive and negative infinity
+ - Implement backtracking and theory proposition
+ - Simplify matrix by removing unused variables using Gaussian elimination
+
+References
+==========
+
+.. [1] Dutertre, B., de Moura, L.:
+       A Fast Linear-Arithmetic Solver for DPLL(T)
+       https://link.springer.com/chapter/10.1007/11817963_11
+"""
+from sympy.solvers.solveset import linear_eq_to_matrix
+from sympy.matrices.dense import eye
+from sympy.assumptions import Predicate
+from sympy.assumptions.assume import AppliedPredicate
+from sympy.assumptions.ask import Q
+from sympy.core import Dummy
+from sympy.core.mul import Mul
+from sympy.core.add import Add
+from sympy.core.relational import Eq, Ne
+from sympy.core.sympify import sympify
+from sympy.core.singleton import S
+from sympy.core.numbers import Rational, oo
+from sympy.matrices.dense import Matrix
+
+class UnhandledInput(Exception):
+    """
+    Raised while creating an LRASolver if non-linearity
+    or non-rational numbers are present.
+    """
+
+# predicates that LRASolver understands and makes use of
+ALLOWED_PRED = {Q.eq, Q.gt, Q.lt, Q.le, Q.ge}
+
+# if true ~Q.gt(x, y) implies Q.le(x, y)
+HANDLE_NEGATION = True
+
+class LRASolver():
+    """
+    Linear Arithmetic Solver for DPLL(T) implemented with an algorithm based on
+    the Dual Simplex method. Uses Bland's pivoting rule to avoid cycling.
+
+    References
+    ==========
+
+    .. [1] Dutertre, B., de Moura, L.:
+           A Fast Linear-Arithmetic Solver for DPLL(T)
+           https://link.springer.com/chapter/10.1007/11817963_11
+    """
+
+    def __init__(self, A, slack_variables, nonslack_variables, enc_to_boundary, s_subs, testing_mode):
+        """
+        Use the "from_encoded_cnf" method to create a new LRASolver.
+        """
+        self.run_checks = testing_mode
+        self.s_subs = s_subs  # used only for test_lra_theory.test_random_problems
+
+        if any(not isinstance(a, Rational) for a in A):
+            raise UnhandledInput("Non-rational numbers are not handled")
+        if any(not isinstance(b.bound, Rational) for b in enc_to_boundary.values()):
+            raise UnhandledInput("Non-rational numbers are not handled")
+        m, n = len(slack_variables), len(slack_variables)+len(nonslack_variables)
+        if m != 0:
+            assert A.shape == (m, n)
+        if self.run_checks:
+            assert A[:, n-m:] == -eye(m)
+
+        self.enc_to_boundary = enc_to_boundary  # mapping of int to Boundary objects
+        self.boundary_to_enc = {value: key for key, value in enc_to_boundary.items()}
+        self.A = A
+        self.slack = slack_variables
+        self.nonslack = nonslack_variables
+        self.all_var = nonslack_variables + slack_variables
+
+        self.slack_set = set(slack_variables)
+
+        self.is_sat = True  # While True, all constraints asserted so far are satisfiable
+        self.result = None  # always one of: (True, assignment), (False, conflict clause), None
+
+    @staticmethod
+    def from_encoded_cnf(encoded_cnf, testing_mode=False):
+        """
+        Creates an LRASolver from an EncodedCNF object
+        and a list of conflict clauses for propositions
+        that can be simplified to True or False.
+
+        Parameters
+        ==========
+
+        encoded_cnf : EncodedCNF
+
+        testing_mode : bool
+            Setting testing_mode to True enables some slow assert statements
+            and sorting to reduce nonterministic behavior.
+
+        Returns
+        =======
+
+        (lra, conflicts)
+
+        lra : LRASolver
+
+        conflicts : list
+            Contains a one-literal conflict clause for each proposition
+            that can be simplified to True or False.
+
+        Example
+        =======
+
+        >>> from sympy.core.relational import Eq
+        >>> from sympy.assumptions.cnf import CNF, EncodedCNF
+        >>> from sympy.assumptions.ask import Q
+        >>> from sympy.logic.algorithms.lra_theory import LRASolver
+        >>> from sympy.abc import x, y, z
+        >>> phi = (x >= 0) & ((x + y <= 2) | (x + 2 * y - z >= 6))
+        >>> phi = phi & (Eq(x + y, 2) | (x + 2 * y - z > 4))
+        >>> phi = phi & Q.gt(2, 1)
+        >>> cnf = CNF.from_prop(phi)
+        >>> enc = EncodedCNF()
+        >>> enc.from_cnf(cnf)
+        >>> lra, conflicts = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+        >>> lra #doctest: +SKIP
+        
+        >>> conflicts #doctest: +SKIP
+        [[4]]
+        """
+        # This function has three main jobs:
+        # - raise errors if the input formula is not handled
+        # - preprocesses the formula into a matrix and single variable constraints
+        # - create one-literal conflict clauses from predicates that are always True
+        #   or always False such as Q.gt(3, 2)
+        #
+        # See the preprocessing section of "A Fast Linear-Arithmetic Solver for DPLL(T)"
+        # for an explanation of how the formula is converted into a matrix
+        # and a set of single variable constraints.
+
+        encoding = {}  # maps int to boundary
+        A = []
+
+        basic = []
+        s_count = 0
+        s_subs = {}
+        nonbasic = []
+
+        if testing_mode:
+            # sort to reduce nondeterminism
+            encoded_cnf_items = sorted(encoded_cnf.encoding.items(), key=lambda x: str(x))
+        else:
+            encoded_cnf_items = encoded_cnf.encoding.items()
+
+        empty_var = Dummy()
+        var_to_lra_var = {}
+        conflicts = []
+
+        for prop, enc in encoded_cnf_items:
+            if isinstance(prop, Predicate):
+                prop = prop(empty_var)
+            if not isinstance(prop, AppliedPredicate):
+                if prop == True:
+                    conflicts.append([enc])
+                    continue
+                if prop == False:
+                    conflicts.append([-enc])
+                    continue
+
+                raise ValueError(f"Unhandled Predicate: {prop}")
+
+            assert prop.function in ALLOWED_PRED
+            if prop.lhs == S.NaN or prop.rhs == S.NaN:
+                raise ValueError(f"{prop} contains nan")
+            if prop.lhs.is_imaginary or prop.rhs.is_imaginary:
+                raise UnhandledInput(f"{prop} contains an imaginary component")
+            if prop.lhs == oo or prop.rhs == oo:
+                raise UnhandledInput(f"{prop} contains infinity")
+
+            prop = _eval_binrel(prop)  # simplify variable-less quantities to True / False if possible
+            if prop == True:
+                conflicts.append([enc])
+                continue
+            elif prop == False:
+                conflicts.append([-enc])
+                continue
+            elif prop is None:
+                raise UnhandledInput(f"{prop} could not be simplified")
+
+            expr = prop.lhs - prop.rhs
+            if prop.function in [Q.ge, Q.gt]:
+                expr = -expr
+
+            # expr should be less than (or equal to) 0
+            # otherwise prop is False
+            if prop.function in [Q.le, Q.ge]:
+                bool = (expr <= 0)
+            elif prop.function in [Q.lt, Q.gt]:
+                bool = (expr < 0)
+            else:
+                assert prop.function == Q.eq
+                bool = Eq(expr, 0)
+
+            if bool == True:
+                conflicts.append([enc])
+                continue
+            elif bool == False:
+                conflicts.append([-enc])
+                continue
+
+
+            vars, const = _sep_const_terms(expr)  # example: (2x + 3y + 2) --> (2x + 3y), (2)
+            vars, var_coeff = _sep_const_coeff(vars)  # examples: (2x) --> (x, 2); (2x + 3y) --> (2x + 3y), (1)
+            const = const / var_coeff
+
+            terms = _list_terms(vars)  # example: (2x + 3y) --> [2x, 3y]
+            for term in terms:
+                term, _ = _sep_const_coeff(term)
+                assert len(term.free_symbols) > 0
+                if term not in var_to_lra_var:
+                    var_to_lra_var[term] = LRAVariable(term)
+                    nonbasic.append(term)
+
+            if len(terms) > 1:
+                if vars not in s_subs:
+                    s_count += 1
+                    d = Dummy(f"s{s_count}")
+                    var_to_lra_var[d] = LRAVariable(d)
+                    basic.append(d)
+                    s_subs[vars] = d
+                    A.append(vars - d)
+                var = s_subs[vars]
+            else:
+                var = terms[0]
+
+            assert var_coeff != 0
+
+            equality = prop.function == Q.eq
+            upper = var_coeff > 0 if not equality else None
+            strict = prop.function in [Q.gt, Q.lt]
+            b = Boundary(var_to_lra_var[var], -const, upper, equality, strict)
+            encoding[enc] = b
+
+        fs = [v.free_symbols for v in nonbasic + basic]
+        assert all(len(syms) > 0 for syms in fs)
+        fs_count = sum(len(syms) for syms in fs)
+        if len(fs) > 0 and  len(set.union(*fs)) < fs_count:
+            raise UnhandledInput("Nonlinearity is not handled")
+
+        A, _ = linear_eq_to_matrix(A, nonbasic + basic)
+        nonbasic = [var_to_lra_var[nb] for nb in nonbasic]
+        basic = [var_to_lra_var[b] for b in basic]
+        for idx, var in enumerate(nonbasic + basic):
+            var.col_idx = idx
+
+        return LRASolver(A, basic, nonbasic, encoding, s_subs, testing_mode), conflicts
+
+    def reset_bounds(self):
+        """
+        Resets the state of the LRASolver to before
+        anything was asserted.
+        """
+        self.result = None
+        for var in self.all_var:
+            var.lower = LRARational(-float("inf"), 0)
+            var.lower_from_eq = False
+            var.lower_from_neg = False
+            var.upper = LRARational(float("inf"), 0)
+            var.upper_from_eq= False
+            var.lower_from_neg = False
+            var.assign = LRARational(0, 0)
+
+    def assert_lit(self, enc_constraint):
+        """
+        Assert a literal representing a constraint
+        and update the internal state accordingly.
+
+        Note that due to peculiarities of this implementation
+        asserting ~(x > 0) will assert (x <= 0) but asserting
+        ~Eq(x, 0) will not do anything.
+
+        Parameters
+        ==========
+
+        enc_constraint : int
+            A mapping of encodings to constraints
+            can be found in `self.enc_to_boundary`.
+
+        Returns
+        =======
+
+        None or (False, explanation)
+
+        explanation : set of ints
+            A conflict clause that "explains" why
+            the literals asserted so far are unsatisfiable.
+        """
+        if abs(enc_constraint) not in self.enc_to_boundary:
+            return None
+
+        if not HANDLE_NEGATION and enc_constraint < 0:
+            return None
+
+        boundary = self.enc_to_boundary[abs(enc_constraint)]
+        sym, c, negated = boundary.var, boundary.bound, enc_constraint < 0
+
+        if boundary.equality and negated:
+            return None # negated equality is not handled and should only appear in conflict clauses
+
+        upper = boundary.upper != negated
+        if boundary.strict != negated:
+            delta = -1 if upper else 1
+            c = LRARational(c, delta)
+        else:
+            c = LRARational(c, 0)
+
+        if boundary.equality:
+            res1 = self._assert_lower(sym, c, from_equality=True, from_neg=negated)
+            if res1 and res1[0] == False:
+                res = res1
+            else:
+                res2 = self._assert_upper(sym, c, from_equality=True, from_neg=negated)
+                res =  res2
+        elif upper:
+            res = self._assert_upper(sym, c, from_neg=negated)
+        else:
+            res = self._assert_lower(sym, c, from_neg=negated)
+
+        if self.is_sat and sym not in self.slack_set:
+            self.is_sat = res is None
+        else:
+            self.is_sat = False
+
+        return res
+
+    def _assert_upper(self, xi, ci, from_equality=False, from_neg=False):
+        """
+        Adjusts the upper bound on variable xi if the new upper bound is
+        more limiting. The assignment of variable xi is adjusted to be
+        within the new bound if needed.
+
+        Also calls `self._update` to update the assignment for slack variables
+        to keep all equalities satisfied.
+        """
+        if self.result:
+            assert self.result[0] != False
+        self.result = None
+        if ci >= xi.upper:
+            return None
+        if ci < xi.lower:
+            assert (xi.lower[1] >= 0) is True
+            assert (ci[1] <= 0) is True
+
+            lit1, neg1 = Boundary.from_lower(xi)
+
+            lit2 = Boundary(var=xi, const=ci[0], strict=ci[1] != 0, upper=True, equality=from_equality)
+            if from_neg:
+                lit2 = lit2.get_negated()
+            neg2 = -1 if from_neg else 1
+
+            conflict = [-neg1*self.boundary_to_enc[lit1], -neg2*self.boundary_to_enc[lit2]]
+            self.result = False, conflict
+            return self.result
+        xi.upper = ci
+        xi.upper_from_eq = from_equality
+        xi.upper_from_neg = from_neg
+        if xi in self.nonslack and xi.assign > ci:
+            self._update(xi, ci)
+
+        if self.run_checks and all(v.assign[0] != float("inf") and v.assign[0] != -float("inf")
+                                   for v in self.all_var):
+            M = self.A
+            X = Matrix([v.assign[0] for v in self.all_var])
+            assert all(abs(val) < 10 ** (-10) for val in M * X)
+
+        return None
+
+    def _assert_lower(self, xi, ci, from_equality=False, from_neg=False):
+        """
+        Adjusts the lower bound on variable xi if the new lower bound is
+        more limiting. The assignment of variable xi is adjusted to be
+        within the new bound if needed.
+
+        Also calls `self._update` to update the assignment for slack variables
+        to keep all equalities satisfied.
+        """
+        if self.result:
+            assert self.result[0] != False
+        self.result = None
+        if ci <= xi.lower:
+            return None
+        if ci > xi.upper:
+            assert (xi.upper[1] <= 0) is True
+            assert (ci[1] >= 0) is True
+
+            lit1, neg1 = Boundary.from_upper(xi)
+
+            lit2 = Boundary(var=xi, const=ci[0], strict=ci[1] != 0, upper=False, equality=from_equality)
+            if from_neg:
+                lit2 = lit2.get_negated()
+            neg2 = -1 if from_neg else 1
+
+            conflict = [-neg1*self.boundary_to_enc[lit1],-neg2*self.boundary_to_enc[lit2]]
+            self.result = False, conflict
+            return self.result
+        xi.lower = ci
+        xi.lower_from_eq = from_equality
+        xi.lower_from_neg = from_neg
+        if xi in self.nonslack and xi.assign < ci:
+            self._update(xi, ci)
+
+        if self.run_checks and all(v.assign[0] != float("inf") and v.assign[0] != -float("inf")
+                                   for v in self.all_var):
+            M = self.A
+            X = Matrix([v.assign[0] for v in self.all_var])
+            assert all(abs(val) < 10 ** (-10) for val in M * X)
+
+        return None
+
+    def _update(self, xi, v):
+        """
+        Updates all slack variables that have equations that contain
+        variable xi so that they stay satisfied given xi is equal to v.
+        """
+        i = xi.col_idx
+        for j, b in enumerate(self.slack):
+            aji = self.A[j, i]
+            b.assign = b.assign + (v - xi.assign)*aji
+        xi.assign = v
+
+    def check(self):
+        """
+        Searches for an assignment that satisfies all constraints
+        or determines that no such assignment exists and gives
+        a minimal conflict clause that "explains" why the
+        constraints are unsatisfiable.
+
+        Returns
+        =======
+
+        (True, assignment) or (False, explanation)
+
+        assignment : dict of LRAVariables to values
+            Assigned values are tuples that represent a rational number
+            plus some infinatesimal delta.
+
+        explanation : set of ints
+        """
+        if self.is_sat:
+            return True, {var: var.assign for var in self.all_var}
+        if self.result:
+            return self.result
+
+        from sympy.matrices.dense import Matrix
+        M = self.A.copy()
+        basic = {s: i for i, s in enumerate(self.slack)}  # contains the row index associated with each basic variable
+        nonbasic = set(self.nonslack)
+        while True:
+            if self.run_checks:
+                # nonbasic variables must always be within bounds
+                assert all(((nb.assign >= nb.lower) == True) and ((nb.assign <= nb.upper) == True) for nb in nonbasic)
+
+                # assignments for x must always satisfy Ax = 0
+                # probably have to turn this off when dealing with strict ineq
+                if all(v.assign[0] != float("inf") and v.assign[0] != -float("inf")
+                                   for v in self.all_var):
+                    X = Matrix([v.assign[0] for v in self.all_var])
+                    assert all(abs(val) < 10**(-10) for val in M*X)
+
+                # check upper and lower match this format:
+                # x <= rat + delta iff x < rat
+                # x >= rat - delta iff x > rat
+                # this wouldn't make sense:
+                # x <= rat - delta
+                # x >= rat + delta
+                assert all(x.upper[1] <= 0 for x in self.all_var)
+                assert all(x.lower[1] >= 0 for x in self.all_var)
+
+            cand = [b for b in basic if b.assign < b.lower or b.assign > b.upper]
+
+            if len(cand) == 0:
+                return True, {var: var.assign for var in self.all_var}
+
+            xi = min(cand, key=lambda v: v.col_idx) # Bland's rule
+            i = basic[xi]
+
+            if xi.assign < xi.lower:
+                cand = [nb for nb in nonbasic
+                        if (M[i, nb.col_idx] > 0 and nb.assign < nb.upper)
+                        or (M[i, nb.col_idx] < 0 and nb.assign > nb.lower)]
+                if len(cand) == 0:
+                    N_plus = [nb for nb in nonbasic if M[i, nb.col_idx] > 0]
+                    N_minus = [nb for nb in nonbasic if M[i, nb.col_idx] < 0]
+
+                    conflict = []
+                    conflict += [Boundary.from_upper(nb) for nb in N_plus]
+                    conflict += [Boundary.from_lower(nb) for nb in N_minus]
+                    conflict.append(Boundary.from_lower(xi))
+                    conflict = [-neg*self.boundary_to_enc[c] for c, neg in conflict]
+                    return False, conflict
+                xj = min(cand, key=str)
+                M = self._pivot_and_update(M, basic, nonbasic, xi, xj, xi.lower)
+
+            if xi.assign > xi.upper:
+                cand = [nb for nb in nonbasic
+                        if (M[i, nb.col_idx] < 0 and nb.assign < nb.upper)
+                        or (M[i, nb.col_idx] > 0 and nb.assign > nb.lower)]
+
+                if len(cand) == 0:
+                    N_plus = [nb for nb in nonbasic if M[i, nb.col_idx] > 0]
+                    N_minus = [nb for nb in nonbasic if M[i, nb.col_idx] < 0]
+
+                    conflict = []
+                    conflict += [Boundary.from_upper(nb) for nb in N_minus]
+                    conflict += [Boundary.from_lower(nb) for nb in N_plus]
+                    conflict.append(Boundary.from_upper(xi))
+
+                    conflict = [-neg*self.boundary_to_enc[c] for c, neg in conflict]
+                    return False, conflict
+                xj = min(cand, key=lambda v: v.col_idx)
+                M = self._pivot_and_update(M, basic, nonbasic, xi, xj, xi.upper)
+
+    def _pivot_and_update(self, M, basic, nonbasic, xi, xj, v):
+        """
+        Pivots basic variable xi with nonbasic variable xj,
+        and sets value of xi to v and adjusts the values of all basic variables
+        to keep equations satisfied.
+        """
+        i, j = basic[xi], xj.col_idx
+        assert M[i, j] != 0
+        theta = (v - xi.assign)*(1/M[i, j])
+        xi.assign = v
+        xj.assign = xj.assign + theta
+        for xk in basic:
+            if xk != xi:
+                k = basic[xk]
+                akj = M[k, j]
+                xk.assign = xk.assign + theta*akj
+        # pivot
+        basic[xj] = basic[xi]
+        del basic[xi]
+        nonbasic.add(xi)
+        nonbasic.remove(xj)
+        return self._pivot(M, i, j)
+
+    @staticmethod
+    def _pivot(M, i, j):
+        """
+        Performs a pivot operation about entry i, j of M by performing
+        a series of row operations on a copy of M and returning the result.
+        The original M is left unmodified.
+
+        Conceptually, M represents a system of equations and pivoting
+        can be thought of as rearranging equation i to be in terms of
+        variable j and then substituting in the rest of the equations
+        to get rid of other occurances of variable j.
+
+        Example
+        =======
+
+        >>> from sympy.matrices.dense import Matrix
+        >>> from sympy.logic.algorithms.lra_theory import LRASolver
+        >>> from sympy import var
+        >>> Matrix(3, 3, var('a:i'))
+        Matrix([
+        [a, b, c],
+        [d, e, f],
+        [g, h, i]])
+
+        This matrix is equivalent to:
+        0 = a*x + b*y + c*z
+        0 = d*x + e*y + f*z
+        0 = g*x + h*y + i*z
+
+        >>> LRASolver._pivot(_, 1, 0)
+        Matrix([
+        [ 0, -a*e/d + b, -a*f/d + c],
+        [-1,       -e/d,       -f/d],
+        [ 0,  h - e*g/d,  i - f*g/d]])
+
+        We rearrange equation 1 in terms of variable 0 (x)
+        and substitute to remove x from the other equations.
+
+        0 = 0 + (-a*e/d + b)*y + (-a*f/d + c)*z
+        0 = -x + (-e/d)*y + (-f/d)*z
+        0 = 0 + (h - e*g/d)*y + (i - f*g/d)*z
+        """
+        _, _, Mij = M[i, :], M[:, j], M[i, j]
+        if Mij == 0:
+            raise ZeroDivisionError("Tried to pivot about zero-valued entry.")
+        A = M.copy()
+        A[i, :] = -A[i, :]/Mij
+        for row in range(M.shape[0]):
+            if row != i:
+                A[row, :] = A[row, :] + A[row, j] * A[i, :]
+
+        return A
+
+
+def _sep_const_coeff(expr):
+    """
+    Example
+    =======
+
+    >>> from sympy.logic.algorithms.lra_theory import _sep_const_coeff
+    >>> from sympy.abc import x, y
+    >>> _sep_const_coeff(2*x)
+    (x, 2)
+    >>> _sep_const_coeff(2*x + 3*y)
+    (2*x + 3*y, 1)
+    """
+    if isinstance(expr, Add):
+        return expr, sympify(1)
+
+    if isinstance(expr, Mul):
+        coeffs = expr.args
+    else:
+        coeffs = [expr]
+
+    var, const = [], []
+    for c in coeffs:
+        c = sympify(c)
+        if len(c.free_symbols)==0:
+            const.append(c)
+        else:
+            var.append(c)
+    return Mul(*var), Mul(*const)
+
+
+def _list_terms(expr):
+    if not isinstance(expr, Add):
+        return [expr]
+
+    return expr.args
+
+
+def _sep_const_terms(expr):
+    """
+    Example
+    =======
+
+    >>> from sympy.logic.algorithms.lra_theory import _sep_const_terms
+    >>> from sympy.abc import x, y
+    >>> _sep_const_terms(2*x + 3*y + 2)
+    (2*x + 3*y, 2)
+    """
+    if isinstance(expr, Add):
+        terms = expr.args
+    else:
+        terms = [expr]
+
+    var, const = [], []
+    for t in terms:
+        if len(t.free_symbols) == 0:
+            const.append(t)
+        else:
+            var.append(t)
+    return sum(var), sum(const)
+
+
+def _eval_binrel(binrel):
+    """
+    Simplify binary relation to True / False if possible.
+    """
+    if not (len(binrel.lhs.free_symbols) == 0 and len(binrel.rhs.free_symbols) == 0):
+        return binrel
+    if binrel.function == Q.lt:
+        res = binrel.lhs < binrel.rhs
+    elif binrel.function == Q.gt:
+        res = binrel.lhs > binrel.rhs
+    elif binrel.function == Q.le:
+        res = binrel.lhs <= binrel.rhs
+    elif binrel.function == Q.ge:
+        res = binrel.lhs >= binrel.rhs
+    elif binrel.function == Q.eq:
+        res = Eq(binrel.lhs, binrel.rhs)
+    elif binrel.function == Q.ne:
+        res = Ne(binrel.lhs, binrel.rhs)
+
+    if res == True or res == False:
+        return res
+    else:
+        return None
+
+
+class Boundary:
+    """
+    Represents an upper or lower bound or an equality between a symbol
+    and some constant.
+    """
+    def __init__(self, var, const, upper, equality, strict=None):
+        if not equality in [True, False]:
+            assert equality in [True, False]
+
+
+        self.var = var
+        if isinstance(const, tuple):
+            s = const[1] != 0
+            if strict:
+                assert s == strict
+            self.bound = const[0]
+            self.strict = s
+        else:
+            self.bound = const
+            self.strict = strict
+        self.upper = upper if not equality else None
+        self.equality = equality
+        self.strict = strict
+        assert self.strict is not None
+
+    @staticmethod
+    def from_upper(var):
+        neg = -1 if var.upper_from_neg else 1
+        b = Boundary(var, var.upper[0], True, var.upper_from_eq, var.upper[1] != 0)
+        if neg < 0:
+            b = b.get_negated()
+        return b, neg
+
+    @staticmethod
+    def from_lower(var):
+        neg = -1 if var.lower_from_neg else 1
+        b = Boundary(var, var.lower[0], False, var.lower_from_eq, var.lower[1] != 0)
+        if neg < 0:
+            b = b.get_negated()
+        return b, neg
+
+    def get_negated(self):
+        return Boundary(self.var, self.bound, not self.upper, self.equality, not self.strict)
+
+    def get_inequality(self):
+        if self.equality:
+            return Eq(self.var.var, self.bound)
+        elif self.upper and self.strict:
+            return self.var.var < self.bound
+        elif not self.upper and self.strict:
+            return self.var.var > self.bound
+        elif self.upper:
+            return self.var.var <= self.bound
+        else:
+            return self.var.var >= self.bound
+
+    def __repr__(self):
+        return repr("Boundary(" + repr(self.get_inequality()) + ")")
+
+    def __eq__(self, other):
+        other = (other.var, other.bound, other.strict, other.upper, other.equality)
+        return (self.var, self.bound, self.strict, self.upper, self.equality) == other
+
+    def __hash__(self):
+        return hash((self.var, self.bound, self.strict, self.upper, self.equality))
+
+
+class LRARational():
+    """
+    Represents a rational plus or minus some amount
+    of arbitrary small deltas.
+    """
+    def __init__(self, rational, delta):
+        self.value = (rational, delta)
+
+    def __lt__(self, other):
+        return self.value < other.value
+
+    def __le__(self, other):
+        return self.value <= other.value
+
+    def __eq__(self, other):
+        return self.value == other.value
+
+    def __add__(self, other):
+        return LRARational(self.value[0] + other.value[0], self.value[1] + other.value[1])
+
+    def __sub__(self, other):
+        return LRARational(self.value[0] - other.value[0], self.value[1] - other.value[1])
+
+    def __mul__(self, other):
+        assert not isinstance(other, LRARational)
+        return LRARational(self.value[0] * other, self.value[1] * other)
+
+    def __getitem__(self, index):
+        return self.value[index]
+
+    def __repr__(self):
+        return repr(self.value)
+
+
+class LRAVariable():
+    """
+    Object to keep track of upper and lower bounds
+    on `self.var`.
+    """
+    def __init__(self, var):
+        self.upper = LRARational(float("inf"), 0)
+        self.upper_from_eq = False
+        self.upper_from_neg = False
+        self.lower = LRARational(-float("inf"), 0)
+        self.lower_from_eq = False
+        self.lower_from_neg = False
+        self.assign = LRARational(0,0)
+        self.var = var
+        self.col_idx = None
+
+    def __repr__(self):
+        return repr(self.var)
+
+    def __eq__(self, other):
+        if not isinstance(other, LRAVariable):
+            return False
+        return other.var == self.var
+
+    def __hash__(self):
+        return hash(self.var)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/minisat22_wrapper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/minisat22_wrapper.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d5c1f8f14f04309f7cb8197cc05d01a3c108545
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/minisat22_wrapper.py
@@ -0,0 +1,46 @@
+from sympy.assumptions.cnf import EncodedCNF
+
+def minisat22_satisfiable(expr, all_models=False, minimal=False):
+
+    if not isinstance(expr, EncodedCNF):
+        exprs = EncodedCNF()
+        exprs.add_prop(expr)
+        expr = exprs
+
+    from pysat.solvers import Minisat22
+
+    # Return UNSAT when False (encoded as 0) is present in the CNF
+    if {0} in expr.data:
+        if all_models:
+            return (f for f in [False])
+        return False
+
+    r = Minisat22(expr.data)
+
+    if minimal:
+        r.set_phases([-(i+1) for i in range(r.nof_vars())])
+
+    if not r.solve():
+        return False
+
+    if not all_models:
+        return {expr.symbols[abs(lit) - 1]: lit > 0 for lit in r.get_model()}
+
+    else:
+        # Make solutions SymPy compatible by creating a generator
+        def _gen(results):
+            satisfiable = False
+            while results.solve():
+                sol = results.get_model()
+                yield {expr.symbols[abs(lit) - 1]: lit > 0 for lit in sol}
+                if minimal:
+                    results.add_clause([-i for i in sol if i>0])
+                else:
+                    results.add_clause([-i for i in sol])
+                satisfiable = True
+            if not satisfiable:
+                yield False
+            raise StopIteration
+
+
+        return _gen(r)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/pycosat_wrapper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/pycosat_wrapper.py
new file mode 100644
index 0000000000000000000000000000000000000000..5ff498b7e3f6b73d95e9b949598ef32df4ecf226
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/pycosat_wrapper.py
@@ -0,0 +1,41 @@
+from sympy.assumptions.cnf import EncodedCNF
+
+
+def pycosat_satisfiable(expr, all_models=False):
+    import pycosat
+    if not isinstance(expr, EncodedCNF):
+        exprs = EncodedCNF()
+        exprs.add_prop(expr)
+        expr = exprs
+
+    # Return UNSAT when False (encoded as 0) is present in the CNF
+    if {0} in expr.data:
+        if all_models:
+            return (f for f in [False])
+        return False
+
+    if not all_models:
+        r = pycosat.solve(expr.data)
+        result = (r != "UNSAT")
+        if not result:
+            return result
+        return {expr.symbols[abs(lit) - 1]: lit > 0 for lit in r}
+    else:
+        r = pycosat.itersolve(expr.data)
+        result = (r != "UNSAT")
+        if not result:
+            return result
+
+        # Make solutions SymPy compatible by creating a generator
+        def _gen(results):
+            satisfiable = False
+            try:
+                while True:
+                    sol = next(results)
+                    yield {expr.symbols[abs(lit) - 1]: lit > 0 for lit in sol}
+                    satisfiable = True
+            except StopIteration:
+                if not satisfiable:
+                    yield False
+
+        return _gen(r)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/z3_wrapper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/z3_wrapper.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe44f713a2edfd5286c0f81b737212146766b11b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/algorithms/z3_wrapper.py
@@ -0,0 +1,115 @@
+from sympy.printing.smtlib import smtlib_code
+from sympy.assumptions.assume import AppliedPredicate
+from sympy.assumptions.cnf import EncodedCNF
+from sympy.assumptions.ask import Q
+
+from sympy.core import Add, Mul
+from sympy.core.relational import Equality, LessThan, GreaterThan, StrictLessThan, StrictGreaterThan
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import Pow
+from sympy.functions.elementary.miscellaneous import Min, Max
+from sympy.logic.boolalg import And, Or, Xor, Implies
+from sympy.logic.boolalg import Not, ITE
+from sympy.assumptions.relation.equality import StrictGreaterThanPredicate, StrictLessThanPredicate, GreaterThanPredicate, LessThanPredicate, EqualityPredicate
+from sympy.external import import_module
+
+def z3_satisfiable(expr, all_models=False):
+    if not isinstance(expr, EncodedCNF):
+        exprs = EncodedCNF()
+        exprs.add_prop(expr)
+        expr = exprs
+
+    z3 = import_module("z3")
+    if z3 is None:
+        raise ImportError("z3 is not installed")
+
+    s = encoded_cnf_to_z3_solver(expr, z3)
+
+    res = str(s.check())
+    if res == "unsat":
+        return False
+    elif res == "sat":
+        return z3_model_to_sympy_model(s.model(), expr)
+    else:
+        return None
+
+
+def z3_model_to_sympy_model(z3_model, enc_cnf):
+    rev_enc = {value : key for key, value in enc_cnf.encoding.items()}
+    return {rev_enc[int(var.name()[1:])] : bool(z3_model[var]) for var in z3_model}
+
+
+def clause_to_assertion(clause):
+    clause_strings = [f"d{abs(lit)}" if lit > 0 else f"(not d{abs(lit)})" for lit in clause]
+    return "(assert (or " + " ".join(clause_strings) + "))"
+
+
+def encoded_cnf_to_z3_solver(enc_cnf, z3):
+    def dummify_bool(pred):
+        return False
+        assert isinstance(pred, AppliedPredicate)
+
+        if pred.function in [Q.positive, Q.negative, Q.zero]:
+            return pred
+        else:
+            return False
+
+    s = z3.Solver()
+
+    declarations = [f"(declare-const d{var} Bool)" for var in enc_cnf.variables]
+    assertions = [clause_to_assertion(clause) for clause in enc_cnf.data]
+
+    symbols = set()
+    for pred, enc in enc_cnf.encoding.items():
+        if not isinstance(pred, AppliedPredicate):
+            continue
+        if pred.function not in (Q.gt, Q.lt, Q.ge, Q.le, Q.ne, Q.eq, Q.positive, Q.negative, Q.extended_negative, Q.extended_positive, Q.zero, Q.nonzero, Q.nonnegative, Q.nonpositive, Q.extended_nonzero, Q.extended_nonnegative, Q.extended_nonpositive):
+            continue
+
+        pred_str = smtlib_code(pred, auto_declare=False, auto_assert=False, known_functions=known_functions)
+
+        symbols |= pred.free_symbols
+        pred = pred_str
+        clause = f"(implies d{enc} {pred})"
+        assertion = "(assert " + clause + ")"
+        assertions.append(assertion)
+
+    for sym in symbols:
+        declarations.append(f"(declare-const {sym} Real)")
+
+    declarations = "\n".join(declarations)
+    assertions = "\n".join(assertions)
+    s.from_string(declarations)
+    s.from_string(assertions)
+
+    return s
+
+
+known_functions = {
+            Add: '+',
+            Mul: '*',
+
+            Equality: '=',
+            LessThan: '<=',
+            GreaterThan: '>=',
+            StrictLessThan: '<',
+            StrictGreaterThan: '>',
+
+            EqualityPredicate(): '=',
+            LessThanPredicate(): '<=',
+            GreaterThanPredicate(): '>=',
+            StrictLessThanPredicate(): '<',
+            StrictGreaterThanPredicate(): '>',
+
+            Abs: 'abs',
+            Min: 'min',
+            Max: 'max',
+            Pow: '^',
+
+            And: 'and',
+            Or: 'or',
+            Xor: 'xor',
+            Not: 'not',
+            ITE: 'ite',
+            Implies: '=>',
+        }
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/boolalg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/boolalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e11a9b6361ac5d7e355d5d4fb176d8df443e07e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/boolalg.py
@@ -0,0 +1,3587 @@
+"""
+Boolean algebra module for SymPy
+"""
+
+from __future__ import annotations
+from typing import TYPE_CHECKING, overload, Any
+from collections.abc import Iterable, Mapping
+
+from collections import defaultdict
+from itertools import chain, combinations, product, permutations
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.cache import cacheit
+from sympy.core.containers import Tuple
+from sympy.core.decorators import sympify_method_args, sympify_return
+from sympy.core.function import Application, Derivative
+from sympy.core.kind import BooleanKind, NumberKind
+from sympy.core.numbers import Number
+from sympy.core.operations import LatticeOp
+from sympy.core.singleton import Singleton, S
+from sympy.core.sorting import ordered
+from sympy.core.sympify import _sympy_converter, _sympify, sympify
+from sympy.utilities.iterables import sift, ibin
+from sympy.utilities.misc import filldedent
+
+
+def as_Boolean(e):
+    """Like ``bool``, return the Boolean value of an expression, e,
+    which can be any instance of :py:class:`~.Boolean` or ``bool``.
+
+    Examples
+    ========
+
+    >>> from sympy import true, false, nan
+    >>> from sympy.logic.boolalg import as_Boolean
+    >>> from sympy.abc import x
+    >>> as_Boolean(0) is false
+    True
+    >>> as_Boolean(1) is true
+    True
+    >>> as_Boolean(x)
+    x
+    >>> as_Boolean(2)
+    Traceback (most recent call last):
+    ...
+    TypeError: expecting bool or Boolean, not `2`.
+    >>> as_Boolean(nan)
+    Traceback (most recent call last):
+    ...
+    TypeError: expecting bool or Boolean, not `nan`.
+
+    """
+    from sympy.core.symbol import Symbol
+    if e == True:
+        return true
+    if e == False:
+        return false
+    if isinstance(e, Symbol):
+        z = e.is_zero
+        if z is None:
+            return e
+        return false if z else true
+    if isinstance(e, Boolean):
+        return e
+    raise TypeError('expecting bool or Boolean, not `%s`.' % e)
+
+
+@sympify_method_args
+class Boolean(Basic):
+    """A Boolean object is an object for which logic operations make sense."""
+
+    __slots__ = ()
+
+    kind = BooleanKind
+
+    if TYPE_CHECKING:
+
+        def __new__(cls, *args: Basic | complex) -> Boolean:
+            ...
+
+        @overload # type: ignore
+        def subs(self, arg1: Mapping[Basic | complex, Boolean | complex], arg2: None=None) -> Boolean: ...
+        @overload
+        def subs(self, arg1: Iterable[tuple[Basic | complex, Boolean | complex]], arg2: None=None, **kwargs: Any) -> Boolean: ...
+        @overload
+        def subs(self, arg1: Boolean | complex, arg2: Boolean | complex) -> Boolean: ...
+        @overload
+        def subs(self, arg1: Mapping[Basic | complex, Basic | complex], arg2: None=None, **kwargs: Any) -> Basic: ...
+        @overload
+        def subs(self, arg1: Iterable[tuple[Basic | complex, Basic | complex]], arg2: None=None, **kwargs: Any) -> Basic: ...
+        @overload
+        def subs(self, arg1: Basic | complex, arg2: Basic | complex, **kwargs: Any) -> Basic: ...
+
+        def subs(self, arg1: Mapping[Basic | complex, Basic | complex] | Basic | complex, # type: ignore
+                 arg2: Basic | complex | None = None, **kwargs: Any) -> Basic:
+            ...
+
+        def simplify(self, **kwargs) -> Boolean:
+            ...
+
+    @sympify_return([('other', 'Boolean')], NotImplemented)
+    def __and__(self, other):
+        return And(self, other)
+
+    __rand__ = __and__
+
+    @sympify_return([('other', 'Boolean')], NotImplemented)
+    def __or__(self, other):
+        return Or(self, other)
+
+    __ror__ = __or__
+
+    def __invert__(self):
+        """Overloading for ~"""
+        return Not(self)
+
+    @sympify_return([('other', 'Boolean')], NotImplemented)
+    def __rshift__(self, other):
+        return Implies(self, other)
+
+    @sympify_return([('other', 'Boolean')], NotImplemented)
+    def __lshift__(self, other):
+        return Implies(other, self)
+
+    __rrshift__ = __lshift__
+    __rlshift__ = __rshift__
+
+    @sympify_return([('other', 'Boolean')], NotImplemented)
+    def __xor__(self, other):
+        return Xor(self, other)
+
+    __rxor__ = __xor__
+
+    def equals(self, other):
+        """
+        Returns ``True`` if the given formulas have the same truth table.
+        For two formulas to be equal they must have the same literals.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import A, B, C
+        >>> from sympy import And, Or, Not
+        >>> (A >> B).equals(~B >> ~A)
+        True
+        >>> Not(And(A, B, C)).equals(And(Not(A), Not(B), Not(C)))
+        False
+        >>> Not(And(A, Not(A))).equals(Or(B, Not(B)))
+        False
+
+        """
+        from sympy.logic.inference import satisfiable
+        from sympy.core.relational import Relational
+
+        if self.has(Relational) or other.has(Relational):
+            raise NotImplementedError('handling of relationals')
+        return self.atoms() == other.atoms() and \
+            not satisfiable(Not(Equivalent(self, other)))
+
+    def to_nnf(self, simplify=True):
+        # override where necessary
+        return self
+
+    def as_set(self):
+        """
+        Rewrites Boolean expression in terms of real sets.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Eq, Or, And
+        >>> x = Symbol('x', real=True)
+        >>> Eq(x, 0).as_set()
+        {0}
+        >>> (x > 0).as_set()
+        Interval.open(0, oo)
+        >>> And(-2 < x, x < 2).as_set()
+        Interval.open(-2, 2)
+        >>> Or(x < -2, 2 < x).as_set()
+        Union(Interval.open(-oo, -2), Interval.open(2, oo))
+
+        """
+        from sympy.calculus.util import periodicity
+        from sympy.core.relational import Relational
+
+        free = self.free_symbols
+        if len(free) == 1:
+            x = free.pop()
+            if x.kind is NumberKind:
+                reps = {}
+                for r in self.atoms(Relational):
+                    if periodicity(r, x) not in (0, None):
+                        s = r._eval_as_set()
+                        if s in (S.EmptySet, S.UniversalSet, S.Reals):
+                            reps[r] = s.as_relational(x)
+                            continue
+                        raise NotImplementedError(filldedent('''
+                            as_set is not implemented for relationals
+                            with periodic solutions
+                            '''))
+                new = self.subs(reps)
+                if new.func != self.func:
+                    return new.as_set()  # restart with new obj
+                else:
+                    return new._eval_as_set()
+
+            return self._eval_as_set()
+        else:
+            raise NotImplementedError("Sorry, as_set has not yet been"
+                                      " implemented for multivariate"
+                                      " expressions")
+
+    @property
+    def binary_symbols(self):
+        from sympy.core.relational import Eq, Ne
+        return set().union(*[i.binary_symbols for i in self.args
+                           if i.is_Boolean or i.is_Symbol
+                           or isinstance(i, (Eq, Ne))])
+
+    def _eval_refine(self, assumptions):
+        from sympy.assumptions import ask
+        ret = ask(self, assumptions)
+        if ret is True:
+            return true
+        elif ret is False:
+            return false
+        return None
+
+
+class BooleanAtom(Boolean):
+    """
+    Base class of :py:class:`~.BooleanTrue` and :py:class:`~.BooleanFalse`.
+    """
+    is_Boolean = True
+    is_Atom = True
+    _op_priority = 11  # higher than Expr
+
+    def simplify(self, *a, **kw):
+        return self
+
+    def expand(self, *a, **kw):
+        return self
+
+    @property
+    def canonical(self):
+        return self
+
+    def _noop(self, other=None):
+        raise TypeError('BooleanAtom not allowed in this context.')
+
+    __add__ = _noop
+    __radd__ = _noop
+    __sub__ = _noop
+    __rsub__ = _noop
+    __mul__ = _noop
+    __rmul__ = _noop
+    __pow__ = _noop
+    __rpow__ = _noop
+    __truediv__ = _noop
+    __rtruediv__ = _noop
+    __mod__ = _noop
+    __rmod__ = _noop
+    _eval_power = _noop
+
+    def __lt__(self, other):
+        raise TypeError(filldedent('''
+            A Boolean argument can only be used in
+            Eq and Ne; all other relationals expect
+            real expressions.
+        '''))
+
+    __le__ = __lt__
+    __gt__ = __lt__
+    __ge__ = __lt__
+    # \\\
+
+    def _eval_simplify(self, **kwargs):
+        return self
+
+
+class BooleanTrue(BooleanAtom, metaclass=Singleton):
+    """
+    SymPy version of ``True``, a singleton that can be accessed via ``S.true``.
+
+    This is the SymPy version of ``True``, for use in the logic module. The
+    primary advantage of using ``true`` instead of ``True`` is that shorthand Boolean
+    operations like ``~`` and ``>>`` will work as expected on this class, whereas with
+    True they act bitwise on 1. Functions in the logic module will return this
+    class when they evaluate to true.
+
+    Notes
+    =====
+
+    There is liable to be some confusion as to when ``True`` should
+    be used and when ``S.true`` should be used in various contexts
+    throughout SymPy. An important thing to remember is that
+    ``sympify(True)`` returns ``S.true``. This means that for the most
+    part, you can just use ``True`` and it will automatically be converted
+    to ``S.true`` when necessary, similar to how you can generally use 1
+    instead of ``S.One``.
+
+    The rule of thumb is:
+
+    "If the boolean in question can be replaced by an arbitrary symbolic
+    ``Boolean``, like ``Or(x, y)`` or ``x > 1``, use ``S.true``.
+    Otherwise, use ``True``"
+
+    In other words, use ``S.true`` only on those contexts where the
+    boolean is being used as a symbolic representation of truth.
+    For example, if the object ends up in the ``.args`` of any expression,
+    then it must necessarily be ``S.true`` instead of ``True``, as
+    elements of ``.args`` must be ``Basic``. On the other hand,
+    ``==`` is not a symbolic operation in SymPy, since it always returns
+    ``True`` or ``False``, and does so in terms of structural equality
+    rather than mathematical, so it should return ``True``. The assumptions
+    system should use ``True`` and ``False``. Aside from not satisfying
+    the above rule of thumb, the assumptions system uses a three-valued logic
+    (``True``, ``False``, ``None``), whereas ``S.true`` and ``S.false``
+    represent a two-valued logic. When in doubt, use ``True``.
+
+    "``S.true == True is True``."
+
+    While "``S.true is True``" is ``False``, "``S.true == True``"
+    is ``True``, so if there is any doubt over whether a function or
+    expression will return ``S.true`` or ``True``, just use ``==``
+    instead of ``is`` to do the comparison, and it will work in either
+    case.  Finally, for boolean flags, it's better to just use ``if x``
+    instead of ``if x is True``. To quote PEP 8:
+
+    Do not compare boolean values to ``True`` or ``False``
+    using ``==``.
+
+    * Yes:   ``if greeting:``
+    * No:    ``if greeting == True:``
+    * Worse: ``if greeting is True:``
+
+    Examples
+    ========
+
+    >>> from sympy import sympify, true, false, Or
+    >>> sympify(True)
+    True
+    >>> _ is True, _ is true
+    (False, True)
+
+    >>> Or(true, false)
+    True
+    >>> _ is true
+    True
+
+    Python operators give a boolean result for true but a
+    bitwise result for True
+
+    >>> ~true, ~True  # doctest: +SKIP
+    (False, -2)
+    >>> true >> true, True >> True
+    (True, 0)
+
+    See Also
+    ========
+
+    sympy.logic.boolalg.BooleanFalse
+
+    """
+    def __bool__(self):
+        return True
+
+    def __hash__(self):
+        return hash(True)
+
+    def __eq__(self, other):
+        if other is True:
+            return True
+        if other is False:
+            return False
+        return super().__eq__(other)
+
+    @property
+    def negated(self):
+        return false
+
+    def as_set(self):
+        """
+        Rewrite logic operators and relationals in terms of real sets.
+
+        Examples
+        ========
+
+        >>> from sympy import true
+        >>> true.as_set()
+        UniversalSet
+
+        """
+        return S.UniversalSet
+
+
+class BooleanFalse(BooleanAtom, metaclass=Singleton):
+    """
+    SymPy version of ``False``, a singleton that can be accessed via ``S.false``.
+
+    This is the SymPy version of ``False``, for use in the logic module. The
+    primary advantage of using ``false`` instead of ``False`` is that shorthand
+    Boolean operations like ``~`` and ``>>`` will work as expected on this class,
+    whereas with ``False`` they act bitwise on 0. Functions in the logic module
+    will return this class when they evaluate to false.
+
+    Notes
+    ======
+
+    See the notes section in :py:class:`sympy.logic.boolalg.BooleanTrue`
+
+    Examples
+    ========
+
+    >>> from sympy import sympify, true, false, Or
+    >>> sympify(False)
+    False
+    >>> _ is False, _ is false
+    (False, True)
+
+    >>> Or(true, false)
+    True
+    >>> _ is true
+    True
+
+    Python operators give a boolean result for false but a
+    bitwise result for False
+
+    >>> ~false, ~False  # doctest: +SKIP
+    (True, -1)
+    >>> false >> false, False >> False
+    (True, 0)
+
+    See Also
+    ========
+
+    sympy.logic.boolalg.BooleanTrue
+
+    """
+    def __bool__(self):
+        return False
+
+    def __hash__(self):
+        return hash(False)
+
+    def __eq__(self, other):
+        if other is True:
+            return False
+        if other is False:
+            return True
+        return super().__eq__(other)
+
+    @property
+    def negated(self):
+        return true
+
+    def as_set(self):
+        """
+        Rewrite logic operators and relationals in terms of real sets.
+
+        Examples
+        ========
+
+        >>> from sympy import false
+        >>> false.as_set()
+        EmptySet
+        """
+        return S.EmptySet
+
+
+true = BooleanTrue()
+false = BooleanFalse()
+# We want S.true and S.false to work, rather than S.BooleanTrue and
+# S.BooleanFalse, but making the class and instance names the same causes some
+# major issues (like the inability to import the class directly from this
+# file).
+S.true = true
+S.false = false
+
+_sympy_converter[bool] = lambda x: true if x else false
+
+
+class BooleanFunction(Application, Boolean):
+    """Boolean function is a function that lives in a boolean space
+    It is used as base class for :py:class:`~.And`, :py:class:`~.Or`,
+    :py:class:`~.Not`, etc.
+    """
+    is_Boolean = True
+
+    def _eval_simplify(self, **kwargs):
+        rv = simplify_univariate(self)
+        if not isinstance(rv, BooleanFunction):
+            return rv.simplify(**kwargs)
+        rv = rv.func(*[a.simplify(**kwargs) for a in rv.args])
+        return simplify_logic(rv)
+
+    def simplify(self, **kwargs):
+        from sympy.simplify.simplify import simplify
+        return simplify(self, **kwargs)
+
+    def __lt__(self, other):
+        raise TypeError(filldedent('''
+            A Boolean argument can only be used in
+            Eq and Ne; all other relationals expect
+            real expressions.
+        '''))
+    __le__ = __lt__
+    __ge__ = __lt__
+    __gt__ = __lt__
+
+    @classmethod
+    def binary_check_and_simplify(self, *args):
+        return [as_Boolean(i) for i in args]
+
+    def to_nnf(self, simplify=True):
+        return self._to_nnf(*self.args, simplify=simplify)
+
+    def to_anf(self, deep=True):
+        return self._to_anf(*self.args, deep=deep)
+
+    @classmethod
+    def _to_nnf(cls, *args, **kwargs):
+        simplify = kwargs.get('simplify', True)
+        argset = set()
+        for arg in args:
+            if not is_literal(arg):
+                arg = arg.to_nnf(simplify)
+            if simplify:
+                if isinstance(arg, cls):
+                    arg = arg.args
+                else:
+                    arg = (arg,)
+                for a in arg:
+                    if Not(a) in argset:
+                        return cls.zero
+                    argset.add(a)
+            else:
+                argset.add(arg)
+        return cls(*argset)
+
+    @classmethod
+    def _to_anf(cls, *args, **kwargs):
+        deep = kwargs.get('deep', True)
+        new_args = []
+        for arg in args:
+            if deep:
+                if not is_literal(arg) or isinstance(arg, Not):
+                    arg = arg.to_anf(deep=deep)
+            new_args.append(arg)
+        return cls(*new_args, remove_true=False)
+
+    # the diff method below is copied from Expr class
+    def diff(self, *symbols, **assumptions):
+        assumptions.setdefault("evaluate", True)
+        return Derivative(self, *symbols, **assumptions)
+
+    def _eval_derivative(self, x):
+        if x in self.binary_symbols:
+            from sympy.core.relational import Eq
+            from sympy.functions.elementary.piecewise import Piecewise
+            return Piecewise(
+                (0, Eq(self.subs(x, 0), self.subs(x, 1))),
+                (1, True))
+        elif x in self.free_symbols:
+            # not implemented, see https://www.encyclopediaofmath.org/
+            # index.php/Boolean_differential_calculus
+            pass
+        else:
+            return S.Zero
+
+
+class And(LatticeOp, BooleanFunction):
+    """
+    Logical AND function.
+
+    It evaluates its arguments in order, returning false immediately
+    when an argument is false and true if they are all true.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy import And
+    >>> x & y
+    x & y
+
+    Notes
+    =====
+
+    The ``&`` operator is provided as a convenience, but note that its use
+    here is different from its normal use in Python, which is bitwise
+    and. Hence, ``And(a, b)`` and ``a & b`` will produce different results if
+    ``a`` and ``b`` are integers.
+
+    >>> And(x, y).subs(x, 1)
+    y
+
+    """
+    zero = false
+    identity = true
+
+    nargs = None
+
+    if TYPE_CHECKING:
+
+        def __new__(cls, *args: Boolean | bool) -> Boolean: # type: ignore
+            ...
+
+        @property
+        def args(self) -> tuple[Boolean, ...]:
+            ...
+
+    @classmethod
+    def _new_args_filter(cls, args):
+        args = BooleanFunction.binary_check_and_simplify(*args)
+        args = LatticeOp._new_args_filter(args, And)
+        newargs = []
+        rel = set()
+        for x in ordered(args):
+            if x.is_Relational:
+                c = x.canonical
+                if c in rel:
+                    continue
+                elif c.negated.canonical in rel:
+                    return [false]
+                else:
+                    rel.add(c)
+            newargs.append(x)
+        return newargs
+
+    def _eval_subs(self, old, new):
+        args = []
+        bad = None
+        for i in self.args:
+            try:
+                i = i.subs(old, new)
+            except TypeError:
+                # store TypeError
+                if bad is None:
+                    bad = i
+                continue
+            if i == False:
+                return false
+            elif i != True:
+                args.append(i)
+        if bad is not None:
+            # let it raise
+            bad.subs(old, new)
+        # If old is And, replace the parts of the arguments with new if all
+        # are there
+        if isinstance(old, And):
+            old_set = set(old.args)
+            if old_set.issubset(args):
+                args = set(args) - old_set
+                args.add(new)
+
+        return self.func(*args)
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.core.relational import Equality, Relational
+        from sympy.solvers.solveset import linear_coeffs
+        # standard simplify
+        rv = super()._eval_simplify(**kwargs)
+        if not isinstance(rv, And):
+            return rv
+
+        # simplify args that are equalities involving
+        # symbols so x == 0 & x == y -> x==0 & y == 0
+        Rel, nonRel = sift(rv.args, lambda i: isinstance(i, Relational),
+                           binary=True)
+        if not Rel:
+            return rv
+        eqs, other = sift(Rel, lambda i: isinstance(i, Equality), binary=True)
+
+        measure = kwargs['measure']
+        if eqs:
+            ratio = kwargs['ratio']
+            reps = {}
+            sifted = {}
+            # group by length of free symbols
+            sifted = sift(ordered([
+                (i.free_symbols, i) for i in eqs]),
+                lambda x: len(x[0]))
+            eqs = []
+            nonlineqs = []
+            while 1 in sifted:
+                for free, e in sifted.pop(1):
+                    x = free.pop()
+                    if (e.lhs != x or x in e.rhs.free_symbols) and x not in reps:
+                        try:
+                            m, b = linear_coeffs(
+                                Add(e.lhs, -e.rhs, evaluate=False), x)
+                            enew = e.func(x, -b/m)
+                            if measure(enew) <= ratio*measure(e):
+                                e = enew
+                            else:
+                                eqs.append(e)
+                                continue
+                        except ValueError:
+                            pass
+                    if x in reps:
+                        eqs.append(e.subs(x, reps[x]))
+                    elif e.lhs == x and x not in e.rhs.free_symbols:
+                        reps[x] = e.rhs
+                        eqs.append(e)
+                    else:
+                        # x is not yet identified, but may be later
+                        nonlineqs.append(e)
+                resifted = defaultdict(list)
+                for k in sifted:
+                    for f, e in sifted[k]:
+                        e = e.xreplace(reps)
+                        f = e.free_symbols
+                        resifted[len(f)].append((f, e))
+                sifted = resifted
+            for k in sifted:
+                eqs.extend([e for f, e in sifted[k]])
+            nonlineqs = [ei.subs(reps) for ei in nonlineqs]
+            other = [ei.subs(reps) for ei in other]
+            rv = rv.func(*([i.canonical for i in (eqs + nonlineqs + other)] + nonRel))
+        patterns = _simplify_patterns_and()
+        threeterm_patterns = _simplify_patterns_and3()
+        return _apply_patternbased_simplification(rv, patterns,
+                                                  measure, false,
+                                                  threeterm_patterns=threeterm_patterns)
+
+    def _eval_as_set(self):
+        from sympy.sets.sets import Intersection
+        return Intersection(*[arg.as_set() for arg in self.args])
+
+    def _eval_rewrite_as_Nor(self, *args, **kwargs):
+        return Nor(*[Not(arg) for arg in self.args])
+
+    def to_anf(self, deep=True):
+        if deep:
+            result = And._to_anf(*self.args, deep=deep)
+            return distribute_xor_over_and(result)
+        return self
+
+
+class Or(LatticeOp, BooleanFunction):
+    """
+    Logical OR function
+
+    It evaluates its arguments in order, returning true immediately
+    when an  argument is true, and false if they are all false.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y
+    >>> from sympy import Or
+    >>> x | y
+    x | y
+
+    Notes
+    =====
+
+    The ``|`` operator is provided as a convenience, but note that its use
+    here is different from its normal use in Python, which is bitwise
+    or. Hence, ``Or(a, b)`` and ``a | b`` will return different things if
+    ``a`` and ``b`` are integers.
+
+    >>> Or(x, y).subs(x, 0)
+    y
+
+    """
+    zero = true
+    identity = false
+
+    if TYPE_CHECKING:
+
+        def __new__(cls, *args: Boolean | bool) -> Boolean: # type: ignore
+            ...
+
+        @property
+        def args(self) -> tuple[Boolean, ...]:
+            ...
+
+    @classmethod
+    def _new_args_filter(cls, args):
+        newargs = []
+        rel = []
+        args = BooleanFunction.binary_check_and_simplify(*args)
+        for x in args:
+            if x.is_Relational:
+                c = x.canonical
+                if c in rel:
+                    continue
+                nc = c.negated.canonical
+                if any(r == nc for r in rel):
+                    return [true]
+                rel.append(c)
+            newargs.append(x)
+        return LatticeOp._new_args_filter(newargs, Or)
+
+    def _eval_subs(self, old, new):
+        args = []
+        bad = None
+        for i in self.args:
+            try:
+                i = i.subs(old, new)
+            except TypeError:
+                # store TypeError
+                if bad is None:
+                    bad = i
+                continue
+            if i == True:
+                return true
+            elif i != False:
+                args.append(i)
+        if bad is not None:
+            # let it raise
+            bad.subs(old, new)
+        # If old is Or, replace the parts of the arguments with new if all
+        # are there
+        if isinstance(old, Or):
+            old_set = set(old.args)
+            if old_set.issubset(args):
+                args = set(args) - old_set
+                args.add(new)
+
+        return self.func(*args)
+
+    def _eval_as_set(self):
+        from sympy.sets.sets import Union
+        return Union(*[arg.as_set() for arg in self.args])
+
+    def _eval_rewrite_as_Nand(self, *args, **kwargs):
+        return Nand(*[Not(arg) for arg in self.args])
+
+    def _eval_simplify(self, **kwargs):
+        from sympy.core.relational import Le, Ge, Eq
+        lege = self.atoms(Le, Ge)
+        if lege:
+            reps = {i: self.func(
+                Eq(i.lhs, i.rhs), i.strict) for i in lege}
+            return self.xreplace(reps)._eval_simplify(**kwargs)
+        # standard simplify
+        rv = super()._eval_simplify(**kwargs)
+        if not isinstance(rv, Or):
+            return rv
+        patterns = _simplify_patterns_or()
+        return _apply_patternbased_simplification(rv, patterns,
+                                                  kwargs['measure'], true)
+
+    def to_anf(self, deep=True):
+        args = range(1, len(self.args) + 1)
+        args = (combinations(self.args, j) for j in args)
+        args = chain.from_iterable(args)  # powerset
+        args = (And(*arg) for arg in args)
+        args = (to_anf(x, deep=deep) if deep else x for x in args)
+        return Xor(*list(args), remove_true=False)
+
+
+class Not(BooleanFunction):
+    """
+    Logical Not function (negation)
+
+
+    Returns ``true`` if the statement is ``false`` or ``False``.
+    Returns ``false`` if the statement is ``true`` or ``True``.
+
+    Examples
+    ========
+
+    >>> from sympy import Not, And, Or
+    >>> from sympy.abc import x, A, B
+    >>> Not(True)
+    False
+    >>> Not(False)
+    True
+    >>> Not(And(True, False))
+    True
+    >>> Not(Or(True, False))
+    False
+    >>> Not(And(And(True, x), Or(x, False)))
+    ~x
+    >>> ~x
+    ~x
+    >>> Not(And(Or(A, B), Or(~A, ~B)))
+    ~((A | B) & (~A | ~B))
+
+    Notes
+    =====
+
+    - The ``~`` operator is provided as a convenience, but note that its use
+      here is different from its normal use in Python, which is bitwise
+      not. In particular, ``~a`` and ``Not(a)`` will be different if ``a`` is
+      an integer. Furthermore, since bools in Python subclass from ``int``,
+      ``~True`` is the same as ``~1`` which is ``-2``, which has a boolean
+      value of True.  To avoid this issue, use the SymPy boolean types
+      ``true`` and ``false``.
+
+    - As of Python 3.12, the bitwise not operator ``~`` used on a
+      Python ``bool`` is deprecated and will emit a warning.
+
+    >>> from sympy import true
+    >>> ~True  # doctest: +SKIP
+    -2
+    >>> ~true
+    False
+
+    """
+
+    is_Not = True
+
+    @classmethod
+    def eval(cls, arg):
+        if isinstance(arg, Number) or arg in (True, False):
+            return false if arg else true
+        if arg.is_Not:
+            return arg.args[0]
+        # Simplify Relational objects.
+        if arg.is_Relational:
+            return arg.negated
+
+    def _eval_as_set(self):
+        """
+        Rewrite logic operators and relationals in terms of real sets.
+
+        Examples
+        ========
+
+        >>> from sympy import Not, Symbol
+        >>> x = Symbol('x')
+        >>> Not(x > 0).as_set()
+        Interval(-oo, 0)
+        """
+        return self.args[0].as_set().complement(S.Reals)
+
+    def to_nnf(self, simplify=True):
+        if is_literal(self):
+            return self
+
+        expr = self.args[0]
+
+        func, args = expr.func, expr.args
+
+        if func == And:
+            return Or._to_nnf(*[Not(arg) for arg in args], simplify=simplify)
+
+        if func == Or:
+            return And._to_nnf(*[Not(arg) for arg in args], simplify=simplify)
+
+        if func == Implies:
+            a, b = args
+            return And._to_nnf(a, Not(b), simplify=simplify)
+
+        if func == Equivalent:
+            return And._to_nnf(Or(*args), Or(*[Not(arg) for arg in args]),
+                               simplify=simplify)
+
+        if func == Xor:
+            result = []
+            for i in range(1, len(args)+1, 2):
+                for neg in combinations(args, i):
+                    clause = [Not(s) if s in neg else s for s in args]
+                    result.append(Or(*clause))
+            return And._to_nnf(*result, simplify=simplify)
+
+        if func == ITE:
+            a, b, c = args
+            return And._to_nnf(Or(a, Not(c)), Or(Not(a), Not(b)), simplify=simplify)
+
+        raise ValueError("Illegal operator %s in expression" % func)
+
+    def to_anf(self, deep=True):
+        return Xor._to_anf(true, self.args[0], deep=deep)
+
+
+class Xor(BooleanFunction):
+    """
+    Logical XOR (exclusive OR) function.
+
+
+    Returns True if an odd number of the arguments are True and the rest are
+    False.
+
+    Returns False if an even number of the arguments are True and the rest are
+    False.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Xor
+    >>> from sympy import symbols
+    >>> x, y = symbols('x y')
+    >>> Xor(True, False)
+    True
+    >>> Xor(True, True)
+    False
+    >>> Xor(True, False, True, True, False)
+    True
+    >>> Xor(True, False, True, False)
+    False
+    >>> x ^ y
+    x ^ y
+
+    Notes
+    =====
+
+    The ``^`` operator is provided as a convenience, but note that its use
+    here is different from its normal use in Python, which is bitwise xor. In
+    particular, ``a ^ b`` and ``Xor(a, b)`` will be different if ``a`` and
+    ``b`` are integers.
+
+    >>> Xor(x, y).subs(y, 0)
+    x
+
+    """
+    def __new__(cls, *args, remove_true=True, **kwargs):
+        argset = set()
+        obj = super().__new__(cls, *args, **kwargs)
+        for arg in obj._args:
+            if isinstance(arg, Number) or arg in (True, False):
+                if arg:
+                    arg = true
+                else:
+                    continue
+            if isinstance(arg, Xor):
+                for a in arg.args:
+                    argset.remove(a) if a in argset else argset.add(a)
+            elif arg in argset:
+                argset.remove(arg)
+            else:
+                argset.add(arg)
+        rel = [(r, r.canonical, r.negated.canonical)
+               for r in argset if r.is_Relational]
+        odd = False  # is number of complimentary pairs odd? start 0 -> False
+        remove = []
+        for i, (r, c, nc) in enumerate(rel):
+            for j in range(i + 1, len(rel)):
+                rj, cj = rel[j][:2]
+                if cj == nc:
+                    odd = not odd
+                    break
+                elif cj == c:
+                    break
+            else:
+                continue
+            remove.append((r, rj))
+        if odd:
+            argset.remove(true) if true in argset else argset.add(true)
+        for a, b in remove:
+            argset.remove(a)
+            argset.remove(b)
+        if len(argset) == 0:
+            return false
+        elif len(argset) == 1:
+            return argset.pop()
+        elif True in argset and remove_true:
+            argset.remove(True)
+            return Not(Xor(*argset))
+        else:
+            obj._args = tuple(ordered(argset))
+            obj._argset = frozenset(argset)
+            return obj
+
+    # XXX: This should be cached on the object rather than using cacheit
+    # Maybe it can be computed in __new__?
+    @property  # type: ignore
+    @cacheit
+    def args(self):
+        return tuple(ordered(self._argset))
+
+    def to_nnf(self, simplify=True):
+        args = []
+        for i in range(0, len(self.args)+1, 2):
+            for neg in combinations(self.args, i):
+                clause = [Not(s) if s in neg else s for s in self.args]
+                args.append(Or(*clause))
+        return And._to_nnf(*args, simplify=simplify)
+
+    def _eval_rewrite_as_Or(self, *args, **kwargs):
+        a = self.args
+        return Or(*[_convert_to_varsSOP(x, self.args)
+                    for x in _get_odd_parity_terms(len(a))])
+
+    def _eval_rewrite_as_And(self, *args, **kwargs):
+        a = self.args
+        return And(*[_convert_to_varsPOS(x, self.args)
+                     for x in _get_even_parity_terms(len(a))])
+
+    def _eval_simplify(self, **kwargs):
+        # as standard simplify uses simplify_logic which writes things as
+        # And and Or, we only simplify the partial expressions before using
+        # patterns
+        rv = self.func(*[a.simplify(**kwargs) for a in self.args])
+        rv = rv.to_anf()
+        if not isinstance(rv, Xor):  # This shouldn't really happen here
+            return rv
+        patterns = _simplify_patterns_xor()
+        return _apply_patternbased_simplification(rv, patterns,
+                                                  kwargs['measure'], None)
+
+    def _eval_subs(self, old, new):
+        # If old is Xor, replace the parts of the arguments with new if all
+        # are there
+        if isinstance(old, Xor):
+            old_set = set(old.args)
+            if old_set.issubset(self.args):
+                args = set(self.args) - old_set
+                args.add(new)
+                return self.func(*args)
+
+
+class Nand(BooleanFunction):
+    """
+    Logical NAND function.
+
+    It evaluates its arguments in order, giving True immediately if any
+    of them are False, and False if they are all True.
+
+    Returns True if any of the arguments are False
+    Returns False if all arguments are True
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Nand
+    >>> from sympy import symbols
+    >>> x, y = symbols('x y')
+    >>> Nand(False, True)
+    True
+    >>> Nand(True, True)
+    False
+    >>> Nand(x, y)
+    ~(x & y)
+
+    """
+    @classmethod
+    def eval(cls, *args):
+        return Not(And(*args))
+
+
+class Nor(BooleanFunction):
+    """
+    Logical NOR function.
+
+    It evaluates its arguments in order, giving False immediately if any
+    of them are True, and True if they are all False.
+
+    Returns False if any argument is True
+    Returns True if all arguments are False
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Nor
+    >>> from sympy import symbols
+    >>> x, y = symbols('x y')
+
+    >>> Nor(True, False)
+    False
+    >>> Nor(True, True)
+    False
+    >>> Nor(False, True)
+    False
+    >>> Nor(False, False)
+    True
+    >>> Nor(x, y)
+    ~(x | y)
+
+    """
+    @classmethod
+    def eval(cls, *args):
+        return Not(Or(*args))
+
+
+class Xnor(BooleanFunction):
+    """
+    Logical XNOR function.
+
+    Returns False if an odd number of the arguments are True and the rest are
+    False.
+
+    Returns True if an even number of the arguments are True and the rest are
+    False.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Xnor
+    >>> from sympy import symbols
+    >>> x, y = symbols('x y')
+    >>> Xnor(True, False)
+    False
+    >>> Xnor(True, True)
+    True
+    >>> Xnor(True, False, True, True, False)
+    False
+    >>> Xnor(True, False, True, False)
+    True
+
+    """
+    @classmethod
+    def eval(cls, *args):
+        return Not(Xor(*args))
+
+
+class Implies(BooleanFunction):
+    r"""
+    Logical implication.
+
+    A implies B is equivalent to if A then B. Mathematically, it is written
+    as `A \Rightarrow B` and is equivalent to `\neg A \vee B` or ``~A | B``.
+
+    Accepts two Boolean arguments; A and B.
+    Returns False if A is True and B is False
+    Returns True otherwise.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Implies
+    >>> from sympy import symbols
+    >>> x, y = symbols('x y')
+
+    >>> Implies(True, False)
+    False
+    >>> Implies(False, False)
+    True
+    >>> Implies(True, True)
+    True
+    >>> Implies(False, True)
+    True
+    >>> x >> y
+    Implies(x, y)
+    >>> y << x
+    Implies(x, y)
+
+    Notes
+    =====
+
+    The ``>>`` and ``<<`` operators are provided as a convenience, but note
+    that their use here is different from their normal use in Python, which is
+    bit shifts. Hence, ``Implies(a, b)`` and ``a >> b`` will return different
+    things if ``a`` and ``b`` are integers.  In particular, since Python
+    considers ``True`` and ``False`` to be integers, ``True >> True`` will be
+    the same as ``1 >> 1``, i.e., 0, which has a truth value of False.  To
+    avoid this issue, use the SymPy objects ``true`` and ``false``.
+
+    >>> from sympy import true, false
+    >>> True >> False
+    1
+    >>> true >> false
+    False
+
+    """
+    @classmethod
+    def eval(cls, *args):
+        try:
+            newargs = []
+            for x in args:
+                if isinstance(x, Number) or x in (0, 1):
+                    newargs.append(bool(x))
+                else:
+                    newargs.append(x)
+            A, B = newargs
+        except ValueError:
+            raise ValueError(
+                "%d operand(s) used for an Implies "
+                "(pairs are required): %s" % (len(args), str(args)))
+        if A in (True, False) or B in (True, False):
+            return Or(Not(A), B)
+        elif A == B:
+            return true
+        elif A.is_Relational and B.is_Relational:
+            if A.canonical == B.canonical:
+                return true
+            if A.negated.canonical == B.canonical:
+                return B
+        else:
+            return Basic.__new__(cls, *args)
+
+    def to_nnf(self, simplify=True):
+        a, b = self.args
+        return Or._to_nnf(Not(a), b, simplify=simplify)
+
+    def to_anf(self, deep=True):
+        a, b = self.args
+        return Xor._to_anf(true, a, And(a, b), deep=deep)
+
+
+class Equivalent(BooleanFunction):
+    """
+    Equivalence relation.
+
+    ``Equivalent(A, B)`` is True iff A and B are both True or both False.
+
+    Returns True if all of the arguments are logically equivalent.
+    Returns False otherwise.
+
+    For two arguments, this is equivalent to :py:class:`~.Xnor`.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Equivalent, And
+    >>> from sympy.abc import x
+    >>> Equivalent(False, False, False)
+    True
+    >>> Equivalent(True, False, False)
+    False
+    >>> Equivalent(x, And(x, True))
+    True
+
+    """
+    def __new__(cls, *args, **options):
+        from sympy.core.relational import Relational
+        args = [_sympify(arg) for arg in args]
+
+        argset = set(args)
+        for x in args:
+            if isinstance(x, Number) or x in [True, False]:  # Includes 0, 1
+                argset.discard(x)
+                argset.add(bool(x))
+        rel = []
+        for r in argset:
+            if isinstance(r, Relational):
+                rel.append((r, r.canonical, r.negated.canonical))
+        remove = []
+        for i, (r, c, nc) in enumerate(rel):
+            for j in range(i + 1, len(rel)):
+                rj, cj = rel[j][:2]
+                if cj == nc:
+                    return false
+                elif cj == c:
+                    remove.append((r, rj))
+                    break
+        for a, b in remove:
+            argset.remove(a)
+            argset.remove(b)
+            argset.add(True)
+        if len(argset) <= 1:
+            return true
+        if True in argset:
+            argset.discard(True)
+            return And(*argset)
+        if False in argset:
+            argset.discard(False)
+            return And(*[Not(arg) for arg in argset])
+        _args = frozenset(argset)
+        obj = super().__new__(cls, _args)
+        obj._argset = _args
+        return obj
+
+    # XXX: This should be cached on the object rather than using cacheit
+    # Maybe it can be computed in __new__?
+    @property  # type: ignore
+    @cacheit
+    def args(self):
+        return tuple(ordered(self._argset))
+
+    def to_nnf(self, simplify=True):
+        args = []
+        for a, b in zip(self.args, self.args[1:]):
+            args.append(Or(Not(a), b))
+        args.append(Or(Not(self.args[-1]), self.args[0]))
+        return And._to_nnf(*args, simplify=simplify)
+
+    def to_anf(self, deep=True):
+        a = And(*self.args)
+        b = And(*[to_anf(Not(arg), deep=False) for arg in self.args])
+        b = distribute_xor_over_and(b)
+        return Xor._to_anf(a, b, deep=deep)
+
+
+class ITE(BooleanFunction):
+    """
+    If-then-else clause.
+
+    ``ITE(A, B, C)`` evaluates and returns the result of B if A is true
+    else it returns the result of C. All args must be Booleans.
+
+    From a logic gate perspective, ITE corresponds to a 2-to-1 multiplexer,
+    where A is the select signal.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import ITE, And, Xor, Or
+    >>> from sympy.abc import x, y, z
+    >>> ITE(True, False, True)
+    False
+    >>> ITE(Or(True, False), And(True, True), Xor(True, True))
+    True
+    >>> ITE(x, y, z)
+    ITE(x, y, z)
+    >>> ITE(True, x, y)
+    x
+    >>> ITE(False, x, y)
+    y
+    >>> ITE(x, y, y)
+    y
+
+    Trying to use non-Boolean args will generate a TypeError:
+
+    >>> ITE(True, [], ())
+    Traceback (most recent call last):
+    ...
+    TypeError: expecting bool, Boolean or ITE, not `[]`
+
+    """
+    def __new__(cls, *args, **kwargs):
+        from sympy.core.relational import Eq, Ne
+        if len(args) != 3:
+            raise ValueError('expecting exactly 3 args')
+        a, b, c = args
+        # check use of binary symbols
+        if isinstance(a, (Eq, Ne)):
+            # in this context, we can evaluate the Eq/Ne
+            # if one arg is a binary symbol and the other
+            # is true/false
+            b, c = map(as_Boolean, (b, c))
+            bin_syms = set().union(*[i.binary_symbols for i in (b, c)])
+            if len(set(a.args) - bin_syms) == 1:
+                # one arg is a binary_symbols
+                _a = a
+                if a.lhs is true:
+                    a = a.rhs
+                elif a.rhs is true:
+                    a = a.lhs
+                elif a.lhs is false:
+                    a = Not(a.rhs)
+                elif a.rhs is false:
+                    a = Not(a.lhs)
+                else:
+                    # binary can only equal True or False
+                    a = false
+                if isinstance(_a, Ne):
+                    a = Not(a)
+        else:
+            a, b, c = BooleanFunction.binary_check_and_simplify(
+                a, b, c)
+        rv = None
+        if kwargs.get('evaluate', True):
+            rv = cls.eval(a, b, c)
+        if rv is None:
+            rv = BooleanFunction.__new__(cls, a, b, c, evaluate=False)
+        return rv
+
+    @classmethod
+    def eval(cls, *args):
+        from sympy.core.relational import Eq, Ne
+        # do the args give a singular result?
+        a, b, c = args
+        if isinstance(a, (Ne, Eq)):
+            _a = a
+            if true in a.args:
+                a = a.lhs if a.rhs is true else a.rhs
+            elif false in a.args:
+                a = Not(a.lhs) if a.rhs is false else Not(a.rhs)
+            else:
+                _a = None
+            if _a is not None and isinstance(_a, Ne):
+                a = Not(a)
+        if a is true:
+            return b
+        if a is false:
+            return c
+        if b == c:
+            return b
+        else:
+            # or maybe the results allow the answer to be expressed
+            # in terms of the condition
+            if b is true and c is false:
+                return a
+            if b is false and c is true:
+                return Not(a)
+        if [a, b, c] != args:
+            return cls(a, b, c, evaluate=False)
+
+    def to_nnf(self, simplify=True):
+        a, b, c = self.args
+        return And._to_nnf(Or(Not(a), b), Or(a, c), simplify=simplify)
+
+    def _eval_as_set(self):
+        return self.to_nnf().as_set()
+
+    def _eval_rewrite_as_Piecewise(self, *args, **kwargs):
+        from sympy.functions.elementary.piecewise import Piecewise
+        return Piecewise((args[1], args[0]), (args[2], True))
+
+
+class Exclusive(BooleanFunction):
+    """
+    True if only one or no argument is true.
+
+    ``Exclusive(A, B, C)`` is equivalent to ``~(A & B) & ~(A & C) & ~(B & C)``.
+
+    For two arguments, this is equivalent to :py:class:`~.Xor`.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Exclusive
+    >>> Exclusive(False, False, False)
+    True
+    >>> Exclusive(False, True, False)
+    True
+    >>> Exclusive(False, True, True)
+    False
+
+    """
+    @classmethod
+    def eval(cls, *args):
+        and_args = []
+        for a, b in combinations(args, 2):
+            and_args.append(Not(And(a, b)))
+        return And(*and_args)
+
+
+# end class definitions. Some useful methods
+
+
+def conjuncts(expr):
+    """Return a list of the conjuncts in ``expr``.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import conjuncts
+    >>> from sympy.abc import A, B
+    >>> conjuncts(A & B)
+    frozenset({A, B})
+    >>> conjuncts(A | B)
+    frozenset({A | B})
+
+    """
+    return And.make_args(expr)
+
+
+def disjuncts(expr):
+    """Return a list of the disjuncts in ``expr``.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import disjuncts
+    >>> from sympy.abc import A, B
+    >>> disjuncts(A | B)
+    frozenset({A, B})
+    >>> disjuncts(A & B)
+    frozenset({A & B})
+
+    """
+    return Or.make_args(expr)
+
+
+def distribute_and_over_or(expr):
+    """
+    Given a sentence ``expr`` consisting of conjunctions and disjunctions
+    of literals, return an equivalent sentence in CNF.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import distribute_and_over_or, And, Or, Not
+    >>> from sympy.abc import A, B, C
+    >>> distribute_and_over_or(Or(A, And(Not(B), Not(C))))
+    (A | ~B) & (A | ~C)
+
+    """
+    return _distribute((expr, And, Or))
+
+
+def distribute_or_over_and(expr):
+    """
+    Given a sentence ``expr`` consisting of conjunctions and disjunctions
+    of literals, return an equivalent sentence in DNF.
+
+    Note that the output is NOT simplified.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import distribute_or_over_and, And, Or, Not
+    >>> from sympy.abc import A, B, C
+    >>> distribute_or_over_and(And(Or(Not(A), B), C))
+    (B & C) | (C & ~A)
+
+    """
+    return _distribute((expr, Or, And))
+
+
+def distribute_xor_over_and(expr):
+    """
+    Given a sentence ``expr`` consisting of conjunction and
+    exclusive disjunctions of literals, return an
+    equivalent exclusive disjunction.
+
+    Note that the output is NOT simplified.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import distribute_xor_over_and, And, Xor, Not
+    >>> from sympy.abc import A, B, C
+    >>> distribute_xor_over_and(And(Xor(Not(A), B), C))
+    (B & C) ^ (C & ~A)
+    """
+    return _distribute((expr, Xor, And))
+
+
+def _distribute(info):
+    """
+    Distributes ``info[1]`` over ``info[2]`` with respect to ``info[0]``.
+    """
+    if isinstance(info[0], info[2]):
+        for arg in info[0].args:
+            if isinstance(arg, info[1]):
+                conj = arg
+                break
+        else:
+            return info[0]
+        rest = info[2](*[a for a in info[0].args if a is not conj])
+        return info[1](*list(map(_distribute,
+                                 [(info[2](c, rest), info[1], info[2])
+                                  for c in conj.args])), remove_true=False)
+    elif isinstance(info[0], info[1]):
+        return info[1](*list(map(_distribute,
+                                 [(x, info[1], info[2])
+                                  for x in info[0].args])),
+                       remove_true=False)
+    else:
+        return info[0]
+
+
+def to_anf(expr, deep=True):
+    r"""
+    Converts expr to Algebraic Normal Form (ANF).
+
+    ANF is a canonical normal form, which means that two
+    equivalent formulas will convert to the same ANF.
+
+    A logical expression is in ANF if it has the form
+
+    .. math:: 1 \oplus a \oplus b \oplus ab \oplus abc
+
+    i.e. it can be:
+        - purely true,
+        - purely false,
+        - conjunction of variables,
+        - exclusive disjunction.
+
+    The exclusive disjunction can only contain true, variables
+    or conjunction of variables. No negations are permitted.
+
+    If ``deep`` is ``False``, arguments of the boolean
+    expression are considered variables, i.e. only the
+    top-level expression is converted to ANF.
+
+    Examples
+    ========
+    >>> from sympy.logic.boolalg import And, Or, Not, Implies, Equivalent
+    >>> from sympy.logic.boolalg import to_anf
+    >>> from sympy.abc import A, B, C
+    >>> to_anf(Not(A))
+    A ^ True
+    >>> to_anf(And(Or(A, B), Not(C)))
+    A ^ B ^ (A & B) ^ (A & C) ^ (B & C) ^ (A & B & C)
+    >>> to_anf(Implies(Not(A), Equivalent(B, C)), deep=False)
+    True ^ ~A ^ (~A & (Equivalent(B, C)))
+
+    """
+    expr = sympify(expr)
+
+    if is_anf(expr):
+        return expr
+    return expr.to_anf(deep=deep)
+
+
+def to_nnf(expr, simplify=True):
+    """
+    Converts ``expr`` to Negation Normal Form (NNF).
+
+    A logical expression is in NNF if it
+    contains only :py:class:`~.And`, :py:class:`~.Or` and :py:class:`~.Not`,
+    and :py:class:`~.Not` is applied only to literals.
+    If ``simplify`` is ``True``, the result contains no redundant clauses.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B, C, D
+    >>> from sympy.logic.boolalg import Not, Equivalent, to_nnf
+    >>> to_nnf(Not((~A & ~B) | (C & D)))
+    (A | B) & (~C | ~D)
+    >>> to_nnf(Equivalent(A >> B, B >> A))
+    (A | ~B | (A & ~B)) & (B | ~A | (B & ~A))
+
+    """
+    if is_nnf(expr, simplify):
+        return expr
+    return expr.to_nnf(simplify)
+
+
+def to_cnf(expr, simplify=False, force=False):
+    """
+    Convert a propositional logical sentence ``expr`` to conjunctive normal
+    form: ``((A | ~B | ...) & (B | C | ...) & ...)``.
+    If ``simplify`` is ``True``, ``expr`` is evaluated to its simplest CNF
+    form using the Quine-McCluskey algorithm; this may take a long
+    time. If there are more than 8 variables the ``force`` flag must be set
+    to ``True`` to simplify (default is ``False``).
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import to_cnf
+    >>> from sympy.abc import A, B, D
+    >>> to_cnf(~(A | B) | D)
+    (D | ~A) & (D | ~B)
+    >>> to_cnf((A | B) & (A | ~A), True)
+    A | B
+
+    """
+    expr = sympify(expr)
+    if not isinstance(expr, BooleanFunction):
+        return expr
+
+    if simplify:
+        if not force and len(_find_predicates(expr)) > 8:
+            raise ValueError(filldedent('''
+            To simplify a logical expression with more
+            than 8 variables may take a long time and requires
+            the use of `force=True`.'''))
+        return simplify_logic(expr, 'cnf', True, force=force)
+
+    # Don't convert unless we have to
+    if is_cnf(expr):
+        return expr
+
+    expr = eliminate_implications(expr)
+    res = distribute_and_over_or(expr)
+
+    return res
+
+
+def to_dnf(expr, simplify=False, force=False):
+    """
+    Convert a propositional logical sentence ``expr`` to disjunctive normal
+    form: ``((A & ~B & ...) | (B & C & ...) | ...)``.
+    If ``simplify`` is ``True``, ``expr`` is evaluated to its simplest DNF form using
+    the Quine-McCluskey algorithm; this may take a long
+    time. If there are more than 8 variables, the ``force`` flag must be set to
+    ``True`` to simplify (default is ``False``).
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import to_dnf
+    >>> from sympy.abc import A, B, C
+    >>> to_dnf(B & (A | C))
+    (A & B) | (B & C)
+    >>> to_dnf((A & B) | (A & ~B) | (B & C) | (~B & C), True)
+    A | C
+
+    """
+    expr = sympify(expr)
+    if not isinstance(expr, BooleanFunction):
+        return expr
+
+    if simplify:
+        if not force and len(_find_predicates(expr)) > 8:
+            raise ValueError(filldedent('''
+            To simplify a logical expression with more
+            than 8 variables may take a long time and requires
+            the use of `force=True`.'''))
+        return simplify_logic(expr, 'dnf', True, force=force)
+
+    # Don't convert unless we have to
+    if is_dnf(expr):
+        return expr
+
+    expr = eliminate_implications(expr)
+    return distribute_or_over_and(expr)
+
+
+def is_anf(expr):
+    r"""
+    Checks if ``expr``  is in Algebraic Normal Form (ANF).
+
+    A logical expression is in ANF if it has the form
+
+    .. math:: 1 \oplus a \oplus b \oplus ab \oplus abc
+
+    i.e. it is purely true, purely false, conjunction of
+    variables or exclusive disjunction. The exclusive
+    disjunction can only contain true, variables or
+    conjunction of variables. No negations are permitted.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import And, Not, Xor, true, is_anf
+    >>> from sympy.abc import A, B, C
+    >>> is_anf(true)
+    True
+    >>> is_anf(A)
+    True
+    >>> is_anf(And(A, B, C))
+    True
+    >>> is_anf(Xor(A, Not(B)))
+    False
+
+    """
+    expr = sympify(expr)
+
+    if is_literal(expr) and not isinstance(expr, Not):
+        return True
+
+    if isinstance(expr, And):
+        for arg in expr.args:
+            if not arg.is_Symbol:
+                return False
+        return True
+
+    elif isinstance(expr, Xor):
+        for arg in expr.args:
+            if isinstance(arg, And):
+                for a in arg.args:
+                    if not a.is_Symbol:
+                        return False
+            elif is_literal(arg):
+                if isinstance(arg, Not):
+                    return False
+            else:
+                return False
+        return True
+
+    else:
+        return False
+
+
+def is_nnf(expr, simplified=True):
+    """
+    Checks if ``expr`` is in Negation Normal Form (NNF).
+
+    A logical expression is in NNF if it
+    contains only :py:class:`~.And`, :py:class:`~.Or` and :py:class:`~.Not`,
+    and :py:class:`~.Not` is applied only to literals.
+    If ``simplified`` is ``True``, checks if result contains no redundant clauses.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B, C
+    >>> from sympy.logic.boolalg import Not, is_nnf
+    >>> is_nnf(A & B | ~C)
+    True
+    >>> is_nnf((A | ~A) & (B | C))
+    False
+    >>> is_nnf((A | ~A) & (B | C), False)
+    True
+    >>> is_nnf(Not(A & B) | C)
+    False
+    >>> is_nnf((A >> B) & (B >> A))
+    False
+
+    """
+
+    expr = sympify(expr)
+    if is_literal(expr):
+        return True
+
+    stack = [expr]
+
+    while stack:
+        expr = stack.pop()
+        if expr.func in (And, Or):
+            if simplified:
+                args = expr.args
+                for arg in args:
+                    if Not(arg) in args:
+                        return False
+            stack.extend(expr.args)
+
+        elif not is_literal(expr):
+            return False
+
+    return True
+
+
+def is_cnf(expr):
+    """
+    Test whether or not an expression is in conjunctive normal form.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import is_cnf
+    >>> from sympy.abc import A, B, C
+    >>> is_cnf(A | B | C)
+    True
+    >>> is_cnf(A & B & C)
+    True
+    >>> is_cnf((A & B) | C)
+    False
+
+    """
+    return _is_form(expr, And, Or)
+
+
+def is_dnf(expr):
+    """
+    Test whether or not an expression is in disjunctive normal form.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import is_dnf
+    >>> from sympy.abc import A, B, C
+    >>> is_dnf(A | B | C)
+    True
+    >>> is_dnf(A & B & C)
+    True
+    >>> is_dnf((A & B) | C)
+    True
+    >>> is_dnf(A & (B | C))
+    False
+
+    """
+    return _is_form(expr, Or, And)
+
+
+def _is_form(expr, function1, function2):
+    """
+    Test whether or not an expression is of the required form.
+
+    """
+    expr = sympify(expr)
+
+    vals = function1.make_args(expr) if isinstance(expr, function1) else [expr]
+    for lit in vals:
+        if isinstance(lit, function2):
+            vals2 = function2.make_args(lit) if isinstance(lit, function2) else [lit]
+            for l in vals2:
+                if is_literal(l) is False:
+                    return False
+        elif is_literal(lit) is False:
+            return False
+
+    return True
+
+
+def eliminate_implications(expr):
+    """
+    Change :py:class:`~.Implies` and :py:class:`~.Equivalent` into
+    :py:class:`~.And`, :py:class:`~.Or`, and :py:class:`~.Not`.
+    That is, return an expression that is equivalent to ``expr``, but has only
+    ``&``, ``|``, and ``~`` as logical
+    operators.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import Implies, Equivalent, \
+         eliminate_implications
+    >>> from sympy.abc import A, B, C
+    >>> eliminate_implications(Implies(A, B))
+    B | ~A
+    >>> eliminate_implications(Equivalent(A, B))
+    (A | ~B) & (B | ~A)
+    >>> eliminate_implications(Equivalent(A, B, C))
+    (A | ~C) & (B | ~A) & (C | ~B)
+
+    """
+    return to_nnf(expr, simplify=False)
+
+
+def is_literal(expr):
+    """
+    Returns True if expr is a literal, else False.
+
+    Examples
+    ========
+
+    >>> from sympy import Or, Q
+    >>> from sympy.abc import A, B
+    >>> from sympy.logic.boolalg import is_literal
+    >>> is_literal(A)
+    True
+    >>> is_literal(~A)
+    True
+    >>> is_literal(Q.zero(A))
+    True
+    >>> is_literal(A + B)
+    True
+    >>> is_literal(Or(A, B))
+    False
+
+    """
+    from sympy.assumptions import AppliedPredicate
+
+    if isinstance(expr, Not):
+        return is_literal(expr.args[0])
+    elif expr in (True, False) or isinstance(expr, AppliedPredicate) or expr.is_Atom:
+        return True
+    elif not isinstance(expr, BooleanFunction) and all(
+            (isinstance(expr, AppliedPredicate) or a.is_Atom) for a in expr.args):
+        return True
+    return False
+
+
+def to_int_repr(clauses, symbols):
+    """
+    Takes clauses in CNF format and puts them into an integer representation.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import to_int_repr
+    >>> from sympy.abc import x, y
+    >>> to_int_repr([x | y, y], [x, y]) == [{1, 2}, {2}]
+    True
+
+    """
+
+    # Convert the symbol list into a dict
+    symbols = dict(zip(symbols, range(1, len(symbols) + 1)))
+
+    def append_symbol(arg, symbols):
+        if isinstance(arg, Not):
+            return -symbols[arg.args[0]]
+        else:
+            return symbols[arg]
+
+    return [{append_symbol(arg, symbols) for arg in Or.make_args(c)}
+            for c in clauses]
+
+
+def term_to_integer(term):
+    """
+    Return an integer corresponding to the base-2 digits given by *term*.
+
+    Parameters
+    ==========
+
+    term : a string or list of ones and zeros
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import term_to_integer
+    >>> term_to_integer([1, 0, 0])
+    4
+    >>> term_to_integer('100')
+    4
+
+    """
+
+    return int(''.join(list(map(str, list(term)))), 2)
+
+
+integer_to_term = ibin  # XXX could delete?
+
+
+def truth_table(expr, variables, input=True):
+    """
+    Return a generator of all possible configurations of the input variables,
+    and the result of the boolean expression for those values.
+
+    Parameters
+    ==========
+
+    expr : Boolean expression
+
+    variables : list of variables
+
+    input : bool (default ``True``)
+        Indicates whether to return the input combinations.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import truth_table
+    >>> from sympy.abc import x,y
+    >>> table = truth_table(x >> y, [x, y])
+    >>> for t in table:
+    ...     print('{0} -> {1}'.format(*t))
+    [0, 0] -> True
+    [0, 1] -> True
+    [1, 0] -> False
+    [1, 1] -> True
+
+    >>> table = truth_table(x | y, [x, y])
+    >>> list(table)
+    [([0, 0], False), ([0, 1], True), ([1, 0], True), ([1, 1], True)]
+
+    If ``input`` is ``False``, ``truth_table`` returns only a list of truth values.
+    In this case, the corresponding input values of variables can be
+    deduced from the index of a given output.
+
+    >>> from sympy.utilities.iterables import ibin
+    >>> vars = [y, x]
+    >>> values = truth_table(x >> y, vars, input=False)
+    >>> values = list(values)
+    >>> values
+    [True, False, True, True]
+
+    >>> for i, value in enumerate(values):
+    ...     print('{0} -> {1}'.format(list(zip(
+    ...     vars, ibin(i, len(vars)))), value))
+    [(y, 0), (x, 0)] -> True
+    [(y, 0), (x, 1)] -> False
+    [(y, 1), (x, 0)] -> True
+    [(y, 1), (x, 1)] -> True
+
+    """
+    variables = [sympify(v) for v in variables]
+
+    expr = sympify(expr)
+    if not isinstance(expr, BooleanFunction) and not is_literal(expr):
+        return
+
+    table = product((0, 1), repeat=len(variables))
+    for term in table:
+        value = expr.xreplace(dict(zip(variables, term)))
+
+        if input:
+            yield list(term), value
+        else:
+            yield value
+
+
+def _check_pair(minterm1, minterm2):
+    """
+    Checks if a pair of minterms differs by only one bit. If yes, returns
+    index, else returns `-1`.
+    """
+    # Early termination seems to be faster than list comprehension,
+    # at least for large examples.
+    index = -1
+    for x, i in enumerate(minterm1):  # zip(minterm1, minterm2) is slower
+        if i != minterm2[x]:
+            if index == -1:
+                index = x
+            else:
+                return -1
+    return index
+
+
+def _convert_to_varsSOP(minterm, variables):
+    """
+    Converts a term in the expansion of a function from binary to its
+    variable form (for SOP).
+    """
+    temp = [variables[n] if val == 1 else Not(variables[n])
+            for n, val in enumerate(minterm) if val != 3]
+    return And(*temp)
+
+
+def _convert_to_varsPOS(maxterm, variables):
+    """
+    Converts a term in the expansion of a function from binary to its
+    variable form (for POS).
+    """
+    temp = [variables[n] if val == 0 else Not(variables[n])
+            for n, val in enumerate(maxterm) if val != 3]
+    return Or(*temp)
+
+
+def _convert_to_varsANF(term, variables):
+    """
+    Converts a term in the expansion of a function from binary to its
+    variable form (for ANF).
+
+    Parameters
+    ==========
+
+    term : list of 1's and 0's (complementation pattern)
+    variables : list of variables
+
+    """
+    temp = [variables[n] for n, t in enumerate(term) if t == 1]
+
+    if not temp:
+        return true
+
+    return And(*temp)
+
+
+def _get_odd_parity_terms(n):
+    """
+    Returns a list of lists, with all possible combinations of n zeros and ones
+    with an odd number of ones.
+    """
+    return [e for e in [ibin(i, n) for i in range(2**n)] if sum(e) % 2 == 1]
+
+
+def _get_even_parity_terms(n):
+    """
+    Returns a list of lists, with all possible combinations of n zeros and ones
+    with an even number of ones.
+    """
+    return [e for e in [ibin(i, n) for i in range(2**n)] if sum(e) % 2 == 0]
+
+
+def _simplified_pairs(terms):
+    """
+    Reduces a set of minterms, if possible, to a simplified set of minterms
+    with one less variable in the terms using QM method.
+    """
+    if not terms:
+        return []
+
+    simplified_terms = []
+    todo = list(range(len(terms)))
+
+    # Count number of ones as _check_pair can only potentially match if there
+    # is at most a difference of a single one
+    termdict = defaultdict(list)
+    for n, term in enumerate(terms):
+        ones = sum(1 for t in term if t == 1)
+        termdict[ones].append(n)
+
+    variables = len(terms[0])
+    for k in range(variables):
+        for i in termdict[k]:
+            for j in termdict[k+1]:
+                index = _check_pair(terms[i], terms[j])
+                if index != -1:
+                    # Mark terms handled
+                    todo[i] = todo[j] = None
+                    # Copy old term
+                    newterm = terms[i][:]
+                    # Set differing position to don't care
+                    newterm[index] = 3
+                    # Add if not already there
+                    if newterm not in simplified_terms:
+                        simplified_terms.append(newterm)
+
+    if simplified_terms:
+        # Further simplifications only among the new terms
+        simplified_terms = _simplified_pairs(simplified_terms)
+
+    # Add remaining, non-simplified, terms
+    simplified_terms.extend([terms[i] for i in todo if i is not None])
+    return simplified_terms
+
+
+def _rem_redundancy(l1, terms):
+    """
+    After the truth table has been sufficiently simplified, use the prime
+    implicant table method to recognize and eliminate redundant pairs,
+    and return the essential arguments.
+    """
+
+    if not terms:
+        return []
+
+    nterms = len(terms)
+    nl1 = len(l1)
+
+    # Create dominating matrix
+    dommatrix = [[0]*nl1 for n in range(nterms)]
+    colcount = [0]*nl1
+    rowcount = [0]*nterms
+    for primei, prime in enumerate(l1):
+        for termi, term in enumerate(terms):
+            # Check prime implicant covering term
+            if all(t == 3 or t == mt for t, mt in zip(prime, term)):
+                dommatrix[termi][primei] = 1
+                colcount[primei] += 1
+                rowcount[termi] += 1
+
+    # Keep track if anything changed
+    anythingchanged = True
+    # Then, go again
+    while anythingchanged:
+        anythingchanged = False
+
+        for rowi in range(nterms):
+            # Still non-dominated?
+            if rowcount[rowi]:
+                row = dommatrix[rowi]
+                for row2i in range(nterms):
+                    # Still non-dominated?
+                    if rowi != row2i and rowcount[rowi] and (rowcount[rowi] <= rowcount[row2i]):
+                        row2 = dommatrix[row2i]
+                        if all(row2[n] >= row[n] for n in range(nl1)):
+                            # row2 dominating row, remove row2
+                            rowcount[row2i] = 0
+                            anythingchanged = True
+                            for primei, prime in enumerate(row2):
+                                if prime:
+                                    # Make corresponding entry 0
+                                    dommatrix[row2i][primei] = 0
+                                    colcount[primei] -= 1
+
+        colcache = {}
+
+        for coli in range(nl1):
+            # Still non-dominated?
+            if colcount[coli]:
+                if coli in colcache:
+                    col = colcache[coli]
+                else:
+                    col = [dommatrix[i][coli] for i in range(nterms)]
+                    colcache[coli] = col
+                for col2i in range(nl1):
+                    # Still non-dominated?
+                    if coli != col2i and colcount[col2i] and (colcount[coli] >= colcount[col2i]):
+                        if col2i in colcache:
+                            col2 = colcache[col2i]
+                        else:
+                            col2 = [dommatrix[i][col2i] for i in range(nterms)]
+                            colcache[col2i] = col2
+                        if all(col[n] >= col2[n] for n in range(nterms)):
+                            # col dominating col2, remove col2
+                            colcount[col2i] = 0
+                            anythingchanged = True
+                            for termi, term in enumerate(col2):
+                                if term and dommatrix[termi][col2i]:
+                                    # Make corresponding entry 0
+                                    dommatrix[termi][col2i] = 0
+                                    rowcount[termi] -= 1
+
+        if not anythingchanged:
+            # Heuristically select the prime implicant covering most terms
+            maxterms = 0
+            bestcolidx = -1
+            for coli in range(nl1):
+                s = colcount[coli]
+                if s > maxterms:
+                    bestcolidx = coli
+                    maxterms = s
+
+            # In case we found a prime implicant covering at least two terms
+            if bestcolidx != -1 and maxterms > 1:
+                for primei, prime in enumerate(l1):
+                    if primei != bestcolidx:
+                        for termi, term in enumerate(colcache[bestcolidx]):
+                            if term and dommatrix[termi][primei]:
+                                # Make corresponding entry 0
+                                dommatrix[termi][primei] = 0
+                                anythingchanged = True
+                                rowcount[termi] -= 1
+                                colcount[primei] -= 1
+
+    return [l1[i] for i in range(nl1) if colcount[i]]
+
+
+def _input_to_binlist(inputlist, variables):
+    binlist = []
+    bits = len(variables)
+    for val in inputlist:
+        if isinstance(val, int):
+            binlist.append(ibin(val, bits))
+        elif isinstance(val, dict):
+            nonspecvars = list(variables)
+            for key in val.keys():
+                nonspecvars.remove(key)
+            for t in product((0, 1), repeat=len(nonspecvars)):
+                d = dict(zip(nonspecvars, t))
+                d.update(val)
+                binlist.append([d[v] for v in variables])
+        elif isinstance(val, (list, tuple)):
+            if len(val) != bits:
+                raise ValueError("Each term must contain {bits} bits as there are"
+                                 "\n{bits} variables (or be an integer)."
+                                 "".format(bits=bits))
+            binlist.append(list(val))
+        else:
+            raise TypeError("A term list can only contain lists,"
+                            " ints or dicts.")
+    return binlist
+
+
+def SOPform(variables, minterms, dontcares=None):
+    """
+    The SOPform function uses simplified_pairs and a redundant group-
+    eliminating algorithm to convert the list of all input combos that
+    generate '1' (the minterms) into the smallest sum-of-products form.
+
+    The variables must be given as the first argument.
+
+    Return a logical :py:class:`~.Or` function (i.e., the "sum of products" or
+    "SOP" form) that gives the desired outcome. If there are inputs that can
+    be ignored, pass them as a list, too.
+
+    The result will be one of the (perhaps many) functions that satisfy
+    the conditions.
+
+    Examples
+    ========
+
+    >>> from sympy.logic import SOPform
+    >>> from sympy import symbols
+    >>> w, x, y, z = symbols('w x y z')
+    >>> minterms = [[0, 0, 0, 1], [0, 0, 1, 1],
+    ...             [0, 1, 1, 1], [1, 0, 1, 1], [1, 1, 1, 1]]
+    >>> dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]]
+    >>> SOPform([w, x, y, z], minterms, dontcares)
+    (y & z) | (~w & ~x)
+
+    The terms can also be represented as integers:
+
+    >>> minterms = [1, 3, 7, 11, 15]
+    >>> dontcares = [0, 2, 5]
+    >>> SOPform([w, x, y, z], minterms, dontcares)
+    (y & z) | (~w & ~x)
+
+    They can also be specified using dicts, which does not have to be fully
+    specified:
+
+    >>> minterms = [{w: 0, x: 1}, {y: 1, z: 1, x: 0}]
+    >>> SOPform([w, x, y, z], minterms)
+    (x & ~w) | (y & z & ~x)
+
+    Or a combination:
+
+    >>> minterms = [4, 7, 11, [1, 1, 1, 1]]
+    >>> dontcares = [{w : 0, x : 0, y: 0}, 5]
+    >>> SOPform([w, x, y, z], minterms, dontcares)
+    (w & y & z) | (~w & ~y) | (x & z & ~w)
+
+    See also
+    ========
+
+    POSform
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Quine-McCluskey_algorithm
+    .. [2] https://en.wikipedia.org/wiki/Don%27t-care_term
+
+    """
+    if not minterms:
+        return false
+
+    variables = tuple(map(sympify, variables))
+
+
+    minterms = _input_to_binlist(minterms, variables)
+    dontcares = _input_to_binlist((dontcares or []), variables)
+    for d in dontcares:
+        if d in minterms:
+            raise ValueError('%s in minterms is also in dontcares' % d)
+
+    return _sop_form(variables, minterms, dontcares)
+
+
+def _sop_form(variables, minterms, dontcares):
+    new = _simplified_pairs(minterms + dontcares)
+    essential = _rem_redundancy(new, minterms)
+    return Or(*[_convert_to_varsSOP(x, variables) for x in essential])
+
+
+def POSform(variables, minterms, dontcares=None):
+    """
+    The POSform function uses simplified_pairs and a redundant-group
+    eliminating algorithm to convert the list of all input combinations
+    that generate '1' (the minterms) into the smallest product-of-sums form.
+
+    The variables must be given as the first argument.
+
+    Return a logical :py:class:`~.And` function (i.e., the "product of sums"
+    or "POS" form) that gives the desired outcome. If there are inputs that can
+    be ignored, pass them as a list, too.
+
+    The result will be one of the (perhaps many) functions that satisfy
+    the conditions.
+
+    Examples
+    ========
+
+    >>> from sympy.logic import POSform
+    >>> from sympy import symbols
+    >>> w, x, y, z = symbols('w x y z')
+    >>> minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1],
+    ...             [1, 0, 1, 1], [1, 1, 1, 1]]
+    >>> dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]]
+    >>> POSform([w, x, y, z], minterms, dontcares)
+    z & (y | ~w)
+
+    The terms can also be represented as integers:
+
+    >>> minterms = [1, 3, 7, 11, 15]
+    >>> dontcares = [0, 2, 5]
+    >>> POSform([w, x, y, z], minterms, dontcares)
+    z & (y | ~w)
+
+    They can also be specified using dicts, which does not have to be fully
+    specified:
+
+    >>> minterms = [{w: 0, x: 1}, {y: 1, z: 1, x: 0}]
+    >>> POSform([w, x, y, z], minterms)
+    (x | y) & (x | z) & (~w | ~x)
+
+    Or a combination:
+
+    >>> minterms = [4, 7, 11, [1, 1, 1, 1]]
+    >>> dontcares = [{w : 0, x : 0, y: 0}, 5]
+    >>> POSform([w, x, y, z], minterms, dontcares)
+    (w | x) & (y | ~w) & (z | ~y)
+
+    See also
+    ========
+
+    SOPform
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Quine-McCluskey_algorithm
+    .. [2] https://en.wikipedia.org/wiki/Don%27t-care_term
+
+    """
+    if not minterms:
+        return false
+
+    variables = tuple(map(sympify, variables))
+    minterms = _input_to_binlist(minterms, variables)
+    dontcares = _input_to_binlist((dontcares or []), variables)
+    for d in dontcares:
+        if d in minterms:
+            raise ValueError('%s in minterms is also in dontcares' % d)
+
+    maxterms = []
+    for t in product((0, 1), repeat=len(variables)):
+        t = list(t)
+        if (t not in minterms) and (t not in dontcares):
+            maxterms.append(t)
+
+    new = _simplified_pairs(maxterms + dontcares)
+    essential = _rem_redundancy(new, maxterms)
+    return And(*[_convert_to_varsPOS(x, variables) for x in essential])
+
+
+def ANFform(variables, truthvalues):
+    """
+    The ANFform function converts the list of truth values to
+    Algebraic Normal Form (ANF).
+
+    The variables must be given as the first argument.
+
+    Return True, False, logical :py:class:`~.And` function (i.e., the
+    "Zhegalkin monomial") or logical :py:class:`~.Xor` function (i.e.,
+    the "Zhegalkin polynomial"). When True and False
+    are represented by 1 and 0, respectively, then
+    :py:class:`~.And` is multiplication and :py:class:`~.Xor` is addition.
+
+    Formally a "Zhegalkin monomial" is the product (logical
+    And) of a finite set of distinct variables, including
+    the empty set whose product is denoted 1 (True).
+    A "Zhegalkin polynomial" is the sum (logical Xor) of a
+    set of Zhegalkin monomials, with the empty set denoted
+    by 0 (False).
+
+    Parameters
+    ==========
+
+    variables : list of variables
+    truthvalues : list of 1's and 0's (result column of truth table)
+
+    Examples
+    ========
+    >>> from sympy.logic.boolalg import ANFform
+    >>> from sympy.abc import x, y
+    >>> ANFform([x], [1, 0])
+    x ^ True
+    >>> ANFform([x, y], [0, 1, 1, 1])
+    x ^ y ^ (x & y)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Zhegalkin_polynomial
+
+    """
+
+    n_vars = len(variables)
+    n_values = len(truthvalues)
+
+    if n_values != 2 ** n_vars:
+        raise ValueError("The number of truth values must be equal to 2^%d, "
+                         "got %d" % (n_vars, n_values))
+
+    variables = tuple(map(sympify, variables))
+
+    coeffs = anf_coeffs(truthvalues)
+    terms = []
+
+    for i, t in enumerate(product((0, 1), repeat=n_vars)):
+        if coeffs[i] == 1:
+            terms.append(t)
+
+    return Xor(*[_convert_to_varsANF(x, variables) for x in terms],
+               remove_true=False)
+
+
+def anf_coeffs(truthvalues):
+    """
+    Convert a list of truth values of some boolean expression
+    to the list of coefficients of the polynomial mod 2 (exclusive
+    disjunction) representing the boolean expression in ANF
+    (i.e., the "Zhegalkin polynomial").
+
+    There are `2^n` possible Zhegalkin monomials in `n` variables, since
+    each monomial is fully specified by the presence or absence of
+    each variable.
+
+    We can enumerate all the monomials. For example, boolean
+    function with four variables ``(a, b, c, d)`` can contain
+    up to `2^4 = 16` monomials. The 13-th monomial is the
+    product ``a & b & d``, because 13 in binary is 1, 1, 0, 1.
+
+    A given monomial's presence or absence in a polynomial corresponds
+    to that monomial's coefficient being 1 or 0 respectively.
+
+    Examples
+    ========
+    >>> from sympy.logic.boolalg import anf_coeffs, bool_monomial, Xor
+    >>> from sympy.abc import a, b, c
+    >>> truthvalues = [0, 1, 1, 0, 0, 1, 0, 1]
+    >>> coeffs = anf_coeffs(truthvalues)
+    >>> coeffs
+    [0, 1, 1, 0, 0, 0, 1, 0]
+    >>> polynomial = Xor(*[
+    ...     bool_monomial(k, [a, b, c])
+    ...     for k, coeff in enumerate(coeffs) if coeff == 1
+    ... ])
+    >>> polynomial
+    b ^ c ^ (a & b)
+
+    """
+
+    s = '{:b}'.format(len(truthvalues))
+    n = len(s) - 1
+
+    if len(truthvalues) != 2**n:
+        raise ValueError("The number of truth values must be a power of two, "
+                         "got %d" % len(truthvalues))
+
+    coeffs = [[v] for v in truthvalues]
+
+    for i in range(n):
+        tmp = []
+        for j in range(2 ** (n-i-1)):
+            tmp.append(coeffs[2*j] +
+                list(map(lambda x, y: x^y, coeffs[2*j], coeffs[2*j+1])))
+        coeffs = tmp
+
+    return coeffs[0]
+
+
+def bool_minterm(k, variables):
+    """
+    Return the k-th minterm.
+
+    Minterms are numbered by a binary encoding of the complementation
+    pattern of the variables. This convention assigns the value 1 to
+    the direct form and 0 to the complemented form.
+
+    Parameters
+    ==========
+
+    k : int or list of 1's and 0's (complementation pattern)
+    variables : list of variables
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import bool_minterm
+    >>> from sympy.abc import x, y, z
+    >>> bool_minterm([1, 0, 1], [x, y, z])
+    x & z & ~y
+    >>> bool_minterm(6, [x, y, z])
+    x & y & ~z
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Canonical_normal_form#Indexing_minterms
+
+    """
+    if isinstance(k, int):
+        k = ibin(k, len(variables))
+    variables = tuple(map(sympify, variables))
+    return _convert_to_varsSOP(k, variables)
+
+
+def bool_maxterm(k, variables):
+    """
+    Return the k-th maxterm.
+
+    Each maxterm is assigned an index based on the opposite
+    conventional binary encoding used for minterms. The maxterm
+    convention assigns the value 0 to the direct form and 1 to
+    the complemented form.
+
+    Parameters
+    ==========
+
+    k : int or list of 1's and 0's (complementation pattern)
+    variables : list of variables
+
+    Examples
+    ========
+    >>> from sympy.logic.boolalg import bool_maxterm
+    >>> from sympy.abc import x, y, z
+    >>> bool_maxterm([1, 0, 1], [x, y, z])
+    y | ~x | ~z
+    >>> bool_maxterm(6, [x, y, z])
+    z | ~x | ~y
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Canonical_normal_form#Indexing_maxterms
+
+    """
+    if isinstance(k, int):
+        k = ibin(k, len(variables))
+    variables = tuple(map(sympify, variables))
+    return _convert_to_varsPOS(k, variables)
+
+
+def bool_monomial(k, variables):
+    """
+    Return the k-th monomial.
+
+    Monomials are numbered by a binary encoding of the presence and
+    absences of the variables. This convention assigns the value
+    1 to the presence of variable and 0 to the absence of variable.
+
+    Each boolean function can be uniquely represented by a
+    Zhegalkin Polynomial (Algebraic Normal Form). The Zhegalkin
+    Polynomial of the boolean function with `n` variables can contain
+    up to `2^n` monomials. We can enumerate all the monomials.
+    Each monomial is fully specified by the presence or absence
+    of each variable.
+
+    For example, boolean function with four variables ``(a, b, c, d)``
+    can contain up to `2^4 = 16` monomials. The 13-th monomial is the
+    product ``a & b & d``, because 13 in binary is 1, 1, 0, 1.
+
+    Parameters
+    ==========
+
+    k : int or list of 1's and 0's
+    variables : list of variables
+
+    Examples
+    ========
+    >>> from sympy.logic.boolalg import bool_monomial
+    >>> from sympy.abc import x, y, z
+    >>> bool_monomial([1, 0, 1], [x, y, z])
+    x & z
+    >>> bool_monomial(6, [x, y, z])
+    x & y
+
+    """
+    if isinstance(k, int):
+        k = ibin(k, len(variables))
+    variables = tuple(map(sympify, variables))
+    return _convert_to_varsANF(k, variables)
+
+
+def _find_predicates(expr):
+    """Helper to find logical predicates in BooleanFunctions.
+
+    A logical predicate is defined here as anything within a BooleanFunction
+    that is not a BooleanFunction itself.
+
+    """
+    if not isinstance(expr, BooleanFunction):
+        return {expr}
+    return set().union(*(map(_find_predicates, expr.args)))
+
+
+def simplify_logic(expr, form=None, deep=True, force=False, dontcare=None):
+    """
+    This function simplifies a boolean function to its simplified version
+    in SOP or POS form. The return type is an :py:class:`~.Or` or
+    :py:class:`~.And` object in SymPy.
+
+    Parameters
+    ==========
+
+    expr : Boolean
+
+    form : string (``'cnf'`` or ``'dnf'``) or ``None`` (default).
+        If ``'cnf'`` or ``'dnf'``, the simplest expression in the corresponding
+        normal form is returned; if ``None``, the answer is returned
+        according to the form with fewest args (in CNF by default).
+
+    deep : bool (default ``True``)
+        Indicates whether to recursively simplify any
+        non-boolean functions contained within the input.
+
+    force : bool (default ``False``)
+        As the simplifications require exponential time in the number
+        of variables, there is by default a limit on expressions with
+        8 variables. When the expression has more than 8 variables
+        only symbolical simplification (controlled by ``deep``) is
+        made. By setting ``force`` to ``True``, this limit is removed. Be
+        aware that this can lead to very long simplification times.
+
+    dontcare : Boolean
+        Optimize expression under the assumption that inputs where this
+        expression is true are don't care. This is useful in e.g. Piecewise
+        conditions, where later conditions do not need to consider inputs that
+        are converted by previous conditions. For example, if a previous
+        condition is ``And(A, B)``, the simplification of expr can be made
+        with don't cares for ``And(A, B)``.
+
+    Examples
+    ========
+
+    >>> from sympy.logic import simplify_logic
+    >>> from sympy.abc import x, y, z
+    >>> b = (~x & ~y & ~z) | ( ~x & ~y & z)
+    >>> simplify_logic(b)
+    ~x & ~y
+    >>> simplify_logic(x | y, dontcare=y)
+    x
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Don%27t-care_term
+
+    """
+
+    if form not in (None, 'cnf', 'dnf'):
+        raise ValueError("form can be cnf or dnf only")
+    expr = sympify(expr)
+    # check for quick exit if form is given: right form and all args are
+    # literal and do not involve Not
+    if form:
+        form_ok = False
+        if form == 'cnf':
+            form_ok = is_cnf(expr)
+        elif form == 'dnf':
+            form_ok = is_dnf(expr)
+
+        if form_ok and all(is_literal(a)
+                for a in expr.args):
+            return expr
+    from sympy.core.relational import Relational
+    if deep:
+        variables = expr.atoms(Relational)
+        from sympy.simplify.simplify import simplify
+        s = tuple(map(simplify, variables))
+        expr = expr.xreplace(dict(zip(variables, s)))
+    if not isinstance(expr, BooleanFunction):
+        return expr
+    # Replace Relationals with Dummys to possibly
+    # reduce the number of variables
+    repl = {}
+    undo = {}
+    from sympy.core.symbol import Dummy
+    variables = expr.atoms(Relational)
+    if dontcare is not None:
+        dontcare = sympify(dontcare)
+        variables.update(dontcare.atoms(Relational))
+    while variables:
+        var = variables.pop()
+        if var.is_Relational:
+            d = Dummy()
+            undo[d] = var
+            repl[var] = d
+            nvar = var.negated
+            if nvar in variables:
+                repl[nvar] = Not(d)
+                variables.remove(nvar)
+
+    expr = expr.xreplace(repl)
+
+    if dontcare is not None:
+        dontcare = dontcare.xreplace(repl)
+
+    # Get new variables after replacing
+    variables = _find_predicates(expr)
+    if not force and len(variables) > 8:
+        return expr.xreplace(undo)
+    if dontcare is not None:
+        # Add variables from dontcare
+        dcvariables = _find_predicates(dontcare)
+        variables.update(dcvariables)
+        # if too many restore to variables only
+        if not force and len(variables) > 8:
+            variables = _find_predicates(expr)
+            dontcare = None
+    # group into constants and variable values
+    c, v = sift(ordered(variables), lambda x: x in (True, False), binary=True)
+    variables = c + v
+    # standardize constants to be 1 or 0 in keeping with truthtable
+    c = [1 if i == True else 0 for i in c]
+    truthtable = _get_truthtable(v, expr, c)
+    if dontcare is not None:
+        dctruthtable = _get_truthtable(v, dontcare, c)
+        truthtable = [t for t in truthtable if t not in dctruthtable]
+    else:
+        dctruthtable = []
+    big = len(truthtable) >= (2 ** (len(variables) - 1))
+    if form == 'dnf' or form is None and big:
+        return _sop_form(variables, truthtable, dctruthtable).xreplace(undo)
+    return POSform(variables, truthtable, dctruthtable).xreplace(undo)
+
+
+def _get_truthtable(variables, expr, const):
+    """ Return a list of all combinations leading to a True result for ``expr``.
+    """
+    _variables = variables.copy()
+    def _get_tt(inputs):
+        if _variables:
+            v = _variables.pop()
+            tab = [[i[0].xreplace({v: false}), [0] + i[1]] for i in inputs if i[0] is not false]
+            tab.extend([[i[0].xreplace({v: true}), [1] + i[1]] for i in inputs if i[0] is not false])
+            return _get_tt(tab)
+        return inputs
+    res = [const + k[1] for k in _get_tt([[expr, []]]) if k[0]]
+    if res == [[]]:
+        return []
+    else:
+        return res
+
+
+def _finger(eq):
+    """
+    Assign a 5-item fingerprint to each symbol in the equation:
+    [
+    # of times it appeared as a Symbol;
+    # of times it appeared as a Not(symbol);
+    # of times it appeared as a Symbol in an And or Or;
+    # of times it appeared as a Not(Symbol) in an And or Or;
+    a sorted tuple of tuples, (i, j, k), where i is the number of arguments
+    in an And or Or with which it appeared as a Symbol, and j is
+    the number of arguments that were Not(Symbol); k is the number
+    of times that (i, j) was seen.
+    ]
+
+    Examples
+    ========
+
+    >>> from sympy.logic.boolalg import _finger as finger
+    >>> from sympy import And, Or, Not, Xor, to_cnf, symbols
+    >>> from sympy.abc import a, b, x, y
+    >>> eq = Or(And(Not(y), a), And(Not(y), b), And(x, y))
+    >>> dict(finger(eq))
+    {(0, 0, 1, 0, ((2, 0, 1),)): [x],
+    (0, 0, 1, 0, ((2, 1, 1),)): [a, b],
+    (0, 0, 1, 2, ((2, 0, 1),)): [y]}
+    >>> dict(finger(x & ~y))
+    {(0, 1, 0, 0, ()): [y], (1, 0, 0, 0, ()): [x]}
+
+    In the following, the (5, 2, 6) means that there were 6 Or
+    functions in which a symbol appeared as itself amongst 5 arguments in
+    which there were also 2 negated symbols, e.g. ``(a0 | a1 | a2 | ~a3 | ~a4)``
+    is counted once for a0, a1 and a2.
+
+    >>> dict(finger(to_cnf(Xor(*symbols('a:5')))))
+    {(0, 0, 8, 8, ((5, 0, 1), (5, 2, 6), (5, 4, 1))): [a0, a1, a2, a3, a4]}
+
+    The equation must not have more than one level of nesting:
+
+    >>> dict(finger(And(Or(x, y), y)))
+    {(0, 0, 1, 0, ((2, 0, 1),)): [x], (1, 0, 1, 0, ((2, 0, 1),)): [y]}
+    >>> dict(finger(And(Or(x, And(a, x)), y)))
+    Traceback (most recent call last):
+    ...
+    NotImplementedError: unexpected level of nesting
+
+    So y and x have unique fingerprints, but a and b do not.
+    """
+    f = eq.free_symbols
+    d = dict(list(zip(f, [[0]*4 + [defaultdict(int)] for fi in f])))
+    for a in eq.args:
+        if a.is_Symbol:
+            d[a][0] += 1
+        elif a.is_Not:
+            d[a.args[0]][1] += 1
+        else:
+            o = len(a.args), sum(isinstance(ai, Not) for ai in a.args)
+            for ai in a.args:
+                if ai.is_Symbol:
+                    d[ai][2] += 1
+                    d[ai][-1][o] += 1
+                elif ai.is_Not:
+                    d[ai.args[0]][3] += 1
+                else:
+                    raise NotImplementedError('unexpected level of nesting')
+    inv = defaultdict(list)
+    for k, v in ordered(iter(d.items())):
+        v[-1] = tuple(sorted([i + (j,) for i, j in v[-1].items()]))
+        inv[tuple(v)].append(k)
+    return inv
+
+
+def bool_map(bool1, bool2):
+    """
+    Return the simplified version of *bool1*, and the mapping of variables
+    that makes the two expressions *bool1* and *bool2* represent the same
+    logical behaviour for some correspondence between the variables
+    of each.
+    If more than one mappings of this sort exist, one of them
+    is returned.
+
+    For example, ``And(x, y)`` is logically equivalent to ``And(a, b)`` for
+    the mapping ``{x: a, y: b}`` or ``{x: b, y: a}``.
+    If no such mapping exists, return ``False``.
+
+    Examples
+    ========
+
+    >>> from sympy import SOPform, bool_map, Or, And, Not, Xor
+    >>> from sympy.abc import w, x, y, z, a, b, c, d
+    >>> function1 = SOPform([x, z, y],[[1, 0, 1], [0, 0, 1]])
+    >>> function2 = SOPform([a, b, c],[[1, 0, 1], [1, 0, 0]])
+    >>> bool_map(function1, function2)
+    (y & ~z, {y: a, z: b})
+
+    The results are not necessarily unique, but they are canonical. Here,
+    ``(w, z)`` could be ``(a, d)`` or ``(d, a)``:
+
+    >>> eq =  Or(And(Not(y), w), And(Not(y), z), And(x, y))
+    >>> eq2 = Or(And(Not(c), a), And(Not(c), d), And(b, c))
+    >>> bool_map(eq, eq2)
+    ((x & y) | (w & ~y) | (z & ~y), {w: a, x: b, y: c, z: d})
+    >>> eq = And(Xor(a, b), c, And(c,d))
+    >>> bool_map(eq, eq.subs(c, x))
+    (c & d & (a | b) & (~a | ~b), {a: a, b: b, c: d, d: x})
+
+    """
+
+    def match(function1, function2):
+        """Return the mapping that equates variables between two
+        simplified boolean expressions if possible.
+
+        By "simplified" we mean that a function has been denested
+        and is either an And (or an Or) whose arguments are either
+        symbols (x), negated symbols (Not(x)), or Or (or an And) whose
+        arguments are only symbols or negated symbols. For example,
+        ``And(x, Not(y), Or(w, Not(z)))``.
+
+        Basic.match is not robust enough (see issue 4835) so this is
+        a workaround that is valid for simplified boolean expressions
+        """
+
+        # do some quick checks
+        if function1.__class__ != function2.__class__:
+            return None  # maybe simplification makes them the same?
+        if len(function1.args) != len(function2.args):
+            return None  # maybe simplification makes them the same?
+        if function1.is_Symbol:
+            return {function1: function2}
+
+        # get the fingerprint dictionaries
+        f1 = _finger(function1)
+        f2 = _finger(function2)
+
+        # more quick checks
+        if len(f1) != len(f2):
+            return False
+
+        # assemble the match dictionary if possible
+        matchdict = {}
+        for k in f1.keys():
+            if k not in f2:
+                return False
+            if len(f1[k]) != len(f2[k]):
+                return False
+            for i, x in enumerate(f1[k]):
+                matchdict[x] = f2[k][i]
+        return matchdict
+
+    a = simplify_logic(bool1)
+    b = simplify_logic(bool2)
+    m = match(a, b)
+    if m:
+        return a, m
+    return m
+
+
+def _apply_patternbased_simplification(rv, patterns, measure,
+                                       dominatingvalue,
+                                       replacementvalue=None,
+                                       threeterm_patterns=None):
+    """
+    Replace patterns of Relational
+
+    Parameters
+    ==========
+
+    rv : Expr
+        Boolean expression
+
+    patterns : tuple
+        Tuple of tuples, with (pattern to simplify, simplified pattern) with
+        two terms.
+
+    measure : function
+        Simplification measure.
+
+    dominatingvalue : Boolean or ``None``
+        The dominating value for the function of consideration.
+        For example, for :py:class:`~.And` ``S.false`` is dominating.
+        As soon as one expression is ``S.false`` in :py:class:`~.And`,
+        the whole expression is ``S.false``.
+
+    replacementvalue : Boolean or ``None``, optional
+        The resulting value for the whole expression if one argument
+        evaluates to ``dominatingvalue``.
+        For example, for :py:class:`~.Nand` ``S.false`` is dominating, but
+        in this case the resulting value is ``S.true``. Default is ``None``.
+        If ``replacementvalue`` is ``None`` and ``dominatingvalue`` is not
+        ``None``, ``replacementvalue = dominatingvalue``.
+
+    threeterm_patterns : tuple, optional
+        Tuple of tuples, with (pattern to simplify, simplified pattern) with
+        three terms.
+
+    """
+    from sympy.core.relational import Relational, _canonical
+
+    if replacementvalue is None and dominatingvalue is not None:
+        replacementvalue = dominatingvalue
+    # Use replacement patterns for Relationals
+    Rel, nonRel = sift(rv.args, lambda i: isinstance(i, Relational),
+                       binary=True)
+    if len(Rel) <= 1:
+        return rv
+    Rel, nonRealRel = sift(Rel, lambda i: not any(s.is_real is False
+                                                  for s in i.free_symbols),
+                           binary=True)
+    Rel = [i.canonical for i in Rel]
+
+    if threeterm_patterns and len(Rel) >= 3:
+        Rel = _apply_patternbased_threeterm_simplification(Rel,
+                            threeterm_patterns, rv.func, dominatingvalue,
+                            replacementvalue, measure)
+
+    Rel = _apply_patternbased_twoterm_simplification(Rel, patterns,
+                    rv.func, dominatingvalue, replacementvalue, measure)
+
+    rv = rv.func(*([_canonical(i) for i in ordered(Rel)]
+                 + nonRel + nonRealRel))
+    return rv
+
+
+def _apply_patternbased_twoterm_simplification(Rel, patterns, func,
+                                               dominatingvalue,
+                                               replacementvalue,
+                                               measure):
+    """ Apply pattern-based two-term simplification."""
+    from sympy.functions.elementary.miscellaneous import Min, Max
+    from sympy.core.relational import Ge, Gt, _Inequality
+    changed = True
+    while changed and len(Rel) >= 2:
+        changed = False
+        # Use only < or <=
+        Rel = [r.reversed if isinstance(r, (Ge, Gt)) else r for r in Rel]
+        # Sort based on ordered
+        Rel = list(ordered(Rel))
+        # Eq and Ne must be tested reversed as well
+        rtmp = [(r, ) if isinstance(r, _Inequality) else (r, r.reversed) for r in Rel]
+        # Create a list of possible replacements
+        results = []
+        # Try all combinations of possibly reversed relational
+        for ((i, pi), (j, pj)) in combinations(enumerate(rtmp), 2):
+            for pattern, simp in patterns:
+                res = []
+                for p1, p2 in product(pi, pj):
+                    # use SymPy matching
+                    oldexpr = Tuple(p1, p2)
+                    tmpres = oldexpr.match(pattern)
+                    if tmpres:
+                        res.append((tmpres, oldexpr))
+
+                if res:
+                    for tmpres, oldexpr in res:
+                        # we have a matching, compute replacement
+                        np = simp.xreplace(tmpres)
+                        if np == dominatingvalue:
+                            # if dominatingvalue, the whole expression
+                            # will be replacementvalue
+                            return [replacementvalue]
+                        # add replacement
+                        if not isinstance(np, ITE) and not np.has(Min, Max):
+                            # We only want to use ITE and Min/Max replacements if
+                            # they simplify to a relational
+                            costsaving = measure(func(*oldexpr.args)) - measure(np)
+                            if costsaving > 0:
+                                results.append((costsaving, ([i, j], np)))
+        if results:
+            # Sort results based on complexity
+            results = sorted(results,
+                                           key=lambda pair: pair[0], reverse=True)
+            # Replace the one providing most simplification
+            replacement = results[0][1]
+            idx, newrel = replacement
+            idx.sort()
+            # Remove the old relationals
+            for index in reversed(idx):
+                del Rel[index]
+            if dominatingvalue is None or newrel != Not(dominatingvalue):
+                # Insert the new one (no need to insert a value that will
+                # not affect the result)
+                if newrel.func == func:
+                    for a in newrel.args:
+                        Rel.append(a)
+                else:
+                    Rel.append(newrel)
+            # We did change something so try again
+            changed = True
+    return Rel
+
+
+def _apply_patternbased_threeterm_simplification(Rel, patterns, func,
+                                                 dominatingvalue,
+                                                 replacementvalue,
+                                                 measure):
+    """ Apply pattern-based three-term simplification."""
+    from sympy.functions.elementary.miscellaneous import Min, Max
+    from sympy.core.relational import Le, Lt, _Inequality
+    changed = True
+    while changed and len(Rel) >= 3:
+        changed = False
+        # Use only > or >=
+        Rel = [r.reversed if isinstance(r, (Le, Lt)) else r for r in Rel]
+        # Sort based on ordered
+        Rel = list(ordered(Rel))
+        # Create a list of possible replacements
+        results = []
+        # Eq and Ne must be tested reversed as well
+        rtmp = [(r, ) if isinstance(r, _Inequality) else (r, r.reversed) for r in Rel]
+        # Try all combinations of possibly reversed relational
+        for ((i, pi), (j, pj), (k, pk)) in permutations(enumerate(rtmp), 3):
+            for pattern, simp in patterns:
+                res = []
+                for p1, p2, p3 in product(pi, pj, pk):
+                    # use SymPy matching
+                    oldexpr = Tuple(p1, p2, p3)
+                    tmpres = oldexpr.match(pattern)
+                    if tmpres:
+                        res.append((tmpres, oldexpr))
+
+                if res:
+                    for tmpres, oldexpr in res:
+                        # we have a matching, compute replacement
+                        np = simp.xreplace(tmpres)
+                        if np == dominatingvalue:
+                            # if dominatingvalue, the whole expression
+                            # will be replacementvalue
+                            return [replacementvalue]
+                        # add replacement
+                        if not isinstance(np, ITE) and not np.has(Min, Max):
+                            # We only want to use ITE and Min/Max replacements if
+                            # they simplify to a relational
+                            costsaving = measure(func(*oldexpr.args)) - measure(np)
+                            if costsaving > 0:
+                                results.append((costsaving, ([i, j, k], np)))
+        if results:
+            # Sort results based on complexity
+            results = sorted(results,
+                                           key=lambda pair: pair[0], reverse=True)
+            # Replace the one providing most simplification
+            replacement = results[0][1]
+            idx, newrel = replacement
+            idx.sort()
+            # Remove the old relationals
+            for index in reversed(idx):
+                del Rel[index]
+            if dominatingvalue is None or newrel != Not(dominatingvalue):
+                # Insert the new one (no need to insert a value that will
+                # not affect the result)
+                if newrel.func == func:
+                    for a in newrel.args:
+                        Rel.append(a)
+                else:
+                    Rel.append(newrel)
+            # We did change something so try again
+            changed = True
+    return Rel
+
+
+@cacheit
+def _simplify_patterns_and():
+    """ Two-term patterns for And."""
+
+    from sympy.core import Wild
+    from sympy.core.relational import Eq, Ne, Ge, Gt, Le, Lt
+    from sympy.functions.elementary.complexes import Abs
+    from sympy.functions.elementary.miscellaneous import Min, Max
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    # Relationals patterns should be in alphabetical order
+    # (pattern1, pattern2, simplified)
+    # Do not use Ge, Gt
+    _matchers_and = ((Tuple(Eq(a, b), Lt(a, b)), false),
+                     #(Tuple(Eq(a, b), Lt(b, a)), S.false),
+                     #(Tuple(Le(b, a), Lt(a, b)), S.false),
+                     #(Tuple(Lt(b, a), Le(a, b)), S.false),
+                     (Tuple(Lt(b, a), Lt(a, b)), false),
+                     (Tuple(Eq(a, b), Le(b, a)), Eq(a, b)),
+                     #(Tuple(Eq(a, b), Le(a, b)), Eq(a, b)),
+                     #(Tuple(Le(b, a), Lt(b, a)), Gt(a, b)),
+                     (Tuple(Le(b, a), Le(a, b)), Eq(a, b)),
+                     #(Tuple(Le(b, a), Ne(a, b)), Gt(a, b)),
+                     #(Tuple(Lt(b, a), Ne(a, b)), Gt(a, b)),
+                     (Tuple(Le(a, b), Lt(a, b)), Lt(a, b)),
+                     (Tuple(Le(a, b), Ne(a, b)), Lt(a, b)),
+                     (Tuple(Lt(a, b), Ne(a, b)), Lt(a, b)),
+                     # Sign
+                     (Tuple(Eq(a, b), Eq(a, -b)), And(Eq(a, S.Zero), Eq(b, S.Zero))),
+                     # Min/Max/ITE
+                     (Tuple(Le(b, a), Le(c, a)), Ge(a, Max(b, c))),
+                     (Tuple(Le(b, a), Lt(c, a)), ITE(b > c, Ge(a, b), Gt(a, c))),
+                     (Tuple(Lt(b, a), Lt(c, a)), Gt(a, Max(b, c))),
+                     (Tuple(Le(a, b), Le(a, c)), Le(a, Min(b, c))),
+                     (Tuple(Le(a, b), Lt(a, c)), ITE(b < c, Le(a, b), Lt(a, c))),
+                     (Tuple(Lt(a, b), Lt(a, c)), Lt(a, Min(b, c))),
+                     (Tuple(Le(a, b), Le(c, a)), ITE(Eq(b, c), Eq(a, b), ITE(b < c, false, And(Le(a, b), Ge(a, c))))),
+                     (Tuple(Le(c, a), Le(a, b)), ITE(Eq(b, c), Eq(a, b), ITE(b < c, false, And(Le(a, b), Ge(a, c))))),
+                     (Tuple(Lt(a, b), Lt(c, a)), ITE(b < c, false, And(Lt(a, b), Gt(a, c)))),
+                     (Tuple(Lt(c, a), Lt(a, b)), ITE(b < c, false, And(Lt(a, b), Gt(a, c)))),
+                     (Tuple(Le(a, b), Lt(c, a)), ITE(b <= c, false, And(Le(a, b), Gt(a, c)))),
+                     (Tuple(Le(c, a), Lt(a, b)), ITE(b <= c, false, And(Lt(a, b), Ge(a, c)))),
+                     (Tuple(Eq(a, b), Eq(a, c)), ITE(Eq(b, c), Eq(a, b), false)),
+                     (Tuple(Lt(a, b), Lt(-b, a)), ITE(b > 0, Lt(Abs(a), b), false)),
+                     (Tuple(Le(a, b), Le(-b, a)), ITE(b >= 0, Le(Abs(a), b), false)),
+                     )
+    return _matchers_and
+
+
+@cacheit
+def _simplify_patterns_and3():
+    """ Three-term patterns for And."""
+
+    from sympy.core import Wild
+    from sympy.core.relational import Eq, Ge, Gt
+
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    # Relationals patterns should be in alphabetical order
+    # (pattern1, pattern2, pattern3, simplified)
+    # Do not use Le, Lt
+    _matchers_and = ((Tuple(Ge(a, b), Ge(b, c), Gt(c, a)), false),
+                     (Tuple(Ge(a, b), Gt(b, c), Gt(c, a)), false),
+                     (Tuple(Gt(a, b), Gt(b, c), Gt(c, a)), false),
+                     # (Tuple(Ge(c, a), Gt(a, b), Gt(b, c)), S.false),
+                     # Lower bound relations
+                     # Commented out combinations that does not simplify
+                     (Tuple(Ge(a, b), Ge(a, c), Ge(b, c)), And(Ge(a, b), Ge(b, c))),
+                     (Tuple(Ge(a, b), Ge(a, c), Gt(b, c)), And(Ge(a, b), Gt(b, c))),
+                     # (Tuple(Ge(a, b), Gt(a, c), Ge(b, c)), And(Ge(a, b), Ge(b, c))),
+                     (Tuple(Ge(a, b), Gt(a, c), Gt(b, c)), And(Ge(a, b), Gt(b, c))),
+                     # (Tuple(Gt(a, b), Ge(a, c), Ge(b, c)), And(Gt(a, b), Ge(b, c))),
+                     (Tuple(Ge(a, c), Gt(a, b), Gt(b, c)), And(Gt(a, b), Gt(b, c))),
+                     (Tuple(Ge(b, c), Gt(a, b), Gt(a, c)), And(Gt(a, b), Ge(b, c))),
+                     (Tuple(Gt(a, b), Gt(a, c), Gt(b, c)), And(Gt(a, b), Gt(b, c))),
+                     # Upper bound relations
+                     # Commented out combinations that does not simplify
+                     (Tuple(Ge(b, a), Ge(c, a), Ge(b, c)), And(Ge(c, a), Ge(b, c))),
+                     (Tuple(Ge(b, a), Ge(c, a), Gt(b, c)), And(Ge(c, a), Gt(b, c))),
+                     # (Tuple(Ge(b, a), Gt(c, a), Ge(b, c)), And(Gt(c, a), Ge(b, c))),
+                     (Tuple(Ge(b, a), Gt(c, a), Gt(b, c)), And(Gt(c, a), Gt(b, c))),
+                     # (Tuple(Gt(b, a), Ge(c, a), Ge(b, c)), And(Ge(c, a), Ge(b, c))),
+                     (Tuple(Ge(c, a), Gt(b, a), Gt(b, c)), And(Ge(c, a), Gt(b, c))),
+                     (Tuple(Ge(b, c), Gt(b, a), Gt(c, a)), And(Gt(c, a), Ge(b, c))),
+                     (Tuple(Gt(b, a), Gt(c, a), Gt(b, c)), And(Gt(c, a), Gt(b, c))),
+                     # Circular relation
+                     (Tuple(Ge(a, b), Ge(b, c), Ge(c, a)), And(Eq(a, b), Eq(b, c))),
+                     )
+    return _matchers_and
+
+
+@cacheit
+def _simplify_patterns_or():
+    """ Two-term patterns for Or."""
+
+    from sympy.core import Wild
+    from sympy.core.relational import Eq, Ne, Ge, Gt, Le, Lt
+    from sympy.functions.elementary.complexes import Abs
+    from sympy.functions.elementary.miscellaneous import Min, Max
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    # Relationals patterns should be in alphabetical order
+    # (pattern1, pattern2, simplified)
+    # Do not use Ge, Gt
+    _matchers_or = ((Tuple(Le(b, a), Le(a, b)), true),
+                    #(Tuple(Le(b, a), Lt(a, b)), true),
+                    (Tuple(Le(b, a), Ne(a, b)), true),
+                    #(Tuple(Le(a, b), Lt(b, a)), true),
+                    #(Tuple(Le(a, b), Ne(a, b)), true),
+                    #(Tuple(Eq(a, b), Le(b, a)), Ge(a, b)),
+                    #(Tuple(Eq(a, b), Lt(b, a)), Ge(a, b)),
+                    (Tuple(Eq(a, b), Le(a, b)), Le(a, b)),
+                    (Tuple(Eq(a, b), Lt(a, b)), Le(a, b)),
+                    #(Tuple(Le(b, a), Lt(b, a)), Ge(a, b)),
+                    (Tuple(Lt(b, a), Lt(a, b)), Ne(a, b)),
+                    (Tuple(Lt(b, a), Ne(a, b)), Ne(a, b)),
+                    (Tuple(Le(a, b), Lt(a, b)), Le(a, b)),
+                    #(Tuple(Lt(a, b), Ne(a, b)), Ne(a, b)),
+                    (Tuple(Eq(a, b), Ne(a, c)), ITE(Eq(b, c), true, Ne(a, c))),
+                    (Tuple(Ne(a, b), Ne(a, c)), ITE(Eq(b, c), Ne(a, b), true)),
+                    # Min/Max/ITE
+                    (Tuple(Le(b, a), Le(c, a)), Ge(a, Min(b, c))),
+                    #(Tuple(Ge(b, a), Ge(c, a)), Ge(Min(b, c), a)),
+                    (Tuple(Le(b, a), Lt(c, a)), ITE(b > c, Lt(c, a), Le(b, a))),
+                    (Tuple(Lt(b, a), Lt(c, a)), Gt(a, Min(b, c))),
+                    #(Tuple(Gt(b, a), Gt(c, a)), Gt(Min(b, c), a)),
+                    (Tuple(Le(a, b), Le(a, c)), Le(a, Max(b, c))),
+                    #(Tuple(Le(b, a), Le(c, a)), Le(Max(b, c), a)),
+                    (Tuple(Le(a, b), Lt(a, c)), ITE(b >= c, Le(a, b), Lt(a, c))),
+                    (Tuple(Lt(a, b), Lt(a, c)), Lt(a, Max(b, c))),
+                    #(Tuple(Lt(b, a), Lt(c, a)), Lt(Max(b, c), a)),
+                    (Tuple(Le(a, b), Le(c, a)), ITE(b >= c, true, Or(Le(a, b), Ge(a, c)))),
+                    (Tuple(Le(c, a), Le(a, b)), ITE(b >= c, true, Or(Le(a, b), Ge(a, c)))),
+                    (Tuple(Lt(a, b), Lt(c, a)), ITE(b > c, true, Or(Lt(a, b), Gt(a, c)))),
+                    (Tuple(Lt(c, a), Lt(a, b)), ITE(b > c, true, Or(Lt(a, b), Gt(a, c)))),
+                    (Tuple(Le(a, b), Lt(c, a)), ITE(b >= c, true, Or(Le(a, b), Gt(a, c)))),
+                    (Tuple(Le(c, a), Lt(a, b)), ITE(b >= c, true, Or(Lt(a, b), Ge(a, c)))),
+                    (Tuple(Lt(b, a), Lt(a, -b)), ITE(b >= 0, Gt(Abs(a), b), true)),
+                    (Tuple(Le(b, a), Le(a, -b)), ITE(b > 0, Ge(Abs(a), b), true)),
+                    )
+    return _matchers_or
+
+
+@cacheit
+def _simplify_patterns_xor():
+    """ Two-term patterns for Xor."""
+
+    from sympy.functions.elementary.miscellaneous import Min, Max
+    from sympy.core import Wild
+    from sympy.core.relational import Eq, Ne, Ge, Gt, Le, Lt
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    # Relationals patterns should be in alphabetical order
+    # (pattern1, pattern2, simplified)
+    # Do not use Ge, Gt
+    _matchers_xor = (#(Tuple(Le(b, a), Lt(a, b)), true),
+                     #(Tuple(Lt(b, a), Le(a, b)), true),
+                     #(Tuple(Eq(a, b), Le(b, a)), Gt(a, b)),
+                     #(Tuple(Eq(a, b), Lt(b, a)), Ge(a, b)),
+                     (Tuple(Eq(a, b), Le(a, b)), Lt(a, b)),
+                     (Tuple(Eq(a, b), Lt(a, b)), Le(a, b)),
+                     (Tuple(Le(a, b), Lt(a, b)), Eq(a, b)),
+                     (Tuple(Le(a, b), Le(b, a)), Ne(a, b)),
+                     (Tuple(Le(b, a), Ne(a, b)), Le(a, b)),
+                     # (Tuple(Lt(b, a), Lt(a, b)), Ne(a, b)),
+                     (Tuple(Lt(b, a), Ne(a, b)), Lt(a, b)),
+                     # (Tuple(Le(a, b), Lt(a, b)), Eq(a, b)),
+                     # (Tuple(Le(a, b), Ne(a, b)), Ge(a, b)),
+                     # (Tuple(Lt(a, b), Ne(a, b)), Gt(a, b)),
+                     # Min/Max/ITE
+                     (Tuple(Le(b, a), Le(c, a)),
+                      And(Ge(a, Min(b, c)), Lt(a, Max(b, c)))),
+                     (Tuple(Le(b, a), Lt(c, a)),
+                      ITE(b > c, And(Gt(a, c), Lt(a, b)),
+                          And(Ge(a, b), Le(a, c)))),
+                     (Tuple(Lt(b, a), Lt(c, a)),
+                      And(Gt(a, Min(b, c)), Le(a, Max(b, c)))),
+                     (Tuple(Le(a, b), Le(a, c)),
+                      And(Le(a, Max(b, c)), Gt(a, Min(b, c)))),
+                     (Tuple(Le(a, b), Lt(a, c)),
+                      ITE(b < c, And(Lt(a, c), Gt(a, b)),
+                          And(Le(a, b), Ge(a, c)))),
+                     (Tuple(Lt(a, b), Lt(a, c)),
+                      And(Lt(a, Max(b, c)), Ge(a, Min(b, c)))),
+                     )
+    return _matchers_xor
+
+
+def simplify_univariate(expr):
+    """return a simplified version of univariate boolean expression, else ``expr``"""
+    from sympy.functions.elementary.piecewise import Piecewise
+    from sympy.core.relational import Eq, Ne
+    if not isinstance(expr, BooleanFunction):
+        return expr
+    if expr.atoms(Eq, Ne):
+        return expr
+    c = expr
+    free = c.free_symbols
+    if len(free) != 1:
+        return c
+    x = free.pop()
+    ok, i = Piecewise((0, c), evaluate=False
+            )._intervals(x, err_on_Eq=True)
+    if not ok:
+        return c
+    if not i:
+        return false
+    args = []
+    for a, b, _, _ in i:
+        if a is S.NegativeInfinity:
+            if b is S.Infinity:
+                c = true
+            else:
+                if c.subs(x, b) == True:
+                    c = (x <= b)
+                else:
+                    c = (x < b)
+        else:
+            incl_a = (c.subs(x, a) == True)
+            incl_b = (c.subs(x, b) == True)
+            if incl_a and incl_b:
+                if b.is_infinite:
+                    c = (x >= a)
+                else:
+                    c = And(a <= x, x <= b)
+            elif incl_a:
+                c = And(a <= x, x < b)
+            elif incl_b:
+                if b.is_infinite:
+                    c = (x > a)
+                else:
+                    c = And(a < x, x <= b)
+            else:
+                c = And(a < x, x < b)
+        args.append(c)
+    return Or(*args)
+
+
+# Classes corresponding to logic gates
+# Used in gateinputcount method
+BooleanGates = (And, Or, Xor, Nand, Nor, Not, Xnor, ITE)
+
+def gateinputcount(expr):
+    """
+    Return the total number of inputs for the logic gates realizing the
+    Boolean expression.
+
+    Returns
+    =======
+
+    int
+        Number of gate inputs
+
+    Note
+    ====
+
+    Not all Boolean functions count as gate here, only those that are
+    considered to be standard gates. These are: :py:class:`~.And`,
+    :py:class:`~.Or`, :py:class:`~.Xor`, :py:class:`~.Not`, and
+    :py:class:`~.ITE` (multiplexer). :py:class:`~.Nand`, :py:class:`~.Nor`,
+    and :py:class:`~.Xnor` will be evaluated to ``Not(And())`` etc.
+
+    Examples
+    ========
+
+    >>> from sympy.logic import And, Or, Nand, Not, gateinputcount
+    >>> from sympy.abc import x, y, z
+    >>> expr = And(x, y)
+    >>> gateinputcount(expr)
+    2
+    >>> gateinputcount(Or(expr, z))
+    4
+
+    Note that ``Nand`` is automatically evaluated to ``Not(And())`` so
+
+    >>> gateinputcount(Nand(x, y, z))
+    4
+    >>> gateinputcount(Not(And(x, y, z)))
+    4
+
+    Although this can be avoided by using ``evaluate=False``
+
+    >>> gateinputcount(Nand(x, y, z, evaluate=False))
+    3
+
+    Also note that a comparison will count as a Boolean variable:
+
+    >>> gateinputcount(And(x > z, y >= 2))
+    2
+
+    As will a symbol:
+    >>> gateinputcount(x)
+    0
+
+    """
+    if not isinstance(expr, Boolean):
+        raise TypeError("Expression must be Boolean")
+    if isinstance(expr, BooleanGates):
+        return len(expr.args) + sum(gateinputcount(x) for x in expr.args)
+    return 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/inference.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/inference.py
new file mode 100644
index 0000000000000000000000000000000000000000..c3798231c09ae351ea7e7026d622b834fea3e3fa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/inference.py
@@ -0,0 +1,340 @@
+"""Inference in propositional logic"""
+
+from sympy.logic.boolalg import And, Not, conjuncts, to_cnf, BooleanFunction
+from sympy.core.sorting import ordered
+from sympy.core.sympify import sympify
+from sympy.external.importtools import import_module
+
+
+def literal_symbol(literal):
+    """
+    The symbol in this literal (without the negation).
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A
+    >>> from sympy.logic.inference import literal_symbol
+    >>> literal_symbol(A)
+    A
+    >>> literal_symbol(~A)
+    A
+
+    """
+
+    if literal is True or literal is False:
+        return literal
+    elif literal.is_Symbol:
+        return literal
+    elif literal.is_Not:
+        return literal_symbol(literal.args[0])
+    else:
+        raise ValueError("Argument must be a boolean literal.")
+
+
+def satisfiable(expr, algorithm=None, all_models=False, minimal=False, use_lra_theory=False):
+    """
+    Check satisfiability of a propositional sentence.
+    Returns a model when it succeeds.
+    Returns {true: true} for trivially true expressions.
+
+    On setting all_models to True, if given expr is satisfiable then
+    returns a generator of models. However, if expr is unsatisfiable
+    then returns a generator containing the single element False.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B
+    >>> from sympy.logic.inference import satisfiable
+    >>> satisfiable(A & ~B)
+    {A: True, B: False}
+    >>> satisfiable(A & ~A)
+    False
+    >>> satisfiable(True)
+    {True: True}
+    >>> next(satisfiable(A & ~A, all_models=True))
+    False
+    >>> models = satisfiable((A >> B) & B, all_models=True)
+    >>> next(models)
+    {A: False, B: True}
+    >>> next(models)
+    {A: True, B: True}
+    >>> def use_models(models):
+    ...     for model in models:
+    ...         if model:
+    ...             # Do something with the model.
+    ...             print(model)
+    ...         else:
+    ...             # Given expr is unsatisfiable.
+    ...             print("UNSAT")
+    >>> use_models(satisfiable(A >> ~A, all_models=True))
+    {A: False}
+    >>> use_models(satisfiable(A ^ A, all_models=True))
+    UNSAT
+
+    """
+    if use_lra_theory:
+        if algorithm is not None and algorithm != "dpll2":
+            raise ValueError(f"Currently only dpll2 can handle using lra theory. {algorithm} is not handled.")
+        algorithm = "dpll2"
+
+    if algorithm is None or algorithm == "pycosat":
+        pycosat = import_module('pycosat')
+        if pycosat is not None:
+            algorithm = "pycosat"
+        else:
+            if algorithm == "pycosat":
+                raise ImportError("pycosat module is not present")
+            # Silently fall back to dpll2 if pycosat
+            # is not installed
+            algorithm = "dpll2"
+
+    if algorithm=="minisat22":
+        pysat = import_module('pysat')
+        if pysat is None:
+            algorithm = "dpll2"
+
+    if algorithm=="z3":
+        z3 = import_module('z3')
+        if z3 is None:
+            algorithm = "dpll2"
+
+    if algorithm == "dpll":
+        from sympy.logic.algorithms.dpll import dpll_satisfiable
+        return dpll_satisfiable(expr)
+    elif algorithm == "dpll2":
+        from sympy.logic.algorithms.dpll2 import dpll_satisfiable
+        return dpll_satisfiable(expr, all_models, use_lra_theory=use_lra_theory)
+    elif algorithm == "pycosat":
+        from sympy.logic.algorithms.pycosat_wrapper import pycosat_satisfiable
+        return pycosat_satisfiable(expr, all_models)
+    elif algorithm == "minisat22":
+        from sympy.logic.algorithms.minisat22_wrapper import minisat22_satisfiable
+        return minisat22_satisfiable(expr, all_models, minimal)
+    elif algorithm == "z3":
+        from sympy.logic.algorithms.z3_wrapper import z3_satisfiable
+        return z3_satisfiable(expr, all_models)
+
+    raise NotImplementedError
+
+
+def valid(expr):
+    """
+    Check validity of a propositional sentence.
+    A valid propositional sentence is True under every assignment.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B
+    >>> from sympy.logic.inference import valid
+    >>> valid(A | ~A)
+    True
+    >>> valid(A | B)
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Validity
+
+    """
+    return not satisfiable(Not(expr))
+
+
+def pl_true(expr, model=None, deep=False):
+    """
+    Returns whether the given assignment is a model or not.
+
+    If the assignment does not specify the value for every proposition,
+    this may return None to indicate 'not obvious'.
+
+    Parameters
+    ==========
+
+    model : dict, optional, default: {}
+        Mapping of symbols to boolean values to indicate assignment.
+    deep: boolean, optional, default: False
+        Gives the value of the expression under partial assignments
+        correctly. May still return None to indicate 'not obvious'.
+
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B
+    >>> from sympy.logic.inference import pl_true
+    >>> pl_true( A & B, {A: True, B: True})
+    True
+    >>> pl_true(A & B, {A: False})
+    False
+    >>> pl_true(A & B, {A: True})
+    >>> pl_true(A & B, {A: True}, deep=True)
+    >>> pl_true(A >> (B >> A))
+    >>> pl_true(A >> (B >> A), deep=True)
+    True
+    >>> pl_true(A & ~A)
+    >>> pl_true(A & ~A, deep=True)
+    False
+    >>> pl_true(A & B & (~A | ~B), {A: True})
+    >>> pl_true(A & B & (~A | ~B), {A: True}, deep=True)
+    False
+
+    """
+
+    from sympy.core.symbol import Symbol
+
+    boolean = (True, False)
+
+    def _validate(expr):
+        if isinstance(expr, Symbol) or expr in boolean:
+            return True
+        if not isinstance(expr, BooleanFunction):
+            return False
+        return all(_validate(arg) for arg in expr.args)
+
+    if expr in boolean:
+        return expr
+    expr = sympify(expr)
+    if not _validate(expr):
+        raise ValueError("%s is not a valid boolean expression" % expr)
+    if not model:
+        model = {}
+    model = {k: v for k, v in model.items() if v in boolean}
+    result = expr.subs(model)
+    if result in boolean:
+        return bool(result)
+    if deep:
+        model = dict.fromkeys(result.atoms(), True)
+        if pl_true(result, model):
+            if valid(result):
+                return True
+        else:
+            if not satisfiable(result):
+                return False
+    return None
+
+
+def entails(expr, formula_set=None):
+    """
+    Check whether the given expr_set entail an expr.
+    If formula_set is empty then it returns the validity of expr.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import A, B, C
+    >>> from sympy.logic.inference import entails
+    >>> entails(A, [A >> B, B >> C])
+    False
+    >>> entails(C, [A >> B, B >> C, A])
+    True
+    >>> entails(A >> B)
+    False
+    >>> entails(A >> (B >> A))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Logical_consequence
+
+    """
+    if formula_set:
+        formula_set = list(formula_set)
+    else:
+        formula_set = []
+    formula_set.append(Not(expr))
+    return not satisfiable(And(*formula_set))
+
+
+class KB:
+    """Base class for all knowledge bases"""
+    def __init__(self, sentence=None):
+        self.clauses_ = set()
+        if sentence:
+            self.tell(sentence)
+
+    def tell(self, sentence):
+        raise NotImplementedError
+
+    def ask(self, query):
+        raise NotImplementedError
+
+    def retract(self, sentence):
+        raise NotImplementedError
+
+    @property
+    def clauses(self):
+        return list(ordered(self.clauses_))
+
+
+class PropKB(KB):
+    """A KB for Propositional Logic.  Inefficient, with no indexing."""
+
+    def tell(self, sentence):
+        """Add the sentence's clauses to the KB
+
+        Examples
+        ========
+
+        >>> from sympy.logic.inference import PropKB
+        >>> from sympy.abc import x, y
+        >>> l = PropKB()
+        >>> l.clauses
+        []
+
+        >>> l.tell(x | y)
+        >>> l.clauses
+        [x | y]
+
+        >>> l.tell(y)
+        >>> l.clauses
+        [y, x | y]
+
+        """
+        for c in conjuncts(to_cnf(sentence)):
+            self.clauses_.add(c)
+
+    def ask(self, query):
+        """Checks if the query is true given the set of clauses.
+
+        Examples
+        ========
+
+        >>> from sympy.logic.inference import PropKB
+        >>> from sympy.abc import x, y
+        >>> l = PropKB()
+        >>> l.tell(x & ~y)
+        >>> l.ask(x)
+        True
+        >>> l.ask(y)
+        False
+
+        """
+        return entails(query, self.clauses_)
+
+    def retract(self, sentence):
+        """Remove the sentence's clauses from the KB
+
+        Examples
+        ========
+
+        >>> from sympy.logic.inference import PropKB
+        >>> from sympy.abc import x, y
+        >>> l = PropKB()
+        >>> l.clauses
+        []
+
+        >>> l.tell(x | y)
+        >>> l.clauses
+        [x | y]
+
+        >>> l.retract(x | y)
+        >>> l.clauses
+        []
+
+        """
+        for c in conjuncts(to_cnf(sentence)):
+            self.clauses_.discard(c)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_boolalg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_boolalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..88cdd647fdcc723faee328f71df96030841a3edb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_boolalg.py
@@ -0,0 +1,1367 @@
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+from sympy.core.numbers import oo
+from sympy.core.relational import Equality, Eq, Ne
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.functions import Piecewise
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.sets.sets import Interval, Union
+from sympy.sets.contains import Contains
+from sympy.simplify.simplify import simplify
+from sympy.logic.boolalg import (
+    And, Boolean, Equivalent, ITE, Implies, Nand, Nor, Not, Or,
+    POSform, SOPform, Xor, Xnor, conjuncts, disjuncts,
+    distribute_or_over_and, distribute_and_over_or,
+    eliminate_implications, is_nnf, is_cnf, is_dnf, simplify_logic,
+    to_nnf, to_cnf, to_dnf, to_int_repr, bool_map, true, false,
+    BooleanAtom, is_literal, term_to_integer,
+    truth_table, as_Boolean, to_anf, is_anf, distribute_xor_over_and,
+    anf_coeffs, ANFform, bool_minterm, bool_maxterm, bool_monomial,
+    _check_pair, _convert_to_varsSOP, _convert_to_varsPOS, Exclusive,
+    gateinputcount)
+from sympy.assumptions.cnf import CNF
+
+from sympy.testing.pytest import raises, XFAIL, slow
+
+from itertools import combinations, permutations, product
+
+A, B, C, D = symbols('A:D')
+a, b, c, d, e, w, x, y, z = symbols('a:e w:z')
+
+
+def test_overloading():
+    """Test that |, & are overloaded as expected"""
+
+    assert A & B == And(A, B)
+    assert A | B == Or(A, B)
+    assert (A & B) | C == Or(And(A, B), C)
+    assert A >> B == Implies(A, B)
+    assert A << B == Implies(B, A)
+    assert ~A == Not(A)
+    assert A ^ B == Xor(A, B)
+
+
+def test_And():
+    assert And() is true
+    assert And(A) == A
+    assert And(True) is true
+    assert And(False) is false
+    assert And(True, True) is true
+    assert And(True, False) is false
+    assert And(False, False) is false
+    assert And(True, A) == A
+    assert And(False, A) is false
+    assert And(True, True, True) is true
+    assert And(True, True, A) == A
+    assert And(True, False, A) is false
+    assert And(1, A) == A
+    raises(TypeError, lambda: And(2, A))
+    assert And(A < 1, A >= 1) is false
+    e = A > 1
+    assert And(e, e.canonical) == e.canonical
+    g, l, ge, le = A > B, B < A, A >= B, B <= A
+    assert And(g, l, ge, le) == And(ge, g)
+    assert {And(*i) for i in permutations((l, g, le, ge))} == {And(ge, g)}
+    assert And(And(Eq(a, 0), Eq(b, 0)), And(Ne(a, 0), Eq(c, 0))) is false
+
+
+def test_Or():
+    assert Or() is false
+    assert Or(A) == A
+    assert Or(True) is true
+    assert Or(False) is false
+    assert Or(True, True) is true
+    assert Or(True, False) is true
+    assert Or(False, False) is false
+    assert Or(True, A) is true
+    assert Or(False, A) == A
+    assert Or(True, False, False) is true
+    assert Or(True, False, A) is true
+    assert Or(False, False, A) == A
+    assert Or(1, A) is true
+    raises(TypeError, lambda: Or(2, A))
+    assert Or(A < 1, A >= 1) is true
+    e = A > 1
+    assert Or(e, e.canonical) == e
+    g, l, ge, le = A > B, B < A, A >= B, B <= A
+    assert Or(g, l, ge, le) == Or(g, ge)
+
+
+def test_Xor():
+    assert Xor() is false
+    assert Xor(A) == A
+    assert Xor(A, A) is false
+    assert Xor(True, A, A) is true
+    assert Xor(A, A, A, A, A) == A
+    assert Xor(True, False, False, A, B) == ~Xor(A, B)
+    assert Xor(True) is true
+    assert Xor(False) is false
+    assert Xor(True, True) is false
+    assert Xor(True, False) is true
+    assert Xor(False, False) is false
+    assert Xor(True, A) == ~A
+    assert Xor(False, A) == A
+    assert Xor(True, False, False) is true
+    assert Xor(True, False, A) == ~A
+    assert Xor(False, False, A) == A
+    assert isinstance(Xor(A, B), Xor)
+    assert Xor(A, B, Xor(C, D)) == Xor(A, B, C, D)
+    assert Xor(A, B, Xor(B, C)) == Xor(A, C)
+    assert Xor(A < 1, A >= 1, B) == Xor(0, 1, B) == Xor(1, 0, B)
+    e = A > 1
+    assert Xor(e, e.canonical) == Xor(0, 0) == Xor(1, 1)
+
+
+def test_rewrite_as_And():
+    expr = x ^ y
+    assert expr.rewrite(And) == (x | y) & (~x | ~y)
+
+
+def test_rewrite_as_Or():
+    expr = x ^ y
+    assert expr.rewrite(Or) == (x & ~y) | (y & ~x)
+
+
+def test_rewrite_as_Nand():
+    expr = (y & z) | (z & ~w)
+    assert expr.rewrite(Nand) == ~(~(y & z) & ~(z & ~w))
+
+
+def test_rewrite_as_Nor():
+    expr = z & (y | ~w)
+    assert expr.rewrite(Nor) == ~(~z | ~(y | ~w))
+
+
+def test_Not():
+    raises(TypeError, lambda: Not(True, False))
+    assert Not(True) is false
+    assert Not(False) is true
+    assert Not(0) is true
+    assert Not(1) is false
+    assert Not(2) is false
+
+
+def test_Nand():
+    assert Nand() is false
+    assert Nand(A) == ~A
+    assert Nand(True) is false
+    assert Nand(False) is true
+    assert Nand(True, True) is false
+    assert Nand(True, False) is true
+    assert Nand(False, False) is true
+    assert Nand(True, A) == ~A
+    assert Nand(False, A) is true
+    assert Nand(True, True, True) is false
+    assert Nand(True, True, A) == ~A
+    assert Nand(True, False, A) is true
+
+
+def test_Nor():
+    assert Nor() is true
+    assert Nor(A) == ~A
+    assert Nor(True) is false
+    assert Nor(False) is true
+    assert Nor(True, True) is false
+    assert Nor(True, False) is false
+    assert Nor(False, False) is true
+    assert Nor(True, A) is false
+    assert Nor(False, A) == ~A
+    assert Nor(True, True, True) is false
+    assert Nor(True, True, A) is false
+    assert Nor(True, False, A) is false
+
+
+def test_Xnor():
+    assert Xnor() is true
+    assert Xnor(A) == ~A
+    assert Xnor(A, A) is true
+    assert Xnor(True, A, A) is false
+    assert Xnor(A, A, A, A, A) == ~A
+    assert Xnor(True) is false
+    assert Xnor(False) is true
+    assert Xnor(True, True) is true
+    assert Xnor(True, False) is false
+    assert Xnor(False, False) is true
+    assert Xnor(True, A) == A
+    assert Xnor(False, A) == ~A
+    assert Xnor(True, False, False) is false
+    assert Xnor(True, False, A) == A
+    assert Xnor(False, False, A) == ~A
+
+
+def test_Implies():
+    raises(ValueError, lambda: Implies(A, B, C))
+    assert Implies(True, True) is true
+    assert Implies(True, False) is false
+    assert Implies(False, True) is true
+    assert Implies(False, False) is true
+    assert Implies(0, A) is true
+    assert Implies(1, 1) is true
+    assert Implies(1, 0) is false
+    assert A >> B == B << A
+    assert (A < 1) >> (A >= 1) == (A >= 1)
+    assert (A < 1) >> (S.One > A) is true
+    assert A >> A is true
+
+
+def test_Equivalent():
+    assert Equivalent(A, B) == Equivalent(B, A) == Equivalent(A, B, A)
+    assert Equivalent() is true
+    assert Equivalent(A, A) == Equivalent(A) is true
+    assert Equivalent(True, True) == Equivalent(False, False) is true
+    assert Equivalent(True, False) == Equivalent(False, True) is false
+    assert Equivalent(A, True) == A
+    assert Equivalent(A, False) == Not(A)
+    assert Equivalent(A, B, True) == A & B
+    assert Equivalent(A, B, False) == ~A & ~B
+    assert Equivalent(1, A) == A
+    assert Equivalent(0, A) == Not(A)
+    assert Equivalent(A, Equivalent(B, C)) != Equivalent(Equivalent(A, B), C)
+    assert Equivalent(A < 1, A >= 1) is false
+    assert Equivalent(A < 1, A >= 1, 0) is false
+    assert Equivalent(A < 1, A >= 1, 1) is false
+    assert Equivalent(A < 1, S.One > A) == Equivalent(1, 1) == Equivalent(0, 0)
+    assert Equivalent(Equality(A, B), Equality(B, A)) is true
+
+
+def test_Exclusive():
+    assert Exclusive(False, False, False) is true
+    assert Exclusive(True, False, False) is true
+    assert Exclusive(True, True, False) is false
+    assert Exclusive(True, True, True) is false
+
+
+def test_equals():
+    assert Not(Or(A, B)).equals(And(Not(A), Not(B))) is True
+    assert Equivalent(A, B).equals((A >> B) & (B >> A)) is True
+    assert ((A | ~B) & (~A | B)).equals((~A & ~B) | (A & B)) is True
+    assert (A >> B).equals(~A >> ~B) is False
+    assert (A >> (B >> A)).equals(A >> (C >> A)) is False
+    raises(NotImplementedError, lambda: (A & B).equals(A > B))
+
+
+def test_simplification_boolalg():
+    """
+    Test working of simplification methods.
+    """
+    set1 = [[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 1, 0]]
+    set2 = [[0, 0, 0], [0, 1, 0], [1, 0, 1], [1, 1, 1]]
+    assert SOPform([x, y, z], set1) == Or(And(Not(x), z), And(Not(z), x))
+    assert Not(SOPform([x, y, z], set2)) == \
+           Not(Or(And(Not(x), Not(z)), And(x, z)))
+    assert POSform([x, y, z], set1 + set2) is true
+    assert SOPform([x, y, z], set1 + set2) is true
+    assert SOPform([Dummy(), Dummy(), Dummy()], set1 + set2) is true
+
+    minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], [1, 0, 1, 1],
+                [1, 1, 1, 1]]
+    dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]]
+    assert (
+        SOPform([w, x, y, z], minterms, dontcares) ==
+        Or(And(y, z), And(Not(w), Not(x))))
+    assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z)
+
+    minterms = [1, 3, 7, 11, 15]
+    dontcares = [0, 2, 5]
+    assert (
+        SOPform([w, x, y, z], minterms, dontcares) ==
+        Or(And(y, z), And(Not(w), Not(x))))
+    assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z)
+
+    minterms = [1, [0, 0, 1, 1], 7, [1, 0, 1, 1],
+                [1, 1, 1, 1]]
+    dontcares = [0, [0, 0, 1, 0], 5]
+    assert (
+        SOPform([w, x, y, z], minterms, dontcares) ==
+        Or(And(y, z), And(Not(w), Not(x))))
+    assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z)
+
+    minterms = [1, {y: 1, z: 1}]
+    dontcares = [0, [0, 0, 1, 0], 5]
+    assert (
+        SOPform([w, x, y, z], minterms, dontcares) ==
+        Or(And(y, z), And(Not(w), Not(x))))
+    assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z)
+
+    minterms = [{y: 1, z: 1}, 1]
+    dontcares = [[0, 0, 0, 0]]
+
+    minterms = [[0, 0, 0]]
+    raises(ValueError, lambda: SOPform([w, x, y, z], minterms))
+    raises(ValueError, lambda: POSform([w, x, y, z], minterms))
+
+    raises(TypeError, lambda: POSform([w, x, y, z], ["abcdefg"]))
+
+    # test simplification
+    ans = And(A, Or(B, C))
+    assert simplify_logic(A & (B | C)) == ans
+    assert simplify_logic((A & B) | (A & C)) == ans
+    assert simplify_logic(Implies(A, B)) == Or(Not(A), B)
+    assert simplify_logic(Equivalent(A, B)) == \
+           Or(And(A, B), And(Not(A), Not(B)))
+    assert simplify_logic(And(Equality(A, 2), C)) == And(Equality(A, 2), C)
+    assert simplify_logic(And(Equality(A, 2), A)) == And(Equality(A, 2), A)
+    assert simplify_logic(And(Equality(A, B), C)) == And(Equality(A, B), C)
+    assert simplify_logic(Or(And(Equality(A, 3), B), And(Equality(A, 3), C))) \
+           == And(Equality(A, 3), Or(B, C))
+    b = (~x & ~y & ~z) | (~x & ~y & z)
+    e = And(A, b)
+    assert simplify_logic(e) == A & ~x & ~y
+    raises(ValueError, lambda: simplify_logic(A & (B | C), form='blabla'))
+    assert simplify(Or(x <= y, And(x < y, z))) == (x <= y)
+    assert simplify(Or(x <= y, And(y > x, z))) == (x <= y)
+    assert simplify(Or(x >= y, And(y < x, z))) == (x >= y)
+
+    # Check that expressions with nine variables or more are not simplified
+    # (without the force-flag)
+    a, b, c, d, e, f, g, h, j = symbols('a b c d e f g h j')
+    expr = a & b & c & d & e & f & g & h & j | \
+           a & b & c & d & e & f & g & h & ~j
+    # This expression can be simplified to get rid of the j variables
+    assert simplify_logic(expr) == expr
+
+    # Test dontcare
+    assert simplify_logic((a & b) | c | d, dontcare=(a & b)) == c | d
+
+    # check input
+    ans = SOPform([x, y], [[1, 0]])
+    assert SOPform([x, y], [[1, 0]]) == ans
+    assert POSform([x, y], [[1, 0]]) == ans
+
+    raises(ValueError, lambda: SOPform([x], [[1]], [[1]]))
+    assert SOPform([x], [[1]], [[0]]) is true
+    assert SOPform([x], [[0]], [[1]]) is true
+    assert SOPform([x], [], []) is false
+
+    raises(ValueError, lambda: POSform([x], [[1]], [[1]]))
+    assert POSform([x], [[1]], [[0]]) is true
+    assert POSform([x], [[0]], [[1]]) is true
+    assert POSform([x], [], []) is false
+
+    # check working of simplify
+    assert simplify((A & B) | (A & C)) == And(A, Or(B, C))
+    assert simplify(And(x, Not(x))) == False
+    assert simplify(Or(x, Not(x))) == True
+    assert simplify(And(Eq(x, 0), Eq(x, y))) == And(Eq(x, 0), Eq(y, 0))
+    assert And(Eq(x - 1, 0), Eq(x, y)).simplify() == And(Eq(x, 1), Eq(y, 1))
+    assert And(Ne(x - 1, 0), Ne(x, y)).simplify() == And(Ne(x, 1), Ne(x, y))
+    assert And(Eq(x - 1, 0), Ne(x, y)).simplify() == And(Eq(x, 1), Ne(y, 1))
+    assert And(Eq(x - 1, 0), Eq(x, z + y), Eq(y + x, 0)).simplify(
+    ) == And(Eq(x, 1), Eq(y, -1), Eq(z, 2))
+    assert And(Eq(x - 1, 0), Eq(x + 2, 3)).simplify() == Eq(x, 1)
+    assert And(Ne(x - 1, 0), Ne(x + 2, 3)).simplify() == Ne(x, 1)
+    assert And(Eq(x - 1, 0), Eq(x + 2, 2)).simplify() == False
+    assert And(Ne(x - 1, 0), Ne(x + 2, 2)).simplify(
+    ) == And(Ne(x, 1), Ne(x, 0))
+    assert simplify(Xor(x, ~x)) == True
+
+
+def test_bool_map():
+    """
+    Test working of bool_map function.
+    """
+
+    minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], [1, 0, 1, 1],
+                [1, 1, 1, 1]]
+    assert bool_map(Not(Not(a)), a) == (a, {a: a})
+    assert bool_map(SOPform([w, x, y, z], minterms),
+                    POSform([w, x, y, z], minterms)) == \
+           (And(Or(Not(w), y), Or(Not(x), y), z), {x: x, w: w, z: z, y: y})
+    assert bool_map(SOPform([x, z, y], [[1, 0, 1]]),
+                    SOPform([a, b, c], [[1, 0, 1]])) != False
+    function1 = SOPform([x, z, y], [[1, 0, 1], [0, 0, 1]])
+    function2 = SOPform([a, b, c], [[1, 0, 1], [1, 0, 0]])
+    assert bool_map(function1, function2) == \
+           (function1, {y: a, z: b})
+    assert bool_map(Xor(x, y), ~Xor(x, y)) == False
+    assert bool_map(And(x, y), Or(x, y)) is None
+    assert bool_map(And(x, y), And(x, y, z)) is None
+    # issue 16179
+    assert bool_map(Xor(x, y, z), ~Xor(x, y, z)) == False
+    assert bool_map(Xor(a, x, y, z), ~Xor(a, x, y, z)) == False
+
+
+def test_bool_symbol():
+    """Test that mixing symbols with boolean values
+    works as expected"""
+
+    assert And(A, True) == A
+    assert And(A, True, True) == A
+    assert And(A, False) is false
+    assert And(A, True, False) is false
+    assert Or(A, True) is true
+    assert Or(A, False) == A
+
+
+def test_is_boolean():
+    assert isinstance(True, Boolean) is False
+    assert isinstance(true, Boolean) is True
+    assert 1 == True
+    assert 1 != true
+    assert (1 == true) is False
+    assert 0 == False
+    assert 0 != false
+    assert (0 == false) is False
+    assert true.is_Boolean is True
+    assert (A & B).is_Boolean
+    assert (A | B).is_Boolean
+    assert (~A).is_Boolean
+    assert (A ^ B).is_Boolean
+    assert A.is_Boolean != isinstance(A, Boolean)
+    assert isinstance(A, Boolean)
+
+
+def test_subs():
+    assert (A & B).subs(A, True) == B
+    assert (A & B).subs(A, False) is false
+    assert (A & B).subs(B, True) == A
+    assert (A & B).subs(B, False) is false
+    assert (A & B).subs({A: True, B: True}) is true
+    assert (A | B).subs(A, True) is true
+    assert (A | B).subs(A, False) == B
+    assert (A | B).subs(B, True) is true
+    assert (A | B).subs(B, False) == A
+    assert (A | B).subs({A: True, B: True}) is true
+
+
+"""
+we test for axioms of boolean algebra
+see https://en.wikipedia.org/wiki/Boolean_algebra_(structure)
+"""
+
+
+def test_commutative():
+    """Test for commutativity of And and Or"""
+    A, B = map(Boolean, symbols('A,B'))
+
+    assert A & B == B & A
+    assert A | B == B | A
+
+
+def test_and_associativity():
+    """Test for associativity of And"""
+
+    assert (A & B) & C == A & (B & C)
+
+
+def test_or_assicativity():
+    assert ((A | B) | C) == (A | (B | C))
+
+
+def test_double_negation():
+    a = Boolean()
+    assert ~(~a) == a
+
+
+# test methods
+
+def test_eliminate_implications():
+    assert eliminate_implications(Implies(A, B, evaluate=False)) == (~A) | B
+    assert eliminate_implications(
+        A >> (C >> Not(B))) == Or(Or(Not(B), Not(C)), Not(A))
+    assert eliminate_implications(Equivalent(A, B, C, D)) == \
+           (~A | B) & (~B | C) & (~C | D) & (~D | A)
+
+
+def test_conjuncts():
+    assert conjuncts(A & B & C) == {A, B, C}
+    assert conjuncts((A | B) & C) == {A | B, C}
+    assert conjuncts(A) == {A}
+    assert conjuncts(True) == {True}
+    assert conjuncts(False) == {False}
+
+
+def test_disjuncts():
+    assert disjuncts(A | B | C) == {A, B, C}
+    assert disjuncts((A | B) & C) == {(A | B) & C}
+    assert disjuncts(A) == {A}
+    assert disjuncts(True) == {True}
+    assert disjuncts(False) == {False}
+
+
+def test_distribute():
+    assert distribute_and_over_or(Or(And(A, B), C)) == And(Or(A, C), Or(B, C))
+    assert distribute_or_over_and(And(A, Or(B, C))) == Or(And(A, B), And(A, C))
+    assert distribute_xor_over_and(And(A, Xor(B, C))) == Xor(And(A, B), And(A, C))
+
+
+def test_to_anf():
+    x, y, z = symbols('x,y,z')
+    assert to_anf(And(x, y)) == And(x, y)
+    assert to_anf(Or(x, y)) == Xor(x, y, And(x, y))
+    assert to_anf(Or(Implies(x, y), And(x, y), y)) == \
+           Xor(x, True, x & y, remove_true=False)
+    assert to_anf(Or(Nand(x, y), Nor(x, y), Xnor(x, y), Implies(x, y))) == True
+    assert to_anf(Or(x, Not(y), Nor(x, z), And(x, y), Nand(y, z))) == \
+           Xor(True, And(y, z), And(x, y, z), remove_true=False)
+    assert to_anf(Xor(x, y)) == Xor(x, y)
+    assert to_anf(Not(x)) == Xor(x, True, remove_true=False)
+    assert to_anf(Nand(x, y)) == Xor(True, And(x, y), remove_true=False)
+    assert to_anf(Nor(x, y)) == Xor(x, y, True, And(x, y), remove_true=False)
+    assert to_anf(Implies(x, y)) == Xor(x, True, And(x, y), remove_true=False)
+    assert to_anf(Equivalent(x, y)) == Xor(x, y, True, remove_true=False)
+    assert to_anf(Nand(x | y, x >> y), deep=False) == \
+           Xor(True, And(Or(x, y), Implies(x, y)), remove_true=False)
+    assert to_anf(Nor(x ^ y, x & y), deep=False) == \
+           Xor(True, Or(Xor(x, y), And(x, y)), remove_true=False)
+    # issue 25218
+    assert to_anf(x ^ ~(x ^ y ^ ~y)) == False
+
+
+def test_to_nnf():
+    assert to_nnf(true) is true
+    assert to_nnf(false) is false
+    assert to_nnf(A) == A
+    assert to_nnf(A | ~A | B) is true
+    assert to_nnf(A & ~A & B) is false
+    assert to_nnf(A >> B) == ~A | B
+    assert to_nnf(Equivalent(A, B, C)) == (~A | B) & (~B | C) & (~C | A)
+    assert to_nnf(A ^ B ^ C) == \
+           (A | B | C) & (~A | ~B | C) & (A | ~B | ~C) & (~A | B | ~C)
+    assert to_nnf(ITE(A, B, C)) == (~A | B) & (A | C)
+    assert to_nnf(Not(A | B | C)) == ~A & ~B & ~C
+    assert to_nnf(Not(A & B & C)) == ~A | ~B | ~C
+    assert to_nnf(Not(A >> B)) == A & ~B
+    assert to_nnf(Not(Equivalent(A, B, C))) == And(Or(A, B, C), Or(~A, ~B, ~C))
+    assert to_nnf(Not(A ^ B ^ C)) == \
+           (~A | B | C) & (A | ~B | C) & (A | B | ~C) & (~A | ~B | ~C)
+    assert to_nnf(Not(ITE(A, B, C))) == (~A | ~B) & (A | ~C)
+    assert to_nnf((A >> B) ^ (B >> A)) == (A & ~B) | (~A & B)
+    assert to_nnf((A >> B) ^ (B >> A), False) == \
+           (~A | ~B | A | B) & ((A & ~B) | (~A & B))
+    assert ITE(A, 1, 0).to_nnf() == A
+    assert ITE(A, 0, 1).to_nnf() == ~A
+    # although ITE can hold non-Boolean, it will complain if
+    # an attempt is made to convert the ITE to Boolean nnf
+    raises(TypeError, lambda: ITE(A < 1, [1], B).to_nnf())
+
+
+def test_to_cnf():
+    assert to_cnf(~(B | C)) == And(Not(B), Not(C))
+    assert to_cnf((A & B) | C) == And(Or(A, C), Or(B, C))
+    assert to_cnf(A >> B) == (~A) | B
+    assert to_cnf(A >> (B & C)) == (~A | B) & (~A | C)
+    assert to_cnf(A & (B | C) | ~A & (B | C), True) == B | C
+    assert to_cnf(A & B) == And(A, B)
+
+    assert to_cnf(Equivalent(A, B)) == And(Or(A, Not(B)), Or(B, Not(A)))
+    assert to_cnf(Equivalent(A, B & C)) == \
+           (~A | B) & (~A | C) & (~B | ~C | A)
+    assert to_cnf(Equivalent(A, B | C), True) == \
+           And(Or(Not(B), A), Or(Not(C), A), Or(B, C, Not(A)))
+    assert to_cnf(A + 1) == A + 1
+
+
+def test_issue_18904():
+    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15 = symbols('x1:16')
+    eq = ((x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8 & x9) |
+          (x1 & x2 & x3 & x4 & x5 & x6 & x7 & x10 & x9) |
+          (x1 & x11 & x3 & x12 & x5 & x13 & x14 & x15 & x9))
+    assert is_cnf(to_cnf(eq))
+    raises(ValueError, lambda: to_cnf(eq, simplify=True))
+    for f, t in zip((And, Or), (to_cnf, to_dnf)):
+        eq = f(x1, x2, x3, x4, x5, x6, x7, x8, x9)
+        raises(ValueError, lambda: to_cnf(eq, simplify=True))
+        assert t(eq, simplify=True, force=True) == eq
+
+
+def test_issue_9949():
+    assert is_cnf(to_cnf((b > -5) | (a > 2) & (a < 4)))
+
+
+def test_to_CNF():
+    assert CNF.CNF_to_cnf(CNF.to_CNF(~(B | C))) == to_cnf(~(B | C))
+    assert CNF.CNF_to_cnf(CNF.to_CNF((A & B) | C)) == to_cnf((A & B) | C)
+    assert CNF.CNF_to_cnf(CNF.to_CNF(A >> B)) == to_cnf(A >> B)
+    assert CNF.CNF_to_cnf(CNF.to_CNF(A >> (B & C))) == to_cnf(A >> (B & C))
+    assert CNF.CNF_to_cnf(CNF.to_CNF(A & (B | C) | ~A & (B | C))) == to_cnf(A & (B | C) | ~A & (B | C))
+    assert CNF.CNF_to_cnf(CNF.to_CNF(A & B)) == to_cnf(A & B)
+
+
+def test_to_dnf():
+    assert to_dnf(~(B | C)) == And(Not(B), Not(C))
+    assert to_dnf(A & (B | C)) == Or(And(A, B), And(A, C))
+    assert to_dnf(A >> B) == (~A) | B
+    assert to_dnf(A >> (B & C)) == (~A) | (B & C)
+    assert to_dnf(A | B) == A | B
+
+    assert to_dnf(Equivalent(A, B), True) == \
+           Or(And(A, B), And(Not(A), Not(B)))
+    assert to_dnf(Equivalent(A, B & C), True) == \
+           Or(And(A, B, C), And(Not(A), Not(B)), And(Not(A), Not(C)))
+    assert to_dnf(A + 1) == A + 1
+
+
+def test_to_int_repr():
+    x, y, z = map(Boolean, symbols('x,y,z'))
+
+    def sorted_recursive(arg):
+        try:
+            return sorted(sorted_recursive(x) for x in arg)
+        except TypeError:  # arg is not a sequence
+            return arg
+
+    assert sorted_recursive(to_int_repr([x | y, z | x], [x, y, z])) == \
+           sorted_recursive([[1, 2], [1, 3]])
+    assert sorted_recursive(to_int_repr([x | y, z | ~x], [x, y, z])) == \
+           sorted_recursive([[1, 2], [3, -1]])
+
+
+def test_is_anf():
+    x, y = symbols('x,y')
+    assert is_anf(true) is True
+    assert is_anf(false) is True
+    assert is_anf(x) is True
+    assert is_anf(And(x, y)) is True
+    assert is_anf(Xor(x, y, And(x, y))) is True
+    assert is_anf(Xor(x, y, Or(x, y))) is False
+    assert is_anf(Xor(Not(x), y)) is False
+
+
+def test_is_nnf():
+    assert is_nnf(true) is True
+    assert is_nnf(A) is True
+    assert is_nnf(~A) is True
+    assert is_nnf(A & B) is True
+    assert is_nnf((A & B) | (~A & A) | (~B & B) | (~A & ~B), False) is True
+    assert is_nnf((A | B) & (~A | ~B)) is True
+    assert is_nnf(Not(Or(A, B))) is False
+    assert is_nnf(A ^ B) is False
+    assert is_nnf((A & B) | (~A & A) | (~B & B) | (~A & ~B), True) is False
+
+
+def test_is_cnf():
+    assert is_cnf(x) is True
+    assert is_cnf(x | y | z) is True
+    assert is_cnf(x & y & z) is True
+    assert is_cnf((x | y) & z) is True
+    assert is_cnf((x & y) | z) is False
+    assert is_cnf(~(x & y) | z) is False
+
+
+def test_is_dnf():
+    assert is_dnf(x) is True
+    assert is_dnf(x | y | z) is True
+    assert is_dnf(x & y & z) is True
+    assert is_dnf((x & y) | z) is True
+    assert is_dnf((x | y) & z) is False
+    assert is_dnf(~(x | y) & z) is False
+
+
+def test_ITE():
+    A, B, C = symbols('A:C')
+    assert ITE(True, False, True) is false
+    assert ITE(True, True, False) is true
+    assert ITE(False, True, False) is false
+    assert ITE(False, False, True) is true
+    assert isinstance(ITE(A, B, C), ITE)
+
+    A = True
+    assert ITE(A, B, C) == B
+    A = False
+    assert ITE(A, B, C) == C
+    B = True
+    assert ITE(And(A, B), B, C) == C
+    assert ITE(Or(A, False), And(B, True), False) is false
+    assert ITE(x, A, B) == Not(x)
+    assert ITE(x, B, A) == x
+    assert ITE(1, x, y) == x
+    assert ITE(0, x, y) == y
+    raises(TypeError, lambda: ITE(2, x, y))
+    raises(TypeError, lambda: ITE(1, [], y))
+    raises(TypeError, lambda: ITE(1, (), y))
+    raises(TypeError, lambda: ITE(1, y, []))
+    assert ITE(1, 1, 1) is S.true
+    assert isinstance(ITE(1, 1, 1, evaluate=False), ITE)
+
+    assert ITE(Eq(x, True), y, x) == ITE(x, y, x)
+    assert ITE(Eq(x, False), y, x) == ITE(~x, y, x)
+    assert ITE(Ne(x, True), y, x) == ITE(~x, y, x)
+    assert ITE(Ne(x, False), y, x) == ITE(x, y, x)
+    assert ITE(Eq(S.true, x), y, x) == ITE(x, y, x)
+    assert ITE(Eq(S.false, x), y, x) == ITE(~x, y, x)
+    assert ITE(Ne(S.true, x), y, x) == ITE(~x, y, x)
+    assert ITE(Ne(S.false, x), y, x) == ITE(x, y, x)
+    # 0 and 1 in the context are not treated as True/False
+    # so the equality must always be False since dissimilar
+    # objects cannot be equal
+    assert ITE(Eq(x, 0), y, x) == x
+    assert ITE(Eq(x, 1), y, x) == x
+    assert ITE(Ne(x, 0), y, x) == y
+    assert ITE(Ne(x, 1), y, x) == y
+    assert ITE(Eq(x, 0), y, z).subs(x, 0) == y
+    assert ITE(Eq(x, 0), y, z).subs(x, 1) == z
+    raises(ValueError, lambda: ITE(x > 1, y, x, z))
+
+
+def test_is_literal():
+    assert is_literal(True) is True
+    assert is_literal(False) is True
+    assert is_literal(A) is True
+    assert is_literal(~A) is True
+    assert is_literal(Or(A, B)) is False
+    assert is_literal(Q.zero(A)) is True
+    assert is_literal(Not(Q.zero(A))) is True
+    assert is_literal(Or(A, B)) is False
+    assert is_literal(And(Q.zero(A), Q.zero(B))) is False
+    assert is_literal(x < 3)
+    assert not is_literal(x + y < 3)
+
+
+def test_operators():
+    # Mostly test __and__, __rand__, and so on
+    assert True & A == A & True == A
+    assert False & A == A & False == False
+    assert A & B == And(A, B)
+    assert True | A == A | True == True
+    assert False | A == A | False == A
+    assert A | B == Or(A, B)
+    assert ~A == Not(A)
+    assert True >> A == A << True == A
+    assert False >> A == A << False == True
+    assert A >> True == True << A == True
+    assert A >> False == False << A == ~A
+    assert A >> B == B << A == Implies(A, B)
+    assert True ^ A == A ^ True == ~A
+    assert False ^ A == A ^ False == A
+    assert A ^ B == Xor(A, B)
+
+
+def test_true_false():
+    assert true is S.true
+    assert false is S.false
+    assert true is not True
+    assert false is not False
+    assert true
+    assert not false
+    assert true == True
+    assert false == False
+    assert not (true == False)
+    assert not (false == True)
+    assert not (true == false)
+
+    assert hash(true) == hash(True)
+    assert hash(false) == hash(False)
+    assert len({true, True}) == len({false, False}) == 1
+
+    assert isinstance(true, BooleanAtom)
+    assert isinstance(false, BooleanAtom)
+    # We don't want to subclass from bool, because bool subclasses from
+    # int. But operators like &, |, ^, <<, >>, and ~ act differently on 0 and
+    # 1 then we want them to on true and false.  See the docstrings of the
+    # various And, Or, etc. functions for examples.
+    assert not isinstance(true, bool)
+    assert not isinstance(false, bool)
+
+    # Note: using 'is' comparison is important here. We want these to return
+    # true and false, not True and False
+
+    assert Not(true) is false
+    assert Not(True) is false
+    assert Not(false) is true
+    assert Not(False) is true
+    assert ~true is false
+    assert ~false is true
+
+    for T, F in product((True, true), (False, false)):
+        assert And(T, F) is false
+        assert And(F, T) is false
+        assert And(F, F) is false
+        assert And(T, T) is true
+        assert And(T, x) == x
+        assert And(F, x) is false
+        if not (T is True and F is False):
+            assert T & F is false
+            assert F & T is false
+        if F is not False:
+            assert F & F is false
+        if T is not True:
+            assert T & T is true
+
+        assert Or(T, F) is true
+        assert Or(F, T) is true
+        assert Or(F, F) is false
+        assert Or(T, T) is true
+        assert Or(T, x) is true
+        assert Or(F, x) == x
+        if not (T is True and F is False):
+            assert T | F is true
+            assert F | T is true
+        if F is not False:
+            assert F | F is false
+        if T is not True:
+            assert T | T is true
+
+        assert Xor(T, F) is true
+        assert Xor(F, T) is true
+        assert Xor(F, F) is false
+        assert Xor(T, T) is false
+        assert Xor(T, x) == ~x
+        assert Xor(F, x) == x
+        if not (T is True and F is False):
+            assert T ^ F is true
+            assert F ^ T is true
+        if F is not False:
+            assert F ^ F is false
+        if T is not True:
+            assert T ^ T is false
+
+        assert Nand(T, F) is true
+        assert Nand(F, T) is true
+        assert Nand(F, F) is true
+        assert Nand(T, T) is false
+        assert Nand(T, x) == ~x
+        assert Nand(F, x) is true
+
+        assert Nor(T, F) is false
+        assert Nor(F, T) is false
+        assert Nor(F, F) is true
+        assert Nor(T, T) is false
+        assert Nor(T, x) is false
+        assert Nor(F, x) == ~x
+
+        assert Implies(T, F) is false
+        assert Implies(F, T) is true
+        assert Implies(F, F) is true
+        assert Implies(T, T) is true
+        assert Implies(T, x) == x
+        assert Implies(F, x) is true
+        assert Implies(x, T) is true
+        assert Implies(x, F) == ~x
+        if not (T is True and F is False):
+            assert T >> F is false
+            assert F << T is false
+            assert F >> T is true
+            assert T << F is true
+        if F is not False:
+            assert F >> F is true
+            assert F << F is true
+        if T is not True:
+            assert T >> T is true
+            assert T << T is true
+
+        assert Equivalent(T, F) is false
+        assert Equivalent(F, T) is false
+        assert Equivalent(F, F) is true
+        assert Equivalent(T, T) is true
+        assert Equivalent(T, x) == x
+        assert Equivalent(F, x) == ~x
+        assert Equivalent(x, T) == x
+        assert Equivalent(x, F) == ~x
+
+        assert ITE(T, T, T) is true
+        assert ITE(T, T, F) is true
+        assert ITE(T, F, T) is false
+        assert ITE(T, F, F) is false
+        assert ITE(F, T, T) is true
+        assert ITE(F, T, F) is false
+        assert ITE(F, F, T) is true
+        assert ITE(F, F, F) is false
+
+    assert all(i.simplify(1, 2) is i for i in (S.true, S.false))
+
+
+def test_bool_as_set():
+    assert ITE(y <= 0, False, y >= 1).as_set() == Interval(1, oo)
+    assert And(x <= 2, x >= -2).as_set() == Interval(-2, 2)
+    assert Or(x >= 2, x <= -2).as_set() == Interval(-oo, -2) + Interval(2, oo)
+    assert Not(x > 2).as_set() == Interval(-oo, 2)
+    # issue 10240
+    assert Not(And(x > 2, x < 3)).as_set() == \
+           Union(Interval(-oo, 2), Interval(3, oo))
+    assert true.as_set() == S.UniversalSet
+    assert false.as_set() is S.EmptySet
+    assert x.as_set() == S.UniversalSet
+    assert And(Or(x < 1, x > 3), x < 2).as_set() == Interval.open(-oo, 1)
+    assert And(x < 1, sin(x) < 3).as_set() == (x < 1).as_set()
+    raises(NotImplementedError, lambda: (sin(x) < 1).as_set())
+    # watch for object morph in as_set
+    assert Eq(-1, cos(2 * x) ** 2 / sin(2 * x) ** 2).as_set() is S.EmptySet
+
+
+@XFAIL
+def test_multivariate_bool_as_set():
+    x, y = symbols('x,y')
+
+    assert And(x >= 0, y >= 0).as_set() == Interval(0, oo) * Interval(0, oo)
+    assert Or(x >= 0, y >= 0).as_set() == S.Reals * S.Reals - \
+           Interval(-oo, 0, True, True) * Interval(-oo, 0, True, True)
+
+
+def test_all_or_nothing():
+    x = symbols('x', extended_real=True)
+    args = x >= -oo, x <= oo
+    v = And(*args)
+    if v.func is And:
+        assert len(v.args) == len(args) - args.count(S.true)
+    else:
+        assert v == True
+    v = Or(*args)
+    if v.func is Or:
+        assert len(v.args) == 2
+    else:
+        assert v == True
+
+
+def test_canonical_atoms():
+    assert true.canonical == true
+    assert false.canonical == false
+
+
+def test_negated_atoms():
+    assert true.negated == false
+    assert false.negated == true
+
+
+def test_issue_8777():
+    assert And(x > 2, x < oo).as_set() == Interval(2, oo, left_open=True)
+    assert And(x >= 1, x < oo).as_set() == Interval(1, oo)
+    assert (x < oo).as_set() == Interval(-oo, oo)
+    assert (x > -oo).as_set() == Interval(-oo, oo)
+
+
+def test_issue_8975():
+    assert Or(And(-oo < x, x <= -2), And(2 <= x, x < oo)).as_set() == \
+           Interval(-oo, -2) + Interval(2, oo)
+
+
+def test_term_to_integer():
+    assert term_to_integer([1, 0, 1, 0, 0, 1, 0]) == 82
+    assert term_to_integer('0010101000111001') == 10809
+
+
+def test_issue_21971():
+    a, b, c, d = symbols('a b c d')
+    f = a & b & c | a & c
+    assert f.subs(a & c, d) == b & d | d
+    assert f.subs(a & b & c, d) == a & c | d
+
+    f = (a | b | c) & (a | c)
+    assert f.subs(a | c, d) == (b | d) & d
+    assert f.subs(a | b | c, d) == (a | c) & d
+
+    f = (a ^ b ^ c) & (a ^ c)
+    assert f.subs(a ^ c, d) == (b ^ d) & d
+    assert f.subs(a ^ b ^ c, d) == (a ^ c) & d
+
+
+def test_truth_table():
+    assert list(truth_table(And(x, y), [x, y], input=False)) == \
+           [False, False, False, True]
+    assert list(truth_table(x | y, [x, y], input=False)) == \
+           [False, True, True, True]
+    assert list(truth_table(x >> y, [x, y], input=False)) == \
+           [True, True, False, True]
+    assert list(truth_table(And(x, y), [x, y])) == \
+           [([0, 0], False), ([0, 1], False), ([1, 0], False), ([1, 1], True)]
+
+
+def test_issue_8571():
+    for t in (S.true, S.false):
+        raises(TypeError, lambda: +t)
+        raises(TypeError, lambda: -t)
+        raises(TypeError, lambda: abs(t))
+        # use int(bool(t)) to get 0 or 1
+        raises(TypeError, lambda: int(t))
+
+        for o in [S.Zero, S.One, x]:
+            for _ in range(2):
+                raises(TypeError, lambda: o + t)
+                raises(TypeError, lambda: o - t)
+                raises(TypeError, lambda: o % t)
+                raises(TypeError, lambda: o * t)
+                raises(TypeError, lambda: o / t)
+                raises(TypeError, lambda: o ** t)
+                o, t = t, o  # do again in reversed order
+
+
+def test_expand_relational():
+    n = symbols('n', negative=True)
+    p, q = symbols('p q', positive=True)
+    r = ((n + q * (-n / q + 1)) / (q * (-n / q + 1)) < 0)
+    assert r is not S.false
+    assert r.expand() is S.false
+    assert (q > 0).expand() is S.true
+
+
+def test_issue_12717():
+    assert S.true.is_Atom == True
+    assert S.false.is_Atom == True
+
+
+def test_as_Boolean():
+    nz = symbols('nz', nonzero=True)
+    assert all(as_Boolean(i) is S.true for i in (True, S.true, 1, nz))
+    z = symbols('z', zero=True)
+    assert all(as_Boolean(i) is S.false for i in (False, S.false, 0, z))
+    assert all(as_Boolean(i) == i for i in (x, x < 0))
+    for i in (2, S(2), x + 1, []):
+        raises(TypeError, lambda: as_Boolean(i))
+
+
+def test_binary_symbols():
+    assert ITE(x < 1, y, z).binary_symbols == {y, z}
+    for f in (Eq, Ne):
+        assert f(x, 1).binary_symbols == set()
+        assert f(x, True).binary_symbols == {x}
+        assert f(x, False).binary_symbols == {x}
+    assert S.true.binary_symbols == set()
+    assert S.false.binary_symbols == set()
+    assert x.binary_symbols == {x}
+    assert And(x, Eq(y, False), Eq(z, 1)).binary_symbols == {x, y}
+    assert Q.prime(x).binary_symbols == set()
+    assert Q.lt(x, 1).binary_symbols == set()
+    assert Q.is_true(x).binary_symbols == {x}
+    assert Q.eq(x, True).binary_symbols == {x}
+    assert Q.prime(x).binary_symbols == set()
+
+
+def test_BooleanFunction_diff():
+    assert And(x, y).diff(x) == Piecewise((0, Eq(y, False)), (1, True))
+
+
+def test_issue_14700():
+    A, B, C, D, E, F, G, H = symbols('A B C D E F G H')
+    q = ((B & D & H & ~F) | (B & H & ~C & ~D) | (B & H & ~C & ~F) |
+         (B & H & ~D & ~G) | (B & H & ~F & ~G) | (C & G & ~B & ~D) |
+         (C & G & ~D & ~H) | (C & G & ~F & ~H) | (D & F & H & ~B) |
+         (D & F & ~G & ~H) | (B & D & F & ~C & ~H) | (D & E & F & ~B & ~C) |
+         (D & F & ~A & ~B & ~C) | (D & F & ~A & ~C & ~H) |
+         (A & B & D & F & ~E & ~H))
+    soldnf = ((B & D & H & ~F) | (D & F & H & ~B) | (B & H & ~C & ~D) |
+              (B & H & ~D & ~G) | (C & G & ~B & ~D) | (C & G & ~D & ~H) |
+              (C & G & ~F & ~H) | (D & F & ~G & ~H) | (D & E & F & ~C & ~H) |
+              (D & F & ~A & ~C & ~H) | (A & B & D & F & ~E & ~H))
+    solcnf = ((B | C | D) & (B | D | G) & (C | D | H) & (C | F | H) &
+              (D | G | H) & (F | G | H) & (B | F | ~D | ~H) &
+              (~B | ~D | ~F | ~H) & (D | ~B | ~C | ~G | ~H) &
+              (A | H | ~C | ~D | ~F | ~G) & (H | ~C | ~D | ~E | ~F | ~G) &
+              (B | E | H | ~A | ~D | ~F | ~G))
+    assert simplify_logic(q, "dnf") == soldnf
+    assert simplify_logic(q, "cnf") == solcnf
+
+    minterms = [[0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1],
+                [0, 0, 1, 1], [1, 0, 1, 1]]
+    dontcares = [[1, 0, 0, 0], [1, 0, 0, 1], [1, 1, 0, 0], [1, 1, 0, 1]]
+    assert SOPform([w, x, y, z], minterms) == (x & ~w) | (y & z & ~x)
+    # Should not be more complicated with don't cares
+    assert SOPform([w, x, y, z], minterms, dontcares) == \
+           (x & ~w) | (y & z & ~x)
+
+
+def test_issue_25115():
+    cond = Contains(x, S.Integers)
+    # Previously this raised an exception:
+    assert simplify_logic(cond) == cond
+
+
+def test_relational_simplification():
+    w, x, y, z = symbols('w x y z', real=True)
+    d, e = symbols('d e', real=False)
+    # Test all combinations or sign and order
+    assert Or(x >= y, x < y).simplify() == S.true
+    assert Or(x >= y, y > x).simplify() == S.true
+    assert Or(x >= y, -x > -y).simplify() == S.true
+    assert Or(x >= y, -y < -x).simplify() == S.true
+    assert Or(-x <= -y, x < y).simplify() == S.true
+    assert Or(-x <= -y, -x > -y).simplify() == S.true
+    assert Or(-x <= -y, y > x).simplify() == S.true
+    assert Or(-x <= -y, -y < -x).simplify() == S.true
+    assert Or(y <= x, x < y).simplify() == S.true
+    assert Or(y <= x, y > x).simplify() == S.true
+    assert Or(y <= x, -x > -y).simplify() == S.true
+    assert Or(y <= x, -y < -x).simplify() == S.true
+    assert Or(-y >= -x, x < y).simplify() == S.true
+    assert Or(-y >= -x, y > x).simplify() == S.true
+    assert Or(-y >= -x, -x > -y).simplify() == S.true
+    assert Or(-y >= -x, -y < -x).simplify() == S.true
+
+    assert Or(x < y, x >= y).simplify() == S.true
+    assert Or(y > x, x >= y).simplify() == S.true
+    assert Or(-x > -y, x >= y).simplify() == S.true
+    assert Or(-y < -x, x >= y).simplify() == S.true
+    assert Or(x < y, -x <= -y).simplify() == S.true
+    assert Or(-x > -y, -x <= -y).simplify() == S.true
+    assert Or(y > x, -x <= -y).simplify() == S.true
+    assert Or(-y < -x, -x <= -y).simplify() == S.true
+    assert Or(x < y, y <= x).simplify() == S.true
+    assert Or(y > x, y <= x).simplify() == S.true
+    assert Or(-x > -y, y <= x).simplify() == S.true
+    assert Or(-y < -x, y <= x).simplify() == S.true
+    assert Or(x < y, -y >= -x).simplify() == S.true
+    assert Or(y > x, -y >= -x).simplify() == S.true
+    assert Or(-x > -y, -y >= -x).simplify() == S.true
+    assert Or(-y < -x, -y >= -x).simplify() == S.true
+
+    # Some other tests
+    assert Or(x >= y, w < z, x <= y).simplify() == S.true
+    assert And(x >= y, x < y).simplify() == S.false
+    assert Or(x >= y, Eq(y, x)).simplify() == (x >= y)
+    assert And(x >= y, Eq(y, x)).simplify() == Eq(x, y)
+    assert And(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y).simplify() == \
+           (Eq(x, y) & (x >= 1) & (y >= 5) & (y > z))
+    assert Or(Eq(x, y), x >= y, w < y, z < y).simplify() == \
+           (x >= y) | (y > z) | (w < y)
+    assert And(Eq(x, y), x >= y, w < y, y >= z, z < y).simplify() == \
+           Eq(x, y) & (y > z) & (w < y)
+    # assert And(Eq(x, y), x >= y, w < y, y >= z, z < y).simplify(relational_minmax=True) == \
+    #    And(Eq(x, y), y > Max(w, z))
+    # assert Or(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y).simplify(relational_minmax=True) == \
+    #    (Eq(x, y) | (x >= 1) | (y > Min(2, z)))
+    assert And(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y).simplify() == \
+           (Eq(x, y) & (x >= 1) & (y >= 5) & (y > z))
+    assert (Eq(x, y) & Eq(d, e) & (x >= y) & (d >= e)).simplify() == \
+           (Eq(x, y) & Eq(d, e) & (d >= e))
+    assert And(Eq(x, y), Eq(x, -y)).simplify() == And(Eq(x, 0), Eq(y, 0))
+    assert Xor(x >= y, x <= y).simplify() == Ne(x, y)
+    assert And(x > 1, x < -1, Eq(x, y)).simplify() == S.false
+    # From #16690
+    assert And(x >= y, Eq(y, 0)).simplify() == And(x >= 0, Eq(y, 0))
+    assert Or(Ne(x, 1), Ne(x, 2)).simplify() == S.true
+    assert And(Eq(x, 1), Ne(2, x)).simplify() == Eq(x, 1)
+    assert Or(Eq(x, 1), Ne(2, x)).simplify() == Ne(x, 2)
+
+
+def test_issue_8373():
+    x = symbols('x', real=True)
+    assert Or(x < 1, x > -1).simplify() == S.true
+    assert Or(x < 1, x >= 1).simplify() == S.true
+    assert And(x < 1, x >= 1).simplify() == S.false
+    assert Or(x <= 1, x >= 1).simplify() == S.true
+
+
+def test_issue_7950():
+    x = symbols('x', real=True)
+    assert And(Eq(x, 1), Eq(x, 2)).simplify() == S.false
+
+
+@slow
+def test_relational_simplification_numerically():
+    def test_simplification_numerically_function(original, simplified):
+        symb = original.free_symbols
+        n = len(symb)
+        valuelist = list(set(combinations(list(range(-(n - 1), n)) * n, n)))
+        for values in valuelist:
+            sublist = dict(zip(symb, values))
+            originalvalue = original.subs(sublist)
+            simplifiedvalue = simplified.subs(sublist)
+            assert originalvalue == simplifiedvalue, "Original: {}\nand" \
+                                                     " simplified: {}\ndo not evaluate to the same value for {}" \
+                                                     "".format(original, simplified, sublist)
+
+    w, x, y, z = symbols('w x y z', real=True)
+    d, e = symbols('d e', real=False)
+
+    expressions = (And(Eq(x, y), x >= y, w < y, y >= z, z < y),
+                   And(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y),
+                   Or(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y),
+                   And(x >= y, Eq(y, x)),
+                   Or(And(Eq(x, y), x >= y, w < y, Or(y >= z, z < y)),
+                      And(Eq(x, y), x >= 1, 2 < y, y >= -1, z < y)),
+                   (Eq(x, y) & Eq(d, e) & (x >= y) & (d >= e)),
+                   )
+
+    for expression in expressions:
+        test_simplification_numerically_function(expression,
+                                                 expression.simplify())
+
+
+def test_relational_simplification_patterns_numerically():
+    from sympy.core import Wild
+    from sympy.logic.boolalg import _simplify_patterns_and, \
+        _simplify_patterns_or, _simplify_patterns_xor
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    symb = [a, b, c]
+    patternlists = [[And, _simplify_patterns_and()],
+                    [Or, _simplify_patterns_or()],
+                    [Xor, _simplify_patterns_xor()]]
+    valuelist = list(set(combinations(list(range(-2, 3)) * 3, 3)))
+    # Skip combinations of +/-2 and 0, except for all 0
+    valuelist = [v for v in valuelist if any(w % 2 for w in v) or not any(v)]
+    for func, patternlist in patternlists:
+        for pattern in patternlist:
+            original = func(*pattern[0].args)
+            simplified = pattern[1]
+            for values in valuelist:
+                sublist = dict(zip(symb, values))
+                originalvalue = original.xreplace(sublist)
+                simplifiedvalue = simplified.xreplace(sublist)
+                assert originalvalue == simplifiedvalue, "Original: {}\nand" \
+                                                         " simplified: {}\ndo not evaluate to the same value for" \
+                                                         "{}".format(pattern[0], simplified, sublist)
+
+
+def test_issue_16803():
+    n = symbols('n')
+    # No simplification done, but should not raise an exception
+    assert ((n > 3) | (n < 0) | ((n > 0) & (n < 3))).simplify() == \
+           (n > 3) | (n < 0) | ((n > 0) & (n < 3))
+
+
+def test_issue_17530():
+    r = {x: oo, y: oo}
+    assert Or(x + y > 0, x - y < 0).subs(r)
+    assert not And(x + y < 0, x - y < 0).subs(r)
+    raises(TypeError, lambda: Or(x + y < 0, x - y < 0).subs(r))
+    raises(TypeError, lambda: And(x + y > 0, x - y < 0).subs(r))
+    raises(TypeError, lambda: And(x + y > 0, x - y < 0).subs(r))
+
+
+def test_anf_coeffs():
+    assert anf_coeffs([1, 0]) == [1, 1]
+    assert anf_coeffs([0, 0, 0, 1]) == [0, 0, 0, 1]
+    assert anf_coeffs([0, 1, 1, 1]) == [0, 1, 1, 1]
+    assert anf_coeffs([1, 1, 1, 0]) == [1, 0, 0, 1]
+    assert anf_coeffs([1, 0, 0, 0]) == [1, 1, 1, 1]
+    assert anf_coeffs([1, 0, 0, 1]) == [1, 1, 1, 0]
+    assert anf_coeffs([1, 1, 0, 1]) == [1, 0, 1, 1]
+
+
+def test_ANFform():
+    x, y = symbols('x,y')
+    assert ANFform([x], [1, 1]) == True
+    assert ANFform([x], [0, 0]) == False
+    assert ANFform([x], [1, 0]) == Xor(x, True, remove_true=False)
+    assert ANFform([x, y], [1, 1, 1, 0]) == \
+           Xor(True, And(x, y), remove_true=False)
+
+
+def test_bool_minterm():
+    x, y = symbols('x,y')
+    assert bool_minterm(3, [x, y]) == And(x, y)
+    assert bool_minterm([1, 0], [x, y]) == And(Not(y), x)
+
+
+def test_bool_maxterm():
+    x, y = symbols('x,y')
+    assert bool_maxterm(2, [x, y]) == Or(Not(x), y)
+    assert bool_maxterm([0, 1], [x, y]) == Or(Not(y), x)
+
+
+def test_bool_monomial():
+    x, y = symbols('x,y')
+    assert bool_monomial(1, [x, y]) == y
+    assert bool_monomial([1, 1], [x, y]) == And(x, y)
+
+
+def test_check_pair():
+    assert _check_pair([0, 1, 0], [0, 1, 1]) == 2
+    assert _check_pair([0, 1, 0], [1, 1, 1]) == -1
+
+
+def test_issue_19114():
+    expr = (B & C) | (A & ~C) | (~A & ~B)
+    # Expression is minimal, but there are multiple minimal forms possible
+    res1 = (A & B) | (C & ~A) | (~B & ~C)
+    result = to_dnf(expr, simplify=True)
+    assert result in (expr, res1)
+
+
+def test_issue_20870():
+    result = SOPform([a, b, c, d], [1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15])
+    expected = ((d & ~b) | (a & b & c) | (a & ~c & ~d) |
+                (b & ~a & ~c) | (c & ~a & ~d))
+    assert result == expected
+
+
+def test_convert_to_varsSOP():
+    assert _convert_to_varsSOP([0, 1, 0], [x, y, z]) == And(Not(x), y, Not(z))
+    assert _convert_to_varsSOP([3, 1, 0], [x, y, z]) == And(y, Not(z))
+
+
+def test_convert_to_varsPOS():
+    assert _convert_to_varsPOS([0, 1, 0], [x, y, z]) == Or(x, Not(y), z)
+    assert _convert_to_varsPOS([3, 1, 0], [x, y, z]) == Or(Not(y), z)
+
+
+def test_gateinputcount():
+    a, b, c, d, e = symbols('a:e')
+    assert gateinputcount(And(a, b)) == 2
+    assert gateinputcount(a | b & c & d ^ (e | a)) == 9
+    assert gateinputcount(And(a, True)) == 0
+    raises(TypeError, lambda: gateinputcount(a * b))
+
+
+def test_refine():
+    # relational
+    assert not refine(x < 0, ~(x < 0))
+    assert refine(x < 0, (x < 0))
+    assert refine(x < 0, (0 > x)) is S.true
+    assert refine(x < 0, (y < 0)) == (x < 0)
+    assert not refine(x <= 0, ~(x <= 0))
+    assert refine(x <= 0, (x <= 0))
+    assert refine(x <= 0, (0 >= x)) is S.true
+    assert refine(x <= 0, (y <= 0)) == (x <= 0)
+    assert not refine(x > 0, ~(x > 0))
+    assert refine(x > 0, (x > 0))
+    assert refine(x > 0, (0 < x)) is S.true
+    assert refine(x > 0, (y > 0)) == (x > 0)
+    assert not refine(x >= 0, ~(x >= 0))
+    assert refine(x >= 0, (x >= 0))
+    assert refine(x >= 0, (0 <= x)) is S.true
+    assert refine(x >= 0, (y >= 0)) == (x >= 0)
+    assert not refine(Eq(x, 0), ~(Eq(x, 0)))
+    assert refine(Eq(x, 0), (Eq(x, 0)))
+    assert refine(Eq(x, 0), (Eq(0, x))) is S.true
+    assert refine(Eq(x, 0), (Eq(y, 0))) == Eq(x, 0)
+    assert not refine(Ne(x, 0), ~(Ne(x, 0)))
+    assert refine(Ne(x, 0), (Ne(0, x))) is S.true
+    assert refine(Ne(x, 0), (Ne(x, 0)))
+    assert refine(Ne(x, 0), (Ne(y, 0))) == (Ne(x, 0))
+
+    # boolean functions
+    assert refine(And(x > 0, y > 0), (x > 0)) == (y > 0)
+    assert refine(And(x > 0, y > 0), (x > 0) & (y > 0)) is S.true
+
+    # predicates
+    assert refine(Q.positive(x), Q.positive(x)) is S.true
+    assert refine(Q.positive(x), Q.negative(x)) is S.false
+    assert refine(Q.positive(x), Q.real(x)) == Q.positive(x)
+
+
+def test_relational_threeterm_simplification_patterns_numerically():
+    from sympy.core import Wild
+    from sympy.logic.boolalg import _simplify_patterns_and3
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    symb = [a, b, c]
+    patternlists = [[And, _simplify_patterns_and3()]]
+    valuelist = list(set(combinations(list(range(-2, 3)) * 3, 3)))
+    # Skip combinations of +/-2 and 0, except for all 0
+    valuelist = [v for v in valuelist if any(w % 2 for w in v) or not any(v)]
+    for func, patternlist in patternlists:
+        for pattern in patternlist:
+            original = func(*pattern[0].args)
+            simplified = pattern[1]
+            for values in valuelist:
+                sublist = dict(zip(symb, values))
+                originalvalue = original.xreplace(sublist)
+                simplifiedvalue = simplified.xreplace(sublist)
+                assert originalvalue == simplifiedvalue, "Original: {}\nand" \
+                                                         " simplified: {}\ndo not evaluate to the same value for" \
+                                                         "{}".format(pattern[0], simplified, sublist)
+
+
+def test_issue_25451():
+    x = Or(And(a, c), Eq(a, b))
+    assert isinstance(x, Or)
+    assert set(x.args) == {And(a, c), Eq(a, b)}
+
+
+def test_issue_26985():
+    a, b, c, d = symbols('a b c d')
+
+    # Expression before applying to_anf
+    x = Xor(c, And(a, b), And(a, c))
+    y = Xor(a, b, And(a, c))
+
+    # Applying to_anf
+    result = Xor(Xor(d, And(x, y)), And(x, y))
+    result_anf = to_anf(Xor(to_anf(Xor(d, And(x, y))), And(x, y)))
+
+    assert result_anf == d
+    assert result == d
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_dimacs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_dimacs.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a9a51a39d33fb807688614cb5809b621ce21a2c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_dimacs.py
@@ -0,0 +1,234 @@
+"""Various tests on satisfiability using dimacs cnf file syntax
+You can find lots of cnf files in
+ftp://dimacs.rutgers.edu/pub/challenge/satisfiability/benchmarks/cnf/
+"""
+
+from sympy.logic.utilities.dimacs import load
+from sympy.logic.algorithms.dpll import dpll_satisfiable
+
+
+def test_f1():
+    assert bool(dpll_satisfiable(load(f1)))
+
+
+def test_f2():
+    assert bool(dpll_satisfiable(load(f2)))
+
+
+def test_f3():
+    assert bool(dpll_satisfiable(load(f3)))
+
+
+def test_f4():
+    assert not bool(dpll_satisfiable(load(f4)))
+
+
+def test_f5():
+    assert bool(dpll_satisfiable(load(f5)))
+
+f1 = """c  simple example
+c Resolution: SATISFIABLE
+c
+p cnf 3 2
+1 -3 0
+2 3 -1 0
+"""
+
+
+f2 = """c  an example from Quinn's text, 16 variables and 18 clauses.
+c Resolution: SATISFIABLE
+c
+p cnf 16 18
+  1    2  0
+ -2   -4  0
+  3    4  0
+ -4   -5  0
+  5   -6  0
+  6   -7  0
+  6    7  0
+  7  -16  0
+  8   -9  0
+ -8  -14  0
+  9   10  0
+  9  -10  0
+-10  -11  0
+ 10   12  0
+ 11   12  0
+ 13   14  0
+ 14  -15  0
+ 15   16  0
+"""
+
+f3 = """c
+p cnf 6 9
+-1 0
+-3 0
+2 -1 0
+2 -4 0
+5 -4 0
+-1 -3 0
+-4 -6 0
+1 3 -2 0
+4 6 -2 -5 0
+"""
+
+f4 = """c
+c file:   hole6.cnf [http://people.sc.fsu.edu/~jburkardt/data/cnf/hole6.cnf]
+c
+c SOURCE: John Hooker (jh38+@andrew.cmu.edu)
+c
+c DESCRIPTION: Pigeon hole problem of placing n (for file 'holen.cnf') pigeons
+c              in n+1 holes without placing 2 pigeons in the same hole
+c
+c NOTE: Part of the collection at the Forschungsinstitut fuer
+c       anwendungsorientierte Wissensverarbeitung in Ulm Germany.
+c
+c NOTE: Not satisfiable
+c
+p cnf 42 133
+-1     -7    0
+-1     -13   0
+-1     -19   0
+-1     -25   0
+-1     -31   0
+-1     -37   0
+-7     -13   0
+-7     -19   0
+-7     -25   0
+-7     -31   0
+-7     -37   0
+-13    -19   0
+-13    -25   0
+-13    -31   0
+-13    -37   0
+-19    -25   0
+-19    -31   0
+-19    -37   0
+-25    -31   0
+-25    -37   0
+-31    -37   0
+-2     -8    0
+-2     -14   0
+-2     -20   0
+-2     -26   0
+-2     -32   0
+-2     -38   0
+-8     -14   0
+-8     -20   0
+-8     -26   0
+-8     -32   0
+-8     -38   0
+-14    -20   0
+-14    -26   0
+-14    -32   0
+-14    -38   0
+-20    -26   0
+-20    -32   0
+-20    -38   0
+-26    -32   0
+-26    -38   0
+-32    -38   0
+-3     -9    0
+-3     -15   0
+-3     -21   0
+-3     -27   0
+-3     -33   0
+-3     -39   0
+-9     -15   0
+-9     -21   0
+-9     -27   0
+-9     -33   0
+-9     -39   0
+-15    -21   0
+-15    -27   0
+-15    -33   0
+-15    -39   0
+-21    -27   0
+-21    -33   0
+-21    -39   0
+-27    -33   0
+-27    -39   0
+-33    -39   0
+-4     -10   0
+-4     -16   0
+-4     -22   0
+-4     -28   0
+-4     -34   0
+-4     -40   0
+-10    -16   0
+-10    -22   0
+-10    -28   0
+-10    -34   0
+-10    -40   0
+-16    -22   0
+-16    -28   0
+-16    -34   0
+-16    -40   0
+-22    -28   0
+-22    -34   0
+-22    -40   0
+-28    -34   0
+-28    -40   0
+-34    -40   0
+-5     -11   0
+-5     -17   0
+-5     -23   0
+-5     -29   0
+-5     -35   0
+-5     -41   0
+-11    -17   0
+-11    -23   0
+-11    -29   0
+-11    -35   0
+-11    -41   0
+-17    -23   0
+-17    -29   0
+-17    -35   0
+-17    -41   0
+-23    -29   0
+-23    -35   0
+-23    -41   0
+-29    -35   0
+-29    -41   0
+-35    -41   0
+-6     -12   0
+-6     -18   0
+-6     -24   0
+-6     -30   0
+-6     -36   0
+-6     -42   0
+-12    -18   0
+-12    -24   0
+-12    -30   0
+-12    -36   0
+-12    -42   0
+-18    -24   0
+-18    -30   0
+-18    -36   0
+-18    -42   0
+-24    -30   0
+-24    -36   0
+-24    -42   0
+-30    -36   0
+-30    -42   0
+-36    -42   0
+ 6      5      4      3      2      1    0
+ 12     11     10     9      8      7    0
+ 18     17     16     15     14     13   0
+ 24     23     22     21     20     19   0
+ 30     29     28     27     26     25   0
+ 36     35     34     33     32     31   0
+ 42     41     40     39     38     37   0
+"""
+
+f5 = """c  simple example requiring variable selection
+c
+c NOTE: Satisfiable
+c
+p cnf 5 5
+1 2 3 0
+1 -2 3 0
+4 5 -3 0
+1 -4 -3 0
+-1 -5 0
+"""
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_inference.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_inference.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff37b1b104f6f106ec5df7809fd34959bce35917
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_inference.py
@@ -0,0 +1,396 @@
+"""For more tests on satisfiability, see test_dimacs"""
+
+from sympy.assumptions.ask import Q
+from sympy.core.symbol import symbols
+from sympy.core.relational import Unequality
+from sympy.logic.boolalg import And, Or, Implies, Equivalent, true, false
+from sympy.logic.inference import literal_symbol, \
+     pl_true, satisfiable, valid, entails, PropKB
+from sympy.logic.algorithms.dpll import dpll, dpll_satisfiable, \
+    find_pure_symbol, find_unit_clause, unit_propagate, \
+    find_pure_symbol_int_repr, find_unit_clause_int_repr, \
+    unit_propagate_int_repr
+from sympy.logic.algorithms.dpll2 import dpll_satisfiable as dpll2_satisfiable
+
+from sympy.logic.algorithms.z3_wrapper import z3_satisfiable
+from sympy.assumptions.cnf import CNF, EncodedCNF
+from sympy.logic.tests.test_lra_theory import make_random_problem
+from sympy.core.random import randint
+
+from sympy.testing.pytest import raises, skip
+from sympy.external import import_module
+
+
+def test_literal():
+    A, B = symbols('A,B')
+    assert literal_symbol(True) is True
+    assert literal_symbol(False) is False
+    assert literal_symbol(A) is A
+    assert literal_symbol(~A) is A
+
+
+def test_find_pure_symbol():
+    A, B, C = symbols('A,B,C')
+    assert find_pure_symbol([A], [A]) == (A, True)
+    assert find_pure_symbol([A, B], [~A | B, ~B | A]) == (None, None)
+    assert find_pure_symbol([A, B, C], [ A | ~B, ~B | ~C, C | A]) == (A, True)
+    assert find_pure_symbol([A, B, C], [~A | B, B | ~C, C | A]) == (B, True)
+    assert find_pure_symbol([A, B, C], [~A | ~B, ~B | ~C, C | A]) == (B, False)
+    assert find_pure_symbol(
+        [A, B, C], [~A | B, ~B | ~C, C | A]) == (None, None)
+
+
+def test_find_pure_symbol_int_repr():
+    assert find_pure_symbol_int_repr([1], [{1}]) == (1, True)
+    assert find_pure_symbol_int_repr([1, 2],
+                [{-1, 2}, {-2, 1}]) == (None, None)
+    assert find_pure_symbol_int_repr([1, 2, 3],
+                [{1, -2}, {-2, -3}, {3, 1}]) == (1, True)
+    assert find_pure_symbol_int_repr([1, 2, 3],
+                [{-1, 2}, {2, -3}, {3, 1}]) == (2, True)
+    assert find_pure_symbol_int_repr([1, 2, 3],
+                [{-1, -2}, {-2, -3}, {3, 1}]) == (2, False)
+    assert find_pure_symbol_int_repr([1, 2, 3],
+                [{-1, 2}, {-2, -3}, {3, 1}]) == (None, None)
+
+
+def test_unit_clause():
+    A, B, C = symbols('A,B,C')
+    assert find_unit_clause([A], {}) == (A, True)
+    assert find_unit_clause([A, ~A], {}) == (A, True)  # Wrong ??
+    assert find_unit_clause([A | B], {A: True}) == (B, True)
+    assert find_unit_clause([A | B], {B: True}) == (A, True)
+    assert find_unit_clause(
+        [A | B | C, B | ~C, A | ~B], {A: True}) == (B, False)
+    assert find_unit_clause([A | B | C, B | ~C, A | B], {A: True}) == (B, True)
+    assert find_unit_clause([A | B | C, B | ~C, A ], {}) == (A, True)
+
+
+def test_unit_clause_int_repr():
+    assert find_unit_clause_int_repr(map(set, [[1]]), {}) == (1, True)
+    assert find_unit_clause_int_repr(map(set, [[1], [-1]]), {}) == (1, True)
+    assert find_unit_clause_int_repr([{1, 2}], {1: True}) == (2, True)
+    assert find_unit_clause_int_repr([{1, 2}], {2: True}) == (1, True)
+    assert find_unit_clause_int_repr(map(set,
+        [[1, 2, 3], [2, -3], [1, -2]]), {1: True}) == (2, False)
+    assert find_unit_clause_int_repr(map(set,
+        [[1, 2, 3], [3, -3], [1, 2]]), {1: True}) == (2, True)
+
+    A, B, C = symbols('A,B,C')
+    assert find_unit_clause([A | B | C, B | ~C, A ], {}) == (A, True)
+
+
+def test_unit_propagate():
+    A, B, C = symbols('A,B,C')
+    assert unit_propagate([A | B], A) == []
+    assert unit_propagate([A | B, ~A | C, ~C | B, A], A) == [C, ~C | B, A]
+
+
+def test_unit_propagate_int_repr():
+    assert unit_propagate_int_repr([{1, 2}], 1) == []
+    assert unit_propagate_int_repr(map(set,
+        [[1, 2], [-1, 3], [-3, 2], [1]]), 1) == [{3}, {-3, 2}]
+
+
+def test_dpll():
+    """This is also tested in test_dimacs"""
+    A, B, C = symbols('A,B,C')
+    assert dpll([A | B], [A, B], {A: True, B: True}) == {A: True, B: True}
+
+
+def test_dpll_satisfiable():
+    A, B, C = symbols('A,B,C')
+    assert dpll_satisfiable( A & ~A ) is False
+    assert dpll_satisfiable( A & ~B ) == {A: True, B: False}
+    assert dpll_satisfiable(
+        A | B ) in ({A: True}, {B: True}, {A: True, B: True})
+    assert dpll_satisfiable(
+        (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False})
+    assert dpll_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False},
+            {A: True, C: True}, {B: True, C: True})
+    assert dpll_satisfiable( A & B & C  ) == {A: True, B: True, C: True}
+    assert dpll_satisfiable( (A | B) & (A >> B) ) == {B: True}
+    assert dpll_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True}
+    assert dpll_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False}
+
+
+def test_dpll2_satisfiable():
+    A, B, C = symbols('A,B,C')
+    assert dpll2_satisfiable( A & ~A ) is False
+    assert dpll2_satisfiable( A & ~B ) == {A: True, B: False}
+    assert dpll2_satisfiable(
+        A | B ) in ({A: True}, {B: True}, {A: True, B: True})
+    assert dpll2_satisfiable(
+        (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False})
+    assert dpll2_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False, C: True},
+        {A: True, B: True, C: True})
+    assert dpll2_satisfiable( A & B & C  ) == {A: True, B: True, C: True}
+    assert dpll2_satisfiable( (A | B) & (A >> B) ) in ({B: True, A: False},
+        {B: True, A: True})
+    assert dpll2_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True}
+    assert dpll2_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False}
+
+
+def test_minisat22_satisfiable():
+    A, B, C = symbols('A,B,C')
+    minisat22_satisfiable = lambda expr: satisfiable(expr, algorithm="minisat22")
+    assert minisat22_satisfiable( A & ~A ) is False
+    assert minisat22_satisfiable( A & ~B ) == {A: True, B: False}
+    assert minisat22_satisfiable(
+        A | B ) in ({A: True}, {B: False}, {A: False, B: True}, {A: True, B: True}, {A: True, B: False})
+    assert minisat22_satisfiable(
+        (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False})
+    assert minisat22_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False, C: True},
+        {A: True, B: True, C: True}, {A: False, B: True, C: True}, {A: True, B: False, C: False})
+    assert minisat22_satisfiable( A & B & C  ) == {A: True, B: True, C: True}
+    assert minisat22_satisfiable( (A | B) & (A >> B) ) in ({B: True, A: False},
+        {B: True, A: True})
+    assert minisat22_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True}
+    assert minisat22_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False}
+
+def test_minisat22_minimal_satisfiable():
+    A, B, C = symbols('A,B,C')
+    minisat22_satisfiable = lambda expr, minimal=True: satisfiable(expr, algorithm="minisat22", minimal=True)
+    assert minisat22_satisfiable( A & ~A ) is False
+    assert minisat22_satisfiable( A & ~B ) == {A: True, B: False}
+    assert minisat22_satisfiable(
+        A | B ) in ({A: True}, {B: False}, {A: False, B: True}, {A: True, B: True}, {A: True, B: False})
+    assert minisat22_satisfiable(
+        (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False})
+    assert minisat22_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False, C: True},
+        {A: True, B: True, C: True}, {A: False, B: True, C: True}, {A: True, B: False, C: False})
+    assert minisat22_satisfiable( A & B & C  ) == {A: True, B: True, C: True}
+    assert minisat22_satisfiable( (A | B) & (A >> B) ) in ({B: True, A: False},
+        {B: True, A: True})
+    assert minisat22_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True}
+    assert minisat22_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False}
+    g = satisfiable((A | B | C),algorithm="minisat22",minimal=True,all_models=True)
+    sol = next(g)
+    first_solution = {key for key, value in sol.items() if value}
+    sol=next(g)
+    second_solution = {key for key, value in sol.items() if value}
+    sol=next(g)
+    third_solution = {key for key, value in sol.items() if value}
+    assert not first_solution <= second_solution
+    assert not second_solution <= third_solution
+    assert not first_solution <= third_solution
+
+def test_satisfiable():
+    A, B, C = symbols('A,B,C')
+    assert satisfiable(A & (A >> B) & ~B) is False
+
+
+def test_valid():
+    A, B, C = symbols('A,B,C')
+    assert valid(A >> (B >> A)) is True
+    assert valid((A >> (B >> C)) >> ((A >> B) >> (A >> C))) is True
+    assert valid((~B >> ~A) >> (A >> B)) is True
+    assert valid(A | B | C) is False
+    assert valid(A >> B) is False
+
+
+def test_pl_true():
+    A, B, C = symbols('A,B,C')
+    assert pl_true(True) is True
+    assert pl_true( A & B, {A: True, B: True}) is True
+    assert pl_true( A | B, {A: True}) is True
+    assert pl_true( A | B, {B: True}) is True
+    assert pl_true( A | B, {A: None, B: True}) is True
+    assert pl_true( A >> B, {A: False}) is True
+    assert pl_true( A | B | ~C, {A: False, B: True, C: True}) is True
+    assert pl_true(Equivalent(A, B), {A: False, B: False}) is True
+
+    # test for false
+    assert pl_true(False) is False
+    assert pl_true( A & B, {A: False, B: False}) is False
+    assert pl_true( A & B, {A: False}) is False
+    assert pl_true( A & B, {B: False}) is False
+    assert pl_true( A | B, {A: False, B: False}) is False
+
+    #test for None
+    assert pl_true(B, {B: None}) is None
+    assert pl_true( A & B, {A: True, B: None}) is None
+    assert pl_true( A >> B, {A: True, B: None}) is None
+    assert pl_true(Equivalent(A, B), {A: None}) is None
+    assert pl_true(Equivalent(A, B), {A: True, B: None}) is None
+
+    # Test for deep
+    assert pl_true(A | B, {A: False}, deep=True) is None
+    assert pl_true(~A & ~B, {A: False}, deep=True) is None
+    assert pl_true(A | B, {A: False, B: False}, deep=True) is False
+    assert pl_true(A & B & (~A | ~B), {A: True}, deep=True) is False
+    assert pl_true((C >> A) >> (B >> A), {C: True}, deep=True) is True
+
+
+def test_pl_true_wrong_input():
+    from sympy.core.numbers import pi
+    raises(ValueError, lambda: pl_true('John Cleese'))
+    raises(ValueError, lambda: pl_true(42 + pi + pi ** 2))
+    raises(ValueError, lambda: pl_true(42))
+
+
+def test_entails():
+    A, B, C = symbols('A, B, C')
+    assert entails(A, [A >> B, ~B]) is False
+    assert entails(B, [Equivalent(A, B), A]) is True
+    assert entails((A >> B) >> (~A >> ~B)) is False
+    assert entails((A >> B) >> (~B >> ~A)) is True
+
+
+def test_PropKB():
+    A, B, C = symbols('A,B,C')
+    kb = PropKB()
+    assert kb.ask(A >> B) is False
+    assert kb.ask(A >> (B >> A)) is True
+    kb.tell(A >> B)
+    kb.tell(B >> C)
+    assert kb.ask(A) is False
+    assert kb.ask(B) is False
+    assert kb.ask(C) is False
+    assert kb.ask(~A) is False
+    assert kb.ask(~B) is False
+    assert kb.ask(~C) is False
+    assert kb.ask(A >> C) is True
+    kb.tell(A)
+    assert kb.ask(A) is True
+    assert kb.ask(B) is True
+    assert kb.ask(C) is True
+    assert kb.ask(~C) is False
+    kb.retract(A)
+    assert kb.ask(C) is False
+
+
+def test_propKB_tolerant():
+    """"tolerant to bad input"""
+    kb = PropKB()
+    A, B, C = symbols('A,B,C')
+    assert kb.ask(B) is False
+
+def test_satisfiable_non_symbols():
+    x, y = symbols('x y')
+    assumptions = Q.zero(x*y)
+    facts = Implies(Q.zero(x*y), Q.zero(x) | Q.zero(y))
+    query = ~Q.zero(x) & ~Q.zero(y)
+    refutations = [
+        {Q.zero(x): True, Q.zero(x*y): True},
+        {Q.zero(y): True, Q.zero(x*y): True},
+        {Q.zero(x): True, Q.zero(y): True, Q.zero(x*y): True},
+        {Q.zero(x): True, Q.zero(y): False, Q.zero(x*y): True},
+        {Q.zero(x): False, Q.zero(y): True, Q.zero(x*y): True}]
+    assert not satisfiable(And(assumptions, facts, query), algorithm='dpll')
+    assert satisfiable(And(assumptions, facts, ~query), algorithm='dpll') in refutations
+    assert not satisfiable(And(assumptions, facts, query), algorithm='dpll2')
+    assert satisfiable(And(assumptions, facts, ~query), algorithm='dpll2') in refutations
+
+def test_satisfiable_bool():
+    from sympy.core.singleton import S
+    assert satisfiable(true) == {true: true}
+    assert satisfiable(S.true) == {true: true}
+    assert satisfiable(false) is False
+    assert satisfiable(S.false) is False
+
+
+def test_satisfiable_all_models():
+    from sympy.abc import A, B
+    assert next(satisfiable(False, all_models=True)) is False
+    assert list(satisfiable((A >> ~A) & A, all_models=True)) == [False]
+    assert list(satisfiable(True, all_models=True)) == [{true: true}]
+
+    models = [{A: True, B: False}, {A: False, B: True}]
+    result = satisfiable(A ^ B, all_models=True)
+    models.remove(next(result))
+    models.remove(next(result))
+    raises(StopIteration, lambda: next(result))
+    assert not models
+
+    assert list(satisfiable(Equivalent(A, B), all_models=True)) == \
+    [{A: False, B: False}, {A: True, B: True}]
+
+    models = [{A: False, B: False}, {A: False, B: True}, {A: True, B: True}]
+    for model in satisfiable(A >> B, all_models=True):
+        models.remove(model)
+    assert not models
+
+    # This is a santiy test to check that only the required number
+    # of solutions are generated. The expr below has 2**100 - 1 models
+    # which would time out the test if all are generated at once.
+    from sympy.utilities.iterables import numbered_symbols
+    from sympy.logic.boolalg import Or
+    sym = numbered_symbols()
+    X = [next(sym) for i in range(100)]
+    result = satisfiable(Or(*X), all_models=True)
+    for i in range(10):
+        assert next(result)
+
+
+def test_z3():
+    z3 = import_module("z3")
+
+    if not z3:
+        skip("z3 not installed.")
+    A, B, C = symbols('A,B,C')
+    x, y, z = symbols('x,y,z')
+    assert z3_satisfiable((x >= 2) & (x < 1)) is False
+    assert z3_satisfiable( A & ~A ) is False
+
+    model = z3_satisfiable(A & (~A | B | C))
+    assert bool(model) is True
+    assert model[A] is True
+
+    # test nonlinear function
+    assert z3_satisfiable((x ** 2 >= 2) & (x < 1) & (x > -1)) is False
+
+
+def test_z3_vs_lra_dpll2():
+    z3 = import_module("z3")
+    if z3 is None:
+        skip("z3 not installed.")
+
+    def boolean_formula_to_encoded_cnf(bf):
+        cnf = CNF.from_prop(bf)
+        enc = EncodedCNF()
+        enc.from_cnf(cnf)
+        return enc
+
+    def make_random_cnf(num_clauses=5, num_constraints=10, num_var=2):
+        assert num_clauses <= num_constraints
+        constraints = make_random_problem(num_variables=num_var, num_constraints=num_constraints, rational=False)
+        clauses = [[cons] for cons in constraints[:num_clauses]]
+        for cons in constraints[num_clauses:]:
+            if isinstance(cons, Unequality):
+                cons = ~cons
+            i = randint(0, num_clauses-1)
+            clauses[i].append(cons)
+
+        clauses = [Or(*clause) for clause in clauses]
+        cnf = And(*clauses)
+        return boolean_formula_to_encoded_cnf(cnf)
+
+    lra_dpll2_satisfiable = lambda x: dpll2_satisfiable(x, use_lra_theory=True)
+
+    for _ in range(50):
+        cnf = make_random_cnf(num_clauses=10, num_constraints=15, num_var=2)
+
+        try:
+            z3_sat = z3_satisfiable(cnf)
+        except z3.z3types.Z3Exception:
+            continue
+
+        lra_dpll2_sat = lra_dpll2_satisfiable(cnf) is not False
+
+        assert z3_sat == lra_dpll2_sat
+
+def test_issue_27733():
+    x, y = symbols('x,y')
+    clauses = [[1, -3, -2], [5, 7, -8, -6, -4], [-10, -9, 10, 11, -4], [-12, 13, 14], [-10, 9, -6, 11, -4],
+               [16, -15, 18, -19, -17], [11, -6, 10, -9], [9, 11, -10, -9], [2, -3, -1], [-13, 12], [-15, 3, -17],
+               [-16, -15, 19, -17], [-6, -9, 10, 11, -4], [20, -1, -2], [-23, -22, -21], [10, 11, -10, -9],
+               [9, 11, -4, -10], [24, -6, -4], [-14, 12], [-10, -9, 9, -6, 11], [25, -27, -26], [-15, 19, -18, -17],
+               [5, 8, -7, -6, -4], [-30, -29, 28], [12], [14]]
+
+    encoding = {Q.gt(y, i): i for i in range(1, 31) if i != 11 and i != 12}
+    encoding[Q.gt(x, 0)] = 11
+    encoding[Q.lt(x, 0)] = 12
+
+    cnf = EncodedCNF(clauses, encoding)
+    assert satisfiable(cnf, use_lra_theory=True) is False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_lra_theory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_lra_theory.py
new file mode 100644
index 0000000000000000000000000000000000000000..207a3c5ba2c1b16ee5323382deee0863a5dfb595
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/tests/test_lra_theory.py
@@ -0,0 +1,440 @@
+from sympy.core.numbers import Rational, I, oo
+from sympy.core.relational import Eq
+from sympy.core.symbol import symbols
+from sympy.core.singleton import S
+from sympy.matrices.dense import Matrix
+from sympy.matrices.dense import randMatrix
+from sympy.assumptions.ask import Q
+from sympy.logic.boolalg import And
+from sympy.abc import x, y, z
+from sympy.assumptions.cnf import CNF, EncodedCNF
+from sympy.functions.elementary.trigonometric import cos
+from sympy.external import import_module
+
+from sympy.logic.algorithms.lra_theory import LRASolver, UnhandledInput, LRARational, HANDLE_NEGATION
+from sympy.core.random import random, choice, randint
+from sympy.core.sympify import sympify
+from sympy.ntheory.generate import randprime
+from sympy.core.relational import StrictLessThan, StrictGreaterThan
+import itertools
+
+from sympy.testing.pytest import raises, XFAIL, skip
+
+def make_random_problem(num_variables=2, num_constraints=2, sparsity=.1, rational=True,
+                        disable_strict = False, disable_nonstrict=False, disable_equality=False):
+    def rand(sparsity=sparsity):
+        if random() < sparsity:
+            return sympify(0)
+        if rational:
+            int1, int2 = [randprime(0, 50) for _ in range(2)]
+            return Rational(int1, int2) * choice([-1, 1])
+        else:
+            return randint(1, 10) * choice([-1, 1])
+
+    variables = symbols('x1:%s' % (num_variables + 1))
+    constraints = []
+    for _ in range(num_constraints):
+        lhs, rhs = sum(rand() * x for x in variables), rand(sparsity=0) # sparsity=0  bc of bug with smtlib_code
+        options = []
+        if not disable_equality:
+            options += [Eq(lhs, rhs)]
+        if not disable_nonstrict:
+            options += [lhs <= rhs, lhs >= rhs]
+        if not disable_strict:
+            options += [lhs < rhs, lhs > rhs]
+
+        constraints.append(choice(options))
+
+    return constraints
+
+def check_if_satisfiable_with_z3(constraints):
+    from sympy.external.importtools import import_module
+    from sympy.printing.smtlib import smtlib_code
+    from sympy.logic.boolalg import And
+    boolean_formula = And(*constraints)
+    z3 = import_module("z3")
+    if z3:
+        smtlib_string = smtlib_code(boolean_formula)
+        s = z3.Solver()
+        s.from_string(smtlib_string)
+        res = str(s.check())
+        if res == 'sat':
+            return True
+        elif res == 'unsat':
+            return False
+        else:
+            raise ValueError(f"z3 was not able to check the satisfiability of {boolean_formula}")
+
+def find_rational_assignment(constr, assignment, iter=20):
+    eps = sympify(1)
+
+    for _ in range(iter):
+        assign = {key: val[0] + val[1]*eps for key, val in assignment.items()}
+        try:
+            for cons in constr:
+                assert cons.subs(assign) == True
+            return assign
+        except AssertionError:
+            eps = eps/2
+
+    return None
+
+def boolean_formula_to_encoded_cnf(bf):
+    cnf = CNF.from_prop(bf)
+    enc = EncodedCNF()
+    enc.from_cnf(cnf)
+    return enc
+
+
+def test_from_encoded_cnf():
+    s1, s2 = symbols("s1 s2")
+
+    # Test preprocessing
+    # Example is from section 3 of paper.
+    phi = (x >= 0) & ((x + y <= 2) | (x + 2 * y - z >= 6)) & (Eq(x + y, 2) | (x + 2 * y - z > 4))
+    enc = boolean_formula_to_encoded_cnf(phi)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    assert lra.A.shape == (2, 5)
+    assert str(lra.slack) == '[_s1, _s2]'
+    assert str(lra.nonslack) == '[x, y, z]'
+    assert lra.A == Matrix([[ 1,  1, 0, -1,  0],
+                            [-1, -2, 1,  0, -1]])
+    assert {(str(b.var), b.bound, b.upper, b.equality, b.strict) for b in lra.enc_to_boundary.values()} == {('_s1', 2, None, True, False),
+    ('_s1', 2, True, False, False),
+    ('_s2', -4, True, False, True),
+    ('_s2', -6, True, False, False),
+    ('x', 0, False, False, False)}
+
+
+def test_problem():
+    from sympy.logic.algorithms.lra_theory import LRASolver
+    from sympy.assumptions.cnf import CNF, EncodedCNF
+    cons = [-2 * x - 2 * y >= 7, -9 * y >= 7, -6 * y >= 5]
+    cnf = CNF().from_prop(And(*cons))
+    enc = EncodedCNF()
+    enc.from_cnf(cnf)
+    lra, _ = LRASolver.from_encoded_cnf(enc)
+    lra.assert_lit(1)
+    lra.assert_lit(2)
+    lra.assert_lit(3)
+    is_sat, assignment = lra.check()
+    assert is_sat is True
+
+
+def test_random_problems():
+    z3 = import_module("z3")
+    if z3 is None:
+        skip("z3 is not installed")
+
+    special_cases = []; x1, x2, x3 = symbols("x1 x2 x3")
+    special_cases.append([x1 - 3 * x2 <= -5, 6 * x1 + 4 * x2 <= 0, -7 * x1 + 3 * x2 <= 3])
+    special_cases.append([-3 * x1 >= 3, Eq(4 * x1, -1)])
+    special_cases.append([-4 * x1 < 4, 6 * x1 <= -6])
+    special_cases.append([-3 * x2 >= 7, 6 * x1 <= -5, -3 * x2 <= -4])
+    special_cases.append([x + y >= 2, x + y <= 1])
+    special_cases.append([x >= 0, x + y <= 2, x + 2 * y - z >= 6])  # from paper example
+    special_cases.append([-2 * x1 - 2 * x2 >= 7, -9 * x1 >= 7, -6 * x1 >= 5])
+    special_cases.append([2 * x1 > -3, -9 * x1 < -6, 9 * x1 <= 6])
+    special_cases.append([-2*x1 < -4, 9*x1 > -9])
+    special_cases.append([-6*x1 >= -1, -8*x1 + x2 >= 5, -8*x1 + 7*x2 < 4, x1 > 7])
+    special_cases.append([Eq(x1, 2), Eq(5*x1, -2), Eq(-7*x2, -6), Eq(9*x1 + 10*x2, 9)])
+    special_cases.append([Eq(3*x1, 6), Eq(x1 - 8*x2, -9), Eq(-7*x1 + 5*x2, 3), Eq(3*x2, 7)])
+    special_cases.append([-4*x1 < 4, 6*x1 <= -6])
+    special_cases.append([-3*x1 + 8*x2 >= -8, -10*x2 > 9, 8*x1 - 4*x2 < 8, 10*x1 - 9*x2 >= -9])
+    special_cases.append([x1 + 5*x2 >= -6, 9*x1 - 3*x2 >= -9, 6*x1 + 6*x2 < -10, -3*x1 + 3*x2 < -7])
+    special_cases.append([-9*x1 < 7, -5*x1 - 7*x2 < -1, 3*x1 + 7*x2 > 1, -6*x1 - 6*x2 > 9])
+    special_cases.append([9*x1 - 6*x2 >= -7, 9*x1 + 4*x2 < -8, -7*x2 <= 1, 10*x2 <= -7])
+
+    feasible_count = 0
+    for i in range(50):
+        if i % 8 == 0:
+            constraints = make_random_problem(num_variables=1, num_constraints=2, rational=False)
+        elif i % 8 == 1:
+            constraints = make_random_problem(num_variables=2, num_constraints=4, rational=False, disable_equality=True,
+                                              disable_nonstrict=True)
+        elif i % 8 == 2:
+            constraints = make_random_problem(num_variables=2, num_constraints=4, rational=False, disable_strict=True)
+        elif i % 8 == 3:
+            constraints = make_random_problem(num_variables=3, num_constraints=12, rational=False)
+        else:
+            constraints = make_random_problem(num_variables=3, num_constraints=6, rational=False)
+
+        if i < len(special_cases):
+            constraints = special_cases[i]
+
+        if False in constraints or True in constraints:
+            continue
+
+        phi = And(*constraints)
+        if phi == False:
+            continue
+        cnf = CNF.from_prop(phi); enc = EncodedCNF()
+        enc.from_cnf(cnf)
+        assert all(0 not in clause for clause in enc.data)
+
+        lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+        s_subs = lra.s_subs
+
+        lra.run_checks = True
+        s_subs_rev = {value: key for key, value in s_subs.items()}
+        lits = {lit for clause in enc.data for lit in clause}
+
+        bounds = [(lra.enc_to_boundary[l], l) for l in lits if l in lra.enc_to_boundary]
+        bounds = sorted(bounds, key=lambda x: (str(x[0].var), x[0].bound, str(x[0].upper))) # to remove nondeterminism
+
+        for b, l in bounds:
+            if lra.result and lra.result[0] == False:
+                break
+            lra.assert_lit(l)
+
+        feasible = lra.check()
+
+        if feasible[0] == True:
+            feasible_count += 1
+            assert check_if_satisfiable_with_z3(constraints) is True
+            cons_funcs = [cons.func for cons in constraints]
+            assignment = feasible[1]
+            assignment = {key.var : value for key, value in assignment.items()}
+            if not (StrictLessThan in cons_funcs or StrictGreaterThan in cons_funcs):
+                assignment = {key: value[0] for key, value in assignment.items()}
+                for cons in constraints:
+                    assert cons.subs(assignment) == True
+
+            else:
+                rat_assignment = find_rational_assignment(constraints, assignment)
+                assert rat_assignment is not None
+        else:
+            assert check_if_satisfiable_with_z3(constraints) is False
+
+            conflict = feasible[1]
+            assert len(conflict) >= 2
+            conflict = {lra.enc_to_boundary[-l].get_inequality() for l in conflict}
+            conflict = {clause.subs(s_subs_rev) for clause in conflict}
+            assert check_if_satisfiable_with_z3(conflict) is False
+
+            # check that conflict clause is probably minimal
+            for subset in itertools.combinations(conflict, len(conflict)-1):
+                assert check_if_satisfiable_with_z3(subset) is True
+
+
+@XFAIL
+def test_pos_neg_zero():
+    bf = Q.positive(x) & Q.negative(x) & Q.zero(y)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 3
+    assert lra.check()[0] == False
+
+    bf = Q.positive(x) & Q.lt(x, -1)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+
+    bf = Q.positive(x) & Q.zero(x)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+
+    bf = Q.positive(x) & Q.zero(y)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == True
+
+
+@XFAIL
+def test_pos_neg_infinite():
+    bf = Q.positive_infinite(x) & Q.lt(x, 10000000) & Q.positive_infinite(y)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 3
+    assert lra.check()[0] == False
+
+    bf = Q.positive_infinite(x) & Q.gt(x, 10000000) & Q.positive_infinite(y)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 3
+    assert lra.check()[0] == True
+
+    bf = Q.positive_infinite(x) & Q.negative_infinite(x)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in enc.encoding.values():
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+
+
+def test_binrel_evaluation():
+    bf = Q.gt(3, 2)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, conflicts = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    assert len(lra.enc_to_boundary) == 0
+    assert conflicts == [[1]]
+
+    bf = Q.lt(3, 2)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, conflicts = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    assert len(lra.enc_to_boundary) == 0
+    assert conflicts == [[-1]]
+
+
+def test_negation():
+    assert HANDLE_NEGATION is True
+    bf = Q.gt(x, 1) & ~Q.gt(x, 0)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for clause in enc.data:
+        for lit in clause:
+            lra.assert_lit(lit)
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+    assert sorted(lra.check()[1]) in [[-1, 2], [-2, 1]]
+
+    bf = ~Q.gt(x, 1) & ~Q.lt(x, 0)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for clause in enc.data:
+        for lit in clause:
+            lra.assert_lit(lit)
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == True
+
+    bf = ~Q.gt(x, 0) & ~Q.lt(x, 1)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for clause in enc.data:
+        for lit in clause:
+            lra.assert_lit(lit)
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+
+    bf = ~Q.gt(x, 0) & ~Q.le(x, 0)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for clause in enc.data:
+        for lit in clause:
+            lra.assert_lit(lit)
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+
+    bf = ~Q.le(x+y, 2) & ~Q.ge(x-y, 2) & ~Q.ge(y, 0)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for clause in enc.data:
+        for lit in clause:
+            lra.assert_lit(lit)
+    assert len(lra.enc_to_boundary) == 3
+    assert lra.check()[0] == False
+    assert len(lra.check()[1]) == 3
+    assert all(i > 0 for i in lra.check()[1])
+
+
+def test_unhandled_input():
+    nan = S.NaN
+    bf = Q.gt(3, nan) & Q.gt(x, nan)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    raises(ValueError, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True))
+
+    bf = Q.gt(3, I) & Q.gt(x, I)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True))
+
+    bf = Q.gt(3, float("inf")) & Q.gt(x, float("inf"))
+    enc = boolean_formula_to_encoded_cnf(bf)
+    raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True))
+
+    bf = Q.gt(3, oo) & Q.gt(x, oo)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True))
+
+    # test non-linearity
+    bf = Q.gt(x**2 + x, 2)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True))
+
+    bf = Q.gt(cos(x) + x, 2)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True))
+
+@XFAIL
+def test_infinite_strict_inequalities():
+    # Extensive testing of the interaction between strict inequalities
+    # and constraints containing infinity is needed because
+    # the paper's rule for strict inequalities don't work when
+    # infinite numbers are allowed. Using the paper's rules you
+    # can end up with situations where oo + delta > oo is considered
+    # True when oo + delta should be equal to oo.
+    # See https://math.stackexchange.com/questions/4757069/can-this-method-of-converting-strict-inequalities-to-equisatisfiable-nonstrict-i
+    bf = (-x - y >= -float("inf")) & (x > 0) & (y >= float("inf"))
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for lit in sorted(enc.encoding.values()):
+        if lra.assert_lit(lit) is not None:
+            break
+    assert len(lra.enc_to_boundary) == 3
+    assert lra.check()[0] == True
+
+
+def test_pivot():
+    for _ in range(10):
+        m = randMatrix(5)
+        rref = m.rref()
+        for _ in range(5):
+            i, j = randint(0, 4), randint(0, 4)
+            if m[i, j] != 0:
+                assert LRASolver._pivot(m, i, j).rref() == rref
+
+
+def test_reset_bounds():
+    bf = Q.ge(x, 1) & Q.lt(x, 1)
+    enc = boolean_formula_to_encoded_cnf(bf)
+    lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
+    for clause in enc.data:
+        for lit in clause:
+            lra.assert_lit(lit)
+    assert len(lra.enc_to_boundary) == 2
+    assert lra.check()[0] == False
+
+    lra.reset_bounds()
+    assert lra.check()[0] == True
+    for var in lra.all_var:
+        assert var.upper == LRARational(float("inf"), 0)
+        assert var.upper_from_eq == False
+        assert var.upper_from_neg == False
+        assert var.lower == LRARational(-float("inf"), 0)
+        assert var.lower_from_eq == False
+        assert var.lower_from_neg == False
+        assert var.assign == LRARational(0, 0)
+        assert var.var is not None
+        assert var.col_idx is not None
+
+
+def test_empty_cnf():
+    cnf = CNF()
+    enc = EncodedCNF()
+    enc.from_cnf(cnf)
+    lra, conflict = LRASolver.from_encoded_cnf(enc)
+    assert len(conflict) == 0
+    assert lra.check() == (True, {})
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/utilities/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/utilities/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..3526c3e53d624bc70afe2df05f123c835781364c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/utilities/__init__.py
@@ -0,0 +1,3 @@
+from .dimacs import load_file
+
+__all__ = ['load_file']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/utilities/dimacs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/utilities/dimacs.py
new file mode 100644
index 0000000000000000000000000000000000000000..51302d8052c8ed8443239c1e21a2f063cf34e4ab
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/logic/utilities/dimacs.py
@@ -0,0 +1,69 @@
+"""For reading in DIMACS file format
+
+www.cs.ubc.ca/~hoos/SATLIB/Benchmarks/SAT/satformat.ps
+
+"""
+
+from sympy.core import Symbol
+from sympy.logic.boolalg import And, Or
+import re
+from pathlib import Path
+
+
+def load(s):
+    """Loads a boolean expression from a string.
+
+    Examples
+    ========
+
+    >>> from sympy.logic.utilities.dimacs import load
+    >>> load('1')
+    cnf_1
+    >>> load('1 2')
+    cnf_1 | cnf_2
+    >>> load('1 \\n 2')
+    cnf_1 & cnf_2
+    >>> load('1 2 \\n 3')
+    cnf_3 & (cnf_1 | cnf_2)
+    """
+    clauses = []
+
+    lines = s.split('\n')
+
+    pComment = re.compile(r'c.*')
+    pStats = re.compile(r'p\s*cnf\s*(\d*)\s*(\d*)')
+
+    while len(lines) > 0:
+        line = lines.pop(0)
+
+        # Only deal with lines that aren't comments
+        if not pComment.match(line):
+            m = pStats.match(line)
+
+            if not m:
+                nums = line.rstrip('\n').split(' ')
+                list = []
+                for lit in nums:
+                    if lit != '':
+                        if int(lit) == 0:
+                            continue
+                        num = abs(int(lit))
+                        sign = True
+                        if int(lit) < 0:
+                            sign = False
+
+                        if sign:
+                            list.append(Symbol("cnf_%s" % num))
+                        else:
+                            list.append(~Symbol("cnf_%s" % num))
+
+                if len(list) > 0:
+                    clauses.append(Or(*list))
+
+    return And(*clauses)
+
+
+def load_file(location):
+    """Loads a boolean expression from a file."""
+    s = Path(location).read_text()
+    return load(s)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..37b558f3f03f149dae6af20254e9b88192f7f1ed
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/__init__.py
@@ -0,0 +1,72 @@
+"""A module that handles matrices.
+
+Includes functions for fast creating matrices like zero, one/eye, random
+matrix, etc.
+"""
+from .exceptions import ShapeError, NonSquareMatrixError
+from .kind import MatrixKind
+from .dense import (
+    GramSchmidt, casoratian, diag, eye, hessian, jordan_cell,
+    list2numpy, matrix2numpy, matrix_multiply_elementwise, ones,
+    randMatrix, rot_axis1, rot_axis2, rot_axis3, rot_ccw_axis1,
+    rot_ccw_axis2, rot_ccw_axis3, rot_givens,
+    symarray, wronskian, zeros)
+from .dense import MutableDenseMatrix
+from .matrixbase import DeferredVector, MatrixBase
+
+MutableMatrix = MutableDenseMatrix
+Matrix = MutableMatrix
+
+from .sparse import MutableSparseMatrix
+from .sparsetools import banded
+from .immutable import ImmutableDenseMatrix, ImmutableSparseMatrix
+
+ImmutableMatrix = ImmutableDenseMatrix
+SparseMatrix = MutableSparseMatrix
+
+from .expressions import (
+    MatrixSlice, BlockDiagMatrix, BlockMatrix, FunctionMatrix, Identity,
+    Inverse, MatAdd, MatMul, MatPow, MatrixExpr, MatrixSymbol, Trace,
+    Transpose, ZeroMatrix, OneMatrix, blockcut, block_collapse, matrix_symbols, Adjoint,
+    hadamard_product, HadamardProduct, HadamardPower, Determinant, det,
+    diagonalize_vector, DiagMatrix, DiagonalMatrix, DiagonalOf, trace,
+    DotProduct, kronecker_product, KroneckerProduct,
+    PermutationMatrix, MatrixPermute, MatrixSet, Permanent, per)
+
+from .utilities import dotprodsimp
+
+__all__ = [
+    'ShapeError', 'NonSquareMatrixError', 'MatrixKind',
+
+    'GramSchmidt', 'casoratian', 'diag', 'eye', 'hessian', 'jordan_cell',
+    'list2numpy', 'matrix2numpy', 'matrix_multiply_elementwise', 'ones',
+    'randMatrix', 'rot_axis1', 'rot_axis2', 'rot_axis3', 'symarray',
+    'wronskian', 'zeros', 'rot_ccw_axis1', 'rot_ccw_axis2', 'rot_ccw_axis3',
+    'rot_givens',
+
+    'MutableDenseMatrix',
+
+    'DeferredVector', 'MatrixBase',
+
+    'Matrix', 'MutableMatrix',
+
+    'MutableSparseMatrix',
+
+    'banded',
+
+    'ImmutableDenseMatrix', 'ImmutableSparseMatrix',
+
+    'ImmutableMatrix', 'SparseMatrix',
+
+    'MatrixSlice', 'BlockDiagMatrix', 'BlockMatrix', 'FunctionMatrix',
+    'Identity', 'Inverse', 'MatAdd', 'MatMul', 'MatPow', 'MatrixExpr',
+    'MatrixSymbol', 'Trace', 'Transpose', 'ZeroMatrix', 'OneMatrix',
+    'blockcut', 'block_collapse', 'matrix_symbols', 'Adjoint',
+    'hadamard_product', 'HadamardProduct', 'HadamardPower', 'Determinant',
+    'det', 'diagonalize_vector', 'DiagMatrix', 'DiagonalMatrix',
+    'DiagonalOf', 'trace', 'DotProduct', 'kronecker_product',
+    'KroneckerProduct', 'PermutationMatrix', 'MatrixPermute', 'MatrixSet',
+    'Permanent', 'per',
+
+    'dotprodsimp',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/benchmarks/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/benchmarks/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/benchmarks/bench_matrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/benchmarks/bench_matrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..4fb845600533c4c6fef196fe5a45b98890f4ad78
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/benchmarks/bench_matrix.py
@@ -0,0 +1,21 @@
+from sympy.core.numbers import Integer
+from sympy.matrices.dense import (eye, zeros)
+
+i3 = Integer(3)
+M = eye(100)
+
+
+def timeit_Matrix__getitem_ii():
+    M[3, 3]
+
+
+def timeit_Matrix__getitem_II():
+    M[i3, i3]
+
+
+def timeit_Matrix__getslice():
+    M[:, :]
+
+
+def timeit_Matrix_zeronm():
+    zeros(100, 100)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/common.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/common.py
new file mode 100644
index 0000000000000000000000000000000000000000..bcb54726fe1a0c36658d8bf63b974db5a3ce8bad
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/common.py
@@ -0,0 +1,3258 @@
+"""
+A module containing deprecated matrix mixin classes.
+
+The classes in this module are deprecated and will be removed in a future
+release. They are kept here for backwards compatibility in case downstream
+code was subclassing them.
+
+Importing anything else from this module is deprecated so anything here
+should either not be used or should be imported from somewhere else.
+"""
+from __future__ import annotations
+from collections import defaultdict
+from collections.abc import Iterable
+from inspect import isfunction
+from functools import reduce
+
+from sympy.assumptions.refine import refine
+from sympy.core import SympifyError, Add
+from sympy.core.basic import Atom
+from sympy.core.decorators import call_highest_priority
+from sympy.core.logic import fuzzy_and, FuzzyBool
+from sympy.core.numbers import Integer
+from sympy.core.mod import Mod
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.complexes import Abs, re, im
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from .utilities import _dotprodsimp, _simplify
+from sympy.polys.polytools import Poly
+from sympy.utilities.iterables import flatten, is_sequence
+from sympy.utilities.misc import as_int, filldedent
+from sympy.tensor.array import NDimArray
+
+from .utilities import _get_intermediate_simp_bool
+
+
+# These exception types were previously defined in this module but were moved
+# to exceptions.py. We reimport them here for backwards compatibility in case
+# downstream code was importing them from here.
+from .exceptions import ( # noqa: F401
+    MatrixError, ShapeError, NonSquareMatrixError, NonInvertibleMatrixError,
+    NonPositiveDefiniteMatrixError
+)
+
+
+_DEPRECATED_MIXINS = (
+    'MatrixShaping',
+    'MatrixSpecial',
+    'MatrixProperties',
+    'MatrixOperations',
+    'MatrixArithmetic',
+    'MatrixCommon',
+    'MatrixDeterminant',
+    'MatrixReductions',
+    'MatrixSubspaces',
+    'MatrixEigen',
+    'MatrixCalculus',
+    'MatrixDeprecated',
+)
+
+
+class _MatrixDeprecatedMeta(type):
+
+    #
+    # Override the default __instancecheck__ implementation to ensure that
+    # e.g. isinstance(M, MatrixCommon) still works when M is one of the
+    # matrix classes. Matrix no longer inherits from MatrixCommon so
+    # isinstance(M, MatrixCommon) would now return False by default.
+    #
+    # There were lots of places in the codebase where this was being done
+    # so it seems likely that downstream code may be doing it too. All use
+    # of these mixins is deprecated though so we give a deprecation warning
+    # unconditionally if they are being used with isinstance.
+    #
+    # Any code seeing this deprecation warning should be changed to use
+    # isinstance(M, MatrixBase) instead which also works in previous versions
+    # of SymPy.
+    #
+
+    def __instancecheck__(cls, instance):
+
+        sympy_deprecation_warning(
+            f"""
+            Checking whether an object is an instance of {cls.__name__} is
+            deprecated.
+
+            Use `isinstance(obj, Matrix)` instead of `isinstance(obj, {cls.__name__})`.
+            """,
+            deprecated_since_version="1.13",
+            active_deprecations_target="deprecated-matrix-mixins",
+            stacklevel=3,
+        )
+
+        from sympy.matrices.matrixbase import MatrixBase
+        from sympy.matrices.matrices import (
+            MatrixDeterminant,
+            MatrixReductions,
+            MatrixSubspaces,
+            MatrixEigen,
+            MatrixCalculus,
+            MatrixDeprecated
+        )
+
+        all_mixins = (
+            MatrixRequired,
+            MatrixShaping,
+            MatrixSpecial,
+            MatrixProperties,
+            MatrixOperations,
+            MatrixArithmetic,
+            MatrixCommon,
+            MatrixDeterminant,
+            MatrixReductions,
+            MatrixSubspaces,
+            MatrixEigen,
+            MatrixCalculus,
+            MatrixDeprecated
+        )
+
+        if cls in all_mixins and isinstance(instance, MatrixBase):
+            return True
+        else:
+            return super().__instancecheck__(instance)
+
+
+class MatrixRequired(metaclass=_MatrixDeprecatedMeta):
+    """Deprecated mixin class for making matrix classes."""
+
+    rows: int
+    cols: int
+    _simplify = None
+
+    def __init_subclass__(cls, **kwargs):
+
+        # Warn if any downstream code is subclassing this class or any of the
+        # deprecated mixin classes that are all ultimately subclasses of this
+        # class.
+        #
+        # We don't want to warn about the deprecated mixins themselves being
+        # created, but only about them being used as mixins by downstream code.
+        # Otherwise just importing this module would trigger a warning.
+        # Ultimately the whole module should be deprecated and removed but for
+        # SymPy 1.13 it is premature to do that given that this module was the
+        # main way to import matrix exception types in all previous versions.
+
+        if cls.__name__ not in _DEPRECATED_MIXINS:
+            sympy_deprecation_warning(
+                f"""
+                Inheriting from the Matrix mixin classes is deprecated.
+
+                The class {cls.__name__} is subclassing a deprecated mixin.
+                """,
+                deprecated_since_version="1.13",
+                active_deprecations_target="deprecated-matrix-mixins",
+                stacklevel=3,
+            )
+
+        super().__init_subclass__(**kwargs)
+
+    @classmethod
+    def _new(cls, *args, **kwargs):
+        """`_new` must, at minimum, be callable as
+        `_new(rows, cols, mat) where mat is a flat list of the
+        elements of the matrix."""
+        raise NotImplementedError("Subclasses must implement this.")
+
+    def __eq__(self, other):
+        raise NotImplementedError("Subclasses must implement this.")
+
+    def __getitem__(self, key):
+        """Implementations of __getitem__ should accept ints, in which
+        case the matrix is indexed as a flat list, tuples (i,j) in which
+        case the (i,j) entry is returned, slices, or mixed tuples (a,b)
+        where a and b are any combination of slices and integers."""
+        raise NotImplementedError("Subclasses must implement this.")
+
+    def __len__(self):
+        """The total number of entries in the matrix."""
+        raise NotImplementedError("Subclasses must implement this.")
+
+    @property
+    def shape(self):
+        raise NotImplementedError("Subclasses must implement this.")
+
+
+class MatrixShaping(MatrixRequired):
+    """Provides basic matrix shaping and extracting of submatrices"""
+
+    def _eval_col_del(self, col):
+        def entry(i, j):
+            return self[i, j] if j < col else self[i, j + 1]
+        return self._new(self.rows, self.cols - 1, entry)
+
+    def _eval_col_insert(self, pos, other):
+
+        def entry(i, j):
+            if j < pos:
+                return self[i, j]
+            elif pos <= j < pos + other.cols:
+                return other[i, j - pos]
+            return self[i, j - other.cols]
+
+        return self._new(self.rows, self.cols + other.cols, entry)
+
+    def _eval_col_join(self, other):
+        rows = self.rows
+
+        def entry(i, j):
+            if i < rows:
+                return self[i, j]
+            return other[i - rows, j]
+
+        return classof(self, other)._new(self.rows + other.rows, self.cols,
+                                         entry)
+
+    def _eval_extract(self, rowsList, colsList):
+        mat = list(self)
+        cols = self.cols
+        indices = (i * cols + j for i in rowsList for j in colsList)
+        return self._new(len(rowsList), len(colsList),
+                         [mat[i] for i in indices])
+
+    def _eval_get_diag_blocks(self):
+        sub_blocks = []
+
+        def recurse_sub_blocks(M):
+            for i in range(1, M.shape[0] + 1):
+                if i == 1:
+                    to_the_right = M[0, i:]
+                    to_the_bottom = M[i:, 0]
+                else:
+                    to_the_right = M[:i, i:]
+                    to_the_bottom = M[i:, :i]
+                if any(to_the_right) or any(to_the_bottom):
+                    continue
+                sub_blocks.append(M[:i, :i])
+                if M.shape != M[:i, :i].shape:
+                    recurse_sub_blocks(M[i:, i:])
+                return
+
+        recurse_sub_blocks(self)
+        return sub_blocks
+
+    def _eval_row_del(self, row):
+        def entry(i, j):
+            return self[i, j] if i < row else self[i + 1, j]
+        return self._new(self.rows - 1, self.cols, entry)
+
+    def _eval_row_insert(self, pos, other):
+        entries = list(self)
+        insert_pos = pos * self.cols
+        entries[insert_pos:insert_pos] = list(other)
+        return self._new(self.rows + other.rows, self.cols, entries)
+
+    def _eval_row_join(self, other):
+        cols = self.cols
+
+        def entry(i, j):
+            if j < cols:
+                return self[i, j]
+            return other[i, j - cols]
+
+        return classof(self, other)._new(self.rows, self.cols + other.cols,
+                                         entry)
+
+    def _eval_tolist(self):
+        return [list(self[i,:]) for i in range(self.rows)]
+
+    def _eval_todok(self):
+        dok = {}
+        rows, cols = self.shape
+        for i in range(rows):
+            for j in range(cols):
+                val = self[i, j]
+                if val != self.zero:
+                    dok[i, j] = val
+        return dok
+
+    def _eval_vec(self):
+        rows = self.rows
+
+        def entry(n, _):
+            # we want to read off the columns first
+            j = n // rows
+            i = n - j * rows
+            return self[i, j]
+
+        return self._new(len(self), 1, entry)
+
+    def _eval_vech(self, diagonal):
+        c = self.cols
+        v = []
+        if diagonal:
+            for j in range(c):
+                for i in range(j, c):
+                    v.append(self[i, j])
+        else:
+            for j in range(c):
+                for i in range(j + 1, c):
+                    v.append(self[i, j])
+        return self._new(len(v), 1, v)
+
+    def col_del(self, col):
+        """Delete the specified column."""
+        if col < 0:
+            col += self.cols
+        if not 0 <= col < self.cols:
+            raise IndexError("Column {} is out of range.".format(col))
+        return self._eval_col_del(col)
+
+    def col_insert(self, pos, other):
+        """Insert one or more columns at the given column position.
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(3, 1)
+        >>> M.col_insert(1, V)
+        Matrix([
+        [0, 1, 0, 0],
+        [0, 1, 0, 0],
+        [0, 1, 0, 0]])
+
+        See Also
+        ========
+
+        col
+        row_insert
+        """
+        # Allows you to build a matrix even if it is null matrix
+        if not self:
+            return type(self)(other)
+
+        pos = as_int(pos)
+
+        if pos < 0:
+            pos = self.cols + pos
+        if pos < 0:
+            pos = 0
+        elif pos > self.cols:
+            pos = self.cols
+
+        if self.rows != other.rows:
+            raise ShapeError(
+                "The matrices have incompatible number of rows ({} and {})"
+                .format(self.rows, other.rows))
+
+        return self._eval_col_insert(pos, other)
+
+    def col_join(self, other):
+        """Concatenates two matrices along self's last and other's first row.
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(1, 3)
+        >>> M.col_join(V)
+        Matrix([
+        [0, 0, 0],
+        [0, 0, 0],
+        [0, 0, 0],
+        [1, 1, 1]])
+
+        See Also
+        ========
+
+        col
+        row_join
+        """
+        # A null matrix can always be stacked (see  #10770)
+        if self.rows == 0 and self.cols != other.cols:
+            return self._new(0, other.cols, []).col_join(other)
+
+        if self.cols != other.cols:
+            raise ShapeError(
+                "The matrices have incompatible number of columns ({} and {})"
+                .format(self.cols, other.cols))
+        return self._eval_col_join(other)
+
+    def col(self, j):
+        """Elementary column selector.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> eye(2).col(0)
+        Matrix([
+        [1],
+        [0]])
+
+        See Also
+        ========
+
+        row
+        col_del
+        col_join
+        col_insert
+        """
+        return self[:, j]
+
+    def extract(self, rowsList, colsList):
+        r"""Return a submatrix by specifying a list of rows and columns.
+        Negative indices can be given. All indices must be in the range
+        $-n \le i < n$ where $n$ is the number of rows or columns.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(4, 3, range(12))
+        >>> m
+        Matrix([
+        [0,  1,  2],
+        [3,  4,  5],
+        [6,  7,  8],
+        [9, 10, 11]])
+        >>> m.extract([0, 1, 3], [0, 1])
+        Matrix([
+        [0,  1],
+        [3,  4],
+        [9, 10]])
+
+        Rows or columns can be repeated:
+
+        >>> m.extract([0, 0, 1], [-1])
+        Matrix([
+        [2],
+        [2],
+        [5]])
+
+        Every other row can be taken by using range to provide the indices:
+
+        >>> m.extract(range(0, m.rows, 2), [-1])
+        Matrix([
+        [2],
+        [8]])
+
+        RowsList or colsList can also be a list of booleans, in which case
+        the rows or columns corresponding to the True values will be selected:
+
+        >>> m.extract([0, 1, 2, 3], [True, False, True])
+        Matrix([
+        [0,  2],
+        [3,  5],
+        [6,  8],
+        [9, 11]])
+        """
+
+        if not is_sequence(rowsList) or not is_sequence(colsList):
+            raise TypeError("rowsList and colsList must be iterable")
+        # ensure rowsList and colsList are lists of integers
+        if rowsList and all(isinstance(i, bool) for i in rowsList):
+            rowsList = [index for index, item in enumerate(rowsList) if item]
+        if colsList and all(isinstance(i, bool) for i in colsList):
+            colsList = [index for index, item in enumerate(colsList) if item]
+
+        # ensure everything is in range
+        rowsList = [a2idx(k, self.rows) for k in rowsList]
+        colsList = [a2idx(k, self.cols) for k in colsList]
+
+        return self._eval_extract(rowsList, colsList)
+
+    def get_diag_blocks(self):
+        """Obtains the square sub-matrices on the main diagonal of a square matrix.
+
+        Useful for inverting symbolic matrices or solving systems of
+        linear equations which may be decoupled by having a block diagonal
+        structure.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y, z
+        >>> A = Matrix([[1, 3, 0, 0], [y, z*z, 0, 0], [0, 0, x, 0], [0, 0, 0, 0]])
+        >>> a1, a2, a3 = A.get_diag_blocks()
+        >>> a1
+        Matrix([
+        [1,    3],
+        [y, z**2]])
+        >>> a2
+        Matrix([[x]])
+        >>> a3
+        Matrix([[0]])
+
+        """
+        return self._eval_get_diag_blocks()
+
+    @classmethod
+    def hstack(cls, *args):
+        """Return a matrix formed by joining args horizontally (i.e.
+        by repeated application of row_join).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, eye
+        >>> Matrix.hstack(eye(2), 2*eye(2))
+        Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2]])
+        """
+        if len(args) == 0:
+            return cls._new()
+
+        kls = type(args[0])
+        return reduce(kls.row_join, args)
+
+    def reshape(self, rows, cols):
+        """Reshape the matrix. Total number of elements must remain the same.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 3, lambda i, j: 1)
+        >>> m
+        Matrix([
+        [1, 1, 1],
+        [1, 1, 1]])
+        >>> m.reshape(1, 6)
+        Matrix([[1, 1, 1, 1, 1, 1]])
+        >>> m.reshape(3, 2)
+        Matrix([
+        [1, 1],
+        [1, 1],
+        [1, 1]])
+
+        """
+        if self.rows * self.cols != rows * cols:
+            raise ValueError("Invalid reshape parameters %d %d" % (rows, cols))
+        return self._new(rows, cols, lambda i, j: self[i * cols + j])
+
+    def row_del(self, row):
+        """Delete the specified row."""
+        if row < 0:
+            row += self.rows
+        if not 0 <= row < self.rows:
+            raise IndexError("Row {} is out of range.".format(row))
+
+        return self._eval_row_del(row)
+
+    def row_insert(self, pos, other):
+        """Insert one or more rows at the given row position.
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(1, 3)
+        >>> M.row_insert(1, V)
+        Matrix([
+        [0, 0, 0],
+        [1, 1, 1],
+        [0, 0, 0],
+        [0, 0, 0]])
+
+        See Also
+        ========
+
+        row
+        col_insert
+        """
+        # Allows you to build a matrix even if it is null matrix
+        if not self:
+            return self._new(other)
+
+        pos = as_int(pos)
+
+        if pos < 0:
+            pos = self.rows + pos
+        if pos < 0:
+            pos = 0
+        elif pos > self.rows:
+            pos = self.rows
+
+        if self.cols != other.cols:
+            raise ShapeError(
+                "The matrices have incompatible number of columns ({} and {})"
+                .format(self.cols, other.cols))
+
+        return self._eval_row_insert(pos, other)
+
+    def row_join(self, other):
+        """Concatenates two matrices along self's last and rhs's first column
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(3, 1)
+        >>> M.row_join(V)
+        Matrix([
+        [0, 0, 0, 1],
+        [0, 0, 0, 1],
+        [0, 0, 0, 1]])
+
+        See Also
+        ========
+
+        row
+        col_join
+        """
+        # A null matrix can always be stacked (see  #10770)
+        if self.cols == 0 and self.rows != other.rows:
+            return self._new(other.rows, 0, []).row_join(other)
+
+        if self.rows != other.rows:
+            raise ShapeError(
+                "The matrices have incompatible number of rows ({} and {})"
+                .format(self.rows, other.rows))
+        return self._eval_row_join(other)
+
+    def diagonal(self, k=0):
+        """Returns the kth diagonal of self. The main diagonal
+        corresponds to `k=0`; diagonals above and below correspond to
+        `k > 0` and `k < 0`, respectively. The values of `self[i, j]`
+        for which `j - i = k`, are returned in order of increasing
+        `i + j`, starting with `i + j = |k|`.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(3, 3, lambda i, j: j - i); m
+        Matrix([
+        [ 0,  1, 2],
+        [-1,  0, 1],
+        [-2, -1, 0]])
+        >>> _.diagonal()
+        Matrix([[0, 0, 0]])
+        >>> m.diagonal(1)
+        Matrix([[1, 1]])
+        >>> m.diagonal(-2)
+        Matrix([[-2]])
+
+        Even though the diagonal is returned as a Matrix, the element
+        retrieval can be done with a single index:
+
+        >>> Matrix.diag(1, 2, 3).diagonal()[1]  # instead of [0, 1]
+        2
+
+        See Also
+        ========
+
+        diag
+        """
+        rv = []
+        k = as_int(k)
+        r = 0 if k > 0 else -k
+        c = 0 if r else k
+        while True:
+            if r == self.rows or c == self.cols:
+                break
+            rv.append(self[r, c])
+            r += 1
+            c += 1
+        if not rv:
+            raise ValueError(filldedent('''
+            The %s diagonal is out of range [%s, %s]''' % (
+            k, 1 - self.rows, self.cols - 1)))
+        return self._new(1, len(rv), rv)
+
+    def row(self, i):
+        """Elementary row selector.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> eye(2).row(0)
+        Matrix([[1, 0]])
+
+        See Also
+        ========
+
+        col
+        row_del
+        row_join
+        row_insert
+        """
+        return self[i, :]
+
+    @property
+    def shape(self):
+        """The shape (dimensions) of the matrix as the 2-tuple (rows, cols).
+
+        Examples
+        ========
+
+        >>> from sympy import zeros
+        >>> M = zeros(2, 3)
+        >>> M.shape
+        (2, 3)
+        >>> M.rows
+        2
+        >>> M.cols
+        3
+        """
+        return (self.rows, self.cols)
+
+    def todok(self):
+        """Return the matrix as dictionary of keys.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix.eye(3)
+        >>> M.todok()
+        {(0, 0): 1, (1, 1): 1, (2, 2): 1}
+        """
+        return self._eval_todok()
+
+    def tolist(self):
+        """Return the Matrix as a nested Python list.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, ones
+        >>> m = Matrix(3, 3, range(9))
+        >>> m
+        Matrix([
+        [0, 1, 2],
+        [3, 4, 5],
+        [6, 7, 8]])
+        >>> m.tolist()
+        [[0, 1, 2], [3, 4, 5], [6, 7, 8]]
+        >>> ones(3, 0).tolist()
+        [[], [], []]
+
+        When there are no rows then it will not be possible to tell how
+        many columns were in the original matrix:
+
+        >>> ones(0, 3).tolist()
+        []
+
+        """
+        if not self.rows:
+            return []
+        if not self.cols:
+            return [[] for i in range(self.rows)]
+        return self._eval_tolist()
+
+    def todod(M):
+        """Returns matrix as dict of dicts containing non-zero elements of the Matrix
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[0, 1],[0, 3]])
+        >>> A
+        Matrix([
+        [0, 1],
+        [0, 3]])
+        >>> A.todod()
+        {0: {1: 1}, 1: {1: 3}}
+
+
+        """
+        rowsdict = {}
+        Mlol = M.tolist()
+        for i, Mi in enumerate(Mlol):
+            row = {j: Mij for j, Mij in enumerate(Mi) if Mij}
+            if row:
+                rowsdict[i] = row
+        return rowsdict
+
+    def vec(self):
+        """Return the Matrix converted into a one column matrix by stacking columns
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m=Matrix([[1, 3], [2, 4]])
+        >>> m
+        Matrix([
+        [1, 3],
+        [2, 4]])
+        >>> m.vec()
+        Matrix([
+        [1],
+        [2],
+        [3],
+        [4]])
+
+        See Also
+        ========
+
+        vech
+        """
+        return self._eval_vec()
+
+    def vech(self, diagonal=True, check_symmetry=True):
+        """Reshapes the matrix into a column vector by stacking the
+        elements in the lower triangle.
+
+        Parameters
+        ==========
+
+        diagonal : bool, optional
+            If ``True``, it includes the diagonal elements.
+
+        check_symmetry : bool, optional
+            If ``True``, it checks whether the matrix is symmetric.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m=Matrix([[1, 2], [2, 3]])
+        >>> m
+        Matrix([
+        [1, 2],
+        [2, 3]])
+        >>> m.vech()
+        Matrix([
+        [1],
+        [2],
+        [3]])
+        >>> m.vech(diagonal=False)
+        Matrix([[2]])
+
+        Notes
+        =====
+
+        This should work for symmetric matrices and ``vech`` can
+        represent symmetric matrices in vector form with less size than
+        ``vec``.
+
+        See Also
+        ========
+
+        vec
+        """
+        if not self.is_square:
+            raise NonSquareMatrixError
+
+        if check_symmetry and not self.is_symmetric():
+            raise ValueError("The matrix is not symmetric.")
+
+        return self._eval_vech(diagonal)
+
+    @classmethod
+    def vstack(cls, *args):
+        """Return a matrix formed by joining args vertically (i.e.
+        by repeated application of col_join).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, eye
+        >>> Matrix.vstack(eye(2), 2*eye(2))
+        Matrix([
+        [1, 0],
+        [0, 1],
+        [2, 0],
+        [0, 2]])
+        """
+        if len(args) == 0:
+            return cls._new()
+
+        kls = type(args[0])
+        return reduce(kls.col_join, args)
+
+
+class MatrixSpecial(MatrixRequired):
+    """Construction of special matrices"""
+
+    @classmethod
+    def _eval_diag(cls, rows, cols, diag_dict):
+        """diag_dict is a defaultdict containing
+        all the entries of the diagonal matrix."""
+        def entry(i, j):
+            return diag_dict[(i, j)]
+        return cls._new(rows, cols, entry)
+
+    @classmethod
+    def _eval_eye(cls, rows, cols):
+        vals = [cls.zero]*(rows*cols)
+        vals[::cols+1] = [cls.one]*min(rows, cols)
+        return cls._new(rows, cols, vals, copy=False)
+
+    @classmethod
+    def _eval_jordan_block(cls, size: int, eigenvalue, band='upper'):
+        if band == 'lower':
+            def entry(i, j):
+                if i == j:
+                    return eigenvalue
+                elif j + 1 == i:
+                    return cls.one
+                return cls.zero
+        else:
+            def entry(i, j):
+                if i == j:
+                    return eigenvalue
+                elif i + 1 == j:
+                    return cls.one
+                return cls.zero
+        return cls._new(size, size, entry)
+
+    @classmethod
+    def _eval_ones(cls, rows, cols):
+        def entry(i, j):
+            return cls.one
+        return cls._new(rows, cols, entry)
+
+    @classmethod
+    def _eval_zeros(cls, rows, cols):
+        return cls._new(rows, cols, [cls.zero]*(rows*cols), copy=False)
+
+    @classmethod
+    def _eval_wilkinson(cls, n):
+        def entry(i, j):
+            return cls.one if i + 1 == j else cls.zero
+
+        D = cls._new(2*n + 1, 2*n + 1, entry)
+
+        wminus = cls.diag(list(range(-n, n + 1)), unpack=True) + D + D.T
+        wplus = abs(cls.diag(list(range(-n, n + 1)), unpack=True)) + D + D.T
+
+        return wminus, wplus
+
+    @classmethod
+    def diag(kls, *args, strict=False, unpack=True, rows=None, cols=None, **kwargs):
+        """Returns a matrix with the specified diagonal.
+        If matrices are passed, a block-diagonal matrix
+        is created (i.e. the "direct sum" of the matrices).
+
+        kwargs
+        ======
+
+        rows : rows of the resulting matrix; computed if
+               not given.
+
+        cols : columns of the resulting matrix; computed if
+               not given.
+
+        cls : class for the resulting matrix
+
+        unpack : bool which, when True (default), unpacks a single
+        sequence rather than interpreting it as a Matrix.
+
+        strict : bool which, when False (default), allows Matrices to
+        have variable-length rows.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> Matrix.diag(1, 2, 3)
+        Matrix([
+        [1, 0, 0],
+        [0, 2, 0],
+        [0, 0, 3]])
+
+        The current default is to unpack a single sequence. If this is
+        not desired, set `unpack=False` and it will be interpreted as
+        a matrix.
+
+        >>> Matrix.diag([1, 2, 3]) == Matrix.diag(1, 2, 3)
+        True
+
+        When more than one element is passed, each is interpreted as
+        something to put on the diagonal. Lists are converted to
+        matrices. Filling of the diagonal always continues from
+        the bottom right hand corner of the previous item: this
+        will create a block-diagonal matrix whether the matrices
+        are square or not.
+
+        >>> col = [1, 2, 3]
+        >>> row = [[4, 5]]
+        >>> Matrix.diag(col, row)
+        Matrix([
+        [1, 0, 0],
+        [2, 0, 0],
+        [3, 0, 0],
+        [0, 4, 5]])
+
+        When `unpack` is False, elements within a list need not all be
+        of the same length. Setting `strict` to True would raise a
+        ValueError for the following:
+
+        >>> Matrix.diag([[1, 2, 3], [4, 5], [6]], unpack=False)
+        Matrix([
+        [1, 2, 3],
+        [4, 5, 0],
+        [6, 0, 0]])
+
+        The type of the returned matrix can be set with the ``cls``
+        keyword.
+
+        >>> from sympy import ImmutableMatrix
+        >>> from sympy.utilities.misc import func_name
+        >>> func_name(Matrix.diag(1, cls=ImmutableMatrix))
+        'ImmutableDenseMatrix'
+
+        A zero dimension matrix can be used to position the start of
+        the filling at the start of an arbitrary row or column:
+
+        >>> from sympy import ones
+        >>> r2 = ones(0, 2)
+        >>> Matrix.diag(r2, 1, 2)
+        Matrix([
+        [0, 0, 1, 0],
+        [0, 0, 0, 2]])
+
+        See Also
+        ========
+        eye
+        diagonal
+        .dense.diag
+        .expressions.blockmatrix.BlockMatrix
+        .sparsetools.banded
+       """
+        from sympy.matrices.matrixbase import MatrixBase
+        from sympy.matrices.dense import Matrix
+        from sympy.matrices import SparseMatrix
+        klass = kwargs.get('cls', kls)
+        if unpack and len(args) == 1 and is_sequence(args[0]) and \
+                not isinstance(args[0], MatrixBase):
+            args = args[0]
+
+        # fill a default dict with the diagonal entries
+        diag_entries = defaultdict(int)
+        rmax = cmax = 0  # keep track of the biggest index seen
+        for m in args:
+            if isinstance(m, list):
+                if strict:
+                    # if malformed, Matrix will raise an error
+                    _ = Matrix(m)
+                    r, c = _.shape
+                    m = _.tolist()
+                else:
+                    r, c, smat = SparseMatrix._handle_creation_inputs(m)
+                    for (i, j), _ in smat.items():
+                        diag_entries[(i + rmax, j + cmax)] = _
+                    m = []  # to skip process below
+            elif hasattr(m, 'shape'):  # a Matrix
+                # convert to list of lists
+                r, c = m.shape
+                m = m.tolist()
+            else:  # in this case, we're a single value
+                diag_entries[(rmax, cmax)] = m
+                rmax += 1
+                cmax += 1
+                continue
+            # process list of lists
+            for i, mi in enumerate(m):
+                for j, _ in enumerate(mi):
+                    diag_entries[(i + rmax, j + cmax)] = _
+            rmax += r
+            cmax += c
+        if rows is None:
+            rows, cols = cols, rows
+        if rows is None:
+            rows, cols = rmax, cmax
+        else:
+            cols = rows if cols is None else cols
+        if rows < rmax or cols < cmax:
+            raise ValueError(filldedent('''
+                The constructed matrix is {} x {} but a size of {} x {}
+                was specified.'''.format(rmax, cmax, rows, cols)))
+        return klass._eval_diag(rows, cols, diag_entries)
+
+    @classmethod
+    def eye(kls, rows, cols=None, **kwargs):
+        """Returns an identity matrix.
+
+        Parameters
+        ==========
+
+        rows : rows of the matrix
+        cols : cols of the matrix (if None, cols=rows)
+
+        kwargs
+        ======
+        cls : class of the returned matrix
+        """
+        if cols is None:
+            cols = rows
+        if rows < 0 or cols < 0:
+            raise ValueError("Cannot create a {} x {} matrix. "
+                             "Both dimensions must be positive".format(rows, cols))
+        klass = kwargs.get('cls', kls)
+        rows, cols = as_int(rows), as_int(cols)
+
+        return klass._eval_eye(rows, cols)
+
+    @classmethod
+    def jordan_block(kls, size=None, eigenvalue=None, *, band='upper', **kwargs):
+        """Returns a Jordan block
+
+        Parameters
+        ==========
+
+        size : Integer, optional
+            Specifies the shape of the Jordan block matrix.
+
+        eigenvalue : Number or Symbol
+            Specifies the value for the main diagonal of the matrix.
+
+            .. note::
+                The keyword ``eigenval`` is also specified as an alias
+                of this keyword, but it is not recommended to use.
+
+                We may deprecate the alias in later release.
+
+        band : 'upper' or 'lower', optional
+            Specifies the position of the off-diagonal to put `1` s on.
+
+        cls : Matrix, optional
+            Specifies the matrix class of the output form.
+
+            If it is not specified, the class type where the method is
+            being executed on will be returned.
+
+        Returns
+        =======
+
+        Matrix
+            A Jordan block matrix.
+
+        Raises
+        ======
+
+        ValueError
+            If insufficient arguments are given for matrix size
+            specification, or no eigenvalue is given.
+
+        Examples
+        ========
+
+        Creating a default Jordan block:
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x
+        >>> Matrix.jordan_block(4, x)
+        Matrix([
+        [x, 1, 0, 0],
+        [0, x, 1, 0],
+        [0, 0, x, 1],
+        [0, 0, 0, x]])
+
+        Creating an alternative Jordan block matrix where `1` is on
+        lower off-diagonal:
+
+        >>> Matrix.jordan_block(4, x, band='lower')
+        Matrix([
+        [x, 0, 0, 0],
+        [1, x, 0, 0],
+        [0, 1, x, 0],
+        [0, 0, 1, x]])
+
+        Creating a Jordan block with keyword arguments
+
+        >>> Matrix.jordan_block(size=4, eigenvalue=x)
+        Matrix([
+        [x, 1, 0, 0],
+        [0, x, 1, 0],
+        [0, 0, x, 1],
+        [0, 0, 0, x]])
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Jordan_matrix
+        """
+        klass = kwargs.pop('cls', kls)
+
+        eigenval = kwargs.get('eigenval', None)
+        if eigenvalue is None and eigenval is None:
+            raise ValueError("Must supply an eigenvalue")
+        elif eigenvalue != eigenval and None not in (eigenval, eigenvalue):
+            raise ValueError(
+                "Inconsistent values are given: 'eigenval'={}, "
+                "'eigenvalue'={}".format(eigenval, eigenvalue))
+        else:
+            if eigenval is not None:
+                eigenvalue = eigenval
+
+        if size is None:
+            raise ValueError("Must supply a matrix size")
+
+        size = as_int(size)
+        return klass._eval_jordan_block(size, eigenvalue, band)
+
+    @classmethod
+    def ones(kls, rows, cols=None, **kwargs):
+        """Returns a matrix of ones.
+
+        Parameters
+        ==========
+
+        rows : rows of the matrix
+        cols : cols of the matrix (if None, cols=rows)
+
+        kwargs
+        ======
+        cls : class of the returned matrix
+        """
+        if cols is None:
+            cols = rows
+        klass = kwargs.get('cls', kls)
+        rows, cols = as_int(rows), as_int(cols)
+
+        return klass._eval_ones(rows, cols)
+
+    @classmethod
+    def zeros(kls, rows, cols=None, **kwargs):
+        """Returns a matrix of zeros.
+
+        Parameters
+        ==========
+
+        rows : rows of the matrix
+        cols : cols of the matrix (if None, cols=rows)
+
+        kwargs
+        ======
+        cls : class of the returned matrix
+        """
+        if cols is None:
+            cols = rows
+        if rows < 0 or cols < 0:
+            raise ValueError("Cannot create a {} x {} matrix. "
+                             "Both dimensions must be positive".format(rows, cols))
+        klass = kwargs.get('cls', kls)
+        rows, cols = as_int(rows), as_int(cols)
+
+        return klass._eval_zeros(rows, cols)
+
+    @classmethod
+    def companion(kls, poly):
+        """Returns a companion matrix of a polynomial.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, Poly, Symbol, symbols
+        >>> x = Symbol('x')
+        >>> c0, c1, c2, c3, c4 = symbols('c0:5')
+        >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x)
+        >>> Matrix.companion(p)
+        Matrix([
+        [0, 0, 0, 0, -c0],
+        [1, 0, 0, 0, -c1],
+        [0, 1, 0, 0, -c2],
+        [0, 0, 1, 0, -c3],
+        [0, 0, 0, 1, -c4]])
+        """
+        poly = kls._sympify(poly)
+        if not isinstance(poly, Poly):
+            raise ValueError("{} must be a Poly instance.".format(poly))
+        if not poly.is_monic:
+            raise ValueError("{} must be a monic polynomial.".format(poly))
+        if not poly.is_univariate:
+            raise ValueError(
+                "{} must be a univariate polynomial.".format(poly))
+
+        size = poly.degree()
+        if not size >= 1:
+            raise ValueError(
+                "{} must have degree not less than 1.".format(poly))
+
+        coeffs = poly.all_coeffs()
+        def entry(i, j):
+            if j == size - 1:
+                return -coeffs[-1 - i]
+            elif i == j + 1:
+                return kls.one
+            return kls.zero
+        return kls._new(size, size, entry)
+
+
+    @classmethod
+    def wilkinson(kls, n, **kwargs):
+        """Returns two square Wilkinson Matrix of size 2*n + 1
+        $W_{2n + 1}^-, W_{2n + 1}^+ =$ Wilkinson(n)
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> wminus, wplus = Matrix.wilkinson(3)
+        >>> wminus
+        Matrix([
+        [-3,  1,  0, 0, 0, 0, 0],
+        [ 1, -2,  1, 0, 0, 0, 0],
+        [ 0,  1, -1, 1, 0, 0, 0],
+        [ 0,  0,  1, 0, 1, 0, 0],
+        [ 0,  0,  0, 1, 1, 1, 0],
+        [ 0,  0,  0, 0, 1, 2, 1],
+        [ 0,  0,  0, 0, 0, 1, 3]])
+        >>> wplus
+        Matrix([
+        [3, 1, 0, 0, 0, 0, 0],
+        [1, 2, 1, 0, 0, 0, 0],
+        [0, 1, 1, 1, 0, 0, 0],
+        [0, 0, 1, 0, 1, 0, 0],
+        [0, 0, 0, 1, 1, 1, 0],
+        [0, 0, 0, 0, 1, 2, 1],
+        [0, 0, 0, 0, 0, 1, 3]])
+
+        References
+        ==========
+
+        .. [1] https://blogs.mathworks.com/cleve/2013/04/15/wilkinsons-matrices-2/
+        .. [2] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Claredon Press, Oxford, 1965, 662 pp.
+
+        """
+        klass = kwargs.get('cls', kls)
+        n = as_int(n)
+        return klass._eval_wilkinson(n)
+
+class MatrixProperties(MatrixRequired):
+    """Provides basic properties of a matrix."""
+
+    def _eval_atoms(self, *types):
+        result = set()
+        for i in self:
+            result.update(i.atoms(*types))
+        return result
+
+    def _eval_free_symbols(self):
+        return set().union(*(i.free_symbols for i in self if i))
+
+    def _eval_has(self, *patterns):
+        return any(a.has(*patterns) for a in self)
+
+    def _eval_is_anti_symmetric(self, simpfunc):
+        if not all(simpfunc(self[i, j] + self[j, i]).is_zero for i in range(self.rows) for j in range(self.cols)):
+            return False
+        return True
+
+    def _eval_is_diagonal(self):
+        for i in range(self.rows):
+            for j in range(self.cols):
+                if i != j and self[i, j]:
+                    return False
+        return True
+
+    # _eval_is_hermitian is called by some general SymPy
+    # routines and has a different *args signature.  Make
+    # sure the names don't clash by adding `_matrix_` in name.
+    def _eval_is_matrix_hermitian(self, simpfunc):
+        mat = self._new(self.rows, self.cols, lambda i, j: simpfunc(self[i, j] - self[j, i].conjugate()))
+        return mat.is_zero_matrix
+
+    def _eval_is_Identity(self) -> FuzzyBool:
+        def dirac(i, j):
+            if i == j:
+                return 1
+            return 0
+
+        return all(self[i, j] == dirac(i, j)
+                for i in range(self.rows)
+                for j in range(self.cols))
+
+    def _eval_is_lower_hessenberg(self):
+        return all(self[i, j].is_zero
+                   for i in range(self.rows)
+                   for j in range(i + 2, self.cols))
+
+    def _eval_is_lower(self):
+        return all(self[i, j].is_zero
+                   for i in range(self.rows)
+                   for j in range(i + 1, self.cols))
+
+    def _eval_is_symbolic(self):
+        return self.has(Symbol)
+
+    def _eval_is_symmetric(self, simpfunc):
+        mat = self._new(self.rows, self.cols, lambda i, j: simpfunc(self[i, j] - self[j, i]))
+        return mat.is_zero_matrix
+
+    def _eval_is_zero_matrix(self):
+        if any(i.is_zero == False for i in self):
+            return False
+        if any(i.is_zero is None for i in self):
+            return None
+        return True
+
+    def _eval_is_upper_hessenberg(self):
+        return all(self[i, j].is_zero
+                   for i in range(2, self.rows)
+                   for j in range(min(self.cols, (i - 1))))
+
+    def _eval_values(self):
+        return [i for i in self if not i.is_zero]
+
+    def _has_positive_diagonals(self):
+        diagonal_entries = (self[i, i] for i in range(self.rows))
+        return fuzzy_and(x.is_positive for x in diagonal_entries)
+
+    def _has_nonnegative_diagonals(self):
+        diagonal_entries = (self[i, i] for i in range(self.rows))
+        return fuzzy_and(x.is_nonnegative for x in diagonal_entries)
+
+    def atoms(self, *types):
+        """Returns the atoms that form the current object.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import Matrix
+        >>> Matrix([[x]])
+        Matrix([[x]])
+        >>> _.atoms()
+        {x}
+        >>> Matrix([[x, y], [y, x]])
+        Matrix([
+        [x, y],
+        [y, x]])
+        >>> _.atoms()
+        {x, y}
+        """
+
+        types = tuple(t if isinstance(t, type) else type(t) for t in types)
+        if not types:
+            types = (Atom,)
+        return self._eval_atoms(*types)
+
+    @property
+    def free_symbols(self):
+        """Returns the free symbols within the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> from sympy import Matrix
+        >>> Matrix([[x], [1]]).free_symbols
+        {x}
+        """
+        return self._eval_free_symbols()
+
+    def has(self, *patterns):
+        """Test whether any subexpression matches any of the patterns.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, SparseMatrix, Float
+        >>> from sympy.abc import x, y
+        >>> A = Matrix(((1, x), (0.2, 3)))
+        >>> B = SparseMatrix(((1, x), (0.2, 3)))
+        >>> A.has(x)
+        True
+        >>> A.has(y)
+        False
+        >>> A.has(Float)
+        True
+        >>> B.has(x)
+        True
+        >>> B.has(y)
+        False
+        >>> B.has(Float)
+        True
+        """
+        return self._eval_has(*patterns)
+
+    def is_anti_symmetric(self, simplify=True):
+        """Check if matrix M is an antisymmetric matrix,
+        that is, M is a square matrix with all M[i, j] == -M[j, i].
+
+        When ``simplify=True`` (default), the sum M[i, j] + M[j, i] is
+        simplified before testing to see if it is zero. By default,
+        the SymPy simplify function is used. To use a custom function
+        set simplify to a function that accepts a single argument which
+        returns a simplified expression. To skip simplification, set
+        simplify to False but note that although this will be faster,
+        it may induce false negatives.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, symbols
+        >>> m = Matrix(2, 2, [0, 1, -1, 0])
+        >>> m
+        Matrix([
+        [ 0, 1],
+        [-1, 0]])
+        >>> m.is_anti_symmetric()
+        True
+        >>> x, y = symbols('x y')
+        >>> m = Matrix(2, 3, [0, 0, x, -y, 0, 0])
+        >>> m
+        Matrix([
+        [ 0, 0, x],
+        [-y, 0, 0]])
+        >>> m.is_anti_symmetric()
+        False
+
+        >>> from sympy.abc import x, y
+        >>> m = Matrix(3, 3, [0, x**2 + 2*x + 1, y,
+        ...                   -(x + 1)**2, 0, x*y,
+        ...                   -y, -x*y, 0])
+
+        Simplification of matrix elements is done by default so even
+        though two elements which should be equal and opposite would not
+        pass an equality test, the matrix is still reported as
+        anti-symmetric:
+
+        >>> m[0, 1] == -m[1, 0]
+        False
+        >>> m.is_anti_symmetric()
+        True
+
+        If ``simplify=False`` is used for the case when a Matrix is already
+        simplified, this will speed things up. Here, we see that without
+        simplification the matrix does not appear anti-symmetric:
+
+        >>> print(m.is_anti_symmetric(simplify=False))
+        None
+
+        But if the matrix were already expanded, then it would appear
+        anti-symmetric and simplification in the is_anti_symmetric routine
+        is not needed:
+
+        >>> m = m.expand()
+        >>> m.is_anti_symmetric(simplify=False)
+        True
+        """
+        # accept custom simplification
+        simpfunc = simplify
+        if not isfunction(simplify):
+            simpfunc = _simplify if simplify else lambda x: x
+
+        if not self.is_square:
+            return False
+        return self._eval_is_anti_symmetric(simpfunc)
+
+    def is_diagonal(self):
+        """Check if matrix is diagonal,
+        that is matrix in which the entries outside the main diagonal are all zero.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, diag
+        >>> m = Matrix(2, 2, [1, 0, 0, 2])
+        >>> m
+        Matrix([
+        [1, 0],
+        [0, 2]])
+        >>> m.is_diagonal()
+        True
+
+        >>> m = Matrix(2, 2, [1, 1, 0, 2])
+        >>> m
+        Matrix([
+        [1, 1],
+        [0, 2]])
+        >>> m.is_diagonal()
+        False
+
+        >>> m = diag(1, 2, 3)
+        >>> m
+        Matrix([
+        [1, 0, 0],
+        [0, 2, 0],
+        [0, 0, 3]])
+        >>> m.is_diagonal()
+        True
+
+        See Also
+        ========
+
+        is_lower
+        is_upper
+        sympy.matrices.matrixbase.MatrixCommon.is_diagonalizable
+        diagonalize
+        """
+        return self._eval_is_diagonal()
+
+    @property
+    def is_weakly_diagonally_dominant(self):
+        r"""Tests if the matrix is row weakly diagonally dominant.
+
+        Explanation
+        ===========
+
+        A $n, n$ matrix $A$ is row weakly diagonally dominant if
+
+        .. math::
+            \left|A_{i, i}\right| \ge \sum_{j = 0, j \neq i}^{n-1}
+            \left|A_{i, j}\right| \quad {\text{for all }}
+            i \in \{ 0, ..., n-1 \}
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]])
+        >>> A.is_weakly_diagonally_dominant
+        True
+
+        >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]])
+        >>> A.is_weakly_diagonally_dominant
+        False
+
+        >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]])
+        >>> A.is_weakly_diagonally_dominant
+        True
+
+        Notes
+        =====
+
+        If you want to test whether a matrix is column diagonally
+        dominant, you can apply the test after transposing the matrix.
+        """
+        if not self.is_square:
+            return False
+
+        rows, cols = self.shape
+
+        def test_row(i):
+            summation = self.zero
+            for j in range(cols):
+                if i != j:
+                    summation += Abs(self[i, j])
+            return (Abs(self[i, i]) - summation).is_nonnegative
+
+        return fuzzy_and(test_row(i) for i in range(rows))
+
+    @property
+    def is_strongly_diagonally_dominant(self):
+        r"""Tests if the matrix is row strongly diagonally dominant.
+
+        Explanation
+        ===========
+
+        A $n, n$ matrix $A$ is row strongly diagonally dominant if
+
+        .. math::
+            \left|A_{i, i}\right| > \sum_{j = 0, j \neq i}^{n-1}
+            \left|A_{i, j}\right| \quad {\text{for all }}
+            i \in \{ 0, ..., n-1 \}
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]])
+        >>> A.is_strongly_diagonally_dominant
+        False
+
+        >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]])
+        >>> A.is_strongly_diagonally_dominant
+        False
+
+        >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]])
+        >>> A.is_strongly_diagonally_dominant
+        True
+
+        Notes
+        =====
+
+        If you want to test whether a matrix is column diagonally
+        dominant, you can apply the test after transposing the matrix.
+        """
+        if not self.is_square:
+            return False
+
+        rows, cols = self.shape
+
+        def test_row(i):
+            summation = self.zero
+            for j in range(cols):
+                if i != j:
+                    summation += Abs(self[i, j])
+            return (Abs(self[i, i]) - summation).is_positive
+
+        return fuzzy_and(test_row(i) for i in range(rows))
+
+    @property
+    def is_hermitian(self):
+        """Checks if the matrix is Hermitian.
+
+        In a Hermitian matrix element i,j is the complex conjugate of
+        element j,i.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy import I
+        >>> from sympy.abc import x
+        >>> a = Matrix([[1, I], [-I, 1]])
+        >>> a
+        Matrix([
+        [ 1, I],
+        [-I, 1]])
+        >>> a.is_hermitian
+        True
+        >>> a[0, 0] = 2*I
+        >>> a.is_hermitian
+        False
+        >>> a[0, 0] = x
+        >>> a.is_hermitian
+        >>> a[0, 1] = a[1, 0]*I
+        >>> a.is_hermitian
+        False
+        """
+        if not self.is_square:
+            return False
+
+        return self._eval_is_matrix_hermitian(_simplify)
+
+    @property
+    def is_Identity(self) -> FuzzyBool:
+        if not self.is_square:
+            return False
+        return self._eval_is_Identity()
+
+    @property
+    def is_lower_hessenberg(self):
+        r"""Checks if the matrix is in the lower-Hessenberg form.
+
+        The lower hessenberg matrix has zero entries
+        above the first superdiagonal.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[1, 2, 0, 0], [5, 2, 3, 0], [3, 4, 3, 7], [5, 6, 1, 1]])
+        >>> a
+        Matrix([
+        [1, 2, 0, 0],
+        [5, 2, 3, 0],
+        [3, 4, 3, 7],
+        [5, 6, 1, 1]])
+        >>> a.is_lower_hessenberg
+        True
+
+        See Also
+        ========
+
+        is_upper_hessenberg
+        is_lower
+        """
+        return self._eval_is_lower_hessenberg()
+
+    @property
+    def is_lower(self):
+        """Check if matrix is a lower triangular matrix. True can be returned
+        even if the matrix is not square.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, [1, 0, 0, 1])
+        >>> m
+        Matrix([
+        [1, 0],
+        [0, 1]])
+        >>> m.is_lower
+        True
+
+        >>> m = Matrix(4, 3, [0, 0, 0, 2, 0, 0, 1, 4, 0, 6, 6, 5])
+        >>> m
+        Matrix([
+        [0, 0, 0],
+        [2, 0, 0],
+        [1, 4, 0],
+        [6, 6, 5]])
+        >>> m.is_lower
+        True
+
+        >>> from sympy.abc import x, y
+        >>> m = Matrix(2, 2, [x**2 + y, y**2 + x, 0, x + y])
+        >>> m
+        Matrix([
+        [x**2 + y, x + y**2],
+        [       0,    x + y]])
+        >>> m.is_lower
+        False
+
+        See Also
+        ========
+
+        is_upper
+        is_diagonal
+        is_lower_hessenberg
+        """
+        return self._eval_is_lower()
+
+    @property
+    def is_square(self):
+        """Checks if a matrix is square.
+
+        A matrix is square if the number of rows equals the number of columns.
+        The empty matrix is square by definition, since the number of rows and
+        the number of columns are both zero.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[1, 2, 3], [4, 5, 6]])
+        >>> b = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+        >>> c = Matrix([])
+        >>> a.is_square
+        False
+        >>> b.is_square
+        True
+        >>> c.is_square
+        True
+        """
+        return self.rows == self.cols
+
+    def is_symbolic(self):
+        """Checks if any elements contain Symbols.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.is_symbolic()
+        True
+
+        """
+        return self._eval_is_symbolic()
+
+    def is_symmetric(self, simplify=True):
+        """Check if matrix is symmetric matrix,
+        that is square matrix and is equal to its transpose.
+
+        By default, simplifications occur before testing symmetry.
+        They can be skipped using 'simplify=False'; while speeding things a bit,
+        this may however induce false negatives.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, [0, 1, 1, 2])
+        >>> m
+        Matrix([
+        [0, 1],
+        [1, 2]])
+        >>> m.is_symmetric()
+        True
+
+        >>> m = Matrix(2, 2, [0, 1, 2, 0])
+        >>> m
+        Matrix([
+        [0, 1],
+        [2, 0]])
+        >>> m.is_symmetric()
+        False
+
+        >>> m = Matrix(2, 3, [0, 0, 0, 0, 0, 0])
+        >>> m
+        Matrix([
+        [0, 0, 0],
+        [0, 0, 0]])
+        >>> m.is_symmetric()
+        False
+
+        >>> from sympy.abc import x, y
+        >>> m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
+        >>> m
+        Matrix([
+        [         1, x**2 + 2*x + 1, y],
+        [(x + 1)**2,              2, 0],
+        [         y,              0, 3]])
+        >>> m.is_symmetric()
+        True
+
+        If the matrix is already simplified, you may speed-up is_symmetric()
+        test by using 'simplify=False'.
+
+        >>> bool(m.is_symmetric(simplify=False))
+        False
+        >>> m1 = m.expand()
+        >>> m1.is_symmetric(simplify=False)
+        True
+        """
+        simpfunc = simplify
+        if not isfunction(simplify):
+            simpfunc = _simplify if simplify else lambda x: x
+
+        if not self.is_square:
+            return False
+
+        return self._eval_is_symmetric(simpfunc)
+
+    @property
+    def is_upper_hessenberg(self):
+        """Checks if the matrix is the upper-Hessenberg form.
+
+        The upper hessenberg matrix has zero entries
+        below the first subdiagonal.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[1, 4, 2, 3], [3, 4, 1, 7], [0, 2, 3, 4], [0, 0, 1, 3]])
+        >>> a
+        Matrix([
+        [1, 4, 2, 3],
+        [3, 4, 1, 7],
+        [0, 2, 3, 4],
+        [0, 0, 1, 3]])
+        >>> a.is_upper_hessenberg
+        True
+
+        See Also
+        ========
+
+        is_lower_hessenberg
+        is_upper
+        """
+        return self._eval_is_upper_hessenberg()
+
+    @property
+    def is_upper(self):
+        """Check if matrix is an upper triangular matrix. True can be returned
+        even if the matrix is not square.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, [1, 0, 0, 1])
+        >>> m
+        Matrix([
+        [1, 0],
+        [0, 1]])
+        >>> m.is_upper
+        True
+
+        >>> m = Matrix(4, 3, [5, 1, 9, 0, 4, 6, 0, 0, 5, 0, 0, 0])
+        >>> m
+        Matrix([
+        [5, 1, 9],
+        [0, 4, 6],
+        [0, 0, 5],
+        [0, 0, 0]])
+        >>> m.is_upper
+        True
+
+        >>> m = Matrix(2, 3, [4, 2, 5, 6, 1, 1])
+        >>> m
+        Matrix([
+        [4, 2, 5],
+        [6, 1, 1]])
+        >>> m.is_upper
+        False
+
+        See Also
+        ========
+
+        is_lower
+        is_diagonal
+        is_upper_hessenberg
+        """
+        return all(self[i, j].is_zero
+                   for i in range(1, self.rows)
+                   for j in range(min(i, self.cols)))
+
+    @property
+    def is_zero_matrix(self):
+        """Checks if a matrix is a zero matrix.
+
+        A matrix is zero if every element is zero.  A matrix need not be square
+        to be considered zero.  The empty matrix is zero by the principle of
+        vacuous truth.  For a matrix that may or may not be zero (e.g.
+        contains a symbol), this will be None
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, zeros
+        >>> from sympy.abc import x
+        >>> a = Matrix([[0, 0], [0, 0]])
+        >>> b = zeros(3, 4)
+        >>> c = Matrix([[0, 1], [0, 0]])
+        >>> d = Matrix([])
+        >>> e = Matrix([[x, 0], [0, 0]])
+        >>> a.is_zero_matrix
+        True
+        >>> b.is_zero_matrix
+        True
+        >>> c.is_zero_matrix
+        False
+        >>> d.is_zero_matrix
+        True
+        >>> e.is_zero_matrix
+        """
+        return self._eval_is_zero_matrix()
+
+    def values(self):
+        """Return non-zero values of self."""
+        return self._eval_values()
+
+
+class MatrixOperations(MatrixRequired):
+    """Provides basic matrix shape and elementwise
+    operations.  Should not be instantiated directly."""
+
+    def _eval_adjoint(self):
+        return self.transpose().conjugate()
+
+    def _eval_applyfunc(self, f):
+        out = self._new(self.rows, self.cols, [f(x) for x in self])
+        return out
+
+    def _eval_as_real_imag(self):  # type: ignore
+        return (self.applyfunc(re), self.applyfunc(im))
+
+    def _eval_conjugate(self):
+        return self.applyfunc(lambda x: x.conjugate())
+
+    def _eval_permute_cols(self, perm):
+        # apply the permutation to a list
+        mapping = list(perm)
+
+        def entry(i, j):
+            return self[i, mapping[j]]
+
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_permute_rows(self, perm):
+        # apply the permutation to a list
+        mapping = list(perm)
+
+        def entry(i, j):
+            return self[mapping[i], j]
+
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_trace(self):
+        return sum(self[i, i] for i in range(self.rows))
+
+    def _eval_transpose(self):
+        return self._new(self.cols, self.rows, lambda i, j: self[j, i])
+
+    def adjoint(self):
+        """Conjugate transpose or Hermitian conjugation."""
+        return self._eval_adjoint()
+
+    def applyfunc(self, f):
+        """Apply a function to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, lambda i, j: i*2+j)
+        >>> m
+        Matrix([
+        [0, 1],
+        [2, 3]])
+        >>> m.applyfunc(lambda i: 2*i)
+        Matrix([
+        [0, 2],
+        [4, 6]])
+
+        """
+        if not callable(f):
+            raise TypeError("`f` must be callable.")
+
+        return self._eval_applyfunc(f)
+
+    def as_real_imag(self, deep=True, **hints):
+        """Returns a tuple containing the (real, imaginary) part of matrix."""
+        # XXX: Ignoring deep and hints...
+        return self._eval_as_real_imag()
+
+    def conjugate(self):
+        """Return the by-element conjugation.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix, I
+        >>> a = SparseMatrix(((1, 2 + I), (3, 4), (I, -I)))
+        >>> a
+        Matrix([
+        [1, 2 + I],
+        [3,     4],
+        [I,    -I]])
+        >>> a.C
+        Matrix([
+        [ 1, 2 - I],
+        [ 3,     4],
+        [-I,     I]])
+
+        See Also
+        ========
+
+        transpose: Matrix transposition
+        H: Hermite conjugation
+        sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation
+        """
+        return self._eval_conjugate()
+
+    def doit(self, **hints):
+        return self.applyfunc(lambda x: x.doit(**hints))
+
+    def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False):
+        """Apply evalf() to each element of self."""
+        options = {'subs':subs, 'maxn':maxn, 'chop':chop, 'strict':strict,
+                'quad':quad, 'verbose':verbose}
+        return self.applyfunc(lambda i: i.evalf(n, **options))
+
+    def expand(self, deep=True, modulus=None, power_base=True, power_exp=True,
+               mul=True, log=True, multinomial=True, basic=True, **hints):
+        """Apply core.function.expand to each entry of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> from sympy import Matrix
+        >>> Matrix(1, 1, [x*(x+1)])
+        Matrix([[x*(x + 1)]])
+        >>> _.expand()
+        Matrix([[x**2 + x]])
+
+        """
+        return self.applyfunc(lambda x: x.expand(
+            deep, modulus, power_base, power_exp, mul, log, multinomial, basic,
+            **hints))
+
+    @property
+    def H(self):
+        """Return Hermite conjugate.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, I
+        >>> m = Matrix((0, 1 + I, 2, 3))
+        >>> m
+        Matrix([
+        [    0],
+        [1 + I],
+        [    2],
+        [    3]])
+        >>> m.H
+        Matrix([[0, 1 - I, 2, 3]])
+
+        See Also
+        ========
+
+        conjugate: By-element conjugation
+        sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation
+        """
+        return self.T.C
+
+    def permute(self, perm, orientation='rows', direction='forward'):
+        r"""Permute the rows or columns of a matrix by the given list of
+        swaps.
+
+        Parameters
+        ==========
+
+        perm : Permutation, list, or list of lists
+            A representation for the permutation.
+
+            If it is ``Permutation``, it is used directly with some
+            resizing with respect to the matrix size.
+
+            If it is specified as list of lists,
+            (e.g., ``[[0, 1], [0, 2]]``), then the permutation is formed
+            from applying the product of cycles. The direction how the
+            cyclic product is applied is described in below.
+
+            If it is specified as a list, the list should represent
+            an array form of a permutation. (e.g., ``[1, 2, 0]``) which
+            would would form the swapping function
+            `0 \mapsto 1, 1 \mapsto 2, 2\mapsto 0`.
+
+        orientation : 'rows', 'cols'
+            A flag to control whether to permute the rows or the columns
+
+        direction : 'forward', 'backward'
+            A flag to control whether to apply the permutations from
+            the start of the list first, or from the back of the list
+            first.
+
+            For example, if the permutation specification is
+            ``[[0, 1], [0, 2]]``,
+
+            If the flag is set to ``'forward'``, the cycle would be
+            formed as `0 \mapsto 2, 2 \mapsto 1, 1 \mapsto 0`.
+
+            If the flag is set to ``'backward'``, the cycle would be
+            formed as `0 \mapsto 1, 1 \mapsto 2, 2 \mapsto 0`.
+
+            If the argument ``perm`` is not in a form of list of lists,
+            this flag takes no effect.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='forward')
+        Matrix([
+        [0, 0, 1],
+        [1, 0, 0],
+        [0, 1, 0]])
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='backward')
+        Matrix([
+        [0, 1, 0],
+        [0, 0, 1],
+        [1, 0, 0]])
+
+        Notes
+        =====
+
+        If a bijective function
+        `\sigma : \mathbb{N}_0 \rightarrow \mathbb{N}_0` denotes the
+        permutation.
+
+        If the matrix `A` is the matrix to permute, represented as
+        a horizontal or a vertical stack of vectors:
+
+        .. math::
+            A =
+            \begin{bmatrix}
+            a_0 \\ a_1 \\ \vdots \\ a_{n-1}
+            \end{bmatrix} =
+            \begin{bmatrix}
+            \alpha_0 & \alpha_1 & \cdots & \alpha_{n-1}
+            \end{bmatrix}
+
+        If the matrix `B` is the result, the permutation of matrix rows
+        is defined as:
+
+        .. math::
+            B := \begin{bmatrix}
+            a_{\sigma(0)} \\ a_{\sigma(1)} \\ \vdots \\ a_{\sigma(n-1)}
+            \end{bmatrix}
+
+        And the permutation of matrix columns is defined as:
+
+        .. math::
+            B := \begin{bmatrix}
+            \alpha_{\sigma(0)} & \alpha_{\sigma(1)} &
+            \cdots & \alpha_{\sigma(n-1)}
+            \end{bmatrix}
+        """
+        from sympy.combinatorics import Permutation
+
+        # allow british variants and `columns`
+        if direction == 'forwards':
+            direction = 'forward'
+        if direction == 'backwards':
+            direction = 'backward'
+        if orientation == 'columns':
+            orientation = 'cols'
+
+        if direction not in ('forward', 'backward'):
+            raise TypeError("direction='{}' is an invalid kwarg. "
+                            "Try 'forward' or 'backward'".format(direction))
+        if orientation not in ('rows', 'cols'):
+            raise TypeError("orientation='{}' is an invalid kwarg. "
+                            "Try 'rows' or 'cols'".format(orientation))
+
+        if not isinstance(perm, (Permutation, Iterable)):
+            raise ValueError(
+                "{} must be a list, a list of lists, "
+                "or a SymPy permutation object.".format(perm))
+
+        # ensure all swaps are in range
+        max_index = self.rows if orientation == 'rows' else self.cols
+        if not all(0 <= t <= max_index for t in flatten(list(perm))):
+            raise IndexError("`swap` indices out of range.")
+
+        if perm and not isinstance(perm, Permutation) and \
+            isinstance(perm[0], Iterable):
+            if direction == 'forward':
+                perm = list(reversed(perm))
+            perm = Permutation(perm, size=max_index+1)
+        else:
+            perm = Permutation(perm, size=max_index+1)
+
+        if orientation == 'rows':
+            return self._eval_permute_rows(perm)
+        if orientation == 'cols':
+            return self._eval_permute_cols(perm)
+
+    def permute_cols(self, swaps, direction='forward'):
+        """Alias for
+        ``self.permute(swaps, orientation='cols', direction=direction)``
+
+        See Also
+        ========
+
+        permute
+        """
+        return self.permute(swaps, orientation='cols', direction=direction)
+
+    def permute_rows(self, swaps, direction='forward'):
+        """Alias for
+        ``self.permute(swaps, orientation='rows', direction=direction)``
+
+        See Also
+        ========
+
+        permute
+        """
+        return self.permute(swaps, orientation='rows', direction=direction)
+
+    def refine(self, assumptions=True):
+        """Apply refine to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Matrix, Abs, sqrt, Q
+        >>> x = Symbol('x')
+        >>> Matrix([[Abs(x)**2, sqrt(x**2)],[sqrt(x**2), Abs(x)**2]])
+        Matrix([
+        [ Abs(x)**2, sqrt(x**2)],
+        [sqrt(x**2),  Abs(x)**2]])
+        >>> _.refine(Q.real(x))
+        Matrix([
+        [  x**2, Abs(x)],
+        [Abs(x),   x**2]])
+
+        """
+        return self.applyfunc(lambda x: refine(x, assumptions))
+
+    def replace(self, F, G, map=False, simultaneous=True, exact=None):
+        """Replaces Function F in Matrix entries with Function G.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Function, Matrix
+        >>> F, G = symbols('F, G', cls=Function)
+        >>> M = Matrix(2, 2, lambda i, j: F(i+j)) ; M
+        Matrix([
+        [F(0), F(1)],
+        [F(1), F(2)]])
+        >>> N = M.replace(F,G)
+        >>> N
+        Matrix([
+        [G(0), G(1)],
+        [G(1), G(2)]])
+        """
+        return self.applyfunc(
+            lambda x: x.replace(F, G, map=map, simultaneous=simultaneous, exact=exact))
+
+    def rot90(self, k=1):
+        """Rotates Matrix by 90 degrees
+
+        Parameters
+        ==========
+
+        k : int
+            Specifies how many times the matrix is rotated by 90 degrees
+            (clockwise when positive, counter-clockwise when negative).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, symbols
+        >>> A = Matrix(2, 2, symbols('a:d'))
+        >>> A
+        Matrix([
+        [a, b],
+        [c, d]])
+
+        Rotating the matrix clockwise one time:
+
+        >>> A.rot90(1)
+        Matrix([
+        [c, a],
+        [d, b]])
+
+        Rotating the matrix anticlockwise two times:
+
+        >>> A.rot90(-2)
+        Matrix([
+        [d, c],
+        [b, a]])
+        """
+
+        mod = k%4
+        if mod == 0:
+            return self
+        if mod == 1:
+            return self[::-1, ::].T
+        if mod == 2:
+            return self[::-1, ::-1]
+        if mod == 3:
+            return self[::, ::-1].T
+
+    def simplify(self, **kwargs):
+        """Apply simplify to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import SparseMatrix, sin, cos
+        >>> SparseMatrix(1, 1, [x*sin(y)**2 + x*cos(y)**2])
+        Matrix([[x*sin(y)**2 + x*cos(y)**2]])
+        >>> _.simplify()
+        Matrix([[x]])
+        """
+        return self.applyfunc(lambda x: x.simplify(**kwargs))
+
+    def subs(self, *args, **kwargs):  # should mirror core.basic.subs
+        """Return a new matrix with subs applied to each entry.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import SparseMatrix, Matrix
+        >>> SparseMatrix(1, 1, [x])
+        Matrix([[x]])
+        >>> _.subs(x, y)
+        Matrix([[y]])
+        >>> Matrix(_).subs(y, x)
+        Matrix([[x]])
+        """
+
+        if len(args) == 1 and  not isinstance(args[0], (dict, set)) and iter(args[0]) and not is_sequence(args[0]):
+            args = (list(args[0]),)
+
+        return self.applyfunc(lambda x: x.subs(*args, **kwargs))
+
+    def trace(self):
+        """
+        Returns the trace of a square matrix i.e. the sum of the
+        diagonal elements.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix(2, 2, [1, 2, 3, 4])
+        >>> A.trace()
+        5
+
+        """
+        if self.rows != self.cols:
+            raise NonSquareMatrixError()
+        return self._eval_trace()
+
+    def transpose(self):
+        """
+        Returns the transpose of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix(2, 2, [1, 2, 3, 4])
+        >>> A.transpose()
+        Matrix([
+        [1, 3],
+        [2, 4]])
+
+        >>> from sympy import Matrix, I
+        >>> m=Matrix(((1, 2+I), (3, 4)))
+        >>> m
+        Matrix([
+        [1, 2 + I],
+        [3,     4]])
+        >>> m.transpose()
+        Matrix([
+        [    1, 3],
+        [2 + I, 4]])
+        >>> m.T == m.transpose()
+        True
+
+        See Also
+        ========
+
+        conjugate: By-element conjugation
+
+        """
+        return self._eval_transpose()
+
+    @property
+    def T(self):
+        '''Matrix transposition'''
+        return self.transpose()
+
+    @property
+    def C(self):
+        '''By-element conjugation'''
+        return self.conjugate()
+
+    def n(self, *args, **kwargs):
+        """Apply evalf() to each element of self."""
+        return self.evalf(*args, **kwargs)
+
+    def xreplace(self, rule):  # should mirror core.basic.xreplace
+        """Return a new matrix with xreplace applied to each entry.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import SparseMatrix, Matrix
+        >>> SparseMatrix(1, 1, [x])
+        Matrix([[x]])
+        >>> _.xreplace({x: y})
+        Matrix([[y]])
+        >>> Matrix(_).xreplace({y: x})
+        Matrix([[x]])
+        """
+        return self.applyfunc(lambda x: x.xreplace(rule))
+
+    def _eval_simplify(self, **kwargs):
+        # XXX: We can't use self.simplify here as mutable subclasses will
+        # override simplify and have it return None
+        return MatrixOperations.simplify(self, **kwargs)
+
+    def _eval_trigsimp(self, **opts):
+        from sympy.simplify.trigsimp import trigsimp
+        return self.applyfunc(lambda x: trigsimp(x, **opts))
+
+    def upper_triangular(self, k=0):
+        """Return the elements on and above the kth diagonal of a matrix.
+        If k is not specified then simply returns upper-triangular portion
+        of a matrix
+
+        Examples
+        ========
+
+        >>> from sympy import ones
+        >>> A = ones(4)
+        >>> A.upper_triangular()
+        Matrix([
+        [1, 1, 1, 1],
+        [0, 1, 1, 1],
+        [0, 0, 1, 1],
+        [0, 0, 0, 1]])
+
+        >>> A.upper_triangular(2)
+        Matrix([
+        [0, 0, 1, 1],
+        [0, 0, 0, 1],
+        [0, 0, 0, 0],
+        [0, 0, 0, 0]])
+
+        >>> A.upper_triangular(-1)
+        Matrix([
+        [1, 1, 1, 1],
+        [1, 1, 1, 1],
+        [0, 1, 1, 1],
+        [0, 0, 1, 1]])
+
+        """
+
+        def entry(i, j):
+            return self[i, j] if i + k <= j else self.zero
+
+        return self._new(self.rows, self.cols, entry)
+
+
+    def lower_triangular(self, k=0):
+        """Return the elements on and below the kth diagonal of a matrix.
+        If k is not specified then simply returns lower-triangular portion
+        of a matrix
+
+        Examples
+        ========
+
+        >>> from sympy import ones
+        >>> A = ones(4)
+        >>> A.lower_triangular()
+        Matrix([
+        [1, 0, 0, 0],
+        [1, 1, 0, 0],
+        [1, 1, 1, 0],
+        [1, 1, 1, 1]])
+
+        >>> A.lower_triangular(-2)
+        Matrix([
+        [0, 0, 0, 0],
+        [0, 0, 0, 0],
+        [1, 0, 0, 0],
+        [1, 1, 0, 0]])
+
+        >>> A.lower_triangular(1)
+        Matrix([
+        [1, 1, 0, 0],
+        [1, 1, 1, 0],
+        [1, 1, 1, 1],
+        [1, 1, 1, 1]])
+
+        """
+
+        def entry(i, j):
+            return self[i, j] if i + k >= j else self.zero
+
+        return self._new(self.rows, self.cols, entry)
+
+
+
+class MatrixArithmetic(MatrixRequired):
+    """Provides basic matrix arithmetic operations.
+    Should not be instantiated directly."""
+
+    _op_priority = 10.01
+
+    def _eval_Abs(self):
+        return self._new(self.rows, self.cols, lambda i, j: Abs(self[i, j]))
+
+    def _eval_add(self, other):
+        return self._new(self.rows, self.cols,
+                         lambda i, j: self[i, j] + other[i, j])
+
+    def _eval_matrix_mul(self, other):
+        def entry(i, j):
+            vec = [self[i,k]*other[k,j] for k in range(self.cols)]
+            try:
+                return Add(*vec)
+            except (TypeError, SympifyError):
+                # Some matrices don't work with `sum` or `Add`
+                # They don't work with `sum` because `sum` tries to add `0`
+                # Fall back to a safe way to multiply if the `Add` fails.
+                return reduce(lambda a, b: a + b, vec)
+
+        return self._new(self.rows, other.cols, entry)
+
+    def _eval_matrix_mul_elementwise(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other[i,j])
+
+    def _eval_matrix_rmul(self, other):
+        def entry(i, j):
+            return sum(other[i,k]*self[k,j] for k in range(other.cols))
+        return self._new(other.rows, self.cols, entry)
+
+    def _eval_pow_by_recursion(self, num):
+        if num == 1:
+            return self
+
+        if num % 2 == 1:
+            a, b = self, self._eval_pow_by_recursion(num - 1)
+        else:
+            a = b = self._eval_pow_by_recursion(num // 2)
+
+        return a.multiply(b)
+
+    def _eval_pow_by_cayley(self, exp):
+        from sympy.discrete.recurrences import linrec_coeffs
+        row = self.shape[0]
+        p = self.charpoly()
+
+        coeffs = (-p).all_coeffs()[1:]
+        coeffs = linrec_coeffs(coeffs, exp)
+        new_mat = self.eye(row)
+        ans = self.zeros(row)
+
+        for i in range(row):
+            ans += coeffs[i]*new_mat
+            new_mat *= self
+
+        return ans
+
+    def _eval_pow_by_recursion_dotprodsimp(self, num, prevsimp=None):
+        if prevsimp is None:
+            prevsimp = [True]*len(self)
+
+        if num == 1:
+            return self
+
+        if num % 2 == 1:
+            a, b = self, self._eval_pow_by_recursion_dotprodsimp(num - 1,
+                    prevsimp=prevsimp)
+        else:
+            a = b = self._eval_pow_by_recursion_dotprodsimp(num // 2,
+                    prevsimp=prevsimp)
+
+        m     = a.multiply(b, dotprodsimp=False)
+        lenm  = len(m)
+        elems = [None]*lenm
+
+        for i in range(lenm):
+            if prevsimp[i]:
+                elems[i], prevsimp[i] = _dotprodsimp(m[i], withsimp=True)
+            else:
+                elems[i] = m[i]
+
+        return m._new(m.rows, m.cols, elems)
+
+    def _eval_scalar_mul(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other)
+
+    def _eval_scalar_rmul(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: other*self[i,j])
+
+    def _eval_Mod(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: Mod(self[i, j], other))
+
+    # Python arithmetic functions
+    def __abs__(self):
+        """Returns a new matrix with entry-wise absolute values."""
+        return self._eval_Abs()
+
+    @call_highest_priority('__radd__')
+    def __add__(self, other):
+        """Return self + other, raising ShapeError if shapes do not match."""
+        if isinstance(other, NDimArray): # Matrix and array addition is currently not implemented
+            return NotImplemented
+        other = _matrixify(other)
+        # matrix-like objects can have shapes.  This is
+        # our first sanity check.
+        if hasattr(other, 'shape'):
+            if self.shape != other.shape:
+                raise ShapeError("Matrix size mismatch: %s + %s" % (
+                    self.shape, other.shape))
+
+        # honest SymPy matrices defer to their class's routine
+        if getattr(other, 'is_Matrix', False):
+            # call the highest-priority class's _eval_add
+            a, b = self, other
+            if a.__class__ != classof(a, b):
+                b, a = a, b
+            return a._eval_add(b)
+        # Matrix-like objects can be passed to CommonMatrix routines directly.
+        if getattr(other, 'is_MatrixLike', False):
+            return MatrixArithmetic._eval_add(self, other)
+
+        raise TypeError('cannot add %s and %s' % (type(self), type(other)))
+
+    @call_highest_priority('__rtruediv__')
+    def __truediv__(self, other):
+        return self * (self.one / other)
+
+    @call_highest_priority('__rmatmul__')
+    def __matmul__(self, other):
+        other = _matrixify(other)
+        if not getattr(other, 'is_Matrix', False) and not getattr(other, 'is_MatrixLike', False):
+            return NotImplemented
+
+        return self.__mul__(other)
+
+    def __mod__(self, other):
+        return self.applyfunc(lambda x: x % other)
+
+    @call_highest_priority('__rmul__')
+    def __mul__(self, other):
+        """Return self*other where other is either a scalar or a matrix
+        of compatible dimensions.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[1, 2, 3], [4, 5, 6]])
+        >>> 2*A == A*2 == Matrix([[2, 4, 6], [8, 10, 12]])
+        True
+        >>> B = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+        >>> A*B
+        Matrix([
+        [30, 36, 42],
+        [66, 81, 96]])
+        >>> B*A
+        Traceback (most recent call last):
+        ...
+        ShapeError: Matrices size mismatch.
+        >>>
+
+        See Also
+        ========
+
+        matrix_multiply_elementwise
+        """
+
+        return self.multiply(other)
+
+    def multiply(self, other, dotprodsimp=None):
+        """Same as __mul__() but with optional simplification.
+
+        Parameters
+        ==========
+
+        dotprodsimp : bool, optional
+            Specifies whether intermediate term algebraic simplification is used
+            during matrix multiplications to control expression blowup and thus
+            speed up calculation. Default is off.
+        """
+
+        isimpbool = _get_intermediate_simp_bool(False, dotprodsimp)
+        other = _matrixify(other)
+        # matrix-like objects can have shapes.  This is
+        # our first sanity check. Double check other is not explicitly not a Matrix.
+        if (hasattr(other, 'shape') and len(other.shape) == 2 and
+            (getattr(other, 'is_Matrix', True) or
+             getattr(other, 'is_MatrixLike', True))):
+            if self.shape[1] != other.shape[0]:
+                raise ShapeError("Matrix size mismatch: %s * %s." % (
+                    self.shape, other.shape))
+
+        # honest SymPy matrices defer to their class's routine
+        if getattr(other, 'is_Matrix', False):
+            m = self._eval_matrix_mul(other)
+            if isimpbool:
+                return m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m])
+            return m
+
+        # Matrix-like objects can be passed to CommonMatrix routines directly.
+        if getattr(other, 'is_MatrixLike', False):
+            return MatrixArithmetic._eval_matrix_mul(self, other)
+
+        # if 'other' is not iterable then scalar multiplication.
+        if not isinstance(other, Iterable):
+            try:
+                return self._eval_scalar_mul(other)
+            except TypeError:
+                pass
+
+        return NotImplemented
+
+    def multiply_elementwise(self, other):
+        """Return the Hadamard product (elementwise product) of A and B
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[0, 1, 2], [3, 4, 5]])
+        >>> B = Matrix([[1, 10, 100], [100, 10, 1]])
+        >>> A.multiply_elementwise(B)
+        Matrix([
+        [  0, 10, 200],
+        [300, 40,   5]])
+
+        See Also
+        ========
+
+        sympy.matrices.matrixbase.MatrixBase.cross
+        sympy.matrices.matrixbase.MatrixBase.dot
+        multiply
+        """
+        if self.shape != other.shape:
+            raise ShapeError("Matrix shapes must agree {} != {}".format(self.shape, other.shape))
+
+        return self._eval_matrix_mul_elementwise(other)
+
+    def __neg__(self):
+        return self._eval_scalar_mul(-1)
+
+    @call_highest_priority('__rpow__')
+    def __pow__(self, exp):
+        """Return self**exp a scalar or symbol."""
+
+        return self.pow(exp)
+
+
+    def pow(self, exp, method=None):
+        r"""Return self**exp a scalar or symbol.
+
+        Parameters
+        ==========
+
+        method : multiply, mulsimp, jordan, cayley
+            If multiply then it returns exponentiation using recursion.
+            If jordan then Jordan form exponentiation will be used.
+            If cayley then the exponentiation is done using Cayley-Hamilton
+            theorem.
+            If mulsimp then the exponentiation is done using recursion
+            with dotprodsimp. This specifies whether intermediate term
+            algebraic simplification is used during naive matrix power to
+            control expression blowup and thus speed up calculation.
+            If None, then it heuristically decides which method to use.
+
+        """
+
+        if method is not None and method not in ['multiply', 'mulsimp', 'jordan', 'cayley']:
+            raise TypeError('No such method')
+        if self.rows != self.cols:
+            raise NonSquareMatrixError()
+        a = self
+        jordan_pow = getattr(a, '_matrix_pow_by_jordan_blocks', None)
+        exp = sympify(exp)
+
+        if exp.is_zero:
+            return a._new(a.rows, a.cols, lambda i, j: int(i == j))
+        if exp == 1:
+            return a
+
+        diagonal = getattr(a, 'is_diagonal', None)
+        if diagonal is not None and diagonal():
+            return a._new(a.rows, a.cols, lambda i, j: a[i,j]**exp if i == j else 0)
+
+        if exp.is_Number and exp % 1 == 0:
+            if a.rows == 1:
+                return a._new([[a[0]**exp]])
+            if exp < 0:
+                exp = -exp
+                a = a.inv()
+        # When certain conditions are met,
+        # Jordan block algorithm is faster than
+        # computation by recursion.
+        if method == 'jordan':
+            try:
+                return jordan_pow(exp)
+            except MatrixError:
+                if method == 'jordan':
+                    raise
+
+        elif method == 'cayley':
+            if not exp.is_Number or exp % 1 != 0:
+                raise ValueError("cayley method is only valid for integer powers")
+            return a._eval_pow_by_cayley(exp)
+
+        elif method == "mulsimp":
+            if not exp.is_Number or exp % 1 != 0:
+                raise ValueError("mulsimp method is only valid for integer powers")
+            return a._eval_pow_by_recursion_dotprodsimp(exp)
+
+        elif method == "multiply":
+            if not exp.is_Number or exp % 1 != 0:
+                raise ValueError("multiply method is only valid for integer powers")
+            return a._eval_pow_by_recursion(exp)
+
+        elif method is None and exp.is_Number and exp % 1 == 0:
+            if exp.is_Float:
+                exp = Integer(exp)
+            # Decide heuristically which method to apply
+            if a.rows == 2 and exp > 100000:
+                return jordan_pow(exp)
+            elif _get_intermediate_simp_bool(True, None):
+                return a._eval_pow_by_recursion_dotprodsimp(exp)
+            elif exp > 10000:
+                return a._eval_pow_by_cayley(exp)
+            else:
+                return a._eval_pow_by_recursion(exp)
+
+        if jordan_pow:
+            try:
+                return jordan_pow(exp)
+            except NonInvertibleMatrixError:
+                # Raised by jordan_pow on zero determinant matrix unless exp is
+                # definitely known to be a non-negative integer.
+                # Here we raise if n is definitely not a non-negative integer
+                # but otherwise we can leave this as an unevaluated MatPow.
+                if exp.is_integer is False or exp.is_nonnegative is False:
+                    raise
+
+        from sympy.matrices.expressions import MatPow
+        return MatPow(a, exp)
+
+    @call_highest_priority('__add__')
+    def __radd__(self, other):
+        return self + other
+
+    @call_highest_priority('__matmul__')
+    def __rmatmul__(self, other):
+        other = _matrixify(other)
+        if not getattr(other, 'is_Matrix', False) and not getattr(other, 'is_MatrixLike', False):
+            return NotImplemented
+
+        return self.__rmul__(other)
+
+    @call_highest_priority('__mul__')
+    def __rmul__(self, other):
+        return self.rmultiply(other)
+
+    def rmultiply(self, other, dotprodsimp=None):
+        """Same as __rmul__() but with optional simplification.
+
+        Parameters
+        ==========
+
+        dotprodsimp : bool, optional
+            Specifies whether intermediate term algebraic simplification is used
+            during matrix multiplications to control expression blowup and thus
+            speed up calculation. Default is off.
+        """
+        isimpbool = _get_intermediate_simp_bool(False, dotprodsimp)
+        other = _matrixify(other)
+        # matrix-like objects can have shapes.  This is
+        # our first sanity check. Double check other is not explicitly not a Matrix.
+        if (hasattr(other, 'shape') and len(other.shape) == 2 and
+            (getattr(other, 'is_Matrix', True) or
+             getattr(other, 'is_MatrixLike', True))):
+            if self.shape[0] != other.shape[1]:
+                raise ShapeError("Matrix size mismatch.")
+
+        # honest SymPy matrices defer to their class's routine
+        if getattr(other, 'is_Matrix', False):
+            m = self._eval_matrix_rmul(other)
+            if isimpbool:
+                return m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m])
+            return m
+        # Matrix-like objects can be passed to CommonMatrix routines directly.
+        if getattr(other, 'is_MatrixLike', False):
+            return MatrixArithmetic._eval_matrix_rmul(self, other)
+
+        # if 'other' is not iterable then scalar multiplication.
+        if not isinstance(other, Iterable):
+            try:
+                return self._eval_scalar_rmul(other)
+            except TypeError:
+                pass
+
+        return NotImplemented
+
+    @call_highest_priority('__sub__')
+    def __rsub__(self, a):
+        return (-self) + a
+
+    @call_highest_priority('__rsub__')
+    def __sub__(self, a):
+        return self + (-a)
+
+
+class MatrixCommon(MatrixArithmetic, MatrixOperations, MatrixProperties,
+                  MatrixSpecial, MatrixShaping):
+    """All common matrix operations including basic arithmetic, shaping,
+    and special matrices like `zeros`, and `eye`."""
+    _diff_wrt: bool = True
+
+
+class _MinimalMatrix:
+    """Class providing the minimum functionality
+    for a matrix-like object and implementing every method
+    required for a `MatrixRequired`.  This class does not have everything
+    needed to become a full-fledged SymPy object, but it will satisfy the
+    requirements of anything inheriting from `MatrixRequired`.  If you wish
+    to make a specialized matrix type, make sure to implement these
+    methods and properties with the exception of `__init__` and `__repr__`
+    which are included for convenience."""
+
+    is_MatrixLike = True
+    _sympify = staticmethod(sympify)
+    _class_priority = 3
+    zero = S.Zero
+    one = S.One
+
+    is_Matrix = True
+    is_MatrixExpr = False
+
+    @classmethod
+    def _new(cls, *args, **kwargs):
+        return cls(*args, **kwargs)
+
+    def __init__(self, rows, cols=None, mat=None, copy=False):
+        if isfunction(mat):
+            # if we passed in a function, use that to populate the indices
+            mat = [mat(i, j) for i in range(rows) for j in range(cols)]
+        if cols is None and mat is None:
+            mat = rows
+        rows, cols = getattr(mat, 'shape', (rows, cols))
+        try:
+            # if we passed in a list of lists, flatten it and set the size
+            if cols is None and mat is None:
+                mat = rows
+            cols = len(mat[0])
+            rows = len(mat)
+            mat = [x for l in mat for x in l]
+        except (IndexError, TypeError):
+            pass
+        self.mat = tuple(self._sympify(x) for x in mat)
+        self.rows, self.cols = rows, cols
+        if self.rows is None or self.cols is None:
+            raise NotImplementedError("Cannot initialize matrix with given parameters")
+
+    def __getitem__(self, key):
+        def _normalize_slices(row_slice, col_slice):
+            """Ensure that row_slice and col_slice do not have
+            `None` in their arguments.  Any integers are converted
+            to slices of length 1"""
+            if not isinstance(row_slice, slice):
+                row_slice = slice(row_slice, row_slice + 1, None)
+            row_slice = slice(*row_slice.indices(self.rows))
+
+            if not isinstance(col_slice, slice):
+                col_slice = slice(col_slice, col_slice + 1, None)
+            col_slice = slice(*col_slice.indices(self.cols))
+
+            return (row_slice, col_slice)
+
+        def _coord_to_index(i, j):
+            """Return the index in _mat corresponding
+            to the (i,j) position in the matrix. """
+            return i * self.cols + j
+
+        if isinstance(key, tuple):
+            i, j = key
+            if isinstance(i, slice) or isinstance(j, slice):
+                # if the coordinates are not slices, make them so
+                # and expand the slices so they don't contain `None`
+                i, j = _normalize_slices(i, j)
+
+                rowsList, colsList = list(range(self.rows))[i], \
+                                     list(range(self.cols))[j]
+                indices = (i * self.cols + j for i in rowsList for j in
+                           colsList)
+                return self._new(len(rowsList), len(colsList),
+                                 [self.mat[i] for i in indices])
+
+            # if the key is a tuple of ints, change
+            # it to an array index
+            key = _coord_to_index(i, j)
+        return self.mat[key]
+
+    def __eq__(self, other):
+        try:
+            classof(self, other)
+        except TypeError:
+            return False
+        return (
+            self.shape == other.shape and list(self) == list(other))
+
+    def __len__(self):
+        return self.rows*self.cols
+
+    def __repr__(self):
+        return "_MinimalMatrix({}, {}, {})".format(self.rows, self.cols,
+                                                   self.mat)
+
+    @property
+    def shape(self):
+        return (self.rows, self.cols)
+
+
+class _CastableMatrix: # this is needed here ONLY FOR TESTS.
+    def as_mutable(self):
+        return self
+
+    def as_immutable(self):
+        return self
+
+
+class _MatrixWrapper:
+    """Wrapper class providing the minimum functionality for a matrix-like
+    object: .rows, .cols, .shape, indexability, and iterability. CommonMatrix
+    math operations should work on matrix-like objects. This one is intended for
+    matrix-like objects which use the same indexing format as SymPy with respect
+    to returning matrix elements instead of rows for non-tuple indexes.
+    """
+
+    is_Matrix     = False # needs to be here because of __getattr__
+    is_MatrixLike = True
+
+    def __init__(self, mat, shape):
+        self.mat = mat
+        self.shape = shape
+        self.rows, self.cols = shape
+
+    def __getitem__(self, key):
+        if isinstance(key, tuple):
+            return sympify(self.mat.__getitem__(key))
+
+        return sympify(self.mat.__getitem__((key // self.rows, key % self.cols)))
+
+    def __iter__(self): # supports numpy.matrix and numpy.array
+        mat = self.mat
+        cols = self.cols
+
+        return iter(sympify(mat[r, c]) for r in range(self.rows) for c in range(cols))
+
+
+def _matrixify(mat):
+    """If `mat` is a Matrix or is matrix-like,
+    return a Matrix or MatrixWrapper object.  Otherwise
+    `mat` is passed through without modification."""
+
+    if getattr(mat, 'is_Matrix', False) or getattr(mat, 'is_MatrixLike', False):
+        return mat
+
+    if not(getattr(mat, 'is_Matrix', True) or getattr(mat, 'is_MatrixLike', True)):
+        return mat
+
+    shape = None
+
+    if hasattr(mat, 'shape'): # numpy, scipy.sparse
+        if len(mat.shape) == 2:
+            shape = mat.shape
+    elif hasattr(mat, 'rows') and hasattr(mat, 'cols'): # mpmath
+        shape = (mat.rows, mat.cols)
+
+    if shape:
+        return _MatrixWrapper(mat, shape)
+
+    return mat
+
+
+def a2idx(j, n=None):
+    """Return integer after making positive and validating against n."""
+    if not isinstance(j, int):
+        jindex = getattr(j, '__index__', None)
+        if jindex is not None:
+            j = jindex()
+        else:
+            raise IndexError("Invalid index a[%r]" % (j,))
+    if n is not None:
+        if j < 0:
+            j += n
+        if not (j >= 0 and j < n):
+            raise IndexError("Index out of range: a[%s]" % (j,))
+    return int(j)
+
+
+def classof(A, B):
+    """
+    Get the type of the result when combining matrices of different types.
+
+    Currently the strategy is that immutability is contagious.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, ImmutableMatrix
+    >>> from sympy.matrices.matrixbase import classof
+    >>> M = Matrix([[1, 2], [3, 4]]) # a Mutable Matrix
+    >>> IM = ImmutableMatrix([[1, 2], [3, 4]])
+    >>> classof(M, IM)
+    
+    """
+    priority_A = getattr(A, '_class_priority', None)
+    priority_B = getattr(B, '_class_priority', None)
+    if None not in (priority_A, priority_B):
+        if A._class_priority > B._class_priority:
+            return A.__class__
+        else:
+            return B.__class__
+
+    try:
+        import numpy
+    except ImportError:
+        pass
+    else:
+        if isinstance(A, numpy.ndarray):
+            return B.__class__
+        if isinstance(B, numpy.ndarray):
+            return A.__class__
+
+    raise TypeError("Incompatible classes %s, %s" % (A.__class__, B.__class__))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/decompositions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/decompositions.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8dd466d84c957b870396a050fd25ec21e7113a3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/decompositions.py
@@ -0,0 +1,1621 @@
+import copy
+
+from sympy.core import S
+from sympy.core.function import expand_mul
+from sympy.functions.elementary.miscellaneous import Min, sqrt
+from sympy.functions.elementary.complexes import sign
+
+from .exceptions import NonSquareMatrixError, NonPositiveDefiniteMatrixError
+from .utilities import _get_intermediate_simp, _iszero
+from .determinant import _find_reasonable_pivot_naive
+
+
+def _rank_decomposition(M, iszerofunc=_iszero, simplify=False):
+    r"""Returns a pair of matrices (`C`, `F`) with matching rank
+    such that `A = C F`.
+
+    Parameters
+    ==========
+
+    iszerofunc : Function, optional
+        A function used for detecting whether an element can
+        act as a pivot.  ``lambda x: x.is_zero`` is used by default.
+
+    simplify : Bool or Function, optional
+        A function used to simplify elements when looking for a
+        pivot. By default SymPy's ``simplify`` is used.
+
+    Returns
+    =======
+
+    (C, F) : Matrices
+        `C` and `F` are full-rank matrices with rank as same as `A`,
+        whose product gives `A`.
+
+        See Notes for additional mathematical details.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([
+    ...     [1, 3, 1, 4],
+    ...     [2, 7, 3, 9],
+    ...     [1, 5, 3, 1],
+    ...     [1, 2, 0, 8]
+    ... ])
+    >>> C, F = A.rank_decomposition()
+    >>> C
+    Matrix([
+    [1, 3, 4],
+    [2, 7, 9],
+    [1, 5, 1],
+    [1, 2, 8]])
+    >>> F
+    Matrix([
+    [1, 0, -2, 0],
+    [0, 1,  1, 0],
+    [0, 0,  0, 1]])
+    >>> C * F == A
+    True
+
+    Notes
+    =====
+
+    Obtaining `F`, an RREF of `A`, is equivalent to creating a
+    product
+
+    .. math::
+        E_n E_{n-1} ... E_1 A = F
+
+    where `E_n, E_{n-1}, \dots, E_1` are the elimination matrices or
+    permutation matrices equivalent to each row-reduction step.
+
+    The inverse of the same product of elimination matrices gives
+    `C`:
+
+    .. math::
+        C = \left(E_n E_{n-1} \dots E_1\right)^{-1}
+
+    It is not necessary, however, to actually compute the inverse:
+    the columns of `C` are those from the original matrix with the
+    same column indices as the indices of the pivot columns of `F`.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Rank_factorization
+
+    .. [2] Piziak, R.; Odell, P. L. (1 June 1999).
+        "Full Rank Factorization of Matrices".
+        Mathematics Magazine. 72 (3): 193. doi:10.2307/2690882
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.rref
+    """
+
+    F, pivot_cols = M.rref(simplify=simplify, iszerofunc=iszerofunc,
+            pivots=True)
+    rank = len(pivot_cols)
+
+    C = M.extract(range(M.rows), pivot_cols)
+    F = F[:rank, :]
+
+    return C, F
+
+
+def _liupc(M):
+    """Liu's algorithm, for pre-determination of the Elimination Tree of
+    the given matrix, used in row-based symbolic Cholesky factorization.
+
+    Examples
+    ========
+
+    >>> from sympy import SparseMatrix
+    >>> S = SparseMatrix([
+    ... [1, 0, 3, 2],
+    ... [0, 0, 1, 0],
+    ... [4, 0, 0, 5],
+    ... [0, 6, 7, 0]])
+    >>> S.liupc()
+    ([[0], [], [0], [1, 2]], [4, 3, 4, 4])
+
+    References
+    ==========
+
+    .. [1] Symbolic Sparse Cholesky Factorization using Elimination Trees,
+           Jeroen Van Grondelle (1999)
+           https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582
+    """
+    # Algorithm 2.4, p 17 of reference
+
+    # get the indices of the elements that are non-zero on or below diag
+    R = [[] for r in range(M.rows)]
+
+    for r, c, _ in M.row_list():
+        if c <= r:
+            R[r].append(c)
+
+    inf     = len(R)  # nothing will be this large
+    parent  = [inf]*M.rows
+    virtual = [inf]*M.rows
+
+    for r in range(M.rows):
+        for c in R[r][:-1]:
+            while virtual[c] < r:
+                t          = virtual[c]
+                virtual[c] = r
+                c          = t
+
+            if virtual[c] == inf:
+                parent[c] = virtual[c] = r
+
+    return R, parent
+
+def _row_structure_symbolic_cholesky(M):
+    """Symbolic cholesky factorization, for pre-determination of the
+    non-zero structure of the Cholesky factororization.
+
+    Examples
+    ========
+
+    >>> from sympy import SparseMatrix
+    >>> S = SparseMatrix([
+    ... [1, 0, 3, 2],
+    ... [0, 0, 1, 0],
+    ... [4, 0, 0, 5],
+    ... [0, 6, 7, 0]])
+    >>> S.row_structure_symbolic_cholesky()
+    [[0], [], [0], [1, 2]]
+
+    References
+    ==========
+
+    .. [1] Symbolic Sparse Cholesky Factorization using Elimination Trees,
+           Jeroen Van Grondelle (1999)
+           https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582
+    """
+
+    R, parent = M.liupc()
+    inf       = len(R)  # this acts as infinity
+    Lrow      = copy.deepcopy(R)
+
+    for k in range(M.rows):
+        for j in R[k]:
+            while j != inf and j != k:
+                Lrow[k].append(j)
+                j = parent[j]
+
+        Lrow[k] = sorted(set(Lrow[k]))
+
+    return Lrow
+
+
+def _cholesky(M, hermitian=True):
+    """Returns the Cholesky-type decomposition L of a matrix A
+    such that L * L.H == A if hermitian flag is True,
+    or L * L.T == A if hermitian is False.
+
+    A must be a Hermitian positive-definite matrix if hermitian is True,
+    or a symmetric matrix if it is False.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    >>> A.cholesky()
+    Matrix([
+    [ 5, 0, 0],
+    [ 3, 3, 0],
+    [-1, 1, 3]])
+    >>> A.cholesky() * A.cholesky().T
+    Matrix([
+    [25, 15, -5],
+    [15, 18,  0],
+    [-5,  0, 11]])
+
+    The matrix can have complex entries:
+
+    >>> from sympy import I
+    >>> A = Matrix(((9, 3*I), (-3*I, 5)))
+    >>> A.cholesky()
+    Matrix([
+    [ 3, 0],
+    [-I, 2]])
+    >>> A.cholesky() * A.cholesky().H
+    Matrix([
+    [   9, 3*I],
+    [-3*I,   5]])
+
+    Non-hermitian Cholesky-type decomposition may be useful when the
+    matrix is not positive-definite.
+
+    >>> A = Matrix([[1, 2], [2, 1]])
+    >>> L = A.cholesky(hermitian=False)
+    >>> L
+    Matrix([
+    [1,         0],
+    [2, sqrt(3)*I]])
+    >>> L*L.T == A
+    True
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.LDLdecomposition
+    sympy.matrices.matrixbase.MatrixBase.LUdecomposition
+    QRdecomposition
+    """
+
+    from .dense import MutableDenseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if hermitian and not M.is_hermitian:
+        raise ValueError("Matrix must be Hermitian.")
+    if not hermitian and not M.is_symmetric():
+        raise ValueError("Matrix must be symmetric.")
+
+    L   = MutableDenseMatrix.zeros(M.rows, M.rows)
+
+    if hermitian:
+        for i in range(M.rows):
+            for j in range(i):
+                L[i, j] = ((1 / L[j, j])*(M[i, j] -
+                    sum(L[i, k]*L[j, k].conjugate() for k in range(j))))
+
+            Lii2 = (M[i, i] -
+                sum(L[i, k]*L[i, k].conjugate() for k in range(i)))
+
+            if Lii2.is_positive is False:
+                raise NonPositiveDefiniteMatrixError(
+                    "Matrix must be positive-definite")
+
+            L[i, i] = sqrt(Lii2)
+
+    else:
+        for i in range(M.rows):
+            for j in range(i):
+                L[i, j] = ((1 / L[j, j])*(M[i, j] -
+                    sum(L[i, k]*L[j, k] for k in range(j))))
+
+            L[i, i] = sqrt(M[i, i] -
+                sum(L[i, k]**2 for k in range(i)))
+
+    return M._new(L)
+
+def _cholesky_sparse(M, hermitian=True):
+    """
+    Returns the Cholesky decomposition L of a matrix A
+    such that L * L.T = A
+
+    A must be a square, symmetric, positive-definite
+    and non-singular matrix
+
+    Examples
+    ========
+
+    >>> from sympy import SparseMatrix
+    >>> A = SparseMatrix(((25,15,-5),(15,18,0),(-5,0,11)))
+    >>> A.cholesky()
+    Matrix([
+    [ 5, 0, 0],
+    [ 3, 3, 0],
+    [-1, 1, 3]])
+    >>> A.cholesky() * A.cholesky().T == A
+    True
+
+    The matrix can have complex entries:
+
+    >>> from sympy import I
+    >>> A = SparseMatrix(((9, 3*I), (-3*I, 5)))
+    >>> A.cholesky()
+    Matrix([
+    [ 3, 0],
+    [-I, 2]])
+    >>> A.cholesky() * A.cholesky().H
+    Matrix([
+    [   9, 3*I],
+    [-3*I,   5]])
+
+    Non-hermitian Cholesky-type decomposition may be useful when the
+    matrix is not positive-definite.
+
+    >>> A = SparseMatrix([[1, 2], [2, 1]])
+    >>> L = A.cholesky(hermitian=False)
+    >>> L
+    Matrix([
+    [1,         0],
+    [2, sqrt(3)*I]])
+    >>> L*L.T == A
+    True
+
+    See Also
+    ========
+
+    sympy.matrices.sparse.SparseMatrix.LDLdecomposition
+    sympy.matrices.matrixbase.MatrixBase.LUdecomposition
+    QRdecomposition
+    """
+
+    from .dense import MutableDenseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if hermitian and not M.is_hermitian:
+        raise ValueError("Matrix must be Hermitian.")
+    if not hermitian and not M.is_symmetric():
+        raise ValueError("Matrix must be symmetric.")
+
+    dps       = _get_intermediate_simp(expand_mul, expand_mul)
+    Crowstruc = M.row_structure_symbolic_cholesky()
+    C         = MutableDenseMatrix.zeros(M.rows)
+
+    for i in range(len(Crowstruc)):
+        for j in Crowstruc[i]:
+            if i != j:
+                C[i, j] = M[i, j]
+                summ    = 0
+
+                for p1 in Crowstruc[i]:
+                    if p1 < j:
+                        for p2 in Crowstruc[j]:
+                            if p2 < j:
+                                if p1 == p2:
+                                    if hermitian:
+                                        summ += C[i, p1]*C[j, p1].conjugate()
+                                    else:
+                                        summ += C[i, p1]*C[j, p1]
+                            else:
+                                break
+                        else:
+                            break
+
+                C[i, j] = dps((C[i, j] - summ) / C[j, j])
+
+            else: # i == j
+                C[j, j] = M[j, j]
+                summ    = 0
+
+                for k in Crowstruc[j]:
+                    if k < j:
+                        if hermitian:
+                            summ += C[j, k]*C[j, k].conjugate()
+                        else:
+                            summ += C[j, k]**2
+                    else:
+                        break
+
+                Cjj2 = dps(C[j, j] - summ)
+
+                if hermitian and Cjj2.is_positive is False:
+                    raise NonPositiveDefiniteMatrixError(
+                        "Matrix must be positive-definite")
+
+                C[j, j] = sqrt(Cjj2)
+
+    return M._new(C)
+
+
+def _LDLdecomposition(M, hermitian=True):
+    """Returns the LDL Decomposition (L, D) of matrix A,
+    such that L * D * L.H == A if hermitian flag is True, or
+    L * D * L.T == A if hermitian is False.
+    This method eliminates the use of square root.
+    Further this ensures that all the diagonal entries of L are 1.
+    A must be a Hermitian positive-definite matrix if hermitian is True,
+    or a symmetric matrix otherwise.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, eye
+    >>> A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    >>> L, D = A.LDLdecomposition()
+    >>> L
+    Matrix([
+    [   1,   0, 0],
+    [ 3/5,   1, 0],
+    [-1/5, 1/3, 1]])
+    >>> D
+    Matrix([
+    [25, 0, 0],
+    [ 0, 9, 0],
+    [ 0, 0, 9]])
+    >>> L * D * L.T * A.inv() == eye(A.rows)
+    True
+
+    The matrix can have complex entries:
+
+    >>> from sympy import I
+    >>> A = Matrix(((9, 3*I), (-3*I, 5)))
+    >>> L, D = A.LDLdecomposition()
+    >>> L
+    Matrix([
+    [   1, 0],
+    [-I/3, 1]])
+    >>> D
+    Matrix([
+    [9, 0],
+    [0, 4]])
+    >>> L*D*L.H == A
+    True
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.cholesky
+    sympy.matrices.matrixbase.MatrixBase.LUdecomposition
+    QRdecomposition
+    """
+
+    from .dense import MutableDenseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if hermitian and not M.is_hermitian:
+        raise ValueError("Matrix must be Hermitian.")
+    if not hermitian and not M.is_symmetric():
+        raise ValueError("Matrix must be symmetric.")
+
+    D   = MutableDenseMatrix.zeros(M.rows, M.rows)
+    L   = MutableDenseMatrix.eye(M.rows)
+
+    if hermitian:
+        for i in range(M.rows):
+            for j in range(i):
+                L[i, j] = (1 / D[j, j])*(M[i, j] - sum(
+                    L[i, k]*L[j, k].conjugate()*D[k, k] for k in range(j)))
+
+            D[i, i] = (M[i, i] -
+                sum(L[i, k]*L[i, k].conjugate()*D[k, k] for k in range(i)))
+
+            if D[i, i].is_positive is False:
+                raise NonPositiveDefiniteMatrixError(
+                    "Matrix must be positive-definite")
+
+    else:
+        for i in range(M.rows):
+            for j in range(i):
+                L[i, j] = (1 / D[j, j])*(M[i, j] - sum(
+                    L[i, k]*L[j, k]*D[k, k] for k in range(j)))
+
+            D[i, i] = M[i, i] - sum(L[i, k]**2*D[k, k] for k in range(i))
+
+    return M._new(L), M._new(D)
+
+def _LDLdecomposition_sparse(M, hermitian=True):
+    """
+    Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix
+    ``A``, such that ``L * D * L.T == A``. ``A`` must be a square,
+    symmetric, positive-definite and non-singular.
+
+    This method eliminates the use of square root and ensures that all
+    the diagonal entries of L are 1.
+
+    Examples
+    ========
+
+    >>> from sympy import SparseMatrix
+    >>> A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    >>> L, D = A.LDLdecomposition()
+    >>> L
+    Matrix([
+    [   1,   0, 0],
+    [ 3/5,   1, 0],
+    [-1/5, 1/3, 1]])
+    >>> D
+    Matrix([
+    [25, 0, 0],
+    [ 0, 9, 0],
+    [ 0, 0, 9]])
+    >>> L * D * L.T == A
+    True
+
+    """
+
+    from .dense import MutableDenseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if hermitian and not M.is_hermitian:
+        raise ValueError("Matrix must be Hermitian.")
+    if not hermitian and not M.is_symmetric():
+        raise ValueError("Matrix must be symmetric.")
+
+    dps       = _get_intermediate_simp(expand_mul, expand_mul)
+    Lrowstruc = M.row_structure_symbolic_cholesky()
+    L         = MutableDenseMatrix.eye(M.rows)
+    D         = MutableDenseMatrix.zeros(M.rows, M.cols)
+
+    for i in range(len(Lrowstruc)):
+        for j in Lrowstruc[i]:
+            if i != j:
+                L[i, j] = M[i, j]
+                summ    = 0
+
+                for p1 in Lrowstruc[i]:
+                    if p1 < j:
+                        for p2 in Lrowstruc[j]:
+                            if p2 < j:
+                                if p1 == p2:
+                                    if hermitian:
+                                        summ += L[i, p1]*L[j, p1].conjugate()*D[p1, p1]
+                                    else:
+                                        summ += L[i, p1]*L[j, p1]*D[p1, p1]
+                            else:
+                                break
+                    else:
+                        break
+
+                L[i, j] = dps((L[i, j] - summ) / D[j, j])
+
+            else: # i == j
+                D[i, i] = M[i, i]
+                summ    = 0
+
+                for k in Lrowstruc[i]:
+                    if k < i:
+                        if hermitian:
+                            summ += L[i, k]*L[i, k].conjugate()*D[k, k]
+                        else:
+                            summ += L[i, k]**2*D[k, k]
+                    else:
+                        break
+
+                D[i, i] = dps(D[i, i] - summ)
+
+                if hermitian and D[i, i].is_positive is False:
+                    raise NonPositiveDefiniteMatrixError(
+                        "Matrix must be positive-definite")
+
+    return M._new(L), M._new(D)
+
+
+def _LUdecomposition(M, iszerofunc=_iszero, simpfunc=None, rankcheck=False):
+    """Returns (L, U, perm) where L is a lower triangular matrix with unit
+    diagonal, U is an upper triangular matrix, and perm is a list of row
+    swap index pairs. If A is the original matrix, then
+    ``A = (L*U).permuteBkwd(perm)``, and the row permutation matrix P such
+    that $P A = L U$ can be computed by ``P = eye(A.rows).permuteFwd(perm)``.
+
+    See documentation for LUCombined for details about the keyword argument
+    rankcheck, iszerofunc, and simpfunc.
+
+    Parameters
+    ==========
+
+    rankcheck : bool, optional
+        Determines if this function should detect the rank
+        deficiency of the matrixis and should raise a
+        ``ValueError``.
+
+    iszerofunc : function, optional
+        A function which determines if a given expression is zero.
+
+        The function should be a callable that takes a single
+        SymPy expression and returns a 3-valued boolean value
+        ``True``, ``False``, or ``None``.
+
+        It is internally used by the pivot searching algorithm.
+        See the notes section for a more information about the
+        pivot searching algorithm.
+
+    simpfunc : function or None, optional
+        A function that simplifies the input.
+
+        If this is specified as a function, this function should be
+        a callable that takes a single SymPy expression and returns
+        an another SymPy expression that is algebraically
+        equivalent.
+
+        If ``None``, it indicates that the pivot search algorithm
+        should not attempt to simplify any candidate pivots.
+
+        It is internally used by the pivot searching algorithm.
+        See the notes section for a more information about the
+        pivot searching algorithm.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> a = Matrix([[4, 3], [6, 3]])
+    >>> L, U, _ = a.LUdecomposition()
+    >>> L
+    Matrix([
+    [  1, 0],
+    [3/2, 1]])
+    >>> U
+    Matrix([
+    [4,    3],
+    [0, -3/2]])
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.cholesky
+    sympy.matrices.dense.DenseMatrix.LDLdecomposition
+    QRdecomposition
+    LUdecomposition_Simple
+    LUdecompositionFF
+    LUsolve
+    """
+
+    combined, p = M.LUdecomposition_Simple(iszerofunc=iszerofunc,
+        simpfunc=simpfunc, rankcheck=rankcheck)
+
+    # L is lower triangular ``M.rows x M.rows``
+    # U is upper triangular ``M.rows x M.cols``
+    # L has unit diagonal. For each column in combined, the subcolumn
+    # below the diagonal of combined is shared by L.
+    # If L has more columns than combined, then the remaining subcolumns
+    # below the diagonal of L are zero.
+    # The upper triangular portion of L and combined are equal.
+    def entry_L(i, j):
+        if i < j:
+            # Super diagonal entry
+            return M.zero
+        elif i == j:
+            return M.one
+        elif j < combined.cols:
+            return combined[i, j]
+
+        # Subdiagonal entry of L with no corresponding
+        # entry in combined
+        return M.zero
+
+    def entry_U(i, j):
+        return M.zero if i > j else combined[i, j]
+
+    L = M._new(combined.rows, combined.rows, entry_L)
+    U = M._new(combined.rows, combined.cols, entry_U)
+
+    return L, U, p
+
+def _LUdecomposition_Simple(M, iszerofunc=_iszero, simpfunc=None,
+        rankcheck=False):
+    r"""Compute the PLU decomposition of the matrix.
+
+    Parameters
+    ==========
+
+    rankcheck : bool, optional
+        Determines if this function should detect the rank
+        deficiency of the matrixis and should raise a
+        ``ValueError``.
+
+    iszerofunc : function, optional
+        A function which determines if a given expression is zero.
+
+        The function should be a callable that takes a single
+        SymPy expression and returns a 3-valued boolean value
+        ``True``, ``False``, or ``None``.
+
+        It is internally used by the pivot searching algorithm.
+        See the notes section for a more information about the
+        pivot searching algorithm.
+
+    simpfunc : function or None, optional
+        A function that simplifies the input.
+
+        If this is specified as a function, this function should be
+        a callable that takes a single SymPy expression and returns
+        an another SymPy expression that is algebraically
+        equivalent.
+
+        If ``None``, it indicates that the pivot search algorithm
+        should not attempt to simplify any candidate pivots.
+
+        It is internally used by the pivot searching algorithm.
+        See the notes section for a more information about the
+        pivot searching algorithm.
+
+    Returns
+    =======
+
+    (lu, row_swaps) : (Matrix, list)
+        If the original matrix is a $m, n$ matrix:
+
+        *lu* is a $m, n$ matrix, which contains result of the
+        decomposition in a compressed form. See the notes section
+        to see how the matrix is compressed.
+
+        *row_swaps* is a $m$-element list where each element is a
+        pair of row exchange indices.
+
+        ``A = (L*U).permute_backward(perm)``, and the row
+        permutation matrix $P$ from the formula $P A = L U$ can be
+        computed by ``P=eye(A.row).permute_forward(perm)``.
+
+    Raises
+    ======
+
+    ValueError
+        Raised if ``rankcheck=True`` and the matrix is found to
+        be rank deficient during the computation.
+
+    Notes
+    =====
+
+    About the PLU decomposition:
+
+    PLU decomposition is a generalization of a LU decomposition
+    which can be extended for rank-deficient matrices.
+
+    It can further be generalized for non-square matrices, and this
+    is the notation that SymPy is using.
+
+    PLU decomposition is a decomposition of a $m, n$ matrix $A$ in
+    the form of $P A = L U$ where
+
+    * $L$ is a $m, m$ lower triangular matrix with unit diagonal
+        entries.
+    * $U$ is a $m, n$ upper triangular matrix.
+    * $P$ is a $m, m$ permutation matrix.
+
+    So, for a square matrix, the decomposition would look like:
+
+    .. math::
+        L = \begin{bmatrix}
+        1 & 0 & 0 & \cdots & 0 \\
+        L_{1, 0} & 1 & 0 & \cdots & 0 \\
+        L_{2, 0} & L_{2, 1} & 1 & \cdots & 0 \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots & 1
+        \end{bmatrix}
+
+    .. math::
+        U = \begin{bmatrix}
+        U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\
+        0 & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\
+        0 & 0 & U_{2, 2} & \cdots & U_{2, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        0 & 0 & 0 & \cdots & U_{n-1, n-1}
+        \end{bmatrix}
+
+    And for a matrix with more rows than the columns,
+    the decomposition would look like:
+
+    .. math::
+        L = \begin{bmatrix}
+        1 & 0 & 0 & \cdots & 0 & 0 & \cdots & 0 \\
+        L_{1, 0} & 1 & 0 & \cdots & 0 & 0 & \cdots & 0 \\
+        L_{2, 0} & L_{2, 1} & 1 & \cdots & 0 & 0 & \cdots & 0 \\
+        \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots
+        & \vdots \\
+        L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots & 1 & 0
+        & \cdots & 0 \\
+        L_{n, 0} & L_{n, 1} & L_{n, 2} & \cdots & L_{n, n-1} & 1
+        & \cdots & 0 \\
+        \vdots & \vdots & \vdots & \ddots & \vdots & \vdots
+        & \ddots & \vdots \\
+        L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots & L_{m-1, n-1}
+        & 0 & \cdots & 1 \\
+        \end{bmatrix}
+
+    .. math::
+        U = \begin{bmatrix}
+        U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\
+        0 & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\
+        0 & 0 & U_{2, 2} & \cdots & U_{2, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        0 & 0 & 0 & \cdots & U_{n-1, n-1} \\
+        0 & 0 & 0 & \cdots & 0 \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        0 & 0 & 0 & \cdots & 0
+        \end{bmatrix}
+
+    Finally, for a matrix with more columns than the rows, the
+    decomposition would look like:
+
+    .. math::
+        L = \begin{bmatrix}
+        1 & 0 & 0 & \cdots & 0 \\
+        L_{1, 0} & 1 & 0 & \cdots & 0 \\
+        L_{2, 0} & L_{2, 1} & 1 & \cdots & 0 \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots & 1
+        \end{bmatrix}
+
+    .. math::
+        U = \begin{bmatrix}
+        U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, m-1}
+        & \cdots & U_{0, n-1} \\
+        0 & U_{1, 1} & U_{1, 2} & \cdots & U_{1, m-1}
+        & \cdots & U_{1, n-1} \\
+        0 & 0 & U_{2, 2} & \cdots & U_{2, m-1}
+        & \cdots & U_{2, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots
+        & \cdots & \vdots \\
+        0 & 0 & 0 & \cdots & U_{m-1, m-1}
+        & \cdots & U_{m-1, n-1} \\
+        \end{bmatrix}
+
+    About the compressed LU storage:
+
+    The results of the decomposition are often stored in compressed
+    forms rather than returning $L$ and $U$ matrices individually.
+
+    It may be less intiuitive, but it is commonly used for a lot of
+    numeric libraries because of the efficiency.
+
+    The storage matrix is defined as following for this specific
+    method:
+
+    * The subdiagonal elements of $L$ are stored in the subdiagonal
+        portion of $LU$, that is $LU_{i, j} = L_{i, j}$ whenever
+        $i > j$.
+    * The elements on the diagonal of $L$ are all 1, and are not
+        explicitly stored.
+    * $U$ is stored in the upper triangular portion of $LU$, that is
+        $LU_{i, j} = U_{i, j}$ whenever $i <= j$.
+    * For a case of $m > n$, the right side of the $L$ matrix is
+        trivial to store.
+    * For a case of $m < n$, the below side of the $U$ matrix is
+        trivial to store.
+
+    So, for a square matrix, the compressed output matrix would be:
+
+    .. math::
+        LU = \begin{bmatrix}
+        U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\
+        L_{1, 0} & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\
+        L_{2, 0} & L_{2, 1} & U_{2, 2} & \cdots & U_{2, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots & U_{n-1, n-1}
+        \end{bmatrix}
+
+    For a matrix with more rows than the columns, the compressed
+    output matrix would be:
+
+    .. math::
+        LU = \begin{bmatrix}
+        U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\
+        L_{1, 0} & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\
+        L_{2, 0} & L_{2, 1} & U_{2, 2} & \cdots & U_{2, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots
+        & U_{n-1, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots \\
+        L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots
+        & L_{m-1, n-1} \\
+        \end{bmatrix}
+
+    For a matrix with more columns than the rows, the compressed
+    output matrix would be:
+
+    .. math::
+        LU = \begin{bmatrix}
+        U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, m-1}
+        & \cdots & U_{0, n-1} \\
+        L_{1, 0} & U_{1, 1} & U_{1, 2} & \cdots & U_{1, m-1}
+        & \cdots & U_{1, n-1} \\
+        L_{2, 0} & L_{2, 1} & U_{2, 2} & \cdots & U_{2, m-1}
+        & \cdots & U_{2, n-1} \\
+        \vdots & \vdots & \vdots & \ddots & \vdots
+        & \cdots & \vdots \\
+        L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots & U_{m-1, m-1}
+        & \cdots & U_{m-1, n-1} \\
+        \end{bmatrix}
+
+    About the pivot searching algorithm:
+
+    When a matrix contains symbolic entries, the pivot search algorithm
+    differs from the case where every entry can be categorized as zero or
+    nonzero.
+    The algorithm searches column by column through the submatrix whose
+    top left entry coincides with the pivot position.
+    If it exists, the pivot is the first entry in the current search
+    column that iszerofunc guarantees is nonzero.
+    If no such candidate exists, then each candidate pivot is simplified
+    if simpfunc is not None.
+    The search is repeated, with the difference that a candidate may be
+    the pivot if ``iszerofunc()`` cannot guarantee that it is nonzero.
+    In the second search the pivot is the first candidate that
+    iszerofunc can guarantee is nonzero.
+    If no such candidate exists, then the pivot is the first candidate
+    for which iszerofunc returns None.
+    If no such candidate exists, then the search is repeated in the next
+    column to the right.
+    The pivot search algorithm differs from the one in ``rref()``, which
+    relies on ``_find_reasonable_pivot()``.
+    Future versions of ``LUdecomposition_simple()`` may use
+    ``_find_reasonable_pivot()``.
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.LUdecomposition
+    LUdecompositionFF
+    LUsolve
+    """
+
+    if rankcheck:
+        # https://github.com/sympy/sympy/issues/9796
+        pass
+
+    if S.Zero in M.shape:
+        # Define LU decomposition of a matrix with no entries as a matrix
+        # of the same dimensions with all zero entries.
+        return M.zeros(M.rows, M.cols), []
+
+    dps       = _get_intermediate_simp()
+    lu        = M.as_mutable()
+    row_swaps = []
+
+    pivot_col = 0
+
+    for pivot_row in range(0, lu.rows - 1):
+        # Search for pivot. Prefer entry that iszeropivot determines
+        # is nonzero, over entry that iszeropivot cannot guarantee
+        # is  zero.
+        # XXX ``_find_reasonable_pivot`` uses slow zero testing. Blocked by bug #10279
+        # Future versions of LUdecomposition_simple can pass iszerofunc and simpfunc
+        # to _find_reasonable_pivot().
+        # In pass 3 of _find_reasonable_pivot(), the predicate in ``if x.equals(S.Zero):``
+        # calls sympy.simplify(), and not the simplification function passed in via
+        # the keyword argument simpfunc.
+        iszeropivot = True
+
+        while pivot_col != M.cols and iszeropivot:
+            sub_col = (lu[r, pivot_col] for r in range(pivot_row, M.rows))
+
+            pivot_row_offset, pivot_value, is_assumed_non_zero, ind_simplified_pairs =\
+                _find_reasonable_pivot_naive(sub_col, iszerofunc, simpfunc)
+
+            iszeropivot = pivot_value is None
+
+            if iszeropivot:
+                # All candidate pivots in this column are zero.
+                # Proceed to next column.
+                pivot_col += 1
+
+        if rankcheck and pivot_col != pivot_row:
+            # All entries including and below the pivot position are
+            # zero, which indicates that the rank of the matrix is
+            # strictly less than min(num rows, num cols)
+            # Mimic behavior of previous implementation, by throwing a
+            # ValueError.
+            raise ValueError("Rank of matrix is strictly less than"
+                                " number of rows or columns."
+                                " Pass keyword argument"
+                                " rankcheck=False to compute"
+                                " the LU decomposition of this matrix.")
+
+        candidate_pivot_row = None if pivot_row_offset is None else pivot_row + pivot_row_offset
+
+        if candidate_pivot_row is None and iszeropivot:
+            # If candidate_pivot_row is None and iszeropivot is True
+            # after pivot search has completed, then the submatrix
+            # below and to the right of (pivot_row, pivot_col) is
+            # all zeros, indicating that Gaussian elimination is
+            # complete.
+            return lu, row_swaps
+
+        # Update entries simplified during pivot search.
+        for offset, val in ind_simplified_pairs:
+            lu[pivot_row + offset, pivot_col] = val
+
+        if pivot_row != candidate_pivot_row:
+            # Row swap book keeping:
+            # Record which rows were swapped.
+            # Update stored portion of L factor by multiplying L on the
+            # left and right with the current permutation.
+            # Swap rows of U.
+            row_swaps.append([pivot_row, candidate_pivot_row])
+
+            # Update L.
+            lu[pivot_row, 0:pivot_row], lu[candidate_pivot_row, 0:pivot_row] = \
+                lu[candidate_pivot_row, 0:pivot_row], lu[pivot_row, 0:pivot_row]
+
+            # Swap pivot row of U with candidate pivot row.
+            lu[pivot_row, pivot_col:lu.cols], lu[candidate_pivot_row, pivot_col:lu.cols] = \
+                lu[candidate_pivot_row, pivot_col:lu.cols], lu[pivot_row, pivot_col:lu.cols]
+
+        # Introduce zeros below the pivot by adding a multiple of the
+        # pivot row to a row under it, and store the result in the
+        # row under it.
+        # Only entries in the target row whose index is greater than
+        # start_col may be nonzero.
+        start_col = pivot_col + 1
+
+        for row in range(pivot_row + 1, lu.rows):
+            # Store factors of L in the subcolumn below
+            # (pivot_row, pivot_row).
+            lu[row, pivot_row] = \
+                dps(lu[row, pivot_col]/lu[pivot_row, pivot_col])
+
+            # Form the linear combination of the pivot row and the current
+            # row below the pivot row that zeros the entries below the pivot.
+            # Employing slicing instead of a loop here raises
+            # NotImplementedError: Cannot add Zero to MutableSparseMatrix
+            # in sympy/matrices/tests/test_sparse.py.
+            # c = pivot_row + 1 if pivot_row == pivot_col else pivot_col
+            for c in range(start_col, lu.cols):
+                lu[row, c] = dps(lu[row, c] - lu[row, pivot_row]*lu[pivot_row, c])
+
+        if pivot_row != pivot_col:
+            # matrix rank < min(num rows, num cols),
+            # so factors of L are not stored directly below the pivot.
+            # These entries are zero by construction, so don't bother
+            # computing them.
+            for row in range(pivot_row + 1, lu.rows):
+                lu[row, pivot_col] = M.zero
+
+        pivot_col += 1
+
+        if pivot_col == lu.cols:
+            # All candidate pivots are zero implies that Gaussian
+            # elimination is complete.
+            return lu, row_swaps
+
+    if rankcheck:
+        if iszerofunc(
+                lu[Min(lu.rows, lu.cols) - 1, Min(lu.rows, lu.cols) - 1]):
+            raise ValueError("Rank of matrix is strictly less than"
+                                " number of rows or columns."
+                                " Pass keyword argument"
+                                " rankcheck=False to compute"
+                                " the LU decomposition of this matrix.")
+
+    return lu, row_swaps
+
+def _LUdecompositionFF(M):
+    """Compute a fraction-free LU decomposition.
+
+    Returns 4 matrices P, L, D, U such that PA = L D**-1 U.
+    If the elements of the matrix belong to some integral domain I, then all
+    elements of L, D and U are guaranteed to belong to I.
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.LUdecomposition
+    LUdecomposition_Simple
+    LUsolve
+
+    References
+    ==========
+
+    .. [1] W. Zhou & D.J. Jeffrey, "Fraction-free matrix factors: new forms
+        for LU and QR factors". Frontiers in Computer Science in China,
+        Vol 2, no. 1, pp. 67-80, 2008.
+    """
+
+    from sympy.matrices import SparseMatrix
+
+    zeros    = SparseMatrix.zeros
+    eye      = SparseMatrix.eye
+    n, m     = M.rows, M.cols
+    U, L, P  = M.as_mutable(), eye(n), eye(n)
+    DD       = zeros(n, n)
+    oldpivot = 1
+
+    for k in range(n - 1):
+        if U[k, k] == 0:
+            for kpivot in range(k + 1, n):
+                if U[kpivot, k]:
+                    break
+            else:
+                raise ValueError("Matrix is not full rank")
+
+            U[k, k:], U[kpivot, k:] = U[kpivot, k:], U[k, k:]
+            L[k, :k], L[kpivot, :k] = L[kpivot, :k], L[k, :k]
+            P[k, :], P[kpivot, :]   = P[kpivot, :], P[k, :]
+
+        L [k, k] = Ukk = U[k, k]
+        DD[k, k] = oldpivot * Ukk
+
+        for i in range(k + 1, n):
+            L[i, k] = Uik = U[i, k]
+
+            for j in range(k + 1, m):
+                U[i, j] = (Ukk * U[i, j] - U[k, j] * Uik) / oldpivot
+
+            U[i, k] = 0
+
+        oldpivot = Ukk
+
+    DD[n - 1, n - 1] = oldpivot
+
+    return P, L, DD, U
+
+def _singular_value_decomposition(A):
+    r"""Returns a Condensed Singular Value decomposition.
+
+    Explanation
+    ===========
+
+    A Singular Value decomposition is a decomposition in the form $A = U \Sigma V^H$
+    where
+
+    - $U, V$ are column orthogonal matrix.
+    - $\Sigma$ is a diagonal matrix, where the main diagonal contains singular
+      values of matrix A.
+
+    A column orthogonal matrix satisfies
+    $\mathbb{I} = U^H U$ while a full orthogonal matrix satisfies
+    relation $\mathbb{I} = U U^H = U^H U$ where $\mathbb{I}$ is an identity
+    matrix with matching dimensions.
+
+    For matrices which are not square or are rank-deficient, it is
+    sufficient to return a column orthogonal matrix because augmenting
+    them may introduce redundant computations.
+    In condensed Singular Value Decomposition we only return column orthogonal
+    matrices because of this reason
+
+    If you want to augment the results to return a full orthogonal
+    decomposition, you should use the following procedures.
+
+    - Augment the $U, V$ matrices with columns that are orthogonal to every
+      other columns and make it square.
+    - Augment the $\Sigma$ matrix with zero rows to make it have the same
+      shape as the original matrix.
+
+    The procedure will be illustrated in the examples section.
+
+    Examples
+    ========
+
+    we take a full rank matrix first:
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[1, 2],[2,1]])
+    >>> U, S, V = A.singular_value_decomposition()
+    >>> U
+    Matrix([
+    [ sqrt(2)/2, sqrt(2)/2],
+    [-sqrt(2)/2, sqrt(2)/2]])
+    >>> S
+    Matrix([
+    [1, 0],
+    [0, 3]])
+    >>> V
+    Matrix([
+    [-sqrt(2)/2, sqrt(2)/2],
+    [ sqrt(2)/2, sqrt(2)/2]])
+
+    If a matrix if square and full rank both U, V
+    are orthogonal in both directions
+
+    >>> U * U.H
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    >>> U.H * U
+    Matrix([
+    [1, 0],
+    [0, 1]])
+
+    >>> V * V.H
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    >>> V.H * V
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    >>> A == U * S * V.H
+    True
+
+    >>> C = Matrix([
+    ...         [1, 0, 0, 0, 2],
+    ...         [0, 0, 3, 0, 0],
+    ...         [0, 0, 0, 0, 0],
+    ...         [0, 2, 0, 0, 0],
+    ...     ])
+    >>> U, S, V = C.singular_value_decomposition()
+
+    >>> V.H * V
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> V * V.H
+    Matrix([
+    [1/5, 0, 0, 0, 2/5],
+    [  0, 1, 0, 0,   0],
+    [  0, 0, 1, 0,   0],
+    [  0, 0, 0, 0,   0],
+    [2/5, 0, 0, 0, 4/5]])
+
+    If you want to augment the results to be a full orthogonal
+    decomposition, you should augment $V$ with an another orthogonal
+    column.
+
+    You are able to append an arbitrary standard basis that are linearly
+    independent to every other columns and you can run the Gram-Schmidt
+    process to make them augmented as orthogonal basis.
+
+    >>> V_aug = V.row_join(Matrix([[0,0,0,0,1],
+    ... [0,0,0,1,0]]).H)
+    >>> V_aug = V_aug.QRdecomposition()[0]
+    >>> V_aug
+    Matrix([
+    [0,   sqrt(5)/5, 0, -2*sqrt(5)/5, 0],
+    [1,           0, 0,            0, 0],
+    [0,           0, 1,            0, 0],
+    [0,           0, 0,            0, 1],
+    [0, 2*sqrt(5)/5, 0,    sqrt(5)/5, 0]])
+    >>> V_aug.H * V_aug
+    Matrix([
+    [1, 0, 0, 0, 0],
+    [0, 1, 0, 0, 0],
+    [0, 0, 1, 0, 0],
+    [0, 0, 0, 1, 0],
+    [0, 0, 0, 0, 1]])
+    >>> V_aug * V_aug.H
+    Matrix([
+    [1, 0, 0, 0, 0],
+    [0, 1, 0, 0, 0],
+    [0, 0, 1, 0, 0],
+    [0, 0, 0, 1, 0],
+    [0, 0, 0, 0, 1]])
+
+    Similarly we augment U
+
+    >>> U_aug = U.row_join(Matrix([0,0,1,0]))
+    >>> U_aug = U_aug.QRdecomposition()[0]
+    >>> U_aug
+    Matrix([
+    [0, 1, 0, 0],
+    [0, 0, 1, 0],
+    [0, 0, 0, 1],
+    [1, 0, 0, 0]])
+
+    >>> U_aug.H * U_aug
+    Matrix([
+    [1, 0, 0, 0],
+    [0, 1, 0, 0],
+    [0, 0, 1, 0],
+    [0, 0, 0, 1]])
+    >>> U_aug * U_aug.H
+    Matrix([
+    [1, 0, 0, 0],
+    [0, 1, 0, 0],
+    [0, 0, 1, 0],
+    [0, 0, 0, 1]])
+
+    We add 2 zero columns and one row to S
+
+    >>> S_aug = S.col_join(Matrix([[0,0,0]]))
+    >>> S_aug = S_aug.row_join(Matrix([[0,0,0,0],
+    ... [0,0,0,0]]).H)
+    >>> S_aug
+    Matrix([
+    [2,       0, 0, 0, 0],
+    [0, sqrt(5), 0, 0, 0],
+    [0,       0, 3, 0, 0],
+    [0,       0, 0, 0, 0]])
+
+
+
+    >>> U_aug * S_aug * V_aug.H == C
+    True
+
+    """
+
+    AH = A.H
+    m, n = A.shape
+    if m >= n:
+        V, S = (AH * A).diagonalize()
+
+        ranked = []
+        for i, x in enumerate(S.diagonal()):
+            if not x.is_zero:
+                ranked.append(i)
+
+        V = V[:, ranked]
+
+        Singular_vals = [sqrt(S[i, i]) for i in range(S.rows) if i in ranked]
+
+        S = S.diag(*Singular_vals)
+        V, _ = V.QRdecomposition()
+        U = A * V * S.inv()
+    else:
+        U, S = (A * AH).diagonalize()
+
+        ranked = []
+        for i, x in enumerate(S.diagonal()):
+            if not x.is_zero:
+                ranked.append(i)
+
+        U = U[:, ranked]
+        Singular_vals = [sqrt(S[i, i]) for i in range(S.rows) if i in ranked]
+
+        S = S.diag(*Singular_vals)
+        U, _ = U.QRdecomposition()
+        V = AH * U * S.inv()
+
+    return U, S, V
+
+def _QRdecomposition_optional(M, normalize=True):
+    def dot(u, v):
+        return u.dot(v, hermitian=True)
+
+    dps = _get_intermediate_simp(expand_mul, expand_mul)
+
+    A = M.as_mutable()
+    ranked = []
+
+    Q = A
+    R = A.zeros(A.cols)
+
+    for j in range(A.cols):
+        for i in range(j):
+            if Q[:, i].is_zero_matrix:
+                continue
+
+            R[i, j] = dot(Q[:, i], Q[:, j]) / dot(Q[:, i], Q[:, i])
+            R[i, j] = dps(R[i, j])
+            Q[:, j] -= Q[:, i] * R[i, j]
+
+        Q[:, j] = dps(Q[:, j])
+        if Q[:, j].is_zero_matrix is not True:
+            ranked.append(j)
+            R[j, j] = M.one
+
+    Q = Q.extract(range(Q.rows), ranked)
+    R = R.extract(ranked, range(R.cols))
+
+    if normalize:
+        # Normalization
+        for i in range(Q.cols):
+            norm = Q[:, i].norm()
+            Q[:, i] /= norm
+            R[i, :] *= norm
+
+    return M.__class__(Q), M.__class__(R)
+
+
+def _QRdecomposition(M):
+    r"""Returns a QR decomposition.
+
+    Explanation
+    ===========
+
+    A QR decomposition is a decomposition in the form $A = Q R$
+    where
+
+    - $Q$ is a column orthogonal matrix.
+    - $R$ is a upper triangular (trapezoidal) matrix.
+
+    A column orthogonal matrix satisfies
+    $\mathbb{I} = Q^H Q$ while a full orthogonal matrix satisfies
+    relation $\mathbb{I} = Q Q^H = Q^H Q$ where $I$ is an identity
+    matrix with matching dimensions.
+
+    For matrices which are not square or are rank-deficient, it is
+    sufficient to return a column orthogonal matrix because augmenting
+    them may introduce redundant computations.
+    And an another advantage of this is that you can easily inspect the
+    matrix rank by counting the number of columns of $Q$.
+
+    If you want to augment the results to return a full orthogonal
+    decomposition, you should use the following procedures.
+
+    - Augment the $Q$ matrix with columns that are orthogonal to every
+      other columns and make it square.
+    - Augment the $R$ matrix with zero rows to make it have the same
+      shape as the original matrix.
+
+    The procedure will be illustrated in the examples section.
+
+    Examples
+    ========
+
+    A full rank matrix example:
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[12, -51, 4], [6, 167, -68], [-4, 24, -41]])
+    >>> Q, R = A.QRdecomposition()
+    >>> Q
+    Matrix([
+    [ 6/7, -69/175, -58/175],
+    [ 3/7, 158/175,   6/175],
+    [-2/7,    6/35,  -33/35]])
+    >>> R
+    Matrix([
+    [14,  21, -14],
+    [ 0, 175, -70],
+    [ 0,   0,  35]])
+
+    If the matrix is square and full rank, the $Q$ matrix becomes
+    orthogonal in both directions, and needs no augmentation.
+
+    >>> Q * Q.H
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> Q.H * Q
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+
+    >>> A == Q*R
+    True
+
+    A rank deficient matrix example:
+
+    >>> A = Matrix([[12, -51, 0], [6, 167, 0], [-4, 24, 0]])
+    >>> Q, R = A.QRdecomposition()
+    >>> Q
+    Matrix([
+    [ 6/7, -69/175],
+    [ 3/7, 158/175],
+    [-2/7,    6/35]])
+    >>> R
+    Matrix([
+    [14,  21, 0],
+    [ 0, 175, 0]])
+
+    QRdecomposition might return a matrix Q that is rectangular.
+    In this case the orthogonality condition might be satisfied as
+    $\mathbb{I} = Q.H*Q$ but not in the reversed product
+    $\mathbb{I} = Q * Q.H$.
+
+    >>> Q.H * Q
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    >>> Q * Q.H
+    Matrix([
+    [27261/30625,   348/30625, -1914/6125],
+    [  348/30625, 30589/30625,   198/6125],
+    [ -1914/6125,    198/6125,   136/1225]])
+
+    If you want to augment the results to be a full orthogonal
+    decomposition, you should augment $Q$ with an another orthogonal
+    column.
+
+    You are able to append an identity matrix,
+    and you can run the Gram-Schmidt
+    process to make them augmented as orthogonal basis.
+
+    >>> Q_aug = Q.row_join(Matrix.eye(3))
+    >>> Q_aug = Q_aug.QRdecomposition()[0]
+    >>> Q_aug
+    Matrix([
+    [ 6/7, -69/175, 58/175],
+    [ 3/7, 158/175, -6/175],
+    [-2/7,    6/35,  33/35]])
+    >>> Q_aug.H * Q_aug
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> Q_aug * Q_aug.H
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+
+    Augmenting the $R$ matrix with zero row is straightforward.
+
+    >>> R_aug = R.col_join(Matrix([[0, 0, 0]]))
+    >>> R_aug
+    Matrix([
+    [14,  21, 0],
+    [ 0, 175, 0],
+    [ 0,   0, 0]])
+    >>> Q_aug * R_aug == A
+    True
+
+    A zero matrix example:
+
+    >>> from sympy import Matrix
+    >>> A = Matrix.zeros(3, 4)
+    >>> Q, R = A.QRdecomposition()
+
+    They may return matrices with zero rows and columns.
+
+    >>> Q
+    Matrix(3, 0, [])
+    >>> R
+    Matrix(0, 4, [])
+    >>> Q*R
+    Matrix([
+    [0, 0, 0, 0],
+    [0, 0, 0, 0],
+    [0, 0, 0, 0]])
+
+    As the same augmentation rule described above, $Q$ can be augmented
+    with columns of an identity matrix and $R$ can be augmented with
+    rows of a zero matrix.
+
+    >>> Q_aug = Q.row_join(Matrix.eye(3))
+    >>> R_aug = R.col_join(Matrix.zeros(3, 4))
+    >>> Q_aug * Q_aug.T
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> R_aug
+    Matrix([
+    [0, 0, 0, 0],
+    [0, 0, 0, 0],
+    [0, 0, 0, 0]])
+    >>> Q_aug * R_aug == A
+    True
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.cholesky
+    sympy.matrices.dense.DenseMatrix.LDLdecomposition
+    sympy.matrices.matrixbase.MatrixBase.LUdecomposition
+    QRsolve
+    """
+    return _QRdecomposition_optional(M, normalize=True)
+
+def _upper_hessenberg_decomposition(A):
+    """Converts a matrix into Hessenberg matrix H.
+
+    Returns 2 matrices H, P s.t.
+    $P H P^{T} = A$, where H is an upper hessenberg matrix
+    and P is an orthogonal matrix
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([
+    ...     [1,2,3],
+    ...     [-3,5,6],
+    ...     [4,-8,9],
+    ... ])
+    >>> H, P = A.upper_hessenberg_decomposition()
+    >>> H
+    Matrix([
+    [1,    6/5,    17/5],
+    [5, 213/25, -134/25],
+    [0, 216/25,  137/25]])
+    >>> P
+    Matrix([
+    [1,    0,   0],
+    [0, -3/5, 4/5],
+    [0,  4/5, 3/5]])
+    >>> P * H * P.H == A
+    True
+
+
+    References
+    ==========
+
+    .. [#] https://mathworld.wolfram.com/HessenbergDecomposition.html
+    """
+
+    M = A.as_mutable()
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+
+    n = M.cols
+    P = M.eye(n)
+    H = M
+
+    for j in range(n - 2):
+
+        u = H[j + 1:, j]
+
+        if u[1:, :].is_zero_matrix:
+            continue
+
+        if sign(u[0]) != 0:
+            u[0] = u[0] + sign(u[0]) * u.norm()
+        else:
+            u[0] = u[0] + u.norm()
+
+        v = u / u.norm()
+
+        H[j + 1:, :] = H[j + 1:, :] - 2 * v * (v.H * H[j + 1:, :])
+        H[:, j + 1:] = H[:, j + 1:] - (H[:, j + 1:] * (2 * v)) * v.H
+        P[:, j + 1:] = P[:, j + 1:] - (P[:, j + 1:] * (2 * v)) * v.H
+
+    return H, P
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/dense.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/dense.py
new file mode 100644
index 0000000000000000000000000000000000000000..98bf9931df54f67abfd9c4dc810b46fdcf70288f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/dense.py
@@ -0,0 +1,1094 @@
+from __future__ import annotations
+import random
+
+from sympy.core.basic import Basic
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import is_sequence
+
+from .exceptions import ShapeError
+from .decompositions import _cholesky, _LDLdecomposition
+from .matrixbase import MatrixBase
+from .repmatrix import MutableRepMatrix, RepMatrix
+from .solvers import _lower_triangular_solve, _upper_triangular_solve
+
+
+__doctest_requires__ = {('symarray',): ['numpy']}
+
+
+def _iszero(x):
+    """Returns True if x is zero."""
+    return x.is_zero
+
+
+class DenseMatrix(RepMatrix):
+    """Matrix implementation based on DomainMatrix as the internal representation"""
+
+    #
+    # DenseMatrix is a superclass for both MutableDenseMatrix and
+    # ImmutableDenseMatrix. Methods shared by both classes but not for the
+    # Sparse classes should be implemented here.
+    #
+
+    is_MatrixExpr: bool = False
+
+    _op_priority = 10.01
+    _class_priority = 4
+
+    @property
+    def _mat(self):
+        sympy_deprecation_warning(
+            """
+            The private _mat attribute of Matrix is deprecated. Use the
+            .flat() method instead.
+            """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-private-matrix-attributes"
+        )
+
+        return self.flat()
+
+    def _eval_inverse(self, **kwargs):
+        return self.inv(method=kwargs.get('method', 'GE'),
+                        iszerofunc=kwargs.get('iszerofunc', _iszero),
+                        try_block_diag=kwargs.get('try_block_diag', False))
+
+    def as_immutable(self):
+        """Returns an Immutable version of this Matrix
+        """
+        from .immutable import ImmutableDenseMatrix as cls
+        return cls._fromrep(self._rep.copy())
+
+    def as_mutable(self):
+        """Returns a mutable version of this matrix
+
+        Examples
+        ========
+
+        >>> from sympy import ImmutableMatrix
+        >>> X = ImmutableMatrix([[1, 2], [3, 4]])
+        >>> Y = X.as_mutable()
+        >>> Y[1, 1] = 5 # Can set values in Y
+        >>> Y
+        Matrix([
+        [1, 2],
+        [3, 5]])
+        """
+        return Matrix(self)
+
+    def cholesky(self, hermitian=True):
+        return _cholesky(self, hermitian=hermitian)
+
+    def LDLdecomposition(self, hermitian=True):
+        return _LDLdecomposition(self, hermitian=hermitian)
+
+    def lower_triangular_solve(self, rhs):
+        return _lower_triangular_solve(self, rhs)
+
+    def upper_triangular_solve(self, rhs):
+        return _upper_triangular_solve(self, rhs)
+
+    cholesky.__doc__               = _cholesky.__doc__
+    LDLdecomposition.__doc__       = _LDLdecomposition.__doc__
+    lower_triangular_solve.__doc__ = _lower_triangular_solve.__doc__
+    upper_triangular_solve.__doc__ = _upper_triangular_solve.__doc__
+
+
+def _force_mutable(x):
+    """Return a matrix as a Matrix, otherwise return x."""
+    if getattr(x, 'is_Matrix', False):
+        return x.as_mutable()
+    elif isinstance(x, Basic):
+        return x
+    elif hasattr(x, '__array__'):
+        a = x.__array__()
+        if len(a.shape) == 0:
+            return sympify(a)
+        return Matrix(x)
+    return x
+
+
+class MutableDenseMatrix(DenseMatrix, MutableRepMatrix):
+
+    def simplify(self, **kwargs):
+        """Applies simplify to the elements of a matrix in place.
+
+        This is a shortcut for M.applyfunc(lambda x: simplify(x, ratio, measure))
+
+        See Also
+        ========
+
+        sympy.simplify.simplify.simplify
+        """
+        from sympy.simplify.simplify import simplify as _simplify
+        for (i, j), element in self.todok().items():
+            self[i, j] = _simplify(element, **kwargs)
+
+
+MutableMatrix = Matrix = MutableDenseMatrix
+
+###########
+# Numpy Utility Functions:
+# list2numpy, matrix2numpy, symmarray
+###########
+
+
+def list2numpy(l, dtype=object):  # pragma: no cover
+    """Converts Python list of SymPy expressions to a NumPy array.
+
+    See Also
+    ========
+
+    matrix2numpy
+    """
+    from numpy import empty
+    a = empty(len(l), dtype)
+    for i, s in enumerate(l):
+        a[i] = s
+    return a
+
+
+def matrix2numpy(m, dtype=object):  # pragma: no cover
+    """Converts SymPy's matrix to a NumPy array.
+
+    See Also
+    ========
+
+    list2numpy
+    """
+    from numpy import empty
+    a = empty(m.shape, dtype)
+    for i in range(m.rows):
+        for j in range(m.cols):
+            a[i, j] = m[i, j]
+    return a
+
+
+###########
+# Rotation matrices:
+# rot_givens, rot_axis[123], rot_ccw_axis[123]
+###########
+
+
+def rot_givens(i, j, theta, dim=3):
+    r"""Returns a a Givens rotation matrix, a a rotation in the
+    plane spanned by two coordinates axes.
+
+    Explanation
+    ===========
+
+    The Givens rotation corresponds to a generalization of rotation
+    matrices to any number of dimensions, given by:
+
+    .. math::
+        G(i, j, \theta) =
+            \begin{bmatrix}
+                1   & \cdots &    0   & \cdots &    0   & \cdots &    0   \\
+                \vdots & \ddots & \vdots &        & \vdots &        & \vdots \\
+                0   & \cdots &    c   & \cdots &   -s   & \cdots &    0   \\
+                \vdots &        & \vdots & \ddots & \vdots &        & \vdots \\
+                0   & \cdots &    s   & \cdots &    c   & \cdots &    0   \\
+                \vdots &        & \vdots &        & \vdots & \ddots & \vdots \\
+                0   & \cdots &    0   & \cdots &    0   & \cdots &    1
+            \end{bmatrix}
+
+    Where $c = \cos(\theta)$ and $s = \sin(\theta)$ appear at the intersections
+    ``i``\th and ``j``\th rows and columns.
+
+    For fixed ``i > j``\, the non-zero elements of a Givens matrix are
+    given by:
+
+    - $g_{kk} = 1$ for $k \ne i,\,j$
+    - $g_{kk} = c$ for $k = i,\,j$
+    - $g_{ji} = -g_{ij} = -s$
+
+    Parameters
+    ==========
+
+    i : int between ``0`` and ``dim - 1``
+        Represents first axis
+    j : int between ``0`` and ``dim - 1``
+        Represents second axis
+    dim : int bigger than 1
+        Number of dimensions. Defaults to 3.
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_givens
+
+    A counterclockwise rotation of pi/3 (60 degrees) around
+    the third axis (z-axis):
+
+    >>> rot_givens(1, 0, pi/3)
+    Matrix([
+    [      1/2, -sqrt(3)/2, 0],
+    [sqrt(3)/2,        1/2, 0],
+    [        0,          0, 1]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_givens(1, 0, pi/2)
+    Matrix([
+    [0, -1, 0],
+    [1,  0, 0],
+    [0,  0, 1]])
+
+    This can be generalized to any number
+    of dimensions:
+
+    >>> rot_givens(1, 0, pi/2, dim=4)
+    Matrix([
+    [0, -1, 0, 0],
+    [1,  0, 0, 0],
+    [0,  0, 1, 0],
+    [0,  0, 0, 1]])
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Givens_rotation
+
+    See Also
+    ========
+
+    rot_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (clockwise around the x axis)
+    rot_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (clockwise around the y axis)
+    rot_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (clockwise around the z axis)
+    rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (counterclockwise around the x axis)
+    rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (counterclockwise around the y axis)
+    rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (counterclockwise around the z axis)
+    """
+    if not isinstance(dim, int) or dim < 2:
+        raise ValueError('dim must be an integer biggen than one, '
+                         'got {}.'.format(dim))
+
+    if i == j:
+        raise ValueError('i and j must be different, '
+                         'got ({}, {})'.format(i, j))
+
+    for ij in [i, j]:
+        if not isinstance(ij, int) or ij < 0 or ij > dim - 1:
+            raise ValueError('i and j must be integers between 0 and '
+                             '{}, got i={} and j={}.'.format(dim-1, i, j))
+
+    theta = sympify(theta)
+    c = cos(theta)
+    s = sin(theta)
+    M = eye(dim)
+    M[i, i] = c
+    M[j, j] = c
+    M[i, j] = s
+    M[j, i] = -s
+    return M
+
+
+def rot_axis3(theta):
+    r"""Returns a rotation matrix for a rotation of theta (in radians)
+    about the 3-axis.
+
+    Explanation
+    ===========
+
+    For a right-handed coordinate system, this corresponds to a
+    clockwise rotation around the `z`-axis, given by:
+
+    .. math::
+
+        R  = \begin{bmatrix}
+                 \cos(\theta) & \sin(\theta) & 0 \\
+                -\sin(\theta) & \cos(\theta) & 0 \\
+                            0 &            0 & 1
+            \end{bmatrix}
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_axis3
+
+    A rotation of pi/3 (60 degrees):
+
+    >>> theta = pi/3
+    >>> rot_axis3(theta)
+    Matrix([
+    [       1/2, sqrt(3)/2, 0],
+    [-sqrt(3)/2,       1/2, 0],
+    [         0,         0, 1]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_axis3(pi/2)
+    Matrix([
+    [ 0, 1, 0],
+    [-1, 0, 0],
+    [ 0, 0, 1]])
+
+    See Also
+    ========
+
+    rot_givens: Returns a Givens rotation matrix (generalized rotation for
+        any number of dimensions)
+    rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (counterclockwise around the z axis)
+    rot_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (clockwise around the x axis)
+    rot_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (clockwise around the y axis)
+    """
+    return rot_givens(0, 1, theta, dim=3)
+
+
+def rot_axis2(theta):
+    r"""Returns a rotation matrix for a rotation of theta (in radians)
+    about the 2-axis.
+
+    Explanation
+    ===========
+
+    For a right-handed coordinate system, this corresponds to a
+    clockwise rotation around the `y`-axis, given by:
+
+    .. math::
+
+        R  = \begin{bmatrix}
+                \cos(\theta) & 0 & -\sin(\theta) \\
+                           0 & 1 &             0 \\
+                \sin(\theta) & 0 &  \cos(\theta)
+            \end{bmatrix}
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_axis2
+
+    A rotation of pi/3 (60 degrees):
+
+    >>> theta = pi/3
+    >>> rot_axis2(theta)
+    Matrix([
+    [      1/2, 0, -sqrt(3)/2],
+    [        0, 1,          0],
+    [sqrt(3)/2, 0,        1/2]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_axis2(pi/2)
+    Matrix([
+    [0, 0, -1],
+    [0, 1,  0],
+    [1, 0,  0]])
+
+    See Also
+    ========
+
+    rot_givens: Returns a Givens rotation matrix (generalized rotation for
+        any number of dimensions)
+    rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (clockwise around the y axis)
+    rot_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (counterclockwise around the x axis)
+    rot_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (counterclockwise around the z axis)
+    """
+    return rot_givens(2, 0, theta, dim=3)
+
+
+def rot_axis1(theta):
+    r"""Returns a rotation matrix for a rotation of theta (in radians)
+    about the 1-axis.
+
+    Explanation
+    ===========
+
+    For a right-handed coordinate system, this corresponds to a
+    clockwise rotation around the `x`-axis, given by:
+
+    .. math::
+
+        R  = \begin{bmatrix}
+                1 &             0 &            0 \\
+                0 &  \cos(\theta) & \sin(\theta) \\
+                0 & -\sin(\theta) & \cos(\theta)
+            \end{bmatrix}
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_axis1
+
+    A rotation of pi/3 (60 degrees):
+
+    >>> theta = pi/3
+    >>> rot_axis1(theta)
+    Matrix([
+    [1,          0,         0],
+    [0,        1/2, sqrt(3)/2],
+    [0, -sqrt(3)/2,       1/2]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_axis1(pi/2)
+    Matrix([
+    [1,  0, 0],
+    [0,  0, 1],
+    [0, -1, 0]])
+
+    See Also
+    ========
+
+    rot_givens: Returns a Givens rotation matrix (generalized rotation for
+        any number of dimensions)
+    rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (counterclockwise around the x axis)
+    rot_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (clockwise around the y axis)
+    rot_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (clockwise around the z axis)
+    """
+    return rot_givens(1, 2, theta, dim=3)
+
+
+def rot_ccw_axis3(theta):
+    r"""Returns a rotation matrix for a rotation of theta (in radians)
+    about the 3-axis.
+
+    Explanation
+    ===========
+
+    For a right-handed coordinate system, this corresponds to a
+    counterclockwise rotation around the `z`-axis, given by:
+
+    .. math::
+
+        R  = \begin{bmatrix}
+                \cos(\theta) & -\sin(\theta) & 0 \\
+                \sin(\theta) &  \cos(\theta) & 0 \\
+                           0 &             0 & 1
+            \end{bmatrix}
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_ccw_axis3
+
+    A rotation of pi/3 (60 degrees):
+
+    >>> theta = pi/3
+    >>> rot_ccw_axis3(theta)
+    Matrix([
+    [      1/2, -sqrt(3)/2, 0],
+    [sqrt(3)/2,        1/2, 0],
+    [        0,          0, 1]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_ccw_axis3(pi/2)
+    Matrix([
+    [0, -1, 0],
+    [1,  0, 0],
+    [0,  0, 1]])
+
+    See Also
+    ========
+
+    rot_givens: Returns a Givens rotation matrix (generalized rotation for
+        any number of dimensions)
+    rot_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (clockwise around the z axis)
+    rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (counterclockwise around the x axis)
+    rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (counterclockwise around the y axis)
+    """
+    return rot_givens(1, 0, theta, dim=3)
+
+
+def rot_ccw_axis2(theta):
+    r"""Returns a rotation matrix for a rotation of theta (in radians)
+    about the 2-axis.
+
+    Explanation
+    ===========
+
+    For a right-handed coordinate system, this corresponds to a
+    counterclockwise rotation around the `y`-axis, given by:
+
+    .. math::
+
+        R  = \begin{bmatrix}
+                 \cos(\theta) & 0 & \sin(\theta) \\
+                            0 & 1 &            0 \\
+                -\sin(\theta) & 0 & \cos(\theta)
+            \end{bmatrix}
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_ccw_axis2
+
+    A rotation of pi/3 (60 degrees):
+
+    >>> theta = pi/3
+    >>> rot_ccw_axis2(theta)
+    Matrix([
+    [       1/2, 0, sqrt(3)/2],
+    [         0, 1,         0],
+    [-sqrt(3)/2, 0,       1/2]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_ccw_axis2(pi/2)
+    Matrix([
+    [ 0,  0,  1],
+    [ 0,  1,  0],
+    [-1,  0,  0]])
+
+    See Also
+    ========
+
+    rot_givens: Returns a Givens rotation matrix (generalized rotation for
+        any number of dimensions)
+    rot_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (clockwise around the y axis)
+    rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (counterclockwise around the x axis)
+    rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (counterclockwise around the z axis)
+    """
+    return rot_givens(0, 2, theta, dim=3)
+
+
+def rot_ccw_axis1(theta):
+    r"""Returns a rotation matrix for a rotation of theta (in radians)
+    about the 1-axis.
+
+    Explanation
+    ===========
+
+    For a right-handed coordinate system, this corresponds to a
+    counterclockwise rotation around the `x`-axis, given by:
+
+    .. math::
+
+        R  = \begin{bmatrix}
+                1 &            0 &             0 \\
+                0 & \cos(\theta) & -\sin(\theta) \\
+                0 & \sin(\theta) &  \cos(\theta)
+            \end{bmatrix}
+
+    Examples
+    ========
+
+    >>> from sympy import pi, rot_ccw_axis1
+
+    A rotation of pi/3 (60 degrees):
+
+    >>> theta = pi/3
+    >>> rot_ccw_axis1(theta)
+    Matrix([
+    [1,         0,          0],
+    [0,       1/2, -sqrt(3)/2],
+    [0, sqrt(3)/2,        1/2]])
+
+    If we rotate by pi/2 (90 degrees):
+
+    >>> rot_ccw_axis1(pi/2)
+    Matrix([
+    [1, 0,  0],
+    [0, 0, -1],
+    [0, 1,  0]])
+
+    See Also
+    ========
+
+    rot_givens: Returns a Givens rotation matrix (generalized rotation for
+        any number of dimensions)
+    rot_axis1: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 1-axis (clockwise around the x axis)
+    rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 2-axis (counterclockwise around the y axis)
+    rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians)
+        about the 3-axis (counterclockwise around the z axis)
+    """
+    return rot_givens(2, 1, theta, dim=3)
+
+
+@doctest_depends_on(modules=('numpy',))
+def symarray(prefix, shape, **kwargs):  # pragma: no cover
+    r"""Create a numpy ndarray of symbols (as an object array).
+
+    The created symbols are named ``prefix_i1_i2_``...  You should thus provide a
+    non-empty prefix if you want your symbols to be unique for different output
+    arrays, as SymPy symbols with identical names are the same object.
+
+    Parameters
+    ----------
+
+    prefix : string
+      A prefix prepended to the name of every symbol.
+
+    shape : int or tuple
+      Shape of the created array.  If an int, the array is one-dimensional; for
+      more than one dimension the shape must be a tuple.
+
+    \*\*kwargs : dict
+      keyword arguments passed on to Symbol
+
+    Examples
+    ========
+    These doctests require numpy.
+
+    >>> from sympy import symarray
+    >>> symarray('', 3)
+    [_0 _1 _2]
+
+    If you want multiple symarrays to contain distinct symbols, you *must*
+    provide unique prefixes:
+
+    >>> a = symarray('', 3)
+    >>> b = symarray('', 3)
+    >>> a[0] == b[0]
+    True
+    >>> a = symarray('a', 3)
+    >>> b = symarray('b', 3)
+    >>> a[0] == b[0]
+    False
+
+    Creating symarrays with a prefix:
+
+    >>> symarray('a', 3)
+    [a_0 a_1 a_2]
+
+    For more than one dimension, the shape must be given as a tuple:
+
+    >>> symarray('a', (2, 3))
+    [[a_0_0 a_0_1 a_0_2]
+     [a_1_0 a_1_1 a_1_2]]
+    >>> symarray('a', (2, 3, 2))
+    [[[a_0_0_0 a_0_0_1]
+      [a_0_1_0 a_0_1_1]
+      [a_0_2_0 a_0_2_1]]
+    
+     [[a_1_0_0 a_1_0_1]
+      [a_1_1_0 a_1_1_1]
+      [a_1_2_0 a_1_2_1]]]
+
+    For setting assumptions of the underlying Symbols:
+
+    >>> [s.is_real for s in symarray('a', 2, real=True)]
+    [True, True]
+    """
+    from numpy import empty, ndindex
+    arr = empty(shape, dtype=object)
+    for index in ndindex(shape):
+        arr[index] = Symbol('%s_%s' % (prefix, '_'.join(map(str, index))),
+                            **kwargs)
+    return arr
+
+
+###############
+# Functions
+###############
+
+def casoratian(seqs, n, zero=True):
+    """Given linear difference operator L of order 'k' and homogeneous
+       equation Ly = 0 we want to compute kernel of L, which is a set
+       of 'k' sequences: a(n), b(n), ... z(n).
+
+       Solutions of L are linearly independent iff their Casoratian,
+       denoted as C(a, b, ..., z), do not vanish for n = 0.
+
+       Casoratian is defined by k x k determinant::
+
+                  +  a(n)     b(n)     . . . z(n)     +
+                  |  a(n+1)   b(n+1)   . . . z(n+1)   |
+                  |    .         .     .        .     |
+                  |    .         .       .      .     |
+                  |    .         .         .    .     |
+                  +  a(n+k-1) b(n+k-1) . . . z(n+k-1) +
+
+       It proves very useful in rsolve_hyper() where it is applied
+       to a generating set of a recurrence to factor out linearly
+       dependent solutions and return a basis:
+
+       >>> from sympy import Symbol, casoratian, factorial
+       >>> n = Symbol('n', integer=True)
+
+       Exponential and factorial are linearly independent:
+
+       >>> casoratian([2**n, factorial(n)], n) != 0
+       True
+
+    """
+
+    seqs = list(map(sympify, seqs))
+
+    if not zero:
+        f = lambda i, j: seqs[j].subs(n, n + i)
+    else:
+        f = lambda i, j: seqs[j].subs(n, i)
+
+    k = len(seqs)
+
+    return Matrix(k, k, f).det()
+
+
+def eye(*args, **kwargs):
+    """Create square identity matrix n x n
+
+    See Also
+    ========
+
+    diag
+    zeros
+    ones
+    """
+
+    return Matrix.eye(*args, **kwargs)
+
+
+def diag(*values, strict=True, unpack=False, **kwargs):
+    """Returns a matrix with the provided values placed on the
+    diagonal. If non-square matrices are included, they will
+    produce a block-diagonal matrix.
+
+    Examples
+    ========
+
+    This version of diag is a thin wrapper to Matrix.diag that differs
+    in that it treats all lists like matrices -- even when a single list
+    is given. If this is not desired, either put a `*` before the list or
+    set `unpack=True`.
+
+    >>> from sympy import diag
+
+    >>> diag([1, 2, 3], unpack=True)  # = diag(1,2,3) or diag(*[1,2,3])
+    Matrix([
+    [1, 0, 0],
+    [0, 2, 0],
+    [0, 0, 3]])
+
+    >>> diag([1, 2, 3])  # a column vector
+    Matrix([
+    [1],
+    [2],
+    [3]])
+
+    See Also
+    ========
+    .matrixbase.MatrixBase.eye
+    .matrixbase.MatrixBase.diagonal
+    .matrixbase.MatrixBase.diag
+    .expressions.blockmatrix.BlockMatrix
+    """
+    return Matrix.diag(*values, strict=strict, unpack=unpack, **kwargs)
+
+
+def GramSchmidt(vlist, orthonormal=False):
+    """Apply the Gram-Schmidt process to a set of vectors.
+
+    Parameters
+    ==========
+
+    vlist : List of Matrix
+        Vectors to be orthogonalized for.
+
+    orthonormal : Bool, optional
+        If true, return an orthonormal basis.
+
+    Returns
+    =======
+
+    vlist : List of Matrix
+        Orthogonalized vectors
+
+    Notes
+    =====
+
+    This routine is mostly duplicate from ``Matrix.orthogonalize``,
+    except for some difference that this always raises error when
+    linearly dependent vectors are found, and the keyword ``normalize``
+    has been named as ``orthonormal`` in this function.
+
+    See Also
+    ========
+
+    .matrixbase.MatrixBase.orthogonalize
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
+    """
+    return MutableDenseMatrix.orthogonalize(
+        *vlist, normalize=orthonormal, rankcheck=True
+    )
+
+
+def hessian(f, varlist, constraints=()):
+    """Compute Hessian matrix for a function f wrt parameters in varlist
+    which may be given as a sequence or a row/column vector. A list of
+    constraints may optionally be given.
+
+    Examples
+    ========
+
+    >>> from sympy import Function, hessian, pprint
+    >>> from sympy.abc import x, y
+    >>> f = Function('f')(x, y)
+    >>> g1 = Function('g')(x, y)
+    >>> g2 = x**2 + 3*y
+    >>> pprint(hessian(f, (x, y), [g1, g2]))
+    [                   d               d            ]
+    [     0        0    --(g(x, y))     --(g(x, y))  ]
+    [                   dx              dy           ]
+    [                                                ]
+    [     0        0        2*x              3       ]
+    [                                                ]
+    [                     2               2          ]
+    [d                   d               d           ]
+    [--(g(x, y))  2*x   ---(f(x, y))   -----(f(x, y))]
+    [dx                   2            dy dx         ]
+    [                   dx                           ]
+    [                                                ]
+    [                     2               2          ]
+    [d                   d               d           ]
+    [--(g(x, y))   3   -----(f(x, y))   ---(f(x, y)) ]
+    [dy                dy dx              2          ]
+    [                                   dy           ]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hessian_matrix
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.jacobian
+    wronskian
+    """
+    # f is the expression representing a function f, return regular matrix
+    if isinstance(varlist, MatrixBase):
+        if 1 not in varlist.shape:
+            raise ShapeError("`varlist` must be a column or row vector.")
+        if varlist.cols == 1:
+            varlist = varlist.T
+        varlist = varlist.tolist()[0]
+    if is_sequence(varlist):
+        n = len(varlist)
+        if not n:
+            raise ShapeError("`len(varlist)` must not be zero.")
+    else:
+        raise ValueError("Improper variable list in hessian function")
+    if not getattr(f, 'diff'):
+        # check differentiability
+        raise ValueError("Function `f` (%s) is not differentiable" % f)
+    m = len(constraints)
+    N = m + n
+    out = zeros(N)
+    for k, g in enumerate(constraints):
+        if not getattr(g, 'diff'):
+            # check differentiability
+            raise ValueError("Function `f` (%s) is not differentiable" % f)
+        for i in range(n):
+            out[k, i + m] = g.diff(varlist[i])
+    for i in range(n):
+        for j in range(i, n):
+            out[i + m, j + m] = f.diff(varlist[i]).diff(varlist[j])
+    for i in range(N):
+        for j in range(i + 1, N):
+            out[j, i] = out[i, j]
+    return out
+
+
+def jordan_cell(eigenval, n):
+    """
+    Create a Jordan block:
+
+    Examples
+    ========
+
+    >>> from sympy import jordan_cell
+    >>> from sympy.abc import x
+    >>> jordan_cell(x, 4)
+    Matrix([
+    [x, 1, 0, 0],
+    [0, x, 1, 0],
+    [0, 0, x, 1],
+    [0, 0, 0, x]])
+    """
+
+    return Matrix.jordan_block(size=n, eigenvalue=eigenval)
+
+
+def matrix_multiply_elementwise(A, B):
+    """Return the Hadamard product (elementwise product) of A and B
+
+    >>> from sympy import Matrix, matrix_multiply_elementwise
+    >>> A = Matrix([[0, 1, 2], [3, 4, 5]])
+    >>> B = Matrix([[1, 10, 100], [100, 10, 1]])
+    >>> matrix_multiply_elementwise(A, B)
+    Matrix([
+    [  0, 10, 200],
+    [300, 40,   5]])
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.__mul__
+    """
+    return A.multiply_elementwise(B)
+
+
+def ones(*args, **kwargs):
+    """Returns a matrix of ones with ``rows`` rows and ``cols`` columns;
+    if ``cols`` is omitted a square matrix will be returned.
+
+    See Also
+    ========
+
+    zeros
+    eye
+    diag
+    """
+
+    if 'c' in kwargs:
+        kwargs['cols'] = kwargs.pop('c')
+
+    return Matrix.ones(*args, **kwargs)
+
+
+def randMatrix(r, c=None, min=0, max=99, seed=None, symmetric=False,
+               percent=100, prng=None):
+    """Create random matrix with dimensions ``r`` x ``c``. If ``c`` is omitted
+    the matrix will be square. If ``symmetric`` is True the matrix must be
+    square. If ``percent`` is less than 100 then only approximately the given
+    percentage of elements will be non-zero.
+
+    The pseudo-random number generator used to generate matrix is chosen in the
+    following way.
+
+    * If ``prng`` is supplied, it will be used as random number generator.
+      It should be an instance of ``random.Random``, or at least have
+      ``randint`` and ``shuffle`` methods with same signatures.
+    * if ``prng`` is not supplied but ``seed`` is supplied, then new
+      ``random.Random`` with given ``seed`` will be created;
+    * otherwise, a new ``random.Random`` with default seed will be used.
+
+    Examples
+    ========
+
+    >>> from sympy import randMatrix
+    >>> randMatrix(3) # doctest:+SKIP
+    [25, 45, 27]
+    [44, 54,  9]
+    [23, 96, 46]
+    >>> randMatrix(3, 2) # doctest:+SKIP
+    [87, 29]
+    [23, 37]
+    [90, 26]
+    >>> randMatrix(3, 3, 0, 2) # doctest:+SKIP
+    [0, 2, 0]
+    [2, 0, 1]
+    [0, 0, 1]
+    >>> randMatrix(3, symmetric=True) # doctest:+SKIP
+    [85, 26, 29]
+    [26, 71, 43]
+    [29, 43, 57]
+    >>> A = randMatrix(3, seed=1)
+    >>> B = randMatrix(3, seed=2)
+    >>> A == B
+    False
+    >>> A == randMatrix(3, seed=1)
+    True
+    >>> randMatrix(3, symmetric=True, percent=50) # doctest:+SKIP
+    [77, 70,  0],
+    [70,  0,  0],
+    [ 0,  0, 88]
+    """
+    # Note that ``Random()`` is equivalent to ``Random(None)``
+    prng = prng or random.Random(seed)
+
+    if c is None:
+        c = r
+
+    if symmetric and r != c:
+        raise ValueError('For symmetric matrices, r must equal c, but %i != %i' % (r, c))
+
+    ij = range(r * c)
+    if percent != 100:
+        ij = prng.sample(ij, int(len(ij)*percent // 100))
+
+    m = zeros(r, c)
+
+    if not symmetric:
+        for ijk in ij:
+            i, j = divmod(ijk, c)
+            m[i, j] = prng.randint(min, max)
+    else:
+        for ijk in ij:
+            i, j = divmod(ijk, c)
+            if i <= j:
+                m[i, j] = m[j, i] = prng.randint(min, max)
+
+    return m
+
+
+def wronskian(functions, var, method='bareiss'):
+    """
+    Compute Wronskian for [] of functions
+
+    ::
+
+                         | f1       f2        ...   fn      |
+                         | f1'      f2'       ...   fn'     |
+                         |  .        .        .      .      |
+        W(f1, ..., fn) = |  .        .         .     .      |
+                         |  .        .          .    .      |
+                         |  (n)      (n)            (n)     |
+                         | D   (f1) D   (f2)  ...  D   (fn) |
+
+    see: https://en.wikipedia.org/wiki/Wronskian
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.jacobian
+    hessian
+    """
+
+    functions = [sympify(f) for f in functions]
+    n = len(functions)
+    if n == 0:
+        return S.One
+    W = Matrix(n, n, lambda i, j: functions[i].diff(var, j))
+    return W.det(method)
+
+
+def zeros(*args, **kwargs):
+    """Returns a matrix of zeros with ``rows`` rows and ``cols`` columns;
+    if ``cols`` is omitted a square matrix will be returned.
+
+    See Also
+    ========
+
+    ones
+    eye
+    diag
+    """
+
+    if 'c' in kwargs:
+        kwargs['cols'] = kwargs.pop('c')
+
+    return Matrix.zeros(*args, **kwargs)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/determinant.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/determinant.py
new file mode 100644
index 0000000000000000000000000000000000000000..9206c0714999ebe0cde5c4300d9b3293939177df
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/determinant.py
@@ -0,0 +1,1021 @@
+from types import FunctionType
+
+from sympy.core.cache import cacheit
+from sympy.core.numbers import Float, Integer
+from sympy.core.singleton import S
+from sympy.core.symbol import uniquely_named_symbol
+from sympy.core.mul import Mul
+from sympy.polys import PurePoly, cancel
+from sympy.functions.combinatorial.numbers import nC
+from sympy.polys.matrices.domainmatrix import DomainMatrix
+from sympy.polys.matrices.ddm import DDM
+
+from .exceptions import NonSquareMatrixError
+from .utilities import (
+    _get_intermediate_simp, _get_intermediate_simp_bool,
+    _iszero, _is_zero_after_expand_mul, _dotprodsimp, _simplify)
+
+
+def _find_reasonable_pivot(col, iszerofunc=_iszero, simpfunc=_simplify):
+    """ Find the lowest index of an item in ``col`` that is
+    suitable for a pivot.  If ``col`` consists only of
+    Floats, the pivot with the largest norm is returned.
+    Otherwise, the first element where ``iszerofunc`` returns
+    False is used.  If ``iszerofunc`` does not return false,
+    items are simplified and retested until a suitable
+    pivot is found.
+
+    Returns a 4-tuple
+        (pivot_offset, pivot_val, assumed_nonzero, newly_determined)
+    where pivot_offset is the index of the pivot, pivot_val is
+    the (possibly simplified) value of the pivot, assumed_nonzero
+    is True if an assumption that the pivot was non-zero
+    was made without being proved, and newly_determined are
+    elements that were simplified during the process of pivot
+    finding."""
+
+    newly_determined = []
+    col = list(col)
+    # a column that contains a mix of floats and integers
+    # but at least one float is considered a numerical
+    # column, and so we do partial pivoting
+    if all(isinstance(x, (Float, Integer)) for x in col) and any(
+            isinstance(x, Float) for x in col):
+        col_abs = [abs(x) for x in col]
+        max_value = max(col_abs)
+        if iszerofunc(max_value):
+            # just because iszerofunc returned True, doesn't
+            # mean the value is numerically zero.  Make sure
+            # to replace all entries with numerical zeros
+            if max_value != 0:
+                newly_determined = [(i, 0) for i, x in enumerate(col) if x != 0]
+            return (None, None, False, newly_determined)
+        index = col_abs.index(max_value)
+        return (index, col[index], False, newly_determined)
+
+    # PASS 1 (iszerofunc directly)
+    possible_zeros = []
+    for i, x in enumerate(col):
+        is_zero = iszerofunc(x)
+        # is someone wrote a custom iszerofunc, it may return
+        # BooleanFalse or BooleanTrue instead of True or False,
+        # so use == for comparison instead of `is`
+        if is_zero == False:
+            # we found something that is definitely not zero
+            return (i, x, False, newly_determined)
+        possible_zeros.append(is_zero)
+
+    # by this point, we've found no certain non-zeros
+    if all(possible_zeros):
+        # if everything is definitely zero, we have
+        # no pivot
+        return (None, None, False, newly_determined)
+
+    # PASS 2 (iszerofunc after simplify)
+    # we haven't found any for-sure non-zeros, so
+    # go through the elements iszerofunc couldn't
+    # make a determination about and opportunistically
+    # simplify to see if we find something
+    for i, x in enumerate(col):
+        if possible_zeros[i] is not None:
+            continue
+        simped = simpfunc(x)
+        is_zero = iszerofunc(simped)
+        if is_zero in (True, False):
+            newly_determined.append((i, simped))
+        if is_zero == False:
+            return (i, simped, False, newly_determined)
+        possible_zeros[i] = is_zero
+
+    # after simplifying, some things that were recognized
+    # as zeros might be zeros
+    if all(possible_zeros):
+        # if everything is definitely zero, we have
+        # no pivot
+        return (None, None, False, newly_determined)
+
+    # PASS 3 (.equals(0))
+    # some expressions fail to simplify to zero, but
+    # ``.equals(0)`` evaluates to True.  As a last-ditch
+    # attempt, apply ``.equals`` to these expressions
+    for i, x in enumerate(col):
+        if possible_zeros[i] is not None:
+            continue
+        if x.equals(S.Zero):
+            # ``.iszero`` may return False with
+            # an implicit assumption (e.g., ``x.equals(0)``
+            # when ``x`` is a symbol), so only treat it
+            # as proved when ``.equals(0)`` returns True
+            possible_zeros[i] = True
+            newly_determined.append((i, S.Zero))
+
+    if all(possible_zeros):
+        return (None, None, False, newly_determined)
+
+    # at this point there is nothing that could definitely
+    # be a pivot.  To maintain compatibility with existing
+    # behavior, we'll assume that an illdetermined thing is
+    # non-zero.  We should probably raise a warning in this case
+    i = possible_zeros.index(None)
+    return (i, col[i], True, newly_determined)
+
+
+def _find_reasonable_pivot_naive(col, iszerofunc=_iszero, simpfunc=None):
+    """
+    Helper that computes the pivot value and location from a
+    sequence of contiguous matrix column elements. As a side effect
+    of the pivot search, this function may simplify some of the elements
+    of the input column. A list of these simplified entries and their
+    indices are also returned.
+    This function mimics the behavior of _find_reasonable_pivot(),
+    but does less work trying to determine if an indeterminate candidate
+    pivot simplifies to zero. This more naive approach can be much faster,
+    with the trade-off that it may erroneously return a pivot that is zero.
+
+    ``col`` is a sequence of contiguous column entries to be searched for
+    a suitable pivot.
+    ``iszerofunc`` is a callable that returns a Boolean that indicates
+    if its input is zero, or None if no such determination can be made.
+    ``simpfunc`` is a callable that simplifies its input. It must return
+    its input if it does not simplify its input. Passing in
+    ``simpfunc=None`` indicates that the pivot search should not attempt
+    to simplify any candidate pivots.
+
+    Returns a 4-tuple:
+    (pivot_offset, pivot_val, assumed_nonzero, newly_determined)
+    ``pivot_offset`` is the sequence index of the pivot.
+    ``pivot_val`` is the value of the pivot.
+    pivot_val and col[pivot_index] are equivalent, but will be different
+    when col[pivot_index] was simplified during the pivot search.
+    ``assumed_nonzero`` is a boolean indicating if the pivot cannot be
+    guaranteed to be zero. If assumed_nonzero is true, then the pivot
+    may or may not be non-zero. If assumed_nonzero is false, then
+    the pivot is non-zero.
+    ``newly_determined`` is a list of index-value pairs of pivot candidates
+    that were simplified during the pivot search.
+    """
+
+    # indeterminates holds the index-value pairs of each pivot candidate
+    # that is neither zero or non-zero, as determined by iszerofunc().
+    # If iszerofunc() indicates that a candidate pivot is guaranteed
+    # non-zero, or that every candidate pivot is zero then the contents
+    # of indeterminates are unused.
+    # Otherwise, the only viable candidate pivots are symbolic.
+    # In this case, indeterminates will have at least one entry,
+    # and all but the first entry are ignored when simpfunc is None.
+    indeterminates = []
+    for i, col_val in enumerate(col):
+        col_val_is_zero = iszerofunc(col_val)
+        if col_val_is_zero == False:
+            # This pivot candidate is non-zero.
+            return i, col_val, False, []
+        elif col_val_is_zero is None:
+            # The candidate pivot's comparison with zero
+            # is indeterminate.
+            indeterminates.append((i, col_val))
+
+    if len(indeterminates) == 0:
+        # All candidate pivots are guaranteed to be zero, i.e. there is
+        # no pivot.
+        return None, None, False, []
+
+    if simpfunc is None:
+        # Caller did not pass in a simplification function that might
+        # determine if an indeterminate pivot candidate is guaranteed
+        # to be nonzero, so assume the first indeterminate candidate
+        # is non-zero.
+        return indeterminates[0][0], indeterminates[0][1], True, []
+
+    # newly_determined holds index-value pairs of candidate pivots
+    # that were simplified during the search for a non-zero pivot.
+    newly_determined = []
+    for i, col_val in indeterminates:
+        tmp_col_val = simpfunc(col_val)
+        if id(col_val) != id(tmp_col_val):
+            # simpfunc() simplified this candidate pivot.
+            newly_determined.append((i, tmp_col_val))
+            if iszerofunc(tmp_col_val) == False:
+                # Candidate pivot simplified to a guaranteed non-zero value.
+                return i, tmp_col_val, False, newly_determined
+
+    return indeterminates[0][0], indeterminates[0][1], True, newly_determined
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _berkowitz_toeplitz_matrix(M):
+    """Return (A,T) where T the Toeplitz matrix used in the Berkowitz algorithm
+    corresponding to ``M`` and A is the first principal submatrix.
+    """
+
+    # the 0 x 0 case is trivial
+    if M.rows == 0 and M.cols == 0:
+        return M._new(1,1, [M.one])
+
+    #
+    # Partition M = [ a_11  R ]
+    #                  [ C     A ]
+    #
+
+    a, R = M[0,0],   M[0, 1:]
+    C, A = M[1:, 0], M[1:,1:]
+
+    #
+    # The Toeplitz matrix looks like
+    #
+    #  [ 1                                     ]
+    #  [ -a         1                          ]
+    #  [ -RC       -a        1                 ]
+    #  [ -RAC     -RC       -a       1         ]
+    #  [ -RA**2C -RAC      -RC      -a       1 ]
+    #  etc.
+
+    # Compute the diagonal entries.
+    # Because multiplying matrix times vector is so much
+    # more efficient than matrix times matrix, recursively
+    # compute -R * A**n * C.
+    diags = [C]
+    for i in range(M.rows - 2):
+        diags.append(A.multiply(diags[i], dotprodsimp=None))
+    diags = [(-R).multiply(d, dotprodsimp=None)[0, 0] for d in diags]
+    diags = [M.one, -a] + diags
+
+    def entry(i,j):
+        if j > i:
+            return M.zero
+        return diags[i - j]
+
+    toeplitz = M._new(M.cols + 1, M.rows, entry)
+    return (A, toeplitz)
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _berkowitz_vector(M):
+    """ Run the Berkowitz algorithm and return a vector whose entries
+        are the coefficients of the characteristic polynomial of ``M``.
+
+        Given N x N matrix, efficiently compute
+        coefficients of characteristic polynomials of ``M``
+        without division in the ground domain.
+
+        This method is particularly useful for computing determinant,
+        principal minors and characteristic polynomial when ``M``
+        has complicated coefficients e.g. polynomials. Semi-direct
+        usage of this algorithm is also important in computing
+        efficiently sub-resultant PRS.
+
+        Assuming that M is a square matrix of dimension N x N and
+        I is N x N identity matrix, then the Berkowitz vector is
+        an N x 1 vector whose entries are coefficients of the
+        polynomial
+
+                        charpoly(M) = det(t*I - M)
+
+        As a consequence, all polynomials generated by Berkowitz
+        algorithm are monic.
+
+        For more information on the implemented algorithm refer to:
+
+        [1] S.J. Berkowitz, On computing the determinant in small
+            parallel time using a small number of processors, ACM,
+            Information Processing Letters 18, 1984, pp. 147-150
+
+        [2] M. Keber, Division-Free computation of sub-resultants
+            using Bezout matrices, Tech. Report MPI-I-2006-1-006,
+            Saarbrucken, 2006
+    """
+
+    # handle the trivial cases
+    if M.rows == 0 and M.cols == 0:
+        return M._new(1, 1, [M.one])
+    elif M.rows == 1 and M.cols == 1:
+        return M._new(2, 1, [M.one, -M[0,0]])
+
+    submat, toeplitz = _berkowitz_toeplitz_matrix(M)
+
+    return toeplitz.multiply(_berkowitz_vector(submat), dotprodsimp=None)
+
+
+def _adjugate(M, method="berkowitz"):
+    """Returns the adjugate, or classical adjoint, of
+    a matrix.  That is, the transpose of the matrix of cofactors.
+
+    https://en.wikipedia.org/wiki/Adjugate
+
+    Parameters
+    ==========
+
+    method : string, optional
+        Method to use to find the cofactors, can be "bareiss", "berkowitz",
+        "bird", "laplace" or "lu".
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2], [3, 4]])
+    >>> M.adjugate()
+    Matrix([
+    [ 4, -2],
+    [-3,  1]])
+
+    See Also
+    ========
+
+    cofactor_matrix
+    sympy.matrices.matrixbase.MatrixBase.transpose
+    """
+
+    return M.cofactor_matrix(method=method).transpose()
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _charpoly(M, x='lambda', simplify=_simplify):
+    """Computes characteristic polynomial det(x*I - M) where I is
+    the identity matrix.
+
+    A PurePoly is returned, so using different variables for ``x`` does
+    not affect the comparison or the polynomials:
+
+    Parameters
+    ==========
+
+    x : string, optional
+        Name for the "lambda" variable, defaults to "lambda".
+
+    simplify : function, optional
+        Simplification function to use on the characteristic polynomial
+        calculated. Defaults to ``simplify``.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.abc import x, y
+    >>> M = Matrix([[1, 3], [2, 0]])
+    >>> M.charpoly()
+    PurePoly(lambda**2 - lambda - 6, lambda, domain='ZZ')
+    >>> M.charpoly(x) == M.charpoly(y)
+    True
+    >>> M.charpoly(x) == M.charpoly(y)
+    True
+
+    Specifying ``x`` is optional; a symbol named ``lambda`` is used by
+    default (which looks good when pretty-printed in unicode):
+
+    >>> M.charpoly().as_expr()
+    lambda**2 - lambda - 6
+
+    And if ``x`` clashes with an existing symbol, underscores will
+    be prepended to the name to make it unique:
+
+    >>> M = Matrix([[1, 2], [x, 0]])
+    >>> M.charpoly(x).as_expr()
+    _x**2 - _x - 2*x
+
+    Whether you pass a symbol or not, the generator can be obtained
+    with the gen attribute since it may not be the same as the symbol
+    that was passed:
+
+    >>> M.charpoly(x).gen
+    _x
+    >>> M.charpoly(x).gen == x
+    False
+
+    Notes
+    =====
+
+    The Samuelson-Berkowitz algorithm is used to compute
+    the characteristic polynomial efficiently and without any
+    division operations.  Thus the characteristic polynomial over any
+    commutative ring without zero divisors can be computed.
+
+    If the determinant det(x*I - M) can be found out easily as
+    in the case of an upper or a lower triangular matrix, then
+    instead of Samuelson-Berkowitz algorithm, eigenvalues are computed
+    and the characteristic polynomial with their help.
+
+    See Also
+    ========
+
+    det
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    # Use DomainMatrix. We are already going to convert this to a Poly so there
+    # is no need to worry about expanding powers etc. Also since this algorithm
+    # does not require division or zero detection it is fine to use EX.
+    #
+    # M.to_DM() will fall back on EXRAW rather than EX. EXRAW is a lot faster
+    # for elementary arithmetic because it does not call cancel for each
+    # operation but it generates large unsimplified results that are slow in
+    # the subsequent call to simplify. Using EX instead is faster overall
+    # but at least in some cases EXRAW+simplify gives a simpler result so we
+    # preserve that existing behaviour of charpoly for now...
+    dM = M.to_DM()
+
+    K = dM.domain
+
+    cp = dM.charpoly()
+
+    x = uniquely_named_symbol(x, [M], modify=lambda s: '_' + s)
+
+    if K.is_EXRAW or simplify is not _simplify:
+        # XXX: Converting back to Expr is expensive. We only do it if the
+        # caller supplied a custom simplify function for backwards
+        # compatibility or otherwise if the domain was EX. For any other domain
+        # there should be no benefit in simplifying at this stage because Poly
+        # will put everything into canonical form anyway.
+        berk_vector = [K.to_sympy(c) for c in cp]
+        berk_vector = [simplify(a) for a in berk_vector]
+        p = PurePoly(berk_vector, x)
+
+    else:
+        # Convert from the list of domain elements directly to Poly.
+        p = PurePoly(cp, x, domain=K)
+
+    return p
+
+
+def _cofactor(M, i, j, method="berkowitz"):
+    """Calculate the cofactor of an element.
+
+    Parameters
+    ==========
+
+    method : string, optional
+        Method to use to find the cofactors, can be "bareiss", "berkowitz",
+        "bird", "laplace" or "lu".
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2], [3, 4]])
+    >>> M.cofactor(0, 1)
+    -3
+
+    See Also
+    ========
+
+    cofactor_matrix
+    minor
+    minor_submatrix
+    """
+
+    if not M.is_square or M.rows < 1:
+        raise NonSquareMatrixError()
+
+    return S.NegativeOne**((i + j) % 2) * M.minor(i, j, method)
+
+
+def _cofactor_matrix(M, method="berkowitz"):
+    """Return a matrix containing the cofactor of each element.
+
+    Parameters
+    ==========
+
+    method : string, optional
+        Method to use to find the cofactors, can be "bareiss", "berkowitz",
+        "bird", "laplace" or "lu".
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2], [3, 4]])
+    >>> M.cofactor_matrix()
+    Matrix([
+    [ 4, -3],
+    [-2,  1]])
+
+    See Also
+    ========
+
+    cofactor
+    minor
+    minor_submatrix
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    return M._new(M.rows, M.cols,
+            lambda i, j: M.cofactor(i, j, method))
+
+def _per(M):
+    """Returns the permanent of a matrix. Unlike determinant,
+    permanent is defined for both square and non-square matrices.
+
+    For an m x n matrix, with m less than or equal to n,
+    it is given as the sum over the permutations s of size
+    less than or equal to m on [1, 2, . . . n] of the product
+    from i = 1 to m of M[i, s[i]]. Taking the transpose will
+    not affect the value of the permanent.
+
+    In the case of a square matrix, this is the same as the permutation
+    definition of the determinant, but it does not take the sign of the
+    permutation into account. Computing the permanent with this definition
+    is quite inefficient, so here the Ryser formula is used.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> M.per()
+    450
+    >>> M = Matrix([1, 5, 7])
+    >>> M.per()
+    13
+
+    References
+    ==========
+
+    .. [1] Prof. Frank Ben's notes: https://math.berkeley.edu/~bernd/ban275.pdf
+    .. [2] Wikipedia article on Permanent: https://en.wikipedia.org/wiki/Permanent_%28mathematics%29
+    .. [3] https://reference.wolfram.com/language/ref/Permanent.html
+    .. [4] Permanent of a rectangular matrix : https://arxiv.org/pdf/0904.3251.pdf
+    """
+    import itertools
+
+    m, n = M.shape
+    if m > n:
+        M = M.T
+        m, n = n, m
+    s = list(range(n))
+
+    subsets = []
+    for i in range(1, m + 1):
+        subsets += list(map(list, itertools.combinations(s, i)))
+
+    perm = 0
+    for subset in subsets:
+        prod = 1
+        sub_len = len(subset)
+        for i in range(m):
+            prod *= sum(M[i, j] for j in subset)
+        perm += prod * S.NegativeOne**sub_len * nC(n - sub_len, m - sub_len)
+    perm *= S.NegativeOne**m
+    return perm.simplify()
+
+def _det_DOM(M):
+    DOM = DomainMatrix.from_Matrix(M, field=True, extension=True)
+    K = DOM.domain
+    return K.to_sympy(DOM.det())
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _det(M, method="bareiss", iszerofunc=None):
+    """Computes the determinant of a matrix if ``M`` is a concrete matrix object
+    otherwise return an expressions ``Determinant(M)`` if ``M`` is a
+    ``MatrixSymbol`` or other expression.
+
+    Parameters
+    ==========
+
+    method : string, optional
+        Specifies the algorithm used for computing the matrix determinant.
+
+        If the matrix is at most 3x3, a hard-coded formula is used and the
+        specified method is ignored. Otherwise, it defaults to
+        ``'bareiss'``.
+
+        Also, if the matrix is an upper or a lower triangular matrix, determinant
+        is computed by simple multiplication of diagonal elements, and the
+        specified method is ignored.
+
+        If it is set to ``'domain-ge'``, then Gaussian elimination method will
+        be used via using DomainMatrix.
+
+        If it is set to ``'bareiss'``, Bareiss' fraction-free algorithm will
+        be used.
+
+        If it is set to ``'berkowitz'``, Berkowitz' algorithm will be used.
+
+        If it is set to ``'bird'``, Bird's algorithm will be used [1]_.
+
+        If it is set to ``'laplace'``, Laplace's algorithm will be used.
+
+        Otherwise, if it is set to ``'lu'``, LU decomposition will be used.
+
+        .. note::
+            For backward compatibility, legacy keys like "bareis" and
+            "det_lu" can still be used to indicate the corresponding
+            methods.
+            And the keys are also case-insensitive for now. However, it is
+            suggested to use the precise keys for specifying the method.
+
+    iszerofunc : FunctionType or None, optional
+        If it is set to ``None``, it will be defaulted to ``_iszero`` if the
+        method is set to ``'bareiss'``, and ``_is_zero_after_expand_mul`` if
+        the method is set to ``'lu'``.
+
+        It can also accept any user-specified zero testing function, if it
+        is formatted as a function which accepts a single symbolic argument
+        and returns ``True`` if it is tested as zero and ``False`` if it
+        tested as non-zero, and also ``None`` if it is undecidable.
+
+    Returns
+    =======
+
+    det : Basic
+        Result of determinant.
+
+    Raises
+    ======
+
+    ValueError
+        If unrecognized keys are given for ``method`` or ``iszerofunc``.
+
+    NonSquareMatrixError
+        If attempted to calculate determinant from a non-square matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, eye, det
+    >>> I3 = eye(3)
+    >>> det(I3)
+    1
+    >>> M = Matrix([[1, 2], [3, 4]])
+    >>> det(M)
+    -2
+    >>> det(M) == M.det()
+    True
+    >>> M.det(method="domain-ge")
+    -2
+
+    References
+    ==========
+
+    .. [1] Bird, R. S. (2011). A simple division-free algorithm for computing
+           determinants. Inf. Process. Lett., 111(21), 1072-1074. doi:
+           10.1016/j.ipl.2011.08.006
+    """
+
+    # sanitize `method`
+    method = method.lower()
+
+    if method == "bareis":
+        method = "bareiss"
+    elif method == "det_lu":
+        method = "lu"
+
+    if method not in ("bareiss", "berkowitz", "lu", "domain-ge", "bird",
+                      "laplace"):
+        raise ValueError("Determinant method '%s' unrecognized" % method)
+
+    if iszerofunc is None:
+        if method == "bareiss":
+            iszerofunc = _is_zero_after_expand_mul
+        elif method == "lu":
+            iszerofunc = _iszero
+
+    elif not isinstance(iszerofunc, FunctionType):
+        raise ValueError("Zero testing method '%s' unrecognized" % iszerofunc)
+
+    n = M.rows
+
+    if n == M.cols: # square check is done in individual method functions
+        if n == 0:
+            return M.one
+        elif n == 1:
+            return M[0, 0]
+        elif n == 2:
+            m = M[0, 0] * M[1, 1] - M[0, 1] * M[1, 0]
+            return _get_intermediate_simp(_dotprodsimp)(m)
+        elif n == 3:
+            m =  (M[0, 0] * M[1, 1] * M[2, 2]
+                + M[0, 1] * M[1, 2] * M[2, 0]
+                + M[0, 2] * M[1, 0] * M[2, 1]
+                - M[0, 2] * M[1, 1] * M[2, 0]
+                - M[0, 0] * M[1, 2] * M[2, 1]
+                - M[0, 1] * M[1, 0] * M[2, 2])
+            return _get_intermediate_simp(_dotprodsimp)(m)
+
+    dets = []
+    for b in M.strongly_connected_components():
+        if method == "domain-ge": # uses DomainMatrix to evaluate determinant
+            det = _det_DOM(M[b, b])
+        elif method == "bareiss":
+            det = M[b, b]._eval_det_bareiss(iszerofunc=iszerofunc)
+        elif method == "berkowitz":
+            det = M[b, b]._eval_det_berkowitz()
+        elif method == "lu":
+            det = M[b, b]._eval_det_lu(iszerofunc=iszerofunc)
+        elif method == "bird":
+            det = M[b, b]._eval_det_bird()
+        elif method == "laplace":
+            det = M[b, b]._eval_det_laplace()
+        dets.append(det)
+    return Mul(*dets)
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _det_bareiss(M, iszerofunc=_is_zero_after_expand_mul):
+    """Compute matrix determinant using Bareiss' fraction-free
+    algorithm which is an extension of the well known Gaussian
+    elimination method. This approach is best suited for dense
+    symbolic matrices and will result in a determinant with
+    minimal number of fractions. It means that less term
+    rewriting is needed on resulting formulae.
+
+    Parameters
+    ==========
+
+    iszerofunc : function, optional
+        The function to use to determine zeros when doing an LU decomposition.
+        Defaults to ``lambda x: x.is_zero``.
+
+    TODO: Implement algorithm for sparse matrices (SFF),
+    http://www.eecis.udel.edu/~saunders/papers/sffge/it5.ps.
+    """
+
+    # Recursively implemented Bareiss' algorithm as per Deanna Richelle Leggett's
+    # thesis http://www.math.usm.edu/perry/Research/Thesis_DRL.pdf
+    def bareiss(mat, cumm=1):
+        if mat.rows == 0:
+            return mat.one
+        elif mat.rows == 1:
+            return mat[0, 0]
+
+        # find a pivot and extract the remaining matrix
+        # With the default iszerofunc, _find_reasonable_pivot slows down
+        # the computation by the factor of 2.5 in one test.
+        # Relevant issues: #10279 and #13877.
+        pivot_pos, pivot_val, _, _ = _find_reasonable_pivot(mat[:, 0], iszerofunc=iszerofunc)
+        if pivot_pos is None:
+            return mat.zero
+
+        # if we have a valid pivot, we'll do a "row swap", so keep the
+        # sign of the det
+        sign = (-1) ** (pivot_pos % 2)
+
+        # we want every row but the pivot row and every column
+        rows = [i for i in range(mat.rows) if i != pivot_pos]
+        cols = list(range(mat.cols))
+        tmp_mat = mat.extract(rows, cols)
+
+        def entry(i, j):
+            ret = (pivot_val*tmp_mat[i, j + 1] - mat[pivot_pos, j + 1]*tmp_mat[i, 0]) / cumm
+            if _get_intermediate_simp_bool(True):
+                return _dotprodsimp(ret)
+            elif not ret.is_Atom:
+                return cancel(ret)
+            return ret
+
+        return sign*bareiss(M._new(mat.rows - 1, mat.cols - 1, entry), pivot_val)
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    if M.rows == 0:
+        return M.one
+        # sympy/matrices/tests/test_matrices.py contains a test that
+        # suggests that the determinant of a 0 x 0 matrix is one, by
+        # convention.
+
+    return bareiss(M)
+
+
+def _det_berkowitz(M):
+    """ Use the Berkowitz algorithm to compute the determinant."""
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    if M.rows == 0:
+        return M.one
+        # sympy/matrices/tests/test_matrices.py contains a test that
+        # suggests that the determinant of a 0 x 0 matrix is one, by
+        # convention.
+
+    berk_vector = _berkowitz_vector(M)
+    return (-1)**(len(berk_vector) - 1) * berk_vector[-1]
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _det_LU(M, iszerofunc=_iszero, simpfunc=None):
+    """ Computes the determinant of a matrix from its LU decomposition.
+    This function uses the LU decomposition computed by
+    LUDecomposition_Simple().
+
+    The keyword arguments iszerofunc and simpfunc are passed to
+    LUDecomposition_Simple().
+    iszerofunc is a callable that returns a boolean indicating if its
+    input is zero, or None if it cannot make the determination.
+    simpfunc is a callable that simplifies its input.
+    The default is simpfunc=None, which indicate that the pivot search
+    algorithm should not attempt to simplify any candidate pivots.
+    If simpfunc fails to simplify its input, then it must return its input
+    instead of a copy.
+
+    Parameters
+    ==========
+
+    iszerofunc : function, optional
+        The function to use to determine zeros when doing an LU decomposition.
+        Defaults to ``lambda x: x.is_zero``.
+
+    simpfunc : function, optional
+        The simplification function to use when looking for zeros for pivots.
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    if M.rows == 0:
+        return M.one
+        # sympy/matrices/tests/test_matrices.py contains a test that
+        # suggests that the determinant of a 0 x 0 matrix is one, by
+        # convention.
+
+    lu, row_swaps = M.LUdecomposition_Simple(iszerofunc=iszerofunc,
+            simpfunc=simpfunc)
+    # P*A = L*U => det(A) = det(L)*det(U)/det(P) = det(P)*det(U).
+    # Lower triangular factor L encoded in lu has unit diagonal => det(L) = 1.
+    # P is a permutation matrix => det(P) in {-1, 1} => 1/det(P) = det(P).
+    # LUdecomposition_Simple() returns a list of row exchange index pairs, rather
+    # than a permutation matrix, but det(P) = (-1)**len(row_swaps).
+
+    # Avoid forming the potentially time consuming  product of U's diagonal entries
+    # if the product is zero.
+    # Bottom right entry of U is 0 => det(A) = 0.
+    # It may be impossible to determine if this entry of U is zero when it is symbolic.
+    if iszerofunc(lu[lu.rows-1, lu.rows-1]):
+        return M.zero
+
+    # Compute det(P)
+    det = -M.one if len(row_swaps)%2 else M.one
+
+    # Compute det(U) by calculating the product of U's diagonal entries.
+    # The upper triangular portion of lu is the upper triangular portion of the
+    # U factor in the LU decomposition.
+    for k in range(lu.rows):
+        det *= lu[k, k]
+
+    # return det(P)*det(U)
+    return det
+
+
+@cacheit
+def __det_laplace(M):
+    """Compute the determinant of a matrix using Laplace expansion.
+
+    This is a recursive function, and it should not be called directly.
+    Use _det_laplace() instead. The reason for splitting this function
+    into two is to allow caching of determinants of submatrices. While
+    one could also define this function inside _det_laplace(), that
+    would remove the advantage of using caching in Cramer Solve.
+    """
+    n = M.shape[0]
+    if n == 1:
+        return M[0]
+    elif n == 2:
+        return M[0, 0] * M[1, 1] - M[0, 1] * M[1, 0]
+    else:
+        return sum((-1) ** i * M[0, i] *
+                   __det_laplace(M.minor_submatrix(0, i)) for i in range(n))
+
+
+def _det_laplace(M):
+    """Compute the determinant of a matrix using Laplace expansion.
+
+    While Laplace expansion is not the most efficient method of computing
+    a determinant, it is a simple one, and it has the advantage of
+    being division free. To improve efficiency, this function uses
+    caching to avoid recomputing determinants of submatrices.
+    """
+    if not M.is_square:
+        raise NonSquareMatrixError()
+    if M.shape[0] == 0:
+        return M.one
+        # sympy/matrices/tests/test_matrices.py contains a test that
+        # suggests that the determinant of a 0 x 0 matrix is one, by
+        # convention.
+    return __det_laplace(M.as_immutable())
+
+
+def _det_bird(M):
+    r"""Compute the determinant of a matrix using Bird's algorithm.
+
+    Bird's algorithm is a simple division-free algorithm for computing, which
+    is of lower order than the Laplace's algorithm. It is described in [1]_.
+
+    References
+    ==========
+
+    .. [1] Bird, R. S. (2011). A simple division-free algorithm for computing
+           determinants. Inf. Process. Lett., 111(21), 1072-1074. doi:
+           10.1016/j.ipl.2011.08.006
+    """
+    def mu(X):
+        n = X.shape[0]
+        zero = X.domain.zero
+
+        total = zero
+        diag_sums = [zero]
+        for i in reversed(range(1, n)):
+            total -= X[i][i]
+            diag_sums.append(total)
+        diag_sums = diag_sums[::-1]
+
+        elems = [[zero] * i + [diag_sums[i]] + X_i[i + 1:] for i, X_i in
+                 enumerate(X)]
+        return DDM(elems, X.shape, X.domain)
+
+    Mddm = M._rep.to_ddm()
+    n = M.shape[0]
+    if n == 0:
+        return M.one
+        # sympy/matrices/tests/test_matrices.py contains a test that
+        # suggests that the determinant of a 0 x 0 matrix is one, by
+        # convention.
+    Fn1 = Mddm
+    for _ in range(n - 1):
+        Fn1 = mu(Fn1).matmul(Mddm)
+    detA = Fn1[0][0]
+    if n % 2 == 0:
+        detA = -detA
+
+    return Mddm.domain.to_sympy(detA)
+
+
+def _minor(M, i, j, method="berkowitz"):
+    """Return the (i,j) minor of ``M``.  That is,
+    return the determinant of the matrix obtained by deleting
+    the `i`th row and `j`th column from ``M``.
+
+    Parameters
+    ==========
+
+    i, j : int
+        The row and column to exclude to obtain the submatrix.
+
+    method : string, optional
+        Method to use to find the determinant of the submatrix, can be
+        "bareiss", "berkowitz", "bird", "laplace" or "lu".
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> M.minor(1, 1)
+    -12
+
+    See Also
+    ========
+
+    minor_submatrix
+    cofactor
+    det
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    return M.minor_submatrix(i, j).det(method=method)
+
+
+def _minor_submatrix(M, i, j):
+    """Return the submatrix obtained by removing the `i`th row
+    and `j`th column from ``M`` (works with Pythonic negative indices).
+
+    Parameters
+    ==========
+
+    i, j : int
+        The row and column to exclude to obtain the submatrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> M.minor_submatrix(1, 1)
+    Matrix([
+    [1, 3],
+    [7, 9]])
+
+    See Also
+    ========
+
+    minor
+    cofactor
+    """
+
+    if i < 0:
+        i += M.rows
+    if j < 0:
+        j += M.cols
+
+    if not 0 <= i < M.rows or not 0 <= j < M.cols:
+        raise ValueError("`i` and `j` must satisfy 0 <= i < ``M.rows`` "
+                            "(%d)" % M.rows + "and 0 <= j < ``M.cols`` (%d)." % M.cols)
+
+    rows = [a for a in range(M.rows) if a != i]
+    cols = [a for a in range(M.cols) if a != j]
+
+    return M.extract(rows, cols)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/eigen.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/eigen.py
new file mode 100644
index 0000000000000000000000000000000000000000..87b2418efcece1c0b158ec56995bb011286feb3c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/eigen.py
@@ -0,0 +1,1346 @@
+from types import FunctionType
+from collections import Counter
+
+from mpmath import mp, workprec
+from mpmath.libmp.libmpf import prec_to_dps
+
+from sympy.core.sorting import default_sort_key
+from sympy.core.evalf import DEFAULT_MAXPREC, PrecisionExhausted
+from sympy.core.logic import fuzzy_and, fuzzy_or
+from sympy.core.numbers import Float
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.polys import roots, CRootOf, ZZ, QQ, EX
+from sympy.polys.matrices import DomainMatrix
+from sympy.polys.matrices.eigen import dom_eigenvects, dom_eigenvects_to_sympy
+from sympy.polys.polytools import gcd
+
+from .exceptions import MatrixError, NonSquareMatrixError
+from .determinant import _find_reasonable_pivot
+
+from .utilities import _iszero, _simplify
+
+
+__doctest_requires__ = {
+    ('_is_indefinite',
+     '_is_negative_definite',
+     '_is_negative_semidefinite',
+     '_is_positive_definite',
+     '_is_positive_semidefinite'): ['matplotlib'],
+}
+
+
+def _eigenvals_eigenvects_mpmath(M):
+    norm2 = lambda v: mp.sqrt(sum(i**2 for i in v))
+
+    v1 = None
+    prec = max(x._prec for x in M.atoms(Float))
+    eps = 2**-prec
+
+    while prec < DEFAULT_MAXPREC:
+        with workprec(prec):
+            A = mp.matrix(M.evalf(n=prec_to_dps(prec)))
+            E, ER = mp.eig(A)
+            v2 = norm2([i for e in E for i in (mp.re(e), mp.im(e))])
+            if v1 is not None and mp.fabs(v1 - v2) < eps:
+                return E, ER
+            v1 = v2
+        prec *= 2
+
+    # we get here because the next step would have taken us
+    # past MAXPREC or because we never took a step; in case
+    # of the latter, we refuse to send back a solution since
+    # it would not have been verified; we also resist taking
+    # a small step to arrive exactly at MAXPREC since then
+    # the two calculations might be artificially close.
+    raise PrecisionExhausted
+
+
+def _eigenvals_mpmath(M, multiple=False):
+    """Compute eigenvalues using mpmath"""
+    E, _ = _eigenvals_eigenvects_mpmath(M)
+    result = [_sympify(x) for x in E]
+    if multiple:
+        return result
+    return dict(Counter(result))
+
+
+def _eigenvects_mpmath(M):
+    E, ER = _eigenvals_eigenvects_mpmath(M)
+    result = []
+    for i in range(M.rows):
+        eigenval = _sympify(E[i])
+        eigenvect = _sympify(ER[:, i])
+        result.append((eigenval, 1, [eigenvect]))
+
+    return result
+
+
+# This function is a candidate for caching if it gets implemented for matrices.
+def _eigenvals(
+    M, error_when_incomplete=True, *, simplify=False, multiple=False,
+    rational=False, **flags):
+    r"""Compute eigenvalues of the matrix.
+
+    Parameters
+    ==========
+
+    error_when_incomplete : bool, optional
+        If it is set to ``True``, it will raise an error if not all
+        eigenvalues are computed. This is caused by ``roots`` not returning
+        a full list of eigenvalues.
+
+    simplify : bool or function, optional
+        If it is set to ``True``, it attempts to return the most
+        simplified form of expressions returned by applying default
+        simplification method in every routine.
+
+        If it is set to ``False``, it will skip simplification in this
+        particular routine to save computation resources.
+
+        If a function is passed to, it will attempt to apply
+        the particular function as simplification method.
+
+    rational : bool, optional
+        If it is set to ``True``, every floating point numbers would be
+        replaced with rationals before computation. It can solve some
+        issues of ``roots`` routine not working well with floats.
+
+    multiple : bool, optional
+        If it is set to ``True``, the result will be in the form of a
+        list.
+
+        If it is set to ``False``, the result will be in the form of a
+        dictionary.
+
+    Returns
+    =======
+
+    eigs : list or dict
+        Eigenvalues of a matrix. The return format would be specified by
+        the key ``multiple``.
+
+    Raises
+    ======
+
+    MatrixError
+        If not enough roots had got computed.
+
+    NonSquareMatrixError
+        If attempted to compute eigenvalues from a non-square matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix(3, 3, [0, 1, 1, 1, 0, 0, 1, 1, 1])
+    >>> M.eigenvals()
+    {-1: 1, 0: 1, 2: 1}
+
+    See Also
+    ========
+
+    MatrixBase.charpoly
+    eigenvects
+
+    Notes
+    =====
+
+    Eigenvalues of a matrix $A$ can be computed by solving a matrix
+    equation $\det(A - \lambda I) = 0$
+
+    It's not always possible to return radical solutions for
+    eigenvalues for matrices larger than $4, 4$ shape due to
+    Abel-Ruffini theorem.
+
+    If there is no radical solution is found for the eigenvalue,
+    it may return eigenvalues in the form of
+    :class:`sympy.polys.rootoftools.ComplexRootOf`.
+    """
+    if not M:
+        if multiple:
+            return []
+        return {}
+
+    if not M.is_square:
+        raise NonSquareMatrixError("{} must be a square matrix.".format(M))
+
+    if M._rep.domain not in (ZZ, QQ):
+        # Skip this check for ZZ/QQ because it can be slow
+        if all(x.is_number for x in M) and M.has(Float):
+            return _eigenvals_mpmath(M, multiple=multiple)
+
+    if rational:
+        from sympy.simplify import nsimplify
+        M = M.applyfunc(
+            lambda x: nsimplify(x, rational=True) if x.has(Float) else x)
+
+    if multiple:
+        return _eigenvals_list(
+            M, error_when_incomplete=error_when_incomplete, simplify=simplify,
+            **flags)
+    return _eigenvals_dict(
+        M, error_when_incomplete=error_when_incomplete, simplify=simplify,
+        **flags)
+
+
+eigenvals_error_message = \
+"It is not always possible to express the eigenvalues of a matrix " + \
+"of size 5x5 or higher in radicals. " + \
+"We have CRootOf, but domains other than the rationals are not " + \
+"currently supported. " + \
+"If there are no symbols in the matrix, " + \
+"it should still be possible to compute numeric approximations " + \
+"of the eigenvalues using " + \
+"M.evalf().eigenvals() or M.charpoly().nroots()."
+
+
+def _eigenvals_list(
+    M, error_when_incomplete=True, simplify=False, **flags):
+    iblocks = M.strongly_connected_components()
+    all_eigs = []
+    is_dom = M._rep.domain in (ZZ, QQ)
+    for b in iblocks:
+
+        # Fast path for a 1x1 block:
+        if is_dom and len(b) == 1:
+            index = b[0]
+            val = M[index, index]
+            all_eigs.append(val)
+            continue
+
+        block = M[b, b]
+
+        if isinstance(simplify, FunctionType):
+            charpoly = block.charpoly(simplify=simplify)
+        else:
+            charpoly = block.charpoly()
+
+        eigs = roots(charpoly, multiple=True, **flags)
+
+        if len(eigs) != block.rows:
+            try:
+                eigs = charpoly.all_roots(multiple=True)
+            except NotImplementedError:
+                if error_when_incomplete:
+                    raise MatrixError(eigenvals_error_message)
+                else:
+                    eigs = []
+
+        all_eigs += eigs
+
+    if not simplify:
+        return all_eigs
+    if not isinstance(simplify, FunctionType):
+        simplify = _simplify
+    return [simplify(value) for value in all_eigs]
+
+
+def _eigenvals_dict(
+    M, error_when_incomplete=True, simplify=False, **flags):
+    iblocks = M.strongly_connected_components()
+    all_eigs = {}
+    is_dom = M._rep.domain in (ZZ, QQ)
+    for b in iblocks:
+
+        # Fast path for a 1x1 block:
+        if is_dom and len(b) == 1:
+            index = b[0]
+            val = M[index, index]
+            all_eigs[val] = all_eigs.get(val, 0) + 1
+            continue
+
+        block = M[b, b]
+
+        if isinstance(simplify, FunctionType):
+            charpoly = block.charpoly(simplify=simplify)
+        else:
+            charpoly = block.charpoly()
+
+        eigs = roots(charpoly, multiple=False, **flags)
+
+        if sum(eigs.values()) != block.rows:
+            try:
+                eigs = dict(charpoly.all_roots(multiple=False))
+            except NotImplementedError:
+                if error_when_incomplete:
+                    raise MatrixError(eigenvals_error_message)
+                else:
+                    eigs = {}
+
+        for k, v in eigs.items():
+            if k in all_eigs:
+                all_eigs[k] += v
+            else:
+                all_eigs[k] = v
+
+    if not simplify:
+        return all_eigs
+    if not isinstance(simplify, FunctionType):
+        simplify = _simplify
+    return {simplify(key): value for key, value in all_eigs.items()}
+
+
+def _eigenspace(M, eigenval, iszerofunc=_iszero, simplify=False):
+    """Get a basis for the eigenspace for a particular eigenvalue"""
+    m   = M - M.eye(M.rows) * eigenval
+    ret = m.nullspace(iszerofunc=iszerofunc)
+
+    # The nullspace for a real eigenvalue should be non-trivial.
+    # If we didn't find an eigenvector, try once more a little harder
+    if len(ret) == 0 and simplify:
+        ret = m.nullspace(iszerofunc=iszerofunc, simplify=True)
+    if len(ret) == 0:
+        raise NotImplementedError(
+            "Can't evaluate eigenvector for eigenvalue {}".format(eigenval))
+    return ret
+
+
+def _eigenvects_DOM(M, **kwargs):
+    DOM = DomainMatrix.from_Matrix(M, field=True, extension=True)
+    DOM = DOM.to_dense()
+
+    if DOM.domain != EX:
+        rational, algebraic = dom_eigenvects(DOM)
+        eigenvects = dom_eigenvects_to_sympy(
+            rational, algebraic, M.__class__, **kwargs)
+        eigenvects = sorted(eigenvects, key=lambda x: default_sort_key(x[0]))
+
+        return eigenvects
+    return None
+
+
+def _eigenvects_sympy(M, iszerofunc, simplify=True, **flags):
+    eigenvals = M.eigenvals(rational=False, **flags)
+
+    # Make sure that we have all roots in radical form
+    for x in eigenvals:
+        if x.has(CRootOf):
+            raise MatrixError(
+                "Eigenvector computation is not implemented if the matrix have "
+                "eigenvalues in CRootOf form")
+
+    eigenvals = sorted(eigenvals.items(), key=default_sort_key)
+    ret = []
+    for val, mult in eigenvals:
+        vects = _eigenspace(M, val, iszerofunc=iszerofunc, simplify=simplify)
+        ret.append((val, mult, vects))
+    return ret
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _eigenvects(M, error_when_incomplete=True, iszerofunc=_iszero, *, chop=False, **flags):
+    """Compute eigenvectors of the matrix.
+
+    Parameters
+    ==========
+
+    error_when_incomplete : bool, optional
+        Raise an error when not all eigenvalues are computed. This is
+        caused by ``roots`` not returning a full list of eigenvalues.
+
+    iszerofunc : function, optional
+        Specifies a zero testing function to be used in ``rref``.
+
+        Default value is ``_iszero``, which uses SymPy's naive and fast
+        default assumption handler.
+
+        It can also accept any user-specified zero testing function, if it
+        is formatted as a function which accepts a single symbolic argument
+        and returns ``True`` if it is tested as zero and ``False`` if it
+        is tested as non-zero, and ``None`` if it is undecidable.
+
+    simplify : bool or function, optional
+        If ``True``, ``as_content_primitive()`` will be used to tidy up
+        normalization artifacts.
+
+        It will also be used by the ``nullspace`` routine.
+
+    chop : bool or positive number, optional
+        If the matrix contains any Floats, they will be changed to Rationals
+        for computation purposes, but the answers will be returned after
+        being evaluated with evalf. The ``chop`` flag is passed to ``evalf``.
+        When ``chop=True`` a default precision will be used; a number will
+        be interpreted as the desired level of precision.
+
+    Returns
+    =======
+
+    ret : [(eigenval, multiplicity, eigenspace), ...]
+        A ragged list containing tuples of data obtained by ``eigenvals``
+        and ``nullspace``.
+
+        ``eigenspace`` is a list containing the ``eigenvector`` for each
+        eigenvalue.
+
+        ``eigenvector`` is a vector in the form of a ``Matrix``. e.g.
+        a vector of length 3 is returned as ``Matrix([a_1, a_2, a_3])``.
+
+    Raises
+    ======
+
+    NotImplementedError
+        If failed to compute nullspace.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix(3, 3, [0, 1, 1, 1, 0, 0, 1, 1, 1])
+    >>> M.eigenvects()
+    [(-1, 1, [Matrix([
+    [-1],
+    [ 1],
+    [ 0]])]), (0, 1, [Matrix([
+    [ 0],
+    [-1],
+    [ 1]])]), (2, 1, [Matrix([
+    [2/3],
+    [1/3],
+    [  1]])])]
+
+    See Also
+    ========
+
+    eigenvals
+    MatrixBase.nullspace
+    """
+    simplify = flags.get('simplify', True)
+    primitive = flags.get('simplify', False)
+    flags.pop('simplify', None)  # remove this if it's there
+    flags.pop('multiple', None)  # remove this if it's there
+
+    if not isinstance(simplify, FunctionType):
+        simpfunc = _simplify if simplify else lambda x: x
+
+    has_floats = M.has(Float)
+    if has_floats:
+        if all(x.is_number for x in M):
+            return _eigenvects_mpmath(M)
+        from sympy.simplify import nsimplify
+        M = M.applyfunc(lambda x: nsimplify(x, rational=True))
+
+    ret = _eigenvects_DOM(M)
+    if ret is None:
+        ret = _eigenvects_sympy(M, iszerofunc, simplify=simplify, **flags)
+
+    if primitive:
+        # if the primitive flag is set, get rid of any common
+        # integer denominators
+        def denom_clean(l):
+            return [(v / gcd(list(v))).applyfunc(simpfunc) for v in l]
+
+        ret = [(val, mult, denom_clean(es)) for val, mult, es in ret]
+
+    if has_floats:
+        # if we had floats to start with, turn the eigenvectors to floats
+        ret = [(val.evalf(chop=chop), mult, [v.evalf(chop=chop) for v in es])
+                for val, mult, es in ret]
+
+    return ret
+
+
+def _is_diagonalizable_with_eigen(M, reals_only=False):
+    """See _is_diagonalizable. This function returns the bool along with the
+    eigenvectors to avoid calculating them again in functions like
+    ``diagonalize``."""
+
+    if not M.is_square:
+        return False, []
+
+    eigenvecs = M.eigenvects(simplify=True)
+
+    for val, mult, basis in eigenvecs:
+        if reals_only and not val.is_real: # if we have a complex eigenvalue
+            return False, eigenvecs
+
+        if mult != len(basis): # if the geometric multiplicity doesn't equal the algebraic
+            return False, eigenvecs
+
+    return True, eigenvecs
+
+def _is_diagonalizable(M, reals_only=False, **kwargs):
+    """Returns ``True`` if a matrix is diagonalizable.
+
+    Parameters
+    ==========
+
+    reals_only : bool, optional
+        If ``True``, it tests whether the matrix can be diagonalized
+        to contain only real numbers on the diagonal.
+
+
+        If ``False``, it tests whether the matrix can be diagonalized
+        at all, even with numbers that may not be real.
+
+    Examples
+    ========
+
+    Example of a diagonalizable matrix:
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2, 0], [0, 3, 0], [2, -4, 2]])
+    >>> M.is_diagonalizable()
+    True
+
+    Example of a non-diagonalizable matrix:
+
+    >>> M = Matrix([[0, 1], [0, 0]])
+    >>> M.is_diagonalizable()
+    False
+
+    Example of a matrix that is diagonalized in terms of non-real entries:
+
+    >>> M = Matrix([[0, 1], [-1, 0]])
+    >>> M.is_diagonalizable(reals_only=False)
+    True
+    >>> M.is_diagonalizable(reals_only=True)
+    False
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.is_diagonal
+    diagonalize
+    """
+    if not M.is_square:
+        return False
+
+    if all(e.is_real for e in M) and M.is_symmetric():
+        return True
+
+    if all(e.is_complex for e in M) and M.is_hermitian:
+        return True
+
+    return _is_diagonalizable_with_eigen(M, reals_only=reals_only)[0]
+
+
+#G&VL, Matrix Computations, Algo 5.4.2
+def _householder_vector(x):
+    if not x.cols == 1:
+        raise ValueError("Input must be a column matrix")
+    v = x.copy()
+    v_plus = x.copy()
+    v_minus = x.copy()
+    q = x[0, 0] / abs(x[0, 0])
+    norm_x = x.norm()
+    v_plus[0, 0] = x[0, 0] + q * norm_x
+    v_minus[0, 0] = x[0, 0] - q * norm_x
+    if x[1:, 0].norm() == 0:
+        bet = 0
+        v[0, 0] = 1
+    else:
+        if v_plus.norm() <= v_minus.norm():
+            v = v_plus
+        else:
+            v = v_minus
+        v = v / v[0]
+        bet = 2 / (v.norm() ** 2)
+    return v, bet
+
+
+def _bidiagonal_decmp_hholder(M):
+    m = M.rows
+    n = M.cols
+    A = M.as_mutable()
+    U, V = A.eye(m), A.eye(n)
+    for i in range(min(m, n)):
+        v, bet = _householder_vector(A[i:, i])
+        hh_mat = A.eye(m - i) - bet * v * v.H
+        A[i:, i:] = hh_mat * A[i:, i:]
+        temp = A.eye(m)
+        temp[i:, i:] = hh_mat
+        U = U * temp
+        if i + 1 <= n - 2:
+            v, bet = _householder_vector(A[i, i+1:].T)
+            hh_mat = A.eye(n - i - 1) - bet * v * v.H
+            A[i:, i+1:] = A[i:, i+1:] * hh_mat
+            temp = A.eye(n)
+            temp[i+1:, i+1:] = hh_mat
+            V = temp * V
+    return U, A, V
+
+
+def _eval_bidiag_hholder(M):
+    m = M.rows
+    n = M.cols
+    A = M.as_mutable()
+    for i in range(min(m, n)):
+        v, bet = _householder_vector(A[i:, i])
+        hh_mat = A.eye(m-i) - bet * v * v.H
+        A[i:, i:] = hh_mat * A[i:, i:]
+        if i + 1 <= n - 2:
+            v, bet = _householder_vector(A[i, i+1:].T)
+            hh_mat = A.eye(n - i - 1) - bet * v * v.H
+            A[i:, i+1:] = A[i:, i+1:] * hh_mat
+    return A
+
+
+def _bidiagonal_decomposition(M, upper=True):
+    """
+    Returns $(U,B,V.H)$ for
+
+    $$A = UBV^{H}$$
+
+    where $A$ is the input matrix, and $B$ is its Bidiagonalized form
+
+    Note: Bidiagonal Computation can hang for symbolic matrices.
+
+    Parameters
+    ==========
+
+    upper : bool. Whether to do upper bidiagnalization or lower.
+                True for upper and False for lower.
+
+    References
+    ==========
+
+    .. [1] Algorithm 5.4.2, Matrix computations by Golub and Van Loan, 4th edition
+    .. [2] Complex Matrix Bidiagonalization, https://github.com/vslobody/Householder-Bidiagonalization
+
+    """
+
+    if not isinstance(upper, bool):
+        raise ValueError("upper must be a boolean")
+
+    if upper:
+        return _bidiagonal_decmp_hholder(M)
+
+    X = _bidiagonal_decmp_hholder(M.H)
+    return X[2].H, X[1].H, X[0].H
+
+
+def _bidiagonalize(M, upper=True):
+    """
+    Returns $B$, the Bidiagonalized form of the input matrix.
+
+    Note: Bidiagonal Computation can hang for symbolic matrices.
+
+    Parameters
+    ==========
+
+    upper : bool. Whether to do upper bidiagnalization or lower.
+                True for upper and False for lower.
+
+    References
+    ==========
+
+    .. [1] Algorithm 5.4.2, Matrix computations by Golub and Van Loan, 4th edition
+    .. [2] Complex Matrix Bidiagonalization : https://github.com/vslobody/Householder-Bidiagonalization
+
+    """
+
+    if not isinstance(upper, bool):
+        raise ValueError("upper must be a boolean")
+
+    if upper:
+        return _eval_bidiag_hholder(M)
+    return _eval_bidiag_hholder(M.H).H
+
+
+def _diagonalize(M, reals_only=False, sort=False, normalize=False):
+    """
+    Return (P, D), where D is diagonal and
+
+        D = P^-1 * M * P
+
+    where M is current matrix.
+
+    Parameters
+    ==========
+
+    reals_only : bool. Whether to throw an error if complex numbers are need
+                    to diagonalize. (Default: False)
+
+    sort : bool. Sort the eigenvalues along the diagonal. (Default: False)
+
+    normalize : bool. If True, normalize the columns of P. (Default: False)
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix(3, 3, [1, 2, 0, 0, 3, 0, 2, -4, 2])
+    >>> M
+    Matrix([
+    [1,  2, 0],
+    [0,  3, 0],
+    [2, -4, 2]])
+    >>> (P, D) = M.diagonalize()
+    >>> D
+    Matrix([
+    [1, 0, 0],
+    [0, 2, 0],
+    [0, 0, 3]])
+    >>> P
+    Matrix([
+    [-1, 0, -1],
+    [ 0, 0, -1],
+    [ 2, 1,  2]])
+    >>> P.inv() * M * P
+    Matrix([
+    [1, 0, 0],
+    [0, 2, 0],
+    [0, 0, 3]])
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.is_diagonal
+    is_diagonalizable
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError()
+
+    is_diagonalizable, eigenvecs = _is_diagonalizable_with_eigen(M,
+                reals_only=reals_only)
+
+    if not is_diagonalizable:
+        raise MatrixError("Matrix is not diagonalizable")
+
+    if sort:
+        eigenvecs = sorted(eigenvecs, key=default_sort_key)
+
+    p_cols, diag = [], []
+
+    for val, mult, basis in eigenvecs:
+        diag   += [val] * mult
+        p_cols += basis
+
+    if normalize:
+        p_cols = [v / v.norm() for v in p_cols]
+
+    return M.hstack(*p_cols), M.diag(*diag)
+
+
+def _fuzzy_positive_definite(M):
+    positive_diagonals = M._has_positive_diagonals()
+    if positive_diagonals is False:
+        return False
+
+    if positive_diagonals and M.is_strongly_diagonally_dominant:
+        return True
+
+    return None
+
+
+def _fuzzy_positive_semidefinite(M):
+    nonnegative_diagonals = M._has_nonnegative_diagonals()
+    if nonnegative_diagonals is False:
+        return False
+
+    if nonnegative_diagonals and M.is_weakly_diagonally_dominant:
+        return True
+
+    return None
+
+
+def _is_positive_definite(M):
+    if not M.is_hermitian:
+        if not M.is_square:
+            return False
+        M = M + M.H
+
+    fuzzy = _fuzzy_positive_definite(M)
+    if fuzzy is not None:
+        return fuzzy
+
+    return _is_positive_definite_GE(M)
+
+
+def _is_positive_semidefinite(M):
+    if not M.is_hermitian:
+        if not M.is_square:
+            return False
+        M = M + M.H
+
+    fuzzy = _fuzzy_positive_semidefinite(M)
+    if fuzzy is not None:
+        return fuzzy
+
+    return _is_positive_semidefinite_cholesky(M)
+
+
+def _is_negative_definite(M):
+    return _is_positive_definite(-M)
+
+
+def _is_negative_semidefinite(M):
+    return _is_positive_semidefinite(-M)
+
+
+def _is_indefinite(M):
+    if M.is_hermitian:
+        eigen = M.eigenvals()
+        args1        = [x.is_positive for x in eigen.keys()]
+        any_positive = fuzzy_or(args1)
+        args2        = [x.is_negative for x in eigen.keys()]
+        any_negative = fuzzy_or(args2)
+
+        return fuzzy_and([any_positive, any_negative])
+
+    elif M.is_square:
+        return (M + M.H).is_indefinite
+
+    return False
+
+
+def _is_positive_definite_GE(M):
+    """A division-free gaussian elimination method for testing
+    positive-definiteness."""
+    M = M.as_mutable()
+    size = M.rows
+
+    for i in range(size):
+        is_positive = M[i, i].is_positive
+        if is_positive is not True:
+            return is_positive
+        for j in range(i+1, size):
+            M[j, i+1:] = M[i, i] * M[j, i+1:] - M[j, i] * M[i, i+1:]
+    return True
+
+
+def _is_positive_semidefinite_cholesky(M):
+    """Uses Cholesky factorization with complete pivoting
+
+    References
+    ==========
+
+    .. [1] http://eprints.ma.man.ac.uk/1199/1/covered/MIMS_ep2008_116.pdf
+
+    .. [2] https://www.value-at-risk.net/cholesky-factorization/
+    """
+    M = M.as_mutable()
+    for k in range(M.rows):
+        diags = [M[i, i] for i in range(k, M.rows)]
+        pivot, pivot_val, nonzero, _ = _find_reasonable_pivot(diags)
+
+        if nonzero:
+            return None
+
+        if pivot is None:
+            for i in range(k+1, M.rows):
+                for j in range(k, M.cols):
+                    iszero = M[i, j].is_zero
+                    if iszero is None:
+                        return None
+                    elif iszero is False:
+                        return False
+            return True
+
+        if M[k, k].is_negative or pivot_val.is_negative:
+            return False
+        elif not (M[k, k].is_nonnegative and pivot_val.is_nonnegative):
+            return None
+
+        if pivot > 0:
+            M.col_swap(k, k+pivot)
+            M.row_swap(k, k+pivot)
+
+        M[k, k] = sqrt(M[k, k])
+        M[k, k+1:] /= M[k, k]
+        M[k+1:, k+1:] -= M[k, k+1:].H * M[k, k+1:]
+
+    return M[-1, -1].is_nonnegative
+
+
+_doc_positive_definite = \
+    r"""Finds out the definiteness of a matrix.
+
+    Explanation
+    ===========
+
+    A square real matrix $A$ is:
+
+    - A positive definite matrix if $x^T A x > 0$
+      for all non-zero real vectors $x$.
+    - A positive semidefinite matrix if $x^T A x \geq 0$
+      for all non-zero real vectors $x$.
+    - A negative definite matrix if $x^T A x < 0$
+      for all non-zero real vectors $x$.
+    - A negative semidefinite matrix if $x^T A x \leq 0$
+      for all non-zero real vectors $x$.
+    - An indefinite matrix if there exists non-zero real vectors
+      $x, y$ with $x^T A x > 0 > y^T A y$.
+
+    A square complex matrix $A$ is:
+
+    - A positive definite matrix if $\text{re}(x^H A x) > 0$
+      for all non-zero complex vectors $x$.
+    - A positive semidefinite matrix if $\text{re}(x^H A x) \geq 0$
+      for all non-zero complex vectors $x$.
+    - A negative definite matrix if $\text{re}(x^H A x) < 0$
+      for all non-zero complex vectors $x$.
+    - A negative semidefinite matrix if $\text{re}(x^H A x) \leq 0$
+      for all non-zero complex vectors $x$.
+    - An indefinite matrix if there exists non-zero complex vectors
+      $x, y$ with $\text{re}(x^H A x) > 0 > \text{re}(y^H A y)$.
+
+    A matrix need not be symmetric or hermitian to be positive definite.
+
+    - A real non-symmetric matrix is positive definite if and only if
+      $\frac{A + A^T}{2}$ is positive definite.
+    - A complex non-hermitian matrix is positive definite if and only if
+      $\frac{A + A^H}{2}$ is positive definite.
+
+    And this extension can apply for all the definitions above.
+
+    However, for complex cases, you can restrict the definition of
+    $\text{re}(x^H A x) > 0$ to $x^H A x > 0$ and require the matrix
+    to be hermitian.
+    But we do not present this restriction for computation because you
+    can check ``M.is_hermitian`` independently with this and use
+    the same procedure.
+
+    Examples
+    ========
+
+    An example of symmetric positive definite matrix:
+
+    .. plot::
+        :context: reset
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy import Matrix, symbols
+        >>> from sympy.plotting import plot3d
+        >>> a, b = symbols('a b')
+        >>> x = Matrix([a, b])
+
+        >>> A = Matrix([[1, 0], [0, 1]])
+        >>> A.is_positive_definite
+        True
+        >>> A.is_positive_semidefinite
+        True
+
+        >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1))
+
+    An example of symmetric positive semidefinite matrix:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> A = Matrix([[1, -1], [-1, 1]])
+        >>> A.is_positive_definite
+        False
+        >>> A.is_positive_semidefinite
+        True
+
+        >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1))
+
+    An example of symmetric negative definite matrix:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> A = Matrix([[-1, 0], [0, -1]])
+        >>> A.is_negative_definite
+        True
+        >>> A.is_negative_semidefinite
+        True
+        >>> A.is_indefinite
+        False
+
+        >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1))
+
+    An example of symmetric indefinite matrix:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> A = Matrix([[1, 2], [2, -1]])
+        >>> A.is_indefinite
+        True
+
+        >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1))
+
+    An example of non-symmetric positive definite matrix.
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> A = Matrix([[1, 2], [-2, 1]])
+        >>> A.is_positive_definite
+        True
+        >>> A.is_positive_semidefinite
+        True
+
+        >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1))
+
+    Notes
+    =====
+
+    Although some people trivialize the definition of positive definite
+    matrices only for symmetric or hermitian matrices, this restriction
+    is not correct because it does not classify all instances of
+    positive definite matrices from the definition $x^T A x > 0$ or
+    $\text{re}(x^H A x) > 0$.
+
+    For instance, ``Matrix([[1, 2], [-2, 1]])`` presented in
+    the example above is an example of real positive definite matrix
+    that is not symmetric.
+
+    However, since the following formula holds true;
+
+    .. math::
+        \text{re}(x^H A x) > 0 \iff
+        \text{re}(x^H \frac{A + A^H}{2} x) > 0
+
+    We can classify all positive definite matrices that may or may not
+    be symmetric or hermitian by transforming the matrix to
+    $\frac{A + A^T}{2}$ or $\frac{A + A^H}{2}$
+    (which is guaranteed to be always real symmetric or complex
+    hermitian) and we can defer most of the studies to symmetric or
+    hermitian positive definite matrices.
+
+    But it is a different problem for the existence of Cholesky
+    decomposition. Because even though a non symmetric or a non
+    hermitian matrix can be positive definite, Cholesky or LDL
+    decomposition does not exist because the decompositions require the
+    matrix to be symmetric or hermitian.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Definiteness_of_a_matrix#Eigenvalues
+
+    .. [2] https://mathworld.wolfram.com/PositiveDefiniteMatrix.html
+
+    .. [3] Johnson, C. R. "Positive Definite Matrices." Amer.
+        Math. Monthly 77, 259-264 1970.
+    """
+
+_is_positive_definite.__doc__     = _doc_positive_definite
+_is_positive_semidefinite.__doc__ = _doc_positive_definite
+_is_negative_definite.__doc__     = _doc_positive_definite
+_is_negative_semidefinite.__doc__ = _doc_positive_definite
+_is_indefinite.__doc__            = _doc_positive_definite
+
+
+def _jordan_form(M, calc_transform=True, *, chop=False):
+    """Return $(P, J)$ where $J$ is a Jordan block
+    matrix and $P$ is a matrix such that $M = P J P^{-1}$
+
+    Parameters
+    ==========
+
+    calc_transform : bool
+        If ``False``, then only $J$ is returned.
+
+    chop : bool
+        All matrices are converted to exact types when computing
+        eigenvalues and eigenvectors.  As a result, there may be
+        approximation errors.  If ``chop==True``, these errors
+        will be truncated.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[ 6,  5, -2, -3], [-3, -1,  3,  3], [ 2,  1, -2, -3], [-1,  1,  5,  5]])
+    >>> P, J = M.jordan_form()
+    >>> J
+    Matrix([
+    [2, 1, 0, 0],
+    [0, 2, 0, 0],
+    [0, 0, 2, 1],
+    [0, 0, 0, 2]])
+
+    See Also
+    ========
+
+    jordan_block
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Only square matrices have Jordan forms")
+
+    mat        = M
+    has_floats = M.has(Float)
+
+    if has_floats:
+        try:
+            max_prec = max(term._prec for term in M.values() if isinstance(term, Float))
+        except ValueError:
+            # if no term in the matrix is explicitly a Float calling max()
+            # will throw a error so setting max_prec to default value of 53
+            max_prec = 53
+
+        # setting minimum max_dps to 15 to prevent loss of precision in
+        # matrix containing non evaluated expressions
+        max_dps = max(prec_to_dps(max_prec), 15)
+
+    def restore_floats(*args):
+        """If ``has_floats`` is `True`, cast all ``args`` as
+        matrices of floats."""
+
+        if has_floats:
+            args = [m.evalf(n=max_dps, chop=chop) for m in args]
+        if len(args) == 1:
+            return args[0]
+
+        return args
+
+    # cache calculations for some speedup
+    mat_cache = {}
+
+    def eig_mat(val, pow):
+        """Cache computations of ``(M - val*I)**pow`` for quick
+        retrieval"""
+
+        if (val, pow) in mat_cache:
+            return mat_cache[(val, pow)]
+
+        if (val, pow - 1) in mat_cache:
+            mat_cache[(val, pow)] = mat_cache[(val, pow - 1)].multiply(
+                    mat_cache[(val, 1)], dotprodsimp=None)
+        else:
+            mat_cache[(val, pow)] = (mat - val*M.eye(M.rows)).pow(pow)
+
+        return mat_cache[(val, pow)]
+
+    # helper functions
+    def nullity_chain(val, algebraic_multiplicity):
+        """Calculate the sequence  [0, nullity(E), nullity(E**2), ...]
+        until it is constant where ``E = M - val*I``"""
+
+        # mat.rank() is faster than computing the null space,
+        # so use the rank-nullity theorem
+        cols    = M.cols
+        ret     = [0]
+        nullity = cols - eig_mat(val, 1).rank()
+        i       = 2
+
+        while nullity != ret[-1]:
+            ret.append(nullity)
+
+            if nullity == algebraic_multiplicity:
+                break
+
+            nullity  = cols - eig_mat(val, i).rank()
+            i       += 1
+
+            # Due to issues like #7146 and #15872, SymPy sometimes
+            # gives the wrong rank. In this case, raise an error
+            # instead of returning an incorrect matrix
+            if nullity < ret[-1] or nullity > algebraic_multiplicity:
+                raise MatrixError(
+                    "SymPy had encountered an inconsistent "
+                    "result while computing Jordan block: "
+                    "{}".format(M))
+
+        return ret
+
+    def blocks_from_nullity_chain(d):
+        """Return a list of the size of each Jordan block.
+        If d_n is the nullity of E**n, then the number
+        of Jordan blocks of size n is
+
+            2*d_n - d_(n-1) - d_(n+1)"""
+
+        # d[0] is always the number of columns, so skip past it
+        mid = [2*d[n] - d[n - 1] - d[n + 1] for n in range(1, len(d) - 1)]
+        # d is assumed to plateau with "d[ len(d) ] == d[-1]", so
+        # 2*d_n - d_(n-1) - d_(n+1) == d_n - d_(n-1)
+        end = [d[-1] - d[-2]] if len(d) > 1 else [d[0]]
+
+        return mid + end
+
+    def pick_vec(small_basis, big_basis):
+        """Picks a vector from big_basis that isn't in
+        the subspace spanned by small_basis"""
+
+        if len(small_basis) == 0:
+            return big_basis[0]
+
+        for v in big_basis:
+            _, pivots = M.hstack(*(small_basis + [v])).echelon_form(
+                    with_pivots=True)
+
+            if pivots[-1] == len(small_basis):
+                return v
+
+    # roots doesn't like Floats, so replace them with Rationals
+    if has_floats:
+        from sympy.simplify import nsimplify
+        mat = mat.applyfunc(lambda x: nsimplify(x, rational=True))
+
+    # first calculate the jordan block structure
+    eigs = mat.eigenvals()
+
+    # Make sure that we have all roots in radical form
+    for x in eigs:
+        if x.has(CRootOf):
+            raise MatrixError(
+                "Jordan normal form is not implemented if the matrix have "
+                "eigenvalues in CRootOf form")
+
+    # most matrices have distinct eigenvalues
+    # and so are diagonalizable.  In this case, don't
+    # do extra work!
+    if len(eigs.keys()) == mat.cols:
+        blocks     = sorted(eigs.keys(), key=default_sort_key)
+        jordan_mat = mat.diag(*blocks)
+
+        if not calc_transform:
+            return restore_floats(jordan_mat)
+
+        jordan_basis = [eig_mat(eig, 1).nullspace()[0]
+                for eig in blocks]
+        basis_mat    = mat.hstack(*jordan_basis)
+
+        return restore_floats(basis_mat, jordan_mat)
+
+    block_structure = []
+
+    for eig in sorted(eigs.keys(), key=default_sort_key):
+        algebraic_multiplicity = eigs[eig]
+        chain = nullity_chain(eig, algebraic_multiplicity)
+        block_sizes = blocks_from_nullity_chain(chain)
+
+        # if block_sizes =       = [a, b, c, ...], then the number of
+        # Jordan blocks of size 1 is a, of size 2 is b, etc.
+        # create an array that has (eig, block_size) with one
+        # entry for each block
+        size_nums = [(i+1, num) for i, num in enumerate(block_sizes)]
+
+        # we expect larger Jordan blocks to come earlier
+        size_nums.reverse()
+
+        block_structure.extend(
+            [(eig, size) for size, num in size_nums for _ in range(num)])
+
+    jordan_form_size = sum(size for eig, size in block_structure)
+
+    if jordan_form_size != M.rows:
+        raise MatrixError(
+            "SymPy had encountered an inconsistent result while "
+            "computing Jordan block. : {}".format(M))
+
+    blocks     = (mat.jordan_block(size=size, eigenvalue=eig) for eig, size in block_structure)
+    jordan_mat = mat.diag(*blocks)
+
+    if not calc_transform:
+        return restore_floats(jordan_mat)
+
+    # For each generalized eigenspace, calculate a basis.
+    # We start by looking for a vector in null( (A - eig*I)**n )
+    # which isn't in null( (A - eig*I)**(n-1) ) where n is
+    # the size of the Jordan block
+    #
+    # Ideally we'd just loop through block_structure and
+    # compute each generalized eigenspace.  However, this
+    # causes a lot of unneeded computation.  Instead, we
+    # go through the eigenvalues separately, since we know
+    # their generalized eigenspaces must have bases that
+    # are linearly independent.
+    jordan_basis = []
+
+    for eig in sorted(eigs.keys(), key=default_sort_key):
+        eig_basis = []
+
+        for block_eig, size in block_structure:
+            if block_eig != eig:
+                continue
+
+            null_big   = (eig_mat(eig, size)).nullspace()
+            null_small = (eig_mat(eig, size - 1)).nullspace()
+
+            # we want to pick something that is in the big basis
+            # and not the small, but also something that is independent
+            # of any other generalized eigenvectors from a different
+            # generalized eigenspace sharing the same eigenvalue.
+            vec      = pick_vec(null_small + eig_basis, null_big)
+            new_vecs = [eig_mat(eig, i).multiply(vec, dotprodsimp=None)
+                    for i in range(size)]
+
+            eig_basis.extend(new_vecs)
+            jordan_basis.extend(reversed(new_vecs))
+
+    basis_mat = mat.hstack(*jordan_basis)
+
+    return restore_floats(basis_mat, jordan_mat)
+
+
+def _left_eigenvects(M, **flags):
+    """Returns left eigenvectors and eigenvalues.
+
+    This function returns the list of triples (eigenval, multiplicity,
+    basis) for the left eigenvectors. Options are the same as for
+    eigenvects(), i.e. the ``**flags`` arguments gets passed directly to
+    eigenvects().
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[0, 1, 1], [1, 0, 0], [1, 1, 1]])
+    >>> M.eigenvects()
+    [(-1, 1, [Matrix([
+    [-1],
+    [ 1],
+    [ 0]])]), (0, 1, [Matrix([
+    [ 0],
+    [-1],
+    [ 1]])]), (2, 1, [Matrix([
+    [2/3],
+    [1/3],
+    [  1]])])]
+    >>> M.left_eigenvects()
+    [(-1, 1, [Matrix([[-2, 1, 1]])]), (0, 1, [Matrix([[-1, -1, 1]])]), (2,
+    1, [Matrix([[1, 1, 1]])])]
+
+    """
+
+    eigs = M.transpose().eigenvects(**flags)
+
+    return [(val, mult, [l.transpose() for l in basis]) for val, mult, basis in eigs]
+
+
+def _singular_values(M):
+    """Compute the singular values of a Matrix
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, Symbol
+    >>> x = Symbol('x', real=True)
+    >>> M = Matrix([[0, 1, 0], [0, x, 0], [-1, 0, 0]])
+    >>> M.singular_values()
+    [sqrt(x**2 + 1), 1, 0]
+
+    See Also
+    ========
+
+    condition_number
+    """
+
+    if M.rows >= M.cols:
+        valmultpairs = M.H.multiply(M).eigenvals()
+    else:
+        valmultpairs = M.multiply(M.H).eigenvals()
+
+    # Expands result from eigenvals into a simple list
+    vals = []
+
+    for k, v in valmultpairs.items():
+        vals += [sqrt(k)] * v  # dangerous! same k in several spots!
+
+    # Pad with zeros if singular values are computed in reverse way,
+    # to give consistent format.
+    if len(vals) < M.cols:
+        vals += [M.zero] * (M.cols - len(vals))
+
+    # sort them in descending order
+    vals.sort(reverse=True, key=default_sort_key)
+
+    return vals
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/exceptions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/exceptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..bfc7cfa0bdffd59ff2bc5a9cd85cf9b04ed1a63d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/exceptions.py
@@ -0,0 +1,26 @@
+"""
+Exceptions raised by the matrix module.
+"""
+
+
+class MatrixError(Exception):
+    pass
+
+
+class ShapeError(ValueError, MatrixError):
+    """Wrong matrix shape"""
+    pass
+
+
+class NonSquareMatrixError(ShapeError):
+    pass
+
+
+class NonInvertibleMatrixError(ValueError, MatrixError):
+    """The matrix in not invertible (division by multidimensional zero error)."""
+    pass
+
+
+class NonPositiveDefiniteMatrixError(ValueError, MatrixError):
+    """The matrix is not a positive-definite matrix."""
+    pass
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..5f4ab203ab74165d1003cdedd83945ea3fcf8f47
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/__init__.py
@@ -0,0 +1,62 @@
+""" A module which handles Matrix Expressions """
+
+from .slice import MatrixSlice
+from .blockmatrix import BlockMatrix, BlockDiagMatrix, block_collapse, blockcut
+from .companion import CompanionMatrix
+from .funcmatrix import FunctionMatrix
+from .inverse import Inverse
+from .matadd import MatAdd
+from .matexpr import MatrixExpr, MatrixSymbol, matrix_symbols
+from .matmul import MatMul
+from .matpow import MatPow
+from .trace import Trace, trace
+from .determinant import Determinant, det, Permanent, per
+from .transpose import Transpose
+from .adjoint import Adjoint
+from .hadamard import hadamard_product, HadamardProduct, hadamard_power, HadamardPower
+from .diagonal import DiagonalMatrix, DiagonalOf, DiagMatrix, diagonalize_vector
+from .dotproduct import DotProduct
+from .kronecker import kronecker_product, KroneckerProduct, combine_kronecker
+from .permutation import PermutationMatrix, MatrixPermute
+from .sets import MatrixSet
+from .special import ZeroMatrix, Identity, OneMatrix
+
+__all__ = [
+    'MatrixSlice',
+
+    'BlockMatrix', 'BlockDiagMatrix', 'block_collapse', 'blockcut',
+    'FunctionMatrix',
+
+    'CompanionMatrix',
+
+    'Inverse',
+
+    'MatAdd',
+
+    'Identity', 'MatrixExpr', 'MatrixSymbol', 'ZeroMatrix', 'OneMatrix',
+    'matrix_symbols', 'MatrixSet',
+
+    'MatMul',
+
+    'MatPow',
+
+    'Trace', 'trace',
+
+    'Determinant', 'det',
+
+    'Transpose',
+
+    'Adjoint',
+
+    'hadamard_product', 'HadamardProduct', 'hadamard_power', 'HadamardPower',
+
+    'DiagonalMatrix', 'DiagonalOf', 'DiagMatrix', 'diagonalize_vector',
+
+    'DotProduct',
+
+    'kronecker_product', 'KroneckerProduct', 'combine_kronecker',
+
+    'PermutationMatrix', 'MatrixPermute',
+
+    'Permanent', 'per'
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/_shape.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/_shape.py
new file mode 100644
index 0000000000000000000000000000000000000000..a95d481bf8e1edf4c62992044cd50563b335caac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/_shape.py
@@ -0,0 +1,102 @@
+from sympy.core.relational import Eq
+from sympy.core.expr import Expr
+from sympy.core.numbers import Integer
+from sympy.logic.boolalg import Boolean, And
+from sympy.matrices.expressions.matexpr import MatrixExpr
+from sympy.matrices.exceptions import ShapeError
+from typing import Union
+
+
+def is_matadd_valid(*args: MatrixExpr) -> Boolean:
+    """Return the symbolic condition how ``MatAdd``, ``HadamardProduct``
+    makes sense.
+
+    Parameters
+    ==========
+
+    args
+        The list of arguments of matrices to be tested for.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, symbols
+    >>> from sympy.matrices.expressions._shape import is_matadd_valid
+
+    >>> m, n, p, q = symbols('m n p q')
+    >>> A = MatrixSymbol('A', m, n)
+    >>> B = MatrixSymbol('B', p, q)
+    >>> is_matadd_valid(A, B)
+    Eq(m, p) & Eq(n, q)
+    """
+    rows, cols = zip(*(arg.shape for arg in args))
+    return And(
+        *(Eq(i, j) for i, j in zip(rows[:-1], rows[1:])),
+        *(Eq(i, j) for i, j in zip(cols[:-1], cols[1:])),
+    )
+
+
+def is_matmul_valid(*args: Union[MatrixExpr, Expr]) -> Boolean:
+    """Return the symbolic condition how ``MatMul`` makes sense
+
+    Parameters
+    ==========
+
+    args
+        The list of arguments of matrices and scalar expressions to be tested
+        for.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, symbols
+    >>> from sympy.matrices.expressions._shape import is_matmul_valid
+
+    >>> m, n, p, q = symbols('m n p q')
+    >>> A = MatrixSymbol('A', m, n)
+    >>> B = MatrixSymbol('B', p, q)
+    >>> is_matmul_valid(A, B)
+    Eq(n, p)
+    """
+    rows, cols = zip(*(arg.shape for arg in args if isinstance(arg, MatrixExpr)))
+    return And(*(Eq(i, j) for i, j in zip(cols[:-1], rows[1:])))
+
+
+def is_square(arg: MatrixExpr, /) -> Boolean:
+    """Return the symbolic condition how the matrix is assumed to be square
+
+    Parameters
+    ==========
+
+    arg
+        The matrix to be tested for.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, symbols
+    >>> from sympy.matrices.expressions._shape import is_square
+
+    >>> m, n = symbols('m n')
+    >>> A = MatrixSymbol('A', m, n)
+    >>> is_square(A)
+    Eq(m, n)
+    """
+    return Eq(arg.rows, arg.cols)
+
+
+def validate_matadd_integer(*args: MatrixExpr) -> None:
+    """Validate matrix shape for addition only for integer values"""
+    rows, cols = zip(*(x.shape for x in args))
+    if len(set(filter(lambda x: isinstance(x, (int, Integer)), rows))) > 1:
+        raise ShapeError(f"Matrices have mismatching shape: {rows}")
+    if len(set(filter(lambda x: isinstance(x, (int, Integer)), cols))) > 1:
+        raise ShapeError(f"Matrices have mismatching shape: {cols}")
+
+
+def validate_matmul_integer(*args: MatrixExpr) -> None:
+    """Validate matrix shape for multiplication only for integer values"""
+    for A, B in zip(args[:-1], args[1:]):
+        i, j = A.cols, B.rows
+        if isinstance(i, (int, Integer)) and isinstance(j, (int, Integer)) and i != j:
+            raise ShapeError("Matrices are not aligned", i, j)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/adjoint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/adjoint.py
new file mode 100644
index 0000000000000000000000000000000000000000..2039a7b2eb8eeacb02435979121c4133a11d8e02
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/adjoint.py
@@ -0,0 +1,60 @@
+from sympy.core import Basic
+from sympy.functions import adjoint, conjugate
+from sympy.matrices.expressions.matexpr import MatrixExpr
+
+
+class Adjoint(MatrixExpr):
+    """
+    The Hermitian adjoint of a matrix expression.
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the adjoint, use the ``adjoint()``
+    function.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Adjoint, adjoint
+    >>> A = MatrixSymbol('A', 3, 5)
+    >>> B = MatrixSymbol('B', 5, 3)
+    >>> Adjoint(A*B)
+    Adjoint(A*B)
+    >>> adjoint(A*B)
+    Adjoint(B)*Adjoint(A)
+    >>> adjoint(A*B) == Adjoint(A*B)
+    False
+    >>> adjoint(A*B) == Adjoint(A*B).doit()
+    True
+    """
+    is_Adjoint = True
+
+    def doit(self, **hints):
+        arg = self.arg
+        if hints.get('deep', True) and isinstance(arg, Basic):
+            return adjoint(arg.doit(**hints))
+        else:
+            return adjoint(self.arg)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    @property
+    def shape(self):
+        return self.arg.shape[::-1]
+
+    def _entry(self, i, j, **kwargs):
+        return conjugate(self.arg._entry(j, i, **kwargs))
+
+    def _eval_adjoint(self):
+        return self.arg
+
+    def _eval_transpose(self):
+        return self.arg.conjugate()
+
+    def _eval_conjugate(self):
+        return self.arg.transpose()
+
+    def _eval_trace(self):
+        from sympy.matrices.expressions.trace import Trace
+        return conjugate(Trace(self.arg))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/applyfunc.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/applyfunc.py
new file mode 100644
index 0000000000000000000000000000000000000000..c0363658447a8dc37a152b30e45533bac582b10c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/applyfunc.py
@@ -0,0 +1,204 @@
+from sympy.core.expr import ExprBuilder
+from sympy.core.function import (Function, FunctionClass, Lambda)
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import sympify, _sympify
+from sympy.matrices.expressions import MatrixExpr
+from sympy.matrices.matrixbase import MatrixBase
+
+
+class ElementwiseApplyFunction(MatrixExpr):
+    r"""
+    Apply function to a matrix elementwise without evaluating.
+
+    Examples
+    ========
+
+    It can be created by calling ``.applyfunc()`` on a matrix
+    expression:
+
+    >>> from sympy import MatrixSymbol
+    >>> from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction
+    >>> from sympy import exp
+    >>> X = MatrixSymbol("X", 3, 3)
+    >>> X.applyfunc(exp)
+    Lambda(_d, exp(_d)).(X)
+
+    Otherwise using the class constructor:
+
+    >>> from sympy import eye
+    >>> expr = ElementwiseApplyFunction(exp, eye(3))
+    >>> expr
+    Lambda(_d, exp(_d)).(Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]]))
+    >>> expr.doit()
+    Matrix([
+    [E, 1, 1],
+    [1, E, 1],
+    [1, 1, E]])
+
+    Notice the difference with the real mathematical functions:
+
+    >>> exp(eye(3))
+    Matrix([
+    [E, 0, 0],
+    [0, E, 0],
+    [0, 0, E]])
+    """
+
+    def __new__(cls, function, expr):
+        expr = _sympify(expr)
+        if not expr.is_Matrix:
+            raise ValueError("{} must be a matrix instance.".format(expr))
+
+        if expr.shape == (1, 1):
+            # Check if the function returns a matrix, in that case, just apply
+            # the function instead of creating an ElementwiseApplyFunc object:
+            ret = function(expr)
+            if isinstance(ret, MatrixExpr):
+                return ret
+
+        if not isinstance(function, (FunctionClass, Lambda)):
+            d = Dummy('d')
+            function = Lambda(d, function(d))
+
+        function = sympify(function)
+        if not isinstance(function, (FunctionClass, Lambda)):
+            raise ValueError(
+                "{} should be compatible with SymPy function classes."
+                .format(function))
+
+        if 1 not in function.nargs:
+            raise ValueError(
+                '{} should be able to accept 1 arguments.'.format(function))
+
+        if not isinstance(function, Lambda):
+            d = Dummy('d')
+            function = Lambda(d, function(d))
+
+        obj = MatrixExpr.__new__(cls, function, expr)
+        return obj
+
+    @property
+    def function(self):
+        return self.args[0]
+
+    @property
+    def expr(self):
+        return self.args[1]
+
+    @property
+    def shape(self):
+        return self.expr.shape
+
+    def doit(self, **hints):
+        deep = hints.get("deep", True)
+        expr = self.expr
+        if deep:
+            expr = expr.doit(**hints)
+        function = self.function
+        if isinstance(function, Lambda) and function.is_identity:
+            # This is a Lambda containing the identity function.
+            return expr
+        if isinstance(expr, MatrixBase):
+            return expr.applyfunc(self.function)
+        elif isinstance(expr, ElementwiseApplyFunction):
+            return ElementwiseApplyFunction(
+                lambda x: self.function(expr.function(x)),
+                expr.expr
+            ).doit(**hints)
+        else:
+            return self
+
+    def _entry(self, i, j, **kwargs):
+        return self.function(self.expr._entry(i, j, **kwargs))
+
+    def _get_function_fdiff(self):
+        d = Dummy("d")
+        function = self.function(d)
+        fdiff = function.diff(d)
+        if isinstance(fdiff, Function):
+            fdiff = type(fdiff)
+        else:
+            fdiff = Lambda(d, fdiff)
+        return fdiff
+
+    def _eval_derivative(self, x):
+        from sympy.matrices.expressions.hadamard import hadamard_product
+        dexpr = self.expr.diff(x)
+        fdiff = self._get_function_fdiff()
+        return hadamard_product(
+            dexpr,
+            ElementwiseApplyFunction(fdiff, self.expr)
+        )
+
+    def _eval_derivative_matrix_lines(self, x):
+        from sympy.matrices.expressions.special import Identity
+        from sympy.tensor.array.expressions.array_expressions import ArrayContraction
+        from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal
+        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+
+        fdiff = self._get_function_fdiff()
+        lr = self.expr._eval_derivative_matrix_lines(x)
+        ewdiff = ElementwiseApplyFunction(fdiff, self.expr)
+        if 1 in x.shape:
+            # Vector:
+            iscolumn = self.shape[1] == 1
+            for i in lr:
+                if iscolumn:
+                    ptr1 = i.first_pointer
+                    ptr2 = Identity(self.shape[1])
+                else:
+                    ptr1 = Identity(self.shape[0])
+                    ptr2 = i.second_pointer
+
+                subexpr = ExprBuilder(
+                    ArrayDiagonal,
+                    [
+                        ExprBuilder(
+                            ArrayTensorProduct,
+                            [
+                                ewdiff,
+                                ptr1,
+                                ptr2,
+                            ]
+                        ),
+                        (0, 2) if iscolumn else (1, 4)
+                    ],
+                    validator=ArrayDiagonal._validate
+                )
+                i._lines = [subexpr]
+                i._first_pointer_parent = subexpr.args[0].args
+                i._first_pointer_index = 1
+                i._second_pointer_parent = subexpr.args[0].args
+                i._second_pointer_index = 2
+        else:
+            # Matrix case:
+            for i in lr:
+                ptr1 = i.first_pointer
+                ptr2 = i.second_pointer
+                newptr1 = Identity(ptr1.shape[1])
+                newptr2 = Identity(ptr2.shape[1])
+                subexpr = ExprBuilder(
+                    ArrayContraction,
+                    [
+                        ExprBuilder(
+                            ArrayTensorProduct,
+                            [ptr1, newptr1, ewdiff, ptr2, newptr2]
+                        ),
+                        (1, 2, 4),
+                        (5, 7, 8),
+                    ],
+                    validator=ArrayContraction._validate
+                )
+                i._first_pointer_parent = subexpr.args[0].args
+                i._first_pointer_index = 1
+                i._second_pointer_parent = subexpr.args[0].args
+                i._second_pointer_index = 4
+                i._lines = [subexpr]
+        return lr
+
+    def _eval_transpose(self):
+        from sympy.matrices.expressions.transpose import Transpose
+        return self.func(self.function, Transpose(self.expr).doit())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/blockmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/blockmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..0125d6233ba7cf8c0b590fbb655d9c7c447e0bd4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/blockmatrix.py
@@ -0,0 +1,975 @@
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core import Basic, Add, Mul, S
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.complexes import re, im
+from sympy.strategies import typed, exhaust, condition, do_one, unpack
+from sympy.strategies.traverse import bottom_up
+from sympy.utilities.iterables import is_sequence, sift
+from sympy.utilities.misc import filldedent
+
+from sympy.matrices import Matrix, ShapeError
+from sympy.matrices.exceptions import NonInvertibleMatrixError
+from sympy.matrices.expressions.determinant import det, Determinant
+from sympy.matrices.expressions.inverse import Inverse
+from sympy.matrices.expressions.matadd import MatAdd
+from sympy.matrices.expressions.matexpr import MatrixExpr, MatrixElement
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.matrices.expressions.matpow import MatPow
+from sympy.matrices.expressions.slice import MatrixSlice
+from sympy.matrices.expressions.special import ZeroMatrix, Identity
+from sympy.matrices.expressions.trace import trace
+from sympy.matrices.expressions.transpose import Transpose, transpose
+
+
+class BlockMatrix(MatrixExpr):
+    """A BlockMatrix is a Matrix comprised of other matrices.
+
+    The submatrices are stored in a SymPy Matrix object but accessed as part of
+    a Matrix Expression
+
+    >>> from sympy import (MatrixSymbol, BlockMatrix, symbols,
+    ...     Identity, ZeroMatrix, block_collapse)
+    >>> n,m,l = symbols('n m l')
+    >>> X = MatrixSymbol('X', n, n)
+    >>> Y = MatrixSymbol('Y', m, m)
+    >>> Z = MatrixSymbol('Z', n, m)
+    >>> B = BlockMatrix([[X, Z], [ZeroMatrix(m,n), Y]])
+    >>> print(B)
+    Matrix([
+    [X, Z],
+    [0, Y]])
+
+    >>> C = BlockMatrix([[Identity(n), Z]])
+    >>> print(C)
+    Matrix([[I, Z]])
+
+    >>> print(block_collapse(C*B))
+    Matrix([[X, Z + Z*Y]])
+
+    Some matrices might be comprised of rows of blocks with
+    the matrices in each row having the same height and the
+    rows all having the same total number of columns but
+    not having the same number of columns for each matrix
+    in each row. In this case, the matrix is not a block
+    matrix and should be instantiated by Matrix.
+
+    >>> from sympy import ones, Matrix
+    >>> dat = [
+    ... [ones(3,2), ones(3,3)*2],
+    ... [ones(2,3)*3, ones(2,2)*4]]
+    ...
+    >>> BlockMatrix(dat)
+    Traceback (most recent call last):
+    ...
+    ValueError:
+    Although this matrix is comprised of blocks, the blocks do not fill
+    the matrix in a size-symmetric fashion. To create a full matrix from
+    these arguments, pass them directly to Matrix.
+    >>> Matrix(dat)
+    Matrix([
+    [1, 1, 2, 2, 2],
+    [1, 1, 2, 2, 2],
+    [1, 1, 2, 2, 2],
+    [3, 3, 3, 4, 4],
+    [3, 3, 3, 4, 4]])
+
+    See Also
+    ========
+    sympy.matrices.matrixbase.MatrixBase.irregular
+    """
+    def __new__(cls, *args, **kwargs):
+        from sympy.matrices.immutable import ImmutableDenseMatrix
+        isMat = lambda i: getattr(i, 'is_Matrix', False)
+        if len(args) != 1 or \
+                not is_sequence(args[0]) or \
+                len({isMat(r) for r in args[0]}) != 1:
+            raise ValueError(filldedent('''
+                expecting a sequence of 1 or more rows
+                containing Matrices.'''))
+        rows = args[0] if args else []
+        if not isMat(rows):
+            if rows and isMat(rows[0]):
+                rows = [rows]  # rows is not list of lists or []
+            # regularity check
+            # same number of matrices in each row
+            blocky = ok = len({len(r) for r in rows}) == 1
+            if ok:
+                # same number of rows for each matrix in a row
+                for r in rows:
+                    ok = len({i.rows for i in r}) == 1
+                    if not ok:
+                        break
+                blocky = ok
+                if ok:
+                    # same number of cols for each matrix in each col
+                    for c in range(len(rows[0])):
+                        ok = len({rows[i][c].cols
+                            for i in range(len(rows))}) == 1
+                        if not ok:
+                            break
+            if not ok:
+                # same total cols in each row
+                ok = len({
+                    sum(i.cols for i in r) for r in rows}) == 1
+                if blocky and ok:
+                    raise ValueError(filldedent('''
+                        Although this matrix is comprised of blocks,
+                        the blocks do not fill the matrix in a
+                        size-symmetric fashion. To create a full matrix
+                        from these arguments, pass them directly to
+                        Matrix.'''))
+                raise ValueError(filldedent('''
+                    When there are not the same number of rows in each
+                    row's matrices or there are not the same number of
+                    total columns in each row, the matrix is not a
+                    block matrix. If this matrix is known to consist of
+                    blocks fully filling a 2-D space then see
+                    Matrix.irregular.'''))
+        mat = ImmutableDenseMatrix(rows, evaluate=False)
+        obj = Basic.__new__(cls, mat)
+        return obj
+
+    @property
+    def shape(self):
+        numrows = numcols = 0
+        M = self.blocks
+        for i in range(M.shape[0]):
+            numrows += M[i, 0].shape[0]
+        for i in range(M.shape[1]):
+            numcols += M[0, i].shape[1]
+        return (numrows, numcols)
+
+    @property
+    def blockshape(self):
+        return self.blocks.shape
+
+    @property
+    def blocks(self):
+        return self.args[0]
+
+    @property
+    def rowblocksizes(self):
+        return [self.blocks[i, 0].rows for i in range(self.blockshape[0])]
+
+    @property
+    def colblocksizes(self):
+        return [self.blocks[0, i].cols for i in range(self.blockshape[1])]
+
+    def structurally_equal(self, other):
+        return (isinstance(other, BlockMatrix)
+            and self.shape == other.shape
+            and self.blockshape == other.blockshape
+            and self.rowblocksizes == other.rowblocksizes
+            and self.colblocksizes == other.colblocksizes)
+
+    def _blockmul(self, other):
+        if (isinstance(other, BlockMatrix) and
+                self.colblocksizes == other.rowblocksizes):
+            return BlockMatrix(self.blocks*other.blocks)
+
+        return self * other
+
+    def _blockadd(self, other):
+        if (isinstance(other, BlockMatrix)
+                and self.structurally_equal(other)):
+            return BlockMatrix(self.blocks + other.blocks)
+
+        return self + other
+
+    def _eval_transpose(self):
+        # Flip all the individual matrices
+        matrices = [transpose(matrix) for matrix in self.blocks]
+        # Make a copy
+        M = Matrix(self.blockshape[0], self.blockshape[1], matrices)
+        # Transpose the block structure
+        M = M.transpose()
+        return BlockMatrix(M)
+
+    def _eval_adjoint(self):
+        return BlockMatrix(
+            Matrix(self.blockshape[0], self.blockshape[1], self.blocks).adjoint()
+        )
+
+    def _eval_trace(self):
+        if self.rowblocksizes == self.colblocksizes:
+            blocks = [self.blocks[i, i] for i in range(self.blockshape[0])]
+            return Add(*[trace(block) for block in blocks])
+
+    def _eval_determinant(self):
+        if self.blockshape == (1, 1):
+            return det(self.blocks[0, 0])
+        if self.blockshape == (2, 2):
+            [[A, B],
+             [C, D]] = self.blocks.tolist()
+            if ask(Q.invertible(A)):
+                return det(A)*det(D - C*A.I*B)
+            elif ask(Q.invertible(D)):
+                return det(D)*det(A - B*D.I*C)
+        return Determinant(self)
+
+    def _eval_as_real_imag(self):
+        real_matrices = [re(matrix) for matrix in self.blocks]
+        real_matrices = Matrix(self.blockshape[0], self.blockshape[1], real_matrices)
+
+        im_matrices = [im(matrix) for matrix in self.blocks]
+        im_matrices = Matrix(self.blockshape[0], self.blockshape[1], im_matrices)
+
+        return (BlockMatrix(real_matrices), BlockMatrix(im_matrices))
+
+    def _eval_derivative(self, x):
+        return BlockMatrix(self.blocks.diff(x))
+
+    def transpose(self):
+        """Return transpose of matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import MatrixSymbol, BlockMatrix, ZeroMatrix
+        >>> from sympy.abc import m, n
+        >>> X = MatrixSymbol('X', n, n)
+        >>> Y = MatrixSymbol('Y', m, m)
+        >>> Z = MatrixSymbol('Z', n, m)
+        >>> B = BlockMatrix([[X, Z], [ZeroMatrix(m,n), Y]])
+        >>> B.transpose()
+        Matrix([
+        [X.T,  0],
+        [Z.T, Y.T]])
+        >>> _.transpose()
+        Matrix([
+        [X, Z],
+        [0, Y]])
+        """
+        return self._eval_transpose()
+
+    def schur(self, mat = 'A', generalized = False):
+        """Return the Schur Complement of the 2x2 BlockMatrix
+
+        Parameters
+        ==========
+
+        mat : String, optional
+            The matrix with respect to which the
+            Schur Complement is calculated. 'A' is
+            used by default
+
+        generalized : bool, optional
+            If True, returns the generalized Schur
+            Component which uses Moore-Penrose Inverse
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, MatrixSymbol, BlockMatrix
+        >>> m, n = symbols('m n')
+        >>> A = MatrixSymbol('A', n, n)
+        >>> B = MatrixSymbol('B', n, m)
+        >>> C = MatrixSymbol('C', m, n)
+        >>> D = MatrixSymbol('D', m, m)
+        >>> X = BlockMatrix([[A, B], [C, D]])
+
+        The default Schur Complement is evaluated with "A"
+
+        >>> X.schur()
+        -C*A**(-1)*B + D
+        >>> X.schur('D')
+        A - B*D**(-1)*C
+
+        Schur complement with non-invertible matrices is not
+        defined. Instead, the generalized Schur complement can
+        be calculated which uses the Moore-Penrose Inverse. To
+        achieve this, `generalized` must be set to `True`
+
+        >>> X.schur('B', generalized=True)
+        C - D*(B.T*B)**(-1)*B.T*A
+        >>> X.schur('C', generalized=True)
+        -A*(C.T*C)**(-1)*C.T*D + B
+
+        Returns
+        =======
+
+        M : Matrix
+            The Schur Complement Matrix
+
+        Raises
+        ======
+
+        ShapeError
+            If the block matrix is not a 2x2 matrix
+
+        NonInvertibleMatrixError
+            If given matrix is non-invertible
+
+        References
+        ==========
+
+        .. [1] Wikipedia Article on Schur Component : https://en.wikipedia.org/wiki/Schur_complement
+
+        See Also
+        ========
+
+        sympy.matrices.matrixbase.MatrixBase.pinv
+        """
+
+        if self.blockshape == (2, 2):
+            [[A, B],
+             [C, D]] = self.blocks.tolist()
+            d={'A' : A, 'B' : B, 'C' : C, 'D' : D}
+            try:
+                inv = (d[mat].T*d[mat]).inv()*d[mat].T if generalized else d[mat].inv()
+                if mat == 'A':
+                    return D - C * inv * B
+                elif mat == 'B':
+                    return C - D * inv * A
+                elif mat == 'C':
+                    return B - A * inv * D
+                elif mat == 'D':
+                    return A - B * inv * C
+                #For matrices where no sub-matrix is square
+                return self
+            except NonInvertibleMatrixError:
+                raise NonInvertibleMatrixError('The given matrix is not invertible. Please set generalized=True \
+            to compute the generalized Schur Complement which uses Moore-Penrose Inverse')
+        else:
+            raise ShapeError('Schur Complement can only be calculated for 2x2 block matrices')
+
+    def LDUdecomposition(self):
+        """Returns the Block LDU decomposition of
+        a 2x2 Block Matrix
+
+        Returns
+        =======
+
+        (L, D, U) : Matrices
+            L : Lower Diagonal Matrix
+            D : Diagonal Matrix
+            U : Upper Diagonal Matrix
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, MatrixSymbol, BlockMatrix, block_collapse
+        >>> m, n = symbols('m n')
+        >>> A = MatrixSymbol('A', n, n)
+        >>> B = MatrixSymbol('B', n, m)
+        >>> C = MatrixSymbol('C', m, n)
+        >>> D = MatrixSymbol('D', m, m)
+        >>> X = BlockMatrix([[A, B], [C, D]])
+        >>> L, D, U = X.LDUdecomposition()
+        >>> block_collapse(L*D*U)
+        Matrix([
+        [A, B],
+        [C, D]])
+
+        Raises
+        ======
+
+        ShapeError
+            If the block matrix is not a 2x2 matrix
+
+        NonInvertibleMatrixError
+            If the matrix "A" is non-invertible
+
+        See Also
+        ========
+        sympy.matrices.expressions.blockmatrix.BlockMatrix.UDLdecomposition
+        sympy.matrices.expressions.blockmatrix.BlockMatrix.LUdecomposition
+        """
+        if self.blockshape == (2,2):
+            [[A, B],
+             [C, D]] = self.blocks.tolist()
+            try:
+                AI = A.I
+            except NonInvertibleMatrixError:
+                raise NonInvertibleMatrixError('Block LDU decomposition cannot be calculated when\
+                    "A" is singular')
+            Ip = Identity(B.shape[0])
+            Iq = Identity(B.shape[1])
+            Z = ZeroMatrix(*B.shape)
+            L = BlockMatrix([[Ip, Z], [C*AI, Iq]])
+            D = BlockDiagMatrix(A, self.schur())
+            U = BlockMatrix([[Ip, AI*B],[Z.T, Iq]])
+            return L, D, U
+        else:
+            raise ShapeError("Block LDU decomposition is supported only for 2x2 block matrices")
+
+    def UDLdecomposition(self):
+        """Returns the Block UDL decomposition of
+        a 2x2 Block Matrix
+
+        Returns
+        =======
+
+        (U, D, L) : Matrices
+            U : Upper Diagonal Matrix
+            D : Diagonal Matrix
+            L : Lower Diagonal Matrix
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, MatrixSymbol, BlockMatrix, block_collapse
+        >>> m, n = symbols('m n')
+        >>> A = MatrixSymbol('A', n, n)
+        >>> B = MatrixSymbol('B', n, m)
+        >>> C = MatrixSymbol('C', m, n)
+        >>> D = MatrixSymbol('D', m, m)
+        >>> X = BlockMatrix([[A, B], [C, D]])
+        >>> U, D, L = X.UDLdecomposition()
+        >>> block_collapse(U*D*L)
+        Matrix([
+        [A, B],
+        [C, D]])
+
+        Raises
+        ======
+
+        ShapeError
+            If the block matrix is not a 2x2 matrix
+
+        NonInvertibleMatrixError
+            If the matrix "D" is non-invertible
+
+        See Also
+        ========
+        sympy.matrices.expressions.blockmatrix.BlockMatrix.LDUdecomposition
+        sympy.matrices.expressions.blockmatrix.BlockMatrix.LUdecomposition
+        """
+        if self.blockshape == (2,2):
+            [[A, B],
+             [C, D]] = self.blocks.tolist()
+            try:
+                DI = D.I
+            except NonInvertibleMatrixError:
+                raise NonInvertibleMatrixError('Block UDL decomposition cannot be calculated when\
+                    "D" is singular')
+            Ip = Identity(A.shape[0])
+            Iq = Identity(B.shape[1])
+            Z = ZeroMatrix(*B.shape)
+            U = BlockMatrix([[Ip, B*DI], [Z.T, Iq]])
+            D = BlockDiagMatrix(self.schur('D'), D)
+            L = BlockMatrix([[Ip, Z],[DI*C, Iq]])
+            return U, D, L
+        else:
+            raise ShapeError("Block UDL decomposition is supported only for 2x2 block matrices")
+
+    def LUdecomposition(self):
+        """Returns the Block LU decomposition of
+        a 2x2 Block Matrix
+
+        Returns
+        =======
+
+        (L, U) : Matrices
+            L : Lower Diagonal Matrix
+            U : Upper Diagonal Matrix
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, MatrixSymbol, BlockMatrix, block_collapse
+        >>> m, n = symbols('m n')
+        >>> A = MatrixSymbol('A', n, n)
+        >>> B = MatrixSymbol('B', n, m)
+        >>> C = MatrixSymbol('C', m, n)
+        >>> D = MatrixSymbol('D', m, m)
+        >>> X = BlockMatrix([[A, B], [C, D]])
+        >>> L, U = X.LUdecomposition()
+        >>> block_collapse(L*U)
+        Matrix([
+        [A, B],
+        [C, D]])
+
+        Raises
+        ======
+
+        ShapeError
+            If the block matrix is not a 2x2 matrix
+
+        NonInvertibleMatrixError
+            If the matrix "A" is non-invertible
+
+        See Also
+        ========
+        sympy.matrices.expressions.blockmatrix.BlockMatrix.UDLdecomposition
+        sympy.matrices.expressions.blockmatrix.BlockMatrix.LDUdecomposition
+        """
+        if self.blockshape == (2,2):
+            [[A, B],
+             [C, D]] = self.blocks.tolist()
+            try:
+                A = A**S.Half
+                AI = A.I
+            except NonInvertibleMatrixError:
+                raise NonInvertibleMatrixError('Block LU decomposition cannot be calculated when\
+                    "A" is singular')
+            Z = ZeroMatrix(*B.shape)
+            Q = self.schur()**S.Half
+            L = BlockMatrix([[A, Z], [C*AI, Q]])
+            U = BlockMatrix([[A, AI*B],[Z.T, Q]])
+            return L, U
+        else:
+            raise ShapeError("Block LU decomposition is supported only for 2x2 block matrices")
+
+    def _entry(self, i, j, **kwargs):
+        # Find row entry
+        orig_i, orig_j = i, j
+        for row_block, numrows in enumerate(self.rowblocksizes):
+            cmp = i < numrows
+            if cmp == True:
+                break
+            elif cmp == False:
+                i -= numrows
+            elif row_block < self.blockshape[0] - 1:
+                # Can't tell which block and it's not the last one, return unevaluated
+                return MatrixElement(self, orig_i, orig_j)
+        for col_block, numcols in enumerate(self.colblocksizes):
+            cmp = j < numcols
+            if cmp == True:
+                break
+            elif cmp == False:
+                j -= numcols
+            elif col_block < self.blockshape[1] - 1:
+                return MatrixElement(self, orig_i, orig_j)
+        return self.blocks[row_block, col_block][i, j]
+
+    @property
+    def is_Identity(self):
+        if self.blockshape[0] != self.blockshape[1]:
+            return False
+        for i in range(self.blockshape[0]):
+            for j in range(self.blockshape[1]):
+                if i==j and not self.blocks[i, j].is_Identity:
+                    return False
+                if i!=j and not self.blocks[i, j].is_ZeroMatrix:
+                    return False
+        return True
+
+    @property
+    def is_structurally_symmetric(self):
+        return self.rowblocksizes == self.colblocksizes
+
+    def equals(self, other):
+        if self == other:
+            return True
+        if (isinstance(other, BlockMatrix) and self.blocks == other.blocks):
+            return True
+        return super().equals(other)
+
+
+class BlockDiagMatrix(BlockMatrix):
+    """A sparse matrix with block matrices along its diagonals
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, BlockDiagMatrix, symbols
+    >>> n, m, l = symbols('n m l')
+    >>> X = MatrixSymbol('X', n, n)
+    >>> Y = MatrixSymbol('Y', m, m)
+    >>> BlockDiagMatrix(X, Y)
+    Matrix([
+    [X, 0],
+    [0, Y]])
+
+    Notes
+    =====
+
+    If you want to get the individual diagonal blocks, use
+    :meth:`get_diag_blocks`.
+
+    See Also
+    ========
+
+    sympy.matrices.dense.diag
+    """
+    def __new__(cls, *mats):
+        return Basic.__new__(BlockDiagMatrix, *[_sympify(m) for m in mats])
+
+    @property
+    def diag(self):
+        return self.args
+
+    @property
+    def blocks(self):
+        from sympy.matrices.immutable import ImmutableDenseMatrix
+        mats = self.args
+        data = [[mats[i] if i == j else ZeroMatrix(mats[i].rows, mats[j].cols)
+                        for j in range(len(mats))]
+                        for i in range(len(mats))]
+        return ImmutableDenseMatrix(data, evaluate=False)
+
+    @property
+    def shape(self):
+        return (sum(block.rows for block in self.args),
+                sum(block.cols for block in self.args))
+
+    @property
+    def blockshape(self):
+        n = len(self.args)
+        return (n, n)
+
+    @property
+    def rowblocksizes(self):
+        return [block.rows for block in self.args]
+
+    @property
+    def colblocksizes(self):
+        return [block.cols for block in self.args]
+
+    def _all_square_blocks(self):
+        """Returns true if all blocks are square"""
+        return all(mat.is_square for mat in self.args)
+
+    def _eval_determinant(self):
+        if self._all_square_blocks():
+            return Mul(*[det(mat) for mat in self.args])
+        # At least one block is non-square.  Since the entire matrix must be square we know there must
+        # be at least two blocks in this matrix, in which case the entire matrix is necessarily rank-deficient
+        return S.Zero
+
+    def _eval_inverse(self, expand='ignored'):
+        if self._all_square_blocks():
+            return BlockDiagMatrix(*[mat.inverse() for mat in self.args])
+        # See comment in _eval_determinant()
+        raise NonInvertibleMatrixError('Matrix det == 0; not invertible.')
+
+    def _eval_transpose(self):
+        return BlockDiagMatrix(*[mat.transpose() for mat in self.args])
+
+    def _blockmul(self, other):
+        if (isinstance(other, BlockDiagMatrix) and
+                self.colblocksizes == other.rowblocksizes):
+            return BlockDiagMatrix(*[a*b for a, b in zip(self.args, other.args)])
+        else:
+            return BlockMatrix._blockmul(self, other)
+
+    def _blockadd(self, other):
+        if (isinstance(other, BlockDiagMatrix) and
+                self.blockshape == other.blockshape and
+                self.rowblocksizes == other.rowblocksizes and
+                self.colblocksizes == other.colblocksizes):
+            return BlockDiagMatrix(*[a + b for a, b in zip(self.args, other.args)])
+        else:
+            return BlockMatrix._blockadd(self, other)
+
+    def get_diag_blocks(self):
+        """Return the list of diagonal blocks of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import BlockDiagMatrix, Matrix
+
+        >>> A = Matrix([[1, 2], [3, 4]])
+        >>> B = Matrix([[5, 6], [7, 8]])
+        >>> M = BlockDiagMatrix(A, B)
+
+        How to get diagonal blocks from the block diagonal matrix:
+
+        >>> diag_blocks = M.get_diag_blocks()
+        >>> diag_blocks[0]
+        Matrix([
+        [1, 2],
+        [3, 4]])
+        >>> diag_blocks[1]
+        Matrix([
+        [5, 6],
+        [7, 8]])
+        """
+        return self.args
+
+
+def block_collapse(expr):
+    """Evaluates a block matrix expression
+
+    >>> from sympy import MatrixSymbol, BlockMatrix, symbols, Identity, ZeroMatrix, block_collapse
+    >>> n,m,l = symbols('n m l')
+    >>> X = MatrixSymbol('X', n, n)
+    >>> Y = MatrixSymbol('Y', m, m)
+    >>> Z = MatrixSymbol('Z', n, m)
+    >>> B = BlockMatrix([[X, Z], [ZeroMatrix(m, n), Y]])
+    >>> print(B)
+    Matrix([
+    [X, Z],
+    [0, Y]])
+
+    >>> C = BlockMatrix([[Identity(n), Z]])
+    >>> print(C)
+    Matrix([[I, Z]])
+
+    >>> print(block_collapse(C*B))
+    Matrix([[X, Z + Z*Y]])
+    """
+    from sympy.strategies.util import expr_fns
+
+    hasbm = lambda expr: isinstance(expr, MatrixExpr) and expr.has(BlockMatrix)
+
+    conditioned_rl = condition(
+        hasbm,
+        typed(
+            {MatAdd: do_one(bc_matadd, bc_block_plus_ident),
+             MatMul: do_one(bc_matmul, bc_dist),
+             MatPow: bc_matmul,
+             Transpose: bc_transpose,
+             Inverse: bc_inverse,
+             BlockMatrix: do_one(bc_unpack, deblock)}
+        )
+    )
+
+    rule = exhaust(
+        bottom_up(
+            exhaust(conditioned_rl),
+            fns=expr_fns
+        )
+    )
+
+    result = rule(expr)
+    doit = getattr(result, 'doit', None)
+    if doit is not None:
+        return doit()
+    else:
+        return result
+
+def bc_unpack(expr):
+    if expr.blockshape == (1, 1):
+        return expr.blocks[0, 0]
+    return expr
+
+def bc_matadd(expr):
+    args = sift(expr.args, lambda M: isinstance(M, BlockMatrix))
+    blocks = args[True]
+    if not blocks:
+        return expr
+
+    nonblocks = args[False]
+    block = blocks[0]
+    for b in blocks[1:]:
+        block = block._blockadd(b)
+    if nonblocks:
+        return MatAdd(*nonblocks) + block
+    else:
+        return block
+
+def bc_block_plus_ident(expr):
+    idents = [arg for arg in expr.args if arg.is_Identity]
+    if not idents:
+        return expr
+
+    blocks = [arg for arg in expr.args if isinstance(arg, BlockMatrix)]
+    if (blocks and all(b.structurally_equal(blocks[0]) for b in blocks)
+               and blocks[0].is_structurally_symmetric):
+        block_id = BlockDiagMatrix(*[Identity(k)
+                                        for k in blocks[0].rowblocksizes])
+        rest = [arg for arg in expr.args if not arg.is_Identity and not isinstance(arg, BlockMatrix)]
+        return MatAdd(block_id * len(idents), *blocks, *rest).doit()
+
+    return expr
+
+def bc_dist(expr):
+    """ Turn  a*[X, Y] into [a*X, a*Y] """
+    factor, mat = expr.as_coeff_mmul()
+    if factor == 1:
+        return expr
+
+    unpacked = unpack(mat)
+
+    if isinstance(unpacked, BlockDiagMatrix):
+        B = unpacked.diag
+        new_B = [factor * mat for mat in B]
+        return BlockDiagMatrix(*new_B)
+    elif isinstance(unpacked, BlockMatrix):
+        B = unpacked.blocks
+        new_B = [
+            [factor * B[i, j] for j in range(B.cols)] for i in range(B.rows)]
+        return BlockMatrix(new_B)
+    return expr
+
+
+def bc_matmul(expr):
+    if isinstance(expr, MatPow):
+        if expr.args[1].is_Integer and expr.args[1] > 0:
+            factor, matrices = 1, [expr.args[0]]*expr.args[1]
+        else:
+            return expr
+    else:
+        factor, matrices = expr.as_coeff_matrices()
+
+    i = 0
+    while (i+1 < len(matrices)):
+        A, B = matrices[i:i+2]
+        if isinstance(A, BlockMatrix) and isinstance(B, BlockMatrix):
+            matrices[i] = A._blockmul(B)
+            matrices.pop(i+1)
+        elif isinstance(A, BlockMatrix):
+            matrices[i] = A._blockmul(BlockMatrix([[B]]))
+            matrices.pop(i+1)
+        elif isinstance(B, BlockMatrix):
+            matrices[i] = BlockMatrix([[A]])._blockmul(B)
+            matrices.pop(i+1)
+        else:
+            i+=1
+    return MatMul(factor, *matrices).doit()
+
+def bc_transpose(expr):
+    collapse = block_collapse(expr.arg)
+    return collapse._eval_transpose()
+
+
+def bc_inverse(expr):
+    if isinstance(expr.arg, BlockDiagMatrix):
+        return expr.inverse()
+
+    expr2 = blockinverse_1x1(expr)
+    if expr != expr2:
+        return expr2
+    return blockinverse_2x2(Inverse(reblock_2x2(expr.arg)))
+
+def blockinverse_1x1(expr):
+    if isinstance(expr.arg, BlockMatrix) and expr.arg.blockshape == (1, 1):
+        mat = Matrix([[expr.arg.blocks[0].inverse()]])
+        return BlockMatrix(mat)
+    return expr
+
+
+def blockinverse_2x2(expr):
+    if isinstance(expr.arg, BlockMatrix) and expr.arg.blockshape == (2, 2):
+        # See: Inverses of 2x2 Block Matrices, Tzon-Tzer Lu and Sheng-Hua Shiou
+        [[A, B],
+         [C, D]] = expr.arg.blocks.tolist()
+
+        formula = _choose_2x2_inversion_formula(A, B, C, D)
+        if formula != None:
+            MI = expr.arg.schur(formula).I
+        if formula == 'A':
+            AI = A.I
+            return BlockMatrix([[AI + AI * B * MI * C * AI, -AI * B * MI], [-MI * C * AI, MI]])
+        if formula == 'B':
+            BI = B.I
+            return BlockMatrix([[-MI * D * BI, MI], [BI + BI * A * MI * D * BI, -BI * A * MI]])
+        if formula == 'C':
+            CI = C.I
+            return BlockMatrix([[-CI * D * MI, CI + CI * D * MI * A * CI], [MI, -MI * A * CI]])
+        if formula == 'D':
+            DI = D.I
+            return BlockMatrix([[MI, -MI * B * DI], [-DI * C * MI, DI + DI * C * MI * B * DI]])
+
+    return expr
+
+
+def _choose_2x2_inversion_formula(A, B, C, D):
+    """
+    Assuming [[A, B], [C, D]] would form a valid square block matrix, find
+    which of the classical 2x2 block matrix inversion formulas would be
+    best suited.
+
+    Returns 'A', 'B', 'C', 'D' to represent the algorithm involving inversion
+    of the given argument or None if the matrix cannot be inverted using
+    any of those formulas.
+    """
+    # Try to find a known invertible matrix.  Note that the Schur complement
+    # is currently not being considered for this
+    A_inv = ask(Q.invertible(A))
+    if A_inv == True:
+        return 'A'
+    B_inv = ask(Q.invertible(B))
+    if B_inv == True:
+        return 'B'
+    C_inv = ask(Q.invertible(C))
+    if C_inv == True:
+        return 'C'
+    D_inv = ask(Q.invertible(D))
+    if D_inv == True:
+        return 'D'
+    # Otherwise try to find a matrix that isn't known to be non-invertible
+    if A_inv != False:
+        return 'A'
+    if B_inv != False:
+        return 'B'
+    if C_inv != False:
+        return 'C'
+    if D_inv != False:
+        return 'D'
+    return None
+
+
+def deblock(B):
+    """ Flatten a BlockMatrix of BlockMatrices """
+    if not isinstance(B, BlockMatrix) or not B.blocks.has(BlockMatrix):
+        return B
+    wrap = lambda x: x if isinstance(x, BlockMatrix) else BlockMatrix([[x]])
+    bb = B.blocks.applyfunc(wrap)  # everything is a block
+
+    try:
+        MM = Matrix(0, sum(bb[0, i].blocks.shape[1] for i in range(bb.shape[1])), [])
+        for row in range(0, bb.shape[0]):
+            M = Matrix(bb[row, 0].blocks)
+            for col in range(1, bb.shape[1]):
+                M = M.row_join(bb[row, col].blocks)
+            MM = MM.col_join(M)
+
+        return BlockMatrix(MM)
+    except ShapeError:
+        return B
+
+
+def reblock_2x2(expr):
+    """
+    Reblock a BlockMatrix so that it has 2x2 blocks of block matrices.  If
+    possible in such a way that the matrix continues to be invertible using the
+    classical 2x2 block inversion formulas.
+    """
+    if not isinstance(expr, BlockMatrix) or not all(d > 2 for d in expr.blockshape):
+        return expr
+
+    BM = BlockMatrix  # for brevity's sake
+    rowblocks, colblocks = expr.blockshape
+    blocks = expr.blocks
+    for i in range(1, rowblocks):
+        for j in range(1, colblocks):
+            # try to split rows at i and cols at j
+            A = bc_unpack(BM(blocks[:i, :j]))
+            B = bc_unpack(BM(blocks[:i, j:]))
+            C = bc_unpack(BM(blocks[i:, :j]))
+            D = bc_unpack(BM(blocks[i:, j:]))
+
+            formula = _choose_2x2_inversion_formula(A, B, C, D)
+            if formula is not None:
+                return BlockMatrix([[A, B], [C, D]])
+
+    # else: nothing worked, just split upper left corner
+    return BM([[blocks[0, 0], BM(blocks[0, 1:])],
+               [BM(blocks[1:, 0]), BM(blocks[1:, 1:])]])
+
+
+def bounds(sizes):
+    """ Convert sequence of numbers into pairs of low-high pairs
+
+    >>> from sympy.matrices.expressions.blockmatrix import bounds
+    >>> bounds((1, 10, 50))
+    [(0, 1), (1, 11), (11, 61)]
+    """
+    low = 0
+    rv = []
+    for size in sizes:
+        rv.append((low, low + size))
+        low += size
+    return rv
+
+def blockcut(expr, rowsizes, colsizes):
+    """ Cut a matrix expression into Blocks
+
+    >>> from sympy import ImmutableMatrix, blockcut
+    >>> M = ImmutableMatrix(4, 4, range(16))
+    >>> B = blockcut(M, (1, 3), (1, 3))
+    >>> type(B).__name__
+    'BlockMatrix'
+    >>> ImmutableMatrix(B.blocks[0, 1])
+    Matrix([[1, 2, 3]])
+    """
+
+    rowbounds = bounds(rowsizes)
+    colbounds = bounds(colsizes)
+    return BlockMatrix([[MatrixSlice(expr, rowbound, colbound)
+                         for colbound in colbounds]
+                         for rowbound in rowbounds])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/companion.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/companion.py
new file mode 100644
index 0000000000000000000000000000000000000000..6969c917f63806cb1f5417804e01ecc1350d1406
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/companion.py
@@ -0,0 +1,56 @@
+from sympy.core.singleton import S
+from sympy.core.sympify import _sympify
+from sympy.polys.polytools import Poly
+
+from .matexpr import MatrixExpr
+
+
+class CompanionMatrix(MatrixExpr):
+    """A symbolic companion matrix of a polynomial.
+
+    Examples
+    ========
+
+    >>> from sympy import Poly, Symbol, symbols
+    >>> from sympy.matrices.expressions import CompanionMatrix
+    >>> x = Symbol('x')
+    >>> c0, c1, c2, c3, c4 = symbols('c0:5')
+    >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x)
+    >>> CompanionMatrix(p)
+    CompanionMatrix(Poly(x**5 + c4*x**4 + c3*x**3 + c2*x**2 + c1*x + c0,
+    x, domain='ZZ[c0,c1,c2,c3,c4]'))
+    """
+    def __new__(cls, poly):
+        poly = _sympify(poly)
+        if not isinstance(poly, Poly):
+            raise ValueError("{} must be a Poly instance.".format(poly))
+        if not poly.is_monic:
+            raise ValueError("{} must be a monic polynomial.".format(poly))
+        if not poly.is_univariate:
+            raise ValueError(
+                "{} must be a univariate polynomial.".format(poly))
+        if not poly.degree() >= 1:
+            raise ValueError(
+                "{} must have degree not less than 1.".format(poly))
+
+        return super().__new__(cls, poly)
+
+
+    @property
+    def shape(self):
+        poly = self.args[0]
+        size = poly.degree()
+        return size, size
+
+
+    def _entry(self, i, j):
+        if j == self.cols - 1:
+            return -self.args[0].all_coeffs()[-1 - i]
+        elif i == j + 1:
+            return S.One
+        return S.Zero
+
+
+    def as_explicit(self):
+        from sympy.matrices.immutable import ImmutableDenseMatrix
+        return ImmutableDenseMatrix.companion(self.args[0])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/determinant.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/determinant.py
new file mode 100644
index 0000000000000000000000000000000000000000..b323b3f93a5a0404bf2205f39d25b931d173b6d9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/determinant.py
@@ -0,0 +1,148 @@
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.singleton import S
+from sympy.core.sympify import sympify
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.matrixbase import MatrixBase
+
+
+class Determinant(Expr):
+    """Matrix Determinant
+
+    Represents the determinant of a matrix expression.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Determinant, eye
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> Determinant(A)
+    Determinant(A)
+    >>> Determinant(eye(3)).doit()
+    1
+    """
+    is_commutative = True
+
+    def __new__(cls, mat):
+        mat = sympify(mat)
+        if not mat.is_Matrix:
+            raise TypeError("Input to Determinant, %s, not a matrix" % str(mat))
+
+        if mat.is_square is False:
+            raise NonSquareMatrixError("Det of a non-square matrix")
+
+        return Basic.__new__(cls, mat)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    @property
+    def kind(self):
+        return self.arg.kind.element_kind
+
+    def doit(self, **hints):
+        arg = self.arg
+        if hints.get('deep', True):
+            arg = arg.doit(**hints)
+
+        result = arg._eval_determinant()
+        if result is not None:
+            return result
+
+        return self
+
+
+def det(matexpr):
+    """ Matrix Determinant
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, det, eye
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> det(A)
+    Determinant(A)
+    >>> det(eye(3))
+    1
+    """
+
+    return Determinant(matexpr).doit()
+
+class Permanent(Expr):
+    """Matrix Permanent
+
+    Represents the permanent of a matrix expression.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Permanent, ones
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> Permanent(A)
+    Permanent(A)
+    >>> Permanent(ones(3, 3)).doit()
+    6
+    """
+
+    def __new__(cls, mat):
+        mat = sympify(mat)
+        if not mat.is_Matrix:
+            raise TypeError("Input to Permanent, %s, not a matrix" % str(mat))
+
+        return Basic.__new__(cls, mat)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    def doit(self, expand=False, **hints):
+        if isinstance(self.arg, MatrixBase):
+            return self.arg.per()
+        else:
+            return self
+
+def per(matexpr):
+    """ Matrix Permanent
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Matrix, per, ones
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> per(A)
+    Permanent(A)
+    >>> per(ones(5, 5))
+    120
+    >>> M = Matrix([1, 2, 5])
+    >>> per(M)
+    8
+    """
+
+    return Permanent(matexpr).doit()
+
+from sympy.assumptions.ask import ask, Q
+from sympy.assumptions.refine import handlers_dict
+
+
+def refine_Determinant(expr, assumptions):
+    """
+    >>> from sympy import MatrixSymbol, Q, assuming, refine, det
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> det(X)
+    Determinant(X)
+    >>> with assuming(Q.orthogonal(X)):
+    ...     print(refine(det(X)))
+    1
+    """
+    if ask(Q.orthogonal(expr.arg), assumptions):
+        return S.One
+    elif ask(Q.singular(expr.arg), assumptions):
+        return S.Zero
+    elif ask(Q.unit_triangular(expr.arg), assumptions):
+        return S.One
+
+    return expr
+
+
+handlers_dict['Determinant'] = refine_Determinant
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/diagonal.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/diagonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba8a0216588143e3e251dab84c25f038fad550a4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/diagonal.py
@@ -0,0 +1,220 @@
+from sympy.core.sympify import _sympify
+
+from sympy.matrices.expressions import MatrixExpr
+from sympy.core import S, Eq, Ge
+from sympy.core.mul import Mul
+from sympy.functions.special.tensor_functions import KroneckerDelta
+
+
+class DiagonalMatrix(MatrixExpr):
+    """DiagonalMatrix(M) will create a matrix expression that
+    behaves as though all off-diagonal elements,
+    `M[i, j]` where `i != j`, are zero.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, DiagonalMatrix, Symbol
+    >>> n = Symbol('n', integer=True)
+    >>> m = Symbol('m', integer=True)
+    >>> D = DiagonalMatrix(MatrixSymbol('x', 2, 3))
+    >>> D[1, 2]
+    0
+    >>> D[1, 1]
+    x[1, 1]
+
+    The length of the diagonal -- the lesser of the two dimensions of `M` --
+    is accessed through the `diagonal_length` property:
+
+    >>> D.diagonal_length
+    2
+    >>> DiagonalMatrix(MatrixSymbol('x', n + 1, n)).diagonal_length
+    n
+
+    When one of the dimensions is symbolic the other will be treated as
+    though it is smaller:
+
+    >>> tall = DiagonalMatrix(MatrixSymbol('x', n, 3))
+    >>> tall.diagonal_length
+    3
+    >>> tall[10, 1]
+    0
+
+    When the size of the diagonal is not known, a value of None will
+    be returned:
+
+    >>> DiagonalMatrix(MatrixSymbol('x', n, m)).diagonal_length is None
+    True
+
+    """
+    arg = property(lambda self: self.args[0])
+
+    shape = property(lambda self: self.arg.shape)  # type:ignore
+
+    @property
+    def diagonal_length(self):
+        r, c = self.shape
+        if r.is_Integer and c.is_Integer:
+            m = min(r, c)
+        elif r.is_Integer and not c.is_Integer:
+            m = r
+        elif c.is_Integer and not r.is_Integer:
+            m = c
+        elif r == c:
+            m = r
+        else:
+            try:
+                m = min(r, c)
+            except TypeError:
+                m = None
+        return m
+
+    def _entry(self, i, j, **kwargs):
+        if self.diagonal_length is not None:
+            if Ge(i, self.diagonal_length) is S.true:
+                return S.Zero
+            elif Ge(j, self.diagonal_length) is S.true:
+                return S.Zero
+        eq = Eq(i, j)
+        if eq is S.true:
+            return self.arg[i, i]
+        elif eq is S.false:
+            return S.Zero
+        return self.arg[i, j]*KroneckerDelta(i, j)
+
+
+class DiagonalOf(MatrixExpr):
+    """DiagonalOf(M) will create a matrix expression that
+    is equivalent to the diagonal of `M`, represented as
+    a single column matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, DiagonalOf, Symbol
+    >>> n = Symbol('n', integer=True)
+    >>> m = Symbol('m', integer=True)
+    >>> x = MatrixSymbol('x', 2, 3)
+    >>> diag = DiagonalOf(x)
+    >>> diag.shape
+    (2, 1)
+
+    The diagonal can be addressed like a matrix or vector and will
+    return the corresponding element of the original matrix:
+
+    >>> diag[1, 0] == diag[1] == x[1, 1]
+    True
+
+    The length of the diagonal -- the lesser of the two dimensions of `M` --
+    is accessed through the `diagonal_length` property:
+
+    >>> diag.diagonal_length
+    2
+    >>> DiagonalOf(MatrixSymbol('x', n + 1, n)).diagonal_length
+    n
+
+    When only one of the dimensions is symbolic the other will be
+    treated as though it is smaller:
+
+    >>> dtall = DiagonalOf(MatrixSymbol('x', n, 3))
+    >>> dtall.diagonal_length
+    3
+
+    When the size of the diagonal is not known, a value of None will
+    be returned:
+
+    >>> DiagonalOf(MatrixSymbol('x', n, m)).diagonal_length is None
+    True
+
+    """
+    arg = property(lambda self: self.args[0])
+    @property
+    def shape(self):
+        r, c = self.arg.shape
+        if r.is_Integer and c.is_Integer:
+            m = min(r, c)
+        elif r.is_Integer and not c.is_Integer:
+            m = r
+        elif c.is_Integer and not r.is_Integer:
+            m = c
+        elif r == c:
+            m = r
+        else:
+            try:
+                m = min(r, c)
+            except TypeError:
+                m = None
+        return m, S.One
+
+    @property
+    def diagonal_length(self):
+        return self.shape[0]
+
+    def _entry(self, i, j, **kwargs):
+        return self.arg._entry(i, i, **kwargs)
+
+
+class DiagMatrix(MatrixExpr):
+    """
+    Turn a vector into a diagonal matrix.
+    """
+    def __new__(cls, vector):
+        vector = _sympify(vector)
+        obj = MatrixExpr.__new__(cls, vector)
+        shape = vector.shape
+        dim = shape[1] if shape[0] == 1 else shape[0]
+        if vector.shape[0] != 1:
+            obj._iscolumn = True
+        else:
+            obj._iscolumn = False
+        obj._shape = (dim, dim)
+        obj._vector = vector
+        return obj
+
+    @property
+    def shape(self):
+        return self._shape
+
+    def _entry(self, i, j, **kwargs):
+        if self._iscolumn:
+            result = self._vector._entry(i, 0, **kwargs)
+        else:
+            result = self._vector._entry(0, j, **kwargs)
+        if i != j:
+            result *= KroneckerDelta(i, j)
+        return result
+
+    def _eval_transpose(self):
+        return self
+
+    def as_explicit(self):
+        from sympy.matrices.dense import diag
+        return diag(*list(self._vector.as_explicit()))
+
+    def doit(self, **hints):
+        from sympy.assumptions import ask, Q
+        from sympy.matrices.expressions.matmul import MatMul
+        from sympy.matrices.expressions.transpose import Transpose
+        from sympy.matrices.dense import eye
+        from sympy.matrices.matrixbase import MatrixBase
+        vector = self._vector
+        # This accounts for shape (1, 1) and identity matrices, among others:
+        if ask(Q.diagonal(vector)):
+            return vector
+        if isinstance(vector, MatrixBase):
+            ret = eye(max(vector.shape))
+            for i in range(ret.shape[0]):
+                ret[i, i] = vector[i]
+            return type(vector)(ret)
+        if vector.is_MatMul:
+            matrices = [arg for arg in vector.args if arg.is_Matrix]
+            scalars = [arg for arg in vector.args if arg not in matrices]
+            if scalars:
+                return Mul.fromiter(scalars)*DiagMatrix(MatMul.fromiter(matrices).doit()).doit()
+        if isinstance(vector, Transpose):
+            vector = vector.arg
+        return DiagMatrix(vector)
+
+
+def diagonalize_vector(vector):
+    return DiagMatrix(vector).doit()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/dotproduct.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/dotproduct.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a413f8c79a221505f0c082d7f19f78597a2befc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/dotproduct.py
@@ -0,0 +1,55 @@
+from sympy.core import Basic, Expr
+from sympy.core.sympify import _sympify
+from sympy.matrices.expressions.transpose import transpose
+
+
+class DotProduct(Expr):
+    """
+    Dot product of vector matrices
+
+    The input should be two 1 x n or n x 1 matrices. The output represents the
+    scalar dotproduct.
+
+    This is similar to using MatrixElement and MatMul, except DotProduct does
+    not require that one vector to be a row vector and the other vector to be
+    a column vector.
+
+    >>> from sympy import MatrixSymbol, DotProduct
+    >>> A = MatrixSymbol('A', 1, 3)
+    >>> B = MatrixSymbol('B', 1, 3)
+    >>> DotProduct(A, B)
+    DotProduct(A, B)
+    >>> DotProduct(A, B).doit()
+    A[0, 0]*B[0, 0] + A[0, 1]*B[0, 1] + A[0, 2]*B[0, 2]
+    """
+
+    def __new__(cls, arg1, arg2):
+        arg1, arg2 = _sympify((arg1, arg2))
+
+        if not arg1.is_Matrix:
+            raise TypeError("Argument 1 of DotProduct is not a matrix")
+        if not arg2.is_Matrix:
+            raise TypeError("Argument 2 of DotProduct is not a matrix")
+        if not (1 in arg1.shape):
+            raise TypeError("Argument 1 of DotProduct is not a vector")
+        if not (1 in arg2.shape):
+            raise TypeError("Argument 2 of DotProduct is not a vector")
+
+        if set(arg1.shape) != set(arg2.shape):
+            raise TypeError("DotProduct arguments are not the same length")
+
+        return Basic.__new__(cls, arg1, arg2)
+
+    def doit(self, expand=False, **hints):
+        if self.args[0].shape == self.args[1].shape:
+            if self.args[0].shape[0] == 1:
+                mul = self.args[0]*transpose(self.args[1])
+            else:
+                mul = transpose(self.args[0])*self.args[1]
+        else:
+            if self.args[0].shape[0] == 1:
+                mul = self.args[0]*self.args[1]
+            else:
+                mul = transpose(self.args[0])*transpose(self.args[1])
+
+        return mul[0]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/factorizations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/factorizations.py
new file mode 100644
index 0000000000000000000000000000000000000000..aff2bb81ecff99d8e733f282ac2dd187d76ce895
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/factorizations.py
@@ -0,0 +1,62 @@
+from sympy.matrices.expressions import MatrixExpr
+from sympy.assumptions.ask import Q
+
+class Factorization(MatrixExpr):
+    arg = property(lambda self: self.args[0])
+    shape = property(lambda self: self.arg.shape)  # type: ignore
+
+class LofLU(Factorization):
+    @property
+    def predicates(self):
+        return (Q.lower_triangular,)
+class UofLU(Factorization):
+    @property
+    def predicates(self):
+        return (Q.upper_triangular,)
+
+class LofCholesky(LofLU): pass
+class UofCholesky(UofLU): pass
+
+class QofQR(Factorization):
+    @property
+    def predicates(self):
+        return (Q.orthogonal,)
+class RofQR(Factorization):
+    @property
+    def predicates(self):
+        return (Q.upper_triangular,)
+
+class EigenVectors(Factorization):
+    @property
+    def predicates(self):
+        return (Q.orthogonal,)
+class EigenValues(Factorization):
+    @property
+    def predicates(self):
+        return (Q.diagonal,)
+
+class UofSVD(Factorization):
+    @property
+    def predicates(self):
+        return (Q.orthogonal,)
+class SofSVD(Factorization):
+    @property
+    def predicates(self):
+        return (Q.diagonal,)
+class VofSVD(Factorization):
+    @property
+    def predicates(self):
+        return (Q.orthogonal,)
+
+
+def lu(expr):
+    return LofLU(expr), UofLU(expr)
+
+def qr(expr):
+    return QofQR(expr), RofQR(expr)
+
+def eig(expr):
+    return EigenValues(expr), EigenVectors(expr)
+
+def svd(expr):
+    return UofSVD(expr), SofSVD(expr), VofSVD(expr)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/fourier.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/fourier.py
new file mode 100644
index 0000000000000000000000000000000000000000..5fa9222c2a9b218f42636267235d5dd44c25f8bb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/fourier.py
@@ -0,0 +1,91 @@
+from sympy.core.sympify import _sympify
+from sympy.matrices.expressions import MatrixExpr
+from sympy.core.numbers import I
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+
+
+class DFT(MatrixExpr):
+    r"""
+    Returns a discrete Fourier transform matrix. The matrix is scaled
+    with :math:`\frac{1}{\sqrt{n}}` so that it is unitary.
+
+    Parameters
+    ==========
+
+    n : integer or Symbol
+        Size of the transform.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import n
+    >>> from sympy.matrices.expressions.fourier import DFT
+    >>> DFT(3)
+    DFT(3)
+    >>> DFT(3).as_explicit()
+    Matrix([
+    [sqrt(3)/3,                sqrt(3)/3,                sqrt(3)/3],
+    [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3,  sqrt(3)*exp(2*I*pi/3)/3],
+    [sqrt(3)/3,  sqrt(3)*exp(2*I*pi/3)/3, sqrt(3)*exp(-2*I*pi/3)/3]])
+    >>> DFT(n).shape
+    (n, n)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/DFT_matrix
+
+    """
+
+    def __new__(cls, n):
+        n = _sympify(n)
+        cls._check_dim(n)
+
+        obj = super().__new__(cls, n)
+        return obj
+
+    n = property(lambda self: self.args[0])  # type: ignore
+    shape = property(lambda self: (self.n, self.n))  # type: ignore
+
+    def _entry(self, i, j, **kwargs):
+        w = exp(-2*S.Pi*I/self.n)
+        return w**(i*j) / sqrt(self.n)
+
+    def _eval_inverse(self):
+        return IDFT(self.n)
+
+
+class IDFT(DFT):
+    r"""
+    Returns an inverse discrete Fourier transform matrix. The matrix is scaled
+    with :math:`\frac{1}{\sqrt{n}}` so that it is unitary.
+
+    Parameters
+    ==========
+
+    n : integer or Symbol
+        Size of the transform
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.expressions.fourier import DFT, IDFT
+    >>> IDFT(3)
+    IDFT(3)
+    >>> IDFT(4)*DFT(4)
+    I
+
+    See Also
+    ========
+
+    DFT
+
+    """
+    def _entry(self, i, j, **kwargs):
+        w = exp(-2*S.Pi*I/self.n)
+        return w**(-i*j) / sqrt(self.n)
+
+    def _eval_inverse(self):
+        return DFT(self.n)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/funcmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/funcmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..91106edb489b73ac9dd6cb94adc508c0db75d3a5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/funcmatrix.py
@@ -0,0 +1,118 @@
+from .matexpr import MatrixExpr
+from sympy.core.function import FunctionClass, Lambda
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import _sympify, sympify
+from sympy.matrices import Matrix
+from sympy.functions.elementary.complexes import re, im
+
+
+class FunctionMatrix(MatrixExpr):
+    """Represents a matrix using a function (``Lambda``) which gives
+    outputs according to the coordinates of each matrix entries.
+
+    Parameters
+    ==========
+
+    rows : nonnegative integer. Can be symbolic.
+
+    cols : nonnegative integer. Can be symbolic.
+
+    lamda : Function, Lambda or str
+        If it is a SymPy ``Function`` or ``Lambda`` instance,
+        it should be able to accept two arguments which represents the
+        matrix coordinates.
+
+        If it is a pure string containing Python ``lambda`` semantics,
+        it is interpreted by the SymPy parser and casted into a SymPy
+        ``Lambda`` instance.
+
+    Examples
+    ========
+
+    Creating a ``FunctionMatrix`` from ``Lambda``:
+
+    >>> from sympy import FunctionMatrix, symbols, Lambda, MatPow
+    >>> i, j, n, m = symbols('i,j,n,m')
+    >>> FunctionMatrix(n, m, Lambda((i, j), i + j))
+    FunctionMatrix(n, m, Lambda((i, j), i + j))
+
+    Creating a ``FunctionMatrix`` from a SymPy function:
+
+    >>> from sympy import KroneckerDelta
+    >>> X = FunctionMatrix(3, 3, KroneckerDelta)
+    >>> X.as_explicit()
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+
+    Creating a ``FunctionMatrix`` from a SymPy undefined function:
+
+    >>> from sympy import Function
+    >>> f = Function('f')
+    >>> X = FunctionMatrix(3, 3, f)
+    >>> X.as_explicit()
+    Matrix([
+    [f(0, 0), f(0, 1), f(0, 2)],
+    [f(1, 0), f(1, 1), f(1, 2)],
+    [f(2, 0), f(2, 1), f(2, 2)]])
+
+    Creating a ``FunctionMatrix`` from Python ``lambda``:
+
+    >>> FunctionMatrix(n, m, 'lambda i, j: i + j')
+    FunctionMatrix(n, m, Lambda((i, j), i + j))
+
+    Example of lazy evaluation of matrix product:
+
+    >>> Y = FunctionMatrix(1000, 1000, Lambda((i, j), i + j))
+    >>> isinstance(Y*Y, MatPow) # this is an expression object
+    True
+    >>> (Y**2)[10,10] # So this is evaluated lazily
+    342923500
+
+    Notes
+    =====
+
+    This class provides an alternative way to represent an extremely
+    dense matrix with entries in some form of a sequence, in a most
+    sparse way.
+    """
+    def __new__(cls, rows, cols, lamda):
+        rows, cols = _sympify(rows), _sympify(cols)
+        cls._check_dim(rows)
+        cls._check_dim(cols)
+
+        lamda = sympify(lamda)
+        if not isinstance(lamda, (FunctionClass, Lambda)):
+            raise ValueError(
+                "{} should be compatible with SymPy function classes."
+                .format(lamda))
+
+        if 2 not in lamda.nargs:
+            raise ValueError(
+                '{} should be able to accept 2 arguments.'.format(lamda))
+
+        if not isinstance(lamda, Lambda):
+            i, j = Dummy('i'), Dummy('j')
+            lamda = Lambda((i, j), lamda(i, j))
+
+        return super().__new__(cls, rows, cols, lamda)
+
+    @property
+    def shape(self):
+        return self.args[0:2]
+
+    @property
+    def lamda(self):
+        return self.args[2]
+
+    def _entry(self, i, j, **kwargs):
+        return self.lamda(i, j)
+
+    def _eval_trace(self):
+        from sympy.matrices.expressions.trace import Trace
+        from sympy.concrete.summations import Sum
+        return Trace(self).rewrite(Sum).doit()
+
+    def _eval_as_real_imag(self):
+        return (re(Matrix(self)), im(Matrix(self)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/hadamard.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/hadamard.py
new file mode 100644
index 0000000000000000000000000000000000000000..38c9033ebea3a7bfc569223978dc6ef3890206cf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/hadamard.py
@@ -0,0 +1,464 @@
+from collections import Counter
+
+from sympy.core import Mul, sympify
+from sympy.core.add import Add
+from sympy.core.expr import ExprBuilder
+from sympy.core.sorting import default_sort_key
+from sympy.functions.elementary.exponential import log
+from sympy.matrices.expressions.matexpr import MatrixExpr
+from sympy.matrices.expressions._shape import validate_matadd_integer as validate
+from sympy.matrices.expressions.special import ZeroMatrix, OneMatrix
+from sympy.strategies import (
+    unpack, flatten, condition, exhaust, rm_id, sort
+)
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+
+def hadamard_product(*matrices):
+    """
+    Return the elementwise (aka Hadamard) product of matrices.
+
+    Examples
+    ========
+
+    >>> from sympy import hadamard_product, MatrixSymbol
+    >>> A = MatrixSymbol('A', 2, 3)
+    >>> B = MatrixSymbol('B', 2, 3)
+    >>> hadamard_product(A)
+    A
+    >>> hadamard_product(A, B)
+    HadamardProduct(A, B)
+    >>> hadamard_product(A, B)[0, 1]
+    A[0, 1]*B[0, 1]
+    """
+    if not matrices:
+        raise TypeError("Empty Hadamard product is undefined")
+    if len(matrices) == 1:
+        return matrices[0]
+    return HadamardProduct(*matrices).doit()
+
+
+class HadamardProduct(MatrixExpr):
+    """
+    Elementwise product of matrix expressions
+
+    Examples
+    ========
+
+    Hadamard product for matrix symbols:
+
+    >>> from sympy import hadamard_product, HadamardProduct, MatrixSymbol
+    >>> A = MatrixSymbol('A', 5, 5)
+    >>> B = MatrixSymbol('B', 5, 5)
+    >>> isinstance(hadamard_product(A, B), HadamardProduct)
+    True
+
+    Notes
+    =====
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the product, use the function
+    ``hadamard_product()`` or ``HadamardProduct.doit``
+    """
+    is_HadamardProduct = True
+
+    def __new__(cls, *args, evaluate=False, check=None):
+        args = list(map(sympify, args))
+        if len(args) == 0:
+            # We currently don't have a way to support one-matrices of generic dimensions:
+            raise ValueError("HadamardProduct needs at least one argument")
+
+        if not all(isinstance(arg, MatrixExpr) for arg in args):
+            raise TypeError("Mix of Matrix and Scalar symbols")
+
+        if check is not None:
+            sympy_deprecation_warning(
+                "Passing check to HadamardProduct is deprecated and the check argument will be removed in a future version.",
+                deprecated_since_version="1.11",
+                active_deprecations_target='remove-check-argument-from-matrix-operations')
+
+        if check is not False:
+            validate(*args)
+
+        obj = super().__new__(cls, *args)
+        if evaluate:
+            obj = obj.doit(deep=False)
+        return obj
+
+    @property
+    def shape(self):
+        return self.args[0].shape
+
+    def _entry(self, i, j, **kwargs):
+        return Mul(*[arg._entry(i, j, **kwargs) for arg in self.args])
+
+    def _eval_transpose(self):
+        from sympy.matrices.expressions.transpose import transpose
+        return HadamardProduct(*list(map(transpose, self.args)))
+
+    def doit(self, **hints):
+        expr = self.func(*(i.doit(**hints) for i in self.args))
+        # Check for explicit matrices:
+        from sympy.matrices.matrixbase import MatrixBase
+        from sympy.matrices.immutable import ImmutableMatrix
+
+        explicit = [i for i in expr.args if isinstance(i, MatrixBase)]
+        if explicit:
+            remainder = [i for i in expr.args if i not in explicit]
+            expl_mat = ImmutableMatrix([
+                Mul.fromiter(i) for i in zip(*explicit)
+            ]).reshape(*self.shape)
+            expr = HadamardProduct(*([expl_mat] + remainder))
+
+        return canonicalize(expr)
+
+    def _eval_derivative(self, x):
+        terms = []
+        args = list(self.args)
+        for i in range(len(args)):
+            factors = args[:i] + [args[i].diff(x)] + args[i+1:]
+            terms.append(hadamard_product(*factors))
+        return Add.fromiter(terms)
+
+    def _eval_derivative_matrix_lines(self, x):
+        from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal
+        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+        from sympy.matrices.expressions.matexpr import _make_matrix
+
+        with_x_ind = [i for i, arg in enumerate(self.args) if arg.has(x)]
+        lines = []
+        for ind in with_x_ind:
+            left_args = self.args[:ind]
+            right_args = self.args[ind+1:]
+
+            d = self.args[ind]._eval_derivative_matrix_lines(x)
+            hadam = hadamard_product(*(right_args + left_args))
+            diagonal = [(0, 2), (3, 4)]
+            diagonal = [e for j, e in enumerate(diagonal) if self.shape[j] != 1]
+            for i in d:
+                l1 = i._lines[i._first_line_index]
+                l2 = i._lines[i._second_line_index]
+                subexpr = ExprBuilder(
+                    ArrayDiagonal,
+                    [
+                        ExprBuilder(
+                            ArrayTensorProduct,
+                            [
+                                ExprBuilder(_make_matrix, [l1]),
+                                hadam,
+                                ExprBuilder(_make_matrix, [l2]),
+                            ]
+                        ),
+                    *diagonal],
+
+                )
+                i._first_pointer_parent = subexpr.args[0].args[0].args
+                i._first_pointer_index = 0
+                i._second_pointer_parent = subexpr.args[0].args[2].args
+                i._second_pointer_index = 0
+                i._lines = [subexpr]
+                lines.append(i)
+
+        return lines
+
+
+# TODO Implement algorithm for rewriting Hadamard product as diagonal matrix
+# if matmul identy matrix is multiplied.
+def canonicalize(x):
+    """Canonicalize the Hadamard product ``x`` with mathematical properties.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, HadamardProduct
+    >>> from sympy import OneMatrix, ZeroMatrix
+    >>> from sympy.matrices.expressions.hadamard import canonicalize
+    >>> from sympy import init_printing
+    >>> init_printing(use_unicode=False)
+
+    >>> A = MatrixSymbol('A', 2, 2)
+    >>> B = MatrixSymbol('B', 2, 2)
+    >>> C = MatrixSymbol('C', 2, 2)
+
+    Hadamard product associativity:
+
+    >>> X = HadamardProduct(A, HadamardProduct(B, C))
+    >>> X
+    A.*(B.*C)
+    >>> canonicalize(X)
+    A.*B.*C
+
+    Hadamard product commutativity:
+
+    >>> X = HadamardProduct(A, B)
+    >>> Y = HadamardProduct(B, A)
+    >>> X
+    A.*B
+    >>> Y
+    B.*A
+    >>> canonicalize(X)
+    A.*B
+    >>> canonicalize(Y)
+    A.*B
+
+    Hadamard product identity:
+
+    >>> X = HadamardProduct(A, OneMatrix(2, 2))
+    >>> X
+    A.*1
+    >>> canonicalize(X)
+    A
+
+    Absorbing element of Hadamard product:
+
+    >>> X = HadamardProduct(A, ZeroMatrix(2, 2))
+    >>> X
+    A.*0
+    >>> canonicalize(X)
+    0
+
+    Rewriting to Hadamard Power
+
+    >>> X = HadamardProduct(A, A, A)
+    >>> X
+    A.*A.*A
+    >>> canonicalize(X)
+     .3
+    A
+
+    Notes
+    =====
+
+    As the Hadamard product is associative, nested products can be flattened.
+
+    The Hadamard product is commutative so that factors can be sorted for
+    canonical form.
+
+    A matrix of only ones is an identity for Hadamard product,
+    so every matrices of only ones can be removed.
+
+    Any zero matrix will make the whole product a zero matrix.
+
+    Duplicate elements can be collected and rewritten as HadamardPower
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hadamard_product_(matrices)
+    """
+    # Associativity
+    rule = condition(
+            lambda x: isinstance(x, HadamardProduct),
+            flatten
+        )
+    fun = exhaust(rule)
+    x = fun(x)
+
+    # Identity
+    fun = condition(
+            lambda x: isinstance(x, HadamardProduct),
+            rm_id(lambda x: isinstance(x, OneMatrix))
+        )
+    x = fun(x)
+
+    # Absorbing by Zero Matrix
+    def absorb(x):
+        if any(isinstance(c, ZeroMatrix) for c in x.args):
+            return ZeroMatrix(*x.shape)
+        else:
+            return x
+    fun = condition(
+            lambda x: isinstance(x, HadamardProduct),
+            absorb
+        )
+    x = fun(x)
+
+    # Rewriting with HadamardPower
+    if isinstance(x, HadamardProduct):
+        tally = Counter(x.args)
+
+        new_arg = []
+        for base, exp in tally.items():
+            if exp == 1:
+                new_arg.append(base)
+            else:
+                new_arg.append(HadamardPower(base, exp))
+
+        x = HadamardProduct(*new_arg)
+
+    # Commutativity
+    fun = condition(
+            lambda x: isinstance(x, HadamardProduct),
+            sort(default_sort_key)
+        )
+    x = fun(x)
+
+    # Unpacking
+    x = unpack(x)
+    return x
+
+
+def hadamard_power(base, exp):
+    base = sympify(base)
+    exp = sympify(exp)
+    if exp == 1:
+        return base
+    if not base.is_Matrix:
+        return base**exp
+    if exp.is_Matrix:
+        raise ValueError("cannot raise expression to a matrix")
+    return HadamardPower(base, exp)
+
+
+class HadamardPower(MatrixExpr):
+    r"""
+    Elementwise power of matrix expressions
+
+    Parameters
+    ==========
+
+    base : scalar or matrix
+
+    exp : scalar or matrix
+
+    Notes
+    =====
+
+    There are four definitions for the hadamard power which can be used.
+    Let's consider `A, B` as `(m, n)` matrices, and `a, b` as scalars.
+
+    Matrix raised to a scalar exponent:
+
+    .. math::
+        A^{\circ b} = \begin{bmatrix}
+        A_{0, 0}^b   & A_{0, 1}^b   & \cdots & A_{0, n-1}^b   \\
+        A_{1, 0}^b   & A_{1, 1}^b   & \cdots & A_{1, n-1}^b   \\
+        \vdots       & \vdots       & \ddots & \vdots         \\
+        A_{m-1, 0}^b & A_{m-1, 1}^b & \cdots & A_{m-1, n-1}^b
+        \end{bmatrix}
+
+    Scalar raised to a matrix exponent:
+
+    .. math::
+        a^{\circ B} = \begin{bmatrix}
+        a^{B_{0, 0}}   & a^{B_{0, 1}}   & \cdots & a^{B_{0, n-1}}   \\
+        a^{B_{1, 0}}   & a^{B_{1, 1}}   & \cdots & a^{B_{1, n-1}}   \\
+        \vdots         & \vdots         & \ddots & \vdots           \\
+        a^{B_{m-1, 0}} & a^{B_{m-1, 1}} & \cdots & a^{B_{m-1, n-1}}
+        \end{bmatrix}
+
+    Matrix raised to a matrix exponent:
+
+    .. math::
+        A^{\circ B} = \begin{bmatrix}
+        A_{0, 0}^{B_{0, 0}}     & A_{0, 1}^{B_{0, 1}}     &
+        \cdots & A_{0, n-1}^{B_{0, n-1}}     \\
+        A_{1, 0}^{B_{1, 0}}     & A_{1, 1}^{B_{1, 1}}     &
+        \cdots & A_{1, n-1}^{B_{1, n-1}}     \\
+        \vdots                  & \vdots                  &
+        \ddots & \vdots                      \\
+        A_{m-1, 0}^{B_{m-1, 0}} & A_{m-1, 1}^{B_{m-1, 1}} &
+        \cdots & A_{m-1, n-1}^{B_{m-1, n-1}}
+        \end{bmatrix}
+
+    Scalar raised to a scalar exponent:
+
+    .. math::
+        a^{\circ b} = a^b
+    """
+
+    def __new__(cls, base, exp):
+        base = sympify(base)
+        exp = sympify(exp)
+
+        if base.is_scalar and exp.is_scalar:
+            return base ** exp
+
+        if isinstance(base, MatrixExpr) and isinstance(exp, MatrixExpr):
+            validate(base, exp)
+
+        obj = super().__new__(cls, base, exp)
+        return obj
+
+    @property
+    def base(self):
+        return self._args[0]
+
+    @property
+    def exp(self):
+        return self._args[1]
+
+    @property
+    def shape(self):
+        if self.base.is_Matrix:
+            return self.base.shape
+        return self.exp.shape
+
+    def _entry(self, i, j, **kwargs):
+        base = self.base
+        exp = self.exp
+
+        if base.is_Matrix:
+            a = base._entry(i, j, **kwargs)
+        elif base.is_scalar:
+            a = base
+        else:
+            raise ValueError(
+                'The base {} must be a scalar or a matrix.'.format(base))
+
+        if exp.is_Matrix:
+            b = exp._entry(i, j, **kwargs)
+        elif exp.is_scalar:
+            b = exp
+        else:
+            raise ValueError(
+                'The exponent {} must be a scalar or a matrix.'.format(exp))
+
+        return a ** b
+
+    def _eval_transpose(self):
+        from sympy.matrices.expressions.transpose import transpose
+        return HadamardPower(transpose(self.base), self.exp)
+
+    def _eval_derivative(self, x):
+        dexp = self.exp.diff(x)
+        logbase = self.base.applyfunc(log)
+        dlbase = logbase.diff(x)
+        return hadamard_product(
+            dexp*logbase + self.exp*dlbase,
+            self
+        )
+
+    def _eval_derivative_matrix_lines(self, x):
+        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+        from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal
+        from sympy.matrices.expressions.matexpr import _make_matrix
+
+        lr = self.base._eval_derivative_matrix_lines(x)
+        for i in lr:
+            diagonal = [(1, 2), (3, 4)]
+            diagonal = [e for j, e in enumerate(diagonal) if self.base.shape[j] != 1]
+            l1 = i._lines[i._first_line_index]
+            l2 = i._lines[i._second_line_index]
+            subexpr = ExprBuilder(
+                ArrayDiagonal,
+                [
+                    ExprBuilder(
+                        ArrayTensorProduct,
+                        [
+                            ExprBuilder(_make_matrix, [l1]),
+                            self.exp*hadamard_power(self.base, self.exp-1),
+                            ExprBuilder(_make_matrix, [l2]),
+                        ]
+                    ),
+                *diagonal],
+                validator=ArrayDiagonal._validate
+            )
+            i._first_pointer_parent = subexpr.args[0].args[0].args
+            i._first_pointer_index = 0
+            i._first_line_index = 0
+            i._second_pointer_parent = subexpr.args[0].args[2].args
+            i._second_pointer_index = 0
+            i._second_line_index = 0
+            i._lines = [subexpr]
+        return lr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/inverse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/inverse.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfc3feccd7126a761f18f23599eed9413c86a9e5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/inverse.py
@@ -0,0 +1,112 @@
+from sympy.core.sympify import _sympify
+from sympy.core import S, Basic
+
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.expressions.matpow import MatPow
+
+
+class Inverse(MatPow):
+    """
+    The multiplicative inverse of a matrix expression
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the inverse, use the ``.inverse()``
+    method of matrices.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Inverse
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> B = MatrixSymbol('B', 3, 3)
+    >>> Inverse(A)
+    A**(-1)
+    >>> A.inverse() == Inverse(A)
+    True
+    >>> (A*B).inverse()
+    B**(-1)*A**(-1)
+    >>> Inverse(A*B)
+    (A*B)**(-1)
+
+    """
+    is_Inverse = True
+    exp = S.NegativeOne
+
+    def __new__(cls, mat, exp=S.NegativeOne):
+        # exp is there to make it consistent with
+        # inverse.func(*inverse.args) == inverse
+        mat = _sympify(mat)
+        exp = _sympify(exp)
+        if not mat.is_Matrix:
+            raise TypeError("mat should be a matrix")
+        if mat.is_square is False:
+            raise NonSquareMatrixError("Inverse of non-square matrix %s" % mat)
+        return Basic.__new__(cls, mat, exp)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    @property
+    def shape(self):
+        return self.arg.shape
+
+    def _eval_inverse(self):
+        return self.arg
+
+    def _eval_transpose(self):
+        return Inverse(self.arg.transpose())
+
+    def _eval_adjoint(self):
+        return Inverse(self.arg.adjoint())
+
+    def _eval_conjugate(self):
+        return Inverse(self.arg.conjugate())
+
+    def _eval_determinant(self):
+        from sympy.matrices.expressions.determinant import det
+        return 1/det(self.arg)
+
+    def doit(self, **hints):
+        if 'inv_expand' in hints and hints['inv_expand'] == False:
+            return self
+
+        arg = self.arg
+        if hints.get('deep', True):
+            arg = arg.doit(**hints)
+
+        return arg.inverse()
+
+    def _eval_derivative_matrix_lines(self, x):
+        arg = self.args[0]
+        lines = arg._eval_derivative_matrix_lines(x)
+        for line in lines:
+            line.first_pointer *= -self.T
+            line.second_pointer *= self
+        return lines
+
+
+from sympy.assumptions.ask import ask, Q
+from sympy.assumptions.refine import handlers_dict
+
+
+def refine_Inverse(expr, assumptions):
+    """
+    >>> from sympy import MatrixSymbol, Q, assuming, refine
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> X.I
+    X**(-1)
+    >>> with assuming(Q.orthogonal(X)):
+    ...     print(refine(X.I))
+    X.T
+    """
+    if ask(Q.orthogonal(expr), assumptions):
+        return expr.arg.T
+    elif ask(Q.unitary(expr), assumptions):
+        return expr.arg.conjugate()
+    elif ask(Q.singular(expr), assumptions):
+        raise ValueError("Inverse of singular matrix %s" % expr.arg)
+
+    return expr
+
+handlers_dict['Inverse'] = refine_Inverse
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/kronecker.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/kronecker.py
new file mode 100644
index 0000000000000000000000000000000000000000..1dd175cb0d500af3e786e2d0dbf6b010947840b4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/kronecker.py
@@ -0,0 +1,434 @@
+"""Implementation of the Kronecker product"""
+from functools import reduce
+from math import prod
+
+from sympy.core import Mul, sympify
+from sympy.functions import adjoint
+from sympy.matrices.exceptions import ShapeError
+from sympy.matrices.expressions.matexpr import MatrixExpr
+from sympy.matrices.expressions.transpose import transpose
+from sympy.matrices.expressions.special import Identity
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.strategies import (
+    canon, condition, distribute, do_one, exhaust, flatten, typed, unpack)
+from sympy.strategies.traverse import bottom_up
+from sympy.utilities import sift
+
+from .matadd import MatAdd
+from .matmul import MatMul
+from .matpow import MatPow
+
+
+def kronecker_product(*matrices):
+    """
+    The Kronecker product of two or more arguments.
+
+    This computes the explicit Kronecker product for subclasses of
+    ``MatrixBase`` i.e. explicit matrices. Otherwise, a symbolic
+    ``KroneckerProduct`` object is returned.
+
+
+    Examples
+    ========
+
+    For ``MatrixSymbol`` arguments a ``KroneckerProduct`` object is returned.
+    Elements of this matrix can be obtained by indexing, or for MatrixSymbols
+    with known dimension the explicit matrix can be obtained with
+    ``.as_explicit()``
+
+    >>> from sympy import kronecker_product, MatrixSymbol
+    >>> A = MatrixSymbol('A', 2, 2)
+    >>> B = MatrixSymbol('B', 2, 2)
+    >>> kronecker_product(A)
+    A
+    >>> kronecker_product(A, B)
+    KroneckerProduct(A, B)
+    >>> kronecker_product(A, B)[0, 1]
+    A[0, 0]*B[0, 1]
+    >>> kronecker_product(A, B).as_explicit()
+    Matrix([
+        [A[0, 0]*B[0, 0], A[0, 0]*B[0, 1], A[0, 1]*B[0, 0], A[0, 1]*B[0, 1]],
+        [A[0, 0]*B[1, 0], A[0, 0]*B[1, 1], A[0, 1]*B[1, 0], A[0, 1]*B[1, 1]],
+        [A[1, 0]*B[0, 0], A[1, 0]*B[0, 1], A[1, 1]*B[0, 0], A[1, 1]*B[0, 1]],
+        [A[1, 0]*B[1, 0], A[1, 0]*B[1, 1], A[1, 1]*B[1, 0], A[1, 1]*B[1, 1]]])
+
+    For explicit matrices the Kronecker product is returned as a Matrix
+
+    >>> from sympy import Matrix, kronecker_product
+    >>> sigma_x = Matrix([
+    ... [0, 1],
+    ... [1, 0]])
+    ...
+    >>> Isigma_y = Matrix([
+    ... [0, 1],
+    ... [-1, 0]])
+    ...
+    >>> kronecker_product(sigma_x, Isigma_y)
+    Matrix([
+    [ 0, 0,  0, 1],
+    [ 0, 0, -1, 0],
+    [ 0, 1,  0, 0],
+    [-1, 0,  0, 0]])
+
+    See Also
+    ========
+        KroneckerProduct
+
+    """
+    if not matrices:
+        raise TypeError("Empty Kronecker product is undefined")
+    if len(matrices) == 1:
+        return matrices[0]
+    else:
+        return KroneckerProduct(*matrices).doit()
+
+
+class KroneckerProduct(MatrixExpr):
+    """
+    The Kronecker product of two or more arguments.
+
+    The Kronecker product is a non-commutative product of matrices.
+    Given two matrices of dimension (m, n) and (s, t) it produces a matrix
+    of dimension (m s, n t).
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the product, use the function
+    ``kronecker_product()`` or call the ``.doit()`` or  ``.as_explicit()``
+    methods.
+
+    >>> from sympy import KroneckerProduct, MatrixSymbol
+    >>> A = MatrixSymbol('A', 5, 5)
+    >>> B = MatrixSymbol('B', 5, 5)
+    >>> isinstance(KroneckerProduct(A, B), KroneckerProduct)
+    True
+    """
+    is_KroneckerProduct = True
+
+    def __new__(cls, *args, check=True):
+        args = list(map(sympify, args))
+        if all(a.is_Identity for a in args):
+            ret = Identity(prod(a.rows for a in args))
+            if all(isinstance(a, MatrixBase) for a in args):
+                return ret.as_explicit()
+            else:
+                return ret
+
+        if check:
+            validate(*args)
+        return super().__new__(cls, *args)
+
+    @property
+    def shape(self):
+        rows, cols = self.args[0].shape
+        for mat in self.args[1:]:
+            rows *= mat.rows
+            cols *= mat.cols
+        return (rows, cols)
+
+    def _entry(self, i, j, **kwargs):
+        result = 1
+        for mat in reversed(self.args):
+            i, m = divmod(i, mat.rows)
+            j, n = divmod(j, mat.cols)
+            result *= mat[m, n]
+        return result
+
+    def _eval_adjoint(self):
+        return KroneckerProduct(*list(map(adjoint, self.args))).doit()
+
+    def _eval_conjugate(self):
+        return KroneckerProduct(*[a.conjugate() for a in self.args]).doit()
+
+    def _eval_transpose(self):
+        return KroneckerProduct(*list(map(transpose, self.args))).doit()
+
+    def _eval_trace(self):
+        from .trace import trace
+        return Mul(*[trace(a) for a in self.args])
+
+    def _eval_determinant(self):
+        from .determinant import det, Determinant
+        if not all(a.is_square for a in self.args):
+            return Determinant(self)
+
+        m = self.rows
+        return Mul(*[det(a)**(m/a.rows) for a in self.args])
+
+    def _eval_inverse(self):
+        try:
+            return KroneckerProduct(*[a.inverse() for a in self.args])
+        except ShapeError:
+            from sympy.matrices.expressions.inverse import Inverse
+            return Inverse(self)
+
+    def structurally_equal(self, other):
+        '''Determine whether two matrices have the same Kronecker product structure
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerProduct, MatrixSymbol, symbols
+        >>> m, n = symbols(r'm, n', integer=True)
+        >>> A = MatrixSymbol('A', m, m)
+        >>> B = MatrixSymbol('B', n, n)
+        >>> C = MatrixSymbol('C', m, m)
+        >>> D = MatrixSymbol('D', n, n)
+        >>> KroneckerProduct(A, B).structurally_equal(KroneckerProduct(C, D))
+        True
+        >>> KroneckerProduct(A, B).structurally_equal(KroneckerProduct(D, C))
+        False
+        >>> KroneckerProduct(A, B).structurally_equal(C)
+        False
+        '''
+        # Inspired by BlockMatrix
+        return (isinstance(other, KroneckerProduct)
+                and self.shape == other.shape
+                and len(self.args) == len(other.args)
+                and all(a.shape == b.shape for (a, b) in zip(self.args, other.args)))
+
+    def has_matching_shape(self, other):
+        '''Determine whether two matrices have the appropriate structure to bring matrix
+        multiplication inside the KroneckerProdut
+
+        Examples
+        ========
+        >>> from sympy import KroneckerProduct, MatrixSymbol, symbols
+        >>> m, n = symbols(r'm, n', integer=True)
+        >>> A = MatrixSymbol('A', m, n)
+        >>> B = MatrixSymbol('B', n, m)
+        >>> KroneckerProduct(A, B).has_matching_shape(KroneckerProduct(B, A))
+        True
+        >>> KroneckerProduct(A, B).has_matching_shape(KroneckerProduct(A, B))
+        False
+        >>> KroneckerProduct(A, B).has_matching_shape(A)
+        False
+        '''
+        return (isinstance(other, KroneckerProduct)
+                and self.cols == other.rows
+                and len(self.args) == len(other.args)
+                and all(a.cols == b.rows for (a, b) in zip(self.args, other.args)))
+
+    def _eval_expand_kroneckerproduct(self, **hints):
+        return flatten(canon(typed({KroneckerProduct: distribute(KroneckerProduct, MatAdd)}))(self))
+
+    def _kronecker_add(self, other):
+        if self.structurally_equal(other):
+            return self.__class__(*[a + b for (a, b) in zip(self.args, other.args)])
+        else:
+            return self + other
+
+    def _kronecker_mul(self, other):
+        if self.has_matching_shape(other):
+            return self.__class__(*[a*b for (a, b) in zip(self.args, other.args)])
+        else:
+            return self * other
+
+    def doit(self, **hints):
+        deep = hints.get('deep', True)
+        if deep:
+            args = [arg.doit(**hints) for arg in self.args]
+        else:
+            args = self.args
+        return canonicalize(KroneckerProduct(*args))
+
+
+def validate(*args):
+    if not all(arg.is_Matrix for arg in args):
+        raise TypeError("Mix of Matrix and Scalar symbols")
+
+
+# rules
+
+def extract_commutative(kron):
+    c_part = []
+    nc_part = []
+    for arg in kron.args:
+        c, nc = arg.args_cnc()
+        c_part.extend(c)
+        nc_part.append(Mul._from_args(nc))
+
+    c_part = Mul(*c_part)
+    if c_part != 1:
+        return c_part*KroneckerProduct(*nc_part)
+    return kron
+
+
+def matrix_kronecker_product(*matrices):
+    """Compute the Kronecker product of a sequence of SymPy Matrices.
+
+    This is the standard Kronecker product of matrices [1].
+
+    Parameters
+    ==========
+
+    matrices : tuple of MatrixBase instances
+        The matrices to take the Kronecker product of.
+
+    Returns
+    =======
+
+    matrix : MatrixBase
+        The Kronecker product matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.matrices.expressions.kronecker import (
+    ... matrix_kronecker_product)
+
+    >>> m1 = Matrix([[1,2],[3,4]])
+    >>> m2 = Matrix([[1,0],[0,1]])
+    >>> matrix_kronecker_product(m1, m2)
+    Matrix([
+    [1, 0, 2, 0],
+    [0, 1, 0, 2],
+    [3, 0, 4, 0],
+    [0, 3, 0, 4]])
+    >>> matrix_kronecker_product(m2, m1)
+    Matrix([
+    [1, 2, 0, 0],
+    [3, 4, 0, 0],
+    [0, 0, 1, 2],
+    [0, 0, 3, 4]])
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Kronecker_product
+    """
+    # Make sure we have a sequence of Matrices
+    if not all(isinstance(m, MatrixBase) for m in matrices):
+        raise TypeError(
+            'Sequence of Matrices expected, got: %s' % repr(matrices)
+        )
+
+    # Pull out the first element in the product.
+    matrix_expansion = matrices[-1]
+    # Do the kronecker product working from right to left.
+    for mat in reversed(matrices[:-1]):
+        rows = mat.rows
+        cols = mat.cols
+        # Go through each row appending kronecker product to.
+        # running matrix_expansion.
+        for i in range(rows):
+            start = matrix_expansion*mat[i*cols]
+            # Go through each column joining each item
+            for j in range(cols - 1):
+                start = start.row_join(
+                    matrix_expansion*mat[i*cols + j + 1]
+                )
+            # If this is the first element, make it the start of the
+            # new row.
+            if i == 0:
+                next = start
+            else:
+                next = next.col_join(start)
+        matrix_expansion = next
+
+    MatrixClass = max(matrices, key=lambda M: M._class_priority).__class__
+    if isinstance(matrix_expansion, MatrixClass):
+        return matrix_expansion
+    else:
+        return MatrixClass(matrix_expansion)
+
+
+def explicit_kronecker_product(kron):
+    # Make sure we have a sequence of Matrices
+    if not all(isinstance(m, MatrixBase) for m in kron.args):
+        return kron
+
+    return matrix_kronecker_product(*kron.args)
+
+
+rules = (unpack,
+         explicit_kronecker_product,
+         flatten,
+         extract_commutative)
+
+canonicalize = exhaust(condition(lambda x: isinstance(x, KroneckerProduct),
+                                 do_one(*rules)))
+
+
+def _kronecker_dims_key(expr):
+    if isinstance(expr, KroneckerProduct):
+        return tuple(a.shape for a in expr.args)
+    else:
+        return (0,)
+
+
+def kronecker_mat_add(expr):
+    args = sift(expr.args, _kronecker_dims_key)
+    nonkrons = args.pop((0,), None)
+    if not args:
+        return expr
+
+    krons = [reduce(lambda x, y: x._kronecker_add(y), group)
+             for group in args.values()]
+
+    if not nonkrons:
+        return MatAdd(*krons)
+    else:
+        return MatAdd(*krons) + nonkrons
+
+
+def kronecker_mat_mul(expr):
+    # modified from block matrix code
+    factor, matrices = expr.as_coeff_matrices()
+
+    i = 0
+    while i < len(matrices) - 1:
+        A, B = matrices[i:i+2]
+        if isinstance(A, KroneckerProduct) and isinstance(B, KroneckerProduct):
+            matrices[i] = A._kronecker_mul(B)
+            matrices.pop(i+1)
+        else:
+            i += 1
+
+    return factor*MatMul(*matrices)
+
+
+def kronecker_mat_pow(expr):
+    if isinstance(expr.base, KroneckerProduct) and all(a.is_square for a in expr.base.args):
+        return KroneckerProduct(*[MatPow(a, expr.exp) for a in expr.base.args])
+    else:
+        return expr
+
+
+def combine_kronecker(expr):
+    """Combine KronekeckerProduct with expression.
+
+    If possible write operations on KroneckerProducts of compatible shapes
+    as a single KroneckerProduct.
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.expressions import combine_kronecker
+    >>> from sympy import MatrixSymbol, KroneckerProduct, symbols
+    >>> m, n = symbols(r'm, n', integer=True)
+    >>> A = MatrixSymbol('A', m, n)
+    >>> B = MatrixSymbol('B', n, m)
+    >>> combine_kronecker(KroneckerProduct(A, B)*KroneckerProduct(B, A))
+    KroneckerProduct(A*B, B*A)
+    >>> combine_kronecker(KroneckerProduct(A, B)+KroneckerProduct(B.T, A.T))
+    KroneckerProduct(A + B.T, B + A.T)
+    >>> C = MatrixSymbol('C', n, n)
+    >>> D = MatrixSymbol('D', m, m)
+    >>> combine_kronecker(KroneckerProduct(C, D)**m)
+    KroneckerProduct(C**m, D**m)
+    """
+    def haskron(expr):
+        return isinstance(expr, MatrixExpr) and expr.has(KroneckerProduct)
+
+    rule = exhaust(
+        bottom_up(exhaust(condition(haskron, typed(
+            {MatAdd: kronecker_mat_add,
+             MatMul: kronecker_mat_mul,
+             MatPow: kronecker_mat_pow})))))
+    result = rule(expr)
+    doit = getattr(result, 'doit', None)
+    if doit is not None:
+        return doit()
+    else:
+        return result
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matadd.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matadd.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfae1e5010e4077c7210c85c4315ed2404f245d7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matadd.py
@@ -0,0 +1,155 @@
+from functools import reduce
+import operator
+
+from sympy.core import Basic, sympify
+from sympy.core.add import add, Add, _could_extract_minus_sign
+from sympy.core.sorting import default_sort_key
+from sympy.functions import adjoint
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.matrices.expressions.transpose import transpose
+from sympy.strategies import (rm_id, unpack, flatten, sort, condition,
+    exhaust, do_one, glom)
+from sympy.matrices.expressions.matexpr import MatrixExpr
+from sympy.matrices.expressions.special import ZeroMatrix, GenericZeroMatrix
+from sympy.matrices.expressions._shape import validate_matadd_integer as validate
+from sympy.utilities.iterables import sift
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+# XXX: MatAdd should perhaps not subclass directly from Add
+class MatAdd(MatrixExpr, Add):
+    """A Sum of Matrix Expressions
+
+    MatAdd inherits from and operates like SymPy Add
+
+    Examples
+    ========
+
+    >>> from sympy import MatAdd, MatrixSymbol
+    >>> A = MatrixSymbol('A', 5, 5)
+    >>> B = MatrixSymbol('B', 5, 5)
+    >>> C = MatrixSymbol('C', 5, 5)
+    >>> MatAdd(A, B, C)
+    A + B + C
+    """
+    is_MatAdd = True
+
+    identity = GenericZeroMatrix()
+
+    def __new__(cls, *args, evaluate=False, check=None, _sympify=True):
+        if not args:
+            return cls.identity
+
+        # This must be removed aggressively in the constructor to avoid
+        # TypeErrors from GenericZeroMatrix().shape
+        args = list(filter(lambda i: cls.identity != i, args))
+        if _sympify:
+            args = list(map(sympify, args))
+
+        if not all(isinstance(arg, MatrixExpr) for arg in args):
+            raise TypeError("Mix of Matrix and Scalar symbols")
+
+        obj = Basic.__new__(cls, *args)
+
+        if check is not None:
+            sympy_deprecation_warning(
+                "Passing check to MatAdd is deprecated and the check argument will be removed in a future version.",
+                deprecated_since_version="1.11",
+                active_deprecations_target='remove-check-argument-from-matrix-operations')
+
+        if check is not False:
+            validate(*args)
+
+        if evaluate:
+            obj = cls._evaluate(obj)
+
+        return obj
+
+    @classmethod
+    def _evaluate(cls, expr):
+        return canonicalize(expr)
+
+    @property
+    def shape(self):
+        return self.args[0].shape
+
+    def could_extract_minus_sign(self):
+        return _could_extract_minus_sign(self)
+
+    def expand(self, **kwargs):
+        expanded = super(MatAdd, self).expand(**kwargs)
+        return self._evaluate(expanded)
+
+    def _entry(self, i, j, **kwargs):
+        return Add(*[arg._entry(i, j, **kwargs) for arg in self.args])
+
+    def _eval_transpose(self):
+        return MatAdd(*[transpose(arg) for arg in self.args]).doit()
+
+    def _eval_adjoint(self):
+        return MatAdd(*[adjoint(arg) for arg in self.args]).doit()
+
+    def _eval_trace(self):
+        from .trace import trace
+        return Add(*[trace(arg) for arg in self.args]).doit()
+
+    def doit(self, **hints):
+        deep = hints.get('deep', True)
+        if deep:
+            args = [arg.doit(**hints) for arg in self.args]
+        else:
+            args = self.args
+        return canonicalize(MatAdd(*args))
+
+    def _eval_derivative_matrix_lines(self, x):
+        add_lines = [arg._eval_derivative_matrix_lines(x) for arg in self.args]
+        return [j for i in add_lines for j in i]
+
+add.register_handlerclass((Add, MatAdd), MatAdd)
+
+
+factor_of = lambda arg: arg.as_coeff_mmul()[0]
+matrix_of = lambda arg: unpack(arg.as_coeff_mmul()[1])
+def combine(cnt, mat):
+    if cnt == 1:
+        return mat
+    else:
+        return cnt * mat
+
+
+def merge_explicit(matadd):
+    """ Merge explicit MatrixBase arguments
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, eye, Matrix, MatAdd, pprint
+    >>> from sympy.matrices.expressions.matadd import merge_explicit
+    >>> A = MatrixSymbol('A', 2, 2)
+    >>> B = eye(2)
+    >>> C = Matrix([[1, 2], [3, 4]])
+    >>> X = MatAdd(A, B, C)
+    >>> pprint(X)
+        [1  0]   [1  2]
+    A + [    ] + [    ]
+        [0  1]   [3  4]
+    >>> pprint(merge_explicit(X))
+        [2  2]
+    A + [    ]
+        [3  5]
+    """
+    groups = sift(matadd.args, lambda arg: isinstance(arg, MatrixBase))
+    if len(groups[True]) > 1:
+        return MatAdd(*(groups[False] + [reduce(operator.add, groups[True])]))
+    else:
+        return matadd
+
+
+rules = (rm_id(lambda x: x == 0 or isinstance(x, ZeroMatrix)),
+         unpack,
+         flatten,
+         glom(matrix_of, factor_of, combine),
+         merge_explicit,
+         sort(default_sort_key))
+
+canonicalize = exhaust(condition(lambda x: isinstance(x, MatAdd),
+                                 do_one(*rules)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matexpr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matexpr.py
new file mode 100644
index 0000000000000000000000000000000000000000..a4e99296ccfcbdac5e09a86ecee020adf9831c73
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matexpr.py
@@ -0,0 +1,888 @@
+from __future__ import annotations
+from functools import wraps
+
+from sympy.core import S, Integer, Basic, Mul, Add
+from sympy.core.assumptions import check_assumptions
+from sympy.core.decorators import call_highest_priority
+from sympy.core.expr import Expr, ExprBuilder
+from sympy.core.logic import FuzzyBool
+from sympy.core.symbol import Str, Dummy, symbols, Symbol
+from sympy.core.sympify import SympifyError, _sympify
+from sympy.external.gmpy import SYMPY_INTS
+from sympy.functions import conjugate, adjoint
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.kind import MatrixKind
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.multipledispatch import dispatch
+from sympy.utilities.misc import filldedent
+
+
+def _sympifyit(arg, retval=None):
+    # This version of _sympifyit sympifies MutableMatrix objects
+    def deco(func):
+        @wraps(func)
+        def __sympifyit_wrapper(a, b):
+            try:
+                b = _sympify(b)
+                return func(a, b)
+            except SympifyError:
+                return retval
+
+        return __sympifyit_wrapper
+
+    return deco
+
+
+class MatrixExpr(Expr):
+    """Superclass for Matrix Expressions
+
+    MatrixExprs represent abstract matrices, linear transformations represented
+    within a particular basis.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> y = MatrixSymbol('y', 3, 1)
+    >>> x = (A.T*A).I * A * y
+
+    See Also
+    ========
+
+    MatrixSymbol, MatAdd, MatMul, Transpose, Inverse
+    """
+    __slots__: tuple[str, ...] = ()
+
+    # Should not be considered iterable by the
+    # sympy.utilities.iterables.iterable function. Subclass that actually are
+    # iterable (i.e., explicit matrices) should set this to True.
+    _iterable = False
+
+    _op_priority = 11.0
+
+    is_Matrix: bool = True
+    is_MatrixExpr: bool = True
+    is_Identity: FuzzyBool = None
+    is_Inverse = False
+    is_Transpose = False
+    is_ZeroMatrix = False
+    is_MatAdd = False
+    is_MatMul = False
+
+    is_commutative = False
+    is_number = False
+    is_symbol = False
+    is_scalar = False
+
+    kind: MatrixKind = MatrixKind()
+
+    def __new__(cls, *args, **kwargs):
+        args = map(_sympify, args)
+        return Basic.__new__(cls, *args, **kwargs)
+
+    # The following is adapted from the core Expr object
+
+    @property
+    def shape(self) -> tuple[Expr, Expr]:
+        raise NotImplementedError
+
+    @property
+    def _add_handler(self):
+        return MatAdd
+
+    @property
+    def _mul_handler(self):
+        return MatMul
+
+    def __neg__(self):
+        return MatMul(S.NegativeOne, self).doit()
+
+    def __abs__(self):
+        raise NotImplementedError
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__radd__')
+    def __add__(self, other):
+        return MatAdd(self, other).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__add__')
+    def __radd__(self, other):
+        return MatAdd(other, self).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__rsub__')
+    def __sub__(self, other):
+        return MatAdd(self, -other).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__sub__')
+    def __rsub__(self, other):
+        return MatAdd(other, -self).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__rmul__')
+    def __mul__(self, other):
+        return MatMul(self, other).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__rmul__')
+    def __matmul__(self, other):
+        return MatMul(self, other).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__mul__')
+    def __rmul__(self, other):
+        return MatMul(other, self).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__mul__')
+    def __rmatmul__(self, other):
+        return MatMul(other, self).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__rpow__')
+    def __pow__(self, other):
+        return MatPow(self, other).doit()
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__pow__')
+    def __rpow__(self, other):
+        raise NotImplementedError("Matrix Power not defined")
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__rtruediv__')
+    def __truediv__(self, other):
+        return self * other**S.NegativeOne
+
+    @_sympifyit('other', NotImplemented)
+    @call_highest_priority('__truediv__')
+    def __rtruediv__(self, other):
+        raise NotImplementedError()
+        #return MatMul(other, Pow(self, S.NegativeOne))
+
+    @property
+    def rows(self):
+        return self.shape[0]
+
+    @property
+    def cols(self):
+        return self.shape[1]
+
+    @property
+    def is_square(self) -> bool | None:
+        rows, cols = self.shape
+        if isinstance(rows, Integer) and isinstance(cols, Integer):
+            return rows == cols
+        if rows == cols:
+            return True
+        return None
+
+    def _eval_conjugate(self):
+        from sympy.matrices.expressions.adjoint import Adjoint
+        return Adjoint(Transpose(self))
+
+    def as_real_imag(self, deep=True, **hints):
+        return self._eval_as_real_imag()
+
+    def _eval_as_real_imag(self):
+        real = S.Half * (self + self._eval_conjugate())
+        im = (self - self._eval_conjugate())/(2*S.ImaginaryUnit)
+        return (real, im)
+
+    def _eval_inverse(self):
+        return Inverse(self)
+
+    def _eval_determinant(self):
+        return Determinant(self)
+
+    def _eval_transpose(self):
+        return Transpose(self)
+
+    def _eval_trace(self):
+        return None
+
+    def _eval_power(self, exp):
+        """
+        Override this in sub-classes to implement simplification of powers.  The cases where the exponent
+        is -1, 0, 1 are already covered in MatPow.doit(), so implementations can exclude these cases.
+        """
+        return MatPow(self, exp)
+
+    def _eval_simplify(self, **kwargs):
+        if self.is_Atom:
+            return self
+        else:
+            from sympy.simplify import simplify
+            return self.func(*[simplify(x, **kwargs) for x in self.args])
+
+    def _eval_adjoint(self):
+        from sympy.matrices.expressions.adjoint import Adjoint
+        return Adjoint(self)
+
+    def _eval_derivative_n_times(self, x, n):
+        return Basic._eval_derivative_n_times(self, x, n)
+
+    def _eval_derivative(self, x):
+        # `x` is a scalar:
+        if self.has(x):
+            # See if there are other methods using it:
+            return super()._eval_derivative(x)
+        else:
+            return ZeroMatrix(*self.shape)
+
+    @classmethod
+    def _check_dim(cls, dim):
+        """Helper function to check invalid matrix dimensions"""
+        ok = not dim.is_Float and check_assumptions(
+            dim, integer=True, nonnegative=True)
+        if ok is False:
+            raise ValueError(
+                "The dimension specification {} should be "
+                "a nonnegative integer.".format(dim))
+
+
+    def _entry(self, i, j, **kwargs):
+        raise NotImplementedError(
+            "Indexing not implemented for %s" % self.__class__.__name__)
+
+    def adjoint(self):
+        return adjoint(self)
+
+    def as_coeff_Mul(self, rational=False):
+        """Efficiently extract the coefficient of a product."""
+        return S.One, self
+
+    def conjugate(self):
+        return conjugate(self)
+
+    def transpose(self):
+        from sympy.matrices.expressions.transpose import transpose
+        return transpose(self)
+
+    @property
+    def T(self):
+        '''Matrix transposition'''
+        return self.transpose()
+
+    def inverse(self):
+        if self.is_square is False:
+            raise NonSquareMatrixError('Inverse of non-square matrix')
+        return self._eval_inverse()
+
+    def inv(self):
+        return self.inverse()
+
+    def det(self):
+        from sympy.matrices.expressions.determinant import det
+        return det(self)
+
+    @property
+    def I(self):
+        return self.inverse()
+
+    def valid_index(self, i, j):
+        def is_valid(idx):
+            return isinstance(idx, (int, Integer, Symbol, Expr))
+        return (is_valid(i) and is_valid(j) and
+                (self.rows is None or
+                (i >= -self.rows) != False and (i < self.rows) != False) and
+                (j >= -self.cols) != False and (j < self.cols) != False)
+
+    def __getitem__(self, key):
+        if not isinstance(key, tuple) and isinstance(key, slice):
+            from sympy.matrices.expressions.slice import MatrixSlice
+            return MatrixSlice(self, key, (0, None, 1))
+        if isinstance(key, tuple) and len(key) == 2:
+            i, j = key
+            if isinstance(i, slice) or isinstance(j, slice):
+                from sympy.matrices.expressions.slice import MatrixSlice
+                return MatrixSlice(self, i, j)
+            i, j = _sympify(i), _sympify(j)
+            if self.valid_index(i, j) != False:
+                return self._entry(i, j)
+            else:
+                raise IndexError("Invalid indices (%s, %s)" % (i, j))
+        elif isinstance(key, (SYMPY_INTS, Integer)):
+            # row-wise decomposition of matrix
+            rows, cols = self.shape
+            # allow single indexing if number of columns is known
+            if not isinstance(cols, Integer):
+                raise IndexError(filldedent('''
+                    Single indexing is only supported when the number
+                    of columns is known.'''))
+            key = _sympify(key)
+            i = key // cols
+            j = key % cols
+            if self.valid_index(i, j) != False:
+                return self._entry(i, j)
+            else:
+                raise IndexError("Invalid index %s" % key)
+        elif isinstance(key, (Symbol, Expr)):
+            raise IndexError(filldedent('''
+                Only integers may be used when addressing the matrix
+                with a single index.'''))
+        raise IndexError("Invalid index, wanted %s[i,j]" % self)
+
+    def _is_shape_symbolic(self) -> bool:
+        return (not isinstance(self.rows, (SYMPY_INTS, Integer))
+            or not isinstance(self.cols, (SYMPY_INTS, Integer)))
+
+    def as_explicit(self):
+        """
+        Returns a dense Matrix with elements represented explicitly
+
+        Returns an object of type ImmutableDenseMatrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Identity
+        >>> I = Identity(3)
+        >>> I
+        I
+        >>> I.as_explicit()
+        Matrix([
+        [1, 0, 0],
+        [0, 1, 0],
+        [0, 0, 1]])
+
+        See Also
+        ========
+        as_mutable: returns mutable Matrix type
+
+        """
+        if self._is_shape_symbolic():
+            raise ValueError(
+                'Matrix with symbolic shape '
+                'cannot be represented explicitly.')
+        from sympy.matrices.immutable import ImmutableDenseMatrix
+        return ImmutableDenseMatrix([[self[i, j]
+                            for j in range(self.cols)]
+                            for i in range(self.rows)])
+
+    def as_mutable(self):
+        """
+        Returns a dense, mutable matrix with elements represented explicitly
+
+        Examples
+        ========
+
+        >>> from sympy import Identity
+        >>> I = Identity(3)
+        >>> I
+        I
+        >>> I.shape
+        (3, 3)
+        >>> I.as_mutable()
+        Matrix([
+        [1, 0, 0],
+        [0, 1, 0],
+        [0, 0, 1]])
+
+        See Also
+        ========
+        as_explicit: returns ImmutableDenseMatrix
+        """
+        return self.as_explicit().as_mutable()
+
+    def __array__(self, dtype=object, copy=None):
+        if copy is not None and not copy:
+            raise TypeError("Cannot implement copy=False when converting Matrix to ndarray")
+        from numpy import empty
+        a = empty(self.shape, dtype=object)
+        for i in range(self.rows):
+            for j in range(self.cols):
+                a[i, j] = self[i, j]
+        return a
+
+    def equals(self, other):
+        """
+        Test elementwise equality between matrices, potentially of different
+        types
+
+        >>> from sympy import Identity, eye
+        >>> Identity(3).equals(eye(3))
+        True
+        """
+        return self.as_explicit().equals(other)
+
+    def canonicalize(self):
+        return self
+
+    def as_coeff_mmul(self):
+        return S.One, MatMul(self)
+
+    @staticmethod
+    def from_index_summation(expr, first_index=None, last_index=None, dimensions=None):
+        r"""
+        Parse expression of matrices with explicitly summed indices into a
+        matrix expression without indices, if possible.
+
+        This transformation expressed in mathematical notation:
+
+        `\sum_{j=0}^{N-1} A_{i,j} B_{j,k} \Longrightarrow \mathbf{A}\cdot \mathbf{B}`
+
+        Optional parameter ``first_index``: specify which free index to use as
+        the index starting the expression.
+
+        Examples
+        ========
+
+        >>> from sympy import MatrixSymbol, MatrixExpr, Sum
+        >>> from sympy.abc import i, j, k, l, N
+        >>> A = MatrixSymbol("A", N, N)
+        >>> B = MatrixSymbol("B", N, N)
+        >>> expr = Sum(A[i, j]*B[j, k], (j, 0, N-1))
+        >>> MatrixExpr.from_index_summation(expr)
+        A*B
+
+        Transposition is detected:
+
+        >>> expr = Sum(A[j, i]*B[j, k], (j, 0, N-1))
+        >>> MatrixExpr.from_index_summation(expr)
+        A.T*B
+
+        Detect the trace:
+
+        >>> expr = Sum(A[i, i], (i, 0, N-1))
+        >>> MatrixExpr.from_index_summation(expr)
+        Trace(A)
+
+        More complicated expressions:
+
+        >>> expr = Sum(A[i, j]*B[k, j]*A[l, k], (j, 0, N-1), (k, 0, N-1))
+        >>> MatrixExpr.from_index_summation(expr)
+        A*B.T*A.T
+        """
+        from sympy.tensor.array.expressions.from_indexed_to_array import convert_indexed_to_array
+        from sympy.tensor.array.expressions.from_array_to_matrix import convert_array_to_matrix
+        first_indices = []
+        if first_index is not None:
+            first_indices.append(first_index)
+        if last_index is not None:
+            first_indices.append(last_index)
+        arr = convert_indexed_to_array(expr, first_indices=first_indices)
+        return convert_array_to_matrix(arr)
+
+    def applyfunc(self, func):
+        from .applyfunc import ElementwiseApplyFunction
+        return ElementwiseApplyFunction(func, self)
+
+
+@dispatch(MatrixExpr, Expr)
+def _eval_is_eq(lhs, rhs): # noqa:F811
+    return False
+
+@dispatch(MatrixExpr, MatrixExpr)  # type: ignore
+def _eval_is_eq(lhs, rhs): # noqa:F811
+    if lhs.shape != rhs.shape:
+        return False
+    if (lhs - rhs).is_ZeroMatrix:
+        return True
+
+def get_postprocessor(cls):
+    def _postprocessor(expr):
+        # To avoid circular imports, we can't have MatMul/MatAdd on the top level
+        mat_class = {Mul: MatMul, Add: MatAdd}[cls]
+        nonmatrices = []
+        matrices = []
+        for term in expr.args:
+            if isinstance(term, MatrixExpr):
+                matrices.append(term)
+            else:
+                nonmatrices.append(term)
+
+        if not matrices:
+            return cls._from_args(nonmatrices)
+
+        if nonmatrices:
+            if cls == Mul:
+                for i in range(len(matrices)):
+                    if not matrices[i].is_MatrixExpr:
+                        # If one of the matrices explicit, absorb the scalar into it
+                        # (doit will combine all explicit matrices into one, so it
+                        # doesn't matter which)
+                        matrices[i] = matrices[i].__mul__(cls._from_args(nonmatrices))
+                        nonmatrices = []
+                        break
+
+            else:
+                # Maintain the ability to create Add(scalar, matrix) without
+                # raising an exception. That way different algorithms can
+                # replace matrix expressions with non-commutative symbols to
+                # manipulate them like non-commutative scalars.
+                return cls._from_args(nonmatrices + [mat_class(*matrices).doit(deep=False)])
+
+        if mat_class == MatAdd:
+            return mat_class(*matrices).doit(deep=False)
+        return mat_class(cls._from_args(nonmatrices), *matrices).doit(deep=False)
+    return _postprocessor
+
+
+Basic._constructor_postprocessor_mapping[MatrixExpr] = {
+    "Mul": [get_postprocessor(Mul)],
+    "Add": [get_postprocessor(Add)],
+}
+
+
+def _matrix_derivative(expr, x, old_algorithm=False):
+
+    if isinstance(expr, MatrixBase) or isinstance(x, MatrixBase):
+        # Do not use array expressions for explicit matrices:
+        old_algorithm = True
+
+    if old_algorithm:
+        return _matrix_derivative_old_algorithm(expr, x)
+
+    from sympy.tensor.array.expressions.from_matrix_to_array import convert_matrix_to_array
+    from sympy.tensor.array.expressions.arrayexpr_derivatives import array_derive
+    from sympy.tensor.array.expressions.from_array_to_matrix import convert_array_to_matrix
+
+    array_expr = convert_matrix_to_array(expr)
+    diff_array_expr = array_derive(array_expr, x)
+    diff_matrix_expr = convert_array_to_matrix(diff_array_expr)
+    return diff_matrix_expr
+
+
+def _matrix_derivative_old_algorithm(expr, x):
+    from sympy.tensor.array.array_derivatives import ArrayDerivative
+    lines = expr._eval_derivative_matrix_lines(x)
+
+    parts = [i.build() for i in lines]
+
+    from sympy.tensor.array.expressions.from_array_to_matrix import convert_array_to_matrix
+
+    parts = [[convert_array_to_matrix(j) for j in i] for i in parts]
+
+    def _get_shape(elem):
+        if isinstance(elem, MatrixExpr):
+            return elem.shape
+        return 1, 1
+
+    def get_rank(parts):
+        return sum(j not in (1, None) for i in parts for j in _get_shape(i))
+
+    ranks = [get_rank(i) for i in parts]
+    rank = ranks[0]
+
+    def contract_one_dims(parts):
+        if len(parts) == 1:
+            return parts[0]
+        else:
+            p1, p2 = parts[:2]
+            if p2.is_Matrix:
+                p2 = p2.T
+            if p1 == Identity(1):
+                pbase = p2
+            elif p2 == Identity(1):
+                pbase = p1
+            else:
+                pbase = p1*p2
+            if len(parts) == 2:
+                return pbase
+            else:  # len(parts) > 2
+                if pbase.is_Matrix:
+                    raise ValueError("")
+                return pbase*Mul.fromiter(parts[2:])
+
+    if rank <= 2:
+        return Add.fromiter([contract_one_dims(i) for i in parts])
+
+    return ArrayDerivative(expr, x)
+
+
+class MatrixElement(Expr):
+    parent = property(lambda self: self.args[0])
+    i = property(lambda self: self.args[1])
+    j = property(lambda self: self.args[2])
+    _diff_wrt = True
+    is_symbol = True
+    is_commutative = True
+
+    def __new__(cls, name, n, m):
+        n, m = map(_sympify, (n, m))
+        if isinstance(name, str):
+            name = Symbol(name)
+        else:
+            if isinstance(name, MatrixBase):
+                if n.is_Integer and m.is_Integer:
+                    return name[n, m]
+                name = _sympify(name)  # change mutable into immutable
+            else:
+                name = _sympify(name)
+                if not isinstance(name.kind, MatrixKind):
+                    raise TypeError("First argument of MatrixElement should be a matrix")
+            if not getattr(name, 'valid_index', lambda n, m: True)(n, m):
+                raise IndexError('indices out of range')
+        obj = Expr.__new__(cls, name, n, m)
+        return obj
+
+    @property
+    def symbol(self):
+        return self.args[0]
+
+    def doit(self, **hints):
+        deep = hints.get('deep', True)
+        if deep:
+            args = [arg.doit(**hints) for arg in self.args]
+        else:
+            args = self.args
+        return args[0][args[1], args[2]]
+
+    @property
+    def indices(self):
+        return self.args[1:]
+
+    def _eval_derivative(self, v):
+
+        if not isinstance(v, MatrixElement):
+            return self.parent.diff(v)[self.i, self.j]
+
+        M = self.args[0]
+
+        m, n = self.parent.shape
+
+        if M == v.args[0]:
+            return KroneckerDelta(self.args[1], v.args[1], (0, m-1)) * \
+                   KroneckerDelta(self.args[2], v.args[2], (0, n-1))
+
+        if isinstance(M, Inverse):
+            from sympy.concrete.summations import Sum
+            i, j = self.args[1:]
+            i1, i2 = symbols("z1, z2", cls=Dummy)
+            Y = M.args[0]
+            r1, r2 = Y.shape
+            return -Sum(M[i, i1]*Y[i1, i2].diff(v)*M[i2, j], (i1, 0, r1-1), (i2, 0, r2-1))
+
+        if self.has(v.args[0]):
+            return None
+
+        return S.Zero
+
+
+class MatrixSymbol(MatrixExpr):
+    """Symbolic representation of a Matrix object
+
+    Creates a SymPy Symbol to represent a Matrix. This matrix has a shape and
+    can be included in Matrix Expressions
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Identity
+    >>> A = MatrixSymbol('A', 3, 4) # A 3 by 4 Matrix
+    >>> B = MatrixSymbol('B', 4, 3) # A 4 by 3 Matrix
+    >>> A.shape
+    (3, 4)
+    >>> 2*A*B + Identity(3)
+    I + 2*A*B
+    """
+    is_commutative = False
+    is_symbol = True
+    _diff_wrt = True
+
+    def __new__(cls, name, n, m):
+        n, m = _sympify(n), _sympify(m)
+
+        cls._check_dim(m)
+        cls._check_dim(n)
+
+        if isinstance(name, str):
+            name = Str(name)
+        obj = Basic.__new__(cls, name, n, m)
+        return obj
+
+    @property
+    def shape(self):
+        return self.args[1], self.args[2]
+
+    @property
+    def name(self):
+        return self.args[0].name
+
+    def _entry(self, i, j, **kwargs):
+        return MatrixElement(self, i, j)
+
+    @property
+    def free_symbols(self):
+        return {self}
+
+    def _eval_simplify(self, **kwargs):
+        return self
+
+    def _eval_derivative(self, x):
+        # x is a scalar:
+        return ZeroMatrix(self.shape[0], self.shape[1])
+
+    def _eval_derivative_matrix_lines(self, x):
+        if self != x:
+            first = ZeroMatrix(x.shape[0], self.shape[0]) if self.shape[0] != 1 else S.Zero
+            second = ZeroMatrix(x.shape[1], self.shape[1]) if self.shape[1] != 1 else S.Zero
+            return [_LeftRightArgs(
+                [first, second],
+            )]
+        else:
+            first = Identity(self.shape[0]) if self.shape[0] != 1 else S.One
+            second = Identity(self.shape[1]) if self.shape[1] != 1 else S.One
+            return [_LeftRightArgs(
+                [first, second],
+            )]
+
+
+def matrix_symbols(expr):
+    return [sym for sym in expr.free_symbols if sym.is_Matrix]
+
+
+class _LeftRightArgs:
+    r"""
+    Helper class to compute matrix derivatives.
+
+    The logic: when an expression is derived by a matrix `X_{mn}`, two lines of
+    matrix multiplications are created: the one contracted to `m` (first line),
+    and the one contracted to `n` (second line).
+
+    Transposition flips the side by which new matrices are connected to the
+    lines.
+
+    The trace connects the end of the two lines.
+    """
+
+    def __init__(self, lines, higher=S.One):
+        self._lines = list(lines)
+        self._first_pointer_parent = self._lines
+        self._first_pointer_index = 0
+        self._first_line_index = 0
+        self._second_pointer_parent = self._lines
+        self._second_pointer_index = 1
+        self._second_line_index = 1
+        self.higher = higher
+
+    @property
+    def first_pointer(self):
+        return self._first_pointer_parent[self._first_pointer_index]
+
+    @first_pointer.setter
+    def first_pointer(self, value):
+        self._first_pointer_parent[self._first_pointer_index] = value
+
+    @property
+    def second_pointer(self):
+        return self._second_pointer_parent[self._second_pointer_index]
+
+    @second_pointer.setter
+    def second_pointer(self, value):
+        self._second_pointer_parent[self._second_pointer_index] = value
+
+    def __repr__(self):
+        built = [self._build(i) for i in self._lines]
+        return "_LeftRightArgs(lines=%s, higher=%s)" % (
+            built,
+            self.higher,
+        )
+
+    def transpose(self):
+        self._first_pointer_parent, self._second_pointer_parent = self._second_pointer_parent, self._first_pointer_parent
+        self._first_pointer_index, self._second_pointer_index = self._second_pointer_index, self._first_pointer_index
+        self._first_line_index, self._second_line_index = self._second_line_index, self._first_line_index
+        return self
+
+    @staticmethod
+    def _build(expr):
+        if isinstance(expr, ExprBuilder):
+            return expr.build()
+        if isinstance(expr, list):
+            if len(expr) == 1:
+                return expr[0]
+            else:
+                return expr[0](*[_LeftRightArgs._build(i) for i in expr[1]])
+        else:
+            return expr
+
+    def build(self):
+        data = [self._build(i) for i in self._lines]
+        if self.higher != 1:
+            data += [self._build(self.higher)]
+        data = list(data)
+        return data
+
+    def matrix_form(self):
+        if self.first != 1 and self.higher != 1:
+            raise ValueError("higher dimensional array cannot be represented")
+
+        def _get_shape(elem):
+            if isinstance(elem, MatrixExpr):
+                return elem.shape
+            return (None, None)
+
+        if _get_shape(self.first)[1] != _get_shape(self.second)[1]:
+            # Remove one-dimensional identity matrices:
+            # (this is needed by `a.diff(a)` where `a` is a vector)
+            if _get_shape(self.second) == (1, 1):
+                return self.first*self.second[0, 0]
+            if _get_shape(self.first) == (1, 1):
+                return self.first[1, 1]*self.second.T
+            raise ValueError("incompatible shapes")
+        if self.first != 1:
+            return self.first*self.second.T
+        else:
+            return self.higher
+
+    def rank(self):
+        """
+        Number of dimensions different from trivial (warning: not related to
+        matrix rank).
+        """
+        rank = 0
+        if self.first != 1:
+            rank += sum(i != 1 for i in self.first.shape)
+        if self.second != 1:
+            rank += sum(i != 1 for i in self.second.shape)
+        if self.higher != 1:
+            rank += 2
+        return rank
+
+    def _multiply_pointer(self, pointer, other):
+        from ...tensor.array.expressions.array_expressions import ArrayTensorProduct
+        from ...tensor.array.expressions.array_expressions import ArrayContraction
+
+        subexpr = ExprBuilder(
+            ArrayContraction,
+            [
+                ExprBuilder(
+                    ArrayTensorProduct,
+                    [
+                        pointer,
+                        other
+                    ]
+                ),
+                (1, 2)
+            ],
+            validator=ArrayContraction._validate
+        )
+
+        return subexpr
+
+    def append_first(self, other):
+        self.first_pointer *= other
+
+    def append_second(self, other):
+        self.second_pointer *= other
+
+
+def _make_matrix(x):
+    from sympy.matrices.immutable import ImmutableDenseMatrix
+    if isinstance(x, MatrixExpr):
+        return x
+    return ImmutableDenseMatrix([[x]])
+
+
+from .matmul import MatMul
+from .matadd import MatAdd
+from .matpow import MatPow
+from .transpose import Transpose
+from .inverse import Inverse
+from .special import ZeroMatrix, Identity
+from .determinant import Determinant
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matmul.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matmul.py
new file mode 100644
index 0000000000000000000000000000000000000000..1c46f7ff5251d89793423f92ea02d7243601de3f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matmul.py
@@ -0,0 +1,496 @@
+from sympy.assumptions.ask import ask, Q
+from sympy.assumptions.refine import handlers_dict
+from sympy.core import Basic, sympify, S
+from sympy.core.mul import mul, Mul
+from sympy.core.numbers import Number, Integer
+from sympy.core.symbol import Dummy
+from sympy.functions import adjoint
+from sympy.strategies import (rm_id, unpack, typed, flatten, exhaust,
+        do_one, new)
+from sympy.matrices.exceptions import NonInvertibleMatrixError
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.matrices.expressions._shape import validate_matmul_integer as validate
+
+from .inverse import Inverse
+from .matexpr import MatrixExpr
+from .matpow import MatPow
+from .transpose import transpose
+from .permutation import PermutationMatrix
+from .special import ZeroMatrix, Identity, GenericIdentity, OneMatrix
+
+
+# XXX: MatMul should perhaps not subclass directly from Mul
+class MatMul(MatrixExpr, Mul):
+    """
+    A product of matrix expressions
+
+    Examples
+    ========
+
+    >>> from sympy import MatMul, MatrixSymbol
+    >>> A = MatrixSymbol('A', 5, 4)
+    >>> B = MatrixSymbol('B', 4, 3)
+    >>> C = MatrixSymbol('C', 3, 6)
+    >>> MatMul(A, B, C)
+    A*B*C
+    """
+    is_MatMul = True
+
+    identity = GenericIdentity()
+
+    def __new__(cls, *args, evaluate=False, check=None, _sympify=True):
+        if not args:
+            return cls.identity
+
+        # This must be removed aggressively in the constructor to avoid
+        # TypeErrors from GenericIdentity().shape
+        args = list(filter(lambda i: cls.identity != i, args))
+        if _sympify:
+            args = list(map(sympify, args))
+        obj = Basic.__new__(cls, *args)
+        factor, matrices = obj.as_coeff_matrices()
+
+        if check is not None:
+            sympy_deprecation_warning(
+                "Passing check to MatMul is deprecated and the check argument will be removed in a future version.",
+                deprecated_since_version="1.11",
+                active_deprecations_target='remove-check-argument-from-matrix-operations')
+
+        if check is not False:
+            validate(*matrices)
+
+        if not matrices:
+            # Should it be
+            #
+            # return Basic.__neq__(cls, factor, GenericIdentity()) ?
+            return factor
+
+        if evaluate:
+            return cls._evaluate(obj)
+
+        return obj
+
+    @classmethod
+    def _evaluate(cls, expr):
+        return canonicalize(expr)
+
+    @property
+    def shape(self):
+        matrices = [arg for arg in self.args if arg.is_Matrix]
+        return (matrices[0].rows, matrices[-1].cols)
+
+    def _entry(self, i, j, expand=True, **kwargs):
+        # Avoid cyclic imports
+        from sympy.concrete.summations import Sum
+        from sympy.matrices.immutable import ImmutableMatrix
+
+        coeff, matrices = self.as_coeff_matrices()
+
+        if len(matrices) == 1:  # situation like 2*X, matmul is just X
+            return coeff * matrices[0][i, j]
+
+        indices = [None]*(len(matrices) + 1)
+        ind_ranges = [None]*(len(matrices) - 1)
+        indices[0] = i
+        indices[-1] = j
+
+        def f():
+            counter = 1
+            while True:
+                yield Dummy("i_%i" % counter)
+                counter += 1
+
+        dummy_generator = kwargs.get("dummy_generator", f())
+
+        for i in range(1, len(matrices)):
+            indices[i] = next(dummy_generator)
+
+        for i, arg in enumerate(matrices[:-1]):
+            ind_ranges[i] = arg.shape[1] - 1
+        matrices = [arg._entry(indices[i], indices[i+1], dummy_generator=dummy_generator) for i, arg in enumerate(matrices)]
+        expr_in_sum = Mul.fromiter(matrices)
+        if any(v.has(ImmutableMatrix) for v in matrices):
+            expand = True
+        result = coeff*Sum(
+                expr_in_sum,
+                *zip(indices[1:-1], [0]*len(ind_ranges), ind_ranges)
+            )
+
+        # Don't waste time in result.doit() if the sum bounds are symbolic
+        if not any(isinstance(v, (Integer, int)) for v in ind_ranges):
+            expand = False
+        return result.doit() if expand else result
+
+    def as_coeff_matrices(self):
+        scalars = [x for x in self.args if not x.is_Matrix]
+        matrices = [x for x in self.args if x.is_Matrix]
+        coeff = Mul(*scalars)
+        if coeff.is_commutative is False:
+            raise NotImplementedError("noncommutative scalars in MatMul are not supported.")
+
+        return coeff, matrices
+
+    def as_coeff_mmul(self):
+        coeff, matrices = self.as_coeff_matrices()
+        return coeff, MatMul(*matrices)
+
+    def expand(self, **kwargs):
+        expanded = super(MatMul, self).expand(**kwargs)
+        return self._evaluate(expanded)
+
+    def _eval_transpose(self):
+        """Transposition of matrix multiplication.
+
+        Notes
+        =====
+
+        The following rules are applied.
+
+        Transposition for matrix multiplied with another matrix:
+        `\\left(A B\\right)^{T} = B^{T} A^{T}`
+
+        Transposition for matrix multiplied with scalar:
+        `\\left(c A\\right)^{T} = c A^{T}`
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Transpose
+        """
+        coeff, matrices = self.as_coeff_matrices()
+        return MatMul(
+            coeff, *[transpose(arg) for arg in matrices[::-1]]).doit()
+
+    def _eval_adjoint(self):
+        return MatMul(*[adjoint(arg) for arg in self.args[::-1]]).doit()
+
+    def _eval_trace(self):
+        factor, mmul = self.as_coeff_mmul()
+        if factor != 1:
+            from .trace import trace
+            return factor * trace(mmul.doit())
+
+    def _eval_determinant(self):
+        from sympy.matrices.expressions.determinant import Determinant
+        factor, matrices = self.as_coeff_matrices()
+        square_matrices = only_squares(*matrices)
+        return factor**self.rows * Mul(*list(map(Determinant, square_matrices)))
+
+    def _eval_inverse(self):
+        if all(arg.is_square for arg in self.args if isinstance(arg, MatrixExpr)):
+            return MatMul(*(
+                arg.inverse() if isinstance(arg, MatrixExpr) else arg**-1
+                    for arg in self.args[::-1]
+                )
+            ).doit()
+        return Inverse(self)
+
+    def doit(self, **hints):
+        deep = hints.get('deep', True)
+        if deep:
+            args = tuple(arg.doit(**hints) for arg in self.args)
+        else:
+            args = self.args
+
+        # treat scalar*MatrixSymbol or scalar*MatPow separately
+        expr = canonicalize(MatMul(*args))
+        return expr
+
+    # Needed for partial compatibility with Mul
+    def args_cnc(self, cset=False, warn=True, **kwargs):
+        coeff_c = [x for x in self.args if x.is_commutative]
+        coeff_nc = [x for x in self.args if not x.is_commutative]
+        if cset:
+            clen = len(coeff_c)
+            coeff_c = set(coeff_c)
+            if clen and warn and len(coeff_c) != clen:
+                raise ValueError('repeated commutative arguments: %s' %
+                                 [ci for ci in coeff_c if list(self.args).count(ci) > 1])
+        return [coeff_c, coeff_nc]
+
+    def _eval_derivative_matrix_lines(self, x):
+        from .transpose import Transpose
+        with_x_ind = [i for i, arg in enumerate(self.args) if arg.has(x)]
+        lines = []
+        for ind in with_x_ind:
+            left_args = self.args[:ind]
+            right_args = self.args[ind+1:]
+
+            if right_args:
+                right_mat = MatMul.fromiter(right_args)
+            else:
+                right_mat = Identity(self.shape[1])
+            if left_args:
+                left_rev = MatMul.fromiter([Transpose(i).doit() if i.is_Matrix else i for i in reversed(left_args)])
+            else:
+                left_rev = Identity(self.shape[0])
+
+            d = self.args[ind]._eval_derivative_matrix_lines(x)
+            for i in d:
+                i.append_first(left_rev)
+                i.append_second(right_mat)
+                lines.append(i)
+
+        return lines
+
+mul.register_handlerclass((Mul, MatMul), MatMul)
+
+
+# Rules
+def newmul(*args):
+    if args[0] == 1:
+        args = args[1:]
+    return new(MatMul, *args)
+
+def any_zeros(mul):
+    if any(arg.is_zero or (arg.is_Matrix and arg.is_ZeroMatrix)
+                       for arg in mul.args):
+        matrices = [arg for arg in mul.args if arg.is_Matrix]
+        return ZeroMatrix(matrices[0].rows, matrices[-1].cols)
+    return mul
+
+def merge_explicit(matmul):
+    """ Merge explicit MatrixBase arguments
+
+    >>> from sympy import MatrixSymbol, Matrix, MatMul, pprint
+    >>> from sympy.matrices.expressions.matmul import merge_explicit
+    >>> A = MatrixSymbol('A', 2, 2)
+    >>> B = Matrix([[1, 1], [1, 1]])
+    >>> C = Matrix([[1, 2], [3, 4]])
+    >>> X = MatMul(A, B, C)
+    >>> pprint(X)
+      [1  1] [1  2]
+    A*[    ]*[    ]
+      [1  1] [3  4]
+    >>> pprint(merge_explicit(X))
+      [4  6]
+    A*[    ]
+      [4  6]
+
+    >>> X = MatMul(B, A, C)
+    >>> pprint(X)
+    [1  1]   [1  2]
+    [    ]*A*[    ]
+    [1  1]   [3  4]
+    >>> pprint(merge_explicit(X))
+    [1  1]   [1  2]
+    [    ]*A*[    ]
+    [1  1]   [3  4]
+    """
+    if not any(isinstance(arg, MatrixBase) for arg in matmul.args):
+        return matmul
+    newargs = []
+    last = matmul.args[0]
+    for arg in matmul.args[1:]:
+        if isinstance(arg, (MatrixBase, Number)) and isinstance(last, (MatrixBase, Number)):
+            last = last * arg
+        else:
+            newargs.append(last)
+            last = arg
+    newargs.append(last)
+
+    return MatMul(*newargs)
+
+def remove_ids(mul):
+    """ Remove Identities from a MatMul
+
+    This is a modified version of sympy.strategies.rm_id.
+    This is necessary because MatMul may contain both MatrixExprs and Exprs
+    as args.
+
+    See Also
+    ========
+
+    sympy.strategies.rm_id
+    """
+    # Separate Exprs from MatrixExprs in args
+    factor, mmul = mul.as_coeff_mmul()
+    # Apply standard rm_id for MatMuls
+    result = rm_id(lambda x: x.is_Identity is True)(mmul)
+    if result != mmul:
+        return newmul(factor, *result.args)  # Recombine and return
+    else:
+        return mul
+
+def factor_in_front(mul):
+    factor, matrices = mul.as_coeff_matrices()
+    if factor != 1:
+        return newmul(factor, *matrices)
+    return mul
+
+def combine_powers(mul):
+    r"""Combine consecutive powers with the same base into one, e.g.
+    $$A \times A^2 \Rightarrow A^3$$
+
+    This also cancels out the possible matrix inverses using the
+    knowledgebase of :class:`~.Inverse`, e.g.,
+    $$ Y \times X \times X^{-1} \Rightarrow Y $$
+    """
+    factor, args = mul.as_coeff_matrices()
+    new_args = [args[0]]
+
+    for i in range(1, len(args)):
+        A = new_args[-1]
+        B = args[i]
+
+        if isinstance(B, Inverse) and isinstance(B.arg, MatMul):
+            Bargs = B.arg.args
+            l = len(Bargs)
+            if list(Bargs) == new_args[-l:]:
+                new_args = new_args[:-l] + [Identity(B.shape[0])]
+                continue
+
+        if isinstance(A, Inverse) and isinstance(A.arg, MatMul):
+            Aargs = A.arg.args
+            l = len(Aargs)
+            if list(Aargs) == args[i:i+l]:
+                identity = Identity(A.shape[0])
+                new_args[-1] = identity
+                for j in range(i, i+l):
+                    args[j] = identity
+                continue
+
+        if A.is_square == False or B.is_square == False:
+            new_args.append(B)
+            continue
+
+        if isinstance(A, MatPow):
+            A_base, A_exp = A.args
+        else:
+            A_base, A_exp = A, S.One
+
+        if isinstance(B, MatPow):
+            B_base, B_exp = B.args
+        else:
+            B_base, B_exp = B, S.One
+
+        if A_base == B_base:
+            new_exp = A_exp + B_exp
+            new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
+            continue
+        elif not isinstance(B_base, MatrixBase):
+            try:
+                B_base_inv = B_base.inverse()
+            except NonInvertibleMatrixError:
+                B_base_inv = None
+            if B_base_inv is not None and A_base == B_base_inv:
+                new_exp = A_exp - B_exp
+                new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
+                continue
+        new_args.append(B)
+
+    return newmul(factor, *new_args)
+
+def combine_permutations(mul):
+    """Refine products of permutation matrices as the products of cycles.
+    """
+    args = mul.args
+    l = len(args)
+    if l < 2:
+        return mul
+
+    result = [args[0]]
+    for i in range(1, l):
+        A = result[-1]
+        B = args[i]
+        if isinstance(A, PermutationMatrix) and \
+            isinstance(B, PermutationMatrix):
+            cycle_1 = A.args[0]
+            cycle_2 = B.args[0]
+            result[-1] = PermutationMatrix(cycle_1 * cycle_2)
+        else:
+            result.append(B)
+
+    return MatMul(*result)
+
+def combine_one_matrices(mul):
+    """
+    Combine products of OneMatrix
+
+    e.g. OneMatrix(2, 3) * OneMatrix(3, 4) -> 3 * OneMatrix(2, 4)
+    """
+    factor, args = mul.as_coeff_matrices()
+    new_args = [args[0]]
+
+    for B in args[1:]:
+        A = new_args[-1]
+        if not isinstance(A, OneMatrix) or not isinstance(B, OneMatrix):
+            new_args.append(B)
+            continue
+        new_args.pop()
+        new_args.append(OneMatrix(A.shape[0], B.shape[1]))
+        factor *= A.shape[1]
+
+    return newmul(factor, *new_args)
+
+def distribute_monom(mul):
+    """
+    Simplify MatMul expressions but distributing
+    rational term to MatMul.
+
+    e.g. 2*(A+B) -> 2*A + 2*B
+    """
+    args = mul.args
+    if len(args) == 2:
+        from .matadd import MatAdd
+        if args[0].is_MatAdd and args[1].is_Rational:
+            return MatAdd(*[MatMul(mat, args[1]).doit() for mat in args[0].args])
+        if args[1].is_MatAdd and args[0].is_Rational:
+            return MatAdd(*[MatMul(args[0], mat).doit() for mat in args[1].args])
+    return mul
+
+rules = (
+    distribute_monom, any_zeros, remove_ids, combine_one_matrices, combine_powers, unpack, rm_id(lambda x: x == 1),
+    merge_explicit, factor_in_front, flatten, combine_permutations)
+
+canonicalize = exhaust(typed({MatMul: do_one(*rules)}))
+
+def only_squares(*matrices):
+    """factor matrices only if they are square"""
+    if matrices[0].rows != matrices[-1].cols:
+        raise RuntimeError("Invalid matrices being multiplied")
+    out = []
+    start = 0
+    for i, M in enumerate(matrices):
+        if M.cols == matrices[start].rows:
+            out.append(MatMul(*matrices[start:i+1]).doit())
+            start = i+1
+    return out
+
+
+def refine_MatMul(expr, assumptions):
+    """
+    >>> from sympy import MatrixSymbol, Q, assuming, refine
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> expr = X * X.T
+    >>> print(expr)
+    X*X.T
+    >>> with assuming(Q.orthogonal(X)):
+    ...     print(refine(expr))
+    I
+    """
+    newargs = []
+    exprargs = []
+
+    for args in expr.args:
+        if args.is_Matrix:
+            exprargs.append(args)
+        else:
+            newargs.append(args)
+
+    last = exprargs[0]
+    for arg in exprargs[1:]:
+        if arg == last.T and ask(Q.orthogonal(arg), assumptions):
+            last = Identity(arg.shape[0])
+        elif arg == last.conjugate() and ask(Q.unitary(arg), assumptions):
+            last = Identity(arg.shape[0])
+        else:
+            newargs.append(last)
+            last = arg
+    newargs.append(last)
+
+    return MatMul(*newargs)
+
+
+handlers_dict['MatMul'] = refine_MatMul
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matpow.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matpow.py
new file mode 100644
index 0000000000000000000000000000000000000000..b6472995e134e9e5ebfd28a901480665d1531275
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/matpow.py
@@ -0,0 +1,150 @@
+from .matexpr import MatrixExpr
+from .special import Identity
+from sympy.core import S
+from sympy.core.expr import ExprBuilder
+from sympy.core.cache import cacheit
+from sympy.core.power import Pow
+from sympy.core.sympify import _sympify
+from sympy.matrices import MatrixBase
+from sympy.matrices.exceptions import NonSquareMatrixError
+
+
+class MatPow(MatrixExpr):
+    def __new__(cls, base, exp, evaluate=False, **options):
+        base = _sympify(base)
+        if not base.is_Matrix:
+            raise TypeError("MatPow base should be a matrix")
+
+        if base.is_square is False:
+            raise NonSquareMatrixError("Power of non-square matrix %s" % base)
+
+        exp = _sympify(exp)
+        obj = super().__new__(cls, base, exp)
+
+        if evaluate:
+            obj = obj.doit(deep=False)
+
+        return obj
+
+    @property
+    def base(self):
+        return self.args[0]
+
+    @property
+    def exp(self):
+        return self.args[1]
+
+    @property
+    def shape(self):
+        return self.base.shape
+
+    @cacheit
+    def _get_explicit_matrix(self):
+        return self.base.as_explicit()**self.exp
+
+    def _entry(self, i, j, **kwargs):
+        from sympy.matrices.expressions import MatMul
+        A = self.doit()
+        if isinstance(A, MatPow):
+            # We still have a MatPow, make an explicit MatMul out of it.
+            if A.exp.is_Integer and A.exp.is_positive:
+                A = MatMul(*[A.base for k in range(A.exp)])
+            elif not self._is_shape_symbolic():
+                return A._get_explicit_matrix()[i, j]
+            else:
+                # Leave the expression unevaluated:
+                from sympy.matrices.expressions.matexpr import MatrixElement
+                return MatrixElement(self, i, j)
+        return A[i, j]
+
+    def doit(self, **hints):
+        if hints.get('deep', True):
+            base, exp = (arg.doit(**hints) for arg in self.args)
+        else:
+            base, exp = self.args
+
+        # combine all powers, e.g. (A ** 2) ** 3 -> A ** 6
+        while isinstance(base, MatPow):
+            exp *= base.args[1]
+            base = base.args[0]
+
+        if isinstance(base, MatrixBase):
+            # Delegate
+            return base ** exp
+
+        # Handle simple cases so that _eval_power() in MatrixExpr sub-classes can ignore them
+        if exp == S.One:
+            return base
+        if exp == S.Zero:
+            return Identity(base.rows)
+        if exp == S.NegativeOne:
+            from sympy.matrices.expressions import Inverse
+            return Inverse(base).doit(**hints)
+
+        eval_power = getattr(base, '_eval_power', None)
+        if eval_power is not None:
+            return eval_power(exp)
+
+        return MatPow(base, exp)
+
+    def _eval_transpose(self):
+        base, exp = self.args
+        return MatPow(base.transpose(), exp)
+
+    def _eval_adjoint(self):
+        base, exp = self.args
+        return MatPow(base.adjoint(), exp)
+
+    def _eval_conjugate(self):
+        base, exp = self.args
+        return MatPow(base.conjugate(), exp)
+
+    def _eval_derivative(self, x):
+        return Pow._eval_derivative(self, x)
+
+    def _eval_derivative_matrix_lines(self, x):
+        from sympy.tensor.array.expressions.array_expressions import ArrayContraction
+        from ...tensor.array.expressions.array_expressions import ArrayTensorProduct
+        from .matmul import MatMul
+        from .inverse import Inverse
+        exp = self.exp
+        if self.base.shape == (1, 1) and not exp.has(x):
+            lr = self.base._eval_derivative_matrix_lines(x)
+            for i in lr:
+                subexpr = ExprBuilder(
+                    ArrayContraction,
+                    [
+                        ExprBuilder(
+                            ArrayTensorProduct,
+                            [
+                                Identity(1),
+                                i._lines[0],
+                                exp*self.base**(exp-1),
+                                i._lines[1],
+                                Identity(1),
+                            ]
+                        ),
+                        (0, 3, 4), (5, 7, 8)
+                    ],
+                    validator=ArrayContraction._validate
+                )
+                i._first_pointer_parent = subexpr.args[0].args
+                i._first_pointer_index = 0
+                i._second_pointer_parent = subexpr.args[0].args
+                i._second_pointer_index = 4
+                i._lines = [subexpr]
+            return lr
+        if (exp > 0) == True:
+            newexpr = MatMul.fromiter([self.base for i in range(exp)])
+        elif (exp == -1) == True:
+            return Inverse(self.base)._eval_derivative_matrix_lines(x)
+        elif (exp < 0) == True:
+            newexpr = MatMul.fromiter([Inverse(self.base) for i in range(-exp)])
+        elif (exp == 0) == True:
+            return self.doit()._eval_derivative_matrix_lines(x)
+        else:
+            raise NotImplementedError("cannot evaluate %s derived by %s" % (self, x))
+        return newexpr._eval_derivative_matrix_lines(x)
+
+    def _eval_inverse(self):
+        return MatPow(self.base, -self.exp)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/permutation.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/permutation.py
new file mode 100644
index 0000000000000000000000000000000000000000..5634fa941a53d8890583fe61bb29bc34f4e6000d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/permutation.py
@@ -0,0 +1,303 @@
+from sympy.core import S
+from sympy.core.sympify import _sympify
+from sympy.functions import KroneckerDelta
+
+from .matexpr import MatrixExpr
+from .special import ZeroMatrix, Identity, OneMatrix
+
+
+class PermutationMatrix(MatrixExpr):
+    """A Permutation Matrix
+
+    Parameters
+    ==========
+
+    perm : Permutation
+        The permutation the matrix uses.
+
+        The size of the permutation determines the matrix size.
+
+        See the documentation of
+        :class:`sympy.combinatorics.permutations.Permutation` for
+        the further information of how to create a permutation object.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, PermutationMatrix
+    >>> from sympy.combinatorics import Permutation
+
+    Creating a permutation matrix:
+
+    >>> p = Permutation(1, 2, 0)
+    >>> P = PermutationMatrix(p)
+    >>> P = P.as_explicit()
+    >>> P
+    Matrix([
+    [0, 1, 0],
+    [0, 0, 1],
+    [1, 0, 0]])
+
+    Permuting a matrix row and column:
+
+    >>> M = Matrix([0, 1, 2])
+    >>> Matrix(P*M)
+    Matrix([
+    [1],
+    [2],
+    [0]])
+
+    >>> Matrix(M.T*P)
+    Matrix([[2, 0, 1]])
+
+    See Also
+    ========
+
+    sympy.combinatorics.permutations.Permutation
+    """
+
+    def __new__(cls, perm):
+        from sympy.combinatorics.permutations import Permutation
+
+        perm = _sympify(perm)
+        if not isinstance(perm, Permutation):
+            raise ValueError(
+                "{} must be a SymPy Permutation instance.".format(perm))
+
+        return super().__new__(cls, perm)
+
+    @property
+    def shape(self):
+        size = self.args[0].size
+        return (size, size)
+
+    @property
+    def is_Identity(self):
+        return self.args[0].is_Identity
+
+    def doit(self, **hints):
+        if self.is_Identity:
+            return Identity(self.rows)
+        return self
+
+    def _entry(self, i, j, **kwargs):
+        perm = self.args[0]
+        return KroneckerDelta(perm.apply(i), j)
+
+    def _eval_power(self, exp):
+        return PermutationMatrix(self.args[0] ** exp).doit()
+
+    def _eval_inverse(self):
+        return PermutationMatrix(self.args[0] ** -1)
+
+    _eval_transpose = _eval_adjoint = _eval_inverse
+
+    def _eval_determinant(self):
+        sign = self.args[0].signature()
+        if sign == 1:
+            return S.One
+        elif sign == -1:
+            return S.NegativeOne
+        raise NotImplementedError
+
+    def _eval_rewrite_as_BlockDiagMatrix(self, *args, **kwargs):
+        from sympy.combinatorics.permutations import Permutation
+        from .blockmatrix import BlockDiagMatrix
+
+        perm = self.args[0]
+        full_cyclic_form = perm.full_cyclic_form
+
+        cycles_picks = []
+
+        # Stage 1. Decompose the cycles into the blockable form.
+        a, b, c = 0, 0, 0
+        flag = False
+        for cycle in full_cyclic_form:
+            l = len(cycle)
+            m = max(cycle)
+
+            if not flag:
+                if m + 1 > a + l:
+                    flag = True
+                    temp = [cycle]
+                    b = m
+                    c = l
+                else:
+                    cycles_picks.append([cycle])
+                    a += l
+
+            else:
+                if m > b:
+                    if m + 1 == a + c + l:
+                        temp.append(cycle)
+                        cycles_picks.append(temp)
+                        flag = False
+                        a = m+1
+                    else:
+                        b = m
+                        temp.append(cycle)
+                        c += l
+                else:
+                    if b + 1 == a + c + l:
+                        temp.append(cycle)
+                        cycles_picks.append(temp)
+                        flag = False
+                        a = b+1
+                    else:
+                        temp.append(cycle)
+                        c += l
+
+        # Stage 2. Normalize each decomposed cycles and build matrix.
+        p = 0
+        args = []
+        for pick in cycles_picks:
+            new_cycles = []
+            l = 0
+            for cycle in pick:
+                new_cycle = [i - p for i in cycle]
+                new_cycles.append(new_cycle)
+                l += len(cycle)
+            p += l
+            perm = Permutation(new_cycles)
+            mat = PermutationMatrix(perm)
+            args.append(mat)
+
+        return BlockDiagMatrix(*args)
+
+
+class MatrixPermute(MatrixExpr):
+    r"""Symbolic representation for permuting matrix rows or columns.
+
+    Parameters
+    ==========
+
+    perm : Permutation, PermutationMatrix
+        The permutation to use for permuting the matrix.
+        The permutation can be resized to the suitable one,
+
+    axis : 0 or 1
+        The axis to permute alongside.
+        If `0`, it will permute the matrix rows.
+        If `1`, it will permute the matrix columns.
+
+    Notes
+    =====
+
+    This follows the same notation used in
+    :meth:`sympy.matrices.matrixbase.MatrixBase.permute`.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, MatrixPermute
+    >>> from sympy.combinatorics import Permutation
+
+    Permuting the matrix rows:
+
+    >>> p = Permutation(1, 2, 0)
+    >>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> B = MatrixPermute(A, p, axis=0)
+    >>> B.as_explicit()
+    Matrix([
+    [4, 5, 6],
+    [7, 8, 9],
+    [1, 2, 3]])
+
+    Permuting the matrix columns:
+
+    >>> B = MatrixPermute(A, p, axis=1)
+    >>> B.as_explicit()
+    Matrix([
+    [2, 3, 1],
+    [5, 6, 4],
+    [8, 9, 7]])
+
+    See Also
+    ========
+
+    sympy.matrices.matrixbase.MatrixBase.permute
+    """
+    def __new__(cls, mat, perm, axis=S.Zero):
+        from sympy.combinatorics.permutations import Permutation
+
+        mat = _sympify(mat)
+        if not mat.is_Matrix:
+            raise ValueError(
+                "{} must be a SymPy matrix instance.".format(perm))
+
+        perm = _sympify(perm)
+        if isinstance(perm, PermutationMatrix):
+            perm = perm.args[0]
+
+        if not isinstance(perm, Permutation):
+            raise ValueError(
+                "{} must be a SymPy Permutation or a PermutationMatrix " \
+                "instance".format(perm))
+
+        axis = _sympify(axis)
+        if axis not in (0, 1):
+            raise ValueError("The axis must be 0 or 1.")
+
+        mat_size = mat.shape[axis]
+        if mat_size != perm.size:
+            try:
+                perm = perm.resize(mat_size)
+            except ValueError:
+                raise ValueError(
+                    "Size does not match between the permutation {} "
+                    "and the matrix {} threaded over the axis {} "
+                    "and cannot be converted."
+                    .format(perm, mat, axis))
+
+        return super().__new__(cls, mat, perm, axis)
+
+    def doit(self, deep=True, **hints):
+        mat, perm, axis = self.args
+
+        if deep:
+            mat = mat.doit(deep=deep, **hints)
+            perm = perm.doit(deep=deep, **hints)
+
+        if perm.is_Identity:
+            return mat
+
+        if mat.is_Identity:
+            if axis is S.Zero:
+                return PermutationMatrix(perm)
+            elif axis is S.One:
+                return PermutationMatrix(perm**-1)
+
+        if isinstance(mat, (ZeroMatrix, OneMatrix)):
+            return mat
+
+        if isinstance(mat, MatrixPermute) and mat.args[2] == axis:
+            return MatrixPermute(mat.args[0], perm * mat.args[1], axis)
+
+        return self
+
+    @property
+    def shape(self):
+        return self.args[0].shape
+
+    def _entry(self, i, j, **kwargs):
+        mat, perm, axis = self.args
+
+        if axis == 0:
+            return mat[perm.apply(i), j]
+        elif axis == 1:
+            return mat[i, perm.apply(j)]
+
+    def _eval_rewrite_as_MatMul(self, *args, **kwargs):
+        from .matmul import MatMul
+
+        mat, perm, axis = self.args
+
+        deep = kwargs.get("deep", True)
+
+        if deep:
+            mat = mat.rewrite(MatMul)
+
+        if axis == 0:
+            return MatMul(PermutationMatrix(perm), mat)
+        elif axis == 1:
+            return MatMul(mat, PermutationMatrix(perm**-1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/sets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/sets.py
new file mode 100644
index 0000000000000000000000000000000000000000..ab4930ea8f1b058977a8dd1abdc62f1f5e2195c1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/sets.py
@@ -0,0 +1,68 @@
+from sympy.core.assumptions import check_assumptions
+from sympy.core.logic import fuzzy_and
+from sympy.core.sympify import _sympify
+from sympy.matrices.kind import MatrixKind
+from sympy.sets.sets import Set, SetKind
+from sympy.core.kind import NumberKind
+from .matexpr import MatrixExpr
+
+
+class MatrixSet(Set):
+    """
+    MatrixSet represents the set of matrices with ``shape = (n, m)`` over the
+    given set.
+
+    Examples
+    ========
+
+    >>> from sympy.matrices import MatrixSet
+    >>> from sympy import S, I, Matrix
+    >>> M = MatrixSet(2, 2, set=S.Reals)
+    >>> X = Matrix([[1, 2], [3, 4]])
+    >>> X in M
+    True
+    >>> X = Matrix([[1, 2], [I, 4]])
+    >>> X in M
+    False
+
+    """
+    is_empty = False
+
+    def __new__(cls, n, m, set):
+        n, m, set = _sympify(n), _sympify(m), _sympify(set)
+        cls._check_dim(n)
+        cls._check_dim(m)
+        if not isinstance(set, Set):
+            raise TypeError("{} should be an instance of Set.".format(set))
+        return Set.__new__(cls, n, m, set)
+
+    @property
+    def shape(self):
+        return self.args[:2]
+
+    @property
+    def set(self):
+        return self.args[2]
+
+    def _contains(self, other):
+        if not isinstance(other, MatrixExpr):
+            raise TypeError("{} should be an instance of MatrixExpr.".format(other))
+        if other.shape != self.shape:
+            are_symbolic = any(_sympify(x).is_Symbol for x in other.shape + self.shape)
+            if are_symbolic:
+                return None
+            return False
+        return fuzzy_and(self.set.contains(x) for x in other)
+
+    @classmethod
+    def _check_dim(cls, dim):
+        """Helper function to check invalid matrix dimensions"""
+        ok = not dim.is_Float and check_assumptions(
+            dim, integer=True, nonnegative=True)
+        if ok is False:
+            raise ValueError(
+                "The dimension specification {} should be "
+                "a nonnegative integer.".format(dim))
+
+    def _kind(self):
+        return SetKind(MatrixKind(NumberKind))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/slice.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/slice.py
new file mode 100644
index 0000000000000000000000000000000000000000..1904b49f29c503fb4c0c909532f8342fb0f4b135
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/slice.py
@@ -0,0 +1,114 @@
+from sympy.matrices.expressions.matexpr import MatrixExpr
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.functions.elementary.integers import floor
+
+def normalize(i, parentsize):
+    if isinstance(i, slice):
+        i = (i.start, i.stop, i.step)
+    if not isinstance(i, (tuple, list, Tuple)):
+        if (i < 0) == True:
+            i += parentsize
+        i = (i, i+1, 1)
+    i = list(i)
+    if len(i) == 2:
+        i.append(1)
+    start, stop, step = i
+    start = start or 0
+    if stop is None:
+        stop = parentsize
+    if (start < 0) == True:
+        start += parentsize
+    if (stop < 0) == True:
+        stop += parentsize
+    step = step or 1
+
+    if ((stop - start) * step < 1) == True:
+        raise IndexError()
+
+    return (start, stop, step)
+
+class MatrixSlice(MatrixExpr):
+    """ A MatrixSlice of a Matrix Expression
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSlice, ImmutableMatrix
+    >>> M = ImmutableMatrix(4, 4, range(16))
+    >>> M
+    Matrix([
+    [ 0,  1,  2,  3],
+    [ 4,  5,  6,  7],
+    [ 8,  9, 10, 11],
+    [12, 13, 14, 15]])
+
+    >>> B = MatrixSlice(M, (0, 2), (2, 4))
+    >>> ImmutableMatrix(B)
+    Matrix([
+    [2, 3],
+    [6, 7]])
+    """
+    parent = property(lambda self: self.args[0])
+    rowslice = property(lambda self: self.args[1])
+    colslice = property(lambda self: self.args[2])
+
+    def __new__(cls, parent, rowslice, colslice):
+        rowslice = normalize(rowslice, parent.shape[0])
+        colslice = normalize(colslice, parent.shape[1])
+        if not (len(rowslice) == len(colslice) == 3):
+            raise IndexError()
+        if ((0 > rowslice[0]) == True or
+            (parent.shape[0] < rowslice[1]) == True or
+            (0 > colslice[0]) == True or
+            (parent.shape[1] < colslice[1]) == True):
+            raise IndexError()
+        if isinstance(parent, MatrixSlice):
+            return mat_slice_of_slice(parent, rowslice, colslice)
+        return Basic.__new__(cls, parent, Tuple(*rowslice), Tuple(*colslice))
+
+    @property
+    def shape(self):
+        rows = self.rowslice[1] - self.rowslice[0]
+        rows = rows if self.rowslice[2] == 1 else floor(rows/self.rowslice[2])
+        cols = self.colslice[1] - self.colslice[0]
+        cols = cols if self.colslice[2] == 1 else floor(cols/self.colslice[2])
+        return rows, cols
+
+    def _entry(self, i, j, **kwargs):
+        return self.parent._entry(i*self.rowslice[2] + self.rowslice[0],
+                                  j*self.colslice[2] + self.colslice[0],
+                                  **kwargs)
+
+    @property
+    def on_diag(self):
+        return self.rowslice == self.colslice
+
+
+def slice_of_slice(s, t):
+    start1, stop1, step1 = s
+    start2, stop2, step2 = t
+
+    start = start1 + start2*step1
+    step = step1 * step2
+    stop = start1 + step1*stop2
+
+    if stop > stop1:
+        raise IndexError()
+
+    return start, stop, step
+
+
+def mat_slice_of_slice(parent, rowslice, colslice):
+    """ Collapse nested matrix slices
+
+    >>> from sympy import MatrixSymbol
+    >>> X = MatrixSymbol('X', 10, 10)
+    >>> X[:, 1:5][5:8, :]
+    X[5:8, 1:5]
+    >>> X[1:9:2, 2:6][1:3, 2]
+    X[3:7:2, 4:5]
+    """
+    row = slice_of_slice(parent.rowslice, rowslice)
+    col = slice_of_slice(parent.colslice, colslice)
+    return MatrixSlice(parent.parent, row, col)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/special.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/special.py
new file mode 100644
index 0000000000000000000000000000000000000000..d1e426f16ada0e4245b644867974b41b6f86b5cc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/special.py
@@ -0,0 +1,299 @@
+from sympy.assumptions.ask import ask, Q
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.sympify import _sympify
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.exceptions import NonInvertibleMatrixError
+from .matexpr import MatrixExpr
+
+
+class ZeroMatrix(MatrixExpr):
+    """The Matrix Zero 0 - additive identity
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, ZeroMatrix
+    >>> A = MatrixSymbol('A', 3, 5)
+    >>> Z = ZeroMatrix(3, 5)
+    >>> A + Z
+    A
+    >>> Z*A.T
+    0
+    """
+    is_ZeroMatrix = True
+
+    def __new__(cls, m, n):
+        m, n = _sympify(m), _sympify(n)
+        cls._check_dim(m)
+        cls._check_dim(n)
+
+        return super().__new__(cls, m, n)
+
+    @property
+    def shape(self):
+        return (self.args[0], self.args[1])
+
+    def _eval_power(self, exp):
+        # exp = -1, 0, 1 are already handled at this stage
+        if (exp < 0) == True:
+            raise NonInvertibleMatrixError("Matrix det == 0; not invertible")
+        return self
+
+    def _eval_transpose(self):
+        return ZeroMatrix(self.cols, self.rows)
+
+    def _eval_adjoint(self):
+        return ZeroMatrix(self.cols, self.rows)
+
+    def _eval_trace(self):
+        return S.Zero
+
+    def _eval_determinant(self):
+        return S.Zero
+
+    def _eval_inverse(self):
+        raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+
+    def _eval_as_real_imag(self):
+        return (self, self)
+
+    def _eval_conjugate(self):
+        return self
+
+    def _entry(self, i, j, **kwargs):
+        return S.Zero
+
+
+class GenericZeroMatrix(ZeroMatrix):
+    """
+    A zero matrix without a specified shape
+
+    This exists primarily so MatAdd() with no arguments can return something
+    meaningful.
+    """
+    def __new__(cls):
+        # super(ZeroMatrix, cls) instead of super(GenericZeroMatrix, cls)
+        # because ZeroMatrix.__new__ doesn't have the same signature
+        return super(ZeroMatrix, cls).__new__(cls)
+
+    @property
+    def rows(self):
+        raise TypeError("GenericZeroMatrix does not have a specified shape")
+
+    @property
+    def cols(self):
+        raise TypeError("GenericZeroMatrix does not have a specified shape")
+
+    @property
+    def shape(self):
+        raise TypeError("GenericZeroMatrix does not have a specified shape")
+
+    # Avoid Matrix.__eq__ which might call .shape
+    def __eq__(self, other):
+        return isinstance(other, GenericZeroMatrix)
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __hash__(self):
+        return super().__hash__()
+
+
+
+class Identity(MatrixExpr):
+    """The Matrix Identity I - multiplicative identity
+
+    Examples
+    ========
+
+    >>> from sympy import Identity, MatrixSymbol
+    >>> A = MatrixSymbol('A', 3, 5)
+    >>> I = Identity(3)
+    >>> I*A
+    A
+    """
+
+    is_Identity = True
+
+    def __new__(cls, n):
+        n = _sympify(n)
+        cls._check_dim(n)
+
+        return super().__new__(cls, n)
+
+    @property
+    def rows(self):
+        return self.args[0]
+
+    @property
+    def cols(self):
+        return self.args[0]
+
+    @property
+    def shape(self):
+        return (self.args[0], self.args[0])
+
+    @property
+    def is_square(self):
+        return True
+
+    def _eval_transpose(self):
+        return self
+
+    def _eval_trace(self):
+        return self.rows
+
+    def _eval_inverse(self):
+        return self
+
+    def _eval_as_real_imag(self):
+        return (self, ZeroMatrix(*self.shape))
+
+    def _eval_conjugate(self):
+        return self
+
+    def _eval_adjoint(self):
+        return self
+
+    def _entry(self, i, j, **kwargs):
+        eq = Eq(i, j)
+        if eq is S.true:
+            return S.One
+        elif eq is S.false:
+            return S.Zero
+        return KroneckerDelta(i, j, (0, self.cols-1))
+
+    def _eval_determinant(self):
+        return S.One
+
+    def _eval_power(self, exp):
+        return self
+
+
+class GenericIdentity(Identity):
+    """
+    An identity matrix without a specified shape
+
+    This exists primarily so MatMul() with no arguments can return something
+    meaningful.
+    """
+    def __new__(cls):
+        # super(Identity, cls) instead of super(GenericIdentity, cls) because
+        # Identity.__new__ doesn't have the same signature
+        return super(Identity, cls).__new__(cls)
+
+    @property
+    def rows(self):
+        raise TypeError("GenericIdentity does not have a specified shape")
+
+    @property
+    def cols(self):
+        raise TypeError("GenericIdentity does not have a specified shape")
+
+    @property
+    def shape(self):
+        raise TypeError("GenericIdentity does not have a specified shape")
+
+    @property
+    def is_square(self):
+        return True
+
+    # Avoid Matrix.__eq__ which might call .shape
+    def __eq__(self, other):
+        return isinstance(other, GenericIdentity)
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __hash__(self):
+        return super().__hash__()
+
+
+class OneMatrix(MatrixExpr):
+    """
+    Matrix whose all entries are ones.
+    """
+    def __new__(cls, m, n, evaluate=False):
+        m, n = _sympify(m), _sympify(n)
+        cls._check_dim(m)
+        cls._check_dim(n)
+
+        if evaluate:
+            condition = Eq(m, 1) & Eq(n, 1)
+            if condition == True:
+                return Identity(1)
+
+        obj = super().__new__(cls, m, n)
+        return obj
+
+    @property
+    def shape(self):
+        return self._args
+
+    @property
+    def is_Identity(self):
+        return self._is_1x1() == True
+
+    def as_explicit(self):
+        from sympy.matrices.immutable import ImmutableDenseMatrix
+        return ImmutableDenseMatrix.ones(*self.shape)
+
+    def doit(self, **hints):
+        args = self.args
+        if hints.get('deep', True):
+            args = [a.doit(**hints) for a in args]
+        return self.func(*args, evaluate=True)
+
+    def _eval_power(self, exp):
+        # exp = -1, 0, 1 are already handled at this stage
+        if self._is_1x1() == True:
+            return Identity(1)
+        if (exp < 0) == True:
+            raise NonInvertibleMatrixError("Matrix det == 0; not invertible")
+        if ask(Q.integer(exp)):
+            return self.shape[0] ** (exp - 1) * OneMatrix(*self.shape)
+        return super()._eval_power(exp)
+
+    def _eval_transpose(self):
+        return OneMatrix(self.cols, self.rows)
+
+    def _eval_adjoint(self):
+        return OneMatrix(self.cols, self.rows)
+
+    def _eval_trace(self):
+        return S.One*self.rows
+
+    def _is_1x1(self):
+        """Returns true if the matrix is known to be 1x1"""
+        shape = self.shape
+        return Eq(shape[0], 1) & Eq(shape[1], 1)
+
+    def _eval_determinant(self):
+        condition = self._is_1x1()
+        if condition == True:
+            return S.One
+        elif condition == False:
+            return S.Zero
+        else:
+            from sympy.matrices.expressions.determinant import Determinant
+            return Determinant(self)
+
+    def _eval_inverse(self):
+        condition = self._is_1x1()
+        if condition == True:
+            return Identity(1)
+        elif condition == False:
+            raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+        else:
+            from .inverse import Inverse
+            return Inverse(self)
+
+    def _eval_as_real_imag(self):
+        return (self, ZeroMatrix(*self.shape))
+
+    def _eval_conjugate(self):
+        return self
+
+    def _entry(self, i, j, **kwargs):
+        return S.One
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_adjoint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_adjoint.py
new file mode 100644
index 0000000000000000000000000000000000000000..7106b5740b1dc7c32f2c6f5ecb9d286b5e1dd222
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_adjoint.py
@@ -0,0 +1,34 @@
+from sympy.core import symbols, S
+from sympy.functions import adjoint, conjugate, transpose
+from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose
+from sympy.matrices import eye, Matrix
+
+n, m, l, k, p = symbols('n m l k p', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+
+
+def test_adjoint():
+    Sq = MatrixSymbol('Sq', n, n)
+
+    assert Adjoint(A).shape == (m, n)
+    assert Adjoint(A*B).shape == (l, n)
+    assert adjoint(Adjoint(A)) == A
+    assert isinstance(Adjoint(Adjoint(A)), Adjoint)
+
+    assert conjugate(Adjoint(A)) == Transpose(A)
+    assert transpose(Adjoint(A)) == Adjoint(Transpose(A))
+
+    assert Adjoint(eye(3)).doit() == eye(3)
+
+    assert Adjoint(S(5)).doit() == S(5)
+
+    assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
+
+    assert adjoint(trace(Sq)) == conjugate(trace(Sq))
+    assert trace(adjoint(Sq)) == conjugate(trace(Sq))
+
+    assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
+
+    assert Adjoint(A*B).doit() == Adjoint(B) * Adjoint(A)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_applyfunc.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_applyfunc.py
new file mode 100644
index 0000000000000000000000000000000000000000..d98732e2751e53938d96d7ea56c916e6fee4578e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_applyfunc.py
@@ -0,0 +1,118 @@
+from sympy.core.symbol import symbols, Dummy
+from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction
+from sympy.core.function import Lambda
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.trigonometric import sin
+from sympy.matrices.dense import Matrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.simplify.simplify import simplify
+
+
+X = MatrixSymbol("X", 3, 3)
+Y = MatrixSymbol("Y", 3, 3)
+
+k = symbols("k")
+Xk = MatrixSymbol("X", k, k)
+
+Xd = X.as_explicit()
+
+x, y, z, t = symbols("x y z t")
+
+
+def test_applyfunc_matrix():
+    x = Dummy('x')
+    double = Lambda(x, x**2)
+
+    expr = ElementwiseApplyFunction(double, Xd)
+    assert isinstance(expr, ElementwiseApplyFunction)
+    assert expr.doit() == Xd.applyfunc(lambda x: x**2)
+    assert expr.shape == (3, 3)
+    assert expr.func(*expr.args) == expr
+    assert simplify(expr) == expr
+    assert expr[0, 0] == double(Xd[0, 0])
+
+    expr = ElementwiseApplyFunction(double, X)
+    assert isinstance(expr, ElementwiseApplyFunction)
+    assert isinstance(expr.doit(), ElementwiseApplyFunction)
+    assert expr == X.applyfunc(double)
+    assert expr.func(*expr.args) == expr
+
+    expr = ElementwiseApplyFunction(exp, X*Y)
+    assert expr.expr == X*Y
+    assert expr.function.dummy_eq(Lambda(x, exp(x)))
+    assert expr.dummy_eq((X*Y).applyfunc(exp))
+    assert expr.func(*expr.args) == expr
+
+    assert isinstance(X*expr, MatMul)
+    assert (X*expr).shape == (3, 3)
+    Z = MatrixSymbol("Z", 2, 3)
+    assert (Z*expr).shape == (2, 3)
+
+    expr = ElementwiseApplyFunction(exp, Z.T)*ElementwiseApplyFunction(exp, Z)
+    assert expr.shape == (3, 3)
+    expr = ElementwiseApplyFunction(exp, Z)*ElementwiseApplyFunction(exp, Z.T)
+    assert expr.shape == (2, 2)
+
+    M = Matrix([[x, y], [z, t]])
+    expr = ElementwiseApplyFunction(sin, M)
+    assert isinstance(expr, ElementwiseApplyFunction)
+    assert expr.function.dummy_eq(Lambda(x, sin(x)))
+    assert expr.expr == M
+    assert expr.doit() == M.applyfunc(sin)
+    assert expr.doit() == Matrix([[sin(x), sin(y)], [sin(z), sin(t)]])
+    assert expr.func(*expr.args) == expr
+
+    expr = ElementwiseApplyFunction(double, Xk)
+    assert expr.doit() == expr
+    assert expr.subs(k, 2).shape == (2, 2)
+    assert (expr*expr).shape == (k, k)
+    M = MatrixSymbol("M", k, t)
+    expr2 = M.T*expr*M
+    assert isinstance(expr2, MatMul)
+    assert expr2.args[1] == expr
+    assert expr2.shape == (t, t)
+    expr3 = expr*M
+    assert expr3.shape == (k, t)
+
+    expr1 = ElementwiseApplyFunction(lambda x: x+1, Xk)
+    expr2 = ElementwiseApplyFunction(lambda x: x, Xk)
+    assert expr1 != expr2
+
+
+def test_applyfunc_entry():
+
+    af = X.applyfunc(sin)
+    assert af[0, 0] == sin(X[0, 0])
+
+    af = Xd.applyfunc(sin)
+    assert af[0, 0] == sin(X[0, 0])
+
+
+def test_applyfunc_as_explicit():
+
+    af = X.applyfunc(sin)
+    assert af.as_explicit() == Matrix([
+        [sin(X[0, 0]), sin(X[0, 1]), sin(X[0, 2])],
+        [sin(X[1, 0]), sin(X[1, 1]), sin(X[1, 2])],
+        [sin(X[2, 0]), sin(X[2, 1]), sin(X[2, 2])],
+    ])
+
+
+def test_applyfunc_transpose():
+
+    af = Xk.applyfunc(sin)
+    assert af.T.dummy_eq(Xk.T.applyfunc(sin))
+
+
+def test_applyfunc_shape_11_matrices():
+    M = MatrixSymbol("M", 1, 1)
+
+    double = Lambda(x, x*2)
+
+    expr = M.applyfunc(sin)
+    assert isinstance(expr, ElementwiseApplyFunction)
+
+    expr = M.applyfunc(double)
+    assert isinstance(expr, MatMul)
+    assert expr == 2*M
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d4893cd9a4b3e47dd8e84db33031f7f6f3201fd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py
@@ -0,0 +1,469 @@
+from sympy.matrices.expressions.trace import Trace
+from sympy.testing.pytest import raises, slow
+from sympy.matrices.expressions.blockmatrix import (
+    block_collapse, bc_matmul, bc_block_plus_ident, BlockDiagMatrix,
+    BlockMatrix, bc_dist, bc_matadd, bc_transpose, bc_inverse,
+    blockcut, reblock_2x2, deblock)
+from sympy.matrices.expressions import (
+    MatrixSymbol, Identity, trace, det, ZeroMatrix, OneMatrix)
+from sympy.matrices.expressions.inverse import Inverse
+from sympy.matrices.expressions.matpow import MatPow
+from sympy.matrices.expressions.transpose import Transpose
+from sympy.matrices.exceptions import NonInvertibleMatrixError
+from sympy.matrices import (
+    Matrix, ImmutableMatrix, ImmutableSparseMatrix, zeros)
+from sympy.core import Tuple, Expr, S, Function
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions import transpose, im, re
+
+i, j, k, l, m, n, p = symbols('i:n, p', integer=True)
+A = MatrixSymbol('A', n, n)
+B = MatrixSymbol('B', n, n)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+G = MatrixSymbol('G', n, n)
+H = MatrixSymbol('H', n, n)
+b1 = BlockMatrix([[G, H]])
+b2 = BlockMatrix([[G], [H]])
+
+def test_bc_matmul():
+    assert bc_matmul(H*b1*b2*G) == BlockMatrix([[(H*G*G + H*H*H)*G]])
+
+def test_bc_matadd():
+    assert bc_matadd(BlockMatrix([[G, H]]) + BlockMatrix([[H, H]])) == \
+            BlockMatrix([[G+H, H+H]])
+
+def test_bc_transpose():
+    assert bc_transpose(Transpose(BlockMatrix([[A, B], [C, D]]))) == \
+            BlockMatrix([[A.T, C.T], [B.T, D.T]])
+
+def test_bc_dist_diag():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', m, m)
+    C = MatrixSymbol('C', l, l)
+    X = BlockDiagMatrix(A, B, C)
+
+    assert bc_dist(X+X).equals(BlockDiagMatrix(2*A, 2*B, 2*C))
+
+def test_block_plus_ident():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    Z = MatrixSymbol('Z', n + m, n + m)
+    assert bc_block_plus_ident(X + Identity(m + n) + Z) == \
+            BlockDiagMatrix(Identity(n), Identity(m)) + X + Z
+
+def test_BlockMatrix():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, k)
+    C = MatrixSymbol('C', l, m)
+    D = MatrixSymbol('D', l, k)
+    M = MatrixSymbol('M', m + k, p)
+    N = MatrixSymbol('N', l + n, k + m)
+    X = BlockMatrix(Matrix([[A, B], [C, D]]))
+
+    assert X.__class__(*X.args) == X
+
+    # block_collapse does nothing on normal inputs
+    E = MatrixSymbol('E', n, m)
+    assert block_collapse(A + 2*E) == A + 2*E
+    F = MatrixSymbol('F', m, m)
+    assert block_collapse(E.T*A*F) == E.T*A*F
+
+    assert X.shape == (l + n, k + m)
+    assert X.blockshape == (2, 2)
+    assert transpose(X) == BlockMatrix(Matrix([[A.T, C.T], [B.T, D.T]]))
+    assert transpose(X).shape == X.shape[::-1]
+
+    # Test that BlockMatrices and MatrixSymbols can still mix
+    assert (X*M).is_MatMul
+    assert X._blockmul(M).is_MatMul
+    assert (X*M).shape == (n + l, p)
+    assert (X + N).is_MatAdd
+    assert X._blockadd(N).is_MatAdd
+    assert (X + N).shape == X.shape
+
+    E = MatrixSymbol('E', m, 1)
+    F = MatrixSymbol('F', k, 1)
+
+    Y = BlockMatrix(Matrix([[E], [F]]))
+
+    assert (X*Y).shape == (l + n, 1)
+    assert block_collapse(X*Y).blocks[0, 0] == A*E + B*F
+    assert block_collapse(X*Y).blocks[1, 0] == C*E + D*F
+
+    # block_collapse passes down into container objects, transposes, and inverse
+    assert block_collapse(transpose(X*Y)) == transpose(block_collapse(X*Y))
+    assert block_collapse(Tuple(X*Y, 2*X)) == (
+        block_collapse(X*Y), block_collapse(2*X))
+
+    # Make sure that MatrixSymbols will enter 1x1 BlockMatrix if it simplifies
+    Ab = BlockMatrix([[A]])
+    Z = MatrixSymbol('Z', *A.shape)
+    assert block_collapse(Ab + Z) == A + Z
+
+def test_block_collapse_explicit_matrices():
+    A = Matrix([[1, 2], [3, 4]])
+    assert block_collapse(BlockMatrix([[A]])) == A
+
+    A = ImmutableSparseMatrix([[1, 2], [3, 4]])
+    assert block_collapse(BlockMatrix([[A]])) == A
+
+def test_issue_17624():
+    a = MatrixSymbol("a", 2, 2)
+    z = ZeroMatrix(2, 2)
+    b = BlockMatrix([[a, z], [z, z]])
+    assert block_collapse(b * b) == BlockMatrix([[a**2, z], [z, z]])
+    assert block_collapse(b * b * b) == BlockMatrix([[a**3, z], [z, z]])
+
+def test_issue_18618():
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert A == Matrix(BlockDiagMatrix(A))
+
+def test_BlockMatrix_trace():
+    A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD']
+    X = BlockMatrix([[A, B], [C, D]])
+    assert trace(X) == trace(A) + trace(D)
+    assert trace(BlockMatrix([ZeroMatrix(n, n)])) == 0
+
+def test_BlockMatrix_Determinant():
+    A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD']
+    X = BlockMatrix([[A, B], [C, D]])
+    from sympy.assumptions.ask import Q
+    from sympy.assumptions.assume import assuming
+    with assuming(Q.invertible(A)):
+        assert det(X) == det(A) * det(X.schur('A'))
+
+    assert isinstance(det(X), Expr)
+    assert det(BlockMatrix([A])) == det(A)
+    assert det(BlockMatrix([ZeroMatrix(n, n)])) == 0
+
+def test_squareBlockMatrix():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    Y = BlockMatrix([[A]])
+
+    assert X.is_square
+
+    Q = X + Identity(m + n)
+    assert (block_collapse(Q) ==
+        BlockMatrix([[A + Identity(n), B], [C, D + Identity(m)]]))
+
+    assert (X + MatrixSymbol('Q', n + m, n + m)).is_MatAdd
+    assert (X * MatrixSymbol('Q', n + m, n + m)).is_MatMul
+
+    assert block_collapse(Y.I) == A.I
+
+    assert isinstance(X.inverse(), Inverse)
+
+    assert not X.is_Identity
+
+    Z = BlockMatrix([[Identity(n), B], [C, D]])
+    assert not Z.is_Identity
+
+
+def test_BlockMatrix_2x2_inverse_symbolic():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, k - m)
+    C = MatrixSymbol('C', k - n, m)
+    D = MatrixSymbol('D', k - n, k - m)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert X.is_square and X.shape == (k, k)
+    assert isinstance(block_collapse(X.I), Inverse)  # Can't invert when none of the blocks is square
+
+    # test code path where only A is invertible
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = ZeroMatrix(m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [A.I + A.I * B * X.schur('A').I * C * A.I, -A.I * B * X.schur('A').I],
+        [-X.schur('A').I * C * A.I, X.schur('A').I],
+    ])
+
+    # test code path where only B is invertible
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, n)
+    C = ZeroMatrix(m, m)
+    D = MatrixSymbol('D', m, n)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [-X.schur('B').I * D * B.I, X.schur('B').I],
+        [B.I + B.I * A * X.schur('B').I * D * B.I, -B.I * A * X.schur('B').I],
+    ])
+
+    # test code path where only C is invertible
+    A = MatrixSymbol('A', n, m)
+    B = ZeroMatrix(n, n)
+    C = MatrixSymbol('C', m, m)
+    D = MatrixSymbol('D', m, n)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [-C.I * D * X.schur('C').I, C.I + C.I * D * X.schur('C').I * A * C.I],
+        [X.schur('C').I, -X.schur('C').I * A * C.I],
+    ])
+
+    # test code path where only D is invertible
+    A = ZeroMatrix(n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [X.schur('D').I, -X.schur('D').I * B * D.I],
+        [-D.I * C * X.schur('D').I, D.I + D.I * C * X.schur('D').I * B * D.I],
+    ])
+
+
+def test_BlockMatrix_2x2_inverse_numeric():
+    """Test 2x2 block matrix inversion numerically for all 4 formulas"""
+    M = Matrix([[1, 2], [3, 4]])
+    # rank deficient matrices that have full rank when two of them combined
+    D1 = Matrix([[1, 2], [2, 4]])
+    D2 = Matrix([[1, 3], [3, 9]])
+    D3 = Matrix([[1, 4], [4, 16]])
+    assert D1.rank() == D2.rank() == D3.rank() == 1
+    assert (D1 + D2).rank() == (D2 + D3).rank() == (D3 + D1).rank() == 2
+
+    # Only A is invertible
+    K = BlockMatrix([[M, D1], [D2, D3]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+    # Only B is invertible
+    K = BlockMatrix([[D1, M], [D2, D3]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+    # Only C is invertible
+    K = BlockMatrix([[D1, D2], [M, D3]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+    # Only D is invertible
+    K = BlockMatrix([[D1, D2], [D3, M]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+
+
+@slow
+def test_BlockMatrix_3x3_symbolic():
+    # Only test one of these, instead of all permutations, because it's slow
+    rowblocksizes = (n, m, k)
+    colblocksizes = (m, k, n)
+    K = BlockMatrix([
+        [MatrixSymbol('M%s%s' % (rows, cols), rows, cols) for cols in colblocksizes]
+        for rows in rowblocksizes
+    ])
+    collapse = block_collapse(K.I)
+    assert isinstance(collapse, BlockMatrix)
+
+
+def test_BlockDiagMatrix():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', m, m)
+    C = MatrixSymbol('C', l, l)
+    M = MatrixSymbol('M', n + m + l, n + m + l)
+
+    X = BlockDiagMatrix(A, B, C)
+    Y = BlockDiagMatrix(A, 2*B, 3*C)
+
+    assert X.blocks[1, 1] == B
+    assert X.shape == (n + m + l, n + m + l)
+    assert all(X.blocks[i, j].is_ZeroMatrix if i != j else X.blocks[i, j] in [A, B, C]
+            for i in range(3) for j in range(3))
+    assert X.__class__(*X.args) == X
+    assert X.get_diag_blocks() == (A, B, C)
+
+    assert isinstance(block_collapse(X.I * X), Identity)
+
+    assert bc_matmul(X*X) == BlockDiagMatrix(A*A, B*B, C*C)
+    assert block_collapse(X*X) == BlockDiagMatrix(A*A, B*B, C*C)
+    #XXX: should be == ??
+    assert block_collapse(X + X).equals(BlockDiagMatrix(2*A, 2*B, 2*C))
+    assert block_collapse(X*Y) == BlockDiagMatrix(A*A, 2*B*B, 3*C*C)
+    assert block_collapse(X + Y) == BlockDiagMatrix(2*A, 3*B, 4*C)
+
+    # Ensure that BlockDiagMatrices can still interact with normal MatrixExprs
+    assert (X*(2*M)).is_MatMul
+    assert (X + (2*M)).is_MatAdd
+
+    assert (X._blockmul(M)).is_MatMul
+    assert (X._blockadd(M)).is_MatAdd
+
+def test_BlockDiagMatrix_nonsquare():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', k, l)
+    X = BlockDiagMatrix(A, B)
+    assert X.shape == (n + k, m + l)
+    assert X.shape == (n + k, m + l)
+    assert X.rowblocksizes == [n, k]
+    assert X.colblocksizes == [m, l]
+    C = MatrixSymbol('C', n, m)
+    D = MatrixSymbol('D', k, l)
+    Y = BlockDiagMatrix(C, D)
+    assert block_collapse(X + Y) == BlockDiagMatrix(A + C, B + D)
+    assert block_collapse(X * Y.T) == BlockDiagMatrix(A * C.T, B * D.T)
+    raises(NonInvertibleMatrixError, lambda: BlockDiagMatrix(A, C.T).inverse())
+
+def test_BlockDiagMatrix_determinant():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', m, m)
+    assert det(BlockDiagMatrix()) == 1
+    assert det(BlockDiagMatrix(A)) == det(A)
+    assert det(BlockDiagMatrix(A, B)) == det(A) * det(B)
+
+    # non-square blocks
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', n, m)
+    assert det(BlockDiagMatrix(C, D)) == 0
+
+def test_BlockDiagMatrix_trace():
+    assert trace(BlockDiagMatrix()) == 0
+    assert trace(BlockDiagMatrix(ZeroMatrix(n, n))) == 0
+    A = MatrixSymbol('A', n, n)
+    assert trace(BlockDiagMatrix(A)) == trace(A)
+    B = MatrixSymbol('B', m, m)
+    assert trace(BlockDiagMatrix(A, B)) == trace(A) + trace(B)
+
+    # non-square blocks
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', n, m)
+    assert isinstance(trace(BlockDiagMatrix(C, D)), Trace)
+
+def test_BlockDiagMatrix_transpose():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', k, l)
+    assert transpose(BlockDiagMatrix()) == BlockDiagMatrix()
+    assert transpose(BlockDiagMatrix(A)) == BlockDiagMatrix(A.T)
+    assert transpose(BlockDiagMatrix(A, B)) == BlockDiagMatrix(A.T, B.T)
+
+def test_issue_2460():
+    bdm1 = BlockDiagMatrix(Matrix([i]), Matrix([j]))
+    bdm2 = BlockDiagMatrix(Matrix([k]), Matrix([l]))
+    assert block_collapse(bdm1 + bdm2) == BlockDiagMatrix(Matrix([i + k]), Matrix([j + l]))
+
+def test_blockcut():
+    A = MatrixSymbol('A', n, m)
+    B = blockcut(A, (n/2, n/2), (m/2, m/2))
+    assert B == BlockMatrix([[A[:n/2, :m/2], A[:n/2, m/2:]],
+                             [A[n/2:, :m/2], A[n/2:, m/2:]]])
+
+    M = ImmutableMatrix(4, 4, range(16))
+    B = blockcut(M, (2, 2), (2, 2))
+    assert M == ImmutableMatrix(B)
+
+    B = blockcut(M, (1, 3), (2, 2))
+    assert ImmutableMatrix(B.blocks[0, 1]) == ImmutableMatrix([[2, 3]])
+
+def test_reblock_2x2():
+    B = BlockMatrix([[MatrixSymbol('A_%d%d'%(i,j), 2, 2)
+                            for j in range(3)]
+                            for i in range(3)])
+    assert B.blocks.shape == (3, 3)
+
+    BB = reblock_2x2(B)
+    assert BB.blocks.shape == (2, 2)
+
+    assert B.shape == BB.shape
+    assert B.as_explicit() == BB.as_explicit()
+
+def test_deblock():
+    B = BlockMatrix([[MatrixSymbol('A_%d%d'%(i,j), n, n)
+                    for j in range(4)]
+                    for i in range(4)])
+
+    assert deblock(reblock_2x2(B)) == B
+
+def test_block_collapse_type():
+    bm1 = BlockDiagMatrix(ImmutableMatrix([1]), ImmutableMatrix([2]))
+    bm2 = BlockDiagMatrix(ImmutableMatrix([3]), ImmutableMatrix([4]))
+
+    assert bm1.T.__class__ == BlockDiagMatrix
+    assert block_collapse(bm1 - bm2).__class__ == BlockDiagMatrix
+    assert block_collapse(Inverse(bm1)).__class__ == BlockDiagMatrix
+    assert block_collapse(Transpose(bm1)).__class__ == BlockDiagMatrix
+    assert bc_transpose(Transpose(bm1)).__class__ == BlockDiagMatrix
+    assert bc_inverse(Inverse(bm1)).__class__ == BlockDiagMatrix
+
+def test_invalid_block_matrix():
+    raises(ValueError, lambda: BlockMatrix([
+        [Identity(2), Identity(5)],
+    ]))
+    raises(ValueError, lambda: BlockMatrix([
+        [Identity(n), Identity(m)],
+    ]))
+    raises(ValueError, lambda: BlockMatrix([
+        [ZeroMatrix(n, n), ZeroMatrix(n, n)],
+        [ZeroMatrix(n, n - 1), ZeroMatrix(n, n + 1)],
+    ]))
+    raises(ValueError, lambda: BlockMatrix([
+        [ZeroMatrix(n - 1, n), ZeroMatrix(n, n)],
+        [ZeroMatrix(n + 1, n), ZeroMatrix(n, n)],
+    ]))
+
+def test_block_lu_decomposition():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+
+    #LDU decomposition
+    L, D, U = X.LDUdecomposition()
+    assert block_collapse(L*D*U) == X
+
+    #UDL decomposition
+    U, D, L = X.UDLdecomposition()
+    assert block_collapse(U*D*L) == X
+
+    #LU decomposition
+    L, U = X.LUdecomposition()
+    assert block_collapse(L*U) == X
+
+def test_issue_21866():
+    n  = 10
+    I  = Identity(n)
+    O  = ZeroMatrix(n, n)
+    A  = BlockMatrix([[  I,  O,  O,  O ],
+                      [  O,  I,  O,  O ],
+                      [  O,  O,  I,  O ],
+                      [  I,  O,  O,  I ]])
+    Ainv = block_collapse(A.inv())
+    AinvT = BlockMatrix([[  I,  O,  O,  O ],
+                      [  O,  I,  O,  O ],
+                      [  O,  O,  I,  O ],
+                      [  -I,  O,  O,  I ]])
+    assert Ainv == AinvT
+
+
+def test_adjoint_and_special_matrices():
+    A = Identity(3)
+    B = OneMatrix(3, 2)
+    C = ZeroMatrix(2, 3)
+    D = Identity(2)
+    X = BlockMatrix([[A, B], [C, D]])
+    X2 = BlockMatrix([[A, S.ImaginaryUnit*B], [C, D]])
+    assert X.adjoint() == BlockMatrix([[A, ZeroMatrix(3, 2)], [OneMatrix(2, 3), D]])
+    assert re(X) == X
+    assert X2.adjoint() == BlockMatrix([[A, ZeroMatrix(3, 2)], [-S.ImaginaryUnit*OneMatrix(2, 3), D]])
+    assert im(X2) == BlockMatrix([[ZeroMatrix(3, 3), OneMatrix(3, 2)], [ZeroMatrix(2, 3), ZeroMatrix(2, 2)]])
+
+
+def test_block_matrix_derivative():
+    x = symbols('x')
+    A = Matrix(3, 3, [Function(f'a{i}')(x) for i in range(9)])
+    bc = BlockMatrix([[A[:2, :2], A[:2, 2]], [A[2, :2], A[2:, 2]]])
+    assert Matrix(bc.diff(x)) - A.diff(x) == zeros(3, 3)
+
+
+def test_transpose_inverse_commute():
+    n = Symbol('n')
+    I = Identity(n)
+    Z = ZeroMatrix(n, n)
+    A = BlockMatrix([[I, Z], [Z, I]])
+
+    assert block_collapse(A.transpose().inverse()) == A
+    assert block_collapse(A.inverse().transpose()) == A
+
+    assert block_collapse(MatPow(A.transpose(), -2)) == MatPow(A, -2)
+    assert block_collapse(MatPow(A, -2).transpose()) == MatPow(A, -2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_companion.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_companion.py
new file mode 100644
index 0000000000000000000000000000000000000000..edc592c29098eddce0c6352806aa73d5d889e999
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_companion.py
@@ -0,0 +1,48 @@
+from sympy.core.expr import unchanged
+from sympy.core.symbol import Symbol, symbols
+from sympy.matrices.immutable import ImmutableDenseMatrix
+from sympy.matrices.expressions.companion import CompanionMatrix
+from sympy.polys.polytools import Poly
+from sympy.testing.pytest import raises
+
+
+def test_creation():
+    x = Symbol('x')
+    y = Symbol('y')
+    raises(ValueError, lambda: CompanionMatrix(1))
+    raises(ValueError, lambda: CompanionMatrix(Poly([1], x)))
+    raises(ValueError, lambda: CompanionMatrix(Poly([2, 1], x)))
+    raises(ValueError, lambda: CompanionMatrix(Poly(x*y, [x, y])))
+    assert unchanged(CompanionMatrix, Poly([1, 2, 3], x))
+
+
+def test_shape():
+    c0, c1, c2 = symbols('c0:3')
+    x = Symbol('x')
+    assert CompanionMatrix(Poly([1, c0], x)).shape == (1, 1)
+    assert CompanionMatrix(Poly([1, c1, c0], x)).shape == (2, 2)
+    assert CompanionMatrix(Poly([1, c2, c1, c0], x)).shape == (3, 3)
+
+
+def test_entry():
+    c0, c1, c2 = symbols('c0:3')
+    x = Symbol('x')
+    A = CompanionMatrix(Poly([1, c2, c1, c0], x))
+    assert A[0, 0] == 0
+    assert A[1, 0] == 1
+    assert A[1, 1] == 0
+    assert A[2, 1] == 1
+    assert A[0, 2] == -c0
+    assert A[1, 2] == -c1
+    assert A[2, 2] == -c2
+
+
+def test_as_explicit():
+    c0, c1, c2 = symbols('c0:3')
+    x = Symbol('x')
+    assert CompanionMatrix(Poly([1, c0], x)).as_explicit() == \
+        ImmutableDenseMatrix([-c0])
+    assert CompanionMatrix(Poly([1, c1, c0], x)).as_explicit() == \
+        ImmutableDenseMatrix([[0, -c0], [1, -c1]])
+    assert CompanionMatrix(Poly([1, c2, c1, c0], x)).as_explicit() == \
+        ImmutableDenseMatrix([[0, 0, -c0], [1, 0, -c1], [0, 1, -c2]])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_derivatives.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_derivatives.py
new file mode 100644
index 0000000000000000000000000000000000000000..77484c994dda62eea9771a76afd8b3caeadacb93
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_derivatives.py
@@ -0,0 +1,477 @@
+"""
+Some examples have been taken from:
+
+http://www.math.uwaterloo.ca/~hwolkowi//matrixcookbook.pdf
+"""
+from sympy import KroneckerProduct
+from sympy.combinatorics import Permutation
+from sympy.concrete.summations import Sum
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.expressions.determinant import Determinant
+from sympy.matrices.expressions.diagonal import DiagMatrix
+from sympy.matrices.expressions.hadamard import (HadamardPower, HadamardProduct, hadamard_product)
+from sympy.matrices.expressions.inverse import Inverse
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.special import OneMatrix
+from sympy.matrices.expressions.trace import Trace
+from sympy.matrices.expressions.matadd import MatAdd
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.matrices.expressions.special import (Identity, ZeroMatrix)
+from sympy.tensor.array.array_derivatives import ArrayDerivative
+from sympy.matrices.expressions import hadamard_power
+from sympy.tensor.array.expressions.array_expressions import ArrayAdd, ArrayTensorProduct, PermuteDims
+
+i, j, k = symbols("i j k")
+m, n = symbols("m n")
+
+X = MatrixSymbol("X", k, k)
+x = MatrixSymbol("x", k, 1)
+y = MatrixSymbol("y", k, 1)
+
+A = MatrixSymbol("A", k, k)
+B = MatrixSymbol("B", k, k)
+C = MatrixSymbol("C", k, k)
+D = MatrixSymbol("D", k, k)
+
+a = MatrixSymbol("a", k, 1)
+b = MatrixSymbol("b", k, 1)
+c = MatrixSymbol("c", k, 1)
+d = MatrixSymbol("d", k, 1)
+
+
+KDelta = lambda i, j: KroneckerDelta(i, j, (0, k-1))
+
+
+def _check_derivative_with_explicit_matrix(expr, x, diffexpr, dim=2):
+    # TODO: this is commented because it slows down the tests.
+    return
+
+    expr = expr.xreplace({k: dim})
+    x = x.xreplace({k: dim})
+    diffexpr = diffexpr.xreplace({k: dim})
+
+    expr = expr.as_explicit()
+    x = x.as_explicit()
+    diffexpr = diffexpr.as_explicit()
+
+    assert expr.diff(x).reshape(*diffexpr.shape).tomatrix() == diffexpr
+
+
+def test_matrix_derivative_by_scalar():
+    assert A.diff(i) == ZeroMatrix(k, k)
+    assert (A*(X + B)*c).diff(i) == ZeroMatrix(k, 1)
+    assert x.diff(i) == ZeroMatrix(k, 1)
+    assert (x.T*y).diff(i) == ZeroMatrix(1, 1)
+    assert (x*x.T).diff(i) == ZeroMatrix(k, k)
+    assert (x + y).diff(i) == ZeroMatrix(k, 1)
+    assert hadamard_power(x, 2).diff(i) == ZeroMatrix(k, 1)
+    assert hadamard_power(x, i).diff(i).dummy_eq(
+        HadamardProduct(x.applyfunc(log), HadamardPower(x, i)))
+    assert hadamard_product(x, y).diff(i) == ZeroMatrix(k, 1)
+    assert hadamard_product(i*OneMatrix(k, 1), x, y).diff(i) == hadamard_product(x, y)
+    assert (i*x).diff(i) == x
+    assert (sin(i)*A*B*x).diff(i) == cos(i)*A*B*x
+    assert x.applyfunc(sin).diff(i) == ZeroMatrix(k, 1)
+    assert Trace(i**2*X).diff(i) == 2*i*Trace(X)
+
+    mu = symbols("mu")
+    expr = (2*mu*x)
+    assert expr.diff(x) == 2*mu*Identity(k)
+
+
+def test_one_matrix():
+    assert MatMul(x.T, OneMatrix(k, 1)).diff(x) == OneMatrix(k, 1)
+
+
+def test_matrix_derivative_non_matrix_result():
+    # This is a 4-dimensional array:
+    I = Identity(k)
+    AdA = PermuteDims(ArrayTensorProduct(I, I), Permutation(3)(1, 2))
+    assert A.diff(A) == AdA
+    assert A.T.diff(A) == PermuteDims(ArrayTensorProduct(I, I), Permutation(3)(1, 2, 3))
+    assert (2*A).diff(A) == PermuteDims(ArrayTensorProduct(2*I, I), Permutation(3)(1, 2))
+    assert MatAdd(A, A).diff(A) == ArrayAdd(AdA, AdA)
+    assert (A + B).diff(A) == AdA
+
+
+def test_matrix_derivative_trivial_cases():
+    # Cookbook example 33:
+    # TODO: find a way to represent a four-dimensional zero-array:
+    assert X.diff(A) == ArrayDerivative(X, A)
+
+
+def test_matrix_derivative_with_inverse():
+
+    # Cookbook example 61:
+    expr = a.T*Inverse(X)*b
+    assert expr.diff(X) == -Inverse(X).T*a*b.T*Inverse(X).T
+
+    # Cookbook example 62:
+    expr = Determinant(Inverse(X))
+    # Not implemented yet:
+    # assert expr.diff(X) == -Determinant(X.inv())*(X.inv()).T
+
+    # Cookbook example 63:
+    expr = Trace(A*Inverse(X)*B)
+    assert expr.diff(X) == -(X**(-1)*B*A*X**(-1)).T
+
+    # Cookbook example 64:
+    expr = Trace(Inverse(X + A))
+    assert expr.diff(X) == -(Inverse(X + A)).T**2
+
+
+def test_matrix_derivative_vectors_and_scalars():
+
+    assert x.diff(x) == Identity(k)
+    assert x[i, 0].diff(x[m, 0]).doit() == KDelta(m, i)
+
+    assert x.T.diff(x) == Identity(k)
+
+    # Cookbook example 69:
+    expr = x.T*a
+    assert expr.diff(x) == a
+    assert expr[0, 0].diff(x[m, 0]).doit() == a[m, 0]
+    expr = a.T*x
+    assert expr.diff(x) == a
+
+    # Cookbook example 70:
+    expr = a.T*X*b
+    assert expr.diff(X) == a*b.T
+
+    # Cookbook example 71:
+    expr = a.T*X.T*b
+    assert expr.diff(X) == b*a.T
+
+    # Cookbook example 72:
+    expr = a.T*X*a
+    assert expr.diff(X) == a*a.T
+    expr = a.T*X.T*a
+    assert expr.diff(X) == a*a.T
+
+    # Cookbook example 77:
+    expr = b.T*X.T*X*c
+    assert expr.diff(X) == X*b*c.T + X*c*b.T
+
+    # Cookbook example 78:
+    expr = (B*x + b).T*C*(D*x + d)
+    assert expr.diff(x) == B.T*C*(D*x + d) + D.T*C.T*(B*x + b)
+
+    # Cookbook example 81:
+    expr = x.T*B*x
+    assert expr.diff(x) == B*x + B.T*x
+
+    # Cookbook example 82:
+    expr = b.T*X.T*D*X*c
+    assert expr.diff(X) == D.T*X*b*c.T + D*X*c*b.T
+
+    # Cookbook example 83:
+    expr = (X*b + c).T*D*(X*b + c)
+    assert expr.diff(X) == D*(X*b + c)*b.T + D.T*(X*b + c)*b.T
+    assert str(expr[0, 0].diff(X[m, n]).doit()) == \
+        'b[n, 0]*Sum((c[_i_1, 0] + Sum(X[_i_1, _i_3]*b[_i_3, 0], (_i_3, 0, k - 1)))*D[_i_1, m], (_i_1, 0, k - 1)) + Sum((c[_i_2, 0] + Sum(X[_i_2, _i_4]*b[_i_4, 0], (_i_4, 0, k - 1)))*D[m, _i_2]*b[n, 0], (_i_2, 0, k - 1))'
+
+    # See https://github.com/sympy/sympy/issues/16504#issuecomment-1018339957
+    expr = x*x.T*x
+    I = Identity(k)
+    assert expr.diff(x) == KroneckerProduct(I, x.T*x) + 2*x*x.T
+
+
+def test_matrix_derivatives_of_traces():
+
+    expr = Trace(A)*A
+    I = Identity(k)
+    assert expr.diff(A) == ArrayAdd(ArrayTensorProduct(I, A), PermuteDims(ArrayTensorProduct(Trace(A)*I, I), Permutation(3)(1, 2)))
+    assert expr[i, j].diff(A[m, n]).doit() == (
+        KDelta(i, m)*KDelta(j, n)*Trace(A) +
+        KDelta(m, n)*A[i, j]
+    )
+
+    ## First order:
+
+    # Cookbook example 99:
+    expr = Trace(X)
+    assert expr.diff(X) == Identity(k)
+    assert expr.rewrite(Sum).diff(X[m, n]).doit() == KDelta(m, n)
+
+    # Cookbook example 100:
+    expr = Trace(X*A)
+    assert expr.diff(X) == A.T
+    assert expr.rewrite(Sum).diff(X[m, n]).doit() == A[n, m]
+
+    # Cookbook example 101:
+    expr = Trace(A*X*B)
+    assert expr.diff(X) == A.T*B.T
+    assert expr.rewrite(Sum).diff(X[m, n]).doit().dummy_eq((A.T*B.T)[m, n])
+
+    # Cookbook example 102:
+    expr = Trace(A*X.T*B)
+    assert expr.diff(X) == B*A
+
+    # Cookbook example 103:
+    expr = Trace(X.T*A)
+    assert expr.diff(X) == A
+
+    # Cookbook example 104:
+    expr = Trace(A*X.T)
+    assert expr.diff(X) == A
+
+    # Cookbook example 105:
+    # TODO: TensorProduct is not supported
+    #expr = Trace(TensorProduct(A, X))
+    #assert expr.diff(X) == Trace(A)*Identity(k)
+
+    ## Second order:
+
+    # Cookbook example 106:
+    expr = Trace(X**2)
+    assert expr.diff(X) == 2*X.T
+
+    # Cookbook example 107:
+    expr = Trace(X**2*B)
+    assert expr.diff(X) == (X*B + B*X).T
+    expr = Trace(MatMul(X, X, B))
+    assert expr.diff(X) == (X*B + B*X).T
+
+    # Cookbook example 108:
+    expr = Trace(X.T*B*X)
+    assert expr.diff(X) == B*X + B.T*X
+
+    # Cookbook example 109:
+    expr = Trace(B*X*X.T)
+    assert expr.diff(X) == B*X + B.T*X
+
+    # Cookbook example 110:
+    expr = Trace(X*X.T*B)
+    assert expr.diff(X) == B*X + B.T*X
+
+    # Cookbook example 111:
+    expr = Trace(X*B*X.T)
+    assert expr.diff(X) == X*B.T + X*B
+
+    # Cookbook example 112:
+    expr = Trace(B*X.T*X)
+    assert expr.diff(X) == X*B.T + X*B
+
+    # Cookbook example 113:
+    expr = Trace(X.T*X*B)
+    assert expr.diff(X) == X*B.T + X*B
+
+    # Cookbook example 114:
+    expr = Trace(A*X*B*X)
+    assert expr.diff(X) == A.T*X.T*B.T + B.T*X.T*A.T
+
+    # Cookbook example 115:
+    expr = Trace(X.T*X)
+    assert expr.diff(X) == 2*X
+    expr = Trace(X*X.T)
+    assert expr.diff(X) == 2*X
+
+    # Cookbook example 116:
+    expr = Trace(B.T*X.T*C*X*B)
+    assert expr.diff(X) == C.T*X*B*B.T + C*X*B*B.T
+
+    # Cookbook example 117:
+    expr = Trace(X.T*B*X*C)
+    assert expr.diff(X) == B*X*C + B.T*X*C.T
+
+    # Cookbook example 118:
+    expr = Trace(A*X*B*X.T*C)
+    assert expr.diff(X) == A.T*C.T*X*B.T + C*A*X*B
+
+    # Cookbook example 119:
+    expr = Trace((A*X*B + C)*(A*X*B + C).T)
+    assert expr.diff(X) == 2*A.T*(A*X*B + C)*B.T
+
+    # Cookbook example 120:
+    # TODO: no support for TensorProduct.
+    # expr = Trace(TensorProduct(X, X))
+    # expr = Trace(X)*Trace(X)
+    # expr.diff(X) == 2*Trace(X)*Identity(k)
+
+    # Higher Order
+
+    # Cookbook example 121:
+    expr = Trace(X**k)
+    #assert expr.diff(X) == k*(X**(k-1)).T
+
+    # Cookbook example 122:
+    expr = Trace(A*X**k)
+    #assert expr.diff(X) == # Needs indices
+
+    # Cookbook example 123:
+    expr = Trace(B.T*X.T*C*X*X.T*C*X*B)
+    assert expr.diff(X) == C*X*X.T*C*X*B*B.T + C.T*X*B*B.T*X.T*C.T*X + C*X*B*B.T*X.T*C*X + C.T*X*X.T*C.T*X*B*B.T
+
+    # Other
+
+    # Cookbook example 124:
+    expr = Trace(A*X**(-1)*B)
+    assert expr.diff(X) == -Inverse(X).T*A.T*B.T*Inverse(X).T
+
+    # Cookbook example 125:
+    expr = Trace(Inverse(X.T*C*X)*A)
+    # Warning: result in the cookbook is equivalent if B and C are symmetric:
+    assert expr.diff(X) == - X.inv().T*A.T*X.inv()*C.inv().T*X.inv().T - X.inv().T*A*X.inv()*C.inv()*X.inv().T
+
+    # Cookbook example 126:
+    expr = Trace((X.T*C*X).inv()*(X.T*B*X))
+    assert expr.diff(X) == -2*C*X*(X.T*C*X).inv()*X.T*B*X*(X.T*C*X).inv() + 2*B*X*(X.T*C*X).inv()
+
+    # Cookbook example 127:
+    expr = Trace((A + X.T*C*X).inv()*(X.T*B*X))
+    # Warning: result in the cookbook is equivalent if B and C are symmetric:
+    assert expr.diff(X) == B*X*Inverse(A + X.T*C*X) - C*X*Inverse(A + X.T*C*X)*X.T*B*X*Inverse(A + X.T*C*X) - C.T*X*Inverse(A.T + (C*X).T*X)*X.T*B.T*X*Inverse(A.T + (C*X).T*X) + B.T*X*Inverse(A.T + (C*X).T*X)
+
+
+def test_derivatives_of_complicated_matrix_expr():
+    expr = a.T*(A*X*(X.T*B + X*A) + B.T*X.T*(a*b.T*(X*D*X.T + X*(X.T*B + A*X)*D*B - X.T*C.T*A)*B + B*(X*D.T + B*A*X*A.T - 3*X*D))*B + 42*X*B*X.T*A.T*(X + X.T))*b
+    result = (B*(B*A*X*A.T - 3*X*D + X*D.T) + a*b.T*(X*(A*X + X.T*B)*D*B + X*D*X.T - X.T*C.T*A)*B)*B*b*a.T*B.T + B**2*b*a.T*B.T*X.T*a*b.T*X*D + 42*A*X*B.T*X.T*a*b.T + B*D*B**3*b*a.T*B.T*X.T*a*b.T*X + B*b*a.T*A*X + a*b.T*(42*X + 42*X.T)*A*X*B.T + b*a.T*X*B*a*b.T*B.T**2*X*D.T + b*a.T*X*B*a*b.T*B.T**3*D.T*(B.T*X + X.T*A.T) + 42*b*a.T*X*B*X.T*A.T + A.T*(42*X + 42*X.T)*b*a.T*X*B + A.T*B.T**2*X*B*a*b.T*B.T*A + A.T*a*b.T*(A.T*X.T + B.T*X) + A.T*X.T*b*a.T*X*B*a*b.T*B.T**3*D.T + B.T*X*B*a*b.T*B.T*D - 3*B.T*X*B*a*b.T*B.T*D.T - C.T*A*B**2*b*a.T*B.T*X.T*a*b.T + X.T*A.T*a*b.T*A.T
+    assert expr.diff(X) == result
+
+
+def test_mixed_deriv_mixed_expressions():
+
+    expr = 3*Trace(A)
+    assert expr.diff(A) == 3*Identity(k)
+
+    expr = k
+    deriv = expr.diff(A)
+    assert isinstance(deriv, ZeroMatrix)
+    assert deriv == ZeroMatrix(k, k)
+
+    expr = Trace(A)**2
+    assert expr.diff(A) == (2*Trace(A))*Identity(k)
+
+    expr = Trace(A)*A
+    I = Identity(k)
+    assert expr.diff(A) == ArrayAdd(ArrayTensorProduct(I, A), PermuteDims(ArrayTensorProduct(Trace(A)*I, I), Permutation(3)(1, 2)))
+
+    expr = Trace(Trace(A)*A)
+    assert expr.diff(A) == (2*Trace(A))*Identity(k)
+
+    expr = Trace(Trace(Trace(A)*A)*A)
+    assert expr.diff(A) == (3*Trace(A)**2)*Identity(k)
+
+
+def test_derivatives_matrix_norms():
+
+    expr = x.T*y
+    assert expr.diff(x) == y
+    assert expr[0, 0].diff(x[m, 0]).doit() == y[m, 0]
+
+    expr = (x.T*y)**S.Half
+    assert expr.diff(x) == y/(2*sqrt(x.T*y))
+
+    expr = (x.T*x)**S.Half
+    assert expr.diff(x) == x*(x.T*x)**Rational(-1, 2)
+
+    expr = (c.T*a*x.T*b)**S.Half
+    assert expr.diff(x) == b*a.T*c/sqrt(c.T*a*x.T*b)/2
+
+    expr = (c.T*a*x.T*b)**Rational(1, 3)
+    assert expr.diff(x) == b*a.T*c*(c.T*a*x.T*b)**Rational(-2, 3)/3
+
+    expr = (a.T*X*b)**S.Half
+    assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*b.T
+
+    expr = d.T*x*(a.T*X*b)**S.Half*y.T*c
+    assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*x.T*d*y.T*c*b.T
+
+
+def test_derivatives_elementwise_applyfunc():
+
+    expr = x.applyfunc(tan)
+    assert expr.diff(x).dummy_eq(
+        DiagMatrix(x.applyfunc(lambda x: tan(x)**2 + 1)))
+    assert expr[i, 0].diff(x[m, 0]).doit() == (tan(x[i, 0])**2 + 1)*KDelta(i, m)
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = (i**2*x).applyfunc(sin)
+    assert expr.diff(i).dummy_eq(
+        HadamardProduct((2*i)*x, (i**2*x).applyfunc(cos)))
+    assert expr[i, 0].diff(i).doit() == 2*i*x[i, 0]*cos(i**2*x[i, 0])
+    _check_derivative_with_explicit_matrix(expr, i, expr.diff(i))
+
+    expr = (log(i)*A*B).applyfunc(sin)
+    assert expr.diff(i).dummy_eq(
+        HadamardProduct(A*B/i, (log(i)*A*B).applyfunc(cos)))
+    _check_derivative_with_explicit_matrix(expr, i, expr.diff(i))
+
+    expr = A*x.applyfunc(exp)
+    # TODO: restore this result (currently returning the transpose):
+    #  assert expr.diff(x).dummy_eq(DiagMatrix(x.applyfunc(exp))*A.T)
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = x.T*A*x + k*y.applyfunc(sin).T*x
+    assert expr.diff(x).dummy_eq(A.T*x + A*x + k*y.applyfunc(sin))
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = x.applyfunc(sin).T*y
+    # TODO: restore (currently returning the transpose):
+    #  assert expr.diff(x).dummy_eq(DiagMatrix(x.applyfunc(cos))*y)
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = (a.T * X * b).applyfunc(sin)
+    assert expr.diff(X).dummy_eq(a*(a.T*X*b).applyfunc(cos)*b.T)
+    _check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T * X.applyfunc(sin) * b
+    assert expr.diff(X).dummy_eq(
+        DiagMatrix(a)*X.applyfunc(cos)*DiagMatrix(b))
+    _check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T * (A*X*B).applyfunc(sin) * b
+    assert expr.diff(X).dummy_eq(
+        A.T*DiagMatrix(a)*(A*X*B).applyfunc(cos)*DiagMatrix(b)*B.T)
+    _check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T * (A*X*b).applyfunc(sin) * b.T
+    # TODO: not implemented
+    #assert expr.diff(X) == ...
+    #_check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T*A*X.applyfunc(sin)*B*b
+    assert expr.diff(X).dummy_eq(
+        HadamardProduct(A.T * a * b.T * B.T, X.applyfunc(cos)))
+
+    expr = a.T * (A*X.applyfunc(sin)*B).applyfunc(log) * b
+    # TODO: wrong
+    # assert expr.diff(X) == A.T*DiagMatrix(a)*(A*X.applyfunc(sin)*B).applyfunc(Lambda(k, 1/k))*DiagMatrix(b)*B.T
+
+    expr = a.T * (X.applyfunc(sin)).applyfunc(log) * b
+    # TODO: wrong
+    # assert expr.diff(X) == DiagMatrix(a)*X.applyfunc(sin).applyfunc(Lambda(k, 1/k))*DiagMatrix(b)
+
+
+def test_derivatives_of_hadamard_expressions():
+
+    # Hadamard Product
+
+    expr = hadamard_product(a, x, b)
+    assert expr.diff(x) == DiagMatrix(hadamard_product(b, a))
+
+    expr = a.T*hadamard_product(A, X, B)*b
+    assert expr.diff(X) == HadamardProduct(a*b.T, A, B)
+
+    # Hadamard Power
+
+    expr = hadamard_power(x, 2)
+    assert expr.diff(x).doit() == 2*DiagMatrix(x)
+
+    expr = hadamard_power(x.T, 2)
+    assert expr.diff(x).doit() == 2*DiagMatrix(x)
+
+    expr = hadamard_power(x, S.Half)
+    assert expr.diff(x) == S.Half*DiagMatrix(hadamard_power(x, Rational(-1, 2)))
+
+    expr = hadamard_power(a.T*X*b, 2)
+    assert expr.diff(X) == 2*a*a.T*X*b*b.T
+
+    expr = hadamard_power(a.T*X*b, S.Half)
+    assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*b.T
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_determinant.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_determinant.py
new file mode 100644
index 0000000000000000000000000000000000000000..d1a66c728f076f8c769d2519ee47c8a9cc90a90e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_determinant.py
@@ -0,0 +1,65 @@
+from sympy.core import S, symbols
+from sympy.matrices import eye, ones, Matrix, ShapeError
+from sympy.matrices.expressions import (
+    Identity, MatrixExpr, MatrixSymbol, Determinant,
+    det, per, ZeroMatrix, Transpose,
+    Permanent, MatMul
+)
+from sympy.matrices.expressions.special import OneMatrix
+from sympy.testing.pytest import raises
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+
+n = symbols('n', integer=True)
+A = MatrixSymbol('A', n, n)
+B = MatrixSymbol('B', n, n)
+C = MatrixSymbol('C', 3, 4)
+
+
+def test_det():
+    assert isinstance(Determinant(A), Determinant)
+    assert not isinstance(Determinant(A), MatrixExpr)
+    raises(ShapeError, lambda: Determinant(C))
+    assert det(eye(3)) == 1
+    assert det(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 17
+    _ = A / det(A)  # Make sure this is possible
+
+    raises(TypeError, lambda: Determinant(S.One))
+
+    assert Determinant(A).arg is A
+
+
+def test_eval_determinant():
+    assert det(Identity(n)) == 1
+    assert det(ZeroMatrix(n, n)) == 0
+    assert det(OneMatrix(n, n)) == Determinant(OneMatrix(n, n))
+    assert det(OneMatrix(1, 1)) == 1
+    assert det(OneMatrix(2, 2)) == 0
+    assert det(Transpose(A)) == det(A)
+    assert Determinant(MatMul(eye(2), eye(2))).doit(deep=True) == 1
+
+
+def test_refine():
+    assert refine(det(A), Q.orthogonal(A)) == 1
+    assert refine(det(A), Q.singular(A)) == 0
+    assert refine(det(A), Q.unit_triangular(A)) == 1
+    assert refine(det(A), Q.normal(A)) == det(A)
+
+
+def test_commutative():
+    det_a = Determinant(A)
+    det_b = Determinant(B)
+    assert det_a.is_commutative
+    assert det_b.is_commutative
+    assert det_a * det_b == det_b * det_a
+
+
+def test_permanent():
+    assert isinstance(Permanent(A), Permanent)
+    assert not isinstance(Permanent(A), MatrixExpr)
+    assert isinstance(Permanent(C), Permanent)
+    assert Permanent(ones(3, 3)).doit() == 6
+    _ = C / per(C)
+    assert per(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 103
+    raises(TypeError, lambda: Permanent(S.One))
+    assert Permanent(A).arg is A
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_diagonal.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_diagonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e4f7ea4c178121c33eeb26c09675403d274c1e8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_diagonal.py
@@ -0,0 +1,156 @@
+from sympy.matrices.expressions import MatrixSymbol
+from sympy.matrices.expressions.diagonal import DiagonalMatrix, DiagonalOf, DiagMatrix, diagonalize_vector
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core.symbol import Symbol
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import Matrix
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.matrices.expressions.special import Identity
+from sympy.testing.pytest import raises
+
+
+n = Symbol('n')
+m = Symbol('m')
+
+
+def test_DiagonalMatrix():
+    x = MatrixSymbol('x', n, m)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length is None
+    assert D.shape == (n, m)
+
+    x = MatrixSymbol('x', n, n)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length == n
+    assert D.shape == (n, n)
+    assert D[1, 2] == 0
+    assert D[1, 1] == x[1, 1]
+    i = Symbol('i')
+    j = Symbol('j')
+    x = MatrixSymbol('x', 3, 3)
+    ij = DiagonalMatrix(x)[i, j]
+    assert ij != 0
+    assert ij.subs({i:0, j:0}) == x[0, 0]
+    assert ij.subs({i:0, j:1}) == 0
+    assert ij.subs({i:1, j:1}) == x[1, 1]
+    assert ask(Q.diagonal(D))  # affirm that D is diagonal
+
+    x = MatrixSymbol('x', n, 3)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length == 3
+    assert D.shape == (n, 3)
+    assert D[2, m] == KroneckerDelta(2, m)*x[2, m]
+    assert D[3, m] == 0
+    raises(IndexError, lambda: D[m, 3])
+
+    x = MatrixSymbol('x', 3, n)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length == 3
+    assert D.shape == (3, n)
+    assert D[m, 2] == KroneckerDelta(m, 2)*x[m, 2]
+    assert D[m, 3] == 0
+    raises(IndexError, lambda: D[3, m])
+
+    x = MatrixSymbol('x', n, m)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length is None
+    assert D.shape == (n, m)
+    assert D[m, 4] != 0
+
+    x = MatrixSymbol('x', 3, 4)
+    assert [DiagonalMatrix(x)[i] for i in range(12)] == [
+        x[0, 0], 0, 0, 0, 0, x[1, 1], 0, 0, 0, 0, x[2, 2], 0]
+
+    # shape is retained, issue 12427
+    assert (
+        DiagonalMatrix(MatrixSymbol('x', 3, 4))*
+        DiagonalMatrix(MatrixSymbol('x', 4, 2))).shape == (3, 2)
+
+
+def test_DiagonalOf():
+    x = MatrixSymbol('x', n, n)
+    d = DiagonalOf(x)
+    assert d.shape == (n, 1)
+    assert d.diagonal_length == n
+    assert d[2, 0] == d[2] == x[2, 2]
+
+    x = MatrixSymbol('x', n, m)
+    d = DiagonalOf(x)
+    assert d.shape == (None, 1)
+    assert d.diagonal_length is None
+    assert d[2, 0] == d[2] == x[2, 2]
+
+    d = DiagonalOf(MatrixSymbol('x', 4, 3))
+    assert d.shape == (3, 1)
+    d = DiagonalOf(MatrixSymbol('x', n, 3))
+    assert d.shape == (3, 1)
+    d = DiagonalOf(MatrixSymbol('x', 3, n))
+    assert d.shape == (3, 1)
+    x = MatrixSymbol('x', n, m)
+    assert [DiagonalOf(x)[i] for i in range(4)] ==[
+        x[0, 0], x[1, 1], x[2, 2], x[3, 3]]
+
+
+def test_DiagMatrix():
+    x = MatrixSymbol('x', n, 1)
+    d = DiagMatrix(x)
+    assert d.shape == (n, n)
+    assert d[0, 1] == 0
+    assert d[0, 0] == x[0, 0]
+
+    a = MatrixSymbol('a', 1, 1)
+    d = diagonalize_vector(a)
+    assert isinstance(d, MatrixSymbol)
+    assert a == d
+    assert diagonalize_vector(Identity(3)) == Identity(3)
+    assert DiagMatrix(Identity(3)).doit() == Identity(3)
+    assert isinstance(DiagMatrix(Identity(3)), DiagMatrix)
+
+    # A diagonal matrix is equal to its transpose:
+    assert DiagMatrix(x).T == DiagMatrix(x)
+    assert diagonalize_vector(x.T) == DiagMatrix(x)
+
+    dx = DiagMatrix(x)
+    assert dx[0, 0] == x[0, 0]
+    assert dx[1, 1] == x[1, 0]
+    assert dx[0, 1] == 0
+    assert dx[0, m] == x[0, 0]*KroneckerDelta(0, m)
+
+    z = MatrixSymbol('z', 1, n)
+    dz = DiagMatrix(z)
+    assert dz[0, 0] == z[0, 0]
+    assert dz[1, 1] == z[0, 1]
+    assert dz[0, 1] == 0
+    assert dz[0, m] == z[0, m]*KroneckerDelta(0, m)
+
+    v = MatrixSymbol('v', 3, 1)
+    dv = DiagMatrix(v)
+    assert dv.as_explicit() == Matrix([
+        [v[0, 0], 0, 0],
+        [0, v[1, 0], 0],
+        [0, 0, v[2, 0]],
+    ])
+
+    v = MatrixSymbol('v', 1, 3)
+    dv = DiagMatrix(v)
+    assert dv.as_explicit() == Matrix([
+        [v[0, 0], 0, 0],
+        [0, v[0, 1], 0],
+        [0, 0, v[0, 2]],
+    ])
+
+    dv = DiagMatrix(3*v)
+    assert dv.args == (3*v,)
+    assert dv.doit() == 3*DiagMatrix(v)
+    assert isinstance(dv.doit(), MatMul)
+
+    a = MatrixSymbol("a", 3, 1).as_explicit()
+    expr = DiagMatrix(a)
+    result = Matrix([
+        [a[0, 0], 0, 0],
+        [0, a[1, 0], 0],
+        [0, 0, a[2, 0]],
+    ])
+    assert expr.doit() == result
+    expr = DiagMatrix(a.T)
+    assert expr.doit() == result
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py
new file mode 100644
index 0000000000000000000000000000000000000000..abf8ab8e935cbd3039f25f83d3603ac444e5a7bb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py
@@ -0,0 +1,35 @@
+from sympy.core.expr import unchanged
+from sympy.core.mul import Mul
+from sympy.matrices import Matrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.dotproduct import DotProduct
+from sympy.testing.pytest import raises
+
+
+A = Matrix(3, 1, [1, 2, 3])
+B = Matrix(3, 1, [1, 3, 5])
+C = Matrix(4, 1, [1, 2, 4, 5])
+D = Matrix(2, 2, [1, 2, 3, 4])
+
+def test_docproduct():
+    assert DotProduct(A, B).doit() == 22
+    assert DotProduct(A.T, B).doit() == 22
+    assert DotProduct(A, B.T).doit() == 22
+    assert DotProduct(A.T, B.T).doit() == 22
+
+    raises(TypeError, lambda: DotProduct(1, A))
+    raises(TypeError, lambda: DotProduct(A, 1))
+    raises(TypeError, lambda: DotProduct(A, D))
+    raises(TypeError, lambda: DotProduct(D, A))
+
+    raises(TypeError, lambda: DotProduct(B, C).doit())
+
+def test_dotproduct_symbolic():
+    A = MatrixSymbol('A', 3, 1)
+    B = MatrixSymbol('B', 3, 1)
+
+    dot = DotProduct(A, B)
+    assert dot.is_scalar == True
+    assert unchanged(Mul, 2, dot)
+    # XXX Fix forced evaluation for arithmetics with matrix expressions
+    assert dot * A == (A[0, 0]*B[0, 0] + A[1, 0]*B[1, 0] + A[2, 0]*B[2, 0])*A
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_factorizations.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_factorizations.py
new file mode 100644
index 0000000000000000000000000000000000000000..a0319acabbb7409dfa5c24ceca39e25ff0240618
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_factorizations.py
@@ -0,0 +1,29 @@
+from sympy.matrices.expressions.factorizations import lu, LofCholesky, qr, svd
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core.symbol import Symbol
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+
+n = Symbol('n')
+X = MatrixSymbol('X', n, n)
+
+def test_LU():
+    L, U = lu(X)
+    assert L.shape == U.shape == X.shape
+    assert ask(Q.lower_triangular(L))
+    assert ask(Q.upper_triangular(U))
+
+def test_Cholesky():
+    LofCholesky(X)
+
+def test_QR():
+    Q_, R = qr(X)
+    assert Q_.shape == R.shape == X.shape
+    assert ask(Q.orthogonal(Q_))
+    assert ask(Q.upper_triangular(R))
+
+def test_svd():
+    U, S, V = svd(X)
+    assert U.shape == S.shape == V.shape == X.shape
+    assert ask(Q.orthogonal(U))
+    assert ask(Q.orthogonal(V))
+    assert ask(Q.diagonal(S))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_fourier.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_fourier.py
new file mode 100644
index 0000000000000000000000000000000000000000..0230c8a0957ed28fb0a5cc1e9ee77ecae797265b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_fourier.py
@@ -0,0 +1,44 @@
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core.numbers import (I, Rational)
+from sympy.core.singleton import S
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.simplify.simplify import simplify
+from sympy.core.symbol import symbols
+from sympy.matrices.expressions.fourier import DFT, IDFT
+from sympy.matrices import det, Matrix, Identity
+from sympy.testing.pytest import raises
+
+
+def test_dft_creation():
+    assert DFT(2)
+    assert DFT(0)
+    raises(ValueError, lambda: DFT(-1))
+    raises(ValueError, lambda: DFT(2.0))
+    raises(ValueError, lambda: DFT(2 + 1j))
+
+    n = symbols('n')
+    assert DFT(n)
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: DFT(n))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: DFT(n))
+
+
+def test_dft():
+    n, i, j = symbols('n i j')
+    assert DFT(4).shape == (4, 4)
+    assert ask(Q.unitary(DFT(4)))
+    assert Abs(simplify(det(Matrix(DFT(4))))) == 1
+    assert DFT(n)*IDFT(n) == Identity(n)
+    assert DFT(n)[i, j] == exp(-2*S.Pi*I/n)**(i*j) / sqrt(n)
+
+
+def test_dft2():
+    assert DFT(1).as_explicit() == Matrix([[1]])
+    assert DFT(2).as_explicit() == 1/sqrt(2)*Matrix([[1,1],[1,-1]])
+    assert DFT(4).as_explicit() == Matrix([[S.Half,  S.Half,  S.Half, S.Half],
+                                           [S.Half, -I/2, Rational(-1,2),  I/2],
+                                           [S.Half, Rational(-1,2),  S.Half, Rational(-1,2)],
+                                           [S.Half,  I/2, Rational(-1,2), -I/2]])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..e4850fe5c739b9390fac6afa10757b5babf821c6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py
@@ -0,0 +1,54 @@
+from sympy.core import symbols, Lambda
+from sympy.core.sympify import SympifyError
+from sympy.functions import KroneckerDelta
+from sympy.matrices import Matrix
+from sympy.matrices.expressions import FunctionMatrix, MatrixExpr, Identity
+from sympy.testing.pytest import raises
+
+
+def test_funcmatrix_creation():
+    i, j, k = symbols('i j k')
+    assert FunctionMatrix(2, 2, Lambda((i, j), 0))
+    assert FunctionMatrix(0, 0, Lambda((i, j), 0))
+
+    raises(ValueError, lambda: FunctionMatrix(-1, 0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2.0, 0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2j, 0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(0, -1, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(0, 2.0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(0, 2j, Lambda((i, j), 0)))
+
+    raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda(i, 0)))
+    raises(SympifyError, lambda: FunctionMatrix(2, 2, lambda i, j: 0))
+    raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda((i,), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda((i, j, k), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2, 2, i+j))
+    assert FunctionMatrix(2, 2, "lambda i, j: 0") == \
+        FunctionMatrix(2, 2, Lambda((i, j), 0))
+
+    m = FunctionMatrix(2, 2, KroneckerDelta)
+    assert m.as_explicit() == Identity(2).as_explicit()
+    assert m.args[2].dummy_eq(Lambda((i, j), KroneckerDelta(i, j)))
+
+    n = symbols('n')
+    assert FunctionMatrix(n, n, Lambda((i, j), 0))
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: FunctionMatrix(n, n, Lambda((i, j), 0)))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: FunctionMatrix(n, n, Lambda((i, j), 0)))
+
+
+def test_funcmatrix():
+    i, j = symbols('i,j')
+    X = FunctionMatrix(3, 3, Lambda((i, j), i - j))
+    assert X[1, 1] == 0
+    assert X[1, 2] == -1
+    assert X.shape == (3, 3)
+    assert X.rows == X.cols == 3
+    assert Matrix(X) == Matrix(3, 3, lambda i, j: i - j)
+    assert isinstance(X*X + X, MatrixExpr)
+
+
+def test_replace_issue():
+    X = FunctionMatrix(3, 3, KroneckerDelta)
+    assert X.replace(lambda x: True, lambda x: x) == X
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_hadamard.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_hadamard.py
new file mode 100644
index 0000000000000000000000000000000000000000..800fa830a9b089103d69b372db93ebcea541d02b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_hadamard.py
@@ -0,0 +1,141 @@
+from sympy.matrices.dense import Matrix, eye
+from sympy.matrices.exceptions import ShapeError
+from sympy.matrices.expressions.matadd import MatAdd
+from sympy.matrices.expressions.special import Identity, OneMatrix, ZeroMatrix
+from sympy.core import symbols
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+from sympy.matrices import MatrixSymbol
+from sympy.matrices.expressions import (HadamardProduct, hadamard_product, HadamardPower, hadamard_power)
+
+n, m, k = symbols('n,m,k')
+Z = MatrixSymbol('Z', n, n)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', n, m)
+C = MatrixSymbol('C', m, k)
+
+
+def test_HadamardProduct():
+    assert HadamardProduct(A, B, A).shape == A.shape
+
+    raises(TypeError,  lambda: HadamardProduct(A, n))
+    raises(TypeError,  lambda: HadamardProduct(A, 1))
+
+    assert HadamardProduct(A, 2*B, -A)[1, 1] == \
+            -2 * A[1, 1] * B[1, 1] * A[1, 1]
+
+    mix = HadamardProduct(Z*A, B)*C
+    assert mix.shape == (n, k)
+
+    assert set(HadamardProduct(A, B, A).T.args) == {A.T, A.T, B.T}
+
+
+def test_HadamardProduct_isnt_commutative():
+    assert HadamardProduct(A, B) != HadamardProduct(B, A)
+
+
+def test_mixed_indexing():
+    X = MatrixSymbol('X', 2, 2)
+    Y = MatrixSymbol('Y', 2, 2)
+    Z = MatrixSymbol('Z', 2, 2)
+
+    assert (X*HadamardProduct(Y, Z))[0, 0] == \
+            X[0, 0]*Y[0, 0]*Z[0, 0] + X[0, 1]*Y[1, 0]*Z[1, 0]
+
+
+def test_canonicalize():
+    X = MatrixSymbol('X', 2, 2)
+    Y = MatrixSymbol('Y', 2, 2)
+    with warns_deprecated_sympy():
+        expr = HadamardProduct(X, check=False)
+    assert isinstance(expr, HadamardProduct)
+    expr2 = expr.doit() # unpack is called
+    assert isinstance(expr2, MatrixSymbol)
+    Z = ZeroMatrix(2, 2)
+    U = OneMatrix(2, 2)
+    assert HadamardProduct(Z, X).doit() == Z
+    assert HadamardProduct(U, X, X, U).doit() == HadamardPower(X, 2)
+    assert HadamardProduct(X, U, Y).doit() == HadamardProduct(X, Y)
+    assert HadamardProduct(X, Z, U, Y).doit() == Z
+
+
+def test_hadamard():
+    m, n, p = symbols('m, n, p', integer=True)
+    A = MatrixSymbol('A', m, n)
+    B = MatrixSymbol('B', m, n)
+    X = MatrixSymbol('X', m, m)
+    I = Identity(m)
+
+    raises(TypeError, lambda: hadamard_product())
+    assert hadamard_product(A) == A
+    assert isinstance(hadamard_product(A, B), HadamardProduct)
+    assert hadamard_product(A, B).doit() == hadamard_product(A, B)
+    assert hadamard_product(X, I) == HadamardProduct(I, X)
+    assert isinstance(hadamard_product(X, I), HadamardProduct)
+
+    a = MatrixSymbol("a", k, 1)
+    expr = MatAdd(ZeroMatrix(k, 1), OneMatrix(k, 1))
+    expr = HadamardProduct(expr, a)
+    assert expr.doit() == a
+
+    raises(ValueError, lambda: HadamardProduct())
+
+
+def test_hadamard_product_with_explicit_mat():
+    A = MatrixSymbol("A", 3, 3).as_explicit()
+    B = MatrixSymbol("B", 3, 3).as_explicit()
+    X = MatrixSymbol("X", 3, 3)
+    expr = hadamard_product(A, B)
+    ret = Matrix([i*j for i, j in zip(A, B)]).reshape(3, 3)
+    assert expr == ret
+    expr = hadamard_product(A, X, B)
+    assert expr == HadamardProduct(ret, X)
+    expr = hadamard_product(eye(3), A)
+    assert expr == Matrix([[A[0, 0], 0, 0], [0, A[1, 1], 0], [0, 0, A[2, 2]]])
+    expr = hadamard_product(eye(3), eye(3))
+    assert expr == eye(3)
+
+
+def test_hadamard_power():
+    m, n, p = symbols('m, n, p', integer=True)
+    A = MatrixSymbol('A', m, n)
+
+    assert hadamard_power(A, 1) == A
+    assert isinstance(hadamard_power(A, 2), HadamardPower)
+    assert hadamard_power(A, n).T == hadamard_power(A.T, n)
+    assert hadamard_power(A, n)[0, 0] == A[0, 0]**n
+    assert hadamard_power(m, n) == m**n
+    raises(ValueError, lambda: hadamard_power(A, A))
+
+
+def test_hadamard_power_explicit():
+    A = MatrixSymbol('A', 2, 2)
+    B = MatrixSymbol('B', 2, 2)
+    a, b = symbols('a b')
+
+    assert HadamardPower(a, b) == a**b
+
+    assert HadamardPower(a, B).as_explicit() == \
+        Matrix([
+            [a**B[0, 0], a**B[0, 1]],
+            [a**B[1, 0], a**B[1, 1]]])
+
+    assert HadamardPower(A, b).as_explicit() == \
+        Matrix([
+            [A[0, 0]**b, A[0, 1]**b],
+            [A[1, 0]**b, A[1, 1]**b]])
+
+    assert HadamardPower(A, B).as_explicit() == \
+        Matrix([
+            [A[0, 0]**B[0, 0], A[0, 1]**B[0, 1]],
+            [A[1, 0]**B[1, 0], A[1, 1]**B[1, 1]]])
+
+
+def test_shape_error():
+    A = MatrixSymbol('A', 2, 3)
+    B = MatrixSymbol('B', 3, 3)
+    raises(ShapeError, lambda: HadamardProduct(A, B))
+    raises(ShapeError, lambda: HadamardPower(A, B))
+    A = MatrixSymbol('A', 3, 2)
+    raises(ShapeError, lambda: HadamardProduct(A, B))
+    raises(ShapeError, lambda: HadamardPower(A, B))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_indexing.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_indexing.py
new file mode 100644
index 0000000000000000000000000000000000000000..500761f248eef5f627c2a7344a6817aca0b8a802
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_indexing.py
@@ -0,0 +1,299 @@
+from sympy.concrete.summations import Sum
+from sympy.core.symbol import symbols, Symbol, Dummy
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import eye
+from sympy.matrices.expressions.blockmatrix import BlockMatrix
+from sympy.matrices.expressions.hadamard import HadamardPower
+from sympy.matrices.expressions.matexpr import (MatrixSymbol,
+    MatrixExpr, MatrixElement)
+from sympy.matrices.expressions.matpow import MatPow
+from sympy.matrices.expressions.special import (ZeroMatrix, Identity,
+    OneMatrix)
+from sympy.matrices.expressions.trace import Trace, trace
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+from sympy.testing.pytest import XFAIL, raises
+
+k, l, m, n = symbols('k l m n', integer=True)
+i, j = symbols('i j', integer=True)
+
+W = MatrixSymbol('W', k, l)
+X = MatrixSymbol('X', l, m)
+Y = MatrixSymbol('Y', l, m)
+Z = MatrixSymbol('Z', m, n)
+
+X1 = MatrixSymbol('X1', m, m)
+X2 = MatrixSymbol('X2', m, m)
+X3 = MatrixSymbol('X3', m, m)
+X4 = MatrixSymbol('X4', m, m)
+
+A = MatrixSymbol('A', 2, 2)
+B = MatrixSymbol('B', 2, 2)
+x = MatrixSymbol('x', 1, 2)
+y = MatrixSymbol('x', 2, 1)
+
+
+def test_symbolic_indexing():
+    x12 = X[1, 2]
+    assert all(s in str(x12) for s in ['1', '2', X.name])
+    # We don't care about the exact form of this.  We do want to make sure
+    # that all of these features are present
+
+
+def test_add_index():
+    assert (X + Y)[i, j] == X[i, j] + Y[i, j]
+
+
+def test_mul_index():
+    assert (A*y)[0, 0] == A[0, 0]*y[0, 0] + A[0, 1]*y[1, 0]
+    assert (A*B).as_mutable() == (A.as_mutable() * B.as_mutable())
+    X = MatrixSymbol('X', n, m)
+    Y = MatrixSymbol('Y', m, k)
+
+    result = (X*Y)[4,2]
+    expected = Sum(X[4, i]*Y[i, 2], (i, 0, m - 1))
+    assert result.args[0].dummy_eq(expected.args[0], i)
+    assert result.args[1][1:] == expected.args[1][1:]
+
+
+def test_pow_index():
+    Q = MatPow(A, 2)
+    assert Q[0, 0] == A[0, 0]**2 + A[0, 1]*A[1, 0]
+    n = symbols("n")
+    Q2 = A**n
+    assert Q2[0, 0] == 2*(
+            -sqrt((A[0, 0] + A[1, 1])**2 - 4*A[0, 0]*A[1, 1] +
+            4*A[0, 1]*A[1, 0])/2 + A[0, 0]/2 + A[1, 1]/2
+        )**n * \
+        A[0, 1]*A[1, 0]/(
+            (sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] +
+                  A[1, 1]**2) + A[0, 0] - A[1, 1])*
+            sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + A[1, 1]**2)
+        ) - 2*(
+            sqrt((A[0, 0] + A[1, 1])**2 - 4*A[0, 0]*A[1, 1] +
+            4*A[0, 1]*A[1, 0])/2 + A[0, 0]/2 + A[1, 1]/2
+        )**n * A[0, 1]*A[1, 0]/(
+            (-sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] +
+            A[1, 1]**2) + A[0, 0] - A[1, 1])*
+            sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + A[1, 1]**2)
+        )
+
+
+def test_transpose_index():
+    assert X.T[i, j] == X[j, i]
+
+
+def test_Identity_index():
+    I = Identity(3)
+    assert I[0, 0] == I[1, 1] == I[2, 2] == 1
+    assert I[1, 0] == I[0, 1] == I[2, 1] == 0
+    assert I[i, 0].delta_range == (0, 2)
+    raises(IndexError, lambda: I[3, 3])
+
+
+def test_block_index():
+    I = Identity(3)
+    Z = ZeroMatrix(3, 3)
+    B = BlockMatrix([[I, I], [I, I]])
+    e3 = ImmutableMatrix(eye(3))
+    BB = BlockMatrix([[e3, e3], [e3, e3]])
+    assert B[0, 0] == B[3, 0] == B[0, 3] == B[3, 3] == 1
+    assert B[4, 3] == B[5, 1] == 0
+
+    BB = BlockMatrix([[e3, e3], [e3, e3]])
+    assert B.as_explicit() == BB.as_explicit()
+
+    BI = BlockMatrix([[I, Z], [Z, I]])
+
+    assert BI.as_explicit().equals(eye(6))
+
+
+def test_block_index_symbolic():
+    # Note that these matrices may be zero-sized and indices may be negative, which causes
+    # all naive simplifications given in the comments to be invalid
+    A1 = MatrixSymbol('A1', n, k)
+    A2 = MatrixSymbol('A2', n, l)
+    A3 = MatrixSymbol('A3', m, k)
+    A4 = MatrixSymbol('A4', m, l)
+    A = BlockMatrix([[A1, A2], [A3, A4]])
+    assert A[0, 0] == MatrixElement(A, 0, 0)  # Cannot be A1[0, 0]
+    assert A[n - 1, k - 1] == A1[n - 1, k - 1]
+    assert A[n, k] == A4[0, 0]
+    assert A[n + m - 1, 0] == MatrixElement(A, n + m - 1, 0)  # Cannot be A3[m - 1, 0]
+    assert A[0, k + l - 1] == MatrixElement(A, 0, k + l - 1)  # Cannot be A2[0, l - 1]
+    assert A[n + m - 1, k + l - 1] == MatrixElement(A, n + m - 1, k + l - 1)  # Cannot be A4[m - 1, l - 1]
+    assert A[i, j] == MatrixElement(A, i, j)
+    assert A[n + i, k + j] == MatrixElement(A, n + i, k + j)  # Cannot be A4[i, j]
+    assert A[n - i - 1, k - j - 1] == MatrixElement(A, n - i - 1, k - j - 1)  # Cannot be A1[n - i - 1, k - j - 1]
+
+
+def test_block_index_symbolic_nonzero():
+    # All invalid simplifications from test_block_index_symbolic() that become valid if all
+    # matrices have nonzero size and all indices are nonnegative
+    k, l, m, n = symbols('k l m n', integer=True, positive=True)
+    i, j = symbols('i j', integer=True, nonnegative=True)
+    A1 = MatrixSymbol('A1', n, k)
+    A2 = MatrixSymbol('A2', n, l)
+    A3 = MatrixSymbol('A3', m, k)
+    A4 = MatrixSymbol('A4', m, l)
+    A = BlockMatrix([[A1, A2], [A3, A4]])
+    assert A[0, 0] == A1[0, 0]
+    assert A[n + m - 1, 0] == A3[m - 1, 0]
+    assert A[0, k + l - 1] == A2[0, l - 1]
+    assert A[n + m - 1, k + l - 1] == A4[m - 1, l - 1]
+    assert A[i, j] == MatrixElement(A, i, j)
+    assert A[n + i, k + j] == A4[i, j]
+    assert A[n - i - 1, k - j - 1] == A1[n - i - 1, k - j - 1]
+    assert A[2 * n, 2 * k] == A4[n, k]
+
+
+def test_block_index_large():
+    n, m, k = symbols('n m k', integer=True, positive=True)
+    i = symbols('i', integer=True, nonnegative=True)
+    A1 = MatrixSymbol('A1', n, n)
+    A2 = MatrixSymbol('A2', n, m)
+    A3 = MatrixSymbol('A3', n, k)
+    A4 = MatrixSymbol('A4', m, n)
+    A5 = MatrixSymbol('A5', m, m)
+    A6 = MatrixSymbol('A6', m, k)
+    A7 = MatrixSymbol('A7', k, n)
+    A8 = MatrixSymbol('A8', k, m)
+    A9 = MatrixSymbol('A9', k, k)
+    A = BlockMatrix([[A1, A2, A3], [A4, A5, A6], [A7, A8, A9]])
+    assert A[n + i, n + i] == MatrixElement(A, n + i, n + i)
+
+
+@XFAIL
+def test_block_index_symbolic_fail():
+    # To make this work, symbolic matrix dimensions would need to be somehow assumed nonnegative
+    # even if the symbols aren't specified as such.  Then 2 * n < n would correctly evaluate to
+    # False in BlockMatrix._entry()
+    A1 = MatrixSymbol('A1', n, 1)
+    A2 = MatrixSymbol('A2', m, 1)
+    A = BlockMatrix([[A1], [A2]])
+    assert A[2 * n, 0] == A2[n, 0]
+
+
+def test_slicing():
+    A.as_explicit()[0, :]  # does not raise an error
+
+
+def test_errors():
+    raises(IndexError, lambda: Identity(2)[1, 2, 3, 4, 5])
+    raises(IndexError, lambda: Identity(2)[[1, 2, 3, 4, 5]])
+
+
+def test_matrix_expression_to_indices():
+    i, j = symbols("i, j")
+    i1, i2, i3 = symbols("i_1:4")
+
+    def replace_dummies(expr):
+        repl = {i: Symbol(i.name) for i in expr.atoms(Dummy)}
+        return expr.xreplace(repl)
+
+    expr = W*X*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+        Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = Z.T*X.T*W.T
+    assert replace_dummies(expr._entry(i, j)) == \
+        Sum(W[j, i2]*X[i2, i1]*Z[i1, i], (i1, 0, m-1), (i2, 0, l-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j), i) == expr
+
+    expr = W*X*Z + W*Y*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+        Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) +\
+        Sum(W[i, i1]*Y[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = 2*W*X*Z + 3*W*Y*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+        2*Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) +\
+        3*Sum(W[i, i1]*Y[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = W*(X + Y)*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+            Sum(W[i, i1]*(X[i1, i2] + Y[i1, i2])*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = A*B**2*A
+    #assert replace_dummies(expr._entry(i, j)) == \
+    #        Sum(A[i, i1]*B[i1, i2]*B[i2, i3]*A[i3, j], (i1, 0, 1), (i2, 0, 1), (i3, 0, 1))
+
+    # Check that different dummies are used in sub-multiplications:
+    expr = (X1*X2 + X2*X1)*X3
+    assert replace_dummies(expr._entry(i, j)) == \
+           Sum((Sum(X1[i, i2] * X2[i2, i1], (i2, 0, m - 1)) + Sum(X1[i3, i1] * X2[i, i3], (i3, 0, m - 1))) * X3[
+               i1, j], (i1, 0, m - 1))
+
+
+def test_matrix_expression_from_index_summation():
+    from sympy.abc import a,b,c,d
+    A = MatrixSymbol("A", k, k)
+    B = MatrixSymbol("B", k, k)
+    C = MatrixSymbol("C", k, k)
+    w1 = MatrixSymbol("w1", k, 1)
+
+    i0, i1, i2, i3, i4 = symbols("i0:5", cls=Dummy)
+
+    expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr, a) == W*X*Z
+    expr = Sum(W.T[b,a]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr, a) == W*X*Z
+    expr = Sum(A[b, a]*B[b, c]*C[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixSymbol.from_index_summation(expr, a) == A.T*B*C
+    expr = Sum(A[b, a]*B[c, b]*C[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixSymbol.from_index_summation(expr, a) == A.T*B.T*C
+    expr = Sum(C[c, d]*A[b, a]*B[c, b], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixSymbol.from_index_summation(expr, a) == A.T*B.T*C
+    expr = Sum(A[a, b] + B[a, b], (a, 0, k-1), (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == OneMatrix(1, k)*A*OneMatrix(k, 1) + OneMatrix(1, k)*B*OneMatrix(k, 1)
+    expr = Sum(A[a, b]**2, (a, 0, k - 1), (b, 0, k - 1))
+    assert MatrixExpr.from_index_summation(expr, a) == Trace(A * A.T)
+    expr = Sum(A[a, b]**3, (a, 0, k - 1), (b, 0, k - 1))
+    assert MatrixExpr.from_index_summation(expr, a) == Trace(HadamardPower(A.T, 2) * A)
+    expr = Sum((A[a, b] + B[a, b])*C[b, c], (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == (A+B)*C
+    expr = Sum((A[a, b] + B[b, a])*C[b, c], (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == (A+B.T)*C
+    expr = Sum(A[a, b]*A[b, c]*A[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A**3
+    expr = Sum(A[a, b]*A[b, c]*B[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A**2*B
+
+    # Parse the trace of a matrix:
+
+    expr = Sum(A[a, a], (a, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, None) == trace(A)
+    expr = Sum(A[a, a]*B[b, c]*C[c, d], (a, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, b) == trace(A)*B*C
+
+    # Check wrong sum ranges (should raise an exception):
+
+    ## Case 1: 0 to m instead of 0 to m-1
+    expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m))
+    raises(ValueError, lambda: MatrixExpr.from_index_summation(expr, a))
+    ## Case 2: 1 to m-1 instead of 0 to m-1
+    expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 1, m-1))
+    raises(ValueError, lambda: MatrixExpr.from_index_summation(expr, a))
+
+    # Parse nested sums:
+    expr = Sum(A[a, b]*Sum(B[b, c]*C[c, d], (c, 0, k-1)), (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A*B*C
+
+    # Test Kronecker delta:
+    expr = Sum(A[a, b]*KroneckerDelta(b, c)*B[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A*B
+
+    expr = Sum(KroneckerDelta(i1, m)*KroneckerDelta(i2, n)*A[i, i1]*A[j, i2], (i1, 0, k-1), (i2, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, m) == ArrayTensorProduct(A.T, A)
+
+    # Test numbered indices:
+    expr = Sum(A[i1, i2]*w1[i2, 0], (i2, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, i1) == MatrixElement(A*w1, i1, 0)
+
+    expr = Sum(A[i1, i2]*B[i2, 0], (i2, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, i1) == MatrixElement(A*B, i1, 0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_inverse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_inverse.py
new file mode 100644
index 0000000000000000000000000000000000000000..4bcc7d4de2b2bee4c4922bda8bc48a52aa205961
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_inverse.py
@@ -0,0 +1,69 @@
+from sympy.core import symbols, S
+from sympy.matrices.expressions import MatrixSymbol, Inverse, MatPow, ZeroMatrix, OneMatrix
+from sympy.matrices.exceptions import NonInvertibleMatrixError, NonSquareMatrixError
+from sympy.matrices import eye, Identity
+from sympy.testing.pytest import raises
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+
+n, m, l = symbols('n m l', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+
+
+def test_inverse():
+    assert Inverse(C).args == (C, S.NegativeOne)
+    assert Inverse(C).shape == (n, n)
+    assert Inverse(A*E).shape == (n, n)
+    assert Inverse(E*A).shape == (m, m)
+    assert Inverse(C).inverse() == C
+    assert Inverse(Inverse(C)).doit() == C
+    assert isinstance(Inverse(Inverse(C)), Inverse)
+
+    assert Inverse(*Inverse(E*A).args) == Inverse(E*A)
+
+    assert C.inverse().inverse() == C
+
+    assert C.inverse()*C == Identity(C.rows)
+
+    assert Identity(n).inverse() == Identity(n)
+    assert (3*Identity(n)).inverse() == Identity(n)/3
+
+    # Simplifies Muls if possible (i.e. submatrices are square)
+    assert (C*D).inverse() == D.I*C.I
+    # But still works when not possible
+    assert isinstance((A*E).inverse(), Inverse)
+    assert Inverse(C*D).doit(inv_expand=False) == Inverse(C*D)
+
+    assert Inverse(eye(3)).doit() == eye(3)
+    assert Inverse(eye(3)).doit(deep=False) == eye(3)
+
+    assert OneMatrix(1, 1).I == Identity(1)
+    assert isinstance(OneMatrix(n, n).I, Inverse)
+
+def test_inverse_non_invertible():
+    raises(NonInvertibleMatrixError, lambda: ZeroMatrix(n, n).I)
+    raises(NonInvertibleMatrixError, lambda: OneMatrix(2, 2).I)
+
+def test_refine():
+    assert refine(C.I, Q.orthogonal(C)) == C.T
+
+
+def test_inverse_matpow_canonicalization():
+    A = MatrixSymbol('A', 3, 3)
+    assert Inverse(MatPow(A, 3)).doit() == MatPow(Inverse(A), 3).doit()
+
+
+def test_nonsquare_error():
+    A = MatrixSymbol('A', 3, 4)
+    raises(NonSquareMatrixError, lambda: Inverse(A))
+
+
+def test_adjoint_trnaspose_conjugate():
+    A = MatrixSymbol('A', n, n)
+    assert A.transpose().inverse() == A.inverse().transpose()
+    assert A.conjugate().inverse() == A.inverse().conjugate()
+    assert A.adjoint().inverse() == A.inverse().adjoint()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_kronecker.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_kronecker.py
new file mode 100644
index 0000000000000000000000000000000000000000..b4444716a76a52e3638dd7a36238a9f459179083
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_kronecker.py
@@ -0,0 +1,150 @@
+from sympy.core.mod import Mod
+from sympy.core.numbers import I
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.integers import floor
+from sympy.matrices.dense import (Matrix, eye)
+from sympy.matrices import MatrixSymbol, Identity
+from sympy.matrices.expressions import det, trace
+
+from sympy.matrices.expressions.kronecker import (KroneckerProduct,
+                                                  kronecker_product,
+                                                  combine_kronecker)
+
+
+mat1 = Matrix([[1, 2 * I], [1 + I, 3]])
+mat2 = Matrix([[2 * I, 3], [4 * I, 2]])
+
+i, j, k, n, m, o, p, x = symbols('i,j,k,n,m,o,p,x')
+Z = MatrixSymbol('Z', n, n)
+W = MatrixSymbol('W', m, m)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', n, m)
+C = MatrixSymbol('C', m, k)
+
+
+def test_KroneckerProduct():
+    assert isinstance(KroneckerProduct(A, B), KroneckerProduct)
+    assert KroneckerProduct(A, B).subs(A, C) == KroneckerProduct(C, B)
+    assert KroneckerProduct(A, C).shape == (n*m, m*k)
+    assert (KroneckerProduct(A, C) + KroneckerProduct(-A, C)).is_ZeroMatrix
+    assert (KroneckerProduct(W, Z) * KroneckerProduct(W.I, Z.I)).is_Identity
+
+
+def test_KroneckerProduct_identity():
+    assert KroneckerProduct(Identity(m), Identity(n)) == Identity(m*n)
+    assert KroneckerProduct(eye(2), eye(3)) == eye(6)
+
+
+def test_KroneckerProduct_explicit():
+    X = MatrixSymbol('X', 2, 2)
+    Y = MatrixSymbol('Y', 2, 2)
+    kp = KroneckerProduct(X, Y)
+    assert kp.shape == (4, 4)
+    assert kp.as_explicit() == Matrix(
+        [
+            [X[0, 0]*Y[0, 0], X[0, 0]*Y[0, 1], X[0, 1]*Y[0, 0], X[0, 1]*Y[0, 1]],
+            [X[0, 0]*Y[1, 0], X[0, 0]*Y[1, 1], X[0, 1]*Y[1, 0], X[0, 1]*Y[1, 1]],
+            [X[1, 0]*Y[0, 0], X[1, 0]*Y[0, 1], X[1, 1]*Y[0, 0], X[1, 1]*Y[0, 1]],
+            [X[1, 0]*Y[1, 0], X[1, 0]*Y[1, 1], X[1, 1]*Y[1, 0], X[1, 1]*Y[1, 1]]
+        ]
+    )
+
+
+def test_tensor_product_adjoint():
+    assert KroneckerProduct(I*A, B).adjoint() == \
+        -I*KroneckerProduct(A.adjoint(), B.adjoint())
+    assert KroneckerProduct(mat1, mat2).adjoint() == \
+        kronecker_product(mat1.adjoint(), mat2.adjoint())
+
+
+def test_tensor_product_conjugate():
+    assert KroneckerProduct(I*A, B).conjugate() == \
+        -I*KroneckerProduct(A.conjugate(), B.conjugate())
+    assert KroneckerProduct(mat1, mat2).conjugate() == \
+        kronecker_product(mat1.conjugate(), mat2.conjugate())
+
+
+def test_tensor_product_transpose():
+    assert KroneckerProduct(I*A, B).transpose() == \
+        I*KroneckerProduct(A.transpose(), B.transpose())
+    assert KroneckerProduct(mat1, mat2).transpose() == \
+        kronecker_product(mat1.transpose(), mat2.transpose())
+
+
+def test_KroneckerProduct_is_associative():
+    assert kronecker_product(A, kronecker_product(
+        B, C)) == kronecker_product(kronecker_product(A, B), C)
+    assert kronecker_product(A, kronecker_product(
+        B, C)) == KroneckerProduct(A, B, C)
+
+
+def test_KroneckerProduct_is_bilinear():
+    assert kronecker_product(x*A, B) == x*kronecker_product(A, B)
+    assert kronecker_product(A, x*B) == x*kronecker_product(A, B)
+
+
+def test_KroneckerProduct_determinant():
+    kp = kronecker_product(W, Z)
+    assert det(kp) == det(W)**n * det(Z)**m
+
+
+def test_KroneckerProduct_trace():
+    kp = kronecker_product(W, Z)
+    assert trace(kp) == trace(W)*trace(Z)
+
+
+def test_KroneckerProduct_isnt_commutative():
+    assert KroneckerProduct(A, B) != KroneckerProduct(B, A)
+    assert KroneckerProduct(A, B).is_commutative is False
+
+
+def test_KroneckerProduct_extracts_commutative_part():
+    assert kronecker_product(x * A, 2 * B) == x * \
+        2 * KroneckerProduct(A, B)
+
+
+def test_KroneckerProduct_inverse():
+    kp = kronecker_product(W, Z)
+    assert kp.inverse() == kronecker_product(W.inverse(), Z.inverse())
+
+
+def test_KroneckerProduct_combine_add():
+    kp1 = kronecker_product(A, B)
+    kp2 = kronecker_product(C, W)
+    assert combine_kronecker(kp1*kp2) == kronecker_product(A*C, B*W)
+
+
+def test_KroneckerProduct_combine_mul():
+    X = MatrixSymbol('X', m, n)
+    Y = MatrixSymbol('Y', m, n)
+    kp1 = kronecker_product(A, X)
+    kp2 = kronecker_product(B, Y)
+    assert combine_kronecker(kp1+kp2) == kronecker_product(A+B, X+Y)
+
+
+def test_KroneckerProduct_combine_pow():
+    X = MatrixSymbol('X', n, n)
+    Y = MatrixSymbol('Y', n, n)
+    assert combine_kronecker(KroneckerProduct(
+        X, Y)**x) == KroneckerProduct(X**x, Y**x)
+    assert combine_kronecker(x * KroneckerProduct(X, Y)
+                             ** 2) == x * KroneckerProduct(X**2, Y**2)
+    assert combine_kronecker(
+        x * (KroneckerProduct(X, Y)**2) * KroneckerProduct(A, B)) == x * KroneckerProduct(X**2 * A, Y**2 * B)
+    # cannot simplify because of non-square arguments to kronecker product:
+    assert combine_kronecker(KroneckerProduct(A, B.T) ** m) == KroneckerProduct(A, B.T) ** m
+
+
+def test_KroneckerProduct_expand():
+    X = MatrixSymbol('X', n, n)
+    Y = MatrixSymbol('Y', n, n)
+
+    assert KroneckerProduct(X + Y, Y + Z).expand(kroneckerproduct=True) == \
+        KroneckerProduct(X, Y) + KroneckerProduct(X, Z) + \
+        KroneckerProduct(Y, Y) + KroneckerProduct(Y, Z)
+
+def test_KroneckerProduct_entry():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', o, p)
+
+    assert KroneckerProduct(A, B)._entry(i, j) == A[Mod(floor(i/o), n), Mod(floor(j/p), m)]*B[Mod(i, o), Mod(j, p)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matadd.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matadd.py
new file mode 100644
index 0000000000000000000000000000000000000000..43229ae8c2e42f0253a5f3eceefa5fffe7a99f29
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matadd.py
@@ -0,0 +1,58 @@
+from sympy.matrices.expressions import MatrixSymbol, MatAdd, MatPow, MatMul
+from sympy.matrices.expressions.special import GenericZeroMatrix, ZeroMatrix
+from sympy.matrices.exceptions import ShapeError
+from sympy.matrices import eye, ImmutableMatrix
+from sympy.core import Add, Basic, S
+from sympy.core.add import add
+from sympy.testing.pytest import XFAIL, raises
+
+X = MatrixSymbol('X', 2, 2)
+Y = MatrixSymbol('Y', 2, 2)
+
+def test_evaluate():
+    assert MatAdd(X, X, evaluate=True) == add(X, X, evaluate=True) == MatAdd(X, X).doit()
+
+def test_sort_key():
+    assert MatAdd(Y, X).doit().args == add(Y, X).doit().args == (X, Y)
+
+
+def test_matadd_sympify():
+    assert isinstance(MatAdd(eye(1), eye(1)).args[0], Basic)
+    assert isinstance(add(eye(1), eye(1)).args[0], Basic)
+
+
+def test_matadd_of_matrices():
+    assert MatAdd(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2))
+    assert add(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2))
+
+
+def test_doit_args():
+    A = ImmutableMatrix([[1, 2], [3, 4]])
+    B = ImmutableMatrix([[2, 3], [4, 5]])
+    assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2
+    assert MatAdd(A, MatMul(A, B)).doit() == A + A*B
+    assert (MatAdd(A, X, MatMul(A, B), Y, MatAdd(2*A, B)).doit() ==
+    add(A, X, MatMul(A, B), Y, add(2*A, B)).doit() ==
+    MatAdd(3*A + A*B + B, X, Y))
+
+
+def test_generic_identity():
+    assert MatAdd.identity == GenericZeroMatrix()
+    assert MatAdd.identity != S.Zero
+
+
+def test_zero_matrix_add():
+    assert Add(ZeroMatrix(2, 2), ZeroMatrix(2, 2)) == ZeroMatrix(2, 2)
+
+@XFAIL
+def test_matrix_Add_with_scalar():
+    raises(TypeError, lambda: Add(0, ZeroMatrix(2, 2)))
+
+
+def test_shape_error():
+    A = MatrixSymbol('A', 2, 3)
+    B = MatrixSymbol('B', 3, 3)
+    raises(ShapeError, lambda: MatAdd(A, B))
+
+    A = MatrixSymbol('A', 3, 2)
+    raises(ShapeError, lambda: MatAdd(A, B))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matexpr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matexpr.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2319e8d8097c2ad3519eab783c4665623c55b80
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matexpr.py
@@ -0,0 +1,592 @@
+from sympy.concrete.summations import Sum
+from sympy.core.exprtools import gcd_terms
+from sympy.core.function import (diff, expand)
+from sympy.core.relational import Eq
+from sympy.core.symbol import (Dummy, Symbol, Str)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import zeros
+from sympy.polys.polytools import factor
+
+from sympy.core import (S, symbols, Add, Mul, SympifyError, Rational,
+                    Function)
+from sympy.functions import sin, cos, tan, sqrt, cbrt, exp
+from sympy.simplify import simplify
+from sympy.matrices import (ImmutableMatrix, Inverse, MatAdd, MatMul,
+        MatPow, Matrix, MatrixExpr, MatrixSymbol,
+        SparseMatrix, Transpose, Adjoint, MatrixSet)
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.expressions.determinant import Determinant, det
+from sympy.matrices.expressions.matexpr import MatrixElement
+from sympy.matrices.expressions.special import ZeroMatrix, Identity
+from sympy.testing.pytest import raises, XFAIL, skip
+from importlib.metadata import version
+
+n, m, l, k, p = symbols('n m l k p', integer=True)
+x = symbols('x')
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+w = MatrixSymbol('w', n, 1)
+
+
+def test_matrix_symbol_creation():
+    assert MatrixSymbol('A', 2, 2)
+    assert MatrixSymbol('A', 0, 0)
+    raises(ValueError, lambda: MatrixSymbol('A', -1, 2))
+    raises(ValueError, lambda: MatrixSymbol('A', 2.0, 2))
+    raises(ValueError, lambda: MatrixSymbol('A', 2j, 2))
+    raises(ValueError, lambda: MatrixSymbol('A', 2, -1))
+    raises(ValueError, lambda: MatrixSymbol('A', 2, 2.0))
+    raises(ValueError, lambda: MatrixSymbol('A', 2, 2j))
+
+    n = symbols('n')
+    assert MatrixSymbol('A', n, n)
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: MatrixSymbol('A', n, n))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: MatrixSymbol('A', n, n))
+
+
+def test_matexpr_properties():
+    assert A.shape == (n, m)
+    assert (A * B).shape == (n, l)
+    assert A[0, 1].indices == (0, 1)
+    assert A[0, 0].symbol == A
+    assert A[0, 0].symbol.name == 'A'
+
+
+def test_matexpr():
+    assert (x*A).shape == A.shape
+    assert (x*A).__class__ == MatMul
+    assert 2*A - A - A == ZeroMatrix(*A.shape)
+    assert (A*B).shape == (n, l)
+
+
+def test_matexpr_subs():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', m, l)
+    C = MatrixSymbol('C', m, l)
+
+    assert A.subs(n, m).shape == (m, m)
+    assert (A*B).subs(B, C) == A*C
+    assert (A*B).subs(l, n).is_square
+
+    W = MatrixSymbol("W", 3, 3)
+    X = MatrixSymbol("X", 2, 2)
+    Y = MatrixSymbol("Y", 1, 2)
+    Z = MatrixSymbol("Z", n, 2)
+    # no restrictions on Symbol replacement
+    assert X.subs(X, Y) == Y
+    # it might be better to just change the name
+    y = Str('y')
+    assert X.subs(Str("X"), y).args == (y, 2, 2)
+    # it's ok to introduce a wider matrix
+    assert X[1, 1].subs(X, W) == W[1, 1]
+    # but for a given MatrixExpression, only change
+    # name if indexing on the new shape is valid.
+    # Here, X is 2,2; Y is 1,2 and Y[1, 1] is out
+    # of range so an error is raised
+    raises(IndexError, lambda: X[1, 1].subs(X, Y))
+    # here, [0, 1] is in range so the subs succeeds
+    assert X[0, 1].subs(X, Y) == Y[0, 1]
+    # and here the size of n will accept any index
+    # in the first position
+    assert W[2, 1].subs(W, Z) == Z[2, 1]
+    # but not in the second position
+    raises(IndexError, lambda: W[2, 2].subs(W, Z))
+    # any matrix should raise if invalid
+    raises(IndexError, lambda: W[2, 2].subs(W, zeros(2)))
+
+    A = SparseMatrix([[1, 2], [3, 4]])
+    B = Matrix([[1, 2], [3, 4]])
+    C, D = MatrixSymbol('C', 2, 2), MatrixSymbol('D', 2, 2)
+
+    assert (C*D).subs({C: A, D: B}) == MatMul(A, B)
+
+
+def test_addition():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, m)
+
+    assert isinstance(A + B, MatAdd)
+    assert (A + B).shape == A.shape
+    assert isinstance(A - A + 2*B, MatMul)
+
+    raises(TypeError, lambda: A + 1)
+    raises(TypeError, lambda: 5 + A)
+    raises(TypeError, lambda: 5 - A)
+
+    assert A + ZeroMatrix(n, m) - A == ZeroMatrix(n, m)
+    raises(TypeError, lambda: ZeroMatrix(n, m) + S.Zero)
+
+
+def test_multiplication():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', m, l)
+    C = MatrixSymbol('C', n, n)
+
+    assert (2*A*B).shape == (n, l)
+    assert (A*0*B) == ZeroMatrix(n, l)
+    assert (2*A).shape == A.shape
+
+    assert A * ZeroMatrix(m, m) * B == ZeroMatrix(n, l)
+
+    assert C * Identity(n) * C.I == Identity(n)
+
+    assert B/2 == S.Half*B
+    raises(NotImplementedError, lambda: 2/B)
+
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, n)
+    assert Identity(n) * (A + B) == A + B
+
+    assert A**2*A == A**3
+    assert A**2*(A.I)**3 == A.I
+    assert A**3*(A.I)**2 == A
+
+
+def test_MatPow():
+    A = MatrixSymbol('A', n, n)
+
+    AA = MatPow(A, 2)
+    assert AA.exp == 2
+    assert AA.base == A
+    assert (A**n).exp == n
+
+    assert A**0 == Identity(n)
+    assert A**1 == A
+    assert A**2 == AA
+    assert A**-1 == Inverse(A)
+    assert (A**-1)**-1 == A
+    assert (A**2)**3 == A**6
+    assert A**S.Half == sqrt(A)
+    assert A**Rational(1, 3) == cbrt(A)
+    raises(NonSquareMatrixError, lambda: MatrixSymbol('B', 3, 2)**2)
+
+
+def test_MatrixSymbol():
+    n, m, t = symbols('n,m,t')
+    X = MatrixSymbol('X', n, m)
+    assert X.shape == (n, m)
+    raises(TypeError, lambda: MatrixSymbol('X', n, m)(t))  # issue 5855
+    assert X.doit() == X
+
+
+def test_dense_conversion():
+    X = MatrixSymbol('X', 2, 2)
+    assert ImmutableMatrix(X) == ImmutableMatrix(2, 2, lambda i, j: X[i, j])
+    assert Matrix(X) == Matrix(2, 2, lambda i, j: X[i, j])
+
+
+def test_free_symbols():
+    assert (C*D).free_symbols == {C, D}
+
+
+def test_zero_matmul():
+    assert isinstance(S.Zero * MatrixSymbol('X', 2, 2), MatrixExpr)
+
+
+def test_matadd_simplify():
+    A = MatrixSymbol('A', 1, 1)
+    assert simplify(MatAdd(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
+        MatAdd(A, Matrix([[1]]))
+
+
+def test_matmul_simplify():
+    A = MatrixSymbol('A', 1, 1)
+    assert simplify(MatMul(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
+        MatMul(A, Matrix([[1]]))
+
+
+def test_invariants():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', m, l)
+    X = MatrixSymbol('X', n, n)
+    objs = [Identity(n), ZeroMatrix(m, n), A, MatMul(A, B), MatAdd(A, A),
+            Transpose(A), Adjoint(A), Inverse(X), MatPow(X, 2), MatPow(X, -1),
+            MatPow(X, 0)]
+    for obj in objs:
+        assert obj == obj.__class__(*obj.args)
+
+
+def test_matexpr_indexing():
+    A = MatrixSymbol('A', n, m)
+    A[1, 2]
+    A[l, k]
+    A[l + 1, k + 1]
+    A = MatrixSymbol('A', 2, 1)
+    for i in range(-2, 2):
+        for j in range(-1, 1):
+            A[i, j]
+
+
+def test_single_indexing():
+    A = MatrixSymbol('A', 2, 3)
+    assert A[1] == A[0, 1]
+    assert A[int(1)] == A[0, 1]
+    assert A[3] == A[1, 0]
+    assert list(A[:2, :2]) == [A[0, 0], A[0, 1], A[1, 0], A[1, 1]]
+    raises(IndexError, lambda: A[6])
+    raises(IndexError, lambda: A[n])
+    B = MatrixSymbol('B', n, m)
+    raises(IndexError, lambda: B[1])
+    B = MatrixSymbol('B', n, 3)
+    assert B[3] == B[1, 0]
+
+
+def test_MatrixElement_commutative():
+    assert A[0, 1]*A[1, 0] == A[1, 0]*A[0, 1]
+
+
+def test_MatrixSymbol_determinant():
+    A = MatrixSymbol('A', 4, 4)
+    assert A.as_explicit().det() == A[0, 0]*A[1, 1]*A[2, 2]*A[3, 3] - \
+        A[0, 0]*A[1, 1]*A[2, 3]*A[3, 2] - A[0, 0]*A[1, 2]*A[2, 1]*A[3, 3] + \
+        A[0, 0]*A[1, 2]*A[2, 3]*A[3, 1] + A[0, 0]*A[1, 3]*A[2, 1]*A[3, 2] - \
+        A[0, 0]*A[1, 3]*A[2, 2]*A[3, 1] - A[0, 1]*A[1, 0]*A[2, 2]*A[3, 3] + \
+        A[0, 1]*A[1, 0]*A[2, 3]*A[3, 2] + A[0, 1]*A[1, 2]*A[2, 0]*A[3, 3] - \
+        A[0, 1]*A[1, 2]*A[2, 3]*A[3, 0] - A[0, 1]*A[1, 3]*A[2, 0]*A[3, 2] + \
+        A[0, 1]*A[1, 3]*A[2, 2]*A[3, 0] + A[0, 2]*A[1, 0]*A[2, 1]*A[3, 3] - \
+        A[0, 2]*A[1, 0]*A[2, 3]*A[3, 1] - A[0, 2]*A[1, 1]*A[2, 0]*A[3, 3] + \
+        A[0, 2]*A[1, 1]*A[2, 3]*A[3, 0] + A[0, 2]*A[1, 3]*A[2, 0]*A[3, 1] - \
+        A[0, 2]*A[1, 3]*A[2, 1]*A[3, 0] - A[0, 3]*A[1, 0]*A[2, 1]*A[3, 2] + \
+        A[0, 3]*A[1, 0]*A[2, 2]*A[3, 1] + A[0, 3]*A[1, 1]*A[2, 0]*A[3, 2] - \
+        A[0, 3]*A[1, 1]*A[2, 2]*A[3, 0] - A[0, 3]*A[1, 2]*A[2, 0]*A[3, 1] + \
+        A[0, 3]*A[1, 2]*A[2, 1]*A[3, 0]
+
+    B = MatrixSymbol('B', 4, 4)
+    assert Determinant(A + B).doit() == det(A + B) == (A + B).det()
+
+
+def test_MatrixElement_diff():
+    assert (A[3, 0]*A[0, 0]).diff(A[0, 0]) == A[3, 0]
+
+
+def test_MatrixElement_doit():
+    u = MatrixSymbol('u', 2, 1)
+    v = ImmutableMatrix([3, 5])
+    assert u[0, 0].subs(u, v).doit() == v[0, 0]
+
+
+def test_identity_powers():
+    M = Identity(n)
+    assert MatPow(M, 3).doit() == M**3
+    assert M**n == M
+    assert MatPow(M, 0).doit() == M**2
+    assert M**-2 == M
+    assert MatPow(M, -2).doit() == M**0
+    N = Identity(3)
+    assert MatPow(N, 2).doit() == N**n
+    assert MatPow(N, 3).doit() == N
+    assert MatPow(N, -2).doit() == N**4
+    assert MatPow(N, 2).doit() == N**0
+
+
+def test_Zero_power():
+    z1 = ZeroMatrix(n, n)
+    assert z1**4 == z1
+    raises(ValueError, lambda:z1**-2)
+    assert z1**0 == Identity(n)
+    assert MatPow(z1, 2).doit() == z1**2
+    raises(ValueError, lambda:MatPow(z1, -2).doit())
+    z2 = ZeroMatrix(3, 3)
+    assert MatPow(z2, 4).doit() == z2**4
+    raises(ValueError, lambda:z2**-3)
+    assert z2**3 == MatPow(z2, 3).doit()
+    assert z2**0 == Identity(3)
+    raises(ValueError, lambda:MatPow(z2, -1).doit())
+
+
+def test_matrixelement_diff():
+    dexpr = diff((D*w)[k,0], w[p,0])
+
+    assert w[k, p].diff(w[k, p]) == 1
+    assert w[k, p].diff(w[0, 0]) == KroneckerDelta(0, k, (0, n-1))*KroneckerDelta(0, p, (0, 0))
+    _i_1 = Dummy("_i_1")
+    assert dexpr.dummy_eq(Sum(KroneckerDelta(_i_1, p, (0, n-1))*D[k, _i_1], (_i_1, 0, n - 1)))
+    assert dexpr.doit() == D[k, p]
+
+
+def test_MatrixElement_with_values():
+    x, y, z, w = symbols("x y z w")
+    M = Matrix([[x, y], [z, w]])
+    i, j = symbols("i, j")
+    Mij = M[i, j]
+    assert isinstance(Mij, MatrixElement)
+    Ms = SparseMatrix([[2, 3], [4, 5]])
+    msij = Ms[i, j]
+    assert isinstance(msij, MatrixElement)
+    for oi, oj in [(0, 0), (0, 1), (1, 0), (1, 1)]:
+        assert Mij.subs({i: oi, j: oj}) == M[oi, oj]
+        assert msij.subs({i: oi, j: oj}) == Ms[oi, oj]
+    A = MatrixSymbol("A", 2, 2)
+    assert A[0, 0].subs(A, M) == x
+    assert A[i, j].subs(A, M) == M[i, j]
+    assert M[i, j].subs(M, A) == A[i, j]
+
+    assert isinstance(M[3*i - 2, j], MatrixElement)
+    assert M[3*i - 2, j].subs({i: 1, j: 0}) == M[1, 0]
+    assert isinstance(M[i, 0], MatrixElement)
+    assert M[i, 0].subs(i, 0) == M[0, 0]
+    assert M[0, i].subs(i, 1) == M[0, 1]
+
+    assert M[i, j].diff(x) == Matrix([[1, 0], [0, 0]])[i, j]
+
+    raises(ValueError, lambda: M[i, 2])
+    raises(ValueError, lambda: M[i, -1])
+    raises(ValueError, lambda: M[2, i])
+    raises(ValueError, lambda: M[-1, i])
+
+
+def test_inv():
+    B = MatrixSymbol('B', 3, 3)
+    assert B.inv() == B**-1
+
+    # https://github.com/sympy/sympy/issues/19162
+    X = MatrixSymbol('X', 1, 1).as_explicit()
+    assert X.inv() == Matrix([[1/X[0, 0]]])
+
+    X = MatrixSymbol('X', 2, 2).as_explicit()
+    detX = X[0, 0]*X[1, 1] - X[0, 1]*X[1, 0]
+    invX = Matrix([[ X[1, 1], -X[0, 1]],
+                   [-X[1, 0],  X[0, 0]]]) / detX
+    assert X.inv() == invX
+
+
+@XFAIL
+def test_factor_expand():
+    A = MatrixSymbol("A", n, n)
+    B = MatrixSymbol("B", n, n)
+    expr1 = (A + B)*(C + D)
+    expr2 = A*C + B*C + A*D + B*D
+    assert expr1 != expr2
+    assert expand(expr1) == expr2
+    assert factor(expr2) == expr1
+
+    expr = B**(-1)*(A**(-1)*B**(-1) - A**(-1)*C*B**(-1))**(-1)*A**(-1)
+    I = Identity(n)
+    # Ideally we get the first, but we at least don't want a wrong answer
+    assert factor(expr) in [I - C, B**-1*(A**-1*(I - C)*B**-1)**-1*A**-1]
+
+def test_numpy_conversion():
+    try:
+        from numpy import array, array_equal
+    except ImportError:
+        skip('NumPy must be available to test creating matrices from ndarrays')
+    A = MatrixSymbol('A', 2, 2)
+    np_array = array([[MatrixElement(A, 0, 0), MatrixElement(A, 0, 1)],
+    [MatrixElement(A, 1, 0), MatrixElement(A, 1, 1)]])
+    assert array_equal(array(A), np_array)
+    assert array_equal(array(A, copy=True), np_array)
+    if(int(version('numpy').split('.')[0]) >= 2): #run this test only if numpy is new enough that copy variable is passed properly.
+        raises(TypeError, lambda: array(A, copy=False))
+
+def test_issue_2749():
+    A = MatrixSymbol("A", 5, 2)
+    assert (A.T * A).I.as_explicit() == Matrix([[(A.T * A).I[0, 0], (A.T * A).I[0, 1]], \
+    [(A.T * A).I[1, 0], (A.T * A).I[1, 1]]])
+
+
+def test_issue_2750():
+    x = MatrixSymbol('x', 1, 1)
+    assert (x.T*x).as_explicit()**-1 == Matrix([[x[0, 0]**(-2)]])
+
+
+def test_issue_7842():
+    A = MatrixSymbol('A', 3, 1)
+    B = MatrixSymbol('B', 2, 1)
+    assert Eq(A, B) == False
+    assert Eq(A[1,0], B[1, 0]).func is Eq
+    A = ZeroMatrix(2, 3)
+    B = ZeroMatrix(2, 3)
+    assert Eq(A, B) == True
+
+
+def test_issue_21195():
+    t = symbols('t')
+    x = Function('x')(t)
+    dx = x.diff(t)
+    exp1 = cos(x) + cos(x)*dx
+    exp2 = sin(x) + tan(x)*(dx.diff(t))
+    exp3 = sin(x)*sin(t)*(dx.diff(t)).diff(t)
+    A = Matrix([[exp1], [exp2], [exp3]])
+    B = Matrix([[exp1.diff(x)], [exp2.diff(x)], [exp3.diff(x)]])
+    assert A.diff(x) == B
+
+
+def test_issue_24859():
+    A = MatrixSymbol('A', 2, 3)
+    B = MatrixSymbol('B', 3, 2)
+    J = A*B
+    Jinv = Matrix(J).adjugate()
+    u = MatrixSymbol('u', 2, 3)
+    Jk = Jinv.subs(A, A + x*u)
+
+    expected = B[0, 1]*u[1, 0] + B[1, 1]*u[1, 1] + B[2, 1]*u[1, 2]
+    assert Jk[0, 0].diff(x) == expected
+    assert diff(Jk[0, 0], x).doit() == expected
+
+
+def test_MatMul_postprocessor():
+    z = zeros(2)
+    z1 = ZeroMatrix(2, 2)
+    assert Mul(0, z) == Mul(z, 0) in [z, z1]
+
+    M = Matrix([[1, 2], [3, 4]])
+    Mx = Matrix([[x, 2*x], [3*x, 4*x]])
+    assert Mul(x, M) == Mul(M, x) == Mx
+
+    A = MatrixSymbol("A", 2, 2)
+    assert Mul(A, M) == MatMul(A, M)
+    assert Mul(M, A) == MatMul(M, A)
+    # Scalars should be absorbed into constant matrices
+    a = Mul(x, M, A)
+    b = Mul(M, x, A)
+    c = Mul(M, A, x)
+    assert a == b == c == MatMul(Mx, A)
+    a = Mul(x, A, M)
+    b = Mul(A, x, M)
+    c = Mul(A, M, x)
+    assert a == b == c == MatMul(A, Mx)
+    assert Mul(M, M) == M**2
+    assert Mul(A, M, M) == MatMul(A, M**2)
+    assert Mul(M, M, A) == MatMul(M**2, A)
+    assert Mul(M, A, M) == MatMul(M, A, M)
+
+    assert Mul(A, x, M, M, x) == MatMul(A, Mx**2)
+
+
+@XFAIL
+def test_MatAdd_postprocessor_xfail():
+    # This is difficult to get working because of the way that Add processes
+    # its args.
+    z = zeros(2)
+    assert Add(z, S.NaN) == Add(S.NaN, z)
+
+
+def test_MatAdd_postprocessor():
+    # Some of these are nonsensical, but we do not raise errors for Add
+    # because that breaks algorithms that want to replace matrices with dummy
+    # symbols.
+
+    z = zeros(2)
+
+    assert Add(0, z) == Add(z, 0) == z
+
+    a = Add(S.Infinity, z)
+    assert a == Add(z, S.Infinity)
+    assert isinstance(a, Add)
+    assert a.args == (S.Infinity, z)
+
+    a = Add(S.ComplexInfinity, z)
+    assert a == Add(z, S.ComplexInfinity)
+    assert isinstance(a, Add)
+    assert a.args == (S.ComplexInfinity, z)
+
+    a = Add(z, S.NaN)
+    # assert a == Add(S.NaN, z) # See the XFAIL above
+    assert isinstance(a, Add)
+    assert a.args == (S.NaN, z)
+
+    M = Matrix([[1, 2], [3, 4]])
+    a = Add(x, M)
+    assert a == Add(M, x)
+    assert isinstance(a, Add)
+    assert a.args == (x, M)
+
+    A = MatrixSymbol("A", 2, 2)
+    assert Add(A, M) == Add(M, A) == A + M
+
+    # Scalars should be absorbed into constant matrices (producing an error)
+    a = Add(x, M, A)
+    assert a == Add(M, x, A) == Add(M, A, x) == Add(x, A, M) == Add(A, x, M) == Add(A, M, x)
+    assert isinstance(a, Add)
+    assert a.args == (x, A + M)
+
+    assert Add(M, M) == 2*M
+    assert Add(M, A, M) == Add(M, M, A) == Add(A, M, M) == A + 2*M
+
+    a = Add(A, x, M, M, x)
+    assert isinstance(a, Add)
+    assert a.args == (2*x, A + 2*M)
+
+
+def test_simplify_matrix_expressions():
+    # Various simplification functions
+    assert type(gcd_terms(C*D + D*C)) == MatAdd
+    a = gcd_terms(2*C*D + 4*D*C)
+    assert type(a) == MatAdd
+    assert a.args == (2*C*D, 4*D*C)
+
+
+def test_exp():
+    A = MatrixSymbol('A', 2, 2)
+    B = MatrixSymbol('B', 2, 2)
+    expr1 = exp(A)*exp(B)
+    expr2 = exp(B)*exp(A)
+    assert expr1 != expr2
+    assert expr1 - expr2 != 0
+    assert not isinstance(expr1, exp)
+    assert not isinstance(expr2, exp)
+
+
+def test_invalid_args():
+    raises(SympifyError, lambda: MatrixSymbol(1, 2, 'A'))
+
+
+def test_matrixsymbol_from_symbol():
+    # The label should be preserved during doit and subs
+    A_label = Symbol('A', complex=True)
+    A = MatrixSymbol(A_label, 2, 2)
+
+    A_1 = A.doit()
+    A_2 = A.subs(2, 3)
+    assert A_1.args == A.args
+    assert A_2.args[0] == A.args[0]
+
+
+def test_as_explicit():
+    Z = MatrixSymbol('Z', 2, 3)
+    assert Z.as_explicit() == ImmutableMatrix([
+        [Z[0, 0], Z[0, 1], Z[0, 2]],
+        [Z[1, 0], Z[1, 1], Z[1, 2]],
+    ])
+    raises(ValueError, lambda: A.as_explicit())
+
+
+def test_MatrixSet():
+    M = MatrixSet(2, 2, set=S.Reals)
+    assert M.shape == (2, 2)
+    assert M.set == S.Reals
+    X = Matrix([[1, 2], [3, 4]])
+    assert X in M
+    X = ZeroMatrix(2, 2)
+    assert X in M
+    raises(TypeError, lambda: A in M)
+    raises(TypeError, lambda: 1 in M)
+    M = MatrixSet(n, m, set=S.Reals)
+    assert A in M
+    raises(TypeError, lambda: C in M)
+    raises(TypeError, lambda: X in M)
+    M = MatrixSet(2, 2, set={1, 2, 3})
+    X = Matrix([[1, 2], [3, 4]])
+    Y = Matrix([[1, 2]])
+    assert (X in M) == S.false
+    assert (Y in M) == S.false
+    raises(ValueError, lambda: MatrixSet(2, -2, S.Reals))
+    raises(ValueError, lambda: MatrixSet(2.4, -1, S.Reals))
+    raises(TypeError, lambda: MatrixSet(2, 2, (1, 2, 3)))
+
+
+def test_matrixsymbol_solving():
+    A = MatrixSymbol('A', 2, 2)
+    B = MatrixSymbol('B', 2, 2)
+    Z = ZeroMatrix(2, 2)
+    assert -(-A + B) - A + B == Z
+    assert (-(-A + B) - A + B).simplify() == Z
+    assert (-(-A + B) - A + B).expand() == Z
+    assert (-(-A + B) - A + B - Z).simplify() == Z
+    assert (-(-A + B) - A + B - Z).expand() == Z
+    assert (A*(A + B) + B*(A.T + B.T)).expand() == A**2 + A*B + B*A.T + B*B.T
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matmul.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matmul.py
new file mode 100644
index 0000000000000000000000000000000000000000..813926e2c83e27716f4f894ebebd09b2a576f046
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matmul.py
@@ -0,0 +1,193 @@
+from sympy.core import I, symbols, Basic, Mul, S
+from sympy.core.mul import mul
+from sympy.functions import adjoint, transpose
+from sympy.matrices.exceptions import ShapeError
+from sympy.matrices import (Identity, Inverse, Matrix, MatrixSymbol, ZeroMatrix,
+        eye, ImmutableMatrix)
+from sympy.matrices.expressions import Adjoint, Transpose, det, MatPow
+from sympy.matrices.expressions.special import GenericIdentity
+from sympy.matrices.expressions.matmul import (factor_in_front, remove_ids,
+        MatMul, combine_powers, any_zeros, unpack, only_squares)
+from sympy.strategies import null_safe
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+from sympy.core.symbol import Symbol
+
+from sympy.testing.pytest import XFAIL, raises
+
+n, m, l, k = symbols('n m l k', integer=True)
+x = symbols('x')
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+
+def test_evaluate():
+    assert MatMul(C, C, evaluate=True) == MatMul(C, C).doit()
+
+def test_adjoint():
+    assert adjoint(A*B) == Adjoint(B)*Adjoint(A)
+    assert adjoint(2*A*B) == 2*Adjoint(B)*Adjoint(A)
+    assert adjoint(2*I*C) == -2*I*Adjoint(C)
+
+    M = Matrix(2, 2, [1, 2 + I, 3, 4])
+    MA = Matrix(2, 2, [1, 3, 2 - I, 4])
+    assert adjoint(M) == MA
+    assert adjoint(2*M) == 2*MA
+    assert adjoint(MatMul(2, M)) == MatMul(2, MA).doit()
+
+
+def test_transpose():
+    assert transpose(A*B) == Transpose(B)*Transpose(A)
+    assert transpose(2*A*B) == 2*Transpose(B)*Transpose(A)
+    assert transpose(2*I*C) == 2*I*Transpose(C)
+
+    M = Matrix(2, 2, [1, 2 + I, 3, 4])
+    MT = Matrix(2, 2, [1, 3, 2 + I, 4])
+    assert transpose(M) == MT
+    assert transpose(2*M) == 2*MT
+    assert transpose(x*M) == x*MT
+    assert transpose(MatMul(2, M)) == MatMul(2, MT).doit()
+
+
+def test_factor_in_front():
+    assert factor_in_front(MatMul(A, 2, B, evaluate=False)) ==\
+                           MatMul(2, A, B, evaluate=False)
+
+
+def test_remove_ids():
+    assert remove_ids(MatMul(A, Identity(m), B, evaluate=False)) == \
+                      MatMul(A, B, evaluate=False)
+    assert null_safe(remove_ids)(MatMul(Identity(n), evaluate=False)) == \
+                                 MatMul(Identity(n), evaluate=False)
+
+
+def test_combine_powers():
+    assert combine_powers(MatMul(D, Inverse(D), D, evaluate=False)) == \
+                 MatMul(Identity(n), D, evaluate=False)
+    assert combine_powers(MatMul(B.T, Inverse(E*A), E, A, B, evaluate=False)) == \
+        MatMul(B.T, Identity(m), B, evaluate=False)
+    assert combine_powers(MatMul(A, E, Inverse(A*E), D, evaluate=False)) == \
+        MatMul(Identity(n), D, evaluate=False)
+
+
+def test_any_zeros():
+    assert any_zeros(MatMul(A, ZeroMatrix(m, k), evaluate=False)) == \
+                     ZeroMatrix(n, k)
+
+
+def test_unpack():
+    assert unpack(MatMul(A, evaluate=False)) == A
+    x = MatMul(A, B)
+    assert unpack(x) == x
+
+
+def test_only_squares():
+    assert only_squares(C) == [C]
+    assert only_squares(C, D) == [C, D]
+    assert only_squares(C, A, A.T, D) == [C, A*A.T, D]
+
+
+def test_determinant():
+    assert det(2*C) == 2**n*det(C)
+    assert det(2*C*D) == 2**n*det(C)*det(D)
+    assert det(3*C*A*A.T*D) == 3**n*det(C)*det(A*A.T)*det(D)
+
+
+def test_doit():
+    assert MatMul(C, 2, D).args == (C, 2, D)
+    assert MatMul(C, 2, D).doit().args == (2, C, D)
+    assert MatMul(C, Transpose(D*C)).args == (C, Transpose(D*C))
+    assert MatMul(C, Transpose(D*C)).doit(deep=True).args == (C, C.T, D.T)
+
+
+def test_doit_drills_down():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    Y = ImmutableMatrix([[2, 3], [4, 5]])
+    assert MatMul(X, MatPow(Y, 2)).doit() == X*Y**2
+    assert MatMul(C, Transpose(D*C)).doit().args == (C, C.T, D.T)
+
+
+def test_doit_deep_false_still_canonical():
+    assert (MatMul(C, Transpose(D*C), 2).doit(deep=False).args ==
+            (2, C, Transpose(D*C)))
+
+
+def test_matmul_scalar_Matrix_doit():
+    # Issue 9053
+    X = Matrix([[1, 2], [3, 4]])
+    assert MatMul(2, X).doit() == 2*X
+
+
+def test_matmul_sympify():
+    assert isinstance(MatMul(eye(1), eye(1)).args[0], Basic)
+
+
+def test_collapse_MatrixBase():
+    A = Matrix([[1, 1], [1, 1]])
+    B = Matrix([[1, 2], [3, 4]])
+    assert MatMul(A, B).doit() == ImmutableMatrix([[4, 6], [4, 6]])
+
+
+def test_refine():
+    assert refine(C*C.T*D, Q.orthogonal(C)).doit() == D
+
+    kC = k*C
+    assert refine(kC*C.T, Q.orthogonal(C)).doit() == k*Identity(n)
+    assert refine(kC* kC.T, Q.orthogonal(C)).doit() == (k**2)*Identity(n)
+
+def test_matmul_no_matrices():
+    assert MatMul(1) == 1
+    assert MatMul(n, m) == n*m
+    assert not isinstance(MatMul(n, m), MatMul)
+
+def test_matmul_args_cnc():
+    assert MatMul(n, A, A.T).args_cnc() == [[n], [A, A.T]]
+    assert MatMul(A, A.T).args_cnc() == [[], [A, A.T]]
+
+@XFAIL
+def test_matmul_args_cnc_symbols():
+    # Not currently supported
+    a, b = symbols('a b', commutative=False)
+    assert MatMul(n, a, b, A, A.T).args_cnc() == [[n], [a, b, A, A.T]]
+    assert MatMul(n, a, A, b, A.T).args_cnc() == [[n], [a, A, b, A.T]]
+
+def test_issue_12950():
+    M = Matrix([[Symbol("x")]]) * MatrixSymbol("A", 1, 1)
+    assert MatrixSymbol("A", 1, 1).as_explicit()[0]*Symbol('x') == M.as_explicit()[0]
+
+def test_construction_with_Mul():
+    assert Mul(C, D) == MatMul(C, D)
+    assert Mul(D, C) == MatMul(D, C)
+
+def test_construction_with_mul():
+    assert mul(C, D) == MatMul(C, D)
+    assert mul(D, C) == MatMul(D, C)
+    assert mul(C, D) != MatMul(D, C)
+
+def test_generic_identity():
+    assert MatMul.identity == GenericIdentity()
+    assert MatMul.identity != S.One
+
+
+def test_issue_23519():
+    N = Symbol("N", integer=True)
+    M1 = MatrixSymbol("M1", N, N)
+    M2 = MatrixSymbol("M2", N, N)
+    I = Identity(N)
+    z = (M2 + 2 * (M2 + I) * M1 + I)
+    assert z.coeff(M1) == 2*I + 2*M2
+
+
+def test_shape_error():
+    A = MatrixSymbol('A', 2, 2)
+    B = MatrixSymbol('B', 3, 3)
+    raises(ShapeError, lambda: MatMul(A, B))
+
+
+def test_matmul_transpose():
+    # https://github.com/sympy/sympy/issues/9503
+    M = Matrix(2, 2, [1, 2 + I, 3, 4])
+    a = Symbol('a')
+    assert (MatMul(a, M).T).expand() == (a*Matrix([[1, 3],[2 + I, 4]])).expand()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matpow.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matpow.py
new file mode 100644
index 0000000000000000000000000000000000000000..2afb5fdc2aa652c321de52aba43db63da60941fd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_matpow.py
@@ -0,0 +1,217 @@
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.simplify.powsimp import powsimp
+from sympy.testing.pytest import raises
+from sympy.core.expr import unchanged
+from sympy.core import symbols, S
+from sympy.matrices import Identity, MatrixSymbol, ImmutableMatrix, ZeroMatrix, OneMatrix, Matrix
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.expressions import MatPow, MatAdd, MatMul
+from sympy.matrices.expressions.inverse import Inverse
+from sympy.matrices.expressions.matexpr import MatrixElement
+
+n, m, l, k = symbols('n m l k', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+
+
+def test_entry_matrix():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    assert MatPow(X, 0)[0, 0] == 1
+    assert MatPow(X, 0)[0, 1] == 0
+    assert MatPow(X, 1)[0, 0] == 1
+    assert MatPow(X, 1)[0, 1] == 2
+    assert MatPow(X, 2)[0, 0] == 7
+
+
+def test_entry_symbol():
+    from sympy.concrete import Sum
+    assert MatPow(C, 0)[0, 0] == 1
+    assert MatPow(C, 0)[0, 1] == 0
+    assert MatPow(C, 1)[0, 0] == C[0, 0]
+    assert isinstance(MatPow(C, 2)[0, 0], Sum)
+    assert isinstance(MatPow(C, n)[0, 0], MatrixElement)
+
+
+def test_as_explicit_symbol():
+    X = MatrixSymbol('X', 2, 2)
+    assert MatPow(X, 0).as_explicit() == ImmutableMatrix(Identity(2))
+    assert MatPow(X, 1).as_explicit() == X.as_explicit()
+    assert MatPow(X, 2).as_explicit() == (X.as_explicit())**2
+    assert MatPow(X, n).as_explicit() == ImmutableMatrix([
+        [(X ** n)[0, 0], (X ** n)[0, 1]],
+        [(X ** n)[1, 0], (X ** n)[1, 1]],
+    ])
+
+    a = MatrixSymbol("a", 3, 1)
+    b = MatrixSymbol("b", 3, 1)
+    c = MatrixSymbol("c", 3, 1)
+
+    expr = (a.T*b)**S.Half
+    assert expr.as_explicit() == Matrix([[sqrt(a[0, 0]*b[0, 0] + a[1, 0]*b[1, 0] + a[2, 0]*b[2, 0])]])
+
+    expr = c*(a.T*b)**S.Half
+    m = sqrt(a[0, 0]*b[0, 0] + a[1, 0]*b[1, 0] + a[2, 0]*b[2, 0])
+    assert expr.as_explicit() == Matrix([[c[0, 0]*m], [c[1, 0]*m], [c[2, 0]*m]])
+
+    expr = (a*b.T)**S.Half
+    denom = sqrt(a[0, 0]*b[0, 0] + a[1, 0]*b[1, 0] + a[2, 0]*b[2, 0])
+    expected = (a*b.T).as_explicit()/denom
+    assert expr.as_explicit() == expected
+
+    expr = X**-1
+    det = X[0, 0]*X[1, 1] - X[1, 0]*X[0, 1]
+    expected = Matrix([[X[1, 1], -X[0, 1]], [-X[1, 0], X[0, 0]]])/det
+    assert expr.as_explicit() == expected
+
+    expr = X**m
+    assert expr.as_explicit() == X.as_explicit()**m
+
+
+def test_as_explicit_matrix():
+    A = ImmutableMatrix([[1, 2], [3, 4]])
+    assert MatPow(A, 0).as_explicit() == ImmutableMatrix(Identity(2))
+    assert MatPow(A, 1).as_explicit() == A
+    assert MatPow(A, 2).as_explicit() == A**2
+    assert MatPow(A, -1).as_explicit() == A.inv()
+    assert MatPow(A, -2).as_explicit() == (A.inv())**2
+    # less expensive than testing on a 2x2
+    A = ImmutableMatrix([4])
+    assert MatPow(A, S.Half).as_explicit() == A**S.Half
+
+
+def test_doit_symbol():
+    assert MatPow(C, 0).doit() == Identity(n)
+    assert MatPow(C, 1).doit() == C
+    assert MatPow(C, -1).doit() == C.I
+    for r in [2, S.Half, S.Pi, n]:
+        assert MatPow(C, r).doit() == MatPow(C, r)
+
+
+def test_doit_matrix():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    assert MatPow(X, 0).doit() == ImmutableMatrix(Identity(2))
+    assert MatPow(X, 1).doit() == X
+    assert MatPow(X, 2).doit() == X**2
+    assert MatPow(X, -1).doit() == X.inv()
+    assert MatPow(X, -2).doit() == (X.inv())**2
+    # less expensive than testing on a 2x2
+    assert MatPow(ImmutableMatrix([4]), S.Half).doit() == ImmutableMatrix([2])
+    X = ImmutableMatrix([[0, 2], [0, 4]]) # det() == 0
+    raises(ValueError, lambda: MatPow(X,-1).doit())
+    raises(ValueError, lambda: MatPow(X,-2).doit())
+
+
+def test_nonsquare():
+    A = MatrixSymbol('A', 2, 3)
+    B = ImmutableMatrix([[1, 2, 3], [4, 5, 6]])
+    for r in [-1, 0, 1, 2, S.Half, S.Pi, n]:
+        raises(NonSquareMatrixError, lambda: MatPow(A, r))
+        raises(NonSquareMatrixError, lambda: MatPow(B, r))
+
+
+def test_doit_equals_pow(): #17179
+    X = ImmutableMatrix ([[1,0],[0,1]])
+    assert MatPow(X, n).doit() == X**n == X
+
+
+def test_doit_nested_MatrixExpr():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    Y = ImmutableMatrix([[2, 3], [4, 5]])
+    assert MatPow(MatMul(X, Y), 2).doit() == (X*Y)**2
+    assert MatPow(MatAdd(X, Y), 2).doit() == (X + Y)**2
+
+
+def test_identity_power():
+    k = Identity(n)
+    assert MatPow(k, 4).doit() == k
+    assert MatPow(k, n).doit() == k
+    assert MatPow(k, -3).doit() == k
+    assert MatPow(k, 0).doit() == k
+    l = Identity(3)
+    assert MatPow(l, n).doit() == l
+    assert MatPow(l, -1).doit() == l
+    assert MatPow(l, 0).doit() == l
+
+
+def test_zero_power():
+    z1 = ZeroMatrix(n, n)
+    assert MatPow(z1, 3).doit() == z1
+    raises(ValueError, lambda:MatPow(z1, -1).doit())
+    assert MatPow(z1, 0).doit() == Identity(n)
+    assert MatPow(z1, n).doit() == z1
+    raises(ValueError, lambda:MatPow(z1, -2).doit())
+    z2 = ZeroMatrix(4, 4)
+    assert MatPow(z2, n).doit() == z2
+    raises(ValueError, lambda:MatPow(z2, -3).doit())
+    assert MatPow(z2, 2).doit() == z2
+    assert MatPow(z2, 0).doit() == Identity(4)
+    raises(ValueError, lambda:MatPow(z2, -1).doit())
+
+
+def test_OneMatrix_power():
+    o = OneMatrix(3, 3)
+    assert o ** 0 == Identity(3)
+    assert o ** 1 == o
+    assert o * o == o ** 2 == 3 * o
+    assert o * o * o == o ** 3 == 9 * o
+
+    o = OneMatrix(n, n)
+    assert o * o == o ** 2 == n * o
+    # powsimp necessary as n ** (n - 2) * n does not produce n ** (n - 1)
+    assert powsimp(o ** (n - 1) * o) == o ** n == n ** (n - 1) * o
+
+
+def test_transpose_power():
+    from sympy.matrices.expressions.transpose import Transpose as TP
+
+    assert (C*D).T**5 == ((C*D)**5).T == (D.T * C.T)**5
+    assert ((C*D).T**5).T == (C*D)**5
+
+    assert (C.T.I.T)**7 == C**-7
+    assert (C.T**l).T**k == C**(l*k)
+
+    assert ((E.T * A.T)**5).T == (A*E)**5
+    assert ((A*E).T**5).T**7 == (A*E)**35
+    assert TP(TP(C**2 * D**3)**5).doit() == (C**2 * D**3)**5
+
+    assert ((D*C)**-5).T**-5 == ((D*C)**25).T
+    assert (((D*C)**l).T**k).T == (D*C)**(l*k)
+
+
+def test_Inverse():
+    assert Inverse(MatPow(C, 0)).doit() == Identity(n)
+    assert Inverse(MatPow(C, 1)).doit() == Inverse(C)
+    assert Inverse(MatPow(C, 2)).doit() == MatPow(C, -2)
+    assert Inverse(MatPow(C, -1)).doit() == C
+
+    assert MatPow(Inverse(C), 0).doit() == Identity(n)
+    assert MatPow(Inverse(C), 1).doit() == Inverse(C)
+    assert MatPow(Inverse(C), 2).doit() == MatPow(C, -2)
+    assert MatPow(Inverse(C), -1).doit() == C
+
+
+def test_combine_powers():
+    assert (C ** 1) ** 1 == C
+    assert (C ** 2) ** 3 == MatPow(C, 6)
+    assert (C ** -2) ** -3 == MatPow(C, 6)
+    assert (C ** -1) ** -1 == C
+    assert (((C ** 2) ** 3) ** 4) ** 5 == MatPow(C, 120)
+    assert (C ** n) ** n == C ** (n ** 2)
+
+
+def test_unchanged():
+    assert unchanged(MatPow, C, 0)
+    assert unchanged(MatPow, C, 1)
+    assert unchanged(MatPow, Inverse(C), -1)
+    assert unchanged(Inverse, MatPow(C, -1), -1)
+    assert unchanged(MatPow, MatPow(C, -1), -1)
+    assert unchanged(MatPow, MatPow(C, 1), 1)
+
+
+def test_no_exponentiation():
+    # if this passes, Pow.as_numer_denom should recognize
+    # MatAdd as exponent
+    raises(NotImplementedError, lambda: 3**(-2*C))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_permutation.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_permutation.py
new file mode 100644
index 0000000000000000000000000000000000000000..41a924f6636afb2e5b6560987e38a0fa0c861f1e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_permutation.py
@@ -0,0 +1,166 @@
+from sympy.combinatorics import Permutation
+from sympy.core.expr import unchanged
+from sympy.matrices import Matrix
+from sympy.matrices.expressions import \
+    MatMul, BlockDiagMatrix, Determinant, Inverse
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.special import ZeroMatrix, OneMatrix, Identity
+from sympy.matrices.expressions.permutation import \
+    MatrixPermute, PermutationMatrix
+from sympy.testing.pytest import raises
+from sympy.core.symbol import Symbol
+
+
+def test_PermutationMatrix_basic():
+    p = Permutation([1, 0])
+    assert unchanged(PermutationMatrix, p)
+    raises(ValueError, lambda: PermutationMatrix((0, 1, 2)))
+    assert PermutationMatrix(p).as_explicit() == Matrix([[0, 1], [1, 0]])
+    assert isinstance(PermutationMatrix(p)*MatrixSymbol('A', 2, 2), MatMul)
+
+
+def test_PermutationMatrix_matmul():
+    p = Permutation([1, 2, 0])
+    P = PermutationMatrix(p)
+    M = Matrix([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
+    assert (P*M).as_explicit() == P.as_explicit()*M
+    assert (M*P).as_explicit() == M*P.as_explicit()
+
+    P1 = PermutationMatrix(Permutation([1, 2, 0]))
+    P2 = PermutationMatrix(Permutation([2, 1, 0]))
+    P3 = PermutationMatrix(Permutation([1, 0, 2]))
+    assert P1*P2 == P3
+
+
+def test_PermutationMatrix_matpow():
+    p1 = Permutation([1, 2, 0])
+    P1 = PermutationMatrix(p1)
+    p2 = Permutation([2, 0, 1])
+    P2 = PermutationMatrix(p2)
+    assert P1**2 == P2
+    assert P1**3 == Identity(3)
+
+
+def test_PermutationMatrix_identity():
+    p = Permutation([0, 1])
+    assert PermutationMatrix(p).is_Identity
+
+    p = Permutation([1, 0])
+    assert not PermutationMatrix(p).is_Identity
+
+
+def test_PermutationMatrix_determinant():
+    P = PermutationMatrix(Permutation([0, 1, 2]))
+    assert Determinant(P).doit() == 1
+    P = PermutationMatrix(Permutation([0, 2, 1]))
+    assert Determinant(P).doit() == -1
+    P = PermutationMatrix(Permutation([2, 0, 1]))
+    assert Determinant(P).doit() == 1
+
+
+def test_PermutationMatrix_inverse():
+    P = PermutationMatrix(Permutation(0, 1, 2))
+    assert Inverse(P).doit() == PermutationMatrix(Permutation(0, 2, 1))
+
+
+def test_PermutationMatrix_rewrite_BlockDiagMatrix():
+    P = PermutationMatrix(Permutation([0, 1, 2, 3, 4, 5]))
+    P0 = PermutationMatrix(Permutation([0]))
+    assert P.rewrite(BlockDiagMatrix) == \
+        BlockDiagMatrix(P0, P0, P0, P0, P0, P0)
+
+    P = PermutationMatrix(Permutation([0, 1, 3, 2, 4, 5]))
+    P10 = PermutationMatrix(Permutation(0, 1))
+    assert P.rewrite(BlockDiagMatrix) == \
+        BlockDiagMatrix(P0, P0, P10, P0, P0)
+
+    P = PermutationMatrix(Permutation([1, 0, 3, 2, 5, 4]))
+    assert P.rewrite(BlockDiagMatrix) == \
+        BlockDiagMatrix(P10, P10, P10)
+
+    P = PermutationMatrix(Permutation([0, 4, 3, 2, 1, 5]))
+    P3210 = PermutationMatrix(Permutation([3, 2, 1, 0]))
+    assert P.rewrite(BlockDiagMatrix) == \
+        BlockDiagMatrix(P0, P3210, P0)
+
+    P = PermutationMatrix(Permutation([0, 4, 2, 3, 1, 5]))
+    P3120 = PermutationMatrix(Permutation([3, 1, 2, 0]))
+    assert P.rewrite(BlockDiagMatrix) == \
+        BlockDiagMatrix(P0, P3120, P0)
+
+    P = PermutationMatrix(Permutation(0, 3)(1, 4)(2, 5))
+    assert P.rewrite(BlockDiagMatrix) == BlockDiagMatrix(P)
+
+
+def test_MartrixPermute_basic():
+    p = Permutation(0, 1)
+    P = PermutationMatrix(p)
+    A = MatrixSymbol('A', 2, 2)
+
+    raises(ValueError, lambda: MatrixPermute(Symbol('x'), p))
+    raises(ValueError, lambda: MatrixPermute(A, Symbol('x')))
+
+    assert MatrixPermute(A, P) == MatrixPermute(A, p)
+    raises(ValueError, lambda: MatrixPermute(A, p, 2))
+
+    pp = Permutation(0, 1, size=3)
+    assert MatrixPermute(A, pp) == MatrixPermute(A, p)
+    pp = Permutation(0, 1, 2)
+    raises(ValueError, lambda: MatrixPermute(A, pp))
+
+
+def test_MatrixPermute_shape():
+    p = Permutation(0, 1)
+    A = MatrixSymbol('A', 2, 3)
+    assert MatrixPermute(A, p).shape == (2, 3)
+
+
+def test_MatrixPermute_explicit():
+    p = Permutation(0, 1, 2)
+    A = MatrixSymbol('A', 3, 3)
+    AA = A.as_explicit()
+    assert MatrixPermute(A, p, 0).as_explicit() == \
+        AA.permute(p, orientation='rows')
+    assert MatrixPermute(A, p, 1).as_explicit() == \
+        AA.permute(p, orientation='cols')
+
+
+def test_MatrixPermute_rewrite_MatMul():
+    p = Permutation(0, 1, 2)
+    A = MatrixSymbol('A', 3, 3)
+
+    assert MatrixPermute(A, p, 0).rewrite(MatMul).as_explicit() == \
+        MatrixPermute(A, p, 0).as_explicit()
+    assert MatrixPermute(A, p, 1).rewrite(MatMul).as_explicit() == \
+        MatrixPermute(A, p, 1).as_explicit()
+
+
+def test_MatrixPermute_doit():
+    p = Permutation(0, 1, 2)
+    A = MatrixSymbol('A', 3, 3)
+    assert MatrixPermute(A, p).doit() == MatrixPermute(A, p)
+
+    p = Permutation(0, size=3)
+    A = MatrixSymbol('A', 3, 3)
+    assert MatrixPermute(A, p).doit().as_explicit() == \
+        MatrixPermute(A, p).as_explicit()
+
+    p = Permutation(0, 1, 2)
+    A = Identity(3)
+    assert MatrixPermute(A, p, 0).doit().as_explicit() == \
+        MatrixPermute(A, p, 0).as_explicit()
+    assert MatrixPermute(A, p, 1).doit().as_explicit() == \
+        MatrixPermute(A, p, 1).as_explicit()
+
+    A = ZeroMatrix(3, 3)
+    assert MatrixPermute(A, p).doit() == A
+    A = OneMatrix(3, 3)
+    assert MatrixPermute(A, p).doit() == A
+
+    A = MatrixSymbol('A', 4, 4)
+    p1 = Permutation(0, 1, 2, 3)
+    p2 = Permutation(0, 2, 3, 1)
+    expr = MatrixPermute(MatrixPermute(A, p1, 0), p2, 0)
+    assert expr.as_explicit() == expr.doit().as_explicit()
+    expr = MatrixPermute(MatrixPermute(A, p1, 1), p2, 1)
+    assert expr.as_explicit() == expr.doit().as_explicit()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_sets.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_sets.py
new file mode 100644
index 0000000000000000000000000000000000000000..e811c7968c5a22d65f1c99e995aaa7e5e59d15c4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_sets.py
@@ -0,0 +1,42 @@
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.matrices import Matrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.sets import MatrixSet
+from sympy.matrices.expressions.special import ZeroMatrix
+from sympy.testing.pytest import raises
+from sympy.sets.sets import SetKind
+from sympy.matrices.kind import MatrixKind
+from sympy.core.kind import NumberKind
+
+
+def test_MatrixSet():
+    n, m = symbols('n m', integer=True)
+    A = MatrixSymbol('A', n, m)
+    C = MatrixSymbol('C', n, n)
+
+    M = MatrixSet(2, 2, set=S.Reals)
+    assert M.shape == (2, 2)
+    assert M.set == S.Reals
+    X = Matrix([[1, 2], [3, 4]])
+    assert X in M
+    X = ZeroMatrix(2, 2)
+    assert X in M
+    raises(TypeError, lambda: A in M)
+    raises(TypeError, lambda: 1 in M)
+    M = MatrixSet(n, m, set=S.Reals)
+    assert A in M
+    raises(TypeError, lambda: C in M)
+    raises(TypeError, lambda: X in M)
+    M = MatrixSet(2, 2, set={1, 2, 3})
+    X = Matrix([[1, 2], [3, 4]])
+    Y = Matrix([[1, 2]])
+    assert (X in M) == S.false
+    assert (Y in M) == S.false
+    raises(ValueError, lambda: MatrixSet(2, -2, S.Reals))
+    raises(ValueError, lambda: MatrixSet(2.4, -1, S.Reals))
+    raises(TypeError, lambda: MatrixSet(2, 2, (1, 2, 3)))
+
+
+def test_SetKind_MatrixSet():
+    assert MatrixSet(2, 2, set=S.Reals).kind is SetKind(MatrixKind(NumberKind))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_slice.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_slice.py
new file mode 100644
index 0000000000000000000000000000000000000000..36490719e26908b9e913ed99b7673d602647c492
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_slice.py
@@ -0,0 +1,65 @@
+from sympy.matrices.expressions.slice import MatrixSlice
+from sympy.matrices.expressions import MatrixSymbol
+from sympy.abc import a, b, c, d, k, l, m, n
+from sympy.testing.pytest import raises, XFAIL
+from sympy.functions.elementary.integers import floor
+from sympy.assumptions import assuming, Q
+
+
+X = MatrixSymbol('X', n, m)
+Y = MatrixSymbol('Y', m, k)
+
+def test_shape():
+    B = MatrixSlice(X, (a, b), (c, d))
+    assert B.shape == (b - a, d - c)
+
+def test_entry():
+    B = MatrixSlice(X, (a, b), (c, d))
+    assert B[0,0] == X[a, c]
+    assert B[k,l] == X[a+k, c+l]
+    raises(IndexError, lambda : MatrixSlice(X, 1, (2, 5))[1, 0])
+
+    assert X[1::2, :][1, 3] == X[1+2, 3]
+    assert X[:, 1::2][3, 1] == X[3, 1+2]
+
+def test_on_diag():
+    assert not MatrixSlice(X, (a, b), (c, d)).on_diag
+    assert MatrixSlice(X, (a, b), (a, b)).on_diag
+
+def test_inputs():
+    assert MatrixSlice(X, 1, (2, 5)) == MatrixSlice(X, (1, 2), (2, 5))
+    assert MatrixSlice(X, 1, (2, 5)).shape == (1, 3)
+
+def test_slicing():
+    assert X[1:5, 2:4] == MatrixSlice(X, (1, 5), (2, 4))
+    assert X[1, 2:4] == MatrixSlice(X, 1, (2, 4))
+    assert X[1:5, :].shape == (4, X.shape[1])
+    assert X[:, 1:5].shape == (X.shape[0], 4)
+
+    assert X[::2, ::2].shape == (floor(n/2), floor(m/2))
+    assert X[2, :] == MatrixSlice(X, 2, (0, m))
+    assert X[k, :] == MatrixSlice(X, k, (0, m))
+
+def test_exceptions():
+    X = MatrixSymbol('x', 10, 20)
+    raises(IndexError, lambda: X[0:12, 2])
+    raises(IndexError, lambda: X[0:9, 22])
+    raises(IndexError, lambda: X[-1:5, 2])
+
+@XFAIL
+def test_symmetry():
+    X = MatrixSymbol('x', 10, 10)
+    Y = X[:5, 5:]
+    with assuming(Q.symmetric(X)):
+        assert Y.T == X[5:, :5]
+
+def test_slice_of_slice():
+    X = MatrixSymbol('x', 10, 10)
+    assert X[2, :][:, 3][0, 0] == X[2, 3]
+    assert X[:5, :5][:4, :4] == X[:4, :4]
+    assert X[1:5, 2:6][1:3, 2] == X[2:4, 4]
+    assert X[1:9:2, 2:6][1:3, 2] == X[3:7:2, 4]
+
+def test_negative_index():
+    X = MatrixSymbol('x', 10, 10)
+    assert X[-1, :] == X[9, :]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_special.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_special.py
new file mode 100644
index 0000000000000000000000000000000000000000..beeaf1d76a63673b6622709cda598dfcb295bba4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_special.py
@@ -0,0 +1,228 @@
+from sympy.core.add import Add
+from sympy.core.expr import unchanged
+from sympy.core.mul import Mul
+from sympy.core.symbol import symbols
+from sympy.core.relational import Eq
+from sympy.concrete.summations import Sum
+from sympy.functions.elementary.complexes import im, re
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.matrices.immutable import ImmutableDenseMatrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.matadd import MatAdd
+from sympy.matrices.expressions.special import (
+    ZeroMatrix, GenericZeroMatrix, Identity, GenericIdentity, OneMatrix)
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.testing.pytest import raises
+
+
+def test_zero_matrix_creation():
+    assert unchanged(ZeroMatrix, 2, 2)
+    assert unchanged(ZeroMatrix, 0, 0)
+    raises(ValueError, lambda: ZeroMatrix(-1, 2))
+    raises(ValueError, lambda: ZeroMatrix(2.0, 2))
+    raises(ValueError, lambda: ZeroMatrix(2j, 2))
+    raises(ValueError, lambda: ZeroMatrix(2, -1))
+    raises(ValueError, lambda: ZeroMatrix(2, 2.0))
+    raises(ValueError, lambda: ZeroMatrix(2, 2j))
+
+    n = symbols('n')
+    assert unchanged(ZeroMatrix, n, n)
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: ZeroMatrix(n, n))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: ZeroMatrix(n, n))
+
+
+def test_generic_zero_matrix():
+    z = GenericZeroMatrix()
+    n = symbols('n', integer=True)
+    A = MatrixSymbol("A", n, n)
+
+    assert z == z
+    assert z != A
+    assert A != z
+
+    assert z.is_ZeroMatrix
+
+    raises(TypeError, lambda: z.shape)
+    raises(TypeError, lambda: z.rows)
+    raises(TypeError, lambda: z.cols)
+
+    assert MatAdd() == z
+    assert MatAdd(z, A) == MatAdd(A)
+    # Make sure it is hashable
+    hash(z)
+
+
+def test_identity_matrix_creation():
+    assert Identity(2)
+    assert Identity(0)
+    raises(ValueError, lambda: Identity(-1))
+    raises(ValueError, lambda: Identity(2.0))
+    raises(ValueError, lambda: Identity(2j))
+
+    n = symbols('n')
+    assert Identity(n)
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: Identity(n))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: Identity(n))
+
+
+def test_generic_identity():
+    I = GenericIdentity()
+    n = symbols('n', integer=True)
+    A = MatrixSymbol("A", n, n)
+
+    assert I == I
+    assert I != A
+    assert A != I
+
+    assert I.is_Identity
+    assert I**-1 == I
+
+    raises(TypeError, lambda: I.shape)
+    raises(TypeError, lambda: I.rows)
+    raises(TypeError, lambda: I.cols)
+
+    assert MatMul() == I
+    assert MatMul(I, A) == MatMul(A)
+    # Make sure it is hashable
+    hash(I)
+
+
+def test_one_matrix_creation():
+    assert OneMatrix(2, 2)
+    assert OneMatrix(0, 0)
+    assert Eq(OneMatrix(1, 1), Identity(1))
+    raises(ValueError, lambda: OneMatrix(-1, 2))
+    raises(ValueError, lambda: OneMatrix(2.0, 2))
+    raises(ValueError, lambda: OneMatrix(2j, 2))
+    raises(ValueError, lambda: OneMatrix(2, -1))
+    raises(ValueError, lambda: OneMatrix(2, 2.0))
+    raises(ValueError, lambda: OneMatrix(2, 2j))
+
+    n = symbols('n')
+    assert OneMatrix(n, n)
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: OneMatrix(n, n))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: OneMatrix(n, n))
+
+
+def test_ZeroMatrix():
+    n, m = symbols('n m', integer=True)
+    A = MatrixSymbol('A', n, m)
+    Z = ZeroMatrix(n, m)
+
+    assert A + Z == A
+    assert A*Z.T == ZeroMatrix(n, n)
+    assert Z*A.T == ZeroMatrix(n, n)
+    assert A - A == ZeroMatrix(*A.shape)
+
+    assert Z
+
+    assert Z.transpose() == ZeroMatrix(m, n)
+    assert Z.conjugate() == Z
+    assert Z.adjoint() == ZeroMatrix(m, n)
+    assert re(Z) == Z
+    assert im(Z) == Z
+
+    assert ZeroMatrix(n, n)**0 == Identity(n)
+    assert ZeroMatrix(3, 3).as_explicit() == ImmutableDenseMatrix.zeros(3, 3)
+
+
+def test_ZeroMatrix_doit():
+    n = symbols('n', integer=True)
+    Znn = ZeroMatrix(Add(n, n, evaluate=False), n)
+    assert isinstance(Znn.rows, Add)
+    assert Znn.doit() == ZeroMatrix(2*n, n)
+    assert isinstance(Znn.doit().rows, Mul)
+
+
+def test_OneMatrix():
+    n, m = symbols('n m', integer=True)
+    A = MatrixSymbol('A', n, m)
+    U = OneMatrix(n, m)
+
+    assert U.shape == (n, m)
+    assert isinstance(A + U, Add)
+    assert U.transpose() == OneMatrix(m, n)
+    assert U.conjugate() == U
+    assert U.adjoint() == OneMatrix(m, n)
+    assert re(U) == U
+    assert im(U) == ZeroMatrix(n, m)
+
+    assert OneMatrix(n, n) ** 0 == Identity(n)
+
+    U = OneMatrix(n, n)
+    assert U[1, 2] == 1
+
+    U = OneMatrix(2, 3)
+    assert U.as_explicit() == ImmutableDenseMatrix.ones(2, 3)
+
+
+def test_OneMatrix_doit():
+    n = symbols('n', integer=True)
+    Unn = OneMatrix(Add(n, n, evaluate=False), n)
+    assert isinstance(Unn.rows, Add)
+    assert Unn.doit() == OneMatrix(2 * n, n)
+    assert isinstance(Unn.doit().rows, Mul)
+
+
+def test_OneMatrix_mul():
+    n, m, k = symbols('n m k', integer=True)
+    w = MatrixSymbol('w', n, 1)
+    assert OneMatrix(n, m) * OneMatrix(m, k) == OneMatrix(n, k) * m
+    assert w * OneMatrix(1, 1) == w
+    assert OneMatrix(1, 1) * w.T == w.T
+
+
+def test_Identity():
+    n, m = symbols('n m', integer=True)
+    A = MatrixSymbol('A', n, m)
+    i, j = symbols('i j')
+
+    In = Identity(n)
+    Im = Identity(m)
+
+    assert A*Im == A
+    assert In*A == A
+
+    assert In.transpose() == In
+    assert In.inverse() == In
+    assert In.conjugate() == In
+    assert In.adjoint() == In
+    assert re(In) == In
+    assert im(In) == ZeroMatrix(n, n)
+
+    assert In[i, j] != 0
+    assert Sum(In[i, j], (i, 0, n-1), (j, 0, n-1)).subs(n,3).doit() == 3
+    assert Sum(Sum(In[i, j], (i, 0, n-1)), (j, 0, n-1)).subs(n,3).doit() == 3
+
+    # If range exceeds the limit `(0, n-1)`, do not remove `Piecewise`:
+    expr = Sum(In[i, j], (i, 0, n-1))
+    assert expr.doit() == 1
+    expr = Sum(In[i, j], (i, 0, n-2))
+    assert expr.doit().dummy_eq(
+        Piecewise(
+            (1, (j >= 0) & (j <= n-2)),
+            (0, True)
+        )
+    )
+    expr = Sum(In[i, j], (i, 1, n-1))
+    assert expr.doit().dummy_eq(
+        Piecewise(
+            (1, (j >= 1) & (j <= n-1)),
+            (0, True)
+        )
+    )
+    assert Identity(3).as_explicit() == ImmutableDenseMatrix.eye(3)
+
+
+def test_Identity_doit():
+    n = symbols('n', integer=True)
+    Inn = Identity(Add(n, n, evaluate=False))
+    assert isinstance(Inn.rows, Add)
+    assert Inn.doit() == Identity(2*n)
+    assert isinstance(Inn.doit().rows, Mul)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_trace.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_trace.py
new file mode 100644
index 0000000000000000000000000000000000000000..3bd66bec2377dae634ff486f42cc474eda7b23b1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_trace.py
@@ -0,0 +1,116 @@
+from sympy.core import Lambda, S, symbols
+from sympy.concrete import Sum
+from sympy.functions import adjoint, conjugate, transpose
+from sympy.matrices import eye, Matrix, ShapeError, ImmutableMatrix
+from sympy.matrices.expressions import (
+    Adjoint, Identity, FunctionMatrix, MatrixExpr, MatrixSymbol, Trace,
+    ZeroMatrix, trace, MatPow, MatAdd, MatMul
+)
+from sympy.matrices.expressions.special import OneMatrix
+from sympy.testing.pytest import raises
+from sympy.abc import i
+
+
+n = symbols('n', integer=True)
+A = MatrixSymbol('A', n, n)
+B = MatrixSymbol('B', n, n)
+C = MatrixSymbol('C', 3, 4)
+
+
+def test_Trace():
+    assert isinstance(Trace(A), Trace)
+    assert not isinstance(Trace(A), MatrixExpr)
+    raises(ShapeError, lambda: Trace(C))
+    assert trace(eye(3)) == 3
+    assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15
+
+    assert adjoint(Trace(A)) == trace(Adjoint(A))
+    assert conjugate(Trace(A)) == trace(Adjoint(A))
+    assert transpose(Trace(A)) == Trace(A)
+
+    _ = A / Trace(A)  # Make sure this is possible
+
+    # Some easy simplifications
+    assert trace(Identity(5)) == 5
+    assert trace(ZeroMatrix(5, 5)) == 0
+    assert trace(OneMatrix(1, 1)) == 1
+    assert trace(OneMatrix(2, 2)) == 2
+    assert trace(OneMatrix(n, n)) == n
+    assert trace(2*A*B) == 2*Trace(A*B)
+    assert trace(A.T) == trace(A)
+
+    i, j = symbols('i j')
+    F = FunctionMatrix(3, 3, Lambda((i, j), i + j))
+    assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2)
+
+    raises(TypeError, lambda: Trace(S.One))
+
+    assert Trace(A).arg is A
+
+    assert str(trace(A)) == str(Trace(A).doit())
+
+    assert Trace(A).is_commutative is True
+
+def test_Trace_A_plus_B():
+    assert trace(A + B) == Trace(A) + Trace(B)
+    assert Trace(A + B).arg == MatAdd(A, B)
+    assert Trace(A + B).doit() == Trace(A) + Trace(B)
+
+
+def test_Trace_MatAdd_doit():
+    # See issue #9028
+    X = ImmutableMatrix([[1, 2, 3]]*3)
+    Y = MatrixSymbol('Y', 3, 3)
+    q = MatAdd(X, 2*X, Y, -3*Y)
+    assert Trace(q).arg == q
+    assert Trace(q).doit() == 18 - 2*Trace(Y)
+
+
+def test_Trace_MatPow_doit():
+    X = Matrix([[1, 2], [3, 4]])
+    assert Trace(X).doit() == 5
+    q = MatPow(X, 2)
+    assert Trace(q).arg == q
+    assert Trace(q).doit() == 29
+
+
+def test_Trace_MutableMatrix_plus():
+    # See issue #9043
+    X = Matrix([[1, 2], [3, 4]])
+    assert Trace(X) + Trace(X) == 2*Trace(X)
+
+
+def test_Trace_doit_deep_False():
+    X = Matrix([[1, 2], [3, 4]])
+    q = MatPow(X, 2)
+    assert Trace(q).doit(deep=False).arg == q
+    q = MatAdd(X, 2*X)
+    assert Trace(q).doit(deep=False).arg == q
+    q = MatMul(X, 2*X)
+    assert Trace(q).doit(deep=False).arg == q
+
+
+def test_trace_constant_factor():
+    # Issue 9052: gave 2*Trace(MatMul(A)) instead of 2*Trace(A)
+    assert trace(2*A) == 2*Trace(A)
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    assert trace(MatMul(2, X)) == 10
+
+
+def test_trace_rewrite():
+    assert trace(A).rewrite(Sum) == Sum(A[i, i], (i, 0, n - 1))
+    assert trace(eye(3)).rewrite(Sum) == 3
+
+
+def test_trace_normalize():
+    assert Trace(B*A) != Trace(A*B)
+    assert Trace(B*A)._normalize() == Trace(A*B)
+    assert Trace(B*A.T)._normalize() == Trace(A*B.T)
+
+
+def test_trace_as_explicit():
+    raises(ValueError, lambda: Trace(A).as_explicit())
+
+    X = MatrixSymbol("X", 3, 3)
+    assert Trace(X).as_explicit() == X[0, 0] + X[1, 1] + X[2, 2]
+    assert Trace(eye(3)).as_explicit() == 3
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_transpose.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_transpose.py
new file mode 100644
index 0000000000000000000000000000000000000000..a1a6113873426d99bacf85484d3b66781f300af7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/tests/test_transpose.py
@@ -0,0 +1,69 @@
+from sympy.functions import adjoint, conjugate, transpose
+from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose
+from sympy.matrices import eye, Matrix
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+
+n, m, l, k, p = symbols('n m l k p', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+
+
+def test_transpose():
+    Sq = MatrixSymbol('Sq', n, n)
+
+    assert transpose(A) == Transpose(A)
+    assert Transpose(A).shape == (m, n)
+    assert Transpose(A*B).shape == (l, n)
+    assert transpose(Transpose(A)) == A
+    assert isinstance(Transpose(Transpose(A)), Transpose)
+
+    assert adjoint(Transpose(A)) == Adjoint(Transpose(A))
+    assert conjugate(Transpose(A)) == Adjoint(A)
+
+    assert Transpose(eye(3)).doit() == eye(3)
+
+    assert Transpose(S(5)).doit() == S(5)
+
+    assert Transpose(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
+
+    assert transpose(trace(Sq)) == trace(Sq)
+    assert trace(Transpose(Sq)) == trace(Sq)
+
+    assert Transpose(Sq)[0, 1] == Sq[1, 0]
+
+    assert Transpose(A*B).doit() == Transpose(B) * Transpose(A)
+
+
+def test_transpose_MatAdd_MatMul():
+    # Issue 16807
+    from sympy.functions.elementary.trigonometric import cos
+
+    x = symbols('x')
+    M = MatrixSymbol('M', 3, 3)
+    N = MatrixSymbol('N', 3, 3)
+
+    assert (N + (cos(x) * M)).T == cos(x)*M.T + N.T
+
+
+def test_refine():
+    assert refine(C.T, Q.symmetric(C)) == C
+
+
+def test_transpose1x1():
+    m = MatrixSymbol('m', 1, 1)
+    assert m == refine(m.T)
+    assert m == refine(m.T.T)
+
+def test_issue_9817():
+    from sympy.matrices.expressions import Identity
+    v = MatrixSymbol('v', 3, 1)
+    A = MatrixSymbol('A', 3, 3)
+    x = Matrix([i + 1 for i in range(3)])
+    X = Identity(3)
+    quadratic = v.T * A * v
+    subbed = quadratic.xreplace({v:x, A:X})
+    assert subbed.as_explicit() == Matrix([[14]])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/trace.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/trace.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5f9f94ea7486dc21b47c2e2e783a93280b180e0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/trace.py
@@ -0,0 +1,167 @@
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr, ExprBuilder
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import uniquely_named_symbol
+from sympy.core.sympify import sympify
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.matrices.exceptions import NonSquareMatrixError
+
+
+class Trace(Expr):
+    """Matrix Trace
+
+    Represents the trace of a matrix expression.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Trace, eye
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> Trace(A)
+    Trace(A)
+    >>> Trace(eye(3))
+    Trace(Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]]))
+    >>> Trace(eye(3)).simplify()
+    3
+    """
+    is_Trace = True
+    is_commutative = True
+
+    def __new__(cls, mat):
+        mat = sympify(mat)
+
+        if not mat.is_Matrix:
+            raise TypeError("input to Trace, %s, is not a matrix" % str(mat))
+
+        if mat.is_square is False:
+            raise NonSquareMatrixError("Trace of a non-square matrix")
+
+        return Basic.__new__(cls, mat)
+
+    def _eval_transpose(self):
+        return self
+
+    def _eval_derivative(self, v):
+        from sympy.concrete.summations import Sum
+        from .matexpr import MatrixElement
+        if isinstance(v, MatrixElement):
+            return self.rewrite(Sum).diff(v)
+        expr = self.doit()
+        if isinstance(expr, Trace):
+            # Avoid looping infinitely:
+            raise NotImplementedError
+        return expr._eval_derivative(v)
+
+    def _eval_derivative_matrix_lines(self, x):
+        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct, ArrayContraction
+        r = self.args[0]._eval_derivative_matrix_lines(x)
+        for lr in r:
+            if lr.higher == 1:
+                lr.higher = ExprBuilder(
+                    ArrayContraction,
+                    [
+                        ExprBuilder(
+                            ArrayTensorProduct,
+                            [
+                                lr._lines[0],
+                                lr._lines[1],
+                            ]
+                        ),
+                        (1, 3),
+                    ],
+                    validator=ArrayContraction._validate
+                )
+            else:
+                # This is not a matrix line:
+                lr.higher = ExprBuilder(
+                    ArrayContraction,
+                    [
+                        ExprBuilder(
+                            ArrayTensorProduct,
+                            [
+                                lr._lines[0],
+                                lr._lines[1],
+                                lr.higher,
+                            ]
+                        ),
+                        (1, 3), (0, 2)
+                    ]
+                )
+            lr._lines = [S.One, S.One]
+            lr._first_pointer_parent = lr._lines
+            lr._second_pointer_parent = lr._lines
+            lr._first_pointer_index = 0
+            lr._second_pointer_index = 1
+        return r
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    def doit(self, **hints):
+        if hints.get('deep', True):
+            arg = self.arg.doit(**hints)
+            result = arg._eval_trace()
+            if result is not None:
+                return result
+            else:
+                return Trace(arg)
+        else:
+            # _eval_trace would go too deep here
+            if isinstance(self.arg, MatrixBase):
+                return trace(self.arg)
+            else:
+                return Trace(self.arg)
+
+    def as_explicit(self):
+        return Trace(self.arg.as_explicit()).doit()
+
+    def _normalize(self):
+        # Normalization of trace of matrix products. Use transposition and
+        # cyclic properties of traces to make sure the arguments of the matrix
+        # product are sorted and the first argument is not a transposition.
+        from sympy.matrices.expressions.matmul import MatMul
+        from sympy.matrices.expressions.transpose import Transpose
+        trace_arg = self.arg
+        if isinstance(trace_arg, MatMul):
+
+            def get_arg_key(x):
+                a = trace_arg.args[x]
+                if isinstance(a, Transpose):
+                    a = a.arg
+                return default_sort_key(a)
+
+            indmin = min(range(len(trace_arg.args)), key=get_arg_key)
+            if isinstance(trace_arg.args[indmin], Transpose):
+                trace_arg = Transpose(trace_arg).doit()
+                indmin = min(range(len(trace_arg.args)), key=lambda x: default_sort_key(trace_arg.args[x]))
+            trace_arg = MatMul.fromiter(trace_arg.args[indmin:] + trace_arg.args[:indmin])
+            return Trace(trace_arg)
+        return self
+
+    def _eval_rewrite_as_Sum(self, expr, **kwargs):
+        from sympy.concrete.summations import Sum
+        i = uniquely_named_symbol('i', [expr])
+        s = Sum(self.arg[i, i], (i, 0, self.arg.rows - 1))
+        return s.doit()
+
+
+def trace(expr):
+    """Trace of a Matrix.  Sum of the diagonal elements.
+
+    Examples
+    ========
+
+    >>> from sympy import trace, Symbol, MatrixSymbol, eye
+    >>> n = Symbol('n')
+    >>> X = MatrixSymbol('X', n, n)  # A square matrix
+    >>> trace(2*X)
+    2*Trace(X)
+    >>> trace(eye(3))
+    3
+    """
+    return Trace(expr).doit()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/transpose.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/transpose.py
new file mode 100644
index 0000000000000000000000000000000000000000..b11f7fc21490aab219420610ca529d81d6995d40
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/expressions/transpose.py
@@ -0,0 +1,103 @@
+from sympy.core.basic import Basic
+from sympy.matrices.expressions.matexpr import MatrixExpr
+
+
+class Transpose(MatrixExpr):
+    """
+    The transpose of a matrix expression.
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the transpose, use the ``transpose()``
+    function, or the ``.T`` attribute of matrices.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Transpose, transpose
+    >>> A = MatrixSymbol('A', 3, 5)
+    >>> B = MatrixSymbol('B', 5, 3)
+    >>> Transpose(A)
+    A.T
+    >>> A.T == transpose(A) == Transpose(A)
+    True
+    >>> Transpose(A*B)
+    (A*B).T
+    >>> transpose(A*B)
+    B.T*A.T
+
+    """
+    is_Transpose = True
+
+    def doit(self, **hints):
+        arg = self.arg
+        if hints.get('deep', True) and isinstance(arg, Basic):
+            arg = arg.doit(**hints)
+        _eval_transpose = getattr(arg, '_eval_transpose', None)
+        if _eval_transpose is not None:
+            result = _eval_transpose()
+            return result if result is not None else Transpose(arg)
+        else:
+            return Transpose(arg)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    @property
+    def shape(self):
+        return self.arg.shape[::-1]
+
+    def _entry(self, i, j, expand=False, **kwargs):
+        return self.arg._entry(j, i, expand=expand, **kwargs)
+
+    def _eval_adjoint(self):
+        return self.arg.conjugate()
+
+    def _eval_conjugate(self):
+        return self.arg.adjoint()
+
+    def _eval_transpose(self):
+        return self.arg
+
+    def _eval_trace(self):
+        from .trace import Trace
+        return Trace(self.arg)  # Trace(X.T) => Trace(X)
+
+    def _eval_determinant(self):
+        from sympy.matrices.expressions.determinant import det
+        return det(self.arg)
+
+    def _eval_derivative(self, x):
+        # x is a scalar:
+        return self.arg._eval_derivative(x)
+
+    def _eval_derivative_matrix_lines(self, x):
+        lines = self.args[0]._eval_derivative_matrix_lines(x)
+        return [i.transpose() for i in lines]
+
+
+def transpose(expr):
+    """Matrix transpose"""
+    return Transpose(expr).doit(deep=False)
+
+
+from sympy.assumptions.ask import ask, Q
+from sympy.assumptions.refine import handlers_dict
+
+
+def refine_Transpose(expr, assumptions):
+    """
+    >>> from sympy import MatrixSymbol, Q, assuming, refine
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> X.T
+    X.T
+    >>> with assuming(Q.symmetric(X)):
+    ...     print(refine(X.T))
+    X
+    """
+    if ask(Q.symmetric(expr), assumptions):
+        return expr.arg
+
+    return expr
+
+handlers_dict['Transpose'] = refine_Transpose
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/graph.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/graph.py
new file mode 100644
index 0000000000000000000000000000000000000000..4c6356db884cfcd3c759ada07ac559f43dbcbbcb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/graph.py
@@ -0,0 +1,279 @@
+from sympy.utilities.iterables import \
+    flatten, connected_components, strongly_connected_components
+from .exceptions import NonSquareMatrixError
+
+
+def _connected_components(M):
+    """Returns the list of connected vertices of the graph when
+    a square matrix is viewed as a weighted graph.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([
+    ...     [66, 0, 0, 68, 0, 0, 0, 0, 67],
+    ...     [0, 55, 0, 0, 0, 0, 54, 53, 0],
+    ...     [0, 0, 0, 0, 1, 2, 0, 0, 0],
+    ...     [86, 0, 0, 88, 0, 0, 0, 0, 87],
+    ...     [0, 0, 10, 0, 11, 12, 0, 0, 0],
+    ...     [0, 0, 20, 0, 21, 22, 0, 0, 0],
+    ...     [0, 45, 0, 0, 0, 0, 44, 43, 0],
+    ...     [0, 35, 0, 0, 0, 0, 34, 33, 0],
+    ...     [76, 0, 0, 78, 0, 0, 0, 0, 77]])
+    >>> A.connected_components()
+    [[0, 3, 8], [1, 6, 7], [2, 4, 5]]
+
+    Notes
+    =====
+
+    Even if any symbolic elements of the matrix can be indeterminate
+    to be zero mathematically, this only takes the account of the
+    structural aspect of the matrix, so they will considered to be
+    nonzero.
+    """
+    if not M.is_square:
+        raise NonSquareMatrixError
+
+    V = range(M.rows)
+    E = sorted(M.todok().keys())
+    return connected_components((V, E))
+
+
+def _strongly_connected_components(M):
+    """Returns the list of strongly connected vertices of the graph when
+    a square matrix is viewed as a weighted graph.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([
+    ...     [44, 0, 0, 0, 43, 0, 45, 0, 0],
+    ...     [0, 66, 62, 61, 0, 68, 0, 60, 67],
+    ...     [0, 0, 22, 21, 0, 0, 0, 20, 0],
+    ...     [0, 0, 12, 11, 0, 0, 0, 10, 0],
+    ...     [34, 0, 0, 0, 33, 0, 35, 0, 0],
+    ...     [0, 86, 82, 81, 0, 88, 0, 80, 87],
+    ...     [54, 0, 0, 0, 53, 0, 55, 0, 0],
+    ...     [0, 0, 2, 1, 0, 0, 0, 0, 0],
+    ...     [0, 76, 72, 71, 0, 78, 0, 70, 77]])
+    >>> A.strongly_connected_components()
+    [[0, 4, 6], [2, 3, 7], [1, 5, 8]]
+    """
+    if not M.is_square:
+        raise NonSquareMatrixError
+
+    # RepMatrix uses the more efficient DomainMatrix.scc() method
+    rep = getattr(M, '_rep', None)
+    if rep is not None:
+        return rep.scc()
+
+    V = range(M.rows)
+    E = sorted(M.todok().keys())
+    return strongly_connected_components((V, E))
+
+
+def _connected_components_decomposition(M):
+    """Decomposes a square matrix into block diagonal form only
+    using the permutations.
+
+    Explanation
+    ===========
+
+    The decomposition is in a form of $A = P^{-1} B P$ where $P$ is a
+    permutation matrix and $B$ is a block diagonal matrix.
+
+    Returns
+    =======
+
+    P, B : PermutationMatrix, BlockDiagMatrix
+        *P* is a permutation matrix for the similarity transform
+        as in the explanation. And *B* is the block diagonal matrix of
+        the result of the permutation.
+
+        If you would like to get the diagonal blocks from the
+        BlockDiagMatrix, see
+        :meth:`~sympy.matrices.expressions.blockmatrix.BlockDiagMatrix.get_diag_blocks`.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, pprint
+    >>> A = Matrix([
+    ...     [66, 0, 0, 68, 0, 0, 0, 0, 67],
+    ...     [0, 55, 0, 0, 0, 0, 54, 53, 0],
+    ...     [0, 0, 0, 0, 1, 2, 0, 0, 0],
+    ...     [86, 0, 0, 88, 0, 0, 0, 0, 87],
+    ...     [0, 0, 10, 0, 11, 12, 0, 0, 0],
+    ...     [0, 0, 20, 0, 21, 22, 0, 0, 0],
+    ...     [0, 45, 0, 0, 0, 0, 44, 43, 0],
+    ...     [0, 35, 0, 0, 0, 0, 34, 33, 0],
+    ...     [76, 0, 0, 78, 0, 0, 0, 0, 77]])
+
+    >>> P, B = A.connected_components_decomposition()
+    >>> pprint(P)
+    PermutationMatrix((1 3)(2 8 5 7 4 6))
+    >>> pprint(B)
+    [[66  68  67]                            ]
+    [[          ]                            ]
+    [[86  88  87]       0             0      ]
+    [[          ]                            ]
+    [[76  78  77]                            ]
+    [                                        ]
+    [              [55  54  53]              ]
+    [              [          ]              ]
+    [     0        [45  44  43]       0      ]
+    [              [          ]              ]
+    [              [35  34  33]              ]
+    [                                        ]
+    [                            [0   1   2 ]]
+    [                            [          ]]
+    [     0             0        [10  11  12]]
+    [                            [          ]]
+    [                            [20  21  22]]
+
+    >>> P = P.as_explicit()
+    >>> B = B.as_explicit()
+    >>> P.T*B*P == A
+    True
+
+    Notes
+    =====
+
+    This problem corresponds to the finding of the connected components
+    of a graph, when a matrix is viewed as a weighted graph.
+    """
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.matrices.expressions.blockmatrix import BlockDiagMatrix
+    from sympy.matrices.expressions.permutation import PermutationMatrix
+
+    iblocks = M.connected_components()
+
+    p = Permutation(flatten(iblocks))
+    P = PermutationMatrix(p)
+
+    blocks = []
+    for b in iblocks:
+        blocks.append(M[b, b])
+    B = BlockDiagMatrix(*blocks)
+    return P, B
+
+
+def _strongly_connected_components_decomposition(M, lower=True):
+    """Decomposes a square matrix into block triangular form only
+    using the permutations.
+
+    Explanation
+    ===========
+
+    The decomposition is in a form of $A = P^{-1} B P$ where $P$ is a
+    permutation matrix and $B$ is a block diagonal matrix.
+
+    Parameters
+    ==========
+
+    lower : bool
+        Makes $B$ lower block triangular when ``True``.
+        Otherwise, makes $B$ upper block triangular.
+
+    Returns
+    =======
+
+    P, B : PermutationMatrix, BlockMatrix
+        *P* is a permutation matrix for the similarity transform
+        as in the explanation. And *B* is the block triangular matrix of
+        the result of the permutation.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, pprint
+    >>> A = Matrix([
+    ...     [44, 0, 0, 0, 43, 0, 45, 0, 0],
+    ...     [0, 66, 62, 61, 0, 68, 0, 60, 67],
+    ...     [0, 0, 22, 21, 0, 0, 0, 20, 0],
+    ...     [0, 0, 12, 11, 0, 0, 0, 10, 0],
+    ...     [34, 0, 0, 0, 33, 0, 35, 0, 0],
+    ...     [0, 86, 82, 81, 0, 88, 0, 80, 87],
+    ...     [54, 0, 0, 0, 53, 0, 55, 0, 0],
+    ...     [0, 0, 2, 1, 0, 0, 0, 0, 0],
+    ...     [0, 76, 72, 71, 0, 78, 0, 70, 77]])
+
+    A lower block triangular decomposition:
+
+    >>> P, B = A.strongly_connected_components_decomposition()
+    >>> pprint(P)
+    PermutationMatrix((8)(1 4 3 2 6)(5 7))
+    >>> pprint(B)
+    [[44  43  45]   [0  0  0]     [0  0  0]  ]
+    [[          ]   [       ]     [       ]  ]
+    [[34  33  35]   [0  0  0]     [0  0  0]  ]
+    [[          ]   [       ]     [       ]  ]
+    [[54  53  55]   [0  0  0]     [0  0  0]  ]
+    [                                        ]
+    [ [0  0  0]    [22  21  20]   [0  0  0]  ]
+    [ [       ]    [          ]   [       ]  ]
+    [ [0  0  0]    [12  11  10]   [0  0  0]  ]
+    [ [       ]    [          ]   [       ]  ]
+    [ [0  0  0]    [2   1   0 ]   [0  0  0]  ]
+    [                                        ]
+    [ [0  0  0]    [62  61  60]  [66  68  67]]
+    [ [       ]    [          ]  [          ]]
+    [ [0  0  0]    [82  81  80]  [86  88  87]]
+    [ [       ]    [          ]  [          ]]
+    [ [0  0  0]    [72  71  70]  [76  78  77]]
+
+    >>> P = P.as_explicit()
+    >>> B = B.as_explicit()
+    >>> P.T * B * P == A
+    True
+
+    An upper block triangular decomposition:
+
+    >>> P, B = A.strongly_connected_components_decomposition(lower=False)
+    >>> pprint(P)
+    PermutationMatrix((0 1 5 7 4 3 2 8 6))
+    >>> pprint(B)
+    [[66  68  67]  [62  61  60]   [0  0  0]  ]
+    [[          ]  [          ]   [       ]  ]
+    [[86  88  87]  [82  81  80]   [0  0  0]  ]
+    [[          ]  [          ]   [       ]  ]
+    [[76  78  77]  [72  71  70]   [0  0  0]  ]
+    [                                        ]
+    [ [0  0  0]    [22  21  20]   [0  0  0]  ]
+    [ [       ]    [          ]   [       ]  ]
+    [ [0  0  0]    [12  11  10]   [0  0  0]  ]
+    [ [       ]    [          ]   [       ]  ]
+    [ [0  0  0]    [2   1   0 ]   [0  0  0]  ]
+    [                                        ]
+    [ [0  0  0]     [0  0  0]    [44  43  45]]
+    [ [       ]     [       ]    [          ]]
+    [ [0  0  0]     [0  0  0]    [34  33  35]]
+    [ [       ]     [       ]    [          ]]
+    [ [0  0  0]     [0  0  0]    [54  53  55]]
+
+    >>> P = P.as_explicit()
+    >>> B = B.as_explicit()
+    >>> P.T * B * P == A
+    True
+    """
+    from sympy.combinatorics.permutations import Permutation
+    from sympy.matrices.expressions.blockmatrix import BlockMatrix
+    from sympy.matrices.expressions.permutation import PermutationMatrix
+
+    iblocks = M.strongly_connected_components()
+    if not lower:
+        iblocks = list(reversed(iblocks))
+
+    p = Permutation(flatten(iblocks))
+    P = PermutationMatrix(p)
+
+    rows = []
+    for a in iblocks:
+        cols = []
+        for b in iblocks:
+            cols.append(M[a, b])
+        rows.append(cols)
+    B = BlockMatrix(rows)
+    return P, B
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/immutable.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/immutable.py
new file mode 100644
index 0000000000000000000000000000000000000000..7ec2174bf1c785e1a4698e1b55078d300e62dafe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/immutable.py
@@ -0,0 +1,196 @@
+from mpmath.matrices.matrices import _matrix
+
+from sympy.core import Basic, Dict, Tuple
+from sympy.core.numbers import Integer
+from sympy.core.cache import cacheit
+from sympy.core.sympify import _sympy_converter as sympify_converter, _sympify
+from sympy.matrices.dense import DenseMatrix
+from sympy.matrices.expressions import MatrixExpr
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.matrices.repmatrix import RepMatrix
+from sympy.matrices.sparse import SparseRepMatrix
+from sympy.multipledispatch import dispatch
+
+
+def sympify_matrix(arg):
+    return arg.as_immutable()
+
+
+sympify_converter[MatrixBase] = sympify_matrix
+
+
+def sympify_mpmath_matrix(arg):
+    mat = [_sympify(x) for x in arg]
+    return ImmutableDenseMatrix(arg.rows, arg.cols, mat)
+
+
+sympify_converter[_matrix] = sympify_mpmath_matrix
+
+
+class ImmutableRepMatrix(RepMatrix, MatrixExpr): # type: ignore
+    """Immutable matrix based on RepMatrix
+
+    Uses DomainMAtrix as the internal representation.
+    """
+
+    #
+    # This is a subclass of RepMatrix that adds/overrides some methods to make
+    # the instances Basic and immutable. ImmutableRepMatrix is a superclass for
+    # both ImmutableDenseMatrix and ImmutableSparseMatrix.
+    #
+
+    def __new__(cls, *args, **kwargs):
+        return cls._new(*args, **kwargs)
+
+    __hash__ = MatrixExpr.__hash__
+
+    def copy(self):
+        return self
+
+    @property
+    def cols(self):
+        return self._cols
+
+    @property
+    def rows(self):
+        return self._rows
+
+    @property
+    def shape(self):
+        return self._rows, self._cols
+
+    def as_immutable(self):
+        return self
+
+    def _entry(self, i, j, **kwargs):
+        return self[i, j]
+
+    def __setitem__(self, *args):
+        raise TypeError("Cannot set values of {}".format(self.__class__))
+
+    def is_diagonalizable(self, reals_only=False, **kwargs):
+        return super().is_diagonalizable(
+            reals_only=reals_only, **kwargs)
+
+    is_diagonalizable.__doc__ = SparseRepMatrix.is_diagonalizable.__doc__
+    is_diagonalizable = cacheit(is_diagonalizable)
+
+    def analytic_func(self, f, x):
+        return self.as_mutable().analytic_func(f, x).as_immutable()
+
+
+class ImmutableDenseMatrix(DenseMatrix, ImmutableRepMatrix):  # type: ignore
+    """Create an immutable version of a matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import eye, ImmutableMatrix
+    >>> ImmutableMatrix(eye(3))
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> _[0, 0] = 42
+    Traceback (most recent call last):
+    ...
+    TypeError: Cannot set values of ImmutableDenseMatrix
+    """
+
+    # MatrixExpr is set as NotIterable, but we want explicit matrices to be
+    # iterable
+    _iterable = True
+    _class_priority = 8
+    _op_priority = 10.001
+
+    @classmethod
+    def _new(cls, *args, **kwargs):
+        if len(args) == 1 and isinstance(args[0], ImmutableDenseMatrix):
+            return args[0]
+        if kwargs.get('copy', True) is False:
+            if len(args) != 3:
+                raise TypeError("'copy=False' requires a matrix be initialized as rows,cols,[list]")
+            rows, cols, flat_list = args
+        else:
+            rows, cols, flat_list = cls._handle_creation_inputs(*args, **kwargs)
+            flat_list = list(flat_list) # create a shallow copy
+
+        rep = cls._flat_list_to_DomainMatrix(rows, cols, flat_list)
+
+        return cls._fromrep(rep)
+
+    @classmethod
+    def _fromrep(cls, rep):
+        rows, cols = rep.shape
+        flat_list = rep.to_sympy().to_list_flat()
+        obj = Basic.__new__(cls,
+            Integer(rows),
+            Integer(cols),
+            Tuple(*flat_list, sympify=False))
+        obj._rows = rows
+        obj._cols = cols
+        obj._rep = rep
+        return obj
+
+
+# make sure ImmutableDenseMatrix is aliased as ImmutableMatrix
+ImmutableMatrix = ImmutableDenseMatrix
+
+
+class ImmutableSparseMatrix(SparseRepMatrix, ImmutableRepMatrix):  # type:ignore
+    """Create an immutable version of a sparse matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import eye, ImmutableSparseMatrix
+    >>> ImmutableSparseMatrix(1, 1, {})
+    Matrix([[0]])
+    >>> ImmutableSparseMatrix(eye(3))
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> _[0, 0] = 42
+    Traceback (most recent call last):
+    ...
+    TypeError: Cannot set values of ImmutableSparseMatrix
+    >>> _.shape
+    (3, 3)
+    """
+    is_Matrix = True
+    _class_priority = 9
+
+    @classmethod
+    def _new(cls, *args, **kwargs):
+        rows, cols, smat = cls._handle_creation_inputs(*args, **kwargs)
+
+        rep = cls._smat_to_DomainMatrix(rows, cols, smat)
+
+        return cls._fromrep(rep)
+
+    @classmethod
+    def _fromrep(cls, rep):
+        rows, cols = rep.shape
+        smat = rep.to_sympy().to_dok()
+        obj = Basic.__new__(cls, Integer(rows), Integer(cols), Dict(smat))
+        obj._rows = rows
+        obj._cols = cols
+        obj._rep = rep
+        return obj
+
+
+@dispatch(ImmutableDenseMatrix, ImmutableDenseMatrix)
+def _eval_is_eq(lhs, rhs): # noqa:F811
+    """Helper method for Equality with matrices.sympy.
+
+    Relational automatically converts matrices to ImmutableDenseMatrix
+    instances, so this method only applies here.  Returns True if the
+    matrices are definitively the same, False if they are definitively
+    different, and None if undetermined (e.g. if they contain Symbols).
+    Returning None triggers default handling of Equalities.
+
+    """
+    if lhs.shape != rhs.shape:
+        return False
+    return (lhs - rhs).is_zero_matrix
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/inverse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/inverse.py
new file mode 100644
index 0000000000000000000000000000000000000000..61d9e12edf013d2f5555d61786343aa3840edfd3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/inverse.py
@@ -0,0 +1,524 @@
+from sympy.polys.matrices.exceptions import DMNonInvertibleMatrixError
+from sympy.polys.domains import EX
+
+from .exceptions import MatrixError, NonSquareMatrixError, NonInvertibleMatrixError
+from .utilities import _iszero
+
+
+def _pinv_full_rank(M):
+    """Subroutine for full row or column rank matrices.
+
+    For full row rank matrices, inverse of ``A * A.H`` Exists.
+    For full column rank matrices, inverse of ``A.H * A`` Exists.
+
+    This routine can apply for both cases by checking the shape
+    and have small decision.
+    """
+
+    if M.is_zero_matrix:
+        return M.H
+
+    if M.rows >= M.cols:
+        return M.H.multiply(M).inv().multiply(M.H)
+    else:
+        return M.H.multiply(M.multiply(M.H).inv())
+
+def _pinv_rank_decomposition(M):
+    """Subroutine for rank decomposition
+
+    With rank decompositions, `A` can be decomposed into two full-
+    rank matrices, and each matrix can take pseudoinverse
+    individually.
+    """
+
+    if M.is_zero_matrix:
+        return M.H
+
+    B, C = M.rank_decomposition()
+
+    Bp = _pinv_full_rank(B)
+    Cp = _pinv_full_rank(C)
+
+    return Cp.multiply(Bp)
+
+def _pinv_diagonalization(M):
+    """Subroutine using diagonalization
+
+    This routine can sometimes fail if SymPy's eigenvalue
+    computation is not reliable.
+    """
+
+    if M.is_zero_matrix:
+        return M.H
+
+    A  = M
+    AH = M.H
+
+    try:
+        if M.rows >= M.cols:
+            P, D   = AH.multiply(A).diagonalize(normalize=True)
+            D_pinv = D.applyfunc(lambda x: 0 if _iszero(x) else 1 / x)
+
+            return P.multiply(D_pinv).multiply(P.H).multiply(AH)
+
+        else:
+            P, D   = A.multiply(AH).diagonalize(
+                        normalize=True)
+            D_pinv = D.applyfunc(lambda x: 0 if _iszero(x) else 1 / x)
+
+            return AH.multiply(P).multiply(D_pinv).multiply(P.H)
+
+    except MatrixError:
+        raise NotImplementedError(
+            'pinv for rank-deficient matrices where '
+            'diagonalization of A.H*A fails is not supported yet.')
+
+def _pinv(M, method='RD'):
+    """Calculate the Moore-Penrose pseudoinverse of the matrix.
+
+    The Moore-Penrose pseudoinverse exists and is unique for any matrix.
+    If the matrix is invertible, the pseudoinverse is the same as the
+    inverse.
+
+    Parameters
+    ==========
+
+    method : String, optional
+        Specifies the method for computing the pseudoinverse.
+
+        If ``'RD'``, Rank-Decomposition will be used.
+
+        If ``'ED'``, Diagonalization will be used.
+
+    Examples
+    ========
+
+    Computing pseudoinverse by rank decomposition :
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[1, 2, 3], [4, 5, 6]])
+    >>> A.pinv()
+    Matrix([
+    [-17/18,  4/9],
+    [  -1/9,  1/9],
+    [ 13/18, -2/9]])
+
+    Computing pseudoinverse by diagonalization :
+
+    >>> B = A.pinv(method='ED')
+    >>> B.simplify()
+    >>> B
+    Matrix([
+    [-17/18,  4/9],
+    [  -1/9,  1/9],
+    [ 13/18, -2/9]])
+
+    See Also
+    ========
+
+    inv
+    pinv_solve
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse
+
+    """
+
+    # Trivial case: pseudoinverse of all-zero matrix is its transpose.
+    if M.is_zero_matrix:
+        return M.H
+
+    if method == 'RD':
+        return _pinv_rank_decomposition(M)
+    elif method == 'ED':
+        return _pinv_diagonalization(M)
+    else:
+        raise ValueError('invalid pinv method %s' % repr(method))
+
+
+def _verify_invertible(M, iszerofunc=_iszero):
+    """Initial check to see if a matrix is invertible. Raises or returns
+    determinant for use in _inv_ADJ."""
+
+    if not M.is_square:
+        raise NonSquareMatrixError("A Matrix must be square to invert.")
+
+    d    = M.det(method='berkowitz')
+    zero = d.equals(0)
+
+    if zero is None: # if equals() can't decide, will rref be able to?
+        ok   = M.rref(simplify=True)[0]
+        zero = any(iszerofunc(ok[j, j]) for j in range(ok.rows))
+
+    if zero:
+        raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+
+    return d
+
+def _inv_ADJ(M, iszerofunc=_iszero):
+    """Calculates the inverse using the adjugate matrix and a determinant.
+
+    See Also
+    ========
+
+    inv
+    inverse_GE
+    inverse_LU
+    inverse_CH
+    inverse_LDL
+    """
+
+    d = _verify_invertible(M, iszerofunc=iszerofunc)
+
+    return M.adjugate() / d
+
+def _inv_GE(M, iszerofunc=_iszero):
+    """Calculates the inverse using Gaussian elimination.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_LU
+    inverse_CH
+    inverse_LDL
+    """
+
+    from .dense import Matrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("A Matrix must be square to invert.")
+
+    big = Matrix.hstack(M.as_mutable(), Matrix.eye(M.rows))
+    red = big.rref(iszerofunc=iszerofunc, simplify=True)[0]
+
+    if any(iszerofunc(red[j, j]) for j in range(red.rows)):
+        raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+
+    return M._new(red[:, big.rows:])
+
+def _inv_LU(M, iszerofunc=_iszero):
+    """Calculates the inverse using LU decomposition.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_GE
+    inverse_CH
+    inverse_LDL
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError("A Matrix must be square to invert.")
+    if M.free_symbols:
+        _verify_invertible(M, iszerofunc=iszerofunc)
+
+    return M.LUsolve(M.eye(M.rows), iszerofunc=_iszero)
+
+def _inv_CH(M, iszerofunc=_iszero):
+    """Calculates the inverse using cholesky decomposition.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_GE
+    inverse_LU
+    inverse_LDL
+    """
+
+    _verify_invertible(M, iszerofunc=iszerofunc)
+
+    return M.cholesky_solve(M.eye(M.rows))
+
+def _inv_LDL(M, iszerofunc=_iszero):
+    """Calculates the inverse using LDL decomposition.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_GE
+    inverse_LU
+    inverse_CH
+    """
+
+    _verify_invertible(M, iszerofunc=iszerofunc)
+
+    return M.LDLsolve(M.eye(M.rows))
+
+def _inv_QR(M, iszerofunc=_iszero):
+    """Calculates the inverse using QR decomposition.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_GE
+    inverse_CH
+    inverse_LDL
+    """
+
+    _verify_invertible(M, iszerofunc=iszerofunc)
+
+    return M.QRsolve(M.eye(M.rows))
+
+def _try_DM(M, use_EX=False):
+    """Try to convert a matrix to a ``DomainMatrix``."""
+    dM = M.to_DM()
+    K = dM.domain
+
+    # Return DomainMatrix if a domain is found. Only use EX if use_EX=True.
+    if not use_EX and K.is_EXRAW:
+        return None
+    elif K.is_EXRAW:
+        return dM.convert_to(EX)
+    else:
+        return dM
+
+
+def _use_exact_domain(dom):
+    """Check whether to convert to an exact domain."""
+    # DomainMatrix can handle RR and CC with partial pivoting. Other inexact
+    # domains like RR[a,b,...] can only be handled by converting to an exact
+    # domain like QQ[a,b,...]
+    if dom.is_RR or dom.is_CC:
+        return False
+    else:
+        return not dom.is_Exact
+
+
+def _inv_DM(dM, cancel=True):
+    """Calculates the inverse using ``DomainMatrix``.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_GE
+    inverse_CH
+    inverse_LDL
+    sympy.polys.matrices.domainmatrix.DomainMatrix.inv
+    """
+    m, n = dM.shape
+    dom = dM.domain
+
+    if m != n:
+        raise NonSquareMatrixError("A Matrix must be square to invert.")
+
+    # Convert RR[a,b,...] to QQ[a,b,...]
+    use_exact = _use_exact_domain(dom)
+
+    if use_exact:
+        dom_exact = dom.get_exact()
+        dM = dM.convert_to(dom_exact)
+
+    try:
+        dMi, den = dM.inv_den()
+    except DMNonInvertibleMatrixError:
+        raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+
+    if use_exact:
+        dMi = dMi.convert_to(dom)
+        den = dom.convert_from(den, dom_exact)
+
+    if cancel:
+        # Convert to field and cancel with the denominator.
+        if not dMi.domain.is_Field:
+            dMi = dMi.to_field()
+        Mi = (dMi / den).to_Matrix()
+    else:
+        # Convert to Matrix and divide without cancelling
+        Mi = dMi.to_Matrix() / dMi.domain.to_sympy(den)
+
+    return Mi
+
+def _inv_block(M, iszerofunc=_iszero):
+    """Calculates the inverse using BLOCKWISE inversion.
+
+    See Also
+    ========
+
+    inv
+    inverse_ADJ
+    inverse_GE
+    inverse_CH
+    inverse_LDL
+    """
+    from sympy.matrices.expressions.blockmatrix import BlockMatrix
+    i = M.shape[0]
+    if i <= 20 :
+        return M.inv(method="LU", iszerofunc=_iszero)
+    A = M[:i // 2, :i //2]
+    B = M[:i // 2, i // 2:]
+    C = M[i // 2:, :i // 2]
+    D = M[i // 2:, i // 2:]
+    try:
+        D_inv = _inv_block(D)
+    except NonInvertibleMatrixError:
+        return M.inv(method="LU", iszerofunc=_iszero)
+    B_D_i = B*D_inv
+    BDC = B_D_i*C
+    A_n = A - BDC
+    try:
+        A_n = _inv_block(A_n)
+    except NonInvertibleMatrixError:
+        return M.inv(method="LU", iszerofunc=_iszero)
+    B_n = -A_n*B_D_i
+    dc = D_inv*C
+    C_n = -dc*A_n
+    D_n = D_inv + dc*-B_n
+    nn = BlockMatrix([[A_n, B_n], [C_n, D_n]]).as_explicit()
+    return nn
+
+def _inv(M, method=None, iszerofunc=_iszero, try_block_diag=False):
+    """
+    Return the inverse of a matrix using the method indicated. The default
+    is DM if a suitable domain is found or otherwise GE for dense matrices
+    LDL for sparse matrices.
+
+    Parameters
+    ==========
+
+    method : ('DM', 'DMNC', 'GE', 'LU', 'ADJ', 'CH', 'LDL', 'QR')
+
+    iszerofunc : function, optional
+        Zero-testing function to use.
+
+    try_block_diag : bool, optional
+        If True then will try to form block diagonal matrices using the
+        method get_diag_blocks(), invert these individually, and then
+        reconstruct the full inverse matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import SparseMatrix, Matrix
+    >>> A = SparseMatrix([
+    ... [ 2, -1,  0],
+    ... [-1,  2, -1],
+    ... [ 0,  0,  2]])
+    >>> A.inv('CH')
+    Matrix([
+    [2/3, 1/3, 1/6],
+    [1/3, 2/3, 1/3],
+    [  0,   0, 1/2]])
+    >>> A.inv(method='LDL') # use of 'method=' is optional
+    Matrix([
+    [2/3, 1/3, 1/6],
+    [1/3, 2/3, 1/3],
+    [  0,   0, 1/2]])
+    >>> A * _
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> A = Matrix(A)
+    >>> A.inv('CH')
+    Matrix([
+    [2/3, 1/3, 1/6],
+    [1/3, 2/3, 1/3],
+    [  0,   0, 1/2]])
+    >>> A.inv('ADJ') == A.inv('GE') == A.inv('LU') == A.inv('CH') == A.inv('LDL') == A.inv('QR')
+    True
+
+    Notes
+    =====
+
+    According to the ``method`` keyword, it calls the appropriate method:
+
+        DM .... Use DomainMatrix ``inv_den`` method
+        DMNC .... Use DomainMatrix ``inv_den`` method without cancellation
+        GE .... inverse_GE(); default for dense matrices
+        LU .... inverse_LU()
+        ADJ ... inverse_ADJ()
+        CH ... inverse_CH()
+        LDL ... inverse_LDL(); default for sparse matrices
+        QR ... inverse_QR()
+
+    Note, the GE and LU methods may require the matrix to be simplified
+    before it is inverted in order to properly detect zeros during
+    pivoting. In difficult cases a custom zero detection function can
+    be provided by setting the ``iszerofunc`` argument to a function that
+    should return True if its argument is zero. The ADJ routine computes
+    the determinant and uses that to detect singular matrices in addition
+    to testing for zeros on the diagonal.
+
+    See Also
+    ========
+
+    inverse_ADJ
+    inverse_GE
+    inverse_LU
+    inverse_CH
+    inverse_LDL
+
+    Raises
+    ======
+
+    ValueError
+        If the determinant of the matrix is zero.
+    """
+
+    from sympy.matrices import diag, SparseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("A Matrix must be square to invert.")
+
+    if try_block_diag:
+        blocks = M.get_diag_blocks()
+        r      = []
+
+        for block in blocks:
+            r.append(block.inv(method=method, iszerofunc=iszerofunc))
+
+        return diag(*r)
+
+    # Default: Use DomainMatrix if the domain is not EX.
+    # If DM is requested explicitly then use it even if the domain is EX.
+    if method is None and iszerofunc is _iszero:
+        dM = _try_DM(M, use_EX=False)
+        if dM is not None:
+            method = 'DM'
+    elif method in ("DM", "DMNC"):
+        dM = _try_DM(M, use_EX=True)
+
+    # A suitable domain was not found, fall back to GE for dense matrices
+    # and LDL for sparse matrices.
+    if method is None:
+        if isinstance(M, SparseMatrix):
+            method = 'LDL'
+        else:
+            method = 'GE'
+
+    if method == "DM":
+        rv = _inv_DM(dM)
+    elif method == "DMNC":
+        rv = _inv_DM(dM, cancel=False)
+    elif method == "GE":
+        rv = M.inverse_GE(iszerofunc=iszerofunc)
+    elif method == "LU":
+        rv = M.inverse_LU(iszerofunc=iszerofunc)
+    elif method == "ADJ":
+        rv = M.inverse_ADJ(iszerofunc=iszerofunc)
+    elif method == "CH":
+        rv = M.inverse_CH(iszerofunc=iszerofunc)
+    elif method == "LDL":
+        rv = M.inverse_LDL(iszerofunc=iszerofunc)
+    elif method == "QR":
+        rv = M.inverse_QR(iszerofunc=iszerofunc)
+    elif method == "BLOCK":
+        rv = M.inverse_BLOCK(iszerofunc=iszerofunc)
+    else:
+        raise ValueError("Inversion method unrecognized")
+
+    return M._new(rv)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/kind.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/kind.py
new file mode 100644
index 0000000000000000000000000000000000000000..f9f53ffe16f7cbde60213e49071a2a74e80e5c6c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/kind.py
@@ -0,0 +1,97 @@
+# sympy.matrices.kind
+
+from sympy.core.kind import Kind, _NumberKind, NumberKind
+from sympy.core.mul import Mul
+
+
+class MatrixKind(Kind):
+    """
+    Kind for all matrices in SymPy.
+
+    Basic class for this kind is ``MatrixBase`` and ``MatrixExpr``,
+    but any expression representing the matrix can have this.
+
+    Parameters
+    ==========
+
+    element_kind : Kind
+        Kind of the element. Default is
+        :class:`sympy.core.kind.NumberKind`,
+        which means that the matrix contains only numbers.
+
+    Examples
+    ========
+
+    Any instance of matrix class has kind ``MatrixKind``:
+
+    >>> from sympy import MatrixSymbol
+    >>> A = MatrixSymbol('A', 2, 2)
+    >>> A.kind
+    MatrixKind(NumberKind)
+
+    An expression representing a matrix may not be an instance of
+    the Matrix class, but it will have kind ``MatrixKind``:
+
+    >>> from sympy import MatrixExpr, Integral
+    >>> from sympy.abc import x
+    >>> intM = Integral(A, x)
+    >>> isinstance(intM, MatrixExpr)
+    False
+    >>> intM.kind
+    MatrixKind(NumberKind)
+
+    Use ``isinstance()`` to check for ``MatrixKind`` without specifying the
+    element kind. Use ``is`` to check the kind including the element kind:
+
+    >>> from sympy import Matrix
+    >>> from sympy.core import NumberKind
+    >>> from sympy.matrices import MatrixKind
+    >>> M = Matrix([1, 2])
+    >>> isinstance(M.kind, MatrixKind)
+    True
+    >>> M.kind is MatrixKind(NumberKind)
+    True
+
+    See Also
+    ========
+
+    sympy.core.kind.NumberKind
+    sympy.core.kind.UndefinedKind
+    sympy.core.containers.TupleKind
+    sympy.sets.sets.SetKind
+
+    """
+    def __new__(cls, element_kind=NumberKind):
+        obj = super().__new__(cls, element_kind)
+        obj.element_kind = element_kind
+        return obj
+
+    def __repr__(self):
+        return "MatrixKind(%s)" % self.element_kind
+
+
+@Mul._kind_dispatcher.register(_NumberKind, MatrixKind)
+def num_mat_mul(k1, k2):
+    """
+    Return MatrixKind. The element kind is selected by recursive dispatching.
+    Do not need to dispatch in reversed order because KindDispatcher
+    searches for this automatically.
+    """
+    # Deal with Mul._kind_dispatcher's commutativity
+    # XXX: this function is called with either k1 or k2 as MatrixKind because
+    # the Mul kind dispatcher is commutative. Maybe it shouldn't be. Need to
+    # swap the args here because NumberKind does not have an element_kind
+    # attribute.
+    if not isinstance(k2, MatrixKind):
+        k1, k2 = k2, k1
+    elemk = Mul._kind_dispatcher(k1, k2.element_kind)
+    return MatrixKind(elemk)
+
+
+@Mul._kind_dispatcher.register(MatrixKind, MatrixKind)
+def mat_mat_mul(k1, k2):
+    """
+    Return MatrixKind. The element kind is selected by recursive dispatching.
+    """
+    elemk = Mul._kind_dispatcher(k1.element_kind, k2.element_kind)
+    return MatrixKind(elemk)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..fed41a626cb395ac0529071317630d853e0d3a96
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/matrices.py
@@ -0,0 +1,687 @@
+#
+# A module consisting of deprecated matrix classes. New code should not be
+# added here.
+#
+from sympy.core.basic import Basic
+from sympy.core.symbol import Dummy
+
+from .common import MatrixCommon
+
+from .exceptions import NonSquareMatrixError
+
+from .utilities import _iszero, _is_zero_after_expand_mul, _simplify
+
+from .determinant import (
+    _find_reasonable_pivot, _find_reasonable_pivot_naive,
+    _adjugate, _charpoly, _cofactor, _cofactor_matrix, _per,
+    _det, _det_bareiss, _det_berkowitz, _det_bird, _det_laplace, _det_LU,
+    _minor, _minor_submatrix)
+
+from .reductions import _is_echelon, _echelon_form, _rank, _rref
+from .subspaces import _columnspace, _nullspace, _rowspace, _orthogonalize
+
+from .eigen import (
+    _eigenvals, _eigenvects,
+    _bidiagonalize, _bidiagonal_decomposition,
+    _is_diagonalizable, _diagonalize,
+    _is_positive_definite, _is_positive_semidefinite,
+    _is_negative_definite, _is_negative_semidefinite, _is_indefinite,
+    _jordan_form, _left_eigenvects, _singular_values)
+
+
+# This class was previously defined in this module, but was moved to
+# sympy.matrices.matrixbase. We import it here for backwards compatibility in
+# case someone was importing it from here.
+from .matrixbase import MatrixBase
+
+
+__doctest_requires__ = {
+    ('MatrixEigen.is_indefinite',
+     'MatrixEigen.is_negative_definite',
+     'MatrixEigen.is_negative_semidefinite',
+     'MatrixEigen.is_positive_definite',
+     'MatrixEigen.is_positive_semidefinite'): ['matplotlib'],
+}
+
+
+class MatrixDeterminant(MatrixCommon):
+    """Provides basic matrix determinant operations. Should not be instantiated
+    directly. See ``determinant.py`` for their implementations."""
+
+    def _eval_det_bareiss(self, iszerofunc=_is_zero_after_expand_mul):
+        return _det_bareiss(self, iszerofunc=iszerofunc)
+
+    def _eval_det_berkowitz(self):
+        return _det_berkowitz(self)
+
+    def _eval_det_lu(self, iszerofunc=_iszero, simpfunc=None):
+        return _det_LU(self, iszerofunc=iszerofunc, simpfunc=simpfunc)
+
+    def _eval_det_bird(self):
+        return _det_bird(self)
+
+    def _eval_det_laplace(self):
+        return _det_laplace(self)
+
+    def _eval_determinant(self): # for expressions.determinant.Determinant
+        return _det(self)
+
+    def adjugate(self, method="berkowitz"):
+        return _adjugate(self, method=method)
+
+    def charpoly(self, x='lambda', simplify=_simplify):
+        return _charpoly(self, x=x, simplify=simplify)
+
+    def cofactor(self, i, j, method="berkowitz"):
+        return _cofactor(self, i, j, method=method)
+
+    def cofactor_matrix(self, method="berkowitz"):
+        return _cofactor_matrix(self, method=method)
+
+    def det(self, method="bareiss", iszerofunc=None):
+        return _det(self, method=method, iszerofunc=iszerofunc)
+
+    def per(self):
+        return _per(self)
+
+    def minor(self, i, j, method="berkowitz"):
+        return _minor(self, i, j, method=method)
+
+    def minor_submatrix(self, i, j):
+        return _minor_submatrix(self, i, j)
+
+    _find_reasonable_pivot.__doc__       = _find_reasonable_pivot.__doc__
+    _find_reasonable_pivot_naive.__doc__ = _find_reasonable_pivot_naive.__doc__
+    _eval_det_bareiss.__doc__            = _det_bareiss.__doc__
+    _eval_det_berkowitz.__doc__          = _det_berkowitz.__doc__
+    _eval_det_bird.__doc__            = _det_bird.__doc__
+    _eval_det_laplace.__doc__            = _det_laplace.__doc__
+    _eval_det_lu.__doc__                 = _det_LU.__doc__
+    _eval_determinant.__doc__            = _det.__doc__
+    adjugate.__doc__                     = _adjugate.__doc__
+    charpoly.__doc__                     = _charpoly.__doc__
+    cofactor.__doc__                     = _cofactor.__doc__
+    cofactor_matrix.__doc__              = _cofactor_matrix.__doc__
+    det.__doc__                          = _det.__doc__
+    per.__doc__                          = _per.__doc__
+    minor.__doc__                        = _minor.__doc__
+    minor_submatrix.__doc__              = _minor_submatrix.__doc__
+
+
+class MatrixReductions(MatrixDeterminant):
+    """Provides basic matrix row/column operations. Should not be instantiated
+    directly. See ``reductions.py`` for some of their implementations."""
+
+    def echelon_form(self, iszerofunc=_iszero, simplify=False, with_pivots=False):
+        return _echelon_form(self, iszerofunc=iszerofunc, simplify=simplify,
+                with_pivots=with_pivots)
+
+    @property
+    def is_echelon(self):
+        return _is_echelon(self)
+
+    def rank(self, iszerofunc=_iszero, simplify=False):
+        return _rank(self, iszerofunc=iszerofunc, simplify=simplify)
+
+    def rref_rhs(self, rhs):
+        """Return reduced row-echelon form of matrix, matrix showing
+        rhs after reduction steps. ``rhs`` must have the same number
+        of rows as ``self``.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, symbols
+        >>> r1, r2 = symbols('r1 r2')
+        >>> Matrix([[1, 1], [2, 1]]).rref_rhs(Matrix([r1, r2]))
+        (Matrix([
+        [1, 0],
+        [0, 1]]), Matrix([
+        [ -r1 + r2],
+        [2*r1 - r2]]))
+        """
+        r, _ = _rref(self.hstack(self, self.eye(self.rows), rhs))
+        return r[:, :self.cols], r[:, -rhs.cols:]
+
+    def rref(self, iszerofunc=_iszero, simplify=False, pivots=True,
+            normalize_last=True):
+        return _rref(self, iszerofunc=iszerofunc, simplify=simplify,
+            pivots=pivots, normalize_last=normalize_last)
+
+    echelon_form.__doc__ = _echelon_form.__doc__
+    is_echelon.__doc__   = _is_echelon.__doc__
+    rank.__doc__         = _rank.__doc__
+    rref.__doc__         = _rref.__doc__
+
+    def _normalize_op_args(self, op, col, k, col1, col2, error_str="col"):
+        """Validate the arguments for a row/column operation.  ``error_str``
+        can be one of "row" or "col" depending on the arguments being parsed."""
+        if op not in ["n->kn", "n<->m", "n->n+km"]:
+            raise ValueError("Unknown {} operation '{}'. Valid col operations "
+                             "are 'n->kn', 'n<->m', 'n->n+km'".format(error_str, op))
+
+        # define self_col according to error_str
+        self_cols = self.cols if error_str == 'col' else self.rows
+
+        # normalize and validate the arguments
+        if op == "n->kn":
+            col = col if col is not None else col1
+            if col is None or k is None:
+                raise ValueError("For a {0} operation 'n->kn' you must provide the "
+                                 "kwargs `{0}` and `k`".format(error_str))
+            if not 0 <= col < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col))
+
+        elif op == "n<->m":
+            # we need two cols to swap. It does not matter
+            # how they were specified, so gather them together and
+            # remove `None`
+            cols = {col, k, col1, col2}.difference([None])
+            if len(cols) > 2:
+                # maybe the user left `k` by mistake?
+                cols = {col, col1, col2}.difference([None])
+            if len(cols) != 2:
+                raise ValueError("For a {0} operation 'n<->m' you must provide the "
+                                 "kwargs `{0}1` and `{0}2`".format(error_str))
+            col1, col2 = cols
+            if not 0 <= col1 < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col1))
+            if not 0 <= col2 < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2))
+
+        elif op == "n->n+km":
+            col = col1 if col is None else col
+            col2 = col1 if col2 is None else col2
+            if col is None or col2 is None or k is None:
+                raise ValueError("For a {0} operation 'n->n+km' you must provide the "
+                                 "kwargs `{0}`, `k`, and `{0}2`".format(error_str))
+            if col == col2:
+                raise ValueError("For a {0} operation 'n->n+km' `{0}` and `{0}2` must "
+                                 "be different.".format(error_str))
+            if not 0 <= col < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col))
+            if not 0 <= col2 < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2))
+
+        else:
+            raise ValueError('invalid operation %s' % repr(op))
+
+        return op, col, k, col1, col2
+
+    def _eval_col_op_multiply_col_by_const(self, col, k):
+        def entry(i, j):
+            if j == col:
+                return k * self[i, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_col_op_swap(self, col1, col2):
+        def entry(i, j):
+            if j == col1:
+                return self[i, col2]
+            elif j == col2:
+                return self[i, col1]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_col_op_add_multiple_to_other_col(self, col, k, col2):
+        def entry(i, j):
+            if j == col:
+                return self[i, j] + k * self[i, col2]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_row_op_swap(self, row1, row2):
+        def entry(i, j):
+            if i == row1:
+                return self[row2, j]
+            elif i == row2:
+                return self[row1, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_row_op_multiply_row_by_const(self, row, k):
+        def entry(i, j):
+            if i == row:
+                return k * self[i, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_row_op_add_multiple_to_other_row(self, row, k, row2):
+        def entry(i, j):
+            if i == row:
+                return self[i, j] + k * self[row2, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def elementary_col_op(self, op="n->kn", col=None, k=None, col1=None, col2=None):
+        """Performs the elementary column operation `op`.
+
+        `op` may be one of
+
+            * ``"n->kn"`` (column n goes to k*n)
+            * ``"n<->m"`` (swap column n and column m)
+            * ``"n->n+km"`` (column n goes to column n + k*column m)
+
+        Parameters
+        ==========
+
+        op : string; the elementary row operation
+        col : the column to apply the column operation
+        k : the multiple to apply in the column operation
+        col1 : one column of a column swap
+        col2 : second column of a column swap or column "m" in the column operation
+               "n->n+km"
+        """
+
+        op, col, k, col1, col2 = self._normalize_op_args(op, col, k, col1, col2, "col")
+
+        # now that we've validated, we're all good to dispatch
+        if op == "n->kn":
+            return self._eval_col_op_multiply_col_by_const(col, k)
+        if op == "n<->m":
+            return self._eval_col_op_swap(col1, col2)
+        if op == "n->n+km":
+            return self._eval_col_op_add_multiple_to_other_col(col, k, col2)
+
+    def elementary_row_op(self, op="n->kn", row=None, k=None, row1=None, row2=None):
+        """Performs the elementary row operation `op`.
+
+        `op` may be one of
+
+            * ``"n->kn"`` (row n goes to k*n)
+            * ``"n<->m"`` (swap row n and row m)
+            * ``"n->n+km"`` (row n goes to row n + k*row m)
+
+        Parameters
+        ==========
+
+        op : string; the elementary row operation
+        row : the row to apply the row operation
+        k : the multiple to apply in the row operation
+        row1 : one row of a row swap
+        row2 : second row of a row swap or row "m" in the row operation
+               "n->n+km"
+        """
+
+        op, row, k, row1, row2 = self._normalize_op_args(op, row, k, row1, row2, "row")
+
+        # now that we've validated, we're all good to dispatch
+        if op == "n->kn":
+            return self._eval_row_op_multiply_row_by_const(row, k)
+        if op == "n<->m":
+            return self._eval_row_op_swap(row1, row2)
+        if op == "n->n+km":
+            return self._eval_row_op_add_multiple_to_other_row(row, k, row2)
+
+
+class MatrixSubspaces(MatrixReductions):
+    """Provides methods relating to the fundamental subspaces of a matrix.
+    Should not be instantiated directly. See ``subspaces.py`` for their
+    implementations."""
+
+    def columnspace(self, simplify=False):
+        return _columnspace(self, simplify=simplify)
+
+    def nullspace(self, simplify=False, iszerofunc=_iszero):
+        return _nullspace(self, simplify=simplify, iszerofunc=iszerofunc)
+
+    def rowspace(self, simplify=False):
+        return _rowspace(self, simplify=simplify)
+
+    # This is a classmethod but is converted to such later in order to allow
+    # assignment of __doc__ since that does not work for already wrapped
+    # classmethods in Python 3.6.
+    def orthogonalize(cls, *vecs, **kwargs):
+        return _orthogonalize(cls, *vecs, **kwargs)
+
+    columnspace.__doc__   = _columnspace.__doc__
+    nullspace.__doc__     = _nullspace.__doc__
+    rowspace.__doc__      = _rowspace.__doc__
+    orthogonalize.__doc__ = _orthogonalize.__doc__
+
+    orthogonalize         = classmethod(orthogonalize)  # type:ignore
+
+
+class MatrixEigen(MatrixSubspaces):
+    """Provides basic matrix eigenvalue/vector operations.
+    Should not be instantiated directly. See ``eigen.py`` for their
+    implementations."""
+
+    def eigenvals(self, error_when_incomplete=True, **flags):
+        return _eigenvals(self, error_when_incomplete=error_when_incomplete, **flags)
+
+    def eigenvects(self, error_when_incomplete=True, iszerofunc=_iszero, **flags):
+        return _eigenvects(self, error_when_incomplete=error_when_incomplete,
+                iszerofunc=iszerofunc, **flags)
+
+    def is_diagonalizable(self, reals_only=False, **kwargs):
+        return _is_diagonalizable(self, reals_only=reals_only, **kwargs)
+
+    def diagonalize(self, reals_only=False, sort=False, normalize=False):
+        return _diagonalize(self, reals_only=reals_only, sort=sort,
+                normalize=normalize)
+
+    def bidiagonalize(self, upper=True):
+        return _bidiagonalize(self, upper=upper)
+
+    def bidiagonal_decomposition(self, upper=True):
+        return _bidiagonal_decomposition(self, upper=upper)
+
+    @property
+    def is_positive_definite(self):
+        return _is_positive_definite(self)
+
+    @property
+    def is_positive_semidefinite(self):
+        return _is_positive_semidefinite(self)
+
+    @property
+    def is_negative_definite(self):
+        return _is_negative_definite(self)
+
+    @property
+    def is_negative_semidefinite(self):
+        return _is_negative_semidefinite(self)
+
+    @property
+    def is_indefinite(self):
+        return _is_indefinite(self)
+
+    def jordan_form(self, calc_transform=True, **kwargs):
+        return _jordan_form(self, calc_transform=calc_transform, **kwargs)
+
+    def left_eigenvects(self, **flags):
+        return _left_eigenvects(self, **flags)
+
+    def singular_values(self):
+        return _singular_values(self)
+
+    eigenvals.__doc__                  = _eigenvals.__doc__
+    eigenvects.__doc__                 = _eigenvects.__doc__
+    is_diagonalizable.__doc__          = _is_diagonalizable.__doc__
+    diagonalize.__doc__                = _diagonalize.__doc__
+    is_positive_definite.__doc__       = _is_positive_definite.__doc__
+    is_positive_semidefinite.__doc__   = _is_positive_semidefinite.__doc__
+    is_negative_definite.__doc__       = _is_negative_definite.__doc__
+    is_negative_semidefinite.__doc__   = _is_negative_semidefinite.__doc__
+    is_indefinite.__doc__              = _is_indefinite.__doc__
+    jordan_form.__doc__                = _jordan_form.__doc__
+    left_eigenvects.__doc__            = _left_eigenvects.__doc__
+    singular_values.__doc__            = _singular_values.__doc__
+    bidiagonalize.__doc__              = _bidiagonalize.__doc__
+    bidiagonal_decomposition.__doc__   = _bidiagonal_decomposition.__doc__
+
+
+class MatrixCalculus(MatrixCommon):
+    """Provides calculus-related matrix operations."""
+
+    def diff(self, *args, evaluate=True, **kwargs):
+        """Calculate the derivative of each element in the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.diff(x)
+        Matrix([
+        [1, 0],
+        [0, 0]])
+
+        See Also
+        ========
+
+        integrate
+        limit
+        """
+        # XXX this should be handled here rather than in Derivative
+        from sympy.tensor.array.array_derivatives import ArrayDerivative
+        deriv = ArrayDerivative(self, *args, evaluate=evaluate)
+        # XXX This can rather changed to always return immutable matrix
+        if not isinstance(self, Basic) and evaluate:
+            return deriv.as_mutable()
+        return deriv
+
+    def _eval_derivative(self, arg):
+        return self.applyfunc(lambda x: x.diff(arg))
+
+    def integrate(self, *args, **kwargs):
+        """Integrate each element of the matrix.  ``args`` will
+        be passed to the ``integrate`` function.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.integrate((x, ))
+        Matrix([
+        [x**2/2, x*y],
+        [     x,   0]])
+        >>> M.integrate((x, 0, 2))
+        Matrix([
+        [2, 2*y],
+        [2,   0]])
+
+        See Also
+        ========
+
+        limit
+        diff
+        """
+        return self.applyfunc(lambda x: x.integrate(*args, **kwargs))
+
+    def jacobian(self, X):
+        """Calculates the Jacobian matrix (derivative of a vector-valued function).
+
+        Parameters
+        ==========
+
+        ``self`` : vector of expressions representing functions f_i(x_1, ..., x_n).
+        X : set of x_i's in order, it can be a list or a Matrix
+
+        Both ``self`` and X can be a row or a column matrix in any order
+        (i.e., jacobian() should always work).
+
+        Examples
+        ========
+
+        >>> from sympy import sin, cos, Matrix
+        >>> from sympy.abc import rho, phi
+        >>> X = Matrix([rho*cos(phi), rho*sin(phi), rho**2])
+        >>> Y = Matrix([rho, phi])
+        >>> X.jacobian(Y)
+        Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)],
+        [   2*rho,             0]])
+        >>> X = Matrix([rho*cos(phi), rho*sin(phi)])
+        >>> X.jacobian(Y)
+        Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)]])
+
+        See Also
+        ========
+
+        hessian
+        wronskian
+        """
+        if not isinstance(X, MatrixBase):
+            X = self._new(X)
+        # Both X and ``self`` can be a row or a column matrix, so we need to make
+        # sure all valid combinations work, but everything else fails:
+        if self.shape[0] == 1:
+            m = self.shape[1]
+        elif self.shape[1] == 1:
+            m = self.shape[0]
+        else:
+            raise TypeError("``self`` must be a row or a column matrix")
+        if X.shape[0] == 1:
+            n = X.shape[1]
+        elif X.shape[1] == 1:
+            n = X.shape[0]
+        else:
+            raise TypeError("X must be a row or a column matrix")
+
+        # m is the number of functions and n is the number of variables
+        # computing the Jacobian is now easy:
+        return self._new(m, n, lambda j, i: self[j].diff(X[i]))
+
+    def limit(self, *args):
+        """Calculate the limit of each element in the matrix.
+        ``args`` will be passed to the ``limit`` function.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.limit(x, 2)
+        Matrix([
+        [2, y],
+        [1, 0]])
+
+        See Also
+        ========
+
+        integrate
+        diff
+        """
+        return self.applyfunc(lambda x: x.limit(*args))
+
+
+# https://github.com/sympy/sympy/pull/12854
+class MatrixDeprecated(MatrixCommon):
+    """A class to house deprecated matrix methods."""
+    def berkowitz_charpoly(self, x=Dummy('lambda'), simplify=_simplify):
+        return self.charpoly(x=x)
+
+    def berkowitz_det(self):
+        """Computes determinant using Berkowitz method.
+
+        See Also
+        ========
+
+        det
+        berkowitz
+        """
+        return self.det(method='berkowitz')
+
+    def berkowitz_eigenvals(self, **flags):
+        """Computes eigenvalues of a Matrix using Berkowitz method.
+
+        See Also
+        ========
+
+        berkowitz
+        """
+        return self.eigenvals(**flags)
+
+    def berkowitz_minors(self):
+        """Computes principal minors using Berkowitz method.
+
+        See Also
+        ========
+
+        berkowitz
+        """
+        sign, minors = self.one, []
+
+        for poly in self.berkowitz():
+            minors.append(sign * poly[-1])
+            sign = -sign
+
+        return tuple(minors)
+
+    def berkowitz(self):
+        from sympy.matrices import zeros
+        berk = ((1,),)
+        if not self:
+            return berk
+
+        if not self.is_square:
+            raise NonSquareMatrixError()
+
+        A, N = self, self.rows
+        transforms = [0] * (N - 1)
+
+        for n in range(N, 1, -1):
+            T, k = zeros(n + 1, n), n - 1
+
+            R, C = -A[k, :k], A[:k, k]
+            A, a = A[:k, :k], -A[k, k]
+
+            items = [C]
+
+            for i in range(0, n - 2):
+                items.append(A * items[i])
+
+            for i, B in enumerate(items):
+                items[i] = (R * B)[0, 0]
+
+            items = [self.one, a] + items
+
+            for i in range(n):
+                T[i:, i] = items[:n - i + 1]
+
+            transforms[k - 1] = T
+
+        polys = [self._new([self.one, -A[0, 0]])]
+
+        for i, T in enumerate(transforms):
+            polys.append(T * polys[i])
+
+        return berk + tuple(map(tuple, polys))
+
+    def cofactorMatrix(self, method="berkowitz"):
+        return self.cofactor_matrix(method=method)
+
+    def det_bareis(self):
+        return _det_bareiss(self)
+
+    def det_LU_decomposition(self):
+        """Compute matrix determinant using LU decomposition.
+
+
+        Note that this method fails if the LU decomposition itself
+        fails. In particular, if the matrix has no inverse this method
+        will fail.
+
+        TODO: Implement algorithm for sparse matrices (SFF),
+        https://www.eecis.udel.edu/~saunders/papers/sffge/it5.ps
+
+        See Also
+        ========
+
+
+        det
+        det_bareiss
+        berkowitz_det
+        """
+        return self.det(method='lu')
+
+    def jordan_cell(self, eigenval, n):
+        return self.jordan_block(size=n, eigenvalue=eigenval)
+
+    def jordan_cells(self, calc_transformation=True):
+        P, J = self.jordan_form()
+        return P, J.get_diag_blocks()
+
+    def minorEntry(self, i, j, method="berkowitz"):
+        return self.minor(i, j, method=method)
+
+    def minorMatrix(self, i, j):
+        return self.minor_submatrix(i, j)
+
+    def permuteBkwd(self, perm):
+        """Permute the rows of the matrix with the given permutation in reverse."""
+        return self.permute_rows(perm, direction='backward')
+
+    def permuteFwd(self, perm):
+        """Permute the rows of the matrix with the given permutation."""
+        return self.permute_rows(perm, direction='forward')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/matrixbase.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/matrixbase.py
new file mode 100644
index 0000000000000000000000000000000000000000..49acc04043b30e003f7eed256f2e06e6a6556401
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/matrixbase.py
@@ -0,0 +1,5428 @@
+from __future__ import annotations
+from collections import defaultdict
+from collections.abc import Iterable
+from inspect import isfunction
+from functools import reduce
+
+from sympy.assumptions.refine import refine
+from sympy.core import SympifyError, Add
+from sympy.core.basic import Atom, Basic
+from sympy.core.kind import UndefinedKind
+from sympy.core.numbers import Integer
+from sympy.core.mod import Mod
+from sympy.core.symbol import Symbol, Dummy
+from sympy.core.sympify import sympify, _sympify
+from sympy.core.function import diff
+from sympy.polys import cancel
+from sympy.functions.elementary.complexes import Abs, re, im
+from sympy.printing import sstr
+from sympy.functions.elementary.miscellaneous import Max, Min, sqrt
+from sympy.functions.special.tensor_functions import KroneckerDelta, LeviCivita
+from sympy.core.singleton import S
+from sympy.printing.defaults import Printable
+from sympy.printing.str import StrPrinter
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.combinatorial.factorials import binomial, factorial
+
+import mpmath as mp
+from collections.abc import Callable
+from sympy.utilities.iterables import reshape
+from sympy.core.expr import Expr
+from sympy.core.power import Pow
+from sympy.core.symbol import uniquely_named_symbol
+
+from .utilities import _dotprodsimp, _simplify as _utilities_simplify
+from sympy.polys.polytools import Poly
+from sympy.utilities.iterables import flatten, is_sequence
+from sympy.utilities.misc import as_int, filldedent
+from sympy.core.decorators import call_highest_priority
+from sympy.core.logic import fuzzy_and, FuzzyBool
+from sympy.tensor.array import NDimArray
+from sympy.utilities.iterables import NotIterable
+
+from .utilities import _get_intermediate_simp_bool
+
+from .kind import MatrixKind
+
+from .exceptions import (
+    MatrixError, ShapeError, NonSquareMatrixError, NonInvertibleMatrixError,
+)
+
+from .utilities import _iszero, _is_zero_after_expand_mul
+
+from .determinant import (
+    _find_reasonable_pivot, _find_reasonable_pivot_naive,
+    _adjugate, _charpoly, _cofactor, _cofactor_matrix, _per,
+    _det, _det_bareiss, _det_berkowitz, _det_bird, _det_laplace, _det_LU,
+    _minor, _minor_submatrix)
+
+from .reductions import _is_echelon, _echelon_form, _rank, _rref
+
+from .solvers import (
+    _diagonal_solve, _lower_triangular_solve, _upper_triangular_solve,
+    _cholesky_solve, _LDLsolve, _LUsolve, _QRsolve, _gauss_jordan_solve,
+    _pinv_solve, _cramer_solve, _solve, _solve_least_squares)
+
+from .inverse import (
+    _pinv, _inv_ADJ, _inv_GE, _inv_LU, _inv_CH, _inv_LDL, _inv_QR,
+    _inv, _inv_block)
+
+from .subspaces import _columnspace, _nullspace, _rowspace, _orthogonalize
+
+from .eigen import (
+    _eigenvals, _eigenvects,
+    _bidiagonalize, _bidiagonal_decomposition,
+    _is_diagonalizable, _diagonalize,
+    _is_positive_definite, _is_positive_semidefinite,
+    _is_negative_definite, _is_negative_semidefinite, _is_indefinite,
+    _jordan_form, _left_eigenvects, _singular_values)
+
+from .decompositions import (
+    _rank_decomposition, _cholesky, _LDLdecomposition,
+    _LUdecomposition, _LUdecomposition_Simple, _LUdecompositionFF,
+    _singular_value_decomposition, _QRdecomposition, _upper_hessenberg_decomposition)
+
+from .graph import (
+    _connected_components, _connected_components_decomposition,
+    _strongly_connected_components, _strongly_connected_components_decomposition)
+
+
+__doctest_requires__ = {
+    ('MatrixBase.is_indefinite',
+     'MatrixBase.is_positive_definite',
+     'MatrixBase.is_positive_semidefinite',
+     'MatrixBase.is_negative_definite',
+     'MatrixBase.is_negative_semidefinite'): ['matplotlib'],
+}
+
+
+class MatrixBase(Printable):
+    """All common matrix operations including basic arithmetic, shaping,
+    and special matrices like `zeros`, and `eye`."""
+
+    _op_priority = 10.01
+
+    # Added just for numpy compatibility
+    __array_priority__ = 11
+
+    is_Matrix = True
+    _class_priority = 3
+    _sympify = staticmethod(sympify)
+    zero = S.Zero
+    one = S.One
+
+    _diff_wrt: bool = True
+    rows: int
+    cols: int
+    _simplify = None
+
+    @classmethod
+    def _new(cls, *args, **kwargs):
+        """`_new` must, at minimum, be callable as
+        `_new(rows, cols, mat) where mat is a flat list of the
+        elements of the matrix."""
+        raise NotImplementedError("Subclasses must implement this.")
+
+    def __eq__(self, other):
+        raise NotImplementedError("Subclasses must implement this.")
+
+    def __getitem__(self, key):
+        """Implementations of __getitem__ should accept ints, in which
+        case the matrix is indexed as a flat list, tuples (i,j) in which
+        case the (i,j) entry is returned, slices, or mixed tuples (a,b)
+        where a and b are any combination of slices and integers."""
+        raise NotImplementedError("Subclasses must implement this.")
+
+    @property
+    def shape(self):
+        """The shape (dimensions) of the matrix as the 2-tuple (rows, cols).
+
+        Examples
+        ========
+
+        >>> from sympy import zeros
+        >>> M = zeros(2, 3)
+        >>> M.shape
+        (2, 3)
+        >>> M.rows
+        2
+        >>> M.cols
+        3
+        """
+        return (self.rows, self.cols)
+
+    def _eval_col_del(self, col):
+        def entry(i, j):
+            return self[i, j] if j < col else self[i, j + 1]
+        return self._new(self.rows, self.cols - 1, entry)
+
+    def _eval_col_insert(self, pos, other):
+
+        def entry(i, j):
+            if j < pos:
+                return self[i, j]
+            elif pos <= j < pos + other.cols:
+                return other[i, j - pos]
+            return self[i, j - other.cols]
+
+        return self._new(self.rows, self.cols + other.cols, entry)
+
+    def _eval_col_join(self, other):
+        rows = self.rows
+
+        def entry(i, j):
+            if i < rows:
+                return self[i, j]
+            return other[i - rows, j]
+
+        return classof(self, other)._new(self.rows + other.rows, self.cols,
+                                         entry)
+
+    def _eval_extract(self, rowsList, colsList):
+        mat = list(self)
+        cols = self.cols
+        indices = (i * cols + j for i in rowsList for j in colsList)
+        return self._new(len(rowsList), len(colsList),
+                         [mat[i] for i in indices])
+
+    def _eval_get_diag_blocks(self):
+        sub_blocks = []
+
+        def recurse_sub_blocks(M):
+            for i in range(1, M.shape[0] + 1):
+                if i == 1:
+                    to_the_right = M[0, i:]
+                    to_the_bottom = M[i:, 0]
+                else:
+                    to_the_right = M[:i, i:]
+                    to_the_bottom = M[i:, :i]
+                if any(to_the_right) or any(to_the_bottom):
+                    continue
+                sub_blocks.append(M[:i, :i])
+                if M.shape != M[:i, :i].shape:
+                    recurse_sub_blocks(M[i:, i:])
+                return
+
+        recurse_sub_blocks(self)
+        return sub_blocks
+
+    def _eval_row_del(self, row):
+        def entry(i, j):
+            return self[i, j] if i < row else self[i + 1, j]
+        return self._new(self.rows - 1, self.cols, entry)
+
+    def _eval_row_insert(self, pos, other):
+        entries = list(self)
+        insert_pos = pos * self.cols
+        entries[insert_pos:insert_pos] = list(other)
+        return self._new(self.rows + other.rows, self.cols, entries)
+
+    def _eval_row_join(self, other):
+        cols = self.cols
+
+        def entry(i, j):
+            if j < cols:
+                return self[i, j]
+            return other[i, j - cols]
+
+        return classof(self, other)._new(self.rows, self.cols + other.cols,
+                                         entry)
+
+    def _eval_tolist(self):
+        return [list(self[i,:]) for i in range(self.rows)]
+
+    def _eval_todok(self):
+        dok = {}
+        rows, cols = self.shape
+        for i in range(rows):
+            for j in range(cols):
+                val = self[i, j]
+                if val != self.zero:
+                    dok[i, j] = val
+        return dok
+
+    @classmethod
+    def _eval_from_dok(cls, rows, cols, dok):
+        out_flat = [cls.zero] * (rows * cols)
+        for (i, j), val in dok.items():
+            out_flat[i * cols + j] = val
+        return cls._new(rows, cols, out_flat)
+
+    def _eval_vec(self):
+        rows = self.rows
+
+        def entry(n, _):
+            # we want to read off the columns first
+            j = n // rows
+            i = n - j * rows
+            return self[i, j]
+
+        return self._new(len(self), 1, entry)
+
+    def _eval_vech(self, diagonal):
+        c = self.cols
+        v = []
+        if diagonal:
+            for j in range(c):
+                for i in range(j, c):
+                    v.append(self[i, j])
+        else:
+            for j in range(c):
+                for i in range(j + 1, c):
+                    v.append(self[i, j])
+        return self._new(len(v), 1, v)
+
+    def col_del(self, col):
+        """Delete the specified column."""
+        if col < 0:
+            col += self.cols
+        if not 0 <= col < self.cols:
+            raise IndexError("Column {} is out of range.".format(col))
+        return self._eval_col_del(col)
+
+    def col_insert(self, pos, other):
+        """Insert one or more columns at the given column position.
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(3, 1)
+        >>> M.col_insert(1, V)
+        Matrix([
+        [0, 1, 0, 0],
+        [0, 1, 0, 0],
+        [0, 1, 0, 0]])
+
+        See Also
+        ========
+
+        col
+        row_insert
+        """
+        # Allows you to build a matrix even if it is null matrix
+        if not self:
+            return type(self)(other)
+
+        pos = as_int(pos)
+
+        if pos < 0:
+            pos = self.cols + pos
+        if pos < 0:
+            pos = 0
+        elif pos > self.cols:
+            pos = self.cols
+
+        if self.rows != other.rows:
+            raise ShapeError(
+                "The matrices have incompatible number of rows ({} and {})"
+                .format(self.rows, other.rows))
+
+        return self._eval_col_insert(pos, other)
+
+    def col_join(self, other):
+        """Concatenates two matrices along self's last and other's first row.
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(1, 3)
+        >>> M.col_join(V)
+        Matrix([
+        [0, 0, 0],
+        [0, 0, 0],
+        [0, 0, 0],
+        [1, 1, 1]])
+
+        See Also
+        ========
+
+        col
+        row_join
+        """
+        # A null matrix can always be stacked (see  #10770)
+        if self.rows == 0 and self.cols != other.cols:
+            return self._new(0, other.cols, []).col_join(other)
+
+        if self.cols != other.cols:
+            raise ShapeError(
+                "The matrices have incompatible number of columns ({} and {})"
+                .format(self.cols, other.cols))
+        return self._eval_col_join(other)
+
+    def col(self, j):
+        """Elementary column selector.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> eye(2).col(0)
+        Matrix([
+        [1],
+        [0]])
+
+        See Also
+        ========
+
+        row
+        col_del
+        col_join
+        col_insert
+        """
+        return self[:, j]
+
+    def extract(self, rowsList, colsList):
+        r"""Return a submatrix by specifying a list of rows and columns.
+        Negative indices can be given. All indices must be in the range
+        $-n \le i < n$ where $n$ is the number of rows or columns.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(4, 3, range(12))
+        >>> m
+        Matrix([
+        [0,  1,  2],
+        [3,  4,  5],
+        [6,  7,  8],
+        [9, 10, 11]])
+        >>> m.extract([0, 1, 3], [0, 1])
+        Matrix([
+        [0,  1],
+        [3,  4],
+        [9, 10]])
+
+        Rows or columns can be repeated:
+
+        >>> m.extract([0, 0, 1], [-1])
+        Matrix([
+        [2],
+        [2],
+        [5]])
+
+        Every other row can be taken by using range to provide the indices:
+
+        >>> m.extract(range(0, m.rows, 2), [-1])
+        Matrix([
+        [2],
+        [8]])
+
+        RowsList or colsList can also be a list of booleans, in which case
+        the rows or columns corresponding to the True values will be selected:
+
+        >>> m.extract([0, 1, 2, 3], [True, False, True])
+        Matrix([
+        [0,  2],
+        [3,  5],
+        [6,  8],
+        [9, 11]])
+        """
+
+        if not is_sequence(rowsList) or not is_sequence(colsList):
+            raise TypeError("rowsList and colsList must be iterable")
+        # ensure rowsList and colsList are lists of integers
+        if rowsList and all(isinstance(i, bool) for i in rowsList):
+            rowsList = [index for index, item in enumerate(rowsList) if item]
+        if colsList and all(isinstance(i, bool) for i in colsList):
+            colsList = [index for index, item in enumerate(colsList) if item]
+
+        # ensure everything is in range
+        rowsList = [a2idx(k, self.rows) for k in rowsList]
+        colsList = [a2idx(k, self.cols) for k in colsList]
+
+        return self._eval_extract(rowsList, colsList)
+
+    def get_diag_blocks(self):
+        """Obtains the square sub-matrices on the main diagonal of a square matrix.
+
+        Useful for inverting symbolic matrices or solving systems of
+        linear equations which may be decoupled by having a block diagonal
+        structure.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y, z
+        >>> A = Matrix([[1, 3, 0, 0], [y, z*z, 0, 0], [0, 0, x, 0], [0, 0, 0, 0]])
+        >>> a1, a2, a3 = A.get_diag_blocks()
+        >>> a1
+        Matrix([
+        [1,    3],
+        [y, z**2]])
+        >>> a2
+        Matrix([[x]])
+        >>> a3
+        Matrix([[0]])
+
+        """
+        return self._eval_get_diag_blocks()
+
+    @classmethod
+    def hstack(cls, *args):
+        """Return a matrix formed by joining args horizontally (i.e.
+        by repeated application of row_join).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, eye
+        >>> Matrix.hstack(eye(2), 2*eye(2))
+        Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2]])
+        """
+        if len(args) == 0:
+            return cls._new()
+
+        kls = type(args[0])
+        return reduce(kls.row_join, args)
+
+    def reshape(self, rows, cols):
+        """Reshape the matrix. Total number of elements must remain the same.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 3, lambda i, j: 1)
+        >>> m
+        Matrix([
+        [1, 1, 1],
+        [1, 1, 1]])
+        >>> m.reshape(1, 6)
+        Matrix([[1, 1, 1, 1, 1, 1]])
+        >>> m.reshape(3, 2)
+        Matrix([
+        [1, 1],
+        [1, 1],
+        [1, 1]])
+
+        """
+        if self.rows * self.cols != rows * cols:
+            raise ValueError("Invalid reshape parameters %d %d" % (rows, cols))
+        dok = {divmod(i*self.cols + j, cols):
+            v for (i, j), v in self.todok().items()}
+        return self._eval_from_dok(rows, cols, dok)
+
+    def row_del(self, row):
+        """Delete the specified row."""
+        if row < 0:
+            row += self.rows
+        if not 0 <= row < self.rows:
+            raise IndexError("Row {} is out of range.".format(row))
+
+        return self._eval_row_del(row)
+
+    def row_insert(self, pos, other):
+        """Insert one or more rows at the given row position.
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(1, 3)
+        >>> M.row_insert(1, V)
+        Matrix([
+        [0, 0, 0],
+        [1, 1, 1],
+        [0, 0, 0],
+        [0, 0, 0]])
+
+        See Also
+        ========
+
+        row
+        col_insert
+        """
+        # Allows you to build a matrix even if it is null matrix
+        if not self:
+            return self._new(other)
+
+        pos = as_int(pos)
+
+        if pos < 0:
+            pos = self.rows + pos
+        if pos < 0:
+            pos = 0
+        elif pos > self.rows:
+            pos = self.rows
+
+        if self.cols != other.cols:
+            raise ShapeError(
+                "The matrices have incompatible number of columns ({} and {})"
+                .format(self.cols, other.cols))
+
+        return self._eval_row_insert(pos, other)
+
+    def row_join(self, other):
+        """Concatenates two matrices along self's last and rhs's first column
+
+        Examples
+        ========
+
+        >>> from sympy import zeros, ones
+        >>> M = zeros(3)
+        >>> V = ones(3, 1)
+        >>> M.row_join(V)
+        Matrix([
+        [0, 0, 0, 1],
+        [0, 0, 0, 1],
+        [0, 0, 0, 1]])
+
+        See Also
+        ========
+
+        row
+        col_join
+        """
+        # A null matrix can always be stacked (see  #10770)
+        if self.cols == 0 and self.rows != other.rows:
+            return self._new(other.rows, 0, []).row_join(other)
+
+        if self.rows != other.rows:
+            raise ShapeError(
+                "The matrices have incompatible number of rows ({} and {})"
+                .format(self.rows, other.rows))
+        return self._eval_row_join(other)
+
+    def diagonal(self, k=0):
+        """Returns the kth diagonal of self. The main diagonal
+        corresponds to `k=0`; diagonals above and below correspond to
+        `k > 0` and `k < 0`, respectively. The values of `self[i, j]`
+        for which `j - i = k`, are returned in order of increasing
+        `i + j`, starting with `i + j = |k|`.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(3, 3, lambda i, j: j - i); m
+        Matrix([
+        [ 0,  1, 2],
+        [-1,  0, 1],
+        [-2, -1, 0]])
+        >>> _.diagonal()
+        Matrix([[0, 0, 0]])
+        >>> m.diagonal(1)
+        Matrix([[1, 1]])
+        >>> m.diagonal(-2)
+        Matrix([[-2]])
+
+        Even though the diagonal is returned as a Matrix, the element
+        retrieval can be done with a single index:
+
+        >>> Matrix.diag(1, 2, 3).diagonal()[1]  # instead of [0, 1]
+        2
+
+        See Also
+        ========
+
+        diag
+        """
+        rv = []
+        k = as_int(k)
+        r = 0 if k > 0 else -k
+        c = 0 if r else k
+        while True:
+            if r == self.rows or c == self.cols:
+                break
+            rv.append(self[r, c])
+            r += 1
+            c += 1
+        if not rv:
+            raise ValueError(filldedent('''
+            The %s diagonal is out of range [%s, %s]''' % (
+            k, 1 - self.rows, self.cols - 1)))
+        return self._new(1, len(rv), rv)
+
+    def row(self, i):
+        """Elementary row selector.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> eye(2).row(0)
+        Matrix([[1, 0]])
+
+        See Also
+        ========
+
+        col
+        row_del
+        row_join
+        row_insert
+        """
+        return self[i, :]
+
+    def todok(self):
+        """Return the matrix as dictionary of keys.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix.eye(3)
+        >>> M.todok()
+        {(0, 0): 1, (1, 1): 1, (2, 2): 1}
+        """
+        return self._eval_todok()
+
+    @classmethod
+    def from_dok(cls, rows, cols, dok):
+        """Create a matrix from a dictionary of keys.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> d = {(0, 0): 1, (1, 2): 3, (2, 1): 4}
+        >>> Matrix.from_dok(3, 3, d)
+        Matrix([
+        [1, 0, 0],
+        [0, 0, 3],
+        [0, 4, 0]])
+        """
+        dok = {ij: cls._sympify(val) for ij, val in dok.items()}
+        return cls._eval_from_dok(rows, cols, dok)
+
+    def tolist(self):
+        """Return the Matrix as a nested Python list.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, ones
+        >>> m = Matrix(3, 3, range(9))
+        >>> m
+        Matrix([
+        [0, 1, 2],
+        [3, 4, 5],
+        [6, 7, 8]])
+        >>> m.tolist()
+        [[0, 1, 2], [3, 4, 5], [6, 7, 8]]
+        >>> ones(3, 0).tolist()
+        [[], [], []]
+
+        When there are no rows then it will not be possible to tell how
+        many columns were in the original matrix:
+
+        >>> ones(0, 3).tolist()
+        []
+
+        """
+        if not self.rows:
+            return []
+        if not self.cols:
+            return [[] for i in range(self.rows)]
+        return self._eval_tolist()
+
+    def todod(M):
+        """Returns matrix as dict of dicts containing non-zero elements of the Matrix
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[0, 1],[0, 3]])
+        >>> A
+        Matrix([
+        [0, 1],
+        [0, 3]])
+        >>> A.todod()
+        {0: {1: 1}, 1: {1: 3}}
+
+
+        """
+        rowsdict = {}
+        Mlol = M.tolist()
+        for i, Mi in enumerate(Mlol):
+            row = {j: Mij for j, Mij in enumerate(Mi) if Mij}
+            if row:
+                rowsdict[i] = row
+        return rowsdict
+
+    def vec(self):
+        """Return the Matrix converted into a one column matrix by stacking columns
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m=Matrix([[1, 3], [2, 4]])
+        >>> m
+        Matrix([
+        [1, 3],
+        [2, 4]])
+        >>> m.vec()
+        Matrix([
+        [1],
+        [2],
+        [3],
+        [4]])
+
+        See Also
+        ========
+
+        vech
+        """
+        return self._eval_vec()
+
+    def vech(self, diagonal=True, check_symmetry=True):
+        """Reshapes the matrix into a column vector by stacking the
+        elements in the lower triangle.
+
+        Parameters
+        ==========
+
+        diagonal : bool, optional
+            If ``True``, it includes the diagonal elements.
+
+        check_symmetry : bool, optional
+            If ``True``, it checks whether the matrix is symmetric.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m=Matrix([[1, 2], [2, 3]])
+        >>> m
+        Matrix([
+        [1, 2],
+        [2, 3]])
+        >>> m.vech()
+        Matrix([
+        [1],
+        [2],
+        [3]])
+        >>> m.vech(diagonal=False)
+        Matrix([[2]])
+
+        Notes
+        =====
+
+        This should work for symmetric matrices and ``vech`` can
+        represent symmetric matrices in vector form with less size than
+        ``vec``.
+
+        See Also
+        ========
+
+        vec
+        """
+        if not self.is_square:
+            raise NonSquareMatrixError
+
+        if check_symmetry and not self.is_symmetric():
+            raise ValueError("The matrix is not symmetric.")
+
+        return self._eval_vech(diagonal)
+
+    @classmethod
+    def vstack(cls, *args):
+        """Return a matrix formed by joining args vertically (i.e.
+        by repeated application of col_join).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, eye
+        >>> Matrix.vstack(eye(2), 2*eye(2))
+        Matrix([
+        [1, 0],
+        [0, 1],
+        [2, 0],
+        [0, 2]])
+        """
+        if len(args) == 0:
+            return cls._new()
+
+        kls = type(args[0])
+        return reduce(kls.col_join, args)
+
+    @classmethod
+    def _eval_diag(cls, rows, cols, diag_dict):
+        """diag_dict is a defaultdict containing
+        all the entries of the diagonal matrix."""
+        def entry(i, j):
+            return diag_dict[(i, j)]
+        return cls._new(rows, cols, entry)
+
+    @classmethod
+    def _eval_eye(cls, rows, cols):
+        vals = [cls.zero]*(rows*cols)
+        vals[::cols+1] = [cls.one]*min(rows, cols)
+        return cls._new(rows, cols, vals, copy=False)
+
+    @classmethod
+    def _eval_jordan_block(cls, size: int, eigenvalue, band='upper'):
+        if band == 'lower':
+            def entry(i, j):
+                if i == j:
+                    return eigenvalue
+                elif j + 1 == i:
+                    return cls.one
+                return cls.zero
+        else:
+            def entry(i, j):
+                if i == j:
+                    return eigenvalue
+                elif i + 1 == j:
+                    return cls.one
+                return cls.zero
+        return cls._new(size, size, entry)
+
+    @classmethod
+    def _eval_ones(cls, rows, cols):
+        def entry(i, j):
+            return cls.one
+        return cls._new(rows, cols, entry)
+
+    @classmethod
+    def _eval_zeros(cls, rows, cols):
+        return cls._new(rows, cols, [cls.zero]*(rows*cols), copy=False)
+
+    @classmethod
+    def _eval_wilkinson(cls, n):
+        def entry(i, j):
+            return cls.one if i + 1 == j else cls.zero
+
+        D = cls._new(2*n + 1, 2*n + 1, entry)
+
+        wminus = cls.diag(list(range(-n, n + 1)), unpack=True) + D + D.T
+        wplus = abs(cls.diag(list(range(-n, n + 1)), unpack=True)) + D + D.T
+
+        return wminus, wplus
+
+    @classmethod
+    def diag(kls, *args, strict=False, unpack=True, rows=None, cols=None, **kwargs):
+        """Returns a matrix with the specified diagonal.
+        If matrices are passed, a block-diagonal matrix
+        is created (i.e. the "direct sum" of the matrices).
+
+        kwargs
+        ======
+
+        rows : rows of the resulting matrix; computed if
+               not given.
+
+        cols : columns of the resulting matrix; computed if
+               not given.
+
+        cls : class for the resulting matrix
+
+        unpack : bool which, when True (default), unpacks a single
+        sequence rather than interpreting it as a Matrix.
+
+        strict : bool which, when False (default), allows Matrices to
+        have variable-length rows.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> Matrix.diag(1, 2, 3)
+        Matrix([
+        [1, 0, 0],
+        [0, 2, 0],
+        [0, 0, 3]])
+
+        The current default is to unpack a single sequence. If this is
+        not desired, set `unpack=False` and it will be interpreted as
+        a matrix.
+
+        >>> Matrix.diag([1, 2, 3]) == Matrix.diag(1, 2, 3)
+        True
+
+        When more than one element is passed, each is interpreted as
+        something to put on the diagonal. Lists are converted to
+        matrices. Filling of the diagonal always continues from
+        the bottom right hand corner of the previous item: this
+        will create a block-diagonal matrix whether the matrices
+        are square or not.
+
+        >>> col = [1, 2, 3]
+        >>> row = [[4, 5]]
+        >>> Matrix.diag(col, row)
+        Matrix([
+        [1, 0, 0],
+        [2, 0, 0],
+        [3, 0, 0],
+        [0, 4, 5]])
+
+        When `unpack` is False, elements within a list need not all be
+        of the same length. Setting `strict` to True would raise a
+        ValueError for the following:
+
+        >>> Matrix.diag([[1, 2, 3], [4, 5], [6]], unpack=False)
+        Matrix([
+        [1, 2, 3],
+        [4, 5, 0],
+        [6, 0, 0]])
+
+        The type of the returned matrix can be set with the ``cls``
+        keyword.
+
+        >>> from sympy import ImmutableMatrix
+        >>> from sympy.utilities.misc import func_name
+        >>> func_name(Matrix.diag(1, cls=ImmutableMatrix))
+        'ImmutableDenseMatrix'
+
+        A zero dimension matrix can be used to position the start of
+        the filling at the start of an arbitrary row or column:
+
+        >>> from sympy import ones
+        >>> r2 = ones(0, 2)
+        >>> Matrix.diag(r2, 1, 2)
+        Matrix([
+        [0, 0, 1, 0],
+        [0, 0, 0, 2]])
+
+        See Also
+        ========
+        eye
+        diagonal
+        .dense.diag
+        .expressions.blockmatrix.BlockMatrix
+        .sparsetools.banded
+       """
+        from sympy.matrices.matrixbase import MatrixBase
+        from sympy.matrices.dense import Matrix
+        from sympy.matrices import SparseMatrix
+        klass = kwargs.get('cls', kls)
+        if unpack and len(args) == 1 and is_sequence(args[0]) and \
+                not isinstance(args[0], MatrixBase):
+            args = args[0]
+
+        # fill a default dict with the diagonal entries
+        diag_entries = defaultdict(int)
+        rmax = cmax = 0  # keep track of the biggest index seen
+        for m in args:
+            if isinstance(m, list):
+                if strict:
+                    # if malformed, Matrix will raise an error
+                    _ = Matrix(m)
+                    r, c = _.shape
+                    m = _.tolist()
+                else:
+                    r, c, smat = SparseMatrix._handle_creation_inputs(m)
+                    for (i, j), _ in smat.items():
+                        diag_entries[(i + rmax, j + cmax)] = _
+                    m = []  # to skip process below
+            elif hasattr(m, 'shape'):  # a Matrix
+                # convert to list of lists
+                r, c = m.shape
+                m = m.tolist()
+            else:  # in this case, we're a single value
+                diag_entries[(rmax, cmax)] = m
+                rmax += 1
+                cmax += 1
+                continue
+            # process list of lists
+            for i, mi in enumerate(m):
+                for j, _ in enumerate(mi):
+                    diag_entries[(i + rmax, j + cmax)] = _
+            rmax += r
+            cmax += c
+        if rows is None:
+            rows, cols = cols, rows
+        if rows is None:
+            rows, cols = rmax, cmax
+        else:
+            cols = rows if cols is None else cols
+        if rows < rmax or cols < cmax:
+            raise ValueError(filldedent('''
+                The constructed matrix is {} x {} but a size of {} x {}
+                was specified.'''.format(rmax, cmax, rows, cols)))
+        return klass._eval_diag(rows, cols, diag_entries)
+
+    @classmethod
+    def eye(kls, rows, cols=None, **kwargs):
+        """Returns an identity matrix.
+
+        Parameters
+        ==========
+
+        rows : rows of the matrix
+        cols : cols of the matrix (if None, cols=rows)
+
+        kwargs
+        ======
+        cls : class of the returned matrix
+        """
+        if cols is None:
+            cols = rows
+        if rows < 0 or cols < 0:
+            raise ValueError("Cannot create a {} x {} matrix. "
+                             "Both dimensions must be positive".format(rows, cols))
+        klass = kwargs.get('cls', kls)
+        rows, cols = as_int(rows), as_int(cols)
+
+        return klass._eval_eye(rows, cols)
+
+    @classmethod
+    def jordan_block(kls, size=None, eigenvalue=None, *, band='upper', **kwargs):
+        """Returns a Jordan block
+
+        Parameters
+        ==========
+
+        size : Integer, optional
+            Specifies the shape of the Jordan block matrix.
+
+        eigenvalue : Number or Symbol
+            Specifies the value for the main diagonal of the matrix.
+
+            .. note::
+                The keyword ``eigenval`` is also specified as an alias
+                of this keyword, but it is not recommended to use.
+
+                We may deprecate the alias in later release.
+
+        band : 'upper' or 'lower', optional
+            Specifies the position of the off-diagonal to put `1` s on.
+
+        cls : Matrix, optional
+            Specifies the matrix class of the output form.
+
+            If it is not specified, the class type where the method is
+            being executed on will be returned.
+
+        Returns
+        =======
+
+        Matrix
+            A Jordan block matrix.
+
+        Raises
+        ======
+
+        ValueError
+            If insufficient arguments are given for matrix size
+            specification, or no eigenvalue is given.
+
+        Examples
+        ========
+
+        Creating a default Jordan block:
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x
+        >>> Matrix.jordan_block(4, x)
+        Matrix([
+        [x, 1, 0, 0],
+        [0, x, 1, 0],
+        [0, 0, x, 1],
+        [0, 0, 0, x]])
+
+        Creating an alternative Jordan block matrix where `1` is on
+        lower off-diagonal:
+
+        >>> Matrix.jordan_block(4, x, band='lower')
+        Matrix([
+        [x, 0, 0, 0],
+        [1, x, 0, 0],
+        [0, 1, x, 0],
+        [0, 0, 1, x]])
+
+        Creating a Jordan block with keyword arguments
+
+        >>> Matrix.jordan_block(size=4, eigenvalue=x)
+        Matrix([
+        [x, 1, 0, 0],
+        [0, x, 1, 0],
+        [0, 0, x, 1],
+        [0, 0, 0, x]])
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Jordan_matrix
+        """
+        klass = kwargs.pop('cls', kls)
+
+        eigenval = kwargs.get('eigenval', None)
+        if eigenvalue is None and eigenval is None:
+            raise ValueError("Must supply an eigenvalue")
+        elif eigenvalue != eigenval and None not in (eigenval, eigenvalue):
+            raise ValueError(
+                "Inconsistent values are given: 'eigenval'={}, "
+                "'eigenvalue'={}".format(eigenval, eigenvalue))
+        else:
+            if eigenval is not None:
+                eigenvalue = eigenval
+
+        if size is None:
+            raise ValueError("Must supply a matrix size")
+
+        size = as_int(size)
+        return klass._eval_jordan_block(size, eigenvalue, band)
+
+    @classmethod
+    def ones(kls, rows, cols=None, **kwargs):
+        """Returns a matrix of ones.
+
+        Parameters
+        ==========
+
+        rows : rows of the matrix
+        cols : cols of the matrix (if None, cols=rows)
+
+        kwargs
+        ======
+        cls : class of the returned matrix
+        """
+        if cols is None:
+            cols = rows
+        klass = kwargs.get('cls', kls)
+        rows, cols = as_int(rows), as_int(cols)
+
+        return klass._eval_ones(rows, cols)
+
+    @classmethod
+    def zeros(kls, rows, cols=None, **kwargs):
+        """Returns a matrix of zeros.
+
+        Parameters
+        ==========
+
+        rows : rows of the matrix
+        cols : cols of the matrix (if None, cols=rows)
+
+        kwargs
+        ======
+        cls : class of the returned matrix
+        """
+        if cols is None:
+            cols = rows
+        if rows < 0 or cols < 0:
+            raise ValueError("Cannot create a {} x {} matrix. "
+                             "Both dimensions must be positive".format(rows, cols))
+        klass = kwargs.get('cls', kls)
+        rows, cols = as_int(rows), as_int(cols)
+
+        return klass._eval_zeros(rows, cols)
+
+    @classmethod
+    def companion(kls, poly):
+        """Returns a companion matrix of a polynomial.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, Poly, Symbol, symbols
+        >>> x = Symbol('x')
+        >>> c0, c1, c2, c3, c4 = symbols('c0:5')
+        >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x)
+        >>> Matrix.companion(p)
+        Matrix([
+        [0, 0, 0, 0, -c0],
+        [1, 0, 0, 0, -c1],
+        [0, 1, 0, 0, -c2],
+        [0, 0, 1, 0, -c3],
+        [0, 0, 0, 1, -c4]])
+        """
+        poly = kls._sympify(poly)
+        if not isinstance(poly, Poly):
+            raise ValueError("{} must be a Poly instance.".format(poly))
+        if not poly.is_monic:
+            raise ValueError("{} must be a monic polynomial.".format(poly))
+        if not poly.is_univariate:
+            raise ValueError(
+                "{} must be a univariate polynomial.".format(poly))
+
+        size = poly.degree()
+        if not size >= 1:
+            raise ValueError(
+                "{} must have degree not less than 1.".format(poly))
+
+        coeffs = poly.all_coeffs()
+        def entry(i, j):
+            if j == size - 1:
+                return -coeffs[-1 - i]
+            elif i == j + 1:
+                return kls.one
+            return kls.zero
+        return kls._new(size, size, entry)
+
+
+    @classmethod
+    def wilkinson(kls, n, **kwargs):
+        """Returns two square Wilkinson Matrix of size 2*n + 1
+        $W_{2n + 1}^-, W_{2n + 1}^+ =$ Wilkinson(n)
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> wminus, wplus = Matrix.wilkinson(3)
+        >>> wminus
+        Matrix([
+        [-3,  1,  0, 0, 0, 0, 0],
+        [ 1, -2,  1, 0, 0, 0, 0],
+        [ 0,  1, -1, 1, 0, 0, 0],
+        [ 0,  0,  1, 0, 1, 0, 0],
+        [ 0,  0,  0, 1, 1, 1, 0],
+        [ 0,  0,  0, 0, 1, 2, 1],
+        [ 0,  0,  0, 0, 0, 1, 3]])
+        >>> wplus
+        Matrix([
+        [3, 1, 0, 0, 0, 0, 0],
+        [1, 2, 1, 0, 0, 0, 0],
+        [0, 1, 1, 1, 0, 0, 0],
+        [0, 0, 1, 0, 1, 0, 0],
+        [0, 0, 0, 1, 1, 1, 0],
+        [0, 0, 0, 0, 1, 2, 1],
+        [0, 0, 0, 0, 0, 1, 3]])
+
+        References
+        ==========
+
+        .. [1] https://blogs.mathworks.com/cleve/2013/04/15/wilkinsons-matrices-2/
+        .. [2] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Claredon Press, Oxford, 1965, 662 pp.
+
+        """
+        klass = kwargs.get('cls', kls)
+        n = as_int(n)
+        return klass._eval_wilkinson(n)
+
+    # The RepMatrix subclass uses more efficient sparse implementations of
+    # _eval_iter_values and other things.
+
+    def _eval_iter_values(self):
+        return (i for i in self if i is not S.Zero)
+
+    def _eval_values(self):
+        return list(self.iter_values())
+
+    def _eval_iter_items(self):
+        for i in range(self.rows):
+            for j in range(self.cols):
+                if self[i, j]:
+                    yield (i, j), self[i, j]
+
+    def _eval_atoms(self, *types):
+        values = self.values()
+        if len(values) < self.rows * self.cols and isinstance(S.Zero, types):
+            s = {S.Zero}
+        else:
+            s = set()
+        return s.union(*[v.atoms(*types) for v in values])
+
+    def _eval_free_symbols(self):
+        return set().union(*(i.free_symbols for i in set(self.values())))
+
+    def _eval_has(self, *patterns):
+        return any(a.has(*patterns) for a in self.iter_values())
+
+    def _eval_is_symbolic(self):
+        return self.has(Symbol)
+
+    # _eval_is_hermitian is called by some general SymPy
+    # routines and has a different *args signature.  Make
+    # sure the names don't clash by adding `_matrix_` in name.
+    def _eval_is_matrix_hermitian(self, simpfunc):
+        herm = lambda i, j: simpfunc(self[i, j] - self[j, i].adjoint()).is_zero
+        return fuzzy_and(herm(i, j) for (i, j), v in self.iter_items())
+
+    def _eval_is_zero_matrix(self):
+        return fuzzy_and(v.is_zero for v in self.iter_values())
+
+    def _eval_is_Identity(self) -> FuzzyBool:
+        one = self.one
+        zero = self.zero
+        ident = lambda i, j, v: v is one if i == j else v is zero
+        return all(ident(i, j, v) for (i, j), v in self.iter_items())
+
+    def _eval_is_diagonal(self):
+        return fuzzy_and(v.is_zero for (i, j), v in self.iter_items() if i != j)
+
+    def _eval_is_lower(self):
+        return all(v.is_zero for (i, j), v in self.iter_items() if i < j)
+
+    def _eval_is_upper(self):
+        return all(v.is_zero for (i, j), v in self.iter_items() if i > j)
+
+    def _eval_is_lower_hessenberg(self):
+        return all(v.is_zero for (i, j), v in self.iter_items() if i + 1 < j)
+
+    def _eval_is_upper_hessenberg(self):
+        return all(v.is_zero for (i, j), v in self.iter_items() if i > j + 1)
+
+    def _eval_is_symmetric(self, simpfunc):
+        sym = lambda i, j: simpfunc(self[i, j] - self[j, i]).is_zero
+        return fuzzy_and(sym(i, j) for (i, j), v in self.iter_items())
+
+    def _eval_is_anti_symmetric(self, simpfunc):
+        anti = lambda i, j: simpfunc(self[i, j] + self[j, i]).is_zero
+        return fuzzy_and(anti(i, j) for (i, j), v in self.iter_items())
+
+    def _has_positive_diagonals(self):
+        diagonal_entries = (self[i, i] for i in range(self.rows))
+        return fuzzy_and(x.is_positive for x in diagonal_entries)
+
+    def _has_nonnegative_diagonals(self):
+        diagonal_entries = (self[i, i] for i in range(self.rows))
+        return fuzzy_and(x.is_nonnegative for x in diagonal_entries)
+
+    def atoms(self, *types):
+        """Returns the atoms that form the current object.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import Matrix
+        >>> Matrix([[x]])
+        Matrix([[x]])
+        >>> _.atoms()
+        {x}
+        >>> Matrix([[x, y], [y, x]])
+        Matrix([
+        [x, y],
+        [y, x]])
+        >>> _.atoms()
+        {x, y}
+        """
+
+        types = tuple(t if isinstance(t, type) else type(t) for t in types)
+        if not types:
+            types = (Atom,)
+        return self._eval_atoms(*types)
+
+    @property
+    def free_symbols(self):
+        """Returns the free symbols within the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> from sympy import Matrix
+        >>> Matrix([[x], [1]]).free_symbols
+        {x}
+        """
+        return self._eval_free_symbols()
+
+    def has(self, *patterns):
+        """Test whether any subexpression matches any of the patterns.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, SparseMatrix, Float
+        >>> from sympy.abc import x, y
+        >>> A = Matrix(((1, x), (0.2, 3)))
+        >>> B = SparseMatrix(((1, x), (0.2, 3)))
+        >>> A.has(x)
+        True
+        >>> A.has(y)
+        False
+        >>> A.has(Float)
+        True
+        >>> B.has(x)
+        True
+        >>> B.has(y)
+        False
+        >>> B.has(Float)
+        True
+        """
+        return self._eval_has(*patterns)
+
+    def is_anti_symmetric(self, simplify=True):
+        """Check if matrix M is an antisymmetric matrix,
+        that is, M is a square matrix with all M[i, j] == -M[j, i].
+
+        When ``simplify=True`` (default), the sum M[i, j] + M[j, i] is
+        simplified before testing to see if it is zero. By default,
+        the SymPy simplify function is used. To use a custom function
+        set simplify to a function that accepts a single argument which
+        returns a simplified expression. To skip simplification, set
+        simplify to False but note that although this will be faster,
+        it may induce false negatives.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, symbols
+        >>> m = Matrix(2, 2, [0, 1, -1, 0])
+        >>> m
+        Matrix([
+        [ 0, 1],
+        [-1, 0]])
+        >>> m.is_anti_symmetric()
+        True
+        >>> x, y = symbols('x y')
+        >>> m = Matrix(2, 3, [0, 0, x, -y, 0, 0])
+        >>> m
+        Matrix([
+        [ 0, 0, x],
+        [-y, 0, 0]])
+        >>> m.is_anti_symmetric()
+        False
+
+        >>> from sympy.abc import x, y
+        >>> m = Matrix(3, 3, [0, x**2 + 2*x + 1, y,
+        ...                   -(x + 1)**2, 0, x*y,
+        ...                   -y, -x*y, 0])
+
+        Simplification of matrix elements is done by default so even
+        though two elements which should be equal and opposite would not
+        pass an equality test, the matrix is still reported as
+        anti-symmetric:
+
+        >>> m[0, 1] == -m[1, 0]
+        False
+        >>> m.is_anti_symmetric()
+        True
+
+        If ``simplify=False`` is used for the case when a Matrix is already
+        simplified, this will speed things up. Here, we see that without
+        simplification the matrix does not appear anti-symmetric:
+
+        >>> print(m.is_anti_symmetric(simplify=False))
+        None
+
+        But if the matrix were already expanded, then it would appear
+        anti-symmetric and simplification in the is_anti_symmetric routine
+        is not needed:
+
+        >>> m = m.expand()
+        >>> m.is_anti_symmetric(simplify=False)
+        True
+        """
+        # accept custom simplification
+        simpfunc = simplify
+        if not isfunction(simplify):
+            simpfunc = _utilities_simplify if simplify else lambda x: x
+
+        if not self.is_square:
+            return False
+        return self._eval_is_anti_symmetric(simpfunc)
+
+    def is_diagonal(self):
+        """Check if matrix is diagonal,
+        that is matrix in which the entries outside the main diagonal are all zero.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, diag
+        >>> m = Matrix(2, 2, [1, 0, 0, 2])
+        >>> m
+        Matrix([
+        [1, 0],
+        [0, 2]])
+        >>> m.is_diagonal()
+        True
+
+        >>> m = Matrix(2, 2, [1, 1, 0, 2])
+        >>> m
+        Matrix([
+        [1, 1],
+        [0, 2]])
+        >>> m.is_diagonal()
+        False
+
+        >>> m = diag(1, 2, 3)
+        >>> m
+        Matrix([
+        [1, 0, 0],
+        [0, 2, 0],
+        [0, 0, 3]])
+        >>> m.is_diagonal()
+        True
+
+        See Also
+        ========
+
+        is_lower
+        is_upper
+        sympy.matrices.matrixbase.MatrixBase.is_diagonalizable
+        diagonalize
+        """
+        return self._eval_is_diagonal()
+
+    @property
+    def is_weakly_diagonally_dominant(self):
+        r"""Tests if the matrix is row weakly diagonally dominant.
+
+        Explanation
+        ===========
+
+        A $n, n$ matrix $A$ is row weakly diagonally dominant if
+
+        .. math::
+            \left|A_{i, i}\right| \ge \sum_{j = 0, j \neq i}^{n-1}
+            \left|A_{i, j}\right| \quad {\text{for all }}
+            i \in \{ 0, ..., n-1 \}
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]])
+        >>> A.is_weakly_diagonally_dominant
+        True
+
+        >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]])
+        >>> A.is_weakly_diagonally_dominant
+        False
+
+        >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]])
+        >>> A.is_weakly_diagonally_dominant
+        True
+
+        Notes
+        =====
+
+        If you want to test whether a matrix is column diagonally
+        dominant, you can apply the test after transposing the matrix.
+        """
+        if not self.is_square:
+            return False
+
+        rows, cols = self.shape
+
+        def test_row(i):
+            summation = self.zero
+            for j in range(cols):
+                if i != j:
+                    summation += Abs(self[i, j])
+            return (Abs(self[i, i]) - summation).is_nonnegative
+
+        return fuzzy_and(test_row(i) for i in range(rows))
+
+    @property
+    def is_strongly_diagonally_dominant(self):
+        r"""Tests if the matrix is row strongly diagonally dominant.
+
+        Explanation
+        ===========
+
+        A $n, n$ matrix $A$ is row strongly diagonally dominant if
+
+        .. math::
+            \left|A_{i, i}\right| > \sum_{j = 0, j \neq i}^{n-1}
+            \left|A_{i, j}\right| \quad {\text{for all }}
+            i \in \{ 0, ..., n-1 \}
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]])
+        >>> A.is_strongly_diagonally_dominant
+        False
+
+        >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]])
+        >>> A.is_strongly_diagonally_dominant
+        False
+
+        >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]])
+        >>> A.is_strongly_diagonally_dominant
+        True
+
+        Notes
+        =====
+
+        If you want to test whether a matrix is column diagonally
+        dominant, you can apply the test after transposing the matrix.
+        """
+        if not self.is_square:
+            return False
+
+        rows, cols = self.shape
+
+        def test_row(i):
+            summation = self.zero
+            for j in range(cols):
+                if i != j:
+                    summation += Abs(self[i, j])
+            return (Abs(self[i, i]) - summation).is_positive
+
+        return fuzzy_and(test_row(i) for i in range(rows))
+
+    @property
+    def is_hermitian(self):
+        """Checks if the matrix is Hermitian.
+
+        In a Hermitian matrix element i,j is the complex conjugate of
+        element j,i.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy import I
+        >>> from sympy.abc import x
+        >>> a = Matrix([[1, I], [-I, 1]])
+        >>> a
+        Matrix([
+        [ 1, I],
+        [-I, 1]])
+        >>> a.is_hermitian
+        True
+        >>> a[0, 0] = 2*I
+        >>> a.is_hermitian
+        False
+        >>> a[0, 0] = x
+        >>> a.is_hermitian
+        >>> a[0, 1] = a[1, 0]*I
+        >>> a.is_hermitian
+        False
+        """
+        if not self.is_square:
+            return False
+
+        return self._eval_is_matrix_hermitian(_utilities_simplify)
+
+    @property
+    def is_Identity(self) -> FuzzyBool:
+        if not self.is_square:
+            return False
+        return self._eval_is_Identity()
+
+    @property
+    def is_lower_hessenberg(self):
+        r"""Checks if the matrix is in the lower-Hessenberg form.
+
+        The lower hessenberg matrix has zero entries
+        above the first superdiagonal.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[1, 2, 0, 0], [5, 2, 3, 0], [3, 4, 3, 7], [5, 6, 1, 1]])
+        >>> a
+        Matrix([
+        [1, 2, 0, 0],
+        [5, 2, 3, 0],
+        [3, 4, 3, 7],
+        [5, 6, 1, 1]])
+        >>> a.is_lower_hessenberg
+        True
+
+        See Also
+        ========
+
+        is_upper_hessenberg
+        is_lower
+        """
+        return self._eval_is_lower_hessenberg()
+
+    @property
+    def is_lower(self):
+        """Check if matrix is a lower triangular matrix. True can be returned
+        even if the matrix is not square.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, [1, 0, 0, 1])
+        >>> m
+        Matrix([
+        [1, 0],
+        [0, 1]])
+        >>> m.is_lower
+        True
+
+        >>> m = Matrix(4, 3, [0, 0, 0, 2, 0, 0, 1, 4, 0, 6, 6, 5])
+        >>> m
+        Matrix([
+        [0, 0, 0],
+        [2, 0, 0],
+        [1, 4, 0],
+        [6, 6, 5]])
+        >>> m.is_lower
+        True
+
+        >>> from sympy.abc import x, y
+        >>> m = Matrix(2, 2, [x**2 + y, y**2 + x, 0, x + y])
+        >>> m
+        Matrix([
+        [x**2 + y, x + y**2],
+        [       0,    x + y]])
+        >>> m.is_lower
+        False
+
+        See Also
+        ========
+
+        is_upper
+        is_diagonal
+        is_lower_hessenberg
+        """
+        return self._eval_is_lower()
+
+    @property
+    def is_square(self):
+        """Checks if a matrix is square.
+
+        A matrix is square if the number of rows equals the number of columns.
+        The empty matrix is square by definition, since the number of rows and
+        the number of columns are both zero.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[1, 2, 3], [4, 5, 6]])
+        >>> b = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+        >>> c = Matrix([])
+        >>> a.is_square
+        False
+        >>> b.is_square
+        True
+        >>> c.is_square
+        True
+        """
+        return self.rows == self.cols
+
+    def is_symbolic(self):
+        """Checks if any elements contain Symbols.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.is_symbolic()
+        True
+
+        """
+        return self._eval_is_symbolic()
+
+    def is_symmetric(self, simplify=True):
+        """Check if matrix is symmetric matrix,
+        that is square matrix and is equal to its transpose.
+
+        By default, simplifications occur before testing symmetry.
+        They can be skipped using 'simplify=False'; while speeding things a bit,
+        this may however induce false negatives.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, [0, 1, 1, 2])
+        >>> m
+        Matrix([
+        [0, 1],
+        [1, 2]])
+        >>> m.is_symmetric()
+        True
+
+        >>> m = Matrix(2, 2, [0, 1, 2, 0])
+        >>> m
+        Matrix([
+        [0, 1],
+        [2, 0]])
+        >>> m.is_symmetric()
+        False
+
+        >>> m = Matrix(2, 3, [0, 0, 0, 0, 0, 0])
+        >>> m
+        Matrix([
+        [0, 0, 0],
+        [0, 0, 0]])
+        >>> m.is_symmetric()
+        False
+
+        >>> from sympy.abc import x, y
+        >>> m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
+        >>> m
+        Matrix([
+        [         1, x**2 + 2*x + 1, y],
+        [(x + 1)**2,              2, 0],
+        [         y,              0, 3]])
+        >>> m.is_symmetric()
+        True
+
+        If the matrix is already simplified, you may speed-up is_symmetric()
+        test by using 'simplify=False'.
+
+        >>> bool(m.is_symmetric(simplify=False))
+        False
+        >>> m1 = m.expand()
+        >>> m1.is_symmetric(simplify=False)
+        True
+        """
+        simpfunc = simplify
+        if not isfunction(simplify):
+            simpfunc = _utilities_simplify if simplify else lambda x: x
+
+        if not self.is_square:
+            return False
+
+        return self._eval_is_symmetric(simpfunc)
+
+    @property
+    def is_upper_hessenberg(self):
+        """Checks if the matrix is the upper-Hessenberg form.
+
+        The upper hessenberg matrix has zero entries
+        below the first subdiagonal.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[1, 4, 2, 3], [3, 4, 1, 7], [0, 2, 3, 4], [0, 0, 1, 3]])
+        >>> a
+        Matrix([
+        [1, 4, 2, 3],
+        [3, 4, 1, 7],
+        [0, 2, 3, 4],
+        [0, 0, 1, 3]])
+        >>> a.is_upper_hessenberg
+        True
+
+        See Also
+        ========
+
+        is_lower_hessenberg
+        is_upper
+        """
+        return self._eval_is_upper_hessenberg()
+
+    @property
+    def is_upper(self):
+        """Check if matrix is an upper triangular matrix. True can be returned
+        even if the matrix is not square.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, [1, 0, 0, 1])
+        >>> m
+        Matrix([
+        [1, 0],
+        [0, 1]])
+        >>> m.is_upper
+        True
+
+        >>> m = Matrix(4, 3, [5, 1, 9, 0, 4, 6, 0, 0, 5, 0, 0, 0])
+        >>> m
+        Matrix([
+        [5, 1, 9],
+        [0, 4, 6],
+        [0, 0, 5],
+        [0, 0, 0]])
+        >>> m.is_upper
+        True
+
+        >>> m = Matrix(2, 3, [4, 2, 5, 6, 1, 1])
+        >>> m
+        Matrix([
+        [4, 2, 5],
+        [6, 1, 1]])
+        >>> m.is_upper
+        False
+
+        See Also
+        ========
+
+        is_lower
+        is_diagonal
+        is_upper_hessenberg
+        """
+        return self._eval_is_upper()
+
+    @property
+    def is_zero_matrix(self):
+        """Checks if a matrix is a zero matrix.
+
+        A matrix is zero if every element is zero.  A matrix need not be square
+        to be considered zero.  The empty matrix is zero by the principle of
+        vacuous truth.  For a matrix that may or may not be zero (e.g.
+        contains a symbol), this will be None
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, zeros
+        >>> from sympy.abc import x
+        >>> a = Matrix([[0, 0], [0, 0]])
+        >>> b = zeros(3, 4)
+        >>> c = Matrix([[0, 1], [0, 0]])
+        >>> d = Matrix([])
+        >>> e = Matrix([[x, 0], [0, 0]])
+        >>> a.is_zero_matrix
+        True
+        >>> b.is_zero_matrix
+        True
+        >>> c.is_zero_matrix
+        False
+        >>> d.is_zero_matrix
+        True
+        >>> e.is_zero_matrix
+        """
+        return self._eval_is_zero_matrix()
+
+    def values(self):
+        """Return non-zero values of self.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix([[0, 1], [2, 3]])
+        >>> m.values()
+        [1, 2, 3]
+
+        See Also
+        ========
+
+        iter_values
+        tolist
+        flat
+        """
+        return self._eval_values()
+
+    def iter_values(self):
+        """
+        Iterate over non-zero values of self.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix([[0, 1], [2, 3]])
+        >>> list(m.iter_values())
+        [1, 2, 3]
+
+        See Also
+        ========
+
+        values
+        """
+        return self._eval_iter_values()
+
+    def iter_items(self):
+        """Iterate over indices and values of nonzero items.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix([[0, 1], [2, 3]])
+        >>> list(m.iter_items())
+        [((0, 1), 1), ((1, 0), 2), ((1, 1), 3)]
+
+        See Also
+        ========
+
+        iter_values
+        todok
+        """
+        return self._eval_iter_items()
+
+    def _eval_adjoint(self):
+        return self.transpose().applyfunc(lambda x: x.adjoint())
+
+    def _eval_applyfunc(self, f):
+        cols = self.cols
+        size = self.rows*self.cols
+
+        dok = self.todok()
+        valmap = {v: f(v) for v in dok.values()}
+
+        if len(dok) < size and ((fzero := f(S.Zero)) is not S.Zero):
+            out_flat = [fzero]*size
+            for (i, j), v in dok.items():
+                out_flat[i*cols + j] = valmap[v]
+            out = self._new(self.rows, self.cols, out_flat)
+        else:
+            fdok = {ij: valmap[v] for ij, v in dok.items()}
+            out = self.from_dok(self.rows, self.cols, fdok)
+
+        return out
+
+    def _eval_as_real_imag(self):  # type: ignore
+        return (self.applyfunc(re), self.applyfunc(im))
+
+    def _eval_conjugate(self):
+        return self.applyfunc(lambda x: x.conjugate())
+
+    def _eval_permute_cols(self, perm):
+        # apply the permutation to a list
+        mapping = list(perm)
+
+        def entry(i, j):
+            return self[i, mapping[j]]
+
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_permute_rows(self, perm):
+        # apply the permutation to a list
+        mapping = list(perm)
+
+        def entry(i, j):
+            return self[mapping[i], j]
+
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_trace(self):
+        return sum(self[i, i] for i in range(self.rows))
+
+    def _eval_transpose(self):
+        return self._new(self.cols, self.rows, lambda i, j: self[j, i])
+
+    def adjoint(self):
+        """Conjugate transpose or Hermitian conjugation."""
+        return self._eval_adjoint()
+
+    def applyfunc(self, f):
+        """Apply a function to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix(2, 2, lambda i, j: i*2+j)
+        >>> m
+        Matrix([
+        [0, 1],
+        [2, 3]])
+        >>> m.applyfunc(lambda i: 2*i)
+        Matrix([
+        [0, 2],
+        [4, 6]])
+
+        """
+        if not callable(f):
+            raise TypeError("`f` must be callable.")
+
+        return self._eval_applyfunc(f)
+
+    def as_real_imag(self, deep=True, **hints):
+        """Returns a tuple containing the (real, imaginary) part of matrix."""
+        # XXX: Ignoring deep and hints...
+        return self._eval_as_real_imag()
+
+    def conjugate(self):
+        """Return the by-element conjugation.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix, I
+        >>> a = SparseMatrix(((1, 2 + I), (3, 4), (I, -I)))
+        >>> a
+        Matrix([
+        [1, 2 + I],
+        [3,     4],
+        [I,    -I]])
+        >>> a.C
+        Matrix([
+        [ 1, 2 - I],
+        [ 3,     4],
+        [-I,     I]])
+
+        See Also
+        ========
+
+        transpose: Matrix transposition
+        H: Hermite conjugation
+        sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation
+        """
+        return self._eval_conjugate()
+
+    def doit(self, **hints):
+        return self.applyfunc(lambda x: x.doit(**hints))
+
+    def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False):
+        """Apply evalf() to each element of self."""
+        options = {'subs':subs, 'maxn':maxn, 'chop':chop, 'strict':strict,
+                'quad':quad, 'verbose':verbose}
+        return self.applyfunc(lambda i: i.evalf(n, **options))
+
+    def expand(self, deep=True, modulus=None, power_base=True, power_exp=True,
+               mul=True, log=True, multinomial=True, basic=True, **hints):
+        """Apply core.function.expand to each entry of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x
+        >>> from sympy import Matrix
+        >>> Matrix(1, 1, [x*(x+1)])
+        Matrix([[x*(x + 1)]])
+        >>> _.expand()
+        Matrix([[x**2 + x]])
+
+        """
+        return self.applyfunc(lambda x: x.expand(
+            deep, modulus, power_base, power_exp, mul, log, multinomial, basic,
+            **hints))
+
+    @property
+    def H(self):
+        """Return Hermite conjugate.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, I
+        >>> m = Matrix((0, 1 + I, 2, 3))
+        >>> m
+        Matrix([
+        [    0],
+        [1 + I],
+        [    2],
+        [    3]])
+        >>> m.H
+        Matrix([[0, 1 - I, 2, 3]])
+
+        See Also
+        ========
+
+        conjugate: By-element conjugation
+        sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation
+        """
+        return self.adjoint()
+
+    def permute(self, perm, orientation='rows', direction='forward'):
+        r"""Permute the rows or columns of a matrix by the given list of
+        swaps.
+
+        Parameters
+        ==========
+
+        perm : Permutation, list, or list of lists
+            A representation for the permutation.
+
+            If it is ``Permutation``, it is used directly with some
+            resizing with respect to the matrix size.
+
+            If it is specified as list of lists,
+            (e.g., ``[[0, 1], [0, 2]]``), then the permutation is formed
+            from applying the product of cycles. The direction how the
+            cyclic product is applied is described in below.
+
+            If it is specified as a list, the list should represent
+            an array form of a permutation. (e.g., ``[1, 2, 0]``) which
+            would would form the swapping function
+            `0 \mapsto 1, 1 \mapsto 2, 2\mapsto 0`.
+
+        orientation : 'rows', 'cols'
+            A flag to control whether to permute the rows or the columns
+
+        direction : 'forward', 'backward'
+            A flag to control whether to apply the permutations from
+            the start of the list first, or from the back of the list
+            first.
+
+            For example, if the permutation specification is
+            ``[[0, 1], [0, 2]]``,
+
+            If the flag is set to ``'forward'``, the cycle would be
+            formed as `0 \mapsto 2, 2 \mapsto 1, 1 \mapsto 0`.
+
+            If the flag is set to ``'backward'``, the cycle would be
+            formed as `0 \mapsto 1, 1 \mapsto 2, 2 \mapsto 0`.
+
+            If the argument ``perm`` is not in a form of list of lists,
+            this flag takes no effect.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='forward')
+        Matrix([
+        [0, 0, 1],
+        [1, 0, 0],
+        [0, 1, 0]])
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='backward')
+        Matrix([
+        [0, 1, 0],
+        [0, 0, 1],
+        [1, 0, 0]])
+
+        Notes
+        =====
+
+        If a bijective function
+        `\sigma : \mathbb{N}_0 \rightarrow \mathbb{N}_0` denotes the
+        permutation.
+
+        If the matrix `A` is the matrix to permute, represented as
+        a horizontal or a vertical stack of vectors:
+
+        .. math::
+            A =
+            \begin{bmatrix}
+            a_0 \\ a_1 \\ \vdots \\ a_{n-1}
+            \end{bmatrix} =
+            \begin{bmatrix}
+            \alpha_0 & \alpha_1 & \cdots & \alpha_{n-1}
+            \end{bmatrix}
+
+        If the matrix `B` is the result, the permutation of matrix rows
+        is defined as:
+
+        .. math::
+            B := \begin{bmatrix}
+            a_{\sigma(0)} \\ a_{\sigma(1)} \\ \vdots \\ a_{\sigma(n-1)}
+            \end{bmatrix}
+
+        And the permutation of matrix columns is defined as:
+
+        .. math::
+            B := \begin{bmatrix}
+            \alpha_{\sigma(0)} & \alpha_{\sigma(1)} &
+            \cdots & \alpha_{\sigma(n-1)}
+            \end{bmatrix}
+        """
+        from sympy.combinatorics import Permutation
+
+        # allow british variants and `columns`
+        if direction == 'forwards':
+            direction = 'forward'
+        if direction == 'backwards':
+            direction = 'backward'
+        if orientation == 'columns':
+            orientation = 'cols'
+
+        if direction not in ('forward', 'backward'):
+            raise TypeError("direction='{}' is an invalid kwarg. "
+                            "Try 'forward' or 'backward'".format(direction))
+        if orientation not in ('rows', 'cols'):
+            raise TypeError("orientation='{}' is an invalid kwarg. "
+                            "Try 'rows' or 'cols'".format(orientation))
+
+        if not isinstance(perm, (Permutation, Iterable)):
+            raise ValueError(
+                "{} must be a list, a list of lists, "
+                "or a SymPy permutation object.".format(perm))
+
+        # ensure all swaps are in range
+        max_index = self.rows if orientation == 'rows' else self.cols
+        if not all(0 <= t <= max_index for t in flatten(list(perm))):
+            raise IndexError("`swap` indices out of range.")
+
+        if perm and not isinstance(perm, Permutation) and \
+            isinstance(perm[0], Iterable):
+            if direction == 'forward':
+                perm = list(reversed(perm))
+            perm = Permutation(perm, size=max_index+1)
+        else:
+            perm = Permutation(perm, size=max_index+1)
+
+        if orientation == 'rows':
+            return self._eval_permute_rows(perm)
+        if orientation == 'cols':
+            return self._eval_permute_cols(perm)
+
+    def permute_cols(self, swaps, direction='forward'):
+        """Alias for
+        ``self.permute(swaps, orientation='cols', direction=direction)``
+
+        See Also
+        ========
+
+        permute
+        """
+        return self.permute(swaps, orientation='cols', direction=direction)
+
+    def permute_rows(self, swaps, direction='forward'):
+        """Alias for
+        ``self.permute(swaps, orientation='rows', direction=direction)``
+
+        See Also
+        ========
+
+        permute
+        """
+        return self.permute(swaps, orientation='rows', direction=direction)
+
+    def refine(self, assumptions=True):
+        """Apply refine to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Matrix, Abs, sqrt, Q
+        >>> x = Symbol('x')
+        >>> Matrix([[Abs(x)**2, sqrt(x**2)],[sqrt(x**2), Abs(x)**2]])
+        Matrix([
+        [ Abs(x)**2, sqrt(x**2)],
+        [sqrt(x**2),  Abs(x)**2]])
+        >>> _.refine(Q.real(x))
+        Matrix([
+        [  x**2, Abs(x)],
+        [Abs(x),   x**2]])
+
+        """
+        return self.applyfunc(lambda x: refine(x, assumptions))
+
+    def replace(self, F, G, map=False, simultaneous=True, exact=None):
+        """Replaces Function F in Matrix entries with Function G.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, Function, Matrix
+        >>> F, G = symbols('F, G', cls=Function)
+        >>> M = Matrix(2, 2, lambda i, j: F(i+j)) ; M
+        Matrix([
+        [F(0), F(1)],
+        [F(1), F(2)]])
+        >>> N = M.replace(F,G)
+        >>> N
+        Matrix([
+        [G(0), G(1)],
+        [G(1), G(2)]])
+        """
+        kwargs = {'map': map, 'simultaneous': simultaneous, 'exact': exact}
+
+        if map:
+
+            d = {}
+            def func(eij):
+                eij, dij = eij.replace(F, G, **kwargs)
+                d.update(dij)
+                return eij
+
+            M = self.applyfunc(func)
+            return M, d
+
+        else:
+            return self.applyfunc(lambda i: i.replace(F, G, **kwargs))
+
+    def rot90(self, k=1):
+        """Rotates Matrix by 90 degrees
+
+        Parameters
+        ==========
+
+        k : int
+            Specifies how many times the matrix is rotated by 90 degrees
+            (clockwise when positive, counter-clockwise when negative).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, symbols
+        >>> A = Matrix(2, 2, symbols('a:d'))
+        >>> A
+        Matrix([
+        [a, b],
+        [c, d]])
+
+        Rotating the matrix clockwise one time:
+
+        >>> A.rot90(1)
+        Matrix([
+        [c, a],
+        [d, b]])
+
+        Rotating the matrix anticlockwise two times:
+
+        >>> A.rot90(-2)
+        Matrix([
+        [d, c],
+        [b, a]])
+        """
+
+        mod = k%4
+        if mod == 0:
+            return self
+        if mod == 1:
+            return self[::-1, ::].T
+        if mod == 2:
+            return self[::-1, ::-1]
+        if mod == 3:
+            return self[::, ::-1].T
+
+    def simplify(self, **kwargs):
+        """Apply simplify to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import SparseMatrix, sin, cos
+        >>> SparseMatrix(1, 1, [x*sin(y)**2 + x*cos(y)**2])
+        Matrix([[x*sin(y)**2 + x*cos(y)**2]])
+        >>> _.simplify()
+        Matrix([[x]])
+        """
+        return self.applyfunc(lambda x: x.simplify(**kwargs))
+
+    def subs(self, *args, **kwargs):  # should mirror core.basic.subs
+        """Return a new matrix with subs applied to each entry.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import SparseMatrix, Matrix
+        >>> SparseMatrix(1, 1, [x])
+        Matrix([[x]])
+        >>> _.subs(x, y)
+        Matrix([[y]])
+        >>> Matrix(_).subs(y, x)
+        Matrix([[x]])
+        """
+
+        if len(args) == 1 and  not isinstance(args[0], (dict, set)) and iter(args[0]) and not is_sequence(args[0]):
+            args = (list(args[0]),)
+
+        return self.applyfunc(lambda x: x.subs(*args, **kwargs))
+
+    def trace(self):
+        """
+        Returns the trace of a square matrix i.e. the sum of the
+        diagonal elements.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix(2, 2, [1, 2, 3, 4])
+        >>> A.trace()
+        5
+
+        """
+        if self.rows != self.cols:
+            raise NonSquareMatrixError()
+        return self._eval_trace()
+
+    def transpose(self):
+        """
+        Returns the transpose of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix(2, 2, [1, 2, 3, 4])
+        >>> A.transpose()
+        Matrix([
+        [1, 3],
+        [2, 4]])
+
+        >>> from sympy import Matrix, I
+        >>> m=Matrix(((1, 2+I), (3, 4)))
+        >>> m
+        Matrix([
+        [1, 2 + I],
+        [3,     4]])
+        >>> m.transpose()
+        Matrix([
+        [    1, 3],
+        [2 + I, 4]])
+        >>> m.T == m.transpose()
+        True
+
+        See Also
+        ========
+
+        conjugate: By-element conjugation
+
+        """
+        return self._eval_transpose()
+
+    @property
+    def T(self):
+        '''Matrix transposition'''
+        return self.transpose()
+
+    @property
+    def C(self):
+        '''By-element conjugation'''
+        return self.conjugate()
+
+    def n(self, *args, **kwargs):
+        """Apply evalf() to each element of self."""
+        return self.evalf(*args, **kwargs)
+
+    def xreplace(self, rule):  # should mirror core.basic.xreplace
+        """Return a new matrix with xreplace applied to each entry.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y
+        >>> from sympy import SparseMatrix, Matrix
+        >>> SparseMatrix(1, 1, [x])
+        Matrix([[x]])
+        >>> _.xreplace({x: y})
+        Matrix([[y]])
+        >>> Matrix(_).xreplace({y: x})
+        Matrix([[x]])
+        """
+        return self.applyfunc(lambda x: x.xreplace(rule))
+
+    def _eval_simplify(self, **kwargs):
+        # XXX: We can't use self.simplify here as mutable subclasses will
+        # override simplify and have it return None
+        return self.applyfunc(lambda x: x.simplify(**kwargs))
+
+    def _eval_trigsimp(self, **opts):
+        from sympy.simplify.trigsimp import trigsimp
+        return self.applyfunc(lambda x: trigsimp(x, **opts))
+
+    def upper_triangular(self, k=0):
+        """Return the elements on and above the kth diagonal of a matrix.
+        If k is not specified then simply returns upper-triangular portion
+        of a matrix
+
+        Examples
+        ========
+
+        >>> from sympy import ones
+        >>> A = ones(4)
+        >>> A.upper_triangular()
+        Matrix([
+        [1, 1, 1, 1],
+        [0, 1, 1, 1],
+        [0, 0, 1, 1],
+        [0, 0, 0, 1]])
+
+        >>> A.upper_triangular(2)
+        Matrix([
+        [0, 0, 1, 1],
+        [0, 0, 0, 1],
+        [0, 0, 0, 0],
+        [0, 0, 0, 0]])
+
+        >>> A.upper_triangular(-1)
+        Matrix([
+        [1, 1, 1, 1],
+        [1, 1, 1, 1],
+        [0, 1, 1, 1],
+        [0, 0, 1, 1]])
+
+        """
+
+        def entry(i, j):
+            return self[i, j] if i + k <= j else self.zero
+
+        return self._new(self.rows, self.cols, entry)
+
+    def lower_triangular(self, k=0):
+        """Return the elements on and below the kth diagonal of a matrix.
+        If k is not specified then simply returns lower-triangular portion
+        of a matrix
+
+        Examples
+        ========
+
+        >>> from sympy import ones
+        >>> A = ones(4)
+        >>> A.lower_triangular()
+        Matrix([
+        [1, 0, 0, 0],
+        [1, 1, 0, 0],
+        [1, 1, 1, 0],
+        [1, 1, 1, 1]])
+
+        >>> A.lower_triangular(-2)
+        Matrix([
+        [0, 0, 0, 0],
+        [0, 0, 0, 0],
+        [1, 0, 0, 0],
+        [1, 1, 0, 0]])
+
+        >>> A.lower_triangular(1)
+        Matrix([
+        [1, 1, 0, 0],
+        [1, 1, 1, 0],
+        [1, 1, 1, 1],
+        [1, 1, 1, 1]])
+
+        """
+
+        def entry(i, j):
+            return self[i, j] if i + k >= j else self.zero
+
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_Abs(self):
+        return self._new(self.rows, self.cols, lambda i, j: Abs(self[i, j]))
+
+    def _eval_add(self, other):
+        return self._new(self.rows, self.cols,
+                         lambda i, j: self[i, j] + other[i, j])
+
+    def _eval_matrix_mul(self, other):
+        def entry(i, j):
+            vec = [self[i,k]*other[k,j] for k in range(self.cols)]
+            try:
+                return Add(*vec)
+            except (TypeError, SympifyError):
+                # Some matrices don't work with `sum` or `Add`
+                # They don't work with `sum` because `sum` tries to add `0`
+                # Fall back to a safe way to multiply if the `Add` fails.
+                return reduce(lambda a, b: a + b, vec)
+
+        return self._new(self.rows, other.cols, entry)
+
+    def _eval_matrix_mul_elementwise(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other[i,j])
+
+    def _eval_matrix_rmul(self, other):
+        def entry(i, j):
+            return sum(other[i,k]*self[k,j] for k in range(other.cols))
+        return self._new(other.rows, self.cols, entry)
+
+    def _eval_pow_by_recursion(self, num):
+        if num == 1:
+            return self
+
+        if num % 2 == 1:
+            a, b = self, self._eval_pow_by_recursion(num - 1)
+        else:
+            a = b = self._eval_pow_by_recursion(num // 2)
+
+        return a.multiply(b)
+
+    def _eval_pow_by_cayley(self, exp):
+        from sympy.discrete.recurrences import linrec_coeffs
+        row = self.shape[0]
+        p = self.charpoly()
+
+        coeffs = (-p).all_coeffs()[1:]
+        coeffs = linrec_coeffs(coeffs, exp)
+        new_mat = self.eye(row)
+        ans = self.zeros(row)
+
+        for i in range(row):
+            ans += coeffs[i]*new_mat
+            new_mat *= self
+
+        return ans
+
+    def _eval_pow_by_recursion_dotprodsimp(self, num, prevsimp=None):
+        if prevsimp is None:
+            prevsimp = [True]*len(self)
+
+        if num == 1:
+            return self
+
+        if num % 2 == 1:
+            a, b = self, self._eval_pow_by_recursion_dotprodsimp(num - 1,
+                    prevsimp=prevsimp)
+        else:
+            a = b = self._eval_pow_by_recursion_dotprodsimp(num // 2,
+                    prevsimp=prevsimp)
+
+        m     = a.multiply(b, dotprodsimp=False)
+        lenm  = len(m)
+        elems = [None]*lenm
+
+        for i in range(lenm):
+            if prevsimp[i]:
+                elems[i], prevsimp[i] = _dotprodsimp(m[i], withsimp=True)
+            else:
+                elems[i] = m[i]
+
+        return m._new(m.rows, m.cols, elems)
+
+    def _eval_scalar_mul(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other)
+
+    def _eval_scalar_rmul(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: other*self[i,j])
+
+    def _eval_Mod(self, other):
+        return self._new(self.rows, self.cols, lambda i, j: Mod(self[i, j], other))
+
+    # Python arithmetic functions
+    def __abs__(self):
+        """Returns a new matrix with entry-wise absolute values."""
+        return self._eval_Abs()
+
+    @call_highest_priority('__radd__')
+    def __add__(self, other):
+        """Return self + other, raising ShapeError if shapes do not match."""
+
+        other, T = _coerce_operand(self, other)
+
+        if T != "is_matrix":
+            return NotImplemented
+
+        if self.shape != other.shape:
+            raise ShapeError(f"Matrix size mismatch: {self.shape} + {other.shape}.")
+
+        # Unify matrix types
+        a, b = self, other
+        if a.__class__ != classof(a, b):
+            b, a = a, b
+
+        return a._eval_add(b)
+
+    @call_highest_priority('__rtruediv__')
+    def __truediv__(self, other):
+        return self * (self.one / other)
+
+    @call_highest_priority('__rmatmul__')
+    def __matmul__(self, other):
+        self, other, T = _unify_with_other(self, other)
+
+        if T != "is_matrix":
+            return NotImplemented
+
+        return self.__mul__(other)
+
+    def __mod__(self, other):
+        return self.applyfunc(lambda x: x % other)
+
+    @call_highest_priority('__rmul__')
+    def __mul__(self, other):
+        """Return self*other where other is either a scalar or a matrix
+        of compatible dimensions.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[1, 2, 3], [4, 5, 6]])
+        >>> 2*A == A*2 == Matrix([[2, 4, 6], [8, 10, 12]])
+        True
+        >>> B = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+        >>> A*B
+        Matrix([
+        [30, 36, 42],
+        [66, 81, 96]])
+        >>> B*A
+        Traceback (most recent call last):
+        ...
+        ShapeError: Matrices size mismatch.
+        >>>
+
+        See Also
+        ========
+
+        matrix_multiply_elementwise
+        """
+
+        return self.multiply(other)
+
+    def multiply(self, other, dotprodsimp=None):
+        """Same as __mul__() but with optional simplification.
+
+        Parameters
+        ==========
+
+        dotprodsimp : bool, optional
+            Specifies whether intermediate term algebraic simplification is used
+            during matrix multiplications to control expression blowup and thus
+            speed up calculation. Default is off.
+        """
+
+        isimpbool = _get_intermediate_simp_bool(False, dotprodsimp)
+
+        self, other, T = _unify_with_other(self, other)
+
+        if T == "possible_scalar":
+            try:
+                return self._eval_scalar_mul(other)
+            except TypeError:
+                return NotImplemented
+
+        elif T == "is_matrix":
+
+            if self.shape[1] != other.shape[0]:
+                raise ShapeError(f"Matrix size mismatch: {self.shape} * {other.shape}.")
+
+            m = self._eval_matrix_mul(other)
+
+            if isimpbool:
+                m = m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m])
+
+            return m
+
+        else:
+            return NotImplemented
+
+    def multiply_elementwise(self, other):
+        """Return the Hadamard product (elementwise product) of A and B
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[0, 1, 2], [3, 4, 5]])
+        >>> B = Matrix([[1, 10, 100], [100, 10, 1]])
+        >>> A.multiply_elementwise(B)
+        Matrix([
+        [  0, 10, 200],
+        [300, 40,   5]])
+
+        See Also
+        ========
+
+        sympy.matrices.matrixbase.MatrixBase.cross
+        sympy.matrices.matrixbase.MatrixBase.dot
+        multiply
+        """
+        if self.shape != other.shape:
+            raise ShapeError("Matrix shapes must agree {} != {}".format(self.shape, other.shape))
+
+        return self._eval_matrix_mul_elementwise(other)
+
+    def __neg__(self):
+        return self._eval_scalar_mul(-1)
+
+    @call_highest_priority('__rpow__')
+    def __pow__(self, exp):
+        """Return self**exp a scalar or symbol."""
+
+        return self.pow(exp)
+
+
+    def pow(self, exp, method=None):
+        r"""Return self**exp a scalar or symbol.
+
+        Parameters
+        ==========
+
+        method : multiply, mulsimp, jordan, cayley
+            If multiply then it returns exponentiation using recursion.
+            If jordan then Jordan form exponentiation will be used.
+            If cayley then the exponentiation is done using Cayley-Hamilton
+            theorem.
+            If mulsimp then the exponentiation is done using recursion
+            with dotprodsimp. This specifies whether intermediate term
+            algebraic simplification is used during naive matrix power to
+            control expression blowup and thus speed up calculation.
+            If None, then it heuristically decides which method to use.
+
+        """
+
+        if method is not None and method not in ['multiply', 'mulsimp', 'jordan', 'cayley']:
+            raise TypeError('No such method')
+        if self.rows != self.cols:
+            raise NonSquareMatrixError()
+        a = self
+        jordan_pow = getattr(a, '_matrix_pow_by_jordan_blocks', None)
+        exp = sympify(exp)
+
+        if exp.is_zero:
+            return a._new(a.rows, a.cols, lambda i, j: int(i == j))
+        if exp == 1:
+            return a
+
+        diagonal = getattr(a, 'is_diagonal', None)
+        if diagonal is not None and diagonal():
+            return a._new(a.rows, a.cols, lambda i, j: a[i,j]**exp if i == j else 0)
+
+        if exp.is_Number and exp % 1 == 0:
+            if a.rows == 1:
+                return a._new([[a[0]**exp]])
+            if exp < 0:
+                exp = -exp
+                a = a.inv()
+        # When certain conditions are met,
+        # Jordan block algorithm is faster than
+        # computation by recursion.
+        if method == 'jordan':
+            try:
+                return jordan_pow(exp)
+            except MatrixError:
+                if method == 'jordan':
+                    raise
+
+        elif method == 'cayley':
+            if not exp.is_Number or exp % 1 != 0:
+                raise ValueError("cayley method is only valid for integer powers")
+            return a._eval_pow_by_cayley(exp)
+
+        elif method == "mulsimp":
+            if not exp.is_Number or exp % 1 != 0:
+                raise ValueError("mulsimp method is only valid for integer powers")
+            return a._eval_pow_by_recursion_dotprodsimp(exp)
+
+        elif method == "multiply":
+            if not exp.is_Number or exp % 1 != 0:
+                raise ValueError("multiply method is only valid for integer powers")
+            return a._eval_pow_by_recursion(exp)
+
+        elif method is None and exp.is_Number and exp % 1 == 0:
+            if exp.is_Float:
+                exp = Integer(exp)
+            # Decide heuristically which method to apply
+            if a.rows == 2 and exp > 100000:
+                return jordan_pow(exp)
+            elif _get_intermediate_simp_bool(True, None):
+                return a._eval_pow_by_recursion_dotprodsimp(exp)
+            elif exp > 10000:
+                return a._eval_pow_by_cayley(exp)
+            else:
+                return a._eval_pow_by_recursion(exp)
+
+        if jordan_pow:
+            try:
+                return jordan_pow(exp)
+            except NonInvertibleMatrixError:
+                # Raised by jordan_pow on zero determinant matrix unless exp is
+                # definitely known to be a non-negative integer.
+                # Here we raise if n is definitely not a non-negative integer
+                # but otherwise we can leave this as an unevaluated MatPow.
+                if exp.is_integer is False or exp.is_nonnegative is False:
+                    raise
+
+        from sympy.matrices.expressions import MatPow
+        return MatPow(a, exp)
+
+    @call_highest_priority('__add__')
+    def __radd__(self, other):
+        return self.__add__(other)
+
+    @call_highest_priority('__matmul__')
+    def __rmatmul__(self, other):
+        self, other, T = _unify_with_other(self, other)
+
+        if T != "is_matrix":
+            return NotImplemented
+
+        return self.__rmul__(other)
+
+    @call_highest_priority('__mul__')
+    def __rmul__(self, other):
+        return self.rmultiply(other)
+
+    def rmultiply(self, other, dotprodsimp=None):
+        """Same as __rmul__() but with optional simplification.
+
+        Parameters
+        ==========
+
+        dotprodsimp : bool, optional
+            Specifies whether intermediate term algebraic simplification is used
+            during matrix multiplications to control expression blowup and thus
+            speed up calculation. Default is off.
+        """
+        isimpbool = _get_intermediate_simp_bool(False, dotprodsimp)
+        self, other, T = _unify_with_other(self, other)
+
+        if T == "possible_scalar":
+            try:
+                return self._eval_scalar_rmul(other)
+            except TypeError:
+                return NotImplemented
+
+        elif T == "is_matrix":
+            if self.shape[0] != other.shape[1]:
+                raise ShapeError("Matrix size mismatch.")
+
+            m = self._eval_matrix_rmul(other)
+
+            if isimpbool:
+                return m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m])
+
+            return m
+
+        else:
+            return NotImplemented
+
+    @call_highest_priority('__sub__')
+    def __rsub__(self, a):
+        return (-self) + a
+
+    @call_highest_priority('__rsub__')
+    def __sub__(self, a):
+        return self + (-a)
+
+    def _eval_det_bareiss(self, iszerofunc=_is_zero_after_expand_mul):
+        return _det_bareiss(self, iszerofunc=iszerofunc)
+
+    def _eval_det_berkowitz(self):
+        return _det_berkowitz(self)
+
+    def _eval_det_lu(self, iszerofunc=_iszero, simpfunc=None):
+        return _det_LU(self, iszerofunc=iszerofunc, simpfunc=simpfunc)
+
+    def _eval_det_bird(self):
+        return _det_bird(self)
+
+    def _eval_det_laplace(self):
+        return _det_laplace(self)
+
+    def _eval_determinant(self): # for expressions.determinant.Determinant
+        return _det(self)
+
+    def adjugate(self, method="berkowitz"):
+        return _adjugate(self, method=method)
+
+    def charpoly(self, x='lambda', simplify=_utilities_simplify):
+        return _charpoly(self, x=x, simplify=simplify)
+
+    def cofactor(self, i, j, method="berkowitz"):
+        return _cofactor(self, i, j, method=method)
+
+    def cofactor_matrix(self, method="berkowitz"):
+        return _cofactor_matrix(self, method=method)
+
+    def det(self, method="bareiss", iszerofunc=None):
+        return _det(self, method=method, iszerofunc=iszerofunc)
+
+    def per(self):
+        return _per(self)
+
+    def minor(self, i, j, method="berkowitz"):
+        return _minor(self, i, j, method=method)
+
+    def minor_submatrix(self, i, j):
+        return _minor_submatrix(self, i, j)
+
+    _find_reasonable_pivot.__doc__       = _find_reasonable_pivot.__doc__
+    _find_reasonable_pivot_naive.__doc__ = _find_reasonable_pivot_naive.__doc__
+    _eval_det_bareiss.__doc__            = _det_bareiss.__doc__
+    _eval_det_berkowitz.__doc__          = _det_berkowitz.__doc__
+    _eval_det_bird.__doc__            = _det_bird.__doc__
+    _eval_det_laplace.__doc__            = _det_laplace.__doc__
+    _eval_det_lu.__doc__                 = _det_LU.__doc__
+    _eval_determinant.__doc__            = _det.__doc__
+    adjugate.__doc__                     = _adjugate.__doc__
+    charpoly.__doc__                     = _charpoly.__doc__
+    cofactor.__doc__                     = _cofactor.__doc__
+    cofactor_matrix.__doc__              = _cofactor_matrix.__doc__
+    det.__doc__                          = _det.__doc__
+    per.__doc__                          = _per.__doc__
+    minor.__doc__                        = _minor.__doc__
+    minor_submatrix.__doc__              = _minor_submatrix.__doc__
+
+    def echelon_form(self, iszerofunc=_iszero, simplify=False, with_pivots=False):
+        return _echelon_form(self, iszerofunc=iszerofunc, simplify=simplify,
+                with_pivots=with_pivots)
+
+    @property
+    def is_echelon(self):
+        return _is_echelon(self)
+
+    def rank(self, iszerofunc=_iszero, simplify=False):
+        return _rank(self, iszerofunc=iszerofunc, simplify=simplify)
+
+    def rref_rhs(self, rhs):
+        """Return reduced row-echelon form of matrix, matrix showing
+        rhs after reduction steps. ``rhs`` must have the same number
+        of rows as ``self``.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, symbols
+        >>> r1, r2 = symbols('r1 r2')
+        >>> Matrix([[1, 1], [2, 1]]).rref_rhs(Matrix([r1, r2]))
+        (Matrix([
+        [1, 0],
+        [0, 1]]), Matrix([
+        [ -r1 + r2],
+        [2*r1 - r2]]))
+        """
+        r, _ = _rref(self.hstack(self, self.eye(self.rows), rhs))
+        return r[:, :self.cols], r[:, -rhs.cols:]
+
+    def rref(self, iszerofunc=_iszero, simplify=False, pivots=True,
+            normalize_last=True):
+        return _rref(self, iszerofunc=iszerofunc, simplify=simplify,
+            pivots=pivots, normalize_last=normalize_last)
+
+    echelon_form.__doc__ = _echelon_form.__doc__
+    is_echelon.__doc__   = _is_echelon.__doc__
+    rank.__doc__         = _rank.__doc__
+    rref.__doc__         = _rref.__doc__
+
+    def _normalize_op_args(self, op, col, k, col1, col2, error_str="col"):
+        """Validate the arguments for a row/column operation.  ``error_str``
+        can be one of "row" or "col" depending on the arguments being parsed."""
+        if op not in ["n->kn", "n<->m", "n->n+km"]:
+            raise ValueError("Unknown {} operation '{}'. Valid col operations "
+                             "are 'n->kn', 'n<->m', 'n->n+km'".format(error_str, op))
+
+        # define self_col according to error_str
+        self_cols = self.cols if error_str == 'col' else self.rows
+
+        # normalize and validate the arguments
+        if op == "n->kn":
+            col = col if col is not None else col1
+            if col is None or k is None:
+                raise ValueError("For a {0} operation 'n->kn' you must provide the "
+                                 "kwargs `{0}` and `k`".format(error_str))
+            if not 0 <= col < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col))
+
+        elif op == "n<->m":
+            # we need two cols to swap. It does not matter
+            # how they were specified, so gather them together and
+            # remove `None`
+            cols = {col, k, col1, col2}.difference([None])
+            if len(cols) > 2:
+                # maybe the user left `k` by mistake?
+                cols = {col, col1, col2}.difference([None])
+            if len(cols) != 2:
+                raise ValueError("For a {0} operation 'n<->m' you must provide the "
+                                 "kwargs `{0}1` and `{0}2`".format(error_str))
+            col1, col2 = cols
+            if not 0 <= col1 < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col1))
+            if not 0 <= col2 < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2))
+
+        elif op == "n->n+km":
+            col = col1 if col is None else col
+            col2 = col1 if col2 is None else col2
+            if col is None or col2 is None or k is None:
+                raise ValueError("For a {0} operation 'n->n+km' you must provide the "
+                                 "kwargs `{0}`, `k`, and `{0}2`".format(error_str))
+            if col == col2:
+                raise ValueError("For a {0} operation 'n->n+km' `{0}` and `{0}2` must "
+                                 "be different.".format(error_str))
+            if not 0 <= col < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col))
+            if not 0 <= col2 < self_cols:
+                raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2))
+
+        else:
+            raise ValueError('invalid operation %s' % repr(op))
+
+        return op, col, k, col1, col2
+
+    def _eval_col_op_multiply_col_by_const(self, col, k):
+        def entry(i, j):
+            if j == col:
+                return k * self[i, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_col_op_swap(self, col1, col2):
+        def entry(i, j):
+            if j == col1:
+                return self[i, col2]
+            elif j == col2:
+                return self[i, col1]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_col_op_add_multiple_to_other_col(self, col, k, col2):
+        def entry(i, j):
+            if j == col:
+                return self[i, j] + k * self[i, col2]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_row_op_swap(self, row1, row2):
+        def entry(i, j):
+            if i == row1:
+                return self[row2, j]
+            elif i == row2:
+                return self[row1, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_row_op_multiply_row_by_const(self, row, k):
+        def entry(i, j):
+            if i == row:
+                return k * self[i, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def _eval_row_op_add_multiple_to_other_row(self, row, k, row2):
+        def entry(i, j):
+            if i == row:
+                return self[i, j] + k * self[row2, j]
+            return self[i, j]
+        return self._new(self.rows, self.cols, entry)
+
+    def elementary_col_op(self, op="n->kn", col=None, k=None, col1=None, col2=None):
+        """Performs the elementary column operation `op`.
+
+        `op` may be one of
+
+            * ``"n->kn"`` (column n goes to k*n)
+            * ``"n<->m"`` (swap column n and column m)
+            * ``"n->n+km"`` (column n goes to column n + k*column m)
+
+        Parameters
+        ==========
+
+        op : string; the elementary row operation
+        col : the column to apply the column operation
+        k : the multiple to apply in the column operation
+        col1 : one column of a column swap
+        col2 : second column of a column swap or column "m" in the column operation
+               "n->n+km"
+        """
+
+        op, col, k, col1, col2 = self._normalize_op_args(op, col, k, col1, col2, "col")
+
+        # now that we've validated, we're all good to dispatch
+        if op == "n->kn":
+            return self._eval_col_op_multiply_col_by_const(col, k)
+        if op == "n<->m":
+            return self._eval_col_op_swap(col1, col2)
+        if op == "n->n+km":
+            return self._eval_col_op_add_multiple_to_other_col(col, k, col2)
+
+    def elementary_row_op(self, op="n->kn", row=None, k=None, row1=None, row2=None):
+        """Performs the elementary row operation `op`.
+
+        `op` may be one of
+
+            * ``"n->kn"`` (row n goes to k*n)
+            * ``"n<->m"`` (swap row n and row m)
+            * ``"n->n+km"`` (row n goes to row n + k*row m)
+
+        Parameters
+        ==========
+
+        op : string; the elementary row operation
+        row : the row to apply the row operation
+        k : the multiple to apply in the row operation
+        row1 : one row of a row swap
+        row2 : second row of a row swap or row "m" in the row operation
+               "n->n+km"
+        """
+
+        op, row, k, row1, row2 = self._normalize_op_args(op, row, k, row1, row2, "row")
+
+        # now that we've validated, we're all good to dispatch
+        if op == "n->kn":
+            return self._eval_row_op_multiply_row_by_const(row, k)
+        if op == "n<->m":
+            return self._eval_row_op_swap(row1, row2)
+        if op == "n->n+km":
+            return self._eval_row_op_add_multiple_to_other_row(row, k, row2)
+
+    def columnspace(self, simplify=False):
+        return _columnspace(self, simplify=simplify)
+
+    def nullspace(self, simplify=False, iszerofunc=_iszero):
+        return _nullspace(self, simplify=simplify, iszerofunc=iszerofunc)
+
+    def rowspace(self, simplify=False):
+        return _rowspace(self, simplify=simplify)
+
+    # This is a classmethod but is converted to such later in order to allow
+    # assignment of __doc__ since that does not work for already wrapped
+    # classmethods in Python 3.6.
+    def orthogonalize(cls, *vecs, **kwargs):
+        return _orthogonalize(cls, *vecs, **kwargs)
+
+    columnspace.__doc__   = _columnspace.__doc__
+    nullspace.__doc__     = _nullspace.__doc__
+    rowspace.__doc__      = _rowspace.__doc__
+    orthogonalize.__doc__ = _orthogonalize.__doc__
+
+    orthogonalize         = classmethod(orthogonalize)  # type:ignore
+
+    def eigenvals(self, error_when_incomplete=True, **flags):
+        return _eigenvals(self, error_when_incomplete=error_when_incomplete, **flags)
+
+    def eigenvects(self, error_when_incomplete=True, iszerofunc=_iszero, **flags):
+        return _eigenvects(self, error_when_incomplete=error_when_incomplete,
+                iszerofunc=iszerofunc, **flags)
+
+    def is_diagonalizable(self, reals_only=False, **kwargs):
+        return _is_diagonalizable(self, reals_only=reals_only, **kwargs)
+
+    def diagonalize(self, reals_only=False, sort=False, normalize=False):
+        return _diagonalize(self, reals_only=reals_only, sort=sort,
+                normalize=normalize)
+
+    def bidiagonalize(self, upper=True):
+        return _bidiagonalize(self, upper=upper)
+
+    def bidiagonal_decomposition(self, upper=True):
+        return _bidiagonal_decomposition(self, upper=upper)
+
+    @property
+    def is_positive_definite(self):
+        return _is_positive_definite(self)
+
+    @property
+    def is_positive_semidefinite(self):
+        return _is_positive_semidefinite(self)
+
+    @property
+    def is_negative_definite(self):
+        return _is_negative_definite(self)
+
+    @property
+    def is_negative_semidefinite(self):
+        return _is_negative_semidefinite(self)
+
+    @property
+    def is_indefinite(self):
+        return _is_indefinite(self)
+
+    def jordan_form(self, calc_transform=True, **kwargs):
+        return _jordan_form(self, calc_transform=calc_transform, **kwargs)
+
+    def left_eigenvects(self, **flags):
+        return _left_eigenvects(self, **flags)
+
+    def singular_values(self):
+        return _singular_values(self)
+
+    eigenvals.__doc__                  = _eigenvals.__doc__
+    eigenvects.__doc__                 = _eigenvects.__doc__
+    is_diagonalizable.__doc__          = _is_diagonalizable.__doc__
+    diagonalize.__doc__                = _diagonalize.__doc__
+    is_positive_definite.__doc__       = _is_positive_definite.__doc__
+    is_positive_semidefinite.__doc__   = _is_positive_semidefinite.__doc__
+    is_negative_definite.__doc__       = _is_negative_definite.__doc__
+    is_negative_semidefinite.__doc__   = _is_negative_semidefinite.__doc__
+    is_indefinite.__doc__              = _is_indefinite.__doc__
+    jordan_form.__doc__                = _jordan_form.__doc__
+    left_eigenvects.__doc__            = _left_eigenvects.__doc__
+    singular_values.__doc__            = _singular_values.__doc__
+    bidiagonalize.__doc__              = _bidiagonalize.__doc__
+    bidiagonal_decomposition.__doc__   = _bidiagonal_decomposition.__doc__
+
+    def diff(self, *args, evaluate=True, **kwargs):
+        """Calculate the derivative of each element in the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.diff(x)
+        Matrix([
+        [1, 0],
+        [0, 0]])
+
+        See Also
+        ========
+
+        integrate
+        limit
+        """
+        # XXX this should be handled here rather than in Derivative
+        from sympy.tensor.array.array_derivatives import ArrayDerivative
+        deriv = ArrayDerivative(self, *args, evaluate=evaluate)
+        # XXX This can rather changed to always return immutable matrix
+        if not isinstance(self, Basic) and evaluate:
+            return deriv.as_mutable()
+        return deriv
+
+    def _eval_derivative(self, arg):
+        return self.applyfunc(lambda x: x.diff(arg))
+
+    def integrate(self, *args, **kwargs):
+        """Integrate each element of the matrix.  ``args`` will
+        be passed to the ``integrate`` function.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.integrate((x, ))
+        Matrix([
+        [x**2/2, x*y],
+        [     x,   0]])
+        >>> M.integrate((x, 0, 2))
+        Matrix([
+        [2, 2*y],
+        [2,   0]])
+
+        See Also
+        ========
+
+        limit
+        diff
+        """
+        return self.applyfunc(lambda x: x.integrate(*args, **kwargs))
+
+    def jacobian(self, X):
+        """Calculates the Jacobian matrix (derivative of a vector-valued function).
+
+        Parameters
+        ==========
+
+        ``self`` : vector of expressions representing functions f_i(x_1, ..., x_n).
+        X : set of x_i's in order, it can be a list or a Matrix
+
+        Both ``self`` and X can be a row or a column matrix in any order
+        (i.e., jacobian() should always work).
+
+        Examples
+        ========
+
+        >>> from sympy import sin, cos, Matrix
+        >>> from sympy.abc import rho, phi
+        >>> X = Matrix([rho*cos(phi), rho*sin(phi), rho**2])
+        >>> Y = Matrix([rho, phi])
+        >>> X.jacobian(Y)
+        Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)],
+        [   2*rho,             0]])
+        >>> X = Matrix([rho*cos(phi), rho*sin(phi)])
+        >>> X.jacobian(Y)
+        Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)]])
+
+        See Also
+        ========
+
+        hessian
+        wronskian
+        """
+        from sympy.matrices.matrixbase import MatrixBase
+        if not isinstance(X, MatrixBase):
+            X = self._new(X)
+        # Both X and ``self`` can be a row or a column matrix, so we need to make
+        # sure all valid combinations work, but everything else fails:
+        if self.shape[0] == 1:
+            m = self.shape[1]
+        elif self.shape[1] == 1:
+            m = self.shape[0]
+        else:
+            raise TypeError("``self`` must be a row or a column matrix")
+        if X.shape[0] == 1:
+            n = X.shape[1]
+        elif X.shape[1] == 1:
+            n = X.shape[0]
+        else:
+            raise TypeError("X must be a row or a column matrix")
+
+        # m is the number of functions and n is the number of variables
+        # computing the Jacobian is now easy:
+        return self._new(m, n, lambda j, i: self[j].diff(X[i]))
+
+    def limit(self, *args):
+        """Calculate the limit of each element in the matrix.
+        ``args`` will be passed to the ``limit`` function.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x, y
+        >>> M = Matrix([[x, y], [1, 0]])
+        >>> M.limit(x, 2)
+        Matrix([
+        [2, y],
+        [1, 0]])
+
+        See Also
+        ========
+
+        integrate
+        diff
+        """
+        return self.applyfunc(lambda x: x.limit(*args))
+
+    def berkowitz_charpoly(self, x=Dummy('lambda'), simplify=_utilities_simplify):
+        return self.charpoly(x=x)
+
+    def berkowitz_det(self):
+        """Computes determinant using Berkowitz method.
+
+        See Also
+        ========
+
+        det
+        """
+        return self.det(method='berkowitz')
+
+    def berkowitz_eigenvals(self, **flags):
+        """Computes eigenvalues of a Matrix using Berkowitz method."""
+        return self.eigenvals(**flags)
+
+    def berkowitz_minors(self):
+        """Computes principal minors using Berkowitz method."""
+        sign, minors = self.one, []
+
+        for poly in self.berkowitz():
+            minors.append(sign * poly[-1])
+            sign = -sign
+
+        return tuple(minors)
+
+    def berkowitz(self):
+        from sympy.matrices import zeros
+        berk = ((1,),)
+        if not self:
+            return berk
+
+        if not self.is_square:
+            raise NonSquareMatrixError()
+
+        A, N = self, self.rows
+        transforms = [0] * (N - 1)
+
+        for n in range(N, 1, -1):
+            T, k = zeros(n + 1, n), n - 1
+
+            R, C = -A[k, :k], A[:k, k]
+            A, a = A[:k, :k], -A[k, k]
+
+            items = [C]
+
+            for i in range(0, n - 2):
+                items.append(A * items[i])
+
+            for i, B in enumerate(items):
+                items[i] = (R * B)[0, 0]
+
+            items = [self.one, a] + items
+
+            for i in range(n):
+                T[i:, i] = items[:n - i + 1]
+
+            transforms[k - 1] = T
+
+        polys = [self._new([self.one, -A[0, 0]])]
+
+        for i, T in enumerate(transforms):
+            polys.append(T * polys[i])
+
+        return berk + tuple(map(tuple, polys))
+
+    def cofactorMatrix(self, method="berkowitz"):
+        return self.cofactor_matrix(method=method)
+
+    def det_bareis(self):
+        return _det_bareiss(self)
+
+    def det_LU_decomposition(self):
+        """Compute matrix determinant using LU decomposition.
+
+
+        Note that this method fails if the LU decomposition itself
+        fails. In particular, if the matrix has no inverse this method
+        will fail.
+
+        TODO: Implement algorithm for sparse matrices (SFF),
+        http://www.eecis.udel.edu/~saunders/papers/sffge/it5.ps.
+
+        See Also
+        ========
+
+
+        det
+        berkowitz_det
+        """
+        return self.det(method='lu')
+
+    def jordan_cell(self, eigenval, n):
+        return self.jordan_block(size=n, eigenvalue=eigenval)
+
+    def jordan_cells(self, calc_transformation=True):
+        P, J = self.jordan_form()
+        return P, J.get_diag_blocks()
+
+    def minorEntry(self, i, j, method="berkowitz"):
+        return self.minor(i, j, method=method)
+
+    def minorMatrix(self, i, j):
+        return self.minor_submatrix(i, j)
+
+    def permuteBkwd(self, perm):
+        """Permute the rows of the matrix with the given permutation in reverse."""
+        return self.permute_rows(perm, direction='backward')
+
+    def permuteFwd(self, perm):
+        """Permute the rows of the matrix with the given permutation."""
+        return self.permute_rows(perm, direction='forward')
+
+    @property
+    def kind(self) -> MatrixKind:
+        elem_kinds = {e.kind for e in self.flat()}
+        if len(elem_kinds) == 1:
+            elemkind, = elem_kinds
+        else:
+            elemkind = UndefinedKind
+        return MatrixKind(elemkind)
+
+    def flat(self):
+        """
+        Returns a flat list of all elements in the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> m = Matrix([[0, 2], [3, 4]])
+        >>> m.flat()
+        [0, 2, 3, 4]
+
+        See Also
+        ========
+
+        tolist
+        values
+        """
+        return [self[i, j] for i in range(self.rows) for j in range(self.cols)]
+
+    def __array__(self, dtype=object, copy=None):
+        if copy is not None and not copy:
+            raise TypeError("Cannot implement copy=False when converting Matrix to ndarray")
+        from .dense import matrix2numpy
+        return matrix2numpy(self, dtype=dtype)
+
+    def __len__(self):
+        """Return the number of elements of ``self``.
+
+        Implemented mainly so bool(Matrix()) == False.
+        """
+        return self.rows * self.cols
+
+    def _matrix_pow_by_jordan_blocks(self, num):
+        from sympy.matrices import diag, MutableMatrix
+
+        def jordan_cell_power(jc, n):
+            N = jc.shape[0]
+            l = jc[0,0]
+            if l.is_zero:
+                if N == 1 and n.is_nonnegative:
+                    jc[0,0] = l**n
+                elif not (n.is_integer and n.is_nonnegative):
+                    raise NonInvertibleMatrixError("Non-invertible matrix can only be raised to a nonnegative integer")
+                else:
+                    for i in range(N):
+                        jc[0,i] = KroneckerDelta(i, n)
+            else:
+                for i in range(N):
+                    bn = binomial(n, i)
+                    if isinstance(bn, binomial):
+                        bn = bn._eval_expand_func()
+                    jc[0,i] = l**(n-i)*bn
+            for i in range(N):
+                for j in range(1, N-i):
+                    jc[j,i+j] = jc [j-1,i+j-1]
+
+        P, J = self.jordan_form()
+        jordan_cells = J.get_diag_blocks()
+        # Make sure jordan_cells matrices are mutable:
+        jordan_cells = [MutableMatrix(j) for j in jordan_cells]
+        for j in jordan_cells:
+            jordan_cell_power(j, num)
+        return self._new(P.multiply(diag(*jordan_cells))
+                .multiply(P.inv()))
+
+    def __str__(self):
+        if S.Zero in self.shape:
+            return 'Matrix(%s, %s, [])' % (self.rows, self.cols)
+        return "Matrix(%s)" % str(self.tolist())
+
+    def _format_str(self, printer=None):
+        if not printer:
+            printer = StrPrinter()
+        # Handle zero dimensions:
+        if S.Zero in self.shape:
+            return 'Matrix(%s, %s, [])' % (self.rows, self.cols)
+        if self.rows == 1:
+            return "Matrix([%s])" % self.table(printer, rowsep=',\n')
+        return "Matrix([\n%s])" % self.table(printer, rowsep=',\n')
+
+    @classmethod
+    def irregular(cls, ntop, *matrices, **kwargs):
+        """Return a matrix filled by the given matrices which
+        are listed in order of appearance from left to right, top to
+        bottom as they first appear in the matrix. They must fill the
+        matrix completely.
+
+        Examples
+        ========
+
+        >>> from sympy import ones, Matrix
+        >>> Matrix.irregular(3, ones(2,1), ones(3,3)*2, ones(2,2)*3,
+        ...   ones(1,1)*4, ones(2,2)*5, ones(1,2)*6, ones(1,2)*7)
+        Matrix([
+            [1, 2, 2, 2, 3, 3],
+            [1, 2, 2, 2, 3, 3],
+            [4, 2, 2, 2, 5, 5],
+            [6, 6, 7, 7, 5, 5]])
+        """
+        ntop = as_int(ntop)
+        # make sure we are working with explicit matrices
+        b = [i.as_explicit() if hasattr(i, 'as_explicit') else i
+            for i in matrices]
+        q = list(range(len(b)))
+        dat = [i.rows for i in b]
+        active = [q.pop(0) for _ in range(ntop)]
+        cols = sum(b[i].cols for i in active)
+        rows = []
+        while any(dat):
+            r = []
+            for a, j in enumerate(active):
+                r.extend(b[j][-dat[j], :])
+                dat[j] -= 1
+                if dat[j] == 0 and q:
+                    active[a] = q.pop(0)
+            if len(r) != cols:
+                raise ValueError(filldedent('''
+                    Matrices provided do not appear to fill
+                    the space completely.'''))
+            rows.append(r)
+        return cls._new(rows)
+
+    @classmethod
+    def _handle_ndarray(cls, arg):
+        # NumPy array or matrix or some other object that implements
+        # __array__. So let's first use this method to get a
+        # numpy.array() and then make a Python list out of it.
+        arr = arg.__array__()
+        if len(arr.shape) == 2:
+            rows, cols = arr.shape[0], arr.shape[1]
+            flat_list = [cls._sympify(i) for i in arr.ravel()]
+            return rows, cols, flat_list
+        elif len(arr.shape) == 1:
+            flat_list = [cls._sympify(i) for i in arr]
+            return arr.shape[0], 1, flat_list
+        else:
+            raise NotImplementedError(
+                "SymPy supports just 1D and 2D matrices")
+
+    @classmethod
+    def _handle_creation_inputs(cls, *args, **kwargs):
+        """Return the number of rows, cols and flat matrix elements.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, I
+
+        Matrix can be constructed as follows:
+
+        * from a nested list of iterables
+
+        >>> Matrix( ((1, 2+I), (3, 4)) )
+        Matrix([
+        [1, 2 + I],
+        [3,     4]])
+
+        * from un-nested iterable (interpreted as a column)
+
+        >>> Matrix( [1, 2] )
+        Matrix([
+        [1],
+        [2]])
+
+        * from un-nested iterable with dimensions
+
+        >>> Matrix(1, 2, [1, 2] )
+        Matrix([[1, 2]])
+
+        * from no arguments (a 0 x 0 matrix)
+
+        >>> Matrix()
+        Matrix(0, 0, [])
+
+        * from a rule
+
+        >>> Matrix(2, 2, lambda i, j: i/(j + 1) )
+        Matrix([
+        [0,   0],
+        [1, 1/2]])
+
+        See Also
+        ========
+        irregular - filling a matrix with irregular blocks
+        """
+        from sympy.matrices import SparseMatrix
+        from sympy.matrices.expressions.matexpr import MatrixSymbol
+        from sympy.matrices.expressions.blockmatrix import BlockMatrix
+
+        flat_list = None
+
+        if len(args) == 1:
+            # Matrix(SparseMatrix(...))
+            if isinstance(args[0], SparseMatrix):
+                return args[0].rows, args[0].cols, flatten(args[0].tolist())
+
+            # Matrix(Matrix(...))
+            elif isinstance(args[0], MatrixBase):
+                return args[0].rows, args[0].cols, args[0].flat()
+
+            # Matrix(MatrixSymbol('X', 2, 2))
+            elif isinstance(args[0], Basic) and args[0].is_Matrix:
+                return args[0].rows, args[0].cols, args[0].as_explicit().flat()
+
+            elif isinstance(args[0], mp.matrix):
+                M = args[0]
+                flat_list = [cls._sympify(x) for x in M]
+                return M.rows, M.cols, flat_list
+
+            # Matrix(numpy.ones((2, 2)))
+            elif hasattr(args[0], "__array__"):
+                return cls._handle_ndarray(args[0])
+
+            # Matrix([1, 2, 3]) or Matrix([[1, 2], [3, 4]])
+            elif is_sequence(args[0]) \
+                    and not isinstance(args[0], DeferredVector):
+                dat = list(args[0])
+                ismat = lambda i: isinstance(i, MatrixBase) and (
+                    evaluate or isinstance(i, (BlockMatrix, MatrixSymbol)))
+                raw = lambda i: is_sequence(i) and not ismat(i)
+                evaluate = kwargs.get('evaluate', True)
+
+
+                if evaluate:
+
+                    def make_explicit(x):
+                        """make Block and Symbol explicit"""
+                        if isinstance(x, BlockMatrix):
+                            return x.as_explicit()
+                        elif isinstance(x, MatrixSymbol) and all(_.is_Integer for _ in x.shape):
+                            return x.as_explicit()
+                        else:
+                            return x
+
+                    def make_explicit_row(row):
+                        # Could be list or could be list of lists
+                        if isinstance(row, (list, tuple)):
+                            return [make_explicit(x) for x in row]
+                        else:
+                            return make_explicit(row)
+
+                    if isinstance(dat, (list, tuple)):
+                        dat = [make_explicit_row(row) for row in dat]
+
+                if len(dat) == 0:
+                    rows = cols = 0
+                    flat_list = []
+                elif all(raw(i) for i in dat) and len(dat[0]) == 0:
+                    if not all(len(i) == 0 for i in dat):
+                        raise ValueError('mismatched dimensions')
+                    rows = len(dat)
+                    cols = 0
+                    flat_list = []
+                elif not any(raw(i) or ismat(i) for i in dat):
+                    # a column as a list of values
+                    flat_list = [cls._sympify(i) for i in dat]
+                    rows = len(flat_list)
+                    cols = 1 if rows else 0
+                elif evaluate and all(ismat(i) for i in dat):
+                    # a column as a list of matrices
+                    ncol = {i.cols for i in dat if any(i.shape)}
+                    if ncol:
+                        if len(ncol) != 1:
+                            raise ValueError('mismatched dimensions')
+                        flat_list = [_ for i in dat for r in i.tolist() for _ in r]
+                        cols = ncol.pop()
+                        rows = len(flat_list)//cols
+                    else:
+                        rows = cols = 0
+                        flat_list = []
+                elif evaluate and any(ismat(i) for i in dat):
+                    ncol = set()
+                    flat_list = []
+                    for i in dat:
+                        if ismat(i):
+                            flat_list.extend(
+                                [k for j in i.tolist() for k in j])
+                            if any(i.shape):
+                                ncol.add(i.cols)
+                        elif raw(i):
+                            if i:
+                                ncol.add(len(i))
+                                flat_list.extend([cls._sympify(ij) for ij in i])
+                        else:
+                            ncol.add(1)
+                            flat_list.append(i)
+                        if len(ncol) > 1:
+                            raise ValueError('mismatched dimensions')
+                    cols = ncol.pop()
+                    rows = len(flat_list)//cols
+                else:
+                    # list of lists; each sublist is a logical row
+                    # which might consist of many rows if the values in
+                    # the row are matrices
+                    flat_list = []
+                    ncol = set()
+                    rows = cols = 0
+                    for row in dat:
+                        if not is_sequence(row) and \
+                                not getattr(row, 'is_Matrix', False):
+                            raise ValueError('expecting list of lists')
+
+                        if hasattr(row, '__array__'):
+                            if 0 in row.shape:
+                                continue
+
+                        if evaluate and all(ismat(i) for i in row):
+                            r, c, flatT = cls._handle_creation_inputs(
+                                [i.T for i in row])
+                            T = reshape(flatT, [c])
+                            flat = \
+                                [T[i][j] for j in range(c) for i in range(r)]
+                            r, c = c, r
+                        else:
+                            r = 1
+                            if getattr(row, 'is_Matrix', False):
+                                c = 1
+                                flat = [row]
+                            else:
+                                c = len(row)
+                                flat = [cls._sympify(i) for i in row]
+                        ncol.add(c)
+                        if len(ncol) > 1:
+                            raise ValueError('mismatched dimensions')
+                        flat_list.extend(flat)
+                        rows += r
+                    cols = ncol.pop() if ncol else 0
+
+        elif len(args) == 3:
+            rows = as_int(args[0])
+            cols = as_int(args[1])
+
+            if rows < 0 or cols < 0:
+                raise ValueError("Cannot create a {} x {} matrix. "
+                                 "Both dimensions must be positive".format(rows, cols))
+
+            # Matrix(2, 2, lambda i, j: i+j)
+            if len(args) == 3 and isinstance(args[2], Callable):
+                op = args[2]
+                flat_list = []
+                for i in range(rows):
+                    flat_list.extend(
+                        [cls._sympify(op(cls._sympify(i), cls._sympify(j)))
+                         for j in range(cols)])
+
+            # Matrix(2, 2, [1, 2, 3, 4])
+            elif len(args) == 3 and is_sequence(args[2]):
+                flat_list = args[2]
+                if len(flat_list) != rows * cols:
+                    raise ValueError(
+                        'List length should be equal to rows*columns')
+                flat_list = [cls._sympify(i) for i in flat_list]
+
+
+        # Matrix()
+        elif len(args) == 0:
+            # Empty Matrix
+            rows = cols = 0
+            flat_list = []
+
+        if flat_list is None:
+            raise TypeError(filldedent('''
+                Data type not understood; expecting list of lists
+                or lists of values.'''))
+
+        return rows, cols, flat_list
+
+    def _setitem(self, key, value):
+        """Helper to set value at location given by key.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, I, zeros, ones
+        >>> m = Matrix(((1, 2+I), (3, 4)))
+        >>> m
+        Matrix([
+        [1, 2 + I],
+        [3,     4]])
+        >>> m[1, 0] = 9
+        >>> m
+        Matrix([
+        [1, 2 + I],
+        [9,     4]])
+        >>> m[1, 0] = [[0, 1]]
+
+        To replace row r you assign to position r*m where m
+        is the number of columns:
+
+        >>> M = zeros(4)
+        >>> m = M.cols
+        >>> M[3*m] = ones(1, m)*2; M
+        Matrix([
+        [0, 0, 0, 0],
+        [0, 0, 0, 0],
+        [0, 0, 0, 0],
+        [2, 2, 2, 2]])
+
+        And to replace column c you can assign to position c:
+
+        >>> M[2] = ones(m, 1)*4; M
+        Matrix([
+        [0, 0, 4, 0],
+        [0, 0, 4, 0],
+        [0, 0, 4, 0],
+        [2, 2, 4, 2]])
+        """
+        from .dense import Matrix
+
+        is_slice = isinstance(key, slice)
+        i, j = key = self.key2ij(key)
+        is_mat = isinstance(value, MatrixBase)
+        if isinstance(i, slice) or isinstance(j, slice):
+            if is_mat:
+                self.copyin_matrix(key, value)
+                return
+            if not isinstance(value, Expr) and is_sequence(value):
+                self.copyin_list(key, value)
+                return
+            raise ValueError('unexpected value: %s' % value)
+        else:
+            if (not is_mat and
+                    not isinstance(value, Basic) and is_sequence(value)):
+                value = Matrix(value)
+                is_mat = True
+            if is_mat:
+                if is_slice:
+                    key = (slice(*divmod(i, self.cols)),
+                           slice(*divmod(j, self.cols)))
+                else:
+                    key = (slice(i, i + value.rows),
+                           slice(j, j + value.cols))
+                self.copyin_matrix(key, value)
+            else:
+                return i, j, self._sympify(value)
+            return
+
+    def add(self, b):
+        """Return self + b."""
+        return self + b
+
+    def condition_number(self):
+        """Returns the condition number of a matrix.
+
+        This is the maximum singular value divided by the minimum singular value
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, S
+        >>> A = Matrix([[1, 0, 0], [0, 10, 0], [0, 0, S.One/10]])
+        >>> A.condition_number()
+        100
+
+        See Also
+        ========
+
+        singular_values
+        """
+
+        if not self:
+            return self.zero
+        singularvalues = self.singular_values()
+        return Max(*singularvalues) / Min(*singularvalues)
+
+    def copy(self):
+        """
+        Returns the copy of a matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix(2, 2, [1, 2, 3, 4])
+        >>> A.copy()
+        Matrix([
+        [1, 2],
+        [3, 4]])
+
+        """
+        return self._new(self.rows, self.cols, self.flat())
+
+    def cross(self, b):
+        r"""
+        Return the cross product of ``self`` and ``b`` relaxing the condition
+        of compatible dimensions: if each has 3 elements, a matrix of the
+        same type and shape as ``self`` will be returned. If ``b`` has the same
+        shape as ``self`` then common identities for the cross product (like
+        `a \times b = - b \times a`) will hold.
+
+        Parameters
+        ==========
+            b : 3x1 or 1x3 Matrix
+
+        See Also
+        ========
+
+        dot
+        hat
+        vee
+        multiply
+        multiply_elementwise
+        """
+        from sympy.matrices.expressions.matexpr import MatrixExpr
+
+        if not isinstance(b, (MatrixBase, MatrixExpr)):
+            raise TypeError(
+                "{} must be a Matrix, not {}.".format(b, type(b)))
+
+        if not (self.rows * self.cols == b.rows * b.cols == 3):
+            raise ShapeError("Dimensions incorrect for cross product: %s x %s" %
+                             ((self.rows, self.cols), (b.rows, b.cols)))
+        else:
+            return self._new(self.rows, self.cols, (
+                (self[1] * b[2] - self[2] * b[1]),
+                (self[2] * b[0] - self[0] * b[2]),
+                (self[0] * b[1] - self[1] * b[0])))
+
+    def hat(self):
+        r"""
+        Return the skew-symmetric matrix representing the cross product,
+        so that ``self.hat() * b`` is equivalent to  ``self.cross(b)``.
+
+        Examples
+        ========
+
+        Calling ``hat`` creates a skew-symmetric 3x3 Matrix from a 3x1 Matrix:
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([1, 2, 3])
+        >>> a.hat()
+        Matrix([
+        [ 0, -3,  2],
+        [ 3,  0, -1],
+        [-2,  1,  0]])
+
+        Multiplying it with another 3x1 Matrix calculates the cross product:
+
+        >>> b = Matrix([3, 2, 1])
+        >>> a.hat() * b
+        Matrix([
+        [-4],
+        [ 8],
+        [-4]])
+
+        Which is equivalent to calling the ``cross`` method:
+
+        >>> a.cross(b)
+        Matrix([
+        [-4],
+        [ 8],
+        [-4]])
+
+        See Also
+        ========
+
+        dot
+        cross
+        vee
+        multiply
+        multiply_elementwise
+        """
+
+        if self.shape != (3, 1):
+            raise ShapeError("Dimensions incorrect, expected (3, 1), got " +
+                             str(self.shape))
+        else:
+            x, y, z = self
+            return self._new(3, 3, (
+                 0, -z,  y,
+                 z,  0, -x,
+                -y,  x,  0))
+
+    def vee(self):
+        r"""
+        Return a 3x1 vector from a skew-symmetric matrix representing the cross product,
+        so that ``self * b`` is equivalent to  ``self.vee().cross(b)``.
+
+        Examples
+        ========
+
+        Calling ``vee`` creates a vector from a skew-symmetric Matrix:
+
+        >>> from sympy import Matrix
+        >>> A = Matrix([[0, -3, 2], [3, 0, -1], [-2, 1, 0]])
+        >>> a = A.vee()
+        >>> a
+        Matrix([
+        [1],
+        [2],
+        [3]])
+
+        Calculating the matrix product of the original matrix with a vector
+        is equivalent to a cross product:
+
+        >>> b = Matrix([3, 2, 1])
+        >>> A * b
+        Matrix([
+        [-4],
+        [ 8],
+        [-4]])
+
+        >>> a.cross(b)
+        Matrix([
+        [-4],
+        [ 8],
+        [-4]])
+
+        ``vee`` can also be used to retrieve angular velocity expressions.
+        Defining a rotation matrix:
+
+        >>> from sympy import rot_ccw_axis3, trigsimp
+        >>> from sympy.physics.mechanics import dynamicsymbols
+        >>> theta = dynamicsymbols('theta')
+        >>> R = rot_ccw_axis3(theta)
+        >>> R
+        Matrix([
+        [cos(theta(t)), -sin(theta(t)), 0],
+        [sin(theta(t)),  cos(theta(t)), 0],
+        [            0,              0, 1]])
+
+        We can retrieve the angular velocity:
+
+        >>> Omega = R.T * R.diff()
+        >>> Omega = trigsimp(Omega)
+        >>> Omega.vee()
+        Matrix([
+        [                      0],
+        [                      0],
+        [Derivative(theta(t), t)]])
+
+        See Also
+        ========
+
+        dot
+        cross
+        hat
+        multiply
+        multiply_elementwise
+        """
+
+        if self.shape != (3, 3):
+            raise ShapeError("Dimensions incorrect, expected (3, 3), got " +
+                             str(self.shape))
+        elif not self.is_anti_symmetric():
+            raise ValueError("Matrix is not skew-symmetric")
+        else:
+            return self._new(3, 1, (
+                 self[2, 1],
+                 self[0, 2],
+                 self[1, 0]))
+
+    @property
+    def D(self):
+        """Return Dirac conjugate (if ``self.rows == 4``).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, I, eye
+        >>> m = Matrix((0, 1 + I, 2, 3))
+        >>> m.D
+        Matrix([[0, 1 - I, -2, -3]])
+        >>> m = (eye(4) + I*eye(4))
+        >>> m[0, 3] = 2
+        >>> m.D
+        Matrix([
+        [1 - I,     0,      0,      0],
+        [    0, 1 - I,      0,      0],
+        [    0,     0, -1 + I,      0],
+        [    2,     0,      0, -1 + I]])
+
+        If the matrix does not have 4 rows an AttributeError will be raised
+        because this property is only defined for matrices with 4 rows.
+
+        >>> Matrix(eye(2)).D
+        Traceback (most recent call last):
+        ...
+        AttributeError: Matrix has no attribute D.
+
+        See Also
+        ========
+
+        sympy.matrices.matrixbase.MatrixBase.conjugate: By-element conjugation
+        sympy.matrices.matrixbase.MatrixBase.H: Hermite conjugation
+        """
+        from sympy.physics.matrices import mgamma
+        if self.rows != 4:
+            # In Python 3.2, properties can only return an AttributeError
+            # so we can't raise a ShapeError -- see commit which added the
+            # first line of this inline comment. Also, there is no need
+            # for a message since MatrixBase will raise the AttributeError
+            raise AttributeError
+        return self.H * mgamma(0)
+
+    def dot(self, b, hermitian=None, conjugate_convention=None):
+        """Return the dot or inner product of two vectors of equal length.
+        Here ``self`` must be a ``Matrix`` of size 1 x n or n x 1, and ``b``
+        must be either a matrix of size 1 x n, n x 1, or a list/tuple of length n.
+        A scalar is returned.
+
+        By default, ``dot`` does not conjugate ``self`` or ``b``, even if there are
+        complex entries. Set ``hermitian=True`` (and optionally a ``conjugate_convention``)
+        to compute the hermitian inner product.
+
+        Possible kwargs are ``hermitian`` and ``conjugate_convention``.
+
+        If ``conjugate_convention`` is ``"left"``, ``"math"`` or ``"maths"``,
+        the conjugate of the first vector (``self``) is used.  If ``"right"``
+        or ``"physics"`` is specified, the conjugate of the second vector ``b`` is used.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+        >>> v = Matrix([1, 1, 1])
+        >>> M.row(0).dot(v)
+        6
+        >>> M.col(0).dot(v)
+        12
+        >>> v = [3, 2, 1]
+        >>> M.row(0).dot(v)
+        10
+
+        >>> from sympy import I
+        >>> q = Matrix([1*I, 1*I, 1*I])
+        >>> q.dot(q, hermitian=False)
+        -3
+
+        >>> q.dot(q, hermitian=True)
+        3
+
+        >>> q1 = Matrix([1, 1, 1*I])
+        >>> q.dot(q1, hermitian=True, conjugate_convention="maths")
+        1 - 2*I
+        >>> q.dot(q1, hermitian=True, conjugate_convention="physics")
+        1 + 2*I
+
+
+        See Also
+        ========
+
+        cross
+        multiply
+        multiply_elementwise
+        """
+        from .dense import Matrix
+
+        if not isinstance(b, MatrixBase):
+            if is_sequence(b):
+                if len(b) != self.cols and len(b) != self.rows:
+                    raise ShapeError(
+                        "Dimensions incorrect for dot product: %s, %s" % (
+                            self.shape, len(b)))
+                return self.dot(Matrix(b))
+            else:
+                raise TypeError(
+                    "`b` must be an ordered iterable or Matrix, not %s." %
+                    type(b))
+
+        if (1 not in self.shape) or (1 not in b.shape):
+            raise ShapeError
+        if len(self) != len(b):
+            raise ShapeError(
+                "Dimensions incorrect for dot product: %s, %s" % (self.shape, b.shape))
+
+        mat = self
+        n = len(mat)
+        if mat.shape != (1, n):
+            mat = mat.reshape(1, n)
+        if b.shape != (n, 1):
+            b = b.reshape(n, 1)
+
+        # Now ``mat`` is a row vector and ``b`` is a column vector.
+
+        # If it so happens that only conjugate_convention is passed
+        # then automatically set hermitian to True. If only hermitian
+        # is true but no conjugate_convention is not passed then
+        # automatically set it to ``"maths"``
+
+        if conjugate_convention is not None and hermitian is None:
+            hermitian = True
+        if hermitian and conjugate_convention is None:
+            conjugate_convention = "maths"
+
+        if hermitian == True:
+            if conjugate_convention in ("maths", "left", "math"):
+                mat = mat.conjugate()
+            elif conjugate_convention in ("physics", "right"):
+                b = b.conjugate()
+            else:
+                raise ValueError("Unknown conjugate_convention was entered."
+                                 " conjugate_convention must be one of the"
+                                 " following: math, maths, left, physics or right.")
+        return (mat * b)[0]
+
+    def dual(self):
+        """Returns the dual of a matrix.
+
+        A dual of a matrix is:
+
+        ``(1/2)*levicivita(i, j, k, l)*M(k, l)`` summed over indices `k` and `l`
+
+        Since the levicivita method is anti_symmetric for any pairwise
+        exchange of indices, the dual of a symmetric matrix is the zero
+        matrix. Strictly speaking the dual defined here assumes that the
+        'matrix' `M` is a contravariant anti_symmetric second rank tensor,
+        so that the dual is a covariant second rank tensor.
+
+        """
+        from sympy.matrices import zeros
+
+        M, n = self[:, :], self.rows
+        work = zeros(n)
+        if self.is_symmetric():
+            return work
+
+        for i in range(1, n):
+            for j in range(1, n):
+                acum = 0
+                for k in range(1, n):
+                    acum += LeviCivita(i, j, 0, k) * M[0, k]
+                work[i, j] = acum
+                work[j, i] = -acum
+
+        for l in range(1, n):
+            acum = 0
+            for a in range(1, n):
+                for b in range(1, n):
+                    acum += LeviCivita(0, l, a, b) * M[a, b]
+            acum /= 2
+            work[0, l] = -acum
+            work[l, 0] = acum
+
+        return work
+
+    def _eval_matrix_exp_jblock(self):
+        """A helper function to compute an exponential of a Jordan block
+        matrix
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Matrix
+        >>> l = Symbol('lamda')
+
+        A trivial example of 1*1 Jordan block:
+
+        >>> m = Matrix.jordan_block(1, l)
+        >>> m._eval_matrix_exp_jblock()
+        Matrix([[exp(lamda)]])
+
+        An example of 3*3 Jordan block:
+
+        >>> m = Matrix.jordan_block(3, l)
+        >>> m._eval_matrix_exp_jblock()
+        Matrix([
+        [exp(lamda), exp(lamda), exp(lamda)/2],
+        [         0, exp(lamda),   exp(lamda)],
+        [         0,          0,   exp(lamda)]])
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Matrix_function#Jordan_decomposition
+        """
+        size = self.rows
+        l = self[0, 0]
+        exp_l = exp(l)
+
+        bands = {i: exp_l / factorial(i) for i in range(size)}
+
+        from .sparsetools import banded
+        return self.__class__(banded(size, bands))
+
+
+    def analytic_func(self, f, x):
+        """
+        Computes f(A) where A is a Square Matrix
+        and f is an analytic function.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Matrix, S, log
+
+        >>> x = Symbol('x')
+        >>> m = Matrix([[S(5)/4, S(3)/4], [S(3)/4, S(5)/4]])
+        >>> f = log(x)
+        >>> m.analytic_func(f, x)
+        Matrix([
+        [     0, log(2)],
+        [log(2),      0]])
+
+        Parameters
+        ==========
+
+        f : Expr
+            Analytic Function
+        x : Symbol
+            parameter of f
+
+        """
+
+        f, x = _sympify(f), _sympify(x)
+        if not self.is_square:
+            raise NonSquareMatrixError
+        if not x.is_symbol:
+            raise ValueError("{} must be a symbol.".format(x))
+        if x not in f.free_symbols:
+            raise ValueError(
+                "{} must be a parameter of {}.".format(x, f))
+        if x in self.free_symbols:
+            raise ValueError(
+                "{} must not be a parameter of {}.".format(x, self))
+
+        eigen = self.eigenvals()
+        max_mul = max(eigen.values())
+        derivative = {}
+        dd = f
+        for i in range(max_mul - 1):
+            dd = diff(dd, x)
+            derivative[i + 1] = dd
+        n = self.shape[0]
+        r = self.zeros(n)
+        f_val = self.zeros(n, 1)
+        row = 0
+
+        for i in eigen:
+            mul = eigen[i]
+            f_val[row] = f.subs(x, i)
+            if f_val[row].is_number and not f_val[row].is_complex:
+                raise ValueError(
+                    "Cannot evaluate the function because the "
+                    "function {} is not analytic at the given "
+                    "eigenvalue {}".format(f, f_val[row]))
+            val = 1
+            for a in range(n):
+                r[row, a] = val
+                val *= i
+            if mul > 1:
+                coe = [1 for ii in range(n)]
+                deri = 1
+                while mul > 1:
+                    row = row + 1
+                    mul -= 1
+                    d_i = derivative[deri].subs(x, i)
+                    if d_i.is_number and not d_i.is_complex:
+                        raise ValueError(
+                            "Cannot evaluate the function because the "
+                            "derivative {} is not analytic at the given "
+                            "eigenvalue {}".format(derivative[deri], d_i))
+                    f_val[row] = d_i
+                    for a in range(n):
+                        if a - deri + 1 <= 0:
+                            r[row, a] = 0
+                            coe[a] = 0
+                            continue
+                        coe[a] = coe[a]*(a - deri + 1)
+                        r[row, a] = coe[a]*pow(i, a - deri)
+                    deri += 1
+            row += 1
+        c = r.solve(f_val)
+        ans = self.zeros(n)
+        pre = self.eye(n)
+        for i in range(n):
+            ans = ans + c[i]*pre
+            pre *= self
+        return ans
+
+
+    def exp(self):
+        """Return the exponential of a square matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Matrix
+
+        >>> t = Symbol('t')
+        >>> m = Matrix([[0, 1], [-1, 0]]) * t
+        >>> m.exp()
+        Matrix([
+        [    exp(I*t)/2 + exp(-I*t)/2, -I*exp(I*t)/2 + I*exp(-I*t)/2],
+        [I*exp(I*t)/2 - I*exp(-I*t)/2,      exp(I*t)/2 + exp(-I*t)/2]])
+        """
+        if not self.is_square:
+            raise NonSquareMatrixError(
+                "Exponentiation is valid only for square matrices")
+        try:
+            P, J = self.jordan_form()
+            cells = J.get_diag_blocks()
+        except MatrixError:
+            raise NotImplementedError(
+                "Exponentiation is implemented only for matrices for which the Jordan normal form can be computed")
+
+        blocks = [cell._eval_matrix_exp_jblock() for cell in cells]
+        from sympy.matrices import diag
+        eJ = diag(*blocks)
+        # n = self.rows
+        ret = P.multiply(eJ, dotprodsimp=None).multiply(P.inv(), dotprodsimp=None)
+        if all(value.is_real for value in self.values()):
+            return type(self)(re(ret))
+        else:
+            return type(self)(ret)
+
+    def _eval_matrix_log_jblock(self):
+        """Helper function to compute logarithm of a jordan block.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol, Matrix
+        >>> l = Symbol('lamda')
+
+        A trivial example of 1*1 Jordan block:
+
+        >>> m = Matrix.jordan_block(1, l)
+        >>> m._eval_matrix_log_jblock()
+        Matrix([[log(lamda)]])
+
+        An example of 3*3 Jordan block:
+
+        >>> m = Matrix.jordan_block(3, l)
+        >>> m._eval_matrix_log_jblock()
+        Matrix([
+        [log(lamda),    1/lamda, -1/(2*lamda**2)],
+        [         0, log(lamda),         1/lamda],
+        [         0,          0,      log(lamda)]])
+        """
+        size = self.rows
+        l = self[0, 0]
+
+        if l.is_zero:
+            raise MatrixError(
+                'Could not take logarithm or reciprocal for the given '
+                'eigenvalue {}'.format(l))
+
+        bands = {0: log(l)}
+        for i in range(1, size):
+            bands[i] = -((-l) ** -i) / i
+
+        from .sparsetools import banded
+        return self.__class__(banded(size, bands))
+
+    def log(self, simplify=cancel):
+        """Return the logarithm of a square matrix.
+
+        Parameters
+        ==========
+
+        simplify : function, bool
+            The function to simplify the result with.
+
+            Default is ``cancel``, which is effective to reduce the
+            expression growing for taking reciprocals and inverses for
+            symbolic matrices.
+
+        Examples
+        ========
+
+        >>> from sympy import S, Matrix
+
+        Examples for positive-definite matrices:
+
+        >>> m = Matrix([[1, 1], [0, 1]])
+        >>> m.log()
+        Matrix([
+        [0, 1],
+        [0, 0]])
+
+        >>> m = Matrix([[S(5)/4, S(3)/4], [S(3)/4, S(5)/4]])
+        >>> m.log()
+        Matrix([
+        [     0, log(2)],
+        [log(2),      0]])
+
+        Examples for non positive-definite matrices:
+
+        >>> m = Matrix([[S(3)/4, S(5)/4], [S(5)/4, S(3)/4]])
+        >>> m.log()
+        Matrix([
+        [         I*pi/2, log(2) - I*pi/2],
+        [log(2) - I*pi/2,          I*pi/2]])
+
+        >>> m = Matrix(
+        ...     [[0, 0, 0, 1],
+        ...      [0, 0, 1, 0],
+        ...      [0, 1, 0, 0],
+        ...      [1, 0, 0, 0]])
+        >>> m.log()
+        Matrix([
+        [ I*pi/2,       0,       0, -I*pi/2],
+        [      0,  I*pi/2, -I*pi/2,       0],
+        [      0, -I*pi/2,  I*pi/2,       0],
+        [-I*pi/2,       0,       0,  I*pi/2]])
+        """
+        if not self.is_square:
+            raise NonSquareMatrixError(
+                "Logarithm is valid only for square matrices")
+
+        try:
+            if simplify:
+                P, J = simplify(self).jordan_form()
+            else:
+                P, J = self.jordan_form()
+
+            cells = J.get_diag_blocks()
+        except MatrixError:
+            raise NotImplementedError(
+                "Logarithm is implemented only for matrices for which "
+                "the Jordan normal form can be computed")
+
+        blocks = [
+            cell._eval_matrix_log_jblock()
+            for cell in cells]
+        from sympy.matrices import diag
+        eJ = diag(*blocks)
+
+        if simplify:
+            ret = simplify(P * eJ * simplify(P.inv()))
+            ret = self.__class__(ret)
+        else:
+            ret = P * eJ * P.inv()
+
+        return ret
+
+    def is_nilpotent(self):
+        """Checks if a matrix is nilpotent.
+
+        A matrix B is nilpotent if for some integer k, B**k is
+        a zero matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> a = Matrix([[0, 0, 0], [1, 0, 0], [1, 1, 0]])
+        >>> a.is_nilpotent()
+        True
+
+        >>> a = Matrix([[1, 0, 1], [1, 0, 0], [1, 1, 0]])
+        >>> a.is_nilpotent()
+        False
+        """
+        if not self:
+            return True
+        if not self.is_square:
+            raise NonSquareMatrixError(
+                "Nilpotency is valid only for square matrices")
+        x = uniquely_named_symbol('x', self, modify=lambda s: '_' + s)
+        p = self.charpoly(x)
+        if p.args[0] == x ** self.rows:
+            return True
+        return False
+
+    def key2bounds(self, keys):
+        """Converts a key with potentially mixed types of keys (integer and slice)
+        into a tuple of ranges and raises an error if any index is out of ``self``'s
+        range.
+
+        See Also
+        ========
+
+        key2ij
+        """
+        islice, jslice = [isinstance(k, slice) for k in keys]
+        if islice:
+            if not self.rows:
+                rlo = rhi = 0
+            else:
+                rlo, rhi = keys[0].indices(self.rows)[:2]
+        else:
+            rlo = a2idx(keys[0], self.rows)
+            rhi = rlo + 1
+        if jslice:
+            if not self.cols:
+                clo = chi = 0
+            else:
+                clo, chi = keys[1].indices(self.cols)[:2]
+        else:
+            clo = a2idx(keys[1], self.cols)
+            chi = clo + 1
+        return rlo, rhi, clo, chi
+
+    def key2ij(self, key):
+        """Converts key into canonical form, converting integers or indexable
+        items into valid integers for ``self``'s range or returning slices
+        unchanged.
+
+        See Also
+        ========
+
+        key2bounds
+        """
+        if is_sequence(key):
+            if not len(key) == 2:
+                raise TypeError('key must be a sequence of length 2')
+            return [a2idx(i, n) if not isinstance(i, slice) else i
+                    for i, n in zip(key, self.shape)]
+        elif isinstance(key, slice):
+            return key.indices(len(self))[:2]
+        else:
+            return divmod(a2idx(key, len(self)), self.cols)
+
+    def normalized(self, iszerofunc=_iszero):
+        """Return the normalized version of ``self``.
+
+        Parameters
+        ==========
+
+        iszerofunc : Function, optional
+            A function to determine whether ``self`` is a zero vector.
+            The default ``_iszero`` tests to see if each element is
+            exactly zero.
+
+        Returns
+        =======
+
+        Matrix
+            Normalized vector form of ``self``.
+            It has the same length as a unit vector. However, a zero vector
+            will be returned for a vector with norm 0.
+
+        Raises
+        ======
+
+        ShapeError
+            If the matrix is not in a vector form.
+
+        See Also
+        ========
+
+        norm
+        """
+        if self.rows != 1 and self.cols != 1:
+            raise ShapeError("A Matrix must be a vector to normalize.")
+        norm = self.norm()
+        if iszerofunc(norm):
+            out = self.zeros(self.rows, self.cols)
+        else:
+            out = self.applyfunc(lambda i: i / norm)
+        return out
+
+    def norm(self, ord=None):
+        """Return the Norm of a Matrix or Vector.
+
+        In the simplest case this is the geometric size of the vector
+        Other norms can be specified by the ord parameter
+
+
+        =====  ============================  ==========================
+        ord    norm for matrices             norm for vectors
+        =====  ============================  ==========================
+        None   Frobenius norm                2-norm
+        'fro'  Frobenius norm                - does not exist
+        inf    maximum row sum               max(abs(x))
+        -inf   --                            min(abs(x))
+        1      maximum column sum            as below
+        -1     --                            as below
+        2      2-norm (largest sing. value)  as below
+        -2     smallest singular value       as below
+        other  - does not exist              sum(abs(x)**ord)**(1./ord)
+        =====  ============================  ==========================
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, Symbol, trigsimp, cos, sin, oo
+        >>> x = Symbol('x', real=True)
+        >>> v = Matrix([cos(x), sin(x)])
+        >>> trigsimp( v.norm() )
+        1
+        >>> v.norm(10)
+        (sin(x)**10 + cos(x)**10)**(1/10)
+        >>> A = Matrix([[1, 1], [1, 1]])
+        >>> A.norm(1) # maximum sum of absolute values of A is 2
+        2
+        >>> A.norm(2) # Spectral norm (max of |Ax|/|x| under 2-vector-norm)
+        2
+        >>> A.norm(-2) # Inverse spectral norm (smallest singular value)
+        0
+        >>> A.norm() # Frobenius Norm
+        2
+        >>> A.norm(oo) # Infinity Norm
+        2
+        >>> Matrix([1, -2]).norm(oo)
+        2
+        >>> Matrix([-1, 2]).norm(-oo)
+        1
+
+        See Also
+        ========
+
+        normalized
+        """
+        # Row or Column Vector Norms
+        vals = list(self.values()) or [0]
+        if S.One in self.shape:
+            if ord in (2, None):  # Common case sqrt()
+                return sqrt(Add(*(abs(i) ** 2 for i in vals)))
+
+            elif ord == 1:  # sum(abs(x))
+                return Add(*(abs(i) for i in vals))
+
+            elif ord is S.Infinity:  # max(abs(x))
+                return Max(*[abs(i) for i in vals])
+
+            elif ord is S.NegativeInfinity:  # min(abs(x))
+                return Min(*[abs(i) for i in vals])
+
+            # Otherwise generalize the 2-norm, Sum(x_i**ord)**(1/ord)
+            # Note that while useful this is not mathematically a norm
+            try:
+                return Pow(Add(*(abs(i) ** ord for i in vals)), S.One / ord)
+            except (NotImplementedError, TypeError):
+                raise ValueError("Expected order to be Number, Symbol, oo")
+
+        # Matrix Norms
+        else:
+            if ord == 1:  # Maximum column sum
+                m = self.applyfunc(abs)
+                return Max(*[sum(m.col(i)) for i in range(m.cols)])
+
+            elif ord == 2:  # Spectral Norm
+                # Maximum singular value
+                return Max(*self.singular_values())
+
+            elif ord == -2:
+                # Minimum singular value
+                return Min(*self.singular_values())
+
+            elif ord is S.Infinity:   # Infinity Norm - Maximum row sum
+                m = self.applyfunc(abs)
+                return Max(*[sum(m.row(i)) for i in range(m.rows)])
+
+            elif (ord is None or isinstance(ord,
+                                            str) and ord.lower() in
+                ['f', 'fro', 'frobenius', 'vector']):
+                # Reshape as vector and send back to norm function
+                return self.vec().norm(ord=2)
+
+            else:
+                raise NotImplementedError("Matrix Norms under development")
+
+    def print_nonzero(self, symb="X"):
+        """Shows location of non-zero entries for fast shape lookup.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, eye
+        >>> m = Matrix(2, 3, lambda i, j: i*3+j)
+        >>> m
+        Matrix([
+        [0, 1, 2],
+        [3, 4, 5]])
+        >>> m.print_nonzero()
+        [ XX]
+        [XXX]
+        >>> m = eye(4)
+        >>> m.print_nonzero("x")
+        [x   ]
+        [ x  ]
+        [  x ]
+        [   x]
+
+        """
+        s = []
+        for i in range(self.rows):
+            line = []
+            for j in range(self.cols):
+                if self[i, j] == 0:
+                    line.append(" ")
+                else:
+                    line.append(str(symb))
+            s.append("[%s]" % ''.join(line))
+        print('\n'.join(s))
+
+    def project(self, v):
+        """Return the projection of ``self`` onto the line containing ``v``.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, S, sqrt
+        >>> V = Matrix([sqrt(3)/2, S.Half])
+        >>> x = Matrix([[1, 0]])
+        >>> V.project(x)
+        Matrix([[sqrt(3)/2, 0]])
+        >>> V.project(-x)
+        Matrix([[sqrt(3)/2, 0]])
+        """
+        return v * (self.dot(v) / v.dot(v))
+
+    def table(self, printer, rowstart='[', rowend=']', rowsep='\n',
+              colsep=', ', align='right'):
+        r"""
+        String form of Matrix as a table.
+
+        ``printer`` is the printer to use for on the elements (generally
+        something like StrPrinter())
+
+        ``rowstart`` is the string used to start each row (by default '[').
+
+        ``rowend`` is the string used to end each row (by default ']').
+
+        ``rowsep`` is the string used to separate rows (by default a newline).
+
+        ``colsep`` is the string used to separate columns (by default ', ').
+
+        ``align`` defines how the elements are aligned. Must be one of 'left',
+        'right', or 'center'.  You can also use '<', '>', and '^' to mean the
+        same thing, respectively.
+
+        This is used by the string printer for Matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, StrPrinter
+        >>> M = Matrix([[1, 2], [-33, 4]])
+        >>> printer = StrPrinter()
+        >>> M.table(printer)
+        '[  1, 2]\n[-33, 4]'
+        >>> print(M.table(printer))
+        [  1, 2]
+        [-33, 4]
+        >>> print(M.table(printer, rowsep=',\n'))
+        [  1, 2],
+        [-33, 4]
+        >>> print('[%s]' % M.table(printer, rowsep=',\n'))
+        [[  1, 2],
+        [-33, 4]]
+        >>> print(M.table(printer, colsep=' '))
+        [  1 2]
+        [-33 4]
+        >>> print(M.table(printer, align='center'))
+        [ 1 , 2]
+        [-33, 4]
+        >>> print(M.table(printer, rowstart='{', rowend='}'))
+        {  1, 2}
+        {-33, 4}
+        """
+        # Handle zero dimensions:
+        if S.Zero in self.shape:
+            return '[]'
+        # Build table of string representations of the elements
+        res = []
+        # Track per-column max lengths for pretty alignment
+        maxlen = [0] * self.cols
+        for i in range(self.rows):
+            res.append([])
+            for j in range(self.cols):
+                s = printer._print(self[i, j])
+                res[-1].append(s)
+                maxlen[j] = max(len(s), maxlen[j])
+        # Patch strings together
+        align = {
+            'left': 'ljust',
+            'right': 'rjust',
+            'center': 'center',
+            '<': 'ljust',
+            '>': 'rjust',
+            '^': 'center',
+        }[align]
+        for i, row in enumerate(res):
+            for j, elem in enumerate(row):
+                row[j] = getattr(elem, align)(maxlen[j])
+            res[i] = rowstart + colsep.join(row) + rowend
+        return rowsep.join(res)
+
+    def rank_decomposition(self, iszerofunc=_iszero, simplify=False):
+        return _rank_decomposition(self, iszerofunc=iszerofunc,
+                simplify=simplify)
+
+    def cholesky(self, hermitian=True):
+        raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix')
+
+    def LDLdecomposition(self, hermitian=True):
+        raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix')
+
+    def LUdecomposition(self, iszerofunc=_iszero, simpfunc=None,
+            rankcheck=False):
+        return _LUdecomposition(self, iszerofunc=iszerofunc, simpfunc=simpfunc,
+                rankcheck=rankcheck)
+
+    def LUdecomposition_Simple(self, iszerofunc=_iszero, simpfunc=None,
+            rankcheck=False):
+        return _LUdecomposition_Simple(self, iszerofunc=iszerofunc,
+                simpfunc=simpfunc, rankcheck=rankcheck)
+
+    def LUdecompositionFF(self):
+        return _LUdecompositionFF(self)
+
+    def singular_value_decomposition(self):
+        return _singular_value_decomposition(self)
+
+    def QRdecomposition(self):
+        return _QRdecomposition(self)
+
+    def upper_hessenberg_decomposition(self):
+        return _upper_hessenberg_decomposition(self)
+
+    def diagonal_solve(self, rhs):
+        return _diagonal_solve(self, rhs)
+
+    def lower_triangular_solve(self, rhs):
+        raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix')
+
+    def upper_triangular_solve(self, rhs):
+        raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix')
+
+    def cholesky_solve(self, rhs):
+        return _cholesky_solve(self, rhs)
+
+    def LDLsolve(self, rhs):
+        return _LDLsolve(self, rhs)
+
+    def LUsolve(self, rhs, iszerofunc=_iszero):
+        return _LUsolve(self, rhs, iszerofunc=iszerofunc)
+
+    def QRsolve(self, b):
+        return _QRsolve(self, b)
+
+    def gauss_jordan_solve(self, B, freevar=False):
+        return _gauss_jordan_solve(self, B, freevar=freevar)
+
+    def pinv_solve(self, B, arbitrary_matrix=None):
+        return _pinv_solve(self, B, arbitrary_matrix=arbitrary_matrix)
+
+    def cramer_solve(self, rhs, det_method="laplace"):
+        return _cramer_solve(self, rhs, det_method=det_method)
+
+    def solve(self, rhs, method='GJ'):
+        return _solve(self, rhs, method=method)
+
+    def solve_least_squares(self, rhs, method='CH'):
+        return _solve_least_squares(self, rhs, method=method)
+
+    def pinv(self, method='RD'):
+        return _pinv(self, method=method)
+
+    def inverse_ADJ(self, iszerofunc=_iszero):
+        return _inv_ADJ(self, iszerofunc=iszerofunc)
+
+    def inverse_BLOCK(self, iszerofunc=_iszero):
+        return _inv_block(self, iszerofunc=iszerofunc)
+
+    def inverse_GE(self, iszerofunc=_iszero):
+        return _inv_GE(self, iszerofunc=iszerofunc)
+
+    def inverse_LU(self, iszerofunc=_iszero):
+        return _inv_LU(self, iszerofunc=iszerofunc)
+
+    def inverse_CH(self, iszerofunc=_iszero):
+        return _inv_CH(self, iszerofunc=iszerofunc)
+
+    def inverse_LDL(self, iszerofunc=_iszero):
+        return _inv_LDL(self, iszerofunc=iszerofunc)
+
+    def inverse_QR(self, iszerofunc=_iszero):
+        return _inv_QR(self, iszerofunc=iszerofunc)
+
+    def inv(self, method=None, iszerofunc=_iszero, try_block_diag=False):
+        return _inv(self, method=method, iszerofunc=iszerofunc,
+                try_block_diag=try_block_diag)
+
+    def connected_components(self):
+        return _connected_components(self)
+
+    def connected_components_decomposition(self):
+        return _connected_components_decomposition(self)
+
+    def strongly_connected_components(self):
+        return _strongly_connected_components(self)
+
+    def strongly_connected_components_decomposition(self, lower=True):
+        return _strongly_connected_components_decomposition(self, lower=lower)
+
+    _sage_ = Basic._sage_
+
+    rank_decomposition.__doc__     = _rank_decomposition.__doc__
+    cholesky.__doc__               = _cholesky.__doc__
+    LDLdecomposition.__doc__       = _LDLdecomposition.__doc__
+    LUdecomposition.__doc__        = _LUdecomposition.__doc__
+    LUdecomposition_Simple.__doc__ = _LUdecomposition_Simple.__doc__
+    LUdecompositionFF.__doc__      = _LUdecompositionFF.__doc__
+    singular_value_decomposition.__doc__ = _singular_value_decomposition.__doc__
+    QRdecomposition.__doc__        = _QRdecomposition.__doc__
+    upper_hessenberg_decomposition.__doc__ = _upper_hessenberg_decomposition.__doc__
+
+    diagonal_solve.__doc__         = _diagonal_solve.__doc__
+    lower_triangular_solve.__doc__ = _lower_triangular_solve.__doc__
+    upper_triangular_solve.__doc__ = _upper_triangular_solve.__doc__
+    cholesky_solve.__doc__         = _cholesky_solve.__doc__
+    LDLsolve.__doc__               = _LDLsolve.__doc__
+    LUsolve.__doc__                = _LUsolve.__doc__
+    QRsolve.__doc__                = _QRsolve.__doc__
+    gauss_jordan_solve.__doc__     = _gauss_jordan_solve.__doc__
+    pinv_solve.__doc__             = _pinv_solve.__doc__
+    cramer_solve.__doc__           = _cramer_solve.__doc__
+    solve.__doc__                  = _solve.__doc__
+    solve_least_squares.__doc__    = _solve_least_squares.__doc__
+
+    pinv.__doc__                   = _pinv.__doc__
+    inverse_ADJ.__doc__            = _inv_ADJ.__doc__
+    inverse_GE.__doc__             = _inv_GE.__doc__
+    inverse_LU.__doc__             = _inv_LU.__doc__
+    inverse_CH.__doc__             = _inv_CH.__doc__
+    inverse_LDL.__doc__            = _inv_LDL.__doc__
+    inverse_QR.__doc__             = _inv_QR.__doc__
+    inverse_BLOCK.__doc__          = _inv_block.__doc__
+    inv.__doc__                    = _inv.__doc__
+
+    connected_components.__doc__   = _connected_components.__doc__
+    connected_components_decomposition.__doc__ = \
+        _connected_components_decomposition.__doc__
+    strongly_connected_components.__doc__   = \
+        _strongly_connected_components.__doc__
+    strongly_connected_components_decomposition.__doc__ = \
+        _strongly_connected_components_decomposition.__doc__
+
+
+def _convert_matrix(typ, mat):
+    """Convert mat to a Matrix of type typ."""
+    from sympy.matrices.matrixbase import MatrixBase
+    if getattr(mat, "is_Matrix", False) and not isinstance(mat, MatrixBase):
+        # This is needed for interop between Matrix and the redundant matrix
+        # mixin types like _MinimalMatrix etc. If anyone should happen to be
+        # using those then this keeps them working. Really _MinimalMatrix etc
+        # should be deprecated and removed though.
+        return typ(*mat.shape, list(mat))
+    else:
+        return typ(mat)
+
+
+def _has_matrix_shape(other):
+    shape = getattr(other, 'shape', None)
+    if shape is None:
+        return False
+    return isinstance(shape, tuple) and len(shape) == 2
+
+
+def _has_rows_cols(other):
+    return hasattr(other, 'rows') and hasattr(other, 'cols')
+
+
+def _coerce_operand(self, other):
+    """Convert other to a Matrix, or check for possible scalar."""
+
+    INVALID = None, 'invalid_type'
+
+    # Disallow mixing Matrix and Array
+    if isinstance(other, NDimArray):
+        return INVALID
+
+    is_Matrix = getattr(other, 'is_Matrix', None)
+
+    # Return a Matrix as-is
+    if is_Matrix:
+        return other, 'is_matrix'
+
+    # Try to convert numpy array, mpmath matrix etc.
+    if is_Matrix is None:
+        if _has_matrix_shape(other) or _has_rows_cols(other):
+            return _convert_matrix(type(self), other), 'is_matrix'
+
+    # Could be a scalar but only if not iterable...
+    if not isinstance(other, Iterable):
+        return other, 'possible_scalar'
+
+    return INVALID
+
+
+def classof(A, B):
+    """
+    Get the type of the result when combining matrices of different types.
+
+    Currently the strategy is that immutability is contagious.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, ImmutableMatrix
+    >>> from sympy.matrices.matrixbase import classof
+    >>> M = Matrix([[1, 2], [3, 4]]) # a Mutable Matrix
+    >>> IM = ImmutableMatrix([[1, 2], [3, 4]])
+    >>> classof(M, IM)
+    
+    """
+    priority_A = getattr(A, '_class_priority', None)
+    priority_B = getattr(B, '_class_priority', None)
+    if None not in (priority_A, priority_B):
+        if A._class_priority > B._class_priority:
+            return A.__class__
+        else:
+            return B.__class__
+
+    try:
+        import numpy
+    except ImportError:
+        pass
+    else:
+        if isinstance(A, numpy.ndarray):
+            return B.__class__
+        if isinstance(B, numpy.ndarray):
+            return A.__class__
+
+    raise TypeError("Incompatible classes %s, %s" % (A.__class__, B.__class__))
+
+
+def _unify_with_other(self, other):
+    """Unify self and other into a single matrix type, or check for scalar."""
+    other, T = _coerce_operand(self, other)
+
+    if T == "is_matrix":
+        typ = classof(self, other)
+        if typ != self.__class__:
+            self = _convert_matrix(typ, self)
+        if typ != other.__class__:
+            other = _convert_matrix(typ, other)
+
+    return self, other, T
+
+
+def a2idx(j, n=None):
+    """Return integer after making positive and validating against n."""
+    if not isinstance(j, int):
+        jindex = getattr(j, '__index__', None)
+        if jindex is not None:
+            j = jindex()
+        else:
+            raise IndexError("Invalid index a[%r]" % (j,))
+    if n is not None:
+        if j < 0:
+            j += n
+        if not (j >= 0 and j < n):
+            raise IndexError("Index out of range: a[%s]" % (j,))
+    return int(j)
+
+
+class DeferredVector(Symbol, NotIterable): # type: ignore
+    """A vector whose components are deferred (e.g. for use with lambdify).
+
+    Examples
+    ========
+
+    >>> from sympy import DeferredVector, lambdify
+    >>> X = DeferredVector( 'X' )
+    >>> X
+    X
+    >>> expr = (X[0] + 2, X[2] + 3)
+    >>> func = lambdify( X, expr)
+    >>> func( [1, 2, 3] )
+    (3, 6)
+    """
+
+    def __getitem__(self, i):
+        if i == -0:
+            i = 0
+        if i < 0:
+            raise IndexError('DeferredVector index out of range')
+        component_name = '%s[%d]' % (self.name, i)
+        return Symbol(component_name)
+
+    def __str__(self):
+        return sstr(self)
+
+    def __repr__(self):
+        return "DeferredVector('%s')" % self.name
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/normalforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/normalforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..61a7d26bbdb8c8a3e8e3044d39b2403b2e14b7d5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/normalforms.py
@@ -0,0 +1,156 @@
+'''Functions returning normal forms of matrices'''
+
+from sympy.polys.domains.integerring import ZZ
+from sympy.polys.polytools import Poly
+from sympy.polys.matrices import DomainMatrix
+from sympy.polys.matrices.normalforms import (
+        smith_normal_form as _snf,
+        is_smith_normal_form as _is_snf,
+        smith_normal_decomp as _snd,
+        invariant_factors as _invf,
+        hermite_normal_form as _hnf,
+    )
+
+
+def _to_domain(m, domain=None):
+    """Convert Matrix to DomainMatrix"""
+    # XXX: deprecated support for RawMatrix:
+    ring = getattr(m, "ring", None)
+    m = m.applyfunc(lambda e: e.as_expr() if isinstance(e, Poly) else e)
+
+    dM = DomainMatrix.from_Matrix(m)
+
+    domain = domain or ring
+    if domain is not None:
+        dM = dM.convert_to(domain)
+    return dM
+
+
+def smith_normal_form(m, domain=None):
+    '''
+    Return the Smith Normal Form of a matrix `m` over the ring `domain`.
+    This will only work if the ring is a principal ideal domain.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, ZZ
+    >>> from sympy.matrices.normalforms import smith_normal_form
+    >>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]])
+    >>> print(smith_normal_form(m, domain=ZZ))
+    Matrix([[1, 0, 0], [0, 10, 0], [0, 0, 30]])
+
+    '''
+    dM = _to_domain(m, domain)
+    return _snf(dM).to_Matrix()
+
+
+def is_smith_normal_form(m, domain=None):
+    '''
+    Checks that the matrix is in Smith Normal Form
+    '''
+    dM = _to_domain(m, domain)
+    return _is_snf(dM)
+
+
+def smith_normal_decomp(m, domain=None):
+    '''
+    Return the Smith Normal Decomposition of a matrix `m` over the ring
+    `domain`. This will only work if the ring is a principal ideal domain.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, ZZ
+    >>> from sympy.matrices.normalforms import smith_normal_decomp
+    >>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]])
+    >>> a, s, t = smith_normal_decomp(m, domain=ZZ)
+    >>> assert a == s * m * t
+    '''
+    dM = _to_domain(m, domain)
+    a, s, t = _snd(dM)
+    return a.to_Matrix(), s.to_Matrix(), t.to_Matrix()
+
+
+def invariant_factors(m, domain=None):
+    '''
+    Return the tuple of abelian invariants for a matrix `m`
+    (as in the Smith-Normal form)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Smith_normal_form#Algorithm
+    .. [2] https://web.archive.org/web/20200331143852/https://sierra.nmsu.edu/morandi/notes/SmithNormalForm.pdf
+
+    '''
+    dM = _to_domain(m, domain)
+    factors = _invf(dM)
+    factors = tuple(dM.domain.to_sympy(f) for f in factors)
+    # XXX: deprecated.
+    if hasattr(m, "ring"):
+        if m.ring.is_PolynomialRing:
+            K = m.ring
+            to_poly = lambda f: Poly(f, K.symbols, domain=K.domain)
+            factors = tuple(to_poly(f) for f in factors)
+    return factors
+
+
+def hermite_normal_form(A, *, D=None, check_rank=False):
+    r"""
+    Compute the Hermite Normal Form of a Matrix *A* of integers.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.matrices.normalforms import hermite_normal_form
+    >>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]])
+    >>> print(hermite_normal_form(m))
+    Matrix([[10, 0, 2], [0, 15, 3], [0, 0, 2]])
+
+    Parameters
+    ==========
+
+    A : $m \times n$ ``Matrix`` of integers.
+
+    D : int, optional
+        Let $W$ be the HNF of *A*. If known in advance, a positive integer *D*
+        being any multiple of $\det(W)$ may be provided. In this case, if *A*
+        also has rank $m$, then we may use an alternative algorithm that works
+        mod *D* in order to prevent coefficient explosion.
+
+    check_rank : boolean, optional (default=False)
+        The basic assumption is that, if you pass a value for *D*, then
+        you already believe that *A* has rank $m$, so we do not waste time
+        checking it for you. If you do want this to be checked (and the
+        ordinary, non-modulo *D* algorithm to be used if the check fails), then
+        set *check_rank* to ``True``.
+
+    Returns
+    =======
+
+    ``Matrix``
+        The HNF of matrix *A*.
+
+    Raises
+    ======
+
+    DMDomainError
+        If the domain of the matrix is not :ref:`ZZ`.
+
+    DMShapeError
+        If the mod *D* algorithm is used but the matrix has more rows than
+        columns.
+
+    References
+    ==========
+
+    .. [1] Cohen, H. *A Course in Computational Algebraic Number Theory.*
+       (See Algorithms 2.4.5 and 2.4.8.)
+
+    """
+    # Accept any of Python int, SymPy Integer, and ZZ itself:
+    if D is not None and not ZZ.of_type(D):
+        D = ZZ(int(D))
+    return _hnf(A._rep, D=D, check_rank=check_rank).to_Matrix()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/reductions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/reductions.py
new file mode 100644
index 0000000000000000000000000000000000000000..aace8c0336358e1869a34d99f79390cc0c0163fe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/reductions.py
@@ -0,0 +1,387 @@
+from types import FunctionType
+
+from sympy.polys.polyerrors import CoercionFailed
+from sympy.polys.domains import ZZ, QQ
+
+from .utilities import _get_intermediate_simp, _iszero, _dotprodsimp, _simplify
+from .determinant import _find_reasonable_pivot
+
+
+def _row_reduce_list(mat, rows, cols, one, iszerofunc, simpfunc,
+                normalize_last=True, normalize=True, zero_above=True):
+    """Row reduce a flat list representation of a matrix and return a tuple
+    (rref_matrix, pivot_cols, swaps) where ``rref_matrix`` is a flat list,
+    ``pivot_cols`` are the pivot columns and ``swaps`` are any row swaps that
+    were used in the process of row reduction.
+
+    Parameters
+    ==========
+
+    mat : list
+        list of matrix elements, must be ``rows`` * ``cols`` in length
+
+    rows, cols : integer
+        number of rows and columns in flat list representation
+
+    one : SymPy object
+        represents the value one, from ``Matrix.one``
+
+    iszerofunc : determines if an entry can be used as a pivot
+
+    simpfunc : used to simplify elements and test if they are
+        zero if ``iszerofunc`` returns `None`
+
+    normalize_last : indicates where all row reduction should
+        happen in a fraction-free manner and then the rows are
+        normalized (so that the pivots are 1), or whether
+        rows should be normalized along the way (like the naive
+        row reduction algorithm)
+
+    normalize : whether pivot rows should be normalized so that
+        the pivot value is 1
+
+    zero_above : whether entries above the pivot should be zeroed.
+        If ``zero_above=False``, an echelon matrix will be returned.
+    """
+
+    def get_col(i):
+        return mat[i::cols]
+
+    def row_swap(i, j):
+        mat[i*cols:(i + 1)*cols], mat[j*cols:(j + 1)*cols] = \
+            mat[j*cols:(j + 1)*cols], mat[i*cols:(i + 1)*cols]
+
+    def cross_cancel(a, i, b, j):
+        """Does the row op row[i] = a*row[i] - b*row[j]"""
+        q = (j - i)*cols
+        for p in range(i*cols, (i + 1)*cols):
+            mat[p] = isimp(a*mat[p] - b*mat[p + q])
+
+    isimp = _get_intermediate_simp(_dotprodsimp)
+    piv_row, piv_col = 0, 0
+    pivot_cols = []
+    swaps = []
+
+    # use a fraction free method to zero above and below each pivot
+    while piv_col < cols and piv_row < rows:
+        pivot_offset, pivot_val, \
+        assumed_nonzero, newly_determined = _find_reasonable_pivot(
+                get_col(piv_col)[piv_row:], iszerofunc, simpfunc)
+
+        # _find_reasonable_pivot may have simplified some things
+        # in the process.  Let's not let them go to waste
+        for (offset, val) in newly_determined:
+            offset += piv_row
+            mat[offset*cols + piv_col] = val
+
+        if pivot_offset is None:
+            piv_col += 1
+            continue
+
+        pivot_cols.append(piv_col)
+        if pivot_offset != 0:
+            row_swap(piv_row, pivot_offset + piv_row)
+            swaps.append((piv_row, pivot_offset + piv_row))
+
+        # if we aren't normalizing last, we normalize
+        # before we zero the other rows
+        if normalize_last is False:
+            i, j = piv_row, piv_col
+            mat[i*cols + j] = one
+            for p in range(i*cols + j + 1, (i + 1)*cols):
+                mat[p] = isimp(mat[p] / pivot_val)
+            # after normalizing, the pivot value is 1
+            pivot_val = one
+
+        # zero above and below the pivot
+        for row in range(rows):
+            # don't zero our current row
+            if row == piv_row:
+                continue
+            # don't zero above the pivot unless we're told.
+            if zero_above is False and row < piv_row:
+                continue
+            # if we're already a zero, don't do anything
+            val = mat[row*cols + piv_col]
+            if iszerofunc(val):
+                continue
+
+            cross_cancel(pivot_val, row, val, piv_row)
+        piv_row += 1
+
+    # normalize each row
+    if normalize_last is True and normalize is True:
+        for piv_i, piv_j in enumerate(pivot_cols):
+            pivot_val = mat[piv_i*cols + piv_j]
+            mat[piv_i*cols + piv_j] = one
+            for p in range(piv_i*cols + piv_j + 1, (piv_i + 1)*cols):
+                mat[p] = isimp(mat[p] / pivot_val)
+
+    return mat, tuple(pivot_cols), tuple(swaps)
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _row_reduce(M, iszerofunc, simpfunc, normalize_last=True,
+                normalize=True, zero_above=True):
+
+    mat, pivot_cols, swaps = _row_reduce_list(list(M), M.rows, M.cols, M.one,
+            iszerofunc, simpfunc, normalize_last=normalize_last,
+            normalize=normalize, zero_above=zero_above)
+
+    return M._new(M.rows, M.cols, mat), pivot_cols, swaps
+
+
+def _is_echelon(M, iszerofunc=_iszero):
+    """Returns `True` if the matrix is in echelon form. That is, all rows of
+    zeros are at the bottom, and below each leading non-zero in a row are
+    exclusively zeros."""
+
+    if M.rows <= 0 or M.cols <= 0:
+        return True
+
+    zeros_below = all(iszerofunc(t) for t in M[1:, 0])
+
+    if iszerofunc(M[0, 0]):
+        return zeros_below and _is_echelon(M[:, 1:], iszerofunc)
+
+    return zeros_below and _is_echelon(M[1:, 1:], iszerofunc)
+
+
+def _echelon_form(M, iszerofunc=_iszero, simplify=False, with_pivots=False):
+    """Returns a matrix row-equivalent to ``M`` that is in echelon form. Note
+    that echelon form of a matrix is *not* unique, however, properties like the
+    row space and the null space are preserved.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix([[1, 2], [3, 4]])
+    >>> M.echelon_form()
+    Matrix([
+    [1,  2],
+    [0, -2]])
+    """
+
+    simpfunc = simplify if isinstance(simplify, FunctionType) else _simplify
+
+    mat, pivots, _ = _row_reduce(M, iszerofunc, simpfunc,
+            normalize_last=True, normalize=False, zero_above=False)
+
+    if with_pivots:
+        return mat, pivots
+
+    return mat
+
+
+# This functions is a candidate for caching if it gets implemented for matrices.
+def _rank(M, iszerofunc=_iszero, simplify=False):
+    """Returns the rank of a matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.abc import x
+    >>> m = Matrix([[1, 2], [x, 1 - 1/x]])
+    >>> m.rank()
+    2
+    >>> n = Matrix(3, 3, range(1, 10))
+    >>> n.rank()
+    2
+    """
+
+    def _permute_complexity_right(M, iszerofunc):
+        """Permute columns with complicated elements as
+        far right as they can go.  Since the ``sympy`` row reduction
+        algorithms start on the left, having complexity right-shifted
+        speeds things up.
+
+        Returns a tuple (mat, perm) where perm is a permutation
+        of the columns to perform to shift the complex columns right, and mat
+        is the permuted matrix."""
+
+        def complexity(i):
+            # the complexity of a column will be judged by how many
+            # element's zero-ness cannot be determined
+            return sum(1 if iszerofunc(e) is None else 0 for e in M[:, i])
+
+        complex = [(complexity(i), i) for i in range(M.cols)]
+        perm    = [j for (i, j) in sorted(complex)]
+
+        return (M.permute(perm, orientation='cols'), perm)
+
+    simpfunc = simplify if isinstance(simplify, FunctionType) else _simplify
+
+    # for small matrices, we compute the rank explicitly
+    # if is_zero on elements doesn't answer the question
+    # for small matrices, we fall back to the full routine.
+    if M.rows <= 0 or M.cols <= 0:
+        return 0
+
+    if M.rows <= 1 or M.cols <= 1:
+        zeros = [iszerofunc(x) for x in M]
+
+        if False in zeros:
+            return 1
+
+    if M.rows == 2 and M.cols == 2:
+        zeros = [iszerofunc(x) for x in M]
+
+        if False not in zeros and None not in zeros:
+            return 0
+
+        d = M.det()
+
+        if iszerofunc(d) and False in zeros:
+            return 1
+        if iszerofunc(d) is False:
+            return 2
+
+    mat, _       = _permute_complexity_right(M, iszerofunc=iszerofunc)
+    _, pivots, _ = _row_reduce(mat, iszerofunc, simpfunc, normalize_last=True,
+            normalize=False, zero_above=False)
+
+    return len(pivots)
+
+
+def _to_DM_ZZ_QQ(M):
+    # We have to test for _rep here because there are tests that otherwise fail
+    # with e.g. "AttributeError: 'SubspaceOnlyMatrix' object has no attribute
+    # '_rep'." There is almost certainly no value in such tests. The
+    # presumption seems to be that someone could create a new class by
+    # inheriting some of the Matrix classes and not the full set that is used
+    # by the standard Matrix class but if anyone tried that it would fail in
+    # many ways.
+    if not hasattr(M, '_rep'):
+        return None
+
+    rep = M._rep
+    K = rep.domain
+
+    if K.is_ZZ:
+        return rep
+    elif K.is_QQ:
+        try:
+            return rep.convert_to(ZZ)
+        except CoercionFailed:
+            return rep
+    else:
+        if not all(e.is_Rational for e in M):
+            return None
+        try:
+            return rep.convert_to(ZZ)
+        except CoercionFailed:
+            return rep.convert_to(QQ)
+
+
+def _rref_dm(dM):
+    """Compute the reduced row echelon form of a DomainMatrix."""
+    K = dM.domain
+
+    if K.is_ZZ:
+        dM_rref, den, pivots = dM.rref_den(keep_domain=False)
+        dM_rref = dM_rref.to_field() / den
+    elif K.is_QQ:
+        dM_rref, pivots = dM.rref()
+    else:
+        assert False  # pragma: no cover
+
+    M_rref = dM_rref.to_Matrix()
+
+    return M_rref, pivots
+
+
+def _rref(M, iszerofunc=_iszero, simplify=False, pivots=True,
+        normalize_last=True):
+    """Return reduced row-echelon form of matrix and indices
+    of pivot vars.
+
+    Parameters
+    ==========
+
+    iszerofunc : Function
+        A function used for detecting whether an element can
+        act as a pivot.  ``lambda x: x.is_zero`` is used by default.
+
+    simplify : Function
+        A function used to simplify elements when looking for a pivot.
+        By default SymPy's ``simplify`` is used.
+
+    pivots : True or False
+        If ``True``, a tuple containing the row-reduced matrix and a tuple
+        of pivot columns is returned.  If ``False`` just the row-reduced
+        matrix is returned.
+
+    normalize_last : True or False
+        If ``True``, no pivots are normalized to `1` until after all
+        entries above and below each pivot are zeroed.  This means the row
+        reduction algorithm is fraction free until the very last step.
+        If ``False``, the naive row reduction procedure is used where
+        each pivot is normalized to be `1` before row operations are
+        used to zero above and below the pivot.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.abc import x
+    >>> m = Matrix([[1, 2], [x, 1 - 1/x]])
+    >>> m.rref()
+    (Matrix([
+    [1, 0],
+    [0, 1]]), (0, 1))
+    >>> rref_matrix, rref_pivots = m.rref()
+    >>> rref_matrix
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    >>> rref_pivots
+    (0, 1)
+
+    ``iszerofunc`` can correct rounding errors in matrices with float
+    values. In the following example, calling ``rref()`` leads to
+    floating point errors, incorrectly row reducing the matrix.
+    ``iszerofunc= lambda x: abs(x) < 1e-9`` sets sufficiently small numbers
+    to zero, avoiding this error.
+
+    >>> m = Matrix([[0.9, -0.1, -0.2, 0], [-0.8, 0.9, -0.4, 0], [-0.1, -0.8, 0.6, 0]])
+    >>> m.rref()
+    (Matrix([
+    [1, 0, 0, 0],
+    [0, 1, 0, 0],
+    [0, 0, 1, 0]]), (0, 1, 2))
+    >>> m.rref(iszerofunc=lambda x:abs(x)<1e-9)
+    (Matrix([
+    [1, 0, -0.301369863013699, 0],
+    [0, 1, -0.712328767123288, 0],
+    [0, 0,         0,          0]]), (0, 1))
+
+    Notes
+    =====
+
+    The default value of ``normalize_last=True`` can provide significant
+    speedup to row reduction, especially on matrices with symbols.  However,
+    if you depend on the form row reduction algorithm leaves entries
+    of the matrix, set ``normalize_last=False``
+    """
+    # Try to use DomainMatrix for ZZ or QQ
+    dM = _to_DM_ZZ_QQ(M)
+
+    if dM is not None:
+        # Use DomainMatrix for ZZ or QQ
+        mat, pivot_cols = _rref_dm(dM)
+    else:
+        # Use the generic Matrix routine.
+        if isinstance(simplify, FunctionType):
+            simpfunc = simplify
+        else:
+            simpfunc = _simplify
+
+        mat, pivot_cols, _ = _row_reduce(M, iszerofunc, simpfunc,
+                normalize_last, normalize=True, zero_above=True)
+
+    if pivots:
+        return mat, pivot_cols
+    else:
+        return mat
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/repmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/repmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..57f32fae34786f68f579fad7de38c9e3cf43e131
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/repmatrix.py
@@ -0,0 +1,1034 @@
+from collections import defaultdict
+
+from operator import index as index_
+
+from sympy.core.expr import Expr
+from sympy.core.kind import Kind, NumberKind, UndefinedKind
+from sympy.core.numbers import Integer, Rational
+from sympy.core.sympify import _sympify, SympifyError
+from sympy.core.singleton import S
+from sympy.polys.domains import ZZ, QQ, GF, EXRAW
+from sympy.polys.matrices import DomainMatrix
+from sympy.polys.matrices.exceptions import DMNonInvertibleMatrixError
+from sympy.polys.polyerrors import CoercionFailed, NotInvertible
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.misc import filldedent, as_int
+
+from .exceptions import ShapeError, NonSquareMatrixError, NonInvertibleMatrixError
+from .matrixbase import classof, MatrixBase
+from .kind import MatrixKind
+
+
+class RepMatrix(MatrixBase):
+    """Matrix implementation based on DomainMatrix as an internal representation.
+
+    The RepMatrix class is a superclass for Matrix, ImmutableMatrix,
+    SparseMatrix and ImmutableSparseMatrix which are the main usable matrix
+    classes in SymPy. Most methods on this class are simply forwarded to
+    DomainMatrix.
+    """
+
+    #
+    # MatrixBase is the common superclass for all of the usable explicit matrix
+    # classes in SymPy. The idea is that MatrixBase is an abstract class though
+    # and that subclasses will implement the lower-level methods.
+    #
+    # RepMatrix is a subclass of MatrixBase that uses DomainMatrix as an
+    # internal representation and delegates lower-level methods to
+    # DomainMatrix. All of SymPy's standard explicit matrix classes subclass
+    # RepMatrix and so use DomainMatrix internally.
+    #
+    # A RepMatrix uses an internal DomainMatrix with the domain set to ZZ, QQ
+    # or EXRAW. The EXRAW domain is equivalent to the previous implementation
+    # of Matrix that used Expr for the elements. The ZZ and QQ domains are used
+    # when applicable just because they are compatible with the previous
+    # implementation but are much more efficient. Other domains such as QQ[x]
+    # are not used because they differ from Expr in some way (e.g. automatic
+    # expansion of powers and products).
+    #
+
+    _rep: DomainMatrix
+
+    def __eq__(self, other):
+        # Skip sympify for mutable matrices...
+        if not isinstance(other, RepMatrix):
+            try:
+                other = _sympify(other)
+            except SympifyError:
+                return NotImplemented
+            if not isinstance(other, RepMatrix):
+                return NotImplemented
+
+        return self._rep.unify_eq(other._rep)
+
+    def to_DM(self, domain=None, **kwargs):
+        """Convert to a :class:`~.DomainMatrix`.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix([[1, 2], [3, 4]])
+        >>> M.to_DM()
+        DomainMatrix({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ)
+
+        The :meth:`DomainMatrix.to_Matrix` method can be used to convert back:
+
+        >>> M.to_DM().to_Matrix() == M
+        True
+
+        The domain can be given explicitly or otherwise it will be chosen by
+        :func:`construct_domain`. Any keyword arguments (besides ``domain``)
+        are passed to :func:`construct_domain`:
+
+        >>> from sympy import QQ, symbols
+        >>> x = symbols('x')
+        >>> M = Matrix([[x, 1], [1, x]])
+        >>> M
+        Matrix([
+        [x, 1],
+        [1, x]])
+        >>> M.to_DM().domain
+        ZZ[x]
+        >>> M.to_DM(field=True).domain
+        ZZ(x)
+        >>> M.to_DM(domain=QQ[x]).domain
+        QQ[x]
+
+        See Also
+        ========
+
+        DomainMatrix
+        DomainMatrix.to_Matrix
+        DomainMatrix.convert_to
+        DomainMatrix.choose_domain
+        construct_domain
+        """
+        if domain is not None:
+            if kwargs:
+                raise TypeError("Options cannot be used with domain parameter")
+            return self._rep.convert_to(domain)
+
+        rep = self._rep
+        dom = rep.domain
+
+        # If the internal DomainMatrix is already ZZ or QQ then we can maybe
+        # bypass calling construct_domain or performing any conversions. Some
+        # kwargs might affect this though e.g. field=True (not sure if there
+        # are others).
+        if not kwargs:
+            if dom.is_ZZ:
+                return rep.copy()
+            elif dom.is_QQ:
+                # All elements might be integers
+                try:
+                    return rep.convert_to(ZZ)
+                except CoercionFailed:
+                    pass
+                return rep.copy()
+
+        # Let construct_domain choose a domain
+        rep_dom = rep.choose_domain(**kwargs)
+
+        # XXX: There should be an option to construct_domain to choose EXRAW
+        # instead of EX. At least converting to EX does not initially trigger
+        # EX.simplify which is what we want here but should probably be
+        # considered a bug in EX. Perhaps also this could be handled in
+        # DomainMatrix.choose_domain rather than here...
+        if rep_dom.domain.is_EX:
+            rep_dom = rep_dom.convert_to(EXRAW)
+
+        return rep_dom
+
+    @classmethod
+    def _unify_element_sympy(cls, rep, element):
+        domain = rep.domain
+        element = _sympify(element)
+
+        if domain != EXRAW:
+            # The domain can only be ZZ, QQ or EXRAW
+            if element.is_Integer:
+                new_domain = domain
+            elif element.is_Rational:
+                new_domain = QQ
+            else:
+                new_domain = EXRAW
+
+            # XXX: This converts the domain for all elements in the matrix
+            # which can be slow. This happens e.g. if __setitem__ changes one
+            # element to something that does not fit in the domain
+            if new_domain != domain:
+                rep = rep.convert_to(new_domain)
+                domain = new_domain
+
+            if domain != EXRAW:
+                element = new_domain.from_sympy(element)
+
+        if domain == EXRAW and not isinstance(element, Expr):
+            sympy_deprecation_warning(
+                """
+                non-Expr objects in a Matrix is deprecated. Matrix represents
+                a mathematical matrix. To represent a container of non-numeric
+                entities, Use a list of lists, TableForm, NumPy array, or some
+                other data structure instead.
+                """,
+                deprecated_since_version="1.9",
+                active_deprecations_target="deprecated-non-expr-in-matrix",
+                stacklevel=4,
+            )
+
+        return rep, element
+
+    @classmethod
+    def _dod_to_DomainMatrix(cls, rows, cols, dod, types):
+
+        if not all(issubclass(typ, Expr) for typ in types):
+            sympy_deprecation_warning(
+                """
+                non-Expr objects in a Matrix is deprecated. Matrix represents
+                a mathematical matrix. To represent a container of non-numeric
+                entities, Use a list of lists, TableForm, NumPy array, or some
+                other data structure instead.
+                """,
+                deprecated_since_version="1.9",
+                active_deprecations_target="deprecated-non-expr-in-matrix",
+                stacklevel=6,
+            )
+
+        rep = DomainMatrix(dod, (rows, cols), EXRAW)
+
+        if all(issubclass(typ, Rational) for typ in types):
+            if all(issubclass(typ, Integer) for typ in types):
+                rep = rep.convert_to(ZZ)
+            else:
+                rep = rep.convert_to(QQ)
+
+        return rep
+
+    @classmethod
+    def _flat_list_to_DomainMatrix(cls, rows, cols, flat_list):
+
+        elements_dod = defaultdict(dict)
+        for n, element in enumerate(flat_list):
+            if element != 0:
+                i, j = divmod(n, cols)
+                elements_dod[i][j] = element
+
+        types = set(map(type, flat_list))
+
+        rep = cls._dod_to_DomainMatrix(rows, cols, elements_dod, types)
+        return rep
+
+    @classmethod
+    def _smat_to_DomainMatrix(cls, rows, cols, smat):
+
+        elements_dod = defaultdict(dict)
+        for (i, j), element in smat.items():
+            if element != 0:
+                elements_dod[i][j] = element
+
+        types = set(map(type, smat.values()))
+
+        rep = cls._dod_to_DomainMatrix(rows, cols, elements_dod, types)
+        return rep
+
+    def flat(self):
+        return self._rep.to_sympy().to_list_flat()
+
+    def _eval_tolist(self):
+        return self._rep.to_sympy().to_list()
+
+    def _eval_todok(self):
+        return self._rep.to_sympy().to_dok()
+
+    @classmethod
+    def _eval_from_dok(cls, rows, cols, dok):
+        return cls._fromrep(cls._smat_to_DomainMatrix(rows, cols, dok))
+
+    def _eval_values(self):
+        return list(self._eval_iter_values())
+
+    def _eval_iter_values(self):
+        rep = self._rep
+        K = rep.domain
+        values = rep.iter_values()
+        if not K.is_EXRAW:
+            values = map(K.to_sympy, values)
+        return values
+
+    def _eval_iter_items(self):
+        rep = self._rep
+        K = rep.domain
+        to_sympy = K.to_sympy
+        items = rep.iter_items()
+        if not K.is_EXRAW:
+            items = ((i, to_sympy(v)) for i, v in items)
+        return items
+
+    def copy(self):
+        return self._fromrep(self._rep.copy())
+
+    @property
+    def kind(self) -> MatrixKind:
+        domain = self._rep.domain
+        element_kind: Kind
+        if domain in (ZZ, QQ):
+            element_kind = NumberKind
+        elif domain == EXRAW:
+            kinds = {e.kind for e in self.values()}
+            if len(kinds) == 1:
+                [element_kind] = kinds
+            else:
+                element_kind = UndefinedKind
+        else: # pragma: no cover
+            raise RuntimeError("Domain should only be ZZ, QQ or EXRAW")
+        return MatrixKind(element_kind)
+
+    def _eval_has(self, *patterns):
+        # if the matrix has any zeros, see if S.Zero
+        # has the pattern.  If _smat is full length,
+        # the matrix has no zeros.
+        zhas = False
+        dok = self.todok()
+        if len(dok) != self.rows*self.cols:
+            zhas = S.Zero.has(*patterns)
+        return zhas or any(value.has(*patterns) for value in dok.values())
+
+    def _eval_is_Identity(self):
+        if not all(self[i, i] == 1 for i in range(self.rows)):
+            return False
+        return len(self.todok()) == self.rows
+
+    def _eval_is_symmetric(self, simpfunc):
+        diff = (self - self.T).applyfunc(simpfunc)
+        return len(diff.values()) == 0
+
+    def _eval_transpose(self):
+        """Returns the transposed SparseMatrix of this SparseMatrix.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix
+        >>> a = SparseMatrix(((1, 2), (3, 4)))
+        >>> a
+        Matrix([
+        [1, 2],
+        [3, 4]])
+        >>> a.T
+        Matrix([
+        [1, 3],
+        [2, 4]])
+        """
+        return self._fromrep(self._rep.transpose())
+
+    def _eval_col_join(self, other):
+        return self._fromrep(self._rep.vstack(other._rep))
+
+    def _eval_row_join(self, other):
+        return self._fromrep(self._rep.hstack(other._rep))
+
+    def _eval_extract(self, rowsList, colsList):
+        return self._fromrep(self._rep.extract(rowsList, colsList))
+
+    def __getitem__(self, key):
+        return _getitem_RepMatrix(self, key)
+
+    @classmethod
+    def _eval_zeros(cls, rows, cols):
+        rep = DomainMatrix.zeros((rows, cols), ZZ)
+        return cls._fromrep(rep)
+
+    @classmethod
+    def _eval_eye(cls, rows, cols):
+        rep = DomainMatrix.eye((rows, cols), ZZ)
+        return cls._fromrep(rep)
+
+    def _eval_add(self, other):
+        return classof(self, other)._fromrep(self._rep + other._rep)
+
+    def _eval_matrix_mul(self, other):
+        return classof(self, other)._fromrep(self._rep * other._rep)
+
+    def _eval_matrix_mul_elementwise(self, other):
+        selfrep, otherrep = self._rep.unify(other._rep)
+        newrep = selfrep.mul_elementwise(otherrep)
+        return classof(self, other)._fromrep(newrep)
+
+    def _eval_scalar_mul(self, other):
+        rep, other = self._unify_element_sympy(self._rep, other)
+        return self._fromrep(rep.scalarmul(other))
+
+    def _eval_scalar_rmul(self, other):
+        rep, other = self._unify_element_sympy(self._rep, other)
+        return self._fromrep(rep.rscalarmul(other))
+
+    def _eval_Abs(self):
+        return self._fromrep(self._rep.applyfunc(abs))
+
+    def _eval_conjugate(self):
+        rep = self._rep
+        domain = rep.domain
+        if domain in (ZZ, QQ):
+            return self.copy()
+        else:
+            return self._fromrep(rep.applyfunc(lambda e: e.conjugate()))
+
+    def equals(self, other, failing_expression=False):
+        """Applies ``equals`` to corresponding elements of the matrices,
+        trying to prove that the elements are equivalent, returning True
+        if they are, False if any pair is not, and None (or the first
+        failing expression if failing_expression is True) if it cannot
+        be decided if the expressions are equivalent or not. This is, in
+        general, an expensive operation.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.abc import x
+        >>> A = Matrix([x*(x - 1), 0])
+        >>> B = Matrix([x**2 - x, 0])
+        >>> A == B
+        False
+        >>> A.simplify() == B.simplify()
+        True
+        >>> A.equals(B)
+        True
+        >>> A.equals(2)
+        False
+
+        See Also
+        ========
+        sympy.core.expr.Expr.equals
+        """
+        if self.shape != getattr(other, 'shape', None):
+            return False
+
+        rv = True
+        for i in range(self.rows):
+            for j in range(self.cols):
+                ans = self[i, j].equals(other[i, j], failing_expression)
+                if ans is False:
+                    return False
+                elif ans is not True and rv is True:
+                    rv = ans
+        return rv
+
+    def inv_mod(M, m):
+        r"""
+        Returns the inverse of the integer matrix ``M`` modulo ``m``.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> A = Matrix(2, 2, [1, 2, 3, 4])
+        >>> A.inv_mod(5)
+        Matrix([
+        [3, 1],
+        [4, 2]])
+        >>> A.inv_mod(3)
+        Matrix([
+        [1, 1],
+        [0, 1]])
+
+        """
+
+        if not M.is_square:
+            raise NonSquareMatrixError()
+
+        try:
+            m = as_int(m)
+        except ValueError:
+            raise TypeError("inv_mod: modulus m must be an integer")
+
+        K = GF(m, symmetric=False)
+
+        try:
+            dM = M.to_DM(K)
+        except CoercionFailed:
+            raise ValueError("inv_mod: matrix entries must be integers")
+
+        if K.is_Field:
+            try:
+                dMi = dM.inv()
+            except DMNonInvertibleMatrixError as exc:
+                msg = f'Matrix is not invertible (mod {m})'
+                raise NonInvertibleMatrixError(msg) from exc
+        else:
+            dMadj, det = dM.adj_det()
+            try:
+                detinv = 1 / det
+            except NotInvertible:
+                msg = f'Matrix is not invertible (mod {m})'
+                raise NonInvertibleMatrixError(msg)
+            dMi = dMadj * detinv
+
+        return dMi.to_Matrix()
+
+    def lll(self, delta=0.75):
+        """LLL-reduced basis for the rowspace of a matrix of integers.
+
+        Performs the Lenstra–Lenstra–Lovász (LLL) basis reduction algorithm.
+
+        The implementation is provided by :class:`~DomainMatrix`. See
+        :meth:`~DomainMatrix.lll` for more details.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix([[1, 0, 0, 0, -20160],
+        ...             [0, 1, 0, 0, 33768],
+        ...             [0, 0, 1, 0, 39578],
+        ...             [0, 0, 0, 1, 47757]])
+        >>> M.lll()
+        Matrix([
+        [ 10, -3,  -2,  8,  -4],
+        [  3, -9,   8,  1, -11],
+        [ -3, 13,  -9, -3,  -9],
+        [-12, -7, -11,  9,  -1]])
+
+        See Also
+        ========
+
+        lll_transform
+        sympy.polys.matrices.domainmatrix.DomainMatrix.lll
+        """
+        delta = QQ.from_sympy(_sympify(delta))
+        dM = self._rep.convert_to(ZZ)
+        basis = dM.lll(delta=delta)
+        return self._fromrep(basis)
+
+    def lll_transform(self, delta=0.75):
+        """LLL-reduced basis and transformation matrix.
+
+        Performs the Lenstra–Lenstra–Lovász (LLL) basis reduction algorithm.
+
+        The implementation is provided by :class:`~DomainMatrix`. See
+        :meth:`~DomainMatrix.lll_transform` for more details.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix([[1, 0, 0, 0, -20160],
+        ...             [0, 1, 0, 0, 33768],
+        ...             [0, 0, 1, 0, 39578],
+        ...             [0, 0, 0, 1, 47757]])
+        >>> B, T = M.lll_transform()
+        >>> B
+        Matrix([
+        [ 10, -3,  -2,  8,  -4],
+        [  3, -9,   8,  1, -11],
+        [ -3, 13,  -9, -3,  -9],
+        [-12, -7, -11,  9,  -1]])
+        >>> T
+        Matrix([
+        [ 10, -3,  -2,  8],
+        [  3, -9,   8,  1],
+        [ -3, 13,  -9, -3],
+        [-12, -7, -11,  9]])
+
+        The transformation matrix maps the original basis to the LLL-reduced
+        basis:
+
+        >>> T * M == B
+        True
+
+        See Also
+        ========
+
+        lll
+        sympy.polys.matrices.domainmatrix.DomainMatrix.lll_transform
+        """
+        delta = QQ.from_sympy(_sympify(delta))
+        dM = self._rep.convert_to(ZZ)
+        basis, transform = dM.lll_transform(delta=delta)
+        B = self._fromrep(basis)
+        T = self._fromrep(transform)
+        return B, T
+
+
+class MutableRepMatrix(RepMatrix):
+    """Mutable matrix based on DomainMatrix as the internal representation"""
+
+    #
+    # MutableRepMatrix is a subclass of RepMatrix that adds/overrides methods
+    # to make the instances mutable. MutableRepMatrix is a superclass for both
+    # MutableDenseMatrix and MutableSparseMatrix.
+    #
+
+    is_zero = False
+
+    def __new__(cls, *args, **kwargs):
+        return cls._new(*args, **kwargs)
+
+    @classmethod
+    def _new(cls, *args, copy=True, **kwargs):
+        if copy is False:
+            # The input was rows, cols, [list].
+            # It should be used directly without creating a copy.
+            if len(args) != 3:
+                raise TypeError("'copy=False' requires a matrix be initialized as rows,cols,[list]")
+            rows, cols, flat_list = args
+        else:
+            rows, cols, flat_list = cls._handle_creation_inputs(*args, **kwargs)
+            flat_list = list(flat_list) # create a shallow copy
+
+        rep = cls._flat_list_to_DomainMatrix(rows, cols, flat_list)
+
+        return cls._fromrep(rep)
+
+    @classmethod
+    def _fromrep(cls, rep):
+        obj = super().__new__(cls)
+        obj.rows, obj.cols = rep.shape
+        obj._rep = rep
+        return obj
+
+    def copy(self):
+        return self._fromrep(self._rep.copy())
+
+    def as_mutable(self):
+        return self.copy()
+
+    def __setitem__(self, key, value):
+        """
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, I, zeros, ones
+        >>> m = Matrix(((1, 2+I), (3, 4)))
+        >>> m
+        Matrix([
+        [1, 2 + I],
+        [3,     4]])
+        >>> m[1, 0] = 9
+        >>> m
+        Matrix([
+        [1, 2 + I],
+        [9,     4]])
+        >>> m[1, 0] = [[0, 1]]
+
+        To replace row r you assign to position r*m where m
+        is the number of columns:
+
+        >>> M = zeros(4)
+        >>> m = M.cols
+        >>> M[3*m] = ones(1, m)*2; M
+        Matrix([
+        [0, 0, 0, 0],
+        [0, 0, 0, 0],
+        [0, 0, 0, 0],
+        [2, 2, 2, 2]])
+
+        And to replace column c you can assign to position c:
+
+        >>> M[2] = ones(m, 1)*4; M
+        Matrix([
+        [0, 0, 4, 0],
+        [0, 0, 4, 0],
+        [0, 0, 4, 0],
+        [2, 2, 4, 2]])
+        """
+        rv = self._setitem(key, value)
+        if rv is not None:
+            i, j, value = rv
+            self._rep, value = self._unify_element_sympy(self._rep, value)
+            self._rep.rep.setitem(i, j, value)
+
+    def _eval_col_del(self, col):
+        self._rep = DomainMatrix.hstack(self._rep[:,:col], self._rep[:,col+1:])
+        self.cols -= 1
+
+    def _eval_row_del(self, row):
+        self._rep = DomainMatrix.vstack(self._rep[:row,:], self._rep[row+1:, :])
+        self.rows -= 1
+
+    def _eval_col_insert(self, col, other):
+        other = self._new(other)
+        return self.hstack(self[:,:col], other, self[:,col:])
+
+    def _eval_row_insert(self, row, other):
+        other = self._new(other)
+        return self.vstack(self[:row,:], other, self[row:,:])
+
+    def col_op(self, j, f):
+        """In-place operation on col j using two-arg functor whose args are
+        interpreted as (self[i, j], i).
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.col_op(1, lambda v, i: v + 2*M[i, 0]); M
+        Matrix([
+        [1, 2, 0],
+        [0, 1, 0],
+        [0, 0, 1]])
+
+        See Also
+        ========
+        col
+        row_op
+        """
+        for i in range(self.rows):
+            self[i, j] = f(self[i, j], i)
+
+    def col_swap(self, i, j):
+        """Swap the two given columns of the matrix in-place.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix([[1, 0], [1, 0]])
+        >>> M
+        Matrix([
+        [1, 0],
+        [1, 0]])
+        >>> M.col_swap(0, 1)
+        >>> M
+        Matrix([
+        [0, 1],
+        [0, 1]])
+
+        See Also
+        ========
+
+        col
+        row_swap
+        """
+        for k in range(0, self.rows):
+            self[k, i], self[k, j] = self[k, j], self[k, i]
+
+    def row_op(self, i, f):
+        """In-place operation on row ``i`` using two-arg functor whose args are
+        interpreted as ``(self[i, j], j)``.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.row_op(1, lambda v, j: v + 2*M[0, j]); M
+        Matrix([
+        [1, 0, 0],
+        [2, 1, 0],
+        [0, 0, 1]])
+
+        See Also
+        ========
+        row
+        zip_row_op
+        col_op
+
+        """
+        for j in range(self.cols):
+            self[i, j] = f(self[i, j], j)
+
+    #The next three methods give direct support for the most common row operations inplace.
+    def row_mult(self,i,factor):
+        """Multiply the given row by the given factor in-place.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.row_mult(1,7); M
+        Matrix([
+        [1, 0, 0],
+        [0, 7, 0],
+        [0, 0, 1]])
+
+        """
+        for j in range(self.cols):
+            self[i,j] *= factor
+
+    def row_add(self,s,t,k):
+        """Add k times row s (source) to row t (target) in place.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.row_add(0, 2,3); M
+        Matrix([
+        [1, 0, 0],
+        [0, 1, 0],
+        [3, 0, 1]])
+        """
+
+        for j in range(self.cols):
+            self[t,j] += k*self[s,j]
+
+    def row_swap(self, i, j):
+        """Swap the two given rows of the matrix in-place.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> M = Matrix([[0, 1], [1, 0]])
+        >>> M
+        Matrix([
+        [0, 1],
+        [1, 0]])
+        >>> M.row_swap(0, 1)
+        >>> M
+        Matrix([
+        [1, 0],
+        [0, 1]])
+
+        See Also
+        ========
+
+        row
+        col_swap
+        """
+        for k in range(0, self.cols):
+            self[i, k], self[j, k] = self[j, k], self[i, k]
+
+    def zip_row_op(self, i, k, f):
+        """In-place operation on row ``i`` using two-arg functor whose args are
+        interpreted as ``(self[i, j], self[k, j])``.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> M = eye(3)
+        >>> M.zip_row_op(1, 0, lambda v, u: v + 2*u); M
+        Matrix([
+        [1, 0, 0],
+        [2, 1, 0],
+        [0, 0, 1]])
+
+        See Also
+        ========
+        row
+        row_op
+        col_op
+
+        """
+        for j in range(self.cols):
+            self[i, j] = f(self[i, j], self[k, j])
+
+    def copyin_list(self, key, value):
+        """Copy in elements from a list.
+
+        Parameters
+        ==========
+
+        key : slice
+            The section of this matrix to replace.
+        value : iterable
+            The iterable to copy values from.
+
+        Examples
+        ========
+
+        >>> from sympy import eye
+        >>> I = eye(3)
+        >>> I[:2, 0] = [1, 2] # col
+        >>> I
+        Matrix([
+        [1, 0, 0],
+        [2, 1, 0],
+        [0, 0, 1]])
+        >>> I[1, :2] = [[3, 4]]
+        >>> I
+        Matrix([
+        [1, 0, 0],
+        [3, 4, 0],
+        [0, 0, 1]])
+
+        See Also
+        ========
+
+        copyin_matrix
+        """
+        if not is_sequence(value):
+            raise TypeError("`value` must be an ordered iterable, not %s." % type(value))
+        return self.copyin_matrix(key, type(self)(value))
+
+    def copyin_matrix(self, key, value):
+        """Copy in values from a matrix into the given bounds.
+
+        Parameters
+        ==========
+
+        key : slice
+            The section of this matrix to replace.
+        value : Matrix
+            The matrix to copy values from.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix, eye
+        >>> M = Matrix([[0, 1], [2, 3], [4, 5]])
+        >>> I = eye(3)
+        >>> I[:3, :2] = M
+        >>> I
+        Matrix([
+        [0, 1, 0],
+        [2, 3, 0],
+        [4, 5, 1]])
+        >>> I[0, 1] = M
+        >>> I
+        Matrix([
+        [0, 0, 1],
+        [2, 2, 3],
+        [4, 4, 5]])
+
+        See Also
+        ========
+
+        copyin_list
+        """
+        rlo, rhi, clo, chi = self.key2bounds(key)
+        shape = value.shape
+        dr, dc = rhi - rlo, chi - clo
+        if shape != (dr, dc):
+            raise ShapeError(filldedent("The Matrix `value` doesn't have the "
+                                        "same dimensions "
+                                        "as the in sub-Matrix given by `key`."))
+
+        for i in range(value.rows):
+            for j in range(value.cols):
+                self[i + rlo, j + clo] = value[i, j]
+
+    def fill(self, value):
+        """Fill self with the given value.
+
+        Notes
+        =====
+
+        Unless many values are going to be deleted (i.e. set to zero)
+        this will create a matrix that is slower than a dense matrix in
+        operations.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix
+        >>> M = SparseMatrix.zeros(3); M
+        Matrix([
+        [0, 0, 0],
+        [0, 0, 0],
+        [0, 0, 0]])
+        >>> M.fill(1); M
+        Matrix([
+        [1, 1, 1],
+        [1, 1, 1],
+        [1, 1, 1]])
+
+        See Also
+        ========
+
+        zeros
+        ones
+        """
+        value = _sympify(value)
+        if not value:
+            self._rep = DomainMatrix.zeros(self.shape, EXRAW)
+        else:
+            elements_dod = {i: dict.fromkeys(range(self.cols), value) for i in range(self.rows)}
+            self._rep = DomainMatrix(elements_dod, self.shape, EXRAW)
+
+
+def _getitem_RepMatrix(self, key):
+    """Return portion of self defined by key. If the key involves a slice
+    then a list will be returned (if key is a single slice) or a matrix
+    (if key was a tuple involving a slice).
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, I
+    >>> m = Matrix([
+    ... [1, 2 + I],
+    ... [3, 4    ]])
+
+    If the key is a tuple that does not involve a slice then that element
+    is returned:
+
+    >>> m[1, 0]
+    3
+
+    When a tuple key involves a slice, a matrix is returned. Here, the
+    first column is selected (all rows, column 0):
+
+    >>> m[:, 0]
+    Matrix([
+    [1],
+    [3]])
+
+    If the slice is not a tuple then it selects from the underlying
+    list of elements that are arranged in row order and a list is
+    returned if a slice is involved:
+
+    >>> m[0]
+    1
+    >>> m[::2]
+    [1, 3]
+    """
+    if isinstance(key, tuple):
+        i, j = key
+        try:
+            return self._rep.getitem_sympy(index_(i), index_(j))
+        except (TypeError, IndexError):
+            if (isinstance(i, Expr) and not i.is_number) or (isinstance(j, Expr) and not j.is_number):
+                if ((j < 0) is True) or ((j >= self.shape[1]) is True) or\
+                   ((i < 0) is True) or ((i >= self.shape[0]) is True):
+                    raise ValueError("index out of boundary")
+                from sympy.matrices.expressions.matexpr import MatrixElement
+                return MatrixElement(self, i, j)
+
+            if isinstance(i, slice):
+                i = range(self.rows)[i]
+            elif is_sequence(i):
+                pass
+            else:
+                i = [i]
+            if isinstance(j, slice):
+                j = range(self.cols)[j]
+            elif is_sequence(j):
+                pass
+            else:
+                j = [j]
+            return self.extract(i, j)
+
+    else:
+        # Index/slice like a flattened list
+        rows, cols = self.shape
+
+        # Raise the appropriate exception:
+        if not rows * cols:
+            return [][key]
+
+        rep = self._rep.rep
+        domain = rep.domain
+        is_slice = isinstance(key, slice)
+
+        if is_slice:
+            values = [rep.getitem(*divmod(n, cols)) for n in range(rows * cols)[key]]
+        else:
+            values = [rep.getitem(*divmod(index_(key), cols))]
+
+        if domain != EXRAW:
+            to_sympy = domain.to_sympy
+            values = [to_sympy(val) for val in values]
+
+        if is_slice:
+            return values
+        else:
+            return values[0]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/solvers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/solvers.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fba990df80dcf46304ecb1412f5382f60948c51
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/solvers.py
@@ -0,0 +1,942 @@
+from sympy.core.function import expand_mul
+from sympy.core.symbol import Dummy, uniquely_named_symbol, symbols
+from sympy.utilities.iterables import numbered_symbols
+
+from .exceptions import ShapeError, NonSquareMatrixError, NonInvertibleMatrixError
+from .eigen import _fuzzy_positive_definite
+from .utilities import _get_intermediate_simp, _iszero
+
+
+def _diagonal_solve(M, rhs):
+    """Solves ``Ax = B`` efficiently, where A is a diagonal Matrix,
+    with non-zero diagonal entries.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, eye
+    >>> A = eye(2)*2
+    >>> B = Matrix([[1, 2], [3, 4]])
+    >>> A.diagonal_solve(B) == B/2
+    True
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    if not M.is_diagonal():
+        raise TypeError("Matrix should be diagonal")
+    if rhs.rows != M.rows:
+        raise TypeError("Size mismatch")
+
+    return M._new(
+        rhs.rows, rhs.cols, lambda i, j: rhs[i, j] / M[i, i])
+
+
+def _lower_triangular_solve(M, rhs):
+    """Solves ``Ax = B``, where A is a lower triangular matrix.
+
+    See Also
+    ========
+
+    upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    from .dense import MutableDenseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if rhs.rows != M.rows:
+        raise ShapeError("Matrices size mismatch.")
+    if not M.is_lower:
+        raise ValueError("Matrix must be lower triangular.")
+
+    dps = _get_intermediate_simp()
+    X   = MutableDenseMatrix.zeros(M.rows, rhs.cols)
+
+    for j in range(rhs.cols):
+        for i in range(M.rows):
+            if M[i, i] == 0:
+                raise TypeError("Matrix must be non-singular.")
+
+            X[i, j] = dps((rhs[i, j] - sum(M[i, k]*X[k, j]
+                                        for k in range(i))) / M[i, i])
+
+    return M._new(X)
+
+def _lower_triangular_solve_sparse(M, rhs):
+    """Solves ``Ax = B``, where A is a lower triangular matrix.
+
+    See Also
+    ========
+
+    upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if rhs.rows != M.rows:
+        raise ShapeError("Matrices size mismatch.")
+    if not M.is_lower:
+        raise ValueError("Matrix must be lower triangular.")
+
+    dps  = _get_intermediate_simp()
+    rows = [[] for i in range(M.rows)]
+
+    for i, j, v in M.row_list():
+        if i > j:
+            rows[i].append((j, v))
+
+    X = rhs.as_mutable()
+
+    for j in range(rhs.cols):
+        for i in range(rhs.rows):
+            for u, v in rows[i]:
+                X[i, j] -= v*X[u, j]
+
+            X[i, j] = dps(X[i, j] / M[i, i])
+
+    return M._new(X)
+
+
+def _upper_triangular_solve(M, rhs):
+    """Solves ``Ax = B``, where A is an upper triangular matrix.
+
+    See Also
+    ========
+
+    lower_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    from .dense import MutableDenseMatrix
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if rhs.rows != M.rows:
+        raise ShapeError("Matrix size mismatch.")
+    if not M.is_upper:
+        raise TypeError("Matrix is not upper triangular.")
+
+    dps = _get_intermediate_simp()
+    X   = MutableDenseMatrix.zeros(M.rows, rhs.cols)
+
+    for j in range(rhs.cols):
+        for i in reversed(range(M.rows)):
+            if M[i, i] == 0:
+                raise ValueError("Matrix must be non-singular.")
+
+            X[i, j] = dps((rhs[i, j] - sum(M[i, k]*X[k, j]
+                                        for k in range(i + 1, M.rows))) / M[i, i])
+
+    return M._new(X)
+
+def _upper_triangular_solve_sparse(M, rhs):
+    """Solves ``Ax = B``, where A is an upper triangular matrix.
+
+    See Also
+    ========
+
+    lower_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    if not M.is_square:
+        raise NonSquareMatrixError("Matrix must be square.")
+    if rhs.rows != M.rows:
+        raise ShapeError("Matrix size mismatch.")
+    if not M.is_upper:
+        raise TypeError("Matrix is not upper triangular.")
+
+    dps  = _get_intermediate_simp()
+    rows = [[] for i in range(M.rows)]
+
+    for i, j, v in M.row_list():
+        if i < j:
+            rows[i].append((j, v))
+
+    X = rhs.as_mutable()
+
+    for j in range(rhs.cols):
+        for i in reversed(range(rhs.rows)):
+            for u, v in reversed(rows[i]):
+                X[i, j] -= v*X[u, j]
+
+            X[i, j] = dps(X[i, j] / M[i, i])
+
+    return M._new(X)
+
+
+def _cholesky_solve(M, rhs):
+    """Solves ``Ax = B`` using Cholesky decomposition,
+    for a general square non-singular matrix.
+    For a non-square matrix with rows > cols,
+    the least squares solution is returned.
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    gauss_jordan_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    if M.rows < M.cols:
+        raise NotImplementedError(
+            'Under-determined System. Try M.gauss_jordan_solve(rhs)')
+
+    hermitian = True
+    reform    = False
+
+    if M.is_symmetric():
+        hermitian = False
+    elif not M.is_hermitian:
+        reform = True
+
+    if reform or _fuzzy_positive_definite(M) is False:
+        H         = M.H
+        M         = H.multiply(M)
+        rhs       = H.multiply(rhs)
+        hermitian = not M.is_symmetric()
+
+    L = M.cholesky(hermitian=hermitian)
+    Y = L.lower_triangular_solve(rhs)
+
+    if hermitian:
+        return (L.H).upper_triangular_solve(Y)
+    else:
+        return (L.T).upper_triangular_solve(Y)
+
+
+def _LDLsolve(M, rhs):
+    """Solves ``Ax = B`` using LDL decomposition,
+    for a general square and non-singular matrix.
+
+    For a non-square matrix with rows > cols,
+    the least squares solution is returned.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, eye
+    >>> A = eye(2)*2
+    >>> B = Matrix([[1, 2], [3, 4]])
+    >>> A.LDLsolve(B) == B/2
+    True
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.LDLdecomposition
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LUsolve
+    QRsolve
+    pinv_solve
+    cramer_solve
+    """
+
+    if M.rows < M.cols:
+        raise NotImplementedError(
+            'Under-determined System. Try M.gauss_jordan_solve(rhs)')
+
+    hermitian = True
+    reform    = False
+
+    if M.is_symmetric():
+        hermitian = False
+    elif not M.is_hermitian:
+        reform = True
+
+    if reform or _fuzzy_positive_definite(M) is False:
+        H         = M.H
+        M         = H.multiply(M)
+        rhs       = H.multiply(rhs)
+        hermitian = not M.is_symmetric()
+
+    L, D = M.LDLdecomposition(hermitian=hermitian)
+    Y    = L.lower_triangular_solve(rhs)
+    Z    = D.diagonal_solve(Y)
+
+    if hermitian:
+        return (L.H).upper_triangular_solve(Z)
+    else:
+        return (L.T).upper_triangular_solve(Z)
+
+
+def _LUsolve(M, rhs, iszerofunc=_iszero):
+    """Solve the linear system ``Ax = rhs`` for ``x`` where ``A = M``.
+
+    This is for symbolic matrices, for real or complex ones use
+    mpmath.lu_solve or mpmath.qr_solve.
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    QRsolve
+    pinv_solve
+    LUdecomposition
+    cramer_solve
+    """
+
+    if rhs.rows != M.rows:
+        raise ShapeError(
+            "``M`` and ``rhs`` must have the same number of rows.")
+
+    m = M.rows
+    n = M.cols
+
+    if m < n:
+        raise NotImplementedError("Underdetermined systems not supported.")
+
+    try:
+        A, perm = M.LUdecomposition_Simple(
+            iszerofunc=iszerofunc, rankcheck=True)
+    except ValueError:
+        raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+
+    dps = _get_intermediate_simp()
+    b   = rhs.permute_rows(perm).as_mutable()
+
+    # forward substitution, all diag entries are scaled to 1
+    for i in range(m):
+        for j in range(min(i, n)):
+            scale = A[i, j]
+            b.zip_row_op(i, j, lambda x, y: dps(x - scale * y))
+
+    # consistency check for overdetermined systems
+    if m > n:
+        for i in range(n, m):
+            for j in range(b.cols):
+                if not iszerofunc(b[i, j]):
+                    raise ValueError("The system is inconsistent.")
+
+        b = b[0:n, :]   # truncate zero rows if consistent
+
+    # backward substitution
+    for i in range(n - 1, -1, -1):
+        for j in range(i + 1, n):
+            scale = A[i, j]
+            b.zip_row_op(i, j, lambda x, y: dps(x - scale * y))
+
+        scale = A[i, i]
+        b.row_op(i, lambda x, _: dps(scale**-1 * x))
+
+    return rhs.__class__(b)
+
+
+def _QRsolve(M, b):
+    """Solve the linear system ``Ax = b``.
+
+    ``M`` is the matrix ``A``, the method argument is the vector
+    ``b``.  The method returns the solution vector ``x``.  If ``b`` is a
+    matrix, the system is solved for each column of ``b`` and the
+    return value is a matrix of the same shape as ``b``.
+
+    This method is slower (approximately by a factor of 2) but
+    more stable for floating-point arithmetic than the LUsolve method.
+    However, LUsolve usually uses an exact arithmetic, so you do not need
+    to use QRsolve.
+
+    This is mainly for educational purposes and symbolic matrices, for real
+    (or complex) matrices use mpmath.qr_solve.
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    pinv_solve
+    QRdecomposition
+    cramer_solve
+    """
+
+    dps  = _get_intermediate_simp(expand_mul, expand_mul)
+    Q, R = M.QRdecomposition()
+    y    = Q.T * b
+
+    # back substitution to solve R*x = y:
+    # We build up the result "backwards" in the vector 'x' and reverse it
+    # only in the end.
+    x = []
+    n = R.rows
+
+    for j in range(n - 1, -1, -1):
+        tmp = y[j, :]
+
+        for k in range(j + 1, n):
+            tmp -= R[j, k] * x[n - 1 - k]
+
+        tmp = dps(tmp)
+
+        x.append(tmp / R[j, j])
+
+    return M.vstack(*x[::-1])
+
+
+def _gauss_jordan_solve(M, B, freevar=False):
+    """
+    Solves ``Ax = B`` using Gauss Jordan elimination.
+
+    There may be zero, one, or infinite solutions.  If one solution
+    exists, it will be returned. If infinite solutions exist, it will
+    be returned parametrically. If no solutions exist, It will throw
+    ValueError.
+
+    Parameters
+    ==========
+
+    B : Matrix
+        The right hand side of the equation to be solved for.  Must have
+        the same number of rows as matrix A.
+
+    freevar : boolean, optional
+        Flag, when set to `True` will return the indices of the free
+        variables in the solutions (column Matrix), for a system that is
+        undetermined (e.g. A has more columns than rows), for which
+        infinite solutions are possible, in terms of arbitrary
+        values of free variables. Default `False`.
+
+    Returns
+    =======
+
+    x : Matrix
+        The matrix that will satisfy ``Ax = B``.  Will have as many rows as
+        matrix A has columns, and as many columns as matrix B.
+
+    params : Matrix
+        If the system is underdetermined (e.g. A has more columns than
+        rows), infinite solutions are possible, in terms of arbitrary
+        parameters. These arbitrary parameters are returned as params
+        Matrix.
+
+    free_var_index : List, optional
+        If the system is underdetermined (e.g. A has more columns than
+        rows), infinite solutions are possible, in terms of arbitrary
+        values of free variables. Then the indices of the free variables
+        in the solutions (column Matrix) are returned by free_var_index,
+        if the flag `freevar` is set to `True`.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[1, 2, 1, 1], [1, 2, 2, -1], [2, 4, 0, 6]])
+    >>> B = Matrix([7, 12, 4])
+    >>> sol, params = A.gauss_jordan_solve(B)
+    >>> sol
+    Matrix([
+    [-2*tau0 - 3*tau1 + 2],
+    [                 tau0],
+    [           2*tau1 + 5],
+    [                 tau1]])
+    >>> params
+    Matrix([
+    [tau0],
+    [tau1]])
+    >>> taus_zeroes = { tau:0 for tau in params }
+    >>> sol_unique = sol.xreplace(taus_zeroes)
+    >>> sol_unique
+        Matrix([
+    [2],
+    [0],
+    [5],
+    [0]])
+
+
+    >>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 10]])
+    >>> B = Matrix([3, 6, 9])
+    >>> sol, params = A.gauss_jordan_solve(B)
+    >>> sol
+    Matrix([
+    [-1],
+    [ 2],
+    [ 0]])
+    >>> params
+    Matrix(0, 1, [])
+
+    >>> A = Matrix([[2, -7], [-1, 4]])
+    >>> B = Matrix([[-21, 3], [12, -2]])
+    >>> sol, params = A.gauss_jordan_solve(B)
+    >>> sol
+    Matrix([
+    [0, -2],
+    [3, -1]])
+    >>> params
+    Matrix(0, 2, [])
+
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[1, 2, 1, 1], [1, 2, 2, -1], [2, 4, 0, 6]])
+    >>> B = Matrix([7, 12, 4])
+    >>> sol, params, freevars = A.gauss_jordan_solve(B, freevar=True)
+    >>> sol
+    Matrix([
+    [-2*tau0 - 3*tau1 + 2],
+    [                 tau0],
+    [           2*tau1 + 5],
+    [                 tau1]])
+    >>> params
+    Matrix([
+    [tau0],
+    [tau1]])
+    >>> freevars
+    [1, 3]
+
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gaussian_elimination
+
+    """
+
+    from sympy.matrices import Matrix, zeros
+
+    cls      = M.__class__
+    aug      = M.hstack(M.copy(), B.copy())
+    B_cols   = B.cols
+    row, col = aug[:, :-B_cols].shape
+
+    # solve by reduced row echelon form
+    A, pivots = aug.rref(simplify=True)
+    A, v      = A[:, :-B_cols], A[:, -B_cols:]
+    pivots    = list(filter(lambda p: p < col, pivots))
+    rank      = len(pivots)
+
+    # Get index of free symbols (free parameters)
+    # non-pivots columns are free variables
+    free_var_index = [c for c in range(A.cols) if c not in pivots]
+
+    # Bring to block form
+    permutation = Matrix(pivots + free_var_index).T
+
+    # check for existence of solutions
+    # rank of aug Matrix should be equal to rank of coefficient matrix
+    if not v[rank:, :].is_zero_matrix:
+        raise ValueError("Linear system has no solution")
+
+    # Free parameters
+    # what are current unnumbered free symbol names?
+    name = uniquely_named_symbol('tau', [aug],
+            compare=lambda i: str(i).rstrip('1234567890'),
+            modify=lambda s: '_' + s).name
+    gen  = numbered_symbols(name)
+    tau  = Matrix([next(gen) for k in range((col - rank)*B_cols)]).reshape(
+            col - rank, B_cols)
+
+    # Full parametric solution
+    V        = A[:rank, free_var_index]
+    vt       = v[:rank, :]
+    free_sol = tau.vstack(vt - V * tau, tau)
+
+    # Undo permutation
+    sol = zeros(col, B_cols)
+
+    for k in range(col):
+        sol[permutation[k], :] = free_sol[k,:]
+
+    sol, tau = cls(sol), cls(tau)
+
+    if freevar:
+        return sol, tau, free_var_index
+    else:
+        return sol, tau
+
+
+def _pinv_solve(M, B, arbitrary_matrix=None):
+    """Solve ``Ax = B`` using the Moore-Penrose pseudoinverse.
+
+    There may be zero, one, or infinite solutions.  If one solution
+    exists, it will be returned.  If infinite solutions exist, one will
+    be returned based on the value of arbitrary_matrix.  If no solutions
+    exist, the least-squares solution is returned.
+
+    Parameters
+    ==========
+
+    B : Matrix
+        The right hand side of the equation to be solved for.  Must have
+        the same number of rows as matrix A.
+    arbitrary_matrix : Matrix
+        If the system is underdetermined (e.g. A has more columns than
+        rows), infinite solutions are possible, in terms of an arbitrary
+        matrix.  This parameter may be set to a specific matrix to use
+        for that purpose; if so, it must be the same shape as x, with as
+        many rows as matrix A has columns, and as many columns as matrix
+        B.  If left as None, an appropriate matrix containing dummy
+        symbols in the form of ``wn_m`` will be used, with n and m being
+        row and column position of each symbol.
+
+    Returns
+    =======
+
+    x : Matrix
+        The matrix that will satisfy ``Ax = B``.  Will have as many rows as
+        matrix A has columns, and as many columns as matrix B.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[1, 2, 3], [4, 5, 6]])
+    >>> B = Matrix([7, 8])
+    >>> A.pinv_solve(B)
+    Matrix([
+    [ _w0_0/6 - _w1_0/3 + _w2_0/6 - 55/18],
+    [-_w0_0/3 + 2*_w1_0/3 - _w2_0/3 + 1/9],
+    [ _w0_0/6 - _w1_0/3 + _w2_0/6 + 59/18]])
+    >>> A.pinv_solve(B, arbitrary_matrix=Matrix([0, 0, 0]))
+    Matrix([
+    [-55/18],
+    [   1/9],
+    [ 59/18]])
+
+    See Also
+    ========
+
+    sympy.matrices.dense.DenseMatrix.lower_triangular_solve
+    sympy.matrices.dense.DenseMatrix.upper_triangular_solve
+    gauss_jordan_solve
+    cholesky_solve
+    diagonal_solve
+    LDLsolve
+    LUsolve
+    QRsolve
+    pinv
+
+    Notes
+    =====
+
+    This may return either exact solutions or least squares solutions.
+    To determine which, check ``A * A.pinv() * B == B``.  It will be
+    True if exact solutions exist, and False if only a least-squares
+    solution exists.  Be aware that the left hand side of that equation
+    may need to be simplified to correctly compare to the right hand
+    side.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#Obtaining_all_solutions_of_a_linear_system
+
+    """
+
+    from sympy.matrices import eye
+
+    A      = M
+    A_pinv = M.pinv()
+
+    if arbitrary_matrix is None:
+        rows, cols       = A.cols, B.cols
+        w                = symbols('w:{}_:{}'.format(rows, cols), cls=Dummy)
+        arbitrary_matrix = M.__class__(cols, rows, w).T
+
+    return A_pinv.multiply(B) + (eye(A.cols) -
+            A_pinv.multiply(A)).multiply(arbitrary_matrix)
+
+
+def _cramer_solve(M, rhs, det_method="laplace"):
+    """Solves system of linear equations using Cramer's rule.
+
+    This method is relatively inefficient compared to other methods.
+    However it only uses a single division, assuming a division-free determinant
+    method is provided. This is helpful to minimize the chance of divide-by-zero
+    cases in symbolic solutions to linear systems.
+
+    Parameters
+    ==========
+    M : Matrix
+        The matrix representing the left hand side of the equation.
+    rhs : Matrix
+        The matrix representing the right hand side of the equation.
+    det_method : str or callable
+        The method to use to calculate the determinant of the matrix.
+        The default is ``'laplace'``.  If a callable is passed, it should take a
+        single argument, the matrix, and return the determinant of the matrix.
+
+    Returns
+    =======
+    x : Matrix
+        The matrix that will satisfy ``Ax = B``.  Will have as many rows as
+        matrix A has columns, and as many columns as matrix B.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> A = Matrix([[0, -6, 1], [0, -6, -1], [-5, -2, 3]])
+    >>> B = Matrix([[-30, -9], [-18, -27], [-26, 46]])
+    >>> x = A.cramer_solve(B)
+    >>> x
+    Matrix([
+    [ 0, -5],
+    [ 4,  3],
+    [-6,  9]])
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Cramer%27s_rule#Explicit_formulas_for_small_systems
+
+    """
+    from .dense import zeros
+
+    def entry(i, j):
+        return rhs[i, sol] if j == col else M[i, j]
+
+    if det_method == "bird":
+        from .determinant import _det_bird
+        det = _det_bird
+    elif det_method == "laplace":
+        from .determinant import _det_laplace
+        det = _det_laplace
+    elif isinstance(det_method, str):
+        det = lambda matrix: matrix.det(method=det_method)
+    else:
+        det = det_method
+    det_M = det(M)
+    x = zeros(*rhs.shape)
+    for sol in range(rhs.shape[1]):
+        for col in range(rhs.shape[0]):
+            x[col, sol] = det(M.__class__(*M.shape, entry)) / det_M
+    return M.__class__(x)
+
+
+def _solve(M, rhs, method='GJ'):
+    """Solves linear equation where the unique solution exists.
+
+    Parameters
+    ==========
+
+    rhs : Matrix
+        Vector representing the right hand side of the linear equation.
+
+    method : string, optional
+        If set to ``'GJ'`` or ``'GE'``, the Gauss-Jordan elimination will be
+        used, which is implemented in the routine ``gauss_jordan_solve``.
+
+        If set to ``'LU'``, ``LUsolve`` routine will be used.
+
+        If set to ``'QR'``, ``QRsolve`` routine will be used.
+
+        If set to ``'PINV'``, ``pinv_solve`` routine will be used.
+
+        If set to ``'CRAMER'``, ``cramer_solve`` routine will be used.
+
+        It also supports the methods available for special linear systems
+
+        For positive definite systems:
+
+        If set to ``'CH'``, ``cholesky_solve`` routine will be used.
+
+        If set to ``'LDL'``, ``LDLsolve`` routine will be used.
+
+        To use a different method and to compute the solution via the
+        inverse, use a method defined in the .inv() docstring.
+
+    Returns
+    =======
+
+    solutions : Matrix
+        Vector representing the solution.
+
+    Raises
+    ======
+
+    ValueError
+        If there is not a unique solution then a ``ValueError`` will be
+        raised.
+
+        If ``M`` is not square, a ``ValueError`` and a different routine
+        for solving the system will be suggested.
+    """
+
+    if method in ('GJ', 'GE'):
+        try:
+            soln, param = M.gauss_jordan_solve(rhs)
+
+            if param:
+                raise NonInvertibleMatrixError("Matrix det == 0; not invertible. "
+                "Try ``M.gauss_jordan_solve(rhs)`` to obtain a parametric solution.")
+
+        except ValueError:
+            raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
+
+        return soln
+
+    elif method == 'LU':
+        return M.LUsolve(rhs)
+    elif method == 'CH':
+        return M.cholesky_solve(rhs)
+    elif method == 'QR':
+        return M.QRsolve(rhs)
+    elif method == 'LDL':
+        return M.LDLsolve(rhs)
+    elif method == 'PINV':
+        return M.pinv_solve(rhs)
+    elif method == 'CRAMER':
+        return M.cramer_solve(rhs)
+    else:
+        return M.inv(method=method).multiply(rhs)
+
+
+def _solve_least_squares(M, rhs, method='CH'):
+    """Return the least-square fit to the data.
+
+    Parameters
+    ==========
+
+    rhs : Matrix
+        Vector representing the right hand side of the linear equation.
+
+    method : string or boolean, optional
+        If set to ``'CH'``, ``cholesky_solve`` routine will be used.
+
+        If set to ``'LDL'``, ``LDLsolve`` routine will be used.
+
+        If set to ``'QR'``, ``QRsolve`` routine will be used.
+
+        If set to ``'PINV'``, ``pinv_solve`` routine will be used.
+
+        Otherwise, the conjugate of ``M`` will be used to create a system
+        of equations that is passed to ``solve`` along with the hint
+        defined by ``method``.
+
+    Returns
+    =======
+
+    solutions : Matrix
+        Vector representing the solution.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, ones
+    >>> A = Matrix([1, 2, 3])
+    >>> B = Matrix([2, 3, 4])
+    >>> S = Matrix(A.row_join(B))
+    >>> S
+    Matrix([
+    [1, 2],
+    [2, 3],
+    [3, 4]])
+
+    If each line of S represent coefficients of Ax + By
+    and x and y are [2, 3] then S*xy is:
+
+    >>> r = S*Matrix([2, 3]); r
+    Matrix([
+    [ 8],
+    [13],
+    [18]])
+
+    But let's add 1 to the middle value and then solve for the
+    least-squares value of xy:
+
+    >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy
+    Matrix([
+    [ 5/3],
+    [10/3]])
+
+    The error is given by S*xy - r:
+
+    >>> S*xy - r
+    Matrix([
+    [1/3],
+    [1/3],
+    [1/3]])
+    >>> _.norm().n(2)
+    0.58
+
+    If a different xy is used, the norm will be higher:
+
+    >>> xy += ones(2, 1)/10
+    >>> (S*xy - r).norm().n(2)
+    1.5
+
+    """
+
+    if method == 'CH':
+        return M.cholesky_solve(rhs)
+    elif method == 'QR':
+        return M.QRsolve(rhs)
+    elif method == 'LDL':
+        return M.LDLsolve(rhs)
+    elif method == 'PINV':
+        return M.pinv_solve(rhs)
+    else:
+        t = M.H
+        return (t * M).solve(t * rhs, method=method)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/sparse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/sparse.py
new file mode 100644
index 0000000000000000000000000000000000000000..95a7b3ca0ac29cf4409ec1eeecd059f9643e9bbc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/sparse.py
@@ -0,0 +1,473 @@
+from collections.abc import Callable
+
+from sympy.core.containers import Dict
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.misc import as_int
+
+from .matrixbase import MatrixBase
+from .repmatrix import MutableRepMatrix, RepMatrix
+
+from .utilities import _iszero
+
+from .decompositions import (
+    _liupc, _row_structure_symbolic_cholesky, _cholesky_sparse,
+    _LDLdecomposition_sparse)
+
+from .solvers import (
+    _lower_triangular_solve_sparse, _upper_triangular_solve_sparse)
+
+
+class SparseRepMatrix(RepMatrix):
+    """
+    A sparse matrix (a matrix with a large number of zero elements).
+
+    Examples
+    ========
+
+    >>> from sympy import SparseMatrix, ones
+    >>> SparseMatrix(2, 2, range(4))
+    Matrix([
+    [0, 1],
+    [2, 3]])
+    >>> SparseMatrix(2, 2, {(1, 1): 2})
+    Matrix([
+    [0, 0],
+    [0, 2]])
+
+    A SparseMatrix can be instantiated from a ragged list of lists:
+
+    >>> SparseMatrix([[1, 2, 3], [1, 2], [1]])
+    Matrix([
+    [1, 2, 3],
+    [1, 2, 0],
+    [1, 0, 0]])
+
+    For safety, one may include the expected size and then an error
+    will be raised if the indices of any element are out of range or
+    (for a flat list) if the total number of elements does not match
+    the expected shape:
+
+    >>> SparseMatrix(2, 2, [1, 2])
+    Traceback (most recent call last):
+    ...
+    ValueError: List length (2) != rows*columns (4)
+
+    Here, an error is not raised because the list is not flat and no
+    element is out of range:
+
+    >>> SparseMatrix(2, 2, [[1, 2]])
+    Matrix([
+    [1, 2],
+    [0, 0]])
+
+    But adding another element to the first (and only) row will cause
+    an error to be raised:
+
+    >>> SparseMatrix(2, 2, [[1, 2, 3]])
+    Traceback (most recent call last):
+    ...
+    ValueError: The location (0, 2) is out of designated range: (1, 1)
+
+    To autosize the matrix, pass None for rows:
+
+    >>> SparseMatrix(None, [[1, 2, 3]])
+    Matrix([[1, 2, 3]])
+    >>> SparseMatrix(None, {(1, 1): 1, (3, 3): 3})
+    Matrix([
+    [0, 0, 0, 0],
+    [0, 1, 0, 0],
+    [0, 0, 0, 0],
+    [0, 0, 0, 3]])
+
+    Values that are themselves a Matrix are automatically expanded:
+
+    >>> SparseMatrix(4, 4, {(1, 1): ones(2)})
+    Matrix([
+    [0, 0, 0, 0],
+    [0, 1, 1, 0],
+    [0, 1, 1, 0],
+    [0, 0, 0, 0]])
+
+    A ValueError is raised if the expanding matrix tries to overwrite
+    a different element already present:
+
+    >>> SparseMatrix(3, 3, {(0, 0): ones(2), (1, 1): 2})
+    Traceback (most recent call last):
+    ...
+    ValueError: collision at (1, 1)
+
+    See Also
+    ========
+    DenseMatrix
+    MutableSparseMatrix
+    ImmutableSparseMatrix
+    """
+
+    @classmethod
+    def _handle_creation_inputs(cls, *args, **kwargs):
+        if len(args) == 1 and isinstance(args[0], MatrixBase):
+            rows = args[0].rows
+            cols = args[0].cols
+            smat = args[0].todok()
+            return rows, cols, smat
+
+        smat = {}
+        # autosizing
+        if len(args) == 2 and args[0] is None:
+            args = [None, None, args[1]]
+
+        if len(args) == 3:
+            r, c = args[:2]
+            if r is c is None:
+                rows = cols = None
+            elif None in (r, c):
+                raise ValueError(
+                    'Pass rows=None and no cols for autosizing.')
+            else:
+                rows, cols = as_int(args[0]), as_int(args[1])
+
+            if isinstance(args[2], Callable):
+                op = args[2]
+
+                if None in (rows, cols):
+                    raise ValueError(
+                        "{} and {} must be integers for this "
+                        "specification.".format(rows, cols))
+
+                row_indices = [cls._sympify(i) for i in range(rows)]
+                col_indices = [cls._sympify(j) for j in range(cols)]
+
+                for i in row_indices:
+                    for j in col_indices:
+                        value = cls._sympify(op(i, j))
+                        if value != cls.zero:
+                            smat[i, j] = value
+
+                return rows, cols, smat
+
+            elif isinstance(args[2], (dict, Dict)):
+                def update(i, j, v):
+                    # update smat and make sure there are no collisions
+                    if v:
+                        if (i, j) in smat and v != smat[i, j]:
+                            raise ValueError(
+                                "There is a collision at {} for {} and {}."
+                                .format((i, j), v, smat[i, j])
+                            )
+                        smat[i, j] = v
+
+                # manual copy, copy.deepcopy() doesn't work
+                for (r, c), v in args[2].items():
+                    if isinstance(v, MatrixBase):
+                        for (i, j), vv in v.todok().items():
+                            update(r + i, c + j, vv)
+                    elif isinstance(v, (list, tuple)):
+                        _, _, smat = cls._handle_creation_inputs(v, **kwargs)
+                        for i, j in smat:
+                            update(r + i, c + j, smat[i, j])
+                    else:
+                        v = cls._sympify(v)
+                        update(r, c, cls._sympify(v))
+
+            elif is_sequence(args[2]):
+                flat = not any(is_sequence(i) for i in args[2])
+                if not flat:
+                    _, _, smat = \
+                        cls._handle_creation_inputs(args[2], **kwargs)
+                else:
+                    flat_list = args[2]
+                    if len(flat_list) != rows * cols:
+                        raise ValueError(
+                            "The length of the flat list ({}) does not "
+                            "match the specified size ({} * {})."
+                            .format(len(flat_list), rows, cols)
+                        )
+
+                    for i in range(rows):
+                        for j in range(cols):
+                            value = flat_list[i*cols + j]
+                            value = cls._sympify(value)
+                            if value != cls.zero:
+                                smat[i, j] = value
+
+            if rows is None:  # autosizing
+                keys = smat.keys()
+                rows = max(r for r, _ in keys) + 1 if keys else 0
+                cols = max(c for _, c in keys) + 1 if keys else 0
+
+            else:
+                for i, j in smat.keys():
+                    if i and i >= rows or j and j >= cols:
+                        raise ValueError(
+                            "The location {} is out of the designated range"
+                            "[{}, {}]x[{}, {}]"
+                            .format((i, j), 0, rows - 1, 0, cols - 1)
+                        )
+
+            return rows, cols, smat
+
+        elif len(args) == 1 and isinstance(args[0], (list, tuple)):
+            # list of values or lists
+            v = args[0]
+            c = 0
+            for i, row in enumerate(v):
+                if not isinstance(row, (list, tuple)):
+                    row = [row]
+                for j, vv in enumerate(row):
+                    if vv != cls.zero:
+                        smat[i, j] = cls._sympify(vv)
+                c = max(c, len(row))
+            rows = len(v) if c else 0
+            cols = c
+            return rows, cols, smat
+
+        else:
+            # handle full matrix forms with _handle_creation_inputs
+            rows, cols, mat = super()._handle_creation_inputs(*args)
+            for i in range(rows):
+                for j in range(cols):
+                    value = mat[cols*i + j]
+                    if value != cls.zero:
+                        smat[i, j] = value
+
+            return rows, cols, smat
+
+    @property
+    def _smat(self):
+
+        sympy_deprecation_warning(
+            """
+            The private _smat attribute of SparseMatrix is deprecated. Use the
+            .todok() method instead.
+            """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-private-matrix-attributes"
+        )
+
+        return self.todok()
+
+    def _eval_inverse(self, **kwargs):
+        return self.inv(method=kwargs.get('method', 'LDL'),
+                        iszerofunc=kwargs.get('iszerofunc', _iszero),
+                        try_block_diag=kwargs.get('try_block_diag', False))
+
+    def applyfunc(self, f):
+        """Apply a function to each element of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix
+        >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j)
+        >>> m
+        Matrix([
+        [0, 1],
+        [2, 3]])
+        >>> m.applyfunc(lambda i: 2*i)
+        Matrix([
+        [0, 2],
+        [4, 6]])
+
+        """
+        if not callable(f):
+            raise TypeError("`f` must be callable.")
+
+        # XXX: This only applies the function to the nonzero elements of the
+        # matrix so is inconsistent with DenseMatrix.applyfunc e.g.
+        #   zeros(2, 2).applyfunc(lambda x: x + 1)
+        dok = {}
+        for k, v in self.todok().items():
+            fv = f(v)
+            if fv != 0:
+                dok[k] = fv
+
+        return self._new(self.rows, self.cols, dok)
+
+    def as_immutable(self):
+        """Returns an Immutable version of this Matrix."""
+        from .immutable import ImmutableSparseMatrix
+        return ImmutableSparseMatrix(self)
+
+    def as_mutable(self):
+        """Returns a mutable version of this matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import ImmutableMatrix
+        >>> X = ImmutableMatrix([[1, 2], [3, 4]])
+        >>> Y = X.as_mutable()
+        >>> Y[1, 1] = 5 # Can set values in Y
+        >>> Y
+        Matrix([
+        [1, 2],
+        [3, 5]])
+        """
+        return MutableSparseMatrix(self)
+
+    def col_list(self):
+        """Returns a column-sorted list of non-zero elements of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix
+        >>> a=SparseMatrix(((1, 2), (3, 4)))
+        >>> a
+        Matrix([
+        [1, 2],
+        [3, 4]])
+        >>> a.CL
+        [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)]
+
+        See Also
+        ========
+
+        sympy.matrices.sparse.SparseMatrix.row_list
+        """
+        return [tuple(k + (self[k],)) for k in sorted(self.todok().keys(), key=lambda k: list(reversed(k)))]
+
+    def nnz(self):
+        """Returns the number of non-zero elements in Matrix."""
+        return len(self.todok())
+
+    def row_list(self):
+        """Returns a row-sorted list of non-zero elements of the matrix.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix
+        >>> a = SparseMatrix(((1, 2), (3, 4)))
+        >>> a
+        Matrix([
+        [1, 2],
+        [3, 4]])
+        >>> a.RL
+        [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)]
+
+        See Also
+        ========
+
+        sympy.matrices.sparse.SparseMatrix.col_list
+        """
+        return [tuple(k + (self[k],)) for k in
+            sorted(self.todok().keys(), key=list)]
+
+    def scalar_multiply(self, scalar):
+        "Scalar element-wise multiplication"
+        return scalar * self
+
+    def solve_least_squares(self, rhs, method='LDL'):
+        """Return the least-square fit to the data.
+
+        By default the cholesky_solve routine is used (method='CH'); other
+        methods of matrix inversion can be used. To find out which are
+        available, see the docstring of the .inv() method.
+
+        Examples
+        ========
+
+        >>> from sympy import SparseMatrix, Matrix, ones
+        >>> A = Matrix([1, 2, 3])
+        >>> B = Matrix([2, 3, 4])
+        >>> S = SparseMatrix(A.row_join(B))
+        >>> S
+        Matrix([
+        [1, 2],
+        [2, 3],
+        [3, 4]])
+
+        If each line of S represent coefficients of Ax + By
+        and x and y are [2, 3] then S*xy is:
+
+        >>> r = S*Matrix([2, 3]); r
+        Matrix([
+        [ 8],
+        [13],
+        [18]])
+
+        But let's add 1 to the middle value and then solve for the
+        least-squares value of xy:
+
+        >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy
+        Matrix([
+        [ 5/3],
+        [10/3]])
+
+        The error is given by S*xy - r:
+
+        >>> S*xy - r
+        Matrix([
+        [1/3],
+        [1/3],
+        [1/3]])
+        >>> _.norm().n(2)
+        0.58
+
+        If a different xy is used, the norm will be higher:
+
+        >>> xy += ones(2, 1)/10
+        >>> (S*xy - r).norm().n(2)
+        1.5
+
+        """
+        t = self.T
+        return (t*self).inv(method=method)*t*rhs
+
+    def solve(self, rhs, method='LDL'):
+        """Return solution to self*soln = rhs using given inversion method.
+
+        For a list of possible inversion methods, see the .inv() docstring.
+        """
+        if not self.is_square:
+            if self.rows < self.cols:
+                raise ValueError('Under-determined system.')
+            elif self.rows > self.cols:
+                raise ValueError('For over-determined system, M, having '
+                    'more rows than columns, try M.solve_least_squares(rhs).')
+        else:
+            return self.inv(method=method).multiply(rhs)
+
+    RL = property(row_list, None, None, "Alternate faster representation")
+    CL = property(col_list, None, None, "Alternate faster representation")
+
+    def liupc(self):
+        return _liupc(self)
+
+    def row_structure_symbolic_cholesky(self):
+        return _row_structure_symbolic_cholesky(self)
+
+    def cholesky(self, hermitian=True):
+        return _cholesky_sparse(self, hermitian=hermitian)
+
+    def LDLdecomposition(self, hermitian=True):
+        return _LDLdecomposition_sparse(self, hermitian=hermitian)
+
+    def lower_triangular_solve(self, rhs):
+        return _lower_triangular_solve_sparse(self, rhs)
+
+    def upper_triangular_solve(self, rhs):
+        return _upper_triangular_solve_sparse(self, rhs)
+
+    liupc.__doc__                           = _liupc.__doc__
+    row_structure_symbolic_cholesky.__doc__ = _row_structure_symbolic_cholesky.__doc__
+    cholesky.__doc__                        = _cholesky_sparse.__doc__
+    LDLdecomposition.__doc__                = _LDLdecomposition_sparse.__doc__
+    lower_triangular_solve.__doc__          = lower_triangular_solve.__doc__
+    upper_triangular_solve.__doc__          = upper_triangular_solve.__doc__
+
+
+class MutableSparseMatrix(SparseRepMatrix, MutableRepMatrix):
+
+    @classmethod
+    def _new(cls, *args, **kwargs):
+        rows, cols, smat = cls._handle_creation_inputs(*args, **kwargs)
+
+        rep = cls._smat_to_DomainMatrix(rows, cols, smat)
+
+        return cls._fromrep(rep)
+
+
+SparseMatrix = MutableSparseMatrix
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/sparsetools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/sparsetools.py
new file mode 100644
index 0000000000000000000000000000000000000000..50048f6dc7e5cf160366963d16427987616ddce7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/sparsetools.py
@@ -0,0 +1,300 @@
+from sympy.core.containers import Dict
+from sympy.core.symbol import Dummy
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.misc import as_int, filldedent
+
+from .sparse import MutableSparseMatrix as SparseMatrix
+
+
+def _doktocsr(dok):
+    """Converts a sparse matrix to Compressed Sparse Row (CSR) format.
+
+    Parameters
+    ==========
+
+    A : contains non-zero elements sorted by key (row, column)
+    JA : JA[i] is the column corresponding to A[i]
+    IA : IA[i] contains the index in A for the first non-zero element
+        of row[i]. Thus IA[i+1] - IA[i] gives number of non-zero
+        elements row[i]. The length of IA is always 1 more than the
+        number of rows in the matrix.
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.sparsetools import _doktocsr
+    >>> from sympy import SparseMatrix, diag
+    >>> m = SparseMatrix(diag(1, 2, 3))
+    >>> m[2, 0] = -1
+    >>> _doktocsr(m)
+    [[1, 2, -1, 3], [0, 1, 0, 2], [0, 1, 2, 4], [3, 3]]
+
+    """
+    row, JA, A = [list(i) for i in zip(*dok.row_list())]
+    IA = [0]*((row[0] if row else 0) + 1)
+    for i, r in enumerate(row):
+        IA.extend([i]*(r - row[i - 1]))  # if i = 0 nothing is extended
+    IA.extend([len(A)]*(dok.rows - len(IA) + 1))
+    shape = [dok.rows, dok.cols]
+    return [A, JA, IA, shape]
+
+
+def _csrtodok(csr):
+    """Converts a CSR representation to DOK representation.
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.sparsetools import _csrtodok
+    >>> _csrtodok([[5, 8, 3, 6], [0, 1, 2, 1], [0, 0, 2, 3, 4], [4, 3]])
+    Matrix([
+    [0, 0, 0],
+    [5, 8, 0],
+    [0, 0, 3],
+    [0, 6, 0]])
+
+    """
+    smat = {}
+    A, JA, IA, shape = csr
+    for i in range(len(IA) - 1):
+        indices = slice(IA[i], IA[i + 1])
+        for l, m in zip(A[indices], JA[indices]):
+            smat[i, m] = l
+    return SparseMatrix(*shape, smat)
+
+
+def banded(*args, **kwargs):
+    """Returns a SparseMatrix from the given dictionary describing
+    the diagonals of the matrix. The keys are positive for upper
+    diagonals and negative for those below the main diagonal. The
+    values may be:
+
+    * expressions or single-argument functions,
+
+    * lists or tuples of values,
+
+    * matrices
+
+    Unless dimensions are given, the size of the returned matrix will
+    be large enough to contain the largest non-zero value provided.
+
+    kwargs
+    ======
+
+    rows : rows of the resulting matrix; computed if
+           not given.
+
+    cols : columns of the resulting matrix; computed if
+           not given.
+
+    Examples
+    ========
+
+    >>> from sympy import banded, ones, Matrix
+    >>> from sympy.abc import x
+
+    If explicit values are given in tuples,
+    the matrix will autosize to contain all values, otherwise
+    a single value is filled onto the entire diagonal:
+
+    >>> banded({1: (1, 2, 3), -1: (4, 5, 6), 0: x})
+    Matrix([
+    [x, 1, 0, 0],
+    [4, x, 2, 0],
+    [0, 5, x, 3],
+    [0, 0, 6, x]])
+
+    A function accepting a single argument can be used to fill the
+    diagonal as a function of diagonal index (which starts at 0).
+    The size (or shape) of the matrix must be given to obtain more
+    than a 1x1 matrix:
+
+    >>> s = lambda d: (1 + d)**2
+    >>> banded(5, {0: s, 2: s, -2: 2})
+    Matrix([
+    [1, 0, 1,  0,  0],
+    [0, 4, 0,  4,  0],
+    [2, 0, 9,  0,  9],
+    [0, 2, 0, 16,  0],
+    [0, 0, 2,  0, 25]])
+
+    The diagonal of matrices placed on a diagonal will coincide
+    with the indicated diagonal:
+
+    >>> vert = Matrix([1, 2, 3])
+    >>> banded({0: vert}, cols=3)
+    Matrix([
+    [1, 0, 0],
+    [2, 1, 0],
+    [3, 2, 1],
+    [0, 3, 2],
+    [0, 0, 3]])
+
+    >>> banded(4, {0: ones(2)})
+    Matrix([
+    [1, 1, 0, 0],
+    [1, 1, 0, 0],
+    [0, 0, 1, 1],
+    [0, 0, 1, 1]])
+
+    Errors are raised if the designated size will not hold
+    all values an integral number of times. Here, the rows
+    are designated as odd (but an even number is required to
+    hold the off-diagonal 2x2 ones):
+
+    >>> banded({0: 2, 1: ones(2)}, rows=5)
+    Traceback (most recent call last):
+    ...
+    ValueError:
+    sequence does not fit an integral number of times in the matrix
+
+    And here, an even number of rows is given...but the square
+    matrix has an even number of columns, too. As we saw
+    in the previous example, an odd number is required:
+
+    >>> banded(4, {0: 2, 1: ones(2)})  # trying to make 4x4 and cols must be odd
+    Traceback (most recent call last):
+    ...
+    ValueError:
+    sequence does not fit an integral number of times in the matrix
+
+    A way around having to count rows is to enclosing matrix elements
+    in a tuple and indicate the desired number of them to the right:
+
+    >>> banded({0: 2, 2: (ones(2),)*3})
+    Matrix([
+    [2, 0, 1, 1, 0, 0, 0, 0],
+    [0, 2, 1, 1, 0, 0, 0, 0],
+    [0, 0, 2, 0, 1, 1, 0, 0],
+    [0, 0, 0, 2, 1, 1, 0, 0],
+    [0, 0, 0, 0, 2, 0, 1, 1],
+    [0, 0, 0, 0, 0, 2, 1, 1]])
+
+    An error will be raised if more than one value
+    is written to a given entry. Here, the ones overlap
+    with the main diagonal if they are placed on the
+    first diagonal:
+
+    >>> banded({0: (2,)*5, 1: (ones(2),)*3})
+    Traceback (most recent call last):
+    ...
+    ValueError: collision at (1, 1)
+
+    By placing a 0 at the bottom left of the 2x2 matrix of
+    ones, the collision is avoided:
+
+    >>> u2 = Matrix([
+    ... [1, 1],
+    ... [0, 1]])
+    >>> banded({0: [2]*5, 1: [u2]*3})
+    Matrix([
+    [2, 1, 1, 0, 0, 0, 0],
+    [0, 2, 1, 0, 0, 0, 0],
+    [0, 0, 2, 1, 1, 0, 0],
+    [0, 0, 0, 2, 1, 0, 0],
+    [0, 0, 0, 0, 2, 1, 1],
+    [0, 0, 0, 0, 0, 0, 1]])
+    """
+    try:
+        if len(args) not in (1, 2, 3):
+            raise TypeError
+        if not isinstance(args[-1], (dict, Dict)):
+            raise TypeError
+        if len(args) == 1:
+            rows = kwargs.get('rows', None)
+            cols = kwargs.get('cols', None)
+            if rows is not None:
+                rows = as_int(rows)
+            if cols is not None:
+                cols = as_int(cols)
+        elif len(args) == 2:
+            rows = cols = as_int(args[0])
+        else:
+            rows, cols = map(as_int, args[:2])
+        # fails with ValueError if any keys are not ints
+        _ = all(as_int(k) for k in args[-1])
+    except (ValueError, TypeError):
+        raise TypeError(filldedent(
+            '''unrecognized input to banded:
+            expecting [[row,] col,] {int: value}'''))
+    def rc(d):
+        # return row,col coord of diagonal start
+        r = -d if d < 0 else 0
+        c = 0 if r else d
+        return r, c
+    smat = {}
+    undone = []
+    tba = Dummy()
+    # first handle objects with size
+    for d, v in args[-1].items():
+        r, c = rc(d)
+        # note: only list and tuple are recognized since this
+        # will allow other Basic objects like Tuple
+        # into the matrix if so desired
+        if isinstance(v, (list, tuple)):
+            extra = 0
+            for i, vi in enumerate(v):
+                i += extra
+                if is_sequence(vi):
+                    vi = SparseMatrix(vi)
+                    smat[r + i, c + i] = vi
+                    extra += min(vi.shape) - 1
+                else:
+                    smat[r + i, c + i] = vi
+        elif is_sequence(v):
+            v = SparseMatrix(v)
+            rv, cv = v.shape
+            if rows and cols:
+                nr, xr = divmod(rows - r, rv)
+                nc, xc = divmod(cols - c, cv)
+                x = xr or xc
+                do = min(nr, nc)
+            elif rows:
+                do, x = divmod(rows - r, rv)
+            elif cols:
+                do, x = divmod(cols - c, cv)
+            else:
+                do = 1
+                x = 0
+            if x:
+                raise ValueError(filldedent('''
+                    sequence does not fit an integral number of times
+                    in the matrix'''))
+            j = min(v.shape)
+            for i in range(do):
+                smat[r, c] = v
+                r += j
+                c += j
+        elif v:
+            smat[r, c] = tba
+            undone.append((d, v))
+    s = SparseMatrix(None, smat)  # to expand matrices
+    smat = s.todok()
+    # check for dim errors here
+    if rows is not None and rows < s.rows:
+        raise ValueError('Designated rows %s < needed %s' % (rows, s.rows))
+    if cols is not None and cols < s.cols:
+        raise ValueError('Designated cols %s < needed %s' % (cols, s.cols))
+    if rows is cols is None:
+        rows = s.rows
+        cols = s.cols
+    elif rows is not None and cols is None:
+        cols = max(rows, s.cols)
+    elif cols is not None and rows is None:
+        rows = max(cols, s.rows)
+    def update(i, j, v):
+        # update smat and make sure there are
+        # no collisions
+        if v:
+            if (i, j) in smat and smat[i, j] not in (tba, v):
+                raise ValueError('collision at %s' % ((i, j),))
+            smat[i, j] = v
+    if undone:
+        for d, vi in undone:
+            r, c = rc(d)
+            v = vi if callable(vi) else lambda _: vi
+            i = 0
+            while r + i < rows and c + i < cols:
+                update(r + i, c + i, v(i))
+                i += 1
+    return SparseMatrix(rows, cols, smat)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/subspaces.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/subspaces.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ab0b71b4289ebaeb6394059c6a7cd49d3a148a1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/subspaces.py
@@ -0,0 +1,174 @@
+from .utilities import _iszero
+
+
+def _columnspace(M, simplify=False):
+    """Returns a list of vectors (Matrix objects) that span columnspace of ``M``
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6])
+    >>> M
+    Matrix([
+    [ 1,  3, 0],
+    [-2, -6, 0],
+    [ 3,  9, 6]])
+    >>> M.columnspace()
+    [Matrix([
+    [ 1],
+    [-2],
+    [ 3]]), Matrix([
+    [0],
+    [0],
+    [6]])]
+
+    See Also
+    ========
+
+    nullspace
+    rowspace
+    """
+
+    reduced, pivots = M.echelon_form(simplify=simplify, with_pivots=True)
+
+    return [M.col(i) for i in pivots]
+
+
+def _nullspace(M, simplify=False, iszerofunc=_iszero):
+    """Returns list of vectors (Matrix objects) that span nullspace of ``M``
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6])
+    >>> M
+    Matrix([
+    [ 1,  3, 0],
+    [-2, -6, 0],
+    [ 3,  9, 6]])
+    >>> M.nullspace()
+    [Matrix([
+    [-3],
+    [ 1],
+    [ 0]])]
+
+    See Also
+    ========
+
+    columnspace
+    rowspace
+    """
+
+    reduced, pivots = M.rref(iszerofunc=iszerofunc, simplify=simplify)
+
+    free_vars = [i for i in range(M.cols) if i not in pivots]
+    basis     = []
+
+    for free_var in free_vars:
+        # for each free variable, we will set it to 1 and all others
+        # to 0.  Then, we will use back substitution to solve the system
+        vec           = [M.zero] * M.cols
+        vec[free_var] = M.one
+
+        for piv_row, piv_col in enumerate(pivots):
+            vec[piv_col] -= reduced[piv_row, free_var]
+
+        basis.append(vec)
+
+    return [M._new(M.cols, 1, b) for b in basis]
+
+
+def _rowspace(M, simplify=False):
+    """Returns a list of vectors that span the row space of ``M``.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6])
+    >>> M
+    Matrix([
+    [ 1,  3, 0],
+    [-2, -6, 0],
+    [ 3,  9, 6]])
+    >>> M.rowspace()
+    [Matrix([[1, 3, 0]]), Matrix([[0, 0, 6]])]
+    """
+
+    reduced, pivots = M.echelon_form(simplify=simplify, with_pivots=True)
+
+    return [reduced.row(i) for i in range(len(pivots))]
+
+
+def _orthogonalize(cls, *vecs, normalize=False, rankcheck=False):
+    """Apply the Gram-Schmidt orthogonalization procedure
+    to vectors supplied in ``vecs``.
+
+    Parameters
+    ==========
+
+    vecs
+        vectors to be made orthogonal
+
+    normalize : bool
+        If ``True``, return an orthonormal basis.
+
+    rankcheck : bool
+        If ``True``, the computation does not stop when encountering
+        linearly dependent vectors.
+
+        If ``False``, it will raise ``ValueError`` when any zero
+        or linearly dependent vectors are found.
+
+    Returns
+    =======
+
+    list
+        List of orthogonal (or orthonormal) basis vectors.
+
+    Examples
+    ========
+
+    >>> from sympy import I, Matrix
+    >>> v = [Matrix([1, I]), Matrix([1, -I])]
+    >>> Matrix.orthogonalize(*v)
+    [Matrix([
+    [1],
+    [I]]), Matrix([
+    [ 1],
+    [-I]])]
+
+    See Also
+    ========
+
+    MatrixBase.QRdecomposition
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
+    """
+    from .decompositions import _QRdecomposition_optional
+
+    if not vecs:
+        return []
+
+    all_row_vecs = (vecs[0].rows == 1)
+
+    vecs = [x.vec() for x in vecs]
+    M = cls.hstack(*vecs)
+    Q, R = _QRdecomposition_optional(M, normalize=normalize)
+
+    if rankcheck and Q.cols < len(vecs):
+        raise ValueError("GramSchmidt: vector set not linearly independent")
+
+    ret = []
+    for i in range(Q.cols):
+        if all_row_vecs:
+            col = cls(Q[:, i].T)
+        else:
+            col = cls(Q[:, i])
+        ret.append(col)
+    return ret
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_commonmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_commonmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..6735adc1a9d4f9934a55c7ee70b087a19d3a48b4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_commonmatrix.py
@@ -0,0 +1,1266 @@
+#
+# Code for testing deprecated matrix classes. New test code should not be added
+# here. Instead, add it to test_matrixbase.py.
+#
+# This entire test module and the corresponding sympy/matrices/common.py
+# module will be removed in a future release.
+#
+from sympy.testing.pytest import raises, XFAIL, warns_deprecated_sympy
+
+from sympy.assumptions import Q
+from sympy.core.expr import Expr
+from sympy.core.add import Add
+from sympy.core.function import Function
+from sympy.core.kind import NumberKind, UndefinedKind
+from sympy.core.numbers import I, Integer, oo, pi, Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.matrices.exceptions import ShapeError, NonSquareMatrixError
+from sympy.matrices.kind import MatrixKind
+from sympy.matrices.common import (
+    _MinimalMatrix, _CastableMatrix, MatrixShaping, MatrixProperties,
+    MatrixOperations, MatrixArithmetic, MatrixSpecial)
+from sympy.matrices.matrices import MatrixCalculus
+from sympy.matrices import (Matrix, diag, eye,
+    matrix_multiply_elementwise, ones, zeros, SparseMatrix, banded,
+    MutableDenseMatrix, MutableSparseMatrix, ImmutableDenseMatrix,
+    ImmutableSparseMatrix)
+from sympy.polys.polytools import Poly
+from sympy.utilities.iterables import flatten
+from sympy.tensor.array.dense_ndim_array import ImmutableDenseNDimArray as Array
+
+from sympy.abc import x, y, z
+
+
+def test_matrix_deprecated_isinstance():
+
+    # Test that e.g. isinstance(M, MatrixCommon) still gives True when M is a
+    # Matrix for each of the deprecated matrix classes.
+
+    from sympy.matrices.common import (
+        MatrixRequired,
+        MatrixShaping,
+        MatrixSpecial,
+        MatrixProperties,
+        MatrixOperations,
+        MatrixArithmetic,
+        MatrixCommon
+    )
+    from sympy.matrices.matrices import (
+        MatrixDeterminant,
+        MatrixReductions,
+        MatrixSubspaces,
+        MatrixEigen,
+        MatrixCalculus,
+        MatrixDeprecated
+    )
+    from sympy import (
+        Matrix,
+        ImmutableMatrix,
+        SparseMatrix,
+        ImmutableSparseMatrix
+    )
+    all_mixins = (
+        MatrixRequired,
+        MatrixShaping,
+        MatrixSpecial,
+        MatrixProperties,
+        MatrixOperations,
+        MatrixArithmetic,
+        MatrixCommon,
+        MatrixDeterminant,
+        MatrixReductions,
+        MatrixSubspaces,
+        MatrixEigen,
+        MatrixCalculus,
+        MatrixDeprecated
+    )
+    all_matrices = (
+        Matrix,
+        ImmutableMatrix,
+        SparseMatrix,
+        ImmutableSparseMatrix
+    )
+
+    Ms = [M([[1, 2], [3, 4]]) for M in all_matrices]
+    t = ()
+
+    for mixin in all_mixins:
+        for M in Ms:
+            with warns_deprecated_sympy():
+                assert isinstance(M, mixin) is True
+        with warns_deprecated_sympy():
+            assert isinstance(t, mixin) is False
+
+
+# classes to test the deprecated matrix classes. We use warns_deprecated_sympy
+# to suppress the deprecation warnings because subclassing the deprecated
+# classes causes a warning to be raised.
+
+with warns_deprecated_sympy():
+    class ShapingOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixShaping):
+        pass
+
+
+def eye_Shaping(n):
+    return ShapingOnlyMatrix(n, n, lambda i, j: int(i == j))
+
+
+def zeros_Shaping(n):
+    return ShapingOnlyMatrix(n, n, lambda i, j: 0)
+
+
+with warns_deprecated_sympy():
+    class PropertiesOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixProperties):
+        pass
+
+
+def eye_Properties(n):
+    return PropertiesOnlyMatrix(n, n, lambda i, j: int(i == j))
+
+
+def zeros_Properties(n):
+    return PropertiesOnlyMatrix(n, n, lambda i, j: 0)
+
+
+with warns_deprecated_sympy():
+    class OperationsOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixOperations):
+        pass
+
+
+def eye_Operations(n):
+    return OperationsOnlyMatrix(n, n, lambda i, j: int(i == j))
+
+
+def zeros_Operations(n):
+    return OperationsOnlyMatrix(n, n, lambda i, j: 0)
+
+
+with warns_deprecated_sympy():
+    class ArithmeticOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixArithmetic):
+        pass
+
+
+def eye_Arithmetic(n):
+    return ArithmeticOnlyMatrix(n, n, lambda i, j: int(i == j))
+
+
+def zeros_Arithmetic(n):
+    return ArithmeticOnlyMatrix(n, n, lambda i, j: 0)
+
+
+with warns_deprecated_sympy():
+    class SpecialOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixSpecial):
+        pass
+
+
+with warns_deprecated_sympy():
+    class CalculusOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixCalculus):
+        pass
+
+
+def test__MinimalMatrix():
+    x = _MinimalMatrix(2, 3, [1, 2, 3, 4, 5, 6])
+    assert x.rows == 2
+    assert x.cols == 3
+    assert x[2] == 3
+    assert x[1, 1] == 5
+    assert list(x) == [1, 2, 3, 4, 5, 6]
+    assert list(x[1, :]) == [4, 5, 6]
+    assert list(x[:, 1]) == [2, 5]
+    assert list(x[:, :]) == list(x)
+    assert x[:, :] == x
+    assert _MinimalMatrix(x) == x
+    assert _MinimalMatrix([[1, 2, 3], [4, 5, 6]]) == x
+    assert _MinimalMatrix(([1, 2, 3], [4, 5, 6])) == x
+    assert _MinimalMatrix([(1, 2, 3), (4, 5, 6)]) == x
+    assert _MinimalMatrix(((1, 2, 3), (4, 5, 6))) == x
+    assert not (_MinimalMatrix([[1, 2], [3, 4], [5, 6]]) == x)
+
+
+def test_kind():
+    assert Matrix([[1, 2], [3, 4]]).kind == MatrixKind(NumberKind)
+    assert Matrix([[0, 0], [0, 0]]).kind == MatrixKind(NumberKind)
+    assert Matrix(0, 0, []).kind == MatrixKind(NumberKind)
+    assert Matrix([[x]]).kind == MatrixKind(NumberKind)
+    assert Matrix([[1, Matrix([[1]])]]).kind == MatrixKind(UndefinedKind)
+    assert SparseMatrix([[1]]).kind == MatrixKind(NumberKind)
+    assert SparseMatrix([[1, Matrix([[1]])]]).kind == MatrixKind(UndefinedKind)
+
+
+# ShapingOnlyMatrix tests
+def test_vec():
+    m = ShapingOnlyMatrix(2, 2, [1, 3, 2, 4])
+    m_vec = m.vec()
+    assert m_vec.cols == 1
+    for i in range(4):
+        assert m_vec[i] == i + 1
+
+
+def test_todok():
+    a, b, c, d = symbols('a:d')
+    m1 = MutableDenseMatrix([[a, b], [c, d]])
+    m2 = ImmutableDenseMatrix([[a, b], [c, d]])
+    m3 = MutableSparseMatrix([[a, b], [c, d]])
+    m4 = ImmutableSparseMatrix([[a, b], [c, d]])
+    assert m1.todok() == m2.todok() == m3.todok() == m4.todok() == \
+        {(0, 0): a, (0, 1): b, (1, 0): c, (1, 1): d}
+
+
+def test_tolist():
+    lst = [[S.One, S.Half, x*y, S.Zero], [x, y, z, x**2], [y, -S.One, z*x, 3]]
+    flat_lst = [S.One, S.Half, x*y, S.Zero, x, y, z, x**2, y, -S.One, z*x, 3]
+    m = ShapingOnlyMatrix(3, 4, flat_lst)
+    assert m.tolist() == lst
+
+def test_todod():
+    m = ShapingOnlyMatrix(3, 2, [[S.One, 0], [0, S.Half], [x, 0]])
+    dict = {0: {0: S.One}, 1: {1: S.Half}, 2: {0: x}}
+    assert m.todod() == dict
+
+def test_row_col_del():
+    e = ShapingOnlyMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    raises(IndexError, lambda: e.row_del(5))
+    raises(IndexError, lambda: e.row_del(-5))
+    raises(IndexError, lambda: e.col_del(5))
+    raises(IndexError, lambda: e.col_del(-5))
+
+    assert e.row_del(2) == e.row_del(-1) == Matrix([[1, 2, 3], [4, 5, 6]])
+    assert e.col_del(2) == e.col_del(-1) == Matrix([[1, 2], [4, 5], [7, 8]])
+
+    assert e.row_del(1) == e.row_del(-2) == Matrix([[1, 2, 3], [7, 8, 9]])
+    assert e.col_del(1) == e.col_del(-2) == Matrix([[1, 3], [4, 6], [7, 9]])
+
+
+def test_get_diag_blocks1():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    assert a.get_diag_blocks() == [a]
+    assert b.get_diag_blocks() == [b]
+    assert c.get_diag_blocks() == [c]
+
+
+def test_get_diag_blocks2():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    A, B, C, D = diag(a, b, b), diag(a, b, c), diag(a, c, b), diag(c, c, b)
+    A = ShapingOnlyMatrix(A.rows, A.cols, A)
+    B = ShapingOnlyMatrix(B.rows, B.cols, B)
+    C = ShapingOnlyMatrix(C.rows, C.cols, C)
+    D = ShapingOnlyMatrix(D.rows, D.cols, D)
+
+    assert A.get_diag_blocks() == [a, b, b]
+    assert B.get_diag_blocks() == [a, b, c]
+    assert C.get_diag_blocks() == [a, c, b]
+    assert D.get_diag_blocks() == [c, c, b]
+
+
+def test_shape():
+    m = ShapingOnlyMatrix(1, 2, [0, 0])
+    assert m.shape == (1, 2)
+
+
+def test_reshape():
+    m0 = eye_Shaping(3)
+    assert m0.reshape(1, 9) == Matrix(1, 9, (1, 0, 0, 0, 1, 0, 0, 0, 1))
+    m1 = ShapingOnlyMatrix(3, 4, lambda i, j: i + j)
+    assert m1.reshape(
+        4, 3) == Matrix(((0, 1, 2), (3, 1, 2), (3, 4, 2), (3, 4, 5)))
+    assert m1.reshape(2, 6) == Matrix(((0, 1, 2, 3, 1, 2), (3, 4, 2, 3, 4, 5)))
+
+
+def test_row_col():
+    m = ShapingOnlyMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    assert m.row(0) == Matrix(1, 3, [1, 2, 3])
+    assert m.col(0) == Matrix(3, 1, [1, 4, 7])
+
+
+def test_row_join():
+    assert eye_Shaping(3).row_join(Matrix([7, 7, 7])) == \
+           Matrix([[1, 0, 0, 7],
+                   [0, 1, 0, 7],
+                   [0, 0, 1, 7]])
+
+
+def test_col_join():
+    assert eye_Shaping(3).col_join(Matrix([[7, 7, 7]])) == \
+           Matrix([[1, 0, 0],
+                   [0, 1, 0],
+                   [0, 0, 1],
+                   [7, 7, 7]])
+
+
+def test_row_insert():
+    r4 = Matrix([[4, 4, 4]])
+    for i in range(-4, 5):
+        l = [1, 0, 0]
+        l.insert(i, 4)
+        assert flatten(eye_Shaping(3).row_insert(i, r4).col(0).tolist()) == l
+
+
+def test_col_insert():
+    c4 = Matrix([4, 4, 4])
+    for i in range(-4, 5):
+        l = [0, 0, 0]
+        l.insert(i, 4)
+        assert flatten(zeros_Shaping(3).col_insert(i, c4).row(0).tolist()) == l
+    # issue 13643
+    assert eye_Shaping(6).col_insert(3, Matrix([[2, 2], [2, 2], [2, 2], [2, 2], [2, 2], [2, 2]])) == \
+           Matrix([[1, 0, 0, 2, 2, 0, 0, 0],
+                   [0, 1, 0, 2, 2, 0, 0, 0],
+                   [0, 0, 1, 2, 2, 0, 0, 0],
+                   [0, 0, 0, 2, 2, 1, 0, 0],
+                   [0, 0, 0, 2, 2, 0, 1, 0],
+                   [0, 0, 0, 2, 2, 0, 0, 1]])
+
+
+def test_extract():
+    m = ShapingOnlyMatrix(4, 3, lambda i, j: i*3 + j)
+    assert m.extract([0, 1, 3], [0, 1]) == Matrix(3, 2, [0, 1, 3, 4, 9, 10])
+    assert m.extract([0, 3], [0, 0, 2]) == Matrix(2, 3, [0, 0, 2, 9, 9, 11])
+    assert m.extract(range(4), range(3)) == m
+    raises(IndexError, lambda: m.extract([4], [0]))
+    raises(IndexError, lambda: m.extract([0], [3]))
+
+
+def test_hstack():
+    m = ShapingOnlyMatrix(4, 3, lambda i, j: i*3 + j)
+    m2 = ShapingOnlyMatrix(3, 4, lambda i, j: i*3 + j)
+    assert m == m.hstack(m)
+    assert m.hstack(m, m, m) == ShapingOnlyMatrix.hstack(m, m, m) == Matrix([
+                [0,  1,  2, 0,  1,  2, 0,  1,  2],
+                [3,  4,  5, 3,  4,  5, 3,  4,  5],
+                [6,  7,  8, 6,  7,  8, 6,  7,  8],
+                [9, 10, 11, 9, 10, 11, 9, 10, 11]])
+    raises(ShapeError, lambda: m.hstack(m, m2))
+    assert Matrix.hstack() == Matrix()
+
+    # test regression #12938
+    M1 = Matrix.zeros(0, 0)
+    M2 = Matrix.zeros(0, 1)
+    M3 = Matrix.zeros(0, 2)
+    M4 = Matrix.zeros(0, 3)
+    m = ShapingOnlyMatrix.hstack(M1, M2, M3, M4)
+    assert m.rows == 0 and m.cols == 6
+
+
+def test_vstack():
+    m = ShapingOnlyMatrix(4, 3, lambda i, j: i*3 + j)
+    m2 = ShapingOnlyMatrix(3, 4, lambda i, j: i*3 + j)
+    assert m == m.vstack(m)
+    assert m.vstack(m, m, m) == ShapingOnlyMatrix.vstack(m, m, m) == Matrix([
+                                [0,  1,  2],
+                                [3,  4,  5],
+                                [6,  7,  8],
+                                [9, 10, 11],
+                                [0,  1,  2],
+                                [3,  4,  5],
+                                [6,  7,  8],
+                                [9, 10, 11],
+                                [0,  1,  2],
+                                [3,  4,  5],
+                                [6,  7,  8],
+                                [9, 10, 11]])
+    raises(ShapeError, lambda: m.vstack(m, m2))
+    assert Matrix.vstack() == Matrix()
+
+
+# PropertiesOnlyMatrix tests
+def test_atoms():
+    m = PropertiesOnlyMatrix(2, 2, [1, 2, x, 1 - 1/x])
+    assert m.atoms() == {S.One, S(2), S.NegativeOne, x}
+    assert m.atoms(Symbol) == {x}
+
+
+def test_free_symbols():
+    assert PropertiesOnlyMatrix([[x], [0]]).free_symbols == {x}
+
+
+def test_has():
+    A = PropertiesOnlyMatrix(((x, y), (2, 3)))
+    assert A.has(x)
+    assert not A.has(z)
+    assert A.has(Symbol)
+
+    A = PropertiesOnlyMatrix(((2, y), (2, 3)))
+    assert not A.has(x)
+
+
+def test_is_anti_symmetric():
+    x = symbols('x')
+    assert PropertiesOnlyMatrix(2, 1, [1, 2]).is_anti_symmetric() is False
+    m = PropertiesOnlyMatrix(3, 3, [0, x**2 + 2*x + 1, y, -(x + 1)**2, 0, x*y, -y, -x*y, 0])
+    assert m.is_anti_symmetric() is True
+    assert m.is_anti_symmetric(simplify=False) is False
+    assert m.is_anti_symmetric(simplify=lambda x: x) is False
+
+    m = PropertiesOnlyMatrix(3, 3, [x.expand() for x in m])
+    assert m.is_anti_symmetric(simplify=False) is True
+    m = PropertiesOnlyMatrix(3, 3, [x.expand() for x in [S.One] + list(m)[1:]])
+    assert m.is_anti_symmetric() is False
+
+
+def test_diagonal_symmetrical():
+    m = PropertiesOnlyMatrix(2, 2, [0, 1, 1, 0])
+    assert not m.is_diagonal()
+    assert m.is_symmetric()
+    assert m.is_symmetric(simplify=False)
+
+    m = PropertiesOnlyMatrix(2, 2, [1, 0, 0, 1])
+    assert m.is_diagonal()
+
+    m = PropertiesOnlyMatrix(3, 3, diag(1, 2, 3))
+    assert m.is_diagonal()
+    assert m.is_symmetric()
+
+    m = PropertiesOnlyMatrix(3, 3, [1, 0, 0, 0, 2, 0, 0, 0, 3])
+    assert m == diag(1, 2, 3)
+
+    m = PropertiesOnlyMatrix(2, 3, zeros(2, 3))
+    assert not m.is_symmetric()
+    assert m.is_diagonal()
+
+    m = PropertiesOnlyMatrix(((5, 0), (0, 6), (0, 0)))
+    assert m.is_diagonal()
+
+    m = PropertiesOnlyMatrix(((5, 0, 0), (0, 6, 0)))
+    assert m.is_diagonal()
+
+    m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
+    assert m.is_symmetric()
+    assert not m.is_symmetric(simplify=False)
+    assert m.expand().is_symmetric(simplify=False)
+
+
+def test_is_hermitian():
+    a = PropertiesOnlyMatrix([[1, I], [-I, 1]])
+    assert a.is_hermitian
+    a = PropertiesOnlyMatrix([[2*I, I], [-I, 1]])
+    assert a.is_hermitian is False
+    a = PropertiesOnlyMatrix([[x, I], [-I, 1]])
+    assert a.is_hermitian is None
+    a = PropertiesOnlyMatrix([[x, 1], [-I, 1]])
+    assert a.is_hermitian is False
+
+
+def test_is_Identity():
+    assert eye_Properties(3).is_Identity
+    assert not PropertiesOnlyMatrix(zeros(3)).is_Identity
+    assert not PropertiesOnlyMatrix(ones(3)).is_Identity
+    # issue 6242
+    assert not PropertiesOnlyMatrix([[1, 0, 0]]).is_Identity
+
+
+def test_is_symbolic():
+    a = PropertiesOnlyMatrix([[x, x], [x, x]])
+    assert a.is_symbolic() is True
+    a = PropertiesOnlyMatrix([[1, 2, 3, 4], [5, 6, 7, 8]])
+    assert a.is_symbolic() is False
+    a = PropertiesOnlyMatrix([[1, 2, 3, 4], [5, 6, x, 8]])
+    assert a.is_symbolic() is True
+    a = PropertiesOnlyMatrix([[1, x, 3]])
+    assert a.is_symbolic() is True
+    a = PropertiesOnlyMatrix([[1, 2, 3]])
+    assert a.is_symbolic() is False
+    a = PropertiesOnlyMatrix([[1], [x], [3]])
+    assert a.is_symbolic() is True
+    a = PropertiesOnlyMatrix([[1], [2], [3]])
+    assert a.is_symbolic() is False
+
+
+def test_is_upper():
+    a = PropertiesOnlyMatrix([[1, 2, 3]])
+    assert a.is_upper is True
+    a = PropertiesOnlyMatrix([[1], [2], [3]])
+    assert a.is_upper is False
+
+
+def test_is_lower():
+    a = PropertiesOnlyMatrix([[1, 2, 3]])
+    assert a.is_lower is False
+    a = PropertiesOnlyMatrix([[1], [2], [3]])
+    assert a.is_lower is True
+
+
+def test_is_square():
+    m = PropertiesOnlyMatrix([[1], [1]])
+    m2 = PropertiesOnlyMatrix([[2, 2], [2, 2]])
+    assert not m.is_square
+    assert m2.is_square
+
+
+def test_is_symmetric():
+    m = PropertiesOnlyMatrix(2, 2, [0, 1, 1, 0])
+    assert m.is_symmetric()
+    m = PropertiesOnlyMatrix(2, 2, [0, 1, 0, 1])
+    assert not m.is_symmetric()
+
+
+def test_is_hessenberg():
+    A = PropertiesOnlyMatrix([[3, 4, 1], [2, 4, 5], [0, 1, 2]])
+    assert A.is_upper_hessenberg
+    A = PropertiesOnlyMatrix(3, 3, [3, 2, 0, 4, 4, 1, 1, 5, 2])
+    assert A.is_lower_hessenberg
+    A = PropertiesOnlyMatrix(3, 3, [3, 2, -1, 4, 4, 1, 1, 5, 2])
+    assert A.is_lower_hessenberg is False
+    assert A.is_upper_hessenberg is False
+
+    A = PropertiesOnlyMatrix([[3, 4, 1], [2, 4, 5], [3, 1, 2]])
+    assert not A.is_upper_hessenberg
+
+
+def test_is_zero():
+    assert PropertiesOnlyMatrix(0, 0, []).is_zero_matrix
+    assert PropertiesOnlyMatrix([[0, 0], [0, 0]]).is_zero_matrix
+    assert PropertiesOnlyMatrix(zeros(3, 4)).is_zero_matrix
+    assert not PropertiesOnlyMatrix(eye(3)).is_zero_matrix
+    assert PropertiesOnlyMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert PropertiesOnlyMatrix([[x, 1], [0, 0]]).is_zero_matrix == False
+    a = Symbol('a', nonzero=True)
+    assert PropertiesOnlyMatrix([[a, 0], [0, 0]]).is_zero_matrix == False
+
+
+def test_values():
+    assert set(PropertiesOnlyMatrix(2, 2, [0, 1, 2, 3]
+        ).values()) == {1, 2, 3}
+    x = Symbol('x', real=True)
+    assert set(PropertiesOnlyMatrix(2, 2, [x, 0, 0, 1]
+        ).values()) == {x, 1}
+
+
+# OperationsOnlyMatrix tests
+def test_applyfunc():
+    m0 = OperationsOnlyMatrix(eye(3))
+    assert m0.applyfunc(lambda x: 2*x) == eye(3)*2
+    assert m0.applyfunc(lambda x: 0) == zeros(3)
+    assert m0.applyfunc(lambda x: 1) == ones(3)
+
+
+def test_adjoint():
+    dat = [[0, I], [1, 0]]
+    ans = OperationsOnlyMatrix([[0, 1], [-I, 0]])
+    assert ans.adjoint() == Matrix(dat)
+
+
+def test_as_real_imag():
+    m1 = OperationsOnlyMatrix(2, 2, [1, 2, 3, 4])
+    m3 = OperationsOnlyMatrix(2, 2,
+        [1 + S.ImaginaryUnit, 2 + 2*S.ImaginaryUnit,
+        3 + 3*S.ImaginaryUnit, 4 + 4*S.ImaginaryUnit])
+
+    a, b = m3.as_real_imag()
+    assert a == m1
+    assert b == m1
+
+
+def test_conjugate():
+    M = OperationsOnlyMatrix([[0, I, 5],
+                [1, 2, 0]])
+
+    assert M.T == Matrix([[0, 1],
+                          [I, 2],
+                          [5, 0]])
+
+    assert M.C == Matrix([[0, -I, 5],
+                          [1,  2, 0]])
+    assert M.C == M.conjugate()
+
+    assert M.H == M.T.C
+    assert M.H == Matrix([[ 0, 1],
+                          [-I, 2],
+                          [ 5, 0]])
+
+
+def test_doit():
+    a = OperationsOnlyMatrix([[Add(x, x, evaluate=False)]])
+    assert a[0] != 2*x
+    assert a.doit() == Matrix([[2*x]])
+
+
+def test_evalf():
+    a = OperationsOnlyMatrix(2, 1, [sqrt(5), 6])
+    assert all(a.evalf()[i] == a[i].evalf() for i in range(2))
+    assert all(a.evalf(2)[i] == a[i].evalf(2) for i in range(2))
+    assert all(a.n(2)[i] == a[i].n(2) for i in range(2))
+
+
+def test_expand():
+    m0 = OperationsOnlyMatrix([[x*(x + y), 2], [((x + y)*y)*x, x*(y + x*(x + y))]])
+    # Test if expand() returns a matrix
+    m1 = m0.expand()
+    assert m1 == Matrix(
+        [[x*y + x**2, 2], [x*y**2 + y*x**2, x*y + y*x**2 + x**3]])
+
+    a = Symbol('a', real=True)
+
+    assert OperationsOnlyMatrix(1, 1, [exp(I*a)]).expand(complex=True) == \
+           Matrix([cos(a) + I*sin(a)])
+
+
+def test_refine():
+    m0 = OperationsOnlyMatrix([[Abs(x)**2, sqrt(x**2)],
+                 [sqrt(x**2)*Abs(y)**2, sqrt(y**2)*Abs(x)**2]])
+    m1 = m0.refine(Q.real(x) & Q.real(y))
+    assert m1 == Matrix([[x**2, Abs(x)], [y**2*Abs(x), x**2*Abs(y)]])
+
+    m1 = m0.refine(Q.positive(x) & Q.positive(y))
+    assert m1 == Matrix([[x**2, x], [x*y**2, x**2*y]])
+
+    m1 = m0.refine(Q.negative(x) & Q.negative(y))
+    assert m1 == Matrix([[x**2, -x], [-x*y**2, -x**2*y]])
+
+
+def test_replace():
+    F, G = symbols('F, G', cls=Function)
+    K = OperationsOnlyMatrix(2, 2, lambda i, j: G(i+j))
+    M = OperationsOnlyMatrix(2, 2, lambda i, j: F(i+j))
+    N = M.replace(F, G)
+    assert N == K
+
+
+def test_replace_map():
+    F, G = symbols('F, G', cls=Function)
+    K = OperationsOnlyMatrix(2, 2, [(G(0), {F(0): G(0)}), (G(1), {F(1): G(1)}), (G(1), {F(1) \
+                                                                              : G(1)}), (G(2), {F(2): G(2)})])
+    M = OperationsOnlyMatrix(2, 2, lambda i, j: F(i+j))
+    N = M.replace(F, G, True)
+    assert N == K
+
+
+def test_rot90():
+    A = Matrix([[1, 2], [3, 4]])
+    assert A == A.rot90(0) == A.rot90(4)
+    assert A.rot90(2) == A.rot90(-2) == A.rot90(6) == Matrix(((4, 3), (2, 1)))
+    assert A.rot90(3) == A.rot90(-1) == A.rot90(7) == Matrix(((2, 4), (1, 3)))
+    assert A.rot90() == A.rot90(-7) == A.rot90(-3) == Matrix(((3, 1), (4, 2)))
+
+def test_simplify():
+    n = Symbol('n')
+    f = Function('f')
+
+    M = OperationsOnlyMatrix([[            1/x + 1/y,                 (x + x*y) / x  ],
+                [ (f(x) + y*f(x))/f(x), 2 * (1/n - cos(n * pi)/n) / pi ]])
+    assert M.simplify() == Matrix([[ (x + y)/(x * y),                        1 + y ],
+                        [           1 + y, 2*((1 - 1*cos(pi*n))/(pi*n)) ]])
+    eq = (1 + x)**2
+    M = OperationsOnlyMatrix([[eq]])
+    assert M.simplify() == Matrix([[eq]])
+    assert M.simplify(ratio=oo) == Matrix([[eq.simplify(ratio=oo)]])
+
+    # https://github.com/sympy/sympy/issues/19353
+    m = Matrix([[30, 2], [3, 4]])
+    assert (1/(m.trace())).simplify() == Rational(1, 34)
+
+
+def test_subs():
+    assert OperationsOnlyMatrix([[1, x], [x, 4]]).subs(x, 5) == Matrix([[1, 5], [5, 4]])
+    assert OperationsOnlyMatrix([[x, 2], [x + y, 4]]).subs([[x, -1], [y, -2]]) == \
+           Matrix([[-1, 2], [-3, 4]])
+    assert OperationsOnlyMatrix([[x, 2], [x + y, 4]]).subs([(x, -1), (y, -2)]) == \
+           Matrix([[-1, 2], [-3, 4]])
+    assert OperationsOnlyMatrix([[x, 2], [x + y, 4]]).subs({x: -1, y: -2}) == \
+           Matrix([[-1, 2], [-3, 4]])
+    assert OperationsOnlyMatrix([[x*y]]).subs({x: y - 1, y: x - 1}, simultaneous=True) == \
+           Matrix([[(x - 1)*(y - 1)]])
+
+
+def test_trace():
+    M = OperationsOnlyMatrix([[1, 0, 0],
+                [0, 5, 0],
+                [0, 0, 8]])
+    assert M.trace() == 14
+
+
+def test_xreplace():
+    assert OperationsOnlyMatrix([[1, x], [x, 4]]).xreplace({x: 5}) == \
+           Matrix([[1, 5], [5, 4]])
+    assert OperationsOnlyMatrix([[x, 2], [x + y, 4]]).xreplace({x: -1, y: -2}) == \
+           Matrix([[-1, 2], [-3, 4]])
+
+
+def test_permute():
+    a = OperationsOnlyMatrix(3, 4, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
+
+    raises(IndexError, lambda: a.permute([[0, 5]]))
+    raises(ValueError, lambda: a.permute(Symbol('x')))
+    b = a.permute_rows([[0, 2], [0, 1]])
+    assert a.permute([[0, 2], [0, 1]]) == b == Matrix([
+                                            [5,  6,  7,  8],
+                                            [9, 10, 11, 12],
+                                            [1,  2,  3,  4]])
+
+    b = a.permute_cols([[0, 2], [0, 1]])
+    assert a.permute([[0, 2], [0, 1]], orientation='cols') == b ==\
+                            Matrix([
+                            [ 2,  3, 1,  4],
+                            [ 6,  7, 5,  8],
+                            [10, 11, 9, 12]])
+
+    b = a.permute_cols([[0, 2], [0, 1]], direction='backward')
+    assert a.permute([[0, 2], [0, 1]], orientation='cols', direction='backward') == b ==\
+                            Matrix([
+                            [ 3, 1,  2,  4],
+                            [ 7, 5,  6,  8],
+                            [11, 9, 10, 12]])
+
+    assert a.permute([1, 2, 0, 3]) == Matrix([
+                                            [5,  6,  7,  8],
+                                            [9, 10, 11, 12],
+                                            [1,  2,  3,  4]])
+
+    from sympy.combinatorics import Permutation
+    assert a.permute(Permutation([1, 2, 0, 3])) == Matrix([
+                                            [5,  6,  7,  8],
+                                            [9, 10, 11, 12],
+                                            [1,  2,  3,  4]])
+
+def test_upper_triangular():
+
+    A = OperationsOnlyMatrix([
+                [1, 1, 1, 1],
+                [1, 1, 1, 1],
+                [1, 1, 1, 1],
+                [1, 1, 1, 1]
+            ])
+
+    R = A.upper_triangular(2)
+    assert R == OperationsOnlyMatrix([
+                        [0, 0, 1, 1],
+                        [0, 0, 0, 1],
+                        [0, 0, 0, 0],
+                        [0, 0, 0, 0]
+                    ])
+
+    R = A.upper_triangular(-2)
+    assert R == OperationsOnlyMatrix([
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [0, 1, 1, 1]
+                    ])
+
+    R = A.upper_triangular()
+    assert R == OperationsOnlyMatrix([
+                        [1, 1, 1, 1],
+                        [0, 1, 1, 1],
+                        [0, 0, 1, 1],
+                        [0, 0, 0, 1]
+                    ])
+
+def test_lower_triangular():
+    A = OperationsOnlyMatrix([
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1]
+                    ])
+
+    L = A.lower_triangular()
+    assert L == ArithmeticOnlyMatrix([
+                        [1, 0, 0, 0],
+                        [1, 1, 0, 0],
+                        [1, 1, 1, 0],
+                        [1, 1, 1, 1]])
+
+    L = A.lower_triangular(2)
+    assert L == ArithmeticOnlyMatrix([
+                        [1, 1, 1, 0],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1]
+                    ])
+
+    L = A.lower_triangular(-2)
+    assert L == ArithmeticOnlyMatrix([
+                        [0, 0, 0, 0],
+                        [0, 0, 0, 0],
+                        [1, 0, 0, 0],
+                        [1, 1, 0, 0]
+                    ])
+
+
+# ArithmeticOnlyMatrix tests
+def test_abs():
+    m = ArithmeticOnlyMatrix([[1, -2], [x, y]])
+    assert abs(m) == ArithmeticOnlyMatrix([[1, 2], [Abs(x), Abs(y)]])
+
+
+def test_add():
+    m = ArithmeticOnlyMatrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
+    assert m + m == ArithmeticOnlyMatrix([[2, 4, 6], [2*x, 2*y, 2*x], [4*y, -100, 2*z*x]])
+    n = ArithmeticOnlyMatrix(1, 2, [1, 2])
+    raises(ShapeError, lambda: m + n)
+
+
+def test_multiplication():
+    a = ArithmeticOnlyMatrix((
+        (1, 2),
+        (3, 1),
+        (0, 6),
+    ))
+
+    b = ArithmeticOnlyMatrix((
+        (1, 2),
+        (3, 0),
+    ))
+
+    raises(ShapeError, lambda: b*a)
+    raises(TypeError, lambda: a*{})
+
+    c = a*b
+    assert c[0, 0] == 7
+    assert c[0, 1] == 2
+    assert c[1, 0] == 6
+    assert c[1, 1] == 6
+    assert c[2, 0] == 18
+    assert c[2, 1] == 0
+
+    try:
+        eval('c = a @ b')
+    except SyntaxError:
+        pass
+    else:
+        assert c[0, 0] == 7
+        assert c[0, 1] == 2
+        assert c[1, 0] == 6
+        assert c[1, 1] == 6
+        assert c[2, 0] == 18
+        assert c[2, 1] == 0
+
+    h = a.multiply_elementwise(c)
+    assert h == matrix_multiply_elementwise(a, c)
+    assert h[0, 0] == 7
+    assert h[0, 1] == 4
+    assert h[1, 0] == 18
+    assert h[1, 1] == 6
+    assert h[2, 0] == 0
+    assert h[2, 1] == 0
+    raises(ShapeError, lambda: a.multiply_elementwise(b))
+
+    c = b * Symbol("x")
+    assert isinstance(c, ArithmeticOnlyMatrix)
+    assert c[0, 0] == x
+    assert c[0, 1] == 2*x
+    assert c[1, 0] == 3*x
+    assert c[1, 1] == 0
+
+    c2 = x * b
+    assert c == c2
+
+    c = 5 * b
+    assert isinstance(c, ArithmeticOnlyMatrix)
+    assert c[0, 0] == 5
+    assert c[0, 1] == 2*5
+    assert c[1, 0] == 3*5
+    assert c[1, 1] == 0
+
+    try:
+        eval('c = 5 @ b')
+    except SyntaxError:
+        pass
+    else:
+        assert isinstance(c, ArithmeticOnlyMatrix)
+        assert c[0, 0] == 5
+        assert c[0, 1] == 2*5
+        assert c[1, 0] == 3*5
+        assert c[1, 1] == 0
+
+    # https://github.com/sympy/sympy/issues/22353
+    A = Matrix(ones(3, 1))
+    _h = -Rational(1, 2)
+    B = Matrix([_h, _h, _h])
+    assert A.multiply_elementwise(B) == Matrix([
+        [_h],
+        [_h],
+        [_h]])
+
+
+def test_matmul():
+    a = Matrix([[1, 2], [3, 4]])
+
+    assert a.__matmul__(2) == NotImplemented
+
+    assert a.__rmatmul__(2) == NotImplemented
+
+    #This is done this way because @ is only supported in Python 3.5+
+    #To check 2@a case
+    try:
+        eval('2 @ a')
+    except SyntaxError:
+        pass
+    except TypeError:  #TypeError is raised in case of NotImplemented is returned
+        pass
+
+    #Check a@2 case
+    try:
+        eval('a @ 2')
+    except SyntaxError:
+        pass
+    except TypeError:  #TypeError is raised in case of NotImplemented is returned
+        pass
+
+
+def test_non_matmul():
+    """
+    Test that if explicitly specified as non-matrix, mul reverts
+    to scalar multiplication.
+    """
+    class foo(Expr):
+        is_Matrix=False
+        is_MatrixLike=False
+        shape = (1, 1)
+
+    A = Matrix([[1, 2], [3, 4]])
+    b = foo()
+    assert b*A == Matrix([[b, 2*b], [3*b, 4*b]])
+    assert A*b == Matrix([[b, 2*b], [3*b, 4*b]])
+
+
+def test_power():
+    raises(NonSquareMatrixError, lambda: Matrix((1, 2))**2)
+
+    A = ArithmeticOnlyMatrix([[2, 3], [4, 5]])
+    assert (A**5)[:] == (6140, 8097, 10796, 14237)
+    A = ArithmeticOnlyMatrix([[2, 1, 3], [4, 2, 4], [6, 12, 1]])
+    assert (A**3)[:] == (290, 262, 251, 448, 440, 368, 702, 954, 433)
+    assert A**0 == eye(3)
+    assert A**1 == A
+    assert (ArithmeticOnlyMatrix([[2]]) ** 100)[0, 0] == 2**100
+    assert ArithmeticOnlyMatrix([[1, 2], [3, 4]])**Integer(2) == ArithmeticOnlyMatrix([[7, 10], [15, 22]])
+    A = Matrix([[1,2],[4,5]])
+    assert A.pow(20, method='cayley') == A.pow(20, method='multiply')
+
+def test_neg():
+    n = ArithmeticOnlyMatrix(1, 2, [1, 2])
+    assert -n == ArithmeticOnlyMatrix(1, 2, [-1, -2])
+
+
+def test_sub():
+    n = ArithmeticOnlyMatrix(1, 2, [1, 2])
+    assert n - n == ArithmeticOnlyMatrix(1, 2, [0, 0])
+
+
+def test_div():
+    n = ArithmeticOnlyMatrix(1, 2, [1, 2])
+    assert n/2 == ArithmeticOnlyMatrix(1, 2, [S.Half, S(2)/2])
+
+# SpecialOnlyMatrix tests
+def test_eye():
+    assert list(SpecialOnlyMatrix.eye(2, 2)) == [1, 0, 0, 1]
+    assert list(SpecialOnlyMatrix.eye(2)) == [1, 0, 0, 1]
+    assert type(SpecialOnlyMatrix.eye(2)) == SpecialOnlyMatrix
+    assert type(SpecialOnlyMatrix.eye(2, cls=Matrix)) == Matrix
+
+
+def test_ones():
+    assert list(SpecialOnlyMatrix.ones(2, 2)) == [1, 1, 1, 1]
+    assert list(SpecialOnlyMatrix.ones(2)) == [1, 1, 1, 1]
+    assert SpecialOnlyMatrix.ones(2, 3) == Matrix([[1, 1, 1], [1, 1, 1]])
+    assert type(SpecialOnlyMatrix.ones(2)) == SpecialOnlyMatrix
+    assert type(SpecialOnlyMatrix.ones(2, cls=Matrix)) == Matrix
+
+
+def test_zeros():
+    assert list(SpecialOnlyMatrix.zeros(2, 2)) == [0, 0, 0, 0]
+    assert list(SpecialOnlyMatrix.zeros(2)) == [0, 0, 0, 0]
+    assert SpecialOnlyMatrix.zeros(2, 3) == Matrix([[0, 0, 0], [0, 0, 0]])
+    assert type(SpecialOnlyMatrix.zeros(2)) == SpecialOnlyMatrix
+    assert type(SpecialOnlyMatrix.zeros(2, cls=Matrix)) == Matrix
+
+
+def test_diag_make():
+    diag = SpecialOnlyMatrix.diag
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    assert diag(a, b, b) == Matrix([
+        [1, 2, 0, 0, 0, 0],
+        [2, 3, 0, 0, 0, 0],
+        [0, 0, 3, x, 0, 0],
+        [0, 0, y, 3, 0, 0],
+        [0, 0, 0, 0, 3, x],
+        [0, 0, 0, 0, y, 3],
+    ])
+    assert diag(a, b, c) == Matrix([
+        [1, 2, 0, 0, 0, 0, 0],
+        [2, 3, 0, 0, 0, 0, 0],
+        [0, 0, 3, x, 0, 0, 0],
+        [0, 0, y, 3, 0, 0, 0],
+        [0, 0, 0, 0, 3, x, 3],
+        [0, 0, 0, 0, y, 3, z],
+        [0, 0, 0, 0, x, y, z],
+    ])
+    assert diag(a, c, b) == Matrix([
+        [1, 2, 0, 0, 0, 0, 0],
+        [2, 3, 0, 0, 0, 0, 0],
+        [0, 0, 3, x, 3, 0, 0],
+        [0, 0, y, 3, z, 0, 0],
+        [0, 0, x, y, z, 0, 0],
+        [0, 0, 0, 0, 0, 3, x],
+        [0, 0, 0, 0, 0, y, 3],
+    ])
+    a = Matrix([x, y, z])
+    b = Matrix([[1, 2], [3, 4]])
+    c = Matrix([[5, 6]])
+    # this "wandering diagonal" is what makes this
+    # a block diagonal where each block is independent
+    # of the others
+    assert diag(a, 7, b, c) == Matrix([
+        [x, 0, 0, 0, 0, 0],
+        [y, 0, 0, 0, 0, 0],
+        [z, 0, 0, 0, 0, 0],
+        [0, 7, 0, 0, 0, 0],
+        [0, 0, 1, 2, 0, 0],
+        [0, 0, 3, 4, 0, 0],
+        [0, 0, 0, 0, 5, 6]])
+    raises(ValueError, lambda: diag(a, 7, b, c, rows=5))
+    assert diag(1) == Matrix([[1]])
+    assert diag(1, rows=2) == Matrix([[1, 0], [0, 0]])
+    assert diag(1, cols=2) == Matrix([[1, 0], [0, 0]])
+    assert diag(1, rows=3, cols=2) == Matrix([[1, 0], [0, 0], [0, 0]])
+    assert diag(*[2, 3]) == Matrix([
+        [2, 0],
+        [0, 3]])
+    assert diag(Matrix([2, 3])) == Matrix([
+        [2],
+        [3]])
+    assert diag([1, [2, 3], 4], unpack=False) == \
+            diag([[1], [2, 3], [4]], unpack=False) == Matrix([
+        [1, 0],
+        [2, 3],
+        [4, 0]])
+    assert type(diag(1)) == SpecialOnlyMatrix
+    assert type(diag(1, cls=Matrix)) == Matrix
+    assert Matrix.diag([1, 2, 3]) == Matrix.diag(1, 2, 3)
+    assert Matrix.diag([1, 2, 3], unpack=False).shape == (3, 1)
+    assert Matrix.diag([[1, 2, 3]]).shape == (3, 1)
+    assert Matrix.diag([[1, 2, 3]], unpack=False).shape == (1, 3)
+    assert Matrix.diag([[[1, 2, 3]]]).shape == (1, 3)
+    # kerning can be used to move the starting point
+    assert Matrix.diag(ones(0, 2), 1, 2) == Matrix([
+        [0, 0, 1, 0],
+        [0, 0, 0, 2]])
+    assert Matrix.diag(ones(2, 0), 1, 2) == Matrix([
+        [0, 0],
+        [0, 0],
+        [1, 0],
+        [0, 2]])
+
+
+def test_diagonal():
+    m = Matrix(3, 3, range(9))
+    d = m.diagonal()
+    assert d == m.diagonal(0)
+    assert tuple(d) == (0, 4, 8)
+    assert tuple(m.diagonal(1)) == (1, 5)
+    assert tuple(m.diagonal(-1)) == (3, 7)
+    assert tuple(m.diagonal(2)) == (2,)
+    assert type(m.diagonal()) == type(m)
+    s = SparseMatrix(3, 3, {(1, 1): 1})
+    assert type(s.diagonal()) == type(s)
+    assert type(m) != type(s)
+    raises(ValueError, lambda: m.diagonal(3))
+    raises(ValueError, lambda: m.diagonal(-3))
+    raises(ValueError, lambda: m.diagonal(pi))
+    M = ones(2, 3)
+    assert banded({i: list(M.diagonal(i))
+        for i in range(1-M.rows, M.cols)}) == M
+
+
+def test_jordan_block():
+    assert SpecialOnlyMatrix.jordan_block(3, 2) == SpecialOnlyMatrix.jordan_block(3, eigenvalue=2) \
+            == SpecialOnlyMatrix.jordan_block(size=3, eigenvalue=2) \
+            == SpecialOnlyMatrix.jordan_block(3, 2, band='upper') \
+            == SpecialOnlyMatrix.jordan_block(
+                size=3, eigenval=2, eigenvalue=2) \
+            == Matrix([
+                [2, 1, 0],
+                [0, 2, 1],
+                [0, 0, 2]])
+
+    assert SpecialOnlyMatrix.jordan_block(3, 2, band='lower') == Matrix([
+                    [2, 0, 0],
+                    [1, 2, 0],
+                    [0, 1, 2]])
+    # missing eigenvalue
+    raises(ValueError, lambda: SpecialOnlyMatrix.jordan_block(2))
+    # non-integral size
+    raises(ValueError, lambda: SpecialOnlyMatrix.jordan_block(3.5, 2))
+    # size not specified
+    raises(ValueError, lambda: SpecialOnlyMatrix.jordan_block(eigenvalue=2))
+    # inconsistent eigenvalue
+    raises(ValueError,
+    lambda: SpecialOnlyMatrix.jordan_block(
+        eigenvalue=2, eigenval=4))
+
+    # Using alias keyword
+    assert SpecialOnlyMatrix.jordan_block(size=3, eigenvalue=2) == \
+        SpecialOnlyMatrix.jordan_block(size=3, eigenval=2)
+
+
+def test_orthogonalize():
+    m = Matrix([[1, 2], [3, 4]])
+    assert m.orthogonalize(Matrix([[2], [1]])) == [Matrix([[2], [1]])]
+    assert m.orthogonalize(Matrix([[2], [1]]), normalize=True) == \
+        [Matrix([[2*sqrt(5)/5], [sqrt(5)/5]])]
+    assert m.orthogonalize(Matrix([[1], [2]]), Matrix([[-1], [4]])) == \
+        [Matrix([[1], [2]]), Matrix([[Rational(-12, 5)], [Rational(6, 5)]])]
+    assert m.orthogonalize(Matrix([[0], [0]]), Matrix([[-1], [4]])) == \
+        [Matrix([[-1], [4]])]
+    assert m.orthogonalize(Matrix([[0], [0]])) == []
+
+    n = Matrix([[9, 1, 9], [3, 6, 10], [8, 5, 2]])
+    vecs = [Matrix([[-5], [1]]), Matrix([[-5], [2]]), Matrix([[-5], [-2]])]
+    assert n.orthogonalize(*vecs) == \
+        [Matrix([[-5], [1]]), Matrix([[Rational(5, 26)], [Rational(25, 26)]])]
+
+    vecs = [Matrix([0, 0, 0]), Matrix([1, 2, 3]), Matrix([1, 4, 5])]
+    raises(ValueError, lambda: Matrix.orthogonalize(*vecs, rankcheck=True))
+
+    vecs = [Matrix([1, 2, 3]), Matrix([4, 5, 6]), Matrix([7, 8, 9])]
+    raises(ValueError, lambda: Matrix.orthogonalize(*vecs, rankcheck=True))
+
+def test_wilkinson():
+
+    wminus, wplus = Matrix.wilkinson(1)
+    assert wminus == Matrix([
+                                [-1, 1, 0],
+                                [1, 0, 1],
+                                [0, 1, 1]])
+    assert wplus == Matrix([
+                            [1, 1, 0],
+                            [1, 0, 1],
+                            [0, 1, 1]])
+
+    wminus, wplus = Matrix.wilkinson(3)
+    assert wminus == Matrix([
+                                [-3,  1,  0, 0, 0, 0, 0],
+                                [1, -2,  1, 0, 0, 0, 0],
+                                [0,  1, -1, 1, 0, 0, 0],
+                                [0,  0,  1, 0, 1, 0, 0],
+                                [0,  0,  0, 1, 1, 1, 0],
+                                [0,  0,  0, 0, 1, 2, 1],
+
+      [0,  0,  0, 0, 0, 1, 3]])
+
+    assert wplus == Matrix([
+                            [3, 1, 0, 0, 0, 0, 0],
+                            [1, 2, 1, 0, 0, 0, 0],
+                            [0, 1, 1, 1, 0, 0, 0],
+                            [0, 0, 1, 0, 1, 0, 0],
+                            [0, 0, 0, 1, 1, 1, 0],
+                            [0, 0, 0, 0, 1, 2, 1],
+                            [0, 0, 0, 0, 0, 1, 3]])
+
+
+# CalculusOnlyMatrix tests
+@XFAIL
+def test_diff():
+    x, y = symbols('x y')
+    m = CalculusOnlyMatrix(2, 1, [x, y])
+    # TODO: currently not working as ``_MinimalMatrix`` cannot be sympified:
+    assert m.diff(x) == Matrix(2, 1, [1, 0])
+
+
+def test_integrate():
+    x, y = symbols('x y')
+    m = CalculusOnlyMatrix(2, 1, [x, y])
+    assert m.integrate(x) == Matrix(2, 1, [x**2/2, y*x])
+
+
+def test_jacobian2():
+    rho, phi = symbols("rho,phi")
+    X = CalculusOnlyMatrix(3, 1, [rho*cos(phi), rho*sin(phi), rho**2])
+    Y = CalculusOnlyMatrix(2, 1, [rho, phi])
+    J = Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)],
+        [   2*rho,             0],
+    ])
+    assert X.jacobian(Y) == J
+
+    m = CalculusOnlyMatrix(2, 2, [1, 2, 3, 4])
+    m2 = CalculusOnlyMatrix(4, 1, [1, 2, 3, 4])
+    raises(TypeError, lambda: m.jacobian(Matrix([1, 2])))
+    raises(TypeError, lambda: m2.jacobian(m))
+
+
+def test_limit():
+    x, y = symbols('x y')
+    m = CalculusOnlyMatrix(2, 1, [1/x, y])
+    assert m.limit(x, 5) == Matrix(2, 1, [Rational(1, 5), y])
+
+
+def test_issue_13774():
+    M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    v = [1, 1, 1]
+    raises(TypeError, lambda: M*v)
+    raises(TypeError, lambda: v*M)
+
+def test_companion():
+    x = Symbol('x')
+    y = Symbol('y')
+    raises(ValueError, lambda: Matrix.companion(1))
+    raises(ValueError, lambda: Matrix.companion(Poly([1], x)))
+    raises(ValueError, lambda: Matrix.companion(Poly([2, 1], x)))
+    raises(ValueError, lambda: Matrix.companion(Poly(x*y, [x, y])))
+
+    c0, c1, c2 = symbols('c0:3')
+    assert Matrix.companion(Poly([1, c0], x)) == Matrix([-c0])
+    assert Matrix.companion(Poly([1, c1, c0], x)) == \
+        Matrix([[0, -c0], [1, -c1]])
+    assert Matrix.companion(Poly([1, c2, c1, c0], x)) == \
+        Matrix([[0, 0, -c0], [1, 0, -c1], [0, 1, -c2]])
+
+def test_issue_10589():
+    x, y, z = symbols("x, y z")
+    M1 = Matrix([x, y, z])
+    M1 = M1.subs(zip([x, y, z], [1, 2, 3]))
+    assert M1 == Matrix([[1], [2], [3]])
+
+    M2 = Matrix([[x, x, x, x, x], [x, x, x, x, x], [x, x, x, x, x]])
+    M2 = M2.subs(zip([x], [1]))
+    assert M2 == Matrix([[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]])
+
+def test_rmul_pr19860():
+    class Foo(ImmutableDenseMatrix):
+        _op_priority = MutableDenseMatrix._op_priority + 0.01
+
+    a = Matrix(2, 2, [1, 2, 3, 4])
+    b = Foo(2, 2, [1, 2, 3, 4])
+
+    # This would throw a RecursionError: maximum recursion depth
+    # since b always has higher priority even after a.as_mutable()
+    c = a*b
+
+    assert isinstance(c, Foo)
+    assert c == Matrix([[7, 10], [15, 22]])
+
+
+def test_issue_18956():
+    A = Array([[1, 2], [3, 4]])
+    B = Matrix([[1,2],[3,4]])
+    raises(TypeError, lambda: B + A)
+    raises(TypeError, lambda: A + B)
+
+
+def test__eq__():
+    class My(object):
+        def __iter__(self):
+            yield 1
+            yield 2
+            return
+        def __getitem__(self, i):
+            return list(self)[i]
+    a = Matrix(2, 1, [1, 2])
+    assert a != My()
+    class My_sympy(My):
+        def _sympy_(self):
+            return Matrix(self)
+    assert a == My_sympy()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_decompositions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_decompositions.py
new file mode 100644
index 0000000000000000000000000000000000000000..d169ec3a8846fed786981e62d932fd860b6d4951
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_decompositions.py
@@ -0,0 +1,474 @@
+from sympy.core.function import expand_mul
+from sympy.core.numbers import I, Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.complexes import Abs
+from sympy.simplify.simplify import simplify
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices import Matrix, zeros, eye, SparseMatrix
+from sympy.abc import x, y, z
+from sympy.testing.pytest import raises, slow
+from sympy.testing.matrices import allclose
+
+
+def test_LUdecomp():
+    testmat = Matrix([[0, 2, 5, 3],
+                      [3, 3, 7, 4],
+                      [8, 4, 0, 2],
+                      [-2, 6, 3, 4]])
+    L, U, p = testmat.LUdecomposition()
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - testmat == zeros(4)
+
+    testmat = Matrix([[6, -2, 7, 4],
+                      [0, 3, 6, 7],
+                      [1, -2, 7, 4],
+                      [-9, 2, 6, 3]])
+    L, U, p = testmat.LUdecomposition()
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - testmat == zeros(4)
+
+    # non-square
+    testmat = Matrix([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9],
+                      [10, 11, 12]])
+    L, U, p = testmat.LUdecomposition(rankcheck=False)
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - testmat == zeros(4, 3)
+
+    # square and singular
+    testmat = Matrix([[1, 2, 3],
+                      [2, 4, 6],
+                      [4, 5, 6]])
+    L, U, p = testmat.LUdecomposition(rankcheck=False)
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - testmat == zeros(3)
+
+    M = Matrix(((1, x, 1), (2, y, 0), (y, 0, z)))
+    L, U, p = M.LUdecomposition()
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - M == zeros(3)
+
+    mL = Matrix((
+        (1, 0, 0),
+        (2, 3, 0),
+    ))
+    assert mL.is_lower is True
+    assert mL.is_upper is False
+    mU = Matrix((
+        (1, 2, 3),
+        (0, 4, 5),
+    ))
+    assert mU.is_lower is False
+    assert mU.is_upper is True
+
+    # test FF LUdecomp
+    M = Matrix([[1, 3, 3],
+                [3, 2, 6],
+                [3, 2, 2]])
+    P, L, Dee, U = M.LUdecompositionFF()
+    assert P*M == L*Dee.inv()*U
+
+    M = Matrix([[1,  2, 3,  4],
+                [3, -1, 2,  3],
+                [3,  1, 3, -2],
+                [6, -1, 0,  2]])
+    P, L, Dee, U = M.LUdecompositionFF()
+    assert P*M == L*Dee.inv()*U
+
+    M = Matrix([[0, 0, 1],
+                [2, 3, 0],
+                [3, 1, 4]])
+    P, L, Dee, U = M.LUdecompositionFF()
+    assert P*M == L*Dee.inv()*U
+
+    # issue 15794
+    M = Matrix(
+        [[1, 2, 3],
+        [4, 5, 6],
+        [7, 8, 9]]
+    )
+    raises(ValueError, lambda : M.LUdecomposition_Simple(rankcheck=True))
+
+def test_singular_value_decompositionD():
+    A = Matrix([[1, 2], [2, 1]])
+    U, S, V = A.singular_value_decomposition()
+    assert U * S * V.T == A
+    assert U.T * U == eye(U.cols)
+    assert V.T * V == eye(V.cols)
+
+    B = Matrix([[1, 2]])
+    U, S, V = B.singular_value_decomposition()
+
+    assert U * S * V.T == B
+    assert U.T * U == eye(U.cols)
+    assert V.T * V == eye(V.cols)
+
+    C = Matrix([
+        [1, 0, 0, 0, 2],
+        [0, 0, 3, 0, 0],
+        [0, 0, 0, 0, 0],
+        [0, 2, 0, 0, 0],
+    ])
+
+    U, S, V = C.singular_value_decomposition()
+
+    assert U * S * V.T == C
+    assert U.T * U == eye(U.cols)
+    assert V.T * V == eye(V.cols)
+
+    D = Matrix([[Rational(1, 3), sqrt(2)], [0, Rational(1, 4)]])
+    U, S, V = D.singular_value_decomposition()
+    assert simplify(U.T * U) == eye(U.cols)
+    assert simplify(V.T * V) == eye(V.cols)
+    assert simplify(U * S * V.T) == D
+
+
+def test_QR():
+    A = Matrix([[1, 2], [2, 3]])
+    Q, S = A.QRdecomposition()
+    R = Rational
+    assert Q == Matrix([
+        [  5**R(-1, 2),  (R(2)/5)*(R(1)/5)**R(-1, 2)],
+        [2*5**R(-1, 2), (-R(1)/5)*(R(1)/5)**R(-1, 2)]])
+    assert S == Matrix([[5**R(1, 2), 8*5**R(-1, 2)], [0, (R(1)/5)**R(1, 2)]])
+    assert Q*S == A
+    assert Q.T * Q == eye(2)
+
+    A = Matrix([[1, 1, 1], [1, 1, 3], [2, 3, 4]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[12, 0, -51], [6, 0, 167], [-4, 0, 24]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    x = Symbol('x')
+    A = Matrix([x])
+    Q, R = A.QRdecomposition()
+    assert Q == Matrix([x / Abs(x)])
+    assert R == Matrix([Abs(x)])
+
+    A = Matrix([[x, 0], [0, x]])
+    Q, R = A.QRdecomposition()
+    assert Q == x / Abs(x) * Matrix([[1, 0], [0, 1]])
+    assert R == Abs(x) * Matrix([[1, 0], [0, 1]])
+
+
+def test_QR_non_square():
+    # Narrow (cols < rows) matrices
+    A = Matrix([[9, 0, 26], [12, 0, -7], [0, 4, 4], [0, -3, -3]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[1, -1, 4], [1, 4, -2], [1, 4, 2], [1, -1, 0]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix(2, 1, [1, 2])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    # Wide (cols > rows) matrices
+    A = Matrix([[1, 2, 3], [4, 5, 6]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[1, 2, 3, 4], [1, 4, 9, 16], [1, 8, 27, 64]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix(1, 2, [1, 2])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+def test_QR_trivial():
+    # Rank deficient matrices
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    # Zero rank matrices
+    A = Matrix([[0, 0, 0]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[0, 0, 0]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[0, 0, 0], [0, 0, 0]])
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[0, 0, 0], [0, 0, 0]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    # Rank deficient matrices with zero norm from beginning columns
+    A = Matrix([[0, 0, 0], [1, 2, 3]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[0, 0, 0, 0], [1, 2, 3, 4], [0, 0, 0, 0]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[0, 0, 0, 0], [1, 2, 3, 4], [0, 0, 0, 0], [2, 4, 6, 8]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+    A = Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 2, 3]]).T
+    Q, R = A.QRdecomposition()
+    assert Q.T * Q == eye(Q.cols)
+    assert R.is_upper
+    assert A == Q*R
+
+
+def test_QR_float():
+    A = Matrix([[1, 1], [1, 1.01]])
+    Q, R = A.QRdecomposition()
+    assert allclose(Q * R, A)
+    assert allclose(Q * Q.T, Matrix.eye(2))
+    assert allclose(Q.T * Q, Matrix.eye(2))
+
+    A = Matrix([[1, 1], [1, 1.001]])
+    Q, R = A.QRdecomposition()
+    assert allclose(Q * R, A)
+    assert allclose(Q * Q.T, Matrix.eye(2))
+    assert allclose(Q.T * Q, Matrix.eye(2))
+
+
+def test_LUdecomposition_Simple_iszerofunc():
+    # Test if callable passed to matrices.LUdecomposition_Simple() as iszerofunc keyword argument is used inside
+    # matrices.LUdecomposition_Simple()
+    magic_string = "I got passed in!"
+    def goofyiszero(value):
+        raise ValueError(magic_string)
+
+    try:
+        lu, p = Matrix([[1, 0], [0, 1]]).LUdecomposition_Simple(iszerofunc=goofyiszero)
+    except ValueError as err:
+        assert magic_string == err.args[0]
+        return
+
+    assert False
+
+def test_LUdecomposition_iszerofunc():
+    # Test if callable passed to matrices.LUdecomposition() as iszerofunc keyword argument is used inside
+    # matrices.LUdecomposition_Simple()
+    magic_string = "I got passed in!"
+    def goofyiszero(value):
+        raise ValueError(magic_string)
+
+    try:
+        l, u, p = Matrix([[1, 0], [0, 1]]).LUdecomposition(iszerofunc=goofyiszero)
+    except ValueError as err:
+        assert magic_string == err.args[0]
+        return
+
+    assert False
+
+def test_LDLdecomposition():
+    raises(NonSquareMatrixError, lambda: Matrix((1, 2)).LDLdecomposition())
+    raises(ValueError, lambda: Matrix(((1, 2), (3, 4))).LDLdecomposition())
+    raises(ValueError, lambda: Matrix(((5 + I, 0), (0, 1))).LDLdecomposition())
+    raises(ValueError, lambda: Matrix(((1, 5), (5, 1))).LDLdecomposition())
+    raises(ValueError, lambda: Matrix(((1, 2), (3, 4))).LDLdecomposition(hermitian=False))
+    A = Matrix(((1, 5), (5, 1)))
+    L, D = A.LDLdecomposition(hermitian=False)
+    assert L * D * L.T == A
+    A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L, D = A.LDLdecomposition()
+    assert L * D * L.T == A
+    assert L.is_lower
+    assert L == Matrix([[1, 0, 0], [ Rational(3, 5), 1, 0], [Rational(-1, 5), Rational(1, 3), 1]])
+    assert D.is_diagonal()
+    assert D == Matrix([[25, 0, 0], [0, 9, 0], [0, 0, 9]])
+    A = Matrix(((4, -2*I, 2 + 2*I), (2*I, 2, -1 + I), (2 - 2*I, -1 - I, 11)))
+    L, D = A.LDLdecomposition()
+    assert expand_mul(L * D * L.H) == A
+    assert L.expand() == Matrix([[1, 0, 0], [I/2, 1, 0], [S.Half - I/2, 0, 1]])
+    assert D.expand() == Matrix(((4, 0, 0), (0, 1, 0), (0, 0, 9)))
+
+    raises(NonSquareMatrixError, lambda: SparseMatrix((1, 2)).LDLdecomposition())
+    raises(ValueError, lambda: SparseMatrix(((1, 2), (3, 4))).LDLdecomposition())
+    raises(ValueError, lambda: SparseMatrix(((5 + I, 0), (0, 1))).LDLdecomposition())
+    raises(ValueError, lambda: SparseMatrix(((1, 5), (5, 1))).LDLdecomposition())
+    raises(ValueError, lambda: SparseMatrix(((1, 2), (3, 4))).LDLdecomposition(hermitian=False))
+    A = SparseMatrix(((1, 5), (5, 1)))
+    L, D = A.LDLdecomposition(hermitian=False)
+    assert L * D * L.T == A
+    A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L, D = A.LDLdecomposition()
+    assert L * D * L.T == A
+    assert L.is_lower
+    assert L == Matrix([[1, 0, 0], [ Rational(3, 5), 1, 0], [Rational(-1, 5), Rational(1, 3), 1]])
+    assert D.is_diagonal()
+    assert D == Matrix([[25, 0, 0], [0, 9, 0], [0, 0, 9]])
+    A = SparseMatrix(((4, -2*I, 2 + 2*I), (2*I, 2, -1 + I), (2 - 2*I, -1 - I, 11)))
+    L, D = A.LDLdecomposition()
+    assert expand_mul(L * D * L.H) == A
+    assert L == Matrix(((1, 0, 0), (I/2, 1, 0), (S.Half - I/2, 0, 1)))
+    assert D == Matrix(((4, 0, 0), (0, 1, 0), (0, 0, 9)))
+
+def test_pinv_succeeds_with_rank_decomposition_method():
+    # Test rank decomposition method of pseudoinverse succeeding
+    As = [Matrix([
+        [61, 89, 55, 20, 71, 0],
+        [62, 96, 85, 85, 16, 0],
+        [69, 56, 17,  4, 54, 0],
+        [10, 54, 91, 41, 71, 0],
+        [ 7, 30, 10, 48, 90, 0],
+        [0,0,0,0,0,0]])]
+    for A in As:
+        A_pinv = A.pinv(method="RD")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+def test_rank_decomposition():
+    a = Matrix(0, 0, [])
+    c, f = a.rank_decomposition()
+    assert f.is_echelon
+    assert c.cols == f.rows == a.rank()
+    assert c * f == a
+
+    a = Matrix(1, 1, [5])
+    c, f = a.rank_decomposition()
+    assert f.is_echelon
+    assert c.cols == f.rows == a.rank()
+    assert c * f == a
+
+    a = Matrix(3, 3, [1, 2, 3, 1, 2, 3, 1, 2, 3])
+    c, f = a.rank_decomposition()
+    assert f.is_echelon
+    assert c.cols == f.rows == a.rank()
+    assert c * f == a
+
+    a = Matrix([
+        [0, 0, 1, 2, 2, -5, 3],
+        [-1, 5, 2, 2, 1, -7, 5],
+        [0, 0, -2, -3, -3, 8, -5],
+        [-1, 5, 0, -1, -2, 1, 0]])
+    c, f = a.rank_decomposition()
+    assert f.is_echelon
+    assert c.cols == f.rows == a.rank()
+    assert c * f == a
+
+
+@slow
+def test_upper_hessenberg_decomposition():
+    A = Matrix([
+        [1, 0, sqrt(3)],
+        [sqrt(2), Rational(1, 2), 2],
+        [1, Rational(1, 4), 3],
+    ])
+    H, P = A.upper_hessenberg_decomposition()
+    assert simplify(P * P.H) == eye(P.cols)
+    assert simplify(P.H * P) == eye(P.cols)
+    assert H.is_upper_hessenberg
+    assert (simplify(P * H * P.H)) == A
+
+
+    B = Matrix([
+        [1, 2, 10],
+        [8, 2, 5],
+        [3, 12, 34],
+    ])
+    H, P = B.upper_hessenberg_decomposition()
+    assert simplify(P * P.H) == eye(P.cols)
+    assert simplify(P.H * P) == eye(P.cols)
+    assert H.is_upper_hessenberg
+    assert simplify(P * H * P.H) == B
+
+    C = Matrix([
+        [1, sqrt(2), 2, 3],
+        [0, 5, 3, 4],
+        [1, 1, 4, sqrt(5)],
+        [0, 2, 2, 3]
+    ])
+
+    H, P = C.upper_hessenberg_decomposition()
+    assert simplify(P * P.H) == eye(P.cols)
+    assert simplify(P.H * P) == eye(P.cols)
+    assert H.is_upper_hessenberg
+    assert simplify(P * H * P.H) == C
+
+    D = Matrix([
+        [1, 2, 3],
+        [-3, 5, 6],
+        [4, -8, 9],
+    ])
+    H, P = D.upper_hessenberg_decomposition()
+    assert simplify(P * P.H) == eye(P.cols)
+    assert simplify(P.H * P) == eye(P.cols)
+    assert H.is_upper_hessenberg
+    assert simplify(P * H * P.H) == D
+
+    E = Matrix([
+        [1, 0, 0, 0],
+        [0, 1, 0, 0],
+        [1, 1, 0, 1],
+        [1, 1, 1, 0]
+    ])
+
+    H, P = E.upper_hessenberg_decomposition()
+    assert simplify(P * P.H) == eye(P.cols)
+    assert simplify(P.H * P) == eye(P.cols)
+    assert H.is_upper_hessenberg
+    assert simplify(P * H * P.H) == E
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_determinant.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_determinant.py
new file mode 100644
index 0000000000000000000000000000000000000000..82b42ccf67efa4757bf270782bdf1d65e0efa306
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_determinant.py
@@ -0,0 +1,280 @@
+import random
+import pytest
+from sympy.core.numbers import I
+from sympy.core.numbers import Rational
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.polys.polytools import Poly
+from sympy.matrices import Matrix, eye, ones
+from sympy.abc import x, y, z
+from sympy.testing.pytest import raises
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.functions.combinatorial.factorials import factorial, subfactorial
+
+
+@pytest.mark.parametrize("method", [
+    # Evaluating these directly because they are never reached via M.det()
+    Matrix._eval_det_bareiss, Matrix._eval_det_berkowitz,
+    Matrix._eval_det_bird, Matrix._eval_det_laplace, Matrix._eval_det_lu
+])
+@pytest.mark.parametrize("M, sol", [
+    (Matrix(), 1),
+    (Matrix([[0]]), 0),
+    (Matrix([[5]]), 5),
+])
+def test_eval_determinant(method, M, sol):
+    assert method(M) == sol
+
+
+@pytest.mark.parametrize("method", [
+    "domain-ge", "bareiss", "berkowitz", "bird", "laplace", "lu"])
+@pytest.mark.parametrize("M, sol", [
+    (Matrix(( (-3,  2),
+              ( 8, -5) )), -1),
+    (Matrix(( (x,   1),
+              (y, 2*y) )), 2*x*y - y),
+    (Matrix(( (1, 1, 1),
+              (1, 2, 3),
+              (1, 3, 6) )), 1),
+    (Matrix(( ( 3, -2,  0, 5),
+              (-2,  1, -2, 2),
+              ( 0, -2,  5, 0),
+              ( 5,  0,  3, 4) )), -289),
+    (Matrix(( ( 1,  2,  3,  4),
+              ( 5,  6,  7,  8),
+              ( 9, 10, 11, 12),
+              (13, 14, 15, 16) )), 0),
+    (Matrix(( (3, 2, 0, 0, 0),
+              (0, 3, 2, 0, 0),
+              (0, 0, 3, 2, 0),
+              (0, 0, 0, 3, 2),
+              (2, 0, 0, 0, 3) )), 275),
+    (Matrix(( ( 3,  0,  0, 0),
+              (-2,  1,  0, 0),
+              ( 0, -2,  5, 0),
+              ( 5,  0,  3, 4) )), 60),
+    (Matrix(( ( 1,  0,  0,  0),
+              ( 5,  0,  0,  0),
+              ( 9, 10, 11, 0),
+              (13, 14, 15, 16) )), 0),
+    (Matrix(( (3, 2, 0, 0, 0),
+              (0, 3, 2, 0, 0),
+              (0, 0, 3, 2, 0),
+              (0, 0, 0, 3, 2),
+              (0, 0, 0, 0, 3) )), 243),
+    (Matrix(( (1, 0,  1,  2, 12),
+              (2, 0,  1,  1,  4),
+              (2, 1,  1, -1,  3),
+              (3, 2, -1,  1,  8),
+              (1, 1,  1,  0,  6) )), -55),
+    (Matrix(( (-5,  2,  3,  4,  5),
+              ( 1, -4,  3,  4,  5),
+              ( 1,  2, -3,  4,  5),
+              ( 1,  2,  3, -2,  5),
+              ( 1,  2,  3,  4, -1) )), 11664),
+    (Matrix(( ( 2,  7, -1, 3, 2),
+              ( 0,  0,  1, 0, 1),
+              (-2,  0,  7, 0, 2),
+              (-3, -2,  4, 5, 3),
+              ( 1,  0,  0, 0, 1) )), 123),
+    (Matrix(( (x, y, z),
+              (1, 0, 0),
+              (y, z, x) )), z**2 - x*y),
+])
+def test_determinant(method, M, sol):
+    assert M.det(method=method) == sol
+
+
+def test_issue_13835():
+    a = symbols('a')
+    M = lambda n: Matrix([[i + a*j for i in range(n)]
+                          for j in range(n)])
+    assert M(5).det() == 0
+    assert M(6).det() == 0
+    assert M(7).det() == 0
+
+
+def test_issue_14517():
+    M = Matrix([
+        [   0, 10*I,    10*I,       0],
+        [10*I,    0,       0,    10*I],
+        [10*I,    0, 5 + 2*I,    10*I],
+        [   0, 10*I,    10*I, 5 + 2*I]])
+    ev = M.eigenvals()
+    # test one random eigenvalue, the computation is a little slow
+    test_ev = random.choice(list(ev.keys()))
+    assert (M - test_ev*eye(4)).det() == 0
+
+
+@pytest.mark.parametrize("method", [
+    "bareis", "det_lu", "det_LU", "Bareis", "BAREISS", "BERKOWITZ", "LU"])
+@pytest.mark.parametrize("M, sol", [
+    (Matrix(( ( 3, -2,  0, 5),
+              (-2,  1, -2, 2),
+              ( 0, -2,  5, 0),
+              ( 5,  0,  3, 4) )), -289),
+    (Matrix(( (-5,  2,  3,  4,  5),
+              ( 1, -4,  3,  4,  5),
+              ( 1,  2, -3,  4,  5),
+              ( 1,  2,  3, -2,  5),
+              ( 1,  2,  3,  4, -1) )), 11664),
+])
+def test_legacy_det(method, M, sol):
+    # Minimal support for legacy keys for 'method' in det()
+    # Partially copied from test_determinant()
+    assert M.det(method=method) == sol
+
+
+def eye_Determinant(n):
+    return Matrix(n, n, lambda i, j: int(i == j))
+
+def zeros_Determinant(n):
+    return Matrix(n, n, lambda i, j: 0)
+
+def test_det():
+    a = Matrix(2, 3, [1, 2, 3, 4, 5, 6])
+    raises(NonSquareMatrixError, lambda: a.det())
+
+    z = zeros_Determinant(2)
+    ey = eye_Determinant(2)
+    assert z.det() == 0
+    assert ey.det() == 1
+
+    x = Symbol('x')
+    a = Matrix(0, 0, [])
+    b = Matrix(1, 1, [5])
+    c = Matrix(2, 2, [1, 2, 3, 4])
+    d = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 8])
+    e = Matrix(4, 4,
+        [x, 1, 2, 3, 4, 5, 6, 7, 2, 9, 10, 11, 12, 13, 14, 14])
+    from sympy.abc import i, j, k, l, m, n
+    f = Matrix(3, 3, [i, l, m, 0, j, n, 0, 0, k])
+    g = Matrix(3, 3, [i, 0, 0, l, j, 0, m, n, k])
+    h = Matrix(3, 3, [x**3, 0, 0, i, x**-1, 0, j, k, x**-2])
+    # the method keyword for `det` doesn't kick in until 4x4 matrices,
+    # so there is no need to test all methods on smaller ones
+
+    assert a.det() == 1
+    assert b.det() == 5
+    assert c.det() == -2
+    assert d.det() == 3
+    assert e.det() == 4*x - 24
+    assert e.det(method="domain-ge") == 4*x - 24
+    assert e.det(method='bareiss') == 4*x - 24
+    assert e.det(method='berkowitz') == 4*x - 24
+    assert f.det() == i*j*k
+    assert g.det() == i*j*k
+    assert h.det() == 1
+    raises(ValueError, lambda: e.det(iszerofunc="test"))
+
+def test_permanent():
+    M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert M.per() == 450
+    for i in range(1, 12):
+        assert ones(i, i).per() == ones(i, i).T.per() == factorial(i)
+        assert (ones(i, i)-eye(i)).per() == (ones(i, i)-eye(i)).T.per() == subfactorial(i)
+
+    a1, a2, a3, a4, a5 = symbols('a_1 a_2 a_3 a_4 a_5')
+    M = Matrix([a1, a2, a3, a4, a5])
+    assert M.per() == M.T.per() == a1 + a2 + a3 + a4 + a5
+
+def test_adjugate():
+    x = Symbol('x')
+    e = Matrix(4, 4,
+        [x, 1, 2, 3, 4, 5, 6, 7, 2, 9, 10, 11, 12, 13, 14, 14])
+
+    adj = Matrix([
+        [   4,         -8,         4,         0],
+        [  76, -14*x - 68,  14*x - 8, -4*x + 24],
+        [-122, 17*x + 142, -21*x + 4,  8*x - 48],
+        [  48,  -4*x - 72,       8*x, -4*x + 24]])
+    assert e.adjugate() == adj
+    assert e.adjugate(method='bareiss') == adj
+    assert e.adjugate(method='berkowitz') == adj
+    assert e.adjugate(method='bird') == adj
+    assert e.adjugate(method='laplace') == adj
+
+    a = Matrix(2, 3, [1, 2, 3, 4, 5, 6])
+    raises(NonSquareMatrixError, lambda: a.adjugate())
+
+def test_util():
+    R = Rational
+
+    v1 = Matrix(1, 3, [1, 2, 3])
+    v2 = Matrix(1, 3, [3, 4, 5])
+    assert v1.norm() == sqrt(14)
+    assert v1.project(v2) == Matrix(1, 3, [R(39)/25, R(52)/25, R(13)/5])
+    assert Matrix.zeros(1, 2) == Matrix(1, 2, [0, 0])
+    assert ones(1, 2) == Matrix(1, 2, [1, 1])
+    assert v1.copy() == v1
+    # cofactor
+    assert eye(3) == eye(3).cofactor_matrix()
+    test = Matrix([[1, 3, 2], [2, 6, 3], [2, 3, 6]])
+    assert test.cofactor_matrix() == \
+        Matrix([[27, -6, -6], [-12, 2, 3], [-3, 1, 0]])
+    test = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert test.cofactor_matrix() == \
+        Matrix([[-3, 6, -3], [6, -12, 6], [-3, 6, -3]])
+
+def test_cofactor_and_minors():
+    x = Symbol('x')
+    e = Matrix(4, 4,
+        [x, 1, 2, 3, 4, 5, 6, 7, 2, 9, 10, 11, 12, 13, 14, 14])
+
+    m = Matrix([
+        [ x,  1,  3],
+        [ 2,  9, 11],
+        [12, 13, 14]])
+    cm = Matrix([
+        [ 4,         76,       -122,        48],
+        [-8, -14*x - 68, 17*x + 142, -4*x - 72],
+        [ 4,   14*x - 8,  -21*x + 4,       8*x],
+        [ 0,  -4*x + 24,   8*x - 48, -4*x + 24]])
+    sub = Matrix([
+            [x, 1,  2],
+            [4, 5,  6],
+            [2, 9, 10]])
+
+    assert e.minor_submatrix(1, 2) == m
+    assert e.minor_submatrix(-1, -1) == sub
+    assert e.minor(1, 2) == -17*x - 142
+    assert e.cofactor(1, 2) == 17*x + 142
+    assert e.cofactor_matrix() == cm
+    assert e.cofactor_matrix(method="bareiss") == cm
+    assert e.cofactor_matrix(method="berkowitz") == cm
+    assert e.cofactor_matrix(method="bird") == cm
+    assert e.cofactor_matrix(method="laplace") == cm
+
+    raises(ValueError, lambda: e.cofactor(4, 5))
+    raises(ValueError, lambda: e.minor(4, 5))
+    raises(ValueError, lambda: e.minor_submatrix(4, 5))
+
+    a = Matrix(2, 3, [1, 2, 3, 4, 5, 6])
+    assert a.minor_submatrix(0, 0) == Matrix([[5, 6]])
+
+    raises(ValueError, lambda:
+        Matrix(0, 0, []).minor_submatrix(0, 0))
+    raises(NonSquareMatrixError, lambda: a.cofactor(0, 0))
+    raises(NonSquareMatrixError, lambda: a.minor(0, 0))
+    raises(NonSquareMatrixError, lambda: a.cofactor_matrix())
+
+def test_charpoly():
+    x, y = Symbol('x'), Symbol('y')
+    z, t = Symbol('z'), Symbol('t')
+
+    from sympy.abc import a,b,c
+
+    m = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+
+    assert eye_Determinant(3).charpoly(x) == Poly((x - 1)**3, x)
+    assert eye_Determinant(3).charpoly(y) == Poly((y - 1)**3, y)
+    assert m.charpoly() == Poly(x**3 - 15*x**2 - 18*x, x)
+    raises(NonSquareMatrixError, lambda: Matrix([[1], [2]]).charpoly())
+    n = Matrix(4, 4, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+    assert n.charpoly() == Poly(x**4, x)
+
+    n = Matrix(4, 4, [45, 0, 0, 0, 0, 23, 0, 0, 0, 0, 87, 0, 0, 0, 0, 12])
+    assert n.charpoly() == Poly(x**4 - 167*x**3 + 8811*x**2 - 173457*x + 1080540, x)
+
+    n = Matrix(3, 3, [x, 0, 0, a, y, 0, b, c, z])
+    assert n.charpoly() == Poly(t**3 - (x+y+z)*t**2 + t*(x*y+y*z+x*z) - x*y*z, t)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_domains.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_domains.py
new file mode 100644
index 0000000000000000000000000000000000000000..26a54b8879a5c65f3a01b4886d223c08309e733d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_domains.py
@@ -0,0 +1,113 @@
+# Test Matrix/DomainMatrix interaction.
+
+
+from sympy import GF, ZZ, QQ, EXRAW
+from sympy.polys.matrices import DomainMatrix, DM
+
+from sympy import (
+    Matrix,
+    MutableMatrix,
+    ImmutableMatrix,
+    SparseMatrix,
+    MutableDenseMatrix,
+    ImmutableDenseMatrix,
+    MutableSparseMatrix,
+    ImmutableSparseMatrix,
+)
+from sympy import symbols, S, sqrt
+
+from sympy.testing.pytest import raises
+
+
+x, y = symbols('x y')
+
+
+MATRIX_TYPES = (
+    Matrix,
+    MutableMatrix,
+    ImmutableMatrix,
+    SparseMatrix,
+    MutableDenseMatrix,
+    ImmutableDenseMatrix,
+    MutableSparseMatrix,
+    ImmutableSparseMatrix,
+)
+IMMUTABLE = (
+    ImmutableMatrix,
+    ImmutableDenseMatrix,
+    ImmutableSparseMatrix,
+)
+
+
+def DMs(items, domain):
+    return DM(items, domain).to_sparse()
+
+
+def test_Matrix_rep_domain():
+
+    for Mat in MATRIX_TYPES:
+
+        M = Mat([[1, 2], [3, 4]])
+        assert M._rep == DMs([[1, 2], [3, 4]], ZZ)
+        assert (M / 2)._rep == DMs([[(1,2), 1], [(3,2), 2]], QQ)
+        if not isinstance(M, IMMUTABLE):
+            M[0, 0] = x
+            assert M._rep == DMs([[x, 2], [3, 4]], EXRAW)
+
+        M = Mat([[S(1)/2, 2], [3, 4]])
+        assert M._rep == DMs([[(1,2), 2], [3, 4]], QQ)
+        if not isinstance(M, IMMUTABLE):
+            M[0, 0] = x
+            assert M._rep == DMs([[x, 2], [3, 4]], EXRAW)
+
+        dM = DMs([[1, 2], [3, 4]], ZZ)
+        assert Mat._fromrep(dM)._rep == dM
+
+    # XXX: This is not intended. Perhaps it should be coerced to EXRAW?
+    # The private _fromrep method is never called like this but perhaps it
+    # should be guarded.
+    #
+    # It is not clear how to integrate domains other than ZZ, QQ and EXRAW with
+    # the rest of Matrix or if the public type for this needs to be something
+    # different from Matrix somehow.
+    K = QQ.algebraic_field(sqrt(2))
+    dM = DM([[1, 2], [3, 4]], K)
+    assert Mat._fromrep(dM)._rep.domain == K
+
+
+def test_Matrix_to_DM():
+
+    M = Matrix([[1, 2], [3, 4]])
+    assert M.to_DM() == DMs([[1, 2], [3, 4]], ZZ)
+    assert M.to_DM() is not M._rep
+    assert M.to_DM(field=True) == DMs([[1, 2], [3, 4]], QQ)
+    assert M.to_DM(domain=QQ) == DMs([[1, 2], [3, 4]], QQ)
+    assert M.to_DM(domain=QQ[x]) == DMs([[1, 2], [3, 4]], QQ[x])
+    assert M.to_DM(domain=GF(3)) == DMs([[1, 2], [0, 1]], GF(3))
+
+    M = Matrix([[1, 2], [3, 4]])
+    M[0, 0] = x
+    assert M._rep.domain == EXRAW
+    M[0, 0] = 1
+    assert M.to_DM() == DMs([[1, 2], [3, 4]], ZZ)
+
+    M = Matrix([[S(1)/2, 2], [3, 4]])
+    assert M.to_DM() == DMs([[QQ(1,2), 2], [3, 4]], QQ)
+
+    M = Matrix([[x, 2], [3, 4]])
+    assert M.to_DM() == DMs([[x, 2], [3, 4]], ZZ[x])
+    assert M.to_DM(field=True) == DMs([[x, 2], [3, 4]], ZZ.frac_field(x))
+
+    M = Matrix([[1/x, 2], [3, 4]])
+    assert M.to_DM() == DMs([[1/x, 2], [3, 4]], ZZ.frac_field(x))
+
+    M = Matrix([[1, sqrt(2)], [3, 4]])
+    K = QQ.algebraic_field(sqrt(2))
+    sqrt2 = K.from_sympy(sqrt(2)) # XXX: Maybe K(sqrt(2)) should work
+    M_K = DomainMatrix([[K(1), sqrt2], [K(3), K(4)]], (2, 2), K)
+    assert M.to_DM() == DMs([[1, sqrt(2)], [3, 4]], EXRAW)
+    assert M.to_DM(extension=True) == M_K.to_sparse()
+
+    # Options cannot be used with the domain parameter
+    M = Matrix([[1, 2], [3, 4]])
+    raises(TypeError, lambda: M.to_DM(domain=QQ, field=True))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_eigen.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_eigen.py
new file mode 100644
index 0000000000000000000000000000000000000000..fcf96325519879e0683d29e2ddc32db7bf83baa4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_eigen.py
@@ -0,0 +1,712 @@
+from sympy.core.evalf import N
+from sympy.core.numbers import (Float, I, Rational)
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.matrices import eye, Matrix
+from sympy.core.singleton import S
+from sympy.testing.pytest import raises, XFAIL
+from sympy.matrices.exceptions import NonSquareMatrixError, MatrixError
+from sympy.matrices.expressions.fourier import DFT
+from sympy.simplify.simplify import simplify
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.testing.pytest import slow
+from sympy.testing.matrices import allclose
+
+
+def test_eigen():
+    R = Rational
+    M = Matrix.eye(3)
+    assert M.eigenvals(multiple=False) == {S.One: 3}
+    assert M.eigenvals(multiple=True) == [1, 1, 1]
+
+    assert M.eigenvects() == (
+        [(1, 3, [Matrix([1, 0, 0]),
+                 Matrix([0, 1, 0]),
+                 Matrix([0, 0, 1])])])
+
+    assert M.left_eigenvects() == (
+        [(1, 3, [Matrix([[1, 0, 0]]),
+                 Matrix([[0, 1, 0]]),
+                 Matrix([[0, 0, 1]])])])
+
+    M = Matrix([[0, 1, 1],
+                [1, 0, 0],
+                [1, 1, 1]])
+
+    assert M.eigenvals() == {2*S.One: 1, -S.One: 1, S.Zero: 1}
+
+    assert M.eigenvects() == (
+        [
+            (-1, 1, [Matrix([-1, 1, 0])]),
+            ( 0, 1, [Matrix([0, -1, 1])]),
+            ( 2, 1, [Matrix([R(2, 3), R(1, 3), 1])])
+        ])
+
+    assert M.left_eigenvects() == (
+        [
+            (-1, 1, [Matrix([[-2, 1, 1]])]),
+            (0, 1, [Matrix([[-1, -1, 1]])]),
+            (2, 1, [Matrix([[1, 1, 1]])])
+        ])
+
+    a = Symbol('a')
+    M = Matrix([[a, 0],
+                [0, 1]])
+
+    assert M.eigenvals() == {a: 1, S.One: 1}
+
+    M = Matrix([[1, -1],
+                [1,  3]])
+    assert M.eigenvects() == ([(2, 2, [Matrix(2, 1, [-1, 1])])])
+    assert M.left_eigenvects() == ([(2, 2, [Matrix([[1, 1]])])])
+
+    M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    a = R(15, 2)
+    b = 3*33**R(1, 2)
+    c = R(13, 2)
+    d = (R(33, 8) + 3*b/8)
+    e = (R(33, 8) - 3*b/8)
+
+    def NS(e, n):
+        return str(N(e, n))
+    r = [
+        (a - b/2, 1, [Matrix([(12 + 24/(c - b/2))/((c - b/2)*e) + 3/(c - b/2),
+                              (6 + 12/(c - b/2))/e, 1])]),
+        (      0, 1, [Matrix([1, -2, 1])]),
+        (a + b/2, 1, [Matrix([(12 + 24/(c + b/2))/((c + b/2)*d) + 3/(c + b/2),
+                              (6 + 12/(c + b/2))/d, 1])]),
+    ]
+    r1 = [(NS(r[i][0], 2), NS(r[i][1], 2),
+        [NS(j, 2) for j in r[i][2][0]]) for i in range(len(r))]
+    r = M.eigenvects()
+    r2 = [(NS(r[i][0], 2), NS(r[i][1], 2),
+        [NS(j, 2) for j in r[i][2][0]]) for i in range(len(r))]
+    assert sorted(r1) == sorted(r2)
+
+    eps = Symbol('eps', real=True)
+
+    M = Matrix([[abs(eps), I*eps    ],
+                [-I*eps,   abs(eps) ]])
+
+    assert M.eigenvects() == (
+        [
+            ( 0, 1, [Matrix([[-I*eps/abs(eps)], [1]])]),
+            ( 2*abs(eps), 1, [ Matrix([[I*eps/abs(eps)], [1]]) ] ),
+        ])
+
+    assert M.left_eigenvects() == (
+        [
+            (0, 1, [Matrix([[I*eps/Abs(eps), 1]])]),
+            (2*Abs(eps), 1, [Matrix([[-I*eps/Abs(eps), 1]])])
+        ])
+
+    M = Matrix(3, 3, [1, 2, 0, 0, 3, 0, 2, -4, 2])
+    M._eigenvects = M.eigenvects(simplify=False)
+    assert max(i.q for i in M._eigenvects[0][2][0]) > 1
+    M._eigenvects = M.eigenvects(simplify=True)
+    assert max(i.q for i in M._eigenvects[0][2][0]) == 1
+
+    M = Matrix([[Rational(1, 4), 1], [1, 1]])
+    assert M.eigenvects() == [
+        (Rational(5, 8) - sqrt(73)/8, 1, [Matrix([[-sqrt(73)/8 - Rational(3, 8)], [1]])]),
+        (Rational(5, 8) + sqrt(73)/8, 1, [Matrix([[Rational(-3, 8) + sqrt(73)/8], [1]])])]
+
+    # issue 10719
+    assert Matrix([]).eigenvals() == {}
+    assert Matrix([]).eigenvals(multiple=True) == []
+    assert Matrix([]).eigenvects() == []
+
+    # issue 15119
+    raises(NonSquareMatrixError,
+           lambda: Matrix([[1, 2], [0, 4], [0, 0]]).eigenvals())
+    raises(NonSquareMatrixError,
+           lambda: Matrix([[1, 0], [3, 4], [5, 6]]).eigenvals())
+    raises(NonSquareMatrixError,
+           lambda: Matrix([[1, 2, 3], [0, 5, 6]]).eigenvals())
+    raises(NonSquareMatrixError,
+           lambda: Matrix([[1, 0, 0], [4, 5, 0]]).eigenvals())
+    raises(NonSquareMatrixError,
+           lambda: Matrix([[1, 2, 3], [0, 5, 6]]).eigenvals(
+               error_when_incomplete = False))
+    raises(NonSquareMatrixError,
+           lambda: Matrix([[1, 0, 0], [4, 5, 0]]).eigenvals(
+               error_when_incomplete = False))
+
+    m = Matrix([[1, 2], [3, 4]])
+    assert isinstance(m.eigenvals(simplify=True, multiple=False), dict)
+    assert isinstance(m.eigenvals(simplify=True, multiple=True), list)
+    assert isinstance(m.eigenvals(simplify=lambda x: x, multiple=False), dict)
+    assert isinstance(m.eigenvals(simplify=lambda x: x, multiple=True), list)
+
+
+def test_float_eigenvals():
+    m = Matrix([[1, .6, .6], [.6, .9, .9], [.9, .6, .6]])
+    evals = [
+        Rational(5, 4) - sqrt(385)/20,
+        sqrt(385)/20 + Rational(5, 4),
+        S.Zero]
+
+    n_evals = m.eigenvals(rational=True, multiple=True)
+    n_evals = sorted(n_evals)
+    s_evals = [x.evalf() for x in evals]
+    s_evals = sorted(s_evals)
+
+    for x, y in zip(n_evals, s_evals):
+        assert abs(x-y) < 10**-9
+
+
+@XFAIL
+def test_eigen_vects():
+    m = Matrix(2, 2, [1, 0, 0, I])
+    raises(NotImplementedError, lambda: m.is_diagonalizable(True))
+    # !!! bug because of eigenvects() or roots(x**2 + (-1 - I)*x + I, x)
+    # see issue 5292
+    assert not m.is_diagonalizable(True)
+    raises(MatrixError, lambda: m.diagonalize(True))
+    (P, D) = m.diagonalize(True)
+
+def test_issue_8240():
+    # Eigenvalues of large triangular matrices
+    x, y = symbols('x y')
+    n = 200
+
+    diagonal_variables = [Symbol('x%s' % i) for i in range(n)]
+    M = [[0 for i in range(n)] for j in range(n)]
+    for i in range(n):
+        M[i][i] = diagonal_variables[i]
+    M = Matrix(M)
+
+    eigenvals = M.eigenvals()
+    assert len(eigenvals) == n
+    for i in range(n):
+        assert eigenvals[diagonal_variables[i]] == 1
+
+    eigenvals = M.eigenvals(multiple=True)
+    assert set(eigenvals) == set(diagonal_variables)
+
+    # with multiplicity
+    M = Matrix([[x, 0, 0], [1, y, 0], [2, 3, x]])
+    eigenvals = M.eigenvals()
+    assert eigenvals == {x: 2, y: 1}
+
+    eigenvals = M.eigenvals(multiple=True)
+    assert len(eigenvals) == 3
+    assert eigenvals.count(x) == 2
+    assert eigenvals.count(y) == 1
+
+
+def test_eigenvals():
+    M = Matrix([[0, 1, 1],
+                [1, 0, 0],
+                [1, 1, 1]])
+    assert M.eigenvals() == {2*S.One: 1, -S.One: 1, S.Zero: 1}
+
+    m = Matrix([
+        [3,  0,  0, 0, -3],
+        [0, -3, -3, 0,  3],
+        [0,  3,  0, 3,  0],
+        [0,  0,  3, 0,  3],
+        [3,  0,  0, 3,  0]])
+
+    # XXX Used dry-run test because arbitrary symbol that appears in
+    # CRootOf may not be unique.
+    assert m.eigenvals()
+
+
+def test_eigenvects():
+    M = Matrix([[0, 1, 1],
+                [1, 0, 0],
+                [1, 1, 1]])
+    vecs = M.eigenvects()
+    for val, mult, vec_list in vecs:
+        assert len(vec_list) == 1
+        assert M*vec_list[0] == val*vec_list[0]
+
+
+def test_left_eigenvects():
+    M = Matrix([[0, 1, 1],
+                [1, 0, 0],
+                [1, 1, 1]])
+    vecs = M.left_eigenvects()
+    for val, mult, vec_list in vecs:
+        assert len(vec_list) == 1
+        assert vec_list[0]*M == val*vec_list[0]
+
+
+@slow
+def test_bidiagonalize():
+    M = Matrix([[1, 0, 0],
+                [0, 1, 0],
+                [0, 0, 1]])
+    assert M.bidiagonalize() == M
+    assert M.bidiagonalize(upper=False) == M
+    assert M.bidiagonalize() == M
+    assert M.bidiagonal_decomposition() == (M, M, M)
+    assert M.bidiagonal_decomposition(upper=False) == (M, M, M)
+    assert M.bidiagonalize() == M
+
+    import random
+    #Real Tests
+    for real_test in range(2):
+        test_values = []
+        row = 2
+        col = 2
+        for _ in range(row * col):
+            value = random.randint(-1000000000, 1000000000)
+            test_values = test_values + [value]
+        # L     -> Lower Bidiagonalization
+        # M     -> Mutable Matrix
+        # N     -> Immutable Matrix
+        # 0     -> Bidiagonalized form
+        # 1,2,3 -> Bidiagonal_decomposition matrices
+        # 4     -> Product of 1 2 3
+        M = Matrix(row, col, test_values)
+        N = ImmutableMatrix(M)
+
+        N1, N2, N3 = N.bidiagonal_decomposition()
+        M1, M2, M3 = M.bidiagonal_decomposition()
+        M0 = M.bidiagonalize()
+        N0 = N.bidiagonalize()
+
+        N4 = N1 * N2 * N3
+        M4 = M1 * M2 * M3
+
+        N2.simplify()
+        N4.simplify()
+        N0.simplify()
+
+        M0.simplify()
+        M2.simplify()
+        M4.simplify()
+
+        LM0 = M.bidiagonalize(upper=False)
+        LM1, LM2, LM3 = M.bidiagonal_decomposition(upper=False)
+        LN0 = N.bidiagonalize(upper=False)
+        LN1, LN2, LN3 = N.bidiagonal_decomposition(upper=False)
+
+        LN4 = LN1 * LN2 * LN3
+        LM4 = LM1 * LM2 * LM3
+
+        LN2.simplify()
+        LN4.simplify()
+        LN0.simplify()
+
+        LM0.simplify()
+        LM2.simplify()
+        LM4.simplify()
+
+        assert M == M4
+        assert M2 == M0
+        assert N == N4
+        assert N2 == N0
+        assert M == LM4
+        assert LM2 == LM0
+        assert N == LN4
+        assert LN2 == LN0
+
+    #Complex Tests
+    for complex_test in range(2):
+        test_values = []
+        size = 2
+        for _ in range(size * size):
+            real = random.randint(-1000000000, 1000000000)
+            comp = random.randint(-1000000000, 1000000000)
+            value = real + comp * I
+            test_values = test_values + [value]
+        M = Matrix(size, size, test_values)
+        N = ImmutableMatrix(M)
+        # L     -> Lower Bidiagonalization
+        # M     -> Mutable Matrix
+        # N     -> Immutable Matrix
+        # 0     -> Bidiagonalized form
+        # 1,2,3 -> Bidiagonal_decomposition matrices
+        # 4     -> Product of 1 2 3
+        N1, N2, N3 = N.bidiagonal_decomposition()
+        M1, M2, M3 = M.bidiagonal_decomposition()
+        M0 = M.bidiagonalize()
+        N0 = N.bidiagonalize()
+
+        N4 = N1 * N2 * N3
+        M4 = M1 * M2 * M3
+
+        N2.simplify()
+        N4.simplify()
+        N0.simplify()
+
+        M0.simplify()
+        M2.simplify()
+        M4.simplify()
+
+        LM0 = M.bidiagonalize(upper=False)
+        LM1, LM2, LM3 = M.bidiagonal_decomposition(upper=False)
+        LN0 = N.bidiagonalize(upper=False)
+        LN1, LN2, LN3 = N.bidiagonal_decomposition(upper=False)
+
+        LN4 = LN1 * LN2 * LN3
+        LM4 = LM1 * LM2 * LM3
+
+        LN2.simplify()
+        LN4.simplify()
+        LN0.simplify()
+
+        LM0.simplify()
+        LM2.simplify()
+        LM4.simplify()
+
+        assert M == M4
+        assert M2 == M0
+        assert N == N4
+        assert N2 == N0
+        assert M == LM4
+        assert LM2 == LM0
+        assert N == LN4
+        assert LN2 == LN0
+
+    M = Matrix(18, 8, range(1, 145))
+    M = M.applyfunc(lambda i: Float(i))
+    assert M.bidiagonal_decomposition()[1] == M.bidiagonalize()
+    assert M.bidiagonal_decomposition(upper=False)[1] == M.bidiagonalize(upper=False)
+    a, b, c = M.bidiagonal_decomposition()
+    diff = a * b * c - M
+    assert abs(max(diff)) < 10**-12
+
+
+def test_diagonalize():
+    m = Matrix(2, 2, [0, -1, 1, 0])
+    raises(MatrixError, lambda: m.diagonalize(reals_only=True))
+    P, D = m.diagonalize()
+    assert D.is_diagonal()
+    assert D == Matrix([
+                 [-I, 0],
+                 [ 0, I]])
+
+    # make sure we use floats out if floats are passed in
+    m = Matrix(2, 2, [0, .5, .5, 0])
+    P, D = m.diagonalize()
+    assert all(isinstance(e, Float) for e in D.values())
+    assert all(isinstance(e, Float) for e in P.values())
+
+    _, D2 = m.diagonalize(reals_only=True)
+    assert D == D2
+
+    m = Matrix(
+        [[0, 1, 0, 0], [1, 0, 0, 0.002], [0.002, 0, 0, 1], [0, 0, 1, 0]])
+    P, D = m.diagonalize()
+    assert allclose(P*D, m*P)
+
+
+def test_is_diagonalizable():
+    a, b, c = symbols('a b c')
+    m = Matrix(2, 2, [a, c, c, b])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+    assert not Matrix(2, 2, [1, 1, 0, 1]).is_diagonalizable()
+
+    m = Matrix(2, 2, [0, -1, 1, 0])
+    assert m.is_diagonalizable()
+    assert not m.is_diagonalizable(reals_only=True)
+
+
+def test_jordan_form():
+    m = Matrix(3, 2, [-3, 1, -3, 20, 3, 10])
+    raises(NonSquareMatrixError, lambda: m.jordan_form())
+
+    # the next two tests test the cases where the old
+    # algorithm failed due to the fact that the block structure can
+    # *NOT* be determined  from algebraic and geometric multiplicity alone
+    # This can be seen most easily when one lets compute the J.c.f. of a matrix that
+    # is in J.c.f already.
+    m = Matrix(4, 4, [2, 1, 0, 0,
+                    0, 2, 1, 0,
+                    0, 0, 2, 0,
+                    0, 0, 0, 2
+    ])
+    P, J = m.jordan_form()
+    assert m == J
+
+    m = Matrix(4, 4, [2, 1, 0, 0,
+                    0, 2, 0, 0,
+                    0, 0, 2, 1,
+                    0, 0, 0, 2
+    ])
+    P, J = m.jordan_form()
+    assert m == J
+
+    A = Matrix([[ 2,  4,  1,  0],
+                [-4,  2,  0,  1],
+                [ 0,  0,  2,  4],
+                [ 0,  0, -4,  2]])
+    P, J = A.jordan_form()
+    assert simplify(P*J*P.inv()) == A
+
+    assert Matrix(1, 1, [1]).jordan_form() == (Matrix([1]), Matrix([1]))
+    assert Matrix(1, 1, [1]).jordan_form(calc_transform=False) == Matrix([1])
+
+    # If we have eigenvalues in CRootOf form, raise errors
+    m = Matrix([[3, 0, 0, 0, -3], [0, -3, -3, 0, 3], [0, 3, 0, 3, 0], [0, 0, 3, 0, 3], [3, 0, 0, 3, 0]])
+    raises(MatrixError, lambda: m.jordan_form())
+
+    # make sure that if the input has floats, the output does too
+    m = Matrix([
+        [                0.6875, 0.125 + 0.1875*sqrt(3)],
+        [0.125 + 0.1875*sqrt(3),                 0.3125]])
+    P, J = m.jordan_form()
+    assert all(isinstance(x, Float) or x == 0 for x in P)
+    assert all(isinstance(x, Float) or x == 0 for x in J)
+
+
+def test_singular_values():
+    x = Symbol('x', real=True)
+
+    A = Matrix([[0, 1*I], [2, 0]])
+    # if singular values can be sorted, they should be in decreasing order
+    assert A.singular_values() == [2, 1]
+
+    A = eye(3)
+    A[1, 1] = x
+    A[2, 2] = 5
+    vals = A.singular_values()
+    # since Abs(x) cannot be sorted, test set equality
+    assert set(vals) == {5, 1, Abs(x)}
+
+    A = Matrix([[sin(x), cos(x)], [-cos(x), sin(x)]])
+    vals = [sv.trigsimp() for sv in A.singular_values()]
+    assert vals == [S.One, S.One]
+
+    A = Matrix([
+        [2, 4],
+        [1, 3],
+        [0, 0],
+        [0, 0]
+        ])
+    assert A.singular_values() == \
+        [sqrt(sqrt(221) + 15), sqrt(15 - sqrt(221))]
+    assert A.T.singular_values() == \
+        [sqrt(sqrt(221) + 15), sqrt(15 - sqrt(221)), 0, 0]
+
+def test___eq__():
+    assert (Matrix(
+        [[0, 1, 1],
+        [1, 0, 0],
+        [1, 1, 1]]) == {}) is False
+
+
+def test_definite():
+    # Examples from Gilbert Strang, "Introduction to Linear Algebra"
+    # Positive definite matrices
+    m = Matrix([[2, -1, 0], [-1, 2, -1], [0, -1, 2]])
+    assert m.is_positive_definite == True
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    m = Matrix([[5, 4], [4, 5]])
+    assert m.is_positive_definite == True
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    # Positive semidefinite matrices
+    m = Matrix([[2, -1, -1], [-1, 2, -1], [-1, -1, 2]])
+    assert m.is_positive_definite == False
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    m = Matrix([[1, 2], [2, 4]])
+    assert m.is_positive_definite == False
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    # Examples from Mathematica documentation
+    # Non-hermitian positive definite matrices
+    m = Matrix([[2, 3], [4, 8]])
+    assert m.is_positive_definite == True
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    # Hermetian matrices
+    m = Matrix([[1, 2*I], [-I, 4]])
+    assert m.is_positive_definite == True
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    # Symbolic matrices examples
+    a = Symbol('a', positive=True)
+    b = Symbol('b', negative=True)
+    m = Matrix([[a, 0, 0], [0, a, 0], [0, 0, a]])
+    assert m.is_positive_definite == True
+    assert m.is_positive_semidefinite == True
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == False
+
+    m = Matrix([[b, 0, 0], [0, b, 0], [0, 0, b]])
+    assert m.is_positive_definite == False
+    assert m.is_positive_semidefinite == False
+    assert m.is_negative_definite == True
+    assert m.is_negative_semidefinite == True
+    assert m.is_indefinite == False
+
+    m = Matrix([[a, 0], [0, b]])
+    assert m.is_positive_definite == False
+    assert m.is_positive_semidefinite == False
+    assert m.is_negative_definite == False
+    assert m.is_negative_semidefinite == False
+    assert m.is_indefinite == True
+
+    m = Matrix([
+        [0.0228202735623867, 0.00518748979085398,
+         -0.0743036351048907, -0.00709135324903921],
+        [0.00518748979085398, 0.0349045359786350,
+         0.0830317991056637, 0.00233147902806909],
+        [-0.0743036351048907, 0.0830317991056637,
+         1.15859676366277, 0.340359081555988],
+        [-0.00709135324903921, 0.00233147902806909,
+         0.340359081555988, 0.928147644848199]
+    ])
+    assert m.is_positive_definite == True
+    assert m.is_positive_semidefinite == True
+    assert m.is_indefinite == False
+
+    # test for issue 19547: https://github.com/sympy/sympy/issues/19547
+    m = Matrix([
+        [0, 0, 0],
+        [0, 1, 2],
+        [0, 2, 1]
+    ])
+    assert not m.is_positive_definite
+    assert not m.is_positive_semidefinite
+
+
+def test_positive_semidefinite_cholesky():
+    from sympy.matrices.eigen import _is_positive_semidefinite_cholesky
+
+    m = Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+    assert _is_positive_semidefinite_cholesky(m) == True
+    m = Matrix([[0, 0, 0], [0, 5, -10*I], [0, 10*I, 5]])
+    assert _is_positive_semidefinite_cholesky(m) == False
+    m = Matrix([[1, 0, 0], [0, 0, 0], [0, 0, -1]])
+    assert _is_positive_semidefinite_cholesky(m) == False
+    m = Matrix([[0, 1], [1, 0]])
+    assert _is_positive_semidefinite_cholesky(m) == False
+
+    # https://www.value-at-risk.net/cholesky-factorization/
+    m = Matrix([[4, -2, -6], [-2, 10, 9], [-6, 9, 14]])
+    assert _is_positive_semidefinite_cholesky(m) == True
+    m = Matrix([[9, -3, 3], [-3, 2, 1], [3, 1, 6]])
+    assert _is_positive_semidefinite_cholesky(m) == True
+    m = Matrix([[4, -2, 2], [-2, 1, -1], [2, -1, 5]])
+    assert _is_positive_semidefinite_cholesky(m) == True
+    m = Matrix([[1, 2, -1], [2, 5, 1], [-1, 1, 9]])
+    assert _is_positive_semidefinite_cholesky(m) == False
+
+
+def test_issue_20582():
+    A = Matrix([
+        [5, -5, -3, 2, -7],
+        [-2, -5, 0, 2, 1],
+        [-2, -7, -5, -2, -6],
+        [7, 10, 3, 9, -2],
+        [4, -10, 3, -8, -4]
+    ])
+    # XXX Used dry-run test because arbitrary symbol that appears in
+    # CRootOf may not be unique.
+    assert A.eigenvects()
+
+def test_issue_19210():
+    t = Symbol('t')
+    H = Matrix([[3, 0, 0, 0], [0, 1 , 2, 0], [0, 2, 2, 0], [0, 0, 0, 4]])
+    A = (-I * H * t).jordan_form()
+    assert A == (Matrix([
+                    [0, 1,                  0,                0],
+                    [0, 0, -4/(-1 + sqrt(17)), 4/(1 + sqrt(17))],
+                    [0, 0,                  1,                1],
+                    [1, 0,                  0,                0]]), Matrix([
+                    [-4*I*t,      0,                         0,                         0],
+                    [     0, -3*I*t,                         0,                         0],
+                    [     0,      0, t*(-3*I/2 + sqrt(17)*I/2),                         0],
+                    [     0,      0,                         0, t*(-sqrt(17)*I/2 - 3*I/2)]]))
+
+
+def test_issue_20275():
+    # XXX We use complex expansions because complex exponentials are not
+    # recognized by polys.domains
+    A = DFT(3).as_explicit().expand(complex=True)
+    eigenvects = A.eigenvects()
+    assert eigenvects[0] == (
+        -1, 1,
+        [Matrix([[1 - sqrt(3)], [1], [1]])]
+    )
+    assert eigenvects[1] == (
+        1, 1,
+        [Matrix([[1 + sqrt(3)], [1], [1]])]
+    )
+    assert eigenvects[2] == (
+        -I, 1,
+        [Matrix([[0], [-1], [1]])]
+    )
+
+    A = DFT(4).as_explicit().expand(complex=True)
+    eigenvects = A.eigenvects()
+    assert eigenvects[0] == (
+        -1, 1,
+        [Matrix([[-1], [1], [1], [1]])]
+    )
+    assert eigenvects[1] == (
+        1, 2,
+        [Matrix([[1], [0], [1], [0]]), Matrix([[2], [1], [0], [1]])]
+    )
+    assert eigenvects[2] == (
+        -I, 1,
+        [Matrix([[0], [-1], [0], [1]])]
+    )
+
+    # XXX We skip test for some parts of eigenvectors which are very
+    # complicated and fragile under expression tree changes
+    A = DFT(5).as_explicit().expand(complex=True)
+    eigenvects = A.eigenvects()
+    assert eigenvects[0] == (
+        -1, 1,
+        [Matrix([[1 - sqrt(5)], [1], [1], [1], [1]])]
+    )
+    assert eigenvects[1] == (
+        1, 2,
+        [Matrix([[S(1)/2 + sqrt(5)/2], [0], [1], [1], [0]]),
+         Matrix([[S(1)/2 + sqrt(5)/2], [1], [0], [0], [1]])]
+    )
+
+
+def test_issue_20752():
+    b = symbols('b', nonzero=True)
+    m = Matrix([[0, 0, 0], [0, b, 0], [0, 0, b]])
+    assert m.is_positive_semidefinite is None
+
+
+def test_issue_25282():
+    dd = sd = [0] * 11 + [1]
+    ds = [2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]
+    ss = ds.copy()
+    ss[8] = 2
+
+    def rotate(x, i):
+        return x[i:] + x[:i]
+
+    mat = []
+    for i in range(12):
+        mat.append(rotate(ss, i) + rotate(sd, i))
+    for i in range(12):
+        mat.append(rotate(ds, i) + rotate(dd, i))
+
+    assert sum(Matrix(mat).eigenvals().values()) == 24
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_graph.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_graph.py
new file mode 100644
index 0000000000000000000000000000000000000000..0bf3c819a9477387f53560a034d7949fd76a654f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_graph.py
@@ -0,0 +1,108 @@
+from sympy.combinatorics import Permutation
+from sympy.core.symbol import symbols
+from sympy.matrices import Matrix
+from sympy.matrices.expressions import (
+    PermutationMatrix, BlockDiagMatrix, BlockMatrix)
+
+
+def test_connected_components():
+    a, b, c, d, e, f, g, h, i, j, k, l, m = symbols('a:m')
+
+    M = Matrix([
+        [a, 0, 0, 0, b, 0, 0, 0, 0, 0, c, 0, 0],
+        [0, d, 0, 0, 0, e, 0, 0, 0, 0, 0, f, 0],
+        [0, 0, g, 0, 0, 0, h, 0, 0, 0, 0, 0, i],
+        [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+        [m, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
+        [0, m, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
+        [0, 0, m, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
+        [j, 0, 0, 0, k, 0, 0, 1, 0, 0, l, 0, 0],
+        [0, j, 0, 0, 0, k, 0, 0, 1, 0, 0, l, 0],
+        [0, 0, j, 0, 0, 0, k, 0, 0, 1, 0, 0, l],
+        [0, 0, 0, 0, d, 0, 0, 0, 0, 0, 1, 0, 0],
+        [0, 0, 0, 0, 0, d, 0, 0, 0, 0, 0, 1, 0],
+        [0, 0, 0, 0, 0, 0, d, 0, 0, 0, 0, 0, 1]])
+    cc = M.connected_components()
+    assert cc == [[0, 4, 7, 10], [1, 5, 8, 11], [2, 6, 9, 12], [3]]
+
+    P, B = M.connected_components_decomposition()
+    p = Permutation([0, 4, 7, 10, 1, 5, 8, 11, 2, 6, 9, 12, 3])
+    assert P == PermutationMatrix(p)
+
+    B0 = Matrix([
+        [a, b, 0, c],
+        [m, 1, 0, 0],
+        [j, k, 1, l],
+        [0, d, 0, 1]])
+    B1 = Matrix([
+        [d, e, 0, f],
+        [m, 1, 0, 0],
+        [j, k, 1, l],
+        [0, d, 0, 1]])
+    B2 = Matrix([
+        [g, h, 0, i],
+        [m, 1, 0, 0],
+        [j, k, 1, l],
+        [0, d, 0, 1]])
+    B3 = Matrix([[1]])
+    assert B == BlockDiagMatrix(B0, B1, B2, B3)
+
+
+def test_strongly_connected_components():
+    M = Matrix([
+        [11, 14, 10, 0, 15, 0],
+        [0, 44, 0, 0, 45, 0],
+        [1, 4, 0, 0, 5, 0],
+        [0, 0, 0, 22, 0, 23],
+        [0, 54, 0, 0, 55, 0],
+        [0, 0, 0, 32, 0, 33]])
+    scc = M.strongly_connected_components()
+    assert scc == [[1, 4], [0, 2], [3, 5]]
+
+    P, B = M.strongly_connected_components_decomposition()
+    p = Permutation([1, 4, 0, 2, 3, 5])
+    assert P == PermutationMatrix(p)
+    assert B == BlockMatrix([
+        [
+            Matrix([[44, 45], [54, 55]]),
+            Matrix.zeros(2, 2),
+            Matrix.zeros(2, 2)
+        ],
+        [
+            Matrix([[14, 15], [4, 5]]),
+            Matrix([[11, 10], [1, 0]]),
+            Matrix.zeros(2, 2)
+        ],
+        [
+            Matrix.zeros(2, 2),
+            Matrix.zeros(2, 2),
+            Matrix([[22, 23], [32, 33]])
+        ]
+    ])
+    P = P.as_explicit()
+    B = B.as_explicit()
+    assert P.T * B * P == M
+
+    P, B = M.strongly_connected_components_decomposition(lower=False)
+    p = Permutation([3, 5, 0, 2, 1, 4])
+    assert P == PermutationMatrix(p)
+    assert B == BlockMatrix([
+        [
+            Matrix([[22, 23], [32, 33]]),
+            Matrix.zeros(2, 2),
+            Matrix.zeros(2, 2)
+        ],
+        [
+            Matrix.zeros(2, 2),
+            Matrix([[11, 10], [1, 0]]),
+            Matrix([[14, 15], [4, 5]])
+        ],
+        [
+            Matrix.zeros(2, 2),
+            Matrix.zeros(2, 2),
+            Matrix([[44, 45], [54, 55]])
+        ]
+    ])
+    P = P.as_explicit()
+    B = B.as_explicit()
+    assert P.T * B * P == M
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_immutable.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_immutable.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b83c1f9fae7f83be9d5f7dd4b484781dc128faf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_immutable.py
@@ -0,0 +1,136 @@
+from itertools import product
+
+from sympy.core.relational import (Equality, Unequality)
+from sympy.core.singleton import S
+from sympy.core.sympify import sympify
+from sympy.integrals.integrals import integrate
+from sympy.matrices.dense import (Matrix, eye, zeros)
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.matrices import SparseMatrix
+from sympy.matrices.immutable import \
+    ImmutableDenseMatrix, ImmutableSparseMatrix
+from sympy.abc import x, y
+from sympy.testing.pytest import raises
+
+IM = ImmutableDenseMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+ISM = ImmutableSparseMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+ieye = ImmutableDenseMatrix(eye(3))
+
+
+def test_creation():
+    assert IM.shape == ISM.shape == (3, 3)
+    assert IM[1, 2] == ISM[1, 2] == 6
+    assert IM[2, 2] == ISM[2, 2] == 9
+
+
+def test_immutability():
+    with raises(TypeError):
+        IM[2, 2] = 5
+    with raises(TypeError):
+        ISM[2, 2] = 5
+
+
+def test_slicing():
+    assert IM[1, :] == ImmutableDenseMatrix([[4, 5, 6]])
+    assert IM[:2, :2] == ImmutableDenseMatrix([[1, 2], [4, 5]])
+    assert ISM[1, :] == ImmutableSparseMatrix([[4, 5, 6]])
+    assert ISM[:2, :2] == ImmutableSparseMatrix([[1, 2], [4, 5]])
+
+
+def test_subs():
+    A = ImmutableMatrix([[1, 2], [3, 4]])
+    B = ImmutableMatrix([[1, 2], [x, 4]])
+    C = ImmutableMatrix([[-x, x*y], [-(x + y), y**2]])
+    assert B.subs(x, 3) == A
+    assert (x*B).subs(x, 3) == 3*A
+    assert (x*eye(2) + B).subs(x, 3) == 3*eye(2) + A
+    assert C.subs([[x, -1], [y, -2]]) == A
+    assert C.subs([(x, -1), (y, -2)]) == A
+    assert C.subs({x: -1, y: -2}) == A
+    assert C.subs({x: y - 1, y: x - 1}, simultaneous=True) == \
+        ImmutableMatrix([[1 - y, (x - 1)*(y - 1)], [2 - x - y, (x - 1)**2]])
+
+
+def test_as_immutable():
+    data = [[1, 2], [3, 4]]
+    X = Matrix(data)
+    assert sympify(X) == X.as_immutable() == ImmutableMatrix(data)
+
+    data = {(0, 0): 1, (0, 1): 2, (1, 0): 3, (1, 1): 4}
+    X = SparseMatrix(2, 2, data)
+    assert sympify(X) == X.as_immutable() == ImmutableSparseMatrix(2, 2, data)
+
+
+def test_function_return_types():
+    # Lets ensure that decompositions of immutable matrices remain immutable
+    # I.e. do MatrixBase methods return the correct class?
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    Y = ImmutableMatrix([[1], [0]])
+    q, r = X.QRdecomposition()
+    assert (type(q), type(r)) == (ImmutableMatrix, ImmutableMatrix)
+
+    assert type(X.LUsolve(Y)) == ImmutableMatrix
+    assert type(X.QRsolve(Y)) == ImmutableMatrix
+
+    X = ImmutableMatrix([[5, 2], [2, 7]])
+    assert X.T == X
+    assert X.is_symmetric
+    assert type(X.cholesky()) == ImmutableMatrix
+    L, D = X.LDLdecomposition()
+    assert (type(L), type(D)) == (ImmutableMatrix, ImmutableMatrix)
+
+    X = ImmutableMatrix([[1, 2], [2, 1]])
+    assert X.is_diagonalizable()
+    assert X.det() == -3
+    assert X.norm(2) == 3
+
+    assert type(X.eigenvects()[0][2][0]) == ImmutableMatrix
+
+    assert type(zeros(3, 3).as_immutable().nullspace()[0]) == ImmutableMatrix
+
+    X = ImmutableMatrix([[1, 0], [2, 1]])
+    assert type(X.lower_triangular_solve(Y)) == ImmutableMatrix
+    assert type(X.T.upper_triangular_solve(Y)) == ImmutableMatrix
+
+    assert type(X.minor_submatrix(0, 0)) == ImmutableMatrix
+
+# issue 6279
+# https://github.com/sympy/sympy/issues/6279
+# Test that Immutable _op_ Immutable => Immutable and not MatExpr
+
+
+def test_immutable_evaluation():
+    X = ImmutableMatrix(eye(3))
+    A = ImmutableMatrix(3, 3, range(9))
+    assert isinstance(X + A, ImmutableMatrix)
+    assert isinstance(X * A, ImmutableMatrix)
+    assert isinstance(X * 2, ImmutableMatrix)
+    assert isinstance(2 * X, ImmutableMatrix)
+    assert isinstance(A**2, ImmutableMatrix)
+
+
+def test_deterimant():
+    assert ImmutableMatrix(4, 4, lambda i, j: i + j).det() == 0
+
+
+def test_Equality():
+    assert Equality(IM, IM) is S.true
+    assert Unequality(IM, IM) is S.false
+    assert Equality(IM, IM.subs(1, 2)) is S.false
+    assert Unequality(IM, IM.subs(1, 2)) is S.true
+    assert Equality(IM, 2) is S.false
+    assert Unequality(IM, 2) is S.true
+    M = ImmutableMatrix([x, y])
+    assert Equality(M, IM) is S.false
+    assert Unequality(M, IM) is S.true
+    assert Equality(M, M.subs(x, 2)).subs(x, 2) is S.true
+    assert Unequality(M, M.subs(x, 2)).subs(x, 2) is S.false
+    assert Equality(M, M.subs(x, 2)).subs(x, 3) is S.false
+    assert Unequality(M, M.subs(x, 2)).subs(x, 3) is S.true
+
+
+def test_integrate():
+    intIM = integrate(IM, x)
+    assert intIM.shape == IM.shape
+    assert all(intIM[i, j] == (1 + j + 3*i)*x for i, j in
+                product(range(3), range(3)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_interactions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_interactions.py
new file mode 100644
index 0000000000000000000000000000000000000000..f4fc3268368e8dd632fc0df187d57ea5e845120c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_interactions.py
@@ -0,0 +1,77 @@
+"""
+We have a few different kind of Matrices
+Matrix, ImmutableMatrix, MatrixExpr
+
+Here we test the extent to which they cooperate
+"""
+
+from sympy.core.symbol import symbols
+from sympy.matrices import (Matrix, MatrixSymbol, eye, Identity,
+        ImmutableMatrix)
+from sympy.matrices.expressions import MatrixExpr, MatAdd
+from sympy.matrices.matrixbase import classof
+from sympy.testing.pytest import raises
+
+SM = MatrixSymbol('X', 3, 3)
+SV = MatrixSymbol('v', 3, 1)
+MM = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+IM = ImmutableMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+meye = eye(3)
+imeye = ImmutableMatrix(eye(3))
+ideye = Identity(3)
+a, b, c = symbols('a,b,c')
+
+
+def test_IM_MM():
+    assert isinstance(MM + IM, ImmutableMatrix)
+    assert isinstance(IM + MM, ImmutableMatrix)
+    assert isinstance(2*IM + MM, ImmutableMatrix)
+    assert MM.equals(IM)
+
+
+def test_ME_MM():
+    assert isinstance(Identity(3) + MM, MatrixExpr)
+    assert isinstance(SM + MM, MatAdd)
+    assert isinstance(MM + SM, MatAdd)
+    assert (Identity(3) + MM)[1, 1] == 6
+
+
+def test_equality():
+    a, b, c = Identity(3), eye(3), ImmutableMatrix(eye(3))
+    for x in [a, b, c]:
+        for y in [a, b, c]:
+            assert x.equals(y)
+
+
+def test_matrix_symbol_MM():
+    X = MatrixSymbol('X', 3, 3)
+    Y = eye(3) + X
+    assert Y[1, 1] == 1 + X[1, 1]
+
+
+def test_matrix_symbol_vector_matrix_multiplication():
+    A = MM * SV
+    B = IM * SV
+    assert A == B
+    C = (SV.T * MM.T).T
+    assert B == C
+    D = (SV.T * IM.T).T
+    assert C == D
+
+
+def test_indexing_interactions():
+    assert (a * IM)[1, 1] == 5*a
+    assert (SM + IM)[1, 1] == SM[1, 1] + IM[1, 1]
+    assert (SM * IM)[1, 1] == SM[1, 0]*IM[0, 1] + SM[1, 1]*IM[1, 1] + \
+        SM[1, 2]*IM[2, 1]
+
+
+def test_classof():
+    A = Matrix(3, 3, range(9))
+    B = ImmutableMatrix(3, 3, range(9))
+    C = MatrixSymbol('C', 3, 3)
+    assert classof(A, A) == Matrix
+    assert classof(B, B) == ImmutableMatrix
+    assert classof(A, B) == ImmutableMatrix
+    assert classof(B, A) == ImmutableMatrix
+    raises(TypeError, lambda: classof(A, C))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..d9d97341de570e078d652dddce58fb8f5cb99e43
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_matrices.py
@@ -0,0 +1,3487 @@
+#
+# Code for testing deprecated matrix classes. New test code should not be added
+# here. Instead, add it to test_matrixbase.py.
+#
+# This entire test module and the corresponding sympy/matrices/matrices.py
+# module will be removed in a future release.
+#
+import random
+import concurrent.futures
+from collections.abc import Hashable
+
+from sympy.core.add import Add
+from sympy.core.function import Function, diff, expand
+from sympy.core.numbers import (E, Float, I, Integer, Rational, nan, oo, pi)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt)
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.integrals.integrals import integrate
+from sympy.matrices.expressions.transpose import transpose
+from sympy.physics.quantum.operator import HermitianOperator, Operator, Dagger
+from sympy.polys.polytools import (Poly, PurePoly)
+from sympy.polys.rootoftools import RootOf
+from sympy.printing.str import sstr
+from sympy.sets.sets import FiniteSet
+from sympy.simplify.simplify import (signsimp, simplify)
+from sympy.simplify.trigsimp import trigsimp
+from sympy.matrices.exceptions import (ShapeError, MatrixError,
+    NonSquareMatrixError)
+from sympy.matrices.matrixbase import DeferredVector
+from sympy.matrices.determinant import _find_reasonable_pivot_naive
+from sympy.matrices.utilities import _simplify
+from sympy.matrices import (
+    GramSchmidt, ImmutableMatrix, ImmutableSparseMatrix, Matrix,
+    SparseMatrix, casoratian, diag, eye, hessian,
+    matrix_multiply_elementwise, ones, randMatrix, rot_axis1, rot_axis2,
+    rot_axis3, wronskian, zeros, MutableDenseMatrix, ImmutableDenseMatrix,
+    MatrixSymbol, dotprodsimp, rot_ccw_axis1, rot_ccw_axis2, rot_ccw_axis3)
+from sympy.matrices.utilities import _dotprodsimp_state
+from sympy.core import Tuple, Wild
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.utilities.iterables import flatten, capture, iterable
+from sympy.utilities.exceptions import ignore_warnings
+from sympy.testing.pytest import (raises, XFAIL, slow, skip, skip_under_pyodide,
+                                  warns_deprecated_sympy)
+from sympy.assumptions import Q
+from sympy.tensor.array import Array
+from sympy.tensor.array.array_derivatives import ArrayDerivative
+from sympy.matrices.expressions import MatPow
+from sympy.algebras import Quaternion
+
+from sympy import O
+
+from sympy.abc import a, b, c, d, x, y, z, t
+
+
+# don't re-order this list
+classes = (Matrix, SparseMatrix, ImmutableMatrix, ImmutableSparseMatrix)
+
+
+# Test the deprecated matrixmixins
+from sympy.matrices.common import _MinimalMatrix, _CastableMatrix
+from sympy.matrices.matrices import MatrixSubspaces, MatrixReductions
+
+
+with warns_deprecated_sympy():
+    class SubspaceOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixSubspaces):
+        pass
+
+
+with warns_deprecated_sympy():
+    class ReductionsOnlyMatrix(_MinimalMatrix, _CastableMatrix, MatrixReductions):
+        pass
+
+
+def eye_Reductions(n):
+    return ReductionsOnlyMatrix(n, n, lambda i, j: int(i == j))
+
+
+def zeros_Reductions(n):
+    return ReductionsOnlyMatrix(n, n, lambda i, j: 0)
+
+
+def test_args():
+    for n, cls in enumerate(classes):
+        m = cls.zeros(3, 2)
+        # all should give back the same type of arguments, e.g. ints for shape
+        assert m.shape == (3, 2) and all(type(i) is int for i in m.shape)
+        assert m.rows == 3 and type(m.rows) is int
+        assert m.cols == 2 and type(m.cols) is int
+        if not n % 2:
+            assert type(m.flat()) in (list, tuple, Tuple)
+        else:
+            assert type(m.todok()) is dict
+
+
+def test_deprecated_mat_smat():
+    for cls in Matrix, ImmutableMatrix:
+        m = cls.zeros(3, 2)
+        with warns_deprecated_sympy():
+            mat = m._mat
+        assert mat == m.flat()
+    for cls in SparseMatrix, ImmutableSparseMatrix:
+        m = cls.zeros(3, 2)
+        with warns_deprecated_sympy():
+            smat = m._smat
+        assert smat == m.todok()
+
+
+def test_division():
+    v = Matrix(1, 2, [x, y])
+    assert v/z == Matrix(1, 2, [x/z, y/z])
+
+
+def test_sum():
+    m = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
+    assert m + m == Matrix([[2, 4, 6], [2*x, 2*y, 2*x], [4*y, -100, 2*z*x]])
+    n = Matrix(1, 2, [1, 2])
+    raises(ShapeError, lambda: m + n)
+
+def test_abs():
+    m = Matrix(1, 2, [-3, x])
+    n = Matrix(1, 2, [3, Abs(x)])
+    assert abs(m) == n
+
+def test_addition():
+    a = Matrix((
+        (1, 2),
+        (3, 1),
+    ))
+
+    b = Matrix((
+        (1, 2),
+        (3, 0),
+    ))
+
+    assert a + b == a.add(b) == Matrix([[2, 4], [6, 1]])
+
+
+def test_fancy_index_matrix():
+    for M in (Matrix, SparseMatrix):
+        a = M(3, 3, range(9))
+        assert a == a[:, :]
+        assert a[1, :] == Matrix(1, 3, [3, 4, 5])
+        assert a[:, 1] == Matrix([1, 4, 7])
+        assert a[[0, 1], :] == Matrix([[0, 1, 2], [3, 4, 5]])
+        assert a[[0, 1], 2] == a[[0, 1], [2]]
+        assert a[2, [0, 1]] == a[[2], [0, 1]]
+        assert a[:, [0, 1]] == Matrix([[0, 1], [3, 4], [6, 7]])
+        assert a[0, 0] == 0
+        assert a[0:2, :] == Matrix([[0, 1, 2], [3, 4, 5]])
+        assert a[:, 0:2] == Matrix([[0, 1], [3, 4], [6, 7]])
+        assert a[::2, 1] == a[[0, 2], 1]
+        assert a[1, ::2] == a[1, [0, 2]]
+        a = M(3, 3, range(9))
+        assert a[[0, 2, 1, 2, 1], :] == Matrix([
+            [0, 1, 2],
+            [6, 7, 8],
+            [3, 4, 5],
+            [6, 7, 8],
+            [3, 4, 5]])
+        assert a[:, [0,2,1,2,1]] == Matrix([
+            [0, 2, 1, 2, 1],
+            [3, 5, 4, 5, 4],
+            [6, 8, 7, 8, 7]])
+
+    a = SparseMatrix.zeros(3)
+    a[1, 2] = 2
+    a[0, 1] = 3
+    a[2, 0] = 4
+    assert a.extract([1, 1], [2]) == Matrix([
+    [2],
+    [2]])
+    assert a.extract([1, 0], [2, 2, 2]) == Matrix([
+    [2, 2, 2],
+    [0, 0, 0]])
+    assert a.extract([1, 0, 1, 2], [2, 0, 1, 0]) == Matrix([
+        [2, 0, 0, 0],
+        [0, 0, 3, 0],
+        [2, 0, 0, 0],
+        [0, 4, 0, 4]])
+
+
+def test_multiplication():
+    a = Matrix((
+        (1, 2),
+        (3, 1),
+        (0, 6),
+    ))
+
+    b = Matrix((
+        (1, 2),
+        (3, 0),
+    ))
+
+    c = a*b
+    assert c[0, 0] == 7
+    assert c[0, 1] == 2
+    assert c[1, 0] == 6
+    assert c[1, 1] == 6
+    assert c[2, 0] == 18
+    assert c[2, 1] == 0
+
+    try:
+        eval('c = a @ b')
+    except SyntaxError:
+        pass
+    else:
+        assert c[0, 0] == 7
+        assert c[0, 1] == 2
+        assert c[1, 0] == 6
+        assert c[1, 1] == 6
+        assert c[2, 0] == 18
+        assert c[2, 1] == 0
+
+    h = matrix_multiply_elementwise(a, c)
+    assert h == a.multiply_elementwise(c)
+    assert h[0, 0] == 7
+    assert h[0, 1] == 4
+    assert h[1, 0] == 18
+    assert h[1, 1] == 6
+    assert h[2, 0] == 0
+    assert h[2, 1] == 0
+    raises(ShapeError, lambda: matrix_multiply_elementwise(a, b))
+
+    c = b * Symbol("x")
+    assert isinstance(c, Matrix)
+    assert c[0, 0] == x
+    assert c[0, 1] == 2*x
+    assert c[1, 0] == 3*x
+    assert c[1, 1] == 0
+
+    c2 = x * b
+    assert c == c2
+
+    c = 5 * b
+    assert isinstance(c, Matrix)
+    assert c[0, 0] == 5
+    assert c[0, 1] == 2*5
+    assert c[1, 0] == 3*5
+    assert c[1, 1] == 0
+
+    try:
+        eval('c = 5 @ b')
+    except SyntaxError:
+        pass
+    else:
+        assert isinstance(c, Matrix)
+        assert c[0, 0] == 5
+        assert c[0, 1] == 2*5
+        assert c[1, 0] == 3*5
+        assert c[1, 1] == 0
+
+
+def test_multiplication_inf_zero():
+
+    M = Matrix([[oo, 0], [0, oo]])
+    assert M ** 2 == M
+
+    M = Matrix([[oo, oo], [0, 0]])
+    assert M ** 2 == Matrix([[nan, nan], [nan, nan]])
+
+    A = Matrix([
+        [0, 0, 0, -S(1)/2],
+        [0, 1, 0, 0],
+        [0, 0, 1, 0],
+        [-S(1)/2, 0, 0, 0]])
+
+    B = Matrix([
+        [pi*x**2, 0, pi*b*x**4/8 + pi*a*x**4/8 + O(x**5), pi*x**4/2 + pi*b**2*x**6/32 + pi*a*b*x**6/48 + pi*a**2*x**6/32 + O(x**7)],
+        [0, pi*x**4/4, O(x**6), O(x**8)],
+        [pi*b*x**4/8 + pi*a*x**4/8 + O(x**5), O(x**6), pi*b**2*x**6/32 + pi*a*b*x**6/48 + pi*a**2*x**6/32 + O(x**7), pi*b*x**6/12 + pi*a*x**6/12 + O(x**7)],
+        [pi*x**4/2 + pi*b**2*x**6/32 + pi*a*b*x**6/48 + pi*a**2*x**6/32 + O(x**7), O(x**8), pi*b*x**6/12 + pi*a*x**6/12 + O(x**7), pi*x**6/3 + 3*pi*b**2*x**8/64 + pi*a*b*x**8/32 + 3*pi*a**2*x**8/64 + O(x**9)]])
+
+    C = Matrix([
+    [-pi*x**4/4 - pi*b**2*x**6/64 - pi*a*b*x**6/96 - pi*a**2*x**6/64 + O(x**7),   O(x**8),                       -pi*b*x**6/24 - pi*a*x**6/24 + O(x**7), -pi*x**6/6 - 3*pi*b**2*x**8/128 - pi*a*b*x**8/64 - 3*pi*a**2*x**8/128 + O(x**9)],
+    [                                                                        0, pi*x**4/4,                                                      O(x**6),                                                                         O(x**8)],
+    [                                      pi*b*x**4/8 + pi*a*x**4/8 + O(x**5),   O(x**6), pi*b**2*x**6/32 + pi*a*b*x**6/48 + pi*a**2*x**6/32 + O(x**7),                                           pi*b*x**6/12 + pi*a*x**6/12 + O(x**7)],
+    [                                                               -pi*x**2/2,         0,                       -pi*b*x**4/16 - pi*a*x**4/16 + O(x**5),       -pi*x**4/4 - pi*b**2*x**6/64 - pi*a*b*x**6/96 - pi*a**2*x**6/64 + O(x**7)]])
+
+    C2 = Matrix(4, 4, lambda i, j: Add(*(A[i,k]*B[k,j] for k in range(4))))
+
+    assert A*B == C == C2
+
+
+def test_power():
+    raises(NonSquareMatrixError, lambda: Matrix((1, 2))**2)
+
+    R = Rational
+    A = Matrix([[2, 3], [4, 5]])
+    assert (A**-3)[:] == [R(-269)/8, R(153)/8, R(51)/2, R(-29)/2]
+    assert (A**5)[:] == [6140, 8097, 10796, 14237]
+    A = Matrix([[2, 1, 3], [4, 2, 4], [6, 12, 1]])
+    assert (A**3)[:] == [290, 262, 251, 448, 440, 368, 702, 954, 433]
+    assert A**0 == eye(3)
+    assert A**1 == A
+    assert (Matrix([[2]]) ** 100)[0, 0] == 2**100
+    assert eye(2)**10000000 == eye(2)
+    assert Matrix([[1, 2], [3, 4]])**Integer(2) == Matrix([[7, 10], [15, 22]])
+
+    A = Matrix([[33, 24], [48, 57]])
+    assert (A**S.Half)[:] == [5, 2, 4, 7]
+    A = Matrix([[0, 4], [-1, 5]])
+    assert (A**S.Half)**2 == A
+
+    assert Matrix([[1, 0], [1, 1]])**S.Half == Matrix([[1, 0], [S.Half, 1]])
+    assert Matrix([[1, 0], [1, 1]])**0.5 == Matrix([[1, 0], [0.5, 1]])
+    from sympy.abc import n
+    assert Matrix([[1, a], [0, 1]])**n == Matrix([[1, a*n], [0, 1]])
+    assert Matrix([[b, a], [0, b]])**n == Matrix([[b**n, a*b**(n-1)*n], [0, b**n]])
+    assert Matrix([
+        [a**n, a**(n - 1)*n, (a**n*n**2 - a**n*n)/(2*a**2)],
+        [   0,         a**n,                  a**(n - 1)*n],
+        [   0,            0,                          a**n]])
+    assert Matrix([[a, 1, 0], [0, a, 0], [0, 0, b]])**n == Matrix([
+        [a**n, a**(n-1)*n, 0],
+        [0, a**n, 0],
+        [0, 0, b**n]])
+
+    A = Matrix([[1, 0], [1, 7]])
+    assert A._matrix_pow_by_jordan_blocks(S(3)) == A._eval_pow_by_recursion(3)
+    A = Matrix([[2]])
+    assert A**10 == Matrix([[2**10]]) == A._matrix_pow_by_jordan_blocks(S(10)) == \
+        A._eval_pow_by_recursion(10)
+
+    # testing a matrix that cannot be jordan blocked issue 11766
+    m = Matrix([[3, 0, 0, 0, -3], [0, -3, -3, 0, 3], [0, 3, 0, 3, 0], [0, 0, 3, 0, 3], [3, 0, 0, 3, 0]])
+    raises(MatrixError, lambda: m._matrix_pow_by_jordan_blocks(S(10)))
+
+    # test issue 11964
+    raises(MatrixError, lambda: Matrix([[1, 1], [3, 3]])._matrix_pow_by_jordan_blocks(S(-10)))
+    A = Matrix([[0, 1, 0], [0, 0, 1], [0, 0, 0]])  # Nilpotent jordan block size 3
+    assert A**10.0 == Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+    raises(ValueError, lambda: A**2.1)
+    raises(ValueError, lambda: A**Rational(3, 2))
+    A = Matrix([[8, 1], [3, 2]])
+    assert A**10.0 == Matrix([[1760744107, 272388050], [817164150, 126415807]])
+    A = Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])  # Nilpotent jordan block size 1
+    assert A**10.0 == Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+    A = Matrix([[0, 1, 0], [0, 0, 1], [0, 0, 1]])  # Nilpotent jordan block size 2
+    assert A**10.0 == Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+    n = Symbol('n', integer=True)
+    assert isinstance(A**n, MatPow)
+    n = Symbol('n', integer=True, negative=True)
+    raises(ValueError, lambda: A**n)
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert A**n == Matrix([
+        [KroneckerDelta(0, n), KroneckerDelta(1, n), -KroneckerDelta(0, n) - KroneckerDelta(1, n) + 1],
+        [                   0, KroneckerDelta(0, n),                         1 - KroneckerDelta(0, n)],
+        [                   0,                    0,                                                1]])
+    assert A**(n + 2) == Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+    raises(ValueError, lambda: A**Rational(3, 2))
+    A = Matrix([[0, 0, 1], [3, 0, 1], [4, 3, 1]])
+    assert A**5.0 == Matrix([[168,  72,  89], [291, 144, 161], [572, 267, 329]])
+    assert A**5.0 == A**5
+    A = Matrix([[0, 1, 0],[-1, 0, 0],[0, 0, 0]])
+    n = Symbol("n")
+    An = A**n
+    assert An.subs(n, 2).doit() == A**2
+    raises(ValueError, lambda: An.subs(n, -2).doit())
+    assert An * An == A**(2*n)
+
+    # concretizing behavior for non-integer and complex powers
+    A = Matrix([[0,0,0],[0,0,0],[0,0,0]])
+    n = Symbol('n', integer=True, positive=True)
+    assert A**n == A
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert A**n == diag(0**n, 0**n, 0**n)
+    assert (A**n).subs(n, 0) == eye(3)
+    assert (A**n).subs(n, 1) == zeros(3)
+    A = Matrix ([[2,0,0],[0,2,0],[0,0,2]])
+    assert A**2.1 == diag (2**2.1, 2**2.1, 2**2.1)
+    assert A**I == diag (2**I, 2**I, 2**I)
+    A = Matrix([[0, 1, 0], [0, 0, 1], [0, 0, 1]])
+    raises(ValueError, lambda: A**2.1)
+    raises(ValueError, lambda: A**I)
+    A = Matrix([[S.Half, S.Half], [S.Half, S.Half]])
+    assert A**S.Half == A
+    A = Matrix([[1, 1],[3, 3]])
+    assert A**S.Half == Matrix ([[S.Half, S.Half], [3*S.Half, 3*S.Half]])
+
+
+def test_issue_17247_expression_blowup_1():
+    M = Matrix([[1+x, 1-x], [1-x, 1+x]])
+    with dotprodsimp(True):
+        assert M.exp().expand() == Matrix([
+            [ (exp(2*x) + exp(2))/2, (-exp(2*x) + exp(2))/2],
+            [(-exp(2*x) + exp(2))/2,  (exp(2*x) + exp(2))/2]])
+
+def test_issue_17247_expression_blowup_2():
+    M = Matrix([[1+x, 1-x], [1-x, 1+x]])
+    with dotprodsimp(True):
+        P, J = M.jordan_form ()
+        assert P*J*P.inv()
+
+def test_issue_17247_expression_blowup_3():
+    M = Matrix([[1+x, 1-x], [1-x, 1+x]])
+    with dotprodsimp(True):
+        assert M**100 == Matrix([
+            [633825300114114700748351602688*x**100 + 633825300114114700748351602688, 633825300114114700748351602688 - 633825300114114700748351602688*x**100],
+            [633825300114114700748351602688 - 633825300114114700748351602688*x**100, 633825300114114700748351602688*x**100 + 633825300114114700748351602688]])
+
+def test_issue_17247_expression_blowup_4():
+# This matrix takes extremely long on current master even with intermediate simplification so an abbreviated version is used. It is left here for test in case of future optimizations.
+#     M = Matrix(S('''[
+#         [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128,       3/64 + 13*I/64,         -23/32 - 59*I/256,      15/128 - 3*I/32,        19/256 + 551*I/1024],
+#         [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024,  119/128 + 143*I/128, -10879/2048 + 4343*I/4096,  129/256 - 549*I/512, 42533/16384 + 29103*I/8192],
+#         [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64,         -9/32 - I/16,        183/256 - 97*I/128,       3/64 + 13*I/64,          -23/32 - 59*I/256],
+#         [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512, -219/128 + 115*I/256,   6301/4096 - 6609*I/1024,  119/128 + 143*I/128,  -10879/2048 + 4343*I/4096],
+#         [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64,         1/4 - 5*I/16,          65/128 + 87*I/64,         -9/32 - I/16,         183/256 - 97*I/128],
+#         [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128,     85/256 - 33*I/16,      805/128 + 2415*I/512, -219/128 + 115*I/256,    6301/4096 - 6609*I/1024],
+#         [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16,            1/4 + I/2,          -129/64 - 9*I/64,         1/4 - 5*I/16,           65/128 + 87*I/64],
+#         [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128,     125/64 + 87*I/64,     -2063/256 + 541*I/128,     85/256 - 33*I/16,       805/128 + 2415*I/512],
+#         [             -4*I,            27/2 + 6*I,                -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,              1/2 - I,           9/4 + 55*I/16,                 -3/4,           45/32 - 37*I/16,            1/4 + I/2,           -129/64 - 9*I/64],
+#         [      1/4 + 5*I/2,       -23/8 - 57*I/16,      1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,       -5/8 - 39*I/16,     2473/256 + 137*I/64,    -149/64 + 49*I/32,     -177/128 - 1369*I/128,     125/64 + 87*I/64,      -2063/256 + 541*I/128],
+#         [               -4,               9 - 5*I,              -4*I,            27/2 + 6*I,                -2,         17/4 - 13*I/2,                1 + I,           -19/4 + 5*I/4,              1/2 - I,             9/4 + 55*I/16,                 -3/4,            45/32 - 37*I/16],
+#         [             -2*I,        119/8 + 29*I/4,       1/4 + 5*I/2,       -23/8 - 57*I/16,      1/4 + 13*I/4,    -825/64 - 147*I/32,             21/8 + I,      -537/64 + 143*I/16,       -5/8 - 39*I/16,       2473/256 + 137*I/64,    -149/64 + 49*I/32,      -177/128 - 1369*I/128]]'''))
+#     assert M**10 == Matrix([
+#         [    7*(-221393644768594642173548179825793834595 - 1861633166167425978847110897013541127952*I)/9671406556917033397649408,      15*(31670992489131684885307005100073928751695 + 10329090958303458811115024718207404523808*I)/77371252455336267181195264,   7*(-3710978679372178839237291049477017392703 + 1377706064483132637295566581525806894169*I)/19342813113834066795298816,            (9727707023582419994616144751727760051598 - 59261571067013123836477348473611225724433*I)/9671406556917033397649408,      (31896723509506857062605551443641668183707 + 54643444538699269118869436271152084599580*I)/38685626227668133590597632,       (-2024044860947539028275487595741003997397402 + 130959428791783397562960461903698670485863*I)/309485009821345068724781056,     3*(26190251453797590396533756519358368860907 - 27221191754180839338002754608545400941638*I)/77371252455336267181195264,      (1154643595139959842768960128434994698330461 + 3385496216250226964322872072260446072295634*I)/618970019642690137449562112,     3*(-31849347263064464698310044805285774295286 - 11877437776464148281991240541742691164309*I)/77371252455336267181195264,     (4661330392283532534549306589669150228040221 - 4171259766019818631067810706563064103956871*I)/1237940039285380274899124224,        (9598353794289061833850770474812760144506 + 358027153990999990968244906482319780943983*I)/309485009821345068724781056,     (-9755135335127734571547571921702373498554177 - 4837981372692695195747379349593041939686540*I)/2475880078570760549798248448],
+#         [(-379516731607474268954110071392894274962069 - 422272153179747548473724096872271700878296*I)/77371252455336267181195264, (41324748029613152354787280677832014263339501 - 12715121258662668420833935373453570749288074*I)/1237940039285380274899124224, (-339216903907423793947110742819264306542397 + 494174755147303922029979279454787373566517*I)/77371252455336267181195264, (-18121350839962855576667529908850640619878381 - 37413012454129786092962531597292531089199003*I)/1237940039285380274899124224, (2489661087330511608618880408199633556675926 + 1137821536550153872137379935240732287260863*I)/309485009821345068724781056, (-136644109701594123227587016790354220062972119 + 110130123468183660555391413889600443583585272*I)/4951760157141521099596496896, (1488043981274920070468141664150073426459593 - 9691968079933445130866371609614474474327650*I)/1237940039285380274899124224,  27*(4636797403026872518131756991410164760195942 + 3369103221138229204457272860484005850416533*I)/4951760157141521099596496896, (-8534279107365915284081669381642269800472363 + 2241118846262661434336333368511372725482742*I)/1237940039285380274899124224,  (60923350128174260992536531692058086830950875 - 263673488093551053385865699805250505661590126*I)/9903520314283042199192993792, (18520943561240714459282253753348921824172569 + 24846649186468656345966986622110971925703604*I)/4951760157141521099596496896,  (-232781130692604829085973604213529649638644431 + 35981505277760667933017117949103953338570617*I)/9903520314283042199192993792],
+#         [      (8742968295129404279528270438201520488950 + 3061473358639249112126847237482570858327*I)/4835703278458516698824704,      (-245657313712011778432792959787098074935273 + 253113767861878869678042729088355086740856*I)/38685626227668133590597632,      (1947031161734702327107371192008011621193 - 19462330079296259148177542369999791122762*I)/9671406556917033397649408,        (552856485625209001527688949522750288619217 + 392928441196156725372494335248099016686580*I)/77371252455336267181195264,      (-44542866621905323121630214897126343414629 + 3265340021421335059323962377647649632959*I)/19342813113834066795298816,          (136272594005759723105646069956434264218730 - 330975364731707309489523680957584684763587*I)/38685626227668133590597632,       (27392593965554149283318732469825168894401 + 75157071243800133880129376047131061115278*I)/38685626227668133590597632,      7*(-357821652913266734749960136017214096276154 - 45509144466378076475315751988405961498243*I)/309485009821345068724781056,       (104485001373574280824835174390219397141149 - 99041000529599568255829489765415726168162*I)/77371252455336267181195264,      (1198066993119982409323525798509037696321291 + 4249784165667887866939369628840569844519936*I)/618970019642690137449562112,       (-114985392587849953209115599084503853611014 - 52510376847189529234864487459476242883449*I)/77371252455336267181195264,      (6094620517051332877965959223269600650951573 - 4683469779240530439185019982269137976201163*I)/1237940039285380274899124224],
+#         [ (611292255597977285752123848828590587708323 - 216821743518546668382662964473055912169502*I)/77371252455336267181195264,  (-1144023204575811464652692396337616594307487 + 12295317806312398617498029126807758490062855*I)/309485009821345068724781056, (-374093027769390002505693378578475235158281 - 573533923565898290299607461660384634333639*I)/77371252455336267181195264,   (47405570632186659000138546955372796986832987 - 2837476058950808941605000274055970055096534*I)/1237940039285380274899124224,   (-571573207393621076306216726219753090535121 + 533381457185823100878764749236639320783831*I)/77371252455336267181195264,     (-7096548151856165056213543560958582513797519 - 24035731898756040059329175131592138642195366*I)/618970019642690137449562112,  (2396762128833271142000266170154694033849225 + 1448501087375679588770230529017516492953051*I)/309485009821345068724781056, (-150609293845161968447166237242456473262037053 + 92581148080922977153207018003184520294188436*I)/4951760157141521099596496896, 5*(270278244730804315149356082977618054486347 - 1997830155222496880429743815321662710091562*I)/1237940039285380274899124224,   (62978424789588828258068912690172109324360330 + 44803641177219298311493356929537007630129097*I)/2475880078570760549798248448, 19*(-451431106327656743945775812536216598712236 + 114924966793632084379437683991151177407937*I)/1237940039285380274899124224,   (63417747628891221594106738815256002143915995 - 261508229397507037136324178612212080871150958*I)/9903520314283042199192993792],
+#         [     (-2144231934021288786200752920446633703357 + 2305614436009705803670842248131563850246*I)/1208925819614629174706176,       (-90720949337459896266067589013987007078153 - 221951119475096403601562347412753844534569*I)/19342813113834066795298816,      (11590973613116630788176337262688659880376 + 6514520676308992726483494976339330626159*I)/4835703278458516698824704,      3*(-131776217149000326618649542018343107657237 + 79095042939612668486212006406818285287004*I)/38685626227668133590597632,       (10100577916793945997239221374025741184951 - 28631383488085522003281589065994018550748*I)/9671406556917033397649408,         67*(10090295594251078955008130473573667572549 + 10449901522697161049513326446427839676762*I)/77371252455336267181195264,       (-54270981296988368730689531355811033930513 - 3413683117592637309471893510944045467443*I)/19342813113834066795298816,         (440372322928679910536575560069973699181278 - 736603803202303189048085196176918214409081*I)/77371252455336267181195264,        (33220374714789391132887731139763250155295 + 92055083048787219934030779066298919603554*I)/38685626227668133590597632,      5*(-594638554579967244348856981610805281527116 - 82309245323128933521987392165716076704057*I)/309485009821345068724781056,       (128056368815300084550013708313312073721955 - 114619107488668120303579745393765245911404*I)/77371252455336267181195264,       21*(59839959255173222962789517794121843393573 + 241507883613676387255359616163487405826334*I)/618970019642690137449562112],
+#         [ (-13454485022325376674626653802541391955147 + 184471402121905621396582628515905949793486*I)/19342813113834066795298816,   (-6158730123400322562149780662133074862437105 - 3416173052604643794120262081623703514107476*I)/154742504910672534362390528,  (770558003844914708453618983120686116100419 - 127758381209767638635199674005029818518766*I)/77371252455336267181195264,   (-4693005771813492267479835161596671660631703 + 12703585094750991389845384539501921531449948*I)/309485009821345068724781056,   (-295028157441149027913545676461260860036601 - 841544569970643160358138082317324743450770*I)/77371252455336267181195264,     (56716442796929448856312202561538574275502893 + 7216818824772560379753073185990186711454778*I)/1237940039285380274899124224,  15*(-87061038932753366532685677510172566368387 + 61306141156647596310941396434445461895538*I)/154742504910672534362390528,    (-3455315109680781412178133042301025723909347 - 24969329563196972466388460746447646686670670*I)/618970019642690137449562112,   (2453418854160886481106557323699250865361849 + 1497886802326243014471854112161398141242514*I)/309485009821345068724781056, (-151343224544252091980004429001205664193082173 + 90471883264187337053549090899816228846836628*I)/4951760157141521099596496896,   (1652018205533026103358164026239417416432989 - 9959733619236515024261775397109724431400162*I)/1237940039285380274899124224,  3*(40676374242956907656984876692623172736522006 + 31023357083037817469535762230872667581366205*I)/4951760157141521099596496896],
+#         [     (-1226990509403328460274658603410696548387 - 4131739423109992672186585941938392788458*I)/1208925819614629174706176,         (162392818524418973411975140074368079662703 + 23706194236915374831230612374344230400704*I)/9671406556917033397649408,      (-3935678233089814180000602553655565621193 + 2283744757287145199688061892165659502483*I)/1208925819614629174706176,         (-2400210250844254483454290806930306285131 - 315571356806370996069052930302295432758205*I)/19342813113834066795298816,       (13365917938215281056563183751673390817910 + 15911483133819801118348625831132324863881*I)/4835703278458516698824704,        3*(-215950551370668982657516660700301003897855 + 51684341999223632631602864028309400489378*I)/38685626227668133590597632,        (20886089946811765149439844691320027184765 - 30806277083146786592790625980769214361844*I)/9671406556917033397649408,        (562180634592713285745940856221105667874855 + 1031543963988260765153550559766662245114916*I)/77371252455336267181195264,       (-65820625814810177122941758625652476012867 - 12429918324787060890804395323920477537595*I)/19342813113834066795298816,         (319147848192012911298771180196635859221089 - 402403304933906769233365689834404519960394*I)/38685626227668133590597632,        (23035615120921026080284733394359587955057 + 115351677687031786114651452775242461310624*I)/38685626227668133590597632,      (-3426830634881892756966440108592579264936130 - 1022954961164128745603407283836365128598559*I)/309485009821345068724781056],
+#         [ (-192574788060137531023716449082856117537757 - 69222967328876859586831013062387845780692*I)/19342813113834066795298816,     (2736383768828013152914815341491629299773262 - 2773252698016291897599353862072533475408743*I)/77371252455336267181195264,  (-23280005281223837717773057436155921656805 + 214784953368021840006305033048142888879224*I)/19342813113834066795298816,     (-3035247484028969580570400133318947903462326 - 2195168903335435855621328554626336958674325*I)/77371252455336267181195264,     (984552428291526892214541708637840971548653 - 64006622534521425620714598573494988589378*I)/77371252455336267181195264,      (-3070650452470333005276715136041262898509903 + 7286424705750810474140953092161794621989080*I)/154742504910672534362390528,    (-147848877109756404594659513386972921139270 - 416306113044186424749331418059456047650861*I)/38685626227668133590597632,    (55272118474097814260289392337160619494260781 + 7494019668394781211907115583302403519488058*I)/1237940039285380274899124224,     (-581537886583682322424771088996959213068864 + 542191617758465339135308203815256798407429*I)/77371252455336267181195264,    (-6422548983676355789975736799494791970390991 - 23524183982209004826464749309156698827737702*I)/618970019642690137449562112,     7*(180747195387024536886923192475064903482083 + 84352527693562434817771649853047924991804*I)/154742504910672534362390528, (-135485179036717001055310712747643466592387031 + 102346575226653028836678855697782273460527608*I)/4951760157141521099596496896],
+#         [        (3384238362616083147067025892852431152105 + 156724444932584900214919898954874618256*I)/604462909807314587353088,        (-59558300950677430189587207338385764871866 + 114427143574375271097298201388331237478857*I)/4835703278458516698824704,      (-1356835789870635633517710130971800616227 - 7023484098542340388800213478357340875410*I)/1208925819614629174706176,          (234884918567993750975181728413524549575881 + 79757294640629983786895695752733890213506*I)/9671406556917033397649408,        (-7632732774935120473359202657160313866419 + 2905452608512927560554702228553291839465*I)/1208925819614629174706176,           (52291747908702842344842889809762246649489 - 520996778817151392090736149644507525892649*I)/19342813113834066795298816,        (17472406829219127839967951180375981717322 + 23464704213841582137898905375041819568669*I)/4835703278458516698824704,        (-911026971811893092350229536132730760943307 + 150799318130900944080399439626714846752360*I)/38685626227668133590597632,         (26234457233977042811089020440646443590687 - 45650293039576452023692126463683727692890*I)/9671406556917033397649408,       3*(288348388717468992528382586652654351121357 + 454526517721403048270274049572136109264668*I)/77371252455336267181195264,        (-91583492367747094223295011999405657956347 - 12704691128268298435362255538069612411331*I)/19342813113834066795298816,          (411208730251327843849027957710164064354221 - 569898526380691606955496789378230959965898*I)/38685626227668133590597632],
+#         [    (27127513117071487872628354831658811211795 - 37765296987901990355760582016892124833857*I)/4835703278458516698824704,     (1741779916057680444272938534338833170625435 + 3083041729779495966997526404685535449810378*I)/77371252455336267181195264, 3*(-60642236251815783728374561836962709533401 - 24630301165439580049891518846174101510744*I)/19342813113834066795298816,      3*(445885207364591681637745678755008757483408 - 350948497734812895032502179455610024541643*I)/38685626227668133590597632,    (-47373295621391195484367368282471381775684 + 219122969294089357477027867028071400054973*I)/19342813113834066795298816,       (-2801565819673198722993348253876353741520438 - 2250142129822658548391697042460298703335701*I)/77371252455336267181195264,      (801448252275607253266997552356128790317119 - 50890367688077858227059515894356594900558*I)/77371252455336267181195264,    (-5082187758525931944557763799137987573501207 + 11610432359082071866576699236013484487676124*I)/309485009821345068724781056,     (-328925127096560623794883760398247685166830 - 643447969697471610060622160899409680422019*I)/77371252455336267181195264,    15*(2954944669454003684028194956846659916299765 + 33434406416888505837444969347824812608566*I)/1237940039285380274899124224,      (-415749104352001509942256567958449835766827 + 479330966144175743357171151440020955412219*I)/77371252455336267181195264,  3*(-4639987285852134369449873547637372282914255 - 11994411888966030153196659207284951579243273*I)/1237940039285380274899124224],
+#         [       (-478846096206269117345024348666145495601 + 1249092488629201351470551186322814883283*I)/302231454903657293676544,         (-17749319421930878799354766626365926894989 - 18264580106418628161818752318217357231971*I)/1208925819614629174706176,         (2801110795431528876849623279389579072819 + 363258850073786330770713557775566973248*I)/604462909807314587353088,          (-59053496693129013745775512127095650616252 + 78143588734197260279248498898321500167517*I)/4835703278458516698824704,         (-283186724922498212468162690097101115349 - 6443437753863179883794497936345437398276*I)/1208925819614629174706176,            (188799118826748909206887165661384998787543 + 84274736720556630026311383931055307398820*I)/9671406556917033397649408,         (-5482217151670072904078758141270295025989 + 1818284338672191024475557065444481298568*I)/1208925819614629174706176,          (56564463395350195513805521309731217952281 - 360208541416798112109946262159695452898431*I)/19342813113834066795298816,        11*(1259539805728870739006416869463689438068 + 1409136581547898074455004171305324917387*I)/4835703278458516698824704,       5*(-123701190701414554945251071190688818343325 + 30997157322590424677294553832111902279712*I)/38685626227668133590597632,          (16130917381301373033736295883982414239781 - 32752041297570919727145380131926943374516*I)/9671406556917033397649408,          (650301385108223834347093740500375498354925 + 899526407681131828596801223402866051809258*I)/77371252455336267181195264],
+#         [      (9011388245256140876590294262420614839483 + 8167917972423946282513000869327525382672*I)/1208925819614629174706176,       (-426393174084720190126376382194036323028924 + 180692224825757525982858693158209545430621*I)/9671406556917033397649408,     (24588556702197802674765733448108154175535 - 45091766022876486566421953254051868331066*I)/4835703278458516698824704,      (1872113939365285277373877183750416985089691 + 3030392393733212574744122057679633775773130*I)/77371252455336267181195264,    (-222173405538046189185754954524429864167549 - 75193157893478637039381059488387511299116*I)/19342813113834066795298816,        (2670821320766222522963689317316937579844558 - 2645837121493554383087981511645435472169191*I)/77371252455336267181195264,     5*(-2100110309556476773796963197283876204940 + 41957457246479840487980315496957337371937*I)/19342813113834066795298816,     (-5733743755499084165382383818991531258980593 - 3328949988392698205198574824396695027195732*I)/154742504910672534362390528,      (707827994365259025461378911159398206329247 - 265730616623227695108042528694302299777294*I)/77371252455336267181195264,    (-1442501604682933002895864804409322823788319 + 11504137805563265043376405214378288793343879*I)/309485009821345068724781056,         (-56130472299445561499538726459719629522285 - 61117552419727805035810982426639329818864*I)/9671406556917033397649408,    (39053692321126079849054272431599539429908717 - 10209127700342570953247177602860848130710666*I)/1237940039285380274899124224]])
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512],
+        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64],
+        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128],
+        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16],
+        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M**10 == Matrix(S('''[
+            [     7369525394972778926719607798014571861/604462909807314587353088 - 229284202061790301477392339912557559*I/151115727451828646838272,   -19704281515163975949388435612632058035/1208925819614629174706176 + 14319858347987648723768698170712102887*I/302231454903657293676544,      -3623281909451783042932142262164941211/604462909807314587353088 - 6039240602494288615094338643452320495*I/604462909807314587353088,    109260497799140408739847239685705357695/2417851639229258349412352 - 7427566006564572463236368211555511431*I/2417851639229258349412352, -16095803767674394244695716092817006641/2417851639229258349412352 + 10336681897356760057393429626719177583*I/1208925819614629174706176,    -42207883340488041844332828574359769743/2417851639229258349412352 - 182332262671671273188016400290188468499*I/4835703278458516698824704],
+            [50566491050825573392726324995779608259/1208925819614629174706176 - 90047007594468146222002432884052362145*I/2417851639229258349412352,  74273703462900000967697427843983822011/1208925819614629174706176 + 265947522682943571171988741842776095421*I/1208925819614629174706176, -116900341394390200556829767923360888429/2417851639229258349412352 - 53153263356679268823910621474478756845*I/2417851639229258349412352, 195407378023867871243426523048612490249/1208925819614629174706176 - 1242417915995360200584837585002906728929*I/9671406556917033397649408,   -863597594389821970177319682495878193/302231454903657293676544 + 476936100741548328800725360758734300481*I/9671406556917033397649408, -3154451590535653853562472176601754835575/19342813113834066795298816 - 232909875490506237386836489998407329215*I/2417851639229258349412352],
+            [   -1715444997702484578716037230949868543/302231454903657293676544 + 5009695651321306866158517287924120777*I/302231454903657293676544,     -30551582497996879620371947949342101301/604462909807314587353088 - 7632518367986526187139161303331519629*I/151115727451828646838272,           312680739924495153190604170938220575/18889465931478580854784 - 108664334509328818765959789219208459*I/75557863725914323419136,    -14693696966703036206178521686918865509/604462909807314587353088 + 72345386220900843930147151999899692401*I/1208925819614629174706176,  -8218872496728882299722894680635296519/1208925819614629174706176 - 16776782833358893712645864791807664983*I/1208925819614629174706176,      143237839169380078671242929143670635137/2417851639229258349412352 + 2883817094806115974748882735218469447*I/2417851639229258349412352],
+            [   3087979417831061365023111800749855987/151115727451828646838272 + 34441942370802869368851419102423997089*I/604462909807314587353088, -148309181940158040917731426845476175667/604462909807314587353088 - 263987151804109387844966835369350904919*I/9671406556917033397649408,   50259518594816377378747711930008883165/1208925819614629174706176 - 95713974916869240305450001443767979653*I/2417851639229258349412352,  153466447023875527996457943521467271119/2417851639229258349412352 + 517285524891117105834922278517084871349*I/2417851639229258349412352,  -29184653615412989036678939366291205575/604462909807314587353088 - 27551322282526322041080173287022121083*I/1208925819614629174706176,   196404220110085511863671393922447671649/1208925819614629174706176 - 1204712019400186021982272049902206202145*I/9671406556917033397649408],
+            [     -2632581805949645784625606590600098779/151115727451828646838272 - 589957435912868015140272627522612771*I/37778931862957161709568,     26727850893953715274702844733506310247/302231454903657293676544 - 10825791956782128799168209600694020481*I/302231454903657293676544,      -1036348763702366164044671908440791295/151115727451828646838272 + 3188624571414467767868303105288107375*I/151115727451828646838272,     -36814959939970644875593411585393242449/604462909807314587353088 - 18457555789119782404850043842902832647*I/302231454903657293676544,      12454491297984637815063964572803058647/604462909807314587353088 - 340489532842249733975074349495329171*I/302231454903657293676544,      -19547211751145597258386735573258916681/604462909807314587353088 + 87299583775782199663414539883938008933*I/1208925819614629174706176],
+            [  -40281994229560039213253423262678393183/604462909807314587353088 - 2939986850065527327299273003299736641*I/604462909807314587353088, 331940684638052085845743020267462794181/2417851639229258349412352 - 284574901963624403933361315517248458969*I/1208925819614629174706176,      6453843623051745485064693628073010961/302231454903657293676544 + 36062454107479732681350914931391590957*I/604462909807314587353088,  -147665869053634695632880753646441962067/604462909807314587353088 - 305987938660447291246597544085345123927*I/9671406556917033397649408,  107821369195275772166593879711259469423/2417851639229258349412352 - 11645185518211204108659001435013326687*I/302231454903657293676544,     64121228424717666402009446088588091619/1208925819614629174706176 + 265557133337095047883844369272389762133*I/1208925819614629174706176]]'''))
+
+def test_issue_17247_expression_blowup_5():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.charpoly('x') == PurePoly(x**6 + (-6 - 6*I)*x**5 + 36*I*x**4, x, domain='EX')
+
+def test_issue_17247_expression_blowup_6():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.det('bareiss') == 0
+
+def test_issue_17247_expression_blowup_7():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.det('berkowitz') == 0
+
+def test_issue_17247_expression_blowup_8():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.det('lu') == 0
+
+def test_issue_17247_expression_blowup_9():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.rref() == (Matrix([
+            [1, 0, -1, -2, -3, -4, -5, -6],
+            [0, 1,  2,  3,  4,  5,  6,  7],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0]]), (0, 1))
+
+def test_issue_17247_expression_blowup_10():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.cofactor(0, 0) == 0
+
+def test_issue_17247_expression_blowup_11():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.cofactor_matrix() == Matrix(6, 6, [0]*36)
+
+def test_issue_17247_expression_blowup_12():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.eigenvals() == {6: 1, 6*I: 1, 0: 4}
+
+def test_issue_17247_expression_blowup_13():
+    M = Matrix([
+        [    0, 1 - x, x + 1, 1 - x],
+        [1 - x, x + 1,     0, x + 1],
+        [    0, 1 - x, x + 1, 1 - x],
+        [    0,     0,     1 - x, 0]])
+
+    ev = M.eigenvects()
+    assert ev[0] == (0, 2, [Matrix([0, -1, 0, 1])])
+    assert ev[1][0] == x - sqrt(2)*(x - 1) + 1
+    assert ev[1][1] == 1
+    assert ev[1][2][0].expand(deep=False, numer=True) == Matrix([
+        [(-x + sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [-4*x/(x**2 - 2*x + 1) + (x + 1)*(x - sqrt(2)*(x - 1) + 1)/(x**2 - 2*x + 1)],
+        [(-x + sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [1]
+    ])
+
+    assert ev[2][0] == x + sqrt(2)*(x - 1) + 1
+    assert ev[2][1] == 1
+    assert ev[2][2][0].expand(deep=False, numer=True) == Matrix([
+        [(-x - sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [-4*x/(x**2 - 2*x + 1) + (x + 1)*(x + sqrt(2)*(x - 1) + 1)/(x**2 - 2*x + 1)],
+        [(-x - sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [1]
+    ])
+
+
+def test_issue_17247_expression_blowup_14():
+    M = Matrix(8, 8, ([1+x, 1-x]*4 + [1-x, 1+x]*4)*4)
+    with dotprodsimp(True):
+        assert M.echelon_form() == Matrix([
+            [x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x],
+            [    0,   4*x,     0,   4*x,     0,   4*x,     0,   4*x],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0]])
+
+def test_issue_17247_expression_blowup_15():
+    M = Matrix(8, 8, ([1+x, 1-x]*4 + [1-x, 1+x]*4)*4)
+    with dotprodsimp(True):
+        assert M.rowspace() == [Matrix([[x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x]]), Matrix([[0, 4*x, 0, 4*x, 0, 4*x, 0, 4*x]])]
+
+def test_issue_17247_expression_blowup_16():
+    M = Matrix(8, 8, ([1+x, 1-x]*4 + [1-x, 1+x]*4)*4)
+    with dotprodsimp(True):
+        assert M.columnspace() == [Matrix([[x + 1],[1 - x],[x + 1],[1 - x],[x + 1],[1 - x],[x + 1],[1 - x]]), Matrix([[1 - x],[x + 1],[1 - x],[x + 1],[1 - x],[x + 1],[1 - x],[x + 1]])]
+
+def test_issue_17247_expression_blowup_17():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.nullspace() == [
+            Matrix([[1],[-2],[1],[0],[0],[0],[0],[0]]),
+            Matrix([[2],[-3],[0],[1],[0],[0],[0],[0]]),
+            Matrix([[3],[-4],[0],[0],[1],[0],[0],[0]]),
+            Matrix([[4],[-5],[0],[0],[0],[1],[0],[0]]),
+            Matrix([[5],[-6],[0],[0],[0],[0],[1],[0]]),
+            Matrix([[6],[-7],[0],[0],[0],[0],[0],[1]])]
+
+def test_issue_17247_expression_blowup_18():
+    M = Matrix(6, 6, ([1+x, 1-x]*3 + [1-x, 1+x]*3)*3)
+    with dotprodsimp(True):
+        assert not M.is_nilpotent()
+
+def test_issue_17247_expression_blowup_19():
+    M = Matrix(S('''[
+        [             -3/4,                     0,         1/4 + I/2,                     0],
+        [                0, -177/128 - 1369*I/128,                 0, -2063/256 + 541*I/128],
+        [          1/2 - I,                     0,                 0,                     0],
+        [                0,                     0,                 0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert not M.is_diagonalizable()
+
+def test_issue_17247_expression_blowup_20():
+    M = Matrix([
+    [x + 1,  1 - x,      0,      0],
+    [1 - x,  x + 1,      0,  x + 1],
+    [    0,  1 - x,  x + 1,      0],
+    [    0,      0,      0,  x + 1]])
+    with dotprodsimp(True):
+        assert M.diagonalize() == (Matrix([
+            [1,  1, 0, (x + 1)/(x - 1)],
+            [1, -1, 0,               0],
+            [1,  1, 1,               0],
+            [0,  0, 0,               1]]),
+            Matrix([
+            [2,   0,     0,     0],
+            [0, 2*x,     0,     0],
+            [0,   0, x + 1,     0],
+            [0,   0,     0, x + 1]]))
+
+def test_issue_17247_expression_blowup_21():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='GE') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+def test_issue_17247_expression_blowup_22():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='LU') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+def test_issue_17247_expression_blowup_23():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='ADJ').expand() == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+def test_issue_17247_expression_blowup_24():
+    M = SparseMatrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='CH') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+def test_issue_17247_expression_blowup_25():
+    M = SparseMatrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='LDL') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+def test_issue_17247_expression_blowup_26():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024],
+        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64],
+        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512],
+        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64],
+        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128],
+        [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16],
+        [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.rank() == 4
+
+def test_issue_17247_expression_blowup_27():
+    M = Matrix([
+        [    0, 1 - x, x + 1, 1 - x],
+        [1 - x, x + 1,     0, x + 1],
+        [    0, 1 - x, x + 1, 1 - x],
+        [    0,     0,     1 - x, 0]])
+    with dotprodsimp(True):
+        P, J = M.jordan_form()
+        assert P.expand() == Matrix(S('''[
+            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
+            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
+            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
+            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]''')).expand()
+        assert J == Matrix(S('''[
+            [0, 1,                       0,                       0],
+            [0, 0,                       0,                       0],
+            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
+            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]]'''))
+
+def test_issue_17247_expression_blowup_28():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.singular_values() == S('''[
+            sqrt(14609315/131072 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
+            sqrt(14609315/131072 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
+            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2),
+            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2)]''')
+
+
+def test_issue_16823():
+    # This still needs to be fixed if not using dotprodsimp.
+    M = Matrix(S('''[
+        [1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I,15/128-3/32*I,19/256+551/1024*I],
+        [21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I,129/256-549/512*I,42533/16384+29103/8192*I],
+        [-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I],
+        [1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I],
+        [-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I],
+        [1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I],
+        [-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I],
+        [-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I],
+        [0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I],
+        [1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I],
+        [0,-4*I,0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I],
+        [0,1/4+1/2*I,1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I]]'''))
+    with dotprodsimp(True):
+        assert M.rank() == 8
+
+
+def test_issue_18531():
+    # solve_linear_system still needs fixing but the rref works.
+    M = Matrix([
+        [1, 1, 1, 1, 1, 0, 1, 0, 0],
+        [1 + sqrt(2), -1 + sqrt(2), 1 - sqrt(2), -sqrt(2) - 1, 1, 1, -1, 1, 1],
+        [-5 + 2*sqrt(2), -5 - 2*sqrt(2), -5 - 2*sqrt(2), -5 + 2*sqrt(2), -7, 2, -7, -2, 0],
+        [-3*sqrt(2) - 1, 1 - 3*sqrt(2), -1 + 3*sqrt(2), 1 + 3*sqrt(2), -7, -5, 7, -5, 3],
+        [7 - 4*sqrt(2), 4*sqrt(2) + 7, 4*sqrt(2) + 7, 7 - 4*sqrt(2), 7, -12, 7, 12, 0],
+        [-1 + 3*sqrt(2), 1 + 3*sqrt(2), -3*sqrt(2) - 1, 1 - 3*sqrt(2), 7, -5, -7, -5, 3],
+        [-3 + 2*sqrt(2), -3 - 2*sqrt(2), -3 - 2*sqrt(2), -3 + 2*sqrt(2), -1, 2, -1, -2, 0],
+        [1 - sqrt(2), -sqrt(2) - 1, 1 + sqrt(2), -1 + sqrt(2), -1, 1, 1, 1, 1]
+        ])
+    with dotprodsimp(True):
+        assert M.rref() == (Matrix([
+            [1, 0, 0, 0, 0, 0, 0, 0,  S(1)/2],
+            [0, 1, 0, 0, 0, 0, 0, 0, -S(1)/2],
+            [0, 0, 1, 0, 0, 0, 0, 0,  S(1)/2],
+            [0, 0, 0, 1, 0, 0, 0, 0, -S(1)/2],
+            [0, 0, 0, 0, 1, 0, 0, 0,    0],
+            [0, 0, 0, 0, 0, 1, 0, 0, -S(1)/2],
+            [0, 0, 0, 0, 0, 0, 1, 0,    0],
+            [0, 0, 0, 0, 0, 0, 0, 1, -S(1)/2]]), (0, 1, 2, 3, 4, 5, 6, 7))
+
+
+def test_creation():
+    raises(ValueError, lambda: Matrix(5, 5, range(20)))
+    raises(ValueError, lambda: Matrix(5, -1, []))
+    raises(IndexError, lambda: Matrix((1, 2))[2])
+    with raises(IndexError):
+        Matrix((1, 2))[3] = 5
+
+    assert Matrix() == Matrix([]) == Matrix(0, 0, [])
+    assert Matrix([[]]) == Matrix(1, 0, [])
+    assert Matrix([[], []]) == Matrix(2, 0, [])
+
+    # anything used to be allowed in a matrix
+    with warns_deprecated_sympy():
+        assert Matrix([[[1], (2,)]]).tolist() == [[[1], (2,)]]
+    with warns_deprecated_sympy():
+        assert Matrix([[[1], (2,)]]).T.tolist() == [[[1]], [(2,)]]
+    M = Matrix([[0]])
+    with warns_deprecated_sympy():
+        M[0, 0] = S.EmptySet
+
+    a = Matrix([[x, 0], [0, 0]])
+    m = a
+    assert m.cols == m.rows
+    assert m.cols == 2
+    assert m[:] == [x, 0, 0, 0]
+
+    b = Matrix(2, 2, [x, 0, 0, 0])
+    m = b
+    assert m.cols == m.rows
+    assert m.cols == 2
+    assert m[:] == [x, 0, 0, 0]
+
+    assert a == b
+
+    assert Matrix(b) == b
+
+    c23 = Matrix(2, 3, range(1, 7))
+    c13 = Matrix(1, 3, range(7, 10))
+    c = Matrix([c23, c13])
+    assert c.cols == 3
+    assert c.rows == 3
+    assert c[:] == [1, 2, 3, 4, 5, 6, 7, 8, 9]
+
+    assert Matrix(eye(2)) == eye(2)
+    assert ImmutableMatrix(ImmutableMatrix(eye(2))) == ImmutableMatrix(eye(2))
+    assert ImmutableMatrix(c) == c.as_immutable()
+    assert Matrix(ImmutableMatrix(c)) == ImmutableMatrix(c).as_mutable()
+
+    assert c is not Matrix(c)
+
+    dat = [[ones(3,2), ones(3,3)*2], [ones(2,3)*3, ones(2,2)*4]]
+    M = Matrix(dat)
+    assert M == Matrix([
+        [1, 1, 2, 2, 2],
+        [1, 1, 2, 2, 2],
+        [1, 1, 2, 2, 2],
+        [3, 3, 3, 4, 4],
+        [3, 3, 3, 4, 4]])
+    assert M.tolist() != dat
+    # keep block form if evaluate=False
+    assert Matrix(dat, evaluate=False).tolist() == dat
+    A = MatrixSymbol("A", 2, 2)
+    dat = [ones(2), A]
+    assert Matrix(dat) == Matrix([
+    [      1,       1],
+    [      1,       1],
+    [A[0, 0], A[0, 1]],
+    [A[1, 0], A[1, 1]]])
+    with warns_deprecated_sympy():
+        assert Matrix(dat, evaluate=False).tolist() == [[i] for i in dat]
+
+    # 0-dim tolerance
+    assert Matrix([ones(2), ones(0)]) == Matrix([ones(2)])
+    raises(ValueError, lambda: Matrix([ones(2), ones(0, 3)]))
+    raises(ValueError, lambda: Matrix([ones(2), ones(3, 0)]))
+
+    # mix of Matrix and iterable
+    M = Matrix([[1, 2], [3, 4]])
+    M2 = Matrix([M, (5, 6)])
+    assert M2 == Matrix([[1, 2], [3, 4], [5, 6]])
+
+
+def test_irregular_block():
+    assert Matrix.irregular(3, ones(2,1), ones(3,3)*2, ones(2,2)*3,
+        ones(1,1)*4, ones(2,2)*5, ones(1,2)*6, ones(1,2)*7) == Matrix([
+        [1, 2, 2, 2, 3, 3],
+        [1, 2, 2, 2, 3, 3],
+        [4, 2, 2, 2, 5, 5],
+        [6, 6, 7, 7, 5, 5]])
+
+
+def test_tolist():
+    lst = [[S.One, S.Half, x*y, S.Zero], [x, y, z, x**2], [y, -S.One, z*x, 3]]
+    m = Matrix(lst)
+    assert m.tolist() == lst
+
+
+def test_as_mutable():
+    assert zeros(0, 3).as_mutable() == zeros(0, 3)
+    assert zeros(0, 3).as_immutable() == ImmutableMatrix(zeros(0, 3))
+    assert zeros(3, 0).as_immutable() == ImmutableMatrix(zeros(3, 0))
+
+
+def test_slicing():
+    m0 = eye(4)
+    assert m0[:3, :3] == eye(3)
+    assert m0[2:4, 0:2] == zeros(2)
+
+    m1 = Matrix(3, 3, lambda i, j: i + j)
+    assert m1[0, :] == Matrix(1, 3, (0, 1, 2))
+    assert m1[1:3, 1] == Matrix(2, 1, (2, 3))
+
+    m2 = Matrix([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]])
+    assert m2[:, -1] == Matrix(4, 1, [3, 7, 11, 15])
+    assert m2[-2:, :] == Matrix([[8, 9, 10, 11], [12, 13, 14, 15]])
+
+
+def test_submatrix_assignment():
+    m = zeros(4)
+    m[2:4, 2:4] = eye(2)
+    assert m == Matrix(((0, 0, 0, 0),
+                        (0, 0, 0, 0),
+                        (0, 0, 1, 0),
+                        (0, 0, 0, 1)))
+    m[:2, :2] = eye(2)
+    assert m == eye(4)
+    m[:, 0] = Matrix(4, 1, (1, 2, 3, 4))
+    assert m == Matrix(((1, 0, 0, 0),
+                        (2, 1, 0, 0),
+                        (3, 0, 1, 0),
+                        (4, 0, 0, 1)))
+    m[:, :] = zeros(4)
+    assert m == zeros(4)
+    m[:, :] = [(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16)]
+    assert m == Matrix(((1, 2, 3, 4),
+                        (5, 6, 7, 8),
+                        (9, 10, 11, 12),
+                        (13, 14, 15, 16)))
+    m[:2, 0] = [0, 0]
+    assert m == Matrix(((0, 2, 3, 4),
+                        (0, 6, 7, 8),
+                        (9, 10, 11, 12),
+                        (13, 14, 15, 16)))
+
+
+def test_extract():
+    m = Matrix(4, 3, lambda i, j: i*3 + j)
+    assert m.extract([0, 1, 3], [0, 1]) == Matrix(3, 2, [0, 1, 3, 4, 9, 10])
+    assert m.extract([0, 3], [0, 0, 2]) == Matrix(2, 3, [0, 0, 2, 9, 9, 11])
+    assert m.extract(range(4), range(3)) == m
+    raises(IndexError, lambda: m.extract([4], [0]))
+    raises(IndexError, lambda: m.extract([0], [3]))
+
+
+def test_reshape():
+    m0 = eye(3)
+    assert m0.reshape(1, 9) == Matrix(1, 9, (1, 0, 0, 0, 1, 0, 0, 0, 1))
+    m1 = Matrix(3, 4, lambda i, j: i + j)
+    assert m1.reshape(
+        4, 3) == Matrix(((0, 1, 2), (3, 1, 2), (3, 4, 2), (3, 4, 5)))
+    assert m1.reshape(2, 6) == Matrix(((0, 1, 2, 3, 1, 2), (3, 4, 2, 3, 4, 5)))
+
+
+def test_applyfunc():
+    m0 = eye(3)
+    assert m0.applyfunc(lambda x: 2*x) == eye(3)*2
+    assert m0.applyfunc(lambda x: 0) == zeros(3)
+
+
+def test_expand():
+    m0 = Matrix([[x*(x + y), 2], [((x + y)*y)*x, x*(y + x*(x + y))]])
+    # Test if expand() returns a matrix
+    m1 = m0.expand()
+    assert m1 == Matrix(
+        [[x*y + x**2, 2], [x*y**2 + y*x**2, x*y + y*x**2 + x**3]])
+
+    a = Symbol('a', real=True)
+
+    assert Matrix([exp(I*a)]).expand(complex=True) == \
+        Matrix([cos(a) + I*sin(a)])
+
+    assert Matrix([[0, 1, 2], [0, 0, -1], [0, 0, 0]]).exp() == Matrix([
+        [1, 1, Rational(3, 2)],
+        [0, 1, -1],
+        [0, 0, 1]]
+    )
+
+def test_refine():
+    m0 = Matrix([[Abs(x)**2, sqrt(x**2)],
+                [sqrt(x**2)*Abs(y)**2, sqrt(y**2)*Abs(x)**2]])
+    m1 = m0.refine(Q.real(x) & Q.real(y))
+    assert m1 == Matrix([[x**2, Abs(x)], [y**2*Abs(x), x**2*Abs(y)]])
+
+    m1 = m0.refine(Q.positive(x) & Q.positive(y))
+    assert m1 == Matrix([[x**2, x], [x*y**2, x**2*y]])
+
+    m1 = m0.refine(Q.negative(x) & Q.negative(y))
+    assert m1 == Matrix([[x**2, -x], [-x*y**2, -x**2*y]])
+
+def test_random():
+    M = randMatrix(3, 3)
+    M = randMatrix(3, 3, seed=3)
+    assert M == randMatrix(3, 3, seed=3)
+
+    M = randMatrix(3, 4, 0, 150)
+    M = randMatrix(3, seed=4, symmetric=True)
+    assert M == randMatrix(3, seed=4, symmetric=True)
+
+    S = M.copy()
+    S.simplify()
+    assert S == M  # doesn't fail when elements are Numbers, not int
+
+    rng = random.Random(4)
+    assert M == randMatrix(3, symmetric=True, prng=rng)
+
+    # Ensure symmetry
+    for size in (10, 11): # Test odd and even
+        for percent in (100, 70, 30):
+            M = randMatrix(size, symmetric=True, percent=percent, prng=rng)
+            assert M == M.T
+
+    M = randMatrix(10, min=1, percent=70)
+    zero_count = 0
+    for i in range(M.shape[0]):
+        for j in range(M.shape[1]):
+            if M[i, j] == 0:
+                zero_count += 1
+    assert zero_count == 30
+
+def test_inverse():
+    A = eye(4)
+    assert A.inv() == eye(4)
+    assert A.inv(method="LU") == eye(4)
+    assert A.inv(method="ADJ") == eye(4)
+    assert A.inv(method="CH") == eye(4)
+    assert A.inv(method="LDL") == eye(4)
+    assert A.inv(method="QR") == eye(4)
+    A = Matrix([[2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    Ainv = A.inv()
+    assert A*Ainv == eye(3)
+    assert A.inv(method="LU") == Ainv
+    assert A.inv(method="ADJ") == Ainv
+    assert A.inv(method="CH") == Ainv
+    assert A.inv(method="LDL") == Ainv
+    assert A.inv(method="QR") == Ainv
+
+    AA = Matrix([[0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0],
+            [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0],
+            [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
+            [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0],
+            [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0],
+            [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1],
+            [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0],
+            [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1],
+            [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1],
+            [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0],
+            [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0],
+            [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0],
+            [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1],
+            [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0],
+            [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0],
+            [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0],
+            [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1],
+            [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1],
+            [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1],
+            [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+            [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1],
+            [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1],
+            [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0],
+            [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0],
+            [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]])
+    assert AA.inv(method="BLOCK") * AA == eye(AA.shape[0])
+    # test that immutability is not a problem
+    cls = ImmutableMatrix
+    m = cls([[48, 49, 31],
+             [ 9, 71, 94],
+             [59, 28, 65]])
+    assert all(type(m.inv(s)) is cls for s in 'GE ADJ LU CH LDL QR'.split())
+    cls = ImmutableSparseMatrix
+    m = cls([[48, 49, 31],
+             [ 9, 71, 94],
+             [59, 28, 65]])
+    assert all(type(m.inv(s)) is cls for s in 'GE ADJ LU CH LDL QR'.split())
+
+
+def test_jacobian_hessian():
+    L = Matrix(1, 2, [x**2*y, 2*y**2 + x*y])
+    syms = [x, y]
+    assert L.jacobian(syms) == Matrix([[2*x*y, x**2], [y, 4*y + x]])
+
+    L = Matrix(1, 2, [x, x**2*y**3])
+    assert L.jacobian(syms) == Matrix([[1, 0], [2*x*y**3, x**2*3*y**2]])
+
+    f = x**2*y
+    syms = [x, y]
+    assert hessian(f, syms) == Matrix([[2*y, 2*x], [2*x, 0]])
+
+    f = x**2*y**3
+    assert hessian(f, syms) == \
+        Matrix([[2*y**3, 6*x*y**2], [6*x*y**2, 6*x**2*y]])
+
+    f = z + x*y**2
+    g = x**2 + 2*y**3
+    ans = Matrix([[0,   2*y],
+                  [2*y, 2*x]])
+    assert ans == hessian(f, Matrix([x, y]))
+    assert ans == hessian(f, Matrix([x, y]).T)
+    assert hessian(f, (y, x), [g]) == Matrix([
+        [     0, 6*y**2, 2*x],
+        [6*y**2,    2*x, 2*y],
+        [   2*x,    2*y,   0]])
+
+
+def test_wronskian():
+    assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
+    assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
+    assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
+    assert wronskian([1, x, x**2], x) == 2
+    w1 = -6*exp(x)*sin(x)*x + 6*cos(x)*exp(x)*x**2 - 6*exp(x)*cos(x)*x - \
+        exp(x)*cos(x)*x**3 + exp(x)*sin(x)*x**3
+    assert wronskian([exp(x), cos(x), x**3], x).expand() == w1
+    assert wronskian([exp(x), cos(x), x**3], x, method='berkowitz').expand() \
+        == w1
+    w2 = -x**3*cos(x)**2 - x**3*sin(x)**2 - 6*x*cos(x)**2 - 6*x*sin(x)**2
+    assert wronskian([sin(x), cos(x), x**3], x).expand() == w2
+    assert wronskian([sin(x), cos(x), x**3], x, method='berkowitz').expand() \
+        == w2
+    assert wronskian([], x) == 1
+
+
+def test_subs():
+    assert Matrix([[1, x], [x, 4]]).subs(x, 5) == Matrix([[1, 5], [5, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).subs([[x, -1], [y, -2]]) == \
+        Matrix([[-1, 2], [-3, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).subs([(x, -1), (y, -2)]) == \
+        Matrix([[-1, 2], [-3, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).subs({x: -1, y: -2}) == \
+        Matrix([[-1, 2], [-3, 4]])
+    assert Matrix([x*y]).subs({x: y - 1, y: x - 1}, simultaneous=True) == \
+        Matrix([(x - 1)*(y - 1)])
+
+    for cls in classes:
+        assert Matrix([[2, 0], [0, 2]]) == cls.eye(2).subs(1, 2)
+
+def test_xreplace():
+    assert Matrix([[1, x], [x, 4]]).xreplace({x: 5}) == \
+        Matrix([[1, 5], [5, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).xreplace({x: -1, y: -2}) == \
+        Matrix([[-1, 2], [-3, 4]])
+    for cls in classes:
+        assert Matrix([[2, 0], [0, 2]]) == cls.eye(2).xreplace({1: 2})
+
+def test_simplify():
+    n = Symbol('n')
+    f = Function('f')
+
+    M = Matrix([[            1/x + 1/y,                 (x + x*y) / x  ],
+                [ (f(x) + y*f(x))/f(x), 2 * (1/n - cos(n * pi)/n) / pi ]])
+    M.simplify()
+    assert M == Matrix([[ (x + y)/(x * y),                        1 + y ],
+                        [           1 + y, 2*((1 - 1*cos(pi*n))/(pi*n)) ]])
+    eq = (1 + x)**2
+    M = Matrix([[eq]])
+    M.simplify()
+    assert M == Matrix([[eq]])
+    M.simplify(ratio=oo)
+    assert M == Matrix([[eq.simplify(ratio=oo)]])
+
+
+def test_transpose():
+    M = Matrix([[1, 2, 3, 4, 5, 6, 7, 8, 9, 0],
+                [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]])
+    assert M.T == Matrix( [ [1, 1],
+                            [2, 2],
+                            [3, 3],
+                            [4, 4],
+                            [5, 5],
+                            [6, 6],
+                            [7, 7],
+                            [8, 8],
+                            [9, 9],
+                            [0, 0] ])
+    assert M.T.T == M
+    assert M.T == M.transpose()
+
+
+def test_conjugate():
+    M = Matrix([[0, I, 5],
+                [1, 2, 0]])
+
+    assert M.T == Matrix([[0, 1],
+                          [I, 2],
+                          [5, 0]])
+
+    assert M.C == Matrix([[0, -I, 5],
+                          [1,  2, 0]])
+    assert M.C == M.conjugate()
+
+    assert M.H == M.T.C
+    assert M.H == Matrix([[ 0, 1],
+                          [-I, 2],
+                          [ 5, 0]])
+
+
+def test_conj_dirac():
+    raises(AttributeError, lambda: eye(3).D)
+
+    M = Matrix([[1, I, I, I],
+                [0, 1, I, I],
+                [0, 0, 1, I],
+                [0, 0, 0, 1]])
+
+    assert M.D == Matrix([[ 1,  0,  0,  0],
+                          [-I,  1,  0,  0],
+                          [-I, -I, -1,  0],
+                          [-I, -I,  I, -1]])
+
+
+def test_trace():
+    M = Matrix([[1, 0, 0],
+                [0, 5, 0],
+                [0, 0, 8]])
+    assert M.trace() == 14
+
+
+def test_shape():
+    M = Matrix([[x, 0, 0],
+                [0, y, 0]])
+    assert M.shape == (2, 3)
+
+
+def test_col_row_op():
+    M = Matrix([[x, 0, 0],
+                [0, y, 0]])
+    M.row_op(1, lambda r, j: r + j + 1)
+    assert M == Matrix([[x,     0, 0],
+                        [1, y + 2, 3]])
+
+    M.col_op(0, lambda c, j: c + y**j)
+    assert M == Matrix([[x + 1,     0, 0],
+                        [1 + y, y + 2, 3]])
+
+    # neither row nor slice give copies that allow the original matrix to
+    # be changed
+    assert M.row(0) == Matrix([[x + 1, 0, 0]])
+    r1 = M.row(0)
+    r1[0] = 42
+    assert M[0, 0] == x + 1
+    r1 = M[0, :-1]  # also testing negative slice
+    r1[0] = 42
+    assert M[0, 0] == x + 1
+    c1 = M.col(0)
+    assert c1 == Matrix([x + 1, 1 + y])
+    c1[0] = 0
+    assert M[0, 0] == x + 1
+    c1 = M[:, 0]
+    c1[0] = 42
+    assert M[0, 0] == x + 1
+
+
+def test_row_mult():
+    M = Matrix([[1,2,3],
+               [4,5,6]])
+    M.row_mult(1,3)
+    assert M[1,0] == 12
+    assert M[0,0] == 1
+    assert M[1,2] == 18
+
+
+def test_row_add():
+    M = Matrix([[1,2,3],
+               [4,5,6],
+               [1,1,1]])
+    M.row_add(2,0,5)
+    assert M[0,0] == 6
+    assert M[1,0] == 4
+    assert M[0,2] == 8
+
+
+def test_zip_row_op():
+    for cls in classes[:2]: # XXX: immutable matrices don't support row ops
+        M = cls.eye(3)
+        M.zip_row_op(1, 0, lambda v, u: v + 2*u)
+        assert M == cls([[1, 0, 0],
+                         [2, 1, 0],
+                         [0, 0, 1]])
+
+        M = cls.eye(3)*2
+        M[0, 1] = -1
+        M.zip_row_op(1, 0, lambda v, u: v + 2*u); M
+        assert M == cls([[2, -1, 0],
+                         [4,  0, 0],
+                         [0,  0, 2]])
+
+def test_issue_3950():
+    m = Matrix([1, 2, 3])
+    a = Matrix([1, 2, 3])
+    b = Matrix([2, 2, 3])
+    assert not (m in [])
+    assert not (m in [1])
+    assert m != 1
+    assert m == a
+    assert m != b
+
+
+def test_issue_3981():
+    class Index1:
+        def __index__(self):
+            return 1
+
+    class Index2:
+        def __index__(self):
+            return 2
+    index1 = Index1()
+    index2 = Index2()
+
+    m = Matrix([1, 2, 3])
+
+    assert m[index2] == 3
+
+    m[index2] = 5
+    assert m[2] == 5
+
+    m = Matrix([[1, 2, 3], [4, 5, 6]])
+    assert m[index1, index2] == 6
+    assert m[1, index2] == 6
+    assert m[index1, 2] == 6
+
+    m[index1, index2] = 4
+    assert m[1, 2] == 4
+    m[1, index2] = 6
+    assert m[1, 2] == 6
+    m[index1, 2] = 8
+    assert m[1, 2] == 8
+
+
+def test_evalf():
+    a = Matrix([sqrt(5), 6])
+    assert all(a.evalf()[i] == a[i].evalf() for i in range(2))
+    assert all(a.evalf(2)[i] == a[i].evalf(2) for i in range(2))
+    assert all(a.n(2)[i] == a[i].n(2) for i in range(2))
+
+
+def test_is_symbolic():
+    a = Matrix([[x, x], [x, x]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1, 2, 3, 4], [5, 6, 7, 8]])
+    assert a.is_symbolic() is False
+    a = Matrix([[1, 2, 3, 4], [5, 6, x, 8]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1, x, 3]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1, 2, 3]])
+    assert a.is_symbolic() is False
+    a = Matrix([[1], [x], [3]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1], [2], [3]])
+    assert a.is_symbolic() is False
+
+
+def test_is_upper():
+    a = Matrix([[1, 2, 3]])
+    assert a.is_upper is True
+    a = Matrix([[1], [2], [3]])
+    assert a.is_upper is False
+    a = zeros(4, 2)
+    assert a.is_upper is True
+
+
+def test_is_lower():
+    a = Matrix([[1, 2, 3]])
+    assert a.is_lower is False
+    a = Matrix([[1], [2], [3]])
+    assert a.is_lower is True
+
+
+def test_is_nilpotent():
+    a = Matrix(4, 4, [0, 2, 1, 6, 0, 0, 1, 2, 0, 0, 0, 3, 0, 0, 0, 0])
+    assert a.is_nilpotent()
+    a = Matrix([[1, 0], [0, 1]])
+    assert not a.is_nilpotent()
+    a = Matrix([])
+    assert a.is_nilpotent()
+
+
+def test_zeros_ones_fill():
+    n, m = 3, 5
+
+    a = zeros(n, m)
+    a.fill( 5 )
+
+    b = 5 * ones(n, m)
+
+    assert a == b
+    assert a.rows == b.rows == 3
+    assert a.cols == b.cols == 5
+    assert a.shape == b.shape == (3, 5)
+    assert zeros(2) == zeros(2, 2)
+    assert ones(2) == ones(2, 2)
+    assert zeros(2, 3) == Matrix(2, 3, [0]*6)
+    assert ones(2, 3) == Matrix(2, 3, [1]*6)
+
+    a.fill(0)
+    assert a == zeros(n, m)
+
+
+def test_empty_zeros():
+    a = zeros(0)
+    assert a == Matrix()
+    a = zeros(0, 2)
+    assert a.rows == 0
+    assert a.cols == 2
+    a = zeros(2, 0)
+    assert a.rows == 2
+    assert a.cols == 0
+
+
+def test_issue_3749():
+    a = Matrix([[x**2, x*y], [x*sin(y), x*cos(y)]])
+    assert a.diff(x) == Matrix([[2*x, y], [sin(y), cos(y)]])
+    assert Matrix([
+        [x, -x, x**2],
+        [exp(x), 1/x - exp(-x), x + 1/x]]).limit(x, oo) == \
+        Matrix([[oo, -oo, oo], [oo, 0, oo]])
+    assert Matrix([
+        [(exp(x) - 1)/x, 2*x + y*x, x**x ],
+        [1/x, abs(x), abs(sin(x + 1))]]).limit(x, 0) == \
+        Matrix([[1, 0, 1], [oo, 0, sin(1)]])
+    assert a.integrate(x) == Matrix([
+        [Rational(1, 3)*x**3, y*x**2/2],
+        [x**2*sin(y)/2, x**2*cos(y)/2]])
+
+
+def test_inv_iszerofunc():
+    A = eye(4)
+    A.col_swap(0, 1)
+    for method in "GE", "LU":
+        assert A.inv(method=method, iszerofunc=lambda x: x == 0) == \
+            A.inv(method="ADJ")
+
+
+def test_jacobian_metrics():
+    rho, phi = symbols("rho,phi")
+    X = Matrix([rho*cos(phi), rho*sin(phi)])
+    Y = Matrix([rho, phi])
+    J = X.jacobian(Y)
+    assert J == X.jacobian(Y.T)
+    assert J == (X.T).jacobian(Y)
+    assert J == (X.T).jacobian(Y.T)
+    g = J.T*eye(J.shape[0])*J
+    g = g.applyfunc(trigsimp)
+    assert g == Matrix([[1, 0], [0, rho**2]])
+
+
+def test_jacobian2():
+    rho, phi = symbols("rho,phi")
+    X = Matrix([rho*cos(phi), rho*sin(phi), rho**2])
+    Y = Matrix([rho, phi])
+    J = Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)],
+        [   2*rho,             0],
+    ])
+    assert X.jacobian(Y) == J
+
+
+def test_issue_4564():
+    X = Matrix([exp(x + y + z), exp(x + y + z), exp(x + y + z)])
+    Y = Matrix([x, y, z])
+    for i in range(1, 3):
+        for j in range(1, 3):
+            X_slice = X[:i, :]
+            Y_slice = Y[:j, :]
+            J = X_slice.jacobian(Y_slice)
+            assert J.rows == i
+            assert J.cols == j
+            for k in range(j):
+                assert J[:, k] == X_slice
+
+
+def test_nonvectorJacobian():
+    X = Matrix([[exp(x + y + z), exp(x + y + z)],
+                [exp(x + y + z), exp(x + y + z)]])
+    raises(TypeError, lambda: X.jacobian(Matrix([x, y, z])))
+    X = X[0, :]
+    Y = Matrix([[x, y], [x, z]])
+    raises(TypeError, lambda: X.jacobian(Y))
+    raises(TypeError, lambda: X.jacobian(Matrix([ [x, y], [x, z] ])))
+
+
+def test_vec():
+    m = Matrix([[1, 3], [2, 4]])
+    m_vec = m.vec()
+    assert m_vec.cols == 1
+    for i in range(4):
+        assert m_vec[i] == i + 1
+
+
+def test_vech():
+    m = Matrix([[1, 2], [2, 3]])
+    m_vech = m.vech()
+    assert m_vech.cols == 1
+    for i in range(3):
+        assert m_vech[i] == i + 1
+    m_vech = m.vech(diagonal=False)
+    assert m_vech[0] == 2
+
+    m = Matrix([[1, x*(x + y)], [y*x + x**2, 1]])
+    m_vech = m.vech(diagonal=False)
+    assert m_vech[0] == y*x + x**2
+
+    m = Matrix([[1, x*(x + y)], [y*x, 1]])
+    m_vech = m.vech(diagonal=False, check_symmetry=False)
+    assert m_vech[0] == y*x
+
+    raises(ShapeError, lambda: Matrix([[1, 3]]).vech())
+    raises(ValueError, lambda: Matrix([[1, 3], [2, 4]]).vech())
+    raises(ShapeError, lambda: Matrix([[1, 3]]).vech())
+    raises(ValueError, lambda: Matrix([[1, 3], [2, 4]]).vech())
+
+
+def test_diag():
+    # mostly tested in testcommonmatrix.py
+    assert diag([1, 2, 3]) == Matrix([1, 2, 3])
+    m = [1, 2, [3]]
+    raises(ValueError, lambda: diag(m))
+    assert diag(m, strict=False) == Matrix([1, 2, 3])
+
+
+def test_get_diag_blocks1():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    assert a.get_diag_blocks() == [a]
+    assert b.get_diag_blocks() == [b]
+    assert c.get_diag_blocks() == [c]
+
+
+def test_get_diag_blocks2():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    assert diag(a, b, b).get_diag_blocks() == [a, b, b]
+    assert diag(a, b, c).get_diag_blocks() == [a, b, c]
+    assert diag(a, c, b).get_diag_blocks() == [a, c, b]
+    assert diag(c, c, b).get_diag_blocks() == [c, c, b]
+
+
+def test_inv_block():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    A = diag(a, b, b)
+    assert A.inv(try_block_diag=True) == diag(a.inv(), b.inv(), b.inv())
+    A = diag(a, b, c)
+    assert A.inv(try_block_diag=True) == diag(a.inv(), b.inv(), c.inv())
+    A = diag(a, c, b)
+    assert A.inv(try_block_diag=True) == diag(a.inv(), c.inv(), b.inv())
+    A = diag(a, a, b, a, c, a)
+    assert A.inv(try_block_diag=True) == diag(
+        a.inv(), a.inv(), b.inv(), a.inv(), c.inv(), a.inv())
+    assert A.inv(try_block_diag=True, method="ADJ") == diag(
+        a.inv(method="ADJ"), a.inv(method="ADJ"), b.inv(method="ADJ"),
+        a.inv(method="ADJ"), c.inv(method="ADJ"), a.inv(method="ADJ"))
+
+
+def test_creation_args():
+    """
+    Check that matrix dimensions can be specified using any reasonable type
+    (see issue 4614).
+    """
+    raises(ValueError, lambda: zeros(3, -1))
+    raises(TypeError, lambda: zeros(1, 2, 3, 4))
+    assert zeros(int(3)) == zeros(3)
+    assert zeros(Integer(3)) == zeros(3)
+    raises(ValueError, lambda: zeros(3.))
+    assert eye(int(3)) == eye(3)
+    assert eye(Integer(3)) == eye(3)
+    raises(ValueError, lambda: eye(3.))
+    assert ones(int(3), Integer(4)) == ones(3, 4)
+    raises(TypeError, lambda: Matrix(5))
+    raises(TypeError, lambda: Matrix(1, 2))
+    raises(ValueError, lambda: Matrix([1, [2]]))
+
+
+def test_diagonal_symmetrical():
+    m = Matrix(2, 2, [0, 1, 1, 0])
+    assert not m.is_diagonal()
+    assert m.is_symmetric()
+    assert m.is_symmetric(simplify=False)
+
+    m = Matrix(2, 2, [1, 0, 0, 1])
+    assert m.is_diagonal()
+
+    m = diag(1, 2, 3)
+    assert m.is_diagonal()
+    assert m.is_symmetric()
+
+    m = Matrix(3, 3, [1, 0, 0, 0, 2, 0, 0, 0, 3])
+    assert m == diag(1, 2, 3)
+
+    m = Matrix(2, 3, zeros(2, 3))
+    assert not m.is_symmetric()
+    assert m.is_diagonal()
+
+    m = Matrix(((5, 0), (0, 6), (0, 0)))
+    assert m.is_diagonal()
+
+    m = Matrix(((5, 0, 0), (0, 6, 0)))
+    assert m.is_diagonal()
+
+    m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
+    assert m.is_symmetric()
+    assert not m.is_symmetric(simplify=False)
+    assert m.expand().is_symmetric(simplify=False)
+
+
+def test_diagonalization():
+    m = Matrix([[1, 2+I], [2-I, 3]])
+    assert m.is_diagonalizable()
+
+    m = Matrix(3, 2, [-3, 1, -3, 20, 3, 10])
+    assert not m.is_diagonalizable()
+    assert not m.is_symmetric()
+    raises(NonSquareMatrixError, lambda: m.diagonalize())
+
+    # diagonalizable
+    m = diag(1, 2, 3)
+    (P, D) = m.diagonalize()
+    assert P == eye(3)
+    assert D == m
+
+    m = Matrix(2, 2, [0, 1, 1, 0])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+
+    m = Matrix(2, 2, [1, 0, 0, 3])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+    assert P == eye(2)
+    assert D == m
+
+    m = Matrix(2, 2, [1, 1, 0, 0])
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+
+    m = Matrix(3, 3, [1, 2, 0, 0, 3, 0, 2, -4, 2])
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+    for i in P:
+        assert i.as_numer_denom()[1] == 1
+
+    m = Matrix(2, 2, [1, 0, 0, 0])
+    assert m.is_diagonal()
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+    assert P == Matrix([[0, 1], [1, 0]])
+
+    # diagonalizable, complex only
+    m = Matrix(2, 2, [0, 1, -1, 0])
+    assert not m.is_diagonalizable(True)
+    raises(MatrixError, lambda: m.diagonalize(True))
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+
+    # not diagonalizable
+    m = Matrix(2, 2, [0, 1, 0, 0])
+    assert not m.is_diagonalizable()
+    raises(MatrixError, lambda: m.diagonalize())
+
+    m = Matrix(3, 3, [-3, 1, -3, 20, 3, 10, 2, -2, 4])
+    assert not m.is_diagonalizable()
+    raises(MatrixError, lambda: m.diagonalize())
+
+    # symbolic
+    a, b, c, d = symbols('a b c d')
+    m = Matrix(2, 2, [a, c, c, b])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+
+
+def test_issue_15887():
+    # Mutable matrix should not use cache
+    a = MutableDenseMatrix([[0, 1], [1, 0]])
+    assert a.is_diagonalizable() is True
+    a[1, 0] = 0
+    assert a.is_diagonalizable() is False
+
+    a = MutableDenseMatrix([[0, 1], [1, 0]])
+    a.diagonalize()
+    a[1, 0] = 0
+    raises(MatrixError, lambda: a.diagonalize())
+
+
+def test_jordan_form():
+
+    m = Matrix(3, 2, [-3, 1, -3, 20, 3, 10])
+    raises(NonSquareMatrixError, lambda: m.jordan_form())
+
+    # diagonalizable
+    m = Matrix(3, 3, [7, -12, 6, 10, -19, 10, 12, -24, 13])
+    Jmust = Matrix(3, 3, [-1, 0, 0, 0, 1, 0, 0, 0, 1])
+    P, J = m.jordan_form()
+    assert Jmust == J
+    assert Jmust == m.diagonalize()[1]
+
+    # m = Matrix(3, 3, [0, 6, 3, 1, 3, 1, -2, 2, 1])
+    # m.jordan_form()  # very long
+    # m.jordan_form()  #
+
+    # diagonalizable, complex only
+
+    # Jordan cells
+    # complexity: one of eigenvalues is zero
+    m = Matrix(3, 3, [0, 1, 0, -4, 4, 0, -2, 1, 2])
+    # The blocks are ordered according to the value of their eigenvalues,
+    # in order to make the matrix compatible with .diagonalize()
+    Jmust = Matrix(3, 3, [2, 1, 0, 0, 2, 0, 0, 0, 2])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    # complexity: all of eigenvalues are equal
+    m = Matrix(3, 3, [2, 6, -15, 1, 1, -5, 1, 2, -6])
+    # Jmust = Matrix(3, 3, [-1, 0, 0, 0, -1, 1, 0, 0, -1])
+    # same here see 1456ff
+    Jmust = Matrix(3, 3, [-1, 1, 0, 0, -1, 0, 0, 0, -1])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    # complexity: two of eigenvalues are zero
+    m = Matrix(3, 3, [4, -5, 2, 5, -7, 3, 6, -9, 4])
+    Jmust = Matrix(3, 3, [0, 1, 0, 0, 0, 0, 0, 0, 1])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    m = Matrix(4, 4, [6, 5, -2, -3, -3, -1, 3, 3, 2, 1, -2, -3, -1, 1, 5, 5])
+    Jmust = Matrix(4, 4, [2, 1, 0, 0,
+                          0, 2, 0, 0,
+              0, 0, 2, 1,
+              0, 0, 0, 2]
+              )
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    m = Matrix(4, 4, [6, 2, -8, -6, -3, 2, 9, 6, 2, -2, -8, -6, -1, 0, 3, 4])
+    # Jmust = Matrix(4, 4, [2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, -2])
+    # same here see 1456ff
+    Jmust = Matrix(4, 4, [-2, 0, 0, 0,
+                           0, 2, 1, 0,
+                           0, 0, 2, 0,
+                           0, 0, 0, 2])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    m = Matrix(4, 4, [5, 4, 2, 1, 0, 1, -1, -1, -1, -1, 3, 0, 1, 1, -1, 2])
+    assert not m.is_diagonalizable()
+    Jmust = Matrix(4, 4, [1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 1, 0, 0, 0, 4])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    # checking for maximum precision to remain unchanged
+    m = Matrix([[Float('1.0', precision=110), Float('2.0', precision=110)],
+                [Float('3.14159265358979323846264338327', precision=110), Float('4.0', precision=110)]])
+    P, J = m.jordan_form()
+    for term in J.values():
+        if isinstance(term, Float):
+            assert term._prec == 110
+
+
+def test_jordan_form_complex_issue_9274():
+    A = Matrix([[ 2,  4,  1,  0],
+                [-4,  2,  0,  1],
+                [ 0,  0,  2,  4],
+                [ 0,  0, -4,  2]])
+    p = 2 - 4*I
+    q = 2 + 4*I
+    Jmust1 = Matrix([[p, 1, 0, 0],
+                     [0, p, 0, 0],
+                     [0, 0, q, 1],
+                     [0, 0, 0, q]])
+    Jmust2 = Matrix([[q, 1, 0, 0],
+                     [0, q, 0, 0],
+                     [0, 0, p, 1],
+                     [0, 0, 0, p]])
+    P, J = A.jordan_form()
+    assert J == Jmust1 or J == Jmust2
+    assert simplify(P*J*P.inv()) == A
+
+def test_issue_10220():
+    # two non-orthogonal Jordan blocks with eigenvalue 1
+    M = Matrix([[1, 0, 0, 1],
+                [0, 1, 1, 0],
+                [0, 0, 1, 1],
+                [0, 0, 0, 1]])
+    P, J = M.jordan_form()
+    assert P == Matrix([[0, 1, 0, 1],
+                        [1, 0, 0, 0],
+                        [0, 1, 0, 0],
+                        [0, 0, 1, 0]])
+    assert J == Matrix([
+                        [1, 1, 0, 0],
+                        [0, 1, 1, 0],
+                        [0, 0, 1, 0],
+                        [0, 0, 0, 1]])
+
+def test_jordan_form_issue_15858():
+    A = Matrix([
+        [1, 1, 1, 0],
+        [-2, -1, 0, -1],
+        [0, 0, -1, -1],
+        [0, 0, 2, 1]])
+    (P, J) = A.jordan_form()
+    assert P.expand() == Matrix([
+        [    -I,          -I/2,      I,           I/2],
+        [-1 + I,             0, -1 - I,             0],
+        [     0, -S(1)/2 - I/2,      0, -S(1)/2 + I/2],
+        [     0,             1,      0,             1]])
+    assert J == Matrix([
+        [-I, 1, 0, 0],
+        [0, -I, 0, 0],
+        [0, 0, I, 1],
+        [0, 0, 0, I]])
+
+def test_Matrix_berkowitz_charpoly():
+    UA, K_i, K_w = symbols('UA K_i K_w')
+
+    A = Matrix([[-K_i - UA + K_i**2/(K_i + K_w),       K_i*K_w/(K_i + K_w)],
+                [           K_i*K_w/(K_i + K_w), -K_w + K_w**2/(K_i + K_w)]])
+
+    charpoly = A.charpoly(x)
+
+    assert charpoly == \
+        Poly(x**2 + (K_i*UA + K_w*UA + 2*K_i*K_w)/(K_i + K_w)*x +
+        K_i*K_w*UA/(K_i + K_w), x, domain='ZZ(K_i,K_w,UA)')
+
+    assert type(charpoly) is PurePoly
+
+    A = Matrix([[1, 3], [2, 0]])
+    assert A.charpoly() == A.charpoly(x) == PurePoly(x**2 - x - 6)
+
+    A = Matrix([[1, 2], [x, 0]])
+    p = A.charpoly(x)
+    assert p.gen != x
+    assert p.as_expr().subs(p.gen, x) == x**2 - 3*x
+
+
+def test_exp_jordan_block():
+    l = Symbol('lamda')
+
+    m = Matrix.jordan_block(1, l)
+    assert m._eval_matrix_exp_jblock() == Matrix([[exp(l)]])
+
+    m = Matrix.jordan_block(3, l)
+    assert m._eval_matrix_exp_jblock() == \
+        Matrix([
+            [exp(l), exp(l), exp(l)/2],
+            [0, exp(l), exp(l)],
+            [0, 0, exp(l)]])
+
+
+def test_exp():
+    m = Matrix([[3, 4], [0, -2]])
+    m_exp = Matrix([[exp(3), -4*exp(-2)/5 + 4*exp(3)/5], [0, exp(-2)]])
+    assert m.exp() == m_exp
+    assert exp(m) == m_exp
+
+    m = Matrix([[1, 0], [0, 1]])
+    assert m.exp() == Matrix([[E, 0], [0, E]])
+    assert exp(m) == Matrix([[E, 0], [0, E]])
+
+    m = Matrix([[1, -1], [1, 1]])
+    assert m.exp() == Matrix([[E*cos(1), -E*sin(1)], [E*sin(1), E*cos(1)]])
+
+
+def test_log():
+    l = Symbol('lamda')
+
+    m = Matrix.jordan_block(1, l)
+    assert m._eval_matrix_log_jblock() == Matrix([[log(l)]])
+
+    m = Matrix.jordan_block(4, l)
+    assert m._eval_matrix_log_jblock() == \
+        Matrix(
+            [
+                [log(l), 1/l, -1/(2*l**2), 1/(3*l**3)],
+                [0, log(l), 1/l, -1/(2*l**2)],
+                [0, 0, log(l), 1/l],
+                [0, 0, 0, log(l)]
+            ]
+        )
+
+    m = Matrix(
+        [[0, 0, 1],
+        [0, 0, 0],
+        [-1, 0, 0]]
+    )
+    raises(MatrixError, lambda: m.log())
+
+
+def test_has():
+    A = Matrix(((x, y), (2, 3)))
+    assert A.has(x)
+    assert not A.has(z)
+    assert A.has(Symbol)
+
+    A = A.subs(x, 2)
+    assert not A.has(x)
+
+
+def test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1():
+    # Test if matrices._find_reasonable_pivot_naive()
+    # finds a guaranteed non-zero pivot when the
+    # some of the candidate pivots are symbolic expressions.
+    # Keyword argument: simpfunc=None indicates that no simplifications
+    # should be performed during the search.
+    x = Symbol('x')
+    column = Matrix(3, 1, [x, cos(x)**2 + sin(x)**2, S.Half])
+    pivot_offset, pivot_val, pivot_assumed_nonzero, simplified =\
+        _find_reasonable_pivot_naive(column)
+    assert pivot_val == S.Half
+
+def test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2():
+    # Test if matrices._find_reasonable_pivot_naive()
+    # finds a guaranteed non-zero pivot when the
+    # some of the candidate pivots are symbolic expressions.
+    # Keyword argument: simpfunc=_simplify indicates that the search
+    # should attempt to simplify candidate pivots.
+    x = Symbol('x')
+    column = Matrix(3, 1,
+                    [x,
+                     cos(x)**2+sin(x)**2+x**2,
+                     cos(x)**2+sin(x)**2])
+    pivot_offset, pivot_val, pivot_assumed_nonzero, simplified =\
+        _find_reasonable_pivot_naive(column, simpfunc=_simplify)
+    assert pivot_val == 1
+
+def test_find_reasonable_pivot_naive_simplifies():
+    # Test if matrices._find_reasonable_pivot_naive()
+    # simplifies candidate pivots, and reports
+    # their offsets correctly.
+    x = Symbol('x')
+    column = Matrix(3, 1,
+                    [x,
+                     cos(x)**2+sin(x)**2+x,
+                     cos(x)**2+sin(x)**2])
+    pivot_offset, pivot_val, pivot_assumed_nonzero, simplified =\
+        _find_reasonable_pivot_naive(column, simpfunc=_simplify)
+
+    assert len(simplified) == 2
+    assert simplified[0][0] == 1
+    assert simplified[0][1] == 1+x
+    assert simplified[1][0] == 2
+    assert simplified[1][1] == 1
+
+def test_errors():
+    raises(ValueError, lambda: Matrix([[1, 2], [1]]))
+    raises(IndexError, lambda: Matrix([[1, 2]])[1.2, 5])
+    raises(IndexError, lambda: Matrix([[1, 2]])[1, 5.2])
+    raises(ValueError, lambda: randMatrix(3, c=4, symmetric=True))
+    raises(ValueError, lambda: Matrix([1, 2]).reshape(4, 6))
+    raises(ShapeError,
+        lambda: Matrix([[1, 2], [3, 4]]).copyin_matrix([1, 0], Matrix([1, 2])))
+    raises(TypeError, lambda: Matrix([[1, 2], [3, 4]]).copyin_list([0,
+           1], set()))
+    raises(NonSquareMatrixError, lambda: Matrix([[1, 2, 3], [2, 3, 0]]).inv())
+    raises(ShapeError,
+        lambda: Matrix(1, 2, [1, 2]).row_join(Matrix([[1, 2], [3, 4]])))
+    raises(
+        ShapeError, lambda: Matrix([1, 2]).col_join(Matrix([[1, 2], [3, 4]])))
+    raises(ShapeError, lambda: Matrix([1]).row_insert(1, Matrix([[1,
+           2], [3, 4]])))
+    raises(ShapeError, lambda: Matrix([1]).col_insert(1, Matrix([[1,
+           2], [3, 4]])))
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).trace())
+    raises(TypeError, lambda: Matrix([1]).applyfunc(1))
+    raises(ValueError, lambda: Matrix([[1, 2], [3, 4]]).minor(4, 5))
+    raises(ValueError, lambda: Matrix([[1, 2], [3, 4]]).minor_submatrix(4, 5))
+    raises(TypeError, lambda: Matrix([1, 2, 3]).cross(1))
+    raises(TypeError, lambda: Matrix([1, 2, 3]).dot(1))
+    raises(ShapeError, lambda: Matrix([1, 2, 3]).dot(Matrix([1, 2])))
+    raises(ShapeError, lambda: Matrix([1, 2]).dot([]))
+    raises(TypeError, lambda: Matrix([1, 2]).dot('a'))
+    raises(ShapeError, lambda: Matrix([1, 2]).dot([1, 2, 3]))
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2, 3]).exp())
+    raises(ShapeError, lambda: Matrix([[1, 2], [3, 4]]).normalized())
+    raises(ValueError, lambda: Matrix([1, 2]).inv(method='not a method'))
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).inverse_GE())
+    raises(ValueError, lambda: Matrix([[1, 2], [1, 2]]).inverse_GE())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).inverse_ADJ())
+    raises(ValueError, lambda: Matrix([[1, 2], [1, 2]]).inverse_ADJ())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).inverse_LU())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).is_nilpotent())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).det())
+    raises(ValueError,
+        lambda: Matrix([[1, 2], [3, 4]]).det(method='Not a real method'))
+    raises(ValueError,
+        lambda: Matrix([[1, 2, 3, 4], [5, 6, 7, 8],
+        [9, 10, 11, 12], [13, 14, 15, 16]]).det(iszerofunc="Not function"))
+    raises(ValueError,
+        lambda: Matrix([[1, 2, 3, 4], [5, 6, 7, 8],
+        [9, 10, 11, 12], [13, 14, 15, 16]]).det(iszerofunc=False))
+    raises(ValueError,
+        lambda: hessian(Matrix([[1, 2], [3, 4]]), Matrix([[1, 2], [2, 1]])))
+    raises(ValueError, lambda: hessian(Matrix([[1, 2], [3, 4]]), []))
+    raises(ValueError, lambda: hessian(Symbol('x')**2, 'a'))
+    raises(IndexError, lambda: eye(3)[5, 2])
+    raises(IndexError, lambda: eye(3)[2, 5])
+    M = Matrix(((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16)))
+    raises(ValueError, lambda: M.det('method=LU_decomposition()'))
+    V = Matrix([[10, 10, 10]])
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(ValueError, lambda: M.row_insert(4.7, V))
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(ValueError, lambda: M.col_insert(-4.2, V))
+
+def test_len():
+    assert len(Matrix()) == 0
+    assert len(Matrix([[1, 2]])) == len(Matrix([[1], [2]])) == 2
+    assert len(Matrix(0, 2, lambda i, j: 0)) == \
+        len(Matrix(2, 0, lambda i, j: 0)) == 0
+    assert len(Matrix([[0, 1, 2], [3, 4, 5]])) == 6
+    assert Matrix([1]) == Matrix([[1]])
+    assert not Matrix()
+    assert Matrix() == Matrix([])
+
+
+def test_integrate():
+    A = Matrix(((1, 4, x), (y, 2, 4), (10, 5, x**2)))
+    assert A.integrate(x) == \
+        Matrix(((x, 4*x, x**2/2), (x*y, 2*x, 4*x), (10*x, 5*x, x**3/3)))
+    assert A.integrate(y) == \
+        Matrix(((y, 4*y, x*y), (y**2/2, 2*y, 4*y), (10*y, 5*y, y*x**2)))
+
+
+def test_limit():
+    A = Matrix(((1, 4, sin(x)/x), (y, 2, 4), (10, 5, x**2 + 1)))
+    assert A.limit(x, 0) == Matrix(((1, 4, 1), (y, 2, 4), (10, 5, 1)))
+
+
+def test_diff():
+    A = MutableDenseMatrix(((1, 4, x), (y, 2, 4), (10, 5, x**2 + 1)))
+    assert isinstance(A.diff(x), type(A))
+    assert A.diff(x) == MutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert A.diff(y) == MutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    assert diff(A, x) == MutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert diff(A, y) == MutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    A_imm = A.as_immutable()
+    assert isinstance(A_imm.diff(x), type(A_imm))
+    assert A_imm.diff(x) == ImmutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert A_imm.diff(y) == ImmutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    assert diff(A_imm, x) == ImmutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert diff(A_imm, y) == ImmutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    assert A.diff(x, evaluate=False) == ArrayDerivative(A, x, evaluate=False)
+    assert diff(A, x, evaluate=False) == ArrayDerivative(A, x, evaluate=False)
+
+
+def test_diff_by_matrix():
+
+    # Derive matrix by matrix:
+
+    A = MutableDenseMatrix([[x, y], [z, t]])
+    assert A.diff(A) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+    assert diff(A, A) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+
+    A_imm = A.as_immutable()
+    assert A_imm.diff(A_imm) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+    assert diff(A_imm, A_imm) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+
+    # Derive a constant matrix:
+    assert A.diff(a) == MutableDenseMatrix([[0, 0], [0, 0]])
+
+    B = ImmutableDenseMatrix([a, b])
+    assert A.diff(B) == Array.zeros(2, 1, 2, 2)
+    assert A.diff(A) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+
+    # Test diff with tuples:
+
+    dB = B.diff([[a, b]])
+    assert dB.shape == (2, 2, 1)
+    assert dB == Array([[[1], [0]], [[0], [1]]])
+
+    f = Function("f")
+    fxyz = f(x, y, z)
+    assert fxyz.diff([[x, y, z]]) == Array([fxyz.diff(x), fxyz.diff(y), fxyz.diff(z)])
+    assert fxyz.diff(([x, y, z], 2)) == Array([
+        [fxyz.diff(x, 2), fxyz.diff(x, y), fxyz.diff(x, z)],
+        [fxyz.diff(x, y), fxyz.diff(y, 2), fxyz.diff(y, z)],
+        [fxyz.diff(x, z), fxyz.diff(z, y), fxyz.diff(z, 2)],
+    ])
+
+    expr = sin(x)*exp(y)
+    assert expr.diff([[x, y]]) == Array([cos(x)*exp(y), sin(x)*exp(y)])
+    assert expr.diff(y, ((x, y),)) == Array([cos(x)*exp(y), sin(x)*exp(y)])
+    assert expr.diff(x, ((x, y),)) == Array([-sin(x)*exp(y), cos(x)*exp(y)])
+    assert expr.diff(((y, x),), [[x, y]]) == Array([[cos(x)*exp(y), -sin(x)*exp(y)], [sin(x)*exp(y), cos(x)*exp(y)]])
+
+    # Test different notations:
+
+    assert fxyz.diff(x).diff(y).diff(x) == fxyz.diff(((x, y, z),), 3)[0, 1, 0]
+    assert fxyz.diff(z).diff(y).diff(x) == fxyz.diff(((x, y, z),), 3)[2, 1, 0]
+    assert fxyz.diff([[x, y, z]], ((z, y, x),)) == Array([[fxyz.diff(i).diff(j) for i in (x, y, z)] for j in (z, y, x)])
+
+    # Test scalar derived by matrix remains matrix:
+    res = x.diff(Matrix([[x, y]]))
+    assert isinstance(res, ImmutableDenseMatrix)
+    assert res == Matrix([[1, 0]])
+    res = (x**3).diff(Matrix([[x, y]]))
+    assert isinstance(res, ImmutableDenseMatrix)
+    assert res == Matrix([[3*x**2, 0]])
+
+
+def test_getattr():
+    A = Matrix(((1, 4, x), (y, 2, 4), (10, 5, x**2 + 1)))
+    raises(AttributeError, lambda: A.nonexistantattribute)
+    assert getattr(A, 'diff')(x) == Matrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+
+
+def test_hessenberg():
+    A = Matrix([[3, 4, 1], [2, 4, 5], [0, 1, 2]])
+    assert A.is_upper_hessenberg
+    A = A.T
+    assert A.is_lower_hessenberg
+    A[0, -1] = 1
+    assert A.is_lower_hessenberg is False
+
+    A = Matrix([[3, 4, 1], [2, 4, 5], [3, 1, 2]])
+    assert not A.is_upper_hessenberg
+
+    A = zeros(5, 2)
+    assert A.is_upper_hessenberg
+
+
+def test_cholesky():
+    raises(NonSquareMatrixError, lambda: Matrix((1, 2)).cholesky())
+    raises(ValueError, lambda: Matrix(((1, 2), (3, 4))).cholesky())
+    raises(ValueError, lambda: Matrix(((5 + I, 0), (0, 1))).cholesky())
+    raises(ValueError, lambda: Matrix(((1, 5), (5, 1))).cholesky())
+    raises(ValueError, lambda: Matrix(((1, 2), (3, 4))).cholesky(hermitian=False))
+    assert Matrix(((5 + I, 0), (0, 1))).cholesky(hermitian=False) == Matrix([
+        [sqrt(5 + I), 0], [0, 1]])
+    A = Matrix(((1, 5), (5, 1)))
+    L = A.cholesky(hermitian=False)
+    assert L == Matrix([[1, 0], [5, 2*sqrt(6)*I]])
+    assert L*L.T == A
+    A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L = A.cholesky()
+    assert L * L.T == A
+    assert L.is_lower
+    assert L == Matrix([[5, 0, 0], [3, 3, 0], [-1, 1, 3]])
+    A = Matrix(((4, -2*I, 2 + 2*I), (2*I, 2, -1 + I), (2 - 2*I, -1 - I, 11)))
+    assert A.cholesky().expand() == Matrix(((2, 0, 0), (I, 1, 0), (1 - I, 0, 3)))
+
+    raises(NonSquareMatrixError, lambda: SparseMatrix((1, 2)).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((1, 2), (3, 4))).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((5 + I, 0), (0, 1))).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((1, 5), (5, 1))).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((1, 2), (3, 4))).cholesky(hermitian=False))
+    assert SparseMatrix(((5 + I, 0), (0, 1))).cholesky(hermitian=False) == Matrix([
+        [sqrt(5 + I), 0], [0, 1]])
+    A = SparseMatrix(((1, 5), (5, 1)))
+    L = A.cholesky(hermitian=False)
+    assert L == Matrix([[1, 0], [5, 2*sqrt(6)*I]])
+    assert L*L.T == A
+    A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L = A.cholesky()
+    assert L * L.T == A
+    assert L.is_lower
+    assert L == Matrix([[5, 0, 0], [3, 3, 0], [-1, 1, 3]])
+    A = SparseMatrix(((4, -2*I, 2 + 2*I), (2*I, 2, -1 + I), (2 - 2*I, -1 - I, 11)))
+    assert A.cholesky() == Matrix(((2, 0, 0), (I, 1, 0), (1 - I, 0, 3)))
+
+
+def test_matrix_norm():
+    # Vector Tests
+    # Test columns and symbols
+    x = Symbol('x', real=True)
+    v = Matrix([cos(x), sin(x)])
+    assert trigsimp(v.norm(2)) == 1
+    assert v.norm(10) == Pow(cos(x)**10 + sin(x)**10, Rational(1, 10))
+
+    # Test Rows
+    A = Matrix([[5, Rational(3, 2)]])
+    assert A.norm() == Pow(25 + Rational(9, 4), S.Half)
+    assert A.norm(oo) == max(A)
+    assert A.norm(-oo) == min(A)
+
+    # Matrix Tests
+    # Intuitive test
+    A = Matrix([[1, 1], [1, 1]])
+    assert A.norm(2) == 2
+    assert A.norm(-2) == 0
+    assert A.norm('frobenius') == 2
+    assert eye(10).norm(2) == eye(10).norm(-2) == 1
+    assert A.norm(oo) == 2
+
+    # Test with Symbols and more complex entries
+    A = Matrix([[3, y, y], [x, S.Half, -pi]])
+    assert (A.norm('fro')
+           == sqrt(Rational(37, 4) + 2*abs(y)**2 + pi**2 + x**2))
+
+    # Check non-square
+    A = Matrix([[1, 2, -3], [4, 5, Rational(13, 2)]])
+    assert A.norm(2) == sqrt(Rational(389, 8) + sqrt(78665)/8)
+    assert A.norm(-2) is S.Zero
+    assert A.norm('frobenius') == sqrt(389)/2
+
+    # Test properties of matrix norms
+    # https://en.wikipedia.org/wiki/Matrix_norm#Definition
+    # Two matrices
+    A = Matrix([[1, 2], [3, 4]])
+    B = Matrix([[5, 5], [-2, 2]])
+    C = Matrix([[0, -I], [I, 0]])
+    D = Matrix([[1, 0], [0, -1]])
+    L = [A, B, C, D]
+    alpha = Symbol('alpha', real=True)
+
+    for order in ['fro', 2, -2]:
+        # Zero Check
+        assert zeros(3).norm(order) is S.Zero
+        # Check Triangle Inequality for all Pairs of Matrices
+        for X in L:
+            for Y in L:
+                dif = (X.norm(order) + Y.norm(order) -
+                    (X + Y).norm(order))
+                assert (dif >= 0)
+        # Scalar multiplication linearity
+        for M in [A, B, C, D]:
+            dif = simplify((alpha*M).norm(order) -
+                    abs(alpha) * M.norm(order))
+            assert dif == 0
+
+    # Test Properties of Vector Norms
+    # https://en.wikipedia.org/wiki/Vector_norm
+    # Two column vectors
+    a = Matrix([1, 1 - 1*I, -3])
+    b = Matrix([S.Half, 1*I, 1])
+    c = Matrix([-1, -1, -1])
+    d = Matrix([3, 2, I])
+    e = Matrix([Integer(1e2), Rational(1, 1e2), 1])
+    L = [a, b, c, d, e]
+    alpha = Symbol('alpha', real=True)
+
+    for order in [1, 2, -1, -2, S.Infinity, S.NegativeInfinity, pi]:
+        # Zero Check
+        if order > 0:
+            assert Matrix([0, 0, 0]).norm(order) is S.Zero
+        # Triangle inequality on all pairs
+        if order >= 1:  # Triangle InEq holds only for these norms
+            for X in L:
+                for Y in L:
+                    dif = (X.norm(order) + Y.norm(order) -
+                        (X + Y).norm(order))
+                    assert simplify(dif >= 0) is S.true
+        # Linear to scalar multiplication
+        if order in [1, 2, -1, -2, S.Infinity, S.NegativeInfinity]:
+            for X in L:
+                dif = simplify((alpha*X).norm(order) -
+                    (abs(alpha) * X.norm(order)))
+                assert dif == 0
+
+    # ord=1
+    M = Matrix(3, 3, [1, 3, 0, -2, -1, 0, 3, 9, 6])
+    assert M.norm(1) == 13
+
+
+def test_condition_number():
+    x = Symbol('x', real=True)
+    A = eye(3)
+    A[0, 0] = 10
+    A[2, 2] = Rational(1, 10)
+    assert A.condition_number() == 100
+
+    A[1, 1] = x
+    assert A.condition_number() == Max(10, Abs(x)) / Min(Rational(1, 10), Abs(x))
+
+    M = Matrix([[cos(x), sin(x)], [-sin(x), cos(x)]])
+    Mc = M.condition_number()
+    assert all(Float(1.).epsilon_eq(Mc.subs(x, val).evalf()) for val in
+        [Rational(1, 5), S.Half, Rational(1, 10), pi/2, pi, pi*Rational(7, 4) ])
+
+    #issue 10782
+    assert Matrix([]).condition_number() == 0
+
+
+def test_equality():
+    A = Matrix(((1, 2, 3), (4, 5, 6), (7, 8, 9)))
+    B = Matrix(((9, 8, 7), (6, 5, 4), (3, 2, 1)))
+    assert A == A[:, :]
+    assert not A != A[:, :]
+    assert not A == B
+    assert A != B
+    assert A != 10
+    assert not A == 10
+
+    # A SparseMatrix can be equal to a Matrix
+    C = SparseMatrix(((1, 0, 0), (0, 1, 0), (0, 0, 1)))
+    D = Matrix(((1, 0, 0), (0, 1, 0), (0, 0, 1)))
+    assert C == D
+    assert not C != D
+
+
+def test_col_join():
+    assert eye(3).col_join(Matrix([[7, 7, 7]])) == \
+        Matrix([[1, 0, 0],
+                [0, 1, 0],
+                [0, 0, 1],
+                [7, 7, 7]])
+
+
+def test_row_insert():
+    r4 = Matrix([[4, 4, 4]])
+    for i in range(-4, 5):
+        l = [1, 0, 0]
+        l.insert(i, 4)
+        assert flatten(eye(3).row_insert(i, r4).col(0).tolist()) == l
+
+
+def test_col_insert():
+    c4 = Matrix([4, 4, 4])
+    for i in range(-4, 5):
+        l = [0, 0, 0]
+        l.insert(i, 4)
+        assert flatten(zeros(3).col_insert(i, c4).row(0).tolist()) == l
+
+
+def test_normalized():
+    assert Matrix([3, 4]).normalized() == \
+        Matrix([Rational(3, 5), Rational(4, 5)])
+
+    # Zero vector trivial cases
+    assert Matrix([0, 0, 0]).normalized() == Matrix([0, 0, 0])
+
+    # Machine precision error truncation trivial cases
+    m = Matrix([0,0,1.e-100])
+    assert m.normalized(
+    iszerofunc=lambda x: x.evalf(n=10, chop=True).is_zero
+    ) == Matrix([0, 0, 0])
+
+
+def test_print_nonzero():
+    assert capture(lambda: eye(3).print_nonzero()) == \
+        '[X  ]\n[ X ]\n[  X]\n'
+    assert capture(lambda: eye(3).print_nonzero('.')) == \
+        '[.  ]\n[ . ]\n[  .]\n'
+
+
+def test_zeros_eye():
+    assert Matrix.eye(3) == eye(3)
+    assert Matrix.zeros(3) == zeros(3)
+    assert ones(3, 4) == Matrix(3, 4, [1]*12)
+
+    i = Matrix([[1, 0], [0, 1]])
+    z = Matrix([[0, 0], [0, 0]])
+    for cls in classes:
+        m = cls.eye(2)
+        assert i == m  # but m == i will fail if m is immutable
+        assert i == eye(2, cls=cls)
+        assert type(m) == cls
+        m = cls.zeros(2)
+        assert z == m
+        assert z == zeros(2, cls=cls)
+        assert type(m) == cls
+
+
+def test_is_zero():
+    assert Matrix().is_zero_matrix
+    assert Matrix([[0, 0], [0, 0]]).is_zero_matrix
+    assert zeros(3, 4).is_zero_matrix
+    assert not eye(3).is_zero_matrix
+    assert Matrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert SparseMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert ImmutableMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert ImmutableSparseMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert Matrix([[x, 1], [0, 0]]).is_zero_matrix == False
+    a = Symbol('a', nonzero=True)
+    assert Matrix([[a, 0], [0, 0]]).is_zero_matrix == False
+
+
+def test_rotation_matrices():
+    # This tests the rotation matrices by rotating about an axis and back.
+    theta = pi/3
+    r3_plus = rot_axis3(theta)
+    r3_minus = rot_axis3(-theta)
+    r2_plus = rot_axis2(theta)
+    r2_minus = rot_axis2(-theta)
+    r1_plus = rot_axis1(theta)
+    r1_minus = rot_axis1(-theta)
+    assert r3_minus*r3_plus*eye(3) == eye(3)
+    assert r2_minus*r2_plus*eye(3) == eye(3)
+    assert r1_minus*r1_plus*eye(3) == eye(3)
+
+    # Check the correctness of the trace of the rotation matrix
+    assert r1_plus.trace() == 1 + 2*cos(theta)
+    assert r2_plus.trace() == 1 + 2*cos(theta)
+    assert r3_plus.trace() == 1 + 2*cos(theta)
+
+    # Check that a rotation with zero angle doesn't change anything.
+    assert rot_axis1(0) == eye(3)
+    assert rot_axis2(0) == eye(3)
+    assert rot_axis3(0) == eye(3)
+
+    # Check left-hand convention
+    # see Issue #24529
+    q1 = Quaternion.from_axis_angle([1, 0, 0], pi / 2)
+    q2 = Quaternion.from_axis_angle([0, 1, 0], pi / 2)
+    q3 = Quaternion.from_axis_angle([0, 0, 1], pi / 2)
+    assert rot_axis1(- pi / 2) == q1.to_rotation_matrix()
+    assert rot_axis2(- pi / 2) == q2.to_rotation_matrix()
+    assert rot_axis3(- pi / 2) == q3.to_rotation_matrix()
+    # Check right-hand convention
+    assert rot_ccw_axis1(+ pi / 2) == q1.to_rotation_matrix()
+    assert rot_ccw_axis2(+ pi / 2) == q2.to_rotation_matrix()
+    assert rot_ccw_axis3(+ pi / 2) == q3.to_rotation_matrix()
+
+
+def test_DeferredVector():
+    assert str(DeferredVector("vector")[4]) == "vector[4]"
+    assert sympify(DeferredVector("d")) == DeferredVector("d")
+    raises(IndexError, lambda: DeferredVector("d")[-1])
+    assert str(DeferredVector("d")) == "d"
+    assert repr(DeferredVector("test")) == "DeferredVector('test')"
+
+def test_DeferredVector_not_iterable():
+    assert not iterable(DeferredVector('X'))
+
+def test_DeferredVector_Matrix():
+    raises(TypeError, lambda: Matrix(DeferredVector("V")))
+
+def test_GramSchmidt():
+    R = Rational
+    m1 = Matrix(1, 2, [1, 2])
+    m2 = Matrix(1, 2, [2, 3])
+    assert GramSchmidt([m1, m2]) == \
+        [Matrix(1, 2, [1, 2]), Matrix(1, 2, [R(2)/5, R(-1)/5])]
+    assert GramSchmidt([m1.T, m2.T]) == \
+        [Matrix(2, 1, [1, 2]), Matrix(2, 1, [R(2)/5, R(-1)/5])]
+    # from wikipedia
+    assert GramSchmidt([Matrix([3, 1]), Matrix([2, 2])], True) == [
+        Matrix([3*sqrt(10)/10, sqrt(10)/10]),
+        Matrix([-sqrt(10)/10, 3*sqrt(10)/10])]
+    # https://github.com/sympy/sympy/issues/9488
+    L = FiniteSet(Matrix([1]))
+    assert GramSchmidt(L) == [Matrix([[1]])]
+
+
+def test_casoratian():
+    assert casoratian([1, 2, 3, 4], 1) == 0
+    assert casoratian([1, 2, 3, 4], 1, zero=False) == 0
+
+
+def test_zero_dimension_multiply():
+    assert (Matrix()*zeros(0, 3)).shape == (0, 3)
+    assert zeros(3, 0)*zeros(0, 3) == zeros(3, 3)
+    assert zeros(0, 3)*zeros(3, 0) == Matrix()
+
+
+def test_slice_issue_2884():
+    m = Matrix(2, 2, range(4))
+    assert m[1, :] == Matrix([[2, 3]])
+    assert m[-1, :] == Matrix([[2, 3]])
+    assert m[:, 1] == Matrix([[1, 3]]).T
+    assert m[:, -1] == Matrix([[1, 3]]).T
+    raises(IndexError, lambda: m[2, :])
+    raises(IndexError, lambda: m[2, 2])
+
+
+def test_slice_issue_3401():
+    assert zeros(0, 3)[:, -1].shape == (0, 1)
+    assert zeros(3, 0)[0, :] == Matrix(1, 0, [])
+
+
+def test_copyin():
+    s = zeros(3, 3)
+    s[3] = 1
+    assert s[:, 0] == Matrix([0, 1, 0])
+    assert s[3] == 1
+    assert s[3: 4] == [1]
+    s[1, 1] = 42
+    assert s[1, 1] == 42
+    assert s[1, 1:] == Matrix([[42, 0]])
+    s[1, 1:] = Matrix([[5, 6]])
+    assert s[1, :] == Matrix([[1, 5, 6]])
+    s[1, 1:] = [[42, 43]]
+    assert s[1, :] == Matrix([[1, 42, 43]])
+    s[0, 0] = 17
+    assert s[:, :1] == Matrix([17, 1, 0])
+    s[0, 0] = [1, 1, 1]
+    assert s[:, 0] == Matrix([1, 1, 1])
+    s[0, 0] = Matrix([1, 1, 1])
+    assert s[:, 0] == Matrix([1, 1, 1])
+    s[0, 0] = SparseMatrix([1, 1, 1])
+    assert s[:, 0] == Matrix([1, 1, 1])
+
+
+def test_invertible_check():
+    # sometimes a singular matrix will have a pivot vector shorter than
+    # the number of rows in a matrix...
+    assert Matrix([[1, 2], [1, 2]]).rref() == (Matrix([[1, 2], [0, 0]]), (0,))
+    raises(ValueError, lambda: Matrix([[1, 2], [1, 2]]).inv())
+    m = Matrix([
+        [-1, -1,  0],
+        [ x,  1,  1],
+        [ 1,  x, -1],
+    ])
+    assert len(m.rref()[1]) != m.rows
+    # in addition, unless simplify=True in the call to rref, the identity
+    # matrix will be returned even though m is not invertible
+    assert m.rref()[0] != eye(3)
+    assert m.rref(simplify=signsimp)[0] != eye(3)
+    raises(ValueError, lambda: m.inv(method="ADJ"))
+    raises(ValueError, lambda: m.inv(method="GE"))
+    raises(ValueError, lambda: m.inv(method="LU"))
+
+
+def test_issue_3959():
+    x, y = symbols('x, y')
+    e = x*y
+    assert e.subs(x, Matrix([3, 5, 3])) == Matrix([3, 5, 3])*y
+
+
+def test_issue_5964():
+    assert str(Matrix([[1, 2], [3, 4]])) == 'Matrix([[1, 2], [3, 4]])'
+
+
+def test_issue_7604():
+    x, y = symbols("x y")
+    assert sstr(Matrix([[x, 2*y], [y**2, x + 3]])) == \
+        'Matrix([\n[   x,   2*y],\n[y**2, x + 3]])'
+
+
+def test_is_Identity():
+    assert eye(3).is_Identity
+    assert eye(3).as_immutable().is_Identity
+    assert not zeros(3).is_Identity
+    assert not ones(3).is_Identity
+    # issue 6242
+    assert not Matrix([[1, 0, 0]]).is_Identity
+    # issue 8854
+    assert SparseMatrix(3,3, {(0,0):1, (1,1):1, (2,2):1}).is_Identity
+    assert not SparseMatrix(2,3, range(6)).is_Identity
+    assert not SparseMatrix(3,3, {(0,0):1, (1,1):1}).is_Identity
+    assert not SparseMatrix(3,3, {(0,0):1, (1,1):1, (2,2):1, (0,1):2, (0,2):3}).is_Identity
+
+
+def test_dot():
+    assert ones(1, 3).dot(ones(3, 1)) == 3
+    assert ones(1, 3).dot([1, 1, 1]) == 3
+    assert Matrix([1, 2, 3]).dot(Matrix([1, 2, 3])) == 14
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I])) == -5 + I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I]), hermitian=False) == -5 + I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I]), hermitian=True) == 13 + I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I]), hermitian=True, conjugate_convention="physics") == 13 - I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([4, 5*I, 6]), hermitian=True, conjugate_convention="right") == 4 + 8*I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([4, 5*I, 6]), hermitian=True, conjugate_convention="left") == 4 - 8*I
+    assert Matrix([I, 2*I]).dot(Matrix([I, 2*I]), hermitian=False, conjugate_convention="left") == -5
+    assert Matrix([I, 2*I]).dot(Matrix([I, 2*I]), conjugate_convention="left") == 5
+    raises(ValueError, lambda: Matrix([1, 2]).dot(Matrix([3, 4]), hermitian=True, conjugate_convention="test"))
+
+
+def test_dual():
+    B_x, B_y, B_z, E_x, E_y, E_z = symbols(
+        'B_x B_y B_z E_x E_y E_z', real=True)
+    F = Matrix((
+        (   0,  E_x,  E_y,  E_z),
+        (-E_x,    0,  B_z, -B_y),
+        (-E_y, -B_z,    0,  B_x),
+        (-E_z,  B_y, -B_x,    0)
+    ))
+    Fd = Matrix((
+        (  0, -B_x, -B_y, -B_z),
+        (B_x,    0,  E_z, -E_y),
+        (B_y, -E_z,    0,  E_x),
+        (B_z,  E_y, -E_x,    0)
+    ))
+    assert F.dual().equals(Fd)
+    assert eye(3).dual().equals(zeros(3))
+    assert F.dual().dual().equals(-F)
+
+
+def test_anti_symmetric():
+    assert Matrix([1, 2]).is_anti_symmetric() is False
+    m = Matrix(3, 3, [0, x**2 + 2*x + 1, y, -(x + 1)**2, 0, x*y, -y, -x*y, 0])
+    assert m.is_anti_symmetric() is True
+    assert m.is_anti_symmetric(simplify=False) is None
+    assert m.is_anti_symmetric(simplify=lambda x: x) is None
+
+    # tweak to fail
+    m[2, 1] = -m[2, 1]
+    assert m.is_anti_symmetric() is None
+    # untweak
+    m[2, 1] = -m[2, 1]
+
+    m = m.expand()
+    assert m.is_anti_symmetric(simplify=False) is True
+    m[0, 0] = 1
+    assert m.is_anti_symmetric() is False
+
+
+def test_normalize_sort_diogonalization():
+    A = Matrix(((1, 2), (2, 1)))
+    P, Q = A.diagonalize(normalize=True)
+    assert P*P.T == P.T*P == eye(P.cols)
+    P, Q = A.diagonalize(normalize=True, sort=True)
+    assert P*P.T == P.T*P == eye(P.cols)
+    assert P*Q*P.inv() == A
+
+
+def test_issue_5321():
+    raises(ValueError, lambda: Matrix([[1, 2, 3], Matrix(0, 1, [])]))
+
+
+def test_issue_5320():
+    assert Matrix.hstack(eye(2), 2*eye(2)) == Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2]
+    ])
+    assert Matrix.vstack(eye(2), 2*eye(2)) == Matrix([
+        [1, 0],
+        [0, 1],
+        [2, 0],
+        [0, 2]
+    ])
+    cls = SparseMatrix
+    assert cls.hstack(cls(eye(2)), cls(2*eye(2))) == Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2]
+    ])
+
+def test_issue_11944():
+    A = Matrix([[1]])
+    AIm = sympify(A)
+    assert Matrix.hstack(AIm, A) == Matrix([[1, 1]])
+    assert Matrix.vstack(AIm, A) == Matrix([[1], [1]])
+
+def test_cross():
+    a = [1, 2, 3]
+    b = [3, 4, 5]
+    col = Matrix([-2, 4, -2])
+    row = col.T
+
+    def test(M, ans):
+        assert ans == M
+        assert type(M) == cls
+    for cls in classes:
+        A = cls(a)
+        B = cls(b)
+        test(A.cross(B), col)
+        test(A.cross(B.T), col)
+        test(A.T.cross(B.T), row)
+        test(A.T.cross(B), row)
+    raises(ShapeError, lambda:
+        Matrix(1, 2, [1, 1]).cross(Matrix(1, 2, [1, 1])))
+
+def test_hat_vee():
+    v1 = Matrix([x, y, z])
+    v2 = Matrix([a, b, c])
+    assert v1.hat() * v2 == v1.cross(v2)
+    assert v1.hat().is_anti_symmetric()
+    assert v1.hat().vee() == v1
+
+def test_hash():
+    for cls in classes[-2:]:
+        s = {cls.eye(1), cls.eye(1)}
+        assert len(s) == 1 and s.pop() == cls.eye(1)
+    # issue 3979
+    for cls in classes[:2]:
+        assert not isinstance(cls.eye(1), Hashable)
+
+
+@XFAIL
+def test_issue_3979():
+    # when this passes, delete this and change the [1:2]
+    # to [:2] in the test_hash above for issue 3979
+    cls = classes[0]
+    raises(AttributeError, lambda: hash(cls.eye(1)))
+
+
+def test_adjoint():
+    dat = [[0, I], [1, 0]]
+    ans = Matrix([[0, 1], [-I, 0]])
+    for cls in classes:
+        assert ans == cls(dat).adjoint()
+
+
+def test_adjoint_with_operator():
+    # Regression test for issue 25130: adjoint() should propagate to operators
+    import sympy.physics.quantum
+    a = sympy.physics.quantum.operator.Operator('a')
+    a_dag = sympy.physics.quantum.Dagger(a)
+    dat = [[0, I * a], [0, a_dag]]
+    ans = Matrix([[0, 0], [-I * a_dag, a]])
+    for cls in classes:
+        assert ans == cls(dat).adjoint()
+
+
+def test_simplify_immutable():
+    assert simplify(ImmutableMatrix([[sin(x)**2 + cos(x)**2]])) == \
+                    ImmutableMatrix([[1]])
+
+def test_replace():
+    F, G = symbols('F, G', cls=Function)
+    K = Matrix(2, 2, lambda i, j: G(i+j))
+    M = Matrix(2, 2, lambda i, j: F(i+j))
+    N = M.replace(F, G)
+    assert N == K
+
+
+def test_atoms():
+    m = Matrix([[1, 2], [x, 1 - 1/x]])
+    assert m.atoms() == {S.One,S(2),S.NegativeOne, x}
+    assert m.atoms(Symbol) == {x}
+
+
+def test_pinv():
+    # Pseudoinverse of an invertible matrix is the inverse.
+    A1 = Matrix([[a, b], [c, d]])
+    assert simplify(A1.pinv(method="RD")) == simplify(A1.inv())
+
+    # Test the four properties of the pseudoinverse for various matrices.
+    As = [Matrix([[13, 104], [2212, 3], [-3, 5]]),
+          Matrix([[1, 7, 9], [11, 17, 19]]),
+          Matrix([a, b])]
+
+    for A in As:
+        A_pinv = A.pinv(method="RD")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+    # XXX Pinv with diagonalization makes expression too complicated.
+    for A in As:
+        A_pinv = simplify(A.pinv(method="ED"))
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+    # XXX Computing pinv using diagonalization makes an expression that
+    # is too complicated to simplify.
+    # A1 = Matrix([[a, b], [c, d]])
+    # assert simplify(A1.pinv(method="ED")) == simplify(A1.inv())
+    # so this is tested numerically at a fixed random point
+
+    from sympy.core.numbers import comp
+    q = A1.pinv(method="ED")
+    w = A1.inv()
+    reps = {a: -73633, b: 11362, c: 55486, d: 62570}
+    assert all(
+        comp(i.n(), j.n())
+        for i, j in zip(q.subs(reps), w.subs(reps))
+        )
+
+
+@slow
+def test_pinv_rank_deficient_when_diagonalization_fails():
+    # Test the four properties of the pseudoinverse for matrices when
+    # diagonalization of A.H*A fails.
+    As = [
+        Matrix([
+            [61, 89, 55, 20, 71, 0],
+            [62, 96, 85, 85, 16, 0],
+            [69, 56, 17,  4, 54, 0],
+            [10, 54, 91, 41, 71, 0],
+            [ 7, 30, 10, 48, 90, 0],
+            [0, 0, 0, 0, 0, 0]])
+    ]
+    for A in As:
+        A_pinv = A.pinv(method="ED")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert AAp.H == AAp
+
+        # Here ApA.H and ApA are equivalent expressions but they are very
+        # complicated expressions involving RootOfs. Using simplify would be
+        # too slow and so would evalf so we substitute approximate values for
+        # the RootOfs and then evalf which is less accurate but good enough to
+        # confirm that these two matrices are equivalent.
+        #
+        # assert ApA.H == ApA  # <--- would fail (structural equality)
+        # assert simplify(ApA.H - ApA).is_zero_matrix  # <--- too slow
+        # (ApA.H - ApA).evalf()  # <--- too slow
+
+        def allclose(M1, M2):
+            rootofs = M1.atoms(RootOf)
+            rootofs_approx = {r: r.evalf() for r in rootofs}
+            diff_approx = (M1 - M2).xreplace(rootofs_approx).evalf()
+            return all(abs(e) < 1e-10 for e in diff_approx)
+
+        assert allclose(ApA.H, ApA)
+
+
+def test_issue_7201():
+    assert ones(0, 1) + ones(0, 1) == Matrix(0, 1, [])
+    assert ones(1, 0) + ones(1, 0) == Matrix(1, 0, [])
+
+def test_free_symbols():
+    for M in ImmutableMatrix, ImmutableSparseMatrix, Matrix, SparseMatrix:
+        assert M([[x], [0]]).free_symbols == {x}
+
+def test_from_ndarray():
+    """See issue 7465."""
+    try:
+        from numpy import array
+    except ImportError:
+        skip('NumPy must be available to test creating matrices from ndarrays')
+
+    assert Matrix(array([1, 2, 3])) == Matrix([1, 2, 3])
+    assert Matrix(array([[1, 2, 3]])) == Matrix([[1, 2, 3]])
+    assert Matrix(array([[1, 2, 3], [4, 5, 6]])) == \
+        Matrix([[1, 2, 3], [4, 5, 6]])
+    assert Matrix(array([x, y, z])) == Matrix([x, y, z])
+    raises(NotImplementedError,
+        lambda: Matrix(array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])))
+    assert Matrix([array([1, 2]), array([3, 4])]) == Matrix([[1, 2], [3, 4]])
+    assert Matrix([array([1, 2]), [3, 4]]) == Matrix([[1, 2], [3, 4]])
+    assert Matrix([array([]), array([])]) == Matrix(2, 0, []) != Matrix(0, 0, [])
+
+def test_17522_numpy():
+    from sympy.matrices.common import _matrixify
+    try:
+        from numpy import array, matrix
+    except ImportError:
+        skip('NumPy must be available to test indexing matrixified NumPy ndarrays and matrices')
+
+    m = _matrixify(array([[1, 2], [3, 4]]))
+    assert m[3] == 4
+    assert list(m) == [1, 2, 3, 4]
+
+    with ignore_warnings(PendingDeprecationWarning):
+        m = _matrixify(matrix([[1, 2], [3, 4]]))
+    assert m[3] == 4
+    assert list(m) == [1, 2, 3, 4]
+
+def test_17522_mpmath():
+    from sympy.matrices.common import _matrixify
+    try:
+        from mpmath import matrix
+    except ImportError:
+        skip('mpmath must be available to test indexing matrixified mpmath matrices')
+
+    m = _matrixify(matrix([[1, 2], [3, 4]]))
+    assert m[3] == 4.0
+    assert list(m) == [1.0, 2.0, 3.0, 4.0]
+
+def test_17522_scipy():
+    from sympy.matrices.common import _matrixify
+    try:
+        from scipy.sparse import csr_matrix
+    except ImportError:
+        skip('SciPy must be available to test indexing matrixified SciPy sparse matrices')
+
+    m = _matrixify(csr_matrix([[1, 2], [3, 4]]))
+    assert m[3] == 4
+    assert list(m) == [1, 2, 3, 4]
+
+def test_hermitian():
+    a = Matrix([[1, I], [-I, 1]])
+    assert a.is_hermitian
+    a[0, 0] = 2*I
+    assert a.is_hermitian is False
+    a[0, 0] = x
+    assert a.is_hermitian is None
+    a[0, 1] = a[1, 0]*I
+    assert a.is_hermitian is False
+    b = HermitianOperator("b")
+    c = Operator("c")
+    assert Matrix([[b]]).is_hermitian is True
+    assert Matrix([[b, c], [Dagger(c), b]]).is_hermitian is True
+    assert Matrix([[b, c], [c, b]]).is_hermitian is False
+    assert Matrix([[b, c], [transpose(c), b]]).is_hermitian is False
+
+def test_doit():
+    a = Matrix([[Add(x,x, evaluate=False)]])
+    assert a[0] != 2*x
+    assert a.doit() == Matrix([[2*x]])
+
+def test_issue_9457_9467_9876():
+    # for row_del(index)
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    M.row_del(1)
+    assert M == Matrix([[1, 2, 3], [3, 4, 5]])
+    N = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    N.row_del(-2)
+    assert N == Matrix([[1, 2, 3], [3, 4, 5]])
+    O = Matrix([[1, 2, 3], [5, 6, 7], [9, 10, 11]])
+    O.row_del(-1)
+    assert O == Matrix([[1, 2, 3], [5, 6, 7]])
+    P = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: P.row_del(10))
+    Q = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: Q.row_del(-10))
+
+    # for col_del(index)
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    M.col_del(1)
+    assert M == Matrix([[1, 3], [2, 4], [3, 5]])
+    N = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    N.col_del(-2)
+    assert N == Matrix([[1, 3], [2, 4], [3, 5]])
+    P = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: P.col_del(10))
+    Q = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: Q.col_del(-10))
+
+def test_issue_9422():
+    x, y = symbols('x y', commutative=False)
+    a, b = symbols('a b')
+    M = eye(2)
+    M1 = Matrix(2, 2, [x, y, y, z])
+    assert y*x*M != x*y*M
+    assert b*a*M == a*b*M
+    assert x*M1 != M1*x
+    assert a*M1 == M1*a
+    assert y*x*M == Matrix([[y*x, 0], [0, y*x]])
+
+
+def test_issue_10770():
+    M = Matrix([])
+    a = ['col_insert', 'row_join'], Matrix([9, 6, 3])
+    b = ['row_insert', 'col_join'], a[1].T
+    c = ['row_insert', 'col_insert'], Matrix([[1, 2], [3, 4]])
+    for ops, m in (a, b, c):
+        for op in ops:
+            f = getattr(M, op)
+            new = f(m) if 'join' in op else f(42, m)
+            assert new == m and id(new) != id(m)
+
+
+def test_issue_10658():
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert A.extract([0, 1, 2], [True, True, False]) == \
+        Matrix([[1, 2], [4, 5], [7, 8]])
+    assert A.extract([0, 1, 2], [True, False, False]) == Matrix([[1], [4], [7]])
+    assert A.extract([True, False, False], [0, 1, 2]) == Matrix([[1, 2, 3]])
+    assert A.extract([True, False, True], [0, 1, 2]) == \
+        Matrix([[1, 2, 3], [7, 8, 9]])
+    assert A.extract([0, 1, 2], [False, False, False]) == Matrix(3, 0, [])
+    assert A.extract([False, False, False], [0, 1, 2]) == Matrix(0, 3, [])
+    assert A.extract([True, False, True], [False, True, False]) == \
+        Matrix([[2], [8]])
+
+def test_opportunistic_simplification():
+    # this test relates to issue #10718, #9480, #11434
+
+    # issue #9480
+    m = Matrix([[-5 + 5*sqrt(2), -5], [-5*sqrt(2)/2 + 5, -5*sqrt(2)/2]])
+    assert m.rank() == 1
+
+    # issue #10781
+    m = Matrix([[3+3*sqrt(3)*I, -9],[4,-3+3*sqrt(3)*I]])
+    assert simplify(m.rref()[0] - Matrix([[1, -9/(3 + 3*sqrt(3)*I)], [0, 0]])) == zeros(2, 2)
+
+    # issue #11434
+    ax,ay,bx,by,cx,cy,dx,dy,ex,ey,t0,t1 = symbols('a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1')
+    m = Matrix([[ax,ay,ax*t0,ay*t0,0],[bx,by,bx*t0,by*t0,0],[cx,cy,cx*t0,cy*t0,1],[dx,dy,dx*t0,dy*t0,1],[ex,ey,2*ex*t1-ex*t0,2*ey*t1-ey*t0,0]])
+    assert m.rank() == 4
+
+def test_partial_pivoting():
+    # example from https://en.wikipedia.org/wiki/Pivot_element
+    # partial pivoting with back substitution gives a perfect result
+    # naive pivoting give an error ~1e-13, so anything better than
+    # 1e-15 is good
+    mm=Matrix([[0.003, 59.14, 59.17], [5.291, -6.13, 46.78]])
+    assert (mm.rref()[0] - Matrix([[1.0,   0, 10.0],
+                                   [  0, 1.0,  1.0]])).norm() < 1e-15
+
+    # issue #11549
+    m_mixed = Matrix([[6e-17, 1.0, 4],
+                      [ -1.0,   0, 8],
+                      [    0,   0, 1]])
+    m_float = Matrix([[6e-17,  1.0, 4.],
+                      [ -1.0,   0., 8.],
+                      [   0.,   0., 1.]])
+    m_inv = Matrix([[  0,    -1.0,  8.0],
+                    [1.0, 6.0e-17, -4.0],
+                    [  0,       0,    1]])
+    # this example is numerically unstable and involves a matrix with a norm >= 8,
+    # this comparing the difference of the results with 1e-15 is numerically sound.
+    assert (m_mixed.inv() - m_inv).norm() < 1e-15
+    assert (m_float.inv() - m_inv).norm() < 1e-15
+
+def test_iszero_substitution():
+    """ When doing numerical computations, all elements that pass
+    the iszerofunc test should be set to numerically zero if they
+    aren't already. """
+
+    # Matrix from issue #9060
+    m = Matrix([[0.9, -0.1, -0.2, 0],[-0.8, 0.9, -0.4, 0],[-0.1, -0.8, 0.6, 0]])
+    m_rref = m.rref(iszerofunc=lambda x: abs(x)<6e-15)[0]
+    m_correct = Matrix([[1.0,   0, -0.301369863013699, 0],[  0, 1.0, -0.712328767123288, 0],[  0,   0,                  0, 0]])
+    m_diff = m_rref - m_correct
+    assert m_diff.norm() < 1e-15
+    # if a zero-substitution wasn't made, this entry will be -1.11022302462516e-16
+    assert m_rref[2,2] == 0
+
+def test_issue_11238():
+    from sympy.geometry.point import Point
+    xx = 8*tan(pi*Rational(13, 45))/(tan(pi*Rational(13, 45)) + sqrt(3))
+    yy = (-8*sqrt(3)*tan(pi*Rational(13, 45))**2 + 24*tan(pi*Rational(13, 45)))/(-3 + tan(pi*Rational(13, 45))**2)
+    p1 = Point(0, 0)
+    p2 = Point(1, -sqrt(3))
+    p0 = Point(xx,yy)
+    m1 = Matrix([p1 - simplify(p0), p2 - simplify(p0)])
+    m2 = Matrix([p1 - p0, p2 - p0])
+    m3 = Matrix([simplify(p1 - p0), simplify(p2 - p0)])
+
+    # This system has expressions which are zero and
+    # cannot be easily proved to be such, so without
+    # numerical testing, these assertions will fail.
+    Z = lambda x: abs(x.n()) < 1e-20
+    assert m1.rank(simplify=True, iszerofunc=Z) == 1
+    assert m2.rank(simplify=True, iszerofunc=Z) == 1
+    assert m3.rank(simplify=True, iszerofunc=Z) == 1
+
+def test_as_real_imag():
+    m1 = Matrix(2,2,[1,2,3,4])
+    m2 = m1*S.ImaginaryUnit
+    m3 = m1 + m2
+
+    for kls in classes:
+        a,b = kls(m3).as_real_imag()
+        assert list(a) == list(m1)
+        assert list(b) == list(m1)
+
+def test_deprecated():
+    # Maintain tests for deprecated functions.  We must capture
+    # the deprecation warnings.  When the deprecated functionality is
+    # removed, the corresponding tests should be removed.
+
+    m = Matrix(3, 3, [0, 1, 0, -4, 4, 0, -2, 1, 2])
+    P, Jcells = m.jordan_cells()
+    assert Jcells[1] == Matrix(1, 1, [2])
+    assert Jcells[0] == Matrix(2, 2, [2, 1, 0, 2])
+
+
+def test_issue_14489():
+    from sympy.core.mod import Mod
+    A = Matrix([-1, 1, 2])
+    B = Matrix([10, 20, -15])
+
+    assert Mod(A, 3) == Matrix([2, 1, 2])
+    assert Mod(B, 4) == Matrix([2, 0, 1])
+
+def test_issue_14943():
+    # Test that __array__ accepts the optional dtype argument
+    try:
+        from numpy import array
+    except ImportError:
+        skip('NumPy must be available to test creating matrices from ndarrays')
+
+    M = Matrix([[1,2], [3,4]])
+    assert array(M, dtype=float).dtype.name == 'float64'
+
+def test_case_6913():
+    m = MatrixSymbol('m', 1, 1)
+    a = Symbol("a")
+    a = m[0, 0]>0
+    assert str(a) == 'm[0, 0] > 0'
+
+def test_issue_11948():
+    A = MatrixSymbol('A', 3, 3)
+    a = Wild('a')
+    assert A.match(a) == {a: A}
+
+def test_gramschmidt_conjugate_dot():
+    vecs = [Matrix([1, I]), Matrix([1, -I])]
+    assert Matrix.orthogonalize(*vecs) == \
+        [Matrix([[1], [I]]), Matrix([[1], [-I]])]
+
+    vecs = [Matrix([1, I, 0]), Matrix([I, 0, -I])]
+    assert Matrix.orthogonalize(*vecs) == \
+        [Matrix([[1], [I], [0]]), Matrix([[I/2], [S(1)/2], [-I]])]
+
+    mat = Matrix([[1, I], [1, -I]])
+    Q, R = mat.QRdecomposition()
+    assert Q * Q.H == Matrix.eye(2)
+
+def test_issue_8207():
+    a = Matrix(MatrixSymbol('a', 3, 1))
+    b = Matrix(MatrixSymbol('b', 3, 1))
+    c = a.dot(b)
+    d = diff(c, a[0, 0])
+    e = diff(d, a[0, 0])
+    assert d == b[0, 0]
+    assert e == 0
+
+def test_func():
+    from sympy.simplify.simplify import nthroot
+
+    A = Matrix([[1, 2],[0, 3]])
+    assert A.analytic_func(sin(x*t), x) == Matrix([[sin(t), sin(3*t) - sin(t)], [0, sin(3*t)]])
+
+    A = Matrix([[2, 1],[1, 2]])
+    assert (pi * A / 6).analytic_func(cos(x), x) == Matrix([[sqrt(3)/4, -sqrt(3)/4], [-sqrt(3)/4, sqrt(3)/4]])
+
+
+    raises(ValueError, lambda : zeros(5).analytic_func(log(x), x))
+    raises(ValueError, lambda : (A*x).analytic_func(log(x), x))
+
+    A = Matrix([[0, -1, -2, 3], [0, -1, -2, 3], [0, 1, 0, -1], [0, 0, -1, 1]])
+    assert A.analytic_func(exp(x), x) == A.exp()
+    raises(ValueError, lambda : A.analytic_func(sqrt(x), x))
+
+    A = Matrix([[41, 12],[12, 34]])
+    assert simplify(A.analytic_func(sqrt(x), x)**2) == A
+
+    A = Matrix([[3, -12, 4], [-1, 0, -2], [-1, 5, -1]])
+    assert simplify(A.analytic_func(nthroot(x, 3), x)**3) == A
+
+    A = Matrix([[2, 0, 0, 0], [1, 2, 0, 0], [0, 1, 3, 0], [0, 0, 1, 3]])
+    assert A.analytic_func(exp(x), x) == A.exp()
+
+    A = Matrix([[0, 2, 1, 6], [0, 0, 1, 2], [0, 0, 0, 3], [0, 0, 0, 0]])
+    assert A.analytic_func(exp(x*t), x) == expand(simplify((A*t).exp()))
+
+
+@skip_under_pyodide("Cannot create threads under pyodide.")
+def test_issue_19809():
+
+    def f():
+        assert _dotprodsimp_state.state == None
+        m = Matrix([[1]])
+        m = m * m
+        return True
+
+    with dotprodsimp(True):
+        with concurrent.futures.ThreadPoolExecutor() as executor:
+            future = executor.submit(f)
+            assert future.result()
+
+
+def test_issue_23276():
+    M = Matrix([x, y])
+    assert integrate(M, (x, 0, 1), (y, 0, 1)) == Matrix([
+        [S.Half],
+        [S.Half]])
+
+
+# SubspaceOnlyMatrix tests
+def test_columnspace_one():
+    m = SubspaceOnlyMatrix([[ 1,  2,  0,  2,  5],
+                            [-2, -5,  1, -1, -8],
+                            [ 0, -3,  3,  4,  1],
+                            [ 3,  6,  0, -7,  2]])
+
+    basis = m.columnspace()
+    assert basis[0] == Matrix([1, -2, 0, 3])
+    assert basis[1] == Matrix([2, -5, -3, 6])
+    assert basis[2] == Matrix([2, -1, 4, -7])
+
+    assert len(basis) == 3
+    assert Matrix.hstack(m, *basis).columnspace() == basis
+
+
+def test_rowspace():
+    m = SubspaceOnlyMatrix([[ 1,  2,  0,  2,  5],
+                            [-2, -5,  1, -1, -8],
+                            [ 0, -3,  3,  4,  1],
+                            [ 3,  6,  0, -7,  2]])
+
+    basis = m.rowspace()
+    assert basis[0] == Matrix([[1, 2, 0, 2, 5]])
+    assert basis[1] == Matrix([[0, -1, 1, 3, 2]])
+    assert basis[2] == Matrix([[0, 0, 0, 5, 5]])
+
+    assert len(basis) == 3
+
+
+def test_nullspace_one():
+    m = SubspaceOnlyMatrix([[ 1,  2,  0,  2,  5],
+                            [-2, -5,  1, -1, -8],
+                            [ 0, -3,  3,  4,  1],
+                            [ 3,  6,  0, -7,  2]])
+
+    basis = m.nullspace()
+    assert basis[0] == Matrix([-2, 1, 1, 0, 0])
+    assert basis[1] == Matrix([-1, -1, 0, -1, 1])
+    # make sure the null space is really gets zeroed
+    assert all(e.is_zero for e in m*basis[0])
+    assert all(e.is_zero for e in m*basis[1])
+
+
+# ReductionsOnlyMatrix tests
+def test_row_op():
+    e = eye_Reductions(3)
+
+    raises(ValueError, lambda: e.elementary_row_op("abc"))
+    raises(ValueError, lambda: e.elementary_row_op())
+    raises(ValueError, lambda: e.elementary_row_op('n->kn', row=5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->kn', row=-5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=1, row2=5))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=5, row2=1))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=-5, row2=1))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=1, row2=-5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=1, row2=5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=5, row2=1, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=-5, row2=1, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=1, row2=-5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=1, row2=1, k=5))
+
+    # test various ways to set arguments
+    assert e.elementary_row_op("n->kn", 0, 5) == Matrix([[5, 0, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->kn", 1, 5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->kn", row=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->kn", row1=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n<->m", 0, 1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n<->m", row1=0, row2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n<->m", row=0, row2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->n+km", 0, 5, 1) == Matrix([[1, 5, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->n+km", row=0, k=5, row2=1) == Matrix([[1, 5, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->n+km", row1=0, k=5, row2=1) == Matrix([[1, 5, 0], [0, 1, 0], [0, 0, 1]])
+
+    # make sure the matrix doesn't change size
+    a = ReductionsOnlyMatrix(2, 3, [0]*6)
+    assert a.elementary_row_op("n->kn", 1, 5) == Matrix(2, 3, [0]*6)
+    assert a.elementary_row_op("n<->m", 0, 1) == Matrix(2, 3, [0]*6)
+    assert a.elementary_row_op("n->n+km", 0, 5, 1) == Matrix(2, 3, [0]*6)
+
+
+def test_col_op():
+    e = eye_Reductions(3)
+
+    raises(ValueError, lambda: e.elementary_col_op("abc"))
+    raises(ValueError, lambda: e.elementary_col_op())
+    raises(ValueError, lambda: e.elementary_col_op('n->kn', col=5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->kn', col=-5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=1, col2=5))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=5, col2=1))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=-5, col2=1))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=1, col2=-5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=1, col2=5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=5, col2=1, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=-5, col2=1, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=1, col2=-5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=1, col2=1, k=5))
+
+    # test various ways to set arguments
+    assert e.elementary_col_op("n->kn", 0, 5) == Matrix([[5, 0, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->kn", 1, 5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->kn", col=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->kn", col1=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n<->m", 0, 1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n<->m", col1=0, col2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n<->m", col=0, col2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->n+km", 0, 5, 1) == Matrix([[1, 0, 0], [5, 1, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->n+km", col=0, k=5, col2=1) == Matrix([[1, 0, 0], [5, 1, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->n+km", col1=0, k=5, col2=1) == Matrix([[1, 0, 0], [5, 1, 0], [0, 0, 1]])
+
+    # make sure the matrix doesn't change size
+    a = ReductionsOnlyMatrix(2, 3, [0]*6)
+    assert a.elementary_col_op("n->kn", 1, 5) == Matrix(2, 3, [0]*6)
+    assert a.elementary_col_op("n<->m", 0, 1) == Matrix(2, 3, [0]*6)
+    assert a.elementary_col_op("n->n+km", 0, 5, 1) == Matrix(2, 3, [0]*6)
+
+
+def test_is_echelon():
+    zro = zeros_Reductions(3)
+    ident = eye_Reductions(3)
+
+    assert zro.is_echelon
+    assert ident.is_echelon
+
+    a = ReductionsOnlyMatrix(0, 0, [])
+    assert a.is_echelon
+
+    a = ReductionsOnlyMatrix(2, 3, [3, 2, 1, 0, 0, 6])
+    assert a.is_echelon
+
+    a = ReductionsOnlyMatrix(2, 3, [0, 0, 6, 3, 2, 1])
+    assert not a.is_echelon
+
+    x = Symbol('x')
+    a = ReductionsOnlyMatrix(3, 1, [x, 0, 0])
+    assert a.is_echelon
+
+    a = ReductionsOnlyMatrix(3, 1, [x, x, 0])
+    assert not a.is_echelon
+
+    a = ReductionsOnlyMatrix(3, 3, [0, 0, 0, 1, 2, 3, 0, 0, 0])
+    assert not a.is_echelon
+
+
+def test_echelon_form():
+    # echelon form is not unique, but the result
+    # must be row-equivalent to the original matrix
+    # and it must be in echelon form.
+
+    a = zeros_Reductions(3)
+    e = eye_Reductions(3)
+
+    # we can assume the zero matrix and the identity matrix shouldn't change
+    assert a.echelon_form() == a
+    assert e.echelon_form() == e
+
+    a = ReductionsOnlyMatrix(0, 0, [])
+    assert a.echelon_form() == a
+
+    a = ReductionsOnlyMatrix(1, 1, [5])
+    assert a.echelon_form() == a
+
+    # now we get to the real tests
+
+    def verify_row_null_space(mat, rows, nulls):
+        for v in nulls:
+            assert all(t.is_zero for t in a_echelon*v)
+        for v in rows:
+            if not all(t.is_zero for t in v):
+                assert not all(t.is_zero for t in a_echelon*v.transpose())
+
+    a = ReductionsOnlyMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    nulls = [Matrix([
+                     [ 1],
+                     [-2],
+                     [ 1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+
+    a = ReductionsOnlyMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 8])
+    nulls = []
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    a = ReductionsOnlyMatrix(3, 3, [2, 1, 3, 0, 0, 0, 2, 1, 3])
+    nulls = [Matrix([
+             [Rational(-1, 2)],
+             [   1],
+             [   0]]),
+             Matrix([
+             [Rational(-3, 2)],
+             [   0],
+             [   1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    # this one requires a row swap
+    a = ReductionsOnlyMatrix(3, 3, [2, 1, 3, 0, 0, 0, 1, 1, 3])
+    nulls = [Matrix([
+             [   0],
+             [  -3],
+             [   1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    a = ReductionsOnlyMatrix(3, 3, [0, 3, 3, 0, 2, 2, 0, 1, 1])
+    nulls = [Matrix([
+             [1],
+             [0],
+             [0]]),
+             Matrix([
+             [ 0],
+             [-1],
+             [ 1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    a = ReductionsOnlyMatrix(2, 3, [2, 2, 3, 3, 3, 0])
+    nulls = [Matrix([
+             [-1],
+             [1],
+             [0]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+
+def test_rref():
+    e = ReductionsOnlyMatrix(0, 0, [])
+    assert e.rref(pivots=False) == e
+
+    e = ReductionsOnlyMatrix(1, 1, [1])
+    a = ReductionsOnlyMatrix(1, 1, [5])
+    assert e.rref(pivots=False) == a.rref(pivots=False) == e
+
+    a = ReductionsOnlyMatrix(3, 1, [1, 2, 3])
+    assert a.rref(pivots=False) == Matrix([[1], [0], [0]])
+
+    a = ReductionsOnlyMatrix(1, 3, [1, 2, 3])
+    assert a.rref(pivots=False) == Matrix([[1, 2, 3]])
+
+    a = ReductionsOnlyMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    assert a.rref(pivots=False) == Matrix([
+                                     [1, 0, -1],
+                                     [0, 1,  2],
+                                     [0, 0,  0]])
+
+    a = ReductionsOnlyMatrix(3, 3, [1, 2, 3, 1, 2, 3, 1, 2, 3])
+    b = ReductionsOnlyMatrix(3, 3, [1, 2, 3, 0, 0, 0, 0, 0, 0])
+    c = ReductionsOnlyMatrix(3, 3, [0, 0, 0, 1, 2, 3, 0, 0, 0])
+    d = ReductionsOnlyMatrix(3, 3, [0, 0, 0, 0, 0, 0, 1, 2, 3])
+    assert a.rref(pivots=False) == \
+            b.rref(pivots=False) == \
+            c.rref(pivots=False) == \
+            d.rref(pivots=False) == b
+
+    e = eye_Reductions(3)
+    z = zeros_Reductions(3)
+    assert e.rref(pivots=False) == e
+    assert z.rref(pivots=False) == z
+
+    a = ReductionsOnlyMatrix([
+            [ 0, 0,  1,  2,  2, -5,  3],
+            [-1, 5,  2,  2,  1, -7,  5],
+            [ 0, 0, -2, -3, -3,  8, -5],
+            [-1, 5,  0, -1, -2,  1,  0]])
+    mat, pivot_offsets = a.rref()
+    assert mat == Matrix([
+                     [1, -5, 0, 0, 1,  1, -1],
+                     [0,  0, 1, 0, 0, -1,  1],
+                     [0,  0, 0, 1, 1, -2,  1],
+                     [0,  0, 0, 0, 0,  0,  0]])
+    assert pivot_offsets == (0, 2, 3)
+
+    a = ReductionsOnlyMatrix([[Rational(1, 19),  Rational(1, 5),    2,    3],
+                        [   4,    5,    6,    7],
+                        [   8,    9,   10,   11],
+                        [  12,   13,   14,   15]])
+    assert a.rref(pivots=False) == Matrix([
+                                         [1, 0, 0, Rational(-76, 157)],
+                                         [0, 1, 0,  Rational(-5, 157)],
+                                         [0, 0, 1, Rational(238, 157)],
+                                         [0, 0, 0,       0]])
+
+    x = Symbol('x')
+    a = ReductionsOnlyMatrix(2, 3, [x, 1, 1, sqrt(x), x, 1])
+    for i, j in zip(a.rref(pivots=False),
+            [1, 0, sqrt(x)*(-x + 1)/(-x**Rational(5, 2) + x),
+                0, 1, 1/(sqrt(x) + x + 1)]):
+        assert simplify(i - j).is_zero
+
+
+def test_rref_rhs():
+    a, b, c, d = symbols('a b c d')
+    A = Matrix([[0, 0], [0, 0], [1, 2], [3, 4]])
+    B = Matrix([a, b, c, d])
+    assert A.rref_rhs(B) == (Matrix([
+    [1, 0],
+    [0, 1],
+    [0, 0],
+    [0, 0]]), Matrix([
+    [   -2*c + d],
+    [3*c/2 - d/2],
+    [          a],
+    [          b]]))
+
+
+def test_issue_17827():
+    C = Matrix([
+        [3, 4, -1, 1],
+        [9, 12, -3, 3],
+        [0, 2, 1, 3],
+        [2, 3, 0, -2],
+        [0, 3, 3, -5],
+        [8, 15, 0, 6]
+    ])
+    # Tests for row/col within valid range
+    D = C.elementary_row_op('n<->m', row1=2, row2=5)
+    E = C.elementary_row_op('n->n+km', row1=5, row2=3, k=-4)
+    F = C.elementary_row_op('n->kn', row=5, k=2)
+    assert(D[5, :] == Matrix([[0, 2, 1, 3]]))
+    assert(E[5, :] == Matrix([[0, 3, 0, 14]]))
+    assert(F[5, :] == Matrix([[16, 30, 0, 12]]))
+    # Tests for row/col out of range
+    raises(ValueError, lambda: C.elementary_row_op('n<->m', row1=2, row2=6))
+    raises(ValueError, lambda: C.elementary_row_op('n->kn', row=7, k=2))
+    raises(ValueError, lambda: C.elementary_row_op('n->n+km', row1=-1, row2=5, k=2))
+
+def test_rank():
+    m = Matrix([[1, 2], [x, 1 - 1/x]])
+    assert m.rank() == 2
+    n = Matrix(3, 3, range(1, 10))
+    assert n.rank() == 2
+    p = zeros(3)
+    assert p.rank() == 0
+
+def test_issue_11434():
+    ax, ay, bx, by, cx, cy, dx, dy, ex, ey, t0, t1 = \
+        symbols('a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1')
+    M = Matrix([[ax, ay, ax*t0, ay*t0, 0],
+                [bx, by, bx*t0, by*t0, 0],
+                [cx, cy, cx*t0, cy*t0, 1],
+                [dx, dy, dx*t0, dy*t0, 1],
+                [ex, ey, 2*ex*t1 - ex*t0, 2*ey*t1 - ey*t0, 0]])
+    assert M.rank() == 4
+
+def test_rank_regression_from_so():
+    # see:
+    # https://stackoverflow.com/questions/19072700/why-does-sympy-give-me-the-wrong-answer-when-i-row-reduce-a-symbolic-matrix
+
+    nu, lamb = symbols('nu, lambda')
+    A = Matrix([[-3*nu,         1,                  0,  0],
+                [ 3*nu, -2*nu - 1,                  2,  0],
+                [    0,      2*nu, (-1*nu) - lamb - 2,  3],
+                [    0,         0,          nu + lamb, -3]])
+    expected_reduced = Matrix([[1, 0, 0, 1/(nu**2*(-lamb - nu))],
+                               [0, 1, 0,    3/(nu*(-lamb - nu))],
+                               [0, 0, 1,         3/(-lamb - nu)],
+                               [0, 0, 0,                      0]])
+    expected_pivots = (0, 1, 2)
+
+    reduced, pivots = A.rref()
+
+    assert simplify(expected_reduced - reduced) == zeros(*A.shape)
+    assert pivots == expected_pivots
+
+def test_issue_15872():
+    A = Matrix([[1, 1, 1, 0], [-2, -1, 0, -1], [0, 0, -1, -1], [0, 0, 2, 1]])
+    B = A - Matrix.eye(4) * I
+    assert B.rank() == 3
+    assert (B**2).rank() == 2
+    assert (B**3).rank() == 2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_matrixbase.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_matrixbase.py
new file mode 100644
index 0000000000000000000000000000000000000000..a77f51596c6622dc427feeeb9383214592fab632
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_matrixbase.py
@@ -0,0 +1,3795 @@
+import concurrent.futures
+import random
+from collections.abc import Hashable
+
+from sympy import (
+    Abs, Add, Array, DeferredVector, E, Expr, FiniteSet, Float, Function,
+    GramSchmidt, I, ImmutableDenseMatrix, ImmutableMatrix,
+    ImmutableSparseMatrix, Integer, KroneckerDelta, MatPow, Matrix,
+    MatrixSymbol, Max, Min, MutableDenseMatrix, MutableSparseMatrix, Poly, Pow,
+    PurePoly, Q, Quaternion, Rational, RootOf, S, SparseMatrix, Symbol, Tuple,
+    Wild, banded, casoratian, cos, diag, diff, exp, expand, eye, floor, hessian,
+    integrate, log, matrix_multiply_elementwise, nan, ones, oo, pi, randMatrix,
+    rot_axis1, rot_axis2, rot_axis3, rot_ccw_axis1, rot_ccw_axis2,
+    rot_ccw_axis3, signsimp, simplify, sin, sqrt, sstr, symbols, sympify, tan,
+    trigsimp, wronskian, zeros, cancel)
+from sympy.abc import a, b, c, d, t, x, y, z
+from sympy.core.kind import NumberKind, UndefinedKind
+from sympy.matrices.determinant import _find_reasonable_pivot_naive
+from sympy.matrices.exceptions import (
+    MatrixError, NonSquareMatrixError, ShapeError)
+from sympy.matrices.kind import MatrixKind
+from sympy.matrices.utilities import _dotprodsimp_state, _simplify, dotprodsimp
+from sympy.tensor.array.array_derivatives import ArrayDerivative
+from sympy.testing.pytest import (
+    ignore_warnings, raises, skip, skip_under_pyodide, slow,
+    warns_deprecated_sympy)
+from sympy.utilities.iterables import capture, iterable
+from importlib.metadata import version
+
+all_classes = (Matrix, SparseMatrix, ImmutableMatrix, ImmutableSparseMatrix)
+mutable_classes = (Matrix, SparseMatrix)
+immutable_classes = (ImmutableMatrix, ImmutableSparseMatrix)
+
+
+def test__MinimalMatrix():
+    x = Matrix(2, 3, [1, 2, 3, 4, 5, 6])
+    assert x.rows == 2
+    assert x.cols == 3
+    assert x[2] == 3
+    assert x[1, 1] == 5
+    assert list(x) == [1, 2, 3, 4, 5, 6]
+    assert list(x[1, :]) == [4, 5, 6]
+    assert list(x[:, 1]) == [2, 5]
+    assert list(x[:, :]) == list(x)
+    assert x[:, :] == x
+    assert Matrix(x) == x
+    assert Matrix([[1, 2, 3], [4, 5, 6]]) == x
+    assert Matrix(([1, 2, 3], [4, 5, 6])) == x
+    assert Matrix([(1, 2, 3), (4, 5, 6)]) == x
+    assert Matrix(((1, 2, 3), (4, 5, 6))) == x
+    assert not (Matrix([[1, 2], [3, 4], [5, 6]]) == x)
+
+
+def test_kind():
+    assert Matrix([[1, 2], [3, 4]]).kind == MatrixKind(NumberKind)
+    assert Matrix([[0, 0], [0, 0]]).kind == MatrixKind(NumberKind)
+    assert Matrix(0, 0, []).kind == MatrixKind(NumberKind)
+    assert Matrix([[x]]).kind == MatrixKind(NumberKind)
+    assert Matrix([[1, Matrix([[1]])]]).kind == MatrixKind(UndefinedKind)
+    assert SparseMatrix([[1]]).kind == MatrixKind(NumberKind)
+    assert SparseMatrix([[1, Matrix([[1]])]]).kind == MatrixKind(UndefinedKind)
+
+
+def test_todok():
+    a, b, c, d = symbols('a:d')
+    m1 = MutableDenseMatrix([[a, b], [c, d]])
+    m2 = ImmutableDenseMatrix([[a, b], [c, d]])
+    m3 = MutableSparseMatrix([[a, b], [c, d]])
+    m4 = ImmutableSparseMatrix([[a, b], [c, d]])
+    assert m1.todok() == m2.todok() == m3.todok() == m4.todok() == \
+        {(0, 0): a, (0, 1): b, (1, 0): c, (1, 1): d}
+
+
+def test_tolist():
+    lst = [[S.One, S.Half, x*y, S.Zero], [x, y, z, x**2], [y, -S.One, z*x, 3]]
+    flat_lst = [S.One, S.Half, x*y, S.Zero, x, y, z, x**2, y, -S.One, z*x, 3]
+    m = Matrix(3, 4, flat_lst)
+    assert m.tolist() == lst
+
+
+def test_todod():
+    m = Matrix([[S.One, 0], [0, S.Half], [x, 0]])
+    dict = {0: {0: S.One}, 1: {1: S.Half}, 2: {0: x}}
+    assert m.todod() == dict
+
+
+def test_row_col_del():
+    e = ImmutableMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    raises(IndexError, lambda: e.row_del(5))
+    raises(IndexError, lambda: e.row_del(-5))
+    raises(IndexError, lambda: e.col_del(5))
+    raises(IndexError, lambda: e.col_del(-5))
+
+    assert e.row_del(2) == e.row_del(-1) == Matrix([[1, 2, 3], [4, 5, 6]])
+    assert e.col_del(2) == e.col_del(-1) == Matrix([[1, 2], [4, 5], [7, 8]])
+
+    assert e.row_del(1) == e.row_del(-2) == Matrix([[1, 2, 3], [7, 8, 9]])
+    assert e.col_del(1) == e.col_del(-2) == Matrix([[1, 3], [4, 6], [7, 9]])
+
+
+def test_get_diag_blocks1():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    assert a.get_diag_blocks() == [a]
+    assert b.get_diag_blocks() == [b]
+    assert c.get_diag_blocks() == [c]
+
+
+def test_get_diag_blocks2():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    A, B, C, D = diag(a, b, b), diag(a, b, c), diag(a, c, b), diag(c, c, b)
+    A = Matrix(A.rows, A.cols, A)
+    B = Matrix(B.rows, B.cols, B)
+    C = Matrix(C.rows, C.cols, C)
+    D = Matrix(D.rows, D.cols, D)
+
+    assert A.get_diag_blocks() == [a, b, b]
+    assert B.get_diag_blocks() == [a, b, c]
+    assert C.get_diag_blocks() == [a, c, b]
+    assert D.get_diag_blocks() == [c, c, b]
+
+
+def test_row_col():
+    m = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    assert m.row(0) == Matrix(1, 3, [1, 2, 3])
+    assert m.col(0) == Matrix(3, 1, [1, 4, 7])
+
+
+def test_row_join():
+    assert eye(3).row_join(Matrix([7, 7, 7])) == \
+           Matrix([[1, 0, 0, 7],
+                   [0, 1, 0, 7],
+                   [0, 0, 1, 7]])
+
+
+def test_col_join():
+    assert eye(3).col_join(Matrix([[7, 7, 7]])) == \
+           Matrix([[1, 0, 0],
+                   [0, 1, 0],
+                   [0, 0, 1],
+                   [7, 7, 7]])
+
+
+def test_row_insert():
+    r4 = Matrix([[4, 4, 4]])
+    for i in range(-4, 5):
+        l = [1, 0, 0]
+        l.insert(i, 4)
+        assert eye(3).row_insert(i, r4).col(0).flat() == l
+
+
+def test_col_insert():
+    c4 = Matrix([4, 4, 4])
+    for i in range(-4, 5):
+        l = [0, 0, 0]
+        l.insert(i, 4)
+        assert zeros(3).col_insert(i, c4).row(0).flat() == l
+    # issue 13643
+    assert eye(6).col_insert(3, Matrix([[2, 2], [2, 2], [2, 2], [2, 2], [2, 2], [2, 2]])) == \
+           Matrix([[1, 0, 0, 2, 2, 0, 0, 0],
+                   [0, 1, 0, 2, 2, 0, 0, 0],
+                   [0, 0, 1, 2, 2, 0, 0, 0],
+                   [0, 0, 0, 2, 2, 1, 0, 0],
+                   [0, 0, 0, 2, 2, 0, 1, 0],
+                   [0, 0, 0, 2, 2, 0, 0, 1]])
+
+
+def test_extract():
+    m = Matrix(4, 3, lambda i, j: i*3 + j)
+    assert m.extract([0, 1, 3], [0, 1]) == Matrix(3, 2, [0, 1, 3, 4, 9, 10])
+    assert m.extract([0, 3], [0, 0, 2]) == Matrix(2, 3, [0, 0, 2, 9, 9, 11])
+    assert m.extract(range(4), range(3)) == m
+    raises(IndexError, lambda: m.extract([4], [0]))
+    raises(IndexError, lambda: m.extract([0], [3]))
+
+
+def test_hstack():
+    m = Matrix(4, 3, lambda i, j: i*3 + j)
+    m2 = Matrix(3, 4, lambda i, j: i*3 + j)
+    assert m == m.hstack(m)
+    assert m.hstack(m, m, m) == Matrix.hstack(m, m, m) == Matrix([
+                [0,  1,  2, 0,  1,  2, 0,  1,  2],
+                [3,  4,  5, 3,  4,  5, 3,  4,  5],
+                [6,  7,  8, 6,  7,  8, 6,  7,  8],
+                [9, 10, 11, 9, 10, 11, 9, 10, 11]])
+    raises(ShapeError, lambda: m.hstack(m, m2))
+    assert Matrix.hstack() == Matrix()
+
+    # test regression #12938
+    M1 = Matrix.zeros(0, 0)
+    M2 = Matrix.zeros(0, 1)
+    M3 = Matrix.zeros(0, 2)
+    M4 = Matrix.zeros(0, 3)
+    m = Matrix.hstack(M1, M2, M3, M4)
+    assert m.rows == 0 and m.cols == 6
+
+
+def test_vstack():
+    m = Matrix(4, 3, lambda i, j: i*3 + j)
+    m2 = Matrix(3, 4, lambda i, j: i*3 + j)
+    assert m == m.vstack(m)
+    assert m.vstack(m, m, m) == Matrix.vstack(m, m, m) == Matrix([
+                                [0,  1,  2],
+                                [3,  4,  5],
+                                [6,  7,  8],
+                                [9, 10, 11],
+                                [0,  1,  2],
+                                [3,  4,  5],
+                                [6,  7,  8],
+                                [9, 10, 11],
+                                [0,  1,  2],
+                                [3,  4,  5],
+                                [6,  7,  8],
+                                [9, 10, 11]])
+    raises(ShapeError, lambda: m.vstack(m, m2))
+    assert Matrix.vstack() == Matrix()
+
+
+def test_has():
+    A = Matrix(((x, y), (2, 3)))
+    assert A.has(x)
+    assert not A.has(z)
+    assert A.has(Symbol)
+
+    A = Matrix(((2, y), (2, 3)))
+    assert not A.has(x)
+
+
+def test_is_anti_symmetric():
+    x = symbols('x')
+    assert Matrix(2, 1, [1, 2]).is_anti_symmetric() is False
+    m = Matrix(3, 3, [0, x**2 + 2*x + 1, y, -(x + 1)**2, 0, x*y, -y, -x*y, 0])
+    assert m.is_anti_symmetric() is True
+    assert m.is_anti_symmetric(simplify=False) is None
+    assert m.is_anti_symmetric(simplify=lambda x: x) is None
+
+    m = Matrix(3, 3, [x.expand() for x in m])
+    assert m.is_anti_symmetric(simplify=False) is True
+    m = Matrix(3, 3, [x.expand() for x in [S.One] + list(m)[1:]])
+    assert m.is_anti_symmetric() is False
+
+
+def test_is_hermitian():
+    a = Matrix([[1, I], [-I, 1]])
+    assert a.is_hermitian
+    a = Matrix([[2*I, I], [-I, 1]])
+    assert a.is_hermitian is False
+    a = Matrix([[x, I], [-I, 1]])
+    assert a.is_hermitian is None
+    a = Matrix([[x, 1], [-I, 1]])
+    assert a.is_hermitian is False
+
+
+def test_is_symbolic():
+    a = Matrix([[x, x], [x, x]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1, 2, 3, 4], [5, 6, 7, 8]])
+    assert a.is_symbolic() is False
+    a = Matrix([[1, 2, 3, 4], [5, 6, x, 8]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1, x, 3]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1, 2, 3]])
+    assert a.is_symbolic() is False
+    a = Matrix([[1], [x], [3]])
+    assert a.is_symbolic() is True
+    a = Matrix([[1], [2], [3]])
+    assert a.is_symbolic() is False
+
+
+def test_is_square():
+    m = Matrix([[1], [1]])
+    m2 = Matrix([[2, 2], [2, 2]])
+    assert not m.is_square
+    assert m2.is_square
+
+
+def test_is_symmetric():
+    m = Matrix(2, 2, [0, 1, 1, 0])
+    assert m.is_symmetric()
+    m = Matrix(2, 2, [0, 1, 0, 1])
+    assert not m.is_symmetric()
+
+
+def test_is_hessenberg():
+    A = Matrix([[3, 4, 1], [2, 4, 5], [0, 1, 2]])
+    assert A.is_upper_hessenberg
+    A = Matrix(3, 3, [3, 2, 0, 4, 4, 1, 1, 5, 2])
+    assert A.is_lower_hessenberg
+    A = Matrix(3, 3, [3, 2, -1, 4, 4, 1, 1, 5, 2])
+    assert A.is_lower_hessenberg is False
+    assert A.is_upper_hessenberg is False
+
+    A = Matrix([[3, 4, 1], [2, 4, 5], [3, 1, 2]])
+    assert not A.is_upper_hessenberg
+
+
+def test_values():
+    assert set(Matrix(2, 2, [0, 1, 2, 3]
+        ).values()) == {1, 2, 3}
+    x = Symbol('x', real=True)
+    assert set(Matrix(2, 2, [x, 0, 0, 1]
+        ).values()) == {x, 1}
+
+
+def test_conjugate():
+    M = Matrix([[0, I, 5],
+                [1, 2, 0]])
+
+    assert M.T == Matrix([[0, 1],
+                          [I, 2],
+                          [5, 0]])
+
+    assert M.C == Matrix([[0, -I, 5],
+                          [1,  2, 0]])
+    assert M.C == M.conjugate()
+
+    assert M.H == M.T.C
+    assert M.H == Matrix([[ 0, 1],
+                          [-I, 2],
+                          [ 5, 0]])
+
+
+def test_doit():
+    a = Matrix([[Add(x, x, evaluate=False)]])
+    assert a[0] != 2*x
+    assert a.doit() == Matrix([[2*x]])
+
+
+def test_evalf():
+    a = Matrix(2, 1, [sqrt(5), 6])
+    assert all(a.evalf()[i] == a[i].evalf() for i in range(2))
+    assert all(a.evalf(2)[i] == a[i].evalf(2) for i in range(2))
+    assert all(a.n(2)[i] == a[i].n(2) for i in range(2))
+
+
+def test_replace():
+    F, G = symbols('F, G', cls=Function)
+    K = Matrix(2, 2, lambda i, j: G(i+j))
+    M = Matrix(2, 2, lambda i, j: F(i+j))
+    N = M.replace(F, G)
+    assert N == K
+
+
+def test_replace_map():
+    F, G = symbols('F, G', cls=Function)
+    M = Matrix(2, 2, lambda i, j: F(i+j))
+    N, d = M.replace(F, G, True)
+    assert N == Matrix(2, 2, lambda i, j: G(i+j))
+    assert d == {F(0): G(0), F(1): G(1), F(2): G(2)}
+
+def test_numpy_conversion():
+    try:
+        from numpy import array, array_equal
+    except ImportError:
+        skip('NumPy must be available to test creating matrices from ndarrays')
+    A = Matrix([[1,2], [3,4]])
+    np_array = array([[1,2], [3,4]])
+    assert array_equal(array(A), np_array)
+    assert array_equal(array(A, copy=True), np_array)
+    if(int(version('numpy').split('.')[0]) >= 2): #run this test only if numpy is new enough that copy variable is passed properly.
+        raises(TypeError, lambda: array(A, copy=False))
+
+def test_rot90():
+    A = Matrix([[1, 2], [3, 4]])
+    assert A == A.rot90(0) == A.rot90(4)
+    assert A.rot90(2) == A.rot90(-2) == A.rot90(6) == Matrix(((4, 3), (2, 1)))
+    assert A.rot90(3) == A.rot90(-1) == A.rot90(7) == Matrix(((2, 4), (1, 3)))
+    assert A.rot90() == A.rot90(-7) == A.rot90(-3) == Matrix(((3, 1), (4, 2)))
+
+
+def test_subs():
+    assert Matrix([[1, x], [x, 4]]).subs(x, 5) == Matrix([[1, 5], [5, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).subs([[x, -1], [y, -2]]) == \
+           Matrix([[-1, 2], [-3, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).subs([(x, -1), (y, -2)]) == \
+           Matrix([[-1, 2], [-3, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).subs({x: -1, y: -2}) == \
+           Matrix([[-1, 2], [-3, 4]])
+    assert Matrix([[x*y]]).subs({x: y - 1, y: x - 1}, simultaneous=True) == \
+           Matrix([[(x - 1)*(y - 1)]])
+
+
+def test_permute():
+    a = Matrix(3, 4, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
+
+    raises(IndexError, lambda: a.permute([[0, 5]]))
+    raises(ValueError, lambda: a.permute(Symbol('x')))
+    b = a.permute_rows([[0, 2], [0, 1]])
+    assert a.permute([[0, 2], [0, 1]]) == b == Matrix([
+                                            [5,  6,  7,  8],
+                                            [9, 10, 11, 12],
+                                            [1,  2,  3,  4]])
+
+    b = a.permute_cols([[0, 2], [0, 1]])
+    assert a.permute([[0, 2], [0, 1]], orientation='cols') == b ==\
+                            Matrix([
+                            [ 2,  3, 1,  4],
+                            [ 6,  7, 5,  8],
+                            [10, 11, 9, 12]])
+
+    b = a.permute_cols([[0, 2], [0, 1]], direction='backward')
+    assert a.permute([[0, 2], [0, 1]], orientation='cols', direction='backward') == b ==\
+                            Matrix([
+                            [ 3, 1,  2,  4],
+                            [ 7, 5,  6,  8],
+                            [11, 9, 10, 12]])
+
+    assert a.permute([1, 2, 0, 3]) == Matrix([
+                                            [5,  6,  7,  8],
+                                            [9, 10, 11, 12],
+                                            [1,  2,  3,  4]])
+
+    from sympy.combinatorics import Permutation
+    assert a.permute(Permutation([1, 2, 0, 3])) == Matrix([
+                                            [5,  6,  7,  8],
+                                            [9, 10, 11, 12],
+                                            [1,  2,  3,  4]])
+
+def test_upper_triangular():
+
+    A = Matrix([
+                [1, 1, 1, 1],
+                [1, 1, 1, 1],
+                [1, 1, 1, 1],
+                [1, 1, 1, 1]
+            ])
+
+    R = A.upper_triangular(2)
+    assert R == Matrix([
+                        [0, 0, 1, 1],
+                        [0, 0, 0, 1],
+                        [0, 0, 0, 0],
+                        [0, 0, 0, 0]
+                    ])
+
+    R = A.upper_triangular(-2)
+    assert R == Matrix([
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [0, 1, 1, 1]
+                    ])
+
+    R = A.upper_triangular()
+    assert R == Matrix([
+                        [1, 1, 1, 1],
+                        [0, 1, 1, 1],
+                        [0, 0, 1, 1],
+                        [0, 0, 0, 1]
+                    ])
+
+
+def test_lower_triangular():
+    A = Matrix([
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1]
+                    ])
+
+    L = A.lower_triangular()
+    assert L == Matrix([
+                        [1, 0, 0, 0],
+                        [1, 1, 0, 0],
+                        [1, 1, 1, 0],
+                        [1, 1, 1, 1]])
+
+    L = A.lower_triangular(2)
+    assert L == Matrix([
+                        [1, 1, 1, 0],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1],
+                        [1, 1, 1, 1]
+                    ])
+
+    L = A.lower_triangular(-2)
+    assert L == Matrix([
+                        [0, 0, 0, 0],
+                        [0, 0, 0, 0],
+                        [1, 0, 0, 0],
+                        [1, 1, 0, 0]
+                    ])
+
+
+def test_add():
+    m = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
+    assert m + m == Matrix([[2, 4, 6], [2*x, 2*y, 2*x], [4*y, -100, 2*z*x]])
+    n = Matrix(1, 2, [1, 2])
+    raises(ShapeError, lambda: m + n)
+
+
+def test_matmul():
+    a = Matrix([[1, 2], [3, 4]])
+
+    assert a.__matmul__(2) == NotImplemented
+
+    assert a.__rmatmul__(2) == NotImplemented
+
+    #This is done this way because @ is only supported in Python 3.5+
+    #To check 2@a case
+    try:
+        eval('2 @ a')
+    except SyntaxError:
+        pass
+    except TypeError:  #TypeError is raised in case of NotImplemented is returned
+        pass
+
+    #Check a@2 case
+    try:
+        eval('a @ 2')
+    except SyntaxError:
+        pass
+    except TypeError:  #TypeError is raised in case of NotImplemented is returned
+        pass
+
+
+def test_non_matmul():
+    """
+    Test that if explicitly specified as non-matrix, mul reverts
+    to scalar multiplication.
+    """
+    class foo(Expr):
+        is_Matrix=False
+        is_MatrixLike=False
+        shape = (1, 1)
+
+    A = Matrix([[1, 2], [3, 4]])
+    b = foo()
+    assert b*A == Matrix([[b, 2*b], [3*b, 4*b]])
+    assert A*b == Matrix([[b, 2*b], [3*b, 4*b]])
+
+
+def test_neg():
+    n = Matrix(1, 2, [1, 2])
+    assert -n == Matrix(1, 2, [-1, -2])
+
+
+def test_sub():
+    n = Matrix(1, 2, [1, 2])
+    assert n - n == Matrix(1, 2, [0, 0])
+
+
+def test_div():
+    n = Matrix(1, 2, [1, 2])
+    assert n/2 == Matrix(1, 2, [S.Half, S(2)/2])
+
+
+def test_eye():
+    assert list(Matrix.eye(2, 2)) == [1, 0, 0, 1]
+    assert list(Matrix.eye(2)) == [1, 0, 0, 1]
+    assert type(Matrix.eye(2)) == Matrix
+    assert type(Matrix.eye(2, cls=Matrix)) == Matrix
+
+
+def test_ones():
+    assert list(Matrix.ones(2, 2)) == [1, 1, 1, 1]
+    assert list(Matrix.ones(2)) == [1, 1, 1, 1]
+    assert Matrix.ones(2, 3) == Matrix([[1, 1, 1], [1, 1, 1]])
+    assert type(Matrix.ones(2)) == Matrix
+    assert type(Matrix.ones(2, cls=Matrix)) == Matrix
+
+
+def test_zeros():
+    assert list(Matrix.zeros(2, 2)) == [0, 0, 0, 0]
+    assert list(Matrix.zeros(2)) == [0, 0, 0, 0]
+    assert Matrix.zeros(2, 3) == Matrix([[0, 0, 0], [0, 0, 0]])
+    assert type(Matrix.zeros(2)) == Matrix
+    assert type(Matrix.zeros(2, cls=Matrix)) == Matrix
+
+
+def test_diag_make():
+    diag = Matrix.diag
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    assert diag(a, b, b) == Matrix([
+        [1, 2, 0, 0, 0, 0],
+        [2, 3, 0, 0, 0, 0],
+        [0, 0, 3, x, 0, 0],
+        [0, 0, y, 3, 0, 0],
+        [0, 0, 0, 0, 3, x],
+        [0, 0, 0, 0, y, 3],
+    ])
+    assert diag(a, b, c) == Matrix([
+        [1, 2, 0, 0, 0, 0, 0],
+        [2, 3, 0, 0, 0, 0, 0],
+        [0, 0, 3, x, 0, 0, 0],
+        [0, 0, y, 3, 0, 0, 0],
+        [0, 0, 0, 0, 3, x, 3],
+        [0, 0, 0, 0, y, 3, z],
+        [0, 0, 0, 0, x, y, z],
+    ])
+    assert diag(a, c, b) == Matrix([
+        [1, 2, 0, 0, 0, 0, 0],
+        [2, 3, 0, 0, 0, 0, 0],
+        [0, 0, 3, x, 3, 0, 0],
+        [0, 0, y, 3, z, 0, 0],
+        [0, 0, x, y, z, 0, 0],
+        [0, 0, 0, 0, 0, 3, x],
+        [0, 0, 0, 0, 0, y, 3],
+    ])
+    a = Matrix([x, y, z])
+    b = Matrix([[1, 2], [3, 4]])
+    c = Matrix([[5, 6]])
+    # this "wandering diagonal" is what makes this
+    # a block diagonal where each block is independent
+    # of the others
+    assert diag(a, 7, b, c) == Matrix([
+        [x, 0, 0, 0, 0, 0],
+        [y, 0, 0, 0, 0, 0],
+        [z, 0, 0, 0, 0, 0],
+        [0, 7, 0, 0, 0, 0],
+        [0, 0, 1, 2, 0, 0],
+        [0, 0, 3, 4, 0, 0],
+        [0, 0, 0, 0, 5, 6]])
+    raises(ValueError, lambda: diag(a, 7, b, c, rows=5))
+    assert diag(1) == Matrix([[1]])
+    assert diag(1, rows=2) == Matrix([[1, 0], [0, 0]])
+    assert diag(1, cols=2) == Matrix([[1, 0], [0, 0]])
+    assert diag(1, rows=3, cols=2) == Matrix([[1, 0], [0, 0], [0, 0]])
+    assert diag(*[2, 3]) == Matrix([
+        [2, 0],
+        [0, 3]])
+    assert diag(Matrix([2, 3])) == Matrix([
+        [2],
+        [3]])
+    assert diag([1, [2, 3], 4], unpack=False) == \
+            diag([[1], [2, 3], [4]], unpack=False) == Matrix([
+        [1, 0],
+        [2, 3],
+        [4, 0]])
+    assert type(diag(1)) == Matrix
+    assert type(diag(1, cls=Matrix)) == Matrix
+    assert Matrix.diag([1, 2, 3]) == Matrix.diag(1, 2, 3)
+    assert Matrix.diag([1, 2, 3], unpack=False).shape == (3, 1)
+    assert Matrix.diag([[1, 2, 3]]).shape == (3, 1)
+    assert Matrix.diag([[1, 2, 3]], unpack=False).shape == (1, 3)
+    assert Matrix.diag([[[1, 2, 3]]]).shape == (1, 3)
+    # kerning can be used to move the starting point
+    assert Matrix.diag(ones(0, 2), 1, 2) == Matrix([
+        [0, 0, 1, 0],
+        [0, 0, 0, 2]])
+    assert Matrix.diag(ones(2, 0), 1, 2) == Matrix([
+        [0, 0],
+        [0, 0],
+        [1, 0],
+        [0, 2]])
+
+
+def test_diagonal():
+    m = Matrix(3, 3, range(9))
+    d = m.diagonal()
+    assert d == m.diagonal(0)
+    assert tuple(d) == (0, 4, 8)
+    assert tuple(m.diagonal(1)) == (1, 5)
+    assert tuple(m.diagonal(-1)) == (3, 7)
+    assert tuple(m.diagonal(2)) == (2,)
+    assert type(m.diagonal()) == type(m)
+    s = SparseMatrix(3, 3, {(1, 1): 1})
+    assert type(s.diagonal()) == type(s)
+    assert type(m) != type(s)
+    raises(ValueError, lambda: m.diagonal(3))
+    raises(ValueError, lambda: m.diagonal(-3))
+    raises(ValueError, lambda: m.diagonal(pi))
+    M = ones(2, 3)
+    assert banded({i: list(M.diagonal(i))
+        for i in range(1-M.rows, M.cols)}) == M
+
+
+def test_jordan_block():
+    assert Matrix.jordan_block(3, 2) == Matrix.jordan_block(3, eigenvalue=2) \
+            == Matrix.jordan_block(size=3, eigenvalue=2) \
+            == Matrix.jordan_block(3, 2, band='upper') \
+            == Matrix.jordan_block(
+                size=3, eigenval=2, eigenvalue=2) \
+            == Matrix([
+                [2, 1, 0],
+                [0, 2, 1],
+                [0, 0, 2]])
+
+    assert Matrix.jordan_block(3, 2, band='lower') == Matrix([
+                    [2, 0, 0],
+                    [1, 2, 0],
+                    [0, 1, 2]])
+    # missing eigenvalue
+    raises(ValueError, lambda: Matrix.jordan_block(2))
+    # non-integral size
+    raises(ValueError, lambda: Matrix.jordan_block(3.5, 2))
+    # size not specified
+    raises(ValueError, lambda: Matrix.jordan_block(eigenvalue=2))
+    # inconsistent eigenvalue
+    raises(ValueError,
+    lambda: Matrix.jordan_block(
+        eigenvalue=2, eigenval=4))
+
+    # Using alias keyword
+    assert Matrix.jordan_block(size=3, eigenvalue=2) == \
+        Matrix.jordan_block(size=3, eigenval=2)
+
+
+def test_orthogonalize():
+    m = Matrix([[1, 2], [3, 4]])
+    assert m.orthogonalize(Matrix([[2], [1]])) == [Matrix([[2], [1]])]
+    assert m.orthogonalize(Matrix([[2], [1]]), normalize=True) == \
+        [Matrix([[2*sqrt(5)/5], [sqrt(5)/5]])]
+    assert m.orthogonalize(Matrix([[1], [2]]), Matrix([[-1], [4]])) == \
+        [Matrix([[1], [2]]), Matrix([[Rational(-12, 5)], [Rational(6, 5)]])]
+    assert m.orthogonalize(Matrix([[0], [0]]), Matrix([[-1], [4]])) == \
+        [Matrix([[-1], [4]])]
+    assert m.orthogonalize(Matrix([[0], [0]])) == []
+
+    n = Matrix([[9, 1, 9], [3, 6, 10], [8, 5, 2]])
+    vecs = [Matrix([[-5], [1]]), Matrix([[-5], [2]]), Matrix([[-5], [-2]])]
+    assert n.orthogonalize(*vecs) == \
+        [Matrix([[-5], [1]]), Matrix([[Rational(5, 26)], [Rational(25, 26)]])]
+
+    vecs = [Matrix([0, 0, 0]), Matrix([1, 2, 3]), Matrix([1, 4, 5])]
+    raises(ValueError, lambda: Matrix.orthogonalize(*vecs, rankcheck=True))
+
+    vecs = [Matrix([1, 2, 3]), Matrix([4, 5, 6]), Matrix([7, 8, 9])]
+    raises(ValueError, lambda: Matrix.orthogonalize(*vecs, rankcheck=True))
+
+def test_wilkinson():
+
+    wminus, wplus = Matrix.wilkinson(1)
+    assert wminus == Matrix([
+                                [-1, 1, 0],
+                                [1, 0, 1],
+                                [0, 1, 1]])
+    assert wplus == Matrix([
+                            [1, 1, 0],
+                            [1, 0, 1],
+                            [0, 1, 1]])
+
+    wminus, wplus = Matrix.wilkinson(3)
+    assert wminus == Matrix([
+                                [-3,  1,  0, 0, 0, 0, 0],
+                                [1, -2,  1, 0, 0, 0, 0],
+                                [0,  1, -1, 1, 0, 0, 0],
+                                [0,  0,  1, 0, 1, 0, 0],
+                                [0,  0,  0, 1, 1, 1, 0],
+                                [0,  0,  0, 0, 1, 2, 1],
+
+      [0,  0,  0, 0, 0, 1, 3]])
+
+    assert wplus == Matrix([
+                            [3, 1, 0, 0, 0, 0, 0],
+                            [1, 2, 1, 0, 0, 0, 0],
+                            [0, 1, 1, 1, 0, 0, 0],
+                            [0, 0, 1, 0, 1, 0, 0],
+                            [0, 0, 0, 1, 1, 1, 0],
+                            [0, 0, 0, 0, 1, 2, 1],
+                            [0, 0, 0, 0, 0, 1, 3]])
+
+
+def test_limit():
+    x, y = symbols('x y')
+    m = Matrix(2, 1, [1/x, y])
+    assert m.limit(x, 5) == Matrix(2, 1, [Rational(1, 5), y])
+    A = Matrix(((1, 4, sin(x)/x), (y, 2, 4), (10, 5, x**2 + 1)))
+    assert A.limit(x, 0) == Matrix(((1, 4, 1), (y, 2, 4), (10, 5, 1)))
+
+
+def test_issue_13774():
+    M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    v = [1, 1, 1]
+    raises(TypeError, lambda: M*v)
+    raises(TypeError, lambda: v*M)
+
+
+def test_companion():
+    x = Symbol('x')
+    y = Symbol('y')
+    raises(ValueError, lambda: Matrix.companion(1))
+    raises(ValueError, lambda: Matrix.companion(Poly([1], x)))
+    raises(ValueError, lambda: Matrix.companion(Poly([2, 1], x)))
+    raises(ValueError, lambda: Matrix.companion(Poly(x*y, [x, y])))
+
+    c0, c1, c2 = symbols('c0:3')
+    assert Matrix.companion(Poly([1, c0], x)) == Matrix([-c0])
+    assert Matrix.companion(Poly([1, c1, c0], x)) == \
+        Matrix([[0, -c0], [1, -c1]])
+    assert Matrix.companion(Poly([1, c2, c1, c0], x)) == \
+        Matrix([[0, 0, -c0], [1, 0, -c1], [0, 1, -c2]])
+
+
+def test_issue_10589():
+    x, y, z = symbols("x, y z")
+    M1 = Matrix([x, y, z])
+    M1 = M1.subs(zip([x, y, z], [1, 2, 3]))
+    assert M1 == Matrix([[1], [2], [3]])
+
+    M2 = Matrix([[x, x, x, x, x], [x, x, x, x, x], [x, x, x, x, x]])
+    M2 = M2.subs(zip([x], [1]))
+    assert M2 == Matrix([[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]])
+
+
+def test_rmul_pr19860():
+    class Foo(ImmutableDenseMatrix):
+        _op_priority = MutableDenseMatrix._op_priority + 0.01
+
+    a = Matrix(2, 2, [1, 2, 3, 4])
+    b = Foo(2, 2, [1, 2, 3, 4])
+
+    # This would throw a RecursionError: maximum recursion depth
+    # since b always has higher priority even after a.as_mutable()
+    c = a*b
+
+    assert isinstance(c, Foo)
+    assert c == Matrix([[7, 10], [15, 22]])
+
+
+def test_issue_18956():
+    A = Array([[1, 2], [3, 4]])
+    B = Matrix([[1,2],[3,4]])
+    raises(TypeError, lambda: B + A)
+    raises(TypeError, lambda: A + B)
+
+
+def test__eq__():
+    class My(object):
+        def __iter__(self):
+            yield 1
+            yield 2
+            return
+        def __getitem__(self, i):
+            return list(self)[i]
+    a = Matrix(2, 1, [1, 2])
+    assert a != My()
+    class My_sympy(My):
+        def _sympy_(self):
+            return Matrix(self)
+    assert a == My_sympy()
+
+
+def test_args():
+    for n, cls in enumerate(all_classes):
+        m = cls.zeros(3, 2)
+        # all should give back the same type of arguments, e.g. ints for shape
+        assert m.shape == (3, 2) and all(type(i) is int for i in m.shape)
+        assert m.rows == 3 and type(m.rows) is int
+        assert m.cols == 2 and type(m.cols) is int
+        if not n % 2:
+            assert type(m.flat()) in (list, tuple, Tuple)
+        else:
+            assert type(m.todok()) is dict
+
+
+def test_deprecated_mat_smat():
+    for cls in Matrix, ImmutableMatrix:
+        m = cls.zeros(3, 2)
+        with warns_deprecated_sympy():
+            mat = m._mat
+        assert mat == m.flat()
+    for cls in SparseMatrix, ImmutableSparseMatrix:
+        m = cls.zeros(3, 2)
+        with warns_deprecated_sympy():
+            smat = m._smat
+        assert smat == m.todok()
+
+
+def test_division():
+    v = Matrix(1, 2, [x, y])
+    assert v/z == Matrix(1, 2, [x/z, y/z])
+
+
+def test_sum():
+    m = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
+    assert m + m == Matrix([[2, 4, 6], [2*x, 2*y, 2*x], [4*y, -100, 2*z*x]])
+    n = Matrix(1, 2, [1, 2])
+    raises(ShapeError, lambda: m + n)
+
+
+def test_abs():
+    m = Matrix([[1, -2], [x, y]])
+    assert abs(m) == Matrix([[1, 2], [Abs(x), Abs(y)]])
+    m = Matrix(1, 2, [-3, x])
+    n = Matrix(1, 2, [3, Abs(x)])
+    assert abs(m) == n
+
+
+def test_addition():
+    a = Matrix((
+        (1, 2),
+        (3, 1),
+    ))
+
+    b = Matrix((
+        (1, 2),
+        (3, 0),
+    ))
+
+    assert a + b == a.add(b) == Matrix([[2, 4], [6, 1]])
+
+
+def test_fancy_index_matrix():
+    for M in (Matrix, SparseMatrix):
+        a = M(3, 3, range(9))
+        assert a == a[:, :]
+        assert a[1, :] == Matrix(1, 3, [3, 4, 5])
+        assert a[:, 1] == Matrix([1, 4, 7])
+        assert a[[0, 1], :] == Matrix([[0, 1, 2], [3, 4, 5]])
+        assert a[[0, 1], 2] == a[[0, 1], [2]]
+        assert a[2, [0, 1]] == a[[2], [0, 1]]
+        assert a[:, [0, 1]] == Matrix([[0, 1], [3, 4], [6, 7]])
+        assert a[0, 0] == 0
+        assert a[0:2, :] == Matrix([[0, 1, 2], [3, 4, 5]])
+        assert a[:, 0:2] == Matrix([[0, 1], [3, 4], [6, 7]])
+        assert a[::2, 1] == a[[0, 2], 1]
+        assert a[1, ::2] == a[1, [0, 2]]
+        a = M(3, 3, range(9))
+        assert a[[0, 2, 1, 2, 1], :] == Matrix([
+            [0, 1, 2],
+            [6, 7, 8],
+            [3, 4, 5],
+            [6, 7, 8],
+            [3, 4, 5]])
+        assert a[:, [0,2,1,2,1]] == Matrix([
+            [0, 2, 1, 2, 1],
+            [3, 5, 4, 5, 4],
+            [6, 8, 7, 8, 7]])
+
+    a = SparseMatrix.zeros(3)
+    a[1, 2] = 2
+    a[0, 1] = 3
+    a[2, 0] = 4
+    assert a.extract([1, 1], [2]) == Matrix([
+    [2],
+    [2]])
+    assert a.extract([1, 0], [2, 2, 2]) == Matrix([
+    [2, 2, 2],
+    [0, 0, 0]])
+    assert a.extract([1, 0, 1, 2], [2, 0, 1, 0]) == Matrix([
+        [2, 0, 0, 0],
+        [0, 0, 3, 0],
+        [2, 0, 0, 0],
+        [0, 4, 0, 4]])
+
+
+def test_multiplication():
+    a = Matrix((
+        (1, 2),
+        (3, 1),
+        (0, 6),
+    ))
+
+    b = Matrix((
+        (1, 2),
+        (3, 0),
+    ))
+
+    raises(ShapeError, lambda: b*a)
+    raises(TypeError, lambda: a*{})
+
+    c = a*b
+    assert c[0, 0] == 7
+    assert c[0, 1] == 2
+    assert c[1, 0] == 6
+    assert c[1, 1] == 6
+    assert c[2, 0] == 18
+    assert c[2, 1] == 0
+
+    c = a @ b
+    assert c[0, 0] == 7
+    assert c[0, 1] == 2
+    assert c[1, 0] == 6
+    assert c[1, 1] == 6
+    assert c[2, 0] == 18
+    assert c[2, 1] == 0
+
+    h = matrix_multiply_elementwise(a, c)
+    assert h == a.multiply_elementwise(c)
+    assert h[0, 0] == 7
+    assert h[0, 1] == 4
+    assert h[1, 0] == 18
+    assert h[1, 1] == 6
+    assert h[2, 0] == 0
+    assert h[2, 1] == 0
+    raises(ShapeError, lambda: matrix_multiply_elementwise(a, b))
+
+    c = b * Symbol("x")
+    assert isinstance(c, Matrix)
+    assert c[0, 0] == x
+    assert c[0, 1] == 2*x
+    assert c[1, 0] == 3*x
+    assert c[1, 1] == 0
+
+    c2 = x * b
+    assert c == c2
+
+    c = 5 * b
+    assert isinstance(c, Matrix)
+    assert c[0, 0] == 5
+    assert c[0, 1] == 2*5
+    assert c[1, 0] == 3*5
+    assert c[1, 1] == 0
+
+    M = Matrix([[oo, 0], [0, oo]])
+    assert M ** 2 == M
+
+    M = Matrix([[oo, oo], [0, 0]])
+    assert M ** 2 == Matrix([[nan, nan], [nan, nan]])
+
+    # https://github.com/sympy/sympy/issues/22353
+    A = Matrix(ones(3, 1))
+    _h = -Rational(1, 2)
+    B = Matrix([_h, _h, _h])
+    assert A.multiply_elementwise(B) == Matrix([
+        [_h],
+        [_h],
+        [_h]])
+
+
+def test_power():
+    raises(NonSquareMatrixError, lambda: Matrix((1, 2))**2)
+
+    A = Matrix([[2, 3], [4, 5]])
+    assert A**5 == Matrix([[6140, 8097], [10796, 14237]])
+    A = Matrix([[2, 1, 3], [4, 2, 4], [6, 12, 1]])
+    assert A**3 == Matrix([[290, 262, 251], [448, 440, 368], [702, 954, 433]])
+    assert A**0 == eye(3)
+    assert A**1 == A
+    assert (Matrix([[2]]) ** 100)[0, 0] == 2**100
+    assert Matrix([[1, 2], [3, 4]])**Integer(2) == Matrix([[7, 10], [15, 22]])
+    A = Matrix([[1,2],[4,5]])
+    assert A.pow(20, method='cayley') == A.pow(20, method='multiply')
+    assert A**Integer(2) == Matrix([[9, 12], [24, 33]])
+    assert eye(2)**10000000 == eye(2)
+
+    A = Matrix([[33, 24], [48, 57]])
+    assert (A**S.Half)[:] == [5, 2, 4, 7]
+    A = Matrix([[0, 4], [-1, 5]])
+    assert (A**S.Half)**2 == A
+
+    assert Matrix([[1, 0], [1, 1]])**S.Half == Matrix([[1, 0], [S.Half, 1]])
+    assert Matrix([[1, 0], [1, 1]])**0.5 == Matrix([[1, 0], [0.5, 1]])
+    from sympy.abc import n
+    assert Matrix([[1, a], [0, 1]])**n == Matrix([[1, a*n], [0, 1]])
+    assert Matrix([[b, a], [0, b]])**n == Matrix([[b**n, a*b**(n-1)*n], [0, b**n]])
+    assert Matrix([
+        [a**n, a**(n - 1)*n, (a**n*n**2 - a**n*n)/(2*a**2)],
+        [   0,         a**n,                  a**(n - 1)*n],
+        [   0,            0,                          a**n]])
+    assert Matrix([[a, 1, 0], [0, a, 0], [0, 0, b]])**n == Matrix([
+        [a**n, a**(n-1)*n, 0],
+        [0, a**n, 0],
+        [0, 0, b**n]])
+
+    A = Matrix([[1, 0], [1, 7]])
+    assert A._matrix_pow_by_jordan_blocks(S(3)) == A._eval_pow_by_recursion(3)
+    A = Matrix([[2]])
+    assert A**10 == Matrix([[2**10]]) == A._matrix_pow_by_jordan_blocks(S(10)) == \
+        A._eval_pow_by_recursion(10)
+
+    # testing a matrix that cannot be jordan blocked issue 11766
+    m = Matrix([[3, 0, 0, 0, -3], [0, -3, -3, 0, 3], [0, 3, 0, 3, 0], [0, 0, 3, 0, 3], [3, 0, 0, 3, 0]])
+    raises(MatrixError, lambda: m._matrix_pow_by_jordan_blocks(S(10)))
+
+    # test issue 11964
+    raises(MatrixError, lambda: Matrix([[1, 1], [3, 3]])._matrix_pow_by_jordan_blocks(S(-10)))
+    A = Matrix([[0, 1, 0], [0, 0, 1], [0, 0, 0]])  # Nilpotent jordan block size 3
+    assert A**10.0 == Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+    raises(ValueError, lambda: A**2.1)
+    raises(ValueError, lambda: A**Rational(3, 2))
+    A = Matrix([[8, 1], [3, 2]])
+    assert A**10.0 == Matrix([[1760744107, 272388050], [817164150, 126415807]])
+    A = Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])  # Nilpotent jordan block size 1
+    assert A**10.0 == Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+    A = Matrix([[0, 1, 0], [0, 0, 1], [0, 0, 1]])  # Nilpotent jordan block size 2
+    assert A**10.0 == Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+    n = Symbol('n', integer=True)
+    assert isinstance(A**n, MatPow)
+    n = Symbol('n', integer=True, negative=True)
+    raises(ValueError, lambda: A**n)
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert A**n == Matrix([
+        [KroneckerDelta(0, n), KroneckerDelta(1, n), -KroneckerDelta(0, n) - KroneckerDelta(1, n) + 1],
+        [                   0, KroneckerDelta(0, n),                         1 - KroneckerDelta(0, n)],
+        [                   0,                    0,                                                1]])
+    assert A**(n + 2) == Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+    raises(ValueError, lambda: A**Rational(3, 2))
+    A = Matrix([[0, 0, 1], [3, 0, 1], [4, 3, 1]])
+    assert A**5.0 == Matrix([[168,  72,  89], [291, 144, 161], [572, 267, 329]])
+    assert A**5.0 == A**5
+    A = Matrix([[0, 1, 0],[-1, 0, 0],[0, 0, 0]])
+    n = Symbol("n")
+    An = A**n
+    assert An.subs(n, 2).doit() == A**2
+    raises(ValueError, lambda: An.subs(n, -2).doit())
+    assert An * An == A**(2*n)
+
+    # concretizing behavior for non-integer and complex powers
+    A = Matrix([[0,0,0],[0,0,0],[0,0,0]])
+    n = Symbol('n', integer=True, positive=True)
+    assert A**n == A
+    n = Symbol('n', integer=True, nonnegative=True)
+    assert A**n == diag(0**n, 0**n, 0**n)
+    assert (A**n).subs(n, 0) == eye(3)
+    assert (A**n).subs(n, 1) == zeros(3)
+    A = Matrix ([[2,0,0],[0,2,0],[0,0,2]])
+    assert A**2.1 == diag (2**2.1, 2**2.1, 2**2.1)
+    assert A**I == diag (2**I, 2**I, 2**I)
+    A = Matrix([[0, 1, 0], [0, 0, 1], [0, 0, 1]])
+    raises(ValueError, lambda: A**2.1)
+    raises(ValueError, lambda: A**I)
+    A = Matrix([[S.Half, S.Half], [S.Half, S.Half]])
+    assert A**S.Half == A
+    A = Matrix([[1, 1],[3, 3]])
+    assert A**S.Half == Matrix ([[S.Half, S.Half], [3*S.Half, 3*S.Half]])
+
+
+def test_issue_17247_expression_blowup_1():
+    M = Matrix([[1+x, 1-x], [1-x, 1+x]])
+    with dotprodsimp(True):
+        assert M.exp().expand() == Matrix([
+            [ (exp(2*x) + exp(2))/2, (-exp(2*x) + exp(2))/2],
+            [(-exp(2*x) + exp(2))/2,  (exp(2*x) + exp(2))/2]])
+
+
+def test_issue_17247_expression_blowup_2():
+    M = Matrix([[1+x, 1-x], [1-x, 1+x]])
+    with dotprodsimp(True):
+        P, J = M.jordan_form ()
+        assert P*J*P.inv()
+
+
+def test_issue_17247_expression_blowup_3():
+    M = Matrix([[1+x, 1-x], [1-x, 1+x]])
+    with dotprodsimp(True):
+        assert M**100 == Matrix([
+            [633825300114114700748351602688*x**100 + 633825300114114700748351602688, 633825300114114700748351602688 - 633825300114114700748351602688*x**100],
+            [633825300114114700748351602688 - 633825300114114700748351602688*x**100, 633825300114114700748351602688*x**100 + 633825300114114700748351602688]])
+
+
+def test_issue_17247_expression_blowup_4():
+# This matrix takes extremely long on current master even with intermediate simplification so an abbreviated version is used. It is left here for test in case of future optimizations.
+#     M = Matrix(S('''[
+#         [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128,       3/64 + 13*I/64,         -23/32 - 59*I/256,      15/128 - 3*I/32,        19/256 + 551*I/1024],
+#         [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024,  119/128 + 143*I/128, -10879/2048 + 4343*I/4096,  129/256 - 549*I/512, 42533/16384 + 29103*I/8192],
+#         [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64,         -9/32 - I/16,        183/256 - 97*I/128,       3/64 + 13*I/64,          -23/32 - 59*I/256],
+#         [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512, -219/128 + 115*I/256,   6301/4096 - 6609*I/1024,  119/128 + 143*I/128,  -10879/2048 + 4343*I/4096],
+#         [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64,         1/4 - 5*I/16,          65/128 + 87*I/64,         -9/32 - I/16,         183/256 - 97*I/128],
+#         [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128,     85/256 - 33*I/16,      805/128 + 2415*I/512, -219/128 + 115*I/256,    6301/4096 - 6609*I/1024],
+#         [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16,            1/4 + I/2,          -129/64 - 9*I/64,         1/4 - 5*I/16,           65/128 + 87*I/64],
+#         [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128,     125/64 + 87*I/64,     -2063/256 + 541*I/128,     85/256 - 33*I/16,       805/128 + 2415*I/512],
+#         [             -4*I,            27/2 + 6*I,                -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,              1/2 - I,           9/4 + 55*I/16,                 -3/4,           45/32 - 37*I/16,            1/4 + I/2,           -129/64 - 9*I/64],
+#         [      1/4 + 5*I/2,       -23/8 - 57*I/16,      1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,       -5/8 - 39*I/16,     2473/256 + 137*I/64,    -149/64 + 49*I/32,     -177/128 - 1369*I/128,     125/64 + 87*I/64,      -2063/256 + 541*I/128],
+#         [               -4,               9 - 5*I,              -4*I,            27/2 + 6*I,                -2,         17/4 - 13*I/2,                1 + I,           -19/4 + 5*I/4,              1/2 - I,             9/4 + 55*I/16,                 -3/4,            45/32 - 37*I/16],
+#         [             -2*I,        119/8 + 29*I/4,       1/4 + 5*I/2,       -23/8 - 57*I/16,      1/4 + 13*I/4,    -825/64 - 147*I/32,             21/8 + I,      -537/64 + 143*I/16,       -5/8 - 39*I/16,       2473/256 + 137*I/64,    -149/64 + 49*I/32,      -177/128 - 1369*I/128]]'''))
+#     assert M**10 == Matrix([
+#         [    7*(-221393644768594642173548179825793834595 - 1861633166167425978847110897013541127952*I)/9671406556917033397649408,      15*(31670992489131684885307005100073928751695 + 10329090958303458811115024718207404523808*I)/77371252455336267181195264,   7*(-3710978679372178839237291049477017392703 + 1377706064483132637295566581525806894169*I)/19342813113834066795298816,            (9727707023582419994616144751727760051598 - 59261571067013123836477348473611225724433*I)/9671406556917033397649408,      (31896723509506857062605551443641668183707 + 54643444538699269118869436271152084599580*I)/38685626227668133590597632,       (-2024044860947539028275487595741003997397402 + 130959428791783397562960461903698670485863*I)/309485009821345068724781056,     3*(26190251453797590396533756519358368860907 - 27221191754180839338002754608545400941638*I)/77371252455336267181195264,      (1154643595139959842768960128434994698330461 + 3385496216250226964322872072260446072295634*I)/618970019642690137449562112,     3*(-31849347263064464698310044805285774295286 - 11877437776464148281991240541742691164309*I)/77371252455336267181195264,     (4661330392283532534549306589669150228040221 - 4171259766019818631067810706563064103956871*I)/1237940039285380274899124224,        (9598353794289061833850770474812760144506 + 358027153990999990968244906482319780943983*I)/309485009821345068724781056,     (-9755135335127734571547571921702373498554177 - 4837981372692695195747379349593041939686540*I)/2475880078570760549798248448],
+#         [(-379516731607474268954110071392894274962069 - 422272153179747548473724096872271700878296*I)/77371252455336267181195264, (41324748029613152354787280677832014263339501 - 12715121258662668420833935373453570749288074*I)/1237940039285380274899124224, (-339216903907423793947110742819264306542397 + 494174755147303922029979279454787373566517*I)/77371252455336267181195264, (-18121350839962855576667529908850640619878381 - 37413012454129786092962531597292531089199003*I)/1237940039285380274899124224, (2489661087330511608618880408199633556675926 + 1137821536550153872137379935240732287260863*I)/309485009821345068724781056, (-136644109701594123227587016790354220062972119 + 110130123468183660555391413889600443583585272*I)/4951760157141521099596496896, (1488043981274920070468141664150073426459593 - 9691968079933445130866371609614474474327650*I)/1237940039285380274899124224,  27*(4636797403026872518131756991410164760195942 + 3369103221138229204457272860484005850416533*I)/4951760157141521099596496896, (-8534279107365915284081669381642269800472363 + 2241118846262661434336333368511372725482742*I)/1237940039285380274899124224,  (60923350128174260992536531692058086830950875 - 263673488093551053385865699805250505661590126*I)/9903520314283042199192993792, (18520943561240714459282253753348921824172569 + 24846649186468656345966986622110971925703604*I)/4951760157141521099596496896,  (-232781130692604829085973604213529649638644431 + 35981505277760667933017117949103953338570617*I)/9903520314283042199192993792],
+#         [      (8742968295129404279528270438201520488950 + 3061473358639249112126847237482570858327*I)/4835703278458516698824704,      (-245657313712011778432792959787098074935273 + 253113767861878869678042729088355086740856*I)/38685626227668133590597632,      (1947031161734702327107371192008011621193 - 19462330079296259148177542369999791122762*I)/9671406556917033397649408,        (552856485625209001527688949522750288619217 + 392928441196156725372494335248099016686580*I)/77371252455336267181195264,      (-44542866621905323121630214897126343414629 + 3265340021421335059323962377647649632959*I)/19342813113834066795298816,          (136272594005759723105646069956434264218730 - 330975364731707309489523680957584684763587*I)/38685626227668133590597632,       (27392593965554149283318732469825168894401 + 75157071243800133880129376047131061115278*I)/38685626227668133590597632,      7*(-357821652913266734749960136017214096276154 - 45509144466378076475315751988405961498243*I)/309485009821345068724781056,       (104485001373574280824835174390219397141149 - 99041000529599568255829489765415726168162*I)/77371252455336267181195264,      (1198066993119982409323525798509037696321291 + 4249784165667887866939369628840569844519936*I)/618970019642690137449562112,       (-114985392587849953209115599084503853611014 - 52510376847189529234864487459476242883449*I)/77371252455336267181195264,      (6094620517051332877965959223269600650951573 - 4683469779240530439185019982269137976201163*I)/1237940039285380274899124224],
+#         [ (611292255597977285752123848828590587708323 - 216821743518546668382662964473055912169502*I)/77371252455336267181195264,  (-1144023204575811464652692396337616594307487 + 12295317806312398617498029126807758490062855*I)/309485009821345068724781056, (-374093027769390002505693378578475235158281 - 573533923565898290299607461660384634333639*I)/77371252455336267181195264,   (47405570632186659000138546955372796986832987 - 2837476058950808941605000274055970055096534*I)/1237940039285380274899124224,   (-571573207393621076306216726219753090535121 + 533381457185823100878764749236639320783831*I)/77371252455336267181195264,     (-7096548151856165056213543560958582513797519 - 24035731898756040059329175131592138642195366*I)/618970019642690137449562112,  (2396762128833271142000266170154694033849225 + 1448501087375679588770230529017516492953051*I)/309485009821345068724781056, (-150609293845161968447166237242456473262037053 + 92581148080922977153207018003184520294188436*I)/4951760157141521099596496896, 5*(270278244730804315149356082977618054486347 - 1997830155222496880429743815321662710091562*I)/1237940039285380274899124224,   (62978424789588828258068912690172109324360330 + 44803641177219298311493356929537007630129097*I)/2475880078570760549798248448, 19*(-451431106327656743945775812536216598712236 + 114924966793632084379437683991151177407937*I)/1237940039285380274899124224,   (63417747628891221594106738815256002143915995 - 261508229397507037136324178612212080871150958*I)/9903520314283042199192993792],
+#         [     (-2144231934021288786200752920446633703357 + 2305614436009705803670842248131563850246*I)/1208925819614629174706176,       (-90720949337459896266067589013987007078153 - 221951119475096403601562347412753844534569*I)/19342813113834066795298816,      (11590973613116630788176337262688659880376 + 6514520676308992726483494976339330626159*I)/4835703278458516698824704,      3*(-131776217149000326618649542018343107657237 + 79095042939612668486212006406818285287004*I)/38685626227668133590597632,       (10100577916793945997239221374025741184951 - 28631383488085522003281589065994018550748*I)/9671406556917033397649408,         67*(10090295594251078955008130473573667572549 + 10449901522697161049513326446427839676762*I)/77371252455336267181195264,       (-54270981296988368730689531355811033930513 - 3413683117592637309471893510944045467443*I)/19342813113834066795298816,         (440372322928679910536575560069973699181278 - 736603803202303189048085196176918214409081*I)/77371252455336267181195264,        (33220374714789391132887731139763250155295 + 92055083048787219934030779066298919603554*I)/38685626227668133590597632,      5*(-594638554579967244348856981610805281527116 - 82309245323128933521987392165716076704057*I)/309485009821345068724781056,       (128056368815300084550013708313312073721955 - 114619107488668120303579745393765245911404*I)/77371252455336267181195264,       21*(59839959255173222962789517794121843393573 + 241507883613676387255359616163487405826334*I)/618970019642690137449562112],
+#         [ (-13454485022325376674626653802541391955147 + 184471402121905621396582628515905949793486*I)/19342813113834066795298816,   (-6158730123400322562149780662133074862437105 - 3416173052604643794120262081623703514107476*I)/154742504910672534362390528,  (770558003844914708453618983120686116100419 - 127758381209767638635199674005029818518766*I)/77371252455336267181195264,   (-4693005771813492267479835161596671660631703 + 12703585094750991389845384539501921531449948*I)/309485009821345068724781056,   (-295028157441149027913545676461260860036601 - 841544569970643160358138082317324743450770*I)/77371252455336267181195264,     (56716442796929448856312202561538574275502893 + 7216818824772560379753073185990186711454778*I)/1237940039285380274899124224,  15*(-87061038932753366532685677510172566368387 + 61306141156647596310941396434445461895538*I)/154742504910672534362390528,    (-3455315109680781412178133042301025723909347 - 24969329563196972466388460746447646686670670*I)/618970019642690137449562112,   (2453418854160886481106557323699250865361849 + 1497886802326243014471854112161398141242514*I)/309485009821345068724781056, (-151343224544252091980004429001205664193082173 + 90471883264187337053549090899816228846836628*I)/4951760157141521099596496896,   (1652018205533026103358164026239417416432989 - 9959733619236515024261775397109724431400162*I)/1237940039285380274899124224,  3*(40676374242956907656984876692623172736522006 + 31023357083037817469535762230872667581366205*I)/4951760157141521099596496896],
+#         [     (-1226990509403328460274658603410696548387 - 4131739423109992672186585941938392788458*I)/1208925819614629174706176,         (162392818524418973411975140074368079662703 + 23706194236915374831230612374344230400704*I)/9671406556917033397649408,      (-3935678233089814180000602553655565621193 + 2283744757287145199688061892165659502483*I)/1208925819614629174706176,         (-2400210250844254483454290806930306285131 - 315571356806370996069052930302295432758205*I)/19342813113834066795298816,       (13365917938215281056563183751673390817910 + 15911483133819801118348625831132324863881*I)/4835703278458516698824704,        3*(-215950551370668982657516660700301003897855 + 51684341999223632631602864028309400489378*I)/38685626227668133590597632,        (20886089946811765149439844691320027184765 - 30806277083146786592790625980769214361844*I)/9671406556917033397649408,        (562180634592713285745940856221105667874855 + 1031543963988260765153550559766662245114916*I)/77371252455336267181195264,       (-65820625814810177122941758625652476012867 - 12429918324787060890804395323920477537595*I)/19342813113834066795298816,         (319147848192012911298771180196635859221089 - 402403304933906769233365689834404519960394*I)/38685626227668133590597632,        (23035615120921026080284733394359587955057 + 115351677687031786114651452775242461310624*I)/38685626227668133590597632,      (-3426830634881892756966440108592579264936130 - 1022954961164128745603407283836365128598559*I)/309485009821345068724781056],
+#         [ (-192574788060137531023716449082856117537757 - 69222967328876859586831013062387845780692*I)/19342813113834066795298816,     (2736383768828013152914815341491629299773262 - 2773252698016291897599353862072533475408743*I)/77371252455336267181195264,  (-23280005281223837717773057436155921656805 + 214784953368021840006305033048142888879224*I)/19342813113834066795298816,     (-3035247484028969580570400133318947903462326 - 2195168903335435855621328554626336958674325*I)/77371252455336267181195264,     (984552428291526892214541708637840971548653 - 64006622534521425620714598573494988589378*I)/77371252455336267181195264,      (-3070650452470333005276715136041262898509903 + 7286424705750810474140953092161794621989080*I)/154742504910672534362390528,    (-147848877109756404594659513386972921139270 - 416306113044186424749331418059456047650861*I)/38685626227668133590597632,    (55272118474097814260289392337160619494260781 + 7494019668394781211907115583302403519488058*I)/1237940039285380274899124224,     (-581537886583682322424771088996959213068864 + 542191617758465339135308203815256798407429*I)/77371252455336267181195264,    (-6422548983676355789975736799494791970390991 - 23524183982209004826464749309156698827737702*I)/618970019642690137449562112,     7*(180747195387024536886923192475064903482083 + 84352527693562434817771649853047924991804*I)/154742504910672534362390528, (-135485179036717001055310712747643466592387031 + 102346575226653028836678855697782273460527608*I)/4951760157141521099596496896],
+#         [        (3384238362616083147067025892852431152105 + 156724444932584900214919898954874618256*I)/604462909807314587353088,        (-59558300950677430189587207338385764871866 + 114427143574375271097298201388331237478857*I)/4835703278458516698824704,      (-1356835789870635633517710130971800616227 - 7023484098542340388800213478357340875410*I)/1208925819614629174706176,          (234884918567993750975181728413524549575881 + 79757294640629983786895695752733890213506*I)/9671406556917033397649408,        (-7632732774935120473359202657160313866419 + 2905452608512927560554702228553291839465*I)/1208925819614629174706176,           (52291747908702842344842889809762246649489 - 520996778817151392090736149644507525892649*I)/19342813113834066795298816,        (17472406829219127839967951180375981717322 + 23464704213841582137898905375041819568669*I)/4835703278458516698824704,        (-911026971811893092350229536132730760943307 + 150799318130900944080399439626714846752360*I)/38685626227668133590597632,         (26234457233977042811089020440646443590687 - 45650293039576452023692126463683727692890*I)/9671406556917033397649408,       3*(288348388717468992528382586652654351121357 + 454526517721403048270274049572136109264668*I)/77371252455336267181195264,        (-91583492367747094223295011999405657956347 - 12704691128268298435362255538069612411331*I)/19342813113834066795298816,          (411208730251327843849027957710164064354221 - 569898526380691606955496789378230959965898*I)/38685626227668133590597632],
+#         [    (27127513117071487872628354831658811211795 - 37765296987901990355760582016892124833857*I)/4835703278458516698824704,     (1741779916057680444272938534338833170625435 + 3083041729779495966997526404685535449810378*I)/77371252455336267181195264, 3*(-60642236251815783728374561836962709533401 - 24630301165439580049891518846174101510744*I)/19342813113834066795298816,      3*(445885207364591681637745678755008757483408 - 350948497734812895032502179455610024541643*I)/38685626227668133590597632,    (-47373295621391195484367368282471381775684 + 219122969294089357477027867028071400054973*I)/19342813113834066795298816,       (-2801565819673198722993348253876353741520438 - 2250142129822658548391697042460298703335701*I)/77371252455336267181195264,      (801448252275607253266997552356128790317119 - 50890367688077858227059515894356594900558*I)/77371252455336267181195264,    (-5082187758525931944557763799137987573501207 + 11610432359082071866576699236013484487676124*I)/309485009821345068724781056,     (-328925127096560623794883760398247685166830 - 643447969697471610060622160899409680422019*I)/77371252455336267181195264,    15*(2954944669454003684028194956846659916299765 + 33434406416888505837444969347824812608566*I)/1237940039285380274899124224,      (-415749104352001509942256567958449835766827 + 479330966144175743357171151440020955412219*I)/77371252455336267181195264,  3*(-4639987285852134369449873547637372282914255 - 11994411888966030153196659207284951579243273*I)/1237940039285380274899124224],
+#         [       (-478846096206269117345024348666145495601 + 1249092488629201351470551186322814883283*I)/302231454903657293676544,         (-17749319421930878799354766626365926894989 - 18264580106418628161818752318217357231971*I)/1208925819614629174706176,         (2801110795431528876849623279389579072819 + 363258850073786330770713557775566973248*I)/604462909807314587353088,          (-59053496693129013745775512127095650616252 + 78143588734197260279248498898321500167517*I)/4835703278458516698824704,         (-283186724922498212468162690097101115349 - 6443437753863179883794497936345437398276*I)/1208925819614629174706176,            (188799118826748909206887165661384998787543 + 84274736720556630026311383931055307398820*I)/9671406556917033397649408,         (-5482217151670072904078758141270295025989 + 1818284338672191024475557065444481298568*I)/1208925819614629174706176,          (56564463395350195513805521309731217952281 - 360208541416798112109946262159695452898431*I)/19342813113834066795298816,        11*(1259539805728870739006416869463689438068 + 1409136581547898074455004171305324917387*I)/4835703278458516698824704,       5*(-123701190701414554945251071190688818343325 + 30997157322590424677294553832111902279712*I)/38685626227668133590597632,          (16130917381301373033736295883982414239781 - 32752041297570919727145380131926943374516*I)/9671406556917033397649408,          (650301385108223834347093740500375498354925 + 899526407681131828596801223402866051809258*I)/77371252455336267181195264],
+#         [      (9011388245256140876590294262420614839483 + 8167917972423946282513000869327525382672*I)/1208925819614629174706176,       (-426393174084720190126376382194036323028924 + 180692224825757525982858693158209545430621*I)/9671406556917033397649408,     (24588556702197802674765733448108154175535 - 45091766022876486566421953254051868331066*I)/4835703278458516698824704,      (1872113939365285277373877183750416985089691 + 3030392393733212574744122057679633775773130*I)/77371252455336267181195264,    (-222173405538046189185754954524429864167549 - 75193157893478637039381059488387511299116*I)/19342813113834066795298816,        (2670821320766222522963689317316937579844558 - 2645837121493554383087981511645435472169191*I)/77371252455336267181195264,     5*(-2100110309556476773796963197283876204940 + 41957457246479840487980315496957337371937*I)/19342813113834066795298816,     (-5733743755499084165382383818991531258980593 - 3328949988392698205198574824396695027195732*I)/154742504910672534362390528,      (707827994365259025461378911159398206329247 - 265730616623227695108042528694302299777294*I)/77371252455336267181195264,    (-1442501604682933002895864804409322823788319 + 11504137805563265043376405214378288793343879*I)/309485009821345068724781056,         (-56130472299445561499538726459719629522285 - 61117552419727805035810982426639329818864*I)/9671406556917033397649408,    (39053692321126079849054272431599539429908717 - 10209127700342570953247177602860848130710666*I)/1237940039285380274899124224]])
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512],
+        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64],
+        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128],
+        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16],
+        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M**10 == Matrix(S('''[
+            [     7369525394972778926719607798014571861/604462909807314587353088 - 229284202061790301477392339912557559*I/151115727451828646838272,   -19704281515163975949388435612632058035/1208925819614629174706176 + 14319858347987648723768698170712102887*I/302231454903657293676544,      -3623281909451783042932142262164941211/604462909807314587353088 - 6039240602494288615094338643452320495*I/604462909807314587353088,    109260497799140408739847239685705357695/2417851639229258349412352 - 7427566006564572463236368211555511431*I/2417851639229258349412352, -16095803767674394244695716092817006641/2417851639229258349412352 + 10336681897356760057393429626719177583*I/1208925819614629174706176,    -42207883340488041844332828574359769743/2417851639229258349412352 - 182332262671671273188016400290188468499*I/4835703278458516698824704],
+            [50566491050825573392726324995779608259/1208925819614629174706176 - 90047007594468146222002432884052362145*I/2417851639229258349412352,  74273703462900000967697427843983822011/1208925819614629174706176 + 265947522682943571171988741842776095421*I/1208925819614629174706176, -116900341394390200556829767923360888429/2417851639229258349412352 - 53153263356679268823910621474478756845*I/2417851639229258349412352, 195407378023867871243426523048612490249/1208925819614629174706176 - 1242417915995360200584837585002906728929*I/9671406556917033397649408,   -863597594389821970177319682495878193/302231454903657293676544 + 476936100741548328800725360758734300481*I/9671406556917033397649408, -3154451590535653853562472176601754835575/19342813113834066795298816 - 232909875490506237386836489998407329215*I/2417851639229258349412352],
+            [   -1715444997702484578716037230949868543/302231454903657293676544 + 5009695651321306866158517287924120777*I/302231454903657293676544,     -30551582497996879620371947949342101301/604462909807314587353088 - 7632518367986526187139161303331519629*I/151115727451828646838272,           312680739924495153190604170938220575/18889465931478580854784 - 108664334509328818765959789219208459*I/75557863725914323419136,    -14693696966703036206178521686918865509/604462909807314587353088 + 72345386220900843930147151999899692401*I/1208925819614629174706176,  -8218872496728882299722894680635296519/1208925819614629174706176 - 16776782833358893712645864791807664983*I/1208925819614629174706176,      143237839169380078671242929143670635137/2417851639229258349412352 + 2883817094806115974748882735218469447*I/2417851639229258349412352],
+            [   3087979417831061365023111800749855987/151115727451828646838272 + 34441942370802869368851419102423997089*I/604462909807314587353088, -148309181940158040917731426845476175667/604462909807314587353088 - 263987151804109387844966835369350904919*I/9671406556917033397649408,   50259518594816377378747711930008883165/1208925819614629174706176 - 95713974916869240305450001443767979653*I/2417851639229258349412352,  153466447023875527996457943521467271119/2417851639229258349412352 + 517285524891117105834922278517084871349*I/2417851639229258349412352,  -29184653615412989036678939366291205575/604462909807314587353088 - 27551322282526322041080173287022121083*I/1208925819614629174706176,   196404220110085511863671393922447671649/1208925819614629174706176 - 1204712019400186021982272049902206202145*I/9671406556917033397649408],
+            [     -2632581805949645784625606590600098779/151115727451828646838272 - 589957435912868015140272627522612771*I/37778931862957161709568,     26727850893953715274702844733506310247/302231454903657293676544 - 10825791956782128799168209600694020481*I/302231454903657293676544,      -1036348763702366164044671908440791295/151115727451828646838272 + 3188624571414467767868303105288107375*I/151115727451828646838272,     -36814959939970644875593411585393242449/604462909807314587353088 - 18457555789119782404850043842902832647*I/302231454903657293676544,      12454491297984637815063964572803058647/604462909807314587353088 - 340489532842249733975074349495329171*I/302231454903657293676544,      -19547211751145597258386735573258916681/604462909807314587353088 + 87299583775782199663414539883938008933*I/1208925819614629174706176],
+            [  -40281994229560039213253423262678393183/604462909807314587353088 - 2939986850065527327299273003299736641*I/604462909807314587353088, 331940684638052085845743020267462794181/2417851639229258349412352 - 284574901963624403933361315517248458969*I/1208925819614629174706176,      6453843623051745485064693628073010961/302231454903657293676544 + 36062454107479732681350914931391590957*I/604462909807314587353088,  -147665869053634695632880753646441962067/604462909807314587353088 - 305987938660447291246597544085345123927*I/9671406556917033397649408,  107821369195275772166593879711259469423/2417851639229258349412352 - 11645185518211204108659001435013326687*I/302231454903657293676544,     64121228424717666402009446088588091619/1208925819614629174706176 + 265557133337095047883844369272389762133*I/1208925819614629174706176]]'''))
+
+
+def test_issue_17247_expression_blowup_5():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.charpoly('x') == PurePoly(x**6 + (-6 - 6*I)*x**5 + 36*I*x**4, x, domain='EX')
+
+
+def test_issue_17247_expression_blowup_6():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.det('bareiss') == 0
+
+
+def test_issue_17247_expression_blowup_7():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.det('berkowitz') == 0
+
+
+def test_issue_17247_expression_blowup_8():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.det('lu') == 0
+
+
+def test_issue_17247_expression_blowup_9():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.rref() == (Matrix([
+            [1, 0, -1, -2, -3, -4, -5, -6],
+            [0, 1,  2,  3,  4,  5,  6,  7],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0],
+            [0, 0,  0,  0,  0,  0,  0,  0]]), (0, 1))
+
+
+def test_issue_17247_expression_blowup_10():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.cofactor(0, 0) == 0
+
+
+def test_issue_17247_expression_blowup_11():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.cofactor_matrix() == Matrix(6, 6, [0]*36)
+
+
+def test_issue_17247_expression_blowup_12():
+    M = Matrix(6, 6, lambda i, j: 1 + (-1)**(i+j)*I)
+    with dotprodsimp(True):
+        assert M.eigenvals() == {6: 1, 6*I: 1, 0: 4}
+
+
+def test_issue_17247_expression_blowup_13():
+    M = Matrix([
+        [    0, 1 - x, x + 1, 1 - x],
+        [1 - x, x + 1,     0, x + 1],
+        [    0, 1 - x, x + 1, 1 - x],
+        [    0,     0,     1 - x, 0]])
+
+    ev = M.eigenvects()
+    assert ev[0] == (0, 2, [Matrix([0, -1, 0, 1])])
+    assert ev[1][0] == x - sqrt(2)*(x - 1) + 1
+    assert ev[1][1] == 1
+    assert ev[1][2][0].expand(deep=False, numer=True) == Matrix([
+        [(-x + sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [-4*x/(x**2 - 2*x + 1) + (x + 1)*(x - sqrt(2)*(x - 1) + 1)/(x**2 - 2*x + 1)],
+        [(-x + sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [1]
+    ])
+
+    assert ev[2][0] == x + sqrt(2)*(x - 1) + 1
+    assert ev[2][1] == 1
+    assert ev[2][2][0].expand(deep=False, numer=True) == Matrix([
+        [(-x - sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [-4*x/(x**2 - 2*x + 1) + (x + 1)*(x + sqrt(2)*(x - 1) + 1)/(x**2 - 2*x + 1)],
+        [(-x - sqrt(2)*(x - 1) - 1)/(x - 1)],
+        [1]
+    ])
+
+
+def test_issue_17247_expression_blowup_14():
+    M = Matrix(8, 8, ([1+x, 1-x]*4 + [1-x, 1+x]*4)*4)
+    with dotprodsimp(True):
+        assert M.echelon_form() == Matrix([
+            [x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x],
+            [    0,   4*x,     0,   4*x,     0,   4*x,     0,   4*x],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0],
+            [    0,     0,     0,     0,     0,     0,     0,     0]])
+
+
+def test_issue_17247_expression_blowup_15():
+    M = Matrix(8, 8, ([1+x, 1-x]*4 + [1-x, 1+x]*4)*4)
+    with dotprodsimp(True):
+        assert M.rowspace() == [Matrix([[x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x, x + 1, 1 - x]]), Matrix([[0, 4*x, 0, 4*x, 0, 4*x, 0, 4*x]])]
+
+
+def test_issue_17247_expression_blowup_16():
+    M = Matrix(8, 8, ([1+x, 1-x]*4 + [1-x, 1+x]*4)*4)
+    with dotprodsimp(True):
+        assert M.columnspace() == [Matrix([[x + 1],[1 - x],[x + 1],[1 - x],[x + 1],[1 - x],[x + 1],[1 - x]]), Matrix([[1 - x],[x + 1],[1 - x],[x + 1],[1 - x],[x + 1],[1 - x],[x + 1]])]
+
+
+def test_issue_17247_expression_blowup_17():
+    M = Matrix(8, 8, [x+i for i in range (64)])
+    with dotprodsimp(True):
+        assert M.nullspace() == [
+            Matrix([[1],[-2],[1],[0],[0],[0],[0],[0]]),
+            Matrix([[2],[-3],[0],[1],[0],[0],[0],[0]]),
+            Matrix([[3],[-4],[0],[0],[1],[0],[0],[0]]),
+            Matrix([[4],[-5],[0],[0],[0],[1],[0],[0]]),
+            Matrix([[5],[-6],[0],[0],[0],[0],[1],[0]]),
+            Matrix([[6],[-7],[0],[0],[0],[0],[0],[1]])]
+
+
+def test_issue_17247_expression_blowup_18():
+    M = Matrix(6, 6, ([1+x, 1-x]*3 + [1-x, 1+x]*3)*3)
+    with dotprodsimp(True):
+        assert not M.is_nilpotent()
+
+
+def test_issue_17247_expression_blowup_19():
+    M = Matrix(S('''[
+        [             -3/4,                     0,         1/4 + I/2,                     0],
+        [                0, -177/128 - 1369*I/128,                 0, -2063/256 + 541*I/128],
+        [          1/2 - I,                     0,                 0,                     0],
+        [                0,                     0,                 0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert not M.is_diagonalizable()
+
+
+def test_issue_17247_expression_blowup_20():
+    M = Matrix([
+    [x + 1,  1 - x,      0,      0],
+    [1 - x,  x + 1,      0,  x + 1],
+    [    0,  1 - x,  x + 1,      0],
+    [    0,      0,      0,  x + 1]])
+    with dotprodsimp(True):
+        assert M.diagonalize() == (Matrix([
+            [1,  1, 0, (x + 1)/(x - 1)],
+            [1, -1, 0,               0],
+            [1,  1, 1,               0],
+            [0,  0, 0,               1]]),
+            Matrix([
+            [2,   0,     0,     0],
+            [0, 2*x,     0,     0],
+            [0,   0, x + 1,     0],
+            [0,   0,     0, x + 1]]))
+
+
+def test_issue_17247_expression_blowup_21():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='GE') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+
+def test_issue_17247_expression_blowup_22():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='LU') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+
+def test_issue_17247_expression_blowup_23():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='ADJ').expand() == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+
+def test_issue_17247_expression_blowup_24():
+    M = SparseMatrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='CH') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+
+def test_issue_17247_expression_blowup_25():
+    M = SparseMatrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.inv(method='LDL') == Matrix(S('''[
+            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
+            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
+            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
+            [0, 0, 0, -11328/952745 + 87616*I/952745]]'''))
+
+
+def test_issue_17247_expression_blowup_26():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024],
+        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64],
+        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512],
+        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64],
+        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128],
+        [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16],
+        [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.rank() == 4
+
+
+def test_issue_17247_expression_blowup_27():
+    M = Matrix([
+        [    0, 1 - x, x + 1, 1 - x],
+        [1 - x, x + 1,     0, x + 1],
+        [    0, 1 - x, x + 1, 1 - x],
+        [    0,     0,     1 - x, 0]])
+    with dotprodsimp(True):
+        P, J = M.jordan_form()
+        assert P.expand() == Matrix(S('''[
+            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
+            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
+            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
+            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]''')).expand()
+        assert J == Matrix(S('''[
+            [0, 1,                       0,                       0],
+            [0, 0,                       0,                       0],
+            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
+            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]]'''))
+
+
+def test_issue_17247_expression_blowup_28():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.singular_values() == S('''[
+            sqrt(14609315/131072 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
+            sqrt(14609315/131072 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
+            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2),
+            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2)]''')
+
+
+def test_issue_16823():
+    # This still needs to be fixed if not using dotprodsimp.
+    M = Matrix(S('''[
+        [1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I,15/128-3/32*I,19/256+551/1024*I],
+        [21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I,129/256-549/512*I,42533/16384+29103/8192*I],
+        [-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I],
+        [1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I],
+        [-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I],
+        [1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I],
+        [-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I],
+        [-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I],
+        [0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I],
+        [1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I],
+        [0,-4*I,0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I],
+        [0,1/4+1/2*I,1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I]]'''))
+    with dotprodsimp(True):
+        assert M.rank() == 8
+
+
+def test_issue_18531():
+    # solve_linear_system still needs fixing but the rref works.
+    M = Matrix([
+        [1, 1, 1, 1, 1, 0, 1, 0, 0],
+        [1 + sqrt(2), -1 + sqrt(2), 1 - sqrt(2), -sqrt(2) - 1, 1, 1, -1, 1, 1],
+        [-5 + 2*sqrt(2), -5 - 2*sqrt(2), -5 - 2*sqrt(2), -5 + 2*sqrt(2), -7, 2, -7, -2, 0],
+        [-3*sqrt(2) - 1, 1 - 3*sqrt(2), -1 + 3*sqrt(2), 1 + 3*sqrt(2), -7, -5, 7, -5, 3],
+        [7 - 4*sqrt(2), 4*sqrt(2) + 7, 4*sqrt(2) + 7, 7 - 4*sqrt(2), 7, -12, 7, 12, 0],
+        [-1 + 3*sqrt(2), 1 + 3*sqrt(2), -3*sqrt(2) - 1, 1 - 3*sqrt(2), 7, -5, -7, -5, 3],
+        [-3 + 2*sqrt(2), -3 - 2*sqrt(2), -3 - 2*sqrt(2), -3 + 2*sqrt(2), -1, 2, -1, -2, 0],
+        [1 - sqrt(2), -sqrt(2) - 1, 1 + sqrt(2), -1 + sqrt(2), -1, 1, 1, 1, 1]
+        ])
+    with dotprodsimp(True):
+        assert M.rref() == (Matrix([
+            [1, 0, 0, 0, 0, 0, 0, 0,  S(1)/2],
+            [0, 1, 0, 0, 0, 0, 0, 0, -S(1)/2],
+            [0, 0, 1, 0, 0, 0, 0, 0,  S(1)/2],
+            [0, 0, 0, 1, 0, 0, 0, 0, -S(1)/2],
+            [0, 0, 0, 0, 1, 0, 0, 0,    0],
+            [0, 0, 0, 0, 0, 1, 0, 0, -S(1)/2],
+            [0, 0, 0, 0, 0, 0, 1, 0,    0],
+            [0, 0, 0, 0, 0, 0, 0, 1, -S(1)/2]]), (0, 1, 2, 3, 4, 5, 6, 7))
+
+
+def test_creation():
+    raises(ValueError, lambda: Matrix(5, 5, range(20)))
+    raises(ValueError, lambda: Matrix(5, -1, []))
+    raises(IndexError, lambda: Matrix((1, 2))[2])
+    with raises(IndexError):
+        Matrix((1, 2))[3] = 5
+
+    assert Matrix() == Matrix([]) == Matrix(0, 0, [])
+    assert Matrix([[]]) == Matrix(1, 0, [])
+    assert Matrix([[], []]) == Matrix(2, 0, [])
+
+    # anything used to be allowed in a matrix
+    with warns_deprecated_sympy():
+        assert Matrix([[[1], (2,)]]).tolist() == [[[1], (2,)]]
+    with warns_deprecated_sympy():
+        assert Matrix([[[1], (2,)]]).T.tolist() == [[[1]], [(2,)]]
+    M = Matrix([[0]])
+    with warns_deprecated_sympy():
+        M[0, 0] = S.EmptySet
+
+    a = Matrix([[x, 0], [0, 0]])
+    m = a
+    assert m.cols == m.rows
+    assert m.cols == 2
+    assert m[:] == [x, 0, 0, 0]
+
+    b = Matrix(2, 2, [x, 0, 0, 0])
+    m = b
+    assert m.cols == m.rows
+    assert m.cols == 2
+    assert m[:] == [x, 0, 0, 0]
+
+    assert a == b
+
+    assert Matrix(b) == b
+
+    c23 = Matrix(2, 3, range(1, 7))
+    c13 = Matrix(1, 3, range(7, 10))
+    c = Matrix([c23, c13])
+    assert c.cols == 3
+    assert c.rows == 3
+    assert c[:] == [1, 2, 3, 4, 5, 6, 7, 8, 9]
+
+    assert Matrix(eye(2)) == eye(2)
+    assert ImmutableMatrix(ImmutableMatrix(eye(2))) == ImmutableMatrix(eye(2))
+    assert ImmutableMatrix(c) == c.as_immutable()
+    assert Matrix(ImmutableMatrix(c)) == ImmutableMatrix(c).as_mutable()
+
+    assert c is not Matrix(c)
+
+    dat = [[ones(3,2), ones(3,3)*2], [ones(2,3)*3, ones(2,2)*4]]
+    M = Matrix(dat)
+    assert M == Matrix([
+        [1, 1, 2, 2, 2],
+        [1, 1, 2, 2, 2],
+        [1, 1, 2, 2, 2],
+        [3, 3, 3, 4, 4],
+        [3, 3, 3, 4, 4]])
+    assert M.tolist() != dat
+    # keep block form if evaluate=False
+    assert Matrix(dat, evaluate=False).tolist() == dat
+    A = MatrixSymbol("A", 2, 2)
+    dat = [ones(2), A]
+    assert Matrix(dat) == Matrix([
+    [      1,       1],
+    [      1,       1],
+    [A[0, 0], A[0, 1]],
+    [A[1, 0], A[1, 1]]])
+    with warns_deprecated_sympy():
+        assert Matrix(dat, evaluate=False).tolist() == [[i] for i in dat]
+
+    # 0-dim tolerance
+    assert Matrix([ones(2), ones(0)]) == Matrix([ones(2)])
+    raises(ValueError, lambda: Matrix([ones(2), ones(0, 3)]))
+    raises(ValueError, lambda: Matrix([ones(2), ones(3, 0)]))
+
+    # mix of Matrix and iterable
+    M = Matrix([[1, 2], [3, 4]])
+    M2 = Matrix([M, (5, 6)])
+    assert M2 == Matrix([[1, 2], [3, 4], [5, 6]])
+
+
+def test_irregular_block():
+    assert Matrix.irregular(3, ones(2,1), ones(3,3)*2, ones(2,2)*3,
+        ones(1,1)*4, ones(2,2)*5, ones(1,2)*6, ones(1,2)*7) == Matrix([
+        [1, 2, 2, 2, 3, 3],
+        [1, 2, 2, 2, 3, 3],
+        [4, 2, 2, 2, 5, 5],
+        [6, 6, 7, 7, 5, 5]])
+
+
+def test_slicing():
+    m0 = eye(4)
+    assert m0[:3, :3] == eye(3)
+    assert m0[2:4, 0:2] == zeros(2)
+
+    m1 = Matrix(3, 3, lambda i, j: i + j)
+    assert m1[0, :] == Matrix(1, 3, (0, 1, 2))
+    assert m1[1:3, 1] == Matrix(2, 1, (2, 3))
+
+    m2 = Matrix([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]])
+    assert m2[:, -1] == Matrix(4, 1, [3, 7, 11, 15])
+    assert m2[-2:, :] == Matrix([[8, 9, 10, 11], [12, 13, 14, 15]])
+
+
+def test_submatrix_assignment():
+    m = zeros(4)
+    m[2:4, 2:4] = eye(2)
+    assert m == Matrix(((0, 0, 0, 0),
+                        (0, 0, 0, 0),
+                        (0, 0, 1, 0),
+                        (0, 0, 0, 1)))
+    m[:2, :2] = eye(2)
+    assert m == eye(4)
+    m[:, 0] = Matrix(4, 1, (1, 2, 3, 4))
+    assert m == Matrix(((1, 0, 0, 0),
+                        (2, 1, 0, 0),
+                        (3, 0, 1, 0),
+                        (4, 0, 0, 1)))
+    m[:, :] = zeros(4)
+    assert m == zeros(4)
+    m[:, :] = [(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16)]
+    assert m == Matrix(((1, 2, 3, 4),
+                        (5, 6, 7, 8),
+                        (9, 10, 11, 12),
+                        (13, 14, 15, 16)))
+    m[:2, 0] = [0, 0]
+    assert m == Matrix(((0, 2, 3, 4),
+                        (0, 6, 7, 8),
+                        (9, 10, 11, 12),
+                        (13, 14, 15, 16)))
+
+
+def test_reshape():
+    m0 = eye(3)
+    assert m0.reshape(1, 9) == Matrix(1, 9, (1, 0, 0, 0, 1, 0, 0, 0, 1))
+    m1 = Matrix(3, 4, lambda i, j: i + j)
+    assert m1.reshape(
+        4, 3) == Matrix(((0, 1, 2), (3, 1, 2), (3, 4, 2), (3, 4, 5)))
+    assert m1.reshape(2, 6) == Matrix(((0, 1, 2, 3, 1, 2), (3, 4, 2, 3, 4, 5)))
+
+
+def test_applyfunc():
+    m0 = eye(3)
+    assert m0.applyfunc(lambda x: 2*x) == eye(3)*2
+    assert m0.applyfunc(lambda x: 0) == zeros(3)
+
+
+def test_expand():
+    m0 = Matrix([[x*(x + y), 2], [((x + y)*y)*x, x*(y + x*(x + y))]])
+    # Test if expand() returns a matrix
+    m1 = m0.expand()
+    assert m1 == Matrix(
+        [[x*y + x**2, 2], [x*y**2 + y*x**2, x*y + y*x**2 + x**3]])
+
+    a = Symbol('a', real=True)
+
+    assert Matrix([exp(I*a)]).expand(complex=True) == \
+        Matrix([cos(a) + I*sin(a)])
+
+    assert Matrix([[0, 1, 2], [0, 0, -1], [0, 0, 0]]).exp() == Matrix([
+        [1, 1, Rational(3, 2)],
+        [0, 1, -1],
+        [0, 0, 1]]
+    )
+
+
+def test_refine():
+    m0 = Matrix([[Abs(x)**2, sqrt(x**2)],
+                [sqrt(x**2)*Abs(y)**2, sqrt(y**2)*Abs(x)**2]])
+    m1 = m0.refine(Q.real(x) & Q.real(y))
+    assert m1 == Matrix([[x**2, Abs(x)], [y**2*Abs(x), x**2*Abs(y)]])
+
+    m1 = m0.refine(Q.positive(x) & Q.positive(y))
+    assert m1 == Matrix([[x**2, x], [x*y**2, x**2*y]])
+
+    m1 = m0.refine(Q.negative(x) & Q.negative(y))
+    assert m1 == Matrix([[x**2, -x], [-x*y**2, -x**2*y]])
+
+
+def test_random():
+    M = randMatrix(3, 3)
+    M = randMatrix(3, 3, seed=3)
+    assert M == randMatrix(3, 3, seed=3)
+
+    M = randMatrix(3, 4, 0, 150)
+    M = randMatrix(3, seed=4, symmetric=True)
+    assert M == randMatrix(3, seed=4, symmetric=True)
+
+    S = M.copy()
+    S.simplify()
+    assert S == M  # doesn't fail when elements are Numbers, not int
+
+    rng = random.Random(4)
+    assert M == randMatrix(3, symmetric=True, prng=rng)
+
+    # Ensure symmetry
+    for size in (10, 11): # Test odd and even
+        for percent in (100, 70, 30):
+            M = randMatrix(size, symmetric=True, percent=percent, prng=rng)
+            assert M == M.T
+
+    M = randMatrix(10, min=1, percent=70)
+    zero_count = 0
+    for i in range(M.shape[0]):
+        for j in range(M.shape[1]):
+            if M[i, j] == 0:
+                zero_count += 1
+    assert zero_count == 30
+
+
+def test_inverse():
+    A = eye(4)
+    assert A.inv() == eye(4)
+    assert A.inv(method="LU") == eye(4)
+    assert A.inv(method="ADJ") == eye(4)
+    assert A.inv(method="CH") == eye(4)
+    assert A.inv(method="LDL") == eye(4)
+    assert A.inv(method="QR") == eye(4)
+    A = Matrix([[2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    Ainv = A.inv()
+    assert A*Ainv == eye(3)
+    assert A.inv(method="LU") == Ainv
+    assert A.inv(method="ADJ") == Ainv
+    assert A.inv(method="CH") == Ainv
+    assert A.inv(method="LDL") == Ainv
+    assert A.inv(method="QR") == Ainv
+
+    AA = Matrix([[0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0],
+            [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0],
+            [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
+            [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0],
+            [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0],
+            [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1],
+            [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0],
+            [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1],
+            [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1],
+            [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0],
+            [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0],
+            [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0],
+            [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1],
+            [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0],
+            [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0],
+            [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0],
+            [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1],
+            [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1],
+            [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1],
+            [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+            [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1],
+            [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1],
+            [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0],
+            [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0],
+            [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]])
+    assert AA.inv(method="BLOCK") * AA == eye(AA.shape[0])
+    # test that immutability is not a problem
+    cls = ImmutableMatrix
+    m = cls([[48, 49, 31],
+             [ 9, 71, 94],
+             [59, 28, 65]])
+    assert all(type(m.inv(s)) is cls for s in 'GE ADJ LU CH LDL QR'.split())
+    cls = ImmutableSparseMatrix
+    m = cls([[48, 49, 31],
+             [ 9, 71, 94],
+             [59, 28, 65]])
+    assert all(type(m.inv(s)) is cls for s in 'GE ADJ LU CH LDL QR'.split())
+
+
+def test_inverse_symbolic_float_issue_26821():
+    Tau, Tau_syn_in, Tau_syn_ex, C_m, Tau_syn_gap = symbols("Tau Tau_syn_in Tau_syn_ex C_m Tau_syn_gap")
+    __h = symbols("__h")
+
+    M = Matrix([
+        [0,0,0,0,0,(1.0*Tau*__h-1.0*Tau_syn_in*__h)/(2.0*Tau-1.0*Tau_syn_in),-1.0*Tau*Tau_syn_in/(2.0*Tau-1.0*Tau_syn_in)],
+        [0,0,0,0,0,(-1.0*Tau*__h+1.0*Tau_syn_in*__h)/(2.0*Tau*Tau_syn_in-1.0*Tau_syn_in**2),1.0],
+        [0,(1.0*Tau*__h-1.0*Tau_syn_ex*__h)/(2.0*Tau-1.0*Tau_syn_ex),-1.0*Tau*Tau_syn_ex/(2.0*Tau-1.0*Tau_syn_ex),0,0,0,0],
+        [0,(-1.0*Tau*__h+1.0*Tau_syn_ex*__h)/(2.0*Tau*Tau_syn_ex-1.0*Tau_syn_ex**2),1.0,0,0,0,0],
+        [0,0,0,(1.0*Tau*__h-1.0*Tau_syn_gap*__h)/(2.0*Tau-1.0*Tau_syn_gap),-1.0*Tau*Tau_syn_gap/(2.0*Tau-1.0*Tau_syn_gap),0,0],
+        [0,0,0,(-1.0*Tau*__h+1.0*Tau_syn_gap*__h)/(2.0*Tau*Tau_syn_gap-1.0*Tau_syn_gap**2),1.0,0,0],
+        [1.0,-1.0*Tau*Tau_syn_ex*__h/(2.0*C_m*Tau-1.0*C_m*Tau_syn_ex),0,-1.0*Tau*Tau_syn_gap*__h/(2.0*C_m*Tau-1.0*C_m*Tau_syn_gap),0,-1.0*Tau*Tau_syn_in*__h/(2.0*C_m*Tau-1.0*C_m*Tau_syn_in),0]
+    ])
+
+    Mi = M.inv()
+
+    assert (M*Mi - eye(7)).applyfunc(cancel) == zeros(7)
+
+    # https://github.com/sympy/sympy/issues/26821
+    # Previously very large floats were in the result.
+    assert max(abs(f) for f in Mi.atoms(Float)) < 1e3
+
+
+@slow
+def test_matrix_exponential_issue_26821():
+    # The symbol names matter in the original bug...
+    a, b, c, d, e = symbols("Tau, Tau_syn_in, Tau_syn_ex, C_m, Tau_syn_gap")
+    t = symbols("__h")
+    M = Matrix([
+        [      0,  1.0,       0,    0,       0,    0,    0],
+        [-1/b**2, -2/b,       0,    0,       0,    0,    0],
+        [      0,    0,       0,  1.0,       0,    0,    0],
+        [      0,    0, -1/c**2, -2/c,       0,    0,    0],
+        [      0,    0,       0,    0,       0,    1,    0],
+        [      0,    0,       0,    0, -1/e**2, -2/e,    0],
+        [    1/d,    0,     1/d,    0,     1/d,    0, -1/a]
+    ])
+
+    Me = (t*M).exp()
+    assert (Me.diff(t) - M*Me).applyfunc(cancel) == zeros(7)
+    # https://github.com/sympy/sympy/issues/26821
+    # Previously very large floats were in the result.
+    assert max(abs(f) for f in Me.atoms(Float)) < 1e3
+
+
+def test_jacobian_hessian():
+    L = Matrix(1, 2, [x**2*y, 2*y**2 + x*y])
+    syms = [x, y]
+    assert L.jacobian(syms) == Matrix([[2*x*y, x**2], [y, 4*y + x]])
+
+    L = Matrix(1, 2, [x, x**2*y**3])
+    assert L.jacobian(syms) == Matrix([[1, 0], [2*x*y**3, x**2*3*y**2]])
+
+    f = x**2*y
+    syms = [x, y]
+    assert hessian(f, syms) == Matrix([[2*y, 2*x], [2*x, 0]])
+
+    f = x**2*y**3
+    assert hessian(f, syms) == \
+        Matrix([[2*y**3, 6*x*y**2], [6*x*y**2, 6*x**2*y]])
+
+    f = z + x*y**2
+    g = x**2 + 2*y**3
+    ans = Matrix([[0,   2*y],
+                  [2*y, 2*x]])
+    assert ans == hessian(f, Matrix([x, y]))
+    assert ans == hessian(f, Matrix([x, y]).T)
+    assert hessian(f, (y, x), [g]) == Matrix([
+        [     0, 6*y**2, 2*x],
+        [6*y**2,    2*x, 2*y],
+        [   2*x,    2*y,   0]])
+
+
+def test_wronskian():
+    assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
+    assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
+    assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
+    assert wronskian([1, x, x**2], x) == 2
+    w1 = -6*exp(x)*sin(x)*x + 6*cos(x)*exp(x)*x**2 - 6*exp(x)*cos(x)*x - \
+        exp(x)*cos(x)*x**3 + exp(x)*sin(x)*x**3
+    assert wronskian([exp(x), cos(x), x**3], x).expand() == w1
+    assert wronskian([exp(x), cos(x), x**3], x, method='berkowitz').expand() \
+        == w1
+    w2 = -x**3*cos(x)**2 - x**3*sin(x)**2 - 6*x*cos(x)**2 - 6*x*sin(x)**2
+    assert wronskian([sin(x), cos(x), x**3], x).expand() == w2
+    assert wronskian([sin(x), cos(x), x**3], x, method='berkowitz').expand() \
+        == w2
+    assert wronskian([], x) == 1
+
+
+def test_xreplace():
+    assert Matrix([[1, x], [x, 4]]).xreplace({x: 5}) == \
+        Matrix([[1, 5], [5, 4]])
+    assert Matrix([[x, 2], [x + y, 4]]).xreplace({x: -1, y: -2}) == \
+        Matrix([[-1, 2], [-3, 4]])
+    for cls in all_classes:
+        assert Matrix([[2, 0], [0, 2]]) == cls.eye(2).xreplace({1: 2})
+
+
+def test_simplify():
+    n = Symbol('n')
+    f = Function('f')
+
+    M = Matrix([[            1/x + 1/y,                 (x + x*y) / x  ],
+                [ (f(x) + y*f(x))/f(x), 2 * (1/n - cos(n * pi)/n) / pi ]])
+    M.simplify()
+    assert M == Matrix([[ (x + y)/(x * y),                        1 + y ],
+                        [           1 + y, 2*((1 - 1*cos(pi*n))/(pi*n)) ]])
+    eq = (1 + x)**2
+    M = Matrix([[eq]])
+    M.simplify()
+    assert M == Matrix([[eq]])
+    M.simplify(ratio=oo)
+    assert M == Matrix([[eq.simplify(ratio=oo)]])
+
+    n = Symbol('n')
+    f = Function('f')
+
+    M = ImmutableMatrix([
+        [            1/x + 1/y,                 (x + x*y) / x  ],
+        [ (f(x) + y*f(x))/f(x), 2 * (1/n - cos(n * pi)/n) / pi ]
+    ])
+    assert M.simplify() == Matrix([
+        [ (x + y)/(x * y),                        1 + y ],
+        [           1 + y, 2*((1 - 1*cos(pi*n))/(pi*n)) ]
+    ])
+
+    eq = (1 + x)**2
+    M = ImmutableMatrix([[eq]])
+    assert M.simplify() == Matrix([[eq]])
+    assert M.simplify(ratio=oo) == Matrix([[eq.simplify(ratio=oo)]])
+
+    assert simplify(ImmutableMatrix([[sin(x)**2 + cos(x)**2]])) == \
+                    ImmutableMatrix([[1]])
+
+    # https://github.com/sympy/sympy/issues/19353
+    m = Matrix([[30, 2], [3, 4]])
+    assert (1/(m.trace())).simplify() == Rational(1, 34)
+
+def test_transpose():
+    M = Matrix([[1, 2, 3, 4, 5, 6, 7, 8, 9, 0],
+                [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]])
+    assert M.T == Matrix( [ [1, 1],
+                            [2, 2],
+                            [3, 3],
+                            [4, 4],
+                            [5, 5],
+                            [6, 6],
+                            [7, 7],
+                            [8, 8],
+                            [9, 9],
+                            [0, 0] ])
+    assert M.T.T == M
+    assert M.T == M.transpose()
+
+
+def test_conj_dirac():
+    raises(AttributeError, lambda: eye(3).D)
+
+    M = Matrix([[1, I, I, I],
+                [0, 1, I, I],
+                [0, 0, 1, I],
+                [0, 0, 0, 1]])
+
+    assert M.D == Matrix([[ 1,  0,  0,  0],
+                          [-I,  1,  0,  0],
+                          [-I, -I, -1,  0],
+                          [-I, -I,  I, -1]])
+
+
+def test_trace():
+    M = Matrix([[1, 0, 0],
+                [0, 5, 0],
+                [0, 0, 8]])
+    assert M.trace() == 14
+
+
+def test_shape():
+    m = Matrix(1, 2, [0, 0])
+    assert m.shape == (1, 2)
+    M = Matrix([[x, 0, 0],
+                [0, y, 0]])
+    assert M.shape == (2, 3)
+
+
+def test_col_row_op():
+    M = Matrix([[x, 0, 0],
+                [0, y, 0]])
+    M.row_op(1, lambda r, j: r + j + 1)
+    assert M == Matrix([[x,     0, 0],
+                        [1, y + 2, 3]])
+
+    M.col_op(0, lambda c, j: c + y**j)
+    assert M == Matrix([[x + 1,     0, 0],
+                        [1 + y, y + 2, 3]])
+
+    # neither row nor slice give copies that allow the original matrix to
+    # be changed
+    assert M.row(0) == Matrix([[x + 1, 0, 0]])
+    r1 = M.row(0)
+    r1[0] = 42
+    assert M[0, 0] == x + 1
+    r1 = M[0, :-1]  # also testing negative slice
+    r1[0] = 42
+    assert M[0, 0] == x + 1
+    c1 = M.col(0)
+    assert c1 == Matrix([x + 1, 1 + y])
+    c1[0] = 0
+    assert M[0, 0] == x + 1
+    c1 = M[:, 0]
+    c1[0] = 42
+    assert M[0, 0] == x + 1
+
+
+def test_row_mult():
+    M = Matrix([[1,2,3],
+               [4,5,6]])
+    M.row_mult(1,3)
+    assert M[1,0] == 12
+    assert M[0,0] == 1
+    assert M[1,2] == 18
+
+
+def test_row_add():
+    M = Matrix([[1,2,3],
+               [4,5,6],
+               [1,1,1]])
+    M.row_add(2,0,5)
+    assert M[0,0] == 6
+    assert M[1,0] == 4
+    assert M[0,2] == 8
+
+
+def test_zip_row_op():
+    for cls in mutable_classes: # XXX: immutable matrices don't support row ops
+        M = cls.eye(3)
+        M.zip_row_op(1, 0, lambda v, u: v + 2*u)
+        assert M == cls([[1, 0, 0],
+                         [2, 1, 0],
+                         [0, 0, 1]])
+
+        M = cls.eye(3)*2
+        M[0, 1] = -1
+        M.zip_row_op(1, 0, lambda v, u: v + 2*u); M
+        assert M == cls([[2, -1, 0],
+                         [4,  0, 0],
+                         [0,  0, 2]])
+
+
+def test_issue_3950():
+    m = Matrix([1, 2, 3])
+    a = Matrix([1, 2, 3])
+    b = Matrix([2, 2, 3])
+    assert not (m in [])
+    assert not (m in [1])
+    assert m != 1
+    assert m == a
+    assert m != b
+
+
+def test_issue_3981():
+    class Index1:
+        def __index__(self):
+            return 1
+
+    class Index2:
+        def __index__(self):
+            return 2
+    index1 = Index1()
+    index2 = Index2()
+
+    m = Matrix([1, 2, 3])
+
+    assert m[index2] == 3
+
+    m[index2] = 5
+    assert m[2] == 5
+
+    m = Matrix([[1, 2, 3], [4, 5, 6]])
+    assert m[index1, index2] == 6
+    assert m[1, index2] == 6
+    assert m[index1, 2] == 6
+
+    m[index1, index2] = 4
+    assert m[1, 2] == 4
+    m[1, index2] = 6
+    assert m[1, 2] == 6
+    m[index1, 2] = 8
+    assert m[1, 2] == 8
+
+
+def test_is_upper():
+    a = Matrix([[1, 2, 3]])
+    assert a.is_upper is True
+    a = Matrix([[1], [2], [3]])
+    assert a.is_upper is False
+    a = zeros(4, 2)
+    assert a.is_upper is True
+
+
+def test_is_lower():
+    a = Matrix([[1, 2, 3]])
+    assert a.is_lower is False
+    a = Matrix([[1], [2], [3]])
+    assert a.is_lower is True
+
+
+def test_is_nilpotent():
+    a = Matrix(4, 4, [0, 2, 1, 6, 0, 0, 1, 2, 0, 0, 0, 3, 0, 0, 0, 0])
+    assert a.is_nilpotent()
+    a = Matrix([[1, 0], [0, 1]])
+    assert not a.is_nilpotent()
+    a = Matrix([])
+    assert a.is_nilpotent()
+
+
+def test_zeros_ones_fill():
+    n, m = 3, 5
+
+    a = zeros(n, m)
+    a.fill( 5 )
+
+    b = 5 * ones(n, m)
+
+    assert a == b
+    assert a.rows == b.rows == 3
+    assert a.cols == b.cols == 5
+    assert a.shape == b.shape == (3, 5)
+    assert zeros(2) == zeros(2, 2)
+    assert ones(2) == ones(2, 2)
+    assert zeros(2, 3) == Matrix(2, 3, [0]*6)
+    assert ones(2, 3) == Matrix(2, 3, [1]*6)
+
+    a.fill(0)
+    assert a == zeros(n, m)
+
+
+def test_empty_zeros():
+    a = zeros(0)
+    assert a == Matrix()
+    a = zeros(0, 2)
+    assert a.rows == 0
+    assert a.cols == 2
+    a = zeros(2, 0)
+    assert a.rows == 2
+    assert a.cols == 0
+
+
+def test_issue_3749():
+    a = Matrix([[x**2, x*y], [x*sin(y), x*cos(y)]])
+    assert a.diff(x) == Matrix([[2*x, y], [sin(y), cos(y)]])
+    assert Matrix([
+        [x, -x, x**2],
+        [exp(x), 1/x - exp(-x), x + 1/x]]).limit(x, oo) == \
+        Matrix([[oo, -oo, oo], [oo, 0, oo]])
+    assert Matrix([
+        [(exp(x) - 1)/x, 2*x + y*x, x**x ],
+        [1/x, abs(x), abs(sin(x + 1))]]).limit(x, 0) == \
+        Matrix([[1, 0, 1], [oo, 0, sin(1)]])
+    assert a.integrate(x) == Matrix([
+        [Rational(1, 3)*x**3, y*x**2/2],
+        [x**2*sin(y)/2, x**2*cos(y)/2]])
+
+
+def test_inv_iszerofunc():
+    A = eye(4)
+    A.col_swap(0, 1)
+    for method in "GE", "LU":
+        assert A.inv(method=method, iszerofunc=lambda x: x == 0) == \
+            A.inv(method="ADJ")
+
+
+def test_jacobian_metrics():
+    rho, phi = symbols("rho,phi")
+    X = Matrix([rho*cos(phi), rho*sin(phi)])
+    Y = Matrix([rho, phi])
+    J = X.jacobian(Y)
+    assert J == X.jacobian(Y.T)
+    assert J == (X.T).jacobian(Y)
+    assert J == (X.T).jacobian(Y.T)
+    g = J.T*eye(J.shape[0])*J
+    g = g.applyfunc(trigsimp)
+    assert g == Matrix([[1, 0], [0, rho**2]])
+
+
+def test_jacobian2():
+    rho, phi = symbols("rho,phi")
+    X = Matrix([rho*cos(phi), rho*sin(phi), rho**2])
+    Y = Matrix([rho, phi])
+    J = Matrix([
+        [cos(phi), -rho*sin(phi)],
+        [sin(phi),  rho*cos(phi)],
+        [   2*rho,             0],
+    ])
+    assert X.jacobian(Y) == J
+
+
+def test_issue_4564():
+    X = Matrix([exp(x + y + z), exp(x + y + z), exp(x + y + z)])
+    Y = Matrix([x, y, z])
+    for i in range(1, 3):
+        for j in range(1, 3):
+            X_slice = X[:i, :]
+            Y_slice = Y[:j, :]
+            J = X_slice.jacobian(Y_slice)
+            assert J.rows == i
+            assert J.cols == j
+            for k in range(j):
+                assert J[:, k] == X_slice
+
+
+def test_nonvectorJacobian():
+    X = Matrix([[exp(x + y + z), exp(x + y + z)],
+                [exp(x + y + z), exp(x + y + z)]])
+    raises(TypeError, lambda: X.jacobian(Matrix([x, y, z])))
+    X = X[0, :]
+    Y = Matrix([[x, y], [x, z]])
+    raises(TypeError, lambda: X.jacobian(Y))
+    raises(TypeError, lambda: X.jacobian(Matrix([ [x, y], [x, z] ])))
+
+
+def test_vec():
+    m = Matrix([[1, 3], [2, 4]])
+    m_vec = m.vec()
+    assert m_vec.cols == 1
+    for i in range(4):
+        assert m_vec[i] == i + 1
+
+
+def test_vech():
+    m = Matrix([[1, 2], [2, 3]])
+    m_vech = m.vech()
+    assert m_vech.cols == 1
+    for i in range(3):
+        assert m_vech[i] == i + 1
+    m_vech = m.vech(diagonal=False)
+    assert m_vech[0] == 2
+
+    m = Matrix([[1, x*(x + y)], [y*x + x**2, 1]])
+    m_vech = m.vech(diagonal=False)
+    assert m_vech[0] == y*x + x**2
+
+    m = Matrix([[1, x*(x + y)], [y*x, 1]])
+    m_vech = m.vech(diagonal=False, check_symmetry=False)
+    assert m_vech[0] == y*x
+
+    raises(ShapeError, lambda: Matrix([[1, 3]]).vech())
+    raises(ValueError, lambda: Matrix([[1, 3], [2, 4]]).vech())
+    raises(ShapeError, lambda: Matrix([[1, 3]]).vech())
+    raises(ValueError, lambda: Matrix([[1, 3], [2, 4]]).vech())
+
+
+def test_diag():
+    # mostly tested in testcommonmatrix.py
+    assert diag([1, 2, 3]) == Matrix([1, 2, 3])
+    m = [1, 2, [3]]
+    raises(ValueError, lambda: diag(m))
+    assert diag(m, strict=False) == Matrix([1, 2, 3])
+
+
+def test_inv_block():
+    a = Matrix([[1, 2], [2, 3]])
+    b = Matrix([[3, x], [y, 3]])
+    c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
+    A = diag(a, b, b)
+    assert A.inv(try_block_diag=True) == diag(a.inv(), b.inv(), b.inv())
+    A = diag(a, b, c)
+    assert A.inv(try_block_diag=True) == diag(a.inv(), b.inv(), c.inv())
+    A = diag(a, c, b)
+    assert A.inv(try_block_diag=True) == diag(a.inv(), c.inv(), b.inv())
+    A = diag(a, a, b, a, c, a)
+    assert A.inv(try_block_diag=True) == diag(
+        a.inv(), a.inv(), b.inv(), a.inv(), c.inv(), a.inv())
+    assert A.inv(try_block_diag=True, method="ADJ") == diag(
+        a.inv(method="ADJ"), a.inv(method="ADJ"), b.inv(method="ADJ"),
+        a.inv(method="ADJ"), c.inv(method="ADJ"), a.inv(method="ADJ"))
+
+
+def test_creation_args():
+    """
+    Check that matrix dimensions can be specified using any reasonable type
+    (see issue 4614).
+    """
+    raises(ValueError, lambda: zeros(3, -1))
+    raises(TypeError, lambda: zeros(1, 2, 3, 4))
+    assert zeros(int(3)) == zeros(3)
+    assert zeros(Integer(3)) == zeros(3)
+    raises(ValueError, lambda: zeros(3.))
+    assert eye(int(3)) == eye(3)
+    assert eye(Integer(3)) == eye(3)
+    raises(ValueError, lambda: eye(3.))
+    assert ones(int(3), Integer(4)) == ones(3, 4)
+    raises(TypeError, lambda: Matrix(5))
+    raises(TypeError, lambda: Matrix(1, 2))
+    raises(ValueError, lambda: Matrix([1, [2]]))
+
+
+def test_diagonal_symmetrical():
+    m = Matrix(2, 2, [0, 1, 1, 0])
+    assert not m.is_diagonal()
+    assert m.is_symmetric()
+    assert m.is_symmetric(simplify=False)
+
+    m = Matrix(2, 2, [1, 0, 0, 1])
+    assert m.is_diagonal()
+
+    m = diag(1, 2, 3)
+    assert m.is_diagonal()
+    assert m.is_symmetric()
+
+    m = Matrix(3, 3, [1, 0, 0, 0, 2, 0, 0, 0, 3])
+    assert m == diag(1, 2, 3)
+
+    m = Matrix(2, 3, zeros(2, 3))
+    assert not m.is_symmetric()
+    assert m.is_diagonal()
+
+    m = Matrix(((5, 0), (0, 6), (0, 0)))
+    assert m.is_diagonal()
+
+    m = Matrix(((5, 0, 0), (0, 6, 0)))
+    assert m.is_diagonal()
+
+    m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
+    assert m.is_symmetric()
+    assert not m.is_symmetric(simplify=False)
+    assert m.expand().is_symmetric(simplify=False)
+
+
+def test_diagonalization():
+    m = Matrix([[1, 2+I], [2-I, 3]])
+    assert m.is_diagonalizable()
+
+    m = Matrix(3, 2, [-3, 1, -3, 20, 3, 10])
+    assert not m.is_diagonalizable()
+    assert not m.is_symmetric()
+    raises(NonSquareMatrixError, lambda: m.diagonalize())
+
+    # diagonalizable
+    m = diag(1, 2, 3)
+    (P, D) = m.diagonalize()
+    assert P == eye(3)
+    assert D == m
+
+    m = Matrix(2, 2, [0, 1, 1, 0])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+
+    m = Matrix(2, 2, [1, 0, 0, 3])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+    assert P == eye(2)
+    assert D == m
+
+    m = Matrix(2, 2, [1, 1, 0, 0])
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+
+    m = Matrix(3, 3, [1, 2, 0, 0, 3, 0, 2, -4, 2])
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+    for i in P:
+        assert i.as_numer_denom()[1] == 1
+
+    m = Matrix(2, 2, [1, 0, 0, 0])
+    assert m.is_diagonal()
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+    assert P == Matrix([[0, 1], [1, 0]])
+
+    # diagonalizable, complex only
+    m = Matrix(2, 2, [0, 1, -1, 0])
+    assert not m.is_diagonalizable(True)
+    raises(MatrixError, lambda: m.diagonalize(True))
+    assert m.is_diagonalizable()
+    (P, D) = m.diagonalize()
+    assert P.inv() * m * P == D
+
+    # not diagonalizable
+    m = Matrix(2, 2, [0, 1, 0, 0])
+    assert not m.is_diagonalizable()
+    raises(MatrixError, lambda: m.diagonalize())
+
+    m = Matrix(3, 3, [-3, 1, -3, 20, 3, 10, 2, -2, 4])
+    assert not m.is_diagonalizable()
+    raises(MatrixError, lambda: m.diagonalize())
+
+    # symbolic
+    a, b, c, d = symbols('a b c d')
+    m = Matrix(2, 2, [a, c, c, b])
+    assert m.is_symmetric()
+    assert m.is_diagonalizable()
+
+
+def test_issue_15887():
+    # Mutable matrix should not use cache
+    a = MutableDenseMatrix([[0, 1], [1, 0]])
+    assert a.is_diagonalizable() is True
+    a[1, 0] = 0
+    assert a.is_diagonalizable() is False
+
+    a = MutableDenseMatrix([[0, 1], [1, 0]])
+    a.diagonalize()
+    a[1, 0] = 0
+    raises(MatrixError, lambda: a.diagonalize())
+
+
+def test_jordan_form():
+
+    m = Matrix(3, 2, [-3, 1, -3, 20, 3, 10])
+    raises(NonSquareMatrixError, lambda: m.jordan_form())
+
+    # diagonalizable
+    m = Matrix(3, 3, [7, -12, 6, 10, -19, 10, 12, -24, 13])
+    Jmust = Matrix(3, 3, [-1, 0, 0, 0, 1, 0, 0, 0, 1])
+    P, J = m.jordan_form()
+    assert Jmust == J
+    assert Jmust == m.diagonalize()[1]
+
+    # m = Matrix(3, 3, [0, 6, 3, 1, 3, 1, -2, 2, 1])
+    # m.jordan_form()  # very long
+    # m.jordan_form()  #
+
+    # diagonalizable, complex only
+
+    # Jordan cells
+    # complexity: one of eigenvalues is zero
+    m = Matrix(3, 3, [0, 1, 0, -4, 4, 0, -2, 1, 2])
+    # The blocks are ordered according to the value of their eigenvalues,
+    # in order to make the matrix compatible with .diagonalize()
+    Jmust = Matrix(3, 3, [2, 1, 0, 0, 2, 0, 0, 0, 2])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    # complexity: all of eigenvalues are equal
+    m = Matrix(3, 3, [2, 6, -15, 1, 1, -5, 1, 2, -6])
+    # Jmust = Matrix(3, 3, [-1, 0, 0, 0, -1, 1, 0, 0, -1])
+    # same here see 1456ff
+    Jmust = Matrix(3, 3, [-1, 1, 0, 0, -1, 0, 0, 0, -1])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    # complexity: two of eigenvalues are zero
+    m = Matrix(3, 3, [4, -5, 2, 5, -7, 3, 6, -9, 4])
+    Jmust = Matrix(3, 3, [0, 1, 0, 0, 0, 0, 0, 0, 1])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    m = Matrix(4, 4, [6, 5, -2, -3, -3, -1, 3, 3, 2, 1, -2, -3, -1, 1, 5, 5])
+    Jmust = Matrix(4, 4, [2, 1, 0, 0,
+                          0, 2, 0, 0,
+              0, 0, 2, 1,
+              0, 0, 0, 2]
+              )
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    m = Matrix(4, 4, [6, 2, -8, -6, -3, 2, 9, 6, 2, -2, -8, -6, -1, 0, 3, 4])
+    # Jmust = Matrix(4, 4, [2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, -2])
+    # same here see 1456ff
+    Jmust = Matrix(4, 4, [-2, 0, 0, 0,
+                           0, 2, 1, 0,
+                           0, 0, 2, 0,
+                           0, 0, 0, 2])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    m = Matrix(4, 4, [5, 4, 2, 1, 0, 1, -1, -1, -1, -1, 3, 0, 1, 1, -1, 2])
+    assert not m.is_diagonalizable()
+    Jmust = Matrix(4, 4, [1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 1, 0, 0, 0, 4])
+    P, J = m.jordan_form()
+    assert Jmust == J
+
+    # checking for maximum precision to remain unchanged
+    m = Matrix([[Float('1.0', precision=110), Float('2.0', precision=110)],
+                [Float('3.14159265358979323846264338327', precision=110), Float('4.0', precision=110)]])
+    P, J = m.jordan_form()
+    for term in J.values():
+        if isinstance(term, Float):
+            assert term._prec == 110
+
+
+def test_jordan_form_complex_issue_9274():
+    A = Matrix([[ 2,  4,  1,  0],
+                [-4,  2,  0,  1],
+                [ 0,  0,  2,  4],
+                [ 0,  0, -4,  2]])
+    p = 2 - 4*I
+    q = 2 + 4*I
+    Jmust1 = Matrix([[p, 1, 0, 0],
+                     [0, p, 0, 0],
+                     [0, 0, q, 1],
+                     [0, 0, 0, q]])
+    Jmust2 = Matrix([[q, 1, 0, 0],
+                     [0, q, 0, 0],
+                     [0, 0, p, 1],
+                     [0, 0, 0, p]])
+    P, J = A.jordan_form()
+    assert J == Jmust1 or J == Jmust2
+    assert simplify(P*J*P.inv()) == A
+
+
+def test_issue_10220():
+    # two non-orthogonal Jordan blocks with eigenvalue 1
+    M = Matrix([[1, 0, 0, 1],
+                [0, 1, 1, 0],
+                [0, 0, 1, 1],
+                [0, 0, 0, 1]])
+    P, J = M.jordan_form()
+    assert P == Matrix([[0, 1, 0, 1],
+                        [1, 0, 0, 0],
+                        [0, 1, 0, 0],
+                        [0, 0, 1, 0]])
+    assert J == Matrix([
+                        [1, 1, 0, 0],
+                        [0, 1, 1, 0],
+                        [0, 0, 1, 0],
+                        [0, 0, 0, 1]])
+
+
+def test_jordan_form_issue_15858():
+    A = Matrix([
+        [1, 1, 1, 0],
+        [-2, -1, 0, -1],
+        [0, 0, -1, -1],
+        [0, 0, 2, 1]])
+    (P, J) = A.jordan_form()
+    assert P.expand() == Matrix([
+        [    -I,          -I/2,      I,           I/2],
+        [-1 + I,             0, -1 - I,             0],
+        [     0, -S(1)/2 - I/2,      0, -S(1)/2 + I/2],
+        [     0,             1,      0,             1]])
+    assert J == Matrix([
+        [-I, 1, 0, 0],
+        [0, -I, 0, 0],
+        [0, 0, I, 1],
+        [0, 0, 0, I]])
+
+
+def test_Matrix_berkowitz_charpoly():
+    UA, K_i, K_w = symbols('UA K_i K_w')
+
+    A = Matrix([[-K_i - UA + K_i**2/(K_i + K_w),       K_i*K_w/(K_i + K_w)],
+                [           K_i*K_w/(K_i + K_w), -K_w + K_w**2/(K_i + K_w)]])
+
+    charpoly = A.charpoly(x)
+
+    assert charpoly == \
+        Poly(x**2 + (K_i*UA + K_w*UA + 2*K_i*K_w)/(K_i + K_w)*x +
+        K_i*K_w*UA/(K_i + K_w), x, domain='ZZ(K_i,K_w,UA)')
+
+    assert type(charpoly) is PurePoly
+
+    A = Matrix([[1, 3], [2, 0]])
+    assert A.charpoly() == A.charpoly(x) == PurePoly(x**2 - x - 6)
+
+    A = Matrix([[1, 2], [x, 0]])
+    p = A.charpoly(x)
+    assert p.gen != x
+    assert p.as_expr().subs(p.gen, x) == x**2 - 3*x
+
+
+def test_exp_jordan_block():
+    l = Symbol('lamda')
+
+    m = Matrix.jordan_block(1, l)
+    assert m._eval_matrix_exp_jblock() == Matrix([[exp(l)]])
+
+    m = Matrix.jordan_block(3, l)
+    assert m._eval_matrix_exp_jblock() == \
+        Matrix([
+            [exp(l), exp(l), exp(l)/2],
+            [0, exp(l), exp(l)],
+            [0, 0, exp(l)]])
+
+
+def test_exp():
+    m = Matrix([[3, 4], [0, -2]])
+    m_exp = Matrix([[exp(3), -4*exp(-2)/5 + 4*exp(3)/5], [0, exp(-2)]])
+    assert m.exp() == m_exp
+    assert exp(m) == m_exp
+
+    m = Matrix([[1, 0], [0, 1]])
+    assert m.exp() == Matrix([[E, 0], [0, E]])
+    assert exp(m) == Matrix([[E, 0], [0, E]])
+
+    m = Matrix([[1, -1], [1, 1]])
+    assert m.exp() == Matrix([[E*cos(1), -E*sin(1)], [E*sin(1), E*cos(1)]])
+
+
+def test_log():
+    l = Symbol('lamda')
+
+    m = Matrix.jordan_block(1, l)
+    assert m._eval_matrix_log_jblock() == Matrix([[log(l)]])
+
+    m = Matrix.jordan_block(4, l)
+    assert m._eval_matrix_log_jblock() == \
+        Matrix(
+            [
+                [log(l), 1/l, -1/(2*l**2), 1/(3*l**3)],
+                [0, log(l), 1/l, -1/(2*l**2)],
+                [0, 0, log(l), 1/l],
+                [0, 0, 0, log(l)]
+            ]
+        )
+
+    m = Matrix(
+        [[0, 0, 1],
+        [0, 0, 0],
+        [-1, 0, 0]]
+    )
+    raises(MatrixError, lambda: m.log())
+
+
+def test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1():
+    # Test if matrices._find_reasonable_pivot_naive()
+    # finds a guaranteed non-zero pivot when the
+    # some of the candidate pivots are symbolic expressions.
+    # Keyword argument: simpfunc=None indicates that no simplifications
+    # should be performed during the search.
+    x = Symbol('x')
+    column = Matrix(3, 1, [x, cos(x)**2 + sin(x)**2, S.Half])
+    pivot_offset, pivot_val, pivot_assumed_nonzero, simplified =\
+        _find_reasonable_pivot_naive(column)
+    assert pivot_val == S.Half
+
+
+def test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2():
+    # Test if matrices._find_reasonable_pivot_naive()
+    # finds a guaranteed non-zero pivot when the
+    # some of the candidate pivots are symbolic expressions.
+    # Keyword argument: simpfunc=_simplify indicates that the search
+    # should attempt to simplify candidate pivots.
+    x = Symbol('x')
+    column = Matrix(3, 1,
+                    [x,
+                     cos(x)**2+sin(x)**2+x**2,
+                     cos(x)**2+sin(x)**2])
+    pivot_offset, pivot_val, pivot_assumed_nonzero, simplified =\
+        _find_reasonable_pivot_naive(column, simpfunc=_simplify)
+    assert pivot_val == 1
+
+
+def test_find_reasonable_pivot_naive_simplifies():
+    # Test if matrices._find_reasonable_pivot_naive()
+    # simplifies candidate pivots, and reports
+    # their offsets correctly.
+    x = Symbol('x')
+    column = Matrix(3, 1,
+                    [x,
+                     cos(x)**2+sin(x)**2+x,
+                     cos(x)**2+sin(x)**2])
+    pivot_offset, pivot_val, pivot_assumed_nonzero, simplified =\
+        _find_reasonable_pivot_naive(column, simpfunc=_simplify)
+
+    assert len(simplified) == 2
+    assert simplified[0][0] == 1
+    assert simplified[0][1] == 1+x
+    assert simplified[1][0] == 2
+    assert simplified[1][1] == 1
+
+
+def test_errors():
+    raises(ValueError, lambda: Matrix([[1, 2], [1]]))
+    raises(IndexError, lambda: Matrix([[1, 2]])[1.2, 5])
+    raises(IndexError, lambda: Matrix([[1, 2]])[1, 5.2])
+    raises(ValueError, lambda: randMatrix(3, c=4, symmetric=True))
+    raises(ValueError, lambda: Matrix([1, 2]).reshape(4, 6))
+    raises(ShapeError,
+        lambda: Matrix([[1, 2], [3, 4]]).copyin_matrix([1, 0], Matrix([1, 2])))
+    raises(TypeError, lambda: Matrix([[1, 2], [3, 4]]).copyin_list([0,
+           1], set()))
+    raises(NonSquareMatrixError, lambda: Matrix([[1, 2, 3], [2, 3, 0]]).inv())
+    raises(ShapeError,
+        lambda: Matrix(1, 2, [1, 2]).row_join(Matrix([[1, 2], [3, 4]])))
+    raises(
+        ShapeError, lambda: Matrix([1, 2]).col_join(Matrix([[1, 2], [3, 4]])))
+    raises(ShapeError, lambda: Matrix([1]).row_insert(1, Matrix([[1,
+           2], [3, 4]])))
+    raises(ShapeError, lambda: Matrix([1]).col_insert(1, Matrix([[1,
+           2], [3, 4]])))
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).trace())
+    raises(TypeError, lambda: Matrix([1]).applyfunc(1))
+    raises(ValueError, lambda: Matrix([[1, 2], [3, 4]]).minor(4, 5))
+    raises(ValueError, lambda: Matrix([[1, 2], [3, 4]]).minor_submatrix(4, 5))
+    raises(TypeError, lambda: Matrix([1, 2, 3]).cross(1))
+    raises(TypeError, lambda: Matrix([1, 2, 3]).dot(1))
+    raises(ShapeError, lambda: Matrix([1, 2, 3]).dot(Matrix([1, 2])))
+    raises(ShapeError, lambda: Matrix([1, 2]).dot([]))
+    raises(TypeError, lambda: Matrix([1, 2]).dot('a'))
+    raises(ShapeError, lambda: Matrix([1, 2]).dot([1, 2, 3]))
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2, 3]).exp())
+    raises(ShapeError, lambda: Matrix([[1, 2], [3, 4]]).normalized())
+    raises(ValueError, lambda: Matrix([1, 2]).inv(method='not a method'))
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).inverse_GE())
+    raises(ValueError, lambda: Matrix([[1, 2], [1, 2]]).inverse_GE())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).inverse_ADJ())
+    raises(ValueError, lambda: Matrix([[1, 2], [1, 2]]).inverse_ADJ())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).inverse_LU())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).is_nilpotent())
+    raises(NonSquareMatrixError, lambda: Matrix([1, 2]).det())
+    raises(ValueError,
+        lambda: Matrix([[1, 2], [3, 4]]).det(method='Not a real method'))
+    raises(ValueError,
+        lambda: Matrix([[1, 2, 3, 4], [5, 6, 7, 8],
+        [9, 10, 11, 12], [13, 14, 15, 16]]).det(iszerofunc="Not function"))
+    raises(ValueError,
+        lambda: Matrix([[1, 2, 3, 4], [5, 6, 7, 8],
+        [9, 10, 11, 12], [13, 14, 15, 16]]).det(iszerofunc=False))
+    raises(ValueError,
+        lambda: hessian(Matrix([[1, 2], [3, 4]]), Matrix([[1, 2], [2, 1]])))
+    raises(ValueError, lambda: hessian(Matrix([[1, 2], [3, 4]]), []))
+    raises(ValueError, lambda: hessian(Symbol('x')**2, 'a'))
+    raises(IndexError, lambda: eye(3)[5, 2])
+    raises(IndexError, lambda: eye(3)[2, 5])
+    M = Matrix(((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16)))
+    raises(ValueError, lambda: M.det('method=LU_decomposition()'))
+    V = Matrix([[10, 10, 10]])
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(ValueError, lambda: M.row_insert(4.7, V))
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(ValueError, lambda: M.col_insert(-4.2, V))
+
+
+def test_len():
+    assert len(Matrix()) == 0
+    assert len(Matrix([[1, 2]])) == len(Matrix([[1], [2]])) == 2
+    assert len(Matrix(0, 2, lambda i, j: 0)) == \
+        len(Matrix(2, 0, lambda i, j: 0)) == 0
+    assert len(Matrix([[0, 1, 2], [3, 4, 5]])) == 6
+    assert Matrix([1]) == Matrix([[1]])
+    assert not Matrix()
+    assert Matrix() == Matrix([])
+
+
+def test_integrate():
+    A = Matrix(((1, 4, x), (y, 2, 4), (10, 5, x**2)))
+    assert A.integrate(x) == \
+        Matrix(((x, 4*x, x**2/2), (x*y, 2*x, 4*x), (10*x, 5*x, x**3/3)))
+    assert A.integrate(y) == \
+        Matrix(((y, 4*y, x*y), (y**2/2, 2*y, 4*y), (10*y, 5*y, y*x**2)))
+    m = Matrix(2, 1, [x, y])
+    assert m.integrate(x) == Matrix(2, 1, [x**2/2, y*x])
+
+
+def test_diff():
+    A = MutableDenseMatrix(((1, 4, x), (y, 2, 4), (10, 5, x**2 + 1)))
+    assert isinstance(A.diff(x), type(A))
+    assert A.diff(x) == MutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert A.diff(y) == MutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    assert diff(A, x) == MutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert diff(A, y) == MutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    A_imm = A.as_immutable()
+    assert isinstance(A_imm.diff(x), type(A_imm))
+    assert A_imm.diff(x) == ImmutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert A_imm.diff(y) == ImmutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    assert diff(A_imm, x) == ImmutableDenseMatrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+    assert diff(A_imm, y) == ImmutableDenseMatrix(((0, 0, 0), (1, 0, 0), (0, 0, 0)))
+
+    assert A.diff(x, evaluate=False) == ArrayDerivative(A, x, evaluate=False)
+    assert diff(A, x, evaluate=False) == ArrayDerivative(A, x, evaluate=False)
+
+
+def test_diff_by_matrix():
+
+    # Derive matrix by matrix:
+
+    A = MutableDenseMatrix([[x, y], [z, t]])
+    assert A.diff(A) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+    assert diff(A, A) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+
+    A_imm = A.as_immutable()
+    assert A_imm.diff(A_imm) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+    assert diff(A_imm, A_imm) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+
+    # Derive a constant matrix:
+    assert A.diff(a) == MutableDenseMatrix([[0, 0], [0, 0]])
+
+    B = ImmutableDenseMatrix([a, b])
+    assert A.diff(B) == Array.zeros(2, 1, 2, 2)
+    assert A.diff(A) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]])
+
+    # Test diff with tuples:
+
+    dB = B.diff([[a, b]])
+    assert dB.shape == (2, 2, 1)
+    assert dB == Array([[[1], [0]], [[0], [1]]])
+
+    f = Function("f")
+    fxyz = f(x, y, z)
+    assert fxyz.diff([[x, y, z]]) == Array([fxyz.diff(x), fxyz.diff(y), fxyz.diff(z)])
+    assert fxyz.diff(([x, y, z], 2)) == Array([
+        [fxyz.diff(x, 2), fxyz.diff(x, y), fxyz.diff(x, z)],
+        [fxyz.diff(x, y), fxyz.diff(y, 2), fxyz.diff(y, z)],
+        [fxyz.diff(x, z), fxyz.diff(z, y), fxyz.diff(z, 2)],
+    ])
+
+    expr = sin(x)*exp(y)
+    assert expr.diff([[x, y]]) == Array([cos(x)*exp(y), sin(x)*exp(y)])
+    assert expr.diff(y, ((x, y),)) == Array([cos(x)*exp(y), sin(x)*exp(y)])
+    assert expr.diff(x, ((x, y),)) == Array([-sin(x)*exp(y), cos(x)*exp(y)])
+    assert expr.diff(((y, x),), [[x, y]]) == Array([[cos(x)*exp(y), -sin(x)*exp(y)], [sin(x)*exp(y), cos(x)*exp(y)]])
+
+    # Test different notations:
+
+    assert fxyz.diff(x).diff(y).diff(x) == fxyz.diff(((x, y, z),), 3)[0, 1, 0]
+    assert fxyz.diff(z).diff(y).diff(x) == fxyz.diff(((x, y, z),), 3)[2, 1, 0]
+    assert fxyz.diff([[x, y, z]], ((z, y, x),)) == Array([[fxyz.diff(i).diff(j) for i in (x, y, z)] for j in (z, y, x)])
+
+    # Test scalar derived by matrix remains matrix:
+    res = x.diff(Matrix([[x, y]]))
+    assert isinstance(res, ImmutableDenseMatrix)
+    assert res == Matrix([[1, 0]])
+    res = (x**3).diff(Matrix([[x, y]]))
+    assert isinstance(res, ImmutableDenseMatrix)
+    assert res == Matrix([[3*x**2, 0]])
+
+
+def test_getattr():
+    A = Matrix(((1, 4, x), (y, 2, 4), (10, 5, x**2 + 1)))
+    raises(AttributeError, lambda: A.nonexistantattribute)
+    assert getattr(A, 'diff')(x) == Matrix(((0, 0, 1), (0, 0, 0), (0, 0, 2*x)))
+
+
+def test_hessenberg():
+    A = Matrix([[3, 4, 1], [2, 4, 5], [0, 1, 2]])
+    assert A.is_upper_hessenberg
+    A = A.T
+    assert A.is_lower_hessenberg
+    A[0, -1] = 1
+    assert A.is_lower_hessenberg is False
+
+    A = Matrix([[3, 4, 1], [2, 4, 5], [3, 1, 2]])
+    assert not A.is_upper_hessenberg
+
+    A = zeros(5, 2)
+    assert A.is_upper_hessenberg
+
+
+def test_cholesky():
+    raises(NonSquareMatrixError, lambda: Matrix((1, 2)).cholesky())
+    raises(ValueError, lambda: Matrix(((1, 2), (3, 4))).cholesky())
+    raises(ValueError, lambda: Matrix(((5 + I, 0), (0, 1))).cholesky())
+    raises(ValueError, lambda: Matrix(((1, 5), (5, 1))).cholesky())
+    raises(ValueError, lambda: Matrix(((1, 2), (3, 4))).cholesky(hermitian=False))
+    assert Matrix(((5 + I, 0), (0, 1))).cholesky(hermitian=False) == Matrix([
+        [sqrt(5 + I), 0], [0, 1]])
+    A = Matrix(((1, 5), (5, 1)))
+    L = A.cholesky(hermitian=False)
+    assert L == Matrix([[1, 0], [5, 2*sqrt(6)*I]])
+    assert L*L.T == A
+    A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L = A.cholesky()
+    assert L * L.T == A
+    assert L.is_lower
+    assert L == Matrix([[5, 0, 0], [3, 3, 0], [-1, 1, 3]])
+    A = Matrix(((4, -2*I, 2 + 2*I), (2*I, 2, -1 + I), (2 - 2*I, -1 - I, 11)))
+    assert A.cholesky().expand() == Matrix(((2, 0, 0), (I, 1, 0), (1 - I, 0, 3)))
+
+    raises(NonSquareMatrixError, lambda: SparseMatrix((1, 2)).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((1, 2), (3, 4))).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((5 + I, 0), (0, 1))).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((1, 5), (5, 1))).cholesky())
+    raises(ValueError, lambda: SparseMatrix(((1, 2), (3, 4))).cholesky(hermitian=False))
+    assert SparseMatrix(((5 + I, 0), (0, 1))).cholesky(hermitian=False) == Matrix([
+        [sqrt(5 + I), 0], [0, 1]])
+    A = SparseMatrix(((1, 5), (5, 1)))
+    L = A.cholesky(hermitian=False)
+    assert L == Matrix([[1, 0], [5, 2*sqrt(6)*I]])
+    assert L*L.T == A
+    A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L = A.cholesky()
+    assert L * L.T == A
+    assert L.is_lower
+    assert L == Matrix([[5, 0, 0], [3, 3, 0], [-1, 1, 3]])
+    A = SparseMatrix(((4, -2*I, 2 + 2*I), (2*I, 2, -1 + I), (2 - 2*I, -1 - I, 11)))
+    assert A.cholesky() == Matrix(((2, 0, 0), (I, 1, 0), (1 - I, 0, 3)))
+
+
+def test_matrix_norm():
+    # Vector Tests
+    # Test columns and symbols
+    x = Symbol('x', real=True)
+    v = Matrix([cos(x), sin(x)])
+    assert trigsimp(v.norm(2)) == 1
+    assert v.norm(10) == Pow(cos(x)**10 + sin(x)**10, Rational(1, 10))
+
+    # Test Rows
+    A = Matrix([[5, Rational(3, 2)]])
+    assert A.norm() == Pow(25 + Rational(9, 4), S.Half)
+    assert A.norm(oo) == max(A)
+    assert A.norm(-oo) == min(A)
+
+    # Matrix Tests
+    # Intuitive test
+    A = Matrix([[1, 1], [1, 1]])
+    assert A.norm(2) == 2
+    assert A.norm(-2) == 0
+    assert A.norm('frobenius') == 2
+    assert eye(10).norm(2) == eye(10).norm(-2) == 1
+    assert A.norm(oo) == 2
+
+    # Test with Symbols and more complex entries
+    A = Matrix([[3, y, y], [x, S.Half, -pi]])
+    assert (A.norm('fro')
+           == sqrt(Rational(37, 4) + 2*abs(y)**2 + pi**2 + x**2))
+
+    # Check non-square
+    A = Matrix([[1, 2, -3], [4, 5, Rational(13, 2)]])
+    assert A.norm(2) == sqrt(Rational(389, 8) + sqrt(78665)/8)
+    assert A.norm(-2) is S.Zero
+    assert A.norm('frobenius') == sqrt(389)/2
+
+    # Test properties of matrix norms
+    # https://en.wikipedia.org/wiki/Matrix_norm#Definition
+    # Two matrices
+    A = Matrix([[1, 2], [3, 4]])
+    B = Matrix([[5, 5], [-2, 2]])
+    C = Matrix([[0, -I], [I, 0]])
+    D = Matrix([[1, 0], [0, -1]])
+    L = [A, B, C, D]
+    alpha = Symbol('alpha', real=True)
+
+    for order in ['fro', 2, -2]:
+        # Zero Check
+        assert zeros(3).norm(order) is S.Zero
+        # Check Triangle Inequality for all Pairs of Matrices
+        for X in L:
+            for Y in L:
+                dif = (X.norm(order) + Y.norm(order) -
+                    (X + Y).norm(order))
+                assert (dif >= 0)
+        # Scalar multiplication linearity
+        for M in [A, B, C, D]:
+            dif = simplify((alpha*M).norm(order) -
+                    abs(alpha) * M.norm(order))
+            assert dif == 0
+
+    # Test Properties of Vector Norms
+    # https://en.wikipedia.org/wiki/Vector_norm
+    # Two column vectors
+    a = Matrix([1, 1 - 1*I, -3])
+    b = Matrix([S.Half, 1*I, 1])
+    c = Matrix([-1, -1, -1])
+    d = Matrix([3, 2, I])
+    e = Matrix([Integer(1e2), Rational(1, 1e2), 1])
+    L = [a, b, c, d, e]
+    alpha = Symbol('alpha', real=True)
+
+    for order in [1, 2, -1, -2, S.Infinity, S.NegativeInfinity, pi]:
+        # Zero Check
+        if order > 0:
+            assert Matrix([0, 0, 0]).norm(order) is S.Zero
+        # Triangle inequality on all pairs
+        if order >= 1:  # Triangle InEq holds only for these norms
+            for X in L:
+                for Y in L:
+                    dif = (X.norm(order) + Y.norm(order) -
+                        (X + Y).norm(order))
+                    assert simplify(dif >= 0) is S.true
+        # Linear to scalar multiplication
+        if order in [1, 2, -1, -2, S.Infinity, S.NegativeInfinity]:
+            for X in L:
+                dif = simplify((alpha*X).norm(order) -
+                    (abs(alpha) * X.norm(order)))
+                assert dif == 0
+
+    # ord=1
+    M = Matrix(3, 3, [1, 3, 0, -2, -1, 0, 3, 9, 6])
+    assert M.norm(1) == 13
+
+
+def test_condition_number():
+    x = Symbol('x', real=True)
+    A = eye(3)
+    A[0, 0] = 10
+    A[2, 2] = Rational(1, 10)
+    assert A.condition_number() == 100
+
+    A[1, 1] = x
+    assert A.condition_number() == Max(10, Abs(x)) / Min(Rational(1, 10), Abs(x))
+
+    M = Matrix([[cos(x), sin(x)], [-sin(x), cos(x)]])
+    Mc = M.condition_number()
+    assert all(Float(1.).epsilon_eq(Mc.subs(x, val).evalf()) for val in
+        [Rational(1, 5), S.Half, Rational(1, 10), pi/2, pi, pi*Rational(7, 4) ])
+
+    #issue 10782
+    assert Matrix([]).condition_number() == 0
+
+
+def test_equality():
+    A = Matrix(((1, 2, 3), (4, 5, 6), (7, 8, 9)))
+    B = Matrix(((9, 8, 7), (6, 5, 4), (3, 2, 1)))
+    assert A == A[:, :]
+    assert not A != A[:, :]
+    assert not A == B
+    assert A != B
+    assert A != 10
+    assert not A == 10
+
+    # A SparseMatrix can be equal to a Matrix
+    C = SparseMatrix(((1, 0, 0), (0, 1, 0), (0, 0, 1)))
+    D = Matrix(((1, 0, 0), (0, 1, 0), (0, 0, 1)))
+    assert C == D
+    assert not C != D
+
+
+def test_normalized():
+    assert Matrix([3, 4]).normalized() == \
+        Matrix([Rational(3, 5), Rational(4, 5)])
+
+    # Zero vector trivial cases
+    assert Matrix([0, 0, 0]).normalized() == Matrix([0, 0, 0])
+
+    # Machine precision error truncation trivial cases
+    m = Matrix([0,0,1.e-100])
+    assert m.normalized(
+    iszerofunc=lambda x: x.evalf(n=10, chop=True).is_zero
+    ) == Matrix([0, 0, 0])
+
+
+def test_print_nonzero():
+    assert capture(lambda: eye(3).print_nonzero()) == \
+        '[X  ]\n[ X ]\n[  X]\n'
+    assert capture(lambda: eye(3).print_nonzero('.')) == \
+        '[.  ]\n[ . ]\n[  .]\n'
+
+
+def test_zeros_eye():
+    assert Matrix.eye(3) == eye(3)
+    assert Matrix.zeros(3) == zeros(3)
+    assert ones(3, 4) == Matrix(3, 4, [1]*12)
+
+    i = Matrix([[1, 0], [0, 1]])
+    z = Matrix([[0, 0], [0, 0]])
+    for cls in all_classes:
+        m = cls.eye(2)
+        assert i == m  # but m == i will fail if m is immutable
+        assert i == eye(2, cls=cls)
+        assert type(m) == cls
+        m = cls.zeros(2)
+        assert z == m
+        assert z == zeros(2, cls=cls)
+        assert type(m) == cls
+
+
+def test_is_zero():
+    assert Matrix().is_zero_matrix
+    assert Matrix([[0, 0], [0, 0]]).is_zero_matrix
+    assert zeros(3, 4).is_zero_matrix
+    assert not eye(3).is_zero_matrix
+    assert Matrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert SparseMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert ImmutableMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert ImmutableSparseMatrix([[x, 0], [0, 0]]).is_zero_matrix == None
+    assert Matrix([[x, 1], [0, 0]]).is_zero_matrix == False
+    a = Symbol('a', nonzero=True)
+    assert Matrix([[a, 0], [0, 0]]).is_zero_matrix == False
+
+
+def test_rotation_matrices():
+    # This tests the rotation matrices by rotating about an axis and back.
+    theta = pi/3
+    r3_plus = rot_axis3(theta)
+    r3_minus = rot_axis3(-theta)
+    r2_plus = rot_axis2(theta)
+    r2_minus = rot_axis2(-theta)
+    r1_plus = rot_axis1(theta)
+    r1_minus = rot_axis1(-theta)
+    assert r3_minus*r3_plus*eye(3) == eye(3)
+    assert r2_minus*r2_plus*eye(3) == eye(3)
+    assert r1_minus*r1_plus*eye(3) == eye(3)
+
+    # Check the correctness of the trace of the rotation matrix
+    assert r1_plus.trace() == 1 + 2*cos(theta)
+    assert r2_plus.trace() == 1 + 2*cos(theta)
+    assert r3_plus.trace() == 1 + 2*cos(theta)
+
+    # Check that a rotation with zero angle doesn't change anything.
+    assert rot_axis1(0) == eye(3)
+    assert rot_axis2(0) == eye(3)
+    assert rot_axis3(0) == eye(3)
+
+    # Check left-hand convention
+    # see Issue #24529
+    q1 = Quaternion.from_axis_angle([1, 0, 0], pi / 2)
+    q2 = Quaternion.from_axis_angle([0, 1, 0], pi / 2)
+    q3 = Quaternion.from_axis_angle([0, 0, 1], pi / 2)
+    assert rot_axis1(- pi / 2) == q1.to_rotation_matrix()
+    assert rot_axis2(- pi / 2) == q2.to_rotation_matrix()
+    assert rot_axis3(- pi / 2) == q3.to_rotation_matrix()
+    # Check right-hand convention
+    assert rot_ccw_axis1(+ pi / 2) == q1.to_rotation_matrix()
+    assert rot_ccw_axis2(+ pi / 2) == q2.to_rotation_matrix()
+    assert rot_ccw_axis3(+ pi / 2) == q3.to_rotation_matrix()
+
+
+def test_DeferredVector():
+    assert str(DeferredVector("vector")[4]) == "vector[4]"
+    assert sympify(DeferredVector("d")) == DeferredVector("d")
+    raises(IndexError, lambda: DeferredVector("d")[-1])
+    assert str(DeferredVector("d")) == "d"
+    assert repr(DeferredVector("test")) == "DeferredVector('test')"
+
+
+def test_DeferredVector_not_iterable():
+    assert not iterable(DeferredVector('X'))
+
+
+def test_DeferredVector_Matrix():
+    raises(TypeError, lambda: Matrix(DeferredVector("V")))
+
+
+def test_GramSchmidt():
+    R = Rational
+    m1 = Matrix(1, 2, [1, 2])
+    m2 = Matrix(1, 2, [2, 3])
+    assert GramSchmidt([m1, m2]) == \
+        [Matrix(1, 2, [1, 2]), Matrix(1, 2, [R(2)/5, R(-1)/5])]
+    assert GramSchmidt([m1.T, m2.T]) == \
+        [Matrix(2, 1, [1, 2]), Matrix(2, 1, [R(2)/5, R(-1)/5])]
+    # from wikipedia
+    assert GramSchmidt([Matrix([3, 1]), Matrix([2, 2])], True) == [
+        Matrix([3*sqrt(10)/10, sqrt(10)/10]),
+        Matrix([-sqrt(10)/10, 3*sqrt(10)/10])]
+    # https://github.com/sympy/sympy/issues/9488
+    L = FiniteSet(Matrix([1]))
+    assert GramSchmidt(L) == [Matrix([[1]])]
+
+
+def test_casoratian():
+    assert casoratian([1, 2, 3, 4], 1) == 0
+    assert casoratian([1, 2, 3, 4], 1, zero=False) == 0
+
+
+def test_zero_dimension_multiply():
+    assert (Matrix()*zeros(0, 3)).shape == (0, 3)
+    assert zeros(3, 0)*zeros(0, 3) == zeros(3, 3)
+    assert zeros(0, 3)*zeros(3, 0) == Matrix()
+
+
+def test_slice_issue_2884():
+    m = Matrix(2, 2, range(4))
+    assert m[1, :] == Matrix([[2, 3]])
+    assert m[-1, :] == Matrix([[2, 3]])
+    assert m[:, 1] == Matrix([[1, 3]]).T
+    assert m[:, -1] == Matrix([[1, 3]]).T
+    raises(IndexError, lambda: m[2, :])
+    raises(IndexError, lambda: m[2, 2])
+
+
+def test_slice_issue_3401():
+    assert zeros(0, 3)[:, -1].shape == (0, 1)
+    assert zeros(3, 0)[0, :] == Matrix(1, 0, [])
+
+
+def test_copyin():
+    s = zeros(3, 3)
+    s[3] = 1
+    assert s[:, 0] == Matrix([0, 1, 0])
+    assert s[3] == 1
+    assert s[3: 4] == [1]
+    s[1, 1] = 42
+    assert s[1, 1] == 42
+    assert s[1, 1:] == Matrix([[42, 0]])
+    s[1, 1:] = Matrix([[5, 6]])
+    assert s[1, :] == Matrix([[1, 5, 6]])
+    s[1, 1:] = [[42, 43]]
+    assert s[1, :] == Matrix([[1, 42, 43]])
+    s[0, 0] = 17
+    assert s[:, :1] == Matrix([17, 1, 0])
+    s[0, 0] = [1, 1, 1]
+    assert s[:, 0] == Matrix([1, 1, 1])
+    s[0, 0] = Matrix([1, 1, 1])
+    assert s[:, 0] == Matrix([1, 1, 1])
+    s[0, 0] = SparseMatrix([1, 1, 1])
+    assert s[:, 0] == Matrix([1, 1, 1])
+
+
+def test_invertible_check():
+    # sometimes a singular matrix will have a pivot vector shorter than
+    # the number of rows in a matrix...
+    assert Matrix([[1, 2], [1, 2]]).rref() == (Matrix([[1, 2], [0, 0]]), (0,))
+    raises(ValueError, lambda: Matrix([[1, 2], [1, 2]]).inv())
+    m = Matrix([
+        [-1, -1,  0],
+        [ x,  1,  1],
+        [ 1,  x, -1],
+    ])
+    assert len(m.rref()[1]) != m.rows
+    # in addition, unless simplify=True in the call to rref, the identity
+    # matrix will be returned even though m is not invertible
+    assert m.rref()[0] != eye(3)
+    assert m.rref(simplify=signsimp)[0] != eye(3)
+    raises(ValueError, lambda: m.inv(method="ADJ"))
+    raises(ValueError, lambda: m.inv(method="GE"))
+    raises(ValueError, lambda: m.inv(method="LU"))
+
+
+def test_issue_3959():
+    x, y = symbols('x, y')
+    e = x*y
+    assert e.subs(x, Matrix([3, 5, 3])) == Matrix([3, 5, 3])*y
+
+
+def test_issue_5964():
+    assert str(Matrix([[1, 2], [3, 4]])) == 'Matrix([[1, 2], [3, 4]])'
+
+
+def test_issue_7604():
+    x, y = symbols("x y")
+    assert sstr(Matrix([[x, 2*y], [y**2, x + 3]])) == \
+        'Matrix([\n[   x,   2*y],\n[y**2, x + 3]])'
+
+
+def test_is_Identity():
+    assert eye(3).is_Identity
+    assert eye(3).as_immutable().is_Identity
+    assert not zeros(3).is_Identity
+    assert not ones(3).is_Identity
+    # issue 6242
+    assert not Matrix([[1, 0, 0]]).is_Identity
+    # issue 8854
+    assert SparseMatrix(3,3, {(0,0):1, (1,1):1, (2,2):1}).is_Identity
+    assert not SparseMatrix(2,3, range(6)).is_Identity
+    assert not SparseMatrix(3,3, {(0,0):1, (1,1):1}).is_Identity
+    assert not SparseMatrix(3,3, {(0,0):1, (1,1):1, (2,2):1, (0,1):2, (0,2):3}).is_Identity
+
+
+def test_dot():
+    assert ones(1, 3).dot(ones(3, 1)) == 3
+    assert ones(1, 3).dot([1, 1, 1]) == 3
+    assert Matrix([1, 2, 3]).dot(Matrix([1, 2, 3])) == 14
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I])) == -5 + I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I]), hermitian=False) == -5 + I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I]), hermitian=True) == 13 + I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([I, 2, 3*I]), hermitian=True, conjugate_convention="physics") == 13 - I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([4, 5*I, 6]), hermitian=True, conjugate_convention="right") == 4 + 8*I
+    assert Matrix([1, 2, 3*I]).dot(Matrix([4, 5*I, 6]), hermitian=True, conjugate_convention="left") == 4 - 8*I
+    assert Matrix([I, 2*I]).dot(Matrix([I, 2*I]), hermitian=False, conjugate_convention="left") == -5
+    assert Matrix([I, 2*I]).dot(Matrix([I, 2*I]), conjugate_convention="left") == 5
+    raises(ValueError, lambda: Matrix([1, 2]).dot(Matrix([3, 4]), hermitian=True, conjugate_convention="test"))
+
+
+def test_dual():
+    B_x, B_y, B_z, E_x, E_y, E_z = symbols(
+        'B_x B_y B_z E_x E_y E_z', real=True)
+    F = Matrix((
+        (   0,  E_x,  E_y,  E_z),
+        (-E_x,    0,  B_z, -B_y),
+        (-E_y, -B_z,    0,  B_x),
+        (-E_z,  B_y, -B_x,    0)
+    ))
+    Fd = Matrix((
+        (  0, -B_x, -B_y, -B_z),
+        (B_x,    0,  E_z, -E_y),
+        (B_y, -E_z,    0,  E_x),
+        (B_z,  E_y, -E_x,    0)
+    ))
+    assert F.dual().equals(Fd)
+    assert eye(3).dual().equals(zeros(3))
+    assert F.dual().dual().equals(-F)
+
+
+def test_anti_symmetric():
+    assert Matrix([1, 2]).is_anti_symmetric() is False
+    m = Matrix(3, 3, [0, x**2 + 2*x + 1, y, -(x + 1)**2, 0, x*y, -y, -x*y, 0])
+    assert m.is_anti_symmetric() is True
+    assert m.is_anti_symmetric(simplify=False) is None
+    assert m.is_anti_symmetric(simplify=lambda x: x) is None
+
+    # tweak to fail
+    m[2, 1] = -m[2, 1]
+    assert m.is_anti_symmetric() is None
+    # untweak
+    m[2, 1] = -m[2, 1]
+
+    m = m.expand()
+    assert m.is_anti_symmetric(simplify=False) is True
+    m[0, 0] = 1
+    assert m.is_anti_symmetric() is False
+
+
+def test_normalize_sort_diogonalization():
+    A = Matrix(((1, 2), (2, 1)))
+    P, Q = A.diagonalize(normalize=True)
+    assert P*P.T == P.T*P == eye(P.cols)
+    P, Q = A.diagonalize(normalize=True, sort=True)
+    assert P*P.T == P.T*P == eye(P.cols)
+    assert P*Q*P.inv() == A
+
+
+def test_issue_5321():
+    raises(ValueError, lambda: Matrix([[1, 2, 3], Matrix(0, 1, [])]))
+
+
+def test_issue_5320():
+    assert Matrix.hstack(eye(2), 2*eye(2)) == Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2]
+    ])
+    assert Matrix.vstack(eye(2), 2*eye(2)) == Matrix([
+        [1, 0],
+        [0, 1],
+        [2, 0],
+        [0, 2]
+    ])
+    cls = SparseMatrix
+    assert cls.hstack(cls(eye(2)), cls(2*eye(2))) == Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2]
+    ])
+
+
+def test_issue_11944():
+    A = Matrix([[1]])
+    AIm = sympify(A)
+    assert Matrix.hstack(AIm, A) == Matrix([[1, 1]])
+    assert Matrix.vstack(AIm, A) == Matrix([[1], [1]])
+
+
+def test_cross():
+    a = [1, 2, 3]
+    b = [3, 4, 5]
+    col = Matrix([-2, 4, -2])
+    row = col.T
+
+    def test(M, ans):
+        assert ans == M
+        assert type(M) == cls
+    for cls in all_classes:
+        A = cls(a)
+        B = cls(b)
+        test(A.cross(B), col)
+        test(A.cross(B.T), col)
+        test(A.T.cross(B.T), row)
+        test(A.T.cross(B), row)
+    raises(ShapeError, lambda:
+        Matrix(1, 2, [1, 1]).cross(Matrix(1, 2, [1, 1])))
+
+
+def test_hat_vee():
+    v1 = Matrix([x, y, z])
+    v2 = Matrix([a, b, c])
+    assert v1.hat() * v2 == v1.cross(v2)
+    assert v1.hat().is_anti_symmetric()
+    assert v1.hat().vee() == v1
+
+
+def test_hash():
+    for cls in immutable_classes:
+        s = {cls.eye(1), cls.eye(1)}
+        assert len(s) == 1 and s.pop() == cls.eye(1)
+    # issue 3979
+    for cls in mutable_classes:
+        assert not isinstance(cls.eye(1), Hashable)
+
+
+def test_adjoint():
+    dat = [[0, I], [1, 0]]
+    ans = Matrix([[0, 1], [-I, 0]])
+    for cls in all_classes:
+        assert ans == cls(dat).adjoint()
+
+
+def test_atoms():
+    m = Matrix([[1, 2], [x, 1 - 1/x]])
+    assert m.atoms() == {S.One,S(2),S.NegativeOne, x}
+    assert m.atoms(Symbol) == {x}
+
+
+def test_pinv():
+    # Pseudoinverse of an invertible matrix is the inverse.
+    A1 = Matrix([[a, b], [c, d]])
+    assert simplify(A1.pinv(method="RD")) == simplify(A1.inv())
+
+    # Test the four properties of the pseudoinverse for various matrices.
+    As = [Matrix([[13, 104], [2212, 3], [-3, 5]]),
+          Matrix([[1, 7, 9], [11, 17, 19]]),
+          Matrix([a, b])]
+
+    for A in As:
+        A_pinv = A.pinv(method="RD")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+    # XXX Pinv with diagonalization makes expression too complicated.
+    for A in As:
+        A_pinv = simplify(A.pinv(method="ED"))
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+    # XXX Computing pinv using diagonalization makes an expression that
+    # is too complicated to simplify.
+    # A1 = Matrix([[a, b], [c, d]])
+    # assert simplify(A1.pinv(method="ED")) == simplify(A1.inv())
+    # so this is tested numerically at a fixed random point
+
+    from sympy.core.numbers import comp
+    q = A1.pinv(method="ED")
+    w = A1.inv()
+    reps = {a: -73633, b: 11362, c: 55486, d: 62570}
+    assert all(
+        comp(i.n(), j.n())
+        for i, j in zip(q.subs(reps), w.subs(reps))
+        )
+
+
+@slow
+def test_pinv_rank_deficient_when_diagonalization_fails():
+    # Test the four properties of the pseudoinverse for matrices when
+    # diagonalization of A.H*A fails.
+    As = [
+        Matrix([
+            [61, 89, 55, 20, 71, 0],
+            [62, 96, 85, 85, 16, 0],
+            [69, 56, 17,  4, 54, 0],
+            [10, 54, 91, 41, 71, 0],
+            [ 7, 30, 10, 48, 90, 0],
+            [0, 0, 0, 0, 0, 0]])
+    ]
+    for A in As:
+        A_pinv = A.pinv(method="ED")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert AAp.H == AAp
+
+        # Here ApA.H and ApA are equivalent expressions but they are very
+        # complicated expressions involving RootOfs. Using simplify would be
+        # too slow and so would evalf so we substitute approximate values for
+        # the RootOfs and then evalf which is less accurate but good enough to
+        # confirm that these two matrices are equivalent.
+        #
+        # assert ApA.H == ApA  # <--- would fail (structural equality)
+        # assert simplify(ApA.H - ApA).is_zero_matrix  # <--- too slow
+        # (ApA.H - ApA).evalf()  # <--- too slow
+
+        def allclose(M1, M2):
+            rootofs = M1.atoms(RootOf)
+            rootofs_approx = {r: r.evalf() for r in rootofs}
+            diff_approx = (M1 - M2).xreplace(rootofs_approx).evalf()
+            return all(abs(e) < 1e-10 for e in diff_approx)
+
+        assert allclose(ApA.H, ApA)
+
+
+def test_issue_7201():
+    assert ones(0, 1) + ones(0, 1) == Matrix(0, 1, [])
+    assert ones(1, 0) + ones(1, 0) == Matrix(1, 0, [])
+
+
+def test_free_symbols():
+    for M in ImmutableMatrix, ImmutableSparseMatrix, Matrix, SparseMatrix:
+        assert M([[x], [0]]).free_symbols == {x}
+
+
+def test_from_ndarray():
+    """See issue 7465."""
+    try:
+        from numpy import array
+    except ImportError:
+        skip('NumPy must be available to test creating matrices from ndarrays')
+
+    assert Matrix(array([1, 2, 3])) == Matrix([1, 2, 3])
+    assert Matrix(array([[1, 2, 3]])) == Matrix([[1, 2, 3]])
+    assert Matrix(array([[1, 2, 3], [4, 5, 6]])) == \
+        Matrix([[1, 2, 3], [4, 5, 6]])
+    assert Matrix(array([x, y, z])) == Matrix([x, y, z])
+    raises(NotImplementedError,
+        lambda: Matrix(array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])))
+    assert Matrix([array([1, 2]), array([3, 4])]) == Matrix([[1, 2], [3, 4]])
+    assert Matrix([array([1, 2]), [3, 4]]) == Matrix([[1, 2], [3, 4]])
+    assert Matrix([array([]), array([])]) == Matrix(2, 0, []) != Matrix([])
+
+
+def test_17522_numpy():
+    from sympy.matrices.common import _matrixify
+    try:
+        from numpy import array, matrix
+    except ImportError:
+        skip('NumPy must be available to test indexing matrixified NumPy ndarrays and matrices')
+
+    m = _matrixify(array([[1, 2], [3, 4]]))
+    assert m[3] == 4
+    assert list(m) == [1, 2, 3, 4]
+
+    with ignore_warnings(PendingDeprecationWarning):
+        m = _matrixify(matrix([[1, 2], [3, 4]]))
+    assert m[3] == 4
+    assert list(m) == [1, 2, 3, 4]
+
+
+def test_17522_mpmath():
+    from sympy.matrices.common import _matrixify
+    try:
+        from mpmath import matrix
+    except ImportError:
+        skip('mpmath must be available to test indexing matrixified mpmath matrices')
+
+    m = _matrixify(matrix([[1, 2], [3, 4]]))
+    assert m[3] == 4.0
+    assert list(m) == [1.0, 2.0, 3.0, 4.0]
+
+
+def test_17522_scipy():
+    from sympy.matrices.common import _matrixify
+    try:
+        from scipy.sparse import csr_matrix
+    except ImportError:
+        skip('SciPy must be available to test indexing matrixified SciPy sparse matrices')
+
+    m = _matrixify(csr_matrix([[1, 2], [3, 4]]))
+    assert m[3] == 4
+    assert list(m) == [1, 2, 3, 4]
+
+
+def test_hermitian():
+    a = Matrix([[1, I], [-I, 1]])
+    assert a.is_hermitian
+    a[0, 0] = 2*I
+    assert a.is_hermitian is False
+    a[0, 0] = x
+    assert a.is_hermitian is None
+    a[0, 1] = a[1, 0]*I
+    assert a.is_hermitian is False
+
+
+def test_issue_9457_9467_9876():
+    # for row_del(index)
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    M.row_del(1)
+    assert M == Matrix([[1, 2, 3], [3, 4, 5]])
+    N = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    N.row_del(-2)
+    assert N == Matrix([[1, 2, 3], [3, 4, 5]])
+    O = Matrix([[1, 2, 3], [5, 6, 7], [9, 10, 11]])
+    O.row_del(-1)
+    assert O == Matrix([[1, 2, 3], [5, 6, 7]])
+    P = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: P.row_del(10))
+    Q = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: Q.row_del(-10))
+
+    # for col_del(index)
+    M = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    M.col_del(1)
+    assert M == Matrix([[1, 3], [2, 4], [3, 5]])
+    N = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    N.col_del(-2)
+    assert N == Matrix([[1, 3], [2, 4], [3, 5]])
+    P = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: P.col_del(10))
+    Q = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
+    raises(IndexError, lambda: Q.col_del(-10))
+
+
+def test_issue_9422():
+    x, y = symbols('x y', commutative=False)
+    a, b = symbols('a b')
+    M = eye(2)
+    M1 = Matrix(2, 2, [x, y, y, z])
+    assert y*x*M != x*y*M
+    assert b*a*M == a*b*M
+    assert x*M1 != M1*x
+    assert a*M1 == M1*a
+    assert y*x*M == Matrix([[y*x, 0], [0, y*x]])
+
+
+def test_issue_10770():
+    M = Matrix([])
+    a = ['col_insert', 'row_join'], Matrix([9, 6, 3])
+    b = ['row_insert', 'col_join'], a[1].T
+    c = ['row_insert', 'col_insert'], Matrix([[1, 2], [3, 4]])
+    for ops, m in (a, b, c):
+        for op in ops:
+            f = getattr(M, op)
+            new = f(m) if 'join' in op else f(42, m)
+            assert new == m and id(new) != id(m)
+
+
+def test_issue_10658():
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert A.extract([0, 1, 2], [True, True, False]) == \
+        Matrix([[1, 2], [4, 5], [7, 8]])
+    assert A.extract([0, 1, 2], [True, False, False]) == Matrix([[1], [4], [7]])
+    assert A.extract([True, False, False], [0, 1, 2]) == Matrix([[1, 2, 3]])
+    assert A.extract([True, False, True], [0, 1, 2]) == \
+        Matrix([[1, 2, 3], [7, 8, 9]])
+    assert A.extract([0, 1, 2], [False, False, False]) == Matrix(3, 0, [])
+    assert A.extract([False, False, False], [0, 1, 2]) == Matrix(0, 3, [])
+    assert A.extract([True, False, True], [False, True, False]) == \
+        Matrix([[2], [8]])
+
+
+def test_opportunistic_simplification():
+    # this test relates to issue #10718, #9480, #11434
+
+    # issue #9480
+    m = Matrix([[-5 + 5*sqrt(2), -5], [-5*sqrt(2)/2 + 5, -5*sqrt(2)/2]])
+    assert m.rank() == 1
+
+    # issue #10781
+    m = Matrix([[3+3*sqrt(3)*I, -9],[4,-3+3*sqrt(3)*I]])
+    assert simplify(m.rref()[0] - Matrix([[1, -9/(3 + 3*sqrt(3)*I)], [0, 0]])) == zeros(2, 2)
+
+    # issue #11434
+    ax,ay,bx,by,cx,cy,dx,dy,ex,ey,t0,t1 = symbols('a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1')
+    m = Matrix([[ax,ay,ax*t0,ay*t0,0],[bx,by,bx*t0,by*t0,0],[cx,cy,cx*t0,cy*t0,1],[dx,dy,dx*t0,dy*t0,1],[ex,ey,2*ex*t1-ex*t0,2*ey*t1-ey*t0,0]])
+    assert m.rank() == 4
+
+
+def test_partial_pivoting():
+    # example from https://en.wikipedia.org/wiki/Pivot_element
+    # partial pivoting with back substitution gives a perfect result
+    # naive pivoting give an error ~1e-13, so anything better than
+    # 1e-15 is good
+    mm=Matrix([[0.003, 59.14, 59.17], [5.291, -6.13, 46.78]])
+    assert (mm.rref()[0] - Matrix([[1.0,   0, 10.0],
+                                   [  0, 1.0,  1.0]])).norm() < 1e-15
+
+    # issue #11549
+    m_mixed = Matrix([[6e-17, 1.0, 4],
+                      [ -1.0,   0, 8],
+                      [    0,   0, 1]])
+    m_float = Matrix([[6e-17,  1.0, 4.],
+                      [ -1.0,   0., 8.],
+                      [   0.,   0., 1.]])
+    m_inv = Matrix([[  0,    -1.0,  8.0],
+                    [1.0, 6.0e-17, -4.0],
+                    [  0,       0,    1]])
+    # this example is numerically unstable and involves a matrix with a norm >= 8,
+    # this comparing the difference of the results with 1e-15 is numerically sound.
+    assert (m_mixed.inv() - m_inv).norm() < 1e-15
+    assert (m_float.inv() - m_inv).norm() < 1e-15
+
+
+def test_iszero_substitution():
+    """ When doing numerical computations, all elements that pass
+    the iszerofunc test should be set to numerically zero if they
+    aren't already. """
+
+    # Matrix from issue #9060
+    m = Matrix([[0.9, -0.1, -0.2, 0],[-0.8, 0.9, -0.4, 0],[-0.1, -0.8, 0.6, 0]])
+    m_rref = m.rref(iszerofunc=lambda x: abs(x)<6e-15)[0]
+    m_correct = Matrix([[1.0,   0, -0.301369863013699, 0],[  0, 1.0, -0.712328767123288, 0],[  0,   0,                  0, 0]])
+    m_diff = m_rref - m_correct
+    assert m_diff.norm() < 1e-15
+    # if a zero-substitution wasn't made, this entry will be -1.11022302462516e-16
+    assert m_rref[2,2] == 0
+
+
+def test_issue_11238():
+    from sympy.geometry.point import Point
+    xx = 8*tan(pi*Rational(13, 45))/(tan(pi*Rational(13, 45)) + sqrt(3))
+    yy = (-8*sqrt(3)*tan(pi*Rational(13, 45))**2 + 24*tan(pi*Rational(13, 45)))/(-3 + tan(pi*Rational(13, 45))**2)
+    p1 = Point(0, 0)
+    p2 = Point(1, -sqrt(3))
+    p0 = Point(xx,yy)
+    m1 = Matrix([p1 - simplify(p0), p2 - simplify(p0)])
+    m2 = Matrix([p1 - p0, p2 - p0])
+    m3 = Matrix([simplify(p1 - p0), simplify(p2 - p0)])
+
+    # This system has expressions which are zero and
+    # cannot be easily proved to be such, so without
+    # numerical testing, these assertions will fail.
+    Z = lambda x: abs(x.n()) < 1e-20
+    assert m1.rank(simplify=True, iszerofunc=Z) == 1
+    assert m2.rank(simplify=True, iszerofunc=Z) == 1
+    assert m3.rank(simplify=True, iszerofunc=Z) == 1
+
+
+def test_as_real_imag():
+    m1 = Matrix(2,2,[1,2,3,4])
+    m2 = m1*S.ImaginaryUnit
+    m3 = m1 + m2
+
+    for kls in all_classes:
+        a,b = kls(m3).as_real_imag()
+        assert list(a) == list(m1)
+        assert list(b) == list(m1)
+
+
+def test_deprecated():
+    # Maintain tests for deprecated functions.  We must capture
+    # the deprecation warnings.  When the deprecated functionality is
+    # removed, the corresponding tests should be removed.
+
+    m = Matrix(3, 3, [0, 1, 0, -4, 4, 0, -2, 1, 2])
+    P, Jcells = m.jordan_cells()
+    assert Jcells[1] == Matrix(1, 1, [2])
+    assert Jcells[0] == Matrix(2, 2, [2, 1, 0, 2])
+
+
+def test_issue_14489():
+    from sympy.core.mod import Mod
+    A = Matrix([-1, 1, 2])
+    B = Matrix([10, 20, -15])
+
+    assert Mod(A, 3) == Matrix([2, 1, 2])
+    assert Mod(B, 4) == Matrix([2, 0, 1])
+
+
+def test_issue_14943():
+    # Test that __array__ accepts the optional dtype argument
+    try:
+        from numpy import array
+    except ImportError:
+        skip('NumPy must be available to test creating matrices from ndarrays')
+
+    M = Matrix([[1,2], [3,4]])
+    assert array(M, dtype=float).dtype.name == 'float64'
+
+
+def test_case_6913():
+    m = MatrixSymbol('m', 1, 1)
+    a = Symbol("a")
+    a = m[0, 0]>0
+    assert str(a) == 'm[0, 0] > 0'
+
+
+def test_issue_11948():
+    A = MatrixSymbol('A', 3, 3)
+    a = Wild('a')
+    assert A.match(a) == {a: A}
+
+
+def test_gramschmidt_conjugate_dot():
+    vecs = [Matrix([1, I]), Matrix([1, -I])]
+    assert Matrix.orthogonalize(*vecs) == \
+        [Matrix([[1], [I]]), Matrix([[1], [-I]])]
+
+    vecs = [Matrix([1, I, 0]), Matrix([I, 0, -I])]
+    assert Matrix.orthogonalize(*vecs) == \
+        [Matrix([[1], [I], [0]]), Matrix([[I/2], [S(1)/2], [-I]])]
+
+    mat = Matrix([[1, I], [1, -I]])
+    Q, R = mat.QRdecomposition()
+    assert Q * Q.H == Matrix.eye(2)
+
+
+def test_issue_8207():
+    a = Matrix(MatrixSymbol('a', 3, 1))
+    b = Matrix(MatrixSymbol('b', 3, 1))
+    c = a.dot(b)
+    d = diff(c, a[0, 0])
+    e = diff(d, a[0, 0])
+    assert d == b[0, 0]
+    assert e == 0
+
+
+def test_func():
+    from sympy.simplify.simplify import nthroot
+
+    A = Matrix([[1, 2],[0, 3]])
+    assert A.analytic_func(sin(x*t), x) == Matrix([[sin(t), sin(3*t) - sin(t)], [0, sin(3*t)]])
+
+    A = Matrix([[2, 1],[1, 2]])
+    assert (pi * A / 6).analytic_func(cos(x), x) == Matrix([[sqrt(3)/4, -sqrt(3)/4], [-sqrt(3)/4, sqrt(3)/4]])
+
+
+    raises(ValueError, lambda : zeros(5).analytic_func(log(x), x))
+    raises(ValueError, lambda : (A*x).analytic_func(log(x), x))
+
+    A = Matrix([[0, -1, -2, 3], [0, -1, -2, 3], [0, 1, 0, -1], [0, 0, -1, 1]])
+    assert A.analytic_func(exp(x), x) == A.exp()
+    raises(ValueError, lambda : A.analytic_func(sqrt(x), x))
+
+    A = Matrix([[41, 12],[12, 34]])
+    assert simplify(A.analytic_func(sqrt(x), x)**2) == A
+
+    A = Matrix([[3, -12, 4], [-1, 0, -2], [-1, 5, -1]])
+    assert simplify(A.analytic_func(nthroot(x, 3), x)**3) == A
+
+    A = Matrix([[2, 0, 0, 0], [1, 2, 0, 0], [0, 1, 3, 0], [0, 0, 1, 3]])
+    assert A.analytic_func(exp(x), x) == A.exp()
+
+    A = Matrix([[0, 2, 1, 6], [0, 0, 1, 2], [0, 0, 0, 3], [0, 0, 0, 0]])
+    assert A.analytic_func(exp(x*t), x) == expand(simplify((A*t).exp()))
+
+
+@skip_under_pyodide("Cannot create threads under pyodide.")
+def test_issue_19809():
+
+    def f():
+        assert _dotprodsimp_state.state == None
+        m = Matrix([[1]])
+        m = m * m
+        return True
+
+    with dotprodsimp(True):
+        with concurrent.futures.ThreadPoolExecutor() as executor:
+            future = executor.submit(f)
+            assert future.result()
+
+
+def test_issue_23276():
+    M = Matrix([x, y])
+    assert integrate(M, (x, 0, 1), (y, 0, 1)) == Matrix([
+        [S.Half],
+        [S.Half]])
+
+
+def test_issue_27225():
+    # https://github.com/sympy/sympy/issues/27225
+    raises(TypeError, lambda : floor(Matrix([1, 1, 0])))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_normalforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_normalforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..47ee52d73539f7fb79295443e1cf7e0a49e30a5e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_normalforms.py
@@ -0,0 +1,111 @@
+from sympy.testing.pytest import warns_deprecated_sympy
+
+from sympy.core.symbol import Symbol
+from sympy.polys.polytools import Poly
+from sympy.matrices import Matrix, randMatrix
+from sympy.matrices.normalforms import (
+    invariant_factors,
+    smith_normal_form,
+    smith_normal_decomp,
+    hermite_normal_form,
+    is_smith_normal_form,
+)
+from sympy.polys.domains import ZZ, QQ
+from sympy.core.numbers import Integer
+
+import random
+
+
+def test_smith_normal():
+    m = Matrix([[12,6,4,8],[3,9,6,12],[2,16,14,28],[20,10,10,20]])
+    smf = Matrix([[1, 0, 0, 0], [0, 10, 0, 0], [0, 0, 30, 0], [0, 0, 0, 0]])
+    assert smith_normal_form(m) == smf
+
+    a, s, t = smith_normal_decomp(m)
+    assert a == s * m * t
+
+    x = Symbol('x')
+    with warns_deprecated_sympy():
+        m = Matrix([[Poly(x-1), Poly(1, x),Poly(-1,x)],
+                    [0, Poly(x), Poly(-1,x)],
+                    [Poly(0,x),Poly(-1,x),Poly(x)]])
+    invs = 1, x - 1, x**2 - 1
+    assert invariant_factors(m, domain=QQ[x]) == invs
+
+    m = Matrix([[2, 4]])
+    smf = Matrix([[2, 0]])
+    assert smith_normal_form(m) == smf
+
+    prng = random.Random(0)
+    for i in range(6):
+        for j in range(6):
+            for _ in range(10 if i*j else 1):
+                m = randMatrix(i, j, max=5, percent=50, prng=prng)
+                a, s, t = smith_normal_decomp(m)
+                assert a == s * m * t
+                assert is_smith_normal_form(a)
+                s.inv().to_DM(ZZ)
+                t.inv().to_DM(ZZ)
+
+                a, s, t = smith_normal_decomp(m, QQ)
+                assert a == s * m * t
+                assert is_smith_normal_form(a)
+                s.inv()
+                t.inv()
+
+
+def test_smith_normal_deprecated():
+    from sympy.polys.solvers import RawMatrix as Matrix
+
+    with warns_deprecated_sympy():
+        m = Matrix([[12, 6, 4,8],[3,9,6,12],[2,16,14,28],[20,10,10,20]])
+    setattr(m, 'ring', ZZ)
+    with warns_deprecated_sympy():
+        smf = Matrix([[1, 0, 0, 0], [0, 10, 0, 0], [0, 0, 30, 0], [0, 0, 0, 0]])
+    assert smith_normal_form(m) == smf
+
+    x = Symbol('x')
+    with warns_deprecated_sympy():
+        m = Matrix([[Poly(x-1), Poly(1, x),Poly(-1,x)],
+                    [0, Poly(x), Poly(-1,x)],
+                    [Poly(0,x),Poly(-1,x),Poly(x)]])
+    setattr(m, 'ring', QQ[x])
+    invs = (Poly(1, x, domain='QQ'), Poly(x - 1, domain='QQ'), Poly(x**2 - 1, domain='QQ'))
+    assert invariant_factors(m) == invs
+
+    with warns_deprecated_sympy():
+        m = Matrix([[2, 4]])
+    setattr(m, 'ring', ZZ)
+    with warns_deprecated_sympy():
+        smf = Matrix([[2, 0]])
+    assert smith_normal_form(m) == smf
+
+
+def test_hermite_normal():
+    m = Matrix([[2, 7, 17, 29, 41], [3, 11, 19, 31, 43], [5, 13, 23, 37, 47]])
+    hnf = Matrix([[1, 0, 0], [0, 2, 1], [0, 0, 1]])
+    assert hermite_normal_form(m) == hnf
+
+    tr_hnf = Matrix([[37, 0, 19], [222, -6, 113], [48, 0, 25], [0, 2, 1], [0, 0, 1]])
+    assert hermite_normal_form(m.transpose()) == tr_hnf
+
+    m = Matrix([[8, 28, 68, 116, 164], [3, 11, 19, 31, 43], [5, 13, 23, 37, 47]])
+    hnf = Matrix([[4, 0, 0], [0, 2, 1], [0, 0, 1]])
+    assert hermite_normal_form(m) == hnf
+    assert hermite_normal_form(m, D=8) == hnf
+    assert hermite_normal_form(m, D=ZZ(8)) == hnf
+    assert hermite_normal_form(m, D=Integer(8)) == hnf
+
+    m = Matrix([[10, 8, 6, 30, 2], [45, 36, 27, 18, 9], [5, 4, 3, 2, 1]])
+    hnf = Matrix([[26, 2], [0, 9], [0, 1]])
+    assert hermite_normal_form(m) == hnf
+
+    m = Matrix([[2, 7], [0, 0], [0, 0]])
+    hnf = Matrix([[1], [0], [0]])
+    assert hermite_normal_form(m) == hnf
+
+
+def test_issue_23410():
+    A = Matrix([[1, 12], [0, 8], [0, 5]])
+    H = Matrix([[1, 0], [0, 8], [0, 5]])
+    assert hermite_normal_form(A) == H
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_reductions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_reductions.py
new file mode 100644
index 0000000000000000000000000000000000000000..32c98c6f249b1afafc8193f4248dc9493bb803e0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_reductions.py
@@ -0,0 +1,351 @@
+from sympy.core.numbers import I
+from sympy.core.symbol import symbols
+from sympy.testing.pytest import raises
+from sympy.matrices import Matrix, zeros, eye
+from sympy.core.symbol import Symbol
+from sympy.core.numbers import Rational
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.simplify.simplify import simplify
+from sympy.abc import x
+
+
+# Matrix tests
+def test_row_op():
+    e = eye(3)
+
+    raises(ValueError, lambda: e.elementary_row_op("abc"))
+    raises(ValueError, lambda: e.elementary_row_op())
+    raises(ValueError, lambda: e.elementary_row_op('n->kn', row=5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->kn', row=-5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=1, row2=5))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=5, row2=1))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=-5, row2=1))
+    raises(ValueError, lambda: e.elementary_row_op('n<->m', row1=1, row2=-5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=1, row2=5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=5, row2=1, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=-5, row2=1, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=1, row2=-5, k=5))
+    raises(ValueError, lambda: e.elementary_row_op('n->n+km', row1=1, row2=1, k=5))
+
+    # test various ways to set arguments
+    assert e.elementary_row_op("n->kn", 0, 5) == Matrix([[5, 0, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->kn", 1, 5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->kn", row=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->kn", row1=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n<->m", 0, 1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n<->m", row1=0, row2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n<->m", row=0, row2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->n+km", 0, 5, 1) == Matrix([[1, 5, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->n+km", row=0, k=5, row2=1) == Matrix([[1, 5, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_row_op("n->n+km", row1=0, k=5, row2=1) == Matrix([[1, 5, 0], [0, 1, 0], [0, 0, 1]])
+
+    # make sure the matrix doesn't change size
+    a = Matrix(2, 3, [0]*6)
+    assert a.elementary_row_op("n->kn", 1, 5) == Matrix(2, 3, [0]*6)
+    assert a.elementary_row_op("n<->m", 0, 1) == Matrix(2, 3, [0]*6)
+    assert a.elementary_row_op("n->n+km", 0, 5, 1) == Matrix(2, 3, [0]*6)
+
+
+def test_col_op():
+    e = eye(3)
+
+    raises(ValueError, lambda: e.elementary_col_op("abc"))
+    raises(ValueError, lambda: e.elementary_col_op())
+    raises(ValueError, lambda: e.elementary_col_op('n->kn', col=5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->kn', col=-5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=1, col2=5))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=5, col2=1))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=-5, col2=1))
+    raises(ValueError, lambda: e.elementary_col_op('n<->m', col1=1, col2=-5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=1, col2=5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=5, col2=1, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=-5, col2=1, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=1, col2=-5, k=5))
+    raises(ValueError, lambda: e.elementary_col_op('n->n+km', col1=1, col2=1, k=5))
+
+    # test various ways to set arguments
+    assert e.elementary_col_op("n->kn", 0, 5) == Matrix([[5, 0, 0], [0, 1, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->kn", 1, 5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->kn", col=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->kn", col1=1, k=5) == Matrix([[1, 0, 0], [0, 5, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n<->m", 0, 1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n<->m", col1=0, col2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n<->m", col=0, col2=1) == Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->n+km", 0, 5, 1) == Matrix([[1, 0, 0], [5, 1, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->n+km", col=0, k=5, col2=1) == Matrix([[1, 0, 0], [5, 1, 0], [0, 0, 1]])
+    assert e.elementary_col_op("n->n+km", col1=0, k=5, col2=1) == Matrix([[1, 0, 0], [5, 1, 0], [0, 0, 1]])
+
+    # make sure the matrix doesn't change size
+    a = Matrix(2, 3, [0]*6)
+    assert a.elementary_col_op("n->kn", 1, 5) == Matrix(2, 3, [0]*6)
+    assert a.elementary_col_op("n<->m", 0, 1) == Matrix(2, 3, [0]*6)
+    assert a.elementary_col_op("n->n+km", 0, 5, 1) == Matrix(2, 3, [0]*6)
+
+
+def test_is_echelon():
+    zro = zeros(3)
+    ident = eye(3)
+
+    assert zro.is_echelon
+    assert ident.is_echelon
+
+    a = Matrix(0, 0, [])
+    assert a.is_echelon
+
+    a = Matrix(2, 3, [3, 2, 1, 0, 0, 6])
+    assert a.is_echelon
+
+    a = Matrix(2, 3, [0, 0, 6, 3, 2, 1])
+    assert not a.is_echelon
+
+    x = Symbol('x')
+    a = Matrix(3, 1, [x, 0, 0])
+    assert a.is_echelon
+
+    a = Matrix(3, 1, [x, x, 0])
+    assert not a.is_echelon
+
+    a = Matrix(3, 3, [0, 0, 0, 1, 2, 3, 0, 0, 0])
+    assert not a.is_echelon
+
+
+def test_echelon_form():
+    # echelon form is not unique, but the result
+    # must be row-equivalent to the original matrix
+    # and it must be in echelon form.
+
+    a = zeros(3)
+    e = eye(3)
+
+    # we can assume the zero matrix and the identity matrix shouldn't change
+    assert a.echelon_form() == a
+    assert e.echelon_form() == e
+
+    a = Matrix(0, 0, [])
+    assert a.echelon_form() == a
+
+    a = Matrix(1, 1, [5])
+    assert a.echelon_form() == a
+
+    # now we get to the real tests
+
+    def verify_row_null_space(mat, rows, nulls):
+        for v in nulls:
+            assert all(t.is_zero for t in a_echelon*v)
+        for v in rows:
+            if not all(t.is_zero for t in v):
+                assert not all(t.is_zero for t in a_echelon*v.transpose())
+
+    a = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    nulls = [Matrix([
+                     [ 1],
+                     [-2],
+                     [ 1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+
+    a = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 8])
+    nulls = []
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    a = Matrix(3, 3, [2, 1, 3, 0, 0, 0, 2, 1, 3])
+    nulls = [Matrix([
+             [Rational(-1, 2)],
+             [   1],
+             [   0]]),
+             Matrix([
+             [Rational(-3, 2)],
+             [   0],
+             [   1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    # this one requires a row swap
+    a = Matrix(3, 3, [2, 1, 3, 0, 0, 0, 1, 1, 3])
+    nulls = [Matrix([
+             [   0],
+             [  -3],
+             [   1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    a = Matrix(3, 3, [0, 3, 3, 0, 2, 2, 0, 1, 1])
+    nulls = [Matrix([
+             [1],
+             [0],
+             [0]]),
+             Matrix([
+             [ 0],
+             [-1],
+             [ 1]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+    a = Matrix(2, 3, [2, 2, 3, 3, 3, 0])
+    nulls = [Matrix([
+             [-1],
+             [1],
+             [0]])]
+    rows = [a[i, :] for i in range(a.rows)]
+    a_echelon = a.echelon_form()
+    assert a_echelon.is_echelon
+    verify_row_null_space(a, rows, nulls)
+
+
+def test_rref():
+    e = Matrix(0, 0, [])
+    assert e.rref(pivots=False) == e
+
+    e = Matrix(1, 1, [1])
+    a = Matrix(1, 1, [5])
+    assert e.rref(pivots=False) == a.rref(pivots=False) == e
+
+    a = Matrix(3, 1, [1, 2, 3])
+    assert a.rref(pivots=False) == Matrix([[1], [0], [0]])
+
+    a = Matrix(1, 3, [1, 2, 3])
+    assert a.rref(pivots=False) == Matrix([[1, 2, 3]])
+
+    a = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    assert a.rref(pivots=False) == Matrix([
+                                     [1, 0, -1],
+                                     [0, 1,  2],
+                                     [0, 0,  0]])
+
+    a = Matrix(3, 3, [1, 2, 3, 1, 2, 3, 1, 2, 3])
+    b = Matrix(3, 3, [1, 2, 3, 0, 0, 0, 0, 0, 0])
+    c = Matrix(3, 3, [0, 0, 0, 1, 2, 3, 0, 0, 0])
+    d = Matrix(3, 3, [0, 0, 0, 0, 0, 0, 1, 2, 3])
+    assert a.rref(pivots=False) == \
+            b.rref(pivots=False) == \
+            c.rref(pivots=False) == \
+            d.rref(pivots=False) == b
+
+    e = eye(3)
+    z = zeros(3)
+    assert e.rref(pivots=False) == e
+    assert z.rref(pivots=False) == z
+
+    a = Matrix([
+            [ 0, 0,  1,  2,  2, -5,  3],
+            [-1, 5,  2,  2,  1, -7,  5],
+            [ 0, 0, -2, -3, -3,  8, -5],
+            [-1, 5,  0, -1, -2,  1,  0]])
+    mat, pivot_offsets = a.rref()
+    assert mat == Matrix([
+                     [1, -5, 0, 0, 1,  1, -1],
+                     [0,  0, 1, 0, 0, -1,  1],
+                     [0,  0, 0, 1, 1, -2,  1],
+                     [0,  0, 0, 0, 0,  0,  0]])
+    assert pivot_offsets == (0, 2, 3)
+
+    a = Matrix([[Rational(1, 19),  Rational(1, 5),    2,    3],
+                        [   4,    5,    6,    7],
+                        [   8,    9,   10,   11],
+                        [  12,   13,   14,   15]])
+    assert a.rref(pivots=False) == Matrix([
+                                         [1, 0, 0, Rational(-76, 157)],
+                                         [0, 1, 0,  Rational(-5, 157)],
+                                         [0, 0, 1, Rational(238, 157)],
+                                         [0, 0, 0,       0]])
+
+    x = Symbol('x')
+    a = Matrix(2, 3, [x, 1, 1, sqrt(x), x, 1])
+    for i, j in zip(a.rref(pivots=False),
+            [1, 0, sqrt(x)*(-x + 1)/(-x**Rational(5, 2) + x),
+                0, 1, 1/(sqrt(x) + x + 1)]):
+        assert simplify(i - j).is_zero
+
+
+def test_rref_rhs():
+    a, b, c, d = symbols('a b c d')
+    A = Matrix([[0, 0], [0, 0], [1, 2], [3, 4]])
+    B = Matrix([a, b, c, d])
+    assert A.rref_rhs(B) == (Matrix([
+    [1, 0],
+    [0, 1],
+    [0, 0],
+    [0, 0]]), Matrix([
+    [   -2*c + d],
+    [3*c/2 - d/2],
+    [          a],
+    [          b]]))
+
+
+def test_issue_17827():
+    C = Matrix([
+        [3, 4, -1, 1],
+        [9, 12, -3, 3],
+        [0, 2, 1, 3],
+        [2, 3, 0, -2],
+        [0, 3, 3, -5],
+        [8, 15, 0, 6]
+    ])
+    # Tests for row/col within valid range
+    D = C.elementary_row_op('n<->m', row1=2, row2=5)
+    E = C.elementary_row_op('n->n+km', row1=5, row2=3, k=-4)
+    F = C.elementary_row_op('n->kn', row=5, k=2)
+    assert(D[5, :] == Matrix([[0, 2, 1, 3]]))
+    assert(E[5, :] == Matrix([[0, 3, 0, 14]]))
+    assert(F[5, :] == Matrix([[16, 30, 0, 12]]))
+    # Tests for row/col out of range
+    raises(ValueError, lambda: C.elementary_row_op('n<->m', row1=2, row2=6))
+    raises(ValueError, lambda: C.elementary_row_op('n->kn', row=7, k=2))
+    raises(ValueError, lambda: C.elementary_row_op('n->n+km', row1=-1, row2=5, k=2))
+
+def test_rank():
+    m = Matrix([[1, 2], [x, 1 - 1/x]])
+    assert m.rank() == 2
+    n = Matrix(3, 3, range(1, 10))
+    assert n.rank() == 2
+    p = zeros(3)
+    assert p.rank() == 0
+
+def test_issue_11434():
+    ax, ay, bx, by, cx, cy, dx, dy, ex, ey, t0, t1 = \
+        symbols('a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1')
+    M = Matrix([[ax, ay, ax*t0, ay*t0, 0],
+                [bx, by, bx*t0, by*t0, 0],
+                [cx, cy, cx*t0, cy*t0, 1],
+                [dx, dy, dx*t0, dy*t0, 1],
+                [ex, ey, 2*ex*t1 - ex*t0, 2*ey*t1 - ey*t0, 0]])
+    assert M.rank() == 4
+
+def test_rank_regression_from_so():
+    # see:
+    # https://stackoverflow.com/questions/19072700/why-does-sympy-give-me-the-wrong-answer-when-i-row-reduce-a-symbolic-matrix
+
+    nu, lamb = symbols('nu, lambda')
+    A = Matrix([[-3*nu,         1,                  0,  0],
+                [ 3*nu, -2*nu - 1,                  2,  0],
+                [    0,      2*nu, (-1*nu) - lamb - 2,  3],
+                [    0,         0,          nu + lamb, -3]])
+    expected_reduced = Matrix([[1, 0, 0, 1/(nu**2*(-lamb - nu))],
+                               [0, 1, 0,    3/(nu*(-lamb - nu))],
+                               [0, 0, 1,         3/(-lamb - nu)],
+                               [0, 0, 0,                      0]])
+    expected_pivots = (0, 1, 2)
+
+    reduced, pivots = A.rref()
+
+    assert simplify(expected_reduced - reduced) == zeros(*A.shape)
+    assert pivots == expected_pivots
+
+def test_issue_15872():
+    A = Matrix([[1, 1, 1, 0], [-2, -1, 0, -1], [0, 0, -1, -1], [0, 0, 2, 1]])
+    B = A - Matrix.eye(4) * I
+    assert B.rank() == 3
+    assert (B**2).rank() == 2
+    assert (B**3).rank() == 2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_repmatrix.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_repmatrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..ee36de004705f29eaa49ea8e06fd65a8a2baa718
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_repmatrix.py
@@ -0,0 +1,62 @@
+from sympy.testing.pytest import raises
+from sympy.matrices.exceptions import NonSquareMatrixError, NonInvertibleMatrixError
+
+from sympy import Matrix, Rational
+
+
+def test_lll():
+    A = Matrix([[1, 0, 0, 0, -20160],
+                [0, 1, 0, 0, 33768],
+                [0, 0, 1, 0, 39578],
+                [0, 0, 0, 1, 47757]])
+    L = Matrix([[ 10, -3,  -2,  8,  -4],
+                [  3, -9,   8,  1, -11],
+                [ -3, 13,  -9, -3,  -9],
+                [-12, -7, -11,  9,  -1]])
+    T = Matrix([[ 10, -3,  -2,  8],
+                [  3, -9,   8,  1],
+                [ -3, 13,  -9, -3],
+                [-12, -7, -11,  9]])
+    assert A.lll() == L
+    assert A.lll_transform() == (L, T)
+    assert T * A == L
+
+
+def test_matrix_inv_mod():
+    A = Matrix(2, 1, [1, 0])
+    raises(NonSquareMatrixError, lambda: A.inv_mod(2))
+    A = Matrix(2, 2, [1, 0, 0, 0])
+    raises(NonInvertibleMatrixError, lambda: A.inv_mod(2))
+    A = Matrix(2, 2, [1, 2, 3, 4])
+    Ai = Matrix(2, 2, [1, 1, 0, 1])
+    assert A.inv_mod(3) == Ai
+    A = Matrix(2, 2, [1, 0, 0, 1])
+    assert A.inv_mod(2) == A
+    A = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+    raises(NonInvertibleMatrixError, lambda: A.inv_mod(5))
+    A = Matrix(3, 3, [5, 1, 3, 2, 6, 0, 2, 1, 1])
+    Ai = Matrix(3, 3, [6, 8, 0, 1, 5, 6, 5, 6, 4])
+    assert A.inv_mod(9) == Ai
+    A = Matrix(3, 3, [1, 6, -3, 4, 1, -5, 3, -5, 5])
+    Ai = Matrix(3, 3, [4, 3, 3, 1, 2, 5, 1, 5, 1])
+    assert A.inv_mod(6) == Ai
+    A = Matrix(3, 3, [1, 6, 1, 4, 1, 5, 3, 2, 5])
+    Ai = Matrix(3, 3, [6, 0, 3, 6, 6, 4, 1, 6, 1])
+    assert A.inv_mod(7) == Ai
+    A = Matrix([[1, 2], [3, Rational(3,4)]])
+    raises(ValueError, lambda: A.inv_mod(2))
+    A = Matrix([[1, 2], [3, 4]])
+    raises(TypeError, lambda: A.inv_mod(Rational(1, 2)))
+    # https://github.com/sympy/sympy/issues/27663
+    M = Matrix([
+        [2, 3, 1, 4],
+        [1, 5, 3, 2],
+        [3, 2, 4, 1],
+        [4, 1, 2, 5],
+    ])
+    assert M.inv_mod(26) == Matrix([
+        [7, 21, 10, 10],
+        [1, 7, 19, 3],
+        [14, 1, 15, 1],
+        [25, 23, 3, 12],
+    ])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_solvers.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_solvers.py
new file mode 100644
index 0000000000000000000000000000000000000000..c1347062c0482336affbeb4bb9a95aedfcc0ae53
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_solvers.py
@@ -0,0 +1,615 @@
+import pytest
+from sympy.core.function import expand_mul
+from sympy.core.numbers import (I, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.simplify.simplify import simplify
+from sympy.matrices.exceptions import (ShapeError, NonSquareMatrixError)
+from sympy.matrices import (
+    ImmutableMatrix, Matrix, eye, ones, ImmutableDenseMatrix, dotprodsimp)
+from sympy.matrices.determinant import _det_laplace
+from sympy.testing.pytest import raises
+from sympy.matrices.exceptions import NonInvertibleMatrixError
+from sympy.polys.matrices.exceptions import DMShapeError
+from sympy.solvers.solveset import linsolve
+from sympy.abc import x, y
+
+def test_issue_17247_expression_blowup_29():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.gauss_jordan_solve(ones(4, 1)) == (Matrix(S('''[
+            [                          -32549314808672/3306971225785 - 17397006745216*I/3306971225785],
+            [                               67439348256/3306971225785 - 9167503335872*I/3306971225785],
+            [-15091965363354518272/21217636514687010905 + 16890163109293858304*I/21217636514687010905],
+            [                                                          -11328/952745 + 87616*I/952745]]''')), Matrix(0, 1, []))
+
+def test_issue_17247_expression_blowup_30():
+    M = Matrix(S('''[
+        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
+        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
+        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
+        [                0,                     0,                   0, -177/128 - 1369*I/128]]'''))
+    with dotprodsimp(True):
+        assert M.cholesky_solve(ones(4, 1)) == Matrix(S('''[
+            [                          -32549314808672/3306971225785 - 17397006745216*I/3306971225785],
+            [                               67439348256/3306971225785 - 9167503335872*I/3306971225785],
+            [-15091965363354518272/21217636514687010905 + 16890163109293858304*I/21217636514687010905],
+            [                                                          -11328/952745 + 87616*I/952745]]'''))
+
+# @XFAIL # This calculation hangs with dotprodsimp.
+# def test_issue_17247_expression_blowup_31():
+#     M = Matrix([
+#         [x + 1, 1 - x,     0,     0],
+#         [1 - x, x + 1,     0, x + 1],
+#         [    0, 1 - x, x + 1,     0],
+#         [    0,     0,     0, x + 1]])
+#     with dotprodsimp(True):
+#         assert M.LDLsolve(ones(4, 1)) == Matrix([
+#             [(x + 1)/(4*x)],
+#             [(x - 1)/(4*x)],
+#             [(x + 1)/(4*x)],
+#             [    1/(x + 1)]])
+
+
+def test_LUsolve_iszerofunc():
+    # taken from https://github.com/sympy/sympy/issues/24679
+
+    M = Matrix([[(x + 1)**2 - (x**2 + 2*x + 1), x], [x, 0]])
+    b = Matrix([1, 1])
+    is_zero_func = lambda e: False if e._random() else True
+
+    x_exp = Matrix([1/x, (1-(-x**2 - 2*x + (x+1)**2 - 1)/x)/x])
+
+    assert (x_exp - M.LUsolve(b, iszerofunc=is_zero_func)) == Matrix([0, 0])
+
+
+def test_issue_17247_expression_blowup_32():
+    M = Matrix([
+        [x + 1, 1 - x,     0,     0],
+        [1 - x, x + 1,     0, x + 1],
+        [    0, 1 - x, x + 1,     0],
+        [    0,     0,     0, x + 1]])
+    with dotprodsimp(True):
+        assert M.LUsolve(ones(4, 1)) == Matrix([
+            [(x + 1)/(4*x)],
+            [(x - 1)/(4*x)],
+            [(x + 1)/(4*x)],
+            [    1/(x + 1)]])
+
+def test_LUsolve():
+    A = Matrix([[2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    x = Matrix(3, 1, [3, 7, 5])
+    b = A*x
+    soln = A.LUsolve(b)
+    assert soln == x
+    A = Matrix([[0, -1, 2],
+                [5, 10, 7],
+                [8,  3, 4]])
+    x = Matrix(3, 1, [-1, 2, 5])
+    b = A*x
+    soln = A.LUsolve(b)
+    assert soln == x
+    A = Matrix([[2, 1], [1, 0], [1, 0]])   # issue 14548
+    b = Matrix([3, 1, 1])
+    assert A.LUsolve(b) == Matrix([1, 1])
+    b = Matrix([3, 1, 2])                  # inconsistent
+    raises(ValueError, lambda: A.LUsolve(b))
+    A = Matrix([[0, -1, 2],
+                [5, 10, 7],
+                [8,  3, 4],
+                [2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    x = Matrix([2, 1, -4])
+    b = A*x
+    soln = A.LUsolve(b)
+    assert soln == x
+    A = Matrix([[0, -1, 2], [5, 10, 7]])  # underdetermined
+    x = Matrix([-1, 2, 0])
+    b = A*x
+    raises(NotImplementedError, lambda: A.LUsolve(b))
+
+    A = Matrix(4, 4, lambda i, j: 1/(i+j+1) if i != 3 else 0)
+    b = Matrix.zeros(4, 1)
+    raises(NonInvertibleMatrixError, lambda: A.LUsolve(b))
+
+
+def test_LUsolve_noncommutative():
+    a0, a1, a2, a3 = symbols("a:4", commutative=False)
+    b0, b1 = symbols("b:2", commutative=False)
+    A = Matrix([[a0, a1], [a2, a3]])
+    check = A * A.LUsolve(Matrix([b0, b1]))
+    assert check[0, 0].expand() == b0
+    # Because sympy simplification is very limited with noncommutative expressions,
+    # perform an explicit check with the second element
+    assert check[1, 0] == (
+        a2*a0**(-1)*(-a1*(-a2*a0**(-1)*a1 + a3)**(-1)*(-a2*a0**(-1)*b0 + b1) + b0)
+        + a3*(-a2*a0**(-1)*a1 + a3)**(-1)*(-a2*a0**(-1)*b0 + b1)
+    )
+
+
+def test_QRsolve():
+    A = Matrix([[2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    x = Matrix(3, 1, [3, 7, 5])
+    b = A*x
+    soln = A.QRsolve(b)
+    assert soln == x
+    x = Matrix([[1, 2], [3, 4], [5, 6]])
+    b = A*x
+    soln = A.QRsolve(b)
+    assert soln == x
+
+    A = Matrix([[0, -1, 2],
+                [5, 10, 7],
+                [8,  3, 4]])
+    x = Matrix(3, 1, [-1, 2, 5])
+    b = A*x
+    soln = A.QRsolve(b)
+    assert soln == x
+    x = Matrix([[7, 8], [9, 10], [11, 12]])
+    b = A*x
+    soln = A.QRsolve(b)
+    assert soln == x
+
+def test_errors():
+    raises(ShapeError, lambda: Matrix([1]).LUsolve(Matrix([[1, 2], [3, 4]])))
+
+def test_cholesky_solve():
+    A = Matrix([[2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    x = Matrix(3, 1, [3, 7, 5])
+    b = A*x
+    soln = A.cholesky_solve(b)
+    assert soln == x
+    A = Matrix([[0, -1, 2],
+                [5, 10, 7],
+                [8,  3, 4]])
+    x = Matrix(3, 1, [-1, 2, 5])
+    b = A*x
+    soln = A.cholesky_solve(b)
+    assert soln == x
+    A = Matrix(((1, 5), (5, 1)))
+    x = Matrix((4, -3))
+    b = A*x
+    soln = A.cholesky_solve(b)
+    assert soln == x
+    A = Matrix(((9, 3*I), (-3*I, 5)))
+    x = Matrix((-2, 1))
+    b = A*x
+    soln = A.cholesky_solve(b)
+    assert expand_mul(soln) == x
+    A = Matrix(((9*I, 3), (-3 + I, 5)))
+    x = Matrix((2 + 3*I, -1))
+    b = A*x
+    soln = A.cholesky_solve(b)
+    assert expand_mul(soln) == x
+    a00, a01, a11, b0, b1 = symbols('a00, a01, a11, b0, b1')
+    A = Matrix(((a00, a01), (a01, a11)))
+    b = Matrix((b0, b1))
+    x = A.cholesky_solve(b)
+    assert simplify(A*x) == b
+
+
+def test_LDLsolve():
+    A = Matrix([[2, 3, 5],
+                [3, 6, 2],
+                [8, 3, 6]])
+    x = Matrix(3, 1, [3, 7, 5])
+    b = A*x
+    soln = A.LDLsolve(b)
+    assert soln == x
+
+    A = Matrix([[0, -1, 2],
+                [5, 10, 7],
+                [8,  3, 4]])
+    x = Matrix(3, 1, [-1, 2, 5])
+    b = A*x
+    soln = A.LDLsolve(b)
+    assert soln == x
+
+    A = Matrix(((9, 3*I), (-3*I, 5)))
+    x = Matrix((-2, 1))
+    b = A*x
+    soln = A.LDLsolve(b)
+    assert expand_mul(soln) == x
+
+    A = Matrix(((9*I, 3), (-3 + I, 5)))
+    x = Matrix((2 + 3*I, -1))
+    b = A*x
+    soln = A.LDLsolve(b)
+    assert expand_mul(soln) == x
+
+    A = Matrix(((9, 3), (3, 9)))
+    x = Matrix((1, 1))
+    b = A * x
+    soln = A.LDLsolve(b)
+    assert expand_mul(soln) == x
+
+    A = Matrix([[-5, -3, -4], [-3, -7, 7]])
+    x = Matrix([[8], [7], [-2]])
+    b = A * x
+    raises(NotImplementedError, lambda: A.LDLsolve(b))
+
+
+def test_lower_triangular_solve():
+
+    raises(NonSquareMatrixError,
+        lambda: Matrix([1, 0]).lower_triangular_solve(Matrix([0, 1])))
+    raises(ShapeError,
+        lambda: Matrix([[1, 0], [0, 1]]).lower_triangular_solve(Matrix([1])))
+    raises(ValueError,
+        lambda: Matrix([[2, 1], [1, 2]]).lower_triangular_solve(
+            Matrix([[1, 0], [0, 1]])))
+
+    A = Matrix([[1, 0], [0, 1]])
+    B = Matrix([[x, y], [y, x]])
+    C = Matrix([[4, 8], [2, 9]])
+
+    assert A.lower_triangular_solve(B) == B
+    assert A.lower_triangular_solve(C) == C
+
+
+def test_upper_triangular_solve():
+
+    raises(NonSquareMatrixError,
+        lambda: Matrix([1, 0]).upper_triangular_solve(Matrix([0, 1])))
+    raises(ShapeError,
+        lambda: Matrix([[1, 0], [0, 1]]).upper_triangular_solve(Matrix([1])))
+    raises(TypeError,
+        lambda: Matrix([[2, 1], [1, 2]]).upper_triangular_solve(
+            Matrix([[1, 0], [0, 1]])))
+
+    A = Matrix([[1, 0], [0, 1]])
+    B = Matrix([[x, y], [y, x]])
+    C = Matrix([[2, 4], [3, 8]])
+
+    assert A.upper_triangular_solve(B) == B
+    assert A.upper_triangular_solve(C) == C
+
+
+def test_diagonal_solve():
+    raises(TypeError, lambda: Matrix([1, 1]).diagonal_solve(Matrix([1])))
+    A = Matrix([[1, 0], [0, 1]])*2
+    B = Matrix([[x, y], [y, x]])
+    assert A.diagonal_solve(B) == B/2
+
+    A = Matrix([[1, 0], [1, 2]])
+    raises(TypeError, lambda: A.diagonal_solve(B))
+
+def test_pinv_solve():
+    # Fully determined system (unique result, identical to other solvers).
+    A = Matrix([[1, 5], [7, 9]])
+    B = Matrix([12, 13])
+    assert A.pinv_solve(B) == A.cholesky_solve(B)
+    assert A.pinv_solve(B) == A.LDLsolve(B)
+    assert A.pinv_solve(B) == Matrix([sympify('-43/26'), sympify('71/26')])
+    assert A * A.pinv() * B == B
+    # Fully determined, with two-dimensional B matrix.
+    B = Matrix([[12, 13, 14], [15, 16, 17]])
+    assert A.pinv_solve(B) == A.cholesky_solve(B)
+    assert A.pinv_solve(B) == A.LDLsolve(B)
+    assert A.pinv_solve(B) == Matrix([[-33, -37, -41], [69, 75, 81]]) / 26
+    assert A * A.pinv() * B == B
+    # Underdetermined system (infinite results).
+    A = Matrix([[1, 0, 1], [0, 1, 1]])
+    B = Matrix([5, 7])
+    solution = A.pinv_solve(B)
+    w = {}
+    for s in solution.atoms(Symbol):
+        # Extract dummy symbols used in the solution.
+        w[s.name] = s
+    assert solution == Matrix([[w['w0_0']/3 + w['w1_0']/3 - w['w2_0']/3 + 1],
+                               [w['w0_0']/3 + w['w1_0']/3 - w['w2_0']/3 + 3],
+                               [-w['w0_0']/3 - w['w1_0']/3 + w['w2_0']/3 + 4]])
+    assert A * A.pinv() * B == B
+    # Overdetermined system (least squares results).
+    A = Matrix([[1, 0], [0, 0], [0, 1]])
+    B = Matrix([3, 2, 1])
+    assert A.pinv_solve(B) == Matrix([3, 1])
+    # Proof the solution is not exact.
+    assert A * A.pinv() * B != B
+
+def test_pinv_rank_deficient():
+    # Test the four properties of the pseudoinverse for various matrices.
+    As = [Matrix([[1, 1, 1], [2, 2, 2]]),
+          Matrix([[1, 0], [0, 0]]),
+          Matrix([[1, 2], [2, 4], [3, 6]])]
+
+    for A in As:
+        A_pinv = A.pinv(method="RD")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+    for A in As:
+        A_pinv = A.pinv(method="ED")
+        AAp = A * A_pinv
+        ApA = A_pinv * A
+        assert simplify(AAp * A) == A
+        assert simplify(ApA * A_pinv) == A_pinv
+        assert AAp.H == AAp
+        assert ApA.H == ApA
+
+    # Test solving with rank-deficient matrices.
+    A = Matrix([[1, 0], [0, 0]])
+    # Exact, non-unique solution.
+    B = Matrix([3, 0])
+    solution = A.pinv_solve(B)
+    w1 = solution.atoms(Symbol).pop()
+    assert w1.name == 'w1_0'
+    assert solution == Matrix([3, w1])
+    assert A * A.pinv() * B == B
+    # Least squares, non-unique solution.
+    B = Matrix([3, 1])
+    solution = A.pinv_solve(B)
+    w1 = solution.atoms(Symbol).pop()
+    assert w1.name == 'w1_0'
+    assert solution == Matrix([3, w1])
+    assert A * A.pinv() * B != B
+
+def test_gauss_jordan_solve():
+
+    # Square, full rank, unique solution
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 10]])
+    b = Matrix([3, 6, 9])
+    sol, params = A.gauss_jordan_solve(b)
+    assert sol == Matrix([[-1], [2], [0]])
+    assert params == Matrix(0, 1, [])
+
+    # Square, full rank, unique solution, B has more columns than rows
+    A = eye(3)
+    B = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
+    sol, params = A.gauss_jordan_solve(B)
+    assert sol == B
+    assert params == Matrix(0, 4, [])
+
+    # Square, reduced rank, parametrized solution
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    b = Matrix([3, 6, 9])
+    sol, params, freevar = A.gauss_jordan_solve(b, freevar=True)
+    w = {}
+    for s in sol.atoms(Symbol):
+        # Extract dummy symbols used in the solution.
+        w[s.name] = s
+    assert sol == Matrix([[w['tau0'] - 1], [-2*w['tau0'] + 2], [w['tau0']]])
+    assert params == Matrix([[w['tau0']]])
+    assert freevar == [2]
+
+    # Square, reduced rank, parametrized solution, B has two columns
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    B = Matrix([[3, 4], [6, 8], [9, 12]])
+    sol, params, freevar = A.gauss_jordan_solve(B, freevar=True)
+    w = {}
+    for s in sol.atoms(Symbol):
+        # Extract dummy symbols used in the solution.
+        w[s.name] = s
+    assert sol == Matrix([[w['tau0'] - 1, w['tau1'] - Rational(4, 3)],
+                          [-2*w['tau0'] + 2, -2*w['tau1'] + Rational(8, 3)],
+                          [w['tau0'], w['tau1']],])
+    assert params == Matrix([[w['tau0'], w['tau1']]])
+    assert freevar == [2]
+
+    # Square, reduced rank, parametrized solution
+    A = Matrix([[1, 2, 3], [2, 4, 6], [3, 6, 9]])
+    b = Matrix([0, 0, 0])
+    sol, params = A.gauss_jordan_solve(b)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert sol == Matrix([[-2*w['tau0'] - 3*w['tau1']],
+                         [w['tau0']], [w['tau1']]])
+    assert params == Matrix([[w['tau0']], [w['tau1']]])
+
+    # Square, reduced rank, parametrized solution
+    A = Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+    b = Matrix([0, 0, 0])
+    sol, params = A.gauss_jordan_solve(b)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert sol == Matrix([[w['tau0']], [w['tau1']], [w['tau2']]])
+    assert params == Matrix([[w['tau0']], [w['tau1']], [w['tau2']]])
+
+    # Square, reduced rank, no solution
+    A = Matrix([[1, 2, 3], [2, 4, 6], [3, 6, 9]])
+    b = Matrix([0, 0, 1])
+    raises(ValueError, lambda: A.gauss_jordan_solve(b))
+
+    # Rectangular, tall, full rank, unique solution
+    A = Matrix([[1, 5, 3], [2, 1, 6], [1, 7, 9], [1, 4, 3]])
+    b = Matrix([0, 0, 1, 0])
+    sol, params = A.gauss_jordan_solve(b)
+    assert sol == Matrix([[Rational(-1, 2)], [0], [Rational(1, 6)]])
+    assert params == Matrix(0, 1, [])
+
+    # Rectangular, tall, full rank, unique solution, B has less columns than rows
+    A = Matrix([[1, 5, 3], [2, 1, 6], [1, 7, 9], [1, 4, 3]])
+    B = Matrix([[0,0], [0, 0], [1, 2], [0, 0]])
+    sol, params = A.gauss_jordan_solve(B)
+    assert sol == Matrix([[Rational(-1, 2), Rational(-2, 2)], [0, 0], [Rational(1, 6), Rational(2, 6)]])
+    assert params == Matrix(0, 2, [])
+
+    # Rectangular, tall, full rank, no solution
+    A = Matrix([[1, 5, 3], [2, 1, 6], [1, 7, 9], [1, 4, 3]])
+    b = Matrix([0, 0, 0, 1])
+    raises(ValueError, lambda: A.gauss_jordan_solve(b))
+
+    # Rectangular, tall, full rank, no solution, B has two columns (2nd has no solution)
+    A = Matrix([[1, 5, 3], [2, 1, 6], [1, 7, 9], [1, 4, 3]])
+    B = Matrix([[0,0], [0, 0], [1, 0], [0, 1]])
+    raises(ValueError, lambda: A.gauss_jordan_solve(B))
+
+    # Rectangular, tall, full rank, no solution, B has two columns (1st has no solution)
+    A = Matrix([[1, 5, 3], [2, 1, 6], [1, 7, 9], [1, 4, 3]])
+    B = Matrix([[0,0], [0, 0], [0, 1], [1, 0]])
+    raises(ValueError, lambda: A.gauss_jordan_solve(B))
+
+    # Rectangular, tall, reduced rank, parametrized solution
+    A = Matrix([[1, 5, 3], [2, 10, 6], [3, 15, 9], [1, 4, 3]])
+    b = Matrix([0, 0, 0, 1])
+    sol, params = A.gauss_jordan_solve(b)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert sol == Matrix([[-3*w['tau0'] + 5], [-1], [w['tau0']]])
+    assert params == Matrix([[w['tau0']]])
+
+    # Rectangular, tall, reduced rank, no solution
+    A = Matrix([[1, 5, 3], [2, 10, 6], [3, 15, 9], [1, 4, 3]])
+    b = Matrix([0, 0, 1, 1])
+    raises(ValueError, lambda: A.gauss_jordan_solve(b))
+
+    # Rectangular, wide, full rank, parametrized solution
+    A = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 1, 12]])
+    b = Matrix([1, 1, 1])
+    sol, params = A.gauss_jordan_solve(b)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert sol == Matrix([[2*w['tau0'] - 1], [-3*w['tau0'] + 1], [0],
+                         [w['tau0']]])
+    assert params == Matrix([[w['tau0']]])
+
+    # Rectangular, wide, reduced rank, parametrized solution
+    A = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [2, 4, 6, 8]])
+    b = Matrix([0, 1, 0])
+    sol, params = A.gauss_jordan_solve(b)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert sol == Matrix([[w['tau0'] + 2*w['tau1'] + S.Half],
+                         [-2*w['tau0'] - 3*w['tau1'] - Rational(1, 4)],
+                         [w['tau0']], [w['tau1']]])
+    assert params == Matrix([[w['tau0']], [w['tau1']]])
+    # watch out for clashing symbols
+    x0, x1, x2, _x0 = symbols('_tau0 _tau1 _tau2 tau1')
+    M = Matrix([[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, _x0]])
+    A = M[:, :-1]
+    b = M[:, -1:]
+    sol, params = A.gauss_jordan_solve(b)
+    assert params == Matrix(3, 1, [x0, x1, x2])
+    assert sol == Matrix(5, 1, [x0, 0, x1, _x0, x2])
+
+    # Rectangular, wide, reduced rank, no solution
+    A = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [2, 4, 6, 8]])
+    b = Matrix([1, 1, 1])
+    raises(ValueError, lambda: A.gauss_jordan_solve(b))
+
+    # Test for immutable matrix
+    A = ImmutableMatrix([[1, 0], [0, 1]])
+    B = ImmutableMatrix([1, 2])
+    sol, params = A.gauss_jordan_solve(B)
+    assert sol == ImmutableMatrix([1, 2])
+    assert params == ImmutableMatrix(0, 1, [])
+    assert sol.__class__ == ImmutableDenseMatrix
+    assert params.__class__ == ImmutableDenseMatrix
+
+    # Test placement of free variables
+    A = Matrix([[1, 0, 0, 0], [0, 0, 0, 1]])
+    b = Matrix([1, 1])
+    sol, params = A.gauss_jordan_solve(b)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert sol == Matrix([[1], [w['tau0']], [w['tau1']], [1]])
+    assert params == Matrix([[w['tau0']], [w['tau1']]])
+
+
+def test_linsolve_underdetermined_AND_gauss_jordan_solve():
+    #Test placement of free variables as per issue 19815
+    A = Matrix([[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
+                [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
+                [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
+                [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0],
+                [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
+                [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0],
+                [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]])
+    B  = Matrix([1, 2, 1, 1, 1, 1, 1, 2])
+    sol, params = A.gauss_jordan_solve(B)
+    w = {}
+    for s in sol.atoms(Symbol):
+        w[s.name] = s
+    assert params == Matrix([[w['tau0']], [w['tau1']], [w['tau2']],
+                             [w['tau3']], [w['tau4']], [w['tau5']]])
+    assert sol == Matrix([[1 - 1*w['tau2']],
+                          [w['tau2']],
+                          [1 - 1*w['tau0'] + w['tau1']],
+                          [w['tau0']],
+                          [w['tau3'] + w['tau4']],
+                          [-1*w['tau3'] - 1*w['tau4'] - 1*w['tau1']],
+                          [1 - 1*w['tau2']],
+                          [w['tau1']],
+                          [w['tau2']],
+                          [w['tau3']],
+                          [w['tau4']],
+                          [1 - 1*w['tau5']],
+                          [w['tau5']],
+                          [1]])
+
+    from sympy.abc import j,f
+    # https://github.com/sympy/sympy/issues/20046
+    A = Matrix([
+    [1,  1, 1,  1, 1,  1, 1,  1,  1],
+    [0, -1, 0, -1, 0, -1, 0, -1, -j],
+    [0,  0, 0,  0, 1,  1, 1,  1,  f]
+    ])
+
+    sol_1=Matrix(list(linsolve(A))[0])
+
+    tau0, tau1, tau2, tau3, tau4 = symbols('tau:5')
+
+    assert sol_1 == Matrix([[-f - j - tau0 + tau2 + tau4 + 1],
+                          [j - tau1 - tau2 - tau4],
+                          [tau0],
+                          [tau1],
+                          [f - tau2 - tau3 - tau4],
+                          [tau2],
+                          [tau3],
+                          [tau4]])
+
+    # https://github.com/sympy/sympy/issues/19815
+    sol_2 = A[:, : -1 ] * sol_1 - A[:, -1 ]
+    assert sol_2 == Matrix([[0], [0], [0]])
+
+
+@pytest.mark.parametrize("det_method", ["bird", "laplace"])
+@pytest.mark.parametrize("M, rhs", [
+    (Matrix([[2, 3, 5], [3, 6, 2], [8, 3, 6]]), Matrix(3, 1, [3, 7, 5])),
+    (Matrix([[2, 3, 5], [3, 6, 2], [8, 3, 6]]),
+     Matrix([[1, 2], [3, 4], [5, 6]])),
+    (Matrix(2, 2, symbols("a:4")), Matrix(2, 1, symbols("b:2"))),
+])
+def test_cramer_solve(det_method, M, rhs):
+    assert simplify(M.cramer_solve(rhs, det_method=det_method) - M.LUsolve(rhs)
+                    ) == Matrix.zeros(M.rows, rhs.cols)
+
+
+@pytest.mark.parametrize("det_method, error", [
+    ("bird", DMShapeError), (_det_laplace, NonSquareMatrixError)])
+def test_cramer_solve_errors(det_method, error):
+    # Non-square matrix
+    A = Matrix([[0, -1, 2], [5, 10, 7]])
+    b = Matrix([-2, 15])
+    raises(error, lambda: A.cramer_solve(b, det_method=det_method))
+
+
+def test_solve():
+    A = Matrix([[1,2], [2,4]])
+    b = Matrix([[3], [4]])
+    raises(ValueError, lambda: A.solve(b)) #no solution
+    b = Matrix([[ 4], [8]])
+    raises(ValueError, lambda: A.solve(b)) #infinite solution
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_sparse.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_sparse.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d257c8062f220cc06bc0dabdc7ac40ce9dc4adc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_sparse.py
@@ -0,0 +1,745 @@
+from sympy.core.numbers import (Float, I, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import Abs
+from sympy.polys.polytools import PurePoly
+from sympy.matrices import \
+    Matrix, MutableSparseMatrix, ImmutableSparseMatrix, SparseMatrix, eye, \
+    ones, zeros, ShapeError, NonSquareMatrixError
+from sympy.testing.pytest import raises
+
+
+def test_sparse_creation():
+    a = SparseMatrix(2, 2, {(0, 0): [[1, 2], [3, 4]]})
+    assert a == SparseMatrix([[1, 2], [3, 4]])
+    a = SparseMatrix(2, 2, {(0, 0): [[1, 2]]})
+    assert a == SparseMatrix([[1, 2], [0, 0]])
+    a = SparseMatrix(2, 2, {(0, 0): [1, 2]})
+    assert a == SparseMatrix([[1, 0], [2, 0]])
+
+
+def test_sparse_matrix():
+    def sparse_eye(n):
+        return SparseMatrix.eye(n)
+
+    def sparse_zeros(n):
+        return SparseMatrix.zeros(n)
+
+    # creation args
+    raises(TypeError, lambda: SparseMatrix(1, 2))
+
+    a = SparseMatrix((
+        (1, 0),
+        (0, 1)
+    ))
+    assert SparseMatrix(a) == a
+
+    from sympy.matrices import MutableDenseMatrix
+    a = MutableSparseMatrix([])
+    b = MutableDenseMatrix([1, 2])
+    assert a.row_join(b) == b
+    assert a.col_join(b) == b
+    assert type(a.row_join(b)) == type(a)
+    assert type(a.col_join(b)) == type(a)
+
+    # make sure 0 x n matrices get stacked correctly
+    sparse_matrices = [SparseMatrix.zeros(0, n) for n in range(4)]
+    assert SparseMatrix.hstack(*sparse_matrices) == Matrix(0, 6, [])
+    sparse_matrices = [SparseMatrix.zeros(n, 0) for n in range(4)]
+    assert SparseMatrix.vstack(*sparse_matrices) == Matrix(6, 0, [])
+
+    # test element assignment
+    a = SparseMatrix((
+        (1, 0),
+        (0, 1)
+    ))
+
+    a[3] = 4
+    assert a[1, 1] == 4
+    a[3] = 1
+
+    a[0, 0] = 2
+    assert a == SparseMatrix((
+        (2, 0),
+        (0, 1)
+    ))
+    a[1, 0] = 5
+    assert a == SparseMatrix((
+        (2, 0),
+        (5, 1)
+    ))
+    a[1, 1] = 0
+    assert a == SparseMatrix((
+        (2, 0),
+        (5, 0)
+    ))
+    assert a.todok() == {(0, 0): 2, (1, 0): 5}
+
+    # test_multiplication
+    a = SparseMatrix((
+        (1, 2),
+        (3, 1),
+        (0, 6),
+    ))
+
+    b = SparseMatrix((
+        (1, 2),
+        (3, 0),
+    ))
+
+    c = a*b
+    assert c[0, 0] == 7
+    assert c[0, 1] == 2
+    assert c[1, 0] == 6
+    assert c[1, 1] == 6
+    assert c[2, 0] == 18
+    assert c[2, 1] == 0
+
+    try:
+        eval('c = a @ b')
+    except SyntaxError:
+        pass
+    else:
+        assert c[0, 0] == 7
+        assert c[0, 1] == 2
+        assert c[1, 0] == 6
+        assert c[1, 1] == 6
+        assert c[2, 0] == 18
+        assert c[2, 1] == 0
+
+    x = Symbol("x")
+
+    c = b * Symbol("x")
+    assert isinstance(c, SparseMatrix)
+    assert c[0, 0] == x
+    assert c[0, 1] == 2*x
+    assert c[1, 0] == 3*x
+    assert c[1, 1] == 0
+
+    c = 5 * b
+    assert isinstance(c, SparseMatrix)
+    assert c[0, 0] == 5
+    assert c[0, 1] == 2*5
+    assert c[1, 0] == 3*5
+    assert c[1, 1] == 0
+
+    #test_power
+    A = SparseMatrix([[2, 3], [4, 5]])
+    assert (A**5)[:] == [6140, 8097, 10796, 14237]
+    A = SparseMatrix([[2, 1, 3], [4, 2, 4], [6, 12, 1]])
+    assert (A**3)[:] == [290, 262, 251, 448, 440, 368, 702, 954, 433]
+
+    # test_creation
+    x = Symbol("x")
+    a = SparseMatrix([[x, 0], [0, 0]])
+    m = a
+    assert m.cols == m.rows
+    assert m.cols == 2
+    assert m[:] == [x, 0, 0, 0]
+    b = SparseMatrix(2, 2, [x, 0, 0, 0])
+    m = b
+    assert m.cols == m.rows
+    assert m.cols == 2
+    assert m[:] == [x, 0, 0, 0]
+
+    assert a == b
+    S = sparse_eye(3)
+    S.row_del(1)
+    assert S == SparseMatrix([
+                             [1, 0, 0],
+    [0, 0, 1]])
+    S = sparse_eye(3)
+    S.col_del(1)
+    assert S == SparseMatrix([
+                             [1, 0],
+    [0, 0],
+    [0, 1]])
+    S = SparseMatrix.eye(3)
+    S[2, 1] = 2
+    S.col_swap(1, 0)
+    assert S == SparseMatrix([
+        [0, 1, 0],
+        [1, 0, 0],
+        [2, 0, 1]])
+    S.row_swap(0, 1)
+    assert S == SparseMatrix([
+        [1, 0, 0],
+        [0, 1, 0],
+        [2, 0, 1]])
+
+    a = SparseMatrix(1, 2, [1, 2])
+    b = a.copy()
+    c = a.copy()
+    assert a[0] == 1
+    a.row_del(0)
+    assert a == SparseMatrix(0, 2, [])
+    b.col_del(1)
+    assert b == SparseMatrix(1, 1, [1])
+
+    assert SparseMatrix([[1, 2, 3], [1, 2], [1]]) == Matrix([
+        [1, 2, 3],
+        [1, 2, 0],
+        [1, 0, 0]])
+    assert SparseMatrix(4, 4, {(1, 1): sparse_eye(2)}) == Matrix([
+        [0, 0, 0, 0],
+        [0, 1, 0, 0],
+        [0, 0, 1, 0],
+        [0, 0, 0, 0]])
+    raises(ValueError, lambda: SparseMatrix(1, 1, {(1, 1): 1}))
+    assert SparseMatrix(1, 2, [1, 2]).tolist() == [[1, 2]]
+    assert SparseMatrix(2, 2, [1, [2, 3]]).tolist() == [[1, 0], [2, 3]]
+    raises(ValueError, lambda: SparseMatrix(2, 2, [1]))
+    raises(ValueError, lambda: SparseMatrix(1, 1, [[1, 2]]))
+    assert SparseMatrix([.1]).has(Float)
+    # autosizing
+    assert SparseMatrix(None, {(0, 1): 0}).shape == (0, 0)
+    assert SparseMatrix(None, {(0, 1): 1}).shape == (1, 2)
+    assert SparseMatrix(None, None, {(0, 1): 1}).shape == (1, 2)
+    raises(ValueError, lambda: SparseMatrix(None, 1, [[1, 2]]))
+    raises(ValueError, lambda: SparseMatrix(1, None, [[1, 2]]))
+    raises(ValueError, lambda: SparseMatrix(3, 3, {(0, 0): ones(2), (1, 1): 2}))
+
+    # test_determinant
+    x, y = Symbol('x'), Symbol('y')
+
+    assert SparseMatrix(1, 1, [0]).det() == 0
+
+    assert SparseMatrix([[1]]).det() == 1
+
+    assert SparseMatrix(((-3, 2), (8, -5))).det() == -1
+
+    assert SparseMatrix(((x, 1), (y, 2*y))).det() == 2*x*y - y
+
+    assert SparseMatrix(( (1, 1, 1),
+                          (1, 2, 3),
+                          (1, 3, 6) )).det() == 1
+
+    assert SparseMatrix(( ( 3, -2,  0, 5),
+                          (-2,  1, -2, 2),
+                          ( 0, -2,  5, 0),
+                          ( 5,  0,  3, 4) )).det() == -289
+
+    assert SparseMatrix(( ( 1,  2,  3,  4),
+                          ( 5,  6,  7,  8),
+                          ( 9, 10, 11, 12),
+                          (13, 14, 15, 16) )).det() == 0
+
+    assert SparseMatrix(( (3, 2, 0, 0, 0),
+                          (0, 3, 2, 0, 0),
+                          (0, 0, 3, 2, 0),
+                          (0, 0, 0, 3, 2),
+                          (2, 0, 0, 0, 3) )).det() == 275
+
+    assert SparseMatrix(( (1, 0,  1,  2, 12),
+                          (2, 0,  1,  1,  4),
+                          (2, 1,  1, -1,  3),
+                          (3, 2, -1,  1,  8),
+                          (1, 1,  1,  0,  6) )).det() == -55
+
+    assert SparseMatrix(( (-5,  2,  3,  4,  5),
+                          ( 1, -4,  3,  4,  5),
+                          ( 1,  2, -3,  4,  5),
+                          ( 1,  2,  3, -2,  5),
+                          ( 1,  2,  3,  4, -1) )).det() == 11664
+
+    assert SparseMatrix(( ( 3,  0,  0, 0),
+                          (-2,  1,  0, 0),
+                          ( 0, -2,  5, 0),
+                          ( 5,  0,  3, 4) )).det() == 60
+
+    assert SparseMatrix(( ( 1,  0,  0,  0),
+                          ( 5,  0,  0,  0),
+                          ( 9, 10, 11, 0),
+                          (13, 14, 15, 16) )).det() == 0
+
+    assert SparseMatrix(( (3, 2, 0, 0, 0),
+                          (0, 3, 2, 0, 0),
+                          (0, 0, 3, 2, 0),
+                          (0, 0, 0, 3, 2),
+                          (0, 0, 0, 0, 3) )).det() == 243
+
+    assert SparseMatrix(( ( 2,  7, -1, 3, 2),
+                          ( 0,  0,  1, 0, 1),
+                          (-2,  0,  7, 0, 2),
+                          (-3, -2,  4, 5, 3),
+                          ( 1,  0,  0, 0, 1) )).det() == 123
+
+    # test_slicing
+    m0 = sparse_eye(4)
+    assert m0[:3, :3] == sparse_eye(3)
+    assert m0[2:4, 0:2] == sparse_zeros(2)
+
+    m1 = SparseMatrix(3, 3, lambda i, j: i + j)
+    assert m1[0, :] == SparseMatrix(1, 3, (0, 1, 2))
+    assert m1[1:3, 1] == SparseMatrix(2, 1, (2, 3))
+
+    m2 = SparseMatrix(
+        [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]])
+    assert m2[:, -1] == SparseMatrix(4, 1, [3, 7, 11, 15])
+    assert m2[-2:, :] == SparseMatrix([[8, 9, 10, 11], [12, 13, 14, 15]])
+
+    assert SparseMatrix([[1, 2], [3, 4]])[[1], [1]] == Matrix([[4]])
+
+    # test_submatrix_assignment
+    m = sparse_zeros(4)
+    m[2:4, 2:4] = sparse_eye(2)
+    assert m == SparseMatrix([(0, 0, 0, 0),
+                              (0, 0, 0, 0),
+                              (0, 0, 1, 0),
+                              (0, 0, 0, 1)])
+    assert len(m.todok()) == 2
+    m[:2, :2] = sparse_eye(2)
+    assert m == sparse_eye(4)
+    m[:, 0] = SparseMatrix(4, 1, (1, 2, 3, 4))
+    assert m == SparseMatrix([(1, 0, 0, 0),
+                              (2, 1, 0, 0),
+                              (3, 0, 1, 0),
+                              (4, 0, 0, 1)])
+    m[:, :] = sparse_zeros(4)
+    assert m == sparse_zeros(4)
+    m[:, :] = ((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16))
+    assert m == SparseMatrix((( 1,  2,  3,  4),
+                              ( 5,  6,  7,  8),
+                              ( 9, 10, 11, 12),
+                              (13, 14, 15, 16)))
+    m[:2, 0] = [0, 0]
+    assert m == SparseMatrix((( 0,  2,  3,  4),
+                              ( 0,  6,  7,  8),
+                              ( 9, 10, 11, 12),
+                              (13, 14, 15, 16)))
+
+    # test_reshape
+    m0 = sparse_eye(3)
+    assert m0.reshape(1, 9) == SparseMatrix(1, 9, (1, 0, 0, 0, 1, 0, 0, 0, 1))
+    m1 = SparseMatrix(3, 4, lambda i, j: i + j)
+    assert m1.reshape(4, 3) == \
+        SparseMatrix([(0, 1, 2), (3, 1, 2), (3, 4, 2), (3, 4, 5)])
+    assert m1.reshape(2, 6) == \
+        SparseMatrix([(0, 1, 2, 3, 1, 2), (3, 4, 2, 3, 4, 5)])
+
+    # test_applyfunc
+    m0 = sparse_eye(3)
+    assert m0.applyfunc(lambda x: 2*x) == sparse_eye(3)*2
+    assert m0.applyfunc(lambda x: 0 ) == sparse_zeros(3)
+
+    # test__eval_Abs
+    assert abs(SparseMatrix(((x, 1), (y, 2*y)))) == SparseMatrix(((Abs(x), 1), (Abs(y), 2*Abs(y))))
+
+    # test_LUdecomp
+    testmat = SparseMatrix([[ 0, 2, 5, 3],
+                            [ 3, 3, 7, 4],
+                            [ 8, 4, 0, 2],
+                            [-2, 6, 3, 4]])
+    L, U, p = testmat.LUdecomposition()
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - testmat == sparse_zeros(4)
+
+    testmat = SparseMatrix([[ 6, -2, 7, 4],
+                            [ 0,  3, 6, 7],
+                            [ 1, -2, 7, 4],
+                            [-9,  2, 6, 3]])
+    L, U, p = testmat.LUdecomposition()
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - testmat == sparse_zeros(4)
+
+    x, y, z = Symbol('x'), Symbol('y'), Symbol('z')
+    M = Matrix(((1, x, 1), (2, y, 0), (y, 0, z)))
+    L, U, p = M.LUdecomposition()
+    assert L.is_lower
+    assert U.is_upper
+    assert (L*U).permute_rows(p, 'backward') - M == sparse_zeros(3)
+
+    # test_LUsolve
+    A = SparseMatrix([[2, 3, 5],
+                      [3, 6, 2],
+                      [8, 3, 6]])
+    x = SparseMatrix(3, 1, [3, 7, 5])
+    b = A*x
+    soln = A.LUsolve(b)
+    assert soln == x
+    A = SparseMatrix([[0, -1, 2],
+                      [5, 10, 7],
+                      [8,  3, 4]])
+    x = SparseMatrix(3, 1, [-1, 2, 5])
+    b = A*x
+    soln = A.LUsolve(b)
+    assert soln == x
+
+    # test_inverse
+    A = sparse_eye(4)
+    assert A.inv() == sparse_eye(4)
+    assert A.inv(method="CH") == sparse_eye(4)
+    assert A.inv(method="LDL") == sparse_eye(4)
+
+    A = SparseMatrix([[2, 3, 5],
+                      [3, 6, 2],
+                      [7, 2, 6]])
+    Ainv = SparseMatrix(Matrix(A).inv())
+    assert A*Ainv == sparse_eye(3)
+    assert A.inv(method="CH") == Ainv
+    assert A.inv(method="LDL") == Ainv
+
+    A = SparseMatrix([[2, 3, 5],
+                      [3, 6, 2],
+                      [5, 2, 6]])
+    Ainv = SparseMatrix(Matrix(A).inv())
+    assert A*Ainv == sparse_eye(3)
+    assert A.inv(method="CH") == Ainv
+    assert A.inv(method="LDL") == Ainv
+
+    # test_cross
+    v1 = Matrix(1, 3, [1, 2, 3])
+    v2 = Matrix(1, 3, [3, 4, 5])
+    assert v1.cross(v2) == Matrix(1, 3, [-2, 4, -2])
+    assert v1.norm(2)**2 == 14
+
+    # conjugate
+    a = SparseMatrix(((1, 2 + I), (3, 4)))
+    assert a.C == SparseMatrix([
+        [1, 2 - I],
+        [3,     4]
+    ])
+
+    # mul
+    assert a*Matrix(2, 2, [1, 0, 0, 1]) == a
+    assert a + Matrix(2, 2, [1, 1, 1, 1]) == SparseMatrix([
+        [2, 3 + I],
+        [4,     5]
+    ])
+
+    # col join
+    assert a.col_join(sparse_eye(2)) == SparseMatrix([
+        [1, 2 + I],
+        [3,     4],
+        [1,     0],
+        [0,     1]
+    ])
+
+    # row insert
+    assert a.row_insert(2, sparse_eye(2)) == SparseMatrix([
+        [1, 2 + I],
+        [3,     4],
+        [1,     0],
+        [0,     1]
+    ])
+
+    # col insert
+    assert a.col_insert(2, SparseMatrix.zeros(2, 1)) == SparseMatrix([
+        [1, 2 + I, 0],
+        [3,     4, 0],
+    ])
+
+    # symmetric
+    assert not a.is_symmetric(simplify=False)
+
+    # col op
+    M = SparseMatrix.eye(3)*2
+    M[1, 0] = -1
+    M.col_op(1, lambda v, i: v + 2*M[i, 0])
+    assert M == SparseMatrix([
+        [ 2, 4, 0],
+        [-1, 0, 0],
+        [ 0, 0, 2]
+    ])
+
+    # fill
+    M = SparseMatrix.eye(3)
+    M.fill(2)
+    assert M == SparseMatrix([
+        [2, 2, 2],
+        [2, 2, 2],
+        [2, 2, 2],
+    ])
+
+    # test_cofactor
+    assert sparse_eye(3) == sparse_eye(3).cofactor_matrix()
+    test = SparseMatrix([[1, 3, 2], [2, 6, 3], [2, 3, 6]])
+    assert test.cofactor_matrix() == \
+        SparseMatrix([[27, -6, -6], [-12, 2, 3], [-3, 1, 0]])
+    test = SparseMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert test.cofactor_matrix() == \
+        SparseMatrix([[-3, 6, -3], [6, -12, 6], [-3, 6, -3]])
+
+    # test_jacobian
+    x = Symbol('x')
+    y = Symbol('y')
+    L = SparseMatrix(1, 2, [x**2*y, 2*y**2 + x*y])
+    syms = [x, y]
+    assert L.jacobian(syms) == Matrix([[2*x*y, x**2], [y, 4*y + x]])
+
+    L = SparseMatrix(1, 2, [x, x**2*y**3])
+    assert L.jacobian(syms) == SparseMatrix([[1, 0], [2*x*y**3, x**2*3*y**2]])
+
+    # test_QR
+    A = Matrix([[1, 2], [2, 3]])
+    Q, S = A.QRdecomposition()
+    R = Rational
+    assert Q == Matrix([
+        [  5**R(-1, 2),  (R(2)/5)*(R(1)/5)**R(-1, 2)],
+        [2*5**R(-1, 2), (-R(1)/5)*(R(1)/5)**R(-1, 2)]])
+    assert S == Matrix([
+        [5**R(1, 2),     8*5**R(-1, 2)],
+        [         0, (R(1)/5)**R(1, 2)]])
+    assert Q*S == A
+    assert Q.T * Q == sparse_eye(2)
+
+    R = Rational
+    # test nullspace
+    # first test reduced row-ech form
+
+    M = SparseMatrix([[5, 7, 2, 1],
+               [1, 6, 2, -1]])
+    out, tmp = M.rref()
+    assert out == Matrix([[1, 0, -R(2)/23, R(13)/23],
+                          [0, 1,  R(8)/23, R(-6)/23]])
+
+    M = SparseMatrix([[ 1,  3, 0,  2,  6, 3, 1],
+                      [-2, -6, 0, -2, -8, 3, 1],
+                      [ 3,  9, 0,  0,  6, 6, 2],
+                      [-1, -3, 0,  1,  0, 9, 3]])
+
+    out, tmp = M.rref()
+    assert out == Matrix([[1, 3, 0, 0, 2, 0, 0],
+                          [0, 0, 0, 1, 2, 0, 0],
+                          [0, 0, 0, 0, 0, 1, R(1)/3],
+                          [0, 0, 0, 0, 0, 0, 0]])
+    # now check the vectors
+    basis = M.nullspace()
+    assert basis[0] == Matrix([-3, 1, 0, 0, 0, 0, 0])
+    assert basis[1] == Matrix([0, 0, 1, 0, 0, 0, 0])
+    assert basis[2] == Matrix([-2, 0, 0, -2, 1, 0, 0])
+    assert basis[3] == Matrix([0, 0, 0, 0, 0, R(-1)/3, 1])
+
+    # test eigen
+    x = Symbol('x')
+    y = Symbol('y')
+    sparse_eye3 = sparse_eye(3)
+    assert sparse_eye3.charpoly(x) == PurePoly((x - 1)**3)
+    assert sparse_eye3.charpoly(y) == PurePoly((y - 1)**3)
+
+    # test values
+    M = Matrix([( 0, 1, -1),
+                ( 1, 1,  0),
+                (-1, 0,  1)])
+    vals = M.eigenvals()
+    assert sorted(vals.keys()) == [-1, 1, 2]
+
+    R = Rational
+    M = Matrix([[1, 0, 0],
+                [0, 1, 0],
+                [0, 0, 1]])
+    assert M.eigenvects() == [(1, 3, [
+        Matrix([1, 0, 0]),
+        Matrix([0, 1, 0]),
+        Matrix([0, 0, 1])])]
+    M = Matrix([[5, 0, 2],
+                [3, 2, 0],
+                [0, 0, 1]])
+    assert M.eigenvects() == [(1, 1, [Matrix([R(-1)/2, R(3)/2, 1])]),
+                              (2, 1, [Matrix([0, 1, 0])]),
+                              (5, 1, [Matrix([1, 1, 0])])]
+
+    assert M.zeros(3, 5) == SparseMatrix(3, 5, {})
+    A =  SparseMatrix(10, 10, {(0, 0): 18, (0, 9): 12, (1, 4): 18, (2, 7): 16, (3, 9): 12, (4, 2): 19, (5, 7): 16, (6, 2): 12, (9, 7): 18})
+    assert A.row_list() == [(0, 0, 18), (0, 9, 12), (1, 4, 18), (2, 7, 16), (3, 9, 12), (4, 2, 19), (5, 7, 16), (6, 2, 12), (9, 7, 18)]
+    assert A.col_list() == [(0, 0, 18), (4, 2, 19), (6, 2, 12), (1, 4, 18), (2, 7, 16), (5, 7, 16), (9, 7, 18), (0, 9, 12), (3, 9, 12)]
+    assert SparseMatrix.eye(2).nnz() == 2
+
+
+def test_scalar_multiply():
+    assert SparseMatrix([[1, 2]]).scalar_multiply(3) == SparseMatrix([[3, 6]])
+
+
+def test_transpose():
+    assert SparseMatrix(((1, 2), (3, 4))).transpose() == \
+        SparseMatrix(((1, 3), (2, 4)))
+
+
+def test_trace():
+    assert SparseMatrix(((1, 2), (3, 4))).trace() == 5
+    assert SparseMatrix(((0, 0), (0, 4))).trace() == 4
+
+
+def test_CL_RL():
+    assert SparseMatrix(((1, 2), (3, 4))).row_list() == \
+        [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)]
+    assert SparseMatrix(((1, 2), (3, 4))).col_list() == \
+        [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)]
+
+
+def test_add():
+    assert SparseMatrix(((1, 0), (0, 1))) + SparseMatrix(((0, 1), (1, 0))) == \
+        SparseMatrix(((1, 1), (1, 1)))
+    a = SparseMatrix(100, 100, lambda i, j: int(j != 0 and i % j == 0))
+    b = SparseMatrix(100, 100, lambda i, j: int(i != 0 and j % i == 0))
+    assert (len(a.todok()) + len(b.todok()) - len((a + b).todok()) > 0)
+
+
+def test_errors():
+    raises(ValueError, lambda: SparseMatrix(1.4, 2, lambda i, j: 0))
+    raises(TypeError, lambda: SparseMatrix([1, 2, 3], [1, 2]))
+    raises(ValueError, lambda: SparseMatrix([[1, 2], [3, 4]])[(1, 2, 3)])
+    raises(IndexError, lambda: SparseMatrix([[1, 2], [3, 4]])[5])
+    raises(ValueError, lambda: SparseMatrix([[1, 2], [3, 4]])[1, 2, 3])
+    raises(TypeError,
+        lambda: SparseMatrix([[1, 2], [3, 4]]).copyin_list([0, 1], set()))
+    raises(
+        IndexError, lambda: SparseMatrix([[1, 2], [3, 4]])[1, 2])
+    raises(TypeError, lambda: SparseMatrix([1, 2, 3]).cross(1))
+    raises(IndexError, lambda: SparseMatrix(1, 2, [1, 2])[3])
+    raises(ShapeError,
+        lambda: SparseMatrix(1, 2, [1, 2]) + SparseMatrix(2, 1, [2, 1]))
+
+
+def test_len():
+    assert not SparseMatrix()
+    assert SparseMatrix() == SparseMatrix([])
+    assert SparseMatrix() == SparseMatrix([[]])
+
+
+def test_sparse_zeros_sparse_eye():
+    assert SparseMatrix.eye(3) == eye(3, cls=SparseMatrix)
+    assert len(SparseMatrix.eye(3).todok()) == 3
+    assert SparseMatrix.zeros(3) == zeros(3, cls=SparseMatrix)
+    assert len(SparseMatrix.zeros(3).todok()) == 0
+
+
+def test_copyin():
+    s = SparseMatrix(3, 3, {})
+    s[1, 0] = 1
+    assert s[:, 0] == SparseMatrix(Matrix([0, 1, 0]))
+    assert s[3] == 1
+    assert s[3: 4] == [1]
+    s[1, 1] = 42
+    assert s[1, 1] == 42
+    assert s[1, 1:] == SparseMatrix([[42, 0]])
+    s[1, 1:] = Matrix([[5, 6]])
+    assert s[1, :] == SparseMatrix([[1, 5, 6]])
+    s[1, 1:] = [[42, 43]]
+    assert s[1, :] == SparseMatrix([[1, 42, 43]])
+    s[0, 0] = 17
+    assert s[:, :1] == SparseMatrix([17, 1, 0])
+    s[0, 0] = [1, 1, 1]
+    assert s[:, 0] == SparseMatrix([1, 1, 1])
+    s[0, 0] = Matrix([1, 1, 1])
+    assert s[:, 0] == SparseMatrix([1, 1, 1])
+    s[0, 0] = SparseMatrix([1, 1, 1])
+    assert s[:, 0] == SparseMatrix([1, 1, 1])
+
+
+def test_sparse_solve():
+    A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    assert A.cholesky() == Matrix([
+        [ 5, 0, 0],
+        [ 3, 3, 0],
+        [-1, 1, 3]])
+    assert A.cholesky() * A.cholesky().T == Matrix([
+        [25, 15, -5],
+        [15, 18, 0],
+        [-5, 0, 11]])
+
+    A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
+    L, D = A.LDLdecomposition()
+    assert 15*L == Matrix([
+        [15, 0, 0],
+        [ 9, 15, 0],
+        [-3, 5, 15]])
+    assert D == Matrix([
+        [25, 0, 0],
+        [ 0, 9, 0],
+        [ 0, 0, 9]])
+    assert L * D * L.T == A
+
+    A = SparseMatrix(((3, 0, 2), (0, 0, 1), (1, 2, 0)))
+    assert A.inv() * A == SparseMatrix(eye(3))
+
+    A = SparseMatrix([
+        [ 2, -1, 0],
+        [-1, 2, -1],
+        [ 0, 0, 2]])
+    ans = SparseMatrix([
+        [Rational(2, 3), Rational(1, 3), Rational(1, 6)],
+        [Rational(1, 3), Rational(2, 3), Rational(1, 3)],
+        [             0,              0,        S.Half]])
+    assert A.inv(method='CH') == ans
+    assert A.inv(method='LDL') == ans
+    assert A * ans == SparseMatrix(eye(3))
+
+    s = A.solve(A[:, 0], 'LDL')
+    assert A*s == A[:, 0]
+    s = A.solve(A[:, 0], 'CH')
+    assert A*s == A[:, 0]
+    A = A.col_join(A)
+    s = A.solve_least_squares(A[:, 0], 'CH')
+    assert A*s == A[:, 0]
+    s = A.solve_least_squares(A[:, 0], 'LDL')
+    assert A*s == A[:, 0]
+
+
+def test_lower_triangular_solve():
+    raises(NonSquareMatrixError, lambda:
+        SparseMatrix([[1, 2]]).lower_triangular_solve(Matrix([[1, 2]])))
+    raises(ShapeError, lambda:
+        SparseMatrix([[1, 2], [0, 4]]).lower_triangular_solve(Matrix([1])))
+    raises(ValueError, lambda:
+        SparseMatrix([[1, 2], [3, 4]]).lower_triangular_solve(Matrix([[1, 2], [3, 4]])))
+
+    a, b, c, d = symbols('a:d')
+    u, v, w, x = symbols('u:x')
+
+    A = SparseMatrix([[a, 0], [c, d]])
+    B = MutableSparseMatrix([[u, v], [w, x]])
+    C = ImmutableSparseMatrix([[u, v], [w, x]])
+
+    sol = Matrix([[u/a, v/a], [(w - c*u/a)/d, (x - c*v/a)/d]])
+    assert A.lower_triangular_solve(B) == sol
+    assert A.lower_triangular_solve(C) == sol
+
+
+def test_upper_triangular_solve():
+    raises(NonSquareMatrixError, lambda:
+        SparseMatrix([[1, 2]]).upper_triangular_solve(Matrix([[1, 2]])))
+    raises(ShapeError, lambda:
+        SparseMatrix([[1, 2], [0, 4]]).upper_triangular_solve(Matrix([1])))
+    raises(TypeError, lambda:
+        SparseMatrix([[1, 2], [3, 4]]).upper_triangular_solve(Matrix([[1, 2], [3, 4]])))
+
+    a, b, c, d = symbols('a:d')
+    u, v, w, x = symbols('u:x')
+
+    A = SparseMatrix([[a, b], [0, d]])
+    B = MutableSparseMatrix([[u, v], [w, x]])
+    C = ImmutableSparseMatrix([[u, v], [w, x]])
+
+    sol = Matrix([[(u - b*w/d)/a, (v - b*x/d)/a], [w/d, x/d]])
+    assert A.upper_triangular_solve(B) == sol
+    assert A.upper_triangular_solve(C) == sol
+
+
+def test_diagonal_solve():
+    a, d = symbols('a d')
+    u, v, w, x = symbols('u:x')
+
+    A = SparseMatrix([[a, 0], [0, d]])
+    B = MutableSparseMatrix([[u, v], [w, x]])
+    C = ImmutableSparseMatrix([[u, v], [w, x]])
+
+    sol = Matrix([[u/a, v/a], [w/d, x/d]])
+    assert A.diagonal_solve(B) == sol
+    assert A.diagonal_solve(C) == sol
+
+
+def test_hermitian():
+    x = Symbol('x')
+    a = SparseMatrix([[0, I], [-I, 0]])
+    assert a.is_hermitian
+    a = SparseMatrix([[1, I], [-I, 1]])
+    assert a.is_hermitian
+    a[0, 0] = 2*I
+    assert a.is_hermitian is False
+    a[0, 0] = x
+    assert a.is_hermitian is None
+    a[0, 1] = a[1, 0]*I
+    assert a.is_hermitian is False
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_sparsetools.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_sparsetools.py
new file mode 100644
index 0000000000000000000000000000000000000000..244944c31da06460d4bc7beff8bce0f91fea9f14
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_sparsetools.py
@@ -0,0 +1,132 @@
+from sympy.matrices.sparsetools import _doktocsr, _csrtodok, banded
+from sympy.matrices.dense import (Matrix, eye, ones, zeros)
+from sympy.matrices import SparseMatrix
+from sympy.testing.pytest import raises
+
+
+def test_doktocsr():
+    a = SparseMatrix([[1, 2, 0, 0], [0, 3, 9, 0], [0, 1, 4, 0]])
+    b = SparseMatrix(4, 6, [10, 20, 0, 0, 0, 0, 0, 30, 0, 40, 0, 0, 0, 0, 50,
+        60, 70, 0, 0, 0, 0, 0, 0, 80])
+    c = SparseMatrix(4, 4, [0, 0, 0, 0, 0, 12, 0, 2, 15, 0, 12, 0, 0, 0, 0, 4])
+    d = SparseMatrix(10, 10, {(1, 1): 12, (3, 5): 7, (7, 8): 12})
+    e = SparseMatrix([[0, 0, 0], [1, 0, 2], [3, 0, 0]])
+    f = SparseMatrix(7, 8, {(2, 3): 5, (4, 5):12})
+    assert _doktocsr(a) == [[1, 2, 3, 9, 1, 4], [0, 1, 1, 2, 1, 2],
+        [0, 2, 4, 6], [3, 4]]
+    assert _doktocsr(b) == [[10, 20, 30, 40, 50, 60, 70, 80],
+        [0, 1, 1, 3, 2, 3, 4, 5], [0, 2, 4, 7, 8], [4, 6]]
+    assert _doktocsr(c) == [[12, 2, 15, 12, 4], [1, 3, 0, 2, 3],
+        [0, 0, 2, 4, 5], [4, 4]]
+    assert _doktocsr(d) == [[12, 7, 12], [1, 5, 8],
+        [0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3], [10, 10]]
+    assert _doktocsr(e) == [[1, 2, 3], [0, 2, 0], [0, 0, 2, 3], [3, 3]]
+    assert _doktocsr(f) == [[5, 12], [3, 5], [0, 0, 0, 1, 1, 2, 2, 2], [7, 8]]
+
+
+def test_csrtodok():
+    h = [[5, 7, 5], [2, 1, 3], [0, 1, 1, 3], [3, 4]]
+    g = [[12, 5, 4], [2, 4, 2], [0, 1, 2, 3], [3, 7]]
+    i = [[1, 3, 12], [0, 2, 4], [0, 2, 3], [2, 5]]
+    j = [[11, 15, 12, 15], [2, 4, 1, 2], [0, 1, 1, 2, 3, 4], [5, 8]]
+    k = [[1, 3], [2, 1], [0, 1, 1, 2], [3, 3]]
+    m = _csrtodok(h)
+    assert isinstance(m, SparseMatrix)
+    assert m == SparseMatrix(3, 4,
+        {(0, 2): 5, (2, 1): 7, (2, 3): 5})
+    assert _csrtodok(g) == SparseMatrix(3, 7,
+        {(0, 2): 12, (1, 4): 5, (2, 2): 4})
+    assert _csrtodok(i) == SparseMatrix([[1, 0, 3, 0, 0], [0, 0, 0, 0, 12]])
+    assert _csrtodok(j) == SparseMatrix(5, 8,
+        {(0, 2): 11, (2, 4): 15, (3, 1): 12, (4, 2): 15})
+    assert _csrtodok(k) == SparseMatrix(3, 3, {(0, 2): 1, (2, 1): 3})
+
+
+def test_banded():
+    raises(TypeError, lambda: banded())
+    raises(TypeError, lambda: banded(1))
+    raises(TypeError, lambda: banded(1, 2))
+    raises(TypeError, lambda: banded(1, 2, 3))
+    raises(TypeError, lambda: banded(1, 2, 3, 4))
+    raises(ValueError, lambda: banded({0: (1, 2)}, rows=1))
+    raises(ValueError, lambda: banded({0: (1, 2)}, cols=1))
+    raises(ValueError, lambda: banded(1, {0: (1, 2)}))
+    raises(ValueError, lambda: banded(2, 1, {0: (1, 2)}))
+    raises(ValueError, lambda: banded(1, 2, {0: (1, 2)}))
+
+    assert isinstance(banded(2, 4, {}), SparseMatrix)
+    assert banded(2, 4, {}) == zeros(2, 4)
+    assert banded({0: 0, 1: 0}) == zeros(0)
+    assert banded({0: Matrix([1, 2])}) == Matrix([1, 2])
+    assert banded({1: [1, 2, 3, 0], -1: [4, 5, 6]}) == \
+        banded({1: (1, 2, 3), -1: (4, 5, 6)}) == \
+        Matrix([
+        [0, 1, 0, 0],
+        [4, 0, 2, 0],
+        [0, 5, 0, 3],
+        [0, 0, 6, 0]])
+    assert banded(3, 4, {-1: 1, 0: 2, 1: 3}) == \
+        Matrix([
+        [2, 3, 0, 0],
+        [1, 2, 3, 0],
+        [0, 1, 2, 3]])
+    s = lambda d: (1 + d)**2
+    assert banded(5, {0: s, 2: s}) == \
+        Matrix([
+        [1, 0, 1,  0,  0],
+        [0, 4, 0,  4,  0],
+        [0, 0, 9,  0,  9],
+        [0, 0, 0, 16,  0],
+        [0, 0, 0,  0, 25]])
+    assert banded(2, {0: 1}) == \
+        Matrix([
+        [1, 0],
+        [0, 1]])
+    assert banded(2, 3, {0: 1}) == \
+        Matrix([
+        [1, 0, 0],
+        [0, 1, 0]])
+    vert = Matrix([1, 2, 3])
+    assert banded({0: vert}, cols=3) == \
+        Matrix([
+        [1, 0, 0],
+        [2, 1, 0],
+        [3, 2, 1],
+        [0, 3, 2],
+        [0, 0, 3]])
+    assert banded(4, {0: ones(2)}) == \
+        Matrix([
+        [1, 1, 0, 0],
+        [1, 1, 0, 0],
+        [0, 0, 1, 1],
+        [0, 0, 1, 1]])
+    raises(ValueError, lambda: banded({0: 2, 1: ones(2)}, rows=5))
+    assert banded({0: 2, 2: (ones(2),)*3}) == \
+        Matrix([
+        [2, 0, 1, 1, 0, 0, 0, 0],
+        [0, 2, 1, 1, 0, 0, 0, 0],
+        [0, 0, 2, 0, 1, 1, 0, 0],
+        [0, 0, 0, 2, 1, 1, 0, 0],
+        [0, 0, 0, 0, 2, 0, 1, 1],
+        [0, 0, 0, 0, 0, 2, 1, 1]])
+    raises(ValueError, lambda: banded({0: (2,)*5, 1: (ones(2),)*3}))
+    u2 = Matrix([[1, 1], [0, 1]])
+    assert banded({0: (2,)*5, 1: (u2,)*3}) == \
+        Matrix([
+        [2, 1, 1, 0, 0, 0, 0],
+        [0, 2, 1, 0, 0, 0, 0],
+        [0, 0, 2, 1, 1, 0, 0],
+        [0, 0, 0, 2, 1, 0, 0],
+        [0, 0, 0, 0, 2, 1, 1],
+        [0, 0, 0, 0, 0, 0, 1]])
+    assert banded({0:(0, ones(2)), 2: 2}) == \
+        Matrix([
+        [0, 0, 2],
+        [0, 1, 1],
+        [0, 1, 1]])
+    raises(ValueError, lambda: banded({0: (0, ones(2)), 1: 2}))
+    assert banded({0: 1}, cols=3) == banded({0: 1}, rows=3) == eye(3)
+    assert banded({1: 1}, rows=3) == Matrix([
+        [0, 1, 0],
+        [0, 0, 1],
+        [0, 0, 0]])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_subspaces.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_subspaces.py
new file mode 100644
index 0000000000000000000000000000000000000000..0bd853e321eb06f754c17e7bd0c11deb870506f5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/tests/test_subspaces.py
@@ -0,0 +1,109 @@
+from sympy.matrices import Matrix
+from sympy.core.numbers import Rational
+from sympy.core.symbol import symbols
+from sympy.solvers import solve
+
+
+def test_columnspace_one():
+    m = Matrix([[ 1,  2,  0,  2,  5],
+                [-2, -5,  1, -1, -8],
+                [ 0, -3,  3,  4,  1],
+                [ 3,  6,  0, -7,  2]])
+
+    basis = m.columnspace()
+    assert basis[0] == Matrix([1, -2, 0, 3])
+    assert basis[1] == Matrix([2, -5, -3, 6])
+    assert basis[2] == Matrix([2, -1, 4, -7])
+
+    assert len(basis) == 3
+    assert Matrix.hstack(m, *basis).columnspace() == basis
+
+
+def test_rowspace():
+    m = Matrix([[ 1,  2,  0,  2,  5],
+                [-2, -5,  1, -1, -8],
+                [ 0, -3,  3,  4,  1],
+                [ 3,  6,  0, -7,  2]])
+
+    basis = m.rowspace()
+    assert basis[0] == Matrix([[1, 2, 0, 2, 5]])
+    assert basis[1] == Matrix([[0, -1, 1, 3, 2]])
+    assert basis[2] == Matrix([[0, 0, 0, 5, 5]])
+
+    assert len(basis) == 3
+
+
+def test_nullspace_one():
+    m = Matrix([[ 1,  2,  0,  2,  5],
+                [-2, -5,  1, -1, -8],
+                [ 0, -3,  3,  4,  1],
+                [ 3,  6,  0, -7,  2]])
+
+    basis = m.nullspace()
+    assert basis[0] == Matrix([-2, 1, 1, 0, 0])
+    assert basis[1] == Matrix([-1, -1, 0, -1, 1])
+    # make sure the null space is really gets zeroed
+    assert all(e.is_zero for e in m*basis[0])
+    assert all(e.is_zero for e in m*basis[1])
+
+def test_nullspace_second():
+    # first test reduced row-ech form
+    R = Rational
+
+    M = Matrix([[5, 7, 2,  1],
+                [1, 6, 2, -1]])
+    out, tmp = M.rref()
+    assert out == Matrix([[1, 0, -R(2)/23, R(13)/23],
+                          [0, 1,  R(8)/23, R(-6)/23]])
+
+    M = Matrix([[-5, -1,  4, -3, -1],
+                [ 1, -1, -1,  1,  0],
+                [-1,  0,  0,  0,  0],
+                [ 4,  1, -4,  3,  1],
+                [-2,  0,  2, -2, -1]])
+    assert M*M.nullspace()[0] == Matrix(5, 1, [0]*5)
+
+    M = Matrix([[ 1,  3, 0,  2,  6, 3, 1],
+                [-2, -6, 0, -2, -8, 3, 1],
+                [ 3,  9, 0,  0,  6, 6, 2],
+                [-1, -3, 0,  1,  0, 9, 3]])
+    out, tmp = M.rref()
+    assert out == Matrix([[1, 3, 0, 0, 2, 0, 0],
+                          [0, 0, 0, 1, 2, 0, 0],
+                          [0, 0, 0, 0, 0, 1, R(1)/3],
+                          [0, 0, 0, 0, 0, 0, 0]])
+
+    # now check the vectors
+    basis = M.nullspace()
+    assert basis[0] == Matrix([-3, 1, 0, 0, 0, 0, 0])
+    assert basis[1] == Matrix([0, 0, 1, 0, 0, 0, 0])
+    assert basis[2] == Matrix([-2, 0, 0, -2, 1, 0, 0])
+    assert basis[3] == Matrix([0, 0, 0, 0, 0, R(-1)/3, 1])
+
+    # issue 4797; just see that we can do it when rows > cols
+    M = Matrix([[1, 2], [2, 4], [3, 6]])
+    assert M.nullspace()
+
+
+def test_columnspace_second():
+    M = Matrix([[ 1,  2,  0,  2,  5],
+                [-2, -5,  1, -1, -8],
+                [ 0, -3,  3,  4,  1],
+                [ 3,  6,  0, -7,  2]])
+
+    # now check the vectors
+    basis = M.columnspace()
+    assert basis[0] == Matrix([1, -2, 0, 3])
+    assert basis[1] == Matrix([2, -5, -3, 6])
+    assert basis[2] == Matrix([2, -1, 4, -7])
+
+    #check by columnspace definition
+    a, b, c, d, e = symbols('a b c d e')
+    X = Matrix([a, b, c, d, e])
+    for i in range(len(basis)):
+        eq=M*X-basis[i]
+        assert len(solve(eq, X)) != 0
+
+    #check if rank-nullity theorem holds
+    assert M.rank() == len(basis)
+    assert len(M.nullspace()) + len(M.columnspace()) == M.cols
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/utilities.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/utilities.py
new file mode 100644
index 0000000000000000000000000000000000000000..b8a680b47e63615e210e561639a192ba47c642d3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/matrices/utilities.py
@@ -0,0 +1,72 @@
+from contextlib import contextmanager
+from threading import local
+
+from sympy.core.function import expand_mul
+
+
+class DotProdSimpState(local):
+    def __init__(self):
+        self.state = None
+
+_dotprodsimp_state = DotProdSimpState()
+
+@contextmanager
+def dotprodsimp(x):
+    old = _dotprodsimp_state.state
+
+    try:
+        _dotprodsimp_state.state = x
+        yield
+    finally:
+        _dotprodsimp_state.state = old
+
+
+def _dotprodsimp(expr, withsimp=False):
+    """Wrapper for simplify.dotprodsimp to avoid circular imports."""
+    from sympy.simplify.simplify import dotprodsimp as dps
+    return dps(expr, withsimp=withsimp)
+
+
+def _get_intermediate_simp(deffunc=lambda x: x, offfunc=lambda x: x,
+        onfunc=_dotprodsimp, dotprodsimp=None):
+    """Support function for controlling intermediate simplification. Returns a
+    simplification function according to the global setting of dotprodsimp
+    operation.
+
+    ``deffunc``     - Function to be used by default.
+    ``offfunc``     - Function to be used if dotprodsimp has been turned off.
+    ``onfunc``      - Function to be used if dotprodsimp has been turned on.
+    ``dotprodsimp`` - True, False or None. Will be overridden by global
+                      _dotprodsimp_state.state if that is not None.
+    """
+
+    if dotprodsimp is False or _dotprodsimp_state.state is False:
+        return offfunc
+    if dotprodsimp is True or _dotprodsimp_state.state is True:
+        return onfunc
+
+    return deffunc # None, None
+
+
+def _get_intermediate_simp_bool(default=False, dotprodsimp=None):
+    """Same as ``_get_intermediate_simp`` but returns bools instead of functions
+    by default."""
+
+    return _get_intermediate_simp(default, False, True, dotprodsimp)
+
+
+def _iszero(x):
+    """Returns True if x is zero."""
+    return getattr(x, 'is_zero', None)
+
+
+def _is_zero_after_expand_mul(x):
+    """Tests by expand_mul only, suitable for polynomials and rational
+    functions."""
+    return expand_mul(x) == 0
+
+
+def _simplify(expr):
+    """ Wrapper to avoid circular imports. """
+    from sympy.simplify.simplify import simplify
+    return simplify(expr)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..5447651645e3e2e92df3002822e87a773ade0df8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/__init__.py
@@ -0,0 +1,11 @@
+from .core import dispatch
+from .dispatcher import (Dispatcher, halt_ordering, restart_ordering,
+    MDNotImplementedError)
+
+__version__ = '0.4.9'
+
+__all__ = [
+    'dispatch',
+
+    'Dispatcher', 'halt_ordering', 'restart_ordering', 'MDNotImplementedError',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/conflict.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/conflict.py
new file mode 100644
index 0000000000000000000000000000000000000000..98c6742c9c03860233ef0004b241ea3944ac6d4d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/conflict.py
@@ -0,0 +1,68 @@
+from .utils import _toposort, groupby
+
+class AmbiguityWarning(Warning):
+    pass
+
+
+def supercedes(a, b):
+    """ A is consistent and strictly more specific than B """
+    return len(a) == len(b) and all(map(issubclass, a, b))
+
+
+def consistent(a, b):
+    """ It is possible for an argument list to satisfy both A and B """
+    return (len(a) == len(b) and
+            all(issubclass(aa, bb) or issubclass(bb, aa)
+                           for aa, bb in zip(a, b)))
+
+
+def ambiguous(a, b):
+    """ A is consistent with B but neither is strictly more specific """
+    return consistent(a, b) and not (supercedes(a, b) or supercedes(b, a))
+
+
+def ambiguities(signatures):
+    """ All signature pairs such that A is ambiguous with B """
+    signatures = list(map(tuple, signatures))
+    return {(a, b) for a in signatures for b in signatures
+                       if hash(a) < hash(b)
+                       and ambiguous(a, b)
+                       and not any(supercedes(c, a) and supercedes(c, b)
+                                    for c in signatures)}
+
+
+def super_signature(signatures):
+    """ A signature that would break ambiguities """
+    n = len(signatures[0])
+    assert all(len(s) == n for s in signatures)
+
+    return [max([type.mro(sig[i]) for sig in signatures], key=len)[0]
+               for i in range(n)]
+
+
+def edge(a, b, tie_breaker=hash):
+    """ A should be checked before B
+
+    Tie broken by tie_breaker, defaults to ``hash``
+    """
+    if supercedes(a, b):
+        if supercedes(b, a):
+            return tie_breaker(a) > tie_breaker(b)
+        else:
+            return True
+    return False
+
+
+def ordering(signatures):
+    """ A sane ordering of signatures to check, first to last
+
+    Topoological sort of edges as given by ``edge`` and ``supercedes``
+    """
+    signatures = list(map(tuple, signatures))
+    edges = [(a, b) for a in signatures for b in signatures if edge(a, b)]
+    edges = groupby(lambda x: x[0], edges)
+    for s in signatures:
+        if s not in edges:
+            edges[s] = []
+    edges = {k: [b for a, b in v] for k, v in edges.items()}
+    return _toposort(edges)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/core.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/core.py
new file mode 100644
index 0000000000000000000000000000000000000000..2856ff728c4eb97c5a59fffabddb4bf3c8b4baf2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/core.py
@@ -0,0 +1,83 @@
+from __future__ import annotations
+from typing import Any
+
+import inspect
+
+from .dispatcher import Dispatcher, MethodDispatcher, ambiguity_warn
+
+# XXX: This parameter to dispatch isn't documented and isn't used anywhere in
+# sympy. Maybe it should just be removed.
+global_namespace: dict[str, Any] = {}
+
+
+def dispatch(*types, namespace=global_namespace, on_ambiguity=ambiguity_warn):
+    """ Dispatch function on the types of the inputs
+
+    Supports dispatch on all non-keyword arguments.
+
+    Collects implementations based on the function name.  Ignores namespaces.
+
+    If ambiguous type signatures occur a warning is raised when the function is
+    defined suggesting the additional method to break the ambiguity.
+
+    Examples
+    --------
+
+    >>> from sympy.multipledispatch import dispatch
+    >>> @dispatch(int)
+    ... def f(x):
+    ...     return x + 1
+
+    >>> @dispatch(float)
+    ... def f(x): # noqa: F811
+    ...     return x - 1
+
+    >>> f(3)
+    4
+    >>> f(3.0)
+    2.0
+
+    Specify an isolated namespace with the namespace keyword argument
+
+    >>> my_namespace = dict()
+    >>> @dispatch(int, namespace=my_namespace)
+    ... def foo(x):
+    ...     return x + 1
+
+    Dispatch on instance methods within classes
+
+    >>> class MyClass(object):
+    ...     @dispatch(list)
+    ...     def __init__(self, data):
+    ...         self.data = data
+    ...     @dispatch(int)
+    ...     def __init__(self, datum): # noqa: F811
+    ...         self.data = [datum]
+    """
+    types = tuple(types)
+
+    def _(func):
+        name = func.__name__
+
+        if ismethod(func):
+            dispatcher = inspect.currentframe().f_back.f_locals.get(
+                name,
+                MethodDispatcher(name))
+        else:
+            if name not in namespace:
+                namespace[name] = Dispatcher(name)
+            dispatcher = namespace[name]
+
+        dispatcher.add(types, func, on_ambiguity=on_ambiguity)
+        return dispatcher
+    return _
+
+
+def ismethod(func):
+    """ Is func a method?
+
+    Note that this has to work as the method is defined but before the class is
+    defined.  At this stage methods look like functions.
+    """
+    signature = inspect.signature(func)
+    return signature.parameters.get('self', None) is not None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/dispatcher.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/dispatcher.py
new file mode 100644
index 0000000000000000000000000000000000000000..89471d678e1c330138a91ec6a41a324d29a037d7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/dispatcher.py
@@ -0,0 +1,413 @@
+from __future__ import annotations
+
+from warnings import warn
+import inspect
+from .conflict import ordering, ambiguities, super_signature, AmbiguityWarning
+from .utils import expand_tuples
+import itertools as itl
+
+
+class MDNotImplementedError(NotImplementedError):
+    """ A NotImplementedError for multiple dispatch """
+
+
+### Functions for on_ambiguity
+
+def ambiguity_warn(dispatcher, ambiguities):
+    """ Raise warning when ambiguity is detected
+
+    Parameters
+    ----------
+    dispatcher : Dispatcher
+        The dispatcher on which the ambiguity was detected
+    ambiguities : set
+        Set of type signature pairs that are ambiguous within this dispatcher
+
+    See Also:
+        Dispatcher.add
+        warning_text
+    """
+    warn(warning_text(dispatcher.name, ambiguities), AmbiguityWarning)
+
+
+class RaiseNotImplementedError:
+    """Raise ``NotImplementedError`` when called."""
+
+    def __init__(self, dispatcher):
+        self.dispatcher = dispatcher
+
+    def __call__(self, *args, **kwargs):
+        types = tuple(type(a) for a in args)
+        raise NotImplementedError(
+            "Ambiguous signature for %s: <%s>" % (
+            self.dispatcher.name, str_signature(types)
+        ))
+
+def ambiguity_register_error_ignore_dup(dispatcher, ambiguities):
+    """
+    If super signature for ambiguous types is duplicate types, ignore it.
+    Else, register instance of ``RaiseNotImplementedError`` for ambiguous types.
+
+    Parameters
+    ----------
+    dispatcher : Dispatcher
+        The dispatcher on which the ambiguity was detected
+    ambiguities : set
+        Set of type signature pairs that are ambiguous within this dispatcher
+
+    See Also:
+        Dispatcher.add
+        ambiguity_warn
+    """
+    for amb in ambiguities:
+        signature = tuple(super_signature(amb))
+        if len(set(signature)) == 1:
+            continue
+        dispatcher.add(
+            signature, RaiseNotImplementedError(dispatcher),
+            on_ambiguity=ambiguity_register_error_ignore_dup
+        )
+
+###
+
+
+_unresolved_dispatchers: set[Dispatcher] = set()
+_resolve = [True]
+
+
+def halt_ordering():
+    _resolve[0] = False
+
+
+def restart_ordering(on_ambiguity=ambiguity_warn):
+    _resolve[0] = True
+    while _unresolved_dispatchers:
+        dispatcher = _unresolved_dispatchers.pop()
+        dispatcher.reorder(on_ambiguity=on_ambiguity)
+
+
+class Dispatcher:
+    """ Dispatch methods based on type signature
+
+    Use ``dispatch`` to add implementations
+
+    Examples
+    --------
+
+    >>> from sympy.multipledispatch import dispatch
+    >>> @dispatch(int)
+    ... def f(x):
+    ...     return x + 1
+
+    >>> @dispatch(float)
+    ... def f(x): # noqa: F811
+    ...     return x - 1
+
+    >>> f(3)
+    4
+    >>> f(3.0)
+    2.0
+    """
+    __slots__ = '__name__', 'name', 'funcs', 'ordering', '_cache', 'doc'
+
+    def __init__(self, name, doc=None):
+        self.name = self.__name__ = name
+        self.funcs = {}
+        self._cache = {}
+        self.ordering = []
+        self.doc = doc
+
+    def register(self, *types, **kwargs):
+        """ Register dispatcher with new implementation
+
+        >>> from sympy.multipledispatch.dispatcher import Dispatcher
+        >>> f = Dispatcher('f')
+        >>> @f.register(int)
+        ... def inc(x):
+        ...     return x + 1
+
+        >>> @f.register(float)
+        ... def dec(x):
+        ...     return x - 1
+
+        >>> @f.register(list)
+        ... @f.register(tuple)
+        ... def reverse(x):
+        ...     return x[::-1]
+
+        >>> f(1)
+        2
+
+        >>> f(1.0)
+        0.0
+
+        >>> f([1, 2, 3])
+        [3, 2, 1]
+        """
+        def _(func):
+            self.add(types, func, **kwargs)
+            return func
+        return _
+
+    @classmethod
+    def get_func_params(cls, func):
+        if hasattr(inspect, "signature"):
+            sig = inspect.signature(func)
+            return sig.parameters.values()
+
+    @classmethod
+    def get_func_annotations(cls, func):
+        """ Get annotations of function positional parameters
+        """
+        params = cls.get_func_params(func)
+        if params:
+            Parameter = inspect.Parameter
+
+            params = (param for param in params
+                      if param.kind in
+                      (Parameter.POSITIONAL_ONLY,
+                       Parameter.POSITIONAL_OR_KEYWORD))
+
+            annotations = tuple(
+                param.annotation
+                for param in params)
+
+            if not any(ann is Parameter.empty for ann in annotations):
+                return annotations
+
+    def add(self, signature, func, on_ambiguity=ambiguity_warn):
+        """ Add new types/method pair to dispatcher
+
+        >>> from sympy.multipledispatch import Dispatcher
+        >>> D = Dispatcher('add')
+        >>> D.add((int, int), lambda x, y: x + y)
+        >>> D.add((float, float), lambda x, y: x + y)
+
+        >>> D(1, 2)
+        3
+        >>> D(1, 2.0)
+        Traceback (most recent call last):
+        ...
+        NotImplementedError: Could not find signature for add: 
+
+        When ``add`` detects a warning it calls the ``on_ambiguity`` callback
+        with a dispatcher/itself, and a set of ambiguous type signature pairs
+        as inputs.  See ``ambiguity_warn`` for an example.
+        """
+        # Handle annotations
+        if not signature:
+            annotations = self.get_func_annotations(func)
+            if annotations:
+                signature = annotations
+
+        # Handle union types
+        if any(isinstance(typ, tuple) for typ in signature):
+            for typs in expand_tuples(signature):
+                self.add(typs, func, on_ambiguity)
+            return
+
+        for typ in signature:
+            if not isinstance(typ, type):
+                str_sig = ', '.join(c.__name__ if isinstance(c, type)
+                                    else str(c) for c in signature)
+                raise TypeError("Tried to dispatch on non-type: %s\n"
+                                "In signature: <%s>\n"
+                                "In function: %s" %
+                                (typ, str_sig, self.name))
+
+        self.funcs[signature] = func
+        self.reorder(on_ambiguity=on_ambiguity)
+        self._cache.clear()
+
+    def reorder(self, on_ambiguity=ambiguity_warn):
+        if _resolve[0]:
+            self.ordering = ordering(self.funcs)
+            amb = ambiguities(self.funcs)
+            if amb:
+                on_ambiguity(self, amb)
+        else:
+            _unresolved_dispatchers.add(self)
+
+    def __call__(self, *args, **kwargs):
+        types = tuple([type(arg) for arg in args])
+        try:
+            func = self._cache[types]
+        except KeyError:
+            func = self.dispatch(*types)
+            if not func:
+                raise NotImplementedError(
+                    'Could not find signature for %s: <%s>' %
+                    (self.name, str_signature(types)))
+            self._cache[types] = func
+        try:
+            return func(*args, **kwargs)
+
+        except MDNotImplementedError:
+            funcs = self.dispatch_iter(*types)
+            next(funcs)  # burn first
+            for func in funcs:
+                try:
+                    return func(*args, **kwargs)
+                except MDNotImplementedError:
+                    pass
+            raise NotImplementedError("Matching functions for "
+                                      "%s: <%s> found, but none completed successfully"
+                                      % (self.name, str_signature(types)))
+
+    def __str__(self):
+        return "" % self.name
+    __repr__ = __str__
+
+    def dispatch(self, *types):
+        """ Deterimine appropriate implementation for this type signature
+
+        This method is internal.  Users should call this object as a function.
+        Implementation resolution occurs within the ``__call__`` method.
+
+        >>> from sympy.multipledispatch import dispatch
+        >>> @dispatch(int)
+        ... def inc(x):
+        ...     return x + 1
+
+        >>> implementation = inc.dispatch(int)
+        >>> implementation(3)
+        4
+
+        >>> print(inc.dispatch(float))
+        None
+
+        See Also:
+            ``sympy.multipledispatch.conflict`` - module to determine resolution order
+        """
+
+        if types in self.funcs:
+            return self.funcs[types]
+
+        try:
+            return next(self.dispatch_iter(*types))
+        except StopIteration:
+            return None
+
+    def dispatch_iter(self, *types):
+        n = len(types)
+        for signature in self.ordering:
+            if len(signature) == n and all(map(issubclass, types, signature)):
+                result = self.funcs[signature]
+                yield result
+
+    def resolve(self, types):
+        """ Deterimine appropriate implementation for this type signature
+
+        .. deprecated:: 0.4.4
+            Use ``dispatch(*types)`` instead
+        """
+        warn("resolve() is deprecated, use dispatch(*types)",
+             DeprecationWarning)
+
+        return self.dispatch(*types)
+
+    def __getstate__(self):
+        return {'name': self.name,
+                'funcs': self.funcs}
+
+    def __setstate__(self, d):
+        self.name = d['name']
+        self.funcs = d['funcs']
+        self.ordering = ordering(self.funcs)
+        self._cache = {}
+
+    @property
+    def __doc__(self):
+        docs = ["Multiply dispatched method: %s" % self.name]
+
+        if self.doc:
+            docs.append(self.doc)
+
+        other = []
+        for sig in self.ordering[::-1]:
+            func = self.funcs[sig]
+            if func.__doc__:
+                s = 'Inputs: <%s>\n' % str_signature(sig)
+                s += '-' * len(s) + '\n'
+                s += func.__doc__.strip()
+                docs.append(s)
+            else:
+                other.append(str_signature(sig))
+
+        if other:
+            docs.append('Other signatures:\n    ' + '\n    '.join(other))
+
+        return '\n\n'.join(docs)
+
+    def _help(self, *args):
+        return self.dispatch(*map(type, args)).__doc__
+
+    def help(self, *args, **kwargs):
+        """ Print docstring for the function corresponding to inputs """
+        print(self._help(*args))
+
+    def _source(self, *args):
+        func = self.dispatch(*map(type, args))
+        if not func:
+            raise TypeError("No function found")
+        return source(func)
+
+    def source(self, *args, **kwargs):
+        """ Print source code for the function corresponding to inputs """
+        print(self._source(*args))
+
+
+def source(func):
+    s = 'File: %s\n\n' % inspect.getsourcefile(func)
+    s = s + inspect.getsource(func)
+    return s
+
+
+class MethodDispatcher(Dispatcher):
+    """ Dispatch methods based on type signature
+
+    See Also:
+        Dispatcher
+    """
+
+    @classmethod
+    def get_func_params(cls, func):
+        if hasattr(inspect, "signature"):
+            sig = inspect.signature(func)
+            return itl.islice(sig.parameters.values(), 1, None)
+
+    def __get__(self, instance, owner):
+        self.obj = instance
+        self.cls = owner
+        return self
+
+    def __call__(self, *args, **kwargs):
+        types = tuple([type(arg) for arg in args])
+        func = self.dispatch(*types)
+        if not func:
+            raise NotImplementedError('Could not find signature for %s: <%s>' %
+                                      (self.name, str_signature(types)))
+        return func(self.obj, *args, **kwargs)
+
+
+def str_signature(sig):
+    """ String representation of type signature
+
+    >>> from sympy.multipledispatch.dispatcher import str_signature
+    >>> str_signature((int, float))
+    'int, float'
+    """
+    return ', '.join(cls.__name__ for cls in sig)
+
+
+def warning_text(name, amb):
+    """ The text for ambiguity warnings """
+    text = "\nAmbiguities exist in dispatched function %s\n\n" % (name)
+    text += "The following signatures may result in ambiguous behavior:\n"
+    for pair in amb:
+        text += "\t" + \
+            ', '.join('[' + str_signature(s) + ']' for s in pair) + "\n"
+    text += "\n\nConsider making the following additions:\n\n"
+    text += '\n\n'.join(['@dispatch(' + str_signature(super_signature(s))
+                         + ')\ndef %s(...)' % name for s in amb])
+    return text
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_conflict.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_conflict.py
new file mode 100644
index 0000000000000000000000000000000000000000..5d2292c460585ae2a65a01795b38499e67706ff0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_conflict.py
@@ -0,0 +1,62 @@
+from sympy.multipledispatch.conflict import (supercedes, ordering, ambiguities,
+        ambiguous, super_signature, consistent)
+
+
+class A: pass
+class B(A): pass
+class C: pass
+
+
+def test_supercedes():
+    assert supercedes([B], [A])
+    assert supercedes([B, A], [A, A])
+    assert not supercedes([B, A], [A, B])
+    assert not supercedes([A], [B])
+
+
+def test_consistent():
+    assert consistent([A], [A])
+    assert consistent([B], [B])
+    assert not consistent([A], [C])
+    assert consistent([A, B], [A, B])
+    assert consistent([B, A], [A, B])
+    assert not consistent([B, A], [B])
+    assert not consistent([B, A], [B, C])
+
+
+def test_super_signature():
+    assert super_signature([[A]]) == [A]
+    assert super_signature([[A], [B]]) == [B]
+    assert super_signature([[A, B], [B, A]]) == [B, B]
+    assert super_signature([[A, A, B], [A, B, A], [B, A, A]]) == [B, B, B]
+
+
+def test_ambiguous():
+    assert not ambiguous([A], [A])
+    assert not ambiguous([A], [B])
+    assert not ambiguous([B], [B])
+    assert not ambiguous([A, B], [B, B])
+    assert ambiguous([A, B], [B, A])
+
+
+def test_ambiguities():
+    signatures = [[A], [B], [A, B], [B, A], [A, C]]
+    expected = {((A, B), (B, A))}
+    result = ambiguities(signatures)
+    assert set(map(frozenset, expected)) == set(map(frozenset, result))
+
+    signatures = [[A], [B], [A, B], [B, A], [A, C], [B, B]]
+    expected = set()
+    result = ambiguities(signatures)
+    assert set(map(frozenset, expected)) == set(map(frozenset, result))
+
+
+def test_ordering():
+    signatures = [[A, A], [A, B], [B, A], [B, B], [A, C]]
+    ord = ordering(signatures)
+    assert ord[0] == (B, B) or ord[0] == (A, C)
+    assert ord[-1] == (A, A) or ord[-1] == (A, C)
+
+
+def test_type_mro():
+    assert super_signature([[object], [type]]) == [type]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_core.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_core.py
new file mode 100644
index 0000000000000000000000000000000000000000..016270fecc8cda644fc71b5c310b1430b50361f6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_core.py
@@ -0,0 +1,213 @@
+from __future__ import annotations
+from typing import Any
+
+from sympy.multipledispatch import dispatch
+from sympy.multipledispatch.conflict import AmbiguityWarning
+from sympy.testing.pytest import raises, warns
+from functools import partial
+
+test_namespace: dict[str, Any] = {}
+
+orig_dispatch = dispatch
+dispatch = partial(dispatch, namespace=test_namespace)
+
+
+def test_singledispatch():
+    @dispatch(int)
+    def f(x): # noqa:F811
+        return x + 1
+
+    @dispatch(int)
+    def g(x): # noqa:F811
+        return x + 2
+
+    @dispatch(float) # noqa:F811
+    def f(x): # noqa:F811
+        return x - 1
+
+    assert f(1) == 2
+    assert g(1) == 3
+    assert f(1.0) == 0
+
+    assert raises(NotImplementedError, lambda: f('hello'))
+
+
+def test_multipledispatch():
+    @dispatch(int, int)
+    def f(x, y): # noqa:F811
+        return x + y
+
+    @dispatch(float, float) # noqa:F811
+    def f(x, y): # noqa:F811
+        return x - y
+
+    assert f(1, 2) == 3
+    assert f(1.0, 2.0) == -1.0
+
+
+class A: pass
+class B: pass
+class C(A): pass
+class D(C): pass
+class E(C): pass
+
+
+def test_inheritance():
+    @dispatch(A)
+    def f(x): # noqa:F811
+        return 'a'
+
+    @dispatch(B) # noqa:F811
+    def f(x): # noqa:F811
+        return 'b'
+
+    assert f(A()) == 'a'
+    assert f(B()) == 'b'
+    assert f(C()) == 'a'
+
+
+def test_inheritance_and_multiple_dispatch():
+    @dispatch(A, A)
+    def f(x, y): # noqa:F811
+        return type(x), type(y)
+
+    @dispatch(A, B) # noqa:F811
+    def f(x, y): # noqa:F811
+        return 0
+
+    assert f(A(), A()) == (A, A)
+    assert f(A(), C()) == (A, C)
+    assert f(A(), B()) == 0
+    assert f(C(), B()) == 0
+    assert raises(NotImplementedError, lambda: f(B(), B()))
+
+
+def test_competing_solutions():
+    @dispatch(A)
+    def h(x): # noqa:F811
+        return 1
+
+    @dispatch(C) # noqa:F811
+    def h(x): # noqa:F811
+        return 2
+
+    assert h(D()) == 2
+
+
+def test_competing_multiple():
+    @dispatch(A, B)
+    def h(x, y): # noqa:F811
+        return 1
+
+    @dispatch(C, B) # noqa:F811
+    def h(x, y): # noqa:F811
+        return 2
+
+    assert h(D(), B()) == 2
+
+
+def test_competing_ambiguous():
+    test_namespace = {}
+    dispatch = partial(orig_dispatch, namespace=test_namespace)
+
+    @dispatch(A, C)
+    def f(x, y): # noqa:F811
+        return 2
+
+    with warns(AmbiguityWarning, test_stacklevel=False):
+        @dispatch(C, A) # noqa:F811
+        def f(x, y): # noqa:F811
+            return 2
+
+    assert f(A(), C()) == f(C(), A()) == 2
+    # assert raises(Warning, lambda : f(C(), C()))
+
+
+def test_caching_correct_behavior():
+    @dispatch(A)
+    def f(x): # noqa:F811
+        return 1
+
+    assert f(C()) == 1
+
+    @dispatch(C)
+    def f(x): # noqa:F811
+        return 2
+
+    assert f(C()) == 2
+
+
+def test_union_types():
+    @dispatch((A, C))
+    def f(x): # noqa:F811
+        return 1
+
+    assert f(A()) == 1
+    assert f(C()) == 1
+
+
+def test_namespaces():
+    ns1 = {}
+    ns2 = {}
+
+    def foo(x):
+        return 1
+    foo1 = orig_dispatch(int, namespace=ns1)(foo)
+
+    def foo(x):
+        return 2
+    foo2 = orig_dispatch(int, namespace=ns2)(foo)
+
+    assert foo1(0) == 1
+    assert foo2(0) == 2
+
+
+"""
+Fails
+def test_dispatch_on_dispatch():
+    @dispatch(A)
+    @dispatch(C)
+    def q(x): # noqa:F811
+        return 1
+
+    assert q(A()) == 1
+    assert q(C()) == 1
+"""
+
+
+def test_methods():
+    class Foo:
+        @dispatch(float)
+        def f(self, x): # noqa:F811
+            return x - 1
+
+        @dispatch(int) # noqa:F811
+        def f(self, x): # noqa:F811
+            return x + 1
+
+        @dispatch(int)
+        def g(self, x): # noqa:F811
+            return x + 3
+
+
+    foo = Foo()
+    assert foo.f(1) == 2
+    assert foo.f(1.0) == 0.0
+    assert foo.g(1) == 4
+
+
+def test_methods_multiple_dispatch():
+    class Foo:
+        @dispatch(A, A)
+        def f(x, y): # noqa:F811
+            return 1
+
+        @dispatch(A, C) # noqa:F811
+        def f(x, y): # noqa:F811
+            return 2
+
+
+    foo = Foo()
+    assert foo.f(A(), A()) == 1
+    assert foo.f(A(), C()) == 2
+    assert foo.f(C(), C()) == 2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_dispatcher.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_dispatcher.py
new file mode 100644
index 0000000000000000000000000000000000000000..e31ca8a5486b87eb43fc5e6f887caf50d6bfbe20
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/tests/test_dispatcher.py
@@ -0,0 +1,284 @@
+from sympy.multipledispatch.dispatcher import (Dispatcher, MDNotImplementedError,
+                                         MethodDispatcher, halt_ordering,
+                                         restart_ordering,
+                                         ambiguity_register_error_ignore_dup)
+from sympy.testing.pytest import raises, warns
+
+
+def identity(x):
+    return x
+
+
+def inc(x):
+    return x + 1
+
+
+def dec(x):
+    return x - 1
+
+
+def test_dispatcher():
+    f = Dispatcher('f')
+    f.add((int,), inc)
+    f.add((float,), dec)
+
+    with warns(DeprecationWarning, test_stacklevel=False):
+        assert f.resolve((int,)) == inc
+    assert f.dispatch(int) is inc
+
+    assert f(1) == 2
+    assert f(1.0) == 0.0
+
+
+def test_union_types():
+    f = Dispatcher('f')
+    f.register((int, float))(inc)
+
+    assert f(1) == 2
+    assert f(1.0) == 2.0
+
+
+def test_dispatcher_as_decorator():
+    f = Dispatcher('f')
+
+    @f.register(int)
+    def inc(x): # noqa:F811
+        return x + 1
+
+    @f.register(float) # noqa:F811
+    def inc(x): # noqa:F811
+        return x - 1
+
+    assert f(1) == 2
+    assert f(1.0) == 0.0
+
+
+def test_register_instance_method():
+
+    class Test:
+        __init__ = MethodDispatcher('f')
+
+        @__init__.register(list)
+        def _init_list(self, data):
+            self.data = data
+
+        @__init__.register(object)
+        def _init_obj(self, datum):
+            self.data = [datum]
+
+    a = Test(3)
+    b = Test([3])
+    assert a.data == b.data
+
+
+def test_on_ambiguity():
+    f = Dispatcher('f')
+
+    def identity(x): return x
+
+    ambiguities = [False]
+
+    def on_ambiguity(dispatcher, amb):
+        ambiguities[0] = True
+
+    f.add((object, object), identity, on_ambiguity=on_ambiguity)
+    assert not ambiguities[0]
+    f.add((object, float), identity, on_ambiguity=on_ambiguity)
+    assert not ambiguities[0]
+    f.add((float, object), identity, on_ambiguity=on_ambiguity)
+    assert ambiguities[0]
+
+
+def test_raise_error_on_non_class():
+    f = Dispatcher('f')
+    assert raises(TypeError, lambda: f.add((1,), inc))
+
+
+def test_docstring():
+
+    def one(x, y):
+        """ Docstring number one """
+        return x + y
+
+    def two(x, y):
+        """ Docstring number two """
+        return x + y
+
+    def three(x, y):
+        return x + y
+
+    master_doc = 'Doc of the multimethod itself'
+
+    f = Dispatcher('f', doc=master_doc)
+    f.add((object, object), one)
+    f.add((int, int), two)
+    f.add((float, float), three)
+
+    assert one.__doc__.strip() in f.__doc__
+    assert two.__doc__.strip() in f.__doc__
+    assert f.__doc__.find(one.__doc__.strip()) < \
+        f.__doc__.find(two.__doc__.strip())
+    assert 'object, object' in f.__doc__
+    assert master_doc in f.__doc__
+
+
+def test_help():
+    def one(x, y):
+        """ Docstring number one """
+        return x + y
+
+    def two(x, y):
+        """ Docstring number two """
+        return x + y
+
+    def three(x, y):
+        """ Docstring number three """
+        return x + y
+
+    master_doc = 'Doc of the multimethod itself'
+
+    f = Dispatcher('f', doc=master_doc)
+    f.add((object, object), one)
+    f.add((int, int), two)
+    f.add((float, float), three)
+
+    assert f._help(1, 1) == two.__doc__
+    assert f._help(1.0, 2.0) == three.__doc__
+
+
+def test_source():
+    def one(x, y):
+        """ Docstring number one """
+        return x + y
+
+    def two(x, y):
+        """ Docstring number two """
+        return x - y
+
+    master_doc = 'Doc of the multimethod itself'
+
+    f = Dispatcher('f', doc=master_doc)
+    f.add((int, int), one)
+    f.add((float, float), two)
+
+    assert 'x + y' in f._source(1, 1)
+    assert 'x - y' in f._source(1.0, 1.0)
+
+
+def test_source_raises_on_missing_function():
+    f = Dispatcher('f')
+
+    assert raises(TypeError, lambda: f.source(1))
+
+
+def test_halt_method_resolution():
+    g = [0]
+
+    def on_ambiguity(a, b):
+        g[0] += 1
+
+    f = Dispatcher('f')
+
+    halt_ordering()
+
+    def func(*args):
+        pass
+
+    f.add((int, object), func)
+    f.add((object, int), func)
+
+    assert g == [0]
+
+    restart_ordering(on_ambiguity=on_ambiguity)
+
+    assert g == [1]
+
+    assert set(f.ordering) == {(int, object), (object, int)}
+
+
+def test_no_implementations():
+    f = Dispatcher('f')
+    assert raises(NotImplementedError, lambda: f('hello'))
+
+
+def test_register_stacking():
+    f = Dispatcher('f')
+
+    @f.register(list)
+    @f.register(tuple)
+    def rev(x):
+        return x[::-1]
+
+    assert f((1, 2, 3)) == (3, 2, 1)
+    assert f([1, 2, 3]) == [3, 2, 1]
+
+    assert raises(NotImplementedError, lambda: f('hello'))
+    assert rev('hello') == 'olleh'
+
+
+def test_dispatch_method():
+    f = Dispatcher('f')
+
+    @f.register(list)
+    def rev(x):
+        return x[::-1]
+
+    @f.register(int, int)
+    def add(x, y):
+        return x + y
+
+    class MyList(list):
+        pass
+
+    assert f.dispatch(list) is rev
+    assert f.dispatch(MyList) is rev
+    assert f.dispatch(int, int) is add
+
+
+def test_not_implemented():
+    f = Dispatcher('f')
+
+    @f.register(object)
+    def _(x):
+        return 'default'
+
+    @f.register(int)
+    def _(x):
+        if x % 2 == 0:
+            return 'even'
+        else:
+            raise MDNotImplementedError()
+
+    assert f('hello') == 'default'  # default behavior
+    assert f(2) == 'even'          # specialized behavior
+    assert f(3) == 'default'       # fall bac to default behavior
+    assert raises(NotImplementedError, lambda: f(1, 2))
+
+
+def test_not_implemented_error():
+    f = Dispatcher('f')
+
+    @f.register(float)
+    def _(a):
+        raise MDNotImplementedError()
+
+    assert raises(NotImplementedError, lambda: f(1.0))
+
+def test_ambiguity_register_error_ignore_dup():
+    f = Dispatcher('f')
+
+    class A:
+        pass
+    class B(A):
+        pass
+    class C(A):
+        pass
+
+    # suppress warning for registering ambiguous signal
+    f.add((A, B), lambda x,y: None, ambiguity_register_error_ignore_dup)
+    f.add((B, A), lambda x,y: None, ambiguity_register_error_ignore_dup)
+    f.add((A, C), lambda x,y: None, ambiguity_register_error_ignore_dup)
+    f.add((C, A), lambda x,y: None, ambiguity_register_error_ignore_dup)
+
+    # raises error if ambiguous signal is passed
+    assert raises(NotImplementedError, lambda: f(B(), C()))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/utils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..11f563772385124c2fc0d285f7aa6e0747b8b412
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/multipledispatch/utils.py
@@ -0,0 +1,105 @@
+from collections import OrderedDict
+
+
+def expand_tuples(L):
+    """
+    >>> from sympy.multipledispatch.utils import expand_tuples
+    >>> expand_tuples([1, (2, 3)])
+    [(1, 2), (1, 3)]
+
+    >>> expand_tuples([1, 2])
+    [(1, 2)]
+    """
+    if not L:
+        return [()]
+    elif not isinstance(L[0], tuple):
+        rest = expand_tuples(L[1:])
+        return [(L[0],) + t for t in rest]
+    else:
+        rest = expand_tuples(L[1:])
+        return [(item,) + t for t in rest for item in L[0]]
+
+
+# Taken from theano/theano/gof/sched.py
+# Avoids licensing issues because this was written by Matthew Rocklin
+def _toposort(edges):
+    """ Topological sort algorithm by Kahn [1] - O(nodes + vertices)
+
+    inputs:
+        edges - a dict of the form {a: {b, c}} where b and c depend on a
+    outputs:
+        L - an ordered list of nodes that satisfy the dependencies of edges
+
+    >>> from sympy.multipledispatch.utils import _toposort
+    >>> _toposort({1: (2, 3), 2: (3, )})
+    [1, 2, 3]
+
+    Closely follows the wikipedia page [2]
+
+    [1] Kahn, Arthur B. (1962), "Topological sorting of large networks",
+    Communications of the ACM
+    [2] https://en.wikipedia.org/wiki/Toposort#Algorithms
+    """
+    incoming_edges = reverse_dict(edges)
+    incoming_edges = {k: set(val) for k, val in incoming_edges.items()}
+    S = OrderedDict.fromkeys(v for v in edges if v not in incoming_edges)
+    L = []
+
+    while S:
+        n, _ = S.popitem()
+        L.append(n)
+        for m in edges.get(n, ()):
+            assert n in incoming_edges[m]
+            incoming_edges[m].remove(n)
+            if not incoming_edges[m]:
+                S[m] = None
+    if any(incoming_edges.get(v, None) for v in edges):
+        raise ValueError("Input has cycles")
+    return L
+
+
+def reverse_dict(d):
+    """Reverses direction of dependence dict
+
+    >>> d = {'a': (1, 2), 'b': (2, 3), 'c':()}
+    >>> reverse_dict(d)  # doctest: +SKIP
+    {1: ('a',), 2: ('a', 'b'), 3: ('b',)}
+
+    :note: dict order are not deterministic. As we iterate on the
+        input dict, it make the output of this function depend on the
+        dict order. So this function output order should be considered
+        as undeterministic.
+
+    """
+    result = {}
+    for key in d:
+        for val in d[key]:
+            result[val] = result.get(val, ()) + (key, )
+    return result
+
+
+# Taken from toolz
+# Avoids licensing issues because this version was authored by Matthew Rocklin
+def groupby(func, seq):
+    """ Group a collection by a key function
+
+    >>> from sympy.multipledispatch.utils import groupby
+    >>> names = ['Alice', 'Bob', 'Charlie', 'Dan', 'Edith', 'Frank']
+    >>> groupby(len, names)  # doctest: +SKIP
+    {3: ['Bob', 'Dan'], 5: ['Alice', 'Edith', 'Frank'], 7: ['Charlie']}
+
+    >>> iseven = lambda x: x % 2 == 0
+    >>> groupby(iseven, [1, 2, 3, 4, 5, 6, 7, 8])  # doctest: +SKIP
+    {False: [1, 3, 5, 7], True: [2, 4, 6, 8]}
+
+    See Also:
+        ``countby``
+    """
+
+    d = {}
+    for item in seq:
+        key = func(item)
+        if key not in d:
+            d[key] = []
+        d[key].append(item)
+    return d
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..19576c8935da455743d27f0a263caecca94f59f8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/__init__.py
@@ -0,0 +1,67 @@
+"""
+Number theory module (primes, etc)
+"""
+
+from .generate import nextprime, prevprime, prime, primepi, primerange, \
+    randprime, Sieve, sieve, primorial, cycle_length, composite, compositepi
+from .primetest import isprime, is_gaussian_prime, is_mersenne_prime
+from .factor_ import divisors, proper_divisors, factorint, multiplicity, \
+    multiplicity_in_factorial, perfect_power, factor_cache, pollard_pm1, \
+    pollard_rho, primefactors, totient, \
+    divisor_count, proper_divisor_count, divisor_sigma, factorrat, \
+    reduced_totient, primenu, primeomega, mersenne_prime_exponent, \
+    is_perfect, is_abundant, is_deficient, is_amicable, is_carmichael, \
+    abundance, dra, drm
+
+from .partitions_ import npartitions
+from .residue_ntheory import is_primitive_root, is_quad_residue, \
+    legendre_symbol, jacobi_symbol, n_order, sqrt_mod, quadratic_residues, \
+    primitive_root, nthroot_mod, is_nthpow_residue, sqrt_mod_iter, mobius, \
+    discrete_log, quadratic_congruence, polynomial_congruence
+from .multinomial import binomial_coefficients, binomial_coefficients_list, \
+    multinomial_coefficients
+from .continued_fraction import continued_fraction_periodic, \
+    continued_fraction_iterator, continued_fraction_reduce, \
+    continued_fraction_convergents, continued_fraction
+from .digits import count_digits, digits, is_palindromic
+from .egyptian_fraction import egyptian_fraction
+from .ecm import ecm
+from .qs import qs, qs_factor
+__all__ = [
+    'nextprime', 'prevprime', 'prime', 'primepi', 'primerange', 'randprime',
+    'Sieve', 'sieve', 'primorial', 'cycle_length', 'composite', 'compositepi',
+
+    'isprime', 'is_gaussian_prime', 'is_mersenne_prime',
+
+
+    'divisors', 'proper_divisors', 'factorint', 'multiplicity', 'perfect_power',
+    'pollard_pm1', 'factor_cache', 'pollard_rho', 'primefactors', 'totient',
+    'divisor_count', 'proper_divisor_count', 'divisor_sigma', 'factorrat',
+    'reduced_totient', 'primenu', 'primeomega', 'mersenne_prime_exponent',
+    'is_perfect', 'is_abundant', 'is_deficient', 'is_amicable',
+    'is_carmichael', 'abundance', 'dra', 'drm', 'multiplicity_in_factorial',
+
+    'npartitions',
+
+    'is_primitive_root', 'is_quad_residue', 'legendre_symbol',
+    'jacobi_symbol', 'n_order', 'sqrt_mod', 'quadratic_residues',
+    'primitive_root', 'nthroot_mod', 'is_nthpow_residue', 'sqrt_mod_iter',
+    'mobius', 'discrete_log', 'quadratic_congruence', 'polynomial_congruence',
+
+    'binomial_coefficients', 'binomial_coefficients_list',
+    'multinomial_coefficients',
+
+    'continued_fraction_periodic', 'continued_fraction_iterator',
+    'continued_fraction_reduce', 'continued_fraction_convergents',
+    'continued_fraction',
+
+    'digits',
+    'count_digits',
+    'is_palindromic',
+
+    'egyptian_fraction',
+
+    'ecm',
+
+    'qs', 'qs_factor',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/bbp_pi.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/bbp_pi.py
new file mode 100644
index 0000000000000000000000000000000000000000..e2ff4b755d74d4e075ac7195f991c8182d175693
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/bbp_pi.py
@@ -0,0 +1,190 @@
+'''
+This implementation is a heavily modified fixed point implementation of
+BBP_formula for calculating the nth position of pi. The original hosted
+at: https://web.archive.org/web/20151116045029/http://en.literateprograms.org/Pi_with_the_BBP_formula_(Python)
+
+# Permission is hereby granted, free of charge, to any person obtaining
+# a copy of this software and associated documentation files (the
+# "Software"), to deal in the Software without restriction, including
+# without limitation the rights to use, copy, modify, merge, publish,
+# distribute, sub-license, and/or sell copies of the Software, and to
+# permit persons to whom the Software is furnished to do so, subject to
+# the following conditions:
+#
+# The above copyright notice and this permission notice shall be
+# included in all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+Modifications:
+
+1.Once the nth digit and desired number of digits is selected, the
+number of digits of working precision is calculated to ensure that
+the hexadecimal digits returned are accurate. This is calculated as
+
+    int(math.log(start + prec)/math.log(16) + prec + 3)
+    ---------------------------------------   --------
+                      /                          /
+    number of hex digits           additional digits
+
+This was checked by the following code which completed without
+errors (and dig are the digits included in the test_bbp.py file):
+
+    for i in range(0,1000):
+     for j in range(1,1000):
+      a, b = pi_hex_digits(i, j), dig[i:i+j]
+      if a != b:
+        print('%s\n%s'%(a,b))
+
+Deceasing the additional digits by 1 generated errors, so '3' is
+the smallest additional precision needed to calculate the above
+loop without errors. The following trailing 10 digits were also
+checked to be accurate (and the times were slightly faster with
+some of the constant modifications that were made):
+
+    >> from time import time
+    >> t=time();pi_hex_digits(10**2-10 + 1, 10), time()-t
+    ('e90c6cc0ac', 0.0)
+    >> t=time();pi_hex_digits(10**4-10 + 1, 10), time()-t
+    ('26aab49ec6', 0.17100000381469727)
+    >> t=time();pi_hex_digits(10**5-10 + 1, 10), time()-t
+    ('a22673c1a5', 4.7109999656677246)
+    >> t=time();pi_hex_digits(10**6-10 + 1, 10), time()-t
+    ('9ffd342362', 59.985999822616577)
+    >> t=time();pi_hex_digits(10**7-10 + 1, 10), time()-t
+    ('c1a42e06a1', 689.51800012588501)
+
+2. The while loop to evaluate whether the series has converged quits
+when the addition amount `dt` has dropped to zero.
+
+3. the formatting string to convert the decimal to hexadecimal is
+calculated for the given precision.
+
+4. pi_hex_digits(n) changed to have coefficient to the formula in an
+array (perhaps just a matter of preference).
+
+'''
+
+from sympy.utilities.misc import as_int
+
+
+def _series(j, n, prec=14):
+
+    # Left sum from the bbp algorithm
+    s = 0
+    D = _dn(n, prec)
+    D4 = 4 * D
+    d = j
+    for k in range(n + 1):
+        s += (pow(16, n - k, d) << D4) // d
+        d += 8
+
+    # Right sum iterates to infinity for full precision, but we
+    # stop at the point where one iteration is beyond the precision
+    # specified.
+
+    t = 0
+    k = n + 1
+    e = D4 - 4 # 4*(D + n - k)
+    d = 8 * k + j
+    while True:
+        dt = (1 << e) // d
+        if not dt:
+            break
+        t += dt
+        # k += 1
+        e -= 4
+        d += 8
+    total = s + t
+
+    return total
+
+
+def pi_hex_digits(n, prec=14):
+    """Returns a string containing ``prec`` (default 14) digits
+    starting at the nth digit of pi in hex. Counting of digits
+    starts at 0 and the decimal is not counted, so for n = 0 the
+    returned value starts with 3; n = 1 corresponds to the first
+    digit past the decimal point (which in hex is 2).
+
+    Parameters
+    ==========
+
+    n : non-negative integer
+    prec : non-negative integer. default = 14
+
+    Returns
+    =======
+
+    str : Returns a string containing ``prec`` digits
+          starting at the nth digit of pi in hex.
+          If ``prec`` = 0, returns empty string.
+
+    Raises
+    ======
+
+    ValueError
+        If ``n`` < 0 or ``prec`` < 0.
+        Or ``n`` or ``prec`` is not an integer.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.bbp_pi import pi_hex_digits
+    >>> pi_hex_digits(0)
+    '3243f6a8885a30'
+    >>> pi_hex_digits(0, 3)
+    '324'
+
+    These are consistent with the following results
+
+    >>> import math
+    >>> hex(int(math.pi * 2**((14-1)*4)))
+    '0x3243f6a8885a30'
+    >>> hex(int(math.pi * 2**((3-1)*4)))
+    '0x324'
+
+    References
+    ==========
+
+    .. [1] http://www.numberworld.org/digits/Pi/
+    """
+    n, prec = as_int(n), as_int(prec)
+    if n < 0:
+        raise ValueError('n cannot be negative')
+    if prec < 0:
+        raise ValueError('prec cannot be negative')
+    if prec == 0:
+        return ''
+
+    # main of implementation arrays holding formulae coefficients
+    n -= 1
+    a = [4, 2, 1, 1]
+    j = [1, 4, 5, 6]
+
+    #formulae
+    D = _dn(n, prec)
+    x = + (a[0]*_series(j[0], n, prec)
+         - a[1]*_series(j[1], n, prec)
+         - a[2]*_series(j[2], n, prec)
+         - a[3]*_series(j[3], n, prec)) & (16**D - 1)
+
+    s = ("%0" + "%ix" % prec) % (x // 16**(D - prec))
+    return s
+
+
+def _dn(n, prec):
+    # controller for n dependence on precision
+    # n = starting digit index
+    # prec = the number of total digits to compute
+    n += 1  # because we subtract 1 for _series
+
+    # assert int(math.log(n + prec)/math.log(16)) ==\
+    #  ((n + prec).bit_length() - 1) // 4
+    return ((n + prec).bit_length() - 1) // 4 + prec + 3
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/continued_fraction.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/continued_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..62f8e2d729ada3414a87d6f0583e06bee2a2b220
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/continued_fraction.py
@@ -0,0 +1,369 @@
+from __future__ import annotations
+import itertools
+from sympy.core.exprtools import factor_terms
+from sympy.core.numbers import Integer, Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import _sympify
+from sympy.utilities.misc import as_int
+
+
+def continued_fraction(a) -> list:
+    """Return the continued fraction representation of a Rational or
+    quadratic irrational.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.continued_fraction import continued_fraction
+    >>> from sympy import sqrt
+    >>> continued_fraction((1 + 2*sqrt(3))/5)
+    [0, 1, [8, 3, 34, 3]]
+
+    See Also
+    ========
+    continued_fraction_periodic, continued_fraction_reduce, continued_fraction_convergents
+    """
+    e = _sympify(a)
+    if all(i.is_Rational for i in e.atoms()):
+        if e.is_Integer:
+            return continued_fraction_periodic(e, 1, 0)
+        elif e.is_Rational:
+            return continued_fraction_periodic(e.p, e.q, 0)
+        elif e.is_Pow and e.exp is S.Half and e.base.is_Integer:
+            return continued_fraction_periodic(0, 1, e.base)
+        elif e.is_Mul and len(e.args) == 2 and (
+                e.args[0].is_Rational and
+                e.args[1].is_Pow and
+                e.args[1].base.is_Integer and
+                e.args[1].exp is S.Half):
+            a, b = e.args
+            return continued_fraction_periodic(0, a.q, b.base, a.p)
+        else:
+            # this should not have to work very hard- no
+            # simplification, cancel, etc... which should be
+            # done by the user.  e.g. This is a fancy 1 but
+            # the user should simplify it first:
+            # sqrt(2)*(1 + sqrt(2))/(sqrt(2) + 2)
+            p, d = e.expand().as_numer_denom()
+            if d.is_Integer:
+                if p.is_Rational:
+                    return continued_fraction_periodic(p, d)
+                # look for a + b*c
+                # with c = sqrt(s)
+                if p.is_Add and len(p.args) == 2:
+                    a, bc = p.args
+                else:
+                    a = S.Zero
+                    bc = p
+                if a.is_Integer:
+                    b = S.NaN
+                    if bc.is_Mul and len(bc.args) == 2:
+                        b, c = bc.args
+                    elif bc.is_Pow:
+                        b = Integer(1)
+                        c = bc
+                    if b.is_Integer and (
+                            c.is_Pow and c.exp is S.Half and
+                            c.base.is_Integer):
+                        # (a + b*sqrt(c))/d
+                        c = c.base
+                        return continued_fraction_periodic(a, d, c, b)
+    raise ValueError(
+        'expecting a rational or quadratic irrational, not %s' % e)
+
+
+def continued_fraction_periodic(p, q, d=0, s=1) -> list:
+    r"""
+    Find the periodic continued fraction expansion of a quadratic irrational.
+
+    Compute the continued fraction expansion of a rational or a
+    quadratic irrational number, i.e. `\frac{p + s\sqrt{d}}{q}`, where
+    `p`, `q \ne 0` and `d \ge 0` are integers.
+
+    Returns the continued fraction representation (canonical form) as
+    a list of integers, optionally ending (for quadratic irrationals)
+    with list of integers representing the repeating digits.
+
+    Parameters
+    ==========
+
+    p : int
+        the rational part of the number's numerator
+    q : int
+        the denominator of the number
+    d : int, optional
+        the irrational part (discriminator) of the number's numerator
+    s : int, optional
+        the coefficient of the irrational part
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.continued_fraction import continued_fraction_periodic
+    >>> continued_fraction_periodic(3, 2, 7)
+    [2, [1, 4, 1, 1]]
+
+    Golden ratio has the simplest continued fraction expansion:
+
+    >>> continued_fraction_periodic(1, 2, 5)
+    [[1]]
+
+    If the discriminator is zero or a perfect square then the number will be a
+    rational number:
+
+    >>> continued_fraction_periodic(4, 3, 0)
+    [1, 3]
+    >>> continued_fraction_periodic(4, 3, 49)
+    [3, 1, 2]
+
+    See Also
+    ========
+
+    continued_fraction_iterator, continued_fraction_reduce
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Periodic_continued_fraction
+    .. [2] K. Rosen. Elementary Number theory and its applications.
+           Addison-Wesley, 3 Sub edition, pages 379-381, January 1992.
+
+    """
+    from sympy.functions import sqrt, floor
+
+    p, q, d, s = list(map(as_int, [p, q, d, s]))
+
+    if d < 0:
+        raise ValueError("expected non-negative for `d` but got %s" % d)
+
+    if q == 0:
+        raise ValueError("The denominator cannot be 0.")
+
+    if not s:
+        d = 0
+
+    # check for rational case
+    sd = sqrt(d)
+    if sd.is_Integer:
+        return list(continued_fraction_iterator(Rational(p + s*sd, q)))
+
+    # irrational case with sd != Integer
+    if q < 0:
+        p, q, s = -p, -q, -s
+
+    n = (p + s*sd)/q
+    if n < 0:
+        w = floor(-n)
+        f = -n - w
+        one_f = continued_fraction(1 - f)  # 1-f < 1 so cf is [0 ... [...]]
+        one_f[0] -= w + 1
+        return one_f
+
+    d *= s**2
+    sd *= s
+
+    if (d - p**2)%q:
+        d *= q**2
+        sd *= q
+        p *= q
+        q *= q
+
+    terms: list[int] = []
+    pq = {}
+
+    while (p, q) not in pq:
+        pq[(p, q)] = len(terms)
+        terms.append((p + sd)//q)
+        p = terms[-1]*q - p
+        q = (d - p**2)//q
+
+    i = pq[(p, q)]
+    return terms[:i] + [terms[i:]]  # type: ignore
+
+
+def continued_fraction_reduce(cf):
+    """
+    Reduce a continued fraction to a rational or quadratic irrational.
+
+    Compute the rational or quadratic irrational number from its
+    terminating or periodic continued fraction expansion.  The
+    continued fraction expansion (cf) should be supplied as a
+    terminating iterator supplying the terms of the expansion.  For
+    terminating continued fractions, this is equivalent to
+    ``list(continued_fraction_convergents(cf))[-1]``, only a little more
+    efficient.  If the expansion has a repeating part, a list of the
+    repeating terms should be returned as the last element from the
+    iterator.  This is the format returned by
+    continued_fraction_periodic.
+
+    For quadratic irrationals, returns the largest solution found,
+    which is generally the one sought, if the fraction is in canonical
+    form (all terms positive except possibly the first).
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.continued_fraction import continued_fraction_reduce
+    >>> continued_fraction_reduce([1, 2, 3, 4, 5])
+    225/157
+    >>> continued_fraction_reduce([-2, 1, 9, 7, 1, 2])
+    -256/233
+    >>> continued_fraction_reduce([2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8]).n(10)
+    2.718281835
+    >>> continued_fraction_reduce([1, 4, 2, [3, 1]])
+    (sqrt(21) + 287)/238
+    >>> continued_fraction_reduce([[1]])
+    (1 + sqrt(5))/2
+    >>> from sympy.ntheory.continued_fraction import continued_fraction_periodic
+    >>> continued_fraction_reduce(continued_fraction_periodic(8, 5, 13))
+    (sqrt(13) + 8)/5
+
+    See Also
+    ========
+
+    continued_fraction_periodic
+
+    """
+    from sympy.solvers import solve
+
+    period = []
+    x = Dummy('x')
+
+    def untillist(cf):
+        for nxt in cf:
+            if isinstance(nxt, list):
+                period.extend(nxt)
+                yield x
+                break
+            yield nxt
+
+    a = S.Zero
+    for a in continued_fraction_convergents(untillist(cf)):
+        pass
+
+    if period:
+        y = Dummy('y')
+        solns = solve(continued_fraction_reduce(period + [y]) - y, y)
+        solns.sort()
+        pure = solns[-1]
+        rv = a.subs(x, pure).radsimp()
+    else:
+        rv = a
+    if rv.is_Add:
+        rv = factor_terms(rv)
+        if rv.is_Mul and rv.args[0] == -1:
+            rv = rv.func(*rv.args)
+    return rv
+
+
+def continued_fraction_iterator(x):
+    """
+    Return continued fraction expansion of x as iterator.
+
+    Examples
+    ========
+
+    >>> from sympy import Rational, pi
+    >>> from sympy.ntheory.continued_fraction import continued_fraction_iterator
+
+    >>> list(continued_fraction_iterator(Rational(3, 8)))
+    [0, 2, 1, 2]
+    >>> list(continued_fraction_iterator(Rational(-3, 8)))
+    [-1, 1, 1, 1, 2]
+
+    >>> for i, v in enumerate(continued_fraction_iterator(pi)):
+    ...     if i > 7:
+    ...         break
+    ...     print(v)
+    3
+    7
+    15
+    1
+    292
+    1
+    1
+    1
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Continued_fraction
+
+    """
+    from sympy.functions import floor
+    while True:
+        i = floor(x)
+        yield i
+        x -= i
+        if not x:
+            break
+        x = 1/x
+
+
+def continued_fraction_convergents(cf):
+    """
+    Return an iterator over the convergents of a continued fraction (cf).
+
+    The parameter should be in either of the following to forms:
+    - A list of partial quotients, possibly with the last element being a list
+    of repeating partial quotients, such as might be returned by
+    continued_fraction and continued_fraction_periodic.
+    - An iterable returning successive partial quotients of the continued
+    fraction, such as might be returned by continued_fraction_iterator.
+
+    In computing the convergents, the continued fraction need not be strictly
+    in canonical form (all integers, all but the first positive).
+    Rational and negative elements may be present in the expansion.
+
+    Examples
+    ========
+
+    >>> from sympy.core import pi
+    >>> from sympy import S
+    >>> from sympy.ntheory.continued_fraction import \
+            continued_fraction_convergents, continued_fraction_iterator
+
+    >>> list(continued_fraction_convergents([0, 2, 1, 2]))
+    [0, 1/2, 1/3, 3/8]
+
+    >>> list(continued_fraction_convergents([1, S('1/2'), -7, S('1/4')]))
+    [1, 3, 19/5, 7]
+
+    >>> it = continued_fraction_convergents(continued_fraction_iterator(pi))
+    >>> for n in range(7):
+    ...     print(next(it))
+    3
+    22/7
+    333/106
+    355/113
+    103993/33102
+    104348/33215
+    208341/66317
+
+    >>> it = continued_fraction_convergents([1, [1, 2]])  # sqrt(3)
+    >>> for n in range(7):
+    ...     print(next(it))
+    1
+    2
+    5/3
+    7/4
+    19/11
+    26/15
+    71/41
+
+    See Also
+    ========
+
+    continued_fraction_iterator, continued_fraction, continued_fraction_periodic
+
+    """
+    if isinstance(cf, list) and isinstance(cf[-1], list):
+        cf = itertools.chain(cf[:-1], itertools.cycle(cf[-1]))
+    p_2, q_2 = S.Zero, S.One
+    p_1, q_1 = S.One, S.Zero
+    for a in cf:
+        p, q = a*p_1 + p_2, a*q_1 + q_2
+        p_2, q_2 = p_1, q_1
+        p_1, q_1 = p, q
+        yield p/q
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/digits.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/digits.py
new file mode 100644
index 0000000000000000000000000000000000000000..a0414815871f6f888ccd2823546ab2b0c2c9f515
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/digits.py
@@ -0,0 +1,150 @@
+from collections import defaultdict
+
+from sympy.utilities.iterables import multiset, is_palindromic as _palindromic
+from sympy.utilities.misc import as_int
+
+
+def digits(n, b=10, digits=None):
+    """
+    Return a list of the digits of ``n`` in base ``b``. The first
+    element in the list is ``b`` (or ``-b`` if ``n`` is negative).
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.digits import digits
+    >>> digits(35)
+    [10, 3, 5]
+
+    If the number is negative, the negative sign will be placed on the
+    base (which is the first element in the returned list):
+
+    >>> digits(-35)
+    [-10, 3, 5]
+
+    Bases other than 10 (and greater than 1) can be selected with ``b``:
+
+    >>> digits(27, b=2)
+    [2, 1, 1, 0, 1, 1]
+
+    Use the ``digits`` keyword if a certain number of digits is desired:
+
+    >>> digits(35, digits=4)
+    [10, 0, 0, 3, 5]
+
+    Parameters
+    ==========
+
+    n: integer
+        The number whose digits are returned.
+
+    b: integer
+        The base in which digits are computed.
+
+    digits: integer (or None for all digits)
+        The number of digits to be returned (padded with zeros, if
+        necessary).
+
+    See Also
+    ========
+    sympy.core.intfunc.num_digits, count_digits
+    """
+
+    b = as_int(b)
+    n = as_int(n)
+    if b < 2:
+        raise ValueError("b must be greater than 1")
+    else:
+        x, y = abs(n), []
+        while x >= b:
+            x, r = divmod(x, b)
+            y.append(r)
+        y.append(x)
+        y.append(-b if n < 0 else b)
+        y.reverse()
+        ndig = len(y) - 1
+        if digits is not None:
+            if ndig > digits:
+                raise ValueError(
+                    "For %s, at least %s digits are needed." % (n, ndig))
+            elif ndig < digits:
+                y[1:1] = [0]*(digits - ndig)
+        return y
+
+
+def count_digits(n, b=10):
+    """
+    Return a dictionary whose keys are the digits of ``n`` in the
+    given base, ``b``, with keys indicating the digits appearing in the
+    number and values indicating how many times that digit appeared.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import count_digits
+
+    >>> count_digits(1111339)
+    {1: 4, 3: 2, 9: 1}
+
+    The digits returned are always represented in base-10
+    but the number itself can be entered in any format that is
+    understood by Python; the base of the number can also be
+    given if it is different than 10:
+
+    >>> n = 0xFA; n
+    250
+    >>> count_digits(_)
+    {0: 1, 2: 1, 5: 1}
+    >>> count_digits(n, 16)
+    {10: 1, 15: 1}
+
+    The default dictionary will return a 0 for any digit that did
+    not appear in the number. For example, which digits appear 7
+    times in ``77!``:
+
+    >>> from sympy import factorial
+    >>> c77 = count_digits(factorial(77))
+    >>> [i for i in range(10) if c77[i] == 7]
+    [1, 3, 7, 9]
+
+    See Also
+    ========
+    sympy.core.intfunc.num_digits, digits
+    """
+    rv = defaultdict(int, multiset(digits(n, b)).items())
+    rv.pop(b) if b in rv else rv.pop(-b)  # b or -b is there
+    return rv
+
+
+def is_palindromic(n, b=10):
+    """return True if ``n`` is the same when read from left to right
+    or right to left in the given base, ``b``.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import is_palindromic
+
+    >>> all(is_palindromic(i) for i in (-11, 1, 22, 121))
+    True
+
+    The second argument allows you to test numbers in other
+    bases. For example, 88 is palindromic in base-10 but not
+    in base-8:
+
+    >>> is_palindromic(88, 8)
+    False
+
+    On the other hand, a number can be palindromic in base-8 but
+    not in base-10:
+
+    >>> 0o121, is_palindromic(0o121)
+    (81, False)
+
+    Or it might be palindromic in both bases:
+
+    >>> oct(121), is_palindromic(121, 8) and is_palindromic(121)
+    ('0o171', True)
+
+    """
+    return _palindromic(digits(n, b), 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/ecm.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/ecm.py
new file mode 100644
index 0000000000000000000000000000000000000000..498c0c8fdf8478688465c4bae307818e9685b686
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/ecm.py
@@ -0,0 +1,348 @@
+from math import log
+
+from sympy.core.random import _randint
+from sympy.external.gmpy import gcd, invert, sqrt
+from sympy.utilities.misc import as_int
+from .generate import sieve, primerange
+from .primetest import isprime
+
+
+#----------------------------------------------------------------------------#
+#                                                                            #
+#                   Lenstra's Elliptic Curve Factorization                   #
+#                                                                            #
+#----------------------------------------------------------------------------#
+
+
+class Point:
+    """Montgomery form of Points in an elliptic curve.
+    In this form, the addition and doubling of points
+    does not need any y-coordinate information thus
+    decreasing the number of operations.
+    Using Montgomery form we try to perform point addition
+    and doubling in least amount of multiplications.
+
+    The elliptic curve used here is of the form
+    (E : b*y**2*z = x**3 + a*x**2*z + x*z**2).
+    The a_24 parameter is equal to (a + 2)/4.
+
+    References
+    ==========
+
+    .. [1] Kris Gaj, Soonhak Kwon, Patrick Baier, Paul Kohlbrenner, Hoang Le, Mohammed Khaleeluddin, Ramakrishna Bachimanchi,
+           Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware,
+           Cryptographic Hardware and Embedded Systems - CHES 2006 (2006), pp. 119-133,
+           https://doi.org/10.1007/11894063_10
+           https://www.hyperelliptic.org/tanja/SHARCS/talks06/Gaj.pdf
+
+    """
+
+    def __init__(self, x_cord, z_cord, a_24, mod):
+        """
+        Initial parameters for the Point class.
+
+        Parameters
+        ==========
+
+        x_cord : X coordinate of the Point
+        z_cord : Z coordinate of the Point
+        a_24 : Parameter of the elliptic curve in Montgomery form
+        mod : modulus
+        """
+        self.x_cord = x_cord
+        self.z_cord = z_cord
+        self.a_24 = a_24
+        self.mod = mod
+
+    def __eq__(self, other):
+        """Two points are equal if X/Z of both points are equal
+        """
+        if self.a_24 != other.a_24 or self.mod != other.mod:
+            return False
+        return self.x_cord * other.z_cord % self.mod ==\
+            other.x_cord * self.z_cord % self.mod
+
+    def add(self, Q, diff):
+        """
+        Add two points self and Q where diff = self - Q. Moreover the assumption
+        is self.x_cord*Q.x_cord*(self.x_cord - Q.x_cord) != 0. This algorithm
+        requires 6 multiplications. Here the difference between the points
+        is already known and using this algorithm speeds up the addition
+        by reducing the number of multiplication required. Also in the
+        mont_ladder algorithm is constructed in a way so that the difference
+        between intermediate points is always equal to the initial point.
+        So, we always know what the difference between the point is.
+
+
+        Parameters
+        ==========
+
+        Q : point on the curve in Montgomery form
+        diff : self - Q
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.ecm import Point
+        >>> p1 = Point(11, 16, 7, 29)
+        >>> p2 = Point(13, 10, 7, 29)
+        >>> p3 = p2.add(p1, p1)
+        >>> p3.x_cord
+        23
+        >>> p3.z_cord
+        17
+        """
+        u = (self.x_cord - self.z_cord)*(Q.x_cord + Q.z_cord)
+        v = (self.x_cord + self.z_cord)*(Q.x_cord - Q.z_cord)
+        add, subt = u + v, u - v
+        x_cord = diff.z_cord * add * add % self.mod
+        z_cord = diff.x_cord * subt * subt % self.mod
+        return Point(x_cord, z_cord, self.a_24, self.mod)
+
+    def double(self):
+        """
+        Doubles a point in an elliptic curve in Montgomery form.
+        This algorithm requires 5 multiplications.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.ecm import Point
+        >>> p1 = Point(11, 16, 7, 29)
+        >>> p2 = p1.double()
+        >>> p2.x_cord
+        13
+        >>> p2.z_cord
+        10
+        """
+        u = pow(self.x_cord + self.z_cord, 2, self.mod)
+        v = pow(self.x_cord - self.z_cord, 2, self.mod)
+        diff = u - v
+        x_cord = u*v % self.mod
+        z_cord = diff*(v + self.a_24*diff) % self.mod
+        return Point(x_cord, z_cord, self.a_24, self.mod)
+
+    def mont_ladder(self, k):
+        """
+        Scalar multiplication of a point in Montgomery form
+        using Montgomery Ladder Algorithm.
+        A total of 11 multiplications are required in each step of this
+        algorithm.
+
+        Parameters
+        ==========
+
+        k : The positive integer multiplier
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.ecm import Point
+        >>> p1 = Point(11, 16, 7, 29)
+        >>> p3 = p1.mont_ladder(3)
+        >>> p3.x_cord
+        23
+        >>> p3.z_cord
+        17
+        """
+        Q = self
+        R = self.double()
+        for i in bin(k)[3:]:
+            if  i  == '1':
+                Q = R.add(Q, self)
+                R = R.double()
+            else:
+                R = Q.add(R, self)
+                Q = Q.double()
+        return Q
+
+
+def _ecm_one_factor(n, B1=10000, B2=100000, max_curve=200, seed=None):
+    """Returns one factor of n using
+    Lenstra's 2 Stage Elliptic curve Factorization
+    with Suyama's Parameterization. Here Montgomery
+    arithmetic is used for fast computation of addition
+    and doubling of points in elliptic curve.
+
+    Explanation
+    ===========
+
+    This ECM method considers elliptic curves in Montgomery
+    form (E : b*y**2*z = x**3 + a*x**2*z + x*z**2) and involves
+    elliptic curve operations (mod N), where the elements in
+    Z are reduced (mod N). Since N is not a prime, E over FF(N)
+    is not really an elliptic curve but we can still do point additions
+    and doubling as if FF(N) was a field.
+
+    Stage 1 : The basic algorithm involves taking a random point (P) on an
+    elliptic curve in FF(N). The compute k*P using Montgomery ladder algorithm.
+    Let q be an unknown factor of N. Then the order of the curve E, |E(FF(q))|,
+    might be a smooth number that divides k. Then we have k = l * |E(FF(q))|
+    for some l. For any point belonging to the curve E, |E(FF(q))|*P = O,
+    hence k*P = l*|E(FF(q))|*P. Thus kP.z_cord = 0 (mod q), and the unknownn
+    factor of N (q) can be recovered by taking gcd(kP.z_cord, N).
+
+    Stage 2 : This is a continuation of Stage 1 if k*P != O. The idea utilize
+    the fact that even if kP != 0, the value of k might miss just one large
+    prime divisor of |E(FF(q))|. In this case we only need to compute the
+    scalar multiplication by p to get p*k*P = O. Here a second bound B2
+    restrict the size of possible values of p.
+
+    Parameters
+    ==========
+
+    n : Number to be Factored. Assume that it is a composite number.
+    B1 : Stage 1 Bound. Must be an even number.
+    B2 : Stage 2 Bound. Must be an even number.
+    max_curve : Maximum number of curves generated
+
+    Returns
+    =======
+
+    integer | None : a non-trivial divisor of ``n``. ``None`` if not found
+
+    References
+    ==========
+
+    .. [1] Carl Pomerance, Richard Crandall, Prime Numbers: A Computational Perspective,
+           2nd Edition (2005), page 344, ISBN:978-0387252827
+    """
+    randint = _randint(seed)
+
+    # When calculating T, if (B1 - 2*D) is negative, it cannot be calculated.
+    D = min(sqrt(B2), B1 // 2 - 1)
+    sieve.extend(D)
+    beta = [0] * D
+    S = [0] * D
+    k = 1
+    for p in primerange(2, B1 + 1):
+        k *= pow(p, int(log(B1, p)))
+
+    # Pre-calculate the prime numbers to be used in stage 2.
+    # Using the fact that the x-coordinates of point P and its
+    # inverse -P coincide, the number of primes to be checked
+    # in stage 2 can be reduced.
+    deltas_list = []
+    for r in range(B1 + 2*D, B2 + 2*D, 4*D):
+        # d in deltas iff r+(2d+1) and/or r-(2d+1) is prime
+        deltas = {abs(q - r) >> 1 for q in primerange(r - 2*D, r + 2*D)}
+        deltas_list.append(list(deltas))
+
+    for _ in range(max_curve):
+        #Suyama's Parametrization
+        sigma = randint(6, n - 1)
+        u = (sigma**2 - 5) % n
+        v = (4*sigma) % n
+        u_3 = pow(u, 3, n)
+
+        try:
+            # We use the elliptic curve y**2 = x**3 + a*x**2 + x
+            # where a = pow(v - u, 3, n)*(3*u + v)*invert(4*u_3*v, n) - 2
+            # However, we do not declare a because it is more convenient
+            # to use a24 = (a + 2)*invert(4, n) in the calculation.
+            a24 = pow(v - u, 3, n)*(3*u + v)*invert(16*u_3*v, n) % n
+        except ZeroDivisionError:
+            #If the invert(16*u_3*v, n) doesn't exist (i.e., g != 1)
+            g = gcd(2*u_3*v, n)
+            #If g = n, try another curve
+            if g == n:
+                continue
+            return g
+
+        Q = Point(u_3, pow(v, 3, n), a24, n)
+        Q = Q.mont_ladder(k)
+        g = gcd(Q.z_cord, n)
+
+        #Stage 1 factor
+        if g != 1 and g != n:
+            return g
+        #Stage 1 failure. Q.z = 0, Try another curve
+        elif g == n:
+            continue
+
+        #Stage 2 - Improved Standard Continuation
+        S[0] = Q
+        Q2 = Q.double()
+        S[1] = Q2.add(Q, Q)
+        beta[0] = (S[0].x_cord*S[0].z_cord) % n
+        beta[1] = (S[1].x_cord*S[1].z_cord) % n
+        for d in range(2, D):
+            S[d] = S[d - 1].add(Q2, S[d - 2])
+            beta[d] = (S[d].x_cord*S[d].z_cord) % n
+        # i.e., S[i] = Q.mont_ladder(2*i + 1)
+
+        g = 1
+        W = Q.mont_ladder(4*D)
+        T = Q.mont_ladder(B1 - 2*D)
+        R = Q.mont_ladder(B1 + 2*D)
+        for deltas in deltas_list:
+            # R = Q.mont_ladder(r) where r in range(B1 + 2*D, B2 + 2*D, 4*D)
+            alpha = (R.x_cord*R.z_cord) % n
+            for delta in deltas:
+                # We want to calculate
+                # f = R.x_cord * S[delta].z_cord - S[delta].x_cord * R.z_cord
+                f = (R.x_cord - S[delta].x_cord)*\
+                    (R.z_cord + S[delta].z_cord) - alpha + beta[delta]
+                g = (g*f) % n
+            T, R = R, R.add(W, T)
+        g = gcd(n, g)
+
+        #Stage 2 Factor found
+        if g != 1 and g != n:
+            return g
+
+
+def ecm(n, B1=10000, B2=100000, max_curve=200, seed=1234):
+    """Performs factorization using Lenstra's Elliptic curve method.
+
+    This function repeatedly calls ``_ecm_one_factor`` to compute the factors
+    of n. First all the small factors are taken out using trial division.
+    Then ``_ecm_one_factor`` is used to compute one factor at a time.
+
+    Parameters
+    ==========
+
+    n : Number to be Factored
+    B1 : Stage 1 Bound. Must be an even number.
+    B2 : Stage 2 Bound. Must be an even number.
+    max_curve : Maximum number of curves generated
+    seed : Initialize pseudorandom generator
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import ecm
+    >>> ecm(25645121643901801)
+    {5394769, 4753701529}
+    >>> ecm(9804659461513846513)
+    {4641991, 2112166839943}
+    """
+    from .factor_ import _perfect_power
+    n = as_int(n)
+    if B1 % 2 != 0 or B2 % 2 != 0:
+        raise ValueError("both bounds must be even")
+    TF_LIMIT = 100000
+    factors = set()
+    for prime in sieve.primerange(2, TF_LIMIT):
+        if n % prime == 0:
+            factors.add(prime)
+            while(n % prime == 0):
+                n //= prime
+
+    queue = []
+    def check(m):
+        if isprime(m):
+            factors.add(m)
+            return
+        if result := _perfect_power(m, TF_LIMIT):
+            return check(result[0])
+        queue.append(m)
+    check(n)
+    while queue:
+        n = queue.pop()
+        factor = _ecm_one_factor(n, B1, B2, max_curve, seed)
+        if factor is None:
+            raise ValueError("Increase the bounds")
+        check(factor)
+        check(n // factor)
+    return factors
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/egyptian_fraction.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/egyptian_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a42540b372042f596808684fef8e3fc57935b74
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/egyptian_fraction.py
@@ -0,0 +1,223 @@
+from sympy.core.containers import Tuple
+from sympy.core.numbers import (Integer, Rational)
+from sympy.core.singleton import S
+import sympy.polys
+
+from math import gcd
+
+
+def egyptian_fraction(r, algorithm="Greedy"):
+    """
+    Return the list of denominators of an Egyptian fraction
+    expansion [1]_ of the said rational `r`.
+
+    Parameters
+    ==========
+
+    r : Rational or (p, q)
+        a positive rational number, ``p/q``.
+    algorithm : { "Greedy", "Graham Jewett", "Takenouchi", "Golomb" }, optional
+        Denotes the algorithm to be used (the default is "Greedy").
+
+    Examples
+    ========
+
+    >>> from sympy import Rational
+    >>> from sympy.ntheory.egyptian_fraction import egyptian_fraction
+    >>> egyptian_fraction(Rational(3, 7))
+    [3, 11, 231]
+    >>> egyptian_fraction((3, 7), "Graham Jewett")
+    [7, 8, 9, 56, 57, 72, 3192]
+    >>> egyptian_fraction((3, 7), "Takenouchi")
+    [4, 7, 28]
+    >>> egyptian_fraction((3, 7), "Golomb")
+    [3, 15, 35]
+    >>> egyptian_fraction((11, 5), "Golomb")
+    [1, 2, 3, 4, 9, 234, 1118, 2580]
+
+    See Also
+    ========
+
+    sympy.core.numbers.Rational
+
+    Notes
+    =====
+
+    Currently the following algorithms are supported:
+
+    1) Greedy Algorithm
+
+       Also called the Fibonacci-Sylvester algorithm [2]_.
+       At each step, extract the largest unit fraction less
+       than the target and replace the target with the remainder.
+
+       It has some distinct properties:
+
+       a) Given `p/q` in lowest terms, generates an expansion of maximum
+          length `p`. Even as the numerators get large, the number of
+          terms is seldom more than a handful.
+
+       b) Uses minimal memory.
+
+       c) The terms can blow up (standard examples of this are 5/121 and
+          31/311).  The denominator is at most squared at each step
+          (doubly-exponential growth) and typically exhibits
+          singly-exponential growth.
+
+    2) Graham Jewett Algorithm
+
+       The algorithm suggested by the result of Graham and Jewett.
+       Note that this has a tendency to blow up: the length of the
+       resulting expansion is always ``2**(x/gcd(x, y)) - 1``.  See [3]_.
+
+    3) Takenouchi Algorithm
+
+       The algorithm suggested by Takenouchi (1921).
+       Differs from the Graham-Jewett algorithm only in the handling
+       of duplicates.  See [3]_.
+
+    4) Golomb's Algorithm
+
+       A method given by Golumb (1962), using modular arithmetic and
+       inverses.  It yields the same results as a method using continued
+       fractions proposed by Bleicher (1972).  See [4]_.
+
+    If the given rational is greater than or equal to 1, a greedy algorithm
+    of summing the harmonic sequence 1/1 + 1/2 + 1/3 + ... is used, taking
+    all the unit fractions of this sequence until adding one more would be
+    greater than the given number.  This list of denominators is prefixed
+    to the result from the requested algorithm used on the remainder.  For
+    example, if r is 8/3, using the Greedy algorithm, we get [1, 2, 3, 4,
+    5, 6, 7, 14, 420], where the beginning of the sequence, [1, 2, 3, 4, 5,
+    6, 7] is part of the harmonic sequence summing to 363/140, leaving a
+    remainder of 31/420, which yields [14, 420] by the Greedy algorithm.
+    The result of egyptian_fraction(Rational(8, 3), "Golomb") is [1, 2, 3,
+    4, 5, 6, 7, 14, 574, 2788, 6460, 11590, 33062, 113820], and so on.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Egyptian_fraction
+    .. [2] https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions
+    .. [3] https://www.ics.uci.edu/~eppstein/numth/egypt/conflict.html
+    .. [4] https://web.archive.org/web/20180413004012/https://ami.ektf.hu/uploads/papers/finalpdf/AMI_42_from129to134.pdf
+
+    """
+
+    if not isinstance(r, Rational):
+        if isinstance(r, (Tuple, tuple)) and len(r) == 2:
+            r = Rational(*r)
+        else:
+            raise ValueError("Value must be a Rational or tuple of ints")
+    if r <= 0:
+        raise ValueError("Value must be positive")
+
+    # common cases that all methods agree on
+    x, y = r.as_numer_denom()
+    if y == 1 and x == 2:
+        return [Integer(i) for i in [1, 2, 3, 6]]
+    if x == y + 1:
+        return [S.One, y]
+
+    prefix, rem = egypt_harmonic(r)
+    if rem == 0:
+        return prefix
+    # work in Python ints
+    x, y = rem.p, rem.q
+    # assert x < y and gcd(x, y) = 1
+
+    if algorithm == "Greedy":
+        postfix = egypt_greedy(x, y)
+    elif algorithm == "Graham Jewett":
+        postfix = egypt_graham_jewett(x, y)
+    elif algorithm == "Takenouchi":
+        postfix = egypt_takenouchi(x, y)
+    elif algorithm == "Golomb":
+        postfix = egypt_golomb(x, y)
+    else:
+        raise ValueError("Entered invalid algorithm")
+    return prefix + [Integer(i) for i in postfix]
+
+
+def egypt_greedy(x, y):
+    # assumes gcd(x, y) == 1
+    if x == 1:
+        return [y]
+    else:
+        a = (-y) % x
+        b = y*(y//x + 1)
+        c = gcd(a, b)
+        if c > 1:
+            num, denom = a//c, b//c
+        else:
+            num, denom = a, b
+        return [y//x + 1] + egypt_greedy(num, denom)
+
+
+def egypt_graham_jewett(x, y):
+    # assumes gcd(x, y) == 1
+    l = [y] * x
+
+    # l is now a list of integers whose reciprocals sum to x/y.
+    # we shall now proceed to manipulate the elements of l without
+    # changing the reciprocated sum until all elements are unique.
+
+    while len(l) != len(set(l)):
+        l.sort()  # so the list has duplicates. find a smallest pair
+        for i in range(len(l) - 1):
+            if l[i] == l[i + 1]:
+                break
+        # we have now identified a pair of identical
+        # elements: l[i] and l[i + 1].
+        # now comes the application of the result of graham and jewett:
+        l[i + 1] = l[i] + 1
+        # and we just iterate that until the list has no duplicates.
+        l.append(l[i]*(l[i] + 1))
+    return sorted(l)
+
+
+def egypt_takenouchi(x, y):
+    # assumes gcd(x, y) == 1
+    # special cases for 3/y
+    if x == 3:
+        if y % 2 == 0:
+            return [y//2, y]
+        i = (y - 1)//2
+        j = i + 1
+        k = j + i
+        return [j, k, j*k]
+    l = [y] * x
+    while len(l) != len(set(l)):
+        l.sort()
+        for i in range(len(l) - 1):
+            if l[i] == l[i + 1]:
+                break
+        k = l[i]
+        if k % 2 == 0:
+            l[i] = l[i] // 2
+            del l[i + 1]
+        else:
+            l[i], l[i + 1] = (k + 1)//2, k*(k + 1)//2
+    return sorted(l)
+
+
+def egypt_golomb(x, y):
+    # assumes x < y and gcd(x, y) == 1
+    if x == 1:
+        return [y]
+    xp = sympy.polys.ZZ.invert(int(x), int(y))
+    rv = [xp*y]
+    rv.extend(egypt_golomb((x*xp - 1)//y, xp))
+    return sorted(rv)
+
+
+def egypt_harmonic(r):
+    # assumes r is Rational
+    rv = []
+    d = S.One
+    acc = S.Zero
+    while acc + 1/d <= r:
+        acc += 1/d
+        rv.append(d)
+        d += 1
+    return (rv, r - acc)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/elliptic_curve.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/elliptic_curve.py
new file mode 100644
index 0000000000000000000000000000000000000000..c969470a6c19a3d17e637529b6615eeba326e84a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/elliptic_curve.py
@@ -0,0 +1,397 @@
+from sympy.core.numbers import oo
+from sympy.core.symbol import symbols
+from sympy.polys.domains import FiniteField, QQ, RationalField, FF
+from sympy.polys.polytools import Poly
+from sympy.solvers.solvers import solve
+from sympy.utilities.iterables import is_sequence
+from sympy.utilities.misc import as_int
+from .factor_ import divisors
+from .residue_ntheory import polynomial_congruence
+
+
+class EllipticCurve:
+    """
+    Create the following Elliptic Curve over domain.
+
+    `y^{2} + a_{1} x y + a_{3} y = x^{3} + a_{2} x^{2} + a_{4} x + a_{6}`
+
+    The default domain is ``QQ``. If no coefficient ``a1``, ``a2``, ``a3``,
+    is given then it creates a curve with the following form:
+
+    `y^{2} = x^{3} + a_{4} x + a_{6}`
+
+    Examples
+    ========
+
+    References
+    ==========
+
+    .. [1] J. Silverman "A Friendly Introduction to Number Theory" Third Edition
+    .. [2] https://mathworld.wolfram.com/EllipticDiscriminant.html
+    .. [3] G. Hardy, E. Wright "An Introduction to the Theory of Numbers" Sixth Edition
+
+    """
+
+    def __init__(self, a4, a6, a1=0, a2=0, a3=0, modulus=0):
+        if modulus == 0:
+            domain = QQ
+        else:
+            domain = FF(modulus)
+        a1, a2, a3, a4, a6 = map(domain.convert, (a1, a2, a3, a4, a6))
+        self._domain = domain
+        self.modulus = modulus
+        # Calculate discriminant
+        b2 = a1**2 + 4 * a2
+        b4 = 2 * a4 + a1 * a3
+        b6 = a3**2 + 4 * a6
+        b8 = a1**2 * a6 + 4 * a2 * a6 - a1 * a3 * a4 + a2 * a3**2 - a4**2
+        self._b2, self._b4, self._b6, self._b8 = b2, b4, b6, b8
+        self._discrim = -b2**2 * b8 - 8 * b4**3 - 27 * b6**2 + 9 * b2 * b4 * b6
+        self._a1 = a1
+        self._a2 = a2
+        self._a3 = a3
+        self._a4 = a4
+        self._a6 = a6
+        x, y, z = symbols('x y z')
+        self.x, self.y, self.z = x, y, z
+        self._poly = Poly(y**2*z + a1*x*y*z + a3*y*z**2 - x**3 - a2*x**2*z - a4*x*z**2 - a6*z**3, domain=domain)
+        if isinstance(self._domain, FiniteField):
+            self._rank = 0
+        elif isinstance(self._domain, RationalField):
+            self._rank = None
+
+    def __call__(self, x, y, z=1):
+        return EllipticCurvePoint(x, y, z, self)
+
+    def __contains__(self, point):
+        if is_sequence(point):
+            if len(point) == 2:
+                z1 = 1
+            else:
+                z1 = point[2]
+            x1, y1 = point[:2]
+        elif isinstance(point, EllipticCurvePoint):
+            x1, y1, z1 = point.x, point.y, point.z
+        else:
+            raise ValueError('Invalid point.')
+        if self.characteristic == 0 and z1 == 0:
+            return True
+        return self._poly.subs({self.x: x1, self.y: y1, self.z: z1}) == 0
+
+    def __repr__(self):
+        return self._poly.__repr__()
+
+    def minimal(self):
+        """
+        Return minimal Weierstrass equation.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+
+        >>> e1 = EllipticCurve(-10, -20, 0, -1, 1)
+        >>> e1.minimal()
+        Poly(-x**3 + 13392*x*z**2 + y**2*z + 1080432*z**3, x, y, z, domain='QQ')
+
+        """
+        char = self.characteristic
+        if char == 2:
+            return self
+        if char == 3:
+            return EllipticCurve(self._b4/2, self._b6/4, a2=self._b2/4, modulus=self.modulus)
+        c4 = self._b2**2 - 24*self._b4
+        c6 = -self._b2**3 + 36*self._b2*self._b4 - 216*self._b6
+        return EllipticCurve(-27*c4, -54*c6, modulus=self.modulus)
+
+    def points(self):
+        """
+        Return points of curve over Finite Field.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+        >>> e2 = EllipticCurve(1, 1, 1, 1, 1, modulus=5)
+        >>> e2.points()
+        {(0, 2), (1, 4), (2, 0), (2, 2), (3, 0), (3, 1), (4, 0)}
+
+        """
+
+        char = self.characteristic
+        all_pt = set()
+        if char >= 1:
+            for i in range(char):
+                congruence_eq = self._poly.subs({self.x: i, self.z: 1}).expr
+                sol = polynomial_congruence(congruence_eq, char)
+                all_pt.update((i, num) for num in sol)
+            return all_pt
+        else:
+            raise ValueError("Infinitely many points")
+
+    def points_x(self, x):
+        """Returns points on the curve for the given x-coordinate."""
+        pt = []
+        if self._domain == QQ:
+            for y in solve(self._poly.subs(self.x, x)):
+                pt.append((x, y))
+        else:
+            congruence_eq = self._poly.subs({self.x: x, self.z: 1}).expr
+            for y in polynomial_congruence(congruence_eq, self.characteristic):
+                pt.append((x, y))
+        return pt
+
+    def torsion_points(self):
+        """
+        Return torsion points of curve over Rational number.
+
+        Return point objects those are finite order.
+        According to Nagell-Lutz theorem, torsion point p(x, y)
+        x and y are integers, either y = 0 or y**2 is divisor
+        of discriminent. According to Mazur's theorem, there are
+        at most 15 points in torsion collection.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+        >>> e2 = EllipticCurve(-43, 166)
+        >>> sorted(e2.torsion_points())
+        [(-5, -16), (-5, 16), O, (3, -8), (3, 8), (11, -32), (11, 32)]
+
+        """
+        if self.characteristic > 0:
+            raise ValueError("No torsion point for Finite Field.")
+        l = [EllipticCurvePoint.point_at_infinity(self)]
+        for xx in solve(self._poly.subs({self.y: 0, self.z: 1})):
+            if xx.is_rational:
+                l.append(self(xx, 0))
+        for i in divisors(self.discriminant, generator=True):
+            j = int(i**.5)
+            if j**2 == i:
+                for xx in solve(self._poly.subs({self.y: j, self.z: 1})):
+                    if not xx.is_rational:
+                        continue
+                    p = self(xx, j)
+                    if p.order() != oo:
+                        l.extend([p, -p])
+        return l
+
+    @property
+    def characteristic(self):
+        """
+        Return domain characteristic.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+        >>> e2 = EllipticCurve(-43, 166)
+        >>> e2.characteristic
+        0
+
+        """
+        return self._domain.characteristic()
+
+    @property
+    def discriminant(self):
+        """
+        Return curve discriminant.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+        >>> e2 = EllipticCurve(0, 17)
+        >>> e2.discriminant
+        -124848
+
+        """
+        return int(self._discrim)
+
+    @property
+    def is_singular(self):
+        """
+        Return True if curve discriminant is equal to zero.
+        """
+        return self.discriminant == 0
+
+    @property
+    def j_invariant(self):
+        """
+        Return curve j-invariant.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+        >>> e1 = EllipticCurve(-2, 0, 0, 1, 1)
+        >>> e1.j_invariant
+        1404928/389
+
+        """
+        c4 = self._b2**2 - 24*self._b4
+        return self._domain.to_sympy(c4**3 / self._discrim)
+
+    @property
+    def order(self):
+        """
+        Number of points in Finite field.
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+        >>> e2 = EllipticCurve(1, 0, modulus=19)
+        >>> e2.order
+        19
+
+        """
+        if self.characteristic == 0:
+            raise NotImplementedError("Still not implemented")
+        return len(self.points())
+
+    @property
+    def rank(self):
+        """
+        Number of independent points of infinite order.
+
+        For Finite field, it must be 0.
+        """
+        if self._rank is not None:
+            return self._rank
+        raise NotImplementedError("Still not implemented")
+
+
+class EllipticCurvePoint:
+    """
+    Point of Elliptic Curve
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.elliptic_curve import EllipticCurve
+    >>> e1 = EllipticCurve(-17, 16)
+    >>> p1 = e1(0, -4, 1)
+    >>> p2 = e1(1, 0)
+    >>> p1 + p2
+    (15, -56)
+    >>> e3 = EllipticCurve(-1, 9)
+    >>> e3(1, -3) * 3
+    (664/169, 17811/2197)
+    >>> (e3(1, -3) * 3).order()
+    oo
+    >>> e2 = EllipticCurve(-2, 0, 0, 1, 1)
+    >>> p = e2(-1,1)
+    >>> q = e2(0, -1)
+    >>> p+q
+    (4, 8)
+    >>> p-q
+    (1, 0)
+    >>> 3*p-5*q
+    (328/361, -2800/6859)
+    """
+
+    @staticmethod
+    def point_at_infinity(curve):
+        return EllipticCurvePoint(0, 1, 0, curve)
+
+    def __init__(self, x, y, z, curve):
+        dom = curve._domain.convert
+        self.x = dom(x)
+        self.y = dom(y)
+        self.z = dom(z)
+        self._curve = curve
+        self._domain = self._curve._domain
+        if not self._curve.__contains__(self):
+            raise ValueError("The curve does not contain this point")
+
+    def __add__(self, p):
+        if self.z == 0:
+            return p
+        if p.z == 0:
+            return self
+        x1, y1 = self.x/self.z, self.y/self.z
+        x2, y2 = p.x/p.z, p.y/p.z
+        a1 = self._curve._a1
+        a2 = self._curve._a2
+        a3 = self._curve._a3
+        a4 = self._curve._a4
+        a6 = self._curve._a6
+        if x1 != x2:
+            slope = (y1 - y2) / (x1 - x2)
+            yint = (y1 * x2 - y2 * x1) / (x2 - x1)
+        else:
+            if (y1 + y2) == 0:
+                return self.point_at_infinity(self._curve)
+            slope = (3 * x1**2 + 2*a2*x1 + a4 - a1*y1) / (a1 * x1 + a3 + 2 * y1)
+            yint = (-x1**3 + a4*x1 + 2*a6 - a3*y1) / (a1*x1 + a3 + 2*y1)
+        x3 = slope**2 + a1*slope - a2 - x1 - x2
+        y3 = -(slope + a1) * x3 - yint - a3
+        return self._curve(x3, y3, 1)
+
+    def __lt__(self, other):
+        return (self.x, self.y, self.z) < (other.x, other.y, other.z)
+
+    def __mul__(self, n):
+        n = as_int(n)
+        r = self.point_at_infinity(self._curve)
+        if n == 0:
+            return r
+        if n < 0:
+            return -self * -n
+        p = self
+        while n:
+            if n & 1:
+                r = r + p
+            n >>= 1
+            p = p + p
+        return r
+
+    def __rmul__(self, n):
+        return self * n
+
+    def __neg__(self):
+        return EllipticCurvePoint(self.x, -self.y - self._curve._a1*self.x - self._curve._a3, self.z, self._curve)
+
+    def __repr__(self):
+        if self.z == 0:
+            return 'O'
+        dom = self._curve._domain
+        try:
+            return '({}, {})'.format(dom.to_sympy(self.x), dom.to_sympy(self.y))
+        except TypeError:
+            pass
+        return '({}, {})'.format(self.x, self.y)
+
+    def __sub__(self, other):
+        return self.__add__(-other)
+
+    def order(self):
+        """
+        Return point order n where nP = 0.
+
+        """
+        if self.z == 0:
+            return 1
+        if self.y == 0:  # P = -P
+            return 2
+        p = self * 2
+        if p.y == -self.y:  # 2P = -P
+            return 3
+        i = 2
+        if self._domain != QQ:
+            while int(p.x) == p.x and int(p.y) == p.y:
+                p = self + p
+                i += 1
+                if p.z == 0:
+                    return i
+            return oo
+        while p.x.numerator == p.x and p.y.numerator == p.y:
+            p = self + p
+            i += 1
+            if i > 12:
+                return oo
+            if p.z == 0:
+                return i
+        return oo
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/factor_.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/factor_.py
new file mode 100644
index 0000000000000000000000000000000000000000..2dc6ac81c237f000e55014f5e170b27b41335786
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/factor_.py
@@ -0,0 +1,2841 @@
+"""
+Integer factorization
+"""
+from __future__ import annotations
+
+from bisect import bisect_left
+from collections import defaultdict, OrderedDict
+from collections.abc import MutableMapping
+import math
+
+from sympy.core.containers import Dict
+from sympy.core.mul import Mul
+from sympy.core.numbers import Rational, Integer
+from sympy.core.intfunc import num_digits
+from sympy.core.power import Pow
+from sympy.core.random import _randint
+from sympy.core.singleton import S
+from sympy.external.gmpy import (SYMPY_INTS, gcd, sqrt as isqrt,
+                                 sqrtrem, iroot, bit_scan1, remove)
+from .primetest import isprime, MERSENNE_PRIME_EXPONENTS, is_mersenne_prime
+from .generate import sieve, primerange, nextprime
+from .digits import digits
+from sympy.utilities.decorator import deprecated
+from sympy.utilities.iterables import flatten
+from sympy.utilities.misc import as_int, filldedent
+from .ecm import _ecm_one_factor
+
+
+def smoothness(n):
+    """
+    Return the B-smooth and B-power smooth values of n.
+
+    The smoothness of n is the largest prime factor of n; the power-
+    smoothness is the largest divisor raised to its multiplicity.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import smoothness
+    >>> smoothness(2**7*3**2)
+    (3, 128)
+    >>> smoothness(2**4*13)
+    (13, 16)
+    >>> smoothness(2)
+    (2, 2)
+
+    See Also
+    ========
+
+    factorint, smoothness_p
+    """
+
+    if n == 1:
+        return (1, 1)  # not prime, but otherwise this causes headaches
+    facs = factorint(n)
+    return max(facs), max(m**facs[m] for m in facs)
+
+
+def smoothness_p(n, m=-1, power=0, visual=None):
+    """
+    Return a list of [m, (p, (M, sm(p + m), psm(p + m)))...]
+    where:
+
+    1. p**M is the base-p divisor of n
+    2. sm(p + m) is the smoothness of p + m (m = -1 by default)
+    3. psm(p + m) is the power smoothness of p + m
+
+    The list is sorted according to smoothness (default) or by power smoothness
+    if power=1.
+
+    The smoothness of the numbers to the left (m = -1) or right (m = 1) of a
+    factor govern the results that are obtained from the p +/- 1 type factoring
+    methods.
+
+        >>> from sympy.ntheory.factor_ import smoothness_p, factorint
+        >>> smoothness_p(10431, m=1)
+        (1, [(3, (2, 2, 4)), (19, (1, 5, 5)), (61, (1, 31, 31))])
+        >>> smoothness_p(10431)
+        (-1, [(3, (2, 2, 2)), (19, (1, 3, 9)), (61, (1, 5, 5))])
+        >>> smoothness_p(10431, power=1)
+        (-1, [(3, (2, 2, 2)), (61, (1, 5, 5)), (19, (1, 3, 9))])
+
+    If visual=True then an annotated string will be returned:
+
+        >>> print(smoothness_p(21477639576571, visual=1))
+        p**i=4410317**1 has p-1 B=1787, B-pow=1787
+        p**i=4869863**1 has p-1 B=2434931, B-pow=2434931
+
+    This string can also be generated directly from a factorization dictionary
+    and vice versa:
+
+        >>> factorint(17*9)
+        {3: 2, 17: 1}
+        >>> smoothness_p(_)
+        'p**i=3**2 has p-1 B=2, B-pow=2\\np**i=17**1 has p-1 B=2, B-pow=16'
+        >>> smoothness_p(_)
+        {3: 2, 17: 1}
+
+    The table of the output logic is:
+
+        ====== ====== ======= =======
+        |              Visual
+        ------ ----------------------
+        Input  True   False   other
+        ====== ====== ======= =======
+        dict    str    tuple   str
+        str     str    tuple   dict
+        tuple   str    tuple   str
+        n       str    tuple   tuple
+        mul     str    tuple   tuple
+        ====== ====== ======= =======
+
+    See Also
+    ========
+
+    factorint, smoothness
+    """
+
+    # visual must be True, False or other (stored as None)
+    if visual in (1, 0):
+        visual = bool(visual)
+    elif visual not in (True, False):
+        visual = None
+
+    if isinstance(n, str):
+        if visual:
+            return n
+        d = {}
+        for li in n.splitlines():
+            k, v = [int(i) for i in
+                    li.split('has')[0].split('=')[1].split('**')]
+            d[k] = v
+        if visual is not True and visual is not False:
+            return d
+        return smoothness_p(d, visual=False)
+    elif not isinstance(n, tuple):
+        facs = factorint(n, visual=False)
+
+    if power:
+        k = -1
+    else:
+        k = 1
+    if isinstance(n, tuple):
+        rv = n
+    else:
+        rv = (m, sorted([(f,
+                          tuple([M] + list(smoothness(f + m))))
+                         for f, M in list(facs.items())],
+                        key=lambda x: (x[1][k], x[0])))
+
+    if visual is False or (visual is not True) and (type(n) in [int, Mul]):
+        return rv
+    lines = []
+    for dat in rv[1]:
+        dat = flatten(dat)
+        dat.insert(2, m)
+        lines.append('p**i=%i**%i has p%+i B=%i, B-pow=%i' % tuple(dat))
+    return '\n'.join(lines)
+
+
+def multiplicity(p, n):
+    """
+    Find the greatest integer m such that p**m divides n.
+
+    Examples
+    ========
+
+    >>> from sympy import multiplicity, Rational
+    >>> [multiplicity(5, n) for n in [8, 5, 25, 125, 250]]
+    [0, 1, 2, 3, 3]
+    >>> multiplicity(3, Rational(1, 9))
+    -2
+
+    Note: when checking for the multiplicity of a number in a
+    large factorial it is most efficient to send it as an unevaluated
+    factorial or to call ``multiplicity_in_factorial`` directly:
+
+    >>> from sympy.ntheory import multiplicity_in_factorial
+    >>> from sympy import factorial
+    >>> p = factorial(25)
+    >>> n = 2**100
+    >>> nfac = factorial(n, evaluate=False)
+    >>> multiplicity(p, nfac)
+    52818775009509558395695966887
+    >>> _ == multiplicity_in_factorial(p, n)
+    True
+
+    See Also
+    ========
+
+    trailing
+
+    """
+    try:
+        p, n = as_int(p), as_int(n)
+    except ValueError:
+        from sympy.functions.combinatorial.factorials import factorial
+        if all(isinstance(i, (SYMPY_INTS, Rational)) for i in (p, n)):
+            p = Rational(p)
+            n = Rational(n)
+            if p.q == 1:
+                if n.p == 1:
+                    return -multiplicity(p.p, n.q)
+                return multiplicity(p.p, n.p) - multiplicity(p.p, n.q)
+            elif p.p == 1:
+                return multiplicity(p.q, n.q)
+            else:
+                like = min(
+                    multiplicity(p.p, n.p),
+                    multiplicity(p.q, n.q))
+                cross = min(
+                    multiplicity(p.q, n.p),
+                    multiplicity(p.p, n.q))
+                return like - cross
+        elif (isinstance(p, (SYMPY_INTS, Integer)) and
+                isinstance(n, factorial) and
+                isinstance(n.args[0], Integer) and
+                n.args[0] >= 0):
+            return multiplicity_in_factorial(p, n.args[0])
+        raise ValueError('expecting ints or fractions, got %s and %s' % (p, n))
+
+    if n == 0:
+        raise ValueError('no such integer exists: multiplicity of %s is not-defined' %(n))
+    return remove(n, p)[1]
+
+
+def multiplicity_in_factorial(p, n):
+    """return the largest integer ``m`` such that ``p**m`` divides ``n!``
+    without calculating the factorial of ``n``.
+
+    Parameters
+    ==========
+
+    p : Integer
+        positive integer
+    n : Integer
+        non-negative integer
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import multiplicity_in_factorial
+    >>> from sympy import factorial
+
+    >>> multiplicity_in_factorial(2, 3)
+    1
+
+    An instructive use of this is to tell how many trailing zeros
+    a given factorial has. For example, there are 6 in 25!:
+
+    >>> factorial(25)
+    15511210043330985984000000
+    >>> multiplicity_in_factorial(10, 25)
+    6
+
+    For large factorials, it is much faster/feasible to use
+    this function rather than computing the actual factorial:
+
+    >>> multiplicity_in_factorial(factorial(25), 2**100)
+    52818775009509558395695966887
+
+    See Also
+    ========
+
+    multiplicity
+
+    """
+
+    p, n = as_int(p), as_int(n)
+
+    if p <= 0:
+        raise ValueError('expecting positive integer got %s' % p )
+
+    if n < 0:
+        raise ValueError('expecting non-negative integer got %s' % n )
+
+    # keep only the largest of a given multiplicity since those
+    # of a given multiplicity will be goverened by the behavior
+    # of the largest factor
+    f = defaultdict(int)
+    for k, v in factorint(p).items():
+        f[v] = max(k, f[v])
+    # multiplicity of p in n! depends on multiplicity
+    # of prime `k` in p, so we floor divide by `v`
+    # and keep it if smaller than the multiplicity of p
+    # seen so far
+    return min((n + k - sum(digits(n, k)))//(k - 1)//v for v, k in f.items())
+
+
+def _perfect_power(n, next_p=2):
+    """ Return integers ``(b, e)`` such that ``n == b**e`` if ``n`` is a unique
+    perfect power with ``e > 1``, else ``False`` (e.g. 1 is not a perfect power).
+
+    Explanation
+    ===========
+
+    This is a low-level helper for ``perfect_power``, for internal use.
+
+    Parameters
+    ==========
+
+    n : int
+        assume that n is a nonnegative integer
+    next_p : int
+        Assume that n has no factor less than next_p.
+        i.e., all(n % p for p in range(2, next_p)) is True
+
+    Examples
+    ========
+    >>> from sympy.ntheory.factor_ import _perfect_power
+    >>> _perfect_power(16)
+    (2, 4)
+    >>> _perfect_power(17)
+    False
+
+    """
+    if n <= 3:
+        return False
+
+    factors = {}
+    g = 0
+    multi = 1
+
+    def done(n, factors, g, multi):
+        g = gcd(g, multi)
+        if g == 1:
+            return False
+        factors[n] = multi
+        return math.prod(p**(e//g) for p, e in factors.items()), g
+
+    # If n is small, only trial factoring is faster
+    if n <= 1_000_000:
+        n = _factorint_small(factors, n, 1_000, 1_000, next_p)[0]
+        if n > 1:
+            return False
+        g = gcd(*factors.values())
+        if g == 1:
+            return False
+        return math.prod(p**(e//g) for p, e in factors.items()), g
+
+    # divide by 2
+    if next_p < 3:
+        g = bit_scan1(n)
+        if g:
+            if g == 1:
+                return False
+            n >>= g
+            factors[2] = g
+            if n == 1:
+                return 2, g
+            else:
+                # If `m**g`, then we have found perfect power.
+                # Otherwise, there is no possibility of perfect power, especially if `g` is prime.
+                m, _exact = iroot(n, g)
+                if _exact:
+                    return 2*m, g
+                elif isprime(g):
+                    return False
+        next_p = 3
+
+    # square number?
+    while n & 7 == 1: # n % 8 == 1:
+        m, _exact = iroot(n, 2)
+        if _exact:
+            n = m
+            multi <<= 1
+        else:
+            break
+    if n < next_p**3:
+        return done(n, factors, g, multi)
+
+    # trial factoring
+    # Since the maximum value an exponent can take is `log_{next_p}(n)`,
+    # the number of exponents to be checked can be reduced by performing a trial factoring.
+    # The value of `tf_max` needs more consideration.
+    tf_max = n.bit_length()//27 + 24
+    if next_p < tf_max:
+        for p in primerange(next_p, tf_max):
+            m, t = remove(n, p)
+            if t:
+                n = m
+                t *= multi
+                _g = gcd(g, t)
+                if _g == 1:
+                    return False
+                factors[p] = t
+                if n == 1:
+                    return math.prod(p**(e//_g)
+                                        for p, e in factors.items()), _g
+                elif g == 0 or _g < g: # If g is updated
+                    g = _g
+                    m, _exact = iroot(n**multi, g)
+                    if _exact:
+                        return m * math.prod(p**(e//g)
+                                            for p, e in factors.items()), g
+                    elif isprime(g):
+                        return False
+        next_p = tf_max
+    if n < next_p**3:
+        return done(n, factors, g, multi)
+
+    # check iroot
+    if g:
+        # If g is non-zero, the exponent is a divisor of g.
+        # 2 can be omitted since it has already been checked.
+        prime_iter = sorted(factorint(g >> bit_scan1(g)).keys())
+    else:
+        # The maximum possible value of the exponent is `log_{next_p}(n)`.
+        # To compensate for the presence of computational error, 2 is added.
+        prime_iter = primerange(3, int(math.log(n, next_p)) + 2)
+    logn = math.log2(n)
+    threshold = logn / 40 # Threshold for direct calculation
+    for p in prime_iter:
+        if threshold < p:
+            # If p is large, find the power root p directly without `iroot`.
+            while True:
+                b = pow(2, logn / p)
+                rb = int(b + 0.5)
+                if abs(rb - b) < 0.01 and rb**p == n:
+                    n = rb
+                    multi *= p
+                    logn = math.log2(n)
+                else:
+                    break
+        else:
+            while True:
+                m, _exact = iroot(n, p)
+                if _exact:
+                    n = m
+                    multi *= p
+                    logn = math.log2(n)
+                else:
+                    break
+        if n < next_p**(p + 2):
+            break
+    return done(n, factors, g, multi)
+
+
+def perfect_power(n, candidates=None, big=True, factor=True):
+    """
+    Return ``(b, e)`` such that ``n`` == ``b**e`` if ``n`` is a unique
+    perfect power with ``e > 1``, else ``False`` (e.g. 1 is not a
+    perfect power). A ValueError is raised if ``n`` is not Rational.
+
+    By default, the base is recursively decomposed and the exponents
+    collected so the largest possible ``e`` is sought. If ``big=False``
+    then the smallest possible ``e`` (thus prime) will be chosen.
+
+    If ``factor=True`` then simultaneous factorization of ``n`` is
+    attempted since finding a factor indicates the only possible root
+    for ``n``. This is True by default since only a few small factors will
+    be tested in the course of searching for the perfect power.
+
+    The use of ``candidates`` is primarily for internal use; if provided,
+    False will be returned if ``n`` cannot be written as a power with one
+    of the candidates as an exponent and factoring (beyond testing for
+    a factor of 2) will not be attempted.
+
+    Examples
+    ========
+
+    >>> from sympy import perfect_power, Rational
+    >>> perfect_power(16)
+    (2, 4)
+    >>> perfect_power(16, big=False)
+    (4, 2)
+
+    Negative numbers can only have odd perfect powers:
+
+    >>> perfect_power(-4)
+    False
+    >>> perfect_power(-8)
+    (-2, 3)
+
+    Rationals are also recognized:
+
+    >>> perfect_power(Rational(1, 2)**3)
+    (1/2, 3)
+    >>> perfect_power(Rational(-3, 2)**3)
+    (-3/2, 3)
+
+    Notes
+    =====
+
+    To know whether an integer is a perfect power of 2 use
+
+        >>> is2pow = lambda n: bool(n and not n & (n - 1))
+        >>> [(i, is2pow(i)) for i in range(5)]
+        [(0, False), (1, True), (2, True), (3, False), (4, True)]
+
+    It is not necessary to provide ``candidates``. When provided
+    it will be assumed that they are ints. The first one that is
+    larger than the computed maximum possible exponent will signal
+    failure for the routine.
+
+        >>> perfect_power(3**8, [9])
+        False
+        >>> perfect_power(3**8, [2, 4, 8])
+        (3, 8)
+        >>> perfect_power(3**8, [4, 8], big=False)
+        (9, 4)
+
+    See Also
+    ========
+    sympy.core.intfunc.integer_nthroot
+    sympy.ntheory.primetest.is_square
+    """
+    # negative handling
+    if n < 0:
+        if candidates is None:
+            pp = perfect_power(-n, big=True, factor=factor)
+            if not pp:
+                return False
+
+            b, e = pp
+            e2 = e & (-e)
+            b, e = b ** e2, e // e2
+
+            if e <= 1:
+                return False
+
+            if big or isprime(e):
+                return -b, e
+
+            for p in primerange(3, e + 1):
+                if e % p == 0:
+                    return - b ** (e // p), p
+
+        odd_candidates = {i for i in candidates if i % 2}
+        if not odd_candidates:
+            return False
+
+        pp = perfect_power(-n, odd_candidates, big, factor)
+        if pp:
+            return -pp[0], pp[1]
+
+        return False
+
+    # non-integer handling
+    if isinstance(n, Rational) and not isinstance(n, Integer):
+        p, q = n.p, n.q
+
+        if p == 1:
+            qq = perfect_power(q, candidates, big, factor)
+            return (S.One / qq[0], qq[1]) if qq is not False else False
+
+        if not (pp:=perfect_power(p, factor=factor)):
+            return False
+        if not (qq:=perfect_power(q, factor=factor)):
+            return False
+        (num_base, num_exp), (den_base, den_exp) = pp, qq
+
+        def compute_tuple(exponent):
+            """Helper to compute final result given an exponent"""
+            new_num = num_base ** (num_exp // exponent)
+            new_den = den_base ** (den_exp // exponent)
+            return n.func(new_num, new_den), exponent
+
+        if candidates:
+            valid_candidates = [i for i in candidates
+                                if num_exp % i == 0 and den_exp % i == 0]
+            if not valid_candidates:
+                return False
+
+            e = max(valid_candidates) if big else min(valid_candidates)
+            return compute_tuple(e)
+
+        g = math.gcd(num_exp, den_exp)
+        if g == 1:
+            return False
+
+        if big:
+            return compute_tuple(g)
+
+        e = next(p for p in primerange(2, g + 1) if g % p == 0)
+        return compute_tuple(e)
+
+    if candidates is not None:
+        candidates = set(candidates)
+
+    # positive integer handling
+    n = as_int(n)
+
+    if candidates is None and big:
+        return _perfect_power(n)
+
+    if n <= 3:
+        # no unique exponent for 0, 1
+        # 2 and 3 have exponents of 1
+        return False
+    logn = math.log2(n)
+    max_possible = int(logn) + 2  # only check values less than this
+    not_square = n % 10 in [2, 3, 7, 8]  # squares cannot end in 2, 3, 7, 8
+    min_possible = 2 + not_square
+    if not candidates:
+        candidates = primerange(min_possible, max_possible)
+    else:
+        candidates = sorted([i for i in candidates
+            if min_possible <= i < max_possible])
+        if n%2 == 0:
+            e = bit_scan1(n)
+            candidates = [i for i in candidates if e%i == 0]
+        if big:
+            candidates = reversed(candidates)
+        for e in candidates:
+            r, ok = iroot(n, e)
+            if ok:
+                return int(r), e
+        return False
+
+    def _factors():
+        rv = 2 + n % 2
+        while True:
+            yield rv
+            rv = nextprime(rv)
+
+    for fac, e in zip(_factors(), candidates):
+        # see if there is a factor present
+        if factor and n % fac == 0:
+            # find what the potential power is
+            e = remove(n, fac)[1]
+            # if it's a trivial power we are done
+            if e == 1:
+                return False
+
+            # maybe the e-th root of n is exact
+            r, exact = iroot(n, e)
+            if not exact:
+                # Having a factor, we know that e is the maximal
+                # possible value for a root of n.
+                # If n = fac**e*m can be written as a perfect
+                # power then see if m can be written as r**E where
+                # gcd(e, E) != 1 so n = (fac**(e//E)*r)**E
+                m = n//fac**e
+                rE = perfect_power(m, candidates=divisors(e, generator=True))
+                if not rE:
+                    return False
+                else:
+                    r, E = rE
+                    r, e = fac**(e//E)*r, E
+            if not big:
+                e0 = primefactors(e)
+                if e0[0] != e:
+                    r, e = r**(e//e0[0]), e0[0]
+            return int(r), e
+
+        # Weed out downright impossible candidates
+        if logn/e < 40:
+            b = 2.0**(logn/e)
+            if abs(int(b + 0.5) - b) > 0.01:
+                continue
+
+        # now see if the plausible e makes a perfect power
+        r, exact = iroot(n, e)
+        if exact:
+            if big:
+                m = perfect_power(r, big=big, factor=factor)
+                if m:
+                    r, e = m[0], e*m[1]
+            return int(r), e
+
+    return False
+
+
+class FactorCache(MutableMapping):
+    """ Provides a cache for prime factors.
+    ``factor_cache`` is pre-prepared as an instance of ``FactorCache``,
+    and ``factorint`` internally references it to speed up
+    the factorization of prime factors.
+
+    While cache is automatically added during the execution of ``factorint``,
+    users can also manually add prime factors independently.
+
+    >>> from sympy import factor_cache
+    >>> factor_cache[15] = 5
+
+    Furthermore, by customizing ``get_external``,
+    it is also possible to use external databases.
+    The following is an example using http://factordb.com .
+
+    .. code-block:: python
+
+        import requests
+        from sympy import factor_cache
+
+        def get_external(self, n: int) -> list[int] | None:
+            res = requests.get("http://factordb.com/api", params={"query": str(n)})
+            if res.status_code != requests.codes.ok:
+                return None
+            j = res.json()
+            if j.get("status") in ["FF", "P"]:
+                return list(int(p) for p, _ in j.get("factors"))
+
+        factor_cache.get_external = get_external
+
+    Be aware that writing this code will trigger internet access
+    to factordb.com when calling ``factorint``.
+
+    """
+    def __init__(self, maxsize: int | None = None):
+        self._cache: OrderedDict[int, int] = OrderedDict()
+        self.maxsize = maxsize
+
+    def __len__(self) -> int:
+        return len(self._cache)
+
+    def __contains__(self, n) -> bool:
+        return n in self._cache
+
+    def __getitem__(self, n: int) -> int:
+        factor = self.get(n)
+        if factor is None:
+            raise KeyError(f"{n} does not exist.")
+        return factor
+
+    def __setitem__(self, n: int, factor: int):
+        if not (1 < factor <= n and n % factor == 0 and isprime(factor)):
+            raise ValueError(f"{factor} is not a prime factor of {n}")
+        self._cache[n] = max(self._cache.get(n, 0), factor)
+        if self.maxsize is not None and len(self._cache) > self.maxsize:
+            self._cache.popitem(False)
+
+    def __delitem__(self, n: int):
+        if n not in self._cache:
+            raise KeyError(f"{n} does not exist.")
+        del self._cache[n]
+
+    def __iter__(self):
+        return self._cache.__iter__()
+
+    def cache_clear(self) -> None:
+        """ Clear the cache """
+        self._cache = OrderedDict()
+
+    @property
+    def maxsize(self) -> int | None:
+        """ Returns the maximum cache size; if ``None``, it is unlimited. """
+        return self._maxsize
+
+    @maxsize.setter
+    def maxsize(self, value: int | None) -> None:
+        if value is not None and value <= 0:
+            raise ValueError("maxsize must be None or a non-negative integer.")
+        self._maxsize = value
+        if value is not None:
+            while len(self._cache) > value:
+                self._cache.popitem(False)
+
+    def get(self, n: int, default=None):
+        """ Return the prime factor of ``n``.
+        If it does not exist in the cache, return the value of ``default``.
+        """
+        if n <= sieve._list[-1]:
+            if sieve._list[bisect_left(sieve._list, n)] == n:
+                return n
+        if n in self._cache:
+            self._cache.move_to_end(n)
+            return self._cache[n]
+        if factors := self.get_external(n):
+            self.add(n, factors)
+            return self._cache[n]
+        return default
+
+    def add(self, n: int, factors: list[int]) -> None:
+        for p in sorted(factors, reverse=True):
+            self[n] = p
+            n, _ = remove(n, p)
+
+    def get_external(self, n: int) -> list[int] | None:
+        return None
+
+
+factor_cache = FactorCache(maxsize=1000)
+
+
+def pollard_rho(n, s=2, a=1, retries=5, seed=1234, max_steps=None, F=None):
+    r"""
+    Use Pollard's rho method to try to extract a nontrivial factor
+    of ``n``. The returned factor may be a composite number. If no
+    factor is found, ``None`` is returned.
+
+    The algorithm generates pseudo-random values of x with a generator
+    function, replacing x with F(x). If F is not supplied then the
+    function x**2 + ``a`` is used. The first value supplied to F(x) is ``s``.
+    Upon failure (if ``retries`` is > 0) a new ``a`` and ``s`` will be
+    supplied; the ``a`` will be ignored if F was supplied.
+
+    The sequence of numbers generated by such functions generally have a
+    a lead-up to some number and then loop around back to that number and
+    begin to repeat the sequence, e.g. 1, 2, 3, 4, 5, 3, 4, 5 -- this leader
+    and loop look a bit like the Greek letter rho, and thus the name, 'rho'.
+
+    For a given function, very different leader-loop values can be obtained
+    so it is a good idea to allow for retries:
+
+    >>> from sympy.ntheory.generate import cycle_length
+    >>> n = 16843009
+    >>> F = lambda x:(2048*pow(x, 2, n) + 32767) % n
+    >>> for s in range(5):
+    ...     print('loop length = %4i; leader length = %3i' % next(cycle_length(F, s)))
+    ...
+    loop length = 2489; leader length =  43
+    loop length =   78; leader length = 121
+    loop length = 1482; leader length = 100
+    loop length = 1482; leader length = 286
+    loop length = 1482; leader length = 101
+
+    Here is an explicit example where there is a three element leadup to
+    a sequence of 3 numbers (11, 14, 4) that then repeat:
+
+    >>> x=2
+    >>> for i in range(9):
+    ...     print(x)
+    ...     x=(x**2+12)%17
+    ...
+    2
+    16
+    13
+    11
+    14
+    4
+    11
+    14
+    4
+    >>> next(cycle_length(lambda x: (x**2+12)%17, 2))
+    (3, 3)
+    >>> list(cycle_length(lambda x: (x**2+12)%17, 2, values=True))
+    [2, 16, 13, 11, 14, 4]
+
+    Instead of checking the differences of all generated values for a gcd
+    with n, only the kth and 2*kth numbers are checked, e.g. 1st and 2nd,
+    2nd and 4th, 3rd and 6th until it has been detected that the loop has been
+    traversed. Loops may be many thousands of steps long before rho finds a
+    factor or reports failure. If ``max_steps`` is specified, the iteration
+    is cancelled with a failure after the specified number of steps.
+
+    Examples
+    ========
+
+    >>> from sympy import pollard_rho
+    >>> n=16843009
+    >>> F=lambda x:(2048*pow(x,2,n) + 32767) % n
+    >>> pollard_rho(n, F=F)
+    257
+
+    Use the default setting with a bad value of ``a`` and no retries:
+
+    >>> pollard_rho(n, a=n-2, retries=0)
+
+    If retries is > 0 then perhaps the problem will correct itself when
+    new values are generated for a:
+
+    >>> pollard_rho(n, a=n-2, retries=1)
+    257
+
+    References
+    ==========
+
+    .. [1] Richard Crandall & Carl Pomerance (2005), "Prime Numbers:
+           A Computational Perspective", Springer, 2nd edition, 229-231
+
+    """
+    n = int(n)
+    if n < 5:
+        raise ValueError('pollard_rho should receive n > 4')
+    randint = _randint(seed + retries)
+    V = s
+    for i in range(retries + 1):
+        U = V
+        if not F:
+            F = lambda x: (pow(x, 2, n) + a) % n
+        j = 0
+        while 1:
+            if max_steps and (j > max_steps):
+                break
+            j += 1
+            U = F(U)
+            V = F(F(V))  # V is 2x further along than U
+            g = gcd(U - V, n)
+            if g == 1:
+                continue
+            if g == n:
+                break
+            return int(g)
+        V = randint(0, n - 1)
+        a = randint(1, n - 3)  # for x**2 + a, a%n should not be 0 or -2
+        F = None
+    return None
+
+
+def pollard_pm1(n, B=10, a=2, retries=0, seed=1234):
+    """
+    Use Pollard's p-1 method to try to extract a nontrivial factor
+    of ``n``. Either a divisor (perhaps composite) or ``None`` is returned.
+
+    The value of ``a`` is the base that is used in the test gcd(a**M - 1, n).
+    The default is 2.  If ``retries`` > 0 then if no factor is found after the
+    first attempt, a new ``a`` will be generated randomly (using the ``seed``)
+    and the process repeated.
+
+    Note: the value of M is lcm(1..B) = reduce(ilcm, range(2, B + 1)).
+
+    A search is made for factors next to even numbers having a power smoothness
+    less than ``B``. Choosing a larger B increases the likelihood of finding a
+    larger factor but takes longer. Whether a factor of n is found or not
+    depends on ``a`` and the power smoothness of the even number just less than
+    the factor p (hence the name p - 1).
+
+    Although some discussion of what constitutes a good ``a`` some
+    descriptions are hard to interpret. At the modular.math site referenced
+    below it is stated that if gcd(a**M - 1, n) = N then a**M % q**r is 1
+    for every prime power divisor of N. But consider the following:
+
+        >>> from sympy.ntheory.factor_ import smoothness_p, pollard_pm1
+        >>> n=257*1009
+        >>> smoothness_p(n)
+        (-1, [(257, (1, 2, 256)), (1009, (1, 7, 16))])
+
+    So we should (and can) find a root with B=16:
+
+        >>> pollard_pm1(n, B=16, a=3)
+        1009
+
+    If we attempt to increase B to 256 we find that it does not work:
+
+        >>> pollard_pm1(n, B=256)
+        >>>
+
+    But if the value of ``a`` is changed we find that only multiples of
+    257 work, e.g.:
+
+        >>> pollard_pm1(n, B=256, a=257)
+        1009
+
+    Checking different ``a`` values shows that all the ones that did not
+    work had a gcd value not equal to ``n`` but equal to one of the
+    factors:
+
+        >>> from sympy import ilcm, igcd, factorint, Pow
+        >>> M = 1
+        >>> for i in range(2, 256):
+        ...     M = ilcm(M, i)
+        ...
+        >>> set([igcd(pow(a, M, n) - 1, n) for a in range(2, 256) if
+        ...      igcd(pow(a, M, n) - 1, n) != n])
+        {1009}
+
+    But does aM % d for every divisor of n give 1?
+
+        >>> aM = pow(255, M, n)
+        >>> [(d, aM%Pow(*d.args)) for d in factorint(n, visual=True).args]
+        [(257**1, 1), (1009**1, 1)]
+
+    No, only one of them. So perhaps the principle is that a root will
+    be found for a given value of B provided that:
+
+    1) the power smoothness of the p - 1 value next to the root
+       does not exceed B
+    2) a**M % p != 1 for any of the divisors of n.
+
+    By trying more than one ``a`` it is possible that one of them
+    will yield a factor.
+
+    Examples
+    ========
+
+    With the default smoothness bound, this number cannot be cracked:
+
+        >>> from sympy.ntheory import pollard_pm1
+        >>> pollard_pm1(21477639576571)
+
+    Increasing the smoothness bound helps:
+
+        >>> pollard_pm1(21477639576571, B=2000)
+        4410317
+
+    Looking at the smoothness of the factors of this number we find:
+
+        >>> from sympy.ntheory.factor_ import smoothness_p, factorint
+        >>> print(smoothness_p(21477639576571, visual=1))
+        p**i=4410317**1 has p-1 B=1787, B-pow=1787
+        p**i=4869863**1 has p-1 B=2434931, B-pow=2434931
+
+    The B and B-pow are the same for the p - 1 factorizations of the divisors
+    because those factorizations had a very large prime factor:
+
+        >>> factorint(4410317 - 1)
+        {2: 2, 617: 1, 1787: 1}
+        >>> factorint(4869863-1)
+        {2: 1, 2434931: 1}
+
+    Note that until B reaches the B-pow value of 1787, the number is not cracked;
+
+        >>> pollard_pm1(21477639576571, B=1786)
+        >>> pollard_pm1(21477639576571, B=1787)
+        4410317
+
+    The B value has to do with the factors of the number next to the divisor,
+    not the divisors themselves. A worst case scenario is that the number next
+    to the factor p has a large prime divisisor or is a perfect power. If these
+    conditions apply then the power-smoothness will be about p/2 or p. The more
+    realistic is that there will be a large prime factor next to p requiring
+    a B value on the order of p/2. Although primes may have been searched for
+    up to this level, the p/2 is a factor of p - 1, something that we do not
+    know. The modular.math reference below states that 15% of numbers in the
+    range of 10**15 to 15**15 + 10**4 are 10**6 power smooth so a B of 10**6
+    will fail 85% of the time in that range. From 10**8 to 10**8 + 10**3 the
+    percentages are nearly reversed...but in that range the simple trial
+    division is quite fast.
+
+    References
+    ==========
+
+    .. [1] Richard Crandall & Carl Pomerance (2005), "Prime Numbers:
+           A Computational Perspective", Springer, 2nd edition, 236-238
+    .. [2] https://web.archive.org/web/20150716201437/http://modular.math.washington.edu/edu/2007/spring/ent/ent-html/node81.html
+    .. [3] https://www.cs.toronto.edu/~yuvalf/Factorization.pdf
+    """
+
+    n = int(n)
+    if n < 4 or B < 3:
+        raise ValueError('pollard_pm1 should receive n > 3 and B > 2')
+    randint = _randint(seed + B)
+
+    # computing a**lcm(1,2,3,..B) % n for B > 2
+    # it looks weird, but it's right: primes run [2, B]
+    # and the answer's not right until the loop is done.
+    for i in range(retries + 1):
+        aM = a
+        for p in sieve.primerange(2, B + 1):
+            e = int(math.log(B, p))
+            aM = pow(aM, pow(p, e), n)
+        g = gcd(aM - 1, n)
+        if 1 < g < n:
+            return int(g)
+
+        # get a new a:
+        # since the exponent, lcm(1..B), is even, if we allow 'a' to be 'n-1'
+        # then (n - 1)**even % n will be 1 which will give a g of 0 and 1 will
+        # give a zero, too, so we set the range as [2, n-2]. Some references
+        # say 'a' should be coprime to n, but either will detect factors.
+        a = randint(2, n - 2)
+
+
+def _trial(factors, n, candidates, verbose=False):
+    """
+    Helper function for integer factorization. Trial factors ``n`
+    against all integers given in the sequence ``candidates``
+    and updates the dict ``factors`` in-place. Returns the reduced
+    value of ``n`` and a flag indicating whether any factors were found.
+    """
+    if verbose:
+        factors0 = list(factors.keys())
+    nfactors = len(factors)
+    for d in candidates:
+        if n % d == 0:
+            if n != d:
+                factor_cache[n] = d
+            n, m = remove(n // d, d)
+            factors[d] = m + 1
+    if verbose:
+        for k in sorted(set(factors).difference(set(factors0))):
+            print(factor_msg % (k, factors[k]))
+    return int(n), len(factors) != nfactors
+
+
+def _check_termination(factors, n, limit, use_trial, use_rho, use_pm1,
+                       verbose, next_p):
+    """
+    Helper function for integer factorization. Checks if ``n``
+    is a prime or a perfect power, and in those cases updates the factorization.
+    """
+    if verbose:
+        print('Check for termination')
+    if n == 1:
+        if verbose:
+            print(complete_msg)
+        return True
+    if n < next_p**2 or isprime(n):
+        factor_cache[n] = n
+        factors[int(n)] = 1
+        if verbose:
+            print(complete_msg)
+        return True
+
+    # since we've already been factoring there is no need to do
+    # simultaneous factoring with the power check
+    p = _perfect_power(n, next_p)
+    if not p:
+        return False
+    base, exp = p
+    if base < next_p**2 or isprime(base):
+        factor_cache[n] = base
+        factors[base] = exp
+    else:
+        facs = factorint(base, limit, use_trial, use_rho, use_pm1,
+                         verbose=False)
+        for b, e in facs.items():
+            if verbose:
+                print(factor_msg % (b, e))
+            factors[b] = exp*e
+    if verbose:
+        print(complete_msg)
+    return True
+
+
+trial_int_msg = "Trial division with ints [%i ... %i] and fail_max=%i"
+trial_msg = "Trial division with primes [%i ... %i]"
+rho_msg = "Pollard's rho with retries %i, max_steps %i and seed %i"
+pm1_msg = "Pollard's p-1 with smoothness bound %i and seed %i"
+ecm_msg = "Elliptic Curve with B1 bound %i, B2 bound %i, num_curves %i"
+factor_msg = '\t%i ** %i'
+fermat_msg = 'Close factors satisfying Fermat condition found.'
+complete_msg = 'Factorization is complete.'
+
+
+def _factorint_small(factors, n, limit, fail_max, next_p=2):
+    """
+    Return the value of n and either a 0 (indicating that factorization up
+    to the limit was complete) or else the next near-prime that would have
+    been tested.
+
+    Factoring stops if there are fail_max unsuccessful tests in a row.
+
+    If factors of n were found they will be in the factors dictionary as
+    {factor: multiplicity} and the returned value of n will have had those
+    factors removed. The factors dictionary is modified in-place.
+
+    """
+
+    def done(n, d):
+        """return n, d if the sqrt(n) was not reached yet, else
+           n, 0 indicating that factoring is done.
+        """
+        if d*d <= n:
+            return n, d
+        return n, 0
+
+    limit2 = limit**2
+    threshold2 = min(n, limit2)
+
+    if next_p < 3:
+        if not n & 1:
+            m = bit_scan1(n)
+            factors[2] = m
+            n >>= m
+            threshold2 = min(n, limit2)
+        next_p = 3
+        if threshold2 < 9: # next_p**2 = 9
+            return done(n, next_p)
+
+    if next_p < 5:
+        if not n % 3:
+            n //= 3
+            m = 1
+            while not n % 3:
+                n //= 3
+                m += 1
+                if m == 20:
+                    n, mm = remove(n, 3)
+                    m += mm
+                    break
+            factors[3] = m
+            threshold2 = min(n, limit2)
+        next_p = 5
+        if threshold2 < 25: # next_p**2 = 25
+            return done(n, next_p)
+
+    # Because of the order of checks, starting from `min_p = 6k+5`,
+    # useless checks are caused.
+    # We want to calculate
+    # next_p += [-1, -2, 3, 2, 1, 0][next_p % 6]
+    p6 = next_p % 6
+    next_p += (-1 if p6 < 2 else 5) - p6
+
+    fails = 0
+    while fails < fail_max:
+        # next_p % 6 == 5
+        if n % next_p:
+            fails += 1
+        else:
+            n //= next_p
+            m = 1
+            while not n % next_p:
+                n //= next_p
+                m += 1
+                if m == 20:
+                    n, mm = remove(n, next_p)
+                    m += mm
+                    break
+            factors[next_p] = m
+            fails = 0
+            threshold2 = min(n, limit2)
+        next_p += 2
+        if threshold2 < next_p**2:
+            return done(n, next_p)
+
+        # next_p % 6 == 1
+        if n % next_p:
+            fails += 1
+        else:
+            n //= next_p
+            m = 1
+            while not n % next_p:
+                n //= next_p
+                m += 1
+                if m == 20:
+                    n, mm = remove(n, next_p)
+                    m += mm
+                    break
+            factors[next_p] = m
+            fails = 0
+            threshold2 = min(n, limit2)
+        next_p += 4
+        if threshold2 < next_p**2:
+            return done(n, next_p)
+    return done(n, next_p)
+
+
+def factorint(n, limit=None, use_trial=True, use_rho=True, use_pm1=True,
+              use_ecm=True, verbose=False, visual=None, multiple=False):
+    r"""
+    Given a positive integer ``n``, ``factorint(n)`` returns a dict containing
+    the prime factors of ``n`` as keys and their respective multiplicities
+    as values. For example:
+
+    >>> from sympy.ntheory import factorint
+    >>> factorint(2000)    # 2000 = (2**4) * (5**3)
+    {2: 4, 5: 3}
+    >>> factorint(65537)   # This number is prime
+    {65537: 1}
+
+    For input less than 2, factorint behaves as follows:
+
+        - ``factorint(1)`` returns the empty factorization, ``{}``
+        - ``factorint(0)`` returns ``{0:1}``
+        - ``factorint(-n)`` adds ``-1:1`` to the factors and then factors ``n``
+
+    Partial Factorization:
+
+    If ``limit`` (> 3) is specified, the search is stopped after performing
+    trial division up to (and including) the limit (or taking a
+    corresponding number of rho/p-1 steps). This is useful if one has
+    a large number and only is interested in finding small factors (if
+    any). Note that setting a limit does not prevent larger factors
+    from being found early; it simply means that the largest factor may
+    be composite. Since checking for perfect power is relatively cheap, it is
+    done regardless of the limit setting.
+
+    This number, for example, has two small factors and a huge
+    semi-prime factor that cannot be reduced easily:
+
+    >>> from sympy.ntheory import isprime
+    >>> a = 1407633717262338957430697921446883
+    >>> f = factorint(a, limit=10000)
+    >>> f == {991: 1, int(202916782076162456022877024859): 1, 7: 1}
+    True
+    >>> isprime(max(f))
+    False
+
+    This number has a small factor and a residual perfect power whose
+    base is greater than the limit:
+
+    >>> factorint(3*101**7, limit=5)
+    {3: 1, 101: 7}
+
+    List of Factors:
+
+    If ``multiple`` is set to ``True`` then a list containing the
+    prime factors including multiplicities is returned.
+
+    >>> factorint(24, multiple=True)
+    [2, 2, 2, 3]
+
+    Visual Factorization:
+
+    If ``visual`` is set to ``True``, then it will return a visual
+    factorization of the integer.  For example:
+
+    >>> from sympy import pprint
+    >>> pprint(factorint(4200, visual=True))
+     3  1  2  1
+    2 *3 *5 *7
+
+    Note that this is achieved by using the evaluate=False flag in Mul
+    and Pow. If you do other manipulations with an expression where
+    evaluate=False, it may evaluate.  Therefore, you should use the
+    visual option only for visualization, and use the normal dictionary
+    returned by visual=False if you want to perform operations on the
+    factors.
+
+    You can easily switch between the two forms by sending them back to
+    factorint:
+
+    >>> from sympy import Mul
+    >>> regular = factorint(1764); regular
+    {2: 2, 3: 2, 7: 2}
+    >>> pprint(factorint(regular))
+     2  2  2
+    2 *3 *7
+
+    >>> visual = factorint(1764, visual=True); pprint(visual)
+     2  2  2
+    2 *3 *7
+    >>> print(factorint(visual))
+    {2: 2, 3: 2, 7: 2}
+
+    If you want to send a number to be factored in a partially factored form
+    you can do so with a dictionary or unevaluated expression:
+
+    >>> factorint(factorint({4: 2, 12: 3})) # twice to toggle to dict form
+    {2: 10, 3: 3}
+    >>> factorint(Mul(4, 12, evaluate=False))
+    {2: 4, 3: 1}
+
+    The table of the output logic is:
+
+        ====== ====== ======= =======
+                       Visual
+        ------ ----------------------
+        Input  True   False   other
+        ====== ====== ======= =======
+        dict    mul    dict    mul
+        n       mul    dict    dict
+        mul     mul    dict    dict
+        ====== ====== ======= =======
+
+    Notes
+    =====
+
+    Algorithm:
+
+    The function switches between multiple algorithms. Trial division
+    quickly finds small factors (of the order 1-5 digits), and finds
+    all large factors if given enough time. The Pollard rho and p-1
+    algorithms are used to find large factors ahead of time; they
+    will often find factors of the order of 10 digits within a few
+    seconds:
+
+    >>> factors = factorint(12345678910111213141516)
+    >>> for base, exp in sorted(factors.items()):
+    ...     print('%s %s' % (base, exp))
+    ...
+    2 2
+    2507191691 1
+    1231026625769 1
+
+    Any of these methods can optionally be disabled with the following
+    boolean parameters:
+
+        - ``use_trial``: Toggle use of trial division
+        - ``use_rho``: Toggle use of Pollard's rho method
+        - ``use_pm1``: Toggle use of Pollard's p-1 method
+
+    ``factorint`` also periodically checks if the remaining part is
+    a prime number or a perfect power, and in those cases stops.
+
+    For unevaluated factorial, it uses Legendre's formula(theorem).
+
+
+    If ``verbose`` is set to ``True``, detailed progress is printed.
+
+    See Also
+    ========
+
+    smoothness, smoothness_p, divisors
+
+    """
+    if isinstance(n, Dict):
+        n = dict(n)
+    if multiple:
+        fac = factorint(n, limit=limit, use_trial=use_trial,
+                           use_rho=use_rho, use_pm1=use_pm1,
+                           verbose=verbose, visual=False, multiple=False)
+        factorlist = sum(([p] * fac[p] if fac[p] > 0 else [S.One/p]*(-fac[p])
+                               for p in sorted(fac)), [])
+        return factorlist
+
+    factordict = {}
+    if visual and not isinstance(n, (Mul, dict)):
+        factordict = factorint(n, limit=limit, use_trial=use_trial,
+                               use_rho=use_rho, use_pm1=use_pm1,
+                               verbose=verbose, visual=False)
+    elif isinstance(n, Mul):
+        factordict = {int(k): int(v) for k, v in
+            n.as_powers_dict().items()}
+    elif isinstance(n, dict):
+        factordict = n
+    if factordict and isinstance(n, (Mul, dict)):
+        # check it
+        for key in list(factordict.keys()):
+            if isprime(key):
+                continue
+            e = factordict.pop(key)
+            d = factorint(key, limit=limit, use_trial=use_trial, use_rho=use_rho,
+                          use_pm1=use_pm1, verbose=verbose, visual=False)
+            for k, v in d.items():
+                if k in factordict:
+                    factordict[k] += v*e
+                else:
+                    factordict[k] = v*e
+    if visual or (type(n) is dict and
+                  visual is not True and
+                  visual is not False):
+        if factordict == {}:
+            return S.One
+        if -1 in factordict:
+            factordict.pop(-1)
+            args = [S.NegativeOne]
+        else:
+            args = []
+        args.extend([Pow(*i, evaluate=False)
+                     for i in sorted(factordict.items())])
+        return Mul(*args, evaluate=False)
+    elif isinstance(n, (dict, Mul)):
+        return factordict
+
+    assert use_trial or use_rho or use_pm1 or use_ecm
+
+    from sympy.functions.combinatorial.factorials import factorial
+    if isinstance(n, factorial):
+        x = as_int(n.args[0])
+        if x >= 20:
+            factors = {}
+            m = 2 # to initialize the if condition below
+            for p in sieve.primerange(2, x + 1):
+                if m > 1:
+                    m, q = 0, x // p
+                    while q != 0:
+                        m += q
+                        q //= p
+                factors[p] = m
+            if factors and verbose:
+                for k in sorted(factors):
+                    print(factor_msg % (k, factors[k]))
+            if verbose:
+                print(complete_msg)
+            return factors
+        else:
+            # if n < 20!, direct computation is faster
+            # since it uses a lookup table
+            n = n.func(x)
+
+    n = as_int(n)
+    if limit:
+        limit = int(limit)
+        use_ecm = False
+
+    # special cases
+    if n < 0:
+        factors = factorint(
+            -n, limit=limit, use_trial=use_trial, use_rho=use_rho,
+            use_pm1=use_pm1, verbose=verbose, visual=False)
+        factors[-1] = 1
+        return factors
+
+    if limit and limit < 2:
+        if n == 1:
+            return {}
+        return {n: 1}
+    elif n < 10:
+        # doing this we are assured of getting a limit > 2
+        # when we have to compute it later
+        return [{0: 1}, {}, {2: 1}, {3: 1}, {2: 2}, {5: 1},
+                {2: 1, 3: 1}, {7: 1}, {2: 3}, {3: 2}][n]
+
+    factors = {}
+
+    # do simplistic factorization
+    if verbose:
+        sn = str(n)
+        if len(sn) > 50:
+            print('Factoring %s' % sn[:5] + \
+                  '..(%i other digits)..' % (len(sn) - 10) + sn[-5:])
+        else:
+            print('Factoring', n)
+
+    # this is the preliminary factorization for small factors
+    # We want to guarantee that there are no small prime factors,
+    # so we run even if `use_trial` is False.
+    small = 2**15
+    fail_max = 600
+    small = min(small, limit or small)
+    if verbose:
+        print(trial_int_msg % (2, small, fail_max))
+    n, next_p = _factorint_small(factors, n, small, fail_max)
+    if factors and verbose:
+        for k in sorted(factors):
+            print(factor_msg % (k, factors[k]))
+    if next_p == 0:
+        if n > 1:
+            factors[int(n)] = 1
+        if verbose:
+            print(complete_msg)
+        return factors
+    # Check if it exists in the cache
+    while p := factor_cache.get(n):
+        n, e = remove(n, p)
+        factors[int(p)] = int(e)
+    # first check if the simplistic run didn't finish
+    # because of the limit and check for a perfect
+    # power before exiting
+    if limit and next_p > limit:
+        if verbose:
+            print('Exceeded limit:', limit)
+        if _check_termination(factors, n, limit, use_trial,
+                              use_rho, use_pm1, verbose, next_p):
+            return factors
+        if n > 1:
+            factors[int(n)] = 1
+        return factors
+    if _check_termination(factors, n, limit, use_trial,
+                          use_rho, use_pm1, verbose, next_p):
+        return factors
+
+    # continue with more advanced factorization methods
+    # ...do a Fermat test since it's so easy and we need the
+    # square root anyway. Finding 2 factors is easy if they are
+    # "close enough." This is the big root equivalent of dividing by
+    # 2, 3, 5.
+    sqrt_n = isqrt(n)
+    a = sqrt_n + 1
+    # If `n % 4 == 1`, `a` must be odd for `a**2 - n` to be a square number.
+    if (n % 4 == 1) ^ (a & 1):
+        a += 1
+    a2 = a**2
+    b2 = a2 - n
+    for _ in range(3):
+        b, fermat = sqrtrem(b2)
+        if not fermat:
+            if verbose:
+                print(fermat_msg)
+            for r in [a - b, a + b]:
+                facs = factorint(r, limit=limit, use_trial=use_trial,
+                                 use_rho=use_rho, use_pm1=use_pm1,
+                                 verbose=verbose)
+                for k, v in facs.items():
+                    factors[k] = factors.get(k, 0) + v
+                factor_cache.add(n, facs)
+            if verbose:
+                print(complete_msg)
+            return factors
+        b2 += (a + 1) << 2  # equiv to (a + 2)**2 - n
+        a += 2
+
+    # these are the limits for trial division which will
+    # be attempted in parallel with pollard methods
+    low, high = next_p, 2*next_p
+
+    # add 1 to make sure limit is reached in primerange calls
+    _limit = (limit or sqrt_n) + 1
+    iteration = 0
+    while 1:
+        high_ = min(high, _limit)
+
+        # Trial division
+        if use_trial:
+            if verbose:
+                print(trial_msg % (low, high_))
+            ps = sieve.primerange(low, high_)
+            n, found_trial = _trial(factors, n, ps, verbose)
+            next_p = high_
+            if found_trial and _check_termination(factors, n, limit, use_trial,
+                                                  use_rho, use_pm1, verbose, next_p):
+                return factors
+        else:
+            found_trial = False
+
+        if high > _limit:
+            if verbose:
+                print('Exceeded limit:', _limit)
+            if n > 1:
+                factors[int(n)] = 1
+            if verbose:
+                print(complete_msg)
+            return factors
+
+        # Only used advanced methods when no small factors were found
+        if not found_trial:
+            # Pollard p-1
+            if use_pm1:
+                if verbose:
+                    print(pm1_msg % (low, high_))
+                c = pollard_pm1(n, B=low, seed=high_)
+                if c:
+                    if c < next_p**2 or isprime(c):
+                        ps = [c]
+                    else:
+                        ps = factorint(c, limit=limit,
+                                       use_trial=use_trial,
+                                       use_rho=use_rho,
+                                       use_pm1=use_pm1,
+                                       use_ecm=use_ecm,
+                                       verbose=verbose)
+                    n, _ = _trial(factors, n, ps, verbose=False)
+                    if _check_termination(factors, n, limit, use_trial,
+                                          use_rho, use_pm1, verbose, next_p):
+                        return factors
+
+            # Pollard rho
+            if use_rho:
+                if verbose:
+                    print(rho_msg % (1, low, high_))
+                c = pollard_rho(n, retries=1, max_steps=low, seed=high_)
+                if c:
+                    if c < next_p**2 or isprime(c):
+                        ps = [c]
+                    else:
+                        ps = factorint(c, limit=limit,
+                                       use_trial=use_trial,
+                                       use_rho=use_rho,
+                                       use_pm1=use_pm1,
+                                       use_ecm=use_ecm,
+                                       verbose=verbose)
+                    n, _ = _trial(factors, n, ps, verbose=False)
+                    if _check_termination(factors, n, limit, use_trial,
+                                          use_rho, use_pm1, verbose, next_p):
+                        return factors
+        # Use subexponential algorithms if use_ecm
+        # Use pollard algorithms for finding small factors for 3 iterations
+        # if after small factors the number of digits of n >= 25 then use ecm
+        iteration += 1
+        if use_ecm and iteration >= 3 and num_digits(n) >= 24:
+            break
+        low, high = high, high*2
+
+    B1 = 10000
+    B2 = 100*B1
+    num_curves = 50
+    while(1):
+        if verbose:
+            print(ecm_msg % (B1, B2, num_curves))
+        factor = _ecm_one_factor(n, B1, B2, num_curves, seed=B1)
+        if factor:
+            if factor < next_p**2 or isprime(factor):
+                ps = [factor]
+            else:
+                ps = factorint(factor, limit=limit,
+                           use_trial=use_trial,
+                           use_rho=use_rho,
+                           use_pm1=use_pm1,
+                           use_ecm=use_ecm,
+                           verbose=verbose)
+            n, _ = _trial(factors, n, ps, verbose=False)
+            if _check_termination(factors, n, limit, use_trial,
+                                  use_rho, use_pm1, verbose, next_p):
+                return factors
+        B1 *= 5
+        B2 = 100*B1
+        num_curves *= 4
+
+
+def factorrat(rat, limit=None, use_trial=True, use_rho=True, use_pm1=True,
+              verbose=False, visual=None, multiple=False):
+    r"""
+    Given a Rational ``r``, ``factorrat(r)`` returns a dict containing
+    the prime factors of ``r`` as keys and their respective multiplicities
+    as values. For example:
+
+    >>> from sympy import factorrat, S
+    >>> factorrat(S(8)/9)    # 8/9 = (2**3) * (3**-2)
+    {2: 3, 3: -2}
+    >>> factorrat(S(-1)/987)    # -1/789 = -1 * (3**-1) * (7**-1) * (47**-1)
+    {-1: 1, 3: -1, 7: -1, 47: -1}
+
+    Please see the docstring for ``factorint`` for detailed explanations
+    and examples of the following keywords:
+
+        - ``limit``: Integer limit up to which trial division is done
+        - ``use_trial``: Toggle use of trial division
+        - ``use_rho``: Toggle use of Pollard's rho method
+        - ``use_pm1``: Toggle use of Pollard's p-1 method
+        - ``verbose``: Toggle detailed printing of progress
+        - ``multiple``: Toggle returning a list of factors or dict
+        - ``visual``: Toggle product form of output
+    """
+    if multiple:
+        fac = factorrat(rat, limit=limit, use_trial=use_trial,
+                  use_rho=use_rho, use_pm1=use_pm1,
+                  verbose=verbose, visual=False, multiple=False)
+        factorlist = sum(([p] * fac[p] if fac[p] > 0 else [S.One/p]*(-fac[p])
+                               for p, _ in sorted(fac.items(),
+                                                        key=lambda elem: elem[0]
+                                                        if elem[1] > 0
+                                                        else 1/elem[0])), [])
+        return factorlist
+
+    f = factorint(rat.p, limit=limit, use_trial=use_trial,
+                  use_rho=use_rho, use_pm1=use_pm1,
+                  verbose=verbose).copy()
+    f = defaultdict(int, f)
+    for p, e in factorint(rat.q, limit=limit,
+                          use_trial=use_trial,
+                          use_rho=use_rho,
+                          use_pm1=use_pm1,
+                          verbose=verbose).items():
+        f[p] += -e
+
+    if len(f) > 1 and 1 in f:
+        del f[1]
+    if not visual:
+        return dict(f)
+    else:
+        if -1 in f:
+            f.pop(-1)
+            args = [S.NegativeOne]
+        else:
+            args = []
+        args.extend([Pow(*i, evaluate=False)
+                     for i in sorted(f.items())])
+        return Mul(*args, evaluate=False)
+
+
+def primefactors(n, limit=None, verbose=False, **kwargs):
+    """Return a sorted list of n's prime factors, ignoring multiplicity
+    and any composite factor that remains if the limit was set too low
+    for complete factorization. Unlike factorint(), primefactors() does
+    not return -1 or 0.
+
+    Parameters
+    ==========
+
+    n : integer
+    limit, verbose, **kwargs :
+        Additional keyword arguments to be passed to ``factorint``.
+        Since ``kwargs`` is new in version 1.13,
+        ``limit`` and ``verbose`` are retained for compatibility purposes.
+
+    Returns
+    =======
+
+    list(int) : List of prime numbers dividing ``n``
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import primefactors, factorint, isprime
+    >>> primefactors(6)
+    [2, 3]
+    >>> primefactors(-5)
+    [5]
+
+    >>> sorted(factorint(123456).items())
+    [(2, 6), (3, 1), (643, 1)]
+    >>> primefactors(123456)
+    [2, 3, 643]
+
+    >>> sorted(factorint(10000000001, limit=200).items())
+    [(101, 1), (99009901, 1)]
+    >>> isprime(99009901)
+    False
+    >>> primefactors(10000000001, limit=300)
+    [101]
+
+    See Also
+    ========
+
+    factorint, divisors
+
+    """
+    n = int(n)
+    kwargs.update({"visual": None, "multiple": False,
+                   "limit": limit, "verbose": verbose})
+    factors = sorted(factorint(n=n, **kwargs).keys())
+    # We want to calculate
+    # s = [f for f in factors if isprime(f)]
+    s = [f for f in factors[:-1:] if f not in [-1, 0, 1]]
+    if factors and isprime(factors[-1]):
+        s += [factors[-1]]
+    return s
+
+
+def _divisors(n, proper=False):
+    """Helper function for divisors which generates the divisors.
+
+    Parameters
+    ==========
+
+    n : int
+        a nonnegative integer
+    proper: bool
+        If `True`, returns the generator that outputs only the proper divisor (i.e., excluding n).
+
+    """
+    if n <= 1:
+        if not proper and n:
+            yield 1
+        return
+
+    factordict = factorint(n)
+    ps = sorted(factordict.keys())
+
+    def rec_gen(n=0):
+        if n == len(ps):
+            yield 1
+        else:
+            pows = [1]
+            for _ in range(factordict[ps[n]]):
+                pows.append(pows[-1] * ps[n])
+            yield from (p * q for q in rec_gen(n + 1) for p in pows)
+
+    if proper:
+        yield from (p for p in rec_gen() if p != n)
+    else:
+        yield from rec_gen()
+
+
+def divisors(n, generator=False, proper=False):
+    r"""
+    Return all divisors of n sorted from 1..n by default.
+    If generator is ``True`` an unordered generator is returned.
+
+    The number of divisors of n can be quite large if there are many
+    prime factors (counting repeated factors). If only the number of
+    factors is desired use divisor_count(n).
+
+    Examples
+    ========
+
+    >>> from sympy import divisors, divisor_count
+    >>> divisors(24)
+    [1, 2, 3, 4, 6, 8, 12, 24]
+    >>> divisor_count(24)
+    8
+
+    >>> list(divisors(120, generator=True))
+    [1, 2, 4, 8, 3, 6, 12, 24, 5, 10, 20, 40, 15, 30, 60, 120]
+
+    Notes
+    =====
+
+    This is a slightly modified version of Tim Peters referenced at:
+    https://stackoverflow.com/questions/1010381/python-factorization
+
+    See Also
+    ========
+
+    primefactors, factorint, divisor_count
+    """
+    rv = _divisors(as_int(abs(n)), proper)
+    return rv if generator else sorted(rv)
+
+
+def divisor_count(n, modulus=1, proper=False):
+    """
+    Return the number of divisors of ``n``. If ``modulus`` is not 1 then only
+    those that are divisible by ``modulus`` are counted. If ``proper`` is True
+    then the divisor of ``n`` will not be counted.
+
+    Examples
+    ========
+
+    >>> from sympy import divisor_count
+    >>> divisor_count(6)
+    4
+    >>> divisor_count(6, 2)
+    2
+    >>> divisor_count(6, proper=True)
+    3
+
+    See Also
+    ========
+
+    factorint, divisors, totient, proper_divisor_count
+
+    """
+
+    if not modulus:
+        return 0
+    elif modulus != 1:
+        n, r = divmod(n, modulus)
+        if r:
+            return 0
+    if n == 0:
+        return 0
+    n = Mul(*[v + 1 for k, v in factorint(n).items() if k > 1])
+    if n and proper:
+        n -= 1
+    return n
+
+
+def proper_divisors(n, generator=False):
+    """
+    Return all divisors of n except n, sorted by default.
+    If generator is ``True`` an unordered generator is returned.
+
+    Examples
+    ========
+
+    >>> from sympy import proper_divisors, proper_divisor_count
+    >>> proper_divisors(24)
+    [1, 2, 3, 4, 6, 8, 12]
+    >>> proper_divisor_count(24)
+    7
+    >>> list(proper_divisors(120, generator=True))
+    [1, 2, 4, 8, 3, 6, 12, 24, 5, 10, 20, 40, 15, 30, 60]
+
+    See Also
+    ========
+
+    factorint, divisors, proper_divisor_count
+
+    """
+    return divisors(n, generator=generator, proper=True)
+
+
+def proper_divisor_count(n, modulus=1):
+    """
+    Return the number of proper divisors of ``n``.
+
+    Examples
+    ========
+
+    >>> from sympy import proper_divisor_count
+    >>> proper_divisor_count(6)
+    3
+    >>> proper_divisor_count(6, modulus=2)
+    1
+
+    See Also
+    ========
+
+    divisors, proper_divisors, divisor_count
+
+    """
+    return divisor_count(n, modulus=modulus, proper=True)
+
+
+def _udivisors(n):
+    """Helper function for udivisors which generates the unitary divisors.
+
+    Parameters
+    ==========
+
+    n : int
+        a nonnegative integer
+
+    """
+    if n <= 1:
+        if n == 1:
+            yield 1
+        return
+
+    factorpows = [p**e for p, e in factorint(n).items()]
+    # We want to calculate
+    # yield from (math.prod(s) for s in powersets(factorpows))
+    for i in range(2**len(factorpows)):
+        d = 1
+        for k in range(i.bit_length()):
+            if i & 1:
+                d *= factorpows[k]
+            i >>= 1
+        yield d
+
+
+def udivisors(n, generator=False):
+    r"""
+    Return all unitary divisors of n sorted from 1..n by default.
+    If generator is ``True`` an unordered generator is returned.
+
+    The number of unitary divisors of n can be quite large if there are many
+    prime factors. If only the number of unitary divisors is desired use
+    udivisor_count(n).
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import udivisors, udivisor_count
+    >>> udivisors(15)
+    [1, 3, 5, 15]
+    >>> udivisor_count(15)
+    4
+
+    >>> sorted(udivisors(120, generator=True))
+    [1, 3, 5, 8, 15, 24, 40, 120]
+
+    See Also
+    ========
+
+    primefactors, factorint, divisors, divisor_count, udivisor_count
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Unitary_divisor
+    .. [2] https://mathworld.wolfram.com/UnitaryDivisor.html
+
+    """
+    rv = _udivisors(as_int(abs(n)))
+    return rv if generator else sorted(rv)
+
+
+def udivisor_count(n):
+    """
+    Return the number of unitary divisors of ``n``.
+
+    Parameters
+    ==========
+
+    n : integer
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import udivisor_count
+    >>> udivisor_count(120)
+    8
+
+    See Also
+    ========
+
+    factorint, divisors, udivisors, divisor_count, totient
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/UnitaryDivisorFunction.html
+
+    """
+
+    if n == 0:
+        return 0
+    return 2**len([p for p in factorint(n) if p > 1])
+
+
+def _antidivisors(n):
+    """Helper function for antidivisors which generates the antidivisors.
+
+    Parameters
+    ==========
+
+    n : int
+        a nonnegative integer
+
+    """
+    if n <= 2:
+        return
+    for d in _divisors(n):
+        y = 2*d
+        if n > y and n % y:
+            yield y
+    for d in _divisors(2*n-1):
+        if n > d >= 2 and n % d:
+            yield d
+    for d in _divisors(2*n+1):
+        if n > d >= 2 and n % d:
+            yield d
+
+
+def antidivisors(n, generator=False):
+    r"""
+    Return all antidivisors of n sorted from 1..n by default.
+
+    Antidivisors [1]_ of n are numbers that do not divide n by the largest
+    possible margin.  If generator is True an unordered generator is returned.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import antidivisors
+    >>> antidivisors(24)
+    [7, 16]
+
+    >>> sorted(antidivisors(128, generator=True))
+    [3, 5, 15, 17, 51, 85]
+
+    See Also
+    ========
+
+    primefactors, factorint, divisors, divisor_count, antidivisor_count
+
+    References
+    ==========
+
+    .. [1] definition is described in https://oeis.org/A066272/a066272a.html
+
+    """
+    rv = _antidivisors(as_int(abs(n)))
+    return rv if generator else sorted(rv)
+
+
+def antidivisor_count(n):
+    """
+    Return the number of antidivisors [1]_ of ``n``.
+
+    Parameters
+    ==========
+
+    n : integer
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import antidivisor_count
+    >>> antidivisor_count(13)
+    4
+    >>> antidivisor_count(27)
+    5
+
+    See Also
+    ========
+
+    factorint, divisors, antidivisors, divisor_count, totient
+
+    References
+    ==========
+
+    .. [1] formula from https://oeis.org/A066272
+
+    """
+
+    n = as_int(abs(n))
+    if n <= 2:
+        return 0
+    return divisor_count(2*n - 1) + divisor_count(2*n + 1) + \
+        divisor_count(n) - divisor_count(n, 2) - 5
+
+@deprecated("""\
+The `sympy.ntheory.factor_.totient` has been moved to `sympy.functions.combinatorial.numbers.totient`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def totient(n):
+    r"""
+    Calculate the Euler totient function phi(n)
+
+    .. deprecated:: 1.13
+
+        The ``totient`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.totient`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    ``totient(n)`` or `\phi(n)` is the number of positive integers `\leq` n
+    that are relatively prime to n.
+
+    Parameters
+    ==========
+
+    n : integer
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import totient
+    >>> totient(1)
+    1
+    >>> totient(25)
+    20
+    >>> totient(45) == totient(5)*totient(9)
+    True
+
+    See Also
+    ========
+
+    divisor_count
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler%27s_totient_function
+    .. [2] https://mathworld.wolfram.com/TotientFunction.html
+
+    """
+    from sympy.functions.combinatorial.numbers import totient as _totient
+    return _totient(n)
+
+
+@deprecated("""\
+The `sympy.ntheory.factor_.reduced_totient` has been moved to `sympy.functions.combinatorial.numbers.reduced_totient`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def reduced_totient(n):
+    r"""
+    Calculate the Carmichael reduced totient function lambda(n)
+
+    .. deprecated:: 1.13
+
+        The ``reduced_totient`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.reduced_totient`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    ``reduced_totient(n)`` or `\lambda(n)` is the smallest m > 0 such that
+    `k^m \equiv 1 \mod n` for all k relatively prime to n.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import reduced_totient
+    >>> reduced_totient(1)
+    1
+    >>> reduced_totient(8)
+    2
+    >>> reduced_totient(30)
+    4
+
+    See Also
+    ========
+
+    totient
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Carmichael_function
+    .. [2] https://mathworld.wolfram.com/CarmichaelFunction.html
+
+    """
+    from sympy.functions.combinatorial.numbers import reduced_totient as _reduced_totient
+    return _reduced_totient(n)
+
+
+@deprecated("""\
+The `sympy.ntheory.factor_.divisor_sigma` has been moved to `sympy.functions.combinatorial.numbers.divisor_sigma`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def divisor_sigma(n, k=1):
+    r"""
+    Calculate the divisor function `\sigma_k(n)` for positive integer n
+
+    .. deprecated:: 1.13
+
+        The ``divisor_sigma`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.divisor_sigma`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    ``divisor_sigma(n, k)`` is equal to ``sum([x**k for x in divisors(n)])``
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^\omega p_i^{m_i},
+
+    then
+
+    .. math ::
+        \sigma_k(n) = \prod_{i=1}^\omega (1+p_i^k+p_i^{2k}+\cdots
+        + p_i^{m_ik}).
+
+    Parameters
+    ==========
+
+    n : integer
+
+    k : integer, optional
+        power of divisors in the sum
+
+        for k = 0, 1:
+        ``divisor_sigma(n, 0)`` is equal to ``divisor_count(n)``
+        ``divisor_sigma(n, 1)`` is equal to ``sum(divisors(n))``
+
+        Default for k is 1.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import divisor_sigma
+    >>> divisor_sigma(18, 0)
+    6
+    >>> divisor_sigma(39, 1)
+    56
+    >>> divisor_sigma(12, 2)
+    210
+    >>> divisor_sigma(37)
+    38
+
+    See Also
+    ========
+
+    divisor_count, totient, divisors, factorint
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Divisor_function
+
+    """
+    from sympy.functions.combinatorial.numbers import divisor_sigma as func_divisor_sigma
+    return func_divisor_sigma(n, k)
+
+
+def _divisor_sigma(n:int, k:int=1) -> int:
+    r""" Calculate the divisor function `\sigma_k(n)` for positive integer n
+
+    Parameters
+    ==========
+
+    n : int
+        positive integer
+    k : int
+        nonnegative integer
+
+    See Also
+    ========
+
+    sympy.functions.combinatorial.numbers.divisor_sigma
+
+    """
+    if k == 0:
+        return math.prod(e + 1 for e in factorint(n).values())
+    return math.prod((p**(k*(e + 1)) - 1)//(p**k - 1) for p, e in factorint(n).items())
+
+
+def core(n, t=2):
+    r"""
+    Calculate core(n, t) = `core_t(n)` of a positive integer n
+
+    ``core_2(n)`` is equal to the squarefree part of n
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^\omega p_i^{m_i},
+
+    then
+
+    .. math ::
+        core_t(n) = \prod_{i=1}^\omega p_i^{m_i \mod t}.
+
+    Parameters
+    ==========
+
+    n : integer
+
+    t : integer
+        core(n, t) calculates the t-th power free part of n
+
+        ``core(n, 2)`` is the squarefree part of ``n``
+        ``core(n, 3)`` is the cubefree part of ``n``
+
+        Default for t is 2.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import core
+    >>> core(24, 2)
+    6
+    >>> core(9424, 3)
+    1178
+    >>> core(379238)
+    379238
+    >>> core(15**11, 10)
+    15
+
+    See Also
+    ========
+
+    factorint, sympy.solvers.diophantine.diophantine.square_factor
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Square-free_integer#Squarefree_core
+
+    """
+
+    n = as_int(n)
+    t = as_int(t)
+    if n <= 0:
+        raise ValueError("n must be a positive integer")
+    elif t <= 1:
+        raise ValueError("t must be >= 2")
+    else:
+        y = 1
+        for p, e in factorint(n).items():
+            y *= p**(e % t)
+        return y
+
+
+@deprecated("""\
+The `sympy.ntheory.factor_.udivisor_sigma` has been moved to `sympy.functions.combinatorial.numbers.udivisor_sigma`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def udivisor_sigma(n, k=1):
+    r"""
+    Calculate the unitary divisor function `\sigma_k^*(n)` for positive integer n
+
+    .. deprecated:: 1.13
+
+        The ``udivisor_sigma`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.udivisor_sigma`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    ``udivisor_sigma(n, k)`` is equal to ``sum([x**k for x in udivisors(n)])``
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^\omega p_i^{m_i},
+
+    then
+
+    .. math ::
+        \sigma_k^*(n) = \prod_{i=1}^\omega (1+ p_i^{m_ik}).
+
+    Parameters
+    ==========
+
+    k : power of divisors in the sum
+
+        for k = 0, 1:
+        ``udivisor_sigma(n, 0)`` is equal to ``udivisor_count(n)``
+        ``udivisor_sigma(n, 1)`` is equal to ``sum(udivisors(n))``
+
+        Default for k is 1.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import udivisor_sigma
+    >>> udivisor_sigma(18, 0)
+    4
+    >>> udivisor_sigma(74, 1)
+    114
+    >>> udivisor_sigma(36, 3)
+    47450
+    >>> udivisor_sigma(111)
+    152
+
+    See Also
+    ========
+
+    divisor_count, totient, divisors, udivisors, udivisor_count, divisor_sigma,
+    factorint
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/UnitaryDivisorFunction.html
+
+    """
+    from sympy.functions.combinatorial.numbers import udivisor_sigma as _udivisor_sigma
+    return _udivisor_sigma(n, k)
+
+
+@deprecated("""\
+The `sympy.ntheory.factor_.primenu` has been moved to `sympy.functions.combinatorial.numbers.primenu`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def primenu(n):
+    r"""
+    Calculate the number of distinct prime factors for a positive integer n.
+
+    .. deprecated:: 1.13
+
+        The ``primenu`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.primenu`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^k p_i^{m_i},
+
+    then ``primenu(n)`` or `\nu(n)` is:
+
+    .. math ::
+        \nu(n) = k.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import primenu
+    >>> primenu(1)
+    0
+    >>> primenu(30)
+    3
+
+    See Also
+    ========
+
+    factorint
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PrimeFactor.html
+
+    """
+    from sympy.functions.combinatorial.numbers import primenu as _primenu
+    return _primenu(n)
+
+
+@deprecated("""\
+The `sympy.ntheory.factor_.primeomega` has been moved to `sympy.functions.combinatorial.numbers.primeomega`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def primeomega(n):
+    r"""
+    Calculate the number of prime factors counting multiplicities for a
+    positive integer n.
+
+    .. deprecated:: 1.13
+
+        The ``primeomega`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.primeomega`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    If n's prime factorization is:
+
+    .. math ::
+        n = \prod_{i=1}^k p_i^{m_i},
+
+    then ``primeomega(n)``  or `\Omega(n)` is:
+
+    .. math ::
+        \Omega(n) = \sum_{i=1}^k m_i.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import primeomega
+    >>> primeomega(1)
+    0
+    >>> primeomega(20)
+    3
+
+    See Also
+    ========
+
+    factorint
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PrimeFactor.html
+
+    """
+    from sympy.functions.combinatorial.numbers import primeomega as _primeomega
+    return _primeomega(n)
+
+
+def mersenne_prime_exponent(nth):
+    """Returns the exponent ``i`` for the nth Mersenne prime (which
+    has the form `2^i - 1`).
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import mersenne_prime_exponent
+    >>> mersenne_prime_exponent(1)
+    2
+    >>> mersenne_prime_exponent(20)
+    4423
+    """
+    n = as_int(nth)
+    if n < 1:
+        raise ValueError("nth must be a positive integer; mersenne_prime_exponent(1) == 2")
+    if n > 51:
+        raise ValueError("There are only 51 perfect numbers; nth must be less than or equal to 51")
+    return MERSENNE_PRIME_EXPONENTS[n - 1]
+
+
+def is_perfect(n):
+    """Returns True if ``n`` is a perfect number, else False.
+
+    A perfect number is equal to the sum of its positive, proper divisors.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import divisor_sigma
+    >>> from sympy.ntheory.factor_ import is_perfect, divisors
+    >>> is_perfect(20)
+    False
+    >>> is_perfect(6)
+    True
+    >>> 6 == divisor_sigma(6) - 6 == sum(divisors(6)[:-1])
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PerfectNumber.html
+    .. [2] https://en.wikipedia.org/wiki/Perfect_number
+
+    """
+    n = as_int(n)
+    if n < 1:
+        return False
+    if n % 2 == 0:
+        m = (n.bit_length() + 1) >> 1
+        if (1 << (m - 1)) * ((1 << m) - 1) != n:
+            # Even perfect numbers must be of the form `2^{m-1}(2^m-1)`
+            return False
+        return m in MERSENNE_PRIME_EXPONENTS or is_mersenne_prime(2**m - 1)
+
+    # n is an odd integer
+    if n < 10**2000:  # https://www.lirmm.fr/~ochem/opn/
+        return False
+    if n % 105 == 0:  # not divis by 105
+        return False
+    if all(n % m != r for m, r in [(12, 1), (468, 117), (324, 81)]):
+        return False
+    # there are many criteria that the factor structure of n
+    # must meet; since we will have to factor it to test the
+    # structure we will have the factors and can then check
+    # to see whether it is a perfect number or not. So we
+    # skip the structure checks and go straight to the final
+    # test below.
+    result = abundance(n) == 0
+    if result:
+        raise ValueError(filldedent('''In 1888, Sylvester stated: "
+            ...a prolonged meditation on the subject has satisfied
+            me that the existence of any one such [odd perfect number]
+            -- its escape, so to say, from the complex web of conditions
+            which hem it in on all sides -- would be little short of a
+            miracle." I guess SymPy just found that miracle and it
+            factors like this: %s''' % factorint(n)))
+    return result
+
+
+def abundance(n):
+    """Returns the difference between the sum of the positive
+    proper divisors of a number and the number.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import abundance, is_perfect, is_abundant
+    >>> abundance(6)
+    0
+    >>> is_perfect(6)
+    True
+    >>> abundance(10)
+    -2
+    >>> is_abundant(10)
+    False
+    """
+    return _divisor_sigma(n) - 2 * n
+
+
+def is_abundant(n):
+    """Returns True if ``n`` is an abundant number, else False.
+
+    A abundant number is smaller than the sum of its positive proper divisors.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import is_abundant
+    >>> is_abundant(20)
+    True
+    >>> is_abundant(15)
+    False
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/AbundantNumber.html
+
+    """
+    n = as_int(n)
+    if is_perfect(n):
+        return False
+    return n % 6 == 0 or bool(abundance(n) > 0)
+
+
+def is_deficient(n):
+    """Returns True if ``n`` is a deficient number, else False.
+
+    A deficient number is greater than the sum of its positive proper divisors.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import is_deficient
+    >>> is_deficient(20)
+    False
+    >>> is_deficient(15)
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/DeficientNumber.html
+
+    """
+    n = as_int(n)
+    if is_perfect(n):
+        return False
+    return bool(abundance(n) < 0)
+
+
+def is_amicable(m, n):
+    """Returns True if the numbers `m` and `n` are "amicable", else False.
+
+    Amicable numbers are two different numbers so related that the sum
+    of the proper divisors of each is equal to that of the other.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import divisor_sigma
+    >>> from sympy.ntheory.factor_ import is_amicable
+    >>> is_amicable(220, 284)
+    True
+    >>> divisor_sigma(220) == divisor_sigma(284)
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Amicable_numbers
+
+    """
+    return m != n and m + n == _divisor_sigma(m) == _divisor_sigma(n)
+
+
+def is_carmichael(n):
+    """ Returns True if the numbers `n` is Carmichael number, else False.
+
+    Parameters
+    ==========
+
+    n : Integer
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Carmichael_number
+    .. [2] https://oeis.org/A002997
+
+    """
+    if n < 561:
+        return False
+    return n % 2 and not isprime(n) and \
+           all(e == 1 and (n - 1) % (p - 1) == 0 for p, e in factorint(n).items())
+
+
+def find_carmichael_numbers_in_range(x, y):
+    """ Returns a list of the number of Carmichael in the range
+
+    See Also
+    ========
+
+    is_carmichael
+
+    """
+    if 0 <= x <= y:
+        if x % 2 == 0:
+            return [i for i in range(x + 1, y, 2) if is_carmichael(i)]
+        else:
+            return [i for i in range(x, y, 2) if is_carmichael(i)]
+    else:
+        raise ValueError('The provided range is not valid. x and y must be non-negative integers and x <= y')
+
+
+def find_first_n_carmichaels(n):
+    """ Returns the first n Carmichael numbers.
+
+    Parameters
+    ==========
+
+    n : Integer
+
+    See Also
+    ========
+
+    is_carmichael
+
+    """
+    i = 561
+    carmichaels = []
+
+    while len(carmichaels) < n:
+        if is_carmichael(i):
+            carmichaels.append(i)
+        i += 2
+
+    return carmichaels
+
+
+def dra(n, b):
+    """
+    Returns the additive digital root of a natural number ``n`` in base ``b``
+    which is a single digit value obtained by an iterative process of summing
+    digits, on each iteration using the result from the previous iteration to
+    compute a digit sum.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import dra
+    >>> dra(3110, 12)
+    8
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Digital_root
+
+    """
+
+    num = abs(as_int(n))
+    b = as_int(b)
+    if b <= 1:
+        raise ValueError("Base should be an integer greater than 1")
+
+    if num == 0:
+        return 0
+
+    return (1 + (num - 1) % (b - 1))
+
+
+def drm(n, b):
+    """
+    Returns the multiplicative digital root of a natural number ``n`` in a given
+    base ``b`` which is a single digit value obtained by an iterative process of
+    multiplying digits, on each iteration using the result from the previous
+    iteration to compute the digit multiplication.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import drm
+    >>> drm(9876, 10)
+    0
+
+    >>> drm(49, 10)
+    8
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/MultiplicativeDigitalRoot.html
+
+    """
+
+    n = abs(as_int(n))
+    b = as_int(b)
+    if b <= 1:
+        raise ValueError("Base should be an integer greater than 1")
+    while n > b:
+        mul = 1
+        while n > 1:
+            n, r = divmod(n, b)
+            if r == 0:
+                return 0
+            mul *= r
+        n = mul
+    return n
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/generate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/generate.py
new file mode 100644
index 0000000000000000000000000000000000000000..855bb44acfcb6241e6b0bcb81e7a2cfc8ced861f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/generate.py
@@ -0,0 +1,1157 @@
+"""
+Generating and counting primes.
+
+"""
+
+from bisect import bisect, bisect_left
+from itertools import count
+# Using arrays for sieving instead of lists greatly reduces
+# memory consumption
+from array import array as _array
+
+from sympy.core.random import randint
+from sympy.external.gmpy import sqrt
+from .primetest import isprime
+from sympy.utilities.decorator import deprecated
+from sympy.utilities.misc import as_int
+
+
+def _as_int_ceiling(a):
+    """ Wrapping ceiling in as_int will raise an error if there was a problem
+        determining whether the expression was exactly an integer or not."""
+    from sympy.functions.elementary.integers import ceiling
+    return as_int(ceiling(a))
+
+
+class Sieve:
+    """A list of prime numbers, implemented as a dynamically
+    growing sieve of Eratosthenes. When a lookup is requested involving
+    an odd number that has not been sieved, the sieve is automatically
+    extended up to that number. Implementation details limit the number of
+    primes to ``2^32-1``.
+
+    Examples
+    ========
+
+    >>> from sympy import sieve
+    >>> sieve._reset() # this line for doctest only
+    >>> 25 in sieve
+    False
+    >>> sieve._list
+    array('L', [2, 3, 5, 7, 11, 13, 17, 19, 23])
+    """
+
+    # data shared (and updated) by all Sieve instances
+    def __init__(self, sieve_interval=1_000_000):
+        """ Initial parameters for the Sieve class.
+
+        Parameters
+        ==========
+
+        sieve_interval (int): Amount of memory to be used
+
+        Raises
+        ======
+
+        ValueError
+            If ``sieve_interval`` is not positive.
+
+        """
+        self._n = 6
+        self._list = _array('L', [2, 3, 5, 7, 11, 13]) # primes
+        self._tlist = _array('L', [0, 1, 1, 2, 2, 4]) # totient
+        self._mlist = _array('i', [0, 1, -1, -1, 0, -1]) # mobius
+        if sieve_interval <= 0:
+            raise ValueError("sieve_interval should be a positive integer")
+        self.sieve_interval = sieve_interval
+        assert all(len(i) == self._n for i in (self._list, self._tlist, self._mlist))
+
+    def __repr__(self):
+        return ("<%s sieve (%i): %i, %i, %i, ... %i, %i\n"
+             "%s sieve (%i): %i, %i, %i, ... %i, %i\n"
+             "%s sieve (%i): %i, %i, %i, ... %i, %i>") % (
+             'prime', len(self._list),
+                 self._list[0], self._list[1], self._list[2],
+                 self._list[-2], self._list[-1],
+             'totient', len(self._tlist),
+                 self._tlist[0], self._tlist[1],
+                 self._tlist[2], self._tlist[-2], self._tlist[-1],
+             'mobius', len(self._mlist),
+                 self._mlist[0], self._mlist[1],
+                 self._mlist[2], self._mlist[-2], self._mlist[-1])
+
+    def _reset(self, prime=None, totient=None, mobius=None):
+        """Reset all caches (default). To reset one or more set the
+            desired keyword to True."""
+        if all(i is None for i in (prime, totient, mobius)):
+            prime = totient = mobius = True
+        if prime:
+            self._list = self._list[:self._n]
+        if totient:
+            self._tlist = self._tlist[:self._n]
+        if mobius:
+            self._mlist = self._mlist[:self._n]
+
+    def extend(self, n):
+        """Grow the sieve to cover all primes <= n.
+
+        Examples
+        ========
+
+        >>> from sympy import sieve
+        >>> sieve._reset() # this line for doctest only
+        >>> sieve.extend(30)
+        >>> sieve[10] == 29
+        True
+        """
+        n = int(n)
+        # `num` is even at any point in the function.
+        # This satisfies the condition required by `self._primerange`.
+        num = self._list[-1] + 1
+        if n < num:
+            return
+        num2 = num**2
+        while num2 <= n:
+            self._list += _array('L', self._primerange(num, num2))
+            num, num2 = num2, num2**2
+        # Merge the sieves
+        self._list += _array('L', self._primerange(num, n + 1))
+
+    def _primerange(self, a, b):
+        """ Generate all prime numbers in the range (a, b).
+
+        Parameters
+        ==========
+
+        a, b : positive integers assuming the following conditions
+                * a is an even number
+                * 2 < self._list[-1] < a < b < nextprime(self._list[-1])**2
+
+        Yields
+        ======
+
+        p (int): prime numbers such that ``a < p < b``
+
+        Examples
+        ========
+
+        >>> from sympy.ntheory.generate import Sieve
+        >>> s = Sieve()
+        >>> s._list[-1]
+        13
+        >>> list(s._primerange(18, 31))
+        [19, 23, 29]
+
+        """
+        if b % 2:
+            b -= 1
+        while a < b:
+            block_size = min(self.sieve_interval, (b - a) // 2)
+            # Create the list such that block[x] iff (a + 2x + 1) is prime.
+            # Note that even numbers are not considered here.
+            block = [True] * block_size
+            for p in self._list[1:bisect(self._list, sqrt(a + 2 * block_size + 1))]:
+                for t in range((-(a + 1 + p) // 2) % p, block_size, p):
+                    block[t] = False
+            for idx, p in enumerate(block):
+                if p:
+                    yield a + 2 * idx + 1
+            a += 2 * block_size
+
+    def extend_to_no(self, i):
+        """Extend to include the ith prime number.
+
+        Parameters
+        ==========
+
+        i : integer
+
+        Examples
+        ========
+
+        >>> from sympy import sieve
+        >>> sieve._reset() # this line for doctest only
+        >>> sieve.extend_to_no(9)
+        >>> sieve._list
+        array('L', [2, 3, 5, 7, 11, 13, 17, 19, 23])
+
+        Notes
+        =====
+
+        The list is extended by 50% if it is too short, so it is
+        likely that it will be longer than requested.
+        """
+        i = as_int(i)
+        while len(self._list) < i:
+            self.extend(int(self._list[-1] * 1.5))
+
+    def primerange(self, a, b=None):
+        """Generate all prime numbers in the range [2, a) or [a, b).
+
+        Examples
+        ========
+
+        >>> from sympy import sieve, prime
+
+        All primes less than 19:
+
+        >>> print([i for i in sieve.primerange(19)])
+        [2, 3, 5, 7, 11, 13, 17]
+
+        All primes greater than or equal to 7 and less than 19:
+
+        >>> print([i for i in sieve.primerange(7, 19)])
+        [7, 11, 13, 17]
+
+        All primes through the 10th prime
+
+        >>> list(sieve.primerange(prime(10) + 1))
+        [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+
+        """
+        if b is None:
+            b = _as_int_ceiling(a)
+            a = 2
+        else:
+            a = max(2, _as_int_ceiling(a))
+            b = _as_int_ceiling(b)
+        if a >= b:
+            return
+        self.extend(b)
+        yield from self._list[bisect_left(self._list, a):
+                              bisect_left(self._list, b)]
+
+    def totientrange(self, a, b):
+        """Generate all totient numbers for the range [a, b).
+
+        Examples
+        ========
+
+        >>> from sympy import sieve
+        >>> print([i for i in sieve.totientrange(7, 18)])
+        [6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16]
+        """
+        a = max(1, _as_int_ceiling(a))
+        b = _as_int_ceiling(b)
+        n = len(self._tlist)
+        if a >= b:
+            return
+        elif b <= n:
+            for i in range(a, b):
+                yield self._tlist[i]
+        else:
+            self._tlist += _array('L', range(n, b))
+            for i in range(1, n):
+                ti = self._tlist[i]
+                if ti == i - 1:
+                    startindex = (n + i - 1) // i * i
+                    for j in range(startindex, b, i):
+                        self._tlist[j] -= self._tlist[j] // i
+                if i >= a:
+                    yield ti
+
+            for i in range(n, b):
+                ti = self._tlist[i]
+                if ti == i:
+                    for j in range(i, b, i):
+                        self._tlist[j] -= self._tlist[j] // i
+                if i >= a:
+                    yield self._tlist[i]
+
+    def mobiusrange(self, a, b):
+        """Generate all mobius numbers for the range [a, b).
+
+        Parameters
+        ==========
+
+        a : integer
+            First number in range
+
+        b : integer
+            First number outside of range
+
+        Examples
+        ========
+
+        >>> from sympy import sieve
+        >>> print([i for i in sieve.mobiusrange(7, 18)])
+        [-1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1]
+        """
+        a = max(1, _as_int_ceiling(a))
+        b = _as_int_ceiling(b)
+        n = len(self._mlist)
+        if a >= b:
+            return
+        elif b <= n:
+            for i in range(a, b):
+                yield self._mlist[i]
+        else:
+            self._mlist += _array('i', [0]*(b - n))
+            for i in range(1, n):
+                mi = self._mlist[i]
+                startindex = (n + i - 1) // i * i
+                for j in range(startindex, b, i):
+                    self._mlist[j] -= mi
+                if i >= a:
+                    yield mi
+
+            for i in range(n, b):
+                mi = self._mlist[i]
+                for j in range(2 * i, b, i):
+                    self._mlist[j] -= mi
+                if i >= a:
+                    yield mi
+
+    def search(self, n):
+        """Return the indices i, j of the primes that bound n.
+
+        If n is prime then i == j.
+
+        Although n can be an expression, if ceiling cannot convert
+        it to an integer then an n error will be raised.
+
+        Examples
+        ========
+
+        >>> from sympy import sieve
+        >>> sieve.search(25)
+        (9, 10)
+        >>> sieve.search(23)
+        (9, 9)
+        """
+        test = _as_int_ceiling(n)
+        n = as_int(n)
+        if n < 2:
+            raise ValueError("n should be >= 2 but got: %s" % n)
+        if n > self._list[-1]:
+            self.extend(n)
+        b = bisect(self._list, n)
+        if self._list[b - 1] == test:
+            return b, b
+        else:
+            return b, b + 1
+
+    def __contains__(self, n):
+        try:
+            n = as_int(n)
+            assert n >= 2
+        except (ValueError, AssertionError):
+            return False
+        if n % 2 == 0:
+            return n == 2
+        a, b = self.search(n)
+        return a == b
+
+    def __iter__(self):
+        for n in count(1):
+            yield self[n]
+
+    def __getitem__(self, n):
+        """Return the nth prime number"""
+        if isinstance(n, slice):
+            self.extend_to_no(n.stop)
+            start = n.start if n.start is not None else 0
+            if start < 1:
+                # sieve[:5] would be empty (starting at -1), let's
+                # just be explicit and raise.
+                raise IndexError("Sieve indices start at 1.")
+            return self._list[start - 1:n.stop - 1:n.step]
+        else:
+            if n < 1:
+                # offset is one, so forbid explicit access to sieve[0]
+                # (would surprisingly return the last one).
+                raise IndexError("Sieve indices start at 1.")
+            n = as_int(n)
+            self.extend_to_no(n)
+            return self._list[n - 1]
+
+# Generate a global object for repeated use in trial division etc
+sieve = Sieve()
+
+def prime(nth):
+    r"""
+    Return the nth prime number, where primes are indexed starting from 1:
+    prime(1) = 2, prime(2) = 3, etc.
+
+    Parameters
+    ==========
+
+    nth : int
+        The position of the prime number to return (must be a positive integer).
+
+    Returns
+    =======
+
+    int
+        The nth prime number.
+
+    Examples
+    ========
+
+    >>> from sympy import prime
+    >>> prime(10)
+    29
+    >>> prime(1)
+    2
+    >>> prime(100000)
+    1299709
+
+    See Also
+    ========
+
+    sympy.ntheory.primetest.isprime : Test if a number is prime.
+    primerange : Generate all primes in a given range.
+    primepi : Return the number of primes less than or equal to a given number.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Prime_number_theorem
+    .. [2] https://en.wikipedia.org/wiki/Logarithmic_integral_function
+    .. [3] https://en.wikipedia.org/wiki/Skewes%27_number
+    """
+    n = as_int(nth)
+    if n < 1:
+        raise ValueError("nth must be a positive integer; prime(1) == 2")
+
+    # Check if n is within the sieve range
+    if n <= len(sieve._list):
+        return sieve[n]
+
+    from sympy.functions.elementary.exponential import log
+    from sympy.functions.special.error_functions import li
+
+    if n < 1000:
+        # Extend sieve up to 8*n as this is empirically sufficient
+        sieve.extend(8 * n)
+        return sieve[n]
+
+    a = 2
+    # Estimate an upper bound for the nth prime using the prime number theorem
+    b = int(n * (log(n).evalf() + log(log(n)).evalf()))
+
+    # Binary search for the least m such that li(m) > n
+    while a < b:
+        mid = (a + b) >> 1
+        if li(mid).evalf() > n:
+            b = mid
+        else:
+            a = mid + 1
+
+    return nextprime(a - 1, n - _primepi(a - 1))
+
+
+@deprecated("""\
+The `sympy.ntheory.generate.primepi` has been moved to `sympy.functions.combinatorial.numbers.primepi`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def primepi(n):
+    r""" Represents the prime counting function pi(n) = the number
+        of prime numbers less than or equal to n.
+
+        .. deprecated:: 1.13
+
+            The ``primepi`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.primepi`
+            instead. See its documentation for more information. See
+            :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+        Algorithm Description:
+
+        In sieve method, we remove all multiples of prime p
+        except p itself.
+
+        Let phi(i,j) be the number of integers 2 <= k <= i
+        which remain after sieving from primes less than
+        or equal to j.
+        Clearly, pi(n) = phi(n, sqrt(n))
+
+        If j is not a prime,
+        phi(i,j) = phi(i, j - 1)
+
+        if j is a prime,
+        We remove all numbers(except j) whose
+        smallest prime factor is j.
+
+        Let $x= j \times a$ be such a number, where $2 \le a \le i / j$
+        Now, after sieving from primes $\le j - 1$,
+        a must remain
+        (because x, and hence a has no prime factor $\le j - 1$)
+        Clearly, there are phi(i / j, j - 1) such a
+        which remain on sieving from primes $\le j - 1$
+
+        Now, if a is a prime less than equal to j - 1,
+        $x= j \times a$ has smallest prime factor = a, and
+        has already been removed(by sieving from a).
+        So, we do not need to remove it again.
+        (Note: there will be pi(j - 1) such x)
+
+        Thus, number of x, that will be removed are:
+        phi(i / j, j - 1) - phi(j - 1, j - 1)
+        (Note that pi(j - 1) = phi(j - 1, j - 1))
+
+        $\Rightarrow$ phi(i,j) = phi(i, j - 1) - phi(i / j, j - 1) + phi(j - 1, j - 1)
+
+        So,following recursion is used and implemented as dp:
+
+        phi(a, b) = phi(a, b - 1), if b is not a prime
+        phi(a, b) = phi(a, b-1)-phi(a / b, b-1) + phi(b-1, b-1), if b is prime
+
+        Clearly a is always of the form floor(n / k),
+        which can take at most $2\sqrt{n}$ values.
+        Two arrays arr1,arr2 are maintained
+        arr1[i] = phi(i, j),
+        arr2[i] = phi(n // i, j)
+
+        Finally the answer is arr2[1]
+
+        Examples
+        ========
+
+        >>> from sympy import primepi, prime, prevprime, isprime
+        >>> primepi(25)
+        9
+
+        So there are 9 primes less than or equal to 25. Is 25 prime?
+
+        >>> isprime(25)
+        False
+
+        It is not. So the first prime less than 25 must be the
+        9th prime:
+
+        >>> prevprime(25) == prime(9)
+        True
+
+        See Also
+        ========
+
+        sympy.ntheory.primetest.isprime : Test if n is prime
+        primerange : Generate all primes in a given range
+        prime : Return the nth prime
+    """
+    from sympy.functions.combinatorial.numbers import primepi as func_primepi
+    return func_primepi(n)
+
+
+def _primepi(n:int) -> int:
+    r""" Represents the prime counting function pi(n) = the number
+    of prime numbers less than or equal to n.
+
+    Explanation
+    ===========
+
+    In sieve method, we remove all multiples of prime p
+    except p itself.
+
+    Let phi(i,j) be the number of integers 2 <= k <= i
+    which remain after sieving from primes less than
+    or equal to j.
+    Clearly, pi(n) = phi(n, sqrt(n))
+
+    If j is not a prime,
+    phi(i,j) = phi(i, j - 1)
+
+    if j is a prime,
+    We remove all numbers(except j) whose
+    smallest prime factor is j.
+
+    Let $x= j \times a$ be such a number, where $2 \le a \le i / j$
+    Now, after sieving from primes $\le j - 1$,
+    a must remain
+    (because x, and hence a has no prime factor $\le j - 1$)
+    Clearly, there are phi(i / j, j - 1) such a
+    which remain on sieving from primes $\le j - 1$
+
+    Now, if a is a prime less than equal to j - 1,
+    $x= j \times a$ has smallest prime factor = a, and
+    has already been removed(by sieving from a).
+    So, we do not need to remove it again.
+    (Note: there will be pi(j - 1) such x)
+
+    Thus, number of x, that will be removed are:
+    phi(i / j, j - 1) - phi(j - 1, j - 1)
+    (Note that pi(j - 1) = phi(j - 1, j - 1))
+
+    $\Rightarrow$ phi(i,j) = phi(i, j - 1) - phi(i / j, j - 1) + phi(j - 1, j - 1)
+
+    So,following recursion is used and implemented as dp:
+
+    phi(a, b) = phi(a, b - 1), if b is not a prime
+    phi(a, b) = phi(a, b-1)-phi(a / b, b-1) + phi(b-1, b-1), if b is prime
+
+    Clearly a is always of the form floor(n / k),
+    which can take at most $2\sqrt{n}$ values.
+    Two arrays arr1,arr2 are maintained
+    arr1[i] = phi(i, j),
+    arr2[i] = phi(n // i, j)
+
+    Finally the answer is arr2[1]
+
+    Parameters
+    ==========
+
+    n : int
+
+    """
+    if n < 2:
+        return 0
+    if n <= sieve._list[-1]:
+        return sieve.search(n)[0]
+    lim = sqrt(n)
+    arr1 = [(i + 1) >> 1 for i in range(lim + 1)]
+    arr2 = [0] + [(n//i + 1) >> 1 for i in range(1, lim + 1)]
+    skip = [False] * (lim + 1)
+    for i in range(3, lim + 1, 2):
+        # Presently, arr1[k]=phi(k,i - 1),
+        # arr2[k] = phi(n // k,i - 1) # not all k's do this
+        if skip[i]:
+            # skip if i is a composite number
+            continue
+        p = arr1[i - 1]
+        for j in range(i, lim + 1, i):
+            skip[j] = True
+        # update arr2
+        # phi(n/j, i) = phi(n/j, i-1) - phi(n/(i*j), i-1) + phi(i-1, i-1)
+        for j in range(1, min(n // (i * i), lim) + 1, 2):
+            # No need for arr2[j] in j such that skip[j] is True to
+            # compute the final required arr2[1].
+            if skip[j]:
+                continue
+            st = i * j
+            if st <= lim:
+                arr2[j] -= arr2[st] - p
+            else:
+                arr2[j] -= arr1[n // st] - p
+        # update arr1
+        # phi(j, i) = phi(j, i-1) - phi(j/i, i-1) + phi(i-1, i-1)
+        # where the range below i**2 is fixed and
+        # does not need to be calculated.
+        for j in range(lim, min(lim, i*i - 1), -1):
+            arr1[j] -= arr1[j // i] - p
+    return arr2[1]
+
+
+def nextprime(n, ith=1):
+    """ Return the ith prime greater than n.
+
+        Parameters
+        ==========
+
+        n : integer
+        ith : positive integer
+
+        Returns
+        =======
+
+        int : Return the ith prime greater than n
+
+        Raises
+        ======
+
+        ValueError
+            If ``ith <= 0``.
+            If ``n`` or ``ith`` is not an integer.
+
+        Notes
+        =====
+
+        Potential primes are located at 6*j +/- 1. This
+        property is used during searching.
+
+        >>> from sympy import nextprime
+        >>> [(i, nextprime(i)) for i in range(10, 15)]
+        [(10, 11), (11, 13), (12, 13), (13, 17), (14, 17)]
+        >>> nextprime(2, ith=2) # the 2nd prime after 2
+        5
+
+        See Also
+        ========
+
+        prevprime : Return the largest prime smaller than n
+        primerange : Generate all primes in a given range
+
+    """
+    n = int(n)
+    i = as_int(ith)
+    if i <= 0:
+        raise ValueError("ith should be positive")
+    if n < 2:
+        n = 2
+        i -= 1
+    if n <= sieve._list[-2]:
+        l, _ = sieve.search(n)
+        if l + i - 1 < len(sieve._list):
+            return sieve._list[l + i - 1]
+        n = sieve._list[-1]
+        i += l - len(sieve._list)
+    nn = 6*(n//6)
+    if nn == n:
+        n += 1
+        if isprime(n):
+            i -= 1
+            if not i:
+                return n
+        n += 4
+    elif n - nn == 5:
+        n += 2
+        if isprime(n):
+            i -= 1
+            if not i:
+                return n
+        n += 4
+    else:
+        n = nn + 5
+    while 1:
+        if isprime(n):
+            i -= 1
+            if not i:
+                return n
+        n += 2
+        if isprime(n):
+            i -= 1
+            if not i:
+                return n
+        n += 4
+
+
+def prevprime(n):
+    """ Return the largest prime smaller than n.
+
+        Notes
+        =====
+
+        Potential primes are located at 6*j +/- 1. This
+        property is used during searching.
+
+        >>> from sympy import prevprime
+        >>> [(i, prevprime(i)) for i in range(10, 15)]
+        [(10, 7), (11, 7), (12, 11), (13, 11), (14, 13)]
+
+        See Also
+        ========
+
+        nextprime : Return the ith prime greater than n
+        primerange : Generates all primes in a given range
+    """
+    n = _as_int_ceiling(n)
+    if n < 3:
+        raise ValueError("no preceding primes")
+    if n < 8:
+        return {3: 2, 4: 3, 5: 3, 6: 5, 7: 5}[n]
+    if n <= sieve._list[-1]:
+        l, u = sieve.search(n)
+        if l == u:
+            return sieve[l-1]
+        else:
+            return sieve[l]
+    nn = 6*(n//6)
+    if n - nn <= 1:
+        n = nn - 1
+        if isprime(n):
+            return n
+        n -= 4
+    else:
+        n = nn + 1
+    while 1:
+        if isprime(n):
+            return n
+        n -= 2
+        if isprime(n):
+            return n
+        n -= 4
+
+
+def primerange(a, b=None):
+    """ Generate a list of all prime numbers in the range [2, a),
+        or [a, b).
+
+        If the range exists in the default sieve, the values will
+        be returned from there; otherwise values will be returned
+        but will not modify the sieve.
+
+        Examples
+        ========
+
+        >>> from sympy import primerange, prime
+
+        All primes less than 19:
+
+        >>> list(primerange(19))
+        [2, 3, 5, 7, 11, 13, 17]
+
+        All primes greater than or equal to 7 and less than 19:
+
+        >>> list(primerange(7, 19))
+        [7, 11, 13, 17]
+
+        All primes through the 10th prime
+
+        >>> list(primerange(prime(10) + 1))
+        [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+
+        The Sieve method, primerange, is generally faster but it will
+        occupy more memory as the sieve stores values. The default
+        instance of Sieve, named sieve, can be used:
+
+        >>> from sympy import sieve
+        >>> list(sieve.primerange(1, 30))
+        [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+
+        Notes
+        =====
+
+        Some famous conjectures about the occurrence of primes in a given
+        range are [1]:
+
+        - Twin primes: though often not, the following will give 2 primes
+                    an infinite number of times:
+                        primerange(6*n - 1, 6*n + 2)
+        - Legendre's: the following always yields at least one prime
+                        primerange(n**2, (n+1)**2+1)
+        - Bertrand's (proven): there is always a prime in the range
+                        primerange(n, 2*n)
+        - Brocard's: there are at least four primes in the range
+                        primerange(prime(n)**2, prime(n+1)**2)
+
+        The average gap between primes is log(n) [2]; the gap between
+        primes can be arbitrarily large since sequences of composite
+        numbers are arbitrarily large, e.g. the numbers in the sequence
+        n! + 2, n! + 3 ... n! + n are all composite.
+
+        See Also
+        ========
+
+        prime : Return the nth prime
+        nextprime : Return the ith prime greater than n
+        prevprime : Return the largest prime smaller than n
+        randprime : Returns a random prime in a given range
+        primorial : Returns the product of primes based on condition
+        Sieve.primerange : return range from already computed primes
+                           or extend the sieve to contain the requested
+                           range.
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Prime_number
+        .. [2] https://primes.utm.edu/notes/gaps.html
+    """
+    if b is None:
+        a, b = 2, a
+    if a >= b:
+        return
+    # If we already have the range, return it.
+    largest_known_prime = sieve._list[-1]
+    if b <= largest_known_prime:
+        yield from sieve.primerange(a, b)
+        return
+    # If we know some of it, return it.
+    if a <= largest_known_prime:
+        yield from sieve._list[bisect_left(sieve._list, a):]
+        a = largest_known_prime + 1
+    elif a % 2:
+        a -= 1
+    tail = min(b, (largest_known_prime)**2)
+    if a < tail:
+        yield from sieve._primerange(a, tail)
+        a = tail
+    if b <= a:
+        return
+    # otherwise compute, without storing, the desired range.
+    while 1:
+        a = nextprime(a)
+        if a < b:
+            yield a
+        else:
+            return
+
+
+def randprime(a, b):
+    """ Return a random prime number in the range [a, b).
+
+        Bertrand's postulate assures that
+        randprime(a, 2*a) will always succeed for a > 1.
+
+        Note that due to implementation difficulties,
+        the prime numbers chosen are not uniformly random.
+        For example, there are two primes in the range [112, 128),
+        ``113`` and ``127``, but ``randprime(112, 128)`` returns ``127``
+        with a probability of 15/17.
+
+        Examples
+        ========
+
+        >>> from sympy import randprime, isprime
+        >>> randprime(1, 30) #doctest: +SKIP
+        13
+        >>> isprime(randprime(1, 30))
+        True
+
+        See Also
+        ========
+
+        primerange : Generate all primes in a given range
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Bertrand's_postulate
+
+    """
+    if a >= b:
+        return
+    a, b = map(int, (a, b))
+    n = randint(a - 1, b)
+    p = nextprime(n)
+    if p >= b:
+        p = prevprime(b)
+    if p < a:
+        raise ValueError("no primes exist in the specified range")
+    return p
+
+
+def primorial(n, nth=True):
+    """
+    Returns the product of the first n primes (default) or
+    the primes less than or equal to n (when ``nth=False``).
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.generate import primorial, primerange
+    >>> from sympy import factorint, Mul, primefactors, sqrt
+    >>> primorial(4) # the first 4 primes are 2, 3, 5, 7
+    210
+    >>> primorial(4, nth=False) # primes <= 4 are 2 and 3
+    6
+    >>> primorial(1)
+    2
+    >>> primorial(1, nth=False)
+    1
+    >>> primorial(sqrt(101), nth=False)
+    210
+
+    One can argue that the primes are infinite since if you take
+    a set of primes and multiply them together (e.g. the primorial) and
+    then add or subtract 1, the result cannot be divided by any of the
+    original factors, hence either 1 or more new primes must divide this
+    product of primes.
+
+    In this case, the number itself is a new prime:
+
+    >>> factorint(primorial(4) + 1)
+    {211: 1}
+
+    In this case two new primes are the factors:
+
+    >>> factorint(primorial(4) - 1)
+    {11: 1, 19: 1}
+
+    Here, some primes smaller and larger than the primes multiplied together
+    are obtained:
+
+    >>> p = list(primerange(10, 20))
+    >>> sorted(set(primefactors(Mul(*p) + 1)).difference(set(p)))
+    [2, 5, 31, 149]
+
+    See Also
+    ========
+
+    primerange : Generate all primes in a given range
+
+    """
+    if nth:
+        n = as_int(n)
+    else:
+        n = int(n)
+    if n < 1:
+        raise ValueError("primorial argument must be >= 1")
+    p = 1
+    if nth:
+        for i in range(1, n + 1):
+            p *= prime(i)
+    else:
+        for i in primerange(2, n + 1):
+            p *= i
+    return p
+
+
+def cycle_length(f, x0, nmax=None, values=False):
+    """For a given iterated sequence, return a generator that gives
+    the length of the iterated cycle (lambda) and the length of terms
+    before the cycle begins (mu); if ``values`` is True then the
+    terms of the sequence will be returned instead. The sequence is
+    started with value ``x0``.
+
+    Note: more than the first lambda + mu terms may be returned and this
+    is the cost of cycle detection with Brent's method; there are, however,
+    generally less terms calculated than would have been calculated if the
+    proper ending point were determined, e.g. by using Floyd's method.
+
+    >>> from sympy.ntheory.generate import cycle_length
+
+    This will yield successive values of i <-- func(i):
+
+        >>> def gen(func, i):
+        ...     while 1:
+        ...         yield i
+        ...         i = func(i)
+        ...
+
+    A function is defined:
+
+        >>> func = lambda i: (i**2 + 1) % 51
+
+    and given a seed of 4 and the mu and lambda terms calculated:
+
+        >>> next(cycle_length(func, 4))
+        (6, 3)
+
+    We can see what is meant by looking at the output:
+
+        >>> iter = cycle_length(func, 4, values=True)
+        >>> list(iter)
+        [4, 17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14]
+
+    There are 6 repeating values after the first 3.
+
+    If a sequence is suspected of being longer than you might wish, ``nmax``
+    can be used to exit early (and mu will be returned as None):
+
+        >>> next(cycle_length(func, 4, nmax = 4))
+        (4, None)
+        >>> list(cycle_length(func, 4, nmax = 4, values=True))
+        [4, 17, 35, 2]
+
+    Code modified from:
+        https://en.wikipedia.org/wiki/Cycle_detection.
+    """
+
+    nmax = int(nmax or 0)
+
+    # main phase: search successive powers of two
+    power = lam = 1
+    tortoise, hare = x0, f(x0)  # f(x0) is the element/node next to x0.
+    i = 1
+    if values:
+        yield tortoise
+    while tortoise != hare and (not nmax or i < nmax):
+        i += 1
+        if power == lam:   # time to start a new power of two?
+            tortoise = hare
+            power *= 2
+            lam = 0
+        if values:
+            yield hare
+        hare = f(hare)
+        lam += 1
+    if nmax and i == nmax:
+        if values:
+            return
+        else:
+            yield nmax, None
+            return
+    if not values:
+        # Find the position of the first repetition of length lambda
+        mu = 0
+        tortoise = hare = x0
+        for i in range(lam):
+            hare = f(hare)
+        while tortoise != hare:
+            tortoise = f(tortoise)
+            hare = f(hare)
+            mu += 1
+        yield lam, mu
+
+
+def composite(nth):
+    """ Return the nth composite number, with the composite numbers indexed as
+        composite(1) = 4, composite(2) = 6, etc....
+
+        Examples
+        ========
+
+        >>> from sympy import composite
+        >>> composite(36)
+        52
+        >>> composite(1)
+        4
+        >>> composite(17737)
+        20000
+
+        See Also
+        ========
+
+        sympy.ntheory.primetest.isprime : Test if n is prime
+        primerange : Generate all primes in a given range
+        primepi : Return the number of primes less than or equal to n
+        prime : Return the nth prime
+        compositepi : Return the number of positive composite numbers less than or equal to n
+    """
+    n = as_int(nth)
+    if n < 1:
+        raise ValueError("nth must be a positive integer; composite(1) == 4")
+    composite_arr = [4, 6, 8, 9, 10, 12, 14, 15, 16, 18]
+    if n <= 10:
+        return composite_arr[n - 1]
+
+    a, b = 4, sieve._list[-1]
+    if n <= b - _primepi(b) - 1:
+        while a < b - 1:
+            mid = (a + b) >> 1
+            if mid - _primepi(mid) - 1 > n:
+                b = mid
+            else:
+                a = mid
+        if isprime(a):
+            a -= 1
+        return a
+
+    from sympy.functions.elementary.exponential import log
+    from sympy.functions.special.error_functions import li
+    a = 4 # Lower bound for binary search
+    b = int(n*(log(n) + log(log(n)))) # Upper bound for the search.
+
+    while a < b:
+        mid = (a + b) >> 1
+        if mid - li(mid) - 1 > n:
+            b = mid
+        else:
+            a = mid + 1
+
+    n_composites = a - _primepi(a) - 1
+    while n_composites > n:
+        if not isprime(a):
+            n_composites -= 1
+        a -= 1
+    if isprime(a):
+        a -= 1
+    return a
+
+
+def compositepi(n):
+    """ Return the number of positive composite numbers less than or equal to n.
+        The first positive composite is 4, i.e. compositepi(4) = 1.
+
+        Examples
+        ========
+
+        >>> from sympy import compositepi
+        >>> compositepi(25)
+        15
+        >>> compositepi(1000)
+        831
+
+        See Also
+        ========
+
+        sympy.ntheory.primetest.isprime : Test if n is prime
+        primerange : Generate all primes in a given range
+        prime : Return the nth prime
+        primepi : Return the number of primes less than or equal to n
+        composite : Return the nth composite number
+    """
+    n = int(n)
+    if n < 4:
+        return 0
+    return n - _primepi(n) - 1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/modular.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/modular.py
new file mode 100644
index 0000000000000000000000000000000000000000..628a3d8c5a7fb4b6c51ad337df66d74f90282496
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/modular.py
@@ -0,0 +1,291 @@
+from math import prod
+
+from sympy.external.gmpy import gcd, gcdext
+from sympy.ntheory.primetest import isprime
+from sympy.polys.domains import ZZ
+from sympy.polys.galoistools import gf_crt, gf_crt1, gf_crt2
+from sympy.utilities.misc import as_int
+
+
+def symmetric_residue(a, m):
+    """Return the residual mod m such that it is within half of the modulus.
+
+    >>> from sympy.ntheory.modular import symmetric_residue
+    >>> symmetric_residue(1, 6)
+    1
+    >>> symmetric_residue(4, 6)
+    -2
+    """
+    if a <= m // 2:
+        return a
+    return a - m
+
+
+def crt(m, v, symmetric=False, check=True):
+    r"""Chinese Remainder Theorem.
+
+    The moduli in m are assumed to be pairwise coprime.  The output
+    is then an integer f, such that f = v_i mod m_i for each pair out
+    of v and m. If ``symmetric`` is False a positive integer will be
+    returned, else \|f\| will be less than or equal to the LCM of the
+    moduli, and thus f may be negative.
+
+    If the moduli are not co-prime the correct result will be returned
+    if/when the test of the result is found to be incorrect. This result
+    will be None if there is no solution.
+
+    The keyword ``check`` can be set to False if it is known that the moduli
+    are coprime.
+
+    Examples
+    ========
+
+    As an example consider a set of residues ``U = [49, 76, 65]``
+    and a set of moduli ``M = [99, 97, 95]``. Then we have::
+
+       >>> from sympy.ntheory.modular import crt
+
+       >>> crt([99, 97, 95], [49, 76, 65])
+       (639985, 912285)
+
+    This is the correct result because::
+
+       >>> [639985 % m for m in [99, 97, 95]]
+       [49, 76, 65]
+
+    If the moduli are not co-prime, you may receive an incorrect result
+    if you use ``check=False``:
+
+       >>> crt([12, 6, 17], [3, 4, 2], check=False)
+       (954, 1224)
+       >>> [954 % m for m in [12, 6, 17]]
+       [6, 0, 2]
+       >>> crt([12, 6, 17], [3, 4, 2]) is None
+       True
+       >>> crt([3, 6], [2, 5])
+       (5, 6)
+
+    Note: the order of gf_crt's arguments is reversed relative to crt,
+    and that solve_congruence takes residue, modulus pairs.
+
+    Programmer's note: rather than checking that all pairs of moduli share
+    no GCD (an O(n**2) test) and rather than factoring all moduli and seeing
+    that there is no factor in common, a check that the result gives the
+    indicated residuals is performed -- an O(n) operation.
+
+    See Also
+    ========
+
+    solve_congruence
+    sympy.polys.galoistools.gf_crt : low level crt routine used by this routine
+    """
+    if check:
+        m = list(map(as_int, m))
+        v = list(map(as_int, v))
+
+    result = gf_crt(v, m, ZZ)
+    mm = prod(m)
+
+    if check:
+        if not all(v % m == result % m for v, m in zip(v, m)):
+            result = solve_congruence(*list(zip(v, m)),
+                    check=False, symmetric=symmetric)
+            if result is None:
+                return result
+            result, mm = result
+
+    if symmetric:
+        return int(symmetric_residue(result, mm)), int(mm)
+    return int(result), int(mm)
+
+
+def crt1(m):
+    """First part of Chinese Remainder Theorem, for multiple application.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.modular import crt, crt1, crt2
+    >>> m = [99, 97, 95]
+    >>> v = [49, 76, 65]
+
+    The following two codes have the same result.
+
+    >>> crt(m, v)
+    (639985, 912285)
+
+    >>> mm, e, s = crt1(m)
+    >>> crt2(m, v, mm, e, s)
+    (639985, 912285)
+
+    However, it is faster when we want to fix ``m`` and
+    compute for multiple ``v``, i.e. the following cases:
+
+    >>> mm, e, s = crt1(m)
+    >>> vs = [[52, 21, 37], [19, 46, 76]]
+    >>> for v in vs:
+    ...     print(crt2(m, v, mm, e, s))
+    (397042, 912285)
+    (803206, 912285)
+
+    See Also
+    ========
+
+    sympy.polys.galoistools.gf_crt1 : low level crt routine used by this routine
+    sympy.ntheory.modular.crt
+    sympy.ntheory.modular.crt2
+
+    """
+
+    return gf_crt1(m, ZZ)
+
+
+def crt2(m, v, mm, e, s, symmetric=False):
+    """Second part of Chinese Remainder Theorem, for multiple application.
+
+    See ``crt1`` for usage.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.modular import crt1, crt2
+    >>> mm, e, s = crt1([18, 42, 6])
+    >>> crt2([18, 42, 6], [0, 0, 0], mm, e, s)
+    (0, 4536)
+
+    See Also
+    ========
+
+    sympy.polys.galoistools.gf_crt2 : low level crt routine used by this routine
+    sympy.ntheory.modular.crt
+    sympy.ntheory.modular.crt1
+
+    """
+
+    result = gf_crt2(v, m, mm, e, s, ZZ)
+
+    if symmetric:
+        return int(symmetric_residue(result, mm)), int(mm)
+    return int(result), int(mm)
+
+
+def solve_congruence(*remainder_modulus_pairs, **hint):
+    """Compute the integer ``n`` that has the residual ``ai`` when it is
+    divided by ``mi`` where the ``ai`` and ``mi`` are given as pairs to
+    this function: ((a1, m1), (a2, m2), ...). If there is no solution,
+    return None. Otherwise return ``n`` and its modulus.
+
+    The ``mi`` values need not be co-prime. If it is known that the moduli are
+    not co-prime then the hint ``check`` can be set to False (default=True) and
+    the check for a quicker solution via crt() (valid when the moduli are
+    co-prime) will be skipped.
+
+    If the hint ``symmetric`` is True (default is False), the value of ``n``
+    will be within 1/2 of the modulus, possibly negative.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.modular import solve_congruence
+
+    What number is 2 mod 3, 3 mod 5 and 2 mod 7?
+
+    >>> solve_congruence((2, 3), (3, 5), (2, 7))
+    (23, 105)
+    >>> [23 % m for m in [3, 5, 7]]
+    [2, 3, 2]
+
+    If you prefer to work with all remainder in one list and
+    all moduli in another, send the arguments like this:
+
+    >>> solve_congruence(*zip((2, 3, 2), (3, 5, 7)))
+    (23, 105)
+
+    The moduli need not be co-prime; in this case there may or
+    may not be a solution:
+
+    >>> solve_congruence((2, 3), (4, 6)) is None
+    True
+
+    >>> solve_congruence((2, 3), (5, 6))
+    (5, 6)
+
+    The symmetric flag will make the result be within 1/2 of the modulus:
+
+    >>> solve_congruence((2, 3), (5, 6), symmetric=True)
+    (-1, 6)
+
+    See Also
+    ========
+
+    crt : high level routine implementing the Chinese Remainder Theorem
+
+    """
+    def combine(c1, c2):
+        """Return the tuple (a, m) which satisfies the requirement
+        that n = a + i*m satisfy n = a1 + j*m1 and n = a2 = k*m2.
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Method_of_successive_substitution
+        """
+        a1, m1 = c1
+        a2, m2 = c2
+        a, b, c = m1, a2 - a1, m2
+        g = gcd(a, b, c)
+        a, b, c = [i//g for i in [a, b, c]]
+        if a != 1:
+            g, inv_a, _ = gcdext(a, c)
+            if g != 1:
+                return None
+            b *= inv_a
+        a, m = a1 + m1*b, m1*c
+        return a, m
+
+    rm = remainder_modulus_pairs
+    symmetric = hint.get('symmetric', False)
+
+    if hint.get('check', True):
+        rm = [(as_int(r), as_int(m)) for r, m in rm]
+
+        # ignore redundant pairs but raise an error otherwise; also
+        # make sure that a unique set of bases is sent to gf_crt if
+        # they are all prime.
+        #
+        # The routine will work out less-trivial violations and
+        # return None, e.g. for the pairs (1,3) and (14,42) there
+        # is no answer because 14 mod 42 (having a gcd of 14) implies
+        # (14/2) mod (42/2), (14/7) mod (42/7) and (14/14) mod (42/14)
+        # which, being 0 mod 3, is inconsistent with 1 mod 3. But to
+        # preprocess the input beyond checking of another pair with 42
+        # or 3 as the modulus (for this example) is not necessary.
+        uniq = {}
+        for r, m in rm:
+            r %= m
+            if m in uniq:
+                if r != uniq[m]:
+                    return None
+                continue
+            uniq[m] = r
+        rm = [(r, m) for m, r in uniq.items()]
+        del uniq
+
+        # if the moduli are co-prime, the crt will be significantly faster;
+        # checking all pairs for being co-prime gets to be slow but a prime
+        # test is a good trade-off
+        if all(isprime(m) for r, m in rm):
+            r, m = list(zip(*rm))
+            return crt(m, r, symmetric=symmetric, check=False)
+
+    rv = (0, 1)
+    for rmi in rm:
+        rv = combine(rv, rmi)
+        if rv is None:
+            break
+        n, m = rv
+        n = n % m
+    else:
+        if symmetric:
+            return symmetric_residue(n, m), m
+        return n, m
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/multinomial.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/multinomial.py
new file mode 100644
index 0000000000000000000000000000000000000000..8ec50fdb533be547b9a8e60dc47568965bf89436
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/multinomial.py
@@ -0,0 +1,188 @@
+from sympy.utilities.misc import as_int
+
+
+def binomial_coefficients(n):
+    """Return a dictionary containing pairs :math:`{(k1,k2) : C_kn}` where
+    :math:`C_kn` are binomial coefficients and :math:`n=k1+k2`.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import binomial_coefficients
+    >>> binomial_coefficients(9)
+    {(0, 9): 1, (1, 8): 9, (2, 7): 36, (3, 6): 84,
+     (4, 5): 126, (5, 4): 126, (6, 3): 84, (7, 2): 36, (8, 1): 9, (9, 0): 1}
+
+    See Also
+    ========
+
+    binomial_coefficients_list, multinomial_coefficients
+    """
+    n = as_int(n)
+    d = {(0, n): 1, (n, 0): 1}
+    a = 1
+    for k in range(1, n//2 + 1):
+        a = (a * (n - k + 1))//k
+        d[k, n - k] = d[n - k, k] = a
+    return d
+
+
+def binomial_coefficients_list(n):
+    """ Return a list of binomial coefficients as rows of the Pascal's
+    triangle.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import binomial_coefficients_list
+    >>> binomial_coefficients_list(9)
+    [1, 9, 36, 84, 126, 126, 84, 36, 9, 1]
+
+    See Also
+    ========
+
+    binomial_coefficients, multinomial_coefficients
+    """
+    n = as_int(n)
+    d = [1] * (n + 1)
+    a = 1
+    for k in range(1, n//2 + 1):
+        a = (a * (n - k + 1))//k
+        d[k] = d[n - k] = a
+    return d
+
+
+def multinomial_coefficients(m, n):
+    r"""Return a dictionary containing pairs ``{(k1,k2,..,km) : C_kn}``
+    where ``C_kn`` are multinomial coefficients such that
+    ``n=k1+k2+..+km``.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import multinomial_coefficients
+    >>> multinomial_coefficients(2, 5) # indirect doctest
+    {(0, 5): 1, (1, 4): 5, (2, 3): 10, (3, 2): 10, (4, 1): 5, (5, 0): 1}
+
+    Notes
+    =====
+
+    The algorithm is based on the following result:
+
+    .. math::
+        \binom{n}{k_1, \ldots, k_m} =
+        \frac{k_1 + 1}{n - k_1} \sum_{i=2}^m \binom{n}{k_1 + 1, \ldots, k_i - 1, \ldots}
+
+    Code contributed to Sage by Yann Laigle-Chapuy, copied with permission
+    of the author.
+
+    See Also
+    ========
+
+    binomial_coefficients_list, binomial_coefficients
+    """
+    m = as_int(m)
+    n = as_int(n)
+    if not m:
+        if n:
+            return {}
+        return {(): 1}
+    if m == 2:
+        return binomial_coefficients(n)
+    if m >= 2*n and n > 1:
+        return dict(multinomial_coefficients_iterator(m, n))
+    t = [n] + [0] * (m - 1)
+    r = {tuple(t): 1}
+    if n:
+        j = 0  # j will be the leftmost nonzero position
+    else:
+        j = m
+    # enumerate tuples in co-lex order
+    while j < m - 1:
+        # compute next tuple
+        tj = t[j]
+        if j:
+            t[j] = 0
+            t[0] = tj
+        if tj > 1:
+            t[j + 1] += 1
+            j = 0
+            start = 1
+            v = 0
+        else:
+            j += 1
+            start = j + 1
+            v = r[tuple(t)]
+            t[j] += 1
+        # compute the value
+        # NB: the initialization of v was done above
+        for k in range(start, m):
+            if t[k]:
+                t[k] -= 1
+                v += r[tuple(t)]
+                t[k] += 1
+        t[0] -= 1
+        r[tuple(t)] = (v * tj) // (n - t[0])
+    return r
+
+
+def multinomial_coefficients_iterator(m, n, _tuple=tuple):
+    """multinomial coefficient iterator
+
+    This routine has been optimized for `m` large with respect to `n` by taking
+    advantage of the fact that when the monomial tuples `t` are stripped of
+    zeros, their coefficient is the same as that of the monomial tuples from
+    ``multinomial_coefficients(n, n)``. Therefore, the latter coefficients are
+    precomputed to save memory and time.
+
+    >>> from sympy.ntheory.multinomial import multinomial_coefficients
+    >>> m53, m33 = multinomial_coefficients(5,3), multinomial_coefficients(3,3)
+    >>> m53[(0,0,0,1,2)] == m53[(0,0,1,0,2)] == m53[(1,0,2,0,0)] == m33[(0,1,2)]
+    True
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.multinomial import multinomial_coefficients_iterator
+    >>> it = multinomial_coefficients_iterator(20,3)
+    >>> next(it)
+    ((3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), 1)
+    """
+    m = as_int(m)
+    n = as_int(n)
+    if m < 2*n or n == 1:
+        mc = multinomial_coefficients(m, n)
+        yield from mc.items()
+    else:
+        mc = multinomial_coefficients(n, n)
+        mc1 = {}
+        for k, v in mc.items():
+            mc1[_tuple(filter(None, k))] = v
+        mc = mc1
+
+        t = [n] + [0] * (m - 1)
+        t1 = _tuple(t)
+        b = _tuple(filter(None, t1))
+        yield (t1, mc[b])
+        if n:
+            j = 0  # j will be the leftmost nonzero position
+        else:
+            j = m
+        # enumerate tuples in co-lex order
+        while j < m - 1:
+            # compute next tuple
+            tj = t[j]
+            if j:
+                t[j] = 0
+                t[0] = tj
+            if tj > 1:
+                t[j + 1] += 1
+                j = 0
+            else:
+                j += 1
+                t[j] += 1
+
+            t[0] -= 1
+            t1 = _tuple(t)
+            b = _tuple(filter(None, t1))
+            yield (t1, mc[b])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/partitions_.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/partitions_.py
new file mode 100644
index 0000000000000000000000000000000000000000..953fa9e2fef146b0d3a9baad0ec5e1353ad6f237
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/partitions_.py
@@ -0,0 +1,277 @@
+from mpmath.libmp import (fzero, from_int, from_rational,
+    fone, fhalf, bitcount, to_int, mpf_mul, mpf_div, mpf_sub,
+    mpf_add, mpf_sqrt, mpf_pi, mpf_cosh_sinh, mpf_cos, mpf_sin)
+from .residue_ntheory import _sqrt_mod_prime_power, is_quad_residue
+from sympy.utilities.decorator import deprecated
+from sympy.utilities.memoization import recurrence_memo
+
+import math
+from itertools import count
+
+def _pre():
+    maxn = 10**5
+    global _factor, _totient
+    _factor = [0]*maxn
+    _totient = [1]*maxn
+    lim = int(maxn**0.5) + 5
+    for i in range(2, lim):
+        if _factor[i] == 0:
+            for j in range(i*i, maxn, i):
+                if _factor[j] == 0:
+                    _factor[j] = i
+    for i in range(2, maxn):
+        if _factor[i] == 0:
+            _factor[i] = i
+            _totient[i] = i-1
+            continue
+        x = _factor[i]
+        y = i//x
+        if y % x == 0:
+            _totient[i] = _totient[y]*x
+        else:
+            _totient[i] = _totient[y]*(x - 1)
+
+def _a(n, k, prec):
+    """ Compute the inner sum in HRR formula [1]_
+
+    References
+    ==========
+
+    .. [1] https://msp.org/pjm/1956/6-1/pjm-v6-n1-p18-p.pdf
+
+    """
+    if k == 1:
+        return fone
+
+    k1 = k
+    e = 0
+    p = _factor[k]
+    while k1 % p == 0:
+        k1 //= p
+        e += 1
+    k2 = k//k1 # k2 = p^e
+    v = 1 - 24*n
+    pi = mpf_pi(prec)
+
+    if k1 == 1:
+        # k  = p^e
+        if p == 2:
+            mod = 8*k
+            v = mod + v % mod
+            v = (v*pow(9, k - 1, mod)) % mod
+            m = _sqrt_mod_prime_power(v, 2, e + 3)[0]
+            arg = mpf_div(mpf_mul(
+                from_int(4*m), pi, prec), from_int(mod), prec)
+            return mpf_mul(mpf_mul(
+                from_int((-1)**e*(2 - (m % 4))),
+                mpf_sqrt(from_int(k), prec), prec),
+                mpf_sin(arg, prec), prec)
+        if p == 3:
+            mod = 3*k
+            v = mod + v % mod
+            if e > 1:
+                v = (v*pow(64, k//3 - 1, mod)) % mod
+            m = _sqrt_mod_prime_power(v, 3, e + 1)[0]
+            arg = mpf_div(mpf_mul(from_int(4*m), pi, prec),
+                from_int(mod), prec)
+            return mpf_mul(mpf_mul(
+                from_int(2*(-1)**(e + 1)*(3 - 2*(m % 3))),
+                mpf_sqrt(from_int(k//3), prec), prec),
+                mpf_sin(arg, prec), prec)
+        v = k + v % k
+        jacobi3 = -1 if k % 12 in [5, 7] else 1
+        if v % p == 0:
+            if e == 1:
+                return mpf_mul(
+                    from_int(jacobi3),
+                    mpf_sqrt(from_int(k), prec), prec)
+            return fzero
+        if not is_quad_residue(v, p):
+            return fzero
+        _phi = p**(e - 1)*(p - 1)
+        v = (v*pow(576, _phi - 1, k))
+        m = _sqrt_mod_prime_power(v, p, e)[0]
+        arg = mpf_div(
+            mpf_mul(from_int(4*m), pi, prec),
+            from_int(k), prec)
+        return mpf_mul(mpf_mul(
+            from_int(2*jacobi3),
+            mpf_sqrt(from_int(k), prec), prec),
+            mpf_cos(arg, prec), prec)
+
+    if p != 2 or e >= 3:
+        d1, d2 = math.gcd(k1, 24), math.gcd(k2, 24)
+        e = 24//(d1*d2)
+        n1 = ((d2*e*n + (k2**2 - 1)//d1)*
+            pow(e*k2*k2*d2, _totient[k1] - 1, k1)) % k1
+        n2 = ((d1*e*n + (k1**2 - 1)//d2)*
+            pow(e*k1*k1*d1, _totient[k2] - 1, k2)) % k2
+        return mpf_mul(_a(n1, k1, prec), _a(n2, k2, prec), prec)
+    if e == 2:
+        n1 = ((8*n + 5)*pow(128, _totient[k1] - 1, k1)) % k1
+        n2 = (4 + ((n - 2 - (k1**2 - 1)//8)*(k1**2)) % 4) % 4
+        return mpf_mul(mpf_mul(
+            from_int(-1),
+            _a(n1, k1, prec), prec),
+            _a(n2, k2, prec))
+    n1 = ((8*n + 1)*pow(32, _totient[k1] - 1, k1)) % k1
+    n2 = (2 + (n - (k1**2 - 1)//8) % 2) % 2
+    return mpf_mul(_a(n1, k1, prec), _a(n2, k2, prec), prec)
+
+def _d(n, j, prec, sq23pi, sqrt8):
+    """
+    Compute the sinh term in the outer sum of the HRR formula.
+    The constants sqrt(2/3*pi) and sqrt(8) must be precomputed.
+    """
+    j = from_int(j)
+    pi = mpf_pi(prec)
+    a = mpf_div(sq23pi, j, prec)
+    b = mpf_sub(from_int(n), from_rational(1, 24, prec), prec)
+    c = mpf_sqrt(b, prec)
+    ch, sh = mpf_cosh_sinh(mpf_mul(a, c), prec)
+    D = mpf_div(
+        mpf_sqrt(j, prec),
+        mpf_mul(mpf_mul(sqrt8, b), pi), prec)
+    E = mpf_sub(mpf_mul(a, ch), mpf_div(sh, c, prec), prec)
+    return mpf_mul(D, E)
+
+
+@recurrence_memo([1, 1])
+def _partition_rec(n: int, prev) -> int:
+    """ Calculate the partition function P(n)
+
+    Parameters
+    ==========
+
+    n : int
+        nonnegative integer
+
+    """
+    v = 0
+    penta = 0 # pentagonal number: 1, 5, 12, ...
+    for i in count():
+        penta += 3*i + 1
+        np = n - penta
+        if np < 0:
+            break
+        s = prev[np]
+        np -= i + 1
+        # np = n - gp where gp = generalized pentagonal: 2, 7, 15, ...
+        if 0 <= np:
+            s += prev[np]
+        v += -s if i % 2 else s
+    return v
+
+
+def _partition(n: int) -> int:
+    """ Calculate the partition function P(n)
+
+    Parameters
+    ==========
+
+    n : int
+
+    """
+    if n < 0:
+        return 0
+    if (n <= 200_000 and n - _partition_rec.cache_length() < 70 or
+            _partition_rec.cache_length() == 2 and n < 14_400):
+        # There will be 2*10**5 elements created here
+        # and n elements created by partition, so in case we
+        # are going to be working with small n, we just
+        # use partition to calculate (and cache) the values
+        # since lookup is used there while summation, using
+        # _factor and _totient, will be used below. But we
+        # only do so if n is relatively close to the length
+        # of the cache since doing 1 calculation here is about
+        # the same as adding 70 elements to the cache. In addition,
+        # the startup here costs about the same as calculating the first
+        # 14,400 values via partition, so we delay startup here unless n
+        # is smaller than that.
+        return _partition_rec(n)
+    if '_factor' not in globals():
+        _pre()
+    # Estimate number of bits in p(n). This formula could be tidied
+    pbits = int((
+        math.pi*(2*n/3.)**0.5 -
+        math.log(4*n))/math.log(10) + 1) * \
+        math.log2(10)
+    prec = p = int(pbits*1.1 + 100)
+
+    # find the number of terms needed so rounded sum will be accurate
+    # using Rademacher's bound M(n, N) for the remainder after a partial
+    # sum of N terms (https://arxiv.org/pdf/1205.5991.pdf, (1.8))
+    c1 = 44*math.pi**2/(225*math.sqrt(3))
+    c2 = math.pi*math.sqrt(2)/75
+    c3 = math.pi*math.sqrt(2/3)
+    def _M(n, N):
+        sqrt = math.sqrt
+        return c1/sqrt(N) + c2*sqrt(N/(n - 1))*math.sinh(c3*sqrt(n)/N)
+    big = max(9, math.ceil(n**0.5))  # should be too large (for n > 65, ceil should work)
+    assert _M(n, big) < 0.5  # else double big until too large
+    while big > 40 and _M(n, big) < 0.5:
+        big //= 2
+    small = big
+    big = small*2
+    while big - small > 1:
+        N = (big + small)//2
+        if (er := _M(n, N)) < 0.5:
+            big = N
+        elif er >= 0.5:
+            small = N
+    M = big  # done with function M; now have value
+
+    # sanity check for expected size of answer
+    if M > 10**5:  # i.e. M > maxn
+        raise ValueError("Input too big")  # i.e. n > 149832547102
+
+    # calculate it
+    s = fzero
+    sq23pi = mpf_mul(mpf_sqrt(from_rational(2, 3, p), p), mpf_pi(p), p)
+    sqrt8 = mpf_sqrt(from_int(8), p)
+    for q in range(1, M):
+        a = _a(n, q, p)
+        d = _d(n, q, p, sq23pi, sqrt8)
+        s = mpf_add(s, mpf_mul(a, d), prec)
+        # On average, the terms decrease rapidly in magnitude.
+        # Dynamically reducing the precision greatly improves
+        # performance.
+        p = bitcount(abs(to_int(d))) + 50
+    return int(to_int(mpf_add(s, fhalf, prec)))
+
+
+@deprecated("""\
+The `sympy.ntheory.partitions_.npartitions` has been moved to `sympy.functions.combinatorial.numbers.partition`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def npartitions(n, verbose=False):
+    """
+    Calculate the partition function P(n), i.e. the number of ways that
+    n can be written as a sum of positive integers.
+
+    .. deprecated:: 1.13
+
+        The ``npartitions`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.partition`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    P(n) is computed using the Hardy-Ramanujan-Rademacher formula [1]_.
+
+
+    The correctness of this implementation has been tested through $10^{10}$.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import partition
+    >>> partition(25)
+    1958
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/PartitionFunctionP.html
+
+    """
+    from sympy.functions.combinatorial.numbers import partition as func_partition
+    return func_partition(n)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/primetest.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/primetest.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff3cb82cc51bf57ca345a7d72ee715c861f62e2a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/primetest.py
@@ -0,0 +1,830 @@
+"""
+Primality testing
+
+"""
+
+from itertools import count
+
+from sympy.core.sympify import sympify
+from sympy.external.gmpy import (gmpy as _gmpy, gcd, jacobi,
+                                 is_square as gmpy_is_square,
+                                 bit_scan1, is_fermat_prp, is_euler_prp,
+                                 is_selfridge_prp, is_strong_selfridge_prp,
+                                 is_strong_bpsw_prp)
+from sympy.external.ntheory import _lucas_sequence
+from sympy.utilities.misc import as_int, filldedent
+
+# Note: This list should be updated whenever new Mersenne primes are found.
+# Refer: https://www.mersenne.org/
+MERSENNE_PRIME_EXPONENTS = (2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203,
+ 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049,
+ 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583,
+ 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 77232917, 82589933,
+ 136279841)
+
+
+def is_fermat_pseudoprime(n, a):
+    r"""Returns True if ``n`` is prime or is an odd composite integer that
+    is coprime to ``a`` and satisfy the modular arithmetic congruence relation:
+
+    .. math ::
+        a^{n-1} \equiv 1 \pmod{n}
+
+    (where mod refers to the modulo operation).
+
+    Parameters
+    ==========
+
+    n : Integer
+        ``n`` is a positive integer.
+    a : Integer
+        ``a`` is a positive integer.
+        ``a`` and ``n`` should be relatively prime.
+
+    Returns
+    =======
+
+    bool : If ``n`` is prime, it always returns ``True``.
+           The composite number that returns ``True`` is called an Fermat pseudoprime.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import is_fermat_pseudoprime
+    >>> from sympy.ntheory.factor_ import isprime
+    >>> for n in range(1, 1000):
+    ...     if is_fermat_pseudoprime(n, 2) and not isprime(n):
+    ...         print(n)
+    341
+    561
+    645
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fermat_pseudoprime
+    """
+    n, a = as_int(n), as_int(a)
+    if a == 1:
+        return n == 2 or bool(n % 2)
+    return is_fermat_prp(n, a)
+
+
+def is_euler_pseudoprime(n, a):
+    r"""Returns True if ``n`` is prime or is an odd composite integer that
+    is coprime to ``a`` and satisfy the modular arithmetic congruence relation:
+
+    .. math ::
+        a^{(n-1)/2} \equiv \pm 1 \pmod{n}
+
+    (where mod refers to the modulo operation).
+
+    Parameters
+    ==========
+
+    n : Integer
+        ``n`` is a positive integer.
+    a : Integer
+        ``a`` is a positive integer.
+        ``a`` and ``n`` should be relatively prime.
+
+    Returns
+    =======
+
+    bool : If ``n`` is prime, it always returns ``True``.
+           The composite number that returns ``True`` is called an Euler pseudoprime.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import is_euler_pseudoprime
+    >>> from sympy.ntheory.factor_ import isprime
+    >>> for n in range(1, 1000):
+    ...     if is_euler_pseudoprime(n, 2) and not isprime(n):
+    ...         print(n)
+    341
+    561
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler_pseudoprime
+    """
+    n, a = as_int(n), as_int(a)
+    if a < 1:
+        raise ValueError("a should be an integer greater than 0")
+    if n < 1:
+        raise ValueError("n should be an integer greater than 0")
+    if n == 1:
+        return False
+    if a == 1:
+        return n == 2 or bool(n % 2)  # (prime or odd composite)
+    if n % 2 == 0:
+        return n == 2
+    if gcd(n, a) != 1:
+        raise ValueError("The two numbers should be relatively prime")
+    return pow(a, (n - 1) // 2, n) in [1, n - 1]
+
+
+def is_euler_jacobi_pseudoprime(n, a):
+    r"""Returns True if ``n`` is prime or is an odd composite integer that
+    is coprime to ``a`` and satisfy the modular arithmetic congruence relation:
+
+    .. math ::
+        a^{(n-1)/2} \equiv \left(\frac{a}{n}\right) \pmod{n}
+
+    (where mod refers to the modulo operation).
+
+    Parameters
+    ==========
+
+    n : Integer
+        ``n`` is a positive integer.
+    a : Integer
+        ``a`` is a positive integer.
+        ``a`` and ``n`` should be relatively prime.
+
+    Returns
+    =======
+
+    bool : If ``n`` is prime, it always returns ``True``.
+           The composite number that returns ``True`` is called an Euler-Jacobi pseudoprime.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import is_euler_jacobi_pseudoprime
+    >>> from sympy.ntheory.factor_ import isprime
+    >>> for n in range(1, 1000):
+    ...     if is_euler_jacobi_pseudoprime(n, 2) and not isprime(n):
+    ...         print(n)
+    561
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Euler%E2%80%93Jacobi_pseudoprime
+    """
+    n, a = as_int(n), as_int(a)
+    if a == 1:
+        return n == 2 or bool(n % 2)
+    return is_euler_prp(n, a)
+
+
+def is_square(n, prep=True):
+    """Return True if n == a * a for some integer a, else False.
+    If n is suspected of *not* being a square then this is a
+    quick method of confirming that it is not.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import is_square
+    >>> is_square(25)
+    True
+    >>> is_square(2)
+    False
+
+    References
+    ==========
+
+    .. [1]  https://mersenneforum.org/showpost.php?p=110896
+
+    See Also
+    ========
+    sympy.core.intfunc.isqrt
+    """
+    if prep:
+        n = as_int(n)
+        if n < 0:
+            return False
+        if n in (0, 1):
+            return True
+    return gmpy_is_square(n)
+
+
+def _test(n, base, s, t):
+    """Miller-Rabin strong pseudoprime test for one base.
+    Return False if n is definitely composite, True if n is
+    probably prime, with a probability greater than 3/4.
+
+    """
+    # do the Fermat test
+    b = pow(base, t, n)
+    if b == 1 or b == n - 1:
+        return True
+    for _ in range(s - 1):
+        b = pow(b, 2, n)
+        if b == n - 1:
+            return True
+        # see I. Niven et al. "An Introduction to Theory of Numbers", page 78
+        if b == 1:
+            return False
+    return False
+
+
+def mr(n, bases):
+    """Perform a Miller-Rabin strong pseudoprime test on n using a
+    given list of bases/witnesses.
+
+    References
+    ==========
+
+    .. [1] Richard Crandall & Carl Pomerance (2005), "Prime Numbers:
+           A Computational Perspective", Springer, 2nd edition, 135-138
+
+    A list of thresholds and the bases they require are here:
+    https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test#Deterministic_variants
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import mr
+    >>> mr(1373651, [2, 3])
+    False
+    >>> mr(479001599, [31, 73])
+    True
+
+    """
+    from sympy.polys.domains import ZZ
+
+    n = as_int(n)
+    if n < 2 or (n > 2 and n % 2 == 0):
+        return False
+    # remove powers of 2 from n-1 (= t * 2**s)
+    s = bit_scan1(n - 1)
+    t = n >> s
+    for base in bases:
+        # Bases >= n are wrapped, bases < 2 are invalid
+        if base >= n:
+            base %= n
+        if base >= 2:
+            base = ZZ(base)
+            if not _test(n, base, s, t):
+                return False
+    return True
+
+
+def _lucas_extrastrong_params(n):
+    """Calculates the "extra strong" parameters (D, P, Q) for n.
+
+    Parameters
+    ==========
+
+    n : int
+        positive odd integer
+
+    Returns
+    =======
+
+    D, P, Q: "extra strong" parameters.
+             ``(0, 0, 0)`` if we find a nontrivial divisor of ``n``.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import _lucas_extrastrong_params
+    >>> _lucas_extrastrong_params(101)
+    (12, 4, 1)
+    >>> _lucas_extrastrong_params(15)
+    (0, 0, 0)
+
+    References
+    ==========
+    .. [1] OEIS A217719: Extra Strong Lucas Pseudoprimes
+           https://oeis.org/A217719
+    .. [2] https://en.wikipedia.org/wiki/Lucas_pseudoprime
+
+    """
+    for P in count(3):
+        D = P**2 - 4
+        j = jacobi(D, n)
+        if j == -1:
+            return (D, P, 1)
+        elif j == 0 and D % n:
+            return (0, 0, 0)
+
+
+def is_lucas_prp(n):
+    """Standard Lucas compositeness test with Selfridge parameters.  Returns
+    False if n is definitely composite, and True if n is a Lucas probable
+    prime.
+
+    This is typically used in combination with the Miller-Rabin test.
+
+    References
+    ==========
+    .. [1] Robert Baillie, Samuel S. Wagstaff, Lucas Pseudoprimes,
+           Math. Comp. Vol 35, Number 152 (1980), pp. 1391-1417,
+           https://doi.org/10.1090%2FS0025-5718-1980-0583518-6
+           http://mpqs.free.fr/LucasPseudoprimes.pdf
+    .. [2] OEIS A217120: Lucas Pseudoprimes
+           https://oeis.org/A217120
+    .. [3] https://en.wikipedia.org/wiki/Lucas_pseudoprime
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import isprime, is_lucas_prp
+    >>> for i in range(10000):
+    ...     if is_lucas_prp(i) and not isprime(i):
+    ...         print(i)
+    323
+    377
+    1159
+    1829
+    3827
+    5459
+    5777
+    9071
+    9179
+    """
+    n = as_int(n)
+    if n < 2:
+        return False
+    return is_selfridge_prp(n)
+
+
+def is_strong_lucas_prp(n):
+    """Strong Lucas compositeness test with Selfridge parameters.  Returns
+    False if n is definitely composite, and True if n is a strong Lucas
+    probable prime.
+
+    This is often used in combination with the Miller-Rabin test, and
+    in particular, when combined with M-R base 2 creates the strong BPSW test.
+
+    References
+    ==========
+    .. [1] Robert Baillie, Samuel S. Wagstaff, Lucas Pseudoprimes,
+           Math. Comp. Vol 35, Number 152 (1980), pp. 1391-1417,
+           https://doi.org/10.1090%2FS0025-5718-1980-0583518-6
+           http://mpqs.free.fr/LucasPseudoprimes.pdf
+    .. [2] OEIS A217255: Strong Lucas Pseudoprimes
+           https://oeis.org/A217255
+    .. [3] https://en.wikipedia.org/wiki/Lucas_pseudoprime
+    .. [4] https://en.wikipedia.org/wiki/Baillie-PSW_primality_test
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import isprime, is_strong_lucas_prp
+    >>> for i in range(20000):
+    ...     if is_strong_lucas_prp(i) and not isprime(i):
+    ...        print(i)
+    5459
+    5777
+    10877
+    16109
+    18971
+    """
+    n = as_int(n)
+    if n < 2:
+        return False
+    return is_strong_selfridge_prp(n)
+
+
+def is_extra_strong_lucas_prp(n):
+    """Extra Strong Lucas compositeness test.  Returns False if n is
+    definitely composite, and True if n is an "extra strong" Lucas probable
+    prime.
+
+    The parameters are selected using P = 3, Q = 1, then incrementing P until
+    (D|n) == -1.  The test itself is as defined in [1]_, from the
+    Mo and Jones preprint.  The parameter selection and test are the same as
+    used in OEIS A217719, Perl's Math::Prime::Util, and the Lucas pseudoprime
+    page on Wikipedia.
+
+    It is 20-50% faster than the strong test.
+
+    Because of the different parameters selected, there is no relationship
+    between the strong Lucas pseudoprimes and extra strong Lucas pseudoprimes.
+    In particular, one is not a subset of the other.
+
+    References
+    ==========
+    .. [1] Jon Grantham, Frobenius Pseudoprimes,
+           Math. Comp. Vol 70, Number 234 (2001), pp. 873-891,
+           https://doi.org/10.1090%2FS0025-5718-00-01197-2
+    .. [2] OEIS A217719: Extra Strong Lucas Pseudoprimes
+           https://oeis.org/A217719
+    .. [3] https://en.wikipedia.org/wiki/Lucas_pseudoprime
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import isprime, is_extra_strong_lucas_prp
+    >>> for i in range(20000):
+    ...     if is_extra_strong_lucas_prp(i) and not isprime(i):
+    ...        print(i)
+    989
+    3239
+    5777
+    10877
+    """
+    # Implementation notes:
+    #   1) the parameters differ from Thomas R. Nicely's.  His parameter
+    #      selection leads to pseudoprimes that overlap M-R tests, and
+    #      contradict Baillie and Wagstaff's suggestion of (D|n) = -1.
+    #   2) The MathWorld page as of June 2013 specifies Q=-1.  The Lucas
+    #      sequence must have Q=1.  See Grantham theorem 2.3, any of the
+    #      references on the MathWorld page, or run it and see Q=-1 is wrong.
+    n = as_int(n)
+    if n == 2:
+        return True
+    if n < 2 or (n % 2) == 0:
+        return False
+    if gmpy_is_square(n):
+        return False
+
+    D, P, Q = _lucas_extrastrong_params(n)
+    if D == 0:
+        return False
+
+    # remove powers of 2 from n+1 (= k * 2**s)
+    s = bit_scan1(n + 1)
+    k = (n + 1) >> s
+
+    U, V, _ = _lucas_sequence(n, P, Q, k)
+
+    if U == 0 and (V == 2 or V == n - 2):
+        return True
+    for _ in range(1, s):
+        if V == 0:
+            return True
+        V = (V*V - 2) % n
+    return False
+
+
+def proth_test(n):
+    r""" Test if the Proth number `n = k2^m + 1` is prime. where k is a positive odd number and `2^m > k`.
+
+    Parameters
+    ==========
+
+    n : Integer
+        ``n`` is Proth number
+
+    Returns
+    =======
+
+    bool : If ``True``, then ``n`` is the Proth prime
+
+    Raises
+    ======
+
+    ValueError
+        If ``n`` is not Proth number.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import proth_test
+    >>> proth_test(41)
+    True
+    >>> proth_test(57)
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Proth_prime
+
+    """
+    n = as_int(n)
+    if n < 3:
+        raise ValueError("n is not Proth number")
+    m = bit_scan1(n - 1)
+    k = n >> m
+    if m < k.bit_length():
+        raise ValueError("n is not Proth number")
+    if n % 3 == 0:
+        return n == 3
+    if k % 3: # n % 12 == 5
+        return pow(3, n >> 1, n) == n - 1
+    # If `n` is a square number, then `jacobi(a, n) = 1` for any `a`
+    if gmpy_is_square(n):
+        return False
+    # `a` may be chosen at random.
+    # In any case, we want to find `a` such that `jacobi(a, n) = -1`.
+    for a in range(5, n):
+        j = jacobi(a, n)
+        if j == -1:
+            return pow(a, n >> 1, n) == n - 1
+        if j == 0:
+            return False
+
+
+def _lucas_lehmer_primality_test(p):
+    r""" Test if the Mersenne number `M_p = 2^p-1` is prime.
+
+    Parameters
+    ==========
+
+    p : int
+        ``p`` is an odd prime number
+
+    Returns
+    =======
+
+    bool : If ``True``, then `M_p` is the Mersenne prime
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.primetest import _lucas_lehmer_primality_test
+    >>> _lucas_lehmer_primality_test(5) # 2**5 - 1 = 31 is prime
+    True
+    >>> _lucas_lehmer_primality_test(11) # 2**11 - 1 = 2047 is not prime
+    False
+
+    See Also
+    ========
+
+    is_mersenne_prime
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
+
+    """
+    v = 4
+    m = 2**p - 1
+    for _ in range(p - 2):
+        v = pow(v, 2, m) - 2
+    return v == 0
+
+
+def is_mersenne_prime(n):
+    """Returns True if  ``n`` is a Mersenne prime, else False.
+
+    A Mersenne prime is a prime number having the form `2^i - 1`.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import is_mersenne_prime
+    >>> is_mersenne_prime(6)
+    False
+    >>> is_mersenne_prime(127)
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/MersennePrime.html
+
+    """
+    n = as_int(n)
+    if n < 1:
+        return False
+    if n & (n + 1):
+        # n is not Mersenne number
+        return False
+    p = n.bit_length()
+    if p in MERSENNE_PRIME_EXPONENTS:
+        return True
+    if p < 65_000_000 or not isprime(p):
+        # According to GIMPS, verification was completed on September 19, 2023 for p less than 65 million.
+        # https://www.mersenne.org/report_milestones/
+        # If p is composite number, then n=2**p-1 is composite number.
+        return False
+    result = _lucas_lehmer_primality_test(p)
+    if result:
+        raise ValueError(filldedent('''
+            This Mersenne Prime, 2^%s - 1, should
+            be added to SymPy's known values.''' % p))
+    return result
+
+
+_MR_BASES_32 = [15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295,
+                2776, 3620, 560, 3128, 5212, 2657, 2300, 2021, 4652, 1471,
+                9336, 4018, 2398, 20462, 10277, 8028, 2213, 6219, 620, 3763,
+                4852, 5012, 3185, 1333, 6227,5298, 1074, 2391, 5113, 7061,
+                803, 1269, 3875, 422, 751, 580, 4729, 10239, 746, 2951, 556,
+                2206, 3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373,
+                6441, 3344, 17, 15105, 1490, 4154, 2036, 1882, 1813, 467,
+                3307, 14042, 6371, 658, 1005, 903, 737, 1887, 7447, 1888,
+                2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41, 19875,
+                3110, 13221, 8726, 571, 7043, 6943, 1199, 352, 6435, 165,
+                1169, 3315, 978, 233, 3003, 2562, 2994, 10587, 10030, 2377,
+                1902, 5354, 4447, 1555, 263, 27027, 2283, 305, 669, 1912, 601,
+                6186, 429, 1930, 14873, 1784, 1661, 524, 3577, 236, 2360,
+                6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031,
+                2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725,
+                3597, 3366, 14336, 579, 165, 1375, 10018, 12616, 9816, 1371,
+                536, 1867, 10864, 857, 2206, 5788, 434, 8085, 17618, 727,
+                3639, 1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183, 8126,
+                1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566, 5674,
+                411, 522, 1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007,
+                35201, 4706, 1152, 1785, 1028, 1540, 3743, 493, 4474, 2521,
+                26845, 8354, 864, 18915, 5465, 2447, 42, 4511, 1660, 166,
+                1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816, 5197,
+                13330, 7054, 2818, 3199, 811, 922, 350, 7514, 4452, 3449,
+                2663, 4708, 418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194]
+
+
+def isprime(n):
+    """
+    Test if n is a prime number (True) or not (False). For n < 2^64 the
+    answer is definitive; larger n values have a small probability of actually
+    being pseudoprimes.
+
+    Negative numbers (e.g. -2) are not considered prime.
+
+    The first step is looking for trivial factors, which if found enables
+    a quick return.  Next, if the sieve is large enough, use bisection search
+    on the sieve.  For small numbers, a set of deterministic Miller-Rabin
+    tests are performed with bases that are known to have no counterexamples
+    in their range.  Finally if the number is larger than 2^64, a strong
+    BPSW test is performed.  While this is a probable prime test and we
+    believe counterexamples exist, there are no known counterexamples.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import isprime
+    >>> isprime(13)
+    True
+    >>> isprime(15)
+    False
+
+    Notes
+    =====
+
+    This routine is intended only for integer input, not numerical
+    expressions which may represent numbers. Floats are also
+    rejected as input because they represent numbers of limited
+    precision. While it is tempting to permit 7.0 to represent an
+    integer there are errors that may "pass silently" if this is
+    allowed:
+
+    >>> from sympy import Float, S
+    >>> int(1e3) == 1e3 == 10**3
+    True
+    >>> int(1e23) == 1e23
+    True
+    >>> int(1e23) == 10**23
+    False
+
+    >>> near_int = 1 + S(1)/10**19
+    >>> near_int == int(near_int)
+    False
+    >>> n = Float(near_int, 10)  # truncated by precision
+    >>> n % 1 == 0
+    True
+    >>> n = Float(near_int, 20)
+    >>> n % 1 == 0
+    False
+
+    See Also
+    ========
+
+    sympy.ntheory.generate.primerange : Generates all primes in a given range
+    sympy.functions.combinatorial.numbers.primepi : Return the number of primes less than or equal to n
+    sympy.ntheory.generate.prime : Return the nth prime
+
+    References
+    ==========
+    .. [1] https://en.wikipedia.org/wiki/Strong_pseudoprime
+    .. [2] Robert Baillie, Samuel S. Wagstaff, Lucas Pseudoprimes,
+           Math. Comp. Vol 35, Number 152 (1980), pp. 1391-1417,
+           https://doi.org/10.1090%2FS0025-5718-1980-0583518-6
+           http://mpqs.free.fr/LucasPseudoprimes.pdf
+    .. [3] https://en.wikipedia.org/wiki/Baillie-PSW_primality_test
+    """
+    n = as_int(n)
+
+    # Step 1, do quick composite testing via trial division.  The individual
+    # modulo tests benchmark faster than one or two primorial igcds for me.
+    # The point here is just to speedily handle small numbers and many
+    # composites.  Step 2 only requires that n <= 2 get handled here.
+    if n in [2, 3, 5]:
+        return True
+    if n < 2 or (n % 2) == 0 or (n % 3) == 0 or (n % 5) == 0:
+        return False
+    if n < 49:
+        return True
+    if (n %  7) == 0 or (n % 11) == 0 or (n % 13) == 0 or (n % 17) == 0 or \
+       (n % 19) == 0 or (n % 23) == 0 or (n % 29) == 0 or (n % 31) == 0 or \
+       (n % 37) == 0 or (n % 41) == 0 or (n % 43) == 0 or (n % 47) == 0:
+        return False
+    if n < 2809:
+        return True
+    if n < 65077:
+        # There are only five Euler pseudoprimes with a least prime factor greater than 47
+        return pow(2, n >> 1, n) in [1, n - 1] and n not in [8321, 31621, 42799, 49141, 49981]
+
+    # bisection search on the sieve if the sieve is large enough
+    from sympy.ntheory.generate import sieve as s
+    if n <= s._list[-1]:
+        l, u = s.search(n)
+        return l == u
+    from sympy.ntheory.factor_ import factor_cache
+    if (ret := factor_cache.get(n)) is not None:
+        return ret == n
+
+    # If we have GMPY2, skip straight to step 3 and do a strong BPSW test.
+    # This should be a bit faster than our step 2, and for large values will
+    # be a lot faster than our step 3 (C+GMP vs. Python).
+    if _gmpy is not None:
+        return is_strong_bpsw_prp(n)
+
+
+    # Step 2: deterministic Miller-Rabin testing for numbers < 2^64.  See:
+    #    https://miller-rabin.appspot.com/
+    # for lists.  We have made sure the M-R routine will successfully handle
+    # bases larger than n, so we can use the minimal set.
+    # In September 2015 deterministic numbers were extended to over 2^81.
+    #    https://arxiv.org/pdf/1509.00864.pdf
+    #    https://oeis.org/A014233
+    if n < 341531:
+        return mr(n, [9345883071009581737])
+    if n < 4296595241:
+        # Michal Forisek and Jakub Jancina,
+        # Fast Primality Testing for Integers That Fit into a Machine Word
+        # https://ceur-ws.org/Vol-1326/020-Forisek.pdf
+        h = ((n >> 16) ^ n) * 0x45d9f3b
+        h = ((h >> 16) ^ h) * 0x45d9f3b
+        h = ((h >> 16) ^ h) & 255
+        return mr(n, [_MR_BASES_32[h]])
+    if n < 350269456337:
+        return mr(n, [4230279247111683200, 14694767155120705706, 16641139526367750375])
+    if n < 55245642489451:
+        return mr(n, [2, 141889084524735, 1199124725622454117, 11096072698276303650])
+    if n < 7999252175582851:
+        return mr(n, [2, 4130806001517, 149795463772692060, 186635894390467037, 3967304179347715805])
+    if n < 585226005592931977:
+        return mr(n, [2, 123635709730000, 9233062284813009, 43835965440333360, 761179012939631437, 1263739024124850375])
+    if n < 18446744073709551616:
+        return mr(n, [2, 325, 9375, 28178, 450775, 9780504, 1795265022])
+    if n < 318665857834031151167461:
+        return mr(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37])
+    if n < 3317044064679887385961981:
+        return mr(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41])
+
+    # We could do this instead at any point:
+    #if n < 18446744073709551616:
+    #   return mr(n, [2]) and is_extra_strong_lucas_prp(n)
+
+    # Here are tests that are safe for MR routines that don't understand
+    # large bases.
+    #if n < 9080191:
+    #    return mr(n, [31, 73])
+    #if n < 19471033:
+    #    return mr(n, [2, 299417])
+    #if n < 38010307:
+    #    return mr(n, [2, 9332593])
+    #if n < 316349281:
+    #    return mr(n, [11000544, 31481107])
+    #if n < 4759123141:
+    #    return mr(n, [2, 7, 61])
+    #if n < 105936894253:
+    #    return mr(n, [2, 1005905886, 1340600841])
+    #if n < 31858317218647:
+    #    return mr(n, [2, 642735, 553174392, 3046413974])
+    #if n < 3071837692357849:
+    #    return mr(n, [2, 75088, 642735, 203659041, 3613982119])
+    #if n < 18446744073709551616:
+    #    return mr(n, [2, 325, 9375, 28178, 450775, 9780504, 1795265022])
+
+    # Step 3: BPSW.
+    #
+    #  Time for isprime(10**2000 + 4561), no gmpy or gmpy2 installed
+    #     44.0s   old isprime using 46 bases
+    #      5.3s   strong BPSW + one random base
+    #      4.3s   extra strong BPSW + one random base
+    #      4.1s   strong BPSW
+    #      3.2s   extra strong BPSW
+
+    # Classic BPSW from page 1401 of the paper.  See alternate ideas below.
+    return is_strong_bpsw_prp(n)
+
+    # Using extra strong test, which is somewhat faster
+    #return mr(n, [2]) and is_extra_strong_lucas_prp(n)
+
+    # Add a random M-R base
+    #import random
+    #return mr(n, [2, random.randint(3, n-1)]) and is_strong_lucas_prp(n)
+
+
+def is_gaussian_prime(num):
+    r"""Test if num is a Gaussian prime number.
+
+    References
+    ==========
+
+    .. [1] https://oeis.org/wiki/Gaussian_primes
+    """
+
+    num = sympify(num)
+    a, b = num.as_real_imag()
+    a = as_int(a, strict=False)
+    b = as_int(b, strict=False)
+    if a == 0:
+        b = abs(b)
+        return isprime(b) and b % 4 == 3
+    elif b == 0:
+        a = abs(a)
+        return isprime(a) and a % 4 == 3
+    return isprime(a**2 + b**2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/qs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/qs.py
new file mode 100644
index 0000000000000000000000000000000000000000..acc9a7b6e0151695538a99a738ef397166497ba5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/qs.py
@@ -0,0 +1,451 @@
+from math import exp, log
+from sympy.core.random import _randint
+from sympy.external.gmpy import bit_scan1, gcd, invert, sqrt as isqrt
+from sympy.ntheory.factor_ import _perfect_power
+from sympy.ntheory.primetest import isprime
+from sympy.ntheory.residue_ntheory import _sqrt_mod_prime_power
+
+
+class SievePolynomial:
+    def __init__(self, a, b, N):
+        """This class denotes the sieve polynomial.
+        Provide methods to compute `(a*x + b)**2 - N` and
+        `a*x + b` when given `x`.
+
+        Parameters
+        ==========
+
+        a : parameter of the sieve polynomial
+        b : parameter of the sieve polynomial
+        N : number to be factored
+
+        """
+        self.a = a
+        self.b = b
+        self.a2 = a**2
+        self.ab = 2*a*b
+        self.b2 = b**2 - N
+
+    def eval_u(self, x):
+        return self.a*x + self.b
+
+    def eval_v(self, x):
+        return (self.a2*x + self.ab)*x + self.b2
+
+
+class FactorBaseElem:
+    """This class stores an element of the `factor_base`.
+    """
+    def __init__(self, prime, tmem_p, log_p):
+        """
+        Initialization of factor_base_elem.
+
+        Parameters
+        ==========
+
+        prime : prime number of the factor_base
+        tmem_p : Integer square root of x**2 = n mod prime
+        log_p : Compute Natural Logarithm of the prime
+        """
+        self.prime = prime
+        self.tmem_p = tmem_p
+        self.log_p = log_p
+        # `soln1` and `soln2` are solutions to
+        # the equation `(a*x + b)**2 - N = 0 (mod p)`.
+        self.soln1 = None
+        self.soln2 = None
+        self.b_ainv = None
+
+
+def _generate_factor_base(prime_bound, n):
+    """Generate `factor_base` for Quadratic Sieve. The `factor_base`
+    consists of all the points whose ``legendre_symbol(n, p) == 1``
+    and ``p < num_primes``. Along with the prime `factor_base` also stores
+    natural logarithm of prime and the residue n modulo p.
+    It also returns the of primes numbers in the `factor_base` which are
+    close to 1000 and 5000.
+
+    Parameters
+    ==========
+
+    prime_bound : upper prime bound of the factor_base
+    n : integer to be factored
+    """
+    from sympy.ntheory.generate import sieve
+    factor_base = []
+    idx_1000, idx_5000 = None, None
+    for prime in sieve.primerange(1, prime_bound):
+        if pow(n, (prime - 1) // 2, prime) == 1:
+            if prime > 1000 and idx_1000 is None:
+                idx_1000 = len(factor_base) - 1
+            if prime > 5000 and idx_5000 is None:
+                idx_5000 = len(factor_base) - 1
+            residue = _sqrt_mod_prime_power(n, prime, 1)[0]
+            log_p = round(log(prime)*2**10)
+            factor_base.append(FactorBaseElem(prime, residue, log_p))
+    return idx_1000, idx_5000, factor_base
+
+
+def _generate_polynomial(N, M, factor_base, idx_1000, idx_5000, randint):
+    """ Generate sieve polynomials indefinitely.
+    Information such as `soln1` in the `factor_base` associated with
+    the polynomial is modified in place.
+
+    Parameters
+    ==========
+
+    N : Number to be factored
+    M : sieve interval
+    factor_base : factor_base primes
+    idx_1000 : index of prime number in the factor_base near 1000
+    idx_5000 : index of prime number in the factor_base near to 5000
+    randint : A callable that takes two integers (a, b) and returns a random integer
+              n such that a <= n <= b, similar to `random.randint`.
+    """
+    approx_val = log(2*N)/2 - log(M)
+    start = idx_1000 or 0
+    end = idx_5000 or (len(factor_base) - 1)
+    while True:
+        # Choose `a` that is close to `sqrt(2*N) / M`
+        best_a, best_q, best_ratio = None, None, None
+        for _ in range(50):
+            a = 1
+            q = []
+            while log(a) < approx_val:
+                rand_p = 0
+                while(rand_p == 0 or rand_p in q):
+                    rand_p = randint(start, end)
+                p = factor_base[rand_p].prime
+                a *= p
+                q.append(rand_p)
+            ratio = exp(log(a) - approx_val)
+            if best_ratio is None or abs(ratio - 1) < abs(best_ratio - 1):
+                best_q = q
+                best_a = a
+                best_ratio = ratio
+
+        # Set `b` using the Chinese remainder theorem
+        a = best_a
+        q = best_q
+        B = []
+        for val in q:
+            q_l = factor_base[val].prime
+            gamma = factor_base[val].tmem_p * invert(a // q_l, q_l) % q_l
+            if 2*gamma > q_l:
+                gamma = q_l - gamma
+            B.append(a//q_l*gamma)
+        b = sum(B)
+        g = SievePolynomial(a, b, N)
+        for fb in factor_base:
+            if a % fb.prime == 0:
+                fb.soln1 = None
+                continue
+            a_inv = invert(a, fb.prime)
+            fb.b_ainv = [2*b_elem*a_inv % fb.prime for b_elem in B]
+            fb.soln1 = (a_inv*(fb.tmem_p - b)) % fb.prime
+            fb.soln2 = (a_inv*(-fb.tmem_p - b)) % fb.prime
+        yield g
+
+        # Update `b` with Gray code
+        for i in range(1, 2**(len(B)-1)):
+            v = bit_scan1(i)
+            neg_pow = 2*((i >> (v + 1)) % 2) - 1
+            b = g.b + 2*neg_pow*B[v]
+            a = g.a
+            g = SievePolynomial(a, b, N)
+            for fb in factor_base:
+                if fb.soln1 is None:
+                    continue
+                fb.soln1 = (fb.soln1 - neg_pow*fb.b_ainv[v]) % fb.prime
+                fb.soln2 = (fb.soln2 - neg_pow*fb.b_ainv[v]) % fb.prime
+            yield g
+
+
+def _gen_sieve_array(M, factor_base):
+    """Sieve Stage of the Quadratic Sieve. For every prime in the factor_base
+    that does not divide the coefficient `a` we add log_p over the sieve_array
+    such that ``-M <= soln1 + i*p <=  M`` and ``-M <= soln2 + i*p <=  M`` where `i`
+    is an integer. When p = 2 then log_p is only added using
+    ``-M <= soln1 + i*p <=  M``.
+
+    Parameters
+    ==========
+
+    M : sieve interval
+    factor_base : factor_base primes
+    """
+    sieve_array = [0]*(2*M + 1)
+    for factor in factor_base:
+        if factor.soln1 is None: #The prime does not divides a
+            continue
+        for idx in range((M + factor.soln1) % factor.prime, 2*M, factor.prime):
+            sieve_array[idx] += factor.log_p
+        if factor.prime == 2:
+            continue
+        #if prime is 2 then sieve only with soln_1_p
+        for idx in range((M + factor.soln2) % factor.prime, 2*M, factor.prime):
+            sieve_array[idx] += factor.log_p
+    return sieve_array
+
+
+def _check_smoothness(num, factor_base):
+    r""" Check if `num` is smooth with respect to the given `factor_base`
+    and compute its factorization vector.
+
+    Parameters
+    ==========
+
+    num : integer whose smootheness is to be checked
+    factor_base : factor_base primes
+    """
+    if num < 0:
+        num *= -1
+        vec = 1
+    else:
+        vec = 0
+    for i, fb in enumerate(factor_base, 1):
+        if num % fb.prime:
+            continue
+        e = 1
+        num //= fb.prime
+        while num % fb.prime == 0:
+            e += 1
+            num //= fb.prime
+        if e % 2:
+            vec += 1 << i
+    return vec, num
+
+
+def _trial_division_stage(N, M, factor_base, sieve_array, sieve_poly, partial_relations, ERROR_TERM):
+    """Trial division stage. Here we trial divide the values generetated
+    by sieve_poly in the sieve interval and if it is a smooth number then
+    it is stored in `smooth_relations`. Moreover, if we find two partial relations
+    with same large prime then they are combined to form a smooth relation.
+    First we iterate over sieve array and look for values which are greater
+    than accumulated_val, as these values have a high chance of being smooth
+    number. Then using these values we find smooth relations.
+    In general, let ``t**2 = u*p modN`` and ``r**2 = v*p modN`` be two partial relations
+    with the same large prime p. Then they can be combined ``(t*r/p)**2 = u*v modN``
+    to form a smooth relation.
+
+    Parameters
+    ==========
+
+    N : Number to be factored
+    M : sieve interval
+    factor_base : factor_base primes
+    sieve_array : stores log_p values
+    sieve_poly : polynomial from which we find smooth relations
+    partial_relations : stores partial relations with one large prime
+    ERROR_TERM : error term for accumulated_val
+    """
+    accumulated_val = (log(M) + log(N)/2 - ERROR_TERM) * 2**10
+    smooth_relations = []
+    proper_factor = set()
+    partial_relation_upper_bound = 128*factor_base[-1].prime
+    for x, val in enumerate(sieve_array, -M):
+        if val < accumulated_val:
+            continue
+        v = sieve_poly.eval_v(x)
+        vec, num = _check_smoothness(v, factor_base)
+        if num == 1:
+            smooth_relations.append((sieve_poly.eval_u(x), v, vec))
+        elif num < partial_relation_upper_bound and isprime(num):
+            if N % num == 0:
+                proper_factor.add(num)
+                continue
+            u = sieve_poly.eval_u(x)
+            if num in partial_relations:
+                u_prev, v_prev, vec_prev = partial_relations.pop(num)
+                u = u*u_prev*invert(num, N) % N
+                v = v*v_prev // num**2
+                vec ^= vec_prev
+                smooth_relations.append((u, v, vec))
+            else:
+                partial_relations[num] = (u, v, vec)
+    return smooth_relations, proper_factor
+
+
+def _find_factor(N, smooth_relations, col):
+    """ Finds proper factor of N using fast gaussian reduction for modulo 2 matrix.
+
+    Parameters
+    ==========
+
+    N : Number to be factored
+    smooth_relations : Smooth relations vectors matrix
+    col : Number of columns in the matrix
+
+    Reference
+    ==========
+
+    .. [1] A fast algorithm for gaussian elimination over GF(2) and
+    its implementation on the GAPP. Cetin K.Koc, Sarath N.Arachchige
+    """
+    matrix = [s_relation[2] for s_relation in smooth_relations]
+    row = len(matrix)
+    mark = [False] * row
+    for pos in range(col):
+        m = 1 << pos
+        for i in range(row):
+            if p := matrix[i] & m:
+                add_col = p ^ matrix[i]
+                matrix[i] = m
+                mark[i] = True
+                for j in range(i + 1, row):
+                    if matrix[j] & m:
+                        matrix[j] ^= add_col
+                break
+
+    for m, mat, rel in zip(mark, matrix, smooth_relations):
+        if m:
+            continue
+        u, v = rel[0], rel[1]
+        for m1, mat1, rel1 in zip(mark, matrix, smooth_relations):
+            if m1 and mat & mat1:
+                u *= rel1[0]
+                v *= rel1[1]
+        # assert is_square(v)
+        v = isqrt(v)
+        if 1 < (g := gcd(u - v, N)) < N:
+            yield g
+
+
+def qs(N, prime_bound, M, ERROR_TERM=25, seed=1234):
+    """Performs factorization using Self-Initializing Quadratic Sieve.
+    In SIQS, let N be a number to be factored, and this N should not be a
+    perfect power. If we find two integers such that ``X**2 = Y**2 modN`` and
+    ``X != +-Y modN``, then `gcd(X + Y, N)` will reveal a proper factor of N.
+    In order to find these integers X and Y we try to find relations of form
+    t**2 = u modN where u is a product of small primes. If we have enough of
+    these relations then we can form ``(t1*t2...ti)**2 = u1*u2...ui modN`` such that
+    the right hand side is a square, thus we found a relation of ``X**2 = Y**2 modN``.
+
+    Here, several optimizations are done like using multiple polynomials for
+    sieving, fast changing between polynomials and using partial relations.
+    The use of partial relations can speeds up the factoring by 2 times.
+
+    Parameters
+    ==========
+
+    N : Number to be Factored
+    prime_bound : upper bound for primes in the factor base
+    M : Sieve Interval
+    ERROR_TERM : Error term for checking smoothness
+    seed : seed of random number generator
+
+    Returns
+    =======
+
+    set(int) : A set of factors of N without considering multiplicity.
+               Returns ``{N}`` if factorization fails.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import qs
+    >>> qs(25645121643901801, 2000, 10000)
+    {5394769, 4753701529}
+    >>> qs(9804659461513846513, 2000, 10000)
+    {4641991, 2112166839943}
+
+    See Also
+    ========
+
+    qs_factor
+
+    References
+    ==========
+
+    .. [1] https://pdfs.semanticscholar.org/5c52/8a975c1405bd35c65993abf5a4edb667c1db.pdf
+    .. [2] https://www.rieselprime.de/ziki/Self-initializing_quadratic_sieve
+    """
+    return set(qs_factor(N, prime_bound, M, ERROR_TERM, seed))
+
+
+def qs_factor(N, prime_bound, M, ERROR_TERM=25, seed=1234):
+    """ Performs factorization using Self-Initializing Quadratic Sieve.
+
+    Parameters
+    ==========
+
+    N : Number to be Factored
+    prime_bound : upper bound for primes in the factor base
+    M : Sieve Interval
+    ERROR_TERM : Error term for checking smoothness
+    seed : seed of random number generator
+
+    Returns
+    =======
+
+    dict[int, int] : Factors of N.
+                     Returns ``{N: 1}`` if factorization fails.
+                     Note that the key is not always a prime number.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import qs_factor
+    >>> qs_factor(1009 * 100003, 2000, 10000)
+    {1009: 1, 100003: 1}
+
+    See Also
+    ========
+
+    qs
+
+    """
+    if N < 2:
+        raise ValueError("N should be greater than 1")
+    factors = {}
+    smooth_relations = []
+    partial_relations = {}
+    # Eliminate the possibility of even numbers,
+    # prime numbers, and perfect powers.
+    if N % 2 == 0:
+        e = 1
+        N //= 2
+        while N % 2 == 0:
+            N //= 2
+            e += 1
+        factors[2] = e
+    if isprime(N):
+        factors[N] = 1
+        return factors
+    if result := _perfect_power(N, 3):
+        n, e = result
+        factors[n] = e
+        return factors
+    N_copy = N
+    randint = _randint(seed)
+    idx_1000, idx_5000, factor_base = _generate_factor_base(prime_bound, N)
+    threshold = len(factor_base) * 105//100
+    for g in _generate_polynomial(N, M, factor_base, idx_1000, idx_5000, randint):
+        sieve_array = _gen_sieve_array(M, factor_base)
+        s_rel, p_f = _trial_division_stage(N, M, factor_base, sieve_array, g, partial_relations, ERROR_TERM)
+        smooth_relations += s_rel
+        for p in p_f:
+            if N_copy % p:
+                continue
+            e = 1
+            N_copy //= p
+            while N_copy % p == 0:
+                N_copy //= p
+                e += 1
+            factors[p] = e
+        if threshold <= len(smooth_relations):
+            break
+
+    for factor in _find_factor(N, smooth_relations, len(factor_base) + 1):
+        if N_copy % factor == 0:
+            e = 1
+            N_copy //= factor
+            while N_copy % factor == 0:
+                N_copy //= factor
+                e += 1
+            factors[factor] = e
+            if N_copy == 1 or isprime(N_copy):
+                break
+    if N_copy != 1:
+        factors[N_copy] = 1
+    return factors
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/residue_ntheory.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/residue_ntheory.py
new file mode 100644
index 0000000000000000000000000000000000000000..eba024161194605aabebd10ee30bf09acb90270b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/residue_ntheory.py
@@ -0,0 +1,1963 @@
+from __future__ import annotations
+
+from sympy.external.gmpy import (gcd, lcm, invert, sqrt, jacobi,
+                                 bit_scan1, remove)
+from sympy.polys import Poly
+from sympy.polys.domains import ZZ
+from sympy.polys.galoistools import gf_crt1, gf_crt2, linear_congruence, gf_csolve
+from .primetest import isprime
+from .generate import primerange
+from .factor_ import factorint, _perfect_power
+from .modular import crt
+from sympy.utilities.decorator import deprecated
+from sympy.utilities.memoization import recurrence_memo
+from sympy.utilities.misc import as_int
+from sympy.utilities.iterables import iproduct
+from sympy.core.random import _randint, randint
+
+from itertools import product
+
+
+def n_order(a, n):
+    r""" Returns the order of ``a`` modulo ``n``.
+
+    Explanation
+    ===========
+
+    The order of ``a`` modulo ``n`` is the smallest integer
+    ``k`` such that `a^k` leaves a remainder of 1 with ``n``.
+
+    Parameters
+    ==========
+
+    a : integer
+    n : integer, n > 1. a and n should be relatively prime
+
+    Returns
+    =======
+
+    int : the order of ``a`` modulo ``n``
+
+    Raises
+    ======
+
+    ValueError
+        If `n \le 1` or `\gcd(a, n) \neq 1`.
+        If ``a`` or ``n`` is not an integer.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import n_order
+    >>> n_order(3, 7)
+    6
+    >>> n_order(4, 7)
+    3
+
+    See Also
+    ========
+
+    is_primitive_root
+        We say that ``a`` is a primitive root of ``n``
+        when the order of ``a`` modulo ``n`` equals ``totient(n)``
+
+    """
+    a, n = as_int(a), as_int(n)
+    if n <= 1:
+        raise ValueError("n should be an integer greater than 1")
+    a = a % n
+    # Trivial
+    if a == 1:
+        return 1
+    if gcd(a, n) != 1:
+        raise ValueError("The two numbers should be relatively prime")
+    a_order = 1
+    for p, e in factorint(n).items():
+        pe = p**e
+        pe_order = (p - 1) * p**(e - 1)
+        factors = factorint(p - 1)
+        if e > 1:
+            factors[p] = e - 1
+        order = 1
+        for px, ex in factors.items():
+            x = pow(a, pe_order // px**ex, pe)
+            while x != 1:
+                x = pow(x, px, pe)
+                order *= px
+        a_order = lcm(a_order, order)
+    return int(a_order)
+
+
+def _primitive_root_prime_iter(p):
+    r""" Generates the primitive roots for a prime ``p``.
+
+    Explanation
+    ===========
+
+    The primitive roots generated are not necessarily sorted.
+    However, the first one is the smallest primitive root.
+
+    Find the element whose order is ``p-1`` from the smaller one.
+    If we can find the first primitive root ``g``, we can use the following theorem.
+
+    .. math ::
+        \operatorname{ord}(g^k) = \frac{\operatorname{ord}(g)}{\gcd(\operatorname{ord}(g), k)}
+
+    From the assumption that `\operatorname{ord}(g)=p-1`,
+    it is a necessary and sufficient condition for
+    `\operatorname{ord}(g^k)=p-1` that `\gcd(p-1, k)=1`.
+
+    Parameters
+    ==========
+
+    p : odd prime
+
+    Yields
+    ======
+
+    int
+        the primitive roots of ``p``
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _primitive_root_prime_iter
+    >>> sorted(_primitive_root_prime_iter(19))
+    [2, 3, 10, 13, 14, 15]
+
+    References
+    ==========
+
+    .. [1] W. Stein "Elementary Number Theory" (2011), page 44
+
+    """
+    if p == 3:
+        yield 2
+        return
+    # Let p = +-1 (mod 4a). Legendre symbol (a/p) = 1, so `a` is not the primitive root.
+    # Corollary : If p = +-1 (mod 8), then 2 is not the primitive root of p.
+    g_min = 3 if p % 8 in [1, 7] else 2
+    if p < 41:
+        # small case
+        g = 5 if p == 23 else g_min
+    else:
+        v = [(p - 1) // i for i in factorint(p - 1).keys()]
+        for g in range(g_min, p):
+            if all(pow(g, pw, p) != 1 for pw in v):
+                break
+    yield g
+    # g**k is the primitive root of p iff gcd(p - 1, k) = 1
+    for k in range(3, p, 2):
+        if gcd(p - 1, k) == 1:
+            yield pow(g, k, p)
+
+
+def _primitive_root_prime_power_iter(p, e):
+    r""" Generates the primitive roots of `p^e`.
+
+    Explanation
+    ===========
+
+    Let ``g`` be the primitive root of ``p``.
+    If `g^{p-1} \not\equiv 1 \pmod{p^2}`, then ``g`` is primitive root of `p^e`.
+    Thus, if we find a primitive root ``g`` of ``p``,
+    then `g, g+p, g+2p, \ldots, g+(p-1)p` are primitive roots of `p^2` except one.
+    That one satisfies `\hat{g}^{p-1} \equiv 1 \pmod{p^2}`.
+    If ``h`` is the primitive root of `p^2`,
+    then `h, h+p^2, h+2p^2, \ldots, h+(p^{e-2}-1)p^e` are primitive roots of `p^e`.
+
+    Parameters
+    ==========
+
+    p : odd prime
+    e : positive integer
+
+    Yields
+    ======
+
+    int
+        the primitive roots of `p^e`
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _primitive_root_prime_power_iter
+    >>> sorted(_primitive_root_prime_power_iter(5, 2))
+    [2, 3, 8, 12, 13, 17, 22, 23]
+
+    """
+    if e == 1:
+        yield from _primitive_root_prime_iter(p)
+    else:
+        p2 = p**2
+        for g in _primitive_root_prime_iter(p):
+            t = (g - pow(g, 2 - p, p2)) % p2
+            for k in range(0, p2, p):
+                if k != t:
+                    yield from (g + k + m for m in range(0, p**e, p2))
+
+
+def _primitive_root_prime_power2_iter(p, e):
+    r""" Generates the primitive roots of `2p^e`.
+
+    Explanation
+    ===========
+
+    If ``g`` is the primitive root of ``p**e``,
+    then the odd one of ``g`` and ``g+p**e`` is the primitive root of ``2*p**e``.
+
+    Parameters
+    ==========
+
+    p : odd prime
+    e : positive integer
+
+    Yields
+    ======
+
+    int
+        the primitive roots of `2p^e`
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _primitive_root_prime_power2_iter
+    >>> sorted(_primitive_root_prime_power2_iter(5, 2))
+    [3, 13, 17, 23, 27, 33, 37, 47]
+
+    """
+    for g in _primitive_root_prime_power_iter(p, e):
+        if g % 2 == 1:
+            yield g
+        else:
+            yield g + p**e
+
+
+def primitive_root(p, smallest=True):
+    r""" Returns a primitive root of ``p`` or None.
+
+    Explanation
+    ===========
+
+    For the definition of primitive root,
+    see the explanation of ``is_primitive_root``.
+
+    The primitive root of ``p`` exist only for
+    `p = 2, 4, q^e, 2q^e` (``q`` is an odd prime).
+    Now, if we know the primitive root of ``q``,
+    we can calculate the primitive root of `q^e`,
+    and if we know the primitive root of `q^e`,
+    we can calculate the primitive root of `2q^e`.
+    When there is no need to find the smallest primitive root,
+    this property can be used to obtain a fast primitive root.
+    On the other hand, when we want the smallest primitive root,
+    we naively determine whether it is a primitive root or not.
+
+    Parameters
+    ==========
+
+    p : integer, p > 1
+    smallest : if True the smallest primitive root is returned or None
+
+    Returns
+    =======
+
+    int | None :
+        If the primitive root exists, return the primitive root of ``p``.
+        If not, return None.
+
+    Raises
+    ======
+
+    ValueError
+        If `p \le 1` or ``p`` is not an integer.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import primitive_root
+    >>> primitive_root(19)
+    2
+    >>> primitive_root(21) is None
+    True
+    >>> primitive_root(50, smallest=False)
+    27
+
+    See Also
+    ========
+
+    is_primitive_root
+
+    References
+    ==========
+
+    .. [1] W. Stein "Elementary Number Theory" (2011), page 44
+    .. [2] P. Hackman "Elementary Number Theory" (2009), Chapter C
+
+    """
+    p = as_int(p)
+    if p <= 1:
+        raise ValueError("p should be an integer greater than 1")
+    if p <= 4:
+        return p - 1
+    p_even = p % 2 == 0
+    if not p_even:
+        q = p  # p is odd
+    elif p % 4:
+        q = p//2  # p had 1 factor of 2
+    else:
+        return None  # p had more than one factor of 2
+    if isprime(q):
+        e = 1
+    else:
+        m = _perfect_power(q, 3)
+        if not m:
+            return None
+        q, e = m
+        if not isprime(q):
+            return None
+    if not smallest:
+        if p_even:
+            return next(_primitive_root_prime_power2_iter(q, e))
+        return next(_primitive_root_prime_power_iter(q, e))
+    if p_even:
+        for i in range(3, p, 2):
+            if i % q and is_primitive_root(i, p):
+                return i
+    g = next(_primitive_root_prime_iter(q))
+    if e == 1 or pow(g, q - 1, q**2) != 1:
+        return g
+    for i in range(g + 1, p):
+        if i % q and is_primitive_root(i, p):
+            return i
+
+
+def is_primitive_root(a, p):
+    r""" Returns True if ``a`` is a primitive root of ``p``.
+
+    Explanation
+    ===========
+
+    ``a`` is said to be the primitive root of ``p`` if `\gcd(a, p) = 1` and
+    `\phi(p)` is the smallest positive number s.t.
+
+        `a^{\phi(p)} \equiv 1 \pmod{p}`.
+
+    where `\phi(p)` is Euler's totient function.
+
+    The primitive root of ``p`` exist only for
+    `p = 2, 4, q^e, 2q^e` (``q`` is an odd prime).
+    Hence, if it is not such a ``p``, it returns False.
+    To determine the primitive root, we need to know
+    the prime factorization of ``q-1``.
+    The hardness of the determination depends on this complexity.
+
+    Parameters
+    ==========
+
+    a : integer
+    p : integer, ``p`` > 1. ``a`` and ``p`` should be relatively prime
+
+    Returns
+    =======
+
+    bool : If True, ``a`` is the primitive root of ``p``.
+
+    Raises
+    ======
+
+    ValueError
+        If `p \le 1` or `\gcd(a, p) \neq 1`.
+        If ``a`` or ``p`` is not an integer.
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import totient
+    >>> from sympy.ntheory import is_primitive_root, n_order
+    >>> is_primitive_root(3, 10)
+    True
+    >>> is_primitive_root(9, 10)
+    False
+    >>> n_order(3, 10) == totient(10)
+    True
+    >>> n_order(9, 10) == totient(10)
+    False
+
+    See Also
+    ========
+
+    primitive_root
+
+    """
+    a, p = as_int(a), as_int(p)
+    if p <= 1:
+        raise ValueError("p should be an integer greater than 1")
+    a = a % p
+    if gcd(a, p) != 1:
+        raise ValueError("The two numbers should be relatively prime")
+    # Primitive root of p exist only for
+    # p = 2, 4, q**e, 2*q**e (q is odd prime)
+    if p <= 4:
+        # The primitive root is only p-1.
+        return a == p - 1
+    if p % 2:
+        q = p  # p is odd
+    elif p % 4:
+        q = p//2  # p had 1 factor of 2
+    else:
+        return False  # p had more than one factor of 2
+    if isprime(q):
+        group_order = q - 1
+        factors = factorint(q - 1).keys()
+    else:
+        m = _perfect_power(q, 3)
+        if not m:
+            return False
+        q, e = m
+        if not isprime(q):
+            return False
+        group_order = q**(e - 1)*(q - 1)
+        factors = set(factorint(q - 1).keys())
+        factors.add(q)
+    return all(pow(a, group_order // prime, p) != 1 for prime in factors)
+
+
+def _sqrt_mod_tonelli_shanks(a, p):
+    """
+    Returns the square root in the case of ``p`` prime with ``p == 1 (mod 8)``
+
+    Assume that the root exists.
+
+    Parameters
+    ==========
+
+    a : int
+    p : int
+        prime number. should be ``p % 8 == 1``
+
+    Returns
+    =======
+
+    int : Generally, there are two roots, but only one is returned.
+          Which one is returned is random.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _sqrt_mod_tonelli_shanks
+    >>> _sqrt_mod_tonelli_shanks(2, 17) in [6, 11]
+    True
+
+    References
+    ==========
+
+    .. [1] Carl Pomerance, Richard Crandall, Prime Numbers: A Computational Perspective,
+           2nd Edition (2005), page 101, ISBN:978-0387252827
+
+    """
+    s = bit_scan1(p - 1)
+    t = p >> s
+    # find a non-quadratic residue
+    if p % 12 == 5:
+        # Legendre symbol (3/p) == -1 if p % 12 in [5, 7]
+        d = 3
+    elif p % 5 in [2, 3]:
+        # Legendre symbol (5/p) == -1 if p % 5 in [2, 3]
+        d = 5
+    else:
+        while 1:
+            d = randint(6, p - 1)
+            if jacobi(d, p) == -1:
+                break
+    #assert legendre_symbol(d, p) == -1
+    A = pow(a, t, p)
+    D = pow(d, t, p)
+    m = 0
+    for i in range(s):
+        adm = A*pow(D, m, p) % p
+        adm = pow(adm, 2**(s - 1 - i), p)
+        if adm % p == p - 1:
+            m += 2**i
+    #assert A*pow(D, m, p) % p == 1
+    x = pow(a, (t + 1)//2, p)*pow(D, m//2, p) % p
+    return x
+
+
+def sqrt_mod(a, p, all_roots=False):
+    """
+    Find a root of ``x**2 = a mod p``.
+
+    Parameters
+    ==========
+
+    a : integer
+    p : positive integer
+    all_roots : if True the list of roots is returned or None
+
+    Notes
+    =====
+
+    If there is no root it is returned None; else the returned root
+    is less or equal to ``p // 2``; in general is not the smallest one.
+    It is returned ``p // 2`` only if it is the only root.
+
+    Use ``all_roots`` only when it is expected that all the roots fit
+    in memory; otherwise use ``sqrt_mod_iter``.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import sqrt_mod
+    >>> sqrt_mod(11, 43)
+    21
+    >>> sqrt_mod(17, 32, True)
+    [7, 9, 23, 25]
+    """
+    if all_roots:
+        return sorted(sqrt_mod_iter(a, p))
+    p = abs(as_int(p))
+    halfp = p // 2
+    x = None
+    for r in sqrt_mod_iter(a, p):
+        if r < halfp:
+            return r
+        elif r > halfp:
+            return p - r
+        else:
+            x = r
+    return x
+
+
+def sqrt_mod_iter(a, p, domain=int):
+    """
+    Iterate over solutions to ``x**2 = a mod p``.
+
+    Parameters
+    ==========
+
+    a : integer
+    p : positive integer
+    domain : integer domain, ``int``, ``ZZ`` or ``Integer``
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import sqrt_mod_iter
+    >>> list(sqrt_mod_iter(11, 43))
+    [21, 22]
+
+    See Also
+    ========
+
+    sqrt_mod : Same functionality, but you want a sorted list or only one solution.
+
+    """
+    a, p = as_int(a), abs(as_int(p))
+    v = []
+    pv = []
+    _product = product
+    for px, ex in factorint(p).items():
+        if a % px:
+            # `len(rx)` is at most 4
+            rx = _sqrt_mod_prime_power(a, px, ex)
+        else:
+            # `len(list(rx))` can be assumed to be large.
+            # The `itertools.product` is disadvantageous in terms of memory usage.
+            # It is also inferior to iproduct in speed if not all Cartesian products are needed.
+            rx = _sqrt_mod1(a, px, ex)
+            _product = iproduct
+        if not rx:
+            return
+        v.append(rx)
+        pv.append(px**ex)
+    if len(v) == 1:
+        yield from map(domain, v[0])
+    else:
+        mm, e, s = gf_crt1(pv, ZZ)
+        for vx in _product(*v):
+            yield domain(gf_crt2(vx, pv, mm, e, s, ZZ))
+
+
+def _sqrt_mod_prime_power(a, p, k):
+    """
+    Find the solutions to ``x**2 = a mod p**k`` when ``a % p != 0``.
+    If no solution exists, return ``None``.
+    Solutions are returned in an ascending list.
+
+    Parameters
+    ==========
+
+    a : integer
+    p : prime number
+    k : positive integer
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _sqrt_mod_prime_power
+    >>> _sqrt_mod_prime_power(11, 43, 1)
+    [21, 22]
+
+    References
+    ==========
+
+    .. [1] P. Hackman "Elementary Number Theory" (2009), page 160
+    .. [2] http://www.numbertheory.org/php/squareroot.html
+    .. [3] [Gathen99]_
+    """
+    pk = p**k
+    a = a % pk
+
+    if p == 2:
+        # see Ref.[2]
+        if a % 8 != 1:
+            return None
+        # Trivial
+        if k <= 3:
+            return list(range(1, pk, 2))
+        r = 1
+        # r is one of the solutions to x**2 - a = 0 (mod 2**3).
+        # Hensel lift them to solutions of x**2 - a = 0 (mod 2**k)
+        # if r**2 - a = 0 mod 2**nx but not mod 2**(nx+1)
+        # then r + 2**(nx - 1) is a root mod 2**(nx+1)
+        for nx in range(3, k):
+            if ((r**2 - a) >> nx) % 2:
+                r += 1 << (nx - 1)
+        # r is a solution of x**2 - a = 0 (mod 2**k), and
+        # there exist other solutions -r, r+h, -(r+h), and these are all solutions.
+        h = 1 << (k - 1)
+        return sorted([r, pk - r, (r + h) % pk, -(r + h) % pk])
+
+    # If the Legendre symbol (a/p) is not 1, no solution exists.
+    if jacobi(a, p) != 1:
+        return None
+    if p % 4 == 3:
+        res = pow(a, (p + 1) // 4, p)
+    elif p % 8 == 5:
+        res = pow(a, (p + 3) // 8, p)
+        if pow(res, 2, p) != a % p:
+            res = res * pow(2, (p - 1) // 4, p) % p
+    else:
+        res = _sqrt_mod_tonelli_shanks(a, p)
+    if k > 1:
+        # Hensel lifting with Newton iteration, see Ref.[3] chapter 9
+        # with f(x) = x**2 - a; one has f'(a) != 0 (mod p) for p != 2
+        px = p
+        for _ in range(k.bit_length() - 1):
+            px = px**2
+            frinv = invert(2*res, px)
+            res = (res - (res**2 - a)*frinv) % px
+        if k & (k - 1): # If k is not a power of 2
+            frinv = invert(2*res, pk)
+            res = (res - (res**2 - a)*frinv) % pk
+    return sorted([res, pk - res])
+
+
+def _sqrt_mod1(a, p, n):
+    """
+    Find solution to ``x**2 == a mod p**n`` when ``a % p == 0``.
+    If no solution exists, return ``None``.
+
+    Parameters
+    ==========
+
+    a : integer
+    p : prime number, p must divide a
+    n : positive integer
+
+    References
+    ==========
+
+    .. [1] http://www.numbertheory.org/php/squareroot.html
+    """
+    pn = p**n
+    a = a % pn
+    if a == 0:
+        # case gcd(a, p**k) = p**n
+        return range(0, pn, p**((n + 1) // 2))
+    # case gcd(a, p**k) = p**r, r < n
+    a, r = remove(a, p)
+    if r % 2 == 1:
+        return None
+    res = _sqrt_mod_prime_power(a, p, n - r)
+    if res is None:
+        return None
+    m = r // 2
+    return (x for rx in res for x in range(rx*p**m, pn, p**(n - m)))
+
+
+def is_quad_residue(a, p):
+    """
+    Returns True if ``a`` (mod ``p``) is in the set of squares mod ``p``,
+    i.e a % p in set([i**2 % p for i in range(p)]).
+
+    Parameters
+    ==========
+
+    a : integer
+    p : positive integer
+
+    Returns
+    =======
+
+    bool : If True, ``x**2 == a (mod p)`` has solution.
+
+    Raises
+    ======
+
+    ValueError
+        If ``a``, ``p`` is not integer.
+        If ``p`` is not positive.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import is_quad_residue
+    >>> is_quad_residue(21, 100)
+    True
+
+    Indeed, ``pow(39, 2, 100)`` would be 21.
+
+    >>> is_quad_residue(21, 120)
+    False
+
+    That is, for any integer ``x``, ``pow(x, 2, 120)`` is not 21.
+
+    If ``p`` is an odd
+    prime, an iterative method is used to make the determination:
+
+    >>> from sympy.ntheory import is_quad_residue
+    >>> sorted(set([i**2 % 7 for i in range(7)]))
+    [0, 1, 2, 4]
+    >>> [j for j in range(7) if is_quad_residue(j, 7)]
+    [0, 1, 2, 4]
+
+    See Also
+    ========
+
+    legendre_symbol, jacobi_symbol, sqrt_mod
+    """
+    a, p = as_int(a), as_int(p)
+    if p < 1:
+        raise ValueError('p must be > 0')
+    a %= p
+    if a < 2 or p < 3:
+        return True
+    # Since we want to compute the Jacobi symbol,
+    # we separate p into the odd part and the rest.
+    t = bit_scan1(p)
+    if t:
+        # The existence of a solution to a power of 2 is determined
+        # using the logic of `p==2` in `_sqrt_mod_prime_power` and `_sqrt_mod1`.
+        a_ = a % (1 << t)
+        if a_:
+            r = bit_scan1(a_)
+            if r % 2 or (a_ >> r) & 6:
+                return False
+        p >>= t
+        a %= p
+        if a < 2 or p < 3:
+            return True
+    # If Jacobi symbol is -1 or p is prime, can be determined by Jacobi symbol only
+    j = jacobi(a, p)
+    if j == -1 or isprime(p):
+        return j == 1
+    # Checks if `x**2 = a (mod p)` has a solution
+    for px, ex in factorint(p).items():
+        if a % px:
+            if jacobi(a, px) != 1:
+                return False
+        else:
+            a_ = a % px**ex
+            if a_ == 0:
+                continue
+            a_, r = remove(a_, px)
+            if r % 2 or jacobi(a_, px) != 1:
+                return False
+    return True
+
+
+def is_nthpow_residue(a, n, m):
+    """
+    Returns True if ``x**n == a (mod m)`` has solutions.
+
+    References
+    ==========
+
+    .. [1] P. Hackman "Elementary Number Theory" (2009), page 76
+
+    """
+    a = a % m
+    a, n, m = as_int(a), as_int(n), as_int(m)
+    if m <= 0:
+        raise ValueError('m must be > 0')
+    if n < 0:
+        raise ValueError('n must be >= 0')
+    if n == 0:
+        if m == 1:
+            return False
+        return a == 1
+    if a == 0:
+        return True
+    if n == 1:
+        return True
+    if n == 2:
+        return is_quad_residue(a, m)
+    return all(_is_nthpow_residue_bign_prime_power(a, n, p, e)
+               for p, e in factorint(m).items())
+
+
+def _is_nthpow_residue_bign_prime_power(a, n, p, k):
+    r"""
+    Returns True if `x^n = a \pmod{p^k}` has solutions for `n > 2`.
+
+    Parameters
+    ==========
+
+    a : positive integer
+    n : integer, n > 2
+    p : prime number
+    k : positive integer
+
+    """
+    while a % p == 0:
+        a %= pow(p, k)
+        if not a:
+            return True
+        a, mu = remove(a, p)
+        if mu % n:
+            return False
+        k -= mu
+    if p != 2:
+        f = p**(k - 1)*(p - 1) # f = totient(p**k)
+        return pow(a, f // gcd(f, n), pow(p, k)) == 1
+    if n & 1:
+        return True
+    c = min(bit_scan1(n) + 2, k)
+    return a % pow(2, c) == 1
+
+
+def _nthroot_mod1(s, q, p, all_roots):
+    """
+    Root of ``x**q = s mod p``, ``p`` prime and ``q`` divides ``p - 1``.
+    Assume that the root exists.
+
+    Parameters
+    ==========
+
+    s : integer
+    q : integer, n > 2. ``q`` divides ``p - 1``.
+    p : prime number
+    all_roots : if False returns the smallest root, else the list of roots
+
+    Returns
+    =======
+
+    list[int] | int :
+        Root of ``x**q = s mod p``. If ``all_roots == True``,
+        returned ascending list. otherwise, returned an int.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _nthroot_mod1
+    >>> _nthroot_mod1(5, 3, 13, False)
+    7
+    >>> _nthroot_mod1(13, 4, 17, True)
+    [3, 5, 12, 14]
+
+    References
+    ==========
+
+    .. [1] A. M. Johnston, A Generalized qth Root Algorithm,
+           ACM-SIAM Symposium on Discrete Algorithms (1999), pp. 929-930
+
+    """
+    g = next(_primitive_root_prime_iter(p))
+    r = s
+    for qx, ex in factorint(q).items():
+        f = (p - 1) // qx**ex
+        while f % qx == 0:
+            f //= qx
+        z = f*invert(-f, qx)
+        x = (1 + z) // qx
+        t = discrete_log(p, pow(r, f, p), pow(g, f*qx, p))
+        for _ in range(ex):
+            # assert t == discrete_log(p, pow(r, f, p), pow(g, f*qx, p))
+            r = pow(r, x, p)*pow(g, -z*t % (p - 1), p) % p
+            t //= qx
+    res = [r]
+    h = pow(g, (p - 1) // q, p)
+    #assert pow(h, q, p) == 1
+    hx = r
+    for _ in range(q - 1):
+        hx = (hx*h) % p
+        res.append(hx)
+    if all_roots:
+        res.sort()
+        return res
+    return min(res)
+
+
+def _nthroot_mod_prime_power(a, n, p, k):
+    """ Root of ``x**n = a mod p**k``.
+
+    Parameters
+    ==========
+
+    a : integer
+    n : integer, n > 2
+    p : prime number
+    k : positive integer
+
+    Returns
+    =======
+
+    list[int] :
+        Ascending list of roots of ``x**n = a mod p**k``.
+        If no solution exists, return ``[]``.
+
+    """
+    if not _is_nthpow_residue_bign_prime_power(a, n, p, k):
+        return []
+    a_mod_p = a % p
+    if a_mod_p == 0:
+        base_roots = [0]
+    elif (p - 1) % n == 0:
+        base_roots = _nthroot_mod1(a_mod_p, n, p, all_roots=True)
+    else:
+        # The roots of ``x**n - a = 0 (mod p)`` are roots of
+        # ``gcd(x**n - a, x**(p - 1) - 1) = 0 (mod p)``
+        pa = n
+        pb = p - 1
+        b = 1
+        if pa < pb:
+            a_mod_p, pa, b, pb = b, pb, a_mod_p, pa
+        # gcd(x**pa - a, x**pb - b) = gcd(x**pb - b, x**pc - c)
+        # where pc = pa % pb; c = b**-q * a mod p
+        while pb:
+            q, pc = divmod(pa, pb)
+            c = pow(b, -q, p) * a_mod_p % p
+            pa, pb = pb, pc
+            a_mod_p, b = b, c
+        if pa == 1:
+            base_roots = [a_mod_p]
+        elif pa == 2:
+            base_roots = sqrt_mod(a_mod_p, p, all_roots=True)
+        else:
+            base_roots = _nthroot_mod1(a_mod_p, pa, p, all_roots=True)
+    if k == 1:
+        return base_roots
+    a %= p**k
+    tot_roots = set()
+    for root in base_roots:
+        diff = pow(root, n - 1, p)*n % p
+        new_base = p
+        if diff != 0:
+            m_inv = invert(diff, p)
+            for _ in range(k - 1):
+                new_base *= p
+                tmp = pow(root, n, new_base) - a
+                tmp *= m_inv
+                root = (root - tmp) % new_base
+            tot_roots.add(root)
+        else:
+            roots_in_base = {root}
+            for _ in range(k - 1):
+                new_base *= p
+                new_roots = set()
+                for k_ in roots_in_base:
+                    if pow(k_, n, new_base) != a % new_base:
+                        continue
+                    while k_ not in new_roots:
+                        new_roots.add(k_)
+                        k_ = (k_ + (new_base // p)) % new_base
+                roots_in_base = new_roots
+            tot_roots = tot_roots | roots_in_base
+    return sorted(tot_roots)
+
+
+def nthroot_mod(a, n, p, all_roots=False):
+    """
+    Find the solutions to ``x**n = a mod p``.
+
+    Parameters
+    ==========
+
+    a : integer
+    n : positive integer
+    p : positive integer
+    all_roots : if False returns the smallest root, else the list of roots
+
+    Returns
+    =======
+
+        list[int] | int | None :
+            solutions to ``x**n = a mod p``.
+            The table of the output type is:
+
+            ========== ========== ==========
+            all_roots  has roots  Returns
+            ========== ========== ==========
+            True       Yes        list[int]
+            True       No         []
+            False      Yes        int
+            False      No         None
+            ========== ========== ==========
+
+    Raises
+    ======
+
+        ValueError
+            If ``a``, ``n`` or ``p`` is not integer.
+            If ``n`` or ``p`` is not positive.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import nthroot_mod
+    >>> nthroot_mod(11, 4, 19)
+    8
+    >>> nthroot_mod(11, 4, 19, True)
+    [8, 11]
+    >>> nthroot_mod(68, 3, 109)
+    23
+
+    References
+    ==========
+
+    .. [1] P. Hackman "Elementary Number Theory" (2009), page 76
+
+    """
+    a = a % p
+    a, n, p = as_int(a), as_int(n), as_int(p)
+
+    if n < 1:
+        raise ValueError("n should be positive")
+    if p < 1:
+        raise ValueError("p should be positive")
+    if n == 1:
+        return [a] if all_roots else a
+    if n == 2:
+        return sqrt_mod(a, p, all_roots)
+    base = []
+    prime_power = []
+    for q, e in factorint(p).items():
+        tot_roots = _nthroot_mod_prime_power(a, n, q, e)
+        if not tot_roots:
+            return [] if all_roots else None
+        prime_power.append(q**e)
+        base.append(sorted(tot_roots))
+    P, E, S = gf_crt1(prime_power, ZZ)
+    ret = sorted(map(int, {gf_crt2(c, prime_power, P, E, S, ZZ)
+                           for c in product(*base)}))
+    if all_roots:
+        return ret
+    if ret:
+        return ret[0]
+
+
+def quadratic_residues(p) -> list[int]:
+    """
+    Returns the list of quadratic residues.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import quadratic_residues
+    >>> quadratic_residues(7)
+    [0, 1, 2, 4]
+    """
+    p = as_int(p)
+    r = {pow(i, 2, p) for i in range(p // 2 + 1)}
+    return sorted(r)
+
+
+@deprecated("""\
+The `sympy.ntheory.residue_ntheory.legendre_symbol` has been moved to `sympy.functions.combinatorial.numbers.legendre_symbol`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def legendre_symbol(a, p):
+    r"""
+    Returns the Legendre symbol `(a / p)`.
+
+    .. deprecated:: 1.13
+
+        The ``legendre_symbol`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.legendre_symbol`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    For an integer ``a`` and an odd prime ``p``, the Legendre symbol is
+    defined as
+
+    .. math ::
+        \genfrac(){}{}{a}{p} = \begin{cases}
+             0 & \text{if } p \text{ divides } a\\
+             1 & \text{if } a \text{ is a quadratic residue modulo } p\\
+            -1 & \text{if } a \text{ is a quadratic nonresidue modulo } p
+        \end{cases}
+
+    Parameters
+    ==========
+
+    a : integer
+    p : odd prime
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import legendre_symbol
+    >>> [legendre_symbol(i, 7) for i in range(7)]
+    [0, 1, 1, -1, 1, -1, -1]
+    >>> sorted(set([i**2 % 7 for i in range(7)]))
+    [0, 1, 2, 4]
+
+    See Also
+    ========
+
+    is_quad_residue, jacobi_symbol
+
+    """
+    from sympy.functions.combinatorial.numbers import legendre_symbol as _legendre_symbol
+    return _legendre_symbol(a, p)
+
+
+@deprecated("""\
+The `sympy.ntheory.residue_ntheory.jacobi_symbol` has been moved to `sympy.functions.combinatorial.numbers.jacobi_symbol`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def jacobi_symbol(m, n):
+    r"""
+    Returns the Jacobi symbol `(m / n)`.
+
+    .. deprecated:: 1.13
+
+        The ``jacobi_symbol`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.jacobi_symbol`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    For any integer ``m`` and any positive odd integer ``n`` the Jacobi symbol
+    is defined as the product of the Legendre symbols corresponding to the
+    prime factors of ``n``:
+
+    .. math ::
+        \genfrac(){}{}{m}{n} =
+            \genfrac(){}{}{m}{p^{1}}^{\alpha_1}
+            \genfrac(){}{}{m}{p^{2}}^{\alpha_2}
+            ...
+            \genfrac(){}{}{m}{p^{k}}^{\alpha_k}
+            \text{ where } n =
+                p_1^{\alpha_1}
+                p_2^{\alpha_2}
+                ...
+                p_k^{\alpha_k}
+
+    Like the Legendre symbol, if the Jacobi symbol `\genfrac(){}{}{m}{n} = -1`
+    then ``m`` is a quadratic nonresidue modulo ``n``.
+
+    But, unlike the Legendre symbol, if the Jacobi symbol
+    `\genfrac(){}{}{m}{n} = 1` then ``m`` may or may not be a quadratic residue
+    modulo ``n``.
+
+    Parameters
+    ==========
+
+    m : integer
+    n : odd positive integer
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import jacobi_symbol, legendre_symbol
+    >>> from sympy import S
+    >>> jacobi_symbol(45, 77)
+    -1
+    >>> jacobi_symbol(60, 121)
+    1
+
+    The relationship between the ``jacobi_symbol`` and ``legendre_symbol`` can
+    be demonstrated as follows:
+
+    >>> L = legendre_symbol
+    >>> S(45).factors()
+    {3: 2, 5: 1}
+    >>> jacobi_symbol(7, 45) == L(7, 3)**2 * L(7, 5)**1
+    True
+
+    See Also
+    ========
+
+    is_quad_residue, legendre_symbol
+    """
+    from sympy.functions.combinatorial.numbers import jacobi_symbol as _jacobi_symbol
+    return _jacobi_symbol(m, n)
+
+
+@deprecated("""\
+The `sympy.ntheory.residue_ntheory.mobius` has been moved to `sympy.functions.combinatorial.numbers.mobius`.""",
+deprecated_since_version="1.13",
+active_deprecations_target='deprecated-ntheory-symbolic-functions')
+def mobius(n):
+    """
+    Mobius function maps natural number to {-1, 0, 1}
+
+    .. deprecated:: 1.13
+
+        The ``mobius`` function is deprecated. Use :class:`sympy.functions.combinatorial.numbers.mobius`
+        instead. See its documentation for more information. See
+        :ref:`deprecated-ntheory-symbolic-functions` for details.
+
+    It is defined as follows:
+        1) `1` if `n = 1`.
+        2) `0` if `n` has a squared prime factor.
+        3) `(-1)^k` if `n` is a square-free positive integer with `k`
+           number of prime factors.
+
+    It is an important multiplicative function in number theory
+    and combinatorics.  It has applications in mathematical series,
+    algebraic number theory and also physics (Fermion operator has very
+    concrete realization with Mobius Function model).
+
+    Parameters
+    ==========
+
+    n : positive integer
+
+    Examples
+    ========
+
+    >>> from sympy.functions.combinatorial.numbers import mobius
+    >>> mobius(13*7)
+    1
+    >>> mobius(1)
+    1
+    >>> mobius(13*7*5)
+    -1
+    >>> mobius(13**2)
+    0
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/M%C3%B6bius_function
+    .. [2] Thomas Koshy "Elementary Number Theory with Applications"
+
+    """
+    from sympy.functions.combinatorial.numbers import mobius as _mobius
+    return _mobius(n)
+
+
+def _discrete_log_trial_mul(n, a, b, order=None):
+    """
+    Trial multiplication algorithm for computing the discrete logarithm of
+    ``a`` to the base ``b`` modulo ``n``.
+
+    The algorithm finds the discrete logarithm using exhaustive search. This
+    naive method is used as fallback algorithm of ``discrete_log`` when the
+    group order is very small. The value ``n`` must be greater than 1.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _discrete_log_trial_mul
+    >>> _discrete_log_trial_mul(41, 15, 7)
+    3
+
+    See Also
+    ========
+
+    discrete_log
+
+    References
+    ==========
+
+    .. [1] "Handbook of applied cryptography", Menezes, A. J., Van, O. P. C., &
+        Vanstone, S. A. (1997).
+    """
+    a %= n
+    b %= n
+    if order is None:
+        order = n
+    x = 1
+    for i in range(order):
+        if x == a:
+            return i
+        x = x * b % n
+    raise ValueError("Log does not exist")
+
+
+def _discrete_log_shanks_steps(n, a, b, order=None):
+    """
+    Baby-step giant-step algorithm for computing the discrete logarithm of
+    ``a`` to the base ``b`` modulo ``n``.
+
+    The algorithm is a time-memory trade-off of the method of exhaustive
+    search. It uses `O(sqrt(m))` memory, where `m` is the group order.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _discrete_log_shanks_steps
+    >>> _discrete_log_shanks_steps(41, 15, 7)
+    3
+
+    See Also
+    ========
+
+    discrete_log
+
+    References
+    ==========
+
+    .. [1] "Handbook of applied cryptography", Menezes, A. J., Van, O. P. C., &
+        Vanstone, S. A. (1997).
+    """
+    a %= n
+    b %= n
+    if order is None:
+        order = n_order(b, n)
+    m = sqrt(order) + 1
+    T = {}
+    x = 1
+    for i in range(m):
+        T[x] = i
+        x = x * b % n
+    z = pow(b, -m, n)
+    x = a
+    for i in range(m):
+        if x in T:
+            return i * m + T[x]
+        x = x * z % n
+    raise ValueError("Log does not exist")
+
+
+def _discrete_log_pollard_rho(n, a, b, order=None, retries=10, rseed=None):
+    """
+    Pollard's Rho algorithm for computing the discrete logarithm of ``a`` to
+    the base ``b`` modulo ``n``.
+
+    It is a randomized algorithm with the same expected running time as
+    ``_discrete_log_shanks_steps``, but requires a negligible amount of memory.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _discrete_log_pollard_rho
+    >>> _discrete_log_pollard_rho(227, 3**7, 3)
+    7
+
+    See Also
+    ========
+
+    discrete_log
+
+    References
+    ==========
+
+    .. [1] "Handbook of applied cryptography", Menezes, A. J., Van, O. P. C., &
+        Vanstone, S. A. (1997).
+    """
+    a %= n
+    b %= n
+
+    if order is None:
+        order = n_order(b, n)
+    randint = _randint(rseed)
+
+    for i in range(retries):
+        aa = randint(1, order - 1)
+        ba = randint(1, order - 1)
+        xa = pow(b, aa, n) * pow(a, ba, n) % n
+
+        c = xa % 3
+        if c == 0:
+            xb = a * xa % n
+            ab = aa
+            bb = (ba + 1) % order
+        elif c == 1:
+            xb = xa * xa % n
+            ab = (aa + aa) % order
+            bb = (ba + ba) % order
+        else:
+            xb = b * xa % n
+            ab = (aa + 1) % order
+            bb = ba
+
+        for j in range(order):
+            c = xa % 3
+            if c == 0:
+                xa = a * xa % n
+                ba = (ba + 1) % order
+            elif c == 1:
+                xa = xa * xa % n
+                aa = (aa + aa) % order
+                ba = (ba + ba) % order
+            else:
+                xa = b * xa % n
+                aa = (aa + 1) % order
+
+            c = xb % 3
+            if c == 0:
+                xb = a * xb % n
+                bb = (bb + 1) % order
+            elif c == 1:
+                xb = xb * xb % n
+                ab = (ab + ab) % order
+                bb = (bb + bb) % order
+            else:
+                xb = b * xb % n
+                ab = (ab + 1) % order
+
+            c = xb % 3
+            if c == 0:
+                xb = a * xb % n
+                bb = (bb + 1) % order
+            elif c == 1:
+                xb = xb * xb % n
+                ab = (ab + ab) % order
+                bb = (bb + bb) % order
+            else:
+                xb = b * xb % n
+                ab = (ab + 1) % order
+
+            if xa == xb:
+                r = (ba - bb) % order
+                try:
+                    e = invert(r, order) * (ab - aa) % order
+                    if (pow(b, e, n) - a) % n == 0:
+                        return e
+                except ZeroDivisionError:
+                    pass
+                break
+    raise ValueError("Pollard's Rho failed to find logarithm")
+
+
+def _discrete_log_is_smooth(n: int, factorbase: list):
+    """Try to factor n with respect to a given factorbase.
+    Upon success a list of exponents with respect to the factorbase is returned.
+    Otherwise None."""
+    factors = [0]*len(factorbase)
+    for i, p in enumerate(factorbase):
+        while n % p == 0: # divide by p as many times as possible
+            factors[i] += 1
+            n = n // p
+    if n != 1:
+        return None # the number factors if at the end nothing is left
+    return factors
+
+
+def _discrete_log_index_calculus(n, a, b, order, rseed=None):
+    """
+    Index Calculus algorithm for computing the discrete logarithm of ``a`` to
+    the base ``b`` modulo ``n``.
+
+    The group order must be given and prime. It is not suitable for small orders
+    and the algorithm might fail to find a solution in such situations.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _discrete_log_index_calculus
+    >>> _discrete_log_index_calculus(24570203447, 23859756228, 2, 12285101723)
+    4519867240
+
+    See Also
+    ========
+
+    discrete_log
+
+    References
+    ==========
+
+    .. [1] "Handbook of applied cryptography", Menezes, A. J., Van, O. P. C., &
+        Vanstone, S. A. (1997).
+    """
+    randint = _randint(rseed)
+    from math import sqrt, exp, log
+    a %= n
+    b %= n
+    # assert isprime(order), "The order of the base must be prime."
+    # First choose a heuristic the bound B for the factorbase.
+    # We have added an extra term to the asymptotic value which
+    # is closer to the theoretical optimum for n up to 2^70.
+    B = int(exp(0.5 * sqrt( log(n) * log(log(n)) )*( 1 + 1/log(log(n)) )))
+    max = 5 * B * B  # expected number of tries to find a relation
+    factorbase = list(primerange(B)) # compute the factorbase
+    lf = len(factorbase) # length of the factorbase
+    ordermo = order-1
+    abx = a
+    for x in range(order):
+        if abx == 1:
+            return (order - x) % order
+        relationa = _discrete_log_is_smooth(abx, factorbase)
+        if relationa:
+            relationa = [r % order for r in relationa] + [x]
+            break
+        abx = abx * b % n # abx = a*pow(b, x, n) % n
+
+    else:
+        raise ValueError("Index Calculus failed")
+
+    relations = [None] * lf
+    k = 1  # number of relations found
+    kk = 0
+    while k < 3 * lf and kk < max:  # find relations for all primes in our factor base
+        x = randint(1,ordermo)
+        relation = _discrete_log_is_smooth(pow(b,x,n), factorbase)
+        if relation is None:
+            kk += 1
+            continue
+        k += 1
+        kk = 0
+        relation += [ x ]
+        index = lf  # determine the index of the first nonzero entry
+        for i in range(lf):
+            ri = relation[i] % order
+            if ri> 0 and relations[i] is not None:  # make this entry zero if we can
+                for j in range(lf+1):
+                    relation[j] = (relation[j] - ri*relations[i][j]) % order
+            else:
+                relation[i] = ri
+            if relation[i] > 0 and index == lf:  # is this the index of the first nonzero entry?
+                index = i
+        if index == lf or relations[index] is not None:  # the relation contains no new information
+            continue
+        # the relation contains new information
+        rinv = pow(relation[index],-1,order)  # normalize the first nonzero entry
+        for j in range(index,lf+1):
+            relation[j] = rinv * relation[j] % order
+        relations[index] = relation
+        for i in range(lf):  # subtract the new relation from the one for a
+            if relationa[i] > 0 and relations[i] is not None:
+                rbi = relationa[i]
+                for j in range(lf+1):
+                    relationa[j] = (relationa[j] - rbi*relations[i][j]) % order
+            if relationa[i] > 0:  # the index of the first nonzero entry
+                break  # we do not need to reduce further at this point
+        else:  # all unknowns are gone
+            #print(f"Success after {k} relations out of {lf}")
+            x = (order -relationa[lf]) % order
+            if pow(b,x,n) == a:
+                return x
+            raise ValueError("Index Calculus failed")
+    raise ValueError("Index Calculus failed")
+
+
+def _discrete_log_pohlig_hellman(n, a, b, order=None, order_factors=None):
+    """
+    Pohlig-Hellman algorithm for computing the discrete logarithm of ``a`` to
+    the base ``b`` modulo ``n``.
+
+    In order to compute the discrete logarithm, the algorithm takes advantage
+    of the factorization of the group order. It is more efficient when the
+    group order factors into many small primes.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _discrete_log_pohlig_hellman
+    >>> _discrete_log_pohlig_hellman(251, 210, 71)
+    197
+
+    See Also
+    ========
+
+    discrete_log
+
+    References
+    ==========
+
+    .. [1] "Handbook of applied cryptography", Menezes, A. J., Van, O. P. C., &
+        Vanstone, S. A. (1997).
+    """
+    from .modular import crt
+    a %= n
+    b %= n
+
+    if order is None:
+        order = n_order(b, n)
+    if order_factors is None:
+        order_factors = factorint(order)
+    l = [0] * len(order_factors)
+
+    for i, (pi, ri) in enumerate(order_factors.items()):
+        for j in range(ri):
+            aj = pow(a * pow(b, -l[i], n), order // pi**(j + 1), n)
+            bj = pow(b, order // pi, n)
+            cj = discrete_log(n, aj, bj, pi, True)
+            l[i] += cj * pi**j
+
+    d, _ = crt([pi**ri for pi, ri in order_factors.items()], l)
+    return d
+
+
+def discrete_log(n, a, b, order=None, prime_order=None):
+    """
+    Compute the discrete logarithm of ``a`` to the base ``b`` modulo ``n``.
+
+    This is a recursive function to reduce the discrete logarithm problem in
+    cyclic groups of composite order to the problem in cyclic groups of prime
+    order.
+
+    It employs different algorithms depending on the problem (subgroup order
+    size, prime order or not):
+
+        * Trial multiplication
+        * Baby-step giant-step
+        * Pollard's Rho
+        * Index Calculus
+        * Pohlig-Hellman
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import discrete_log
+    >>> discrete_log(41, 15, 7)
+    3
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/DiscreteLogarithm.html
+    .. [2] "Handbook of applied cryptography", Menezes, A. J., Van, O. P. C., &
+        Vanstone, S. A. (1997).
+
+    """
+    from math import sqrt, log
+    n, a, b = as_int(n), as_int(a), as_int(b)
+
+    if n < 1:
+        raise ValueError("n should be positive")
+    if n == 1:
+        return 0
+
+    if order is None:
+        # Compute the order and its factoring in one pass
+        # order = totient(n), factors = factorint(order)
+        factors = {}
+        for px, kx in factorint(n).items():
+            if kx > 1:
+                if px in factors:
+                    factors[px] += kx - 1
+                else:
+                    factors[px] = kx - 1
+            for py, ky in factorint(px - 1).items():
+                if py in factors:
+                    factors[py] += ky
+                else:
+                    factors[py] = ky
+        order = 1
+        for px, kx in factors.items():
+            order *= px**kx
+        # Now the `order` is the order of the group and factors = factorint(order)
+        # The order of `b` divides the order of the group.
+        order_factors = {}
+        for p, e in factors.items():
+            i = 0
+            for _ in range(e):
+                if pow(b, order // p, n) == 1:
+                    order //= p
+                    i += 1
+                else:
+                    break
+            if i < e:
+                order_factors[p] = e - i
+
+    if prime_order is None:
+        prime_order = isprime(order)
+
+    if order < 1000:
+        return _discrete_log_trial_mul(n, a, b, order)
+    elif prime_order:
+        # Shanks and Pollard rho are O(sqrt(order)) while index calculus is O(exp(2*sqrt(log(n)log(log(n)))))
+        # we compare the expected running times to determine the algorithm which is expected to be faster
+        if 4*sqrt(log(n)*log(log(n))) < log(order) - 10:  # the number 10 was determined experimental
+            return _discrete_log_index_calculus(n, a, b, order)
+        elif order < 1000000000000:
+            # Shanks seems typically faster, but uses O(sqrt(order)) memory
+            return _discrete_log_shanks_steps(n, a, b, order)
+        return _discrete_log_pollard_rho(n, a, b, order)
+
+    return _discrete_log_pohlig_hellman(n, a, b, order, order_factors)
+
+
+
+def quadratic_congruence(a, b, c, n):
+    r"""
+    Find the solutions to `a x^2 + b x + c \equiv 0 \pmod{n}`.
+
+    Parameters
+    ==========
+
+    a : int
+    b : int
+    c : int
+    n : int
+        A positive integer.
+
+    Returns
+    =======
+
+    list[int] :
+        A sorted list of solutions. If no solution exists, ``[]``.
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import quadratic_congruence
+    >>> quadratic_congruence(2, 5, 3, 7) # 2x^2 + 5x + 3 = 0 (mod 7)
+    [2, 6]
+    >>> quadratic_congruence(8, 6, 4, 15) # No solution
+    []
+
+    See Also
+    ========
+
+    polynomial_congruence : Solve the polynomial congruence
+
+    """
+    a = as_int(a)
+    b = as_int(b)
+    c = as_int(c)
+    n = as_int(n)
+    if n <= 1:
+        raise ValueError("n should be an integer greater than 1")
+    a %= n
+    b %= n
+    c %= n
+
+    if a == 0:
+        return linear_congruence(b, -c, n)
+    if n == 2:
+        # assert a == 1
+        roots = []
+        if c == 0:
+            roots.append(0)
+        if (b + c) % 2:
+            roots.append(1)
+        return roots
+    if gcd(2*a, n) == 1:
+        inv_a = invert(a, n)
+        b *= inv_a
+        c *= inv_a
+        if b % 2:
+            b += n
+        b >>= 1
+        return sorted((i - b) % n for i in sqrt_mod_iter(b**2 - c, n))
+    res = set()
+    for i in sqrt_mod_iter(b**2 - 4*a*c, 4*a*n):
+        q, rem = divmod(i - b, 2*a)
+        if rem == 0:
+            res.add(q % n)
+
+    return sorted(res)
+
+
+def _valid_expr(expr):
+    """
+    return coefficients of expr if it is a univariate polynomial
+    with integer coefficients else raise a ValueError.
+    """
+
+    if not expr.is_polynomial():
+        raise ValueError("The expression should be a polynomial")
+    polynomial = Poly(expr)
+    if not polynomial.is_univariate:
+        raise ValueError("The expression should be univariate")
+    if not polynomial.domain == ZZ:
+        raise ValueError("The expression should should have integer coefficients")
+    return polynomial.all_coeffs()
+
+
+def polynomial_congruence(expr, m):
+    """
+    Find the solutions to a polynomial congruence equation modulo m.
+
+    Parameters
+    ==========
+
+    expr : integer coefficient polynomial
+    m : positive integer
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory import polynomial_congruence
+    >>> from sympy.abc import x
+    >>> expr = x**6 - 2*x**5 -35
+    >>> polynomial_congruence(expr, 6125)
+    [3257]
+
+    See Also
+    ========
+
+    sympy.polys.galoistools.gf_csolve : low level solving routine used by this routine
+
+    """
+    coefficients = _valid_expr(expr)
+    coefficients = [num % m for num in coefficients]
+    rank = len(coefficients)
+    if rank == 3:
+        return quadratic_congruence(*coefficients, m)
+    if rank == 2:
+        return quadratic_congruence(0, *coefficients, m)
+    if coefficients[0] == 1 and 1 + coefficients[-1] == sum(coefficients):
+        return nthroot_mod(-coefficients[-1], rank - 1, m, True)
+    return gf_csolve(coefficients, m)
+
+
+def binomial_mod(n, m, k):
+    """Compute ``binomial(n, m) % k``.
+
+    Explanation
+    ===========
+
+    Returns ``binomial(n, m) % k`` using a generalization of Lucas'
+    Theorem for prime powers given by Granville [1]_, in conjunction with
+    the Chinese Remainder Theorem.  The residue for each prime power
+    is calculated in time O(log^2(n) + q^4*log(n)log(p) + q^4*p*log^3(p)).
+
+    Parameters
+    ==========
+
+    n : an integer
+    m : an integer
+    k : a positive integer
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import binomial_mod
+    >>> binomial_mod(10, 2, 6)  # binomial(10, 2) = 45
+    3
+    >>> binomial_mod(17, 9, 10)  # binomial(17, 9) = 24310
+    0
+
+    References
+    ==========
+
+    .. [1] Binomial coefficients modulo prime powers, Andrew Granville,
+        Available: https://web.archive.org/web/20170202003812/http://www.dms.umontreal.ca/~andrew/PDF/BinCoeff.pdf
+    """
+    if k < 1: raise ValueError('k is required to be positive')
+    # We decompose q into a product of prime powers and apply
+    # the generalization of Lucas' Theorem given by Granville
+    # to obtain binomial(n, k) mod p^e, and then use the Chinese
+    # Remainder Theorem to obtain the result mod q
+    if n < 0 or m < 0 or m > n: return 0
+    factorisation = factorint(k)
+    residues = [_binomial_mod_prime_power(n, m, p, e) for p, e in factorisation.items()]
+    return crt([p**pw for p, pw in factorisation.items()], residues, check=False)[0]
+
+
+def _binomial_mod_prime_power(n, m, p, q):
+    """Compute ``binomial(n, m) % p**q`` for a prime ``p``.
+
+    Parameters
+    ==========
+
+    n : positive integer
+    m : a nonnegative integer
+    p : a prime
+    q : a positive integer (the prime exponent)
+
+    Examples
+    ========
+
+    >>> from sympy.ntheory.residue_ntheory import _binomial_mod_prime_power
+    >>> _binomial_mod_prime_power(10, 2, 3, 2)  # binomial(10, 2) = 45
+    0
+    >>> _binomial_mod_prime_power(17, 9, 2, 4)  # binomial(17, 9) = 24310
+    6
+
+    References
+    ==========
+
+    .. [1] Binomial coefficients modulo prime powers, Andrew Granville,
+        Available: https://web.archive.org/web/20170202003812/http://www.dms.umontreal.ca/~andrew/PDF/BinCoeff.pdf
+    """
+    # Function/variable naming within this function follows Ref.[1]
+    # n!_p will be used to denote the product of integers <= n not divisible by
+    # p, with binomial(n, m)_p the same as binomial(n, m), but defined using
+    # n!_p in place of n!
+    modulo = pow(p, q)
+
+    def up_factorial(u):
+        """Compute (u*p)!_p modulo p^q."""
+        r = q // 2
+        fac = prod = 1
+        if r == 1 and p == 2 or 2*r + 1 in (p, p*p):
+            if q % 2 == 1: r += 1
+            modulo, div = pow(p, 2*r), pow(p, 2*r - q)
+        else:
+            modulo, div = pow(p, 2*r + 1), pow(p, (2*r + 1) - q)
+        for j in range(1, r + 1):
+            for mul in range((j - 1)*p + 1, j*p):  # ignore jp itself
+                fac *= mul
+                fac %= modulo
+            bj_ = bj(u, j, r)
+            prod *= pow(fac, bj_, modulo)
+            prod %= modulo
+        if p == 2:
+            sm = u // 2
+            for j in range(1, r + 1): sm += j//2 * bj(u, j, r)
+            if sm % 2 == 1: prod *= -1
+        prod %= modulo//div
+        return prod % modulo
+
+    def bj(u, j, r):
+        """Compute the exponent of (j*p)!_p in the calculation of (u*p)!_p."""
+        prod = u
+        for i in range(1, r + 1):
+            if i != j: prod *= u*u - i*i
+        for i in range(1, r + 1):
+            if i != j: prod //= j*j - i*i
+        return prod // j
+
+    def up_plus_v_binom(u, v):
+        """Compute binomial(u*p + v, v)_p modulo p^q."""
+        prod = 1
+        div = invert(factorial(v), modulo)
+        for j in range(1, q):
+            b = div
+            for v_ in range(j*p + 1, j*p + v + 1):
+                b *= v_
+                b %= modulo
+            aj = u
+            for i in range(1, q):
+                if i != j: aj *= u - i
+            for i in range(1, q):
+                if i != j: aj //= j - i
+            aj //= j
+            prod *= pow(b, aj, modulo)
+            prod %= modulo
+        return prod
+
+    @recurrence_memo([1])
+    def factorial(v, prev):
+        """Compute v! modulo p^q."""
+        return v*prev[-1] % modulo
+
+    def factorial_p(n):
+        """Compute n!_p modulo p^q."""
+        u, v = divmod(n, p)
+        return (factorial(v) * up_factorial(u) * up_plus_v_binom(u, v)) % modulo
+
+    prod = 1
+    Nj, Mj, Rj = n, m, n - m
+    # e0 will be the p-adic valuation of binomial(n, m) at p
+    e0 = carry = eq_1 = j = 0
+    while Nj:
+        numerator = factorial_p(Nj % modulo)
+        denominator = factorial_p(Mj % modulo) * factorial_p(Rj % modulo) % modulo
+        Nj, (Mj, mj), (Rj, rj) = Nj//p, divmod(Mj, p), divmod(Rj, p)
+        carry = (mj + rj + carry) // p
+        e0 += carry
+        if j >= q - 1: eq_1 += carry
+        prod *= numerator * invert(denominator, modulo)
+        prod %= modulo
+        j += 1
+
+    mul = pow(1 if p == 2 and q >= 3 else -1, eq_1, modulo)
+    return (pow(p, e0, modulo) * mul * prod) % modulo
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_bbp_pi.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_bbp_pi.py
new file mode 100644
index 0000000000000000000000000000000000000000..69c24970239cc45eef4140bf19dfd7d4f6a7e150
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_bbp_pi.py
@@ -0,0 +1,134 @@
+from sympy.core.random import randint
+
+from sympy.ntheory.bbp_pi import pi_hex_digits
+from sympy.testing.pytest import raises
+
+
+# http://www.herongyang.com/Cryptography/Blowfish-First-8366-Hex-Digits-of-PI.html
+# There are actually 8336 listed there; with the prepended 3 there are 8337
+# below
+dig=''.join('''
+3243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89452821e638d013
+77be5466cf34e90c6cc0ac29b7c97c50dd3f84d5b5b54709179216d5d98979fb1bd1310ba698dfb5
+ac2ffd72dbd01adfb7b8e1afed6a267e96ba7c9045f12c7f9924a19947b3916cf70801f2e2858efc
+16636920d871574e69a458fea3f4933d7e0d95748f728eb658718bcd5882154aee7b54a41dc25a59
+b59c30d5392af26013c5d1b023286085f0ca417918b8db38ef8e79dcb0603a180e6c9e0e8bb01e8a
+3ed71577c1bd314b2778af2fda55605c60e65525f3aa55ab945748986263e8144055ca396a2aab10
+b6b4cc5c341141e8cea15486af7c72e993b3ee1411636fbc2a2ba9c55d741831f6ce5c3e169b8793
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+9ac9aa53fd62a80f00bb25bfe235bdd2f671126905b2040222b6cbcf7ccd769c2b53113ec01640e3
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+5b578fdfe33ac372e6'''.split())
+
+
+def test_hex_pi_nth_digits():
+    assert pi_hex_digits(0) == '3243f6a8885a30'
+    assert pi_hex_digits(1) ==  '243f6a8885a308'
+    assert pi_hex_digits(10000) == '68ac8fcfb8016c'
+    assert pi_hex_digits(13) == '08d313198a2e03'
+    assert pi_hex_digits(0, 3) == '324'
+    assert pi_hex_digits(0, 0) == ''
+    raises(ValueError, lambda: pi_hex_digits(-1))
+    raises(ValueError, lambda: pi_hex_digits(0, -1))
+    raises(ValueError, lambda: pi_hex_digits(3.14))
+
+    # this will pick a random segment to compute every time
+    # it is run. If it ever fails, there is an error in the
+    # computation.
+    n = randint(0, len(dig))
+    prec = randint(0, len(dig) - n)
+    assert pi_hex_digits(n, prec) == dig[n: n + prec]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_continued_fraction.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_continued_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..8ca6088507f1d112e9146cd5249b1143f375c2cf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_continued_fraction.py
@@ -0,0 +1,77 @@
+import itertools
+from sympy.core import GoldenRatio as phi
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.ntheory.continued_fraction import \
+    (continued_fraction_periodic as cf_p,
+     continued_fraction_iterator as cf_i,
+     continued_fraction_convergents as cf_c,
+     continued_fraction_reduce as cf_r,
+     continued_fraction as cf)
+from sympy.testing.pytest import raises
+
+
+def test_continued_fraction():
+    assert cf_p(1, 1, 10, 0) == cf_p(1, 1, 0, 1)
+    assert cf_p(1, -1, 10, 1) == cf_p(-1, 1, 10, -1)
+    t = sqrt(2)
+    assert cf((1 + t)*(1 - t)) == cf(-1)
+    for n in [0, 2, Rational(2, 3), sqrt(2), 3*sqrt(2), 1 + 2*sqrt(3)/5,
+            (2 - 3*sqrt(5))/7, 1 + sqrt(2), (-5 + sqrt(17))/4]:
+        assert (cf_r(cf(n)) - n).expand() == 0
+        assert (cf_r(cf(-n)) + n).expand() == 0
+    raises(ValueError, lambda: cf(sqrt(2 + sqrt(3))))
+    raises(ValueError, lambda: cf(sqrt(2) + sqrt(3)))
+    raises(ValueError, lambda: cf(pi))
+    raises(ValueError, lambda: cf(.1))
+
+    raises(ValueError, lambda: cf_p(1, 0, 0))
+    raises(ValueError, lambda: cf_p(1, 1, -1))
+    assert cf_p(4, 3, 0) == [1, 3]
+    assert cf_p(0, 3, 5) == [0, 1, [2, 1, 12, 1, 2, 2]]
+    assert cf_p(1, 1, 0) == [1]
+    assert cf_p(3, 4, 0) == [0, 1, 3]
+    assert cf_p(4, 5, 0) == [0, 1, 4]
+    assert cf_p(5, 6, 0) == [0, 1, 5]
+    assert cf_p(11, 13, 0) == [0, 1, 5, 2]
+    assert cf_p(16, 19, 0) == [0, 1, 5, 3]
+    assert cf_p(27, 32, 0) == [0, 1, 5, 2, 2]
+    assert cf_p(1, 2, 5) == [[1]]
+    assert cf_p(0, 1, 2) == [1, [2]]
+    assert cf_p(6, 7, 49) == [1, 1, 6]
+    assert cf_p(3796, 1387, 0) == [2, 1, 2, 1, 4]
+    assert cf_p(3245, 10000) == [0, 3, 12, 4, 13]
+    assert cf_p(1932, 2568) == [0, 1, 3, 26, 2]
+    assert cf_p(6589, 2569) == [2, 1, 1, 3, 2, 1, 3, 1, 23]
+
+    def take(iterator, n=7):
+        return list(itertools.islice(iterator, n))
+
+    assert take(cf_i(phi)) == [1, 1, 1, 1, 1, 1, 1]
+    assert take(cf_i(pi)) == [3, 7, 15, 1, 292, 1, 1]
+
+    assert list(cf_i(Rational(17, 12))) == [1, 2, 2, 2]
+    assert list(cf_i(Rational(-17, 12))) == [-2, 1, 1, 2, 2]
+
+    assert list(cf_c([1, 6, 1, 8])) == [S.One, Rational(7, 6), Rational(8, 7), Rational(71, 62)]
+    assert list(cf_c([2])) == [S(2)]
+    assert list(cf_c([1, 1, 1, 1, 1, 1, 1])) == [S.One, S(2), Rational(3, 2), Rational(5, 3),
+                                                 Rational(8, 5), Rational(13, 8), Rational(21, 13)]
+    assert list(cf_c([1, 6, Rational(-1, 2), 4])) == [S.One, Rational(7, 6), Rational(5, 4), Rational(3, 2)]
+    assert take(cf_c([[1]])) == [S.One, S(2), Rational(3, 2), Rational(5, 3), Rational(8, 5),
+                                 Rational(13, 8), Rational(21, 13)]
+    assert take(cf_c([1, [1, 2]])) == [S.One, S(2), Rational(5, 3), Rational(7, 4), Rational(19, 11),
+                                    Rational(26, 15), Rational(71, 41)]
+
+    cf_iter_e = (2 if i == 1 else i // 3 * 2 if i % 3 == 0 else 1 for i in itertools.count(1))
+    assert take(cf_c(cf_iter_e)) == [S(2), S(3), Rational(8, 3), Rational(11, 4), Rational(19, 7),
+                                     Rational(87, 32), Rational(106, 39)]
+
+    assert cf_r([1, 6, 1, 8]) == Rational(71, 62)
+    assert cf_r([3]) == S(3)
+    assert cf_r([-1, 5, 1, 4]) == Rational(-24, 29)
+    assert (cf_r([0, 1, 1, 7, [24, 8]]) - (sqrt(3) + 2)/7).expand() == 0
+    assert cf_r([1, 5, 9]) == Rational(55, 46)
+    assert (cf_r([[1]]) - (sqrt(5) + 1)/2).expand() == 0
+    assert cf_r([-3, 1, 1, [2]]) == -1 - sqrt(2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_digits.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_digits.py
new file mode 100644
index 0000000000000000000000000000000000000000..4284805f4ffe5b9095eacb2e83f2cd8076db3ee4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_digits.py
@@ -0,0 +1,55 @@
+from sympy.ntheory import count_digits, digits, is_palindromic
+from sympy.core.intfunc import num_digits
+
+from sympy.testing.pytest import raises
+
+
+def test_num_digits():
+    # depending on whether one rounds up or down or uses log or log10,
+    # one or more of these will fail if you don't check for the off-by
+    # one condition
+    assert num_digits(2, 2) == 2
+    assert num_digits(2**48 - 1, 2) == 48
+    assert num_digits(1000, 10) == 4
+    assert num_digits(125, 5) == 4
+    assert num_digits(100, 16) == 2
+    assert num_digits(-1000, 10) == 4
+    # if changes are made to the function, this structured test over
+    # this range will expose problems
+    for base in range(2, 100):
+        for e in range(1, 100):
+            n = base**e
+            assert num_digits(n, base) == e + 1
+            assert num_digits(n + 1, base) == e + 1
+            assert num_digits(n - 1, base) == e
+
+
+def test_digits():
+    assert all(digits(n, 2)[1:] == [int(d) for d in format(n, 'b')]
+                for n in range(20))
+    assert all(digits(n, 8)[1:] == [int(d) for d in format(n, 'o')]
+                for n in range(20))
+    assert all(digits(n, 16)[1:] == [int(d, 16) for d in format(n, 'x')]
+                for n in range(20))
+    assert digits(2345, 34) == [34, 2, 0, 33]
+    assert digits(384753, 71) == [71, 1, 5, 23, 4]
+    assert digits(93409, 10) == [10, 9, 3, 4, 0, 9]
+    assert digits(-92838, 11) == [-11, 6, 3, 8, 2, 9]
+    assert digits(35, 10) == [10, 3, 5]
+    assert digits(35, 10, 3) == [10, 0, 3, 5]
+    assert digits(-35, 10, 4) == [-10, 0, 0, 3, 5]
+    raises(ValueError, lambda: digits(2, 2, 1))
+
+
+def test_count_digits():
+    assert count_digits(55, 2) == {1: 5, 0: 1}
+    assert count_digits(55, 10) == {5: 2}
+    n = count_digits(123)
+    assert n[4] == 0 and type(n[4]) is int
+
+
+def test_is_palindromic():
+    assert is_palindromic(-11)
+    assert is_palindromic(11)
+    assert is_palindromic(0o121, 8)
+    assert not is_palindromic(123)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_ecm.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_ecm.py
new file mode 100644
index 0000000000000000000000000000000000000000..7f134e4e1cf68231e9f89242d2b8476b9edeabb8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_ecm.py
@@ -0,0 +1,63 @@
+from sympy.external.gmpy import invert
+from sympy.ntheory.ecm import ecm, Point
+from sympy.testing.pytest import slow
+
+@slow
+def test_ecm():
+    assert ecm(3146531246531241245132451321) == {3, 100327907731, 10454157497791297}
+    assert ecm(46167045131415113) == {43, 2634823, 407485517}
+    assert ecm(631211032315670776841) == {9312934919, 67777885039}
+    assert ecm(398883434337287) == {99476569, 4009823}
+    assert ecm(64211816600515193) == {281719, 359641, 633767}
+    assert ecm(4269021180054189416198169786894227) == {184039, 241603, 333331, 477973, 618619, 974123}
+    assert ecm(4516511326451341281684513) == {3, 39869, 131743543, 95542348571}
+    assert ecm(4132846513818654136451) == {47, 160343, 2802377, 195692803}
+    assert ecm(168541512131094651323) == {79, 113, 11011069, 1714635721}
+    #This takes ~10secs while factorint is not able to factorize this even in ~10mins
+    assert ecm(7060005655815754299976961394452809, B1=100000, B2=1000000) == {6988699669998001, 1010203040506070809}
+
+
+def test_Point():
+    #The curve is of the form y**2 = x**3 + a*x**2 + x
+    mod = 101
+    a = 10
+    a_24 = (a + 2)*invert(4, mod)
+    p1 = Point(10, 17, a_24, mod)
+    p2 = p1.double()
+    assert p2 == Point(68, 56, a_24, mod)
+    p4 = p2.double()
+    assert p4 == Point(22, 64, a_24, mod)
+    p8 = p4.double()
+    assert p8 == Point(71, 95, a_24, mod)
+    p16 = p8.double()
+    assert p16 == Point(5, 16, a_24, mod)
+    p32 = p16.double()
+    assert p32 == Point(33, 96, a_24, mod)
+
+    # p3 = p2 + p1
+    p3 = p2.add(p1, p1)
+    assert p3 == Point(1, 61, a_24, mod)
+    # p5 = p3 + p2 or p4 + p1
+    p5 = p3.add(p2, p1)
+    assert p5 == Point(49, 90, a_24, mod)
+    assert p5 == p4.add(p1, p3)
+    # p6 = 2*p3
+    p6 = p3.double()
+    assert p6 == Point(87, 43, a_24, mod)
+    assert p6 == p4.add(p2, p2)
+    # p7 = p5 + p2
+    p7 = p5.add(p2, p3)
+    assert p7 == Point(69, 23, a_24, mod)
+    assert p7 == p4.add(p3, p1)
+    assert p7 == p6.add(p1, p5)
+    # p9 = p5 + p4
+    p9 = p5.add(p4, p1)
+    assert p9 == Point(56, 99, a_24, mod)
+    assert p9 == p6.add(p3, p3)
+    assert p9 == p7.add(p2, p5)
+    assert p9 == p8.add(p1, p7)
+
+    assert p5 == p1.mont_ladder(5)
+    assert p9 == p1.mont_ladder(9)
+    assert p16 == p1.mont_ladder(16)
+    assert p9 == p3.mont_ladder(3)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_egyptian_fraction.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_egyptian_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9a9fac578d93a88a648bdcf8dc34550cf4a7573
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_egyptian_fraction.py
@@ -0,0 +1,49 @@
+from sympy.core.numbers import Rational
+from sympy.ntheory.egyptian_fraction import egyptian_fraction
+from sympy.core.add import Add
+from sympy.testing.pytest import raises
+from sympy.core.random import random_complex_number
+
+
+def test_egyptian_fraction():
+    def test_equality(r, alg="Greedy"):
+        return r == Add(*[Rational(1, i) for i in egyptian_fraction(r, alg)])
+
+    r = random_complex_number(a=0, c=1, b=0, d=0, rational=True)
+    assert test_equality(r)
+
+    assert egyptian_fraction(Rational(4, 17)) == [5, 29, 1233, 3039345]
+    assert egyptian_fraction(Rational(7, 13), "Greedy") == [2, 26]
+    assert egyptian_fraction(Rational(23, 101), "Greedy") == \
+        [5, 37, 1438, 2985448, 40108045937720]
+    assert egyptian_fraction(Rational(18, 23), "Takenouchi") == \
+        [2, 6, 12, 35, 276, 2415]
+    assert egyptian_fraction(Rational(5, 6), "Graham Jewett") == \
+        [6, 7, 8, 9, 10, 42, 43, 44, 45, 56, 57, 58, 72, 73, 90, 1806, 1807,
+         1808, 1892, 1893, 1980, 3192, 3193, 3306, 5256, 3263442, 3263443,
+         3267056, 3581556, 10192056, 10650056950806]
+    assert egyptian_fraction(Rational(5, 6), "Golomb") == [2, 6, 12, 20, 30]
+    assert egyptian_fraction(Rational(5, 121), "Golomb") == [25, 1225, 3577, 7081, 11737]
+    raises(ValueError, lambda: egyptian_fraction(Rational(-4, 9)))
+    assert egyptian_fraction(Rational(8, 3), "Golomb") == [1, 2, 3, 4, 5, 6, 7,
+                                                           14, 574, 2788, 6460,
+                                                           11590, 33062, 113820]
+    assert egyptian_fraction(Rational(355, 113)) == [1, 2, 3, 4, 5, 6, 7, 8, 9,
+                                                     10, 11, 12, 27, 744, 893588,
+                                                     1251493536607,
+                                                     20361068938197002344405230]
+
+
+def test_input():
+    r = (2,3), Rational(2, 3), (Rational(2), Rational(3))
+    for m in ["Greedy", "Graham Jewett", "Takenouchi", "Golomb"]:
+        for i in r:
+            d = egyptian_fraction(i, m)
+            assert all(i.is_Integer for i in d)
+            if m == "Graham Jewett":
+                assert d == [3, 4, 12]
+            else:
+                assert d == [2, 6]
+    # check prefix
+    d = egyptian_fraction(Rational(5, 3))
+    assert d == [1, 2, 6] and all(i.is_Integer for i in d)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_elliptic_curve.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_elliptic_curve.py
new file mode 100644
index 0000000000000000000000000000000000000000..7d49d8eac72cc622fb92dfca8c54e5cc6c8dfb8f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_elliptic_curve.py
@@ -0,0 +1,20 @@
+from sympy.ntheory.elliptic_curve import EllipticCurve
+
+
+def test_elliptic_curve():
+    # Point addition and multiplication
+    e3 = EllipticCurve(-1, 9)
+    p = e3(0, 3)
+    q = e3(-1, 3)
+    r = p + q
+    assert r.x == 1 and r.y == -3
+    r = 2*p + q
+    assert r.x == 35 and r.y == 207
+    r = -p + q
+    assert r.x == 37 and r.y == 225
+    # Verify result in http://www.lmfdb.org/EllipticCurve/Q
+    # Discriminant
+    assert EllipticCurve(-1, 9).discriminant == -34928
+    assert EllipticCurve(-2731, -55146, 1, 0, 1).discriminant == 25088
+    # Torsion points
+    assert len(EllipticCurve(0, 1).torsion_points()) == 6
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_factor_.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_factor_.py
new file mode 100644
index 0000000000000000000000000000000000000000..5174b842c49ef0e14c1ad38d2d9ad550c2a2a388
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_factor_.py
@@ -0,0 +1,702 @@
+from sympy.core.containers import Dict
+from sympy.core.mul import Mul
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.functions.combinatorial.factorials import factorial as fac
+from sympy.core.numbers import Integer, Rational
+from sympy.external.gmpy import gcd
+
+from sympy.ntheory import (totient,
+    factorint, primefactors, divisors, nextprime,
+    pollard_rho, perfect_power, multiplicity, multiplicity_in_factorial,
+    divisor_count, primorial, pollard_pm1, divisor_sigma,
+    factorrat, reduced_totient)
+from sympy.ntheory.factor_ import (smoothness, smoothness_p, proper_divisors,
+    antidivisors, antidivisor_count, _divisor_sigma, core, udivisors, udivisor_sigma,
+    udivisor_count, proper_divisor_count, primenu, primeomega,
+    mersenne_prime_exponent, is_perfect, is_abundant,
+    is_deficient, is_amicable, is_carmichael, find_carmichael_numbers_in_range,
+    find_first_n_carmichaels, dra, drm, _perfect_power, factor_cache)
+
+from sympy.testing.pytest import raises, slow
+
+from sympy.utilities.iterables import capture
+
+
+def fac_multiplicity(n, p):
+    """Return the power of the prime number p in the
+    factorization of n!"""
+    if p > n:
+        return 0
+    if p > n//2:
+        return 1
+    q, m = n, 0
+    while q >= p:
+        q //= p
+        m += q
+    return m
+
+
+def multiproduct(seq=(), start=1):
+    """
+    Return the product of a sequence of factors with multiplicities,
+    times the value of the parameter ``start``. The input may be a
+    sequence of (factor, exponent) pairs or a dict of such pairs.
+
+        >>> multiproduct({3:7, 2:5}, 4) # = 3**7 * 2**5 * 4
+        279936
+
+    """
+    if not seq:
+        return start
+    if isinstance(seq, dict):
+        seq = iter(seq.items())
+    units = start
+    multi = []
+    for base, exp in seq:
+        if not exp:
+            continue
+        elif exp == 1:
+            units *= base
+        else:
+            if exp % 2:
+                units *= base
+            multi.append((base, exp//2))
+    return units * multiproduct(multi)**2
+
+
+def test_multiplicity():
+    for b in range(2, 20):
+        for i in range(100):
+            assert multiplicity(b, b**i) == i
+            assert multiplicity(b, (b**i) * 23) == i
+            assert multiplicity(b, (b**i) * 1000249) == i
+    # Should be fast
+    assert multiplicity(10, 10**10023) == 10023
+    # Should exit quickly
+    assert multiplicity(10**10, 10**10) == 1
+    # Should raise errors for bad input
+    raises(ValueError, lambda: multiplicity(1, 1))
+    raises(ValueError, lambda: multiplicity(1, 2))
+    raises(ValueError, lambda: multiplicity(1.3, 2))
+    raises(ValueError, lambda: multiplicity(2, 0))
+    raises(ValueError, lambda: multiplicity(1.3, 0))
+
+    # handles Rationals
+    assert multiplicity(10, Rational(30, 7)) == 1
+    assert multiplicity(Rational(2, 7), Rational(4, 7)) == 1
+    assert multiplicity(Rational(1, 7), Rational(3, 49)) == 2
+    assert multiplicity(Rational(2, 7), Rational(7, 2)) == -1
+    assert multiplicity(3, Rational(1, 9)) == -2
+
+
+def test_multiplicity_in_factorial():
+    n = fac(1000)
+    for i in (2, 4, 6, 12, 30, 36, 48, 60, 72, 96):
+        assert multiplicity(i, n) == multiplicity_in_factorial(i, 1000)
+
+
+def test_private_perfect_power():
+    assert _perfect_power(0) is False
+    assert _perfect_power(1) is False
+    assert _perfect_power(2) is False
+    assert _perfect_power(3) is False
+    for x in [2, 3, 5, 6, 7, 12, 15, 105, 100003]:
+        for y in range(2, 100):
+            assert _perfect_power(x**y) == (x, y)
+            if x & 1:
+                assert _perfect_power(x**y, next_p=3) == (x, y)
+            if x == 100003:
+                assert _perfect_power(x**y, next_p=100003) == (x, y)
+            assert _perfect_power(101*x**y) == False
+            # Catalan's conjecture
+            if x**y not in [8, 9]:
+                assert _perfect_power(x**y + 1) == False
+                assert _perfect_power(x**y - 1) == False
+    for x in range(1, 10):
+        for y in range(1, 10):
+            g = gcd(x, y)
+            if g == 1:
+                assert _perfect_power(5**x * 101**y) == False
+            else:
+                assert _perfect_power(5**x * 101**y) == (5**(x//g) * 101**(y//g), g)
+
+
+def test_perfect_power():
+    raises(ValueError, lambda: perfect_power(0.1))
+    assert perfect_power(0) is False
+    assert perfect_power(1) is False
+    assert perfect_power(2) is False
+    assert perfect_power(3) is False
+    assert perfect_power(4) == (2, 2)
+    assert perfect_power(14) is False
+    assert perfect_power(25) == (5, 2)
+    assert perfect_power(22) is False
+    assert perfect_power(22, [2]) is False
+    assert perfect_power(137**(3*5*13)) == (137, 3*5*13)
+    assert perfect_power(137**(3*5*13) + 1) is False
+    assert perfect_power(137**(3*5*13) - 1) is False
+    assert perfect_power(103005006004**7) == (103005006004, 7)
+    assert perfect_power(103005006004**7 + 1) is False
+    assert perfect_power(103005006004**7 - 1) is False
+    assert perfect_power(103005006004**12) == (103005006004, 12)
+    assert perfect_power(103005006004**12 + 1) is False
+    assert perfect_power(103005006004**12 - 1) is False
+    assert perfect_power(2**10007) == (2, 10007)
+    assert perfect_power(2**10007 + 1) is False
+    assert perfect_power(2**10007 - 1) is False
+    assert perfect_power((9**99 + 1)**60) == (9**99 + 1, 60)
+    assert perfect_power((9**99 + 1)**60 + 1) is False
+    assert perfect_power((9**99 + 1)**60 - 1) is False
+    assert perfect_power((10**40000)**2, big=False) == (10**40000, 2)
+    assert perfect_power(10**100000) == (10, 100000)
+    assert perfect_power(10**100001) == (10, 100001)
+    assert perfect_power(13**4, [3, 5]) is False
+    assert perfect_power(3**4, [3, 10], factor=0) is False
+    assert perfect_power(3**3*5**3) == (15, 3)
+    assert perfect_power(2**3*5**5) is False
+    assert perfect_power(2*13**4) is False
+    assert perfect_power(2**5*3**3) is False
+    t = 2**24
+    for d in divisors(24):
+        m = perfect_power(t*3**d)
+        assert m and m[1] == d or d == 1
+        m = perfect_power(t*3**d, big=False)
+        assert m and m[1] == 2 or d == 1 or d == 3, (d, m)
+
+    # negatives and non-integer rationals
+    assert perfect_power(-4) is False
+    assert perfect_power(-8) == (-2, 3)
+    assert perfect_power(-S(1)/8) == (-S(1)/2, 3)
+    assert perfect_power(S(1)/3) == False
+    assert perfect_power(-5**15) == (-5, 15)
+    assert perfect_power(-5**15, big=False) == (-3125, 3)
+    assert perfect_power(-5**15, [15]) == (-5, 15)
+
+    n = -3 ** 60
+    assert perfect_power(n) == (-81, 15)
+    assert perfect_power(n, big=False) == (-3486784401, 3)
+    assert perfect_power(n, [3, 5], big=True) == (-531441, 5)
+    assert perfect_power(n, [3, 5], big=False) == (-3486784401, 3)
+    assert perfect_power(n, [2]) == False
+    assert perfect_power(n, [2, 15]) == (-81, 15)
+    assert perfect_power(n, [2, 13]) == False
+    assert perfect_power(n, [17]) == False
+    assert perfect_power(n, [3]) == (-3486784401, 3)
+    assert perfect_power(n + 1) == False
+
+    r = S(2) ** (2 * 5 * 7) / S(3) ** (2 * 7)
+    assert perfect_power(r) == (S(32) / 3, 14)
+    assert perfect_power(-r) == (-S(1024) / 9, 7)
+    assert perfect_power(r, big=False) == (S(34359738368) / 2187, 2)
+    assert perfect_power(r, [2, 5]) == (S(34359738368) / 2187, 2)
+    assert perfect_power(r, [5, 7]) == (S(1024) / 9, 7)
+    assert perfect_power(r, [5, 7], big=False) == (S(1024) / 9, 7)
+    assert perfect_power(r, [2, 5, 7], big=False) == (S(34359738368) / 2187, 2)
+    assert perfect_power(-r, [5, 7], big=False) == (-S(1024) / 9, 7)
+
+    assert perfect_power(-S(1) / 8) == (-S(1) / 2, 3)
+
+    assert perfect_power((-3)**60) == (3, 60)
+    assert perfect_power((-3)**61) == (-3, 61)
+
+    assert perfect_power(S(2 ** 9) / 3 ** 12) == (S(8)/81, 3)
+    assert perfect_power(Rational(1, 2)**3) == (S.Half, 3)
+    assert perfect_power(Rational(-3, 2)**3) == (-3*S.Half, 3)
+
+
+def test_factor_cache():
+    factor_cache.cache_clear()
+    raises(ValueError, lambda: factor_cache.__setitem__(1, 5))
+    raises(ValueError, lambda: factor_cache.__setitem__(10, 1))
+    raises(ValueError, lambda: factor_cache.__setitem__(10, 10))
+    raises(ValueError, lambda: factor_cache.__setitem__(10, 3))
+    raises(ValueError, lambda: factor_cache.__setitem__(20, 4))
+    factor_cache.maxsize = 3
+    for i in range(2, 10):
+        factor_cache[5*i] = 5
+    assert len(factor_cache) == 3
+    factor_cache.maxsize = 5
+    for i in range(2, 10):
+        factor_cache[5*i] = 5
+    assert len(factor_cache) == 5
+    factor_cache.maxsize = 2
+    assert len(factor_cache) == 2
+    factor_cache.maxsize =1000
+
+    factor_cache.cache_clear()
+    factor_cache[40] = 5
+    assert factor_cache.get(40) == 5
+    assert factor_cache.get(20) is None
+    assert factor_cache[40] == 5
+    raises(KeyError, lambda: factor_cache[10])
+    del factor_cache[40]
+    assert len(factor_cache) == 0
+    raises(KeyError, lambda: factor_cache.__delitem__(40))
+    factor_cache.add(100, [5, 2])
+    assert len(factor_cache) == 2
+    assert factor_cache[100] == 5
+
+    for n in [1000000007, 10000019*20000003]:
+        factorint(n)
+        assert n in factor_cache
+
+    # Restore the initial state
+    factor_cache.cache_clear()
+    factor_cache.maxsize = 1000
+
+
+@slow
+def test_factorint():
+    assert primefactors(123456) == [2, 3, 643]
+    assert factorint(0) == {0: 1}
+    assert factorint(1) == {}
+    assert factorint(-1) == {-1: 1}
+    assert factorint(-2) == {-1: 1, 2: 1}
+    assert factorint(-16) == {-1: 1, 2: 4}
+    assert factorint(2) == {2: 1}
+    assert factorint(126) == {2: 1, 3: 2, 7: 1}
+    assert factorint(123456) == {2: 6, 3: 1, 643: 1}
+    assert factorint(5951757) == {3: 1, 7: 1, 29: 2, 337: 1}
+    assert factorint(64015937) == {7993: 1, 8009: 1}
+    assert factorint(2**(2**6) + 1) == {274177: 1, 67280421310721: 1}
+    #issue 19683
+    assert factorint(10**38 - 1) == {3: 2, 11: 1, 909090909090909091: 1, 1111111111111111111: 1}
+    #issue 17676
+    assert factorint(28300421052393658575) == {3: 1, 5: 2, 11: 2, 43: 1, 2063: 2, 4127: 1, 4129: 1}
+    assert factorint(2063**2 * 4127**1 * 4129**1) == {2063: 2, 4127: 1, 4129: 1}
+    assert factorint(2347**2 * 7039**1 * 7043**1) == {2347: 2, 7039: 1, 7043: 1}
+
+    assert factorint(0, multiple=True) == [0]
+    assert factorint(1, multiple=True) == []
+    assert factorint(-1, multiple=True) == [-1]
+    assert factorint(-2, multiple=True) == [-1, 2]
+    assert factorint(-16, multiple=True) == [-1, 2, 2, 2, 2]
+    assert factorint(2, multiple=True) == [2]
+    assert factorint(24, multiple=True) == [2, 2, 2, 3]
+    assert factorint(126, multiple=True) == [2, 3, 3, 7]
+    assert factorint(123456, multiple=True) == [2, 2, 2, 2, 2, 2, 3, 643]
+    assert factorint(5951757, multiple=True) == [3, 7, 29, 29, 337]
+    assert factorint(64015937, multiple=True) == [7993, 8009]
+    assert factorint(2**(2**6) + 1, multiple=True) == [274177, 67280421310721]
+
+    assert factorint(fac(1, evaluate=False)) == {}
+    assert factorint(fac(7, evaluate=False)) == {2: 4, 3: 2, 5: 1, 7: 1}
+    assert factorint(fac(15, evaluate=False)) == \
+        {2: 11, 3: 6, 5: 3, 7: 2, 11: 1, 13: 1}
+    assert factorint(fac(20, evaluate=False)) == \
+        {2: 18, 3: 8, 5: 4, 7: 2, 11: 1, 13: 1, 17: 1, 19: 1}
+    assert factorint(fac(23, evaluate=False)) == \
+        {2: 19, 3: 9, 5: 4, 7: 3, 11: 2, 13: 1, 17: 1, 19: 1, 23: 1}
+
+    assert multiproduct(factorint(fac(200))) == fac(200)
+    assert multiproduct(factorint(fac(200, evaluate=False))) == fac(200)
+    for b, e in factorint(fac(150)).items():
+        assert e == fac_multiplicity(150, b)
+    for b, e in factorint(fac(150, evaluate=False)).items():
+        assert e == fac_multiplicity(150, b)
+    assert factorint(103005006059**7) == {103005006059: 7}
+    assert factorint(31337**191) == {31337: 191}
+    assert factorint(2**1000 * 3**500 * 257**127 * 383**60) == \
+        {2: 1000, 3: 500, 257: 127, 383: 60}
+    assert len(factorint(fac(10000))) == 1229
+    assert len(factorint(fac(10000, evaluate=False))) == 1229
+    assert factorint(12932983746293756928584532764589230) == \
+        {2: 1, 5: 1, 73: 1, 727719592270351: 1, 63564265087747: 1, 383: 1}
+    assert factorint(727719592270351) == {727719592270351: 1}
+    assert factorint(2**64 + 1, use_trial=False) == factorint(2**64 + 1)
+    for n in range(60000):
+        assert multiproduct(factorint(n)) == n
+    assert pollard_rho(2**64 + 1, seed=1) == 274177
+    assert pollard_rho(19, seed=1) is None
+    assert factorint(3, limit=2) == {3: 1}
+    assert factorint(12345) == {3: 1, 5: 1, 823: 1}
+    assert factorint(
+        12345, limit=3) == {4115: 1, 3: 1}  # the 5 is greater than the limit
+    assert factorint(1, limit=1) == {}
+    assert factorint(0, 3) == {0: 1}
+    assert factorint(12, limit=1) == {12: 1}
+    assert factorint(30, limit=2) == {2: 1, 15: 1}
+    assert factorint(16, limit=2) == {2: 4}
+    assert factorint(124, limit=3) == {2: 2, 31: 1}
+    assert factorint(4*31**2, limit=3) == {2: 2, 31: 2}
+    p1 = nextprime(2**32)
+    p2 = nextprime(2**16)
+    p3 = nextprime(p2)
+    assert factorint(p1*p2*p3) == {p1: 1, p2: 1, p3: 1}
+    assert factorint(13*17*19, limit=15) == {13: 1, 17*19: 1}
+    assert factorint(1951*15013*15053, limit=2000) == {225990689: 1, 1951: 1}
+    assert factorint(primorial(17) + 1, use_pm1=0) == \
+        {int(19026377261): 1, 3467: 1, 277: 1, 105229: 1}
+    # when prime b is closer than approx sqrt(8*p) to prime p then they are
+    # "close" and have a trivial factorization
+    a = nextprime(2**2**8)  # 78 digits
+    b = nextprime(a + 2**2**4)
+    assert 'Fermat' in capture(lambda: factorint(a*b, verbose=1))
+
+    raises(ValueError, lambda: pollard_rho(4))
+    raises(ValueError, lambda: pollard_pm1(3))
+    raises(ValueError, lambda: pollard_pm1(10, B=2))
+    # verbose coverage
+    n = nextprime(2**16)*nextprime(2**17)*nextprime(1901)
+    assert 'with primes' in capture(lambda: factorint(n, verbose=1))
+    capture(lambda: factorint(nextprime(2**16)*1012, verbose=1))
+
+    n = nextprime(2**17)
+    capture(lambda: factorint(n**3, verbose=1))  # perfect power termination
+    capture(lambda: factorint(2*n, verbose=1))  # factoring complete msg
+
+    # exceed 1st
+    n = nextprime(2**17)
+    n *= nextprime(n)
+    assert '1000' in capture(lambda: factorint(n, limit=1000, verbose=1))
+    n *= nextprime(n)
+    assert len(factorint(n)) == 3
+    assert len(factorint(n, limit=p1)) == 3
+    n *= nextprime(2*n)
+    # exceed 2nd
+    assert '2001' in capture(lambda: factorint(n, limit=2000, verbose=1))
+    assert capture(
+        lambda: factorint(n, limit=4000, verbose=1)).count('Pollard') == 2
+    # non-prime pm1 result
+    n = nextprime(8069)
+    n *= nextprime(2*n)*nextprime(2*n, 2)
+    capture(lambda: factorint(n, verbose=1))  # non-prime pm1 result
+    # factor fermat composite
+    p1 = nextprime(2**17)
+    p2 = nextprime(2*p1)
+    assert factorint((p1*p2**2)**3) == {p1: 3, p2: 6}
+    # Test for non integer input
+    raises(ValueError, lambda: factorint(4.5))
+    # test dict/Dict input
+    sans = '2**10*3**3'
+    n = {4: 2, 12: 3}
+    assert str(factorint(n)) == sans
+    assert str(factorint(Dict(n))) == sans
+
+
+def test_divisors_and_divisor_count():
+    assert divisors(-1) == [1]
+    assert divisors(0) == []
+    assert divisors(1) == [1]
+    assert divisors(2) == [1, 2]
+    assert divisors(3) == [1, 3]
+    assert divisors(17) == [1, 17]
+    assert divisors(10) == [1, 2, 5, 10]
+    assert divisors(100) == [1, 2, 4, 5, 10, 20, 25, 50, 100]
+    assert divisors(101) == [1, 101]
+    assert type(divisors(2, generator=True)) is not list
+
+    assert divisor_count(0) == 0
+    assert divisor_count(-1) == 1
+    assert divisor_count(1) == 1
+    assert divisor_count(6) == 4
+    assert divisor_count(12) == 6
+
+    assert divisor_count(180, 3) == divisor_count(180//3)
+    assert divisor_count(2*3*5, 7) == 0
+
+
+def test_proper_divisors_and_proper_divisor_count():
+    assert proper_divisors(-1) == []
+    assert proper_divisors(0) == []
+    assert proper_divisors(1) == []
+    assert proper_divisors(2) == [1]
+    assert proper_divisors(3) == [1]
+    assert proper_divisors(17) == [1]
+    assert proper_divisors(10) == [1, 2, 5]
+    assert proper_divisors(100) == [1, 2, 4, 5, 10, 20, 25, 50]
+    assert proper_divisors(1000000007) == [1]
+    assert type(proper_divisors(2, generator=True)) is not list
+
+    assert proper_divisor_count(0) == 0
+    assert proper_divisor_count(-1) == 0
+    assert proper_divisor_count(1) == 0
+    assert proper_divisor_count(36) == 8
+    assert proper_divisor_count(2*3*5) == 7
+
+
+def test_udivisors_and_udivisor_count():
+    assert udivisors(-1) == [1]
+    assert udivisors(0) == []
+    assert udivisors(1) == [1]
+    assert udivisors(2) == [1, 2]
+    assert udivisors(3) == [1, 3]
+    assert udivisors(17) == [1, 17]
+    assert udivisors(10) == [1, 2, 5, 10]
+    assert udivisors(100) == [1, 4, 25, 100]
+    assert udivisors(101) == [1, 101]
+    assert udivisors(1000) == [1, 8, 125, 1000]
+    assert type(udivisors(2, generator=True)) is not list
+
+    assert udivisor_count(0) == 0
+    assert udivisor_count(-1) == 1
+    assert udivisor_count(1) == 1
+    assert udivisor_count(6) == 4
+    assert udivisor_count(12) == 4
+
+    assert udivisor_count(180) == 8
+    assert udivisor_count(2*3*5*7) == 16
+
+
+def test_issue_6981():
+    S = set(divisors(4)).union(set(divisors(Integer(2))))
+    assert S == {1,2,4}
+
+
+def test_issue_4356():
+    assert factorint(1030903) == {53: 2, 367: 1}
+
+
+def test_divisors():
+    assert divisors(28) == [1, 2, 4, 7, 14, 28]
+    assert list(divisors(3*5*7, 1)) == [1, 3, 5, 15, 7, 21, 35, 105]
+    assert divisors(0) == []
+
+
+def test_divisor_count():
+    assert divisor_count(0) == 0
+    assert divisor_count(6) == 4
+
+
+def test_proper_divisors():
+    assert proper_divisors(-1) == []
+    assert proper_divisors(28) == [1, 2, 4, 7, 14]
+    assert list(proper_divisors(3*5*7, True)) == [1, 3, 5, 15, 7, 21, 35]
+
+
+def test_proper_divisor_count():
+    assert proper_divisor_count(6) == 3
+    assert proper_divisor_count(108) == 11
+
+
+def test_antidivisors():
+    assert antidivisors(-1) == []
+    assert antidivisors(-3) == [2]
+    assert antidivisors(14) == [3, 4, 9]
+    assert antidivisors(237) == [2, 5, 6, 11, 19, 25, 43, 95, 158]
+    assert antidivisors(12345) == [2, 6, 7, 10, 30, 1646, 3527, 4938, 8230]
+    assert antidivisors(393216) == [262144]
+    assert sorted(x for x in antidivisors(3*5*7, 1)) == \
+        [2, 6, 10, 11, 14, 19, 30, 42, 70]
+    assert antidivisors(1) == []
+    assert type(antidivisors(2, generator=True)) is not list
+
+def test_antidivisor_count():
+    assert antidivisor_count(0) == 0
+    assert antidivisor_count(-1) == 0
+    assert antidivisor_count(-4) == 1
+    assert antidivisor_count(20) == 3
+    assert antidivisor_count(25) == 5
+    assert antidivisor_count(38) == 7
+    assert antidivisor_count(180) == 6
+    assert antidivisor_count(2*3*5) == 3
+
+
+def test_smoothness_and_smoothness_p():
+    assert smoothness(1) == (1, 1)
+    assert smoothness(2**4*3**2) == (3, 16)
+
+    assert smoothness_p(10431, m=1) == \
+        (1, [(3, (2, 2, 4)), (19, (1, 5, 5)), (61, (1, 31, 31))])
+    assert smoothness_p(10431) == \
+        (-1, [(3, (2, 2, 2)), (19, (1, 3, 9)), (61, (1, 5, 5))])
+    assert smoothness_p(10431, power=1) == \
+        (-1, [(3, (2, 2, 2)), (61, (1, 5, 5)), (19, (1, 3, 9))])
+    assert smoothness_p(21477639576571, visual=1) == \
+        'p**i=4410317**1 has p-1 B=1787, B-pow=1787\n' + \
+        'p**i=4869863**1 has p-1 B=2434931, B-pow=2434931'
+
+
+def test_visual_factorint():
+    assert factorint(1, visual=1) == 1
+    forty2 = factorint(42, visual=True)
+    assert type(forty2) == Mul
+    assert str(forty2) == '2**1*3**1*7**1'
+    assert factorint(1, visual=True) is S.One
+    no = {"evaluate": False}
+    assert factorint(42**2, visual=True) == Mul(Pow(2, 2, **no),
+                                                Pow(3, 2, **no),
+                                                Pow(7, 2, **no), **no)
+    assert -1 in factorint(-42, visual=True).args
+
+
+def test_factorrat():
+    assert str(factorrat(S(12)/1, visual=True)) == '2**2*3**1'
+    assert str(factorrat(Rational(1, 1), visual=True)) == '1'
+    assert str(factorrat(S(25)/14, visual=True)) == '5**2/(2*7)'
+    assert str(factorrat(Rational(25, 14), visual=True)) == '5**2/(2*7)'
+    assert str(factorrat(S(-25)/14/9, visual=True)) == '-1*5**2/(2*3**2*7)'
+
+    assert factorrat(S(12)/1, multiple=True) == [2, 2, 3]
+    assert factorrat(Rational(1, 1), multiple=True) == []
+    assert factorrat(S(25)/14, multiple=True) == [Rational(1, 7), S.Half, 5, 5]
+    assert factorrat(Rational(25, 14), multiple=True) == [Rational(1, 7), S.Half, 5, 5]
+    assert factorrat(Rational(12, 1), multiple=True) == [2, 2, 3]
+    assert factorrat(S(-25)/14/9, multiple=True) == \
+        [-1, Rational(1, 7), Rational(1, 3), Rational(1, 3), S.Half, 5, 5]
+
+
+def test_visual_io():
+    sm = smoothness_p
+    fi = factorint
+    # with smoothness_p
+    n = 124
+    d = fi(n)
+    m = fi(d, visual=True)
+    t = sm(n)
+    s = sm(t)
+    for th in [d, s, t, n, m]:
+        assert sm(th, visual=True) == s
+        assert sm(th, visual=1) == s
+    for th in [d, s, t, n, m]:
+        assert sm(th, visual=False) == t
+    assert [sm(th, visual=None) for th in [d, s, t, n, m]] == [s, d, s, t, t]
+    assert [sm(th, visual=2) for th in [d, s, t, n, m]] == [s, d, s, t, t]
+
+    # with factorint
+    for th in [d, m, n]:
+        assert fi(th, visual=True) == m
+        assert fi(th, visual=1) == m
+    for th in [d, m, n]:
+        assert fi(th, visual=False) == d
+    assert [fi(th, visual=None) for th in [d, m, n]] == [m, d, d]
+    assert [fi(th, visual=0) for th in [d, m, n]] == [m, d, d]
+
+    # test reevaluation
+    no = {"evaluate": False}
+    assert sm({4: 2}, visual=False) == sm(16)
+    assert sm(Mul(*[Pow(k, v, **no) for k, v in {4: 2, 2: 6}.items()], **no),
+              visual=False) == sm(2**10)
+
+    assert fi({4: 2}, visual=False) == fi(16)
+    assert fi(Mul(*[Pow(k, v, **no) for k, v in {4: 2, 2: 6}.items()], **no),
+              visual=False) == fi(2**10)
+
+
+def test_core():
+    assert core(35**13, 10) == 42875
+    assert core(210**2) == 1
+    assert core(7776, 3) == 36
+    assert core(10**27, 22) == 10**5
+    assert core(537824) == 14
+    assert core(1, 6) == 1
+
+
+def test__divisor_sigma():
+    assert _divisor_sigma(23450) == 50592
+    assert _divisor_sigma(23450, 0) == 24
+    assert _divisor_sigma(23450, 1) == 50592
+    assert _divisor_sigma(23450, 2) == 730747500
+    assert _divisor_sigma(23450, 3) == 14666785333344
+    A000005 = [1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4,
+               4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8]
+    for n, val in enumerate(A000005, 1):
+        assert _divisor_sigma(n, 0) == val
+    A000203 = [1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18,
+               39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48]
+    for n, val in enumerate(A000203, 1):
+        assert _divisor_sigma(n, 1) == val
+    A001157 = [1, 5, 10, 21, 26, 50, 50, 85, 91, 130, 122, 210, 170, 250, 260,
+               341, 290, 455, 362, 546, 500, 610, 530, 850, 651, 850, 820, 1050]
+    for n, val in enumerate(A001157, 1):
+        assert _divisor_sigma(n, 2) == val
+
+
+def test_mersenne_prime_exponent():
+    assert mersenne_prime_exponent(1) == 2
+    assert mersenne_prime_exponent(4) == 7
+    assert mersenne_prime_exponent(10) == 89
+    assert mersenne_prime_exponent(25) == 21701
+    raises(ValueError, lambda: mersenne_prime_exponent(52))
+    raises(ValueError, lambda: mersenne_prime_exponent(0))
+
+
+def test_is_perfect():
+    assert is_perfect(-6) is False
+    assert is_perfect(6) is True
+    assert is_perfect(15) is False
+    assert is_perfect(28) is True
+    assert is_perfect(400) is False
+    assert is_perfect(496) is True
+    assert is_perfect(8128) is True
+    assert is_perfect(10000) is False
+
+
+def test_is_abundant():
+    assert is_abundant(10) is False
+    assert is_abundant(12) is True
+    assert is_abundant(18) is True
+    assert is_abundant(21) is False
+    assert is_abundant(945) is True
+
+
+def test_is_deficient():
+    assert is_deficient(10) is True
+    assert is_deficient(22) is True
+    assert is_deficient(56) is False
+    assert is_deficient(20) is False
+    assert is_deficient(36) is False
+
+
+def test_is_amicable():
+    assert is_amicable(173, 129) is False
+    assert is_amicable(220, 284) is True
+    assert is_amicable(8756, 8756) is False
+
+
+def test_is_carmichael():
+    A002997 = [561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841,
+               29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101]
+    for n in range(1, 5000):
+        assert is_carmichael(n) == (n in A002997)
+    for n in A002997:
+        assert is_carmichael(n)
+
+
+def test_find_carmichael_numbers_in_range():
+    assert find_carmichael_numbers_in_range(0, 561) == []
+    assert find_carmichael_numbers_in_range(561, 562) == [561]
+    assert find_carmichael_numbers_in_range(561, 1105) == find_carmichael_numbers_in_range(561, 562)
+    raises(ValueError, lambda: find_carmichael_numbers_in_range(-2, 2))
+    raises(ValueError, lambda: find_carmichael_numbers_in_range(22, 2))
+
+
+def test_find_first_n_carmichaels():
+    assert find_first_n_carmichaels(0) == []
+    assert find_first_n_carmichaels(1) == [561]
+    assert find_first_n_carmichaels(2) == [561, 1105]
+
+
+def test_dra():
+    assert dra(19, 12) == 8
+    assert dra(2718, 10) == 9
+    assert dra(0, 22) == 0
+    assert dra(23456789, 10) == 8
+    raises(ValueError, lambda: dra(24, -2))
+    raises(ValueError, lambda: dra(24.2, 5))
+
+def test_drm():
+    assert drm(19, 12) == 7
+    assert drm(2718, 10) == 2
+    assert drm(0, 15) == 0
+    assert drm(234161, 10) == 6
+    raises(ValueError, lambda: drm(24, -2))
+    raises(ValueError, lambda: drm(11.6, 9))
+
+
+def test_deprecated_ntheory_symbolic_functions():
+    from sympy.testing.pytest import warns_deprecated_sympy
+
+    with warns_deprecated_sympy():
+        assert primenu(3) == 1
+    with warns_deprecated_sympy():
+        assert primeomega(3) == 1
+    with warns_deprecated_sympy():
+        assert totient(3) == 2
+    with warns_deprecated_sympy():
+        assert reduced_totient(3) == 2
+    with warns_deprecated_sympy():
+        assert divisor_sigma(3) == 4
+    with warns_deprecated_sympy():
+        assert udivisor_sigma(3) == 4
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_generate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_generate.py
new file mode 100644
index 0000000000000000000000000000000000000000..b0e5918ffefede2e86f3be2b07d6c3a01c02e6e0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_generate.py
@@ -0,0 +1,285 @@
+from bisect import bisect, bisect_left
+
+from sympy.functions.combinatorial.numbers import mobius, totient
+from sympy.ntheory.generate import (sieve, Sieve)
+
+from sympy.ntheory import isprime, randprime, nextprime, prevprime, \
+    primerange, primepi, prime, primorial, composite, compositepi
+from sympy.ntheory.generate import cycle_length, _primepi
+from sympy.ntheory.primetest import mr
+from sympy.testing.pytest import raises
+
+def test_prime():
+    assert prime(1) == 2
+    assert prime(2) == 3
+    assert prime(5) == 11
+    assert prime(11) == 31
+    assert prime(57) == 269
+    assert prime(296) == 1949
+    assert prime(559) == 4051
+    assert prime(3000) == 27449
+    assert prime(4096) == 38873
+    assert prime(9096) == 94321
+    assert prime(25023) == 287341
+    assert prime(10000000) == 179424673 # issue #20951
+    assert prime(99999999) == 2038074739
+    raises(ValueError, lambda: prime(0))
+    sieve.extend(3000)
+    assert prime(401) == 2749
+    raises(ValueError, lambda: prime(-1))
+
+
+def test__primepi():
+    assert _primepi(-1) == 0
+    assert _primepi(1) == 0
+    assert _primepi(2) == 1
+    assert _primepi(5) == 3
+    assert _primepi(11) == 5
+    assert _primepi(57) == 16
+    assert _primepi(296) == 62
+    assert _primepi(559) == 102
+    assert _primepi(3000) == 430
+    assert _primepi(4096) == 564
+    assert _primepi(9096) == 1128
+    assert _primepi(25023) == 2763
+    assert _primepi(10**8) == 5761455
+    assert _primepi(253425253) == 13856396
+    assert _primepi(8769575643) == 401464322
+    sieve.extend(3000)
+    assert _primepi(2000) == 303
+
+
+def test_composite():
+    from sympy.ntheory.generate import sieve
+    sieve._reset()
+    assert composite(1) == 4
+    assert composite(2) == 6
+    assert composite(5) == 10
+    assert composite(11) == 20
+    assert composite(41) == 58
+    assert composite(57) == 80
+    assert composite(296) == 370
+    assert composite(559) == 684
+    assert composite(3000) == 3488
+    assert composite(4096) == 4736
+    assert composite(9096) == 10368
+    assert composite(25023) == 28088
+    sieve.extend(3000)
+    assert composite(1957) == 2300
+    assert composite(2568) == 2998
+    raises(ValueError, lambda: composite(0))
+
+
+def test_compositepi():
+    assert compositepi(1) == 0
+    assert compositepi(2) == 0
+    assert compositepi(5) == 1
+    assert compositepi(11) == 5
+    assert compositepi(57) == 40
+    assert compositepi(296) == 233
+    assert compositepi(559) == 456
+    assert compositepi(3000) == 2569
+    assert compositepi(4096) == 3531
+    assert compositepi(9096) == 7967
+    assert compositepi(25023) == 22259
+    assert compositepi(10**8) == 94238544
+    assert compositepi(253425253) == 239568856
+    assert compositepi(8769575643) == 8368111320
+    sieve.extend(3000)
+    assert compositepi(2321) == 1976
+
+
+def test_generate():
+    from sympy.ntheory.generate import sieve
+    sieve._reset()
+    assert nextprime(-4) == 2
+    assert nextprime(2) == 3
+    assert nextprime(5) == 7
+    assert nextprime(12) == 13
+    assert prevprime(3) == 2
+    assert prevprime(7) == 5
+    assert prevprime(13) == 11
+    assert prevprime(19) == 17
+    assert prevprime(20) == 19
+
+    sieve.extend_to_no(9)
+    assert sieve._list[-1] == 23
+
+    assert sieve._list[-1] < 31
+    assert 31 in sieve
+
+    assert nextprime(90) == 97
+    assert nextprime(10**40) == (10**40 + 121)
+    primelist = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
+                 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
+                 79, 83, 89, 97, 101, 103, 107, 109, 113,
+                 127, 131, 137, 139, 149, 151, 157, 163,
+                 167, 173, 179, 181, 191, 193, 197, 199,
+                 211, 223, 227, 229, 233, 239, 241, 251,
+                 257, 263, 269, 271, 277, 281, 283, 293]
+    for i in range(len(primelist) - 2):
+        for j in range(2, len(primelist) - i):
+            assert nextprime(primelist[i], j) == primelist[i + j]
+            if 3 < i:
+                assert nextprime(primelist[i] - 1, j) == primelist[i + j - 1]
+    raises(ValueError, lambda: nextprime(2, 0))
+    raises(ValueError, lambda: nextprime(2, -1))
+    assert prevprime(97) == 89
+    assert prevprime(10**40) == (10**40 - 17)
+
+    raises(ValueError, lambda: Sieve(0))
+    raises(ValueError, lambda: Sieve(-1))
+    for sieve_interval in [1, 10, 11, 1_000_000]:
+        s = Sieve(sieve_interval=sieve_interval)
+        for head in range(s._list[-1] + 1, (s._list[-1] + 1)**2, 2):
+            for tail in range(head + 1, (s._list[-1] + 1)**2):
+                A = list(s._primerange(head, tail))
+                B = primelist[bisect(primelist, head):bisect_left(primelist, tail)]
+                assert A == B
+        for k in range(s._list[-1], primelist[-1] - 1, 2):
+            s = Sieve(sieve_interval=sieve_interval)
+            s.extend(k)
+            assert list(s._list) == primelist[:bisect(primelist, k)]
+            s.extend(primelist[-1])
+            assert list(s._list) == primelist
+
+    assert list(sieve.primerange(10, 1)) == []
+    assert list(sieve.primerange(5, 9)) == [5, 7]
+    sieve._reset(prime=True)
+    assert list(sieve.primerange(2, 13)) == [2, 3, 5, 7, 11]
+    assert list(sieve.primerange(13)) == [2, 3, 5, 7, 11]
+    assert list(sieve.primerange(8)) == [2, 3, 5, 7]
+    assert list(sieve.primerange(-2)) == []
+    assert list(sieve.primerange(29)) == [2, 3, 5, 7, 11, 13, 17, 19, 23]
+    assert list(sieve.primerange(34)) == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
+
+    assert list(sieve.totientrange(5, 15)) == [4, 2, 6, 4, 6, 4, 10, 4, 12, 6]
+    sieve._reset(totient=True)
+    assert list(sieve.totientrange(3, 13)) == [2, 2, 4, 2, 6, 4, 6, 4, 10, 4]
+    assert list(sieve.totientrange(900, 1000)) == [totient(x) for x in range(900, 1000)]
+    assert list(sieve.totientrange(0, 1)) == []
+    assert list(sieve.totientrange(1, 2)) == [1]
+
+    assert list(sieve.mobiusrange(5, 15)) == [-1, 1, -1, 0, 0, 1, -1, 0, -1, 1]
+    sieve._reset(mobius=True)
+    assert list(sieve.mobiusrange(3, 13)) == [-1, 0, -1, 1, -1, 0, 0, 1, -1, 0]
+    assert list(sieve.mobiusrange(1050, 1100)) == [mobius(x) for x in range(1050, 1100)]
+    assert list(sieve.mobiusrange(0, 1)) == []
+    assert list(sieve.mobiusrange(1, 2)) == [1]
+
+    assert list(primerange(10, 1)) == []
+    assert list(primerange(2, 7)) == [2, 3, 5]
+    assert list(primerange(2, 10)) == [2, 3, 5, 7]
+    assert list(primerange(1050, 1100)) == [1051, 1061,
+        1063, 1069, 1087, 1091, 1093, 1097]
+    s = Sieve()
+    for i in range(30, 2350, 376):
+        for j in range(2, 5096, 1139):
+            A = list(s.primerange(i, i + j))
+            B = list(primerange(i, i + j))
+            assert A == B
+    s = Sieve()
+    sieve._reset(prime=True)
+    sieve.extend(13)
+    for i in range(200):
+        for j in range(i, 200):
+            A = list(s.primerange(i, j))
+            B = list(primerange(i, j))
+            assert A == B
+    sieve.extend(1000)
+    for a, b in [(901, 1103), # a < 1000 < b < 1000**2
+                 (806, 1002007), # a < 1000 < 1000**2 < b
+                 (2000, 30001), # 1000 < a < b < 1000**2
+                 (100005, 1010001), # 1000 < a < 1000**2 < b
+                 (1003003, 1005000), # 1000**2 < a < b
+                 ]:
+        assert list(primerange(a, b)) == list(s.primerange(a, b))
+    sieve._reset(prime=True)
+    sieve.extend(100000)
+    assert len(sieve._list) == len(set(sieve._list))
+    s = Sieve()
+    assert s[10] == 29
+
+    assert nextprime(2, 2) == 5
+
+    raises(ValueError, lambda: totient(0))
+
+    raises(ValueError, lambda: primorial(0))
+
+    assert mr(1, [2]) is False
+
+    func = lambda i: (i**2 + 1) % 51
+    assert next(cycle_length(func, 4)) == (6, 3)
+    assert list(cycle_length(func, 4, values=True)) == \
+        [4, 17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14]
+    assert next(cycle_length(func, 4, nmax=5)) == (5, None)
+    assert list(cycle_length(func, 4, nmax=5, values=True)) == \
+        [4, 17, 35, 2, 5]
+    sieve.extend(3000)
+    assert nextprime(2968) == 2969
+    assert prevprime(2930) == 2927
+    raises(ValueError, lambda: prevprime(1))
+    raises(ValueError, lambda: prevprime(-4))
+
+
+def test_randprime():
+    assert randprime(10, 1) is None
+    assert randprime(3, -3) is None
+    assert randprime(2, 3) == 2
+    assert randprime(1, 3) == 2
+    assert randprime(3, 5) == 3
+    raises(ValueError, lambda: randprime(-12, -2))
+    raises(ValueError, lambda: randprime(-10, 0))
+    raises(ValueError, lambda: randprime(20, 22))
+    raises(ValueError, lambda: randprime(0, 2))
+    raises(ValueError, lambda: randprime(1, 2))
+    for a in [100, 300, 500, 250000]:
+        for b in [100, 300, 500, 250000]:
+            p = randprime(a, a + b)
+            assert a <= p < (a + b) and isprime(p)
+
+
+def test_primorial():
+    assert primorial(1) == 2
+    assert primorial(1, nth=0) == 1
+    assert primorial(2) == 6
+    assert primorial(2, nth=0) == 2
+    assert primorial(4, nth=0) == 6
+
+
+def test_search():
+    assert 2 in sieve
+    assert 2.1 not in sieve
+    assert 1 not in sieve
+    assert 2**1000 not in sieve
+    raises(ValueError, lambda: sieve.search(1))
+
+
+def test_sieve_slice():
+    assert sieve[5] == 11
+    assert list(sieve[5:10]) == [sieve[x] for x in range(5, 10)]
+    assert list(sieve[5:10:2]) == [sieve[x] for x in range(5, 10, 2)]
+    assert list(sieve[1:5]) == [2, 3, 5, 7]
+    raises(IndexError, lambda: sieve[:5])
+    raises(IndexError, lambda: sieve[0])
+    raises(IndexError, lambda: sieve[0:5])
+
+def test_sieve_iter():
+    values = []
+    for value in sieve:
+        if value > 7:
+            break
+        values.append(value)
+    assert values == list(sieve[1:5])
+
+
+def test_sieve_repr():
+    assert "sieve" in repr(sieve)
+    assert "prime" in repr(sieve)
+
+
+def test_deprecated_ntheory_symbolic_functions():
+    from sympy.testing.pytest import warns_deprecated_sympy
+
+    with warns_deprecated_sympy():
+        assert primepi(0) == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_hypothesis.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_hypothesis.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8f4cbecdbb7a6b15b0e323700cda11039c968fb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_hypothesis.py
@@ -0,0 +1,24 @@
+from hypothesis import given
+from hypothesis import strategies as st
+from sympy import divisors
+from sympy.functions.combinatorial.numbers import divisor_sigma, totient
+from sympy.ntheory.primetest import is_square
+
+
+@given(n=st.integers(1, 10**10))
+def test_tau_hypothesis(n):
+    div = divisors(n)
+    tau_n = len(div)
+    assert is_square(n) == (tau_n % 2 == 1)
+    sigmas = [divisor_sigma(i) for i in div]
+    totients = [totient(n // i) for i in div]
+    mul = [a * b for a, b in zip(sigmas, totients)]
+    assert n * tau_n == sum(mul)
+
+
+@given(n=st.integers(1, 10**10))
+def test_totient_hypothesis(n):
+    assert totient(n) <= n
+    div = divisors(n)
+    totients = [totient(i) for i in div]
+    assert n == sum(totients)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_modular.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_modular.py
new file mode 100644
index 0000000000000000000000000000000000000000..10ebb1d3d3bdf5f736a6229579ae4c42a805745e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_modular.py
@@ -0,0 +1,34 @@
+from sympy.ntheory.modular import crt, crt1, crt2, solve_congruence
+from sympy.testing.pytest import raises
+
+
+def test_crt():
+    def mcrt(m, v, r, symmetric=False):
+        assert crt(m, v, symmetric)[0] == r
+        mm, e, s = crt1(m)
+        assert crt2(m, v, mm, e, s, symmetric) == (r, mm)
+
+    mcrt([2, 3, 5], [0, 0, 0], 0)
+    mcrt([2, 3, 5], [1, 1, 1], 1)
+
+    mcrt([2, 3, 5], [-1, -1, -1], -1, True)
+    mcrt([2, 3, 5], [-1, -1, -1], 2*3*5 - 1, False)
+
+    assert crt([656, 350], [811, 133], symmetric=True) == (-56917, 114800)
+
+
+def test_modular():
+    assert solve_congruence(*list(zip([3, 4, 2], [12, 35, 17]))) == (1719, 7140)
+    assert solve_congruence(*list(zip([3, 4, 2], [12, 6, 17]))) is None
+    assert solve_congruence(*list(zip([3, 4, 2], [13, 7, 17]))) == (172, 1547)
+    assert solve_congruence(*list(zip([-10, -3, -15], [13, 7, 17]))) == (172, 1547)
+    assert solve_congruence(*list(zip([-10, -3, 1, -15], [13, 7, 7, 17]))) is None
+    assert solve_congruence(
+        *list(zip([-10, -5, 2, -15], [13, 7, 7, 17]))) == (835, 1547)
+    assert solve_congruence(
+        *list(zip([-10, -5, 2, -15], [13, 7, 14, 17]))) == (2382, 3094)
+    assert solve_congruence(
+        *list(zip([-10, 2, 2, -15], [13, 7, 14, 17]))) == (2382, 3094)
+    assert solve_congruence(*list(zip((1, 1, 2), (3, 2, 4)))) is None
+    raises(
+        ValueError, lambda: solve_congruence(*list(zip([3, 4, 2], [12.1, 35, 17]))))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_multinomial.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_multinomial.py
new file mode 100644
index 0000000000000000000000000000000000000000..b455c5cc979b9ba9756c9da88c1694471115cd5d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_multinomial.py
@@ -0,0 +1,48 @@
+from sympy.ntheory.multinomial import (binomial_coefficients, binomial_coefficients_list, multinomial_coefficients)
+from sympy.ntheory.multinomial import multinomial_coefficients_iterator
+
+
+def test_binomial_coefficients_list():
+    assert binomial_coefficients_list(0) == [1]
+    assert binomial_coefficients_list(1) == [1, 1]
+    assert binomial_coefficients_list(2) == [1, 2, 1]
+    assert binomial_coefficients_list(3) == [1, 3, 3, 1]
+    assert binomial_coefficients_list(4) == [1, 4, 6, 4, 1]
+    assert binomial_coefficients_list(5) == [1, 5, 10, 10, 5, 1]
+    assert binomial_coefficients_list(6) == [1, 6, 15, 20, 15, 6, 1]
+
+
+def test_binomial_coefficients():
+    for n in range(15):
+        c = binomial_coefficients(n)
+        l = [c[k] for k in sorted(c)]
+        assert l == binomial_coefficients_list(n)
+
+
+def test_multinomial_coefficients():
+    assert multinomial_coefficients(1, 1) == {(1,): 1}
+    assert multinomial_coefficients(1, 2) == {(2,): 1}
+    assert multinomial_coefficients(1, 3) == {(3,): 1}
+    assert multinomial_coefficients(2, 0) == {(0, 0): 1}
+    assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1}
+    assert multinomial_coefficients(2, 2) == {(2, 0): 1, (0, 2): 1, (1, 1): 2}
+    assert multinomial_coefficients(2, 3) == {(3, 0): 1, (1, 2): 3, (0, 3): 1,
+            (2, 1): 3}
+    assert multinomial_coefficients(3, 1) == {(1, 0, 0): 1, (0, 1, 0): 1,
+            (0, 0, 1): 1}
+    assert multinomial_coefficients(3, 2) == {(0, 1, 1): 2, (0, 0, 2): 1,
+            (1, 1, 0): 2, (0, 2, 0): 1, (1, 0, 1): 2, (2, 0, 0): 1}
+    mc = multinomial_coefficients(3, 3)
+    assert mc == {(2, 1, 0): 3, (0, 3, 0): 1,
+            (1, 0, 2): 3, (0, 2, 1): 3, (0, 1, 2): 3, (3, 0, 0): 1,
+            (2, 0, 1): 3, (1, 2, 0): 3, (1, 1, 1): 6, (0, 0, 3): 1}
+    assert dict(multinomial_coefficients_iterator(2, 0)) == {(0, 0): 1}
+    assert dict(
+        multinomial_coefficients_iterator(2, 1)) == {(0, 1): 1, (1, 0): 1}
+    assert dict(multinomial_coefficients_iterator(2, 2)) == \
+        {(2, 0): 1, (0, 2): 1, (1, 1): 2}
+    assert dict(multinomial_coefficients_iterator(3, 3)) == mc
+    it = multinomial_coefficients_iterator(7, 2)
+    assert [next(it) for i in range(4)] == \
+        [((2, 0, 0, 0, 0, 0, 0), 1), ((1, 1, 0, 0, 0, 0, 0), 2),
+      ((0, 2, 0, 0, 0, 0, 0), 1), ((1, 0, 1, 0, 0, 0, 0), 2)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_partitions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_partitions.py
new file mode 100644
index 0000000000000000000000000000000000000000..8eb7fad3445068ae7ae4033c76c808e3c87347b6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_partitions.py
@@ -0,0 +1,28 @@
+from sympy.ntheory.partitions_ import npartitions, _partition_rec, _partition
+
+
+def test__partition_rec():
+    A000041 = [1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135,
+               176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575]
+    for n, val in enumerate(A000041):
+        assert _partition_rec(n) == val
+
+
+def test__partition():
+    assert [_partition(k) for k in range(13)] == \
+        [1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77]
+    assert _partition(100) == 190569292
+    assert _partition(200) == 3972999029388
+    assert _partition(1000) == 24061467864032622473692149727991
+    assert _partition(1001) == 25032297938763929621013218349796
+    assert _partition(2000) == 4720819175619413888601432406799959512200344166
+    assert _partition(10000) % 10**10 == 6916435144
+    assert _partition(100000) % 10**10 == 9421098519
+    assert _partition(10000000) % 10**10 == 7677288980
+
+
+def test_deprecated_ntheory_symbolic_functions():
+    from sympy.testing.pytest import warns_deprecated_sympy
+
+    with warns_deprecated_sympy():
+        assert npartitions(0) == 1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_primetest.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_primetest.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a56332941d9421bda4d6acc1e4b3406617cee2b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_primetest.py
@@ -0,0 +1,235 @@
+from math import gcd
+
+from sympy.ntheory.generate import Sieve, sieve
+from sympy.ntheory.primetest import (mr, _lucas_extrastrong_params, is_lucas_prp, is_square,
+                                     is_strong_lucas_prp, is_extra_strong_lucas_prp,
+                                     proth_test, isprime, is_euler_pseudoprime,
+                                     is_gaussian_prime, is_fermat_pseudoprime, is_euler_jacobi_pseudoprime,
+                                     MERSENNE_PRIME_EXPONENTS, _lucas_lehmer_primality_test,
+                                     is_mersenne_prime)
+
+from sympy.testing.pytest import slow, raises
+from sympy.core.numbers import I, Float
+
+
+def test_is_fermat_pseudoprime():
+    assert is_fermat_pseudoprime(5, 1)
+    assert is_fermat_pseudoprime(9, 1)
+
+
+def test_euler_pseudoprimes():
+    assert is_euler_pseudoprime(13, 1)
+    assert is_euler_pseudoprime(15, 1)
+    assert is_euler_pseudoprime(17, 6)
+    assert is_euler_pseudoprime(101, 7)
+    assert is_euler_pseudoprime(1009, 10)
+    assert is_euler_pseudoprime(11287, 41)
+
+    raises(ValueError, lambda: is_euler_pseudoprime(0, 4))
+    raises(ValueError, lambda: is_euler_pseudoprime(3, 0))
+    raises(ValueError, lambda: is_euler_pseudoprime(15, 6))
+
+    # A006970
+    euler_prp = [341, 561, 1105, 1729, 1905, 2047, 2465, 3277,
+                 4033, 4681, 5461, 6601, 8321, 8481, 10261, 10585]
+    for p in euler_prp:
+        assert is_euler_pseudoprime(p, 2)
+
+    # A048950
+    euler_prp = [121, 703, 1729, 1891, 2821, 3281, 7381, 8401, 8911, 10585,
+                 12403, 15457, 15841, 16531, 18721, 19345, 23521, 24661, 28009]
+    for p in euler_prp:
+        assert is_euler_pseudoprime(p, 3)
+
+    # A033181
+    absolute_euler_prp = [1729, 2465, 15841, 41041, 46657, 75361,
+                          162401, 172081, 399001, 449065, 488881]
+    for p in absolute_euler_prp:
+        for a in range(2, p):
+            if gcd(a, p) != 1:
+                continue
+            assert is_euler_pseudoprime(p, a)
+
+
+def test_is_euler_jacobi_pseudoprime():
+    assert is_euler_jacobi_pseudoprime(11, 1)
+    assert is_euler_jacobi_pseudoprime(15, 1)
+
+
+def test_lucas_extrastrong_params():
+    assert _lucas_extrastrong_params(3) == (5, 3, 1)
+    assert _lucas_extrastrong_params(5) == (12, 4, 1)
+    assert _lucas_extrastrong_params(7) == (5, 3, 1)
+    assert _lucas_extrastrong_params(9) == (0, 0, 0)
+    assert _lucas_extrastrong_params(11) == (21, 5, 1)
+    assert _lucas_extrastrong_params(59) == (32, 6, 1)
+    assert _lucas_extrastrong_params(479) == (117, 11, 1)
+
+
+def test_is_extra_strong_lucas_prp():
+    assert is_extra_strong_lucas_prp(4) == False
+    assert is_extra_strong_lucas_prp(989) == True
+    assert is_extra_strong_lucas_prp(10877) == True
+    assert is_extra_strong_lucas_prp(9) == False
+    assert is_extra_strong_lucas_prp(16) == False
+    assert is_extra_strong_lucas_prp(169) == False
+
+@slow
+def test_prps():
+    oddcomposites = [n for n in range(1, 10**5) if
+        n % 2 and not isprime(n)]
+    # A checksum would be better.
+    assert sum(oddcomposites) == 2045603465
+    assert [n for n in oddcomposites if mr(n, [2])] == [
+        2047, 3277, 4033, 4681, 8321, 15841, 29341, 42799, 49141,
+        52633, 65281, 74665, 80581, 85489, 88357, 90751]
+    assert [n for n in oddcomposites if mr(n, [3])] == [
+        121, 703, 1891, 3281, 8401, 8911, 10585, 12403, 16531,
+        18721, 19345, 23521, 31621, 44287, 47197, 55969, 63139,
+        74593, 79003, 82513, 87913, 88573, 97567]
+    assert [n for n in oddcomposites if mr(n, [325])] == [
+        9, 25, 27, 49, 65, 81, 325, 341, 343, 697, 1141, 2059,
+        2149, 3097, 3537, 4033, 4681, 4941, 5833, 6517, 7987, 8911,
+        12403, 12913, 15043, 16021, 20017, 22261, 23221, 24649,
+        24929, 31841, 35371, 38503, 43213, 44173, 47197, 50041,
+        55909, 56033, 58969, 59089, 61337, 65441, 68823, 72641,
+        76793, 78409, 85879]
+    assert not any(mr(n, [9345883071009581737]) for n in oddcomposites)
+    assert [n for n in oddcomposites if is_lucas_prp(n)] == [
+        323, 377, 1159, 1829, 3827, 5459, 5777, 9071, 9179, 10877,
+        11419, 11663, 13919, 14839, 16109, 16211, 18407, 18971,
+        19043, 22499, 23407, 24569, 25199, 25877, 26069, 27323,
+        32759, 34943, 35207, 39059, 39203, 39689, 40309, 44099,
+        46979, 47879, 50183, 51983, 53663, 56279, 58519, 60377,
+        63881, 69509, 72389, 73919, 75077, 77219, 79547, 79799,
+        82983, 84419, 86063, 90287, 94667, 97019, 97439]
+    assert [n for n in oddcomposites if is_strong_lucas_prp(n)] == [
+        5459, 5777, 10877, 16109, 18971, 22499, 24569, 25199, 40309,
+        58519, 75077, 97439]
+    assert [n for n in oddcomposites if is_extra_strong_lucas_prp(n)
+            ] == [
+        989, 3239, 5777, 10877, 27971, 29681, 30739, 31631, 39059,
+        72389, 73919, 75077]
+
+
+def test_proth_test():
+    # Proth number
+    A080075 = [3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65,
+               81, 97, 113, 129, 145, 161, 177, 193]
+    # Proth prime
+    A080076 = [3, 5, 13, 17, 41, 97, 113, 193]
+
+    for n in range(200):
+        if n in A080075:
+            assert proth_test(n) == (n in A080076)
+        else:
+            raises(ValueError, lambda: proth_test(n))
+
+
+def test_lucas_lehmer_primality_test():
+    for p in sieve.primerange(3, 100):
+        assert _lucas_lehmer_primality_test(p) == (p in MERSENNE_PRIME_EXPONENTS)
+
+
+def test_is_mersenne_prime():
+    assert is_mersenne_prime(-3) is False
+    assert is_mersenne_prime(3) is True
+    assert is_mersenne_prime(10) is False
+    assert is_mersenne_prime(127) is True
+    assert is_mersenne_prime(511) is False
+    assert is_mersenne_prime(131071) is True
+    assert is_mersenne_prime(2147483647) is True
+
+
+def test_isprime():
+    s = Sieve()
+    s.extend(100000)
+    ps = set(s.primerange(2, 100001))
+    for n in range(100001):
+        # if (n in ps) != isprime(n): print n
+        assert (n in ps) == isprime(n)
+    assert isprime(179424673)
+    assert isprime(20678048681)
+    assert isprime(1968188556461)
+    assert isprime(2614941710599)
+    assert isprime(65635624165761929287)
+    assert isprime(1162566711635022452267983)
+    assert isprime(77123077103005189615466924501)
+    assert isprime(3991617775553178702574451996736229)
+    assert isprime(273952953553395851092382714516720001799)
+    assert isprime(int('''
+531137992816767098689588206552468627329593117727031923199444138200403\
+559860852242739162502265229285668889329486246501015346579337652707239\
+409519978766587351943831270835393219031728127'''))
+
+    # Some Mersenne primes
+    assert isprime(2**61 - 1)
+    assert isprime(2**89 - 1)
+    assert isprime(2**607 - 1)
+    # (but not all Mersenne's are primes
+    assert not isprime(2**601 - 1)
+
+    # pseudoprimes
+    #-------------
+    # to some small bases
+    assert not isprime(2152302898747)
+    assert not isprime(3474749660383)
+    assert not isprime(341550071728321)
+    assert not isprime(3825123056546413051)
+    # passes the base set [2, 3, 7, 61, 24251]
+    assert not isprime(9188353522314541)
+    # large examples
+    assert not isprime(877777777777777777777777)
+    # conjectured psi_12 given at http://mathworld.wolfram.com/StrongPseudoprime.html
+    assert not isprime(318665857834031151167461)
+    # conjectured psi_17 given at http://mathworld.wolfram.com/StrongPseudoprime.html
+    assert not isprime(564132928021909221014087501701)
+    # Arnault's 1993 number; a factor of it is
+    # 400958216639499605418306452084546853005188166041132508774506\
+    # 204738003217070119624271622319159721973358216316508535816696\
+    # 9145233813917169287527980445796800452592031836601
+    assert not isprime(int('''
+803837457453639491257079614341942108138837688287558145837488917522297\
+427376533365218650233616396004545791504202360320876656996676098728404\
+396540823292873879185086916685732826776177102938969773947016708230428\
+687109997439976544144845341155872450633409279022275296229414984230688\
+1685404326457534018329786111298960644845216191652872597534901'''))
+    # Arnault's 1995 number; can be factored as
+    # p1*(313*(p1 - 1) + 1)*(353*(p1 - 1) + 1) where p1 is
+    # 296744956686855105501541746429053327307719917998530433509950\
+    # 755312768387531717701995942385964281211880336647542183455624\
+    # 93168782883
+    assert not isprime(int('''
+288714823805077121267142959713039399197760945927972270092651602419743\
+230379915273311632898314463922594197780311092934965557841894944174093\
+380561511397999942154241693397290542371100275104208013496673175515285\
+922696291677532547504444585610194940420003990443211677661994962953925\
+045269871932907037356403227370127845389912612030924484149472897688540\
+6024976768122077071687938121709811322297802059565867'''))
+    sieve.extend(3000)
+    assert isprime(2819)
+    assert not isprime(2931)
+    raises(ValueError, lambda: isprime(2.0))
+    raises(ValueError, lambda: isprime(Float(2)))
+
+
+def test_is_square():
+    assert [i for i in range(25) if is_square(i)] == [0, 1, 4, 9, 16]
+
+    # issue #17044
+    assert not is_square(60 ** 3)
+    assert not is_square(60 ** 5)
+    assert not is_square(84 ** 7)
+    assert not is_square(105 ** 9)
+    assert not is_square(120 ** 3)
+
+def test_is_gaussianprime():
+    assert is_gaussian_prime(7*I)
+    assert is_gaussian_prime(7)
+    assert is_gaussian_prime(2 + 3*I)
+    assert not is_gaussian_prime(2 + 2*I)
+
+
+def test_issue_27145():
+    #https://github.com/sympy/sympy/issues/27145
+    assert [mr(i,[2,3,5,7]) for i in (1, 2, 6)] == [False, True, False]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_qs.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_qs.py
new file mode 100644
index 0000000000000000000000000000000000000000..16932dd61badf4a467e67fa52e0f473594fd057b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_qs.py
@@ -0,0 +1,110 @@
+from __future__ import annotations
+
+import math
+from sympy.core.random import _randint
+from sympy.ntheory import qs, qs_factor
+from sympy.ntheory.qs import SievePolynomial, _generate_factor_base, \
+    _generate_polynomial, \
+    _gen_sieve_array, _check_smoothness, _trial_division_stage, _find_factor
+from sympy.testing.pytest import slow
+
+
+@slow
+def test_qs_1():
+    assert qs(10009202107, 100, 10000) == {100043, 100049}
+    assert qs(211107295182713951054568361, 1000, 10000) == \
+        {13791315212531, 15307263442931}
+    assert qs(980835832582657*990377764891511, 2000, 10000) == \
+        {980835832582657, 990377764891511}
+    assert qs(18640889198609*20991129234731, 1000, 50000) == \
+        {18640889198609, 20991129234731}
+
+
+def test_qs_2() -> None:
+    n = 10009202107
+    M = 50
+    sieve_poly = SievePolynomial(10, 80, n)
+    assert sieve_poly.eval_v(10) == sieve_poly.eval_u(10)**2 - n == -10009169707
+    assert sieve_poly.eval_v(5) == sieve_poly.eval_u(5)**2 - n == -10009185207
+
+    idx_1000, idx_5000, factor_base = _generate_factor_base(2000, n)
+    assert idx_1000 == 82
+    assert [factor_base[i].prime for i in range(15)] == \
+        [2, 3, 7, 11, 17, 19, 29, 31, 43, 59, 61, 67, 71, 73, 79]
+    assert [factor_base[i].tmem_p for i in range(15)] == \
+        [1, 1, 3, 5, 3, 6, 6, 14, 1, 16, 24, 22, 18, 22, 15]
+    assert [factor_base[i].log_p for i in range(5)] == \
+        [710, 1125, 1993, 2455, 2901]
+
+    it = _generate_polynomial(
+        n, M, factor_base, idx_1000, idx_5000, _randint(0))
+    g = next(it)
+    assert g.a == 1133107
+    assert g.b == 682543
+    assert [factor_base[i].soln1 for i in range(15)] == \
+        [0, 0, 3, 7, 13, 0, 8, 19, 9, 43, 27, 25, 63, 29, 19]
+    assert [factor_base[i].soln2 for i in range(15)] == \
+        [0, 1, 1, 3, 12, 16, 15, 6, 15, 1, 56, 55, 61, 58, 16]
+    assert [factor_base[i].b_ainv for i in range(5)] == \
+        [[0, 0], [0, 2], [3, 0], [3, 9], [13, 13]]
+
+    g_1 = next(it)
+    assert g_1.a == 1133107
+    assert g_1.b == 136765
+
+    sieve_array = _gen_sieve_array(M, factor_base)
+    assert sieve_array[0:5] == [8424, 13603, 1835, 5335, 710]
+
+    assert _check_smoothness(9645, factor_base) == (36028797018963972, 5)
+    assert _check_smoothness(210313, factor_base) == (20992, 1)
+
+    partial_relations: dict[int, tuple[int, int]] = {}
+    smooth_relation, proper_factor = _trial_division_stage(
+        n, M, factor_base, sieve_array, sieve_poly, partial_relations,
+        ERROR_TERM=25*2**10)
+
+    assert partial_relations == {
+        8699: (440, -10009008507, 75557863761098695507973),
+        166741: (490, -10008962007, 524341),
+        131449: (530, -10008921207, 664613997892457936451903530140172325),
+        6653: (550, -10008899607, 19342813113834066795307021)
+    }
+    assert [smooth_relation[i][0] for i in range(5)] == [
+        -250, 1064469, 72819, 231957, 44167]
+    assert [smooth_relation[i][1] for i in range(5)] == [
+        -10009139607, 1133094251961, 5302606761, 53804049849, 1950723889]
+    assert smooth_relation[0][2] == 89213869829863962596973701078031812362502145
+    assert proper_factor == set()
+
+
+def test_qs_3():
+    N = 1817
+    smooth_relations = [
+        (2455024, 637, 8),
+        (-27993000, 81536, 10),
+        (11461840, 12544, 0),
+        (149, 20384, 10),
+        (-31138074, 19208, 2)
+    ]
+    assert next(_find_factor(N, smooth_relations, 4)) == 23
+
+
+def test_qs_4():
+    N = 10007**2 * 10009 * 10037**3 * 10039
+    for factor in qs(N, 1000, 2000):
+        assert N % factor == 0
+        N //= factor
+
+
+def test_qs_factor():
+    assert qs_factor(1009 * 100003, 2000, 10000) == {1009: 1, 100003: 1}
+    n = 1009**2 * 2003**2*30011*400009
+    factors = qs_factor(n, 2000, 10000)
+    assert len(factors) > 1
+    assert math.prod(p**e for p, e in factors.items()) == n
+
+
+def test_issue_27616():
+    #https://github.com/sympy/sympy/issues/27616
+    N = 9804659461513846513 + 1
+    assert qs(N, 5000, 20000) is not None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_residue.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_residue.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d530905f39b88d8d7cc0e861ac6eadb2fa6f98a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/ntheory/tests/test_residue.py
@@ -0,0 +1,349 @@
+from collections import defaultdict
+from sympy.core.containers import Tuple
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.functions.combinatorial.numbers import totient
+from sympy.ntheory import n_order, is_primitive_root, is_quad_residue, \
+    legendre_symbol, jacobi_symbol, primerange, sqrt_mod, \
+    primitive_root, quadratic_residues, is_nthpow_residue, nthroot_mod, \
+    sqrt_mod_iter, mobius, discrete_log, quadratic_congruence, \
+    polynomial_congruence, sieve
+from sympy.ntheory.residue_ntheory import _primitive_root_prime_iter, \
+    _primitive_root_prime_power_iter, _primitive_root_prime_power2_iter, \
+    _nthroot_mod_prime_power, _discrete_log_trial_mul, _discrete_log_shanks_steps, \
+    _discrete_log_pollard_rho, _discrete_log_index_calculus, _discrete_log_pohlig_hellman, \
+    _binomial_mod_prime_power, binomial_mod
+from sympy.polys.domains import ZZ
+from sympy.testing.pytest import raises
+from sympy.core.random import randint, choice
+
+
+def test_residue():
+    assert n_order(2, 13) == 12
+    assert [n_order(a, 7) for a in range(1, 7)] == \
+           [1, 3, 6, 3, 6, 2]
+    assert n_order(5, 17) == 16
+    assert n_order(17, 11) == n_order(6, 11)
+    assert n_order(101, 119) == 6
+    assert n_order(11, (10**50 + 151)**2) == 10000000000000000000000000000000000000000000000030100000000000000000000000000000000000000000000022650
+    raises(ValueError, lambda: n_order(6, 9))
+
+    assert is_primitive_root(2, 7) is False
+    assert is_primitive_root(3, 8) is False
+    assert is_primitive_root(11, 14) is False
+    assert is_primitive_root(12, 17) == is_primitive_root(29, 17)
+    raises(ValueError, lambda: is_primitive_root(3, 6))
+
+    for p in primerange(3, 100):
+        li = list(_primitive_root_prime_iter(p))
+        assert li[0] == min(li)
+        for g in li:
+            assert n_order(g, p) == p - 1
+        assert len(li) == totient(totient(p))
+        for e in range(1, 4):
+            li_power = list(_primitive_root_prime_power_iter(p, e))
+            li_power2 = list(_primitive_root_prime_power2_iter(p, e))
+            assert len(li_power) == len(li_power2) == totient(totient(p**e))
+    assert primitive_root(97) == 5
+    assert n_order(primitive_root(97, False), 97) == totient(97)
+    assert primitive_root(97**2) == 5
+    assert n_order(primitive_root(97**2, False), 97**2) == totient(97**2)
+    assert primitive_root(40487) == 5
+    assert n_order(primitive_root(40487, False), 40487) == totient(40487)
+    # note that primitive_root(40487) + 40487 = 40492 is a primitive root
+    # of 40487**2, but it is not the smallest
+    assert primitive_root(40487**2) == 10
+    assert n_order(primitive_root(40487**2, False), 40487**2) == totient(40487**2)
+    assert primitive_root(82) == 7
+    assert n_order(primitive_root(82, False), 82) == totient(82)
+    p = 10**50 + 151
+    assert primitive_root(p) == 11
+    assert n_order(primitive_root(p, False), p) == totient(p)
+    assert primitive_root(2*p) == 11
+    assert n_order(primitive_root(2*p, False), 2*p) == totient(2*p)
+    assert primitive_root(p**2) == 11
+    assert n_order(primitive_root(p**2, False), p**2) == totient(p**2)
+    assert primitive_root(4 * 11) is None and primitive_root(4 * 11, False) is None
+    assert primitive_root(15) is None and primitive_root(15, False) is None
+    raises(ValueError, lambda: primitive_root(-3))
+
+    assert is_quad_residue(3, 7) is False
+    assert is_quad_residue(10, 13) is True
+    assert is_quad_residue(12364, 139) == is_quad_residue(12364 % 139, 139)
+    assert is_quad_residue(207, 251) is True
+    assert is_quad_residue(0, 1) is True
+    assert is_quad_residue(1, 1) is True
+    assert is_quad_residue(0, 2) == is_quad_residue(1, 2) is True
+    assert is_quad_residue(1, 4) is True
+    assert is_quad_residue(2, 27) is False
+    assert is_quad_residue(13122380800, 13604889600) is True
+    assert [j for j in range(14) if is_quad_residue(j, 14)] == \
+           [0, 1, 2, 4, 7, 8, 9, 11]
+    raises(ValueError, lambda: is_quad_residue(1.1, 2))
+    raises(ValueError, lambda: is_quad_residue(2, 0))
+
+    assert quadratic_residues(S.One) == [0]
+    assert quadratic_residues(1) == [0]
+    assert quadratic_residues(12) == [0, 1, 4, 9]
+    assert quadratic_residues(13) == [0, 1, 3, 4, 9, 10, 12]
+    assert [len(quadratic_residues(i)) for i in range(1, 20)] == \
+      [1, 2, 2, 2, 3, 4, 4, 3, 4, 6, 6, 4, 7, 8, 6, 4, 9, 8, 10]
+
+    assert list(sqrt_mod_iter(6, 2)) == [0]
+    assert sqrt_mod(3, 13) == 4
+    assert sqrt_mod(3, -13) == 4
+    assert sqrt_mod(6, 23) == 11
+    assert sqrt_mod(345, 690) == 345
+    assert sqrt_mod(67, 101) == None
+    assert sqrt_mod(1020, 104729) == None
+
+    for p in range(3, 100):
+        d = defaultdict(list)
+        for i in range(p):
+            d[pow(i, 2, p)].append(i)
+        for i in range(1, p):
+            it = sqrt_mod_iter(i, p)
+            v = sqrt_mod(i, p, True)
+            if v:
+                v = sorted(v)
+                assert d[i] == v
+            else:
+                assert not d[i]
+
+    assert sqrt_mod(9, 27, True) == [3, 6, 12, 15, 21, 24]
+    assert sqrt_mod(9, 81, True) == [3, 24, 30, 51, 57, 78]
+    assert sqrt_mod(9, 3**5, True) == [3, 78, 84, 159, 165, 240]
+    assert sqrt_mod(81, 3**4, True) == [0, 9, 18, 27, 36, 45, 54, 63, 72]
+    assert sqrt_mod(81, 3**5, True) == [9, 18, 36, 45, 63, 72, 90, 99, 117,\
+            126, 144, 153, 171, 180, 198, 207, 225, 234]
+    assert sqrt_mod(81, 3**6, True) == [9, 72, 90, 153, 171, 234, 252, 315,\
+            333, 396, 414, 477, 495, 558, 576, 639, 657, 720]
+    assert sqrt_mod(81, 3**7, True) == [9, 234, 252, 477, 495, 720, 738, 963,\
+            981, 1206, 1224, 1449, 1467, 1692, 1710, 1935, 1953, 2178]
+
+    for a, p in [(26214400, 32768000000), (26214400, 16384000000),
+        (262144, 1048576), (87169610025, 163443018796875),
+        (22315420166400, 167365651248000000)]:
+        assert pow(sqrt_mod(a, p), 2, p) == a
+
+    n = 70
+    a, p = 5**2*3**n*2**n, 5**6*3**(n+1)*2**(n+2)
+    it = sqrt_mod_iter(a, p)
+    for i in range(10):
+        assert pow(next(it), 2, p) == a
+    a, p = 5**2*3**n*2**n, 5**6*3**(n+1)*2**(n+3)
+    it = sqrt_mod_iter(a, p)
+    for i in range(2):
+        assert pow(next(it), 2, p) == a
+    n = 100
+    a, p = 5**2*3**n*2**n, 5**6*3**(n+1)*2**(n+1)
+    it = sqrt_mod_iter(a, p)
+    for i in range(2):
+        assert pow(next(it), 2, p) == a
+
+    assert type(next(sqrt_mod_iter(9, 27))) is int
+    assert type(next(sqrt_mod_iter(9, 27, ZZ))) is type(ZZ(1))
+    assert type(next(sqrt_mod_iter(1, 7, ZZ))) is type(ZZ(1))
+
+    assert is_nthpow_residue(2, 1, 5)
+
+    #issue 10816
+    assert is_nthpow_residue(1, 0, 1) is False
+    assert is_nthpow_residue(1, 0, 2) is True
+    assert is_nthpow_residue(3, 0, 2) is True
+    assert is_nthpow_residue(0, 1, 8) is True
+    assert is_nthpow_residue(2, 3, 2) is True
+    assert is_nthpow_residue(2, 3, 9) is False
+    assert is_nthpow_residue(3, 5, 30) is True
+    assert is_nthpow_residue(21, 11, 20) is True
+    assert is_nthpow_residue(7, 10, 20) is False
+    assert is_nthpow_residue(5, 10, 20) is True
+    assert is_nthpow_residue(3, 10, 48) is False
+    assert is_nthpow_residue(1, 10, 40) is True
+    assert is_nthpow_residue(3, 10, 24) is False
+    assert is_nthpow_residue(1, 10, 24) is True
+    assert is_nthpow_residue(3, 10, 24) is False
+    assert is_nthpow_residue(2, 10, 48) is False
+    assert is_nthpow_residue(81, 3, 972) is False
+    assert is_nthpow_residue(243, 5, 5103) is True
+    assert is_nthpow_residue(243, 3, 1240029) is False
+    assert is_nthpow_residue(36010, 8, 87382) is True
+    assert is_nthpow_residue(28552, 6, 2218) is True
+    assert is_nthpow_residue(92712, 9, 50026) is True
+    x = {pow(i, 56, 1024) for i in range(1024)}
+    assert {a for a in range(1024) if is_nthpow_residue(a, 56, 1024)} == x
+    x = { pow(i, 256, 2048) for i in range(2048)}
+    assert {a for a in range(2048) if is_nthpow_residue(a, 256, 2048)} == x
+    x = { pow(i, 11, 324000) for i in range(1000)}
+    assert [ is_nthpow_residue(a, 11, 324000) for a in x]
+    x = { pow(i, 17, 22217575536) for i in range(1000)}
+    assert [ is_nthpow_residue(a, 17, 22217575536) for a in x]
+    assert is_nthpow_residue(676, 3, 5364)
+    assert is_nthpow_residue(9, 12, 36)
+    assert is_nthpow_residue(32, 10, 41)
+    assert is_nthpow_residue(4, 2, 64)
+    assert is_nthpow_residue(31, 4, 41)
+    assert not is_nthpow_residue(2, 2, 5)
+    assert is_nthpow_residue(8547, 12, 10007)
+    assert is_nthpow_residue(Dummy(even=True) + 3, 3, 2) == True
+    # _nthroot_mod_prime_power
+    for p in primerange(2, 10):
+        for a in range(3):
+            for n in range(3, 5):
+                ans = _nthroot_mod_prime_power(a, n, p, 1)
+                assert isinstance(ans, list)
+                if len(ans) == 0:
+                    for b in range(p):
+                        assert pow(b, n, p) != a % p
+                    for k in range(2, 10):
+                        assert _nthroot_mod_prime_power(a, n, p, k) == []
+                else:
+                    for b in range(p):
+                        pred = pow(b, n, p) == a % p
+                        assert not(pred ^ (b in ans))
+                    for k in range(2, 10):
+                        ans = _nthroot_mod_prime_power(a, n, p, k)
+                        if not ans:
+                            break
+                        for b in ans:
+                            assert pow(b, n , p**k) == a
+
+    assert nthroot_mod(Dummy(odd=True), 3, 2) == 1
+    assert nthroot_mod(29, 31, 74) == 45
+    assert nthroot_mod(1801, 11, 2663) == 44
+    for a, q, p in [(51922, 2, 203017), (43, 3, 109), (1801, 11, 2663),
+          (26118163, 1303, 33333347), (1499, 7, 2663), (595, 6, 2663),
+          (1714, 12, 2663), (28477, 9, 33343)]:
+        r = nthroot_mod(a, q, p)
+        assert pow(r, q, p) == a
+    assert nthroot_mod(11, 3, 109) is None
+    assert nthroot_mod(16, 5, 36, True) == [4, 22]
+    assert nthroot_mod(9, 16, 36, True) == [3, 9, 15, 21, 27, 33]
+    assert nthroot_mod(4, 3, 3249000) is None
+    assert nthroot_mod(36010, 8, 87382, True) == [40208, 47174]
+    assert nthroot_mod(0, 12, 37, True) == [0]
+    assert nthroot_mod(0, 7, 100, True) == [0, 10, 20, 30, 40, 50, 60, 70, 80, 90]
+    assert nthroot_mod(4, 4, 27, True) == [5, 22]
+    assert nthroot_mod(4, 4, 121, True) == [19, 102]
+    assert nthroot_mod(2, 3, 7, True) == []
+    for p in range(1, 20):
+        for a in range(p):
+            for n in range(1, p):
+                ans = nthroot_mod(a, n, p, True)
+                assert isinstance(ans, list)
+                for b in range(p):
+                    pred = pow(b, n, p) == a
+                    assert not(pred ^ (b in ans))
+                ans2 = nthroot_mod(a, n, p, False)
+                if ans2 is None:
+                    assert ans == []
+                else:
+                    assert ans2 in ans
+
+    x = Symbol('x', positive=True)
+    i = Symbol('i', integer=True)
+    assert _discrete_log_trial_mul(587, 2**7, 2) == 7
+    assert _discrete_log_trial_mul(941, 7**18, 7) == 18
+    assert _discrete_log_trial_mul(389, 3**81, 3) == 81
+    assert _discrete_log_trial_mul(191, 19**123, 19) == 123
+    assert _discrete_log_shanks_steps(442879, 7**2, 7) == 2
+    assert _discrete_log_shanks_steps(874323, 5**19, 5) == 19
+    assert _discrete_log_shanks_steps(6876342, 7**71, 7) == 71
+    assert _discrete_log_shanks_steps(2456747, 3**321, 3) == 321
+    assert _discrete_log_pollard_rho(6013199, 2**6, 2, rseed=0) == 6
+    assert _discrete_log_pollard_rho(6138719, 2**19, 2, rseed=0) == 19
+    assert _discrete_log_pollard_rho(36721943, 2**40, 2, rseed=0) == 40
+    assert _discrete_log_pollard_rho(24567899, 3**333, 3, rseed=0) == 333
+    raises(ValueError, lambda: _discrete_log_pollard_rho(11, 7, 31, rseed=0))
+    raises(ValueError, lambda: _discrete_log_pollard_rho(227, 3**7, 5, rseed=0))
+    assert _discrete_log_index_calculus(983, 948, 2, 491) == 183
+    assert _discrete_log_index_calculus(633383, 21794, 2, 316691) == 68048
+    assert _discrete_log_index_calculus(941762639, 68822582, 2, 470881319) == 338029275
+    assert _discrete_log_index_calculus(999231337607, 888188918786, 2, 499615668803) == 142811376514
+    assert _discrete_log_index_calculus(47747730623, 19410045286, 43425105668, 645239603) == 590504662
+    assert _discrete_log_pohlig_hellman(98376431, 11**9, 11) == 9
+    assert _discrete_log_pohlig_hellman(78723213, 11**31, 11) == 31
+    assert _discrete_log_pohlig_hellman(32942478, 11**98, 11) == 98
+    assert _discrete_log_pohlig_hellman(14789363, 11**444, 11) == 444
+    assert discrete_log(1, 0, 2) == 0
+    raises(ValueError, lambda: discrete_log(-4, 1, 3))
+    raises(ValueError, lambda: discrete_log(10, 3, 2))
+    assert discrete_log(587, 2**9, 2) == 9
+    assert discrete_log(2456747, 3**51, 3) == 51
+    assert discrete_log(32942478, 11**127, 11) == 127
+    assert discrete_log(432751500361, 7**324, 7) == 324
+    assert discrete_log(265390227570863,184500076053622, 2) == 17835221372061
+    assert discrete_log(22708823198678103974314518195029102158525052496759285596453269189798311427475159776411276642277139650833937,
+                        17463946429475485293747680247507700244427944625055089103624311227422110546803452417458985046168310373075327,
+                        123456) == 2068031853682195777930683306640554533145512201725884603914601918777510185469769997054750835368413389728895
+    args = 5779, 3528, 6215
+    assert discrete_log(*args) == 687
+    assert discrete_log(*Tuple(*args)) == 687
+    assert quadratic_congruence(400, 85, 125, 1600) == [295, 615, 935, 1255, 1575]
+    assert quadratic_congruence(3, 6, 5, 25) == [3, 20]
+    assert quadratic_congruence(120, 80, 175, 500) == []
+    assert quadratic_congruence(15, 14, 7, 2) == [1]
+    assert quadratic_congruence(8, 15, 7, 29) == [10, 28]
+    assert quadratic_congruence(160, 200, 300, 461) == [144, 431]
+    assert quadratic_congruence(100000, 123456, 7415263, 48112959837082048697) == [30417843635344493501, 36001135160550533083]
+    assert quadratic_congruence(65, 121, 72, 277) == [249, 252]
+    assert quadratic_congruence(5, 10, 14, 2) == [0]
+    assert quadratic_congruence(10, 17, 19, 2) == [1]
+    assert quadratic_congruence(10, 14, 20, 2) == [0, 1]
+    assert quadratic_congruence(2**48-7, 2**48-1, 4, 2**48) == [8249717183797, 31960993774868]
+    assert polynomial_congruence(6*x**5 + 10*x**4 + 5*x**3 + x**2 + x + 1,
+        972000) == [220999, 242999, 463999, 485999, 706999, 728999, 949999, 971999]
+
+    assert polynomial_congruence(x**3 - 10*x**2 + 12*x - 82, 33075) == [30287]
+    assert polynomial_congruence(x**2 + x + 47, 2401) == [785, 1615]
+    assert polynomial_congruence(10*x**2 + 14*x + 20, 2) == [0, 1]
+    assert polynomial_congruence(x**3 + 3, 16) == [5]
+    assert polynomial_congruence(65*x**2 + 121*x + 72, 277) == [249, 252]
+    assert polynomial_congruence(x**4 - 4, 27) == [5, 22]
+    assert polynomial_congruence(35*x**3 - 6*x**2 - 567*x + 2308, 148225) == [86957,
+        111157, 122531, 146731]
+    assert polynomial_congruence(x**16 - 9, 36) == [3, 9, 15, 21, 27, 33]
+    assert polynomial_congruence(x**6 - 2*x**5 - 35, 6125) == [3257]
+    raises(ValueError, lambda: polynomial_congruence(x**x, 6125))
+    raises(ValueError, lambda: polynomial_congruence(x**i, 6125))
+    raises(ValueError, lambda: polynomial_congruence(0.1*x**2 + 6, 100))
+
+    assert binomial_mod(-1, 1, 10) == 0
+    assert binomial_mod(1, -1, 10) == 0
+    raises(ValueError, lambda: binomial_mod(2, 1, -1))
+    assert binomial_mod(51, 10, 10) == 0
+    assert binomial_mod(10**3, 500, 3**6) == 567
+    assert binomial_mod(10**18 - 1, 123456789, 4) == 0
+    assert binomial_mod(10**18, 10**12, (10**5 + 3)**2) == 3744312326
+
+
+def test_binomial_p_pow():
+    n, binomials, binomial = 1000, [1], 1
+    for i in range(1, n + 1):
+        binomial *= n - i + 1
+        binomial //= i
+        binomials.append(binomial)
+
+    # Test powers of two, which the algorithm treats slightly differently
+    trials_2 = 100
+    for _ in range(trials_2):
+        m, power = randint(0, n), randint(1, 20)
+        assert _binomial_mod_prime_power(n, m, 2, power) == binomials[m] % 2**power
+
+    # Test against other prime powers
+    primes = list(sieve.primerange(2*n))
+    trials = 1000
+    for _ in range(trials):
+        m, prime, power = randint(0, n), choice(primes), randint(1, 10)
+        assert _binomial_mod_prime_power(n, m, prime, power) == binomials[m] % prime**power
+
+
+def test_deprecated_ntheory_symbolic_functions():
+    from sympy.testing.pytest import warns_deprecated_sympy
+
+    with warns_deprecated_sympy():
+        assert mobius(3) == -1
+    with warns_deprecated_sympy():
+        assert legendre_symbol(2, 3) == -1
+    with warns_deprecated_sympy():
+        assert jacobi_symbol(2, 3) == -1
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..b39d031bca26bc599eb9eb0e12dfe48f7e6db174
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/__init__.py
@@ -0,0 +1,4 @@
+"""Used for translating a string into a SymPy expression. """
+__all__ = ['parse_expr']
+
+from .sympy_parser import parse_expr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/ast_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/ast_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..95a773d5bec6e130810b7b7925fdff57270aec17
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/ast_parser.py
@@ -0,0 +1,79 @@
+"""
+This module implements the functionality to take any Python expression as a
+string and fix all numbers and other things before evaluating it,
+thus
+
+1/2
+
+returns
+
+Integer(1)/Integer(2)
+
+We use the ast module for this. It is well documented at docs.python.org.
+
+Some tips to understand how this works: use dump() to get a nice
+representation of any node. Then write a string of what you want to get,
+e.g. "Integer(1)", parse it, dump it and you'll see that you need to do
+"Call(Name('Integer', Load()), [node], [], None, None)". You do not need
+to bother with lineno and col_offset, just call fix_missing_locations()
+before returning the node.
+"""
+
+from sympy.core.basic import Basic
+from sympy.core.sympify import SympifyError
+
+from ast import parse, NodeTransformer, Call, Name, Load, \
+    fix_missing_locations, Constant, Tuple
+
+class Transform(NodeTransformer):
+
+    def __init__(self, local_dict, global_dict):
+        NodeTransformer.__init__(self)
+        self.local_dict = local_dict
+        self.global_dict = global_dict
+
+    def visit_Constant(self, node):
+        if isinstance(node.value, int):
+            return fix_missing_locations(Call(func=Name('Integer', Load()),
+                    args=[node], keywords=[]))
+        elif isinstance(node.value, float):
+            return fix_missing_locations(Call(func=Name('Float', Load()),
+                    args=[node], keywords=[]))
+        return node
+
+    def visit_Name(self, node):
+        if node.id in self.local_dict:
+            return node
+        elif node.id in self.global_dict:
+            name_obj = self.global_dict[node.id]
+
+            if isinstance(name_obj, (Basic, type)) or callable(name_obj):
+                return node
+        elif node.id in ['True', 'False']:
+            return node
+        return fix_missing_locations(Call(func=Name('Symbol', Load()),
+                args=[Constant(node.id)], keywords=[]))
+
+    def visit_Lambda(self, node):
+        args = [self.visit(arg) for arg in node.args.args]
+        body = self.visit(node.body)
+        n = Call(func=Name('Lambda', Load()),
+            args=[Tuple(args, Load()), body], keywords=[])
+        return fix_missing_locations(n)
+
+def parse_expr(s, local_dict):
+    """
+    Converts the string "s" to a SymPy expression, in local_dict.
+
+    It converts all numbers to Integers before feeding it to Python and
+    automatically creates Symbols.
+    """
+    global_dict = {}
+    exec('from sympy import *', global_dict)
+    try:
+        a = parse(s.strip(), mode="eval")
+    except SyntaxError:
+        raise SympifyError("Cannot parse %s." % repr(s))
+    a = Transform(local_dict, global_dict).visit(a)
+    e = compile(a, "", "eval")
+    return eval(e, global_dict, local_dict)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/Autolev.g4 b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/Autolev.g4
new file mode 100644
index 0000000000000000000000000000000000000000..94feea5fa4f49e9d1054eca2cd60c996aebff7c2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/Autolev.g4
@@ -0,0 +1,118 @@
+grammar Autolev;
+
+options {
+        language = Python3;
+}
+
+prog:   stat+;
+
+stat:   varDecl
+    |   functionCall
+    |   codeCommands
+    |   massDecl
+    |   inertiaDecl
+    |   assignment
+    |   settings
+    ;
+
+assignment:   vec equals expr #vecAssign
+          |   ID '[' index ']' equals expr #indexAssign
+          |   ID diff? equals expr #regularAssign;
+
+equals:   ('='|'+='|'-='|':='|'*='|'/='|'^=');
+
+index:   expr (',' expr)* ;
+
+diff:   ('\'')+;
+
+functionCall:   ID '(' (expr (',' expr)*)? ')'
+            |   (Mass|Inertia) '(' (ID (',' ID)*)? ')';
+
+varDecl:   varType varDecl2 (',' varDecl2)*;
+
+varType:   Newtonian|Frames|Bodies|Particles|Points|Constants
+       |   Specifieds|Imaginary|Variables ('\'')*|MotionVariables ('\'')*;
+
+varDecl2:   ID ('{' INT ',' INT '}')? (('{' INT ':' INT (',' INT ':' INT)* '}'))? ('{' INT '}')? ('+'|'-')? ('\'')* ('=' expr)?;
+
+ranges:   ('{' INT ':' INT (',' INT ':' INT)* '}');
+
+massDecl:   Mass massDecl2 (',' massDecl2)*;
+
+massDecl2:   ID '=' expr;
+
+inertiaDecl:   Inertia ID ('(' ID ')')? (',' expr)+;
+
+matrix:   '[' expr ((','|';') expr)* ']';
+matrixInOutput:   (ID (ID '=' (FLOAT|INT)?))|FLOAT|INT;
+
+codeCommands:   units
+            |   inputs
+            |   outputs
+            |   codegen
+            |   commands;
+
+settings:   ID (EXP|ID|FLOAT|INT)?;
+
+units:     UnitSystem ID (',' ID)*;
+inputs:    Input inputs2 (',' inputs2)*;
+id_diff:   ID diff?;
+inputs2:   id_diff '=' expr expr?;
+outputs:   Output outputs2 (',' outputs2)*;
+outputs2:  expr expr?;
+codegen:   ID functionCall ('['matrixInOutput (',' matrixInOutput)*']')? ID'.'ID;
+
+commands:  Save ID'.'ID
+        |  Encode ID (',' ID)*;
+
+vec:  ID ('>')+
+   |  '0>'
+   |  '1>>';
+
+expr:   expr '^' expr  # Exponent
+    |   expr ('*'|'/') expr         # MulDiv
+    |   expr ('+'|'-') expr         # AddSub
+    |   EXP                         # exp
+    |   '-' expr                    # negativeOne
+    |   FLOAT                       # float
+    |   INT                         # int
+    |   ID('\'')*                   # id
+    |   vec                         # VectorOrDyadic
+    |   ID '['expr (',' expr)* ']'  # Indexing
+    |   functionCall                # function
+    |   matrix                      # matrices
+    |   '(' expr ')'                # parens
+    |   expr '=' expr               # idEqualsExpr
+    |   expr ':' expr               # colon
+    |   ID? ranges ('\'')*          # rangess
+    ;
+
+// These are to take care of the case insensitivity of Autolev.
+Mass: ('M'|'m')('A'|'a')('S'|'s')('S'|'s');
+Inertia: ('I'|'i')('N'|'n')('E'|'e')('R'|'r')('T'|'t')('I'|'i')('A'|'a');
+Input: ('I'|'i')('N'|'n')('P'|'p')('U'|'u')('T'|'t')('S'|'s')?;
+Output: ('O'|'o')('U'|'u')('T'|'t')('P'|'p')('U'|'u')('T'|'t');
+Save: ('S'|'s')('A'|'a')('V'|'v')('E'|'e');
+UnitSystem: ('U'|'u')('N'|'n')('I'|'i')('T'|'t')('S'|'s')('Y'|'y')('S'|'s')('T'|'t')('E'|'e')('M'|'m');
+Encode: ('E'|'e')('N'|'n')('C'|'c')('O'|'o')('D'|'d')('E'|'e');
+Newtonian: ('N'|'n')('E'|'e')('W'|'w')('T'|'t')('O'|'o')('N'|'n')('I'|'i')('A'|'a')('N'|'n');
+Frames: ('F'|'f')('R'|'r')('A'|'a')('M'|'m')('E'|'e')('S'|'s')?;
+Bodies: ('B'|'b')('O'|'o')('D'|'d')('I'|'i')('E'|'e')('S'|'s')?;
+Particles: ('P'|'p')('A'|'a')('R'|'r')('T'|'t')('I'|'i')('C'|'c')('L'|'l')('E'|'e')('S'|'s')?;
+Points: ('P'|'p')('O'|'o')('I'|'i')('N'|'n')('T'|'t')('S'|'s')?;
+Constants: ('C'|'c')('O'|'o')('N'|'n')('S'|'s')('T'|'t')('A'|'a')('N'|'n')('T'|'t')('S'|'s')?;
+Specifieds: ('S'|'s')('P'|'p')('E'|'e')('C'|'c')('I'|'i')('F'|'f')('I'|'i')('E'|'e')('D'|'d')('S'|'s')?;
+Imaginary: ('I'|'i')('M'|'m')('A'|'a')('G'|'g')('I'|'i')('N'|'n')('A'|'a')('R'|'r')('Y'|'y');
+Variables: ('V'|'v')('A'|'a')('R'|'r')('I'|'i')('A'|'a')('B'|'b')('L'|'l')('E'|'e')('S'|'s')?;
+MotionVariables: ('M'|'m')('O'|'o')('T'|'t')('I'|'i')('O'|'o')('N'|'n')('V'|'v')('A'|'a')('R'|'r')('I'|'i')('A'|'a')('B'|'b')('L'|'l')('E'|'e')('S'|'s')?;
+
+fragment DIFF:   ('\'')*;
+fragment DIGIT:  [0-9];
+INT:   [0-9]+ ;         // match integers
+FLOAT:  DIGIT+ '.' DIGIT*
+     |  '.' DIGIT+;
+EXP:   FLOAT 'E' INT
+|      FLOAT 'E' '-' INT;
+LINE_COMMENT : '%' .*? '\r'? '\n' -> skip ;
+ID:   [a-zA-Z][a-zA-Z0-9_]*;
+WS:   [ \t\r\n&]+ -> skip ; // toss out whitespace
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..ec81bb83325d68e1c11b43a1df5ec56846367e9f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/__init__.py
@@ -0,0 +1,97 @@
+from sympy.external import import_module
+from sympy.utilities.decorator import doctest_depends_on
+
+@doctest_depends_on(modules=('antlr4',))
+def parse_autolev(autolev_code, include_numeric=False):
+    """Parses Autolev code (version 4.1) to SymPy code.
+
+    Parameters
+    =========
+    autolev_code : Can be an str or any object with a readlines() method (such as a file handle or StringIO).
+    include_numeric : boolean, optional
+        If True NumPy, PyDy, or other numeric code is included for numeric evaluation lines in the Autolev code.
+
+    Returns
+    =======
+    sympy_code : str
+        Equivalent SymPy and/or numpy/pydy code as the input code.
+
+
+    Example (Double Pendulum)
+    =========================
+    >>> my_al_text = ("MOTIONVARIABLES' Q{2}', U{2}'",
+    ... "CONSTANTS L,M,G",
+    ... "NEWTONIAN N",
+    ... "FRAMES A,B",
+    ... "SIMPROT(N, A, 3, Q1)",
+    ... "SIMPROT(N, B, 3, Q2)",
+    ... "W_A_N>=U1*N3>",
+    ... "W_B_N>=U2*N3>",
+    ... "POINT O",
+    ... "PARTICLES P,R",
+    ... "P_O_P> = L*A1>",
+    ... "P_P_R> = L*B1>",
+    ... "V_O_N> = 0>",
+    ... "V2PTS(N, A, O, P)",
+    ... "V2PTS(N, B, P, R)",
+    ... "MASS P=M, R=M",
+    ... "Q1' = U1",
+    ... "Q2' = U2",
+    ... "GRAVITY(G*N1>)",
+    ... "ZERO = FR() + FRSTAR()",
+    ... "KANE()",
+    ... "INPUT M=1,G=9.81,L=1",
+    ... "INPUT Q1=.1,Q2=.2,U1=0,U2=0",
+    ... "INPUT TFINAL=10, INTEGSTP=.01",
+    ... "CODE DYNAMICS() some_filename.c")
+    >>> my_al_text = '\\n'.join(my_al_text)
+    >>> from sympy.parsing.autolev import parse_autolev
+    >>> print(parse_autolev(my_al_text, include_numeric=True))
+    import sympy.physics.mechanics as _me
+    import sympy as _sm
+    import math as m
+    import numpy as _np
+    
+    q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
+    q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
+    l, m, g = _sm.symbols('l m g', real=True)
+    frame_n = _me.ReferenceFrame('n')
+    frame_a = _me.ReferenceFrame('a')
+    frame_b = _me.ReferenceFrame('b')
+    frame_a.orient(frame_n, 'Axis', [q1, frame_n.z])
+    frame_b.orient(frame_n, 'Axis', [q2, frame_n.z])
+    frame_a.set_ang_vel(frame_n, u1*frame_n.z)
+    frame_b.set_ang_vel(frame_n, u2*frame_n.z)
+    point_o = _me.Point('o')
+    particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+    particle_r = _me.Particle('r', _me.Point('r_pt'), _sm.Symbol('m'))
+    particle_p.point.set_pos(point_o, l*frame_a.x)
+    particle_r.point.set_pos(particle_p.point, l*frame_b.x)
+    point_o.set_vel(frame_n, 0)
+    particle_p.point.v2pt_theory(point_o,frame_n,frame_a)
+    particle_r.point.v2pt_theory(particle_p.point,frame_n,frame_b)
+    particle_p.mass = m
+    particle_r.mass = m
+    force_p = particle_p.mass*(g*frame_n.x)
+    force_r = particle_r.mass*(g*frame_n.x)
+    kd_eqs = [q1_d - u1, q2_d - u2]
+    forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x)), (particle_r.point,particle_r.mass*(g*frame_n.x))]
+    kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u1, u2], kd_eqs = kd_eqs)
+    fr, frstar = kane.kanes_equations([particle_p, particle_r], forceList)
+    zero = fr+frstar
+    from pydy.system import System
+    sys = System(kane, constants = {l:1, m:1, g:9.81},
+    specifieds={},
+    initial_conditions={q1:.1, q2:.2, u1:0, u2:0},
+    times = _np.linspace(0.0, 10, 10/.01))
+    
+    y=sys.integrate()
+    
+    """
+
+    _autolev = import_module(
+        'sympy.parsing.autolev._parse_autolev_antlr',
+        import_kwargs={'fromlist': ['X']})
+
+    if _autolev is not None:
+        return _autolev.parse_autolev(autolev_code, include_numeric)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..9b71e9f51fd455558a9eb42dc840604c6c96e4b3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/__init__.py
@@ -0,0 +1,5 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevlexer.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevlexer.py
new file mode 100644
index 0000000000000000000000000000000000000000..f3b3b1d27ade809a63d9fd328a1572c17625443e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevlexer.py
@@ -0,0 +1,253 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+from antlr4 import *
+from io import StringIO
+import sys
+if sys.version_info[1] > 5:
+    from typing import TextIO
+else:
+    from typing.io import TextIO
+
+
+def serializedATN():
+    return [
+        4,0,49,393,6,-1,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,
+        2,6,7,6,2,7,7,7,2,8,7,8,2,9,7,9,2,10,7,10,2,11,7,11,2,12,7,12,2,
+        13,7,13,2,14,7,14,2,15,7,15,2,16,7,16,2,17,7,17,2,18,7,18,2,19,7,
+        19,2,20,7,20,2,21,7,21,2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,2,
+        26,7,26,2,27,7,27,2,28,7,28,2,29,7,29,2,30,7,30,2,31,7,31,2,32,7,
+        32,2,33,7,33,2,34,7,34,2,35,7,35,2,36,7,36,2,37,7,37,2,38,7,38,2,
+        39,7,39,2,40,7,40,2,41,7,41,2,42,7,42,2,43,7,43,2,44,7,44,2,45,7,
+        45,2,46,7,46,2,47,7,47,2,48,7,48,2,49,7,49,2,50,7,50,1,0,1,0,1,1,
+        1,1,1,2,1,2,1,3,1,3,1,3,1,4,1,4,1,4,1,5,1,5,1,5,1,6,1,6,1,6,1,7,
+        1,7,1,7,1,8,1,8,1,8,1,9,1,9,1,10,1,10,1,11,1,11,1,12,1,12,1,13,1,
+        13,1,14,1,14,1,15,1,15,1,16,1,16,1,17,1,17,1,18,1,18,1,19,1,19,1,
+        20,1,20,1,21,1,21,1,21,1,22,1,22,1,22,1,22,1,23,1,23,1,24,1,24,1,
+        25,1,25,1,26,1,26,1,26,1,26,1,26,1,27,1,27,1,27,1,27,1,27,1,27,1,
+        27,1,27,1,28,1,28,1,28,1,28,1,28,1,28,3,28,184,8,28,1,29,1,29,1,
+        29,1,29,1,29,1,29,1,29,1,30,1,30,1,30,1,30,1,30,1,31,1,31,1,31,1,
+        31,1,31,1,31,1,31,1,31,1,31,1,31,1,31,1,32,1,32,1,32,1,32,1,32,1,
+        32,1,32,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,34,1,
+        34,1,34,1,34,1,34,1,34,3,34,232,8,34,1,35,1,35,1,35,1,35,1,35,1,
+        35,3,35,240,8,35,1,36,1,36,1,36,1,36,1,36,1,36,1,36,1,36,1,36,3,
+        36,251,8,36,1,37,1,37,1,37,1,37,1,37,1,37,3,37,259,8,37,1,38,1,38,
+        1,38,1,38,1,38,1,38,1,38,1,38,1,38,3,38,270,8,38,1,39,1,39,1,39,
+        1,39,1,39,1,39,1,39,1,39,1,39,1,39,3,39,282,8,39,1,40,1,40,1,40,
+        1,40,1,40,1,40,1,40,1,40,1,40,1,40,1,41,1,41,1,41,1,41,1,41,1,41,
+        1,41,1,41,1,41,3,41,303,8,41,1,42,1,42,1,42,1,42,1,42,1,42,1,42,
+        1,42,1,42,1,42,1,42,1,42,1,42,1,42,1,42,3,42,320,8,42,1,43,5,43,
+        323,8,43,10,43,12,43,326,9,43,1,44,1,44,1,45,4,45,331,8,45,11,45,
+        12,45,332,1,46,4,46,336,8,46,11,46,12,46,337,1,46,1,46,5,46,342,
+        8,46,10,46,12,46,345,9,46,1,46,1,46,4,46,349,8,46,11,46,12,46,350,
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+        364,8,47,1,48,1,48,5,48,368,8,48,10,48,12,48,371,9,48,1,48,3,48,
+        374,8,48,1,48,1,48,1,48,1,48,1,49,1,49,5,49,382,8,49,10,49,12,49,
+        385,9,49,1,50,4,50,388,8,50,11,50,12,50,389,1,50,1,50,1,369,0,51,
+        1,1,3,2,5,3,7,4,9,5,11,6,13,7,15,8,17,9,19,10,21,11,23,12,25,13,
+        27,14,29,15,31,16,33,17,35,18,37,19,39,20,41,21,43,22,45,23,47,24,
+        49,25,51,26,53,27,55,28,57,29,59,30,61,31,63,32,65,33,67,34,69,35,
+        71,36,73,37,75,38,77,39,79,40,81,41,83,42,85,43,87,0,89,0,91,44,
+        93,45,95,46,97,47,99,48,101,49,1,0,24,2,0,77,77,109,109,2,0,65,65,
+        97,97,2,0,83,83,115,115,2,0,73,73,105,105,2,0,78,78,110,110,2,0,
+        69,69,101,101,2,0,82,82,114,114,2,0,84,84,116,116,2,0,80,80,112,
+        112,2,0,85,85,117,117,2,0,79,79,111,111,2,0,86,86,118,118,2,0,89,
+        89,121,121,2,0,67,67,99,99,2,0,68,68,100,100,2,0,87,87,119,119,2,
+        0,70,70,102,102,2,0,66,66,98,98,2,0,76,76,108,108,2,0,71,71,103,
+        103,1,0,48,57,2,0,65,90,97,122,4,0,48,57,65,90,95,95,97,122,4,0,
+        9,10,13,13,32,32,38,38,410,0,1,1,0,0,0,0,3,1,0,0,0,0,5,1,0,0,0,0,
+        7,1,0,0,0,0,9,1,0,0,0,0,11,1,0,0,0,0,13,1,0,0,0,0,15,1,0,0,0,0,17,
+        1,0,0,0,0,19,1,0,0,0,0,21,1,0,0,0,0,23,1,0,0,0,0,25,1,0,0,0,0,27,
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+        9,112,1,0,0,0,11,115,1,0,0,0,13,118,1,0,0,0,15,121,1,0,0,0,17,124,
+        1,0,0,0,19,127,1,0,0,0,21,129,1,0,0,0,23,131,1,0,0,0,25,133,1,0,
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+        224,7,4,0,0,224,68,1,0,0,0,225,226,7,16,0,0,226,227,7,6,0,0,227,
+        228,7,1,0,0,228,229,7,0,0,0,229,231,7,5,0,0,230,232,7,2,0,0,231,
+        230,1,0,0,0,231,232,1,0,0,0,232,70,1,0,0,0,233,234,7,17,0,0,234,
+        235,7,10,0,0,235,236,7,14,0,0,236,237,7,3,0,0,237,239,7,5,0,0,238,
+        240,7,2,0,0,239,238,1,0,0,0,239,240,1,0,0,0,240,72,1,0,0,0,241,242,
+        7,8,0,0,242,243,7,1,0,0,243,244,7,6,0,0,244,245,7,7,0,0,245,246,
+        7,3,0,0,246,247,7,13,0,0,247,248,7,18,0,0,248,250,7,5,0,0,249,251,
+        7,2,0,0,250,249,1,0,0,0,250,251,1,0,0,0,251,74,1,0,0,0,252,253,7,
+        8,0,0,253,254,7,10,0,0,254,255,7,3,0,0,255,256,7,4,0,0,256,258,7,
+        7,0,0,257,259,7,2,0,0,258,257,1,0,0,0,258,259,1,0,0,0,259,76,1,0,
+        0,0,260,261,7,13,0,0,261,262,7,10,0,0,262,263,7,4,0,0,263,264,7,
+        2,0,0,264,265,7,7,0,0,265,266,7,1,0,0,266,267,7,4,0,0,267,269,7,
+        7,0,0,268,270,7,2,0,0,269,268,1,0,0,0,269,270,1,0,0,0,270,78,1,0,
+        0,0,271,272,7,2,0,0,272,273,7,8,0,0,273,274,7,5,0,0,274,275,7,13,
+        0,0,275,276,7,3,0,0,276,277,7,16,0,0,277,278,7,3,0,0,278,279,7,5,
+        0,0,279,281,7,14,0,0,280,282,7,2,0,0,281,280,1,0,0,0,281,282,1,0,
+        0,0,282,80,1,0,0,0,283,284,7,3,0,0,284,285,7,0,0,0,285,286,7,1,0,
+        0,286,287,7,19,0,0,287,288,7,3,0,0,288,289,7,4,0,0,289,290,7,1,0,
+        0,290,291,7,6,0,0,291,292,7,12,0,0,292,82,1,0,0,0,293,294,7,11,0,
+        0,294,295,7,1,0,0,295,296,7,6,0,0,296,297,7,3,0,0,297,298,7,1,0,
+        0,298,299,7,17,0,0,299,300,7,18,0,0,300,302,7,5,0,0,301,303,7,2,
+        0,0,302,301,1,0,0,0,302,303,1,0,0,0,303,84,1,0,0,0,304,305,7,0,0,
+        0,305,306,7,10,0,0,306,307,7,7,0,0,307,308,7,3,0,0,308,309,7,10,
+        0,0,309,310,7,4,0,0,310,311,7,11,0,0,311,312,7,1,0,0,312,313,7,6,
+        0,0,313,314,7,3,0,0,314,315,7,1,0,0,315,316,7,17,0,0,316,317,7,18,
+        0,0,317,319,7,5,0,0,318,320,7,2,0,0,319,318,1,0,0,0,319,320,1,0,
+        0,0,320,86,1,0,0,0,321,323,5,39,0,0,322,321,1,0,0,0,323,326,1,0,
+        0,0,324,322,1,0,0,0,324,325,1,0,0,0,325,88,1,0,0,0,326,324,1,0,0,
+        0,327,328,7,20,0,0,328,90,1,0,0,0,329,331,7,20,0,0,330,329,1,0,0,
+        0,331,332,1,0,0,0,332,330,1,0,0,0,332,333,1,0,0,0,333,92,1,0,0,0,
+        334,336,3,89,44,0,335,334,1,0,0,0,336,337,1,0,0,0,337,335,1,0,0,
+        0,337,338,1,0,0,0,338,339,1,0,0,0,339,343,5,46,0,0,340,342,3,89,
+        44,0,341,340,1,0,0,0,342,345,1,0,0,0,343,341,1,0,0,0,343,344,1,0,
+        0,0,344,353,1,0,0,0,345,343,1,0,0,0,346,348,5,46,0,0,347,349,3,89,
+        44,0,348,347,1,0,0,0,349,350,1,0,0,0,350,348,1,0,0,0,350,351,1,0,
+        0,0,351,353,1,0,0,0,352,335,1,0,0,0,352,346,1,0,0,0,353,94,1,0,0,
+        0,354,355,3,93,46,0,355,356,5,69,0,0,356,357,3,91,45,0,357,364,1,
+        0,0,0,358,359,3,93,46,0,359,360,5,69,0,0,360,361,5,45,0,0,361,362,
+        3,91,45,0,362,364,1,0,0,0,363,354,1,0,0,0,363,358,1,0,0,0,364,96,
+        1,0,0,0,365,369,5,37,0,0,366,368,9,0,0,0,367,366,1,0,0,0,368,371,
+        1,0,0,0,369,370,1,0,0,0,369,367,1,0,0,0,370,373,1,0,0,0,371,369,
+        1,0,0,0,372,374,5,13,0,0,373,372,1,0,0,0,373,374,1,0,0,0,374,375,
+        1,0,0,0,375,376,5,10,0,0,376,377,1,0,0,0,377,378,6,48,0,0,378,98,
+        1,0,0,0,379,383,7,21,0,0,380,382,7,22,0,0,381,380,1,0,0,0,382,385,
+        1,0,0,0,383,381,1,0,0,0,383,384,1,0,0,0,384,100,1,0,0,0,385,383,
+        1,0,0,0,386,388,7,23,0,0,387,386,1,0,0,0,388,389,1,0,0,0,389,387,
+        1,0,0,0,389,390,1,0,0,0,390,391,1,0,0,0,391,392,6,50,0,0,392,102,
+        1,0,0,0,21,0,183,231,239,250,258,269,281,302,319,324,332,337,343,
+        350,352,363,369,373,383,389,1,6,0,0
+    ]
+
+class AutolevLexer(Lexer):
+
+    atn = ATNDeserializer().deserialize(serializedATN())
+
+    decisionsToDFA = [ DFA(ds, i) for i, ds in enumerate(atn.decisionToState) ]
+
+    T__0 = 1
+    T__1 = 2
+    T__2 = 3
+    T__3 = 4
+    T__4 = 5
+    T__5 = 6
+    T__6 = 7
+    T__7 = 8
+    T__8 = 9
+    T__9 = 10
+    T__10 = 11
+    T__11 = 12
+    T__12 = 13
+    T__13 = 14
+    T__14 = 15
+    T__15 = 16
+    T__16 = 17
+    T__17 = 18
+    T__18 = 19
+    T__19 = 20
+    T__20 = 21
+    T__21 = 22
+    T__22 = 23
+    T__23 = 24
+    T__24 = 25
+    T__25 = 26
+    Mass = 27
+    Inertia = 28
+    Input = 29
+    Output = 30
+    Save = 31
+    UnitSystem = 32
+    Encode = 33
+    Newtonian = 34
+    Frames = 35
+    Bodies = 36
+    Particles = 37
+    Points = 38
+    Constants = 39
+    Specifieds = 40
+    Imaginary = 41
+    Variables = 42
+    MotionVariables = 43
+    INT = 44
+    FLOAT = 45
+    EXP = 46
+    LINE_COMMENT = 47
+    ID = 48
+    WS = 49
+
+    channelNames = [ u"DEFAULT_TOKEN_CHANNEL", u"HIDDEN" ]
+
+    modeNames = [ "DEFAULT_MODE" ]
+
+    literalNames = [ "",
+            "'['", "']'", "'='", "'+='", "'-='", "':='", "'*='", "'/='",
+            "'^='", "','", "'''", "'('", "')'", "'{'", "'}'", "':'", "'+'",
+            "'-'", "';'", "'.'", "'>'", "'0>'", "'1>>'", "'^'", "'*'", "'/'" ]
+
+    symbolicNames = [ "",
+            "Mass", "Inertia", "Input", "Output", "Save", "UnitSystem",
+            "Encode", "Newtonian", "Frames", "Bodies", "Particles", "Points",
+            "Constants", "Specifieds", "Imaginary", "Variables", "MotionVariables",
+            "INT", "FLOAT", "EXP", "LINE_COMMENT", "ID", "WS" ]
+
+    ruleNames = [ "T__0", "T__1", "T__2", "T__3", "T__4", "T__5", "T__6",
+                  "T__7", "T__8", "T__9", "T__10", "T__11", "T__12", "T__13",
+                  "T__14", "T__15", "T__16", "T__17", "T__18", "T__19",
+                  "T__20", "T__21", "T__22", "T__23", "T__24", "T__25",
+                  "Mass", "Inertia", "Input", "Output", "Save", "UnitSystem",
+                  "Encode", "Newtonian", "Frames", "Bodies", "Particles",
+                  "Points", "Constants", "Specifieds", "Imaginary", "Variables",
+                  "MotionVariables", "DIFF", "DIGIT", "INT", "FLOAT", "EXP",
+                  "LINE_COMMENT", "ID", "WS" ]
+
+    grammarFileName = "Autolev.g4"
+
+    def __init__(self, input=None, output:TextIO = sys.stdout):
+        super().__init__(input, output)
+        self.checkVersion("4.11.1")
+        self._interp = LexerATNSimulator(self, self.atn, self.decisionsToDFA, PredictionContextCache())
+        self._actions = None
+        self._predicates = None
+
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevlistener.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevlistener.py
new file mode 100644
index 0000000000000000000000000000000000000000..6f391a298a71ecf2d04cf921a919cbb68b181fab
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevlistener.py
@@ -0,0 +1,421 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+from antlr4 import *
+if __name__ is not None and "." in __name__:
+    from .autolevparser import AutolevParser
+else:
+    from autolevparser import AutolevParser
+
+# This class defines a complete listener for a parse tree produced by AutolevParser.
+class AutolevListener(ParseTreeListener):
+
+    # Enter a parse tree produced by AutolevParser#prog.
+    def enterProg(self, ctx:AutolevParser.ProgContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#prog.
+    def exitProg(self, ctx:AutolevParser.ProgContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#stat.
+    def enterStat(self, ctx:AutolevParser.StatContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#stat.
+    def exitStat(self, ctx:AutolevParser.StatContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#vecAssign.
+    def enterVecAssign(self, ctx:AutolevParser.VecAssignContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#vecAssign.
+    def exitVecAssign(self, ctx:AutolevParser.VecAssignContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#indexAssign.
+    def enterIndexAssign(self, ctx:AutolevParser.IndexAssignContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#indexAssign.
+    def exitIndexAssign(self, ctx:AutolevParser.IndexAssignContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#regularAssign.
+    def enterRegularAssign(self, ctx:AutolevParser.RegularAssignContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#regularAssign.
+    def exitRegularAssign(self, ctx:AutolevParser.RegularAssignContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#equals.
+    def enterEquals(self, ctx:AutolevParser.EqualsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#equals.
+    def exitEquals(self, ctx:AutolevParser.EqualsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#index.
+    def enterIndex(self, ctx:AutolevParser.IndexContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#index.
+    def exitIndex(self, ctx:AutolevParser.IndexContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#diff.
+    def enterDiff(self, ctx:AutolevParser.DiffContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#diff.
+    def exitDiff(self, ctx:AutolevParser.DiffContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#functionCall.
+    def enterFunctionCall(self, ctx:AutolevParser.FunctionCallContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#functionCall.
+    def exitFunctionCall(self, ctx:AutolevParser.FunctionCallContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#varDecl.
+    def enterVarDecl(self, ctx:AutolevParser.VarDeclContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#varDecl.
+    def exitVarDecl(self, ctx:AutolevParser.VarDeclContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#varType.
+    def enterVarType(self, ctx:AutolevParser.VarTypeContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#varType.
+    def exitVarType(self, ctx:AutolevParser.VarTypeContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#varDecl2.
+    def enterVarDecl2(self, ctx:AutolevParser.VarDecl2Context):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#varDecl2.
+    def exitVarDecl2(self, ctx:AutolevParser.VarDecl2Context):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#ranges.
+    def enterRanges(self, ctx:AutolevParser.RangesContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#ranges.
+    def exitRanges(self, ctx:AutolevParser.RangesContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#massDecl.
+    def enterMassDecl(self, ctx:AutolevParser.MassDeclContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#massDecl.
+    def exitMassDecl(self, ctx:AutolevParser.MassDeclContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#massDecl2.
+    def enterMassDecl2(self, ctx:AutolevParser.MassDecl2Context):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#massDecl2.
+    def exitMassDecl2(self, ctx:AutolevParser.MassDecl2Context):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#inertiaDecl.
+    def enterInertiaDecl(self, ctx:AutolevParser.InertiaDeclContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#inertiaDecl.
+    def exitInertiaDecl(self, ctx:AutolevParser.InertiaDeclContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#matrix.
+    def enterMatrix(self, ctx:AutolevParser.MatrixContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#matrix.
+    def exitMatrix(self, ctx:AutolevParser.MatrixContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#matrixInOutput.
+    def enterMatrixInOutput(self, ctx:AutolevParser.MatrixInOutputContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#matrixInOutput.
+    def exitMatrixInOutput(self, ctx:AutolevParser.MatrixInOutputContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#codeCommands.
+    def enterCodeCommands(self, ctx:AutolevParser.CodeCommandsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#codeCommands.
+    def exitCodeCommands(self, ctx:AutolevParser.CodeCommandsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#settings.
+    def enterSettings(self, ctx:AutolevParser.SettingsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#settings.
+    def exitSettings(self, ctx:AutolevParser.SettingsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#units.
+    def enterUnits(self, ctx:AutolevParser.UnitsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#units.
+    def exitUnits(self, ctx:AutolevParser.UnitsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#inputs.
+    def enterInputs(self, ctx:AutolevParser.InputsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#inputs.
+    def exitInputs(self, ctx:AutolevParser.InputsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#id_diff.
+    def enterId_diff(self, ctx:AutolevParser.Id_diffContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#id_diff.
+    def exitId_diff(self, ctx:AutolevParser.Id_diffContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#inputs2.
+    def enterInputs2(self, ctx:AutolevParser.Inputs2Context):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#inputs2.
+    def exitInputs2(self, ctx:AutolevParser.Inputs2Context):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#outputs.
+    def enterOutputs(self, ctx:AutolevParser.OutputsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#outputs.
+    def exitOutputs(self, ctx:AutolevParser.OutputsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#outputs2.
+    def enterOutputs2(self, ctx:AutolevParser.Outputs2Context):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#outputs2.
+    def exitOutputs2(self, ctx:AutolevParser.Outputs2Context):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#codegen.
+    def enterCodegen(self, ctx:AutolevParser.CodegenContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#codegen.
+    def exitCodegen(self, ctx:AutolevParser.CodegenContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#commands.
+    def enterCommands(self, ctx:AutolevParser.CommandsContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#commands.
+    def exitCommands(self, ctx:AutolevParser.CommandsContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#vec.
+    def enterVec(self, ctx:AutolevParser.VecContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#vec.
+    def exitVec(self, ctx:AutolevParser.VecContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#parens.
+    def enterParens(self, ctx:AutolevParser.ParensContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#parens.
+    def exitParens(self, ctx:AutolevParser.ParensContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#VectorOrDyadic.
+    def enterVectorOrDyadic(self, ctx:AutolevParser.VectorOrDyadicContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#VectorOrDyadic.
+    def exitVectorOrDyadic(self, ctx:AutolevParser.VectorOrDyadicContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#Exponent.
+    def enterExponent(self, ctx:AutolevParser.ExponentContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#Exponent.
+    def exitExponent(self, ctx:AutolevParser.ExponentContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#MulDiv.
+    def enterMulDiv(self, ctx:AutolevParser.MulDivContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#MulDiv.
+    def exitMulDiv(self, ctx:AutolevParser.MulDivContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#AddSub.
+    def enterAddSub(self, ctx:AutolevParser.AddSubContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#AddSub.
+    def exitAddSub(self, ctx:AutolevParser.AddSubContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#float.
+    def enterFloat(self, ctx:AutolevParser.FloatContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#float.
+    def exitFloat(self, ctx:AutolevParser.FloatContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#int.
+    def enterInt(self, ctx:AutolevParser.IntContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#int.
+    def exitInt(self, ctx:AutolevParser.IntContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#idEqualsExpr.
+    def enterIdEqualsExpr(self, ctx:AutolevParser.IdEqualsExprContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#idEqualsExpr.
+    def exitIdEqualsExpr(self, ctx:AutolevParser.IdEqualsExprContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#negativeOne.
+    def enterNegativeOne(self, ctx:AutolevParser.NegativeOneContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#negativeOne.
+    def exitNegativeOne(self, ctx:AutolevParser.NegativeOneContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#function.
+    def enterFunction(self, ctx:AutolevParser.FunctionContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#function.
+    def exitFunction(self, ctx:AutolevParser.FunctionContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#rangess.
+    def enterRangess(self, ctx:AutolevParser.RangessContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#rangess.
+    def exitRangess(self, ctx:AutolevParser.RangessContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#colon.
+    def enterColon(self, ctx:AutolevParser.ColonContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#colon.
+    def exitColon(self, ctx:AutolevParser.ColonContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#id.
+    def enterId(self, ctx:AutolevParser.IdContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#id.
+    def exitId(self, ctx:AutolevParser.IdContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#exp.
+    def enterExp(self, ctx:AutolevParser.ExpContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#exp.
+    def exitExp(self, ctx:AutolevParser.ExpContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#matrices.
+    def enterMatrices(self, ctx:AutolevParser.MatricesContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#matrices.
+    def exitMatrices(self, ctx:AutolevParser.MatricesContext):
+        pass
+
+
+    # Enter a parse tree produced by AutolevParser#Indexing.
+    def enterIndexing(self, ctx:AutolevParser.IndexingContext):
+        pass
+
+    # Exit a parse tree produced by AutolevParser#Indexing.
+    def exitIndexing(self, ctx:AutolevParser.IndexingContext):
+        pass
+
+
+
+del AutolevParser
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevparser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevparser.py
new file mode 100644
index 0000000000000000000000000000000000000000..e63ef1c110812580d06291ee7c7ec40b6a076cea
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_antlr/autolevparser.py
@@ -0,0 +1,3063 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+from antlr4 import *
+from io import StringIO
+import sys
+if sys.version_info[1] > 5:
+	from typing import TextIO
+else:
+	from typing.io import TextIO
+
+def serializedATN():
+    return [
+        4,1,49,431,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,
+        6,2,7,7,7,2,8,7,8,2,9,7,9,2,10,7,10,2,11,7,11,2,12,7,12,2,13,7,13,
+        2,14,7,14,2,15,7,15,2,16,7,16,2,17,7,17,2,18,7,18,2,19,7,19,2,20,
+        7,20,2,21,7,21,2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,2,26,7,26,
+        2,27,7,27,1,0,4,0,58,8,0,11,0,12,0,59,1,1,1,1,1,1,1,1,1,1,1,1,1,
+        1,3,1,69,8,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
+        3,2,84,8,2,1,2,1,2,1,2,3,2,89,8,2,1,3,1,3,1,4,1,4,1,4,5,4,96,8,4,
+        10,4,12,4,99,9,4,1,5,4,5,102,8,5,11,5,12,5,103,1,6,1,6,1,6,1,6,1,
+        6,5,6,111,8,6,10,6,12,6,114,9,6,3,6,116,8,6,1,6,1,6,1,6,1,6,1,6,
+        1,6,5,6,124,8,6,10,6,12,6,127,9,6,3,6,129,8,6,1,6,3,6,132,8,6,1,
+        7,1,7,1,7,1,7,5,7,138,8,7,10,7,12,7,141,9,7,1,8,1,8,1,8,1,8,1,8,
+        1,8,1,8,1,8,1,8,1,8,5,8,153,8,8,10,8,12,8,156,9,8,1,8,1,8,5,8,160,
+        8,8,10,8,12,8,163,9,8,3,8,165,8,8,1,9,1,9,1,9,1,9,1,9,1,9,3,9,173,
+        8,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,5,9,183,8,9,10,9,12,9,186,9,
+        9,1,9,3,9,189,8,9,1,9,1,9,1,9,3,9,194,8,9,1,9,3,9,197,8,9,1,9,5,
+        9,200,8,9,10,9,12,9,203,9,9,1,9,1,9,3,9,207,8,9,1,10,1,10,1,10,1,
+        10,1,10,1,10,1,10,1,10,5,10,217,8,10,10,10,12,10,220,9,10,1,10,1,
+        10,1,11,1,11,1,11,1,11,5,11,228,8,11,10,11,12,11,231,9,11,1,12,1,
+        12,1,12,1,12,1,13,1,13,1,13,1,13,1,13,3,13,242,8,13,1,13,1,13,4,
+        13,246,8,13,11,13,12,13,247,1,14,1,14,1,14,1,14,5,14,254,8,14,10,
+        14,12,14,257,9,14,1,14,1,14,1,15,1,15,1,15,1,15,3,15,265,8,15,1,
+        15,1,15,3,15,269,8,15,1,16,1,16,1,16,1,16,1,16,3,16,276,8,16,1,17,
+        1,17,3,17,280,8,17,1,18,1,18,1,18,1,18,5,18,286,8,18,10,18,12,18,
+        289,9,18,1,19,1,19,1,19,1,19,5,19,295,8,19,10,19,12,19,298,9,19,
+        1,20,1,20,3,20,302,8,20,1,21,1,21,1,21,1,21,3,21,308,8,21,1,22,1,
+        22,1,22,1,22,5,22,314,8,22,10,22,12,22,317,9,22,1,23,1,23,3,23,321,
+        8,23,1,24,1,24,1,24,1,24,1,24,1,24,5,24,329,8,24,10,24,12,24,332,
+        9,24,1,24,1,24,3,24,336,8,24,1,24,1,24,1,24,1,24,1,25,1,25,1,25,
+        1,25,1,25,1,25,1,25,1,25,5,25,350,8,25,10,25,12,25,353,9,25,3,25,
+        355,8,25,1,26,1,26,4,26,359,8,26,11,26,12,26,360,1,26,1,26,3,26,
+        365,8,26,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,5,27,375,8,27,10,
+        27,12,27,378,9,27,1,27,1,27,1,27,1,27,1,27,1,27,5,27,386,8,27,10,
+        27,12,27,389,9,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,3,
+        27,400,8,27,1,27,1,27,5,27,404,8,27,10,27,12,27,407,9,27,3,27,409,
+        8,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,1,27,
+        1,27,1,27,1,27,5,27,426,8,27,10,27,12,27,429,9,27,1,27,0,1,54,28,
+        0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,
+        46,48,50,52,54,0,7,1,0,3,9,1,0,27,28,1,0,17,18,2,0,10,10,19,19,1,
+        0,44,45,2,0,44,46,48,48,1,0,25,26,483,0,57,1,0,0,0,2,68,1,0,0,0,
+        4,88,1,0,0,0,6,90,1,0,0,0,8,92,1,0,0,0,10,101,1,0,0,0,12,131,1,0,
+        0,0,14,133,1,0,0,0,16,164,1,0,0,0,18,166,1,0,0,0,20,208,1,0,0,0,
+        22,223,1,0,0,0,24,232,1,0,0,0,26,236,1,0,0,0,28,249,1,0,0,0,30,268,
+        1,0,0,0,32,275,1,0,0,0,34,277,1,0,0,0,36,281,1,0,0,0,38,290,1,0,
+        0,0,40,299,1,0,0,0,42,303,1,0,0,0,44,309,1,0,0,0,46,318,1,0,0,0,
+        48,322,1,0,0,0,50,354,1,0,0,0,52,364,1,0,0,0,54,408,1,0,0,0,56,58,
+        3,2,1,0,57,56,1,0,0,0,58,59,1,0,0,0,59,57,1,0,0,0,59,60,1,0,0,0,
+        60,1,1,0,0,0,61,69,3,14,7,0,62,69,3,12,6,0,63,69,3,32,16,0,64,69,
+        3,22,11,0,65,69,3,26,13,0,66,69,3,4,2,0,67,69,3,34,17,0,68,61,1,
+        0,0,0,68,62,1,0,0,0,68,63,1,0,0,0,68,64,1,0,0,0,68,65,1,0,0,0,68,
+        66,1,0,0,0,68,67,1,0,0,0,69,3,1,0,0,0,70,71,3,52,26,0,71,72,3,6,
+        3,0,72,73,3,54,27,0,73,89,1,0,0,0,74,75,5,48,0,0,75,76,5,1,0,0,76,
+        77,3,8,4,0,77,78,5,2,0,0,78,79,3,6,3,0,79,80,3,54,27,0,80,89,1,0,
+        0,0,81,83,5,48,0,0,82,84,3,10,5,0,83,82,1,0,0,0,83,84,1,0,0,0,84,
+        85,1,0,0,0,85,86,3,6,3,0,86,87,3,54,27,0,87,89,1,0,0,0,88,70,1,0,
+        0,0,88,74,1,0,0,0,88,81,1,0,0,0,89,5,1,0,0,0,90,91,7,0,0,0,91,7,
+        1,0,0,0,92,97,3,54,27,0,93,94,5,10,0,0,94,96,3,54,27,0,95,93,1,0,
+        0,0,96,99,1,0,0,0,97,95,1,0,0,0,97,98,1,0,0,0,98,9,1,0,0,0,99,97,
+        1,0,0,0,100,102,5,11,0,0,101,100,1,0,0,0,102,103,1,0,0,0,103,101,
+        1,0,0,0,103,104,1,0,0,0,104,11,1,0,0,0,105,106,5,48,0,0,106,115,
+        5,12,0,0,107,112,3,54,27,0,108,109,5,10,0,0,109,111,3,54,27,0,110,
+        108,1,0,0,0,111,114,1,0,0,0,112,110,1,0,0,0,112,113,1,0,0,0,113,
+        116,1,0,0,0,114,112,1,0,0,0,115,107,1,0,0,0,115,116,1,0,0,0,116,
+        117,1,0,0,0,117,132,5,13,0,0,118,119,7,1,0,0,119,128,5,12,0,0,120,
+        125,5,48,0,0,121,122,5,10,0,0,122,124,5,48,0,0,123,121,1,0,0,0,124,
+        127,1,0,0,0,125,123,1,0,0,0,125,126,1,0,0,0,126,129,1,0,0,0,127,
+        125,1,0,0,0,128,120,1,0,0,0,128,129,1,0,0,0,129,130,1,0,0,0,130,
+        132,5,13,0,0,131,105,1,0,0,0,131,118,1,0,0,0,132,13,1,0,0,0,133,
+        134,3,16,8,0,134,139,3,18,9,0,135,136,5,10,0,0,136,138,3,18,9,0,
+        137,135,1,0,0,0,138,141,1,0,0,0,139,137,1,0,0,0,139,140,1,0,0,0,
+        140,15,1,0,0,0,141,139,1,0,0,0,142,165,5,34,0,0,143,165,5,35,0,0,
+        144,165,5,36,0,0,145,165,5,37,0,0,146,165,5,38,0,0,147,165,5,39,
+        0,0,148,165,5,40,0,0,149,165,5,41,0,0,150,154,5,42,0,0,151,153,5,
+        11,0,0,152,151,1,0,0,0,153,156,1,0,0,0,154,152,1,0,0,0,154,155,1,
+        0,0,0,155,165,1,0,0,0,156,154,1,0,0,0,157,161,5,43,0,0,158,160,5,
+        11,0,0,159,158,1,0,0,0,160,163,1,0,0,0,161,159,1,0,0,0,161,162,1,
+        0,0,0,162,165,1,0,0,0,163,161,1,0,0,0,164,142,1,0,0,0,164,143,1,
+        0,0,0,164,144,1,0,0,0,164,145,1,0,0,0,164,146,1,0,0,0,164,147,1,
+        0,0,0,164,148,1,0,0,0,164,149,1,0,0,0,164,150,1,0,0,0,164,157,1,
+        0,0,0,165,17,1,0,0,0,166,172,5,48,0,0,167,168,5,14,0,0,168,169,5,
+        44,0,0,169,170,5,10,0,0,170,171,5,44,0,0,171,173,5,15,0,0,172,167,
+        1,0,0,0,172,173,1,0,0,0,173,188,1,0,0,0,174,175,5,14,0,0,175,176,
+        5,44,0,0,176,177,5,16,0,0,177,184,5,44,0,0,178,179,5,10,0,0,179,
+        180,5,44,0,0,180,181,5,16,0,0,181,183,5,44,0,0,182,178,1,0,0,0,183,
+        186,1,0,0,0,184,182,1,0,0,0,184,185,1,0,0,0,185,187,1,0,0,0,186,
+        184,1,0,0,0,187,189,5,15,0,0,188,174,1,0,0,0,188,189,1,0,0,0,189,
+        193,1,0,0,0,190,191,5,14,0,0,191,192,5,44,0,0,192,194,5,15,0,0,193,
+        190,1,0,0,0,193,194,1,0,0,0,194,196,1,0,0,0,195,197,7,2,0,0,196,
+        195,1,0,0,0,196,197,1,0,0,0,197,201,1,0,0,0,198,200,5,11,0,0,199,
+        198,1,0,0,0,200,203,1,0,0,0,201,199,1,0,0,0,201,202,1,0,0,0,202,
+        206,1,0,0,0,203,201,1,0,0,0,204,205,5,3,0,0,205,207,3,54,27,0,206,
+        204,1,0,0,0,206,207,1,0,0,0,207,19,1,0,0,0,208,209,5,14,0,0,209,
+        210,5,44,0,0,210,211,5,16,0,0,211,218,5,44,0,0,212,213,5,10,0,0,
+        213,214,5,44,0,0,214,215,5,16,0,0,215,217,5,44,0,0,216,212,1,0,0,
+        0,217,220,1,0,0,0,218,216,1,0,0,0,218,219,1,0,0,0,219,221,1,0,0,
+        0,220,218,1,0,0,0,221,222,5,15,0,0,222,21,1,0,0,0,223,224,5,27,0,
+        0,224,229,3,24,12,0,225,226,5,10,0,0,226,228,3,24,12,0,227,225,1,
+        0,0,0,228,231,1,0,0,0,229,227,1,0,0,0,229,230,1,0,0,0,230,23,1,0,
+        0,0,231,229,1,0,0,0,232,233,5,48,0,0,233,234,5,3,0,0,234,235,3,54,
+        27,0,235,25,1,0,0,0,236,237,5,28,0,0,237,241,5,48,0,0,238,239,5,
+        12,0,0,239,240,5,48,0,0,240,242,5,13,0,0,241,238,1,0,0,0,241,242,
+        1,0,0,0,242,245,1,0,0,0,243,244,5,10,0,0,244,246,3,54,27,0,245,243,
+        1,0,0,0,246,247,1,0,0,0,247,245,1,0,0,0,247,248,1,0,0,0,248,27,1,
+        0,0,0,249,250,5,1,0,0,250,255,3,54,27,0,251,252,7,3,0,0,252,254,
+        3,54,27,0,253,251,1,0,0,0,254,257,1,0,0,0,255,253,1,0,0,0,255,256,
+        1,0,0,0,256,258,1,0,0,0,257,255,1,0,0,0,258,259,5,2,0,0,259,29,1,
+        0,0,0,260,261,5,48,0,0,261,262,5,48,0,0,262,264,5,3,0,0,263,265,
+        7,4,0,0,264,263,1,0,0,0,264,265,1,0,0,0,265,269,1,0,0,0,266,269,
+        5,45,0,0,267,269,5,44,0,0,268,260,1,0,0,0,268,266,1,0,0,0,268,267,
+        1,0,0,0,269,31,1,0,0,0,270,276,3,36,18,0,271,276,3,38,19,0,272,276,
+        3,44,22,0,273,276,3,48,24,0,274,276,3,50,25,0,275,270,1,0,0,0,275,
+        271,1,0,0,0,275,272,1,0,0,0,275,273,1,0,0,0,275,274,1,0,0,0,276,
+        33,1,0,0,0,277,279,5,48,0,0,278,280,7,5,0,0,279,278,1,0,0,0,279,
+        280,1,0,0,0,280,35,1,0,0,0,281,282,5,32,0,0,282,287,5,48,0,0,283,
+        284,5,10,0,0,284,286,5,48,0,0,285,283,1,0,0,0,286,289,1,0,0,0,287,
+        285,1,0,0,0,287,288,1,0,0,0,288,37,1,0,0,0,289,287,1,0,0,0,290,291,
+        5,29,0,0,291,296,3,42,21,0,292,293,5,10,0,0,293,295,3,42,21,0,294,
+        292,1,0,0,0,295,298,1,0,0,0,296,294,1,0,0,0,296,297,1,0,0,0,297,
+        39,1,0,0,0,298,296,1,0,0,0,299,301,5,48,0,0,300,302,3,10,5,0,301,
+        300,1,0,0,0,301,302,1,0,0,0,302,41,1,0,0,0,303,304,3,40,20,0,304,
+        305,5,3,0,0,305,307,3,54,27,0,306,308,3,54,27,0,307,306,1,0,0,0,
+        307,308,1,0,0,0,308,43,1,0,0,0,309,310,5,30,0,0,310,315,3,46,23,
+        0,311,312,5,10,0,0,312,314,3,46,23,0,313,311,1,0,0,0,314,317,1,0,
+        0,0,315,313,1,0,0,0,315,316,1,0,0,0,316,45,1,0,0,0,317,315,1,0,0,
+        0,318,320,3,54,27,0,319,321,3,54,27,0,320,319,1,0,0,0,320,321,1,
+        0,0,0,321,47,1,0,0,0,322,323,5,48,0,0,323,335,3,12,6,0,324,325,5,
+        1,0,0,325,330,3,30,15,0,326,327,5,10,0,0,327,329,3,30,15,0,328,326,
+        1,0,0,0,329,332,1,0,0,0,330,328,1,0,0,0,330,331,1,0,0,0,331,333,
+        1,0,0,0,332,330,1,0,0,0,333,334,5,2,0,0,334,336,1,0,0,0,335,324,
+        1,0,0,0,335,336,1,0,0,0,336,337,1,0,0,0,337,338,5,48,0,0,338,339,
+        5,20,0,0,339,340,5,48,0,0,340,49,1,0,0,0,341,342,5,31,0,0,342,343,
+        5,48,0,0,343,344,5,20,0,0,344,355,5,48,0,0,345,346,5,33,0,0,346,
+        351,5,48,0,0,347,348,5,10,0,0,348,350,5,48,0,0,349,347,1,0,0,0,350,
+        353,1,0,0,0,351,349,1,0,0,0,351,352,1,0,0,0,352,355,1,0,0,0,353,
+        351,1,0,0,0,354,341,1,0,0,0,354,345,1,0,0,0,355,51,1,0,0,0,356,358,
+        5,48,0,0,357,359,5,21,0,0,358,357,1,0,0,0,359,360,1,0,0,0,360,358,
+        1,0,0,0,360,361,1,0,0,0,361,365,1,0,0,0,362,365,5,22,0,0,363,365,
+        5,23,0,0,364,356,1,0,0,0,364,362,1,0,0,0,364,363,1,0,0,0,365,53,
+        1,0,0,0,366,367,6,27,-1,0,367,409,5,46,0,0,368,369,5,18,0,0,369,
+        409,3,54,27,12,370,409,5,45,0,0,371,409,5,44,0,0,372,376,5,48,0,
+        0,373,375,5,11,0,0,374,373,1,0,0,0,375,378,1,0,0,0,376,374,1,0,0,
+        0,376,377,1,0,0,0,377,409,1,0,0,0,378,376,1,0,0,0,379,409,3,52,26,
+        0,380,381,5,48,0,0,381,382,5,1,0,0,382,387,3,54,27,0,383,384,5,10,
+        0,0,384,386,3,54,27,0,385,383,1,0,0,0,386,389,1,0,0,0,387,385,1,
+        0,0,0,387,388,1,0,0,0,388,390,1,0,0,0,389,387,1,0,0,0,390,391,5,
+        2,0,0,391,409,1,0,0,0,392,409,3,12,6,0,393,409,3,28,14,0,394,395,
+        5,12,0,0,395,396,3,54,27,0,396,397,5,13,0,0,397,409,1,0,0,0,398,
+        400,5,48,0,0,399,398,1,0,0,0,399,400,1,0,0,0,400,401,1,0,0,0,401,
+        405,3,20,10,0,402,404,5,11,0,0,403,402,1,0,0,0,404,407,1,0,0,0,405,
+        403,1,0,0,0,405,406,1,0,0,0,406,409,1,0,0,0,407,405,1,0,0,0,408,
+        366,1,0,0,0,408,368,1,0,0,0,408,370,1,0,0,0,408,371,1,0,0,0,408,
+        372,1,0,0,0,408,379,1,0,0,0,408,380,1,0,0,0,408,392,1,0,0,0,408,
+        393,1,0,0,0,408,394,1,0,0,0,408,399,1,0,0,0,409,427,1,0,0,0,410,
+        411,10,16,0,0,411,412,5,24,0,0,412,426,3,54,27,17,413,414,10,15,
+        0,0,414,415,7,6,0,0,415,426,3,54,27,16,416,417,10,14,0,0,417,418,
+        7,2,0,0,418,426,3,54,27,15,419,420,10,3,0,0,420,421,5,3,0,0,421,
+        426,3,54,27,4,422,423,10,2,0,0,423,424,5,16,0,0,424,426,3,54,27,
+        3,425,410,1,0,0,0,425,413,1,0,0,0,425,416,1,0,0,0,425,419,1,0,0,
+        0,425,422,1,0,0,0,426,429,1,0,0,0,427,425,1,0,0,0,427,428,1,0,0,
+        0,428,55,1,0,0,0,429,427,1,0,0,0,50,59,68,83,88,97,103,112,115,125,
+        128,131,139,154,161,164,172,184,188,193,196,201,206,218,229,241,
+        247,255,264,268,275,279,287,296,301,307,315,320,330,335,351,354,
+        360,364,376,387,399,405,408,425,427
+    ]
+
+class AutolevParser ( Parser ):
+
+    grammarFileName = "Autolev.g4"
+
+    atn = ATNDeserializer().deserialize(serializedATN())
+
+    decisionsToDFA = [ DFA(ds, i) for i, ds in enumerate(atn.decisionToState) ]
+
+    sharedContextCache = PredictionContextCache()
+
+    literalNames = [ "", "'['", "']'", "'='", "'+='", "'-='", "':='",
+                     "'*='", "'/='", "'^='", "','", "'''", "'('", "')'",
+                     "'{'", "'}'", "':'", "'+'", "'-'", "';'", "'.'", "'>'",
+                     "'0>'", "'1>>'", "'^'", "'*'", "'/'" ]
+
+    symbolicNames = [ "", "", "", "",
+                      "", "", "", "",
+                      "", "", "", "",
+                      "", "", "", "",
+                      "", "", "", "",
+                      "", "", "", "",
+                      "", "", "", "Mass", "Inertia",
+                      "Input", "Output", "Save", "UnitSystem", "Encode",
+                      "Newtonian", "Frames", "Bodies", "Particles", "Points",
+                      "Constants", "Specifieds", "Imaginary", "Variables",
+                      "MotionVariables", "INT", "FLOAT", "EXP", "LINE_COMMENT",
+                      "ID", "WS" ]
+
+    RULE_prog = 0
+    RULE_stat = 1
+    RULE_assignment = 2
+    RULE_equals = 3
+    RULE_index = 4
+    RULE_diff = 5
+    RULE_functionCall = 6
+    RULE_varDecl = 7
+    RULE_varType = 8
+    RULE_varDecl2 = 9
+    RULE_ranges = 10
+    RULE_massDecl = 11
+    RULE_massDecl2 = 12
+    RULE_inertiaDecl = 13
+    RULE_matrix = 14
+    RULE_matrixInOutput = 15
+    RULE_codeCommands = 16
+    RULE_settings = 17
+    RULE_units = 18
+    RULE_inputs = 19
+    RULE_id_diff = 20
+    RULE_inputs2 = 21
+    RULE_outputs = 22
+    RULE_outputs2 = 23
+    RULE_codegen = 24
+    RULE_commands = 25
+    RULE_vec = 26
+    RULE_expr = 27
+
+    ruleNames =  [ "prog", "stat", "assignment", "equals", "index", "diff",
+                   "functionCall", "varDecl", "varType", "varDecl2", "ranges",
+                   "massDecl", "massDecl2", "inertiaDecl", "matrix", "matrixInOutput",
+                   "codeCommands", "settings", "units", "inputs", "id_diff",
+                   "inputs2", "outputs", "outputs2", "codegen", "commands",
+                   "vec", "expr" ]
+
+    EOF = Token.EOF
+    T__0=1
+    T__1=2
+    T__2=3
+    T__3=4
+    T__4=5
+    T__5=6
+    T__6=7
+    T__7=8
+    T__8=9
+    T__9=10
+    T__10=11
+    T__11=12
+    T__12=13
+    T__13=14
+    T__14=15
+    T__15=16
+    T__16=17
+    T__17=18
+    T__18=19
+    T__19=20
+    T__20=21
+    T__21=22
+    T__22=23
+    T__23=24
+    T__24=25
+    T__25=26
+    Mass=27
+    Inertia=28
+    Input=29
+    Output=30
+    Save=31
+    UnitSystem=32
+    Encode=33
+    Newtonian=34
+    Frames=35
+    Bodies=36
+    Particles=37
+    Points=38
+    Constants=39
+    Specifieds=40
+    Imaginary=41
+    Variables=42
+    MotionVariables=43
+    INT=44
+    FLOAT=45
+    EXP=46
+    LINE_COMMENT=47
+    ID=48
+    WS=49
+
+    def __init__(self, input:TokenStream, output:TextIO = sys.stdout):
+        super().__init__(input, output)
+        self.checkVersion("4.11.1")
+        self._interp = ParserATNSimulator(self, self.atn, self.decisionsToDFA, self.sharedContextCache)
+        self._predicates = None
+
+
+
+
+    class ProgContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def stat(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.StatContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.StatContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_prog
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterProg" ):
+                listener.enterProg(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitProg" ):
+                listener.exitProg(self)
+
+
+
+
+    def prog(self):
+
+        localctx = AutolevParser.ProgContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 0, self.RULE_prog)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 57
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while True:
+                self.state = 56
+                self.stat()
+                self.state = 59
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if not (((_la) & ~0x3f) == 0 and ((1 << _la) & 299067041120256) != 0):
+                    break
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class StatContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def varDecl(self):
+            return self.getTypedRuleContext(AutolevParser.VarDeclContext,0)
+
+
+        def functionCall(self):
+            return self.getTypedRuleContext(AutolevParser.FunctionCallContext,0)
+
+
+        def codeCommands(self):
+            return self.getTypedRuleContext(AutolevParser.CodeCommandsContext,0)
+
+
+        def massDecl(self):
+            return self.getTypedRuleContext(AutolevParser.MassDeclContext,0)
+
+
+        def inertiaDecl(self):
+            return self.getTypedRuleContext(AutolevParser.InertiaDeclContext,0)
+
+
+        def assignment(self):
+            return self.getTypedRuleContext(AutolevParser.AssignmentContext,0)
+
+
+        def settings(self):
+            return self.getTypedRuleContext(AutolevParser.SettingsContext,0)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_stat
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterStat" ):
+                listener.enterStat(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitStat" ):
+                listener.exitStat(self)
+
+
+
+
+    def stat(self):
+
+        localctx = AutolevParser.StatContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 2, self.RULE_stat)
+        try:
+            self.state = 68
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,1,self._ctx)
+            if la_ == 1:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 61
+                self.varDecl()
+                pass
+
+            elif la_ == 2:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 62
+                self.functionCall()
+                pass
+
+            elif la_ == 3:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 63
+                self.codeCommands()
+                pass
+
+            elif la_ == 4:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 64
+                self.massDecl()
+                pass
+
+            elif la_ == 5:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 65
+                self.inertiaDecl()
+                pass
+
+            elif la_ == 6:
+                self.enterOuterAlt(localctx, 6)
+                self.state = 66
+                self.assignment()
+                pass
+
+            elif la_ == 7:
+                self.enterOuterAlt(localctx, 7)
+                self.state = 67
+                self.settings()
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class AssignmentContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_assignment
+
+
+        def copyFrom(self, ctx:ParserRuleContext):
+            super().copyFrom(ctx)
+
+
+
+    class VecAssignContext(AssignmentContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.AssignmentContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def vec(self):
+            return self.getTypedRuleContext(AutolevParser.VecContext,0)
+
+        def equals(self):
+            return self.getTypedRuleContext(AutolevParser.EqualsContext,0)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterVecAssign" ):
+                listener.enterVecAssign(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitVecAssign" ):
+                listener.exitVecAssign(self)
+
+
+    class RegularAssignContext(AssignmentContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.AssignmentContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+        def equals(self):
+            return self.getTypedRuleContext(AutolevParser.EqualsContext,0)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+        def diff(self):
+            return self.getTypedRuleContext(AutolevParser.DiffContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterRegularAssign" ):
+                listener.enterRegularAssign(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitRegularAssign" ):
+                listener.exitRegularAssign(self)
+
+
+    class IndexAssignContext(AssignmentContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.AssignmentContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+        def index(self):
+            return self.getTypedRuleContext(AutolevParser.IndexContext,0)
+
+        def equals(self):
+            return self.getTypedRuleContext(AutolevParser.EqualsContext,0)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterIndexAssign" ):
+                listener.enterIndexAssign(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitIndexAssign" ):
+                listener.exitIndexAssign(self)
+
+
+
+    def assignment(self):
+
+        localctx = AutolevParser.AssignmentContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 4, self.RULE_assignment)
+        self._la = 0 # Token type
+        try:
+            self.state = 88
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,3,self._ctx)
+            if la_ == 1:
+                localctx = AutolevParser.VecAssignContext(self, localctx)
+                self.enterOuterAlt(localctx, 1)
+                self.state = 70
+                self.vec()
+                self.state = 71
+                self.equals()
+                self.state = 72
+                self.expr(0)
+                pass
+
+            elif la_ == 2:
+                localctx = AutolevParser.IndexAssignContext(self, localctx)
+                self.enterOuterAlt(localctx, 2)
+                self.state = 74
+                self.match(AutolevParser.ID)
+                self.state = 75
+                self.match(AutolevParser.T__0)
+                self.state = 76
+                self.index()
+                self.state = 77
+                self.match(AutolevParser.T__1)
+                self.state = 78
+                self.equals()
+                self.state = 79
+                self.expr(0)
+                pass
+
+            elif la_ == 3:
+                localctx = AutolevParser.RegularAssignContext(self, localctx)
+                self.enterOuterAlt(localctx, 3)
+                self.state = 81
+                self.match(AutolevParser.ID)
+                self.state = 83
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if _la==11:
+                    self.state = 82
+                    self.diff()
+
+
+                self.state = 85
+                self.equals()
+                self.state = 86
+                self.expr(0)
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class EqualsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_equals
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterEquals" ):
+                listener.enterEquals(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitEquals" ):
+                listener.exitEquals(self)
+
+
+
+
+    def equals(self):
+
+        localctx = AutolevParser.EqualsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 6, self.RULE_equals)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 90
+            _la = self._input.LA(1)
+            if not(((_la) & ~0x3f) == 0 and ((1 << _la) & 1016) != 0):
+                self._errHandler.recoverInline(self)
+            else:
+                self._errHandler.reportMatch(self)
+                self.consume()
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class IndexContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_index
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterIndex" ):
+                listener.enterIndex(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitIndex" ):
+                listener.exitIndex(self)
+
+
+
+
+    def index(self):
+
+        localctx = AutolevParser.IndexContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 8, self.RULE_index)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 92
+            self.expr(0)
+            self.state = 97
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 93
+                self.match(AutolevParser.T__9)
+                self.state = 94
+                self.expr(0)
+                self.state = 99
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class DiffContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_diff
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterDiff" ):
+                listener.enterDiff(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitDiff" ):
+                listener.exitDiff(self)
+
+
+
+
+    def diff(self):
+
+        localctx = AutolevParser.DiffContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 10, self.RULE_diff)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 101
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while True:
+                self.state = 100
+                self.match(AutolevParser.T__10)
+                self.state = 103
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if not (_la==11):
+                    break
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class FunctionCallContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def Mass(self):
+            return self.getToken(AutolevParser.Mass, 0)
+
+        def Inertia(self):
+            return self.getToken(AutolevParser.Inertia, 0)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_functionCall
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterFunctionCall" ):
+                listener.enterFunctionCall(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitFunctionCall" ):
+                listener.exitFunctionCall(self)
+
+
+
+
+    def functionCall(self):
+
+        localctx = AutolevParser.FunctionCallContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 12, self.RULE_functionCall)
+        self._la = 0 # Token type
+        try:
+            self.state = 131
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [48]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 105
+                self.match(AutolevParser.ID)
+                self.state = 106
+                self.match(AutolevParser.T__11)
+                self.state = 115
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if ((_la) & ~0x3f) == 0 and ((1 << _la) & 404620694540290) != 0:
+                    self.state = 107
+                    self.expr(0)
+                    self.state = 112
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    while _la==10:
+                        self.state = 108
+                        self.match(AutolevParser.T__9)
+                        self.state = 109
+                        self.expr(0)
+                        self.state = 114
+                        self._errHandler.sync(self)
+                        _la = self._input.LA(1)
+
+
+
+                self.state = 117
+                self.match(AutolevParser.T__12)
+                pass
+            elif token in [27, 28]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 118
+                _la = self._input.LA(1)
+                if not(_la==27 or _la==28):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 119
+                self.match(AutolevParser.T__11)
+                self.state = 128
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if _la==48:
+                    self.state = 120
+                    self.match(AutolevParser.ID)
+                    self.state = 125
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    while _la==10:
+                        self.state = 121
+                        self.match(AutolevParser.T__9)
+                        self.state = 122
+                        self.match(AutolevParser.ID)
+                        self.state = 127
+                        self._errHandler.sync(self)
+                        _la = self._input.LA(1)
+
+
+
+                self.state = 130
+                self.match(AutolevParser.T__12)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class VarDeclContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def varType(self):
+            return self.getTypedRuleContext(AutolevParser.VarTypeContext,0)
+
+
+        def varDecl2(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.VarDecl2Context)
+            else:
+                return self.getTypedRuleContext(AutolevParser.VarDecl2Context,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_varDecl
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterVarDecl" ):
+                listener.enterVarDecl(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitVarDecl" ):
+                listener.exitVarDecl(self)
+
+
+
+
+    def varDecl(self):
+
+        localctx = AutolevParser.VarDeclContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 14, self.RULE_varDecl)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 133
+            self.varType()
+            self.state = 134
+            self.varDecl2()
+            self.state = 139
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 135
+                self.match(AutolevParser.T__9)
+                self.state = 136
+                self.varDecl2()
+                self.state = 141
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class VarTypeContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def Newtonian(self):
+            return self.getToken(AutolevParser.Newtonian, 0)
+
+        def Frames(self):
+            return self.getToken(AutolevParser.Frames, 0)
+
+        def Bodies(self):
+            return self.getToken(AutolevParser.Bodies, 0)
+
+        def Particles(self):
+            return self.getToken(AutolevParser.Particles, 0)
+
+        def Points(self):
+            return self.getToken(AutolevParser.Points, 0)
+
+        def Constants(self):
+            return self.getToken(AutolevParser.Constants, 0)
+
+        def Specifieds(self):
+            return self.getToken(AutolevParser.Specifieds, 0)
+
+        def Imaginary(self):
+            return self.getToken(AutolevParser.Imaginary, 0)
+
+        def Variables(self):
+            return self.getToken(AutolevParser.Variables, 0)
+
+        def MotionVariables(self):
+            return self.getToken(AutolevParser.MotionVariables, 0)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_varType
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterVarType" ):
+                listener.enterVarType(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitVarType" ):
+                listener.exitVarType(self)
+
+
+
+
+    def varType(self):
+
+        localctx = AutolevParser.VarTypeContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 16, self.RULE_varType)
+        self._la = 0 # Token type
+        try:
+            self.state = 164
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [34]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 142
+                self.match(AutolevParser.Newtonian)
+                pass
+            elif token in [35]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 143
+                self.match(AutolevParser.Frames)
+                pass
+            elif token in [36]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 144
+                self.match(AutolevParser.Bodies)
+                pass
+            elif token in [37]:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 145
+                self.match(AutolevParser.Particles)
+                pass
+            elif token in [38]:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 146
+                self.match(AutolevParser.Points)
+                pass
+            elif token in [39]:
+                self.enterOuterAlt(localctx, 6)
+                self.state = 147
+                self.match(AutolevParser.Constants)
+                pass
+            elif token in [40]:
+                self.enterOuterAlt(localctx, 7)
+                self.state = 148
+                self.match(AutolevParser.Specifieds)
+                pass
+            elif token in [41]:
+                self.enterOuterAlt(localctx, 8)
+                self.state = 149
+                self.match(AutolevParser.Imaginary)
+                pass
+            elif token in [42]:
+                self.enterOuterAlt(localctx, 9)
+                self.state = 150
+                self.match(AutolevParser.Variables)
+                self.state = 154
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                while _la==11:
+                    self.state = 151
+                    self.match(AutolevParser.T__10)
+                    self.state = 156
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+
+                pass
+            elif token in [43]:
+                self.enterOuterAlt(localctx, 10)
+                self.state = 157
+                self.match(AutolevParser.MotionVariables)
+                self.state = 161
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                while _la==11:
+                    self.state = 158
+                    self.match(AutolevParser.T__10)
+                    self.state = 163
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class VarDecl2Context(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+
+        def INT(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.INT)
+            else:
+                return self.getToken(AutolevParser.INT, i)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_varDecl2
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterVarDecl2" ):
+                listener.enterVarDecl2(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitVarDecl2" ):
+                listener.exitVarDecl2(self)
+
+
+
+
+    def varDecl2(self):
+
+        localctx = AutolevParser.VarDecl2Context(self, self._ctx, self.state)
+        self.enterRule(localctx, 18, self.RULE_varDecl2)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 166
+            self.match(AutolevParser.ID)
+            self.state = 172
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,15,self._ctx)
+            if la_ == 1:
+                self.state = 167
+                self.match(AutolevParser.T__13)
+                self.state = 168
+                self.match(AutolevParser.INT)
+                self.state = 169
+                self.match(AutolevParser.T__9)
+                self.state = 170
+                self.match(AutolevParser.INT)
+                self.state = 171
+                self.match(AutolevParser.T__14)
+
+
+            self.state = 188
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,17,self._ctx)
+            if la_ == 1:
+                self.state = 174
+                self.match(AutolevParser.T__13)
+                self.state = 175
+                self.match(AutolevParser.INT)
+                self.state = 176
+                self.match(AutolevParser.T__15)
+                self.state = 177
+                self.match(AutolevParser.INT)
+                self.state = 184
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                while _la==10:
+                    self.state = 178
+                    self.match(AutolevParser.T__9)
+                    self.state = 179
+                    self.match(AutolevParser.INT)
+                    self.state = 180
+                    self.match(AutolevParser.T__15)
+                    self.state = 181
+                    self.match(AutolevParser.INT)
+                    self.state = 186
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+
+                self.state = 187
+                self.match(AutolevParser.T__14)
+
+
+            self.state = 193
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==14:
+                self.state = 190
+                self.match(AutolevParser.T__13)
+                self.state = 191
+                self.match(AutolevParser.INT)
+                self.state = 192
+                self.match(AutolevParser.T__14)
+
+
+            self.state = 196
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==17 or _la==18:
+                self.state = 195
+                _la = self._input.LA(1)
+                if not(_la==17 or _la==18):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+
+
+            self.state = 201
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==11:
+                self.state = 198
+                self.match(AutolevParser.T__10)
+                self.state = 203
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+            self.state = 206
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==3:
+                self.state = 204
+                self.match(AutolevParser.T__2)
+                self.state = 205
+                self.expr(0)
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class RangesContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def INT(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.INT)
+            else:
+                return self.getToken(AutolevParser.INT, i)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_ranges
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterRanges" ):
+                listener.enterRanges(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitRanges" ):
+                listener.exitRanges(self)
+
+
+
+
+    def ranges(self):
+
+        localctx = AutolevParser.RangesContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 20, self.RULE_ranges)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 208
+            self.match(AutolevParser.T__13)
+            self.state = 209
+            self.match(AutolevParser.INT)
+            self.state = 210
+            self.match(AutolevParser.T__15)
+            self.state = 211
+            self.match(AutolevParser.INT)
+            self.state = 218
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 212
+                self.match(AutolevParser.T__9)
+                self.state = 213
+                self.match(AutolevParser.INT)
+                self.state = 214
+                self.match(AutolevParser.T__15)
+                self.state = 215
+                self.match(AutolevParser.INT)
+                self.state = 220
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+            self.state = 221
+            self.match(AutolevParser.T__14)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class MassDeclContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def Mass(self):
+            return self.getToken(AutolevParser.Mass, 0)
+
+        def massDecl2(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.MassDecl2Context)
+            else:
+                return self.getTypedRuleContext(AutolevParser.MassDecl2Context,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_massDecl
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterMassDecl" ):
+                listener.enterMassDecl(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitMassDecl" ):
+                listener.exitMassDecl(self)
+
+
+
+
+    def massDecl(self):
+
+        localctx = AutolevParser.MassDeclContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 22, self.RULE_massDecl)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 223
+            self.match(AutolevParser.Mass)
+            self.state = 224
+            self.massDecl2()
+            self.state = 229
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 225
+                self.match(AutolevParser.T__9)
+                self.state = 226
+                self.massDecl2()
+                self.state = 231
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class MassDecl2Context(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_massDecl2
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterMassDecl2" ):
+                listener.enterMassDecl2(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitMassDecl2" ):
+                listener.exitMassDecl2(self)
+
+
+
+
+    def massDecl2(self):
+
+        localctx = AutolevParser.MassDecl2Context(self, self._ctx, self.state)
+        self.enterRule(localctx, 24, self.RULE_massDecl2)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 232
+            self.match(AutolevParser.ID)
+            self.state = 233
+            self.match(AutolevParser.T__2)
+            self.state = 234
+            self.expr(0)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class InertiaDeclContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def Inertia(self):
+            return self.getToken(AutolevParser.Inertia, 0)
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_inertiaDecl
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterInertiaDecl" ):
+                listener.enterInertiaDecl(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitInertiaDecl" ):
+                listener.exitInertiaDecl(self)
+
+
+
+
+    def inertiaDecl(self):
+
+        localctx = AutolevParser.InertiaDeclContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 26, self.RULE_inertiaDecl)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 236
+            self.match(AutolevParser.Inertia)
+            self.state = 237
+            self.match(AutolevParser.ID)
+            self.state = 241
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==12:
+                self.state = 238
+                self.match(AutolevParser.T__11)
+                self.state = 239
+                self.match(AutolevParser.ID)
+                self.state = 240
+                self.match(AutolevParser.T__12)
+
+
+            self.state = 245
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while True:
+                self.state = 243
+                self.match(AutolevParser.T__9)
+                self.state = 244
+                self.expr(0)
+                self.state = 247
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if not (_la==10):
+                    break
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class MatrixContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_matrix
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterMatrix" ):
+                listener.enterMatrix(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitMatrix" ):
+                listener.exitMatrix(self)
+
+
+
+
+    def matrix(self):
+
+        localctx = AutolevParser.MatrixContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 28, self.RULE_matrix)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 249
+            self.match(AutolevParser.T__0)
+            self.state = 250
+            self.expr(0)
+            self.state = 255
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10 or _la==19:
+                self.state = 251
+                _la = self._input.LA(1)
+                if not(_la==10 or _la==19):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 252
+                self.expr(0)
+                self.state = 257
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+            self.state = 258
+            self.match(AutolevParser.T__1)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class MatrixInOutputContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def FLOAT(self):
+            return self.getToken(AutolevParser.FLOAT, 0)
+
+        def INT(self):
+            return self.getToken(AutolevParser.INT, 0)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_matrixInOutput
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterMatrixInOutput" ):
+                listener.enterMatrixInOutput(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitMatrixInOutput" ):
+                listener.exitMatrixInOutput(self)
+
+
+
+
+    def matrixInOutput(self):
+
+        localctx = AutolevParser.MatrixInOutputContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 30, self.RULE_matrixInOutput)
+        self._la = 0 # Token type
+        try:
+            self.state = 268
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [48]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 260
+                self.match(AutolevParser.ID)
+
+                self.state = 261
+                self.match(AutolevParser.ID)
+                self.state = 262
+                self.match(AutolevParser.T__2)
+                self.state = 264
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if _la==44 or _la==45:
+                    self.state = 263
+                    _la = self._input.LA(1)
+                    if not(_la==44 or _la==45):
+                        self._errHandler.recoverInline(self)
+                    else:
+                        self._errHandler.reportMatch(self)
+                        self.consume()
+
+
+                pass
+            elif token in [45]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 266
+                self.match(AutolevParser.FLOAT)
+                pass
+            elif token in [44]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 267
+                self.match(AutolevParser.INT)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class CodeCommandsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def units(self):
+            return self.getTypedRuleContext(AutolevParser.UnitsContext,0)
+
+
+        def inputs(self):
+            return self.getTypedRuleContext(AutolevParser.InputsContext,0)
+
+
+        def outputs(self):
+            return self.getTypedRuleContext(AutolevParser.OutputsContext,0)
+
+
+        def codegen(self):
+            return self.getTypedRuleContext(AutolevParser.CodegenContext,0)
+
+
+        def commands(self):
+            return self.getTypedRuleContext(AutolevParser.CommandsContext,0)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_codeCommands
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterCodeCommands" ):
+                listener.enterCodeCommands(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitCodeCommands" ):
+                listener.exitCodeCommands(self)
+
+
+
+
+    def codeCommands(self):
+
+        localctx = AutolevParser.CodeCommandsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 32, self.RULE_codeCommands)
+        try:
+            self.state = 275
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [32]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 270
+                self.units()
+                pass
+            elif token in [29]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 271
+                self.inputs()
+                pass
+            elif token in [30]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 272
+                self.outputs()
+                pass
+            elif token in [48]:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 273
+                self.codegen()
+                pass
+            elif token in [31, 33]:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 274
+                self.commands()
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class SettingsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def EXP(self):
+            return self.getToken(AutolevParser.EXP, 0)
+
+        def FLOAT(self):
+            return self.getToken(AutolevParser.FLOAT, 0)
+
+        def INT(self):
+            return self.getToken(AutolevParser.INT, 0)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_settings
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterSettings" ):
+                listener.enterSettings(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitSettings" ):
+                listener.exitSettings(self)
+
+
+
+
+    def settings(self):
+
+        localctx = AutolevParser.SettingsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 34, self.RULE_settings)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 277
+            self.match(AutolevParser.ID)
+            self.state = 279
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,30,self._ctx)
+            if la_ == 1:
+                self.state = 278
+                _la = self._input.LA(1)
+                if not(((_la) & ~0x3f) == 0 and ((1 << _la) & 404620279021568) != 0):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class UnitsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def UnitSystem(self):
+            return self.getToken(AutolevParser.UnitSystem, 0)
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_units
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterUnits" ):
+                listener.enterUnits(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitUnits" ):
+                listener.exitUnits(self)
+
+
+
+
+    def units(self):
+
+        localctx = AutolevParser.UnitsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 36, self.RULE_units)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 281
+            self.match(AutolevParser.UnitSystem)
+            self.state = 282
+            self.match(AutolevParser.ID)
+            self.state = 287
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 283
+                self.match(AutolevParser.T__9)
+                self.state = 284
+                self.match(AutolevParser.ID)
+                self.state = 289
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class InputsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def Input(self):
+            return self.getToken(AutolevParser.Input, 0)
+
+        def inputs2(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.Inputs2Context)
+            else:
+                return self.getTypedRuleContext(AutolevParser.Inputs2Context,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_inputs
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterInputs" ):
+                listener.enterInputs(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitInputs" ):
+                listener.exitInputs(self)
+
+
+
+
+    def inputs(self):
+
+        localctx = AutolevParser.InputsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 38, self.RULE_inputs)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 290
+            self.match(AutolevParser.Input)
+            self.state = 291
+            self.inputs2()
+            self.state = 296
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 292
+                self.match(AutolevParser.T__9)
+                self.state = 293
+                self.inputs2()
+                self.state = 298
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Id_diffContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+
+        def diff(self):
+            return self.getTypedRuleContext(AutolevParser.DiffContext,0)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_id_diff
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterId_diff" ):
+                listener.enterId_diff(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitId_diff" ):
+                listener.exitId_diff(self)
+
+
+
+
+    def id_diff(self):
+
+        localctx = AutolevParser.Id_diffContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 40, self.RULE_id_diff)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 299
+            self.match(AutolevParser.ID)
+            self.state = 301
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==11:
+                self.state = 300
+                self.diff()
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Inputs2Context(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def id_diff(self):
+            return self.getTypedRuleContext(AutolevParser.Id_diffContext,0)
+
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_inputs2
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterInputs2" ):
+                listener.enterInputs2(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitInputs2" ):
+                listener.exitInputs2(self)
+
+
+
+
+    def inputs2(self):
+
+        localctx = AutolevParser.Inputs2Context(self, self._ctx, self.state)
+        self.enterRule(localctx, 42, self.RULE_inputs2)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 303
+            self.id_diff()
+            self.state = 304
+            self.match(AutolevParser.T__2)
+            self.state = 305
+            self.expr(0)
+            self.state = 307
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,34,self._ctx)
+            if la_ == 1:
+                self.state = 306
+                self.expr(0)
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class OutputsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def Output(self):
+            return self.getToken(AutolevParser.Output, 0)
+
+        def outputs2(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.Outputs2Context)
+            else:
+                return self.getTypedRuleContext(AutolevParser.Outputs2Context,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_outputs
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterOutputs" ):
+                listener.enterOutputs(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitOutputs" ):
+                listener.exitOutputs(self)
+
+
+
+
+    def outputs(self):
+
+        localctx = AutolevParser.OutputsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 44, self.RULE_outputs)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 309
+            self.match(AutolevParser.Output)
+            self.state = 310
+            self.outputs2()
+            self.state = 315
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==10:
+                self.state = 311
+                self.match(AutolevParser.T__9)
+                self.state = 312
+                self.outputs2()
+                self.state = 317
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Outputs2Context(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_outputs2
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterOutputs2" ):
+                listener.enterOutputs2(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitOutputs2" ):
+                listener.exitOutputs2(self)
+
+
+
+
+    def outputs2(self):
+
+        localctx = AutolevParser.Outputs2Context(self, self._ctx, self.state)
+        self.enterRule(localctx, 46, self.RULE_outputs2)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 318
+            self.expr(0)
+            self.state = 320
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,36,self._ctx)
+            if la_ == 1:
+                self.state = 319
+                self.expr(0)
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class CodegenContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def functionCall(self):
+            return self.getTypedRuleContext(AutolevParser.FunctionCallContext,0)
+
+
+        def matrixInOutput(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.MatrixInOutputContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.MatrixInOutputContext,i)
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_codegen
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterCodegen" ):
+                listener.enterCodegen(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitCodegen" ):
+                listener.exitCodegen(self)
+
+
+
+
+    def codegen(self):
+
+        localctx = AutolevParser.CodegenContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 48, self.RULE_codegen)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 322
+            self.match(AutolevParser.ID)
+            self.state = 323
+            self.functionCall()
+            self.state = 335
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==1:
+                self.state = 324
+                self.match(AutolevParser.T__0)
+                self.state = 325
+                self.matrixInOutput()
+                self.state = 330
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                while _la==10:
+                    self.state = 326
+                    self.match(AutolevParser.T__9)
+                    self.state = 327
+                    self.matrixInOutput()
+                    self.state = 332
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+
+                self.state = 333
+                self.match(AutolevParser.T__1)
+
+
+            self.state = 337
+            self.match(AutolevParser.ID)
+            self.state = 338
+            self.match(AutolevParser.T__19)
+            self.state = 339
+            self.match(AutolevParser.ID)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class CommandsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def Save(self):
+            return self.getToken(AutolevParser.Save, 0)
+
+        def ID(self, i:int=None):
+            if i is None:
+                return self.getTokens(AutolevParser.ID)
+            else:
+                return self.getToken(AutolevParser.ID, i)
+
+        def Encode(self):
+            return self.getToken(AutolevParser.Encode, 0)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_commands
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterCommands" ):
+                listener.enterCommands(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitCommands" ):
+                listener.exitCommands(self)
+
+
+
+
+    def commands(self):
+
+        localctx = AutolevParser.CommandsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 50, self.RULE_commands)
+        self._la = 0 # Token type
+        try:
+            self.state = 354
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [31]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 341
+                self.match(AutolevParser.Save)
+                self.state = 342
+                self.match(AutolevParser.ID)
+                self.state = 343
+                self.match(AutolevParser.T__19)
+                self.state = 344
+                self.match(AutolevParser.ID)
+                pass
+            elif token in [33]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 345
+                self.match(AutolevParser.Encode)
+                self.state = 346
+                self.match(AutolevParser.ID)
+                self.state = 351
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                while _la==10:
+                    self.state = 347
+                    self.match(AutolevParser.T__9)
+                    self.state = 348
+                    self.match(AutolevParser.ID)
+                    self.state = 353
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class VecContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_vec
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterVec" ):
+                listener.enterVec(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitVec" ):
+                listener.exitVec(self)
+
+
+
+
+    def vec(self):
+
+        localctx = AutolevParser.VecContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 52, self.RULE_vec)
+        try:
+            self.state = 364
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [48]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 356
+                self.match(AutolevParser.ID)
+                self.state = 358
+                self._errHandler.sync(self)
+                _alt = 1
+                while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                    if _alt == 1:
+                        self.state = 357
+                        self.match(AutolevParser.T__20)
+
+                    else:
+                        raise NoViableAltException(self)
+                    self.state = 360
+                    self._errHandler.sync(self)
+                    _alt = self._interp.adaptivePredict(self._input,41,self._ctx)
+
+                pass
+            elif token in [22]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 362
+                self.match(AutolevParser.T__21)
+                pass
+            elif token in [23]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 363
+                self.match(AutolevParser.T__22)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class ExprContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+
+        def getRuleIndex(self):
+            return AutolevParser.RULE_expr
+
+
+        def copyFrom(self, ctx:ParserRuleContext):
+            super().copyFrom(ctx)
+
+
+    class ParensContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterParens" ):
+                listener.enterParens(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitParens" ):
+                listener.exitParens(self)
+
+
+    class VectorOrDyadicContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def vec(self):
+            return self.getTypedRuleContext(AutolevParser.VecContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterVectorOrDyadic" ):
+                listener.enterVectorOrDyadic(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitVectorOrDyadic" ):
+                listener.exitVectorOrDyadic(self)
+
+
+    class ExponentContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterExponent" ):
+                listener.enterExponent(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitExponent" ):
+                listener.exitExponent(self)
+
+
+    class MulDivContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterMulDiv" ):
+                listener.enterMulDiv(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitMulDiv" ):
+                listener.exitMulDiv(self)
+
+
+    class AddSubContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterAddSub" ):
+                listener.enterAddSub(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitAddSub" ):
+                listener.exitAddSub(self)
+
+
+    class FloatContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def FLOAT(self):
+            return self.getToken(AutolevParser.FLOAT, 0)
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterFloat" ):
+                listener.enterFloat(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitFloat" ):
+                listener.exitFloat(self)
+
+
+    class IntContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def INT(self):
+            return self.getToken(AutolevParser.INT, 0)
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterInt" ):
+                listener.enterInt(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitInt" ):
+                listener.exitInt(self)
+
+
+    class IdEqualsExprContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterIdEqualsExpr" ):
+                listener.enterIdEqualsExpr(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitIdEqualsExpr" ):
+                listener.exitIdEqualsExpr(self)
+
+
+    class NegativeOneContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self):
+            return self.getTypedRuleContext(AutolevParser.ExprContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterNegativeOne" ):
+                listener.enterNegativeOne(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitNegativeOne" ):
+                listener.exitNegativeOne(self)
+
+
+    class FunctionContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def functionCall(self):
+            return self.getTypedRuleContext(AutolevParser.FunctionCallContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterFunction" ):
+                listener.enterFunction(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitFunction" ):
+                listener.exitFunction(self)
+
+
+    class RangessContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def ranges(self):
+            return self.getTypedRuleContext(AutolevParser.RangesContext,0)
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterRangess" ):
+                listener.enterRangess(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitRangess" ):
+                listener.exitRangess(self)
+
+
+    class ColonContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterColon" ):
+                listener.enterColon(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitColon" ):
+                listener.exitColon(self)
+
+
+    class IdContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterId" ):
+                listener.enterId(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitId" ):
+                listener.exitId(self)
+
+
+    class ExpContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def EXP(self):
+            return self.getToken(AutolevParser.EXP, 0)
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterExp" ):
+                listener.enterExp(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitExp" ):
+                listener.exitExp(self)
+
+
+    class MatricesContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def matrix(self):
+            return self.getTypedRuleContext(AutolevParser.MatrixContext,0)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterMatrices" ):
+                listener.enterMatrices(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitMatrices" ):
+                listener.exitMatrices(self)
+
+
+    class IndexingContext(ExprContext):
+
+        def __init__(self, parser, ctx:ParserRuleContext): # actually a AutolevParser.ExprContext
+            super().__init__(parser)
+            self.copyFrom(ctx)
+
+        def ID(self):
+            return self.getToken(AutolevParser.ID, 0)
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(AutolevParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(AutolevParser.ExprContext,i)
+
+
+        def enterRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "enterIndexing" ):
+                listener.enterIndexing(self)
+
+        def exitRule(self, listener:ParseTreeListener):
+            if hasattr( listener, "exitIndexing" ):
+                listener.exitIndexing(self)
+
+
+
+    def expr(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = AutolevParser.ExprContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 54
+        self.enterRecursionRule(localctx, 54, self.RULE_expr, _p)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 408
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,47,self._ctx)
+            if la_ == 1:
+                localctx = AutolevParser.ExpContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+
+                self.state = 367
+                self.match(AutolevParser.EXP)
+                pass
+
+            elif la_ == 2:
+                localctx = AutolevParser.NegativeOneContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 368
+                self.match(AutolevParser.T__17)
+                self.state = 369
+                self.expr(12)
+                pass
+
+            elif la_ == 3:
+                localctx = AutolevParser.FloatContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 370
+                self.match(AutolevParser.FLOAT)
+                pass
+
+            elif la_ == 4:
+                localctx = AutolevParser.IntContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 371
+                self.match(AutolevParser.INT)
+                pass
+
+            elif la_ == 5:
+                localctx = AutolevParser.IdContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 372
+                self.match(AutolevParser.ID)
+                self.state = 376
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,43,self._ctx)
+                while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                    if _alt==1:
+                        self.state = 373
+                        self.match(AutolevParser.T__10)
+                    self.state = 378
+                    self._errHandler.sync(self)
+                    _alt = self._interp.adaptivePredict(self._input,43,self._ctx)
+
+                pass
+
+            elif la_ == 6:
+                localctx = AutolevParser.VectorOrDyadicContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 379
+                self.vec()
+                pass
+
+            elif la_ == 7:
+                localctx = AutolevParser.IndexingContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 380
+                self.match(AutolevParser.ID)
+                self.state = 381
+                self.match(AutolevParser.T__0)
+                self.state = 382
+                self.expr(0)
+                self.state = 387
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                while _la==10:
+                    self.state = 383
+                    self.match(AutolevParser.T__9)
+                    self.state = 384
+                    self.expr(0)
+                    self.state = 389
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+
+                self.state = 390
+                self.match(AutolevParser.T__1)
+                pass
+
+            elif la_ == 8:
+                localctx = AutolevParser.FunctionContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 392
+                self.functionCall()
+                pass
+
+            elif la_ == 9:
+                localctx = AutolevParser.MatricesContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 393
+                self.matrix()
+                pass
+
+            elif la_ == 10:
+                localctx = AutolevParser.ParensContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 394
+                self.match(AutolevParser.T__11)
+                self.state = 395
+                self.expr(0)
+                self.state = 396
+                self.match(AutolevParser.T__12)
+                pass
+
+            elif la_ == 11:
+                localctx = AutolevParser.RangessContext(self, localctx)
+                self._ctx = localctx
+                _prevctx = localctx
+                self.state = 399
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if _la==48:
+                    self.state = 398
+                    self.match(AutolevParser.ID)
+
+
+                self.state = 401
+                self.ranges()
+                self.state = 405
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,46,self._ctx)
+                while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                    if _alt==1:
+                        self.state = 402
+                        self.match(AutolevParser.T__10)
+                    self.state = 407
+                    self._errHandler.sync(self)
+                    _alt = self._interp.adaptivePredict(self._input,46,self._ctx)
+
+                pass
+
+
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 427
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,49,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    self.state = 425
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,48,self._ctx)
+                    if la_ == 1:
+                        localctx = AutolevParser.ExponentContext(self, AutolevParser.ExprContext(self, _parentctx, _parentState))
+                        self.pushNewRecursionContext(localctx, _startState, self.RULE_expr)
+                        self.state = 410
+                        if not self.precpred(self._ctx, 16):
+                            from antlr4.error.Errors import FailedPredicateException
+                            raise FailedPredicateException(self, "self.precpred(self._ctx, 16)")
+                        self.state = 411
+                        self.match(AutolevParser.T__23)
+                        self.state = 412
+                        self.expr(17)
+                        pass
+
+                    elif la_ == 2:
+                        localctx = AutolevParser.MulDivContext(self, AutolevParser.ExprContext(self, _parentctx, _parentState))
+                        self.pushNewRecursionContext(localctx, _startState, self.RULE_expr)
+                        self.state = 413
+                        if not self.precpred(self._ctx, 15):
+                            from antlr4.error.Errors import FailedPredicateException
+                            raise FailedPredicateException(self, "self.precpred(self._ctx, 15)")
+                        self.state = 414
+                        _la = self._input.LA(1)
+                        if not(_la==25 or _la==26):
+                            self._errHandler.recoverInline(self)
+                        else:
+                            self._errHandler.reportMatch(self)
+                            self.consume()
+                        self.state = 415
+                        self.expr(16)
+                        pass
+
+                    elif la_ == 3:
+                        localctx = AutolevParser.AddSubContext(self, AutolevParser.ExprContext(self, _parentctx, _parentState))
+                        self.pushNewRecursionContext(localctx, _startState, self.RULE_expr)
+                        self.state = 416
+                        if not self.precpred(self._ctx, 14):
+                            from antlr4.error.Errors import FailedPredicateException
+                            raise FailedPredicateException(self, "self.precpred(self._ctx, 14)")
+                        self.state = 417
+                        _la = self._input.LA(1)
+                        if not(_la==17 or _la==18):
+                            self._errHandler.recoverInline(self)
+                        else:
+                            self._errHandler.reportMatch(self)
+                            self.consume()
+                        self.state = 418
+                        self.expr(15)
+                        pass
+
+                    elif la_ == 4:
+                        localctx = AutolevParser.IdEqualsExprContext(self, AutolevParser.ExprContext(self, _parentctx, _parentState))
+                        self.pushNewRecursionContext(localctx, _startState, self.RULE_expr)
+                        self.state = 419
+                        if not self.precpred(self._ctx, 3):
+                            from antlr4.error.Errors import FailedPredicateException
+                            raise FailedPredicateException(self, "self.precpred(self._ctx, 3)")
+                        self.state = 420
+                        self.match(AutolevParser.T__2)
+                        self.state = 421
+                        self.expr(4)
+                        pass
+
+                    elif la_ == 5:
+                        localctx = AutolevParser.ColonContext(self, AutolevParser.ExprContext(self, _parentctx, _parentState))
+                        self.pushNewRecursionContext(localctx, _startState, self.RULE_expr)
+                        self.state = 422
+                        if not self.precpred(self._ctx, 2):
+                            from antlr4.error.Errors import FailedPredicateException
+                            raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                        self.state = 423
+                        self.match(AutolevParser.T__15)
+                        self.state = 424
+                        self.expr(3)
+                        pass
+
+
+                self.state = 429
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,49,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+
+    def sempred(self, localctx:RuleContext, ruleIndex:int, predIndex:int):
+        if self._predicates == None:
+            self._predicates = dict()
+        self._predicates[27] = self.expr_sempred
+        pred = self._predicates.get(ruleIndex, None)
+        if pred is None:
+            raise Exception("No predicate with index:" + str(ruleIndex))
+        else:
+            return pred(localctx, predIndex)
+
+    def expr_sempred(self, localctx:ExprContext, predIndex:int):
+            if predIndex == 0:
+                return self.precpred(self._ctx, 16)
+
+
+            if predIndex == 1:
+                return self.precpred(self._ctx, 15)
+
+
+            if predIndex == 2:
+                return self.precpred(self._ctx, 14)
+
+
+            if predIndex == 3:
+                return self.precpred(self._ctx, 3)
+
+
+            if predIndex == 4:
+                return self.precpred(self._ctx, 2)
+
+
+
+
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_build_autolev_antlr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_build_autolev_antlr.py
new file mode 100644
index 0000000000000000000000000000000000000000..8314b2f546c0a18a8e281768b60d66556c852e3b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_build_autolev_antlr.py
@@ -0,0 +1,86 @@
+import os
+import subprocess
+import glob
+
+from sympy.utilities.misc import debug
+
+here = os.path.dirname(__file__)
+grammar_file = os.path.abspath(os.path.join(here, "Autolev.g4"))
+dir_autolev_antlr = os.path.join(here, "_antlr")
+
+header = '''\
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+'''
+
+
+def check_antlr_version():
+    debug("Checking antlr4 version...")
+
+    try:
+        debug(subprocess.check_output(["antlr4"])
+              .decode('utf-8').split("\n")[0])
+        return True
+    except (subprocess.CalledProcessError, FileNotFoundError):
+        debug("The 'antlr4' command line tool is not installed, "
+              "or not on your PATH.\n"
+              "> Please refer to the README.md file for more information.")
+        return False
+
+
+def build_parser(output_dir=dir_autolev_antlr):
+    check_antlr_version()
+
+    debug("Updating ANTLR-generated code in {}".format(output_dir))
+
+    if not os.path.exists(output_dir):
+        os.makedirs(output_dir)
+
+    with open(os.path.join(output_dir, "__init__.py"), "w+") as fp:
+        fp.write(header)
+
+    args = [
+        "antlr4",
+        grammar_file,
+        "-o", output_dir,
+        "-no-visitor",
+    ]
+
+    debug("Running code generation...\n\t$ {}".format(" ".join(args)))
+    subprocess.check_output(args, cwd=output_dir)
+
+    debug("Applying headers, removing unnecessary files and renaming...")
+    # Handle case insensitive file systems. If the files are already
+    # generated, they will be written to autolev* but Autolev*.* won't match them.
+    for path in (glob.glob(os.path.join(output_dir, "Autolev*.*")) or
+        glob.glob(os.path.join(output_dir, "autolev*.*"))):
+
+        # Remove files ending in .interp or .tokens as they are not needed.
+        if not path.endswith(".py"):
+            os.unlink(path)
+            continue
+
+        new_path = os.path.join(output_dir, os.path.basename(path).lower())
+        with open(path, 'r') as f:
+            lines = [line.rstrip().replace('AutolevParser import', 'autolevparser import') +'\n'
+                     for line in f]
+
+        os.unlink(path)
+
+        with open(new_path, "w") as out_file:
+            offset = 0
+            while lines[offset].startswith('#'):
+                offset += 1
+            out_file.write(header)
+            out_file.writelines(lines[offset:])
+
+        debug("\t{}".format(new_path))
+
+    return True
+
+
+if __name__ == "__main__":
+    build_parser()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_listener_autolev_antlr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_listener_autolev_antlr.py
new file mode 100644
index 0000000000000000000000000000000000000000..9ca2f8af88de18036b90788fd29d02707f098213
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_listener_autolev_antlr.py
@@ -0,0 +1,2083 @@
+import collections
+import warnings
+
+from sympy.external import import_module
+
+autolevparser = import_module('sympy.parsing.autolev._antlr.autolevparser',
+                              import_kwargs={'fromlist': ['AutolevParser']})
+autolevlexer = import_module('sympy.parsing.autolev._antlr.autolevlexer',
+                             import_kwargs={'fromlist': ['AutolevLexer']})
+autolevlistener = import_module('sympy.parsing.autolev._antlr.autolevlistener',
+                                import_kwargs={'fromlist': ['AutolevListener']})
+
+AutolevParser = getattr(autolevparser, 'AutolevParser', None)
+AutolevLexer = getattr(autolevlexer, 'AutolevLexer', None)
+AutolevListener = getattr(autolevlistener, 'AutolevListener', None)
+
+
+def strfunc(z):
+    if z == 0:
+        return ""
+    elif z == 1:
+        return "_d"
+    else:
+        return "_" + "d" * z
+
+def declare_phy_entities(self, ctx, phy_type, i, j=None):
+    if phy_type in ("frame", "newtonian"):
+        declare_frames(self, ctx, i, j)
+    elif phy_type == "particle":
+        declare_particles(self, ctx, i, j)
+    elif phy_type == "point":
+        declare_points(self, ctx, i, j)
+    elif phy_type == "bodies":
+        declare_bodies(self, ctx, i, j)
+
+def declare_frames(self, ctx, i, j=None):
+    if "{" in ctx.getText():
+        if j:
+            name1 = ctx.ID().getText().lower() + str(i) + str(j)
+        else:
+            name1 = ctx.ID().getText().lower() + str(i)
+    else:
+        name1 = ctx.ID().getText().lower()
+    name2 = "frame_" + name1
+    if self.getValue(ctx.parentCtx.varType()) == "newtonian":
+        self.newtonian = name2
+
+    self.symbol_table2.update({name1: name2})
+
+    self.symbol_table.update({name1 + "1>": name2 + ".x"})
+    self.symbol_table.update({name1 + "2>": name2 + ".y"})
+    self.symbol_table.update({name1 + "3>": name2 + ".z"})
+
+    self.type2.update({name1: "frame"})
+    self.write(name2 + " = " + "_me.ReferenceFrame('" + name1 + "')\n")
+
+def declare_points(self, ctx, i, j=None):
+    if "{" in ctx.getText():
+        if j:
+            name1 = ctx.ID().getText().lower() + str(i) + str(j)
+        else:
+            name1 = ctx.ID().getText().lower() + str(i)
+    else:
+        name1 = ctx.ID().getText().lower()
+
+    name2 = "point_" + name1
+
+    self.symbol_table2.update({name1: name2})
+    self.type2.update({name1: "point"})
+    self.write(name2 + " = " + "_me.Point('" + name1 + "')\n")
+
+def declare_particles(self, ctx, i, j=None):
+    if "{" in ctx.getText():
+        if j:
+            name1 = ctx.ID().getText().lower() + str(i) + str(j)
+        else:
+            name1 = ctx.ID().getText().lower() + str(i)
+    else:
+        name1 = ctx.ID().getText().lower()
+
+    name2 = "particle_" + name1
+
+    self.symbol_table2.update({name1: name2})
+    self.type2.update({name1: "particle"})
+    self.bodies.update({name1: name2})
+    self.write(name2 + " = " + "_me.Particle('" + name1 + "', " + "_me.Point('" +
+                name1 + "_pt" + "'), " + "_sm.Symbol('m'))\n")
+
+def declare_bodies(self, ctx, i, j=None):
+    if "{" in ctx.getText():
+        if j:
+            name1 = ctx.ID().getText().lower() + str(i) + str(j)
+        else:
+            name1 = ctx.ID().getText().lower() + str(i)
+    else:
+        name1 = ctx.ID().getText().lower()
+
+    name2 = "body_" + name1
+    self.bodies.update({name1: name2})
+    masscenter = name2 + "_cm"
+    refFrame = name2 + "_f"
+
+    self.symbol_table2.update({name1: name2})
+    self.symbol_table2.update({name1 + "o": masscenter})
+    self.symbol_table.update({name1 + "1>": refFrame+".x"})
+    self.symbol_table.update({name1 + "2>": refFrame+".y"})
+    self.symbol_table.update({name1 + "3>": refFrame+".z"})
+
+    self.type2.update({name1: "bodies"})
+    self.type2.update({name1+"o": "point"})
+
+    self.write(masscenter + " = " + "_me.Point('" + name1 + "_cm" + "')\n")
+    if self.newtonian:
+        self.write(masscenter + ".set_vel(" + self.newtonian + ", " + "0)\n")
+    self.write(refFrame + " = " + "_me.ReferenceFrame('" + name1 + "_f" + "')\n")
+    # We set a dummy mass and inertia here.
+    # They will be reset using the setters later in the code anyway.
+    self.write(name2 + " = " + "_me.RigidBody('" + name1 + "', " + masscenter + ", " +
+                refFrame + ", " + "_sm.symbols('m'), (_me.outer(" + refFrame +
+                ".x," + refFrame + ".x)," + masscenter + "))\n")
+
+def inertia_func(self, v1, v2, l, frame):
+
+    if self.type2[v1] == "particle":
+        l.append("_me.inertia_of_point_mass(" + self.bodies[v1] + ".mass, " + self.bodies[v1] +
+                 ".point.pos_from(" + self.symbol_table2[v2] + "), " + frame + ")")
+
+    elif self.type2[v1] == "bodies":
+        # Inertia has been defined about center of mass.
+        if self.inertia_point[v1] == v1 + "o":
+            # Asking point is cm as well
+            if v2 == self.inertia_point[v1]:
+                l.append(self.symbol_table2[v1] + ".inertia[0]")
+
+            # Asking point is not cm
+            else:
+                l.append(self.bodies[v1] + ".inertia[0]" + " + " +
+                         "_me.inertia_of_point_mass(" + self.bodies[v1] +
+                         ".mass, " + self.bodies[v1] + ".masscenter" +
+                         ".pos_from(" + self.symbol_table2[v2] +
+                         "), " + frame + ")")
+
+        # Inertia has been defined about another point
+        else:
+            # Asking point is the defined point
+            if v2 == self.inertia_point[v1]:
+                l.append(self.symbol_table2[v1] + ".inertia[0]")
+            # Asking point is cm
+            elif v2 == v1 + "o":
+                l.append(self.bodies[v1] + ".inertia[0]" + " - " +
+                         "_me.inertia_of_point_mass(" + self.bodies[v1] +
+                         ".mass, " + self.bodies[v1] + ".masscenter" +
+                         ".pos_from(" + self.symbol_table2[self.inertia_point[v1]] +
+                         "), " + frame + ")")
+            # Asking point is some other point
+            else:
+                l.append(self.bodies[v1] + ".inertia[0]" + " - " +
+                         "_me.inertia_of_point_mass(" + self.bodies[v1] +
+                         ".mass, " + self.bodies[v1] + ".masscenter" +
+                         ".pos_from(" + self.symbol_table2[self.inertia_point[v1]] +
+                         "), " + frame + ")" + " + " +
+                         "_me.inertia_of_point_mass(" + self.bodies[v1] +
+                         ".mass, " + self.bodies[v1] + ".masscenter" +
+                         ".pos_from(" + self.symbol_table2[v2] +
+                         "), " + frame + ")")
+
+
+def processConstants(self, ctx):
+    # Process constant declarations of the type: Constants F = 3, g = 9.81
+    name = ctx.ID().getText().lower()
+    if "=" in ctx.getText():
+        self.symbol_table.update({name: name})
+        # self.inputs.update({self.symbol_table[name]: self.getValue(ctx.getChild(2))})
+        self.write(self.symbol_table[name] + " = " + "_sm.S(" + self.getValue(ctx.getChild(2)) + ")\n")
+        self.type.update({name: "constants"})
+        return
+
+    # Constants declarations of the type: Constants A, B
+    else:
+        if "{" not in ctx.getText():
+            self.symbol_table[name] = name
+            self.type[name] = "constants"
+
+    # Process constant declarations of the type: Constants C+, D-
+    if ctx.getChildCount() == 2:
+        # This is set for declaring nonpositive=True and nonnegative=True
+        if ctx.getChild(1).getText() == "+":
+            self.sign[name] = "+"
+        elif ctx.getChild(1).getText() == "-":
+            self.sign[name] = "-"
+    else:
+        if "{" not in ctx.getText():
+            self.sign[name] = "o"
+
+    # Process constant declarations of the type: Constants K{4}, a{1:2, 1:2}, b{1:2}
+    if "{" in ctx.getText():
+        if ":" in ctx.getText():
+            num1 = int(ctx.INT(0).getText())
+            num2 = int(ctx.INT(1).getText()) + 1
+        else:
+            num1 = 1
+            num2 = int(ctx.INT(0).getText()) + 1
+
+        if ":" in ctx.getText():
+            if "," in ctx.getText():
+                num3 = int(ctx.INT(2).getText())
+                num4 = int(ctx.INT(3).getText()) + 1
+                for i in range(num1, num2):
+                    for j in range(num3, num4):
+                        self.symbol_table[name + str(i) + str(j)] = name + str(i) + str(j)
+                        self.type[name + str(i) + str(j)] = "constants"
+                        self.var_list.append(name + str(i) + str(j))
+                        self.sign[name + str(i) + str(j)] = "o"
+            else:
+                for i in range(num1, num2):
+                    self.symbol_table[name + str(i)] = name + str(i)
+                    self.type[name + str(i)] = "constants"
+                    self.var_list.append(name + str(i))
+                    self.sign[name + str(i)] = "o"
+
+        elif "," in ctx.getText():
+            for i in range(1, int(ctx.INT(0).getText()) + 1):
+                for j in range(1, int(ctx.INT(1).getText()) + 1):
+                    self.symbol_table[name] = name + str(i) + str(j)
+                    self.type[name + str(i) + str(j)] = "constants"
+                    self.var_list.append(name + str(i) + str(j))
+                    self.sign[name + str(i) + str(j)] = "o"
+
+        else:
+            for i in range(num1, num2):
+                self.symbol_table[name + str(i)] = name + str(i)
+                self.type[name + str(i)] = "constants"
+                self.var_list.append(name + str(i))
+                self.sign[name + str(i)] = "o"
+
+    if "{" not in ctx.getText():
+        self.var_list.append(name)
+
+
+def writeConstants(self, ctx):
+    l1 = list(filter(lambda x: self.sign[x] == "o", self.var_list))
+    l2 = list(filter(lambda x: self.sign[x] == "+", self.var_list))
+    l3 = list(filter(lambda x: self.sign[x] == "-", self.var_list))
+    try:
+        if self.settings["complex"] == "on":
+            real = ", real=True"
+        elif self.settings["complex"] == "off":
+            real = ""
+    except Exception:
+        real = ", real=True"
+
+    if l1:
+        a = ", ".join(l1) + " = " + "_sm.symbols(" + "'" +\
+            " ".join(l1) + "'" + real + ")\n"
+        self.write(a)
+    if l2:
+        a = ", ".join(l2) + " = " + "_sm.symbols(" + "'" +\
+            " ".join(l2) + "'" + real + ", nonnegative=True)\n"
+        self.write(a)
+    if l3:
+        a = ", ".join(l3) + " = " + "_sm.symbols(" + "'" + \
+            " ".join(l3) + "'" + real + ", nonpositive=True)\n"
+        self.write(a)
+    self.var_list = []
+
+
+def processVariables(self, ctx):
+    # Specified F = x*N1> + y*N2>
+    name = ctx.ID().getText().lower()
+    if "=" in ctx.getText():
+        text = name + "'"*(ctx.getChildCount()-3)
+        self.write(text + " = " + self.getValue(ctx.expr()) + "\n")
+        return
+
+    # Process variables of the type: Variables qA, qB
+    if ctx.getChildCount() == 1:
+        self.symbol_table[name] = name
+        if self.getValue(ctx.parentCtx.getChild(0)) in ("variable", "specified", "motionvariable", "motionvariable'"):
+            self.type.update({name: self.getValue(ctx.parentCtx.getChild(0))})
+
+        self.var_list.append(name)
+        self.sign[name] = 0
+
+    # Process variables of the type: Variables x', y''
+    elif "'" in ctx.getText() and "{" not in ctx.getText():
+        if ctx.getText().count("'") > self.maxDegree:
+            self.maxDegree = ctx.getText().count("'")
+        for i in range(ctx.getChildCount()):
+            self.sign[name + strfunc(i)] = i
+            self.symbol_table[name + "'"*i] = name + strfunc(i)
+            if self.getValue(ctx.parentCtx.getChild(0)) in ("variable", "specified", "motionvariable", "motionvariable'"):
+                self.type.update({name + "'"*i: self.getValue(ctx.parentCtx.getChild(0))})
+            self.var_list.append(name + strfunc(i))
+
+    elif "{" in ctx.getText():
+        # Process variables of the type: Variables x{3}, y{2}
+
+        if "'" in ctx.getText():
+            dash_count = ctx.getText().count("'")
+            if dash_count > self.maxDegree:
+                self.maxDegree = dash_count
+
+        if ":" in ctx.getText():
+            # Variables C{1:2, 1:2}
+            if "," in ctx.getText():
+                num1 = int(ctx.INT(0).getText())
+                num2 = int(ctx.INT(1).getText()) + 1
+                num3 = int(ctx.INT(2).getText())
+                num4 = int(ctx.INT(3).getText()) + 1
+            # Variables C{1:2}
+            else:
+                num1 = int(ctx.INT(0).getText())
+                num2 = int(ctx.INT(1).getText()) + 1
+
+        # Variables C{1,3}
+        elif "," in ctx.getText():
+            num1 = 1
+            num2 = int(ctx.INT(0).getText()) + 1
+            num3 = 1
+            num4 = int(ctx.INT(1).getText()) + 1
+        else:
+            num1 = 1
+            num2 = int(ctx.INT(0).getText()) + 1
+
+        for i in range(num1, num2):
+            try:
+                for j in range(num3, num4):
+                    try:
+                        for z in range(dash_count+1):
+                            self.symbol_table.update({name + str(i) + str(j) + "'"*z: name + str(i) + str(j) + strfunc(z)})
+                            if self.getValue(ctx.parentCtx.getChild(0)) in ("variable", "specified", "motionvariable", "motionvariable'"):
+                                self.type.update({name + str(i) + str(j) +  "'"*z: self.getValue(ctx.parentCtx.getChild(0))})
+                            self.var_list.append(name + str(i) + str(j) + strfunc(z))
+                            self.sign.update({name + str(i) + str(j) + strfunc(z): z})
+                            if dash_count > self.maxDegree:
+                                self.maxDegree = dash_count
+                    except Exception:
+                        self.symbol_table.update({name + str(i) + str(j): name + str(i) + str(j)})
+                        if self.getValue(ctx.parentCtx.getChild(0)) in ("variable", "specified", "motionvariable", "motionvariable'"):
+                            self.type.update({name + str(i) + str(j): self.getValue(ctx.parentCtx.getChild(0))})
+                        self.var_list.append(name + str(i) + str(j))
+                        self.sign.update({name + str(i) + str(j): 0})
+            except Exception:
+                try:
+                    for z in range(dash_count+1):
+                        self.symbol_table.update({name + str(i) + "'"*z: name + str(i) + strfunc(z)})
+                        if self.getValue(ctx.parentCtx.getChild(0)) in ("variable", "specified", "motionvariable", "motionvariable'"):
+                            self.type.update({name + str(i) +  "'"*z: self.getValue(ctx.parentCtx.getChild(0))})
+                        self.var_list.append(name + str(i) + strfunc(z))
+                        self.sign.update({name + str(i) + strfunc(z): z})
+                        if dash_count > self.maxDegree:
+                            self.maxDegree = dash_count
+                except Exception:
+                    self.symbol_table.update({name + str(i): name + str(i)})
+                    if self.getValue(ctx.parentCtx.getChild(0)) in ("variable", "specified", "motionvariable", "motionvariable'"):
+                        self.type.update({name + str(i): self.getValue(ctx.parentCtx.getChild(0))})
+                    self.var_list.append(name + str(i))
+                    self.sign.update({name + str(i): 0})
+
+def writeVariables(self, ctx):
+    #print(self.sign)
+    #print(self.symbol_table)
+    if self.var_list:
+        for i in range(self.maxDegree+1):
+            if i == 0:
+                j = ""
+                t = ""
+            else:
+                j = str(i)
+                t = ", "
+            l = []
+            for k in list(filter(lambda x: self.sign[x] == i, self.var_list)):
+                if i == 0:
+                    l.append(k)
+                if i == 1:
+                    l.append(k[:-1])
+                if i > 1:
+                    l.append(k[:-2])
+            a = ", ".join(list(filter(lambda x: self.sign[x] == i, self.var_list))) + " = " +\
+                "_me.dynamicsymbols(" + "'" + " ".join(l) + "'" + t + j + ")\n"
+            l = []
+            self.write(a)
+        self.maxDegree = 0
+    self.var_list = []
+
+def processImaginary(self, ctx):
+    name = ctx.ID().getText().lower()
+    self.symbol_table[name] = name
+    self.type[name] = "imaginary"
+    self.var_list.append(name)
+
+
+def writeImaginary(self, ctx):
+    a = ", ".join(self.var_list) + " = " + "_sm.symbols(" + "'" + \
+        " ".join(self.var_list) + "')\n"
+    b = ", ".join(self.var_list) + " = " + "_sm.I\n"
+    self.write(a)
+    self.write(b)
+    self.var_list = []
+
+if AutolevListener:
+    class MyListener(AutolevListener):  # type: ignore
+        def __init__(self, include_numeric=False):
+            # Stores data in tree nodes(tree annotation). Especially useful for expr reconstruction.
+            self.tree_property = {}
+
+            # Stores the declared variables, constants etc as they are declared in Autolev and SymPy
+            # {"": ""}.
+            self.symbol_table = collections.OrderedDict()
+
+            # Similar to symbol_table. Used for storing Physical entities like Frames, Points,
+            # Particles, Bodies etc
+            self.symbol_table2 = collections.OrderedDict()
+
+            # Used to store nonpositive, nonnegative etc for constants and number of "'"s (order of diff)
+            # in variables.
+            self.sign = {}
+
+            # Simple list used as a store to pass around variables between the 'process' and 'write'
+            # methods.
+            self.var_list = []
+
+            # Stores the type of a declared variable (constants, variables, specifieds etc)
+            self.type = collections.OrderedDict()
+
+            # Similar to self.type. Used for storing the type of Physical entities like Frames, Points,
+            # Particles, Bodies etc
+            self.type2 = collections.OrderedDict()
+
+            # These lists are used to distinguish matrix, numeric and vector expressions.
+            self.matrix_expr = []
+            self.numeric_expr = []
+            self.vector_expr = []
+            self.fr_expr = []
+
+            self.output_code = []
+
+            # Stores the variables and their rhs for substituting upon the Autolev command EXPLICIT.
+            self.explicit = collections.OrderedDict()
+
+            # Write code to import common dependencies.
+            self.output_code.append("import sympy.physics.mechanics as _me\n")
+            self.output_code.append("import sympy as _sm\n")
+            self.output_code.append("import math as m\n")
+            self.output_code.append("import numpy as _np\n")
+            self.output_code.append("\n")
+
+            # Just a store for the max degree variable in a line.
+            self.maxDegree = 0
+
+            # Stores the input parameters which are then used for codegen and numerical analysis.
+            self.inputs = collections.OrderedDict()
+            # Stores the variables which appear in Output Autolev commands.
+            self.outputs = []
+            # Stores the settings specified by the user. Ex: Complex on/off, Degrees on/off
+            self.settings = {}
+            # Boolean which changes the behaviour of some expression reconstruction
+            # when parsing Input Autolev commands.
+            self.in_inputs = False
+            self.in_outputs = False
+
+            # Stores for the physical entities.
+            self.newtonian = None
+            self.bodies = collections.OrderedDict()
+            self.constants = []
+            self.forces = collections.OrderedDict()
+            self.q_ind = []
+            self.q_dep = []
+            self.u_ind = []
+            self.u_dep = []
+            self.kd_eqs = []
+            self.dependent_variables = []
+            self.kd_equivalents = collections.OrderedDict()
+            self.kd_equivalents2 = collections.OrderedDict()
+            self.kd_eqs_supplied = None
+            self.kane_type = "no_args"
+            self.inertia_point = collections.OrderedDict()
+            self.kane_parsed = False
+            self.t = False
+
+            # PyDy ode code will be included only if this flag is set to True.
+            self.include_numeric = include_numeric
+
+        def write(self, string):
+            self.output_code.append(string)
+
+        def getValue(self, node):
+            return self.tree_property[node]
+
+        def setValue(self, node, value):
+            self.tree_property[node] = value
+
+        def getSymbolTable(self):
+            return self.symbol_table
+
+        def getType(self):
+            return self.type
+
+        def exitVarDecl(self, ctx):
+            # This event method handles variable declarations. The parse tree node varDecl contains
+            # one or more varDecl2 nodes. Eg varDecl for 'Constants a{1:2, 1:2}, b{1:2}' has two varDecl2
+            # nodes(one for a{1:2, 1:2} and one for b{1:2}).
+
+            # Variable declarations are processed and stored in the event method exitVarDecl2.
+            # This stored information is used to write the final SymPy output code in the exitVarDecl event method.
+
+            # determine the type of declaration
+            if self.getValue(ctx.varType()) == "constant":
+                writeConstants(self, ctx)
+            elif self.getValue(ctx.varType()) in\
+            ("variable", "motionvariable", "motionvariable'", "specified"):
+                writeVariables(self, ctx)
+            elif self.getValue(ctx.varType()) == "imaginary":
+                writeImaginary(self, ctx)
+
+        def exitVarType(self, ctx):
+            # Annotate the varType tree node with the type of the variable declaration.
+            name = ctx.getChild(0).getText().lower()
+            if name[-1] == "s" and name != "bodies":
+                self.setValue(ctx, name[:-1])
+            else:
+                self.setValue(ctx, name)
+
+        def exitVarDecl2(self, ctx):
+            # Variable declarations are processed and stored in the event method exitVarDecl2.
+            # This stored information is used to write the final SymPy output code in the exitVarDecl event method.
+            # This is the case for constants, variables, specifieds etc.
+
+            # This isn't the case for all types of declarations though. For instance
+            # Frames A, B, C, N cannot be defined on one line in SymPy. So we do not append A, B, C, N
+            # to a var_list or use exitVarDecl. exitVarDecl2 directly writes out to the file.
+
+            # determine the type of declaration
+            if self.getValue(ctx.parentCtx.varType()) == "constant":
+                processConstants(self, ctx)
+
+            elif self.getValue(ctx.parentCtx.varType()) in \
+            ("variable", "motionvariable", "motionvariable'", "specified"):
+                processVariables(self, ctx)
+
+            elif self.getValue(ctx.parentCtx.varType()) == "imaginary":
+                processImaginary(self, ctx)
+
+            elif self.getValue(ctx.parentCtx.varType()) in ("frame", "newtonian", "point", "particle", "bodies"):
+                if "{" in ctx.getText():
+                    if ":" in ctx.getText() and "," not in ctx.getText():
+                        num1 = int(ctx.INT(0).getText())
+                        num2 = int(ctx.INT(1).getText()) + 1
+                    elif ":" not in ctx.getText() and "," in ctx.getText():
+                        num1 = 1
+                        num2 = int(ctx.INT(0).getText()) + 1
+                        num3 = 1
+                        num4 = int(ctx.INT(1).getText()) + 1
+                    elif ":" in ctx.getText() and "," in ctx.getText():
+                        num1 = int(ctx.INT(0).getText())
+                        num2 = int(ctx.INT(1).getText()) + 1
+                        num3 = int(ctx.INT(2).getText())
+                        num4 = int(ctx.INT(3).getText()) + 1
+                    else:
+                        num1 = 1
+                        num2 = int(ctx.INT(0).getText()) + 1
+                else:
+                    num1 = 1
+                    num2 = 2
+                for i in range(num1, num2):
+                    try:
+                        for j in range(num3, num4):
+                            declare_phy_entities(self, ctx, self.getValue(ctx.parentCtx.varType()), i, j)
+                    except Exception:
+                        declare_phy_entities(self, ctx, self.getValue(ctx.parentCtx.varType()), i)
+        # ================== Subrules of parser rule expr (Start) ====================== #
+
+        def exitId(self, ctx):
+            # Tree annotation for ID which is a labeled subrule of the parser rule expr.
+            # A_C
+            python_keywords = ["and", "as", "assert", "break", "class", "continue", "def", "del", "elif", "else", "except",\
+            "exec", "finally", "for", "from", "global", "if", "import", "in", "is", "lambda", "not", "or", "pass", "print",\
+            "raise", "return", "try", "while", "with", "yield"]
+
+            if ctx.ID().getText().lower() in python_keywords:
+                warnings.warn("Python keywords must not be used as identifiers. Please refer to the list of keywords at https://docs.python.org/2.5/ref/keywords.html",
+                SyntaxWarning)
+
+            if "_" in ctx.ID().getText() and ctx.ID().getText().count('_') == 1:
+                e1, e2 = ctx.ID().getText().lower().split('_')
+                try:
+                    if self.type2[e1] == "frame":
+                        e1 = self.symbol_table2[e1]
+                    elif self.type2[e1] == "bodies":
+                        e1 = self.symbol_table2[e1] + "_f"
+                    if self.type2[e2] == "frame":
+                        e2 = self.symbol_table2[e2]
+                    elif self.type2[e2] == "bodies":
+                        e2 = self.symbol_table2[e2] + "_f"
+
+                    self.setValue(ctx, e1 + ".dcm(" + e2 + ")")
+                except Exception:
+                    self.setValue(ctx, ctx.ID().getText().lower())
+            else:
+                # Reserved constant Pi
+                if ctx.ID().getText().lower() == "pi":
+                    self.setValue(ctx, "_sm.pi")
+                    self.numeric_expr.append(ctx)
+
+                # Reserved variable T (for time)
+                elif ctx.ID().getText().lower() == "t":
+                    self.setValue(ctx, "_me.dynamicsymbols._t")
+                    if not self.in_inputs and not self.in_outputs:
+                        self.t = True
+
+                else:
+                    idText = ctx.ID().getText().lower() + "'"*(ctx.getChildCount() - 1)
+                    if idText in self.type.keys() and self.type[idText] == "matrix":
+                        self.matrix_expr.append(ctx)
+                    if self.in_inputs:
+                        try:
+                            self.setValue(ctx, self.symbol_table[idText])
+                        except Exception:
+                            self.setValue(ctx, idText.lower())
+                    else:
+                        try:
+                            self.setValue(ctx, self.symbol_table[idText])
+                        except Exception:
+                            pass
+
+        def exitInt(self, ctx):
+            # Tree annotation for int which is a labeled subrule of the parser rule expr.
+            int_text = ctx.INT().getText()
+            self.setValue(ctx, int_text)
+            self.numeric_expr.append(ctx)
+
+        def exitFloat(self, ctx):
+            # Tree annotation for float which is a labeled subrule of the parser rule expr.
+            floatText = ctx.FLOAT().getText()
+            self.setValue(ctx, floatText)
+            self.numeric_expr.append(ctx)
+
+        def exitAddSub(self, ctx):
+            # Tree annotation for AddSub which is a labeled subrule of the parser rule expr.
+            # The subrule is expr = expr (+|-) expr
+            if ctx.expr(0) in self.matrix_expr or ctx.expr(1) in self.matrix_expr:
+                self.matrix_expr.append(ctx)
+            if ctx.expr(0) in self.vector_expr or ctx.expr(1) in self.vector_expr:
+                self.vector_expr.append(ctx)
+            if ctx.expr(0) in self.numeric_expr and ctx.expr(1) in self.numeric_expr:
+                self.numeric_expr.append(ctx)
+            self.setValue(ctx, self.getValue(ctx.expr(0)) + ctx.getChild(1).getText() +
+                          self.getValue(ctx.expr(1)))
+
+        def exitMulDiv(self, ctx):
+            # Tree annotation for MulDiv which is a labeled subrule of the parser rule expr.
+            # The subrule is expr = expr (*|/) expr
+            try:
+                if ctx.expr(0) in self.vector_expr and ctx.expr(1) in self.vector_expr:
+                    self.setValue(ctx, "_me.outer(" + self.getValue(ctx.expr(0)) + ", " +
+                                  self.getValue(ctx.expr(1)) + ")")
+                else:
+                    if ctx.expr(0) in self.matrix_expr or ctx.expr(1) in self.matrix_expr:
+                        self.matrix_expr.append(ctx)
+                    if ctx.expr(0) in self.vector_expr or ctx.expr(1) in self.vector_expr:
+                        self.vector_expr.append(ctx)
+                    if ctx.expr(0) in self.numeric_expr and ctx.expr(1) in self.numeric_expr:
+                        self.numeric_expr.append(ctx)
+                    self.setValue(ctx, self.getValue(ctx.expr(0)) + ctx.getChild(1).getText() +
+                                  self.getValue(ctx.expr(1)))
+            except Exception:
+                pass
+
+        def exitNegativeOne(self, ctx):
+            # Tree annotation for negativeOne which is a labeled subrule of the parser rule expr.
+            self.setValue(ctx, "-1*" + self.getValue(ctx.getChild(1)))
+            if ctx.getChild(1) in self.matrix_expr:
+                self.matrix_expr.append(ctx)
+            if ctx.getChild(1) in self.numeric_expr:
+                self.numeric_expr.append(ctx)
+
+        def exitParens(self, ctx):
+            # Tree annotation for parens which is a labeled subrule of the parser rule expr.
+            # The subrule is expr = '(' expr ')'
+            if ctx.expr() in self.matrix_expr:
+                self.matrix_expr.append(ctx)
+            if ctx.expr() in self.vector_expr:
+                self.vector_expr.append(ctx)
+            if ctx.expr() in self.numeric_expr:
+                self.numeric_expr.append(ctx)
+            self.setValue(ctx, "(" + self.getValue(ctx.expr()) + ")")
+
+        def exitExponent(self, ctx):
+            # Tree annotation for Exponent which is a labeled subrule of the parser rule expr.
+            # The subrule is expr = expr ^ expr
+            if ctx.expr(0) in self.matrix_expr or ctx.expr(1) in self.matrix_expr:
+                self.matrix_expr.append(ctx)
+            if ctx.expr(0) in self.vector_expr or ctx.expr(1) in self.vector_expr:
+                self.vector_expr.append(ctx)
+            if ctx.expr(0) in self.numeric_expr and ctx.expr(1) in self.numeric_expr:
+                self.numeric_expr.append(ctx)
+            self.setValue(ctx, self.getValue(ctx.expr(0)) + "**" + self.getValue(ctx.expr(1)))
+
+        def exitExp(self, ctx):
+            s = ctx.EXP().getText()[ctx.EXP().getText().index('E')+1:]
+            if "-" in s:
+                s = s[0] + s[1:].lstrip("0")
+            else:
+                s = s.lstrip("0")
+            self.setValue(ctx, ctx.EXP().getText()[:ctx.EXP().getText().index('E')] +
+                          "*10**(" + s + ")")
+
+        def exitFunction(self, ctx):
+            # Tree annotation for function which is a labeled subrule of the parser rule expr.
+
+            # The difference between this and FunctionCall is that this is used for non standalone functions
+            # appearing in expressions and assignments.
+            # Eg:
+            # When we come across a standalone function say Expand(E, n:m) then it is categorized as FunctionCall
+            # which is a parser rule in itself under rule stat. exitFunctionCall() takes care of it and writes to the file.
+            #
+            # On the other hand, while we come across E_diff = D(E, y), we annotate the tree node
+            # of the function D(E, y) with the SymPy equivalent in exitFunction().
+            # In this case it is the method exitAssignment() that writes the code to the file and not exitFunction().
+
+            ch = ctx.getChild(0)
+            func_name = ch.getChild(0).getText().lower()
+
+            # Expand(y, n:m) *
+            if func_name == "expand":
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    # _sm.Matrix([i.expand() for i in z]).reshape(z.shape[0], z.shape[1])
+                    self.setValue(ctx, "_sm.Matrix([i.expand() for i in " + expr + "])" +
+                                  ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    self.setValue(ctx, "(" + expr + ")" + "." + "expand()")
+
+            # Factor(y, x) *
+            elif func_name == "factor":
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([_sm.factor(i, " + self.getValue(ch.expr(1)) + ") for i in " +
+                                  expr + "])" + ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    self.setValue(ctx, "_sm.factor(" + "(" + expr + ")" +
+                                  ", " + self.getValue(ch.expr(1)) + ")")
+
+            # D(y, x)
+            elif func_name == "d":
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([i.diff(" + self.getValue(ch.expr(1)) + ") for i in " +
+                                  expr + "])" + ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    if ch.getChildCount() == 8:
+                        frame = self.symbol_table2[ch.expr(2).getText().lower()]
+                        self.setValue(ctx, "(" + expr + ")" + "." + "diff(" + self.getValue(ch.expr(1)) +
+                                      ", " + frame + ")")
+                    else:
+                        self.setValue(ctx, "(" + expr + ")" + "." + "diff(" +
+                                      self.getValue(ch.expr(1)) + ")")
+
+            # Dt(y)
+            elif func_name == "dt":
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.vector_expr:
+                    text = "dt("
+                else:
+                    text = "diff(_sm.Symbol('t')"
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([i." + text +
+                                  ") for i in " + expr + "])" +
+                                  ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    if ch.getChildCount() == 6:
+                        frame = self.symbol_table2[ch.expr(1).getText().lower()]
+                        self.setValue(ctx, "(" + expr + ")" + "." + "dt(" +
+                                      frame + ")")
+                    else:
+                        self.setValue(ctx, "(" + expr + ")" + "." + text + ")")
+
+            # Explicit(EXPRESS(IMPLICIT>,C))
+            elif func_name == "explicit":
+                if ch.expr(0) in self.vector_expr:
+                    self.vector_expr.append(ctx)
+                expr = self.getValue(ch.expr(0))
+                if self.explicit.keys():
+                    explicit_list = []
+                    for i in self.explicit.keys():
+                        explicit_list.append(i + ":" + self.explicit[i])
+                    self.setValue(ctx, "(" + expr + ")" + ".subs({" + ", ".join(explicit_list) + "})")
+                else:
+                    self.setValue(ctx, expr)
+
+            # Taylor(y, 0:2, w=a, x=0)
+            # TODO: Currently only works with symbols. Make it work for dynamicsymbols.
+            elif func_name == "taylor":
+                exp = self.getValue(ch.expr(0))
+                order = self.getValue(ch.expr(1).expr(1))
+                x = (ch.getChildCount()-6)//2
+                l = []
+                for i in range(x):
+                    index = 2 + i
+                    child = ch.expr(index)
+                    l.append(".series(" + self.getValue(child.getChild(0)) +
+                             ", " + self.getValue(child.getChild(2)) +
+                             ", " + order + ").removeO()")
+                self.setValue(ctx, "(" + exp + ")" + "".join(l))
+
+            # Evaluate(y, a=x, b=2)
+            elif func_name == "evaluate":
+                expr = self.getValue(ch.expr(0))
+                l = []
+                x = (ch.getChildCount()-4)//2
+                for i in range(x):
+                    index = 1 + i
+                    child = ch.expr(index)
+                    l.append(self.getValue(child.getChild(0)) + ":" +
+                             self.getValue(child.getChild(2)))
+
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([i.subs({" + ",".join(l) + "}) for i in " +
+                                  expr + "])" +
+                                  ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    if self.explicit:
+                        explicit_list = []
+                        for i in self.explicit.keys():
+                            explicit_list.append(i + ":" + self.explicit[i])
+                        self.setValue(ctx, "(" + expr + ")" + ".subs({" + ",".join(explicit_list) +
+                                      "}).subs({" + ",".join(l) + "})")
+                    else:
+                        self.setValue(ctx, "(" + expr + ")" + ".subs({" + ",".join(l) + "})")
+
+            # Polynomial([a, b, c], x)
+            elif func_name == "polynomial":
+                self.setValue(ctx, "_sm.Poly(" + self.getValue(ch.expr(0)) + ", " +
+                              self.getValue(ch.expr(1)) + ")")
+
+            # Roots(Poly, x, 2)
+            # Roots([1; 2; 3; 4])
+            elif func_name == "roots":
+                self.matrix_expr.append(ctx)
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.setValue(ctx, "[i.evalf() for i in " + "_sm.solve(" +
+                                  "_sm.Poly(" + expr + ", " + "x),x)]")
+                else:
+                    self.setValue(ctx, "[i.evalf() for i in " + "_sm.solve(" +
+                                  expr + ", " + self.getValue(ch.expr(1)) + ")]")
+
+            # Transpose(A), Inv(A)
+            elif func_name in ("transpose", "inv", "inverse"):
+                self.matrix_expr.append(ctx)
+                if func_name == "transpose":
+                    e = ".T"
+                elif func_name in ("inv", "inverse"):
+                    e = "**(-1)"
+                self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" + e)
+
+            # Eig(A)
+            elif func_name == "eig":
+                # "_sm.Matrix([i.evalf() for i in " +
+                self.setValue(ctx, "_sm.Matrix([i.evalf() for i in (" +
+                              self.getValue(ch.expr(0)) + ").eigenvals().keys()])")
+
+            # Diagmat(n, m, x)
+            # Diagmat(3, 1)
+            elif func_name == "diagmat":
+                self.matrix_expr.append(ctx)
+                if ch.getChildCount() == 6:
+                    l = []
+                    for i in range(int(self.getValue(ch.expr(0)))):
+                        l.append(self.getValue(ch.expr(1)) + ",")
+
+                    self.setValue(ctx, "_sm.diag(" + ("".join(l))[:-1] + ")")
+
+                elif ch.getChildCount() == 8:
+                    # _sm.Matrix([x if i==j else 0 for i in range(n) for j in range(m)]).reshape(n, m)
+                    n = self.getValue(ch.expr(0))
+                    m = self.getValue(ch.expr(1))
+                    x = self.getValue(ch.expr(2))
+                    self.setValue(ctx, "_sm.Matrix([" + x + " if i==j else 0 for i in range(" +
+                                  n + ") for j in range(" + m + ")]).reshape(" + n + ", " + m + ")")
+
+            # Cols(A)
+            # Cols(A, 1)
+            # Cols(A, 1, 2:4, 3)
+            elif func_name in ("cols", "rows"):
+                self.matrix_expr.append(ctx)
+                if func_name == "cols":
+                    e1 = ".cols"
+                    e2 = ".T."
+                else:
+                    e1 = ".rows"
+                    e2 = "."
+                if ch.getChildCount() == 4:
+                    self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" + e1)
+                elif ch.getChildCount() == 6:
+                    self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" +
+                                  e1[:-1] + "(" + str(int(self.getValue(ch.expr(1))) - 1) + ")")
+                else:
+                    l = []
+                    for i in range(4, ch.getChildCount()):
+                        try:
+                            if ch.getChild(i).getChildCount() > 1 and ch.getChild(i).getChild(1).getText() == ":":
+                                for j in range(int(ch.getChild(i).getChild(0).getText()),
+                                int(ch.getChild(i).getChild(2).getText())+1):
+                                    l.append("(" + self.getValue(ch.getChild(2)) + ")" + e2 +
+                                             "row(" + str(j-1) + ")")
+                            else:
+                                l.append("(" + self.getValue(ch.getChild(2)) + ")" + e2 +
+                                         "row(" + str(int(ch.getChild(i).getText())-1) + ")")
+                        except Exception:
+                            pass
+                    self.setValue(ctx, "_sm.Matrix([" + ",".join(l) + "])")
+
+            # Det(A) Trace(A)
+            elif func_name in ["det", "trace"]:
+                self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" + "." +
+                              func_name + "()")
+
+            # Element(A, 2, 3)
+            elif func_name == "element":
+                self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" + "[" +
+                              str(int(self.getValue(ch.expr(1)))-1) + "," +
+                              str(int(self.getValue(ch.expr(2)))-1) + "]")
+
+            elif func_name in \
+            ["cos", "sin", "tan", "cosh", "sinh", "tanh", "acos", "asin", "atan",
+            "log", "exp", "sqrt", "factorial", "floor", "sign"]:
+                self.setValue(ctx, "_sm." + func_name + "(" + self.getValue(ch.expr(0)) + ")")
+
+            elif func_name == "ceil":
+                self.setValue(ctx, "_sm.ceiling" + "(" + self.getValue(ch.expr(0)) + ")")
+
+            elif func_name == "sqr":
+                self.setValue(ctx, "(" + self.getValue(ch.expr(0)) +
+                              ")" + "**2")
+
+            elif func_name == "log10":
+                self.setValue(ctx, "_sm.log" +
+                              "(" + self.getValue(ch.expr(0)) + ", 10)")
+
+            elif func_name == "atan2":
+                self.setValue(ctx, "_sm.atan2" + "(" + self.getValue(ch.expr(0)) + ", " +
+                              self.getValue(ch.expr(1)) + ")")
+
+            elif func_name in ["int", "round"]:
+                self.setValue(ctx, func_name +
+                              "(" + self.getValue(ch.expr(0)) + ")")
+
+            elif func_name == "abs":
+                self.setValue(ctx, "_sm.Abs(" + self.getValue(ch.expr(0)) + ")")
+
+            elif func_name in ["max", "min"]:
+                # max(x, y, z)
+                l = []
+                for i in range(1, ch.getChildCount()):
+                    if ch.getChild(i) in self.tree_property.keys():
+                        l.append(self.getValue(ch.getChild(i)))
+                    elif ch.getChild(i).getText() in [",", "(", ")"]:
+                        l.append(ch.getChild(i).getText())
+                self.setValue(ctx, "_sm." + ch.getChild(0).getText().capitalize() + "".join(l))
+
+            # Coef(y, x)
+            elif func_name == "coef":
+                #A41_A53=COEF([RHS(U4);RHS(U5)],[U1,U2,U3])
+                if ch.expr(0) in self.matrix_expr and ch.expr(1) in self.matrix_expr:
+                    icount = jcount = 0
+                    for i in range(ch.expr(0).getChild(0).getChildCount()):
+                        try:
+                            ch.expr(0).getChild(0).getChild(i).getRuleIndex()
+                            icount+=1
+                        except Exception:
+                            pass
+                    for j in range(ch.expr(1).getChild(0).getChildCount()):
+                        try:
+                            ch.expr(1).getChild(0).getChild(j).getRuleIndex()
+                            jcount+=1
+                        except Exception:
+                            pass
+                    l = []
+                    for i in range(icount):
+                        for j in range(jcount):
+                            # a41_a53[i,j] = u4.expand().coeff(u1)
+                            l.append(self.getValue(ch.expr(0).getChild(0).expr(i)) + ".expand().coeff("
+                                     + self.getValue(ch.expr(1).getChild(0).expr(j)) + ")")
+                    self.setValue(ctx, "_sm.Matrix([" + ", ".join(l) + "]).reshape(" + str(icount) + ", " + str(jcount) + ")")
+                else:
+                    self.setValue(ctx, "(" + self.getValue(ch.expr(0)) +
+                                  ")" + ".expand().coeff(" + self.getValue(ch.expr(1)) + ")")
+
+            # Exclude(y, x) Include(y, x)
+            elif func_name in ("exclude", "include"):
+                if func_name == "exclude":
+                    e = "0"
+                else:
+                    e = "1"
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([i.collect(" + self.getValue(ch.expr(1)) + "])" +
+                                  ".coeff(" + self.getValue(ch.expr(1)) + "," + e + ")" + "for i in " + expr + ")" +
+                                  ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    self.setValue(ctx, "(" + expr +
+                                  ")" + ".collect(" + self.getValue(ch.expr(1)) + ")" +
+                                  ".coeff(" + self.getValue(ch.expr(1)) + "," + e + ")")
+
+            # RHS(y)
+            elif func_name == "rhs":
+                self.setValue(ctx, self.explicit[self.getValue(ch.expr(0))])
+
+            # Arrange(y, n, x) *
+            elif func_name == "arrange":
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([i.collect(" + self.getValue(ch.expr(2)) +
+                                  ")" + "for i in " + expr + "])"+
+                                  ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    self.setValue(ctx, "(" + expr +
+                                  ")" + ".collect(" + self.getValue(ch.expr(2)) + ")")
+
+            # Replace(y, sin(x)=3)
+            elif func_name == "replace":
+                l = []
+                for i in range(1, ch.getChildCount()):
+                    try:
+                        if ch.getChild(i).getChild(1).getText() == "=":
+                            l.append(self.getValue(ch.getChild(i).getChild(0)) +
+                                     ":" + self.getValue(ch.getChild(i).getChild(2)))
+                    except Exception:
+                        pass
+                expr = self.getValue(ch.expr(0))
+                if ch.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                    self.matrix_expr.append(ctx)
+                    self.setValue(ctx, "_sm.Matrix([i.subs({" + ",".join(l) + "}) for i in " +
+                                  expr + "])" +
+                                  ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])")
+                else:
+                    self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" +
+                                  ".subs({" + ",".join(l) + "})")
+
+            # Dot(Loop>, N1>)
+            elif func_name == "dot":
+                l = []
+                num = (ch.expr(1).getChild(0).getChildCount()-1)//2
+                if ch.expr(1) in self.matrix_expr:
+                    for i in range(num):
+                        l.append("_me.dot(" + self.getValue(ch.expr(0)) + ", " + self.getValue(ch.expr(1).getChild(0).expr(i)) + ")")
+                    self.setValue(ctx, "_sm.Matrix([" + ",".join(l) + "]).reshape(" + str(num) + ", " + "1)")
+                else:
+                    self.setValue(ctx, "_me.dot(" + self.getValue(ch.expr(0)) + ", " + self.getValue(ch.expr(1)) + ")")
+            # Cross(w_A_N>, P_NA_AB>)
+            elif func_name == "cross":
+                self.vector_expr.append(ctx)
+                self.setValue(ctx, "_me.cross(" + self.getValue(ch.expr(0)) + ", " + self.getValue(ch.expr(1)) + ")")
+
+            # Mag(P_O_Q>)
+            elif func_name == "mag":
+                self.setValue(ctx, self.getValue(ch.expr(0)) + "." + "magnitude()")
+
+            # MATRIX(A, I_R>>)
+            elif func_name == "matrix":
+                if self.type2[ch.expr(0).getText().lower()] == "frame":
+                    text = ""
+                elif self.type2[ch.expr(0).getText().lower()] == "bodies":
+                    text = "_f"
+                self.setValue(ctx, "(" + self.getValue(ch.expr(1)) + ")" + ".to_matrix(" +
+                              self.symbol_table2[ch.expr(0).getText().lower()] + text + ")")
+
+            # VECTOR(A, ROWS(EIGVECS,1))
+            elif func_name == "vector":
+                if self.type2[ch.expr(0).getText().lower()] == "frame":
+                    text = ""
+                elif self.type2[ch.expr(0).getText().lower()] == "bodies":
+                    text = "_f"
+                v = self.getValue(ch.expr(1))
+                f = self.symbol_table2[ch.expr(0).getText().lower()] + text
+                self.setValue(ctx, v + "[0]*" + f + ".x +" + v + "[1]*" + f + ".y +" +
+                              v + "[2]*" + f + ".z")
+
+            # Express(A2>, B)
+            # Here I am dealing with all the Inertia commands as I expect the users to use Inertia
+            # commands only with Express because SymPy needs the Reference frame to be specified unlike Autolev.
+            elif func_name == "express":
+                self.vector_expr.append(ctx)
+                if self.type2[ch.expr(1).getText().lower()] == "frame":
+                    frame = self.symbol_table2[ch.expr(1).getText().lower()]
+                else:
+                    frame = self.symbol_table2[ch.expr(1).getText().lower()] + "_f"
+                if ch.expr(0).getText().lower() == "1>>":
+                    self.setValue(ctx, "_me.inertia(" + frame + ", 1, 1, 1)")
+
+                elif '_' in ch.expr(0).getText().lower() and ch.expr(0).getText().lower().count('_') == 2\
+                and ch.expr(0).getText().lower()[0] == "i" and ch.expr(0).getText().lower()[-2:] == ">>":
+                    v1 = ch.expr(0).getText().lower()[:-2].split('_')[1]
+                    v2 = ch.expr(0).getText().lower()[:-2].split('_')[2]
+                    l = []
+                    inertia_func(self, v1, v2, l, frame)
+                    self.setValue(ctx, " + ".join(l))
+
+                elif ch.expr(0).getChild(0).getChild(0).getText().lower() == "inertia":
+                    if ch.expr(0).getChild(0).getChildCount() == 4:
+                        l = []
+                        v2 = ch.expr(0).getChild(0).ID(0).getText().lower()
+                        for v1 in self.bodies:
+                            inertia_func(self, v1, v2, l, frame)
+                        self.setValue(ctx, " + ".join(l))
+
+                    else:
+                        l = []
+                        l2 = []
+                        v2 = ch.expr(0).getChild(0).ID(0).getText().lower()
+                        for i in range(1, (ch.expr(0).getChild(0).getChildCount()-2)//2):
+                            l2.append(ch.expr(0).getChild(0).ID(i).getText().lower())
+                        for v1 in l2:
+                            inertia_func(self, v1, v2, l, frame)
+                        self.setValue(ctx, " + ".join(l))
+
+                else:
+                    self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" + ".express(" +
+                                  self.symbol_table2[ch.expr(1).getText().lower()] + ")")
+            # CM(P)
+            elif func_name == "cm":
+                if self.type2[ch.expr(0).getText().lower()] == "point":
+                    text = ""
+                else:
+                    text = ".point"
+                if ch.getChildCount() == 4:
+                    self.setValue(ctx, "_me.functions.center_of_mass(" + self.symbol_table2[ch.expr(0).getText().lower()] +
+                                  text + "," + ", ".join(self.bodies.values()) + ")")
+                else:
+                    bodies = []
+                    for i in range(1, (ch.getChildCount()-1)//2):
+                        bodies.append(self.symbol_table2[ch.expr(i).getText().lower()])
+                    self.setValue(ctx, "_me.functions.center_of_mass(" + self.symbol_table2[ch.expr(0).getText().lower()] +
+                                  text + "," + ", ".join(bodies) + ")")
+
+            # PARTIALS(V_P1_E>,U1)
+            elif func_name == "partials":
+                speeds = []
+                for i in range(1, (ch.getChildCount()-1)//2):
+                    if self.kd_equivalents2:
+                        speeds.append(self.kd_equivalents2[self.symbol_table[ch.expr(i).getText().lower()]])
+                    else:
+                        speeds.append(self.symbol_table[ch.expr(i).getText().lower()])
+                v1, v2, v3 = ch.expr(0).getText().lower().replace(">","").split('_')
+                if self.type2[v2] == "point":
+                    point = self.symbol_table2[v2]
+                elif self.type2[v2] == "particle":
+                    point = self.symbol_table2[v2] + ".point"
+                frame = self.symbol_table2[v3]
+                self.setValue(ctx, point + ".partial_velocity(" + frame + ", " + ",".join(speeds) + ")")
+
+            # UnitVec(A1>+A2>+A3>)
+            elif func_name == "unitvec":
+                self.setValue(ctx, "(" + self.getValue(ch.expr(0)) + ")" + ".normalize()")
+
+            # Units(deg, rad)
+            elif func_name == "units":
+                if ch.expr(0).getText().lower() == "deg" and ch.expr(1).getText().lower() == "rad":
+                    factor = 0.0174533
+                elif ch.expr(0).getText().lower() == "rad" and ch.expr(1).getText().lower() == "deg":
+                    factor = 57.2958
+                self.setValue(ctx, str(factor))
+            # Mass(A)
+            elif func_name == "mass":
+                l = []
+                try:
+                    ch.ID(0).getText().lower()
+                    for i in range((ch.getChildCount()-1)//2):
+                        l.append(self.symbol_table2[ch.ID(i).getText().lower()] + ".mass")
+                    self.setValue(ctx, "+".join(l))
+                except Exception:
+                    for i in self.bodies.keys():
+                        l.append(self.bodies[i] + ".mass")
+                    self.setValue(ctx, "+".join(l))
+
+            # Fr() FrStar()
+            # _me.KanesMethod(n, q_ind, u_ind, kd, velocity_constraints).kanes_equations(pl, fl)[0]
+            elif func_name in ["fr", "frstar"]:
+                if not self.kane_parsed:
+                    if self.kd_eqs:
+                        for i in self.kd_eqs:
+                            self.q_ind.append(self.symbol_table[i.strip().split('-')[0].replace("'","")])
+                            self.u_ind.append(self.symbol_table[i.strip().split('-')[1].replace("'","")])
+
+                    for i in range(len(self.kd_eqs)):
+                        self.kd_eqs[i] = self.symbol_table[self.kd_eqs[i].strip().split('-')[0]] + " - " +\
+                                         self.symbol_table[self.kd_eqs[i].strip().split('-')[1]]
+
+                    # Do all of this if kd_eqs are not specified
+                    if not self.kd_eqs:
+                        self.kd_eqs_supplied = False
+                        self.matrix_expr.append(ctx)
+                        for i in self.type.keys():
+                            if self.type[i] == "motionvariable":
+                                if self.sign[self.symbol_table[i.lower()]] == 0:
+                                    self.q_ind.append(self.symbol_table[i.lower()])
+                                elif self.sign[self.symbol_table[i.lower()]] == 1:
+                                    name = "u_" + self.symbol_table[i.lower()]
+                                    self.symbol_table.update({name: name})
+                                    self.write(name + " = " + "_me.dynamicsymbols('" + name + "')\n")
+                                    if self.symbol_table[i.lower()] not in self.dependent_variables:
+                                        self.u_ind.append(name)
+                                        self.kd_equivalents.update({name: self.symbol_table[i.lower()]})
+                                    else:
+                                        self.u_dep.append(name)
+                                        self.kd_equivalents.update({name: self.symbol_table[i.lower()]})
+
+                        for i in self.kd_equivalents.keys():
+                            self.kd_eqs.append(self.kd_equivalents[i] + "-" + i)
+
+                    if not self.u_ind and not self.kd_eqs:
+                        self.u_ind = self.q_ind.copy()
+                        self.q_ind = []
+
+                # deal with velocity constraints
+                if self.dependent_variables:
+                    for i in self.dependent_variables:
+                        self.u_dep.append(i)
+                        if i in self.u_ind:
+                            self.u_ind.remove(i)
+
+
+                self.u_dep[:] = [i for i in self.u_dep if i not in self.kd_equivalents.values()]
+
+                force_list = []
+                for i in self.forces.keys():
+                    force_list.append("(" + i + "," + self.forces[i] + ")")
+                if self.u_dep:
+                    u_dep_text = ", u_dependent=[" + ", ".join(self.u_dep) + "]"
+                else:
+                    u_dep_text = ""
+                if self.dependent_variables:
+                    velocity_constraints_text = ", velocity_constraints = velocity_constraints"
+                else:
+                    velocity_constraints_text = ""
+                if ctx.parentCtx not in self.fr_expr:
+                    self.write("kd_eqs = [" + ", ".join(self.kd_eqs) + "]\n")
+                    self.write("forceList = " + "[" + ", ".join(force_list) + "]\n")
+                    self.write("kane = _me.KanesMethod(" + self.newtonian + ", " + "q_ind=[" +
+                            ",".join(self.q_ind) + "], " + "u_ind=[" +
+                            ", ".join(self.u_ind) + "]" + u_dep_text + ", " +
+                            "kd_eqs = kd_eqs" + velocity_constraints_text + ")\n")
+                    self.write("fr, frstar = kane." + "kanes_equations([" +
+                                ", ".join(self.bodies.values()) + "], forceList)\n")
+                    self.fr_expr.append(ctx.parentCtx)
+                self.kane_parsed = True
+                self.setValue(ctx, func_name)
+
+        def exitMatrices(self, ctx):
+            # Tree annotation for Matrices which is a labeled subrule of the parser rule expr.
+
+            # MO = [a, b; c, d]
+            # we generate _sm.Matrix([a, b, c, d]).reshape(2, 2)
+            # The reshape values are determined by counting the "," and ";" in the Autolev matrix
+
+            # Eg:
+            # [1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12]
+            # semicolon_count = 3 and rows = 3+1 = 4
+            # comma_count = 8 and cols = 8/rows + 1 = 8/4 + 1 = 3
+
+            # TODO** Parse block matrices
+            self.matrix_expr.append(ctx)
+            l = []
+            semicolon_count = 0
+            comma_count = 0
+            for i in range(ctx.matrix().getChildCount()):
+                child = ctx.matrix().getChild(i)
+                if child == AutolevParser.ExprContext:
+                    l.append(self.getValue(child))
+                elif child.getText() == ";":
+                    semicolon_count += 1
+                    l.append(",")
+                elif child.getText() == ",":
+                    comma_count += 1
+                    l.append(",")
+                else:
+                    try:
+                        try:
+                            l.append(self.getValue(child))
+                        except Exception:
+                            l.append(self.symbol_table[child.getText().lower()])
+                    except Exception:
+                        l.append(child.getText().lower())
+            num_of_rows = semicolon_count + 1
+            num_of_cols = (comma_count//num_of_rows) + 1
+
+            self.setValue(ctx, "_sm.Matrix(" + "".join(l) + ")" + ".reshape(" +
+                          str(num_of_rows) + ", " + str(num_of_cols) + ")")
+
+        def exitVectorOrDyadic(self, ctx):
+            self.vector_expr.append(ctx)
+            ch = ctx.vec()
+
+            if ch.getChild(0).getText() == "0>":
+                self.setValue(ctx, "0")
+
+            elif ch.getChild(0).getText() == "1>>":
+                self.setValue(ctx, "1>>")
+
+            elif "_" in ch.ID().getText() and ch.ID().getText().count('_') == 2:
+                vec_text = ch.getText().lower()
+                v1, v2, v3 = ch.ID().getText().lower().split('_')
+
+                if v1 == "p":
+                    if self.type2[v2] == "point":
+                        e2 = self.symbol_table2[v2]
+                    elif self.type2[v2] == "particle":
+                        e2 = self.symbol_table2[v2] + ".point"
+                    if self.type2[v3] == "point":
+                        e3 = self.symbol_table2[v3]
+                    elif self.type2[v3] == "particle":
+                        e3 = self.symbol_table2[v3] + ".point"
+                    get_vec = e3 + ".pos_from(" + e2 + ")"
+                    self.setValue(ctx, get_vec)
+
+                elif v1 in ("w", "alf"):
+                    if v1 == "w":
+                        text = ".ang_vel_in("
+                    elif v1 == "alf":
+                        text = ".ang_acc_in("
+                    if self.type2[v2] == "bodies":
+                        e2 = self.symbol_table2[v2] + "_f"
+                    elif self.type2[v2] == "frame":
+                        e2 = self.symbol_table2[v2]
+                    if self.type2[v3] == "bodies":
+                        e3 = self.symbol_table2[v3] + "_f"
+                    elif self.type2[v3] == "frame":
+                        e3 = self.symbol_table2[v3]
+                    get_vec = e2 + text + e3 + ")"
+                    self.setValue(ctx, get_vec)
+
+                elif v1 in ("v", "a"):
+                    if v1 == "v":
+                        text = ".vel("
+                    elif v1 == "a":
+                        text = ".acc("
+                    if self.type2[v2] == "point":
+                        e2 = self.symbol_table2[v2]
+                    elif self.type2[v2] == "particle":
+                        e2 = self.symbol_table2[v2] + ".point"
+                    get_vec = e2 + text + self.symbol_table2[v3] + ")"
+                    self.setValue(ctx, get_vec)
+
+                else:
+                    self.setValue(ctx, vec_text.replace(">", ""))
+
+            else:
+                vec_text = ch.getText().lower()
+                name = self.symbol_table[vec_text]
+                self.setValue(ctx, name)
+
+        def exitIndexing(self, ctx):
+            if ctx.getChildCount() == 4:
+                try:
+                    int_text = str(int(self.getValue(ctx.getChild(2))) - 1)
+                except Exception:
+                    int_text = self.getValue(ctx.getChild(2)) + " - 1"
+                self.setValue(ctx, ctx.ID().getText().lower() + "[" + int_text + "]")
+            elif ctx.getChildCount() == 6:
+                try:
+                    int_text1 = str(int(self.getValue(ctx.getChild(2))) - 1)
+                except Exception:
+                    int_text1 = self.getValue(ctx.getChild(2)) + " - 1"
+                try:
+                    int_text2 = str(int(self.getValue(ctx.getChild(4))) - 1)
+                except Exception:
+                    int_text2 = self.getValue(ctx.getChild(2)) + " - 1"
+                self.setValue(ctx, ctx.ID().getText().lower() + "[" + int_text1 + ", " + int_text2 + "]")
+
+
+        # ================== Subrules of parser rule expr (End) ====================== #
+
+        def exitRegularAssign(self, ctx):
+            # Handle assignments of type ID = expr
+            if ctx.equals().getText() in ["=", "+=", "-=", "*=", "/="]:
+                equals = ctx.equals().getText()
+            elif ctx.equals().getText() == ":=":
+                equals = " = "
+            elif ctx.equals().getText() == "^=":
+                equals = "**="
+
+            try:
+                a = ctx.ID().getText().lower() + "'"*ctx.diff().getText().count("'")
+            except Exception:
+                a = ctx.ID().getText().lower()
+
+            if a in self.type.keys() and self.type[a] in ("motionvariable", "motionvariable'") and\
+            self.type[ctx.expr().getText().lower()] in ("motionvariable", "motionvariable'"):
+                b = ctx.expr().getText().lower()
+                if "'" in b and "'" not in a:
+                    a, b = b, a
+                if not self.kane_parsed:
+                    self.kd_eqs.append(a + "-" + b)
+                    self.kd_equivalents.update({self.symbol_table[a]:
+                                                self.symbol_table[b]})
+                    self.kd_equivalents2.update({self.symbol_table[b]:
+                                                    self.symbol_table[a]})
+
+            if a in self.symbol_table.keys() and a in self.type.keys() and self.type[a] in ("variable", "motionvariable"):
+                self.explicit.update({self.symbol_table[a]: self.getValue(ctx.expr())})
+
+            else:
+                if ctx.expr() in self.matrix_expr:
+                    self.type.update({a: "matrix"})
+
+                try:
+                    b = self.symbol_table[a]
+                except KeyError:
+                    self.symbol_table[a] = a
+
+                if "_" in a and a.count("_") == 1:
+                    e1, e2 = a.split('_')
+                    if e1 in self.type2.keys() and self.type2[e1] in ("frame", "bodies")\
+                    and e2 in self.type2.keys() and self.type2[e2] in ("frame", "bodies"):
+                        if self.type2[e1] == "bodies":
+                            t1 = "_f"
+                        else:
+                            t1 = ""
+                        if self.type2[e2] == "bodies":
+                            t2 = "_f"
+                        else:
+                            t2 = ""
+
+                        self.write(self.symbol_table2[e2] + t2 + ".orient(" + self.symbol_table2[e1] +
+                                   t1 + ", 'DCM', " + self.getValue(ctx.expr()) + ")\n")
+                    else:
+                        self.write(self.symbol_table[a] + " " + equals + " " +
+                                    self.getValue(ctx.expr()) + "\n")
+                else:
+                    self.write(self.symbol_table[a] + " " + equals + " " +
+                                self.getValue(ctx.expr()) + "\n")
+
+        def exitIndexAssign(self, ctx):
+            # Handle assignments of type ID[index] = expr
+                if ctx.equals().getText() in ["=", "+=", "-=", "*=", "/="]:
+                    equals = ctx.equals().getText()
+                elif ctx.equals().getText() == ":=":
+                    equals = " = "
+                elif ctx.equals().getText() == "^=":
+                    equals = "**="
+
+                text = ctx.ID().getText().lower()
+                self.type.update({text: "matrix"})
+                # Handle assignments of type ID[2] = expr
+                if ctx.index().getChildCount() == 1:
+                    if ctx.index().getChild(0).getText() == "1":
+                        self.type.update({text: "matrix"})
+                        self.symbol_table.update({text: text})
+                        self.write(text + " = " + "_sm.Matrix([[0]])\n")
+                        self.write(text + "[0] = " + self.getValue(ctx.expr()) + "\n")
+                    else:
+                        # m = m.row_insert(m.shape[0], _sm.Matrix([[0]]))
+                        self.write(text + " = " + text +
+                                   ".row_insert(" + text + ".shape[0]" + ", " + "_sm.Matrix([[0]])" + ")\n")
+                        self.write(text + "[" + text + ".shape[0]-1" + "] = " + self.getValue(ctx.expr()) + "\n")
+
+                # Handle assignments of type ID[2, 2] = expr
+                elif ctx.index().getChildCount() == 3:
+                    l = []
+                    try:
+                        l.append(str(int(self.getValue(ctx.index().getChild(0)))-1))
+                    except Exception:
+                        l.append(self.getValue(ctx.index().getChild(0)) + "-1")
+                    l.append(",")
+                    try:
+                        l.append(str(int(self.getValue(ctx.index().getChild(2)))-1))
+                    except Exception:
+                        l.append(self.getValue(ctx.index().getChild(2)) + "-1")
+                    self.write(self.symbol_table[ctx.ID().getText().lower()] +
+                               "[" + "".join(l) + "]" + " " + equals + " " + self.getValue(ctx.expr()) + "\n")
+
+        def exitVecAssign(self, ctx):
+            # Handle assignments of the type vec = expr
+            ch = ctx.vec()
+            vec_text = ch.getText().lower()
+
+            if "_" in ch.ID().getText():
+                num = ch.ID().getText().count('_')
+
+                if num == 2:
+                    v1, v2, v3 = ch.ID().getText().lower().split('_')
+
+                    if v1 == "p":
+                        if self.type2[v2] == "point":
+                            e2 = self.symbol_table2[v2]
+                        elif self.type2[v2] == "particle":
+                            e2 = self.symbol_table2[v2] + ".point"
+                        if self.type2[v3] == "point":
+                            e3 = self.symbol_table2[v3]
+                        elif self.type2[v3] == "particle":
+                            e3 = self.symbol_table2[v3] + ".point"
+                        # ab.set_pos(na, la*a.x)
+                        self.write(e3 + ".set_pos(" + e2 + ", " + self.getValue(ctx.expr()) + ")\n")
+
+                    elif v1 in ("w", "alf"):
+                        if v1 == "w":
+                            text = ".set_ang_vel("
+                        elif v1 == "alf":
+                            text = ".set_ang_acc("
+                        # a.set_ang_vel(n, qad*a.z)
+                        if self.type2[v2] == "bodies":
+                            e2 = self.symbol_table2[v2] + "_f"
+                        else:
+                            e2 = self.symbol_table2[v2]
+                        if self.type2[v3] == "bodies":
+                            e3 = self.symbol_table2[v3] + "_f"
+                        else:
+                            e3 = self.symbol_table2[v3]
+                        self.write(e2 + text + e3 + ", " + self.getValue(ctx.expr()) + ")\n")
+
+                    elif v1 in ("v", "a"):
+                        if v1 == "v":
+                            text = ".set_vel("
+                        elif v1 == "a":
+                            text = ".set_acc("
+                        if self.type2[v2] == "point":
+                            e2 = self.symbol_table2[v2]
+                        elif self.type2[v2] == "particle":
+                            e2 = self.symbol_table2[v2] + ".point"
+                        self.write(e2 + text + self.symbol_table2[v3] +
+                                   ", " + self.getValue(ctx.expr()) + ")\n")
+                    elif v1 == "i":
+                        if v2 in self.type2.keys() and self.type2[v2] == "bodies":
+                            self.write(self.symbol_table2[v2] + ".inertia = (" + self.getValue(ctx.expr()) +
+                            ", " + self.symbol_table2[v3] + ")\n")
+                            self.inertia_point.update({v2: v3})
+                        elif v2 in self.type2.keys() and self.type2[v2] == "particle":
+                            self.write(ch.ID().getText().lower() + " = " + self.getValue(ctx.expr()) + "\n")
+                        else:
+                            self.write(ch.ID().getText().lower() + " = " + self.getValue(ctx.expr()) + "\n")
+                    else:
+                        self.write(ch.ID().getText().lower() + " = " + self.getValue(ctx.expr()) + "\n")
+
+                elif num == 1:
+                    v1, v2 = ch.ID().getText().lower().split('_')
+
+                    if v1 in ("force", "torque"):
+                        if self.type2[v2] in ("point", "frame"):
+                            e2 = self.symbol_table2[v2]
+                        elif self.type2[v2] == "particle":
+                            e2 = self.symbol_table2[v2] + ".point"
+                        self.symbol_table.update({vec_text: ch.ID().getText().lower()})
+
+                        if e2 in self.forces.keys():
+                            self.forces[e2] = self.forces[e2] + " + " + self.getValue(ctx.expr())
+                        else:
+                            self.forces.update({e2: self.getValue(ctx.expr())})
+                        self.write(ch.ID().getText().lower() + " = " + self.forces[e2] + "\n")
+
+                    else:
+                        name = ch.ID().getText().lower()
+                        self.symbol_table.update({vec_text: name})
+                        self.write(ch.ID().getText().lower() + " = " + self.getValue(ctx.expr()) + "\n")
+                else:
+                    name = ch.ID().getText().lower()
+                    self.symbol_table.update({vec_text: name})
+                    self.write(name + " " + ctx.getChild(1).getText() + " " + self.getValue(ctx.expr()) + "\n")
+            else:
+                name = ch.ID().getText().lower()
+                self.symbol_table.update({vec_text: name})
+                self.write(name + " " + ctx.getChild(1).getText() + " " + self.getValue(ctx.expr()) + "\n")
+
+        def enterInputs2(self, ctx):
+            self.in_inputs = True
+
+        # Inputs
+        def exitInputs2(self, ctx):
+            # Stores numerical values given by the input command which
+            # are used for codegen and numerical analysis.
+            if ctx.getChildCount() == 3:
+                try:
+                    self.inputs.update({self.symbol_table[ctx.id_diff().getText().lower()]: self.getValue(ctx.expr(0))})
+                except Exception:
+                    self.inputs.update({ctx.id_diff().getText().lower(): self.getValue(ctx.expr(0))})
+            elif ctx.getChildCount() == 4:
+                try:
+                    self.inputs.update({self.symbol_table[ctx.id_diff().getText().lower()]:
+                    (self.getValue(ctx.expr(0)), self.getValue(ctx.expr(1)))})
+                except Exception:
+                    self.inputs.update({ctx.id_diff().getText().lower():
+                    (self.getValue(ctx.expr(0)), self.getValue(ctx.expr(1)))})
+
+            self.in_inputs = False
+
+        def enterOutputs(self, ctx):
+            self.in_outputs = True
+        def exitOutputs(self, ctx):
+            self.in_outputs = False
+
+        def exitOutputs2(self, ctx):
+            try:
+                if "[" in ctx.expr(1).getText():
+                    self.outputs.append(self.symbol_table[ctx.expr(0).getText().lower()] +
+                                        ctx.expr(1).getText().lower())
+                else:
+                    self.outputs.append(self.symbol_table[ctx.expr(0).getText().lower()])
+
+            except Exception:
+                pass
+
+        # Code commands
+        def exitCodegen(self, ctx):
+            # Handles the CODE() command ie the solvers and the codgen part.
+            # Uses linsolve for the algebraic solvers and nsolve for non linear solvers.
+
+            if ctx.functionCall().getChild(0).getText().lower() == "algebraic":
+                matrix_name = self.getValue(ctx.functionCall().expr(0))
+                e = []
+                d = []
+                for i in range(1, (ctx.functionCall().getChildCount()-2)//2):
+                    a = self.getValue(ctx.functionCall().expr(i))
+                    e.append(a)
+
+                for i in self.inputs.keys():
+                    d.append(i + ":" + self.inputs[i])
+                self.write(matrix_name + "_list" + " = " + "[]\n")
+                self.write("for i in " + matrix_name + ":  " + matrix_name +
+                           "_list" + ".append(i.subs({" + ", ".join(d) + "}))\n")
+                self.write("print(_sm.linsolve(" + matrix_name + "_list" + ", " + ",".join(e) + "))\n")
+
+            elif ctx.functionCall().getChild(0).getText().lower() == "nonlinear":
+                e = []
+                d = []
+                guess = []
+                for i in range(1, (ctx.functionCall().getChildCount()-2)//2):
+                    a = self.getValue(ctx.functionCall().expr(i))
+                    e.append(a)
+                #print(self.inputs)
+                for i in self.inputs.keys():
+                    if i in self.symbol_table.keys():
+                        if type(self.inputs[i]) is tuple:
+                            j, z = self.inputs[i]
+                        else:
+                            j = self.inputs[i]
+                            z = ""
+                        if i not in e:
+                            if z == "deg":
+                                d.append(i + ":" + "_np.deg2rad(" + j + ")")
+                            else:
+                                d.append(i + ":" + j)
+                        else:
+                            if z == "deg":
+                                guess.append("_np.deg2rad(" + j + ")")
+                            else:
+                                guess.append(j)
+
+                self.write("matrix_list" + " = " + "[]\n")
+                self.write("for i in " + self.getValue(ctx.functionCall().expr(0)) + ":")
+                self.write("matrix_list" + ".append(i.subs({" + ", ".join(d) + "}))\n")
+                self.write("print(_sm.nsolve(matrix_list," + "(" + ",".join(e) + ")" +
+                           ",(" + ",".join(guess) + ")" + "))\n")
+
+            elif ctx.functionCall().getChild(0).getText().lower() in ["ode", "dynamics"] and self.include_numeric:
+                if self.kane_type == "no_args":
+                    for i in self.symbol_table.keys():
+                        try:
+                            if self.type[i] == "constants" or self.type[self.symbol_table[i]] == "constants":
+                                self.constants.append(self.symbol_table[i])
+                        except Exception:
+                            pass
+                    q_add_u = self.q_ind + self.q_dep + self.u_ind + self.u_dep
+                    x0 = []
+                    for i in q_add_u:
+                        try:
+                            if i in self.inputs.keys():
+                                if type(self.inputs[i]) is tuple:
+                                    if self.inputs[i][1] == "deg":
+                                        x0.append(i + ":" + "_np.deg2rad(" + self.inputs[i][0] + ")")
+                                    else:
+                                        x0.append(i + ":" + self.inputs[i][0])
+                                else:
+                                    x0.append(i + ":" + self.inputs[i])
+                            elif self.kd_equivalents[i] in self.inputs.keys():
+                                if type(self.inputs[self.kd_equivalents[i]]) is tuple:
+                                    x0.append(i + ":" + self.inputs[self.kd_equivalents[i]][0])
+                                else:
+                                    x0.append(i + ":" + self.inputs[self.kd_equivalents[i]])
+                        except Exception:
+                            pass
+
+                    # numerical constants
+                    numerical_constants = []
+                    for i in self.constants:
+                        if i in self.inputs.keys():
+                            if type(self.inputs[i]) is tuple:
+                                numerical_constants.append(self.inputs[i][0])
+                            else:
+                                numerical_constants.append(self.inputs[i])
+
+                    # t = linspace
+                    t_final = self.inputs["tfinal"]
+                    integ_stp = self.inputs["integstp"]
+
+                    self.write("from pydy.system import System\n")
+                    const_list = []
+                    if numerical_constants:
+                        for i in range(len(self.constants)):
+                            const_list.append(self.constants[i] + ":" + numerical_constants[i])
+                    specifieds = []
+                    if self.t:
+                        specifieds.append("_me.dynamicsymbols('t')" + ":" + "lambda x, t: t")
+
+                    for i in self.inputs:
+                        if i in self.symbol_table.keys() and self.symbol_table[i] not in\
+                        self.constants + self.q_ind + self.q_dep + self.u_ind + self.u_dep:
+                            specifieds.append(self.symbol_table[i] + ":" + self.inputs[i])
+
+                    self.write("sys = System(kane, constants = {" + ", ".join(const_list) + "},\n" +
+                               "specifieds={" + ", ".join(specifieds) + "},\n" +
+                               "initial_conditions={" + ", ".join(x0) + "},\n" +
+                               "times = _np.linspace(0.0, " + str(t_final) + ", " + str(t_final) +
+                               "/" + str(integ_stp) + "))\n\ny=sys.integrate()\n")
+
+                    # For outputs other than qs and us.
+                    other_outputs = []
+                    for i in self.outputs:
+                        if i not in q_add_u:
+                            if "[" in i:
+                                other_outputs.append((i[:-3] + i[-2], i[:-3] + "[" + str(int(i[-2])-1) + "]"))
+                            else:
+                                other_outputs.append((i, i))
+
+                    for i in other_outputs:
+                        self.write(i[0] + "_out" + " = " + "[]\n")
+                    if other_outputs:
+                        self.write("for i in y:\n")
+                        self.write("    q_u_dict = dict(zip(sys.coordinates+sys.speeds, i))\n")
+                        for i in other_outputs:
+                            self.write(" "*4 + i[0] + "_out" + ".append(" + i[1] + ".subs(q_u_dict)" +
+                                    ".subs(sys.constants).evalf())\n")
+
+        # Standalone function calls (used for dual functions)
+        def exitFunctionCall(self, ctx):
+            # Basically deals with standalone function calls ie functions which are not a part of
+            # expressions and assignments. Autolev Dual functions can both appear in standalone
+            # function calls and also on the right hand side as part of expr or assignment.
+
+            # Dual functions are indicated by a * in the comments below
+
+            # Checks if the function is a statement on its own
+            if ctx.parentCtx.getRuleIndex() == AutolevParser.RULE_stat:
+                func_name = ctx.getChild(0).getText().lower()
+                # Expand(E, n:m) *
+                if func_name == "expand":
+                    # If the first argument is a pre declared variable.
+                    expr = self.getValue(ctx.expr(0))
+                    symbol = self.symbol_table[ctx.expr(0).getText().lower()]
+                    if ctx.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                        self.write(symbol + " = " + "_sm.Matrix([i.expand() for i in " + expr + "])" +
+                                   ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])\n")
+                    else:
+                        self.write(symbol + " = " + symbol + "." + "expand()\n")
+
+                # Factor(E, x) *
+                elif func_name == "factor":
+                    expr = self.getValue(ctx.expr(0))
+                    symbol = self.symbol_table[ctx.expr(0).getText().lower()]
+                    if ctx.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                        self.write(symbol + " = " + "_sm.Matrix([_sm.factor(i," + self.getValue(ctx.expr(1)) +
+                                   ") for i in " + expr + "])" +
+                                   ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])\n")
+                    else:
+                        self.write(expr + " = " + "_sm.factor(" + expr + ", " +
+                                   self.getValue(ctx.expr(1)) + ")\n")
+
+                # Solve(Zero, x, y)
+                elif func_name == "solve":
+                    l = []
+                    l2 = []
+                    num = 0
+                    for i in range(1, ctx.getChildCount()):
+                        if ctx.getChild(i).getText() == ",":
+                            num+=1
+                        try:
+                            l.append(self.getValue(ctx.getChild(i)))
+                        except Exception:
+                            l.append(ctx.getChild(i).getText())
+
+                        if i != 2:
+                            try:
+                                l2.append(self.getValue(ctx.getChild(i)))
+                            except Exception:
+                                pass
+
+                    for i in l2:
+                        self.explicit.update({i: "_sm.solve" + "".join(l) + "[" + i + "]"})
+
+                    self.write("print(_sm.solve" + "".join(l) + ")\n")
+
+                # Arrange(y, n, x) *
+                elif func_name == "arrange":
+                    expr = self.getValue(ctx.expr(0))
+                    symbol = self.symbol_table[ctx.expr(0).getText().lower()]
+
+                    if ctx.expr(0) in self.matrix_expr or (expr in self.type.keys() and self.type[expr] == "matrix"):
+                        self.write(symbol + " = " + "_sm.Matrix([i.collect(" + self.getValue(ctx.expr(2)) +
+                                   ")" + "for i in " + expr + "])" +
+                                   ".reshape((" + expr + ").shape[0], " + "(" + expr + ").shape[1])\n")
+                    else:
+                        self.write(self.getValue(ctx.expr(0)) + ".collect(" +
+                                   self.getValue(ctx.expr(2)) + ")\n")
+
+                # Eig(M, EigenValue, EigenVec)
+                elif func_name == "eig":
+                    self.symbol_table.update({ctx.expr(1).getText().lower(): ctx.expr(1).getText().lower()})
+                    self.symbol_table.update({ctx.expr(2).getText().lower(): ctx.expr(2).getText().lower()})
+                    # _sm.Matrix([i.evalf() for i in (i_s_so).eigenvals().keys()])
+                    self.write(ctx.expr(1).getText().lower() + " = " +
+                               "_sm.Matrix([i.evalf() for i in " +
+                               "(" + self.getValue(ctx.expr(0)) + ")" + ".eigenvals().keys()])\n")
+                    # _sm.Matrix([i[2][0].evalf() for i in (i_s_o).eigenvects()]).reshape(i_s_o.shape[0], i_s_o.shape[1])
+                    self.write(ctx.expr(2).getText().lower() + " = " +
+                               "_sm.Matrix([i[2][0].evalf() for i in " + "(" + self.getValue(ctx.expr(0)) + ")" +
+                               ".eigenvects()]).reshape(" + self.getValue(ctx.expr(0)) + ".shape[0], " +
+                               self.getValue(ctx.expr(0)) + ".shape[1])\n")
+
+                # Simprot(N, A, 3, qA)
+                elif func_name == "simprot":
+                    # A.orient(N, 'Axis', qA, N.z)
+                    if self.type2[ctx.expr(0).getText().lower()] == "frame":
+                        frame1 = self.symbol_table2[ctx.expr(0).getText().lower()]
+                    elif self.type2[ctx.expr(0).getText().lower()] == "bodies":
+                        frame1 = self.symbol_table2[ctx.expr(0).getText().lower()] + "_f"
+                    if self.type2[ctx.expr(1).getText().lower()] == "frame":
+                        frame2 = self.symbol_table2[ctx.expr(1).getText().lower()]
+                    elif self.type2[ctx.expr(1).getText().lower()] == "bodies":
+                        frame2 = self.symbol_table2[ctx.expr(1).getText().lower()] + "_f"
+                    e2 = ""
+                    if ctx.expr(2).getText()[0] == "-":
+                        e2 = "-1*"
+                    if ctx.expr(2).getText() in ("1", "-1"):
+                        e = frame1 + ".x"
+                    elif ctx.expr(2).getText() in ("2", "-2"):
+                        e = frame1 + ".y"
+                    elif ctx.expr(2).getText() in ("3", "-3"):
+                        e = frame1 + ".z"
+                    else:
+                        e = self.getValue(ctx.expr(2))
+                        e2 = ""
+
+                    if "degrees" in self.settings.keys() and self.settings["degrees"] == "off":
+                        value = self.getValue(ctx.expr(3))
+                    else:
+                        if ctx.expr(3) in self.numeric_expr:
+                            value = "_np.deg2rad(" + self.getValue(ctx.expr(3)) + ")"
+                        else:
+                            value = self.getValue(ctx.expr(3))
+                    self.write(frame2 + ".orient(" + frame1 +
+                               ", " + "'Axis'" + ", " + "[" + value +
+                               ", " + e2 + e + "]" + ")\n")
+
+                # Express(A2>, B) *
+                elif func_name == "express":
+                    if self.type2[ctx.expr(1).getText().lower()] == "bodies":
+                        f = "_f"
+                    else:
+                        f = ""
+
+                    if '_' in ctx.expr(0).getText().lower() and ctx.expr(0).getText().count('_') == 2:
+                        vec = ctx.expr(0).getText().lower().replace(">", "").split('_')
+                        v1 = self.symbol_table2[vec[1]]
+                        v2 = self.symbol_table2[vec[2]]
+                        if vec[0] == "p":
+                            self.write(v2 + ".set_pos(" + v1 + ", " + "(" + self.getValue(ctx.expr(0)) +
+                                    ")" + ".express(" + self.symbol_table2[ctx.expr(1).getText().lower()] + f + "))\n")
+                        elif vec[0] == "v":
+                            self.write(v1 + ".set_vel(" + v2 + ", " + "(" + self.getValue(ctx.expr(0)) +
+                                    ")" + ".express(" + self.symbol_table2[ctx.expr(1).getText().lower()] + f + "))\n")
+                        elif vec[0] == "a":
+                            self.write(v1 + ".set_acc(" + v2 + ", " + "(" + self.getValue(ctx.expr(0)) +
+                                    ")" + ".express(" + self.symbol_table2[ctx.expr(1).getText().lower()] + f + "))\n")
+                        else:
+                            self.write(self.getValue(ctx.expr(0)) + " = " + "(" + self.getValue(ctx.expr(0)) + ")" + ".express(" +
+                                        self.symbol_table2[ctx.expr(1).getText().lower()] + f + ")\n")
+                    else:
+                        self.write(self.getValue(ctx.expr(0)) + " = " + "(" + self.getValue(ctx.expr(0)) + ")" + ".express(" +
+                                    self.symbol_table2[ctx.expr(1).getText().lower()] + f + ")\n")
+
+                # Angvel(A, B)
+                elif func_name == "angvel":
+                    self.write("print(" + self.symbol_table2[ctx.expr(1).getText().lower()] +
+                               ".ang_vel_in(" + self.symbol_table2[ctx.expr(0).getText().lower()] + "))\n")
+
+                # v2pts(N, A, O, P)
+                elif func_name in ("v2pts", "a2pts", "v2pt", "a1pt"):
+                    if func_name == "v2pts":
+                        text = ".v2pt_theory("
+                    elif func_name == "a2pts":
+                        text = ".a2pt_theory("
+                    elif func_name == "v1pt":
+                        text = ".v1pt_theory("
+                    elif func_name == "a1pt":
+                        text = ".a1pt_theory("
+                    if self.type2[ctx.expr(1).getText().lower()] == "frame":
+                        frame = self.symbol_table2[ctx.expr(1).getText().lower()]
+                    elif self.type2[ctx.expr(1).getText().lower()] == "bodies":
+                        frame = self.symbol_table2[ctx.expr(1).getText().lower()] + "_f"
+                    expr_list = []
+                    for i in range(2, 4):
+                        if self.type2[ctx.expr(i).getText().lower()] == "point":
+                            expr_list.append(self.symbol_table2[ctx.expr(i).getText().lower()])
+                        elif self.type2[ctx.expr(i).getText().lower()] == "particle":
+                            expr_list.append(self.symbol_table2[ctx.expr(i).getText().lower()] + ".point")
+
+                    self.write(expr_list[1] + text + expr_list[0] +
+                               "," + self.symbol_table2[ctx.expr(0).getText().lower()] + "," +
+                               frame + ")\n")
+
+                # Gravity(g*N1>)
+                elif func_name == "gravity":
+                    for i in self.bodies.keys():
+                        if self.type2[i] == "bodies":
+                            e = self.symbol_table2[i] + ".masscenter"
+                        elif self.type2[i] == "particle":
+                            e = self.symbol_table2[i] + ".point"
+                        if e in self.forces.keys():
+                            self.forces[e] = self.forces[e] + self.symbol_table2[i] +\
+                                             ".mass*(" + self.getValue(ctx.expr(0)) + ")"
+                        else:
+                            self.forces.update({e: self.symbol_table2[i] +
+                                               ".mass*(" + self.getValue(ctx.expr(0)) + ")"})
+                        self.write("force_" + i + " = " + self.forces[e] + "\n")
+
+                # Explicit(EXPRESS(IMPLICIT>,C))
+                elif func_name == "explicit":
+                    if ctx.expr(0) in self.vector_expr:
+                        self.vector_expr.append(ctx)
+                    expr = self.getValue(ctx.expr(0))
+                    if self.explicit.keys():
+                        explicit_list = []
+                        for i in self.explicit.keys():
+                            explicit_list.append(i + ":" + self.explicit[i])
+                        if '_' in ctx.expr(0).getText().lower() and ctx.expr(0).getText().count('_') == 2:
+                            vec = ctx.expr(0).getText().lower().replace(">", "").split('_')
+                            v1 = self.symbol_table2[vec[1]]
+                            v2 = self.symbol_table2[vec[2]]
+                            if vec[0] == "p":
+                                self.write(v2 + ".set_pos(" + v1 + ", " + "(" + expr +
+                                        ")" + ".subs({" + ", ".join(explicit_list) + "}))\n")
+                            elif vec[0] == "v":
+                                self.write(v2 + ".set_vel(" + v1 + ", " + "(" + expr +
+                                        ")" + ".subs({" + ", ".join(explicit_list) + "}))\n")
+                            elif vec[0] == "a":
+                                self.write(v2 + ".set_acc(" + v1 + ", " + "(" + expr +
+                                        ")" + ".subs({" + ", ".join(explicit_list) + "}))\n")
+                            else:
+                                self.write(expr + " = " + "(" + expr + ")" + ".subs({" + ", ".join(explicit_list) + "})\n")
+                        else:
+                            self.write(expr + " = " + "(" + expr + ")" + ".subs({" + ", ".join(explicit_list) + "})\n")
+
+                # Force(O/Q, -k*Stretch*Uvec>)
+                elif func_name in ("force", "torque"):
+
+                    if "/" in ctx.expr(0).getText().lower():
+                        p1 = ctx.expr(0).getText().lower().split('/')[0]
+                        p2 = ctx.expr(0).getText().lower().split('/')[1]
+                        if self.type2[p1] in ("point", "frame"):
+                            pt1 = self.symbol_table2[p1]
+                        elif self.type2[p1] == "particle":
+                            pt1 = self.symbol_table2[p1] + ".point"
+                        if self.type2[p2] in ("point", "frame"):
+                            pt2 = self.symbol_table2[p2]
+                        elif self.type2[p2] == "particle":
+                            pt2 = self.symbol_table2[p2] + ".point"
+                        if pt1 in self.forces.keys():
+                            self.forces[pt1] = self.forces[pt1] + " + -1*("+self.getValue(ctx.expr(1)) + ")"
+                            self.write("force_" + p1 + " = " + self.forces[pt1] + "\n")
+                        else:
+                            self.forces.update({pt1: "-1*("+self.getValue(ctx.expr(1)) + ")"})
+                            self.write("force_" + p1 + " = " + self.forces[pt1] + "\n")
+                        if pt2 in self.forces.keys():
+                            self.forces[pt2] = self.forces[pt2] + "+ " + self.getValue(ctx.expr(1))
+                            self.write("force_" + p2 + " = " + self.forces[pt2] + "\n")
+                        else:
+                            self.forces.update({pt2: self.getValue(ctx.expr(1))})
+                            self.write("force_" + p2 + " = " + self.forces[pt2] + "\n")
+
+                    elif ctx.expr(0).getChildCount() == 1:
+                        p1 = ctx.expr(0).getText().lower()
+                        if self.type2[p1] in ("point", "frame"):
+                            pt1 = self.symbol_table2[p1]
+                        elif self.type2[p1] == "particle":
+                            pt1 = self.symbol_table2[p1] + ".point"
+                        if pt1 in self.forces.keys():
+                            self.forces[pt1] = self.forces[pt1] + "+ -1*(" + self.getValue(ctx.expr(1)) + ")"
+                        else:
+                            self.forces.update({pt1: "-1*(" + self.getValue(ctx.expr(1)) + ")"})
+
+                # Constrain(Dependent[qB])
+                elif func_name == "constrain":
+                    if ctx.getChild(2).getChild(0).getText().lower() == "dependent":
+                        self.write("velocity_constraints = [i for i in dependent]\n")
+                    x = (ctx.expr(0).getChildCount()-2)//2
+                    for i in range(x):
+                        self.dependent_variables.append(self.getValue(ctx.expr(0).expr(i)))
+
+                # Kane()
+                elif func_name == "kane":
+                    if ctx.getChildCount() == 3:
+                        self.kane_type = "no_args"
+
+        # Settings
+        def exitSettings(self, ctx):
+            # Stores settings like Complex on/off, Degrees on/off etc in self.settings.
+            try:
+                self.settings.update({ctx.getChild(0).getText().lower():
+                                     ctx.getChild(1).getText().lower()})
+            except Exception:
+                pass
+
+        def exitMassDecl2(self, ctx):
+            # Used for declaring the masses of particles and rigidbodies.
+            particle = self.symbol_table2[ctx.getChild(0).getText().lower()]
+            if ctx.getText().count("=") == 2:
+                if ctx.expr().expr(1) in self.numeric_expr:
+                    e = "_sm.S(" + self.getValue(ctx.expr().expr(1)) + ")"
+                else:
+                    e = self.getValue(ctx.expr().expr(1))
+                self.symbol_table.update({ctx.expr().expr(0).getText().lower(): ctx.expr().expr(0).getText().lower()})
+                self.write(ctx.expr().expr(0).getText().lower() + " = " + e + "\n")
+                mass = ctx.expr().expr(0).getText().lower()
+            else:
+                try:
+                    if ctx.expr() in self.numeric_expr:
+                        mass = "_sm.S(" + self.getValue(ctx.expr()) + ")"
+                    else:
+                        mass = self.getValue(ctx.expr())
+                except Exception:
+                    a_text = ctx.expr().getText().lower()
+                    self.symbol_table.update({a_text: a_text})
+                    self.type.update({a_text: "constants"})
+                    self.write(a_text + " = " + "_sm.symbols('" + a_text + "')\n")
+                    mass = a_text
+
+            self.write(particle + ".mass = " + mass + "\n")
+
+        def exitInertiaDecl(self, ctx):
+            inertia_list = []
+            try:
+                ctx.ID(1).getText()
+                num = 5
+            except Exception:
+                num = 2
+            for i in range((ctx.getChildCount()-num)//2):
+                try:
+                    if ctx.expr(i) in self.numeric_expr:
+                        inertia_list.append("_sm.S(" + self.getValue(ctx.expr(i)) + ")")
+                    else:
+                        inertia_list.append(self.getValue(ctx.expr(i)))
+                except Exception:
+                    a_text = ctx.expr(i).getText().lower()
+                    self.symbol_table.update({a_text: a_text})
+                    self.type.update({a_text: "constants"})
+                    self.write(a_text + " = " + "_sm.symbols('" + a_text + "')\n")
+                    inertia_list.append(a_text)
+
+            if len(inertia_list) < 6:
+                for i in range(6-len(inertia_list)):
+                    inertia_list.append("0")
+            # body_a.inertia = (_me.inertia(body_a, I1, I2, I3, 0, 0, 0), body_a_cm)
+            try:
+                frame = self.symbol_table2[ctx.ID(1).getText().lower()]
+                point = self.symbol_table2[ctx.ID(0).getText().lower().split('_')[1]]
+                body = self.symbol_table2[ctx.ID(0).getText().lower().split('_')[0]]
+                self.inertia_point.update({ctx.ID(0).getText().lower().split('_')[0]
+                                          : ctx.ID(0).getText().lower().split('_')[1]})
+                self.write(body + ".inertia" + " = " + "(_me.inertia(" + frame + ", " +
+                           ", ".join(inertia_list) + "), " + point + ")\n")
+
+            except Exception:
+                body_name = self.symbol_table2[ctx.ID(0).getText().lower()]
+                body_name_cm = body_name + "_cm"
+                self.inertia_point.update({ctx.ID(0).getText().lower(): ctx.ID(0).getText().lower() + "o"})
+                self.write(body_name + ".inertia" + " = " + "(_me.inertia(" + body_name + "_f" + ", " +
+                           ", ".join(inertia_list) + "), " + body_name_cm + ")\n")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_parse_autolev_antlr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_parse_autolev_antlr.py
new file mode 100644
index 0000000000000000000000000000000000000000..e43924aac30903ade996b31921d3960afae90284
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/_parse_autolev_antlr.py
@@ -0,0 +1,38 @@
+from importlib.metadata import version
+from sympy.external import import_module
+
+
+autolevparser = import_module('sympy.parsing.autolev._antlr.autolevparser',
+                              import_kwargs={'fromlist': ['AutolevParser']})
+autolevlexer = import_module('sympy.parsing.autolev._antlr.autolevlexer',
+                             import_kwargs={'fromlist': ['AutolevLexer']})
+autolevlistener = import_module('sympy.parsing.autolev._antlr.autolevlistener',
+                                import_kwargs={'fromlist': ['AutolevListener']})
+
+AutolevParser = getattr(autolevparser, 'AutolevParser', None)
+AutolevLexer = getattr(autolevlexer, 'AutolevLexer', None)
+AutolevListener = getattr(autolevlistener, 'AutolevListener', None)
+
+
+def parse_autolev(autolev_code, include_numeric):
+    antlr4 = import_module('antlr4')
+    if not antlr4 or not version('antlr4-python3-runtime').startswith('4.11'):
+        raise ImportError("Autolev parsing requires the antlr4 Python package,"
+                          " provided by pip (antlr4-python3-runtime)"
+                          " conda (antlr-python-runtime), version 4.11")
+    try:
+        l = autolev_code.readlines()
+        input_stream = antlr4.InputStream("".join(l))
+    except Exception:
+        input_stream = antlr4.InputStream(autolev_code)
+
+    if AutolevListener:
+        from ._listener_autolev_antlr import MyListener
+        lexer = AutolevLexer(input_stream)
+        token_stream = antlr4.CommonTokenStream(lexer)
+        parser = AutolevParser(token_stream)
+        tree = parser.prog()
+        my_listener = MyListener(include_numeric)
+        walker = antlr4.ParseTreeWalker()
+        walker.walk(my_listener, tree)
+        return "".join(my_listener.output_code)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/README.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/README.txt
new file mode 100644
index 0000000000000000000000000000000000000000..946b006bac33544fadd2dc6d24c22240c8fbc8e4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/README.txt
@@ -0,0 +1,9 @@
+# parsing/tests/test_autolev.py uses the .al files in this directory as inputs and checks
+# the equivalence of the parser generated codes and the respective .py files.
+
+# By default, this directory contains tests for all rules of the parser.
+
+# Additional tests consisting of full physics examples shall be made available soon in
+# the form of another repository. One shall be able to copy the contents of that repo
+# to this folder and use those tests after uncommenting the respective code in
+# parsing/tests/test_autolev.py.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.al
new file mode 100644
index 0000000000000000000000000000000000000000..3bbb4d51b853bfd759df38d666a42adc1cbea190
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.al
@@ -0,0 +1,33 @@
+CONSTANTS G,LB,W,H
+MOTIONVARIABLES' THETA'',PHI'',OMEGA',ALPHA'
+NEWTONIAN N
+BODIES A,B
+SIMPROT(N,A,2,THETA)
+SIMPROT(A,B,3,PHI)
+POINT O
+LA = (LB-H/2)/2
+P_O_AO> = LA*A3>
+P_O_BO> = LB*A3>
+OMEGA = THETA'
+ALPHA = PHI'
+W_A_N> = OMEGA*N2>
+W_B_A> = ALPHA*A3>
+V_O_N> = 0>
+V2PTS(N, A, O, AO)
+V2PTS(N, A, O, BO)
+MASS A=MA, B=MB
+IAXX = 1/12*MA*(2*LA)^2
+IAYY = IAXX
+IAZZ = 0
+IBXX = 1/12*MB*H^2
+IBYY = 1/12*MB*(W^2+H^2)
+IBZZ = 1/12*MB*W^2
+INERTIA A, IAXX, IAYY, IAZZ
+INERTIA B, IBXX, IBYY, IBZZ
+GRAVITY(G*N3>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT LB=0.2,H=0.1,W=0.2,MA=0.01,MB=0.1,G=9.81
+INPUT THETA = 90 DEG, PHI = 0.5 DEG, OMEGA=0, ALPHA=0
+INPUT TFINAL=10, INTEGSTP=0.02
+CODE DYNAMICS() some_filename.c
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py
new file mode 100644
index 0000000000000000000000000000000000000000..4435635720bb38f40366f55bb3ace0f6f6899284
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py
@@ -0,0 +1,55 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+g, lb, w, h = _sm.symbols('g lb w h', real=True)
+theta, phi, omega, alpha = _me.dynamicsymbols('theta phi omega alpha')
+theta_d, phi_d, omega_d, alpha_d = _me.dynamicsymbols('theta_ phi_ omega_ alpha_', 1)
+theta_dd, phi_dd = _me.dynamicsymbols('theta_ phi_', 2)
+frame_n = _me.ReferenceFrame('n')
+body_a_cm = _me.Point('a_cm')
+body_a_cm.set_vel(frame_n, 0)
+body_a_f = _me.ReferenceFrame('a_f')
+body_a = _me.RigidBody('a', body_a_cm, body_a_f, _sm.symbols('m'), (_me.outer(body_a_f.x,body_a_f.x),body_a_cm))
+body_b_cm = _me.Point('b_cm')
+body_b_cm.set_vel(frame_n, 0)
+body_b_f = _me.ReferenceFrame('b_f')
+body_b = _me.RigidBody('b', body_b_cm, body_b_f, _sm.symbols('m'), (_me.outer(body_b_f.x,body_b_f.x),body_b_cm))
+body_a_f.orient(frame_n, 'Axis', [theta, frame_n.y])
+body_b_f.orient(body_a_f, 'Axis', [phi, body_a_f.z])
+point_o = _me.Point('o')
+la = (lb-h/2)/2
+body_a_cm.set_pos(point_o, la*body_a_f.z)
+body_b_cm.set_pos(point_o, lb*body_a_f.z)
+body_a_f.set_ang_vel(frame_n, omega*frame_n.y)
+body_b_f.set_ang_vel(body_a_f, alpha*body_a_f.z)
+point_o.set_vel(frame_n, 0)
+body_a_cm.v2pt_theory(point_o,frame_n,body_a_f)
+body_b_cm.v2pt_theory(point_o,frame_n,body_a_f)
+ma = _sm.symbols('ma')
+body_a.mass = ma
+mb = _sm.symbols('mb')
+body_b.mass = mb
+iaxx = 1/12*ma*(2*la)**2
+iayy = iaxx
+iazz = 0
+ibxx = 1/12*mb*h**2
+ibyy = 1/12*mb*(w**2+h**2)
+ibzz = 1/12*mb*w**2
+body_a.inertia = (_me.inertia(body_a_f, iaxx, iayy, iazz, 0, 0, 0), body_a_cm)
+body_b.inertia = (_me.inertia(body_b_f, ibxx, ibyy, ibzz, 0, 0, 0), body_b_cm)
+force_a = body_a.mass*(g*frame_n.z)
+force_b = body_b.mass*(g*frame_n.z)
+kd_eqs = [theta_d - omega, phi_d - alpha]
+forceList = [(body_a.masscenter,body_a.mass*(g*frame_n.z)), (body_b.masscenter,body_b.mass*(g*frame_n.z))]
+kane = _me.KanesMethod(frame_n, q_ind=[theta,phi], u_ind=[omega, alpha], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([body_a, body_b], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {g:9.81, lb:0.2, w:0.2, h:0.1, ma:0.01, mb:0.1},
+specifieds={},
+initial_conditions={theta:_np.deg2rad(90), phi:_np.deg2rad(0.5), omega:0, alpha:0},
+times = _np.linspace(0.0, 10, 10/0.02))
+
+y=sys.integrate()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.al
new file mode 100644
index 0000000000000000000000000000000000000000..0b6d72a072e093a6cb048a0b7976041ee9c2f4f3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.al
@@ -0,0 +1,25 @@
+MOTIONVARIABLES' Q{2}', U{2}'
+CONSTANTS L,M,G
+NEWTONIAN N
+FRAMES A,B
+SIMPROT(N, A, 3, Q1)
+SIMPROT(N, B, 3, Q2)
+W_A_N>=U1*N3>
+W_B_N>=U2*N3>
+POINT O
+PARTICLES P,R
+P_O_P> = L*A1>
+P_P_R> = L*B1>
+V_O_N> = 0>
+V2PTS(N, A, O, P)
+V2PTS(N, B, P, R)
+MASS P=M, R=M
+Q1' = U1
+Q2' = U2
+GRAVITY(G*N1>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT M=1,G=9.81,L=1
+INPUT Q1=.1,Q2=.2,U1=0,U2=0
+INPUT TFINAL=10, INTEGSTP=.01
+CODE DYNAMICS() some_filename.c
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.py
new file mode 100644
index 0000000000000000000000000000000000000000..12c73c3b4b198399f4c45f5e00d556c859caff74
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.py
@@ -0,0 +1,39 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
+q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
+l, m, g = _sm.symbols('l m g', real=True)
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_a.orient(frame_n, 'Axis', [q1, frame_n.z])
+frame_b.orient(frame_n, 'Axis', [q2, frame_n.z])
+frame_a.set_ang_vel(frame_n, u1*frame_n.z)
+frame_b.set_ang_vel(frame_n, u2*frame_n.z)
+point_o = _me.Point('o')
+particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+particle_r = _me.Particle('r', _me.Point('r_pt'), _sm.Symbol('m'))
+particle_p.point.set_pos(point_o, l*frame_a.x)
+particle_r.point.set_pos(particle_p.point, l*frame_b.x)
+point_o.set_vel(frame_n, 0)
+particle_p.point.v2pt_theory(point_o,frame_n,frame_a)
+particle_r.point.v2pt_theory(particle_p.point,frame_n,frame_b)
+particle_p.mass = m
+particle_r.mass = m
+force_p = particle_p.mass*(g*frame_n.x)
+force_r = particle_r.mass*(g*frame_n.x)
+kd_eqs = [q1_d - u1, q2_d - u2]
+forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x)), (particle_r.point,particle_r.mass*(g*frame_n.x))]
+kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u1, u2], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([particle_p, particle_r], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {l:1, m:1, g:9.81},
+specifieds={},
+initial_conditions={q1:.1, q2:.2, u1:0, u2:0},
+times = _np.linspace(0.0, 10, 10/.01))
+
+y=sys.integrate()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.al
new file mode 100644
index 0000000000000000000000000000000000000000..4892e5ca8cb18cad6b14a2a37cbdc1f7fb8217ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.al
@@ -0,0 +1,19 @@
+CONSTANTS M,K,B,G
+MOTIONVARIABLES' POSITION',SPEED'
+VARIABLES O
+FORCE = O*SIN(T)
+NEWTONIAN CEILING
+POINTS ORIGIN
+V_ORIGIN_CEILING> = 0>
+PARTICLES BLOCK
+P_ORIGIN_BLOCK> = POSITION*CEILING1>
+MASS BLOCK=M
+V_BLOCK_CEILING>=SPEED*CEILING1>
+POSITION' = SPEED
+FORCE_MAGNITUDE = M*G-K*POSITION-B*SPEED+FORCE
+FORCE_BLOCK>=EXPLICIT(FORCE_MAGNITUDE*CEILING1>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT TFINAL=10.0, INTEGSTP=0.01
+INPUT M=1.0, K=1.0, B=0.2, G=9.8, POSITION=0.1, SPEED=-1.0, O=2
+CODE DYNAMICS() dummy_file.c
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a5baab9642ff140e0ee81027a1e8f9152d7050c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.py
@@ -0,0 +1,31 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+m, k, b, g = _sm.symbols('m k b g', real=True)
+position, speed = _me.dynamicsymbols('position speed')
+position_d, speed_d = _me.dynamicsymbols('position_ speed_', 1)
+o = _me.dynamicsymbols('o')
+force = o*_sm.sin(_me.dynamicsymbols._t)
+frame_ceiling = _me.ReferenceFrame('ceiling')
+point_origin = _me.Point('origin')
+point_origin.set_vel(frame_ceiling, 0)
+particle_block = _me.Particle('block', _me.Point('block_pt'), _sm.Symbol('m'))
+particle_block.point.set_pos(point_origin, position*frame_ceiling.x)
+particle_block.mass = m
+particle_block.point.set_vel(frame_ceiling, speed*frame_ceiling.x)
+force_magnitude = m*g-k*position-b*speed+force
+force_block = (force_magnitude*frame_ceiling.x).subs({position_d:speed})
+kd_eqs = [position_d - speed]
+forceList = [(particle_block.point,(force_magnitude*frame_ceiling.x).subs({position_d:speed}))]
+kane = _me.KanesMethod(frame_ceiling, q_ind=[position], u_ind=[speed], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([particle_block], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {m:1.0, k:1.0, b:0.2, g:9.8},
+specifieds={_me.dynamicsymbols('t'):lambda x, t: t, o:2},
+initial_conditions={position:0.1, speed:-1*1.0},
+times = _np.linspace(0.0, 10.0, 10.0/0.01))
+
+y=sys.integrate()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.al
new file mode 100644
index 0000000000000000000000000000000000000000..74f5062d80926db7acd634a04759abce857087e5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.al
@@ -0,0 +1,20 @@
+MOTIONVARIABLES' Q{2}''
+CONSTANTS L,M,G
+NEWTONIAN N
+POINT PN
+V_PN_N> = 0>
+THETA1 = ATAN(Q2/Q1)
+FRAMES A
+SIMPROT(N, A, 3, THETA1)
+PARTICLES P
+P_PN_P> = Q1*N1>+Q2*N2>
+MASS P=M
+V_P_N>=DT(P_P_PN>, N)
+F_V = DOT(EXPRESS(V_P_N>,A), A1>)
+GRAVITY(G*N1>)
+DEPENDENT[1] = F_V
+CONSTRAIN(DEPENDENT[Q1'])
+ZERO=FR()+FRSTAR()
+F_C = MAG(P_P_PN>)-L
+CONFIG[1]=F_C
+ZERO[2]=CONFIG[1]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc972ebd518e77da5e1902c149f2699979865e7f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.py
@@ -0,0 +1,36 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2 = _me.dynamicsymbols('q1 q2')
+q1_d, q2_d = _me.dynamicsymbols('q1_ q2_', 1)
+q1_dd, q2_dd = _me.dynamicsymbols('q1_ q2_', 2)
+l, m, g = _sm.symbols('l m g', real=True)
+frame_n = _me.ReferenceFrame('n')
+point_pn = _me.Point('pn')
+point_pn.set_vel(frame_n, 0)
+theta1 = _sm.atan(q2/q1)
+frame_a = _me.ReferenceFrame('a')
+frame_a.orient(frame_n, 'Axis', [theta1, frame_n.z])
+particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+particle_p.point.set_pos(point_pn, q1*frame_n.x+q2*frame_n.y)
+particle_p.mass = m
+particle_p.point.set_vel(frame_n, (point_pn.pos_from(particle_p.point)).dt(frame_n))
+f_v = _me.dot((particle_p.point.vel(frame_n)).express(frame_a), frame_a.x)
+force_p = particle_p.mass*(g*frame_n.x)
+dependent = _sm.Matrix([[0]])
+dependent[0] = f_v
+velocity_constraints = [i for i in dependent]
+u_q1_d = _me.dynamicsymbols('u_q1_d')
+u_q2_d = _me.dynamicsymbols('u_q2_d')
+kd_eqs = [q1_d-u_q1_d, q2_d-u_q2_d]
+forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x))]
+kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u_q2_d], u_dependent=[u_q1_d], kd_eqs = kd_eqs, velocity_constraints = velocity_constraints)
+fr, frstar = kane.kanes_equations([particle_p], forceList)
+zero = fr+frstar
+f_c = point_pn.pos_from(particle_p.point).magnitude()-l
+config = _sm.Matrix([[0]])
+config[0] = f_c
+zero = zero.row_insert(zero.shape[0], _sm.Matrix([[0]]))
+zero[zero.shape[0]-1] = config[0]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest1.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest1.al
new file mode 100644
index 0000000000000000000000000000000000000000..457e79fd646677c0decdc69f921bc05e9e0dcf51
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest1.al
@@ -0,0 +1,8 @@
+% ruletest1.al
+CONSTANTS F = 3, G = 9.81
+CONSTANTS A, B
+CONSTANTS S, S1, S2+, S3+, S4-
+CONSTANTS K{4}, L{1:3}, P{1:2,1:3}
+CONSTANTS C{2,3}
+E1 = A*F + S2 - G
+E2 = F^2 + K3*K2*G
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest1.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest1.py
new file mode 100644
index 0000000000000000000000000000000000000000..8466392ac930f13f2419c9c04eef9dcc2884e9bd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest1.py
@@ -0,0 +1,15 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+f = _sm.S(3)
+g = _sm.S(9.81)
+a, b = _sm.symbols('a b', real=True)
+s, s1 = _sm.symbols('s s1', real=True)
+s2, s3 = _sm.symbols('s2 s3', real=True, nonnegative=True)
+s4 = _sm.symbols('s4', real=True, nonpositive=True)
+k1, k2, k3, k4, l1, l2, l3, p11, p12, p13, p21, p22, p23 = _sm.symbols('k1 k2 k3 k4 l1 l2 l3 p11 p12 p13 p21 p22 p23', real=True)
+c11, c12, c13, c21, c22, c23 = _sm.symbols('c11 c12 c13 c21 c22 c23', real=True)
+e1 = a*f+s2-g
+e2 = f**2+k3*k2*g
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest10.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest10.al
new file mode 100644
index 0000000000000000000000000000000000000000..9d5f76f063c43bcb5e2a8d4f29619a6952abf9e5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest10.al
@@ -0,0 +1,58 @@
+% ruletest10.al
+
+VARIABLES X,Y
+COMPLEX ON
+CONSTANTS A,B
+E = A*(B*X+Y)^2
+M = [E;E]
+EXPAND(E)
+EXPAND(M)
+FACTOR(E,X)
+FACTOR(M,X)
+
+EQN[1] = A*X + B*Y
+EQN[2] = 2*A*X - 3*B*Y
+SOLVE(EQN, X, Y)
+RHS_Y = RHS(Y)
+E = (X+Y)^2 + 2*X^2
+ARRANGE(E, 2, X)
+
+CONSTANTS A,B,C
+M = [A,B;C,0]
+M2 = EVALUATE(M,A=1,B=2,C=3)
+EIG(M2, EIGVALUE, EIGVEC)
+
+NEWTONIAN N
+FRAMES A
+SIMPROT(N, A, N1>, X)
+DEGREES OFF
+SIMPROT(N, A, N1>, PI/2)
+
+CONSTANTS C{3}
+V> = C1*A1> + C2*A2> + C3*A3>
+POINTS O, P
+P_P_O> = C1*A1>
+EXPRESS(V>,N)
+EXPRESS(P_P_O>,N)
+W_A_N> = C3*A3>
+ANGVEL(A,N)
+
+V2PTS(N,A,O,P)
+PARTICLES P{2}
+V2PTS(N,A,P1,P2)
+A2PTS(N,A,P1,P)
+
+BODIES B{2}
+CONSTANT G
+GRAVITY(G*N1>)
+
+VARIABLE Z
+V> = X*A1> + Y*A3>
+P_P_O> = X*A1> + Y*A2>
+X = 2*Z
+Y = Z
+EXPLICIT(V>)
+EXPLICIT(P_P_O>)
+
+FORCE(O/P1, X*Y*A1>)
+FORCE(P2, X*Y*A1>)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest10.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest10.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b9674e47d5f6132c5a79a33b9d8d55a131942d6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest10.py
@@ -0,0 +1,64 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+a, b = _sm.symbols('a b', real=True)
+e = a*(b*x+y)**2
+m = _sm.Matrix([e,e]).reshape(2, 1)
+e = e.expand()
+m = _sm.Matrix([i.expand() for i in m]).reshape((m).shape[0], (m).shape[1])
+e = _sm.factor(e, x)
+m = _sm.Matrix([_sm.factor(i,x) for i in m]).reshape((m).shape[0], (m).shape[1])
+eqn = _sm.Matrix([[0]])
+eqn[0] = a*x+b*y
+eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
+eqn[eqn.shape[0]-1] = 2*a*x-3*b*y
+print(_sm.solve(eqn,x,y))
+rhs_y = _sm.solve(eqn,x,y)[y]
+e = (x+y)**2+2*x**2
+e.collect(x)
+a, b, c = _sm.symbols('a b c', real=True)
+m = _sm.Matrix([a,b,c,0]).reshape(2, 2)
+m2 = _sm.Matrix([i.subs({a:1,b:2,c:3}) for i in m]).reshape((m).shape[0], (m).shape[1])
+eigvalue = _sm.Matrix([i.evalf() for i in (m2).eigenvals().keys()])
+eigvec = _sm.Matrix([i[2][0].evalf() for i in (m2).eigenvects()]).reshape(m2.shape[0], m2.shape[1])
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+frame_a.orient(frame_n, 'Axis', [x, frame_n.x])
+frame_a.orient(frame_n, 'Axis', [_sm.pi/2, frame_n.x])
+c1, c2, c3 = _sm.symbols('c1 c2 c3', real=True)
+v = c1*frame_a.x+c2*frame_a.y+c3*frame_a.z
+point_o = _me.Point('o')
+point_p = _me.Point('p')
+point_o.set_pos(point_p, c1*frame_a.x)
+v = (v).express(frame_n)
+point_o.set_pos(point_p, (point_o.pos_from(point_p)).express(frame_n))
+frame_a.set_ang_vel(frame_n, c3*frame_a.z)
+print(frame_n.ang_vel_in(frame_a))
+point_p.v2pt_theory(point_o,frame_n,frame_a)
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+particle_p2.point.v2pt_theory(particle_p1.point,frame_n,frame_a)
+point_p.a2pt_theory(particle_p1.point,frame_n,frame_a)
+body_b1_cm = _me.Point('b1_cm')
+body_b1_cm.set_vel(frame_n, 0)
+body_b1_f = _me.ReferenceFrame('b1_f')
+body_b1 = _me.RigidBody('b1', body_b1_cm, body_b1_f, _sm.symbols('m'), (_me.outer(body_b1_f.x,body_b1_f.x),body_b1_cm))
+body_b2_cm = _me.Point('b2_cm')
+body_b2_cm.set_vel(frame_n, 0)
+body_b2_f = _me.ReferenceFrame('b2_f')
+body_b2 = _me.RigidBody('b2', body_b2_cm, body_b2_f, _sm.symbols('m'), (_me.outer(body_b2_f.x,body_b2_f.x),body_b2_cm))
+g = _sm.symbols('g', real=True)
+force_p1 = particle_p1.mass*(g*frame_n.x)
+force_p2 = particle_p2.mass*(g*frame_n.x)
+force_b1 = body_b1.mass*(g*frame_n.x)
+force_b2 = body_b2.mass*(g*frame_n.x)
+z = _me.dynamicsymbols('z')
+v = x*frame_a.x+y*frame_a.z
+point_o.set_pos(point_p, x*frame_a.x+y*frame_a.y)
+v = (v).subs({x:2*z, y:z})
+point_o.set_pos(point_p, (point_o.pos_from(point_p)).subs({x:2*z, y:z}))
+force_o = -1*(x*y*frame_a.x)
+force_p1 = particle_p1.mass*(g*frame_n.x)+ x*y*frame_a.x
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest11.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest11.al
new file mode 100644
index 0000000000000000000000000000000000000000..60934c1ca563024828110bfe984a90d5686b89e4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest11.al
@@ -0,0 +1,6 @@
+VARIABLES X, Y
+CONSTANTS A{1:2, 1:2}, B{1:2}
+EQN[1] = A11*x + A12*y - B1
+EQN[2] = A21*x + A22*y - B2
+INPUT A11=2, A12=5, A21=3, A22=4, B1=7, B2=6
+CODE ALGEBRAIC(EQN, X, Y) some_filename.c
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest11.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest11.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ec2397ea96261d7b582d1f699e3897caae88f20
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest11.py
@@ -0,0 +1,14 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+a11, a12, a21, a22, b1, b2 = _sm.symbols('a11 a12 a21 a22 b1 b2', real=True)
+eqn = _sm.Matrix([[0]])
+eqn[0] = a11*x+a12*y-b1
+eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
+eqn[eqn.shape[0]-1] = a21*x+a22*y-b2
+eqn_list = []
+for i in eqn:  eqn_list.append(i.subs({a11:2, a12:5, a21:3, a22:4, b1:7, b2:6}))
+print(_sm.linsolve(eqn_list, x,y))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest12.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest12.al
new file mode 100644
index 0000000000000000000000000000000000000000..f147f55afd1438436767960e0487d5d9e7161c8f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest12.al
@@ -0,0 +1,7 @@
+VARIABLES X,Y
+CONSTANTS A,B,R
+EQN[1] = A*X^3+B*Y^2-R
+EQN[2] = A*SIN(X)^2 + B*COS(2*Y) - R^2
+INPUT A=2.0, B=3.0, R=1.0
+INPUT X = 30 DEG, Y = 3.14
+CODE NONLINEAR(EQN,X,Y) some_filename.c
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest12.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest12.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d7d996fa649f796a536dba20c1a36554acd8046
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest12.py
@@ -0,0 +1,14 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+a, b, r = _sm.symbols('a b r', real=True)
+eqn = _sm.Matrix([[0]])
+eqn[0] = a*x**3+b*y**2-r
+eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
+eqn[eqn.shape[0]-1] = a*_sm.sin(x)**2+b*_sm.cos(2*y)-r**2
+matrix_list = []
+for i in eqn:matrix_list.append(i.subs({a:2.0, b:3.0, r:1.0}))
+print(_sm.nsolve(matrix_list,(x,y),(_np.deg2rad(30),3.14)))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest2.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest2.al
new file mode 100644
index 0000000000000000000000000000000000000000..17937e58bd20a9fb82f44ccd05f0c081a1aa6c9b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest2.al
@@ -0,0 +1,12 @@
+% ruletest2.al
+VARIABLES X1,X2
+SPECIFIED F1 = X1*X2 + 3*X1^2
+SPECIFIED F2=X1*T+X2*T^2
+VARIABLE X', Y''
+MOTIONVARIABLES Q{3}, U{2}
+VARIABLES P{2}'
+VARIABLE W{3}', R{2}''
+VARIABLES C{1:2, 1:2}
+VARIABLES D{1,3}
+VARIABLES J{1:2}
+IMAGINARY N
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest2.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest2.py
new file mode 100644
index 0000000000000000000000000000000000000000..31c1d9974c2292466b805b91f8254bffaa94e2ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest2.py
@@ -0,0 +1,22 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x1, x2 = _me.dynamicsymbols('x1 x2')
+f1 = x1*x2+3*x1**2
+f2 = x1*_me.dynamicsymbols._t+x2*_me.dynamicsymbols._t**2
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+y_dd = _me.dynamicsymbols('y_', 2)
+q1, q2, q3, u1, u2 = _me.dynamicsymbols('q1 q2 q3 u1 u2')
+p1, p2 = _me.dynamicsymbols('p1 p2')
+p1_d, p2_d = _me.dynamicsymbols('p1_ p2_', 1)
+w1, w2, w3, r1, r2 = _me.dynamicsymbols('w1 w2 w3 r1 r2')
+w1_d, w2_d, w3_d, r1_d, r2_d = _me.dynamicsymbols('w1_ w2_ w3_ r1_ r2_', 1)
+r1_dd, r2_dd = _me.dynamicsymbols('r1_ r2_', 2)
+c11, c12, c21, c22 = _me.dynamicsymbols('c11 c12 c21 c22')
+d11, d12, d13 = _me.dynamicsymbols('d11 d12 d13')
+j1, j2 = _me.dynamicsymbols('j1 j2')
+n = _sm.symbols('n')
+n = _sm.I
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest3.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest3.al
new file mode 100644
index 0000000000000000000000000000000000000000..f263f1802ebca2725481dd5fdd3540bf8e9f11bf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest3.al
@@ -0,0 +1,25 @@
+% ruletest3.al
+FRAMES A, B
+NEWTONIAN N
+
+VARIABLES X{3}
+CONSTANTS L
+
+V1> = X1*A1> + X2*A2> + X3*A3>
+V2> = X1*B1> + X2*B2> + X3*B3>
+V3> = X1*N1> + X2*N2> + X3*N3>
+
+V> = V1> + V2> + V3>
+
+POINTS C, D
+POINTS PO{3}
+
+PARTICLES L
+PARTICLES P{3}
+
+BODIES S
+BODIES R{2}
+
+V4> = X1*S1> + X2*S2> + X3*S3>
+
+P_C_SO> = L*N1>
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest3.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest3.py
new file mode 100644
index 0000000000000000000000000000000000000000..23f79aa571337f200b3ff4d56b5747f7704985c0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest3.py
@@ -0,0 +1,37 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_n = _me.ReferenceFrame('n')
+x1, x2, x3 = _me.dynamicsymbols('x1 x2 x3')
+l = _sm.symbols('l', real=True)
+v1 = x1*frame_a.x+x2*frame_a.y+x3*frame_a.z
+v2 = x1*frame_b.x+x2*frame_b.y+x3*frame_b.z
+v3 = x1*frame_n.x+x2*frame_n.y+x3*frame_n.z
+v = v1+v2+v3
+point_c = _me.Point('c')
+point_d = _me.Point('d')
+point_po1 = _me.Point('po1')
+point_po2 = _me.Point('po2')
+point_po3 = _me.Point('po3')
+particle_l = _me.Particle('l', _me.Point('l_pt'), _sm.Symbol('m'))
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+particle_p3 = _me.Particle('p3', _me.Point('p3_pt'), _sm.Symbol('m'))
+body_s_cm = _me.Point('s_cm')
+body_s_cm.set_vel(frame_n, 0)
+body_s_f = _me.ReferenceFrame('s_f')
+body_s = _me.RigidBody('s', body_s_cm, body_s_f, _sm.symbols('m'), (_me.outer(body_s_f.x,body_s_f.x),body_s_cm))
+body_r1_cm = _me.Point('r1_cm')
+body_r1_cm.set_vel(frame_n, 0)
+body_r1_f = _me.ReferenceFrame('r1_f')
+body_r1 = _me.RigidBody('r1', body_r1_cm, body_r1_f, _sm.symbols('m'), (_me.outer(body_r1_f.x,body_r1_f.x),body_r1_cm))
+body_r2_cm = _me.Point('r2_cm')
+body_r2_cm.set_vel(frame_n, 0)
+body_r2_f = _me.ReferenceFrame('r2_f')
+body_r2 = _me.RigidBody('r2', body_r2_cm, body_r2_f, _sm.symbols('m'), (_me.outer(body_r2_f.x,body_r2_f.x),body_r2_cm))
+v4 = x1*body_s_f.x+x2*body_s_f.y+x3*body_s_f.z
+body_s_cm.set_pos(point_c, l*frame_n.x)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest4.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest4.al
new file mode 100644
index 0000000000000000000000000000000000000000..7302bd7724bad9b763c75fe4230faa42b5070408
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest4.al
@@ -0,0 +1,20 @@
+% ruletest4.al
+
+FRAMES A, B
+MOTIONVARIABLES Q{3}
+SIMPROT(A, B, 1, Q3)
+DCM = A_B
+M = DCM*3 - A_B
+
+VARIABLES R
+CIRCLE_AREA = PI*R^2
+
+VARIABLES U, A
+VARIABLES X, Y
+S = U*T - 1/2*A*T^2
+
+EXPR1 = 2*A*0.5 - 1.25 + 0.25
+EXPR2 = -X^2 + Y^2 + 0.25*(X+Y)^2
+EXPR3 = 0.5E-10
+
+DYADIC>> = A1>*A1> + A2>*A2> + A3>*A3>
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest4.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest4.py
new file mode 100644
index 0000000000000000000000000000000000000000..74b18543e04d6c9e42dd569d2152040c13ae0899
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest4.py
@@ -0,0 +1,20 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+q1, q2, q3 = _me.dynamicsymbols('q1 q2 q3')
+frame_b.orient(frame_a, 'Axis', [q3, frame_a.x])
+dcm = frame_a.dcm(frame_b)
+m = dcm*3-frame_a.dcm(frame_b)
+r = _me.dynamicsymbols('r')
+circle_area = _sm.pi*r**2
+u, a = _me.dynamicsymbols('u a')
+x, y = _me.dynamicsymbols('x y')
+s = u*_me.dynamicsymbols._t-1/2*a*_me.dynamicsymbols._t**2
+expr1 = 2*a*0.5-1.25+0.25
+expr2 = -1*x**2+y**2+0.25*(x+y)**2
+expr3 = 0.5*10**(-10)
+dyadic = _me.outer(frame_a.x, frame_a.x)+_me.outer(frame_a.y, frame_a.y)+_me.outer(frame_a.z, frame_a.z)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest5.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest5.al
new file mode 100644
index 0000000000000000000000000000000000000000..a859dc8bb1f0251af14809681d995c59b31377ba
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest5.al
@@ -0,0 +1,32 @@
+% ruletest5.al
+VARIABLES X', Y'
+
+E1 = (X+Y)^2 + (X-Y)^3
+E2 = (X-Y)^2
+E3 = X^2 + Y^2 + 2*X*Y
+
+M1 = [E1;E2]
+M2 = [(X+Y)^2,(X-Y)^2]
+M3 = M1 + [X;Y]
+
+AM = EXPAND(M1)
+CM = EXPAND([(X+Y)^2,(X-Y)^2])
+EM = EXPAND(M1 + [X;Y])
+F = EXPAND(E1)
+G = EXPAND(E2)
+
+A = FACTOR(E3, X)
+BM = FACTOR(M1, X)
+CM = FACTOR(M1 + [X;Y], X)
+
+A = D(E3, X)
+B = D(E3, Y)
+CM = D(M2, X)
+DM = D(M1 + [X;Y], X)
+FRAMES A, B
+A_B = [1,0,0;1,0,0;1,0,0]
+V1> = X*A1> + Y*A2> + X*Y*A3>
+E> = D(V1>, X, B)
+FM = DT(M1)
+GM = DT([(X+Y)^2,(X-Y)^2])
+H> = DT(V1>, B)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest5.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest5.py
new file mode 100644
index 0000000000000000000000000000000000000000..93684435b402f5b56e2f4a5c3c81500208556423
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest5.py
@@ -0,0 +1,33 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+e1 = (x+y)**2+(x-y)**3
+e2 = (x-y)**2
+e3 = x**2+y**2+2*x*y
+m1 = _sm.Matrix([e1,e2]).reshape(2, 1)
+m2 = _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)
+m3 = m1+_sm.Matrix([x,y]).reshape(2, 1)
+am = _sm.Matrix([i.expand() for i in m1]).reshape((m1).shape[0], (m1).shape[1])
+cm = _sm.Matrix([i.expand() for i in _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)]).reshape((_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[0], (_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[1])
+em = _sm.Matrix([i.expand() for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
+f = (e1).expand()
+g = (e2).expand()
+a = _sm.factor((e3), x)
+bm = _sm.Matrix([_sm.factor(i, x) for i in m1]).reshape((m1).shape[0], (m1).shape[1])
+cm = _sm.Matrix([_sm.factor(i, x) for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
+a = (e3).diff(x)
+b = (e3).diff(y)
+cm = _sm.Matrix([i.diff(x) for i in m2]).reshape((m2).shape[0], (m2).shape[1])
+dm = _sm.Matrix([i.diff(x) for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_b.orient(frame_a, 'DCM', _sm.Matrix([1,0,0,1,0,0,1,0,0]).reshape(3, 3))
+v1 = x*frame_a.x+y*frame_a.y+x*y*frame_a.z
+e = (v1).diff(x, frame_b)
+fm = _sm.Matrix([i.diff(_sm.Symbol('t')) for i in m1]).reshape((m1).shape[0], (m1).shape[1])
+gm = _sm.Matrix([i.diff(_sm.Symbol('t')) for i in _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)]).reshape((_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[0], (_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[1])
+h = (v1).dt(frame_b)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest6.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest6.al
new file mode 100644
index 0000000000000000000000000000000000000000..7ec3ba61590e77772ae631237df048b932fe778c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest6.al
@@ -0,0 +1,41 @@
+% ruletest6.al
+VARIABLES Q{2}
+VARIABLES X,Y,Z
+Q1 = X^2 + Y^2
+Q2 = X-Y
+E = Q1 + Q2
+A = EXPLICIT(E)
+E2 = COS(X)
+E3 = COS(X*Y)
+A = TAYLOR(E2, 0:2, X=0)
+B = TAYLOR(E3, 0:2, X=0, Y=0)
+
+E = EXPAND((X+Y)^2)
+A = EVALUATE(E, X=1, Y=Z)
+BM = EVALUATE([E;2*E], X=1, Y=Z)
+
+E = Q1 + Q2
+A = EVALUATE(E, X=2, Y=Z^2)
+
+CONSTANTS J,K,L
+P1 = POLYNOMIAL([J,K,L],X)
+P2 = POLYNOMIAL(J*X+K,X,1)
+
+ROOT1 = ROOTS(P1, X, 2)
+ROOT2 = ROOTS([1;2;3])
+
+M = [1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]
+
+AM = TRANSPOSE(M) + M
+BM = EIG(M)
+C1 = DIAGMAT(4, 1)
+C2 = DIAGMAT(3, 4, 2)
+DM = INV(M+C1)
+E = DET(M+C1) + TRACE([1,0;0,1])
+F = ELEMENT(M, 2, 3)
+
+A = COLS(M)
+BM = COLS(M, 1)
+CM = COLS(M, 1, 2:4, 3)
+DM = ROWS(M, 1)
+EM = ROWS(M, 1, 2:4, 3)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest6.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest6.py
new file mode 100644
index 0000000000000000000000000000000000000000..85f1a0b49518bb0ae5766cbe91b9c24a1b8e9c20
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest6.py
@@ -0,0 +1,36 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2 = _me.dynamicsymbols('q1 q2')
+x, y, z = _me.dynamicsymbols('x y z')
+e = q1+q2
+a = (e).subs({q1:x**2+y**2, q2:x-y})
+e2 = _sm.cos(x)
+e3 = _sm.cos(x*y)
+a = (e2).series(x, 0, 2).removeO()
+b = (e3).series(x, 0, 2).removeO().series(y, 0, 2).removeO()
+e = ((x+y)**2).expand()
+a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:1,y:z})
+bm = _sm.Matrix([i.subs({x:1,y:z}) for i in _sm.Matrix([e,2*e]).reshape(2, 1)]).reshape((_sm.Matrix([e,2*e]).reshape(2, 1)).shape[0], (_sm.Matrix([e,2*e]).reshape(2, 1)).shape[1])
+e = q1+q2
+a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:2,y:z**2})
+j, k, l = _sm.symbols('j k l', real=True)
+p1 = _sm.Poly(_sm.Matrix([j,k,l]).reshape(1, 3), x)
+p2 = _sm.Poly(j*x+k, x)
+root1 = [i.evalf() for i in _sm.solve(p1, x)]
+root2 = [i.evalf() for i in _sm.solve(_sm.Poly(_sm.Matrix([1,2,3]).reshape(3, 1), x),x)]
+m = _sm.Matrix([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]).reshape(4, 4)
+am = (m).T+m
+bm = _sm.Matrix([i.evalf() for i in (m).eigenvals().keys()])
+c1 = _sm.diag(1,1,1,1)
+c2 = _sm.Matrix([2 if i==j else 0 for i in range(3) for j in range(4)]).reshape(3, 4)
+dm = (m+c1)**(-1)
+e = (m+c1).det()+(_sm.Matrix([1,0,0,1]).reshape(2, 2)).trace()
+f = (m)[1,2]
+a = (m).cols
+bm = (m).col(0)
+cm = _sm.Matrix([(m).T.row(0),(m).T.row(1),(m).T.row(2),(m).T.row(3),(m).T.row(2)])
+dm = (m).row(0)
+em = _sm.Matrix([(m).row(0),(m).row(1),(m).row(2),(m).row(3),(m).row(2)])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest7.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest7.al
new file mode 100644
index 0000000000000000000000000000000000000000..2904a602f589645d22e1d3d378d077dd6a1ec27e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest7.al
@@ -0,0 +1,39 @@
+% ruletest7.al
+VARIABLES X', Y'
+E = COS(X) + SIN(X) + TAN(X)&
++ COSH(X) + SINH(X) + TANH(X)&
++ ACOS(X) + ASIN(X) + ATAN(X)&
++ LOG(X) + EXP(X) + SQRT(X)&
++ FACTORIAL(X) + CEIL(X) +&
+FLOOR(X) + SIGN(X)
+
+E = SQR(X) + LOG10(X)
+
+A = ABS(-1) + INT(1.5) + ROUND(1.9)
+
+E1 = 2*X + 3*Y
+E2 = X + Y
+
+AM = COEF([E1;E2], [X,Y])
+B = COEF(E1, X)
+C = COEF(E2, Y)
+D1 = EXCLUDE(E1, X)
+D2 = INCLUDE(E1, X)
+FM = ARRANGE([E1,E2],2,X)
+F = ARRANGE(E1, 2, Y)
+G = REPLACE(E1, X=2*X)
+GM = REPLACE([E1;E2], X=3)
+
+FRAMES A, B
+VARIABLES THETA
+SIMPROT(A,B,3,THETA)
+V1> = 2*A1> - 3*A2> + A3>
+V2> = B1> + B2> + B3>
+A = DOT(V1>, V2>)
+BM = DOT(V1>, [V2>;2*V2>])
+C> = CROSS(V1>,V2>)
+D = MAG(2*V1>) + MAG(3*V1>)
+DYADIC>> = 3*A1>*A1> + A2>*A2> + 2*A3>*A3>
+AM = MATRIX(B, DYADIC>>)
+M = [1;2;3]
+V> = VECTOR(A, M)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest7.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest7.py
new file mode 100644
index 0000000000000000000000000000000000000000..19147856dc3b0d451184a6bb539c1c331f61a6d2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest7.py
@@ -0,0 +1,35 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+e = _sm.cos(x)+_sm.sin(x)+_sm.tan(x)+_sm.cosh(x)+_sm.sinh(x)+_sm.tanh(x)+_sm.acos(x)+_sm.asin(x)+_sm.atan(x)+_sm.log(x)+_sm.exp(x)+_sm.sqrt(x)+_sm.factorial(x)+_sm.ceiling(x)+_sm.floor(x)+_sm.sign(x)
+e = (x)**2+_sm.log(x, 10)
+a = _sm.Abs(-1*1)+int(1.5)+round(1.9)
+e1 = 2*x+3*y
+e2 = x+y
+am = _sm.Matrix([e1.expand().coeff(x), e1.expand().coeff(y), e2.expand().coeff(x), e2.expand().coeff(y)]).reshape(2, 2)
+b = (e1).expand().coeff(x)
+c = (e2).expand().coeff(y)
+d1 = (e1).collect(x).coeff(x,0)
+d2 = (e1).collect(x).coeff(x,1)
+fm = _sm.Matrix([i.collect(x)for i in _sm.Matrix([e1,e2]).reshape(1, 2)]).reshape((_sm.Matrix([e1,e2]).reshape(1, 2)).shape[0], (_sm.Matrix([e1,e2]).reshape(1, 2)).shape[1])
+f = (e1).collect(y)
+g = (e1).subs({x:2*x})
+gm = _sm.Matrix([i.subs({x:3}) for i in _sm.Matrix([e1,e2]).reshape(2, 1)]).reshape((_sm.Matrix([e1,e2]).reshape(2, 1)).shape[0], (_sm.Matrix([e1,e2]).reshape(2, 1)).shape[1])
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+theta = _me.dynamicsymbols('theta')
+frame_b.orient(frame_a, 'Axis', [theta, frame_a.z])
+v1 = 2*frame_a.x-3*frame_a.y+frame_a.z
+v2 = frame_b.x+frame_b.y+frame_b.z
+a = _me.dot(v1, v2)
+bm = _sm.Matrix([_me.dot(v1, v2),_me.dot(v1, 2*v2)]).reshape(2, 1)
+c = _me.cross(v1, v2)
+d = 2*v1.magnitude()+3*v1.magnitude()
+dyadic = _me.outer(3*frame_a.x, frame_a.x)+_me.outer(frame_a.y, frame_a.y)+_me.outer(2*frame_a.z, frame_a.z)
+am = (dyadic).to_matrix(frame_b)
+m = _sm.Matrix([1,2,3]).reshape(3, 1)
+v = m[0]*frame_a.x +m[1]*frame_a.y +m[2]*frame_a.z
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest8.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest8.al
new file mode 100644
index 0000000000000000000000000000000000000000..4b2462c51e6730f46bf60b4b21ab6cfbf1993640
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest8.al
@@ -0,0 +1,38 @@
+% ruletest8.al
+FRAMES A
+CONSTANTS C{3}
+A>> = EXPRESS(1>>,A)
+PARTICLES P1, P2
+BODIES R
+R_A = [1,1,1;1,1,0;0,0,1]
+POINT O
+MASS P1=M1, P2=M2, R=MR
+INERTIA R, I1, I2, I3
+P_P1_O> = C1*A1>
+P_P2_O> = C2*A2>
+P_RO_O> = C3*A3>
+A>> = EXPRESS(I_P1_O>>, A)
+A>> = EXPRESS(I_P2_O>>, A)
+A>> = EXPRESS(I_R_O>>, A)
+A>> = EXPRESS(INERTIA(O), A)
+A>> = EXPRESS(INERTIA(O, P1, R), A)
+A>> = EXPRESS(I_R_O>>, A)
+A>> = EXPRESS(I_R_RO>>, A)
+
+P_P1_P2> = C1*A1> + C2*A2>
+P_P1_RO> = C3*A1>
+P_P2_RO> = C3*A2>
+
+B> = CM(O)
+B> = CM(O, P1, R)
+B> = CM(P1)
+
+MOTIONVARIABLES U{3}
+V> = U1*A1> + U2*A2> + U3*A3>
+U> = UNITVEC(V> + C1*A1>)
+V_P1_A> = U1*A1>
+A> = PARTIALS(V_P1_A>, U1)
+
+M = MASS(P1,R)
+M = MASS(P2)
+M = MASS()
\ No newline at end of file
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest8.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest8.py
new file mode 100644
index 0000000000000000000000000000000000000000..6809c47138e40027c700536e807ca7cfa5f468d7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest8.py
@@ -0,0 +1,49 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_a = _me.ReferenceFrame('a')
+c1, c2, c3 = _sm.symbols('c1 c2 c3', real=True)
+a = _me.inertia(frame_a, 1, 1, 1)
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+body_r_cm = _me.Point('r_cm')
+body_r_f = _me.ReferenceFrame('r_f')
+body_r = _me.RigidBody('r', body_r_cm, body_r_f, _sm.symbols('m'), (_me.outer(body_r_f.x,body_r_f.x),body_r_cm))
+frame_a.orient(body_r_f, 'DCM', _sm.Matrix([1,1,1,1,1,0,0,0,1]).reshape(3, 3))
+point_o = _me.Point('o')
+m1 = _sm.symbols('m1')
+particle_p1.mass = m1
+m2 = _sm.symbols('m2')
+particle_p2.mass = m2
+mr = _sm.symbols('mr')
+body_r.mass = mr
+i1 = _sm.symbols('i1')
+i2 = _sm.symbols('i2')
+i3 = _sm.symbols('i3')
+body_r.inertia = (_me.inertia(body_r_f, i1, i2, i3, 0, 0, 0), body_r_cm)
+point_o.set_pos(particle_p1.point, c1*frame_a.x)
+point_o.set_pos(particle_p2.point, c2*frame_a.y)
+point_o.set_pos(body_r_cm, c3*frame_a.z)
+a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a)
+a = _me.inertia_of_point_mass(particle_p2.mass, particle_p2.point.pos_from(point_o), frame_a)
+a = body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a) + _me.inertia_of_point_mass(particle_p2.mass, particle_p2.point.pos_from(point_o), frame_a) + body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a) + body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = body_r.inertia[0]
+particle_p2.point.set_pos(particle_p1.point, c1*frame_a.x+c2*frame_a.y)
+body_r_cm.set_pos(particle_p1.point, c3*frame_a.x)
+body_r_cm.set_pos(particle_p2.point, c3*frame_a.y)
+b = _me.functions.center_of_mass(point_o,particle_p1, particle_p2, body_r)
+b = _me.functions.center_of_mass(point_o,particle_p1, body_r)
+b = _me.functions.center_of_mass(particle_p1.point,particle_p1, particle_p2, body_r)
+u1, u2, u3 = _me.dynamicsymbols('u1 u2 u3')
+v = u1*frame_a.x+u2*frame_a.y+u3*frame_a.z
+u = (v+c1*frame_a.x).normalize()
+particle_p1.point.set_vel(frame_a, u1*frame_a.x)
+a = particle_p1.point.partial_velocity(frame_a, u1)
+m = particle_p1.mass+body_r.mass
+m = particle_p2.mass
+m = particle_p1.mass+particle_p2.mass+body_r.mass
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest9.al b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest9.al
new file mode 100644
index 0000000000000000000000000000000000000000..df5c70f05b76fc215f829672e281491b0c96c6a6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest9.al
@@ -0,0 +1,54 @@
+% ruletest9.al
+NEWTONIAN N
+FRAMES A
+A> = 0>
+D>> = EXPRESS(1>>, A)
+
+POINTS PO{2}
+PARTICLES P{2}
+MOTIONVARIABLES' C{3}'
+BODIES R
+P_P1_PO2> = C1*A1>
+V> = 2*P_P1_PO2> + C2*A2>
+
+W_A_N> = C3*A3>
+V> = 2*W_A_N> + C2*A2>
+W_R_N> = C3*A3>
+V> = 2*W_R_N> + C2*A2>
+
+ALF_A_N> = DT(W_A_N>, A)
+V> = 2*ALF_A_N> + C2*A2>
+
+V_P1_A> = C1*A1> + C3*A2>
+A_RO_N> = C2*A2>
+V_A> = CROSS(A_RO_N>, V_P1_A>)
+
+X_B_C> = V_A>
+X_B_D> = 2*X_B_C>
+A_B_C_D_E> = X_B_D>*2
+
+A_B_C = 2*C1*C2*C3
+A_B_C += 2*C1
+A_B_C := 3*C1
+
+MOTIONVARIABLES' Q{2}', U{2}'
+Q1' = U1
+Q2' = U2
+
+VARIABLES X'', Y''
+SPECIFIED YY
+Y'' = X*X'^2 + 1
+YY = X*X'^2 + 1
+
+M[1] = 2*X
+M[2] = 2*Y
+A = 2*M[1]
+
+M = [1,2,3;4,5,6;7,8,9]
+M[1, 2] = 5
+A = M[1, 2]*2
+
+FORCE_RO> = Q1*N1>
+TORQUE_A> = Q2*N3>
+FORCE_RO> = Q2*N2>
+F> = FORCE_RO>*2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest9.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest9.py
new file mode 100644
index 0000000000000000000000000000000000000000..09d8ae4ee8385bde5c38b946458a43c8ffdaa9b8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/autolev/test-examples/ruletest9.py
@@ -0,0 +1,55 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+a = 0
+d = _me.inertia(frame_a, 1, 1, 1)
+point_po1 = _me.Point('po1')
+point_po2 = _me.Point('po2')
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+c1, c2, c3 = _me.dynamicsymbols('c1 c2 c3')
+c1_d, c2_d, c3_d = _me.dynamicsymbols('c1_ c2_ c3_', 1)
+body_r_cm = _me.Point('r_cm')
+body_r_cm.set_vel(frame_n, 0)
+body_r_f = _me.ReferenceFrame('r_f')
+body_r = _me.RigidBody('r', body_r_cm, body_r_f, _sm.symbols('m'), (_me.outer(body_r_f.x,body_r_f.x),body_r_cm))
+point_po2.set_pos(particle_p1.point, c1*frame_a.x)
+v = 2*point_po2.pos_from(particle_p1.point)+c2*frame_a.y
+frame_a.set_ang_vel(frame_n, c3*frame_a.z)
+v = 2*frame_a.ang_vel_in(frame_n)+c2*frame_a.y
+body_r_f.set_ang_vel(frame_n, c3*frame_a.z)
+v = 2*body_r_f.ang_vel_in(frame_n)+c2*frame_a.y
+frame_a.set_ang_acc(frame_n, (frame_a.ang_vel_in(frame_n)).dt(frame_a))
+v = 2*frame_a.ang_acc_in(frame_n)+c2*frame_a.y
+particle_p1.point.set_vel(frame_a, c1*frame_a.x+c3*frame_a.y)
+body_r_cm.set_acc(frame_n, c2*frame_a.y)
+v_a = _me.cross(body_r_cm.acc(frame_n), particle_p1.point.vel(frame_a))
+x_b_c = v_a
+x_b_d = 2*x_b_c
+a_b_c_d_e = x_b_d*2
+a_b_c = 2*c1*c2*c3
+a_b_c += 2*c1
+a_b_c  =  3*c1
+q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
+q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+x_dd, y_dd = _me.dynamicsymbols('x_ y_', 2)
+yy = _me.dynamicsymbols('yy')
+yy = x*x_d**2+1
+m = _sm.Matrix([[0]])
+m[0] = 2*x
+m = m.row_insert(m.shape[0], _sm.Matrix([[0]]))
+m[m.shape[0]-1] = 2*y
+a = 2*m[0]
+m = _sm.Matrix([1,2,3,4,5,6,7,8,9]).reshape(3, 3)
+m[0,1] = 5
+a = m[0, 1]*2
+force_ro = q1*frame_n.x
+torque_a = q2*frame_n.z
+force_ro = q1*frame_n.x + q2*frame_n.y
+f = force_ro*2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/c/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/c/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..18d3d5301cb001c78fc4a9bc04b25aa36f282a93
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/c/__init__.py
@@ -0,0 +1 @@
+"""Used for translating C source code into a SymPy expression"""
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/c/c_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/c/c_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..9e7223f8351205272e803773589649fcf1902f15
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/c/c_parser.py
@@ -0,0 +1,1059 @@
+from sympy.external import import_module
+import os
+
+cin = import_module('clang.cindex', import_kwargs = {'fromlist': ['cindex']})
+
+"""
+This module contains all the necessary Classes and Function used to Parse C and
+C++ code into SymPy expression
+The module serves as a backend for SymPyExpression to parse C code
+It is also dependent on Clang's AST and SymPy's Codegen AST.
+The module only supports the features currently supported by the Clang and
+codegen AST which will be updated as the development of codegen AST and this
+module progresses.
+You might find unexpected bugs and exceptions while using the module, feel free
+to report them to the SymPy Issue Tracker
+
+Features Supported
+==================
+
+- Variable Declarations (integers and reals)
+- Assignment (using integer & floating literal and function calls)
+- Function Definitions and Declaration
+- Function Calls
+- Compound statements, Return statements
+
+Notes
+=====
+
+The module is dependent on an external dependency which needs to be installed
+to use the features of this module.
+
+Clang: The C and C++ compiler which is used to extract an AST from the provided
+C source code.
+
+References
+==========
+
+.. [1] https://github.com/sympy/sympy/issues
+.. [2] https://clang.llvm.org/docs/
+.. [3] https://clang.llvm.org/docs/IntroductionToTheClangAST.html
+
+"""
+
+if cin:
+    from sympy.codegen.ast import (Variable, Integer, Float,
+        FunctionPrototype, FunctionDefinition, FunctionCall,
+        none, Return, Assignment, intc, int8, int16, int64,
+        uint8, uint16, uint32, uint64, float32, float64, float80,
+        aug_assign, bool_, While, CodeBlock)
+    from sympy.codegen.cnodes import (PreDecrement, PostDecrement,
+        PreIncrement, PostIncrement)
+    from sympy.core import Add, Mod, Mul, Pow, Rel
+    from sympy.logic.boolalg import And, as_Boolean, Not, Or
+    from sympy.core.symbol import Symbol
+    from sympy.core.sympify import sympify
+    from sympy.logic.boolalg import (false, true)
+    import sys
+    import tempfile
+
+    class BaseParser:
+        """Base Class for the C parser"""
+
+        def __init__(self):
+            """Initializes the Base parser creating a Clang AST index"""
+            self.index = cin.Index.create()
+
+        def diagnostics(self, out):
+            """Diagostics function for the Clang AST"""
+            for diag in self.tu.diagnostics:
+                # tu = translation unit
+                print('%s %s (line %s, col %s) %s' % (
+                        {
+                            4: 'FATAL',
+                            3: 'ERROR',
+                            2: 'WARNING',
+                            1: 'NOTE',
+                            0: 'IGNORED',
+                        }[diag.severity],
+                        diag.location.file,
+                        diag.location.line,
+                        diag.location.column,
+                        diag.spelling
+                    ), file=out)
+
+    class CCodeConverter(BaseParser):
+        """The Code Convereter for Clang AST
+
+        The converter object takes the C source code or file as input and
+        converts them to SymPy Expressions.
+        """
+
+        def __init__(self):
+            """Initializes the code converter"""
+            super().__init__()
+            self._py_nodes = []
+            self._data_types = {
+                "void": {
+                    cin.TypeKind.VOID: none
+                },
+                "bool": {
+                    cin.TypeKind.BOOL: bool_
+                },
+                "int": {
+                    cin.TypeKind.SCHAR: int8,
+                    cin.TypeKind.SHORT: int16,
+                    cin.TypeKind.INT: intc,
+                    cin.TypeKind.LONG: int64,
+                    cin.TypeKind.UCHAR: uint8,
+                    cin.TypeKind.USHORT: uint16,
+                    cin.TypeKind.UINT: uint32,
+                    cin.TypeKind.ULONG: uint64
+                },
+                "float": {
+                    cin.TypeKind.FLOAT: float32,
+                    cin.TypeKind.DOUBLE: float64,
+                    cin.TypeKind.LONGDOUBLE: float80
+                }
+            }
+
+        def parse(self, filename, flags):
+            """Function to parse a file with C source code
+
+            It takes the filename as an attribute and creates a Clang AST
+            Translation Unit parsing the file.
+            Then the transformation function is called on the translation unit,
+            whose results are collected into a list which is returned by the
+            function.
+
+            Parameters
+            ==========
+
+            filename : string
+                Path to the C file to be parsed
+
+            flags: list
+                Arguments to be passed to Clang while parsing the C code
+
+            Returns
+            =======
+
+            py_nodes: list
+                A list of SymPy AST nodes
+
+            """
+            filepath = os.path.abspath(filename)
+            self.tu = self.index.parse(
+                filepath,
+                args=flags,
+                options=cin.TranslationUnit.PARSE_DETAILED_PROCESSING_RECORD
+            )
+            for child in self.tu.cursor.get_children():
+                if child.kind == cin.CursorKind.VAR_DECL or child.kind == cin.CursorKind.FUNCTION_DECL:
+                    self._py_nodes.append(self.transform(child))
+            return self._py_nodes
+
+        def parse_str(self, source, flags):
+            """Function to parse a string with C source code
+
+            It takes the source code as an attribute, stores it in a temporary
+            file and creates a Clang AST Translation Unit parsing the file.
+            Then the transformation function is called on the translation unit,
+            whose results are collected into a list which is returned by the
+            function.
+
+            Parameters
+            ==========
+
+            source : string
+                A string containing the C source code to be parsed
+
+            flags: list
+                Arguments to be passed to Clang while parsing the C code
+
+            Returns
+            =======
+
+            py_nodes: list
+                A list of SymPy AST nodes
+
+            """
+            file = tempfile.NamedTemporaryFile(mode = 'w+', suffix = '.cpp')
+            file.write(source)
+            file.flush()
+            file.seek(0)
+            self.tu = self.index.parse(
+                file.name,
+                args=flags,
+                options=cin.TranslationUnit.PARSE_DETAILED_PROCESSING_RECORD
+            )
+            file.close()
+            for child in self.tu.cursor.get_children():
+                if child.kind == cin.CursorKind.VAR_DECL or child.kind == cin.CursorKind.FUNCTION_DECL:
+                    self._py_nodes.append(self.transform(child))
+            return self._py_nodes
+
+        def transform(self, node):
+            """Transformation Function for Clang AST nodes
+
+            It determines the kind of node and calls the respective
+            transformation function for that node.
+
+            Raises
+            ======
+
+            NotImplementedError : if the transformation for the provided node
+            is not implemented
+
+            """
+            handler = getattr(self, 'transform_%s' % node.kind.name.lower(), None)
+
+            if handler is None:
+                print(
+                    "Ignoring node of type %s (%s)" % (
+                        node.kind,
+                        ' '.join(
+                            t.spelling for t in node.get_tokens())
+                        ),
+                    file=sys.stderr
+                )
+
+            return handler(node)
+
+        def transform_var_decl(self, node):
+            """Transformation Function for Variable Declaration
+
+            Used to create nodes for variable declarations and assignments with
+            values or function call for the respective nodes in the clang AST
+
+            Returns
+            =======
+
+            A variable node as Declaration, with the initial value if given
+
+            Raises
+            ======
+
+            NotImplementedError : if called for data types not currently
+            implemented
+
+            Notes
+            =====
+
+            The function currently supports following data types:
+
+            Boolean:
+                bool, _Bool
+
+            Integer:
+                8-bit: signed char and unsigned char
+                16-bit: short, short int, signed short,
+                    signed short int, unsigned short, unsigned short int
+                32-bit: int, signed int, unsigned int
+                64-bit: long, long int, signed long,
+                    signed long int, unsigned long, unsigned long int
+
+            Floating point:
+                Single Precision: float
+                Double Precision: double
+                Extended Precision: long double
+
+            """
+            if node.type.kind in self._data_types["int"]:
+                type = self._data_types["int"][node.type.kind]
+            elif node.type.kind in self._data_types["float"]:
+                type = self._data_types["float"][node.type.kind]
+            elif node.type.kind in self._data_types["bool"]:
+                type = self._data_types["bool"][node.type.kind]
+            else:
+                raise NotImplementedError("Only bool, int "
+                    "and float are supported")
+            try:
+                children = node.get_children()
+                child = next(children)
+
+                #ignoring namespace and type details for the variable
+                while child.kind == cin.CursorKind.NAMESPACE_REF or child.kind == cin.CursorKind.TYPE_REF:
+                    child = next(children)
+
+                val = self.transform(child)
+
+                supported_rhs = [
+                    cin.CursorKind.INTEGER_LITERAL,
+                    cin.CursorKind.FLOATING_LITERAL,
+                    cin.CursorKind.UNEXPOSED_EXPR,
+                    cin.CursorKind.BINARY_OPERATOR,
+                    cin.CursorKind.PAREN_EXPR,
+                    cin.CursorKind.UNARY_OPERATOR,
+                    cin.CursorKind.CXX_BOOL_LITERAL_EXPR
+                ]
+
+                if child.kind in supported_rhs:
+                    if isinstance(val, str):
+                        value = Symbol(val)
+                    elif isinstance(val, bool):
+                        if node.type.kind in self._data_types["int"]:
+                            value = Integer(0) if val == False else Integer(1)
+                        elif node.type.kind in self._data_types["float"]:
+                            value = Float(0.0) if val == False else Float(1.0)
+                        elif node.type.kind in self._data_types["bool"]:
+                            value = sympify(val)
+                    elif isinstance(val, (Integer, int, Float, float)):
+                        if node.type.kind in self._data_types["int"]:
+                            value = Integer(val)
+                        elif node.type.kind in self._data_types["float"]:
+                            value = Float(val)
+                        elif node.type.kind in self._data_types["bool"]:
+                            value = sympify(bool(val))
+                    else:
+                        value = val
+
+                    return Variable(
+                    node.spelling
+                    ).as_Declaration(
+                        type = type,
+                        value = value
+                    )
+
+                elif child.kind == cin.CursorKind.CALL_EXPR:
+                    return Variable(
+                        node.spelling
+                        ).as_Declaration(
+                            value = val
+                        )
+
+                else:
+                    raise NotImplementedError("Given "
+                        "variable declaration \"{}\" "
+                        "is not possible to parse yet!"
+                        .format(" ".join(
+                            t.spelling for t in node.get_tokens()
+                            )
+                        ))
+
+            except StopIteration:
+                return Variable(
+                node.spelling
+                ).as_Declaration(
+                    type = type
+                )
+
+        def transform_function_decl(self, node):
+            """Transformation Function For Function Declaration
+
+            Used to create nodes for function declarations and definitions for
+            the respective nodes in the clang AST
+
+            Returns
+            =======
+
+            function : Codegen AST node
+                - FunctionPrototype node if function body is not present
+                - FunctionDefinition node if the function body is present
+
+
+            """
+
+            if node.result_type.kind in self._data_types["int"]:
+                ret_type = self._data_types["int"][node.result_type.kind]
+            elif node.result_type.kind in self._data_types["float"]:
+                ret_type = self._data_types["float"][node.result_type.kind]
+            elif node.result_type.kind in self._data_types["bool"]:
+                ret_type = self._data_types["bool"][node.result_type.kind]
+            elif node.result_type.kind in self._data_types["void"]:
+                ret_type = self._data_types["void"][node.result_type.kind]
+            else:
+                raise NotImplementedError("Only void, bool, int "
+                    "and float are supported")
+            body = []
+            param = []
+
+            # Subsequent nodes will be the parameters for the function.
+            for child in node.get_children():
+                decl = self.transform(child)
+                if child.kind == cin.CursorKind.PARM_DECL:
+                    param.append(decl)
+                elif child.kind == cin.CursorKind.COMPOUND_STMT:
+                    for val in decl:
+                        body.append(val)
+                else:
+                    body.append(decl)
+
+            if body == []:
+                function = FunctionPrototype(
+                    return_type = ret_type,
+                    name = node.spelling,
+                    parameters = param
+                )
+            else:
+                function = FunctionDefinition(
+                    return_type = ret_type,
+                    name = node.spelling,
+                    parameters = param,
+                    body = body
+                )
+            return function
+
+        def transform_parm_decl(self, node):
+            """Transformation function for Parameter Declaration
+
+            Used to create parameter nodes for the required functions for the
+            respective nodes in the clang AST
+
+            Returns
+            =======
+
+            param : Codegen AST Node
+                Variable node with the value and type of the variable
+
+            Raises
+            ======
+
+            ValueError if multiple children encountered in the parameter node
+
+            """
+            if node.type.kind in self._data_types["int"]:
+                type = self._data_types["int"][node.type.kind]
+            elif node.type.kind in self._data_types["float"]:
+                type = self._data_types["float"][node.type.kind]
+            elif node.type.kind in self._data_types["bool"]:
+                type = self._data_types["bool"][node.type.kind]
+            else:
+                raise NotImplementedError("Only bool, int "
+                    "and float are supported")
+            try:
+                children = node.get_children()
+                child = next(children)
+
+                # Any namespace nodes can be ignored
+                while child.kind in [cin.CursorKind.NAMESPACE_REF,
+                                     cin.CursorKind.TYPE_REF,
+                                     cin.CursorKind.TEMPLATE_REF]:
+                    child = next(children)
+
+                # If there is a child, it is the default value of the parameter.
+                lit = self.transform(child)
+                if node.type.kind in self._data_types["int"]:
+                    val = Integer(lit)
+                elif node.type.kind in self._data_types["float"]:
+                    val = Float(lit)
+                elif node.type.kind in self._data_types["bool"]:
+                    val = sympify(bool(lit))
+                else:
+                    raise NotImplementedError("Only bool, int "
+                        "and float are supported")
+
+                param = Variable(
+                    node.spelling
+                ).as_Declaration(
+                    type = type,
+                    value = val
+                )
+            except StopIteration:
+                param = Variable(
+                    node.spelling
+                ).as_Declaration(
+                    type = type
+                )
+
+            try:
+                self.transform(next(children))
+                raise ValueError("Can't handle multiple children on parameter")
+            except StopIteration:
+                pass
+
+            return param
+
+        def transform_integer_literal(self, node):
+            """Transformation function for integer literal
+
+            Used to get the value and type of the given integer literal.
+
+            Returns
+            =======
+
+            val : list
+                List with two arguments type and Value
+                type contains the type of the integer
+                value contains the value stored in the variable
+
+            Notes
+            =====
+
+            Only Base Integer type supported for now
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except StopIteration:
+                # No tokens
+                value = node.literal
+            return int(value)
+
+        def transform_floating_literal(self, node):
+            """Transformation function for floating literal
+
+            Used to get the value and type of the given floating literal.
+
+            Returns
+            =======
+
+            val : list
+                List with two arguments type and Value
+                type contains the type of float
+                value contains the value stored in the variable
+
+            Notes
+            =====
+
+            Only Base Float type supported for now
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except (StopIteration, ValueError):
+                # No tokens
+                value = node.literal
+            return float(value)
+
+        def transform_string_literal(self, node):
+            #TODO: No string type in AST
+            #type =
+            #try:
+            #    value = next(node.get_tokens()).spelling
+            #except (StopIteration, ValueError):
+                # No tokens
+            #    value = node.literal
+            #val = [type, value]
+            #return val
+            pass
+
+        def transform_character_literal(self, node):
+            """Transformation function for character literal
+
+            Used to get the value of the given character literal.
+
+            Returns
+            =======
+
+            val : int
+                val contains the ascii value of the character literal
+
+            Notes
+            =====
+
+            Only for cases where character is assigned to a integer value,
+            since character literal is not in SymPy AST
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except (StopIteration, ValueError):
+                # No tokens
+                value = node.literal
+            return ord(str(value[1]))
+
+        def transform_cxx_bool_literal_expr(self, node):
+            """Transformation function for boolean literal
+
+            Used to get the value of the given boolean literal.
+
+            Returns
+            =======
+
+            value : bool
+                value contains the boolean value of the variable
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except (StopIteration, ValueError):
+                value = node.literal
+            return True if value == 'true' else False
+
+        def transform_unexposed_decl(self,node):
+            """Transformation function for unexposed declarations"""
+            pass
+
+        def transform_unexposed_expr(self, node):
+            """Transformation function for unexposed expression
+
+            Unexposed expressions are used to wrap float, double literals and
+            expressions
+
+            Returns
+            =======
+
+            expr : Codegen AST Node
+                the result from the wrapped expression
+
+            None : NoneType
+                No children are found for the node
+
+            Raises
+            ======
+
+            ValueError if the expression contains multiple children
+
+            """
+            # Ignore unexposed nodes; pass whatever is the first
+            # (and should be only) child unaltered.
+            try:
+                children = node.get_children()
+                expr = self.transform(next(children))
+            except StopIteration:
+                return None
+
+            try:
+                next(children)
+                raise ValueError("Unexposed expression has > 1 children.")
+            except StopIteration:
+                pass
+
+            return expr
+
+        def transform_decl_ref_expr(self, node):
+            """Returns the name of the declaration reference"""
+            return node.spelling
+
+        def transform_call_expr(self, node):
+            """Transformation function for a call expression
+
+            Used to create function call nodes for the function calls present
+            in the C code
+
+            Returns
+            =======
+
+            FunctionCall : Codegen AST Node
+                FunctionCall node with parameters if any parameters are present
+
+            """
+            param = []
+            children = node.get_children()
+            child = next(children)
+
+            while child.kind == cin.CursorKind.NAMESPACE_REF:
+                child = next(children)
+            while child.kind == cin.CursorKind.TYPE_REF:
+                child = next(children)
+
+            first_child = self.transform(child)
+            try:
+                for child in children:
+                    arg = self.transform(child)
+                    if child.kind == cin.CursorKind.INTEGER_LITERAL:
+                        param.append(Integer(arg))
+                    elif child.kind == cin.CursorKind.FLOATING_LITERAL:
+                        param.append(Float(arg))
+                    else:
+                        param.append(arg)
+                return FunctionCall(first_child, param)
+
+            except StopIteration:
+                return FunctionCall(first_child)
+
+        def transform_return_stmt(self, node):
+            """Returns the Return Node for a return statement"""
+            return Return(next(node.get_children()).spelling)
+
+        def transform_compound_stmt(self, node):
+            """Transformation function for compound statements
+
+            Returns
+            =======
+
+            expr : list
+                list of Nodes for the expressions present in the statement
+
+            None : NoneType
+                if the compound statement is empty
+
+            """
+            expr = []
+            children = node.get_children()
+
+            for child in children:
+                expr.append(self.transform(child))
+            return expr
+
+        def transform_decl_stmt(self, node):
+            """Transformation function for declaration statements
+
+            These statements are used to wrap different kinds of declararions
+            like variable or function declaration
+            The function calls the transformer function for the child of the
+            given node
+
+            Returns
+            =======
+
+            statement : Codegen AST Node
+                contains the node returned by the children node for the type of
+                declaration
+
+            Raises
+            ======
+
+            ValueError if multiple children present
+
+            """
+            try:
+                children = node.get_children()
+                statement = self.transform(next(children))
+            except StopIteration:
+                pass
+
+            try:
+                self.transform(next(children))
+                raise ValueError("Don't know how to handle multiple statements")
+            except StopIteration:
+                pass
+
+            return statement
+
+        def transform_paren_expr(self, node):
+            """Transformation function for Parenthesized expressions
+
+            Returns the result from its children nodes
+
+            """
+            return self.transform(next(node.get_children()))
+
+        def transform_compound_assignment_operator(self, node):
+            """Transformation function for handling shorthand operators
+
+            Returns
+            =======
+
+            augmented_assignment_expression: Codegen AST node
+                    shorthand assignment expression represented as Codegen AST
+
+            Raises
+            ======
+
+            NotImplementedError
+                If the shorthand operator for bitwise operators
+                (~=, ^=, &=, |=, <<=, >>=) is encountered
+
+            """
+            return self.transform_binary_operator(node)
+
+        def transform_unary_operator(self, node):
+            """Transformation function for handling unary operators
+
+            Returns
+            =======
+
+            unary_expression: Codegen AST node
+                    simplified unary expression represented as Codegen AST
+
+            Raises
+            ======
+
+            NotImplementedError
+                If dereferencing operator(*), address operator(&) or
+                bitwise NOT operator(~) is encountered
+
+            """
+            # supported operators list
+            operators_list = ['+', '-', '++', '--', '!']
+            tokens = list(node.get_tokens())
+
+            # it can be either pre increment/decrement or any other operator from the list
+            if tokens[0].spelling in operators_list:
+                child = self.transform(next(node.get_children()))
+                # (decl_ref) e.g.; int a = ++b; or simply ++b;
+                if isinstance(child, str):
+                    if tokens[0].spelling == '+':
+                        return Symbol(child)
+                    if tokens[0].spelling == '-':
+                        return Mul(Symbol(child), -1)
+                    if tokens[0].spelling == '++':
+                        return PreIncrement(Symbol(child))
+                    if tokens[0].spelling == '--':
+                        return PreDecrement(Symbol(child))
+                    if tokens[0].spelling == '!':
+                        return Not(Symbol(child))
+                # e.g.; int a = -1; or int b = -(1 + 2);
+                else:
+                    if tokens[0].spelling == '+':
+                        return child
+                    if tokens[0].spelling == '-':
+                        return Mul(child, -1)
+                    if tokens[0].spelling == '!':
+                        return Not(sympify(bool(child)))
+
+            # it can be either post increment/decrement
+            # since variable name is obtained in token[0].spelling
+            elif tokens[1].spelling in ['++', '--']:
+                child = self.transform(next(node.get_children()))
+                if tokens[1].spelling == '++':
+                    return PostIncrement(Symbol(child))
+                if tokens[1].spelling == '--':
+                    return PostDecrement(Symbol(child))
+            else:
+                raise NotImplementedError("Dereferencing operator, "
+                    "Address operator and bitwise NOT operator "
+                    "have not been implemented yet!")
+
+        def transform_binary_operator(self, node):
+            """Transformation function for handling binary operators
+
+            Returns
+            =======
+
+            binary_expression: Codegen AST node
+                    simplified binary expression represented as Codegen AST
+
+            Raises
+            ======
+
+            NotImplementedError
+                If a bitwise operator or
+                unary operator(which is a child of any binary
+                operator in Clang AST) is encountered
+
+            """
+            # get all the tokens of assignment
+            # and store it in the tokens list
+            tokens = list(node.get_tokens())
+
+            # supported operators list
+            operators_list = ['+', '-', '*', '/', '%','=',
+            '>', '>=', '<', '<=', '==', '!=', '&&', '||', '+=', '-=',
+            '*=', '/=', '%=']
+
+            # this stack will contain variable content
+            # and type of variable in the rhs
+            combined_variables_stack = []
+
+            # this stack will contain operators
+            # to be processed in the rhs
+            operators_stack = []
+
+            # iterate through every token
+            for token in tokens:
+                # token is either '(', ')' or
+                # any of the supported operators from the operator list
+                if token.kind == cin.TokenKind.PUNCTUATION:
+
+                    # push '(' to the operators stack
+                    if token.spelling == '(':
+                        operators_stack.append('(')
+
+                    elif token.spelling == ')':
+                        # keep adding the expression to the
+                        # combined variables stack unless
+                        # '(' is found
+                        while (operators_stack
+                            and operators_stack[-1] != '('):
+                            if len(combined_variables_stack) < 2:
+                                raise NotImplementedError(
+                                    "Unary operators as a part of "
+                                    "binary operators is not "
+                                    "supported yet!")
+                            rhs = combined_variables_stack.pop()
+                            lhs = combined_variables_stack.pop()
+                            operator = operators_stack.pop()
+                            combined_variables_stack.append(
+                                self.perform_operation(
+                                lhs, rhs, operator))
+
+                        # pop '('
+                        operators_stack.pop()
+
+                    # token is an operator (supported)
+                    elif token.spelling in operators_list:
+                        while (operators_stack
+                            and self.priority_of(token.spelling)
+                            <= self.priority_of(
+                            operators_stack[-1])):
+                            if len(combined_variables_stack) < 2:
+                                raise NotImplementedError(
+                                    "Unary operators as a part of "
+                                    "binary operators is not "
+                                    "supported yet!")
+                            rhs = combined_variables_stack.pop()
+                            lhs = combined_variables_stack.pop()
+                            operator = operators_stack.pop()
+                            combined_variables_stack.append(
+                                self.perform_operation(
+                                lhs, rhs, operator))
+
+                        # push current operator
+                        operators_stack.append(token.spelling)
+
+                    # token is a bitwise operator
+                    elif token.spelling in ['&', '|', '^', '<<', '>>']:
+                        raise NotImplementedError(
+                            "Bitwise operator has not been "
+                            "implemented yet!")
+
+                    # token is a shorthand bitwise operator
+                    elif token.spelling in ['&=', '|=', '^=', '<<=',
+                    '>>=']:
+                        raise NotImplementedError(
+                            "Shorthand bitwise operator has not been "
+                            "implemented yet!")
+                    else:
+                        raise NotImplementedError(
+                            "Given token {} is not implemented yet!"
+                            .format(token.spelling))
+
+                # token is an identifier(variable)
+                elif token.kind == cin.TokenKind.IDENTIFIER:
+                    combined_variables_stack.append(
+                        [token.spelling, 'identifier'])
+
+                # token is a literal
+                elif token.kind == cin.TokenKind.LITERAL:
+                    combined_variables_stack.append(
+                        [token.spelling, 'literal'])
+
+                # token is a keyword, either true or false
+                elif (token.kind == cin.TokenKind.KEYWORD
+                    and token.spelling in ['true', 'false']):
+                    combined_variables_stack.append(
+                        [token.spelling, 'boolean'])
+                else:
+                    raise NotImplementedError(
+                        "Given token {} is not implemented yet!"
+                        .format(token.spelling))
+
+            # process remaining operators
+            while operators_stack:
+                if len(combined_variables_stack) < 2:
+                    raise NotImplementedError(
+                        "Unary operators as a part of "
+                        "binary operators is not "
+                        "supported yet!")
+                rhs = combined_variables_stack.pop()
+                lhs = combined_variables_stack.pop()
+                operator = operators_stack.pop()
+                combined_variables_stack.append(
+                    self.perform_operation(lhs, rhs, operator))
+
+            return combined_variables_stack[-1][0]
+
+        def priority_of(self, op):
+            """To get the priority of given operator"""
+            if op in ['=', '+=', '-=', '*=', '/=', '%=']:
+                return 1
+            if op in ['&&', '||']:
+                return 2
+            if op in ['<', '<=', '>', '>=', '==', '!=']:
+                return 3
+            if op in ['+', '-']:
+                return 4
+            if op in ['*', '/', '%']:
+                return 5
+            return 0
+
+        def perform_operation(self, lhs, rhs, op):
+            """Performs operation supported by the SymPy core
+
+            Returns
+            =======
+
+            combined_variable: list
+                contains variable content and type of variable
+
+            """
+            lhs_value = self.get_expr_for_operand(lhs)
+            rhs_value = self.get_expr_for_operand(rhs)
+            if op == '+':
+                return [Add(lhs_value, rhs_value), 'expr']
+            if op == '-':
+                return [Add(lhs_value, -rhs_value), 'expr']
+            if op == '*':
+                return [Mul(lhs_value, rhs_value), 'expr']
+            if op == '/':
+                return [Mul(lhs_value, Pow(rhs_value, Integer(-1))), 'expr']
+            if op == '%':
+                return [Mod(lhs_value, rhs_value), 'expr']
+            if op in ['<', '<=', '>', '>=', '==', '!=']:
+                return [Rel(lhs_value, rhs_value, op), 'expr']
+            if op == '&&':
+                return [And(as_Boolean(lhs_value), as_Boolean(rhs_value)), 'expr']
+            if op == '||':
+                return [Or(as_Boolean(lhs_value), as_Boolean(rhs_value)), 'expr']
+            if op == '=':
+                return [Assignment(Variable(lhs_value), rhs_value), 'expr']
+            if op in ['+=', '-=', '*=', '/=', '%=']:
+                return [aug_assign(Variable(lhs_value), op[0], rhs_value), 'expr']
+
+        def get_expr_for_operand(self, combined_variable):
+            """Gives out SymPy Codegen AST node
+
+            AST node returned is corresponding to
+            combined variable passed.Combined variable contains
+            variable content and type of variable
+
+            """
+            if combined_variable[1] == 'identifier':
+                return Symbol(combined_variable[0])
+            if combined_variable[1] == 'literal':
+                if '.' in combined_variable[0]:
+                    return Float(float(combined_variable[0]))
+                else:
+                    return Integer(int(combined_variable[0]))
+            if combined_variable[1] == 'expr':
+                return combined_variable[0]
+            if combined_variable[1] == 'boolean':
+                    return true if combined_variable[0] == 'true' else false
+
+        def transform_null_stmt(self, node):
+            """Handles Null Statement and returns None"""
+            return none
+
+        def transform_while_stmt(self, node):
+            """Transformation function for handling while statement
+
+            Returns
+            =======
+
+            while statement : Codegen AST Node
+                contains the while statement node having condition and
+                statement block
+
+            """
+            children = node.get_children()
+
+            condition = self.transform(next(children))
+            statements = self.transform(next(children))
+
+            if isinstance(statements, list):
+                statement_block = CodeBlock(*statements)
+            else:
+                statement_block = CodeBlock(statements)
+
+            return While(condition, statement_block)
+
+
+
+else:
+    class CCodeConverter():  # type: ignore
+        def __init__(self, *args, **kwargs):
+            raise ImportError("Module not Installed")
+
+
+def parse_c(source):
+    """Function for converting a C source code
+
+    The function reads the source code present in the given file and parses it
+    to give out SymPy Expressions
+
+    Returns
+    =======
+
+    src : list
+        List of Python expression strings
+
+    """
+    converter = CCodeConverter()
+    if os.path.exists(source):
+        src = converter.parse(source, flags = [])
+    else:
+        src = converter.parse_str(source, flags = [])
+    return src
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/fortran/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/fortran/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..c65e37cf3de2dddbcee0fa5c7eeac2fdc9f685db
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/fortran/__init__.py
@@ -0,0 +1 @@
+"""Used for translating Fortran source code into a SymPy expression. """
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/fortran/fortran_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/fortran/fortran_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..504249f6119a59a90d91c5e989f893cffe20e643
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/fortran/fortran_parser.py
@@ -0,0 +1,347 @@
+from sympy.external import import_module
+
+lfortran = import_module('lfortran')
+
+if lfortran:
+    from sympy.codegen.ast import (Variable, IntBaseType, FloatBaseType, String,
+                                   Return, FunctionDefinition, Assignment)
+    from sympy.core import Add, Mul, Integer, Float
+    from sympy.core.symbol import Symbol
+
+    asr_mod = lfortran.asr
+    asr = lfortran.asr.asr
+    src_to_ast = lfortran.ast.src_to_ast
+    ast_to_asr = lfortran.semantic.ast_to_asr.ast_to_asr
+
+    """
+    This module contains all the necessary Classes and Function used to Parse
+    Fortran code into SymPy expression
+
+    The module and its API are currently under development and experimental.
+    It is also dependent on LFortran for the ASR that is converted to SymPy syntax
+    which is also under development.
+    The module only supports the features currently supported by the LFortran ASR
+    which will be updated as the development of LFortran and this module progresses
+
+    You might find unexpected bugs and exceptions while using the module, feel free
+    to report them to the SymPy Issue Tracker
+
+    The API for the module might also change while in development if better and
+    more effective ways are discovered for the process
+
+    Features Supported
+    ==================
+
+    - Variable Declarations (integers and reals)
+    - Function Definitions
+    - Assignments and Basic Binary Operations
+
+
+    Notes
+    =====
+
+    The module depends on an external dependency
+
+    LFortran : Required to parse Fortran source code into ASR
+
+
+    References
+    ==========
+
+    .. [1] https://github.com/sympy/sympy/issues
+    .. [2] https://gitlab.com/lfortran/lfortran
+    .. [3] https://docs.lfortran.org/
+
+    """
+
+
+    class ASR2PyVisitor(asr.ASTVisitor):  # type: ignore
+        """
+        Visitor Class for LFortran ASR
+
+        It is a Visitor class derived from asr.ASRVisitor which visits all the
+        nodes of the LFortran ASR and creates corresponding AST node for each
+        ASR node
+
+        """
+
+        def __init__(self):
+            """Initialize the Parser"""
+            self._py_ast = []
+
+        def visit_TranslationUnit(self, node):
+            """
+            Function to visit all the elements of the Translation Unit
+            created by LFortran ASR
+            """
+            for s in node.global_scope.symbols:
+                sym = node.global_scope.symbols[s]
+                self.visit(sym)
+            for item in node.items:
+                self.visit(item)
+
+        def visit_Assignment(self, node):
+            """Visitor Function for Assignment
+
+            Visits each Assignment is the LFortran ASR and creates corresponding
+            assignment for SymPy.
+
+            Notes
+            =====
+
+            The function currently only supports variable assignment and binary
+            operation assignments of varying multitudes. Any type of numberS or
+            array is not supported.
+
+            Raises
+            ======
+
+            NotImplementedError() when called for Numeric assignments or Arrays
+
+            """
+            # TODO: Arithmetic Assignment
+            if isinstance(node.target, asr.Variable):
+                target = node.target
+                value = node.value
+                if isinstance(value, asr.Variable):
+                    new_node = Assignment(
+                            Variable(
+                                    target.name
+                                ),
+                            Variable(
+                                    value.name
+                                )
+                        )
+                elif (type(value) == asr.BinOp):
+                    exp_ast = call_visitor(value)
+                    for expr in exp_ast:
+                        new_node = Assignment(
+                                Variable(target.name),
+                                expr
+                            )
+                else:
+                    raise NotImplementedError("Numeric assignments not supported")
+            else:
+                raise NotImplementedError("Arrays not supported")
+            self._py_ast.append(new_node)
+
+        def visit_BinOp(self, node):
+            """Visitor Function for Binary Operations
+
+            Visits each binary operation present in the LFortran ASR like addition,
+            subtraction, multiplication, division and creates the corresponding
+            operation node in SymPy's AST
+
+            In case of more than one binary operations, the function calls the
+            call_visitor() function on the child nodes of the binary operations
+            recursively until all the operations have been processed.
+
+            Notes
+            =====
+
+            The function currently only supports binary operations with Variables
+            or other binary operations. Numerics are not supported as of yet.
+
+            Raises
+            ======
+
+            NotImplementedError() when called for Numeric assignments
+
+            """
+            # TODO: Integer Binary Operations
+            op = node.op
+            lhs = node.left
+            rhs = node.right
+
+            if (type(lhs) == asr.Variable):
+                left_value = Symbol(lhs.name)
+            elif(type(lhs) == asr.BinOp):
+                l_exp_ast = call_visitor(lhs)
+                for exp in l_exp_ast:
+                    left_value = exp
+            else:
+                raise NotImplementedError("Numbers Currently not supported")
+
+            if (type(rhs) == asr.Variable):
+                right_value = Symbol(rhs.name)
+            elif(type(rhs) == asr.BinOp):
+                r_exp_ast = call_visitor(rhs)
+                for exp in r_exp_ast:
+                    right_value = exp
+            else:
+                raise NotImplementedError("Numbers Currently not supported")
+
+            if isinstance(op, asr.Add):
+                new_node = Add(left_value, right_value)
+            elif isinstance(op, asr.Sub):
+                new_node = Add(left_value, -right_value)
+            elif isinstance(op, asr.Div):
+                new_node = Mul(left_value, 1/right_value)
+            elif isinstance(op, asr.Mul):
+                new_node = Mul(left_value, right_value)
+
+            self._py_ast.append(new_node)
+
+        def visit_Variable(self, node):
+            """Visitor Function for Variable Declaration
+
+            Visits each variable declaration present in the ASR and creates a
+            Symbol declaration for each variable
+
+            Notes
+            =====
+
+            The functions currently only support declaration of integer and
+            real variables. Other data types are still under development.
+
+            Raises
+            ======
+
+            NotImplementedError() when called for unsupported data types
+
+            """
+            if isinstance(node.type, asr.Integer):
+                var_type = IntBaseType(String('integer'))
+                value = Integer(0)
+            elif isinstance(node.type, asr.Real):
+                var_type = FloatBaseType(String('real'))
+                value = Float(0.0)
+            else:
+                raise NotImplementedError("Data type not supported")
+
+            if not (node.intent == 'in'):
+                new_node = Variable(
+                    node.name
+                ).as_Declaration(
+                    type = var_type,
+                    value = value
+                )
+                self._py_ast.append(new_node)
+
+        def visit_Sequence(self, seq):
+            """Visitor Function for code sequence
+
+            Visits a code sequence/ block and calls the visitor function on all the
+            children of the code block to create corresponding code in python
+
+            """
+            if seq is not None:
+                for node in seq:
+                    self._py_ast.append(call_visitor(node))
+
+        def visit_Num(self, node):
+            """Visitor Function for Numbers in ASR
+
+            This function is currently under development and will be updated
+            with improvements in the LFortran ASR
+
+            """
+            # TODO:Numbers when the LFortran ASR is updated
+            # self._py_ast.append(Integer(node.n))
+            pass
+
+        def visit_Function(self, node):
+            """Visitor Function for function Definitions
+
+            Visits each function definition present in the ASR and creates a
+            function definition node in the Python AST with all the elements of the
+            given function
+
+            The functions declare all the variables required as SymPy symbols in
+            the function before the function definition
+
+            This function also the call_visior_function to parse the contents of
+            the function body
+
+            """
+            # TODO: Return statement, variable declaration
+            fn_args = [Variable(arg_iter.name) for arg_iter in node.args]
+            fn_body = []
+            fn_name = node.name
+            for i in node.body:
+                fn_ast = call_visitor(i)
+            try:
+                fn_body_expr = fn_ast
+            except UnboundLocalError:
+                fn_body_expr = []
+            for sym in node.symtab.symbols:
+                decl = call_visitor(node.symtab.symbols[sym])
+                for symbols in decl:
+                    fn_body.append(symbols)
+            for elem in fn_body_expr:
+                fn_body.append(elem)
+            fn_body.append(
+                Return(
+                    Variable(
+                        node.return_var.name
+                    )
+                )
+            )
+            if isinstance(node.return_var.type, asr.Integer):
+                ret_type = IntBaseType(String('integer'))
+            elif isinstance(node.return_var.type, asr.Real):
+                ret_type = FloatBaseType(String('real'))
+            else:
+                raise NotImplementedError("Data type not supported")
+            new_node = FunctionDefinition(
+                        return_type = ret_type,
+                        name = fn_name,
+                        parameters = fn_args,
+                        body = fn_body
+                    )
+            self._py_ast.append(new_node)
+
+        def ret_ast(self):
+            """Returns the AST nodes"""
+            return self._py_ast
+else:
+    class ASR2PyVisitor():  # type: ignore
+        def __init__(self, *args, **kwargs):
+            raise ImportError('lfortran not available')
+
+def call_visitor(fort_node):
+    """Calls the AST Visitor on the Module
+
+    This function is used to call the AST visitor for a program or module
+    It imports all the required modules and calls the visit() function
+    on the given node
+
+    Parameters
+    ==========
+
+    fort_node : LFortran ASR object
+        Node for the operation for which the NodeVisitor is called
+
+    Returns
+    =======
+
+    res_ast : list
+        list of SymPy AST Nodes
+
+    """
+    v = ASR2PyVisitor()
+    v.visit(fort_node)
+    res_ast = v.ret_ast()
+    return res_ast
+
+
+def src_to_sympy(src):
+    """Wrapper function to convert the given Fortran source code to SymPy Expressions
+
+    Parameters
+    ==========
+
+    src : string
+        A string with the Fortran source code
+
+    Returns
+    =======
+
+    py_src : string
+        A string with the Python source code compatible with SymPy
+
+    """
+    a_ast = src_to_ast(src, translation_unit=False)
+    a = ast_to_asr(a_ast)
+    py_src = call_visitor(a)
+    return py_src
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/LICENSE.txt b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/LICENSE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6bbfda911b2afada41a568218e31a6502dc68f44
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/LICENSE.txt
@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright 2016, latex2sympy
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/LaTeX.g4 b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/LaTeX.g4
new file mode 100644
index 0000000000000000000000000000000000000000..fc2c30f9817931e2060b549a39f98a6a4f9cb1f7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/LaTeX.g4
@@ -0,0 +1,312 @@
+/*
+ ANTLR4 LaTeX Math Grammar
+
+ Ported from latex2sympy by @augustt198 https://github.com/augustt198/latex2sympy See license in
+ LICENSE.txt
+ */
+
+/*
+ After changing this file, it is necessary to run `python setup.py antlr` in the root directory of
+ the repository. This will regenerate the code in `sympy/parsing/latex/_antlr/*.py`.
+ */
+
+grammar LaTeX;
+
+options {
+	language = Python3;
+}
+
+WS: [ \t\r\n]+ -> skip;
+THINSPACE: ('\\,' | '\\thinspace') -> skip;
+MEDSPACE: ('\\:' | '\\medspace') -> skip;
+THICKSPACE: ('\\;' | '\\thickspace') -> skip;
+QUAD: '\\quad' -> skip;
+QQUAD: '\\qquad' -> skip;
+NEGTHINSPACE: ('\\!' | '\\negthinspace') -> skip;
+NEGMEDSPACE: '\\negmedspace' -> skip;
+NEGTHICKSPACE: '\\negthickspace' -> skip;
+CMD_LEFT: '\\left' -> skip;
+CMD_RIGHT: '\\right' -> skip;
+
+IGNORE:
+	(
+		'\\vrule'
+		| '\\vcenter'
+		| '\\vbox'
+		| '\\vskip'
+		| '\\vspace'
+		| '\\hfil'
+		| '\\*'
+		| '\\-'
+		| '\\.'
+		| '\\/'
+		| '\\"'
+		| '\\('
+		| '\\='
+	) -> skip;
+
+ADD: '+';
+SUB: '-';
+MUL: '*';
+DIV: '/';
+
+L_PAREN: '(';
+R_PAREN: ')';
+L_BRACE: '{';
+R_BRACE: '}';
+L_BRACE_LITERAL: '\\{';
+R_BRACE_LITERAL: '\\}';
+L_BRACKET: '[';
+R_BRACKET: ']';
+
+BAR: '|';
+
+R_BAR: '\\right|';
+L_BAR: '\\left|';
+
+L_ANGLE: '\\langle';
+R_ANGLE: '\\rangle';
+FUNC_LIM: '\\lim';
+LIM_APPROACH_SYM:
+	'\\to'
+	| '\\rightarrow'
+	| '\\Rightarrow'
+	| '\\longrightarrow'
+	| '\\Longrightarrow';
+FUNC_INT:
+    '\\int'
+    | '\\int\\limits';
+FUNC_SUM: '\\sum';
+FUNC_PROD: '\\prod';
+
+FUNC_EXP: '\\exp';
+FUNC_LOG: '\\log';
+FUNC_LG: '\\lg';
+FUNC_LN: '\\ln';
+FUNC_SIN: '\\sin';
+FUNC_COS: '\\cos';
+FUNC_TAN: '\\tan';
+FUNC_CSC: '\\csc';
+FUNC_SEC: '\\sec';
+FUNC_COT: '\\cot';
+
+FUNC_ARCSIN: '\\arcsin';
+FUNC_ARCCOS: '\\arccos';
+FUNC_ARCTAN: '\\arctan';
+FUNC_ARCCSC: '\\arccsc';
+FUNC_ARCSEC: '\\arcsec';
+FUNC_ARCCOT: '\\arccot';
+
+FUNC_SINH: '\\sinh';
+FUNC_COSH: '\\cosh';
+FUNC_TANH: '\\tanh';
+FUNC_ARSINH: '\\arsinh';
+FUNC_ARCOSH: '\\arcosh';
+FUNC_ARTANH: '\\artanh';
+
+L_FLOOR: '\\lfloor';
+R_FLOOR: '\\rfloor';
+L_CEIL: '\\lceil';
+R_CEIL: '\\rceil';
+
+FUNC_SQRT: '\\sqrt';
+FUNC_OVERLINE: '\\overline';
+
+CMD_TIMES: '\\times';
+CMD_CDOT: '\\cdot';
+CMD_DIV: '\\div';
+CMD_FRAC:
+    '\\frac'
+    | '\\dfrac'
+    | '\\tfrac';
+CMD_BINOM: '\\binom';
+CMD_DBINOM: '\\dbinom';
+CMD_TBINOM: '\\tbinom';
+
+CMD_MATHIT: '\\mathit';
+
+UNDERSCORE: '_';
+CARET: '^';
+COLON: ':';
+
+fragment WS_CHAR: [ \t\r\n];
+DIFFERENTIAL: 'd' WS_CHAR*? ([a-zA-Z] | '\\' [a-zA-Z]+);
+
+LETTER: [a-zA-Z];
+DIGIT: [0-9];
+
+EQUAL: (('&' WS_CHAR*?)? '=') | ('=' (WS_CHAR*? '&')?);
+NEQ: '\\neq';
+
+LT: '<';
+LTE: ('\\leq' | '\\le' | LTE_Q | LTE_S);
+LTE_Q: '\\leqq';
+LTE_S: '\\leqslant';
+
+GT: '>';
+GTE: ('\\geq' | '\\ge' | GTE_Q | GTE_S);
+GTE_Q: '\\geqq';
+GTE_S: '\\geqslant';
+
+BANG: '!';
+
+SINGLE_QUOTES: '\''+;
+
+SYMBOL: '\\' [a-zA-Z]+;
+
+math: relation;
+
+relation:
+	relation (EQUAL | LT | LTE | GT | GTE | NEQ) relation
+	| expr;
+
+equality: expr EQUAL expr;
+
+expr: additive;
+
+additive: additive (ADD | SUB) additive | mp;
+
+// mult part
+mp:
+	mp (MUL | CMD_TIMES | CMD_CDOT | DIV | CMD_DIV | COLON) mp
+	| unary;
+
+mp_nofunc:
+	mp_nofunc (
+		MUL
+		| CMD_TIMES
+		| CMD_CDOT
+		| DIV
+		| CMD_DIV
+		| COLON
+	) mp_nofunc
+	| unary_nofunc;
+
+unary: (ADD | SUB) unary | postfix+;
+
+unary_nofunc:
+	(ADD | SUB) unary_nofunc
+	| postfix postfix_nofunc*;
+
+postfix: exp postfix_op*;
+postfix_nofunc: exp_nofunc postfix_op*;
+postfix_op: BANG | eval_at;
+
+eval_at:
+	BAR (eval_at_sup | eval_at_sub | eval_at_sup eval_at_sub);
+
+eval_at_sub: UNDERSCORE L_BRACE (expr | equality) R_BRACE;
+
+eval_at_sup: CARET L_BRACE (expr | equality) R_BRACE;
+
+exp: exp CARET (atom | L_BRACE expr R_BRACE) subexpr? | comp;
+
+exp_nofunc:
+	exp_nofunc CARET (atom | L_BRACE expr R_BRACE) subexpr?
+	| comp_nofunc;
+
+comp:
+	group
+	| abs_group
+	| func
+	| atom
+	| floor
+	| ceil;
+
+comp_nofunc:
+	group
+	| abs_group
+	| atom
+	| floor
+	| ceil;
+
+group:
+	L_PAREN expr R_PAREN
+	| L_BRACKET expr R_BRACKET
+	| L_BRACE expr R_BRACE
+	| L_BRACE_LITERAL expr R_BRACE_LITERAL;
+
+abs_group: BAR expr BAR;
+
+number: DIGIT+ (',' DIGIT DIGIT DIGIT)* ('.' DIGIT+)?;
+
+atom: (LETTER | SYMBOL) (subexpr? SINGLE_QUOTES? | SINGLE_QUOTES? subexpr?)
+	| number
+	| DIFFERENTIAL
+	| mathit
+	| frac
+	| binom
+	| bra
+	| ket;
+
+bra: L_ANGLE expr (R_BAR | BAR);
+ket: (L_BAR | BAR) expr R_ANGLE;
+
+mathit: CMD_MATHIT L_BRACE mathit_text R_BRACE;
+mathit_text: LETTER*;
+
+frac: CMD_FRAC (upperd = DIGIT | L_BRACE upper = expr R_BRACE)
+    (lowerd = DIGIT | L_BRACE lower = expr R_BRACE);
+
+binom:
+	(CMD_BINOM | CMD_DBINOM | CMD_TBINOM) L_BRACE n = expr R_BRACE L_BRACE k = expr R_BRACE;
+
+floor: L_FLOOR val = expr R_FLOOR;
+ceil: L_CEIL val = expr R_CEIL;
+
+func_normal:
+	FUNC_EXP
+	| FUNC_LOG
+	| FUNC_LG
+	| FUNC_LN
+	| FUNC_SIN
+	| FUNC_COS
+	| FUNC_TAN
+	| FUNC_CSC
+	| FUNC_SEC
+	| FUNC_COT
+	| FUNC_ARCSIN
+	| FUNC_ARCCOS
+	| FUNC_ARCTAN
+	| FUNC_ARCCSC
+	| FUNC_ARCSEC
+	| FUNC_ARCCOT
+	| FUNC_SINH
+	| FUNC_COSH
+	| FUNC_TANH
+	| FUNC_ARSINH
+	| FUNC_ARCOSH
+	| FUNC_ARTANH;
+
+func:
+	func_normal (subexpr? supexpr? | supexpr? subexpr?) (
+		L_PAREN func_arg R_PAREN
+		| func_arg_noparens
+	)
+	| (LETTER | SYMBOL) (subexpr? SINGLE_QUOTES? | SINGLE_QUOTES? subexpr?) // e.g. f(x), f_1'(x)
+	L_PAREN args R_PAREN
+	| FUNC_INT (subexpr supexpr | supexpr subexpr)? (
+		additive? DIFFERENTIAL
+		| frac
+		| additive
+	)
+	| FUNC_SQRT (L_BRACKET root = expr R_BRACKET)? L_BRACE base = expr R_BRACE
+	| FUNC_OVERLINE L_BRACE base = expr R_BRACE
+	| (FUNC_SUM | FUNC_PROD) (subeq supexpr | supexpr subeq) mp
+	| FUNC_LIM limit_sub mp;
+
+args: (expr ',' args) | expr;
+
+limit_sub:
+	UNDERSCORE L_BRACE (LETTER | SYMBOL) LIM_APPROACH_SYM expr (
+		CARET ((L_BRACE (ADD | SUB) R_BRACE) | ADD | SUB)
+	)? R_BRACE;
+
+func_arg: expr | (expr ',' func_arg);
+func_arg_noparens: mp_nofunc;
+
+subexpr: UNDERSCORE (atom | L_BRACE expr R_BRACE);
+supexpr: CARET (atom | L_BRACE expr R_BRACE);
+
+subeq: UNDERSCORE L_BRACE equality R_BRACE;
+supeq: UNDERSCORE L_BRACE equality R_BRACE;
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..9466d37b8b06f1f292c73f975e44d21c96da10d1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/__init__.py
@@ -0,0 +1,204 @@
+from sympy.external import import_module
+from sympy.utilities.decorator import doctest_depends_on
+from re import compile as rcompile
+
+from sympy.parsing.latex.lark import LarkLaTeXParser, TransformToSymPyExpr, parse_latex_lark # noqa
+
+from .errors import LaTeXParsingError  # noqa
+
+
+IGNORE_L = r"\s*[{]*\s*"
+IGNORE_R = r"\s*[}]*\s*"
+NO_LEFT = r"(? len(latex_str):
+            e = len(latex_str)
+            eellipsis = ""
+
+        if x[3] in END_DELIM_REPR:
+            err = (f"Extra '{x[2]}' at index {x[0]} or "
+                   "missing corresponding "
+                   f"'{BEGIN_DELIM_REPR[MATRIX_DELIMS_INV[x[3]]]}' "
+                   f"in LaTeX string: {sellipsis}{latex_str[s:e]}"
+                   f"{eellipsis}")
+            raise LaTeXParsingError(err)
+
+        if x[7] is None:
+            err = (f"Extra '{x[2]}' at index {x[0]} or "
+                   "missing corresponding "
+                   f"'{END_DELIM_REPR[MATRIX_DELIMS[x[3]]]}' "
+                   f"in LaTeX string: {sellipsis}{latex_str[s:e]}"
+                   f"{eellipsis}")
+            raise LaTeXParsingError(err)
+
+        correct_end_regex = MATRIX_DELIMS[x[3]]
+        sellipsis = "..." if x[0] > 0 else ""
+        eellipsis = "..." if x[5] < len(latex_str) else ""
+        if x[7] != correct_end_regex:
+            err = ("Expected "
+                   f"'{END_DELIM_REPR[correct_end_regex]}' "
+                   f"to close the '{x[2]}' at index {x[0]} but "
+                   f"found '{x[6]}' at index {x[4]} of LaTeX "
+                   f"string instead: {sellipsis}{latex_str[x[0]:x[5]]}"
+                   f"{eellipsis}")
+            raise LaTeXParsingError(err)
+
+__doctest_requires__ = {('parse_latex',): ['antlr4', 'lark']}
+
+
+@doctest_depends_on(modules=('antlr4', 'lark'))
+def parse_latex(s, strict=False, backend="antlr"):
+    r"""Converts the input LaTeX string ``s`` to a SymPy ``Expr``.
+
+    Parameters
+    ==========
+
+    s : str
+        The LaTeX string to parse. In Python source containing LaTeX,
+        *raw strings* (denoted with ``r"``, like this one) are preferred,
+        as LaTeX makes liberal use of the ``\`` character, which would
+        trigger escaping in normal Python strings.
+    backend : str, optional
+        Currently, there are two backends supported: ANTLR, and Lark.
+        The default setting is to use the ANTLR backend, which can be
+        changed to Lark if preferred.
+
+        Use ``backend="antlr"`` for the ANTLR-based parser, and
+        ``backend="lark"`` for the Lark-based parser.
+
+        The ``backend`` option is case-sensitive, and must be in
+        all lowercase.
+    strict : bool, optional
+        This option is only available with the ANTLR backend.
+
+        If True, raise an exception if the string cannot be parsed as
+        valid LaTeX. If False, try to recover gracefully from common
+        mistakes.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.latex import parse_latex
+    >>> expr = parse_latex(r"\frac {1 + \sqrt {\a}} {\b}")
+    >>> expr
+    (sqrt(a) + 1)/b
+    >>> expr.evalf(4, subs=dict(a=5, b=2))
+    1.618
+    >>> func = parse_latex(r"\int_1^\alpha \dfrac{\mathrm{d}t}{t}", backend="lark")
+    >>> func.evalf(subs={"alpha": 2})
+    0.693147180559945
+    """
+
+    check_matrix_delimiters(s)
+
+    if backend == "antlr":
+        _latex = import_module(
+            'sympy.parsing.latex._parse_latex_antlr',
+            import_kwargs={'fromlist': ['X']})
+
+        if _latex is not None:
+            return _latex.parse_latex(s, strict)
+    elif backend == "lark":
+        return parse_latex_lark(s)
+    else:
+        raise NotImplementedError(f"Using the '{backend}' backend in the LaTeX" \
+                                   " parser is not supported.")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d690e1eb8631ee7731fc1875769d3a4704a1743
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/__init__.py
@@ -0,0 +1,9 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated from ../LaTeX.g4, derived from latex2sympy
+#     latex2sympy is licensed under the MIT license
+#     https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/latexlexer.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/latexlexer.py
new file mode 100644
index 0000000000000000000000000000000000000000..46ca959736c967782eef360b9b3268ccd0be0979
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/latexlexer.py
@@ -0,0 +1,512 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated from ../LaTeX.g4, derived from latex2sympy
+#     latex2sympy is licensed under the MIT license
+#     https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+from antlr4 import *
+from io import StringIO
+import sys
+if sys.version_info[1] > 5:
+    from typing import TextIO
+else:
+    from typing.io import TextIO
+
+
+def serializedATN():
+    return [
+        4,0,91,911,6,-1,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,
+        2,6,7,6,2,7,7,7,2,8,7,8,2,9,7,9,2,10,7,10,2,11,7,11,2,12,7,12,2,
+        13,7,13,2,14,7,14,2,15,7,15,2,16,7,16,2,17,7,17,2,18,7,18,2,19,7,
+        19,2,20,7,20,2,21,7,21,2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,2,
+        26,7,26,2,27,7,27,2,28,7,28,2,29,7,29,2,30,7,30,2,31,7,31,2,32,7,
+        32,2,33,7,33,2,34,7,34,2,35,7,35,2,36,7,36,2,37,7,37,2,38,7,38,2,
+        39,7,39,2,40,7,40,2,41,7,41,2,42,7,42,2,43,7,43,2,44,7,44,2,45,7,
+        45,2,46,7,46,2,47,7,47,2,48,7,48,2,49,7,49,2,50,7,50,2,51,7,51,2,
+        52,7,52,2,53,7,53,2,54,7,54,2,55,7,55,2,56,7,56,2,57,7,57,2,58,7,
+        58,2,59,7,59,2,60,7,60,2,61,7,61,2,62,7,62,2,63,7,63,2,64,7,64,2,
+        65,7,65,2,66,7,66,2,67,7,67,2,68,7,68,2,69,7,69,2,70,7,70,2,71,7,
+        71,2,72,7,72,2,73,7,73,2,74,7,74,2,75,7,75,2,76,7,76,2,77,7,77,2,
+        78,7,78,2,79,7,79,2,80,7,80,2,81,7,81,2,82,7,82,2,83,7,83,2,84,7,
+        84,2,85,7,85,2,86,7,86,2,87,7,87,2,88,7,88,2,89,7,89,2,90,7,90,2,
+        91,7,91,1,0,1,0,1,1,1,1,1,2,4,2,191,8,2,11,2,12,2,192,1,2,1,2,1,
+        3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,3,3,209,8,3,1,3,1,
+        3,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,3,4,224,8,4,1,4,1,
+        4,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,3,5,241,8,
+        5,1,5,1,5,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,7,1,7,1,7,1,7,1,7,1,
+        7,1,7,1,7,1,7,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,
+        8,1,8,1,8,3,8,277,8,8,1,8,1,8,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,
+        9,1,9,1,9,1,9,1,9,1,9,1,9,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,
+        1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,11,1,11,1,11,1,11,
+        1,11,1,11,1,11,1,11,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,
+        1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
+        1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
+        1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
+        1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,3,13,
+        381,8,13,1,13,1,13,1,14,1,14,1,15,1,15,1,16,1,16,1,17,1,17,1,18,
+        1,18,1,19,1,19,1,20,1,20,1,21,1,21,1,22,1,22,1,22,1,23,1,23,1,23,
+        1,24,1,24,1,25,1,25,1,26,1,26,1,27,1,27,1,27,1,27,1,27,1,27,1,27,
+        1,27,1,28,1,28,1,28,1,28,1,28,1,28,1,28,1,29,1,29,1,29,1,29,1,29,
+        1,29,1,29,1,29,1,30,1,30,1,30,1,30,1,30,1,30,1,30,1,30,1,31,1,31,
+        1,31,1,31,1,31,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
+        1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
+        1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
+        1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
+        1,32,1,32,1,32,1,32,1,32,1,32,3,32,504,8,32,1,33,1,33,1,33,1,33,
+        1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,3,33,521,
+        8,33,1,34,1,34,1,34,1,34,1,34,1,35,1,35,1,35,1,35,1,35,1,35,1,36,
+        1,36,1,36,1,36,1,36,1,37,1,37,1,37,1,37,1,37,1,38,1,38,1,38,1,38,
+        1,39,1,39,1,39,1,39,1,40,1,40,1,40,1,40,1,40,1,41,1,41,1,41,1,41,
+        1,41,1,42,1,42,1,42,1,42,1,42,1,43,1,43,1,43,1,43,1,43,1,44,1,44,
+        1,44,1,44,1,44,1,45,1,45,1,45,1,45,1,45,1,46,1,46,1,46,1,46,1,46,
+        1,46,1,46,1,46,1,47,1,47,1,47,1,47,1,47,1,47,1,47,1,47,1,48,1,48,
+        1,48,1,48,1,48,1,48,1,48,1,48,1,49,1,49,1,49,1,49,1,49,1,49,1,49,
+        1,49,1,50,1,50,1,50,1,50,1,50,1,50,1,50,1,50,1,51,1,51,1,51,1,51,
+        1,51,1,51,1,51,1,51,1,52,1,52,1,52,1,52,1,52,1,52,1,53,1,53,1,53,
+        1,53,1,53,1,53,1,54,1,54,1,54,1,54,1,54,1,54,1,55,1,55,1,55,1,55,
+        1,55,1,55,1,55,1,55,1,56,1,56,1,56,1,56,1,56,1,56,1,56,1,56,1,57,
+        1,57,1,57,1,57,1,57,1,57,1,57,1,57,1,58,1,58,1,58,1,58,1,58,1,58,
+        1,58,1,58,1,59,1,59,1,59,1,59,1,59,1,59,1,59,1,59,1,60,1,60,1,60,
+        1,60,1,60,1,60,1,60,1,61,1,61,1,61,1,61,1,61,1,61,1,61,1,62,1,62,
+        1,62,1,62,1,62,1,62,1,63,1,63,1,63,1,63,1,63,1,63,1,63,1,63,1,63,
+        1,63,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,65,1,65,1,65,1,65,1,65,
+        1,65,1,66,1,66,1,66,1,66,1,66,1,67,1,67,1,67,1,67,1,67,1,67,1,67,
+        1,67,1,67,1,67,1,67,1,67,1,67,1,67,1,67,1,67,1,67,3,67,753,8,67,
+        1,68,1,68,1,68,1,68,1,68,1,68,1,68,1,69,1,69,1,69,1,69,1,69,1,69,
+        1,69,1,69,1,70,1,70,1,70,1,70,1,70,1,70,1,70,1,70,1,71,1,71,1,71,
+        1,71,1,71,1,71,1,71,1,71,1,72,1,72,1,73,1,73,1,74,1,74,1,75,1,75,
+        1,76,1,76,5,76,796,8,76,10,76,12,76,799,9,76,1,76,1,76,1,76,4,76,
+        804,8,76,11,76,12,76,805,3,76,808,8,76,1,77,1,77,1,78,1,78,1,79,
+        1,79,5,79,816,8,79,10,79,12,79,819,9,79,3,79,821,8,79,1,79,1,79,
+        1,79,5,79,826,8,79,10,79,12,79,829,9,79,1,79,3,79,832,8,79,3,79,
+        834,8,79,1,80,1,80,1,80,1,80,1,80,1,81,1,81,1,82,1,82,1,82,1,82,
+        1,82,1,82,1,82,1,82,1,82,3,82,852,8,82,1,83,1,83,1,83,1,83,1,83,
+        1,83,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,85,1,85,
+        1,86,1,86,1,86,1,86,1,86,1,86,1,86,1,86,1,86,3,86,881,8,86,1,87,
+        1,87,1,87,1,87,1,87,1,87,1,88,1,88,1,88,1,88,1,88,1,88,1,88,1,88,
+        1,88,1,88,1,89,1,89,1,90,4,90,902,8,90,11,90,12,90,903,1,91,1,91,
+        4,91,908,8,91,11,91,12,91,909,3,797,817,827,0,92,1,1,3,2,5,3,7,4,
+        9,5,11,6,13,7,15,8,17,9,19,10,21,11,23,12,25,13,27,14,29,15,31,16,
+        33,17,35,18,37,19,39,20,41,21,43,22,45,23,47,24,49,25,51,26,53,27,
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+        0,0,579,580,5,116,0,0,580,92,1,0,0,0,581,582,5,92,0,0,582,583,5,
+        97,0,0,583,584,5,114,0,0,584,585,5,99,0,0,585,586,5,115,0,0,586,
+        587,5,105,0,0,587,588,5,110,0,0,588,94,1,0,0,0,589,590,5,92,0,0,
+        590,591,5,97,0,0,591,592,5,114,0,0,592,593,5,99,0,0,593,594,5,99,
+        0,0,594,595,5,111,0,0,595,596,5,115,0,0,596,96,1,0,0,0,597,598,5,
+        92,0,0,598,599,5,97,0,0,599,600,5,114,0,0,600,601,5,99,0,0,601,602,
+        5,116,0,0,602,603,5,97,0,0,603,604,5,110,0,0,604,98,1,0,0,0,605,
+        606,5,92,0,0,606,607,5,97,0,0,607,608,5,114,0,0,608,609,5,99,0,0,
+        609,610,5,99,0,0,610,611,5,115,0,0,611,612,5,99,0,0,612,100,1,0,
+        0,0,613,614,5,92,0,0,614,615,5,97,0,0,615,616,5,114,0,0,616,617,
+        5,99,0,0,617,618,5,115,0,0,618,619,5,101,0,0,619,620,5,99,0,0,620,
+        102,1,0,0,0,621,622,5,92,0,0,622,623,5,97,0,0,623,624,5,114,0,0,
+        624,625,5,99,0,0,625,626,5,99,0,0,626,627,5,111,0,0,627,628,5,116,
+        0,0,628,104,1,0,0,0,629,630,5,92,0,0,630,631,5,115,0,0,631,632,5,
+        105,0,0,632,633,5,110,0,0,633,634,5,104,0,0,634,106,1,0,0,0,635,
+        636,5,92,0,0,636,637,5,99,0,0,637,638,5,111,0,0,638,639,5,115,0,
+        0,639,640,5,104,0,0,640,108,1,0,0,0,641,642,5,92,0,0,642,643,5,116,
+        0,0,643,644,5,97,0,0,644,645,5,110,0,0,645,646,5,104,0,0,646,110,
+        1,0,0,0,647,648,5,92,0,0,648,649,5,97,0,0,649,650,5,114,0,0,650,
+        651,5,115,0,0,651,652,5,105,0,0,652,653,5,110,0,0,653,654,5,104,
+        0,0,654,112,1,0,0,0,655,656,5,92,0,0,656,657,5,97,0,0,657,658,5,
+        114,0,0,658,659,5,99,0,0,659,660,5,111,0,0,660,661,5,115,0,0,661,
+        662,5,104,0,0,662,114,1,0,0,0,663,664,5,92,0,0,664,665,5,97,0,0,
+        665,666,5,114,0,0,666,667,5,116,0,0,667,668,5,97,0,0,668,669,5,110,
+        0,0,669,670,5,104,0,0,670,116,1,0,0,0,671,672,5,92,0,0,672,673,5,
+        108,0,0,673,674,5,102,0,0,674,675,5,108,0,0,675,676,5,111,0,0,676,
+        677,5,111,0,0,677,678,5,114,0,0,678,118,1,0,0,0,679,680,5,92,0,0,
+        680,681,5,114,0,0,681,682,5,102,0,0,682,683,5,108,0,0,683,684,5,
+        111,0,0,684,685,5,111,0,0,685,686,5,114,0,0,686,120,1,0,0,0,687,
+        688,5,92,0,0,688,689,5,108,0,0,689,690,5,99,0,0,690,691,5,101,0,
+        0,691,692,5,105,0,0,692,693,5,108,0,0,693,122,1,0,0,0,694,695,5,
+        92,0,0,695,696,5,114,0,0,696,697,5,99,0,0,697,698,5,101,0,0,698,
+        699,5,105,0,0,699,700,5,108,0,0,700,124,1,0,0,0,701,702,5,92,0,0,
+        702,703,5,115,0,0,703,704,5,113,0,0,704,705,5,114,0,0,705,706,5,
+        116,0,0,706,126,1,0,0,0,707,708,5,92,0,0,708,709,5,111,0,0,709,710,
+        5,118,0,0,710,711,5,101,0,0,711,712,5,114,0,0,712,713,5,108,0,0,
+        713,714,5,105,0,0,714,715,5,110,0,0,715,716,5,101,0,0,716,128,1,
+        0,0,0,717,718,5,92,0,0,718,719,5,116,0,0,719,720,5,105,0,0,720,721,
+        5,109,0,0,721,722,5,101,0,0,722,723,5,115,0,0,723,130,1,0,0,0,724,
+        725,5,92,0,0,725,726,5,99,0,0,726,727,5,100,0,0,727,728,5,111,0,
+        0,728,729,5,116,0,0,729,132,1,0,0,0,730,731,5,92,0,0,731,732,5,100,
+        0,0,732,733,5,105,0,0,733,734,5,118,0,0,734,134,1,0,0,0,735,736,
+        5,92,0,0,736,737,5,102,0,0,737,738,5,114,0,0,738,739,5,97,0,0,739,
+        753,5,99,0,0,740,741,5,92,0,0,741,742,5,100,0,0,742,743,5,102,0,
+        0,743,744,5,114,0,0,744,745,5,97,0,0,745,753,5,99,0,0,746,747,5,
+        92,0,0,747,748,5,116,0,0,748,749,5,102,0,0,749,750,5,114,0,0,750,
+        751,5,97,0,0,751,753,5,99,0,0,752,735,1,0,0,0,752,740,1,0,0,0,752,
+        746,1,0,0,0,753,136,1,0,0,0,754,755,5,92,0,0,755,756,5,98,0,0,756,
+        757,5,105,0,0,757,758,5,110,0,0,758,759,5,111,0,0,759,760,5,109,
+        0,0,760,138,1,0,0,0,761,762,5,92,0,0,762,763,5,100,0,0,763,764,5,
+        98,0,0,764,765,5,105,0,0,765,766,5,110,0,0,766,767,5,111,0,0,767,
+        768,5,109,0,0,768,140,1,0,0,0,769,770,5,92,0,0,770,771,5,116,0,0,
+        771,772,5,98,0,0,772,773,5,105,0,0,773,774,5,110,0,0,774,775,5,111,
+        0,0,775,776,5,109,0,0,776,142,1,0,0,0,777,778,5,92,0,0,778,779,5,
+        109,0,0,779,780,5,97,0,0,780,781,5,116,0,0,781,782,5,104,0,0,782,
+        783,5,105,0,0,783,784,5,116,0,0,784,144,1,0,0,0,785,786,5,95,0,0,
+        786,146,1,0,0,0,787,788,5,94,0,0,788,148,1,0,0,0,789,790,5,58,0,
+        0,790,150,1,0,0,0,791,792,7,0,0,0,792,152,1,0,0,0,793,797,5,100,
+        0,0,794,796,3,151,75,0,795,794,1,0,0,0,796,799,1,0,0,0,797,798,1,
+        0,0,0,797,795,1,0,0,0,798,807,1,0,0,0,799,797,1,0,0,0,800,808,7,
+        1,0,0,801,803,5,92,0,0,802,804,7,1,0,0,803,802,1,0,0,0,804,805,1,
+        0,0,0,805,803,1,0,0,0,805,806,1,0,0,0,806,808,1,0,0,0,807,800,1,
+        0,0,0,807,801,1,0,0,0,808,154,1,0,0,0,809,810,7,1,0,0,810,156,1,
+        0,0,0,811,812,7,2,0,0,812,158,1,0,0,0,813,817,5,38,0,0,814,816,3,
+        151,75,0,815,814,1,0,0,0,816,819,1,0,0,0,817,818,1,0,0,0,817,815,
+        1,0,0,0,818,821,1,0,0,0,819,817,1,0,0,0,820,813,1,0,0,0,820,821,
+        1,0,0,0,821,822,1,0,0,0,822,834,5,61,0,0,823,831,5,61,0,0,824,826,
+        3,151,75,0,825,824,1,0,0,0,826,829,1,0,0,0,827,828,1,0,0,0,827,825,
+        1,0,0,0,828,830,1,0,0,0,829,827,1,0,0,0,830,832,5,38,0,0,831,827,
+        1,0,0,0,831,832,1,0,0,0,832,834,1,0,0,0,833,820,1,0,0,0,833,823,
+        1,0,0,0,834,160,1,0,0,0,835,836,5,92,0,0,836,837,5,110,0,0,837,838,
+        5,101,0,0,838,839,5,113,0,0,839,162,1,0,0,0,840,841,5,60,0,0,841,
+        164,1,0,0,0,842,843,5,92,0,0,843,844,5,108,0,0,844,845,5,101,0,0,
+        845,852,5,113,0,0,846,847,5,92,0,0,847,848,5,108,0,0,848,852,5,101,
+        0,0,849,852,3,167,83,0,850,852,3,169,84,0,851,842,1,0,0,0,851,846,
+        1,0,0,0,851,849,1,0,0,0,851,850,1,0,0,0,852,166,1,0,0,0,853,854,
+        5,92,0,0,854,855,5,108,0,0,855,856,5,101,0,0,856,857,5,113,0,0,857,
+        858,5,113,0,0,858,168,1,0,0,0,859,860,5,92,0,0,860,861,5,108,0,0,
+        861,862,5,101,0,0,862,863,5,113,0,0,863,864,5,115,0,0,864,865,5,
+        108,0,0,865,866,5,97,0,0,866,867,5,110,0,0,867,868,5,116,0,0,868,
+        170,1,0,0,0,869,870,5,62,0,0,870,172,1,0,0,0,871,872,5,92,0,0,872,
+        873,5,103,0,0,873,874,5,101,0,0,874,881,5,113,0,0,875,876,5,92,0,
+        0,876,877,5,103,0,0,877,881,5,101,0,0,878,881,3,175,87,0,879,881,
+        3,177,88,0,880,871,1,0,0,0,880,875,1,0,0,0,880,878,1,0,0,0,880,879,
+        1,0,0,0,881,174,1,0,0,0,882,883,5,92,0,0,883,884,5,103,0,0,884,885,
+        5,101,0,0,885,886,5,113,0,0,886,887,5,113,0,0,887,176,1,0,0,0,888,
+        889,5,92,0,0,889,890,5,103,0,0,890,891,5,101,0,0,891,892,5,113,0,
+        0,892,893,5,115,0,0,893,894,5,108,0,0,894,895,5,97,0,0,895,896,5,
+        110,0,0,896,897,5,116,0,0,897,178,1,0,0,0,898,899,5,33,0,0,899,180,
+        1,0,0,0,900,902,5,39,0,0,901,900,1,0,0,0,902,903,1,0,0,0,903,901,
+        1,0,0,0,903,904,1,0,0,0,904,182,1,0,0,0,905,907,5,92,0,0,906,908,
+        7,1,0,0,907,906,1,0,0,0,908,909,1,0,0,0,909,907,1,0,0,0,909,910,
+        1,0,0,0,910,184,1,0,0,0,22,0,192,208,223,240,276,380,503,520,752,
+        797,805,807,817,820,827,831,833,851,880,903,909,1,6,0,0
+    ]
+
+class LaTeXLexer(Lexer):
+
+    atn = ATNDeserializer().deserialize(serializedATN())
+
+    decisionsToDFA = [ DFA(ds, i) for i, ds in enumerate(atn.decisionToState) ]
+
+    T__0 = 1
+    T__1 = 2
+    WS = 3
+    THINSPACE = 4
+    MEDSPACE = 5
+    THICKSPACE = 6
+    QUAD = 7
+    QQUAD = 8
+    NEGTHINSPACE = 9
+    NEGMEDSPACE = 10
+    NEGTHICKSPACE = 11
+    CMD_LEFT = 12
+    CMD_RIGHT = 13
+    IGNORE = 14
+    ADD = 15
+    SUB = 16
+    MUL = 17
+    DIV = 18
+    L_PAREN = 19
+    R_PAREN = 20
+    L_BRACE = 21
+    R_BRACE = 22
+    L_BRACE_LITERAL = 23
+    R_BRACE_LITERAL = 24
+    L_BRACKET = 25
+    R_BRACKET = 26
+    BAR = 27
+    R_BAR = 28
+    L_BAR = 29
+    L_ANGLE = 30
+    R_ANGLE = 31
+    FUNC_LIM = 32
+    LIM_APPROACH_SYM = 33
+    FUNC_INT = 34
+    FUNC_SUM = 35
+    FUNC_PROD = 36
+    FUNC_EXP = 37
+    FUNC_LOG = 38
+    FUNC_LG = 39
+    FUNC_LN = 40
+    FUNC_SIN = 41
+    FUNC_COS = 42
+    FUNC_TAN = 43
+    FUNC_CSC = 44
+    FUNC_SEC = 45
+    FUNC_COT = 46
+    FUNC_ARCSIN = 47
+    FUNC_ARCCOS = 48
+    FUNC_ARCTAN = 49
+    FUNC_ARCCSC = 50
+    FUNC_ARCSEC = 51
+    FUNC_ARCCOT = 52
+    FUNC_SINH = 53
+    FUNC_COSH = 54
+    FUNC_TANH = 55
+    FUNC_ARSINH = 56
+    FUNC_ARCOSH = 57
+    FUNC_ARTANH = 58
+    L_FLOOR = 59
+    R_FLOOR = 60
+    L_CEIL = 61
+    R_CEIL = 62
+    FUNC_SQRT = 63
+    FUNC_OVERLINE = 64
+    CMD_TIMES = 65
+    CMD_CDOT = 66
+    CMD_DIV = 67
+    CMD_FRAC = 68
+    CMD_BINOM = 69
+    CMD_DBINOM = 70
+    CMD_TBINOM = 71
+    CMD_MATHIT = 72
+    UNDERSCORE = 73
+    CARET = 74
+    COLON = 75
+    DIFFERENTIAL = 76
+    LETTER = 77
+    DIGIT = 78
+    EQUAL = 79
+    NEQ = 80
+    LT = 81
+    LTE = 82
+    LTE_Q = 83
+    LTE_S = 84
+    GT = 85
+    GTE = 86
+    GTE_Q = 87
+    GTE_S = 88
+    BANG = 89
+    SINGLE_QUOTES = 90
+    SYMBOL = 91
+
+    channelNames = [ u"DEFAULT_TOKEN_CHANNEL", u"HIDDEN" ]
+
+    modeNames = [ "DEFAULT_MODE" ]
+
+    literalNames = [ "",
+            "','", "'.'", "'\\quad'", "'\\qquad'", "'\\negmedspace'", "'\\negthickspace'",
+            "'\\left'", "'\\right'", "'+'", "'-'", "'*'", "'/'", "'('",
+            "')'", "'{'", "'}'", "'\\{'", "'\\}'", "'['", "']'", "'|'",
+            "'\\right|'", "'\\left|'", "'\\langle'", "'\\rangle'", "'\\lim'",
+            "'\\sum'", "'\\prod'", "'\\exp'", "'\\log'", "'\\lg'", "'\\ln'",
+            "'\\sin'", "'\\cos'", "'\\tan'", "'\\csc'", "'\\sec'", "'\\cot'",
+            "'\\arcsin'", "'\\arccos'", "'\\arctan'", "'\\arccsc'", "'\\arcsec'",
+            "'\\arccot'", "'\\sinh'", "'\\cosh'", "'\\tanh'", "'\\arsinh'",
+            "'\\arcosh'", "'\\artanh'", "'\\lfloor'", "'\\rfloor'", "'\\lceil'",
+            "'\\rceil'", "'\\sqrt'", "'\\overline'", "'\\times'", "'\\cdot'",
+            "'\\div'", "'\\binom'", "'\\dbinom'", "'\\tbinom'", "'\\mathit'",
+            "'_'", "'^'", "':'", "'\\neq'", "'<'", "'\\leqq'", "'\\leqslant'",
+            "'>'", "'\\geqq'", "'\\geqslant'", "'!'" ]
+
+    symbolicNames = [ "",
+            "WS", "THINSPACE", "MEDSPACE", "THICKSPACE", "QUAD", "QQUAD",
+            "NEGTHINSPACE", "NEGMEDSPACE", "NEGTHICKSPACE", "CMD_LEFT",
+            "CMD_RIGHT", "IGNORE", "ADD", "SUB", "MUL", "DIV", "L_PAREN",
+            "R_PAREN", "L_BRACE", "R_BRACE", "L_BRACE_LITERAL", "R_BRACE_LITERAL",
+            "L_BRACKET", "R_BRACKET", "BAR", "R_BAR", "L_BAR", "L_ANGLE",
+            "R_ANGLE", "FUNC_LIM", "LIM_APPROACH_SYM", "FUNC_INT", "FUNC_SUM",
+            "FUNC_PROD", "FUNC_EXP", "FUNC_LOG", "FUNC_LG", "FUNC_LN", "FUNC_SIN",
+            "FUNC_COS", "FUNC_TAN", "FUNC_CSC", "FUNC_SEC", "FUNC_COT",
+            "FUNC_ARCSIN", "FUNC_ARCCOS", "FUNC_ARCTAN", "FUNC_ARCCSC",
+            "FUNC_ARCSEC", "FUNC_ARCCOT", "FUNC_SINH", "FUNC_COSH", "FUNC_TANH",
+            "FUNC_ARSINH", "FUNC_ARCOSH", "FUNC_ARTANH", "L_FLOOR", "R_FLOOR",
+            "L_CEIL", "R_CEIL", "FUNC_SQRT", "FUNC_OVERLINE", "CMD_TIMES",
+            "CMD_CDOT", "CMD_DIV", "CMD_FRAC", "CMD_BINOM", "CMD_DBINOM",
+            "CMD_TBINOM", "CMD_MATHIT", "UNDERSCORE", "CARET", "COLON",
+            "DIFFERENTIAL", "LETTER", "DIGIT", "EQUAL", "NEQ", "LT", "LTE",
+            "LTE_Q", "LTE_S", "GT", "GTE", "GTE_Q", "GTE_S", "BANG", "SINGLE_QUOTES",
+            "SYMBOL" ]
+
+    ruleNames = [ "T__0", "T__1", "WS", "THINSPACE", "MEDSPACE", "THICKSPACE",
+                  "QUAD", "QQUAD", "NEGTHINSPACE", "NEGMEDSPACE", "NEGTHICKSPACE",
+                  "CMD_LEFT", "CMD_RIGHT", "IGNORE", "ADD", "SUB", "MUL",
+                  "DIV", "L_PAREN", "R_PAREN", "L_BRACE", "R_BRACE", "L_BRACE_LITERAL",
+                  "R_BRACE_LITERAL", "L_BRACKET", "R_BRACKET", "BAR", "R_BAR",
+                  "L_BAR", "L_ANGLE", "R_ANGLE", "FUNC_LIM", "LIM_APPROACH_SYM",
+                  "FUNC_INT", "FUNC_SUM", "FUNC_PROD", "FUNC_EXP", "FUNC_LOG",
+                  "FUNC_LG", "FUNC_LN", "FUNC_SIN", "FUNC_COS", "FUNC_TAN",
+                  "FUNC_CSC", "FUNC_SEC", "FUNC_COT", "FUNC_ARCSIN", "FUNC_ARCCOS",
+                  "FUNC_ARCTAN", "FUNC_ARCCSC", "FUNC_ARCSEC", "FUNC_ARCCOT",
+                  "FUNC_SINH", "FUNC_COSH", "FUNC_TANH", "FUNC_ARSINH",
+                  "FUNC_ARCOSH", "FUNC_ARTANH", "L_FLOOR", "R_FLOOR", "L_CEIL",
+                  "R_CEIL", "FUNC_SQRT", "FUNC_OVERLINE", "CMD_TIMES", "CMD_CDOT",
+                  "CMD_DIV", "CMD_FRAC", "CMD_BINOM", "CMD_DBINOM", "CMD_TBINOM",
+                  "CMD_MATHIT", "UNDERSCORE", "CARET", "COLON", "WS_CHAR",
+                  "DIFFERENTIAL", "LETTER", "DIGIT", "EQUAL", "NEQ", "LT",
+                  "LTE", "LTE_Q", "LTE_S", "GT", "GTE", "GTE_Q", "GTE_S",
+                  "BANG", "SINGLE_QUOTES", "SYMBOL" ]
+
+    grammarFileName = "LaTeX.g4"
+
+    def __init__(self, input=None, output:TextIO = sys.stdout):
+        super().__init__(input, output)
+        self.checkVersion("4.11.1")
+        self._interp = LexerATNSimulator(self, self.atn, self.decisionsToDFA, PredictionContextCache())
+        self._actions = None
+        self._predicates = None
+
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/latexparser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/latexparser.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6f58119055ded8f77380bbef52c77ddd6a01cfe
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_antlr/latexparser.py
@@ -0,0 +1,3652 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated from ../LaTeX.g4, derived from latex2sympy
+#     latex2sympy is licensed under the MIT license
+#     https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+from antlr4 import *
+from io import StringIO
+import sys
+if sys.version_info[1] > 5:
+	from typing import TextIO
+else:
+	from typing.io import TextIO
+
+def serializedATN():
+    return [
+        4,1,91,522,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,
+        6,2,7,7,7,2,8,7,8,2,9,7,9,2,10,7,10,2,11,7,11,2,12,7,12,2,13,7,13,
+        2,14,7,14,2,15,7,15,2,16,7,16,2,17,7,17,2,18,7,18,2,19,7,19,2,20,
+        7,20,2,21,7,21,2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,2,26,7,26,
+        2,27,7,27,2,28,7,28,2,29,7,29,2,30,7,30,2,31,7,31,2,32,7,32,2,33,
+        7,33,2,34,7,34,2,35,7,35,2,36,7,36,2,37,7,37,2,38,7,38,2,39,7,39,
+        2,40,7,40,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,5,1,91,8,1,10,1,12,1,94,
+        9,1,1,2,1,2,1,2,1,2,1,3,1,3,1,4,1,4,1,4,1,4,1,4,1,4,5,4,108,8,4,
+        10,4,12,4,111,9,4,1,5,1,5,1,5,1,5,1,5,1,5,5,5,119,8,5,10,5,12,5,
+        122,9,5,1,6,1,6,1,6,1,6,1,6,1,6,5,6,130,8,6,10,6,12,6,133,9,6,1,
+        7,1,7,1,7,4,7,138,8,7,11,7,12,7,139,3,7,142,8,7,1,8,1,8,1,8,1,8,
+        5,8,148,8,8,10,8,12,8,151,9,8,3,8,153,8,8,1,9,1,9,5,9,157,8,9,10,
+        9,12,9,160,9,9,1,10,1,10,5,10,164,8,10,10,10,12,10,167,9,10,1,11,
+        1,11,3,11,171,8,11,1,12,1,12,1,12,1,12,1,12,1,12,3,12,179,8,12,1,
+        13,1,13,1,13,1,13,3,13,185,8,13,1,13,1,13,1,14,1,14,1,14,1,14,3,
+        14,193,8,14,1,14,1,14,1,15,1,15,1,15,1,15,1,15,1,15,1,15,1,15,1,
+        15,1,15,3,15,207,8,15,1,15,3,15,210,8,15,5,15,212,8,15,10,15,12,
+        15,215,9,15,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,3,
+        16,227,8,16,1,16,3,16,230,8,16,5,16,232,8,16,10,16,12,16,235,9,16,
+        1,17,1,17,1,17,1,17,1,17,1,17,3,17,243,8,17,1,18,1,18,1,18,1,18,
+        1,18,3,18,250,8,18,1,19,1,19,1,19,1,19,1,19,1,19,1,19,1,19,1,19,
+        1,19,1,19,1,19,1,19,1,19,1,19,1,19,3,19,268,8,19,1,20,1,20,1,20,
+        1,20,1,21,4,21,275,8,21,11,21,12,21,276,1,21,1,21,1,21,1,21,5,21,
+        283,8,21,10,21,12,21,286,9,21,1,21,1,21,4,21,290,8,21,11,21,12,21,
+        291,3,21,294,8,21,1,22,1,22,3,22,298,8,22,1,22,3,22,301,8,22,1,22,
+        3,22,304,8,22,1,22,3,22,307,8,22,3,22,309,8,22,1,22,1,22,1,22,1,
+        22,1,22,1,22,1,22,3,22,318,8,22,1,23,1,23,1,23,1,23,1,24,1,24,1,
+        24,1,24,1,25,1,25,1,25,1,25,1,25,1,26,5,26,334,8,26,10,26,12,26,
+        337,9,26,1,27,1,27,1,27,1,27,1,27,1,27,3,27,345,8,27,1,27,1,27,1,
+        27,1,27,1,27,3,27,352,8,27,1,28,1,28,1,28,1,28,1,28,1,28,1,28,1,
+        28,1,29,1,29,1,29,1,29,1,30,1,30,1,30,1,30,1,31,1,31,1,32,1,32,3,
+        32,374,8,32,1,32,3,32,377,8,32,1,32,3,32,380,8,32,1,32,3,32,383,
+        8,32,3,32,385,8,32,1,32,1,32,1,32,1,32,1,32,3,32,392,8,32,1,32,1,
+        32,3,32,396,8,32,1,32,3,32,399,8,32,1,32,3,32,402,8,32,1,32,3,32,
+        405,8,32,3,32,407,8,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,
+        32,1,32,1,32,3,32,420,8,32,1,32,3,32,423,8,32,1,32,1,32,1,32,3,32,
+        428,8,32,1,32,1,32,1,32,1,32,1,32,3,32,435,8,32,1,32,1,32,1,32,1,
+        32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,3,
+        32,453,8,32,1,32,1,32,1,32,1,32,1,32,1,32,3,32,461,8,32,1,33,1,33,
+        1,33,1,33,1,33,3,33,468,8,33,1,34,1,34,1,34,1,34,1,34,1,34,1,34,
+        1,34,1,34,1,34,1,34,3,34,481,8,34,3,34,483,8,34,1,34,1,34,1,35,1,
+        35,1,35,1,35,1,35,3,35,492,8,35,1,36,1,36,1,37,1,37,1,37,1,37,1,
+        37,1,37,3,37,502,8,37,1,38,1,38,1,38,1,38,1,38,1,38,3,38,510,8,38,
+        1,39,1,39,1,39,1,39,1,39,1,40,1,40,1,40,1,40,1,40,1,40,0,6,2,8,10,
+        12,30,32,41,0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,
+        38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,
+        0,9,2,0,79,82,85,86,1,0,15,16,3,0,17,18,65,67,75,75,2,0,77,77,91,
+        91,1,0,27,28,2,0,27,27,29,29,1,0,69,71,1,0,37,58,1,0,35,36,563,0,
+        82,1,0,0,0,2,84,1,0,0,0,4,95,1,0,0,0,6,99,1,0,0,0,8,101,1,0,0,0,
+        10,112,1,0,0,0,12,123,1,0,0,0,14,141,1,0,0,0,16,152,1,0,0,0,18,154,
+        1,0,0,0,20,161,1,0,0,0,22,170,1,0,0,0,24,172,1,0,0,0,26,180,1,0,
+        0,0,28,188,1,0,0,0,30,196,1,0,0,0,32,216,1,0,0,0,34,242,1,0,0,0,
+        36,249,1,0,0,0,38,267,1,0,0,0,40,269,1,0,0,0,42,274,1,0,0,0,44,317,
+        1,0,0,0,46,319,1,0,0,0,48,323,1,0,0,0,50,327,1,0,0,0,52,335,1,0,
+        0,0,54,338,1,0,0,0,56,353,1,0,0,0,58,361,1,0,0,0,60,365,1,0,0,0,
+        62,369,1,0,0,0,64,460,1,0,0,0,66,467,1,0,0,0,68,469,1,0,0,0,70,491,
+        1,0,0,0,72,493,1,0,0,0,74,495,1,0,0,0,76,503,1,0,0,0,78,511,1,0,
+        0,0,80,516,1,0,0,0,82,83,3,2,1,0,83,1,1,0,0,0,84,85,6,1,-1,0,85,
+        86,3,6,3,0,86,92,1,0,0,0,87,88,10,2,0,0,88,89,7,0,0,0,89,91,3,2,
+        1,3,90,87,1,0,0,0,91,94,1,0,0,0,92,90,1,0,0,0,92,93,1,0,0,0,93,3,
+        1,0,0,0,94,92,1,0,0,0,95,96,3,6,3,0,96,97,5,79,0,0,97,98,3,6,3,0,
+        98,5,1,0,0,0,99,100,3,8,4,0,100,7,1,0,0,0,101,102,6,4,-1,0,102,103,
+        3,10,5,0,103,109,1,0,0,0,104,105,10,2,0,0,105,106,7,1,0,0,106,108,
+        3,8,4,3,107,104,1,0,0,0,108,111,1,0,0,0,109,107,1,0,0,0,109,110,
+        1,0,0,0,110,9,1,0,0,0,111,109,1,0,0,0,112,113,6,5,-1,0,113,114,3,
+        14,7,0,114,120,1,0,0,0,115,116,10,2,0,0,116,117,7,2,0,0,117,119,
+        3,10,5,3,118,115,1,0,0,0,119,122,1,0,0,0,120,118,1,0,0,0,120,121,
+        1,0,0,0,121,11,1,0,0,0,122,120,1,0,0,0,123,124,6,6,-1,0,124,125,
+        3,16,8,0,125,131,1,0,0,0,126,127,10,2,0,0,127,128,7,2,0,0,128,130,
+        3,12,6,3,129,126,1,0,0,0,130,133,1,0,0,0,131,129,1,0,0,0,131,132,
+        1,0,0,0,132,13,1,0,0,0,133,131,1,0,0,0,134,135,7,1,0,0,135,142,3,
+        14,7,0,136,138,3,18,9,0,137,136,1,0,0,0,138,139,1,0,0,0,139,137,
+        1,0,0,0,139,140,1,0,0,0,140,142,1,0,0,0,141,134,1,0,0,0,141,137,
+        1,0,0,0,142,15,1,0,0,0,143,144,7,1,0,0,144,153,3,16,8,0,145,149,
+        3,18,9,0,146,148,3,20,10,0,147,146,1,0,0,0,148,151,1,0,0,0,149,147,
+        1,0,0,0,149,150,1,0,0,0,150,153,1,0,0,0,151,149,1,0,0,0,152,143,
+        1,0,0,0,152,145,1,0,0,0,153,17,1,0,0,0,154,158,3,30,15,0,155,157,
+        3,22,11,0,156,155,1,0,0,0,157,160,1,0,0,0,158,156,1,0,0,0,158,159,
+        1,0,0,0,159,19,1,0,0,0,160,158,1,0,0,0,161,165,3,32,16,0,162,164,
+        3,22,11,0,163,162,1,0,0,0,164,167,1,0,0,0,165,163,1,0,0,0,165,166,
+        1,0,0,0,166,21,1,0,0,0,167,165,1,0,0,0,168,171,5,89,0,0,169,171,
+        3,24,12,0,170,168,1,0,0,0,170,169,1,0,0,0,171,23,1,0,0,0,172,178,
+        5,27,0,0,173,179,3,28,14,0,174,179,3,26,13,0,175,176,3,28,14,0,176,
+        177,3,26,13,0,177,179,1,0,0,0,178,173,1,0,0,0,178,174,1,0,0,0,178,
+        175,1,0,0,0,179,25,1,0,0,0,180,181,5,73,0,0,181,184,5,21,0,0,182,
+        185,3,6,3,0,183,185,3,4,2,0,184,182,1,0,0,0,184,183,1,0,0,0,185,
+        186,1,0,0,0,186,187,5,22,0,0,187,27,1,0,0,0,188,189,5,74,0,0,189,
+        192,5,21,0,0,190,193,3,6,3,0,191,193,3,4,2,0,192,190,1,0,0,0,192,
+        191,1,0,0,0,193,194,1,0,0,0,194,195,5,22,0,0,195,29,1,0,0,0,196,
+        197,6,15,-1,0,197,198,3,34,17,0,198,213,1,0,0,0,199,200,10,2,0,0,
+        200,206,5,74,0,0,201,207,3,44,22,0,202,203,5,21,0,0,203,204,3,6,
+        3,0,204,205,5,22,0,0,205,207,1,0,0,0,206,201,1,0,0,0,206,202,1,0,
+        0,0,207,209,1,0,0,0,208,210,3,74,37,0,209,208,1,0,0,0,209,210,1,
+        0,0,0,210,212,1,0,0,0,211,199,1,0,0,0,212,215,1,0,0,0,213,211,1,
+        0,0,0,213,214,1,0,0,0,214,31,1,0,0,0,215,213,1,0,0,0,216,217,6,16,
+        -1,0,217,218,3,36,18,0,218,233,1,0,0,0,219,220,10,2,0,0,220,226,
+        5,74,0,0,221,227,3,44,22,0,222,223,5,21,0,0,223,224,3,6,3,0,224,
+        225,5,22,0,0,225,227,1,0,0,0,226,221,1,0,0,0,226,222,1,0,0,0,227,
+        229,1,0,0,0,228,230,3,74,37,0,229,228,1,0,0,0,229,230,1,0,0,0,230,
+        232,1,0,0,0,231,219,1,0,0,0,232,235,1,0,0,0,233,231,1,0,0,0,233,
+        234,1,0,0,0,234,33,1,0,0,0,235,233,1,0,0,0,236,243,3,38,19,0,237,
+        243,3,40,20,0,238,243,3,64,32,0,239,243,3,44,22,0,240,243,3,58,29,
+        0,241,243,3,60,30,0,242,236,1,0,0,0,242,237,1,0,0,0,242,238,1,0,
+        0,0,242,239,1,0,0,0,242,240,1,0,0,0,242,241,1,0,0,0,243,35,1,0,0,
+        0,244,250,3,38,19,0,245,250,3,40,20,0,246,250,3,44,22,0,247,250,
+        3,58,29,0,248,250,3,60,30,0,249,244,1,0,0,0,249,245,1,0,0,0,249,
+        246,1,0,0,0,249,247,1,0,0,0,249,248,1,0,0,0,250,37,1,0,0,0,251,252,
+        5,19,0,0,252,253,3,6,3,0,253,254,5,20,0,0,254,268,1,0,0,0,255,256,
+        5,25,0,0,256,257,3,6,3,0,257,258,5,26,0,0,258,268,1,0,0,0,259,260,
+        5,21,0,0,260,261,3,6,3,0,261,262,5,22,0,0,262,268,1,0,0,0,263,264,
+        5,23,0,0,264,265,3,6,3,0,265,266,5,24,0,0,266,268,1,0,0,0,267,251,
+        1,0,0,0,267,255,1,0,0,0,267,259,1,0,0,0,267,263,1,0,0,0,268,39,1,
+        0,0,0,269,270,5,27,0,0,270,271,3,6,3,0,271,272,5,27,0,0,272,41,1,
+        0,0,0,273,275,5,78,0,0,274,273,1,0,0,0,275,276,1,0,0,0,276,274,1,
+        0,0,0,276,277,1,0,0,0,277,284,1,0,0,0,278,279,5,1,0,0,279,280,5,
+        78,0,0,280,281,5,78,0,0,281,283,5,78,0,0,282,278,1,0,0,0,283,286,
+        1,0,0,0,284,282,1,0,0,0,284,285,1,0,0,0,285,293,1,0,0,0,286,284,
+        1,0,0,0,287,289,5,2,0,0,288,290,5,78,0,0,289,288,1,0,0,0,290,291,
+        1,0,0,0,291,289,1,0,0,0,291,292,1,0,0,0,292,294,1,0,0,0,293,287,
+        1,0,0,0,293,294,1,0,0,0,294,43,1,0,0,0,295,308,7,3,0,0,296,298,3,
+        74,37,0,297,296,1,0,0,0,297,298,1,0,0,0,298,300,1,0,0,0,299,301,
+        5,90,0,0,300,299,1,0,0,0,300,301,1,0,0,0,301,309,1,0,0,0,302,304,
+        5,90,0,0,303,302,1,0,0,0,303,304,1,0,0,0,304,306,1,0,0,0,305,307,
+        3,74,37,0,306,305,1,0,0,0,306,307,1,0,0,0,307,309,1,0,0,0,308,297,
+        1,0,0,0,308,303,1,0,0,0,309,318,1,0,0,0,310,318,3,42,21,0,311,318,
+        5,76,0,0,312,318,3,50,25,0,313,318,3,54,27,0,314,318,3,56,28,0,315,
+        318,3,46,23,0,316,318,3,48,24,0,317,295,1,0,0,0,317,310,1,0,0,0,
+        317,311,1,0,0,0,317,312,1,0,0,0,317,313,1,0,0,0,317,314,1,0,0,0,
+        317,315,1,0,0,0,317,316,1,0,0,0,318,45,1,0,0,0,319,320,5,30,0,0,
+        320,321,3,6,3,0,321,322,7,4,0,0,322,47,1,0,0,0,323,324,7,5,0,0,324,
+        325,3,6,3,0,325,326,5,31,0,0,326,49,1,0,0,0,327,328,5,72,0,0,328,
+        329,5,21,0,0,329,330,3,52,26,0,330,331,5,22,0,0,331,51,1,0,0,0,332,
+        334,5,77,0,0,333,332,1,0,0,0,334,337,1,0,0,0,335,333,1,0,0,0,335,
+        336,1,0,0,0,336,53,1,0,0,0,337,335,1,0,0,0,338,344,5,68,0,0,339,
+        345,5,78,0,0,340,341,5,21,0,0,341,342,3,6,3,0,342,343,5,22,0,0,343,
+        345,1,0,0,0,344,339,1,0,0,0,344,340,1,0,0,0,345,351,1,0,0,0,346,
+        352,5,78,0,0,347,348,5,21,0,0,348,349,3,6,3,0,349,350,5,22,0,0,350,
+        352,1,0,0,0,351,346,1,0,0,0,351,347,1,0,0,0,352,55,1,0,0,0,353,354,
+        7,6,0,0,354,355,5,21,0,0,355,356,3,6,3,0,356,357,5,22,0,0,357,358,
+        5,21,0,0,358,359,3,6,3,0,359,360,5,22,0,0,360,57,1,0,0,0,361,362,
+        5,59,0,0,362,363,3,6,3,0,363,364,5,60,0,0,364,59,1,0,0,0,365,366,
+        5,61,0,0,366,367,3,6,3,0,367,368,5,62,0,0,368,61,1,0,0,0,369,370,
+        7,7,0,0,370,63,1,0,0,0,371,384,3,62,31,0,372,374,3,74,37,0,373,372,
+        1,0,0,0,373,374,1,0,0,0,374,376,1,0,0,0,375,377,3,76,38,0,376,375,
+        1,0,0,0,376,377,1,0,0,0,377,385,1,0,0,0,378,380,3,76,38,0,379,378,
+        1,0,0,0,379,380,1,0,0,0,380,382,1,0,0,0,381,383,3,74,37,0,382,381,
+        1,0,0,0,382,383,1,0,0,0,383,385,1,0,0,0,384,373,1,0,0,0,384,379,
+        1,0,0,0,385,391,1,0,0,0,386,387,5,19,0,0,387,388,3,70,35,0,388,389,
+        5,20,0,0,389,392,1,0,0,0,390,392,3,72,36,0,391,386,1,0,0,0,391,390,
+        1,0,0,0,392,461,1,0,0,0,393,406,7,3,0,0,394,396,3,74,37,0,395,394,
+        1,0,0,0,395,396,1,0,0,0,396,398,1,0,0,0,397,399,5,90,0,0,398,397,
+        1,0,0,0,398,399,1,0,0,0,399,407,1,0,0,0,400,402,5,90,0,0,401,400,
+        1,0,0,0,401,402,1,0,0,0,402,404,1,0,0,0,403,405,3,74,37,0,404,403,
+        1,0,0,0,404,405,1,0,0,0,405,407,1,0,0,0,406,395,1,0,0,0,406,401,
+        1,0,0,0,407,408,1,0,0,0,408,409,5,19,0,0,409,410,3,66,33,0,410,411,
+        5,20,0,0,411,461,1,0,0,0,412,419,5,34,0,0,413,414,3,74,37,0,414,
+        415,3,76,38,0,415,420,1,0,0,0,416,417,3,76,38,0,417,418,3,74,37,
+        0,418,420,1,0,0,0,419,413,1,0,0,0,419,416,1,0,0,0,419,420,1,0,0,
+        0,420,427,1,0,0,0,421,423,3,8,4,0,422,421,1,0,0,0,422,423,1,0,0,
+        0,423,424,1,0,0,0,424,428,5,76,0,0,425,428,3,54,27,0,426,428,3,8,
+        4,0,427,422,1,0,0,0,427,425,1,0,0,0,427,426,1,0,0,0,428,461,1,0,
+        0,0,429,434,5,63,0,0,430,431,5,25,0,0,431,432,3,6,3,0,432,433,5,
+        26,0,0,433,435,1,0,0,0,434,430,1,0,0,0,434,435,1,0,0,0,435,436,1,
+        0,0,0,436,437,5,21,0,0,437,438,3,6,3,0,438,439,5,22,0,0,439,461,
+        1,0,0,0,440,441,5,64,0,0,441,442,5,21,0,0,442,443,3,6,3,0,443,444,
+        5,22,0,0,444,461,1,0,0,0,445,452,7,8,0,0,446,447,3,78,39,0,447,448,
+        3,76,38,0,448,453,1,0,0,0,449,450,3,76,38,0,450,451,3,78,39,0,451,
+        453,1,0,0,0,452,446,1,0,0,0,452,449,1,0,0,0,453,454,1,0,0,0,454,
+        455,3,10,5,0,455,461,1,0,0,0,456,457,5,32,0,0,457,458,3,68,34,0,
+        458,459,3,10,5,0,459,461,1,0,0,0,460,371,1,0,0,0,460,393,1,0,0,0,
+        460,412,1,0,0,0,460,429,1,0,0,0,460,440,1,0,0,0,460,445,1,0,0,0,
+        460,456,1,0,0,0,461,65,1,0,0,0,462,463,3,6,3,0,463,464,5,1,0,0,464,
+        465,3,66,33,0,465,468,1,0,0,0,466,468,3,6,3,0,467,462,1,0,0,0,467,
+        466,1,0,0,0,468,67,1,0,0,0,469,470,5,73,0,0,470,471,5,21,0,0,471,
+        472,7,3,0,0,472,473,5,33,0,0,473,482,3,6,3,0,474,480,5,74,0,0,475,
+        476,5,21,0,0,476,477,7,1,0,0,477,481,5,22,0,0,478,481,5,15,0,0,479,
+        481,5,16,0,0,480,475,1,0,0,0,480,478,1,0,0,0,480,479,1,0,0,0,481,
+        483,1,0,0,0,482,474,1,0,0,0,482,483,1,0,0,0,483,484,1,0,0,0,484,
+        485,5,22,0,0,485,69,1,0,0,0,486,492,3,6,3,0,487,488,3,6,3,0,488,
+        489,5,1,0,0,489,490,3,70,35,0,490,492,1,0,0,0,491,486,1,0,0,0,491,
+        487,1,0,0,0,492,71,1,0,0,0,493,494,3,12,6,0,494,73,1,0,0,0,495,501,
+        5,73,0,0,496,502,3,44,22,0,497,498,5,21,0,0,498,499,3,6,3,0,499,
+        500,5,22,0,0,500,502,1,0,0,0,501,496,1,0,0,0,501,497,1,0,0,0,502,
+        75,1,0,0,0,503,509,5,74,0,0,504,510,3,44,22,0,505,506,5,21,0,0,506,
+        507,3,6,3,0,507,508,5,22,0,0,508,510,1,0,0,0,509,504,1,0,0,0,509,
+        505,1,0,0,0,510,77,1,0,0,0,511,512,5,73,0,0,512,513,5,21,0,0,513,
+        514,3,4,2,0,514,515,5,22,0,0,515,79,1,0,0,0,516,517,5,73,0,0,517,
+        518,5,21,0,0,518,519,3,4,2,0,519,520,5,22,0,0,520,81,1,0,0,0,59,
+        92,109,120,131,139,141,149,152,158,165,170,178,184,192,206,209,213,
+        226,229,233,242,249,267,276,284,291,293,297,300,303,306,308,317,
+        335,344,351,373,376,379,382,384,391,395,398,401,404,406,419,422,
+        427,434,452,460,467,480,482,491,501,509
+    ]
+
+class LaTeXParser ( Parser ):
+
+    grammarFileName = "LaTeX.g4"
+
+    atn = ATNDeserializer().deserialize(serializedATN())
+
+    decisionsToDFA = [ DFA(ds, i) for i, ds in enumerate(atn.decisionToState) ]
+
+    sharedContextCache = PredictionContextCache()
+
+    literalNames = [ "", "','", "'.'", "", "",
+                     "", "", "'\\quad'", "'\\qquad'",
+                     "", "'\\negmedspace'", "'\\negthickspace'",
+                     "'\\left'", "'\\right'", "", "'+'", "'-'",
+                     "'*'", "'/'", "'('", "')'", "'{'", "'}'", "'\\{'",
+                     "'\\}'", "'['", "']'", "'|'", "'\\right|'", "'\\left|'",
+                     "'\\langle'", "'\\rangle'", "'\\lim'", "",
+                     "", "'\\sum'", "'\\prod'", "'\\exp'", "'\\log'",
+                     "'\\lg'", "'\\ln'", "'\\sin'", "'\\cos'", "'\\tan'",
+                     "'\\csc'", "'\\sec'", "'\\cot'", "'\\arcsin'", "'\\arccos'",
+                     "'\\arctan'", "'\\arccsc'", "'\\arcsec'", "'\\arccot'",
+                     "'\\sinh'", "'\\cosh'", "'\\tanh'", "'\\arsinh'", "'\\arcosh'",
+                     "'\\artanh'", "'\\lfloor'", "'\\rfloor'", "'\\lceil'",
+                     "'\\rceil'", "'\\sqrt'", "'\\overline'", "'\\times'",
+                     "'\\cdot'", "'\\div'", "", "'\\binom'", "'\\dbinom'",
+                     "'\\tbinom'", "'\\mathit'", "'_'", "'^'", "':'", "",
+                     "", "", "", "'\\neq'", "'<'",
+                     "", "'\\leqq'", "'\\leqslant'", "'>'", "",
+                     "'\\geqq'", "'\\geqslant'", "'!'" ]
+
+    symbolicNames = [ "", "", "", "WS", "THINSPACE",
+                      "MEDSPACE", "THICKSPACE", "QUAD", "QQUAD", "NEGTHINSPACE",
+                      "NEGMEDSPACE", "NEGTHICKSPACE", "CMD_LEFT", "CMD_RIGHT",
+                      "IGNORE", "ADD", "SUB", "MUL", "DIV", "L_PAREN", "R_PAREN",
+                      "L_BRACE", "R_BRACE", "L_BRACE_LITERAL", "R_BRACE_LITERAL",
+                      "L_BRACKET", "R_BRACKET", "BAR", "R_BAR", "L_BAR",
+                      "L_ANGLE", "R_ANGLE", "FUNC_LIM", "LIM_APPROACH_SYM",
+                      "FUNC_INT", "FUNC_SUM", "FUNC_PROD", "FUNC_EXP", "FUNC_LOG",
+                      "FUNC_LG", "FUNC_LN", "FUNC_SIN", "FUNC_COS", "FUNC_TAN",
+                      "FUNC_CSC", "FUNC_SEC", "FUNC_COT", "FUNC_ARCSIN",
+                      "FUNC_ARCCOS", "FUNC_ARCTAN", "FUNC_ARCCSC", "FUNC_ARCSEC",
+                      "FUNC_ARCCOT", "FUNC_SINH", "FUNC_COSH", "FUNC_TANH",
+                      "FUNC_ARSINH", "FUNC_ARCOSH", "FUNC_ARTANH", "L_FLOOR",
+                      "R_FLOOR", "L_CEIL", "R_CEIL", "FUNC_SQRT", "FUNC_OVERLINE",
+                      "CMD_TIMES", "CMD_CDOT", "CMD_DIV", "CMD_FRAC", "CMD_BINOM",
+                      "CMD_DBINOM", "CMD_TBINOM", "CMD_MATHIT", "UNDERSCORE",
+                      "CARET", "COLON", "DIFFERENTIAL", "LETTER", "DIGIT",
+                      "EQUAL", "NEQ", "LT", "LTE", "LTE_Q", "LTE_S", "GT",
+                      "GTE", "GTE_Q", "GTE_S", "BANG", "SINGLE_QUOTES",
+                      "SYMBOL" ]
+
+    RULE_math = 0
+    RULE_relation = 1
+    RULE_equality = 2
+    RULE_expr = 3
+    RULE_additive = 4
+    RULE_mp = 5
+    RULE_mp_nofunc = 6
+    RULE_unary = 7
+    RULE_unary_nofunc = 8
+    RULE_postfix = 9
+    RULE_postfix_nofunc = 10
+    RULE_postfix_op = 11
+    RULE_eval_at = 12
+    RULE_eval_at_sub = 13
+    RULE_eval_at_sup = 14
+    RULE_exp = 15
+    RULE_exp_nofunc = 16
+    RULE_comp = 17
+    RULE_comp_nofunc = 18
+    RULE_group = 19
+    RULE_abs_group = 20
+    RULE_number = 21
+    RULE_atom = 22
+    RULE_bra = 23
+    RULE_ket = 24
+    RULE_mathit = 25
+    RULE_mathit_text = 26
+    RULE_frac = 27
+    RULE_binom = 28
+    RULE_floor = 29
+    RULE_ceil = 30
+    RULE_func_normal = 31
+    RULE_func = 32
+    RULE_args = 33
+    RULE_limit_sub = 34
+    RULE_func_arg = 35
+    RULE_func_arg_noparens = 36
+    RULE_subexpr = 37
+    RULE_supexpr = 38
+    RULE_subeq = 39
+    RULE_supeq = 40
+
+    ruleNames =  [ "math", "relation", "equality", "expr", "additive", "mp",
+                   "mp_nofunc", "unary", "unary_nofunc", "postfix", "postfix_nofunc",
+                   "postfix_op", "eval_at", "eval_at_sub", "eval_at_sup",
+                   "exp", "exp_nofunc", "comp", "comp_nofunc", "group",
+                   "abs_group", "number", "atom", "bra", "ket", "mathit",
+                   "mathit_text", "frac", "binom", "floor", "ceil", "func_normal",
+                   "func", "args", "limit_sub", "func_arg", "func_arg_noparens",
+                   "subexpr", "supexpr", "subeq", "supeq" ]
+
+    EOF = Token.EOF
+    T__0=1
+    T__1=2
+    WS=3
+    THINSPACE=4
+    MEDSPACE=5
+    THICKSPACE=6
+    QUAD=7
+    QQUAD=8
+    NEGTHINSPACE=9
+    NEGMEDSPACE=10
+    NEGTHICKSPACE=11
+    CMD_LEFT=12
+    CMD_RIGHT=13
+    IGNORE=14
+    ADD=15
+    SUB=16
+    MUL=17
+    DIV=18
+    L_PAREN=19
+    R_PAREN=20
+    L_BRACE=21
+    R_BRACE=22
+    L_BRACE_LITERAL=23
+    R_BRACE_LITERAL=24
+    L_BRACKET=25
+    R_BRACKET=26
+    BAR=27
+    R_BAR=28
+    L_BAR=29
+    L_ANGLE=30
+    R_ANGLE=31
+    FUNC_LIM=32
+    LIM_APPROACH_SYM=33
+    FUNC_INT=34
+    FUNC_SUM=35
+    FUNC_PROD=36
+    FUNC_EXP=37
+    FUNC_LOG=38
+    FUNC_LG=39
+    FUNC_LN=40
+    FUNC_SIN=41
+    FUNC_COS=42
+    FUNC_TAN=43
+    FUNC_CSC=44
+    FUNC_SEC=45
+    FUNC_COT=46
+    FUNC_ARCSIN=47
+    FUNC_ARCCOS=48
+    FUNC_ARCTAN=49
+    FUNC_ARCCSC=50
+    FUNC_ARCSEC=51
+    FUNC_ARCCOT=52
+    FUNC_SINH=53
+    FUNC_COSH=54
+    FUNC_TANH=55
+    FUNC_ARSINH=56
+    FUNC_ARCOSH=57
+    FUNC_ARTANH=58
+    L_FLOOR=59
+    R_FLOOR=60
+    L_CEIL=61
+    R_CEIL=62
+    FUNC_SQRT=63
+    FUNC_OVERLINE=64
+    CMD_TIMES=65
+    CMD_CDOT=66
+    CMD_DIV=67
+    CMD_FRAC=68
+    CMD_BINOM=69
+    CMD_DBINOM=70
+    CMD_TBINOM=71
+    CMD_MATHIT=72
+    UNDERSCORE=73
+    CARET=74
+    COLON=75
+    DIFFERENTIAL=76
+    LETTER=77
+    DIGIT=78
+    EQUAL=79
+    NEQ=80
+    LT=81
+    LTE=82
+    LTE_Q=83
+    LTE_S=84
+    GT=85
+    GTE=86
+    GTE_Q=87
+    GTE_S=88
+    BANG=89
+    SINGLE_QUOTES=90
+    SYMBOL=91
+
+    def __init__(self, input:TokenStream, output:TextIO = sys.stdout):
+        super().__init__(input, output)
+        self.checkVersion("4.11.1")
+        self._interp = ParserATNSimulator(self, self.atn, self.decisionsToDFA, self.sharedContextCache)
+        self._predicates = None
+
+
+
+
+    class MathContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def relation(self):
+            return self.getTypedRuleContext(LaTeXParser.RelationContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_math
+
+
+
+
+    def math(self):
+
+        localctx = LaTeXParser.MathContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 0, self.RULE_math)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 82
+            self.relation(0)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class RelationContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def relation(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.RelationContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.RelationContext,i)
+
+
+        def EQUAL(self):
+            return self.getToken(LaTeXParser.EQUAL, 0)
+
+        def LT(self):
+            return self.getToken(LaTeXParser.LT, 0)
+
+        def LTE(self):
+            return self.getToken(LaTeXParser.LTE, 0)
+
+        def GT(self):
+            return self.getToken(LaTeXParser.GT, 0)
+
+        def GTE(self):
+            return self.getToken(LaTeXParser.GTE, 0)
+
+        def NEQ(self):
+            return self.getToken(LaTeXParser.NEQ, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_relation
+
+
+
+    def relation(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = LaTeXParser.RelationContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 2
+        self.enterRecursionRule(localctx, 2, self.RULE_relation, _p)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 85
+            self.expr()
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 92
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,0,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    localctx = LaTeXParser.RelationContext(self, _parentctx, _parentState)
+                    self.pushNewRecursionContext(localctx, _startState, self.RULE_relation)
+                    self.state = 87
+                    if not self.precpred(self._ctx, 2):
+                        from antlr4.error.Errors import FailedPredicateException
+                        raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                    self.state = 88
+                    _la = self._input.LA(1)
+                    if not((((_la - 79)) & ~0x3f) == 0 and ((1 << (_la - 79)) & 207) != 0):
+                        self._errHandler.recoverInline(self)
+                    else:
+                        self._errHandler.reportMatch(self)
+                        self.consume()
+                    self.state = 89
+                    self.relation(3)
+                self.state = 94
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,0,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+    class EqualityContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.ExprContext,i)
+
+
+        def EQUAL(self):
+            return self.getToken(LaTeXParser.EQUAL, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_equality
+
+
+
+
+    def equality(self):
+
+        localctx = LaTeXParser.EqualityContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 4, self.RULE_equality)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 95
+            self.expr()
+            self.state = 96
+            self.match(LaTeXParser.EQUAL)
+            self.state = 97
+            self.expr()
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class ExprContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def additive(self):
+            return self.getTypedRuleContext(LaTeXParser.AdditiveContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_expr
+
+
+
+
+    def expr(self):
+
+        localctx = LaTeXParser.ExprContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 6, self.RULE_expr)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 99
+            self.additive(0)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class AdditiveContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def mp(self):
+            return self.getTypedRuleContext(LaTeXParser.MpContext,0)
+
+
+        def additive(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.AdditiveContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.AdditiveContext,i)
+
+
+        def ADD(self):
+            return self.getToken(LaTeXParser.ADD, 0)
+
+        def SUB(self):
+            return self.getToken(LaTeXParser.SUB, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_additive
+
+
+
+    def additive(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = LaTeXParser.AdditiveContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 8
+        self.enterRecursionRule(localctx, 8, self.RULE_additive, _p)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 102
+            self.mp(0)
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 109
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,1,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    localctx = LaTeXParser.AdditiveContext(self, _parentctx, _parentState)
+                    self.pushNewRecursionContext(localctx, _startState, self.RULE_additive)
+                    self.state = 104
+                    if not self.precpred(self._ctx, 2):
+                        from antlr4.error.Errors import FailedPredicateException
+                        raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                    self.state = 105
+                    _la = self._input.LA(1)
+                    if not(_la==15 or _la==16):
+                        self._errHandler.recoverInline(self)
+                    else:
+                        self._errHandler.reportMatch(self)
+                        self.consume()
+                    self.state = 106
+                    self.additive(3)
+                self.state = 111
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,1,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+    class MpContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def unary(self):
+            return self.getTypedRuleContext(LaTeXParser.UnaryContext,0)
+
+
+        def mp(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.MpContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.MpContext,i)
+
+
+        def MUL(self):
+            return self.getToken(LaTeXParser.MUL, 0)
+
+        def CMD_TIMES(self):
+            return self.getToken(LaTeXParser.CMD_TIMES, 0)
+
+        def CMD_CDOT(self):
+            return self.getToken(LaTeXParser.CMD_CDOT, 0)
+
+        def DIV(self):
+            return self.getToken(LaTeXParser.DIV, 0)
+
+        def CMD_DIV(self):
+            return self.getToken(LaTeXParser.CMD_DIV, 0)
+
+        def COLON(self):
+            return self.getToken(LaTeXParser.COLON, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_mp
+
+
+
+    def mp(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = LaTeXParser.MpContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 10
+        self.enterRecursionRule(localctx, 10, self.RULE_mp, _p)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 113
+            self.unary()
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 120
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,2,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    localctx = LaTeXParser.MpContext(self, _parentctx, _parentState)
+                    self.pushNewRecursionContext(localctx, _startState, self.RULE_mp)
+                    self.state = 115
+                    if not self.precpred(self._ctx, 2):
+                        from antlr4.error.Errors import FailedPredicateException
+                        raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                    self.state = 116
+                    _la = self._input.LA(1)
+                    if not((((_la - 17)) & ~0x3f) == 0 and ((1 << (_la - 17)) & 290200700988686339) != 0):
+                        self._errHandler.recoverInline(self)
+                    else:
+                        self._errHandler.reportMatch(self)
+                        self.consume()
+                    self.state = 117
+                    self.mp(3)
+                self.state = 122
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,2,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+    class Mp_nofuncContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def unary_nofunc(self):
+            return self.getTypedRuleContext(LaTeXParser.Unary_nofuncContext,0)
+
+
+        def mp_nofunc(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.Mp_nofuncContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.Mp_nofuncContext,i)
+
+
+        def MUL(self):
+            return self.getToken(LaTeXParser.MUL, 0)
+
+        def CMD_TIMES(self):
+            return self.getToken(LaTeXParser.CMD_TIMES, 0)
+
+        def CMD_CDOT(self):
+            return self.getToken(LaTeXParser.CMD_CDOT, 0)
+
+        def DIV(self):
+            return self.getToken(LaTeXParser.DIV, 0)
+
+        def CMD_DIV(self):
+            return self.getToken(LaTeXParser.CMD_DIV, 0)
+
+        def COLON(self):
+            return self.getToken(LaTeXParser.COLON, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_mp_nofunc
+
+
+
+    def mp_nofunc(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = LaTeXParser.Mp_nofuncContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 12
+        self.enterRecursionRule(localctx, 12, self.RULE_mp_nofunc, _p)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 124
+            self.unary_nofunc()
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 131
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,3,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    localctx = LaTeXParser.Mp_nofuncContext(self, _parentctx, _parentState)
+                    self.pushNewRecursionContext(localctx, _startState, self.RULE_mp_nofunc)
+                    self.state = 126
+                    if not self.precpred(self._ctx, 2):
+                        from antlr4.error.Errors import FailedPredicateException
+                        raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                    self.state = 127
+                    _la = self._input.LA(1)
+                    if not((((_la - 17)) & ~0x3f) == 0 and ((1 << (_la - 17)) & 290200700988686339) != 0):
+                        self._errHandler.recoverInline(self)
+                    else:
+                        self._errHandler.reportMatch(self)
+                        self.consume()
+                    self.state = 128
+                    self.mp_nofunc(3)
+                self.state = 133
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,3,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+    class UnaryContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def unary(self):
+            return self.getTypedRuleContext(LaTeXParser.UnaryContext,0)
+
+
+        def ADD(self):
+            return self.getToken(LaTeXParser.ADD, 0)
+
+        def SUB(self):
+            return self.getToken(LaTeXParser.SUB, 0)
+
+        def postfix(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.PostfixContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.PostfixContext,i)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_unary
+
+
+
+
+    def unary(self):
+
+        localctx = LaTeXParser.UnaryContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 14, self.RULE_unary)
+        self._la = 0 # Token type
+        try:
+            self.state = 141
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [15, 16]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 134
+                _la = self._input.LA(1)
+                if not(_la==15 or _la==16):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 135
+                self.unary()
+                pass
+            elif token in [19, 21, 23, 25, 27, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 64, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 137
+                self._errHandler.sync(self)
+                _alt = 1
+                while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                    if _alt == 1:
+                        self.state = 136
+                        self.postfix()
+
+                    else:
+                        raise NoViableAltException(self)
+                    self.state = 139
+                    self._errHandler.sync(self)
+                    _alt = self._interp.adaptivePredict(self._input,4,self._ctx)
+
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Unary_nofuncContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def unary_nofunc(self):
+            return self.getTypedRuleContext(LaTeXParser.Unary_nofuncContext,0)
+
+
+        def ADD(self):
+            return self.getToken(LaTeXParser.ADD, 0)
+
+        def SUB(self):
+            return self.getToken(LaTeXParser.SUB, 0)
+
+        def postfix(self):
+            return self.getTypedRuleContext(LaTeXParser.PostfixContext,0)
+
+
+        def postfix_nofunc(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.Postfix_nofuncContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.Postfix_nofuncContext,i)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_unary_nofunc
+
+
+
+
+    def unary_nofunc(self):
+
+        localctx = LaTeXParser.Unary_nofuncContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 16, self.RULE_unary_nofunc)
+        self._la = 0 # Token type
+        try:
+            self.state = 152
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [15, 16]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 143
+                _la = self._input.LA(1)
+                if not(_la==15 or _la==16):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 144
+                self.unary_nofunc()
+                pass
+            elif token in [19, 21, 23, 25, 27, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 64, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 145
+                self.postfix()
+                self.state = 149
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,6,self._ctx)
+                while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                    if _alt==1:
+                        self.state = 146
+                        self.postfix_nofunc()
+                    self.state = 151
+                    self._errHandler.sync(self)
+                    _alt = self._interp.adaptivePredict(self._input,6,self._ctx)
+
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class PostfixContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def exp(self):
+            return self.getTypedRuleContext(LaTeXParser.ExpContext,0)
+
+
+        def postfix_op(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.Postfix_opContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.Postfix_opContext,i)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_postfix
+
+
+
+
+    def postfix(self):
+
+        localctx = LaTeXParser.PostfixContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 18, self.RULE_postfix)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 154
+            self.exp(0)
+            self.state = 158
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,8,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    self.state = 155
+                    self.postfix_op()
+                self.state = 160
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,8,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Postfix_nofuncContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def exp_nofunc(self):
+            return self.getTypedRuleContext(LaTeXParser.Exp_nofuncContext,0)
+
+
+        def postfix_op(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.Postfix_opContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.Postfix_opContext,i)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_postfix_nofunc
+
+
+
+
+    def postfix_nofunc(self):
+
+        localctx = LaTeXParser.Postfix_nofuncContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 20, self.RULE_postfix_nofunc)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 161
+            self.exp_nofunc(0)
+            self.state = 165
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,9,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    self.state = 162
+                    self.postfix_op()
+                self.state = 167
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,9,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Postfix_opContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def BANG(self):
+            return self.getToken(LaTeXParser.BANG, 0)
+
+        def eval_at(self):
+            return self.getTypedRuleContext(LaTeXParser.Eval_atContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_postfix_op
+
+
+
+
+    def postfix_op(self):
+
+        localctx = LaTeXParser.Postfix_opContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 22, self.RULE_postfix_op)
+        try:
+            self.state = 170
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [89]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 168
+                self.match(LaTeXParser.BANG)
+                pass
+            elif token in [27]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 169
+                self.eval_at()
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Eval_atContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def BAR(self):
+            return self.getToken(LaTeXParser.BAR, 0)
+
+        def eval_at_sup(self):
+            return self.getTypedRuleContext(LaTeXParser.Eval_at_supContext,0)
+
+
+        def eval_at_sub(self):
+            return self.getTypedRuleContext(LaTeXParser.Eval_at_subContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_eval_at
+
+
+
+
+    def eval_at(self):
+
+        localctx = LaTeXParser.Eval_atContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 24, self.RULE_eval_at)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 172
+            self.match(LaTeXParser.BAR)
+            self.state = 178
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,11,self._ctx)
+            if la_ == 1:
+                self.state = 173
+                self.eval_at_sup()
+                pass
+
+            elif la_ == 2:
+                self.state = 174
+                self.eval_at_sub()
+                pass
+
+            elif la_ == 3:
+                self.state = 175
+                self.eval_at_sup()
+                self.state = 176
+                self.eval_at_sub()
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Eval_at_subContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def UNDERSCORE(self):
+            return self.getToken(LaTeXParser.UNDERSCORE, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def equality(self):
+            return self.getTypedRuleContext(LaTeXParser.EqualityContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_eval_at_sub
+
+
+
+
+    def eval_at_sub(self):
+
+        localctx = LaTeXParser.Eval_at_subContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 26, self.RULE_eval_at_sub)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 180
+            self.match(LaTeXParser.UNDERSCORE)
+            self.state = 181
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 184
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,12,self._ctx)
+            if la_ == 1:
+                self.state = 182
+                self.expr()
+                pass
+
+            elif la_ == 2:
+                self.state = 183
+                self.equality()
+                pass
+
+
+            self.state = 186
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Eval_at_supContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def CARET(self):
+            return self.getToken(LaTeXParser.CARET, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def equality(self):
+            return self.getTypedRuleContext(LaTeXParser.EqualityContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_eval_at_sup
+
+
+
+
+    def eval_at_sup(self):
+
+        localctx = LaTeXParser.Eval_at_supContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 28, self.RULE_eval_at_sup)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 188
+            self.match(LaTeXParser.CARET)
+            self.state = 189
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 192
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,13,self._ctx)
+            if la_ == 1:
+                self.state = 190
+                self.expr()
+                pass
+
+            elif la_ == 2:
+                self.state = 191
+                self.equality()
+                pass
+
+
+            self.state = 194
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class ExpContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def comp(self):
+            return self.getTypedRuleContext(LaTeXParser.CompContext,0)
+
+
+        def exp(self):
+            return self.getTypedRuleContext(LaTeXParser.ExpContext,0)
+
+
+        def CARET(self):
+            return self.getToken(LaTeXParser.CARET, 0)
+
+        def atom(self):
+            return self.getTypedRuleContext(LaTeXParser.AtomContext,0)
+
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def subexpr(self):
+            return self.getTypedRuleContext(LaTeXParser.SubexprContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_exp
+
+
+
+    def exp(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = LaTeXParser.ExpContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 30
+        self.enterRecursionRule(localctx, 30, self.RULE_exp, _p)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 197
+            self.comp()
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 213
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,16,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    localctx = LaTeXParser.ExpContext(self, _parentctx, _parentState)
+                    self.pushNewRecursionContext(localctx, _startState, self.RULE_exp)
+                    self.state = 199
+                    if not self.precpred(self._ctx, 2):
+                        from antlr4.error.Errors import FailedPredicateException
+                        raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                    self.state = 200
+                    self.match(LaTeXParser.CARET)
+                    self.state = 206
+                    self._errHandler.sync(self)
+                    token = self._input.LA(1)
+                    if token in [27, 29, 30, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                        self.state = 201
+                        self.atom()
+                        pass
+                    elif token in [21]:
+                        self.state = 202
+                        self.match(LaTeXParser.L_BRACE)
+                        self.state = 203
+                        self.expr()
+                        self.state = 204
+                        self.match(LaTeXParser.R_BRACE)
+                        pass
+                    else:
+                        raise NoViableAltException(self)
+
+                    self.state = 209
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,15,self._ctx)
+                    if la_ == 1:
+                        self.state = 208
+                        self.subexpr()
+
+
+                self.state = 215
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,16,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+    class Exp_nofuncContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def comp_nofunc(self):
+            return self.getTypedRuleContext(LaTeXParser.Comp_nofuncContext,0)
+
+
+        def exp_nofunc(self):
+            return self.getTypedRuleContext(LaTeXParser.Exp_nofuncContext,0)
+
+
+        def CARET(self):
+            return self.getToken(LaTeXParser.CARET, 0)
+
+        def atom(self):
+            return self.getTypedRuleContext(LaTeXParser.AtomContext,0)
+
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def subexpr(self):
+            return self.getTypedRuleContext(LaTeXParser.SubexprContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_exp_nofunc
+
+
+
+    def exp_nofunc(self, _p:int=0):
+        _parentctx = self._ctx
+        _parentState = self.state
+        localctx = LaTeXParser.Exp_nofuncContext(self, self._ctx, _parentState)
+        _prevctx = localctx
+        _startState = 32
+        self.enterRecursionRule(localctx, 32, self.RULE_exp_nofunc, _p)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 217
+            self.comp_nofunc()
+            self._ctx.stop = self._input.LT(-1)
+            self.state = 233
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,19,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    if self._parseListeners is not None:
+                        self.triggerExitRuleEvent()
+                    _prevctx = localctx
+                    localctx = LaTeXParser.Exp_nofuncContext(self, _parentctx, _parentState)
+                    self.pushNewRecursionContext(localctx, _startState, self.RULE_exp_nofunc)
+                    self.state = 219
+                    if not self.precpred(self._ctx, 2):
+                        from antlr4.error.Errors import FailedPredicateException
+                        raise FailedPredicateException(self, "self.precpred(self._ctx, 2)")
+                    self.state = 220
+                    self.match(LaTeXParser.CARET)
+                    self.state = 226
+                    self._errHandler.sync(self)
+                    token = self._input.LA(1)
+                    if token in [27, 29, 30, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                        self.state = 221
+                        self.atom()
+                        pass
+                    elif token in [21]:
+                        self.state = 222
+                        self.match(LaTeXParser.L_BRACE)
+                        self.state = 223
+                        self.expr()
+                        self.state = 224
+                        self.match(LaTeXParser.R_BRACE)
+                        pass
+                    else:
+                        raise NoViableAltException(self)
+
+                    self.state = 229
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,18,self._ctx)
+                    if la_ == 1:
+                        self.state = 228
+                        self.subexpr()
+
+
+                self.state = 235
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,19,self._ctx)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.unrollRecursionContexts(_parentctx)
+        return localctx
+
+
+    class CompContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def group(self):
+            return self.getTypedRuleContext(LaTeXParser.GroupContext,0)
+
+
+        def abs_group(self):
+            return self.getTypedRuleContext(LaTeXParser.Abs_groupContext,0)
+
+
+        def func(self):
+            return self.getTypedRuleContext(LaTeXParser.FuncContext,0)
+
+
+        def atom(self):
+            return self.getTypedRuleContext(LaTeXParser.AtomContext,0)
+
+
+        def floor(self):
+            return self.getTypedRuleContext(LaTeXParser.FloorContext,0)
+
+
+        def ceil(self):
+            return self.getTypedRuleContext(LaTeXParser.CeilContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_comp
+
+
+
+
+    def comp(self):
+
+        localctx = LaTeXParser.CompContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 34, self.RULE_comp)
+        try:
+            self.state = 242
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,20,self._ctx)
+            if la_ == 1:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 236
+                self.group()
+                pass
+
+            elif la_ == 2:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 237
+                self.abs_group()
+                pass
+
+            elif la_ == 3:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 238
+                self.func()
+                pass
+
+            elif la_ == 4:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 239
+                self.atom()
+                pass
+
+            elif la_ == 5:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 240
+                self.floor()
+                pass
+
+            elif la_ == 6:
+                self.enterOuterAlt(localctx, 6)
+                self.state = 241
+                self.ceil()
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Comp_nofuncContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def group(self):
+            return self.getTypedRuleContext(LaTeXParser.GroupContext,0)
+
+
+        def abs_group(self):
+            return self.getTypedRuleContext(LaTeXParser.Abs_groupContext,0)
+
+
+        def atom(self):
+            return self.getTypedRuleContext(LaTeXParser.AtomContext,0)
+
+
+        def floor(self):
+            return self.getTypedRuleContext(LaTeXParser.FloorContext,0)
+
+
+        def ceil(self):
+            return self.getTypedRuleContext(LaTeXParser.CeilContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_comp_nofunc
+
+
+
+
+    def comp_nofunc(self):
+
+        localctx = LaTeXParser.Comp_nofuncContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 36, self.RULE_comp_nofunc)
+        try:
+            self.state = 249
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,21,self._ctx)
+            if la_ == 1:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 244
+                self.group()
+                pass
+
+            elif la_ == 2:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 245
+                self.abs_group()
+                pass
+
+            elif la_ == 3:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 246
+                self.atom()
+                pass
+
+            elif la_ == 4:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 247
+                self.floor()
+                pass
+
+            elif la_ == 5:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 248
+                self.ceil()
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class GroupContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def L_PAREN(self):
+            return self.getToken(LaTeXParser.L_PAREN, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_PAREN(self):
+            return self.getToken(LaTeXParser.R_PAREN, 0)
+
+        def L_BRACKET(self):
+            return self.getToken(LaTeXParser.L_BRACKET, 0)
+
+        def R_BRACKET(self):
+            return self.getToken(LaTeXParser.R_BRACKET, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def L_BRACE_LITERAL(self):
+            return self.getToken(LaTeXParser.L_BRACE_LITERAL, 0)
+
+        def R_BRACE_LITERAL(self):
+            return self.getToken(LaTeXParser.R_BRACE_LITERAL, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_group
+
+
+
+
+    def group(self):
+
+        localctx = LaTeXParser.GroupContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 38, self.RULE_group)
+        try:
+            self.state = 267
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [19]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 251
+                self.match(LaTeXParser.L_PAREN)
+                self.state = 252
+                self.expr()
+                self.state = 253
+                self.match(LaTeXParser.R_PAREN)
+                pass
+            elif token in [25]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 255
+                self.match(LaTeXParser.L_BRACKET)
+                self.state = 256
+                self.expr()
+                self.state = 257
+                self.match(LaTeXParser.R_BRACKET)
+                pass
+            elif token in [21]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 259
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 260
+                self.expr()
+                self.state = 261
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            elif token in [23]:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 263
+                self.match(LaTeXParser.L_BRACE_LITERAL)
+                self.state = 264
+                self.expr()
+                self.state = 265
+                self.match(LaTeXParser.R_BRACE_LITERAL)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Abs_groupContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def BAR(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.BAR)
+            else:
+                return self.getToken(LaTeXParser.BAR, i)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_abs_group
+
+
+
+
+    def abs_group(self):
+
+        localctx = LaTeXParser.Abs_groupContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 40, self.RULE_abs_group)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 269
+            self.match(LaTeXParser.BAR)
+            self.state = 270
+            self.expr()
+            self.state = 271
+            self.match(LaTeXParser.BAR)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class NumberContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def DIGIT(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.DIGIT)
+            else:
+                return self.getToken(LaTeXParser.DIGIT, i)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_number
+
+
+
+
+    def number(self):
+
+        localctx = LaTeXParser.NumberContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 42, self.RULE_number)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 274
+            self._errHandler.sync(self)
+            _alt = 1
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt == 1:
+                    self.state = 273
+                    self.match(LaTeXParser.DIGIT)
+
+                else:
+                    raise NoViableAltException(self)
+                self.state = 276
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,23,self._ctx)
+
+            self.state = 284
+            self._errHandler.sync(self)
+            _alt = self._interp.adaptivePredict(self._input,24,self._ctx)
+            while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                if _alt==1:
+                    self.state = 278
+                    self.match(LaTeXParser.T__0)
+                    self.state = 279
+                    self.match(LaTeXParser.DIGIT)
+                    self.state = 280
+                    self.match(LaTeXParser.DIGIT)
+                    self.state = 281
+                    self.match(LaTeXParser.DIGIT)
+                self.state = 286
+                self._errHandler.sync(self)
+                _alt = self._interp.adaptivePredict(self._input,24,self._ctx)
+
+            self.state = 293
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,26,self._ctx)
+            if la_ == 1:
+                self.state = 287
+                self.match(LaTeXParser.T__1)
+                self.state = 289
+                self._errHandler.sync(self)
+                _alt = 1
+                while _alt!=2 and _alt!=ATN.INVALID_ALT_NUMBER:
+                    if _alt == 1:
+                        self.state = 288
+                        self.match(LaTeXParser.DIGIT)
+
+                    else:
+                        raise NoViableAltException(self)
+                    self.state = 291
+                    self._errHandler.sync(self)
+                    _alt = self._interp.adaptivePredict(self._input,25,self._ctx)
+
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class AtomContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def LETTER(self):
+            return self.getToken(LaTeXParser.LETTER, 0)
+
+        def SYMBOL(self):
+            return self.getToken(LaTeXParser.SYMBOL, 0)
+
+        def subexpr(self):
+            return self.getTypedRuleContext(LaTeXParser.SubexprContext,0)
+
+
+        def SINGLE_QUOTES(self):
+            return self.getToken(LaTeXParser.SINGLE_QUOTES, 0)
+
+        def number(self):
+            return self.getTypedRuleContext(LaTeXParser.NumberContext,0)
+
+
+        def DIFFERENTIAL(self):
+            return self.getToken(LaTeXParser.DIFFERENTIAL, 0)
+
+        def mathit(self):
+            return self.getTypedRuleContext(LaTeXParser.MathitContext,0)
+
+
+        def frac(self):
+            return self.getTypedRuleContext(LaTeXParser.FracContext,0)
+
+
+        def binom(self):
+            return self.getTypedRuleContext(LaTeXParser.BinomContext,0)
+
+
+        def bra(self):
+            return self.getTypedRuleContext(LaTeXParser.BraContext,0)
+
+
+        def ket(self):
+            return self.getTypedRuleContext(LaTeXParser.KetContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_atom
+
+
+
+
+    def atom(self):
+
+        localctx = LaTeXParser.AtomContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 44, self.RULE_atom)
+        self._la = 0 # Token type
+        try:
+            self.state = 317
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [77, 91]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 295
+                _la = self._input.LA(1)
+                if not(_la==77 or _la==91):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 308
+                self._errHandler.sync(self)
+                la_ = self._interp.adaptivePredict(self._input,31,self._ctx)
+                if la_ == 1:
+                    self.state = 297
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,27,self._ctx)
+                    if la_ == 1:
+                        self.state = 296
+                        self.subexpr()
+
+
+                    self.state = 300
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,28,self._ctx)
+                    if la_ == 1:
+                        self.state = 299
+                        self.match(LaTeXParser.SINGLE_QUOTES)
+
+
+                    pass
+
+                elif la_ == 2:
+                    self.state = 303
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,29,self._ctx)
+                    if la_ == 1:
+                        self.state = 302
+                        self.match(LaTeXParser.SINGLE_QUOTES)
+
+
+                    self.state = 306
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,30,self._ctx)
+                    if la_ == 1:
+                        self.state = 305
+                        self.subexpr()
+
+
+                    pass
+
+
+                pass
+            elif token in [78]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 310
+                self.number()
+                pass
+            elif token in [76]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 311
+                self.match(LaTeXParser.DIFFERENTIAL)
+                pass
+            elif token in [72]:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 312
+                self.mathit()
+                pass
+            elif token in [68]:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 313
+                self.frac()
+                pass
+            elif token in [69, 70, 71]:
+                self.enterOuterAlt(localctx, 6)
+                self.state = 314
+                self.binom()
+                pass
+            elif token in [30]:
+                self.enterOuterAlt(localctx, 7)
+                self.state = 315
+                self.bra()
+                pass
+            elif token in [27, 29]:
+                self.enterOuterAlt(localctx, 8)
+                self.state = 316
+                self.ket()
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class BraContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def L_ANGLE(self):
+            return self.getToken(LaTeXParser.L_ANGLE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_BAR(self):
+            return self.getToken(LaTeXParser.R_BAR, 0)
+
+        def BAR(self):
+            return self.getToken(LaTeXParser.BAR, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_bra
+
+
+
+
+    def bra(self):
+
+        localctx = LaTeXParser.BraContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 46, self.RULE_bra)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 319
+            self.match(LaTeXParser.L_ANGLE)
+            self.state = 320
+            self.expr()
+            self.state = 321
+            _la = self._input.LA(1)
+            if not(_la==27 or _la==28):
+                self._errHandler.recoverInline(self)
+            else:
+                self._errHandler.reportMatch(self)
+                self.consume()
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class KetContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_ANGLE(self):
+            return self.getToken(LaTeXParser.R_ANGLE, 0)
+
+        def L_BAR(self):
+            return self.getToken(LaTeXParser.L_BAR, 0)
+
+        def BAR(self):
+            return self.getToken(LaTeXParser.BAR, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_ket
+
+
+
+
+    def ket(self):
+
+        localctx = LaTeXParser.KetContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 48, self.RULE_ket)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 323
+            _la = self._input.LA(1)
+            if not(_la==27 or _la==29):
+                self._errHandler.recoverInline(self)
+            else:
+                self._errHandler.reportMatch(self)
+                self.consume()
+            self.state = 324
+            self.expr()
+            self.state = 325
+            self.match(LaTeXParser.R_ANGLE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class MathitContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def CMD_MATHIT(self):
+            return self.getToken(LaTeXParser.CMD_MATHIT, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def mathit_text(self):
+            return self.getTypedRuleContext(LaTeXParser.Mathit_textContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_mathit
+
+
+
+
+    def mathit(self):
+
+        localctx = LaTeXParser.MathitContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 50, self.RULE_mathit)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 327
+            self.match(LaTeXParser.CMD_MATHIT)
+            self.state = 328
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 329
+            self.mathit_text()
+            self.state = 330
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Mathit_textContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def LETTER(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.LETTER)
+            else:
+                return self.getToken(LaTeXParser.LETTER, i)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_mathit_text
+
+
+
+
+    def mathit_text(self):
+
+        localctx = LaTeXParser.Mathit_textContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 52, self.RULE_mathit_text)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 335
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            while _la==77:
+                self.state = 332
+                self.match(LaTeXParser.LETTER)
+                self.state = 337
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class FracContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+            self.upperd = None # Token
+            self.upper = None # ExprContext
+            self.lowerd = None # Token
+            self.lower = None # ExprContext
+
+        def CMD_FRAC(self):
+            return self.getToken(LaTeXParser.CMD_FRAC, 0)
+
+        def L_BRACE(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.L_BRACE)
+            else:
+                return self.getToken(LaTeXParser.L_BRACE, i)
+
+        def R_BRACE(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.R_BRACE)
+            else:
+                return self.getToken(LaTeXParser.R_BRACE, i)
+
+        def DIGIT(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.DIGIT)
+            else:
+                return self.getToken(LaTeXParser.DIGIT, i)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_frac
+
+
+
+
+    def frac(self):
+
+        localctx = LaTeXParser.FracContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 54, self.RULE_frac)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 338
+            self.match(LaTeXParser.CMD_FRAC)
+            self.state = 344
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [78]:
+                self.state = 339
+                localctx.upperd = self.match(LaTeXParser.DIGIT)
+                pass
+            elif token in [21]:
+                self.state = 340
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 341
+                localctx.upper = self.expr()
+                self.state = 342
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+            self.state = 351
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [78]:
+                self.state = 346
+                localctx.lowerd = self.match(LaTeXParser.DIGIT)
+                pass
+            elif token in [21]:
+                self.state = 347
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 348
+                localctx.lower = self.expr()
+                self.state = 349
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class BinomContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+            self.n = None # ExprContext
+            self.k = None # ExprContext
+
+        def L_BRACE(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.L_BRACE)
+            else:
+                return self.getToken(LaTeXParser.L_BRACE, i)
+
+        def R_BRACE(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.R_BRACE)
+            else:
+                return self.getToken(LaTeXParser.R_BRACE, i)
+
+        def CMD_BINOM(self):
+            return self.getToken(LaTeXParser.CMD_BINOM, 0)
+
+        def CMD_DBINOM(self):
+            return self.getToken(LaTeXParser.CMD_DBINOM, 0)
+
+        def CMD_TBINOM(self):
+            return self.getToken(LaTeXParser.CMD_TBINOM, 0)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.ExprContext,i)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_binom
+
+
+
+
+    def binom(self):
+
+        localctx = LaTeXParser.BinomContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 56, self.RULE_binom)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 353
+            _la = self._input.LA(1)
+            if not((((_la - 69)) & ~0x3f) == 0 and ((1 << (_la - 69)) & 7) != 0):
+                self._errHandler.recoverInline(self)
+            else:
+                self._errHandler.reportMatch(self)
+                self.consume()
+            self.state = 354
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 355
+            localctx.n = self.expr()
+            self.state = 356
+            self.match(LaTeXParser.R_BRACE)
+            self.state = 357
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 358
+            localctx.k = self.expr()
+            self.state = 359
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class FloorContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+            self.val = None # ExprContext
+
+        def L_FLOOR(self):
+            return self.getToken(LaTeXParser.L_FLOOR, 0)
+
+        def R_FLOOR(self):
+            return self.getToken(LaTeXParser.R_FLOOR, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_floor
+
+
+
+
+    def floor(self):
+
+        localctx = LaTeXParser.FloorContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 58, self.RULE_floor)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 361
+            self.match(LaTeXParser.L_FLOOR)
+            self.state = 362
+            localctx.val = self.expr()
+            self.state = 363
+            self.match(LaTeXParser.R_FLOOR)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class CeilContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+            self.val = None # ExprContext
+
+        def L_CEIL(self):
+            return self.getToken(LaTeXParser.L_CEIL, 0)
+
+        def R_CEIL(self):
+            return self.getToken(LaTeXParser.R_CEIL, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_ceil
+
+
+
+
+    def ceil(self):
+
+        localctx = LaTeXParser.CeilContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 60, self.RULE_ceil)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 365
+            self.match(LaTeXParser.L_CEIL)
+            self.state = 366
+            localctx.val = self.expr()
+            self.state = 367
+            self.match(LaTeXParser.R_CEIL)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Func_normalContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def FUNC_EXP(self):
+            return self.getToken(LaTeXParser.FUNC_EXP, 0)
+
+        def FUNC_LOG(self):
+            return self.getToken(LaTeXParser.FUNC_LOG, 0)
+
+        def FUNC_LG(self):
+            return self.getToken(LaTeXParser.FUNC_LG, 0)
+
+        def FUNC_LN(self):
+            return self.getToken(LaTeXParser.FUNC_LN, 0)
+
+        def FUNC_SIN(self):
+            return self.getToken(LaTeXParser.FUNC_SIN, 0)
+
+        def FUNC_COS(self):
+            return self.getToken(LaTeXParser.FUNC_COS, 0)
+
+        def FUNC_TAN(self):
+            return self.getToken(LaTeXParser.FUNC_TAN, 0)
+
+        def FUNC_CSC(self):
+            return self.getToken(LaTeXParser.FUNC_CSC, 0)
+
+        def FUNC_SEC(self):
+            return self.getToken(LaTeXParser.FUNC_SEC, 0)
+
+        def FUNC_COT(self):
+            return self.getToken(LaTeXParser.FUNC_COT, 0)
+
+        def FUNC_ARCSIN(self):
+            return self.getToken(LaTeXParser.FUNC_ARCSIN, 0)
+
+        def FUNC_ARCCOS(self):
+            return self.getToken(LaTeXParser.FUNC_ARCCOS, 0)
+
+        def FUNC_ARCTAN(self):
+            return self.getToken(LaTeXParser.FUNC_ARCTAN, 0)
+
+        def FUNC_ARCCSC(self):
+            return self.getToken(LaTeXParser.FUNC_ARCCSC, 0)
+
+        def FUNC_ARCSEC(self):
+            return self.getToken(LaTeXParser.FUNC_ARCSEC, 0)
+
+        def FUNC_ARCCOT(self):
+            return self.getToken(LaTeXParser.FUNC_ARCCOT, 0)
+
+        def FUNC_SINH(self):
+            return self.getToken(LaTeXParser.FUNC_SINH, 0)
+
+        def FUNC_COSH(self):
+            return self.getToken(LaTeXParser.FUNC_COSH, 0)
+
+        def FUNC_TANH(self):
+            return self.getToken(LaTeXParser.FUNC_TANH, 0)
+
+        def FUNC_ARSINH(self):
+            return self.getToken(LaTeXParser.FUNC_ARSINH, 0)
+
+        def FUNC_ARCOSH(self):
+            return self.getToken(LaTeXParser.FUNC_ARCOSH, 0)
+
+        def FUNC_ARTANH(self):
+            return self.getToken(LaTeXParser.FUNC_ARTANH, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_func_normal
+
+
+
+
+    def func_normal(self):
+
+        localctx = LaTeXParser.Func_normalContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 62, self.RULE_func_normal)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 369
+            _la = self._input.LA(1)
+            if not(((_la) & ~0x3f) == 0 and ((1 << _la) & 576460614864470016) != 0):
+                self._errHandler.recoverInline(self)
+            else:
+                self._errHandler.reportMatch(self)
+                self.consume()
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class FuncContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+            self.root = None # ExprContext
+            self.base = None # ExprContext
+
+        def func_normal(self):
+            return self.getTypedRuleContext(LaTeXParser.Func_normalContext,0)
+
+
+        def L_PAREN(self):
+            return self.getToken(LaTeXParser.L_PAREN, 0)
+
+        def func_arg(self):
+            return self.getTypedRuleContext(LaTeXParser.Func_argContext,0)
+
+
+        def R_PAREN(self):
+            return self.getToken(LaTeXParser.R_PAREN, 0)
+
+        def func_arg_noparens(self):
+            return self.getTypedRuleContext(LaTeXParser.Func_arg_noparensContext,0)
+
+
+        def subexpr(self):
+            return self.getTypedRuleContext(LaTeXParser.SubexprContext,0)
+
+
+        def supexpr(self):
+            return self.getTypedRuleContext(LaTeXParser.SupexprContext,0)
+
+
+        def args(self):
+            return self.getTypedRuleContext(LaTeXParser.ArgsContext,0)
+
+
+        def LETTER(self):
+            return self.getToken(LaTeXParser.LETTER, 0)
+
+        def SYMBOL(self):
+            return self.getToken(LaTeXParser.SYMBOL, 0)
+
+        def SINGLE_QUOTES(self):
+            return self.getToken(LaTeXParser.SINGLE_QUOTES, 0)
+
+        def FUNC_INT(self):
+            return self.getToken(LaTeXParser.FUNC_INT, 0)
+
+        def DIFFERENTIAL(self):
+            return self.getToken(LaTeXParser.DIFFERENTIAL, 0)
+
+        def frac(self):
+            return self.getTypedRuleContext(LaTeXParser.FracContext,0)
+
+
+        def additive(self):
+            return self.getTypedRuleContext(LaTeXParser.AdditiveContext,0)
+
+
+        def FUNC_SQRT(self):
+            return self.getToken(LaTeXParser.FUNC_SQRT, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def expr(self, i:int=None):
+            if i is None:
+                return self.getTypedRuleContexts(LaTeXParser.ExprContext)
+            else:
+                return self.getTypedRuleContext(LaTeXParser.ExprContext,i)
+
+
+        def L_BRACKET(self):
+            return self.getToken(LaTeXParser.L_BRACKET, 0)
+
+        def R_BRACKET(self):
+            return self.getToken(LaTeXParser.R_BRACKET, 0)
+
+        def FUNC_OVERLINE(self):
+            return self.getToken(LaTeXParser.FUNC_OVERLINE, 0)
+
+        def mp(self):
+            return self.getTypedRuleContext(LaTeXParser.MpContext,0)
+
+
+        def FUNC_SUM(self):
+            return self.getToken(LaTeXParser.FUNC_SUM, 0)
+
+        def FUNC_PROD(self):
+            return self.getToken(LaTeXParser.FUNC_PROD, 0)
+
+        def subeq(self):
+            return self.getTypedRuleContext(LaTeXParser.SubeqContext,0)
+
+
+        def FUNC_LIM(self):
+            return self.getToken(LaTeXParser.FUNC_LIM, 0)
+
+        def limit_sub(self):
+            return self.getTypedRuleContext(LaTeXParser.Limit_subContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_func
+
+
+
+
+    def func(self):
+
+        localctx = LaTeXParser.FuncContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 64, self.RULE_func)
+        self._la = 0 # Token type
+        try:
+            self.state = 460
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58]:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 371
+                self.func_normal()
+                self.state = 384
+                self._errHandler.sync(self)
+                la_ = self._interp.adaptivePredict(self._input,40,self._ctx)
+                if la_ == 1:
+                    self.state = 373
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==73:
+                        self.state = 372
+                        self.subexpr()
+
+
+                    self.state = 376
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==74:
+                        self.state = 375
+                        self.supexpr()
+
+
+                    pass
+
+                elif la_ == 2:
+                    self.state = 379
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==74:
+                        self.state = 378
+                        self.supexpr()
+
+
+                    self.state = 382
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==73:
+                        self.state = 381
+                        self.subexpr()
+
+
+                    pass
+
+
+                self.state = 391
+                self._errHandler.sync(self)
+                la_ = self._interp.adaptivePredict(self._input,41,self._ctx)
+                if la_ == 1:
+                    self.state = 386
+                    self.match(LaTeXParser.L_PAREN)
+                    self.state = 387
+                    self.func_arg()
+                    self.state = 388
+                    self.match(LaTeXParser.R_PAREN)
+                    pass
+
+                elif la_ == 2:
+                    self.state = 390
+                    self.func_arg_noparens()
+                    pass
+
+
+                pass
+            elif token in [77, 91]:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 393
+                _la = self._input.LA(1)
+                if not(_la==77 or _la==91):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 406
+                self._errHandler.sync(self)
+                la_ = self._interp.adaptivePredict(self._input,46,self._ctx)
+                if la_ == 1:
+                    self.state = 395
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==73:
+                        self.state = 394
+                        self.subexpr()
+
+
+                    self.state = 398
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==90:
+                        self.state = 397
+                        self.match(LaTeXParser.SINGLE_QUOTES)
+
+
+                    pass
+
+                elif la_ == 2:
+                    self.state = 401
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==90:
+                        self.state = 400
+                        self.match(LaTeXParser.SINGLE_QUOTES)
+
+
+                    self.state = 404
+                    self._errHandler.sync(self)
+                    _la = self._input.LA(1)
+                    if _la==73:
+                        self.state = 403
+                        self.subexpr()
+
+
+                    pass
+
+
+                self.state = 408
+                self.match(LaTeXParser.L_PAREN)
+                self.state = 409
+                self.args()
+                self.state = 410
+                self.match(LaTeXParser.R_PAREN)
+                pass
+            elif token in [34]:
+                self.enterOuterAlt(localctx, 3)
+                self.state = 412
+                self.match(LaTeXParser.FUNC_INT)
+                self.state = 419
+                self._errHandler.sync(self)
+                token = self._input.LA(1)
+                if token in [73]:
+                    self.state = 413
+                    self.subexpr()
+                    self.state = 414
+                    self.supexpr()
+                    pass
+                elif token in [74]:
+                    self.state = 416
+                    self.supexpr()
+                    self.state = 417
+                    self.subexpr()
+                    pass
+                elif token in [15, 16, 19, 21, 23, 25, 27, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 64, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                    pass
+                else:
+                    pass
+                self.state = 427
+                self._errHandler.sync(self)
+                la_ = self._interp.adaptivePredict(self._input,49,self._ctx)
+                if la_ == 1:
+                    self.state = 422
+                    self._errHandler.sync(self)
+                    la_ = self._interp.adaptivePredict(self._input,48,self._ctx)
+                    if la_ == 1:
+                        self.state = 421
+                        self.additive(0)
+
+
+                    self.state = 424
+                    self.match(LaTeXParser.DIFFERENTIAL)
+                    pass
+
+                elif la_ == 2:
+                    self.state = 425
+                    self.frac()
+                    pass
+
+                elif la_ == 3:
+                    self.state = 426
+                    self.additive(0)
+                    pass
+
+
+                pass
+            elif token in [63]:
+                self.enterOuterAlt(localctx, 4)
+                self.state = 429
+                self.match(LaTeXParser.FUNC_SQRT)
+                self.state = 434
+                self._errHandler.sync(self)
+                _la = self._input.LA(1)
+                if _la==25:
+                    self.state = 430
+                    self.match(LaTeXParser.L_BRACKET)
+                    self.state = 431
+                    localctx.root = self.expr()
+                    self.state = 432
+                    self.match(LaTeXParser.R_BRACKET)
+
+
+                self.state = 436
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 437
+                localctx.base = self.expr()
+                self.state = 438
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            elif token in [64]:
+                self.enterOuterAlt(localctx, 5)
+                self.state = 440
+                self.match(LaTeXParser.FUNC_OVERLINE)
+                self.state = 441
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 442
+                localctx.base = self.expr()
+                self.state = 443
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            elif token in [35, 36]:
+                self.enterOuterAlt(localctx, 6)
+                self.state = 445
+                _la = self._input.LA(1)
+                if not(_la==35 or _la==36):
+                    self._errHandler.recoverInline(self)
+                else:
+                    self._errHandler.reportMatch(self)
+                    self.consume()
+                self.state = 452
+                self._errHandler.sync(self)
+                token = self._input.LA(1)
+                if token in [73]:
+                    self.state = 446
+                    self.subeq()
+                    self.state = 447
+                    self.supexpr()
+                    pass
+                elif token in [74]:
+                    self.state = 449
+                    self.supexpr()
+                    self.state = 450
+                    self.subeq()
+                    pass
+                else:
+                    raise NoViableAltException(self)
+
+                self.state = 454
+                self.mp(0)
+                pass
+            elif token in [32]:
+                self.enterOuterAlt(localctx, 7)
+                self.state = 456
+                self.match(LaTeXParser.FUNC_LIM)
+                self.state = 457
+                self.limit_sub()
+                self.state = 458
+                self.mp(0)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class ArgsContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def args(self):
+            return self.getTypedRuleContext(LaTeXParser.ArgsContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_args
+
+
+
+
+    def args(self):
+
+        localctx = LaTeXParser.ArgsContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 66, self.RULE_args)
+        try:
+            self.state = 467
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,53,self._ctx)
+            if la_ == 1:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 462
+                self.expr()
+                self.state = 463
+                self.match(LaTeXParser.T__0)
+                self.state = 464
+                self.args()
+                pass
+
+            elif la_ == 2:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 466
+                self.expr()
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Limit_subContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def UNDERSCORE(self):
+            return self.getToken(LaTeXParser.UNDERSCORE, 0)
+
+        def L_BRACE(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.L_BRACE)
+            else:
+                return self.getToken(LaTeXParser.L_BRACE, i)
+
+        def LIM_APPROACH_SYM(self):
+            return self.getToken(LaTeXParser.LIM_APPROACH_SYM, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_BRACE(self, i:int=None):
+            if i is None:
+                return self.getTokens(LaTeXParser.R_BRACE)
+            else:
+                return self.getToken(LaTeXParser.R_BRACE, i)
+
+        def LETTER(self):
+            return self.getToken(LaTeXParser.LETTER, 0)
+
+        def SYMBOL(self):
+            return self.getToken(LaTeXParser.SYMBOL, 0)
+
+        def CARET(self):
+            return self.getToken(LaTeXParser.CARET, 0)
+
+        def ADD(self):
+            return self.getToken(LaTeXParser.ADD, 0)
+
+        def SUB(self):
+            return self.getToken(LaTeXParser.SUB, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_limit_sub
+
+
+
+
+    def limit_sub(self):
+
+        localctx = LaTeXParser.Limit_subContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 68, self.RULE_limit_sub)
+        self._la = 0 # Token type
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 469
+            self.match(LaTeXParser.UNDERSCORE)
+            self.state = 470
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 471
+            _la = self._input.LA(1)
+            if not(_la==77 or _la==91):
+                self._errHandler.recoverInline(self)
+            else:
+                self._errHandler.reportMatch(self)
+                self.consume()
+            self.state = 472
+            self.match(LaTeXParser.LIM_APPROACH_SYM)
+            self.state = 473
+            self.expr()
+            self.state = 482
+            self._errHandler.sync(self)
+            _la = self._input.LA(1)
+            if _la==74:
+                self.state = 474
+                self.match(LaTeXParser.CARET)
+                self.state = 480
+                self._errHandler.sync(self)
+                token = self._input.LA(1)
+                if token in [21]:
+                    self.state = 475
+                    self.match(LaTeXParser.L_BRACE)
+                    self.state = 476
+                    _la = self._input.LA(1)
+                    if not(_la==15 or _la==16):
+                        self._errHandler.recoverInline(self)
+                    else:
+                        self._errHandler.reportMatch(self)
+                        self.consume()
+                    self.state = 477
+                    self.match(LaTeXParser.R_BRACE)
+                    pass
+                elif token in [15]:
+                    self.state = 478
+                    self.match(LaTeXParser.ADD)
+                    pass
+                elif token in [16]:
+                    self.state = 479
+                    self.match(LaTeXParser.SUB)
+                    pass
+                else:
+                    raise NoViableAltException(self)
+
+
+
+            self.state = 484
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Func_argContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def func_arg(self):
+            return self.getTypedRuleContext(LaTeXParser.Func_argContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_func_arg
+
+
+
+
+    def func_arg(self):
+
+        localctx = LaTeXParser.Func_argContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 70, self.RULE_func_arg)
+        try:
+            self.state = 491
+            self._errHandler.sync(self)
+            la_ = self._interp.adaptivePredict(self._input,56,self._ctx)
+            if la_ == 1:
+                self.enterOuterAlt(localctx, 1)
+                self.state = 486
+                self.expr()
+                pass
+
+            elif la_ == 2:
+                self.enterOuterAlt(localctx, 2)
+                self.state = 487
+                self.expr()
+                self.state = 488
+                self.match(LaTeXParser.T__0)
+                self.state = 489
+                self.func_arg()
+                pass
+
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class Func_arg_noparensContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def mp_nofunc(self):
+            return self.getTypedRuleContext(LaTeXParser.Mp_nofuncContext,0)
+
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_func_arg_noparens
+
+
+
+
+    def func_arg_noparens(self):
+
+        localctx = LaTeXParser.Func_arg_noparensContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 72, self.RULE_func_arg_noparens)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 493
+            self.mp_nofunc(0)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class SubexprContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def UNDERSCORE(self):
+            return self.getToken(LaTeXParser.UNDERSCORE, 0)
+
+        def atom(self):
+            return self.getTypedRuleContext(LaTeXParser.AtomContext,0)
+
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_subexpr
+
+
+
+
+    def subexpr(self):
+
+        localctx = LaTeXParser.SubexprContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 74, self.RULE_subexpr)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 495
+            self.match(LaTeXParser.UNDERSCORE)
+            self.state = 501
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [27, 29, 30, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                self.state = 496
+                self.atom()
+                pass
+            elif token in [21]:
+                self.state = 497
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 498
+                self.expr()
+                self.state = 499
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class SupexprContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def CARET(self):
+            return self.getToken(LaTeXParser.CARET, 0)
+
+        def atom(self):
+            return self.getTypedRuleContext(LaTeXParser.AtomContext,0)
+
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def expr(self):
+            return self.getTypedRuleContext(LaTeXParser.ExprContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_supexpr
+
+
+
+
+    def supexpr(self):
+
+        localctx = LaTeXParser.SupexprContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 76, self.RULE_supexpr)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 503
+            self.match(LaTeXParser.CARET)
+            self.state = 509
+            self._errHandler.sync(self)
+            token = self._input.LA(1)
+            if token in [27, 29, 30, 68, 69, 70, 71, 72, 76, 77, 78, 91]:
+                self.state = 504
+                self.atom()
+                pass
+            elif token in [21]:
+                self.state = 505
+                self.match(LaTeXParser.L_BRACE)
+                self.state = 506
+                self.expr()
+                self.state = 507
+                self.match(LaTeXParser.R_BRACE)
+                pass
+            else:
+                raise NoViableAltException(self)
+
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class SubeqContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def UNDERSCORE(self):
+            return self.getToken(LaTeXParser.UNDERSCORE, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def equality(self):
+            return self.getTypedRuleContext(LaTeXParser.EqualityContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_subeq
+
+
+
+
+    def subeq(self):
+
+        localctx = LaTeXParser.SubeqContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 78, self.RULE_subeq)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 511
+            self.match(LaTeXParser.UNDERSCORE)
+            self.state = 512
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 513
+            self.equality()
+            self.state = 514
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+    class SupeqContext(ParserRuleContext):
+        __slots__ = 'parser'
+
+        def __init__(self, parser, parent:ParserRuleContext=None, invokingState:int=-1):
+            super().__init__(parent, invokingState)
+            self.parser = parser
+
+        def UNDERSCORE(self):
+            return self.getToken(LaTeXParser.UNDERSCORE, 0)
+
+        def L_BRACE(self):
+            return self.getToken(LaTeXParser.L_BRACE, 0)
+
+        def equality(self):
+            return self.getTypedRuleContext(LaTeXParser.EqualityContext,0)
+
+
+        def R_BRACE(self):
+            return self.getToken(LaTeXParser.R_BRACE, 0)
+
+        def getRuleIndex(self):
+            return LaTeXParser.RULE_supeq
+
+
+
+
+    def supeq(self):
+
+        localctx = LaTeXParser.SupeqContext(self, self._ctx, self.state)
+        self.enterRule(localctx, 80, self.RULE_supeq)
+        try:
+            self.enterOuterAlt(localctx, 1)
+            self.state = 516
+            self.match(LaTeXParser.UNDERSCORE)
+            self.state = 517
+            self.match(LaTeXParser.L_BRACE)
+            self.state = 518
+            self.equality()
+            self.state = 519
+            self.match(LaTeXParser.R_BRACE)
+        except RecognitionException as re:
+            localctx.exception = re
+            self._errHandler.reportError(self, re)
+            self._errHandler.recover(self, re)
+        finally:
+            self.exitRule()
+        return localctx
+
+
+
+    def sempred(self, localctx:RuleContext, ruleIndex:int, predIndex:int):
+        if self._predicates == None:
+            self._predicates = dict()
+        self._predicates[1] = self.relation_sempred
+        self._predicates[4] = self.additive_sempred
+        self._predicates[5] = self.mp_sempred
+        self._predicates[6] = self.mp_nofunc_sempred
+        self._predicates[15] = self.exp_sempred
+        self._predicates[16] = self.exp_nofunc_sempred
+        pred = self._predicates.get(ruleIndex, None)
+        if pred is None:
+            raise Exception("No predicate with index:" + str(ruleIndex))
+        else:
+            return pred(localctx, predIndex)
+
+    def relation_sempred(self, localctx:RelationContext, predIndex:int):
+            if predIndex == 0:
+                return self.precpred(self._ctx, 2)
+
+
+    def additive_sempred(self, localctx:AdditiveContext, predIndex:int):
+            if predIndex == 1:
+                return self.precpred(self._ctx, 2)
+
+
+    def mp_sempred(self, localctx:MpContext, predIndex:int):
+            if predIndex == 2:
+                return self.precpred(self._ctx, 2)
+
+
+    def mp_nofunc_sempred(self, localctx:Mp_nofuncContext, predIndex:int):
+            if predIndex == 3:
+                return self.precpred(self._ctx, 2)
+
+
+    def exp_sempred(self, localctx:ExpContext, predIndex:int):
+            if predIndex == 4:
+                return self.precpred(self._ctx, 2)
+
+
+    def exp_nofunc_sempred(self, localctx:Exp_nofuncContext, predIndex:int):
+            if predIndex == 5:
+                return self.precpred(self._ctx, 2)
+
+
+
+
+
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_build_latex_antlr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_build_latex_antlr.py
new file mode 100644
index 0000000000000000000000000000000000000000..ee50da5b7861154823812c7773360b53dfd29ff6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_build_latex_antlr.py
@@ -0,0 +1,91 @@
+import os
+import subprocess
+import glob
+
+from sympy.utilities.misc import debug
+
+here = os.path.dirname(__file__)
+grammar_file = os.path.abspath(os.path.join(here, "LaTeX.g4"))
+dir_latex_antlr = os.path.join(here, "_antlr")
+
+header = '''\
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated from ../LaTeX.g4, derived from latex2sympy
+#     latex2sympy is licensed under the MIT license
+#     https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt
+'''
+
+
+def check_antlr_version():
+    debug("Checking antlr4 version...")
+
+    try:
+        debug(subprocess.check_output(["antlr4"])
+              .decode('utf-8').split("\n")[0])
+        return True
+    except (subprocess.CalledProcessError, FileNotFoundError):
+        debug("The 'antlr4' command line tool is not installed, "
+              "or not on your PATH.\n"
+              "> Please refer to the README.md file for more information.")
+        return False
+
+
+def build_parser(output_dir=dir_latex_antlr):
+    check_antlr_version()
+
+    debug("Updating ANTLR-generated code in {}".format(output_dir))
+
+    if not os.path.exists(output_dir):
+        os.makedirs(output_dir)
+
+    with open(os.path.join(output_dir, "__init__.py"), "w+") as fp:
+        fp.write(header)
+
+    args = [
+        "antlr4",
+        grammar_file,
+        "-o", output_dir,
+        # for now, not generating these as latex2sympy did not use them
+        "-no-visitor",
+        "-no-listener",
+    ]
+
+    debug("Running code generation...\n\t$ {}".format(" ".join(args)))
+    subprocess.check_output(args, cwd=output_dir)
+
+    debug("Applying headers, removing unnecessary files and renaming...")
+    # Handle case insensitive file systems. If the files are already
+    # generated, they will be written to latex* but LaTeX*.* won't match them.
+    for path in (glob.glob(os.path.join(output_dir, "LaTeX*.*")) or
+        glob.glob(os.path.join(output_dir, "latex*.*"))):
+
+        # Remove files ending in .interp or .tokens as they are not needed.
+        if not path.endswith(".py"):
+            os.unlink(path)
+            continue
+
+        new_path = os.path.join(output_dir, os.path.basename(path).lower())
+        with open(path, 'r') as f:
+            lines = [line.rstrip() + '\n' for line in f]
+
+        os.unlink(path)
+
+        with open(new_path, "w") as out_file:
+            offset = 0
+            while lines[offset].startswith('#'):
+                offset += 1
+            out_file.write(header)
+            out_file.writelines(lines[offset:])
+
+        debug("\t{}".format(new_path))
+
+    return True
+
+
+if __name__ == "__main__":
+    build_parser()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_parse_latex_antlr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_parse_latex_antlr.py
new file mode 100644
index 0000000000000000000000000000000000000000..26604375b3a9622f8c1dacdb1d678d09c2c3ad41
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/_parse_latex_antlr.py
@@ -0,0 +1,607 @@
+# Ported from latex2sympy by @augustt198
+# https://github.com/augustt198/latex2sympy
+# See license in LICENSE.txt
+from importlib.metadata import version
+import sympy
+from sympy.external import import_module
+from sympy.printing.str import StrPrinter
+from sympy.physics.quantum.state import Bra, Ket
+
+from .errors import LaTeXParsingError
+
+
+LaTeXParser = LaTeXLexer = MathErrorListener = None
+
+try:
+    LaTeXParser = import_module('sympy.parsing.latex._antlr.latexparser',
+                                import_kwargs={'fromlist': ['LaTeXParser']}).LaTeXParser
+    LaTeXLexer = import_module('sympy.parsing.latex._antlr.latexlexer',
+                               import_kwargs={'fromlist': ['LaTeXLexer']}).LaTeXLexer
+except Exception:
+    pass
+
+ErrorListener = import_module('antlr4.error.ErrorListener',
+                              warn_not_installed=True,
+                              import_kwargs={'fromlist': ['ErrorListener']}
+                              )
+
+
+
+if ErrorListener:
+    class MathErrorListener(ErrorListener.ErrorListener):  # type:ignore # noqa:F811
+        def __init__(self, src):
+            super(ErrorListener.ErrorListener, self).__init__()
+            self.src = src
+
+        def syntaxError(self, recog, symbol, line, col, msg, e):
+            fmt = "%s\n%s\n%s"
+            marker = "~" * col + "^"
+
+            if msg.startswith("missing"):
+                err = fmt % (msg, self.src, marker)
+            elif msg.startswith("no viable"):
+                err = fmt % ("I expected something else here", self.src, marker)
+            elif msg.startswith("mismatched"):
+                names = LaTeXParser.literalNames
+                expected = [
+                    names[i] for i in e.getExpectedTokens() if i < len(names)
+                ]
+                if len(expected) < 10:
+                    expected = " ".join(expected)
+                    err = (fmt % ("I expected one of these: " + expected, self.src,
+                                  marker))
+                else:
+                    err = (fmt % ("I expected something else here", self.src,
+                                  marker))
+            else:
+                err = fmt % ("I don't understand this", self.src, marker)
+            raise LaTeXParsingError(err)
+
+
+def parse_latex(sympy, strict=False):
+    antlr4 = import_module('antlr4')
+
+    if None in [antlr4, MathErrorListener] or \
+            not version('antlr4-python3-runtime').startswith('4.11'):
+        raise ImportError("LaTeX parsing requires the antlr4 Python package,"
+                          " provided by pip (antlr4-python3-runtime) or"
+                          " conda (antlr-python-runtime), version 4.11")
+
+    sympy = sympy.strip()
+    matherror = MathErrorListener(sympy)
+
+    stream = antlr4.InputStream(sympy)
+    lex = LaTeXLexer(stream)
+    lex.removeErrorListeners()
+    lex.addErrorListener(matherror)
+
+    tokens = antlr4.CommonTokenStream(lex)
+    parser = LaTeXParser(tokens)
+
+    # remove default console error listener
+    parser.removeErrorListeners()
+    parser.addErrorListener(matherror)
+
+    relation = parser.math().relation()
+    if strict and (relation.start.start != 0 or relation.stop.stop != len(sympy) - 1):
+        raise LaTeXParsingError("Invalid LaTeX")
+    expr = convert_relation(relation)
+
+    return expr
+
+
+def convert_relation(rel):
+    if rel.expr():
+        return convert_expr(rel.expr())
+
+    lh = convert_relation(rel.relation(0))
+    rh = convert_relation(rel.relation(1))
+    if rel.LT():
+        return sympy.StrictLessThan(lh, rh)
+    elif rel.LTE():
+        return sympy.LessThan(lh, rh)
+    elif rel.GT():
+        return sympy.StrictGreaterThan(lh, rh)
+    elif rel.GTE():
+        return sympy.GreaterThan(lh, rh)
+    elif rel.EQUAL():
+        return sympy.Eq(lh, rh)
+    elif rel.NEQ():
+        return sympy.Ne(lh, rh)
+
+
+def convert_expr(expr):
+    return convert_add(expr.additive())
+
+
+def convert_add(add):
+    if add.ADD():
+        lh = convert_add(add.additive(0))
+        rh = convert_add(add.additive(1))
+        return sympy.Add(lh, rh, evaluate=False)
+    elif add.SUB():
+        lh = convert_add(add.additive(0))
+        rh = convert_add(add.additive(1))
+        if hasattr(rh, "is_Atom") and rh.is_Atom:
+            return sympy.Add(lh, -1 * rh, evaluate=False)
+        return sympy.Add(lh, sympy.Mul(-1, rh, evaluate=False), evaluate=False)
+    else:
+        return convert_mp(add.mp())
+
+
+def convert_mp(mp):
+    if hasattr(mp, 'mp'):
+        mp_left = mp.mp(0)
+        mp_right = mp.mp(1)
+    else:
+        mp_left = mp.mp_nofunc(0)
+        mp_right = mp.mp_nofunc(1)
+
+    if mp.MUL() or mp.CMD_TIMES() or mp.CMD_CDOT():
+        lh = convert_mp(mp_left)
+        rh = convert_mp(mp_right)
+        return sympy.Mul(lh, rh, evaluate=False)
+    elif mp.DIV() or mp.CMD_DIV() or mp.COLON():
+        lh = convert_mp(mp_left)
+        rh = convert_mp(mp_right)
+        return sympy.Mul(lh, sympy.Pow(rh, -1, evaluate=False), evaluate=False)
+    else:
+        if hasattr(mp, 'unary'):
+            return convert_unary(mp.unary())
+        else:
+            return convert_unary(mp.unary_nofunc())
+
+
+def convert_unary(unary):
+    if hasattr(unary, 'unary'):
+        nested_unary = unary.unary()
+    else:
+        nested_unary = unary.unary_nofunc()
+    if hasattr(unary, 'postfix_nofunc'):
+        first = unary.postfix()
+        tail = unary.postfix_nofunc()
+        postfix = [first] + tail
+    else:
+        postfix = unary.postfix()
+
+    if unary.ADD():
+        return convert_unary(nested_unary)
+    elif unary.SUB():
+        numabs = convert_unary(nested_unary)
+        # Use Integer(-n) instead of Mul(-1, n)
+        return -numabs
+    elif postfix:
+        return convert_postfix_list(postfix)
+
+
+def convert_postfix_list(arr, i=0):
+    if i >= len(arr):
+        raise LaTeXParsingError("Index out of bounds")
+
+    res = convert_postfix(arr[i])
+    if isinstance(res, sympy.Expr):
+        if i == len(arr) - 1:
+            return res  # nothing to multiply by
+        else:
+            if i > 0:
+                left = convert_postfix(arr[i - 1])
+                right = convert_postfix(arr[i + 1])
+                if isinstance(left, sympy.Expr) and isinstance(
+                        right, sympy.Expr):
+                    left_syms = convert_postfix(arr[i - 1]).atoms(sympy.Symbol)
+                    right_syms = convert_postfix(arr[i + 1]).atoms(
+                        sympy.Symbol)
+                    # if the left and right sides contain no variables and the
+                    # symbol in between is 'x', treat as multiplication.
+                    if not (left_syms or right_syms) and str(res) == 'x':
+                        return convert_postfix_list(arr, i + 1)
+            # multiply by next
+            return sympy.Mul(
+                res, convert_postfix_list(arr, i + 1), evaluate=False)
+    else:  # must be derivative
+        wrt = res[0]
+        if i == len(arr) - 1:
+            raise LaTeXParsingError("Expected expression for derivative")
+        else:
+            expr = convert_postfix_list(arr, i + 1)
+            return sympy.Derivative(expr, wrt)
+
+
+def do_subs(expr, at):
+    if at.expr():
+        at_expr = convert_expr(at.expr())
+        syms = at_expr.atoms(sympy.Symbol)
+        if len(syms) == 0:
+            return expr
+        elif len(syms) > 0:
+            sym = next(iter(syms))
+            return expr.subs(sym, at_expr)
+    elif at.equality():
+        lh = convert_expr(at.equality().expr(0))
+        rh = convert_expr(at.equality().expr(1))
+        return expr.subs(lh, rh)
+
+
+def convert_postfix(postfix):
+    if hasattr(postfix, 'exp'):
+        exp_nested = postfix.exp()
+    else:
+        exp_nested = postfix.exp_nofunc()
+
+    exp = convert_exp(exp_nested)
+    for op in postfix.postfix_op():
+        if op.BANG():
+            if isinstance(exp, list):
+                raise LaTeXParsingError("Cannot apply postfix to derivative")
+            exp = sympy.factorial(exp, evaluate=False)
+        elif op.eval_at():
+            ev = op.eval_at()
+            at_b = None
+            at_a = None
+            if ev.eval_at_sup():
+                at_b = do_subs(exp, ev.eval_at_sup())
+            if ev.eval_at_sub():
+                at_a = do_subs(exp, ev.eval_at_sub())
+            if at_b is not None and at_a is not None:
+                exp = sympy.Add(at_b, -1 * at_a, evaluate=False)
+            elif at_b is not None:
+                exp = at_b
+            elif at_a is not None:
+                exp = at_a
+
+    return exp
+
+
+def convert_exp(exp):
+    if hasattr(exp, 'exp'):
+        exp_nested = exp.exp()
+    else:
+        exp_nested = exp.exp_nofunc()
+
+    if exp_nested:
+        base = convert_exp(exp_nested)
+        if isinstance(base, list):
+            raise LaTeXParsingError("Cannot raise derivative to power")
+        if exp.atom():
+            exponent = convert_atom(exp.atom())
+        elif exp.expr():
+            exponent = convert_expr(exp.expr())
+        return sympy.Pow(base, exponent, evaluate=False)
+    else:
+        if hasattr(exp, 'comp'):
+            return convert_comp(exp.comp())
+        else:
+            return convert_comp(exp.comp_nofunc())
+
+
+def convert_comp(comp):
+    if comp.group():
+        return convert_expr(comp.group().expr())
+    elif comp.abs_group():
+        return sympy.Abs(convert_expr(comp.abs_group().expr()), evaluate=False)
+    elif comp.atom():
+        return convert_atom(comp.atom())
+    elif comp.floor():
+        return convert_floor(comp.floor())
+    elif comp.ceil():
+        return convert_ceil(comp.ceil())
+    elif comp.func():
+        return convert_func(comp.func())
+
+
+def convert_atom(atom):
+    if atom.LETTER():
+        sname = atom.LETTER().getText()
+        if atom.subexpr():
+            if atom.subexpr().expr():  # subscript is expr
+                subscript = convert_expr(atom.subexpr().expr())
+            else:  # subscript is atom
+                subscript = convert_atom(atom.subexpr().atom())
+            sname += '_{' + StrPrinter().doprint(subscript) + '}'
+        if atom.SINGLE_QUOTES():
+            sname += atom.SINGLE_QUOTES().getText()  # put after subscript for easy identify
+        return sympy.Symbol(sname)
+    elif atom.SYMBOL():
+        s = atom.SYMBOL().getText()[1:]
+        if s == "infty":
+            return sympy.oo
+        else:
+            if atom.subexpr():
+                subscript = None
+                if atom.subexpr().expr():  # subscript is expr
+                    subscript = convert_expr(atom.subexpr().expr())
+                else:  # subscript is atom
+                    subscript = convert_atom(atom.subexpr().atom())
+                subscriptName = StrPrinter().doprint(subscript)
+                s += '_{' + subscriptName + '}'
+            return sympy.Symbol(s)
+    elif atom.number():
+        s = atom.number().getText().replace(",", "")
+        return sympy.Number(s)
+    elif atom.DIFFERENTIAL():
+        var = get_differential_var(atom.DIFFERENTIAL())
+        return sympy.Symbol('d' + var.name)
+    elif atom.mathit():
+        text = rule2text(atom.mathit().mathit_text())
+        return sympy.Symbol(text)
+    elif atom.frac():
+        return convert_frac(atom.frac())
+    elif atom.binom():
+        return convert_binom(atom.binom())
+    elif atom.bra():
+        val = convert_expr(atom.bra().expr())
+        return Bra(val)
+    elif atom.ket():
+        val = convert_expr(atom.ket().expr())
+        return Ket(val)
+
+
+def rule2text(ctx):
+    stream = ctx.start.getInputStream()
+    # starting index of starting token
+    startIdx = ctx.start.start
+    # stopping index of stopping token
+    stopIdx = ctx.stop.stop
+
+    return stream.getText(startIdx, stopIdx)
+
+
+def convert_frac(frac):
+    diff_op = False
+    partial_op = False
+    if frac.lower and frac.upper:
+        lower_itv = frac.lower.getSourceInterval()
+        lower_itv_len = lower_itv[1] - lower_itv[0] + 1
+        if (frac.lower.start == frac.lower.stop
+                and frac.lower.start.type == LaTeXLexer.DIFFERENTIAL):
+            wrt = get_differential_var_str(frac.lower.start.text)
+            diff_op = True
+        elif (lower_itv_len == 2 and frac.lower.start.type == LaTeXLexer.SYMBOL
+              and frac.lower.start.text == '\\partial'
+              and (frac.lower.stop.type == LaTeXLexer.LETTER
+                   or frac.lower.stop.type == LaTeXLexer.SYMBOL)):
+            partial_op = True
+            wrt = frac.lower.stop.text
+            if frac.lower.stop.type == LaTeXLexer.SYMBOL:
+                wrt = wrt[1:]
+
+        if diff_op or partial_op:
+            wrt = sympy.Symbol(wrt)
+            if (diff_op and frac.upper.start == frac.upper.stop
+                    and frac.upper.start.type == LaTeXLexer.LETTER
+                    and frac.upper.start.text == 'd'):
+                return [wrt]
+            elif (partial_op and frac.upper.start == frac.upper.stop
+                  and frac.upper.start.type == LaTeXLexer.SYMBOL
+                  and frac.upper.start.text == '\\partial'):
+                return [wrt]
+            upper_text = rule2text(frac.upper)
+
+            expr_top = None
+            if diff_op and upper_text.startswith('d'):
+                expr_top = parse_latex(upper_text[1:])
+            elif partial_op and frac.upper.start.text == '\\partial':
+                expr_top = parse_latex(upper_text[len('\\partial'):])
+            if expr_top:
+                return sympy.Derivative(expr_top, wrt)
+    if frac.upper:
+        expr_top = convert_expr(frac.upper)
+    else:
+        expr_top = sympy.Number(frac.upperd.text)
+    if frac.lower:
+        expr_bot = convert_expr(frac.lower)
+    else:
+        expr_bot = sympy.Number(frac.lowerd.text)
+    inverse_denom = sympy.Pow(expr_bot, -1, evaluate=False)
+    if expr_top == 1:
+        return inverse_denom
+    else:
+        return sympy.Mul(expr_top, inverse_denom, evaluate=False)
+
+def convert_binom(binom):
+    expr_n = convert_expr(binom.n)
+    expr_k = convert_expr(binom.k)
+    return sympy.binomial(expr_n, expr_k, evaluate=False)
+
+def convert_floor(floor):
+    val = convert_expr(floor.val)
+    return sympy.floor(val, evaluate=False)
+
+def convert_ceil(ceil):
+    val = convert_expr(ceil.val)
+    return sympy.ceiling(val, evaluate=False)
+
+def convert_func(func):
+    if func.func_normal():
+        if func.L_PAREN():  # function called with parenthesis
+            arg = convert_func_arg(func.func_arg())
+        else:
+            arg = convert_func_arg(func.func_arg_noparens())
+
+        name = func.func_normal().start.text[1:]
+
+        # change arc -> a
+        if name in [
+                "arcsin", "arccos", "arctan", "arccsc", "arcsec", "arccot"
+        ]:
+            name = "a" + name[3:]
+            expr = getattr(sympy.functions, name)(arg, evaluate=False)
+        if name in ["arsinh", "arcosh", "artanh"]:
+            name = "a" + name[2:]
+            expr = getattr(sympy.functions, name)(arg, evaluate=False)
+
+        if name == "exp":
+            expr = sympy.exp(arg, evaluate=False)
+
+        if name in ("log", "lg", "ln"):
+            if func.subexpr():
+                if func.subexpr().expr():
+                    base = convert_expr(func.subexpr().expr())
+                else:
+                    base = convert_atom(func.subexpr().atom())
+            elif name == "lg":  # ISO 80000-2:2019
+                base = 10
+            elif name in ("ln", "log"):  # SymPy's latex printer prints ln as log by default
+                base = sympy.E
+            expr = sympy.log(arg, base, evaluate=False)
+
+        func_pow = None
+        should_pow = True
+        if func.supexpr():
+            if func.supexpr().expr():
+                func_pow = convert_expr(func.supexpr().expr())
+            else:
+                func_pow = convert_atom(func.supexpr().atom())
+
+        if name in [
+                "sin", "cos", "tan", "csc", "sec", "cot", "sinh", "cosh",
+                "tanh"
+        ]:
+            if func_pow == -1:
+                name = "a" + name
+                should_pow = False
+            expr = getattr(sympy.functions, name)(arg, evaluate=False)
+
+        if func_pow and should_pow:
+            expr = sympy.Pow(expr, func_pow, evaluate=False)
+
+        return expr
+    elif func.LETTER() or func.SYMBOL():
+        if func.LETTER():
+            fname = func.LETTER().getText()
+        elif func.SYMBOL():
+            fname = func.SYMBOL().getText()[1:]
+        fname = str(fname)  # can't be unicode
+        if func.subexpr():
+            if func.subexpr().expr():  # subscript is expr
+                subscript = convert_expr(func.subexpr().expr())
+            else:  # subscript is atom
+                subscript = convert_atom(func.subexpr().atom())
+            subscriptName = StrPrinter().doprint(subscript)
+            fname += '_{' + subscriptName + '}'
+        if func.SINGLE_QUOTES():
+            fname += func.SINGLE_QUOTES().getText()
+        input_args = func.args()
+        output_args = []
+        while input_args.args():  # handle multiple arguments to function
+            output_args.append(convert_expr(input_args.expr()))
+            input_args = input_args.args()
+        output_args.append(convert_expr(input_args.expr()))
+        return sympy.Function(fname)(*output_args)
+    elif func.FUNC_INT():
+        return handle_integral(func)
+    elif func.FUNC_SQRT():
+        expr = convert_expr(func.base)
+        if func.root:
+            r = convert_expr(func.root)
+            return sympy.root(expr, r, evaluate=False)
+        else:
+            return sympy.sqrt(expr, evaluate=False)
+    elif func.FUNC_OVERLINE():
+        expr = convert_expr(func.base)
+        return sympy.conjugate(expr, evaluate=False)
+    elif func.FUNC_SUM():
+        return handle_sum_or_prod(func, "summation")
+    elif func.FUNC_PROD():
+        return handle_sum_or_prod(func, "product")
+    elif func.FUNC_LIM():
+        return handle_limit(func)
+
+
+def convert_func_arg(arg):
+    if hasattr(arg, 'expr'):
+        return convert_expr(arg.expr())
+    else:
+        return convert_mp(arg.mp_nofunc())
+
+
+def handle_integral(func):
+    if func.additive():
+        integrand = convert_add(func.additive())
+    elif func.frac():
+        integrand = convert_frac(func.frac())
+    else:
+        integrand = 1
+
+    int_var = None
+    if func.DIFFERENTIAL():
+        int_var = get_differential_var(func.DIFFERENTIAL())
+    else:
+        for sym in integrand.atoms(sympy.Symbol):
+            s = str(sym)
+            if len(s) > 1 and s[0] == 'd':
+                if s[1] == '\\':
+                    int_var = sympy.Symbol(s[2:])
+                else:
+                    int_var = sympy.Symbol(s[1:])
+                int_sym = sym
+        if int_var:
+            integrand = integrand.subs(int_sym, 1)
+        else:
+            # Assume dx by default
+            int_var = sympy.Symbol('x')
+
+    if func.subexpr():
+        if func.subexpr().atom():
+            lower = convert_atom(func.subexpr().atom())
+        else:
+            lower = convert_expr(func.subexpr().expr())
+        if func.supexpr().atom():
+            upper = convert_atom(func.supexpr().atom())
+        else:
+            upper = convert_expr(func.supexpr().expr())
+        return sympy.Integral(integrand, (int_var, lower, upper))
+    else:
+        return sympy.Integral(integrand, int_var)
+
+
+def handle_sum_or_prod(func, name):
+    val = convert_mp(func.mp())
+    iter_var = convert_expr(func.subeq().equality().expr(0))
+    start = convert_expr(func.subeq().equality().expr(1))
+    if func.supexpr().expr():  # ^{expr}
+        end = convert_expr(func.supexpr().expr())
+    else:  # ^atom
+        end = convert_atom(func.supexpr().atom())
+
+    if name == "summation":
+        return sympy.Sum(val, (iter_var, start, end))
+    elif name == "product":
+        return sympy.Product(val, (iter_var, start, end))
+
+
+def handle_limit(func):
+    sub = func.limit_sub()
+    if sub.LETTER():
+        var = sympy.Symbol(sub.LETTER().getText())
+    elif sub.SYMBOL():
+        var = sympy.Symbol(sub.SYMBOL().getText()[1:])
+    else:
+        var = sympy.Symbol('x')
+    if sub.SUB():
+        direction = "-"
+    elif sub.ADD():
+        direction = "+"
+    else:
+        direction = "+-"
+    approaching = convert_expr(sub.expr())
+    content = convert_mp(func.mp())
+
+    return sympy.Limit(content, var, approaching, direction)
+
+
+def get_differential_var(d):
+    text = get_differential_var_str(d.getText())
+    return sympy.Symbol(text)
+
+
+def get_differential_var_str(text):
+    for i in range(1, len(text)):
+        c = text[i]
+        if not (c == " " or c == "\r" or c == "\n" or c == "\t"):
+            idx = i
+            break
+    text = text[idx:]
+    if text[0] == "\\":
+        text = text[1:]
+    return text
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/errors.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/errors.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8c3ef9f06279df42d4b2054acc4cfe39b6682a5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/errors.py
@@ -0,0 +1,2 @@
+class LaTeXParsingError(Exception):
+    pass
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..92e58d3172e100cc376d0b416b3835d164bd5647
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/__init__.py
@@ -0,0 +1,2 @@
+from .latex_parser import parse_latex_lark, LarkLaTeXParser # noqa
+from .transformer import TransformToSymPyExpr # noqa
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/grammar/greek_symbols.lark b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/grammar/greek_symbols.lark
new file mode 100644
index 0000000000000000000000000000000000000000..7439fab9dcac284dc3c9b5fbfa4fc6db8b29dfd2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/grammar/greek_symbols.lark
@@ -0,0 +1,28 @@
+// Greek symbols
+// TODO: Shouold we include the uppercase variants for the symbols where the uppercase variant doesn't have a separate meaning?
+ALPHA: "\\alpha"
+BETA: "\\beta"
+GAMMA: "\\gamma"
+DELTA: "\\delta" // TODO: Should this be included? Delta usually denotes other things.
+EPSILON: "\\epsilon" |  "\\varepsilon"
+ZETA: "\\zeta"
+ETA: "\\eta"
+THETA: "\\theta" | "\\vartheta"
+// TODO: Should I add iota to the list?
+KAPPA: "\\kappa"
+LAMBDA: "\\lambda" // TODO: What about the uppercase variant?
+MU: "\\mu"
+NU: "\\nu"
+XI: "\\xi"
+// TODO: Should there be a separate note for transforming \pi into sympy.pi?
+RHO: "\\rho" | "\\varrho"
+// TODO: What should we do about sigma?
+TAU: "\\tau"
+UPSILON: "\\upsilon"
+PHI: "\\phi" | "\\varphi"
+CHI: "\\chi"
+PSI: "\\psi"
+OMEGA: "\\omega"
+
+GREEK_SYMBOL: ALPHA | BETA | GAMMA | DELTA | EPSILON | ZETA | ETA | THETA | KAPPA
+    | LAMBDA | MU | NU | XI | RHO | TAU | UPSILON | PHI | CHI | PSI | OMEGA
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/grammar/latex.lark b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/grammar/latex.lark
new file mode 100644
index 0000000000000000000000000000000000000000..43e8d0e9105fa4da9bcdd2c0fa6111f6d523c9a9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/grammar/latex.lark
@@ -0,0 +1,403 @@
+%ignore /[ \t\n\r]+/
+
+%ignore "\\," | "\\thinspace" | "\\:" | "\\medspace" | "\\;" | "\\thickspace"
+%ignore "\\quad" | "\\qquad"
+%ignore "\\!" | "\\negthinspace" | "\\negmedspace" | "\\negthickspace"
+%ignore "\\vrule" | "\\vcenter" | "\\vbox" | "\\vskip" | "\\vspace" | "\\hfill"
+%ignore "\\*" | "\\-" | "\\." | "\\/" | "\\(" | "\\="
+
+%ignore "\\left" | "\\right"
+%ignore "\\limits" | "\\nolimits"
+%ignore "\\displaystyle"
+
+///////////////////// tokens ///////////////////////
+
+// basic binary operators
+ADD: "+"
+SUB: "-"
+MUL: "*"
+DIV: "/"
+
+// tokens with distinct left and right symbols
+L_BRACE: "{"
+R_BRACE: "}"
+L_BRACE_LITERAL: "\\{"
+R_BRACE_LITERAL: "\\}"
+L_BRACKET: "["
+R_BRACKET: "]"
+L_CEIL: "\\lceil"
+R_CEIL: "\\rceil"
+L_FLOOR: "\\lfloor"
+R_FLOOR: "\\rfloor"
+L_PAREN: "("
+R_PAREN: ")"
+
+// limit, integral, sum, and product symbols
+FUNC_LIM:  "\\lim"
+LIM_APPROACH_SYM: "\\to" | "\\rightarrow" | "\\Rightarrow" | "\\longrightarrow" | "\\Longrightarrow"
+FUNC_INT:  "\\int" | "\\intop"
+FUNC_SUM:  "\\sum"
+FUNC_PROD: "\\prod"
+
+// common functions
+FUNC_EXP:  "\\exp"
+FUNC_LOG:  "\\log"
+FUNC_LN:   "\\ln"
+FUNC_LG:   "\\lg"
+FUNC_MIN: "\\min"
+FUNC_MAX: "\\max"
+
+// trigonometric functions
+FUNC_SIN:  "\\sin"
+FUNC_COS:  "\\cos"
+FUNC_TAN:  "\\tan"
+FUNC_CSC:  "\\csc"
+FUNC_SEC:  "\\sec"
+FUNC_COT:  "\\cot"
+
+// inverse trigonometric functions
+FUNC_ARCSIN: "\\arcsin"
+FUNC_ARCCOS: "\\arccos"
+FUNC_ARCTAN: "\\arctan"
+FUNC_ARCCSC: "\\arccsc"
+FUNC_ARCSEC: "\\arcsec"
+FUNC_ARCCOT: "\\arccot"
+
+// hyperbolic trigonometric functions
+FUNC_SINH: "\\sinh"
+FUNC_COSH: "\\cosh"
+FUNC_TANH: "\\tanh"
+FUNC_ARSINH: "\\arsinh"
+FUNC_ARCOSH: "\\arcosh"
+FUNC_ARTANH: "\\artanh"
+
+FUNC_SQRT: "\\sqrt"
+
+// miscellaneous symbols
+CMD_TIMES: "\\times"
+CMD_CDOT:  "\\cdot"
+CMD_DIV:   "\\div"
+CMD_FRAC:  "\\frac" | "\\dfrac" | "\\tfrac" | "\\nicefrac"
+CMD_BINOM: "\\binom" | "\\dbinom" | "\\tbinom"
+CMD_OVERLINE: "\\overline"
+CMD_LANGLE: "\\langle"
+CMD_RANGLE: "\\rangle"
+
+CMD_MATHIT: "\\mathit"
+
+CMD_INFTY: "\\infty"
+
+BANG: "!"
+BAR: "|"
+CARET: "^"
+COLON: ":"
+UNDERSCORE: "_"
+
+// relational symbols
+EQUAL: "="
+NOT_EQUAL: "\\neq" | "\\ne"
+LT: "<"
+LTE: "\\leq" | "\\le" | "\\leqslant"
+GT: ">"
+GTE: "\\geq" | "\\ge" | "\\geqslant"
+
+DIV_SYMBOL: CMD_DIV | DIV
+MUL_SYMBOL: MUL | CMD_TIMES | CMD_CDOT
+
+%import .greek_symbols.GREEK_SYMBOL
+
+UPRIGHT_DIFFERENTIAL_SYMBOL: "\\text{d}" | "\\mathrm{d}"
+DIFFERENTIAL_SYMBOL: "d" | UPRIGHT_DIFFERENTIAL_SYMBOL
+
+// disallow "d" as a variable name because we want to parse "d" as a differential symbol.
+SYMBOL: /[a-zA-Z]'*/
+GREEK_SYMBOL_WITH_PRIMES: GREEK_SYMBOL "'"*
+LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT: /([a-zA-Z]'*)_(([A-Za-z0-9]|[a-zA-Z]+)|\{([A-Za-z0-9]|[a-zA-Z]+'*)\})/
+LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT: /([a-zA-Z]'*)_/ GREEK_SYMBOL | /([a-zA-Z]'*)_/ L_BRACE GREEK_SYMBOL_WITH_PRIMES R_BRACE
+// best to define the variant with braces like that instead of shoving it all into one case like in
+// /([a-zA-Z])_/ L_BRACE? GREEK_SYMBOL R_BRACE? because then we can easily error out on input like
+// r"h_{\theta"
+GREEK_SYMBOL_WITH_LATIN_SUBSCRIPT: GREEK_SYMBOL_WITH_PRIMES /_(([A-Za-z0-9]|[a-zA-Z]+)|\{([A-Za-z0-9]|[a-zA-Z]+'*)\})/
+GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT: GREEK_SYMBOL_WITH_PRIMES /_/ (GREEK_SYMBOL | L_BRACE GREEK_SYMBOL_WITH_PRIMES R_BRACE)
+MULTI_LETTER_SYMBOL: /[a-zA-Z]+(\s+[a-zA-Z]+)*'*/
+
+%import common.DIGIT -> DIGIT
+
+CMD_PRIME: "\\prime"
+CMD_ASTERISK: "\\ast"
+
+PRIMES: "'"+
+STARS: "*"+
+PRIMES_VIA_CMD: CMD_PRIME+
+STARS_VIA_CMD: CMD_ASTERISK+
+
+CMD_IMAGINARY_UNIT: "\\imaginaryunit"
+
+CMD_BEGIN: "\\begin"
+CMD_END: "\\end"
+
+// matrices
+IGNORE_L: /[ \t\n\r]*/ L_BRACE* /[ \t\n\r]*/
+IGNORE_R: /[ \t\n\r]*/ R_BRACE* /[ \t\n\r]*/
+ARRAY_MATRIX_BEGIN: L_BRACE "array" R_BRACE L_BRACE /[^}]*/ R_BRACE
+ARRAY_MATRIX_END: L_BRACE "array" R_BRACE
+AMSMATH_MATRIX: L_BRACE "matrix" R_BRACE
+AMSMATH_PMATRIX: L_BRACE "pmatrix" R_BRACE
+AMSMATH_BMATRIX: L_BRACE "bmatrix" R_BRACE
+// Without the (L|R)_PARENs and (L|R)_BRACKETs, a matrix defined using
+// \begin{array}...\end{array} or \begin{matrix}...\end{matrix} must
+// not qualify as a complete matrix expression; this is done so that
+// if we have \begin{array}...\end{array} or \begin{matrix}...\end{matrix}
+// between BAR pairs, then they should be interpreted as determinants as
+// opposed to sympy.Abs (absolute value) applied to a matrix.
+CMD_BEGIN_AMSPMATRIX_AMSBMATRIX: CMD_BEGIN (AMSMATH_PMATRIX | AMSMATH_BMATRIX)
+CMD_BEGIN_ARRAY_AMSMATRIX: (L_PAREN | L_BRACKET) IGNORE_L CMD_BEGIN (ARRAY_MATRIX_BEGIN | AMSMATH_MATRIX)
+CMD_MATRIX_BEGIN: CMD_BEGIN_AMSPMATRIX_AMSBMATRIX | CMD_BEGIN_ARRAY_AMSMATRIX
+CMD_END_AMSPMATRIX_AMSBMATRIX: CMD_END (AMSMATH_PMATRIX | AMSMATH_BMATRIX)
+CMD_END_ARRAY_AMSMATRIX: CMD_END (ARRAY_MATRIX_END | AMSMATH_MATRIX) IGNORE_R "\\right"? (R_PAREN | R_BRACKET)
+CMD_MATRIX_END: CMD_END_AMSPMATRIX_AMSBMATRIX | CMD_END_ARRAY_AMSMATRIX
+MATRIX_COL_DELIM: "&"
+MATRIX_ROW_DELIM: "\\\\"
+FUNC_MATRIX_TRACE: "\\trace"
+FUNC_MATRIX_ADJUGATE: "\\adjugate"
+
+// determinants
+AMSMATH_VMATRIX: L_BRACE "vmatrix" R_BRACE
+CMD_DETERMINANT_BEGIN_SIMPLE: CMD_BEGIN AMSMATH_VMATRIX
+CMD_DETERMINANT_BEGIN_VARIANT: BAR IGNORE_L CMD_BEGIN (ARRAY_MATRIX_BEGIN | AMSMATH_MATRIX)
+CMD_DETERMINANT_BEGIN: CMD_DETERMINANT_BEGIN_SIMPLE | CMD_DETERMINANT_BEGIN_VARIANT
+CMD_DETERMINANT_END_SIMPLE: CMD_END AMSMATH_VMATRIX
+CMD_DETERMINANT_END_VARIANT: CMD_END (ARRAY_MATRIX_END | AMSMATH_MATRIX) IGNORE_R "\\right"? BAR
+CMD_DETERMINANT_END: CMD_DETERMINANT_END_SIMPLE | CMD_DETERMINANT_END_VARIANT
+FUNC_DETERMINANT: "\\det"
+
+//////////////////// grammar //////////////////////
+
+latex_string: _relation | _expression
+
+_one_letter_symbol: SYMBOL
+    | LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT
+    | LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT
+    | GREEK_SYMBOL_WITH_LATIN_SUBSCRIPT
+    | GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT
+    | GREEK_SYMBOL_WITH_PRIMES
+// LuaTeX-generated outputs of \mathit{foo'} and \mathit{foo}'
+// seem to be the same on the surface. We allow both styles.
+multi_letter_symbol: CMD_MATHIT L_BRACE MULTI_LETTER_SYMBOL R_BRACE
+    | CMD_MATHIT L_BRACE MULTI_LETTER_SYMBOL R_BRACE /'+/
+number: /\d+(\.\d*)?/ | CMD_IMAGINARY_UNIT
+
+_atomic_expr: _one_letter_symbol
+    | multi_letter_symbol
+    | number
+    | CMD_INFTY
+
+group_round_parentheses: L_PAREN _expression R_PAREN
+group_square_brackets: L_BRACKET _expression R_BRACKET
+group_curly_parentheses: L_BRACE _expression R_BRACE
+
+_relation: eq | ne | lt | lte | gt | gte
+
+eq: _expression EQUAL _expression
+ne: _expression NOT_EQUAL _expression
+lt: _expression LT _expression
+lte: _expression LTE _expression
+gt: _expression GT _expression
+gte: _expression GTE _expression
+
+_expression_core: _atomic_expr | group_curly_parentheses
+
+add: _expression ADD _expression_mul
+    | ADD _expression_mul
+sub: _expression SUB _expression_mul
+    | SUB _expression_mul
+mul: _expression_mul MUL_SYMBOL _expression_power
+div: _expression_mul DIV_SYMBOL _expression_power
+
+adjacent_expressions: (_one_letter_symbol | number) _expression_mul
+    | group_round_parentheses (group_round_parentheses | _one_letter_symbol)
+    | _function _function
+    | fraction _expression_mul
+
+_expression_func: _expression_core
+    | group_round_parentheses
+    | fraction
+    | binomial
+    | _function
+    | _integral// | derivative
+    | limit
+    | matrix
+
+_expression_power: _expression_func | superscript | matrix_prime | symbol_prime
+
+_expression_mul: _expression_power
+    | mul | div | adjacent_expressions
+    | summation | product
+
+_expression: _expression_mul | add | sub
+
+_limit_dir: "+" | "-" | L_BRACE ("+" | "-") R_BRACE
+
+limit_dir_expr: _expression CARET _limit_dir
+
+group_curly_parentheses_lim: L_BRACE _expression LIM_APPROACH_SYM (limit_dir_expr | _expression) R_BRACE
+
+limit: FUNC_LIM UNDERSCORE group_curly_parentheses_lim _expression
+
+differential: DIFFERENTIAL_SYMBOL _one_letter_symbol
+
+//_derivative_operator: CMD_FRAC L_BRACE DIFFERENTIAL_SYMBOL R_BRACE L_BRACE differential R_BRACE
+
+//derivative: _derivative_operator _expression
+
+_integral: normal_integral | integral_with_special_fraction
+
+normal_integral: FUNC_INT _expression DIFFERENTIAL_SYMBOL _one_letter_symbol
+    | FUNC_INT (CARET _expression_core UNDERSCORE _expression_core)? _expression? DIFFERENTIAL_SYMBOL _one_letter_symbol
+    | FUNC_INT (UNDERSCORE _expression_core CARET _expression_core)? _expression? DIFFERENTIAL_SYMBOL _one_letter_symbol
+
+group_curly_parentheses_int: L_BRACE _expression? differential R_BRACE
+
+special_fraction: CMD_FRAC group_curly_parentheses_int group_curly_parentheses
+
+integral_with_special_fraction: FUNC_INT special_fraction
+    | FUNC_INT (CARET _expression_core UNDERSCORE _expression_core)? special_fraction
+    | FUNC_INT (UNDERSCORE _expression_core CARET _expression_core)? special_fraction
+
+group_curly_parentheses_special: UNDERSCORE L_BRACE _atomic_expr EQUAL _atomic_expr R_BRACE CARET _expression_core
+    | CARET _expression_core UNDERSCORE L_BRACE _atomic_expr EQUAL _atomic_expr R_BRACE
+
+summation: FUNC_SUM group_curly_parentheses_special _expression
+    | FUNC_SUM group_curly_parentheses_special _expression
+
+product: FUNC_PROD group_curly_parentheses_special _expression
+    | FUNC_PROD group_curly_parentheses_special _expression
+
+superscript: _expression_func CARET (_expression_power | CMD_PRIME | CMD_ASTERISK)
+    | _expression_func CARET L_BRACE (PRIMES | STARS | PRIMES_VIA_CMD | STARS_VIA_CMD) R_BRACE
+
+matrix_prime: (matrix | group_round_parentheses) PRIMES
+
+symbol_prime: (LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT
+    | LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT
+    | GREEK_SYMBOL_WITH_LATIN_SUBSCRIPT
+    | GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT) PRIMES
+
+fraction: _basic_fraction
+    | _simple_fraction
+    | _general_fraction
+
+_basic_fraction: CMD_FRAC DIGIT (DIGIT | SYMBOL | GREEK_SYMBOL_WITH_PRIMES)
+
+_simple_fraction: CMD_FRAC DIGIT group_curly_parentheses
+    | CMD_FRAC group_curly_parentheses (DIGIT | SYMBOL | GREEK_SYMBOL_WITH_PRIMES)
+
+_general_fraction: CMD_FRAC group_curly_parentheses group_curly_parentheses
+
+binomial: _basic_binomial
+    | _simple_binomial
+    | _general_binomial
+
+_basic_binomial: CMD_BINOM DIGIT (DIGIT | SYMBOL | GREEK_SYMBOL_WITH_PRIMES)
+
+_simple_binomial: CMD_BINOM DIGIT group_curly_parentheses
+    | CMD_BINOM group_curly_parentheses (DIGIT | SYMBOL | GREEK_SYMBOL_WITH_PRIMES)
+
+_general_binomial: CMD_BINOM group_curly_parentheses group_curly_parentheses
+
+list_of_expressions: _expression ("," _expression)*
+
+function_applied: _one_letter_symbol L_PAREN list_of_expressions R_PAREN
+
+min: FUNC_MIN L_PAREN list_of_expressions R_PAREN
+
+max: FUNC_MAX L_PAREN list_of_expressions R_PAREN
+
+bra: CMD_LANGLE _expression BAR
+
+ket: BAR _expression CMD_RANGLE
+
+inner_product: CMD_LANGLE _expression BAR _expression CMD_RANGLE
+
+_function: function_applied
+    | abs | floor | ceil
+    | _trigonometric_function | _inverse_trigonometric_function
+    | _trigonometric_function_power
+    | _hyperbolic_trigonometric_function | _inverse_hyperbolic_trigonometric_function
+    | exponential
+    | log
+    | square_root
+    | factorial
+    | conjugate
+    | max | min
+    | bra | ket | inner_product
+    | determinant
+    | trace
+    | adjugate
+
+exponential: FUNC_EXP _expression
+
+log: FUNC_LOG _expression
+    | FUNC_LN _expression
+    | FUNC_LG _expression
+    | FUNC_LOG UNDERSCORE (DIGIT | _one_letter_symbol) _expression
+    | FUNC_LOG UNDERSCORE group_curly_parentheses _expression
+
+square_root: FUNC_SQRT group_curly_parentheses
+    | FUNC_SQRT group_square_brackets group_curly_parentheses
+
+factorial: _expression_func BANG
+
+conjugate: CMD_OVERLINE group_curly_parentheses
+    | CMD_OVERLINE DIGIT
+
+_trigonometric_function: sin | cos | tan | csc | sec | cot
+
+sin: FUNC_SIN _expression
+cos: FUNC_COS _expression
+tan: FUNC_TAN _expression
+csc: FUNC_CSC _expression
+sec: FUNC_SEC _expression
+cot: FUNC_COT _expression
+
+_trigonometric_function_power: sin_power | cos_power | tan_power | csc_power | sec_power | cot_power
+
+sin_power: FUNC_SIN CARET _expression_core _expression
+cos_power: FUNC_COS CARET _expression_core _expression
+tan_power: FUNC_TAN CARET _expression_core _expression
+csc_power: FUNC_CSC CARET _expression_core _expression
+sec_power: FUNC_SEC CARET _expression_core _expression
+cot_power: FUNC_COT CARET _expression_core _expression
+
+_hyperbolic_trigonometric_function: sinh | cosh | tanh
+
+sinh: FUNC_SINH _expression
+cosh: FUNC_COSH _expression
+tanh: FUNC_TANH _expression
+
+_inverse_trigonometric_function: arcsin | arccos | arctan | arccsc | arcsec | arccot
+
+arcsin: FUNC_ARCSIN _expression
+arccos: FUNC_ARCCOS _expression
+arctan: FUNC_ARCTAN _expression
+arccsc: FUNC_ARCCSC _expression
+arcsec: FUNC_ARCSEC _expression
+arccot: FUNC_ARCCOT _expression
+
+_inverse_hyperbolic_trigonometric_function: asinh | acosh | atanh
+
+asinh: FUNC_ARSINH _expression
+acosh: FUNC_ARCOSH _expression
+atanh: FUNC_ARTANH _expression
+
+abs: BAR _expression BAR
+floor: L_FLOOR _expression R_FLOOR
+ceil: L_CEIL _expression R_CEIL
+
+matrix: CMD_MATRIX_BEGIN matrix_body CMD_MATRIX_END
+matrix_body: matrix_row (MATRIX_ROW_DELIM matrix_row)* (MATRIX_ROW_DELIM)?
+matrix_row: _expression (MATRIX_COL_DELIM _expression)*
+determinant: (CMD_DETERMINANT_BEGIN matrix_body CMD_DETERMINANT_END)
+    | FUNC_DETERMINANT _expression
+trace: FUNC_MATRIX_TRACE _expression
+adjugate: FUNC_MATRIX_ADJUGATE _expression
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/latex_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/latex_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..29f594b0de4bfd4648df1554d5863a37afff035f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/latex_parser.py
@@ -0,0 +1,145 @@
+import os
+import logging
+import re
+from pathlib import Path
+
+from sympy.external import import_module
+from sympy.parsing.latex.lark.transformer import TransformToSymPyExpr
+
+_lark = import_module("lark")
+
+
+class LarkLaTeXParser:
+    r"""Class for converting input `\mathrm{\LaTeX}` strings into SymPy Expressions.
+    It holds all the necessary internal data for doing so, and exposes hooks for
+    customizing its behavior.
+
+    Parameters
+    ==========
+
+    print_debug_output : bool, optional
+
+        If set to ``True``, prints debug output to the logger. Defaults to ``False``.
+
+    transform : bool, optional
+
+        If set to ``True``, the class runs the Transformer class on the parse tree
+        generated by running ``Lark.parse`` on the input string. Defaults to ``True``.
+
+        Setting it to ``False`` can help with debugging the `\mathrm{\LaTeX}` grammar.
+
+    grammar_file : str, optional
+
+        The path to the grammar file that the parser should use. If set to ``None``,
+        it uses the default grammar, which is in ``grammar/latex.lark``, relative to
+        the ``sympy/parsing/latex/lark/`` directory.
+
+    transformer : str, optional
+
+        The name of the Transformer class to use. If set to ``None``, it uses the
+        default transformer class, which is :py:func:`TransformToSymPyExpr`.
+
+    """
+    def __init__(self, print_debug_output=False, transform=True, grammar_file=None, transformer=None):
+        grammar_dir_path = os.path.join(os.path.dirname(__file__), "grammar/")
+
+        if grammar_file is None:
+            latex_grammar = Path(os.path.join(grammar_dir_path, "latex.lark")).read_text(encoding="utf-8")
+        else:
+            latex_grammar = Path(grammar_file).read_text(encoding="utf-8")
+
+        self.parser = _lark.Lark(
+            latex_grammar,
+            source_path=grammar_dir_path,
+            parser="earley",
+            start="latex_string",
+            lexer="auto",
+            ambiguity="explicit",
+            propagate_positions=False,
+            maybe_placeholders=False,
+            keep_all_tokens=True)
+
+        self.print_debug_output = print_debug_output
+        self.transform_expr = transform
+
+        if transformer is None:
+            self.transformer = TransformToSymPyExpr()
+        else:
+            self.transformer = transformer()
+
+    def doparse(self, s: str):
+        if self.print_debug_output:
+            _lark.logger.setLevel(logging.DEBUG)
+
+        parse_tree = self.parser.parse(s)
+
+        if not self.transform_expr:
+            # exit early and return the parse tree
+            _lark.logger.debug("expression = %s", s)
+            _lark.logger.debug(parse_tree)
+            _lark.logger.debug(parse_tree.pretty())
+            return parse_tree
+
+        if self.print_debug_output:
+            # print this stuff before attempting to run the transformer
+            _lark.logger.debug("expression = %s", s)
+            # print the `parse_tree` variable
+            _lark.logger.debug(parse_tree.pretty())
+
+        sympy_expression = self.transformer.transform(parse_tree)
+
+        if self.print_debug_output:
+            _lark.logger.debug("SymPy expression = %s", sympy_expression)
+
+        return sympy_expression
+
+
+if _lark is not None:
+    _lark_latex_parser = LarkLaTeXParser()
+
+
+def parse_latex_lark(s: str):
+    """
+    Experimental LaTeX parser using Lark.
+
+    This function is still under development and its API may change with the
+    next releases of SymPy.
+    """
+    if _lark is None:
+        raise ImportError("Lark is probably not installed")
+    return _lark_latex_parser.doparse(s)
+
+
+def _pretty_print_lark_trees(tree, indent=0, show_expr=True):
+    if isinstance(tree, _lark.Token):
+        return tree.value
+
+    data = str(tree.data)
+
+    is_expr = data.startswith("expression")
+
+    if is_expr:
+        data = re.sub(r"^expression", "E", data)
+
+    is_ambig = (data == "_ambig")
+
+    if is_ambig:
+        new_indent = indent + 2
+    else:
+        new_indent = indent
+
+    output = ""
+    show_node = not is_expr or show_expr
+
+    if show_node:
+        output += str(data) + "("
+
+    if is_ambig:
+        output += "\n" + "\n".join([" " * new_indent + _pretty_print_lark_trees(i, new_indent, show_expr) for i in tree.children])
+    else:
+        output += ",".join([_pretty_print_lark_trees(i, new_indent, show_expr) for i in tree.children])
+
+    if show_node:
+        output += ")"
+
+    return output
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/transformer.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/transformer.py
new file mode 100644
index 0000000000000000000000000000000000000000..cbd514b6517336207a57de6d28bcce25858071dc
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/latex/lark/transformer.py
@@ -0,0 +1,730 @@
+import re
+
+import sympy
+from sympy.external import import_module
+from sympy.parsing.latex.errors import LaTeXParsingError
+
+lark = import_module("lark")
+
+if lark:
+    from lark import Transformer, Token, Tree  # type: ignore
+else:
+    class Transformer:  # type: ignore
+        def transform(self, *args):
+            pass
+
+
+    class Token:  # type: ignore
+        pass
+
+
+    class Tree:  # type: ignore
+        pass
+
+
+# noinspection PyPep8Naming,PyMethodMayBeStatic
+class TransformToSymPyExpr(Transformer):
+    """Returns a SymPy expression that is generated by traversing the ``lark.Tree``
+    passed to the ``.transform()`` function.
+
+    Notes
+    =====
+
+    **This class is never supposed to be used directly.**
+
+    In order to tweak the behavior of this class, it has to be subclassed and then after
+    the required modifications are made, the name of the new class should be passed to
+    the :py:class:`LarkLaTeXParser` class by using the ``transformer`` argument in the
+    constructor.
+
+    Parameters
+    ==========
+
+    visit_tokens : bool, optional
+        For information about what this option does, see `here
+        `_.
+
+        Note that the option must be set to ``True`` for the default parser to work.
+    """
+
+    SYMBOL = sympy.Symbol
+    DIGIT = sympy.core.numbers.Integer
+
+    def CMD_INFTY(self, tokens):
+        return sympy.oo
+
+    def GREEK_SYMBOL_WITH_PRIMES(self, tokens):
+        # we omit the first character because it is a backslash. Also, if the variable name has "var" in it,
+        # like "varphi" or "varepsilon", we remove that too
+        variable_name = re.sub("var", "", tokens[1:])
+
+        return sympy.Symbol(variable_name)
+
+    def LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT(self, tokens):
+        base, sub = tokens.value.split("_")
+        if sub.startswith("{"):
+            return sympy.Symbol("%s_{%s}" % (base, sub[1:-1]))
+        else:
+            return sympy.Symbol("%s_{%s}" % (base, sub))
+
+    def GREEK_SYMBOL_WITH_LATIN_SUBSCRIPT(self, tokens):
+        base, sub = tokens.value.split("_")
+        greek_letter = re.sub("var", "", base[1:])
+
+        if sub.startswith("{"):
+            return sympy.Symbol("%s_{%s}" % (greek_letter, sub[1:-1]))
+        else:
+            return sympy.Symbol("%s_{%s}" % (greek_letter, sub))
+
+    def LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT(self, tokens):
+        base, sub = tokens.value.split("_")
+        if sub.startswith("{"):
+            greek_letter = sub[2:-1]
+        else:
+            greek_letter = sub[1:]
+
+        greek_letter = re.sub("var", "", greek_letter)
+        return sympy.Symbol("%s_{%s}" % (base, greek_letter))
+
+
+    def GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT(self, tokens):
+        base, sub = tokens.value.split("_")
+        greek_base = re.sub("var", "", base[1:])
+
+        if sub.startswith("{"):
+            greek_sub = sub[2:-1]
+        else:
+            greek_sub = sub[1:]
+
+        greek_sub = re.sub("var", "", greek_sub)
+        return sympy.Symbol("%s_{%s}" % (greek_base, greek_sub))
+
+    def multi_letter_symbol(self, tokens):
+        if len(tokens) == 4: # no primes (single quotes) on symbol
+            return sympy.Symbol(tokens[2])
+        if len(tokens) == 5: # there are primes on the symbol
+            return sympy.Symbol(tokens[2] + tokens[4])
+
+    def number(self, tokens):
+        if tokens[0].type == "CMD_IMAGINARY_UNIT":
+            return sympy.I
+
+        if "." in tokens[0]:
+            return sympy.core.numbers.Float(tokens[0])
+        else:
+            return sympy.core.numbers.Integer(tokens[0])
+
+    def latex_string(self, tokens):
+        return tokens[0]
+
+    def group_round_parentheses(self, tokens):
+        return tokens[1]
+
+    def group_square_brackets(self, tokens):
+        return tokens[1]
+
+    def group_curly_parentheses(self, tokens):
+        return tokens[1]
+
+    def eq(self, tokens):
+        return sympy.Eq(tokens[0], tokens[2])
+
+    def ne(self, tokens):
+        return sympy.Ne(tokens[0], tokens[2])
+
+    def lt(self, tokens):
+        return sympy.Lt(tokens[0], tokens[2])
+
+    def lte(self, tokens):
+        return sympy.Le(tokens[0], tokens[2])
+
+    def gt(self, tokens):
+        return sympy.Gt(tokens[0], tokens[2])
+
+    def gte(self, tokens):
+        return sympy.Ge(tokens[0], tokens[2])
+
+    def add(self, tokens):
+        if len(tokens) == 2: # +a
+            return tokens[1]
+        if len(tokens) == 3: # a + b
+            lh = tokens[0]
+            rh = tokens[2]
+
+            if self._obj_is_sympy_Matrix(lh) or self._obj_is_sympy_Matrix(rh):
+                return sympy.MatAdd(lh, rh)
+
+            return sympy.Add(lh, rh)
+
+    def sub(self, tokens):
+        if len(tokens) == 2: # -a
+            x = tokens[1]
+
+            if self._obj_is_sympy_Matrix(x):
+                return sympy.MatMul(-1, x)
+
+            return -x
+        if len(tokens) == 3: # a - b
+            lh = tokens[0]
+            rh = tokens[2]
+
+            if self._obj_is_sympy_Matrix(lh) or self._obj_is_sympy_Matrix(rh):
+                return sympy.MatAdd(lh, sympy.MatMul(-1, rh))
+
+            return sympy.Add(lh, -rh)
+
+    def mul(self, tokens):
+        lh = tokens[0]
+        rh = tokens[2]
+
+        if self._obj_is_sympy_Matrix(lh) or self._obj_is_sympy_Matrix(rh):
+            return sympy.MatMul(lh, rh)
+
+        return sympy.Mul(lh, rh)
+
+    def div(self, tokens):
+        return self._handle_division(tokens[0], tokens[2])
+
+    def adjacent_expressions(self, tokens):
+        # Most of the time, if two expressions are next to each other, it means implicit multiplication,
+        # but not always
+        from sympy.physics.quantum import Bra, Ket
+        if isinstance(tokens[0], Ket) and isinstance(tokens[1], Bra):
+            from sympy.physics.quantum import OuterProduct
+            return OuterProduct(tokens[0], tokens[1])
+        elif tokens[0] == sympy.Symbol("d"):
+            # If the leftmost token is a "d", then it is highly likely that this is a differential
+            return tokens[0], tokens[1]
+        elif isinstance(tokens[0], tuple):
+            # then we have a derivative
+            return sympy.Derivative(tokens[1], tokens[0][1])
+        else:
+            return sympy.Mul(tokens[0], tokens[1])
+
+    def superscript(self, tokens):
+        def isprime(x):
+            return isinstance(x, Token) and x.type == "PRIMES"
+
+        def iscmdprime(x):
+            return isinstance(x, Token) and (x.type == "PRIMES_VIA_CMD"
+                                             or x.type == "CMD_PRIME")
+
+        def isstar(x):
+            return isinstance(x, Token) and x.type == "STARS"
+
+        def iscmdstar(x):
+            return isinstance(x, Token) and (x.type == "STARS_VIA_CMD"
+                                             or x.type == "CMD_ASTERISK")
+
+        base = tokens[0]
+        if len(tokens) == 3: # a^b OR a^\prime OR a^\ast
+            sup = tokens[2]
+        if len(tokens) == 5:
+            # a^{'}, a^{''}, ... OR
+            # a^{*}, a^{**}, ... OR
+            # a^{\prime}, a^{\prime\prime}, ... OR
+            # a^{\ast}, a^{\ast\ast}, ...
+            sup = tokens[3]
+
+        if self._obj_is_sympy_Matrix(base):
+            if sup == sympy.Symbol("T"):
+                return sympy.Transpose(base)
+            if sup == sympy.Symbol("H"):
+                return sympy.adjoint(base)
+            if isprime(sup):
+                sup = sup.value
+                if len(sup) % 2 == 0:
+                    return base
+                return sympy.Transpose(base)
+            if iscmdprime(sup):
+                sup = sup.value
+                if (len(sup)/len(r"\prime")) % 2 == 0:
+                    return base
+                return sympy.Transpose(base)
+            if isstar(sup):
+                sup = sup.value
+                # need .doit() in order to be consistent with
+                # sympy.adjoint() which returns the evaluated adjoint
+                # of a matrix
+                if len(sup) % 2 == 0:
+                    return base.doit()
+                return sympy.adjoint(base)
+            if iscmdstar(sup):
+                sup = sup.value
+                # need .doit() for same reason as above
+                if (len(sup)/len(r"\ast")) % 2 == 0:
+                    return base.doit()
+                return sympy.adjoint(base)
+
+        if isprime(sup) or iscmdprime(sup) or isstar(sup) or iscmdstar(sup):
+            raise LaTeXParsingError(f"{base} with superscript {sup} is not understood.")
+
+        return sympy.Pow(base, sup)
+
+    def matrix_prime(self, tokens):
+        base = tokens[0]
+        primes = tokens[1].value
+
+        if not self._obj_is_sympy_Matrix(base):
+            raise LaTeXParsingError(f"({base}){primes} is not understood.")
+
+        if len(primes) % 2 == 0:
+            return base
+
+        return sympy.Transpose(base)
+
+    def symbol_prime(self, tokens):
+        base = tokens[0]
+        primes = tokens[1].value
+
+        return sympy.Symbol(f"{base.name}{primes}")
+
+    def fraction(self, tokens):
+        numerator = tokens[1]
+        if isinstance(tokens[2], tuple):
+            # we only need the variable w.r.t. which we are differentiating
+            _, variable = tokens[2]
+
+            # we will pass this information upwards
+            return "derivative", variable
+        else:
+            denominator = tokens[2]
+            return self._handle_division(numerator, denominator)
+
+    def binomial(self, tokens):
+        return sympy.binomial(tokens[1], tokens[2])
+
+    def normal_integral(self, tokens):
+        underscore_index = None
+        caret_index = None
+
+        if "_" in tokens:
+            # we need to know the index because the next item in the list is the
+            # arguments for the lower bound of the integral
+            underscore_index = tokens.index("_")
+
+        if "^" in tokens:
+            # we need to know the index because the next item in the list is the
+            # arguments for the upper bound of the integral
+            caret_index = tokens.index("^")
+
+        lower_bound = tokens[underscore_index + 1] if underscore_index else None
+        upper_bound = tokens[caret_index + 1] if caret_index else None
+
+        differential_symbol = self._extract_differential_symbol(tokens)
+
+        if differential_symbol is None:
+            raise LaTeXParsingError("Differential symbol was not found in the expression."
+                                    "Valid differential symbols are \"d\", \"\\text{d}, and \"\\mathrm{d}\".")
+
+        # else we can assume that a differential symbol was found
+        differential_variable_index = tokens.index(differential_symbol) + 1
+        differential_variable = tokens[differential_variable_index]
+
+        # we can't simply do something like `if (lower_bound and not upper_bound) ...` because this would
+        # evaluate to `True` if the `lower_bound` is 0 and upper bound is non-zero
+        if lower_bound is not None and upper_bound is None:
+            # then one was given and the other wasn't
+            raise LaTeXParsingError("Lower bound for the integral was found, but upper bound was not found.")
+
+        if upper_bound is not None and lower_bound is None:
+            # then one was given and the other wasn't
+            raise LaTeXParsingError("Upper bound for the integral was found, but lower bound was not found.")
+
+        # check if any expression was given or not. If it wasn't, then set the integrand to 1.
+        if underscore_index is not None and underscore_index == differential_variable_index - 3:
+            # The Token at differential_variable_index - 2 should be the integrand. However, if going one more step
+            # backwards after that gives us the underscore, then that means that there _was_ no integrand.
+            # Example: \int^7_0 dx
+            integrand = 1
+        elif caret_index is not None and caret_index == differential_variable_index - 3:
+            # The Token at differential_variable_index - 2 should be the integrand. However, if going one more step
+            # backwards after that gives us the caret, then that means that there _was_ no integrand.
+            # Example: \int_0^7 dx
+            integrand = 1
+        elif differential_variable_index == 2:
+            # this means we have something like "\int dx", because the "\int" symbol will always be
+            # at index 0 in `tokens`
+            integrand = 1
+        else:
+            # The Token at differential_variable_index - 1 is the differential symbol itself, so we need to go one
+            # more step before that.
+            integrand = tokens[differential_variable_index - 2]
+
+        if lower_bound is not None:
+            # then we have a definite integral
+
+            # we can assume that either both the lower and upper bounds are given, or
+            # neither of them are
+            return sympy.Integral(integrand, (differential_variable, lower_bound, upper_bound))
+        else:
+            # we have an indefinite integral
+            return sympy.Integral(integrand, differential_variable)
+
+    def group_curly_parentheses_int(self, tokens):
+        # return signature is a tuple consisting of the expression in the numerator, along with the variable of
+        # integration
+        if len(tokens) == 3:
+            return 1, tokens[1]
+        elif len(tokens) == 4:
+            return tokens[1], tokens[2]
+        # there are no other possibilities
+
+    def special_fraction(self, tokens):
+        numerator, variable = tokens[1]
+        denominator = tokens[2]
+
+        # We pass the integrand, along with information about the variable of integration, upw
+        return sympy.Mul(numerator, sympy.Pow(denominator, -1)), variable
+
+    def integral_with_special_fraction(self, tokens):
+        underscore_index = None
+        caret_index = None
+
+        if "_" in tokens:
+            # we need to know the index because the next item in the list is the
+            # arguments for the lower bound of the integral
+            underscore_index = tokens.index("_")
+
+        if "^" in tokens:
+            # we need to know the index because the next item in the list is the
+            # arguments for the upper bound of the integral
+            caret_index = tokens.index("^")
+
+        lower_bound = tokens[underscore_index + 1] if underscore_index else None
+        upper_bound = tokens[caret_index + 1] if caret_index else None
+
+        # we can't simply do something like `if (lower_bound and not upper_bound) ...` because this would
+        # evaluate to `True` if the `lower_bound` is 0 and upper bound is non-zero
+        if lower_bound is not None and upper_bound is None:
+            # then one was given and the other wasn't
+            raise LaTeXParsingError("Lower bound for the integral was found, but upper bound was not found.")
+
+        if upper_bound is not None and lower_bound is None:
+            # then one was given and the other wasn't
+            raise LaTeXParsingError("Upper bound for the integral was found, but lower bound was not found.")
+
+        integrand, differential_variable = tokens[-1]
+
+        if lower_bound is not None:
+            # then we have a definite integral
+
+            # we can assume that either both the lower and upper bounds are given, or
+            # neither of them are
+            return sympy.Integral(integrand, (differential_variable, lower_bound, upper_bound))
+        else:
+            # we have an indefinite integral
+            return sympy.Integral(integrand, differential_variable)
+
+    def group_curly_parentheses_special(self, tokens):
+        underscore_index = tokens.index("_")
+        caret_index = tokens.index("^")
+
+        # given the type of expressions we are parsing, we can assume that the lower limit
+        # will always use braces around its arguments. This is because we don't support
+        # converting unconstrained sums into SymPy expressions.
+
+        # first we isolate the bottom limit
+        left_brace_index = tokens.index("{", underscore_index)
+        right_brace_index = tokens.index("}", underscore_index)
+
+        bottom_limit = tokens[left_brace_index + 1: right_brace_index]
+
+        # next, we isolate the upper limit
+        top_limit = tokens[caret_index + 1:]
+
+        # the code below will be useful for supporting things like `\sum_{n = 0}^{n = 5} n^2`
+        # if "{" in top_limit:
+        #     left_brace_index = tokens.index("{", caret_index)
+        #     if left_brace_index != -1:
+        #         # then there's a left brace in the string, and we need to find the closing right brace
+        #         right_brace_index = tokens.index("}", caret_index)
+        #         top_limit = tokens[left_brace_index + 1: right_brace_index]
+
+        # print(f"top  limit = {top_limit}")
+
+        index_variable = bottom_limit[0]
+        lower_limit = bottom_limit[-1]
+        upper_limit = top_limit[0]  # for now, the index will always be 0
+
+        # print(f"return value = ({index_variable}, {lower_limit}, {upper_limit})")
+
+        return index_variable, lower_limit, upper_limit
+
+    def summation(self, tokens):
+        return sympy.Sum(tokens[2], tokens[1])
+
+    def product(self, tokens):
+        return sympy.Product(tokens[2], tokens[1])
+
+    def limit_dir_expr(self, tokens):
+        caret_index = tokens.index("^")
+
+        if "{" in tokens:
+            left_curly_brace_index = tokens.index("{", caret_index)
+            direction = tokens[left_curly_brace_index + 1]
+        else:
+            direction = tokens[caret_index + 1]
+
+        if direction == "+":
+            return tokens[0], "+"
+        elif direction == "-":
+            return tokens[0], "-"
+        else:
+            return tokens[0], "+-"
+
+    def group_curly_parentheses_lim(self, tokens):
+        limit_variable = tokens[1]
+        if isinstance(tokens[3], tuple):
+            destination, direction = tokens[3]
+        else:
+            destination = tokens[3]
+            direction = "+-"
+
+        return limit_variable, destination, direction
+
+    def limit(self, tokens):
+        limit_variable, destination, direction = tokens[2]
+
+        return sympy.Limit(tokens[-1], limit_variable, destination, direction)
+
+    def differential(self, tokens):
+        return tokens[1]
+
+    def derivative(self, tokens):
+        return sympy.Derivative(tokens[-1], tokens[5])
+
+    def list_of_expressions(self, tokens):
+        if len(tokens) == 1:
+            # we return it verbatim because the function_applied node expects
+            # a list
+            return tokens
+        else:
+            def remove_tokens(args):
+                if isinstance(args, Token):
+                    if args.type != "COMMA":
+                        # An unexpected token was encountered
+                        raise LaTeXParsingError("A comma token was expected, but some other token was encountered.")
+                    return False
+                return True
+
+            return filter(remove_tokens, tokens)
+
+    def function_applied(self, tokens):
+        return sympy.Function(tokens[0])(*tokens[2])
+
+    def min(self, tokens):
+        return sympy.Min(*tokens[2])
+
+    def max(self, tokens):
+        return sympy.Max(*tokens[2])
+
+    def bra(self, tokens):
+        from sympy.physics.quantum import Bra
+        return Bra(tokens[1])
+
+    def ket(self, tokens):
+        from sympy.physics.quantum import Ket
+        return Ket(tokens[1])
+
+    def inner_product(self, tokens):
+        from sympy.physics.quantum import Bra, Ket, InnerProduct
+        return InnerProduct(Bra(tokens[1]), Ket(tokens[3]))
+
+    def sin(self, tokens):
+        return sympy.sin(tokens[1])
+
+    def cos(self, tokens):
+        return sympy.cos(tokens[1])
+
+    def tan(self, tokens):
+        return sympy.tan(tokens[1])
+
+    def csc(self, tokens):
+        return sympy.csc(tokens[1])
+
+    def sec(self, tokens):
+        return sympy.sec(tokens[1])
+
+    def cot(self, tokens):
+        return sympy.cot(tokens[1])
+
+    def sin_power(self, tokens):
+        exponent = tokens[2]
+        if exponent == -1:
+            return sympy.asin(tokens[-1])
+        else:
+            return sympy.Pow(sympy.sin(tokens[-1]), exponent)
+
+    def cos_power(self, tokens):
+        exponent = tokens[2]
+        if exponent == -1:
+            return sympy.acos(tokens[-1])
+        else:
+            return sympy.Pow(sympy.cos(tokens[-1]), exponent)
+
+    def tan_power(self, tokens):
+        exponent = tokens[2]
+        if exponent == -1:
+            return sympy.atan(tokens[-1])
+        else:
+            return sympy.Pow(sympy.tan(tokens[-1]), exponent)
+
+    def csc_power(self, tokens):
+        exponent = tokens[2]
+        if exponent == -1:
+            return sympy.acsc(tokens[-1])
+        else:
+            return sympy.Pow(sympy.csc(tokens[-1]), exponent)
+
+    def sec_power(self, tokens):
+        exponent = tokens[2]
+        if exponent == -1:
+            return sympy.asec(tokens[-1])
+        else:
+            return sympy.Pow(sympy.sec(tokens[-1]), exponent)
+
+    def cot_power(self, tokens):
+        exponent = tokens[2]
+        if exponent == -1:
+            return sympy.acot(tokens[-1])
+        else:
+            return sympy.Pow(sympy.cot(tokens[-1]), exponent)
+
+    def arcsin(self, tokens):
+        return sympy.asin(tokens[1])
+
+    def arccos(self, tokens):
+        return sympy.acos(tokens[1])
+
+    def arctan(self, tokens):
+        return sympy.atan(tokens[1])
+
+    def arccsc(self, tokens):
+        return sympy.acsc(tokens[1])
+
+    def arcsec(self, tokens):
+        return sympy.asec(tokens[1])
+
+    def arccot(self, tokens):
+        return sympy.acot(tokens[1])
+
+    def sinh(self, tokens):
+        return sympy.sinh(tokens[1])
+
+    def cosh(self, tokens):
+        return sympy.cosh(tokens[1])
+
+    def tanh(self, tokens):
+        return sympy.tanh(tokens[1])
+
+    def asinh(self, tokens):
+        return sympy.asinh(tokens[1])
+
+    def acosh(self, tokens):
+        return sympy.acosh(tokens[1])
+
+    def atanh(self, tokens):
+        return sympy.atanh(tokens[1])
+
+    def abs(self, tokens):
+        return sympy.Abs(tokens[1])
+
+    def floor(self, tokens):
+        return sympy.floor(tokens[1])
+
+    def ceil(self, tokens):
+        return sympy.ceiling(tokens[1])
+
+    def factorial(self, tokens):
+        return sympy.factorial(tokens[0])
+
+    def conjugate(self, tokens):
+        return sympy.conjugate(tokens[1])
+
+    def square_root(self, tokens):
+        if len(tokens) == 2:
+            # then there was no square bracket argument
+            return sympy.sqrt(tokens[1])
+        elif len(tokens) == 3:
+            # then there _was_ a square bracket argument
+            return sympy.root(tokens[2], tokens[1])
+
+    def exponential(self, tokens):
+        return sympy.exp(tokens[1])
+
+    def log(self, tokens):
+        if tokens[0].type == "FUNC_LG":
+            # we don't need to check if there's an underscore or not because having one
+            # in this case would be meaningless
+            # TODO: ANTLR refers to ISO 80000-2:2019. should we keep base 10 or base 2?
+            return sympy.log(tokens[1], 10)
+        elif tokens[0].type == "FUNC_LN":
+            return sympy.log(tokens[1])
+        elif tokens[0].type == "FUNC_LOG":
+            # we check if a base was specified or not
+            if "_" in tokens:
+                # then a base was specified
+                return sympy.log(tokens[3], tokens[2])
+            else:
+                # a base was not specified
+                return sympy.log(tokens[1])
+
+    def _extract_differential_symbol(self, s: str):
+        differential_symbols = {"d", r"\text{d}", r"\mathrm{d}"}
+
+        differential_symbol = next((symbol for symbol in differential_symbols if symbol in s), None)
+
+        return differential_symbol
+
+    def matrix(self, tokens):
+        def is_matrix_row(x):
+            return (isinstance(x, Tree) and x.data == "matrix_row")
+
+        def is_not_col_delim(y):
+            return (not isinstance(y, Token) or y.type != "MATRIX_COL_DELIM")
+
+        matrix_body = tokens[1].children
+        return sympy.Matrix([[y for y in x.children if is_not_col_delim(y)]
+                             for x in matrix_body if is_matrix_row(x)])
+
+    def determinant(self, tokens):
+        if len(tokens) == 2: # \det A
+            if not self._obj_is_sympy_Matrix(tokens[1]):
+                raise LaTeXParsingError("Cannot take determinant of non-matrix.")
+
+            return tokens[1].det()
+
+        if len(tokens) == 3: # | A |
+            return self.matrix(tokens).det()
+
+    def trace(self, tokens):
+        if not self._obj_is_sympy_Matrix(tokens[1]):
+            raise LaTeXParsingError("Cannot take trace of non-matrix.")
+
+        return sympy.Trace(tokens[1])
+
+    def adjugate(self, tokens):
+        if not self._obj_is_sympy_Matrix(tokens[1]):
+            raise LaTeXParsingError("Cannot take adjugate of non-matrix.")
+
+        # need .doit() since MatAdd does not support .adjugate() method
+        return tokens[1].doit().adjugate()
+
+    def _obj_is_sympy_Matrix(self, obj):
+        if hasattr(obj, "is_Matrix"):
+            return obj.is_Matrix
+
+        return isinstance(obj, sympy.Matrix)
+
+    def _handle_division(self, numerator, denominator):
+        if self._obj_is_sympy_Matrix(denominator):
+            raise LaTeXParsingError("Cannot divide by matrices like this since "
+                                    "it is not clear if left or right multiplication "
+                                    "by the inverse is intended. Try explicitly "
+                                    "multiplying by the inverse instead.")
+
+        if self._obj_is_sympy_Matrix(numerator):
+            return sympy.MatMul(numerator, sympy.Pow(denominator, -1))
+
+        return sympy.Mul(numerator, sympy.Pow(denominator, -1))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/mathematica.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/mathematica.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5824a8c33ee402d03e6c5617eeeea21d4a457d1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/mathematica.py
@@ -0,0 +1,1085 @@
+from __future__ import annotations
+import re
+import typing
+from itertools import product
+from typing import Any, Callable
+
+import sympy
+from sympy import Mul, Add, Pow, Rational, log, exp, sqrt, cos, sin, tan, asin, acos, acot, asec, acsc, sinh, cosh, tanh, asinh, \
+    acosh, atanh, acoth, asech, acsch, expand, im, flatten, polylog, cancel, expand_trig, sign, simplify, \
+    UnevaluatedExpr, S, atan, atan2, Mod, Max, Min, rf, Ei, Si, Ci, airyai, airyaiprime, airybi, primepi, prime, \
+    isprime, cot, sec, csc, csch, sech, coth, Function, I, pi, Tuple, GreaterThan, StrictGreaterThan, StrictLessThan, \
+    LessThan, Equality, Or, And, Lambda, Integer, Dummy, symbols
+from sympy.core.sympify import sympify, _sympify
+from sympy.functions.special.bessel import airybiprime
+from sympy.functions.special.error_functions import li
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+
+def mathematica(s, additional_translations=None):
+    sympy_deprecation_warning(
+        """The ``mathematica`` function for the Mathematica parser is now
+deprecated. Use ``parse_mathematica`` instead.
+The parameter ``additional_translation`` can be replaced by SymPy's
+.replace( ) or .subs( ) methods on the output expression instead.""",
+        deprecated_since_version="1.11",
+        active_deprecations_target="mathematica-parser-new",
+    )
+    parser = MathematicaParser(additional_translations)
+    return sympify(parser._parse_old(s))
+
+
+def parse_mathematica(s):
+    """
+    Translate a string containing a Wolfram Mathematica expression to a SymPy
+    expression.
+
+    If the translator is unable to find a suitable SymPy expression, the
+    ``FullForm`` of the Mathematica expression will be output, using SymPy
+    ``Function`` objects as nodes of the syntax tree.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.mathematica import parse_mathematica
+    >>> parse_mathematica("Sin[x]^2 Tan[y]")
+    sin(x)**2*tan(y)
+    >>> e = parse_mathematica("F[7,5,3]")
+    >>> e
+    F(7, 5, 3)
+    >>> from sympy import Function, Max, Min
+    >>> e.replace(Function("F"), lambda *x: Max(*x)*Min(*x))
+    21
+
+    Both standard input form and Mathematica full form are supported:
+
+    >>> parse_mathematica("x*(a + b)")
+    x*(a + b)
+    >>> parse_mathematica("Times[x, Plus[a, b]]")
+    x*(a + b)
+
+    To get a matrix from Wolfram's code:
+
+    >>> m = parse_mathematica("{{a, b}, {c, d}}")
+    >>> m
+    ((a, b), (c, d))
+    >>> from sympy import Matrix
+    >>> Matrix(m)
+    Matrix([
+    [a, b],
+    [c, d]])
+
+    If the translation into equivalent SymPy expressions fails, an SymPy
+    expression equivalent to Wolfram Mathematica's "FullForm" will be created:
+
+    >>> parse_mathematica("x_.")
+    Optional(Pattern(x, Blank()))
+    >>> parse_mathematica("Plus @@ {x, y, z}")
+    Apply(Plus, (x, y, z))
+    >>> parse_mathematica("f[x_, 3] := x^3 /; x > 0")
+    SetDelayed(f(Pattern(x, Blank()), 3), Condition(x**3, x > 0))
+    """
+    parser = MathematicaParser()
+    return parser.parse(s)
+
+
+def _parse_Function(*args):
+    if len(args) == 1:
+        arg = args[0]
+        Slot = Function("Slot")
+        slots = arg.atoms(Slot)
+        numbers = [a.args[0] for a in slots]
+        number_of_arguments = max(numbers)
+        if isinstance(number_of_arguments, Integer):
+            variables = symbols(f"dummy0:{number_of_arguments}", cls=Dummy)
+            return Lambda(variables, arg.xreplace({Slot(i+1): v for i, v in enumerate(variables)}))
+        return Lambda((), arg)
+    elif len(args) == 2:
+        variables = args[0]
+        body = args[1]
+        return Lambda(variables, body)
+    else:
+        raise SyntaxError("Function node expects 1 or 2 arguments")
+
+
+def _deco(cls):
+    cls._initialize_class()
+    return cls
+
+
+@_deco
+class MathematicaParser:
+    """
+    An instance of this class converts a string of a Wolfram Mathematica
+    expression to a SymPy expression.
+
+    The main parser acts internally in three stages:
+
+    1. tokenizer: tokenizes the Mathematica expression and adds the missing *
+        operators. Handled by ``_from_mathematica_to_tokens(...)``
+    2. full form list: sort the list of strings output by the tokenizer into a
+        syntax tree of nested lists and strings, equivalent to Mathematica's
+        ``FullForm`` expression output. This is handled by the function
+        ``_from_tokens_to_fullformlist(...)``.
+    3. SymPy expression: the syntax tree expressed as full form list is visited
+        and the nodes with equivalent classes in SymPy are replaced. Unknown
+        syntax tree nodes are cast to SymPy ``Function`` objects. This is
+        handled by ``_from_fullformlist_to_sympy(...)``.
+
+    """
+
+    # left: Mathematica, right: SymPy
+    CORRESPONDENCES = {
+        'Sqrt[x]': 'sqrt(x)',
+        'Rational[x,y]': 'Rational(x,y)',
+        'Exp[x]': 'exp(x)',
+        'Log[x]': 'log(x)',
+        'Log[x,y]': 'log(y,x)',
+        'Log2[x]': 'log(x,2)',
+        'Log10[x]': 'log(x,10)',
+        'Mod[x,y]': 'Mod(x,y)',
+        'Max[*x]': 'Max(*x)',
+        'Min[*x]': 'Min(*x)',
+        'Pochhammer[x,y]':'rf(x,y)',
+        'ArcTan[x,y]':'atan2(y,x)',
+        'ExpIntegralEi[x]': 'Ei(x)',
+        'SinIntegral[x]': 'Si(x)',
+        'CosIntegral[x]': 'Ci(x)',
+        'AiryAi[x]': 'airyai(x)',
+        'AiryAiPrime[x]': 'airyaiprime(x)',
+        'AiryBi[x]' :'airybi(x)',
+        'AiryBiPrime[x]' :'airybiprime(x)',
+        'LogIntegral[x]':' li(x)',
+        'PrimePi[x]': 'primepi(x)',
+        'Prime[x]': 'prime(x)',
+        'PrimeQ[x]': 'isprime(x)'
+    }
+
+    # trigonometric, e.t.c.
+    for arc, tri, h in product(('', 'Arc'), (
+            'Sin', 'Cos', 'Tan', 'Cot', 'Sec', 'Csc'), ('', 'h')):
+        fm = arc + tri + h + '[x]'
+        if arc:  # arc func
+            fs = 'a' + tri.lower() + h + '(x)'
+        else:    # non-arc func
+            fs = tri.lower() + h + '(x)'
+        CORRESPONDENCES.update({fm: fs})
+
+    REPLACEMENTS = {
+        ' ': '',
+        '^': '**',
+        '{': '[',
+        '}': ']',
+    }
+
+    RULES = {
+        # a single whitespace to '*'
+        'whitespace': (
+            re.compile(r'''
+                (?:(?<=[a-zA-Z\d])|(?<=\d\.))     # a letter or a number
+                \s+                               # any number of whitespaces
+                (?:(?=[a-zA-Z\d])|(?=\.\d))       # a letter or a number
+                ''', re.VERBOSE),
+            '*'),
+
+        # add omitted '*' character
+        'add*_1': (
+            re.compile(r'''
+                (?:(?<=[])\d])|(?<=\d\.))       # ], ) or a number
+                                                # ''
+                (?=[(a-zA-Z])                   # ( or a single letter
+                ''', re.VERBOSE),
+            '*'),
+
+        # add omitted '*' character (variable letter preceding)
+        'add*_2': (
+            re.compile(r'''
+                (?<=[a-zA-Z])       # a letter
+                \(                  # ( as a character
+                (?=.)               # any characters
+                ''', re.VERBOSE),
+            '*('),
+
+        # convert 'Pi' to 'pi'
+        'Pi': (
+            re.compile(r'''
+                (?:
+                \A|(?<=[^a-zA-Z])
+                )
+                Pi                  # 'Pi' is 3.14159... in Mathematica
+                (?=[^a-zA-Z])
+                ''', re.VERBOSE),
+            'pi'),
+    }
+
+    # Mathematica function name pattern
+    FM_PATTERN = re.compile(r'''
+                (?:
+                \A|(?<=[^a-zA-Z])   # at the top or a non-letter
+                )
+                [A-Z][a-zA-Z\d]*    # Function
+                (?=\[)              # [ as a character
+                ''', re.VERBOSE)
+
+    # list or matrix pattern (for future usage)
+    ARG_MTRX_PATTERN = re.compile(r'''
+                \{.*\}
+                ''', re.VERBOSE)
+
+    # regex string for function argument pattern
+    ARGS_PATTERN_TEMPLATE = r'''
+                (?:
+                \A|(?<=[^a-zA-Z])
+                )
+                {arguments}         # model argument like x, y,...
+                (?=[^a-zA-Z])
+                '''
+
+    # will contain transformed CORRESPONDENCES dictionary
+    TRANSLATIONS: dict[tuple[str, int], dict[str, Any]] = {}
+
+    # cache for a raw users' translation dictionary
+    cache_original: dict[tuple[str, int], dict[str, Any]] = {}
+
+    # cache for a compiled users' translation dictionary
+    cache_compiled: dict[tuple[str, int], dict[str, Any]] = {}
+
+    @classmethod
+    def _initialize_class(cls):
+        # get a transformed CORRESPONDENCES dictionary
+        d = cls._compile_dictionary(cls.CORRESPONDENCES)
+        cls.TRANSLATIONS.update(d)
+
+    def __init__(self, additional_translations=None):
+        self.translations = {}
+
+        # update with TRANSLATIONS (class constant)
+        self.translations.update(self.TRANSLATIONS)
+
+        if additional_translations is None:
+            additional_translations = {}
+
+        # check the latest added translations
+        if self.__class__.cache_original != additional_translations:
+            if not isinstance(additional_translations, dict):
+                raise ValueError('The argument must be dict type')
+
+            # get a transformed additional_translations dictionary
+            d = self._compile_dictionary(additional_translations)
+
+            # update cache
+            self.__class__.cache_original = additional_translations
+            self.__class__.cache_compiled = d
+
+        # merge user's own translations
+        self.translations.update(self.__class__.cache_compiled)
+
+    @classmethod
+    def _compile_dictionary(cls, dic):
+        # for return
+        d = {}
+
+        for fm, fs in dic.items():
+            # check function form
+            cls._check_input(fm)
+            cls._check_input(fs)
+
+            # uncover '*' hiding behind a whitespace
+            fm = cls._apply_rules(fm, 'whitespace')
+            fs = cls._apply_rules(fs, 'whitespace')
+
+            # remove whitespace(s)
+            fm = cls._replace(fm, ' ')
+            fs = cls._replace(fs, ' ')
+
+            # search Mathematica function name
+            m = cls.FM_PATTERN.search(fm)
+
+            # if no-hit
+            if m is None:
+                err = "'{f}' function form is invalid.".format(f=fm)
+                raise ValueError(err)
+
+            # get Mathematica function name like 'Log'
+            fm_name = m.group()
+
+            # get arguments of Mathematica function
+            args, end = cls._get_args(m)
+
+            # function side check. (e.g.) '2*Func[x]' is invalid.
+            if m.start() != 0 or end != len(fm):
+                err = "'{f}' function form is invalid.".format(f=fm)
+                raise ValueError(err)
+
+            # check the last argument's 1st character
+            if args[-1][0] == '*':
+                key_arg = '*'
+            else:
+                key_arg = len(args)
+
+            key = (fm_name, key_arg)
+
+            # convert '*x' to '\\*x' for regex
+            re_args = [x if x[0] != '*' else '\\' + x for x in args]
+
+            # for regex. Example: (?:(x|y|z))
+            xyz = '(?:(' + '|'.join(re_args) + '))'
+
+            # string for regex compile
+            patStr = cls.ARGS_PATTERN_TEMPLATE.format(arguments=xyz)
+
+            pat = re.compile(patStr, re.VERBOSE)
+
+            # update dictionary
+            d[key] = {}
+            d[key]['fs'] = fs  # SymPy function template
+            d[key]['args'] = args  # args are ['x', 'y'] for example
+            d[key]['pat'] = pat
+
+        return d
+
+    def _convert_function(self, s):
+        '''Parse Mathematica function to SymPy one'''
+
+        # compiled regex object
+        pat = self.FM_PATTERN
+
+        scanned = ''                # converted string
+        cur = 0                     # position cursor
+        while True:
+            m = pat.search(s)
+
+            if m is None:
+                # append the rest of string
+                scanned += s
+                break
+
+            # get Mathematica function name
+            fm = m.group()
+
+            # get arguments, and the end position of fm function
+            args, end = self._get_args(m)
+
+            # the start position of fm function
+            bgn = m.start()
+
+            # convert Mathematica function to SymPy one
+            s = self._convert_one_function(s, fm, args, bgn, end)
+
+            # update cursor
+            cur = bgn
+
+            # append converted part
+            scanned += s[:cur]
+
+            # shrink s
+            s = s[cur:]
+
+        return scanned
+
+    def _convert_one_function(self, s, fm, args, bgn, end):
+        # no variable-length argument
+        if (fm, len(args)) in self.translations:
+            key = (fm, len(args))
+
+            # x, y,... model arguments
+            x_args = self.translations[key]['args']
+
+            # make CORRESPONDENCES between model arguments and actual ones
+            d = dict(zip(x_args, args))
+
+        # with variable-length argument
+        elif (fm, '*') in self.translations:
+            key = (fm, '*')
+
+            # x, y,..*args (model arguments)
+            x_args = self.translations[key]['args']
+
+            # make CORRESPONDENCES between model arguments and actual ones
+            d = {}
+            for i, x in enumerate(x_args):
+                if x[0] == '*':
+                    d[x] = ','.join(args[i:])
+                    break
+                d[x] = args[i]
+
+        # out of self.translations
+        else:
+            err = "'{f}' is out of the whitelist.".format(f=fm)
+            raise ValueError(err)
+
+        # template string of converted function
+        template = self.translations[key]['fs']
+
+        # regex pattern for x_args
+        pat = self.translations[key]['pat']
+
+        scanned = ''
+        cur = 0
+        while True:
+            m = pat.search(template)
+
+            if m is None:
+                scanned += template
+                break
+
+            # get model argument
+            x = m.group()
+
+            # get a start position of the model argument
+            xbgn = m.start()
+
+            # add the corresponding actual argument
+            scanned += template[:xbgn] + d[x]
+
+            # update cursor to the end of the model argument
+            cur = m.end()
+
+            # shrink template
+            template = template[cur:]
+
+        # update to swapped string
+        s = s[:bgn] + scanned + s[end:]
+
+        return s
+
+    @classmethod
+    def _get_args(cls, m):
+        '''Get arguments of a Mathematica function'''
+
+        s = m.string                # whole string
+        anc = m.end() + 1           # pointing the first letter of arguments
+        square, curly = [], []      # stack for brackets
+        args = []
+
+        # current cursor
+        cur = anc
+        for i, c in enumerate(s[anc:], anc):
+            # extract one argument
+            if c == ',' and (not square) and (not curly):
+                args.append(s[cur:i])       # add an argument
+                cur = i + 1                 # move cursor
+
+            # handle list or matrix (for future usage)
+            if c == '{':
+                curly.append(c)
+            elif c == '}':
+                curly.pop()
+
+            # seek corresponding ']' with skipping irrevant ones
+            if c == '[':
+                square.append(c)
+            elif c == ']':
+                if square:
+                    square.pop()
+                else:   # empty stack
+                    args.append(s[cur:i])
+                    break
+
+        # the next position to ']' bracket (the function end)
+        func_end = i + 1
+
+        return args, func_end
+
+    @classmethod
+    def _replace(cls, s, bef):
+        aft = cls.REPLACEMENTS[bef]
+        s = s.replace(bef, aft)
+        return s
+
+    @classmethod
+    def _apply_rules(cls, s, bef):
+        pat, aft = cls.RULES[bef]
+        return pat.sub(aft, s)
+
+    @classmethod
+    def _check_input(cls, s):
+        for bracket in (('[', ']'), ('{', '}'), ('(', ')')):
+            if s.count(bracket[0]) != s.count(bracket[1]):
+                err = "'{f}' function form is invalid.".format(f=s)
+                raise ValueError(err)
+
+        if '{' in s:
+            err = "Currently list is not supported."
+            raise ValueError(err)
+
+    def _parse_old(self, s):
+        # input check
+        self._check_input(s)
+
+        # uncover '*' hiding behind a whitespace
+        s = self._apply_rules(s, 'whitespace')
+
+        # remove whitespace(s)
+        s = self._replace(s, ' ')
+
+        # add omitted '*' character
+        s = self._apply_rules(s, 'add*_1')
+        s = self._apply_rules(s, 'add*_2')
+
+        # translate function
+        s = self._convert_function(s)
+
+        # '^' to '**'
+        s = self._replace(s, '^')
+
+        # 'Pi' to 'pi'
+        s = self._apply_rules(s, 'Pi')
+
+        # '{', '}' to '[', ']', respectively
+#        s = cls._replace(s, '{')   # currently list is not taken into account
+#        s = cls._replace(s, '}')
+
+        return s
+
+    def parse(self, s):
+        s2 = self._from_mathematica_to_tokens(s)
+        s3 = self._from_tokens_to_fullformlist(s2)
+        s4 = self._from_fullformlist_to_sympy(s3)
+        return s4
+
+    INFIX = "Infix"
+    PREFIX = "Prefix"
+    POSTFIX = "Postfix"
+    FLAT = "Flat"
+    RIGHT = "Right"
+    LEFT = "Left"
+
+    _mathematica_op_precedence: list[tuple[str, str | None, dict[str, str | Callable]]] = [
+        (POSTFIX, None, {";": lambda x: x + ["Null"] if isinstance(x, list) and x and x[0] == "CompoundExpression" else ["CompoundExpression", x, "Null"]}),
+        (INFIX, FLAT, {";": "CompoundExpression"}),
+        (INFIX, RIGHT, {"=": "Set", ":=": "SetDelayed", "+=": "AddTo", "-=": "SubtractFrom", "*=": "TimesBy", "/=": "DivideBy"}),
+        (INFIX, LEFT, {"//": lambda x, y: [x, y]}),
+        (POSTFIX, None, {"&": "Function"}),
+        (INFIX, LEFT, {"/.": "ReplaceAll"}),
+        (INFIX, RIGHT, {"->": "Rule", ":>": "RuleDelayed"}),
+        (INFIX, LEFT, {"/;": "Condition"}),
+        (INFIX, FLAT, {"|": "Alternatives"}),
+        (POSTFIX, None, {"..": "Repeated", "...": "RepeatedNull"}),
+        (INFIX, FLAT, {"||": "Or"}),
+        (INFIX, FLAT, {"&&": "And"}),
+        (PREFIX, None, {"!": "Not"}),
+        (INFIX, FLAT, {"===": "SameQ", "=!=": "UnsameQ"}),
+        (INFIX, FLAT, {"==": "Equal", "!=": "Unequal", "<=": "LessEqual", "<": "Less", ">=": "GreaterEqual", ">": "Greater"}),
+        (INFIX, None, {";;": "Span"}),
+        (INFIX, FLAT, {"+": "Plus", "-": "Plus"}),
+        (INFIX, FLAT, {"*": "Times", "/": "Times"}),
+        (INFIX, FLAT, {".": "Dot"}),
+        (PREFIX, None, {"-": lambda x: MathematicaParser._get_neg(x),
+                        "+": lambda x: x}),
+        (INFIX, RIGHT, {"^": "Power"}),
+        (INFIX, RIGHT, {"@@": "Apply", "/@": "Map", "//@": "MapAll", "@@@": lambda x, y: ["Apply", x, y, ["List", "1"]]}),
+        (POSTFIX, None, {"'": "Derivative", "!": "Factorial", "!!": "Factorial2", "--": "Decrement"}),
+        (INFIX, None, {"[": lambda x, y: [x, *y], "[[": lambda x, y: ["Part", x, *y]}),
+        (PREFIX, None, {"{": lambda x: ["List", *x], "(": lambda x: x[0]}),
+        (INFIX, None, {"?": "PatternTest"}),
+        (POSTFIX, None, {
+            "_": lambda x: ["Pattern", x, ["Blank"]],
+            "_.": lambda x: ["Optional", ["Pattern", x, ["Blank"]]],
+            "__": lambda x: ["Pattern", x, ["BlankSequence"]],
+            "___": lambda x: ["Pattern", x, ["BlankNullSequence"]],
+        }),
+        (INFIX, None, {"_": lambda x, y: ["Pattern", x, ["Blank", y]]}),
+        (PREFIX, None, {"#": "Slot", "##": "SlotSequence"}),
+    ]
+
+    _missing_arguments_default = {
+        "#": lambda: ["Slot", "1"],
+        "##": lambda: ["SlotSequence", "1"],
+    }
+
+    _literal = r"[A-Za-z][A-Za-z0-9]*"
+    _number = r"(?:[0-9]+(?:\.[0-9]*)?|\.[0-9]+)"
+
+    _enclosure_open = ["(", "[", "[[", "{"]
+    _enclosure_close = [")", "]", "]]", "}"]
+
+    @classmethod
+    def _get_neg(cls, x):
+        return f"-{x}" if isinstance(x, str) and re.match(MathematicaParser._number, x) else ["Times", "-1", x]
+
+    @classmethod
+    def _get_inv(cls, x):
+        return ["Power", x, "-1"]
+
+    _regex_tokenizer = None
+
+    def _get_tokenizer(self):
+        if self._regex_tokenizer is not None:
+            # Check if the regular expression has already been compiled:
+            return self._regex_tokenizer
+        tokens = [self._literal, self._number]
+        tokens_escape = self._enclosure_open[:] + self._enclosure_close[:]
+        for typ, strat, symdict in self._mathematica_op_precedence:
+            for k in symdict:
+                tokens_escape.append(k)
+        tokens_escape.sort(key=lambda x: -len(x))
+        tokens.extend(map(re.escape, tokens_escape))
+        tokens.append(",")
+        tokens.append("\n")
+        tokenizer = re.compile("(" + "|".join(tokens) + ")")
+        self._regex_tokenizer = tokenizer
+        return self._regex_tokenizer
+
+    def _from_mathematica_to_tokens(self, code: str):
+        tokenizer = self._get_tokenizer()
+
+        # Find strings:
+        code_splits: list[str | list] = []
+        while True:
+            string_start = code.find("\"")
+            if string_start == -1:
+                if len(code) > 0:
+                    code_splits.append(code)
+                break
+            match_end = re.search(r'(? 0:
+                code_splits.append(code[:string_start])
+            code_splits.append(["_Str", code[string_start+1:string_end].replace('\\"', '"')])
+            code = code[string_end+1:]
+
+        # Remove comments:
+        for i, code_split in enumerate(code_splits):
+            if isinstance(code_split, list):
+                continue
+            while True:
+                pos_comment_start = code_split.find("(*")
+                if pos_comment_start == -1:
+                    break
+                pos_comment_end = code_split.find("*)")
+                if pos_comment_end == -1 or pos_comment_end < pos_comment_start:
+                    raise SyntaxError("mismatch in comment (*  *) code")
+                code_split = code_split[:pos_comment_start] + code_split[pos_comment_end+2:]
+            code_splits[i] = code_split
+
+        # Tokenize the input strings with a regular expression:
+        token_lists = [tokenizer.findall(i) if isinstance(i, str) and i.isascii() else [i] for i in code_splits]
+        tokens = [j for i in token_lists for j in i]
+
+        # Remove newlines at the beginning
+        while tokens and tokens[0] == "\n":
+            tokens.pop(0)
+        # Remove newlines at the end
+        while tokens and tokens[-1] == "\n":
+            tokens.pop(-1)
+
+        return tokens
+
+    def _is_op(self, token: str | list) -> bool:
+        if isinstance(token, list):
+            return False
+        if re.match(self._literal, token):
+            return False
+        if re.match("-?" + self._number, token):
+            return False
+        return True
+
+    def _is_valid_star1(self, token: str | list) -> bool:
+        if token in (")", "}"):
+            return True
+        return not self._is_op(token)
+
+    def _is_valid_star2(self, token: str | list) -> bool:
+        if token in ("(", "{"):
+            return True
+        return not self._is_op(token)
+
+    def _from_tokens_to_fullformlist(self, tokens: list):
+        stack: list[list] = [[]]
+        open_seq = []
+        pointer: int = 0
+        while pointer < len(tokens):
+            token = tokens[pointer]
+            if token in self._enclosure_open:
+                stack[-1].append(token)
+                open_seq.append(token)
+                stack.append([])
+            elif token == ",":
+                if len(stack[-1]) == 0 and stack[-2][-1] == open_seq[-1]:
+                    raise SyntaxError("%s cannot be followed by comma ," % open_seq[-1])
+                stack[-1] = self._parse_after_braces(stack[-1])
+                stack.append([])
+            elif token in self._enclosure_close:
+                ind = self._enclosure_close.index(token)
+                if self._enclosure_open[ind] != open_seq[-1]:
+                    unmatched_enclosure = SyntaxError("unmatched enclosure")
+                    if token == "]]" and open_seq[-1] == "[":
+                        if open_seq[-2] == "[":
+                            # These two lines would be logically correct, but are
+                            # unnecessary:
+                            # token = "]"
+                            # tokens[pointer] = "]"
+                            tokens.insert(pointer+1, "]")
+                        elif open_seq[-2] == "[[":
+                            if tokens[pointer+1] == "]":
+                                tokens[pointer+1] = "]]"
+                            elif tokens[pointer+1] == "]]":
+                                tokens[pointer+1] = "]]"
+                                tokens.insert(pointer+2, "]")
+                            else:
+                                raise unmatched_enclosure
+                    else:
+                        raise unmatched_enclosure
+                if len(stack[-1]) == 0 and stack[-2][-1] == "(":
+                    raise SyntaxError("( ) not valid syntax")
+                last_stack = self._parse_after_braces(stack[-1], True)
+                stack[-1] = last_stack
+                new_stack_element = []
+                while stack[-1][-1] != open_seq[-1]:
+                    new_stack_element.append(stack.pop())
+                new_stack_element.reverse()
+                if open_seq[-1] == "(" and len(new_stack_element) != 1:
+                    raise SyntaxError("( must be followed by one expression, %i detected" % len(new_stack_element))
+                stack[-1].append(new_stack_element)
+                open_seq.pop(-1)
+            else:
+                stack[-1].append(token)
+            pointer += 1
+        if len(stack) != 1:
+            raise RuntimeError("Stack should have only one element")
+        return self._parse_after_braces(stack[0])
+
+    def _util_remove_newlines(self, lines: list, tokens: list, inside_enclosure: bool):
+        pointer = 0
+        size = len(tokens)
+        while pointer < size:
+            token = tokens[pointer]
+            if token == "\n":
+                if inside_enclosure:
+                    # Ignore newlines inside enclosures
+                    tokens.pop(pointer)
+                    size -= 1
+                    continue
+                if pointer == 0:
+                    tokens.pop(0)
+                    size -= 1
+                    continue
+                if pointer > 1:
+                    try:
+                        prev_expr = self._parse_after_braces(tokens[:pointer], inside_enclosure)
+                    except SyntaxError:
+                        tokens.pop(pointer)
+                        size -= 1
+                        continue
+                else:
+                    prev_expr = tokens[0]
+                if len(prev_expr) > 0 and prev_expr[0] == "CompoundExpression":
+                    lines.extend(prev_expr[1:])
+                else:
+                    lines.append(prev_expr)
+                for i in range(pointer):
+                    tokens.pop(0)
+                size -= pointer
+                pointer = 0
+                continue
+            pointer += 1
+
+    def _util_add_missing_asterisks(self, tokens: list):
+        size: int = len(tokens)
+        pointer: int = 0
+        while pointer < size:
+            if (pointer > 0 and
+                    self._is_valid_star1(tokens[pointer - 1]) and
+                    self._is_valid_star2(tokens[pointer])):
+                # This is a trick to add missing * operators in the expression,
+                # `"*" in op_dict` makes sure the precedence level is the same as "*",
+                # while `not self._is_op( ... )` makes sure this and the previous
+                # expression are not operators.
+                if tokens[pointer] == "(":
+                    # ( has already been processed by now, replace:
+                    tokens[pointer] = "*"
+                    tokens[pointer + 1] = tokens[pointer + 1][0]
+                else:
+                    tokens.insert(pointer, "*")
+                    pointer += 1
+                    size += 1
+            pointer += 1
+
+    def _parse_after_braces(self, tokens: list, inside_enclosure: bool = False):
+        op_dict: dict
+        changed: bool = False
+        lines: list = []
+
+        self._util_remove_newlines(lines, tokens, inside_enclosure)
+
+        for op_type, grouping_strat, op_dict in reversed(self._mathematica_op_precedence):
+            if "*" in op_dict:
+                self._util_add_missing_asterisks(tokens)
+            size: int = len(tokens)
+            pointer: int = 0
+            while pointer < size:
+                token = tokens[pointer]
+                if isinstance(token, str) and token in op_dict:
+                    op_name: str | Callable = op_dict[token]
+                    node: list
+                    first_index: int
+                    if isinstance(op_name, str):
+                        node = [op_name]
+                        first_index = 1
+                    else:
+                        node = []
+                        first_index = 0
+                    if token in ("+", "-") and op_type == self.PREFIX and pointer > 0 and not self._is_op(tokens[pointer - 1]):
+                        # Make sure that PREFIX + - don't match expressions like a + b or a - b,
+                        # the INFIX + - are supposed to match that expression:
+                        pointer += 1
+                        continue
+                    if op_type == self.INFIX:
+                        if pointer == 0 or pointer == size - 1 or self._is_op(tokens[pointer - 1]) or self._is_op(tokens[pointer + 1]):
+                            pointer += 1
+                            continue
+                    changed = True
+                    tokens[pointer] = node
+                    if op_type == self.INFIX:
+                        arg1 = tokens.pop(pointer-1)
+                        arg2 = tokens.pop(pointer)
+                        if token == "/":
+                            arg2 = self._get_inv(arg2)
+                        elif token == "-":
+                            arg2 = self._get_neg(arg2)
+                        pointer -= 1
+                        size -= 2
+                        node.append(arg1)
+                        node_p = node
+                        if grouping_strat == self.FLAT:
+                            while pointer + 2 < size and self._check_op_compatible(tokens[pointer+1], token):
+                                node_p.append(arg2)
+                                other_op = tokens.pop(pointer+1)
+                                arg2 = tokens.pop(pointer+1)
+                                if other_op == "/":
+                                    arg2 = self._get_inv(arg2)
+                                elif other_op == "-":
+                                    arg2 = self._get_neg(arg2)
+                                size -= 2
+                            node_p.append(arg2)
+                        elif grouping_strat == self.RIGHT:
+                            while pointer + 2 < size and tokens[pointer+1] == token:
+                                node_p.append([op_name, arg2])
+                                node_p = node_p[-1]
+                                tokens.pop(pointer+1)
+                                arg2 = tokens.pop(pointer+1)
+                                size -= 2
+                            node_p.append(arg2)
+                        elif grouping_strat == self.LEFT:
+                            while pointer + 1 < size and tokens[pointer+1] == token:
+                                if isinstance(op_name, str):
+                                    node_p[first_index] = [op_name, node_p[first_index], arg2]
+                                else:
+                                    node_p[first_index] = op_name(node_p[first_index], arg2)
+                                tokens.pop(pointer+1)
+                                arg2 = tokens.pop(pointer+1)
+                                size -= 2
+                            node_p.append(arg2)
+                        else:
+                            node.append(arg2)
+                    elif op_type == self.PREFIX:
+                        if grouping_strat is not None:
+                            raise TypeError("'Prefix' op_type should not have a grouping strat")
+                        if pointer == size - 1 or self._is_op(tokens[pointer + 1]):
+                            tokens[pointer] = self._missing_arguments_default[token]()
+                        else:
+                            node.append(tokens.pop(pointer+1))
+                            size -= 1
+                    elif op_type == self.POSTFIX:
+                        if grouping_strat is not None:
+                            raise TypeError("'Prefix' op_type should not have a grouping strat")
+                        if pointer == 0 or self._is_op(tokens[pointer - 1]):
+                            tokens[pointer] = self._missing_arguments_default[token]()
+                        else:
+                            node.append(tokens.pop(pointer-1))
+                            pointer -= 1
+                            size -= 1
+                    if isinstance(op_name, Callable):  # type: ignore
+                        op_call: Callable = typing.cast(Callable, op_name)
+                        new_node = op_call(*node)
+                        node.clear()
+                        if isinstance(new_node, list):
+                            node.extend(new_node)
+                        else:
+                            tokens[pointer] = new_node
+                pointer += 1
+        if len(tokens) > 1 or (len(lines) == 0 and len(tokens) == 0):
+            if changed:
+                # Trick to deal with cases in which an operator with lower
+                # precedence should be transformed before an operator of higher
+                # precedence. Such as in the case of `#&[x]` (that is
+                # equivalent to `Lambda(d_, d_)(x)` in SymPy). In this case the
+                # operator `&` has lower precedence than `[`, but needs to be
+                # evaluated first because otherwise `# (&[x])` is not a valid
+                # expression:
+                return self._parse_after_braces(tokens, inside_enclosure)
+            raise SyntaxError("unable to create a single AST for the expression")
+        if len(lines) > 0:
+            if tokens[0] and tokens[0][0] == "CompoundExpression":
+                tokens = tokens[0][1:]
+            compound_expression = ["CompoundExpression", *lines, *tokens]
+            return compound_expression
+        return tokens[0]
+
+    def _check_op_compatible(self, op1: str, op2: str):
+        if op1 == op2:
+            return True
+        muldiv = {"*", "/"}
+        addsub = {"+", "-"}
+        if op1 in muldiv and op2 in muldiv:
+            return True
+        if op1 in addsub and op2 in addsub:
+            return True
+        return False
+
+    def _from_fullform_to_fullformlist(self, wmexpr: str):
+        """
+        Parses FullForm[Downvalues[]] generated by Mathematica
+        """
+        out: list = []
+        stack = [out]
+        generator = re.finditer(r'[\[\],]', wmexpr)
+        last_pos = 0
+        for match in generator:
+            if match is None:
+                break
+            position = match.start()
+            last_expr = wmexpr[last_pos:position].replace(',', '').replace(']', '').replace('[', '').strip()
+
+            if match.group() == ',':
+                if last_expr != '':
+                    stack[-1].append(last_expr)
+            elif match.group() == ']':
+                if last_expr != '':
+                    stack[-1].append(last_expr)
+                stack.pop()
+            elif match.group() == '[':
+                stack[-1].append([last_expr])
+                stack.append(stack[-1][-1])
+            last_pos = match.end()
+        return out[0]
+
+    def _from_fullformlist_to_fullformsympy(self, pylist: list):
+        from sympy import Function, Symbol
+
+        def converter(expr):
+            if isinstance(expr, list):
+                if len(expr) > 0:
+                    head = expr[0]
+                    args = [converter(arg) for arg in expr[1:]]
+                    return Function(head)(*args)
+                else:
+                    raise ValueError("Empty list of expressions")
+            elif isinstance(expr, str):
+                return Symbol(expr)
+            else:
+                return _sympify(expr)
+
+        return converter(pylist)
+
+    _node_conversions = {
+        "Times": Mul,
+        "Plus": Add,
+        "Power": Pow,
+        "Rational": Rational,
+        "Log": lambda *a: log(*reversed(a)),
+        "Log2": lambda x: log(x, 2),
+        "Log10": lambda x: log(x, 10),
+        "Exp": exp,
+        "Sqrt": sqrt,
+
+        "Sin": sin,
+        "Cos": cos,
+        "Tan": tan,
+        "Cot": cot,
+        "Sec": sec,
+        "Csc": csc,
+
+        "ArcSin": asin,
+        "ArcCos": acos,
+        "ArcTan": lambda *a: atan2(*reversed(a)) if len(a) == 2 else atan(*a),
+        "ArcCot": acot,
+        "ArcSec": asec,
+        "ArcCsc": acsc,
+
+        "Sinh": sinh,
+        "Cosh": cosh,
+        "Tanh": tanh,
+        "Coth": coth,
+        "Sech": sech,
+        "Csch": csch,
+
+        "ArcSinh": asinh,
+        "ArcCosh": acosh,
+        "ArcTanh": atanh,
+        "ArcCoth": acoth,
+        "ArcSech": asech,
+        "ArcCsch": acsch,
+
+        "Expand": expand,
+        "Im": im,
+        "Re": sympy.re,
+        "Flatten": flatten,
+        "Polylog": polylog,
+        "Cancel": cancel,
+        # Gamma=gamma,
+        "TrigExpand": expand_trig,
+        "Sign": sign,
+        "Simplify": simplify,
+        "Defer": UnevaluatedExpr,
+        "Identity": S,
+        # Sum=Sum_doit,
+        # Module=With,
+        # Block=With,
+        "Null": lambda *a: S.Zero,
+        "Mod": Mod,
+        "Max": Max,
+        "Min": Min,
+        "Pochhammer": rf,
+        "ExpIntegralEi": Ei,
+        "SinIntegral": Si,
+        "CosIntegral": Ci,
+        "AiryAi": airyai,
+        "AiryAiPrime": airyaiprime,
+        "AiryBi": airybi,
+        "AiryBiPrime": airybiprime,
+        "LogIntegral": li,
+        "PrimePi": primepi,
+        "Prime": prime,
+        "PrimeQ": isprime,
+
+        "List": Tuple,
+        "Greater": StrictGreaterThan,
+        "GreaterEqual": GreaterThan,
+        "Less": StrictLessThan,
+        "LessEqual": LessThan,
+        "Equal": Equality,
+        "Or": Or,
+        "And": And,
+
+        "Function": _parse_Function,
+    }
+
+    _atom_conversions = {
+        "I": I,
+        "Pi": pi,
+    }
+
+    def _from_fullformlist_to_sympy(self, full_form_list):
+
+        def recurse(expr):
+            if isinstance(expr, list):
+                if isinstance(expr[0], list):
+                    head = recurse(expr[0])
+                else:
+                    head = self._node_conversions.get(expr[0], Function(expr[0]))
+                return head(*[recurse(arg) for arg in expr[1:]])
+            else:
+                return self._atom_conversions.get(expr, sympify(expr))
+
+        return recurse(full_form_list)
+
+    def _from_fullformsympy_to_sympy(self, mform):
+
+        expr = mform
+        for mma_form, sympy_node in self._node_conversions.items():
+            expr = expr.replace(Function(mma_form), sympy_node)
+        return expr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/maxima.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/maxima.py
new file mode 100644
index 0000000000000000000000000000000000000000..7a8ee5b17bb03a36e338803cb10f9ebf22763c2c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/maxima.py
@@ -0,0 +1,71 @@
+import re
+from sympy.concrete.products import product
+from sympy.concrete.summations import Sum
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.trigonometric import (cos, sin)
+
+
+class MaximaHelpers:
+    def maxima_expand(expr):
+        return expr.expand()
+
+    def maxima_float(expr):
+        return expr.evalf()
+
+    def maxima_trigexpand(expr):
+        return expr.expand(trig=True)
+
+    def maxima_sum(a1, a2, a3, a4):
+        return Sum(a1, (a2, a3, a4)).doit()
+
+    def maxima_product(a1, a2, a3, a4):
+        return product(a1, (a2, a3, a4))
+
+    def maxima_csc(expr):
+        return 1/sin(expr)
+
+    def maxima_sec(expr):
+        return 1/cos(expr)
+
+sub_dict = {
+    'pi': re.compile(r'%pi'),
+    'E': re.compile(r'%e'),
+    'I': re.compile(r'%i'),
+    '**': re.compile(r'\^'),
+    'oo': re.compile(r'\binf\b'),
+    '-oo': re.compile(r'\bminf\b'),
+    "'-'": re.compile(r'\bminus\b'),
+    'maxima_expand': re.compile(r'\bexpand\b'),
+    'maxima_float': re.compile(r'\bfloat\b'),
+    'maxima_trigexpand': re.compile(r'\btrigexpand'),
+    'maxima_sum': re.compile(r'\bsum\b'),
+    'maxima_product': re.compile(r'\bproduct\b'),
+    'cancel': re.compile(r'\bratsimp\b'),
+    'maxima_csc': re.compile(r'\bcsc\b'),
+    'maxima_sec': re.compile(r'\bsec\b')
+}
+
+var_name = re.compile(r'^\s*(\w+)\s*:')
+
+
+def parse_maxima(str, globals=None, name_dict={}):
+    str = str.strip()
+    str = str.rstrip('; ')
+
+    for k, v in sub_dict.items():
+        str = v.sub(k, str)
+
+    assign_var = None
+    var_match = var_name.search(str)
+    if var_match:
+        assign_var = var_match.group(1)
+        str = str[var_match.end():].strip()
+
+    dct = MaximaHelpers.__dict__.copy()
+    dct.update(name_dict)
+    obj = sympify(str, locals=dct)
+
+    if assign_var and globals:
+        globals[assign_var] = obj
+
+    return obj
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/sym_expr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/sym_expr.py
new file mode 100644
index 0000000000000000000000000000000000000000..9dbd0e94eb51147b51825fcf15cbec5ae18bb1b6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/sym_expr.py
@@ -0,0 +1,279 @@
+from sympy.printing import pycode, ccode, fcode
+from sympy.external import import_module
+from sympy.utilities.decorator import doctest_depends_on
+
+lfortran = import_module('lfortran')
+cin = import_module('clang.cindex', import_kwargs = {'fromlist': ['cindex']})
+
+if lfortran:
+    from sympy.parsing.fortran.fortran_parser import src_to_sympy
+if cin:
+    from sympy.parsing.c.c_parser import parse_c
+
+@doctest_depends_on(modules=['lfortran', 'clang.cindex'])
+class SymPyExpression:  # type: ignore
+    """Class to store and handle SymPy expressions
+
+    This class will hold SymPy Expressions and handle the API for the
+    conversion to and from different languages.
+
+    It works with the C and the Fortran Parser to generate SymPy expressions
+    which are stored here and which can be converted to multiple language's
+    source code.
+
+    Notes
+    =====
+
+    The module and its API are currently under development and experimental
+    and can be changed during development.
+
+    The Fortran parser does not support numeric assignments, so all the
+    variables have been Initialized to zero.
+
+    The module also depends on external dependencies:
+
+    - LFortran which is required to use the Fortran parser
+    - Clang which is required for the C parser
+
+    Examples
+    ========
+
+    Example of parsing C code:
+
+    >>> from sympy.parsing.sym_expr import SymPyExpression
+    >>> src = '''
+    ... int a,b;
+    ... float c = 2, d =4;
+    ... '''
+    >>> a = SymPyExpression(src, 'c')
+    >>> a.return_expr()
+    [Declaration(Variable(a, type=intc)),
+    Declaration(Variable(b, type=intc)),
+    Declaration(Variable(c, type=float32, value=2.0)),
+    Declaration(Variable(d, type=float32, value=4.0))]
+
+    An example of variable definition:
+
+    >>> from sympy.parsing.sym_expr import SymPyExpression
+    >>> src2 = '''
+    ... integer :: a, b, c, d
+    ... real :: p, q, r, s
+    ... '''
+    >>> p = SymPyExpression()
+    >>> p.convert_to_expr(src2, 'f')
+    >>> p.convert_to_c()
+    ['int a = 0', 'int b = 0', 'int c = 0', 'int d = 0', 'double p = 0.0', 'double q = 0.0', 'double r = 0.0', 'double s = 0.0']
+
+    An example of Assignment:
+
+    >>> from sympy.parsing.sym_expr import SymPyExpression
+    >>> src3 = '''
+    ... integer :: a, b, c, d, e
+    ... d = a + b - c
+    ... e = b * d + c * e / a
+    ... '''
+    >>> p = SymPyExpression(src3, 'f')
+    >>> p.convert_to_python()
+    ['a = 0', 'b = 0', 'c = 0', 'd = 0', 'e = 0', 'd = a + b - c', 'e = b*d + c*e/a']
+
+    An example of function definition:
+
+    >>> from sympy.parsing.sym_expr import SymPyExpression
+    >>> src = '''
+    ... integer function f(a,b)
+    ... integer, intent(in) :: a, b
+    ... integer :: r
+    ... end function
+    ... '''
+    >>> a = SymPyExpression(src, 'f')
+    >>> a.convert_to_python()
+    ['def f(a, b):\\n   f = 0\\n    r = 0\\n    return f']
+
+    """
+
+    def __init__(self, source_code = None, mode = None):
+        """Constructor for SymPyExpression class"""
+        super().__init__()
+        if not(mode or source_code):
+            self._expr = []
+        elif mode:
+            if source_code:
+                if mode.lower() == 'f':
+                    if lfortran:
+                        self._expr = src_to_sympy(source_code)
+                    else:
+                        raise ImportError("LFortran is not installed, cannot parse Fortran code")
+                elif mode.lower() == 'c':
+                    if cin:
+                        self._expr = parse_c(source_code)
+                    else:
+                        raise ImportError("Clang is not installed, cannot parse C code")
+                else:
+                    raise NotImplementedError(
+                        'Parser for specified language is not implemented'
+                    )
+            else:
+                raise ValueError('Source code not present')
+        else:
+            raise ValueError('Please specify a mode for conversion')
+
+    def convert_to_expr(self, src_code, mode):
+        """Converts the given source code to SymPy Expressions
+
+        Attributes
+        ==========
+
+        src_code : String
+            the source code or filename of the source code that is to be
+            converted
+
+        mode: String
+            the mode to determine which parser is to be used according to
+            the language of the source code
+            f or F for Fortran
+            c or C for C/C++
+
+        Examples
+        ========
+
+        >>> from sympy.parsing.sym_expr import SymPyExpression
+        >>> src3 = '''
+        ... integer function f(a,b) result(r)
+        ... integer, intent(in) :: a, b
+        ... integer :: x
+        ... r = a + b -x
+        ... end function
+        ... '''
+        >>> p = SymPyExpression()
+        >>> p.convert_to_expr(src3, 'f')
+        >>> p.return_expr()
+        [FunctionDefinition(integer, name=f, parameters=(Variable(a), Variable(b)), body=CodeBlock(
+        Declaration(Variable(r, type=integer, value=0)),
+        Declaration(Variable(x, type=integer, value=0)),
+        Assignment(Variable(r), a + b - x),
+        Return(Variable(r))
+        ))]
+
+
+
+
+        """
+        if mode.lower() == 'f':
+            if lfortran:
+                self._expr = src_to_sympy(src_code)
+            else:
+                raise ImportError("LFortran is not installed, cannot parse Fortran code")
+        elif mode.lower() == 'c':
+            if cin:
+                self._expr = parse_c(src_code)
+            else:
+                raise ImportError("Clang is not installed, cannot parse C code")
+        else:
+            raise NotImplementedError(
+                "Parser for specified language has not been implemented"
+            )
+
+    def convert_to_python(self):
+        """Returns a list with Python code for the SymPy expressions
+
+        Examples
+        ========
+
+        >>> from sympy.parsing.sym_expr import SymPyExpression
+        >>> src2 = '''
+        ... integer :: a, b, c, d
+        ... real :: p, q, r, s
+        ... c = a/b
+        ... d = c/a
+        ... s = p/q
+        ... r = q/p
+        ... '''
+        >>> p = SymPyExpression(src2, 'f')
+        >>> p.convert_to_python()
+        ['a = 0', 'b = 0', 'c = 0', 'd = 0', 'p = 0.0', 'q = 0.0', 'r = 0.0', 's = 0.0', 'c = a/b', 'd = c/a', 's = p/q', 'r = q/p']
+
+        """
+        self._pycode = []
+        for iter in self._expr:
+            self._pycode.append(pycode(iter))
+        return self._pycode
+
+    def convert_to_c(self):
+        """Returns a list with the c source code for the SymPy expressions
+
+
+        Examples
+        ========
+
+        >>> from sympy.parsing.sym_expr import SymPyExpression
+        >>> src2 = '''
+        ... integer :: a, b, c, d
+        ... real :: p, q, r, s
+        ... c = a/b
+        ... d = c/a
+        ... s = p/q
+        ... r = q/p
+        ... '''
+        >>> p = SymPyExpression()
+        >>> p.convert_to_expr(src2, 'f')
+        >>> p.convert_to_c()
+        ['int a = 0', 'int b = 0', 'int c = 0', 'int d = 0', 'double p = 0.0', 'double q = 0.0', 'double r = 0.0', 'double s = 0.0', 'c = a/b;', 'd = c/a;', 's = p/q;', 'r = q/p;']
+
+        """
+        self._ccode = []
+        for iter in self._expr:
+            self._ccode.append(ccode(iter))
+        return self._ccode
+
+    def convert_to_fortran(self):
+        """Returns a list with the fortran source code for the SymPy expressions
+
+        Examples
+        ========
+
+        >>> from sympy.parsing.sym_expr import SymPyExpression
+        >>> src2 = '''
+        ... integer :: a, b, c, d
+        ... real :: p, q, r, s
+        ... c = a/b
+        ... d = c/a
+        ... s = p/q
+        ... r = q/p
+        ... '''
+        >>> p = SymPyExpression(src2, 'f')
+        >>> p.convert_to_fortran()
+        ['      integer*4 a', '      integer*4 b', '      integer*4 c', '      integer*4 d', '      real*8 p', '      real*8 q', '      real*8 r', '      real*8 s', '      c = a/b', '      d = c/a', '      s = p/q', '      r = q/p']
+
+        """
+        self._fcode = []
+        for iter in self._expr:
+            self._fcode.append(fcode(iter))
+        return self._fcode
+
+    def return_expr(self):
+        """Returns the expression list
+
+        Examples
+        ========
+
+        >>> from sympy.parsing.sym_expr import SymPyExpression
+        >>> src3 = '''
+        ... integer function f(a,b)
+        ... integer, intent(in) :: a, b
+        ... integer :: r
+        ... r = a+b
+        ... f = r
+        ... end function
+        ... '''
+        >>> p = SymPyExpression()
+        >>> p.convert_to_expr(src3, 'f')
+        >>> p.return_expr()
+        [FunctionDefinition(integer, name=f, parameters=(Variable(a), Variable(b)), body=CodeBlock(
+        Declaration(Variable(f, type=integer, value=0)),
+        Declaration(Variable(r, type=integer, value=0)),
+        Assignment(Variable(f), Variable(r)),
+        Return(Variable(f))
+        ))]
+
+        """
+        return self._expr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/sympy_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/sympy_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..9cfda9ce0f73ffa3773031c48b9e9c245f69fe0b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/sympy_parser.py
@@ -0,0 +1,1270 @@
+"""Transform a string with Python-like source code into SymPy expression. """
+from __future__ import annotations
+from tokenize import (generate_tokens, untokenize, TokenError,
+    NUMBER, STRING, NAME, OP, ENDMARKER, ERRORTOKEN, NEWLINE)
+
+from keyword import iskeyword
+
+import ast
+import unicodedata
+from io import StringIO
+import builtins
+import types
+from typing import Any, Callable
+from functools import reduce
+from sympy.assumptions.ask import AssumptionKeys
+from sympy.core.basic import Basic
+from sympy.core import Symbol
+from sympy.core.function import Function
+from sympy.utilities.misc import func_name
+from sympy.functions.elementary.miscellaneous import Max, Min
+
+
+null = ''
+
+TOKEN = tuple[int, str]
+DICT = dict[str, Any]
+TRANS = Callable[[list[TOKEN], DICT, DICT], list[TOKEN]]
+
+def _token_splittable(token_name: str) -> bool:
+    """
+    Predicate for whether a token name can be split into multiple tokens.
+
+    A token is splittable if it does not contain an underscore character and
+    it is not the name of a Greek letter. This is used to implicitly convert
+    expressions like 'xyz' into 'x*y*z'.
+    """
+    if '_' in token_name:
+        return False
+    try:
+        return not unicodedata.lookup('GREEK SMALL LETTER ' + token_name)
+    except KeyError:
+        return len(token_name) > 1
+
+
+def _token_callable(token: TOKEN, local_dict: DICT, global_dict: DICT, nextToken=None):
+    """
+    Predicate for whether a token name represents a callable function.
+
+    Essentially wraps ``callable``, but looks up the token name in the
+    locals and globals.
+    """
+    func = local_dict.get(token[1])
+    if not func:
+        func = global_dict.get(token[1])
+    return callable(func) and not isinstance(func, Symbol)
+
+
+def _add_factorial_tokens(name: str, result: list[TOKEN]) -> list[TOKEN]:
+    if result == [] or result[-1][1] == '(':
+        raise TokenError()
+
+    beginning = [(NAME, name), (OP, '(')]
+    end = [(OP, ')')]
+
+    diff = 0
+    length = len(result)
+
+    for index, token in enumerate(result[::-1]):
+        toknum, tokval = token
+        i = length - index - 1
+
+        if tokval == ')':
+            diff += 1
+        elif tokval == '(':
+            diff -= 1
+
+        if diff == 0:
+            if i - 1 >= 0 and result[i - 1][0] == NAME:
+                return result[:i - 1] + beginning + result[i - 1:] + end
+            else:
+                return result[:i] + beginning + result[i:] + end
+
+    return result
+
+
+class ParenthesisGroup(list[TOKEN]):
+    """List of tokens representing an expression in parentheses."""
+    pass
+
+
+class AppliedFunction:
+    """
+    A group of tokens representing a function and its arguments.
+
+    `exponent` is for handling the shorthand sin^2, ln^2, etc.
+    """
+    def __init__(self, function: TOKEN, args: ParenthesisGroup, exponent=None):
+        if exponent is None:
+            exponent = []
+        self.function = function
+        self.args = args
+        self.exponent = exponent
+        self.items = ['function', 'args', 'exponent']
+
+    def expand(self) -> list[TOKEN]:
+        """Return a list of tokens representing the function"""
+        return [self.function, *self.args]
+
+    def __getitem__(self, index):
+        return getattr(self, self.items[index])
+
+    def __repr__(self):
+        return "AppliedFunction(%s, %s, %s)" % (self.function, self.args,
+                                                self.exponent)
+
+
+def _flatten(result: list[TOKEN | AppliedFunction]):
+    result2: list[TOKEN] = []
+    for tok in result:
+        if isinstance(tok, AppliedFunction):
+            result2.extend(tok.expand())
+        else:
+            result2.append(tok)
+    return result2
+
+
+def _group_parentheses(recursor: TRANS):
+    def _inner(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+        """Group tokens between parentheses with ParenthesisGroup.
+
+        Also processes those tokens recursively.
+
+        """
+        result: list[TOKEN | ParenthesisGroup] = []
+        stacks: list[ParenthesisGroup] = []
+        stacklevel = 0
+        for token in tokens:
+            if token[0] == OP:
+                if token[1] == '(':
+                    stacks.append(ParenthesisGroup([]))
+                    stacklevel += 1
+                elif token[1] == ')':
+                    stacks[-1].append(token)
+                    stack = stacks.pop()
+
+                    if len(stacks) > 0:
+                        # We don't recurse here since the upper-level stack
+                        # would reprocess these tokens
+                        stacks[-1].extend(stack)
+                    else:
+                        # Recurse here to handle nested parentheses
+                        # Strip off the outer parentheses to avoid an infinite loop
+                        inner = stack[1:-1]
+                        inner = recursor(inner,
+                                         local_dict,
+                                         global_dict)
+                        parenGroup = [stack[0]] + inner + [stack[-1]]
+                        result.append(ParenthesisGroup(parenGroup))
+                    stacklevel -= 1
+                    continue
+            if stacklevel:
+                stacks[-1].append(token)
+            else:
+                result.append(token)
+        if stacklevel:
+            raise TokenError("Mismatched parentheses")
+        return result
+    return _inner
+
+
+def _apply_functions(tokens: list[TOKEN | ParenthesisGroup], local_dict: DICT, global_dict: DICT):
+    """Convert a NAME token + ParenthesisGroup into an AppliedFunction.
+
+    Note that ParenthesisGroups, if not applied to any function, are
+    converted back into lists of tokens.
+
+    """
+    result: list[TOKEN | AppliedFunction] = []
+    symbol = None
+    for tok in tokens:
+        if isinstance(tok, ParenthesisGroup):
+            if symbol and _token_callable(symbol, local_dict, global_dict):
+                result[-1] = AppliedFunction(symbol, tok)
+                symbol = None
+            else:
+                result.extend(tok)
+        elif tok[0] == NAME:
+            symbol = tok
+            result.append(tok)
+        else:
+            symbol = None
+            result.append(tok)
+    return result
+
+
+def _implicit_multiplication(tokens: list[TOKEN | AppliedFunction], local_dict: DICT, global_dict: DICT):
+    """Implicitly adds '*' tokens.
+
+    Cases:
+
+    - Two AppliedFunctions next to each other ("sin(x)cos(x)")
+
+    - AppliedFunction next to an open parenthesis ("sin x (cos x + 1)")
+
+    - A close parenthesis next to an AppliedFunction ("(x+2)sin x")\
+
+    - A close parenthesis next to an open parenthesis ("(x+2)(x+3)")
+
+    - AppliedFunction next to an implicitly applied function ("sin(x)cos x")
+
+    """
+    result: list[TOKEN | AppliedFunction] = []
+    skip = False
+    for tok, nextTok in zip(tokens, tokens[1:]):
+        result.append(tok)
+        if skip:
+            skip = False
+            continue
+        if tok[0] == OP and tok[1] == '.' and nextTok[0] == NAME:
+            # Dotted name. Do not do implicit multiplication
+            skip = True
+            continue
+        if isinstance(tok, AppliedFunction):
+            if isinstance(nextTok, AppliedFunction):
+                result.append((OP, '*'))
+            elif nextTok == (OP, '('):
+                # Applied function followed by an open parenthesis
+                if tok.function[1] == "Function":
+                    tok.function = (tok.function[0], 'Symbol')
+                result.append((OP, '*'))
+            elif nextTok[0] == NAME:
+                # Applied function followed by implicitly applied function
+                result.append((OP, '*'))
+        else:
+            if tok == (OP, ')'):
+                if isinstance(nextTok, AppliedFunction):
+                    # Close parenthesis followed by an applied function
+                    result.append((OP, '*'))
+                elif nextTok[0] == NAME:
+                    # Close parenthesis followed by an implicitly applied function
+                    result.append((OP, '*'))
+                elif nextTok == (OP, '('):
+                    # Close parenthesis followed by an open parenthesis
+                    result.append((OP, '*'))
+            elif tok[0] == NAME and not _token_callable(tok, local_dict, global_dict):
+                if isinstance(nextTok, AppliedFunction) or \
+                    (nextTok[0] == NAME and _token_callable(nextTok, local_dict, global_dict)):
+                    # Constant followed by (implicitly applied) function
+                    result.append((OP, '*'))
+                elif nextTok == (OP, '('):
+                    # Constant followed by parenthesis
+                    result.append((OP, '*'))
+                elif nextTok[0] == NAME:
+                    # Constant followed by constant
+                    result.append((OP, '*'))
+    if tokens:
+        result.append(tokens[-1])
+    return result
+
+
+def _implicit_application(tokens: list[TOKEN | AppliedFunction], local_dict: DICT, global_dict: DICT):
+    """Adds parentheses as needed after functions."""
+    result: list[TOKEN | AppliedFunction] = []
+    appendParen = 0  # number of closing parentheses to add
+    skip = 0  # number of tokens to delay before adding a ')' (to
+              # capture **, ^, etc.)
+    exponentSkip = False  # skipping tokens before inserting parentheses to
+                          # work with function exponentiation
+    for tok, nextTok in zip(tokens, tokens[1:]):
+        result.append(tok)
+        if (tok[0] == NAME and nextTok[0] not in [OP, ENDMARKER, NEWLINE]):
+            if _token_callable(tok, local_dict, global_dict, nextTok):  # type: ignore
+                result.append((OP, '('))
+                appendParen += 1
+        # name followed by exponent - function exponentiation
+        elif (tok[0] == NAME and nextTok[0] == OP and nextTok[1] == '**'):
+            if _token_callable(tok, local_dict, global_dict):  # type: ignore
+                exponentSkip = True
+        elif exponentSkip:
+            # if the last token added was an applied function (i.e. the
+            # power of the function exponent) OR a multiplication (as
+            # implicit multiplication would have added an extraneous
+            # multiplication)
+            if (isinstance(tok, AppliedFunction)
+                or (tok[0] == OP and tok[1] == '*')):
+                # don't add anything if the next token is a multiplication
+                # or if there's already a parenthesis (if parenthesis, still
+                # stop skipping tokens)
+                if not (nextTok[0] == OP and nextTok[1] == '*'):
+                    if not(nextTok[0] == OP and nextTok[1] == '('):
+                        result.append((OP, '('))
+                        appendParen += 1
+                    exponentSkip = False
+        elif appendParen:
+            if nextTok[0] == OP and nextTok[1] in ('^', '**', '*'):
+                skip = 1
+                continue
+            if skip:
+                skip -= 1
+                continue
+            result.append((OP, ')'))
+            appendParen -= 1
+
+    if tokens:
+        result.append(tokens[-1])
+
+    if appendParen:
+        result.extend([(OP, ')')] * appendParen)
+    return result
+
+
+def function_exponentiation(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Allows functions to be exponentiated, e.g. ``cos**2(x)``.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.sympy_parser import (parse_expr,
+    ... standard_transformations, function_exponentiation)
+    >>> transformations = standard_transformations + (function_exponentiation,)
+    >>> parse_expr('sin**4(x)', transformations=transformations)
+    sin(x)**4
+    """
+    result: list[TOKEN] = []
+    exponent: list[TOKEN] = []
+    consuming_exponent = False
+    level = 0
+    for tok, nextTok in zip(tokens, tokens[1:]):
+        if tok[0] == NAME and nextTok[0] == OP and nextTok[1] == '**':
+            if _token_callable(tok, local_dict, global_dict):
+                consuming_exponent = True
+        elif consuming_exponent:
+            if tok[0] == NAME and tok[1] == 'Function':
+                tok = (NAME, 'Symbol')
+            exponent.append(tok)
+
+            # only want to stop after hitting )
+            if tok[0] == nextTok[0] == OP and tok[1] == ')' and nextTok[1] == '(':
+                consuming_exponent = False
+            # if implicit multiplication was used, we may have )*( instead
+            if tok[0] == nextTok[0] == OP and tok[1] == '*' and nextTok[1] == '(':
+                consuming_exponent = False
+                del exponent[-1]
+            continue
+        elif exponent and not consuming_exponent:
+            if tok[0] == OP:
+                if tok[1] == '(':
+                    level += 1
+                elif tok[1] == ')':
+                    level -= 1
+            if level == 0:
+                result.append(tok)
+                result.extend(exponent)
+                exponent = []
+                continue
+        result.append(tok)
+    if tokens:
+        result.append(tokens[-1])
+    if exponent:
+        result.extend(exponent)
+    return result
+
+
+def split_symbols_custom(predicate: Callable[[str], bool]):
+    """Creates a transformation that splits symbol names.
+
+    ``predicate`` should return True if the symbol name is to be split.
+
+    For instance, to retain the default behavior but avoid splitting certain
+    symbol names, a predicate like this would work:
+
+
+    >>> from sympy.parsing.sympy_parser import (parse_expr, _token_splittable,
+    ... standard_transformations, implicit_multiplication,
+    ... split_symbols_custom)
+    >>> def can_split(symbol):
+    ...     if symbol not in ('list', 'of', 'unsplittable', 'names'):
+    ...             return _token_splittable(symbol)
+    ...     return False
+    ...
+    >>> transformation = split_symbols_custom(can_split)
+    >>> parse_expr('unsplittable', transformations=standard_transformations +
+    ... (transformation, implicit_multiplication))
+    unsplittable
+    """
+    def _split_symbols(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+        result: list[TOKEN] = []
+        split = False
+        split_previous=False
+
+        for tok in tokens:
+            if split_previous:
+                # throw out closing parenthesis of Symbol that was split
+                split_previous=False
+                continue
+            split_previous=False
+
+            if tok[0] == NAME and tok[1] in ['Symbol', 'Function']:
+                split = True
+
+            elif split and tok[0] == NAME:
+                symbol = tok[1][1:-1]
+
+                if predicate(symbol):
+                    tok_type = result[-2][1]  # Symbol or Function
+                    del result[-2:]  # Get rid of the call to Symbol
+
+                    i = 0
+                    while i < len(symbol):
+                        char = symbol[i]
+                        if char in local_dict or char in global_dict:
+                            result.append((NAME, "%s" % char))
+                        elif char.isdigit():
+                            chars = [char]
+                            for i in range(i + 1, len(symbol)):
+                                if not symbol[i].isdigit():
+                                    i -= 1
+                                    break
+                                chars.append(symbol[i])
+                            char = ''.join(chars)
+                            result.extend([(NAME, 'Number'), (OP, '('),
+                                           (NAME, "'%s'" % char), (OP, ')')])
+                        else:
+                            use = tok_type if i == len(symbol) else 'Symbol'
+                            result.extend([(NAME, use), (OP, '('),
+                                           (NAME, "'%s'" % char), (OP, ')')])
+                        i += 1
+
+                    # Set split_previous=True so will skip
+                    # the closing parenthesis of the original Symbol
+                    split = False
+                    split_previous = True
+                    continue
+
+                else:
+                    split = False
+
+            result.append(tok)
+
+        return result
+
+    return _split_symbols
+
+
+#: Splits symbol names for implicit multiplication.
+#:
+#: Intended to let expressions like ``xyz`` be parsed as ``x*y*z``. Does not
+#: split Greek character names, so ``theta`` will *not* become
+#: ``t*h*e*t*a``. Generally this should be used with
+#: ``implicit_multiplication``.
+split_symbols = split_symbols_custom(_token_splittable)
+
+
+def implicit_multiplication(tokens: list[TOKEN], local_dict: DICT,
+                            global_dict: DICT) -> list[TOKEN]:
+    """Makes the multiplication operator optional in most cases.
+
+    Use this before :func:`implicit_application`, otherwise expressions like
+    ``sin 2x`` will be parsed as ``x * sin(2)`` rather than ``sin(2*x)``.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.sympy_parser import (parse_expr,
+    ... standard_transformations, implicit_multiplication)
+    >>> transformations = standard_transformations + (implicit_multiplication,)
+    >>> parse_expr('3 x y', transformations=transformations)
+    3*x*y
+    """
+    # These are interdependent steps, so we don't expose them separately
+    res1 = _group_parentheses(implicit_multiplication)(tokens, local_dict, global_dict)
+    res2 = _apply_functions(res1, local_dict, global_dict)
+    res3 = _implicit_multiplication(res2, local_dict, global_dict)
+    result = _flatten(res3)
+    return result
+
+
+def implicit_application(tokens: list[TOKEN], local_dict: DICT,
+                         global_dict: DICT) -> list[TOKEN]:
+    """Makes parentheses optional in some cases for function calls.
+
+    Use this after :func:`implicit_multiplication`, otherwise expressions
+    like ``sin 2x`` will be parsed as ``x * sin(2)`` rather than
+    ``sin(2*x)``.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.sympy_parser import (parse_expr,
+    ... standard_transformations, implicit_application)
+    >>> transformations = standard_transformations + (implicit_application,)
+    >>> parse_expr('cot z + csc z', transformations=transformations)
+    cot(z) + csc(z)
+    """
+    res1 = _group_parentheses(implicit_application)(tokens, local_dict, global_dict)
+    res2 = _apply_functions(res1, local_dict, global_dict)
+    res3 = _implicit_application(res2, local_dict, global_dict)
+    result = _flatten(res3)
+    return result
+
+
+def implicit_multiplication_application(result: list[TOKEN], local_dict: DICT,
+                                        global_dict: DICT) -> list[TOKEN]:
+    """Allows a slightly relaxed syntax.
+
+    - Parentheses for single-argument method calls are optional.
+
+    - Multiplication is implicit.
+
+    - Symbol names can be split (i.e. spaces are not needed between
+      symbols).
+
+    - Functions can be exponentiated.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.sympy_parser import (parse_expr,
+    ... standard_transformations, implicit_multiplication_application)
+    >>> parse_expr("10sin**2 x**2 + 3xyz + tan theta",
+    ... transformations=(standard_transformations +
+    ... (implicit_multiplication_application,)))
+    3*x*y*z + 10*sin(x**2)**2 + tan(theta)
+
+    """
+    for step in (split_symbols, implicit_multiplication,
+                 implicit_application, function_exponentiation):
+        result = step(result, local_dict, global_dict)
+
+    return result
+
+
+def auto_symbol(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Inserts calls to ``Symbol``/``Function`` for undefined variables."""
+    result: list[TOKEN] = []
+    prevTok = (-1, '')
+
+    tokens.append((-1, ''))  # so zip traverses all tokens
+    for tok, nextTok in zip(tokens, tokens[1:]):
+        tokNum, tokVal = tok
+        nextTokNum, nextTokVal = nextTok
+        if tokNum == NAME:
+            name = tokVal
+
+            if (name in ['True', 'False', 'None']
+                    or iskeyword(name)
+                    # Don't convert attribute access
+                    or (prevTok[0] == OP and prevTok[1] == '.')
+                    # Don't convert keyword arguments
+                    or (prevTok[0] == OP and prevTok[1] in ('(', ',')
+                        and nextTokNum == OP and nextTokVal == '=')
+                    # the name has already been defined
+                    or name in local_dict and local_dict[name] is not null):
+                result.append((NAME, name))
+                continue
+            elif name in local_dict:
+                local_dict.setdefault(null, set()).add(name)
+                if nextTokVal == '(':
+                    local_dict[name] = Function(name)
+                else:
+                    local_dict[name] = Symbol(name)
+                result.append((NAME, name))
+                continue
+            elif name in global_dict:
+                obj = global_dict[name]
+                if isinstance(obj, (AssumptionKeys, Basic, type)) or callable(obj):
+                    result.append((NAME, name))
+                    continue
+
+            result.extend([
+                (NAME, 'Symbol' if nextTokVal != '(' else 'Function'),
+                (OP, '('),
+                (NAME, repr(str(name))),
+                (OP, ')'),
+            ])
+        else:
+            result.append((tokNum, tokVal))
+
+        prevTok = (tokNum, tokVal)
+
+    return result
+
+
+def lambda_notation(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Substitutes "lambda" with its SymPy equivalent Lambda().
+    However, the conversion does not take place if only "lambda"
+    is passed because that is a syntax error.
+
+    """
+    result: list[TOKEN] = []
+    flag = False
+    toknum, tokval = tokens[0]
+    tokLen = len(tokens)
+
+    if toknum == NAME and tokval == 'lambda':
+        if tokLen == 2 or tokLen == 3 and tokens[1][0] == NEWLINE:
+            # In Python 3.6.7+, inputs without a newline get NEWLINE added to
+            # the tokens
+            result.extend(tokens)
+        elif tokLen > 2:
+            result.extend([
+                (NAME, 'Lambda'),
+                (OP, '('),
+                (OP, '('),
+                (OP, ')'),
+                (OP, ')'),
+            ])
+            for tokNum, tokVal in tokens[1:]:
+                if tokNum == OP and tokVal == ':':
+                    tokVal = ','
+                    flag = True
+                if not flag and tokNum == OP and tokVal in ('*', '**'):
+                    raise TokenError("Starred arguments in lambda not supported")
+                if flag:
+                    result.insert(-1, (tokNum, tokVal))
+                else:
+                    result.insert(-2, (tokNum, tokVal))
+    else:
+        result.extend(tokens)
+
+    return result
+
+
+def factorial_notation(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Allows standard notation for factorial."""
+    result: list[TOKEN] = []
+    nfactorial = 0
+    for toknum, tokval in tokens:
+        if toknum == OP and tokval == "!":
+            # In Python 3.12 "!" are OP instead of ERRORTOKEN
+            nfactorial += 1
+        elif toknum == ERRORTOKEN:
+            op = tokval
+            if op == '!':
+                nfactorial += 1
+            else:
+                nfactorial = 0
+                result.append((OP, op))
+        else:
+            if nfactorial == 1:
+                result = _add_factorial_tokens('factorial', result)
+            elif nfactorial == 2:
+                result = _add_factorial_tokens('factorial2', result)
+            elif nfactorial > 2:
+                raise TokenError
+            nfactorial = 0
+            result.append((toknum, tokval))
+    return result
+
+
+def convert_xor(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Treats XOR, ``^``, as exponentiation, ``**``."""
+    result: list[TOKEN] = []
+    for toknum, tokval in tokens:
+        if toknum == OP:
+            if tokval == '^':
+                result.append((OP, '**'))
+            else:
+                result.append((toknum, tokval))
+        else:
+            result.append((toknum, tokval))
+
+    return result
+
+
+def repeated_decimals(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """
+    Allows 0.2[1] notation to represent the repeated decimal 0.2111... (19/90)
+
+    Run this before auto_number.
+
+    """
+    result: list[TOKEN] = []
+
+    def is_digit(s):
+        return all(i in '0123456789_' for i in s)
+
+    # num will running match any DECIMAL [ INTEGER ]
+    num: list[TOKEN] = []
+    for toknum, tokval in tokens:
+        if toknum == NUMBER:
+            if (not num and '.' in tokval and 'e' not in tokval.lower() and
+                'j' not in tokval.lower()):
+                num.append((toknum, tokval))
+            elif is_digit(tokval) and (len(num) == 2 or
+                    len(num) == 3 and is_digit(num[-1][1])):
+                num.append((toknum, tokval))
+            else:
+                num = []
+        elif toknum == OP:
+            if tokval == '[' and len(num) == 1:
+                num.append((OP, tokval))
+            elif tokval == ']' and len(num) >= 3:
+                num.append((OP, tokval))
+            elif tokval == '.' and not num:
+                # handle .[1]
+                num.append((NUMBER, '0.'))
+            else:
+                num = []
+        else:
+            num = []
+
+        result.append((toknum, tokval))
+
+        if num and num[-1][1] == ']':
+            # pre.post[repetend] = a + b/c + d/e where a = pre, b/c = post,
+            # and d/e = repetend
+            result = result[:-len(num)]
+            pre, post = num[0][1].split('.')
+            repetend = num[2][1]
+            if len(num) == 5:
+                repetend += num[3][1]
+
+            pre = pre.replace('_', '')
+            post = post.replace('_', '')
+            repetend = repetend.replace('_', '')
+
+            zeros = '0'*len(post)
+            post, repetends = [w.lstrip('0') for w in [post, repetend]]
+                                        # or else interpreted as octal
+
+            a = pre or '0'
+            b, c = post or '0', '1' + zeros
+            d, e = repetends, ('9'*len(repetend)) + zeros
+
+            seq = [
+                (OP, '('),
+                    (NAME, 'Integer'),
+                    (OP, '('),
+                        (NUMBER, a),
+                    (OP, ')'),
+                    (OP, '+'),
+                    (NAME, 'Rational'),
+                    (OP, '('),
+                        (NUMBER, b),
+                        (OP, ','),
+                        (NUMBER, c),
+                    (OP, ')'),
+                    (OP, '+'),
+                    (NAME, 'Rational'),
+                    (OP, '('),
+                        (NUMBER, d),
+                        (OP, ','),
+                        (NUMBER, e),
+                    (OP, ')'),
+                (OP, ')'),
+            ]
+            result.extend(seq)
+            num = []
+
+    return result
+
+
+def auto_number(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """
+    Converts numeric literals to use SymPy equivalents.
+
+    Complex numbers use ``I``, integer literals use ``Integer``, and float
+    literals use ``Float``.
+
+    """
+    result: list[TOKEN] = []
+
+    for toknum, tokval in tokens:
+        if toknum == NUMBER:
+            number = tokval
+            postfix = []
+
+            if number.endswith(('j', 'J')):
+                number = number[:-1]
+                postfix = [(OP, '*'), (NAME, 'I')]
+
+            if '.' in number or (('e' in number or 'E' in number) and
+                    not (number.startswith(('0x', '0X')))):
+                seq = [(NAME, 'Float'), (OP, '('),
+                    (NUMBER, repr(str(number))), (OP, ')')]
+            else:
+                seq = [(NAME, 'Integer'), (OP, '('), (
+                    NUMBER, number), (OP, ')')]
+
+            result.extend(seq + postfix)
+        else:
+            result.append((toknum, tokval))
+
+    return result
+
+
+def rationalize(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Converts floats into ``Rational``. Run AFTER ``auto_number``."""
+    result: list[TOKEN] = []
+    passed_float = False
+    for toknum, tokval in tokens:
+        if toknum == NAME:
+            if tokval == 'Float':
+                passed_float = True
+                tokval = 'Rational'
+            result.append((toknum, tokval))
+        elif passed_float == True and toknum == NUMBER:
+            passed_float = False
+            result.append((STRING, tokval))
+        else:
+            result.append((toknum, tokval))
+
+    return result
+
+
+def _transform_equals_sign(tokens: list[TOKEN], local_dict: DICT, global_dict: DICT):
+    """Transforms the equals sign ``=`` to instances of Eq.
+
+    This is a helper function for ``convert_equals_signs``.
+    Works with expressions containing one equals sign and no
+    nesting. Expressions like ``(1=2)=False`` will not work with this
+    and should be used with ``convert_equals_signs``.
+
+    Examples: 1=2     to Eq(1,2)
+              1*2=x   to Eq(1*2, x)
+
+    This does not deal with function arguments yet.
+
+    """
+    result: list[TOKEN] = []
+    if (OP, "=") in tokens:
+        result.append((NAME, "Eq"))
+        result.append((OP, "("))
+        for token in tokens:
+            if token == (OP, "="):
+                result.append((OP, ","))
+                continue
+            result.append(token)
+        result.append((OP, ")"))
+    else:
+        result = tokens
+    return result
+
+
+def convert_equals_signs(tokens: list[TOKEN], local_dict: DICT,
+                         global_dict: DICT) -> list[TOKEN]:
+    """ Transforms all the equals signs ``=`` to instances of Eq.
+
+    Parses the equals signs in the expression and replaces them with
+    appropriate Eq instances. Also works with nested equals signs.
+
+    Does not yet play well with function arguments.
+    For example, the expression ``(x=y)`` is ambiguous and can be interpreted
+    as x being an argument to a function and ``convert_equals_signs`` will not
+    work for this.
+
+    See also
+    ========
+    convert_equality_operators
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.sympy_parser import (parse_expr,
+    ... standard_transformations, convert_equals_signs)
+    >>> parse_expr("1*2=x", transformations=(
+    ... standard_transformations + (convert_equals_signs,)))
+    Eq(2, x)
+    >>> parse_expr("(1*2=x)=False", transformations=(
+    ... standard_transformations + (convert_equals_signs,)))
+    Eq(Eq(2, x), False)
+
+    """
+    res1 = _group_parentheses(convert_equals_signs)(tokens, local_dict, global_dict)
+    res2 = _apply_functions(res1, local_dict, global_dict)
+    res3 = _transform_equals_sign(res2, local_dict, global_dict)
+    result = _flatten(res3)
+    return result
+
+
+#: Standard transformations for :func:`parse_expr`.
+#: Inserts calls to :class:`~.Symbol`, :class:`~.Integer`, and other SymPy
+#: datatypes and allows the use of standard factorial notation (e.g. ``x!``).
+standard_transformations: tuple[TRANS, ...] \
+    = (lambda_notation, auto_symbol, repeated_decimals, auto_number,
+       factorial_notation)
+
+
+def stringify_expr(s: str, local_dict: DICT, global_dict: DICT,
+        transformations: tuple[TRANS, ...]) -> str:
+    """
+    Converts the string ``s`` to Python code, in ``local_dict``
+
+    Generally, ``parse_expr`` should be used.
+    """
+
+    tokens = []
+    input_code = StringIO(s.strip())
+    for toknum, tokval, _, _, _ in generate_tokens(input_code.readline):
+        tokens.append((toknum, tokval))
+
+    for transform in transformations:
+        tokens = transform(tokens, local_dict, global_dict)
+
+    return untokenize(tokens)
+
+
+def eval_expr(code, local_dict: DICT, global_dict: DICT):
+    """
+    Evaluate Python code generated by ``stringify_expr``.
+
+    Generally, ``parse_expr`` should be used.
+    """
+    expr = eval(
+        code, global_dict, local_dict)  # take local objects in preference
+    return expr
+
+
+def parse_expr(s: str, local_dict: DICT | None = None,
+               transformations: tuple[TRANS, ...] | str \
+                   = standard_transformations,
+               global_dict: DICT | None = None, evaluate=True):
+    """Converts the string ``s`` to a SymPy expression, in ``local_dict``.
+
+    .. warning::
+        Note that this function uses ``eval``, and thus shouldn't be used on
+        unsanitized input.
+
+    Parameters
+    ==========
+
+    s : str
+        The string to parse.
+
+    local_dict : dict, optional
+        A dictionary of local variables to use when parsing.
+
+    global_dict : dict, optional
+        A dictionary of global variables. By default, this is initialized
+        with ``from sympy import *``; provide this parameter to override
+        this behavior (for instance, to parse ``"Q & S"``).
+
+    transformations : tuple or str
+        A tuple of transformation functions used to modify the tokens of the
+        parsed expression before evaluation. The default transformations
+        convert numeric literals into their SymPy equivalents, convert
+        undefined variables into SymPy symbols, and allow the use of standard
+        mathematical factorial notation (e.g. ``x!``). Selection via
+        string is available (see below).
+
+    evaluate : bool, optional
+        When False, the order of the arguments will remain as they were in the
+        string and automatic simplification that would normally occur is
+        suppressed. (see examples)
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.sympy_parser import parse_expr
+    >>> parse_expr("1/2")
+    1/2
+    >>> type(_)
+    
+    >>> from sympy.parsing.sympy_parser import standard_transformations,\\
+    ... implicit_multiplication_application
+    >>> transformations = (standard_transformations +
+    ...     (implicit_multiplication_application,))
+    >>> parse_expr("2x", transformations=transformations)
+    2*x
+
+    When evaluate=False, some automatic simplifications will not occur:
+
+    >>> parse_expr("2**3"), parse_expr("2**3", evaluate=False)
+    (8, 2**3)
+
+    In addition the order of the arguments will not be made canonical.
+    This feature allows one to tell exactly how the expression was entered:
+
+    >>> a = parse_expr('1 + x', evaluate=False)
+    >>> b = parse_expr('x + 1', evaluate=False)
+    >>> a == b
+    False
+    >>> a.args
+    (1, x)
+    >>> b.args
+    (x, 1)
+
+    Note, however, that when these expressions are printed they will
+    appear the same:
+
+    >>> assert str(a) == str(b)
+
+    As a convenience, transformations can be seen by printing ``transformations``:
+
+    >>> from sympy.parsing.sympy_parser import transformations
+
+    >>> print(transformations)
+    0: lambda_notation
+    1: auto_symbol
+    2: repeated_decimals
+    3: auto_number
+    4: factorial_notation
+    5: implicit_multiplication_application
+    6: convert_xor
+    7: implicit_application
+    8: implicit_multiplication
+    9: convert_equals_signs
+    10: function_exponentiation
+    11: rationalize
+
+    The ``T`` object provides a way to select these transformations:
+
+    >>> from sympy.parsing.sympy_parser import T
+
+    If you print it, you will see the same list as shown above.
+
+    >>> str(T) == str(transformations)
+    True
+
+    Standard slicing will return a tuple of transformations:
+
+    >>> T[:5] == standard_transformations
+    True
+
+    So ``T`` can be used to specify the parsing transformations:
+
+    >>> parse_expr("2x", transformations=T[:5])
+    Traceback (most recent call last):
+    ...
+    SyntaxError: invalid syntax
+    >>> parse_expr("2x", transformations=T[:6])
+    2*x
+    >>> parse_expr('.3', transformations=T[3, 11])
+    3/10
+    >>> parse_expr('.3x', transformations=T[:])
+    3*x/10
+
+    As a further convenience, strings 'implicit' and 'all' can be used
+    to select 0-5 and all the transformations, respectively.
+
+    >>> parse_expr('.3x', transformations='all')
+    3*x/10
+
+    See Also
+    ========
+
+    stringify_expr, eval_expr, standard_transformations,
+    implicit_multiplication_application
+
+    """
+
+    if local_dict is None:
+        local_dict = {}
+    elif not isinstance(local_dict, dict):
+        raise TypeError('expecting local_dict to be a dict')
+    elif null in local_dict:
+        raise ValueError('cannot use "" in local_dict')
+
+    if global_dict is None:
+        global_dict = {}
+        exec('from sympy import *', global_dict)
+
+        builtins_dict = vars(builtins)
+        for name, obj in builtins_dict.items():
+            if isinstance(obj, types.BuiltinFunctionType):
+                global_dict[name] = obj
+        global_dict['max'] = Max
+        global_dict['min'] = Min
+
+    elif not isinstance(global_dict, dict):
+        raise TypeError('expecting global_dict to be a dict')
+
+    transformations = transformations or ()
+    if isinstance(transformations, str):
+        if transformations == 'all':
+            _transformations = T[:]
+        elif transformations == 'implicit':
+            _transformations = T[:6]
+        else:
+            raise ValueError('unknown transformation group name')
+    else:
+        _transformations = transformations
+
+    code = stringify_expr(s, local_dict, global_dict, _transformations)
+
+    if not evaluate:
+        code = compile(evaluateFalse(code), '', 'eval') # type: ignore
+
+    try:
+        rv = eval_expr(code, local_dict, global_dict)
+        # restore neutral definitions for names
+        for i in local_dict.pop(null, ()):
+            local_dict[i] = null
+        return rv
+    except Exception as e:
+        # restore neutral definitions for names
+        for i in local_dict.pop(null, ()):
+            local_dict[i] = null
+        raise e from ValueError(f"Error from parse_expr with transformed code: {code!r}")
+
+
+def evaluateFalse(s: str):
+    """
+    Replaces operators with the SymPy equivalent and sets evaluate=False.
+    """
+    node = ast.parse(s)
+    transformed_node = EvaluateFalseTransformer().visit(node)
+    # node is a Module, we want an Expression
+    transformed_node = ast.Expression(transformed_node.body[0].value)
+
+    return ast.fix_missing_locations(transformed_node)
+
+
+class EvaluateFalseTransformer(ast.NodeTransformer):
+    operators = {
+        ast.Add: 'Add',
+        ast.Mult: 'Mul',
+        ast.Pow: 'Pow',
+        ast.Sub: 'Add',
+        ast.Div: 'Mul',
+        ast.BitOr: 'Or',
+        ast.BitAnd: 'And',
+        ast.BitXor: 'Not',
+    }
+    functions = (
+        'Abs', 'im', 're', 'sign', 'arg', 'conjugate',
+        'acos', 'acot', 'acsc', 'asec', 'asin', 'atan',
+        'acosh', 'acoth', 'acsch', 'asech', 'asinh', 'atanh',
+        'cos', 'cot', 'csc', 'sec', 'sin', 'tan',
+        'cosh', 'coth', 'csch', 'sech', 'sinh', 'tanh',
+        'exp', 'ln', 'log', 'sqrt', 'cbrt',
+    )
+
+    relational_operators = {
+        ast.NotEq: 'Ne',
+        ast.Lt: 'Lt',
+        ast.LtE: 'Le',
+        ast.Gt: 'Gt',
+        ast.GtE: 'Ge',
+        ast.Eq: 'Eq'
+    }
+    def visit_Compare(self, node):
+        def reducer(acc, op_right):
+            result, left = acc
+            op, right = op_right
+            if op.__class__ not in self.relational_operators:
+                raise ValueError("Only equation or inequality operators are supported")
+            new = ast.Call(
+                func=ast.Name(
+                    id=self.relational_operators[op.__class__], ctx=ast.Load()
+                ),
+                args=[self.visit(left), self.visit(right)],
+                keywords=[ast.keyword(arg="evaluate", value=ast.Constant(value=False))],
+            )
+            return result + [new], right
+
+        args, _ = reduce(
+            reducer, zip(node.ops, node.comparators), ([], node.left)
+        )
+        if len(args) == 1:
+            return args[0]
+        return ast.Call(
+            func=ast.Name(id=self.operators[ast.BitAnd], ctx=ast.Load()),
+            args=args,
+            keywords=[ast.keyword(arg="evaluate", value=ast.Constant(value=False))],
+        )
+
+    def flatten(self, args, func):
+        result = []
+        for arg in args:
+            if isinstance(arg, ast.Call):
+                arg_func = arg.func
+                if isinstance(arg_func, ast.Call):
+                    arg_func = arg_func.func
+                if arg_func.id == func:
+                    result.extend(self.flatten(arg.args, func))
+                else:
+                    result.append(arg)
+            else:
+                result.append(arg)
+        return result
+
+    def visit_BinOp(self, node):
+        if node.op.__class__ in self.operators:
+            sympy_class = self.operators[node.op.__class__]
+            right = self.visit(node.right)
+            left = self.visit(node.left)
+
+            rev = False
+            if isinstance(node.op, ast.Sub):
+                right = ast.Call(
+                    func=ast.Name(id='Mul', ctx=ast.Load()),
+                    args=[ast.UnaryOp(op=ast.USub(), operand=ast.Constant(1)), right],
+                    keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))]
+                )
+            elif isinstance(node.op, ast.Div):
+                if isinstance(node.left, ast.UnaryOp):
+                    left, right = right, left
+                    rev = True
+                    left = ast.Call(
+                    func=ast.Name(id='Pow', ctx=ast.Load()),
+                    args=[left, ast.UnaryOp(op=ast.USub(), operand=ast.Constant(1))],
+                    keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))]
+                )
+                else:
+                    right = ast.Call(
+                    func=ast.Name(id='Pow', ctx=ast.Load()),
+                    args=[right, ast.UnaryOp(op=ast.USub(), operand=ast.Constant(1))],
+                    keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))]
+                )
+
+            if rev:  # undo reversal
+                left, right = right, left
+            new_node = ast.Call(
+                func=ast.Name(id=sympy_class, ctx=ast.Load()),
+                args=[left, right],
+                keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))]
+            )
+
+            if sympy_class in ('Add', 'Mul'):
+                # Denest Add or Mul as appropriate
+                new_node.args = self.flatten(new_node.args, sympy_class)
+
+            return new_node
+        return node
+
+    def visit_Call(self, node):
+        new_node = self.generic_visit(node)
+        if isinstance(node.func, ast.Name) and node.func.id in self.functions:
+            new_node.keywords.append(ast.keyword(arg='evaluate', value=ast.Constant(value=False)))
+        return new_node
+
+
+_transformation = {  # items can be added but never re-ordered
+0: lambda_notation,
+1: auto_symbol,
+2: repeated_decimals,
+3: auto_number,
+4: factorial_notation,
+5: implicit_multiplication_application,
+6: convert_xor,
+7: implicit_application,
+8: implicit_multiplication,
+9: convert_equals_signs,
+10: function_exponentiation,
+11: rationalize}
+
+transformations = '\n'.join('%s: %s' % (i, func_name(f)) for i, f in _transformation.items())
+
+
+class _T():
+    """class to retrieve transformations from a given slice
+
+    EXAMPLES
+    ========
+
+    >>> from sympy.parsing.sympy_parser import T, standard_transformations
+    >>> assert T[:5] == standard_transformations
+    """
+    def __init__(self):
+        self.N = len(_transformation)
+
+    def __str__(self):
+        return transformations
+
+    def __getitem__(self, t):
+        if not type(t) is tuple:
+            t = (t,)
+        i = []
+        for ti in t:
+            if type(ti) is int:
+                i.append(range(self.N)[ti])
+            elif type(ti) is slice:
+                i.extend(range(*ti.indices(self.N)))
+            else:
+                raise TypeError('unexpected slice arg')
+        return tuple([_transformation[_] for _ in i])
+
+T = _T()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_ast_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_ast_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..24572190df72f9be11b5830355b0d6b9e3bb53ad
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_ast_parser.py
@@ -0,0 +1,25 @@
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.parsing.ast_parser import parse_expr
+from sympy.testing.pytest import raises
+from sympy.core.sympify import SympifyError
+import warnings
+
+def test_parse_expr():
+    a, b = symbols('a, b')
+    # tests issue_16393
+    assert parse_expr('a + b', {}) == a + b
+    raises(SympifyError, lambda: parse_expr('a + ', {}))
+
+    # tests Transform.visit_Constant
+    assert parse_expr('1 + 2', {}) == S(3)
+    assert parse_expr('1 + 2.0', {}) == S(3.0)
+
+    # tests Transform.visit_Name
+    assert parse_expr('Rational(1, 2)', {}) == S(1)/2
+    assert parse_expr('a', {'a': a}) == a
+
+    # tests issue_23092
+    with warnings.catch_warnings():
+        warnings.simplefilter('error')
+        assert parse_expr('6 * 7', {}) == S(42)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_autolev.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_autolev.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfcaef13565c5e2187dc6e90113b407a7967c331
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_autolev.py
@@ -0,0 +1,178 @@
+import os
+
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+from sympy.parsing.autolev import parse_autolev
+
+antlr4 = import_module("antlr4")
+
+if not antlr4:
+    disabled = True
+
+FILE_DIR = os.path.dirname(
+    os.path.dirname(os.path.abspath(os.path.realpath(__file__))))
+
+
+def _test_examples(in_filename, out_filename, test_name=""):
+
+    in_file_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                                in_filename)
+    correct_file_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                                     out_filename)
+    with open(in_file_path) as f:
+        generated_code = parse_autolev(f, include_numeric=True)
+
+    with open(correct_file_path) as f:
+        for idx, line1 in enumerate(f):
+            if line1.startswith("#"):
+                break
+            try:
+                line2 = generated_code.split('\n')[idx]
+                assert line1.rstrip() == line2.rstrip()
+            except Exception:
+                msg = 'mismatch in ' + test_name + ' in line no: {0}'
+                raise AssertionError(msg.format(idx+1))
+
+
+def test_rule_tests():
+
+    l = ["ruletest1", "ruletest2", "ruletest3", "ruletest4", "ruletest5",
+         "ruletest6", "ruletest7", "ruletest8", "ruletest9", "ruletest10",
+         "ruletest11", "ruletest12"]
+
+    for i in l:
+        in_filepath = i + ".al"
+        out_filepath = i + ".py"
+        _test_examples(in_filepath, out_filepath, i)
+
+
+def test_pydy_examples():
+
+    l = ["mass_spring_damper", "chaos_pendulum", "double_pendulum",
+         "non_min_pendulum"]
+
+    for i in l:
+        in_filepath = os.path.join("pydy-example-repo", i + ".al")
+        out_filepath = os.path.join("pydy-example-repo", i + ".py")
+        _test_examples(in_filepath, out_filepath, i)
+
+
+def test_autolev_tutorial():
+
+    dir_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                            'autolev-tutorial')
+
+    if os.path.isdir(dir_path):
+        l = ["tutor1", "tutor2", "tutor3", "tutor4", "tutor5", "tutor6",
+             "tutor7"]
+        for i in l:
+            in_filepath = os.path.join("autolev-tutorial", i + ".al")
+            out_filepath = os.path.join("autolev-tutorial", i + ".py")
+            _test_examples(in_filepath, out_filepath, i)
+
+
+def test_dynamics_online():
+
+    dir_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                            'dynamics-online')
+
+    if os.path.isdir(dir_path):
+        ch1 = ["1-4", "1-5", "1-6", "1-7", "1-8", "1-9_1", "1-9_2", "1-9_3"]
+        ch2 = ["2-1", "2-2", "2-3", "2-4", "2-5", "2-6", "2-7", "2-8", "2-9",
+               "circular"]
+        ch3 = ["3-1_1", "3-1_2", "3-2_1", "3-2_2", "3-2_3", "3-2_4", "3-2_5",
+               "3-3"]
+        ch4 = ["4-1_1", "4-2_1", "4-4_1", "4-4_2", "4-5_1", "4-5_2"]
+        chapters = [(ch1, "ch1"), (ch2, "ch2"), (ch3, "ch3"), (ch4, "ch4")]
+        for ch, name in chapters:
+            for i in ch:
+                in_filepath = os.path.join("dynamics-online", name, i + ".al")
+                out_filepath = os.path.join("dynamics-online", name, i + ".py")
+                _test_examples(in_filepath, out_filepath, i)
+
+
+def test_output_01():
+    """Autolev example calculates the position, velocity, and acceleration of a
+    point and expresses in a single reference frame::
+
+          (1) FRAMES C,D,F
+          (2) VARIABLES FD'',DC''
+          (3) CONSTANTS R,L
+          (4) POINTS O,E
+          (5) SIMPROT(F,D,1,FD)
+       -> (6) F_D = [1, 0, 0; 0, COS(FD), -SIN(FD); 0, SIN(FD), COS(FD)]
+          (7) SIMPROT(D,C,2,DC)
+       -> (8) D_C = [COS(DC), 0, SIN(DC); 0, 1, 0; -SIN(DC), 0, COS(DC)]
+          (9) W_C_F> = EXPRESS(W_C_F>, F)
+       -> (10) W_C_F> = FD'*F1> + COS(FD)*DC'*F2> + SIN(FD)*DC'*F3>
+          (11) P_O_E>=R*D2>-L*C1>
+          (12) P_O_E>=EXPRESS(P_O_E>, D)
+       -> (13) P_O_E> = -L*COS(DC)*D1> + R*D2> + L*SIN(DC)*D3>
+          (14) V_E_F>=EXPRESS(DT(P_O_E>,F),D)
+       -> (15) V_E_F> = L*SIN(DC)*DC'*D1> - L*SIN(DC)*FD'*D2> + (R*FD'+L*COS(DC)*DC')*D3>
+          (16) A_E_F>=EXPRESS(DT(V_E_F>,F),D)
+       -> (17) A_E_F> = L*(COS(DC)*DC'^2+SIN(DC)*DC'')*D1> + (-R*FD'^2-2*L*COS(DC)*DC'*FD'-L*SIN(DC)*FD'')*D2> + (R*FD''+L*COS(DC)*DC''-L*SIN(DC)*DC'^2-L*SIN(DC)*FD'^2)*D3>
+
+    """
+
+    if not antlr4:
+        skip('Test skipped: antlr4 is not installed.')
+
+    autolev_input = """\
+FRAMES C,D,F
+VARIABLES FD'',DC''
+CONSTANTS R,L
+POINTS O,E
+SIMPROT(F,D,1,FD)
+SIMPROT(D,C,2,DC)
+W_C_F>=EXPRESS(W_C_F>,F)
+P_O_E>=R*D2>-L*C1>
+P_O_E>=EXPRESS(P_O_E>,D)
+V_E_F>=EXPRESS(DT(P_O_E>,F),D)
+A_E_F>=EXPRESS(DT(V_E_F>,F),D)\
+"""
+
+    sympy_input = parse_autolev(autolev_input)
+
+    g = {}
+    l = {}
+    exec(sympy_input, g, l)
+
+    w_c_f = l['frame_c'].ang_vel_in(l['frame_f'])
+    # P_O_E> means "the position of point E wrt to point O"
+    p_o_e = l['point_e'].pos_from(l['point_o'])
+    v_e_f = l['point_e'].vel(l['frame_f'])
+    a_e_f = l['point_e'].acc(l['frame_f'])
+
+    # NOTE : The Autolev outputs above were manually transformed into
+    # equivalent SymPy physics vector expressions. Would be nice to automate
+    # this transformation.
+    expected_w_c_f = (l['fd'].diff()*l['frame_f'].x +
+                      cos(l['fd'])*l['dc'].diff()*l['frame_f'].y +
+                      sin(l['fd'])*l['dc'].diff()*l['frame_f'].z)
+
+    assert (w_c_f - expected_w_c_f).simplify() == 0
+
+    expected_p_o_e = (-l['l']*cos(l['dc'])*l['frame_d'].x +
+                      l['r']*l['frame_d'].y +
+                      l['l']*sin(l['dc'])*l['frame_d'].z)
+
+    assert (p_o_e - expected_p_o_e).simplify() == 0
+
+    expected_v_e_f = (l['l']*sin(l['dc'])*l['dc'].diff()*l['frame_d'].x -
+                      l['l']*sin(l['dc'])*l['fd'].diff()*l['frame_d'].y +
+                      (l['r']*l['fd'].diff() +
+                       l['l']*cos(l['dc'])*l['dc'].diff())*l['frame_d'].z)
+    assert (v_e_f - expected_v_e_f).simplify() == 0
+
+    expected_a_e_f = (l['l']*(cos(l['dc'])*l['dc'].diff()**2 +
+                              sin(l['dc'])*l['dc'].diff().diff())*l['frame_d'].x +
+                      (-l['r']*l['fd'].diff()**2 -
+                       2*l['l']*cos(l['dc'])*l['dc'].diff()*l['fd'].diff() -
+                       l['l']*sin(l['dc'])*l['fd'].diff().diff())*l['frame_d'].y +
+                      (l['r']*l['fd'].diff().diff() +
+                       l['l']*cos(l['dc'])*l['dc'].diff().diff() -
+                       l['l']*sin(l['dc'])*l['dc'].diff()**2 -
+                       l['l']*sin(l['dc'])*l['fd'].diff()**2)*l['frame_d'].z)
+    assert (a_e_f - expected_a_e_f).simplify() == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_c_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_c_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..b74622e40030cba180cb4fc354216ccca119baec
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_c_parser.py
@@ -0,0 +1,5248 @@
+from sympy.parsing.sym_expr import SymPyExpression
+from sympy.testing.pytest import raises, XFAIL
+from sympy.external import import_module
+
+cin = import_module('clang.cindex', import_kwargs = {'fromlist': ['cindex']})
+
+if cin:
+    from sympy.codegen.ast import (Variable, String, Return,
+        FunctionDefinition, Integer, Float, Declaration, CodeBlock,
+        FunctionPrototype, FunctionCall, NoneToken, Assignment, Type,
+        IntBaseType, SignedIntType, UnsignedIntType, FloatType,
+        AddAugmentedAssignment, SubAugmentedAssignment,
+        MulAugmentedAssignment, DivAugmentedAssignment,
+        ModAugmentedAssignment, While)
+    from sympy.codegen.cnodes import (PreDecrement, PostDecrement,
+        PreIncrement, PostIncrement)
+    from sympy.core import (Add, Mul, Mod, Pow, Rational,
+        StrictLessThan, LessThan, StrictGreaterThan, GreaterThan,
+        Equality, Unequality)
+    from sympy.logic.boolalg import And, Not, Or
+    from sympy.core.symbol import Symbol
+    from sympy.logic.boolalg import (false, true)
+    import os
+
+    def test_variable():
+        c_src1 = (
+            'int a;' + '\n' +
+            'int b;' + '\n'
+        )
+        c_src2 = (
+            'float a;' + '\n'
+            + 'float b;' + '\n'
+        )
+        c_src3 = (
+            'int a;' + '\n' +
+            'float b;' + '\n' +
+            'int c;'
+        )
+        c_src4 = (
+            'int x = 1, y = 6.78;' + '\n' +
+            'float p = 2, q = 9.67;'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+
+        assert res1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+
+        assert res1[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+
+        assert res2[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+            )
+        )
+        assert res2[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+            )
+        )
+
+        assert res3[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+
+        assert res3[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+            )
+        )
+
+        assert res3[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+
+        assert res4[0] == Declaration(
+            Variable(
+                Symbol('x'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+            )
+        )
+
+        assert res4[1] == Declaration(
+            Variable(
+                Symbol('y'),
+                type=IntBaseType(String('intc')),
+                value=Integer(6)
+            )
+        )
+
+        assert res4[2] == Declaration(
+            Variable(
+                Symbol('p'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.0', precision=53)
+            )
+        )
+
+        assert res4[3] == Declaration(
+            Variable(
+                Symbol('q'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('9.67', precision=53)
+            )
+        )
+
+
+    def test_int():
+        c_src1 = 'int a = 1;'
+        c_src2 = (
+            'int a = 1;' + '\n' +
+            'int b = 2;' + '\n'
+        )
+        c_src3 = 'int a = 2.345, b = 5.67;'
+        c_src4 = 'int p = 6, q = 23.45;'
+        c_src5 = "int x = '0', y = 'a';"
+        c_src6 = "int r = true, s = false;"
+
+        # cin.TypeKind.UCHAR
+        c_src_type1 = (
+            "signed char a = 1, b = 5.1;"
+            )
+
+        # cin.TypeKind.SHORT
+        c_src_type2 = (
+            "short a = 1, b = 5.1;"
+            "signed short c = 1, d = 5.1;"
+            "short int e = 1, f = 5.1;"
+            "signed short int g = 1, h = 5.1;"
+            )
+
+        # cin.TypeKind.INT
+        c_src_type3 = (
+            "signed int a = 1, b = 5.1;"
+            "int c = 1, d = 5.1;"
+            )
+
+        # cin.TypeKind.LONG
+        c_src_type4 = (
+            "long a = 1, b = 5.1;"
+            "long int c = 1, d = 5.1;"
+            )
+
+        # cin.TypeKind.UCHAR
+        c_src_type5 = "unsigned char a = 1, b = 5.1;"
+
+        # cin.TypeKind.USHORT
+        c_src_type6 = (
+            "unsigned short a = 1, b = 5.1;"
+            "unsigned short int c = 1, d = 5.1;"
+            )
+
+        # cin.TypeKind.UINT
+        c_src_type7 = "unsigned int a = 1, b = 5.1;"
+
+        # cin.TypeKind.ULONG
+        c_src_type8 = (
+            "unsigned long a = 1, b = 5.1;"
+            "unsigned long int c = 1, d = 5.1;"
+            )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+        res5 = SymPyExpression(c_src5, 'c').return_expr()
+        res6 = SymPyExpression(c_src6, 'c').return_expr()
+
+        res_type1 = SymPyExpression(c_src_type1, 'c').return_expr()
+        res_type2 = SymPyExpression(c_src_type2, 'c').return_expr()
+        res_type3 = SymPyExpression(c_src_type3, 'c').return_expr()
+        res_type4 = SymPyExpression(c_src_type4, 'c').return_expr()
+        res_type5 = SymPyExpression(c_src_type5, 'c').return_expr()
+        res_type6 = SymPyExpression(c_src_type6, 'c').return_expr()
+        res_type7 = SymPyExpression(c_src_type7, 'c').return_expr()
+        res_type8 = SymPyExpression(c_src_type8, 'c').return_expr()
+
+        assert res1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+            )
+        )
+
+        assert res2[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+            )
+        )
+
+        assert res2[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+            )
+        )
+
+        assert res3[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+            )
+        )
+
+        assert res3[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(5)
+            )
+        )
+
+        assert res4[0] == Declaration(
+            Variable(
+                Symbol('p'),
+                type=IntBaseType(String('intc')),
+                value=Integer(6)
+            )
+        )
+
+        assert res4[1] == Declaration(
+            Variable(
+                Symbol('q'),
+                type=IntBaseType(String('intc')),
+                value=Integer(23)
+            )
+        )
+
+        assert res5[0] == Declaration(
+            Variable(
+                Symbol('x'),
+                type=IntBaseType(String('intc')),
+                value=Integer(48)
+            )
+        )
+
+        assert res5[1] == Declaration(
+            Variable(
+                Symbol('y'),
+                type=IntBaseType(String('intc')),
+                value=Integer(97)
+            )
+        )
+
+        assert res6[0] == Declaration(
+            Variable(
+                Symbol('r'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+            )
+        )
+
+        assert res6[1] == Declaration(
+            Variable(
+                Symbol('s'),
+                type=IntBaseType(String('intc')),
+                value=Integer(0)
+            )
+        )
+
+        assert res_type1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=SignedIntType(
+                    String('int8'),
+                    nbits=Integer(8)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type1[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=SignedIntType(
+                    String('int8'),
+                    nbits=Integer(8)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type2[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type2[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type2[2] == Declaration(
+            Variable(Symbol('c'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type2[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type2[4] == Declaration(
+            Variable(
+                Symbol('e'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type2[5] == Declaration(
+            Variable(
+                Symbol('f'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type2[6] == Declaration(
+            Variable(
+                Symbol('g'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type2[7] == Declaration(
+            Variable(
+                Symbol('h'),
+                type=SignedIntType(
+                    String('int16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type3[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type3[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type3[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type3[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=IntBaseType(String('intc')),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type4[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=SignedIntType(
+                    String('int64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type4[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=SignedIntType(
+                    String('int64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type4[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=SignedIntType(
+                    String('int64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type4[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=SignedIntType(
+                    String('int64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type5[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=UnsignedIntType(
+                    String('uint8'),
+                    nbits=Integer(8)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type5[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=UnsignedIntType(
+                    String('uint8'),
+                    nbits=Integer(8)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type6[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=UnsignedIntType(
+                    String('uint16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type6[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=UnsignedIntType(
+                    String('uint16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type6[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=UnsignedIntType(
+                    String('uint16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type6[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=UnsignedIntType(
+                    String('uint16'),
+                    nbits=Integer(16)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type7[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=UnsignedIntType(
+                    String('uint32'),
+                    nbits=Integer(32)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type7[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=UnsignedIntType(
+                    String('uint32'),
+                    nbits=Integer(32)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type8[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=UnsignedIntType(
+                    String('uint64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type8[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=UnsignedIntType(
+                    String('uint64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+        assert res_type8[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=UnsignedIntType(
+                    String('uint64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(1)
+                )
+            )
+
+        assert res_type8[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=UnsignedIntType(
+                    String('uint64'),
+                    nbits=Integer(64)
+                    ),
+                value=Integer(5)
+                )
+            )
+
+
+    def test_float():
+        c_src1 = 'float a = 1.0;'
+        c_src2 = (
+            'float a = 1.25;' + '\n' +
+            'float b = 2.39;' + '\n'
+        )
+        c_src3 = 'float x = 1, y = 2;'
+        c_src4 = 'float p = 5, e = 7.89;'
+        c_src5 = 'float r = true, s = false;'
+
+        # cin.TypeKind.FLOAT
+        c_src_type1 = 'float x = 1, y = 2.5;'
+
+        # cin.TypeKind.DOUBLE
+        c_src_type2 = 'double x = 1, y = 2.5;'
+
+        # cin.TypeKind.LONGDOUBLE
+        c_src_type3 = 'long double x = 1, y = 2.5;'
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+        res5 = SymPyExpression(c_src5, 'c').return_expr()
+
+        res_type1 = SymPyExpression(c_src_type1, 'c').return_expr()
+        res_type2 = SymPyExpression(c_src_type2, 'c').return_expr()
+        res_type3 = SymPyExpression(c_src_type3, 'c').return_expr()
+
+        assert res1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.0', precision=53)
+                )
+            )
+
+        assert res2[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.25', precision=53)
+            )
+        )
+
+        assert res2[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.3900000000000001', precision=53)
+            )
+        )
+
+        assert res3[0] == Declaration(
+            Variable(
+                Symbol('x'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.0', precision=53)
+            )
+        )
+
+        assert res3[1] == Declaration(
+            Variable(
+                Symbol('y'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.0', precision=53)
+            )
+        )
+
+        assert res4[0] == Declaration(
+            Variable(
+                Symbol('p'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                ),
+                value=Float('5.0', precision=53)
+            )
+        )
+
+        assert res4[1] == Declaration(
+            Variable(
+                Symbol('e'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('7.89', precision=53)
+            )
+        )
+
+        assert res5[0] == Declaration(
+            Variable(
+                Symbol('r'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.0', precision=53)
+            )
+        )
+
+        assert res5[1] == Declaration(
+            Variable(
+                Symbol('s'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('0.0', precision=53)
+            )
+        )
+
+        assert res_type1[0] == Declaration(
+            Variable(
+                Symbol('x'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.0', precision=53)
+                )
+            )
+
+        assert res_type1[1] == Declaration(
+            Variable(
+                Symbol('y'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.5', precision=53)
+                )
+            )
+        assert res_type2[0] == Declaration(
+            Variable(
+                Symbol('x'),
+                type=FloatType(
+                    String('float64'),
+                    nbits=Integer(64),
+                    nmant=Integer(52),
+                    nexp=Integer(11)
+                    ),
+                value=Float('1.0', precision=53)
+                )
+            )
+
+        assert res_type2[1] == Declaration(
+            Variable(
+                Symbol('y'),
+                type=FloatType(
+                    String('float64'),
+                    nbits=Integer(64),
+                    nmant=Integer(52),
+                    nexp=Integer(11)
+                    ),
+                value=Float('2.5', precision=53)
+                )
+            )
+
+        assert res_type3[0] == Declaration(
+            Variable(
+                Symbol('x'),
+                type=FloatType(
+                    String('float80'),
+                    nbits=Integer(80),
+                    nmant=Integer(63),
+                    nexp=Integer(15)
+                    ),
+                value=Float('1.0', precision=53)
+                )
+            )
+
+        assert res_type3[1] == Declaration(
+            Variable(
+                Symbol('y'),
+                type=FloatType(
+                    String('float80'),
+                    nbits=Integer(80),
+                    nmant=Integer(63),
+                    nexp=Integer(15)
+                    ),
+                value=Float('2.5', precision=53)
+                )
+            )
+
+
+    def test_bool():
+        c_src1 = (
+            'bool a = true, b = false;'
+        )
+
+        c_src2 = (
+            'bool a = 1, b = 0;'
+        )
+
+        c_src3 = (
+            'bool a = 10, b = 20;'
+        )
+
+        c_src4 = (
+            'bool a = 19.1, b = 9.0, c = 0.0;'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+
+        assert res1[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res1[1] == Declaration(
+            Variable(Symbol('b'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res2[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=true)
+            )
+
+        assert res2[1] == Declaration(
+            Variable(Symbol('b'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res3[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res3[1] == Declaration(
+            Variable(Symbol('b'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res4[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=true)
+            )
+
+        assert res4[1] == Declaration(
+            Variable(Symbol('b'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res4[2] == Declaration(
+            Variable(Symbol('c'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+    @XFAIL # this is expected to fail because of a bug in the C parser.
+    def test_function():
+        c_src1 = (
+            'void fun1()' + '\n' +
+            '{' + '\n' +
+            'int a;' + '\n' +
+            '}'
+        )
+        c_src2 = (
+            'int fun2()' + '\n' +
+            '{'+ '\n' +
+            'int a;' + '\n' +
+            'return a;' + '\n' +
+            '}'
+        )
+        c_src3 = (
+            'float fun3()' + '\n' +
+            '{' + '\n' +
+            'float b;' + '\n' +
+            'return b;' + '\n' +
+            '}'
+        )
+        c_src4 = (
+            'float fun4()' + '\n' +
+            '{}'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+
+        assert res1[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('fun1'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                    )
+                )
+            )
+        )
+
+        assert res2[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun2'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                    )
+                ),
+                Return('a')
+            )
+        )
+
+        assert res3[0] == FunctionDefinition(
+            FloatType(
+                String('float32'),
+                nbits=Integer(32),
+                nmant=Integer(23),
+                nexp=Integer(8)
+                ),
+            name=String('fun3'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('b'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                    )
+                ),
+                Return('b')
+            )
+        )
+
+        assert res4[0] == FunctionPrototype(
+            FloatType(
+                String('float32'),
+                nbits=Integer(32),
+                nmant=Integer(23),
+                nexp=Integer(8)
+                ),
+            name=String('fun4'),
+            parameters=()
+        )
+
+    @XFAIL # this is expected to fail because of a bug in the C parser.
+    def test_parameters():
+        c_src1 = (
+            'void fun1( int a)' + '\n' +
+            '{' + '\n' +
+            'int i;' + '\n' +
+            '}'
+        )
+        c_src2 = (
+            'int fun2(float x, float y)' + '\n' +
+            '{'+ '\n' +
+            'int a;' + '\n' +
+            'return a;' + '\n' +
+            '}'
+        )
+        c_src3 = (
+            'float fun3(int p, float q, int r)' + '\n' +
+            '{' + '\n' +
+            'float b;' + '\n' +
+            'return b;' + '\n' +
+            '}'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+
+        assert res1[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('fun1'),
+            parameters=(
+                Variable(
+                    Symbol('a'),
+                    type=IntBaseType(String('intc'))
+                ),
+            ),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('i'),
+                        type=IntBaseType(String('intc'))
+                    )
+                )
+            )
+        )
+
+        assert res2[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun2'),
+            parameters=(
+                Variable(
+                    Symbol('x'),
+                    type=FloatType(
+                        String('float32'),
+                        nbits=Integer(32),
+                        nmant=Integer(23),
+                        nexp=Integer(8)
+                        )
+                ),
+                Variable(
+                    Symbol('y'),
+                    type=FloatType(
+                        String('float32'),
+                        nbits=Integer(32),
+                        nmant=Integer(23),
+                        nexp=Integer(8)
+                        )
+                )
+            ),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                    )
+                ),
+                Return('a')
+            )
+        )
+
+        assert res3[0] == FunctionDefinition(
+            FloatType(
+                String('float32'),
+                nbits=Integer(32),
+                nmant=Integer(23),
+                nexp=Integer(8)
+                ),
+            name=String('fun3'),
+            parameters=(
+                Variable(
+                    Symbol('p'),
+                    type=IntBaseType(String('intc'))
+                ),
+                Variable(
+                    Symbol('q'),
+                    type=FloatType(
+                        String('float32'),
+                        nbits=Integer(32),
+                        nmant=Integer(23),
+                        nexp=Integer(8)
+                        )
+                ),
+                Variable(
+                    Symbol('r'),
+                    type=IntBaseType(String('intc'))
+                )
+            ),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('b'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                    )
+                ),
+                Return('b')
+            )
+        )
+
+    @XFAIL # this is expected to fail because of a bug in the C parser.
+    def test_function_call():
+        c_src1 = (
+            'int fun1(int x)' + '\n' +
+            '{' + '\n' +
+            'return x;' + '\n' +
+            '}' + '\n' +
+            'void caller()' + '\n' +
+            '{' + '\n' +
+            'int x = fun1(2);' + '\n' +
+            '}'
+        )
+
+        c_src2 = (
+            'int fun2(int a, int b, int c)' + '\n' +
+            '{' + '\n' +
+            'return a;' + '\n' +
+            '}' + '\n' +
+            'void caller()' + '\n' +
+            '{' + '\n' +
+            'int y = fun2(2, 3, 4);' + '\n' +
+            '}'
+        )
+
+        c_src3 = (
+            'int fun3(int a, int b, int c)' + '\n' +
+            '{' + '\n' +
+            'return b;' + '\n' +
+            '}' + '\n' +
+            'void caller()' + '\n' +
+            '{' + '\n' +
+            'int p;' + '\n' +
+            'int q;' + '\n' +
+            'int r;' + '\n' +
+            'int z = fun3(p, q, r);' + '\n' +
+            '}'
+        )
+
+        c_src4 = (
+            'int fun4(float a, float b, int c)' + '\n' +
+            '{' + '\n' +
+            'return c;' + '\n' +
+            '}' + '\n' +
+            'void caller()' + '\n' +
+            '{' + '\n' +
+            'float x;' + '\n' +
+            'float y;' + '\n' +
+            'int z;' + '\n' +
+            'int i = fun4(x, y, z)' + '\n' +
+            '}'
+        )
+
+        c_src5 = (
+            'int fun()' + '\n' +
+            '{' + '\n' +
+            'return 1;' + '\n' +
+            '}' + '\n' +
+            'void caller()' + '\n' +
+            '{' + '\n' +
+            'int a = fun()' + '\n' +
+            '}'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+        res5 = SymPyExpression(c_src5, 'c').return_expr()
+
+
+        assert res1[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun1'),
+            parameters=(Variable(Symbol('x'),
+                type=IntBaseType(String('intc'))
+                ),
+            ),
+            body=CodeBlock(
+                Return('x')
+                )
+            )
+
+        assert res1[1] == FunctionDefinition(
+            NoneToken(),
+            name=String('caller'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('x'),
+                        value=FunctionCall(String('fun1'),
+                            function_args=(
+                                Integer(2),
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res2[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun2'),
+            parameters=(Variable(Symbol('a'),
+                type=IntBaseType(String('intc'))
+                ),
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc'))
+                ),
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc'))
+                )
+            ),
+            body=CodeBlock(
+                Return('a')
+                )
+            )
+
+        assert res2[1] == FunctionDefinition(
+            NoneToken(),
+            name=String('caller'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('y'),
+                        value=FunctionCall(
+                            String('fun2'),
+                            function_args=(
+                                Integer(2),
+                                Integer(3),
+                                Integer(4)
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res3[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun3'),
+            parameters=(
+                Variable(Symbol('a'),
+                    type=IntBaseType(String('intc'))
+                    ),
+                Variable(Symbol('b'),
+                    type=IntBaseType(String('intc'))
+                    ),
+                Variable(Symbol('c'),
+                    type=IntBaseType(String('intc'))
+                    )
+                ),
+            body=CodeBlock(
+                Return('b')
+                )
+            )
+
+        assert res3[1] == FunctionDefinition(
+            NoneToken(),
+            name=String('caller'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('p'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('q'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('r'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('z'),
+                        value=FunctionCall(
+                            String('fun3'),
+                            function_args=(
+                                Symbol('p'),
+                                Symbol('q'),
+                                Symbol('r')
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res4[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun4'),
+            parameters=(Variable(Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+                ),
+            Variable(Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+                ),
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc'))
+                )
+            ),
+            body=CodeBlock(
+                Return('c')
+                )
+            )
+
+        assert res4[1] == FunctionDefinition(
+            NoneToken(),
+            name=String('caller'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('x'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('y'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('z'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('i'),
+                        value=FunctionCall(String('fun4'),
+                            function_args=(
+                                Symbol('x'),
+                                Symbol('y'),
+                                Symbol('z')
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res5[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('fun'),
+            parameters=(),
+            body=CodeBlock(
+                Return('')
+                )
+            )
+
+        assert res5[1] == FunctionDefinition(
+            NoneToken(),
+            name=String('caller'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        value=FunctionCall(String('fun'),
+                            function_args=()
+                            )
+                        )
+                    )
+                )
+            )
+
+
+    def test_parse():
+        c_src1 = (
+            'int a;' + '\n' +
+            'int b;' + '\n'
+        )
+        c_src2 = (
+            'void fun1()' + '\n' +
+            '{' + '\n' +
+            'int a;' + '\n' +
+            '}'
+        )
+
+        f1 = open('..a.h', 'w')
+        f2 = open('..b.h', 'w')
+
+        f1.write(c_src1)
+        f2. write(c_src2)
+
+        f1.close()
+        f2.close()
+
+        res1 = SymPyExpression('..a.h', 'c').return_expr()
+        res2 = SymPyExpression('..b.h', 'c').return_expr()
+
+        os.remove('..a.h')
+        os.remove('..b.h')
+
+        assert res1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+        assert res1[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+        assert res2[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('fun1'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                    )
+                )
+            )
+        )
+
+
+    def test_binary_operators():
+        c_src1 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'a = 1;' + '\n' +
+            '}'
+        )
+        c_src2 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 0;' + '\n' +
+                'a = a + 1;' + '\n' +
+                'a = 3*a - 10;' + '\n' +
+            '}'
+        )
+        c_src3 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 10;' + '\n' +
+                'a = 1 + a - 3 * 6;' + '\n' +
+            '}'
+        )
+        c_src4 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'int b;' + '\n' +
+                'a = 100;' + '\n' +
+                'b = a*a + a*a + a + 19*a + 1 + 24;' + '\n' +
+            '}'
+        )
+        c_src5 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'int b;' + '\n' +
+                'int c;' + '\n' +
+                'int d;' + '\n' +
+                'a = 1;' + '\n' +
+                'b = 2;' + '\n' +
+                'c = b;' + '\n' +
+                'd = ((a+b)*(a+c))*((c-d)*(a+c));' + '\n' +
+            '}'
+        )
+        c_src6 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'int b;' + '\n' +
+                'int c;' + '\n' +
+                'int d;' + '\n' +
+                'a = 1;' + '\n' +
+                'b = 2;' + '\n' +
+                'c = 3;' + '\n' +
+                'd = (a*a*a*a + 3*b*b + b + b + c*d);' + '\n' +
+            '}'
+        )
+        c_src7 = (
+            'void func()'+
+            '{' + '\n' +
+                'float a;' + '\n' +
+                'a = 1.01;' + '\n' +
+            '}'
+        )
+
+        c_src8 = (
+            'void func()'+
+            '{' + '\n' +
+                'float a;' + '\n' +
+                'a = 10.0 + 2.5;' + '\n' +
+            '}'
+        )
+
+        c_src9 = (
+            'void func()'+
+            '{' + '\n' +
+                'float a;' + '\n' +
+                'a = 10.0 / 2.5;' + '\n' +
+            '}'
+        )
+
+        c_src10 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'a = 100 / 4;' + '\n' +
+            '}'
+        )
+
+        c_src11 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'a = 20 - 100 / 4 * 5 + 10;' + '\n' +
+            '}'
+        )
+
+        c_src12 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'a = (20 - 100) / 4 * (5 + 10);' + '\n' +
+            '}'
+        )
+
+        c_src13 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'int b;' + '\n' +
+                'float c;' + '\n' +
+                'c = b/a;' + '\n' +
+            '}'
+        )
+
+        c_src14 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 2;' + '\n' +
+                'int d = 5;' + '\n' +
+                'int n = 10;' + '\n' +
+                'int s;' + '\n' +
+                's = (a/2)*(2*a + (n-1)*d);' + '\n' +
+            '}'
+        )
+
+        c_src15 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a;' + '\n' +
+                'a = 1 % 2;' + '\n' +
+            '}'
+        )
+
+        c_src16 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 2;' + '\n' +
+                'int b;' + '\n' +
+                'b = a % 3;' + '\n' +
+            '}'
+        )
+
+        c_src17 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 100;' + '\n' +
+                'int b = 3;' + '\n' +
+                'int c;' + '\n' +
+                'c = a % b;' + '\n' +
+            '}'
+        )
+
+        c_src18 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 100;' + '\n' +
+                'int b = 3;' + '\n' +
+                'int mod = 1000000007;' + '\n' +
+                'int c;' + '\n' +
+                'c = (a + b * (100/a)) % mod;' + '\n' +
+            '}'
+        )
+
+        c_src19 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 100;' + '\n' +
+                'int b = 3;' + '\n' +
+                'int mod = 1000000007;' + '\n' +
+                'int c;' + '\n' +
+                'c = ((a % mod + b % mod) % mod' \
+                '* (a % mod - b % mod) % mod) % mod;' + '\n' +
+            '}'
+        )
+
+        c_src20 = (
+            'void func()'+
+            '{' + '\n' +
+            'bool a' + '\n' +
+            'bool b;' + '\n' +
+            'a = 1 == 2;' + '\n' +
+            'b = 1 != 2;' + '\n' +
+            '}'
+        )
+
+        c_src21 = (
+            'void func()'+
+            '{' + '\n' +
+            'bool a;' + '\n' +
+            'bool b;' + '\n' +
+            'bool c;' + '\n' +
+            'bool d;' + '\n' +
+            'a = 1 == 2;' + '\n' +
+            'b = 1 <= 2;' + '\n' +
+            'c = 1 > 2;' + '\n' +
+            'd = 1 >= 2;' + '\n' +
+            '}'
+        )
+
+        c_src22 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a = 1;' + '\n' +
+            'int b = 2;' + '\n' +
+
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+            'bool c5;' + '\n' +
+            'bool c6;' + '\n' +
+            'bool c7;' + '\n' +
+            'bool c8;' + '\n' +
+
+            'c1 = a == 1;' + '\n' +
+            'c2 = b == 2;' + '\n' +
+
+            'c3 = 1 != a;' + '\n' +
+            'c4 = 1 != b;' + '\n' +
+
+            'c5 = a < 0;' + '\n' +
+            'c6 = b <= 10;' + '\n' +
+            'c7 = a > 0;' + '\n' +
+            'c8 = b >= 11;' + '\n' +
+            '}'
+        )
+
+        c_src23 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a = 3;' + '\n' +
+            'int b = 4;' + '\n' +
+
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+            'bool c5;' + '\n' +
+            'bool c6;' + '\n' +
+
+            'c1 = a == b;' + '\n' +
+            'c2 = a != b;' + '\n' +
+            'c3 = a < b;' + '\n' +
+            'c4 = a <= b;' + '\n' +
+            'c5 = a > b;' + '\n' +
+            'c6 = a >= b;' + '\n' +
+            '}'
+        )
+
+        c_src24 = (
+            'void func()'+
+            '{' + '\n' +
+            'float a = 1.25'
+            'float b = 2.5;' + '\n' +
+
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+
+            'c1 = a == 1.25;' + '\n' +
+            'c2 = b == 2.54;' + '\n' +
+
+            'c3 = 1.2 != a;' + '\n' +
+            'c4 = 1.5 != b;' + '\n' +
+            '}'
+        )
+
+        c_src25 = (
+            'void func()'+
+            '{' + '\n' +
+            'float a = 1.25' + '\n' +
+            'float b = 2.5;' + '\n' +
+
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+            'bool c5;' + '\n' +
+            'bool c6;' + '\n' +
+
+            'c1 = a == b;' + '\n' +
+            'c2 = a != b;' + '\n' +
+            'c3 = a < b;' + '\n' +
+            'c4 = a <= b;' + '\n' +
+            'c5 = a > b;' + '\n' +
+            'c6 = a >= b;' + '\n' +
+            '}'
+        )
+
+        c_src26 = (
+            'void func()'+
+            '{' + '\n' +
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+            'bool c5;' + '\n' +
+            'bool c6;' + '\n' +
+
+            'c1 = true == true;' + '\n' +
+            'c2 = true == false;' + '\n' +
+            'c3 = false == false;' + '\n' +
+
+            'c4 = true != true;' + '\n' +
+            'c5 = true != false;' + '\n' +
+            'c6 = false != false;' + '\n' +
+            '}'
+        )
+
+        c_src27 = (
+            'void func()'+
+            '{' + '\n' +
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+            'bool c5;' + '\n' +
+            'bool c6;' + '\n' +
+
+            'c1 = true && true;' + '\n' +
+            'c2 = true && false;' + '\n' +
+            'c3 = false && false;' + '\n' +
+
+            'c4 = true || true;' + '\n' +
+            'c5 = true || false;' + '\n' +
+            'c6 = false || false;' + '\n' +
+            '}'
+        )
+
+        c_src28 = (
+            'void func()'+
+            '{' + '\n' +
+            'bool a;' + '\n' +
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+
+            'c1 = a && true;' + '\n' +
+            'c2 = false && a;' + '\n' +
+
+            'c3 = true || a;' + '\n' +
+            'c4 = a || false;' + '\n' +
+            '}'
+        )
+
+        c_src29 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a;' + '\n' +
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+
+            'c1 = a && 1;' + '\n' +
+            'c2 = a && 0;' + '\n' +
+
+            'c3 = a || 1;' + '\n' +
+            'c4 = 0 || a;' + '\n' +
+            '}'
+        )
+
+        c_src30 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a;' + '\n' +
+            'int b;' + '\n' +
+            'bool c;'+ '\n' +
+            'bool d;'+ '\n' +
+
+            'bool c1;' + '\n' +
+            'bool c2;' + '\n' +
+            'bool c3;' + '\n' +
+            'bool c4;' + '\n' +
+            'bool c5;' + '\n' +
+            'bool c6;' + '\n' +
+
+            'c1 = a && b;' + '\n' +
+            'c2 = a && c;' + '\n' +
+            'c3 = c && d;' + '\n' +
+
+            'c4 = a || b;' + '\n' +
+            'c5 = a || c;' + '\n' +
+            'c6 = c || d;' + '\n' +
+            '}'
+        )
+
+        c_src_raise1 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a;' + '\n' +
+            'a = -1;' + '\n' +
+            '}'
+        )
+
+        c_src_raise2 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a;' + '\n' +
+            'a = -+1;' + '\n' +
+            '}'
+        )
+
+        c_src_raise3 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a;' + '\n' +
+            'a = 2*-2;' + '\n' +
+            '}'
+        )
+
+        c_src_raise4 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a;' + '\n' +
+            'a = (int)2.0;' + '\n' +
+            '}'
+        )
+
+        c_src_raise5 = (
+            'void func()'+
+            '{' + '\n' +
+            'int a=100;' + '\n' +
+            'a = (a==100)?(1):(0);' + '\n' +
+            '}'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+        res5 = SymPyExpression(c_src5, 'c').return_expr()
+        res6 = SymPyExpression(c_src6, 'c').return_expr()
+        res7 = SymPyExpression(c_src7, 'c').return_expr()
+        res8 = SymPyExpression(c_src8, 'c').return_expr()
+        res9 = SymPyExpression(c_src9, 'c').return_expr()
+        res10 = SymPyExpression(c_src10, 'c').return_expr()
+        res11 = SymPyExpression(c_src11, 'c').return_expr()
+        res12 = SymPyExpression(c_src12, 'c').return_expr()
+        res13 = SymPyExpression(c_src13, 'c').return_expr()
+        res14 = SymPyExpression(c_src14, 'c').return_expr()
+        res15 = SymPyExpression(c_src15, 'c').return_expr()
+        res16 = SymPyExpression(c_src16, 'c').return_expr()
+        res17 = SymPyExpression(c_src17, 'c').return_expr()
+        res18 = SymPyExpression(c_src18, 'c').return_expr()
+        res19 = SymPyExpression(c_src19, 'c').return_expr()
+        res20 = SymPyExpression(c_src20, 'c').return_expr()
+        res21 = SymPyExpression(c_src21, 'c').return_expr()
+        res22 = SymPyExpression(c_src22, 'c').return_expr()
+        res23 = SymPyExpression(c_src23, 'c').return_expr()
+        res24 = SymPyExpression(c_src24, 'c').return_expr()
+        res25 = SymPyExpression(c_src25, 'c').return_expr()
+        res26 = SymPyExpression(c_src26, 'c').return_expr()
+        res27 = SymPyExpression(c_src27, 'c').return_expr()
+        res28 = SymPyExpression(c_src28, 'c').return_expr()
+        res29 = SymPyExpression(c_src29, 'c').return_expr()
+        res30 = SymPyExpression(c_src30, 'c').return_expr()
+
+        assert res1[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(Variable(Symbol('a')), Integer(1))
+                )
+            )
+
+        assert res2[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                    type=IntBaseType(String('intc')),
+                    value=Integer(0))),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Add(Symbol('a'),
+                        Integer(1))
+                    ),
+                Assignment(Variable(Symbol('a')),
+                    Add(
+                        Mul(
+                            Integer(3),
+                            Symbol('a')),
+                        Integer(-10)
+                        )
+                    )
+                )
+            )
+
+        assert res3[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(10)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Add(
+                        Symbol('a'),
+                        Integer(-17)
+                        )
+                    )
+                )
+            )
+
+        assert res4[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(100)),
+                Assignment(
+                    Variable(Symbol('b')),
+                    Add(
+                        Mul(
+                            Integer(2),
+                        Pow(
+                            Symbol('a'),
+                            Integer(2))
+                        ),
+                        Mul(
+                            Integer(20),
+                            Symbol('a')),
+                        Integer(25)
+                        )
+                    )
+                )
+            )
+
+        assert res5[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('d'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(1)),
+                Assignment(
+                    Variable(Symbol('b')),
+                    Integer(2)
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    Symbol('b')),
+                Assignment(
+                    Variable(Symbol('d')),
+                    Mul(
+                        Add(
+                            Symbol('a'),
+                            Symbol('b')),
+                        Pow(
+                            Add(
+                                Symbol('a'),
+                                Symbol('c')
+                                ),
+                            Integer(2)
+                            ),
+                        Add(
+                            Symbol('c'),
+                            Mul(
+                                Integer(-1),
+                                Symbol('d')
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res6[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('d'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(1)
+                    ),
+                Assignment(
+                    Variable(Symbol('b')),
+                    Integer(2)
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    Integer(3)
+                    ),
+                Assignment(
+                    Variable(Symbol('d')),
+                    Add(
+                        Pow(
+                            Symbol('a'),
+                            Integer(4)
+                            ),
+                        Mul(
+                            Integer(3),
+                            Pow(
+                                Symbol('b'),
+                                Integer(2)
+                                )
+                            ),
+                        Mul(
+                            Integer(2),
+                            Symbol('b')
+                            ),
+                        Mul(
+                            Symbol('c'),
+                            Symbol('d')
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res7[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Float('1.01', precision=53)
+                    )
+                )
+            )
+
+        assert res8[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Float('12.5', precision=53)
+                    )
+                )
+            )
+
+        assert res9[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Float('4.0', precision=53)
+                    )
+                )
+            )
+
+        assert res10[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(25)
+                    )
+                )
+            )
+
+        assert res11[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(-95)
+                    )
+                )
+            )
+
+        assert res12[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(-300)
+                    )
+                )
+            )
+
+        assert res13[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    Mul(
+                        Pow(
+                            Symbol('a'),
+                            Integer(-1)
+                            ),
+                        Symbol('b')
+                        )
+                    )
+                )
+            )
+
+        assert res14[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(2)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('d'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(5)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('n'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(10)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('s'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('s')),
+                    Mul(
+                        Rational(1, 2),
+                        Symbol('a'),
+                        Add(
+                            Mul(
+                                Integer(2),
+                                Symbol('a')
+                                ),
+                            Mul(
+                                Symbol('d'),
+                                Add(
+                                    Symbol('n'),
+                                    Integer(-1)
+                                    )
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res15[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Integer(1)
+                    )
+                )
+            )
+
+        assert res16[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(2)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('b')),
+                    Mod(
+                        Symbol('a'),
+                        Integer(3)
+                        )
+                    )
+                )
+            )
+
+        assert res17[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(100)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(3)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    Mod(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    )
+                )
+            )
+
+        assert res18[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(100)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(3)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('mod'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(1000000007)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    Mod(
+                        Add(
+                            Symbol('a'),
+                            Mul(
+                                Integer(100),
+                                Pow(
+                                    Symbol('a'),
+                                    Integer(-1)
+                                    ),
+                                Symbol('b')
+                                )
+                            ),
+                        Symbol('mod')
+                        )
+                    )
+                )
+            )
+
+        assert res19[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(100)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(3)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('mod'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(1000000007)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    Mod(
+                        Mul(
+                            Add(
+                                Mod(
+                                    Symbol('a'),
+                                    Symbol('mod')
+                                    ),
+                                Mul(
+                                    Integer(-1),
+                                    Mod(
+                                        Symbol('b'),
+                                        Symbol('mod')
+                                        )
+                                    )
+                                ),
+                            Mod(
+                                Add(
+                                    Symbol('a'),
+                                    Symbol('b')
+                                    ),
+                                Symbol('mod')
+                                )
+                            ),
+                        Symbol('mod')
+                        )
+                    )
+                )
+            )
+
+        assert res20[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('b')),
+                    true
+                    )
+                )
+            )
+
+        assert res21[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('d'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('b')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('d')),
+                    false
+                    )
+                )
+            )
+
+        assert res22[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(1)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(2)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c5'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c6'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c7'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c8'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    Equality(
+                        Symbol('a'),
+                        Integer(1)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    Equality(
+                        Symbol('b'),
+                        Integer(2)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    Unequality(
+                        Integer(1),
+                        Symbol('a')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    Unequality(
+                        Integer(1),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c5')),
+                    StrictLessThan(
+                        Symbol('a'),
+                        Integer(0)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c6')),
+                    LessThan(
+                        Symbol('b'),
+                        Integer(10)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c7')),
+                    StrictGreaterThan(
+                        Symbol('a'),
+                        Integer(0)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c8')),
+                    GreaterThan(
+                        Symbol('b'),
+                        Integer(11)
+                        )
+                    )
+                )
+            )
+
+        assert res23[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(3)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(4)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c5'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c6'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    Equality(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    Unequality(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    StrictLessThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    LessThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c5')),
+                    StrictGreaterThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c6')),
+                    GreaterThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    )
+                )
+            )
+
+        assert res24[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            )
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    Equality(
+                        Symbol('a'),
+                        Float('1.25', precision=53)
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    Unequality(
+                        Float('1.2', precision=53),
+                        Symbol('a')
+                        )
+                    )
+                )
+            )
+
+
+        assert res25[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            ),
+                        value=Float('1.25', precision=53)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=FloatType(
+                            String('float32'),
+                            nbits=Integer(32),
+                            nmant=Integer(23),
+                            nexp=Integer(8)
+                            ),
+                        value=Float('2.5', precision=53)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool')
+                            )
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c5'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c6'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    Equality(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    Unequality(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    StrictLessThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    LessThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c5')),
+                    StrictGreaterThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c6')),
+                    GreaterThan(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    )
+                )
+            )
+
+        assert res26[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(), body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c5'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c6'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('c5')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c6')),
+                    false
+                    )
+                )
+            )
+
+        assert res27[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c5'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c6'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c5')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c6')),
+                    false)
+                )
+            )
+
+        assert res28[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    Symbol('a')
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    Symbol('a')
+                    )
+                )
+            )
+
+        assert res29[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    Symbol('a')
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    false
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    true
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    Symbol('a')
+                    )
+                )
+            )
+
+        assert res30[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('d'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c1'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c2'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c3'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c4'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c5'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c6'),
+                        type=Type(String('bool'))
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c1')),
+                    And(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c2')),
+                    And(
+                        Symbol('a'),
+                        Symbol('c')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c3')),
+                    And(
+                        Symbol('c'),
+                        Symbol('d')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c4')),
+                    Or(
+                        Symbol('a'),
+                        Symbol('b')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c5')),
+                    Or(
+                        Symbol('a'),
+                        Symbol('c')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('c6')),
+                    Or(
+                        Symbol('c'),
+                        Symbol('d')
+                        )
+                    )
+                )
+            )
+
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise1, 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise2, 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise3, 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise4, 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise5, 'c'))
+
+
+    @XFAIL
+    def test_var_decl():
+        c_src1 = (
+            'int b = 100;' + '\n' +
+            'int a = b;' + '\n'
+        )
+
+        c_src2 = (
+            'int a = 1;' + '\n' +
+            'int b = a + 1;' + '\n'
+        )
+
+        c_src3 = (
+            'float a = 10.0 + 2.5;' + '\n' +
+            'float b = a * 20.0;' + '\n'
+        )
+
+        c_src4 = (
+            'int a = 1 + 100 - 3 * 6;' + '\n'
+        )
+
+        c_src5 = (
+            'int a = (((1 + 100) * 12) - 3) * (6 - 10);' + '\n'
+        )
+
+        c_src6 = (
+            'int b = 2;' + '\n' +
+            'int c = 3;' + '\n' +
+            'int a = b + c * 4;' + '\n'
+        )
+
+        c_src7 = (
+            'int b = 1;' + '\n' +
+            'int c = b + 2;' + '\n' +
+            'int a = 10 * b * b * c;' + '\n'
+        )
+
+        c_src8 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 1;' + '\n' +
+                'int b = 2;' + '\n' +
+                'int temp = a;' + '\n' +
+                'a = b;' + '\n' +
+                'b = temp;' + '\n' +
+            '}'
+        )
+
+        c_src9 = (
+            'int a = 1;' + '\n' +
+            'int b = 2;' + '\n' +
+            'int c = a;' + '\n' +
+            'int d = a + b + c;' + '\n' +
+            'int e = a*a*a + 3*a*a*b + 3*a*b*b + b*b*b;' + '\n'
+            'int f = (a + b + c) * (a + b - c);' + '\n' +
+            'int g = (a + b + c + d)*(a + b + c + d)*(a * (b - c));'
+            + '\n'
+        )
+
+        c_src10 = (
+            'float a = 10.0;' + '\n' +
+            'float b = 2.5;' + '\n' +
+            'float c = a*a + 2*a*b + b*b;' + '\n'
+        )
+
+        c_src11 = (
+            'float a = 10.0 / 2.5;' + '\n'
+        )
+
+        c_src12 = (
+            'int a = 100 / 4;' + '\n'
+        )
+
+        c_src13 = (
+            'int a = 20 - 100 / 4 * 5 + 10;' + '\n'
+        )
+
+        c_src14 = (
+            'int a = (20 - 100) / 4 * (5 + 10);' + '\n'
+        )
+
+        c_src15 = (
+            'int a = 4;' + '\n' +
+            'int b = 2;' + '\n' +
+            'float c = b/a;' + '\n'
+        )
+
+        c_src16 = (
+            'int a = 2;' + '\n' +
+            'int d = 5;' + '\n' +
+            'int n = 10;' + '\n' +
+            'int s = (a/2)*(2*a + (n-1)*d);' + '\n'
+        )
+
+        c_src17 = (
+            'int a = 1 % 2;' + '\n'
+        )
+
+        c_src18 = (
+            'int a = 2;' + '\n' +
+            'int b = a % 3;' + '\n'
+        )
+
+        c_src19 = (
+            'int a = 100;' + '\n' +
+            'int b = 3;' + '\n' +
+            'int c = a % b;' + '\n'
+        )
+
+        c_src20 = (
+            'int a = 100;' + '\n' +
+            'int b = 3;' + '\n' +
+            'int mod = 1000000007;' + '\n' +
+            'int c = (a + b * (100/a)) % mod;' + '\n'
+        )
+
+        c_src21 = (
+            'int a = 100;' + '\n' +
+            'int b = 3;' + '\n' +
+            'int mod = 1000000007;' + '\n' +
+            'int c = ((a % mod + b % mod) % mod *' \
+            '(a % mod - b % mod) % mod) % mod;' + '\n'
+        )
+
+        c_src22 = (
+            'bool a = 1 == 2, b = 1 != 2;'
+        )
+
+        c_src23 = (
+            'bool a = 1 < 2, b = 1 <= 2, c = 1 > 2, d = 1 >= 2;'
+        )
+
+        c_src24 = (
+            'int a = 1, b = 2;' + '\n' +
+
+            'bool c1 = a == 1;' + '\n' +
+            'bool c2 = b == 2;' + '\n' +
+
+            'bool c3 = 1 != a;' + '\n' +
+            'bool c4 = 1 != b;' + '\n' +
+
+            'bool c5 = a < 0;' + '\n' +
+            'bool c6 = b <= 10;' + '\n' +
+            'bool c7 = a > 0;' + '\n' +
+            'bool c8 = b >= 11;'
+
+        )
+
+        c_src25 = (
+            'int a = 3, b = 4;' + '\n' +
+
+            'bool c1 = a == b;' + '\n' +
+            'bool c2 = a != b;' + '\n' +
+            'bool c3 = a < b;' + '\n' +
+            'bool c4 = a <= b;' + '\n' +
+            'bool c5 = a > b;' + '\n' +
+            'bool c6 = a >= b;'
+        )
+
+        c_src26 = (
+            'float a = 1.25, b = 2.5;' + '\n' +
+
+            'bool c1 = a == 1.25;' + '\n' +
+            'bool c2 = b == 2.54;' + '\n' +
+
+            'bool c3 = 1.2 != a;' + '\n' +
+            'bool c4 = 1.5 != b;'
+        )
+
+        c_src27 = (
+            'float a = 1.25, b = 2.5;' + '\n' +
+
+            'bool c1 = a == b;' + '\n' +
+            'bool c2 = a != b;' + '\n' +
+            'bool c3 = a < b;' + '\n' +
+            'bool c4 = a <= b;' + '\n' +
+            'bool c5 = a > b;' + '\n' +
+            'bool c6 = a >= b;'
+        )
+
+        c_src28 = (
+            'bool c1 = true == true;' + '\n' +
+            'bool c2 = true == false;' + '\n' +
+            'bool c3 = false == false;' + '\n' +
+
+            'bool c4 = true != true;' + '\n' +
+            'bool c5 = true != false;' + '\n' +
+            'bool c6 = false != false;'
+        )
+
+        c_src29 = (
+            'bool c1 = true && true;' + '\n' +
+            'bool c2 = true && false;' + '\n' +
+            'bool c3 = false && false;' + '\n' +
+
+            'bool c4 = true || true;' + '\n' +
+            'bool c5 = true || false;' + '\n' +
+            'bool c6 = false || false;'
+        )
+
+        c_src30 = (
+            'bool a = false;' + '\n' +
+
+            'bool c1 = a && true;' + '\n' +
+            'bool c2 = false && a;' + '\n' +
+
+            'bool c3 = true || a;' + '\n' +
+            'bool c4 = a || false;'
+        )
+
+        c_src31 = (
+            'int a = 1;' + '\n' +
+
+            'bool c1 = a && 1;' + '\n' +
+            'bool c2 = a && 0;' + '\n' +
+
+            'bool c3 = a || 1;' + '\n' +
+            'bool c4 = 0 || a;'
+        )
+
+        c_src32 = (
+            'int a = 1, b = 0;' + '\n' +
+            'bool c = false, d = true;'+ '\n' +
+
+            'bool c1 = a && b;' + '\n' +
+            'bool c2 = a && c;' + '\n' +
+            'bool c3 = c && d;' + '\n' +
+
+            'bool c4 = a || b;' + '\n' +
+            'bool c5 = a || c;' + '\n' +
+            'bool c6 = c || d;'
+        )
+
+        c_src_raise1 = (
+            "char a = 'b';"
+        )
+
+        c_src_raise2 = (
+            'int a[] = {10, 20};'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+        res5 = SymPyExpression(c_src5, 'c').return_expr()
+        res6 = SymPyExpression(c_src6, 'c').return_expr()
+        res7 = SymPyExpression(c_src7, 'c').return_expr()
+        res8 = SymPyExpression(c_src8, 'c').return_expr()
+        res9 = SymPyExpression(c_src9, 'c').return_expr()
+        res10 = SymPyExpression(c_src10, 'c').return_expr()
+        res11 = SymPyExpression(c_src11, 'c').return_expr()
+        res12 = SymPyExpression(c_src12, 'c').return_expr()
+        res13 = SymPyExpression(c_src13, 'c').return_expr()
+        res14 = SymPyExpression(c_src14, 'c').return_expr()
+        res15 = SymPyExpression(c_src15, 'c').return_expr()
+        res16 = SymPyExpression(c_src16, 'c').return_expr()
+        res17 = SymPyExpression(c_src17, 'c').return_expr()
+        res18 = SymPyExpression(c_src18, 'c').return_expr()
+        res19 = SymPyExpression(c_src19, 'c').return_expr()
+        res20 = SymPyExpression(c_src20, 'c').return_expr()
+        res21 = SymPyExpression(c_src21, 'c').return_expr()
+        res22 = SymPyExpression(c_src22, 'c').return_expr()
+        res23 = SymPyExpression(c_src23, 'c').return_expr()
+        res24 = SymPyExpression(c_src24, 'c').return_expr()
+        res25 = SymPyExpression(c_src25, 'c').return_expr()
+        res26 = SymPyExpression(c_src26, 'c').return_expr()
+        res27 = SymPyExpression(c_src27, 'c').return_expr()
+        res28 = SymPyExpression(c_src28, 'c').return_expr()
+        res29 = SymPyExpression(c_src29, 'c').return_expr()
+        res30 = SymPyExpression(c_src30, 'c').return_expr()
+        res31 = SymPyExpression(c_src31, 'c').return_expr()
+        res32 = SymPyExpression(c_src32, 'c').return_expr()
+
+        assert res1[0] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(100)
+                )
+            )
+
+        assert res1[1] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Symbol('b')
+                )
+            )
+
+        assert res2[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res2[1] == Declaration(Variable(Symbol('b'),
+            type=IntBaseType(String('intc')),
+            value=Add(
+                Symbol('a'),
+                Integer(1)
+                )
+            )
+        )
+
+        assert res3[0] == Declaration(
+            Variable(Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('12.5', precision=53)
+                )
+            )
+
+        assert res3[1] == Declaration(
+            Variable(Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Mul(
+                    Float('20.0', precision=53),
+                    Symbol('a')
+                    )
+                )
+            )
+
+        assert res4[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(83)
+                )
+            )
+
+        assert res5[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(-4836)
+                )
+            )
+
+        assert res6[0] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res6[1] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Integer(3)
+                )
+            )
+
+        assert res6[2] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Add(
+                    Symbol('b'),
+                    Mul(
+                        Integer(4),
+                        Symbol('c')
+                        )
+                    )
+                )
+            )
+
+        assert res7[0] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res7[1] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Add(
+                    Symbol('b'),
+                    Integer(2)
+                    )
+                )
+            )
+
+        assert res7[2] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Mul(
+                    Integer(10),
+                    Pow(
+                        Symbol('b'),
+                        Integer(2)
+                        ),
+                    Symbol('c')
+                    )
+                )
+            )
+
+        assert res8[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(1)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(2)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('temp'),
+                        type=IntBaseType(String('intc')),
+                        value=Symbol('a')
+                        )
+                    ),
+                Assignment(
+                    Variable(Symbol('a')),
+                    Symbol('b')
+                    ),
+                Assignment(
+                    Variable(Symbol('b')),
+                    Symbol('temp')
+                    )
+                )
+            )
+
+        assert res9[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res9[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res9[2] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Symbol('a')
+                )
+            )
+
+        assert res9[3] == Declaration(
+            Variable(Symbol('d'),
+                type=IntBaseType(String('intc')),
+                value=Add(
+                    Symbol('a'),
+                    Symbol('b'),
+                    Symbol('c')
+                    )
+                )
+            )
+
+        assert res9[4] == Declaration(
+            Variable(Symbol('e'),
+                type=IntBaseType(String('intc')),
+                value=Add(
+                    Pow(
+                        Symbol('a'),
+                        Integer(3)
+                        ),
+                    Mul(
+                        Integer(3),
+                        Pow(
+                            Symbol('a'),
+                            Integer(2)
+                            ),
+                        Symbol('b')
+                        ),
+                    Mul(
+                        Integer(3),
+                        Symbol('a'),
+                        Pow(
+                            Symbol('b'),
+                            Integer(2)
+                            )
+                        ),
+                    Pow(
+                        Symbol('b'),
+                        Integer(3)
+                        )
+                    )
+                )
+            )
+
+        assert res9[5] == Declaration(
+            Variable(Symbol('f'),
+                type=IntBaseType(String('intc')),
+                value=Mul(
+                    Add(
+                        Symbol('a'),
+                        Symbol('b'),
+                        Mul(
+                            Integer(-1),
+                            Symbol('c')
+                            )
+                        ),
+                    Add(
+                        Symbol('a'),
+                        Symbol('b'),
+                        Symbol('c')
+                        )
+                    )
+                )
+            )
+
+        assert res9[6] == Declaration(
+            Variable(Symbol('g'),
+                type=IntBaseType(String('intc')),
+                value=Mul(
+                    Symbol('a'),
+                    Add(
+                        Symbol('b'),
+                        Mul(
+                            Integer(-1),
+                            Symbol('c')
+                            )
+                        ),
+                    Pow(
+                        Add(
+                            Symbol('a'),
+                            Symbol('b'),
+                            Symbol('c'),
+                            Symbol('d')
+                            ),
+                        Integer(2)
+                        )
+                    )
+                )
+            )
+
+        assert res10[0] == Declaration(
+            Variable(Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('10.0', precision=53)
+                )
+            )
+
+        assert res10[1] == Declaration(
+            Variable(Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.5', precision=53)
+                )
+            )
+
+        assert res10[2] == Declaration(
+            Variable(Symbol('c'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Add(
+                    Pow(
+                        Symbol('a'),
+                        Integer(2)
+                        ),
+                    Mul(
+                        Integer(2),
+                        Symbol('a'),
+                        Symbol('b')
+                        ),
+                    Pow(
+                        Symbol('b'),
+                        Integer(2)
+                        )
+                    )
+                )
+            )
+
+        assert res11[0] == Declaration(
+            Variable(Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('4.0', precision=53)
+                )
+            )
+
+        assert res12[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(25)
+                )
+            )
+
+        assert res13[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(-95)
+                )
+            )
+
+        assert res14[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(-300)
+                )
+            )
+
+        assert res15[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(4)
+                )
+            )
+
+        assert res15[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res15[2] == Declaration(
+            Variable(Symbol('c'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Mul(
+                    Pow(
+                        Symbol('a'),
+                        Integer(-1)
+                        ),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res16[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res16[1] == Declaration(
+            Variable(Symbol('d'),
+                type=IntBaseType(String('intc')),
+                value=Integer(5)
+                )
+            )
+
+        assert res16[2] == Declaration(
+            Variable(Symbol('n'),
+                type=IntBaseType(String('intc')),
+                value=Integer(10)
+                )
+            )
+
+        assert res16[3] == Declaration(
+            Variable(Symbol('s'),
+                type=IntBaseType(String('intc')),
+                value=Mul(
+                    Rational(1, 2),
+                    Symbol('a'),
+                    Add(
+                        Mul(
+                            Integer(2),
+                            Symbol('a')
+                            ),
+                        Mul(
+                            Symbol('d'),
+                            Add(
+                                Symbol('n'),
+                                Integer(-1)
+                                )
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res17[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res18[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res18[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Mod(
+                    Symbol('a'),
+                    Integer(3)
+                    )
+                )
+            )
+
+        assert res19[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(100)
+                )
+            )
+        assert res19[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(3)
+                )
+            )
+
+        assert res19[2] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Mod(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res20[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(100)
+                )
+            )
+
+        assert res20[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(3)
+                )
+            )
+
+        assert res20[2] == Declaration(
+            Variable(Symbol('mod'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1000000007)
+                )
+            )
+
+        assert res20[3] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Mod(
+                    Add(
+                        Symbol('a'),
+                        Mul(
+                            Integer(100),
+                            Pow(
+                                Symbol('a'),
+                                Integer(-1)
+                                ),
+                            Symbol('b')
+                            )
+                        ),
+                    Symbol('mod')
+                    )
+                )
+            )
+
+        assert res21[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(100)
+                )
+            )
+
+        assert res21[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(3)
+                )
+            )
+
+        assert res21[2] == Declaration(
+            Variable(Symbol('mod'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1000000007)
+                )
+            )
+
+        assert res21[3] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Mod(
+                    Mul(
+                        Add(
+                            Symbol('a'),
+                            Mul(
+                                Integer(-1),
+                                Symbol('b')
+                                )
+                            ),
+                        Add(
+                            Symbol('a'),
+                            Symbol('b')
+                            )
+                        ),
+                    Symbol('mod')
+                    )
+                )
+            )
+
+        assert res22[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res22[1] == Declaration(
+            Variable(Symbol('b'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res23[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res23[1] == Declaration(
+            Variable(Symbol('b'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res23[2] == Declaration(
+            Variable(Symbol('c'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res23[3] == Declaration(
+            Variable(Symbol('d'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res24[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res24[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res24[2] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=Equality(
+                    Symbol('a'),
+                    Integer(1)
+                    )
+                )
+            )
+
+        assert res24[3] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=Equality(
+                    Symbol('b'),
+                    Integer(2)
+                    )
+                )
+            )
+
+        assert res24[4] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=Unequality(
+                    Integer(1),
+                    Symbol('a')
+                    )
+                )
+            )
+
+        assert res24[5] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=Unequality(
+                    Integer(1),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res24[6] == Declaration(
+            Variable(Symbol('c5'),
+                type=Type(String('bool')),
+                value=StrictLessThan(Symbol('a'),
+                    Integer(0)
+                    )
+                )
+            )
+
+        assert res24[7] == Declaration(
+            Variable(Symbol('c6'),
+                type=Type(String('bool')),
+                value=LessThan(
+                    Symbol('b'),
+                    Integer(10)
+                    )
+                )
+            )
+
+        assert res24[8] == Declaration(
+            Variable(Symbol('c7'),
+                type=Type(String('bool')),
+                value=StrictGreaterThan(
+                    Symbol('a'),
+                    Integer(0)
+                    )
+                )
+            )
+
+        assert res24[9] == Declaration(
+            Variable(Symbol('c8'),
+                type=Type(String('bool')),
+                value=GreaterThan(
+                    Symbol('b'),
+                    Integer(11)
+                    )
+                )
+            )
+
+        assert res25[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(3)
+                )
+            )
+
+        assert res25[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(4)
+                )
+            )
+
+        assert res25[2] == Declaration(Variable(Symbol('c1'),
+            type=Type(String('bool')),
+            value=Equality(
+                Symbol('a'),
+                Symbol('b')
+                )
+            )
+        )
+
+        assert res25[3] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=Unequality(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res25[4] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=StrictLessThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res25[5] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=LessThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res25[6] == Declaration(
+            Variable(Symbol('c5'),
+                type=Type(String('bool')),
+                value=StrictGreaterThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res25[7] == Declaration(
+            Variable(Symbol('c6'),
+                type=Type(String('bool')),
+                value=GreaterThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res26[0] == Declaration(
+            Variable(Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.25', precision=53)
+                )
+            )
+
+        assert res26[1] == Declaration(
+            Variable(Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.5', precision=53)
+                )
+            )
+
+        assert res26[2] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=Equality(
+                    Symbol('a'),
+                    Float('1.25', precision=53)
+                    )
+                )
+            )
+
+        assert res26[3] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=Equality(
+                    Symbol('b'),
+                    Float('2.54', precision=53)
+                    )
+                )
+            )
+
+        assert res26[4] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=Unequality(
+                    Float('1.2', precision=53),
+                    Symbol('a')
+                    )
+                )
+            )
+
+        assert res26[5] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=Unequality(
+                    Float('1.5', precision=53),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res27[0] == Declaration(
+            Variable(Symbol('a'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('1.25', precision=53)
+                )
+            )
+
+        assert res27[1] == Declaration(
+            Variable(Symbol('b'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.5', precision=53)
+                )
+            )
+
+        assert res27[2] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=Equality(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res27[3] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=Unequality(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res27[4] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=StrictLessThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res27[5] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=LessThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res27[6] == Declaration(
+            Variable(Symbol('c5'),
+                type=Type(String('bool')),
+                value=StrictGreaterThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res27[7] == Declaration(
+            Variable(Symbol('c6'),
+                type=Type(String('bool')),
+                value=GreaterThan(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res28[0] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res28[1] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res28[2] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res28[3] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res28[4] == Declaration(
+            Variable(Symbol('c5'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res28[5] == Declaration(
+            Variable(Symbol('c6'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res29[0] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res29[1] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res29[2] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res29[3] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res29[4] == Declaration(
+            Variable(Symbol('c5'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res29[5] == Declaration(
+            Variable(Symbol('c6'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res30[0] == Declaration(
+            Variable(Symbol('a'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res30[1] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=Symbol('a')
+                )
+            )
+
+        assert res30[2] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res30[3] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res30[4] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=Symbol('a')
+                )
+            )
+
+        assert res31[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res31[1] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=Symbol('a')
+                )
+            )
+
+        assert res31[2] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res31[3] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res31[4] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=Symbol('a')
+                )
+            )
+
+        assert res32[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res32[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(0)
+                )
+            )
+
+        assert res32[2] == Declaration(
+            Variable(Symbol('c'),
+                type=Type(String('bool')),
+                value=false
+                )
+            )
+
+        assert res32[3] == Declaration(
+            Variable(Symbol('d'),
+                type=Type(String('bool')),
+                value=true
+                )
+            )
+
+        assert res32[4] == Declaration(
+            Variable(Symbol('c1'),
+                type=Type(String('bool')),
+                value=And(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res32[5] == Declaration(
+            Variable(Symbol('c2'),
+                type=Type(String('bool')),
+                value=And(
+                    Symbol('a'),
+                    Symbol('c')
+                    )
+                )
+            )
+
+        assert res32[6] == Declaration(
+            Variable(Symbol('c3'),
+                type=Type(String('bool')),
+                value=And(
+                    Symbol('c'),
+                    Symbol('d')
+                    )
+                )
+            )
+
+        assert res32[7] == Declaration(
+            Variable(Symbol('c4'),
+                type=Type(String('bool')),
+                value=Or(
+                    Symbol('a'),
+                    Symbol('b')
+                    )
+                )
+            )
+
+        assert res32[8] == Declaration(
+            Variable(Symbol('c5'),
+                type=Type(String('bool')),
+                value=Or(
+                    Symbol('a'),
+                    Symbol('c')
+                    )
+                )
+            )
+
+        assert res32[9] == Declaration(
+            Variable(Symbol('c6'),
+                type=Type(String('bool')),
+                value=Or(
+                    Symbol('c'),
+                    Symbol('d')
+                    )
+                )
+            )
+
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise1, 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise2, 'c'))
+
+
+    def test_paren_expr():
+        c_src1 = (
+            'int a = (1);'
+            'int b = (1 + 2 * 3);'
+        )
+
+        c_src2 = (
+            'int a = 1, b = 2, c = 3;'
+            'int d = (a);'
+            'int e = (a + 1);'
+            'int f = (a + b * c - d / e);'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+
+        assert res1[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res1[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(7)
+                )
+            )
+
+        assert res2[0] == Declaration(
+            Variable(Symbol('a'),
+                type=IntBaseType(String('intc')),
+                value=Integer(1)
+                )
+            )
+
+        assert res2[1] == Declaration(
+            Variable(Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(2)
+                )
+            )
+
+        assert res2[2] == Declaration(
+            Variable(Symbol('c'),
+                type=IntBaseType(String('intc')),
+                value=Integer(3)
+                )
+            )
+
+        assert res2[3] == Declaration(
+            Variable(Symbol('d'),
+                type=IntBaseType(String('intc')),
+                value=Symbol('a')
+                )
+            )
+
+        assert res2[4] == Declaration(
+            Variable(Symbol('e'),
+                type=IntBaseType(String('intc')),
+                value=Add(
+                    Symbol('a'),
+                    Integer(1)
+                    )
+                )
+            )
+
+        assert res2[5] == Declaration(
+            Variable(Symbol('f'),
+                type=IntBaseType(String('intc')),
+                value=Add(
+                    Symbol('a'),
+                    Mul(
+                        Symbol('b'),
+                        Symbol('c')
+                        ),
+                    Mul(
+                        Integer(-1),
+                        Symbol('d'),
+                        Pow(
+                            Symbol('e'),
+                            Integer(-1)
+                            )
+                        )
+                    )
+                )
+            )
+
+
+    def test_unary_operators():
+        c_src1 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 10;' + '\n' +
+                'int b = 20;' + '\n' +
+                '++a;' + '\n' +
+                '--b;' + '\n' +
+                'a++;' + '\n' +
+                'b--;' + '\n' +
+            '}'
+        )
+
+        c_src2 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 10;' + '\n' +
+                'int b = -100;' + '\n' +
+                'int c = +19;' + '\n' +
+                'int d = ++a;' + '\n' +
+                'int e = --b;' + '\n' +
+                'int f = a++;' + '\n' +
+                'int g = b--;' + '\n' +
+                'bool h = !false;' + '\n' +
+                'bool i = !d;' + '\n' +
+                'bool j = !0;' + '\n' +
+                'bool k = !10.0;' + '\n' +
+            '}'
+        )
+
+        c_src_raise1 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 10;' + '\n' +
+                'int b = ~a;' + '\n' +
+            '}'
+        )
+
+        c_src_raise2 = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 10;' + '\n' +
+                'int b = *&a;' + '\n' +
+            '}'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+
+        assert res1[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(10)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(20)
+                        )
+                    ),
+                PreIncrement(Symbol('a')),
+                PreDecrement(Symbol('b')),
+                PostIncrement(Symbol('a')),
+                PostDecrement(Symbol('b'))
+                )
+            )
+
+        assert res2[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(10)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('b'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(-100)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('c'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(19)
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('d'),
+                        type=IntBaseType(String('intc')),
+                        value=PreIncrement(Symbol('a'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('e'),
+                        type=IntBaseType(String('intc')),
+                        value=PreDecrement(Symbol('b'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('f'),
+                        type=IntBaseType(String('intc')),
+                        value=PostIncrement(Symbol('a'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('g'),
+                        type=IntBaseType(String('intc')),
+                        value=PostDecrement(Symbol('b'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('h'),
+                        type=Type(String('bool')),
+                        value=true
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('i'),
+                        type=Type(String('bool')),
+                        value=Not(Symbol('d'))
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('j'),
+                        type=Type(String('bool')),
+                        value=true
+                        )
+                    ),
+                Declaration(
+                    Variable(Symbol('k'),
+                        type=Type(String('bool')),
+                        value=false
+                        )
+                    )
+                )
+            )
+
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise1, 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(c_src_raise2, 'c'))
+
+
+    def test_compound_assignment_operator():
+        c_src = (
+            'void func()'+
+            '{' + '\n' +
+                'int a = 100;' + '\n' +
+                'a += 10;' + '\n' +
+                'a -= 10;' + '\n' +
+                'a *= 10;' + '\n' +
+                'a /= 10;' + '\n' +
+                'a %= 10;' + '\n' +
+            '}'
+        )
+
+        res = SymPyExpression(c_src, 'c').return_expr()
+
+        assert res[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('a'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(100)
+                        )
+                    ),
+                AddAugmentedAssignment(
+                    Variable(Symbol('a')),
+                    Integer(10)
+                    ),
+                SubAugmentedAssignment(
+                    Variable(Symbol('a')),
+                    Integer(10)
+                    ),
+                MulAugmentedAssignment(
+                    Variable(Symbol('a')),
+                    Integer(10)
+                    ),
+                DivAugmentedAssignment(
+                    Variable(Symbol('a')),
+                    Integer(10)
+                    ),
+                ModAugmentedAssignment(
+                    Variable(Symbol('a')),
+                    Integer(10)
+                    )
+                )
+            )
+
+    @XFAIL # this is expected to fail because of a bug in the C parser.
+    def test_while_stmt():
+        c_src1 = (
+            'void func()'+
+            '{' + '\n' +
+                'int i = 0;' + '\n' +
+                'while(i < 10)' + '\n' +
+                '{' + '\n' +
+                    'i++;' + '\n' +
+                '}'
+            '}'
+        )
+
+        c_src2 = (
+            'void func()'+
+            '{' + '\n' +
+                'int i = 0;' + '\n' +
+                'while(i < 10)' + '\n' +
+                    'i++;' + '\n' +
+            '}'
+        )
+
+        c_src3 = (
+            'void func()'+
+            '{' + '\n' +
+                'int i = 10;' + '\n' +
+                'int cnt = 0;' + '\n' +
+                'while(i > 0)' + '\n' +
+                '{' + '\n' +
+                    'i--;' + '\n' +
+                    'cnt++;' + '\n' +
+                '}' + '\n' +
+            '}'
+        )
+
+        c_src4 = (
+            'int digit_sum(int n)'+
+            '{' + '\n' +
+                'int sum = 0;' + '\n' +
+                'while(n > 0)' + '\n' +
+                '{' + '\n' +
+                    'sum += (n % 10);' + '\n' +
+                    'n /= 10;' + '\n' +
+                '}' + '\n' +
+                'return sum;' + '\n' +
+            '}'
+        )
+
+        c_src5 = (
+            'void func()'+
+            '{' + '\n' +
+                'while(1);' + '\n' +
+            '}'
+        )
+
+        res1 = SymPyExpression(c_src1, 'c').return_expr()
+        res2 = SymPyExpression(c_src2, 'c').return_expr()
+        res3 = SymPyExpression(c_src3, 'c').return_expr()
+        res4 = SymPyExpression(c_src4, 'c').return_expr()
+        res5 = SymPyExpression(c_src5, 'c').return_expr()
+
+        assert res1[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(Symbol('i'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(0)
+                        )
+                    ),
+                While(
+                    StrictLessThan(
+                        Symbol('i'),
+                        Integer(10)
+                        ),
+                    body=CodeBlock(
+                        PostIncrement(
+                            Symbol('i')
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res2[0] == res1[0]
+
+        assert res3[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('i'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(10)
+                        )
+                    ),
+                Declaration(
+                    Variable(
+                        Symbol('cnt'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(0)
+                        )
+                    ),
+                While(
+                    StrictGreaterThan(
+                        Symbol('i'),
+                        Integer(0)
+                        ),
+                    body=CodeBlock(
+                        PostDecrement(
+                            Symbol('i')
+                            ),
+                        PostIncrement(
+                            Symbol('cnt')
+                            )
+                        )
+                    )
+                )
+            )
+
+        assert res4[0] == FunctionDefinition(
+            IntBaseType(String('intc')),
+            name=String('digit_sum'),
+            parameters=(
+                Variable(
+                    Symbol('n'),
+                    type=IntBaseType(String('intc'))
+                    ),
+                ),
+            body=CodeBlock(
+                Declaration(
+                    Variable(
+                        Symbol('sum'),
+                        type=IntBaseType(String('intc')),
+                        value=Integer(0)
+                        )
+                    ),
+                While(
+                    StrictGreaterThan(
+                        Symbol('n'),
+                        Integer(0)
+                        ),
+                    body=CodeBlock(
+                        AddAugmentedAssignment(
+                            Variable(
+                                Symbol('sum')
+                                ),
+                            Mod(
+                                Symbol('n'),
+                                Integer(10)
+                                )
+                            ),
+                        DivAugmentedAssignment(
+                            Variable(
+                                Symbol('n')
+                                ),
+                            Integer(10)
+                            )
+                        )
+                    ),
+                Return('sum')
+                )
+            )
+
+        assert res5[0] == FunctionDefinition(
+            NoneToken(),
+            name=String('func'),
+            parameters=(),
+            body=CodeBlock(
+                While(
+                    Integer(1),
+                    body=CodeBlock(
+                        NoneToken()
+                        )
+                    )
+                )
+            )
+
+
+else:
+    def test_raise():
+        from sympy.parsing.c.c_parser import CCodeConverter
+        raises(ImportError, lambda: CCodeConverter())
+        raises(ImportError, lambda: SymPyExpression(' ', mode = 'c'))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_custom_latex.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_custom_latex.py
new file mode 100644
index 0000000000000000000000000000000000000000..f5eff1c9ec79528c7f9e3a06cf9e2f84c86091ee
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_custom_latex.py
@@ -0,0 +1,69 @@
+import os
+import tempfile
+from pathlib import Path
+
+import sympy
+from sympy.testing.pytest import raises
+from sympy.parsing.latex.lark import LarkLaTeXParser, TransformToSymPyExpr, parse_latex_lark
+from sympy.external import import_module
+
+lark = import_module("lark")
+
+# disable tests if lark is not present
+disabled = lark is None
+
+grammar_file = os.path.join(os.path.dirname(__file__), "../latex/lark/grammar/latex.lark")
+
+modification1 = """
+%override DIV_SYMBOL: DIV
+%override MUL_SYMBOL: MUL | CMD_TIMES
+"""
+
+modification2 = r"""
+%override number: /\d+(,\d*)?/
+"""
+
+def init_custom_parser(modification, transformer=None):
+    latex_grammar = Path(grammar_file).read_text(encoding="utf-8")
+    latex_grammar += modification
+
+    with tempfile.NamedTemporaryFile() as f:
+        f.write(bytes(latex_grammar, encoding="utf8"))
+        f.flush()
+
+        parser = LarkLaTeXParser(grammar_file=f.name, transformer=transformer)
+
+    return parser
+
+def test_custom1():
+    # Removes the parser's ability to understand \cdot and \div.
+
+    parser = init_custom_parser(modification1)
+
+    with raises(lark.exceptions.UnexpectedCharacters):
+        parser.doparse(r"a \cdot b")
+        parser.doparse(r"x \div y")
+
+class CustomTransformer(TransformToSymPyExpr):
+    def number(self, tokens):
+        if "," in tokens[0]:
+            # The Float constructor expects a dot as the decimal separator
+            return sympy.core.numbers.Float(tokens[0].replace(",", "."))
+        else:
+            return sympy.core.numbers.Integer(tokens[0])
+
+def test_custom2():
+    # Makes the parser parse commas as the decimal separator instead of dots
+
+    parser = init_custom_parser(modification2, CustomTransformer)
+
+    with raises(lark.exceptions.UnexpectedCharacters):
+        # Asserting that the default parser cannot parse numbers which have commas as
+        # the decimal separator
+        parse_latex_lark("100,1")
+        parse_latex_lark("0,009")
+
+    parser.doparse("100,1")
+    parser.doparse("0,009")
+    parser.doparse("2,71828")
+    parser.doparse("3,14159")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_fortran_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_fortran_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..9bcd54533ef231dd0a116910453dff0e993bc727
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_fortran_parser.py
@@ -0,0 +1,406 @@
+from sympy.testing.pytest import raises
+from sympy.parsing.sym_expr import SymPyExpression
+from sympy.external import import_module
+
+lfortran = import_module('lfortran')
+
+if lfortran:
+    from sympy.codegen.ast import (Variable, IntBaseType, FloatBaseType, String,
+                                   Return, FunctionDefinition, Assignment,
+                                   Declaration, CodeBlock)
+    from sympy.core import Integer, Float, Add
+    from sympy.core.symbol import Symbol
+
+
+    expr1 = SymPyExpression()
+    expr2 = SymPyExpression()
+    src = """\
+    integer :: a, b, c, d
+    real :: p, q, r, s
+    """
+
+
+    def test_sym_expr():
+        src1 = (
+            src +
+            """\
+            d = a + b -c
+            """
+        )
+        expr3 = SymPyExpression(src,'f')
+        expr4 = SymPyExpression(src1,'f')
+        ls1 = expr3.return_expr()
+        ls2 = expr4.return_expr()
+        for i in range(0, 7):
+            assert isinstance(ls1[i], Declaration)
+            assert isinstance(ls2[i], Declaration)
+        assert isinstance(ls2[8], Assignment)
+        assert ls1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[4] == Declaration(
+            Variable(
+                Symbol('p'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls1[5] == Declaration(
+            Variable(
+                Symbol('q'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls1[6] == Declaration(
+            Variable(
+                Symbol('r'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls1[7] == Declaration(
+            Variable(
+                Symbol('s'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls2[8] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') + Symbol('b') - Symbol('c')
+        )
+
+    def test_assignment():
+        src1 = (
+            src +
+            """\
+            a = b
+            c = d
+            p = q
+            r = s
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(0, 12):
+            if iter < 8:
+                assert isinstance(ls1[iter], Declaration)
+            else:
+                assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('a')),
+            Variable(Symbol('b'))
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('c')),
+            Variable(Symbol('d'))
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('p')),
+            Variable(Symbol('q'))
+        )
+        assert ls1[11] == Assignment(
+            Variable(Symbol('r')),
+            Variable(Symbol('s'))
+        )
+
+
+    def test_binop_add():
+        src1 = (
+            src +
+            """\
+            c = a + b
+            d = a + c
+            s = p + q + r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 11):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') + Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') + Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') + Symbol('q') + Symbol('r')
+        )
+
+
+    def test_binop_sub():
+        src1 = (
+            src +
+            """\
+            c = a - b
+            d = a - c
+            s = p - q - r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 11):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') - Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') - Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') - Symbol('q') - Symbol('r')
+        )
+
+
+    def test_binop_mul():
+        src1 = (
+            src +
+            """\
+            c = a * b
+            d = a * c
+            s = p * q * r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 11):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') * Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') * Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') * Symbol('q') * Symbol('r')
+        )
+
+
+    def test_binop_div():
+        src1 = (
+            src +
+            """\
+            c = a / b
+            d = a / c
+            s = p / q
+            r = q / p
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 12):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') / Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') / Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') / Symbol('q')
+        )
+        assert ls1[11] == Assignment(
+            Variable(Symbol('r')),
+            Symbol('q') / Symbol('p')
+        )
+
+    def test_mul_binop():
+        src1 = (
+            src +
+            """\
+            d = a + b - c
+            c = a * b + d
+            s = p * q / r
+            r = p * s + q / p
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 12):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') + Symbol('b') - Symbol('c')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') * Symbol('b') + Symbol('d')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') * Symbol('q') / Symbol('r')
+        )
+        assert ls1[11] == Assignment(
+            Variable(Symbol('r')),
+            Symbol('p') * Symbol('s') + Symbol('q') / Symbol('p')
+        )
+
+
+    def test_function():
+        src1 = """\
+        integer function f(a,b)
+        integer :: x, y
+        f = x + y
+        end function
+        """
+        expr1.convert_to_expr(src1, 'f')
+        for iter in expr1.return_expr():
+            assert isinstance(iter, FunctionDefinition)
+            assert iter == FunctionDefinition(
+                IntBaseType(String('integer')),
+                name=String('f'),
+                parameters=(
+                    Variable(Symbol('a')),
+                    Variable(Symbol('b'))
+                ),
+                body=CodeBlock(
+                    Declaration(
+                        Variable(
+                            Symbol('a'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('b'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('f'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('x'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('y'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Assignment(
+                        Variable(Symbol('f')),
+                        Add(Symbol('x'), Symbol('y'))
+                    ),
+                    Return(Variable(Symbol('f')))
+                )
+            )
+
+
+    def test_var():
+        expr1.convert_to_expr(src, 'f')
+        ls = expr1.return_expr()
+        for iter in expr1.return_expr():
+            assert isinstance(iter, Declaration)
+        assert ls[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[4] == Declaration(
+            Variable(
+                Symbol('p'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls[5] == Declaration(
+            Variable(
+                Symbol('q'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls[6] == Declaration(
+            Variable(
+                Symbol('r'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls[7] == Declaration(
+            Variable(
+                Symbol('s'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+
+else:
+    def test_raise():
+        from sympy.parsing.fortran.fortran_parser import ASR2PyVisitor
+        raises(ImportError, lambda: ASR2PyVisitor())
+        raises(ImportError, lambda: SymPyExpression(' ', mode = 'f'))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_implicit_multiplication_application.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_implicit_multiplication_application.py
new file mode 100644
index 0000000000000000000000000000000000000000..56df361e77b0c0f94bdb53b03e0dc30a8a10899f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_implicit_multiplication_application.py
@@ -0,0 +1,195 @@
+import sympy
+from sympy.parsing.sympy_parser import (
+    parse_expr,
+    standard_transformations,
+    convert_xor,
+    implicit_multiplication_application,
+    implicit_multiplication,
+    implicit_application,
+    function_exponentiation,
+    split_symbols,
+    split_symbols_custom,
+    _token_splittable
+)
+from sympy.testing.pytest import raises
+
+
+def test_implicit_multiplication():
+    cases = {
+        '5x': '5*x',
+        'abc': 'a*b*c',
+        '3sin(x)': '3*sin(x)',
+        '(x+1)(x+2)': '(x+1)*(x+2)',
+        '(5 x**2)sin(x)': '(5*x**2)*sin(x)',
+        '2 sin(x) cos(x)': '2*sin(x)*cos(x)',
+        'pi x': 'pi*x',
+        'x pi': 'x*pi',
+        'E x': 'E*x',
+        'EulerGamma y': 'EulerGamma*y',
+        'E pi': 'E*pi',
+        'pi (x + 2)': 'pi*(x+2)',
+        '(x + 2) pi': '(x+2)*pi',
+        'pi sin(x)': 'pi*sin(x)',
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (split_symbols,
+                                          implicit_multiplication)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal)
+
+    application = ['sin x', 'cos 2*x', 'sin cos x']
+    for case in application:
+        raises(SyntaxError,
+               lambda: parse_expr(case, transformations=transformations2))
+    raises(TypeError,
+           lambda: parse_expr('sin**2(x)', transformations=transformations2))
+
+
+def test_implicit_application():
+    cases = {
+        'factorial': 'factorial',
+        'sin x': 'sin(x)',
+        'tan y**3': 'tan(y**3)',
+        'cos 2*x': 'cos(2*x)',
+        '(cot)': 'cot',
+        'sin cos tan x': 'sin(cos(tan(x)))'
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (implicit_application,)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal), (implicit, normal)
+
+    multiplication = ['x y', 'x sin x', '2x']
+    for case in multiplication:
+        raises(SyntaxError,
+               lambda: parse_expr(case, transformations=transformations2))
+    raises(TypeError,
+           lambda: parse_expr('sin**2(x)', transformations=transformations2))
+
+
+def test_function_exponentiation():
+    cases = {
+        'sin**2(x)': 'sin(x)**2',
+        'exp^y(z)': 'exp(z)^y',
+        'sin**2(E^(x))': 'sin(E^(x))**2'
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (function_exponentiation,)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal)
+
+    other_implicit = ['x y', 'x sin x', '2x', 'sin x',
+                      'cos 2*x', 'sin cos x']
+    for case in other_implicit:
+        raises(SyntaxError,
+               lambda: parse_expr(case, transformations=transformations2))
+
+    assert parse_expr('x**2', local_dict={ 'x': sympy.Symbol('x') },
+                      transformations=transformations2) == parse_expr('x**2')
+
+
+def test_symbol_splitting():
+    # By default Greek letter names should not be split (lambda is a keyword
+    # so skip it)
+    transformations = standard_transformations + (split_symbols,)
+    greek_letters = ('alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta',
+                     'eta', 'theta', 'iota', 'kappa', 'mu', 'nu', 'xi',
+                     'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon',
+                     'phi', 'chi', 'psi', 'omega')
+
+    for letter in greek_letters:
+        assert(parse_expr(letter, transformations=transformations) ==
+               parse_expr(letter))
+
+    # Make sure symbol splitting resolves names
+    transformations += (implicit_multiplication,)
+    local_dict = { 'e': sympy.E }
+    cases = {
+        'xe': 'E*x',
+        'Iy': 'I*y',
+        'ee': 'E*E',
+    }
+    for case, expected in cases.items():
+        assert(parse_expr(case, local_dict=local_dict,
+                          transformations=transformations) ==
+               parse_expr(expected))
+
+    # Make sure custom splitting works
+    def can_split(symbol):
+        if symbol not in ('unsplittable', 'names'):
+            return _token_splittable(symbol)
+        return False
+    transformations = standard_transformations
+    transformations += (split_symbols_custom(can_split),
+                        implicit_multiplication)
+
+    assert(parse_expr('unsplittable', transformations=transformations) ==
+           parse_expr('unsplittable'))
+    assert(parse_expr('names', transformations=transformations) ==
+           parse_expr('names'))
+    assert(parse_expr('xy', transformations=transformations) ==
+           parse_expr('x*y'))
+    for letter in greek_letters:
+        assert(parse_expr(letter, transformations=transformations) ==
+               parse_expr(letter))
+
+
+def test_all_implicit_steps():
+    cases = {
+        '2x': '2*x',  # implicit multiplication
+        'x y': 'x*y',
+        'xy': 'x*y',
+        'sin x': 'sin(x)',  # add parentheses
+        '2sin x': '2*sin(x)',
+        'x y z': 'x*y*z',
+        'sin(2 * 3x)': 'sin(2 * 3 * x)',
+        'sin(x) (1 + cos(x))': 'sin(x) * (1 + cos(x))',
+        '(x + 2) sin(x)': '(x + 2) * sin(x)',
+        '(x + 2) sin x': '(x + 2) * sin(x)',
+        'sin(sin x)': 'sin(sin(x))',
+        'sin x!': 'sin(factorial(x))',
+        'sin x!!': 'sin(factorial2(x))',
+        'factorial': 'factorial',  # don't apply a bare function
+        'x sin x': 'x * sin(x)',  # both application and multiplication
+        'xy sin x': 'x * y * sin(x)',
+        '(x+2)(x+3)': '(x + 2) * (x+3)',
+        'x**2 + 2xy + y**2': 'x**2 + 2 * x * y + y**2',  # split the xy
+        'pi': 'pi',  # don't mess with constants
+        'None': 'None',
+        'ln sin x': 'ln(sin(x))',  # multiple implicit function applications
+        'sin x**2': 'sin(x**2)',  # implicit application to an exponential
+        'alpha': 'Symbol("alpha")',  # don't split Greek letters/subscripts
+        'x_2': 'Symbol("x_2")',
+        'sin^2 x**2': 'sin(x**2)**2',  # function raised to a power
+        'sin**3(x)': 'sin(x)**3',
+        '(factorial)': 'factorial',
+        'tan 3x': 'tan(3*x)',
+        'sin^2(3*E^(x))': 'sin(3*E**(x))**2',
+        'sin**2(E^(3x))': 'sin(E**(3*x))**2',
+        'sin^2 (3x*E^(x))': 'sin(3*x*E^x)**2',
+        'pi sin x': 'pi*sin(x)',
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (implicit_multiplication_application,)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal)
+
+
+def test_no_methods_implicit_multiplication():
+    # Issue 21020
+    u = sympy.Symbol('u')
+    transformations = standard_transformations + \
+                      (implicit_multiplication,)
+    expr = parse_expr('x.is_polynomial(x)', transformations=transformations)
+    assert expr == True
+    expr = parse_expr('(exp(x) / (1 + exp(2x))).subs(exp(x), u)',
+                      transformations=transformations)
+    assert expr == u/(u**2 + 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex.py
new file mode 100644
index 0000000000000000000000000000000000000000..49a48966eacaa1cd7a242dcd0e7699c992bb1268
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex.py
@@ -0,0 +1,358 @@
+from sympy.testing.pytest import raises, XFAIL
+from sympy.external import import_module
+
+from sympy.concrete.products import Product
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.function import (Derivative, Function)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (E, oo)
+from sympy.core.power import Pow
+from sympy.core.relational import (GreaterThan, LessThan, StrictGreaterThan, StrictLessThan, Unequality)
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import (binomial, factorial)
+from sympy.functions.elementary.complexes import (Abs, conjugate)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.integers import (ceiling, floor)
+from sympy.functions.elementary.miscellaneous import (root, sqrt)
+from sympy.functions.elementary.trigonometric import (asin, cos, csc, sec, sin, tan)
+from sympy.integrals.integrals import Integral
+from sympy.series.limits import Limit
+
+from sympy.core.relational import Eq, Ne, Lt, Le, Gt, Ge
+from sympy.physics.quantum.state import Bra, Ket
+from sympy.abc import x, y, z, a, b, c, t, k, n
+antlr4 = import_module("antlr4")
+
+# disable tests if antlr4-python3-runtime is not present
+disabled = antlr4 is None
+
+theta = Symbol('theta')
+f = Function('f')
+
+
+# shorthand definitions
+def _Add(a, b):
+    return Add(a, b, evaluate=False)
+
+
+def _Mul(a, b):
+    return Mul(a, b, evaluate=False)
+
+
+def _Pow(a, b):
+    return Pow(a, b, evaluate=False)
+
+
+def _Sqrt(a):
+    return sqrt(a, evaluate=False)
+
+
+def _Conjugate(a):
+    return conjugate(a, evaluate=False)
+
+
+def _Abs(a):
+    return Abs(a, evaluate=False)
+
+
+def _factorial(a):
+    return factorial(a, evaluate=False)
+
+
+def _exp(a):
+    return exp(a, evaluate=False)
+
+
+def _log(a, b):
+    return log(a, b, evaluate=False)
+
+
+def _binomial(n, k):
+    return binomial(n, k, evaluate=False)
+
+
+def test_import():
+    from sympy.parsing.latex._build_latex_antlr import (
+        build_parser,
+        check_antlr_version,
+        dir_latex_antlr
+    )
+    # XXX: It would be better to come up with a test for these...
+    del build_parser, check_antlr_version, dir_latex_antlr
+
+
+# These LaTeX strings should parse to the corresponding SymPy expression
+GOOD_PAIRS = [
+    (r"0", 0),
+    (r"1", 1),
+    (r"-3.14", -3.14),
+    (r"(-7.13)(1.5)", _Mul(-7.13, 1.5)),
+    (r"x", x),
+    (r"2x", 2*x),
+    (r"x^2", x**2),
+    (r"x^\frac{1}{2}", _Pow(x, _Pow(2, -1))),
+    (r"x^{3 + 1}", x**_Add(3, 1)),
+    (r"-c", -c),
+    (r"a \cdot b", a * b),
+    (r"a / b", a / b),
+    (r"a \div b", a / b),
+    (r"a + b", a + b),
+    (r"a + b - a", _Add(a+b, -a)),
+    (r"a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2)),
+    (r"(x + y) z", _Mul(_Add(x, y), z)),
+    (r"a'b+ab'", _Add(_Mul(Symbol("a'"), b), _Mul(a, Symbol("b'")))),
+    (r"y''_1", Symbol("y_{1}''")),
+    (r"y_1''", Symbol("y_{1}''")),
+    (r"\left(x + y\right) z", _Mul(_Add(x, y), z)),
+    (r"\left( x + y\right ) z", _Mul(_Add(x, y), z)),
+    (r"\left(  x + y\right ) z", _Mul(_Add(x, y), z)),
+    (r"\left[x + y\right] z", _Mul(_Add(x, y), z)),
+    (r"\left\{x + y\right\} z", _Mul(_Add(x, y), z)),
+    (r"1+1", _Add(1, 1)),
+    (r"0+1", _Add(0, 1)),
+    (r"1*2", _Mul(1, 2)),
+    (r"0*1", _Mul(0, 1)),
+    (r"1 \times 2 ", _Mul(1, 2)),
+    (r"x = y", Eq(x, y)),
+    (r"x \neq y", Ne(x, y)),
+    (r"x < y", Lt(x, y)),
+    (r"x > y", Gt(x, y)),
+    (r"x \leq y", Le(x, y)),
+    (r"x \geq y", Ge(x, y)),
+    (r"x \le y", Le(x, y)),
+    (r"x \ge y", Ge(x, y)),
+    (r"\lfloor x \rfloor", floor(x)),
+    (r"\lceil x \rceil", ceiling(x)),
+    (r"\langle x |", Bra('x')),
+    (r"| x \rangle", Ket('x')),
+    (r"\sin \theta", sin(theta)),
+    (r"\sin(\theta)", sin(theta)),
+    (r"\sin^{-1} a", asin(a)),
+    (r"\sin a \cos b", _Mul(sin(a), cos(b))),
+    (r"\sin \cos \theta", sin(cos(theta))),
+    (r"\sin(\cos \theta)", sin(cos(theta))),
+    (r"\frac{a}{b}", a / b),
+    (r"\dfrac{a}{b}", a / b),
+    (r"\tfrac{a}{b}", a / b),
+    (r"\frac12", _Pow(2, -1)),
+    (r"\frac12y", _Mul(_Pow(2, -1), y)),
+    (r"\frac1234", _Mul(_Pow(2, -1), 34)),
+    (r"\frac2{3}", _Mul(2, _Pow(3, -1))),
+    (r"\frac{\sin{x}}2", _Mul(sin(x), _Pow(2, -1))),
+    (r"\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
+    (r"\frac{7}{3}", _Mul(7, _Pow(3, -1))),
+    (r"(\csc x)(\sec y)", csc(x)*sec(y)),
+    (r"\lim_{x \to 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \rightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \Rightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \longrightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \Longrightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \to 3^{+}} a", Limit(a, x, 3, dir='+')),
+    (r"\lim_{x \to 3^{-}} a", Limit(a, x, 3, dir='-')),
+    (r"\lim_{x \to 3^+} a", Limit(a, x, 3, dir='+')),
+    (r"\lim_{x \to 3^-} a", Limit(a, x, 3, dir='-')),
+    (r"\infty", oo),
+    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(_Pow(x, -1), x, oo)),
+    (r"\frac{d}{dx} x", Derivative(x, x)),
+    (r"\frac{d}{dt} x", Derivative(x, t)),
+    (r"f(x)", f(x)),
+    (r"f(x, y)", f(x, y)),
+    (r"f(x, y, z)", f(x, y, z)),
+    (r"f'_1(x)", Function("f_{1}'")(x)),
+    (r"f_{1}''(x+y)", Function("f_{1}''")(x+y)),
+    (r"\frac{d f(x)}{dx}", Derivative(f(x), x)),
+    (r"\frac{d\theta(x)}{dx}", Derivative(Function('theta')(x), x)),
+    (r"x \neq y", Unequality(x, y)),
+    (r"|x|", _Abs(x)),
+    (r"||x||", _Abs(Abs(x))),
+    (r"|x||y|", _Abs(x)*_Abs(y)),
+    (r"||x||y||", _Abs(_Abs(x)*_Abs(y))),
+    (r"\pi^{|xy|}", Symbol('pi')**_Abs(x*y)),
+    (r"\int x dx", Integral(x, x)),
+    (r"\int x d\theta", Integral(x, theta)),
+    (r"\int (x^2 - y)dx", Integral(x**2 - y, x)),
+    (r"\int x + a dx", Integral(_Add(x, a), x)),
+    (r"\int da", Integral(1, a)),
+    (r"\int_0^7 dx", Integral(1, (x, 0, 7))),
+    (r"\int\limits_{0}^{1} x dx", Integral(x, (x, 0, 1))),
+    (r"\int_a^b x dx", Integral(x, (x, a, b))),
+    (r"\int^b_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^b x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^{b} x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_{a} x dx", Integral(x, (x, a, b))),
+    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
+    (r"\int (x+a)", Integral(_Add(x, a), x)),
+    (r"\int a + b + c dx", Integral(_Add(_Add(a, b), c), x)),
+    (r"\int \frac{dz}{z}", Integral(Pow(z, -1), z)),
+    (r"\int \frac{3 dz}{z}", Integral(3*Pow(z, -1), z)),
+    (r"\int \frac{1}{x} dx", Integral(Pow(x, -1), x)),
+    (r"\int \frac{1}{a} + \frac{1}{b} dx",
+     Integral(_Add(_Pow(a, -1), Pow(b, -1)), x)),
+    (r"\int \frac{3 \cdot d\theta}{\theta}",
+     Integral(3*_Pow(theta, -1), theta)),
+    (r"\int \frac{1}{x} + 1 dx", Integral(_Add(_Pow(x, -1), 1), x)),
+    (r"x_0", Symbol('x_{0}')),
+    (r"x_{1}", Symbol('x_{1}')),
+    (r"x_a", Symbol('x_{a}')),
+    (r"x_{b}", Symbol('x_{b}')),
+    (r"h_\theta", Symbol('h_{theta}')),
+    (r"h_{\theta}", Symbol('h_{theta}')),
+    (r"h_{\theta}(x_0, x_1)",
+     Function('h_{theta}')(Symbol('x_{0}'), Symbol('x_{1}'))),
+    (r"x!", _factorial(x)),
+    (r"100!", _factorial(100)),
+    (r"\theta!", _factorial(theta)),
+    (r"(x + 1)!", _factorial(_Add(x, 1))),
+    (r"(x!)!", _factorial(_factorial(x))),
+    (r"x!!!", _factorial(_factorial(_factorial(x)))),
+    (r"5!7!", _Mul(_factorial(5), _factorial(7))),
+    (r"\sqrt{x}", sqrt(x)),
+    (r"\sqrt{x + b}", sqrt(_Add(x, b))),
+    (r"\sqrt[3]{\sin x}", root(sin(x), 3)),
+    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
+    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
+    (r"\sqrt{\frac{12}{6}}", _Sqrt(_Mul(12, _Pow(6, -1)))),
+    (r"\overline{z}", _Conjugate(z)),
+    (r"\overline{\overline{z}}", _Conjugate(_Conjugate(z))),
+    (r"\overline{x + y}", _Conjugate(_Add(x, y))),
+    (r"\overline{x} + \overline{y}", _Conjugate(x) + _Conjugate(y)),
+    (r"x < y", StrictLessThan(x, y)),
+    (r"x \leq y", LessThan(x, y)),
+    (r"x > y", StrictGreaterThan(x, y)),
+    (r"x \geq y", GreaterThan(x, y)),
+    (r"\mathit{x}", Symbol('x')),
+    (r"\mathit{test}", Symbol('test')),
+    (r"\mathit{TEST}", Symbol('TEST')),
+    (r"\mathit{HELLO world}", Symbol('HELLO world')),
+    (r"\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
+    (r"\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^{10} k^2", Sum(k**2, (k, 1, 10))),
+    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}",
+     Sum(_Pow(_factorial(n), -1), (n, 0, oo))),
+    (r"\prod_{a = b}^{c} x", Product(x, (a, b, c))),
+    (r"\prod_{a = b}^c x", Product(x, (a, b, c))),
+    (r"\prod^{c}_{a = b} x", Product(x, (a, b, c))),
+    (r"\prod^c_{a = b} x", Product(x, (a, b, c))),
+    (r"\exp x", _exp(x)),
+    (r"\exp(x)", _exp(x)),
+    (r"\lg x", _log(x, 10)),
+    (r"\ln x", _log(x, E)),
+    (r"\ln xy", _log(x*y, E)),
+    (r"\log x", _log(x, E)),
+    (r"\log xy", _log(x*y, E)),
+    (r"\log_{2} x", _log(x, 2)),
+    (r"\log_{a} x", _log(x, a)),
+    (r"\log_{11} x", _log(x, 11)),
+    (r"\log_{a^2} x", _log(x, _Pow(a, 2))),
+    (r"[x]", x),
+    (r"[a + b]", _Add(a, b)),
+    (r"\frac{d}{dx} [ \tan x ]", Derivative(tan(x), x)),
+    (r"\binom{n}{k}", _binomial(n, k)),
+    (r"\tbinom{n}{k}", _binomial(n, k)),
+    (r"\dbinom{n}{k}", _binomial(n, k)),
+    (r"\binom{n}{0}", _binomial(n, 0)),
+    (r"x^\binom{n}{k}", _Pow(x, _binomial(n, k))),
+    (r"a \, b", _Mul(a, b)),
+    (r"a \thinspace b", _Mul(a, b)),
+    (r"a \: b", _Mul(a, b)),
+    (r"a \medspace b", _Mul(a, b)),
+    (r"a \; b", _Mul(a, b)),
+    (r"a \thickspace b", _Mul(a, b)),
+    (r"a \quad b", _Mul(a, b)),
+    (r"a \qquad b", _Mul(a, b)),
+    (r"a \! b", _Mul(a, b)),
+    (r"a \negthinspace b", _Mul(a, b)),
+    (r"a \negmedspace b", _Mul(a, b)),
+    (r"a \negthickspace b", _Mul(a, b)),
+    (r"\int x \, dx", Integral(x, x)),
+    (r"\log_2 x", _log(x, 2)),
+    (r"\log_a x", _log(x, a)),
+    (r"5^0 - 4^0", _Add(_Pow(5, 0), _Mul(-1, _Pow(4, 0)))),
+    (r"3x - 1", _Add(_Mul(3, x), -1))
+]
+
+
+def test_parseable():
+    from sympy.parsing.latex import parse_latex
+    for latex_str, sympy_expr in GOOD_PAIRS:
+        assert parse_latex(latex_str) == sympy_expr, latex_str
+
+# These bad LaTeX strings should raise a LaTeXParsingError when parsed
+BAD_STRINGS = [
+    r"(",
+    r")",
+    r"\frac{d}{dx}",
+    r"(\frac{d}{dx})",
+    r"\sqrt{}",
+    r"\sqrt",
+    r"\overline{}",
+    r"\overline",
+    r"{",
+    r"}",
+    r"\mathit{x + y}",
+    r"\mathit{21}",
+    r"\frac{2}{}",
+    r"\frac{}{2}",
+    r"\int",
+    r"!",
+    r"!0",
+    r"_",
+    r"^",
+    r"|",
+    r"||x|",
+    r"()",
+    r"((((((((((((((((()))))))))))))))))",
+    r"-",
+    r"\frac{d}{dx} + \frac{d}{dt}",
+    r"f(x,,y)",
+    r"f(x,y,",
+    r"\sin^x",
+    r"\cos^2",
+    r"@",
+    r"#",
+    r"$",
+    r"%",
+    r"&",
+    r"*",
+    r"" "\\",
+    r"~",
+    r"\frac{(2 + x}{1 - x)}",
+]
+
+def test_not_parseable():
+    from sympy.parsing.latex import parse_latex, LaTeXParsingError
+    for latex_str in BAD_STRINGS:
+        with raises(LaTeXParsingError):
+            parse_latex(latex_str)
+
+# At time of migration from latex2sympy, should fail but doesn't
+FAILING_BAD_STRINGS = [
+    r"\cos 1 \cos",
+    r"f(,",
+    r"f()",
+    r"a \div \div b",
+    r"a \cdot \cdot b",
+    r"a // b",
+    r"a +",
+    r"1.1.1",
+    r"1 +",
+    r"a / b /",
+]
+
+@XFAIL
+def test_failing_not_parseable():
+    from sympy.parsing.latex import parse_latex, LaTeXParsingError
+    for latex_str in FAILING_BAD_STRINGS:
+        with raises(LaTeXParsingError):
+            parse_latex(latex_str)
+
+# In strict mode, FAILING_BAD_STRINGS would fail
+def test_strict_mode():
+    from sympy.parsing.latex import parse_latex, LaTeXParsingError
+    for latex_str in FAILING_BAD_STRINGS:
+        with raises(LaTeXParsingError):
+            parse_latex(latex_str, strict=True)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex_deps.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex_deps.py
new file mode 100644
index 0000000000000000000000000000000000000000..7df44c2b19e34024db6e898f7c4eac962dcaa1c9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex_deps.py
@@ -0,0 +1,16 @@
+from sympy.external import import_module
+from sympy.testing.pytest import ignore_warnings, raises
+
+antlr4 = import_module("antlr4", warn_not_installed=False)
+
+# disable tests if antlr4-python3-runtime is not present
+if antlr4:
+    disabled = True
+
+
+def test_no_import():
+    from sympy.parsing.latex import parse_latex
+
+    with ignore_warnings(UserWarning):
+        with raises(ImportError):
+            parse_latex('1 + 1')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex_lark.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex_lark.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd1f72a66c788ac41d923005ea988664d05a16c1
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_latex_lark.py
@@ -0,0 +1,872 @@
+from sympy.testing.pytest import XFAIL
+from sympy.parsing.latex.lark import parse_latex_lark
+from sympy.external import import_module
+
+from sympy.concrete.products import Product
+from sympy.concrete.summations import Sum
+from sympy.core.function import Derivative, Function
+from sympy.core.numbers import E, oo, Rational
+from sympy.core.power import Pow
+from sympy.core.parameters import evaluate
+from sympy.core.relational import GreaterThan, LessThan, StrictGreaterThan, StrictLessThan, Unequality
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import binomial, factorial
+from sympy.functions.elementary.complexes import Abs, conjugate
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.integers import ceiling, floor
+from sympy.functions.elementary.miscellaneous import root, sqrt, Min, Max
+from sympy.functions.elementary.trigonometric import asin, cos, csc, sec, sin, tan
+from sympy.integrals.integrals import Integral
+from sympy.series.limits import Limit
+from sympy import Matrix, MatAdd, MatMul, Transpose, Trace
+from sympy import I
+
+from sympy.core.relational import Eq, Ne, Lt, Le, Gt, Ge
+from sympy.physics.quantum import Bra, Ket, InnerProduct
+from sympy.abc import x, y, z, a, b, c, d, t, k, n
+
+from .test_latex import theta, f, _Add, _Mul, _Pow, _Sqrt, _Conjugate, _Abs, _factorial, _exp, _binomial
+
+lark = import_module("lark")
+
+# disable tests if lark is not present
+disabled = lark is None
+
+# shorthand definitions that are only needed for the Lark LaTeX parser
+def _Min(*args):
+    return Min(*args, evaluate=False)
+
+
+def _Max(*args):
+    return Max(*args, evaluate=False)
+
+
+def _log(a, b=E):
+    if b == E:
+        return log(a, evaluate=False)
+    else:
+        return log(a, b, evaluate=False)
+
+
+def _MatAdd(a, b):
+    return MatAdd(a, b, evaluate=False)
+
+
+def _MatMul(a, b):
+    return MatMul(a, b, evaluate=False)
+
+
+# These LaTeX strings should parse to the corresponding SymPy expression
+SYMBOL_EXPRESSION_PAIRS = [
+    (r"x_0", Symbol('x_{0}')),
+    (r"x_{1}", Symbol('x_{1}')),
+    (r"x_a", Symbol('x_{a}')),
+    (r"x_{b}", Symbol('x_{b}')),
+    (r"h_\theta", Symbol('h_{theta}')),
+    (r"h_{\theta}", Symbol('h_{theta}')),
+    (r"y''_1", Symbol("y''_{1}")),
+    (r"y_1''", Symbol("y_{1}''")),
+    (r"\mathit{x}", Symbol('x')),
+    (r"\mathit{test}", Symbol('test')),
+    (r"\mathit{TEST}", Symbol('TEST')),
+    (r"\mathit{HELLO world}", Symbol('HELLO world')),
+    (r"a'", Symbol("a'")),
+    (r"a''", Symbol("a''")),
+    (r"\alpha'", Symbol("alpha'")),
+    (r"\alpha''", Symbol("alpha''")),
+    (r"a_b", Symbol("a_{b}")),
+    (r"a_b'", Symbol("a_{b}'")),
+    (r"a'_b", Symbol("a'_{b}")),
+    (r"a'_b'", Symbol("a'_{b}'")),
+    (r"a_{b'}", Symbol("a_{b'}")),
+    (r"a_{b'}'", Symbol("a_{b'}'")),
+    (r"a'_{b'}", Symbol("a'_{b'}")),
+    (r"a'_{b'}'", Symbol("a'_{b'}'")),
+    (r"\mathit{foo}'", Symbol("foo'")),
+    (r"\mathit{foo'}", Symbol("foo'")),
+    (r"\mathit{foo'}'", Symbol("foo''")),
+    (r"a_b''", Symbol("a_{b}''")),
+    (r"a''_b", Symbol("a''_{b}")),
+    (r"a''_b'''", Symbol("a''_{b}'''")),
+    (r"a_{b''}", Symbol("a_{b''}")),
+    (r"a_{b''}''", Symbol("a_{b''}''")),
+    (r"a''_{b''}", Symbol("a''_{b''}")),
+    (r"a''_{b''}'''", Symbol("a''_{b''}'''")),
+    (r"\mathit{foo}''", Symbol("foo''")),
+    (r"\mathit{foo''}", Symbol("foo''")),
+    (r"\mathit{foo''}'''", Symbol("foo'''''")),
+    (r"a_\alpha", Symbol("a_{alpha}")),
+    (r"a_\alpha'", Symbol("a_{alpha}'")),
+    (r"a'_\alpha", Symbol("a'_{alpha}")),
+    (r"a'_\alpha'", Symbol("a'_{alpha}'")),
+    (r"a_{\alpha'}", Symbol("a_{alpha'}")),
+    (r"a_{\alpha'}'", Symbol("a_{alpha'}'")),
+    (r"a'_{\alpha'}", Symbol("a'_{alpha'}")),
+    (r"a'_{\alpha'}'", Symbol("a'_{alpha'}'")),
+    (r"a_\alpha''", Symbol("a_{alpha}''")),
+    (r"a''_\alpha", Symbol("a''_{alpha}")),
+    (r"a''_\alpha'''", Symbol("a''_{alpha}'''")),
+    (r"a_{\alpha''}", Symbol("a_{alpha''}")),
+    (r"a_{\alpha''}''", Symbol("a_{alpha''}''")),
+    (r"a''_{\alpha''}", Symbol("a''_{alpha''}")),
+    (r"a''_{\alpha''}'''", Symbol("a''_{alpha''}'''")),
+    (r"\alpha_b", Symbol("alpha_{b}")),
+    (r"\alpha_b'", Symbol("alpha_{b}'")),
+    (r"\alpha'_b", Symbol("alpha'_{b}")),
+    (r"\alpha'_b'", Symbol("alpha'_{b}'")),
+    (r"\alpha_{b'}", Symbol("alpha_{b'}")),
+    (r"\alpha_{b'}'", Symbol("alpha_{b'}'")),
+    (r"\alpha'_{b'}", Symbol("alpha'_{b'}")),
+    (r"\alpha'_{b'}'", Symbol("alpha'_{b'}'")),
+    (r"\alpha_b''", Symbol("alpha_{b}''")),
+    (r"\alpha''_b", Symbol("alpha''_{b}")),
+    (r"\alpha''_b'''", Symbol("alpha''_{b}'''")),
+    (r"\alpha_{b''}", Symbol("alpha_{b''}")),
+    (r"\alpha_{b''}''", Symbol("alpha_{b''}''")),
+    (r"\alpha''_{b''}", Symbol("alpha''_{b''}")),
+    (r"\alpha''_{b''}'''", Symbol("alpha''_{b''}'''")),
+    (r"\alpha_\beta", Symbol("alpha_{beta}")),
+    (r"\alpha_{\beta}", Symbol("alpha_{beta}")),
+    (r"\alpha_{\beta'}", Symbol("alpha_{beta'}")),
+    (r"\alpha_{\beta''}", Symbol("alpha_{beta''}")),
+    (r"\alpha'_\beta", Symbol("alpha'_{beta}")),
+    (r"\alpha'_{\beta}", Symbol("alpha'_{beta}")),
+    (r"\alpha'_{\beta'}", Symbol("alpha'_{beta'}")),
+    (r"\alpha'_{\beta''}", Symbol("alpha'_{beta''}")),
+    (r"\alpha''_\beta", Symbol("alpha''_{beta}")),
+    (r"\alpha''_{\beta}", Symbol("alpha''_{beta}")),
+    (r"\alpha''_{\beta'}", Symbol("alpha''_{beta'}")),
+    (r"\alpha''_{\beta''}", Symbol("alpha''_{beta''}")),
+    (r"\alpha_\beta'", Symbol("alpha_{beta}'")),
+    (r"\alpha_{\beta}'", Symbol("alpha_{beta}'")),
+    (r"\alpha_{\beta'}'", Symbol("alpha_{beta'}'")),
+    (r"\alpha_{\beta''}'", Symbol("alpha_{beta''}'")),
+    (r"\alpha'_\beta'", Symbol("alpha'_{beta}'")),
+    (r"\alpha'_{\beta}'", Symbol("alpha'_{beta}'")),
+    (r"\alpha'_{\beta'}'", Symbol("alpha'_{beta'}'")),
+    (r"\alpha'_{\beta''}'", Symbol("alpha'_{beta''}'")),
+    (r"\alpha''_\beta'", Symbol("alpha''_{beta}'")),
+    (r"\alpha''_{\beta}'", Symbol("alpha''_{beta}'")),
+    (r"\alpha''_{\beta'}'", Symbol("alpha''_{beta'}'")),
+    (r"\alpha''_{\beta''}'", Symbol("alpha''_{beta''}'")),
+    (r"\alpha_\beta''", Symbol("alpha_{beta}''")),
+    (r"\alpha_{\beta}''", Symbol("alpha_{beta}''")),
+    (r"\alpha_{\beta'}''", Symbol("alpha_{beta'}''")),
+    (r"\alpha_{\beta''}''", Symbol("alpha_{beta''}''")),
+    (r"\alpha'_\beta''", Symbol("alpha'_{beta}''")),
+    (r"\alpha'_{\beta}''", Symbol("alpha'_{beta}''")),
+    (r"\alpha'_{\beta'}''", Symbol("alpha'_{beta'}''")),
+    (r"\alpha'_{\beta''}''", Symbol("alpha'_{beta''}''")),
+    (r"\alpha''_\beta''", Symbol("alpha''_{beta}''")),
+    (r"\alpha''_{\beta}''", Symbol("alpha''_{beta}''")),
+    (r"\alpha''_{\beta'}''", Symbol("alpha''_{beta'}''")),
+    (r"\alpha''_{\beta''}''", Symbol("alpha''_{beta''}''"))
+
+]
+
+UNEVALUATED_SIMPLE_EXPRESSION_PAIRS = [
+    (r"0", 0),
+    (r"1", 1),
+    (r"-3.14", -3.14),
+    (r"(-7.13)(1.5)", _Mul(-7.13, 1.5)),
+    (r"1+1", _Add(1, 1)),
+    (r"0+1", _Add(0, 1)),
+    (r"1*2", _Mul(1, 2)),
+    (r"0*1", _Mul(0, 1)),
+    (r"x", x),
+    (r"2x", 2 * x),
+    (r"3x - 1", _Add(_Mul(3, x), -1)),
+    (r"-c", -c),
+    (r"\infty", oo),
+    (r"a \cdot b", a * b),
+    (r"1 \times 2 ", _Mul(1, 2)),
+    (r"a / b", a / b),
+    (r"a \div b", a / b),
+    (r"a + b", a + b),
+    (r"a + b - a", _Add(a + b, -a)),
+    (r"(x + y) z", _Mul(_Add(x, y), z)),
+    (r"a'b+ab'", _Add(_Mul(Symbol("a'"), b), _Mul(a, Symbol("b'"))))
+]
+
+EVALUATED_SIMPLE_EXPRESSION_PAIRS = [
+    (r"(-7.13)(1.5)", -10.695),
+    (r"1+1", 2),
+    (r"0+1", 1),
+    (r"1*2", 2),
+    (r"0*1", 0),
+    (r"2x", 2 * x),
+    (r"3x - 1", 3 * x - 1),
+    (r"-c", -c),
+    (r"a \cdot b", a * b),
+    (r"1 \times 2 ", 2),
+    (r"a / b", a / b),
+    (r"a \div b", a / b),
+    (r"a + b", a + b),
+    (r"a + b - a", b),
+    (r"(x + y) z", (x + y) * z),
+]
+
+UNEVALUATED_FRACTION_EXPRESSION_PAIRS = [
+    (r"\frac{a}{b}", a / b),
+    (r"\dfrac{a}{b}", a / b),
+    (r"\tfrac{a}{b}", a / b),
+    (r"\frac12", _Mul(1, _Pow(2, -1))),
+    (r"\frac12y", _Mul(_Mul(1, _Pow(2, -1)), y)),
+    (r"\frac1234", _Mul(_Mul(1, _Pow(2, -1)), 34)),
+    (r"\frac2{3}", _Mul(2, _Pow(3, -1))),
+    (r"\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
+    (r"\frac{7}{3}", _Mul(7, _Pow(3, -1)))
+]
+
+EVALUATED_FRACTION_EXPRESSION_PAIRS = [
+    (r"\frac{a}{b}", a / b),
+    (r"\dfrac{a}{b}", a / b),
+    (r"\tfrac{a}{b}", a / b),
+    (r"\frac12", Rational(1, 2)),
+    (r"\frac12y", y / 2),
+    (r"\frac1234", 17),
+    (r"\frac2{3}", Rational(2, 3)),
+    (r"\frac{a + b}{c}", (a + b) / c),
+    (r"\frac{7}{3}", Rational(7, 3))
+]
+
+RELATION_EXPRESSION_PAIRS = [
+    (r"x = y", Eq(x, y)),
+    (r"x \neq y", Ne(x, y)),
+    (r"x < y", Lt(x, y)),
+    (r"x > y", Gt(x, y)),
+    (r"x \leq y", Le(x, y)),
+    (r"x \geq y", Ge(x, y)),
+    (r"x \le y", Le(x, y)),
+    (r"x \ge y", Ge(x, y)),
+    (r"x < y", StrictLessThan(x, y)),
+    (r"x \leq y", LessThan(x, y)),
+    (r"x > y", StrictGreaterThan(x, y)),
+    (r"x \geq y", GreaterThan(x, y)),
+    (r"x \neq y", Unequality(x, y)), # same as 2nd one in the list
+    (r"a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2))
+]
+
+UNEVALUATED_POWER_EXPRESSION_PAIRS = [
+    (r"x^2", x ** 2),
+    (r"x^\frac{1}{2}", _Pow(x, _Mul(1, _Pow(2, -1)))),
+    (r"x^{3 + 1}", x ** _Add(3, 1)),
+    (r"\pi^{|xy|}", Symbol('pi') ** _Abs(x * y)),
+    (r"5^0 - 4^0", _Add(_Pow(5, 0), _Mul(-1, _Pow(4, 0))))
+]
+
+EVALUATED_POWER_EXPRESSION_PAIRS = [
+    (r"x^2", x ** 2),
+    (r"x^\frac{1}{2}", sqrt(x)),
+    (r"x^{3 + 1}", x ** 4),
+    (r"\pi^{|xy|}", Symbol('pi') ** _Abs(x * y)),
+    (r"5^0 - 4^0", 0)
+]
+
+UNEVALUATED_INTEGRAL_EXPRESSION_PAIRS = [
+    (r"\int x dx", Integral(_Mul(1, x), x)),
+    (r"\int x \, dx", Integral(_Mul(1, x), x)),
+    (r"\int x d\theta", Integral(_Mul(1, x), theta)),
+    (r"\int (x^2 - y)dx", Integral(_Mul(1, x ** 2 - y), x)),
+    (r"\int x + a dx", Integral(_Mul(1, _Add(x, a)), x)),
+    (r"\int da", Integral(_Mul(1, 1), a)),
+    (r"\int_0^7 dx", Integral(_Mul(1, 1), (x, 0, 7))),
+    (r"\int\limits_{0}^{1} x dx", Integral(_Mul(1, x), (x, 0, 1))),
+    (r"\int_a^b x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int^b_a x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int_{a}^b x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int^{b}_a x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int_{a}^{b} x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int^{b}_{a} x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
+    (r"\int a + b + c dx", Integral(_Mul(1, _Add(_Add(a, b), c)), x)),
+    (r"\int \frac{dz}{z}", Integral(_Mul(1, _Mul(1, Pow(z, -1))), z)),
+    (r"\int \frac{3 dz}{z}", Integral(_Mul(1, _Mul(3, _Pow(z, -1))), z)),
+    (r"\int \frac{1}{x} dx", Integral(_Mul(1, _Mul(1, Pow(x, -1))), x)),
+    (r"\int \frac{1}{a} + \frac{1}{b} dx",
+     Integral(_Mul(1, _Add(_Mul(1, _Pow(a, -1)), _Mul(1, Pow(b, -1)))), x)),
+    (r"\int \frac{1}{x} + 1 dx", Integral(_Mul(1, _Add(_Mul(1, _Pow(x, -1)), 1)), x))
+]
+
+EVALUATED_INTEGRAL_EXPRESSION_PAIRS = [
+    (r"\int x dx", Integral(x, x)),
+    (r"\int x \, dx", Integral(x, x)),
+    (r"\int x d\theta", Integral(x, theta)),
+    (r"\int (x^2 - y)dx", Integral(x ** 2 - y, x)),
+    (r"\int x + a dx", Integral(x + a, x)),
+    (r"\int da", Integral(1, a)),
+    (r"\int_0^7 dx", Integral(1, (x, 0, 7))),
+    (r"\int\limits_{0}^{1} x dx", Integral(x, (x, 0, 1))),
+    (r"\int_a^b x dx", Integral(x, (x, a, b))),
+    (r"\int^b_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^b x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^{b} x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_{a} x dx", Integral(x, (x, a, b))),
+    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
+    (r"\int a + b + c dx", Integral(a + b + c, x)),
+    (r"\int \frac{dz}{z}", Integral(Pow(z, -1), z)),
+    (r"\int \frac{3 dz}{z}", Integral(3 * Pow(z, -1), z)),
+    (r"\int \frac{1}{x} dx", Integral(1 / x, x)),
+    (r"\int \frac{1}{a} + \frac{1}{b} dx", Integral(1 / a + 1 / b, x)),
+    (r"\int \frac{1}{a} - \frac{1}{b} dx", Integral(1 / a - 1 / b, x)),
+    (r"\int \frac{1}{x} + 1 dx", Integral(1 / x + 1, x))
+]
+
+DERIVATIVE_EXPRESSION_PAIRS = [
+    (r"\frac{d}{dx} x", Derivative(x, x)),
+    (r"\frac{d}{dt} x", Derivative(x, t)),
+    (r"\frac{d}{dx} ( \tan x )", Derivative(tan(x), x)),
+    (r"\frac{d f(x)}{dx}", Derivative(f(x), x)),
+    (r"\frac{d\theta(x)}{dx}", Derivative(Function('theta')(x), x))
+]
+
+TRIGONOMETRIC_EXPRESSION_PAIRS = [
+    (r"\sin \theta", sin(theta)),
+    (r"\sin(\theta)", sin(theta)),
+    (r"\sin^{-1} a", asin(a)),
+    (r"\sin a \cos b", _Mul(sin(a), cos(b))),
+    (r"\sin \cos \theta", sin(cos(theta))),
+    (r"\sin(\cos \theta)", sin(cos(theta))),
+    (r"(\csc x)(\sec y)", csc(x) * sec(y)),
+    (r"\frac{\sin{x}}2", _Mul(sin(x), _Pow(2, -1)))
+]
+
+UNEVALUATED_LIMIT_EXPRESSION_PAIRS = [
+    (r"\lim_{x \to 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \rightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \Rightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \longrightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \Longrightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \to 3^{+}} a", Limit(a, x, 3, dir="+")),
+    (r"\lim_{x \to 3^{-}} a", Limit(a, x, 3, dir="-")),
+    (r"\lim_{x \to 3^+} a", Limit(a, x, 3, dir="+")),
+    (r"\lim_{x \to 3^-} a", Limit(a, x, 3, dir="-")),
+    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(_Mul(1, _Pow(x, -1)), x, oo))
+]
+
+EVALUATED_LIMIT_EXPRESSION_PAIRS = [
+    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(1 / x, x, oo))
+]
+
+UNEVALUATED_SQRT_EXPRESSION_PAIRS = [
+    (r"\sqrt{x}", sqrt(x)),
+    (r"\sqrt{x + b}", sqrt(_Add(x, b))),
+    (r"\sqrt[3]{\sin x}", _Pow(sin(x), _Pow(3, -1))),
+    # the above test needed to be handled differently than the ones below because root
+    # acts differently if its second argument is a number
+    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
+    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
+    (r"\sqrt{\frac{12}{6}}", _Sqrt(_Mul(12, _Pow(6, -1))))
+]
+
+EVALUATED_SQRT_EXPRESSION_PAIRS = [
+    (r"\sqrt{x}", sqrt(x)),
+    (r"\sqrt{x + b}", sqrt(x + b)),
+    (r"\sqrt[3]{\sin x}", root(sin(x), 3)),
+    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
+    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
+    (r"\sqrt{\frac{12}{6}}", sqrt(2))
+]
+
+UNEVALUATED_FACTORIAL_EXPRESSION_PAIRS = [
+    (r"x!", _factorial(x)),
+    (r"100!", _factorial(100)),
+    (r"\theta!", _factorial(theta)),
+    (r"(x + 1)!", _factorial(_Add(x, 1))),
+    (r"(x!)!", _factorial(_factorial(x))),
+    (r"x!!!", _factorial(_factorial(_factorial(x)))),
+    (r"5!7!", _Mul(_factorial(5), _factorial(7)))
+]
+
+EVALUATED_FACTORIAL_EXPRESSION_PAIRS = [
+    (r"x!", factorial(x)),
+    (r"100!", factorial(100)),
+    (r"\theta!", factorial(theta)),
+    (r"(x + 1)!", factorial(x + 1)),
+    (r"(x!)!", factorial(factorial(x))),
+    (r"x!!!", factorial(factorial(factorial(x)))),
+    (r"5!7!", factorial(5) * factorial(7)),
+    (r"24! \times 24!", factorial(24) * factorial(24))
+]
+
+UNEVALUATED_SUM_EXPRESSION_PAIRS = [
+    (r"\sum_{k = 1}^{3} c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum_{k = 1}^3 c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum^{3}_{k = 1} c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum^3_{k = 1} c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum_{k = 1}^{10} k^2", Sum(_Mul(1, k ** 2), (k, 1, 10))),
+    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}",
+     Sum(_Mul(1, _Mul(1, _Pow(_factorial(n), -1))), (n, 0, oo)))
+]
+
+EVALUATED_SUM_EXPRESSION_PAIRS = [
+    (r"\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
+    (r"\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^{10} k^2", Sum(k ** 2, (k, 1, 10))),
+    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}", Sum(1 / factorial(n), (n, 0, oo)))
+]
+
+UNEVALUATED_PRODUCT_EXPRESSION_PAIRS = [
+    (r"\prod_{a = b}^{c} x", Product(x, (a, b, c))),
+    (r"\prod_{a = b}^c x", Product(x, (a, b, c))),
+    (r"\prod^{c}_{a = b} x", Product(x, (a, b, c))),
+    (r"\prod^c_{a = b} x", Product(x, (a, b, c)))
+]
+
+APPLIED_FUNCTION_EXPRESSION_PAIRS = [
+    (r"f(x)", f(x)),
+    (r"f(x, y)", f(x, y)),
+    (r"f(x, y, z)", f(x, y, z)),
+    (r"f'_1(x)", Function("f_{1}'")(x)),
+    (r"f_{1}''(x+y)", Function("f_{1}''")(x + y)),
+    (r"h_{\theta}(x_0, x_1)",
+     Function('h_{theta}')(Symbol('x_{0}'), Symbol('x_{1}')))
+]
+
+UNEVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS = [
+    (r"|x|", _Abs(x)),
+    (r"||x||", _Abs(Abs(x))),
+    (r"|x||y|", _Abs(x) * _Abs(y)),
+    (r"||x||y||", _Abs(_Abs(x) * _Abs(y))),
+    (r"\lfloor x \rfloor", floor(x)),
+    (r"\lceil x \rceil", ceiling(x)),
+    (r"\exp x", _exp(x)),
+    (r"\exp(x)", _exp(x)),
+    (r"\lg x", _log(x, 10)),
+    (r"\ln x", _log(x)),
+    (r"\ln xy", _log(x * y)),
+    (r"\log x", _log(x)),
+    (r"\log xy", _log(x * y)),
+    (r"\log_{2} x", _log(x, 2)),
+    (r"\log_{a} x", _log(x, a)),
+    (r"\log_{11} x", _log(x, 11)),
+    (r"\log_{a^2} x", _log(x, _Pow(a, 2))),
+    (r"\log_2 x", _log(x, 2)),
+    (r"\log_a x", _log(x, a)),
+    (r"\overline{z}", _Conjugate(z)),
+    (r"\overline{\overline{z}}", _Conjugate(_Conjugate(z))),
+    (r"\overline{x + y}", _Conjugate(_Add(x, y))),
+    (r"\overline{x} + \overline{y}", _Conjugate(x) + _Conjugate(y)),
+    (r"\min(a, b)", _Min(a, b)),
+    (r"\min(a, b, c - d, xy)", _Min(a, b, c - d, x * y)),
+    (r"\max(a, b)", _Max(a, b)),
+    (r"\max(a, b, c - d, xy)", _Max(a, b, c - d, x * y)),
+    # physics things don't have an `evaluate=False` variant
+    (r"\langle x |", Bra('x')),
+    (r"| x \rangle", Ket('x')),
+    (r"\langle x | y \rangle", InnerProduct(Bra('x'), Ket('y'))),
+]
+
+EVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS = [
+    (r"|x|", Abs(x)),
+    (r"||x||", Abs(Abs(x))),
+    (r"|x||y|", Abs(x) * Abs(y)),
+    (r"||x||y||", Abs(Abs(x) * Abs(y))),
+    (r"\lfloor x \rfloor", floor(x)),
+    (r"\lceil x \rceil", ceiling(x)),
+    (r"\exp x", exp(x)),
+    (r"\exp(x)", exp(x)),
+    (r"\lg x", log(x, 10)),
+    (r"\ln x", log(x)),
+    (r"\ln xy", log(x * y)),
+    (r"\log x", log(x)),
+    (r"\log xy", log(x * y)),
+    (r"\log_{2} x", log(x, 2)),
+    (r"\log_{a} x", log(x, a)),
+    (r"\log_{11} x", log(x, 11)),
+    (r"\log_{a^2} x", log(x, _Pow(a, 2))),
+    (r"\log_2 x", log(x, 2)),
+    (r"\log_a x", log(x, a)),
+    (r"\overline{z}", conjugate(z)),
+    (r"\overline{\overline{z}}", conjugate(conjugate(z))),
+    (r"\overline{x + y}", conjugate(x + y)),
+    (r"\overline{x} + \overline{y}", conjugate(x) + conjugate(y)),
+    (r"\min(a, b)", Min(a, b)),
+    (r"\min(a, b, c - d, xy)", Min(a, b, c - d, x * y)),
+    (r"\max(a, b)", Max(a, b)),
+    (r"\max(a, b, c - d, xy)", Max(a, b, c - d, x * y)),
+    (r"\langle x |", Bra('x')),
+    (r"| x \rangle", Ket('x')),
+    (r"\langle x | y \rangle", InnerProduct(Bra('x'), Ket('y'))),
+]
+
+SPACING_RELATED_EXPRESSION_PAIRS = [
+    (r"a \, b", _Mul(a, b)),
+    (r"a \thinspace b", _Mul(a, b)),
+    (r"a \: b", _Mul(a, b)),
+    (r"a \medspace b", _Mul(a, b)),
+    (r"a \; b", _Mul(a, b)),
+    (r"a \thickspace b", _Mul(a, b)),
+    (r"a \quad b", _Mul(a, b)),
+    (r"a \qquad b", _Mul(a, b)),
+    (r"a \! b", _Mul(a, b)),
+    (r"a \negthinspace b", _Mul(a, b)),
+    (r"a \negmedspace b", _Mul(a, b)),
+    (r"a \negthickspace b", _Mul(a, b))
+]
+
+UNEVALUATED_BINOMIAL_EXPRESSION_PAIRS = [
+    (r"\binom{n}{k}", _binomial(n, k)),
+    (r"\tbinom{n}{k}", _binomial(n, k)),
+    (r"\dbinom{n}{k}", _binomial(n, k)),
+    (r"\binom{n}{0}", _binomial(n, 0)),
+    (r"x^\binom{n}{k}", _Pow(x, _binomial(n, k)))
+]
+
+EVALUATED_BINOMIAL_EXPRESSION_PAIRS = [
+    (r"\binom{n}{k}", binomial(n, k)),
+    (r"\tbinom{n}{k}", binomial(n, k)),
+    (r"\dbinom{n}{k}", binomial(n, k)),
+    (r"\binom{n}{0}", binomial(n, 0)),
+    (r"x^\binom{n}{k}", x ** binomial(n, k))
+]
+
+MISCELLANEOUS_EXPRESSION_PAIRS = [
+    (r"\left(x + y\right) z", _Mul(_Add(x, y), z)),
+    (r"\left( x + y\right ) z", _Mul(_Add(x, y), z)),
+    (r"\left(  x + y\right ) z", _Mul(_Add(x, y), z)),
+]
+
+UNEVALUATED_LITERAL_COMPLEX_NUMBER_EXPRESSION_PAIRS = [
+    (r"\imaginaryunit^2", _Pow(I, 2)),
+    (r"|\imaginaryunit|", _Abs(I)),
+    (r"\overline{\imaginaryunit}", _Conjugate(I)),
+    (r"\imaginaryunit+\imaginaryunit", _Add(I, I)),
+    (r"\imaginaryunit-\imaginaryunit", _Add(I, -I)),
+    (r"\imaginaryunit*\imaginaryunit", _Mul(I, I)),
+    (r"\imaginaryunit/\imaginaryunit", _Mul(I, _Pow(I, -1))),
+    (r"(1+\imaginaryunit)/|1+\imaginaryunit|", _Mul(_Add(1, I), _Pow(_Abs(_Add(1, I)), -1)))
+]
+
+UNEVALUATED_MATRIX_EXPRESSION_PAIRS = [
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}",
+     Matrix([[a, b], [x, y]])),
+    (r"\begin{pmatrix}a & b \\x & y\\\end{pmatrix}",
+     Matrix([[a, b], [x, y]])),
+    (r"\begin{bmatrix}a & b \\x & y\end{bmatrix}",
+     Matrix([[a, b], [x, y]])),
+    (r"\left(\begin{matrix}a & b \\x & y\end{matrix}\right)",
+     Matrix([[a, b], [x, y]])),
+    (r"\left[\begin{matrix}a & b \\x & y\end{matrix}\right]",
+     Matrix([[a, b], [x, y]])),
+    (r"\left[\begin{array}{cc}a & b \\x & y\end{array}\right]",
+     Matrix([[a, b], [x, y]])),
+    (r"\left(\begin{array}{cc}a & b \\x & y\end{array}\right)",
+     Matrix([[a, b], [x, y]])),
+    (r"\left( { \begin{array}{cc}a & b \\x & y\end{array} } \right)",
+     Matrix([[a, b], [x, y]])),
+    (r"+\begin{pmatrix}a & b \\x & y\end{pmatrix}",
+     Matrix([[a, b], [x, y]])),
+    ((r"\begin{pmatrix}x & y \\a & b\end{pmatrix}+"
+      r"\begin{pmatrix}a & b \\x & y\end{pmatrix}"),
+     _MatAdd(Matrix([[x, y], [a, b]]), Matrix([[a, b], [x, y]]))),
+    (r"-\begin{pmatrix}a & b \\x & y\end{pmatrix}",
+     _MatMul(-1, Matrix([[a, b], [x, y]]))),
+    ((r"\begin{pmatrix}x & y \\a & b\end{pmatrix}-"
+      r"\begin{pmatrix}a & b \\x & y\end{pmatrix}"),
+     _MatAdd(Matrix([[x, y], [a, b]]), _MatMul(-1, Matrix([[a, b], [x, y]])))),
+    ((r"\begin{pmatrix}a & b & c \\x & y & z \\a & b & c \end{pmatrix}*"
+      r"\begin{pmatrix}x & y & z \\a & b & c \\a & b & c \end{pmatrix}*"
+      r"\begin{pmatrix}a & b & c \\x & y & z \\x & y & z \end{pmatrix}"),
+     _MatMul(_MatMul(Matrix([[a, b, c], [x, y, z], [a, b, c]]),
+                     Matrix([[x, y, z], [a, b, c], [a, b, c]])),
+             Matrix([[a, b, c], [x, y, z], [x, y, z]]))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}/2",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(2, -1))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^2",
+     _Pow(Matrix([[a, b], [x, y]]), 2)),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^{-1}",
+     _Pow(Matrix([[a, b], [x, y]]), -1)),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^T",
+     Transpose(Matrix([[a, b], [x, y]]))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^{T}",
+     Transpose(Matrix([[a, b], [x, y]]))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^\mathit{T}",
+     Transpose(Matrix([[a, b], [x, y]]))),
+    (r"\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}^T",
+     Transpose(Matrix([[1, 2], [3, 4]]))),
+    ((r"(\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}+"
+      r"\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}^T)*"
+      r"\begin{bmatrix}1\\0\end{bmatrix}"),
+     _MatMul(_MatAdd(Matrix([[1, 2], [3, 4]]),
+                     Transpose(Matrix([[1, 2], [3, 4]]))),
+                Matrix([[1], [0]]))),
+    ((r"(\begin{pmatrix}a & b \\x & y\end{pmatrix}+"
+      r"\begin{pmatrix}x & y \\a & b\end{pmatrix})^2"),
+    _Pow(_MatAdd(Matrix([[a, b], [x, y]]),
+                 Matrix([[x, y], [a, b]])), 2)),
+    ((r"(\begin{pmatrix}a & b \\x & y\end{pmatrix}+"
+      r"\begin{pmatrix}x & y \\a & b\end{pmatrix})^T"),
+    Transpose(_MatAdd(Matrix([[a, b], [x, y]]),
+                      Matrix([[x, y], [a, b]])))),
+    (r"\overline{\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}}",
+     _Conjugate(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                        Matrix([[I, 2], [3, 4]]))))
+]
+
+EVALUATED_MATRIX_EXPRESSION_PAIRS = [
+    (r"\det\left(\left[   { \begin{array}{cc}a&b\\x&y\end{array} } \right]\right)",
+     Matrix([[a, b], [x, y]]).det()),
+    (r"\det \begin{pmatrix}1&2\\3&4\end{pmatrix}", -2),
+    (r"\det{\begin{pmatrix}1&2\\3&4\end{pmatrix}}", -2),
+    (r"\det(\begin{pmatrix}1&2\\3&4\end{pmatrix})", -2),
+    (r"\det\left(\begin{pmatrix}1&2\\3&4\end{pmatrix}\right)", -2),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}/\begin{vmatrix}a & b \\x & y\end{vmatrix}",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(Matrix([[a, b], [x, y]]).det(), -1))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}/|\begin{matrix}a & b \\x & y\end{matrix}|",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(Matrix([[a, b], [x, y]]).det(), -1))),
+    (r"\frac{\begin{pmatrix}a & b \\x & y\end{pmatrix}}{| { \begin{matrix}a & b \\x & y\end{matrix} } |}",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(Matrix([[a, b], [x, y]]).det(), -1))),
+    (r"\overline{\begin{pmatrix}\imaginaryunit & 1+\imaginaryunit \\-\imaginaryunit & 4\end{pmatrix}}",
+     Matrix([[-I, 1-I], [I, 4]])),
+    (r"\begin{pmatrix}\imaginaryunit & 1+\imaginaryunit \\-\imaginaryunit & 4\end{pmatrix}^H",
+     Matrix([[-I, I], [1-I, 4]])),
+    (r"\trace(\begin{pmatrix}\imaginaryunit & 1+\imaginaryunit \\-\imaginaryunit & 4\end{pmatrix})",
+     Trace(Matrix([[I, 1+I], [-I, 4]]))),
+    (r"\adjugate(\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix})",
+     Matrix([[4, -2], [-3, 1]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^\ast",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\ast}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\ast\ast}",
+     Matrix([[2*I, 4], [6, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\ast\ast\ast}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{*}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{**}",
+     Matrix([[2*I, 4], [6, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{***}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^\prime",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\prime}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\prime\prime}",
+     _MatAdd(Matrix([[I, 2], [3, 4]]),
+             Matrix([[I, 2], [3, 4]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\prime\prime\prime}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{'}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{''}",
+     _MatAdd(Matrix([[I, 2], [3, 4]]),
+             Matrix([[I, 2], [3, 4]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{'''}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})'",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})''",
+     _MatAdd(Matrix([[I, 2], [3, 4]]),
+             Matrix([[I, 2], [3, 4]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})'''",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"\det(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})",
+     (_MatAdd(Matrix([[I, 2], [3, 4]]),
+              Matrix([[I, 2], [3, 4]]))).det()),
+    (r"\trace(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})",
+     Trace(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                   Matrix([[I, 2], [3, 4]])))),
+    (r"\adjugate(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})",
+     (Matrix([[8, -4], [-6, 2*I]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^T",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^H",
+     (Matrix([[-2*I, 6], [4, 8]])))
+]
+
+
+def test_symbol_expressions():
+    expected_failures = {6, 7}
+    for i, (latex_str, sympy_expr) in enumerate(SYMBOL_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_simple_expressions():
+    expected_failures = {20}
+    for i, (latex_str, sympy_expr) in enumerate(UNEVALUATED_SIMPLE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for i, (latex_str, sympy_expr) in enumerate(EVALUATED_SIMPLE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_fraction_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_FRACTION_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_FRACTION_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_relation_expressions():
+    for latex_str, sympy_expr in RELATION_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+def test_power_expressions():
+    expected_failures = {3}
+    for i, (latex_str, sympy_expr) in enumerate(UNEVALUATED_POWER_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for i, (latex_str, sympy_expr) in enumerate(EVALUATED_POWER_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_integral_expressions():
+    expected_failures = {14}
+    for i, (latex_str, sympy_expr) in enumerate(UNEVALUATED_INTEGRAL_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, i
+
+    for i, (latex_str, sympy_expr) in enumerate(EVALUATED_INTEGRAL_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_derivative_expressions():
+    expected_failures = {3, 4}
+    for i, (latex_str, sympy_expr) in enumerate(DERIVATIVE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for i, (latex_str, sympy_expr) in enumerate(DERIVATIVE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_trigonometric_expressions():
+    expected_failures = {3}
+    for i, (latex_str, sympy_expr) in enumerate(TRIGONOMETRIC_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_limit_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_LIMIT_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_square_root_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_SQRT_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_SQRT_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_factorial_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_FACTORIAL_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_FACTORIAL_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_sum_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_SUM_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_SUM_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_product_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_PRODUCT_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+@XFAIL
+def test_applied_function_expressions():
+    expected_failures = {0, 3, 4}  # 0 is ambiguous, and the others require not-yet-added features
+    # not sure why 1, and 2 are failing
+    for i, (latex_str, sympy_expr) in enumerate(APPLIED_FUNCTION_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_common_function_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+# unhandled bug causing these to fail
+@XFAIL
+def test_spacing():
+    for latex_str, sympy_expr in SPACING_RELATED_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_binomial_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_BINOMIAL_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_BINOMIAL_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_miscellaneous_expressions():
+    for latex_str, sympy_expr in MISCELLANEOUS_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_literal_complex_number_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_LITERAL_COMPLEX_NUMBER_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_matrix_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_MATRIX_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_MATRIX_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_mathematica.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_mathematica.py
new file mode 100644
index 0000000000000000000000000000000000000000..df193b6d61f9c82778d8e0a40b893cbe6cb8f06a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_mathematica.py
@@ -0,0 +1,280 @@
+from sympy import sin, Function, symbols, Dummy, Lambda, cos
+from sympy.parsing.mathematica import parse_mathematica, MathematicaParser
+from sympy.core.sympify import sympify
+from sympy.abc import n, w, x, y, z
+from sympy.testing.pytest import raises
+
+
+def test_mathematica():
+    d = {
+        '- 6x': '-6*x',
+        'Sin[x]^2': 'sin(x)**2',
+        '2(x-1)': '2*(x-1)',
+        '3y+8': '3*y+8',
+        'ArcSin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
+        'x+y': 'x+y',
+        '355/113': '355/113',
+        '2.718281828': '2.718281828',
+        'Cos(1/2 * π)': 'Cos(π/2)',
+        'Sin[12]': 'sin(12)',
+        'Exp[Log[4]]': 'exp(log(4))',
+        '(x+1)(x+3)': '(x+1)*(x+3)',
+        'Cos[ArcCos[3.6]]': 'cos(acos(3.6))',
+        'Cos[x]==Sin[y]': 'Eq(cos(x), sin(y))',
+        '2*Sin[x+y]': '2*sin(x+y)',
+        'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
+        'Sin[Cos[x]]': 'sin(cos(x))',
+        '2*Sqrt[x+y]': '2*sqrt(x+y)',   # Test case from the issue 4259
+        '+Sqrt[2]': 'sqrt(2)',
+        '-Sqrt[2]': '-sqrt(2)',
+        '-1/Sqrt[2]': '-1/sqrt(2)',
+        '-(1/Sqrt[3])': '-(1/sqrt(3))',
+        '1/(2*Sqrt[5])': '1/(2*sqrt(5))',
+        'Mod[5,3]': 'Mod(5,3)',
+        '-Mod[5,3]': '-Mod(5,3)',
+        '(x+1)y': '(x+1)*y',
+        'x(y+1)': 'x*(y+1)',
+        'Sin[x]Cos[y]': 'sin(x)*cos(y)',
+        'Sin[x]^2Cos[y]^2': 'sin(x)**2*cos(y)**2',
+        'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
+        'x y': 'x*y',
+        'x  y': 'x*y',
+        '2 x': '2*x',
+        'x 8': 'x*8',
+        '2 8': '2*8',
+        '4.x': '4.*x',
+        '4. 3': '4.*3',
+        '4. 3.': '4.*3.',
+        '1 2 3': '1*2*3',
+        ' -  2 *  Sqrt[  2 3 *   ( 1   +  5 ) ]  ': '-2*sqrt(2*3*(1+5))',
+        'Log[2,4]': 'log(4,2)',
+        'Log[Log[2,4],4]': 'log(4,log(4,2))',
+        'Exp[Sqrt[2]^2Log[2, 8]]': 'exp(sqrt(2)**2*log(8,2))',
+        'ArcSin[Cos[0]]': 'asin(cos(0))',
+        'Log2[16]': 'log(16,2)',
+        'Max[1,-2,3,-4]': 'Max(1,-2,3,-4)',
+        'Min[1,-2,3]': 'Min(1,-2,3)',
+        'Exp[I Pi/2]': 'exp(I*pi/2)',
+        'ArcTan[x,y]': 'atan2(y,x)',
+        'Pochhammer[x,y]': 'rf(x,y)',
+        'ExpIntegralEi[x]': 'Ei(x)',
+        'SinIntegral[x]': 'Si(x)',
+        'CosIntegral[x]': 'Ci(x)',
+        'AiryAi[x]': 'airyai(x)',
+        'AiryAiPrime[5]': 'airyaiprime(5)',
+        'AiryBi[x]': 'airybi(x)',
+        'AiryBiPrime[7]': 'airybiprime(7)',
+        'LogIntegral[4]': ' li(4)',
+        'PrimePi[7]': 'primepi(7)',
+        'Prime[5]': 'prime(5)',
+        'PrimeQ[5]': 'isprime(5)',
+        'Rational[2,19]': 'Rational(2,19)',    # test case for issue 25716
+        }
+
+    for e in d:
+        assert parse_mathematica(e) == sympify(d[e])
+
+    # The parsed form of this expression should not evaluate the Lambda object:
+    assert parse_mathematica("Sin[#]^2 + Cos[#]^2 &[x]") == sin(x)**2 + cos(x)**2
+
+    d1, d2, d3 = symbols("d1:4", cls=Dummy)
+    assert parse_mathematica("Sin[#] + Cos[#3] &").dummy_eq(Lambda((d1, d2, d3), sin(d1) + cos(d3)))
+    assert parse_mathematica("Sin[#^2] &").dummy_eq(Lambda(d1, sin(d1**2)))
+    assert parse_mathematica("Function[x, x^3]") == Lambda(x, x**3)
+    assert parse_mathematica("Function[{x, y}, x^2 + y^2]") == Lambda((x, y), x**2 + y**2)
+
+
+def test_parser_mathematica_tokenizer():
+    parser = MathematicaParser()
+
+    chain = lambda expr: parser._from_tokens_to_fullformlist(parser._from_mathematica_to_tokens(expr))
+
+    # Basic patterns
+    assert chain("x") == "x"
+    assert chain("42") == "42"
+    assert chain(".2") == ".2"
+    assert chain("+x") == "x"
+    assert chain("-1") == "-1"
+    assert chain("- 3") == "-3"
+    assert chain("α") == "α"
+    assert chain("+Sin[x]") == ["Sin", "x"]
+    assert chain("-Sin[x]") == ["Times", "-1", ["Sin", "x"]]
+    assert chain("x(a+1)") == ["Times", "x", ["Plus", "a", "1"]]
+    assert chain("(x)") == "x"
+    assert chain("(+x)") == "x"
+    assert chain("-a") == ["Times", "-1", "a"]
+    assert chain("(-x)") == ["Times", "-1", "x"]
+    assert chain("(x + y)") == ["Plus", "x", "y"]
+    assert chain("3 + 4") == ["Plus", "3", "4"]
+    assert chain("a - 3") == ["Plus", "a", "-3"]
+    assert chain("a - b") == ["Plus", "a", ["Times", "-1", "b"]]
+    assert chain("7 * 8") == ["Times", "7", "8"]
+    assert chain("a + b*c") == ["Plus", "a", ["Times", "b", "c"]]
+    assert chain("a + b* c* d + 2 * e") == ["Plus", "a", ["Times", "b", "c", "d"], ["Times", "2", "e"]]
+    assert chain("a / b") == ["Times", "a", ["Power", "b", "-1"]]
+
+    # Missing asterisk (*) patterns:
+    assert chain("x y") == ["Times", "x", "y"]
+    assert chain("3 4") == ["Times", "3", "4"]
+    assert chain("a[b] c") == ["Times", ["a", "b"], "c"]
+    assert chain("(x) (y)") == ["Times", "x", "y"]
+    assert chain("3 (a)") == ["Times", "3", "a"]
+    assert chain("(a) b") == ["Times", "a", "b"]
+    assert chain("4.2") == "4.2"
+    assert chain("4 2") == ["Times", "4", "2"]
+    assert chain("4  2") == ["Times", "4", "2"]
+    assert chain("3 . 4") == ["Dot", "3", "4"]
+    assert chain("4. 2") == ["Times", "4.", "2"]
+    assert chain("x.y") == ["Dot", "x", "y"]
+    assert chain("4.y") == ["Times", "4.", "y"]
+    assert chain("4 .y") == ["Dot", "4", "y"]
+    assert chain("x.4") == ["Times", "x", ".4"]
+    assert chain("x0.3") == ["Times", "x0", ".3"]
+    assert chain("x. 4") == ["Dot", "x", "4"]
+
+    # Comments
+    assert chain("a (* +b *) + c") == ["Plus", "a", "c"]
+    assert chain("a (* + b *) + (**)c (* +d *) + e") == ["Plus", "a", "c", "e"]
+    assert chain("""a + (*
+    + b
+    *) c + (* d
+    *) e
+    """) == ["Plus", "a", "c", "e"]
+
+    # Operators couples + and -, * and / are mutually associative:
+    # (i.e. expression gets flattened when mixing these operators)
+    assert chain("a*b/c") == ["Times", "a", "b", ["Power", "c", "-1"]]
+    assert chain("a/b*c") == ["Times", "a", ["Power", "b", "-1"], "c"]
+    assert chain("a+b-c") == ["Plus", "a", "b", ["Times", "-1", "c"]]
+    assert chain("a-b+c") == ["Plus", "a", ["Times", "-1", "b"], "c"]
+    assert chain("-a + b -c ") == ["Plus", ["Times", "-1", "a"], "b", ["Times", "-1", "c"]]
+    assert chain("a/b/c*d") == ["Times", "a", ["Power", "b", "-1"], ["Power", "c", "-1"], "d"]
+    assert chain("a/b/c") == ["Times", "a", ["Power", "b", "-1"], ["Power", "c", "-1"]]
+    assert chain("a-b-c") == ["Plus", "a", ["Times", "-1", "b"], ["Times", "-1", "c"]]
+    assert chain("1/a") == ["Times", "1", ["Power", "a", "-1"]]
+    assert chain("1/a/b") == ["Times", "1", ["Power", "a", "-1"], ["Power", "b", "-1"]]
+    assert chain("-1/a*b") == ["Times", "-1", ["Power", "a", "-1"], "b"]
+
+    # Enclosures of various kinds, i.e. ( )  [ ]  [[ ]]  { }
+    assert chain("(a + b) + c") == ["Plus", ["Plus", "a", "b"], "c"]
+    assert chain(" a + (b + c) + d ") == ["Plus", "a", ["Plus", "b", "c"], "d"]
+    assert chain("a * (b + c)") == ["Times", "a", ["Plus", "b", "c"]]
+    assert chain("a b (c d)") == ["Times", "a", "b", ["Times", "c", "d"]]
+    assert chain("{a, b, 2, c}") == ["List", "a", "b", "2", "c"]
+    assert chain("{a, {b, c}}") == ["List", "a", ["List", "b", "c"]]
+    assert chain("{{a}}") == ["List", ["List", "a"]]
+    assert chain("a[b, c]") == ["a", "b", "c"]
+    assert chain("a[[b, c]]") == ["Part", "a", "b", "c"]
+    assert chain("a[b[c]]") == ["a", ["b", "c"]]
+    assert chain("a[[b, c[[d, {e,f}]]]]") == ["Part", "a", "b", ["Part", "c", "d", ["List", "e", "f"]]]
+    assert chain("a[b[[c,d]]]") == ["a", ["Part", "b", "c", "d"]]
+    assert chain("a[[b[c]]]") == ["Part", "a", ["b", "c"]]
+    assert chain("a[[b[[c]]]]") == ["Part", "a", ["Part", "b", "c"]]
+    assert chain("a[[b[c[[d]]]]]") == ["Part", "a", ["b", ["Part", "c", "d"]]]
+    assert chain("a[b[[c[d]]]]") == ["a", ["Part", "b", ["c", "d"]]]
+    assert chain("x[[a+1, b+2, c+3]]") == ["Part", "x", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]]
+    assert chain("x[a+1, b+2, c+3]") == ["x", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]]
+    assert chain("{a+1, b+2, c+3}") == ["List", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]]
+
+    # Flat operator:
+    assert chain("a*b*c*d*e") == ["Times", "a", "b", "c", "d", "e"]
+    assert chain("a +b + c+ d+e") == ["Plus", "a", "b", "c", "d", "e"]
+
+    # Right priority operator:
+    assert chain("a^b") == ["Power", "a", "b"]
+    assert chain("a^b^c") == ["Power", "a", ["Power", "b", "c"]]
+    assert chain("a^b^c^d") == ["Power", "a", ["Power", "b", ["Power", "c", "d"]]]
+
+    # Left priority operator:
+    assert chain("a/.b") == ["ReplaceAll", "a", "b"]
+    assert chain("a/.b/.c/.d") == ["ReplaceAll", ["ReplaceAll", ["ReplaceAll", "a", "b"], "c"], "d"]
+
+    assert chain("a//b") == ["a", "b"]
+    assert chain("a//b//c") == [["a", "b"], "c"]
+    assert chain("a//b//c//d") == [[["a", "b"], "c"], "d"]
+
+    # Compound expressions
+    assert chain("a;b") == ["CompoundExpression", "a", "b"]
+    assert chain("a;") == ["CompoundExpression", "a", "Null"]
+    assert chain("a;b;") == ["CompoundExpression", "a", "b", "Null"]
+    assert chain("a[b;c]") == ["a", ["CompoundExpression", "b", "c"]]
+    assert chain("a[b,c;d,e]") == ["a", "b", ["CompoundExpression", "c", "d"], "e"]
+    assert chain("a[b,c;,d]") == ["a", "b", ["CompoundExpression", "c", "Null"], "d"]
+
+    # New lines
+    assert chain("a\nb\n") == ["CompoundExpression", "a", "b"]
+    assert chain("a\n\nb\n (c \nd)  \n") == ["CompoundExpression", "a", "b", ["Times", "c", "d"]]
+    assert chain("\na; b\nc") == ["CompoundExpression", "a", "b", "c"]
+    assert chain("a + \nb\n") == ["Plus", "a", "b"]
+    assert chain("a\nb; c; d\n e; (f \n g); h + \n i") == ["CompoundExpression", "a", "b", "c", "d", "e", ["Times", "f", "g"], ["Plus", "h", "i"]]
+    assert chain("\n{\na\nb; c; d\n e (f \n g); h + \n i\n\n}\n") == ["List", ["CompoundExpression", ["Times", "a", "b"], "c", ["Times", "d", "e", ["Times", "f", "g"]], ["Plus", "h", "i"]]]
+
+    # Patterns
+    assert chain("y_") == ["Pattern", "y", ["Blank"]]
+    assert chain("y_.") == ["Optional", ["Pattern", "y", ["Blank"]]]
+    assert chain("y__") == ["Pattern", "y", ["BlankSequence"]]
+    assert chain("y___") == ["Pattern", "y", ["BlankNullSequence"]]
+    assert chain("a[b_.,c_]") == ["a", ["Optional", ["Pattern", "b", ["Blank"]]], ["Pattern", "c", ["Blank"]]]
+    assert chain("b_. c") == ["Times", ["Optional", ["Pattern", "b", ["Blank"]]], "c"]
+
+    # Slots for lambda functions
+    assert chain("#") == ["Slot", "1"]
+    assert chain("#3") == ["Slot", "3"]
+    assert chain("#n") == ["Slot", "n"]
+    assert chain("##") == ["SlotSequence", "1"]
+    assert chain("##a") == ["SlotSequence", "a"]
+
+    # Lambda functions
+    assert chain("x&") == ["Function", "x"]
+    assert chain("#&") == ["Function", ["Slot", "1"]]
+    assert chain("#+3&") == ["Function", ["Plus", ["Slot", "1"], "3"]]
+    assert chain("#1 + #2&") == ["Function", ["Plus", ["Slot", "1"], ["Slot", "2"]]]
+    assert chain("# + #&") == ["Function", ["Plus", ["Slot", "1"], ["Slot", "1"]]]
+    assert chain("#&[x]") == [["Function", ["Slot", "1"]], "x"]
+    assert chain("#1 + #2 & [x, y]") == [["Function", ["Plus", ["Slot", "1"], ["Slot", "2"]]], "x", "y"]
+    assert chain("#1^2#2^3&") == ["Function", ["Times", ["Power", ["Slot", "1"], "2"], ["Power", ["Slot", "2"], "3"]]]
+
+    # Strings inside Mathematica expressions:
+    assert chain('"abc"') == ["_Str", "abc"]
+    assert chain('"a\\"b"') == ["_Str", 'a"b']
+    # This expression does not make sense mathematically, it's just testing the parser:
+    assert chain('x + "abc" ^ 3') == ["Plus", "x", ["Power", ["_Str", "abc"], "3"]]
+    assert chain('"a (* b *) c"') == ["_Str", "a (* b *) c"]
+    assert chain('"a" (* b *) ') == ["_Str", "a"]
+    assert chain('"a [ b] "') == ["_Str", "a [ b] "]
+    raises(SyntaxError, lambda: chain('"'))
+    raises(SyntaxError, lambda: chain('"\\"'))
+    raises(SyntaxError, lambda: chain('"abc'))
+    raises(SyntaxError, lambda: chain('"abc\\"def'))
+
+    # Invalid expressions:
+    raises(SyntaxError, lambda: chain("(,"))
+    raises(SyntaxError, lambda: chain("()"))
+    raises(SyntaxError, lambda: chain("a (* b"))
+
+
+def test_parser_mathematica_exp_alt():
+    parser = MathematicaParser()
+
+    convert_chain2 = lambda expr: parser._from_fullformlist_to_fullformsympy(parser._from_fullform_to_fullformlist(expr))
+    convert_chain3 = lambda expr: parser._from_fullformsympy_to_sympy(convert_chain2(expr))
+
+    Sin, Times, Plus, Power = symbols("Sin Times Plus Power", cls=Function)
+
+    full_form1 = "Sin[Times[x, y]]"
+    full_form2 = "Plus[Times[x, y], z]"
+    full_form3 = "Sin[Times[x, Plus[y, z], Power[w, n]]]]"
+    full_form4 = "Rational[Rational[x, y], z]"
+
+    assert parser._from_fullform_to_fullformlist(full_form1) == ["Sin", ["Times", "x", "y"]]
+    assert parser._from_fullform_to_fullformlist(full_form2) == ["Plus", ["Times", "x", "y"], "z"]
+    assert parser._from_fullform_to_fullformlist(full_form3) == ["Sin", ["Times", "x", ["Plus", "y", "z"], ["Power", "w", "n"]]]
+    assert parser._from_fullform_to_fullformlist(full_form4) == ["Rational", ["Rational", "x", "y"], "z"]
+
+    assert convert_chain2(full_form1) == Sin(Times(x, y))
+    assert convert_chain2(full_form2) == Plus(Times(x, y), z)
+    assert convert_chain2(full_form3) == Sin(Times(x, Plus(y, z), Power(w, n)))
+
+    assert convert_chain3(full_form1) == sin(x*y)
+    assert convert_chain3(full_form2) == x*y + z
+    assert convert_chain3(full_form3) == sin(x*(y + z)*w**n)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_maxima.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_maxima.py
new file mode 100644
index 0000000000000000000000000000000000000000..c0bc1db8f1385ed52e8c677a1bcc759f5118d01e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_maxima.py
@@ -0,0 +1,50 @@
+from sympy.parsing.maxima import parse_maxima
+from sympy.core.numbers import (E, Rational, oo)
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.abc import x
+
+n = Symbol('n', integer=True)
+
+
+def test_parser():
+    assert Abs(parse_maxima('float(1/3)') - 0.333333333) < 10**(-5)
+    assert parse_maxima('13^26') == 91733330193268616658399616009
+    assert parse_maxima('sin(%pi/2) + cos(%pi/3)') == Rational(3, 2)
+    assert parse_maxima('log(%e)') == 1
+
+
+def test_injection():
+    parse_maxima('c: x+1', globals=globals())
+    # c created by parse_maxima
+    assert c == x + 1 # noqa:F821
+
+    parse_maxima('g: sqrt(81)', globals=globals())
+    # g created by parse_maxima
+    assert g == 9 # noqa:F821
+
+
+def test_maxima_functions():
+    assert parse_maxima('expand( (x+1)^2)') == x**2 + 2*x + 1
+    assert parse_maxima('factor( x**2 + 2*x + 1)') == (x + 1)**2
+    assert parse_maxima('2*cos(x)^2 + sin(x)^2') == 2*cos(x)**2 + sin(x)**2
+    assert parse_maxima('trigexpand(sin(2*x)+cos(2*x))') == \
+        -1 + 2*cos(x)**2 + 2*cos(x)*sin(x)
+    assert parse_maxima('solve(x^2-4,x)') == [-2, 2]
+    assert parse_maxima('limit((1+1/x)^x,x,inf)') == E
+    assert parse_maxima('limit(sqrt(-x)/x,x,0,minus)') is -oo
+    assert parse_maxima('diff(x^x, x)') == x**x*(1 + log(x))
+    assert parse_maxima('sum(k, k, 1, n)', name_dict={
+        "n": Symbol('n', integer=True),
+        "k": Symbol('k', integer=True)
+    }) == (n**2 + n)/2
+    assert parse_maxima('product(k, k, 1, n)', name_dict={
+        "n": Symbol('n', integer=True),
+        "k": Symbol('k', integer=True)
+    }) == factorial(n)
+    assert parse_maxima('ratsimp((x^2-1)/(x+1))') == x - 1
+    assert Abs( parse_maxima(
+        'float(sec(%pi/3) + csc(%pi/3))') - 3.154700538379252) < 10**(-5)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_sym_expr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_sym_expr.py
new file mode 100644
index 0000000000000000000000000000000000000000..99912805db381b96e7f41a348fe6f90d71adf781
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_sym_expr.py
@@ -0,0 +1,209 @@
+from sympy.parsing.sym_expr import SymPyExpression
+from sympy.testing.pytest import raises
+from sympy.external import import_module
+
+lfortran = import_module('lfortran')
+cin = import_module('clang.cindex', import_kwargs = {'fromlist': ['cindex']})
+
+if lfortran and cin:
+    from sympy.codegen.ast import (Variable, IntBaseType, FloatBaseType, String,
+                                   Declaration, FloatType)
+    from sympy.core import Integer, Float
+    from sympy.core.symbol import Symbol
+
+    expr1 = SymPyExpression()
+    src = """\
+    integer :: a, b, c, d
+    real :: p, q, r, s
+    """
+
+    def test_c_parse():
+        src1 = """\
+        int a, b = 4;
+        float c, d = 2.4;
+        """
+        expr1.convert_to_expr(src1, 'c')
+        ls = expr1.return_expr()
+
+        assert ls[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+        assert ls[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(4)
+            )
+        )
+        assert ls[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+            )
+        )
+        assert ls[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.3999999999999999', precision=53)
+            )
+        )
+
+
+    def test_fortran_parse():
+        expr = SymPyExpression(src, 'f')
+        ls = expr.return_expr()
+
+        assert ls[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[4] == Declaration(
+            Variable(
+                Symbol('p'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+        assert ls[5] == Declaration(
+            Variable(
+                Symbol('q'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+        assert ls[6] == Declaration(
+            Variable(
+                Symbol('r'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+        assert ls[7] == Declaration(
+            Variable(
+                Symbol('s'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+
+
+    def test_convert_py():
+        src1 = (
+            src +
+            """\
+            a = b + c
+            s = p * q / r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        exp_py = expr1.convert_to_python()
+        assert exp_py == [
+            'a = 0',
+            'b = 0',
+            'c = 0',
+            'd = 0',
+            'p = 0.0',
+            'q = 0.0',
+            'r = 0.0',
+            's = 0.0',
+            'a = b + c',
+            's = p*q/r'
+        ]
+
+
+    def test_convert_fort():
+        src1 = (
+            src +
+            """\
+            a = b + c
+            s = p * q / r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        exp_fort = expr1.convert_to_fortran()
+        assert exp_fort == [
+            '      integer*4 a',
+            '      integer*4 b',
+            '      integer*4 c',
+            '      integer*4 d',
+            '      real*8 p',
+            '      real*8 q',
+            '      real*8 r',
+            '      real*8 s',
+            '      a = b + c',
+            '      s = p*q/r'
+        ]
+
+
+    def test_convert_c():
+        src1 = (
+            src +
+            """\
+            a = b + c
+            s = p * q / r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        exp_c = expr1.convert_to_c()
+        assert exp_c == [
+            'int a = 0',
+            'int b = 0',
+            'int c = 0',
+            'int d = 0',
+            'double p = 0.0',
+            'double q = 0.0',
+            'double r = 0.0',
+            'double s = 0.0',
+            'a = b + c;',
+            's = p*q/r;'
+        ]
+
+
+    def test_exceptions():
+        src = 'int a;'
+        raises(ValueError, lambda: SymPyExpression(src))
+        raises(ValueError, lambda: SymPyExpression(mode = 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(src, mode = 'd'))
+
+elif not lfortran and not cin:
+    def test_raise():
+        raises(ImportError, lambda: SymPyExpression('int a;', 'c'))
+        raises(ImportError, lambda: SymPyExpression('integer :: a', 'f'))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_sympy_parser.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_sympy_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..43ecccbe262ffb4093248d891aa7423c8f62c628
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/parsing/tests/test_sympy_parser.py
@@ -0,0 +1,371 @@
+# -*- coding: utf-8 -*-
+
+
+import builtins
+import types
+
+from sympy.assumptions import Q
+from sympy.core import Symbol, Function, Float, Rational, Integer, I, Mul, Pow, Eq, Lt, Le, Gt, Ge, Ne
+from sympy.functions import exp, factorial, factorial2, sin, Min, Max
+from sympy.logic import And
+from sympy.series import Limit
+from sympy.testing.pytest import raises
+
+from sympy.parsing.sympy_parser import (
+    parse_expr, standard_transformations, rationalize, TokenError,
+    split_symbols, implicit_multiplication, convert_equals_signs,
+    convert_xor, function_exponentiation, lambda_notation, auto_symbol,
+    repeated_decimals, implicit_multiplication_application,
+    auto_number, factorial_notation, implicit_application,
+    _transformation, T
+    )
+
+
+def test_sympy_parser():
+    x = Symbol('x')
+    inputs = {
+        '2*x': 2 * x,
+        '3.00': Float(3),
+        '22/7': Rational(22, 7),
+        '2+3j': 2 + 3*I,
+        'exp(x)': exp(x),
+        'x!': factorial(x),
+        'x!!': factorial2(x),
+        '(x + 1)! - 1': factorial(x + 1) - 1,
+        '3.[3]': Rational(10, 3),
+        '.0[3]': Rational(1, 30),
+        '3.2[3]': Rational(97, 30),
+        '1.3[12]': Rational(433, 330),
+        '1 + 3.[3]': Rational(13, 3),
+        '1 + .0[3]': Rational(31, 30),
+        '1 + 3.2[3]': Rational(127, 30),
+        '.[0011]': Rational(1, 909),
+        '0.1[00102] + 1': Rational(366697, 333330),
+        '1.[0191]': Rational(10190, 9999),
+        '10!': 3628800,
+        '-(2)': -Integer(2),
+        '[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)],
+        'Symbol("x").free_symbols': x.free_symbols,
+        "S('S(3).n(n=3)')": Float(3, 3),
+        'factorint(12, visual=True)': Mul(
+            Pow(2, 2, evaluate=False),
+            Pow(3, 1, evaluate=False),
+            evaluate=False),
+        'Limit(sin(x), x, 0, dir="-")': Limit(sin(x), x, 0, dir='-'),
+        'Q.even(x)': Q.even(x),
+
+
+    }
+    for text, result in inputs.items():
+        assert parse_expr(text) == result
+
+    raises(TypeError, lambda:
+        parse_expr('x', standard_transformations))
+    raises(TypeError, lambda:
+        parse_expr('x', transformations=lambda x,y: 1))
+    raises(TypeError, lambda:
+        parse_expr('x', transformations=(lambda x,y: 1,)))
+    raises(TypeError, lambda: parse_expr('x', transformations=((),)))
+    raises(TypeError, lambda: parse_expr('x', {}, [], []))
+    raises(TypeError, lambda: parse_expr('x', [], [], {}))
+    raises(TypeError, lambda: parse_expr('x', [], [], {}))
+
+
+def test_rationalize():
+    inputs = {
+        '0.123': Rational(123, 1000)
+    }
+    transformations = standard_transformations + (rationalize,)
+    for text, result in inputs.items():
+        assert parse_expr(text, transformations=transformations) == result
+
+
+def test_factorial_fail():
+    inputs = ['x!!!', 'x!!!!', '(!)']
+
+
+    for text in inputs:
+        try:
+            parse_expr(text)
+            assert False
+        except TokenError:
+            assert True
+
+
+def test_repeated_fail():
+    inputs = ['1[1]', '.1e1[1]', '0x1[1]', '1.1j[1]', '1.1[1 + 1]',
+        '0.1[[1]]', '0x1.1[1]']
+
+
+    # All are valid Python, so only raise TypeError for invalid indexing
+    for text in inputs:
+        raises(TypeError, lambda: parse_expr(text))
+
+
+    inputs = ['0.1[', '0.1[1', '0.1[]']
+    for text in inputs:
+        raises((TokenError, SyntaxError), lambda: parse_expr(text))
+
+
+def test_repeated_dot_only():
+    assert parse_expr('.[1]') == Rational(1, 9)
+    assert parse_expr('1 + .[1]') == Rational(10, 9)
+
+
+def test_local_dict():
+    local_dict = {
+        'my_function': lambda x: x + 2
+    }
+    inputs = {
+        'my_function(2)': Integer(4)
+    }
+    for text, result in inputs.items():
+        assert parse_expr(text, local_dict=local_dict) == result
+
+
+def test_local_dict_split_implmult():
+    t = standard_transformations + (split_symbols, implicit_multiplication,)
+    w = Symbol('w', real=True)
+    y = Symbol('y')
+    assert parse_expr('yx', local_dict={'x':w}, transformations=t) == y*w
+
+
+def test_local_dict_symbol_to_fcn():
+    x = Symbol('x')
+    d = {'foo': Function('bar')}
+    assert parse_expr('foo(x)', local_dict=d) == d['foo'](x)
+    d = {'foo': Symbol('baz')}
+    raises(TypeError, lambda: parse_expr('foo(x)', local_dict=d))
+
+
+def test_global_dict():
+    global_dict = {
+        'Symbol': Symbol
+    }
+    inputs = {
+        'Q & S': And(Symbol('Q'), Symbol('S'))
+    }
+    for text, result in inputs.items():
+        assert parse_expr(text, global_dict=global_dict) == result
+
+
+def test_no_globals():
+
+    # Replicate creating the default global_dict:
+    default_globals = {}
+    exec('from sympy import *', default_globals)
+    builtins_dict = vars(builtins)
+    for name, obj in builtins_dict.items():
+        if isinstance(obj, types.BuiltinFunctionType):
+            default_globals[name] = obj
+    default_globals['max'] = Max
+    default_globals['min'] = Min
+
+    # Need to include Symbol or parse_expr will not work:
+    default_globals.pop('Symbol')
+    global_dict = {'Symbol':Symbol}
+
+    for name in default_globals:
+        obj = parse_expr(name, global_dict=global_dict)
+        assert obj == Symbol(name)
+
+
+def test_issue_2515():
+    raises(TokenError, lambda: parse_expr('(()'))
+    raises(TokenError, lambda: parse_expr('"""'))
+
+
+def test_issue_7663():
+    x = Symbol('x')
+    e = '2*(x+1)'
+    assert parse_expr(e, evaluate=False) == parse_expr(e, evaluate=False)
+    assert parse_expr(e, evaluate=False).equals(2*(x+1))
+
+def test_recursive_evaluate_false_10560():
+    inputs = {
+        '4*-3' : '4*-3',
+        '-4*3' : '(-4)*3',
+        "-2*x*y": '(-2)*x*y',
+        "x*-4*x": "x*(-4)*x"
+    }
+    for text, result in inputs.items():
+        assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)
+
+
+def test_function_evaluate_false():
+    inputs = [
+        'Abs(0)', 'im(0)', 're(0)', 'sign(0)', 'arg(0)', 'conjugate(0)',
+        'acos(0)', 'acot(0)', 'acsc(0)', 'asec(0)', 'asin(0)', 'atan(0)',
+        'acosh(0)', 'acoth(0)', 'acsch(0)', 'asech(0)', 'asinh(0)', 'atanh(0)',
+        'cos(0)', 'cot(0)', 'csc(0)', 'sec(0)', 'sin(0)', 'tan(0)',
+        'cosh(0)', 'coth(0)', 'csch(0)', 'sech(0)', 'sinh(0)', 'tanh(0)',
+        'exp(0)', 'log(0)', 'sqrt(0)',
+    ]
+    for case in inputs:
+        expr = parse_expr(case, evaluate=False)
+        assert case == str(expr) != str(expr.doit())
+    assert str(parse_expr('ln(0)', evaluate=False)) == 'log(0)'
+    assert str(parse_expr('cbrt(0)', evaluate=False)) == '0**(1/3)'
+
+
+def test_issue_10773():
+    inputs = {
+    '-10/5': '(-10)/5',
+    '-10/-5' : '(-10)/(-5)',
+    }
+    for text, result in inputs.items():
+        assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)
+
+
+def test_split_symbols():
+    transformations = standard_transformations + \
+                      (split_symbols, implicit_multiplication,)
+    x = Symbol('x')
+    y = Symbol('y')
+    xy = Symbol('xy')
+
+
+    assert parse_expr("xy") == xy
+    assert parse_expr("xy", transformations=transformations) == x*y
+
+
+def test_split_symbols_function():
+    transformations = standard_transformations + \
+                      (split_symbols, implicit_multiplication,)
+    x = Symbol('x')
+    y = Symbol('y')
+    a = Symbol('a')
+    f = Function('f')
+
+
+    assert parse_expr("ay(x+1)", transformations=transformations) == a*y*(x+1)
+    assert parse_expr("af(x+1)", transformations=transformations,
+                      local_dict={'f':f}) == a*f(x+1)
+
+
+def test_functional_exponent():
+    t = standard_transformations + (convert_xor, function_exponentiation)
+    x = Symbol('x')
+    y = Symbol('y')
+    a = Symbol('a')
+    yfcn = Function('y')
+    assert parse_expr("sin^2(x)", transformations=t) == (sin(x))**2
+    assert parse_expr("sin^y(x)", transformations=t) == (sin(x))**y
+    assert parse_expr("exp^y(x)", transformations=t) == (exp(x))**y
+    assert parse_expr("E^y(x)", transformations=t) == exp(yfcn(x))
+    assert parse_expr("a^y(x)", transformations=t) == a**(yfcn(x))
+
+
+def test_match_parentheses_implicit_multiplication():
+    transformations = standard_transformations + \
+                      (implicit_multiplication,)
+    raises(TokenError, lambda: parse_expr('(1,2),(3,4]',transformations=transformations))
+
+
+def test_convert_equals_signs():
+    transformations = standard_transformations + \
+                        (convert_equals_signs, )
+    x = Symbol('x')
+    y = Symbol('y')
+    assert parse_expr("1*2=x", transformations=transformations) == Eq(2, x)
+    assert parse_expr("y = x", transformations=transformations) == Eq(y, x)
+    assert parse_expr("(2*y = x) = False",
+        transformations=transformations) == Eq(Eq(2*y, x), False)
+
+
+def test_parse_function_issue_3539():
+    x = Symbol('x')
+    f = Function('f')
+    assert parse_expr('f(x)') == f(x)
+
+def test_issue_24288():
+    assert parse_expr("1 < 2", evaluate=False) == Lt(1, 2, evaluate=False)
+    assert parse_expr("1 <= 2", evaluate=False) == Le(1, 2, evaluate=False)
+    assert parse_expr("1 > 2", evaluate=False) == Gt(1, 2, evaluate=False)
+    assert parse_expr("1 >= 2", evaluate=False) == Ge(1, 2, evaluate=False)
+    assert parse_expr("1 != 2", evaluate=False) == Ne(1, 2, evaluate=False)
+    assert parse_expr("1 == 2", evaluate=False) == Eq(1, 2, evaluate=False)
+    assert parse_expr("1 < 2 < 3", evaluate=False) == And(Lt(1, 2, evaluate=False), Lt(2, 3, evaluate=False), evaluate=False)
+    assert parse_expr("1 <= 2 <= 3", evaluate=False) == And(Le(1, 2, evaluate=False), Le(2, 3, evaluate=False), evaluate=False)
+    assert parse_expr("1 < 2 <= 3 < 4", evaluate=False) == \
+        And(Lt(1, 2, evaluate=False), Le(2, 3, evaluate=False), Lt(3, 4, evaluate=False), evaluate=False)
+    # Valid Python relational operators that SymPy does not decide how to handle them yet
+    raises(ValueError, lambda: parse_expr("1 in 2", evaluate=False))
+    raises(ValueError, lambda: parse_expr("1 is 2", evaluate=False))
+    raises(ValueError, lambda: parse_expr("1 not in 2", evaluate=False))
+    raises(ValueError, lambda: parse_expr("1 is not 2", evaluate=False))
+
+def test_split_symbols_numeric():
+    transformations = (
+        standard_transformations +
+        (implicit_multiplication_application,))
+
+    n = Symbol('n')
+    expr1 = parse_expr('2**n * 3**n')
+    expr2 = parse_expr('2**n3**n', transformations=transformations)
+    assert expr1 == expr2 == 2**n*3**n
+
+    expr1 = parse_expr('n12n34', transformations=transformations)
+    assert expr1 == n*12*n*34
+
+
+def test_unicode_names():
+    assert parse_expr('α') == Symbol('α')
+
+
+def test_python3_features():
+    assert parse_expr("123_456") == 123456
+    assert parse_expr("1.2[3_4]") == parse_expr("1.2[34]") == Rational(611, 495)
+    assert parse_expr("1.2[012_012]") == parse_expr("1.2[012012]") == Rational(400, 333)
+    assert parse_expr('.[3_4]') == parse_expr('.[34]') == Rational(34, 99)
+    assert parse_expr('.1[3_4]') == parse_expr('.1[34]') == Rational(133, 990)
+    assert parse_expr('123_123.123_123[3_4]') == parse_expr('123123.123123[34]') == Rational(12189189189211, 99000000)
+
+
+def test_issue_19501():
+    x = Symbol('x')
+    eq = parse_expr('E**x(1+x)', local_dict={'x': x}, transformations=(
+        standard_transformations +
+        (implicit_multiplication_application,)))
+    assert eq.free_symbols == {x}
+
+
+def test_parsing_definitions():
+    from sympy.abc import x
+    assert len(_transformation) == 12  # if this changes, extend below
+    assert _transformation[0] == lambda_notation
+    assert _transformation[1] == auto_symbol
+    assert _transformation[2] == repeated_decimals
+    assert _transformation[3] == auto_number
+    assert _transformation[4] == factorial_notation
+    assert _transformation[5] == implicit_multiplication_application
+    assert _transformation[6] == convert_xor
+    assert _transformation[7] == implicit_application
+    assert _transformation[8] == implicit_multiplication
+    assert _transformation[9] == convert_equals_signs
+    assert _transformation[10] == function_exponentiation
+    assert _transformation[11] == rationalize
+    assert T[:5] == T[0,1,2,3,4] == standard_transformations
+    t = _transformation
+    assert T[-1, 0] == (t[len(t) - 1], t[0])
+    assert T[:5, 8] == standard_transformations + (t[8],)
+    assert parse_expr('0.3x^2', transformations='all') == 3*x**2/10
+    assert parse_expr('sin 3x', transformations='implicit') == sin(3*x)
+
+
+def test_builtins():
+    cases = [
+        ('abs(x)', 'Abs(x)'),
+        ('max(x, y)', 'Max(x, y)'),
+        ('min(x, y)', 'Min(x, y)'),
+        ('pow(x, y)', 'Pow(x, y)'),
+    ]
+    for built_in_func_call, sympy_func_call in cases:
+        assert parse_expr(built_in_func_call) == parse_expr(sympy_func_call)
+    assert str(parse_expr('pow(38, -1, 97)')) == '23'
+
+
+def test_issue_22822():
+    raises(ValueError, lambda: parse_expr('x', {'': 1}))
+    data = {'some_parameter': None}
+    assert parse_expr('some_parameter is None', data) is True
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..60989896ae8b3f69efc7d2350add8f6f19d85669
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/__init__.py
@@ -0,0 +1,12 @@
+"""
+A module that helps solving problems in physics.
+"""
+
+from . import units
+from .matrices import mgamma, msigma, minkowski_tensor, mdft
+
+__all__ = [
+    'units',
+
+    'mgamma', 'msigma', 'minkowski_tensor', 'mdft',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e0f687cc23c1862b65e55117841cfd7d2b8e3f0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/__init__.py
@@ -0,0 +1,53 @@
+"""Biomechanics extension for SymPy.
+
+Includes biomechanics-related constructs which allows users to extend multibody
+models created using `sympy.physics.mechanics` into biomechanical or
+musculoskeletal models involding musculotendons and activation dynamics.
+
+"""
+
+from .activation import (
+   ActivationBase,
+   FirstOrderActivationDeGroote2016,
+   ZerothOrderActivation,
+)
+from .curve import (
+   CharacteristicCurveCollection,
+   CharacteristicCurveFunction,
+   FiberForceLengthActiveDeGroote2016,
+   FiberForceLengthPassiveDeGroote2016,
+   FiberForceLengthPassiveInverseDeGroote2016,
+   FiberForceVelocityDeGroote2016,
+   FiberForceVelocityInverseDeGroote2016,
+   TendonForceLengthDeGroote2016,
+   TendonForceLengthInverseDeGroote2016,
+)
+from .musculotendon import (
+   MusculotendonBase,
+   MusculotendonDeGroote2016,
+   MusculotendonFormulation,
+)
+
+
+__all__ = [
+   # Musculotendon characteristic curve functions
+   'CharacteristicCurveCollection',
+   'CharacteristicCurveFunction',
+   'FiberForceLengthActiveDeGroote2016',
+   'FiberForceLengthPassiveDeGroote2016',
+   'FiberForceLengthPassiveInverseDeGroote2016',
+   'FiberForceVelocityDeGroote2016',
+   'FiberForceVelocityInverseDeGroote2016',
+   'TendonForceLengthDeGroote2016',
+   'TendonForceLengthInverseDeGroote2016',
+
+   # Activation dynamics classes
+   'ActivationBase',
+   'FirstOrderActivationDeGroote2016',
+   'ZerothOrderActivation',
+
+   # Musculotendon classes
+   'MusculotendonBase',
+   'MusculotendonDeGroote2016',
+   'MusculotendonFormulation',
+]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/_mixin.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/_mixin.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6ff905100fb4d6f346aaf717cfe9a66b4c2cc9a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/_mixin.py
@@ -0,0 +1,53 @@
+"""Mixin classes for sharing functionality between unrelated classes.
+
+This module is named with a leading underscore to signify to users that it's
+"private" and only intended for internal use by the biomechanics module.
+
+"""
+
+
+__all__ = ['_NamedMixin']
+
+
+class _NamedMixin:
+    """Mixin class for adding `name` properties.
+
+    Valid names, as will typically be used by subclasses as a suffix when
+    naming automatically-instantiated symbol attributes, must be nonzero length
+    strings.
+
+    Attributes
+    ==========
+
+    name : str
+        The name identifier associated with the instance. Must be a string of
+        length at least 1.
+
+    """
+
+    @property
+    def name(self) -> str:
+        """The name associated with the class instance."""
+        return self._name
+
+    @name.setter
+    def name(self, name: str) -> None:
+        if hasattr(self, '_name'):
+            msg = (
+                f'Can\'t set attribute `name` to {repr(name)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        if not isinstance(name, str):
+            msg = (
+                f'Name {repr(name)} passed to `name` was of type '
+                f'{type(name)}, must be {str}.'
+            )
+            raise TypeError(msg)
+        if name in {''}:
+            msg = (
+                f'Name {repr(name)} is invalid, must be a nonzero length '
+                f'{type(str)}.'
+            )
+            raise ValueError(msg)
+        self._name = name
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/activation.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/activation.py
new file mode 100644
index 0000000000000000000000000000000000000000..908d9bd2e7b433f91ef6678426c2e4896ab82f27
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/activation.py
@@ -0,0 +1,869 @@
+r"""Activation dynamics for musclotendon models.
+
+Musculotendon models are able to produce active force when they are activated,
+which is when a chemical process has taken place within the muscle fibers
+causing them to voluntarily contract. Biologically this chemical process (the
+diffusion of :math:`\textrm{Ca}^{2+}` ions) is not the input in the system,
+electrical signals from the nervous system are. These are termed excitations.
+Activation dynamics, which relates the normalized excitation level to the
+normalized activation level, can be modeled by the models present in this
+module.
+
+"""
+
+from abc import ABC, abstractmethod
+from functools import cached_property
+
+from sympy.core.symbol import Symbol
+from sympy.core.numbers import Float, Integer, Rational
+from sympy.functions.elementary.hyperbolic import tanh
+from sympy.matrices.dense import MutableDenseMatrix as Matrix, zeros
+from sympy.physics.biomechanics._mixin import _NamedMixin
+from sympy.physics.mechanics import dynamicsymbols
+
+
+__all__ = [
+    'ActivationBase',
+    'FirstOrderActivationDeGroote2016',
+    'ZerothOrderActivation',
+]
+
+
+class ActivationBase(ABC, _NamedMixin):
+    """Abstract base class for all activation dynamics classes to inherit from.
+
+    Notes
+    =====
+
+    Instances of this class cannot be directly instantiated by users. However,
+    it can be used to created custom activation dynamics types through
+    subclassing.
+
+    """
+
+    def __init__(self, name):
+        """Initializer for ``ActivationBase``."""
+        self.name = str(name)
+
+        # Symbols
+        self._e = dynamicsymbols(f"e_{name}")
+        self._a = dynamicsymbols(f"a_{name}")
+
+    @classmethod
+    @abstractmethod
+    def with_defaults(cls, name):
+        """Alternate constructor that provides recommended defaults for
+        constants."""
+        pass
+
+    @property
+    def excitation(self):
+        """Dynamic symbol representing excitation.
+
+        Explanation
+        ===========
+
+        The alias ``e`` can also be used to access the same attribute.
+
+        """
+        return self._e
+
+    @property
+    def e(self):
+        """Dynamic symbol representing excitation.
+
+        Explanation
+        ===========
+
+        The alias ``excitation`` can also be used to access the same attribute.
+
+        """
+        return self._e
+
+    @property
+    def activation(self):
+        """Dynamic symbol representing activation.
+
+        Explanation
+        ===========
+
+        The alias ``a`` can also be used to access the same attribute.
+
+        """
+        return self._a
+
+    @property
+    def a(self):
+        """Dynamic symbol representing activation.
+
+        Explanation
+        ===========
+
+        The alias ``activation`` can also be used to access the same attribute.
+
+        """
+        return self._a
+
+    @property
+    @abstractmethod
+    def order(self):
+        """Order of the (differential) equation governing activation."""
+        pass
+
+    @property
+    @abstractmethod
+    def state_vars(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``x`` can also be used to access the same attribute.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def x(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``state_vars`` can also be used to access the same attribute.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def input_vars(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``r`` can also be used to access the same attribute.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def r(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``input_vars`` can also be used to access the same attribute.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def constants(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        Explanation
+        ===========
+
+        The alias ``p`` can also be used to access the same attribute.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def p(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        Explanation
+        ===========
+
+        The alias ``constants`` can also be used to access the same attribute.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def M(self):
+        """Ordered square matrix of coefficients on the LHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The square matrix that forms part of the LHS of the linear system of
+        ordinary differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        """
+        pass
+
+    @property
+    @abstractmethod
+    def F(self):
+        """Ordered column matrix of equations on the RHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The column matrix that forms the RHS of the linear system of ordinary
+        differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        """
+        pass
+
+    @abstractmethod
+    def rhs(self):
+        """
+
+        Explanation
+        ===========
+
+        The solution to the linear system of ordinary differential equations
+        governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        """
+        pass
+
+    def __eq__(self, other):
+        """Equality check for activation dynamics."""
+        if type(self) != type(other):
+            return False
+        if self.name != other.name:
+            return False
+        return True
+
+    def __repr__(self):
+        """Default representation of activation dynamics."""
+        return f'{self.__class__.__name__}({self.name!r})'
+
+
+class ZerothOrderActivation(ActivationBase):
+    """Simple zeroth-order activation dynamics mapping excitation to
+    activation.
+
+    Explanation
+    ===========
+
+    Zeroth-order activation dynamics are useful in instances where you want to
+    reduce the complexity of your musculotendon dynamics as they simple map
+    exictation to activation. As a result, no additional state equations are
+    introduced to your system. They also remove a potential source of delay
+    between the input and dynamics of your system as no (ordinary) differential
+    equations are involved.
+
+    """
+
+    def __init__(self, name):
+        """Initializer for ``ZerothOrderActivation``.
+
+        Parameters
+        ==========
+
+        name : str
+            The name identifier associated with the instance. Must be a string
+            of length at least 1.
+
+        """
+        super().__init__(name)
+
+        # Zeroth-order activation dynamics has activation equal excitation so
+        # overwrite the symbol for activation with the excitation symbol.
+        self._a = self._e
+
+    @classmethod
+    def with_defaults(cls, name):
+        """Alternate constructor that provides recommended defaults for
+        constants.
+
+        Explanation
+        ===========
+
+        As this concrete class doesn't implement any constants associated with
+        its dynamics, this ``classmethod`` simply creates a standard instance
+        of ``ZerothOrderActivation``. An implementation is provided to ensure
+        a consistent interface between all ``ActivationBase`` concrete classes.
+
+        """
+        return cls(name)
+
+    @property
+    def order(self):
+        """Order of the (differential) equation governing activation."""
+        return 0
+
+    @property
+    def state_vars(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        As zeroth-order activation dynamics simply maps excitation to
+        activation, this class has no associated state variables and so this
+        property return an empty column ``Matrix`` with shape (0, 1).
+
+        The alias ``x`` can also be used to access the same attribute.
+
+        """
+        return zeros(0, 1)
+
+    @property
+    def x(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        As zeroth-order activation dynamics simply maps excitation to
+        activation, this class has no associated state variables and so this
+        property return an empty column ``Matrix`` with shape (0, 1).
+
+        The alias ``state_vars`` can also be used to access the same attribute.
+
+        """
+        return zeros(0, 1)
+
+    @property
+    def input_vars(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        Excitation is the only input in zeroth-order activation dynamics and so
+        this property returns a column ``Matrix`` with one entry, ``e``, and
+        shape (1, 1).
+
+        The alias ``r`` can also be used to access the same attribute.
+
+        """
+        return Matrix([self._e])
+
+    @property
+    def r(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        Excitation is the only input in zeroth-order activation dynamics and so
+        this property returns a column ``Matrix`` with one entry, ``e``, and
+        shape (1, 1).
+
+        The alias ``input_vars`` can also be used to access the same attribute.
+
+        """
+        return Matrix([self._e])
+
+    @property
+    def constants(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        Explanation
+        ===========
+
+        As zeroth-order activation dynamics simply maps excitation to
+        activation, this class has no associated constants and so this property
+        return an empty column ``Matrix`` with shape (0, 1).
+
+        The alias ``p`` can also be used to access the same attribute.
+
+        """
+        return zeros(0, 1)
+
+    @property
+    def p(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        Explanation
+        ===========
+
+        As zeroth-order activation dynamics simply maps excitation to
+        activation, this class has no associated constants and so this property
+        return an empty column ``Matrix`` with shape (0, 1).
+
+        The alias ``constants`` can also be used to access the same attribute.
+
+        """
+        return zeros(0, 1)
+
+    @property
+    def M(self):
+        """Ordered square matrix of coefficients on the LHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The square matrix that forms part of the LHS of the linear system of
+        ordinary differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        As zeroth-order activation dynamics have no state variables, this
+        linear system has dimension 0 and therefore ``M`` is an empty square
+        ``Matrix`` with shape (0, 0).
+
+        """
+        return Matrix([])
+
+    @property
+    def F(self):
+        """Ordered column matrix of equations on the RHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The column matrix that forms the RHS of the linear system of ordinary
+        differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        As zeroth-order activation dynamics have no state variables, this
+        linear system has dimension 0 and therefore ``F`` is an empty column
+        ``Matrix`` with shape (0, 1).
+
+        """
+        return zeros(0, 1)
+
+    def rhs(self):
+        """Ordered column matrix of equations for the solution of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The solution to the linear system of ordinary differential equations
+        governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        As zeroth-order activation dynamics have no state variables, this
+        linear has dimension 0 and therefore this method returns an empty
+        column ``Matrix`` with shape (0, 1).
+
+        """
+        return zeros(0, 1)
+
+
+class FirstOrderActivationDeGroote2016(ActivationBase):
+    r"""First-order activation dynamics based on De Groote et al., 2016 [1]_.
+
+    Explanation
+    ===========
+
+    Gives the first-order activation dynamics equation for the rate of change
+    of activation with respect to time as a function of excitation and
+    activation.
+
+    The function is defined by the equation:
+
+    .. math::
+
+        \frac{da}{dt} = \left(\frac{\frac{1}{2} + a0}{\tau_a \left(\frac{1}{2}
+            + \frac{3a}{2}\right)} + \frac{\left(\frac{1}{2}
+            + \frac{3a}{2}\right) \left(\frac{1}{2} - a0\right)}{\tau_d}\right)
+            \left(e - a\right)
+
+    where
+
+    .. math::
+
+        a0 = \frac{\tanh{\left(b \left(e - a\right) \right)}}{2}
+
+    with constant values of :math:`tau_a = 0.015`, :math:`tau_d = 0.060`, and
+    :math:`b = 10`.
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    def __init__(self,
+        name,
+        activation_time_constant=None,
+        deactivation_time_constant=None,
+        smoothing_rate=None,
+    ):
+        """Initializer for ``FirstOrderActivationDeGroote2016``.
+
+        Parameters
+        ==========
+        activation time constant : Symbol | Number | None
+            The value of the activation time constant governing the delay
+            between excitation and activation when excitation exceeds
+            activation.
+        deactivation time constant : Symbol | Number | None
+            The value of the deactivation time constant governing the delay
+            between excitation and activation when activation exceeds
+            excitation.
+        smoothing_rate : Symbol | Number | None
+            The slope of the hyperbolic tangent function used to smooth between
+            the switching of the equations where excitation exceed activation
+            and where activation exceeds excitation. The recommended value to
+            use is ``10``, but values between ``0.1`` and ``100`` can be used.
+
+        """
+        super().__init__(name)
+
+        # Symbols
+        self.activation_time_constant = activation_time_constant
+        self.deactivation_time_constant = deactivation_time_constant
+        self.smoothing_rate = smoothing_rate
+
+    @classmethod
+    def with_defaults(cls, name):
+        r"""Alternate constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns an instance of ``FirstOrderActivationDeGroote2016`` using the
+        three constant values specified in the original publication.
+
+        These have the values:
+
+        :math:`tau_a = 0.015`
+        :math:`tau_d = 0.060`
+        :math:`b = 10`
+
+        """
+        tau_a = Float('0.015')
+        tau_d = Float('0.060')
+        b = Float('10.0')
+        return cls(name, tau_a, tau_d, b)
+
+    @property
+    def activation_time_constant(self):
+        """Delay constant for activation.
+
+        Explanation
+        ===========
+
+        The alias ```tau_a`` can also be used to access the same attribute.
+
+        """
+        return self._tau_a
+
+    @activation_time_constant.setter
+    def activation_time_constant(self, tau_a):
+        if hasattr(self, '_tau_a'):
+            msg = (
+                f'Can\'t set attribute `activation_time_constant` to '
+                f'{repr(tau_a)} as it is immutable and already has value '
+                f'{self._tau_a}.'
+            )
+            raise AttributeError(msg)
+        self._tau_a = Symbol(f'tau_a_{self.name}') if tau_a is None else tau_a
+
+    @property
+    def tau_a(self):
+        """Delay constant for activation.
+
+        Explanation
+        ===========
+
+        The alias ``activation_time_constant`` can also be used to access the
+        same attribute.
+
+        """
+        return self._tau_a
+
+    @property
+    def deactivation_time_constant(self):
+        """Delay constant for deactivation.
+
+        Explanation
+        ===========
+
+        The alias ``tau_d`` can also be used to access the same attribute.
+
+        """
+        return self._tau_d
+
+    @deactivation_time_constant.setter
+    def deactivation_time_constant(self, tau_d):
+        if hasattr(self, '_tau_d'):
+            msg = (
+                f'Can\'t set attribute `deactivation_time_constant` to '
+                f'{repr(tau_d)} as it is immutable and already has value '
+                f'{self._tau_d}.'
+            )
+            raise AttributeError(msg)
+        self._tau_d = Symbol(f'tau_d_{self.name}') if tau_d is None else tau_d
+
+    @property
+    def tau_d(self):
+        """Delay constant for deactivation.
+
+        Explanation
+        ===========
+
+        The alias ``deactivation_time_constant`` can also be used to access the
+        same attribute.
+
+        """
+        return self._tau_d
+
+    @property
+    def smoothing_rate(self):
+        """Smoothing constant for the hyperbolic tangent term.
+
+        Explanation
+        ===========
+
+        The alias ``b`` can also be used to access the same attribute.
+
+        """
+        return self._b
+
+    @smoothing_rate.setter
+    def smoothing_rate(self, b):
+        if hasattr(self, '_b'):
+            msg = (
+                f'Can\'t set attribute `smoothing_rate` to {b!r} as it is '
+                f'immutable and already has value {self._b!r}.'
+            )
+            raise AttributeError(msg)
+        self._b = Symbol(f'b_{self.name}') if b is None else b
+
+    @property
+    def b(self):
+        """Smoothing constant for the hyperbolic tangent term.
+
+        Explanation
+        ===========
+
+        The alias ``smoothing_rate`` can also be used to access the same
+        attribute.
+
+        """
+        return self._b
+
+    @property
+    def order(self):
+        """Order of the (differential) equation governing activation."""
+        return 1
+
+    @property
+    def state_vars(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``x`` can also be used to access the same attribute.
+
+        """
+        return Matrix([self._a])
+
+    @property
+    def x(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``state_vars`` can also be used to access the same attribute.
+
+        """
+        return Matrix([self._a])
+
+    @property
+    def input_vars(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``r`` can also be used to access the same attribute.
+
+        """
+        return Matrix([self._e])
+
+    @property
+    def r(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``input_vars`` can also be used to access the same attribute.
+
+        """
+        return Matrix([self._e])
+
+    @property
+    def constants(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        Explanation
+        ===========
+
+        The alias ``p`` can also be used to access the same attribute.
+
+        """
+        constants = [self._tau_a, self._tau_d, self._b]
+        symbolic_constants = [c for c in constants if not c.is_number]
+        return Matrix(symbolic_constants) if symbolic_constants else zeros(0, 1)
+
+    @property
+    def p(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Explanation
+        ===========
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        The alias ``constants`` can also be used to access the same attribute.
+
+        """
+        constants = [self._tau_a, self._tau_d, self._b]
+        symbolic_constants = [c for c in constants if not c.is_number]
+        return Matrix(symbolic_constants) if symbolic_constants else zeros(0, 1)
+
+    @property
+    def M(self):
+        """Ordered square matrix of coefficients on the LHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The square matrix that forms part of the LHS of the linear system of
+        ordinary differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        """
+        return Matrix([Integer(1)])
+
+    @property
+    def F(self):
+        """Ordered column matrix of equations on the RHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The column matrix that forms the RHS of the linear system of ordinary
+        differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        """
+        return Matrix([self._da_eqn])
+
+    def rhs(self):
+        """Ordered column matrix of equations for the solution of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The solution to the linear system of ordinary differential equations
+        governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        """
+        return Matrix([self._da_eqn])
+
+    @cached_property
+    def _da_eqn(self):
+        HALF = Rational(1, 2)
+        a0 = HALF * tanh(self._b * (self._e - self._a))
+        a1 = (HALF + Rational(3, 2) * self._a)
+        a2 = (HALF + a0) / (self._tau_a * a1)
+        a3 = a1 * (HALF - a0) / self._tau_d
+        activation_dynamics_equation = (a2 + a3) * (self._e - self._a)
+        return activation_dynamics_equation
+
+    def __eq__(self, other):
+        """Equality check for ``FirstOrderActivationDeGroote2016``."""
+        if type(self) != type(other):
+            return False
+        self_attrs = (self.name, self.tau_a, self.tau_d, self.b)
+        other_attrs = (other.name, other.tau_a, other.tau_d, other.b)
+        if self_attrs == other_attrs:
+            return True
+        return False
+
+    def __repr__(self):
+        """Representation of ``FirstOrderActivationDeGroote2016``."""
+        return (
+            f'{self.__class__.__name__}({self.name!r}, '
+            f'activation_time_constant={self.tau_a!r}, '
+            f'deactivation_time_constant={self.tau_d!r}, '
+            f'smoothing_rate={self.b!r})'
+        )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/curve.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/curve.py
new file mode 100644
index 0000000000000000000000000000000000000000..50535271f51493acc2183d257ce89ff0da4dde5e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/curve.py
@@ -0,0 +1,1763 @@
+"""Implementations of characteristic curves for musculotendon models."""
+
+from dataclasses import dataclass
+
+from sympy.core.expr import UnevaluatedExpr
+from sympy.core.function import ArgumentIndexError, Function
+from sympy.core.numbers import Float, Integer
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.hyperbolic import cosh, sinh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.printing.precedence import PRECEDENCE
+
+
+__all__ = [
+    'CharacteristicCurveCollection',
+    'CharacteristicCurveFunction',
+    'FiberForceLengthActiveDeGroote2016',
+    'FiberForceLengthPassiveDeGroote2016',
+    'FiberForceLengthPassiveInverseDeGroote2016',
+    'FiberForceVelocityDeGroote2016',
+    'FiberForceVelocityInverseDeGroote2016',
+    'TendonForceLengthDeGroote2016',
+    'TendonForceLengthInverseDeGroote2016',
+]
+
+
+class CharacteristicCurveFunction(Function):
+    """Base class for all musculotendon characteristic curve functions."""
+
+    @classmethod
+    def eval(cls):
+        msg = (
+            f'Cannot directly instantiate {cls.__name__!r}, instances of '
+            f'characteristic curves must be of a concrete subclass.'
+
+        )
+        raise TypeError(msg)
+
+    def _print_code(self, printer):
+        """Print code for the function defining the curve using a printer.
+
+        Explanation
+        ===========
+
+        The order of operations may need to be controlled as constant folding
+        the numeric terms within the equations of a musculotendon
+        characteristic curve can sometimes results in a numerically-unstable
+        expression.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print a string representation of the
+            characteristic curve as valid code in the target language.
+
+        """
+        return printer._print(printer.parenthesize(
+            self.doit(deep=False, evaluate=False), PRECEDENCE['Atom'],
+        ))
+
+    _ccode = _print_code
+    _cupycode = _print_code
+    _cxxcode = _print_code
+    _fcode = _print_code
+    _jaxcode = _print_code
+    _lambdacode = _print_code
+    _mpmathcode = _print_code
+    _octave = _print_code
+    _pythoncode = _print_code
+    _numpycode = _print_code
+    _scipycode = _print_code
+
+
+class TendonForceLengthDeGroote2016(CharacteristicCurveFunction):
+    r"""Tendon force-length curve based on De Groote et al., 2016 [1]_.
+
+    Explanation
+    ===========
+
+    Gives the normalized tendon force produced as a function of normalized
+    tendon length.
+
+    The function is defined by the equation:
+
+    $fl^T = c_0 \exp{c_3 \left( \tilde{l}^T - c_1 \right)} - c_2$
+
+    with constant values of $c_0 = 0.2$, $c_1 = 0.995$, $c_2 = 0.25$, and
+    $c_3 = 33.93669377311689$.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces no
+    force when the tendon is in an unstrained state. It also produces a force
+    of 1 normalized unit when the tendon is under a 5% strain.
+
+    Examples
+    ========
+
+    The preferred way to instantiate :class:`TendonForceLengthDeGroote2016` is using
+    the :meth:`~.with_defaults` constructor because this will automatically
+    populate the constants within the characteristic curve equation with the
+    floating point values from the original publication. This constructor takes
+    a single argument corresponding to normalized tendon length. We'll create a
+    :class:`~.Symbol` called ``l_T_tilde`` to represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import TendonForceLengthDeGroote2016
+    >>> l_T_tilde = Symbol('l_T_tilde')
+    >>> fl_T = TendonForceLengthDeGroote2016.with_defaults(l_T_tilde)
+    >>> fl_T
+    TendonForceLengthDeGroote2016(l_T_tilde, 0.2, 0.995, 0.25,
+    33.93669377311689)
+
+    It's also possible to populate the four constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1, c2, c3 = symbols('c0 c1 c2 c3')
+    >>> fl_T = TendonForceLengthDeGroote2016(l_T_tilde, c0, c1, c2, c3)
+    >>> fl_T
+    TendonForceLengthDeGroote2016(l_T_tilde, c0, c1, c2, c3)
+
+    You don't just have to use symbols as the arguments, it's also possible to
+    use expressions. Let's create a new pair of symbols, ``l_T`` and
+    ``l_T_slack``, representing tendon length and tendon slack length
+    respectively. We can then represent ``l_T_tilde`` as an expression, the
+    ratio of these.
+
+    >>> l_T, l_T_slack = symbols('l_T l_T_slack')
+    >>> l_T_tilde = l_T/l_T_slack
+    >>> fl_T = TendonForceLengthDeGroote2016.with_defaults(l_T_tilde)
+    >>> fl_T
+    TendonForceLengthDeGroote2016(l_T/l_T_slack, 0.2, 0.995, 0.25,
+    33.93669377311689)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> fl_T.doit(evaluate=False)
+    -0.25 + 0.2*exp(33.93669377311689*(l_T/l_T_slack - 0.995))
+
+    The function can also be differentiated. We'll differentiate with respect
+    to l_T using the ``diff`` method on an instance with the single positional
+    argument ``l_T``.
+
+    >>> fl_T.diff(l_T)
+    6.787338754623378*exp(33.93669377311689*(l_T/l_T_slack - 0.995))/l_T_slack
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, l_T_tilde):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the tendon force-length function using the
+        four constant values specified in the original publication.
+
+        These have the values:
+
+        $c_0 = 0.2$
+        $c_1 = 0.995$
+        $c_2 = 0.25$
+        $c_3 = 33.93669377311689$
+
+        Parameters
+        ==========
+
+        l_T_tilde : Any (sympifiable)
+            Normalized tendon length.
+
+        """
+        c0 = Float('0.2')
+        c1 = Float('0.995')
+        c2 = Float('0.25')
+        c3 = Float('33.93669377311689')
+        return cls(l_T_tilde, c0, c1, c2, c3)
+
+    @classmethod
+    def eval(cls, l_T_tilde, c0, c1, c2, c3):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        l_T_tilde : Any (sympifiable)
+            Normalized tendon length.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``0.2``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``0.995``.
+        c2 : Any (sympifiable)
+            The third constant in the characteristic equation. The published
+            value is ``0.25``.
+        c3 : Any (sympifiable)
+            The fourth constant in the characteristic equation. The published
+            value is ``33.93669377311689``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``l_T_tilde`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        l_T_tilde, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            l_T_tilde = l_T_tilde.doit(deep=deep, **hints)
+            c0, c1, c2, c3 = [c.doit(deep=deep, **hints) for c in constants]
+        else:
+            c0, c1, c2, c3 = constants
+
+        if evaluate:
+            return c0*exp(c3*(l_T_tilde - c1)) - c2
+
+        return c0*exp(c3*UnevaluatedExpr(l_T_tilde - c1)) - c2
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        l_T_tilde, c0, c1, c2, c3 = self.args
+        if argindex == 1:
+            return c0*c3*exp(c3*UnevaluatedExpr(l_T_tilde - c1))
+        elif argindex == 2:
+            return exp(c3*UnevaluatedExpr(l_T_tilde - c1))
+        elif argindex == 3:
+            return -c0*c3*exp(c3*UnevaluatedExpr(l_T_tilde - c1))
+        elif argindex == 4:
+            return Integer(-1)
+        elif argindex == 5:
+            return c0*(l_T_tilde - c1)*exp(c3*UnevaluatedExpr(l_T_tilde - c1))
+
+        raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """Inverse function.
+
+        Parameters
+        ==========
+
+        argindex : int
+            Value to start indexing the arguments at. Default is ``1``.
+
+        """
+        return TendonForceLengthInverseDeGroote2016
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        l_T_tilde = self.args[0]
+        _l_T_tilde = printer._print(l_T_tilde)
+        return r'\operatorname{fl}^T \left( %s \right)' % _l_T_tilde
+
+
+class TendonForceLengthInverseDeGroote2016(CharacteristicCurveFunction):
+    r"""Inverse tendon force-length curve based on De Groote et al., 2016 [1]_.
+
+    Explanation
+    ===========
+
+    Gives the normalized tendon length that produces a specific normalized
+    tendon force.
+
+    The function is defined by the equation:
+
+    ${fl^T}^{-1} = frac{\log{\frac{fl^T + c_2}{c_0}}}{c_3} + c_1$
+
+    with constant values of $c_0 = 0.2$, $c_1 = 0.995$, $c_2 = 0.25$, and
+    $c_3 = 33.93669377311689$. This function is the exact analytical inverse
+    of the related tendon force-length curve ``TendonForceLengthDeGroote2016``.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces no
+    force when the tendon is in an unstrained state. It also produces a force
+    of 1 normalized unit when the tendon is under a 5% strain.
+
+    Examples
+    ========
+
+    The preferred way to instantiate :class:`TendonForceLengthInverseDeGroote2016` is
+    using the :meth:`~.with_defaults` constructor because this will automatically
+    populate the constants within the characteristic curve equation with the
+    floating point values from the original publication. This constructor takes
+    a single argument corresponding to normalized tendon force-length, which is
+    equal to the tendon force. We'll create a :class:`~.Symbol` called ``fl_T`` to
+    represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import TendonForceLengthInverseDeGroote2016
+    >>> fl_T = Symbol('fl_T')
+    >>> l_T_tilde = TendonForceLengthInverseDeGroote2016.with_defaults(fl_T)
+    >>> l_T_tilde
+    TendonForceLengthInverseDeGroote2016(fl_T, 0.2, 0.995, 0.25,
+    33.93669377311689)
+
+    It's also possible to populate the four constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1, c2, c3 = symbols('c0 c1 c2 c3')
+    >>> l_T_tilde = TendonForceLengthInverseDeGroote2016(fl_T, c0, c1, c2, c3)
+    >>> l_T_tilde
+    TendonForceLengthInverseDeGroote2016(fl_T, c0, c1, c2, c3)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> l_T_tilde.doit(evaluate=False)
+    c1 + log((c2 + fl_T)/c0)/c3
+
+    The function can also be differentiated. We'll differentiate with respect
+    to l_T using the ``diff`` method on an instance with the single positional
+    argument ``l_T``.
+
+    >>> l_T_tilde.diff(fl_T)
+    1/(c3*(c2 + fl_T))
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, fl_T):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the inverse tendon force-length function
+        using the four constant values specified in the original publication.
+
+        These have the values:
+
+        $c_0 = 0.2$
+        $c_1 = 0.995$
+        $c_2 = 0.25$
+        $c_3 = 33.93669377311689$
+
+        Parameters
+        ==========
+
+        fl_T : Any (sympifiable)
+            Normalized tendon force as a function of tendon length.
+
+        """
+        c0 = Float('0.2')
+        c1 = Float('0.995')
+        c2 = Float('0.25')
+        c3 = Float('33.93669377311689')
+        return cls(fl_T, c0, c1, c2, c3)
+
+    @classmethod
+    def eval(cls, fl_T, c0, c1, c2, c3):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        fl_T : Any (sympifiable)
+            Normalized tendon force as a function of tendon length.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``0.2``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``0.995``.
+        c2 : Any (sympifiable)
+            The third constant in the characteristic equation. The published
+            value is ``0.25``.
+        c3 : Any (sympifiable)
+            The fourth constant in the characteristic equation. The published
+            value is ``33.93669377311689``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``l_T_tilde`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        fl_T, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            fl_T = fl_T.doit(deep=deep, **hints)
+            c0, c1, c2, c3 = [c.doit(deep=deep, **hints) for c in constants]
+        else:
+            c0, c1, c2, c3 = constants
+
+        if evaluate:
+            return log((fl_T + c2)/c0)/c3 + c1
+
+        return log(UnevaluatedExpr((fl_T + c2)/c0))/c3 + c1
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        fl_T, c0, c1, c2, c3 = self.args
+        if argindex == 1:
+            return 1/(c3*(fl_T + c2))
+        elif argindex == 2:
+            return -1/(c0*c3)
+        elif argindex == 3:
+            return Integer(1)
+        elif argindex == 4:
+            return 1/(c3*(fl_T + c2))
+        elif argindex == 5:
+            return -log(UnevaluatedExpr((fl_T + c2)/c0))/c3**2
+
+        raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """Inverse function.
+
+        Parameters
+        ==========
+
+        argindex : int
+            Value to start indexing the arguments at. Default is ``1``.
+
+        """
+        return TendonForceLengthDeGroote2016
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        fl_T = self.args[0]
+        _fl_T = printer._print(fl_T)
+        return r'\left( \operatorname{fl}^T \right)^{-1} \left( %s \right)' % _fl_T
+
+
+class FiberForceLengthPassiveDeGroote2016(CharacteristicCurveFunction):
+    r"""Passive muscle fiber force-length curve based on De Groote et al., 2016
+    [1]_.
+
+    Explanation
+    ===========
+
+    The function is defined by the equation:
+
+    $fl^M_{pas} = \frac{\frac{\exp{c_1 \left(\tilde{l^M} - 1\right)}}{c_0} - 1}{\exp{c_1} - 1}$
+
+    with constant values of $c_0 = 0.6$ and $c_1 = 4.0$.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces a
+    passive fiber force very close to 0 for all normalized fiber lengths
+    between 0 and 1.
+
+    Examples
+    ========
+
+    The preferred way to instantiate :class:`FiberForceLengthPassiveDeGroote2016` is
+    using the :meth:`~.with_defaults` constructor because this will automatically
+    populate the constants within the characteristic curve equation with the
+    floating point values from the original publication. This constructor takes
+    a single argument corresponding to normalized muscle fiber length. We'll
+    create a :class:`~.Symbol` called ``l_M_tilde`` to represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import FiberForceLengthPassiveDeGroote2016
+    >>> l_M_tilde = Symbol('l_M_tilde')
+    >>> fl_M = FiberForceLengthPassiveDeGroote2016.with_defaults(l_M_tilde)
+    >>> fl_M
+    FiberForceLengthPassiveDeGroote2016(l_M_tilde, 0.6, 4.0)
+
+    It's also possible to populate the two constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1 = symbols('c0 c1')
+    >>> fl_M = FiberForceLengthPassiveDeGroote2016(l_M_tilde, c0, c1)
+    >>> fl_M
+    FiberForceLengthPassiveDeGroote2016(l_M_tilde, c0, c1)
+
+    You don't just have to use symbols as the arguments, it's also possible to
+    use expressions. Let's create a new pair of symbols, ``l_M`` and
+    ``l_M_opt``, representing muscle fiber length and optimal muscle fiber
+    length respectively. We can then represent ``l_M_tilde`` as an expression,
+    the ratio of these.
+
+    >>> l_M, l_M_opt = symbols('l_M l_M_opt')
+    >>> l_M_tilde = l_M/l_M_opt
+    >>> fl_M = FiberForceLengthPassiveDeGroote2016.with_defaults(l_M_tilde)
+    >>> fl_M
+    FiberForceLengthPassiveDeGroote2016(l_M/l_M_opt, 0.6, 4.0)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> fl_M.doit(evaluate=False)
+    0.0186573603637741*(-1 + exp(6.66666666666667*(l_M/l_M_opt - 1)))
+
+    The function can also be differentiated. We'll differentiate with respect
+    to l_M using the ``diff`` method on an instance with the single positional
+    argument ``l_M``.
+
+    >>> fl_M.diff(l_M)
+    0.12438240242516*exp(6.66666666666667*(l_M/l_M_opt - 1))/l_M_opt
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, l_M_tilde):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the muscle fiber passive force-length
+        function using the four constant values specified in the original
+        publication.
+
+        These have the values:
+
+        $c_0 = 0.6$
+        $c_1 = 4.0$
+
+        Parameters
+        ==========
+
+        l_M_tilde : Any (sympifiable)
+            Normalized muscle fiber length.
+
+        """
+        c0 = Float('0.6')
+        c1 = Float('4.0')
+        return cls(l_M_tilde, c0, c1)
+
+    @classmethod
+    def eval(cls, l_M_tilde, c0, c1):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        l_M_tilde : Any (sympifiable)
+            Normalized muscle fiber length.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``0.6``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``4.0``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``l_T_tilde`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        l_M_tilde, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            l_M_tilde = l_M_tilde.doit(deep=deep, **hints)
+            c0, c1 = [c.doit(deep=deep, **hints) for c in constants]
+        else:
+            c0, c1 = constants
+
+        if evaluate:
+            return (exp((c1*(l_M_tilde - 1))/c0) - 1)/(exp(c1) - 1)
+
+        return (exp((c1*UnevaluatedExpr(l_M_tilde - 1))/c0) - 1)/(exp(c1) - 1)
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        l_M_tilde, c0, c1 = self.args
+        if argindex == 1:
+            return c1*exp(c1*UnevaluatedExpr(l_M_tilde - 1)/c0)/(c0*(exp(c1) - 1))
+        elif argindex == 2:
+            return (
+                -c1*exp(c1*UnevaluatedExpr(l_M_tilde - 1)/c0)
+                *UnevaluatedExpr(l_M_tilde - 1)/(c0**2*(exp(c1) - 1))
+            )
+        elif argindex == 3:
+            return (
+                -exp(c1)*(-1 + exp(c1*UnevaluatedExpr(l_M_tilde - 1)/c0))/(exp(c1) - 1)**2
+                + exp(c1*UnevaluatedExpr(l_M_tilde - 1)/c0)*(l_M_tilde - 1)/(c0*(exp(c1) - 1))
+            )
+
+        raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """Inverse function.
+
+        Parameters
+        ==========
+
+        argindex : int
+            Value to start indexing the arguments at. Default is ``1``.
+
+        """
+        return FiberForceLengthPassiveInverseDeGroote2016
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        l_M_tilde = self.args[0]
+        _l_M_tilde = printer._print(l_M_tilde)
+        return r'\operatorname{fl}^M_{pas} \left( %s \right)' % _l_M_tilde
+
+
+class FiberForceLengthPassiveInverseDeGroote2016(CharacteristicCurveFunction):
+    r"""Inverse passive muscle fiber force-length curve based on De Groote et
+    al., 2016 [1]_.
+
+    Explanation
+    ===========
+
+    Gives the normalized muscle fiber length that produces a specific normalized
+    passive muscle fiber force.
+
+    The function is defined by the equation:
+
+    ${fl^M_{pas}}^{-1} = \frac{c_0 \log{\left(\exp{c_1} - 1\right)fl^M_pas + 1}}{c_1} + 1$
+
+    with constant values of $c_0 = 0.6$ and $c_1 = 4.0$. This function is the
+    exact analytical inverse of the related tendon force-length curve
+    ``FiberForceLengthPassiveDeGroote2016``.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces a
+    passive fiber force very close to 0 for all normalized fiber lengths
+    between 0 and 1.
+
+    Examples
+    ========
+
+    The preferred way to instantiate
+    :class:`FiberForceLengthPassiveInverseDeGroote2016` is using the
+    :meth:`~.with_defaults` constructor because this will automatically populate the
+    constants within the characteristic curve equation with the floating point
+    values from the original publication. This constructor takes a single
+    argument corresponding to the normalized passive muscle fiber length-force
+    component of the muscle fiber force. We'll create a :class:`~.Symbol` called
+    ``fl_M_pas`` to represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import FiberForceLengthPassiveInverseDeGroote2016
+    >>> fl_M_pas = Symbol('fl_M_pas')
+    >>> l_M_tilde = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(fl_M_pas)
+    >>> l_M_tilde
+    FiberForceLengthPassiveInverseDeGroote2016(fl_M_pas, 0.6, 4.0)
+
+    It's also possible to populate the two constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1 = symbols('c0 c1')
+    >>> l_M_tilde = FiberForceLengthPassiveInverseDeGroote2016(fl_M_pas, c0, c1)
+    >>> l_M_tilde
+    FiberForceLengthPassiveInverseDeGroote2016(fl_M_pas, c0, c1)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> l_M_tilde.doit(evaluate=False)
+    c0*log(1 + fl_M_pas*(exp(c1) - 1))/c1 + 1
+
+    The function can also be differentiated. We'll differentiate with respect
+    to fl_M_pas using the ``diff`` method on an instance with the single positional
+    argument ``fl_M_pas``.
+
+    >>> l_M_tilde.diff(fl_M_pas)
+    c0*(exp(c1) - 1)/(c1*(fl_M_pas*(exp(c1) - 1) + 1))
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, fl_M_pas):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the inverse muscle fiber passive force-length
+        function using the four constant values specified in the original
+        publication.
+
+        These have the values:
+
+        $c_0 = 0.6$
+        $c_1 = 4.0$
+
+        Parameters
+        ==========
+
+        fl_M_pas : Any (sympifiable)
+            Normalized passive muscle fiber force as a function of muscle fiber
+            length.
+
+        """
+        c0 = Float('0.6')
+        c1 = Float('4.0')
+        return cls(fl_M_pas, c0, c1)
+
+    @classmethod
+    def eval(cls, fl_M_pas, c0, c1):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        fl_M_pas : Any (sympifiable)
+            Normalized passive muscle fiber force.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``0.6``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``4.0``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``l_T_tilde`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        fl_M_pas, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            fl_M_pas = fl_M_pas.doit(deep=deep, **hints)
+            c0, c1 = [c.doit(deep=deep, **hints) for c in constants]
+        else:
+            c0, c1 = constants
+
+        if evaluate:
+            return c0*log(fl_M_pas*(exp(c1) - 1) + 1)/c1 + 1
+
+        return c0*log(UnevaluatedExpr(fl_M_pas*(exp(c1) - 1)) + 1)/c1 + 1
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        fl_M_pas, c0, c1 = self.args
+        if argindex == 1:
+            return c0*(exp(c1) - 1)/(c1*(fl_M_pas*(exp(c1) - 1) + 1))
+        elif argindex == 2:
+            return log(fl_M_pas*(exp(c1) - 1) + 1)/c1
+        elif argindex == 3:
+            return (
+                c0*fl_M_pas*exp(c1)/(c1*(fl_M_pas*(exp(c1) - 1) + 1))
+                - c0*log(fl_M_pas*(exp(c1) - 1) + 1)/c1**2
+            )
+
+        raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """Inverse function.
+
+        Parameters
+        ==========
+
+        argindex : int
+            Value to start indexing the arguments at. Default is ``1``.
+
+        """
+        return FiberForceLengthPassiveDeGroote2016
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        fl_M_pas = self.args[0]
+        _fl_M_pas = printer._print(fl_M_pas)
+        return r'\left( \operatorname{fl}^M_{pas} \right)^{-1} \left( %s \right)' % _fl_M_pas
+
+
+class FiberForceLengthActiveDeGroote2016(CharacteristicCurveFunction):
+    r"""Active muscle fiber force-length curve based on De Groote et al., 2016
+    [1]_.
+
+    Explanation
+    ===========
+
+    The function is defined by the equation:
+
+    $fl_{\text{act}}^M = c_0 \exp\left(-\frac{1}{2}\left(\frac{\tilde{l}^M - c_1}{c_2 + c_3 \tilde{l}^M}\right)^2\right)
+    + c_4 \exp\left(-\frac{1}{2}\left(\frac{\tilde{l}^M - c_5}{c_6 + c_7 \tilde{l}^M}\right)^2\right)
+    + c_8 \exp\left(-\frac{1}{2}\left(\frac{\tilde{l}^M - c_9}{c_{10} + c_{11} \tilde{l}^M}\right)^2\right)$
+
+    with constant values of $c0 = 0.814$, $c1 = 1.06$, $c2 = 0.162$,
+    $c3 = 0.0633$, $c4 = 0.433$, $c5 = 0.717$, $c6 = -0.0299$, $c7 = 0.2$,
+    $c8 = 0.1$, $c9 = 1.0$, $c10 = 0.354$, and $c11 = 0.0$.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces a
+    active fiber force of 1 at a normalized fiber length of 1, and an active
+    fiber force of 0 at normalized fiber lengths of 0 and 2.
+
+    Examples
+    ========
+
+    The preferred way to instantiate :class:`FiberForceLengthActiveDeGroote2016` is
+    using the :meth:`~.with_defaults` constructor because this will automatically
+    populate the constants within the characteristic curve equation with the
+    floating point values from the original publication. This constructor takes
+    a single argument corresponding to normalized muscle fiber length. We'll
+    create a :class:`~.Symbol` called ``l_M_tilde`` to represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import FiberForceLengthActiveDeGroote2016
+    >>> l_M_tilde = Symbol('l_M_tilde')
+    >>> fl_M = FiberForceLengthActiveDeGroote2016.with_defaults(l_M_tilde)
+    >>> fl_M
+    FiberForceLengthActiveDeGroote2016(l_M_tilde, 0.814, 1.06, 0.162, 0.0633,
+    0.433, 0.717, -0.0299, 0.2, 0.1, 1.0, 0.354, 0.0)
+
+    It's also possible to populate the two constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11 = symbols('c0:12')
+    >>> fl_M = FiberForceLengthActiveDeGroote2016(l_M_tilde, c0, c1, c2, c3,
+    ...     c4, c5, c6, c7, c8, c9, c10, c11)
+    >>> fl_M
+    FiberForceLengthActiveDeGroote2016(l_M_tilde, c0, c1, c2, c3, c4, c5, c6,
+    c7, c8, c9, c10, c11)
+
+    You don't just have to use symbols as the arguments, it's also possible to
+    use expressions. Let's create a new pair of symbols, ``l_M`` and
+    ``l_M_opt``, representing muscle fiber length and optimal muscle fiber
+    length respectively. We can then represent ``l_M_tilde`` as an expression,
+    the ratio of these.
+
+    >>> l_M, l_M_opt = symbols('l_M l_M_opt')
+    >>> l_M_tilde = l_M/l_M_opt
+    >>> fl_M = FiberForceLengthActiveDeGroote2016.with_defaults(l_M_tilde)
+    >>> fl_M
+    FiberForceLengthActiveDeGroote2016(l_M/l_M_opt, 0.814, 1.06, 0.162, 0.0633,
+    0.433, 0.717, -0.0299, 0.2, 0.1, 1.0, 0.354, 0.0)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> fl_M.doit(evaluate=False)
+    0.814*exp(-(l_M/l_M_opt
+    - 1.06)**2/(2*(0.0633*l_M/l_M_opt + 0.162)**2))
+    + 0.433*exp(-(l_M/l_M_opt - 0.717)**2/(2*(0.2*l_M/l_M_opt - 0.0299)**2))
+    + 0.1*exp(-3.98991349867535*(l_M/l_M_opt - 1.0)**2)
+
+    The function can also be differentiated. We'll differentiate with respect
+    to l_M using the ``diff`` method on an instance with the single positional
+    argument ``l_M``.
+
+    >>> fl_M.diff(l_M)
+    ((-0.79798269973507*l_M/l_M_opt
+    + 0.79798269973507)*exp(-3.98991349867535*(l_M/l_M_opt - 1.0)**2)
+    + (0.433*(-l_M/l_M_opt + 0.717)/(0.2*l_M/l_M_opt - 0.0299)**2
+    + 0.0866*(l_M/l_M_opt - 0.717)**2/(0.2*l_M/l_M_opt
+    - 0.0299)**3)*exp(-(l_M/l_M_opt - 0.717)**2/(2*(0.2*l_M/l_M_opt - 0.0299)**2))
+    + (0.814*(-l_M/l_M_opt + 1.06)/(0.0633*l_M/l_M_opt
+    + 0.162)**2 + 0.0515262*(l_M/l_M_opt
+    - 1.06)**2/(0.0633*l_M/l_M_opt
+    + 0.162)**3)*exp(-(l_M/l_M_opt
+    - 1.06)**2/(2*(0.0633*l_M/l_M_opt + 0.162)**2)))/l_M_opt
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, l_M_tilde):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the inverse muscle fiber act force-length
+        function using the four constant values specified in the original
+        publication.
+
+        These have the values:
+
+        $c0 = 0.814$
+        $c1 = 1.06$
+        $c2 = 0.162$
+        $c3 = 0.0633$
+        $c4 = 0.433$
+        $c5 = 0.717$
+        $c6 = -0.0299$
+        $c7 = 0.2$
+        $c8 = 0.1$
+        $c9 = 1.0$
+        $c10 = 0.354$
+        $c11 = 0.0$
+
+        Parameters
+        ==========
+
+        fl_M_act : Any (sympifiable)
+            Normalized passive muscle fiber force as a function of muscle fiber
+            length.
+
+        """
+        c0 = Float('0.814')
+        c1 = Float('1.06')
+        c2 = Float('0.162')
+        c3 = Float('0.0633')
+        c4 = Float('0.433')
+        c5 = Float('0.717')
+        c6 = Float('-0.0299')
+        c7 = Float('0.2')
+        c8 = Float('0.1')
+        c9 = Float('1.0')
+        c10 = Float('0.354')
+        c11 = Float('0.0')
+        return cls(l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11)
+
+    @classmethod
+    def eval(cls, l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        l_M_tilde : Any (sympifiable)
+            Normalized muscle fiber length.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``0.814``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``1.06``.
+        c2 : Any (sympifiable)
+            The third constant in the characteristic equation. The published
+            value is ``0.162``.
+        c3 : Any (sympifiable)
+            The fourth constant in the characteristic equation. The published
+            value is ``0.0633``.
+        c4 : Any (sympifiable)
+            The fifth constant in the characteristic equation. The published
+            value is ``0.433``.
+        c5 : Any (sympifiable)
+            The sixth constant in the characteristic equation. The published
+            value is ``0.717``.
+        c6 : Any (sympifiable)
+            The seventh constant in the characteristic equation. The published
+            value is ``-0.0299``.
+        c7 : Any (sympifiable)
+            The eighth constant in the characteristic equation. The published
+            value is ``0.2``.
+        c8 : Any (sympifiable)
+            The ninth constant in the characteristic equation. The published
+            value is ``0.1``.
+        c9 : Any (sympifiable)
+            The tenth constant in the characteristic equation. The published
+            value is ``1.0``.
+        c10 : Any (sympifiable)
+            The eleventh constant in the characteristic equation. The published
+            value is ``0.354``.
+        c11 : Any (sympifiable)
+            The tweflth constant in the characteristic equation. The published
+            value is ``0.0``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``l_M_tilde`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        l_M_tilde, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            l_M_tilde = l_M_tilde.doit(deep=deep, **hints)
+            constants = [c.doit(deep=deep, **hints) for c in constants]
+        c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11 = constants
+
+        if evaluate:
+            return (
+                c0*exp(-(((l_M_tilde - c1)/(c2 + c3*l_M_tilde))**2)/2)
+                + c4*exp(-(((l_M_tilde - c5)/(c6 + c7*l_M_tilde))**2)/2)
+                + c8*exp(-(((l_M_tilde - c9)/(c10 + c11*l_M_tilde))**2)/2)
+            )
+
+        return (
+            c0*exp(-((UnevaluatedExpr(l_M_tilde - c1)/(c2 + c3*l_M_tilde))**2)/2)
+            + c4*exp(-((UnevaluatedExpr(l_M_tilde - c5)/(c6 + c7*l_M_tilde))**2)/2)
+            + c8*exp(-((UnevaluatedExpr(l_M_tilde - c9)/(c10 + c11*l_M_tilde))**2)/2)
+        )
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11 = self.args
+        if argindex == 1:
+            return (
+                c0*(
+                    c3*(l_M_tilde - c1)**2/(c2 + c3*l_M_tilde)**3
+                    + (c1 - l_M_tilde)/((c2 + c3*l_M_tilde)**2)
+                )*exp(-(l_M_tilde - c1)**2/(2*(c2 + c3*l_M_tilde)**2))
+                + c4*(
+                    c7*(l_M_tilde - c5)**2/(c6 + c7*l_M_tilde)**3
+                    + (c5 - l_M_tilde)/((c6 + c7*l_M_tilde)**2)
+                )*exp(-(l_M_tilde - c5)**2/(2*(c6 + c7*l_M_tilde)**2))
+                + c8*(
+                    c11*(l_M_tilde - c9)**2/(c10 + c11*l_M_tilde)**3
+                    + (c9 - l_M_tilde)/((c10 + c11*l_M_tilde)**2)
+                )*exp(-(l_M_tilde - c9)**2/(2*(c10 + c11*l_M_tilde)**2))
+            )
+        elif argindex == 2:
+            return exp(-(l_M_tilde - c1)**2/(2*(c2 + c3*l_M_tilde)**2))
+        elif argindex == 3:
+            return (
+                c0*(l_M_tilde - c1)/(c2 + c3*l_M_tilde)**2
+                *exp(-(l_M_tilde - c1)**2 /(2*(c2 + c3*l_M_tilde)**2))
+            )
+        elif argindex == 4:
+            return (
+                c0*(l_M_tilde - c1)**2/(c2 + c3*l_M_tilde)**3
+                *exp(-(l_M_tilde - c1)**2/(2*(c2 + c3*l_M_tilde)**2))
+            )
+        elif argindex == 5:
+            return (
+                c0*l_M_tilde*(l_M_tilde - c1)**2/(c2 + c3*l_M_tilde)**3
+                *exp(-(l_M_tilde - c1)**2/(2*(c2 + c3*l_M_tilde)**2))
+            )
+        elif argindex == 6:
+            return exp(-(l_M_tilde - c5)**2/(2*(c6 + c7*l_M_tilde)**2))
+        elif argindex == 7:
+            return (
+                c4*(l_M_tilde - c5)/(c6 + c7*l_M_tilde)**2
+                *exp(-(l_M_tilde - c5)**2 /(2*(c6 + c7*l_M_tilde)**2))
+            )
+        elif argindex == 8:
+            return (
+                c4*(l_M_tilde - c5)**2/(c6 + c7*l_M_tilde)**3
+                *exp(-(l_M_tilde - c5)**2/(2*(c6 + c7*l_M_tilde)**2))
+            )
+        elif argindex == 9:
+            return (
+                c4*l_M_tilde*(l_M_tilde - c5)**2/(c6 + c7*l_M_tilde)**3
+                *exp(-(l_M_tilde - c5)**2/(2*(c6 + c7*l_M_tilde)**2))
+            )
+        elif argindex == 10:
+            return exp(-(l_M_tilde - c9)**2/(2*(c10 + c11*l_M_tilde)**2))
+        elif argindex == 11:
+            return (
+                c8*(l_M_tilde - c9)/(c10 + c11*l_M_tilde)**2
+                *exp(-(l_M_tilde - c9)**2 /(2*(c10 + c11*l_M_tilde)**2))
+            )
+        elif argindex == 12:
+            return (
+                c8*(l_M_tilde - c9)**2/(c10 + c11*l_M_tilde)**3
+                *exp(-(l_M_tilde - c9)**2/(2*(c10 + c11*l_M_tilde)**2))
+            )
+        elif argindex == 13:
+            return (
+                c8*l_M_tilde*(l_M_tilde - c9)**2/(c10 + c11*l_M_tilde)**3
+                *exp(-(l_M_tilde - c9)**2/(2*(c10 + c11*l_M_tilde)**2))
+            )
+
+        raise ArgumentIndexError(self, argindex)
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        l_M_tilde = self.args[0]
+        _l_M_tilde = printer._print(l_M_tilde)
+        return r'\operatorname{fl}^M_{act} \left( %s \right)' % _l_M_tilde
+
+
+class FiberForceVelocityDeGroote2016(CharacteristicCurveFunction):
+    r"""Muscle fiber force-velocity curve based on De Groote et al., 2016 [1]_.
+
+    Explanation
+    ===========
+
+    Gives the normalized muscle fiber force produced as a function of
+    normalized tendon velocity.
+
+    The function is defined by the equation:
+
+    $fv^M = c_0 \log{\left(c_1 \tilde{v}_m + c_2\right) + \sqrt{\left(c_1 \tilde{v}_m + c_2\right)^2 + 1}} + c_3$
+
+    with constant values of $c_0 = -0.318$, $c_1 = -8.149$, $c_2 = -0.374$, and
+    $c_3 = 0.886$.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces a
+    normalized muscle fiber force of 1 when the muscle fibers are contracting
+    isometrically (they have an extension rate of 0).
+
+    Examples
+    ========
+
+    The preferred way to instantiate :class:`FiberForceVelocityDeGroote2016` is using
+    the :meth:`~.with_defaults` constructor because this will automatically populate
+    the constants within the characteristic curve equation with the floating
+    point values from the original publication. This constructor takes a single
+    argument corresponding to normalized muscle fiber extension velocity. We'll
+    create a :class:`~.Symbol` called ``v_M_tilde`` to represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import FiberForceVelocityDeGroote2016
+    >>> v_M_tilde = Symbol('v_M_tilde')
+    >>> fv_M = FiberForceVelocityDeGroote2016.with_defaults(v_M_tilde)
+    >>> fv_M
+    FiberForceVelocityDeGroote2016(v_M_tilde, -0.318, -8.149, -0.374, 0.886)
+
+    It's also possible to populate the four constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1, c2, c3 = symbols('c0 c1 c2 c3')
+    >>> fv_M = FiberForceVelocityDeGroote2016(v_M_tilde, c0, c1, c2, c3)
+    >>> fv_M
+    FiberForceVelocityDeGroote2016(v_M_tilde, c0, c1, c2, c3)
+
+    You don't just have to use symbols as the arguments, it's also possible to
+    use expressions. Let's create a new pair of symbols, ``v_M`` and
+    ``v_M_max``, representing muscle fiber extension velocity and maximum
+    muscle fiber extension velocity respectively. We can then represent
+    ``v_M_tilde`` as an expression, the ratio of these.
+
+    >>> v_M, v_M_max = symbols('v_M v_M_max')
+    >>> v_M_tilde = v_M/v_M_max
+    >>> fv_M = FiberForceVelocityDeGroote2016.with_defaults(v_M_tilde)
+    >>> fv_M
+    FiberForceVelocityDeGroote2016(v_M/v_M_max, -0.318, -8.149, -0.374, 0.886)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> fv_M.doit(evaluate=False)
+    0.886 - 0.318*log(-8.149*v_M/v_M_max - 0.374 + sqrt(1 + (-8.149*v_M/v_M_max
+    - 0.374)**2))
+
+    The function can also be differentiated. We'll differentiate with respect
+    to v_M using the ``diff`` method on an instance with the single positional
+    argument ``v_M``.
+
+    >>> fv_M.diff(v_M)
+    2.591382*(1 + (-8.149*v_M/v_M_max - 0.374)**2)**(-1/2)/v_M_max
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, v_M_tilde):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the muscle fiber force-velocity function
+        using the four constant values specified in the original publication.
+
+        These have the values:
+
+        $c_0 = -0.318$
+        $c_1 = -8.149$
+        $c_2 = -0.374$
+        $c_3 = 0.886$
+
+        Parameters
+        ==========
+
+        v_M_tilde : Any (sympifiable)
+            Normalized muscle fiber extension velocity.
+
+        """
+        c0 = Float('-0.318')
+        c1 = Float('-8.149')
+        c2 = Float('-0.374')
+        c3 = Float('0.886')
+        return cls(v_M_tilde, c0, c1, c2, c3)
+
+    @classmethod
+    def eval(cls, v_M_tilde, c0, c1, c2, c3):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        v_M_tilde : Any (sympifiable)
+            Normalized muscle fiber extension velocity.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``-0.318``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``-8.149``.
+        c2 : Any (sympifiable)
+            The third constant in the characteristic equation. The published
+            value is ``-0.374``.
+        c3 : Any (sympifiable)
+            The fourth constant in the characteristic equation. The published
+            value is ``0.886``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``v_M_tilde`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        v_M_tilde, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            v_M_tilde = v_M_tilde.doit(deep=deep, **hints)
+            c0, c1, c2, c3 = [c.doit(deep=deep, **hints) for c in constants]
+        else:
+            c0, c1, c2, c3 = constants
+
+        if evaluate:
+            return c0*log(c1*v_M_tilde + c2 + sqrt((c1*v_M_tilde + c2)**2 + 1)) + c3
+
+        return c0*log(c1*v_M_tilde + c2 + sqrt(UnevaluatedExpr(c1*v_M_tilde + c2)**2 + 1)) + c3
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        v_M_tilde, c0, c1, c2, c3 = self.args
+        if argindex == 1:
+            return c0*c1/sqrt(UnevaluatedExpr(c1*v_M_tilde + c2)**2 + 1)
+        elif argindex == 2:
+            return log(
+                c1*v_M_tilde + c2
+                + sqrt(UnevaluatedExpr(c1*v_M_tilde + c2)**2 + 1)
+            )
+        elif argindex == 3:
+            return c0*v_M_tilde/sqrt(UnevaluatedExpr(c1*v_M_tilde + c2)**2 + 1)
+        elif argindex == 4:
+            return c0/sqrt(UnevaluatedExpr(c1*v_M_tilde + c2)**2 + 1)
+        elif argindex == 5:
+            return Integer(1)
+
+        raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """Inverse function.
+
+        Parameters
+        ==========
+
+        argindex : int
+            Value to start indexing the arguments at. Default is ``1``.
+
+        """
+        return FiberForceVelocityInverseDeGroote2016
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        v_M_tilde = self.args[0]
+        _v_M_tilde = printer._print(v_M_tilde)
+        return r'\operatorname{fv}^M \left( %s \right)' % _v_M_tilde
+
+
+class FiberForceVelocityInverseDeGroote2016(CharacteristicCurveFunction):
+    r"""Inverse muscle fiber force-velocity curve based on De Groote et al.,
+    2016 [1]_.
+
+    Explanation
+    ===========
+
+    Gives the normalized muscle fiber velocity that produces a specific
+    normalized muscle fiber force.
+
+    The function is defined by the equation:
+
+    ${fv^M}^{-1} = \frac{\sinh{\frac{fv^M - c_3}{c_0}} - c_2}{c_1}$
+
+    with constant values of $c_0 = -0.318$, $c_1 = -8.149$, $c_2 = -0.374$, and
+    $c_3 = 0.886$. This function is the exact analytical inverse of the related
+    muscle fiber force-velocity curve ``FiberForceVelocityDeGroote2016``.
+
+    While it is possible to change the constant values, these were carefully
+    selected in the original publication to give the characteristic curve
+    specific and required properties. For example, the function produces a
+    normalized muscle fiber force of 1 when the muscle fibers are contracting
+    isometrically (they have an extension rate of 0).
+
+    Examples
+    ========
+
+    The preferred way to instantiate :class:`FiberForceVelocityInverseDeGroote2016`
+    is using the :meth:`~.with_defaults` constructor because this will automatically
+    populate the constants within the characteristic curve equation with the
+    floating point values from the original publication. This constructor takes
+    a single argument corresponding to normalized muscle fiber force-velocity
+    component of the muscle fiber force. We'll create a :class:`~.Symbol` called
+    ``fv_M`` to represent this.
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.biomechanics import FiberForceVelocityInverseDeGroote2016
+    >>> fv_M = Symbol('fv_M')
+    >>> v_M_tilde = FiberForceVelocityInverseDeGroote2016.with_defaults(fv_M)
+    >>> v_M_tilde
+    FiberForceVelocityInverseDeGroote2016(fv_M, -0.318, -8.149, -0.374, 0.886)
+
+    It's also possible to populate the four constants with your own values too.
+
+    >>> from sympy import symbols
+    >>> c0, c1, c2, c3 = symbols('c0 c1 c2 c3')
+    >>> v_M_tilde = FiberForceVelocityInverseDeGroote2016(fv_M, c0, c1, c2, c3)
+    >>> v_M_tilde
+    FiberForceVelocityInverseDeGroote2016(fv_M, c0, c1, c2, c3)
+
+    To inspect the actual symbolic expression that this function represents,
+    we can call the :meth:`~.doit` method on an instance. We'll use the keyword
+    argument ``evaluate=False`` as this will keep the expression in its
+    canonical form and won't simplify any constants.
+
+    >>> v_M_tilde.doit(evaluate=False)
+    (-c2 + sinh((-c3 + fv_M)/c0))/c1
+
+    The function can also be differentiated. We'll differentiate with respect
+    to fv_M using the ``diff`` method on an instance with the single positional
+    argument ``fv_M``.
+
+    >>> v_M_tilde.diff(fv_M)
+    cosh((-c3 + fv_M)/c0)/(c0*c1)
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    @classmethod
+    def with_defaults(cls, fv_M):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the inverse muscle fiber force-velocity
+        function using the four constant values specified in the original
+        publication.
+
+        These have the values:
+
+        $c_0 = -0.318$
+        $c_1 = -8.149$
+        $c_2 = -0.374$
+        $c_3 = 0.886$
+
+        Parameters
+        ==========
+
+        fv_M : Any (sympifiable)
+            Normalized muscle fiber extension velocity.
+
+        """
+        c0 = Float('-0.318')
+        c1 = Float('-8.149')
+        c2 = Float('-0.374')
+        c3 = Float('0.886')
+        return cls(fv_M, c0, c1, c2, c3)
+
+    @classmethod
+    def eval(cls, fv_M, c0, c1, c2, c3):
+        """Evaluation of basic inputs.
+
+        Parameters
+        ==========
+
+        fv_M : Any (sympifiable)
+            Normalized muscle fiber force as a function of muscle fiber
+            extension velocity.
+        c0 : Any (sympifiable)
+            The first constant in the characteristic equation. The published
+            value is ``-0.318``.
+        c1 : Any (sympifiable)
+            The second constant in the characteristic equation. The published
+            value is ``-8.149``.
+        c2 : Any (sympifiable)
+            The third constant in the characteristic equation. The published
+            value is ``-0.374``.
+        c3 : Any (sympifiable)
+            The fourth constant in the characteristic equation. The published
+            value is ``0.886``.
+
+        """
+        pass
+
+    def _eval_evalf(self, prec):
+        """Evaluate the expression numerically using ``evalf``."""
+        return self.doit(deep=False, evaluate=False)._eval_evalf(prec)
+
+    def doit(self, deep=True, evaluate=True, **hints):
+        """Evaluate the expression defining the function.
+
+        Parameters
+        ==========
+
+        deep : bool
+            Whether ``doit`` should be recursively called. Default is ``True``.
+        evaluate : bool.
+            Whether the SymPy expression should be evaluated as it is
+            constructed. If ``False``, then no constant folding will be
+            conducted which will leave the expression in a more numerically-
+            stable for values of ``fv_M`` that correspond to a sensible
+            operating range for a musculotendon. Default is ``True``.
+        **kwargs : dict[str, Any]
+            Additional keyword argument pairs to be recursively passed to
+            ``doit``.
+
+        """
+        fv_M, *constants = self.args
+        if deep:
+            hints['evaluate'] = evaluate
+            fv_M = fv_M.doit(deep=deep, **hints)
+            c0, c1, c2, c3 = [c.doit(deep=deep, **hints) for c in constants]
+        else:
+            c0, c1, c2, c3 = constants
+
+        if evaluate:
+            return (sinh((fv_M - c3)/c0) - c2)/c1
+
+        return (sinh(UnevaluatedExpr(fv_M - c3)/c0) - c2)/c1
+
+    def fdiff(self, argindex=1):
+        """Derivative of the function with respect to a single argument.
+
+        Parameters
+        ==========
+
+        argindex : int
+            The index of the function's arguments with respect to which the
+            derivative should be taken. Argument indexes start at ``1``.
+            Default is ``1``.
+
+        """
+        fv_M, c0, c1, c2, c3 = self.args
+        if argindex == 1:
+            return cosh((fv_M - c3)/c0)/(c0*c1)
+        elif argindex == 2:
+            return (c3 - fv_M)*cosh((fv_M - c3)/c0)/(c0**2*c1)
+        elif argindex == 3:
+            return (c2 - sinh((fv_M - c3)/c0))/c1**2
+        elif argindex == 4:
+            return -1/c1
+        elif argindex == 5:
+            return -cosh((fv_M - c3)/c0)/(c0*c1)
+
+        raise ArgumentIndexError(self, argindex)
+
+    def inverse(self, argindex=1):
+        """Inverse function.
+
+        Parameters
+        ==========
+
+        argindex : int
+            Value to start indexing the arguments at. Default is ``1``.
+
+        """
+        return FiberForceVelocityDeGroote2016
+
+    def _latex(self, printer):
+        """Print a LaTeX representation of the function defining the curve.
+
+        Parameters
+        ==========
+
+        printer : Printer
+            The printer to be used to print the LaTeX string representation.
+
+        """
+        fv_M = self.args[0]
+        _fv_M = printer._print(fv_M)
+        return r'\left( \operatorname{fv}^M \right)^{-1} \left( %s \right)' % _fv_M
+
+
+@dataclass(frozen=True)
+class CharacteristicCurveCollection:
+    """Simple data container to group together related characteristic curves."""
+    tendon_force_length: CharacteristicCurveFunction
+    tendon_force_length_inverse: CharacteristicCurveFunction
+    fiber_force_length_passive: CharacteristicCurveFunction
+    fiber_force_length_passive_inverse: CharacteristicCurveFunction
+    fiber_force_length_active: CharacteristicCurveFunction
+    fiber_force_velocity: CharacteristicCurveFunction
+    fiber_force_velocity_inverse: CharacteristicCurveFunction
+
+    def __iter__(self):
+        """Iterator support for ``CharacteristicCurveCollection``."""
+        yield self.tendon_force_length
+        yield self.tendon_force_length_inverse
+        yield self.fiber_force_length_passive
+        yield self.fiber_force_length_passive_inverse
+        yield self.fiber_force_length_active
+        yield self.fiber_force_velocity
+        yield self.fiber_force_velocity_inverse
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/musculotendon.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/musculotendon.py
new file mode 100644
index 0000000000000000000000000000000000000000..e16d66373da9107adee2e3b8418f657ee5879298
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/musculotendon.py
@@ -0,0 +1,1424 @@
+"""Implementations of musculotendon models.
+
+Musculotendon models are a critical component of biomechanical models, one that
+differentiates them from pure multibody systems. Musculotendon models produce a
+force dependent on their level of activation, their length, and their
+extension velocity. Length- and extension velocity-dependent force production
+are governed by force-length and force-velocity characteristics.
+These are normalized functions that are dependent on the musculotendon's state
+and are specific to a given musculotendon model.
+
+"""
+
+from abc import abstractmethod
+from enum import IntEnum, unique
+
+from sympy.core.numbers import Float, Integer
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.matrices.dense import MutableDenseMatrix as Matrix, diag, eye, zeros
+from sympy.physics.biomechanics.activation import ActivationBase
+from sympy.physics.biomechanics.curve import (
+    CharacteristicCurveCollection,
+    FiberForceLengthActiveDeGroote2016,
+    FiberForceLengthPassiveDeGroote2016,
+    FiberForceLengthPassiveInverseDeGroote2016,
+    FiberForceVelocityDeGroote2016,
+    FiberForceVelocityInverseDeGroote2016,
+    TendonForceLengthDeGroote2016,
+    TendonForceLengthInverseDeGroote2016,
+)
+from sympy.physics.biomechanics._mixin import _NamedMixin
+from sympy.physics.mechanics.actuator import ForceActuator
+from sympy.physics.vector.functions import dynamicsymbols
+
+
+__all__ = [
+    'MusculotendonBase',
+    'MusculotendonDeGroote2016',
+    'MusculotendonFormulation',
+]
+
+
+@unique
+class MusculotendonFormulation(IntEnum):
+    """Enumeration of types of musculotendon dynamics formulations.
+
+    Explanation
+    ===========
+
+    An (integer) enumeration is used as it allows for clearer selection of the
+    different formulations of musculotendon dynamics.
+
+    Members
+    =======
+
+    RIGID_TENDON : 0
+        A rigid tendon model.
+    FIBER_LENGTH_EXPLICIT : 1
+        An explicit elastic tendon model with the muscle fiber length (l_M) as
+        the state variable.
+    TENDON_FORCE_EXPLICIT : 2
+        An explicit elastic tendon model with the tendon force (F_T) as the
+        state variable.
+    FIBER_LENGTH_IMPLICIT : 3
+        An implicit elastic tendon model with the muscle fiber length (l_M) as
+        the state variable and the muscle fiber velocity as an additional input
+        variable.
+    TENDON_FORCE_IMPLICIT : 4
+        An implicit elastic tendon model with the tendon force (F_T) as the
+        state variable as the muscle fiber velocity as an additional input
+        variable.
+
+    """
+
+    RIGID_TENDON = 0
+    FIBER_LENGTH_EXPLICIT = 1
+    TENDON_FORCE_EXPLICIT = 2
+    FIBER_LENGTH_IMPLICIT = 3
+    TENDON_FORCE_IMPLICIT = 4
+
+    def __str__(self):
+        """Returns a string representation of the enumeration value.
+
+        Notes
+        =====
+
+        This hard coding is required due to an incompatibility between the
+        ``IntEnum`` implementations in Python 3.10 and Python 3.11
+        (https://github.com/python/cpython/issues/84247). From Python 3.11
+        onwards, the ``__str__`` method uses ``int.__str__``, whereas prior it
+        used ``Enum.__str__``. Once Python 3.11 becomes the minimum version
+        supported by SymPy, this method override can be removed.
+
+        """
+        return str(self.value)
+
+
+_DEFAULT_MUSCULOTENDON_FORMULATION = MusculotendonFormulation.RIGID_TENDON
+
+
+class MusculotendonBase(ForceActuator, _NamedMixin):
+    r"""Abstract base class for all musculotendon classes to inherit from.
+
+    Explanation
+    ===========
+
+    A musculotendon generates a contractile force based on its activation,
+    length, and shortening velocity. This abstract base class is to be inherited
+    by all musculotendon subclasses that implement different characteristic
+    musculotendon curves. Characteristic musculotendon curves are required for
+    the tendon force-length, passive fiber force-length, active fiber force-
+    length, and fiber force-velocity relationships.
+
+    Parameters
+    ==========
+
+    name : str
+        The name identifier associated with the musculotendon. This name is used
+        as a suffix when automatically generated symbols are instantiated. It
+        must be a string of nonzero length.
+    pathway : PathwayBase
+        The pathway that the actuator follows. This must be an instance of a
+        concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+    activation_dynamics : ActivationBase
+        The activation dynamics that will be modeled within the musculotendon.
+        This must be an instance of a concrete subclass of ``ActivationBase``,
+        e.g. ``FirstOrderActivationDeGroote2016``.
+    musculotendon_dynamics : MusculotendonFormulation | int
+        The formulation of musculotendon dynamics that should be used
+        internally, i.e. rigid or elastic tendon model, the choice of
+        musculotendon state etc. This must be a member of the integer
+        enumeration ``MusculotendonFormulation`` or an integer that can be cast
+        to a member. To use a rigid tendon formulation, set this to
+        ``MusculotendonFormulation.RIGID_TENDON`` (or the integer value ``0``,
+        which will be cast to the enumeration member). There are four possible
+        formulations for an elastic tendon model. To use an explicit formulation
+        with the fiber length as the state, set this to
+        ``MusculotendonFormulation.FIBER_LENGTH_EXPLICIT`` (or the integer value
+        ``1``). To use an explicit formulation with the tendon force as the
+        state, set this to ``MusculotendonFormulation.TENDON_FORCE_EXPLICIT``
+        (or the integer value ``2``). To use an implicit formulation with the
+        fiber length as the state, set this to
+        ``MusculotendonFormulation.FIBER_LENGTH_IMPLICIT`` (or the integer value
+        ``3``). To use an implicit formulation with the tendon force as the
+        state, set this to ``MusculotendonFormulation.TENDON_FORCE_IMPLICIT``
+        (or the integer value ``4``). The default is
+        ``MusculotendonFormulation.RIGID_TENDON``, which corresponds to a rigid
+        tendon formulation.
+    tendon_slack_length : Expr | None
+        The length of the tendon when the musculotendon is in its unloaded
+        state. In a rigid tendon model the tendon length is the tendon slack
+        length. In all musculotendon models, tendon slack length is used to
+        normalize tendon length to give
+        :math:`\tilde{l}^T = \frac{l^T}{l^T_{slack}}`.
+    peak_isometric_force : Expr | None
+        The maximum force that the muscle fiber can produce when it is
+        undergoing an isometric contraction (no lengthening velocity). In all
+        musculotendon models, peak isometric force is used to normalized tendon
+        and muscle fiber force to give
+        :math:`\tilde{F}^T = \frac{F^T}{F^M_{max}}`.
+    optimal_fiber_length : Expr | None
+        The muscle fiber length at which the muscle fibers produce no passive
+        force and their maximum active force. In all musculotendon models,
+        optimal fiber length is used to normalize muscle fiber length to give
+        :math:`\tilde{l}^M = \frac{l^M}{l^M_{opt}}`.
+    maximal_fiber_velocity : Expr | None
+        The fiber velocity at which, during muscle fiber shortening, the muscle
+        fibers are unable to produce any active force. In all musculotendon
+        models, maximal fiber velocity is used to normalize muscle fiber
+        extension velocity to give :math:`\tilde{v}^M = \frac{v^M}{v^M_{max}}`.
+    optimal_pennation_angle : Expr | None
+        The pennation angle when muscle fiber length equals the optimal fiber
+        length.
+    fiber_damping_coefficient : Expr | None
+        The coefficient of damping to be used in the damping element in the
+        muscle fiber model.
+    with_defaults : bool
+        Whether ``with_defaults`` alternate constructors should be used when
+        automatically constructing child classes. Default is ``False``.
+
+    """
+
+    def __init__(
+        self,
+        name,
+        pathway,
+        activation_dynamics,
+        *,
+        musculotendon_dynamics=_DEFAULT_MUSCULOTENDON_FORMULATION,
+        tendon_slack_length=None,
+        peak_isometric_force=None,
+        optimal_fiber_length=None,
+        maximal_fiber_velocity=None,
+        optimal_pennation_angle=None,
+        fiber_damping_coefficient=None,
+        with_defaults=False,
+    ):
+        self.name = name
+
+        # Supply a placeholder force to the super initializer, this will be
+        # replaced later
+        super().__init__(Symbol('F'), pathway)
+
+        # Activation dynamics
+        if not isinstance(activation_dynamics, ActivationBase):
+            msg = (
+                f'Can\'t set attribute `activation_dynamics` to '
+                f'{activation_dynamics} as it must be of type '
+                f'`ActivationBase`, not {type(activation_dynamics)}.'
+            )
+            raise TypeError(msg)
+        self._activation_dynamics = activation_dynamics
+        self._child_objects = (self._activation_dynamics, )
+
+        # Constants
+        if tendon_slack_length is not None:
+            self._l_T_slack = tendon_slack_length
+        else:
+            self._l_T_slack = Symbol(f'l_T_slack_{self.name}')
+        if peak_isometric_force is not None:
+            self._F_M_max = peak_isometric_force
+        else:
+            self._F_M_max = Symbol(f'F_M_max_{self.name}')
+        if optimal_fiber_length is not None:
+            self._l_M_opt = optimal_fiber_length
+        else:
+            self._l_M_opt = Symbol(f'l_M_opt_{self.name}')
+        if maximal_fiber_velocity is not None:
+            self._v_M_max = maximal_fiber_velocity
+        else:
+            self._v_M_max = Symbol(f'v_M_max_{self.name}')
+        if optimal_pennation_angle is not None:
+            self._alpha_opt = optimal_pennation_angle
+        else:
+            self._alpha_opt = Symbol(f'alpha_opt_{self.name}')
+        if fiber_damping_coefficient is not None:
+            self._beta = fiber_damping_coefficient
+        else:
+            self._beta = Symbol(f'beta_{self.name}')
+
+        # Musculotendon dynamics
+        self._with_defaults = with_defaults
+        if musculotendon_dynamics == MusculotendonFormulation.RIGID_TENDON:
+            self._rigid_tendon_musculotendon_dynamics()
+        elif musculotendon_dynamics == MusculotendonFormulation.FIBER_LENGTH_EXPLICIT:
+            self._fiber_length_explicit_musculotendon_dynamics()
+        elif musculotendon_dynamics == MusculotendonFormulation.TENDON_FORCE_EXPLICIT:
+            self._tendon_force_explicit_musculotendon_dynamics()
+        elif musculotendon_dynamics == MusculotendonFormulation.FIBER_LENGTH_IMPLICIT:
+            self._fiber_length_implicit_musculotendon_dynamics()
+        elif musculotendon_dynamics == MusculotendonFormulation.TENDON_FORCE_IMPLICIT:
+            self._tendon_force_implicit_musculotendon_dynamics()
+        else:
+            msg = (
+                f'Musculotendon dynamics {repr(musculotendon_dynamics)} '
+                f'passed to `musculotendon_dynamics` was of type '
+                f'{type(musculotendon_dynamics)}, must be '
+                f'{MusculotendonFormulation}.'
+            )
+            raise TypeError(msg)
+        self._musculotendon_dynamics = musculotendon_dynamics
+
+        # Must override the placeholder value in `self._force` now that the
+        # actual force has been calculated by
+        # `self.__musculotendon_dynamics`.
+        # Note that `self._force` assumes forces are expansile, musculotendon
+        # forces are contractile hence the minus sign preceding `self._F_T`
+        # (the tendon force).
+        self._force = -self._F_T
+
+    @classmethod
+    def with_defaults(
+        cls,
+        name,
+        pathway,
+        activation_dynamics,
+        *,
+        musculotendon_dynamics=_DEFAULT_MUSCULOTENDON_FORMULATION,
+        tendon_slack_length=None,
+        peak_isometric_force=None,
+        optimal_fiber_length=None,
+        maximal_fiber_velocity=Float('10.0'),
+        optimal_pennation_angle=Float('0.0'),
+        fiber_damping_coefficient=Float('0.1'),
+    ):
+        r"""Recommended constructor that will use the published constants.
+
+        Explanation
+        ===========
+
+        Returns a new instance of the musculotendon class using recommended
+        values for ``v_M_max``, ``alpha_opt``, and ``beta``. The values are:
+
+            :math:`v^M_{max} = 10`
+            :math:`\alpha_{opt} = 0`
+            :math:`\beta = \frac{1}{10}`
+
+        The musculotendon curves are also instantiated using the constants from
+        the original publication.
+
+        Parameters
+        ==========
+
+        name : str
+            The name identifier associated with the musculotendon. This name is
+            used as a suffix when automatically generated symbols are
+            instantiated. It must be a string of nonzero length.
+        pathway : PathwayBase
+            The pathway that the actuator follows. This must be an instance of a
+            concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+        activation_dynamics : ActivationBase
+            The activation dynamics that will be modeled within the
+            musculotendon. This must be an instance of a concrete subclass of
+            ``ActivationBase``, e.g. ``FirstOrderActivationDeGroote2016``.
+        musculotendon_dynamics : MusculotendonFormulation | int
+            The formulation of musculotendon dynamics that should be used
+            internally, i.e. rigid or elastic tendon model, the choice of
+            musculotendon state etc. This must be a member of the integer
+            enumeration ``MusculotendonFormulation`` or an integer that can be
+            cast to a member. To use a rigid tendon formulation, set this to
+            ``MusculotendonFormulation.RIGID_TENDON`` (or the integer value
+            ``0``, which will be cast to the enumeration member). There are four
+            possible formulations for an elastic tendon model. To use an
+            explicit formulation with the fiber length as the state, set this to
+            ``MusculotendonFormulation.FIBER_LENGTH_EXPLICIT`` (or the integer
+            value ``1``). To use an explicit formulation with the tendon force
+            as the state, set this to
+            ``MusculotendonFormulation.TENDON_FORCE_EXPLICIT`` (or the integer
+            value ``2``). To use an implicit formulation with the fiber length
+            as the state, set this to
+            ``MusculotendonFormulation.FIBER_LENGTH_IMPLICIT`` (or the integer
+            value ``3``). To use an implicit formulation with the tendon force
+            as the state, set this to
+            ``MusculotendonFormulation.TENDON_FORCE_IMPLICIT`` (or the integer
+            value ``4``). The default is
+            ``MusculotendonFormulation.RIGID_TENDON``, which corresponds to a
+            rigid tendon formulation.
+        tendon_slack_length : Expr | None
+            The length of the tendon when the musculotendon is in its unloaded
+            state. In a rigid tendon model the tendon length is the tendon slack
+            length. In all musculotendon models, tendon slack length is used to
+            normalize tendon length to give
+            :math:`\tilde{l}^T = \frac{l^T}{l^T_{slack}}`.
+        peak_isometric_force : Expr | None
+            The maximum force that the muscle fiber can produce when it is
+            undergoing an isometric contraction (no lengthening velocity). In
+            all musculotendon models, peak isometric force is used to normalized
+            tendon and muscle fiber force to give
+            :math:`\tilde{F}^T = \frac{F^T}{F^M_{max}}`.
+        optimal_fiber_length : Expr | None
+            The muscle fiber length at which the muscle fibers produce no
+            passive force and their maximum active force. In all musculotendon
+            models, optimal fiber length is used to normalize muscle fiber
+            length to give :math:`\tilde{l}^M = \frac{l^M}{l^M_{opt}}`.
+        maximal_fiber_velocity : Expr | None
+            The fiber velocity at which, during muscle fiber shortening, the
+            muscle fibers are unable to produce any active force. In all
+            musculotendon models, maximal fiber velocity is used to normalize
+            muscle fiber extension velocity to give
+            :math:`\tilde{v}^M = \frac{v^M}{v^M_{max}}`.
+        optimal_pennation_angle : Expr | None
+            The pennation angle when muscle fiber length equals the optimal
+            fiber length.
+        fiber_damping_coefficient : Expr | None
+            The coefficient of damping to be used in the damping element in the
+            muscle fiber model.
+
+        """
+        return cls(
+            name,
+            pathway,
+            activation_dynamics=activation_dynamics,
+            musculotendon_dynamics=musculotendon_dynamics,
+            tendon_slack_length=tendon_slack_length,
+            peak_isometric_force=peak_isometric_force,
+            optimal_fiber_length=optimal_fiber_length,
+            maximal_fiber_velocity=maximal_fiber_velocity,
+            optimal_pennation_angle=optimal_pennation_angle,
+            fiber_damping_coefficient=fiber_damping_coefficient,
+            with_defaults=True,
+        )
+
+    @abstractmethod
+    def curves(cls):
+        """Return a ``CharacteristicCurveCollection`` of the curves related to
+        the specific model."""
+        pass
+
+    @property
+    def tendon_slack_length(self):
+        r"""Symbol or value corresponding to the tendon slack length constant.
+
+        Explanation
+        ===========
+
+        The length of the tendon when the musculotendon is in its unloaded
+        state. In a rigid tendon model the tendon length is the tendon slack
+        length. In all musculotendon models, tendon slack length is used to
+        normalize tendon length to give
+        :math:`\tilde{l}^T = \frac{l^T}{l^T_{slack}}`.
+
+        The alias ``l_T_slack`` can also be used to access the same attribute.
+
+        """
+        return self._l_T_slack
+
+    @property
+    def l_T_slack(self):
+        r"""Symbol or value corresponding to the tendon slack length constant.
+
+        Explanation
+        ===========
+
+        The length of the tendon when the musculotendon is in its unloaded
+        state. In a rigid tendon model the tendon length is the tendon slack
+        length. In all musculotendon models, tendon slack length is used to
+        normalize tendon length to give
+        :math:`\tilde{l}^T = \frac{l^T}{l^T_{slack}}`.
+
+        The alias ``tendon_slack_length`` can also be used to access the same
+        attribute.
+
+        """
+        return self._l_T_slack
+
+    @property
+    def peak_isometric_force(self):
+        r"""Symbol or value corresponding to the peak isometric force constant.
+
+        Explanation
+        ===========
+
+        The maximum force that the muscle fiber can produce when it is
+        undergoing an isometric contraction (no lengthening velocity). In all
+        musculotendon models, peak isometric force is used to normalized tendon
+        and muscle fiber force to give
+        :math:`\tilde{F}^T = \frac{F^T}{F^M_{max}}`.
+
+        The alias ``F_M_max`` can also be used to access the same attribute.
+
+        """
+        return self._F_M_max
+
+    @property
+    def F_M_max(self):
+        r"""Symbol or value corresponding to the peak isometric force constant.
+
+        Explanation
+        ===========
+
+        The maximum force that the muscle fiber can produce when it is
+        undergoing an isometric contraction (no lengthening velocity). In all
+        musculotendon models, peak isometric force is used to normalized tendon
+        and muscle fiber force to give
+        :math:`\tilde{F}^T = \frac{F^T}{F^M_{max}}`.
+
+        The alias ``peak_isometric_force`` can also be used to access the same
+        attribute.
+
+        """
+        return self._F_M_max
+
+    @property
+    def optimal_fiber_length(self):
+        r"""Symbol or value corresponding to the optimal fiber length constant.
+
+        Explanation
+        ===========
+
+        The muscle fiber length at which the muscle fibers produce no passive
+        force and their maximum active force. In all musculotendon models,
+        optimal fiber length is used to normalize muscle fiber length to give
+        :math:`\tilde{l}^M = \frac{l^M}{l^M_{opt}}`.
+
+        The alias ``l_M_opt`` can also be used to access the same attribute.
+
+        """
+        return self._l_M_opt
+
+    @property
+    def l_M_opt(self):
+        r"""Symbol or value corresponding to the optimal fiber length constant.
+
+        Explanation
+        ===========
+
+        The muscle fiber length at which the muscle fibers produce no passive
+        force and their maximum active force. In all musculotendon models,
+        optimal fiber length is used to normalize muscle fiber length to give
+        :math:`\tilde{l}^M = \frac{l^M}{l^M_{opt}}`.
+
+        The alias ``optimal_fiber_length`` can also be used to access the same
+        attribute.
+
+        """
+        return self._l_M_opt
+
+    @property
+    def maximal_fiber_velocity(self):
+        r"""Symbol or value corresponding to the maximal fiber velocity constant.
+
+        Explanation
+        ===========
+
+        The fiber velocity at which, during muscle fiber shortening, the muscle
+        fibers are unable to produce any active force. In all musculotendon
+        models, maximal fiber velocity is used to normalize muscle fiber
+        extension velocity to give :math:`\tilde{v}^M = \frac{v^M}{v^M_{max}}`.
+
+        The alias ``v_M_max`` can also be used to access the same attribute.
+
+        """
+        return self._v_M_max
+
+    @property
+    def v_M_max(self):
+        r"""Symbol or value corresponding to the maximal fiber velocity constant.
+
+        Explanation
+        ===========
+
+        The fiber velocity at which, during muscle fiber shortening, the muscle
+        fibers are unable to produce any active force. In all musculotendon
+        models, maximal fiber velocity is used to normalize muscle fiber
+        extension velocity to give :math:`\tilde{v}^M = \frac{v^M}{v^M_{max}}`.
+
+        The alias ``maximal_fiber_velocity`` can also be used to access the same
+        attribute.
+
+        """
+        return self._v_M_max
+
+    @property
+    def optimal_pennation_angle(self):
+        """Symbol or value corresponding to the optimal pennation angle
+        constant.
+
+        Explanation
+        ===========
+
+        The pennation angle when muscle fiber length equals the optimal fiber
+        length.
+
+        The alias ``alpha_opt`` can also be used to access the same attribute.
+
+        """
+        return self._alpha_opt
+
+    @property
+    def alpha_opt(self):
+        """Symbol or value corresponding to the optimal pennation angle
+        constant.
+
+        Explanation
+        ===========
+
+        The pennation angle when muscle fiber length equals the optimal fiber
+        length.
+
+        The alias ``optimal_pennation_angle`` can also be used to access the
+        same attribute.
+
+        """
+        return self._alpha_opt
+
+    @property
+    def fiber_damping_coefficient(self):
+        """Symbol or value corresponding to the fiber damping coefficient
+        constant.
+
+        Explanation
+        ===========
+
+        The coefficient of damping to be used in the damping element in the
+        muscle fiber model.
+
+        The alias ``beta`` can also be used to access the same attribute.
+
+        """
+        return self._beta
+
+    @property
+    def beta(self):
+        """Symbol or value corresponding to the fiber damping coefficient
+        constant.
+
+        Explanation
+        ===========
+
+        The coefficient of damping to be used in the damping element in the
+        muscle fiber model.
+
+        The alias ``fiber_damping_coefficient`` can also be used to access the
+        same attribute.
+
+        """
+        return self._beta
+
+    @property
+    def activation_dynamics(self):
+        """Activation dynamics model governing this musculotendon's activation.
+
+        Explanation
+        ===========
+
+        Returns the instance of a subclass of ``ActivationBase`` that governs
+        the relationship between excitation and activation that is used to
+        represent the activation dynamics of this musculotendon.
+
+        """
+        return self._activation_dynamics
+
+    @property
+    def excitation(self):
+        """Dynamic symbol representing excitation.
+
+        Explanation
+        ===========
+
+        The alias ``e`` can also be used to access the same attribute.
+
+        """
+        return self._activation_dynamics._e
+
+    @property
+    def e(self):
+        """Dynamic symbol representing excitation.
+
+        Explanation
+        ===========
+
+        The alias ``excitation`` can also be used to access the same attribute.
+
+        """
+        return self._activation_dynamics._e
+
+    @property
+    def activation(self):
+        """Dynamic symbol representing activation.
+
+        Explanation
+        ===========
+
+        The alias ``a`` can also be used to access the same attribute.
+
+        """
+        return self._activation_dynamics._a
+
+    @property
+    def a(self):
+        """Dynamic symbol representing activation.
+
+        Explanation
+        ===========
+
+        The alias ``activation`` can also be used to access the same attribute.
+
+        """
+        return self._activation_dynamics._a
+
+    @property
+    def musculotendon_dynamics(self):
+        """The choice of rigid or type of elastic tendon musculotendon dynamics.
+
+        Explanation
+        ===========
+
+        The formulation of musculotendon dynamics that should be used
+        internally, i.e. rigid or elastic tendon model, the choice of
+        musculotendon state etc. This must be a member of the integer
+        enumeration ``MusculotendonFormulation`` or an integer that can be cast
+        to a member. To use a rigid tendon formulation, set this to
+        ``MusculotendonFormulation.RIGID_TENDON`` (or the integer value ``0``,
+        which will be cast to the enumeration member). There are four possible
+        formulations for an elastic tendon model. To use an explicit formulation
+        with the fiber length as the state, set this to
+        ``MusculotendonFormulation.FIBER_LENGTH_EXPLICIT`` (or the integer value
+        ``1``). To use an explicit formulation with the tendon force as the
+        state, set this to ``MusculotendonFormulation.TENDON_FORCE_EXPLICIT``
+        (or the integer value ``2``). To use an implicit formulation with the
+        fiber length as the state, set this to
+        ``MusculotendonFormulation.FIBER_LENGTH_IMPLICIT`` (or the integer value
+        ``3``). To use an implicit formulation with the tendon force as the
+        state, set this to ``MusculotendonFormulation.TENDON_FORCE_IMPLICIT``
+        (or the integer value ``4``). The default is
+        ``MusculotendonFormulation.RIGID_TENDON``, which corresponds to a rigid
+        tendon formulation.
+
+        """
+        return self._musculotendon_dynamics
+
+    def _rigid_tendon_musculotendon_dynamics(self):
+        """Rigid tendon musculotendon."""
+        self._l_MT = self.pathway.length
+        self._v_MT = self.pathway.extension_velocity
+        self._l_T = self._l_T_slack
+        self._l_T_tilde = Integer(1)
+        self._l_M = sqrt((self._l_MT - self._l_T)**2 + (self._l_M_opt*sin(self._alpha_opt))**2)
+        self._l_M_tilde = self._l_M/self._l_M_opt
+        self._v_M = self._v_MT*(self._l_MT - self._l_T_slack)/self._l_M
+        self._v_M_tilde = self._v_M/self._v_M_max
+        if self._with_defaults:
+            self._fl_T = self.curves.tendon_force_length.with_defaults(self._l_T_tilde)
+            self._fl_M_pas = self.curves.fiber_force_length_passive.with_defaults(self._l_M_tilde)
+            self._fl_M_act = self.curves.fiber_force_length_active.with_defaults(self._l_M_tilde)
+            self._fv_M = self.curves.fiber_force_velocity.with_defaults(self._v_M_tilde)
+        else:
+            fl_T_constants = symbols(f'c_0:4_fl_T_{self.name}')
+            self._fl_T = self.curves.tendon_force_length(self._l_T_tilde, *fl_T_constants)
+            fl_M_pas_constants = symbols(f'c_0:2_fl_M_pas_{self.name}')
+            self._fl_M_pas = self.curves.fiber_force_length_passive(self._l_M_tilde, *fl_M_pas_constants)
+            fl_M_act_constants = symbols(f'c_0:12_fl_M_act_{self.name}')
+            self._fl_M_act = self.curves.fiber_force_length_active(self._l_M_tilde, *fl_M_act_constants)
+            fv_M_constants = symbols(f'c_0:4_fv_M_{self.name}')
+            self._fv_M = self.curves.fiber_force_velocity(self._v_M_tilde, *fv_M_constants)
+        self._F_M_tilde = self.a*self._fl_M_act*self._fv_M + self._fl_M_pas + self._beta*self._v_M_tilde
+        self._F_T_tilde = self._F_M_tilde
+        self._F_M = self._F_M_tilde*self._F_M_max
+        self._cos_alpha = cos(self._alpha_opt)
+        self._F_T = self._F_M*self._cos_alpha
+
+        # Containers
+        self._state_vars = zeros(0, 1)
+        self._input_vars = zeros(0, 1)
+        self._state_eqns = zeros(0, 1)
+        self._curve_constants = Matrix(
+            fl_T_constants
+            + fl_M_pas_constants
+            + fl_M_act_constants
+            + fv_M_constants
+        ) if not self._with_defaults else zeros(0, 1)
+
+    def _fiber_length_explicit_musculotendon_dynamics(self):
+        """Elastic tendon musculotendon using `l_M_tilde` as a state."""
+        self._l_M_tilde = dynamicsymbols(f'l_M_tilde_{self.name}')
+        self._l_MT = self.pathway.length
+        self._v_MT = self.pathway.extension_velocity
+        self._l_M = self._l_M_tilde*self._l_M_opt
+        self._l_T = self._l_MT - sqrt(self._l_M**2 - (self._l_M_opt*sin(self._alpha_opt))**2)
+        self._l_T_tilde = self._l_T/self._l_T_slack
+        self._cos_alpha = (self._l_MT - self._l_T)/self._l_M
+        if self._with_defaults:
+            self._fl_T = self.curves.tendon_force_length.with_defaults(self._l_T_tilde)
+            self._fl_M_pas = self.curves.fiber_force_length_passive.with_defaults(self._l_M_tilde)
+            self._fl_M_act = self.curves.fiber_force_length_active.with_defaults(self._l_M_tilde)
+        else:
+            fl_T_constants = symbols(f'c_0:4_fl_T_{self.name}')
+            self._fl_T = self.curves.tendon_force_length(self._l_T_tilde, *fl_T_constants)
+            fl_M_pas_constants = symbols(f'c_0:2_fl_M_pas_{self.name}')
+            self._fl_M_pas = self.curves.fiber_force_length_passive(self._l_M_tilde, *fl_M_pas_constants)
+            fl_M_act_constants = symbols(f'c_0:12_fl_M_act_{self.name}')
+            self._fl_M_act = self.curves.fiber_force_length_active(self._l_M_tilde, *fl_M_act_constants)
+        self._F_T_tilde = self._fl_T
+        self._F_T = self._F_T_tilde*self._F_M_max
+        self._F_M = self._F_T/self._cos_alpha
+        self._F_M_tilde = self._F_M/self._F_M_max
+        self._fv_M = (self._F_M_tilde - self._fl_M_pas)/(self.a*self._fl_M_act)
+        if self._with_defaults:
+            self._v_M_tilde = self.curves.fiber_force_velocity_inverse.with_defaults(self._fv_M)
+        else:
+            fv_M_constants = symbols(f'c_0:4_fv_M_{self.name}')
+            self._v_M_tilde = self.curves.fiber_force_velocity_inverse(self._fv_M, *fv_M_constants)
+        self._dl_M_tilde_dt = (self._v_M_max/self._l_M_opt)*self._v_M_tilde
+
+        self._state_vars = Matrix([self._l_M_tilde])
+        self._input_vars = zeros(0, 1)
+        self._state_eqns = Matrix([self._dl_M_tilde_dt])
+        self._curve_constants = Matrix(
+            fl_T_constants
+            + fl_M_pas_constants
+            + fl_M_act_constants
+            + fv_M_constants
+        ) if not self._with_defaults else zeros(0, 1)
+
+    def _tendon_force_explicit_musculotendon_dynamics(self):
+        """Elastic tendon musculotendon using `F_T_tilde` as a state."""
+        self._F_T_tilde = dynamicsymbols(f'F_T_tilde_{self.name}')
+        self._l_MT = self.pathway.length
+        self._v_MT = self.pathway.extension_velocity
+        self._fl_T = self._F_T_tilde
+        if self._with_defaults:
+            self._fl_T_inv = self.curves.tendon_force_length_inverse.with_defaults(self._fl_T)
+        else:
+            fl_T_constants = symbols(f'c_0:4_fl_T_{self.name}')
+            self._fl_T_inv = self.curves.tendon_force_length_inverse(self._fl_T, *fl_T_constants)
+        self._l_T_tilde = self._fl_T_inv
+        self._l_T = self._l_T_tilde*self._l_T_slack
+        self._l_M = sqrt((self._l_MT - self._l_T)**2 + (self._l_M_opt*sin(self._alpha_opt))**2)
+        self._l_M_tilde = self._l_M/self._l_M_opt
+        if self._with_defaults:
+            self._fl_M_pas = self.curves.fiber_force_length_passive.with_defaults(self._l_M_tilde)
+            self._fl_M_act = self.curves.fiber_force_length_active.with_defaults(self._l_M_tilde)
+        else:
+            fl_M_pas_constants = symbols(f'c_0:2_fl_M_pas_{self.name}')
+            self._fl_M_pas = self.curves.fiber_force_length_passive(self._l_M_tilde, *fl_M_pas_constants)
+            fl_M_act_constants = symbols(f'c_0:12_fl_M_act_{self.name}')
+            self._fl_M_act = self.curves.fiber_force_length_active(self._l_M_tilde, *fl_M_act_constants)
+        self._cos_alpha = (self._l_MT - self._l_T)/self._l_M
+        self._F_T = self._F_T_tilde*self._F_M_max
+        self._F_M = self._F_T/self._cos_alpha
+        self._F_M_tilde = self._F_M/self._F_M_max
+        self._fv_M = (self._F_M_tilde - self._fl_M_pas)/(self.a*self._fl_M_act)
+        if self._with_defaults:
+            self._fv_M_inv = self.curves.fiber_force_velocity_inverse.with_defaults(self._fv_M)
+        else:
+            fv_M_constants = symbols(f'c_0:4_fv_M_{self.name}')
+            self._fv_M_inv = self.curves.fiber_force_velocity_inverse(self._fv_M, *fv_M_constants)
+        self._v_M_tilde = self._fv_M_inv
+        self._v_M = self._v_M_tilde*self._v_M_max
+        self._v_T = self._v_MT - (self._v_M/self._cos_alpha)
+        self._v_T_tilde = self._v_T/self._l_T_slack
+        if self._with_defaults:
+            self._fl_T = self.curves.tendon_force_length.with_defaults(self._l_T_tilde)
+        else:
+            self._fl_T = self.curves.tendon_force_length(self._l_T_tilde, *fl_T_constants)
+        self._dF_T_tilde_dt = self._fl_T.diff(dynamicsymbols._t).subs({self._l_T_tilde.diff(dynamicsymbols._t): self._v_T_tilde})
+
+        self._state_vars = Matrix([self._F_T_tilde])
+        self._input_vars = zeros(0, 1)
+        self._state_eqns = Matrix([self._dF_T_tilde_dt])
+        self._curve_constants = Matrix(
+            fl_T_constants
+            + fl_M_pas_constants
+            + fl_M_act_constants
+            + fv_M_constants
+        ) if not self._with_defaults else zeros(0, 1)
+
+    def _fiber_length_implicit_musculotendon_dynamics(self):
+        raise NotImplementedError
+
+    def _tendon_force_implicit_musculotendon_dynamics(self):
+        raise NotImplementedError
+
+    @property
+    def state_vars(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``x`` can also be used to access the same attribute.
+
+        """
+        state_vars = [self._state_vars]
+        for child in self._child_objects:
+            state_vars.append(child.state_vars)
+        return Matrix.vstack(*state_vars)
+
+    @property
+    def x(self):
+        """Ordered column matrix of functions of time that represent the state
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``state_vars`` can also be used to access the same attribute.
+
+        """
+        state_vars = [self._state_vars]
+        for child in self._child_objects:
+            state_vars.append(child.state_vars)
+        return Matrix.vstack(*state_vars)
+
+    @property
+    def input_vars(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``r`` can also be used to access the same attribute.
+
+        """
+        input_vars = [self._input_vars]
+        for child in self._child_objects:
+            input_vars.append(child.input_vars)
+        return Matrix.vstack(*input_vars)
+
+    @property
+    def r(self):
+        """Ordered column matrix of functions of time that represent the input
+        variables.
+
+        Explanation
+        ===========
+
+        The alias ``input_vars`` can also be used to access the same attribute.
+
+        """
+        input_vars = [self._input_vars]
+        for child in self._child_objects:
+            input_vars.append(child.input_vars)
+        return Matrix.vstack(*input_vars)
+
+    @property
+    def constants(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Explanation
+        ===========
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        The alias ``p`` can also be used to access the same attribute.
+
+        """
+        musculotendon_constants = [
+            self._l_T_slack,
+            self._F_M_max,
+            self._l_M_opt,
+            self._v_M_max,
+            self._alpha_opt,
+            self._beta,
+        ]
+        musculotendon_constants = [
+            c for c in musculotendon_constants if not c.is_number
+        ]
+        constants = [
+            Matrix(musculotendon_constants)
+            if musculotendon_constants
+            else zeros(0, 1)
+        ]
+        for child in self._child_objects:
+            constants.append(child.constants)
+        constants.append(self._curve_constants)
+        return Matrix.vstack(*constants)
+
+    @property
+    def p(self):
+        """Ordered column matrix of non-time varying symbols present in ``M``
+        and ``F``.
+
+        Explanation
+        ===========
+
+        Only symbolic constants are returned. If a numeric type (e.g. ``Float``)
+        has been used instead of ``Symbol`` for a constant then that attribute
+        will not be included in the matrix returned by this property. This is
+        because the primary use of this property attribute is to provide an
+        ordered sequence of the still-free symbols that require numeric values
+        during code generation.
+
+        The alias ``constants`` can also be used to access the same attribute.
+
+        """
+        musculotendon_constants = [
+            self._l_T_slack,
+            self._F_M_max,
+            self._l_M_opt,
+            self._v_M_max,
+            self._alpha_opt,
+            self._beta,
+        ]
+        musculotendon_constants = [
+            c for c in musculotendon_constants if not c.is_number
+        ]
+        constants = [
+            Matrix(musculotendon_constants)
+            if musculotendon_constants
+            else zeros(0, 1)
+        ]
+        for child in self._child_objects:
+            constants.append(child.constants)
+        constants.append(self._curve_constants)
+        return Matrix.vstack(*constants)
+
+    @property
+    def M(self):
+        """Ordered square matrix of coefficients on the LHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The square matrix that forms part of the LHS of the linear system of
+        ordinary differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        As zeroth-order activation dynamics have no state variables, this
+        linear system has dimension 0 and therefore ``M`` is an empty square
+        ``Matrix`` with shape (0, 0).
+
+        """
+        M = [eye(len(self._state_vars))]
+        for child in self._child_objects:
+            M.append(child.M)
+        return diag(*M)
+
+    @property
+    def F(self):
+        """Ordered column matrix of equations on the RHS of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The column matrix that forms the RHS of the linear system of ordinary
+        differential equations governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        As zeroth-order activation dynamics have no state variables, this
+        linear system has dimension 0 and therefore ``F`` is an empty column
+        ``Matrix`` with shape (0, 1).
+
+        """
+        F = [self._state_eqns]
+        for child in self._child_objects:
+            F.append(child.F)
+        return Matrix.vstack(*F)
+
+    def rhs(self):
+        """Ordered column matrix of equations for the solution of ``M x' = F``.
+
+        Explanation
+        ===========
+
+        The solution to the linear system of ordinary differential equations
+        governing the activation dynamics:
+
+        ``M(x, r, t, p) x' = F(x, r, t, p)``.
+
+        As zeroth-order activation dynamics have no state variables, this
+        linear has dimension 0 and therefore this method returns an empty
+        column ``Matrix`` with shape (0, 1).
+
+        """
+        is_explicit = (
+            MusculotendonFormulation.FIBER_LENGTH_EXPLICIT,
+            MusculotendonFormulation.TENDON_FORCE_EXPLICIT,
+        )
+        if self.musculotendon_dynamics is MusculotendonFormulation.RIGID_TENDON:
+            child_rhs = [child.rhs() for child in self._child_objects]
+            return Matrix.vstack(*child_rhs)
+        elif self.musculotendon_dynamics in is_explicit:
+            rhs = self._state_eqns
+            child_rhs = [child.rhs() for child in self._child_objects]
+            return Matrix.vstack(rhs, *child_rhs)
+        return self.M.solve(self.F)
+
+    def __repr__(self):
+        """Returns a string representation to reinstantiate the model."""
+        return (
+            f'{self.__class__.__name__}({self.name!r}, '
+            f'pathway={self.pathway!r}, '
+            f'activation_dynamics={self.activation_dynamics!r}, '
+            f'musculotendon_dynamics={self.musculotendon_dynamics}, '
+            f'tendon_slack_length={self._l_T_slack!r}, '
+            f'peak_isometric_force={self._F_M_max!r}, '
+            f'optimal_fiber_length={self._l_M_opt!r}, '
+            f'maximal_fiber_velocity={self._v_M_max!r}, '
+            f'optimal_pennation_angle={self._alpha_opt!r}, '
+            f'fiber_damping_coefficient={self._beta!r})'
+        )
+
+    def __str__(self):
+        """Returns a string representation of the expression for musculotendon
+        force."""
+        return str(self.force)
+
+
+class MusculotendonDeGroote2016(MusculotendonBase):
+    r"""Musculotendon model using the curves of De Groote et al., 2016 [1]_.
+
+    Examples
+    ========
+
+    This class models the musculotendon actuator parametrized by the
+    characteristic curves described in De Groote et al., 2016 [1]_. Like all
+    musculotendon models in SymPy's biomechanics module, it requires a pathway
+    to define its line of action. We'll begin by creating a simple
+    ``LinearPathway`` between two points that our musculotendon will follow.
+    We'll create a point ``O`` to represent the musculotendon's origin and
+    another ``I`` to represent its insertion.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import (LinearPathway, Point,
+    ...     ReferenceFrame, dynamicsymbols)
+
+    >>> N = ReferenceFrame('N')
+    >>> O, I = O, P = symbols('O, I', cls=Point)
+    >>> q, u = dynamicsymbols('q, u', real=True)
+    >>> I.set_pos(O, q*N.x)
+    >>> O.set_vel(N, 0)
+    >>> I.set_vel(N, u*N.x)
+    >>> pathway = LinearPathway(O, I)
+    >>> pathway.attachments
+    (O, I)
+    >>> pathway.length
+    Abs(q(t))
+    >>> pathway.extension_velocity
+    sign(q(t))*Derivative(q(t), t)
+
+    A musculotendon also takes an instance of an activation dynamics model as
+    this will be used to provide symbols for the activation in the formulation
+    of the musculotendon dynamics. We'll use an instance of
+    ``FirstOrderActivationDeGroote2016`` to represent first-order activation
+    dynamics. Note that a single name argument needs to be provided as SymPy
+    will use this as a suffix.
+
+    >>> from sympy.physics.biomechanics import FirstOrderActivationDeGroote2016
+
+    >>> activation = FirstOrderActivationDeGroote2016('muscle')
+    >>> activation.x
+    Matrix([[a_muscle(t)]])
+    >>> activation.r
+    Matrix([[e_muscle(t)]])
+    >>> activation.p
+    Matrix([
+    [tau_a_muscle],
+    [tau_d_muscle],
+    [    b_muscle]])
+    >>> activation.rhs()
+    Matrix([[((1/2 - tanh(b_muscle*(-a_muscle(t) + e_muscle(t)))/2)*(3*...]])
+
+    The musculotendon class requires symbols or values to be passed to represent
+    the constants in the musculotendon dynamics. We'll use SymPy's ``symbols``
+    function to create symbols for the maximum isometric force ``F_M_max``,
+    optimal fiber length ``l_M_opt``, tendon slack length ``l_T_slack``, maximum
+    fiber velocity ``v_M_max``, optimal pennation angle ``alpha_opt, and fiber
+    damping coefficient ``beta``.
+
+    >>> F_M_max = symbols('F_M_max', real=True)
+    >>> l_M_opt = symbols('l_M_opt', real=True)
+    >>> l_T_slack = symbols('l_T_slack', real=True)
+    >>> v_M_max = symbols('v_M_max', real=True)
+    >>> alpha_opt = symbols('alpha_opt', real=True)
+    >>> beta = symbols('beta', real=True)
+
+    We can then import the class ``MusculotendonDeGroote2016`` from the
+    biomechanics module and create an instance by passing in the various objects
+    we have previously instantiated. By default, a musculotendon model with
+    rigid tendon musculotendon dynamics will be created.
+
+    >>> from sympy.physics.biomechanics import MusculotendonDeGroote2016
+
+    >>> rigid_tendon_muscle = MusculotendonDeGroote2016(
+    ...     'muscle',
+    ...     pathway,
+    ...     activation,
+    ...     tendon_slack_length=l_T_slack,
+    ...     peak_isometric_force=F_M_max,
+    ...     optimal_fiber_length=l_M_opt,
+    ...     maximal_fiber_velocity=v_M_max,
+    ...     optimal_pennation_angle=alpha_opt,
+    ...     fiber_damping_coefficient=beta,
+    ... )
+
+    We can inspect the various properties of the musculotendon, including
+    getting the symbolic expression describing the force it produces using its
+    ``force`` attribute.
+
+    >>> rigid_tendon_muscle.force
+    -F_M_max*(beta*(-l_T_slack + Abs(q(t)))*sign(q(t))*Derivative(q(t), t)...
+
+    When we created the musculotendon object, we passed in an instance of an
+    activation dynamics object that governs the activation within the
+    musculotendon. SymPy makes a design choice here that the activation dynamics
+    instance will be treated as a child object of the musculotendon dynamics.
+    Therefore, if we want to inspect the state and input variables associated
+    with the musculotendon model, we will also be returned the state and input
+    variables associated with the child object, or the activation dynamics in
+    this case. As the musculotendon model that we created here uses rigid tendon
+    dynamics, no additional states or inputs relating to the musculotendon are
+    introduces. Consequently, the model has a single state associated with it,
+    the activation, and a single input associated with it, the excitation. The
+    states and inputs can be inspected using the ``x`` and ``r`` attributes
+    respectively. Note that both ``x`` and ``r`` have the alias attributes of
+    ``state_vars`` and ``input_vars``.
+
+    >>> rigid_tendon_muscle.x
+    Matrix([[a_muscle(t)]])
+    >>> rigid_tendon_muscle.r
+    Matrix([[e_muscle(t)]])
+
+    To see which constants are symbolic in the musculotendon model, we can use
+    the ``p`` or ``constants`` attribute. This returns a ``Matrix`` populated
+    by the constants that are represented by a ``Symbol`` rather than a numeric
+    value.
+
+    >>> rigid_tendon_muscle.p
+    Matrix([
+    [           l_T_slack],
+    [             F_M_max],
+    [             l_M_opt],
+    [             v_M_max],
+    [           alpha_opt],
+    [                beta],
+    [        tau_a_muscle],
+    [        tau_d_muscle],
+    [            b_muscle],
+    [     c_0_fl_T_muscle],
+    [     c_1_fl_T_muscle],
+    [     c_2_fl_T_muscle],
+    [     c_3_fl_T_muscle],
+    [ c_0_fl_M_pas_muscle],
+    [ c_1_fl_M_pas_muscle],
+    [ c_0_fl_M_act_muscle],
+    [ c_1_fl_M_act_muscle],
+    [ c_2_fl_M_act_muscle],
+    [ c_3_fl_M_act_muscle],
+    [ c_4_fl_M_act_muscle],
+    [ c_5_fl_M_act_muscle],
+    [ c_6_fl_M_act_muscle],
+    [ c_7_fl_M_act_muscle],
+    [ c_8_fl_M_act_muscle],
+    [ c_9_fl_M_act_muscle],
+    [c_10_fl_M_act_muscle],
+    [c_11_fl_M_act_muscle],
+    [     c_0_fv_M_muscle],
+    [     c_1_fv_M_muscle],
+    [     c_2_fv_M_muscle],
+    [     c_3_fv_M_muscle]])
+
+    Finally, we can call the ``rhs`` method to return a ``Matrix`` that
+    contains as its elements the righthand side of the ordinary differential
+    equations corresponding to each of the musculotendon's states. Like the
+    method with the same name on the ``Method`` classes in SymPy's mechanics
+    module, this returns a column vector where the number of rows corresponds to
+    the number of states. For our example here, we have a single state, the
+    dynamic symbol ``a_muscle(t)``, so the returned value is a 1-by-1
+    ``Matrix``.
+
+    >>> rigid_tendon_muscle.rhs()
+    Matrix([[((1/2 - tanh(b_muscle*(-a_muscle(t) + e_muscle(t)))/2)*(3*...]])
+
+    The musculotendon class supports elastic tendon musculotendon models in
+    addition to rigid tendon ones. You can choose to either use the fiber length
+    or tendon force as an additional state. You can also specify whether an
+    explicit or implicit formulation should be used. To select a formulation,
+    pass a member of the ``MusculotendonFormulation`` enumeration to the
+    ``musculotendon_dynamics`` parameter when calling the constructor. This
+    enumeration is an ``IntEnum``, so you can also pass an integer, however it
+    is recommended to use the enumeration as it is clearer which formulation you
+    are actually selecting. Below, we'll use the ``FIBER_LENGTH_EXPLICIT``
+    member to create a musculotendon with an elastic tendon that will use the
+    (normalized) muscle fiber length as an additional state and will produce
+    the governing ordinary differential equation in explicit form.
+
+    >>> from sympy.physics.biomechanics import MusculotendonFormulation
+
+    >>> elastic_tendon_muscle = MusculotendonDeGroote2016(
+    ...     'muscle',
+    ...     pathway,
+    ...     activation,
+    ...     musculotendon_dynamics=MusculotendonFormulation.FIBER_LENGTH_EXPLICIT,
+    ...     tendon_slack_length=l_T_slack,
+    ...     peak_isometric_force=F_M_max,
+    ...     optimal_fiber_length=l_M_opt,
+    ...     maximal_fiber_velocity=v_M_max,
+    ...     optimal_pennation_angle=alpha_opt,
+    ...     fiber_damping_coefficient=beta,
+    ... )
+
+    >>> elastic_tendon_muscle.force
+    -F_M_max*TendonForceLengthDeGroote2016((-sqrt(l_M_opt**2*...
+    >>> elastic_tendon_muscle.x
+    Matrix([
+    [l_M_tilde_muscle(t)],
+    [        a_muscle(t)]])
+    >>> elastic_tendon_muscle.r
+    Matrix([[e_muscle(t)]])
+    >>> elastic_tendon_muscle.p
+    Matrix([
+    [           l_T_slack],
+    [             F_M_max],
+    [             l_M_opt],
+    [             v_M_max],
+    [           alpha_opt],
+    [                beta],
+    [        tau_a_muscle],
+    [        tau_d_muscle],
+    [            b_muscle],
+    [     c_0_fl_T_muscle],
+    [     c_1_fl_T_muscle],
+    [     c_2_fl_T_muscle],
+    [     c_3_fl_T_muscle],
+    [ c_0_fl_M_pas_muscle],
+    [ c_1_fl_M_pas_muscle],
+    [ c_0_fl_M_act_muscle],
+    [ c_1_fl_M_act_muscle],
+    [ c_2_fl_M_act_muscle],
+    [ c_3_fl_M_act_muscle],
+    [ c_4_fl_M_act_muscle],
+    [ c_5_fl_M_act_muscle],
+    [ c_6_fl_M_act_muscle],
+    [ c_7_fl_M_act_muscle],
+    [ c_8_fl_M_act_muscle],
+    [ c_9_fl_M_act_muscle],
+    [c_10_fl_M_act_muscle],
+    [c_11_fl_M_act_muscle],
+    [     c_0_fv_M_muscle],
+    [     c_1_fv_M_muscle],
+    [     c_2_fv_M_muscle],
+    [     c_3_fv_M_muscle]])
+    >>> elastic_tendon_muscle.rhs()
+    Matrix([
+    [v_M_max*FiberForceVelocityInverseDeGroote2016((l_M_opt*...],
+    [ ((1/2 - tanh(b_muscle*(-a_muscle(t) + e_muscle(t)))/2)*(3*...]])
+
+    It is strongly recommended to use the alternate ``with_defaults``
+    constructor when creating an instance because this will ensure that the
+    published constants are used in the musculotendon characteristic curves.
+
+    >>> elastic_tendon_muscle = MusculotendonDeGroote2016.with_defaults(
+    ...     'muscle',
+    ...     pathway,
+    ...     activation,
+    ...     musculotendon_dynamics=MusculotendonFormulation.FIBER_LENGTH_EXPLICIT,
+    ...     tendon_slack_length=l_T_slack,
+    ...     peak_isometric_force=F_M_max,
+    ...     optimal_fiber_length=l_M_opt,
+    ... )
+
+    >>> elastic_tendon_muscle.x
+    Matrix([
+    [l_M_tilde_muscle(t)],
+    [        a_muscle(t)]])
+    >>> elastic_tendon_muscle.r
+    Matrix([[e_muscle(t)]])
+    >>> elastic_tendon_muscle.p
+    Matrix([
+    [   l_T_slack],
+    [     F_M_max],
+    [     l_M_opt],
+    [tau_a_muscle],
+    [tau_d_muscle],
+    [    b_muscle]])
+
+    Parameters
+    ==========
+
+    name : str
+        The name identifier associated with the musculotendon. This name is used
+        as a suffix when automatically generated symbols are instantiated. It
+        must be a string of nonzero length.
+    pathway : PathwayBase
+        The pathway that the actuator follows. This must be an instance of a
+        concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+    activation_dynamics : ActivationBase
+        The activation dynamics that will be modeled within the musculotendon.
+        This must be an instance of a concrete subclass of ``ActivationBase``,
+        e.g. ``FirstOrderActivationDeGroote2016``.
+    musculotendon_dynamics : MusculotendonFormulation | int
+        The formulation of musculotendon dynamics that should be used
+        internally, i.e. rigid or elastic tendon model, the choice of
+        musculotendon state etc. This must be a member of the integer
+        enumeration ``MusculotendonFormulation`` or an integer that can be cast
+        to a member. To use a rigid tendon formulation, set this to
+        ``MusculotendonFormulation.RIGID_TENDON`` (or the integer value ``0``,
+        which will be cast to the enumeration member). There are four possible
+        formulations for an elastic tendon model. To use an explicit formulation
+        with the fiber length as the state, set this to
+        ``MusculotendonFormulation.FIBER_LENGTH_EXPLICIT`` (or the integer value
+        ``1``). To use an explicit formulation with the tendon force as the
+        state, set this to ``MusculotendonFormulation.TENDON_FORCE_EXPLICIT``
+        (or the integer value ``2``). To use an implicit formulation with the
+        fiber length as the state, set this to
+        ``MusculotendonFormulation.FIBER_LENGTH_IMPLICIT`` (or the integer value
+        ``3``). To use an implicit formulation with the tendon force as the
+        state, set this to ``MusculotendonFormulation.TENDON_FORCE_IMPLICIT``
+        (or the integer value ``4``). The default is
+        ``MusculotendonFormulation.RIGID_TENDON``, which corresponds to a rigid
+        tendon formulation.
+    tendon_slack_length : Expr | None
+        The length of the tendon when the musculotendon is in its unloaded
+        state. In a rigid tendon model the tendon length is the tendon slack
+        length. In all musculotendon models, tendon slack length is used to
+        normalize tendon length to give
+        :math:`\tilde{l}^T = \frac{l^T}{l^T_{slack}}`.
+    peak_isometric_force : Expr | None
+        The maximum force that the muscle fiber can produce when it is
+        undergoing an isometric contraction (no lengthening velocity). In all
+        musculotendon models, peak isometric force is used to normalized tendon
+        and muscle fiber force to give
+        :math:`\tilde{F}^T = \frac{F^T}{F^M_{max}}`.
+    optimal_fiber_length : Expr | None
+        The muscle fiber length at which the muscle fibers produce no passive
+        force and their maximum active force. In all musculotendon models,
+        optimal fiber length is used to normalize muscle fiber length to give
+        :math:`\tilde{l}^M = \frac{l^M}{l^M_{opt}}`.
+    maximal_fiber_velocity : Expr | None
+        The fiber velocity at which, during muscle fiber shortening, the muscle
+        fibers are unable to produce any active force. In all musculotendon
+        models, maximal fiber velocity is used to normalize muscle fiber
+        extension velocity to give :math:`\tilde{v}^M = \frac{v^M}{v^M_{max}}`.
+    optimal_pennation_angle : Expr | None
+        The pennation angle when muscle fiber length equals the optimal fiber
+        length.
+    fiber_damping_coefficient : Expr | None
+        The coefficient of damping to be used in the damping element in the
+        muscle fiber model.
+    with_defaults : bool
+        Whether ``with_defaults`` alternate constructors should be used when
+        automatically constructing child classes. Default is ``False``.
+
+    References
+    ==========
+
+    .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation
+           of direct collocation optimal control problem formulations for
+           solving the muscle redundancy problem, Annals of biomedical
+           engineering, 44(10), (2016) pp. 2922-2936
+
+    """
+
+    curves = CharacteristicCurveCollection(
+        tendon_force_length=TendonForceLengthDeGroote2016,
+        tendon_force_length_inverse=TendonForceLengthInverseDeGroote2016,
+        fiber_force_length_passive=FiberForceLengthPassiveDeGroote2016,
+        fiber_force_length_passive_inverse=FiberForceLengthPassiveInverseDeGroote2016,
+        fiber_force_length_active=FiberForceLengthActiveDeGroote2016,
+        fiber_force_velocity=FiberForceVelocityDeGroote2016,
+        fiber_force_velocity_inverse=FiberForceVelocityInverseDeGroote2016,
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_activation.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_activation.py
new file mode 100644
index 0000000000000000000000000000000000000000..a38742f0d42af48dff95295eae869b2c5ef269de
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_activation.py
@@ -0,0 +1,348 @@
+"""Tests for the ``sympy.physics.biomechanics.activation.py`` module."""
+
+import pytest
+
+from sympy import Symbol
+from sympy.core.numbers import Float, Integer, Rational
+from sympy.functions.elementary.hyperbolic import tanh
+from sympy.matrices import Matrix
+from sympy.matrices.dense import zeros
+from sympy.physics.mechanics import dynamicsymbols
+from sympy.physics.biomechanics import (
+    ActivationBase,
+    FirstOrderActivationDeGroote2016,
+    ZerothOrderActivation,
+)
+from sympy.physics.biomechanics._mixin import _NamedMixin
+from sympy.simplify.simplify import simplify
+
+
+class TestZerothOrderActivation:
+
+    @staticmethod
+    def test_class():
+        assert issubclass(ZerothOrderActivation, ActivationBase)
+        assert issubclass(ZerothOrderActivation, _NamedMixin)
+        assert ZerothOrderActivation.__name__ == 'ZerothOrderActivation'
+
+    @pytest.fixture(autouse=True)
+    def _zeroth_order_activation_fixture(self):
+        self.name = 'name'
+        self.e = dynamicsymbols('e_name')
+        self.instance = ZerothOrderActivation(self.name)
+
+    def test_instance(self):
+        instance = ZerothOrderActivation(self.name)
+        assert isinstance(instance, ZerothOrderActivation)
+
+    def test_with_defaults(self):
+        instance = ZerothOrderActivation.with_defaults(self.name)
+        assert isinstance(instance, ZerothOrderActivation)
+        assert instance == ZerothOrderActivation(self.name)
+
+    def test_name(self):
+        assert hasattr(self.instance, 'name')
+        assert self.instance.name == self.name
+
+    def test_order(self):
+        assert hasattr(self.instance, 'order')
+        assert self.instance.order == 0
+
+    def test_excitation_attribute(self):
+        assert hasattr(self.instance, 'e')
+        assert hasattr(self.instance, 'excitation')
+        e_expected = dynamicsymbols('e_name')
+        assert self.instance.e == e_expected
+        assert self.instance.excitation == e_expected
+        assert self.instance.e is self.instance.excitation
+
+    def test_activation_attribute(self):
+        assert hasattr(self.instance, 'a')
+        assert hasattr(self.instance, 'activation')
+        a_expected = dynamicsymbols('e_name')
+        assert self.instance.a == a_expected
+        assert self.instance.activation == a_expected
+        assert self.instance.a is self.instance.activation is self.instance.e
+
+    def test_state_vars_attribute(self):
+        assert hasattr(self.instance, 'x')
+        assert hasattr(self.instance, 'state_vars')
+        assert self.instance.x == self.instance.state_vars
+        x_expected = zeros(0, 1)
+        assert self.instance.x == x_expected
+        assert self.instance.state_vars == x_expected
+        assert isinstance(self.instance.x, Matrix)
+        assert isinstance(self.instance.state_vars, Matrix)
+        assert self.instance.x.shape == (0, 1)
+        assert self.instance.state_vars.shape == (0, 1)
+
+    def test_input_vars_attribute(self):
+        assert hasattr(self.instance, 'r')
+        assert hasattr(self.instance, 'input_vars')
+        assert self.instance.r == self.instance.input_vars
+        r_expected = Matrix([self.e])
+        assert self.instance.r == r_expected
+        assert self.instance.input_vars == r_expected
+        assert isinstance(self.instance.r, Matrix)
+        assert isinstance(self.instance.input_vars, Matrix)
+        assert self.instance.r.shape == (1, 1)
+        assert self.instance.input_vars.shape == (1, 1)
+
+    def test_constants_attribute(self):
+        assert hasattr(self.instance, 'p')
+        assert hasattr(self.instance, 'constants')
+        assert self.instance.p == self.instance.constants
+        p_expected = zeros(0, 1)
+        assert self.instance.p == p_expected
+        assert self.instance.constants == p_expected
+        assert isinstance(self.instance.p, Matrix)
+        assert isinstance(self.instance.constants, Matrix)
+        assert self.instance.p.shape == (0, 1)
+        assert self.instance.constants.shape == (0, 1)
+
+    def test_M_attribute(self):
+        assert hasattr(self.instance, 'M')
+        M_expected = Matrix([])
+        assert self.instance.M == M_expected
+        assert isinstance(self.instance.M, Matrix)
+        assert self.instance.M.shape == (0, 0)
+
+    def test_F(self):
+        assert hasattr(self.instance, 'F')
+        F_expected = zeros(0, 1)
+        assert self.instance.F == F_expected
+        assert isinstance(self.instance.F, Matrix)
+        assert self.instance.F.shape == (0, 1)
+
+    def test_rhs(self):
+        assert hasattr(self.instance, 'rhs')
+        rhs_expected = zeros(0, 1)
+        rhs = self.instance.rhs()
+        assert rhs == rhs_expected
+        assert isinstance(rhs, Matrix)
+        assert rhs.shape == (0, 1)
+
+    def test_repr(self):
+        expected = 'ZerothOrderActivation(\'name\')'
+        assert repr(self.instance) == expected
+
+
+class TestFirstOrderActivationDeGroote2016:
+
+    @staticmethod
+    def test_class():
+        assert issubclass(FirstOrderActivationDeGroote2016, ActivationBase)
+        assert issubclass(FirstOrderActivationDeGroote2016, _NamedMixin)
+        assert FirstOrderActivationDeGroote2016.__name__ == 'FirstOrderActivationDeGroote2016'
+
+    @pytest.fixture(autouse=True)
+    def _first_order_activation_de_groote_2016_fixture(self):
+        self.name = 'name'
+        self.e = dynamicsymbols('e_name')
+        self.a = dynamicsymbols('a_name')
+        self.tau_a = Symbol('tau_a')
+        self.tau_d = Symbol('tau_d')
+        self.b = Symbol('b')
+        self.instance = FirstOrderActivationDeGroote2016(
+            self.name,
+            self.tau_a,
+            self.tau_d,
+            self.b,
+        )
+
+    def test_instance(self):
+        instance = FirstOrderActivationDeGroote2016(self.name)
+        assert isinstance(instance, FirstOrderActivationDeGroote2016)
+
+    def test_with_defaults(self):
+        instance = FirstOrderActivationDeGroote2016.with_defaults(self.name)
+        assert isinstance(instance, FirstOrderActivationDeGroote2016)
+        assert instance.tau_a == Float('0.015')
+        assert instance.activation_time_constant == Float('0.015')
+        assert instance.tau_d == Float('0.060')
+        assert instance.deactivation_time_constant == Float('0.060')
+        assert instance.b == Float('10.0')
+        assert instance.smoothing_rate == Float('10.0')
+
+    def test_name(self):
+        assert hasattr(self.instance, 'name')
+        assert self.instance.name == self.name
+
+    def test_order(self):
+        assert hasattr(self.instance, 'order')
+        assert self.instance.order == 1
+
+    def test_excitation(self):
+        assert hasattr(self.instance, 'e')
+        assert hasattr(self.instance, 'excitation')
+        e_expected = dynamicsymbols('e_name')
+        assert self.instance.e == e_expected
+        assert self.instance.excitation == e_expected
+        assert self.instance.e is self.instance.excitation
+
+    def test_excitation_is_immutable(self):
+        with pytest.raises(AttributeError):
+            self.instance.e = None
+        with pytest.raises(AttributeError):
+            self.instance.excitation = None
+
+    def test_activation(self):
+        assert hasattr(self.instance, 'a')
+        assert hasattr(self.instance, 'activation')
+        a_expected = dynamicsymbols('a_name')
+        assert self.instance.a == a_expected
+        assert self.instance.activation == a_expected
+
+    def test_activation_is_immutable(self):
+        with pytest.raises(AttributeError):
+            self.instance.a = None
+        with pytest.raises(AttributeError):
+            self.instance.activation = None
+
+    @pytest.mark.parametrize(
+        'tau_a, expected',
+        [
+            (None, Symbol('tau_a_name')),
+            (Symbol('tau_a'), Symbol('tau_a')),
+            (Float('0.015'), Float('0.015')),
+        ]
+    )
+    def test_activation_time_constant(self, tau_a, expected):
+        instance = FirstOrderActivationDeGroote2016(
+            'name', activation_time_constant=tau_a,
+        )
+        assert instance.tau_a == expected
+        assert instance.activation_time_constant == expected
+        assert instance.tau_a is instance.activation_time_constant
+
+    def test_activation_time_constant_is_immutable(self):
+        with pytest.raises(AttributeError):
+            self.instance.tau_a = None
+        with pytest.raises(AttributeError):
+            self.instance.activation_time_constant = None
+
+    @pytest.mark.parametrize(
+        'tau_d, expected',
+        [
+            (None, Symbol('tau_d_name')),
+            (Symbol('tau_d'), Symbol('tau_d')),
+            (Float('0.060'), Float('0.060')),
+        ]
+    )
+    def test_deactivation_time_constant(self, tau_d, expected):
+        instance = FirstOrderActivationDeGroote2016(
+            'name', deactivation_time_constant=tau_d,
+        )
+        assert instance.tau_d == expected
+        assert instance.deactivation_time_constant == expected
+        assert instance.tau_d is instance.deactivation_time_constant
+
+    def test_deactivation_time_constant_is_immutable(self):
+        with pytest.raises(AttributeError):
+            self.instance.tau_d = None
+        with pytest.raises(AttributeError):
+            self.instance.deactivation_time_constant = None
+
+    @pytest.mark.parametrize(
+        'b, expected',
+        [
+            (None, Symbol('b_name')),
+            (Symbol('b'), Symbol('b')),
+            (Integer('10'), Integer('10')),
+        ]
+    )
+    def test_smoothing_rate(self, b, expected):
+        instance = FirstOrderActivationDeGroote2016(
+            'name', smoothing_rate=b,
+        )
+        assert instance.b == expected
+        assert instance.smoothing_rate == expected
+        assert instance.b is instance.smoothing_rate
+
+    def test_smoothing_rate_is_immutable(self):
+        with pytest.raises(AttributeError):
+            self.instance.b = None
+        with pytest.raises(AttributeError):
+            self.instance.smoothing_rate = None
+
+    def test_state_vars(self):
+        assert hasattr(self.instance, 'x')
+        assert hasattr(self.instance, 'state_vars')
+        assert self.instance.x == self.instance.state_vars
+        x_expected = Matrix([self.a])
+        assert self.instance.x == x_expected
+        assert self.instance.state_vars == x_expected
+        assert isinstance(self.instance.x, Matrix)
+        assert isinstance(self.instance.state_vars, Matrix)
+        assert self.instance.x.shape == (1, 1)
+        assert self.instance.state_vars.shape == (1, 1)
+
+    def test_input_vars(self):
+        assert hasattr(self.instance, 'r')
+        assert hasattr(self.instance, 'input_vars')
+        assert self.instance.r == self.instance.input_vars
+        r_expected = Matrix([self.e])
+        assert self.instance.r == r_expected
+        assert self.instance.input_vars == r_expected
+        assert isinstance(self.instance.r, Matrix)
+        assert isinstance(self.instance.input_vars, Matrix)
+        assert self.instance.r.shape == (1, 1)
+        assert self.instance.input_vars.shape == (1, 1)
+
+    def test_constants(self):
+        assert hasattr(self.instance, 'p')
+        assert hasattr(self.instance, 'constants')
+        assert self.instance.p == self.instance.constants
+        p_expected = Matrix([self.tau_a, self.tau_d, self.b])
+        assert self.instance.p == p_expected
+        assert self.instance.constants == p_expected
+        assert isinstance(self.instance.p, Matrix)
+        assert isinstance(self.instance.constants, Matrix)
+        assert self.instance.p.shape == (3, 1)
+        assert self.instance.constants.shape == (3, 1)
+
+    def test_M(self):
+        assert hasattr(self.instance, 'M')
+        M_expected = Matrix([1])
+        assert self.instance.M == M_expected
+        assert isinstance(self.instance.M, Matrix)
+        assert self.instance.M.shape == (1, 1)
+
+    def test_F(self):
+        assert hasattr(self.instance, 'F')
+        da_expr = (
+            ((1/(self.tau_a*(Rational(1, 2) + Rational(3, 2)*self.a)))
+            *(Rational(1, 2) + Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+            + ((Rational(1, 2) + Rational(3, 2)*self.a)/self.tau_d)
+            *(Rational(1, 2) - Rational(1, 2)*tanh(self.b*(self.e - self.a))))
+            *(self.e - self.a)
+        )
+        F_expected = Matrix([da_expr])
+        assert self.instance.F == F_expected
+        assert isinstance(self.instance.F, Matrix)
+        assert self.instance.F.shape == (1, 1)
+
+    def test_rhs(self):
+        assert hasattr(self.instance, 'rhs')
+        da_expr = (
+            ((1/(self.tau_a*(Rational(1, 2) + Rational(3, 2)*self.a)))
+            *(Rational(1, 2) + Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+            + ((Rational(1, 2) + Rational(3, 2)*self.a)/self.tau_d)
+            *(Rational(1, 2) - Rational(1, 2)*tanh(self.b*(self.e - self.a))))
+            *(self.e - self.a)
+        )
+        rhs_expected = Matrix([da_expr])
+        rhs = self.instance.rhs()
+        assert rhs == rhs_expected
+        assert isinstance(rhs, Matrix)
+        assert rhs.shape == (1, 1)
+        assert simplify(self.instance.M.solve(self.instance.F) - rhs) == zeros(1)
+
+    def test_repr(self):
+        expected = (
+            'FirstOrderActivationDeGroote2016(\'name\', '
+            'activation_time_constant=tau_a, '
+            'deactivation_time_constant=tau_d, '
+            'smoothing_rate=b)'
+        )
+        assert repr(self.instance) == expected
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_curve.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_curve.py
new file mode 100644
index 0000000000000000000000000000000000000000..6a8fcbccdb8b4190376b051093b376e936d9d5d3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_curve.py
@@ -0,0 +1,1695 @@
+"""Tests for the ``sympy.physics.biomechanics.characteristic.py`` module."""
+
+import pytest
+
+from sympy.core.expr import UnevaluatedExpr
+from sympy.core.function import Function
+from sympy.core.numbers import Float, Integer
+from sympy.core.symbol import Symbol, symbols
+from sympy.external.importtools import import_module
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.hyperbolic import cosh, sinh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.biomechanics.curve import (
+    CharacteristicCurveCollection,
+    CharacteristicCurveFunction,
+    FiberForceLengthActiveDeGroote2016,
+    FiberForceLengthPassiveDeGroote2016,
+    FiberForceLengthPassiveInverseDeGroote2016,
+    FiberForceVelocityDeGroote2016,
+    FiberForceVelocityInverseDeGroote2016,
+    TendonForceLengthDeGroote2016,
+    TendonForceLengthInverseDeGroote2016,
+)
+from sympy.printing.c import C89CodePrinter, C99CodePrinter, C11CodePrinter
+from sympy.printing.cxx import (
+    CXX98CodePrinter,
+    CXX11CodePrinter,
+    CXX17CodePrinter,
+)
+from sympy.printing.fortran import FCodePrinter
+from sympy.printing.lambdarepr import LambdaPrinter
+from sympy.printing.latex import LatexPrinter
+from sympy.printing.octave import OctaveCodePrinter
+from sympy.printing.numpy import (
+    CuPyPrinter,
+    JaxPrinter,
+    NumPyPrinter,
+    SciPyPrinter,
+)
+from sympy.printing.pycode import MpmathPrinter, PythonCodePrinter
+from sympy.utilities.lambdify import lambdify
+
+jax = import_module('jax')
+numpy = import_module('numpy')
+
+if jax:
+    jax.config.update('jax_enable_x64', True)
+
+
+class TestCharacteristicCurveFunction:
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (C89CodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (C99CodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (C11CodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (CXX98CodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (CXX11CodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (CXX17CodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (FCodePrinter, '      (a + b)*(c + d)*(e + f)'),
+            (OctaveCodePrinter, '(a + b).*(c + d).*(e + f)'),
+            (PythonCodePrinter, '(a + b)*(c + d)*(e + f)'),
+            (NumPyPrinter, '(a + b)*(c + d)*(e + f)'),
+            (SciPyPrinter, '(a + b)*(c + d)*(e + f)'),
+            (CuPyPrinter, '(a + b)*(c + d)*(e + f)'),
+            (JaxPrinter, '(a + b)*(c + d)*(e + f)'),
+            (MpmathPrinter, '(a + b)*(c + d)*(e + f)'),
+            (LambdaPrinter, '(a + b)*(c + d)*(e + f)'),
+        ]
+    )
+    def test_print_code_parenthesize(code_printer, expected):
+
+        class ExampleFunction(CharacteristicCurveFunction):
+
+            @classmethod
+            def eval(cls, a, b):
+                pass
+
+            def doit(self, **kwargs):
+                a, b = self.args
+                return a + b
+
+        a, b, c, d, e, f = symbols('a, b, c, d, e, f')
+        f1 = ExampleFunction(a, b)
+        f2 = ExampleFunction(c, d)
+        f3 = ExampleFunction(e, f)
+        assert code_printer().doprint(f1*f2*f3) == expected
+
+
+class TestTendonForceLengthDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _tendon_force_length_arguments_fixture(self):
+        self.l_T_tilde = Symbol('l_T_tilde')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.c2 = Symbol('c_2')
+        self.c3 = Symbol('c_3')
+        self.constants = (self.c0, self.c1, self.c2, self.c3)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(TendonForceLengthDeGroote2016, Function)
+        assert issubclass(TendonForceLengthDeGroote2016, CharacteristicCurveFunction)
+        assert TendonForceLengthDeGroote2016.__name__ == 'TendonForceLengthDeGroote2016'
+
+    def test_instance(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        assert isinstance(fl_T, TendonForceLengthDeGroote2016)
+        assert str(fl_T) == 'TendonForceLengthDeGroote2016(l_T_tilde, c_0, c_1, c_2, c_3)'
+
+    def test_doit(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants).doit()
+        assert fl_T == self.c0*exp(self.c3*(self.l_T_tilde - self.c1)) - self.c2
+
+    def test_doit_evaluate_false(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants).doit(evaluate=False)
+        assert fl_T == self.c0*exp(self.c3*UnevaluatedExpr(self.l_T_tilde - self.c1)) - self.c2
+
+    def test_with_defaults(self):
+        constants = (
+            Float('0.2'),
+            Float('0.995'),
+            Float('0.25'),
+            Float('33.93669377311689'),
+        )
+        fl_T_manual = TendonForceLengthDeGroote2016(self.l_T_tilde, *constants)
+        fl_T_constants = TendonForceLengthDeGroote2016.with_defaults(self.l_T_tilde)
+        assert fl_T_manual == fl_T_constants
+
+    def test_differentiate_wrt_l_T_tilde(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = self.c0*self.c3*exp(self.c3*UnevaluatedExpr(-self.c1 + self.l_T_tilde))
+        assert fl_T.diff(self.l_T_tilde) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = exp(self.c3*UnevaluatedExpr(-self.c1 + self.l_T_tilde))
+        assert fl_T.diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = -self.c0*self.c3*exp(self.c3*UnevaluatedExpr(self.l_T_tilde - self.c1))
+        assert fl_T.diff(self.c1) == expected
+
+    def test_differentiate_wrt_c2(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = Integer(-1)
+        assert fl_T.diff(self.c2) == expected
+
+    def test_differentiate_wrt_c3(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = self.c0*(self.l_T_tilde - self.c1)*exp(self.c3*UnevaluatedExpr(self.l_T_tilde - self.c1))
+        assert fl_T.diff(self.c3) == expected
+
+    def test_inverse(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        assert fl_T.inverse() is TendonForceLengthInverseDeGroote2016
+
+    def test_function_print_latex(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = r'\operatorname{fl}^T \left( l_{T tilde} \right)'
+        assert LatexPrinter().doprint(fl_T) == expected
+
+    def test_expression_print_latex(self):
+        fl_T = TendonForceLengthDeGroote2016(self.l_T_tilde, *self.constants)
+        expected = r'c_{0} e^{c_{3} \left(- c_{1} + l_{T tilde}\right)} - c_{2}'
+        assert LatexPrinter().doprint(fl_T.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                '(-0.25 + 0.20000000000000001*exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                C99CodePrinter,
+                '(-0.25 + 0.20000000000000001*exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                C11CodePrinter,
+                '(-0.25 + 0.20000000000000001*exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                CXX98CodePrinter,
+                '(-0.25 + 0.20000000000000001*exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                CXX11CodePrinter,
+                '(-0.25 + 0.20000000000000001*std::exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                CXX17CodePrinter,
+                '(-0.25 + 0.20000000000000001*std::exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                FCodePrinter,
+                '      (-0.25d0 + 0.2d0*exp(33.93669377311689d0*(l_T_tilde - 0.995d0)))',
+            ),
+            (
+                OctaveCodePrinter,
+                '(-0.25 + 0.2*exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                PythonCodePrinter,
+                '(-0.25 + 0.2*math.exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                NumPyPrinter,
+                '(-0.25 + 0.2*numpy.exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                SciPyPrinter,
+                '(-0.25 + 0.2*numpy.exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                CuPyPrinter,
+                '(-0.25 + 0.2*cupy.exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                JaxPrinter,
+                '(-0.25 + 0.2*jax.numpy.exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+            (
+                MpmathPrinter,
+                '(mpmath.mpf((1, 1, -2, 1)) + mpmath.mpf((0, 3602879701896397, -54, 52))'
+                '*mpmath.exp(mpmath.mpf((0, 9552330089424741, -48, 54))*(l_T_tilde + '
+                'mpmath.mpf((1, 8962163258467287, -53, 53)))))',
+            ),
+            (
+                LambdaPrinter,
+                '(-0.25 + 0.2*math.exp(33.93669377311689*(l_T_tilde - 0.995)))',
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fl_T = TendonForceLengthDeGroote2016.with_defaults(self.l_T_tilde)
+        assert code_printer().doprint(fl_T) == expected
+
+    def test_derivative_print_code(self):
+        fl_T = TendonForceLengthDeGroote2016.with_defaults(self.l_T_tilde)
+        dfl_T_dl_T_tilde = fl_T.diff(self.l_T_tilde)
+        expected = '6.787338754623378*math.exp(33.93669377311689*(l_T_tilde - 0.995))'
+        assert PythonCodePrinter().doprint(dfl_T_dl_T_tilde) == expected
+
+    def test_lambdify(self):
+        fl_T = TendonForceLengthDeGroote2016.with_defaults(self.l_T_tilde)
+        fl_T_callable = lambdify(self.l_T_tilde, fl_T)
+        assert fl_T_callable(1.0) == pytest.approx(-0.013014055039221595)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fl_T = TendonForceLengthDeGroote2016.with_defaults(self.l_T_tilde)
+        fl_T_callable = lambdify(self.l_T_tilde, fl_T, 'numpy')
+        l_T_tilde = numpy.array([0.95, 1.0, 1.01, 1.05])
+        expected = numpy.array([
+            -0.2065693181344816,
+            -0.0130140550392216,
+            0.0827421191989246,
+            1.04314889144172,
+        ])
+        numpy.testing.assert_allclose(fl_T_callable(l_T_tilde), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fl_T = TendonForceLengthDeGroote2016.with_defaults(self.l_T_tilde)
+        fl_T_callable = jax.jit(lambdify(self.l_T_tilde, fl_T, 'jax'))
+        l_T_tilde = jax.numpy.array([0.95, 1.0, 1.01, 1.05])
+        expected = jax.numpy.array([
+            -0.2065693181344816,
+            -0.0130140550392216,
+            0.0827421191989246,
+            1.04314889144172,
+        ])
+        numpy.testing.assert_allclose(fl_T_callable(l_T_tilde), expected)
+
+
+class TestTendonForceLengthInverseDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _tendon_force_length_inverse_arguments_fixture(self):
+        self.fl_T = Symbol('fl_T')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.c2 = Symbol('c_2')
+        self.c3 = Symbol('c_3')
+        self.constants = (self.c0, self.c1, self.c2, self.c3)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(TendonForceLengthInverseDeGroote2016, Function)
+        assert issubclass(TendonForceLengthInverseDeGroote2016, CharacteristicCurveFunction)
+        assert TendonForceLengthInverseDeGroote2016.__name__ == 'TendonForceLengthInverseDeGroote2016'
+
+    def test_instance(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        assert isinstance(fl_T_inv, TendonForceLengthInverseDeGroote2016)
+        assert str(fl_T_inv) == 'TendonForceLengthInverseDeGroote2016(fl_T, c_0, c_1, c_2, c_3)'
+
+    def test_doit(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants).doit()
+        assert fl_T_inv == log((self.fl_T + self.c2)/self.c0)/self.c3 + self.c1
+
+    def test_doit_evaluate_false(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants).doit(evaluate=False)
+        assert fl_T_inv == log(UnevaluatedExpr((self.fl_T + self.c2)/self.c0))/self.c3 + self.c1
+
+    def test_with_defaults(self):
+        constants = (
+            Float('0.2'),
+            Float('0.995'),
+            Float('0.25'),
+            Float('33.93669377311689'),
+        )
+        fl_T_inv_manual = TendonForceLengthInverseDeGroote2016(self.fl_T, *constants)
+        fl_T_inv_constants = TendonForceLengthInverseDeGroote2016.with_defaults(self.fl_T)
+        assert fl_T_inv_manual == fl_T_inv_constants
+
+    def test_differentiate_wrt_fl_T(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = 1/(self.c3*(self.fl_T + self.c2))
+        assert fl_T_inv.diff(self.fl_T) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = -1/(self.c0*self.c3)
+        assert fl_T_inv.diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = Integer(1)
+        assert fl_T_inv.diff(self.c1) == expected
+
+    def test_differentiate_wrt_c2(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = 1/(self.c3*(self.fl_T + self.c2))
+        assert fl_T_inv.diff(self.c2) == expected
+
+    def test_differentiate_wrt_c3(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = -log(UnevaluatedExpr((self.fl_T + self.c2)/self.c0))/self.c3**2
+        assert fl_T_inv.diff(self.c3) == expected
+
+    def test_inverse(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        assert fl_T_inv.inverse() is TendonForceLengthDeGroote2016
+
+    def test_function_print_latex(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = r'\left( \operatorname{fl}^T \right)^{-1} \left( fl_{T} \right)'
+        assert LatexPrinter().doprint(fl_T_inv) == expected
+
+    def test_expression_print_latex(self):
+        fl_T = TendonForceLengthInverseDeGroote2016(self.fl_T, *self.constants)
+        expected = r'c_{1} + \frac{\log{\left(\frac{c_{2} + fl_{T}}{c_{0}} \right)}}{c_{3}}'
+        assert LatexPrinter().doprint(fl_T.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                '(0.995 + 0.029466630034306838*log(5.0*fl_T + 1.25))',
+            ),
+            (
+                C99CodePrinter,
+                '(0.995 + 0.029466630034306838*log(5.0*fl_T + 1.25))',
+            ),
+            (
+                C11CodePrinter,
+                '(0.995 + 0.029466630034306838*log(5.0*fl_T + 1.25))',
+            ),
+            (
+                CXX98CodePrinter,
+                '(0.995 + 0.029466630034306838*log(5.0*fl_T + 1.25))',
+            ),
+            (
+                CXX11CodePrinter,
+                '(0.995 + 0.029466630034306838*std::log(5.0*fl_T + 1.25))',
+            ),
+            (
+                CXX17CodePrinter,
+                '(0.995 + 0.029466630034306838*std::log(5.0*fl_T + 1.25))',
+            ),
+            (
+                FCodePrinter,
+                '      (0.995d0 + 0.02946663003430684d0*log(5.0d0*fl_T + 1.25d0))',
+            ),
+            (
+                OctaveCodePrinter,
+                '(0.995 + 0.02946663003430684*log(5.0*fl_T + 1.25))',
+            ),
+            (
+                PythonCodePrinter,
+                '(0.995 + 0.02946663003430684*math.log(5.0*fl_T + 1.25))',
+            ),
+            (
+                NumPyPrinter,
+                '(0.995 + 0.02946663003430684*numpy.log(5.0*fl_T + 1.25))',
+            ),
+            (
+                SciPyPrinter,
+                '(0.995 + 0.02946663003430684*numpy.log(5.0*fl_T + 1.25))',
+            ),
+            (
+                CuPyPrinter,
+                '(0.995 + 0.02946663003430684*cupy.log(5.0*fl_T + 1.25))',
+            ),
+            (
+                JaxPrinter,
+                '(0.995 + 0.02946663003430684*jax.numpy.log(5.0*fl_T + 1.25))',
+            ),
+            (
+                MpmathPrinter,
+                '(mpmath.mpf((0, 8962163258467287, -53, 53))'
+                ' + mpmath.mpf((0, 33972711434846347, -60, 55))'
+                '*mpmath.log(mpmath.mpf((0, 5, 0, 3))*fl_T + mpmath.mpf((0, 5, -2, 3))))',
+            ),
+            (
+                LambdaPrinter,
+                '(0.995 + 0.02946663003430684*math.log(5.0*fl_T + 1.25))',
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016.with_defaults(self.fl_T)
+        assert code_printer().doprint(fl_T_inv) == expected
+
+    def test_derivative_print_code(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016.with_defaults(self.fl_T)
+        dfl_T_inv_dfl_T = fl_T_inv.diff(self.fl_T)
+        expected = '1/(33.93669377311689*fl_T + 8.484173443279222)'
+        assert PythonCodePrinter().doprint(dfl_T_inv_dfl_T) == expected
+
+    def test_lambdify(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016.with_defaults(self.fl_T)
+        fl_T_inv_callable = lambdify(self.fl_T, fl_T_inv)
+        assert fl_T_inv_callable(0.0) == pytest.approx(1.0015752885)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016.with_defaults(self.fl_T)
+        fl_T_inv_callable = lambdify(self.fl_T, fl_T_inv, 'numpy')
+        fl_T = numpy.array([-0.2, -0.01, 0.0, 1.01, 1.02, 1.05])
+        expected = numpy.array([
+            0.9541505769,
+            1.0003724019,
+            1.0015752885,
+            1.0492347951,
+            1.0494677341,
+            1.0501557022,
+        ])
+        numpy.testing.assert_allclose(fl_T_inv_callable(fl_T), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fl_T_inv = TendonForceLengthInverseDeGroote2016.with_defaults(self.fl_T)
+        fl_T_inv_callable = jax.jit(lambdify(self.fl_T, fl_T_inv, 'jax'))
+        fl_T = jax.numpy.array([-0.2, -0.01, 0.0, 1.01, 1.02, 1.05])
+        expected = jax.numpy.array([
+            0.9541505769,
+            1.0003724019,
+            1.0015752885,
+            1.0492347951,
+            1.0494677341,
+            1.0501557022,
+        ])
+        numpy.testing.assert_allclose(fl_T_inv_callable(fl_T), expected)
+
+
+class TestFiberForceLengthPassiveDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _fiber_force_length_passive_arguments_fixture(self):
+        self.l_M_tilde = Symbol('l_M_tilde')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.constants = (self.c0, self.c1)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(FiberForceLengthPassiveDeGroote2016, Function)
+        assert issubclass(FiberForceLengthPassiveDeGroote2016, CharacteristicCurveFunction)
+        assert FiberForceLengthPassiveDeGroote2016.__name__ == 'FiberForceLengthPassiveDeGroote2016'
+
+    def test_instance(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        assert isinstance(fl_M_pas, FiberForceLengthPassiveDeGroote2016)
+        assert str(fl_M_pas) == 'FiberForceLengthPassiveDeGroote2016(l_M_tilde, c_0, c_1)'
+
+    def test_doit(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants).doit()
+        assert fl_M_pas == (exp((self.c1*(self.l_M_tilde - 1))/self.c0) - 1)/(exp(self.c1) - 1)
+
+    def test_doit_evaluate_false(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants).doit(evaluate=False)
+        assert fl_M_pas == (exp((self.c1*UnevaluatedExpr(self.l_M_tilde - 1))/self.c0) - 1)/(exp(self.c1) - 1)
+
+    def test_with_defaults(self):
+        constants = (
+            Float('0.6'),
+            Float('4.0'),
+        )
+        fl_M_pas_manual = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *constants)
+        fl_M_pas_constants = FiberForceLengthPassiveDeGroote2016.with_defaults(self.l_M_tilde)
+        assert fl_M_pas_manual == fl_M_pas_constants
+
+    def test_differentiate_wrt_l_M_tilde(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = self.c1*exp(self.c1*UnevaluatedExpr(self.l_M_tilde - 1)/self.c0)/(self.c0*(exp(self.c1) - 1))
+        assert fl_M_pas.diff(self.l_M_tilde) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            -self.c1*exp(self.c1*UnevaluatedExpr(self.l_M_tilde - 1)/self.c0)
+            *UnevaluatedExpr(self.l_M_tilde - 1)/(self.c0**2*(exp(self.c1) - 1))
+        )
+        assert fl_M_pas.diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            -exp(self.c1)*(-1 + exp(self.c1*UnevaluatedExpr(self.l_M_tilde - 1)/self.c0))/(exp(self.c1) - 1)**2
+            + exp(self.c1*UnevaluatedExpr(self.l_M_tilde - 1)/self.c0)*(self.l_M_tilde - 1)/(self.c0*(exp(self.c1) - 1))
+        )
+        assert fl_M_pas.diff(self.c1) == expected
+
+    def test_inverse(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        assert fl_M_pas.inverse() is FiberForceLengthPassiveInverseDeGroote2016
+
+    def test_function_print_latex(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = r'\operatorname{fl}^M_{pas} \left( l_{M tilde} \right)'
+        assert LatexPrinter().doprint(fl_M_pas) == expected
+
+    def test_expression_print_latex(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = r'\frac{e^{\frac{c_{1} \left(l_{M tilde} - 1\right)}{c_{0}}} - 1}{e^{c_{1}} - 1}'
+        assert LatexPrinter().doprint(fl_M_pas.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                '(0.01865736036377405*(-1 + exp(6.666666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                C99CodePrinter,
+                '(0.01865736036377405*(-1 + exp(6.666666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                C11CodePrinter,
+                '(0.01865736036377405*(-1 + exp(6.666666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                CXX98CodePrinter,
+                '(0.01865736036377405*(-1 + exp(6.666666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                CXX11CodePrinter,
+                '(0.01865736036377405*(-1 + std::exp(6.666666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                CXX17CodePrinter,
+                '(0.01865736036377405*(-1 + std::exp(6.666666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                FCodePrinter,
+                '      (0.0186573603637741d0*(-1 + exp(6.666666666666667d0*(l_M_tilde - 1\n'
+                '     @ ))))',
+            ),
+            (
+                OctaveCodePrinter,
+                '(0.0186573603637741*(-1 + exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                PythonCodePrinter,
+                '(0.0186573603637741*(-1 + math.exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                NumPyPrinter,
+                '(0.0186573603637741*(-1 + numpy.exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                SciPyPrinter,
+                '(0.0186573603637741*(-1 + numpy.exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                CuPyPrinter,
+                '(0.0186573603637741*(-1 + cupy.exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                JaxPrinter,
+                '(0.0186573603637741*(-1 + jax.numpy.exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+            (
+                MpmathPrinter,
+                '(mpmath.mpf((0, 672202249456079, -55, 50))*(-1 + mpmath.exp('
+                'mpmath.mpf((0, 7505999378950827, -50, 53))*(l_M_tilde - 1))))',
+            ),
+            (
+                LambdaPrinter,
+                '(0.0186573603637741*(-1 + math.exp(6.66666666666667*(l_M_tilde - 1))))',
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016.with_defaults(self.l_M_tilde)
+        assert code_printer().doprint(fl_M_pas) == expected
+
+    def test_derivative_print_code(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_pas_dl_M_tilde = fl_M_pas.diff(self.l_M_tilde)
+        expected = '0.12438240242516*math.exp(6.66666666666667*(l_M_tilde - 1))'
+        assert PythonCodePrinter().doprint(fl_M_pas_dl_M_tilde) == expected
+
+    def test_lambdify(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_pas_callable = lambdify(self.l_M_tilde, fl_M_pas)
+        assert fl_M_pas_callable(1.0) == pytest.approx(0.0)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_pas_callable = lambdify(self.l_M_tilde, fl_M_pas, 'numpy')
+        l_M_tilde = numpy.array([0.5, 0.8, 0.9, 1.0, 1.1, 1.2, 1.5])
+        expected = numpy.array([
+            -0.0179917778,
+            -0.0137393336,
+            -0.0090783522,
+            0.0,
+            0.0176822155,
+            0.0521224686,
+            0.5043387669,
+        ])
+        numpy.testing.assert_allclose(fl_M_pas_callable(l_M_tilde), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fl_M_pas = FiberForceLengthPassiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_pas_callable = jax.jit(lambdify(self.l_M_tilde, fl_M_pas, 'jax'))
+        l_M_tilde = jax.numpy.array([0.5, 0.8, 0.9, 1.0, 1.1, 1.2, 1.5])
+        expected = jax.numpy.array([
+            -0.0179917778,
+            -0.0137393336,
+            -0.0090783522,
+            0.0,
+            0.0176822155,
+            0.0521224686,
+            0.5043387669,
+        ])
+        numpy.testing.assert_allclose(fl_M_pas_callable(l_M_tilde), expected)
+
+
+class TestFiberForceLengthPassiveInverseDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _fiber_force_length_passive_arguments_fixture(self):
+        self.fl_M_pas = Symbol('fl_M_pas')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.constants = (self.c0, self.c1)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(FiberForceLengthPassiveInverseDeGroote2016, Function)
+        assert issubclass(FiberForceLengthPassiveInverseDeGroote2016, CharacteristicCurveFunction)
+        assert FiberForceLengthPassiveInverseDeGroote2016.__name__ == 'FiberForceLengthPassiveInverseDeGroote2016'
+
+    def test_instance(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        assert isinstance(fl_M_pas_inv, FiberForceLengthPassiveInverseDeGroote2016)
+        assert str(fl_M_pas_inv) == 'FiberForceLengthPassiveInverseDeGroote2016(fl_M_pas, c_0, c_1)'
+
+    def test_doit(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants).doit()
+        assert fl_M_pas_inv == self.c0*log(self.fl_M_pas*(exp(self.c1) - 1) + 1)/self.c1 + 1
+
+    def test_doit_evaluate_false(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants).doit(evaluate=False)
+        assert fl_M_pas_inv == self.c0*log(UnevaluatedExpr(self.fl_M_pas*(exp(self.c1) - 1)) + 1)/self.c1 + 1
+
+    def test_with_defaults(self):
+        constants = (
+            Float('0.6'),
+            Float('4.0'),
+        )
+        fl_M_pas_inv_manual = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *constants)
+        fl_M_pas_inv_constants = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(self.fl_M_pas)
+        assert fl_M_pas_inv_manual == fl_M_pas_inv_constants
+
+    def test_differentiate_wrt_fl_T(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        expected = self.c0*(exp(self.c1) - 1)/(self.c1*(self.fl_M_pas*(exp(self.c1) - 1) + 1))
+        assert fl_M_pas_inv.diff(self.fl_M_pas) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        expected = log(self.fl_M_pas*(exp(self.c1) - 1) + 1)/self.c1
+        assert fl_M_pas_inv.diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        expected = (
+            self.c0*self.fl_M_pas*exp(self.c1)/(self.c1*(self.fl_M_pas*(exp(self.c1) - 1) + 1))
+            - self.c0*log(self.fl_M_pas*(exp(self.c1) - 1) + 1)/self.c1**2
+        )
+        assert fl_M_pas_inv.diff(self.c1) == expected
+
+    def test_inverse(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        assert fl_M_pas_inv.inverse() is FiberForceLengthPassiveDeGroote2016
+
+    def test_function_print_latex(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        expected = r'\left( \operatorname{fl}^M_{pas} \right)^{-1} \left( fl_{M pas} \right)'
+        assert LatexPrinter().doprint(fl_M_pas_inv) == expected
+
+    def test_expression_print_latex(self):
+        fl_T = FiberForceLengthPassiveInverseDeGroote2016(self.fl_M_pas, *self.constants)
+        expected = r'\frac{c_{0} \log{\left(fl_{M pas} \left(e^{c_{1}} - 1\right) + 1 \right)}}{c_{1}} + 1'
+        assert LatexPrinter().doprint(fl_T.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                '(1 + 0.14999999999999999*log(1 + 53.598150033144236*fl_M_pas))',
+            ),
+            (
+                C99CodePrinter,
+                '(1 + 0.14999999999999999*log(1 + 53.598150033144236*fl_M_pas))',
+            ),
+            (
+                C11CodePrinter,
+                '(1 + 0.14999999999999999*log(1 + 53.598150033144236*fl_M_pas))',
+            ),
+            (
+                CXX98CodePrinter,
+                '(1 + 0.14999999999999999*log(1 + 53.598150033144236*fl_M_pas))',
+            ),
+            (
+                CXX11CodePrinter,
+                '(1 + 0.14999999999999999*std::log(1 + 53.598150033144236*fl_M_pas))',
+            ),
+            (
+                CXX17CodePrinter,
+                '(1 + 0.14999999999999999*std::log(1 + 53.598150033144236*fl_M_pas))',
+            ),
+            (
+                FCodePrinter,
+                '      (1 + 0.15d0*log(1.0d0 + 53.5981500331442d0*fl_M_pas))',
+            ),
+            (
+                OctaveCodePrinter,
+                '(1 + 0.15*log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+            (
+                PythonCodePrinter,
+                '(1 + 0.15*math.log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+            (
+                NumPyPrinter,
+                '(1 + 0.15*numpy.log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+            (
+                SciPyPrinter,
+                '(1 + 0.15*numpy.log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+            (
+                CuPyPrinter,
+                '(1 + 0.15*cupy.log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+            (
+                JaxPrinter,
+                '(1 + 0.15*jax.numpy.log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+            (
+                MpmathPrinter,
+                '(1 + mpmath.mpf((0, 5404319552844595, -55, 53))*mpmath.log(1 '
+                '+ mpmath.mpf((0, 942908627019595, -44, 50))*fl_M_pas))',
+            ),
+            (
+                LambdaPrinter,
+                '(1 + 0.15*math.log(1 + 53.5981500331442*fl_M_pas))',
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(self.fl_M_pas)
+        assert code_printer().doprint(fl_M_pas_inv) == expected
+
+    def test_derivative_print_code(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(self.fl_M_pas)
+        dfl_M_pas_inv_dfl_T = fl_M_pas_inv.diff(self.fl_M_pas)
+        expected = '32.1588900198865/(214.392600132577*fl_M_pas + 4.0)'
+        assert PythonCodePrinter().doprint(dfl_M_pas_inv_dfl_T) == expected
+
+    def test_lambdify(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(self.fl_M_pas)
+        fl_M_pas_inv_callable = lambdify(self.fl_M_pas, fl_M_pas_inv)
+        assert fl_M_pas_inv_callable(0.0) == pytest.approx(1.0)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(self.fl_M_pas)
+        fl_M_pas_inv_callable = lambdify(self.fl_M_pas, fl_M_pas_inv, 'numpy')
+        fl_M_pas = numpy.array([-0.01, 0.0, 0.01, 0.02, 0.05, 0.1])
+        expected = numpy.array([
+            0.8848253714,
+            1.0,
+            1.0643754386,
+            1.1092744701,
+            1.1954331425,
+            1.2774998934,
+        ])
+        numpy.testing.assert_allclose(fl_M_pas_inv_callable(fl_M_pas), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fl_M_pas_inv = FiberForceLengthPassiveInverseDeGroote2016.with_defaults(self.fl_M_pas)
+        fl_M_pas_inv_callable = jax.jit(lambdify(self.fl_M_pas, fl_M_pas_inv, 'jax'))
+        fl_M_pas = jax.numpy.array([-0.01, 0.0, 0.01, 0.02, 0.05, 0.1])
+        expected = jax.numpy.array([
+            0.8848253714,
+            1.0,
+            1.0643754386,
+            1.1092744701,
+            1.1954331425,
+            1.2774998934,
+        ])
+        numpy.testing.assert_allclose(fl_M_pas_inv_callable(fl_M_pas), expected)
+
+
+class TestFiberForceLengthActiveDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _fiber_force_length_active_arguments_fixture(self):
+        self.l_M_tilde = Symbol('l_M_tilde')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.c2 = Symbol('c_2')
+        self.c3 = Symbol('c_3')
+        self.c4 = Symbol('c_4')
+        self.c5 = Symbol('c_5')
+        self.c6 = Symbol('c_6')
+        self.c7 = Symbol('c_7')
+        self.c8 = Symbol('c_8')
+        self.c9 = Symbol('c_9')
+        self.c10 = Symbol('c_10')
+        self.c11 = Symbol('c_11')
+        self.constants = (
+            self.c0, self.c1, self.c2, self.c3, self.c4, self.c5,
+            self.c6, self.c7, self.c8, self.c9, self.c10, self.c11,
+        )
+
+    @staticmethod
+    def test_class():
+        assert issubclass(FiberForceLengthActiveDeGroote2016, Function)
+        assert issubclass(FiberForceLengthActiveDeGroote2016, CharacteristicCurveFunction)
+        assert FiberForceLengthActiveDeGroote2016.__name__ == 'FiberForceLengthActiveDeGroote2016'
+
+    def test_instance(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        assert isinstance(fl_M_act, FiberForceLengthActiveDeGroote2016)
+        assert str(fl_M_act) == (
+            'FiberForceLengthActiveDeGroote2016(l_M_tilde, c_0, c_1, c_2, c_3, '
+            'c_4, c_5, c_6, c_7, c_8, c_9, c_10, c_11)'
+        )
+
+    def test_doit(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants).doit()
+        assert fl_M_act == (
+            self.c0*exp(-(((self.l_M_tilde - self.c1)/(self.c2 + self.c3*self.l_M_tilde))**2)/2)
+            + self.c4*exp(-(((self.l_M_tilde - self.c5)/(self.c6 + self.c7*self.l_M_tilde))**2)/2)
+            + self.c8*exp(-(((self.l_M_tilde - self.c9)/(self.c10 + self.c11*self.l_M_tilde))**2)/2)
+        )
+
+    def test_doit_evaluate_false(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants).doit(evaluate=False)
+        assert fl_M_act == (
+            self.c0*exp(-((UnevaluatedExpr(self.l_M_tilde - self.c1)/(self.c2 + self.c3*self.l_M_tilde))**2)/2)
+            + self.c4*exp(-((UnevaluatedExpr(self.l_M_tilde - self.c5)/(self.c6 + self.c7*self.l_M_tilde))**2)/2)
+            + self.c8*exp(-((UnevaluatedExpr(self.l_M_tilde - self.c9)/(self.c10 + self.c11*self.l_M_tilde))**2)/2)
+        )
+
+    def test_with_defaults(self):
+        constants = (
+            Float('0.814'),
+            Float('1.06'),
+            Float('0.162'),
+            Float('0.0633'),
+            Float('0.433'),
+            Float('0.717'),
+            Float('-0.0299'),
+            Float('0.2'),
+            Float('0.1'),
+            Float('1.0'),
+            Float('0.354'),
+            Float('0.0'),
+        )
+        fl_M_act_manual = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *constants)
+        fl_M_act_constants = FiberForceLengthActiveDeGroote2016.with_defaults(self.l_M_tilde)
+        assert fl_M_act_manual == fl_M_act_constants
+
+    def test_differentiate_wrt_l_M_tilde(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c0*(
+                self.c3*(self.l_M_tilde - self.c1)**2/(self.c2 + self.c3*self.l_M_tilde)**3
+                + (self.c1 - self.l_M_tilde)/((self.c2 + self.c3*self.l_M_tilde)**2)
+            )*exp(-(self.l_M_tilde - self.c1)**2/(2*(self.c2 + self.c3*self.l_M_tilde)**2))
+            + self.c4*(
+                self.c7*(self.l_M_tilde - self.c5)**2/(self.c6 + self.c7*self.l_M_tilde)**3
+                + (self.c5 - self.l_M_tilde)/((self.c6 + self.c7*self.l_M_tilde)**2)
+            )*exp(-(self.l_M_tilde - self.c5)**2/(2*(self.c6 + self.c7*self.l_M_tilde)**2))
+            + self.c8*(
+                self.c11*(self.l_M_tilde - self.c9)**2/(self.c10 + self.c11*self.l_M_tilde)**3
+                + (self.c9 - self.l_M_tilde)/((self.c10 + self.c11*self.l_M_tilde)**2)
+            )*exp(-(self.l_M_tilde - self.c9)**2/(2*(self.c10 + self.c11*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.l_M_tilde) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = exp(-(self.l_M_tilde - self.c1)**2/(2*(self.c2 + self.c3*self.l_M_tilde)**2))
+        assert fl_M_act.doit().diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c0*(self.l_M_tilde - self.c1)/(self.c2 + self.c3*self.l_M_tilde)**2
+            *exp(-(self.l_M_tilde - self.c1)**2/(2*(self.c2 + self.c3*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c1) == expected
+
+    def test_differentiate_wrt_c2(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c0*(self.l_M_tilde - self.c1)**2/(self.c2 + self.c3*self.l_M_tilde)**3
+            *exp(-(self.l_M_tilde - self.c1)**2/(2*(self.c2 + self.c3*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c2) == expected
+
+    def test_differentiate_wrt_c3(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c0*self.l_M_tilde*(self.l_M_tilde - self.c1)**2/(self.c2 + self.c3*self.l_M_tilde)**3
+            *exp(-(self.l_M_tilde - self.c1)**2/(2*(self.c2 + self.c3*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c3) == expected
+
+    def test_differentiate_wrt_c4(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = exp(-(self.l_M_tilde - self.c5)**2/(2*(self.c6 + self.c7*self.l_M_tilde)**2))
+        assert fl_M_act.diff(self.c4) == expected
+
+    def test_differentiate_wrt_c5(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c4*(self.l_M_tilde - self.c5)/(self.c6 + self.c7*self.l_M_tilde)**2
+            *exp(-(self.l_M_tilde - self.c5)**2/(2*(self.c6 + self.c7*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c5) == expected
+
+    def test_differentiate_wrt_c6(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c4*(self.l_M_tilde - self.c5)**2/(self.c6 + self.c7*self.l_M_tilde)**3
+            *exp(-(self.l_M_tilde - self.c5)**2/(2*(self.c6 + self.c7*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c6) == expected
+
+    def test_differentiate_wrt_c7(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c4*self.l_M_tilde*(self.l_M_tilde - self.c5)**2/(self.c6 + self.c7*self.l_M_tilde)**3
+            *exp(-(self.l_M_tilde - self.c5)**2/(2*(self.c6 + self.c7*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c7) == expected
+
+    def test_differentiate_wrt_c8(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = exp(-(self.l_M_tilde - self.c9)**2/(2*(self.c10 + self.c11*self.l_M_tilde)**2))
+        assert fl_M_act.diff(self.c8) == expected
+
+    def test_differentiate_wrt_c9(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c8*(self.l_M_tilde - self.c9)/(self.c10 + self.c11*self.l_M_tilde)**2
+            *exp(-(self.l_M_tilde - self.c9)**2/(2*(self.c10 + self.c11*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c9) == expected
+
+    def test_differentiate_wrt_c10(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c8*(self.l_M_tilde - self.c9)**2/(self.c10 + self.c11*self.l_M_tilde)**3
+            *exp(-(self.l_M_tilde - self.c9)**2/(2*(self.c10 + self.c11*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c10) == expected
+
+    def test_differentiate_wrt_c11(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            self.c8*self.l_M_tilde*(self.l_M_tilde - self.c9)**2/(self.c10 + self.c11*self.l_M_tilde)**3
+            *exp(-(self.l_M_tilde - self.c9)**2/(2*(self.c10 + self.c11*self.l_M_tilde)**2))
+        )
+        assert fl_M_act.diff(self.c11) == expected
+
+    def test_function_print_latex(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = r'\operatorname{fl}^M_{act} \left( l_{M tilde} \right)'
+        assert LatexPrinter().doprint(fl_M_act) == expected
+
+    def test_expression_print_latex(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016(self.l_M_tilde, *self.constants)
+        expected = (
+            r'c_{0} e^{- \frac{\left(- c_{1} + l_{M tilde}\right)^{2}}{2 \left(c_{2} + c_{3} l_{M tilde}\right)^{2}}} '
+            r'+ c_{4} e^{- \frac{\left(- c_{5} + l_{M tilde}\right)^{2}}{2 \left(c_{6} + c_{7} l_{M tilde}\right)^{2}}} '
+            r'+ c_{8} e^{- \frac{\left(- c_{9} + l_{M tilde}\right)^{2}}{2 \left(c_{10} + c_{11} l_{M tilde}\right)^{2}}}'
+        )
+        assert LatexPrinter().doprint(fl_M_act.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                (
+                    '(0.81399999999999995*exp(-1.0/2.0*pow(l_M_tilde - 1.0600000000000001, 2)/pow(0.063299999999999995*l_M_tilde + 0.16200000000000001, 2)) + 0.433*exp(-1.0/2.0*pow(l_M_tilde - 0.71699999999999997, 2)/pow(0.20000000000000001*l_M_tilde - 0.029899999999999999, 2)) + 0.10000000000000001*exp(-3.9899134986753491*pow(l_M_tilde - 1.0, 2)))'
+                ),
+            ),
+            (
+                C99CodePrinter,
+                (
+                    '(0.81399999999999995*exp(-1.0/2.0*pow(l_M_tilde - 1.0600000000000001, 2)/pow(0.063299999999999995*l_M_tilde + 0.16200000000000001, 2)) + 0.433*exp(-1.0/2.0*pow(l_M_tilde - 0.71699999999999997, 2)/pow(0.20000000000000001*l_M_tilde - 0.029899999999999999, 2)) + 0.10000000000000001*exp(-3.9899134986753491*pow(l_M_tilde - 1.0, 2)))'
+                ),
+            ),
+            (
+                C11CodePrinter,
+                (
+                    '(0.81399999999999995*exp(-1.0/2.0*pow(l_M_tilde - 1.0600000000000001, 2)/pow(0.063299999999999995*l_M_tilde + 0.16200000000000001, 2)) + 0.433*exp(-1.0/2.0*pow(l_M_tilde - 0.71699999999999997, 2)/pow(0.20000000000000001*l_M_tilde - 0.029899999999999999, 2)) + 0.10000000000000001*exp(-3.9899134986753491*pow(l_M_tilde - 1.0, 2)))'
+                ),
+            ),
+            (
+                CXX98CodePrinter,
+                (
+                    '(0.81399999999999995*exp(-1.0/2.0*std::pow(l_M_tilde - 1.0600000000000001, 2)/std::pow(0.063299999999999995*l_M_tilde + 0.16200000000000001, 2)) + 0.433*exp(-1.0/2.0*std::pow(l_M_tilde - 0.71699999999999997, 2)/std::pow(0.20000000000000001*l_M_tilde - 0.029899999999999999, 2)) + 0.10000000000000001*exp(-3.9899134986753491*std::pow(l_M_tilde - 1.0, 2)))'
+                ),
+            ),
+            (
+                CXX11CodePrinter,
+                (
+                    '(0.81399999999999995*std::exp(-1.0/2.0*std::pow(l_M_tilde - 1.0600000000000001, 2)/std::pow(0.063299999999999995*l_M_tilde + 0.16200000000000001, 2)) + 0.433*std::exp(-1.0/2.0*std::pow(l_M_tilde - 0.71699999999999997, 2)/std::pow(0.20000000000000001*l_M_tilde - 0.029899999999999999, 2)) + 0.10000000000000001*std::exp(-3.9899134986753491*std::pow(l_M_tilde - 1.0, 2)))'
+                ),
+            ),
+            (
+                CXX17CodePrinter,
+                (
+                    '(0.81399999999999995*std::exp(-1.0/2.0*std::pow(l_M_tilde - 1.0600000000000001, 2)/std::pow(0.063299999999999995*l_M_tilde + 0.16200000000000001, 2)) + 0.433*std::exp(-1.0/2.0*std::pow(l_M_tilde - 0.71699999999999997, 2)/std::pow(0.20000000000000001*l_M_tilde - 0.029899999999999999, 2)) + 0.10000000000000001*std::exp(-3.9899134986753491*std::pow(l_M_tilde - 1.0, 2)))'
+                ),
+            ),
+            (
+                FCodePrinter,
+                (
+                    '      (0.814d0*exp(-0.5d0*(l_M_tilde - 1.06d0)**2/(\n'
+                    '     @ 0.063299999999999995d0*l_M_tilde + 0.16200000000000001d0)**2) +\n'
+                    '     @ 0.433d0*exp(-0.5d0*(l_M_tilde - 0.717d0)**2/(\n'
+                    '     @ 0.20000000000000001d0*l_M_tilde - 0.029899999999999999d0)**2) +\n'
+                    '     @ 0.1d0*exp(-3.9899134986753491d0*(l_M_tilde - 1.0d0)**2))'
+                ),
+            ),
+            (
+                OctaveCodePrinter,
+                (
+                    '(0.814*exp(-(l_M_tilde - 1.06).^2./(2*(0.0633*l_M_tilde + 0.162).^2)) + 0.433*exp(-(l_M_tilde - 0.717).^2./(2*(0.2*l_M_tilde - 0.0299).^2)) + 0.1*exp(-3.98991349867535*(l_M_tilde - 1.0).^2))'
+                ),
+            ),
+            (
+                PythonCodePrinter,
+                (
+                    '(0.814*math.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2) + 0.433*math.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + 0.1*math.exp(-3.98991349867535*(l_M_tilde - 1.0)**2))'
+                ),
+            ),
+            (
+                NumPyPrinter,
+                (
+                    '(0.814*numpy.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2) + 0.433*numpy.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + 0.1*numpy.exp(-3.98991349867535*(l_M_tilde - 1.0)**2))'
+                ),
+            ),
+            (
+                SciPyPrinter,
+                (
+                    '(0.814*numpy.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2) + 0.433*numpy.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + 0.1*numpy.exp(-3.98991349867535*(l_M_tilde - 1.0)**2))'
+                ),
+            ),
+            (
+                CuPyPrinter,
+                (
+                    '(0.814*cupy.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2) + 0.433*cupy.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + 0.1*cupy.exp(-3.98991349867535*(l_M_tilde - 1.0)**2))'
+                ),
+            ),
+            (
+                JaxPrinter,
+                (
+                    '(0.814*jax.numpy.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2) + 0.433*jax.numpy.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + 0.1*jax.numpy.exp(-3.98991349867535*(l_M_tilde - 1.0)**2))'
+                ),
+            ),
+            (
+                MpmathPrinter,
+                (
+                    '(mpmath.mpf((0, 7331860193359167, -53, 53))*mpmath.exp(-mpmath.mpf(1)/mpmath.mpf(2)*(l_M_tilde + mpmath.mpf((1, 2386907802506363, -51, 52)))**2/(mpmath.mpf((0, 2280622851300419, -55, 52))*l_M_tilde + mpmath.mpf((0, 5836665117072163, -55, 53)))**2) + mpmath.mpf((0, 7800234554605699, -54, 53))*mpmath.exp(-mpmath.mpf(1)/mpmath.mpf(2)*(l_M_tilde + mpmath.mpf((1, 6458161865649291, -53, 53)))**2/(mpmath.mpf((0, 3602879701896397, -54, 52))*l_M_tilde + mpmath.mpf((1, 8618088246936181, -58, 53)))**2) + mpmath.mpf((0, 3602879701896397, -55, 52))*mpmath.exp(-mpmath.mpf((0, 8984486472937407, -51, 53))*(l_M_tilde + mpmath.mpf((1, 1, 0, 1)))**2))'
+                ),
+            ),
+            (
+                LambdaPrinter,
+                (
+                    '(0.814*math.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2) + 0.433*math.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + 0.1*math.exp(-3.98991349867535*(l_M_tilde - 1.0)**2))'
+                ),
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fl_M_act = FiberForceLengthActiveDeGroote2016.with_defaults(self.l_M_tilde)
+        assert code_printer().doprint(fl_M_act) == expected
+
+    def test_derivative_print_code(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_act_dl_M_tilde = fl_M_act.diff(self.l_M_tilde)
+        expected = (
+            '(0.79798269973507 - 0.79798269973507*l_M_tilde)*math.exp(-3.98991349867535*(l_M_tilde - 1.0)**2) + (0.433*(0.717 - l_M_tilde)/(0.2*l_M_tilde - 0.0299)**2 + 0.0866*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**3)*math.exp(-1/2*(l_M_tilde - 0.717)**2/(0.2*l_M_tilde - 0.0299)**2) + (0.814*(1.06 - l_M_tilde)/(0.0633*l_M_tilde + 0.162)**2 + 0.0515262*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**3)*math.exp(-1/2*(l_M_tilde - 1.06)**2/(0.0633*l_M_tilde + 0.162)**2)'
+        )
+        assert PythonCodePrinter().doprint(fl_M_act_dl_M_tilde) == expected
+
+    def test_lambdify(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_act_callable = lambdify(self.l_M_tilde, fl_M_act)
+        assert fl_M_act_callable(1.0) == pytest.approx(0.9941398866)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_act_callable = lambdify(self.l_M_tilde, fl_M_act, 'numpy')
+        l_M_tilde = numpy.array([0.0, 0.5, 1.0, 1.5, 2.0])
+        expected = numpy.array([
+            0.0018501319,
+            0.0529122812,
+            0.9941398866,
+            0.2312431531,
+            0.0069595432,
+        ])
+        numpy.testing.assert_allclose(fl_M_act_callable(l_M_tilde), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fl_M_act = FiberForceLengthActiveDeGroote2016.with_defaults(self.l_M_tilde)
+        fl_M_act_callable = jax.jit(lambdify(self.l_M_tilde, fl_M_act, 'jax'))
+        l_M_tilde = jax.numpy.array([0.0, 0.5, 1.0, 1.5, 2.0])
+        expected = jax.numpy.array([
+            0.0018501319,
+            0.0529122812,
+            0.9941398866,
+            0.2312431531,
+            0.0069595432,
+        ])
+        numpy.testing.assert_allclose(fl_M_act_callable(l_M_tilde), expected)
+
+
+class TestFiberForceVelocityDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _muscle_fiber_force_velocity_arguments_fixture(self):
+        self.v_M_tilde = Symbol('v_M_tilde')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.c2 = Symbol('c_2')
+        self.c3 = Symbol('c_3')
+        self.constants = (self.c0, self.c1, self.c2, self.c3)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(FiberForceVelocityDeGroote2016, Function)
+        assert issubclass(FiberForceVelocityDeGroote2016, CharacteristicCurveFunction)
+        assert FiberForceVelocityDeGroote2016.__name__ == 'FiberForceVelocityDeGroote2016'
+
+    def test_instance(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        assert isinstance(fv_M, FiberForceVelocityDeGroote2016)
+        assert str(fv_M) == 'FiberForceVelocityDeGroote2016(v_M_tilde, c_0, c_1, c_2, c_3)'
+
+    def test_doit(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants).doit()
+        expected = (
+            self.c0 * log((self.c1 * self.v_M_tilde + self.c2)
+            + sqrt((self.c1 * self.v_M_tilde + self.c2)**2 + 1)) + self.c3
+        )
+        assert fv_M == expected
+
+    def test_doit_evaluate_false(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants).doit(evaluate=False)
+        expected = (
+            self.c0 * log((self.c1 * self.v_M_tilde + self.c2)
+            + sqrt(UnevaluatedExpr(self.c1 * self.v_M_tilde + self.c2)**2 + 1)) + self.c3
+        )
+        assert fv_M == expected
+
+    def test_with_defaults(self):
+        constants = (
+            Float('-0.318'),
+            Float('-8.149'),
+            Float('-0.374'),
+            Float('0.886'),
+        )
+        fv_M_manual = FiberForceVelocityDeGroote2016(self.v_M_tilde, *constants)
+        fv_M_constants = FiberForceVelocityDeGroote2016.with_defaults(self.v_M_tilde)
+        assert fv_M_manual == fv_M_constants
+
+    def test_differentiate_wrt_v_M_tilde(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = (
+            self.c0*self.c1
+            /sqrt(UnevaluatedExpr(self.c1*self.v_M_tilde + self.c2)**2 + 1)
+        )
+        assert fv_M.diff(self.v_M_tilde) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = log(
+            self.c1*self.v_M_tilde + self.c2
+            + sqrt(UnevaluatedExpr(self.c1*self.v_M_tilde + self.c2)**2 + 1)
+        )
+        assert fv_M.diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = (
+            self.c0*self.v_M_tilde
+            /sqrt(UnevaluatedExpr(self.c1*self.v_M_tilde + self.c2)**2 + 1)
+        )
+        assert fv_M.diff(self.c1) == expected
+
+    def test_differentiate_wrt_c2(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = (
+            self.c0
+            /sqrt(UnevaluatedExpr(self.c1*self.v_M_tilde + self.c2)**2 + 1)
+        )
+        assert fv_M.diff(self.c2) == expected
+
+    def test_differentiate_wrt_c3(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = Integer(1)
+        assert fv_M.diff(self.c3) == expected
+
+    def test_inverse(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        assert fv_M.inverse() is FiberForceVelocityInverseDeGroote2016
+
+    def test_function_print_latex(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = r'\operatorname{fv}^M \left( v_{M tilde} \right)'
+        assert LatexPrinter().doprint(fv_M) == expected
+
+    def test_expression_print_latex(self):
+        fv_M = FiberForceVelocityDeGroote2016(self.v_M_tilde, *self.constants)
+        expected = (
+            r'c_{0} \log{\left(c_{1} v_{M tilde} + c_{2} + \sqrt{\left(c_{1} '
+            r'v_{M tilde} + c_{2}\right)^{2} + 1} \right)} + c_{3}'
+        )
+        assert LatexPrinter().doprint(fv_M.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                '(0.88600000000000001 - 0.318*log(-8.1489999999999991*v_M_tilde '
+                '- 0.374 + sqrt(1 + pow(-8.1489999999999991*v_M_tilde - 0.374, 2))))',
+            ),
+            (
+                C99CodePrinter,
+                '(0.88600000000000001 - 0.318*log(-8.1489999999999991*v_M_tilde '
+                '- 0.374 + sqrt(1 + pow(-8.1489999999999991*v_M_tilde - 0.374, 2))))',
+            ),
+            (
+                C11CodePrinter,
+                '(0.88600000000000001 - 0.318*log(-8.1489999999999991*v_M_tilde '
+                '- 0.374 + sqrt(1 + pow(-8.1489999999999991*v_M_tilde - 0.374, 2))))',
+            ),
+            (
+                CXX98CodePrinter,
+                '(0.88600000000000001 - 0.318*log(-8.1489999999999991*v_M_tilde '
+                '- 0.374 + std::sqrt(1 + std::pow(-8.1489999999999991*v_M_tilde - 0.374, 2))))',
+            ),
+            (
+                CXX11CodePrinter,
+                '(0.88600000000000001 - 0.318*std::log(-8.1489999999999991*v_M_tilde '
+                '- 0.374 + std::sqrt(1 + std::pow(-8.1489999999999991*v_M_tilde - 0.374, 2))))',
+            ),
+            (
+                CXX17CodePrinter,
+                '(0.88600000000000001 - 0.318*std::log(-8.1489999999999991*v_M_tilde '
+                '- 0.374 + std::sqrt(1 + std::pow(-8.1489999999999991*v_M_tilde - 0.374, 2))))',
+            ),
+            (
+                FCodePrinter,
+                '      (0.886d0 - 0.318d0*log(-8.1489999999999991d0*v_M_tilde - 0.374d0 +\n'
+                '     @ sqrt(1.0d0 + (-8.149d0*v_M_tilde - 0.374d0)**2)))',
+            ),
+            (
+                OctaveCodePrinter,
+                '(0.886 - 0.318*log(-8.149*v_M_tilde - 0.374 '
+                '+ sqrt(1 + (-8.149*v_M_tilde - 0.374).^2)))',
+            ),
+            (
+                PythonCodePrinter,
+                '(0.886 - 0.318*math.log(-8.149*v_M_tilde - 0.374 '
+                '+ math.sqrt(1 + (-8.149*v_M_tilde - 0.374)**2)))',
+            ),
+            (
+                NumPyPrinter,
+                '(0.886 - 0.318*numpy.log(-8.149*v_M_tilde - 0.374 '
+                '+ numpy.sqrt(1 + (-8.149*v_M_tilde - 0.374)**2)))',
+            ),
+            (
+                SciPyPrinter,
+                '(0.886 - 0.318*numpy.log(-8.149*v_M_tilde - 0.374 '
+                '+ numpy.sqrt(1 + (-8.149*v_M_tilde - 0.374)**2)))',
+            ),
+            (
+                CuPyPrinter,
+                '(0.886 - 0.318*cupy.log(-8.149*v_M_tilde - 0.374 '
+                '+ cupy.sqrt(1 + (-8.149*v_M_tilde - 0.374)**2)))',
+            ),
+            (
+                JaxPrinter,
+                '(0.886 - 0.318*jax.numpy.log(-8.149*v_M_tilde - 0.374 '
+                '+ jax.numpy.sqrt(1 + (-8.149*v_M_tilde - 0.374)**2)))',
+            ),
+            (
+                MpmathPrinter,
+                '(mpmath.mpf((0, 7980378539700519, -53, 53)) '
+                '- mpmath.mpf((0, 5728578726015271, -54, 53))'
+                '*mpmath.log(-mpmath.mpf((0, 4587479170430271, -49, 53))*v_M_tilde '
+                '+ mpmath.mpf((1, 3368692521273131, -53, 52)) '
+                '+ mpmath.sqrt(1 + (-mpmath.mpf((0, 4587479170430271, -49, 53))*v_M_tilde '
+                '+ mpmath.mpf((1, 3368692521273131, -53, 52)))**2)))',
+            ),
+            (
+                LambdaPrinter,
+                '(0.886 - 0.318*math.log(-8.149*v_M_tilde - 0.374 '
+                '+ sqrt(1 + (-8.149*v_M_tilde - 0.374)**2)))',
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fv_M = FiberForceVelocityDeGroote2016.with_defaults(self.v_M_tilde)
+        assert code_printer().doprint(fv_M) == expected
+
+    def test_derivative_print_code(self):
+        fv_M = FiberForceVelocityDeGroote2016.with_defaults(self.v_M_tilde)
+        dfv_M_dv_M_tilde = fv_M.diff(self.v_M_tilde)
+        expected = '2.591382*(1 + (-8.149*v_M_tilde - 0.374)**2)**(-1/2)'
+        assert PythonCodePrinter().doprint(dfv_M_dv_M_tilde) == expected
+
+    def test_lambdify(self):
+        fv_M = FiberForceVelocityDeGroote2016.with_defaults(self.v_M_tilde)
+        fv_M_callable = lambdify(self.v_M_tilde, fv_M)
+        assert fv_M_callable(0.0) == pytest.approx(1.002320622548512)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fv_M = FiberForceVelocityDeGroote2016.with_defaults(self.v_M_tilde)
+        fv_M_callable = lambdify(self.v_M_tilde, fv_M, 'numpy')
+        v_M_tilde = numpy.array([-1.0, -0.5, 0.0, 0.5])
+        expected = numpy.array([
+            0.0120816781,
+            0.2438336294,
+            1.0023206225,
+            1.5850003903,
+        ])
+        numpy.testing.assert_allclose(fv_M_callable(v_M_tilde), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fv_M = FiberForceVelocityDeGroote2016.with_defaults(self.v_M_tilde)
+        fv_M_callable = jax.jit(lambdify(self.v_M_tilde, fv_M, 'jax'))
+        v_M_tilde = jax.numpy.array([-1.0, -0.5, 0.0, 0.5])
+        expected = jax.numpy.array([
+            0.0120816781,
+            0.2438336294,
+            1.0023206225,
+            1.5850003903,
+        ])
+        numpy.testing.assert_allclose(fv_M_callable(v_M_tilde), expected)
+
+
+class TestFiberForceVelocityInverseDeGroote2016:
+
+    @pytest.fixture(autouse=True)
+    def _tendon_force_length_inverse_arguments_fixture(self):
+        self.fv_M = Symbol('fv_M')
+        self.c0 = Symbol('c_0')
+        self.c1 = Symbol('c_1')
+        self.c2 = Symbol('c_2')
+        self.c3 = Symbol('c_3')
+        self.constants = (self.c0, self.c1, self.c2, self.c3)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(FiberForceVelocityInverseDeGroote2016, Function)
+        assert issubclass(FiberForceVelocityInverseDeGroote2016, CharacteristicCurveFunction)
+        assert FiberForceVelocityInverseDeGroote2016.__name__ == 'FiberForceVelocityInverseDeGroote2016'
+
+    def test_instance(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        assert isinstance(fv_M_inv, FiberForceVelocityInverseDeGroote2016)
+        assert str(fv_M_inv) == 'FiberForceVelocityInverseDeGroote2016(fv_M, c_0, c_1, c_2, c_3)'
+
+    def test_doit(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants).doit()
+        assert fv_M_inv == (sinh((self.fv_M - self.c3)/self.c0) - self.c2)/self.c1
+
+    def test_doit_evaluate_false(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants).doit(evaluate=False)
+        assert fv_M_inv == (sinh(UnevaluatedExpr(self.fv_M - self.c3)/self.c0) - self.c2)/self.c1
+
+    def test_with_defaults(self):
+        constants = (
+            Float('-0.318'),
+            Float('-8.149'),
+            Float('-0.374'),
+            Float('0.886'),
+        )
+        fv_M_inv_manual = FiberForceVelocityInverseDeGroote2016(self.fv_M, *constants)
+        fv_M_inv_constants = FiberForceVelocityInverseDeGroote2016.with_defaults(self.fv_M)
+        assert fv_M_inv_manual == fv_M_inv_constants
+
+    def test_differentiate_wrt_fv_M(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = cosh((self.fv_M - self.c3)/self.c0)/(self.c0*self.c1)
+        assert fv_M_inv.diff(self.fv_M) == expected
+
+    def test_differentiate_wrt_c0(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = (self.c3 - self.fv_M)*cosh((self.fv_M - self.c3)/self.c0)/(self.c0**2*self.c1)
+        assert fv_M_inv.diff(self.c0) == expected
+
+    def test_differentiate_wrt_c1(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = (self.c2 - sinh((self.fv_M - self.c3)/self.c0))/self.c1**2
+        assert fv_M_inv.diff(self.c1) == expected
+
+    def test_differentiate_wrt_c2(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = -1/self.c1
+        assert fv_M_inv.diff(self.c2) == expected
+
+    def test_differentiate_wrt_c3(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = -cosh((self.fv_M - self.c3)/self.c0)/(self.c0*self.c1)
+        assert fv_M_inv.diff(self.c3) == expected
+
+    def test_inverse(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        assert fv_M_inv.inverse() is FiberForceVelocityDeGroote2016
+
+    def test_function_print_latex(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = r'\left( \operatorname{fv}^M \right)^{-1} \left( fv_{M} \right)'
+        assert LatexPrinter().doprint(fv_M_inv) == expected
+
+    def test_expression_print_latex(self):
+        fv_M = FiberForceVelocityInverseDeGroote2016(self.fv_M, *self.constants)
+        expected = r'\frac{- c_{2} + \sinh{\left(\frac{- c_{3} + fv_{M}}{c_{0}} \right)}}{c_{1}}'
+        assert LatexPrinter().doprint(fv_M.doit()) == expected
+
+    @pytest.mark.parametrize(
+        'code_printer, expected',
+        [
+            (
+                C89CodePrinter,
+                '(-0.12271444348999878*(0.374 - sinh(3.1446540880503142*(fv_M '
+                '- 0.88600000000000001))))',
+            ),
+            (
+                C99CodePrinter,
+                '(-0.12271444348999878*(0.374 - sinh(3.1446540880503142*(fv_M '
+                '- 0.88600000000000001))))',
+            ),
+            (
+                C11CodePrinter,
+                '(-0.12271444348999878*(0.374 - sinh(3.1446540880503142*(fv_M '
+                '- 0.88600000000000001))))',
+            ),
+            (
+                CXX98CodePrinter,
+                '(-0.12271444348999878*(0.374 - sinh(3.1446540880503142*(fv_M '
+                '- 0.88600000000000001))))',
+            ),
+            (
+                CXX11CodePrinter,
+                '(-0.12271444348999878*(0.374 - std::sinh(3.1446540880503142'
+                '*(fv_M - 0.88600000000000001))))',
+            ),
+            (
+                CXX17CodePrinter,
+                '(-0.12271444348999878*(0.374 - std::sinh(3.1446540880503142'
+                '*(fv_M - 0.88600000000000001))))',
+            ),
+            (
+                FCodePrinter,
+                '      (-0.122714443489999d0*(0.374d0 - sinh(3.1446540880503142d0*(fv_M -\n'
+                '     @ 0.886d0))))',
+            ),
+            (
+                OctaveCodePrinter,
+                '(-0.122714443489999*(0.374 - sinh(3.14465408805031*(fv_M '
+                '- 0.886))))',
+            ),
+            (
+                PythonCodePrinter,
+                '(-0.122714443489999*(0.374 - math.sinh(3.14465408805031*(fv_M '
+                '- 0.886))))',
+            ),
+            (
+                NumPyPrinter,
+                '(-0.122714443489999*(0.374 - numpy.sinh(3.14465408805031'
+                '*(fv_M - 0.886))))',
+            ),
+            (
+                SciPyPrinter,
+                '(-0.122714443489999*(0.374 - numpy.sinh(3.14465408805031'
+                '*(fv_M - 0.886))))',
+            ),
+            (
+                CuPyPrinter,
+                '(-0.122714443489999*(0.374 - cupy.sinh(3.14465408805031*(fv_M '
+                '- 0.886))))',
+            ),
+            (
+                JaxPrinter,
+                '(-0.122714443489999*(0.374 - jax.numpy.sinh(3.14465408805031'
+                '*(fv_M - 0.886))))',
+            ),
+            (
+                MpmathPrinter,
+                '(-mpmath.mpf((0, 8842507551592581, -56, 53))*(mpmath.mpf((0, '
+                '3368692521273131, -53, 52)) - mpmath.sinh(mpmath.mpf((0, '
+                '7081131489576251, -51, 53))*(fv_M + mpmath.mpf((1, '
+                '7980378539700519, -53, 53))))))',
+            ),
+            (
+                LambdaPrinter,
+                '(-0.122714443489999*(0.374 - math.sinh(3.14465408805031*(fv_M '
+                '- 0.886))))',
+            ),
+        ]
+    )
+    def test_print_code(self, code_printer, expected):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016.with_defaults(self.fv_M)
+        assert code_printer().doprint(fv_M_inv) == expected
+
+    def test_derivative_print_code(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016.with_defaults(self.fv_M)
+        dfv_M_inv_dfv_M = fv_M_inv.diff(self.fv_M)
+        expected = (
+            '0.385894476383644*math.cosh(3.14465408805031*fv_M '
+            '- 2.78616352201258)'
+        )
+        assert PythonCodePrinter().doprint(dfv_M_inv_dfv_M) == expected
+
+    def test_lambdify(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016.with_defaults(self.fv_M)
+        fv_M_inv_callable = lambdify(self.fv_M, fv_M_inv)
+        assert fv_M_inv_callable(1.0) == pytest.approx(-0.0009548832444487479)
+
+    @pytest.mark.skipif(numpy is None, reason='NumPy not installed')
+    def test_lambdify_numpy(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016.with_defaults(self.fv_M)
+        fv_M_inv_callable = lambdify(self.fv_M, fv_M_inv, 'numpy')
+        fv_M = numpy.array([0.8, 0.9, 1.0, 1.1, 1.2])
+        expected = numpy.array([
+            -0.0794881459,
+            -0.0404909338,
+            -0.0009548832,
+            0.043061991,
+            0.0959484397,
+        ])
+        numpy.testing.assert_allclose(fv_M_inv_callable(fv_M), expected)
+
+    @pytest.mark.skipif(jax is None, reason='JAX not installed')
+    def test_lambdify_jax(self):
+        fv_M_inv = FiberForceVelocityInverseDeGroote2016.with_defaults(self.fv_M)
+        fv_M_inv_callable = jax.jit(lambdify(self.fv_M, fv_M_inv, 'jax'))
+        fv_M = jax.numpy.array([0.8, 0.9, 1.0, 1.1, 1.2])
+        expected = jax.numpy.array([
+            -0.0794881459,
+            -0.0404909338,
+            -0.0009548832,
+            0.043061991,
+            0.0959484397,
+        ])
+        numpy.testing.assert_allclose(fv_M_inv_callable(fv_M), expected)
+
+
+class TestCharacteristicCurveCollection:
+
+    @staticmethod
+    def test_valid_constructor():
+        curves = CharacteristicCurveCollection(
+            tendon_force_length=TendonForceLengthDeGroote2016,
+            tendon_force_length_inverse=TendonForceLengthInverseDeGroote2016,
+            fiber_force_length_passive=FiberForceLengthPassiveDeGroote2016,
+            fiber_force_length_passive_inverse=FiberForceLengthPassiveInverseDeGroote2016,
+            fiber_force_length_active=FiberForceLengthActiveDeGroote2016,
+            fiber_force_velocity=FiberForceVelocityDeGroote2016,
+            fiber_force_velocity_inverse=FiberForceVelocityInverseDeGroote2016,
+        )
+        assert curves.tendon_force_length is TendonForceLengthDeGroote2016
+        assert curves.tendon_force_length_inverse is TendonForceLengthInverseDeGroote2016
+        assert curves.fiber_force_length_passive is FiberForceLengthPassiveDeGroote2016
+        assert curves.fiber_force_length_passive_inverse is FiberForceLengthPassiveInverseDeGroote2016
+        assert curves.fiber_force_length_active is FiberForceLengthActiveDeGroote2016
+        assert curves.fiber_force_velocity is FiberForceVelocityDeGroote2016
+        assert curves.fiber_force_velocity_inverse is FiberForceVelocityInverseDeGroote2016
+
+    @staticmethod
+    @pytest.mark.skip(reason='kw_only dataclasses only valid in Python >3.10')
+    def test_invalid_constructor_keyword_only():
+        with pytest.raises(TypeError):
+            _ = CharacteristicCurveCollection(
+                TendonForceLengthDeGroote2016,
+                TendonForceLengthInverseDeGroote2016,
+                FiberForceLengthPassiveDeGroote2016,
+                FiberForceLengthPassiveInverseDeGroote2016,
+                FiberForceLengthActiveDeGroote2016,
+                FiberForceVelocityDeGroote2016,
+                FiberForceVelocityInverseDeGroote2016,
+            )
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'kwargs',
+        [
+            {'tendon_force_length': TendonForceLengthDeGroote2016},
+            {
+                'tendon_force_length': TendonForceLengthDeGroote2016,
+                'tendon_force_length_inverse': TendonForceLengthInverseDeGroote2016,
+                'fiber_force_length_passive': FiberForceLengthPassiveDeGroote2016,
+                'fiber_force_length_passive_inverse': FiberForceLengthPassiveInverseDeGroote2016,
+                'fiber_force_length_active': FiberForceLengthActiveDeGroote2016,
+                'fiber_force_velocity': FiberForceVelocityDeGroote2016,
+                'fiber_force_velocity_inverse': FiberForceVelocityInverseDeGroote2016,
+                'extra_kwarg': None,
+            },
+        ]
+    )
+    def test_invalid_constructor_wrong_number_args(kwargs):
+        with pytest.raises(TypeError):
+            _ = CharacteristicCurveCollection(**kwargs)
+
+    @staticmethod
+    def test_instance_is_immutable():
+        curves = CharacteristicCurveCollection(
+            tendon_force_length=TendonForceLengthDeGroote2016,
+            tendon_force_length_inverse=TendonForceLengthInverseDeGroote2016,
+            fiber_force_length_passive=FiberForceLengthPassiveDeGroote2016,
+            fiber_force_length_passive_inverse=FiberForceLengthPassiveInverseDeGroote2016,
+            fiber_force_length_active=FiberForceLengthActiveDeGroote2016,
+            fiber_force_velocity=FiberForceVelocityDeGroote2016,
+            fiber_force_velocity_inverse=FiberForceVelocityInverseDeGroote2016,
+        )
+        with pytest.raises(AttributeError):
+            curves.tendon_force_length = None
+        with pytest.raises(AttributeError):
+            curves.tendon_force_length_inverse = None
+        with pytest.raises(AttributeError):
+            curves.fiber_force_length_passive = None
+        with pytest.raises(AttributeError):
+            curves.fiber_force_length_passive_inverse = None
+        with pytest.raises(AttributeError):
+            curves.fiber_force_length_active = None
+        with pytest.raises(AttributeError):
+            curves.fiber_force_velocity = None
+        with pytest.raises(AttributeError):
+            curves.fiber_force_velocity_inverse = None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_mixin.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_mixin.py
new file mode 100644
index 0000000000000000000000000000000000000000..be079c195f3d961a88f52c94b695666f2a4f2bb5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_mixin.py
@@ -0,0 +1,48 @@
+"""Tests for the ``sympy.physics.biomechanics._mixin.py`` module."""
+
+import pytest
+
+from sympy.physics.biomechanics._mixin import _NamedMixin
+
+
+class TestNamedMixin:
+
+    @staticmethod
+    def test_subclass():
+
+        class Subclass(_NamedMixin):
+
+            def __init__(self, name):
+                self.name = name
+
+        instance = Subclass('name')
+        assert instance.name == 'name'
+
+    @pytest.fixture(autouse=True)
+    def _named_mixin_fixture(self):
+
+        class Subclass(_NamedMixin):
+
+            def __init__(self, name):
+                self.name = name
+
+        self.Subclass = Subclass
+
+    @pytest.mark.parametrize('name', ['a', 'name', 'long_name'])
+    def test_valid_name_argument(self, name):
+        instance = self.Subclass(name)
+        assert instance.name == name
+
+    @pytest.mark.parametrize('invalid_name', [0, 0.0, None, False])
+    def test_invalid_name_argument_not_str(self, invalid_name):
+        with pytest.raises(TypeError):
+            _ = self.Subclass(invalid_name)
+
+    def test_invalid_name_argument_zero_length_str(self):
+        with pytest.raises(ValueError):
+            _ = self.Subclass('')
+
+    def test_name_attribute_is_immutable(self):
+        instance = self.Subclass('name')
+        with pytest.raises(AttributeError):
+            instance.name = 'new_name'
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_musculotendon.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_musculotendon.py
new file mode 100644
index 0000000000000000000000000000000000000000..d0c5a1088214049aaaaa3666854e232d26f77786
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/biomechanics/tests/test_musculotendon.py
@@ -0,0 +1,837 @@
+"""Tests for the ``sympy.physics.biomechanics.musculotendon.py`` module."""
+
+import abc
+
+import pytest
+
+from sympy.core.expr import UnevaluatedExpr
+from sympy.core.numbers import Float, Integer, Rational
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.hyperbolic import tanh
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+from sympy.matrices.dense import MutableDenseMatrix as Matrix, eye, zeros
+from sympy.physics.biomechanics.activation import (
+    FirstOrderActivationDeGroote2016
+)
+from sympy.physics.biomechanics.curve import (
+    CharacteristicCurveCollection,
+    FiberForceLengthActiveDeGroote2016,
+    FiberForceLengthPassiveDeGroote2016,
+    FiberForceLengthPassiveInverseDeGroote2016,
+    FiberForceVelocityDeGroote2016,
+    FiberForceVelocityInverseDeGroote2016,
+    TendonForceLengthDeGroote2016,
+    TendonForceLengthInverseDeGroote2016,
+)
+from sympy.physics.biomechanics.musculotendon import (
+    MusculotendonBase,
+    MusculotendonDeGroote2016,
+    MusculotendonFormulation,
+)
+from sympy.physics.biomechanics._mixin import _NamedMixin
+from sympy.physics.mechanics.actuator import ForceActuator
+from sympy.physics.mechanics.pathway import LinearPathway
+from sympy.physics.vector.frame import ReferenceFrame
+from sympy.physics.vector.functions import dynamicsymbols
+from sympy.physics.vector.point import Point
+from sympy.simplify.simplify import simplify
+
+
+class TestMusculotendonFormulation:
+    @staticmethod
+    def test_rigid_tendon_member():
+        assert MusculotendonFormulation(0) == 0
+        assert MusculotendonFormulation.RIGID_TENDON == 0
+
+    @staticmethod
+    def test_fiber_length_explicit_member():
+        assert MusculotendonFormulation(1) == 1
+        assert MusculotendonFormulation.FIBER_LENGTH_EXPLICIT == 1
+
+    @staticmethod
+    def test_tendon_force_explicit_member():
+        assert MusculotendonFormulation(2) == 2
+        assert MusculotendonFormulation.TENDON_FORCE_EXPLICIT == 2
+
+    @staticmethod
+    def test_fiber_length_implicit_member():
+        assert MusculotendonFormulation(3) == 3
+        assert MusculotendonFormulation.FIBER_LENGTH_IMPLICIT == 3
+
+    @staticmethod
+    def test_tendon_force_implicit_member():
+        assert MusculotendonFormulation(4) == 4
+        assert MusculotendonFormulation.TENDON_FORCE_IMPLICIT == 4
+
+
+class TestMusculotendonBase:
+
+    @staticmethod
+    def test_is_abstract_base_class():
+        assert issubclass(MusculotendonBase, abc.ABC)
+
+    @staticmethod
+    def test_class():
+        assert issubclass(MusculotendonBase, ForceActuator)
+        assert issubclass(MusculotendonBase, _NamedMixin)
+        assert MusculotendonBase.__name__ == 'MusculotendonBase'
+
+    @staticmethod
+    def test_cannot_instantiate_directly():
+        with pytest.raises(TypeError):
+            _ = MusculotendonBase()
+
+
+@pytest.mark.parametrize('musculotendon_concrete', [MusculotendonDeGroote2016])
+class TestMusculotendonRigidTendon:
+
+    @pytest.fixture(autouse=True)
+    def _musculotendon_rigid_tendon_fixture(self, musculotendon_concrete):
+        self.name = 'name'
+        self.N = ReferenceFrame('N')
+        self.q = dynamicsymbols('q')
+        self.origin = Point('pO')
+        self.insertion = Point('pI')
+        self.insertion.set_pos(self.origin, self.q*self.N.x)
+        self.pathway = LinearPathway(self.origin, self.insertion)
+        self.activation = FirstOrderActivationDeGroote2016(self.name)
+        self.e = self.activation.excitation
+        self.a = self.activation.activation
+        self.tau_a = self.activation.activation_time_constant
+        self.tau_d = self.activation.deactivation_time_constant
+        self.b = self.activation.smoothing_rate
+        self.formulation = MusculotendonFormulation.RIGID_TENDON
+        self.l_T_slack = Symbol('l_T_slack')
+        self.F_M_max = Symbol('F_M_max')
+        self.l_M_opt = Symbol('l_M_opt')
+        self.v_M_max = Symbol('v_M_max')
+        self.alpha_opt = Symbol('alpha_opt')
+        self.beta = Symbol('beta')
+        self.instance = musculotendon_concrete(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=self.formulation,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        self.da_expr = (
+            (1/(self.tau_a*(Rational(1, 2) + Rational(3, 2)*self.a)))
+            *(Rational(1, 2) + Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+            + ((Rational(1, 2) + Rational(3, 2)*self.a)/self.tau_d)
+            *(Rational(1, 2) - Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+        )*(self.e - self.a)
+
+    def test_state_vars(self):
+        assert hasattr(self.instance, 'x')
+        assert hasattr(self.instance, 'state_vars')
+        assert self.instance.x == self.instance.state_vars
+        x_expected = Matrix([self.a])
+        assert self.instance.x == x_expected
+        assert self.instance.state_vars == x_expected
+        assert isinstance(self.instance.x, Matrix)
+        assert isinstance(self.instance.state_vars, Matrix)
+        assert self.instance.x.shape == (1, 1)
+        assert self.instance.state_vars.shape == (1, 1)
+
+    def test_input_vars(self):
+        assert hasattr(self.instance, 'r')
+        assert hasattr(self.instance, 'input_vars')
+        assert self.instance.r == self.instance.input_vars
+        r_expected = Matrix([self.e])
+        assert self.instance.r == r_expected
+        assert self.instance.input_vars == r_expected
+        assert isinstance(self.instance.r, Matrix)
+        assert isinstance(self.instance.input_vars, Matrix)
+        assert self.instance.r.shape == (1, 1)
+        assert self.instance.input_vars.shape == (1, 1)
+
+    def test_constants(self):
+        assert hasattr(self.instance, 'p')
+        assert hasattr(self.instance, 'constants')
+        assert self.instance.p == self.instance.constants
+        p_expected = Matrix(
+            [
+                self.l_T_slack,
+                self.F_M_max,
+                self.l_M_opt,
+                self.v_M_max,
+                self.alpha_opt,
+                self.beta,
+                self.tau_a,
+                self.tau_d,
+                self.b,
+                Symbol('c_0_fl_T_name'),
+                Symbol('c_1_fl_T_name'),
+                Symbol('c_2_fl_T_name'),
+                Symbol('c_3_fl_T_name'),
+                Symbol('c_0_fl_M_pas_name'),
+                Symbol('c_1_fl_M_pas_name'),
+                Symbol('c_0_fl_M_act_name'),
+                Symbol('c_1_fl_M_act_name'),
+                Symbol('c_2_fl_M_act_name'),
+                Symbol('c_3_fl_M_act_name'),
+                Symbol('c_4_fl_M_act_name'),
+                Symbol('c_5_fl_M_act_name'),
+                Symbol('c_6_fl_M_act_name'),
+                Symbol('c_7_fl_M_act_name'),
+                Symbol('c_8_fl_M_act_name'),
+                Symbol('c_9_fl_M_act_name'),
+                Symbol('c_10_fl_M_act_name'),
+                Symbol('c_11_fl_M_act_name'),
+                Symbol('c_0_fv_M_name'),
+                Symbol('c_1_fv_M_name'),
+                Symbol('c_2_fv_M_name'),
+                Symbol('c_3_fv_M_name'),
+            ]
+        )
+        assert self.instance.p == p_expected
+        assert self.instance.constants == p_expected
+        assert isinstance(self.instance.p, Matrix)
+        assert isinstance(self.instance.constants, Matrix)
+        assert self.instance.p.shape == (31, 1)
+        assert self.instance.constants.shape == (31, 1)
+
+    def test_M(self):
+        assert hasattr(self.instance, 'M')
+        M_expected = Matrix([1])
+        assert self.instance.M == M_expected
+        assert isinstance(self.instance.M, Matrix)
+        assert self.instance.M.shape == (1, 1)
+
+    def test_F(self):
+        assert hasattr(self.instance, 'F')
+        F_expected = Matrix([self.da_expr])
+        assert self.instance.F == F_expected
+        assert isinstance(self.instance.F, Matrix)
+        assert self.instance.F.shape == (1, 1)
+
+    def test_rhs(self):
+        assert hasattr(self.instance, 'rhs')
+        rhs_expected = Matrix([self.da_expr])
+        rhs = self.instance.rhs()
+        assert isinstance(rhs, Matrix)
+        assert rhs.shape == (1, 1)
+        assert simplify(rhs - rhs_expected) == zeros(1)
+
+
+@pytest.mark.parametrize(
+    'musculotendon_concrete, curve',
+    [
+        (
+            MusculotendonDeGroote2016,
+            CharacteristicCurveCollection(
+                tendon_force_length=TendonForceLengthDeGroote2016,
+                tendon_force_length_inverse=TendonForceLengthInverseDeGroote2016,
+                fiber_force_length_passive=FiberForceLengthPassiveDeGroote2016,
+                fiber_force_length_passive_inverse=FiberForceLengthPassiveInverseDeGroote2016,
+                fiber_force_length_active=FiberForceLengthActiveDeGroote2016,
+                fiber_force_velocity=FiberForceVelocityDeGroote2016,
+                fiber_force_velocity_inverse=FiberForceVelocityInverseDeGroote2016,
+            ),
+        )
+    ],
+)
+class TestFiberLengthExplicit:
+
+    @pytest.fixture(autouse=True)
+    def _musculotendon_fiber_length_explicit_fixture(
+        self,
+        musculotendon_concrete,
+        curve,
+    ):
+        self.name = 'name'
+        self.N = ReferenceFrame('N')
+        self.q = dynamicsymbols('q')
+        self.origin = Point('pO')
+        self.insertion = Point('pI')
+        self.insertion.set_pos(self.origin, self.q*self.N.x)
+        self.pathway = LinearPathway(self.origin, self.insertion)
+        self.activation = FirstOrderActivationDeGroote2016(self.name)
+        self.e = self.activation.excitation
+        self.a = self.activation.activation
+        self.tau_a = self.activation.activation_time_constant
+        self.tau_d = self.activation.deactivation_time_constant
+        self.b = self.activation.smoothing_rate
+        self.formulation = MusculotendonFormulation.FIBER_LENGTH_EXPLICIT
+        self.l_T_slack = Symbol('l_T_slack')
+        self.F_M_max = Symbol('F_M_max')
+        self.l_M_opt = Symbol('l_M_opt')
+        self.v_M_max = Symbol('v_M_max')
+        self.alpha_opt = Symbol('alpha_opt')
+        self.beta = Symbol('beta')
+        self.instance = musculotendon_concrete(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=self.formulation,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+            with_defaults=True,
+        )
+        self.l_M_tilde = dynamicsymbols('l_M_tilde_name')
+        l_MT = self.pathway.length
+        l_M = self.l_M_tilde*self.l_M_opt
+        l_T = l_MT - sqrt(l_M**2 - (self.l_M_opt*sin(self.alpha_opt))**2)
+        fl_T = curve.tendon_force_length.with_defaults(l_T/self.l_T_slack)
+        fl_M_pas = curve.fiber_force_length_passive.with_defaults(self.l_M_tilde)
+        fl_M_act = curve.fiber_force_length_active.with_defaults(self.l_M_tilde)
+        v_M_tilde = curve.fiber_force_velocity_inverse.with_defaults(
+            ((((fl_T*self.F_M_max)/((l_MT - l_T)/l_M))/self.F_M_max) - fl_M_pas)
+            /(self.a*fl_M_act)
+        )
+        self.dl_M_tilde_expr = (self.v_M_max/self.l_M_opt)*v_M_tilde
+        self.da_expr = (
+            (1/(self.tau_a*(Rational(1, 2) + Rational(3, 2)*self.a)))
+            *(Rational(1, 2) + Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+            + ((Rational(1, 2) + Rational(3, 2)*self.a)/self.tau_d)
+            *(Rational(1, 2) - Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+        )*(self.e - self.a)
+
+    def test_state_vars(self):
+        assert hasattr(self.instance, 'x')
+        assert hasattr(self.instance, 'state_vars')
+        assert self.instance.x == self.instance.state_vars
+        x_expected = Matrix([self.l_M_tilde, self.a])
+        assert self.instance.x == x_expected
+        assert self.instance.state_vars == x_expected
+        assert isinstance(self.instance.x, Matrix)
+        assert isinstance(self.instance.state_vars, Matrix)
+        assert self.instance.x.shape == (2, 1)
+        assert self.instance.state_vars.shape == (2, 1)
+
+    def test_input_vars(self):
+        assert hasattr(self.instance, 'r')
+        assert hasattr(self.instance, 'input_vars')
+        assert self.instance.r == self.instance.input_vars
+        r_expected = Matrix([self.e])
+        assert self.instance.r == r_expected
+        assert self.instance.input_vars == r_expected
+        assert isinstance(self.instance.r, Matrix)
+        assert isinstance(self.instance.input_vars, Matrix)
+        assert self.instance.r.shape == (1, 1)
+        assert self.instance.input_vars.shape == (1, 1)
+
+    def test_constants(self):
+        assert hasattr(self.instance, 'p')
+        assert hasattr(self.instance, 'constants')
+        assert self.instance.p == self.instance.constants
+        p_expected = Matrix(
+            [
+                self.l_T_slack,
+                self.F_M_max,
+                self.l_M_opt,
+                self.v_M_max,
+                self.alpha_opt,
+                self.beta,
+                self.tau_a,
+                self.tau_d,
+                self.b,
+            ]
+        )
+        assert self.instance.p == p_expected
+        assert self.instance.constants == p_expected
+        assert isinstance(self.instance.p, Matrix)
+        assert isinstance(self.instance.constants, Matrix)
+        assert self.instance.p.shape == (9, 1)
+        assert self.instance.constants.shape == (9, 1)
+
+    def test_M(self):
+        assert hasattr(self.instance, 'M')
+        M_expected = eye(2)
+        assert self.instance.M == M_expected
+        assert isinstance(self.instance.M, Matrix)
+        assert self.instance.M.shape == (2, 2)
+
+    def test_F(self):
+        assert hasattr(self.instance, 'F')
+        F_expected = Matrix([self.dl_M_tilde_expr, self.da_expr])
+        assert self.instance.F == F_expected
+        assert isinstance(self.instance.F, Matrix)
+        assert self.instance.F.shape == (2, 1)
+
+    def test_rhs(self):
+        assert hasattr(self.instance, 'rhs')
+        rhs_expected = Matrix([self.dl_M_tilde_expr, self.da_expr])
+        rhs = self.instance.rhs()
+        assert isinstance(rhs, Matrix)
+        assert rhs.shape == (2, 1)
+        assert simplify(rhs - rhs_expected) == zeros(2, 1)
+
+
+@pytest.mark.parametrize(
+    'musculotendon_concrete, curve',
+    [
+        (
+            MusculotendonDeGroote2016,
+            CharacteristicCurveCollection(
+                tendon_force_length=TendonForceLengthDeGroote2016,
+                tendon_force_length_inverse=TendonForceLengthInverseDeGroote2016,
+                fiber_force_length_passive=FiberForceLengthPassiveDeGroote2016,
+                fiber_force_length_passive_inverse=FiberForceLengthPassiveInverseDeGroote2016,
+                fiber_force_length_active=FiberForceLengthActiveDeGroote2016,
+                fiber_force_velocity=FiberForceVelocityDeGroote2016,
+                fiber_force_velocity_inverse=FiberForceVelocityInverseDeGroote2016,
+            ),
+        )
+    ],
+)
+class TestTendonForceExplicit:
+
+    @pytest.fixture(autouse=True)
+    def _musculotendon_tendon_force_explicit_fixture(
+        self,
+        musculotendon_concrete,
+        curve,
+    ):
+        self.name = 'name'
+        self.N = ReferenceFrame('N')
+        self.q = dynamicsymbols('q')
+        self.origin = Point('pO')
+        self.insertion = Point('pI')
+        self.insertion.set_pos(self.origin, self.q*self.N.x)
+        self.pathway = LinearPathway(self.origin, self.insertion)
+        self.activation = FirstOrderActivationDeGroote2016(self.name)
+        self.e = self.activation.excitation
+        self.a = self.activation.activation
+        self.tau_a = self.activation.activation_time_constant
+        self.tau_d = self.activation.deactivation_time_constant
+        self.b = self.activation.smoothing_rate
+        self.formulation = MusculotendonFormulation.TENDON_FORCE_EXPLICIT
+        self.l_T_slack = Symbol('l_T_slack')
+        self.F_M_max = Symbol('F_M_max')
+        self.l_M_opt = Symbol('l_M_opt')
+        self.v_M_max = Symbol('v_M_max')
+        self.alpha_opt = Symbol('alpha_opt')
+        self.beta = Symbol('beta')
+        self.instance = musculotendon_concrete(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=self.formulation,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+            with_defaults=True,
+        )
+        self.F_T_tilde = dynamicsymbols('F_T_tilde_name')
+        l_T_tilde = curve.tendon_force_length_inverse.with_defaults(self.F_T_tilde)
+        l_MT = self.pathway.length
+        v_MT = self.pathway.extension_velocity
+        l_T = l_T_tilde*self.l_T_slack
+        l_M = sqrt((l_MT - l_T)**2 + (self.l_M_opt*sin(self.alpha_opt))**2)
+        l_M_tilde = l_M/self.l_M_opt
+        cos_alpha = (l_MT - l_T)/l_M
+        F_T = self.F_T_tilde*self.F_M_max
+        F_M = F_T/cos_alpha
+        F_M_tilde = F_M/self.F_M_max
+        fl_M_pas = curve.fiber_force_length_passive.with_defaults(l_M_tilde)
+        fl_M_act = curve.fiber_force_length_active.with_defaults(l_M_tilde)
+        fv_M = (F_M_tilde - fl_M_pas)/(self.a*fl_M_act)
+        v_M_tilde = curve.fiber_force_velocity_inverse.with_defaults(fv_M)
+        v_M = v_M_tilde*self.v_M_max
+        v_T = v_MT - v_M/cos_alpha
+        v_T_tilde = v_T/self.l_T_slack
+        self.dF_T_tilde_expr = (
+            Float('0.2')*Float('33.93669377311689')*exp(
+                Float('33.93669377311689')*UnevaluatedExpr(l_T_tilde - Float('0.995'))
+            )*v_T_tilde
+        )
+        self.da_expr = (
+            (1/(self.tau_a*(Rational(1, 2) + Rational(3, 2)*self.a)))
+            *(Rational(1, 2) + Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+            + ((Rational(1, 2) + Rational(3, 2)*self.a)/self.tau_d)
+            *(Rational(1, 2) - Rational(1, 2)*tanh(self.b*(self.e - self.a)))
+        )*(self.e - self.a)
+
+    def test_state_vars(self):
+        assert hasattr(self.instance, 'x')
+        assert hasattr(self.instance, 'state_vars')
+        assert self.instance.x == self.instance.state_vars
+        x_expected = Matrix([self.F_T_tilde, self.a])
+        assert self.instance.x == x_expected
+        assert self.instance.state_vars == x_expected
+        assert isinstance(self.instance.x, Matrix)
+        assert isinstance(self.instance.state_vars, Matrix)
+        assert self.instance.x.shape == (2, 1)
+        assert self.instance.state_vars.shape == (2, 1)
+
+    def test_input_vars(self):
+        assert hasattr(self.instance, 'r')
+        assert hasattr(self.instance, 'input_vars')
+        assert self.instance.r == self.instance.input_vars
+        r_expected = Matrix([self.e])
+        assert self.instance.r == r_expected
+        assert self.instance.input_vars == r_expected
+        assert isinstance(self.instance.r, Matrix)
+        assert isinstance(self.instance.input_vars, Matrix)
+        assert self.instance.r.shape == (1, 1)
+        assert self.instance.input_vars.shape == (1, 1)
+
+    def test_constants(self):
+        assert hasattr(self.instance, 'p')
+        assert hasattr(self.instance, 'constants')
+        assert self.instance.p == self.instance.constants
+        p_expected = Matrix(
+            [
+                self.l_T_slack,
+                self.F_M_max,
+                self.l_M_opt,
+                self.v_M_max,
+                self.alpha_opt,
+                self.beta,
+                self.tau_a,
+                self.tau_d,
+                self.b,
+            ]
+        )
+        assert self.instance.p == p_expected
+        assert self.instance.constants == p_expected
+        assert isinstance(self.instance.p, Matrix)
+        assert isinstance(self.instance.constants, Matrix)
+        assert self.instance.p.shape == (9, 1)
+        assert self.instance.constants.shape == (9, 1)
+
+    def test_M(self):
+        assert hasattr(self.instance, 'M')
+        M_expected = eye(2)
+        assert self.instance.M == M_expected
+        assert isinstance(self.instance.M, Matrix)
+        assert self.instance.M.shape == (2, 2)
+
+    def test_F(self):
+        assert hasattr(self.instance, 'F')
+        F_expected = Matrix([self.dF_T_tilde_expr, self.da_expr])
+        assert self.instance.F == F_expected
+        assert isinstance(self.instance.F, Matrix)
+        assert self.instance.F.shape == (2, 1)
+
+    def test_rhs(self):
+        assert hasattr(self.instance, 'rhs')
+        rhs_expected = Matrix([self.dF_T_tilde_expr, self.da_expr])
+        rhs = self.instance.rhs()
+        assert isinstance(rhs, Matrix)
+        assert rhs.shape == (2, 1)
+        assert simplify(rhs - rhs_expected) == zeros(2, 1)
+
+
+class TestMusculotendonDeGroote2016:
+
+    @staticmethod
+    def test_class():
+        assert issubclass(MusculotendonDeGroote2016, ForceActuator)
+        assert issubclass(MusculotendonDeGroote2016, _NamedMixin)
+        assert MusculotendonDeGroote2016.__name__ == 'MusculotendonDeGroote2016'
+
+    @staticmethod
+    def test_instance():
+        origin = Point('pO')
+        insertion = Point('pI')
+        insertion.set_pos(origin, dynamicsymbols('q')*ReferenceFrame('N').x)
+        pathway = LinearPathway(origin, insertion)
+        activation = FirstOrderActivationDeGroote2016('name')
+        l_T_slack = Symbol('l_T_slack')
+        F_M_max = Symbol('F_M_max')
+        l_M_opt = Symbol('l_M_opt')
+        v_M_max = Symbol('v_M_max')
+        alpha_opt = Symbol('alpha_opt')
+        beta = Symbol('beta')
+        instance = MusculotendonDeGroote2016(
+            'name',
+            pathway,
+            activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=l_T_slack,
+            peak_isometric_force=F_M_max,
+            optimal_fiber_length=l_M_opt,
+            maximal_fiber_velocity=v_M_max,
+            optimal_pennation_angle=alpha_opt,
+            fiber_damping_coefficient=beta,
+        )
+        assert isinstance(instance, MusculotendonDeGroote2016)
+
+    @pytest.fixture(autouse=True)
+    def _musculotendon_fixture(self):
+        self.name = 'name'
+        self.N = ReferenceFrame('N')
+        self.q = dynamicsymbols('q')
+        self.origin = Point('pO')
+        self.insertion = Point('pI')
+        self.insertion.set_pos(self.origin, self.q*self.N.x)
+        self.pathway = LinearPathway(self.origin, self.insertion)
+        self.activation = FirstOrderActivationDeGroote2016(self.name)
+        self.l_T_slack = Symbol('l_T_slack')
+        self.F_M_max = Symbol('F_M_max')
+        self.l_M_opt = Symbol('l_M_opt')
+        self.v_M_max = Symbol('v_M_max')
+        self.alpha_opt = Symbol('alpha_opt')
+        self.beta = Symbol('beta')
+
+    def test_with_defaults(self):
+        origin = Point('pO')
+        insertion = Point('pI')
+        insertion.set_pos(origin, dynamicsymbols('q')*ReferenceFrame('N').x)
+        pathway = LinearPathway(origin, insertion)
+        activation = FirstOrderActivationDeGroote2016('name')
+        l_T_slack = Symbol('l_T_slack')
+        F_M_max = Symbol('F_M_max')
+        l_M_opt = Symbol('l_M_opt')
+        v_M_max = Float('10.0')
+        alpha_opt = Float('0.0')
+        beta = Float('0.1')
+        instance = MusculotendonDeGroote2016.with_defaults(
+            'name',
+            pathway,
+            activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=l_T_slack,
+            peak_isometric_force=F_M_max,
+            optimal_fiber_length=l_M_opt,
+        )
+        assert instance.tendon_slack_length == l_T_slack
+        assert instance.peak_isometric_force == F_M_max
+        assert instance.optimal_fiber_length == l_M_opt
+        assert instance.maximal_fiber_velocity == v_M_max
+        assert instance.optimal_pennation_angle == alpha_opt
+        assert instance.fiber_damping_coefficient == beta
+
+    @pytest.mark.parametrize(
+        'l_T_slack, expected',
+        [
+            (None, Symbol('l_T_slack_name')),
+            (Symbol('l_T_slack'), Symbol('l_T_slack')),
+            (Rational(1, 2), Rational(1, 2)),
+            (Float('0.5'), Float('0.5')),
+        ],
+    )
+    def test_tendon_slack_length(self, l_T_slack, expected):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        assert instance.l_T_slack == expected
+        assert instance.tendon_slack_length == expected
+
+    @pytest.mark.parametrize(
+        'F_M_max, expected',
+        [
+            (None, Symbol('F_M_max_name')),
+            (Symbol('F_M_max'), Symbol('F_M_max')),
+            (Integer(1000), Integer(1000)),
+            (Float('1000.0'), Float('1000.0')),
+        ],
+    )
+    def test_peak_isometric_force(self, F_M_max, expected):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        assert instance.F_M_max == expected
+        assert instance.peak_isometric_force == expected
+
+    @pytest.mark.parametrize(
+        'l_M_opt, expected',
+        [
+            (None, Symbol('l_M_opt_name')),
+            (Symbol('l_M_opt'), Symbol('l_M_opt')),
+            (Rational(1, 2), Rational(1, 2)),
+            (Float('0.5'), Float('0.5')),
+        ],
+    )
+    def test_optimal_fiber_length(self, l_M_opt, expected):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        assert instance.l_M_opt == expected
+        assert instance.optimal_fiber_length == expected
+
+    @pytest.mark.parametrize(
+        'v_M_max, expected',
+        [
+            (None, Symbol('v_M_max_name')),
+            (Symbol('v_M_max'), Symbol('v_M_max')),
+            (Integer(10), Integer(10)),
+            (Float('10.0'), Float('10.0')),
+        ],
+    )
+    def test_maximal_fiber_velocity(self, v_M_max, expected):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        assert instance.v_M_max == expected
+        assert instance.maximal_fiber_velocity == expected
+
+    @pytest.mark.parametrize(
+        'alpha_opt, expected',
+        [
+            (None, Symbol('alpha_opt_name')),
+            (Symbol('alpha_opt'), Symbol('alpha_opt')),
+            (Integer(0), Integer(0)),
+            (Float('0.1'), Float('0.1')),
+        ],
+    )
+    def test_optimal_pennation_angle(self, alpha_opt, expected):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        assert instance.alpha_opt == expected
+        assert instance.optimal_pennation_angle == expected
+
+    @pytest.mark.parametrize(
+        'beta, expected',
+        [
+            (None, Symbol('beta_name')),
+            (Symbol('beta'), Symbol('beta')),
+            (Integer(0), Integer(0)),
+            (Rational(1, 10), Rational(1, 10)),
+            (Float('0.1'), Float('0.1')),
+        ],
+    )
+    def test_fiber_damping_coefficient(self, beta, expected):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=beta,
+        )
+        assert instance.beta == expected
+        assert instance.fiber_damping_coefficient == expected
+
+    def test_excitation(self):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+        )
+        assert hasattr(instance, 'e')
+        assert hasattr(instance, 'excitation')
+        e_expected = dynamicsymbols('e_name')
+        assert instance.e == e_expected
+        assert instance.excitation == e_expected
+        assert instance.e is instance.excitation
+
+    def test_excitation_is_immutable(self):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+        )
+        with pytest.raises(AttributeError):
+            instance.e = None
+        with pytest.raises(AttributeError):
+            instance.excitation = None
+
+    def test_activation(self):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+        )
+        assert hasattr(instance, 'a')
+        assert hasattr(instance, 'activation')
+        a_expected = dynamicsymbols('a_name')
+        assert instance.a == a_expected
+        assert instance.activation == a_expected
+
+    def test_activation_is_immutable(self):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+        )
+        with pytest.raises(AttributeError):
+            instance.a = None
+        with pytest.raises(AttributeError):
+            instance.activation = None
+
+    def test_repr(self):
+        instance = MusculotendonDeGroote2016(
+            self.name,
+            self.pathway,
+            self.activation,
+            musculotendon_dynamics=MusculotendonFormulation.RIGID_TENDON,
+            tendon_slack_length=self.l_T_slack,
+            peak_isometric_force=self.F_M_max,
+            optimal_fiber_length=self.l_M_opt,
+            maximal_fiber_velocity=self.v_M_max,
+            optimal_pennation_angle=self.alpha_opt,
+            fiber_damping_coefficient=self.beta,
+        )
+        expected = (
+            'MusculotendonDeGroote2016(\'name\', '
+            'pathway=LinearPathway(pO, pI), '
+            'activation_dynamics=FirstOrderActivationDeGroote2016(\'name\', '
+            'activation_time_constant=tau_a_name, '
+            'deactivation_time_constant=tau_d_name, '
+            'smoothing_rate=b_name), '
+            'musculotendon_dynamics=0, '
+            'tendon_slack_length=l_T_slack, '
+            'peak_isometric_force=F_M_max, '
+            'optimal_fiber_length=l_M_opt, '
+            'maximal_fiber_velocity=v_M_max, '
+            'optimal_pennation_angle=alpha_opt, '
+            'fiber_damping_coefficient=beta)'
+        )
+        assert repr(instance) == expected
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..781429110cab760f8990961c6536e7267a2a371a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/__init__.py
@@ -0,0 +1,10 @@
+__all__ = ['Beam',
+            'Truss',
+            'Cable',
+            'Arch'
+            ]
+
+from .beam import Beam
+from .truss import Truss
+from .cable import Cable
+from .arch import Arch
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/arch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/arch.py
new file mode 100644
index 0000000000000000000000000000000000000000..31e2b41e841638f6a8002da1a7c843a9f5b35555
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/arch.py
@@ -0,0 +1,1025 @@
+"""
+This module can be used to solve probelsm related to 2D parabolic arches
+"""
+from sympy.core.sympify import sympify
+from sympy.core.symbol import Symbol,symbols
+from sympy import diff, sqrt, cos , sin, atan, rad, Min
+from sympy.core.relational import Eq
+from sympy.solvers.solvers import solve
+from sympy.functions import Piecewise
+from sympy.plotting import plot
+from sympy import limit
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.external.importtools import import_module
+
+numpy = import_module('numpy', import_kwargs={'fromlist':['arange']})
+
+class Arch:
+    """
+    This class is used to solve problems related to a three hinged arch(determinate) structure.\n
+    An arch is a curved vertical structure spanning an open space underneath it.\n
+    Arches can be used to reduce the bending moments in long-span structures.\n
+
+    Arches are used in structural engineering(over windows, door and even bridges)\n
+    because they can support a very large mass placed on top of them.
+
+    Example
+    ========
+    >>> from sympy.physics.continuum_mechanics.arch import Arch
+    >>> a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+    >>> a.get_shape_eqn
+    5 - (x - 5)**2/5
+
+    >>> from sympy.physics.continuum_mechanics.arch import Arch
+    >>> a = Arch((0,0),(10,1),crown_x=6)
+    >>> a.get_shape_eqn
+    9/5 - (x - 6)**2/20
+    """
+    def __init__(self,left_support,right_support,**kwargs):
+        self._shape_eqn = None
+        self._left_support  = (sympify(left_support[0]),sympify(left_support[1]))
+        self._right_support  = (sympify(right_support[0]),sympify(right_support[1]))
+        self._crown_x = None
+        self._crown_y = None
+        if 'crown_x' in kwargs:
+            self._crown_x = sympify(kwargs['crown_x'])
+        if 'crown_y' in kwargs:
+            self._crown_y = sympify(kwargs['crown_y'])
+        self._shape_eqn = self.get_shape_eqn
+        self._conc_loads = {}
+        self._distributed_loads = {}
+        self._loads = {'concentrated': self._conc_loads, 'distributed':self._distributed_loads}
+        self._loads_applied = {}
+        self._supports = {'left':'hinge', 'right':'hinge'}
+        self._member = None
+        self._member_force = None
+        self._reaction_force = {Symbol('R_A_x'):0, Symbol('R_A_y'):0, Symbol('R_B_x'):0, Symbol('R_B_y'):0}
+        self._points_disc_x = set()
+        self._points_disc_y = set()
+        self._moment_x  = {}
+        self._moment_y = {}
+        self._load_x = {}
+        self._load_y = {}
+        self._moment_x_func = Piecewise((0,True))
+        self._moment_y_func = Piecewise((0,True))
+        self._load_x_func = Piecewise((0,True))
+        self._load_y_func = Piecewise((0,True))
+        self._bending_moment = None
+        self._shear_force = None
+        self._axial_force = None
+        # self._crown = (sympify(crown[0]),sympify(crown[1]))
+
+    @property
+    def get_shape_eqn(self):
+        "returns the equation of the shape of arch developed"
+        if self._shape_eqn:
+            return self._shape_eqn
+
+        x,y,c = symbols('x y c')
+        a = Symbol('a',positive=False)
+        if self._crown_x and self._crown_y:
+            x0  = self._crown_x
+            y0 = self._crown_y
+            parabola_eqn = a*(x-x0)**2 + y0 - y
+            eq1 = parabola_eqn.subs({x:self._left_support[0], y:self._left_support[1]})
+            solution = solve((eq1),(a))
+            parabola_eqn = solution[0]*(x-x0)**2 + y0
+            if(parabola_eqn.subs({x:self._right_support[0]}) != self._right_support[1]):
+                raise ValueError("provided coordinates of crown and supports are not consistent with parabolic arch")
+
+        elif self._crown_x:
+            x0  = self._crown_x
+            parabola_eqn = a*(x-x0)**2 + c - y
+            eq1 = parabola_eqn.subs({x:self._left_support[0], y:self._left_support[1]})
+            eq2 = parabola_eqn.subs({x:self._right_support[0], y:self._right_support[1]})
+            solution = solve((eq1,eq2),(a,c))
+            if len(solution) <2 or solution[a] == 0:
+                raise ValueError("parabolic arch cannot be constructed with the provided coordinates, try providing crown_y")
+            parabola_eqn = solution[a]*(x-x0)**2+ solution[c]
+            self._crown_y = solution[c]
+
+        else:
+            raise KeyError("please provide crown_x to construct arch")
+
+        return parabola_eqn
+
+    @property
+    def get_loads(self):
+        """
+        return the position of the applied load and angle (for concentrated loads)
+        """
+        return self._loads
+
+    @property
+    def supports(self):
+        """
+        Returns the type of support
+        """
+        return self._supports
+
+    @property
+    def left_support(self):
+        """
+        Returns the position of the left support.
+        """
+        return self._left_support
+
+    @property
+    def right_support(self):
+        """
+        Returns the position of the right support.
+        """
+        return self._right_support
+
+    @property
+    def reaction_force(self):
+        """
+        return the reaction forces generated
+        """
+        return self._reaction_force
+
+    def apply_load(self,order,label,start,mag,end=None,angle=None):
+        """
+        This method adds load to the Arch.
+
+        Parameters
+        ==========
+
+            order : Integer
+                Order of the applied load.
+
+                    - For point/concentrated loads, order = -1
+                    - For distributed load, order = 0
+
+            label : String or Symbol
+                The label of the load
+                - should not use 'A' or 'B' as it is used for supports.
+
+            start : Float
+
+                    - For concentrated/point loads, start is the x coordinate
+                    - For distributed loads, start is the starting position of distributed load
+
+            mag : Sympifyable
+                Magnitude of the applied load. Must be positive
+
+            end : Float
+                Required for distributed loads
+
+                    - For concentrated/point load , end is None(may not be given)
+                    - For distributed loads, end is the end position of distributed load
+
+            angle: Sympifyable
+                The angle in degrees, the load vector makes with the horizontal
+                in the counter-clockwise direction.
+
+        Examples
+        ========
+        For applying distributed load
+
+        >>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+        >>> a.apply_load(0,'C',start=3,end=5,mag=-10)
+
+        For applying point/concentrated_loads
+
+        >>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+        >>> a.apply_load(-1,'C',start=2,mag=15,angle=45)
+
+        """
+        y = Symbol('y')
+        x = Symbol('x')
+        x0 = Symbol('x0')
+        # y0 = Symbol('y0')
+        order= sympify(order)
+        mag = sympify(mag)
+        angle = sympify(angle)
+
+        if label in self._loads_applied:
+            raise ValueError("load with the given label already exists")
+
+        if label in ['A','B']:
+            raise ValueError("cannot use the given label, reserved for supports")
+
+        if order == 0:
+            if end is None or end>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+        >>> a.apply_load(0,'C',start=3,end=5,mag=-10)
+        >>> a.remove_load('C')
+        removed load C: {'start': 3, 'end': 5, 'f_y': -10}
+        """
+        y = Symbol('y')
+        x = Symbol('x')
+        x0 = Symbol('x0')
+
+        if label in self._distributed_loads :
+
+            self._loads_applied.pop(label)
+            start = self._distributed_loads[label]['start']
+            end = self._distributed_loads[label]['end']
+            mag  = self._distributed_loads[label]['f_y']
+            self._points_disc_y.remove(start)
+            self._load_y[start] -= mag*(Min(x,end)-start)
+            self._moment_y[start] += mag*(Min(x,end)-start)*(x0-(start+(Min(x,end)))/2)
+            val = self._distributed_loads.pop(label)
+            print(f"removed load {label}: {val}")
+
+        elif label in self._conc_loads :
+
+            self._loads_applied.pop(label)
+            start = self._conc_loads[label]['x']
+            self._points_disc_x.remove(start)
+            self._points_disc_y.remove(start)
+            self._moment_y[start] += self._conc_loads[label]['f_y']*(x0-start)
+            self._moment_x[start] -= self._conc_loads[label]['f_x']*(y-self._conc_loads[label]['y'])
+            self._load_x[start] -= self._conc_loads[label]['f_x']
+            self._load_y[start] -= self._conc_loads[label]['f_y']
+            val = self._conc_loads.pop(label)
+            print(f"removed load {label}: {val}")
+
+        else :
+            raise ValueError("label not found")
+
+    def change_support_position(self, left_support=None, right_support=None):
+        """
+        Change position of supports.
+        If not provided , defaults to the old value.
+        Parameters
+        ==========
+
+            left_support: tuple (x, y)
+                x: float
+                    x-coordinate value of the left_support
+
+                y: float
+                    y-coordinate value of the left_support
+
+            right_support: tuple (x, y)
+                x: float
+                    x-coordinate value of the right_support
+
+                y: float
+                    y-coordinate value of the right_support
+        """
+        if left_support is not None:
+            self._left_support = (left_support[0],left_support[1])
+
+        if right_support is not None:
+            self._right_support = (right_support[0],right_support[1])
+
+        self._shape_eqn = None
+        self._shape_eqn = self.get_shape_eqn
+
+    def change_crown_position(self,crown_x=None,crown_y=None):
+        """
+        Change the position of the crown/hinge of the arch
+
+        Parameters
+        ==========
+
+            crown_x: Float
+                The x coordinate of the position of the hinge
+                - if not provided, defaults to old value
+
+            crown_y: Float
+                The y coordinate of the position of the hinge
+                - if not provided defaults to None
+        """
+        self._crown_x = crown_x
+        self._crown_y = crown_y
+        self._shape_eqn = None
+        self._shape_eqn = self.get_shape_eqn
+
+    def change_support_type(self,left_support=None,right_support=None):
+        """
+        Add the type for support at each end.
+        Can use roller or hinge support at each end.
+
+        Parameters
+        ==========
+
+            left_support, right_support : string
+                Type of support at respective end
+
+                    - For roller support , left_support/right_support = "roller"
+                    - For hinged support, left_support/right_support = "hinge"
+                    - defaults to hinge if value not provided
+
+        Examples
+        ========
+
+        For applying roller support at right end
+
+        >>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+        >>> a.change_support_type(right_support="roller")
+
+        """
+        support_types = ['roller','hinge']
+        if left_support:
+            if left_support not in support_types:
+                raise ValueError("supports must only be roller or hinge")
+
+            self._supports['left'] = left_support
+
+        if right_support:
+            if right_support not in support_types:
+                raise ValueError("supports must only be roller or hinge")
+
+            self._supports['right'] = right_support
+
+    def add_member(self,y):
+        """
+        This method adds a member/rod at a particular height y.
+        A rod is used for stability of the structure in case of a roller support.
+        """
+        if y>self._crown_y or y>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+        >>> a.apply_load(0,'C',start=3,end=5,mag=-10)
+        >>> a.solve()
+        >>> a.reaction_force
+        {R_A_x: 8, R_A_y: 12, R_B_x: -8, R_B_y: 8}
+
+        >>> from sympy import Symbol
+        >>> t = Symbol('t')
+        >>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(16,0),crown_x=8,crown_y=5)
+        >>> a.apply_load(0,'C',start=3,end=5,mag=t)
+        >>> a.solve()
+        >>> a.reaction_force
+        {R_A_x: -4*t/5, R_A_y: -3*t/2, R_B_x: 4*t/5, R_B_y: -t/2}
+
+        >>> a.bending_moment_at(4)
+        -5*t/2
+        """
+        y = Symbol('y')
+        x = Symbol('x')
+        x0 = Symbol('x0')
+
+        discontinuity_points_x = sorted(self._points_disc_x)
+        discontinuity_points_y = sorted(self._points_disc_y)
+
+        self._moment_x_func = Piecewise((0,True))
+        self._moment_y_func = Piecewise((0,True))
+
+        self._load_x_func = Piecewise((0,True))
+        self._load_y_func = Piecewise((0,True))
+
+        accumulated_x_moment = 0
+        accumulated_y_moment = 0
+
+        accumulated_x_load = 0
+        accumulated_y_load = 0
+
+        for point in discontinuity_points_x:
+            cond = (x >= point)
+            accumulated_x_load += self._load_x[point]
+            accumulated_x_moment += self._moment_x[point]
+            self._load_x_func = Piecewise((accumulated_x_load,cond),(self._load_x_func,True))
+            self._moment_x_func = Piecewise((accumulated_x_moment,cond),(self._moment_x_func,True))
+
+        for point in discontinuity_points_y:
+            cond = (x >= point)
+            accumulated_y_moment += self._moment_y[point]
+            accumulated_y_load += self._load_y[point]
+            self._load_y_func = Piecewise((accumulated_y_load,cond),(self._load_y_func,True))
+            self._moment_y_func = Piecewise((accumulated_y_moment,cond),(self._moment_y_func,True))
+
+        moment_A = self._moment_y_func.subs(x,self._right_support[0]).subs(x0,self._left_support[0]) +\
+                   self._moment_x_func.subs(x,self._right_support[0]).subs(y,self._left_support[1])
+
+        moment_hinge_left = self._moment_y_func.subs(x,self._crown_x).subs(x0,self._crown_x) +\
+                            self._moment_x_func.subs(x,self._crown_x).subs(y,self._crown_y)
+
+        moment_hinge_right = self._moment_y_func.subs(x,self._right_support[0]).subs(x0,self._crown_x)- \
+                             self._moment_y_func.subs(x,self._crown_x).subs(x0,self._crown_x) +\
+                             self._moment_x_func.subs(x,self._right_support[0]).subs(y,self._crown_y) -\
+                             self._moment_x_func.subs(x,self._crown_x).subs(y,self._crown_y)
+
+        net_x = self._load_x_func.subs(x,self._right_support[0])
+        net_y = self._load_y_func.subs(x,self._right_support[0])
+
+        if (self._supports['left']=='roller' or self._supports['right']=='roller') and not self._member:
+            print("member must be added if any of the supports is roller")
+            return
+
+        R_A_x, R_A_y, R_B_x, R_B_y, T = symbols('R_A_x R_A_y R_B_x R_B_y T')
+
+        if self._supports['left'] == 'roller' and self._supports['right'] == 'roller':
+
+            if self._member[2]>=max(self._left_support[1],self._right_support[1]):
+
+                if net_x!=0:
+                    raise ValueError("net force in x direction not possible under the specified conditions")
+
+                else:
+                    eq1 = Eq(R_A_x ,0)
+                    eq2 = Eq(R_B_x, 0)
+                    eq3 = Eq(R_A_y + R_B_y + net_y,0)
+
+                    eq4 = Eq(R_B_y*(self._right_support[0]-self._left_support[0])-\
+                             R_B_x*(self._right_support[1]-self._left_support[1])+moment_A,0)
+
+                    eq5 = Eq(moment_hinge_right + R_B_y*(self._right_support[0]-self._crown_x) +\
+                             T*(self._member[2]-self._crown_y),0)
+                    solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+            elif self._member[2]>=self._left_support[1]:
+                eq1 = Eq(R_A_x ,0)
+                eq2 = Eq(R_B_x, 0)
+                eq3 = Eq(R_A_y + R_B_y + net_y,0)
+                eq4 = Eq(R_B_y*(self._right_support[0]-self._left_support[0])-\
+                         T*(self._member[2]-self._left_support[1])+moment_A,0)
+                eq5 = Eq(T+net_x,0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+            elif self._member[2]>=self._right_support[1]:
+                eq1 = Eq(R_A_x ,0)
+                eq2 = Eq(R_B_x, 0)
+                eq3 = Eq(R_A_y + R_B_y + net_y,0)
+                eq4 = Eq(R_B_y*(self._right_support[0]-self._left_support[0])+\
+                         T*(self._member[2]-self._left_support[1])+moment_A,0)
+                eq5 = Eq(T-net_x,0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+        elif self._supports['left'] == 'roller':
+            if self._member[2]>=max(self._left_support[1], self._right_support[1]):
+                eq1 = Eq(R_A_x ,0)
+                eq2 = Eq(R_B_x+net_x,0)
+                eq3 = Eq(R_A_y + R_B_y + net_y,0)
+                eq4 = Eq(R_B_y*(self._right_support[0]-self._left_support[0])-\
+                         R_B_x*(self._right_support[1]-self._left_support[1])+moment_A,0)
+                eq5 = Eq(moment_hinge_left + R_A_y*(self._left_support[0]-self._crown_x) -\
+                         T*(self._member[2]-self._crown_y),0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+            elif self._member[2]>=self._left_support[1]:
+                eq1 = Eq(R_A_x ,0)
+                eq2 = Eq(R_B_x+ T +net_x,0)
+                eq3 = Eq(R_A_y + R_B_y + net_y,0)
+                eq4 = Eq(R_B_y*(self._right_support[0]-self._left_support[0])-\
+                         R_B_x*(self._right_support[1]-self._left_support[1])-\
+                         T*(self._member[2]-self._left_support[0])+moment_A,0)
+                eq5 = Eq(moment_hinge_left + R_A_y*(self._left_support[0]-self._crown_x)-\
+                         T*(self._member[2]-self._crown_y),0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+            elif self._member[2]>=self._right_support[0]:
+                eq1 = Eq(R_A_x,0)
+                eq2 = Eq(R_B_x- T +net_x,0)
+                eq3 = Eq(R_A_y + R_B_y + net_y,0)
+                eq4 = Eq(moment_hinge_left+R_A_y*(self._left_support[0]-self._crown_x),0)
+                eq5 = Eq(moment_A+R_B_y*(self._right_support[0]-self._left_support[0])-\
+                         R_B_x*(self._right_support[1]-self._left_support[1])+\
+                         T*(self._member[2]-self._left_support[1]),0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+        elif self._supports['right'] == 'roller':
+            if self._member[2]>=max(self._left_support[1], self._right_support[1]):
+                eq1 = Eq(R_B_x,0)
+                eq2 = Eq(R_A_x+net_x,0)
+                eq3 = Eq(R_A_y+R_B_y+net_y,0)
+                eq4 = Eq(moment_hinge_right+R_B_y*(self._right_support[0]-self._crown_x)+\
+                         T*(self._member[2]-self._crown_y),0)
+                eq5 = Eq(moment_A+R_B_y*(self._right_support[0]-self._left_support[0]),0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+            elif self._member[2]>=self._left_support[1]:
+                eq1 = Eq(R_B_x,0)
+                eq2 = Eq(R_A_x+T+net_x,0)
+                eq3 = Eq(R_A_y+R_B_y+net_y,0)
+                eq4 = Eq(moment_hinge_right+R_B_y*(self._right_support[0]-self._crown_x),0)
+                eq5 = Eq(moment_A-T*(self._member[2]-self._left_support[1])+\
+                         R_B_y*(self._right_support[0]-self._left_support[0]),0)
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+
+            elif self._member[2]>=self._right_support[1]:
+                eq1 = Eq(R_B_x,0)
+                eq2 = Eq(R_A_x-T+net_x,0)
+                eq3 = Eq(R_A_y+R_B_y+net_y,0)
+                eq4 = Eq(moment_hinge_right+R_B_y*(self._right_support[0]-self._crown_x)+\
+                         T*(self._member[2]-self._crown_y),0)
+                eq5 = Eq(moment_A+T*(self._member[2]-self._left_support[1])+\
+                         R_B_y*(self._right_support[0]-self._left_support[0]))
+                solution = solve((eq1,eq2,eq3,eq4,eq5),(R_A_x,R_A_y,R_B_x,R_B_y,T))
+        else:
+            eq1 = Eq(R_A_x + R_B_x + net_x,0)
+            eq2 = Eq(R_A_y + R_B_y + net_y,0)
+            eq3 = Eq(R_B_y*(self._right_support[0]-self._left_support[0])-\
+                     R_B_x*(self._right_support[1]-self._left_support[1])+moment_A,0)
+            eq4 = Eq(moment_hinge_right + R_B_y*(self._right_support[0]-self._crown_x) -\
+                     R_B_x*(self._right_support[1]-self._crown_y),0)
+            solution = solve((eq1,eq2,eq3,eq4),(R_A_x,R_A_y,R_B_x,R_B_y))
+
+        for symb in self._reaction_force:
+            self._reaction_force[symb] = solution[symb]
+
+        self._bending_moment = - (self._moment_x_func.subs(x,x0) + self._moment_y_func.subs(x,x0) -\
+                                  solution[R_A_y]*(x0-self._left_support[0]) +\
+                                  solution[R_A_x]*(self._shape_eqn.subs({x:x0})-self._left_support[1]))
+
+        angle  = atan(diff(self._shape_eqn,x))
+
+        fx = (self._load_x_func+solution[R_A_x])
+        fy = (self._load_y_func+solution[R_A_y])
+
+        axial_force = fx*cos(angle) + fy*sin(angle)
+        shear_force = -fx*sin(angle) + fy*cos(angle)
+
+        self._axial_force = axial_force
+        self._shear_force = shear_force
+
+    @doctest_depends_on(modules=('numpy',))
+    def draw(self):
+        """
+        This method returns a plot object containing the diagram of the specified arch along with the supports
+        and forces applied to the structure.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> t = Symbol('t')
+        >>> from sympy.physics.continuum_mechanics.arch import Arch
+        >>> a = Arch((0,0),(40,0),crown_x=20,crown_y=12)
+        >>> a.apply_load(-1,'C',8,150,angle=270)
+        >>> a.apply_load(0,'D',start=20,end=40,mag=-4)
+        >>> a.apply_load(-1,'E',10,t,angle=300)
+        >>> p = a.draw()
+        >>> p # doctest: +ELLIPSIS
+        Plot object containing:
+        [0]: cartesian line: 11.325 - 3*(x - 20)**2/100 for x over (0.0, 40.0)
+        [1]: cartesian line: 12 - 3*(x - 20)**2/100 for x over (0.0, 40.0)
+        ...
+        >>> p.show()
+
+        """
+        x = Symbol('x')
+        markers = []
+        annotations = self._draw_loads()
+        rectangles = []
+        supports = self._draw_supports()
+        markers+=supports
+
+        xmax = self._right_support[0]
+        xmin = self._left_support[0]
+        ymin = min(self._left_support[1],self._right_support[1])
+        ymax = self._crown_y
+
+        lim = max(xmax*1.1-xmin*0.8+1, ymax*1.1-ymin*0.8+1)
+
+        rectangles = self._draw_rectangles()
+
+        filler = self._draw_filler()
+        rectangles+=filler
+
+        if self._member is not None:
+            if(self._member[2]>=self._right_support[1]):
+                markers.append(
+                    {
+                        'args':[[self._member[1]+0.005*lim],[self._member[2]]],
+                        'marker':'o',
+                        'markersize': 4,
+                        'color': 'white',
+                        'markerfacecolor':'none'
+                    }
+                )
+
+            if(self._member[2]>=self._left_support[1]):
+                markers.append(
+                    {
+                        'args':[[self._member[0]-0.005*lim],[self._member[2]]],
+                        'marker':'o',
+                        'markersize': 4,
+                        'color': 'white',
+                        'markerfacecolor':'none'
+                    }
+                )
+
+
+
+        markers.append({
+            'args':[[self._crown_x],[self._crown_y-0.005*lim]],
+            'marker':'o',
+            'markersize': 5,
+            'color':'white',
+            'markerfacecolor':'none',
+        })
+
+        if lim==xmax*1.1-xmin*0.8+1:
+
+            sing_plot = plot(self._shape_eqn-0.015*lim,
+                             self._shape_eqn,
+                             (x, self._left_support[0], self._right_support[0]),
+                             markers=markers,
+                             show=False,
+                             annotations=annotations,
+                             rectangles = rectangles,
+                             xlim=(xmin-0.05*lim, xmax*1.1),
+                             ylim=(xmin-0.05*lim, xmax*1.1),
+                             axis=False,
+                             line_color='brown')
+
+        else:
+            sing_plot = plot(self._shape_eqn-0.015*lim,
+                             self._shape_eqn,
+                             (x, self._left_support[0], self._right_support[0]),
+                             markers=markers,
+                             show=False,
+                             annotations=annotations,
+                             rectangles = rectangles,
+                             xlim=(ymin-0.05*lim, ymax*1.1),
+                             ylim=(ymin-0.05*lim, ymax*1.1),
+                             axis=False,
+                             line_color='brown')
+
+        return sing_plot
+
+
+    def _draw_supports(self):
+        support_markers = []
+
+        xmax = self._right_support[0]
+        xmin = self._left_support[0]
+        ymin = min(self._left_support[1],self._right_support[1])
+        ymax = self._crown_y
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        if self._supports['left']=='roller':
+            support_markers.append(
+                {
+                    'args':[
+                        [self._left_support[0]],
+                        [self._left_support[1]-0.02*max_diff]
+                    ],
+                    'marker':'o',
+                    'markersize':11,
+                    'color':'black',
+                    'markerfacecolor':'none'
+                }
+            )
+        else:
+            support_markers.append(
+                {
+                    'args':[
+                        [self._left_support[0]],
+                        [self._left_support[1]-0.007*max_diff]
+                    ],
+                    'marker':6,
+                    'markersize':15,
+                    'color':'black',
+                    'markerfacecolor':'none'
+                }
+            )
+
+        if self._supports['right']=='roller':
+            support_markers.append(
+                {
+                    'args':[
+                        [self._right_support[0]],
+                        [self._right_support[1]-0.02*max_diff]
+                    ],
+                    'marker':'o',
+                    'markersize':11,
+                    'color':'black',
+                    'markerfacecolor':'none'
+                }
+            )
+        else:
+            support_markers.append(
+                {
+                    'args':[
+                        [self._right_support[0]],
+                        [self._right_support[1]-0.007*max_diff]
+                    ],
+                    'marker':6,
+                    'markersize':15,
+                    'color':'black',
+                    'markerfacecolor':'none'
+                }
+            )
+
+        support_markers.append(
+            {
+                'args':[
+                    [self._right_support[0]],
+                    [self._right_support[1]-0.036*max_diff]
+                ],
+                'marker':'_',
+                'markersize':15,
+                'color':'black',
+                'markerfacecolor':'none'
+            }
+        )
+
+        support_markers.append(
+            {
+                'args':[
+                    [self._left_support[0]],
+                    [self._left_support[1]-0.036*max_diff]
+                ],
+                'marker':'_',
+                'markersize':15,
+                'color':'black',
+                'markerfacecolor':'none'
+            }
+        )
+
+        return support_markers
+
+    def _draw_rectangles(self):
+        member = []
+
+        xmax = self._right_support[0]
+        xmin = self._left_support[0]
+        ymin = min(self._left_support[1],self._right_support[1])
+        ymax = self._crown_y
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        if self._member is not None:
+            if self._member[2]>= max(self._left_support[1],self._right_support[1]):
+                member.append(
+                    {
+                        'xy':(self._member[0],self._member[2]-0.005*max_diff),
+                        'width':self._member[1]-self._member[0],
+                        'height': 0.01*max_diff,
+                        'angle': 0,
+                        'color':'brown',
+                    }
+                )
+
+            elif self._member[2]>=self._left_support[1]:
+                member.append(
+                    {
+                        'xy':(self._member[0],self._member[2]-0.005*max_diff),
+                        'width':self._right_support[0]-self._member[0],
+                        'height': 0.01*max_diff,
+                        'angle': 0,
+                        'color':'brown',
+                    }
+                )
+
+            else:
+                member.append(
+                    {
+                        'xy':(self._member[1],self._member[2]-0.005*max_diff),
+                        'width':abs(self._left_support[0]-self._member[1]),
+                        'height': 0.01*max_diff,
+                        'angle': 180,
+                        'color':'brown',
+                    }
+                )
+
+        if self._distributed_loads:
+            for loads in self._distributed_loads:
+
+                start = self._distributed_loads[loads]['start']
+                end = self._distributed_loads[loads]['end']
+
+                member.append(
+                    {
+                        'xy':(start,self._crown_y+max_diff*0.15),
+                        'width': (end-start),
+                        'height': max_diff*0.01,
+                        'color': 'orange'
+                    }
+                )
+
+
+        return member
+
+    def _draw_loads(self):
+        load_annotations = []
+
+        xmax = self._right_support[0]
+        xmin = self._left_support[0]
+        ymin = min(self._left_support[1],self._right_support[1])
+        ymax = self._crown_y
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        for load in self._conc_loads:
+            x = self._conc_loads[load]['x']
+            y = self._conc_loads[load]['y']
+            angle = self._conc_loads[load]['angle']
+            mag = self._conc_loads[load]['mag']
+            load_annotations.append(
+                {
+                    'text':'',
+                    'xy':(
+                        x+cos(rad(angle))*max_diff*0.08,
+                        y+sin(rad(angle))*max_diff*0.08
+                    ),
+                    'xytext':(x,y),
+                    'fontsize':10,
+                    'fontweight': 'bold',
+                    'arrowprops':{'width':1.5, 'headlength':5, 'headwidth':5, 'facecolor':'blue','edgecolor':'blue'}
+                }
+            )
+            load_annotations.append(
+                {
+                    'text':f'{load}: {mag} N',
+                    'fontsize':10,
+                    'fontweight': 'bold',
+                    'xy': (x+cos(rad(angle))*max_diff*0.12,y+sin(rad(angle))*max_diff*0.12)
+                }
+            )
+
+        for load in self._distributed_loads:
+            start = self._distributed_loads[load]['start']
+            end = self._distributed_loads[load]['end']
+            mag = self._distributed_loads[load]['f_y']
+            x_points = numpy.arange(start,end,(end-start)/(max_diff*0.25))
+            x_points = numpy.append(x_points,end)
+            for point in x_points:
+                if(mag<0):
+                    load_annotations.append(
+                        {
+                            'text':'',
+                            'xy':(point,self._crown_y+max_diff*0.05),
+                            'xytext': (point,self._crown_y+max_diff*0.15),
+                            'arrowprops':{'width':1.5, 'headlength':5, 'headwidth':5, 'facecolor':'orange','edgecolor':'orange'}
+                        }
+                    )
+                else:
+                    load_annotations.append(
+                        {
+                            'text':'',
+                            'xy':(point,self._crown_y+max_diff*0.2),
+                            'xytext': (point,self._crown_y+max_diff*0.15),
+                            'arrowprops':{'width':1.5, 'headlength':5, 'headwidth':5, 'facecolor':'orange','edgecolor':'orange'}
+                        }
+                    )
+            if(mag<0):
+                load_annotations.append(
+                    {
+                        'text':f'{load}: {abs(mag)} N/m',
+                        'fontsize':10,
+                        'fontweight': 'bold',
+                        'xy':((start+end)/2,self._crown_y+max_diff*0.175)
+                    }
+                )
+            else:
+                load_annotations.append(
+                    {
+                        'text':f'{load}: {abs(mag)} N/m',
+                        'fontsize':10,
+                        'fontweight': 'bold',
+                        'xy':((start+end)/2,self._crown_y+max_diff*0.125)
+                    }
+                )
+        return load_annotations
+
+    def _draw_filler(self):
+        x = Symbol('x')
+        filler = []
+        xmax = self._right_support[0]
+        xmin = self._left_support[0]
+        ymin = min(self._left_support[1],self._right_support[1])
+        ymax = self._crown_y
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        x_points = numpy.arange(self._left_support[0],self._right_support[0],(self._right_support[0]-self._left_support[0])/(max_diff*max_diff))
+
+        for point in x_points:
+            filler.append(
+                    {
+                        'xy':(point,self._shape_eqn.subs(x,point)-max_diff*0.015),
+                        'width': (self._right_support[0]-self._left_support[0])/(max_diff*max_diff),
+                        'height': max_diff*0.015,
+                        'color': 'brown'
+                    }
+            )
+
+        return filler
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/beam.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/beam.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfdfc6d3594da6de44c7c42def3e3f5539cb988e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/beam.py
@@ -0,0 +1,3903 @@
+"""
+This module can be used to solve 2D beam bending problems with
+singularity functions in mechanics.
+"""
+
+from sympy.core import S, Symbol, diff, symbols
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.function import (Derivative, Function)
+from sympy.core.mul import Mul
+from sympy.core.relational import Eq
+from sympy.core.sympify import sympify
+from sympy.solvers import linsolve
+from sympy.solvers.ode.ode import dsolve
+from sympy.solvers.solvers import solve
+from sympy.printing import sstr
+from sympy.functions import SingularityFunction, Piecewise, factorial
+from sympy.integrals import integrate
+from sympy.series import limit
+from sympy.plotting import plot, PlotGrid
+from sympy.geometry.entity import GeometryEntity
+from sympy.external import import_module
+from sympy.sets.sets import Interval
+from sympy.utilities.lambdify import lambdify
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.utilities.iterables import iterable
+import warnings
+
+
+__doctest_requires__ = {
+    ('Beam.draw',
+     'Beam.plot_bending_moment',
+     'Beam.plot_deflection',
+     'Beam.plot_ild_moment',
+     'Beam.plot_ild_shear',
+     'Beam.plot_shear_force',
+     'Beam.plot_shear_stress',
+     'Beam.plot_slope'): ['matplotlib'],
+}
+
+
+numpy = import_module('numpy', import_kwargs={'fromlist':['arange']})
+
+
+class Beam:
+    """
+    A Beam is a structural element that is capable of withstanding load
+    primarily by resisting against bending. Beams are characterized by
+    their cross sectional profile(Second moment of area), their length
+    and their material.
+
+    .. note::
+       A consistent sign convention must be used while solving a beam
+       bending problem; the results will
+       automatically follow the chosen sign convention. However, the
+       chosen sign convention must respect the rule that, on the positive
+       side of beam's axis (in respect to current section), a loading force
+       giving positive shear yields a negative moment, as below (the
+       curved arrow shows the positive moment and rotation):
+
+    .. image:: allowed-sign-conventions.png
+
+    Examples
+    ========
+    There is a beam of length 4 meters. A constant distributed load of 6 N/m
+    is applied from half of the beam till the end. There are two simple supports
+    below the beam, one at the starting point and another at the ending point
+    of the beam. The deflection of the beam at the end is restricted.
+
+    Using the sign convention of downwards forces being positive.
+
+    >>> from sympy.physics.continuum_mechanics.beam import Beam
+    >>> from sympy import symbols, Piecewise
+    >>> E, I = symbols('E, I')
+    >>> R1, R2 = symbols('R1, R2')
+    >>> b = Beam(4, E, I)
+    >>> b.apply_load(R1, 0, -1)
+    >>> b.apply_load(6, 2, 0)
+    >>> b.apply_load(R2, 4, -1)
+    >>> b.bc_deflection = [(0, 0), (4, 0)]
+    >>> b.boundary_conditions
+    {'bending_moment': [], 'deflection': [(0, 0), (4, 0)], 'shear_force': [], 'slope': []}
+    >>> b.load
+    R1*SingularityFunction(x, 0, -1) + R2*SingularityFunction(x, 4, -1) + 6*SingularityFunction(x, 2, 0)
+    >>> b.solve_for_reaction_loads(R1, R2)
+    >>> b.load
+    -3*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 2, 0) - 9*SingularityFunction(x, 4, -1)
+    >>> b.shear_force()
+    3*SingularityFunction(x, 0, 0) - 6*SingularityFunction(x, 2, 1) + 9*SingularityFunction(x, 4, 0)
+    >>> b.bending_moment()
+    3*SingularityFunction(x, 0, 1) - 3*SingularityFunction(x, 2, 2) + 9*SingularityFunction(x, 4, 1)
+    >>> b.slope()
+    (-3*SingularityFunction(x, 0, 2)/2 + SingularityFunction(x, 2, 3) - 9*SingularityFunction(x, 4, 2)/2 + 7)/(E*I)
+    >>> b.deflection()
+    (7*x - SingularityFunction(x, 0, 3)/2 + SingularityFunction(x, 2, 4)/4 - 3*SingularityFunction(x, 4, 3)/2)/(E*I)
+    >>> b.deflection().rewrite(Piecewise)
+    (7*x - Piecewise((x**3, x >= 0), (0, True))/2
+         - 3*Piecewise(((x - 4)**3, x >= 4), (0, True))/2
+         + Piecewise(((x - 2)**4, x >= 2), (0, True))/4)/(E*I)
+
+    Calculate the support reactions for a fully symbolic beam of length L.
+    There are two simple supports below the beam, one at the starting point
+    and another at the ending point of the beam. The deflection of the beam
+    at the end is restricted. The beam is loaded with:
+
+    * a downward point load P1 applied at L/4
+    * an upward point load P2 applied at L/8
+    * a counterclockwise moment M1 applied at L/2
+    * a clockwise moment M2 applied at 3*L/4
+    * a distributed constant load q1, applied downward, starting from L/2
+      up to 3*L/4
+    * a distributed constant load q2, applied upward, starting from 3*L/4
+      up to L
+
+    No assumptions are needed for symbolic loads. However, defining a positive
+    length will help the algorithm to compute the solution.
+
+    >>> E, I = symbols('E, I')
+    >>> L = symbols("L", positive=True)
+    >>> P1, P2, M1, M2, q1, q2 = symbols("P1, P2, M1, M2, q1, q2")
+    >>> R1, R2 = symbols('R1, R2')
+    >>> b = Beam(L, E, I)
+    >>> b.apply_load(R1, 0, -1)
+    >>> b.apply_load(R2, L, -1)
+    >>> b.apply_load(P1, L/4, -1)
+    >>> b.apply_load(-P2, L/8, -1)
+    >>> b.apply_load(M1, L/2, -2)
+    >>> b.apply_load(-M2, 3*L/4, -2)
+    >>> b.apply_load(q1, L/2, 0, 3*L/4)
+    >>> b.apply_load(-q2, 3*L/4, 0, L)
+    >>> b.bc_deflection = [(0, 0), (L, 0)]
+    >>> b.solve_for_reaction_loads(R1, R2)
+    >>> print(b.reaction_loads[R1])
+    (-3*L**2*q1 + L**2*q2 - 24*L*P1 + 28*L*P2 - 32*M1 + 32*M2)/(32*L)
+    >>> print(b.reaction_loads[R2])
+    (-5*L**2*q1 + 7*L**2*q2 - 8*L*P1 + 4*L*P2 + 32*M1 - 32*M2)/(32*L)
+    """
+
+    def __init__(self, length, elastic_modulus, second_moment, area=Symbol('A'), variable=Symbol('x'), base_char='C', ild_variable=Symbol('a')):
+        """Initializes the class.
+
+        Parameters
+        ==========
+
+        length : Sympifyable
+            A Symbol or value representing the Beam's length.
+
+        elastic_modulus : Sympifyable
+            A SymPy expression representing the Beam's Modulus of Elasticity.
+            It is a measure of the stiffness of the Beam material. It can
+            also be a continuous function of position along the beam.
+
+        second_moment : Sympifyable or Geometry object
+            Describes the cross-section of the beam via a SymPy expression
+            representing the Beam's second moment of area. It is a geometrical
+            property of an area which reflects how its points are distributed
+            with respect to its neutral axis. It can also be a continuous
+            function of position along the beam. Alternatively ``second_moment``
+            can be a shape object such as a ``Polygon`` from the geometry module
+            representing the shape of the cross-section of the beam. In such cases,
+            it is assumed that the x-axis of the shape object is aligned with the
+            bending axis of the beam. The second moment of area will be computed
+            from the shape object internally.
+
+        area : Symbol/float
+            Represents the cross-section area of beam
+
+        variable : Symbol, optional
+            A Symbol object that will be used as the variable along the beam
+            while representing the load, shear, moment, slope and deflection
+            curve. By default, it is set to ``Symbol('x')``.
+
+        base_char : String, optional
+            A String that will be used as base character to generate sequential
+            symbols for integration constants in cases where boundary conditions
+            are not sufficient to solve them.
+
+        ild_variable : Symbol, optional
+            A Symbol object that will be used as the variable specifying the
+            location of the moving load in ILD calculations. By default, it
+            is set to ``Symbol('a')``.
+        """
+        self.length = length
+        self.elastic_modulus = elastic_modulus
+        if isinstance(second_moment, GeometryEntity):
+            self.cross_section = second_moment
+        else:
+            self.cross_section = None
+            self.second_moment = second_moment
+        self.variable = variable
+        self.ild_variable = ild_variable
+        self._base_char = base_char
+        self._boundary_conditions = {'deflection': [], 'slope': [], 'bending_moment': [], 'shear_force': []}
+        self._load = 0
+        self.area = area
+        self._applied_supports = []
+        self._applied_rotation_hinges = []
+        self._applied_sliding_hinges = []
+        self._rotation_hinge_symbols = []
+        self._sliding_hinge_symbols = []
+        self._support_as_loads = []
+        self._applied_loads = []
+        self._reaction_loads = {}
+        self._ild_reactions = {}
+        self._ild_shear = 0
+        self._ild_moment = 0
+        # _original_load is a copy of _load equations with unsubstituted reaction
+        # forces. It is used for calculating reaction forces in case of I.L.D.
+        self._original_load = 0
+        self._joined_beam = False
+
+    def __str__(self):
+        shape_description = self._cross_section if self._cross_section else self._second_moment
+        str_sol = 'Beam({}, {}, {})'.format(sstr(self._length), sstr(self._elastic_modulus), sstr(shape_description))
+        return str_sol
+
+    @property
+    def reaction_loads(self):
+        """ Returns the reaction forces in a dictionary."""
+        return self._reaction_loads
+
+    @property
+    def rotation_jumps(self):
+        """
+        Returns the value for the rotation jumps in rotation hinges in a dictionary.
+        The rotation jump is the rotation (in radian) in a rotation hinge. This can
+        be seen as a jump in the slope plot.
+        """
+        return self._rotation_jumps
+
+    @property
+    def deflection_jumps(self):
+        """
+        Returns the deflection jumps in sliding hinges in a dictionary.
+        The deflection jump is the deflection (in meters) in a sliding hinge.
+        This can be seen as a jump in the deflection plot.
+        """
+        return self._deflection_jumps
+
+    @property
+    def ild_shear(self):
+        """ Returns the I.L.D. shear equation."""
+        return self._ild_shear
+
+    @property
+    def ild_reactions(self):
+        """ Returns the I.L.D. reaction forces in a dictionary."""
+        return self._ild_reactions
+
+    @property
+    def ild_rotation_jumps(self):
+        """
+        Returns the I.L.D. rotation jumps in rotation hinges in a dictionary.
+        The rotation jump is the rotation (in radian) in a rotation hinge. This can
+        be seen as a jump in the slope plot.
+        """
+        return self._ild_rotations_jumps
+
+    @property
+    def ild_deflection_jumps(self):
+        """
+        Returns the I.L.D. deflection jumps in sliding hinges in a dictionary.
+        The deflection jump is the deflection (in meters) in a sliding hinge.
+        This can be seen as a jump in the deflection plot.
+        """
+        return self._ild_deflection_jumps
+
+    @property
+    def ild_moment(self):
+        """ Returns the I.L.D. moment equation."""
+        return self._ild_moment
+
+    @property
+    def length(self):
+        """Length of the Beam."""
+        return self._length
+
+    @length.setter
+    def length(self, l):
+        self._length = sympify(l)
+
+    @property
+    def area(self):
+        """Cross-sectional area of the Beam. """
+        return self._area
+
+    @area.setter
+    def area(self, a):
+        self._area = sympify(a)
+
+    @property
+    def variable(self):
+        """
+        A symbol that can be used as a variable along the length of the beam
+        while representing load distribution, shear force curve, bending
+        moment, slope curve and the deflection curve. By default, it is set
+        to ``Symbol('x')``, but this property is mutable.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I, A = symbols('E, I, A')
+        >>> x, y, z = symbols('x, y, z')
+        >>> b = Beam(4, E, I)
+        >>> b.variable
+        x
+        >>> b.variable = y
+        >>> b.variable
+        y
+        >>> b = Beam(4, E, I, A, z)
+        >>> b.variable
+        z
+        """
+        return self._variable
+
+    @variable.setter
+    def variable(self, v):
+        if isinstance(v, Symbol):
+            self._variable = v
+        else:
+            raise TypeError("""The variable should be a Symbol object.""")
+
+    @property
+    def elastic_modulus(self):
+        """Young's Modulus of the Beam. """
+        return self._elastic_modulus
+
+    @elastic_modulus.setter
+    def elastic_modulus(self, e):
+        self._elastic_modulus = sympify(e)
+
+    @property
+    def second_moment(self):
+        """Second moment of area of the Beam. """
+        return self._second_moment
+
+    @second_moment.setter
+    def second_moment(self, i):
+        self._cross_section = None
+        if isinstance(i, GeometryEntity):
+            raise ValueError("To update cross-section geometry use `cross_section` attribute")
+        else:
+            self._second_moment = sympify(i)
+
+    @property
+    def cross_section(self):
+        """Cross-section of the beam"""
+        return self._cross_section
+
+    @cross_section.setter
+    def cross_section(self, s):
+        if s:
+            self._second_moment = s.second_moment_of_area()[0]
+        self._cross_section = s
+
+    @property
+    def boundary_conditions(self):
+        """
+        Returns a dictionary of boundary conditions applied on the beam.
+        The dictionary has three keywords namely moment, slope and deflection.
+        The value of each keyword is a list of tuple, where each tuple
+        contains location and value of a boundary condition in the format
+        (location, value).
+
+        Examples
+        ========
+        There is a beam of length 4 meters. The bending moment at 0 should be 4
+        and at 4 it should be 0. The slope of the beam should be 1 at 0. The
+        deflection should be 2 at 0.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(4, E, I)
+        >>> b.bc_deflection = [(0, 2)]
+        >>> b.bc_slope = [(0, 1)]
+        >>> b.boundary_conditions
+        {'bending_moment': [], 'deflection': [(0, 2)], 'shear_force': [], 'slope': [(0, 1)]}
+
+        Here the deflection of the beam should be ``2`` at ``0``.
+        Similarly, the slope of the beam should be ``1`` at ``0``.
+        """
+        return self._boundary_conditions
+
+    @property
+    def bc_shear_force(self):
+        return self._boundary_conditions['shear_force']
+
+    @bc_shear_force.setter
+    def bc_shear_force(self, sf_bcs):
+        self._boundary_conditions['shear_force'] = sf_bcs
+
+    @property
+    def bc_bending_moment(self):
+        return self._boundary_conditions['bending_moment']
+
+    @bc_bending_moment.setter
+    def bc_bending_moment(self, bm_bcs):
+        self._boundary_conditions['bending_moment'] = bm_bcs
+
+    @property
+    def bc_slope(self):
+        return self._boundary_conditions['slope']
+
+    @bc_slope.setter
+    def bc_slope(self, s_bcs):
+        self._boundary_conditions['slope'] = s_bcs
+
+    @property
+    def bc_deflection(self):
+        return self._boundary_conditions['deflection']
+
+    @bc_deflection.setter
+    def bc_deflection(self, d_bcs):
+        self._boundary_conditions['deflection'] = d_bcs
+
+    def join(self, beam, via="fixed"):
+        """
+        This method joins two beams to make a new composite beam system.
+        Passed Beam class instance is attached to the right end of calling
+        object. This method can be used to form beams having Discontinuous
+        values of Elastic modulus or Second moment.
+
+        Parameters
+        ==========
+        beam : Beam class object
+            The Beam object which would be connected to the right of calling
+            object.
+        via : String
+            States the way two Beam object would get connected
+            - For axially fixed Beams, via="fixed"
+            - For Beams connected via rotation hinge, via="hinge"
+
+        Examples
+        ========
+        There is a cantilever beam of length 4 meters. For first 2 meters
+        its moment of inertia is `1.5*I` and `I` for the other end.
+        A pointload of magnitude 4 N is applied from the top at its free end.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> R1, R2 = symbols('R1, R2')
+        >>> b1 = Beam(2, E, 1.5*I)
+        >>> b2 = Beam(2, E, I)
+        >>> b = b1.join(b2, "fixed")
+        >>> b.apply_load(20, 4, -1)
+        >>> b.apply_load(R1, 0, -1)
+        >>> b.apply_load(R2, 0, -2)
+        >>> b.bc_slope = [(0, 0)]
+        >>> b.bc_deflection = [(0, 0)]
+        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.load
+        80*SingularityFunction(x, 0, -2) - 20*SingularityFunction(x, 0, -1) + 20*SingularityFunction(x, 4, -1)
+        >>> b.slope()
+        (-((-80*SingularityFunction(x, 0, 1) + 10*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 4, 2))/I + 120/I)/E + 80.0/(E*I))*SingularityFunction(x, 2, 0)
+        - 0.666666666666667*(-80*SingularityFunction(x, 0, 1) + 10*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 4, 2))*SingularityFunction(x, 0, 0)/(E*I)
+        + 0.666666666666667*(-80*SingularityFunction(x, 0, 1) + 10*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 4, 2))*SingularityFunction(x, 2, 0)/(E*I)
+        """
+        x = self.variable
+        E = self.elastic_modulus
+        new_length = self.length + beam.length
+        if self.elastic_modulus != beam.elastic_modulus:
+            raise NotImplementedError('Joining beams with different Elastic modulus is not implemented.')
+
+        if self.second_moment != beam.second_moment:
+            new_second_moment = Piecewise((self.second_moment, x<=self.length),
+                                    (beam.second_moment, x<=new_length))
+        else:
+            new_second_moment = self.second_moment
+
+        if via == "fixed":
+            new_beam = Beam(new_length, E, new_second_moment, x)
+            new_beam._joined_beam = True
+            return new_beam
+
+        if via == "hinge":
+            new_beam = Beam(new_length, E, new_second_moment, x)
+            new_beam._joined_beam = True
+            new_beam.apply_rotation_hinge(self.length)
+            return new_beam
+
+    def apply_support(self, loc, type="fixed"):
+        """
+        This method applies support to a particular beam object and returns
+        the symbol of the unknown reaction load(s).
+
+        Parameters
+        ==========
+        loc : Sympifyable
+            Location of point at which support is applied.
+        type : String
+            Determines type of Beam support applied. To apply support structure
+            with
+            - zero degree of freedom, type = "fixed"
+            - one degree of freedom, type = "pin"
+            - two degrees of freedom, type = "roller"
+
+        Returns
+        =======
+        Symbol or tuple of Symbol
+            The unknown reaction load as a symbol.
+            - Symbol(reaction_force) if type = "pin" or "roller"
+            - Symbol(reaction_force), Symbol(reaction_moment) if type = "fixed"
+
+        Examples
+        ========
+        There is a beam of length 20 meters. A moment of magnitude 100 Nm is
+        applied in the clockwise direction at the end of the beam. A pointload
+        of magnitude 8 N is applied from the top of the beam at a distance of 10 meters.
+        There is one fixed support at the start of the beam and a roller at the end.
+
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(20, E, I)
+        >>> p0, m0 = b.apply_support(0, 'fixed')
+        >>> p1 = b.apply_support(20, 'roller')
+        >>> b.apply_load(-8, 10, -1)
+        >>> b.apply_load(100, 20, -2)
+        >>> b.solve_for_reaction_loads(p0, m0, p1)
+        >>> b.reaction_loads
+        {M_0: 20, R_0: -2, R_20: 10}
+        >>> b.reaction_loads[p0]
+        -2
+        >>> b.load
+        20*SingularityFunction(x, 0, -2) - 2*SingularityFunction(x, 0, -1)
+        - 8*SingularityFunction(x, 10, -1) + 100*SingularityFunction(x, 20, -2)
+        + 10*SingularityFunction(x, 20, -1)
+        """
+        loc = sympify(loc)
+
+        self._applied_supports.append((loc, type))
+        if type in ("pin", "roller"):
+            reaction_load = Symbol('R_'+str(loc))
+            self.apply_load(reaction_load, loc, -1)
+            self.bc_deflection.append((loc, 0))
+        else:
+            reaction_load = Symbol('R_'+str(loc))
+            reaction_moment = Symbol('M_'+str(loc))
+            self.apply_load(reaction_load, loc, -1)
+            self.apply_load(reaction_moment, loc, -2)
+            self.bc_deflection.append((loc, 0))
+            self.bc_slope.append((loc, 0))
+            self._support_as_loads.append((reaction_moment, loc, -2, None))
+
+        self._support_as_loads.append((reaction_load, loc, -1, None))
+
+        if type in ("pin", "roller"):
+            return reaction_load
+        else:
+            return reaction_load, reaction_moment
+
+    def _get_I(self, loc):
+        """
+        Helper function that returns the Second moment (I) at a location in the beam.
+        """
+        I = self.second_moment
+        if not isinstance(I, Piecewise):
+            return I
+        else:
+            for i in range(len(I.args)):
+                if loc <= I.args[i][1].args[1]:
+                    return I.args[i][0]
+
+    def apply_rotation_hinge(self, loc):
+        """
+        This method applies a rotation hinge at a single location on the beam.
+
+        Parameters
+        ----------
+        loc : Sympifyable
+            Location of point at which hinge is applied.
+
+        Returns
+        =======
+        Symbol
+            The unknown rotation jump multiplied by the elastic modulus and second moment as a symbol.
+
+        Examples
+        ========
+        There is a beam of length 15 meters. Pin supports are placed at distances
+        of 0 and 10 meters. There is a fixed support at the end. There are two rotation hinges
+        in the structure, one at 5 meters and one at 10 meters. A pointload of magnitude
+        10 kN is applied on the hinge at 5 meters. A distributed load of 5 kN works on
+        the structure from 10 meters to the end.
+
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import Symbol
+        >>> E = Symbol('E')
+        >>> I = Symbol('I')
+        >>> b = Beam(15, E, I)
+        >>> r0 = b.apply_support(0, type='pin')
+        >>> r10 = b.apply_support(10, type='pin')
+        >>> r15, m15 = b.apply_support(15, type='fixed')
+        >>> p5 = b.apply_rotation_hinge(5)
+        >>> p12 = b.apply_rotation_hinge(12)
+        >>> b.apply_load(-10, 5, -1)
+        >>> b.apply_load(-5, 10, 0, 15)
+        >>> b.solve_for_reaction_loads(r0, r10, r15, m15)
+        >>> b.reaction_loads
+        {M_15: -75/2, R_0: 0, R_10: 40, R_15: -5}
+        >>> b.rotation_jumps
+        {P_12: -1875/(16*E*I), P_5: 9625/(24*E*I)}
+        >>> b.rotation_jumps[p12]
+        -1875/(16*E*I)
+        >>> b.bending_moment()
+        -9625*SingularityFunction(x, 5, -1)/24 + 10*SingularityFunction(x, 5, 1)
+        - 40*SingularityFunction(x, 10, 1) + 5*SingularityFunction(x, 10, 2)/2
+        + 1875*SingularityFunction(x, 12, -1)/16 + 75*SingularityFunction(x, 15, 0)/2
+        + 5*SingularityFunction(x, 15, 1) - 5*SingularityFunction(x, 15, 2)/2
+        """
+        loc = sympify(loc)
+        E = self.elastic_modulus
+        I = self._get_I(loc)
+
+        rotation_jump = Symbol('P_'+str(loc))
+        self._applied_rotation_hinges.append(loc)
+        self._rotation_hinge_symbols.append(rotation_jump)
+        self.apply_load(E * I * rotation_jump, loc, -3)
+        self.bc_bending_moment.append((loc, 0))
+        return rotation_jump
+
+    def apply_sliding_hinge(self, loc):
+        """
+        This method applies a sliding hinge at a single location on the beam.
+
+        Parameters
+        ----------
+        loc : Sympifyable
+            Location of point at which hinge is applied.
+
+        Returns
+        =======
+        Symbol
+            The unknown deflection jump multiplied by the elastic modulus and second moment as a symbol.
+
+        Examples
+        ========
+        There is a beam of length 13 meters. A fixed support is placed at the beginning.
+        There is a pin support at the end. There is a sliding hinge at a location of 8 meters.
+        A pointload of magnitude 10 kN is applied on the hinge at 5 meters.
+
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> b = Beam(13, 20, 20)
+        >>> r0, m0 = b.apply_support(0, type="fixed")
+        >>> s8 = b.apply_sliding_hinge(8)
+        >>> r13 = b.apply_support(13, type="pin")
+        >>> b.apply_load(-10, 5, -1)
+        >>> b.solve_for_reaction_loads(r0, m0, r13)
+        >>> b.reaction_loads
+        {M_0: -50, R_0: 10, R_13: 0}
+        >>> b.deflection_jumps
+        {W_8: 85/24}
+        >>> b.deflection_jumps[s8]
+        85/24
+        >>> b.bending_moment()
+        50*SingularityFunction(x, 0, 0) - 10*SingularityFunction(x, 0, 1)
+        + 10*SingularityFunction(x, 5, 1) - 4250*SingularityFunction(x, 8, -2)/3
+        >>> b.deflection()
+        -SingularityFunction(x, 0, 2)/16 + SingularityFunction(x, 0, 3)/240
+        - SingularityFunction(x, 5, 3)/240 + 85*SingularityFunction(x, 8, 0)/24
+        """
+        loc = sympify(loc)
+        E = self.elastic_modulus
+        I = self._get_I(loc)
+
+        deflection_jump = Symbol('W_' + str(loc))
+        self._applied_sliding_hinges.append(loc)
+        self._sliding_hinge_symbols.append(deflection_jump)
+        self.apply_load(E * I * deflection_jump, loc, -4)
+        self.bc_shear_force.append((loc, 0))
+        return deflection_jump
+
+    def apply_load(self, value, start, order, end=None):
+        """
+        This method adds up the loads given to a particular beam object.
+
+        Parameters
+        ==========
+        value : Sympifyable
+            The value inserted should have the units [Force/(Distance**(n+1)]
+            where n is the order of applied load.
+            Units for applied loads:
+
+               - For moments, unit = kN*m
+               - For point loads, unit = kN
+               - For constant distributed load, unit = kN/m
+               - For ramp loads, unit = kN/m/m
+               - For parabolic ramp loads, unit = kN/m/m/m
+               - ... so on.
+
+        start : Sympifyable
+            The starting point of the applied load. For point moments and
+            point forces this is the location of application.
+        order : Integer
+            The order of the applied load.
+
+               - For moments, order = -2
+               - For point loads, order =-1
+               - For constant distributed load, order = 0
+               - For ramp loads, order = 1
+               - For parabolic ramp loads, order = 2
+               - ... so on.
+
+        end : Sympifyable, optional
+            An optional argument that can be used if the load has an end point
+            within the length of the beam.
+
+        Examples
+        ========
+        There is a beam of length 4 meters. A moment of magnitude 3 Nm is
+        applied in the clockwise direction at the starting point of the beam.
+        A point load of magnitude 4 N is applied from the top of the beam at
+        2 meters from the starting point and a parabolic ramp load of magnitude
+        2 N/m is applied below the beam starting from 2 meters to 3 meters
+        away from the starting point of the beam.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(4, E, I)
+        >>> b.apply_load(-3, 0, -2)
+        >>> b.apply_load(4, 2, -1)
+        >>> b.apply_load(-2, 2, 2, end=3)
+        >>> b.load
+        -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1) - 2*SingularityFunction(x, 2, 2) + 2*SingularityFunction(x, 3, 0) + 4*SingularityFunction(x, 3, 1) + 2*SingularityFunction(x, 3, 2)
+
+        """
+        x = self.variable
+        value = sympify(value)
+        start = sympify(start)
+        order = sympify(order)
+
+        self._applied_loads.append((value, start, order, end))
+        self._load += value*SingularityFunction(x, start, order)
+        self._original_load += value*SingularityFunction(x, start, order)
+
+        if end:
+            # load has an end point within the length of the beam.
+            self._handle_end(x, value, start, order, end, type="apply")
+
+    def remove_load(self, value, start, order, end=None):
+        """
+        This method removes a particular load present on the beam object.
+        Returns a ValueError if the load passed as an argument is not
+        present on the beam.
+
+        Parameters
+        ==========
+        value : Sympifyable
+            The magnitude of an applied load.
+        start : Sympifyable
+            The starting point of the applied load. For point moments and
+            point forces this is the location of application.
+        order : Integer
+            The order of the applied load.
+            - For moments, order= -2
+            - For point loads, order=-1
+            - For constant distributed load, order=0
+            - For ramp loads, order=1
+            - For parabolic ramp loads, order=2
+            - ... so on.
+        end : Sympifyable, optional
+            An optional argument that can be used if the load has an end point
+            within the length of the beam.
+
+        Examples
+        ========
+        There is a beam of length 4 meters. A moment of magnitude 3 Nm is
+        applied in the clockwise direction at the starting point of the beam.
+        A pointload of magnitude 4 N is applied from the top of the beam at
+        2 meters from the starting point and a parabolic ramp load of magnitude
+        2 N/m is applied below the beam starting from 2 meters to 3 meters
+        away from the starting point of the beam.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(4, E, I)
+        >>> b.apply_load(-3, 0, -2)
+        >>> b.apply_load(4, 2, -1)
+        >>> b.apply_load(-2, 2, 2, end=3)
+        >>> b.load
+        -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1) - 2*SingularityFunction(x, 2, 2) + 2*SingularityFunction(x, 3, 0) + 4*SingularityFunction(x, 3, 1) + 2*SingularityFunction(x, 3, 2)
+        >>> b.remove_load(-2, 2, 2, end = 3)
+        >>> b.load
+        -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1)
+        """
+        x = self.variable
+        value = sympify(value)
+        start = sympify(start)
+        order = sympify(order)
+
+        if (value, start, order, end) in self._applied_loads:
+            self._load -= value*SingularityFunction(x, start, order)
+            self._original_load -= value*SingularityFunction(x, start, order)
+            self._applied_loads.remove((value, start, order, end))
+        else:
+            msg = "No such load distribution exists on the beam object."
+            raise ValueError(msg)
+
+        if end:
+            # load has an end point within the length of the beam.
+            self._handle_end(x, value, start, order, end, type="remove")
+
+    def _handle_end(self, x, value, start, order, end, type):
+        """
+        This functions handles the optional `end` value in the
+        `apply_load` and `remove_load` functions. When the value
+        of end is not NULL, this function will be executed.
+        """
+        if order.is_negative:
+            msg = ("If 'end' is provided the 'order' of the load cannot "
+                    "be negative, i.e. 'end' is only valid for distributed "
+                    "loads.")
+            raise ValueError(msg)
+        # NOTE : A Taylor series can be used to define the summation of
+        # singularity functions that subtract from the load past the end
+        # point such that it evaluates to zero past 'end'.
+        f = value*x**order
+
+        if type == "apply":
+            # iterating for "apply_load" method
+            for i in range(0, order + 1):
+                self._load -= (f.diff(x, i).subs(x, end - start) *
+                                SingularityFunction(x, end, i)/factorial(i))
+                self._original_load -= (f.diff(x, i).subs(x, end - start) *
+                                SingularityFunction(x, end, i)/factorial(i))
+        elif type == "remove":
+            # iterating for "remove_load" method
+            for i in range(0, order + 1):
+                self._load += (f.diff(x, i).subs(x, end - start) *
+                                SingularityFunction(x, end, i)/factorial(i))
+                self._original_load += (f.diff(x, i).subs(x, end - start) *
+                                SingularityFunction(x, end, i)/factorial(i))
+
+
+    @property
+    def load(self):
+        """
+        Returns a Singularity Function expression which represents
+        the load distribution curve of the Beam object.
+
+        Examples
+        ========
+        There is a beam of length 4 meters. A moment of magnitude 3 Nm is
+        applied in the clockwise direction at the starting point of the beam.
+        A point load of magnitude 4 N is applied from the top of the beam at
+        2 meters from the starting point and a parabolic ramp load of magnitude
+        2 N/m is applied below the beam starting from 3 meters away from the
+        starting point of the beam.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(4, E, I)
+        >>> b.apply_load(-3, 0, -2)
+        >>> b.apply_load(4, 2, -1)
+        >>> b.apply_load(-2, 3, 2)
+        >>> b.load
+        -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1) - 2*SingularityFunction(x, 3, 2)
+        """
+        return self._load
+
+    @property
+    def applied_loads(self):
+        """
+        Returns a list of all loads applied on the beam object.
+        Each load in the list is a tuple of form (value, start, order, end).
+
+        Examples
+        ========
+        There is a beam of length 4 meters. A moment of magnitude 3 Nm is
+        applied in the clockwise direction at the starting point of the beam.
+        A pointload of magnitude 4 N is applied from the top of the beam at
+        2 meters from the starting point. Another pointload of magnitude 5 N
+        is applied at same position.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(4, E, I)
+        >>> b.apply_load(-3, 0, -2)
+        >>> b.apply_load(4, 2, -1)
+        >>> b.apply_load(5, 2, -1)
+        >>> b.load
+        -3*SingularityFunction(x, 0, -2) + 9*SingularityFunction(x, 2, -1)
+        >>> b.applied_loads
+        [(-3, 0, -2, None), (4, 2, -1, None), (5, 2, -1, None)]
+        """
+        return self._applied_loads
+
+    def solve_for_reaction_loads(self, *reactions):
+        """
+        Solves for the reaction forces.
+
+        Examples
+        ========
+        There is a beam of length 30 meters. A moment of magnitude 120 Nm is
+        applied in the clockwise direction at the end of the beam. A pointload
+        of magnitude 8 N is applied from the top of the beam at the starting
+        point. There are two simple supports below the beam. One at the end
+        and another one at a distance of 10 meters from the start. The
+        deflection is restricted at both the supports.
+
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> R1, R2 = symbols('R1, R2')
+        >>> b = Beam(30, E, I)
+        >>> b.apply_load(-8, 0, -1)
+        >>> b.apply_load(R1, 10, -1)  # Reaction force at x = 10
+        >>> b.apply_load(R2, 30, -1)  # Reaction force at x = 30
+        >>> b.apply_load(120, 30, -2)
+        >>> b.bc_deflection = [(10, 0), (30, 0)]
+        >>> b.load
+        R1*SingularityFunction(x, 10, -1) + R2*SingularityFunction(x, 30, -1)
+            - 8*SingularityFunction(x, 0, -1) + 120*SingularityFunction(x, 30, -2)
+        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.reaction_loads
+        {R1: 6, R2: 2}
+        >>> b.load
+        -8*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 10, -1)
+            + 120*SingularityFunction(x, 30, -2) + 2*SingularityFunction(x, 30, -1)
+        """
+
+        x = self.variable
+        l = self.length
+        C3 = Symbol('C3')
+        C4 = Symbol('C4')
+        rotation_jumps = tuple(self._rotation_hinge_symbols)
+        deflection_jumps = tuple(self._sliding_hinge_symbols)
+
+        shear_curve = limit(self.shear_force(), x, l)
+        moment_curve = limit(self.bending_moment(), x, l)
+
+        shear_force_eqs = []
+        bending_moment_eqs = []
+        slope_eqs = []
+        deflection_eqs = []
+
+        for position, value in self._boundary_conditions['shear_force']:
+            eqs = self.shear_force().subs(x, position) - value
+            new_eqs = sum(arg for arg in eqs.args if not any(num.is_infinite for num in arg.args))
+            shear_force_eqs.append(new_eqs)
+
+        for position, value in self._boundary_conditions['bending_moment']:
+            eqs = self.bending_moment().subs(x, position) - value
+            new_eqs = sum(arg for arg in eqs.args if not any(num.is_infinite for num in arg.args))
+            bending_moment_eqs.append(new_eqs)
+
+        slope_curve = integrate(self.bending_moment(), x) + C3
+        for position, value in self._boundary_conditions['slope']:
+            eqs = slope_curve.subs(x, position) - value
+            slope_eqs.append(eqs)
+
+        deflection_curve = integrate(slope_curve, x) + C4
+        for position, value in self._boundary_conditions['deflection']:
+            eqs = deflection_curve.subs(x, position) - value
+            deflection_eqs.append(eqs)
+
+        solution = list((linsolve([shear_curve, moment_curve] + shear_force_eqs + bending_moment_eqs + slope_eqs
+                            + deflection_eqs, (C3, C4) + reactions + rotation_jumps + deflection_jumps).args)[0])
+        reaction_index = 2+len(reactions)
+        rotation_index = reaction_index + len(rotation_jumps)
+        reaction_solution = solution[2:reaction_index]
+        rotation_solution = solution[reaction_index:rotation_index]
+        deflection_solution = solution[rotation_index:]
+
+        self._reaction_loads = dict(zip(reactions, reaction_solution))
+        self._rotation_jumps = dict(zip(rotation_jumps, rotation_solution))
+        self._deflection_jumps = dict(zip(deflection_jumps, deflection_solution))
+        self._load = self._load.subs(self._reaction_loads)
+        self._load = self._load.subs(self._rotation_jumps)
+        self._load = self._load.subs(self._deflection_jumps)
+
+    def shear_force(self):
+        """
+        Returns a Singularity Function expression which represents
+        the shear force curve of the Beam object.
+
+        Examples
+        ========
+        There is a beam of length 30 meters. A moment of magnitude 120 Nm is
+        applied in the clockwise direction at the end of the beam. A pointload
+        of magnitude 8 N is applied from the top of the beam at the starting
+        point. There are two simple supports below the beam. One at the end
+        and another one at a distance of 10 meters from the start. The
+        deflection is restricted at both the supports.
+
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> R1, R2 = symbols('R1, R2')
+        >>> b = Beam(30, E, I)
+        >>> b.apply_load(-8, 0, -1)
+        >>> b.apply_load(R1, 10, -1)
+        >>> b.apply_load(R2, 30, -1)
+        >>> b.apply_load(120, 30, -2)
+        >>> b.bc_deflection = [(10, 0), (30, 0)]
+        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.shear_force()
+        8*SingularityFunction(x, 0, 0) - 6*SingularityFunction(x, 10, 0) - 120*SingularityFunction(x, 30, -1) - 2*SingularityFunction(x, 30, 0)
+        """
+        x = self.variable
+        return -integrate(self.load, x)
+
+    def max_shear_force(self):
+        """Returns maximum Shear force and its coordinate
+        in the Beam object."""
+        shear_curve = self.shear_force()
+        x = self.variable
+
+        terms = shear_curve.args
+        singularity = []        # Points at which shear function changes
+        for term in terms:
+            if isinstance(term, Mul):
+                term = term.args[-1]    # SingularityFunction in the term
+            singularity.append(term.args[1])
+        singularity = list(set(singularity))
+        singularity.sort()
+
+        intervals = []    # List of Intervals with discrete value of shear force
+        shear_values = []   # List of values of shear force in each interval
+        for i, s in enumerate(singularity):
+            if s == 0:
+                continue
+            try:
+                shear_slope = Piecewise((float("nan"), x<=singularity[i-1]),(self._load.rewrite(Piecewise), x>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> R1, R2 = symbols('R1, R2')
+        >>> b = Beam(30, E, I)
+        >>> b.apply_load(-8, 0, -1)
+        >>> b.apply_load(R1, 10, -1)
+        >>> b.apply_load(R2, 30, -1)
+        >>> b.apply_load(120, 30, -2)
+        >>> b.bc_deflection = [(10, 0), (30, 0)]
+        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.bending_moment()
+        8*SingularityFunction(x, 0, 1) - 6*SingularityFunction(x, 10, 1) - 120*SingularityFunction(x, 30, 0) - 2*SingularityFunction(x, 30, 1)
+        """
+        x = self.variable
+        return integrate(self.shear_force(), x)
+
+    def max_bmoment(self):
+        """Returns maximum Shear force and its coordinate
+        in the Beam object."""
+        bending_curve = self.bending_moment()
+        x = self.variable
+
+        terms = bending_curve.args
+        singularity = []        # Points at which bending moment changes
+        for term in terms:
+            if isinstance(term, Mul):
+                term = term.args[-1]    # SingularityFunction in the term
+            singularity.append(term.args[1])
+        singularity = list(set(singularity))
+        singularity.sort()
+
+        intervals = []    # List of Intervals with discrete value of bending moment
+        moment_values = []   # List of values of bending moment in each interval
+        for i, s in enumerate(singularity):
+            if s == 0:
+                continue
+            try:
+                moment_slope = Piecewise(
+                    (float("nan"), x <= singularity[i - 1]),
+                    (self.shear_force().rewrite(Piecewise), x < s),
+                    (float("nan"), True))
+                points = solve(moment_slope, x)
+                val = []
+                for point in points:
+                    val.append(abs(bending_curve.subs(x, point)))
+                points.extend([singularity[i-1], s])
+                val += [abs(limit(bending_curve, x, singularity[i-1], '+')), abs(limit(bending_curve, x, s, '-'))]
+                max_moment = max(val)
+                moment_values.append(max_moment)
+                intervals.append(points[val.index(max_moment)])
+
+            # If bending moment in a particular Interval has zero or constant
+            # slope, then above block gives NotImplementedError as solve
+            # can't represent Interval solutions.
+            except NotImplementedError:
+                initial_moment = limit(bending_curve, x, singularity[i-1], '+')
+                final_moment = limit(bending_curve, x, s, '-')
+                # If bending_curve has a constant slope(it is a line).
+                if bending_curve.subs(x, (singularity[i-1] + s)/2) == (initial_moment + final_moment)/2 and initial_moment != final_moment:
+                    moment_values.extend([initial_moment, final_moment])
+                    intervals.extend([singularity[i-1], s])
+                else:    # bending_curve has same value in whole Interval
+                    moment_values.append(final_moment)
+                    intervals.append(Interval(singularity[i-1], s))
+
+        moment_values = list(map(abs, moment_values))
+        maximum_moment = max(moment_values)
+        point = intervals[moment_values.index(maximum_moment)]
+        return (point, maximum_moment)
+
+    def point_cflexure(self):
+        """
+        Returns a Set of point(s) with zero bending moment and
+        where bending moment curve of the beam object changes
+        its sign from negative to positive or vice versa.
+
+        Examples
+        ========
+        There is is 10 meter long overhanging beam. There are
+        two simple supports below the beam. One at the start
+        and another one at a distance of 6 meters from the start.
+        Point loads of magnitude 10KN and 20KN are applied at
+        2 meters and 4 meters from start respectively. A Uniformly
+        distribute load of magnitude of magnitude 3KN/m is also
+        applied on top starting from 6 meters away from starting
+        point till end.
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> b = Beam(10, E, I)
+        >>> b.apply_load(-4, 0, -1)
+        >>> b.apply_load(-46, 6, -1)
+        >>> b.apply_load(10, 2, -1)
+        >>> b.apply_load(20, 4, -1)
+        >>> b.apply_load(3, 6, 0)
+        >>> b.point_cflexure()
+        [10/3]
+        """
+        #Removes the singularity functions of order < 0 from the bending moment equation used in this method
+        non_singular_bending_moment = sum(arg for arg in self.bending_moment().args if not arg.args[1].args[2] < 0)
+
+        # To restrict the range within length of the Beam
+        moment_curve = Piecewise((float("nan"), self.variable<=0),
+                (non_singular_bending_moment, self.variable>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> R1, R2 = symbols('R1, R2')
+        >>> b = Beam(30, E, I)
+        >>> b.apply_load(-8, 0, -1)
+        >>> b.apply_load(R1, 10, -1)
+        >>> b.apply_load(R2, 30, -1)
+        >>> b.apply_load(120, 30, -2)
+        >>> b.bc_deflection = [(10, 0), (30, 0)]
+        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.slope()
+        (-4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2)
+            + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + 4000/3)/(E*I)
+        """
+        x = self.variable
+        E = self.elastic_modulus
+        I = self.second_moment
+
+        if not self._boundary_conditions['slope']:
+            return diff(self.deflection(), x)
+        if isinstance(I, Piecewise) and self._joined_beam:
+            args = I.args
+            slope = 0
+            prev_slope = 0
+            prev_end = 0
+            for i in range(len(args)):
+                if i != 0:
+                    prev_end = args[i-1][1].args[1]
+                slope_value = -S.One/E*integrate(self.bending_moment()/args[i][0], (x, prev_end, x))
+                if i != len(args) - 1:
+                    slope += (prev_slope + slope_value)*SingularityFunction(x, prev_end, 0) - \
+                        (prev_slope + slope_value)*SingularityFunction(x, args[i][1].args[1], 0)
+                else:
+                    slope += (prev_slope + slope_value)*SingularityFunction(x, prev_end, 0)
+                prev_slope = slope_value.subs(x, args[i][1].args[1])
+            return slope
+
+        C3 = Symbol('C3')
+        slope_curve = -integrate(S.One/(E*I)*self.bending_moment(), x) + C3
+
+        bc_eqs = []
+        for position, value in self._boundary_conditions['slope']:
+            eqs = slope_curve.subs(x, position) - value
+            bc_eqs.append(eqs)
+        constants = list(linsolve(bc_eqs, C3))
+        slope_curve = slope_curve.subs({C3: constants[0][0]})
+        return slope_curve
+
+    def deflection(self):
+        """
+        Returns a Singularity Function expression which represents
+        the elastic curve or deflection of the Beam object.
+
+        Examples
+        ========
+        There is a beam of length 30 meters. A moment of magnitude 120 Nm is
+        applied in the clockwise direction at the end of the beam. A pointload
+        of magnitude 8 N is applied from the top of the beam at the starting
+        point. There are two simple supports below the beam. One at the end
+        and another one at a distance of 10 meters from the start. The
+        deflection is restricted at both the supports.
+
+        Using the sign convention of upward forces and clockwise moment
+        being positive.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam
+        >>> from sympy import symbols
+        >>> E, I = symbols('E, I')
+        >>> R1, R2 = symbols('R1, R2')
+        >>> b = Beam(30, E, I)
+        >>> b.apply_load(-8, 0, -1)
+        >>> b.apply_load(R1, 10, -1)
+        >>> b.apply_load(R2, 30, -1)
+        >>> b.apply_load(120, 30, -2)
+        >>> b.bc_deflection = [(10, 0), (30, 0)]
+        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.deflection()
+        (4000*x/3 - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3)
+            + 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000)/(E*I)
+        """
+        x = self.variable
+        E = self.elastic_modulus
+        I = self.second_moment
+        if not self._boundary_conditions['deflection'] and not self._boundary_conditions['slope']:
+            if isinstance(I, Piecewise) and self._joined_beam:
+                args = I.args
+                prev_slope = 0
+                prev_def = 0
+                prev_end = 0
+                deflection = 0
+                for i in range(len(args)):
+                    if i != 0:
+                        prev_end = args[i-1][1].args[1]
+                    slope_value = -S.One/E*integrate(self.bending_moment()/args[i][0], (x, prev_end, x))
+                    recent_segment_slope = prev_slope + slope_value
+                    deflection_value = integrate(recent_segment_slope, (x, prev_end, x))
+                    if i != len(args) - 1:
+                        deflection += (prev_def + deflection_value)*SingularityFunction(x, prev_end, 0) \
+                            - (prev_def + deflection_value)*SingularityFunction(x, args[i][1].args[1], 0)
+                    else:
+                        deflection += (prev_def + deflection_value)*SingularityFunction(x, prev_end, 0)
+                    prev_slope = slope_value.subs(x, args[i][1].args[1])
+                    prev_def = deflection_value.subs(x, args[i][1].args[1])
+                return deflection
+            base_char = self._base_char
+            constants = symbols(base_char + '3:5')
+            return S.One/(E*I)*integrate(-integrate(self.bending_moment(), x), x) + constants[0]*x + constants[1]
+        elif not self._boundary_conditions['deflection']:
+            base_char = self._base_char
+            constant = symbols(base_char + '4')
+            return integrate(self.slope(), x) + constant
+        elif not self._boundary_conditions['slope'] and self._boundary_conditions['deflection']:
+            if isinstance(I, Piecewise) and self._joined_beam:
+                args = I.args
+                prev_slope = 0
+                prev_def = 0
+                prev_end = 0
+                deflection = 0
+                for i in range(len(args)):
+                    if i != 0:
+                        prev_end = args[i-1][1].args[1]
+                    slope_value = -S.One/E*integrate(self.bending_moment()/args[i][0], (x, prev_end, x))
+                    recent_segment_slope = prev_slope + slope_value
+                    deflection_value = integrate(recent_segment_slope, (x, prev_end, x))
+                    if i != len(args) - 1:
+                        deflection += (prev_def + deflection_value)*SingularityFunction(x, prev_end, 0) \
+                            - (prev_def + deflection_value)*SingularityFunction(x, args[i][1].args[1], 0)
+                    else:
+                        deflection += (prev_def + deflection_value)*SingularityFunction(x, prev_end, 0)
+                    prev_slope = slope_value.subs(x, args[i][1].args[1])
+                    prev_def = deflection_value.subs(x, args[i][1].args[1])
+                return deflection
+            base_char = self._base_char
+            C3, C4 = symbols(base_char + '3:5')    # Integration constants
+            slope_curve = -integrate(self.bending_moment(), x) + C3
+            deflection_curve = integrate(slope_curve, x) + C4
+            bc_eqs = []
+            for position, value in self._boundary_conditions['deflection']:
+                eqs = deflection_curve.subs(x, position) - value
+                bc_eqs.append(eqs)
+            constants = list(linsolve(bc_eqs, (C3, C4)))
+            deflection_curve = deflection_curve.subs({C3: constants[0][0], C4: constants[0][1]})
+            return S.One/(E*I)*deflection_curve
+
+        if isinstance(I, Piecewise) and self._joined_beam:
+            args = I.args
+            prev_slope = 0
+            prev_def = 0
+            prev_end = 0
+            deflection = 0
+            for i in range(len(args)):
+                if i != 0:
+                    prev_end = args[i-1][1].args[1]
+                slope_value = S.One/E*integrate(self.bending_moment()/args[i][0], (x, prev_end, x))
+                recent_segment_slope = prev_slope + slope_value
+                deflection_value = integrate(recent_segment_slope, (x, prev_end, x))
+                if i != len(args) - 1:
+                    deflection += (prev_def + deflection_value)*SingularityFunction(x, prev_end, 0) \
+                        - (prev_def + deflection_value)*SingularityFunction(x, args[i][1].args[1], 0)
+                else:
+                    deflection += (prev_def + deflection_value)*SingularityFunction(x, prev_end, 0)
+                prev_slope = slope_value.subs(x, args[i][1].args[1])
+                prev_def = deflection_value.subs(x, args[i][1].args[1])
+            return deflection
+
+        C4 = Symbol('C4')
+        deflection_curve = integrate(self.slope(), x) + C4
+
+        bc_eqs = []
+        for position, value in self._boundary_conditions['deflection']:
+            eqs = deflection_curve.subs(x, position) - value
+            bc_eqs.append(eqs)
+
+        constants = list(linsolve(bc_eqs, C4))
+        deflection_curve = deflection_curve.subs({C4: constants[0][0]})
+        return deflection_curve
+
+    def max_deflection(self):
+        """
+        Returns point of max deflection and its corresponding deflection value
+        in a Beam object.
+        """
+
+        # To restrict the range within length of the Beam
+        slope_curve = Piecewise((float("nan"), self.variable<=0),
+                (self.slope(), self.variable>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> R1, R2 = symbols('R1, R2')
+            >>> b = Beam(8, 200*(10**9), 400*(10**-6), 2)
+            >>> b.apply_load(5000, 2, -1)
+            >>> b.apply_load(R1, 0, -1)
+            >>> b.apply_load(R2, 8, -1)
+            >>> b.apply_load(10000, 4, 0, end=8)
+            >>> b.bc_deflection = [(0, 0), (8, 0)]
+            >>> b.solve_for_reaction_loads(R1, R2)
+            >>> b.plot_shear_stress()
+            Plot object containing:
+            [0]: cartesian line: 6875*SingularityFunction(x, 0, 0) - 2500*SingularityFunction(x, 2, 0)
+            - 5000*SingularityFunction(x, 4, 1) + 15625*SingularityFunction(x, 8, 0)
+            + 5000*SingularityFunction(x, 8, 1) for x over (0.0, 8.0)
+        """
+
+        shear_stress = self.shear_stress()
+        x = self.variable
+        length = self.length
+
+        if subs is None:
+            subs = {}
+        for sym in shear_stress.atoms(Symbol):
+            if sym != x and sym not in subs:
+                raise ValueError('value of %s was not passed.' %sym)
+
+        if length in subs:
+            length = subs[length]
+
+        # Returns Plot of Shear Stress
+        return plot (shear_stress.subs(subs), (x, 0, length),
+        title='Shear Stress', xlabel=r'$\mathrm{x}$', ylabel=r'$\tau$',
+        line_color='r')
+
+
+    def plot_shear_force(self, subs=None):
+        """
+
+        Returns a plot for Shear force present in the Beam object.
+
+        Parameters
+        ==========
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 8 meters. A constant distributed load of 10 KN/m
+        is applied from half of the beam till the end. There are two simple supports
+        below the beam, one at the starting point and another at the ending point
+        of the beam. A pointload of magnitude 5 KN is also applied from top of the
+        beam, at a distance of 4 meters from the starting point.
+        Take E = 200 GPa and I = 400*(10**-6) meter**4.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> R1, R2 = symbols('R1, R2')
+            >>> b = Beam(8, 200*(10**9), 400*(10**-6))
+            >>> b.apply_load(5000, 2, -1)
+            >>> b.apply_load(R1, 0, -1)
+            >>> b.apply_load(R2, 8, -1)
+            >>> b.apply_load(10000, 4, 0, end=8)
+            >>> b.bc_deflection = [(0, 0), (8, 0)]
+            >>> b.solve_for_reaction_loads(R1, R2)
+            >>> b.plot_shear_force()
+            Plot object containing:
+            [0]: cartesian line: 13750*SingularityFunction(x, 0, 0) - 5000*SingularityFunction(x, 2, 0)
+            - 10000*SingularityFunction(x, 4, 1) + 31250*SingularityFunction(x, 8, 0)
+            + 10000*SingularityFunction(x, 8, 1) for x over (0.0, 8.0)
+        """
+        shear_force = self.shear_force()
+        if subs is None:
+            subs = {}
+        for sym in shear_force.atoms(Symbol):
+            if sym == self.variable:
+                continue
+            if sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+        return plot(shear_force.subs(subs), (self.variable, 0, length), title='Shear Force',
+                xlabel=r'$\mathrm{x}$', ylabel=r'$\mathrm{V}$', line_color='g')
+
+    def plot_bending_moment(self, subs=None):
+        """
+
+        Returns a plot for Bending moment present in the Beam object.
+
+        Parameters
+        ==========
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 8 meters. A constant distributed load of 10 KN/m
+        is applied from half of the beam till the end. There are two simple supports
+        below the beam, one at the starting point and another at the ending point
+        of the beam. A pointload of magnitude 5 KN is also applied from top of the
+        beam, at a distance of 4 meters from the starting point.
+        Take E = 200 GPa and I = 400*(10**-6) meter**4.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> R1, R2 = symbols('R1, R2')
+            >>> b = Beam(8, 200*(10**9), 400*(10**-6))
+            >>> b.apply_load(5000, 2, -1)
+            >>> b.apply_load(R1, 0, -1)
+            >>> b.apply_load(R2, 8, -1)
+            >>> b.apply_load(10000, 4, 0, end=8)
+            >>> b.bc_deflection = [(0, 0), (8, 0)]
+            >>> b.solve_for_reaction_loads(R1, R2)
+            >>> b.plot_bending_moment()
+            Plot object containing:
+            [0]: cartesian line: 13750*SingularityFunction(x, 0, 1) - 5000*SingularityFunction(x, 2, 1)
+            - 5000*SingularityFunction(x, 4, 2) + 31250*SingularityFunction(x, 8, 1)
+            + 5000*SingularityFunction(x, 8, 2) for x over (0.0, 8.0)
+        """
+        bending_moment = self.bending_moment()
+        if subs is None:
+            subs = {}
+        for sym in bending_moment.atoms(Symbol):
+            if sym == self.variable:
+                continue
+            if sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+        return plot(bending_moment.subs(subs), (self.variable, 0, length), title='Bending Moment',
+                xlabel=r'$\mathrm{x}$', ylabel=r'$\mathrm{M}$', line_color='b')
+
+    def plot_slope(self, subs=None):
+        """
+
+        Returns a plot for slope of deflection curve of the Beam object.
+
+        Parameters
+        ==========
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 8 meters. A constant distributed load of 10 KN/m
+        is applied from half of the beam till the end. There are two simple supports
+        below the beam, one at the starting point and another at the ending point
+        of the beam. A pointload of magnitude 5 KN is also applied from top of the
+        beam, at a distance of 4 meters from the starting point.
+        Take E = 200 GPa and I = 400*(10**-6) meter**4.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> R1, R2 = symbols('R1, R2')
+            >>> b = Beam(8, 200*(10**9), 400*(10**-6))
+            >>> b.apply_load(5000, 2, -1)
+            >>> b.apply_load(R1, 0, -1)
+            >>> b.apply_load(R2, 8, -1)
+            >>> b.apply_load(10000, 4, 0, end=8)
+            >>> b.bc_deflection = [(0, 0), (8, 0)]
+            >>> b.solve_for_reaction_loads(R1, R2)
+            >>> b.plot_slope()
+            Plot object containing:
+            [0]: cartesian line: -8.59375e-5*SingularityFunction(x, 0, 2) + 3.125e-5*SingularityFunction(x, 2, 2)
+            + 2.08333333333333e-5*SingularityFunction(x, 4, 3) - 0.0001953125*SingularityFunction(x, 8, 2)
+            - 2.08333333333333e-5*SingularityFunction(x, 8, 3) + 0.00138541666666667 for x over (0.0, 8.0)
+        """
+        slope = self.slope()
+        if subs is None:
+            subs = {}
+        for sym in slope.atoms(Symbol):
+            if sym == self.variable:
+                continue
+            if sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+        return plot(slope.subs(subs), (self.variable, 0, length), title='Slope',
+                xlabel=r'$\mathrm{x}$', ylabel=r'$\theta$', line_color='m')
+
+    def plot_deflection(self, subs=None):
+        """
+
+        Returns a plot for deflection curve of the Beam object.
+
+        Parameters
+        ==========
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 8 meters. A constant distributed load of 10 KN/m
+        is applied from half of the beam till the end. There are two simple supports
+        below the beam, one at the starting point and another at the ending point
+        of the beam. A pointload of magnitude 5 KN is also applied from top of the
+        beam, at a distance of 4 meters from the starting point.
+        Take E = 200 GPa and I = 400*(10**-6) meter**4.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> R1, R2 = symbols('R1, R2')
+            >>> b = Beam(8, 200*(10**9), 400*(10**-6))
+            >>> b.apply_load(5000, 2, -1)
+            >>> b.apply_load(R1, 0, -1)
+            >>> b.apply_load(R2, 8, -1)
+            >>> b.apply_load(10000, 4, 0, end=8)
+            >>> b.bc_deflection = [(0, 0), (8, 0)]
+            >>> b.solve_for_reaction_loads(R1, R2)
+            >>> b.plot_deflection()
+            Plot object containing:
+            [0]: cartesian line: 0.00138541666666667*x - 2.86458333333333e-5*SingularityFunction(x, 0, 3)
+            + 1.04166666666667e-5*SingularityFunction(x, 2, 3) + 5.20833333333333e-6*SingularityFunction(x, 4, 4)
+            - 6.51041666666667e-5*SingularityFunction(x, 8, 3) - 5.20833333333333e-6*SingularityFunction(x, 8, 4)
+            for x over (0.0, 8.0)
+        """
+        deflection = self.deflection()
+        if subs is None:
+            subs = {}
+        for sym in deflection.atoms(Symbol):
+            if sym == self.variable:
+                continue
+            if sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+        return plot(deflection.subs(subs), (self.variable, 0, length),
+                    title='Deflection', xlabel=r'$\mathrm{x}$', ylabel=r'$\delta$',
+                    line_color='r')
+
+
+    def plot_loading_results(self, subs=None):
+        """
+        Returns a subplot of Shear Force, Bending Moment,
+        Slope and Deflection of the Beam object.
+
+        Parameters
+        ==========
+
+        subs : dictionary
+               Python dictionary containing Symbols as key and their
+               corresponding values.
+
+        Examples
+        ========
+
+        There is a beam of length 8 meters. A constant distributed load of 10 KN/m
+        is applied from half of the beam till the end. There are two simple supports
+        below the beam, one at the starting point and another at the ending point
+        of the beam. A pointload of magnitude 5 KN is also applied from top of the
+        beam, at a distance of 4 meters from the starting point.
+        Take E = 200 GPa and I = 400*(10**-6) meter**4.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> R1, R2 = symbols('R1, R2')
+            >>> b = Beam(8, 200*(10**9), 400*(10**-6))
+            >>> b.apply_load(5000, 2, -1)
+            >>> b.apply_load(R1, 0, -1)
+            >>> b.apply_load(R2, 8, -1)
+            >>> b.apply_load(10000, 4, 0, end=8)
+            >>> b.bc_deflection = [(0, 0), (8, 0)]
+            >>> b.solve_for_reaction_loads(R1, R2)
+            >>> axes = b.plot_loading_results()
+        """
+        length = self.length
+        variable = self.variable
+        if subs is None:
+            subs = {}
+        for sym in self.deflection().atoms(Symbol):
+            if sym == self.variable:
+                continue
+            if sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if length in subs:
+            length = subs[length]
+        ax1 = plot(self.shear_force().subs(subs), (variable, 0, length),
+                   title="Shear Force", xlabel=r'$\mathrm{x}$', ylabel=r'$\mathrm{V}$',
+                   line_color='g', show=False)
+        ax2 = plot(self.bending_moment().subs(subs), (variable, 0, length),
+                   title="Bending Moment", xlabel=r'$\mathrm{x}$', ylabel=r'$\mathrm{M}$',
+                   line_color='b', show=False)
+        ax3 = plot(self.slope().subs(subs), (variable, 0, length),
+                   title="Slope", xlabel=r'$\mathrm{x}$', ylabel=r'$\theta$',
+                   line_color='m', show=False)
+        ax4 = plot(self.deflection().subs(subs), (variable, 0, length),
+                   title="Deflection", xlabel=r'$\mathrm{x}$', ylabel=r'$\delta$',
+                   line_color='r', show=False)
+
+        return PlotGrid(4, 1, ax1, ax2, ax3, ax4)
+
+    def _solve_for_ild_equations(self, value):
+        """
+
+        Helper function for I.L.D. It takes the unsubstituted
+        copy of the load equation and uses it to calculate shear force and bending
+        moment equations.
+        """
+        x = self.variable
+        a = self.ild_variable
+        load = self._load + value * SingularityFunction(x, a, -1)
+        shear_force = -integrate(load, x)
+        bending_moment = integrate(shear_force, x)
+
+        return shear_force, bending_moment
+
+    def solve_for_ild_reactions(self, value, *reactions):
+        """
+
+        Determines the Influence Line Diagram equations for reaction
+        forces under the effect of a moving load.
+
+        Parameters
+        ==========
+        value : Integer
+            Magnitude of moving load
+        reactions :
+            The reaction forces applied on the beam.
+
+        Warning
+        =======
+        This method creates equations that can give incorrect results when
+        substituting a = 0 or a = l, with l the length of the beam.
+
+        Examples
+        ========
+
+        There is a beam of length 10 meters. There are two simple supports
+        below the beam, one at the starting point and another at the ending
+        point of the beam. Calculate the I.L.D. equations for reaction forces
+        under the effect of a moving load of magnitude 1kN.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy import symbols
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> E, I = symbols('E, I')
+            >>> R_0, R_10 = symbols('R_0, R_10')
+            >>> b = Beam(10, E, I)
+            >>> p0 = b.apply_support(0, 'pin')
+            >>> p10 = b.apply_support(10, 'roller')
+            >>> b.solve_for_ild_reactions(1,R_0,R_10)
+            >>> b.ild_reactions
+            {R_0: -SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/10 - SingularityFunction(a, 10, 1)/10,
+            R_10: -SingularityFunction(a, 0, 1)/10 + SingularityFunction(a, 10, 0) + SingularityFunction(a, 10, 1)/10}
+
+        """
+        shear_force, bending_moment = self._solve_for_ild_equations(value)
+        x = self.variable
+        l = self.length
+        a = self.ild_variable
+
+        rotation_jumps = tuple(self._rotation_hinge_symbols)
+        deflection_jumps = tuple(self._sliding_hinge_symbols)
+
+        C3 = Symbol('C3')
+        C4 = Symbol('C4')
+
+        shear_curve = limit(shear_force, x, l) - value*(SingularityFunction(a, 0, 0) - SingularityFunction(a, l, 0))
+        moment_curve = (limit(bending_moment, x, l) - value * (l * SingularityFunction(a, 0, 0)
+                                                               - SingularityFunction(a, 0, 1)
+                                                               + SingularityFunction(a, l, 1)))
+
+        shear_force_eqs = []
+        bending_moment_eqs = []
+        slope_eqs = []
+        deflection_eqs = []
+
+        for position, val in self._boundary_conditions['shear_force']:
+            eqs = self.shear_force().subs(x, position) - val
+            eqs_without_inf = sum(arg for arg in eqs.args if not any(num.is_infinite for num in arg.args))
+            shear_sinc = value * (SingularityFunction(- a, - position, 0) - SingularityFunction(-a, 0, 0))
+            eqs_with_shear_sinc = eqs_without_inf - shear_sinc
+            shear_force_eqs.append(eqs_with_shear_sinc)
+
+        for position, val in self._boundary_conditions['bending_moment']:
+            eqs = self.bending_moment().subs(x, position) - val
+            eqs_without_inf = sum(arg for arg in eqs.args if not any(num.is_infinite for num in arg.args))
+            moment_sinc = value * (position * SingularityFunction(a, 0, 0)
+                                   - SingularityFunction(a, 0, 1) + SingularityFunction(a, position, 1))
+            eqs_with_moment_sinc = eqs_without_inf - moment_sinc
+            bending_moment_eqs.append(eqs_with_moment_sinc)
+
+        slope_curve = integrate(bending_moment, x) + C3
+        for position, val in self._boundary_conditions['slope']:
+            eqs = slope_curve.subs(x, position) - val + value * (SingularityFunction(-a, 0, 1) + position * SingularityFunction(-a, 0, 0))**2 / 2
+            slope_eqs.append(eqs)
+
+        deflection_curve = integrate(slope_curve, x) + C4
+        for position, val in self._boundary_conditions['deflection']:
+            eqs = deflection_curve.subs(x, position) - val + value * (SingularityFunction(-a, 0, 1) + position * SingularityFunction(-a, 0, 0)) ** 3 / 6
+            deflection_eqs.append(eqs)
+
+        solution = list((linsolve([shear_curve, moment_curve] + shear_force_eqs + bending_moment_eqs + slope_eqs
+                                  + deflection_eqs, (C3, C4) + reactions + rotation_jumps + deflection_jumps).args)[0])
+
+        reaction_index = 2 + len(reactions)
+        rotation_index = reaction_index + len(rotation_jumps)
+        reaction_solution = solution[2:reaction_index]
+        rotation_solution = solution[reaction_index:rotation_index]
+        deflection_solution = solution[rotation_index:]
+
+        self._ild_reactions = dict(zip(reactions, reaction_solution))
+        self._ild_rotations_jumps = dict(zip(rotation_jumps, rotation_solution))
+        self._ild_deflection_jumps = dict(zip(deflection_jumps, deflection_solution))
+
+    def plot_ild_reactions(self, subs=None):
+        """
+
+        Plots the Influence Line Diagram of Reaction Forces
+        under the effect of a moving load. This function
+        should be called after calling solve_for_ild_reactions().
+
+        Parameters
+        ==========
+
+        subs : dictionary
+               Python dictionary containing Symbols as key and their
+               corresponding values.
+
+        Warning
+        =======
+        The values for a = 0 and a = l, with l the length of the beam, in
+        the plot can be incorrect.
+
+        Examples
+        ========
+
+        There is a beam of length 10 meters. A point load of magnitude 5KN
+        is also applied from top of the beam, at a distance of 4 meters
+        from the starting point. There are two simple supports below the
+        beam, located at the starting point and at a distance of 7 meters
+        from the starting point. Plot the I.L.D. equations for reactions
+        at both support points under the effect of a moving load
+        of magnitude 1kN.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy import symbols
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> E, I = symbols('E, I')
+            >>> R_0, R_7 = symbols('R_0, R_7')
+            >>> b = Beam(10, E, I)
+            >>> p0 = b.apply_support(0, 'roller')
+            >>> p7 = b.apply_support(7, 'roller')
+            >>> b.apply_load(5,4,-1)
+            >>> b.solve_for_ild_reactions(1,R_0,R_7)
+            >>> b.ild_reactions
+            {R_0: -SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/7
+            - 3*SingularityFunction(a, 10, 0)/7  - SingularityFunction(a, 10, 1)/7 - 15/7,
+            R_7: -SingularityFunction(a, 0, 1)/7 + 10*SingularityFunction(a, 10, 0)/7 + SingularityFunction(a, 10, 1)/7 - 20/7}
+            >>> b.plot_ild_reactions()
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: -SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/7
+            - 3*SingularityFunction(a, 10, 0)/7 - SingularityFunction(a, 10, 1)/7 - 15/7 for a over (0.0, 10.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: -SingularityFunction(a, 0, 1)/7 + 10*SingularityFunction(a, 10, 0)/7
+            + SingularityFunction(a, 10, 1)/7 - 20/7 for a over (0.0, 10.0)
+
+        """
+        if not self._ild_reactions:
+            raise ValueError("I.L.D. reaction equations not found. Please use solve_for_ild_reactions() to generate the I.L.D. reaction equations.")
+
+        a = self.ild_variable
+        ildplots = []
+
+        if subs is None:
+            subs = {}
+
+        for reaction in self._ild_reactions:
+            for sym in self._ild_reactions[reaction].atoms(Symbol):
+                if sym != a and sym not in subs:
+                    raise ValueError('Value of %s was not passed.' %sym)
+
+        for sym in self._length.atoms(Symbol):
+            if sym != a and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+
+        for reaction in self._ild_reactions:
+            ildplots.append(plot(self._ild_reactions[reaction].subs(subs),
+            (a, 0, self._length.subs(subs)), title='I.L.D. for Reactions',
+            xlabel=a, ylabel=reaction, line_color='blue', show=False))
+
+        return PlotGrid(len(ildplots), 1, *ildplots)
+
+    def solve_for_ild_shear(self, distance, value, *reactions):
+        """
+
+        Determines the Influence Line Diagram equations for shear at a
+        specified point under the effect of a moving load.
+
+        Parameters
+        ==========
+        distance : Integer
+            Distance of the point from the start of the beam
+            for which equations are to be determined
+        value : Integer
+            Magnitude of moving load
+        reactions :
+            The reaction forces applied on the beam.
+
+        Warning
+        =======
+        This method creates equations that can give incorrect results when
+        substituting a = 0 or a = l, with l the length of the beam.
+
+        Examples
+        ========
+
+        There is a beam of length 12 meters. There are two simple supports
+        below the beam, one at the starting point and another at a distance
+        of 8 meters. Calculate the I.L.D. equations for Shear at a distance
+        of 4 meters under the effect of a moving load of magnitude 1kN.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy import symbols
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> E, I = symbols('E, I')
+            >>> R_0, R_8 = symbols('R_0, R_8')
+            >>> b = Beam(12, E, I)
+            >>> p0 = b.apply_support(0, 'roller')
+            >>> p8 = b.apply_support(8, 'roller')
+            >>> b.solve_for_ild_reactions(1, R_0, R_8)
+            >>> b.solve_for_ild_shear(4, 1, R_0, R_8)
+            >>> b.ild_shear
+            -(-SingularityFunction(a, 0, 0) + SingularityFunction(a, 12, 0) + 2)*SingularityFunction(a, 4, 0)
+            - SingularityFunction(-a, 0, 0) - SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/8
+            + SingularityFunction(a, 12, 0)/2 - SingularityFunction(a, 12, 1)/8 + 1
+
+        """
+
+        x = self.variable
+        l = self.length
+        a = self.ild_variable
+
+        shear_force, _ = self._solve_for_ild_equations(value)
+
+        shear_curve1 = value - limit(shear_force, x, distance)
+        shear_curve2 = (limit(shear_force, x, l) - limit(shear_force, x, distance)) - value
+
+        for reaction in reactions:
+            shear_curve1 = shear_curve1.subs(reaction,self._ild_reactions[reaction])
+            shear_curve2 = shear_curve2.subs(reaction,self._ild_reactions[reaction])
+
+        shear_eq = (shear_curve1 - (shear_curve1 - shear_curve2) * SingularityFunction(a, distance, 0)
+                    - value * SingularityFunction(-a, 0, 0) + value * SingularityFunction(a, l, 0))
+
+        self._ild_shear = shear_eq
+
+    def plot_ild_shear(self,subs=None):
+        """
+
+        Plots the Influence Line Diagram for Shear under the effect
+        of a moving load. This function should be called after
+        calling solve_for_ild_shear().
+
+        Parameters
+        ==========
+
+        subs : dictionary
+               Python dictionary containing Symbols as key and their
+               corresponding values.
+
+        Warning
+        =======
+        The values for a = 0 and a = l, with l the length of the beam, in
+        the plot can be incorrect.
+
+        Examples
+        ========
+
+        There is a beam of length 12 meters. There are two simple supports
+        below the beam, one at the starting point and another at a distance
+        of 8 meters. Plot the I.L.D. for Shear at a distance
+        of 4 meters under the effect of a moving load of magnitude 1kN.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy import symbols
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> E, I = symbols('E, I')
+            >>> R_0, R_8 = symbols('R_0, R_8')
+            >>> b = Beam(12, E, I)
+            >>> p0 = b.apply_support(0, 'roller')
+            >>> p8 = b.apply_support(8, 'roller')
+            >>> b.solve_for_ild_reactions(1, R_0, R_8)
+            >>> b.solve_for_ild_shear(4, 1, R_0, R_8)
+            >>> b.ild_shear
+            -(-SingularityFunction(a, 0, 0) + SingularityFunction(a, 12, 0) + 2)*SingularityFunction(a, 4, 0)
+            - SingularityFunction(-a, 0, 0) - SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/8
+            + SingularityFunction(a, 12, 0)/2 - SingularityFunction(a, 12, 1)/8 + 1
+            >>> b.plot_ild_shear()
+            Plot object containing:
+            [0]: cartesian line: -(-SingularityFunction(a, 0, 0) + SingularityFunction(a, 12, 0) + 2)*SingularityFunction(a, 4, 0)
+            - SingularityFunction(-a, 0, 0) - SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/8
+            + SingularityFunction(a, 12, 0)/2 - SingularityFunction(a, 12, 1)/8 + 1 for a over (0.0, 12.0)
+
+        """
+
+        if not self._ild_shear:
+            raise ValueError("I.L.D. shear equation not found. Please use solve_for_ild_shear() to generate the I.L.D. shear equations.")
+
+        l = self._length
+        a = self.ild_variable
+
+        if subs is None:
+            subs = {}
+
+        for sym in self._ild_shear.atoms(Symbol):
+            if sym != a and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+
+        for sym in self._length.atoms(Symbol):
+            if sym != a and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+
+        return plot(self._ild_shear.subs(subs), (a, 0, l),  title='I.L.D. for Shear',
+               xlabel=r'$\mathrm{a}$', ylabel=r'$\mathrm{V}$', line_color='blue',show=True)
+
+    def solve_for_ild_moment(self, distance, value, *reactions):
+        """
+
+        Determines the Influence Line Diagram equations for moment at a
+        specified point under the effect of a moving load.
+
+        Parameters
+        ==========
+        distance : Integer
+            Distance of the point from the start of the beam
+            for which equations are to be determined
+        value : Integer
+            Magnitude of moving load
+        reactions :
+            The reaction forces applied on the beam.
+
+        Warning
+        =======
+        This method creates equations that can give incorrect results when
+        substituting a = 0 or a = l, with l the length of the beam.
+
+        Examples
+        ========
+
+        There is a beam of length 12 meters. There are two simple supports
+        below the beam, one at the starting point and another at a distance
+        of 8 meters. Calculate the I.L.D. equations for Moment at a distance
+        of 4 meters under the effect of a moving load of magnitude 1kN.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy import symbols
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> E, I = symbols('E, I')
+            >>> R_0, R_8 = symbols('R_0, R_8')
+            >>> b = Beam(12, E, I)
+            >>> p0 = b.apply_support(0, 'roller')
+            >>> p8 = b.apply_support(8, 'roller')
+            >>> b.solve_for_ild_reactions(1, R_0, R_8)
+            >>> b.solve_for_ild_moment(4, 1, R_0, R_8)
+            >>> b.ild_moment
+            -(4*SingularityFunction(a, 0, 0) - SingularityFunction(a, 0, 1) + SingularityFunction(a, 4, 1))*SingularityFunction(a, 4, 0)
+            - SingularityFunction(a, 0, 1)/2 + SingularityFunction(a, 4, 1) - 2*SingularityFunction(a, 12, 0)
+            - SingularityFunction(a, 12, 1)/2
+
+        """
+
+        x = self.variable
+        l = self.length
+        a = self.ild_variable
+
+        _, moment = self._solve_for_ild_equations(value)
+
+        moment_curve1 = value*(distance * SingularityFunction(a, 0, 0) - SingularityFunction(a, 0, 1)
+                               + SingularityFunction(a, distance, 1)) - limit(moment, x, distance)
+        moment_curve2 = (limit(moment, x, l)-limit(moment, x, distance)
+                         - value * (l * SingularityFunction(a, 0, 0) - SingularityFunction(a, 0, 1)
+                                    + SingularityFunction(a, l, 1)))
+
+        for reaction in reactions:
+            moment_curve1 = moment_curve1.subs(reaction, self._ild_reactions[reaction])
+            moment_curve2 = moment_curve2.subs(reaction, self._ild_reactions[reaction])
+
+        moment_eq = moment_curve1 - (moment_curve1 - moment_curve2) * SingularityFunction(a, distance, 0)
+
+        self._ild_moment = moment_eq
+
+    def plot_ild_moment(self,subs=None):
+        """
+
+        Plots the Influence Line Diagram for Moment under the effect
+        of a moving load. This function should be called after
+        calling solve_for_ild_moment().
+
+        Parameters
+        ==========
+
+        subs : dictionary
+               Python dictionary containing Symbols as key and their
+               corresponding values.
+
+        Warning
+        =======
+        The values for a = 0 and a = l, with l the length of the beam, in
+        the plot can be incorrect.
+
+        Examples
+        ========
+
+        There is a beam of length 12 meters. There are two simple supports
+        below the beam, one at the starting point and another at a distance
+        of 8 meters. Plot the I.L.D. for Moment at a distance
+        of 4 meters under the effect of a moving load of magnitude 1kN.
+
+        Using the sign convention of downwards forces being positive.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy import symbols
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> E, I = symbols('E, I')
+            >>> R_0, R_8 = symbols('R_0, R_8')
+            >>> b = Beam(12, E, I)
+            >>> p0 = b.apply_support(0, 'roller')
+            >>> p8 = b.apply_support(8, 'roller')
+            >>> b.solve_for_ild_reactions(1, R_0, R_8)
+            >>> b.solve_for_ild_moment(4, 1, R_0, R_8)
+            >>> b.ild_moment
+            -(4*SingularityFunction(a, 0, 0) - SingularityFunction(a, 0, 1) + SingularityFunction(a, 4, 1))*SingularityFunction(a, 4, 0)
+            - SingularityFunction(a, 0, 1)/2 + SingularityFunction(a, 4, 1) - 2*SingularityFunction(a, 12, 0)
+            - SingularityFunction(a, 12, 1)/2
+            >>> b.plot_ild_moment()
+            Plot object containing:
+            [0]: cartesian line: -(4*SingularityFunction(a, 0, 0) - SingularityFunction(a, 0, 1)
+            + SingularityFunction(a, 4, 1))*SingularityFunction(a, 4, 0) - SingularityFunction(a, 0, 1)/2
+            + SingularityFunction(a, 4, 1) - 2*SingularityFunction(a, 12, 0) - SingularityFunction(a, 12, 1)/2 for a over (0.0, 12.0)
+
+        """
+
+        if not self._ild_moment:
+            raise ValueError("I.L.D. moment equation not found. Please use solve_for_ild_moment() to generate the I.L.D. moment equations.")
+
+        a = self.ild_variable
+
+        if subs is None:
+            subs = {}
+
+        for sym in self._ild_moment.atoms(Symbol):
+            if sym != a and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+
+        for sym in self._length.atoms(Symbol):
+            if sym != a and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        return plot(self._ild_moment.subs(subs), (a, 0, self._length), title='I.L.D. for Moment',
+               xlabel=r'$\mathrm{a}$', ylabel=r'$\mathrm{M}$', line_color='blue', show=True)
+
+    @doctest_depends_on(modules=('numpy',))
+    def draw(self, pictorial=True):
+        """
+        Returns a plot object representing the beam diagram of the beam.
+        In particular, the diagram might include:
+
+        * the beam.
+        * vertical black arrows represent point loads and support reaction
+          forces (the latter if they have been added with the ``apply_load``
+          method).
+        * circular arrows represent moments.
+        * shaded areas represent distributed loads.
+        * the support, if ``apply_support`` has been executed.
+        * if a composite beam has been created with the ``join`` method and
+          a hinge has been specified, it will be shown with a white disc.
+
+        The diagram shows positive loads on the upper side of the beam,
+        and negative loads on the lower side. If two or more distributed
+        loads acts along the same direction over the same region, the
+        function will add them up together.
+
+        .. note::
+            The user must be careful while entering load values.
+            The draw function assumes a sign convention which is used
+            for plotting loads.
+            Given a right handed coordinate system with XYZ coordinates,
+            the beam's length is assumed to be along the positive X axis.
+            The draw function recognizes positive loads(with n>-2) as loads
+            acting along negative Y direction and positive moments acting
+            along positive Z direction.
+
+        Parameters
+        ==========
+
+        pictorial: Boolean (default=True)
+            Setting ``pictorial=True`` would simply create a pictorial (scaled)
+            view of the beam diagram. On the other hand, ``pictorial=False``
+            would create a beam diagram with the exact dimensions on the plot.
+
+        Examples
+        ========
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam
+            >>> from sympy import symbols
+            >>> P1, P2, M = symbols('P1, P2, M')
+            >>> E, I = symbols('E, I')
+            >>> b = Beam(50, 20, 30)
+            >>> b.apply_load(-10, 2, -1)
+            >>> b.apply_load(15, 26, -1)
+            >>> b.apply_load(P1, 10, -1)
+            >>> b.apply_load(-P2, 40, -1)
+            >>> b.apply_load(90, 5, 0, 23)
+            >>> b.apply_load(10, 30, 1, 50)
+            >>> b.apply_load(M, 15, -2)
+            >>> b.apply_load(-M, 30, -2)
+            >>> p50 = b.apply_support(50, "pin")
+            >>> p0, m0 = b.apply_support(0, "fixed")
+            >>> p20 = b.apply_support(20, "roller")
+            >>> p = b.draw()  # doctest: +SKIP
+            >>> p  # doctest: +ELLIPSIS,+SKIP
+            Plot object containing:
+            [0]: cartesian line: 25*SingularityFunction(x, 5, 0) - 25*SingularityFunction(x, 23, 0)
+            + SingularityFunction(x, 30, 1) - 20*SingularityFunction(x, 50, 0)
+            - SingularityFunction(x, 50, 1) + 5 for x over (0.0, 50.0)
+            [1]: cartesian line: 5 for x over (0.0, 50.0)
+            ...
+            >>> p.show() # doctest: +SKIP
+
+        """
+        if not numpy:
+            raise ImportError("To use this function numpy module is required")
+
+        loads = list(set(self.applied_loads) - set(self._support_as_loads))
+        if (not pictorial) and any((len(l[0].free_symbols) > 0) and (l[2] >= 0) for l in loads):
+            raise ValueError("`pictorial=False` requires numerical "
+                "distributed loads. Instead, symbolic loads were found. "
+                "Cannot continue.")
+
+        x = self.variable
+
+        # checking whether length is an expression in terms of any Symbol.
+        if isinstance(self.length, Expr):
+            l = list(self.length.atoms(Symbol))
+            # assigning every Symbol a default value of 10
+            l = dict.fromkeys(l, 10)
+            length = self.length.subs(l)
+        else:
+            l = {}
+            length = self.length
+        height = length/10
+
+        rectangles = []
+        rectangles.append({'xy':(0, 0), 'width':length, 'height': height, 'facecolor':"brown"})
+        annotations, markers, load_eq,load_eq1, fill = self._draw_load(pictorial, length, l)
+        support_markers, support_rectangles = self._draw_supports(length, l)
+
+        rectangles += support_rectangles
+        markers += support_markers
+
+        for loc in self._applied_rotation_hinges:
+            ratio = loc / self.length
+            x_pos = float(ratio) * length
+            markers += [{'args':[[x_pos], [height / 2]], 'marker':'o', 'markersize':6, 'color':"white"}]
+
+        for loc in self._applied_sliding_hinges:
+            ratio = loc / self.length
+            x_pos = float(ratio) * length
+            markers += [{'args': [[x_pos], [height / 2]], 'marker':'|', 'markersize':12, 'color':"white"}]
+
+        ylim = (-length, 1.25*length)
+        if fill:
+            # when distributed loads are presents, they might get clipped out
+            # in the figure by the ylim settings.
+            # It might be necessary to compute new limits.
+            _min = min(min(fill["y2"]), min(r["xy"][1] for r in rectangles))
+            _max = max(max(fill["y1"]), max(r["xy"][1] for r in rectangles))
+            if (_min < ylim[0]) or (_max > ylim[1]):
+                offset = abs(_max - _min) * 0.1
+                ylim = (_min - offset, _max + offset)
+
+        sing_plot = plot(height + load_eq, height + load_eq1, (x, 0, length),
+            xlim=(-height, length + height), ylim=ylim,
+            annotations=annotations, markers=markers, rectangles=rectangles,
+            line_color='brown', fill=fill, axis=False, show=False)
+
+        return sing_plot
+
+
+    def _is_load_negative(self, load):
+        """Try to determine if a load is negative or positive, using
+        expansion and doit if necessary.
+
+        Returns
+        =======
+        True: if the load is negative
+        False: if the load is positive
+        None: if it is indeterminate
+
+        """
+        rv = load.is_negative
+        if load.is_Atom or rv is not None:
+            return rv
+        return load.doit().expand().is_negative
+
+    def _draw_load(self, pictorial, length, l):
+        loads = list(set(self.applied_loads) - set(self._support_as_loads))
+        height = length/10
+        x = self.variable
+
+        annotations = []
+        markers = []
+        load_args = []
+        scaled_load = 0
+        load_args1 = []
+        scaled_load1 = 0
+        load_eq = S.Zero     # For positive valued higher order loads
+        load_eq1 = S.Zero    # For negative valued higher order loads
+        fill = None
+
+        # schematic view should use the class convention as much as possible.
+        # However, users can add expressions as symbolic loads, for example
+        # P1 - P2: is this load positive or negative? We can't say.
+        # On these occasions it is better to inform users about the
+        # indeterminate state of those loads.
+        warning_head = "Please, note that this schematic view might not be " \
+            "in agreement with the sign convention used by the Beam class " \
+            "for load-related computations, because it was not possible " \
+            "to determine the sign (hence, the direction) of the " \
+            "following loads:\n"
+        warning_body = ""
+
+        for load in loads:
+            # check if the position of load is in terms of the beam length.
+            if l:
+                pos =  load[1].subs(l)
+            else:
+                pos = load[1]
+
+            # point loads
+            if load[2] == -1:
+                iln = self._is_load_negative(load[0])
+                if iln is None:
+                    warning_body += "* Point load %s located at %s\n" % (load[0], load[1])
+                if iln:
+                    annotations.append({'text':'', 'xy':(pos, 0), 'xytext':(pos, height - 4*height), 'arrowprops':{'width': 1.5, 'headlength': 5, 'headwidth': 5, 'facecolor': 'black'}})
+                else:
+                    annotations.append({'text':'', 'xy':(pos, height),  'xytext':(pos, height*4), 'arrowprops':{"width": 1.5, "headlength": 4, "headwidth": 4, "facecolor": 'black'}})
+            # moment loads
+            elif load[2] == -2:
+                iln = self._is_load_negative(load[0])
+                if iln is None:
+                    warning_body += "* Moment %s located at %s\n" % (load[0], load[1])
+                if self._is_load_negative(load[0]):
+                    markers.append({'args':[[pos], [height/2]], 'marker': r'$\circlearrowright$', 'markersize':15})
+                else:
+                    markers.append({'args':[[pos], [height/2]], 'marker': r'$\circlearrowleft$', 'markersize':15})
+            # higher order loads
+            elif load[2] >= 0:
+                # `fill` will be assigned only when higher order loads are present
+                value, start, order, end = load
+
+                iln = self._is_load_negative(value)
+                if iln is None:
+                    warning_body += "* Distributed load %s from %s to %s\n" % (value, start, end)
+
+                # Positive loads have their separate equations
+                if not iln:
+                    # if pictorial is True we remake the load equation again with
+                    # some constant magnitude values.
+                    if pictorial:
+                        # remake the load equation again with some constant
+                        # magnitude values.
+                        value = 10**(1-order) if order > 0 else length/2
+                    scaled_load += value*SingularityFunction(x, start, order)
+                    if end:
+                        f2 = value*x**order if order >= 0 else length/2*x**order
+                        for i in range(0, order + 1):
+                            scaled_load -= (f2.diff(x, i).subs(x, end - start)*
+                                            SingularityFunction(x, end, i)/factorial(i))
+
+                    if isinstance(scaled_load, Add):
+                        load_args = scaled_load.args
+                    else:
+                        # when the load equation consists of only a single term
+                        load_args = (scaled_load,)
+                    load_eq = Add(*[i.subs(l) for i in load_args])
+
+                # For loads with negative value
+                else:
+                    if pictorial:
+                        # remake the load equation again with some constant
+                        # magnitude values.
+                        value = 10**(1-order) if order > 0 else length/2
+                    scaled_load1 += abs(value)*SingularityFunction(x, start, order)
+                    if end:
+                        f2 = abs(value)*x**order if order >= 0 else length/2*x**order
+                        for i in range(0, order + 1):
+                            scaled_load1 -= (f2.diff(x, i).subs(x, end - start)*
+                                            SingularityFunction(x, end, i)/factorial(i))
+
+                    if isinstance(scaled_load1, Add):
+                        load_args1 = scaled_load1.args
+                    else:
+                        # when the load equation consists of only a single term
+                        load_args1 = (scaled_load1,)
+                    load_eq1 = [i.subs(l) for i in load_args1]
+                    load_eq1 = -Add(*load_eq1) - height
+
+        if len(warning_body) > 0:
+            warnings.warn(warning_head + warning_body)
+
+        xx = numpy.arange(0, float(length), 0.001)
+        yy1 = lambdify([x], height + load_eq.rewrite(Piecewise))(xx)
+        yy2 = lambdify([x], height + load_eq1.rewrite(Piecewise))(xx)
+        if not isinstance(yy1, numpy.ndarray):
+            yy1 *= numpy.ones_like(xx)
+        if not isinstance(yy2, numpy.ndarray):
+            yy2 *= numpy.ones_like(xx)
+        fill = {'x': xx, 'y1': yy1, 'y2': yy2,
+            'color':'darkkhaki', "zorder": -1}
+        return annotations, markers, load_eq, load_eq1, fill
+
+
+    def _draw_supports(self, length, l):
+        height = float(length/10)
+
+        support_markers = []
+        support_rectangles = []
+        for support in self._applied_supports:
+            if l:
+                pos =  support[0].subs(l)
+            else:
+                pos = support[0]
+
+            if support[1] == "pin":
+                support_markers.append({'args':[pos, [0]], 'marker':6, 'markersize':13, 'color':"black"})
+
+            elif support[1] == "roller":
+                support_markers.append({'args':[pos, [-height/2.5]], 'marker':'o', 'markersize':11, 'color':"black"})
+
+            elif support[1] == "fixed":
+                if pos == 0:
+                    support_rectangles.append({'xy':(0, -3*height), 'width':-length/20, 'height':6*height + height, 'fill':False, 'hatch':'/////'})
+                else:
+                    support_rectangles.append({'xy':(length, -3*height), 'width':length/20, 'height': 6*height + height, 'fill':False, 'hatch':'/////'})
+
+        return support_markers, support_rectangles
+
+
+class Beam3D(Beam):
+    """
+    This class handles loads applied in any direction of a 3D space along
+    with unequal values of Second moment along different axes.
+
+    .. note::
+       A consistent sign convention must be used while solving a beam
+       bending problem; the results will
+       automatically follow the chosen sign convention.
+       This class assumes that any kind of distributed load/moment is
+       applied through out the span of a beam.
+
+    Examples
+    ========
+    There is a beam of l meters long. A constant distributed load of magnitude q
+    is applied along y-axis from start till the end of beam. A constant distributed
+    moment of magnitude m is also applied along z-axis from start till the end of beam.
+    Beam is fixed at both of its end. So, deflection of the beam at the both ends
+    is restricted.
+
+    >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+    >>> from sympy import symbols, simplify, collect, factor
+    >>> l, E, G, I, A = symbols('l, E, G, I, A')
+    >>> b = Beam3D(l, E, G, I, A)
+    >>> x, q, m = symbols('x, q, m')
+    >>> b.apply_load(q, 0, 0, dir="y")
+    >>> b.apply_moment_load(m, 0, -1, dir="z")
+    >>> b.shear_force()
+    [0, -q*x, 0]
+    >>> b.bending_moment()
+    [0, 0, -m*x + q*x**2/2]
+    >>> b.bc_slope = [(0, [0, 0, 0]), (l, [0, 0, 0])]
+    >>> b.bc_deflection = [(0, [0, 0, 0]), (l, [0, 0, 0])]
+    >>> b.solve_slope_deflection()
+    >>> factor(b.slope())
+    [0, 0, x*(-l + x)*(-A*G*l**3*q + 2*A*G*l**2*q*x - 12*E*I*l*q
+        - 72*E*I*m + 24*E*I*q*x)/(12*E*I*(A*G*l**2 + 12*E*I))]
+    >>> dx, dy, dz = b.deflection()
+    >>> dy = collect(simplify(dy), x)
+    >>> dx == dz == 0
+    True
+    >>> dy == (x*(12*E*I*l*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q)
+    ... + x*(A*G*l*(3*l*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q) + x*(-2*A*G*l**2*q + 4*A*G*l*m - 24*E*I*q))
+    ... + A*G*(A*G*l**2 + 12*E*I)*(-2*l**2*q + 6*l*m - 4*m*x + q*x**2)
+    ... - 12*E*I*q*(A*G*l**2 + 12*E*I)))/(24*A*E*G*I*(A*G*l**2 + 12*E*I)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://homes.civil.aau.dk/jc/FemteSemester/Beams3D.pdf
+
+    """
+
+    def __init__(self, length, elastic_modulus, shear_modulus, second_moment,
+                 area, variable=Symbol('x')):
+        """Initializes the class.
+
+        Parameters
+        ==========
+        length : Sympifyable
+            A Symbol or value representing the Beam's length.
+        elastic_modulus : Sympifyable
+            A SymPy expression representing the Beam's Modulus of Elasticity.
+            It is a measure of the stiffness of the Beam material.
+        shear_modulus : Sympifyable
+            A SymPy expression representing the Beam's Modulus of rigidity.
+            It is a measure of rigidity of the Beam material.
+        second_moment : Sympifyable or list
+            A list of two elements having SymPy expression representing the
+            Beam's Second moment of area. First value represent Second moment
+            across y-axis and second across z-axis.
+            Single SymPy expression can be passed if both values are same
+        area : Sympifyable
+            A SymPy expression representing the Beam's cross-sectional area
+            in a plane perpendicular to length of the Beam.
+        variable : Symbol, optional
+            A Symbol object that will be used as the variable along the beam
+            while representing the load, shear, moment, slope and deflection
+            curve. By default, it is set to ``Symbol('x')``.
+        """
+        super().__init__(length, elastic_modulus, second_moment, variable)
+        self.shear_modulus = shear_modulus
+        self.area = area
+        self._load_vector = [0, 0, 0]
+        self._moment_load_vector = [0, 0, 0]
+        self._torsion_moment = {}
+        self._load_Singularity = [0, 0, 0]
+        self._slope = [0, 0, 0]
+        self._deflection = [0, 0, 0]
+        self._angular_deflection = 0
+
+    @property
+    def shear_modulus(self):
+        """Young's Modulus of the Beam. """
+        return self._shear_modulus
+
+    @shear_modulus.setter
+    def shear_modulus(self, e):
+        self._shear_modulus = sympify(e)
+
+    @property
+    def second_moment(self):
+        """Second moment of area of the Beam. """
+        return self._second_moment
+
+    @second_moment.setter
+    def second_moment(self, i):
+        if isinstance(i, list):
+            i = [sympify(x) for x in i]
+            self._second_moment = i
+        else:
+            self._second_moment = sympify(i)
+
+    @property
+    def area(self):
+        """Cross-sectional area of the Beam. """
+        return self._area
+
+    @area.setter
+    def area(self, a):
+        self._area = sympify(a)
+
+    @property
+    def load_vector(self):
+        """
+        Returns a three element list representing the load vector.
+        """
+        return self._load_vector
+
+    @property
+    def moment_load_vector(self):
+        """
+        Returns a three element list representing moment loads on Beam.
+        """
+        return self._moment_load_vector
+
+    @property
+    def boundary_conditions(self):
+        """
+        Returns a dictionary of boundary conditions applied on the beam.
+        The dictionary has two keywords namely slope and deflection.
+        The value of each keyword is a list of tuple, where each tuple
+        contains location and value of a boundary condition in the format
+        (location, value). Further each value is a list corresponding to
+        slope or deflection(s) values along three axes at that location.
+
+        Examples
+        ========
+        There is a beam of length 4 meters. The slope at 0 should be 4 along
+        the x-axis and 0 along others. At the other end of beam, deflection
+        along all the three axes should be zero.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+        >>> from sympy import symbols
+        >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+        >>> b = Beam3D(30, E, G, I, A, x)
+        >>> b.bc_slope = [(0, (4, 0, 0))]
+        >>> b.bc_deflection = [(4, [0, 0, 0])]
+        >>> b.boundary_conditions
+        {'bending_moment': [], 'deflection': [(4, [0, 0, 0])], 'shear_force': [], 'slope': [(0, (4, 0, 0))]}
+
+        Here the deflection of the beam should be ``0`` along all the three axes at ``4``.
+        Similarly, the slope of the beam should be ``4`` along x-axis and ``0``
+        along y and z axis at ``0``.
+        """
+        return self._boundary_conditions
+
+    def polar_moment(self):
+        """
+        Returns the polar moment of area of the beam
+        about the X axis with respect to the centroid.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+        >>> from sympy import symbols
+        >>> l, E, G, I, A = symbols('l, E, G, I, A')
+        >>> b = Beam3D(l, E, G, I, A)
+        >>> b.polar_moment()
+        2*I
+        >>> I1 = [9, 15]
+        >>> b = Beam3D(l, E, G, I1, A)
+        >>> b.polar_moment()
+        24
+        """
+        if not iterable(self.second_moment):
+            return 2*self.second_moment
+        return sum(self.second_moment)
+
+    def apply_load(self, value, start, order, dir="y"):
+        """
+        This method adds up the force load to a particular beam object.
+
+        Parameters
+        ==========
+        value : Sympifyable
+            The magnitude of an applied load.
+        dir : String
+            Axis along which load is applied.
+        order : Integer
+            The order of the applied load.
+            - For point loads, order=-1
+            - For constant distributed load, order=0
+            - For ramp loads, order=1
+            - For parabolic ramp loads, order=2
+            - ... so on.
+        """
+        x = self.variable
+        value = sympify(value)
+        start = sympify(start)
+        order = sympify(order)
+
+        if dir == "x":
+            if not order == -1:
+                self._load_vector[0] += value
+            self._load_Singularity[0] += value*SingularityFunction(x, start, order)
+
+        elif dir == "y":
+            if not order == -1:
+                self._load_vector[1] += value
+            self._load_Singularity[1] += value*SingularityFunction(x, start, order)
+
+        else:
+            if not order == -1:
+                self._load_vector[2] += value
+            self._load_Singularity[2] += value*SingularityFunction(x, start, order)
+
+    def apply_moment_load(self, value, start, order, dir="y"):
+        """
+        This method adds up the moment loads to a particular beam object.
+
+        Parameters
+        ==========
+        value : Sympifyable
+            The magnitude of an applied moment.
+        dir : String
+            Axis along which moment is applied.
+        order : Integer
+            The order of the applied load.
+            - For point moments, order=-2
+            - For constant distributed moment, order=-1
+            - For ramp moments, order=0
+            - For parabolic ramp moments, order=1
+            - ... so on.
+        """
+        x = self.variable
+        value = sympify(value)
+        start = sympify(start)
+        order = sympify(order)
+
+        if dir == "x":
+            if not order == -2:
+                self._moment_load_vector[0] += value
+            else:
+                if start in list(self._torsion_moment):
+                    self._torsion_moment[start] += value
+                else:
+                    self._torsion_moment[start] = value
+            self._load_Singularity[0] += value*SingularityFunction(x, start, order)
+        elif dir == "y":
+            if not order == -2:
+                self._moment_load_vector[1] += value
+            self._load_Singularity[0] += value*SingularityFunction(x, start, order)
+        else:
+            if not order == -2:
+                self._moment_load_vector[2] += value
+            self._load_Singularity[0] += value*SingularityFunction(x, start, order)
+
+    def apply_support(self, loc, type="fixed"):
+        if type in ("pin", "roller"):
+            reaction_load = Symbol('R_'+str(loc))
+            self._reaction_loads[reaction_load] = reaction_load
+            self.bc_deflection.append((loc, [0, 0, 0]))
+        else:
+            reaction_load = Symbol('R_'+str(loc))
+            reaction_moment = Symbol('M_'+str(loc))
+            self._reaction_loads[reaction_load] = [reaction_load, reaction_moment]
+            self.bc_deflection.append((loc, [0, 0, 0]))
+            self.bc_slope.append((loc, [0, 0, 0]))
+
+    def solve_for_reaction_loads(self, *reaction):
+        """
+        Solves for the reaction forces.
+
+        Examples
+        ========
+        There is a beam of length 30 meters. It it supported by rollers at
+        of its end. A constant distributed load of magnitude 8 N is applied
+        from start till its end along y-axis. Another linear load having
+        slope equal to 9 is applied along z-axis.
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+        >>> from sympy import symbols
+        >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+        >>> b = Beam3D(30, E, G, I, A, x)
+        >>> b.apply_load(8, start=0, order=0, dir="y")
+        >>> b.apply_load(9*x, start=0, order=0, dir="z")
+        >>> b.bc_deflection = [(0, [0, 0, 0]), (30, [0, 0, 0])]
+        >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+        >>> b.apply_load(R1, start=0, order=-1, dir="y")
+        >>> b.apply_load(R2, start=30, order=-1, dir="y")
+        >>> b.apply_load(R3, start=0, order=-1, dir="z")
+        >>> b.apply_load(R4, start=30, order=-1, dir="z")
+        >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+        >>> b.reaction_loads
+        {R1: -120, R2: -120, R3: -1350, R4: -2700}
+        """
+        x = self.variable
+        l = self.length
+        q = self._load_Singularity
+        shear_curves = [integrate(load, x) for load in q]
+        moment_curves = [integrate(shear, x) for shear in shear_curves]
+        for i in range(3):
+            react = [r for r in reaction if (shear_curves[i].has(r) or moment_curves[i].has(r))]
+            if len(react) == 0:
+                continue
+            shear_curve = limit(shear_curves[i], x, l)
+            moment_curve = limit(moment_curves[i], x, l)
+            sol = list((linsolve([shear_curve, moment_curve], react).args)[0])
+            sol_dict = dict(zip(react, sol))
+            reaction_loads = self._reaction_loads
+            # Check if any of the evaluated reaction exists in another direction
+            # and if it exists then it should have same value.
+            for key in sol_dict:
+                if key in reaction_loads and sol_dict[key] != reaction_loads[key]:
+                    raise ValueError("Ambiguous solution for %s in different directions." % key)
+            self._reaction_loads.update(sol_dict)
+
+    def shear_force(self):
+        """
+        Returns a list of three expressions which represents the shear force
+        curve of the Beam object along all three axes.
+        """
+        x = self.variable
+        q = self._load_vector
+        return [integrate(-q[0], x), integrate(-q[1], x), integrate(-q[2], x)]
+
+    def axial_force(self):
+        """
+        Returns expression of Axial shear force present inside the Beam object.
+        """
+        return self.shear_force()[0]
+
+    def shear_stress(self):
+        """
+        Returns a list of three expressions which represents the shear stress
+        curve of the Beam object along all three axes.
+        """
+        return [self.shear_force()[0]/self._area, self.shear_force()[1]/self._area, self.shear_force()[2]/self._area]
+
+    def axial_stress(self):
+        """
+        Returns expression of Axial stress present inside the Beam object.
+        """
+        return self.axial_force()/self._area
+
+    def bending_moment(self):
+        """
+        Returns a list of three expressions which represents the bending moment
+        curve of the Beam object along all three axes.
+        """
+        x = self.variable
+        m = self._moment_load_vector
+        shear = self.shear_force()
+
+        return [integrate(-m[0], x), integrate(-m[1] + shear[2], x),
+                integrate(-m[2] - shear[1], x) ]
+
+    def torsional_moment(self):
+        """
+        Returns expression of Torsional moment present inside the Beam object.
+        """
+        return self.bending_moment()[0]
+
+    def solve_for_torsion(self):
+        """
+        Solves for the angular deflection due to the torsional effects of
+        moments being applied in the x-direction i.e. out of or into the beam.
+
+        Here, a positive torque means the direction of the torque is positive
+        i.e. out of the beam along the beam-axis. Likewise, a negative torque
+        signifies a torque into the beam cross-section.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+        >>> from sympy import symbols
+        >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+        >>> b = Beam3D(20, E, G, I, A, x)
+        >>> b.apply_moment_load(4, 4, -2, dir='x')
+        >>> b.apply_moment_load(4, 8, -2, dir='x')
+        >>> b.apply_moment_load(4, 8, -2, dir='x')
+        >>> b.solve_for_torsion()
+        >>> b.angular_deflection().subs(x, 3)
+        18/(G*I)
+        """
+        x = self.variable
+        sum_moments = 0
+        for point in list(self._torsion_moment):
+            sum_moments += self._torsion_moment[point]
+        list(self._torsion_moment).sort()
+        pointsList = list(self._torsion_moment)
+        torque_diagram = Piecewise((sum_moments, x<=pointsList[0]), (0, x>=pointsList[0]))
+        for i in range(len(pointsList))[1:]:
+            sum_moments -= self._torsion_moment[pointsList[i-1]]
+            torque_diagram += Piecewise((0, x<=pointsList[i-1]), (sum_moments, x<=pointsList[i]), (0, x>=pointsList[i]))
+        integrated_torque_diagram = integrate(torque_diagram)
+        self._angular_deflection =  integrated_torque_diagram/(self.shear_modulus*self.polar_moment())
+
+    def solve_slope_deflection(self):
+        x = self.variable
+        l = self.length
+        E = self.elastic_modulus
+        G = self.shear_modulus
+        I = self.second_moment
+        if isinstance(I, list):
+            I_y, I_z = I[0], I[1]
+        else:
+            I_y = I_z = I
+        A = self._area
+        load = self._load_vector
+        moment = self._moment_load_vector
+        defl = Function('defl')
+        theta = Function('theta')
+
+        # Finding deflection along x-axis(and corresponding slope value by differentiating it)
+        # Equation used: Derivative(E*A*Derivative(def_x(x), x), x) + load_x = 0
+        eq = Derivative(E*A*Derivative(defl(x), x), x) + load[0]
+        def_x = dsolve(Eq(eq, 0), defl(x)).args[1]
+        # Solving constants originated from dsolve
+        C1 = Symbol('C1')
+        C2 = Symbol('C2')
+        constants = list((linsolve([def_x.subs(x, 0), def_x.subs(x, l)], C1, C2).args)[0])
+        def_x = def_x.subs({C1:constants[0], C2:constants[1]})
+        slope_x = def_x.diff(x)
+        self._deflection[0] = def_x
+        self._slope[0] = slope_x
+
+        # Finding deflection along y-axis and slope across z-axis. System of equation involved:
+        # 1: Derivative(E*I_z*Derivative(theta_z(x), x), x) + G*A*(Derivative(defl_y(x), x) - theta_z(x)) + moment_z = 0
+        # 2: Derivative(G*A*(Derivative(defl_y(x), x) - theta_z(x)), x) + load_y = 0
+        C_i = Symbol('C_i')
+        # Substitute value of `G*A*(Derivative(defl_y(x), x) - theta_z(x))` from (2) in (1)
+        eq1 = Derivative(E*I_z*Derivative(theta(x), x), x) + (integrate(-load[1], x) + C_i) + moment[2]
+        slope_z = dsolve(Eq(eq1, 0)).args[1]
+
+        # Solve for constants originated from using dsolve on eq1
+        constants = list((linsolve([slope_z.subs(x, 0), slope_z.subs(x, l)], C1, C2).args)[0])
+        slope_z = slope_z.subs({C1:constants[0], C2:constants[1]})
+
+        # Put value of slope obtained back in (2) to solve for `C_i` and find deflection across y-axis
+        eq2 = G*A*(Derivative(defl(x), x)) + load[1]*x - C_i - G*A*slope_z
+        def_y = dsolve(Eq(eq2, 0), defl(x)).args[1]
+        # Solve for constants originated from using dsolve on eq2
+        constants = list((linsolve([def_y.subs(x, 0), def_y.subs(x, l)], C1, C_i).args)[0])
+        self._deflection[1] = def_y.subs({C1:constants[0], C_i:constants[1]})
+        self._slope[2] = slope_z.subs(C_i, constants[1])
+
+        # Finding deflection along z-axis and slope across y-axis. System of equation involved:
+        # 1: Derivative(E*I_y*Derivative(theta_y(x), x), x) - G*A*(Derivative(defl_z(x), x) + theta_y(x)) + moment_y = 0
+        # 2: Derivative(G*A*(Derivative(defl_z(x), x) + theta_y(x)), x) + load_z = 0
+
+        # Substitute value of `G*A*(Derivative(defl_y(x), x) + theta_z(x))` from (2) in (1)
+        eq1 = Derivative(E*I_y*Derivative(theta(x), x), x) + (integrate(load[2], x) - C_i) + moment[1]
+        slope_y = dsolve(Eq(eq1, 0)).args[1]
+        # Solve for constants originated from using dsolve on eq1
+        constants = list((linsolve([slope_y.subs(x, 0), slope_y.subs(x, l)], C1, C2).args)[0])
+        slope_y = slope_y.subs({C1:constants[0], C2:constants[1]})
+
+        # Put value of slope obtained back in (2) to solve for `C_i` and find deflection across z-axis
+        eq2 = G*A*(Derivative(defl(x), x)) + load[2]*x - C_i + G*A*slope_y
+        def_z = dsolve(Eq(eq2,0)).args[1]
+        # Solve for constants originated from using dsolve on eq2
+        constants = list((linsolve([def_z.subs(x, 0), def_z.subs(x, l)], C1, C_i).args)[0])
+        self._deflection[2] = def_z.subs({C1:constants[0], C_i:constants[1]})
+        self._slope[1] = slope_y.subs(C_i, constants[1])
+
+    def slope(self):
+        """
+        Returns a three element list representing slope of deflection curve
+        along all the three axes.
+        """
+        return self._slope
+
+    def deflection(self):
+        """
+        Returns a three element list representing deflection curve along all
+        the three axes.
+        """
+        return self._deflection
+
+    def angular_deflection(self):
+        """
+        Returns a function in x depicting how the angular deflection, due to moments
+        in the x-axis on the beam, varies with x.
+        """
+        return self._angular_deflection
+
+    def _plot_shear_force(self, dir, subs=None):
+
+        shear_force = self.shear_force()
+
+        if dir == 'x':
+            dir_num = 0
+            color = 'r'
+
+        elif dir == 'y':
+            dir_num = 1
+            color = 'g'
+
+        elif dir == 'z':
+            dir_num = 2
+            color = 'b'
+
+        if subs is None:
+            subs = {}
+
+        for sym in shear_force[dir_num].atoms(Symbol):
+            if sym != self.variable and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+
+        return plot(shear_force[dir_num].subs(subs), (self.variable, 0, length), show = False, title='Shear Force along %c direction'%dir,
+                xlabel=r'$\mathrm{X}$', ylabel=r'$\mathrm{V(%c)}$'%dir, line_color=color)
+
+    def plot_shear_force(self, dir="all", subs=None):
+
+        """
+
+        Returns a plot for Shear force along all three directions
+        present in the Beam object.
+
+        Parameters
+        ==========
+        dir : string (default : "all")
+            Direction along which shear force plot is required.
+            If no direction is specified, all plots are displayed.
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 20 meters. It is supported by rollers
+        at both of its ends. A linear load having slope equal to 12 is applied
+        along y-axis. A constant distributed load of magnitude 15 N is
+        applied from start till its end along z-axis.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, E, G, I, A, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.plot_shear_force()
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: 0 for x over (0.0, 20.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: -6*x**2 for x over (0.0, 20.0)
+            Plot[2]:Plot object containing:
+            [0]: cartesian line: -15*x for x over (0.0, 20.0)
+
+        """
+
+        dir = dir.lower()
+        # For shear force along x direction
+        if dir == "x":
+            Px = self._plot_shear_force('x', subs)
+            return Px.show()
+        # For shear force along y direction
+        elif dir == "y":
+            Py = self._plot_shear_force('y', subs)
+            return Py.show()
+        # For shear force along z direction
+        elif dir == "z":
+            Pz = self._plot_shear_force('z', subs)
+            return Pz.show()
+        # For shear force along all direction
+        else:
+            Px = self._plot_shear_force('x', subs)
+            Py = self._plot_shear_force('y', subs)
+            Pz = self._plot_shear_force('z', subs)
+            return PlotGrid(3, 1, Px, Py, Pz)
+
+    def _plot_bending_moment(self, dir, subs=None):
+
+        bending_moment = self.bending_moment()
+
+        if dir == 'x':
+            dir_num = 0
+            color = 'g'
+
+        elif dir == 'y':
+            dir_num = 1
+            color = 'c'
+
+        elif dir == 'z':
+            dir_num = 2
+            color = 'm'
+
+        if subs is None:
+            subs = {}
+
+        for sym in bending_moment[dir_num].atoms(Symbol):
+            if sym != self.variable and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+
+        return plot(bending_moment[dir_num].subs(subs), (self.variable, 0, length), show = False, title='Bending Moment along %c direction'%dir,
+                xlabel=r'$\mathrm{X}$', ylabel=r'$\mathrm{M(%c)}$'%dir, line_color=color)
+
+    def plot_bending_moment(self, dir="all", subs=None):
+
+        """
+
+        Returns a plot for bending moment along all three directions
+        present in the Beam object.
+
+        Parameters
+        ==========
+        dir : string (default : "all")
+            Direction along which bending moment plot is required.
+            If no direction is specified, all plots are displayed.
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 20 meters. It is supported by rollers
+        at both of its ends. A linear load having slope equal to 12 is applied
+        along y-axis. A constant distributed load of magnitude 15 N is
+        applied from start till its end along z-axis.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, E, G, I, A, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.plot_bending_moment()
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: 0 for x over (0.0, 20.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: -15*x**2/2 for x over (0.0, 20.0)
+            Plot[2]:Plot object containing:
+            [0]: cartesian line: 2*x**3 for x over (0.0, 20.0)
+
+        """
+
+        dir = dir.lower()
+        # For bending moment along x direction
+        if dir == "x":
+            Px = self._plot_bending_moment('x', subs)
+            return Px.show()
+        # For bending moment along y direction
+        elif dir == "y":
+            Py = self._plot_bending_moment('y', subs)
+            return Py.show()
+        # For bending moment along z direction
+        elif dir == "z":
+            Pz = self._plot_bending_moment('z', subs)
+            return Pz.show()
+        # For bending moment along all direction
+        else:
+            Px = self._plot_bending_moment('x', subs)
+            Py = self._plot_bending_moment('y', subs)
+            Pz = self._plot_bending_moment('z', subs)
+            return PlotGrid(3, 1, Px, Py, Pz)
+
+    def _plot_slope(self, dir, subs=None):
+
+        slope = self.slope()
+
+        if dir == 'x':
+            dir_num = 0
+            color = 'b'
+
+        elif dir == 'y':
+            dir_num = 1
+            color = 'm'
+
+        elif dir == 'z':
+            dir_num = 2
+            color = 'g'
+
+        if subs is None:
+            subs = {}
+
+        for sym in slope[dir_num].atoms(Symbol):
+            if sym != self.variable and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+
+
+        return plot(slope[dir_num].subs(subs), (self.variable, 0, length), show = False, title='Slope along %c direction'%dir,
+                xlabel=r'$\mathrm{X}$', ylabel=r'$\mathrm{\theta(%c)}$'%dir, line_color=color)
+
+    def plot_slope(self, dir="all", subs=None):
+
+        """
+
+        Returns a plot for Slope along all three directions
+        present in the Beam object.
+
+        Parameters
+        ==========
+        dir : string (default : "all")
+            Direction along which Slope plot is required.
+            If no direction is specified, all plots are displayed.
+        subs : dictionary
+            Python dictionary containing Symbols as keys and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 20 meters. It is supported by rollers
+        at both of its ends. A linear load having slope equal to 12 is applied
+        along y-axis. A constant distributed load of magnitude 15 N is
+        applied from start till its end along z-axis.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, 40, 21, 100, 25, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.solve_slope_deflection()
+            >>> b.plot_slope()
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: 0 for x over (0.0, 20.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: -x**3/1600 + 3*x**2/160 - x/8 for x over (0.0, 20.0)
+            Plot[2]:Plot object containing:
+            [0]: cartesian line: x**4/8000 - 19*x**2/172 + 52*x/43 for x over (0.0, 20.0)
+
+        """
+
+        dir = dir.lower()
+        # For Slope along x direction
+        if dir == "x":
+            Px = self._plot_slope('x', subs)
+            return Px.show()
+        # For Slope along y direction
+        elif dir == "y":
+            Py = self._plot_slope('y', subs)
+            return Py.show()
+        # For Slope along z direction
+        elif dir == "z":
+            Pz = self._plot_slope('z', subs)
+            return Pz.show()
+        # For Slope along all direction
+        else:
+            Px = self._plot_slope('x', subs)
+            Py = self._plot_slope('y', subs)
+            Pz = self._plot_slope('z', subs)
+            return PlotGrid(3, 1, Px, Py, Pz)
+
+    def _plot_deflection(self, dir, subs=None):
+
+        deflection = self.deflection()
+
+        if dir == 'x':
+            dir_num = 0
+            color = 'm'
+
+        elif dir == 'y':
+            dir_num = 1
+            color = 'r'
+
+        elif dir == 'z':
+            dir_num = 2
+            color = 'c'
+
+        if subs is None:
+            subs = {}
+
+        for sym in deflection[dir_num].atoms(Symbol):
+            if sym != self.variable and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+
+        return plot(deflection[dir_num].subs(subs), (self.variable, 0, length), show = False, title='Deflection along %c direction'%dir,
+                xlabel=r'$\mathrm{X}$', ylabel=r'$\mathrm{\delta(%c)}$'%dir, line_color=color)
+
+    def plot_deflection(self, dir="all", subs=None):
+
+        """
+
+        Returns a plot for Deflection along all three directions
+        present in the Beam object.
+
+        Parameters
+        ==========
+        dir : string (default : "all")
+            Direction along which deflection plot is required.
+            If no direction is specified, all plots are displayed.
+        subs : dictionary
+            Python dictionary containing Symbols as keys and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 20 meters. It is supported by rollers
+        at both of its ends. A linear load having slope equal to 12 is applied
+        along y-axis. A constant distributed load of magnitude 15 N is
+        applied from start till its end along z-axis.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, 40, 21, 100, 25, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.solve_slope_deflection()
+            >>> b.plot_deflection()
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: 0 for x over (0.0, 20.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: x**5/40000 - 4013*x**3/90300 + 26*x**2/43 + 1520*x/903 for x over (0.0, 20.0)
+            Plot[2]:Plot object containing:
+            [0]: cartesian line: x**4/6400 - x**3/160 + 27*x**2/560 + 2*x/7 for x over (0.0, 20.0)
+
+
+        """
+
+        dir = dir.lower()
+        # For deflection along x direction
+        if dir == "x":
+            Px = self._plot_deflection('x', subs)
+            return Px.show()
+        # For deflection along y direction
+        elif dir == "y":
+            Py = self._plot_deflection('y', subs)
+            return Py.show()
+        # For deflection along z direction
+        elif dir == "z":
+            Pz = self._plot_deflection('z', subs)
+            return Pz.show()
+        # For deflection along all direction
+        else:
+            Px = self._plot_deflection('x', subs)
+            Py = self._plot_deflection('y', subs)
+            Pz = self._plot_deflection('z', subs)
+            return PlotGrid(3, 1, Px, Py, Pz)
+
+    def plot_loading_results(self, dir='x', subs=None):
+
+        """
+
+        Returns a subplot of Shear Force, Bending Moment,
+        Slope and Deflection of the Beam object along the direction specified.
+
+        Parameters
+        ==========
+
+        dir : string (default : "x")
+               Direction along which plots are required.
+               If no direction is specified, plots along x-axis are displayed.
+        subs : dictionary
+               Python dictionary containing Symbols as key and their
+               corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 20 meters. It is supported by rollers
+        at both of its ends. A linear load having slope equal to 12 is applied
+        along y-axis. A constant distributed load of magnitude 15 N is
+        applied from start till its end along z-axis.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, E, G, I, A, x)
+            >>> subs = {E:40, G:21, I:100, A:25}
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.solve_slope_deflection()
+            >>> b.plot_loading_results('y',subs)
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: -6*x**2 for x over (0.0, 20.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: -15*x**2/2 for x over (0.0, 20.0)
+            Plot[2]:Plot object containing:
+            [0]: cartesian line: -x**3/1600 + 3*x**2/160 - x/8 for x over (0.0, 20.0)
+            Plot[3]:Plot object containing:
+            [0]: cartesian line: x**5/40000 - 4013*x**3/90300 + 26*x**2/43 + 1520*x/903 for x over (0.0, 20.0)
+
+        """
+
+        dir = dir.lower()
+        if subs is None:
+            subs = {}
+
+        ax1 = self._plot_shear_force(dir, subs)
+        ax2 = self._plot_bending_moment(dir, subs)
+        ax3 = self._plot_slope(dir, subs)
+        ax4 = self._plot_deflection(dir, subs)
+
+        return PlotGrid(4, 1, ax1, ax2, ax3, ax4)
+
+    def _plot_shear_stress(self, dir, subs=None):
+
+        shear_stress = self.shear_stress()
+
+        if dir == 'x':
+            dir_num = 0
+            color = 'r'
+
+        elif dir == 'y':
+            dir_num = 1
+            color = 'g'
+
+        elif dir == 'z':
+            dir_num = 2
+            color = 'b'
+
+        if subs is None:
+            subs = {}
+
+        for sym in shear_stress[dir_num].atoms(Symbol):
+            if sym != self.variable and sym not in subs:
+                raise ValueError('Value of %s was not passed.' %sym)
+        if self.length in subs:
+            length = subs[self.length]
+        else:
+            length = self.length
+
+        return plot(shear_stress[dir_num].subs(subs), (self.variable, 0, length), show = False, title='Shear stress along %c direction'%dir,
+                xlabel=r'$\mathrm{X}$', ylabel=r'$\tau(%c)$'%dir, line_color=color)
+
+    def plot_shear_stress(self, dir="all", subs=None):
+
+        """
+
+        Returns a plot for Shear Stress along all three directions
+        present in the Beam object.
+
+        Parameters
+        ==========
+        dir : string (default : "all")
+            Direction along which shear stress plot is required.
+            If no direction is specified, all plots are displayed.
+        subs : dictionary
+            Python dictionary containing Symbols as key and their
+            corresponding values.
+
+        Examples
+        ========
+        There is a beam of length 20 meters and area of cross section 2 square
+        meters. It is supported by rollers at both of its ends. A linear load having
+        slope equal to 12 is applied along y-axis. A constant distributed load
+        of magnitude 15 N is applied from start till its end along z-axis.
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, E, G, I, 2, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.plot_shear_stress()
+            PlotGrid object containing:
+            Plot[0]:Plot object containing:
+            [0]: cartesian line: 0 for x over (0.0, 20.0)
+            Plot[1]:Plot object containing:
+            [0]: cartesian line: -3*x**2 for x over (0.0, 20.0)
+            Plot[2]:Plot object containing:
+            [0]: cartesian line: -15*x/2 for x over (0.0, 20.0)
+
+        """
+
+        dir = dir.lower()
+        # For shear stress along x direction
+        if dir == "x":
+            Px = self._plot_shear_stress('x', subs)
+            return Px.show()
+        # For shear stress along y direction
+        elif dir == "y":
+            Py = self._plot_shear_stress('y', subs)
+            return Py.show()
+        # For shear stress along z direction
+        elif dir == "z":
+            Pz = self._plot_shear_stress('z', subs)
+            return Pz.show()
+        # For shear stress along all direction
+        else:
+            Px = self._plot_shear_stress('x', subs)
+            Py = self._plot_shear_stress('y', subs)
+            Pz = self._plot_shear_stress('z', subs)
+            return PlotGrid(3, 1, Px, Py, Pz)
+
+    def _max_shear_force(self, dir):
+        """
+        Helper function for max_shear_force().
+        """
+
+        dir = dir.lower()
+
+        if dir == 'x':
+            dir_num = 0
+
+        elif dir == 'y':
+            dir_num = 1
+
+        elif dir == 'z':
+            dir_num = 2
+
+        if not self.shear_force()[dir_num]:
+            return (0,0)
+        # To restrict the range within length of the Beam
+        load_curve = Piecewise((float("nan"), self.variable<=0),
+                (self._load_vector[dir_num], self.variable>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, 40, 21, 100, 25, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.max_shear_force()
+            [(0, 0), (20, 2400), (20, 300)]
+        """
+
+        max_shear = []
+        max_shear.append(self._max_shear_force('x'))
+        max_shear.append(self._max_shear_force('y'))
+        max_shear.append(self._max_shear_force('z'))
+        return max_shear
+
+    def _max_bending_moment(self, dir):
+        """
+        Helper function for max_bending_moment().
+        """
+
+        dir = dir.lower()
+
+        if dir == 'x':
+            dir_num = 0
+
+        elif dir == 'y':
+            dir_num = 1
+
+        elif dir == 'z':
+            dir_num = 2
+
+        if not self.bending_moment()[dir_num]:
+            return (0,0)
+        # To restrict the range within length of the Beam
+        shear_curve = Piecewise((float("nan"), self.variable<=0),
+                (self.shear_force()[dir_num], self.variable>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, 40, 21, 100, 25, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.max_bending_moment()
+            [(0, 0), (20, 3000), (20, 16000)]
+        """
+
+        max_bmoment = []
+        max_bmoment.append(self._max_bending_moment('x'))
+        max_bmoment.append(self._max_bending_moment('y'))
+        max_bmoment.append(self._max_bending_moment('z'))
+        return max_bmoment
+
+    max_bmoment = max_bending_moment
+
+    def _max_deflection(self, dir):
+        """
+        Helper function for max_Deflection()
+        """
+
+        dir = dir.lower()
+
+        if dir == 'x':
+            dir_num = 0
+
+        elif dir == 'y':
+            dir_num = 1
+
+        elif dir == 'z':
+            dir_num = 2
+
+        if not self.deflection()[dir_num]:
+            return (0,0)
+        # To restrict the range within length of the Beam
+        slope_curve = Piecewise((float("nan"), self.variable<=0),
+                (self.slope()[dir_num], self.variable>> from sympy.physics.continuum_mechanics.beam import Beam3D
+            >>> from sympy import symbols
+            >>> l, E, G, I, A, x = symbols('l, E, G, I, A, x')
+            >>> b = Beam3D(20, 40, 21, 100, 25, x)
+            >>> b.apply_load(15, start=0, order=0, dir="z")
+            >>> b.apply_load(12*x, start=0, order=0, dir="y")
+            >>> b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+            >>> R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+            >>> b.apply_load(R1, start=0, order=-1, dir="z")
+            >>> b.apply_load(R2, start=20, order=-1, dir="z")
+            >>> b.apply_load(R3, start=0, order=-1, dir="y")
+            >>> b.apply_load(R4, start=20, order=-1, dir="y")
+            >>> b.solve_for_reaction_loads(R1, R2, R3, R4)
+            >>> b.solve_slope_deflection()
+            >>> b.max_deflection()
+            [(0, 0), (10, 495/14), (-10 + 10*sqrt(10793)/43, (10 - 10*sqrt(10793)/43)**3/160 - 20/7 + (10 - 10*sqrt(10793)/43)**4/6400 + 20*sqrt(10793)/301 + 27*(10 - 10*sqrt(10793)/43)**2/560)]
+        """
+
+        max_def = []
+        max_def.append(self._max_deflection('x'))
+        max_def.append(self._max_deflection('y'))
+        max_def.append(self._max_deflection('z'))
+        return max_def
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py
new file mode 100644
index 0000000000000000000000000000000000000000..e38c6601b0a12cad83bc7e87597e79937f4667a4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py
@@ -0,0 +1,815 @@
+"""
+This module can be used to solve problems related
+to 2D Cables.
+"""
+
+from sympy.core.sympify import sympify
+from sympy.core.symbol import Symbol,symbols
+from sympy import sin, cos, pi, atan, diff, Piecewise, solve, rad
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.solvers.solveset import linsolve
+from sympy.matrices import Matrix
+from sympy.plotting import plot
+
+class Cable:
+    """
+    Cables are structures in engineering that support
+    the applied transverse loads through the tensile
+    resistance developed in its members.
+
+    Cables are widely used in suspension bridges, tension
+    leg offshore platforms, transmission lines, and find
+    use in several other engineering applications.
+
+    Examples
+    ========
+    A cable is supported at (0, 10) and (10, 10). Two point loads
+    acting vertically downwards act on the cable, one with magnitude 3 kN
+    and acting 2 meters from the left support and 3 meters below it, while
+    the other with magnitude 2 kN is 6 meters from the left support and
+    6 meters below it.
+
+    >>> from sympy.physics.continuum_mechanics.cable import Cable
+    >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+    >>> c.apply_load(-1, ('P', 2, 7, 3, 270))
+    >>> c.apply_load(-1, ('Q', 6, 4, 2, 270))
+    >>> c.loads
+    {'distributed': {}, 'point_load': {'P': [3, 270], 'Q': [2, 270]}}
+    >>> c.loads_position
+    {'P': [2, 7], 'Q': [6, 4]}
+    """
+    def __init__(self, support_1, support_2):
+        """
+        Initializes the class.
+
+        Parameters
+        ==========
+
+        support_1 and support_2 are tuples of the form
+        (label, x, y), where
+
+        label : String or symbol
+            The label of the support
+
+        x : Sympifyable
+            The x coordinate of the position of the support
+
+        y : Sympifyable
+            The y coordinate of the position of the support
+        """
+        self._left_support = []
+        self._right_support = []
+        self._supports = {}
+        self._support_labels = []
+        self._loads = {"distributed": {}, "point_load": {}}
+        self._loads_position = {}
+        self._length = 0
+        self._reaction_loads = {}
+        self._tension = {}
+        self._lowest_x_global = sympify(0)
+        self._lowest_y_global = sympify(0)
+        self._cable_eqn = None
+        self._tension_func = None
+        if support_1[0] == support_2[0]:
+            raise ValueError("Supports can not have the same label")
+
+        elif support_1[1] == support_2[1]:
+            raise ValueError("Supports can not be at the same location")
+
+        x1 = sympify(support_1[1])
+        y1 = sympify(support_1[2])
+        self._supports[support_1[0]] = [x1, y1]
+
+        x2 = sympify(support_2[1])
+        y2 = sympify(support_2[2])
+        self._supports[support_2[0]] = [x2, y2]
+
+        if support_1[1] < support_2[1]:
+            self._left_support.append(x1)
+            self._left_support.append(y1)
+            self._right_support.append(x2)
+            self._right_support.append(y2)
+            self._support_labels.append(support_1[0])
+            self._support_labels.append(support_2[0])
+
+        else:
+            self._left_support.append(x2)
+            self._left_support.append(y2)
+            self._right_support.append(x1)
+            self._right_support.append(y1)
+            self._support_labels.append(support_2[0])
+            self._support_labels.append(support_1[0])
+
+        for i in self._support_labels:
+            self._reaction_loads[Symbol("R_"+ i +"_x")] = 0
+            self._reaction_loads[Symbol("R_"+ i +"_y")] = 0
+
+    @property
+    def supports(self):
+        """
+        Returns the supports of the cable along with their
+        positions.
+        """
+        return self._supports
+
+    @property
+    def left_support(self):
+        """
+        Returns the position of the left support.
+        """
+        return self._left_support
+
+    @property
+    def right_support(self):
+        """
+        Returns the position of the right support.
+        """
+        return self._right_support
+
+    @property
+    def loads(self):
+        """
+        Returns the magnitude and direction of the loads
+        acting on the cable.
+        """
+        return self._loads
+
+    @property
+    def loads_position(self):
+        """
+        Returns the position of the point loads acting on the
+        cable.
+        """
+        return self._loads_position
+
+    @property
+    def length(self):
+        """
+        Returns the length of the cable.
+        """
+        return self._length
+
+    @property
+    def reaction_loads(self):
+        """
+        Returns the reaction forces at the supports, which are
+        initialized to 0.
+        """
+        return self._reaction_loads
+
+    @property
+    def tension(self):
+        """
+        Returns the tension developed in the cable due to the loads
+        applied.
+        """
+        return self._tension
+
+    def tension_at(self, x):
+        """
+        Returns the tension at a given value of x developed due to
+        distributed load.
+        """
+        if 'distributed' not in self._tension.keys():
+            raise ValueError("No distributed load added or solve method not called")
+
+        if x > self._right_support[0] or x < self._left_support[0]:
+            raise ValueError("The value of x should be between the two supports")
+
+        A = self._tension['distributed']
+        X = Symbol('X')
+
+        return A.subs({X:(x-self._lowest_x_global)})
+
+    def apply_length(self, length):
+        """
+        This method specifies the length of the cable
+
+        Parameters
+        ==========
+
+        length : Sympifyable
+            The length of the cable
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_length(20)
+        >>> c.length
+        20
+        """
+        dist = ((self._left_support[0] - self._right_support[0])**2
+                - (self._left_support[1] - self._right_support[1])**2)**(1/2)
+
+        if length < dist:
+            raise ValueError("length should not be less than the distance between the supports")
+
+        self._length = length
+
+    def change_support(self, label, new_support):
+        """
+        This method changes the mentioned support with a new support.
+
+        Parameters
+        ==========
+        label: String or symbol
+            The label of the support to be changed
+
+        new_support: Tuple of the form (new_label, x, y)
+            new_label: String or symbol
+                The label of the new support
+
+            x: Sympifyable
+                The x-coordinate of the position of the new support.
+
+            y: Sympifyable
+                The y-coordinate of the position of the new support.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.supports
+        {'A': [0, 10], 'B': [10, 10]}
+        >>> c.change_support('B', ('C', 5, 6))
+        >>> c.supports
+        {'A': [0, 10], 'C': [5, 6]}
+        """
+        if label not in self._supports:
+            raise ValueError("No support exists with the given label")
+
+        i = self._support_labels.index(label)
+        rem_label = self._support_labels[(i+1)%2]
+        x1 = self._supports[rem_label][0]
+        y1 = self._supports[rem_label][1]
+
+        x = sympify(new_support[1])
+        y = sympify(new_support[2])
+
+        for l in self._loads_position:
+            if l[0] >= max(x, x1) or l[0] <= min(x, x1):
+                raise ValueError("The change in support will throw an existing load out of range")
+
+        self._supports.pop(label)
+        self._left_support.clear()
+        self._right_support.clear()
+        self._reaction_loads.clear()
+        self._support_labels.remove(label)
+
+        self._supports[new_support[0]] = [x, y]
+
+        if x1 < x:
+            self._left_support.append(x1)
+            self._left_support.append(y1)
+            self._right_support.append(x)
+            self._right_support.append(y)
+            self._support_labels.append(new_support[0])
+
+        else:
+            self._left_support.append(x)
+            self._left_support.append(y)
+            self._right_support.append(x1)
+            self._right_support.append(y1)
+            self._support_labels.insert(0, new_support[0])
+
+        for i in self._support_labels:
+            self._reaction_loads[Symbol("R_"+ i +"_x")] = 0
+            self._reaction_loads[Symbol("R_"+ i +"_y")] = 0
+
+    def apply_load(self, order, load):
+        """
+        This method adds load to the cable.
+
+        Parameters
+        ==========
+
+        order : Integer
+            The order of the applied load.
+
+                - For point loads, order = -1
+                - For distributed load, order = 0
+
+        load : tuple
+
+            * For point loads, load is of the form (label, x, y, magnitude, direction), where:
+
+            label : String or symbol
+                The label of the load
+
+            x : Sympifyable
+                The x coordinate of the position of the load
+
+            y : Sympifyable
+                The y coordinate of the position of the load
+
+            magnitude : Sympifyable
+                The magnitude of the load. It must always be positive
+
+            direction : Sympifyable
+                The angle, in degrees, that the load vector makes with the horizontal
+                in the counter-clockwise direction. It takes the values 0 to 360,
+                inclusive.
+
+
+            * For uniformly distributed load, load is of the form (label, magnitude)
+
+            label : String or symbol
+                The label of the load
+
+            magnitude : Sympifyable
+                The magnitude of the load. It must always be positive
+
+        Examples
+        ========
+
+        For a point load of magnitude 12 units inclined at 30 degrees with the horizontal:
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_load(-1, ('Z', 5, 5, 12, 30))
+        >>> c.loads
+        {'distributed': {}, 'point_load': {'Z': [12, 30]}}
+        >>> c.loads_position
+        {'Z': [5, 5]}
+
+
+        For a uniformly distributed load of magnitude 9 units:
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_load(0, ('X', 9))
+        >>> c.loads
+        {'distributed': {'X': 9}, 'point_load': {}}
+        """
+        if order == -1:
+            if len(self._loads["distributed"]) != 0:
+                raise ValueError("Distributed load already exists")
+
+            label = load[0]
+            if label in self._loads["point_load"]:
+                raise ValueError("Label already exists")
+
+            x = sympify(load[1])
+            y = sympify(load[2])
+
+            if x > self._right_support[0] or x < self._left_support[0]:
+                raise ValueError("The load should be positioned between the supports")
+
+            magnitude = sympify(load[3])
+            direction = sympify(load[4])
+
+            self._loads["point_load"][label] = [magnitude, direction]
+            self._loads_position[label] = [x, y]
+
+        elif order == 0:
+            if len(self._loads_position) != 0:
+                raise ValueError("Point load(s) already exist")
+
+            label = load[0]
+            if label in self._loads["distributed"]:
+                raise ValueError("Label already exists")
+
+            magnitude = sympify(load[1])
+
+            self._loads["distributed"][label] = magnitude
+
+        else:
+            raise ValueError("Order should be either -1 or 0")
+
+    def remove_loads(self, *args):
+        """
+        This methods removes the specified loads.
+
+        Parameters
+        ==========
+        This input takes multiple label(s) as input
+        label(s): String or symbol
+            The label(s) of the loads to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_load(-1, ('Z', 5, 5, 12, 30))
+        >>> c.loads
+        {'distributed': {}, 'point_load': {'Z': [12, 30]}}
+        >>> c.remove_loads('Z')
+        >>> c.loads
+        {'distributed': {}, 'point_load': {}}
+        """
+        for i in args:
+            if len(self._loads_position) == 0:
+                if i not in self._loads['distributed']:
+                    raise ValueError("Error removing load " + i + ": no such load exists")
+
+                else:
+                    self._loads['disrtibuted'].pop(i)
+
+            else:
+                if i not in self._loads['point_load']:
+                    raise ValueError("Error removing load " + i + ": no such load exists")
+
+                else:
+                    self._loads['point_load'].pop(i)
+                    self._loads_position.pop(i)
+
+    def solve(self, *args):
+        """
+        This method solves for the reaction forces at the supports, the tension developed in
+        the cable, and updates the length of the cable.
+
+        Parameters
+        ==========
+        This method requires no input when solving for point loads
+        For distributed load, the x and y coordinates of the lowest point of the cable are
+        required as
+
+        x: Sympifyable
+            The x coordinate of the lowest point
+
+        y: Sympifyable
+            The y coordinate of the lowest point
+
+        Examples
+        ========
+        For point loads,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(("A", 0, 10), ("B", 10, 10))
+        >>> c.apply_load(-1, ('Z', 2, 7.26, 3, 270))
+        >>> c.apply_load(-1, ('X', 4, 6, 8, 270))
+        >>> c.solve()
+        >>> c.tension
+        {A_Z: 8.91403453669861, X_B: 19*sqrt(13)/10, Z_X: 4.79150773600774}
+        >>> c.reaction_loads
+        {R_A_x: -5.25547445255474, R_A_y: 7.2, R_B_x: 5.25547445255474, R_B_y: 3.8}
+        >>> c.length
+        5.7560958484519 + 2*sqrt(13)
+
+        For distributed load,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c=Cable(("A", 0, 40),("B", 100, 20))
+        >>> c.apply_load(0, ("X", 850))
+        >>> c.solve(58.58)
+        >>> c.tension
+        {'distributed': 36465.0*sqrt(0.00054335718671383*X**2 + 1)}
+        >>> c.tension_at(0)
+        61717.4130533677
+        >>> c.reaction_loads
+        {R_A_x: 36465.0, R_A_y: -49793.0, R_B_x: 44399.9537590861, R_B_y: 42868.2071025955}
+        """
+
+        if len(self._loads_position) != 0:
+            sorted_position = sorted(self._loads_position.items(), key = lambda item : item[1][0])
+
+            sorted_position.append(self._support_labels[1])
+            sorted_position.insert(0, self._support_labels[0])
+
+            self._tension.clear()
+            moment_sum_from_left_support = 0
+            moment_sum_from_right_support = 0
+            F_x = 0
+            F_y = 0
+            self._length = 0
+            tension_func = []
+            x = symbols('x')
+            for i in range(1, len(sorted_position)-1):
+                if i == 1:
+                    self._length+=sqrt((self._left_support[0] - self._loads_position[sorted_position[i][0]][0])**2 + (self._left_support[1] - self._loads_position[sorted_position[i][0]][1])**2)
+
+                else:
+                    self._length+=sqrt((self._loads_position[sorted_position[i-1][0]][0] - self._loads_position[sorted_position[i][0]][0])**2 + (self._loads_position[sorted_position[i-1][0]][1] - self._loads_position[sorted_position[i][0]][1])**2)
+
+                if i == len(sorted_position)-2:
+                    self._length+=sqrt((self._right_support[0] - self._loads_position[sorted_position[i][0]][0])**2 + (self._right_support[1] - self._loads_position[sorted_position[i][0]][1])**2)
+
+                moment_sum_from_left_support += self._loads['point_load'][sorted_position[i][0]][0] * cos(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._left_support[1] - self._loads_position[sorted_position[i][0]][1])
+                moment_sum_from_left_support += self._loads['point_load'][sorted_position[i][0]][0] * sin(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._left_support[0] - self._loads_position[sorted_position[i][0]][0])
+
+                F_x += self._loads['point_load'][sorted_position[i][0]][0] * cos(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180)
+                F_y += self._loads['point_load'][sorted_position[i][0]][0] * sin(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180)
+
+                label = Symbol(sorted_position[i][0]+"_"+sorted_position[i+1][0])
+                y2 = self._loads_position[sorted_position[i][0]][1]
+                x2 = self._loads_position[sorted_position[i][0]][0]
+                y1 = 0
+                x1 = 0
+
+                if i == len(sorted_position)-2:
+                    x1 = self._right_support[0]
+                    y1 = self._right_support[1]
+
+                else:
+                    x1 = self._loads_position[sorted_position[i+1][0]][0]
+                    y1 = self._loads_position[sorted_position[i+1][0]][1]
+
+                angle_with_horizontal = atan((y1 - y2)/(x1 - x2))
+
+                tension = -(moment_sum_from_left_support)/(abs(self._left_support[1] - self._loads_position[sorted_position[i][0]][1])*cos(angle_with_horizontal) + abs(self._left_support[0] - self._loads_position[sorted_position[i][0]][0])*sin(angle_with_horizontal))
+                self._tension[label] = tension
+                tension_func.append((tension, x<=x1))
+                moment_sum_from_right_support += self._loads['point_load'][sorted_position[i][0]][0] * cos(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._right_support[1] - self._loads_position[sorted_position[i][0]][1])
+                moment_sum_from_right_support += self._loads['point_load'][sorted_position[i][0]][0] * sin(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._right_support[0] - self._loads_position[sorted_position[i][0]][0])
+
+            label = Symbol(sorted_position[0][0]+"_"+sorted_position[1][0])
+            y2 = self._loads_position[sorted_position[1][0]][1]
+            x2 = self._loads_position[sorted_position[1][0]][0]
+            x1 = self._left_support[0]
+            y1 = self._left_support[1]
+
+            angle_with_horizontal = -atan((y2 - y1)/(x2 - x1))
+            tension = -(moment_sum_from_right_support)/(abs(self._right_support[1] - self._loads_position[sorted_position[1][0]][1])*cos(angle_with_horizontal) + abs(self._right_support[0] - self._loads_position[sorted_position[1][0]][0])*sin(angle_with_horizontal))
+            self._tension[label] = tension
+
+            tension_func.insert(0,(tension, x<=x2))
+            self._tension_func = Piecewise(*tension_func)
+            angle_with_horizontal = pi/2 - angle_with_horizontal
+            label = self._support_labels[0]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = -sin(angle_with_horizontal) * tension
+            F_x += -sin(angle_with_horizontal) * tension
+            self._reaction_loads[Symbol("R_"+label+"_y")] = cos(angle_with_horizontal) * tension
+            F_y += cos(angle_with_horizontal) * tension
+
+            label = self._support_labels[1]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = -F_x
+            self._reaction_loads[Symbol("R_"+label+"_y")] = -F_y
+
+        elif len(self._loads['distributed']) != 0 :
+
+            if len(args) == 0:
+                raise ValueError("Provide the lowest point of the cable")
+
+            lowest_x = sympify(args[0])
+            self._lowest_x_global = lowest_x
+
+            a = Symbol('a', positive=True)
+            c = Symbol('c')
+            # augmented matrix form of linsolve
+
+            M = Matrix(
+                [[(self._left_support[0]-lowest_x)**2, 1, self._left_support[1]],
+                [(self._right_support[0]-lowest_x)**2, 1, self._right_support[1]],
+                ])
+
+            coefficient_solution = list(linsolve(M, (a, c)))
+            if len(coefficient_solution) ==0 or coefficient_solution[0][0]== 0:
+                raise ValueError("The lowest point is inconsistent with the supports")
+
+            A = coefficient_solution[0][0]
+            C = coefficient_solution[0][1] + coefficient_solution[0][0]*lowest_x**2
+            B = -2*coefficient_solution[0][0]*lowest_x
+            self._lowest_y_global = coefficient_solution[0][1]
+            lowest_y = self._lowest_y_global
+
+            # y = A*x**2 + B*x + C
+            # shifting origin to lowest point
+            X = Symbol('X')
+            Y = Symbol('Y')
+            Y = A*(X + lowest_x)**2 + B*(X + lowest_x) + C - lowest_y
+
+            temp_list = list(self._loads['distributed'].values())
+            applied_force = temp_list[0]
+
+            horizontal_force_constant = (applied_force * (self._right_support[0] - lowest_x)**2) / (2 * (self._right_support[1] - lowest_y))
+
+            self._tension.clear()
+            tangent_slope_to_curve = diff(Y, X)
+            self._tension['distributed'] = horizontal_force_constant / (cos(atan(tangent_slope_to_curve)))
+
+            label = self._support_labels[0]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = self.tension_at(self._left_support[0]) * cos(atan(tangent_slope_to_curve.subs(X, self._left_support[0] - lowest_x)))
+            self._reaction_loads[Symbol("R_"+label+"_y")] = self.tension_at(self._left_support[0]) * sin(atan(tangent_slope_to_curve.subs(X, self._left_support[0] - lowest_x)))
+
+            label = self._support_labels[1]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = self.tension_at(self._left_support[0]) * cos(atan(tangent_slope_to_curve.subs(X, self._right_support[0] - lowest_x)))
+            self._reaction_loads[Symbol("R_"+label+"_y")] = self.tension_at(self._left_support[0]) * sin(atan(tangent_slope_to_curve.subs(X, self._right_support[0] - lowest_x)))
+
+    def draw(self):
+        """
+        This method is used to obtain a plot for the specified cable with its supports,
+        shape and loads.
+
+        Examples
+        ========
+
+        For point loads,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(("A", 0, 10), ("B", 10, 10))
+        >>> c.apply_load(-1, ('Z', 2, 7.26, 3, 270))
+        >>> c.apply_load(-1, ('X', 4, 6, 8, 270))
+        >>> c.solve()
+        >>> p = c.draw()
+        >>> p  # doctest: +ELLIPSIS
+        Plot object containing:
+        [0]: cartesian line: Piecewise((10 - 1.37*x, x <= 2), (8.52 - 0.63*x, x <= 4), (2*x/3 + 10/3, x <= 10)) for x over (0.0, 10.0)
+        ...
+        >>> p.show()
+
+        For uniformly distributed loads,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c=Cable(("A", 0, 40),("B", 100, 20))
+        >>> c.apply_load(0, ("X", 850))
+        >>> c.solve(58.58)
+        >>> p = c.draw()
+        >>> p # doctest: +ELLIPSIS
+        Plot object containing:
+        [0]: cartesian line: 0.0116550116550117*(x - 58.58)**2 + 0.00447086247086247 for x over (0.0, 100.0)
+        [1]: cartesian line: -7.49552913752915 for x over (0.0, 100.0)
+        ...
+        >>> p.show()
+        """
+        x = Symbol("x")
+        annotations = []
+        support_rectangles = self._draw_supports()
+
+        xy_min = min(self._left_support[0],self._lowest_y_global)
+        xy_max = max(self._right_support[0], max(self._right_support[1],self._left_support[1]))
+        max_diff = xy_max - xy_min
+        if len(self._loads_position) != 0:
+            self._cable_eqn = self._draw_cable(-1)
+            annotations += self._draw_loads(-1)
+
+        elif len(self._loads['distributed']) != 0 :
+            self._cable_eqn = self._draw_cable(0)
+            annotations += self._draw_loads(0)
+
+        if not self._cable_eqn:
+            raise ValueError("solve method not called and/or values provided for loads and supports not adequate")
+
+        cab_plot = plot(*self._cable_eqn,(x,self._left_support[0],self._right_support[0]),
+                        xlim=(xy_min-0.5*max_diff,xy_max+0.5*max_diff),
+                        ylim=(xy_min-0.5*max_diff,xy_max+0.5*max_diff),
+                        rectangles=support_rectangles,show= False,annotations=annotations, axis=False)
+
+        return cab_plot
+
+    def _draw_supports(self):
+        member_rectangles = []
+        xy_min = min(self._left_support[0],self._lowest_y_global)
+        xy_max = max(self._right_support[0], max(self._right_support[1],self._left_support[1]))
+        max_diff = xy_max - xy_min
+
+        supp_width = 0.075*max_diff
+
+        member_rectangles.append(
+            {
+                'xy': (self._left_support[0]-supp_width,self._left_support[1]),
+                'width': supp_width,
+                'height':supp_width,
+                'color':'brown',
+                'fill': False
+            }
+        )
+
+        member_rectangles.append(
+            {
+                'xy': (self._right_support[0],self._right_support[1]),
+                'width': supp_width,
+                'height':supp_width,
+                'color':'brown',
+                'fill': False
+            }
+        )
+
+        return member_rectangles
+
+    def _draw_cable(self,order):
+        xy_min = min(self._left_support[0],self._lowest_y_global)
+        xy_max = max(self._right_support[0], max(self._right_support[1],self._left_support[1]))
+        max_diff = xy_max - xy_min
+        if order == -1 :
+            x,y = symbols('x y')
+            line_func = []
+            sorted_position = sorted(self._loads_position.items(), key = lambda item : item[1][0])
+
+            for i in range(len(sorted_position)):
+                if(i==0):
+                    y = ((sorted_position[i][1][1] - self._left_support[1])*(x-self._left_support[0]))/(sorted_position[i][1][0]- self._left_support[0]) + self._left_support[1]
+                else:
+                    y = ((sorted_position[i][1][1] - sorted_position[i-1][1][1] )*(x-sorted_position[i-1][1][0]))/(sorted_position[i][1][0]- sorted_position[i-1][1][0]) + sorted_position[i-1][1][1]
+                line_func.append((y,x<=sorted_position[i][1][0]))
+
+            y = ((sorted_position[len(sorted_position)-1][1][1] - self._right_support[1])*(x-self._right_support[0]))/(sorted_position[i][1][0]- self._right_support[0]) + self._right_support[1]
+            line_func.append((y,x<=self._right_support[0]))
+            return [Piecewise(*line_func)]
+
+        elif order == 0:
+            x0 = self._lowest_x_global
+            diff_force_height = max_diff*0.075
+
+            a,c,x,y = symbols('a c x y')
+            parabola_eqn = a*(x-x0)**2 + c - y
+
+            points = [(self._left_support[0],self._left_support[1]),(self._right_support[0],self._right_support[1])]
+            equations = []
+            for px, py in points:
+                equations.append(parabola_eqn.subs({x: px, y: py}))
+            solution = solve(equations, (a, c))
+            parabola_eqn = solution[a]*(x-x0)**2 + solution[c]
+            return [parabola_eqn, self._lowest_y_global - diff_force_height]
+
+    def _draw_loads(self,order):
+        xy_min = min(self._left_support[0],self._lowest_y_global)
+        xy_max = max(self._right_support[0], max(self._right_support[1],self._left_support[1]))
+        max_diff = xy_max - xy_min
+        if(order==-1):
+            arrow_length = max_diff*0.1
+            force_arrows = []
+            for key in self._loads['point_load']:
+                force_arrows.append(
+                    {
+                        'text': '',
+                        'xy':(self._loads_position[key][0]+arrow_length*cos(rad(self._loads['point_load'][key][1])),\
+                              self._loads_position[key][1] + arrow_length*sin(rad(self._loads['point_load'][key][1]))),
+                        'xytext': (self._loads_position[key][0],self._loads_position[key][1]),
+                        'arrowprops': {'width': 1, 'headlength':3, 'headwidth':3 , 'facecolor': 'black', }
+                    }
+                )
+                mag = self._loads['point_load'][key][0]
+                force_arrows.append(
+                    {
+                        'text':f'{mag}N',
+                        'xy': (self._loads_position[key][0]+arrow_length*1.6*cos(rad(self._loads['point_load'][key][1])),\
+                               self._loads_position[key][1] + arrow_length*1.6*sin(rad(self._loads['point_load'][key][1]))),
+                    }
+                )
+            return force_arrows
+
+        elif (order == 0):
+            x = symbols('x')
+            force_arrows = []
+            x_val = [self._left_support[0] + ((self._right_support[0]-self._left_support[0])/10)*i for i in range(1,10)]
+            for i in x_val:
+                force_arrows.append(
+                    {
+                        'text':'',
+                        'xytext':(
+                            i,
+                            self._cable_eqn[0].subs(x,i)
+                        ),
+                        'xy':(
+                            i,
+                            self._cable_eqn[1].subs(x,i)
+                        ),
+                        'arrowprops':{'width':1, 'headlength':3.5, 'headwidth':3.5, 'facecolor':'black'}
+                    }
+                )
+            mag = 0
+            for key in self._loads['distributed']:
+                mag += self._loads['distributed'][key]
+
+            force_arrows.append(
+                {
+                    'text':f'{mag} N/m',
+                    'xy':((self._left_support[0]+self._right_support[0])/2,self._lowest_y_global - max_diff*0.15)
+                }
+            )
+            return force_arrows
+
+    def plot_tension(self):
+        """
+        Returns the diagram/plot of the tension generated in the cable at various points.
+
+        Examples
+        ========
+
+        For point loads,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(("A", 0, 10), ("B", 10, 10))
+        >>> c.apply_load(-1, ('Z', 2, 7.26, 3, 270))
+        >>> c.apply_load(-1, ('X', 4, 6, 8, 270))
+        >>> c.solve()
+        >>> p = c.plot_tension()
+        >>> p
+        Plot object containing:
+        [0]: cartesian line: Piecewise((8.91403453669861, x <= 2), (4.79150773600774, x <= 4), (19*sqrt(13)/10, x <= 10)) for x over (0.0, 10.0)
+        >>> p.show()
+
+        For uniformly distributed loads,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c=Cable(("A", 0, 40),("B", 100, 20))
+        >>> c.apply_load(0, ("X", 850))
+        >>> c.solve(58.58)
+        >>> p = c.plot_tension()
+        >>> p
+        Plot object containing:
+        [0]: cartesian line: 36465.0*sqrt(0.00054335718671383*X**2 + 1) for X over (0.0, 100.0)
+        >>> p.show()
+
+        """
+        if len(self._loads_position) != 0:
+            x = symbols('x')
+            tension_plot  = plot(self._tension_func, (x,self._left_support[0],self._right_support[0]), show=False)
+        else:
+            X = symbols('X')
+            tension_plot  = plot(self._tension['distributed'], (X,self._left_support[0],self._right_support[0]), show=False)
+        return tension_plot
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_arch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_arch.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d77062702222d7381a89450e8230b52bac4028c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_arch.py
@@ -0,0 +1,61 @@
+from sympy.physics.continuum_mechanics.arch import Arch
+from sympy import Symbol, simplify
+
+x = Symbol('x')
+t = Symbol('t')
+
+def test_arch_init():
+    a = Arch((0,0),(10,0),crown_x=5,crown_y=5)
+    assert a.get_loads == {'distributed': {}, 'concentrated': {}}
+    assert a.reaction_force == {Symbol('R_A_x'):0, Symbol('R_A_y'):0, Symbol('R_B_x'):0, Symbol('R_B_y'):0}
+    assert a.supports == {'left':'hinge', 'right':'hinge'}
+    assert a.left_support == (0,0)
+    assert a.right_support == (10,0)
+    assert a.get_shape_eqn == 5 - ((x-5)**2)/5
+
+    a = Arch((0,0),(10,1),crown_x=6)
+    a.change_support_type(left_support='roller')
+    a.add_member(0.5)
+    assert a.supports == {'left':'roller', 'right':'hinge'}
+    assert simplify(a.get_shape_eqn) == simplify(9/5 - (x - 6)**2/20)
+
+def test_arch_support():
+    a = Arch((0,0),(40,0),crown_x=20,crown_y=12)
+    a.apply_load(-1,'C',8,150,angle=270)
+    a.apply_load(0,'D',start=20,end=40,mag=-4)
+    a.solve()
+    assert abs(a.reaction_force[Symbol("R_A_x")] - 83.33333333333333) < 10e-12
+    assert abs(a.reaction_force[Symbol("R_B_y")] - 90.00000000000000) < 10e-12
+    assert abs(a.reaction_force[Symbol("R_B_x")] + 83.33333333333333) < 10e-12
+    assert abs(a.reaction_force[Symbol("R_A_y")] - 140.00000000000000) < 10e-12
+
+def test_arch_member():
+    a = Arch((0,0),(40,0),crown_x=20,crown_y=15)
+    a.change_support_type(right_support='roller')
+    a.add_member(0)
+    a.apply_load(-1,'D',start=12,mag=3,angle=270)
+    a.apply_load(-1,'E',start=6,mag=4,angle=270)
+    a.apply_load(-1,'C',start=30,mag=5,angle=270)
+    a.solve()
+    assert a.reaction_force[Symbol("R_A_x")] == 0
+    assert abs(a.reaction_force[Symbol("R_A_y")] - 6.750000000000000) < 10e-12
+    assert a.reaction_force[Symbol("R_B_x")] == 0
+    assert abs(a.reaction_force[Symbol("R_B_y")] - 5.250000000000000) < 10e-12
+
+def test_symbol_magnitude():
+    a = Arch((0,0),(16,0),crown_x=8,crown_y=5)
+    a.apply_load(0,'C',start=3,end=5,mag=t)
+    a.solve()
+    assert a.reaction_force[Symbol("R_A_x")] == -(4*t)/5
+    assert a.reaction_force[Symbol("R_A_y")] == -(3*t)/2
+    assert a.reaction_force[Symbol("R_B_x")] == (4*t)/5
+    assert a.reaction_force[Symbol("R_B_y")] == -t/2
+    assert a.bending_moment_at(4) == -5*t/2
+
+def test_forces():
+    a = Arch((0,0),(40,0),crown_x=20,crown_y=12)
+    a.apply_load(-1,'C',8,150,angle=270)
+    a.apply_load(0,'D',start=20,end=40,mag=-4)
+    a.solve()
+    assert abs(a.axial_force_at(7.999999999999999)-149.430523405935) < 1e-12
+    assert abs(a.shear_force_at(7.999999999999999)-64.9227473161196) < 1e-12
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_beam.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_beam.py
new file mode 100644
index 0000000000000000000000000000000000000000..a6a36fb030f99d9d384e52d4a239351688c7626b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_beam.py
@@ -0,0 +1,1118 @@
+from sympy.core.function import expand
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.sets.sets import Interval
+from sympy.simplify.simplify import simplify
+from sympy.physics.continuum_mechanics.beam import Beam
+from sympy.functions import SingularityFunction, Piecewise, meijerg, Abs, log
+from sympy.testing.pytest import raises
+from sympy.physics.units import meter, newton, kilo, giga, milli
+from sympy.physics.continuum_mechanics.beam import Beam3D
+from sympy.geometry import Circle, Polygon, Point2D, Triangle
+from sympy.core.sympify import sympify
+
+x = Symbol('x')
+y = Symbol('y')
+R1, R2 = symbols('R1, R2')
+
+
+def test_Beam():
+    E = Symbol('E')
+    E_1 = Symbol('E_1')
+    I = Symbol('I')
+    I_1 = Symbol('I_1')
+    A = Symbol('A')
+
+    b = Beam(1, E, I)
+    assert b.length == 1
+    assert b.elastic_modulus == E
+    assert b.second_moment == I
+    assert b.variable == x
+
+    # Test the length setter
+    b.length = 4
+    assert b.length == 4
+
+    # Test the E setter
+    b.elastic_modulus = E_1
+    assert b.elastic_modulus == E_1
+
+    # Test the I setter
+    b.second_moment = I_1
+    assert b.second_moment is I_1
+
+    # Test the variable setter
+    b.variable = y
+    assert b.variable is y
+
+    # Test for all boundary conditions.
+    b.bc_deflection = [(0, 2)]
+    b.bc_slope = [(0, 1)]
+    b.bc_bending_moment = [(0, 5)]
+    b.bc_shear_force = [(2, 1)]
+    assert b.boundary_conditions == {'deflection': [(0, 2)], 'slope': [(0, 1)],
+                                     'bending_moment': [(0, 5)], 'shear_force': [(2, 1)]}
+
+    # Test for shear force boundary condition method
+    b.bc_shear_force.extend([(1, 1), (2, 3)])
+    sf_bcs = b.bc_shear_force
+    assert sf_bcs == [(2, 1), (1, 1), (2, 3)]
+
+    # Test for slope boundary condition method
+    b.bc_bending_moment.extend([(1, 3), (5, 3)])
+    bm_bcs = b.bc_bending_moment
+    assert bm_bcs == [(0, 5), (1, 3), (5, 3)]
+
+    # Test for slope boundary condition method
+    b.bc_slope.extend([(4, 3), (5, 0)])
+    s_bcs = b.bc_slope
+    assert s_bcs == [(0, 1), (4, 3), (5, 0)]
+
+    # Test for deflection boundary condition method
+    b.bc_deflection.extend([(4, 3), (5, 0)])
+    d_bcs = b.bc_deflection
+    assert d_bcs == [(0, 2), (4, 3), (5, 0)]
+
+    # Test for updated boundary conditions
+    bcs_new = b.boundary_conditions
+    assert bcs_new == {
+        'deflection': [(0, 2), (4, 3), (5, 0)],
+        'slope': [(0, 1), (4, 3), (5, 0)],
+        'bending_moment': [(0, 5), (1, 3), (5, 3)],
+        'shear_force': [(2, 1), (1, 1), (2, 3)]}
+
+    b1 = Beam(30, E, I)
+    b1.apply_load(-8, 0, -1)
+    b1.apply_load(R1, 10, -1)
+    b1.apply_load(R2, 30, -1)
+    b1.apply_load(120, 30, -2)
+    b1.bc_deflection = [(10, 0), (30, 0)]
+    b1.solve_for_reaction_loads(R1, R2)
+
+    # Test for finding reaction forces
+    p = b1.reaction_loads
+    q = {R1: 6, R2: 2}
+    assert p == q
+
+    # Test for load distribution function.
+    p = b1.load
+    q = -8*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 10, -1) \
+    + 120*SingularityFunction(x, 30, -2) + 2*SingularityFunction(x, 30, -1)
+    assert p == q
+
+    # Test for shear force distribution function
+    p = b1.shear_force()
+    q = 8*SingularityFunction(x, 0, 0) - 6*SingularityFunction(x, 10, 0) \
+    - 120*SingularityFunction(x, 30, -1) - 2*SingularityFunction(x, 30, 0)
+    assert p == q
+
+    # Test for shear stress distribution function
+    p = b1.shear_stress()
+    q = (8*SingularityFunction(x, 0, 0) - 6*SingularityFunction(x, 10, 0) \
+    - 120*SingularityFunction(x, 30, -1) \
+    - 2*SingularityFunction(x, 30, 0))/A
+    assert p==q
+
+    # Test for bending moment distribution function
+    p = b1.bending_moment()
+    q = 8*SingularityFunction(x, 0, 1) - 6*SingularityFunction(x, 10, 1) \
+    - 120*SingularityFunction(x, 30, 0) - 2*SingularityFunction(x, 30, 1)
+    assert p == q
+
+    # Test for slope distribution function
+    p = b1.slope()
+    q = -4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2) \
+    + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) \
+    + Rational(4000, 3)
+    assert p == q/(E*I)
+
+    # Test for deflection distribution function
+    p = b1.deflection()
+    q = x*Rational(4000, 3) - 4*SingularityFunction(x, 0, 3)/3 \
+    + SingularityFunction(x, 10, 3) + 60*SingularityFunction(x, 30, 2) \
+    + SingularityFunction(x, 30, 3)/3 - 12000
+    assert p == q/(E*I)
+
+    # Test using symbols
+    l = Symbol('l')
+    w0 = Symbol('w0')
+    w2 = Symbol('w2')
+    a1 = Symbol('a1')
+    c = Symbol('c')
+    c1 = Symbol('c1')
+    d = Symbol('d')
+    e = Symbol('e')
+    f = Symbol('f')
+
+    b2 = Beam(l, E, I)
+
+    b2.apply_load(w0, a1, 1)
+    b2.apply_load(w2, c1, -1)
+
+    b2.bc_deflection = [(c, d)]
+    b2.bc_slope = [(e, f)]
+
+    # Test for load distribution function.
+    p = b2.load
+    q = w0*SingularityFunction(x, a1, 1) + w2*SingularityFunction(x, c1, -1)
+    assert p == q
+
+    # Test for shear force distribution function
+    p = b2.shear_force()
+    q = -w0*SingularityFunction(x, a1, 2)/2 \
+    - w2*SingularityFunction(x, c1, 0)
+    assert p == q
+
+    # Test for shear stress distribution function
+    p = b2.shear_stress()
+    q = (-w0*SingularityFunction(x, a1, 2)/2 \
+    - w2*SingularityFunction(x, c1, 0))/A
+    assert p == q
+
+    # Test for bending moment distribution function
+    p = b2.bending_moment()
+    q = -w0*SingularityFunction(x, a1, 3)/6 - w2*SingularityFunction(x, c1, 1)
+    assert p == q
+
+    # Test for slope distribution function
+    p = b2.slope()
+    q = (w0*SingularityFunction(x, a1, 4)/24 + w2*SingularityFunction(x, c1, 2)/2)/(E*I) + (E*I*f - w0*SingularityFunction(e, a1, 4)/24 - w2*SingularityFunction(e, c1, 2)/2)/(E*I)
+    assert expand(p) == expand(q)
+
+    # Test for deflection distribution function
+    p = b2.deflection()
+    q = x*(E*I*f - w0*SingularityFunction(e, a1, 4)/24 \
+    - w2*SingularityFunction(e, c1, 2)/2)/(E*I) \
+    + (w0*SingularityFunction(x, a1, 5)/120 \
+    + w2*SingularityFunction(x, c1, 3)/6)/(E*I) \
+    + (E*I*(-c*f + d) + c*w0*SingularityFunction(e, a1, 4)/24 \
+    + c*w2*SingularityFunction(e, c1, 2)/2 \
+    - w0*SingularityFunction(c, a1, 5)/120 \
+    - w2*SingularityFunction(c, c1, 3)/6)/(E*I)
+    assert simplify(p - q) == 0
+
+    b3 = Beam(9, E, I, 2)
+    b3.apply_load(value=-2, start=2, order=2, end=3)
+    b3.bc_slope.append((0, 2))
+    C3 = symbols('C3')
+    C4 = symbols('C4')
+
+    p = b3.load
+    q = -2*SingularityFunction(x, 2, 2) + 2*SingularityFunction(x, 3, 0) \
+    + 4*SingularityFunction(x, 3, 1) + 2*SingularityFunction(x, 3, 2)
+    assert p == q
+
+    p = b3.shear_force()
+    q = 2*SingularityFunction(x, 2, 3)/3 - 2*SingularityFunction(x, 3, 1) \
+    - 2*SingularityFunction(x, 3, 2) - 2*SingularityFunction(x, 3, 3)/3
+    assert p == q
+
+    p = b3.shear_stress()
+    q = SingularityFunction(x, 2, 3)/3 - 1*SingularityFunction(x, 3, 1) \
+    - 1*SingularityFunction(x, 3, 2) - 1*SingularityFunction(x, 3, 3)/3
+    assert p == q
+
+    p = b3.slope()
+    q = 2 - (SingularityFunction(x, 2, 5)/30 - SingularityFunction(x, 3, 3)/3 \
+    - SingularityFunction(x, 3, 4)/6 - SingularityFunction(x, 3, 5)/30)/(E*I)
+    assert p == q
+
+    p = b3.deflection()
+    q = 2*x - (SingularityFunction(x, 2, 6)/180 \
+    - SingularityFunction(x, 3, 4)/12 - SingularityFunction(x, 3, 5)/30 \
+    - SingularityFunction(x, 3, 6)/180)/(E*I)
+    assert p == q + C4
+
+    b4 = Beam(4, E, I, 3)
+    b4.apply_load(-3, 0, 0, end=3)
+
+    p = b4.load
+    q = -3*SingularityFunction(x, 0, 0) + 3*SingularityFunction(x, 3, 0)
+    assert p == q
+
+    p = b4.shear_force()
+    q = 3*SingularityFunction(x, 0, 1) \
+    - 3*SingularityFunction(x, 3, 1)
+    assert p == q
+
+    p = b4.shear_stress()
+    q = SingularityFunction(x, 0, 1) - SingularityFunction(x, 3, 1)
+    assert p == q
+
+    p = b4.slope()
+    q = -3*SingularityFunction(x, 0, 3)/6 + 3*SingularityFunction(x, 3, 3)/6
+    assert p == q/(E*I) + C3
+
+    p = b4.deflection()
+    q = -3*SingularityFunction(x, 0, 4)/24 + 3*SingularityFunction(x, 3, 4)/24
+    assert p == q/(E*I) + C3*x + C4
+
+    # can't use end with point loads
+    raises(ValueError, lambda: b4.apply_load(-3, 0, -1, end=3))
+    with raises(TypeError):
+        b4.variable = 1
+
+
+def test_insufficient_bconditions():
+    # Test cases when required number of boundary conditions
+    # are not provided to solve the integration constants.
+    L = symbols('L', positive=True)
+    E, I, P, a3, a4 = symbols('E I P a3 a4')
+
+    b = Beam(L, E, I, base_char='a')
+    b.apply_load(R2, L, -1)
+    b.apply_load(R1, 0, -1)
+    b.apply_load(-P, L/2, -1)
+    b.solve_for_reaction_loads(R1, R2)
+
+    p = b.slope()
+    q = P*SingularityFunction(x, 0, 2)/4 - P*SingularityFunction(x, L/2, 2)/2 + P*SingularityFunction(x, L, 2)/4
+    assert p == q/(E*I) + a3
+
+    p = b.deflection()
+    q = P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
+    assert p == q/(E*I) + a3*x + a4
+
+    b.bc_deflection = [(0, 0)]
+    p = b.deflection()
+    q = a3*x + P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
+    assert p == q/(E*I)
+
+    b.bc_deflection = [(0, 0), (L, 0)]
+    p = b.deflection()
+    q = -L**2*P*x/16 + P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
+    assert p == q/(E*I)
+
+
+def test_statically_indeterminate():
+    E = Symbol('E')
+    I = Symbol('I')
+    M1, M2 = symbols('M1, M2')
+    F = Symbol('F')
+    l = Symbol('l', positive=True)
+
+    b5 = Beam(l, E, I)
+    b5.bc_deflection = [(0, 0),(l, 0)]
+    b5.bc_slope = [(0, 0),(l, 0)]
+
+    b5.apply_load(R1, 0, -1)
+    b5.apply_load(M1, 0, -2)
+    b5.apply_load(R2, l, -1)
+    b5.apply_load(M2, l, -2)
+    b5.apply_load(-F, l/2, -1)
+
+    b5.solve_for_reaction_loads(R1, R2, M1, M2)
+    p = b5.reaction_loads
+    q = {R1: F/2, R2: F/2, M1: -F*l/8, M2: F*l/8}
+    assert p == q
+
+
+def test_beam_units():
+    E = Symbol('E')
+    I = Symbol('I')
+    R1, R2 = symbols('R1, R2')
+
+    kN = kilo*newton
+    gN = giga*newton
+
+    b = Beam(8*meter, 200*gN/meter**2, 400*1000000*(milli*meter)**4)
+    b.apply_load(5*kN, 2*meter, -1)
+    b.apply_load(R1, 0*meter, -1)
+    b.apply_load(R2, 8*meter, -1)
+    b.apply_load(10*kN/meter, 4*meter, 0, end=8*meter)
+    b.bc_deflection = [(0*meter, 0*meter), (8*meter, 0*meter)]
+    b.solve_for_reaction_loads(R1, R2)
+    assert b.reaction_loads == {R1: -13750*newton, R2: -31250*newton}
+
+    b = Beam(3*meter, E*newton/meter**2, I*meter**4)
+    b.apply_load(8*kN, 1*meter, -1)
+    b.apply_load(R1, 0*meter, -1)
+    b.apply_load(R2, 3*meter, -1)
+    b.apply_load(12*kN*meter, 2*meter, -2)
+    b.bc_deflection = [(0*meter, 0*meter), (3*meter, 0*meter)]
+    b.solve_for_reaction_loads(R1, R2)
+    assert b.reaction_loads == {R1: newton*Rational(-28000, 3), R2: newton*Rational(4000, 3)}
+    assert b.deflection().subs(x, 1*meter) == 62000*meter/(9*E*I)
+
+
+def test_variable_moment():
+    E = Symbol('E')
+    I = Symbol('I')
+
+    b = Beam(4, E, 2*(4 - x))
+    b.apply_load(20, 4, -1)
+    R, M = symbols('R, M')
+    b.apply_load(R, 0, -1)
+    b.apply_load(M, 0, -2)
+    b.bc_deflection = [(0, 0)]
+    b.bc_slope = [(0, 0)]
+    b.solve_for_reaction_loads(R, M)
+    assert b.slope().expand() == ((10*x*SingularityFunction(x, 0, 0)
+        - 10*(x - 4)*SingularityFunction(x, 4, 0))/E).expand()
+    assert b.deflection().expand() == ((5*x**2*SingularityFunction(x, 0, 0)
+        - 10*Piecewise((0, Abs(x)/4 < 1), (x**2*meijerg(((-1, 1), ()), ((), (-2, 0)), x/4), True))
+        + 40*SingularityFunction(x, 4, 1))/E).expand()
+
+    b = Beam(4, E - x, I)
+    b.apply_load(20, 4, -1)
+    R, M = symbols('R, M')
+    b.apply_load(R, 0, -1)
+    b.apply_load(M, 0, -2)
+    b.bc_deflection = [(0, 0)]
+    b.bc_slope = [(0, 0)]
+    b.solve_for_reaction_loads(R, M)
+    assert b.slope().expand() == ((-80*(-log(-E) + log(-E + x))*SingularityFunction(x, 0, 0)
+        + 80*(-log(-E + 4) + log(-E + x))*SingularityFunction(x, 4, 0) + 20*(-E*log(-E)
+        + E*log(-E + x) + x)*SingularityFunction(x, 0, 0) - 20*(-E*log(-E + 4) + E*log(-E + x)
+        + x - 4)*SingularityFunction(x, 4, 0))/I).expand()
+
+
+def test_composite_beam():
+    E = Symbol('E')
+    I = Symbol('I')
+    b1 = Beam(2, E, 1.5*I)
+    b2 = Beam(2, E, I)
+    b = b1.join(b2, "fixed")
+    b.apply_load(-20, 0, -1)
+    b.apply_load(80, 0, -2)
+    b.apply_load(20, 4, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0)]
+    assert b.length == 4
+    assert b.second_moment == Piecewise((1.5*I, x <= 2), (I, x <= 4))
+    assert b.slope().subs(x, 4) == 120.0/(E*I)
+    assert b.slope().subs(x, 2) == 80.0/(E*I)
+    assert int(b.deflection().subs(x, 4).args[0]) == -302  # Coefficient of 1/(E*I)
+
+    l = symbols('l', positive=True)
+    R1, M1, R2, R3, P = symbols('R1 M1 R2 R3 P')
+    b1 = Beam(2*l, E, I)
+    b2 = Beam(2*l, E, I)
+    b = b1.join(b2,"hinge")
+    b.apply_load(M1, 0, -2)
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(R3, 4*l, -1)
+    b.apply_load(P, 3*l, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0), (l, 0), (4*l, 0)]
+    b.solve_for_reaction_loads(M1, R1, R2, R3)
+    assert b.reaction_loads == {R3: -P/2, R2: P*Rational(-5, 4), M1: -P*l/4, R1: P*Rational(3, 4)}
+    assert b.slope().subs(x, 3*l) == -7*P*l**2/(48*E*I)
+    assert b.deflection().subs(x, 2*l) == 7*P*l**3/(24*E*I)
+    assert b.deflection().subs(x, 3*l) == 5*P*l**3/(16*E*I)
+
+    # When beams having same second moment are joined.
+    b1 = Beam(2, 500, 10)
+    b2 = Beam(2, 500, 10)
+    b = b1.join(b2, "fixed")
+    b.apply_load(M1, 0, -2)
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, 1, -1)
+    b.apply_load(R3, 4, -1)
+    b.apply_load(10, 3, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0), (1, 0), (4, 0)]
+    b.solve_for_reaction_loads(M1, R1, R2, R3)
+    assert b.slope() == -2*SingularityFunction(x, 0, 1)/5625 + SingularityFunction(x, 0, 2)/1875\
+                - 133*SingularityFunction(x, 1, 2)/135000 + SingularityFunction(x, 3, 2)/1000\
+                - 37*SingularityFunction(x, 4, 2)/67500
+    assert b.deflection() == -SingularityFunction(x, 0, 2)/5625 + SingularityFunction(x, 0, 3)/5625\
+                    - 133*SingularityFunction(x, 1, 3)/405000 + SingularityFunction(x, 3, 3)/3000\
+                    - 37*SingularityFunction(x, 4, 3)/202500
+
+
+def test_point_cflexure():
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(10, E, I)
+    b.apply_load(-4, 0, -1)
+    b.apply_load(-46, 6, -1)
+    b.apply_load(10, 2, -1)
+    b.apply_load(20, 4, -1)
+    b.apply_load(3, 6, 0)
+    assert b.point_cflexure() == [Rational(10, 3)]
+
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(15, E, I)
+    r0 = b.apply_support(0, type='pin')
+    r10 = b.apply_support(10, type='pin')
+    r15, m15 = b.apply_support(15, type='fixed')
+    b.apply_rotation_hinge(12)
+    b.apply_load(-10, 5, -1)
+    b.apply_load(-5, 10, 0, 15)
+    b.solve_for_reaction_loads(r0, r10, r15, m15)
+    assert b.point_cflexure() == [Rational(1200, 163), 12, Rational(163, 12)]
+
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(15, E, I)
+    r0 = b.apply_support(0, type='pin')
+    r10 = b.apply_support(10, type='pin')
+    r15, m15 = b.apply_support(15, type='fixed')
+    b.apply_rotation_hinge(5)
+    b.apply_rotation_hinge(12)
+    b.apply_load(-10, 5, -1)
+    b.apply_load(-5, 10, 0, 15)
+    b.solve_for_reaction_loads(r0, r10, r15, m15)
+    with raises(NotImplementedError):
+        b.point_cflexure()
+
+def test_remove_load():
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(4, E, I)
+
+    try:
+        b.remove_load(2, 1, -1)
+    # As no load is applied on beam, ValueError should be returned.
+    except ValueError:
+        assert True
+    else:
+        assert False
+
+    b.apply_load(-3, 0, -2)
+    b.apply_load(4, 2, -1)
+    b.apply_load(-2, 2, 2, end = 3)
+    b.remove_load(-2, 2, 2, end = 3)
+    assert b.load == -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1)
+    assert b.applied_loads == [(-3, 0, -2, None), (4, 2, -1, None)]
+
+    try:
+        b.remove_load(1, 2, -1)
+    # As load of this magnitude was never applied at
+    # this position, method should return a ValueError.
+    except ValueError:
+        assert True
+    else:
+        assert False
+
+    b.remove_load(-3, 0, -2)
+    b.remove_load(4, 2, -1)
+    assert b.load == 0
+    assert b.applied_loads == []
+
+
+def test_apply_support():
+    E = Symbol('E')
+    I = Symbol('I')
+
+    b = Beam(4, E, I)
+    b.apply_support(0, "cantilever")
+    b.apply_load(20, 4, -1)
+    M_0, R_0 = symbols('M_0, R_0')
+    b.solve_for_reaction_loads(R_0, M_0)
+    assert simplify(b.slope()) == simplify((80*SingularityFunction(x, 0, 1) - 10*SingularityFunction(x, 0, 2)
+                + 10*SingularityFunction(x, 4, 2))/(E*I))
+    assert simplify(b.deflection()) == simplify((40*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 0, 3)/3
+                + 10*SingularityFunction(x, 4, 3)/3)/(E*I))
+
+    b = Beam(30, E, I)
+    p0 = b.apply_support(10, "pin")
+    p1 = b.apply_support(30, "roller")
+    b.apply_load(-8, 0, -1)
+    b.apply_load(120, 30, -2)
+    b.solve_for_reaction_loads(p0, p1)
+    assert b.slope() == (-4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2)
+            + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + Rational(4000, 3))/(E*I)
+    assert b.deflection() == (x*Rational(4000, 3) - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3)
+            + 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000)/(E*I)
+    R_10 = Symbol('R_10')
+    R_30 = Symbol('R_30')
+    assert p0 == R_10
+    assert b.reaction_loads == {R_10: 6, R_30: 2}
+    assert b.reaction_loads[p0] == 6
+
+    b = Beam(8, E, I)
+    p0, m0 = b.apply_support(0, "fixed")
+    p1 = b.apply_support(8, "roller")
+    b.apply_load(-5, 0, 0, 8)
+    b.solve_for_reaction_loads(p0, m0, p1)
+    R_0 = Symbol('R_0')
+    M_0 = Symbol('M_0')
+    R_8 = Symbol('R_8')
+    assert p0 == R_0
+    assert m0 == M_0
+    assert p1 == R_8
+    assert b.reaction_loads == {R_0: 25, M_0: -40, R_8: 15}
+    assert b.reaction_loads[m0] == -40
+
+    P = Symbol('P', positive=True)
+    L = Symbol('L', positive=True)
+    b = Beam(L, E, I)
+    b.apply_support(0, type='fixed')
+    b.apply_support(L, type='fixed')
+    b.apply_load(-P, L/2, -1)
+    R_0, R_L, M_0, M_L = symbols('R_0, R_L, M_0, M_L')
+    b.solve_for_reaction_loads(R_0, R_L, M_0, M_L)
+    assert b.reaction_loads == {R_0: P/2, R_L: P/2, M_0: -L*P/8, M_L: L*P/8}
+
+def test_apply_rotation_hinge():
+    b = Beam(15, 20, 20)
+    r0, m0 = b.apply_support(0, type='fixed')
+    r10 = b.apply_support(10, type='pin')
+    r15 = b.apply_support(15, type='pin')
+    p7 = b.apply_rotation_hinge(7)
+    p12 = b.apply_rotation_hinge(12)
+    b.apply_load(-10, 7, -1)
+    b.apply_load(-2, 10, 0, 15)
+    b.solve_for_reaction_loads(r0, m0, r10, r15)
+    R_0, M_0, R_10, R_15, P_7, P_12 = symbols('R_0, M_0, R_10, R_15, P_7, P_12')
+    expected_reactions = {R_0: 20/3, M_0: -140/3, R_10: 31/3, R_15: 3}
+    expected_rotations = {P_7: 2281/2160, P_12: -5137/5184}
+    reaction_symbols = [r0, m0, r10, r15]
+    rotation_symbols = [p7, p12]
+    tolerance = 1e-6
+    assert all(abs(b.reaction_loads[r] - expected_reactions[r]) < tolerance for r in reaction_symbols)
+    assert all(abs(b.rotation_jumps[r] - expected_rotations[r]) < tolerance for r in rotation_symbols)
+    expected_bending_moment = (140 * SingularityFunction(x, 0, 0) / 3 - 20 * SingularityFunction(x, 0, 1) / 3
+        - 11405 * SingularityFunction(x, 7, -1) / 27 + 10 * SingularityFunction(x, 7, 1)
+        - 31 * SingularityFunction(x, 10, 1) / 3 + SingularityFunction(x, 10, 2)
+        + 128425 * SingularityFunction(x, 12, -1) / 324 - 3 * SingularityFunction(x, 15, 1)
+        - SingularityFunction(x, 15, 2))
+    assert b.bending_moment().expand() == expected_bending_moment.expand()
+    expected_slope = (-7*SingularityFunction(x, 0, 1)/60 + SingularityFunction(x, 0, 2)/120
+        + 2281*SingularityFunction(x, 7, 0)/2160 - SingularityFunction(x, 7, 2)/80
+        + 31*SingularityFunction(x, 10, 2)/2400 - SingularityFunction(x, 10, 3)/1200
+        - 5137*SingularityFunction(x, 12, 0)/5184 + 3*SingularityFunction(x, 15, 2)/800
+        + SingularityFunction(x, 15, 3)/1200)
+    assert b.slope().expand() == expected_slope.expand()
+    expected_deflection = (-7 * SingularityFunction(x, 0, 2) / 120 + SingularityFunction(x, 0, 3) / 360
+        + 2281 * SingularityFunction(x, 7, 1) / 2160 - SingularityFunction(x, 7, 3) / 240
+        + 31 * SingularityFunction(x, 10, 3) / 7200 - SingularityFunction(x, 10, 4) / 4800
+        - 5137 * SingularityFunction(x, 12, 1) / 5184 + SingularityFunction(x, 15, 3) / 800
+        + SingularityFunction(x, 15, 4) / 4800)
+    assert b.deflection().expand() == expected_deflection.expand()
+
+    E = Symbol('E')
+    I = Symbol('I')
+    F = Symbol('F')
+    b = Beam(10, E, I)
+    r0, m0 = b.apply_support(0, type="fixed")
+    r10 = b.apply_support(10, type="pin")
+    b.apply_rotation_hinge(6)
+    b.apply_load(F, 8, -1)
+    b.solve_for_reaction_loads(r0, m0, r10)
+    assert b.reaction_loads == {R_0: -F/2, M_0: 3*F, R_10: -F/2}
+    assert (b.bending_moment() == -3*F*SingularityFunction(x, 0, 0) + F*SingularityFunction(x, 0, 1)/2
+            + 17*F*SingularityFunction(x, 6, -1) - F*SingularityFunction(x, 8, 1)
+            + F*SingularityFunction(x, 10, 1)/2)
+    expected_deflection = -(-3*F*SingularityFunction(x, 0, 2)/2 + F*SingularityFunction(x, 0, 3)/12
+            + 17*F*SingularityFunction(x, 6, 1) - F*SingularityFunction(x, 8, 3)/6
+            + F*SingularityFunction(x, 10, 3)/12)/(E*I)
+    assert b.deflection().expand() == expected_deflection.expand()
+
+    E = Symbol('E')
+    I = Symbol('I')
+    F = Symbol('F')
+    l1 = Symbol('l1', positive=True)
+    l2 = Symbol('l2', positive=True)
+    l3 = Symbol('l3', positive=True)
+    L = l1 + l2 + l3
+    b = Beam(L, E, I)
+    r0, m0 = b.apply_support(0, type="fixed")
+    r1 = b.apply_support(L, type="pin")
+    b.apply_rotation_hinge(l1)
+    b.apply_load(F, l1+l2, -1)
+    b.solve_for_reaction_loads(r0, m0, r1)
+    assert b.reaction_loads[r0] == -F*l3/(l2 + l3)
+    assert b.reaction_loads[m0] == F*l1*l3/(l2 + l3)
+    assert b.reaction_loads[r1] == -F*l2/(l2 + l3)
+    expected_bending_moment = (-F*l1*l3*SingularityFunction(x, 0, 0)/(l2 + l3)
+            + F*l2*SingularityFunction(x, l1 + l2 + l3, 1)/(l2 + l3)
+            + F*l3*SingularityFunction(x, 0, 1)/(l2 + l3) - F*SingularityFunction(x, l1 + l2, 1)
+            - (-2*F*l1**3*l3 - 3*F*l1**2*l2*l3 - 3*F*l1**2*l3**2 + F*l2**3*l3 + 3*F*l2**2*l3**2 + 2*F*l2*l3**3)
+            *SingularityFunction(x, l1, -1)/(6*l2**2 + 12*l2*l3 + 6*l3**2))
+    assert simplify(b.bending_moment().expand()) == simplify(expected_bending_moment.expand())
+
+def test_apply_sliding_hinge():
+    b = Beam(13, 20, 20)
+    r0, m0 = b.apply_support(0, type="fixed")
+    w8 = b.apply_sliding_hinge(8)
+    r13 = b.apply_support(13, type="pin")
+    b.apply_load(-10, 5, -1)
+    b.solve_for_reaction_loads(r0, m0, r13)
+    R_0, M_0, R_13, W_8 = symbols('R_0, M_0, R_13 W_8')
+    assert b.reaction_loads == {R_0: 10, M_0: -50, R_13: 0}
+    tolerance = 1e-6
+    assert abs(b.deflection_jumps[w8] - 85/24) < tolerance
+    assert (b.bending_moment() == 50*SingularityFunction(x, 0, 0) - 10*SingularityFunction(x, 0, 1)
+            + 10*SingularityFunction(x, 5, 1) - 4250*SingularityFunction(x, 8, -2)/3)
+    assert (b.deflection() == -SingularityFunction(x, 0, 2)/16 + SingularityFunction(x, 0, 3)/240
+            - SingularityFunction(x, 5, 3)/240 + 85*SingularityFunction(x, 8, 0)/24)
+
+    E = Symbol('E')
+    I = Symbol('I')
+    I2 = Symbol('I2')
+    b1 = Beam(5, E, I)
+    b2 = Beam(8, E, I2)
+    b = b1.join(b2)
+    r0, m0 = b.apply_support(0, type="fixed")
+    b.apply_sliding_hinge(8)
+    r13 = b.apply_support(13, type="pin")
+    b.apply_load(-10, 5, -1)
+    b.solve_for_reaction_loads(r0, m0, r13)
+    W_8 = Symbol('W_8')
+    assert b.deflection_jumps == {W_8: 4250/(3*E*I2)}
+
+    E = Symbol('E')
+    I = Symbol('I')
+    q = Symbol('q')
+    l1 = Symbol('l1', positive=True)
+    l2 = Symbol('l2', positive=True)
+    l3 = Symbol('l3', positive=True)
+    L = l1 + l2 + l3
+    b = Beam(L, E, I)
+    r0 = b.apply_support(0, type="pin")
+    r3 = b.apply_support(l1, type="pin")
+    b.apply_sliding_hinge(l1 + l2)
+    r10 = b.apply_support(L, type="pin")
+    b.apply_load(q, 0, 0, l1)
+    b.solve_for_reaction_loads(r0, r3, r10)
+    assert (b.bending_moment() == l1*q*SingularityFunction(x, 0, 1)/2 + l1*q*SingularityFunction(x, l1, 1)/2
+            - q*SingularityFunction(x, 0, 2)/2 + q*SingularityFunction(x, l1, 2)/2
+            + (-l1**3*l2*q/24 - l1**3*l3*q/24)*SingularityFunction(x, l1 + l2, -2))
+    assert b.deflection() ==(l1**3*q*x/24 - l1*q*SingularityFunction(x, 0, 3)/12
+                             - l1*q*SingularityFunction(x, l1, 3)/12 + q*SingularityFunction(x, 0, 4)/24
+                             - q*SingularityFunction(x, l1, 4)/24
+                             + (l1**3*l2*q/24 + l1**3*l3*q/24)*SingularityFunction(x, l1 + l2, 0))/(E*I)
+
+def test_max_shear_force():
+    E = Symbol('E')
+    I = Symbol('I')
+
+    b = Beam(3, E, I)
+    R, M = symbols('R, M')
+    b.apply_load(R, 0, -1)
+    b.apply_load(M, 0, -2)
+    b.apply_load(2, 3, -1)
+    b.apply_load(4, 2, -1)
+    b.apply_load(2, 2, 0, end=3)
+    b.solve_for_reaction_loads(R, M)
+    assert b.max_shear_force() == (Interval(0, 2), 8)
+
+    l = symbols('l', positive=True)
+    P = Symbol('P')
+    b = Beam(l, E, I)
+    R1, R2 = symbols('R1, R2')
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(P, 0, 0, end=l)
+    b.solve_for_reaction_loads(R1, R2)
+    max_shear = b.max_shear_force()
+    assert max_shear[0] == 0
+    assert simplify(max_shear[1] - (l*Abs(P)/2)) == 0
+
+
+def test_max_bmoment():
+    E = Symbol('E')
+    I = Symbol('I')
+    l, P = symbols('l, P', positive=True)
+
+    b = Beam(l, E, I)
+    R1, R2 = symbols('R1, R2')
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(P, l/2, -1)
+    b.solve_for_reaction_loads(R1, R2)
+    b.reaction_loads
+    assert b.max_bmoment() == (l/2, P*l/4)
+
+    b = Beam(l, E, I)
+    R1, R2 = symbols('R1, R2')
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(P, 0, 0, end=l)
+    b.solve_for_reaction_loads(R1, R2)
+    assert b.max_bmoment() == (l/2, P*l**2/8)
+
+
+def test_max_deflection():
+    E, I, l, F = symbols('E, I, l, F', positive=True)
+    b = Beam(l, E, I)
+    b.bc_deflection = [(0, 0),(l, 0)]
+    b.bc_slope = [(0, 0),(l, 0)]
+    b.apply_load(F/2, 0, -1)
+    b.apply_load(-F*l/8, 0, -2)
+    b.apply_load(F/2, l, -1)
+    b.apply_load(F*l/8, l, -2)
+    b.apply_load(-F, l/2, -1)
+    assert b.max_deflection() == (l/2, F*l**3/(192*E*I))
+
+def test_solve_for_ild_reactions():
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(10, E, I)
+    b.apply_support(0, type="pin")
+    b.apply_support(10, type="pin")
+    R_0, R_10 = symbols('R_0, R_10')
+    b.solve_for_ild_reactions(1, R_0, R_10)
+    a = b.ild_variable
+    assert b.ild_reactions == {R_0: -SingularityFunction(a, 0, 0) + SingularityFunction(a, 0, 1)/10
+                                    - SingularityFunction(a, 10, 1)/10,
+                               R_10: -SingularityFunction(a, 0, 1)/10 + SingularityFunction(a, 10, 0)
+                                     + SingularityFunction(a, 10, 1)/10}
+
+    E = Symbol('E')
+    I = Symbol('I')
+    F = Symbol('F')
+    L = Symbol('L', positive=True)
+    b = Beam(L, E, I)
+    b.apply_support(L, type="fixed")
+    b.apply_load(F, 0, -1)
+    R_L, M_L = symbols('R_L, M_L')
+    b.solve_for_ild_reactions(F, R_L, M_L)
+    a = b.ild_variable
+    assert b.ild_reactions == {R_L: -F*SingularityFunction(a, 0, 0) + F*SingularityFunction(a, L, 0) - F,
+                               M_L: -F*L*SingularityFunction(a, 0, 0) - F*L + F*SingularityFunction(a, 0, 1)
+                                    - F*SingularityFunction(a, L, 1)}
+
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(20, E, I)
+    r0 = b.apply_support(0, type="pin")
+    r5 = b.apply_support(5, type="pin")
+    r10 = b.apply_support(10, type="pin")
+    r20, m20 = b.apply_support(20, type="fixed")
+    b.solve_for_ild_reactions(1, r0, r5, r10, r20, m20)
+    a = b.ild_variable
+    assert b.ild_reactions[r0].subs(a, 4) == -Rational(59, 475)
+    assert b.ild_reactions[r5].subs(a, 4) == -Rational(2296, 2375)
+    assert b.ild_reactions[r10].subs(a, 4) == Rational(243, 2375)
+    assert b.ild_reactions[r20].subs(a, 12) == -Rational(83, 475)
+    assert b.ild_reactions[m20].subs(a, 12) == -Rational(264, 475)
+
+def test_solve_for_ild_shear():
+    E = Symbol('E')
+    I = Symbol('I')
+    F = Symbol('F')
+    L1 = Symbol('L1', positive=True)
+    L2 = Symbol('L2', positive=True)
+    b = Beam(L1 + L2, E, I)
+    r0 = b.apply_support(0, type="pin")
+    rL = b.apply_support(L1 + L2, type="pin")
+    b.solve_for_ild_reactions(F, r0, rL)
+    b.solve_for_ild_shear(L1, F, r0, rL)
+    a = b.ild_variable
+    expected_shear = (-F*L1*SingularityFunction(a, 0, 0)/(L1 + L2) - F*L2*SingularityFunction(a, 0, 0)/(L1 + L2)
+                      - F*SingularityFunction(-a, 0, 0) + F*SingularityFunction(a, L1 + L2, 0) + F
+                      + F*SingularityFunction(a, 0, 1)/(L1 + L2) - F*SingularityFunction(a, L1 + L2, 1)/(L1 + L2)
+                      - (-F*L1*SingularityFunction(a, 0, 0)/(L1 + L2) + F*L1*SingularityFunction(a, L1 + L2, 0)/(L1 + L2)
+                         - F*L2*SingularityFunction(a, 0, 0)/(L1 + L2) + F*L2*SingularityFunction(a, L1 + L2, 0)/(L1 + L2)
+                         + 2*F)*SingularityFunction(a, L1, 0))
+    assert b.ild_shear.expand() == expected_shear.expand()
+
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(20, E, I)
+    r0 = b.apply_support(0, type="pin")
+    r5 = b.apply_support(5, type="pin")
+    r10 = b.apply_support(10, type="pin")
+    r20, m20 = b.apply_support(20, type="fixed")
+    b.solve_for_ild_reactions(1, r0, r5, r10, r20, m20)
+    b.solve_for_ild_shear(6, 1, r0, r5, r10, r20, m20)
+    a = b.ild_variable
+    assert b.ild_shear.subs(a, 12) == Rational(96, 475)
+    assert b.ild_shear.subs(a, 4) == -Rational(216, 2375)
+
+def test_solve_for_ild_moment():
+    E = Symbol('E')
+    I = Symbol('I')
+    F = Symbol('F')
+    L1 = Symbol('L1', positive=True)
+    L2 = Symbol('L2', positive=True)
+    b = Beam(L1 + L2, E, I)
+    r0 = b.apply_support(0, type="pin")
+    rL = b.apply_support(L1 + L2, type="pin")
+    a = b.ild_variable
+    b.solve_for_ild_reactions(F, r0, rL)
+    b.solve_for_ild_moment(L1, F, r0, rL)
+    assert b.ild_moment.subs(a, 3).subs(L1, 5).subs(L2, 5) == -3*F/2
+
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(20, E, I)
+    r0 = b.apply_support(0, type="pin")
+    r5 = b.apply_support(5, type="pin")
+    r10 = b.apply_support(10, type="pin")
+    r20, m20 = b.apply_support(20, type="fixed")
+    b.solve_for_ild_reactions(1, r0, r5, r10, r20, m20)
+    b.solve_for_ild_moment(5, 1, r0, r5, r10, r20, m20)
+    assert b.ild_moment.subs(a, 12) == -Rational(96, 475)
+    assert b.ild_moment.subs(a, 4) == Rational(36, 95)
+
+def test_ild_with_rotation_hinge():
+    E = Symbol('E')
+    I = Symbol('I')
+    F = Symbol('F')
+    L1 = Symbol('L1', positive=True)
+    L2 = Symbol('L2', positive=True)
+    L3 = Symbol('L3', positive=True)
+    b = Beam(L1 + L2 + L3, E, I)
+    r0 = b.apply_support(0, type="pin")
+    r1 = b.apply_support(L1 + L2, type="pin")
+    r2 = b.apply_support(L1 + L2 + L3, type="pin")
+    b.apply_rotation_hinge(L1 + L2)
+    b.solve_for_ild_reactions(F, r0, r1, r2)
+    a = b.ild_variable
+    assert b.ild_reactions[r0].subs(a, 4).subs(L1, 5).subs(L2, 5).subs(L3, 10) == -3*F/5
+    assert b.ild_reactions[r0].subs(a, -10).subs(L1, 5).subs(L2, 5).subs(L3, 10) == 0
+    assert b.ild_reactions[r0].subs(a, 25).subs(L1, 5).subs(L2, 5).subs(L3, 10) == 0
+    assert b.ild_reactions[r1].subs(a, 4).subs(L1, 5).subs(L2, 5).subs(L3, 10) == -2*F/5
+    assert b.ild_reactions[r2].subs(a, 18).subs(L1, 5).subs(L2, 5).subs(L3, 10) == -4*F/5
+    b.solve_for_ild_shear(L1, F, r0, r1, r2)
+    assert b.ild_shear.subs(a, 7).subs(L1, 5).subs(L2, 5).subs(L3, 10) == -3*F/10
+    assert b.ild_shear.subs(a, 70).subs(L1, 5).subs(L2, 5).subs(L3, 10) == 0
+    b.solve_for_ild_moment(L1, F, r0, r1, r2)
+    assert b.ild_moment.subs(a, 1).subs(L1, 5).subs(L2, 5).subs(L3, 10) == -F/2
+    assert b.ild_moment.subs(a, 8).subs(L1, 5).subs(L2, 5).subs(L3, 10) == -F
+
+def test_ild_with_sliding_hinge():
+    b = Beam(13, 200, 200)
+    r0 = b.apply_support(0, type="pin")
+    r6 = b.apply_support(6, type="pin")
+    r13, m13 = b.apply_support(13, type="fixed")
+    w3 = b.apply_sliding_hinge(3)
+    b.solve_for_ild_reactions(1, r0, r6, r13, m13)
+    a = b.ild_variable
+    assert b.ild_reactions[r0].subs(a, 3) == -1
+    assert b.ild_reactions[r6].subs(a, 3) == Rational(9, 14)
+    assert b.ild_reactions[r13].subs(a, 9) == -Rational(207, 343)
+    assert b.ild_reactions[m13].subs(a, 9) == -Rational(60, 49)
+    assert b.ild_reactions[m13].subs(a, 15) == 0
+    assert b.ild_reactions[m13].subs(a, -3) == 0
+    assert b.ild_deflection_jumps[w3].subs(a, 9) == -Rational(9, 35000)
+    b.solve_for_ild_shear(7, 1, r0, r6, r13, m13)
+    assert b.ild_shear.subs(a, 8) == -Rational(200, 343)
+    b.solve_for_ild_moment(8, 1, r0, r6, r13, m13)
+    assert b.ild_moment.subs(a, 3) == -Rational(12, 7)
+
+def test_Beam3D():
+    l, E, G, I, A = symbols('l, E, G, I, A')
+    R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+
+    b = Beam3D(l, E, G, I, A)
+    m, q = symbols('m, q')
+    b.apply_load(q, 0, 0, dir="y")
+    b.apply_moment_load(m, 0, 0, dir="z")
+    b.bc_slope = [(0, [0, 0, 0]), (l, [0, 0, 0])]
+    b.bc_deflection = [(0, [0, 0, 0]), (l, [0, 0, 0])]
+    b.solve_slope_deflection()
+
+    assert b.polar_moment() == 2*I
+    assert b.shear_force() == [0, -q*x, 0]
+    assert b.shear_stress() == [0, -q*x/A, 0]
+    assert b.axial_stress() == 0
+    assert b.bending_moment() == [0, 0, -m*x + q*x**2/2]
+    expected_deflection = (x*(A*G*q*x**3/4 + A*G*x**2*(-l*(A*G*l*(l*q - 2*m) +
+        12*E*I*q)/(A*G*l**2 + 12*E*I)/2 - m) + 3*E*I*l*(A*G*l*(l*q - 2*m) +
+        12*E*I*q)/(A*G*l**2 + 12*E*I) + x*(-A*G*l**2*q/2 +
+        3*A*G*l**2*(A*G*l*(l*q - 2*m) + 12*E*I*q)/(A*G*l**2 + 12*E*I)/4 +
+        A*G*l*m*Rational(3, 2) - 3*E*I*q))/(6*A*E*G*I))
+    dx, dy, dz = b.deflection()
+    assert dx == dz == 0
+    assert simplify(dy - expected_deflection) == 0
+
+    b2 = Beam3D(30, E, G, I, A, x)
+    b2.apply_load(50, start=0, order=0, dir="y")
+    b2.bc_deflection = [(0, [0, 0, 0]), (30, [0, 0, 0])]
+    b2.apply_load(R1, start=0, order=-1, dir="y")
+    b2.apply_load(R2, start=30, order=-1, dir="y")
+    b2.solve_for_reaction_loads(R1, R2)
+    assert b2.reaction_loads == {R1: -750, R2: -750}
+
+    b2.solve_slope_deflection()
+    assert b2.slope() == [0, 0, 25*x**3/(3*E*I) - 375*x**2/(E*I) + 3750*x/(E*I)]
+    expected_deflection = 25*x**4/(12*E*I) - 125*x**3/(E*I) + 1875*x**2/(E*I) - \
+        25*x**2/(A*G) + 750*x/(A*G)
+    dx, dy, dz = b2.deflection()
+    assert dx == dz == 0
+    assert dy == expected_deflection
+
+    # Test for solve_for_reaction_loads
+    b3 = Beam3D(30, E, G, I, A, x)
+    b3.apply_load(8, start=0, order=0, dir="y")
+    b3.apply_load(9*x, start=0, order=0, dir="z")
+    b3.apply_load(R1, start=0, order=-1, dir="y")
+    b3.apply_load(R2, start=30, order=-1, dir="y")
+    b3.apply_load(R3, start=0, order=-1, dir="z")
+    b3.apply_load(R4, start=30, order=-1, dir="z")
+    b3.solve_for_reaction_loads(R1, R2, R3, R4)
+    assert b3.reaction_loads == {R1: -120, R2: -120, R3: -1350, R4: -2700}
+
+
+def test_polar_moment_Beam3D():
+    l, E, G, A, I1, I2 = symbols('l, E, G, A, I1, I2')
+    I = [I1, I2]
+
+    b = Beam3D(l, E, G, I, A)
+    assert b.polar_moment() == I1 + I2
+
+
+def test_parabolic_loads():
+
+    E, I, L = symbols('E, I, L', positive=True, real=True)
+    R, M, P = symbols('R, M, P', real=True)
+
+    # cantilever beam fixed at x=0 and parabolic distributed loading across
+    # length of beam
+    beam = Beam(L, E, I)
+
+    beam.bc_deflection.append((0, 0))
+    beam.bc_slope.append((0, 0))
+    beam.apply_load(R, 0, -1)
+    beam.apply_load(M, 0, -2)
+
+    # parabolic load
+    beam.apply_load(1, 0, 2)
+
+    beam.solve_for_reaction_loads(R, M)
+
+    assert beam.reaction_loads[R] == -L**3/3
+
+    # cantilever beam fixed at x=0 and parabolic distributed loading across
+    # first half of beam
+    beam = Beam(2*L, E, I)
+
+    beam.bc_deflection.append((0, 0))
+    beam.bc_slope.append((0, 0))
+    beam.apply_load(R, 0, -1)
+    beam.apply_load(M, 0, -2)
+
+    # parabolic load from x=0 to x=L
+    beam.apply_load(1, 0, 2, end=L)
+
+    beam.solve_for_reaction_loads(R, M)
+
+    # result should be the same as the prior example
+    assert beam.reaction_loads[R] == -L**3/3
+
+    # check constant load
+    beam = Beam(2*L, E, I)
+    beam.apply_load(P, 0, 0, end=L)
+    loading = beam.load.xreplace({L: 10, E: 20, I: 30, P: 40})
+    assert loading.xreplace({x: 5}) == 40
+    assert loading.xreplace({x: 15}) == 0
+
+    # check ramp load
+    beam = Beam(2*L, E, I)
+    beam.apply_load(P, 0, 1, end=L)
+    assert beam.load == (P*SingularityFunction(x, 0, 1) -
+                         P*SingularityFunction(x, L, 1) -
+                         P*L*SingularityFunction(x, L, 0))
+
+    # check higher order load: x**8 load from x=0 to x=L
+    beam = Beam(2*L, E, I)
+    beam.apply_load(P, 0, 8, end=L)
+    loading = beam.load.xreplace({L: 10, E: 20, I: 30, P: 40})
+    assert loading.xreplace({x: 5}) == 40*5**8
+    assert loading.xreplace({x: 15}) == 0
+
+
+def test_cross_section():
+    I = Symbol('I')
+    l = Symbol('l')
+    E = Symbol('E')
+    C3, C4 = symbols('C3, C4')
+    a, c, g, h, r, n = symbols('a, c, g, h, r, n')
+
+    # test for second_moment and cross_section setter
+    b0 = Beam(l, E, I)
+    assert b0.second_moment == I
+    assert b0.cross_section == None
+    b0.cross_section = Circle((0, 0), 5)
+    assert b0.second_moment == pi*Rational(625, 4)
+    assert b0.cross_section == Circle((0, 0), 5)
+    b0.second_moment = 2*n - 6
+    assert b0.second_moment == 2*n-6
+    assert b0.cross_section == None
+    with raises(ValueError):
+        b0.second_moment = Circle((0, 0), 5)
+
+    # beam with a circular cross-section
+    b1 = Beam(50, E, Circle((0, 0), r))
+    assert b1.cross_section == Circle((0, 0), r)
+    assert b1.second_moment == pi*r*Abs(r)**3/4
+
+    b1.apply_load(-10, 0, -1)
+    b1.apply_load(R1, 5, -1)
+    b1.apply_load(R2, 50, -1)
+    b1.apply_load(90, 45, -2)
+    b1.solve_for_reaction_loads(R1, R2)
+    assert b1.load == (-10*SingularityFunction(x, 0, -1) + 82*SingularityFunction(x, 5, -1)/S(9)
+                         + 90*SingularityFunction(x, 45, -2) + 8*SingularityFunction(x, 50, -1)/9)
+    assert b1.bending_moment() == (10*SingularityFunction(x, 0, 1) - 82*SingularityFunction(x, 5, 1)/9
+                                     - 90*SingularityFunction(x, 45, 0) - 8*SingularityFunction(x, 50, 1)/9)
+    q = (-5*SingularityFunction(x, 0, 2) + 41*SingularityFunction(x, 5, 2)/S(9)
+           + 90*SingularityFunction(x, 45, 1) + 4*SingularityFunction(x, 50, 2)/S(9))/(pi*E*r*Abs(r)**3)
+    assert b1.slope() == C3 + 4*q
+    q = (-5*SingularityFunction(x, 0, 3)/3 + 41*SingularityFunction(x, 5, 3)/27 + 45*SingularityFunction(x, 45, 2)
+           + 4*SingularityFunction(x, 50, 3)/27)/(pi*E*r*Abs(r)**3)
+    assert b1.deflection() == C3*x + C4 + 4*q
+
+    # beam with a recatangular cross-section
+    b2 = Beam(20, E, Polygon((0, 0), (a, 0), (a, c), (0, c)))
+    assert b2.cross_section == Polygon((0, 0), (a, 0), (a, c), (0, c))
+    assert b2.second_moment == a*c**3/12
+    # beam with a triangular cross-section
+    b3 = Beam(15, E, Triangle((0, 0), (g, 0), (g/2, h)))
+    assert b3.cross_section == Triangle(Point2D(0, 0), Point2D(g, 0), Point2D(g/2, h))
+    assert b3.second_moment == g*h**3/36
+
+    # composite beam
+    b = b2.join(b3, "fixed")
+    b.apply_load(-30, 0, -1)
+    b.apply_load(65, 0, -2)
+    b.apply_load(40, 0, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0)]
+
+    assert b.second_moment == Piecewise((a*c**3/12, x <= 20), (g*h**3/36, x <= 35))
+    assert b.cross_section == None
+    assert b.length == 35
+    assert b.slope().subs(x, 7) == 8400/(E*a*c**3)
+    assert b.slope().subs(x, 25) == 52200/(E*g*h**3) + 39600/(E*a*c**3)
+    assert b.deflection().subs(x, 30) == -537000/(E*g*h**3) - 712000/(E*a*c**3)
+
+def test_max_shear_force_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_load(15, start=0, order=0, dir="z")
+    b.apply_load(12*x, start=0, order=0, dir="y")
+    b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+    assert b.max_shear_force() == [(0, 0), (20, 2400), (20, 300)]
+
+def test_max_bending_moment_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_load(15, start=0, order=0, dir="z")
+    b.apply_load(12*x, start=0, order=0, dir="y")
+    b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+    assert b.max_bmoment() == [(0, 0), (20, 3000), (20, 16000)]
+
+def test_max_deflection_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_load(15, start=0, order=0, dir="z")
+    b.apply_load(12*x, start=0, order=0, dir="y")
+    b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+    b.solve_slope_deflection()
+    c = sympify("495/14")
+    p = sympify("-10 + 10*sqrt(10793)/43")
+    q = sympify("(10 - 10*sqrt(10793)/43)**3/160 - 20/7 + (10 - 10*sqrt(10793)/43)**4/6400 + 20*sqrt(10793)/301 + 27*(10 - 10*sqrt(10793)/43)**2/560")
+    assert b.max_deflection() == [(0, 0), (10, c), (p, q)]
+
+def test_torsion_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_moment_load(15, 5, -2, dir='x')
+    b.apply_moment_load(25, 10, -2, dir='x')
+    b.apply_moment_load(-5, 20, -2, dir='x')
+    b.solve_for_torsion()
+    assert b.angular_deflection().subs(x, 3) == sympify("1/40")
+    assert b.angular_deflection().subs(x, 9) == sympify("17/280")
+    assert b.angular_deflection().subs(x, 12) == sympify("53/840")
+    assert b.angular_deflection().subs(x, 17) == sympify("2/35")
+    assert b.angular_deflection().subs(x, 20) == sympify("3/56")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_cable.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_cable.py
new file mode 100644
index 0000000000000000000000000000000000000000..95ae7997af20f31cbd1b36df4a494f66968ecf53
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_cable.py
@@ -0,0 +1,83 @@
+from sympy.physics.continuum_mechanics.cable import Cable
+from sympy.core.symbol import Symbol
+
+
+def test_cable():
+    c = Cable(('A', 0, 10), ('B', 10, 10))
+    assert c.supports == {'A': [0, 10], 'B': [10, 10]}
+    assert c.left_support == [0, 10]
+    assert c.right_support == [10, 10]
+    assert c.loads == {'distributed': {}, 'point_load': {}}
+    assert c.loads_position == {}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    # tests for change_support method
+    c.change_support('A', ('C', 12, 3))
+    assert c.supports == {'B': [10, 10], 'C': [12, 3]}
+    assert c.left_support == [10, 10]
+    assert c.right_support == [12, 3]
+    assert c.reaction_loads == {Symbol("R_B_x"): 0, Symbol("R_B_y"): 0, Symbol("R_C_x"): 0, Symbol("R_C_y"): 0}
+
+    c.change_support('C', ('A', 0, 10))
+
+    # tests for apply_load method for point loads
+    c.apply_load(-1, ('X', 2, 5, 3, 30))
+    c.apply_load(-1, ('Y', 5, 8, 5, 60))
+    assert c.loads == {'distributed': {}, 'point_load': {'X': [3, 30], 'Y': [5, 60]}}
+    assert c.loads_position == {'X': [2, 5], 'Y': [5, 8]}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    # tests for remove_loads method
+    c.remove_loads('X')
+    assert c.loads == {'distributed': {}, 'point_load': {'Y': [5, 60]}}
+    assert c.loads_position == {'Y': [5, 8]}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    c.remove_loads('Y')
+
+    #tests for apply_load method for distributed load
+    c.apply_load(0, ('Z', 9))
+    assert c.loads == {'distributed': {'Z': 9}, 'point_load': {}}
+    assert c.loads_position == {}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    # tests for apply_length method
+    c.apply_length(20)
+    assert c.length == 20
+
+    del c
+    # tests for solve method
+    # for point loads
+    c = Cable(("A", 0, 10), ("B", 5.5, 8))
+    c.apply_load(-1, ('Z', 2, 7.26, 3, 270))
+    c.apply_load(-1, ('X', 4, 6, 8, 270))
+    c.solve()
+    #assert c.tension == {Symbol("Z_X"): 4.79150773600774, Symbol("X_B"): 6.78571428571429, Symbol("A_Z"): 6.89488895397307}
+    assert abs(c.tension[Symbol("A_Z")] - 6.89488895397307) < 10e-12
+    assert abs(c.tension[Symbol("Z_X")] - 4.79150773600774) < 10e-12
+    assert abs(c.tension[Symbol("X_B")] - 6.78571428571429) < 10e-12
+    #assert c.reaction_loads == {Symbol("R_A_x"): -4.06504065040650, Symbol("R_A_y"): 5.56910569105691, Symbol("R_B_x"): 4.06504065040650, Symbol("R_B_y"): 5.43089430894309}
+    assert abs(c.reaction_loads[Symbol("R_A_x")] + 4.06504065040650) < 10e-12
+    assert abs(c.reaction_loads[Symbol("R_A_y")] - 5.56910569105691) < 10e-12
+    assert abs(c.reaction_loads[Symbol("R_B_x")] - 4.06504065040650) < 10e-12
+    assert abs(c.reaction_loads[Symbol("R_B_y")] - 5.43089430894309) < 10e-12
+    assert abs(c.length - 8.25609584845190) < 10e-12
+
+    del c
+    # tests for solve method
+    # for distributed loads
+    c=Cable(("A", 0, 40),("B", 100, 20))
+    c.apply_load(0, ("X", 850))
+    c.solve(58.58, 0)
+
+    # assert c.tension['distributed'] == 36456.8485*sqrt(0.000543529004799705*(X + 0.00135624381275735)**2 + 1)
+    assert abs(c.tension_at(0) - 61717.4130533677) < 10e-11
+    assert abs(c.tension_at(40) - 39738.0809048449) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_A_x")] - 36465.0000000000) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_A_y")] + 49793.0000000000) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_B_x")] - 44399.9537590861) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_B_y")] - 42868.2071025955 ) < 10e-11
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_truss.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_truss.py
new file mode 100644
index 0000000000000000000000000000000000000000..61c89c9e09386257c7c69909dfdb0f37cda8627d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_truss.py
@@ -0,0 +1,100 @@
+from sympy.core.symbol import Symbol, symbols
+from sympy.physics.continuum_mechanics.truss import Truss
+from sympy import sqrt
+
+
+def test_truss():
+    A = Symbol('A')
+    B = Symbol('B')
+    C = Symbol('C')
+    AB, BC, AC = symbols('AB, BC, AC')
+    P = Symbol('P')
+
+    t = Truss()
+    assert t.nodes == []
+    assert t.node_labels == []
+    assert t.node_positions == []
+    assert t.members == {}
+    assert t.loads == {}
+    assert t.supports == {}
+    assert t.reaction_loads == {}
+    assert t.internal_forces == {}
+
+    # testing the add_node method
+    t.add_node((A, 0, 0), (B, 2, 2), (C, 3, 0))
+    assert t.nodes == [(A, 0, 0), (B, 2, 2), (C, 3, 0)]
+    assert t.node_labels == [A, B, C]
+    assert t.node_positions == [(0, 0), (2, 2), (3, 0)]
+    assert t.loads == {}
+    assert t.supports == {}
+    assert t.reaction_loads == {}
+
+    # testing the remove_node method
+    t.remove_node(C)
+    assert t.nodes == [(A, 0, 0), (B, 2, 2)]
+    assert t.node_labels == [A, B]
+    assert t.node_positions == [(0, 0), (2, 2)]
+    assert t.loads == {}
+    assert t.supports == {}
+
+    t.add_node((C, 3, 0))
+
+    # testing the add_member method
+    t.add_member((AB, A, B), (BC, B, C), (AC, A, C))
+    assert t.members == {AB: [A, B], BC: [B, C], AC: [A, C]}
+    assert t.internal_forces == {AB: 0, BC: 0, AC: 0}
+
+    # testing the remove_member method
+    t.remove_member(BC)
+    assert t.members == {AB: [A, B], AC: [A, C]}
+    assert t.internal_forces == {AB: 0, AC: 0}
+
+    t.add_member((BC, B, C))
+
+    D, CD = symbols('D, CD')
+
+    # testing the change_label methods
+    t.change_node_label((B, D))
+    assert t.nodes == [(A, 0, 0), (D, 2, 2), (C, 3, 0)]
+    assert t.node_labels == [A, D, C]
+    assert t.loads == {}
+    assert t.supports == {}
+    assert t.members == {AB: [A, D], BC: [D, C], AC: [A, C]}
+
+    t.change_member_label((BC, CD))
+    assert t.members == {AB: [A, D], CD: [D, C], AC: [A, C]}
+    assert t.internal_forces == {AB: 0, CD: 0, AC: 0}
+
+
+    # testing the apply_load method
+    t.apply_load((A, P, 90), (A, P/4, 90), (A, 2*P,45), (D, P/2, 90))
+    assert t.loads == {A: [[P, 90], [P/4, 90], [2*P, 45]], D: [[P/2, 90]]}
+    assert t.loads[A] == [[P, 90], [P/4, 90], [2*P, 45]]
+
+    # testing the remove_load method
+    t.remove_load((A, P/4, 90))
+    assert t.loads == {A: [[P, 90], [2*P, 45]], D: [[P/2, 90]]}
+    assert t.loads[A] == [[P, 90], [2*P, 45]]
+
+    # testing the apply_support method
+    t.apply_support((A, "pinned"), (D, "roller"))
+    assert t.supports == {A: 'pinned', D: 'roller'}
+    assert t.reaction_loads == {}
+    assert t.loads == {A: [[P, 90], [2*P, 45], [Symbol('R_A_x'), 0], [Symbol('R_A_y'), 90]],  D: [[P/2, 90], [Symbol('R_D_y'), 90]]}
+
+    # testing the remove_support method
+    t.remove_support(A)
+    assert t.supports == {D: 'roller'}
+    assert t.reaction_loads == {}
+    assert t.loads == {A: [[P, 90], [2*P, 45]], D: [[P/2, 90], [Symbol('R_D_y'), 90]]}
+
+    t.apply_support((A, "pinned"))
+
+    # testing the solve method
+    t.solve()
+    assert t.reaction_loads['R_A_x'] == -sqrt(2)*P
+    assert t.reaction_loads['R_A_y'] == -sqrt(2)*P - P
+    assert t.reaction_loads['R_D_y'] == -P/2
+    assert t.internal_forces[AB]/P == 0
+    assert t.internal_forces[CD] == 0
+    assert t.internal_forces[AC] == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/truss.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/truss.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7fd0ea3f5e18574f21e2f656477c7af987d8eb6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/continuum_mechanics/truss.py
@@ -0,0 +1,1108 @@
+"""
+This module can be used to solve problems related
+to 2D Trusses.
+"""
+
+
+from cmath import atan, inf
+from sympy.core.add import Add
+from sympy.core.evalf import INF
+from sympy.core.mul import Mul
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy import Matrix, pi
+from sympy.external.importtools import import_module
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import zeros
+import math
+from sympy.physics.units.quantities import Quantity
+from sympy.plotting import plot
+from sympy.utilities.decorator import doctest_depends_on
+from sympy import sin, cos
+
+
+__doctest_requires__ = {('Truss.draw'): ['matplotlib']}
+
+
+numpy = import_module('numpy', import_kwargs={'fromlist':['arange']})
+
+
+class Truss:
+    """
+    A Truss is an assembly of members such as beams,
+    connected by nodes, that create a rigid structure.
+    In engineering, a truss is a structure that
+    consists of two-force members only.
+
+    Trusses are extremely important in engineering applications
+    and can be seen in numerous real-world applications like bridges.
+
+    Examples
+    ========
+
+    There is a Truss consisting of four nodes and five
+    members connecting the nodes. A force P acts
+    downward on the node D and there also exist pinned
+    and roller joints on the nodes A and B respectively.
+
+    .. image:: truss_example.png
+
+    >>> from sympy.physics.continuum_mechanics.truss import Truss
+    >>> t = Truss()
+    >>> t.add_node(("node_1", 0, 0), ("node_2", 6, 0), ("node_3", 2, 2), ("node_4", 2, 0))
+    >>> t.add_member(("member_1", "node_1", "node_4"), ("member_2", "node_2", "node_4"), ("member_3", "node_1", "node_3"))
+    >>> t.add_member(("member_4", "node_2", "node_3"), ("member_5", "node_3", "node_4"))
+    >>> t.apply_load(("node_4", 10, 270))
+    >>> t.apply_support(("node_1", "pinned"), ("node_2", "roller"))
+    """
+
+    def __init__(self):
+        """
+        Initializes the class
+        """
+        self._nodes = []
+        self._members = {}
+        self._loads = {}
+        self._supports = {}
+        self._node_labels = []
+        self._node_positions = []
+        self._node_position_x = []
+        self._node_position_y = []
+        self._nodes_occupied = {}
+        self._member_lengths = {}
+        self._reaction_loads = {}
+        self._internal_forces = {}
+        self._node_coordinates = {}
+
+    @property
+    def nodes(self):
+        """
+        Returns the nodes of the truss along with their positions.
+        """
+        return self._nodes
+
+    @property
+    def node_labels(self):
+        """
+        Returns the node labels of the truss.
+        """
+        return self._node_labels
+
+    @property
+    def node_positions(self):
+        """
+        Returns the positions of the nodes of the truss.
+        """
+        return self._node_positions
+
+    @property
+    def members(self):
+        """
+        Returns the members of the truss along with the start and end points.
+        """
+        return self._members
+
+    @property
+    def member_lengths(self):
+        """
+        Returns the length of each member of the truss.
+        """
+        return self._member_lengths
+
+    @property
+    def supports(self):
+        """
+        Returns the nodes with provided supports along with the kind of support provided i.e.
+        pinned or roller.
+        """
+        return self._supports
+
+    @property
+    def loads(self):
+        """
+        Returns the loads acting on the truss.
+        """
+        return self._loads
+
+    @property
+    def reaction_loads(self):
+        """
+        Returns the reaction forces for all supports which are all initialized to 0.
+        """
+        return self._reaction_loads
+
+    @property
+    def internal_forces(self):
+        """
+        Returns the internal forces for all members which are all initialized to 0.
+        """
+        return self._internal_forces
+
+    def add_node(self, *args):
+        """
+        This method adds a node to the truss along with its name/label and its location.
+        Multiple nodes can be added at the same time.
+
+        Parameters
+        ==========
+        The input(s) for this method are tuples of the form (label, x, y).
+
+        label:  String or a Symbol
+            The label for a node. It is the only way to identify a particular node.
+
+        x: Sympifyable
+            The x-coordinate of the position of the node.
+
+        y: Sympifyable
+            The y-coordinate of the position of the node.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0))
+        >>> t.nodes
+        [('A', 0, 0)]
+        >>> t.add_node(('B', 3, 0), ('C', 4, 1))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0), ('C', 4, 1)]
+        """
+
+        for i in args:
+            label = i[0]
+            x = i[1]
+            x = sympify(x)
+            y=i[2]
+            y = sympify(y)
+            if label in self._node_coordinates:
+                raise ValueError("Node needs to have a unique label")
+
+            elif [x, y] in self._node_coordinates.values():
+                raise ValueError("A node already exists at the given position")
+
+            else :
+                self._nodes.append((label, x, y))
+                self._node_labels.append(label)
+                self._node_positions.append((x, y))
+                self._node_position_x.append(x)
+                self._node_position_y.append(y)
+                self._node_coordinates[label] = [x, y]
+
+
+
+    def remove_node(self, *args):
+        """
+        This method removes a node from the truss.
+        Multiple nodes can be removed at the same time.
+
+        Parameters
+        ==========
+        The input(s) for this method are the labels of the nodes to be removed.
+
+        label:  String or Symbol
+            The label of the node to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('C', 5, 0))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0), ('C', 5, 0)]
+        >>> t.remove_node('A', 'C')
+        >>> t.nodes
+        [('B', 3, 0)]
+        """
+        for label in args:
+            for i in range(len(self.nodes)):
+                if self._node_labels[i] == label:
+                    x = self._node_position_x[i]
+                    y = self._node_position_y[i]
+
+            if label not in self._node_coordinates:
+                raise ValueError("No such node exists in the truss")
+
+            else:
+                members_duplicate = self._members.copy()
+                for member in members_duplicate:
+                    if label == self._members[member][0] or label == self._members[member][1]:
+                        raise ValueError("The given node already has member attached to it")
+                self._nodes.remove((label, x, y))
+                self._node_labels.remove(label)
+                self._node_positions.remove((x, y))
+                self._node_position_x.remove(x)
+                self._node_position_y.remove(y)
+                if label in self._loads:
+                    self._loads.pop(label)
+                if label in self._supports:
+                    self._supports.pop(label)
+                self._node_coordinates.pop(label)
+
+
+
+    def add_member(self, *args):
+        """
+        This method adds a member between any two nodes in the given truss.
+
+        Parameters
+        ==========
+        The input(s) of the method are tuple(s) of the form (label, start, end).
+
+        label: String or Symbol
+            The label for a member. It is the only way to identify a particular member.
+
+        start: String or Symbol
+            The label of the starting point/node of the member.
+
+        end: String or Symbol
+            The label of the ending point/node of the member.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('C', 2, 2))
+        >>> t.add_member(('AB', 'A', 'B'), ('BC', 'B', 'C'))
+        >>> t.members
+        {'AB': ['A', 'B'], 'BC': ['B', 'C']}
+        """
+        for i in args:
+            label = i[0]
+            start = i[1]
+            end = i[2]
+
+            if start not in self._node_coordinates or end not in self._node_coordinates or start==end:
+                raise ValueError("The start and end points of the member must be unique nodes")
+
+            elif label in self._members:
+                raise ValueError("A member with the same label already exists for the truss")
+
+            elif self._nodes_occupied.get((start, end)):
+                raise ValueError("A member already exists between the two nodes")
+
+            else:
+                self._members[label] = [start, end]
+                self._member_lengths[label] = sqrt((self._node_coordinates[end][0]-self._node_coordinates[start][0])**2 + (self._node_coordinates[end][1]-self._node_coordinates[start][1])**2)
+                self._nodes_occupied[start, end] = True
+                self._nodes_occupied[end, start] = True
+                self._internal_forces[label] = 0
+
+    def remove_member(self, *args):
+        """
+        This method removes members from the given truss.
+
+        Parameters
+        ==========
+        labels: String or Symbol
+            The label for the member to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('C', 2, 2))
+        >>> t.add_member(('AB', 'A', 'B'), ('AC', 'A', 'C'), ('BC', 'B', 'C'))
+        >>> t.members
+        {'AB': ['A', 'B'], 'AC': ['A', 'C'], 'BC': ['B', 'C']}
+        >>> t.remove_member('AC', 'BC')
+        >>> t.members
+        {'AB': ['A', 'B']}
+        """
+        for label in args:
+            if label not in self._members:
+                raise ValueError("No such member exists in the Truss")
+
+            else:
+                self._nodes_occupied.pop((self._members[label][0], self._members[label][1]))
+                self._nodes_occupied.pop((self._members[label][1], self._members[label][0]))
+                self._members.pop(label)
+                self._member_lengths.pop(label)
+                self._internal_forces.pop(label)
+
+    def change_node_label(self, *args):
+        """
+        This method changes the label(s) of the specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are tuple(s) of the form (label, new_label).
+
+        label: String or Symbol
+            The label of the node for which the label has
+            to be changed.
+
+        new_label: String or Symbol
+            The new label of the node.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0)]
+        >>> t.change_node_label(('A', 'C'), ('B', 'D'))
+        >>> t.nodes
+        [('C', 0, 0), ('D', 3, 0)]
+        """
+        for i in args:
+            label = i[0]
+            new_label = i[1]
+            if label not in self._node_coordinates:
+                raise ValueError("No such node exists for the Truss")
+            elif new_label in self._node_coordinates:
+                raise ValueError("A node with the given label already exists")
+            else:
+                for node in self._nodes:
+                    if node[0] == label:
+                        self._nodes[self._nodes.index((label, node[1], node[2]))] = (new_label, node[1], node[2])
+                        self._node_labels[self._node_labels.index(node[0])] = new_label
+                        self._node_coordinates[new_label] = self._node_coordinates[label]
+                        self._node_coordinates.pop(label)
+                        if node[0] in self._supports:
+                            self._supports[new_label] = self._supports[node[0]]
+                            self._supports.pop(node[0])
+                        if new_label in self._supports:
+                            if self._supports[new_label] == 'pinned':
+                                if 'R_'+str(label)+'_x' in self._reaction_loads and 'R_'+str(label)+'_y' in self._reaction_loads:
+                                    self._reaction_loads['R_'+str(new_label)+'_x'] = self._reaction_loads['R_'+str(label)+'_x']
+                                    self._reaction_loads['R_'+str(new_label)+'_y'] = self._reaction_loads['R_'+str(label)+'_y']
+                                    self._reaction_loads.pop('R_'+str(label)+'_x')
+                                    self._reaction_loads.pop('R_'+str(label)+'_y')
+                                self._loads[new_label] = self._loads[label]
+                                for load in self._loads[new_label]:
+                                    if load[1] == 90:
+                                        load[0] -= Symbol('R_'+str(label)+'_y')
+                                        if load[0] == 0:
+                                            self._loads[label].remove(load)
+                                        break
+                                for load in self._loads[new_label]:
+                                    if load[1] == 0:
+                                        load[0] -= Symbol('R_'+str(label)+'_x')
+                                        if load[0] == 0:
+                                            self._loads[label].remove(load)
+                                        break
+                                self.apply_load(new_label, Symbol('R_'+str(new_label)+'_x'), 0)
+                                self.apply_load(new_label, Symbol('R_'+str(new_label)+'_y'), 90)
+                                self._loads.pop(label)
+                            elif self._supports[new_label] == 'roller':
+                                self._loads[new_label] = self._loads[label]
+                                for load in self._loads[label]:
+                                    if load[1] == 90:
+                                        load[0] -= Symbol('R_'+str(label)+'_y')
+                                        if load[0] == 0:
+                                            self._loads[label].remove(load)
+                                        break
+                                self.apply_load(new_label, Symbol('R_'+str(new_label)+'_y'), 90)
+                                self._loads.pop(label)
+                        else:
+                            if label in self._loads:
+                                self._loads[new_label] = self._loads[label]
+                                self._loads.pop(label)
+                        for member in self._members:
+                            if self._members[member][0] == node[0]:
+                                self._members[member][0] = new_label
+                                self._nodes_occupied[(new_label, self._members[member][1])] = True
+                                self._nodes_occupied[(self._members[member][1], new_label)] = True
+                                self._nodes_occupied.pop((label, self._members[member][1]))
+                                self._nodes_occupied.pop((self._members[member][1], label))
+                            elif self._members[member][1] == node[0]:
+                                self._members[member][1] = new_label
+                                self._nodes_occupied[(self._members[member][0], new_label)] = True
+                                self._nodes_occupied[(new_label, self._members[member][0])] = True
+                                self._nodes_occupied.pop((self._members[member][0], label))
+                                self._nodes_occupied.pop((label, self._members[member][0]))
+
+    def change_member_label(self, *args):
+        """
+        This method changes the label(s) of the specified member(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are tuple(s) of the form (label, new_label)
+
+        label: String or Symbol
+            The label of the member for which the label has
+            to be changed.
+
+        new_label: String or Symbol
+            The new label of the member.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('D', 5, 0))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0), ('D', 5, 0)]
+        >>> t.change_node_label(('A', 'C'))
+        >>> t.nodes
+        [('C', 0, 0), ('B', 3, 0), ('D', 5, 0)]
+        >>> t.add_member(('BC', 'B', 'C'), ('BD', 'B', 'D'))
+        >>> t.members
+        {'BC': ['B', 'C'], 'BD': ['B', 'D']}
+        >>> t.change_member_label(('BC', 'BC_new'), ('BD', 'BD_new'))
+        >>> t.members
+        {'BC_new': ['B', 'C'], 'BD_new': ['B', 'D']}
+        """
+        for i in args:
+            label = i[0]
+            new_label = i[1]
+            if label not in self._members:
+                raise ValueError("No such member exists for the Truss")
+            else:
+                members_duplicate = list(self._members).copy()
+                for member in members_duplicate:
+                    if member == label:
+                        self._members[new_label] = [self._members[member][0], self._members[member][1]]
+                        self._members.pop(label)
+                        self._member_lengths[new_label] = self._member_lengths[label]
+                        self._member_lengths.pop(label)
+                        self._internal_forces[new_label] = self._internal_forces[label]
+                        self._internal_forces.pop(label)
+
+    def apply_load(self, *args):
+        """
+        This method applies external load(s) at the specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of the method are tuple(s) of the form (location, magnitude, direction).
+
+        location: String or Symbol
+            Label of the Node at which load is applied.
+
+        magnitude: Sympifyable
+            Magnitude of the load applied. It must always be positive and any changes in
+            the direction of the load are not reflected here.
+
+        direction: Sympifyable
+            The angle, in degrees, that the load vector makes with the horizontal
+            in the counter-clockwise direction. It takes the values 0 to 360,
+            inclusive.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> from sympy import symbols
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> P = symbols('P')
+        >>> t.apply_load(('A', P, 90), ('A', P/2, 45), ('A', P/4, 90))
+        >>> t.loads
+        {'A': [[P, 90], [P/2, 45], [P/4, 90]]}
+        """
+        for i in args:
+            location = i[0]
+            magnitude = i[1]
+            direction = i[2]
+            magnitude = sympify(magnitude)
+            direction = sympify(direction)
+
+            if location not in self._node_coordinates:
+                raise ValueError("Load must be applied at a known node")
+
+            else:
+                if location in self._loads:
+                    self._loads[location].append([magnitude, direction])
+                else:
+                    self._loads[location] = [[magnitude, direction]]
+
+    def remove_load(self, *args):
+        """
+        This method removes already
+        present external load(s) at specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are tuple(s) of the form (location, magnitude, direction).
+
+        location: String or Symbol
+            Label of the Node at which load is applied and is to be removed.
+
+        magnitude: Sympifyable
+            Magnitude of the load applied.
+
+        direction: Sympifyable
+            The angle, in degrees, that the load vector makes with the horizontal
+            in the counter-clockwise direction. It takes the values 0 to 360,
+            inclusive.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> from sympy import symbols
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> P = symbols('P')
+        >>> t.apply_load(('A', P, 90), ('A', P/2, 45), ('A', P/4, 90))
+        >>> t.loads
+        {'A': [[P, 90], [P/2, 45], [P/4, 90]]}
+        >>> t.remove_load(('A', P/4, 90), ('A', P/2, 45))
+        >>> t.loads
+        {'A': [[P, 90]]}
+        """
+        for i in args:
+            location = i[0]
+            magnitude = i[1]
+            direction = i[2]
+            magnitude = sympify(magnitude)
+            direction = sympify(direction)
+
+            if location not in self._node_coordinates:
+                raise ValueError("Load must be removed from a known node")
+
+            else:
+                if [magnitude, direction] not in self._loads[location]:
+                    raise ValueError("No load of this magnitude and direction has been applied at this node")
+                else:
+                    self._loads[location].remove([magnitude, direction])
+            if self._loads[location] == []:
+                self._loads.pop(location)
+
+    def apply_support(self, *args):
+        """
+        This method adds a pinned or roller support at specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are of the form (location, type).
+
+        location: String or Symbol
+            Label of the Node at which support is added.
+
+        type: String
+            Type of the support being provided at the node.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> t.apply_support(('A', 'pinned'), ('B', 'roller'))
+        >>> t.supports
+        {'A': 'pinned', 'B': 'roller'}
+        """
+        for i in args:
+            location = i[0]
+            type = i[1]
+            if location not in self._node_coordinates:
+                raise ValueError("Support must be added on a known node")
+
+            else:
+                if location not in self._supports:
+                    if type == 'pinned':
+                        self.apply_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                        self.apply_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                    elif type == 'roller':
+                        self.apply_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                elif self._supports[location] == 'pinned':
+                    if type == 'roller':
+                        self.remove_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                elif self._supports[location] == 'roller':
+                    if type == 'pinned':
+                        self.apply_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                self._supports[location] = type
+
+    def remove_support(self, *args):
+        """
+        This method removes support from specified node(s.)
+
+        Parameters
+        ==========
+
+        locations: String or Symbol
+            Label of the Node(s) at which support is to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> t.apply_support(('A', 'pinned'), ('B', 'roller'))
+        >>> t.supports
+        {'A': 'pinned', 'B': 'roller'}
+        >>> t.remove_support('A','B')
+        >>> t.supports
+        {}
+        """
+        for location in args:
+
+            if location not in self._node_coordinates:
+                raise ValueError("No such node exists in the Truss")
+
+            elif location not in self._supports:
+                raise ValueError("No support has been added to the given node")
+
+            else:
+                if self._supports[location] == 'pinned':
+                    self.remove_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                    self.remove_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                elif self._supports[location] == 'roller':
+                    self.remove_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                self._supports.pop(location)
+
+    def solve(self):
+        """
+        This method solves for all reaction forces of all supports and all internal forces
+        of all the members in the truss, provided the Truss is solvable.
+
+        A Truss is solvable if the following condition is met,
+
+        2n >= r + m
+
+        Where n is the number of nodes, r is the number of reaction forces, where each pinned
+        support has 2 reaction forces and each roller has 1, and m is the number of members.
+
+        The given condition is derived from the fact that a system of equations is solvable
+        only when the number of variables is lesser than or equal to the number of equations.
+        Equilibrium Equations in x and y directions give two equations per node giving 2n number
+        equations. However, the truss needs to be stable as well and may be unstable if 2n > r + m.
+        The number of variables is simply the sum of the number of reaction forces and member
+        forces.
+
+        .. note::
+           The sign convention for the internal forces present in a member revolves around whether each
+           force is compressive or tensile. While forming equations for each node, internal force due
+           to a member on the node is assumed to be away from the node i.e. each force is assumed to
+           be compressive by default. Hence, a positive value for an internal force implies the
+           presence of compressive force in the member and a negative value implies a tensile force.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(("node_1", 0, 0), ("node_2", 6, 0), ("node_3", 2, 2), ("node_4", 2, 0))
+        >>> t.add_member(("member_1", "node_1", "node_4"), ("member_2", "node_2", "node_4"), ("member_3", "node_1", "node_3"))
+        >>> t.add_member(("member_4", "node_2", "node_3"), ("member_5", "node_3", "node_4"))
+        >>> t.apply_load(("node_4", 10, 270))
+        >>> t.apply_support(("node_1", "pinned"), ("node_2", "roller"))
+        >>> t.solve()
+        >>> t.reaction_loads
+        {'R_node_1_x': 0, 'R_node_1_y': 20/3, 'R_node_2_y': 10/3}
+        >>> t.internal_forces
+        {'member_1': 20/3, 'member_2': 20/3, 'member_3': -20*sqrt(2)/3, 'member_4': -10*sqrt(5)/3, 'member_5': 10}
+        """
+        count_reaction_loads = 0
+        for node in self._nodes:
+            if node[0] in self._supports:
+                if self._supports[node[0]]=='pinned':
+                    count_reaction_loads += 2
+                elif self._supports[node[0]]=='roller':
+                    count_reaction_loads += 1
+        if 2*len(self._nodes) != len(self._members) + count_reaction_loads:
+            raise ValueError("The given truss cannot be solved")
+        coefficients_matrix = [[0 for i in range(2*len(self._nodes))] for j in range(2*len(self._nodes))]
+        load_matrix = zeros(2*len(self.nodes), 1)
+        load_matrix_row = 0
+        for node in self._nodes:
+            if node[0] in self._loads:
+                for load in self._loads[node[0]]:
+                    if load[0]!=Symbol('R_'+str(node[0])+'_x') and load[0]!=Symbol('R_'+str(node[0])+'_y'):
+                        load_matrix[load_matrix_row] -= load[0]*cos(pi*load[1]/180)
+                        load_matrix[load_matrix_row + 1] -= load[0]*sin(pi*load[1]/180)
+            load_matrix_row += 2
+        cols = 0
+        row = 0
+        for node in self._nodes:
+            if node[0] in self._supports:
+                if self._supports[node[0]]=='pinned':
+                    coefficients_matrix[row][cols] += 1
+                    coefficients_matrix[row+1][cols+1] += 1
+                    cols += 2
+                elif self._supports[node[0]]=='roller':
+                    coefficients_matrix[row+1][cols] += 1
+                    cols += 1
+            row += 2
+        for member in self._members:
+            start = self._members[member][0]
+            end = self._members[member][1]
+            length = sqrt((self._node_coordinates[start][0]-self._node_coordinates[end][0])**2 + (self._node_coordinates[start][1]-self._node_coordinates[end][1])**2)
+            start_index = self._node_labels.index(start)
+            end_index = self._node_labels.index(end)
+            horizontal_component_start = (self._node_coordinates[end][0]-self._node_coordinates[start][0])/length
+            vertical_component_start = (self._node_coordinates[end][1]-self._node_coordinates[start][1])/length
+            horizontal_component_end = (self._node_coordinates[start][0]-self._node_coordinates[end][0])/length
+            vertical_component_end = (self._node_coordinates[start][1]-self._node_coordinates[end][1])/length
+            coefficients_matrix[start_index*2][cols] += horizontal_component_start
+            coefficients_matrix[start_index*2+1][cols] += vertical_component_start
+            coefficients_matrix[end_index*2][cols] += horizontal_component_end
+            coefficients_matrix[end_index*2+1][cols] += vertical_component_end
+            cols += 1
+        forces_matrix = (Matrix(coefficients_matrix)**-1)*load_matrix
+        self._reaction_loads = {}
+        i = 0
+        min_load = inf
+        for node in self._nodes:
+            if node[0] in self._loads:
+                for load in self._loads[node[0]]:
+                    if type(load[0]) not in [Symbol, Mul, Add]:
+                        min_load = min(min_load, load[0])
+        for j in range(len(forces_matrix)):
+            if type(forces_matrix[j]) not in [Symbol, Mul, Add]:
+                if abs(forces_matrix[j]/min_load) <1E-10:
+                    forces_matrix[j] = 0
+        for node in self._nodes:
+            if node[0] in self._supports:
+                if self._supports[node[0]]=='pinned':
+                    self._reaction_loads['R_'+str(node[0])+'_x'] = forces_matrix[i]
+                    self._reaction_loads['R_'+str(node[0])+'_y'] = forces_matrix[i+1]
+                    i += 2
+                elif self._supports[node[0]]=='roller':
+                    self._reaction_loads['R_'+str(node[0])+'_y'] = forces_matrix[i]
+                    i += 1
+        for member in self._members:
+            self._internal_forces[member] = forces_matrix[i]
+            i += 1
+        return
+
+    @doctest_depends_on(modules=('numpy',))
+    def draw(self, subs_dict=None):
+        """
+        Returns a plot object of the Truss with all its nodes, members,
+        supports and loads.
+
+        .. note::
+            The user must be careful while entering load values in their
+            directions. The draw function assumes a sign convention that
+            is used for plotting loads.
+
+            Given a right-handed coordinate system with XYZ coordinates,
+            the supports are assumed to be such that the reaction forces of a
+            pinned support is in the +X and +Y direction while those of a
+            roller support is in the +Y direction. For the load, the range
+            of angles, one can input goes all the way to 360 degrees which, in the
+            the plot is the angle that the load vector makes with the positive x-axis in the anticlockwise direction.
+
+            For example, for a 90-degree angle, the load will be a vertically
+            directed along +Y while a 270-degree angle denotes a vertical
+            load as well but along -Y.
+
+        Examples
+        ========
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.truss import Truss
+            >>> import math
+            >>> t = Truss()
+            >>> t.add_node(("A", -4, 0), ("B", 0, 0), ("C", 4, 0), ("D", 8, 0))
+            >>> t.add_node(("E", 6, 2/math.sqrt(3)))
+            >>> t.add_node(("F", 2, 2*math.sqrt(3)))
+            >>> t.add_node(("G", -2, 2/math.sqrt(3)))
+            >>> t.add_member(("AB","A","B"), ("BC","B","C"), ("CD","C","D"))
+            >>> t.add_member(("AG","A","G"), ("GB","G","B"), ("GF","G","F"))
+            >>> t.add_member(("BF","B","F"), ("FC","F","C"), ("CE","C","E"))
+            >>> t.add_member(("FE","F","E"), ("DE","D","E"))
+            >>> t.apply_support(("A","pinned"), ("D","roller"))
+            >>> t.apply_load(("G", 3, 90), ("E", 3, 90), ("F", 2, 90))
+            >>> p = t.draw()
+            >>> p  # doctest: +ELLIPSIS
+            Plot object containing:
+            [0]: cartesian line: 1 for x over (1.0, 1.0)
+            ...
+            >>> p.show()
+        """
+        if not numpy:
+            raise ImportError("To use this function numpy module is required")
+
+        x = Symbol('x')
+
+        markers = []
+        annotations = []
+        rectangles = []
+
+        node_markers = self._draw_nodes(subs_dict)
+        markers += node_markers
+
+        member_rectangles = self._draw_members()
+        rectangles += member_rectangles
+
+        support_markers = self._draw_supports()
+        markers += support_markers
+
+        load_annotations = self._draw_loads()
+        annotations += load_annotations
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+
+        lim = max(xmax*1.1-xmin*0.8+1, ymax*1.1-ymin*0.8+1)
+
+        if lim==xmax*1.1-xmin*0.8+1:
+            sing_plot = plot(1, (x, 1, 1), markers=markers, show=False, annotations=annotations, xlim=(xmin-0.05*lim, xmax*1.1), ylim=(xmin-0.05*lim, xmax*1.1), axis=False, rectangles=rectangles)
+
+        else:
+            sing_plot = plot(1, (x, 1, 1), markers=markers, show=False, annotations=annotations, xlim=(ymin-0.05*lim, ymax*1.1), ylim=(ymin-0.05*lim, ymax*1.1), axis=False, rectangles=rectangles)
+
+        return sing_plot
+
+
+    def _draw_nodes(self, subs_dict):
+        node_markers = []
+
+        for node in self._node_coordinates:
+            if (type(self._node_coordinates[node][0]) in (Symbol, Quantity)):
+                if self._node_coordinates[node][0] in subs_dict:
+                    self._node_coordinates[node][0] = subs_dict[self._node_coordinates[node][0]]
+                else:
+                    raise ValueError("provided substituted dictionary is not adequate")
+            elif (type(self._node_coordinates[node][0]) == Mul):
+                objects = self._node_coordinates[node][0].as_coeff_Mul()
+                for object in objects:
+                    if type(object) in (Symbol, Quantity):
+                        if subs_dict==None or object not in subs_dict:
+                            raise ValueError("provided substituted dictionary is not adequate")
+                        else:
+                            self._node_coordinates[node][0] /= object
+                            self._node_coordinates[node][0] *= subs_dict[object]
+
+            if (type(self._node_coordinates[node][1]) in (Symbol, Quantity)):
+                if self._node_coordinates[node][1] in subs_dict:
+                    self._node_coordinates[node][1] = subs_dict[self._node_coordinates[node][1]]
+                else:
+                    raise ValueError("provided substituted dictionary is not adequate")
+            elif (type(self._node_coordinates[node][1]) == Mul):
+                objects = self._node_coordinates[node][1].as_coeff_Mul()
+                for object in objects:
+                    if type(object) in (Symbol, Quantity):
+                        if subs_dict==None or object not in subs_dict:
+                            raise ValueError("provided substituted dictionary is not adequate")
+                        else:
+                            self._node_coordinates[node][1] /= object
+                            self._node_coordinates[node][1] *= subs_dict[object]
+
+        for node in self._node_coordinates:
+            node_markers.append(
+                {
+                    'args':[[self._node_coordinates[node][0]], [self._node_coordinates[node][1]]],
+                    'marker':'o',
+                    'markersize':5,
+                    'color':'black'
+                }
+            )
+        return node_markers
+
+    def _draw_members(self):
+
+        member_rectangles = []
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        for member in self._members:
+            x1 = self._node_coordinates[self._members[member][0]][0]
+            y1 = self._node_coordinates[self._members[member][0]][1]
+            x2 = self._node_coordinates[self._members[member][1]][0]
+            y2 = self._node_coordinates[self._members[member][1]][1]
+            if x2!=x1 and y2!=y1:
+                if x2>x1:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff*cos(pi/4+atan((y2-y1)/(x2-x1)))/2, y1-0.005*max_diff*sin(pi/4+atan((y2-y1)/(x2-x1)))/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2)+0.005*max_diff/math.sqrt(2),
+                            'height':0.005*max_diff,
+                            'angle':180*atan((y2-y1)/(x2-x1))/pi,
+                            'color':'brown'
+                        }
+                    )
+                else:
+                    member_rectangles.append(
+                        {
+                            'xy':(x2-0.005*max_diff*cos(pi/4+atan((y2-y1)/(x2-x1)))/2, y2-0.005*max_diff*sin(pi/4+atan((y2-y1)/(x2-x1)))/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2)+0.005*max_diff/math.sqrt(2),
+                            'height':0.005*max_diff,
+                            'angle':180*atan((y2-y1)/(x2-x1))/pi,
+                            'color':'brown'
+                        }
+                    )
+            elif y2==y1:
+                if x2>x1:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff/2, y1-0.005*max_diff/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2),
+                            'height':0.005*max_diff,
+                            'angle':90*(1-math.copysign(1, x2-x1)),
+                            'color':'brown'
+                        }
+                    )
+                else:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff/2, y1-0.005*max_diff/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2),
+                            'height':-0.005*max_diff,
+                            'angle':90*(1-math.copysign(1, x2-x1)),
+                            'color':'brown'
+                        }
+                    )
+            else:
+                if y1abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        for node in self._supports:
+            if self._supports[node]=='pinned':
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]]
+                        ],
+                        'marker':6,
+                        'markersize':15,
+                        'color':'black',
+                        'markerfacecolor':'none'
+                    }
+                )
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]-0.035*max_diff]
+                        ],
+                        'marker':'_',
+                        'markersize':14,
+                        'color':'black'
+                    }
+                )
+
+            elif self._supports[node]=='roller':
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]-0.02*max_diff]
+                        ],
+                        'marker':'o',
+                        'markersize':11,
+                        'color':'black',
+                        'markerfacecolor':'none'
+                    }
+                )
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]-0.0375*max_diff]
+                        ],
+                        'marker':'_',
+                        'markersize':14,
+                        'color':'black'
+                    }
+                )
+        return support_markers
+
+    def _draw_loads(self):
+        load_annotations = []
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin+5
+        else:
+            max_diff = 1.1*ymax-0.8*ymin+5
+
+        for node in self._loads:
+            for load in self._loads[node]:
+                if load[0] in [Symbol('R_'+str(node)+'_x'), Symbol('R_'+str(node)+'_y')]:
+                    continue
+                x = self._node_coordinates[node][0]
+                y = self._node_coordinates[node][1]
+                load_annotations.append(
+                    {
+                        'text':'',
+                        'xy':(
+                            x-math.cos(pi*load[1]/180)*(max_diff/100),
+                            y-math.sin(pi*load[1]/180)*(max_diff/100)
+                        ),
+                        'xytext':(
+                            x-(max_diff/100+abs(xmax-xmin)+abs(ymax-ymin))*math.cos(pi*load[1]/180)/20,
+                            y-(max_diff/100+abs(xmax-xmin)+abs(ymax-ymin))*math.sin(pi*load[1]/180)/20
+                        ),
+                        'arrowprops':{'width':1.5, 'headlength':5, 'headwidth':5, 'facecolor':'black'}
+                    }
+                )
+        return load_annotations
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..c4d74895f2e68cb918f00fd7065ca048b32ef06d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/__init__.py
@@ -0,0 +1,17 @@
+from .lti import (TransferFunction, PIDController, Series, MIMOSeries, Parallel, MIMOParallel,
+    Feedback, MIMOFeedback, TransferFunctionMatrix, StateSpace, gbt, bilinear, forward_diff,
+    backward_diff, phase_margin, gain_margin)
+from .control_plots import (pole_zero_numerical_data, pole_zero_plot, step_response_numerical_data,
+    step_response_plot, impulse_response_numerical_data, impulse_response_plot, ramp_response_numerical_data,
+    ramp_response_plot, bode_magnitude_numerical_data, bode_phase_numerical_data, bode_magnitude_plot,
+    bode_phase_plot, bode_plot, nyquist_plot_expr, nyquist_plot, nichols_plot_expr, nichols_plot)
+
+__all__ = ['TransferFunction', 'PIDController', 'Series', 'MIMOSeries', 'Parallel',
+    'MIMOParallel', 'Feedback', 'MIMOFeedback', 'TransferFunctionMatrix', 'StateSpace',
+    'gbt', 'bilinear', 'forward_diff', 'backward_diff', 'phase_margin', 'gain_margin',
+    'pole_zero_numerical_data', 'pole_zero_plot', 'step_response_numerical_data',
+    'step_response_plot', 'impulse_response_numerical_data', 'impulse_response_plot',
+    'ramp_response_numerical_data', 'ramp_response_plot',
+    'bode_magnitude_numerical_data', 'bode_phase_numerical_data',
+    'bode_magnitude_plot', 'bode_phase_plot', 'bode_plot', 'nyquist_plot_expr', 'nyquist_plot',
+    'nichols_plot_expr', 'nichols_plot']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/control_plots.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/control_plots.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a83d3b833a064905619a4d6ba2a74e52ef72afa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/control_plots.py
@@ -0,0 +1,1135 @@
+from sympy.core.numbers import I, pi
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.polys.partfrac import apart
+from sympy.core.symbol import Dummy
+from sympy.external import import_module
+from sympy.functions import arg, Abs
+from sympy.integrals.laplace import _fast_inverse_laplace
+from sympy.physics.control.lti import SISOLinearTimeInvariant
+from sympy.plotting.series import LineOver1DRangeSeries
+from sympy.plotting.plot import plot_parametric
+from sympy.polys.domains import ZZ, QQ
+from sympy.polys.polytools import Poly
+from sympy.printing.latex import latex
+from sympy.geometry.polygon import deg
+
+__all__ = ['pole_zero_numerical_data', 'pole_zero_plot',
+    'step_response_numerical_data', 'step_response_plot',
+    'impulse_response_numerical_data', 'impulse_response_plot',
+    'ramp_response_numerical_data', 'ramp_response_plot',
+    'bode_magnitude_numerical_data', 'bode_phase_numerical_data',
+    'bode_magnitude_plot', 'bode_phase_plot', 'bode_plot',
+    'nyquist_plot_expr', 'nyquist_plot', 'nichols_plot_expr',
+    'nichols_plot']
+
+
+matplotlib = import_module(
+        'matplotlib', import_kwargs={'fromlist': ['pyplot']},
+        catch=(RuntimeError,))
+
+if matplotlib:
+    plt = matplotlib.pyplot
+
+
+def _check_system(system):
+    """Function to check whether the dynamical system passed for plots is
+    compatible or not."""
+    if not isinstance(system, SISOLinearTimeInvariant):
+        raise NotImplementedError("Only SISO LTI systems are currently supported.")
+    sys = system.to_expr()
+    len_free_symbols = len(sys.free_symbols)
+    if len_free_symbols > 1:
+        raise ValueError("Extra degree of freedom found. Make sure"
+            " that there are no free symbols in the dynamical system other"
+            " than the variable of Laplace transform.")
+    if sys.has(exp):
+        # Should test that exp is not part of a constant, in which case
+        # no exception is required, compare exp(s) with s*exp(1)
+        raise NotImplementedError("Time delay terms are not supported.")
+
+
+def _poly_roots(poly):
+    """Function to get the roots of a polynomial."""
+    def _eval(l):
+        return [float(i) if i.is_real else complex(i) for i in l]
+    if poly.domain in (QQ, ZZ):
+        return _eval(poly.all_roots())
+    # XXX: Use all_roots() for irrational coefficients when possible
+    # See https://github.com/sympy/sympy/issues/22943
+    return _eval(poly.nroots())
+
+
+def pole_zero_numerical_data(system):
+    """
+    Returns the numerical data of poles and zeros of the system.
+    It is internally used by ``pole_zero_plot`` to get the data
+    for plotting poles and zeros. Users can use this data to further
+    analyse the dynamics of the system or plot using a different
+    backend/plotting-module.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the pole-zero data is to be computed.
+
+    Returns
+    =======
+
+    tuple : (zeros, poles)
+        zeros = Zeros of the system as a list of Python float/complex.
+        poles = Poles of the system as a list of Python float/complex.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import pole_zero_numerical_data
+    >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+    >>> pole_zero_numerical_data(tf1)
+    ([-1j, 1j], [-2.0, -1.0, (-0.5-0.8660254037844386j), (-0.5+0.8660254037844386j)])
+
+    See Also
+    ========
+
+    pole_zero_plot
+
+    """
+    _check_system(system)
+    system = system.doit()  # Get the equivalent TransferFunction object.
+
+    num_poly = Poly(system.num, system.var)
+    den_poly = Poly(system.den, system.var)
+
+    return _poly_roots(num_poly), _poly_roots(den_poly)
+
+
+def pole_zero_plot(system, pole_color='blue', pole_markersize=10,
+    zero_color='orange', zero_markersize=7, grid=True, show_axes=True,
+    show=True, **kwargs):
+    r"""
+    Returns the Pole-Zero plot (also known as PZ Plot or PZ Map) of a system.
+
+    A Pole-Zero plot is a graphical representation of a system's poles and
+    zeros. It is plotted on a complex plane, with circular markers representing
+    the system's zeros and 'x' shaped markers representing the system's poles.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type systems
+        The system for which the pole-zero plot is to be computed.
+    pole_color : str, tuple, optional
+        The color of the pole points on the plot. Default color
+        is blue. The color can be provided as a matplotlib color string,
+        or a 3-tuple of floats each in the 0-1 range.
+    pole_markersize : Number, optional
+        The size of the markers used to mark the poles in the plot.
+        Default pole markersize is 10.
+    zero_color : str, tuple, optional
+        The color of the zero points on the plot. Default color
+        is orange. The color can be provided as a matplotlib color string,
+        or a 3-tuple of floats each in the 0-1 range.
+    zero_markersize : Number, optional
+        The size of the markers used to mark the zeros in the plot.
+        Default zero markersize is 7.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import pole_zero_plot
+        >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+        >>> pole_zero_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    pole_zero_numerical_data
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Pole%E2%80%93zero_plot
+
+    """
+    zeros, poles = pole_zero_numerical_data(system)
+
+    zero_real = [i.real for i in zeros]
+    zero_imag = [i.imag for i in zeros]
+
+    pole_real = [i.real for i in poles]
+    pole_imag = [i.imag for i in poles]
+
+    plt.plot(pole_real, pole_imag, 'x', mfc='none',
+        markersize=pole_markersize, color=pole_color)
+    plt.plot(zero_real, zero_imag, 'o', markersize=zero_markersize,
+        color=zero_color)
+    plt.xlabel('Real Axis')
+    plt.ylabel('Imaginary Axis')
+    plt.title(f'Poles and Zeros of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def step_response_numerical_data(system, prec=8, lower_limit=0,
+    upper_limit=10, **kwargs):
+    """
+    Returns the numerical values of the points in the step response plot
+    of a SISO continuous-time system. By default, adaptive sampling
+    is used. If the user wants to instead get an uniformly
+    sampled response, then ``adaptive`` kwarg should be passed ``False``
+    and ``n`` must be passed as additional kwargs.
+    Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries`
+    for more details.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the unit step response data is to be computed.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    kwargs :
+        Additional keyword arguments are passed to the underlying
+        :class:`sympy.plotting.series.LineOver1DRangeSeries` class.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = Time-axis values of the points in the step response. NumPy array.
+        y = Amplitude-axis values of the points in the step response. NumPy array.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When ``lower_limit`` parameter is less than 0.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import step_response_numerical_data
+    >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s)
+    >>> step_response_numerical_data(tf1)   # doctest: +SKIP
+    ([0.0, 0.025413462339411542, 0.0484508722725343, ... , 9.670250533855183, 9.844291913708725, 10.0],
+    [0.0, 0.023844582399907256, 0.042894276802320226, ..., 6.828770759094287e-12, 6.456457160755703e-12])
+
+    See Also
+    ========
+
+    step_response_plot
+
+    """
+    if lower_limit < 0:
+        raise ValueError("Lower limit of time must be greater "
+            "than or equal to zero.")
+    _check_system(system)
+    _x = Dummy("x")
+    expr = system.to_expr()/(system.var)
+    expr = apart(expr, system.var, full=True)
+    _y = _fast_inverse_laplace(expr, system.var, _x).evalf(prec)
+    return LineOver1DRangeSeries(_y, (_x, lower_limit, upper_limit),
+        **kwargs).get_points()
+
+
+def step_response_plot(system, color='b', prec=8, lower_limit=0,
+    upper_limit=10, show_axes=False, grid=True, show=True, **kwargs):
+    r"""
+    Returns the unit step response of a continuous-time system. It is
+    the response of the system when the input signal is a step function.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Step Response is to be computed.
+    color : str, tuple, optional
+        The color of the line. Default is Blue.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import step_response_plot
+        >>> tf1 = TransferFunction(8*s**2 + 18*s + 32, s**3 + 6*s**2 + 14*s + 24, s)
+        >>> step_response_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    impulse_response_plot, ramp_response_plot
+
+    References
+    ==========
+
+    .. [1] https://www.mathworks.com/help/control/ref/lti.step.html
+
+    """
+    x, y = step_response_numerical_data(system, prec=prec,
+        lower_limit=lower_limit, upper_limit=upper_limit, **kwargs)
+    plt.plot(x, y, color=color)
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.title(f'Unit Step Response of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def impulse_response_numerical_data(system, prec=8, lower_limit=0,
+    upper_limit=10, **kwargs):
+    """
+    Returns the numerical values of the points in the impulse response plot
+    of a SISO continuous-time system. By default, adaptive sampling
+    is used. If the user wants to instead get an uniformly
+    sampled response, then ``adaptive`` kwarg should be passed ``False``
+    and ``n`` must be passed as additional kwargs.
+    Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries`
+    for more details.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the impulse response data is to be computed.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    kwargs :
+        Additional keyword arguments are passed to the underlying
+        :class:`sympy.plotting.series.LineOver1DRangeSeries` class.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = Time-axis values of the points in the impulse response. NumPy array.
+        y = Amplitude-axis values of the points in the impulse response. NumPy array.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When ``lower_limit`` parameter is less than 0.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import impulse_response_numerical_data
+    >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s)
+    >>> impulse_response_numerical_data(tf1)   # doctest: +SKIP
+    ([0.0, 0.06616480200395854,... , 9.854500743565858, 10.0],
+    [0.9999999799999999, 0.7042848373025861,...,7.170748906965121e-13, -5.1901263495547205e-12])
+
+    See Also
+    ========
+
+    impulse_response_plot
+
+    """
+    if lower_limit < 0:
+        raise ValueError("Lower limit of time must be greater "
+            "than or equal to zero.")
+    _check_system(system)
+    _x = Dummy("x")
+    expr = system.to_expr()
+    expr = apart(expr, system.var, full=True)
+    _y = _fast_inverse_laplace(expr, system.var, _x).evalf(prec)
+    return LineOver1DRangeSeries(_y, (_x, lower_limit, upper_limit),
+        **kwargs).get_points()
+
+
+def impulse_response_plot(system, color='b', prec=8, lower_limit=0,
+    upper_limit=10, show_axes=False, grid=True, show=True, **kwargs):
+    r"""
+    Returns the unit impulse response (Input is the Dirac-Delta Function) of a
+    continuous-time system.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Impulse Response is to be computed.
+    color : str, tuple, optional
+        The color of the line. Default is Blue.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import impulse_response_plot
+        >>> tf1 = TransferFunction(8*s**2 + 18*s + 32, s**3 + 6*s**2 + 14*s + 24, s)
+        >>> impulse_response_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    step_response_plot, ramp_response_plot
+
+    References
+    ==========
+
+    .. [1] https://www.mathworks.com/help/control/ref/dynamicsystem.impulse.html
+
+    """
+    x, y = impulse_response_numerical_data(system, prec=prec,
+        lower_limit=lower_limit, upper_limit=upper_limit, **kwargs)
+    plt.plot(x, y, color=color)
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.title(f'Impulse Response of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def ramp_response_numerical_data(system, slope=1, prec=8,
+    lower_limit=0, upper_limit=10, **kwargs):
+    """
+    Returns the numerical values of the points in the ramp response plot
+    of a SISO continuous-time system. By default, adaptive sampling
+    is used. If the user wants to instead get an uniformly
+    sampled response, then ``adaptive`` kwarg should be passed ``False``
+    and ``n`` must be passed as additional kwargs.
+    Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries`
+    for more details.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the ramp response data is to be computed.
+    slope : Number, optional
+        The slope of the input ramp function. Defaults to 1.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    kwargs :
+        Additional keyword arguments are passed to the underlying
+        :class:`sympy.plotting.series.LineOver1DRangeSeries` class.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = Time-axis values of the points in the ramp response plot. NumPy array.
+        y = Amplitude-axis values of the points in the ramp response plot. NumPy array.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When ``lower_limit`` parameter is less than 0.
+
+        When ``slope`` is negative.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import ramp_response_numerical_data
+    >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s)
+    >>> ramp_response_numerical_data(tf1)   # doctest: +SKIP
+    (([0.0, 0.12166980856813935,..., 9.861246379582118, 10.0],
+    [1.4504508011325967e-09, 0.006046440489058766,..., 0.12499999999568202, 0.12499999999661349]))
+
+    See Also
+    ========
+
+    ramp_response_plot
+
+    """
+    if slope < 0:
+        raise ValueError("Slope must be greater than or equal"
+            " to zero.")
+    if lower_limit < 0:
+        raise ValueError("Lower limit of time must be greater "
+            "than or equal to zero.")
+    _check_system(system)
+    _x = Dummy("x")
+    expr = (slope*system.to_expr())/((system.var)**2)
+    expr = apart(expr, system.var, full=True)
+    _y = _fast_inverse_laplace(expr, system.var, _x).evalf(prec)
+    return LineOver1DRangeSeries(_y, (_x, lower_limit, upper_limit),
+        **kwargs).get_points()
+
+
+def ramp_response_plot(system, slope=1, color='b', prec=8, lower_limit=0,
+    upper_limit=10, show_axes=False, grid=True, show=True, **kwargs):
+    r"""
+    Returns the ramp response of a continuous-time system.
+
+    Ramp function is defined as the straight line
+    passing through origin ($f(x) = mx$). The slope of
+    the ramp function can be varied by the user and
+    the default value is 1.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Ramp Response is to be computed.
+    slope : Number, optional
+        The slope of the input ramp function. Defaults to 1.
+    color : str, tuple, optional
+        The color of the line. Default is Blue.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import ramp_response_plot
+        >>> tf1 = TransferFunction(s, (s+4)*(s+8), s)
+        >>> ramp_response_plot(tf1, upper_limit=2)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    step_response_plot, impulse_response_plot
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Ramp_function
+
+    """
+    x, y = ramp_response_numerical_data(system, slope=slope, prec=prec,
+        lower_limit=lower_limit, upper_limit=upper_limit, **kwargs)
+    plt.plot(x, y, color=color)
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.title(f'Ramp Response of ${latex(system)}$ [Slope = {slope}]', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def bode_magnitude_numerical_data(system, initial_exp=-5, final_exp=5, freq_unit='rad/sec', **kwargs):
+    """
+    Returns the numerical data of the Bode magnitude plot of the system.
+    It is internally used by ``bode_magnitude_plot`` to get the data
+    for plotting Bode magnitude plot. Users can use this data to further
+    analyse the dynamics of the system or plot using a different
+    backend/plotting-module.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the data is to be computed.
+    initial_exp : Number, optional
+        The initial exponent of 10 of the semilog plot. Defaults to -5.
+    final_exp : Number, optional
+        The final exponent of 10 of the semilog plot. Defaults to 5.
+    freq_unit : string, optional
+        User can choose between ``'rad/sec'`` (radians/second) and ``'Hz'`` (Hertz) as frequency units.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = x-axis values of the Bode magnitude plot.
+        y = y-axis values of the Bode magnitude plot.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When incorrect frequency units are given as input.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import bode_magnitude_numerical_data
+    >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+    >>> bode_magnitude_numerical_data(tf1)   # doctest: +SKIP
+    ([1e-05, 1.5148378120533502e-05,..., 68437.36188804005, 100000.0],
+    [-6.020599914256786, -6.0205999155219505,..., -193.4117304087953, -200.00000000260573])
+
+    See Also
+    ========
+
+    bode_magnitude_plot, bode_phase_numerical_data
+
+    """
+    _check_system(system)
+    expr = system.to_expr()
+    freq_units = ('rad/sec', 'Hz')
+    if freq_unit not in freq_units:
+        raise ValueError('Only "rad/sec" and "Hz" are accepted frequency units.')
+
+    _w = Dummy("w", real=True)
+    if freq_unit == 'Hz':
+        repl = I*_w*2*pi
+    else:
+        repl = I*_w
+    w_expr = expr.subs({system.var: repl})
+
+    mag = 20*log(Abs(w_expr), 10)
+
+    x, y = LineOver1DRangeSeries(mag,
+        (_w, 10**initial_exp, 10**final_exp), xscale='log', **kwargs).get_points()
+
+    return x, y
+
+
+def bode_magnitude_plot(system, initial_exp=-5, final_exp=5,
+    color='b', show_axes=False, grid=True, show=True, freq_unit='rad/sec', **kwargs):
+    r"""
+    Returns the Bode magnitude plot of a continuous-time system.
+
+    See ``bode_plot`` for all the parameters.
+    """
+    x, y = bode_magnitude_numerical_data(system, initial_exp=initial_exp,
+        final_exp=final_exp, freq_unit=freq_unit)
+    plt.plot(x, y, color=color, **kwargs)
+    plt.xscale('log')
+
+
+    plt.xlabel('Frequency (%s) [Log Scale]' % freq_unit)
+    plt.ylabel('Magnitude (dB)')
+    plt.title(f'Bode Plot (Magnitude) of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid(True)
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def bode_phase_numerical_data(system, initial_exp=-5, final_exp=5, freq_unit='rad/sec', phase_unit='rad', phase_unwrap = True, **kwargs):
+    """
+    Returns the numerical data of the Bode phase plot of the system.
+    It is internally used by ``bode_phase_plot`` to get the data
+    for plotting Bode phase plot. Users can use this data to further
+    analyse the dynamics of the system or plot using a different
+    backend/plotting-module.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the Bode phase plot data is to be computed.
+    initial_exp : Number, optional
+        The initial exponent of 10 of the semilog plot. Defaults to -5.
+    final_exp : Number, optional
+        The final exponent of 10 of the semilog plot. Defaults to 5.
+    freq_unit : string, optional
+        User can choose between ``'rad/sec'`` (radians/second) and '``'Hz'`` (Hertz) as frequency units.
+    phase_unit : string, optional
+        User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units.
+    phase_unwrap : bool, optional
+        Set to ``True`` by default.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = x-axis values of the Bode phase plot.
+        y = y-axis values of the Bode phase plot.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When incorrect frequency or phase units are given as input.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import bode_phase_numerical_data
+    >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+    >>> bode_phase_numerical_data(tf1)   # doctest: +SKIP
+    ([1e-05, 1.4472354033813751e-05, 2.035581932165858e-05,..., 47577.3248186011, 67884.09326036123, 100000.0],
+    [-2.5000000000291665e-05, -3.6180885085e-05, -5.08895483066e-05,...,-3.1415085799262523, -3.14155265358979])
+
+    See Also
+    ========
+
+    bode_magnitude_plot, bode_phase_numerical_data
+
+    """
+    _check_system(system)
+    expr = system.to_expr()
+    freq_units = ('rad/sec', 'Hz')
+    phase_units = ('rad', 'deg')
+    if freq_unit not in freq_units:
+        raise ValueError('Only "rad/sec" and "Hz" are accepted frequency units.')
+    if phase_unit not in phase_units:
+        raise ValueError('Only "rad" and "deg" are accepted phase units.')
+
+    _w = Dummy("w", real=True)
+    if freq_unit == 'Hz':
+        repl = I*_w*2*pi
+    else:
+        repl = I*_w
+    w_expr = expr.subs({system.var: repl})
+
+    if phase_unit == 'deg':
+        phase = arg(w_expr)*180/pi
+    else:
+        phase = arg(w_expr)
+
+    x, y = LineOver1DRangeSeries(phase,
+        (_w, 10**initial_exp, 10**final_exp), xscale='log', **kwargs).get_points()
+
+    half = None
+    if phase_unwrap:
+        if(phase_unit == 'rad'):
+            half = pi
+        elif(phase_unit == 'deg'):
+            half = 180
+    if half:
+        unit = 2*half
+        for i in range(1, len(y)):
+            diff = y[i] - y[i - 1]
+            if diff > half:      # Jump from -half to half
+                y[i] = (y[i] - unit)
+            elif diff < -half:   # Jump from half to -half
+                y[i] = (y[i] + unit)
+
+    return x, y
+
+
+def bode_phase_plot(system, initial_exp=-5, final_exp=5,
+    color='b', show_axes=False, grid=True, show=True, freq_unit='rad/sec', phase_unit='rad', phase_unwrap=True, **kwargs):
+    r"""
+    Returns the Bode phase plot of a continuous-time system.
+
+    See ``bode_plot`` for all the parameters.
+    """
+    x, y = bode_phase_numerical_data(system, initial_exp=initial_exp,
+        final_exp=final_exp, freq_unit=freq_unit, phase_unit=phase_unit, phase_unwrap=phase_unwrap)
+    plt.plot(x, y, color=color, **kwargs)
+    plt.xscale('log')
+
+    plt.xlabel('Frequency (%s) [Log Scale]' % freq_unit)
+    plt.ylabel('Phase (%s)' % phase_unit)
+    plt.title(f'Bode Plot (Phase) of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid(True)
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def bode_plot(system, initial_exp=-5, final_exp=5,
+    grid=True, show_axes=False, show=True, freq_unit='rad/sec', phase_unit='rad', phase_unwrap=True, **kwargs):
+    r"""
+    Returns the Bode phase and magnitude plots of a continuous-time system.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Bode Plot is to be computed.
+    initial_exp : Number, optional
+        The initial exponent of 10 of the semilog plot. Defaults to -5.
+    final_exp : Number, optional
+        The final exponent of 10 of the semilog plot. Defaults to 5.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    freq_unit : string, optional
+        User can choose between ``'rad/sec'`` (radians/second) and ``'Hz'`` (Hertz) as frequency units.
+    phase_unit : string, optional
+        User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import bode_plot
+        >>> tf1 = TransferFunction(1*s**2 + 0.1*s + 7.5, 1*s**4 + 0.12*s**3 + 9*s**2, s)
+        >>> bode_plot(tf1, initial_exp=0.2, final_exp=0.7)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    bode_magnitude_plot, bode_phase_plot
+
+    """
+    plt.subplot(211)
+    mag = bode_magnitude_plot(system, initial_exp=initial_exp, final_exp=final_exp,
+        show=False, grid=grid, show_axes=show_axes,
+        freq_unit=freq_unit, **kwargs)
+    mag.title(f'Bode Plot of ${latex(system)}$', pad=20)
+    mag.xlabel(None)
+    plt.subplot(212)
+    bode_phase_plot(system, initial_exp=initial_exp, final_exp=final_exp,
+        show=False, grid=grid, show_axes=show_axes, freq_unit=freq_unit, phase_unit=phase_unit, phase_unwrap=phase_unwrap, **kwargs).title(None)
+
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def nyquist_plot_expr(system):
+    """Function to get the expression for Nyquist plot."""
+    s = system.var
+    w = Dummy('w', real=True)
+    repl = I * w
+    expr = system.to_expr()
+    w_expr = expr.subs({s: repl})
+    w_expr = w_expr.as_real_imag()
+    real_expr = w_expr[0]
+    imag_expr = w_expr[1]
+    return real_expr, imag_expr, w
+
+
+def nichols_plot_expr(system):
+    """Function to get the expression for Nichols plot."""
+    s = system.var
+    w = Dummy('w', real=True)
+    sys_expr = system.to_expr()
+    H_jw = sys_expr.subs(s, I*w)
+    mag_expr = Abs(H_jw)
+    mag_dB_expr = 20*log(mag_expr, 10)
+    phase_expr = arg(H_jw)
+    phase_deg_expr = deg(phase_expr)
+    return mag_dB_expr, phase_deg_expr, w
+
+
+def nyquist_plot(system, initial_omega=0.01, final_omega=100, show=True,
+                color='b', **kwargs):
+    r"""
+    Generates the Nyquist plot for a continuous-time system.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The LTI SISO system for which the Nyquist plot is to be generated.
+    initial_omega : float, optional
+        The starting frequency value. Defaults to 0.01.
+    final_omega : float, optional
+        The ending frequency value. Defaults to 100.
+    show : bool, optional
+        If True, the plot is displayed. Default is True.
+    color : str, optional
+        The color of the Nyquist plot. Default is 'b' (blue).
+    grid : bool, optional
+        If True, grid lines are displayed. Default is False.
+    **kwargs
+        Additional keyword arguments for customization.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import nyquist_plot
+        >>> tf1 = TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s)
+        >>> nyquist_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    nichols_plot, bode_plot
+
+    """
+    _check_system(system)
+    real_expr, imag_expr, w = nyquist_plot_expr(system)
+    w_values = [(w, initial_omega, final_omega)]
+    p = plot_parametric(
+        (real_expr, imag_expr),   # The curve
+        (real_expr, -imag_expr),  # Its mirror image
+        *w_values,
+        show=False,
+        line_color=color,
+        adaptive=True,
+        title=f'Nyquist Plot of ${latex(system)}$',
+        xlabel='Real Axis',
+        ylabel='Imaginary Axis',
+        size=(6, 5),
+        kwargs=kwargs)
+    if show:
+        p.show()
+        return
+    return p
+
+
+def nichols_plot(system, initial_omega=0.01, final_omega=100, show=True, color='b', **kwargs):
+    r"""
+    Generates the Nichols plot for a LTI system.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The LTI SISO system for which the Nyquist plot is to be generated.
+    initial_omega : float, optional
+        The starting frequency value. Defaults to 0.01.
+    final_omega : float, optional
+        The ending frequency value. Defaults to 100.
+    show : bool, optional
+        If True, the plot is displayed. Default is True.
+    color : str, optional
+        The color of the Nyquist plot. Default is 'b' (blue).
+    grid : bool, optional
+        If True, grid lines are displayed. Default is False.
+    **kwargs
+        Additional keyword arguments for customization.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import nichols_plot
+        >>> tf1 = TransferFunction(1.5, s**2+14*s+40.02, s)
+        >>> nichols_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    nyquist_plot, bode_plot
+
+    """
+    _check_system(system)
+    magnitude_dB_expr, phase_deg_expr, w = nichols_plot_expr(system)
+    w_values = [(w, initial_omega, final_omega)]
+    p = plot_parametric(
+        (phase_deg_expr, magnitude_dB_expr),
+        *w_values,
+        show=False,
+        line_color=color,
+        title=f'Nichols Plot of ${latex(system)}$',
+        xlabel='Phase [deg]',
+        ylabel='Magnitude [dB]',
+        size=(6,5),
+        kwargs=kwargs)
+    if show:
+        p.show()
+        return
+    return p
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/lti.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/lti.py
new file mode 100644
index 0000000000000000000000000000000000000000..480a1ec71d8c4dd07a51d67304a0b6e20a90691e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/lti.py
@@ -0,0 +1,5001 @@
+from typing import Type
+from sympy import Interval, numer, Rational, solveset
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.evalf import EvalfMixin
+from sympy.core.expr import Expr
+from sympy.core.function import expand
+from sympy.core.logic import fuzzy_and
+from sympy.core.mul import Mul
+from sympy.core.numbers import I, pi, oo
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy, Symbol
+from sympy.functions import Abs
+from sympy.core.sympify import sympify, _sympify
+from sympy.matrices import Matrix, ImmutableMatrix, ImmutableDenseMatrix, eye, ShapeError, zeros
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.matrices.expressions import MatMul, MatAdd
+from sympy.polys import Poly, rootof
+from sympy.polys.polyroots import roots
+from sympy.polys.polytools import (cancel, degree)
+from sympy.series import limit
+from sympy.utilities.misc import filldedent
+from sympy.solvers.ode.systems import linodesolve
+from sympy.solvers.solveset import linsolve, linear_eq_to_matrix
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+__all__ = ['TransferFunction', 'PIDController', 'Series', 'MIMOSeries', 'Parallel', 'MIMOParallel',
+    'Feedback', 'MIMOFeedback', 'TransferFunctionMatrix', 'StateSpace', 'gbt', 'bilinear', 'forward_diff', 'backward_diff',
+    'phase_margin', 'gain_margin']
+
+def _roots(poly, var):
+    """ like roots, but works on higher-order polynomials. """
+    r = roots(poly, var, multiple=True)
+    n = degree(poly)
+    if len(r) != n:
+        r = [rootof(poly, var, k) for k in range(n)]
+    return r
+
+def gbt(tf, sample_per, alpha):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the generalised bilinear transformation method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) = \frac{z-1}{T(\alpha z + (1-\alpha))}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, gbt
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = gbt(tf, T, 0.5)
+    >>> numZ
+    [T/(2*(L + R*T/2)), T/(2*(L + R*T/2))]
+    >>> denZ
+    [1, (-L + R*T/2)/(L + R*T/2)]
+
+    >>> numZ, denZ = gbt(tf, T, 0)
+    >>> numZ
+    [T/L]
+    >>> denZ
+    [1, (-L + R*T)/L]
+
+    >>> numZ, denZ = gbt(tf, T, 1)
+    >>> numZ
+    [T/(L + R*T), 0]
+    >>> denZ
+    [1, -L/(L + R*T)]
+
+    >>> numZ, denZ = gbt(tf, T, 0.3)
+    >>> numZ
+    [3*T/(10*(L + 3*R*T/10)), 7*T/(10*(L + 3*R*T/10))]
+    >>> denZ
+    [1, (-L + 7*R*T/10)/(L + 3*R*T/10)]
+
+    References
+    ==========
+
+    .. [1] https://www.polyu.edu.hk/ama/profile/gfzhang/Research/ZCC09_IJC.pdf
+    """
+    if not tf.is_SISO:
+        raise NotImplementedError("Not implemented for MIMO systems.")
+
+    T = sample_per  # and sample period T
+    s = tf.var
+    z =  s         # dummy discrete variable z
+
+    np = tf.num.as_poly(s).all_coeffs()
+    dp = tf.den.as_poly(s).all_coeffs()
+    alpha = Rational(alpha).limit_denominator(1000)
+
+    # The next line results from multiplying H(z) with z^N/z^N
+    N = max(len(np), len(dp)) - 1
+    num = Add(*[ T**(N-i) * c * (z-1)**i * (alpha * z + 1 - alpha)**(N-i) for c, i in zip(np[::-1], range(len(np))) ])
+    den = Add(*[ T**(N-i) * c * (z-1)**i * (alpha * z + 1 - alpha)**(N-i) for c, i in zip(dp[::-1], range(len(dp))) ])
+
+    num_coefs = num.as_poly(z).all_coeffs()
+    den_coefs = den.as_poly(z).all_coeffs()
+
+    para = den_coefs[0]
+    num_coefs = [coef/para for coef in num_coefs]
+    den_coefs = [coef/para for coef in den_coefs]
+
+    return num_coefs, den_coefs
+
+def bilinear(tf, sample_per):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the bilinear transform method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) = \frac{2}{T}\frac{z-1}{z+1}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, bilinear
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = bilinear(tf, T)
+    >>> numZ
+    [T/(2*(L + R*T/2)), T/(2*(L + R*T/2))]
+    >>> denZ
+    [1, (-L + R*T/2)/(L + R*T/2)]
+    """
+    return gbt(tf, sample_per, S.Half)
+
+def forward_diff(tf, sample_per):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the forward difference transform method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) = \frac{z-1}{T}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, forward_diff
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = forward_diff(tf, T)
+    >>> numZ
+    [T/L]
+    >>> denZ
+    [1, (-L + R*T)/L]
+    """
+    return gbt(tf, sample_per, S.Zero)
+
+def backward_diff(tf, sample_per):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the backward difference transform method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) =  \frac{z-1}{Tz}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, backward_diff
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = backward_diff(tf, T)
+    >>> numZ
+    [T/(L + R*T), 0]
+    >>> denZ
+    [1, -L/(L + R*T)]
+    """
+    return gbt(tf, sample_per, S.One)
+
+def phase_margin(system):
+    r"""
+    Returns the phase margin of a continuous time system.
+    Only applicable to Transfer Functions which can generate valid bode plots.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When time delay terms are present in the system.
+
+    ValueError
+        When a SISO LTI system is not passed.
+
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control import TransferFunction, phase_margin
+    >>> from sympy.abc import s
+
+    >>> tf = TransferFunction(1, s**3 + 2*s**2 + s, s)
+    >>> phase_margin(tf)
+    180*(-pi + atan((-1 + (-2*18**(1/3)/(9 + sqrt(93))**(1/3) + 12**(1/3)*(9 + sqrt(93))**(1/3))**2/36)/(-12**(1/3)*(9 + sqrt(93))**(1/3)/3 + 2*18**(1/3)/(3*(9 + sqrt(93))**(1/3)))))/pi + 180
+    >>> phase_margin(tf).n()
+    21.3863897518751
+
+    >>> tf1 = TransferFunction(s**3, s**2 + 5*s, s)
+    >>> phase_margin(tf1)
+    -180 + 180*(atan(sqrt(2)*(-51/10 - sqrt(101)/10)*sqrt(1 + sqrt(101))/(2*(sqrt(101)/2 + 51/2))) + pi)/pi
+    >>> phase_margin(tf1).n()
+    -25.1783920627277
+
+    >>> tf2 = TransferFunction(1, s + 1, s)
+    >>> phase_margin(tf2)
+    -180
+
+    See Also
+    ========
+
+    gain_margin
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Phase_margin
+
+    """
+    from sympy.functions import arg
+
+    if not isinstance(system, SISOLinearTimeInvariant):
+        raise ValueError("Margins are only applicable for SISO LTI systems.")
+
+    _w = Dummy("w", real=True)
+    repl = I*_w
+    expr = system.to_expr()
+    len_free_symbols = len(expr.free_symbols)
+    if expr.has(exp):
+        raise NotImplementedError("Margins for systems with Time delay terms are not supported.")
+    elif len_free_symbols > 1:
+        raise ValueError("Extra degree of freedom found. Make sure"
+            " that there are no free symbols in the dynamical system other"
+            " than the variable of Laplace transform.")
+
+    w_expr = expr.subs({system.var: repl})
+
+    mag = 20*log(Abs(w_expr), 10)
+    mag_sol = list(solveset(mag, _w, Interval(0, oo, left_open=True)))
+
+    if (len(mag_sol) == 0):
+        pm = S(-180)
+    else:
+        wcp = mag_sol[0]
+        pm = ((arg(w_expr)*S(180)/pi).subs({_w:wcp}) + S(180)) % 360
+
+    if(pm >= 180):
+        pm = pm - 360
+
+    return pm
+
+def gain_margin(system):
+    r"""
+    Returns the gain margin of a continuous time system.
+    Only applicable to Transfer Functions which can generate valid bode plots.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When time delay terms are present in the system.
+
+    ValueError
+        When a SISO LTI system is not passed.
+
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control import TransferFunction, gain_margin
+    >>> from sympy.abc import s
+
+    >>> tf = TransferFunction(1, s**3 + 2*s**2 + s, s)
+    >>> gain_margin(tf)
+    20*log(2)/log(10)
+    >>> gain_margin(tf).n()
+    6.02059991327962
+
+    >>> tf1 = TransferFunction(s**3, s**2 + 5*s, s)
+    >>> gain_margin(tf1)
+    oo
+
+    See Also
+    ========
+
+    phase_margin
+
+    References
+    ==========
+
+    https://en.wikipedia.org/wiki/Bode_plot
+
+    """
+    if not isinstance(system, SISOLinearTimeInvariant):
+        raise ValueError("Margins are only applicable for SISO LTI systems.")
+
+    _w = Dummy("w", real=True)
+    repl = I*_w
+    expr = system.to_expr()
+    len_free_symbols = len(expr.free_symbols)
+    if expr.has(exp):
+        raise NotImplementedError("Margins for systems with Time delay terms are not supported.")
+    elif len_free_symbols > 1:
+        raise ValueError("Extra degree of freedom found. Make sure"
+            " that there are no free symbols in the dynamical system other"
+            " than the variable of Laplace transform.")
+
+    w_expr = expr.subs({system.var: repl})
+
+    mag = 20*log(Abs(w_expr), 10)
+    phase = w_expr
+    phase_sol = list(solveset(numer(phase.as_real_imag()[1].cancel()),_w, Interval(0, oo, left_open = True)))
+
+    if (len(phase_sol) == 0):
+        gm = oo
+    else:
+        wcg = phase_sol[0]
+        gm = -mag.subs({_w:wcg})
+
+    return gm
+
+class LinearTimeInvariant(Basic, EvalfMixin):
+    """A common class for all the Linear Time-Invariant Dynamical Systems."""
+
+    _clstype: Type
+
+    # Users should not directly interact with this class.
+    def __new__(cls, *system, **kwargs):
+        if cls is LinearTimeInvariant:
+            raise NotImplementedError('The LTICommon class is not meant to be used directly.')
+        return super(LinearTimeInvariant, cls).__new__(cls, *system, **kwargs)
+
+    @classmethod
+    def _check_args(cls, args):
+        if not args:
+            raise ValueError("At least 1 argument must be passed.")
+        if not all(isinstance(arg, cls._clstype) for arg in args):
+            raise TypeError(f"All arguments must be of type {cls._clstype}.")
+        var_set = {arg.var for arg in args}
+        if len(var_set) != 1:
+            raise ValueError(filldedent(f"""
+                All transfer functions should use the same complex variable
+                of the Laplace transform. {len(var_set)} different
+                values found."""))
+
+    @property
+    def is_SISO(self):
+        """Returns `True` if the passed LTI system is SISO else returns False."""
+        return self._is_SISO
+
+
+class SISOLinearTimeInvariant(LinearTimeInvariant):
+    """A common class for all the SISO Linear Time-Invariant Dynamical Systems."""
+    # Users should not directly interact with this class.
+
+    @property
+    def num_inputs(self):
+        """Return the number of inputs for SISOLinearTimeInvariant."""
+        return 1
+
+    @property
+    def num_outputs(self):
+        """Return the number of outputs for SISOLinearTimeInvariant."""
+        return 1
+
+    _is_SISO = True
+
+
+class MIMOLinearTimeInvariant(LinearTimeInvariant):
+    """A common class for all the MIMO Linear Time-Invariant Dynamical Systems."""
+    # Users should not directly interact with this class.
+    _is_SISO = False
+
+
+SISOLinearTimeInvariant._clstype = SISOLinearTimeInvariant
+MIMOLinearTimeInvariant._clstype = MIMOLinearTimeInvariant
+
+
+def _check_other_SISO(func):
+    def wrapper(*args, **kwargs):
+        if not isinstance(args[-1], SISOLinearTimeInvariant):
+            return NotImplemented
+        else:
+            return func(*args, **kwargs)
+    return wrapper
+
+
+def _check_other_MIMO(func):
+    def wrapper(*args, **kwargs):
+        if not isinstance(args[-1], MIMOLinearTimeInvariant):
+            return NotImplemented
+        else:
+            return func(*args, **kwargs)
+    return wrapper
+
+
+class TransferFunction(SISOLinearTimeInvariant):
+    r"""
+    A class for representing LTI (Linear, time-invariant) systems that can be strictly described
+    by ratio of polynomials in the Laplace transform complex variable. The arguments
+    are ``num``, ``den``, and ``var``, where ``num`` and ``den`` are numerator and
+    denominator polynomials of the ``TransferFunction`` respectively, and the third argument is
+    a complex variable of the Laplace transform used by these polynomials of the transfer function.
+    ``num`` and ``den`` can be either polynomials or numbers, whereas ``var``
+    has to be a :py:class:`~.Symbol`.
+
+    Explanation
+    ===========
+
+    Generally, a dynamical system representing a physical model can be described in terms of Linear
+    Ordinary Differential Equations like -
+
+            $b_{m}y^{\left(m\right)}+b_{m-1}y^{\left(m-1\right)}+\dots+b_{1}y^{\left(1\right)}+b_{0}y=
+            a_{n}x^{\left(n\right)}+a_{n-1}x^{\left(n-1\right)}+\dots+a_{1}x^{\left(1\right)}+a_{0}x$
+
+    Here, $x$ is the input signal and $y$ is the output signal and superscript on both is the order of derivative
+    (not exponent). Derivative is taken with respect to the independent variable, $t$. Also, generally $m$ is greater
+    than $n$.
+
+    It is not feasible to analyse the properties of such systems in their native form therefore, we use
+    mathematical tools like Laplace transform to get a better perspective. Taking the Laplace transform
+    of both the sides in the equation (at zero initial conditions), we get -
+
+            $\mathcal{L}[b_{m}y^{\left(m\right)}+b_{m-1}y^{\left(m-1\right)}+\dots+b_{1}y^{\left(1\right)}+b_{0}y]=
+            \mathcal{L}[a_{n}x^{\left(n\right)}+a_{n-1}x^{\left(n-1\right)}+\dots+a_{1}x^{\left(1\right)}+a_{0}x]$
+
+    Using the linearity property of Laplace transform and also considering zero initial conditions
+    (i.e. $y(0^{-}) = 0$, $y'(0^{-}) = 0$ and so on), the equation
+    above gets translated to -
+
+            $b_{m}\mathcal{L}[y^{\left(m\right)}]+\dots+b_{1}\mathcal{L}[y^{\left(1\right)}]+b_{0}\mathcal{L}[y]=
+            a_{n}\mathcal{L}[x^{\left(n\right)}]+\dots+a_{1}\mathcal{L}[x^{\left(1\right)}]+a_{0}\mathcal{L}[x]$
+
+    Now, applying Derivative property of Laplace transform,
+
+            $b_{m}s^{m}\mathcal{L}[y]+\dots+b_{1}s\mathcal{L}[y]+b_{0}\mathcal{L}[y]=
+            a_{n}s^{n}\mathcal{L}[x]+\dots+a_{1}s\mathcal{L}[x]+a_{0}\mathcal{L}[x]$
+
+    Here, the superscript on $s$ is **exponent**. Note that the zero initial conditions assumption, mentioned above, is very important
+    and cannot be ignored otherwise the dynamical system cannot be considered time-independent and the simplified equation above
+    cannot be reached.
+
+    Collecting $\mathcal{L}[y]$ and $\mathcal{L}[x]$ terms from both the sides and taking the ratio
+    $\frac{ \mathcal{L}\left\{y\right\} }{ \mathcal{L}\left\{x\right\} }$, we get the typical rational form of transfer
+    function.
+
+    The numerator of the transfer function is, therefore, the Laplace transform of the output signal
+    (The signals are represented as functions of time) and similarly, the denominator
+    of the transfer function is the Laplace transform of the input signal. It is also a convention
+    to denote the input and output signal's Laplace transform with capital alphabets like shown below.
+
+            $H(s) = \frac{Y(s)}{X(s)} = \frac{ \mathcal{L}\left\{y(t)\right\} }{ \mathcal{L}\left\{x(t)\right\} }$
+
+    $s$, also known as complex frequency, is a complex variable in the Laplace domain. It corresponds to the
+    equivalent variable $t$, in the time domain. Transfer functions are sometimes also referred to as the Laplace
+    transform of the system's impulse response. Transfer function, $H$, is represented as a rational
+    function in $s$ like,
+
+            $H(s) =\ \frac{a_{n}s^{n}+a_{n-1}s^{n-1}+\dots+a_{1}s+a_{0}}{b_{m}s^{m}+b_{m-1}s^{m-1}+\dots+b_{1}s+b_{0}}$
+
+    Parameters
+    ==========
+
+    num : Expr, Number
+        The numerator polynomial of the transfer function.
+    den : Expr, Number
+        The denominator polynomial of the transfer function.
+    var : Symbol
+        Complex variable of the Laplace transform used by the
+        polynomials of the transfer function.
+
+    Raises
+    ======
+
+    TypeError
+        When ``var`` is not a Symbol or when ``num`` or ``den`` is not a
+        number or a polynomial.
+    ValueError
+        When ``den`` is zero.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s, p, a
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> tf1 = TransferFunction(s + a, s**2 + s + 1, s)
+    >>> tf1
+    TransferFunction(a + s, s**2 + s + 1, s)
+    >>> tf1.num
+    a + s
+    >>> tf1.den
+    s**2 + s + 1
+    >>> tf1.var
+    s
+    >>> tf1.args
+    (a + s, s**2 + s + 1, s)
+
+    Any complex variable can be used for ``var``.
+
+    >>> tf2 = TransferFunction(a*p**3 - a*p**2 + s*p, p + a**2, p)
+    >>> tf2
+    TransferFunction(a*p**3 - a*p**2 + p*s, a**2 + p, p)
+    >>> tf3 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+    >>> tf3
+    TransferFunction((p - 1)*(p + 3), (p - 1)*(p + 5), p)
+
+    To negate a transfer function the ``-`` operator can be prepended:
+
+    >>> tf4 = TransferFunction(-a + s, p**2 + s, p)
+    >>> -tf4
+    TransferFunction(a - s, p**2 + s, p)
+    >>> tf5 = TransferFunction(s**4 - 2*s**3 + 5*s + 4, s + 4, s)
+    >>> -tf5
+    TransferFunction(-s**4 + 2*s**3 - 5*s - 4, s + 4, s)
+
+    You can use a float or an integer (or other constants) as numerator and denominator:
+
+    >>> tf6 = TransferFunction(1/2, 4, s)
+    >>> tf6.num
+    0.500000000000000
+    >>> tf6.den
+    4
+    >>> tf6.var
+    s
+    >>> tf6.args
+    (0.5, 4, s)
+
+    You can take the integer power of a transfer function using the ``**`` operator:
+
+    >>> tf7 = TransferFunction(s + a, s - a, s)
+    >>> tf7**3
+    TransferFunction((a + s)**3, (-a + s)**3, s)
+    >>> tf7**0
+    TransferFunction(1, 1, s)
+    >>> tf8 = TransferFunction(p + 4, p - 3, p)
+    >>> tf8**-1
+    TransferFunction(p - 3, p + 4, p)
+
+    Addition, subtraction, and multiplication of transfer functions can form
+    unevaluated ``Series`` or ``Parallel`` objects.
+
+    >>> tf9 = TransferFunction(s + 1, s**2 + s + 1, s)
+    >>> tf10 = TransferFunction(s - p, s + 3, s)
+    >>> tf11 = TransferFunction(4*s**2 + 2*s - 4, s - 1, s)
+    >>> tf12 = TransferFunction(1 - s, s**2 + 4, s)
+    >>> tf9 + tf10
+    Parallel(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(-p + s, s + 3, s))
+    >>> tf10 - tf11
+    Parallel(TransferFunction(-p + s, s + 3, s), TransferFunction(-4*s**2 - 2*s + 4, s - 1, s))
+    >>> tf9 * tf10
+    Series(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(-p + s, s + 3, s))
+    >>> tf10 - (tf9 + tf12)
+    Parallel(TransferFunction(-p + s, s + 3, s), TransferFunction(-s - 1, s**2 + s + 1, s), TransferFunction(s - 1, s**2 + 4, s))
+    >>> tf10 - (tf9 * tf12)
+    Parallel(TransferFunction(-p + s, s + 3, s), Series(TransferFunction(-1, 1, s), TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(1 - s, s**2 + 4, s)))
+    >>> tf11 * tf10 * tf9
+    Series(TransferFunction(4*s**2 + 2*s - 4, s - 1, s), TransferFunction(-p + s, s + 3, s), TransferFunction(s + 1, s**2 + s + 1, s))
+    >>> tf9 * tf11 + tf10 * tf12
+    Parallel(Series(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(4*s**2 + 2*s - 4, s - 1, s)), Series(TransferFunction(-p + s, s + 3, s), TransferFunction(1 - s, s**2 + 4, s)))
+    >>> (tf9 + tf12) * (tf10 + tf11)
+    Series(Parallel(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(1 - s, s**2 + 4, s)), Parallel(TransferFunction(-p + s, s + 3, s), TransferFunction(4*s**2 + 2*s - 4, s - 1, s)))
+
+    These unevaluated ``Series`` or ``Parallel`` objects can convert into the
+    resultant transfer function using ``.doit()`` method or by ``.rewrite(TransferFunction)``.
+
+    >>> ((tf9 + tf10) * tf12).doit()
+    TransferFunction((1 - s)*((-p + s)*(s**2 + s + 1) + (s + 1)*(s + 3)), (s + 3)*(s**2 + 4)*(s**2 + s + 1), s)
+    >>> (tf9 * tf10 - tf11 * tf12).rewrite(TransferFunction)
+    TransferFunction(-(1 - s)*(s + 3)*(s**2 + s + 1)*(4*s**2 + 2*s - 4) + (-p + s)*(s - 1)*(s + 1)*(s**2 + 4), (s - 1)*(s + 3)*(s**2 + 4)*(s**2 + s + 1), s)
+
+    See Also
+    ========
+
+    Feedback, Series, Parallel
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Transfer_function
+    .. [2] https://en.wikipedia.org/wiki/Laplace_transform
+
+    """
+    def __new__(cls, num, den, var):
+        num, den = _sympify(num), _sympify(den)
+
+        if not isinstance(var, Symbol):
+            raise TypeError("Variable input must be a Symbol.")
+
+        if den == 0:
+            raise ValueError("TransferFunction cannot have a zero denominator.")
+
+        if (((isinstance(num, (Expr, TransferFunction, Series, Parallel)) and num.has(Symbol)) or num.is_number) and
+            ((isinstance(den, (Expr, TransferFunction, Series, Parallel)) and den.has(Symbol)) or den.is_number)):
+            cls.is_StateSpace_object = False
+            return super(TransferFunction, cls).__new__(cls, num, den, var)
+
+        else:
+            raise TypeError("Unsupported type for numerator or denominator of TransferFunction.")
+
+    @classmethod
+    def from_rational_expression(cls, expr, var=None):
+        r"""
+        Creates a new ``TransferFunction`` efficiently from a rational expression.
+
+        Parameters
+        ==========
+
+        expr : Expr, Number
+            The rational expression representing the ``TransferFunction``.
+        var : Symbol, optional
+            Complex variable of the Laplace transform used by the
+            polynomials of the transfer function.
+
+        Raises
+        ======
+
+        ValueError
+            When ``expr`` is of type ``Number`` and optional parameter ``var``
+            is not passed.
+
+            When ``expr`` has more than one variables and an optional parameter
+            ``var`` is not passed.
+        ZeroDivisionError
+            When denominator of ``expr`` is zero or it has ``ComplexInfinity``
+            in its numerator.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> expr1 = (s + 5)/(3*s**2 + 2*s + 1)
+        >>> tf1 = TransferFunction.from_rational_expression(expr1)
+        >>> tf1
+        TransferFunction(s + 5, 3*s**2 + 2*s + 1, s)
+        >>> expr2 = (a*p**3 - a*p**2 + s*p)/(p + a**2)  # Expr with more than one variables
+        >>> tf2 = TransferFunction.from_rational_expression(expr2, p)
+        >>> tf2
+        TransferFunction(a*p**3 - a*p**2 + p*s, a**2 + p, p)
+
+        In case of conflict between two or more variables in a expression, SymPy will
+        raise a ``ValueError``, if ``var`` is not passed by the user.
+
+        >>> tf = TransferFunction.from_rational_expression((a + a*s)/(s**2 + s + 1))
+        Traceback (most recent call last):
+        ...
+        ValueError: Conflicting values found for positional argument `var` ({a, s}). Specify it manually.
+
+        This can be corrected by specifying the ``var`` parameter manually.
+
+        >>> tf = TransferFunction.from_rational_expression((a + a*s)/(s**2 + s + 1), s)
+        >>> tf
+        TransferFunction(a*s + a, s**2 + s + 1, s)
+
+        ``var`` also need to be specified when ``expr`` is a ``Number``
+
+        >>> tf3 = TransferFunction.from_rational_expression(10, s)
+        >>> tf3
+        TransferFunction(10, 1, s)
+
+        """
+        expr = _sympify(expr)
+        if var is None:
+            _free_symbols = expr.free_symbols
+            _len_free_symbols = len(_free_symbols)
+            if _len_free_symbols == 1:
+                var = list(_free_symbols)[0]
+            elif _len_free_symbols == 0:
+                raise ValueError(filldedent("""
+                    Positional argument `var` not found in the
+                    TransferFunction defined. Specify it manually."""))
+            else:
+                raise ValueError(filldedent("""
+                    Conflicting values found for positional argument `var` ({}).
+                    Specify it manually.""".format(_free_symbols)))
+
+        _num, _den = expr.as_numer_denom()
+        if _den == 0 or _num.has(S.ComplexInfinity):
+            raise ZeroDivisionError("TransferFunction cannot have a zero denominator.")
+        return cls(_num, _den, var)
+
+    @classmethod
+    def from_coeff_lists(cls, num_list, den_list, var):
+        r"""
+        Creates a new ``TransferFunction`` efficiently from a list of coefficients.
+
+        Parameters
+        ==========
+
+        num_list : Sequence
+            Sequence comprising of numerator coefficients.
+        den_list : Sequence
+            Sequence comprising of denominator coefficients.
+        var : Symbol
+            Complex variable of the Laplace transform used by the
+            polynomials of the transfer function.
+
+        Raises
+        ======
+
+        ZeroDivisionError
+            When the constructed denominator is zero.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> num = [1, 0, 2]
+        >>> den = [3, 2, 2, 1]
+        >>> tf = TransferFunction.from_coeff_lists(num, den, s)
+        >>> tf
+        TransferFunction(s**2 + 2, 3*s**3 + 2*s**2 + 2*s + 1, s)
+        >>> #Create a Transfer Function with more than one variable
+        >>> tf1 = TransferFunction.from_coeff_lists([p, 1], [2*p, 0, 4], s)
+        >>> tf1
+        TransferFunction(p*s + 1, 2*p*s**2 + 4, s)
+
+        """
+        num_list = num_list[::-1]
+        den_list = den_list[::-1]
+        num_var_powers = [var**i for i in range(len(num_list))]
+        den_var_powers = [var**i for i in range(len(den_list))]
+
+        _num = sum(coeff * var_power for coeff, var_power in zip(num_list, num_var_powers))
+        _den = sum(coeff * var_power for coeff, var_power in zip(den_list, den_var_powers))
+
+        if _den == 0:
+            raise ZeroDivisionError("TransferFunction cannot have a zero denominator.")
+
+        return cls(_num, _den, var)
+
+    @classmethod
+    def from_zpk(cls, zeros, poles, gain, var):
+        r"""
+        Creates a new ``TransferFunction`` from given zeros, poles and gain.
+
+        Parameters
+        ==========
+
+        zeros : Sequence
+            Sequence comprising of zeros of transfer function.
+        poles : Sequence
+            Sequence comprising of poles of transfer function.
+        gain : Number, Symbol, Expression
+            A scalar value specifying gain of the model.
+        var : Symbol
+            Complex variable of the Laplace transform used by the
+            polynomials of the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, k
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> zeros = [1, 2, 3]
+        >>> poles = [6, 5, 4]
+        >>> gain = 7
+        >>> tf = TransferFunction.from_zpk(zeros, poles, gain, s)
+        >>> tf
+        TransferFunction(7*(s - 3)*(s - 2)*(s - 1), (s - 6)*(s - 5)*(s - 4), s)
+        >>> #Create a Transfer Function with variable poles and zeros
+        >>> tf1 = TransferFunction.from_zpk([p, k], [p + k, p - k], 2, s)
+        >>> tf1
+        TransferFunction(2*(-k + s)*(-p + s), (-k - p + s)*(k - p + s), s)
+        >>> #Complex poles or zeros are acceptable
+        >>> tf2 = TransferFunction.from_zpk([0], [1-1j, 1+1j, 2], -2, s)
+        >>> tf2
+        TransferFunction(-2*s, (s - 2)*(s - 1.0 - 1.0*I)*(s - 1.0 + 1.0*I), s)
+
+        """
+        num_poly = 1
+        den_poly = 1
+        for zero in zeros:
+            num_poly *= var - zero
+        for pole in poles:
+            den_poly *= var - pole
+
+        return cls(gain*num_poly, den_poly, var)
+
+    @property
+    def num(self):
+        """
+        Returns the numerator polynomial of the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction(s**2 + p*s + 3, s - 4, s)
+        >>> G1.num
+        p*s + s**2 + 3
+        >>> G2 = TransferFunction((p + 5)*(p - 3), (p - 3)*(p + 1), p)
+        >>> G2.num
+        (p - 3)*(p + 5)
+
+        """
+        return self.args[0]
+
+    @property
+    def den(self):
+        """
+        Returns the denominator polynomial of the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction(s + 4, p**3 - 2*p + 4, s)
+        >>> G1.den
+        p**3 - 2*p + 4
+        >>> G2 = TransferFunction(3, 4, s)
+        >>> G2.den
+        4
+
+        """
+        return self.args[1]
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable of the Laplace transform used by the polynomials of
+        the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G1.var
+        p
+        >>> G2 = TransferFunction(0, s - 5, s)
+        >>> G2.var
+        s
+
+        """
+        return self.args[2]
+
+    def _eval_subs(self, old, new):
+        arg_num = self.num.subs(old, new)
+        arg_den = self.den.subs(old, new)
+        argnew = TransferFunction(arg_num, arg_den, self.var)
+        return self if old == self.var else argnew
+
+    def _eval_evalf(self, prec):
+        return TransferFunction(
+            self.num._eval_evalf(prec),
+            self.den._eval_evalf(prec),
+            self.var)
+
+    def _eval_simplify(self, **kwargs):
+        tf = cancel(Mul(self.num, 1/self.den, evaluate=False), expand=False).as_numer_denom()
+        num_, den_ = tf[0], tf[1]
+        return TransferFunction(num_, den_, self.var)
+
+    def _eval_rewrite_as_StateSpace(self, *args):
+        """
+        Returns the equivalent space model of the transfer function model.
+        The state space model will be returned in the controllable canonical form.
+
+        Unlike the space state to transfer function model conversion, the transfer function
+        to state space model conversion is not unique. There can be multiple state space
+        representations of a given transfer function model.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control import TransferFunction, StateSpace
+        >>> tf = TransferFunction(s**2 + 1, s**3 + 2*s + 10, s)
+        >>> tf.rewrite(StateSpace)
+        StateSpace(Matrix([
+        [  0,  1, 0],
+        [  0,  0, 1],
+        [-10, -2, 0]]), Matrix([
+        [0],
+        [0],
+        [1]]), Matrix([[1, 0, 1]]), Matrix([[0]]))
+
+        """
+        if not self.is_proper:
+            raise ValueError("Transfer Function must be proper.")
+
+        num_poly = Poly(self.num, self.var)
+        den_poly = Poly(self.den, self.var)
+        n = den_poly.degree()
+
+        num_coeffs = num_poly.all_coeffs()
+        den_coeffs = den_poly.all_coeffs()
+        diff = n - num_poly.degree()
+        num_coeffs = [0]*diff + num_coeffs
+
+        a = den_coeffs[1:]
+        a_mat = Matrix([[(-1)*coefficient/den_coeffs[0] for coefficient in reversed(a)]])
+        vert = zeros(n-1, 1)
+        mat = eye(n-1)
+        A = vert.row_join(mat)
+        A = A.col_join(a_mat)
+
+        B = zeros(n, 1)
+        B[n-1] = 1
+
+        i = n
+        C = []
+        while(i > 0):
+            C.append(num_coeffs[i] - den_coeffs[i]*num_coeffs[0])
+            i -= 1
+        C = Matrix([C])
+
+        D = Matrix([num_coeffs[0]])
+
+        return StateSpace(A, B, C, D)
+
+    def expand(self):
+        """
+        Returns the transfer function with numerator and denominator
+        in expanded form.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction((a - s)**2, (s**2 + a)**2, s)
+        >>> G1.expand()
+        TransferFunction(a**2 - 2*a*s + s**2, a**2 + 2*a*s**2 + s**4, s)
+        >>> G2 = TransferFunction((p + 3*b)*(p - b), (p - b)*(p + 2*b), p)
+        >>> G2.expand()
+        TransferFunction(-3*b**2 + 2*b*p + p**2, -2*b**2 + b*p + p**2, p)
+
+        """
+        return TransferFunction(expand(self.num), expand(self.den), self.var)
+
+    def dc_gain(self):
+        """
+        Computes the gain of the response as the frequency approaches zero.
+
+        The DC gain is infinite for systems with pure integrators.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(s + 3, s**2 - 9, s)
+        >>> tf1.dc_gain()
+        -1/3
+        >>> tf2 = TransferFunction(p**2, p - 3 + p**3, p)
+        >>> tf2.dc_gain()
+        0
+        >>> tf3 = TransferFunction(a*p**2 - b, s + b, s)
+        >>> tf3.dc_gain()
+        (a*p**2 - b)/b
+        >>> tf4 = TransferFunction(1, s, s)
+        >>> tf4.dc_gain()
+        oo
+
+        """
+        m = Mul(self.num, Pow(self.den, -1, evaluate=False), evaluate=False)
+        return limit(m, self.var, 0)
+
+    def poles(self):
+        """
+        Returns the poles of a transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+        >>> tf1.poles()
+        [-5, 1]
+        >>> tf2 = TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+        >>> tf2.poles()
+        [I, I, -I, -I]
+        >>> tf3 = TransferFunction(s**2, a*s + p, s)
+        >>> tf3.poles()
+        [-p/a]
+
+        """
+        return _roots(Poly(self.den, self.var), self.var)
+
+    def zeros(self):
+        """
+        Returns the zeros of a transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+        >>> tf1.zeros()
+        [-3, 1]
+        >>> tf2 = TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+        >>> tf2.zeros()
+        [1, 1]
+        >>> tf3 = TransferFunction(s**2, a*s + p, s)
+        >>> tf3.zeros()
+        [0, 0]
+
+        """
+        return _roots(Poly(self.num, self.var), self.var)
+
+    def eval_frequency(self, other):
+        """
+        Returns the system response at any point in the real or complex plane.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy import I
+        >>> tf1 = TransferFunction(1, s**2 + 2*s + 1, s)
+        >>> omega = 0.1
+        >>> tf1.eval_frequency(I*omega)
+        1/(0.99 + 0.2*I)
+        >>> tf2 = TransferFunction(s**2, a*s + p, s)
+        >>> tf2.eval_frequency(2)
+        4/(2*a + p)
+        >>> tf2.eval_frequency(I*2)
+        -4/(2*I*a + p)
+        """
+        arg_num = self.num.subs(self.var, other)
+        arg_den = self.den.subs(self.var, other)
+        argnew = TransferFunction(arg_num, arg_den, self.var).to_expr()
+        return argnew.expand()
+
+    def is_stable(self):
+        """
+        Returns True if the transfer function is asymptotically stable; else False.
+
+        This would not check the marginal or conditional stability of the system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy import symbols
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> q, r = symbols('q, r', negative=True)
+        >>> tf1 = TransferFunction((1 - s)**2, (s + 1)**2, s)
+        >>> tf1.is_stable()
+        True
+        >>> tf2 = TransferFunction((1 - p)**2, (s**2 + 1)**2, s)
+        >>> tf2.is_stable()
+        False
+        >>> tf3 = TransferFunction(4, q*s - r, s)
+        >>> tf3.is_stable()
+        False
+        >>> tf4 = TransferFunction(p + 1, a*p - s**2, p)
+        >>> tf4.is_stable() is None   # Not enough info about the symbols to determine stability
+        True
+
+        """
+        return fuzzy_and(pole.as_real_imag()[0].is_negative for pole in self.poles())
+
+    def __add__(self, other):
+        if hasattr(other, "is_StateSpace_object") and other.is_StateSpace_object:
+            return Parallel(self, other)
+        elif isinstance(other, (TransferFunction, Series, Feedback)):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Parallel(self, other)
+        elif isinstance(other, Parallel):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            arg_list = list(other.args)
+            return Parallel(self, *arg_list)
+        else:
+            raise ValueError("TransferFunction cannot be added with {}.".
+                format(type(other)))
+
+    def __radd__(self, other):
+        return self + other
+
+    def __sub__(self, other):
+        if hasattr(other, "is_StateSpace_object") and other.is_StateSpace_object:
+            return Parallel(self, -other)
+        elif isinstance(other, (TransferFunction, Series)):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Parallel(self, -other)
+        elif isinstance(other, Parallel):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            arg_list = [-i for i in list(other.args)]
+            return Parallel(self, *arg_list)
+        else:
+            raise ValueError("{} cannot be subtracted from a TransferFunction."
+                .format(type(other)))
+
+    def __rsub__(self, other):
+        return -self + other
+
+    def __mul__(self, other):
+        if hasattr(other, "is_StateSpace_object") and other.is_StateSpace_object:
+            return Series(self, other)
+        elif isinstance(other, (TransferFunction, Parallel, Feedback)):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Series(self, other)
+        elif isinstance(other, Series):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            arg_list = list(other.args)
+            return Series(self, *arg_list)
+        else:
+            raise ValueError("TransferFunction cannot be multiplied with {}."
+                .format(type(other)))
+
+    __rmul__ = __mul__
+
+    def __truediv__(self, other):
+        if isinstance(other, TransferFunction):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Series(self, TransferFunction(other.den, other.num, self.var))
+        elif (isinstance(other, Parallel) and len(other.args
+                ) == 2 and isinstance(other.args[0], TransferFunction)
+            and isinstance(other.args[1], (Series, TransferFunction))):
+
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    Both TransferFunction and Parallel should use the
+                    same complex variable of the Laplace transform."""))
+            if other.args[1] == self:
+                # plant and controller with unit feedback.
+                return Feedback(self, other.args[0])
+            other_arg_list = list(other.args[1].args) if isinstance(
+                other.args[1], Series) else other.args[1]
+            if other_arg_list == other.args[1]:
+                return Feedback(self, other_arg_list)
+            elif self in other_arg_list:
+                other_arg_list.remove(self)
+            else:
+                return Feedback(self, Series(*other_arg_list))
+
+            if len(other_arg_list) == 1:
+                return Feedback(self, *other_arg_list)
+            else:
+                return Feedback(self, Series(*other_arg_list))
+        else:
+            raise ValueError("TransferFunction cannot be divided by {}.".
+                format(type(other)))
+
+    __rtruediv__ = __truediv__
+
+    def __pow__(self, p):
+        p = sympify(p)
+        if not p.is_Integer:
+            raise ValueError("Exponent must be an integer.")
+        if p is S.Zero:
+            return TransferFunction(1, 1, self.var)
+        elif p > 0:
+            num_, den_ = self.num**p, self.den**p
+        else:
+            p = abs(p)
+            num_, den_ = self.den**p, self.num**p
+
+        return TransferFunction(num_, den_, self.var)
+
+    def __neg__(self):
+        return TransferFunction(-self.num, self.den, self.var)
+
+    @property
+    def is_proper(self):
+        """
+        Returns True if degree of the numerator polynomial is less than
+        or equal to degree of the denominator polynomial, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+        >>> tf1.is_proper
+        False
+        >>> tf2 = TransferFunction(p**2 - 4*p, p**3 + 3*p + 2, p)
+        >>> tf2.is_proper
+        True
+
+        """
+        return degree(self.num, self.var) <= degree(self.den, self.var)
+
+    @property
+    def is_strictly_proper(self):
+        """
+        Returns True if degree of the numerator polynomial is strictly less
+        than degree of the denominator polynomial, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf1.is_strictly_proper
+        False
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tf2.is_strictly_proper
+        True
+
+        """
+        return degree(self.num, self.var) < degree(self.den, self.var)
+
+    @property
+    def is_biproper(self):
+        """
+        Returns True if degree of the numerator polynomial is equal to
+        degree of the denominator polynomial, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf1.is_biproper
+        True
+        >>> tf2 = TransferFunction(p**2, p + a, p)
+        >>> tf2.is_biproper
+        False
+
+        """
+        return degree(self.num, self.var) == degree(self.den, self.var)
+
+    def to_expr(self):
+        """
+        Converts a ``TransferFunction`` object to SymPy Expr.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy import Expr
+        >>> tf1 = TransferFunction(s, a*s**2 + 1, s)
+        >>> tf1.to_expr()
+        s/(a*s**2 + 1)
+        >>> isinstance(_, Expr)
+        True
+        >>> tf2 = TransferFunction(1, (p + 3*b)*(b - p), p)
+        >>> tf2.to_expr()
+        1/((b - p)*(3*b + p))
+        >>> tf3 = TransferFunction((s - 2)*(s - 3), (s - 1)*(s - 2)*(s - 3), s)
+        >>> tf3.to_expr()
+        ((s - 3)*(s - 2))/(((s - 3)*(s - 2)*(s - 1)))
+
+        """
+
+        if self.num != 1:
+            return Mul(self.num, Pow(self.den, -1, evaluate=False), evaluate=False)
+        else:
+            return Pow(self.den, -1, evaluate=False)
+
+
+class PIDController(TransferFunction):
+    r"""
+    A class for representing PID (Proportional-Integral-Derivative)
+    controllers in control systems. The PIDController class is a subclass
+    of TransferFunction, representing the controller's transfer function
+    in the Laplace domain. The arguments are ``kp``, ``ki``, ``kd``,
+    ``tf``, and ``var``, where ``kp``, ``ki``, and ``kd`` are the
+    proportional, integral, and derivative gains respectively.``tf``
+    is the derivative filter time constant, which can be used to
+    filter out the noise and ``var`` is the complex variable used in
+    the transfer function.
+
+    Parameters
+    ==========
+
+    kp : Expr, Number
+        Proportional gain. Defaults to ``Symbol('kp')`` if not specified.
+    ki : Expr, Number
+        Integral gain. Defaults to ``Symbol('ki')`` if not specified.
+    kd : Expr, Number
+        Derivative gain. Defaults to ``Symbol('kd')`` if not specified.
+    tf : Expr, Number
+        Derivative filter time constant.  Defaults to ``0`` if not specified.
+    var : Symbol
+        The complex frequency variable.  Defaults to ``s`` if not specified.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.control.lti import PIDController
+    >>> kp, ki, kd = symbols('kp ki kd')
+    >>> p1 = PIDController(kp, ki, kd)
+    >>> print(p1)
+    PIDController(kp, ki, kd, 0, s)
+    >>> p1.doit()
+    TransferFunction(kd*s**2 + ki + kp*s, s, s)
+    >>> p1.kp
+    kp
+    >>> p1.ki
+    ki
+    >>> p1.kd
+    kd
+    >>> p1.tf
+    0
+    >>> p1.var
+    s
+    >>> p1.to_expr()
+    (kd*s**2 + ki + kp*s)/s
+
+    See Also
+    ========
+
+    TransferFunction
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/PID_controller
+    .. [2] https://in.mathworks.com/help/control/ug/proportional-integral-derivative-pid-controllers.html
+
+    """
+    def __new__(cls, kp=Symbol('kp'), ki=Symbol('ki'), kd=Symbol('kd'), tf=0, var=Symbol('s')):
+        kp, ki, kd, tf = _sympify(kp), _sympify(ki), _sympify(kd), _sympify(tf)
+        num = kp*tf*var**2 + kp*var + ki*tf*var + ki + kd*var**2
+        den = tf*var**2 + var
+        obj = TransferFunction.__new__(cls, num, den, var)
+        obj._kp, obj._ki, obj._kd, obj._tf = kp, ki, kd, tf
+        return obj
+
+    def __repr__(self):
+        return f"PIDController({self.kp}, {self.ki}, {self.kd}, {self.tf}, {self.var})"
+
+    __str__ = __repr__
+
+    @property
+    def kp(self):
+        """
+        Returns the Proportional gain (kp) of the PIDController.
+        """
+        return self._kp
+
+    @property
+    def ki(self):
+        """
+        Returns the Integral gain (ki) of the PIDController.
+        """
+        return self._ki
+
+    @property
+    def kd(self):
+        """
+        Returns the Derivative gain (kd) of the PIDController.
+        """
+        return self._kd
+
+    @property
+    def tf(self):
+        """
+        Returns the Derivative filter time constant (tf) of the PIDController.
+        """
+        return self._tf
+
+    def doit(self):
+        """
+        Convert the PIDController into TransferFunction.
+        """
+        return TransferFunction(self.num, self.den, self.var)
+
+
+def _flatten_args(args, _cls):
+    temp_args = []
+    for arg in args:
+        if isinstance(arg, _cls):
+            temp_args.extend(arg.args)
+        else:
+            temp_args.append(arg)
+    return tuple(temp_args)
+
+
+def _dummify_args(_arg, var):
+    dummy_dict = {}
+    dummy_arg_list = []
+
+    for arg in _arg:
+        _s = Dummy()
+        dummy_dict[_s] = var
+        dummy_arg = arg.subs({var: _s})
+        dummy_arg_list.append(dummy_arg)
+
+    return dummy_arg_list, dummy_dict
+
+
+class Series(SISOLinearTimeInvariant):
+    r"""
+    A class for representing a series configuration of SISO systems.
+
+    Parameters
+    ==========
+
+    args : SISOLinearTimeInvariant
+        SISO systems in a series configuration.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``Series(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed, SISO in this case.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s, p, a, b
+    >>> from sympy import Matrix
+    >>> from sympy.physics.control.lti import TransferFunction, Series, Parallel, StateSpace
+    >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+    >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+    >>> tf3 = TransferFunction(p**2, p + s, s)
+    >>> S1 = Series(tf1, tf2)
+    >>> S1
+    Series(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s))
+    >>> S1.var
+    s
+    >>> S2 = Series(tf2, Parallel(tf3, -tf1))
+    >>> S2
+    Series(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), Parallel(TransferFunction(p**2, p + s, s), TransferFunction(-a*p**2 - b*s, -p + s, s)))
+    >>> S2.var
+    s
+    >>> S3 = Series(Parallel(tf1, tf2), Parallel(tf2, tf3))
+    >>> S3
+    Series(Parallel(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)), Parallel(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), TransferFunction(p**2, p + s, s)))
+    >>> S3.var
+    s
+
+    You can get the resultant transfer function by using ``.doit()`` method:
+
+    >>> S3 = Series(tf1, tf2, -tf3)
+    >>> S3.doit()
+    TransferFunction(-p**2*(s**3 - 2)*(a*p**2 + b*s), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+    >>> S4 = Series(tf2, Parallel(tf1, -tf3))
+    >>> S4.doit()
+    TransferFunction((s**3 - 2)*(-p**2*(-p + s) + (p + s)*(a*p**2 + b*s)), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+
+    You can also connect StateSpace which results in SISO
+
+    >>> A1 = Matrix([[-1]])
+    >>> B1 = Matrix([[1]])
+    >>> C1 = Matrix([[-1]])
+    >>> D1 = Matrix([1])
+    >>> A2 = Matrix([[0]])
+    >>> B2 = Matrix([[1]])
+    >>> C2 = Matrix([[1]])
+    >>> D2 = Matrix([[0]])
+    >>> ss1 = StateSpace(A1, B1, C1, D1)
+    >>> ss2 = StateSpace(A2, B2, C2, D2)
+    >>> S5 = Series(ss1, ss2)
+    >>> S5
+    Series(StateSpace(Matrix([[-1]]), Matrix([[1]]), Matrix([[-1]]), Matrix([[1]])), StateSpace(Matrix([[0]]), Matrix([[1]]), Matrix([[1]]), Matrix([[0]])))
+    >>> S5.doit()
+    StateSpace(Matrix([
+    [-1,  0],
+    [-1, 0]]), Matrix([
+    [1],
+    [1]]), Matrix([[0, 1]]), Matrix([[0]]))
+
+    Notes
+    =====
+
+    All the transfer functions should use the same complex variable
+    ``var`` of the Laplace transform.
+
+    See Also
+    ========
+
+    MIMOSeries, Parallel, TransferFunction, Feedback
+
+    """
+    def __new__(cls, *args, evaluate=False):
+
+        args = _flatten_args(args, Series)
+        # For StateSpace series connection
+        if args and any(isinstance(arg, StateSpace) or (hasattr(arg, 'is_StateSpace_object')
+                                            and arg.is_StateSpace_object)for arg in args):
+            # Check for SISO
+            if (args[0].num_inputs == 1) and (args[-1].num_outputs == 1):
+                # Check the interconnection
+                for i in range(1, len(args)):
+                    if args[i].num_inputs != args[i-1].num_outputs:
+                        raise ValueError(filldedent("""Systems with incompatible inputs and outputs
+                            cannot be connected in Series."""))
+                cls._is_series_StateSpace = True
+            else:
+                raise ValueError("To use Series connection for MIMO systems use MIMOSeries instead.")
+        else:
+            cls._is_series_StateSpace = False
+            cls._check_args(args)
+
+        obj = super().__new__(cls, *args)
+
+        return obj.doit() if evaluate else obj
+
+    def __repr__(self):
+        systems_repr = ', '.join(repr(system) for system in self.args)
+        return f"Series({systems_repr})"
+
+    __str__ = __repr__
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, Series, Parallel
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> Series(G1, G2).var
+        p
+        >>> Series(-G3, Parallel(G1, G2)).var
+        p
+
+        """
+        return self.args[0].var
+
+    def doit(self, **hints):
+        """
+        Returns the resultant transfer function or StateSpace obtained after evaluating
+        the series interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> Series(tf2, tf1).doit()
+        TransferFunction((s**3 - 2)*(a*p**2 + b*s), (-p + s)*(s**4 + 5*s + 6), s)
+        >>> Series(-tf1, -tf2).doit()
+        TransferFunction((2 - s**3)*(-a*p**2 - b*s), (-p + s)*(s**4 + 5*s + 6), s)
+
+        Notes
+        =====
+
+        If a series connection contains only TransferFunction components, the equivalent system returned
+        will be a TransferFunction. However, if a StateSpace object is used in any of the arguments,
+        the output will be a StateSpace object.
+
+        """
+        # Check if the system is a StateSpace
+        if self._is_series_StateSpace:
+            # Return the equivalent StateSpace model
+            res = self.args[0]
+            if not isinstance(res, StateSpace):
+                res = res.doit().rewrite(StateSpace)
+            for arg in self.args[1:]:
+                if not isinstance(arg, StateSpace):
+                    arg = arg.doit().rewrite(StateSpace)
+                else:
+                    arg = arg.doit()
+                arg = arg.doit()
+                res = arg * res
+                return res
+
+        _num_arg = (arg.doit().num for arg in self.args)
+        _den_arg = (arg.doit().den for arg in self.args)
+        res_num = Mul(*_num_arg, evaluate=True)
+        res_den = Mul(*_den_arg, evaluate=True)
+        return TransferFunction(res_num, res_den, self.var)
+
+    def _eval_rewrite_as_TransferFunction(self, *args, **kwargs):
+        if self._is_series_StateSpace:
+            return self.doit().rewrite(TransferFunction)[0][0]
+        return self.doit()
+
+    @_check_other_SISO
+    def __add__(self, other):
+
+        if isinstance(other, Parallel):
+            arg_list = list(other.args)
+            return Parallel(self, *arg_list)
+
+        return Parallel(self, other)
+
+    __radd__ = __add__
+
+    @_check_other_SISO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_SISO
+    def __mul__(self, other):
+
+        arg_list = list(self.args)
+        return Series(*arg_list, other)
+
+    def __truediv__(self, other):
+        if isinstance(other, TransferFunction):
+            return Series(*self.args, TransferFunction(other.den, other.num, other.var))
+        elif isinstance(other, Series):
+            tf_self = self.rewrite(TransferFunction)
+            tf_other = other.rewrite(TransferFunction)
+            return tf_self / tf_other
+        elif (isinstance(other, Parallel) and len(other.args) == 2
+            and isinstance(other.args[0], TransferFunction) and isinstance(other.args[1], Series)):
+
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            self_arg_list = set(self.args)
+            other_arg_list = set(other.args[1].args)
+            res = list(self_arg_list ^ other_arg_list)
+            if len(res) == 0:
+                return Feedback(self, other.args[0])
+            elif len(res) == 1:
+                return Feedback(self, *res)
+            else:
+                return Feedback(self, Series(*res))
+        else:
+            raise ValueError("This transfer function expression is invalid.")
+
+    def __neg__(self):
+        return Series(TransferFunction(-1, 1, self.var), self)
+
+    def to_expr(self):
+        """Returns the equivalent ``Expr`` object."""
+        return Mul(*(arg.to_expr() for arg in self.args), evaluate=False)
+
+    @property
+    def is_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is less than or equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+        >>> tf2 = TransferFunction(p**2 - 4*p, p**3 + 3*s + 2, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> S1 = Series(-tf2, tf1)
+        >>> S1.is_proper
+        False
+        >>> S2 = Series(tf1, tf2, tf3)
+        >>> S2.is_proper
+        True
+
+        """
+        return self.doit().is_proper
+
+    @property
+    def is_strictly_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is strictly less than degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**2 + 5*s + 6, s)
+        >>> tf3 = TransferFunction(1, s**2 + s + 1, s)
+        >>> S1 = Series(tf1, tf2)
+        >>> S1.is_strictly_proper
+        False
+        >>> S2 = Series(tf1, tf2, tf3)
+        >>> S2.is_strictly_proper
+        True
+
+        """
+        return self.doit().is_strictly_proper
+
+    @property
+    def is_biproper(self):
+        r"""
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(p, s**2, s)
+        >>> tf3 = TransferFunction(s**2, 1, s)
+        >>> S1 = Series(tf1, -tf2)
+        >>> S1.is_biproper
+        False
+        >>> S2 = Series(tf2, tf3)
+        >>> S2.is_biproper
+        True
+
+        """
+        return self.doit().is_biproper
+
+    @property
+    def is_StateSpace_object(self):
+        return self._is_series_StateSpace
+
+def _mat_mul_compatible(*args):
+    """To check whether shapes are compatible for matrix mul."""
+    return all(args[i].num_outputs == args[i+1].num_inputs for i in range(len(args)-1))
+
+
+class MIMOSeries(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing a series configuration of MIMO systems.
+
+    Parameters
+    ==========
+
+    args : MIMOLinearTimeInvariant
+        MIMO systems in a series configuration.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``MIMOSeries(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+
+        ``num_outputs`` of the MIMO system is not equal to the
+        ``num_inputs`` of its adjacent MIMO system. (Matrix
+        multiplication constraint, basically)
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed, MIMO in this case.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import MIMOSeries, TransferFunctionMatrix, StateSpace
+    >>> from sympy import Matrix, pprint
+    >>> mat_a = Matrix([[5*s], [5]])  # 2 Outputs 1 Input
+    >>> mat_b = Matrix([[5, 1/(6*s**2)]])  # 1 Output 2 Inputs
+    >>> mat_c = Matrix([[1, s], [5/s, 1]])  # 2 Outputs 2 Inputs
+    >>> tfm_a = TransferFunctionMatrix.from_Matrix(mat_a, s)
+    >>> tfm_b = TransferFunctionMatrix.from_Matrix(mat_b, s)
+    >>> tfm_c = TransferFunctionMatrix.from_Matrix(mat_c, s)
+    >>> MIMOSeries(tfm_c, tfm_b, tfm_a)
+    MIMOSeries(TransferFunctionMatrix(((TransferFunction(1, 1, s), TransferFunction(s, 1, s)), (TransferFunction(5, s, s), TransferFunction(1, 1, s)))), TransferFunctionMatrix(((TransferFunction(5, 1, s), TransferFunction(1, 6*s**2, s)),)), TransferFunctionMatrix(((TransferFunction(5*s, 1, s),), (TransferFunction(5, 1, s),))))
+    >>> pprint(_, use_unicode=False)  #  For Better Visualization
+    [5*s]                 [1  s]
+    [---]    [5   1  ]    [-  -]
+    [ 1 ]    [-  ----]    [1  1]
+    [   ]   *[1     2]   *[    ]
+    [ 5 ]    [   6*s ]{t} [5  1]
+    [ - ]                 [-  -]
+    [ 1 ]{t}              [s  1]{t}
+    >>> MIMOSeries(tfm_c, tfm_b, tfm_a).doit()
+    TransferFunctionMatrix(((TransferFunction(150*s**4 + 25*s, 6*s**3, s), TransferFunction(150*s**4 + 5*s, 6*s**2, s)), (TransferFunction(150*s**3 + 25, 6*s**3, s), TransferFunction(150*s**3 + 5, 6*s**2, s))))
+    >>> pprint(_, use_unicode=False)  # (2 Inputs -A-> 2 Outputs) -> (2 Inputs -B-> 1 Output) -> (1 Input -C-> 2 Outputs) is equivalent to (2 Inputs -Series Equivalent-> 2 Outputs).
+    [     4              4      ]
+    [150*s  + 25*s  150*s  + 5*s]
+    [-------------  ------------]
+    [        3             2    ]
+    [     6*s           6*s     ]
+    [                           ]
+    [      3              3     ]
+    [ 150*s  + 25    150*s  + 5 ]
+    [ -----------    ---------- ]
+    [        3             2    ]
+    [     6*s           6*s     ]{t}
+    >>> a1 = Matrix([[4, 1], [2, -3]])
+    >>> b1 = Matrix([[5, 2], [-3, -3]])
+    >>> c1 = Matrix([[2, -4], [0, 1]])
+    >>> d1 = Matrix([[3, 2], [1, -1]])
+    >>> a2 = Matrix([[-3, 4, 2], [-1, -3, 0], [2, 5, 3]])
+    >>> b2 = Matrix([[1, 4], [-3, -3], [-2, 1]])
+    >>> c2 = Matrix([[4, 2, -3], [1, 4, 3]])
+    >>> d2 = Matrix([[-2, 4], [0, 1]])
+    >>> ss1 = StateSpace(a1, b1, c1, d1) #2 inputs, 2 outputs
+    >>> ss2 = StateSpace(a2, b2, c2, d2) #2 inputs, 2 outputs
+    >>> S1 = MIMOSeries(ss1, ss2) #(2 inputs, 2 outputs) -> (2 inputs, 2 outputs)
+    >>> S1
+    MIMOSeries(StateSpace(Matrix([
+            [4,  1],
+            [2, -3]]), Matrix([
+            [ 5,  2],
+            [-3, -3]]), Matrix([
+            [2, -4],
+            [0,  1]]), Matrix([
+            [3,  2],
+            [1, -1]])), StateSpace(Matrix([
+            [-3,  4, 2],
+            [-1, -3, 0],
+            [ 2,  5, 3]]), Matrix([
+            [ 1,  4],
+            [-3, -3],
+            [-2,  1]]), Matrix([
+            [4, 2, -3],
+            [1, 4,  3]]), Matrix([
+            [-2, 4],
+            [ 0, 1]])))
+    >>> S1.doit()
+    StateSpace(Matrix([
+    [ 4,  1,  0,  0, 0],
+    [ 2, -3,  0,  0, 0],
+    [ 2,  0, -3,  4, 2],
+    [-6,  9, -1, -3, 0],
+    [-4,  9,  2,  5, 3]]), Matrix([
+    [  5,  2],
+    [ -3, -3],
+    [  7, -2],
+    [-12, -3],
+    [ -5, -5]]), Matrix([
+    [-4, 12, 4, 2, -3],
+    [ 0,  1, 1, 4,  3]]), Matrix([
+    [-2, -8],
+    [ 1, -1]]))
+
+    Notes
+    =====
+
+    All the transfer function matrices should use the same complex variable ``var`` of the Laplace transform.
+
+    ``MIMOSeries(A, B)`` is not equivalent to ``A*B``. It is always in the reverse order, that is ``B*A``.
+
+    See Also
+    ========
+
+    Series, MIMOParallel
+
+    """
+    def __new__(cls, *args, evaluate=False):
+
+        if args and any(isinstance(arg, StateSpace) or (hasattr(arg, 'is_StateSpace_object')
+                                            and arg.is_StateSpace_object) for arg in args):
+            # Check compatibility
+            for i in range(1, len(args)):
+                if args[i].num_inputs != args[i - 1].num_outputs:
+                    raise ValueError(filldedent("""Systems with incompatible inputs and outputs
+                        cannot be connected in MIMOSeries."""))
+            obj = super().__new__(cls, *args)
+            cls._is_series_StateSpace = True
+        else:
+            cls._check_args(args)
+            cls._is_series_StateSpace = False
+
+            if _mat_mul_compatible(*args):
+                obj = super().__new__(cls, *args)
+
+            else:
+                raise ValueError(filldedent("""
+                    Number of input signals do not match the number
+                    of output signals of adjacent systems for some args."""))
+
+        return obj.doit() if evaluate else obj
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, MIMOSeries, TransferFunctionMatrix
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> tfm_1 = TransferFunctionMatrix([[G1, G2, G3]])
+        >>> tfm_2 = TransferFunctionMatrix([[G1], [G2], [G3]])
+        >>> MIMOSeries(tfm_2, tfm_1).var
+        p
+
+        """
+        return self.args[0].var
+
+    @property
+    def num_inputs(self):
+        """Returns the number of input signals of the series system."""
+        return self.args[0].num_inputs
+
+    @property
+    def num_outputs(self):
+        """Returns the number of output signals of the series system."""
+        return self.args[-1].num_outputs
+
+    @property
+    def shape(self):
+        """Returns the shape of the equivalent MIMO system."""
+        return self.num_outputs, self.num_inputs
+
+    @property
+    def is_StateSpace_object(self):
+        return self._is_series_StateSpace
+
+    def doit(self, cancel=False, **kwargs):
+        """
+        Returns the resultant obtained after evaluating the MIMO systems arranged
+        in a series configuration. For TransferFunction systems it returns a TransferFunctionMatrix
+        and for StateSpace systems it returns the resultant StateSpace system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, MIMOSeries, TransferFunctionMatrix
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tfm1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf2]])
+        >>> tfm2 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf1]])
+        >>> MIMOSeries(tfm2, tfm1).doit()
+        TransferFunctionMatrix(((TransferFunction(2*(-p + s)*(s**3 - 2)*(a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)**2*(s**4 + 5*s + 6)**2, s), TransferFunction((-p + s)**2*(s**3 - 2)*(a*p**2 + b*s) + (-p + s)*(a*p**2 + b*s)**2*(s**4 + 5*s + 6), (-p + s)**3*(s**4 + 5*s + 6), s)), (TransferFunction((-p + s)*(s**3 - 2)**2*(s**4 + 5*s + 6) + (s**3 - 2)*(a*p**2 + b*s)*(s**4 + 5*s + 6)**2, (-p + s)*(s**4 + 5*s + 6)**3, s), TransferFunction(2*(s**3 - 2)*(a*p**2 + b*s), (-p + s)*(s**4 + 5*s + 6), s))))
+
+        """
+        if self._is_series_StateSpace:
+            # Return the equivalent StateSpace model
+            res = self.args[0]
+            if not isinstance(res, StateSpace):
+                res = res.doit().rewrite(StateSpace)
+            for arg in self.args[1:]:
+                if not isinstance(arg, StateSpace):
+                    arg = arg.doit().rewrite(StateSpace)
+                else:
+                    arg = arg.doit()
+                res = arg * res
+            return res
+
+        _arg = (arg.doit()._expr_mat for arg in reversed(self.args))
+
+        if cancel:
+            res = MatMul(*_arg, evaluate=True)
+            return TransferFunctionMatrix.from_Matrix(res, self.var)
+
+        _dummy_args, _dummy_dict = _dummify_args(_arg, self.var)
+        res = MatMul(*_dummy_args, evaluate=True)
+        temp_tfm = TransferFunctionMatrix.from_Matrix(res, self.var)
+        return temp_tfm.subs(_dummy_dict)
+
+    def _eval_rewrite_as_TransferFunctionMatrix(self, *args, **kwargs):
+        if self._is_series_StateSpace:
+            return self.doit().rewrite(TransferFunction)
+        return self.doit()
+
+    @_check_other_MIMO
+    def __add__(self, other):
+
+        if isinstance(other, MIMOParallel):
+            arg_list = list(other.args)
+            return MIMOParallel(self, *arg_list)
+
+        return MIMOParallel(self, other)
+
+    __radd__ = __add__
+
+    @_check_other_MIMO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_MIMO
+    def __mul__(self, other):
+
+        if isinstance(other, MIMOSeries):
+            self_arg_list = list(self.args)
+            other_arg_list = list(other.args)
+            return MIMOSeries(*other_arg_list, *self_arg_list)  # A*B = MIMOSeries(B, A)
+
+        arg_list = list(self.args)
+        return MIMOSeries(other, *arg_list)
+
+    def __neg__(self):
+        arg_list = list(self.args)
+        arg_list[0] = -arg_list[0]
+        return MIMOSeries(*arg_list)
+
+
+class Parallel(SISOLinearTimeInvariant):
+    r"""
+    A class for representing a parallel configuration of SISO systems.
+
+    Parameters
+    ==========
+
+    args : SISOLinearTimeInvariant
+        SISO systems in a parallel arrangement.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``Parallel(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.abc import s, p, a, b
+    >>> from sympy.physics.control.lti import TransferFunction, Parallel, Series, StateSpace
+    >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+    >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+    >>> tf3 = TransferFunction(p**2, p + s, s)
+    >>> P1 = Parallel(tf1, tf2)
+    >>> P1
+    Parallel(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s))
+    >>> P1.var
+    s
+    >>> P2 = Parallel(tf2, Series(tf3, -tf1))
+    >>> P2
+    Parallel(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), Series(TransferFunction(p**2, p + s, s), TransferFunction(-a*p**2 - b*s, -p + s, s)))
+    >>> P2.var
+    s
+    >>> P3 = Parallel(Series(tf1, tf2), Series(tf2, tf3))
+    >>> P3
+    Parallel(Series(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)), Series(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), TransferFunction(p**2, p + s, s)))
+    >>> P3.var
+    s
+
+    You can get the resultant transfer function by using ``.doit()`` method:
+
+    >>> Parallel(tf1, tf2, -tf3).doit()
+    TransferFunction(-p**2*(-p + s)*(s**4 + 5*s + 6) + (-p + s)*(p + s)*(s**3 - 2) + (p + s)*(a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+    >>> Parallel(tf2, Series(tf1, -tf3)).doit()
+    TransferFunction(-p**2*(a*p**2 + b*s)*(s**4 + 5*s + 6) + (-p + s)*(p + s)*(s**3 - 2), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+
+    Parallel can be used to connect SISO ``StateSpace`` systems together.
+
+    >>> A1 = Matrix([[-1]])
+    >>> B1 = Matrix([[1]])
+    >>> C1 = Matrix([[-1]])
+    >>> D1 = Matrix([1])
+    >>> A2 = Matrix([[0]])
+    >>> B2 = Matrix([[1]])
+    >>> C2 = Matrix([[1]])
+    >>> D2 = Matrix([[0]])
+    >>> ss1 = StateSpace(A1, B1, C1, D1)
+    >>> ss2 = StateSpace(A2, B2, C2, D2)
+    >>> P4 = Parallel(ss1, ss2)
+    >>> P4
+    Parallel(StateSpace(Matrix([[-1]]), Matrix([[1]]), Matrix([[-1]]), Matrix([[1]])), StateSpace(Matrix([[0]]), Matrix([[1]]), Matrix([[1]]), Matrix([[0]])))
+
+    ``doit()`` can be used to find ``StateSpace`` equivalent for the system containing ``StateSpace`` objects.
+
+    >>> P4.doit()
+    StateSpace(Matrix([
+    [-1, 0],
+    [ 0, 0]]), Matrix([
+    [1],
+    [1]]), Matrix([[-1, 1]]), Matrix([[1]]))
+    >>> P4.rewrite(TransferFunction)
+    TransferFunction(s*(s + 1) + 1, s*(s + 1), s)
+
+    Notes
+    =====
+
+    All the transfer functions should use the same complex variable
+    ``var`` of the Laplace transform.
+
+    See Also
+    ========
+
+    Series, TransferFunction, Feedback
+
+    """
+
+    def __new__(cls, *args, evaluate=False):
+
+        args = _flatten_args(args, Parallel)
+        # For StateSpace parallel connection
+        if args and any(isinstance(arg, StateSpace) or (hasattr(arg, 'is_StateSpace_object')
+                                                        and arg.is_StateSpace_object) for arg in args):
+            # Check for SISO
+            if all(arg.is_SISO for arg in args):
+                cls._is_parallel_StateSpace = True
+            else:
+                raise ValueError("To use Parallel connection for MIMO systems use MIMOParallel instead.")
+        else:
+            cls._is_parallel_StateSpace = False
+            cls._check_args(args)
+        obj = super().__new__(cls, *args)
+
+        return obj.doit() if evaluate else obj
+
+    def __repr__(self):
+        systems_repr = ', '.join(repr(system) for system in self.args)
+        return f"Parallel({systems_repr})"
+
+    __str__ = __repr__
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel, Series
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> Parallel(G1, G2).var
+        p
+        >>> Parallel(-G3, Series(G1, G2)).var
+        p
+
+        """
+        return self.args[0].var
+
+    def doit(self, **hints):
+        """
+        Returns the resultant transfer function or state space obtained by
+        parallel connection of transfer functions or state space objects.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> Parallel(tf2, tf1).doit()
+        TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s)
+        >>> Parallel(-tf1, -tf2).doit()
+        TransferFunction((2 - s**3)*(-p + s) + (-a*p**2 - b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s)
+
+        """
+        if self._is_parallel_StateSpace:
+            # Return the equivalent StateSpace model
+            res = self.args[0].doit()
+            if not isinstance(res, StateSpace):
+                res = res.rewrite(StateSpace)
+            for arg in self.args[1:]:
+                if not isinstance(arg, StateSpace):
+                    arg = arg.doit().rewrite(StateSpace)
+                res += arg
+            return res
+
+        _arg = (arg.doit().to_expr() for arg in self.args)
+        res = Add(*_arg).as_numer_denom()
+        return TransferFunction(*res, self.var)
+
+    def _eval_rewrite_as_TransferFunction(self, *args, **kwargs):
+        if self._is_parallel_StateSpace:
+            return self.doit().rewrite(TransferFunction)[0][0]
+        return self.doit()
+
+    @_check_other_SISO
+    def __add__(self, other):
+
+        self_arg_list = list(self.args)
+        return Parallel(*self_arg_list, other)
+
+    __radd__ = __add__
+
+    @_check_other_SISO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_SISO
+    def __mul__(self, other):
+
+        if isinstance(other, Series):
+            arg_list = list(other.args)
+            return Series(self, *arg_list)
+
+        return Series(self, other)
+
+    def __neg__(self):
+        return Series(TransferFunction(-1, 1, self.var), self)
+
+    def to_expr(self):
+        """Returns the equivalent ``Expr`` object."""
+        return Add(*(arg.to_expr() for arg in self.args), evaluate=False)
+
+    @property
+    def is_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is less than or equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+        >>> tf2 = TransferFunction(p**2 - 4*p, p**3 + 3*s + 2, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> P1 = Parallel(-tf2, tf1)
+        >>> P1.is_proper
+        False
+        >>> P2 = Parallel(tf2, tf3)
+        >>> P2.is_proper
+        True
+
+        """
+        return self.doit().is_proper
+
+    @property
+    def is_strictly_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is strictly less than degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> P1 = Parallel(tf1, tf2)
+        >>> P1.is_strictly_proper
+        False
+        >>> P2 = Parallel(tf2, tf3)
+        >>> P2.is_strictly_proper
+        True
+
+        """
+        return self.doit().is_strictly_proper
+
+    @property
+    def is_biproper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(p**2, p + s, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> P1 = Parallel(tf1, -tf2)
+        >>> P1.is_biproper
+        True
+        >>> P2 = Parallel(tf2, tf3)
+        >>> P2.is_biproper
+        False
+
+        """
+        return self.doit().is_biproper
+
+    @property
+    def is_StateSpace_object(self):
+        return self._is_parallel_StateSpace
+
+
+class MIMOParallel(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing a parallel configuration of MIMO systems.
+
+    Parameters
+    ==========
+
+    args : MIMOLinearTimeInvariant
+        MIMO Systems in a parallel arrangement.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``MIMOParallel(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+
+        All MIMO systems passed do not have same shape.
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed, MIMO in this case.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunctionMatrix, MIMOParallel, StateSpace
+    >>> from sympy import Matrix, pprint
+    >>> expr_1 = 1/s
+    >>> expr_2 = s/(s**2-1)
+    >>> expr_3 = (2 + s)/(s**2 - 1)
+    >>> expr_4 = 5
+    >>> tfm_a = TransferFunctionMatrix.from_Matrix(Matrix([[expr_1, expr_2], [expr_3, expr_4]]), s)
+    >>> tfm_b = TransferFunctionMatrix.from_Matrix(Matrix([[expr_2, expr_1], [expr_4, expr_3]]), s)
+    >>> tfm_c = TransferFunctionMatrix.from_Matrix(Matrix([[expr_3, expr_4], [expr_1, expr_2]]), s)
+    >>> MIMOParallel(tfm_a, tfm_b, tfm_c)
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(1, s, s), TransferFunction(s, s**2 - 1, s)), (TransferFunction(s + 2, s**2 - 1, s), TransferFunction(5, 1, s)))), TransferFunctionMatrix(((TransferFunction(s, s**2 - 1, s), TransferFunction(1, s, s)), (TransferFunction(5, 1, s), TransferFunction(s + 2, s**2 - 1, s)))), TransferFunctionMatrix(((TransferFunction(s + 2, s**2 - 1, s), TransferFunction(5, 1, s)), (TransferFunction(1, s, s), TransferFunction(s, s**2 - 1, s)))))
+    >>> pprint(_, use_unicode=False)  #  For Better Visualization
+    [  1       s   ]      [  s       1   ]      [s + 2     5   ]
+    [  -     ------]      [------    -   ]      [------    -   ]
+    [  s      2    ]      [ 2        s   ]      [ 2        1   ]
+    [        s  - 1]      [s  - 1        ]      [s  - 1        ]
+    [              ]    + [              ]    + [              ]
+    [s + 2     5   ]      [  5     s + 2 ]      [  1       s   ]
+    [------    -   ]      [  -     ------]      [  -     ------]
+    [ 2        1   ]      [  1      2    ]      [  s      2    ]
+    [s  - 1        ]{t}   [        s  - 1]{t}   [        s  - 1]{t}
+    >>> MIMOParallel(tfm_a, tfm_b, tfm_c).doit()
+    TransferFunctionMatrix(((TransferFunction(s**2 + s*(2*s + 2) - 1, s*(s**2 - 1), s), TransferFunction(2*s**2 + 5*s*(s**2 - 1) - 1, s*(s**2 - 1), s)), (TransferFunction(s**2 + s*(s + 2) + 5*s*(s**2 - 1) - 1, s*(s**2 - 1), s), TransferFunction(5*s**2 + 2*s - 3, s**2 - 1, s))))
+    >>> pprint(_, use_unicode=False)
+    [       2                              2       / 2    \    ]
+    [      s  + s*(2*s + 2) - 1         2*s  + 5*s*\s  - 1/ - 1]
+    [      --------------------         -----------------------]
+    [             / 2    \                       / 2    \      ]
+    [           s*\s  - 1/                     s*\s  - 1/      ]
+    [                                                          ]
+    [ 2                   / 2    \             2               ]
+    [s  + s*(s + 2) + 5*s*\s  - 1/ - 1      5*s  + 2*s - 3     ]
+    [---------------------------------      --------------     ]
+    [              / 2    \                      2             ]
+    [            s*\s  - 1/                     s  - 1         ]{t}
+
+    ``MIMOParallel`` can also be used to connect MIMO ``StateSpace`` systems.
+
+    >>> A1 = Matrix([[4, 1], [2, -3]])
+    >>> B1 = Matrix([[5, 2], [-3, -3]])
+    >>> C1 = Matrix([[2, -4], [0, 1]])
+    >>> D1 = Matrix([[3, 2], [1, -1]])
+    >>> A2 = Matrix([[-3, 4, 2], [-1, -3, 0], [2, 5, 3]])
+    >>> B2 = Matrix([[1, 4], [-3, -3], [-2, 1]])
+    >>> C2 = Matrix([[4, 2, -3], [1, 4, 3]])
+    >>> D2 = Matrix([[-2, 4], [0, 1]])
+    >>> ss1 = StateSpace(A1, B1, C1, D1)
+    >>> ss2 = StateSpace(A2, B2, C2, D2)
+    >>> p1 = MIMOParallel(ss1, ss2)
+    >>> p1
+    MIMOParallel(StateSpace(Matrix([
+    [4,  1],
+    [2, -3]]), Matrix([
+    [ 5,  2],
+    [-3, -3]]), Matrix([
+    [2, -4],
+    [0,  1]]), Matrix([
+    [3,  2],
+    [1, -1]])), StateSpace(Matrix([
+    [-3,  4, 2],
+    [-1, -3, 0],
+    [ 2,  5, 3]]), Matrix([
+    [ 1,  4],
+    [-3, -3],
+    [-2,  1]]), Matrix([
+    [4, 2, -3],
+    [1, 4,  3]]), Matrix([
+    [-2, 4],
+    [ 0, 1]])))
+
+    ``doit()`` can be used to find ``StateSpace`` equivalent for the system containing ``StateSpace`` objects.
+
+    >>> p1.doit()
+    StateSpace(Matrix([
+    [4,  1,  0,  0, 0],
+    [2, -3,  0,  0, 0],
+    [0,  0, -3,  4, 2],
+    [0,  0, -1, -3, 0],
+    [0,  0,  2,  5, 3]]), Matrix([
+    [ 5,  2],
+    [-3, -3],
+    [ 1,  4],
+    [-3, -3],
+    [-2,  1]]), Matrix([
+    [2, -4, 4, 2, -3],
+    [0,  1, 1, 4,  3]]), Matrix([
+    [1, 6],
+    [1, 0]]))
+
+    Notes
+    =====
+
+    All the transfer function matrices should use the same complex variable
+    ``var`` of the Laplace transform.
+
+    See Also
+    ========
+
+    Parallel, MIMOSeries
+
+    """
+
+    def __new__(cls, *args, evaluate=False):
+
+        args = _flatten_args(args, MIMOParallel)
+
+        # For StateSpace Parallel connection
+        if args and any(isinstance(arg, StateSpace) or (hasattr(arg, 'is_StateSpace_object')
+                                    and arg.is_StateSpace_object) for arg in args):
+            if any(arg.num_inputs != args[0].num_inputs or arg.num_outputs != args[0].num_outputs
+                   for arg in args[1:]):
+                raise ShapeError("Systems with incompatible inputs and outputs cannot be "
+                                 "connected in MIMOParallel.")
+            cls._is_parallel_StateSpace = True
+        else:
+            cls._check_args(args)
+            if any(arg.shape != args[0].shape for arg in args):
+                raise TypeError("Shape of all the args is not equal.")
+            cls._is_parallel_StateSpace = False
+        obj = super().__new__(cls, *args)
+
+        return obj.doit() if evaluate else obj
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the systems.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOParallel
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> G4 = TransferFunction(p**2, p**2 - 1, p)
+        >>> tfm_a = TransferFunctionMatrix([[G1, G2], [G3, G4]])
+        >>> tfm_b = TransferFunctionMatrix([[G2, G1], [G4, G3]])
+        >>> MIMOParallel(tfm_a, tfm_b).var
+        p
+
+        """
+        return self.args[0].var
+
+    @property
+    def num_inputs(self):
+        """Returns the number of input signals of the parallel system."""
+        return self.args[0].num_inputs
+
+    @property
+    def num_outputs(self):
+        """Returns the number of output signals of the parallel system."""
+        return self.args[0].num_outputs
+
+    @property
+    def shape(self):
+        """Returns the shape of the equivalent MIMO system."""
+        return self.num_outputs, self.num_inputs
+
+    @property
+    def is_StateSpace_object(self):
+        return self._is_parallel_StateSpace
+
+    def doit(self, **hints):
+        """
+        Returns the resultant transfer function matrix or StateSpace obtained after evaluating
+        the MIMO systems arranged in a parallel configuration.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, MIMOParallel, TransferFunctionMatrix
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> tfm_2 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf2]])
+        >>> MIMOParallel(tfm_1, tfm_2).doit()
+        TransferFunctionMatrix(((TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s), TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s)), (TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s), TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s))))
+
+        """
+        if self._is_parallel_StateSpace:
+            # Return the equivalent StateSpace model.
+            res = self.args[0]
+            if not isinstance(res, StateSpace):
+                res = res.doit().rewrite(StateSpace)
+            for arg in self.args[1:]:
+                if not isinstance(arg, StateSpace):
+                    arg = arg.doit().rewrite(StateSpace)
+                else:
+                    arg = arg.doit()
+                res += arg
+            return res
+        _arg = (arg.doit()._expr_mat for arg in self.args)
+        res = MatAdd(*_arg, evaluate=True)
+        return TransferFunctionMatrix.from_Matrix(res, self.var)
+
+    def _eval_rewrite_as_TransferFunctionMatrix(self, *args, **kwargs):
+        if self._is_parallel_StateSpace:
+            return self.doit().rewrite(TransferFunction)
+        return self.doit()
+
+    @_check_other_MIMO
+    def __add__(self, other):
+
+        self_arg_list = list(self.args)
+        return MIMOParallel(*self_arg_list, other)
+
+    __radd__ = __add__
+
+    @_check_other_MIMO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_MIMO
+    def __mul__(self, other):
+
+        if isinstance(other, MIMOSeries):
+            arg_list = list(other.args)
+            return MIMOSeries(*arg_list, self)
+
+        return MIMOSeries(other, self)
+
+    def __neg__(self):
+        arg_list = [-arg for arg in list(self.args)]
+        return MIMOParallel(*arg_list)
+
+
+class Feedback(SISOLinearTimeInvariant):
+    r"""
+    A class for representing closed-loop feedback interconnection between two
+    SISO input/output systems.
+
+    The first argument, ``sys1``, is the feedforward part of the closed-loop
+    system or in simple words, the dynamical model representing the process
+    to be controlled. The second argument, ``sys2``, is the feedback system
+    and controls the fed back signal to ``sys1``. Both ``sys1`` and ``sys2``
+    can either be ``Series``, ``StateSpace`` or ``TransferFunction`` objects.
+
+    Parameters
+    ==========
+
+    sys1 : Series, StateSpace, TransferFunction
+        The feedforward path system.
+    sys2 : Series, StateSpace, TransferFunction, optional
+        The feedback path system (often a feedback controller).
+        It is the model sitting on the feedback path.
+
+        If not specified explicitly, the sys2 is
+        assumed to be unit (1.0) transfer function.
+    sign : int, optional
+        The sign of feedback. Can either be ``1``
+        (for positive feedback) or ``-1`` (for negative feedback).
+        Default value is `-1`.
+
+    Raises
+    ======
+
+    ValueError
+        When ``sys1`` and ``sys2`` are not using the
+        same complex variable of the Laplace transform.
+
+        When a combination of ``sys1`` and ``sys2`` yields
+        zero denominator.
+
+    TypeError
+        When either ``sys1`` or ``sys2`` is not a ``Series``, ``StateSpace`` or
+        ``TransferFunction`` object.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import StateSpace, TransferFunction, Feedback
+    >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+    >>> controller = TransferFunction(5*s - 10, s + 7, s)
+    >>> F1 = Feedback(plant, controller)
+    >>> F1
+    Feedback(TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s), TransferFunction(5*s - 10, s + 7, s), -1)
+    >>> F1.var
+    s
+    >>> F1.args
+    (TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s), TransferFunction(5*s - 10, s + 7, s), -1)
+
+    You can get the feedforward and feedback path systems by using ``.sys1`` and ``.sys2`` respectively.
+
+    >>> F1.sys1
+    TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+    >>> F1.sys2
+    TransferFunction(5*s - 10, s + 7, s)
+
+    You can get the resultant closed loop transfer function obtained by negative feedback
+    interconnection using ``.doit()`` method.
+
+    >>> F1.doit()
+    TransferFunction((s + 7)*(s**2 - 4*s + 2)*(3*s**2 + 7*s - 3), ((s + 7)*(s**2 - 4*s + 2) + (5*s - 10)*(3*s**2 + 7*s - 3))*(s**2 - 4*s + 2), s)
+    >>> G = TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s)
+    >>> C = TransferFunction(5*s + 10, s + 10, s)
+    >>> F2 = Feedback(G*C, TransferFunction(1, 1, s))
+    >>> F2.doit()
+    TransferFunction((s + 10)*(5*s + 10)*(s**2 + 2*s + 3)*(2*s**2 + 5*s + 1), (s + 10)*((s + 10)*(s**2 + 2*s + 3) + (5*s + 10)*(2*s**2 + 5*s + 1))*(s**2 + 2*s + 3), s)
+
+    To negate a ``Feedback`` object, the ``-`` operator can be prepended:
+
+    >>> -F1
+    Feedback(TransferFunction(-3*s**2 - 7*s + 3, s**2 - 4*s + 2, s), TransferFunction(10 - 5*s, s + 7, s), -1)
+    >>> -F2
+    Feedback(Series(TransferFunction(-1, 1, s), TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s), TransferFunction(5*s + 10, s + 10, s)), TransferFunction(-1, 1, s), -1)
+
+    ``Feedback`` can also be used to connect SISO ``StateSpace`` systems together.
+
+    >>> A1 = Matrix([[-1]])
+    >>> B1 = Matrix([[1]])
+    >>> C1 = Matrix([[-1]])
+    >>> D1 = Matrix([1])
+    >>> A2 = Matrix([[0]])
+    >>> B2 = Matrix([[1]])
+    >>> C2 = Matrix([[1]])
+    >>> D2 = Matrix([[0]])
+    >>> ss1 = StateSpace(A1, B1, C1, D1)
+    >>> ss2 = StateSpace(A2, B2, C2, D2)
+    >>> F3 = Feedback(ss1, ss2)
+    >>> F3
+    Feedback(StateSpace(Matrix([[-1]]), Matrix([[1]]), Matrix([[-1]]), Matrix([[1]])), StateSpace(Matrix([[0]]), Matrix([[1]]), Matrix([[1]]), Matrix([[0]])), -1)
+
+    ``doit()`` can be used to find ``StateSpace`` equivalent for the system containing ``StateSpace`` objects.
+
+    >>> F3.doit()
+    StateSpace(Matrix([
+    [-1, -1],
+    [-1, -1]]), Matrix([
+    [1],
+    [1]]), Matrix([[-1, -1]]), Matrix([[1]]))
+
+    We can also find the equivalent ``TransferFunction`` by using ``rewrite(TransferFunction)`` method.
+
+    >>> F3.rewrite(TransferFunction)
+    TransferFunction(s, s + 2, s)
+
+    See Also
+    ========
+
+    MIMOFeedback, Series, Parallel
+
+    """
+    def __new__(cls, sys1, sys2=None, sign=-1):
+        if not sys2:
+            sys2 = TransferFunction(1, 1, sys1.var)
+
+        if not isinstance(sys1, (TransferFunction, Series, StateSpace, Feedback)):
+            raise TypeError("Unsupported type for `sys1` in Feedback.")
+
+        if not isinstance(sys2, (TransferFunction, Series, StateSpace, Feedback)):
+            raise TypeError("Unsupported type for `sys2` in Feedback.")
+
+        if not (sys1.num_inputs == sys1.num_outputs == sys2.num_inputs ==
+                sys2.num_outputs == 1):
+            raise ValueError("""To use Feedback connection for MIMO systems
+                            use MIMOFeedback instead.""")
+
+        if sign not in [-1, 1]:
+            raise ValueError(filldedent("""
+                Unsupported type for feedback. `sign` arg should
+                either be 1 (positive feedback loop) or -1
+                (negative feedback loop)."""))
+
+        if sys1.is_StateSpace_object or sys2.is_StateSpace_object:
+            cls.is_StateSpace_object = True
+        else:
+            if Mul(sys1.to_expr(), sys2.to_expr()).simplify() == sign:
+                raise ValueError("The equivalent system will have zero denominator.")
+            if sys1.var != sys2.var:
+                raise ValueError(filldedent("""Both `sys1` and `sys2` should be using the
+                same complex variable."""))
+            cls.is_StateSpace_object = False
+
+        return super(SISOLinearTimeInvariant, cls).__new__(cls, sys1, sys2, _sympify(sign))
+
+    def __repr__(self):
+        return f"Feedback({self.sys1}, {self.sys2}, {self.sign})"
+
+    __str__ = __repr__
+
+    @property
+    def sys1(self):
+        """
+        Returns the feedforward system of the feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.sys1
+        TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p)
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - s, p + 2, p)
+        >>> F2 = Feedback(TransferFunction(1, 1, p), G*C*P)
+        >>> F2.sys1
+        TransferFunction(1, 1, p)
+
+        """
+        return self.args[0]
+
+    @property
+    def sys2(self):
+        """
+        Returns the feedback controller of the feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.sys2
+        TransferFunction(5*s - 10, s + 7, s)
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p)
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - s, p + 2, p)
+        >>> F2 = Feedback(TransferFunction(1, 1, p), G*C*P)
+        >>> F2.sys2
+        Series(TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p), TransferFunction(5*p + 10, p + 10, p), TransferFunction(1 - s, p + 2, p))
+
+        """
+        return self.args[1]
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable of the Laplace transform used by all
+        the transfer functions involved in the feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.var
+        s
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p)
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - s, p + 2, p)
+        >>> F2 = Feedback(TransferFunction(1, 1, p), G*C*P)
+        >>> F2.var
+        p
+
+        """
+        return self.sys1.var
+
+    @property
+    def sign(self):
+        """
+        Returns the type of MIMO Feedback model. ``1``
+        for Positive and ``-1`` for Negative.
+        """
+        return self.args[2]
+
+    @property
+    def num(self):
+        """
+        Returns the numerator of the closed loop feedback system.
+        """
+        return self.sys1
+
+    @property
+    def den(self):
+        """
+        Returns the denominator of the closed loop feedback model.
+        """
+        unit = TransferFunction(1, 1, self.var)
+        arg_list = list(self.sys1.args) if isinstance(self.sys1, Series) else [self.sys1]
+        if self.sign == 1:
+            return Parallel(unit, -Series(self.sys2, *arg_list))
+        return Parallel(unit, Series(self.sys2, *arg_list))
+
+    @property
+    def sensitivity(self):
+        """
+        Returns the sensitivity function of the feedback loop.
+
+        Sensitivity of a Feedback system is the ratio
+        of change in the open loop gain to the change in
+        the closed loop gain.
+
+        .. note::
+            This method would not return the complementary
+            sensitivity function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - p, p + 2, p)
+        >>> F_1 = Feedback(P, C)
+        >>> F_1.sensitivity
+        1/((1 - p)*(5*p + 10)/((p + 2)*(p + 10)) + 1)
+
+        """
+
+        return 1/(1 - self.sign*self.sys1.to_expr()*self.sys2.to_expr())
+
+    def doit(self, cancel=False, expand=False, **hints):
+        """
+        Returns the resultant transfer function or state space obtained by
+        feedback connection of transfer functions or state space objects.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback, StateSpace
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.doit()
+        TransferFunction((s + 7)*(s**2 - 4*s + 2)*(3*s**2 + 7*s - 3), ((s + 7)*(s**2 - 4*s + 2) + (5*s - 10)*(3*s**2 + 7*s - 3))*(s**2 - 4*s + 2), s)
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s)
+        >>> F2 = Feedback(G, TransferFunction(1, 1, s))
+        >>> F2.doit()
+        TransferFunction((s**2 + 2*s + 3)*(2*s**2 + 5*s + 1), (s**2 + 2*s + 3)*(3*s**2 + 7*s + 4), s)
+
+        Use kwarg ``expand=True`` to expand the resultant transfer function.
+        Use ``cancel=True`` to cancel out the common terms in numerator and
+        denominator.
+
+        >>> F2.doit(cancel=True, expand=True)
+        TransferFunction(2*s**2 + 5*s + 1, 3*s**2 + 7*s + 4, s)
+        >>> F2.doit(expand=True)
+        TransferFunction(2*s**4 + 9*s**3 + 17*s**2 + 17*s + 3, 3*s**4 + 13*s**3 + 27*s**2 + 29*s + 12, s)
+
+        If the connection contain any ``StateSpace`` object then ``doit()``
+        will return the equivalent ``StateSpace`` object.
+
+        >>> A1 = Matrix([[-1.5, -2], [1, 0]])
+        >>> B1 = Matrix([0.5, 0])
+        >>> C1 = Matrix([[0, 1]])
+        >>> A2 = Matrix([[0, 1], [-5, -2]])
+        >>> B2 = Matrix([0, 3])
+        >>> C2 = Matrix([[0, 1]])
+        >>> ss1 = StateSpace(A1, B1, C1)
+        >>> ss2 = StateSpace(A2, B2, C2)
+        >>> F3 = Feedback(ss1, ss2)
+        >>> F3.doit()
+        StateSpace(Matrix([
+        [-1.5, -2,  0, -0.5],
+        [   1,  0,  0,    0],
+        [   0,  0,  0,    1],
+        [   0,  3, -5,   -2]]), Matrix([
+        [0.5],
+        [  0],
+        [  0],
+        [  0]]), Matrix([[0, 1, 0, 0]]), Matrix([[0]]))
+
+        """
+        if self.is_StateSpace_object:
+            sys1_ss = self.sys1.doit().rewrite(StateSpace)
+            sys2_ss = self.sys2.doit().rewrite(StateSpace)
+            A1, B1, C1, D1 = sys1_ss.A, sys1_ss.B, sys1_ss.C, sys1_ss.D
+            A2, B2, C2, D2 = sys2_ss.A, sys2_ss.B, sys2_ss.C, sys2_ss.D
+
+            # Create identity matrices
+            I_inputs = eye(self.num_inputs)
+            I_outputs = eye(self.num_outputs)
+
+            # Compute F and its inverse
+            F = I_inputs - self.sign * D2 * D1
+            E = F.inv()
+
+            # Compute intermediate matrices
+            E_D2 = E * D2
+            E_C2 = E * C2
+            T1 = I_outputs + self.sign * D1 * E_D2
+            T2 = I_inputs + self.sign * E_D2 * D1
+            A = Matrix.vstack(
+            Matrix.hstack(A1 + self.sign * B1 * E_D2 * C1, self.sign * B1 * E_C2),
+            Matrix.hstack(B2 * T1 * C1, A2 + self.sign * B2 * D1 * E_C2)
+            )
+            B = Matrix.vstack(B1 * T2, B2 * D1 * T2)
+            C = Matrix.hstack(T1 * C1, self.sign * D1 * E_C2)
+            D = D1 * T2
+            return StateSpace(A, B, C, D)
+
+        arg_list = list(self.sys1.args) if isinstance(self.sys1, Series) else [self.sys1]
+        # F_n and F_d are resultant TFs of num and den of Feedback.
+        F_n, unit = self.sys1.doit(), TransferFunction(1, 1, self.sys1.var)
+        if self.sign == -1:
+            F_d = Parallel(unit, Series(self.sys2, *arg_list)).doit()
+        else:
+            F_d = Parallel(unit, -Series(self.sys2, *arg_list)).doit()
+
+        _resultant_tf = TransferFunction(F_n.num * F_d.den, F_n.den * F_d.num, F_n.var)
+
+        if cancel:
+            _resultant_tf = _resultant_tf.simplify()
+
+        if expand:
+            _resultant_tf = _resultant_tf.expand()
+
+        return _resultant_tf
+
+    def _eval_rewrite_as_TransferFunction(self, num, den, sign, **kwargs):
+        if self.is_StateSpace_object:
+            return self.doit().rewrite(TransferFunction)[0][0]
+        return self.doit()
+
+    def to_expr(self):
+        """
+        Converts a ``Feedback`` object to SymPy Expr.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> from sympy import Expr
+        >>> tf1 = TransferFunction(a+s, 1, s)
+        >>> tf2 = TransferFunction(b+s, 1, s)
+        >>> fd1 = Feedback(tf1, tf2)
+        >>> fd1.to_expr()
+        (a + s)/((a + s)*(b + s) + 1)
+        >>> isinstance(_, Expr)
+        True
+        """
+
+        return self.doit().to_expr()
+
+    def __neg__(self):
+        return Feedback(-self.sys1, -self.sys2, self.sign)
+
+
+def _is_invertible(a, b, sign):
+    """
+    Checks whether a given pair of MIMO
+    systems passed is invertible or not.
+    """
+    _mat = eye(a.num_outputs) - sign*(a.doit()._expr_mat)*(b.doit()._expr_mat)
+    _det = _mat.det()
+
+    return _det != 0
+
+
+class MIMOFeedback(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing closed-loop feedback interconnection between two
+    MIMO input/output systems.
+
+    Parameters
+    ==========
+
+    sys1 : MIMOSeries, TransferFunctionMatrix, StateSpace
+        The MIMO system placed on the feedforward path.
+    sys2 : MIMOSeries, TransferFunctionMatrix, StateSpace
+        The system placed on the feedback path
+        (often a feedback controller).
+    sign : int, optional
+        The sign of feedback. Can either be ``1``
+        (for positive feedback) or ``-1`` (for negative feedback).
+        Default value is `-1`.
+
+    Raises
+    ======
+
+    ValueError
+        When ``sys1`` and ``sys2`` are not using the
+        same complex variable of the Laplace transform.
+
+        Forward path model should have an equal number of inputs/outputs
+        to the feedback path outputs/inputs.
+
+        When product of ``sys1`` and ``sys2`` is not a square matrix.
+
+        When the equivalent MIMO system is not invertible.
+
+    TypeError
+        When either ``sys1`` or ``sys2`` is not a ``MIMOSeries``,
+        ``TransferFunctionMatrix`` or a ``StateSpace`` object.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, pprint
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import StateSpace, TransferFunctionMatrix, MIMOFeedback
+    >>> plant_mat = Matrix([[1, 1/s], [0, 1]])
+    >>> controller_mat = Matrix([[10, 0], [0, 10]])  # Constant Gain
+    >>> plant = TransferFunctionMatrix.from_Matrix(plant_mat, s)
+    >>> controller = TransferFunctionMatrix.from_Matrix(controller_mat, s)
+    >>> feedback = MIMOFeedback(plant, controller)  # Negative Feedback (default)
+    >>> pprint(feedback, use_unicode=False)
+    /    [1  1]    [10  0 ]   \-1   [1  1]
+    |    [-  -]    [--  - ]   |     [-  -]
+    |    [1  s]    [1   1 ]   |     [1  s]
+    |I + [    ]   *[      ]   |   * [    ]
+    |    [0  1]    [0   10]   |     [0  1]
+    |    [-  -]    [-   --]   |     [-  -]
+    \    [1  1]{t} [1   1 ]{t}/     [1  1]{t}
+
+    To get the equivalent system matrix, use either ``doit`` or ``rewrite`` method.
+
+    >>> pprint(feedback.doit(), use_unicode=False)
+    [1     1  ]
+    [--  -----]
+    [11  121*s]
+    [         ]
+    [0    1   ]
+    [-    --  ]
+    [1    11  ]{t}
+
+    To negate the ``MIMOFeedback`` object, use ``-`` operator.
+
+    >>> neg_feedback = -feedback
+    >>> pprint(neg_feedback.doit(), use_unicode=False)
+    [-1    -1  ]
+    [---  -----]
+    [11   121*s]
+    [          ]
+    [ 0    -1  ]
+    [ -    --- ]
+    [ 1    11  ]{t}
+
+    ``MIMOFeedback`` can also be used to connect MIMO ``StateSpace`` systems.
+
+    >>> A1 = Matrix([[4, 1], [2, -3]])
+    >>> B1 = Matrix([[5, 2], [-3, -3]])
+    >>> C1 = Matrix([[2, -4], [0, 1]])
+    >>> D1 = Matrix([[3, 2], [1, -1]])
+    >>> A2 = Matrix([[-3, 4, 2], [-1, -3, 0], [2, 5, 3]])
+    >>> B2 = Matrix([[1, 4], [-3, -3], [-2, 1]])
+    >>> C2 = Matrix([[4, 2, -3], [1, 4, 3]])
+    >>> D2 = Matrix([[-2, 4], [0, 1]])
+    >>> ss1 = StateSpace(A1, B1, C1, D1)
+    >>> ss2 = StateSpace(A2, B2, C2, D2)
+    >>> F1 = MIMOFeedback(ss1, ss2)
+    >>> F1
+    MIMOFeedback(StateSpace(Matrix([
+    [4,  1],
+    [2, -3]]), Matrix([
+    [ 5,  2],
+    [-3, -3]]), Matrix([
+    [2, -4],
+    [0,  1]]), Matrix([
+    [3,  2],
+    [1, -1]])), StateSpace(Matrix([
+    [-3,  4, 2],
+    [-1, -3, 0],
+    [ 2,  5, 3]]), Matrix([
+    [ 1,  4],
+    [-3, -3],
+    [-2,  1]]), Matrix([
+    [4, 2, -3],
+    [1, 4,  3]]), Matrix([
+    [-2, 4],
+    [ 0, 1]])), -1)
+
+    ``doit()`` can be used to find ``StateSpace`` equivalent for the system containing ``StateSpace`` objects.
+
+    >>> F1.doit()
+    StateSpace(Matrix([
+    [   3,  -3/4, -15/4, -37/2, -15],
+    [ 7/2, -39/8,   9/8,  39/4,   9],
+    [   3, -41/4, -45/4, -51/2, -19],
+    [-9/2, 129/8,  73/8, 171/4,  36],
+    [-3/2,  47/8,  31/8,  85/4,  18]]), Matrix([
+    [-1/4,  19/4],
+    [ 3/8, -21/8],
+    [ 1/4,  29/4],
+    [ 3/8, -93/8],
+    [ 5/8, -35/8]]), Matrix([
+    [  1, -15/4,  -7/4, -21/2, -9],
+    [1/2, -13/8, -13/8, -19/4, -3]]), Matrix([
+    [-1/4, 11/4],
+    [ 1/8,  9/8]]))
+
+    See Also
+    ========
+
+    Feedback, MIMOSeries, MIMOParallel
+
+    """
+    def __new__(cls, sys1, sys2, sign=-1):
+        if not isinstance(sys1, (TransferFunctionMatrix, MIMOSeries, StateSpace)):
+            raise TypeError("Unsupported type for `sys1` in MIMO Feedback.")
+
+        if not isinstance(sys2, (TransferFunctionMatrix, MIMOSeries, StateSpace)):
+            raise TypeError("Unsupported type for `sys2` in MIMO Feedback.")
+
+        if sys1.num_inputs != sys2.num_outputs or \
+            sys1.num_outputs != sys2.num_inputs:
+            raise ValueError(filldedent("""
+                Product of `sys1` and `sys2` must
+                yield a square matrix."""))
+
+        if sign not in (-1, 1):
+            raise ValueError(filldedent("""
+                Unsupported type for feedback. `sign` arg should
+                either be 1 (positive feedback loop) or -1
+                (negative feedback loop)."""))
+
+        if sys1.is_StateSpace_object or sys2.is_StateSpace_object:
+            cls.is_StateSpace_object = True
+        else:
+            if not _is_invertible(sys1, sys2, sign):
+                raise ValueError("Non-Invertible system inputted.")
+            cls.is_StateSpace_object = False
+
+        if not cls.is_StateSpace_object and sys1.var != sys2.var:
+            raise ValueError(filldedent("""
+                Both `sys1` and `sys2` should be using the
+                same complex variable."""))
+
+        return super().__new__(cls, sys1, sys2, _sympify(sign))
+
+    @property
+    def sys1(self):
+        r"""
+        Returns the system placed on the feedforward path of the MIMO feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(s**2 + s + 1, s**2 - s + 1, s)
+        >>> tf2 = TransferFunction(1, s, s)
+        >>> tf3 = TransferFunction(1, 1, s)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf3, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)
+        >>> F_1.sys1
+        TransferFunctionMatrix(((TransferFunction(s**2 + s + 1, s**2 - s + 1, s), TransferFunction(1, s, s)), (TransferFunction(1, s, s), TransferFunction(s**2 + s + 1, s**2 - s + 1, s))))
+        >>> pprint(_, use_unicode=False)
+        [ 2                    ]
+        [s  + s + 1      1     ]
+        [----------      -     ]
+        [ 2              s     ]
+        [s  - s + 1            ]
+        [                      ]
+        [             2        ]
+        [    1       s  + s + 1]
+        [    -       ----------]
+        [    s        2        ]
+        [            s  - s + 1]{t}
+
+        """
+        return self.args[0]
+
+    @property
+    def sys2(self):
+        r"""
+        Returns the feedback controller of the MIMO feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(s**2, s**3 - s + 1, s)
+        >>> tf2 = TransferFunction(1, s, s)
+        >>> tf3 = TransferFunction(1, 1, s)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2)
+        >>> F_1.sys2
+        TransferFunctionMatrix(((TransferFunction(s**2, s**3 - s + 1, s), TransferFunction(1, 1, s)), (TransferFunction(1, 1, s), TransferFunction(1, s, s))))
+        >>> pprint(_, use_unicode=False)
+        [     2       ]
+        [    s       1]
+        [----------  -]
+        [ 3          1]
+        [s  - s + 1   ]
+        [             ]
+        [    1       1]
+        [    -       -]
+        [    1       s]{t}
+
+        """
+        return self.args[1]
+
+    @property
+    def var(self):
+        r"""
+        Returns the complex variable of the Laplace transform used by all
+        the transfer functions involved in the MIMO feedback loop.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(p, 1 - p, p)
+        >>> tf2 = TransferFunction(1, p, p)
+        >>> tf3 = TransferFunction(1, 1, p)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)  # Positive feedback
+        >>> F_1.var
+        p
+
+        """
+        return self.sys1.var
+
+    @property
+    def sign(self):
+        r"""
+        Returns the type of feedback interconnection of two models. ``1``
+        for Positive and ``-1`` for Negative.
+        """
+        return self.args[2]
+
+    @property
+    def sensitivity(self):
+        r"""
+        Returns the sensitivity function matrix of the feedback loop.
+
+        Sensitivity of a closed-loop system is the ratio of change
+        in the open loop gain to the change in the closed loop gain.
+
+        .. note::
+            This method would not return the complementary
+            sensitivity function.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(p, 1 - p, p)
+        >>> tf2 = TransferFunction(1, p, p)
+        >>> tf3 = TransferFunction(1, 1, p)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)  # Positive feedback
+        >>> F_2 = MIMOFeedback(sys1, sys2)  # Negative feedback
+        >>> pprint(F_1.sensitivity, use_unicode=False)
+        [   4      3      2               5      4      2           ]
+        [- p  + 3*p  - 4*p  + 3*p - 1    p  - 2*p  + 3*p  - 3*p + 1 ]
+        [----------------------------  -----------------------------]
+        [  4      3      2              5      4      3      2      ]
+        [ p  + 3*p  - 8*p  + 8*p - 3   p  + 3*p  - 8*p  + 8*p  - 3*p]
+        [                                                           ]
+        [       4    3    2                  3      2               ]
+        [      p  - p  - p  + p           3*p  - 6*p  + 4*p - 1     ]
+        [ --------------------------    --------------------------  ]
+        [  4      3      2               4      3      2            ]
+        [ p  + 3*p  - 8*p  + 8*p - 3    p  + 3*p  - 8*p  + 8*p - 3  ]
+        >>> pprint(F_2.sensitivity, use_unicode=False)
+        [ 4      3      2           5      4      2          ]
+        [p  - 3*p  + 2*p  + p - 1  p  - 2*p  + 3*p  - 3*p + 1]
+        [------------------------  --------------------------]
+        [   4      3                   5      4      2       ]
+        [  p  - 3*p  + 2*p - 1        p  - 3*p  + 2*p  - p   ]
+        [                                                    ]
+        [     4    3    2               4      3             ]
+        [    p  - p  - p  + p        2*p  - 3*p  + 2*p - 1   ]
+        [  -------------------       ---------------------   ]
+        [   4      3                   4      3              ]
+        [  p  - 3*p  + 2*p - 1        p  - 3*p  + 2*p - 1    ]
+
+        """
+        _sys1_mat = self.sys1.doit()._expr_mat
+        _sys2_mat = self.sys2.doit()._expr_mat
+
+        return (eye(self.sys1.num_inputs) - \
+            self.sign*_sys1_mat*_sys2_mat).inv()
+
+    @property
+    def num_inputs(self):
+        """Returns the number of inputs of the system."""
+        return self.sys1.num_inputs
+
+    @property
+    def num_outputs(self):
+        """Returns the number of outputs of the system."""
+        return self.sys1.num_outputs
+
+    def doit(self, cancel=True, expand=False, **hints):
+        r"""
+        Returns the resultant transfer function matrix obtained by the
+        feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(s, 1 - s, s)
+        >>> tf2 = TransferFunction(1, s, s)
+        >>> tf3 = TransferFunction(5, 1, s)
+        >>> tf4 = TransferFunction(s - 1, s, s)
+        >>> tf5 = TransferFunction(0, 1, s)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+        >>> sys2 = TransferFunctionMatrix([[tf3, tf5], [tf5, tf5]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)
+        >>> pprint(F_1, use_unicode=False)
+        /    [  s      1  ]    [5  0]   \-1   [  s      1  ]
+        |    [-----    -  ]    [-  -]   |     [-----    -  ]
+        |    [1 - s    s  ]    [1  1]   |     [1 - s    s  ]
+        |I - [            ]   *[    ]   |   * [            ]
+        |    [  5    s - 1]    [0  0]   |     [  5    s - 1]
+        |    [  -    -----]    [-  -]   |     [  -    -----]
+        \    [  1      s  ]{t} [1  1]{t}/     [  1      s  ]{t}
+        >>> pprint(F_1.doit(), use_unicode=False)
+        [  -s           s - 1       ]
+        [-------     -----------    ]
+        [6*s - 1     s*(6*s - 1)    ]
+        [                           ]
+        [5*s - 5  (s - 1)*(6*s + 24)]
+        [-------  ------------------]
+        [6*s - 1     s*(6*s - 1)    ]{t}
+
+        If the user wants the resultant ``TransferFunctionMatrix`` object without
+        canceling the common factors then the ``cancel`` kwarg should be passed ``False``.
+
+        >>> pprint(F_1.doit(cancel=False), use_unicode=False)
+        [             s*(s - 1)                              s - 1               ]
+        [         -----------------                       -----------            ]
+        [         (1 - s)*(6*s - 1)                       s*(6*s - 1)            ]
+        [                                                                        ]
+        [s*(25*s - 25) + 5*(1 - s)*(6*s - 1)  s*(s - 1)*(6*s - 1) + s*(25*s - 25)]
+        [-----------------------------------  -----------------------------------]
+        [         (1 - s)*(6*s - 1)                        2                     ]
+        [                                                 s *(6*s - 1)           ]{t}
+
+        If the user wants the expanded form of the resultant transfer function matrix,
+        the ``expand`` kwarg should be passed as ``True``.
+
+        >>> pprint(F_1.doit(expand=True), use_unicode=False)
+        [  -s          s - 1      ]
+        [-------      --------    ]
+        [6*s - 1         2        ]
+        [             6*s  - s    ]
+        [                         ]
+        [            2            ]
+        [5*s - 5  6*s  + 18*s - 24]
+        [-------  ----------------]
+        [6*s - 1         2        ]
+        [             6*s  - s    ]{t}
+
+        """
+        if self.is_StateSpace_object:
+            sys1_ss = self.sys1.doit().rewrite(StateSpace)
+            sys2_ss = self.sys2.doit().rewrite(StateSpace)
+            A1, B1, C1, D1 = sys1_ss.A, sys1_ss.B, sys1_ss.C, sys1_ss.D
+            A2, B2, C2, D2 = sys2_ss.A, sys2_ss.B, sys2_ss.C, sys2_ss.D
+
+            # Create identity matrices
+            I_inputs = eye(self.num_inputs)
+            I_outputs = eye(self.num_outputs)
+
+            # Compute F and its inverse
+            F = I_inputs - self.sign * D2 * D1
+            E = F.inv()
+
+            # Compute intermediate matrices
+            E_D2 = E * D2
+            E_C2 = E * C2
+            T1 = I_outputs + self.sign * D1 * E_D2
+            T2 = I_inputs + self.sign * E_D2 * D1
+            A = Matrix.vstack(
+            Matrix.hstack(A1 + self.sign * B1 * E_D2 * C1, self.sign * B1 * E_C2),
+            Matrix.hstack(B2 * T1 * C1, A2 + self.sign * B2 * D1 * E_C2)
+            )
+            B = Matrix.vstack(B1 * T2, B2 * D1 * T2)
+            C = Matrix.hstack(T1 * C1, self.sign * D1 * E_C2)
+            D = D1 * T2
+            return StateSpace(A, B, C, D)
+
+        _mat = self.sensitivity * self.sys1.doit()._expr_mat
+
+        _resultant_tfm = _to_TFM(_mat, self.var)
+
+        if cancel:
+            _resultant_tfm = _resultant_tfm.simplify()
+
+        if expand:
+            _resultant_tfm = _resultant_tfm.expand()
+
+        return _resultant_tfm
+
+    def _eval_rewrite_as_TransferFunctionMatrix(self, sys1, sys2, sign, **kwargs):
+        return self.doit()
+
+    def __neg__(self):
+        return MIMOFeedback(-self.sys1, -self.sys2, self.sign)
+
+
+def _to_TFM(mat, var):
+    """Private method to convert ImmutableMatrix to TransferFunctionMatrix efficiently"""
+    to_tf = lambda expr: TransferFunction.from_rational_expression(expr, var)
+    arg = [[to_tf(expr) for expr in row] for row in mat.tolist()]
+    return TransferFunctionMatrix(arg)
+
+
+class TransferFunctionMatrix(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing the MIMO (multiple-input and multiple-output)
+    generalization of the SISO (single-input and single-output) transfer function.
+
+    It is a matrix of transfer functions (``TransferFunction``, SISO-``Series`` or SISO-``Parallel``).
+    There is only one argument, ``arg`` which is also the compulsory argument.
+    ``arg`` is expected to be strictly of the type list of lists
+    which holds the transfer functions or reducible to transfer functions.
+
+    Parameters
+    ==========
+
+    arg : Nested ``List`` (strictly).
+        Users are expected to input a nested list of ``TransferFunction``, ``Series``
+        and/or ``Parallel`` objects.
+
+    Examples
+    ========
+
+    .. note::
+        ``pprint()`` can be used for better visualization of ``TransferFunctionMatrix`` objects.
+
+    >>> from sympy.abc import s, p, a
+    >>> from sympy import pprint
+    >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, Series, Parallel
+    >>> tf_1 = TransferFunction(s + a, s**2 + s + 1, s)
+    >>> tf_2 = TransferFunction(p**4 - 3*p + 2, s + p, s)
+    >>> tf_3 = TransferFunction(3, s + 2, s)
+    >>> tf_4 = TransferFunction(-a + p, 9*s - 9, s)
+    >>> tfm_1 = TransferFunctionMatrix([[tf_1], [tf_2], [tf_3]])
+    >>> tfm_1
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(3, s + 2, s),)))
+    >>> tfm_1.var
+    s
+    >>> tfm_1.num_inputs
+    1
+    >>> tfm_1.num_outputs
+    3
+    >>> tfm_1.shape
+    (3, 1)
+    >>> tfm_1.args
+    (((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(3, s + 2, s),)),)
+    >>> tfm_2 = TransferFunctionMatrix([[tf_1, -tf_3], [tf_2, -tf_1], [tf_3, -tf_2]])
+    >>> tfm_2
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s), TransferFunction(-3, s + 2, s)), (TransferFunction(p**4 - 3*p + 2, p + s, s), TransferFunction(-a - s, s**2 + s + 1, s)), (TransferFunction(3, s + 2, s), TransferFunction(-p**4 + 3*p - 2, p + s, s))))
+    >>> pprint(tfm_2, use_unicode=False)  # pretty-printing for better visualization
+    [   a + s           -3       ]
+    [ ----------       -----     ]
+    [  2               s + 2     ]
+    [ s  + s + 1                 ]
+    [                            ]
+    [ 4                          ]
+    [p  - 3*p + 2      -a - s    ]
+    [------------    ----------  ]
+    [   p + s         2          ]
+    [                s  + s + 1  ]
+    [                            ]
+    [                 4          ]
+    [     3        - p  + 3*p - 2]
+    [   -----      --------------]
+    [   s + 2          p + s     ]{t}
+
+    TransferFunctionMatrix can be transposed, if user wants to switch the input and output transfer functions
+
+    >>> tfm_2.transpose()
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s), TransferFunction(p**4 - 3*p + 2, p + s, s), TransferFunction(3, s + 2, s)), (TransferFunction(-3, s + 2, s), TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(-p**4 + 3*p - 2, p + s, s))))
+    >>> pprint(_, use_unicode=False)
+    [             4                          ]
+    [  a + s     p  - 3*p + 2        3       ]
+    [----------  ------------      -----     ]
+    [ 2             p + s          s + 2     ]
+    [s  + s + 1                              ]
+    [                                        ]
+    [                             4          ]
+    [   -3          -a - s     - p  + 3*p - 2]
+    [  -----      ----------   --------------]
+    [  s + 2       2               p + s     ]
+    [             s  + s + 1                 ]{t}
+
+    >>> tf_5 = TransferFunction(5, s, s)
+    >>> tf_6 = TransferFunction(5*s, (2 + s**2), s)
+    >>> tf_7 = TransferFunction(5, (s*(2 + s**2)), s)
+    >>> tf_8 = TransferFunction(5, 1, s)
+    >>> tfm_3 = TransferFunctionMatrix([[tf_5, tf_6], [tf_7, tf_8]])
+    >>> tfm_3
+    TransferFunctionMatrix(((TransferFunction(5, s, s), TransferFunction(5*s, s**2 + 2, s)), (TransferFunction(5, s*(s**2 + 2), s), TransferFunction(5, 1, s))))
+    >>> pprint(tfm_3, use_unicode=False)
+    [    5        5*s  ]
+    [    -       ------]
+    [    s        2    ]
+    [            s  + 2]
+    [                  ]
+    [    5         5   ]
+    [----------    -   ]
+    [  / 2    \    1   ]
+    [s*\s  + 2/        ]{t}
+    >>> tfm_3.var
+    s
+    >>> tfm_3.shape
+    (2, 2)
+    >>> tfm_3.num_outputs
+    2
+    >>> tfm_3.num_inputs
+    2
+    >>> tfm_3.args
+    (((TransferFunction(5, s, s), TransferFunction(5*s, s**2 + 2, s)), (TransferFunction(5, s*(s**2 + 2), s), TransferFunction(5, 1, s))),)
+
+    To access the ``TransferFunction`` at any index in the ``TransferFunctionMatrix``, use the index notation.
+
+    >>> tfm_3[1, 0]  # gives the TransferFunction present at 2nd Row and 1st Col. Similar to that in Matrix classes
+    TransferFunction(5, s*(s**2 + 2), s)
+    >>> tfm_3[0, 0]  # gives the TransferFunction present at 1st Row and 1st Col.
+    TransferFunction(5, s, s)
+    >>> tfm_3[:, 0]  # gives the first column
+    TransferFunctionMatrix(((TransferFunction(5, s, s),), (TransferFunction(5, s*(s**2 + 2), s),)))
+    >>> pprint(_, use_unicode=False)
+    [    5     ]
+    [    -     ]
+    [    s     ]
+    [          ]
+    [    5     ]
+    [----------]
+    [  / 2    \]
+    [s*\s  + 2/]{t}
+    >>> tfm_3[0, :]  # gives the first row
+    TransferFunctionMatrix(((TransferFunction(5, s, s), TransferFunction(5*s, s**2 + 2, s)),))
+    >>> pprint(_, use_unicode=False)
+    [5   5*s  ]
+    [-  ------]
+    [s   2    ]
+    [   s  + 2]{t}
+
+    To negate a transfer function matrix, ``-`` operator can be prepended:
+
+    >>> tfm_4 = TransferFunctionMatrix([[tf_2], [-tf_1], [tf_3]])
+    >>> -tfm_4
+    TransferFunctionMatrix(((TransferFunction(-p**4 + 3*p - 2, p + s, s),), (TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(-3, s + 2, s),)))
+    >>> tfm_5 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, -tf_1]])
+    >>> -tfm_5
+    TransferFunctionMatrix(((TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(-p**4 + 3*p - 2, p + s, s)), (TransferFunction(-3, s + 2, s), TransferFunction(a + s, s**2 + s + 1, s))))
+
+    ``subs()`` returns the ``TransferFunctionMatrix`` object with the value substituted in the expression. This will not
+    mutate your original ``TransferFunctionMatrix``.
+
+    >>> tfm_2.subs(p, 2)  #  substituting p everywhere in tfm_2 with 2.
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s), TransferFunction(-3, s + 2, s)), (TransferFunction(12, s + 2, s), TransferFunction(-a - s, s**2 + s + 1, s)), (TransferFunction(3, s + 2, s), TransferFunction(-12, s + 2, s))))
+    >>> pprint(_, use_unicode=False)
+    [  a + s        -3     ]
+    [----------    -----   ]
+    [ 2            s + 2   ]
+    [s  + s + 1            ]
+    [                      ]
+    [    12        -a - s  ]
+    [  -----     ----------]
+    [  s + 2      2        ]
+    [            s  + s + 1]
+    [                      ]
+    [    3          -12    ]
+    [  -----       -----   ]
+    [  s + 2       s + 2   ]{t}
+    >>> pprint(tfm_2, use_unicode=False) # State of tfm_2 is unchanged after substitution
+    [   a + s           -3       ]
+    [ ----------       -----     ]
+    [  2               s + 2     ]
+    [ s  + s + 1                 ]
+    [                            ]
+    [ 4                          ]
+    [p  - 3*p + 2      -a - s    ]
+    [------------    ----------  ]
+    [   p + s         2          ]
+    [                s  + s + 1  ]
+    [                            ]
+    [                 4          ]
+    [     3        - p  + 3*p - 2]
+    [   -----      --------------]
+    [   s + 2          p + s     ]{t}
+
+    ``subs()`` also supports multiple substitutions.
+
+    >>> tfm_2.subs({p: 2, a: 1})  # substituting p with 2 and a with 1
+    TransferFunctionMatrix(((TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(-3, s + 2, s)), (TransferFunction(12, s + 2, s), TransferFunction(-s - 1, s**2 + s + 1, s)), (TransferFunction(3, s + 2, s), TransferFunction(-12, s + 2, s))))
+    >>> pprint(_, use_unicode=False)
+    [  s + 1        -3     ]
+    [----------    -----   ]
+    [ 2            s + 2   ]
+    [s  + s + 1            ]
+    [                      ]
+    [    12        -s - 1  ]
+    [  -----     ----------]
+    [  s + 2      2        ]
+    [            s  + s + 1]
+    [                      ]
+    [    3          -12    ]
+    [  -----       -----   ]
+    [  s + 2       s + 2   ]{t}
+
+    Users can reduce the ``Series`` and ``Parallel`` elements of the matrix to ``TransferFunction`` by using
+    ``doit()``.
+
+    >>> tfm_6 = TransferFunctionMatrix([[Series(tf_3, tf_4), Parallel(tf_3, tf_4)]])
+    >>> tfm_6
+    TransferFunctionMatrix(((Series(TransferFunction(3, s + 2, s), TransferFunction(-a + p, 9*s - 9, s)), Parallel(TransferFunction(3, s + 2, s), TransferFunction(-a + p, 9*s - 9, s))),))
+    >>> pprint(tfm_6, use_unicode=False)
+    [-a + p    3    -a + p      3  ]
+    [-------*-----  ------- + -----]
+    [9*s - 9 s + 2  9*s - 9   s + 2]{t}
+    >>> tfm_6.doit()
+    TransferFunctionMatrix(((TransferFunction(-3*a + 3*p, (s + 2)*(9*s - 9), s), TransferFunction(27*s + (-a + p)*(s + 2) - 27, (s + 2)*(9*s - 9), s)),))
+    >>> pprint(_, use_unicode=False)
+    [    -3*a + 3*p     27*s + (-a + p)*(s + 2) - 27]
+    [-----------------  ----------------------------]
+    [(s + 2)*(9*s - 9)       (s + 2)*(9*s - 9)      ]{t}
+    >>> tf_9 = TransferFunction(1, s, s)
+    >>> tf_10 = TransferFunction(1, s**2, s)
+    >>> tfm_7 = TransferFunctionMatrix([[Series(tf_9, tf_10), tf_9], [tf_10, Parallel(tf_9, tf_10)]])
+    >>> tfm_7
+    TransferFunctionMatrix(((Series(TransferFunction(1, s, s), TransferFunction(1, s**2, s)), TransferFunction(1, s, s)), (TransferFunction(1, s**2, s), Parallel(TransferFunction(1, s, s), TransferFunction(1, s**2, s)))))
+    >>> pprint(tfm_7, use_unicode=False)
+    [ 1      1   ]
+    [----    -   ]
+    [   2    s   ]
+    [s*s         ]
+    [            ]
+    [ 1    1    1]
+    [ --   -- + -]
+    [  2    2   s]
+    [ s    s     ]{t}
+    >>> tfm_7.doit()
+    TransferFunctionMatrix(((TransferFunction(1, s**3, s), TransferFunction(1, s, s)), (TransferFunction(1, s**2, s), TransferFunction(s**2 + s, s**3, s))))
+    >>> pprint(_, use_unicode=False)
+    [1     1   ]
+    [--    -   ]
+    [ 3    s   ]
+    [s         ]
+    [          ]
+    [     2    ]
+    [1   s  + s]
+    [--  ------]
+    [ 2     3  ]
+    [s     s   ]{t}
+
+    Addition, subtraction, and multiplication of transfer function matrices can form
+    unevaluated ``Series`` or ``Parallel`` objects.
+
+    - For addition and subtraction:
+      All the transfer function matrices must have the same shape.
+
+    - For multiplication (C = A * B):
+      The number of inputs of the first transfer function matrix (A) must be equal to the
+      number of outputs of the second transfer function matrix (B).
+
+    Also, use pretty-printing (``pprint``) to analyse better.
+
+    >>> tfm_8 = TransferFunctionMatrix([[tf_3], [tf_2], [-tf_1]])
+    >>> tfm_9 = TransferFunctionMatrix([[-tf_3]])
+    >>> tfm_10 = TransferFunctionMatrix([[tf_1], [tf_2], [tf_4]])
+    >>> tfm_11 = TransferFunctionMatrix([[tf_4], [-tf_1]])
+    >>> tfm_12 = TransferFunctionMatrix([[tf_4, -tf_1, tf_3], [-tf_2, -tf_4, -tf_3]])
+    >>> tfm_8 + tfm_10
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),))), TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a + p, 9*s - 9, s),))))
+    >>> pprint(_, use_unicode=False)
+    [     3      ]      [   a + s    ]
+    [   -----    ]      [ ---------- ]
+    [   s + 2    ]      [  2         ]
+    [            ]      [ s  + s + 1 ]
+    [ 4          ]      [            ]
+    [p  - 3*p + 2]      [ 4          ]
+    [------------]    + [p  - 3*p + 2]
+    [   p + s    ]      [------------]
+    [            ]      [   p + s    ]
+    [   -a - s   ]      [            ]
+    [ ---------- ]      [   -a + p   ]
+    [  2         ]      [  -------   ]
+    [ s  + s + 1 ]{t}   [  9*s - 9   ]{t}
+    >>> -tfm_10 - tfm_8
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(-a - s, s**2 + s + 1, s),), (TransferFunction(-p**4 + 3*p - 2, p + s, s),), (TransferFunction(a - p, 9*s - 9, s),))), TransferFunctionMatrix(((TransferFunction(-3, s + 2, s),), (TransferFunction(-p**4 + 3*p - 2, p + s, s),), (TransferFunction(a + s, s**2 + s + 1, s),))))
+    >>> pprint(_, use_unicode=False)
+    [    -a - s    ]      [     -3       ]
+    [  ----------  ]      [    -----     ]
+    [   2          ]      [    s + 2     ]
+    [  s  + s + 1  ]      [              ]
+    [              ]      [   4          ]
+    [   4          ]      [- p  + 3*p - 2]
+    [- p  + 3*p - 2]    + [--------------]
+    [--------------]      [    p + s     ]
+    [    p + s     ]      [              ]
+    [              ]      [    a + s     ]
+    [    a - p     ]      [  ----------  ]
+    [   -------    ]      [   2          ]
+    [   9*s - 9    ]{t}   [  s  + s + 1  ]{t}
+    >>> tfm_12 * tfm_8
+    MIMOSeries(TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),))), TransferFunctionMatrix(((TransferFunction(-a + p, 9*s - 9, s), TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(3, s + 2, s)), (TransferFunction(-p**4 + 3*p - 2, p + s, s), TransferFunction(a - p, 9*s - 9, s), TransferFunction(-3, s + 2, s)))))
+    >>> pprint(_, use_unicode=False)
+                                           [     3      ]
+                                           [   -----    ]
+    [    -a + p        -a - s      3  ]    [   s + 2    ]
+    [   -------      ----------  -----]    [            ]
+    [   9*s - 9       2          s + 2]    [ 4          ]
+    [                s  + s + 1       ]    [p  - 3*p + 2]
+    [                                 ]   *[------------]
+    [   4                             ]    [   p + s    ]
+    [- p  + 3*p - 2    a - p      -3  ]    [            ]
+    [--------------   -------    -----]    [   -a - s   ]
+    [    p + s        9*s - 9    s + 2]{t} [ ---------- ]
+                                           [  2         ]
+                                           [ s  + s + 1 ]{t}
+    >>> tfm_12 * tfm_8 * tfm_9
+    MIMOSeries(TransferFunctionMatrix(((TransferFunction(-3, s + 2, s),),)), TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),))), TransferFunctionMatrix(((TransferFunction(-a + p, 9*s - 9, s), TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(3, s + 2, s)), (TransferFunction(-p**4 + 3*p - 2, p + s, s), TransferFunction(a - p, 9*s - 9, s), TransferFunction(-3, s + 2, s)))))
+    >>> pprint(_, use_unicode=False)
+                                           [     3      ]
+                                           [   -----    ]
+    [    -a + p        -a - s      3  ]    [   s + 2    ]
+    [   -------      ----------  -----]    [            ]
+    [   9*s - 9       2          s + 2]    [ 4          ]
+    [                s  + s + 1       ]    [p  - 3*p + 2]    [ -3  ]
+    [                                 ]   *[------------]   *[-----]
+    [   4                             ]    [   p + s    ]    [s + 2]{t}
+    [- p  + 3*p - 2    a - p      -3  ]    [            ]
+    [--------------   -------    -----]    [   -a - s   ]
+    [    p + s        9*s - 9    s + 2]{t} [ ---------- ]
+                                           [  2         ]
+                                           [ s  + s + 1 ]{t}
+    >>> tfm_10 + tfm_8*tfm_9
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a + p, 9*s - 9, s),))), MIMOSeries(TransferFunctionMatrix(((TransferFunction(-3, s + 2, s),),)), TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),)))))
+    >>> pprint(_, use_unicode=False)
+    [   a + s    ]      [     3      ]
+    [ ---------- ]      [   -----    ]
+    [  2         ]      [   s + 2    ]
+    [ s  + s + 1 ]      [            ]
+    [            ]      [ 4          ]
+    [ 4          ]      [p  - 3*p + 2]    [ -3  ]
+    [p  - 3*p + 2]    + [------------]   *[-----]
+    [------------]      [   p + s    ]    [s + 2]{t}
+    [   p + s    ]      [            ]
+    [            ]      [   -a - s   ]
+    [   -a + p   ]      [ ---------- ]
+    [  -------   ]      [  2         ]
+    [  9*s - 9   ]{t}   [ s  + s + 1 ]{t}
+
+    These unevaluated ``Series`` or ``Parallel`` objects can convert into the
+    resultant transfer function matrix using ``.doit()`` method or by
+    ``.rewrite(TransferFunctionMatrix)``.
+
+    >>> (-tfm_8 + tfm_10 + tfm_8*tfm_9).doit()
+    TransferFunctionMatrix(((TransferFunction((a + s)*(s + 2)**3 - 3*(s + 2)**2*(s**2 + s + 1) - 9*(s + 2)*(s**2 + s + 1), (s + 2)**3*(s**2 + s + 1), s),), (TransferFunction((p + s)*(-3*p**4 + 9*p - 6), (p + s)**2*(s + 2), s),), (TransferFunction((-a + p)*(s + 2)*(s**2 + s + 1)**2 + (a + s)*(s + 2)*(9*s - 9)*(s**2 + s + 1) + (3*a + 3*s)*(9*s - 9)*(s**2 + s + 1), (s + 2)*(9*s - 9)*(s**2 + s + 1)**2, s),)))
+    >>> (-tfm_12 * -tfm_8 * -tfm_9).rewrite(TransferFunctionMatrix)
+    TransferFunctionMatrix(((TransferFunction(3*(-3*a + 3*p)*(p + s)*(s + 2)*(s**2 + s + 1)**2 + 3*(-3*a - 3*s)*(p + s)*(s + 2)*(9*s - 9)*(s**2 + s + 1) + 3*(a + s)*(s + 2)**2*(9*s - 9)*(-p**4 + 3*p - 2)*(s**2 + s + 1), (p + s)*(s + 2)**3*(9*s - 9)*(s**2 + s + 1)**2, s),), (TransferFunction(3*(-a + p)*(p + s)*(s + 2)**2*(-p**4 + 3*p - 2)*(s**2 + s + 1) + 3*(3*a + 3*s)*(p + s)**2*(s + 2)*(9*s - 9) + 3*(p + s)*(s + 2)*(9*s - 9)*(-3*p**4 + 9*p - 6)*(s**2 + s + 1), (p + s)**2*(s + 2)**3*(9*s - 9)*(s**2 + s + 1), s),)))
+
+    See Also
+    ========
+
+    TransferFunction, MIMOSeries, MIMOParallel, Feedback
+
+    """
+    def __new__(cls, arg):
+
+        expr_mat_arg = []
+        try:
+            var = arg[0][0].var
+        except TypeError:
+            raise ValueError(filldedent("""
+                `arg` param in TransferFunctionMatrix should
+                strictly be a nested list containing TransferFunction
+                objects."""))
+        for row in arg:
+            temp = []
+            for element in row:
+                if not isinstance(element, SISOLinearTimeInvariant):
+                    raise TypeError(filldedent("""
+                        Each element is expected to be of
+                        type `SISOLinearTimeInvariant`."""))
+
+                if var != element.var:
+                    raise ValueError(filldedent("""
+                        Conflicting value(s) found for `var`. All TransferFunction
+                        instances in TransferFunctionMatrix should use the same
+                        complex variable in Laplace domain."""))
+
+                temp.append(element.to_expr())
+            expr_mat_arg.append(temp)
+
+        if isinstance(arg, (tuple, list, Tuple)):
+            # Making nested Tuple (sympy.core.containers.Tuple) from nested list or nested Python tuple
+            arg = Tuple(*(Tuple(*r, sympify=False) for r in arg), sympify=False)
+
+        obj = super(TransferFunctionMatrix, cls).__new__(cls, arg)
+        obj._expr_mat = ImmutableMatrix(expr_mat_arg)
+        obj.is_StateSpace_object = False
+        return obj
+
+    @classmethod
+    def from_Matrix(cls, matrix, var):
+        """
+        Creates a new ``TransferFunctionMatrix`` efficiently from a SymPy Matrix of ``Expr`` objects.
+
+        Parameters
+        ==========
+
+        matrix : ``ImmutableMatrix`` having ``Expr``/``Number`` elements.
+        var : Symbol
+            Complex variable of the Laplace transform which will be used by the
+            all the ``TransferFunction`` objects in the ``TransferFunctionMatrix``.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunctionMatrix
+        >>> from sympy import Matrix, pprint
+        >>> M = Matrix([[s, 1/s], [1/(s+1), s]])
+        >>> M_tf = TransferFunctionMatrix.from_Matrix(M, s)
+        >>> pprint(M_tf, use_unicode=False)
+        [  s    1]
+        [  -    -]
+        [  1    s]
+        [        ]
+        [  1    s]
+        [-----  -]
+        [s + 1  1]{t}
+        >>> M_tf.elem_poles()
+        [[[], [0]], [[-1], []]]
+        >>> M_tf.elem_zeros()
+        [[[0], []], [[], [0]]]
+
+        """
+        return _to_TFM(matrix, var)
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions or
+        ``Series``/``Parallel`` objects in a transfer function matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p, s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, Series, Parallel
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> G4 = TransferFunction(s + 1, s**2 + s + 1, s)
+        >>> S1 = Series(G1, G2)
+        >>> S2 = Series(-G3, Parallel(G2, -G1))
+        >>> tfm1 = TransferFunctionMatrix([[G1], [G2], [G3]])
+        >>> tfm1.var
+        p
+        >>> tfm2 = TransferFunctionMatrix([[-S1, -S2], [S1, S2]])
+        >>> tfm2.var
+        p
+        >>> tfm3 = TransferFunctionMatrix([[G4]])
+        >>> tfm3.var
+        s
+
+        """
+        return self.args[0][0][0].var
+
+    @property
+    def num_inputs(self):
+        """
+        Returns the number of inputs of the system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> G1 = TransferFunction(s + 3, s**2 - 3, s)
+        >>> G2 = TransferFunction(4, s**2, s)
+        >>> G3 = TransferFunction(p**2 + s**2, p - 3, s)
+        >>> tfm_1 = TransferFunctionMatrix([[G2, -G1, G3], [-G2, -G1, -G3]])
+        >>> tfm_1.num_inputs
+        3
+
+        See Also
+        ========
+
+        num_outputs
+
+        """
+        return self._expr_mat.shape[1]
+
+    @property
+    def num_outputs(self):
+        """
+        Returns the number of outputs of the system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunctionMatrix
+        >>> from sympy import Matrix
+        >>> M_1 = Matrix([[s], [1/s]])
+        >>> TFM = TransferFunctionMatrix.from_Matrix(M_1, s)
+        >>> print(TFM)
+        TransferFunctionMatrix(((TransferFunction(s, 1, s),), (TransferFunction(1, s, s),)))
+        >>> TFM.num_outputs
+        2
+
+        See Also
+        ========
+
+        num_inputs
+
+        """
+        return self._expr_mat.shape[0]
+
+    @property
+    def shape(self):
+        """
+        Returns the shape of the transfer function matrix, that is, ``(# of outputs, # of inputs)``.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> tf1 = TransferFunction(p**2 - 1, s**4 + s**3 - p, p)
+        >>> tf2 = TransferFunction(1 - p, p**2 - 3*p + 7, p)
+        >>> tf3 = TransferFunction(3, 4, p)
+        >>> tfm1 = TransferFunctionMatrix([[tf1, -tf2]])
+        >>> tfm1.shape
+        (1, 2)
+        >>> tfm2 = TransferFunctionMatrix([[-tf2, tf3], [tf1, -tf1]])
+        >>> tfm2.shape
+        (2, 2)
+
+        """
+        return self._expr_mat.shape
+
+    def __neg__(self):
+        neg = -self._expr_mat
+        return _to_TFM(neg, self.var)
+
+    @_check_other_MIMO
+    def __add__(self, other):
+
+        if not isinstance(other, MIMOParallel):
+            return MIMOParallel(self, other)
+        other_arg_list = list(other.args)
+        return MIMOParallel(self, *other_arg_list)
+
+    @_check_other_MIMO
+    def __sub__(self, other):
+        return self + (-other)
+
+    @_check_other_MIMO
+    def __mul__(self, other):
+
+        if not isinstance(other, MIMOSeries):
+            return MIMOSeries(other, self)
+        other_arg_list = list(other.args)
+        return MIMOSeries(*other_arg_list, self)
+
+    def __getitem__(self, key):
+        trunc = self._expr_mat.__getitem__(key)
+        if isinstance(trunc, ImmutableMatrix):
+            return _to_TFM(trunc, self.var)
+        return TransferFunction.from_rational_expression(trunc, self.var)
+
+    def transpose(self):
+        """Returns the transpose of the ``TransferFunctionMatrix`` (switched input and output layers)."""
+        transposed_mat = self._expr_mat.transpose()
+        return _to_TFM(transposed_mat, self.var)
+
+    def elem_poles(self):
+        """
+        Returns the poles of each element of the ``TransferFunctionMatrix``.
+
+        .. note::
+            Actual poles of a MIMO system are NOT the poles of individual elements.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> tf_1 = TransferFunction(3, (s + 1), s)
+        >>> tf_2 = TransferFunction(s + 6, (s + 1)*(s + 2), s)
+        >>> tf_3 = TransferFunction(s + 3, s**2 + 3*s + 2, s)
+        >>> tf_4 = TransferFunction(s + 2, s**2 + 5*s - 10, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, tf_4]])
+        >>> tfm_1
+        TransferFunctionMatrix(((TransferFunction(3, s + 1, s), TransferFunction(s + 6, (s + 1)*(s + 2), s)), (TransferFunction(s + 3, s**2 + 3*s + 2, s), TransferFunction(s + 2, s**2 + 5*s - 10, s))))
+        >>> tfm_1.elem_poles()
+        [[[-1], [-2, -1]], [[-2, -1], [-5/2 + sqrt(65)/2, -sqrt(65)/2 - 5/2]]]
+
+        See Also
+        ========
+
+        elem_zeros
+
+        """
+        return [[element.poles() for element in row] for row in self.doit().args[0]]
+
+    def elem_zeros(self):
+        """
+        Returns the zeros of each element of the ``TransferFunctionMatrix``.
+
+        .. note::
+            Actual zeros of a MIMO system are NOT the zeros of individual elements.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> tf_1 = TransferFunction(3, (s + 1), s)
+        >>> tf_2 = TransferFunction(s + 6, (s + 1)*(s + 2), s)
+        >>> tf_3 = TransferFunction(s + 3, s**2 + 3*s + 2, s)
+        >>> tf_4 = TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, tf_4]])
+        >>> tfm_1
+        TransferFunctionMatrix(((TransferFunction(3, s + 1, s), TransferFunction(s + 6, (s + 1)*(s + 2), s)), (TransferFunction(s + 3, s**2 + 3*s + 2, s), TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s))))
+        >>> tfm_1.elem_zeros()
+        [[[], [-6]], [[-3], [4, 5]]]
+
+        See Also
+        ========
+
+        elem_poles
+
+        """
+        return [[element.zeros() for element in row] for row in self.doit().args[0]]
+
+    def eval_frequency(self, other):
+        """
+        Evaluates system response of each transfer function in the ``TransferFunctionMatrix`` at any point in the real or complex plane.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> from sympy import I
+        >>> tf_1 = TransferFunction(3, (s + 1), s)
+        >>> tf_2 = TransferFunction(s + 6, (s + 1)*(s + 2), s)
+        >>> tf_3 = TransferFunction(s + 3, s**2 + 3*s + 2, s)
+        >>> tf_4 = TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, tf_4]])
+        >>> tfm_1
+        TransferFunctionMatrix(((TransferFunction(3, s + 1, s), TransferFunction(s + 6, (s + 1)*(s + 2), s)), (TransferFunction(s + 3, s**2 + 3*s + 2, s), TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s))))
+        >>> tfm_1.eval_frequency(2)
+        Matrix([
+        [   1, 2/3],
+        [5/12, 3/2]])
+        >>> tfm_1.eval_frequency(I*2)
+        Matrix([
+        [   3/5 - 6*I/5,                -I],
+        [3/20 - 11*I/20, -101/74 + 23*I/74]])
+        """
+        mat = self._expr_mat.subs(self.var, other)
+        return mat.expand()
+
+    def _flat(self):
+        """Returns flattened list of args in TransferFunctionMatrix"""
+        return [elem for tup in self.args[0] for elem in tup]
+
+    def _eval_evalf(self, prec):
+        """Calls evalf() on each transfer function in the transfer function matrix"""
+        dps = prec_to_dps(prec)
+        mat = self._expr_mat.applyfunc(lambda a: a.evalf(n=dps))
+        return _to_TFM(mat, self.var)
+
+    def _eval_simplify(self, **kwargs):
+        """Simplifies the transfer function matrix"""
+        simp_mat = self._expr_mat.applyfunc(lambda a: cancel(a, expand=False))
+        return _to_TFM(simp_mat, self.var)
+
+    def expand(self, **hints):
+        """Expands the transfer function matrix"""
+        expand_mat = self._expr_mat.expand(**hints)
+        return _to_TFM(expand_mat, self.var)
+
+class StateSpace(LinearTimeInvariant):
+    r"""
+    State space model (ssm) of a linear, time invariant control system.
+
+    Represents the standard state-space model with A, B, C, D as state-space matrices.
+    This makes the linear control system:
+
+        (1) x'(t) = A * x(t) + B * u(t);    x in R^n , u in R^k
+        (2) y(t)  = C * x(t) + D * u(t);    y in R^m
+
+    where u(t) is any input signal, y(t) the corresponding output, and x(t) the system's state.
+
+    Parameters
+    ==========
+
+    A : Matrix
+        The State matrix of the state space model.
+    B : Matrix
+        The Input-to-State matrix of the state space model.
+    C : Matrix
+        The State-to-Output matrix of the state space model.
+    D : Matrix
+        The Feedthrough matrix of the state space model.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.physics.control import StateSpace
+
+    The easiest way to create a StateSpaceModel is via four matrices:
+
+    >>> A = Matrix([[1, 2], [1, 0]])
+    >>> B = Matrix([1, 1])
+    >>> C = Matrix([[0, 1]])
+    >>> D = Matrix([0])
+    >>> StateSpace(A, B, C, D)
+    StateSpace(Matrix([
+    [1, 2],
+    [1, 0]]), Matrix([
+    [1],
+    [1]]), Matrix([[0, 1]]), Matrix([[0]]))
+
+    One can use less matrices. The rest will be filled with a minimum of zeros:
+
+    >>> StateSpace(A, B)
+    StateSpace(Matrix([
+    [1, 2],
+    [1, 0]]), Matrix([
+    [1],
+    [1]]), Matrix([[0, 0]]), Matrix([[0]]))
+
+    See Also
+    ========
+
+    TransferFunction, TransferFunctionMatrix
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/State-space_representation
+    .. [2] https://in.mathworks.com/help/control/ref/ss.html
+
+    """
+    def __new__(cls, A=None, B=None, C=None, D=None):
+        if A is None:
+            A = zeros(1)
+        if B is None:
+            B = zeros(A.rows, 1)
+        if C is None:
+            C = zeros(1, A.cols)
+        if D is None:
+            D = zeros(C.rows, B.cols)
+
+        A = _sympify(A)
+        B = _sympify(B)
+        C = _sympify(C)
+        D = _sympify(D)
+
+        if (isinstance(A, ImmutableDenseMatrix) and isinstance(B, ImmutableDenseMatrix) and
+            isinstance(C, ImmutableDenseMatrix) and isinstance(D, ImmutableDenseMatrix)):
+            # Check State Matrix is square
+            if A.rows != A.cols:
+                raise ShapeError("Matrix A must be a square matrix.")
+
+            # Check State and Input matrices have same rows
+            if A.rows != B.rows:
+                raise ShapeError("Matrices A and B must have the same number of rows.")
+
+            # Check Output and Feedthrough matrices have same rows
+            if C.rows != D.rows:
+                raise ShapeError("Matrices C and D must have the same number of rows.")
+
+            # Check State and Output matrices have same columns
+            if A.cols != C.cols:
+                raise ShapeError("Matrices A and C must have the same number of columns.")
+
+            # Check Input and Feedthrough matrices have same columns
+            if B.cols != D.cols:
+                raise ShapeError("Matrices B and D must have the same number of columns.")
+
+            obj = super(StateSpace, cls).__new__(cls, A, B, C, D)
+            obj._A = A
+            obj._B = B
+            obj._C = C
+            obj._D = D
+
+            # Determine if the system is SISO or MIMO
+            num_outputs = D.rows
+            num_inputs = D.cols
+            if num_inputs == 1 and num_outputs == 1:
+                obj._is_SISO = True
+                obj._clstype = SISOLinearTimeInvariant
+            else:
+                obj._is_SISO = False
+                obj._clstype = MIMOLinearTimeInvariant
+            obj.is_StateSpace_object = True
+            return obj
+
+        else:
+            raise TypeError("A, B, C and D inputs must all be sympy Matrices.")
+
+    @property
+    def state_matrix(self):
+        """
+        Returns the state matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.state_matrix
+        Matrix([
+        [1, 2],
+        [1, 0]])
+
+        """
+        return self._A
+
+    @property
+    def input_matrix(self):
+        """
+        Returns the input matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.input_matrix
+        Matrix([
+        [1],
+        [1]])
+
+        """
+        return self._B
+
+    @property
+    def output_matrix(self):
+        """
+        Returns the output matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.output_matrix
+        Matrix([[0, 1]])
+
+        """
+        return self._C
+
+    @property
+    def feedforward_matrix(self):
+        """
+        Returns the feedforward matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.feedforward_matrix
+        Matrix([[0]])
+
+        """
+        return self._D
+
+    A = state_matrix
+    B = input_matrix
+    C = output_matrix
+    D = feedforward_matrix
+
+    @property
+    def num_states(self):
+        """
+        Returns the number of states of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.num_states
+        2
+
+        """
+        return self._A.rows
+
+    @property
+    def num_inputs(self):
+        """
+        Returns the number of inputs of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.num_inputs
+        1
+
+        """
+        return self._D.cols
+
+    @property
+    def num_outputs(self):
+        """
+        Returns the number of outputs of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.num_outputs
+        1
+
+        """
+        return self._D.rows
+
+
+    @property
+    def shape(self):
+        """Returns the shape of the equivalent StateSpace system."""
+        return self.num_outputs, self.num_inputs
+
+    def dsolve(self, initial_conditions=None, input_vector=None, var=Symbol('t')):
+        r"""
+        Returns `y(t)` or output of StateSpace given by the solution of equations:
+            x'(t) = A * x(t) + B * u(t)
+            y(t)  = C * x(t) + D * u(t)
+
+        Parameters
+        ============
+
+        initial_conditions : Matrix
+            The initial conditions of `x` state vector. If not provided, it defaults to a zero vector.
+        input_vector : Matrix
+            The input vector for state space. If not provided, it defaults to a zero vector.
+        var : Symbol
+            The symbol representing time. If not provided, it defaults to `t`.
+
+        Examples
+        ==========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-2, 0], [1, -1]])
+        >>> B = Matrix([[1], [0]])
+        >>> C = Matrix([[2, 1]])
+        >>> ip = Matrix([5])
+        >>> i = Matrix([0, 0])
+        >>> ss = StateSpace(A, B, C)
+        >>> ss.dsolve(input_vector=ip, initial_conditions=i).simplify()
+        Matrix([[15/2 - 5*exp(-t) - 5*exp(-2*t)/2]])
+
+        If no input is provided it defaults to solving the system with zero initial conditions and zero input.
+
+        >>> ss.dsolve()
+        Matrix([[0]])
+
+        References
+        ==========
+        .. [1] https://web.mit.edu/2.14/www/Handouts/StateSpaceResponse.pdf
+        .. [2] https://docs.sympy.org/latest/modules/solvers/ode.html#sympy.solvers.ode.systems.linodesolve
+
+        """
+
+        if not isinstance(var, Symbol):
+            raise ValueError("Variable for representing time must be a Symbol.")
+        if not initial_conditions:
+            initial_conditions = zeros(self._A.shape[0], 1)
+        elif initial_conditions.shape != (self._A.shape[0], 1):
+            raise ShapeError("Initial condition vector should have the same number of "
+                             "rows as the state matrix.")
+        if not input_vector:
+            input_vector = zeros(self._B.shape[1], 1)
+        elif input_vector.shape != (self._B.shape[1], 1):
+            raise ShapeError("Input vector should have the same number of "
+                             "columns as the input matrix.")
+        sol = linodesolve(A=self._A, t=var, b=self._B*input_vector, type='type2', doit=True)
+        mat1 = Matrix(sol)
+        mat2 = mat1.replace(var, 0)
+        free1 = self._A.free_symbols | self._B.free_symbols | input_vector.free_symbols
+        free2 = mat2.free_symbols
+        # Get all the free symbols form the matrix
+        dummy_symbols = list(free2-free1)
+        # Convert the matrix to a Coefficient matrix
+        r1, r2 = linear_eq_to_matrix(mat2, dummy_symbols)
+        s = linsolve((r1, initial_conditions+r2))
+        res_tuple = next(iter(s))
+        for ind, v in enumerate(res_tuple):
+            mat1 = mat1.replace(dummy_symbols[ind], v)
+        res = self._C*mat1 + self._D*input_vector
+        return res
+
+    def _eval_evalf(self, prec):
+        """
+        Returns state space model where numerical expressions are evaluated into floating point numbers.
+        """
+        dps = prec_to_dps(prec)
+        return StateSpace(
+            self._A.evalf(n = dps),
+            self._B.evalf(n = dps),
+            self._C.evalf(n = dps),
+            self._D.evalf(n = dps))
+
+    def _eval_rewrite_as_TransferFunction(self, *args):
+        """
+        Returns the equivalent Transfer Function of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import TransferFunction, StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.rewrite(TransferFunction)
+        [[TransferFunction(12*s + 59, s**2 + 6*s + 8, s)]]
+
+        """
+        s = Symbol('s')
+        n = self._A.shape[0]
+        I = eye(n)
+        G = self._C*(s*I - self._A).solve(self._B) + self._D
+        G = G.simplify()
+        to_tf = lambda expr: TransferFunction.from_rational_expression(expr, s)
+        tf_mat = [[to_tf(expr) for expr in sublist] for sublist in G.tolist()]
+        return tf_mat
+
+    def __add__(self, other):
+        """
+        Add two State Space systems (parallel connection).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A1 = Matrix([[1]])
+        >>> B1 = Matrix([[2]])
+        >>> C1 = Matrix([[-1]])
+        >>> D1 = Matrix([[-2]])
+        >>> A2 = Matrix([[-1]])
+        >>> B2 = Matrix([[-2]])
+        >>> C2 = Matrix([[1]])
+        >>> D2 = Matrix([[2]])
+        >>> ss1 = StateSpace(A1, B1, C1, D1)
+        >>> ss2 = StateSpace(A2, B2, C2, D2)
+        >>> ss1 + ss2
+        StateSpace(Matrix([
+        [1,  0],
+        [0, -1]]), Matrix([
+        [ 2],
+        [-2]]), Matrix([[-1, 1]]), Matrix([[0]]))
+
+        """
+        # Check for scalars
+        if isinstance(other, (int, float, complex, Symbol)):
+            A = self._A
+            B = self._B
+            C = self._C
+            D = self._D.applyfunc(lambda element: element + other)
+
+        else:
+            # Check nature of system
+            if not isinstance(other, StateSpace):
+                raise ValueError("Addition is only supported for 2 State Space models.")
+            # Check dimensions of system
+            elif ((self.num_inputs != other.num_inputs) or (self.num_outputs != other.num_outputs)):
+                raise ShapeError("Systems with incompatible inputs and outputs cannot be added.")
+
+            m1 = (self._A).row_join(zeros(self._A.shape[0], other._A.shape[-1]))
+            m2 = zeros(other._A.shape[0], self._A.shape[-1]).row_join(other._A)
+
+            A = m1.col_join(m2)
+            B = self._B.col_join(other._B)
+            C = self._C.row_join(other._C)
+            D = self._D + other._D
+
+        return StateSpace(A, B, C, D)
+
+    def __radd__(self, other):
+        """
+        Right add two State Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.control import StateSpace
+        >>> s = StateSpace()
+        >>> 5 + s
+        StateSpace(Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[5]]))
+
+        """
+        return self + other
+
+    def __sub__(self, other):
+        """
+        Subtract two State Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A1 = Matrix([[1]])
+        >>> B1 = Matrix([[2]])
+        >>> C1 = Matrix([[-1]])
+        >>> D1 = Matrix([[-2]])
+        >>> A2 = Matrix([[-1]])
+        >>> B2 = Matrix([[-2]])
+        >>> C2 = Matrix([[1]])
+        >>> D2 = Matrix([[2]])
+        >>> ss1 = StateSpace(A1, B1, C1, D1)
+        >>> ss2 = StateSpace(A2, B2, C2, D2)
+        >>> ss1 - ss2
+        StateSpace(Matrix([
+        [1,  0],
+        [0, -1]]), Matrix([
+        [ 2],
+        [-2]]), Matrix([[-1, -1]]), Matrix([[-4]]))
+
+        """
+        return self + (-other)
+
+    def __rsub__(self, other):
+        """
+        Right subtract two tate Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.control import StateSpace
+        >>> s = StateSpace()
+        >>> 5 - s
+        StateSpace(Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[5]]))
+
+        """
+        return other + (-self)
+
+    def __neg__(self):
+        """
+        Returns the negation of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> -ss
+        StateSpace(Matrix([
+        [-5, -1],
+        [ 3, -1]]), Matrix([
+        [2],
+        [5]]), Matrix([[-1, -2]]), Matrix([[0]]))
+
+        """
+        return StateSpace(self._A, self._B, -self._C, -self._D)
+
+    def __mul__(self, other):
+        """
+        Multiplication of two State Space systems (serial connection).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss*5
+        StateSpace(Matrix([
+        [-5, -1],
+        [ 3, -1]]), Matrix([
+        [2],
+        [5]]), Matrix([[5, 10]]), Matrix([[0]]))
+
+        """
+        # Check for scalars
+        if isinstance(other, (int, float, complex, Symbol)):
+            A = self._A
+            B = self._B
+            C = self._C.applyfunc(lambda element: element*other)
+            D = self._D.applyfunc(lambda element: element*other)
+
+        else:
+            # Check nature of system
+            if not isinstance(other, StateSpace):
+                raise ValueError("Multiplication is only supported for 2 State Space models.")
+            # Check dimensions of system
+            elif self.num_inputs != other.num_outputs:
+                raise ShapeError("Systems with incompatible inputs and outputs cannot be multiplied.")
+
+            m1 = (other._A).row_join(zeros(other._A.shape[0], self._A.shape[1]))
+            m2 = (self._B * other._C).row_join(self._A)
+
+            A = m1.col_join(m2)
+            B = (other._B).col_join(self._B * other._D)
+            C = (self._D * other._C).row_join(self._C)
+            D = self._D * other._D
+
+        return StateSpace(A, B, C, D)
+
+    def __rmul__(self, other):
+        """
+        Right multiply two tate Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> 5*ss
+        StateSpace(Matrix([
+        [-5, -1],
+        [ 3, -1]]), Matrix([
+        [10],
+        [25]]), Matrix([[1, 2]]), Matrix([[0]]))
+
+        """
+        if isinstance(other, (int, float, complex, Symbol)):
+            A = self._A
+            C = self._C
+            B = self._B.applyfunc(lambda element: element*other)
+            D = self._D.applyfunc(lambda element: element*other)
+            return StateSpace(A, B, C, D)
+        else:
+            return self*other
+
+    def __repr__(self):
+        A_str = self._A.__repr__()
+        B_str = self._B.__repr__()
+        C_str = self._C.__repr__()
+        D_str = self._D.__repr__()
+
+        return f"StateSpace(\n{A_str},\n\n{B_str},\n\n{C_str},\n\n{D_str})"
+
+
+    def append(self, other):
+        """
+        Returns the first model appended with the second model. The order is preserved.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A1 = Matrix([[1]])
+        >>> B1 = Matrix([[2]])
+        >>> C1 = Matrix([[-1]])
+        >>> D1 = Matrix([[-2]])
+        >>> A2 = Matrix([[-1]])
+        >>> B2 = Matrix([[-2]])
+        >>> C2 = Matrix([[1]])
+        >>> D2 = Matrix([[2]])
+        >>> ss1 = StateSpace(A1, B1, C1, D1)
+        >>> ss2 = StateSpace(A2, B2, C2, D2)
+        >>> ss1.append(ss2)
+        StateSpace(Matrix([
+        [1,  0],
+        [0, -1]]), Matrix([
+        [2,  0],
+        [0, -2]]), Matrix([
+        [-1, 0],
+        [ 0, 1]]), Matrix([
+        [-2, 0],
+        [ 0, 2]]))
+
+        """
+        n = self.num_states + other.num_states
+        m = self.num_inputs + other.num_inputs
+        p = self.num_outputs + other.num_outputs
+
+        A = zeros(n, n)
+        B = zeros(n, m)
+        C = zeros(p, n)
+        D = zeros(p, m)
+
+        A[:self.num_states, :self.num_states] = self._A
+        A[self.num_states:, self.num_states:] = other._A
+        B[:self.num_states, :self.num_inputs] = self._B
+        B[self.num_states:, self.num_inputs:] = other._B
+        C[:self.num_outputs, :self.num_states] = self._C
+        C[self.num_outputs:, self.num_states:] = other._C
+        D[:self.num_outputs, :self.num_inputs] = self._D
+        D[self.num_outputs:, self.num_inputs:] = other._D
+        return StateSpace(A, B, C, D)
+
+    def observability_matrix(self):
+        """
+        Returns the observability matrix of the state space model:
+            [C, C * A^1, C * A^2, .. , C * A^(n-1)]; A in R^(n x n), C in R^(m x k)
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ob = ss.observability_matrix()
+        >>> ob
+        Matrix([
+        [0, 1],
+        [1, 0]])
+
+        References
+        ==========
+        .. [1] https://in.mathworks.com/help/control/ref/statespacemodel.obsv.html
+
+        """
+        n = self.num_states
+        ob = self._C
+        for i in range(1,n):
+            ob = ob.col_join(self._C * self._A**i)
+
+        return ob
+
+    def observable_subspace(self):
+        """
+        Returns the observable subspace of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ob_subspace = ss.observable_subspace()
+        >>> ob_subspace
+        [Matrix([
+        [0],
+        [1]]), Matrix([
+        [1],
+        [0]])]
+
+        """
+        return self.observability_matrix().columnspace()
+
+    def is_observable(self):
+        """
+        Returns if the state space model is observable.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.is_observable()
+        True
+
+        """
+        return self.observability_matrix().rank() == self.num_states
+
+    def controllability_matrix(self):
+        """
+        Returns the controllability matrix of the system:
+            [B, A * B, A^2 * B, .. , A^(n-1) * B]; A in R^(n x n), B in R^(n x m)
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.controllability_matrix()
+        Matrix([
+        [0.5, -0.75],
+        [  0,   0.5]])
+
+        References
+        ==========
+        .. [1] https://in.mathworks.com/help/control/ref/statespacemodel.ctrb.html
+
+        """
+        co = self._B
+        n = self._A.shape[0]
+        for i in range(1, n):
+            co = co.row_join(((self._A)**i) * self._B)
+
+        return co
+
+    def controllable_subspace(self):
+        """
+        Returns the controllable subspace of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> co_subspace = ss.controllable_subspace()
+        >>> co_subspace
+        [Matrix([
+        [0.5],
+        [  0]]), Matrix([
+        [-0.75],
+        [  0.5]])]
+
+        """
+        return self.controllability_matrix().columnspace()
+
+    def is_controllable(self):
+        """
+        Returns if the state space model is controllable.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.is_controllable()
+        True
+
+        """
+        return self.controllability_matrix().rank() == self.num_states
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/test_control_plots.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/test_control_plots.py
new file mode 100644
index 0000000000000000000000000000000000000000..05836c806f93c4a8ff375efe2b8bd5f993db7502
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/test_control_plots.py
@@ -0,0 +1,332 @@
+from math import isclose
+from sympy.core.numbers import I, all_close
+from sympy.core.symbol import Dummy
+from sympy.functions.elementary.complexes import (Abs, arg)
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.abc import s, p, a
+from sympy import pi
+from sympy.external import import_module
+from sympy.physics.control.control_plots import \
+    (pole_zero_numerical_data, pole_zero_plot, step_response_numerical_data,
+    step_response_plot, impulse_response_numerical_data,
+    impulse_response_plot, ramp_response_numerical_data,
+    ramp_response_plot, bode_magnitude_numerical_data,
+    bode_phase_numerical_data, bode_plot, nyquist_plot_expr,
+    nichols_plot_expr)
+
+from sympy.physics.control.lti import (TransferFunction,
+    Series, Parallel, TransferFunctionMatrix)
+from sympy.testing.pytest import raises, skip
+
+matplotlib = import_module(
+        'matplotlib', import_kwargs={'fromlist': ['pyplot']},
+        catch=(RuntimeError,))
+
+numpy = import_module('numpy')
+
+tf1 = TransferFunction(1, p**2 + 0.5*p + 2, p)
+tf2 = TransferFunction(p, 6*p**2 + 3*p + 1, p)
+tf3 = TransferFunction(p, p**3 - 1, p)
+tf4 = TransferFunction(10, p**3, p)
+tf5 = TransferFunction(5, s**2 + 2*s + 10, s)
+tf6 = TransferFunction(1, 1, s)
+tf7 = TransferFunction(4*s*3 + 9*s**2 + 0.1*s + 11, 8*s**6 + 9*s**4 + 11, s)
+tf8 = TransferFunction(5, s**2 + (2+I)*s + 10, s)
+
+ser1 = Series(tf4, TransferFunction(1, p - 5, p))
+ser2 = Series(tf3, TransferFunction(p, p + 2, p))
+
+par1 = Parallel(tf1, tf2)
+
+
+def _to_tuple(a, b):
+    return tuple(a), tuple(b)
+
+def _trim_tuple(a, b):
+    a, b = _to_tuple(a, b)
+    return tuple(a[0: 2] + a[len(a)//2 : len(a)//2 + 1] + a[-2:]), \
+        tuple(b[0: 2] + b[len(b)//2 : len(b)//2 + 1] + b[-2:])
+
+def y_coordinate_equality(plot_data_func, evalf_func, system):
+    """Checks whether the y-coordinate value of the plotted
+    data point is equal to the value of the function at a
+    particular x."""
+    x, y = plot_data_func(system)
+    x, y = _trim_tuple(x, y)
+    y_exp = tuple(evalf_func(system, x_i) for x_i in x)
+    return all(Abs(y_exp_i - y_i) < 1e-8 for y_exp_i, y_i in zip(y_exp, y))
+
+
+def test_errors():
+    if not matplotlib:
+        skip("Matplotlib not the default backend")
+
+    # Invalid `system` check
+    tfm = TransferFunctionMatrix([[tf6, tf5], [tf5, tf6]])
+    expr = 1/(s**2 - 1)
+    raises(NotImplementedError, lambda: pole_zero_plot(tfm))
+    raises(NotImplementedError, lambda: pole_zero_numerical_data(expr))
+    raises(NotImplementedError, lambda: impulse_response_plot(expr))
+    raises(NotImplementedError, lambda: impulse_response_numerical_data(tfm))
+    raises(NotImplementedError, lambda: step_response_plot(tfm))
+    raises(NotImplementedError, lambda: step_response_numerical_data(expr))
+    raises(NotImplementedError, lambda: ramp_response_plot(expr))
+    raises(NotImplementedError, lambda: ramp_response_numerical_data(tfm))
+    raises(NotImplementedError, lambda: bode_plot(tfm))
+
+    # More than 1 variables
+    tf_a = TransferFunction(a, s + 1, s)
+    raises(ValueError, lambda: pole_zero_plot(tf_a))
+    raises(ValueError, lambda: pole_zero_numerical_data(tf_a))
+    raises(ValueError, lambda: impulse_response_plot(tf_a))
+    raises(ValueError, lambda: impulse_response_numerical_data(tf_a))
+    raises(ValueError, lambda: step_response_plot(tf_a))
+    raises(ValueError, lambda: step_response_numerical_data(tf_a))
+    raises(ValueError, lambda: ramp_response_plot(tf_a))
+    raises(ValueError, lambda: ramp_response_numerical_data(tf_a))
+    raises(ValueError, lambda: bode_plot(tf_a))
+
+    # lower_limit > 0 for response plots
+    raises(ValueError, lambda: impulse_response_plot(tf1, lower_limit=-1))
+    raises(ValueError, lambda: step_response_plot(tf1, lower_limit=-0.1))
+    raises(ValueError, lambda: ramp_response_plot(tf1, lower_limit=-4/3))
+
+    # slope in ramp_response_plot() is negative
+    raises(ValueError, lambda: ramp_response_plot(tf1, slope=-0.1))
+
+    # incorrect frequency or phase unit
+    raises(ValueError, lambda: bode_plot(tf1,freq_unit = 'hz'))
+    raises(ValueError, lambda: bode_plot(tf1,phase_unit = 'degree'))
+
+
+def test_pole_zero():
+
+    def pz_tester(sys, expected_value):
+        _z, _p = pole_zero_numerical_data(sys)
+        z_check = all_close(_z, expected_value[0])
+        p_check = all_close(_p, expected_value[1])
+        return p_check and z_check
+
+    exp1 = [[], [-0.24999999999999994-1.3919410907075054j, -0.24999999999999994+1.3919410907075054j]]
+    exp2 = [[0.0], [-0.25-0.3227486121839514j, -0.25+0.3227486121839514j]]
+    exp3 = [[0.0], [0.9999999999999998+0j, -0.5000000000000004-0.8660254037844395j,
+        -0.5000000000000004+0.8660254037844395j]]
+    exp4 = [[], [0.0, 0.0, 0.0, 5.0]]
+    exp5 = [[-5.645751311064592, -0.5000000000000008, -0.3542486889354093],
+        [-0.24999999999999986-0.322748612183951348j,
+        -0.2499999999999998+0.32274861218395134j,
+        -0.24999999999999986-1.3919410907075052j,
+         -0.2499999999999998+1.3919410907075052j]]
+    exp6 = [[], [-1.1641600331447917-3.545808351896439j,
+          -0.8358399668552097+2.5458083518964383j]]
+
+    assert pz_tester(tf1, exp1)
+    assert pz_tester(tf2, exp2)
+    assert pz_tester(tf3, exp3)
+    assert pz_tester(ser1, exp4)
+    assert pz_tester(par1, exp5)
+    assert pz_tester(tf8, exp6)
+
+
+def test_bode():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def bode_phase_evalf(system, point):
+        expr = system.to_expr()
+        _w = Dummy("w", real=True)
+        w_expr = expr.subs({system.var: I*_w})
+        return arg(w_expr).subs({_w: point}).evalf()
+
+    def bode_mag_evalf(system, point):
+        expr = system.to_expr()
+        _w = Dummy("w", real=True)
+        w_expr = expr.subs({system.var: I*_w})
+        return 20*log(Abs(w_expr), 10).subs({_w: point}).evalf()
+
+    def test_bode_data(sys):
+        return y_coordinate_equality(bode_magnitude_numerical_data, bode_mag_evalf, sys) \
+            and y_coordinate_equality(bode_phase_numerical_data, bode_phase_evalf, sys)
+
+    assert test_bode_data(tf1)
+    assert test_bode_data(tf2)
+    assert test_bode_data(tf3)
+    assert test_bode_data(tf4)
+    assert test_bode_data(tf5)
+
+
+def check_point_accuracy(a, b):
+    return all(isclose(*_, rel_tol=1e-1, abs_tol=1e-6
+        ) for _ in zip(a, b))
+
+
+def test_impulse_response():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def impulse_res_tester(sys, expected_value):
+        x, y = _to_tuple(*impulse_response_numerical_data(sys,
+            adaptive=False, n=10))
+        x_check = check_point_accuracy(x, expected_value[0])
+        y_check = check_point_accuracy(y, expected_value[1])
+        return x_check and y_check
+
+    exp1 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 0.544019738507865, 0.01993849743234938, -0.31140243360893216, -0.022852779906491996, 0.1778306498155759,
+        0.01962941084328499, -0.1013115194573652, -0.014975541213105696, 0.0575789724730714))
+    exp2 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.1666666675, 0.08389223412935855,
+        0.02338051973475047, -0.014966807776379383, -0.034645954223054234, -0.040560075735512804,
+        -0.037658628907103885, -0.030149507719590022, -0.021162090730736834, -0.012721292737437523))
+    exp3 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (4.369893391586999e-09, 1.1750333000630964,
+        3.2922404058312473, 9.432290008148343, 28.37098083007151, 86.18577464367974, 261.90356653762115,
+        795.6538758627842, 2416.9920942096983, 7342.159505206647))
+    exp4 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 6.17283950617284, 24.69135802469136,
+        55.555555555555564, 98.76543209876544, 154.320987654321, 222.22222222222226, 302.46913580246917,
+        395.0617283950618, 500.0))
+    exp5 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, -0.10455606138085417,
+        0.06757671513476461, -0.03234567568833768, 0.013582514927757873, -0.005273419510705473,
+        0.0019364083003354075, -0.000680070134067832, 0.00022969845960406913, -7.476094359583917e-05))
+    exp6 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-6.016699583000218e-09, 0.35039802056107394, 3.3728423827689884, 12.119846079276684,
+        25.86101014293389, 29.352480635282088, -30.49475907497664, -273.8717189554019, -863.2381702029659,
+        -1747.0262164682233))
+    exp7 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335,
+        4.444444444444445, 5.555555555555555, 6.666666666666667, 7.777777777777779,
+        8.88888888888889, 10.0), (0.0, 18.934638095560974, 5346.93244680907, 1384609.8718249386,
+        358161126.65801865, 92645770015.70108, 23964739753087.42, 6198974342083139.0, 1.603492601616059e+18,
+        4.147764422869658e+20))
+
+    assert impulse_res_tester(tf1, exp1)
+    assert impulse_res_tester(tf2, exp2)
+    assert impulse_res_tester(tf3, exp3)
+    assert impulse_res_tester(tf4, exp4)
+    assert impulse_res_tester(tf5, exp5)
+    assert impulse_res_tester(tf7, exp6)
+    assert impulse_res_tester(ser1, exp7)
+
+
+def test_step_response():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def step_res_tester(sys, expected_value):
+        x, y = _to_tuple(*step_response_numerical_data(sys,
+            adaptive=False, n=10))
+        x_check = check_point_accuracy(x, expected_value[0])
+        y_check = check_point_accuracy(y, expected_value[1])
+        return x_check and y_check
+
+    exp1 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-1.9193285738516863e-08, 0.42283495488246126, 0.7840485977945262, 0.5546841805655717,
+        0.33903033806932087, 0.4627251747410237, 0.5909907598988051, 0.5247213989553071,
+        0.4486997874319281, 0.4839358435839171))
+    exp2 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 0.13728409095645816, 0.19474559355325086, 0.1974909129243011, 0.16841657696573073,
+        0.12559777736159378, 0.08153828016664713, 0.04360471317348958, 0.015072994568868221,
+        -0.003636420058445484))
+    exp3 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 0.6314542141914303, 2.9356520038101035, 9.37731009663807, 28.452300356688376,
+        86.25721933273988, 261.9236645044672, 795.6435410577224, 2416.9786984578764, 7342.154119725917))
+    exp4 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 2.286236899862826, 18.28989519890261, 61.72839629629631, 146.31916159122088, 285.7796124828532,
+        493.8271703703705, 784.1792566529494, 1170.553292729767, 1666.6667))
+    exp5 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-3.999999997894577e-09, 0.6720357068882895, 0.4429938256137113, 0.5182010838004518,
+        0.4944139147159695, 0.5016379853883338, 0.4995466896527733, 0.5001154784851325,
+        0.49997448824584123, 0.5000039745919259))
+    exp6 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-1.5433688493882158e-09, 0.3428705539937336, 1.1253619102202777, 3.1849962651016517,
+        9.47532757182671, 28.727231099148135, 87.29426924860557, 265.2138681048606, 805.6636260007757,
+        2447.387582370878))
+
+    assert step_res_tester(tf1, exp1)
+    assert step_res_tester(tf2, exp2)
+    assert step_res_tester(tf3, exp3)
+    assert step_res_tester(tf4, exp4)
+    assert step_res_tester(tf5, exp5)
+    assert step_res_tester(ser2, exp6)
+
+
+def test_ramp_response():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def ramp_res_tester(sys, num_points, expected_value, slope=1):
+        x, y = _to_tuple(*ramp_response_numerical_data(sys,
+            slope=slope, adaptive=False, n=num_points))
+        x_check = check_point_accuracy(x, expected_value[0])
+        y_check = check_point_accuracy(y, expected_value[1])
+        return x_check and y_check
+
+    exp1 = ((0.0, 2.0, 4.0, 6.0, 8.0, 10.0), (0.0, 0.7324667795033895, 1.9909720978650398,
+        2.7956587704217783, 3.9224897567931514, 4.85022655284895))
+    exp2 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (2.4360213402019326e-08, 0.10175320182493253, 0.33057612497658406, 0.5967937263298935,
+        0.8431511866718248, 1.0398805391471613, 1.1776043125035738, 1.2600994825747305, 1.2981042689274653,
+        1.304684417610106))
+    exp3 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (-3.9329040468771836e-08,
+        0.34686634635794555, 2.9998828170537903, 12.33303690737476, 40.993913948137795, 127.84145222317912,
+        391.41713691996, 1192.0006858708389, 3623.9808672503405, 11011.728034546572))
+    exp4 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 1.9051973784484078, 30.483158055174524,
+        154.32098765432104, 487.7305288827924, 1190.7483615302544, 2469.1358024691367, 4574.3789056546275,
+        7803.688462124678, 12500.0))
+    exp5 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 3.8844361856975635, 9.141792069209865,
+        14.096349157657231, 19.09783068994694, 24.10179770390321, 29.09907319114121, 34.10040420185154,
+        39.09983919254265, 44.10006013058409))
+    exp6 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 1.1111111111111112, 2.2222222222222223,
+        3.3333333333333335, 4.444444444444445, 5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0))
+
+    assert ramp_res_tester(tf1, 6, exp1)
+    assert ramp_res_tester(tf2, 10, exp2, 1.2)
+    assert ramp_res_tester(tf3, 10, exp3, 1.5)
+    assert ramp_res_tester(tf4, 10, exp4, 3)
+    assert ramp_res_tester(tf5, 10, exp5, 9)
+    assert ramp_res_tester(tf6, 10, exp6)
+
+
+def test_nyquist_plot_expr():
+    r1, i1, w1 = nyquist_plot_expr(tf1)
+    r2, i2, w2 = nyquist_plot_expr(tf2)
+    r3, i3, w3 = nyquist_plot_expr(tf3)
+    r4, i4, w4 = nyquist_plot_expr(tf4)
+    assert r1 == (2 - w1**2)/(0.25*w1**2 + (2 - w1**2)**2)
+    assert i1 == -0.5*w1/(0.25*w1**2 + (2 - w1**2)**2)
+    assert r2 == 3*w2**2/(9*w2**2 + (1 - 6*w2**2)**2)
+    assert i2 == w2*(1 - 6*w2**2)/(9*w2**2 + (1 - 6*w2**2)**2)
+    assert r3 == -w3**4/(w3**6 + 1)
+    assert i3 == -w3/(w3**6 + 1)
+    assert r4 == 0
+    assert i4 == 10/w4**3
+
+
+def test_nichols_expr():
+    m1, p1, w1 = nichols_plot_expr(tf1)
+    m2, p2, w2 = nichols_plot_expr(tf2)
+    m3, p3, w3 = nichols_plot_expr(tf3)
+    m4, p4, w4 = nichols_plot_expr(tf4)
+    assert m1 == 20*log(1/sqrt(w1**4 - 3.75*w1**2 + 4))/log(10)
+    assert p1 == 180*arg(1/(-w1**2 + 0.5*w1*I + 2))/pi
+    assert m2 == 20*log(Abs(w2)/sqrt(36*w2**4 - 3*w2**2 + 1))/log(10)
+    assert p2 == 180*arg(w2*I/(-6*w2**2 + 3*w2*I + 1))/pi
+    assert m3 == 20*log(Abs(w3)/sqrt(w3**6 + 1))/log(10)
+    assert p3 == 180*arg(-w3*I/(w3**3*I + 1))/pi
+    assert m4 == 20*log(10/(w4**2*Abs(w4)))/log(10)
+    assert p4 == 180*arg(I/w4**3)/pi
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/test_lti.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/test_lti.py
new file mode 100644
index 0000000000000000000000000000000000000000..a78a4c9b893d11f5e9e94705637080e2a722796a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/control/tests/test_lti.py
@@ -0,0 +1,2273 @@
+from sympy.core.add import Add
+from sympy.core.function import Function
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, pi, Rational, oo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.special.delta_functions import Heaviside
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import atan
+from sympy.matrices.dense import eye
+from sympy.physics.control.lti import SISOLinearTimeInvariant
+from sympy.polys.polytools import factor
+from sympy.polys.rootoftools import CRootOf
+from sympy.simplify.simplify import simplify
+from sympy.core.containers import Tuple
+from sympy.matrices import ImmutableMatrix, Matrix, ShapeError
+from sympy.functions.elementary.trigonometric import sin, cos
+from sympy.physics.control import (TransferFunction, PIDController, Series, Parallel,
+    Feedback, TransferFunctionMatrix, MIMOSeries, MIMOParallel, MIMOFeedback,
+    StateSpace, gbt, bilinear, forward_diff, backward_diff, phase_margin, gain_margin)
+from sympy.testing.pytest import raises
+
+a, x, b, c, s, g, d, p, k, tau, zeta, wn, T = symbols('a, x, b, c, s, g, d, p, k,\
+    tau, zeta, wn, T')
+a0, a1, a2, a3, b0, b1, b2, b3, c0, c1, c2, c3, d0, d1, d2, d3 = symbols('a0:4,\
+    b0:4, c0:4, d0:4')
+TF1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+TF2 = TransferFunction(k, 1, s)
+TF3 = TransferFunction(a2*p - s, a2*s + p, s)
+
+
+def test_TransferFunction_construction():
+    tf = TransferFunction(s + 1, s**2 + s + 1, s)
+    assert tf.num == (s + 1)
+    assert tf.den == (s**2 + s + 1)
+    assert tf.args == (s + 1, s**2 + s + 1, s)
+
+    tf1 = TransferFunction(s + 4, s - 5, s)
+    assert tf1.num == (s + 4)
+    assert tf1.den == (s - 5)
+    assert tf1.args == (s + 4, s - 5, s)
+
+    # using different polynomial variables.
+    tf2 = TransferFunction(p + 3, p**2 - 9, p)
+    assert tf2.num == (p + 3)
+    assert tf2.den == (p**2 - 9)
+    assert tf2.args == (p + 3, p**2 - 9, p)
+
+    tf3 = TransferFunction(p**3 + 5*p**2 + 4, p**4 + 3*p + 1, p)
+    assert tf3.args == (p**3 + 5*p**2 + 4, p**4 + 3*p + 1, p)
+
+    # no pole-zero cancellation on its own.
+    tf4 = TransferFunction((s + 3)*(s - 1), (s - 1)*(s + 5), s)
+    assert tf4.den == (s - 1)*(s + 5)
+    assert tf4.args == ((s + 3)*(s - 1), (s - 1)*(s + 5), s)
+
+    tf4_ = TransferFunction(p + 2, p + 2, p)
+    assert tf4_.args == (p + 2, p + 2, p)
+
+    tf5 = TransferFunction(s - 1, 4 - p, s)
+    assert tf5.args == (s - 1, 4 - p, s)
+
+    tf5_ = TransferFunction(s - 1, s - 1, s)
+    assert tf5_.args == (s - 1, s - 1, s)
+
+    tf6 = TransferFunction(5, 6, s)
+    assert tf6.num == 5
+    assert tf6.den == 6
+    assert tf6.args == (5, 6, s)
+
+    tf6_ = TransferFunction(1/2, 4, s)
+    assert tf6_.num == 0.5
+    assert tf6_.den == 4
+    assert tf6_.args == (0.500000000000000, 4, s)
+
+    tf7 = TransferFunction(3*s**2 + 2*p + 4*s, 8*p**2 + 7*s, s)
+    tf8 = TransferFunction(3*s**2 + 2*p + 4*s, 8*p**2 + 7*s, p)
+    assert not tf7 == tf8
+
+    tf7_ = TransferFunction(a0*s + a1*s**2 + a2*s**3, b0*p - b1*s, s)
+    tf8_ = TransferFunction(a0*s + a1*s**2 + a2*s**3, b0*p - b1*s, s)
+    assert tf7_ == tf8_
+    assert -(-tf7_) == tf7_ == -(-(-(-tf7_)))
+
+    tf9 = TransferFunction(a*s**3 + b*s**2 + g*s + d, d*p + g*p**2 + g*s, s)
+    assert tf9.args == (a*s**3 + b*s**2 + d + g*s, d*p + g*p**2 + g*s, s)
+
+    tf10 = TransferFunction(p**3 + d, g*s**2 + d*s + a, p)
+    tf10_ = TransferFunction(p**3 + d, g*s**2 + d*s + a, p)
+    assert tf10.args == (d + p**3, a + d*s + g*s**2, p)
+    assert tf10_ == tf10
+
+    tf11 = TransferFunction(a1*s + a0, b2*s**2 + b1*s + b0, s)
+    assert tf11.num == (a0 + a1*s)
+    assert tf11.den == (b0 + b1*s + b2*s**2)
+    assert tf11.args == (a0 + a1*s, b0 + b1*s + b2*s**2, s)
+
+    # when just the numerator is 0, leave the denominator alone.
+    tf12 = TransferFunction(0, p**2 - p + 1, p)
+    assert tf12.args == (0, p**2 - p + 1, p)
+
+    tf13 = TransferFunction(0, 1, s)
+    assert tf13.args == (0, 1, s)
+
+    # float exponents
+    tf14 = TransferFunction(a0*s**0.5 + a2*s**0.6 - a1, a1*p**(-8.7), s)
+    assert tf14.args == (a0*s**0.5 - a1 + a2*s**0.6, a1*p**(-8.7), s)
+
+    tf15 = TransferFunction(a2**2*p**(1/4) + a1*s**(-4/5), a0*s - p, p)
+    assert tf15.args == (a1*s**(-0.8) + a2**2*p**0.25, a0*s - p, p)
+
+    omega_o, k_p, k_o, k_i = symbols('omega_o, k_p, k_o, k_i')
+    tf18 = TransferFunction((k_p + k_o*s + k_i/s), s**2 + 2*omega_o*s + omega_o**2, s)
+    assert tf18.num == k_i/s + k_o*s + k_p
+    assert tf18.args == (k_i/s + k_o*s + k_p, omega_o**2 + 2*omega_o*s + s**2, s)
+
+    # ValueError when denominator is zero.
+    raises(ValueError, lambda: TransferFunction(4, 0, s))
+    raises(ValueError, lambda: TransferFunction(s, 0, s))
+    raises(ValueError, lambda: TransferFunction(0, 0, s))
+
+    raises(TypeError, lambda: TransferFunction(Matrix([1, 2, 3]), s, s))
+
+    raises(TypeError, lambda: TransferFunction(s**2 + 2*s - 1, s + 3, 3))
+    raises(TypeError, lambda: TransferFunction(p + 1, 5 - p, 4))
+    raises(TypeError, lambda: TransferFunction(3, 4, 8))
+
+
+def test_TransferFunction_functions():
+    # classmethod from_rational_expression
+    expr_1 = Mul(0, Pow(s, -1, evaluate=False), evaluate=False)
+    expr_2 = s/0
+    expr_3 = (p*s**2 + 5*s)/(s + 1)**3
+    expr_4 = 6
+    expr_5 = ((2 + 3*s)*(5 + 2*s))/((9 + 3*s)*(5 + 2*s**2))
+    expr_6 = (9*s**4 + 4*s**2 + 8)/((s + 1)*(s + 9))
+    tf = TransferFunction(s + 1, s**2 + 2, s)
+    delay = exp(-s/tau)
+    expr_7 = delay*tf.to_expr()
+    H1 = TransferFunction.from_rational_expression(expr_7, s)
+    H2 = TransferFunction(s + 1, (s**2 + 2)*exp(s/tau), s)
+    expr_8 = Add(2,  3*s/(s**2 + 1), evaluate=False)
+
+    assert TransferFunction.from_rational_expression(expr_1) == TransferFunction(0, s, s)
+    raises(ZeroDivisionError, lambda: TransferFunction.from_rational_expression(expr_2))
+    raises(ValueError, lambda: TransferFunction.from_rational_expression(expr_3))
+    assert TransferFunction.from_rational_expression(expr_3, s) == TransferFunction((p*s**2 + 5*s), (s + 1)**3, s)
+    assert TransferFunction.from_rational_expression(expr_3, p) == TransferFunction((p*s**2 + 5*s), (s + 1)**3, p)
+    raises(ValueError, lambda: TransferFunction.from_rational_expression(expr_4))
+    assert TransferFunction.from_rational_expression(expr_4, s) == TransferFunction(6, 1, s)
+    assert TransferFunction.from_rational_expression(expr_5, s) == \
+        TransferFunction((2 + 3*s)*(5 + 2*s), (9 + 3*s)*(5 + 2*s**2), s)
+    assert TransferFunction.from_rational_expression(expr_6, s) == \
+        TransferFunction((9*s**4 + 4*s**2 + 8), (s + 1)*(s + 9), s)
+    assert H1 == H2
+    assert TransferFunction.from_rational_expression(expr_8, s) == \
+        TransferFunction(2*s**2 + 3*s + 2, s**2 + 1, s)
+
+    # classmethod from_coeff_lists
+    tf1 = TransferFunction.from_coeff_lists([1, 2], [3, 4, 5], s)
+    num2 = [p**2, 2*p]
+    den2 = [p**3, p + 1, 4]
+    tf2 = TransferFunction.from_coeff_lists(num2, den2, s)
+    num3 = [1, 2, 3]
+    den3 = [0, 0]
+
+    assert tf1 == TransferFunction(s + 2, 3*s**2 + 4*s + 5, s)
+    assert tf2 == TransferFunction(p**2*s + 2*p, p**3*s**2 + s*(p + 1) + 4, s)
+    raises(ZeroDivisionError, lambda: TransferFunction.from_coeff_lists(num3, den3, s))
+
+    # classmethod from_zpk
+    zeros = [4]
+    poles = [-1+2j, -1-2j]
+    gain = 3
+    tf1 = TransferFunction.from_zpk(zeros, poles, gain, s)
+
+    assert tf1 == TransferFunction(3*s - 12, (s + 1.0 - 2.0*I)*(s + 1.0 + 2.0*I), s)
+
+    # explicitly cancel poles and zeros.
+    tf0 = TransferFunction(s**5 + s**3 + s, s - s**2, s)
+    a = TransferFunction(-(s**4 + s**2 + 1), s - 1, s)
+    assert tf0.simplify() == simplify(tf0) == a
+
+    tf1 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+    b = TransferFunction(p + 3, p + 5, p)
+    assert tf1.simplify() == simplify(tf1) == b
+
+    # expand the numerator and the denominator.
+    G1 = TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+    G2 = TransferFunction(1, -3, p)
+    c = (a2*s**p + a1*s**s + a0*p**p)*(p**s + s**p)
+    d = (b0*s**s + b1*p**s)*(b2*s*p + p**p)
+    e = a0*p**p*p**s + a0*p**p*s**p + a1*p**s*s**s + a1*s**p*s**s + a2*p**s*s**p + a2*s**(2*p)
+    f = b0*b2*p*s*s**s + b0*p**p*s**s + b1*b2*p*p**s*s + b1*p**p*p**s
+    g = a1*a2*s*s**p + a1*p*s + a2*b1*p*s*s**p + b1*p**2*s
+    G3 = TransferFunction(c, d, s)
+    G4 = TransferFunction(a0*s**s - b0*p**p, (a1*s + b1*s*p)*(a2*s**p + p), p)
+
+    assert G1.expand() == TransferFunction(s**2 - 2*s + 1, s**4 + 2*s**2 + 1, s)
+    assert tf1.expand() == TransferFunction(p**2 + 2*p - 3, p**2 + 4*p - 5, p)
+    assert G2.expand() == G2
+    assert G3.expand() == TransferFunction(e, f, s)
+    assert G4.expand() == TransferFunction(a0*s**s - b0*p**p, g, p)
+
+    # purely symbolic polynomials.
+    p1 = a1*s + a0
+    p2 = b2*s**2 + b1*s + b0
+    SP1 = TransferFunction(p1, p2, s)
+    expect1 = TransferFunction(2.0*s + 1.0, 5.0*s**2 + 4.0*s + 3.0, s)
+    expect1_ = TransferFunction(2*s + 1, 5*s**2 + 4*s + 3, s)
+    assert SP1.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}) == expect1_
+    assert SP1.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}).evalf() == expect1
+    assert expect1_.evalf() == expect1
+
+    c1, d0, d1, d2 = symbols('c1, d0:3')
+    p3, p4 = c1*p, d2*p**3 + d1*p**2 - d0
+    SP2 = TransferFunction(p3, p4, p)
+    expect2 = TransferFunction(2.0*p, 5.0*p**3 + 2.0*p**2 - 3.0, p)
+    expect2_ = TransferFunction(2*p, 5*p**3 + 2*p**2 - 3, p)
+    assert SP2.subs({c1: 2, d0: 3, d1: 2, d2: 5}) == expect2_
+    assert SP2.subs({c1: 2, d0: 3, d1: 2, d2: 5}).evalf() == expect2
+    assert expect2_.evalf() == expect2
+
+    SP3 = TransferFunction(a0*p**3 + a1*s**2 - b0*s + b1, a1*s + p, s)
+    expect3 = TransferFunction(2.0*p**3 + 4.0*s**2 - s + 5.0, p + 4.0*s, s)
+    expect3_ = TransferFunction(2*p**3 + 4*s**2 - s + 5, p + 4*s, s)
+    assert SP3.subs({a0: 2, a1: 4, b0: 1, b1: 5}) == expect3_
+    assert SP3.subs({a0: 2, a1: 4, b0: 1, b1: 5}).evalf() == expect3
+    assert expect3_.evalf() == expect3
+
+    SP4 = TransferFunction(s - a1*p**3, a0*s + p, p)
+    expect4 = TransferFunction(7.0*p**3 + s, p - s, p)
+    expect4_ = TransferFunction(7*p**3 + s, p - s, p)
+    assert SP4.subs({a0: -1, a1: -7}) == expect4_
+    assert SP4.subs({a0: -1, a1: -7}).evalf() == expect4
+    assert expect4_.evalf() == expect4
+
+    # evaluate the transfer function at particular frequencies.
+    assert tf1.eval_frequency(wn) == wn**2/(wn**2 + 4*wn - 5) + 2*wn/(wn**2 + 4*wn - 5) - 3/(wn**2 + 4*wn - 5)
+    assert G1.eval_frequency(1 + I) == S(3)/25 + S(4)*I/25
+    assert G4.eval_frequency(S(5)/3) == \
+        a0*s**s/(a1*a2*s**(S(8)/3) + S(5)*a1*s/3 + 5*a2*b1*s**(S(8)/3)/3 + S(25)*b1*s/9) - 5*3**(S(1)/3)*5**(S(2)/3)*b0/(9*a1*a2*s**(S(8)/3) + 15*a1*s + 15*a2*b1*s**(S(8)/3) + 25*b1*s)
+
+    # Low-frequency (or DC) gain.
+    assert tf0.dc_gain() == 1
+    assert tf1.dc_gain() == Rational(3, 5)
+    assert SP2.dc_gain() == 0
+    assert expect4.dc_gain() == -1
+    assert expect2_.dc_gain() == 0
+    assert TransferFunction(1, s, s).dc_gain() == oo
+
+    # Poles of a transfer function.
+    tf_ = TransferFunction(x**3 - k, k, x)
+    _tf = TransferFunction(k, x**4 - k, x)
+    TF_ = TransferFunction(x**2, x**10 + x + x**2, x)
+    _TF = TransferFunction(x**10 + x + x**2, x**2, x)
+    assert G1.poles() == [I, I, -I, -I]
+    assert G2.poles() == []
+    assert tf1.poles() == [-5, 1]
+    assert expect4_.poles() == [s]
+    assert SP4.poles() == [-a0*s]
+    assert expect3.poles() == [-0.25*p]
+    assert str(expect2.poles()) == str([0.729001428685125, -0.564500714342563 - 0.710198984796332*I, -0.564500714342563 + 0.710198984796332*I])
+    assert str(expect1.poles()) == str([-0.4 - 0.66332495807108*I, -0.4 + 0.66332495807108*I])
+    assert _tf.poles() == [k**(Rational(1, 4)), -k**(Rational(1, 4)), I*k**(Rational(1, 4)), -I*k**(Rational(1, 4))]
+    assert TF_.poles() == [CRootOf(x**9 + x + 1, 0), 0, CRootOf(x**9 + x + 1, 1), CRootOf(x**9 + x + 1, 2),
+        CRootOf(x**9 + x + 1, 3), CRootOf(x**9 + x + 1, 4), CRootOf(x**9 + x + 1, 5), CRootOf(x**9 + x + 1, 6),
+        CRootOf(x**9 + x + 1, 7), CRootOf(x**9 + x + 1, 8)]
+    raises(NotImplementedError, lambda: TransferFunction(x**2, a0*x**10 + x + x**2, x).poles())
+
+    # Stability of a transfer function.
+    q, r = symbols('q, r', negative=True)
+    t = symbols('t', positive=True)
+    TF_ = TransferFunction(s**2 + a0 - a1*p, q*s - r, s)
+    stable_tf = TransferFunction(s**2 + a0 - a1*p, q*s - 1, s)
+    stable_tf_ = TransferFunction(s**2 + a0 - a1*p, q*s - t, s)
+
+    assert G1.is_stable() is False
+    assert G2.is_stable() is True
+    assert tf1.is_stable() is False   # as one pole is +ve, and the other is -ve.
+    assert expect2.is_stable() is False
+    assert expect1.is_stable() is True
+    assert stable_tf.is_stable() is True
+    assert stable_tf_.is_stable() is True
+    assert TF_.is_stable() is False
+    assert expect4_.is_stable() is None   # no assumption provided for the only pole 's'.
+    assert SP4.is_stable() is None
+
+    # Zeros of a transfer function.
+    assert G1.zeros() == [1, 1]
+    assert G2.zeros() == []
+    assert tf1.zeros() == [-3, 1]
+    assert expect4_.zeros() == [7**(Rational(2, 3))*(-s)**(Rational(1, 3))/7, -7**(Rational(2, 3))*(-s)**(Rational(1, 3))/14 -
+        sqrt(3)*7**(Rational(2, 3))*I*(-s)**(Rational(1, 3))/14, -7**(Rational(2, 3))*(-s)**(Rational(1, 3))/14 + sqrt(3)*7**(Rational(2, 3))*I*(-s)**(Rational(1, 3))/14]
+    assert SP4.zeros() == [(s/a1)**(Rational(1, 3)), -(s/a1)**(Rational(1, 3))/2 - sqrt(3)*I*(s/a1)**(Rational(1, 3))/2,
+        -(s/a1)**(Rational(1, 3))/2 + sqrt(3)*I*(s/a1)**(Rational(1, 3))/2]
+    assert str(expect3.zeros()) == str([0.125 - 1.11102430216445*sqrt(-0.405063291139241*p**3 - 1.0),
+        1.11102430216445*sqrt(-0.405063291139241*p**3 - 1.0) + 0.125])
+    assert tf_.zeros() == [k**(Rational(1, 3)), -k**(Rational(1, 3))/2 - sqrt(3)*I*k**(Rational(1, 3))/2,
+        -k**(Rational(1, 3))/2 + sqrt(3)*I*k**(Rational(1, 3))/2]
+    assert _TF.zeros() == [CRootOf(x**9 + x + 1, 0), 0, CRootOf(x**9 + x + 1, 1), CRootOf(x**9 + x + 1, 2),
+        CRootOf(x**9 + x + 1, 3), CRootOf(x**9 + x + 1, 4), CRootOf(x**9 + x + 1, 5), CRootOf(x**9 + x + 1, 6),
+        CRootOf(x**9 + x + 1, 7), CRootOf(x**9 + x + 1, 8)]
+    raises(NotImplementedError, lambda: TransferFunction(a0*x**10 + x + x**2, x**2, x).zeros())
+
+    # negation of TF.
+    tf2 = TransferFunction(s + 3, s**2 - s**3 + 9, s)
+    tf3 = TransferFunction(-3*p + 3, 1 - p, p)
+    assert -tf2 == TransferFunction(-s - 3, s**2 - s**3 + 9, s)
+    assert -tf3 == TransferFunction(3*p - 3, 1 - p, p)
+
+    # taking power of a TF.
+    tf4 = TransferFunction(p + 4, p - 3, p)
+    tf5 = TransferFunction(s**2 + 1, 1 - s, s)
+    expect2 = TransferFunction((s**2 + 1)**3, (1 - s)**3, s)
+    expect1 = TransferFunction((p + 4)**2, (p - 3)**2, p)
+    assert (tf4*tf4).doit() == tf4**2 == pow(tf4, 2) == expect1
+    assert (tf5*tf5*tf5).doit() == tf5**3 == pow(tf5, 3) == expect2
+    assert tf5**0 == pow(tf5, 0) == TransferFunction(1, 1, s)
+    assert Series(tf4).doit()**-1 == tf4**-1 == pow(tf4, -1) == TransferFunction(p - 3, p + 4, p)
+    assert (tf5*tf5).doit()**-1 == tf5**-2 == pow(tf5, -2) == TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+
+    raises(ValueError, lambda: tf4**(s**2 + s - 1))
+    raises(ValueError, lambda: tf5**s)
+    raises(ValueError, lambda: tf4**tf5)
+
+    # SymPy's own functions.
+    tf = TransferFunction(s - 1, s**2 - 2*s + 1, s)
+    tf6 = TransferFunction(s + p, p**2 - 5, s)
+    assert factor(tf) == TransferFunction(s - 1, (s - 1)**2, s)
+    assert tf.num.subs(s, 2) == tf.den.subs(s, 2) == 1
+    # subs & xreplace
+    assert tf.subs(s, 2) == TransferFunction(s - 1, s**2 - 2*s + 1, s)
+    assert tf6.subs(p, 3) == TransferFunction(s + 3, 4, s)
+    assert tf3.xreplace({p: s}) == TransferFunction(-3*s + 3, 1 - s, s)
+    raises(TypeError, lambda: tf3.xreplace({p: exp(2)}))
+    assert tf3.subs(p, exp(2)) == tf3
+
+    tf7 = TransferFunction(a0*s**p + a1*p**s, a2*p - s, s)
+    assert tf7.xreplace({s: k}) == TransferFunction(a0*k**p + a1*p**k, a2*p - k, k)
+    assert tf7.subs(s, k) == TransferFunction(a0*s**p + a1*p**s, a2*p - s, s)
+
+    # Conversion to Expr with to_expr()
+    tf8 = TransferFunction(a0*s**5 + 5*s**2 + 3, s**6 - 3, s)
+    tf9 = TransferFunction((5 + s), (5 + s)*(6 + s), s)
+    tf10 = TransferFunction(0, 1, s)
+    tf11 = TransferFunction(1, 1, s)
+    assert tf8.to_expr() == Mul((a0*s**5 + 5*s**2 + 3), Pow((s**6 - 3), -1, evaluate=False), evaluate=False)
+    assert tf9.to_expr() == Mul((s + 5), Pow((5 + s)*(6 + s), -1, evaluate=False), evaluate=False)
+    assert tf10.to_expr() == Mul(S(0), Pow(1, -1, evaluate=False), evaluate=False)
+    assert tf11.to_expr() == Pow(1, -1, evaluate=False)
+
+
+def test_TransferFunction_addition_and_subtraction():
+    tf1 = TransferFunction(s + 6, s - 5, s)
+    tf2 = TransferFunction(s + 3, s + 1, s)
+    tf3 = TransferFunction(s + 1, s**2 + s + 1, s)
+    tf4 = TransferFunction(p, 2 - p, p)
+
+    # addition
+    assert tf1 + tf2 == Parallel(tf1, tf2)
+    assert tf3 + tf1 == Parallel(tf3, tf1)
+    assert -tf1 + tf2 + tf3 == Parallel(-tf1, tf2, tf3)
+    assert tf1 + (tf2 + tf3) == Parallel(tf1, tf2, tf3)
+
+    c = symbols("c", commutative=False)
+    raises(ValueError, lambda: tf1 + Matrix([1, 2, 3]))
+    raises(ValueError, lambda: tf2 + c)
+    raises(ValueError, lambda: tf3 + tf4)
+    raises(ValueError, lambda: tf1 + (s - 1))
+    raises(ValueError, lambda: tf1 + 8)
+    raises(ValueError, lambda: (1 - p**3) + tf1)
+
+    # subtraction
+    assert tf1 - tf2 == Parallel(tf1, -tf2)
+    assert tf3 - tf2 == Parallel(tf3, -tf2)
+    assert -tf1 - tf3 == Parallel(-tf1, -tf3)
+    assert tf1 - tf2 + tf3 == Parallel(tf1, -tf2, tf3)
+
+    raises(ValueError, lambda: tf1 - Matrix([1, 2, 3]))
+    raises(ValueError, lambda: tf3 - tf4)
+    raises(ValueError, lambda: tf1 - (s - 1))
+    raises(ValueError, lambda: tf1 - 8)
+    raises(ValueError, lambda: (s + 5) - tf2)
+    raises(ValueError, lambda: (1 + p**4) - tf1)
+
+
+def test_TransferFunction_multiplication_and_division():
+    G1 = TransferFunction(s + 3, -s**3 + 9, s)
+    G2 = TransferFunction(s + 1, s - 5, s)
+    G3 = TransferFunction(p, p**4 - 6, p)
+    G4 = TransferFunction(p + 4, p - 5, p)
+    G5 = TransferFunction(s + 6, s - 5, s)
+    G6 = TransferFunction(s + 3, s + 1, s)
+    G7 = TransferFunction(1, 1, s)
+
+    # multiplication
+    assert G1*G2 == Series(G1, G2)
+    assert -G1*G5 == Series(-G1, G5)
+    assert -G2*G5*-G6 == Series(-G2, G5, -G6)
+    assert -G1*-G2*-G5*-G6 == Series(-G1, -G2, -G5, -G6)
+    assert G3*G4 == Series(G3, G4)
+    assert (G1*G2)*-(G5*G6) == \
+        Series(G1, G2, TransferFunction(-1, 1, s), Series(G5, G6))
+    assert G1*G2*(G5 + G6) == Series(G1, G2, Parallel(G5, G6))
+
+    # division - See ``test_Feedback_functions()`` for division by Parallel objects.
+    assert G5/G6 == Series(G5, pow(G6, -1))
+    assert -G3/G4 == Series(-G3, pow(G4, -1))
+    assert (G5*G6)/G7 == Series(G5, G6, pow(G7, -1))
+
+    c = symbols("c", commutative=False)
+    raises(ValueError, lambda: G3 * Matrix([1, 2, 3]))
+    raises(ValueError, lambda: G1 * c)
+    raises(ValueError, lambda: G3 * G5)
+    raises(ValueError, lambda: G5 * (s - 1))
+    raises(ValueError, lambda: 9 * G5)
+
+    raises(ValueError, lambda: G3 / Matrix([1, 2, 3]))
+    raises(ValueError, lambda: G6 / 0)
+    raises(ValueError, lambda: G3 / G5)
+    raises(ValueError, lambda: G5 / 2)
+    raises(ValueError, lambda: G5 / s**2)
+    raises(ValueError, lambda: (s - 4*s**2) / G2)
+    raises(ValueError, lambda: 0 / G4)
+    raises(ValueError, lambda: G7 / (1 + G6))
+    raises(ValueError, lambda: G7 / (G5 * G6))
+    raises(ValueError, lambda: G7 / (G7 + (G5 + G6)))
+
+
+def test_TransferFunction_is_proper():
+    omega_o, zeta, tau = symbols('omega_o, zeta, tau')
+    G1 = TransferFunction(omega_o**2, s**2 + p*omega_o*zeta*s + omega_o**2, omega_o)
+    G2 = TransferFunction(tau - s**3, tau + p**4, tau)
+    G3 = TransferFunction(a*b*s**3 + s**2 - a*p + s, b - s*p**2, p)
+    G4 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+    assert G1.is_proper
+    assert G2.is_proper
+    assert G3.is_proper
+    assert not G4.is_proper
+
+
+def test_TransferFunction_is_strictly_proper():
+    omega_o, zeta, tau = symbols('omega_o, zeta, tau')
+    tf1 = TransferFunction(omega_o**2, s**2 + p*omega_o*zeta*s + omega_o**2, omega_o)
+    tf2 = TransferFunction(tau - s**3, tau + p**4, tau)
+    tf3 = TransferFunction(a*b*s**3 + s**2 - a*p + s, b - s*p**2, p)
+    tf4 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+    assert not tf1.is_strictly_proper
+    assert not tf2.is_strictly_proper
+    assert tf3.is_strictly_proper
+    assert not tf4.is_strictly_proper
+
+
+def test_TransferFunction_is_biproper():
+    tau, omega_o, zeta = symbols('tau, omega_o, zeta')
+    tf1 = TransferFunction(omega_o**2, s**2 + p*omega_o*zeta*s + omega_o**2, omega_o)
+    tf2 = TransferFunction(tau - s**3, tau + p**4, tau)
+    tf3 = TransferFunction(a*b*s**3 + s**2 - a*p + s, b - s*p**2, p)
+    tf4 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+    assert tf1.is_biproper
+    assert tf2.is_biproper
+    assert not tf3.is_biproper
+    assert not tf4.is_biproper
+
+
+def test_PIDController():
+    kp, ki, kd, tf = symbols("kp ki kd tf")
+    p1 = PIDController(kp, ki, kd, tf)
+    p2 = PIDController()
+
+    # Type Checking
+    assert isinstance(p1, PIDController)
+    assert isinstance(p1, TransferFunction)
+
+    # Properties checking
+    assert p1 == PIDController(kp, ki, kd, tf, s)
+    assert p2 == PIDController(kp, ki, kd, 0, s)
+    assert p1.num == kd*s**2 + ki*s*tf + ki + kp*s**2*tf + kp*s
+    assert p1.den == s**2*tf + s
+    assert p1.var == s
+    assert p1.kp == kp
+    assert p1.ki == ki
+    assert p1.kd == kd
+    assert p1.tf == tf
+
+    # Functionality checking
+    assert p1.doit() == TransferFunction(kd*s**2 + ki*s*tf + ki + kp*s**2*tf + kp*s, s**2*tf + s, s)
+    assert p1.is_proper == True
+    assert p1.is_biproper == True
+    assert p1.is_strictly_proper == False
+    assert p2.doit() == TransferFunction(kd*s**2 + ki + kp*s, s, s)
+
+    # Using PIDController with TransferFunction
+    tf1 = TransferFunction(s, s + 1, s)
+    par1 = Parallel(p1, tf1)
+    ser1 = Series(p1, tf1)
+    fed1 = Feedback(p1, tf1)
+    assert par1 == Parallel(PIDController(kp, ki, kd, tf, s), TransferFunction(s, s + 1, s))
+    assert ser1 == Series(PIDController(kp, ki, kd, tf, s), TransferFunction(s, s + 1, s))
+    assert fed1 == Feedback(PIDController(kp, ki, kd, tf, s), TransferFunction(s, s + 1, s))
+    assert par1.doit() == TransferFunction(s*(s**2*tf + s) + (s + 1)*(kd*s**2 + ki*s*tf + ki + kp*s**2*tf + kp*s),
+                                           (s + 1)*(s**2*tf + s), s)
+    assert ser1.doit() == TransferFunction(s*(kd*s**2 + ki*s*tf + ki + kp*s**2*tf + kp*s),
+                                           (s + 1)*(s**2*tf + s), s)
+    assert fed1.doit() == TransferFunction((s + 1)*(s**2*tf + s)*(kd*s**2 + ki*s*tf + ki + kp*s**2*tf + kp*s),
+                                           (s*(kd*s**2 + ki*s*tf + ki + kp*s**2*tf + kp*s) + (s + 1)*(s**2*tf + s))*(s**2*tf + s), s)
+
+
+def test_Series_construction():
+    tf = TransferFunction(a0*s**3 + a1*s**2 - a2*s, b0*p**4 + b1*p**3 - b2*s*p, s)
+    tf2 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf3 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf4 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    inp = Function('X_d')(s)
+    out = Function('X')(s)
+
+    s0 = Series(tf, tf2)
+    assert s0.args == (tf, tf2)
+    assert s0.var == s
+
+    s1 = Series(Parallel(tf, -tf2), tf2)
+    assert s1.args == (Parallel(tf, -tf2), tf2)
+    assert s1.var == s
+
+    tf3_ = TransferFunction(inp, 1, s)
+    tf4_ = TransferFunction(-out, 1, s)
+    s2 = Series(tf, Parallel(tf3_, tf4_), tf2)
+    assert s2.args == (tf, Parallel(tf3_, tf4_), tf2)
+
+    s3 = Series(tf, tf2, tf4)
+    assert s3.args == (tf, tf2, tf4)
+
+    s4 = Series(tf3_, tf4_)
+    assert s4.args == (tf3_, tf4_)
+    assert s4.var == s
+
+    s6 = Series(tf2, tf4, Parallel(tf2, -tf), tf4)
+    assert s6.args == (tf2, tf4, Parallel(tf2, -tf), tf4)
+
+    s7 = Series(tf, tf2)
+    assert s0 == s7
+    assert not s0 == s2
+
+    raises(ValueError, lambda: Series(tf, tf3))
+    raises(ValueError, lambda: Series(tf, tf2, tf3, tf4))
+    raises(ValueError, lambda: Series(-tf3, tf2))
+    raises(TypeError, lambda: Series(2, tf, tf4))
+    raises(TypeError, lambda: Series(s**2 + p*s, tf3, tf2))
+    raises(TypeError, lambda: Series(tf3, Matrix([1, 2, 3, 4])))
+
+
+def test_MIMOSeries_construction():
+    tf_1 = TransferFunction(a0*s**3 + a1*s**2 - a2*s, b0*p**4 + b1*p**3 - b2*s*p, s)
+    tf_2 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf_3 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+
+    tfm_1 = TransferFunctionMatrix([[tf_1, tf_2, tf_3], [-tf_3, -tf_2, tf_1]])
+    tfm_2 = TransferFunctionMatrix([[-tf_2], [-tf_2], [-tf_3]])
+    tfm_3 = TransferFunctionMatrix([[-tf_3]])
+    tfm_4 = TransferFunctionMatrix([[TF3], [TF2], [-TF1]])
+    tfm_5 = TransferFunctionMatrix.from_Matrix(Matrix([1/p]), p)
+
+    s8 = MIMOSeries(tfm_2, tfm_1)
+    assert s8.args == (tfm_2, tfm_1)
+    assert s8.var == s
+    assert s8.shape == (s8.num_outputs, s8.num_inputs) == (2, 1)
+
+    s9 = MIMOSeries(tfm_3, tfm_2, tfm_1)
+    assert s9.args == (tfm_3, tfm_2, tfm_1)
+    assert s9.var == s
+    assert s9.shape == (s9.num_outputs, s9.num_inputs) == (2, 1)
+
+    s11 = MIMOSeries(tfm_3, MIMOParallel(-tfm_2, -tfm_4), tfm_1)
+    assert s11.args == (tfm_3, MIMOParallel(-tfm_2, -tfm_4), tfm_1)
+    assert s11.shape == (s11.num_outputs, s11.num_inputs) == (2, 1)
+
+    # arg cannot be empty tuple.
+    raises(ValueError, lambda: MIMOSeries())
+
+    # arg cannot contain SISO as well as MIMO systems.
+    raises(TypeError, lambda: MIMOSeries(tfm_1, tf_1))
+
+    # for all the adjacent transfer function matrices:
+    # no. of inputs of first TFM must be equal to the no. of outputs of the second TFM.
+    raises(ValueError, lambda: MIMOSeries(tfm_1, tfm_2, -tfm_1))
+
+    # all the TFMs must use the same complex variable.
+    raises(ValueError, lambda: MIMOSeries(tfm_3, tfm_5))
+
+    # Number or expression not allowed in the arguments.
+    raises(TypeError, lambda: MIMOSeries(2, tfm_2, tfm_3))
+    raises(TypeError, lambda: MIMOSeries(s**2 + p*s, -tfm_2, tfm_3))
+    raises(TypeError, lambda: MIMOSeries(Matrix([1/p]), tfm_3))
+
+
+def test_Series_functions():
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    assert tf1*tf2*tf3 == Series(tf1, tf2, tf3) == Series(Series(tf1, tf2), tf3) \
+        == Series(tf1, Series(tf2, tf3))
+    assert tf1*(tf2 + tf3) == Series(tf1, Parallel(tf2, tf3))
+    assert tf1*tf2 + tf5 == Parallel(Series(tf1, tf2), tf5)
+    assert tf1*tf2 - tf5 == Parallel(Series(tf1, tf2), -tf5)
+    assert tf1*tf2 + tf3 + tf5 == Parallel(Series(tf1, tf2), tf3, tf5)
+    assert tf1*tf2 - tf3 - tf5 == Parallel(Series(tf1, tf2), -tf3, -tf5)
+    assert tf1*tf2 - tf3 + tf5 == Parallel(Series(tf1, tf2), -tf3, tf5)
+    assert tf1*tf2 + tf3*tf5 == Parallel(Series(tf1, tf2), Series(tf3, tf5))
+    assert tf1*tf2 - tf3*tf5 == Parallel(Series(tf1, tf2), Series(TransferFunction(-1, 1, s), Series(tf3, tf5)))
+    assert tf2*tf3*(tf2 - tf1)*tf3 == Series(tf2, tf3, Parallel(tf2, -tf1), tf3)
+    assert -tf1*tf2 == Series(-tf1, tf2)
+    assert -(tf1*tf2) == Series(TransferFunction(-1, 1, s), Series(tf1, tf2))
+    raises(ValueError, lambda: tf1*tf2*tf4)
+    raises(ValueError, lambda: tf1*(tf2 - tf4))
+    raises(ValueError, lambda: tf3*Matrix([1, 2, 3]))
+
+    # evaluate=True -> doit()
+    assert Series(tf1, tf2, evaluate=True) == Series(tf1, tf2).doit() == \
+        TransferFunction(k, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Series(tf1, tf2, Parallel(tf1, -tf3), evaluate=True) == Series(tf1, tf2, Parallel(tf1, -tf3)).doit() == \
+        TransferFunction(k*(a2*s + p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2)), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)**2, s)
+    assert Series(tf2, tf1, -tf3, evaluate=True) == Series(tf2, tf1, -tf3).doit() == \
+        TransferFunction(k*(-a2*p + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert not Series(tf1, -tf2, evaluate=False) == Series(tf1, -tf2).doit()
+
+    assert Series(Parallel(tf1, tf2), Parallel(tf2, -tf3)).doit() == \
+        TransferFunction((k*(s**2 + 2*s*wn*zeta + wn**2) + 1)*(-a2*p + k*(a2*s + p) + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Series(-tf1, -tf2, -tf3).doit() == \
+        TransferFunction(k*(-a2*p + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert -Series(tf1, tf2, tf3).doit() == \
+        TransferFunction(-k*(a2*p - s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Series(tf2, tf3, Parallel(tf2, -tf1), tf3).doit() == \
+        TransferFunction(k*(a2*p - s)**2*(k*(s**2 + 2*s*wn*zeta + wn**2) - 1), (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    assert Series(tf1, tf2).rewrite(TransferFunction) == TransferFunction(k, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Series(tf2, tf1, -tf3).rewrite(TransferFunction) == \
+        TransferFunction(k*(-a2*p + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    S1 = Series(Parallel(tf1, tf2), Parallel(tf2, -tf3))
+    assert S1.is_proper
+    assert not S1.is_strictly_proper
+    assert S1.is_biproper
+
+    S2 = Series(tf1, tf2, tf3)
+    assert S2.is_proper
+    assert S2.is_strictly_proper
+    assert not S2.is_biproper
+
+    S3 = Series(tf1, -tf2, Parallel(tf1, -tf3))
+    assert S3.is_proper
+    assert S3.is_strictly_proper
+    assert not S3.is_biproper
+
+
+def test_MIMOSeries_functions():
+    tfm1 = TransferFunctionMatrix([[TF1, TF2, TF3], [-TF3, -TF2, TF1]])
+    tfm2 = TransferFunctionMatrix([[-TF1], [-TF2], [-TF3]])
+    tfm3 = TransferFunctionMatrix([[-TF1]])
+    tfm4 = TransferFunctionMatrix([[-TF2, -TF3], [-TF1, TF2]])
+    tfm5 = TransferFunctionMatrix([[TF2, -TF2], [-TF3, -TF2]])
+    tfm6 = TransferFunctionMatrix([[-TF3], [TF1]])
+    tfm7 = TransferFunctionMatrix([[TF1], [-TF2]])
+
+    assert tfm1*tfm2 + tfm6 == MIMOParallel(MIMOSeries(tfm2, tfm1), tfm6)
+    assert tfm1*tfm2 + tfm7 + tfm6 == MIMOParallel(MIMOSeries(tfm2, tfm1), tfm7, tfm6)
+    assert tfm1*tfm2 - tfm6 - tfm7 == MIMOParallel(MIMOSeries(tfm2, tfm1), -tfm6, -tfm7)
+    assert tfm4*tfm5 + (tfm4 - tfm5) == MIMOParallel(MIMOSeries(tfm5, tfm4), tfm4, -tfm5)
+    assert tfm4*-tfm6 + (-tfm4*tfm6) == MIMOParallel(MIMOSeries(-tfm6, tfm4), MIMOSeries(tfm6, -tfm4))
+
+    raises(ValueError, lambda: tfm1*tfm2 + TF1)
+    raises(TypeError, lambda: tfm1*tfm2 + a0)
+    raises(TypeError, lambda: tfm4*tfm6 - (s - 1))
+    raises(TypeError, lambda: tfm4*-tfm6 - 8)
+    raises(TypeError, lambda: (-1 + p**5) + tfm1*tfm2)
+
+    # Shape criteria.
+
+    raises(TypeError, lambda: -tfm1*tfm2 + tfm4)
+    raises(TypeError, lambda: tfm1*tfm2 - tfm4 + tfm5)
+    raises(TypeError, lambda: tfm1*tfm2 - tfm4*tfm5)
+
+    assert tfm1*tfm2*-tfm3 == MIMOSeries(-tfm3, tfm2, tfm1)
+    assert (tfm1*-tfm2)*tfm3 == MIMOSeries(tfm3, -tfm2, tfm1)
+
+    # Multiplication of a Series object with a SISO TF not allowed.
+
+    raises(ValueError, lambda: tfm4*tfm5*TF1)
+    raises(TypeError, lambda: tfm4*tfm5*a1)
+    raises(TypeError, lambda: tfm4*-tfm5*(s - 2))
+    raises(TypeError, lambda: tfm5*tfm4*9)
+    raises(TypeError, lambda: (-p**3 + 1)*tfm5*tfm4)
+
+    # Transfer function matrix in the arguments.
+    assert (MIMOSeries(tfm2, tfm1, evaluate=True) == MIMOSeries(tfm2, tfm1).doit()
+        == TransferFunctionMatrix(((TransferFunction(-k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (-a2*p + s)*(a2*p - s)*(s**2 + 2*s*wn*zeta + wn**2)**2 - (a2*s + p)**2,
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2, s),),
+        (TransferFunction(k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (-a2*p + s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + (a2*p - s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2),
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2, s),))))
+
+    # doit() should not cancel poles and zeros.
+    mat_1 = Matrix([[1/(1+s), (1+s)/(1+s**2+2*s)**3]])
+    mat_2 = Matrix([[(1+s)], [(1+s**2+2*s)**3/(1+s)]])
+    tm_1, tm_2 = TransferFunctionMatrix.from_Matrix(mat_1, s), TransferFunctionMatrix.from_Matrix(mat_2, s)
+    assert (MIMOSeries(tm_2, tm_1).doit()
+        == TransferFunctionMatrix(((TransferFunction(2*(s + 1)**2*(s**2 + 2*s + 1)**3, (s + 1)**2*(s**2 + 2*s + 1)**3, s),),)))
+    assert MIMOSeries(tm_2, tm_1).doit().simplify() == TransferFunctionMatrix(((TransferFunction(2, 1, s),),))
+
+    # calling doit() will expand the internal Series and Parallel objects.
+    assert (MIMOSeries(-tfm3, -tfm2, tfm1, evaluate=True)
+        == MIMOSeries(-tfm3, -tfm2, tfm1).doit()
+        == TransferFunctionMatrix(((TransferFunction(k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (a2*p - s)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (a2*s + p)**2,
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**3, s),),
+        (TransferFunction(-k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (-a2*p + s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + (a2*p - s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2),
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**3, s),))))
+    assert (MIMOSeries(MIMOParallel(tfm4, tfm5), tfm5, evaluate=True)
+        == MIMOSeries(MIMOParallel(tfm4, tfm5), tfm5).doit()
+        == TransferFunctionMatrix(((TransferFunction(-k*(-a2*s - p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2)), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s), TransferFunction(k*(-a2*p - \
+            k*(a2*s + p) + s), a2*s + p, s)), (TransferFunction(-k*(-a2*s - p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2)), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s), \
+            TransferFunction((-a2*p + s)*(-a2*p - k*(a2*s + p) + s), (a2*s + p)**2, s)))) == MIMOSeries(MIMOParallel(tfm4, tfm5), tfm5).rewrite(TransferFunctionMatrix))
+
+
+def test_Parallel_construction():
+    tf = TransferFunction(a0*s**3 + a1*s**2 - a2*s, b0*p**4 + b1*p**3 - b2*s*p, s)
+    tf2 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf3 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf4 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    inp = Function('X_d')(s)
+    out = Function('X')(s)
+
+    p0 = Parallel(tf, tf2)
+    assert p0.args == (tf, tf2)
+    assert p0.var == s
+
+    p1 = Parallel(Series(tf, -tf2), tf2)
+    assert p1.args == (Series(tf, -tf2), tf2)
+    assert p1.var == s
+
+    tf3_ = TransferFunction(inp, 1, s)
+    tf4_ = TransferFunction(-out, 1, s)
+    p2 = Parallel(tf, Series(tf3_, -tf4_), tf2)
+    assert p2.args == (tf, Series(tf3_, -tf4_), tf2)
+
+    p3 = Parallel(tf, tf2, tf4)
+    assert p3.args == (tf, tf2, tf4)
+
+    p4 = Parallel(tf3_, tf4_)
+    assert p4.args == (tf3_, tf4_)
+    assert p4.var == s
+
+    p5 = Parallel(tf, tf2)
+    assert p0 == p5
+    assert not p0 == p1
+
+    p6 = Parallel(tf2, tf4, Series(tf2, -tf4))
+    assert p6.args == (tf2, tf4, Series(tf2, -tf4))
+
+    p7 = Parallel(tf2, tf4, Series(tf2, -tf), tf4)
+    assert p7.args == (tf2, tf4, Series(tf2, -tf), tf4)
+
+    raises(ValueError, lambda: Parallel(tf, tf3))
+    raises(ValueError, lambda: Parallel(tf, tf2, tf3, tf4))
+    raises(ValueError, lambda: Parallel(-tf3, tf4))
+    raises(TypeError, lambda: Parallel(2, tf, tf4))
+    raises(TypeError, lambda: Parallel(s**2 + p*s, tf3, tf2))
+    raises(TypeError, lambda: Parallel(tf3, Matrix([1, 2, 3, 4])))
+
+
+def test_MIMOParallel_construction():
+    tfm1 = TransferFunctionMatrix([[TF1], [TF2], [TF3]])
+    tfm2 = TransferFunctionMatrix([[-TF3], [TF2], [TF1]])
+    tfm3 = TransferFunctionMatrix([[TF1]])
+    tfm4 = TransferFunctionMatrix([[TF2], [TF1], [TF3]])
+    tfm5 = TransferFunctionMatrix([[TF1, TF2], [TF2, TF1]])
+    tfm6 = TransferFunctionMatrix([[TF2, TF1], [TF1, TF2]])
+    tfm7 = TransferFunctionMatrix.from_Matrix(Matrix([[1/p]]), p)
+
+    p8 = MIMOParallel(tfm1, tfm2)
+    assert p8.args == (tfm1, tfm2)
+    assert p8.var == s
+    assert p8.shape == (p8.num_outputs, p8.num_inputs) == (3, 1)
+
+    p9 = MIMOParallel(MIMOSeries(tfm3, tfm1), tfm2)
+    assert p9.args == (MIMOSeries(tfm3, tfm1), tfm2)
+    assert p9.var == s
+    assert p9.shape == (p9.num_outputs, p9.num_inputs) == (3, 1)
+
+    p10 = MIMOParallel(tfm1, MIMOSeries(tfm3, tfm4), tfm2)
+    assert p10.args == (tfm1, MIMOSeries(tfm3, tfm4), tfm2)
+    assert p10.var == s
+    assert p10.shape == (p10.num_outputs, p10.num_inputs) == (3, 1)
+
+    p11 = MIMOParallel(tfm2, tfm1, tfm4)
+    assert p11.args == (tfm2, tfm1, tfm4)
+    assert p11.shape == (p11.num_outputs, p11.num_inputs) == (3, 1)
+
+    p12 = MIMOParallel(tfm6, tfm5)
+    assert p12.args == (tfm6, tfm5)
+    assert p12.shape == (p12.num_outputs, p12.num_inputs) == (2, 2)
+
+    p13 = MIMOParallel(tfm2, tfm4, MIMOSeries(-tfm3, tfm4), -tfm4)
+    assert p13.args == (tfm2, tfm4, MIMOSeries(-tfm3, tfm4), -tfm4)
+    assert p13.shape == (p13.num_outputs, p13.num_inputs) == (3, 1)
+
+    # arg cannot be empty tuple.
+    raises(TypeError, lambda: MIMOParallel(()))
+
+    # arg cannot contain SISO as well as MIMO systems.
+    raises(TypeError, lambda: MIMOParallel(tfm1, tfm2, TF1))
+
+    # all TFMs must have same shapes.
+    raises(TypeError, lambda: MIMOParallel(tfm1, tfm3, tfm4))
+
+    # all TFMs must be using the same complex variable.
+    raises(ValueError, lambda: MIMOParallel(tfm3, tfm7))
+
+    # Number or expression not allowed in the arguments.
+    raises(TypeError, lambda: MIMOParallel(2, tfm1, tfm4))
+    raises(TypeError, lambda: MIMOParallel(s**2 + p*s, -tfm4, tfm2))
+
+
+def test_Parallel_functions():
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    assert tf1 + tf2 + tf3 == Parallel(tf1, tf2, tf3)
+    assert tf1 + tf2 + tf3 + tf5 == Parallel(tf1, tf2, tf3, tf5)
+    assert tf1 + tf2 - tf3 - tf5 == Parallel(tf1, tf2, -tf3, -tf5)
+    assert tf1 + tf2*tf3 == Parallel(tf1, Series(tf2, tf3))
+    assert tf1 - tf2*tf3 == Parallel(tf1, -Series(tf2,tf3))
+    assert -tf1 - tf2 == Parallel(-tf1, -tf2)
+    assert -(tf1 + tf2) == Series(TransferFunction(-1, 1, s), Parallel(tf1, tf2))
+    assert (tf2 + tf3)*tf1 == Series(Parallel(tf2, tf3), tf1)
+    assert (tf1 + tf2)*(tf3*tf5) == Series(Parallel(tf1, tf2), tf3, tf5)
+    assert -(tf2 + tf3)*-tf5 == Series(TransferFunction(-1, 1, s), Parallel(tf2, tf3), -tf5)
+    assert tf2 + tf3 + tf2*tf1 + tf5 == Parallel(tf2, tf3, Series(tf2, tf1), tf5)
+    assert tf2 + tf3 + tf2*tf1 - tf3 == Parallel(tf2, tf3, Series(tf2, tf1), -tf3)
+    assert (tf1 + tf2 + tf5)*(tf3 + tf5) == Series(Parallel(tf1, tf2, tf5), Parallel(tf3, tf5))
+    raises(ValueError, lambda: tf1 + tf2 + tf4)
+    raises(ValueError, lambda: tf1 - tf2*tf4)
+    raises(ValueError, lambda: tf3 + Matrix([1, 2, 3]))
+
+    # evaluate=True -> doit()
+    assert Parallel(tf1, tf2, evaluate=True) == Parallel(tf1, tf2).doit() == \
+        TransferFunction(k*(s**2 + 2*s*wn*zeta + wn**2) + 1, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Parallel(tf1, tf2, Series(-tf1, tf3), evaluate=True) == \
+        Parallel(tf1, tf2, Series(-tf1, tf3)).doit() == TransferFunction(k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)**2 + \
+            (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2) + (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), (a2*s + p)*(s**2 + \
+                2*s*wn*zeta + wn**2)**2, s)
+    assert Parallel(tf2, tf1, -tf3, evaluate=True) == Parallel(tf2, tf1, -tf3).doit() == \
+        TransferFunction(a2*s + k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2) \
+            , (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert not Parallel(tf1, -tf2, evaluate=False) == Parallel(tf1, -tf2).doit()
+
+    assert Parallel(Series(tf1, tf2), Series(tf2, tf3)).doit() == \
+        TransferFunction(k*(a2*p - s)*(s**2 + 2*s*wn*zeta + wn**2) + k*(a2*s + p), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Parallel(-tf1, -tf2, -tf3).doit() == \
+        TransferFunction(-a2*s - k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) - p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2), \
+            (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert -Parallel(tf1, tf2, tf3).doit() == \
+        TransferFunction(-a2*s - k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) - p - (a2*p - s)*(s**2 + 2*s*wn*zeta + wn**2), \
+            (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Parallel(tf2, tf3, Series(tf2, -tf1), tf3).doit() == \
+        TransferFunction(k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) - k*(a2*s + p) + (2*a2*p - 2*s)*(s**2 + 2*s*wn*zeta \
+            + wn**2), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    assert Parallel(tf1, tf2).rewrite(TransferFunction) == \
+        TransferFunction(k*(s**2 + 2*s*wn*zeta + wn**2) + 1, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Parallel(tf2, tf1, -tf3).rewrite(TransferFunction) == \
+        TransferFunction(a2*s + k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + \
+             wn**2), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    assert Parallel(tf1, Parallel(tf2, tf3)) == Parallel(tf1, tf2, tf3) == Parallel(Parallel(tf1, tf2), tf3)
+
+    P1 = Parallel(Series(tf1, tf2), Series(tf2, tf3))
+    assert P1.is_proper
+    assert not P1.is_strictly_proper
+    assert P1.is_biproper
+
+    P2 = Parallel(tf1, -tf2, -tf3)
+    assert P2.is_proper
+    assert not P2.is_strictly_proper
+    assert P2.is_biproper
+
+    P3 = Parallel(tf1, -tf2, Series(tf1, tf3))
+    assert P3.is_proper
+    assert not P3.is_strictly_proper
+    assert P3.is_biproper
+
+
+def test_MIMOParallel_functions():
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    tfm1 = TransferFunctionMatrix([[TF1], [TF2], [TF3]])
+    tfm2 = TransferFunctionMatrix([[-TF2], [tf5], [-TF1]])
+    tfm3 = TransferFunctionMatrix([[tf5], [-tf5], [TF2]])
+    tfm4 = TransferFunctionMatrix([[TF2, -tf5], [TF1, tf5]])
+    tfm5 = TransferFunctionMatrix([[TF1, TF2], [TF3, -tf5]])
+    tfm6 = TransferFunctionMatrix([[-TF2]])
+    tfm7 = TransferFunctionMatrix([[tf4], [-tf4], [tf4]])
+
+    assert tfm1 + tfm2 + tfm3 == MIMOParallel(tfm1, tfm2, tfm3) == MIMOParallel(MIMOParallel(tfm1, tfm2), tfm3)
+    assert tfm2 - tfm1 - tfm3 == MIMOParallel(tfm2, -tfm1, -tfm3)
+    assert tfm2 - tfm3 + (-tfm1*tfm6*-tfm6) == MIMOParallel(tfm2, -tfm3, MIMOSeries(-tfm6, tfm6, -tfm1))
+    assert tfm1 + tfm1 - (-tfm1*tfm6) == MIMOParallel(tfm1, tfm1, -MIMOSeries(tfm6, -tfm1))
+    assert tfm2 - tfm3 - tfm1 + tfm2 == MIMOParallel(tfm2, -tfm3, -tfm1, tfm2)
+    assert tfm1 + tfm2 - tfm3 - tfm1 == MIMOParallel(tfm1, tfm2, -tfm3, -tfm1)
+    raises(ValueError, lambda: tfm1 + tfm2 + TF2)
+    raises(TypeError, lambda: tfm1 - tfm2 - a1)
+    raises(TypeError, lambda: tfm2 - tfm3 - (s - 1))
+    raises(TypeError, lambda: -tfm3 - tfm2 - 9)
+    raises(TypeError, lambda: (1 - p**3) - tfm3 - tfm2)
+    # All TFMs must use the same complex var. tfm7 uses 'p'.
+    raises(ValueError, lambda: tfm3 - tfm2 - tfm7)
+    raises(ValueError, lambda: tfm2 - tfm1 + tfm7)
+    # (tfm1 +/- tfm2) has (3, 1) shape while tfm4 has (2, 2) shape.
+    raises(TypeError, lambda: tfm1 + tfm2 + tfm4)
+    raises(TypeError, lambda: (tfm1 - tfm2) - tfm4)
+
+    assert (tfm1 + tfm2)*tfm6 == MIMOSeries(tfm6, MIMOParallel(tfm1, tfm2))
+    assert (tfm2 - tfm3)*tfm6*-tfm6 == MIMOSeries(-tfm6, tfm6, MIMOParallel(tfm2, -tfm3))
+    assert (tfm2 - tfm1 - tfm3)*(tfm6 + tfm6) == MIMOSeries(MIMOParallel(tfm6, tfm6), MIMOParallel(tfm2, -tfm1, -tfm3))
+    raises(ValueError, lambda: (tfm4 + tfm5)*TF1)
+    raises(TypeError, lambda: (tfm2 - tfm3)*a2)
+    raises(TypeError, lambda: (tfm3 + tfm2)*(s - 6))
+    raises(TypeError, lambda: (tfm1 + tfm2 + tfm3)*0)
+    raises(TypeError, lambda: (1 - p**3)*(tfm1 + tfm3))
+
+    # (tfm3 - tfm2) has (3, 1) shape while tfm4*tfm5 has (2, 2) shape.
+    raises(ValueError, lambda: (tfm3 - tfm2)*tfm4*tfm5)
+    # (tfm1 - tfm2) has (3, 1) shape while tfm5 has (2, 2) shape.
+    raises(ValueError, lambda: (tfm1 - tfm2)*tfm5)
+
+    # TFM in the arguments.
+    assert (MIMOParallel(tfm1, tfm2, evaluate=True) == MIMOParallel(tfm1, tfm2).doit()
+    == MIMOParallel(tfm1, tfm2).rewrite(TransferFunctionMatrix)
+    == TransferFunctionMatrix(((TransferFunction(-k*(s**2 + 2*s*wn*zeta + wn**2) + 1, s**2 + 2*s*wn*zeta + wn**2, s),), \
+        (TransferFunction(-a0 + a1*s**2 + a2*s + k*(a0 + s), a0 + s, s),), (TransferFunction(-a2*s - p + (a2*p - s)* \
+        (s**2 + 2*s*wn*zeta + wn**2), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s),))))
+
+
+def test_Feedback_construction():
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+    tf6 = TransferFunction(s - p, p + s, p)
+
+    f1 = Feedback(TransferFunction(1, 1, s), tf1*tf2*tf3)
+    assert f1.args == (TransferFunction(1, 1, s), Series(tf1, tf2, tf3), -1)
+    assert f1.sys1 == TransferFunction(1, 1, s)
+    assert f1.sys2 == Series(tf1, tf2, tf3)
+    assert f1.var == s
+
+    f2 = Feedback(tf1, tf2*tf3)
+    assert f2.args == (tf1, Series(tf2, tf3), -1)
+    assert f2.sys1 == tf1
+    assert f2.sys2 == Series(tf2, tf3)
+    assert f2.var == s
+
+    f3 = Feedback(tf1*tf2, tf5)
+    assert f3.args == (Series(tf1, tf2), tf5, -1)
+    assert f3.sys1 == Series(tf1, tf2)
+
+    f4 = Feedback(tf4, tf6)
+    assert f4.args == (tf4, tf6, -1)
+    assert f4.sys1 == tf4
+    assert f4.var == p
+
+    f5 = Feedback(tf5, TransferFunction(1, 1, s))
+    assert f5.args == (tf5, TransferFunction(1, 1, s), -1)
+    assert f5.var == s
+    assert f5 == Feedback(tf5)  # When sys2 is not passed explicitly, it is assumed to be unit tf.
+
+    f6 = Feedback(TransferFunction(1, 1, p), tf4)
+    assert f6.args == (TransferFunction(1, 1, p), tf4, -1)
+    assert f6.var == p
+
+    f7 = -Feedback(tf4*tf6, TransferFunction(1, 1, p))
+    assert f7.args == (Series(TransferFunction(-1, 1, p), Series(tf4, tf6)), -TransferFunction(1, 1, p), -1)
+    assert f7.sys1 == Series(TransferFunction(-1, 1, p), Series(tf4, tf6))
+
+    # denominator can't be a Parallel instance
+    raises(TypeError, lambda: Feedback(tf1, tf2 + tf3))
+    raises(TypeError, lambda: Feedback(tf1, Matrix([1, 2, 3])))
+    raises(TypeError, lambda: Feedback(TransferFunction(1, 1, s), s - 1))
+    raises(TypeError, lambda: Feedback(1, 1))
+    # raises(ValueError, lambda: Feedback(TransferFunction(1, 1, s), TransferFunction(1, 1, s)))
+    raises(ValueError, lambda: Feedback(tf2, tf4*tf5))
+    raises(ValueError, lambda: Feedback(tf2, tf1, 1.5))  # `sign` can only be -1 or 1
+    raises(ValueError, lambda: Feedback(tf1, -tf1**-1))  # denominator can't be zero
+    raises(ValueError, lambda: Feedback(tf4, tf5))  # Both systems should use the same `var`
+
+
+def test_Feedback_functions():
+    tf = TransferFunction(1, 1, s)
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+    tf6 = TransferFunction(s - p, p + s, p)
+
+    assert (tf1*tf2*tf3 / tf3*tf5) == Series(tf1, tf2, tf3, pow(tf3, -1), tf5)
+    assert (tf1*tf2*tf3) / (tf3*tf5) == Series((tf1*tf2*tf3).doit(), pow((tf3*tf5).doit(),-1))
+    assert tf / (tf + tf1) == Feedback(tf, tf1)
+    assert tf / (tf + tf1*tf2*tf3) == Feedback(tf, tf1*tf2*tf3)
+    assert tf1 / (tf + tf1*tf2*tf3) == Feedback(tf1, tf2*tf3)
+    assert (tf1*tf2) / (tf + tf1*tf2) == Feedback(tf1*tf2, tf)
+    assert (tf1*tf2) / (tf + tf1*tf2*tf5) == Feedback(tf1*tf2, tf5)
+    assert (tf1*tf2) / (tf + tf1*tf2*tf5*tf3) in (Feedback(tf1*tf2, tf5*tf3), Feedback(tf1*tf2, tf3*tf5))
+    assert tf4 / (TransferFunction(1, 1, p) + tf4*tf6) == Feedback(tf4, tf6)
+    assert tf5 / (tf + tf5) == Feedback(tf5, tf)
+
+    raises(TypeError, lambda: tf1*tf2*tf3 / (1 + tf1*tf2*tf3))
+    raises(ValueError, lambda: tf2*tf3 / (tf + tf2*tf3*tf4))
+
+    assert Feedback(tf, tf1*tf2*tf3).doit() == \
+        TransferFunction((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), k*(a2*p - s) + \
+        (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(tf, tf1*tf2*tf3).sensitivity == \
+        1/(k*(a2*p - s)/((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)) + 1)
+    assert Feedback(tf1, tf2*tf3).doit() == \
+        TransferFunction((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), (k*(a2*p - s) + \
+        (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2))*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(tf1, tf2*tf3).sensitivity == \
+        1/(k*(a2*p - s)/((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)) + 1)
+    assert Feedback(tf1*tf2, tf5).doit() == \
+        TransferFunction(k*(a0 + s)*(s**2 + 2*s*wn*zeta + wn**2), (k*(-a0 + a1*s**2 + a2*s) + \
+        (a0 + s)*(s**2 + 2*s*wn*zeta + wn**2))*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(tf1*tf2, tf5, 1).sensitivity == \
+        1/(-k*(-a0 + a1*s**2 + a2*s)/((a0 + s)*(s**2 + 2*s*wn*zeta + wn**2)) + 1)
+    assert Feedback(tf4, tf6).doit() == \
+        TransferFunction(p*(p + s)*(a0*p + p**a1 - s), p*(p*(p + s) + (-p + s)*(a0*p + p**a1 - s)), p)
+    assert -Feedback(tf4*tf6, TransferFunction(1, 1, p)).doit() == \
+        TransferFunction(-p*(-p + s)*(p + s)*(a0*p + p**a1 - s), p*(p + s)*(p*(p + s) + (-p + s)*(a0*p + p**a1 - s)), p)
+    assert Feedback(tf, tf).doit() == TransferFunction(1, 2, s)
+
+    assert Feedback(tf1, tf2*tf5).rewrite(TransferFunction) == \
+        TransferFunction((a0 + s)*(s**2 + 2*s*wn*zeta + wn**2), (k*(-a0 + a1*s**2 + a2*s) + \
+        (a0 + s)*(s**2 + 2*s*wn*zeta + wn**2))*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(TransferFunction(1, 1, p), tf4).rewrite(TransferFunction) == \
+        TransferFunction(p, a0*p + p + p**a1 - s, p)
+
+
+def test_Feedback_with_Series():
+    # Solves issue https://github.com/sympy/sympy/issues/26161
+    tf1 = TransferFunction(s+1, 1, s)
+    tf2 = TransferFunction(s+2, 1, s)
+    fd1 = Feedback(tf1, tf2, -1) # Negative Feedback system
+    fd2 = Feedback(tf1, tf2, 1) # Positive Feedback system
+    unit = TransferFunction(1, 1, s)
+
+    # Checking the type
+    assert isinstance(fd1, SISOLinearTimeInvariant)
+    assert isinstance(fd1, Feedback)
+
+    # Testing the numerator and denominator
+    assert fd1.num == tf1
+    assert fd2.num == tf1
+    assert fd1.den == Parallel(unit, Series(tf2, tf1))
+    assert fd2.den == Parallel(unit, -Series(tf2, tf1))
+
+    # Testing the Series and Parallel Combination with Feedback and TransferFunction
+    s1 = Series(tf1, fd1)
+    p1 = Parallel(tf1, fd1)
+    assert tf1 * fd1 == s1
+    assert tf1 + fd1 == p1
+    assert s1.doit() == TransferFunction((s + 1)**2, (s + 1)*(s + 2) + 1, s)
+    assert p1.doit() == TransferFunction(s + (s + 1)*((s + 1)*(s + 2) + 1) + 1, (s + 1)*(s + 2) + 1, s)
+
+    # Testing the use of Feedback and TransferFunction with Feedback
+    fd3 = Feedback(tf1*fd1, tf2, -1)
+    assert fd3 == Feedback(Series(tf1, fd1), tf2)
+    assert fd3.num == tf1 * fd1
+    assert fd3.den == Parallel(unit, Series(tf2, Series(tf1, fd1)))
+
+    # Testing the use of Feedback and TransferFunction with TransferFunction
+    tf3 = TransferFunction(tf1*fd1, tf2, s)
+    assert tf3 == TransferFunction(Series(tf1, fd1), tf2, s)
+    assert tf3.num == tf1*fd1
+
+
+def test_issue_26161():
+    # Issue https://github.com/sympy/sympy/issues/26161
+    Ib, Is, m, h, l2, l1 = symbols('I_b, I_s, m, h, l2, l1',
+                                            real=True, nonnegative=True)
+    KD, KP, v = symbols('K_D, K_P, v', real=True)
+
+    tau1_sq = (Ib + m * h ** 2) / m / g / h
+    tau2 = l2 / v
+    tau3 = v / (l1 + l2)
+    K = v ** 2 / g / (l1 + l2)
+
+    Gtheta = TransferFunction(-K * (tau2 * s + 1), tau1_sq * s ** 2 - 1, s)
+    Gdelta = TransferFunction(1, Is * s ** 2 + c * s, s)
+    Gpsi = TransferFunction(1, tau3 * s, s)
+    Dcont = TransferFunction(KD * s, 1, s)
+    PIcont = TransferFunction(KP, s, s)
+    Gunity = TransferFunction(1, 1, s)
+
+    Ginner = Feedback(Dcont * Gdelta, Gtheta)
+    Gouter = Feedback(PIcont * Ginner * Gpsi, Gunity)
+    assert Gouter == Feedback(Series(PIcont, Series(Ginner, Gpsi)), Gunity)
+    assert Gouter.num == Series(PIcont, Series(Ginner, Gpsi))
+    assert Gouter.den == Parallel(Gunity, Series(Gunity, Series(PIcont, Series(Ginner, Gpsi))))
+    expr = (KD*KP*g*s**3*v**2*(l1 + l2)*(Is*s**2 + c*s)**2*(-g*h*m + s**2*(Ib + h**2*m))*(-KD*g*h*m*s*v**2*(l2*s + v) + \
+            g*v*(l1 + l2)*(Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m))))/((s**2*v*(Is*s**2 + c*s)*(-KD*g*h*m*s*v**2* \
+            (l2*s + v) + g*v*(l1 + l2)*(Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m)))*(KD*KP*g*s*v*(l1 + l2)**2* \
+            (Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m)) + s**2*v*(Is*s**2 + c*s)*(-KD*g*h*m*s*v**2*(l2*s + v) + \
+            g*v*(l1 + l2)*(Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m))))/(l1 + l2)))
+
+    assert (Gouter.to_expr() - expr).simplify() == 0
+
+
+def test_MIMOFeedback_construction():
+    tf1 = TransferFunction(1, s, s)
+    tf2 = TransferFunction(s, s**3 - 1, s)
+    tf3 = TransferFunction(s, s + 1, s)
+    tf4 = TransferFunction(s, s**2 + 1, s)
+
+    tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+    tfm_2 = TransferFunctionMatrix([[tf2, tf3], [tf4, tf1]])
+    tfm_3 = TransferFunctionMatrix([[tf3, tf4], [tf1, tf2]])
+
+    f1 = MIMOFeedback(tfm_1, tfm_2)
+    assert f1.args == (tfm_1, tfm_2, -1)
+    assert f1.sys1 == tfm_1
+    assert f1.sys2 == tfm_2
+    assert f1.var == s
+    assert f1.sign == -1
+    assert -(-f1) == f1
+
+    f2 = MIMOFeedback(tfm_2, tfm_1, 1)
+    assert f2.args == (tfm_2, tfm_1, 1)
+    assert f2.sys1 == tfm_2
+    assert f2.sys2 == tfm_1
+    assert f2.var == s
+    assert f2.sign == 1
+
+    f3 = MIMOFeedback(tfm_1, MIMOSeries(tfm_3, tfm_2))
+    assert f3.args == (tfm_1, MIMOSeries(tfm_3, tfm_2), -1)
+    assert f3.sys1 == tfm_1
+    assert f3.sys2 == MIMOSeries(tfm_3, tfm_2)
+    assert f3.var == s
+    assert f3.sign == -1
+
+    mat = Matrix([[1, 1/s], [0, 1]])
+    sys1 = controller = TransferFunctionMatrix.from_Matrix(mat, s)
+    f4 = MIMOFeedback(sys1, controller)
+    assert f4.args == (sys1, controller, -1)
+    assert f4.sys1 == f4.sys2 == sys1
+
+
+def test_MIMOFeedback_errors():
+    tf1 = TransferFunction(1, s, s)
+    tf2 = TransferFunction(s, s**3 - 1, s)
+    tf3 = TransferFunction(s, s - 1, s)
+    tf4 = TransferFunction(s, s**2 + 1, s)
+    tf5 = TransferFunction(1, 1, s)
+    tf6 = TransferFunction(-1, s - 1, s)
+
+    tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+    tfm_2 = TransferFunctionMatrix([[tf2, tf3], [tf4, tf1]])
+    tfm_3 = TransferFunctionMatrix.from_Matrix(eye(2), var=s)
+    tfm_4 = TransferFunctionMatrix([[tf1, tf5], [tf5, tf5]])
+    tfm_5 = TransferFunctionMatrix([[-tf3, tf3], [tf3, tf6]])
+    # tfm_4 is inverse of tfm_5. Therefore tfm_5*tfm_4 = I
+    tfm_6 = TransferFunctionMatrix([[-tf3]])
+    tfm_7 = TransferFunctionMatrix([[tf3, tf4]])
+
+    # Unsupported Types
+    raises(TypeError, lambda: MIMOFeedback(tf1, tf2))
+    raises(TypeError, lambda: MIMOFeedback(MIMOParallel(tfm_1, tfm_2), tfm_3))
+    # Shape Errors
+    raises(ValueError, lambda: MIMOFeedback(tfm_1, tfm_6, 1))
+    raises(ValueError, lambda: MIMOFeedback(tfm_7, tfm_7))
+    # sign not 1/-1
+    raises(ValueError, lambda: MIMOFeedback(tfm_1, tfm_2, -2))
+    # Non-Invertible Systems
+    raises(ValueError, lambda: MIMOFeedback(tfm_5, tfm_4, 1))
+    raises(ValueError, lambda: MIMOFeedback(tfm_4, -tfm_5))
+    raises(ValueError, lambda: MIMOFeedback(tfm_3, tfm_3, 1))
+    # Variable not same in both the systems
+    tfm_8 = TransferFunctionMatrix.from_Matrix(eye(2), var=p)
+    raises(ValueError, lambda: MIMOFeedback(tfm_1, tfm_8, 1))
+
+
+def test_MIMOFeedback_functions():
+    tf1 = TransferFunction(1, s, s)
+    tf2 = TransferFunction(s, s - 1, s)
+    tf3 = TransferFunction(1, 1, s)
+    tf4 = TransferFunction(-1, s - 1, s)
+
+    tfm_1 = TransferFunctionMatrix.from_Matrix(eye(2), var=s)
+    tfm_2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf3]])
+    tfm_3 = TransferFunctionMatrix([[-tf2, tf2], [tf2, tf4]])
+    tfm_4 = TransferFunctionMatrix([[tf1, tf2], [-tf2, tf1]])
+
+    # sensitivity, doit(), rewrite()
+    F_1 = MIMOFeedback(tfm_2, tfm_3)
+    F_2 = MIMOFeedback(tfm_2, MIMOSeries(tfm_4, -tfm_1), 1)
+
+    assert F_1.sensitivity == Matrix([[S.Half, 0], [0, S.Half]])
+    assert F_2.sensitivity == Matrix([[(-2*s**4 + s**2)/(s**2 - s + 1),
+        (2*s**3 - s**2)/(s**2 - s + 1)], [-s**2, s]])
+
+    assert F_1.doit() == \
+        TransferFunctionMatrix(((TransferFunction(1, 2*s, s),
+        TransferFunction(1, 2, s)), (TransferFunction(1, 2, s),
+        TransferFunction(1, 2, s)))) == F_1.rewrite(TransferFunctionMatrix)
+    assert F_2.doit(cancel=False, expand=True) == \
+        TransferFunctionMatrix(((TransferFunction(-s**5 + 2*s**4 - 2*s**3 + s**2, s**5 - 2*s**4 + 3*s**3 - 2*s**2 + s, s),
+        TransferFunction(-2*s**4 + 2*s**3, s**2 - s + 1, s)), (TransferFunction(0, 1, s), TransferFunction(-s**2 + s, 1, s))))
+    assert F_2.doit(cancel=False) == \
+        TransferFunctionMatrix(((TransferFunction(s*(2*s**3 - s**2)*(s**2 - s + 1) + \
+        (-2*s**4 + s**2)*(s**2 - s + 1), s*(s**2 - s + 1)**2, s), TransferFunction(-2*s**4 + 2*s**3, s**2 - s + 1, s)),
+        (TransferFunction(0, 1, s), TransferFunction(-s**2 + s, 1, s))))
+    assert F_2.doit() == \
+        TransferFunctionMatrix(((TransferFunction(s*(-2*s**2 + s*(2*s - 1) + 1), s**2 - s + 1, s),
+        TransferFunction(-2*s**3*(s - 1), s**2 - s + 1, s)), (TransferFunction(0, 1, s), TransferFunction(s*(1 - s), 1, s))))
+    assert F_2.doit(expand=True) == \
+        TransferFunctionMatrix(((TransferFunction(-s**2 + s, s**2 - s + 1, s), TransferFunction(-2*s**4 + 2*s**3, s**2 - s + 1, s)),
+        (TransferFunction(0, 1, s), TransferFunction(-s**2 + s, 1, s))))
+
+    assert -(F_1.doit()) == (-F_1).doit()  # First negating then calculating vs calculating then negating.
+
+
+def test_TransferFunctionMatrix_construction():
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+
+    tfm3_ = TransferFunctionMatrix([[-TF3]])
+    assert tfm3_.shape == (tfm3_.num_outputs, tfm3_.num_inputs) == (1, 1)
+    assert tfm3_.args == Tuple(Tuple(Tuple(-TF3)))
+    assert tfm3_.var == s
+
+    tfm5 = TransferFunctionMatrix([[TF1, -TF2], [TF3, tf5]])
+    assert tfm5.shape == (tfm5.num_outputs, tfm5.num_inputs) == (2, 2)
+    assert tfm5.args == Tuple(Tuple(Tuple(TF1, -TF2), Tuple(TF3, tf5)))
+    assert tfm5.var == s
+
+    tfm7 = TransferFunctionMatrix([[TF1, TF2], [TF3, -tf5], [-tf5, TF2]])
+    assert tfm7.shape == (tfm7.num_outputs, tfm7.num_inputs) == (3, 2)
+    assert tfm7.args == Tuple(Tuple(Tuple(TF1, TF2), Tuple(TF3, -tf5), Tuple(-tf5, TF2)))
+    assert tfm7.var == s
+
+    # all transfer functions will use the same complex variable. tf4 uses 'p'.
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1], [TF2], [tf4]]))
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1, tf4], [TF3, tf5]]))
+
+    # length of all the lists in the TFM should be equal.
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1], [TF3, tf5]]))
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1, TF3], [tf5]]))
+
+    # lists should only support transfer functions in them.
+    raises(TypeError, lambda: TransferFunctionMatrix([[TF1, TF2], [TF3, Matrix([1, 2])]]))
+    raises(TypeError, lambda: TransferFunctionMatrix([[TF1, Matrix([1, 2])], [TF3, TF2]]))
+
+    # `arg` should strictly be nested list of TransferFunction
+    raises(ValueError, lambda: TransferFunctionMatrix([TF1, TF2, tf5]))
+    raises(ValueError, lambda: TransferFunctionMatrix([TF1]))
+
+def test_TransferFunctionMatrix_functions():
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    #  Classmethod (from_matrix)
+
+    mat_1 = ImmutableMatrix([
+        [s*(s + 1)*(s - 3)/(s**4 + 1), 2],
+        [p, p*(s + 1)/(s*(s**1 + 1))]
+        ])
+    mat_2 = ImmutableMatrix([[(2*s + 1)/(s**2 - 9)]])
+    mat_3 = ImmutableMatrix([[1, 2], [3, 4]])
+    assert TransferFunctionMatrix.from_Matrix(mat_1, s) == \
+        TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)],
+        [TransferFunction(p, 1, s), TransferFunction(p, s, s)]])
+    assert TransferFunctionMatrix.from_Matrix(mat_2, s) == \
+        TransferFunctionMatrix([[TransferFunction(2*s + 1, s**2 - 9, s)]])
+    assert TransferFunctionMatrix.from_Matrix(mat_3, p) == \
+        TransferFunctionMatrix([[TransferFunction(1, 1, p), TransferFunction(2, 1, p)],
+        [TransferFunction(3, 1, p), TransferFunction(4, 1, p)]])
+
+    #  Negating a TFM
+
+    tfm1 = TransferFunctionMatrix([[TF1], [TF2]])
+    assert -tfm1 == TransferFunctionMatrix([[-TF1], [-TF2]])
+
+    tfm2 = TransferFunctionMatrix([[TF1, TF2, TF3], [tf5, -TF1, -TF3]])
+    assert -tfm2 == TransferFunctionMatrix([[-TF1, -TF2, -TF3], [-tf5, TF1, TF3]])
+
+    # subs()
+
+    H_1 = TransferFunctionMatrix.from_Matrix(mat_1, s)
+    H_2 = TransferFunctionMatrix([[TransferFunction(a*p*s, k*s**2, s), TransferFunction(p*s, k*(s**2 - a), s)]])
+    assert H_1.subs(p, 1) == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)], [TransferFunction(1, 1, s), TransferFunction(1, s, s)]])
+    assert H_1.subs({p: 1}) == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)], [TransferFunction(1, 1, s), TransferFunction(1, s, s)]])
+    assert H_1.subs({p: 1, s: 1}) == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)], [TransferFunction(1, 1, s), TransferFunction(1, s, s)]]) # This should ignore `s` as it is `var`
+    assert H_2.subs(p, 2) == TransferFunctionMatrix([[TransferFunction(2*a*s, k*s**2, s), TransferFunction(2*s, k*(-a + s**2), s)]])
+    assert H_2.subs(k, 1) == TransferFunctionMatrix([[TransferFunction(a*p*s, s**2, s), TransferFunction(p*s, -a + s**2, s)]])
+    assert H_2.subs(a, 0) == TransferFunctionMatrix([[TransferFunction(0, k*s**2, s), TransferFunction(p*s, k*s**2, s)]])
+    assert H_2.subs({p: 1, k: 1, a: a0}) == TransferFunctionMatrix([[TransferFunction(a0*s, s**2, s), TransferFunction(s, -a0 + s**2, s)]])
+
+    # eval_frequency()
+    assert H_2.eval_frequency(S(1)/2 + I) == Matrix([[2*a*p/(5*k) - 4*I*a*p/(5*k), I*p/(-a*k - 3*k/4 + I*k) + p/(-2*a*k - 3*k/2 + 2*I*k)]])
+
+    # transpose()
+
+    assert H_1.transpose() == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(p, 1, s)], [TransferFunction(2, 1, s), TransferFunction(p, s, s)]])
+    assert H_2.transpose() == TransferFunctionMatrix([[TransferFunction(a*p*s, k*s**2, s)], [TransferFunction(p*s, k*(-a + s**2), s)]])
+    assert H_1.transpose().transpose() == H_1
+    assert H_2.transpose().transpose() == H_2
+
+    # elem_poles()
+
+    assert H_1.elem_poles() == [[[-sqrt(2)/2 - sqrt(2)*I/2, -sqrt(2)/2 + sqrt(2)*I/2, sqrt(2)/2 - sqrt(2)*I/2, sqrt(2)/2 + sqrt(2)*I/2], []],
+        [[], [0]]]
+    assert H_2.elem_poles() == [[[0, 0], [sqrt(a), -sqrt(a)]]]
+    assert tfm2.elem_poles() == [[[wn*(-zeta + sqrt((zeta - 1)*(zeta + 1))), wn*(-zeta - sqrt((zeta - 1)*(zeta + 1)))], [], [-p/a2]],
+        [[-a0], [wn*(-zeta + sqrt((zeta - 1)*(zeta + 1))), wn*(-zeta - sqrt((zeta - 1)*(zeta + 1)))], [-p/a2]]]
+
+    # elem_zeros()
+
+    assert H_1.elem_zeros() == [[[-1, 0, 3], []], [[], []]]
+    assert H_2.elem_zeros() == [[[0], [0]]]
+    assert tfm2.elem_zeros() == [[[], [], [a2*p]],
+        [[-a2/(2*a1) - sqrt(4*a0*a1 + a2**2)/(2*a1), -a2/(2*a1) + sqrt(4*a0*a1 + a2**2)/(2*a1)], [], [a2*p]]]
+
+    # doit()
+
+    H_3 = TransferFunctionMatrix([[Series(TransferFunction(1, s**3 - 3, s), TransferFunction(s**2 - 2*s + 5, 1, s), TransferFunction(1, s, s))]])
+    H_4 = TransferFunctionMatrix([[Parallel(TransferFunction(s**3 - 3, 4*s**4 - s**2 - 2*s + 5, s), TransferFunction(4 - s**3, 4*s**4 - s**2 - 2*s + 5, s))]])
+
+    assert H_3.doit() == TransferFunctionMatrix([[TransferFunction(s**2 - 2*s + 5, s*(s**3 - 3), s)]])
+    assert H_4.doit() == TransferFunctionMatrix([[TransferFunction(1, 4*s**4 - s**2 - 2*s + 5, s)]])
+
+    # _flat()
+
+    assert H_1._flat() == [TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s), TransferFunction(p, 1, s), TransferFunction(p, s, s)]
+    assert H_2._flat() == [TransferFunction(a*p*s, k*s**2, s), TransferFunction(p*s, k*(-a + s**2), s)]
+    assert H_3._flat() == [Series(TransferFunction(1, s**3 - 3, s), TransferFunction(s**2 - 2*s + 5, 1, s), TransferFunction(1, s, s))]
+    assert H_4._flat() == [Parallel(TransferFunction(s**3 - 3, 4*s**4 - s**2 - 2*s + 5, s), TransferFunction(4 - s**3, 4*s**4 - s**2 - 2*s + 5, s))]
+
+    # evalf()
+
+    assert H_1.evalf() == \
+        TransferFunctionMatrix(((TransferFunction(s*(s - 3.0)*(s + 1.0), s**4 + 1.0, s), TransferFunction(2.0, 1, s)), (TransferFunction(1.0*p, 1, s), TransferFunction(p, s, s))))
+    assert H_2.subs({a:3.141, p:2.88, k:2}).evalf() == \
+        TransferFunctionMatrix(((TransferFunction(4.5230399999999999494093572138808667659759521484375, s, s),
+        TransferFunction(2.87999999999999989341858963598497211933135986328125*s, 2.0*s**2 - 6.282000000000000028421709430404007434844970703125, s)),))
+
+    # simplify()
+
+    H_5 = TransferFunctionMatrix([[TransferFunction(s**5 + s**3 + s, s - s**2, s),
+        TransferFunction((s + 3)*(s - 1), (s - 1)*(s + 5), s)]])
+
+    assert H_5.simplify() == simplify(H_5) == \
+        TransferFunctionMatrix(((TransferFunction(-s**4 - s**2 - 1, s - 1, s), TransferFunction(s + 3, s + 5, s)),))
+
+    # expand()
+
+    assert (H_1.expand()
+            == TransferFunctionMatrix(((TransferFunction(s**3 - 2*s**2 - 3*s, s**4 + 1, s), TransferFunction(2, 1, s)),
+            (TransferFunction(p, 1, s), TransferFunction(p, s, s)))))
+    assert H_5.expand() == \
+        TransferFunctionMatrix(((TransferFunction(s**5 + s**3 + s, -s**2 + s, s), TransferFunction(s**2 + 2*s - 3, s**2 + 4*s - 5, s)),))
+
+def test_TransferFunction_gbt():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 0.5)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_bilinear = TransferFunction(s * numZ[0] + numZ[1], s * denZ[0] + denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(2*(a + b*T/2)) + T/(2*(a + b*T/2)), s + (-a + b*T/2)/(a + b*T/2), s)
+
+    assert S.Zero == (tf_test_bilinear.simplify()-tf_test_manual.simplify()).simplify().num
+
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 0)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_forward = TransferFunction(numZ[0], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(T/a, s + (-a + b*T)/a, s)
+
+    assert S.Zero == (tf_test_forward.simplify()-tf_test_manual.simplify()).simplify().num
+
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 1)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_backward = TransferFunction(s*numZ[0], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(a + b*T), s - a/(a + b*T), s)
+
+    assert S.Zero == (tf_test_backward.simplify()-tf_test_manual.simplify()).simplify().num
+
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 0.3)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_gbt = TransferFunction(s*numZ[0]+numZ[1], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s*3*T/(10*(a + 3*b*T/10)) + 7*T/(10*(a + 3*b*T/10)), s + (-a + 7*b*T/10)/(a + 3*b*T/10), s)
+
+    assert S.Zero == (tf_test_gbt.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_bilinear():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = bilinear(tf, T)
+    # discretized transfer function with coefs from tf.bilinear()
+    tf_test_bilinear = TransferFunction(s*numZ[0]+numZ[1], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(2*(a + b*T/2)) + T/(2*(a + b*T/2)), s + (-a + b*T/2)/(a + b*T/2), s)
+
+    assert S.Zero == (tf_test_bilinear.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_forward_diff():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = forward_diff(tf, T)
+    # discretized transfer function with coefs from tf.forward_diff()
+    tf_test_forward = TransferFunction(numZ[0], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(T/a, s + (-a + b*T)/a, s)
+
+    assert S.Zero == (tf_test_forward.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_backward_diff():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = backward_diff(tf, T)
+    # discretized transfer function with coefs from tf.backward_diff()
+    tf_test_backward = TransferFunction(s*numZ[0]+numZ[1], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(a + b*T), s - a/(a + b*T), s)
+
+    assert S.Zero == (tf_test_backward.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_phase_margin():
+    # Test for phase margin
+    tf1 = TransferFunction(10, p**3 + 1, p)
+    tf2 = TransferFunction(s**2, 10, s)
+    tf3 = TransferFunction(1, a*s+b, s)
+    tf4 = TransferFunction((s + 1)*exp(s/tau), s**2 + 2, s)
+    tf_m = TransferFunctionMatrix([[tf2],[tf3]])
+
+    assert phase_margin(tf1) == -180 + 180*atan(3*sqrt(11))/pi
+    assert phase_margin(tf2) == 0
+
+    raises(NotImplementedError, lambda: phase_margin(tf4))
+    raises(ValueError, lambda: phase_margin(tf3))
+    raises(ValueError, lambda: phase_margin(MIMOSeries(tf_m)))
+
+def test_TransferFunction_gain_margin():
+    # Test for gain margin
+    tf1 = TransferFunction(s**2, 5*(s+1)*(s-5)*(s-10), s)
+    tf2 = TransferFunction(s**2 + 2*s + 1, 1, s)
+    tf3 = TransferFunction(1, a*s+b, s)
+    tf4 = TransferFunction((s + 1)*exp(s/tau), s**2 + 2, s)
+    tf_m = TransferFunctionMatrix([[tf2],[tf3]])
+
+    assert gain_margin(tf1) == -20*log(S(7)/540)/log(10)
+    assert gain_margin(tf2) == oo
+
+    raises(NotImplementedError, lambda: gain_margin(tf4))
+    raises(ValueError, lambda: gain_margin(tf3))
+    raises(ValueError, lambda: gain_margin(MIMOSeries(tf_m)))
+
+
+def test_StateSpace_construction():
+    # using different numbers for a SISO system.
+    A1 = Matrix([[0, 1], [1, 0]])
+    B1 = Matrix([1, 0])
+    C1 = Matrix([[0, 1]])
+    D1 = Matrix([0])
+    ss1 = StateSpace(A1, B1, C1, D1)
+
+    assert ss1.state_matrix == Matrix([[0, 1], [1, 0]])
+    assert ss1.input_matrix == Matrix([1, 0])
+    assert ss1.output_matrix == Matrix([[0, 1]])
+    assert ss1.feedforward_matrix == Matrix([0])
+    assert ss1.args == (Matrix([[0, 1], [1, 0]]), Matrix([[1], [0]]), Matrix([[0, 1]]), Matrix([[0]]))
+
+    # using different symbols for a SISO system.
+    ss2 = StateSpace(Matrix([a0]), Matrix([a1]),
+                    Matrix([a2]), Matrix([a3]))
+
+    assert ss2.state_matrix == Matrix([[a0]])
+    assert ss2.input_matrix == Matrix([[a1]])
+    assert ss2.output_matrix == Matrix([[a2]])
+    assert ss2.feedforward_matrix == Matrix([[a3]])
+    assert ss2.args == (Matrix([[a0]]), Matrix([[a1]]), Matrix([[a2]]), Matrix([[a3]]))
+
+    # using different numbers for a MIMO system.
+    ss3 = StateSpace(Matrix([[-1.5, -2], [1, 0]]),
+                    Matrix([[0.5, 0], [0, 1]]),
+                    Matrix([[0, 1], [0, 2]]),
+                    Matrix([[2, 2], [1, 1]]))
+
+    assert ss3.state_matrix == Matrix([[-1.5, -2], [1,  0]])
+    assert ss3.input_matrix == Matrix([[0.5, 0], [0, 1]])
+    assert ss3.output_matrix == Matrix([[0, 1], [0, 2]])
+    assert ss3.feedforward_matrix == Matrix([[2, 2], [1, 1]])
+    assert ss3.args == (Matrix([[-1.5, -2],
+                                [1,  0]]),
+                        Matrix([[0.5, 0],
+                                [0, 1]]),
+                        Matrix([[0, 1],
+                                [0, 2]]),
+                        Matrix([[2, 2],
+                                [1, 1]]))
+
+    # using different symbols for a MIMO system.
+    A4 = Matrix([[a0, a1], [a2, a3]])
+    B4 = Matrix([[b0, b1], [b2, b3]])
+    C4 = Matrix([[c0, c1], [c2, c3]])
+    D4 = Matrix([[d0, d1], [d2, d3]])
+    ss4 = StateSpace(A4, B4, C4, D4)
+
+    assert ss4.state_matrix == Matrix([[a0, a1], [a2, a3]])
+    assert ss4.input_matrix == Matrix([[b0, b1], [b2, b3]])
+    assert ss4.output_matrix == Matrix([[c0, c1], [c2, c3]])
+    assert ss4.feedforward_matrix == Matrix([[d0, d1], [d2, d3]])
+    assert ss4.args == (Matrix([[a0, a1],
+                                [a2, a3]]),
+                        Matrix([[b0, b1],
+                                [b2, b3]]),
+                        Matrix([[c0, c1],
+                                [c2, c3]]),
+                        Matrix([[d0, d1],
+                                [d2, d3]]))
+
+    # using less matrices. Rest will be filled with a minimum of zeros.
+    ss5 = StateSpace()
+    assert ss5.args == (Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[0]]))
+
+    A6 = Matrix([[0, 1], [1, 0]])
+    B6 = Matrix([1, 1])
+    ss6 = StateSpace(A6, B6)
+
+    assert ss6.state_matrix == Matrix([[0, 1], [1, 0]])
+    assert ss6.input_matrix ==  Matrix([1, 1])
+    assert ss6.output_matrix == Matrix([[0, 0]])
+    assert ss6.feedforward_matrix == Matrix([[0]])
+    assert ss6.args == (Matrix([[0, 1],
+                                [1, 0]]),
+                        Matrix([[1],
+                                [1]]),
+                        Matrix([[0, 0]]),
+                        Matrix([[0]]))
+
+    # Check if the system is SISO or MIMO.
+    # If system is not SISO, then it is definitely MIMO.
+
+    assert ss1.is_SISO == True
+    assert ss2.is_SISO == True
+    assert ss3.is_SISO == False
+    assert ss4.is_SISO == False
+    assert ss5.is_SISO == True
+    assert ss6.is_SISO == True
+
+    # ShapeError if matrices do not fit.
+    raises(ShapeError, lambda: StateSpace(Matrix([s, (s+1)**2]), Matrix([s+1]),
+                                          Matrix([s**2 - 1]), Matrix([2*s])))
+    raises(ShapeError, lambda: StateSpace(Matrix([s]), Matrix([s+1, s**3 + 1]),
+                                          Matrix([s**2 - 1]), Matrix([2*s])))
+    raises(ShapeError, lambda: StateSpace(Matrix([s]), Matrix([s+1]),
+                                          Matrix([[s**2 - 1], [s**2 + 2*s + 1]]), Matrix([2*s])))
+    raises(ShapeError, lambda: StateSpace(Matrix([[-s, -s], [s, 0]]),
+                                                Matrix([[s/2, 0], [0, s]]),
+                                                Matrix([[0, s]]),
+                                                Matrix([[2*s, 2*s], [s, s]])))
+
+    # TypeError if arguments are not sympy matrices.
+    raises(TypeError, lambda: StateSpace(s**2, s+1, 2*s, 1))
+    raises(TypeError, lambda: StateSpace(Matrix([2, 0.5]), Matrix([-1]),
+                                         Matrix([1]), 0))
+def test_StateSpace_add():
+    A1 = Matrix([[4, 1],[2, -3]])
+    B1 = Matrix([[5, 2],[-3, -3]])
+    C1 = Matrix([[2, -4],[0, 1]])
+    D1 = Matrix([[3, 2],[1, -1]])
+    ss1 = StateSpace(A1, B1, C1, D1)
+
+    A2 = Matrix([[-3, 4, 2],[-1, -3, 0],[2, 5, 3]])
+    B2 = Matrix([[1, 4],[-3, -3],[-2, 1]])
+    C2 = Matrix([[4, 2, -3],[1, 4, 3]])
+    D2 = Matrix([[-2, 4],[0, 1]])
+    ss2 = StateSpace(A2, B2, C2, D2)
+    ss3 = StateSpace()
+    ss4 = StateSpace(Matrix([1]), Matrix([2]), Matrix([3]), Matrix([4]))
+
+    expected_add = \
+        StateSpace(
+        Matrix([
+        [4,  1,  0,  0, 0],
+        [2, -3,  0,  0, 0],
+        [0,  0, -3,  4, 2],
+        [0,  0, -1, -3, 0],
+        [0,  0,  2,  5, 3]]),
+        Matrix([
+        [ 5,  2],
+        [-3, -3],
+        [ 1,  4],
+        [-3, -3],
+        [-2,  1]]),
+        Matrix([
+        [2, -4, 4, 2, -3],
+        [0,  1, 1, 4,  3]]),
+        Matrix([
+        [1, 6],
+        [1, 0]]))
+
+    expected_mul = \
+        StateSpace(
+        Matrix([
+        [ -3,   4,  2, 0,  0],
+        [ -1,  -3,  0, 0,  0],
+        [  2,   5,  3, 0,  0],
+        [ 22,  18, -9, 4,  1],
+        [-15, -18,  0, 2, -3]]),
+        Matrix([
+        [  1,   4],
+        [ -3,  -3],
+        [ -2,   1],
+        [-10,  22],
+        [  6, -15]]),
+        Matrix([
+        [14, 14, -3, 2, -4],
+        [ 3, -2, -6, 0,  1]]),
+        Matrix([
+        [-6, 14],
+        [-2,  3]]))
+
+    assert ss1 + ss2 == expected_add
+    assert ss1*ss2 == expected_mul
+    assert ss3 + 1/2 == StateSpace(Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[0.5]]))
+    assert ss4*1.5 == StateSpace(Matrix([[1]]), Matrix([[2]]), Matrix([[4.5]]), Matrix([[6.0]]))
+    assert 1.5*ss4 == StateSpace(Matrix([[1]]), Matrix([[3.0]]), Matrix([[3]]), Matrix([[6.0]]))
+    raises(ShapeError, lambda: ss1 + ss3)
+    raises(ShapeError, lambda: ss2*ss4)
+
+def test_StateSpace_negation():
+    A = Matrix([[a0, a1], [a2, a3]])
+    B = Matrix([[b0, b1], [b2, b3]])
+    C = Matrix([[c0, c1], [c1, c2], [c2, c3]])
+    D = Matrix([[d0, d1], [d1, d2], [d2, d3]])
+    SS = StateSpace(A, B, C, D)
+    SS_neg = -SS
+
+    state_mat = Matrix([[-1, 1], [1, -1]])
+    input_mat = Matrix([1, -1])
+    output_mat = Matrix([[-1, 1]])
+    feedforward_mat = Matrix([1])
+    system = StateSpace(state_mat, input_mat, output_mat, feedforward_mat)
+
+    assert SS_neg == \
+        StateSpace(Matrix([[a0, a1],
+                           [a2, a3]]),
+                   Matrix([[b0, b1],
+                           [b2, b3]]),
+                   Matrix([[-c0, -c1],
+                           [-c1, -c2],
+                           [-c2, -c3]]),
+                   Matrix([[-d0, -d1],
+                           [-d1, -d2],
+                           [-d2, -d3]]))
+    assert -system == \
+        StateSpace(Matrix([[-1,  1],
+                           [ 1, -1]]),
+                   Matrix([[ 1],[-1]]),
+                   Matrix([[1, -1]]),
+                   Matrix([[-1]]))
+    assert -SS_neg == SS
+    assert -(-(-(-system))) == system
+
+def test_SymPy_substitution_functions():
+    # subs
+    ss1 = StateSpace(Matrix([s]), Matrix([(s + 1)**2]), Matrix([s**2 - 1]), Matrix([2*s]))
+    ss2 = StateSpace(Matrix([s + p]), Matrix([(s + 1)*(p - 1)]), Matrix([p**3 - s**3]), Matrix([s - p]))
+
+    assert ss1.subs({s:5}) == StateSpace(Matrix([[5]]), Matrix([[36]]), Matrix([[24]]), Matrix([[10]]))
+    assert ss2.subs({p:1}) == StateSpace(Matrix([[s + 1]]), Matrix([[0]]), Matrix([[1 - s**3]]), Matrix([[s - 1]]))
+
+    # xreplace
+    assert ss1.xreplace({s:p}) == \
+        StateSpace(Matrix([[p]]), Matrix([[(p + 1)**2]]), Matrix([[p**2 - 1]]), Matrix([[2*p]]))
+    assert ss2.xreplace({s:a, p:b}) == \
+        StateSpace(Matrix([[a + b]]), Matrix([[(a + 1)*(b - 1)]]), Matrix([[-a**3 + b**3]]), Matrix([[a - b]]))
+
+    # evalf
+    p1 = a1*s + a0
+    p2 = b2*s**2 + b1*s + b0
+    G = StateSpace(Matrix([p1]), Matrix([p2]))
+    expect = StateSpace(Matrix([[2*s + 1]]), Matrix([[5*s**2 + 4*s + 3]]), Matrix([[0]]), Matrix([[0]]))
+    expect_ = StateSpace(Matrix([[2.0*s + 1.0]]), Matrix([[5.0*s**2 + 4.0*s + 3.0]]), Matrix([[0]]), Matrix([[0]]))
+    assert G.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}) == expect
+    assert G.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}).evalf() == expect_
+    assert expect.evalf() == expect_
+
+def test_conversion():
+    # StateSpace to TransferFunction for SISO
+    A1 = Matrix([[-5, -1], [3, -1]])
+    B1 = Matrix([2, 5])
+    C1 = Matrix([[1, 2]])
+    D1 = Matrix([0])
+    H1 = StateSpace(A1, B1, C1, D1)
+    H3 = StateSpace(Matrix([[a0, a1], [a2, a3]]), B = Matrix([[b1], [b2]]), C = Matrix([[c1, c2]]))
+    tm1 = H1.rewrite(TransferFunction)
+    tm2 = (-H1).rewrite(TransferFunction)
+
+    tf1 = tm1[0][0]
+    tf2 = tm2[0][0]
+
+    assert tf1 == TransferFunction(12*s + 59, s**2 + 6*s + 8, s)
+    assert tf2.num == -tf1.num
+    assert tf2.den == tf1.den
+
+    # StateSpace to TransferFunction for MIMO
+    A2 = Matrix([[-1.5, -2, 3], [1, 0, 1], [2, 1, 1]])
+    B2 = Matrix([[0.5, 0, 1], [0, 1, 2], [2, 2, 3]])
+    C2 = Matrix([[0, 1, 0], [0, 2, 1], [1, 0, 2]])
+    D2 = Matrix([[2, 2, 0], [1, 1, 1], [3, 2, 1]])
+    H2 = StateSpace(A2, B2, C2, D2)
+    tm3 = H2.rewrite(TransferFunction)
+
+    # outputs for input i obtained at Index i-1. Consider input 1
+    assert tm3[0][0] == TransferFunction(2.0*s**3 + 1.0*s**2 - 10.5*s + 4.5, 1.0*s**3 + 0.5*s**2 - 6.5*s - 2.5, s)
+    assert tm3[0][1] == TransferFunction(2.0*s**3 + 2.0*s**2 - 10.5*s - 3.5, 1.0*s**3 + 0.5*s**2 - 6.5*s - 2.5, s)
+    assert tm3[0][2] == TransferFunction(2.0*s**2 + 5.0*s - 0.5, 1.0*s**3 + 0.5*s**2 - 6.5*s - 2.5, s)
+    assert H3.rewrite(TransferFunction) == [[TransferFunction(-c1*(a1*b2 - a3*b1 + b1*s) - c2*(-a0*b2 + a2*b1 + b2*s),
+                                                              -a0*a3 + a0*s + a1*a2 + a3*s - s**2, s)]]
+    # TransferFunction to StateSpace
+    SS = TF1.rewrite(StateSpace)
+    assert SS == \
+        StateSpace(Matrix([[     0,          1],
+                           [-wn**2, -2*wn*zeta]]),
+                   Matrix([[0],
+                           [1]]),
+                   Matrix([[1, 0]]),
+                   Matrix([[0]]))
+    assert SS.rewrite(TransferFunction)[0][0] == TF1
+
+    # Transfer function has to be proper
+    raises(ValueError, lambda: TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s).rewrite(StateSpace))
+
+
+def test_StateSpace_dsolve():
+    # https://web.mit.edu/2.14/www/Handouts/StateSpaceResponse.pdf
+    # https://lpsa.swarthmore.edu/Transient/TransMethSS.html
+    A1 = Matrix([[0, 1], [-2, -3]])
+    B1 = Matrix([[0], [1]])
+    C1 = Matrix([[1, -1]])
+    D1 = Matrix([0])
+    I1 = Matrix([[1], [2]])
+    t = symbols('t')
+    ss1 = StateSpace(A1, B1, C1, D1)
+
+    # Zero input and Zero initial conditions
+    assert ss1.dsolve() == Matrix([[0]])
+    assert ss1.dsolve(initial_conditions=I1) == Matrix([[8*exp(-t) - 9*exp(-2*t)]])
+
+    A2 = Matrix([[-2, 0], [1, -1]])
+    C2 = eye(2,2)
+    I2 = Matrix([2, 3])
+    ss2 = StateSpace(A=A2, C=C2)
+    assert ss2.dsolve(initial_conditions=I2) == Matrix([[2*exp(-2*t)], [5*exp(-t) - 2*exp(-2*t)]])
+
+    A3 = Matrix([[-1, 1], [-4, -4]])
+    B3 = Matrix([[0], [4]])
+    C3 = Matrix([[0, 1]])
+    D3 = Matrix([0])
+    U3 = Matrix([10])
+    ss3 = StateSpace(A3, B3, C3, D3)
+    op = ss3.dsolve(input_vector=U3, var=t)
+    assert str(op.simplify().expand().evalf()[0]) == str(5.0 + 20.7880460155075*exp(-5*t/2)*sin(sqrt(7)*t/2)
+                                            - 5.0*exp(-5*t/2)*cos(sqrt(7)*t/2))
+
+    # Test with Heaviside as input
+    A4 = Matrix([[-1, 1], [-4, -4]])
+    B4 = Matrix([[0], [4]])
+    C4 = Matrix([[0, 1]])
+    U4 = Matrix([[10*Heaviside(t)]])
+    ss4 = StateSpace(A4, B4, C4)
+    op4 = str(ss4.dsolve(var=t, input_vector=U4)[0].simplify().expand().evalf())
+    assert op4 == str(5.0*Heaviside(t) + 20.7880460155075*exp(-5*t/2)*sin(sqrt(7)*t/2)*Heaviside(t)
+                                            - 5.0*exp(-5*t/2)*cos(sqrt(7)*t/2)*Heaviside(t))
+
+    # Test with Symbolic Matrices
+    m, a, x0 = symbols('m a x_0')
+    A5 = Matrix([[0, 1], [0, 0]])
+    B5 = Matrix([[0], [1 / m]])
+    C5 = Matrix([[1, 0]])
+    I5 = Matrix([[x0], [0]])
+    U5 = Matrix([[exp(-a * t)]])
+    ss5 = StateSpace(A5, B5, C5)
+    op5 = ss5.dsolve(initial_conditions=I5, input_vector=U5, var=t).simplify()
+    assert op5[0].args[0][0] == x0 + t/(a*m) - 1/(a**2*m) + exp(-a*t)/(a**2*m)
+    a11, a12, a21, a22, b1, b2, c1, c2, i1, i2 = symbols('a_11 a_12 a_21 a_22 b_1 b_2 c_1 c_2 i_1 i_2')
+    A6 = Matrix([[a11, a12], [a21, a22]])
+    B6 = Matrix([b1, b2])
+    C6 = Matrix([[c1, c2]])
+    I6 = Matrix([i1, i2])
+    ss6 = StateSpace(A6, B6, C6)
+    expr6 = ss6.dsolve(initial_conditions=I6)[0]
+    expr6 = expr6.subs([(a11, 0), (a12, 1), (a21, -2), (a22, -3), (b1, 0), (b2, 1), (c1, 1), (c2, -1), (i1, 1), (i2, 2)])
+    assert expr6 == 8*exp(-t) - 9*exp(-2*t)
+
+
+def test_StateSpace_functions():
+    # https://in.mathworks.com/help/control/ref/statespacemodel.obsv.html
+
+    A_mat = Matrix([[-1.5, -2], [1, 0]])
+    B_mat = Matrix([0.5, 0])
+    C_mat = Matrix([[0, 1]])
+    D_mat = Matrix([1])
+    SS1 = StateSpace(A_mat, B_mat, C_mat, D_mat)
+    SS2 = StateSpace(Matrix([[1, 1], [4, -2]]),Matrix([[0, 1], [0, 2]]),Matrix([[-1, 1], [1, -1]]))
+    SS3 = StateSpace(Matrix([[1, 1], [4, -2]]),Matrix([[1, -1], [1, -1]]))
+    SS4 = StateSpace(Matrix([[a0, a1], [a2, a3]]), Matrix([[b1], [b2]]), Matrix([[c1, c2]]))
+
+    # Observability
+    assert SS1.is_observable() == True
+    assert SS2.is_observable() == False
+    assert SS1.observability_matrix() == Matrix([[0, 1], [1, 0]])
+    assert SS2.observability_matrix() == Matrix([[-1,  1], [ 1, -1], [ 3, -3], [-3,  3]])
+    assert SS1.observable_subspace() == [Matrix([[0], [1]]), Matrix([[1], [0]])]
+    assert SS2.observable_subspace() == [Matrix([[-1], [ 1], [ 3], [-3]])]
+    Qo = SS4.observability_matrix().subs([(a0, 0), (a1, -6), (a2, 1), (a3, -5), (c1, 0), (c2, 1)])
+    assert Qo == Matrix([[0, 1], [1, -5]])
+
+    # Controllability
+    assert SS1.is_controllable() == True
+    assert SS3.is_controllable() == False
+    assert SS1.controllability_matrix() ==  Matrix([[0.5, -0.75], [  0,   0.5]])
+    assert SS3.controllability_matrix() == Matrix([[1, -1, 2, -2], [1, -1, 2, -2]])
+    assert SS1.controllable_subspace() == [Matrix([[0.5], [  0]]), Matrix([[-0.75], [  0.5]])]
+    assert SS3.controllable_subspace() == [Matrix([[1], [1]])]
+    assert SS4.controllable_subspace() == [Matrix([
+                                          [b1],
+                                          [b2]]), Matrix([
+                                          [a0*b1 + a1*b2],
+                                          [a2*b1 + a3*b2]])]
+    Qc = SS4.controllability_matrix().subs([(a0, 0), (a1, 1), (a2, -6), (a3, -5), (b1, 0), (b2, 1)])
+    assert Qc == Matrix([[0, 1], [1, -5]])
+
+    # Append
+    A1 = Matrix([[0, 1], [1, 0]])
+    B1 = Matrix([[0], [1]])
+    C1 = Matrix([[0, 1]])
+    D1 = Matrix([[0]])
+    ss1 = StateSpace(A1, B1, C1, D1)
+    ss2 = StateSpace(Matrix([[1, 0], [0, 1]]), Matrix([[1], [0]]), Matrix([[1, 0]]), Matrix([[1]]))
+    ss3 = ss1.append(ss2)
+    ss4 = SS4.append(ss1)
+
+    assert ss3.num_states == ss1.num_states + ss2.num_states
+    assert ss3.num_inputs == ss1.num_inputs + ss2.num_inputs
+    assert ss3.num_outputs == ss1.num_outputs + ss2.num_outputs
+    assert ss3.state_matrix == Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
+    assert ss3.input_matrix == Matrix([[0, 0], [1, 0], [0, 1], [0, 0]])
+    assert ss3.output_matrix == Matrix([[0, 1, 0, 0], [0, 0, 1, 0]])
+    assert ss3.feedforward_matrix == Matrix([[0, 0], [0, 1]])
+
+    # Using symbolic matrices
+    assert ss4.num_states == SS4.num_states + ss1.num_states
+    assert ss4.num_inputs == SS4.num_inputs + ss1.num_inputs
+    assert ss4.num_outputs == SS4.num_outputs + ss1.num_outputs
+    assert ss4.state_matrix == Matrix([[a0, a1, 0, 0], [a2, a3, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
+    assert ss4.input_matrix == Matrix([[b1, 0], [b2, 0], [0, 0], [0, 1]])
+    assert ss4.output_matrix == Matrix([[c1, c2, 0, 0], [0, 0, 0, 1]])
+    assert ss4.feedforward_matrix == Matrix([[0, 0], [0, 0]])
+
+
+def test_StateSpace_series():
+    # For SISO Systems
+    a1 = Matrix([[0, 1], [1, 0]])
+    b1 = Matrix([[0], [1]])
+    c1 = Matrix([[0, 1]])
+    d1 = Matrix([[0]])
+    a2 = Matrix([[1, 0], [0, 1]])
+    b2 = Matrix([[1], [0]])
+    c2 = Matrix([[1, 0]])
+    d2 = Matrix([[1]])
+
+    ss1 = StateSpace(a1, b1, c1, d1)
+    ss2 = StateSpace(a2, b2, c2, d2)
+    tf1 = TransferFunction(s, s+1, s)
+    ser1 = Series(ss1, ss2)
+    assert ser1 == Series(StateSpace(Matrix([
+                            [0, 1],
+                            [1, 0]]), Matrix([
+                            [0],
+                            [1]]), Matrix([[0, 1]]), Matrix([[0]])), StateSpace(Matrix([
+                            [1, 0],
+                            [0, 1]]), Matrix([
+                            [1],
+                            [0]]), Matrix([[1, 0]]), Matrix([[1]])))
+    assert ser1.doit() == StateSpace(
+                            Matrix([
+                            [0, 1, 0, 0],
+                            [1, 0, 0, 0],
+                            [0, 1, 1, 0],
+                            [0, 0, 0, 1]]),
+                            Matrix([
+                            [0],
+                            [1],
+                            [0],
+                            [0]]),
+                            Matrix([[0, 1, 1, 0]]),
+                            Matrix([[0]]))
+
+    assert ser1.num_inputs == 1
+    assert ser1.num_outputs == 1
+    assert ser1.rewrite(TransferFunction) == TransferFunction(s**2, s**3 - s**2 - s + 1, s)
+    ser2 = Series(ss1)
+    ser3 = Series(ser2, ss2)
+    assert ser3.doit() == ser1.doit()
+
+    # TransferFunction interconnection with StateSpace
+    ser_tf = Series(tf1, ss1)
+    assert ser_tf == Series(TransferFunction(s, s + 1, s), StateSpace(Matrix([
+                            [0, 1],
+                            [1, 0]]), Matrix([
+                            [0],
+                            [1]]), Matrix([[0, 1]]), Matrix([[0]])))
+    assert ser_tf.doit() == StateSpace(
+                            Matrix([
+                            [-1, 0,  0],
+                            [0, 0,  1],
+                            [-1, 1, 0]]),
+                            Matrix([
+                            [1],
+                            [0],
+                            [1]]),
+                            Matrix([[0, 0, 1]]),
+                            Matrix([[0]]))
+    assert ser_tf.rewrite(TransferFunction) == TransferFunction(s**2, s**3 + s**2 - s - 1, s)
+
+    # For MIMO Systems
+    a3 = Matrix([[4, 1], [2, -3]])
+    b3 = Matrix([[5, 2], [-3, -3]])
+    c3 = Matrix([[2, -4], [0, 1]])
+    d3 = Matrix([[3, 2], [1, -1]])
+    a4 = Matrix([[-3, 4, 2], [-1, -3, 0], [2, 5, 3]])
+    b4 = Matrix([[1, 4], [-3, -3], [-2, 1]])
+    c4 = Matrix([[4, 2, -3], [1, 4, 3]])
+    d4 = Matrix([[-2, 4], [0, 1]])
+    ss3 = StateSpace(a3, b3, c3, d3)
+    ss4 = StateSpace(a4, b4, c4, d4)
+    ser4 = MIMOSeries(ss3, ss4)
+    assert ser4 == MIMOSeries(StateSpace(Matrix([
+                    [4,  1],
+                    [2, -3]]), Matrix([
+                    [ 5,  2],
+                    [-3, -3]]), Matrix([
+                    [2, -4],
+                    [0,  1]]), Matrix([
+                    [3,  2],
+                    [1, -1]])), StateSpace(Matrix([
+                    [-3,  4, 2],
+                    [-1, -3, 0],
+                    [ 2,  5, 3]]), Matrix([
+                    [ 1,  4],
+                    [-3, -3],
+                    [-2,  1]]), Matrix([
+                    [4, 2, -3],
+                    [1, 4,  3]]), Matrix([
+                    [-2, 4],
+                    [ 0, 1]])))
+    assert ser4.doit() == StateSpace(
+                        Matrix([
+                        [4,   1,  0, 0,  0],
+                        [2,  -3,  0, 0,  0],
+                        [2,   0,  -3, 4,  2],
+                        [-6,  9, -1, -3,  0],
+                        [-4, 9,  2, 5, 3]]),
+                        Matrix([
+                        [5,   2],
+                        [-3,  -3],
+                        [7,   -2],
+                        [-12,  -3],
+                        [-5, -5]]),
+                        Matrix([
+                        [-4, 12, 4, 2, -3],
+                        [0, 1, 1, 4, 3]]),
+                        Matrix([
+                        [-2, -8],
+                        [1, -1]]))
+    assert ser4.num_inputs == ss3.num_inputs
+    assert ser4.num_outputs == ss4.num_outputs
+    ser5 = MIMOSeries(ss3)
+    ser6 = MIMOSeries(ser5, ss4)
+    assert ser6.doit() == ser4.doit()
+    assert ser6.rewrite(TransferFunctionMatrix) == ser4.rewrite(TransferFunctionMatrix)
+    tf2 = TransferFunction(1, s, s)
+    tf3 = TransferFunction(1, s+1, s)
+    tf4 = TransferFunction(s, s+2, s)
+    tfm = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+    ser6 = MIMOSeries(ss3, tfm)
+    assert ser6 == MIMOSeries(StateSpace(Matrix([
+                        [4,  1],
+                        [2, -3]]), Matrix([
+                        [ 5,  2],
+                        [-3, -3]]), Matrix([
+                        [2, -4],
+                        [0,  1]]), Matrix([
+                        [3,  2],
+                        [1, -1]])), TransferFunctionMatrix((
+                        (TransferFunction(s, s + 1, s), TransferFunction(1, s, s)),
+                        (TransferFunction(1, s + 1, s), TransferFunction(s, s + 2, s)))))
+
+
+def test_StateSpace_parallel():
+    # For SISO system
+    a1 = Matrix([[0, 1], [1, 0]])
+    b1 = Matrix([[0], [1]])
+    c1 = Matrix([[0, 1]])
+    d1 = Matrix([[0]])
+    a2 = Matrix([[1, 0], [0, 1]])
+    b2 = Matrix([[1], [0]])
+    c2 = Matrix([[1, 0]])
+    d2 = Matrix([[1]])
+    ss1 = StateSpace(a1, b1, c1, d1)
+    ss2 = StateSpace(a2, b2, c2, d2)
+    p1 = Parallel(ss1, ss2)
+    assert p1 == Parallel(StateSpace(Matrix([[0, 1], [1, 0]]), Matrix([[0], [1]]), Matrix([[0, 1]]), Matrix([[0]])),
+                          StateSpace(Matrix([[1, 0],[0, 1]]), Matrix([[1],[0]]), Matrix([[1, 0]]), Matrix([[1]])))
+    assert p1.doit() == StateSpace(Matrix([
+                        [0, 1, 0, 0],
+                        [1, 0, 0, 0],
+                        [0, 0, 1, 0],
+                        [0, 0, 0, 1]]),
+                        Matrix([
+                        [0],
+                        [1],
+                        [1],
+                        [0]]),
+                        Matrix([[0, 1, 1, 0]]),
+                        Matrix([[1]]))
+    assert p1.rewrite(TransferFunction) == TransferFunction(s*(s + 2), s**2 - 1, s)
+
+    # Connecting StateSpace with TransferFunction
+    tf1 = TransferFunction(s, s+1, s)
+    p2 = Parallel(ss1, tf1)
+    assert p2 == Parallel(StateSpace(Matrix([
+                        [0, 1],
+                        [1, 0]]), Matrix([
+                        [0],
+                        [1]]), Matrix([[0, 1]]), Matrix([[0]])), TransferFunction(s, s + 1, s))
+    assert p2.doit() == StateSpace(
+                        Matrix([
+                        [0, 1,  0],
+                        [1, 0,  0],
+                        [0, 0, -1]]),
+                        Matrix([
+                        [0],
+                        [1],
+                        [1]]),
+                        Matrix([[0, 1, -1]]),
+                        Matrix([[1]]))
+    assert p2.rewrite(TransferFunction) == TransferFunction(s**2, s**2 - 1, s)
+
+    # For MIMO
+    a3 = Matrix([[4, 1], [2, -3]])
+    b3 = Matrix([[5, 2], [-3, -3]])
+    c3 = Matrix([[2, -4], [0, 1]])
+    d3 = Matrix([[3, 2], [1, -1]])
+    a4 = Matrix([[-3, 4, 2], [-1, -3, 0], [2, 5, 3]])
+    b4 = Matrix([[1, 4], [-3, -3], [-2, 1]])
+    c4 = Matrix([[4, 2, -3], [1, 4, 3]])
+    d4 = Matrix([[-2, 4], [0, 1]])
+    ss3 = StateSpace(a3, b3, c3, d3)
+    ss4 = StateSpace(a4, b4, c4, d4)
+    p3 = MIMOParallel(ss3, ss4)
+    assert p3 == MIMOParallel(StateSpace(Matrix([
+                        [4,  1],
+                        [2, -3]]), Matrix([
+                        [ 5,  2],
+                        [-3, -3]]), Matrix([
+                        [2, -4],
+                        [0,  1]]), Matrix([
+                        [3,  2],
+                        [1, -1]])), StateSpace(Matrix([
+                        [-3,  4, 2],
+                        [-1, -3, 0],
+                        [ 2,  5, 3]]), Matrix([
+                        [ 1,  4],
+                        [-3, -3],
+                        [-2,  1]]), Matrix([
+                        [4, 2, -3],
+                        [1, 4,  3]]), Matrix([
+                        [-2, 4],
+                        [ 0, 1]])))
+    assert p3.doit() == StateSpace(Matrix([
+                        [4, 1, 0, 0, 0],
+                        [2, -3, 0, 0, 0],
+                        [0, 0, -3, 4, 2],
+                        [0, 0, -1, -3, 0],
+                        [0, 0, 2, 5, 3]]),
+                        Matrix([
+                        [5, 2],
+                        [-3, -3],
+                        [1, 4],
+                        [-3, -3],
+                        [-2, 1]]),
+                        Matrix([
+                        [2, -4, 4, 2, -3],
+                        [0, 1, 1, 4, 3]]),
+                        Matrix([
+                        [1, 6],
+                        [1, 0]]))
+
+    # Using StateSpace with MIMOParallel.
+    tf2 = TransferFunction(1, s, s)
+    tf3 = TransferFunction(1, s + 1, s)
+    tf4 = TransferFunction(s, s + 2, s)
+    tfm = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+    p4 = MIMOParallel(tfm, ss3)
+    assert p4 == MIMOParallel(TransferFunctionMatrix((
+                        (TransferFunction(s, s + 1, s), TransferFunction(1, s, s)),
+                        (TransferFunction(1, s + 1, s), TransferFunction(s, s + 2, s)))),
+                        StateSpace(Matrix([
+                        [4, 1],
+                        [2, -3]]), Matrix([
+                        [5, 2],
+                        [-3, -3]]), Matrix([
+                        [2, -4],
+                        [0, 1]]), Matrix([
+                        [3, 2],
+                        [1, -1]])))
+
+
+def test_StateSpace_feedback():
+    # For SISO
+    a1 = Matrix([[0, 1], [1, 0]])
+    b1 = Matrix([[0], [1]])
+    c1 = Matrix([[0, 1]])
+    d1 = Matrix([[0]])
+    a2 = Matrix([[1, 0], [0, 1]])
+    b2 = Matrix([[1], [0]])
+    c2 = Matrix([[1, 0]])
+    d2 = Matrix([[1]])
+    ss1 = StateSpace(a1, b1, c1, d1)
+    ss2 = StateSpace(a2, b2, c2, d2)
+    fd1 = Feedback(ss1, ss2)
+
+    # Negative feedback
+    assert fd1 == Feedback(StateSpace(Matrix([[0, 1], [1, 0]]), Matrix([[0], [1]]), Matrix([[0, 1]]), Matrix([[0]])),
+                          StateSpace(Matrix([[1, 0],[0, 1]]), Matrix([[1],[0]]), Matrix([[1, 0]]), Matrix([[1]])), -1)
+    assert fd1.doit() == StateSpace(Matrix([
+                            [0,  1,  0, 0],
+                            [1, -1, -1, 0],
+                            [0,  1,  1, 0],
+                            [0,  0,  0, 1]]), Matrix([
+                            [0],
+                            [1],
+                            [0],
+                            [0]]), Matrix(
+                            [[0, 1, 0, 0]]), Matrix(
+                            [[0]]))
+    assert fd1.rewrite(TransferFunction) == TransferFunction(s*(s - 1), s**3 - s + 1, s)
+
+    # Positive Feedback
+    fd2 = Feedback(ss1, ss2, 1)
+    assert fd2.doit() == StateSpace(Matrix([
+                            [0, 1, 0, 0],
+                            [1, 1, 1, 0],
+                            [0, 1, 1, 0],
+                            [0, 0, 0, 1]]), Matrix([
+                            [0],
+                            [1],
+                            [0],
+                            [0]]), Matrix(
+                            [[0, 1, 0, 0]]), Matrix(
+                            [[0]]))
+    assert fd2.rewrite(TransferFunction) == TransferFunction(s*(s - 1), s**3 - 2*s**2 - s + 1, s)
+
+    # Connection with TransferFunction
+    tf1 = TransferFunction(s, s+1, s)
+    fd3 = Feedback(ss1, tf1)
+    assert fd3 == Feedback(StateSpace(Matrix([
+                            [0, 1],
+                            [1, 0]]), Matrix([
+                            [0],
+                            [1]]), Matrix([[0, 1]]), Matrix([[0]])),
+                            TransferFunction(s, s + 1, s), -1)
+    assert fd3.doit() == StateSpace (Matrix([
+                            [0,  1,  0],
+                            [1, -1,  1],
+                            [0,  1, -1]]), Matrix([
+                            [0],
+                            [1],
+                            [0]]), Matrix(
+                            [[0, 1, 0]]), Matrix(
+                            [[0]]))
+
+    # For MIMO
+    a3 = Matrix([[4, 1], [2, -3]])
+    b3 = Matrix([[5, 2], [-3, -3]])
+    c3 = Matrix([[2, -4], [0, 1]])
+    d3 = Matrix([[3, 2], [1, -1]])
+    a4 = Matrix([[-3, 4, 2], [-1, -3, 0], [2, 5, 3]])
+    b4 = Matrix([[1, 4], [-3, -3], [-2, 1]])
+    c4 = Matrix([[4, 2, -3], [1, 4, 3]])
+    d4 = Matrix([[-2, 4], [0, 1]])
+    ss3 = StateSpace(a3, b3, c3, d3)
+    ss4 = StateSpace(a4, b4, c4, d4)
+
+    # Negative Feedback
+    fd4 = MIMOFeedback(ss3, ss4)
+    assert fd4 == MIMOFeedback(StateSpace(Matrix([
+                            [4,  1],
+                            [2, -3]]), Matrix([
+                            [ 5,  2],
+                            [-3, -3]]), Matrix([
+                            [2, -4],
+                            [0,  1]]), Matrix([
+                            [3,  2],
+                            [1, -1]])), StateSpace(Matrix([
+                            [-3,  4, 2],
+                            [-1, -3, 0],
+                            [ 2,  5, 3]]), Matrix([
+                            [ 1,  4],
+                            [-3, -3],
+                            [-2,  1]]), Matrix([
+                            [4, 2, -3],
+                            [1, 4,  3]]), Matrix([
+                            [-2, 4],
+                            [ 0, 1]])), -1)
+    assert fd4.doit() == StateSpace(Matrix([
+                            [Rational(3), Rational(-3, 4), Rational(-15, 4), Rational(-37, 2), Rational(-15)],
+                            [Rational(7, 2), Rational(-39, 8), Rational(9, 8), Rational(39, 4), Rational(9)],
+                            [Rational(3), Rational(-41, 4), Rational(-45, 4), Rational(-51, 2), Rational(-19)],
+                            [Rational(-9, 2), Rational(129, 8), Rational(73, 8), Rational(171, 4), Rational(36)],
+                            [Rational(-3, 2), Rational(47, 8), Rational(31, 8), Rational(85, 4), Rational(18)]]), Matrix([
+                            [Rational(-1, 4), Rational(19, 4)],
+                            [Rational(3, 8), Rational(-21, 8)],
+                            [Rational(1, 4), Rational(29, 4)],
+                            [Rational(3, 8), Rational(-93, 8)],
+                            [Rational(5, 8), Rational(-35, 8)]]), Matrix([
+                            [Rational(1), Rational(-15, 4), Rational(-7, 4), Rational(-21, 2), Rational(-9)],
+                            [Rational(1, 2), Rational(-13, 8), Rational(-13, 8), Rational(-19, 4), Rational(-3)]]), Matrix([
+                            [Rational(-1, 4), Rational(11, 4)],
+                            [Rational(1, 8), Rational(9, 8)]]))
+
+    # Positive Feedback
+    fd5 = MIMOFeedback(ss3, ss4, 1)
+    assert fd5.doit() == StateSpace(Matrix([
+                            [Rational(4, 7), Rational(62, 7), Rational(1), Rational(-8), Rational(-69, 7)],
+                            [Rational(32, 7), Rational(-135, 14), Rational(-3, 2), Rational(3), Rational(36, 7)],
+                            [Rational(-10, 7), Rational(41, 7), Rational(-4), Rational(-12), Rational(-97, 7)],
+                            [Rational(12, 7), Rational(-111, 14), Rational(-5, 2), Rational(18), Rational(171, 7)],
+                            [Rational(2, 7), Rational(-29, 14), Rational(-1, 2), Rational(10), Rational(81, 7)]]), Matrix([
+                            [Rational(6, 7), Rational(-17, 7)],
+                            [Rational(-9, 14), Rational(15, 14)],
+                            [Rational(6, 7), Rational(-31, 7)],
+                            [Rational(-27, 14), Rational(87, 14)],
+                            [Rational(-15, 14), Rational(25, 14)]]), Matrix([
+                            [Rational(-2, 7), Rational(11, 7), Rational(1), Rational(-4), Rational(-39, 7)],
+                            [Rational(-2, 7), Rational(15, 14), Rational(-1, 2), Rational(-3), Rational(-18, 7)]]), Matrix([
+                            [Rational(4, 7), Rational(-9, 7)],
+                            [Rational(1, 14), Rational(-11, 14)]]))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/gamma_matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/gamma_matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..40c3d0754438902f304d01c2df354dd09f9ea257
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/gamma_matrices.py
@@ -0,0 +1,716 @@
+"""
+    Module to handle gamma matrices expressed as tensor objects.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, LorentzIndex
+    >>> from sympy.tensor.tensor import tensor_indices
+    >>> i = tensor_indices('i', LorentzIndex)
+    >>> G(i)
+    GammaMatrix(i)
+
+    Note that there is already an instance of GammaMatrixHead in four dimensions:
+    GammaMatrix, which is simply declare as
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix
+    >>> from sympy.tensor.tensor import tensor_indices
+    >>> i = tensor_indices('i', LorentzIndex)
+    >>> GammaMatrix(i)
+    GammaMatrix(i)
+
+    To access the metric tensor
+
+    >>> LorentzIndex.metric
+    metric(LorentzIndex,LorentzIndex)
+
+"""
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.matrices.dense import eye
+from sympy.matrices.expressions.trace import trace
+from sympy.tensor.tensor import TensorIndexType, TensorIndex,\
+    TensMul, TensAdd, tensor_mul, Tensor, TensorHead, TensorSymmetry
+
+
+# DiracSpinorIndex = TensorIndexType('DiracSpinorIndex', dim=4, dummy_name="S")
+
+
+LorentzIndex = TensorIndexType('LorentzIndex', dim=4, dummy_name="L")
+
+
+GammaMatrix = TensorHead("GammaMatrix", [LorentzIndex],
+                         TensorSymmetry.no_symmetry(1), comm=None)
+
+
+def extract_type_tens(expression, component):
+    """
+    Extract from a ``TensExpr`` all tensors with `component`.
+
+    Returns two tensor expressions:
+
+    * the first contains all ``Tensor`` of having `component`.
+    * the second contains all remaining.
+
+
+    """
+    if isinstance(expression, Tensor):
+        sp = [expression]
+    elif isinstance(expression, TensMul):
+        sp = expression.args
+    else:
+        raise ValueError('wrong type')
+
+    # Collect all gamma matrices of the same dimension
+    new_expr = S.One
+    residual_expr = S.One
+    for i in sp:
+        if isinstance(i, Tensor) and i.component == component:
+            new_expr *= i
+        else:
+            residual_expr *= i
+    return new_expr, residual_expr
+
+
+def simplify_gamma_expression(expression):
+    extracted_expr, residual_expr = extract_type_tens(expression, GammaMatrix)
+    res_expr = _simplify_single_line(extracted_expr)
+    return res_expr * residual_expr
+
+
+def simplify_gpgp(ex, sort=True):
+    """
+    simplify products ``G(i)*p(-i)*G(j)*p(-j) -> p(i)*p(-i)``
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        LorentzIndex, simplify_gpgp
+    >>> from sympy.tensor.tensor import tensor_indices, tensor_heads
+    >>> p, q = tensor_heads('p, q', [LorentzIndex])
+    >>> i0,i1,i2,i3,i4,i5 = tensor_indices('i0:6', LorentzIndex)
+    >>> ps = p(i0)*G(-i0)
+    >>> qs = q(i0)*G(-i0)
+    >>> simplify_gpgp(ps*qs*qs)
+    GammaMatrix(-L_0)*p(L_0)*q(L_1)*q(-L_1)
+    """
+    def _simplify_gpgp(ex):
+        components = ex.components
+        a = []
+        comp_map = []
+        for i, comp in enumerate(components):
+            comp_map.extend([i]*comp.rank)
+        dum = [(i[0], i[1], comp_map[i[0]], comp_map[i[1]]) for i in ex.dum]
+        for i in range(len(components)):
+            if components[i] != GammaMatrix:
+                continue
+            for dx in dum:
+                if dx[2] == i:
+                    p_pos1 = dx[3]
+                elif dx[3] == i:
+                    p_pos1 = dx[2]
+                else:
+                    continue
+                comp1 = components[p_pos1]
+                if comp1.comm == 0 and comp1.rank == 1:
+                    a.append((i, p_pos1))
+        if not a:
+            return ex
+        elim = set()
+        tv = []
+        hit = True
+        coeff = S.One
+        ta = None
+        while hit:
+            hit = False
+            for i, ai in enumerate(a[:-1]):
+                if ai[0] in elim:
+                    continue
+                if ai[0] != a[i + 1][0] - 1:
+                    continue
+                if components[ai[1]] != components[a[i + 1][1]]:
+                    continue
+                elim.add(ai[0])
+                elim.add(ai[1])
+                elim.add(a[i + 1][0])
+                elim.add(a[i + 1][1])
+                if not ta:
+                    ta = ex.split()
+                    mu = TensorIndex('mu', LorentzIndex)
+                hit = True
+                if i == 0:
+                    coeff = ex.coeff
+                tx = components[ai[1]](mu)*components[ai[1]](-mu)
+                if len(a) == 2:
+                    tx *= 4  # eye(4)
+                tv.append(tx)
+                break
+
+        if tv:
+            a = [x for j, x in enumerate(ta) if j not in elim]
+            a.extend(tv)
+            t = tensor_mul(*a)*coeff
+            # t = t.replace(lambda x: x.is_Matrix, lambda x: 1)
+            return t
+        else:
+            return ex
+
+    if sort:
+        ex = ex.sorted_components()
+    # this would be better off with pattern matching
+    while 1:
+        t = _simplify_gpgp(ex)
+        if t != ex:
+            ex = t
+        else:
+            return t
+
+
+def gamma_trace(t):
+    """
+    trace of a single line of gamma matrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        gamma_trace, LorentzIndex
+    >>> from sympy.tensor.tensor import tensor_indices, tensor_heads
+    >>> p, q = tensor_heads('p, q', [LorentzIndex])
+    >>> i0,i1,i2,i3,i4,i5 = tensor_indices('i0:6', LorentzIndex)
+    >>> ps = p(i0)*G(-i0)
+    >>> qs = q(i0)*G(-i0)
+    >>> gamma_trace(G(i0)*G(i1))
+    4*metric(i0, i1)
+    >>> gamma_trace(ps*ps) - 4*p(i0)*p(-i0)
+    0
+    >>> gamma_trace(ps*qs + ps*ps) - 4*p(i0)*p(-i0) - 4*p(i0)*q(-i0)
+    0
+
+    """
+    if isinstance(t, TensAdd):
+        res = TensAdd(*[gamma_trace(x) for x in t.args])
+        return res
+    t = _simplify_single_line(t)
+    res = _trace_single_line(t)
+    return res
+
+
+def _simplify_single_line(expression):
+    """
+    Simplify single-line product of gamma matrices.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        LorentzIndex, _simplify_single_line
+    >>> from sympy.tensor.tensor import tensor_indices, TensorHead
+    >>> p = TensorHead('p', [LorentzIndex])
+    >>> i0,i1 = tensor_indices('i0:2', LorentzIndex)
+    >>> _simplify_single_line(G(i0)*G(i1)*p(-i1)*G(-i0)) + 2*G(i0)*p(-i0)
+    0
+
+    """
+    t1, t2 = extract_type_tens(expression, GammaMatrix)
+    if t1 != 1:
+        t1 = kahane_simplify(t1)
+    res = t1*t2
+    return res
+
+
+def _trace_single_line(t):
+    """
+    Evaluate the trace of a single gamma matrix line inside a ``TensExpr``.
+
+    Notes
+    =====
+
+    If there are ``DiracSpinorIndex.auto_left`` and ``DiracSpinorIndex.auto_right``
+    indices trace over them; otherwise traces are not implied (explain)
+
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        LorentzIndex, _trace_single_line
+    >>> from sympy.tensor.tensor import tensor_indices, TensorHead
+    >>> p = TensorHead('p', [LorentzIndex])
+    >>> i0,i1,i2,i3,i4,i5 = tensor_indices('i0:6', LorentzIndex)
+    >>> _trace_single_line(G(i0)*G(i1))
+    4*metric(i0, i1)
+    >>> _trace_single_line(G(i0)*p(-i0)*G(i1)*p(-i1)) - 4*p(i0)*p(-i0)
+    0
+
+    """
+    def _trace_single_line1(t):
+        t = t.sorted_components()
+        components = t.components
+        ncomps = len(components)
+        g = LorentzIndex.metric
+        # gamma matirices are in a[i:j]
+        hit = 0
+        for i in range(ncomps):
+            if components[i] == GammaMatrix:
+                hit = 1
+                break
+
+        for j in range(i + hit, ncomps):
+            if components[j] != GammaMatrix:
+                break
+        else:
+            j = ncomps
+        numG = j - i
+        if numG == 0:
+            tcoeff = t.coeff
+            return t.nocoeff if tcoeff else t
+        if numG % 2 == 1:
+            return TensMul.from_data(S.Zero, [], [], [])
+        elif numG > 4:
+            # find the open matrix indices and connect them:
+            a = t.split()
+            ind1 = a[i].get_indices()[0]
+            ind2 = a[i + 1].get_indices()[0]
+            aa = a[:i] + a[i + 2:]
+            t1 = tensor_mul(*aa)*g(ind1, ind2)
+            t1 = t1.contract_metric(g)
+            args = [t1]
+            sign = 1
+            for k in range(i + 2, j):
+                sign = -sign
+                ind2 = a[k].get_indices()[0]
+                aa = a[:i] + a[i + 1:k] + a[k + 1:]
+                t2 = sign*tensor_mul(*aa)*g(ind1, ind2)
+                t2 = t2.contract_metric(g)
+                t2 = simplify_gpgp(t2, False)
+                args.append(t2)
+            t3 = TensAdd(*args)
+            t3 = _trace_single_line(t3)
+            return t3
+        else:
+            a = t.split()
+            t1 = _gamma_trace1(*a[i:j])
+            a2 = a[:i] + a[j:]
+            t2 = tensor_mul(*a2)
+            t3 = t1*t2
+            if not t3:
+                return t3
+            t3 = t3.contract_metric(g)
+            return t3
+
+    t = t.expand()
+    if isinstance(t, TensAdd):
+        a = [_trace_single_line1(x)*x.coeff for x in t.args]
+        return TensAdd(*a)
+    elif isinstance(t, (Tensor, TensMul)):
+        r = t.coeff*_trace_single_line1(t)
+        return r
+    else:
+        return trace(t)
+
+
+def _gamma_trace1(*a):
+    gctr = 4  # FIXME specific for d=4
+    g = LorentzIndex.metric
+    if not a:
+        return gctr
+    n = len(a)
+    if n%2 == 1:
+        #return TensMul.from_data(S.Zero, [], [], [])
+        return S.Zero
+    if n == 2:
+        ind0 = a[0].get_indices()[0]
+        ind1 = a[1].get_indices()[0]
+        return gctr*g(ind0, ind1)
+    if n == 4:
+        ind0 = a[0].get_indices()[0]
+        ind1 = a[1].get_indices()[0]
+        ind2 = a[2].get_indices()[0]
+        ind3 = a[3].get_indices()[0]
+
+        return gctr*(g(ind0, ind1)*g(ind2, ind3) - \
+           g(ind0, ind2)*g(ind1, ind3) + g(ind0, ind3)*g(ind1, ind2))
+
+
+def kahane_simplify(expression):
+    r"""
+    This function cancels contracted elements in a product of four
+    dimensional gamma matrices, resulting in an expression equal to the given
+    one, without the contracted gamma matrices.
+
+    Parameters
+    ==========
+
+    `expression`    the tensor expression containing the gamma matrices to simplify.
+
+    Notes
+    =====
+
+    If spinor indices are given, the matrices must be given in
+    the order given in the product.
+
+    Algorithm
+    =========
+
+    The idea behind the algorithm is to use some well-known identities,
+    i.e., for contractions enclosing an even number of `\gamma` matrices
+
+    `\gamma^\mu \gamma_{a_1} \cdots \gamma_{a_{2N}} \gamma_\mu = 2 (\gamma_{a_{2N}} \gamma_{a_1} \cdots \gamma_{a_{2N-1}} + \gamma_{a_{2N-1}} \cdots \gamma_{a_1} \gamma_{a_{2N}} )`
+
+    for an odd number of `\gamma` matrices
+
+    `\gamma^\mu \gamma_{a_1} \cdots \gamma_{a_{2N+1}} \gamma_\mu = -2 \gamma_{a_{2N+1}} \gamma_{a_{2N}} \cdots \gamma_{a_{1}}`
+
+    Instead of repeatedly applying these identities to cancel out all contracted indices,
+    it is possible to recognize the links that would result from such an operation,
+    the problem is thus reduced to a simple rearrangement of free gamma matrices.
+
+    Examples
+    ========
+
+    When using, always remember that the original expression coefficient
+    has to be handled separately
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, LorentzIndex
+    >>> from sympy.physics.hep.gamma_matrices import kahane_simplify
+    >>> from sympy.tensor.tensor import tensor_indices
+    >>> i0, i1, i2 = tensor_indices('i0:3', LorentzIndex)
+    >>> ta = G(i0)*G(-i0)
+    >>> kahane_simplify(ta)
+    Matrix([
+    [4, 0, 0, 0],
+    [0, 4, 0, 0],
+    [0, 0, 4, 0],
+    [0, 0, 0, 4]])
+    >>> tb = G(i0)*G(i1)*G(-i0)
+    >>> kahane_simplify(tb)
+    -2*GammaMatrix(i1)
+    >>> t = G(i0)*G(-i0)
+    >>> kahane_simplify(t)
+    Matrix([
+    [4, 0, 0, 0],
+    [0, 4, 0, 0],
+    [0, 0, 4, 0],
+    [0, 0, 0, 4]])
+    >>> t = G(i0)*G(-i0)
+    >>> kahane_simplify(t)
+    Matrix([
+    [4, 0, 0, 0],
+    [0, 4, 0, 0],
+    [0, 0, 4, 0],
+    [0, 0, 0, 4]])
+
+    If there are no contractions, the same expression is returned
+
+    >>> tc = G(i0)*G(i1)
+    >>> kahane_simplify(tc)
+    GammaMatrix(i0)*GammaMatrix(i1)
+
+    References
+    ==========
+
+    [1] Algorithm for Reducing Contracted Products of gamma Matrices,
+    Joseph Kahane, Journal of Mathematical Physics, Vol. 9, No. 10, October 1968.
+    """
+
+    if isinstance(expression, Mul):
+        return expression
+    if isinstance(expression, TensAdd):
+        return TensAdd(*[kahane_simplify(arg) for arg in expression.args])
+
+    if isinstance(expression, Tensor):
+        return expression
+
+    assert isinstance(expression, TensMul)
+
+    gammas = expression.args
+
+    for gamma in gammas:
+        assert gamma.component == GammaMatrix
+
+    free = expression.free
+    # spinor_free = [_ for _ in expression.free_in_args if _[1] != 0]
+
+    # if len(spinor_free) == 2:
+    #     spinor_free.sort(key=lambda x: x[2])
+    #     assert spinor_free[0][1] == 1 and spinor_free[-1][1] == 2
+    #     assert spinor_free[0][2] == 0
+    # elif spinor_free:
+    #     raise ValueError('spinor indices do not match')
+
+    dum = []
+    for dum_pair in expression.dum:
+        if expression.index_types[dum_pair[0]] == LorentzIndex:
+            dum.append((dum_pair[0], dum_pair[1]))
+
+    dum = sorted(dum)
+
+    if len(dum) == 0:  # or GammaMatrixHead:
+        # no contractions in `expression`, just return it.
+        return expression
+
+    # find the `first_dum_pos`, i.e. the position of the first contracted
+    # gamma matrix, Kahane's algorithm as described in his paper requires the
+    # gamma matrix expression to start with a contracted gamma matrix, this is
+    # a workaround which ignores possible initial free indices, and re-adds
+    # them later.
+
+    first_dum_pos = min(map(min, dum))
+
+    # for p1, p2, a1, a2 in expression.dum_in_args:
+    #     if p1 != 0 or p2 != 0:
+    #         # only Lorentz indices, skip Dirac indices:
+    #         continue
+    #     first_dum_pos = min(p1, p2)
+    #     break
+
+    total_number = len(free) + len(dum)*2
+    number_of_contractions = len(dum)
+
+    free_pos = [None]*total_number
+    for i in free:
+        free_pos[i[1]] = i[0]
+
+    # `index_is_free` is a list of booleans, to identify index position
+    # and whether that index is free or dummy.
+    index_is_free = [False]*total_number
+
+    for i, indx in enumerate(free):
+        index_is_free[indx[1]] = True
+
+    # `links` is a dictionary containing the graph described in Kahane's paper,
+    # to every key correspond one or two values, representing the linked indices.
+    # All values in `links` are integers, negative numbers are used in the case
+    # where it is necessary to insert gamma matrices between free indices, in
+    # order to make Kahane's algorithm work (see paper).
+    links = {i: [] for i in range(first_dum_pos, total_number)}
+
+    # `cum_sign` is a step variable to mark the sign of every index, see paper.
+    cum_sign = -1
+    # `cum_sign_list` keeps storage for all `cum_sign` (every index).
+    cum_sign_list = [None]*total_number
+    block_free_count = 0
+
+    # multiply `resulting_coeff` by the coefficient parameter, the rest
+    # of the algorithm ignores a scalar coefficient.
+    resulting_coeff = S.One
+
+    # initialize a list of lists of indices. The outer list will contain all
+    # additive tensor expressions, while the inner list will contain the
+    # free indices (rearranged according to the algorithm).
+    resulting_indices = [[]]
+
+    # start to count the `connected_components`, which together with the number
+    # of contractions, determines a -1 or +1 factor to be multiplied.
+    connected_components = 1
+
+    # First loop: here we fill `cum_sign_list`, and draw the links
+    # among consecutive indices (they are stored in `links`). Links among
+    # non-consecutive indices will be drawn later.
+    for i, is_free in enumerate(index_is_free):
+        # if `expression` starts with free indices, they are ignored here;
+        # they are later added as they are to the beginning of all
+        # `resulting_indices` list of lists of indices.
+        if i < first_dum_pos:
+            continue
+
+        if is_free:
+            block_free_count += 1
+            # if previous index was free as well, draw an arch in `links`.
+            if block_free_count > 1:
+                links[i - 1].append(i)
+                links[i].append(i - 1)
+        else:
+            # Change the sign of the index (`cum_sign`) if the number of free
+            # indices preceding it is even.
+            cum_sign *= 1 if (block_free_count % 2) else -1
+            if block_free_count == 0 and i != first_dum_pos:
+                # check if there are two consecutive dummy indices:
+                # in this case create virtual indices with negative position,
+                # these "virtual" indices represent the insertion of two
+                # gamma^0 matrices to separate consecutive dummy indices, as
+                # Kahane's algorithm requires dummy indices to be separated by
+                # free indices. The product of two gamma^0 matrices is unity,
+                # so the new expression being examined is the same as the
+                # original one.
+                if cum_sign == -1:
+                    links[-1-i] = [-1-i+1]
+                    links[-1-i+1] = [-1-i]
+            if (i - cum_sign) in links:
+                if i != first_dum_pos:
+                    links[i].append(i - cum_sign)
+                if block_free_count != 0:
+                    if i - cum_sign < len(index_is_free):
+                        if index_is_free[i - cum_sign]:
+                            links[i - cum_sign].append(i)
+            block_free_count = 0
+
+        cum_sign_list[i] = cum_sign
+
+    # The previous loop has only created links between consecutive free indices,
+    # it is necessary to properly create links among dummy (contracted) indices,
+    # according to the rules described in Kahane's paper. There is only one exception
+    # to Kahane's rules: the negative indices, which handle the case of some
+    # consecutive free indices (Kahane's paper just describes dummy indices
+    # separated by free indices, hinting that free indices can be added without
+    # altering the expression result).
+    for i in dum:
+        # get the positions of the two contracted indices:
+        pos1 = i[0]
+        pos2 = i[1]
+
+        # create Kahane's upper links, i.e. the upper arcs between dummy
+        # (i.e. contracted) indices:
+        links[pos1].append(pos2)
+        links[pos2].append(pos1)
+
+        # create Kahane's lower links, this corresponds to the arcs below
+        # the line described in the paper:
+
+        # first we move `pos1` and `pos2` according to the sign of the indices:
+        linkpos1 = pos1 + cum_sign_list[pos1]
+        linkpos2 = pos2 + cum_sign_list[pos2]
+
+        # otherwise, perform some checks before creating the lower arcs:
+
+        # make sure we are not exceeding the total number of indices:
+        if linkpos1 >= total_number:
+            continue
+        if linkpos2 >= total_number:
+            continue
+
+        # make sure we are not below the first dummy index in `expression`:
+        if linkpos1 < first_dum_pos:
+            continue
+        if linkpos2 < first_dum_pos:
+            continue
+
+        # check if the previous loop created "virtual" indices between dummy
+        # indices, in such a case relink `linkpos1` and `linkpos2`:
+        if (-1-linkpos1) in links:
+            linkpos1 = -1-linkpos1
+        if (-1-linkpos2) in links:
+            linkpos2 = -1-linkpos2
+
+        # move only if not next to free index:
+        if linkpos1 >= 0 and not index_is_free[linkpos1]:
+            linkpos1 = pos1
+
+        if linkpos2 >=0 and not index_is_free[linkpos2]:
+            linkpos2 = pos2
+
+        # create the lower arcs:
+        if linkpos2 not in links[linkpos1]:
+            links[linkpos1].append(linkpos2)
+        if linkpos1 not in links[linkpos2]:
+            links[linkpos2].append(linkpos1)
+
+    # This loop starts from the `first_dum_pos` index (first dummy index)
+    # walks through the graph deleting the visited indices from `links`,
+    # it adds a gamma matrix for every free index in encounters, while it
+    # completely ignores dummy indices and virtual indices.
+    pointer = first_dum_pos
+    previous_pointer = 0
+    while True:
+        if pointer in links:
+            next_ones = links.pop(pointer)
+        else:
+            break
+
+        if previous_pointer in next_ones:
+            next_ones.remove(previous_pointer)
+
+        previous_pointer = pointer
+
+        if next_ones:
+            pointer = next_ones[0]
+        else:
+            break
+
+        if pointer == previous_pointer:
+            break
+        if pointer >=0 and free_pos[pointer] is not None:
+            for ri in resulting_indices:
+                ri.append(free_pos[pointer])
+
+    # The following loop removes the remaining connected components in `links`.
+    # If there are free indices inside a connected component, it gives a
+    # contribution to the resulting expression given by the factor
+    # `gamma_a gamma_b ... gamma_z + gamma_z ... gamma_b gamma_a`, in Kahanes's
+    # paper represented as  {gamma_a, gamma_b, ... , gamma_z},
+    # virtual indices are ignored. The variable `connected_components` is
+    # increased by one for every connected component this loop encounters.
+
+    # If the connected component has virtual and dummy indices only
+    # (no free indices), it contributes to `resulting_indices` by a factor of two.
+    # The multiplication by two is a result of the
+    # factor {gamma^0, gamma^0} = 2 I, as it appears in Kahane's paper.
+    # Note: curly brackets are meant as in the paper, as a generalized
+    # multi-element anticommutator!
+
+    while links:
+        connected_components += 1
+        pointer = min(links.keys())
+        previous_pointer = pointer
+        # the inner loop erases the visited indices from `links`, and it adds
+        # all free indices to `prepend_indices` list, virtual indices are
+        # ignored.
+        prepend_indices = []
+        while True:
+            if pointer in links:
+                next_ones = links.pop(pointer)
+            else:
+                break
+
+            if previous_pointer in next_ones:
+                if len(next_ones) > 1:
+                    next_ones.remove(previous_pointer)
+
+            previous_pointer = pointer
+
+            if next_ones:
+                pointer = next_ones[0]
+
+            if pointer >= first_dum_pos and free_pos[pointer] is not None:
+                prepend_indices.insert(0, free_pos[pointer])
+        # if `prepend_indices` is void, it means there are no free indices
+        # in the loop (and it can be shown that there must be a virtual index),
+        # loops of virtual indices only contribute by a factor of two:
+        if len(prepend_indices) == 0:
+            resulting_coeff *= 2
+        # otherwise, add the free indices in `prepend_indices` to
+        # the `resulting_indices`:
+        else:
+            expr1 = prepend_indices
+            expr2 = list(reversed(prepend_indices))
+            resulting_indices = [expri + ri for ri in resulting_indices for expri in (expr1, expr2)]
+
+    # sign correction, as described in Kahane's paper:
+    resulting_coeff *= -1 if (number_of_contractions - connected_components + 1) % 2 else 1
+    # power of two factor, as described in Kahane's paper:
+    resulting_coeff *= 2**(number_of_contractions)
+
+    # If `first_dum_pos` is not zero, it means that there are trailing free gamma
+    # matrices in front of `expression`, so multiply by them:
+    resulting_indices = [ free_pos[0:first_dum_pos] + ri for ri in resulting_indices ]
+
+    resulting_expr = S.Zero
+    for i in resulting_indices:
+        temp_expr = S.One
+        for j in i:
+            temp_expr *= GammaMatrix(j)
+        resulting_expr += temp_expr
+
+    t = resulting_coeff * resulting_expr
+    t1 = None
+    if isinstance(t, TensAdd):
+        t1 = t.args[0]
+    elif isinstance(t, TensMul):
+        t1 = t
+    if t1:
+        pass
+    else:
+        t = eye(4)*t
+    return t
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/tests/test_gamma_matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/tests/test_gamma_matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..1552cf0d19be222ba249a7e32c65c8c3abc54ac2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/hep/tests/test_gamma_matrices.py
@@ -0,0 +1,427 @@
+from sympy.matrices.dense import eye, Matrix
+from sympy.tensor.tensor import tensor_indices, TensorHead, tensor_heads, \
+    TensExpr, canon_bp
+from sympy.physics.hep.gamma_matrices import GammaMatrix as G, LorentzIndex, \
+    kahane_simplify, gamma_trace, _simplify_single_line, simplify_gamma_expression
+from sympy import Symbol
+
+
+def _is_tensor_eq(arg1, arg2):
+    arg1 = canon_bp(arg1)
+    arg2 = canon_bp(arg2)
+    if isinstance(arg1, TensExpr):
+        return arg1.equals(arg2)
+    elif isinstance(arg2, TensExpr):
+        return arg2.equals(arg1)
+    return arg1 == arg2
+
+def execute_gamma_simplify_tests_for_function(tfunc, D):
+    """
+    Perform tests to check if sfunc is able to simplify gamma matrix expressions.
+
+    Parameters
+    ==========
+
+    `sfunc`     a function to simplify a `TIDS`, shall return the simplified `TIDS`.
+    `D`         the number of dimension (in most cases `D=4`).
+
+    """
+
+    mu, nu, rho, sigma = tensor_indices("mu, nu, rho, sigma", LorentzIndex)
+    a1, a2, a3, a4, a5, a6 = tensor_indices("a1:7", LorentzIndex)
+    mu11, mu12, mu21, mu31, mu32, mu41, mu51, mu52 = tensor_indices("mu11, mu12, mu21, mu31, mu32, mu41, mu51, mu52", LorentzIndex)
+    mu61, mu71, mu72 = tensor_indices("mu61, mu71, mu72", LorentzIndex)
+    m0, m1, m2, m3, m4, m5, m6 = tensor_indices("m0:7", LorentzIndex)
+
+    def g(xx, yy):
+        return (G(xx)*G(yy) + G(yy)*G(xx))/2
+
+    # Some examples taken from Kahane's paper, 4 dim only:
+    if D == 4:
+        t = (G(a1)*G(mu11)*G(a2)*G(mu21)*G(-a1)*G(mu31)*G(-a2))
+        assert _is_tensor_eq(tfunc(t), -4*G(mu11)*G(mu31)*G(mu21) - 4*G(mu31)*G(mu11)*G(mu21))
+
+        t = (G(a1)*G(mu11)*G(mu12)*\
+                              G(a2)*G(mu21)*\
+                              G(a3)*G(mu31)*G(mu32)*\
+                              G(a4)*G(mu41)*\
+                              G(-a2)*G(mu51)*G(mu52)*\
+                              G(-a1)*G(mu61)*\
+                              G(-a3)*G(mu71)*G(mu72)*\
+                              G(-a4))
+        assert _is_tensor_eq(tfunc(t), \
+            16*G(mu31)*G(mu32)*G(mu72)*G(mu71)*G(mu11)*G(mu52)*G(mu51)*G(mu12)*G(mu61)*G(mu21)*G(mu41) + 16*G(mu31)*G(mu32)*G(mu72)*G(mu71)*G(mu12)*G(mu51)*G(mu52)*G(mu11)*G(mu61)*G(mu21)*G(mu41) + 16*G(mu71)*G(mu72)*G(mu32)*G(mu31)*G(mu11)*G(mu52)*G(mu51)*G(mu12)*G(mu61)*G(mu21)*G(mu41) + 16*G(mu71)*G(mu72)*G(mu32)*G(mu31)*G(mu12)*G(mu51)*G(mu52)*G(mu11)*G(mu61)*G(mu21)*G(mu41))
+
+    # Fully Lorentz-contracted expressions, these return scalars:
+
+    def add_delta(ne):
+        return ne * eye(4)  # DiracSpinorIndex.delta(DiracSpinorIndex.auto_left, -DiracSpinorIndex.auto_right)
+
+    t = (G(mu)*G(-mu))
+    ts = add_delta(D)
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(mu)*G(nu)*G(-mu)*G(-nu))
+    ts = add_delta(2*D - D**2)  # -8
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(mu)*G(nu)*G(-nu)*G(-mu))
+    ts = add_delta(D**2)  # 16
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(mu)*G(nu)*G(-rho)*G(-nu)*G(-mu)*G(rho))
+    ts = add_delta(4*D - 4*D**2 + D**3)  # 16
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(mu)*G(nu)*G(rho)*G(-rho)*G(-nu)*G(-mu))
+    ts = add_delta(D**3)  # 64
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(a1)*G(a2)*G(a3)*G(a4)*G(-a3)*G(-a1)*G(-a2)*G(-a4))
+    ts = add_delta(-8*D + 16*D**2 - 8*D**3 + D**4)  # -32
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(-mu)*G(-nu)*G(-rho)*G(-sigma)*G(nu)*G(mu)*G(sigma)*G(rho))
+    ts = add_delta(-16*D + 24*D**2 - 8*D**3 + D**4)  # 64
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(-mu)*G(nu)*G(-rho)*G(sigma)*G(rho)*G(-nu)*G(mu)*G(-sigma))
+    ts = add_delta(8*D - 12*D**2 + 6*D**3 - D**4)  # -32
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(a1)*G(a2)*G(a3)*G(a4)*G(a5)*G(-a3)*G(-a2)*G(-a1)*G(-a5)*G(-a4))
+    ts = add_delta(64*D - 112*D**2 + 60*D**3 - 12*D**4 + D**5)  # 256
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(a1)*G(a2)*G(a3)*G(a4)*G(a5)*G(-a3)*G(-a1)*G(-a2)*G(-a4)*G(-a5))
+    ts = add_delta(64*D - 120*D**2 + 72*D**3 - 16*D**4 + D**5)  # -128
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(a1)*G(a2)*G(a3)*G(a4)*G(a5)*G(a6)*G(-a3)*G(-a2)*G(-a1)*G(-a6)*G(-a5)*G(-a4))
+    ts = add_delta(416*D - 816*D**2 + 528*D**3 - 144*D**4 + 18*D**5 - D**6)  # -128
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    t = (G(a1)*G(a2)*G(a3)*G(a4)*G(a5)*G(a6)*G(-a2)*G(-a3)*G(-a1)*G(-a6)*G(-a4)*G(-a5))
+    ts = add_delta(416*D - 848*D**2 + 584*D**3 - 172*D**4 + 22*D**5 - D**6)  # -128
+    assert _is_tensor_eq(tfunc(t), ts)
+
+    # Expressions with free indices:
+
+    t = (G(mu)*G(nu)*G(rho)*G(sigma)*G(-mu))
+    assert _is_tensor_eq(tfunc(t), (-2*G(sigma)*G(rho)*G(nu) + (4-D)*G(nu)*G(rho)*G(sigma)))
+
+    t = (G(mu)*G(nu)*G(-mu))
+    assert _is_tensor_eq(tfunc(t), (2-D)*G(nu))
+
+    t = (G(mu)*G(nu)*G(rho)*G(-mu))
+    assert _is_tensor_eq(tfunc(t), 2*G(nu)*G(rho) + 2*G(rho)*G(nu) - (4-D)*G(nu)*G(rho))
+
+    t = 2*G(m2)*G(m0)*G(m1)*G(-m0)*G(-m1)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, (D*(-2*D + 4))*G(m2))
+
+    t = G(m2)*G(m0)*G(m1)*G(-m0)*G(-m2)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, ((-D + 2)**2)*G(m1))
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)*G(-m1)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, (D - 4)*G(m0)*G(m2)*G(m3) + 4*G(m0)*g(m2, m3))
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)*G(-m1)*G(-m0)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, ((D - 4)**2)*G(m2)*G(m3) + (8*D - 16)*g(m2, m3))
+
+    t = G(m2)*G(m0)*G(m1)*G(-m2)*G(-m0)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, ((-D + 2)*(D - 4) + 4)*G(m1))
+
+    t = G(m3)*G(m1)*G(m0)*G(m2)*G(-m3)*G(-m0)*G(-m2)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, (-4*D + (-D + 2)**2*(D - 4) + 8)*G(m1))
+
+    t = 2*G(m0)*G(m1)*G(m2)*G(m3)*G(-m0)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, ((-2*D + 8)*G(m1)*G(m2)*G(m3) - 4*G(m3)*G(m2)*G(m1)))
+
+    t = G(m5)*G(m0)*G(m1)*G(m4)*G(m2)*G(-m4)*G(m3)*G(-m0)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, (((-D + 2)*(-D + 4))*G(m5)*G(m1)*G(m2)*G(m3) + (2*D - 4)*G(m5)*G(m3)*G(m2)*G(m1)))
+
+    t = -G(m0)*G(m1)*G(m2)*G(m3)*G(-m0)*G(m4)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, ((D - 4)*G(m1)*G(m2)*G(m3)*G(m4) + 2*G(m3)*G(m2)*G(m1)*G(m4)))
+
+    t = G(-m5)*G(m0)*G(m1)*G(m2)*G(m3)*G(m4)*G(-m0)*G(m5)
+    st = tfunc(t)
+
+    result1 = ((-D + 4)**2 + 4)*G(m1)*G(m2)*G(m3)*G(m4) +\
+        (4*D - 16)*G(m3)*G(m2)*G(m1)*G(m4) + (4*D - 16)*G(m4)*G(m1)*G(m2)*G(m3)\
+        + 4*G(m2)*G(m1)*G(m4)*G(m3) + 4*G(m3)*G(m4)*G(m1)*G(m2) +\
+        4*G(m4)*G(m3)*G(m2)*G(m1)
+
+    # Kahane's algorithm yields this result, which is equivalent to `result1`
+    # in four dimensions, but is not automatically recognized as equal:
+    result2 = 8*G(m1)*G(m2)*G(m3)*G(m4) + 8*G(m4)*G(m3)*G(m2)*G(m1)
+
+    if D == 4:
+        assert _is_tensor_eq(st, (result1)) or _is_tensor_eq(st, (result2))
+    else:
+        assert _is_tensor_eq(st, (result1))
+
+    # and a few very simple cases, with no contracted indices:
+
+    t = G(m0)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, t)
+
+    t = -7*G(m0)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, t)
+
+    t = 224*G(m0)*G(m1)*G(-m2)*G(m3)
+    st = tfunc(t)
+    assert _is_tensor_eq(st, t)
+
+
+def test_kahane_algorithm():
+    # Wrap this function to convert to and from TIDS:
+
+    def tfunc(e):
+        return _simplify_single_line(e)
+
+    execute_gamma_simplify_tests_for_function(tfunc, D=4)
+
+
+def test_kahane_simplify1():
+    i0,i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15 = tensor_indices('i0:16', LorentzIndex)
+    mu, nu, rho, sigma = tensor_indices("mu, nu, rho, sigma", LorentzIndex)
+    D = 4
+    t = G(i0)*G(i1)
+    r = kahane_simplify(t)
+    assert r.equals(t)
+
+    t = G(i0)*G(i1)*G(-i0)
+    r = kahane_simplify(t)
+    assert r.equals(-2*G(i1))
+    t = G(i0)*G(i1)*G(-i0)
+    r = kahane_simplify(t)
+    assert r.equals(-2*G(i1))
+
+    t = G(i0)*G(i1)
+    r = kahane_simplify(t)
+    assert r.equals(t)
+    t = G(i0)*G(i1)
+    r = kahane_simplify(t)
+    assert r.equals(t)
+    t = G(i0)*G(-i0)
+    r = kahane_simplify(t)
+    assert r.equals(4*eye(4))
+    t = G(i0)*G(-i0)
+    r = kahane_simplify(t)
+    assert r.equals(4*eye(4))
+    t = G(i0)*G(-i0)
+    r = kahane_simplify(t)
+    assert r.equals(4*eye(4))
+    t = G(i0)*G(i1)*G(-i0)
+    r = kahane_simplify(t)
+    assert r.equals(-2*G(i1))
+    t = G(i0)*G(i1)*G(-i0)*G(-i1)
+    r = kahane_simplify(t)
+    assert r.equals((2*D - D**2)*eye(4))
+    t = G(i0)*G(i1)*G(-i0)*G(-i1)
+    r = kahane_simplify(t)
+    assert r.equals((2*D - D**2)*eye(4))
+    t = G(i0)*G(-i0)*G(i1)*G(-i1)
+    r = kahane_simplify(t)
+    assert r.equals(16*eye(4))
+    t = (G(mu)*G(nu)*G(-nu)*G(-mu))
+    r = kahane_simplify(t)
+    assert r.equals(D**2*eye(4))
+    t = (G(mu)*G(nu)*G(-nu)*G(-mu))
+    r = kahane_simplify(t)
+    assert r.equals(D**2*eye(4))
+    t = (G(mu)*G(nu)*G(-nu)*G(-mu))
+    r = kahane_simplify(t)
+    assert r.equals(D**2*eye(4))
+    t = (G(mu)*G(nu)*G(-rho)*G(-nu)*G(-mu)*G(rho))
+    r = kahane_simplify(t)
+    assert r.equals((4*D - 4*D**2 + D**3)*eye(4))
+    t = (G(-mu)*G(-nu)*G(-rho)*G(-sigma)*G(nu)*G(mu)*G(sigma)*G(rho))
+    r = kahane_simplify(t)
+    assert r.equals((-16*D + 24*D**2 - 8*D**3 + D**4)*eye(4))
+    t = (G(-mu)*G(nu)*G(-rho)*G(sigma)*G(rho)*G(-nu)*G(mu)*G(-sigma))
+    r = kahane_simplify(t)
+    assert r.equals((8*D - 12*D**2 + 6*D**3 - D**4)*eye(4))
+
+    # Expressions with free indices:
+    t = (G(mu)*G(nu)*G(rho)*G(sigma)*G(-mu))
+    r = kahane_simplify(t)
+    assert r.equals(-2*G(sigma)*G(rho)*G(nu))
+    t = (G(mu)*G(-mu)*G(rho)*G(sigma))
+    r = kahane_simplify(t)
+    assert r.equals(4*G(rho)*G(sigma))
+    t = (G(rho)*G(sigma)*G(mu)*G(-mu))
+    r = kahane_simplify(t)
+    assert r.equals(4*G(rho)*G(sigma))
+
+def test_gamma_matrix_class():
+    i, j, k = tensor_indices('i,j,k', LorentzIndex)
+
+    # define another type of TensorHead to see if exprs are correctly handled:
+    A = TensorHead('A', [LorentzIndex])
+
+    t = A(k)*G(i)*G(-i)
+    ts = simplify_gamma_expression(t)
+    assert _is_tensor_eq(ts, Matrix([
+        [4, 0, 0, 0],
+        [0, 4, 0, 0],
+        [0, 0, 4, 0],
+        [0, 0, 0, 4]])*A(k))
+
+    t = G(i)*A(k)*G(j)
+    ts = simplify_gamma_expression(t)
+    assert _is_tensor_eq(ts, A(k)*G(i)*G(j))
+
+    execute_gamma_simplify_tests_for_function(simplify_gamma_expression, D=4)
+
+
+def test_gamma_matrix_trace():
+    g = LorentzIndex.metric
+
+    m0, m1, m2, m3, m4, m5, m6 = tensor_indices('m0:7', LorentzIndex)
+    n0, n1, n2, n3, n4, n5 = tensor_indices('n0:6', LorentzIndex)
+
+    # working in D=4 dimensions
+    D = 4
+
+    # traces of odd number of gamma matrices are zero:
+    t = G(m0)
+    t1 = gamma_trace(t)
+    assert t1.equals(0)
+
+    t = G(m0)*G(m1)*G(m2)
+    t1 = gamma_trace(t)
+    assert t1.equals(0)
+
+    t = G(m0)*G(m1)*G(-m0)
+    t1 = gamma_trace(t)
+    assert t1.equals(0)
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)*G(m4)
+    t1 = gamma_trace(t)
+    assert t1.equals(0)
+
+    # traces without internal contractions:
+    t = G(m0)*G(m1)
+    t1 = gamma_trace(t)
+    assert _is_tensor_eq(t1, 4*g(m0, m1))
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)
+    t1 = gamma_trace(t)
+    t2 = -4*g(m0, m2)*g(m1, m3) + 4*g(m0, m1)*g(m2, m3) + 4*g(m0, m3)*g(m1, m2)
+    assert _is_tensor_eq(t1, t2)
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)*G(m4)*G(m5)
+    t1 = gamma_trace(t)
+    t2 = t1*g(-m0, -m5)
+    t2 = t2.contract_metric(g)
+    assert _is_tensor_eq(t2, D*gamma_trace(G(m1)*G(m2)*G(m3)*G(m4)))
+
+    # traces of expressions with internal contractions:
+    t = G(m0)*G(-m0)
+    t1 = gamma_trace(t)
+    assert t1.equals(4*D)
+
+    t = G(m0)*G(m1)*G(-m0)*G(-m1)
+    t1 = gamma_trace(t)
+    assert t1.equals(8*D - 4*D**2)
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)*G(m4)*G(-m0)
+    t1 = gamma_trace(t)
+    t2 = (-4*D)*g(m1, m3)*g(m2, m4) + (4*D)*g(m1, m2)*g(m3, m4) + \
+                 (4*D)*g(m1, m4)*g(m2, m3)
+    assert _is_tensor_eq(t1, t2)
+
+    t = G(-m5)*G(m0)*G(m1)*G(m2)*G(m3)*G(m4)*G(-m0)*G(m5)
+    t1 = gamma_trace(t)
+    t2 = (32*D + 4*(-D + 4)**2 - 64)*(g(m1, m2)*g(m3, m4) - \
+            g(m1, m3)*g(m2, m4) + g(m1, m4)*g(m2, m3))
+    assert _is_tensor_eq(t1, t2)
+
+    t = G(m0)*G(m1)*G(-m0)*G(m3)
+    t1 = gamma_trace(t)
+    assert t1.equals((-4*D + 8)*g(m1, m3))
+
+#    p, q = S1('p,q')
+#    ps = p(m0)*G(-m0)
+#    qs = q(m0)*G(-m0)
+#    t = ps*qs*ps*qs
+#    t1 = gamma_trace(t)
+#    assert t1 == 8*p(m0)*q(-m0)*p(m1)*q(-m1) - 4*p(m0)*p(-m0)*q(m1)*q(-m1)
+
+    t = G(m0)*G(m1)*G(m2)*G(m3)*G(m4)*G(m5)*G(-m0)*G(-m1)*G(-m2)*G(-m3)*G(-m4)*G(-m5)
+    t1 = gamma_trace(t)
+    assert t1.equals(-4*D**6 + 120*D**5 - 1040*D**4 + 3360*D**3 - 4480*D**2 + 2048*D)
+
+    t = G(m0)*G(m1)*G(n1)*G(m2)*G(n2)*G(m3)*G(m4)*G(-n2)*G(-n1)*G(-m0)*G(-m1)*G(-m2)*G(-m3)*G(-m4)
+    t1 = gamma_trace(t)
+    tresu = -7168*D + 16768*D**2 - 14400*D**3 + 5920*D**4 - 1232*D**5 + 120*D**6 - 4*D**7
+    assert t1.equals(tresu)
+
+    # checked with Mathematica
+    # In[1]:= <>> from sympy.physics.hydrogen import R_nl
+    >>> from sympy.abc import r, Z
+    >>> R_nl(1, 0, r, Z)
+    2*sqrt(Z**3)*exp(-Z*r)
+    >>> R_nl(2, 0, r, Z)
+    sqrt(2)*(-Z*r + 2)*sqrt(Z**3)*exp(-Z*r/2)/4
+    >>> R_nl(2, 1, r, Z)
+    sqrt(6)*Z*r*sqrt(Z**3)*exp(-Z*r/2)/12
+
+    For Hydrogen atom, you can just use the default value of Z=1:
+
+    >>> R_nl(1, 0, r)
+    2*exp(-r)
+    >>> R_nl(2, 0, r)
+    sqrt(2)*(2 - r)*exp(-r/2)/4
+    >>> R_nl(3, 0, r)
+    2*sqrt(3)*(2*r**2/9 - 2*r + 3)*exp(-r/3)/27
+
+    For Silver atom, you would use Z=47:
+
+    >>> R_nl(1, 0, r, Z=47)
+    94*sqrt(47)*exp(-47*r)
+    >>> R_nl(2, 0, r, Z=47)
+    47*sqrt(94)*(2 - 47*r)*exp(-47*r/2)/4
+    >>> R_nl(3, 0, r, Z=47)
+    94*sqrt(141)*(4418*r**2/9 - 94*r + 3)*exp(-47*r/3)/27
+
+    The normalization of the radial wavefunction is:
+
+    >>> from sympy import integrate, oo
+    >>> integrate(R_nl(1, 0, r)**2 * r**2, (r, 0, oo))
+    1
+    >>> integrate(R_nl(2, 0, r)**2 * r**2, (r, 0, oo))
+    1
+    >>> integrate(R_nl(2, 1, r)**2 * r**2, (r, 0, oo))
+    1
+
+    It holds for any atomic number:
+
+    >>> integrate(R_nl(1, 0, r, Z=2)**2 * r**2, (r, 0, oo))
+    1
+    >>> integrate(R_nl(2, 0, r, Z=3)**2 * r**2, (r, 0, oo))
+    1
+    >>> integrate(R_nl(2, 1, r, Z=4)**2 * r**2, (r, 0, oo))
+    1
+
+    """
+    # sympify arguments
+    n, l, r, Z = map(S, [n, l, r, Z])
+    # radial quantum number
+    n_r = n - l - 1
+    # rescaled "r"
+    a = 1/Z  # Bohr radius
+    r0 = 2 * r / (n * a)
+    # normalization coefficient
+    C = sqrt((S(2)/(n*a))**3 * factorial(n_r) / (2*n*factorial(n + l)))
+    # This is an equivalent normalization coefficient, that can be found in
+    # some books. Both coefficients seem to be the same fast:
+    # C =  S(2)/n**2 * sqrt(1/a**3 * factorial(n_r) / (factorial(n+l)))
+    return C * r0**l * assoc_laguerre(n_r, 2*l + 1, r0).expand() * exp(-r0/2)
+
+
+def Psi_nlm(n, l, m, r, phi, theta, Z=1):
+    """
+    Returns the Hydrogen wave function psi_{nlm}. It's the product of
+    the radial wavefunction R_{nl} and the spherical harmonic Y_{l}^{m}.
+
+    Parameters
+    ==========
+
+    n : integer
+        Principal Quantum Number which is
+        an integer with possible values as 1, 2, 3, 4,...
+    l : integer
+        ``l`` is the Angular Momentum Quantum Number with
+        values ranging from 0 to ``n-1``.
+    m : integer
+        ``m`` is the Magnetic Quantum Number with values
+        ranging from ``-l`` to ``l``.
+    r :
+        radial coordinate
+    phi :
+        azimuthal angle
+    theta :
+        polar angle
+    Z :
+        atomic number (1 for Hydrogen, 2 for Helium, ...)
+
+    Everything is in Hartree atomic units.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hydrogen import Psi_nlm
+    >>> from sympy import Symbol
+    >>> r=Symbol("r", positive=True)
+    >>> phi=Symbol("phi", real=True)
+    >>> theta=Symbol("theta", real=True)
+    >>> Z=Symbol("Z", positive=True, integer=True, nonzero=True)
+    >>> Psi_nlm(1,0,0,r,phi,theta,Z)
+    Z**(3/2)*exp(-Z*r)/sqrt(pi)
+    >>> Psi_nlm(2,1,1,r,phi,theta,Z)
+    -Z**(5/2)*r*exp(I*phi)*exp(-Z*r/2)*sin(theta)/(8*sqrt(pi))
+
+    Integrating the absolute square of a hydrogen wavefunction psi_{nlm}
+    over the whole space leads 1.
+
+    The normalization of the hydrogen wavefunctions Psi_nlm is:
+
+    >>> from sympy import integrate, conjugate, pi, oo, sin
+    >>> wf=Psi_nlm(2,1,1,r,phi,theta,Z)
+    >>> abs_sqrd=wf*conjugate(wf)
+    >>> jacobi=r**2*sin(theta)
+    >>> integrate(abs_sqrd*jacobi, (r,0,oo), (phi,0,2*pi), (theta,0,pi))
+    1
+    """
+
+    # sympify arguments
+    n, l, m, r, phi, theta, Z = map(S, [n, l, m, r, phi, theta, Z])
+    # check if values for n,l,m make physically sense
+    if n.is_integer and n < 1:
+        raise ValueError("'n' must be positive integer")
+    if l.is_integer and not (n > l):
+        raise ValueError("'n' must be greater than 'l'")
+    if m.is_integer and not (abs(m) <= l):
+        raise ValueError("|'m'| must be less or equal 'l'")
+    # return the hydrogen wave function
+    return R_nl(n, l, r, Z)*Ynm(l, m, theta, phi).expand(func=True)
+
+
+def E_nl(n, Z=1):
+    """
+    Returns the energy of the state (n, l) in Hartree atomic units.
+
+    The energy does not depend on "l".
+
+    Parameters
+    ==========
+
+    n : integer
+        Principal Quantum Number which is
+        an integer with possible values as 1, 2, 3, 4,...
+    Z :
+        Atomic number (1 for Hydrogen, 2 for Helium, ...)
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hydrogen import E_nl
+    >>> from sympy.abc import n, Z
+    >>> E_nl(n, Z)
+    -Z**2/(2*n**2)
+    >>> E_nl(1)
+    -1/2
+    >>> E_nl(2)
+    -1/8
+    >>> E_nl(3)
+    -1/18
+    >>> E_nl(3, 47)
+    -2209/18
+
+    """
+    n, Z = S(n), S(Z)
+    if n.is_integer and (n < 1):
+        raise ValueError("'n' must be positive integer")
+    return -Z**2/(2*n**2)
+
+
+def E_nl_dirac(n, l, spin_up=True, Z=1, c=Float("137.035999037")):
+    """
+    Returns the relativistic energy of the state (n, l, spin) in Hartree atomic
+    units.
+
+    The energy is calculated from the Dirac equation. The rest mass energy is
+    *not* included.
+
+    Parameters
+    ==========
+
+    n : integer
+        Principal Quantum Number which is
+        an integer with possible values as 1, 2, 3, 4,...
+    l : integer
+        ``l`` is the Angular Momentum Quantum Number with
+        values ranging from 0 to ``n-1``.
+    spin_up :
+        True if the electron spin is up (default), otherwise down
+    Z :
+        Atomic number (1 for Hydrogen, 2 for Helium, ...)
+    c :
+        Speed of light in atomic units. Default value is 137.035999037,
+        taken from https://arxiv.org/abs/1012.3627
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hydrogen import E_nl_dirac
+    >>> E_nl_dirac(1, 0)
+    -0.500006656595360
+
+    >>> E_nl_dirac(2, 0)
+    -0.125002080189006
+    >>> E_nl_dirac(2, 1)
+    -0.125000416028342
+    >>> E_nl_dirac(2, 1, False)
+    -0.125002080189006
+
+    >>> E_nl_dirac(3, 0)
+    -0.0555562951740285
+    >>> E_nl_dirac(3, 1)
+    -0.0555558020932949
+    >>> E_nl_dirac(3, 1, False)
+    -0.0555562951740285
+    >>> E_nl_dirac(3, 2)
+    -0.0555556377366884
+    >>> E_nl_dirac(3, 2, False)
+    -0.0555558020932949
+
+    """
+    n, l, Z, c = map(S, [n, l, Z, c])
+    if not (l >= 0):
+        raise ValueError("'l' must be positive or zero")
+    if not (n > l):
+        raise ValueError("'n' must be greater than 'l'")
+    if (l == 0 and spin_up is False):
+        raise ValueError("Spin must be up for l==0.")
+    # skappa is sign*kappa, where sign contains the correct sign
+    if spin_up:
+        skappa = -l - 1
+    else:
+        skappa = -l
+    beta = sqrt(skappa**2 - Z**2/c**2)
+    return c**2/sqrt(1 + Z**2/(n + skappa + beta)**2/c**2) - c**2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/matrices.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..d91466220d63956053b91bd76b948ee677e7c191
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/matrices.py
@@ -0,0 +1,176 @@
+"""Known matrices related to physics"""
+
+from sympy.core.numbers import I
+from sympy.matrices.dense import MutableDenseMatrix as Matrix
+from sympy.utilities.decorator import deprecated
+
+
+def msigma(i):
+    r"""Returns a Pauli matrix `\sigma_i` with `i=1,2,3`.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Pauli_matrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.matrices import msigma
+    >>> msigma(1)
+    Matrix([
+    [0, 1],
+    [1, 0]])
+    """
+    if i == 1:
+        mat = (
+            (0, 1),
+            (1, 0)
+        )
+    elif i == 2:
+        mat = (
+            (0, -I),
+            (I, 0)
+        )
+    elif i == 3:
+        mat = (
+            (1, 0),
+            (0, -1)
+        )
+    else:
+        raise IndexError("Invalid Pauli index")
+    return Matrix(mat)
+
+
+def pat_matrix(m, dx, dy, dz):
+    """Returns the Parallel Axis Theorem matrix to translate the inertia
+    matrix a distance of `(dx, dy, dz)` for a body of mass m.
+
+    Examples
+    ========
+
+    To translate a body having a mass of 2 units a distance of 1 unit along
+    the `x`-axis we get:
+
+    >>> from sympy.physics.matrices import pat_matrix
+    >>> pat_matrix(2, 1, 0, 0)
+    Matrix([
+    [0, 0, 0],
+    [0, 2, 0],
+    [0, 0, 2]])
+
+    """
+    dxdy = -dx*dy
+    dydz = -dy*dz
+    dzdx = -dz*dx
+    dxdx = dx**2
+    dydy = dy**2
+    dzdz = dz**2
+    mat = ((dydy + dzdz, dxdy, dzdx),
+           (dxdy, dxdx + dzdz, dydz),
+           (dzdx, dydz, dydy + dxdx))
+    return m*Matrix(mat)
+
+
+def mgamma(mu, lower=False):
+    r"""Returns a Dirac gamma matrix `\gamma^\mu` in the standard
+    (Dirac) representation.
+
+    Explanation
+    ===========
+
+    If you want `\gamma_\mu`, use ``gamma(mu, True)``.
+
+    We use a convention:
+
+    `\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3`
+
+    `\gamma_5 = i \cdot \gamma_0 \cdot \gamma_1 \cdot \gamma_2 \cdot \gamma_3 = - \gamma^5`
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gamma_matrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.matrices import mgamma
+    >>> mgamma(1)
+    Matrix([
+    [ 0,  0, 0, 1],
+    [ 0,  0, 1, 0],
+    [ 0, -1, 0, 0],
+    [-1,  0, 0, 0]])
+    """
+    if mu not in (0, 1, 2, 3, 5):
+        raise IndexError("Invalid Dirac index")
+    if mu == 0:
+        mat = (
+            (1, 0, 0, 0),
+            (0, 1, 0, 0),
+            (0, 0, -1, 0),
+            (0, 0, 0, -1)
+        )
+    elif mu == 1:
+        mat = (
+            (0, 0, 0, 1),
+            (0, 0, 1, 0),
+            (0, -1, 0, 0),
+            (-1, 0, 0, 0)
+        )
+    elif mu == 2:
+        mat = (
+            (0, 0, 0, -I),
+            (0, 0, I, 0),
+            (0, I, 0, 0),
+            (-I, 0, 0, 0)
+        )
+    elif mu == 3:
+        mat = (
+            (0, 0, 1, 0),
+            (0, 0, 0, -1),
+            (-1, 0, 0, 0),
+            (0, 1, 0, 0)
+        )
+    elif mu == 5:
+        mat = (
+            (0, 0, 1, 0),
+            (0, 0, 0, 1),
+            (1, 0, 0, 0),
+            (0, 1, 0, 0)
+        )
+    m = Matrix(mat)
+    if lower:
+        if mu in (1, 2, 3, 5):
+            m = -m
+    return m
+
+#Minkowski tensor using the convention (+,-,-,-) used in the Quantum Field
+#Theory
+minkowski_tensor = Matrix( (
+    (1, 0, 0, 0),
+    (0, -1, 0, 0),
+    (0, 0, -1, 0),
+    (0, 0, 0, -1)
+))
+
+
+@deprecated(
+    """
+    The sympy.physics.matrices.mdft method is deprecated. Use
+    sympy.DFT(n).as_explicit() instead.
+    """,
+    deprecated_since_version="1.9",
+    active_deprecations_target="deprecated-physics-mdft",
+)
+def mdft(n):
+    r"""
+    .. deprecated:: 1.9
+
+       Use DFT from sympy.matrices.expressions.fourier instead.
+
+       To get identical behavior to ``mdft(n)``, use ``DFT(n).as_explicit()``.
+    """
+    from sympy.matrices.expressions.fourier import DFT
+    return DFT(n).as_mutable()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..afd8c071a2af4fd201d5b2371594b19e4a68edda
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/__init__.py
@@ -0,0 +1,90 @@
+__all__ = [
+    'vector',
+
+    'CoordinateSym', 'ReferenceFrame', 'Dyadic', 'Vector', 'Point', 'cross',
+    'dot', 'express', 'time_derivative', 'outer', 'kinematic_equations',
+    'get_motion_params', 'partial_velocity', 'dynamicsymbols', 'vprint',
+    'vsstrrepr', 'vsprint', 'vpprint', 'vlatex', 'init_vprinting', 'curl',
+    'divergence', 'gradient', 'is_conservative', 'is_solenoidal',
+    'scalar_potential', 'scalar_potential_difference',
+
+    'KanesMethod',
+
+    'RigidBody',
+
+    'linear_momentum', 'angular_momentum', 'kinetic_energy', 'potential_energy',
+    'Lagrangian', 'mechanics_printing', 'mprint', 'msprint', 'mpprint',
+    'mlatex', 'msubs', 'find_dynamicsymbols',
+
+    'inertia', 'inertia_of_point_mass', 'Inertia',
+
+    'Force', 'Torque',
+
+    'Particle',
+
+    'LagrangesMethod',
+
+    'Linearizer',
+
+    'Body',
+
+    'SymbolicSystem', 'System',
+
+    'PinJoint', 'PrismaticJoint', 'CylindricalJoint', 'PlanarJoint',
+    'SphericalJoint', 'WeldJoint',
+
+    'JointsMethod',
+
+    'WrappingCylinder', 'WrappingGeometryBase', 'WrappingSphere',
+
+    'PathwayBase', 'LinearPathway', 'ObstacleSetPathway', 'WrappingPathway',
+
+    'ActuatorBase', 'ForceActuator', 'LinearDamper', 'LinearSpring',
+    'TorqueActuator', 'DuffingSpring', 'CoulombKineticFriction',
+]
+
+from sympy.physics import vector
+
+from sympy.physics.vector import (CoordinateSym, ReferenceFrame, Dyadic, Vector, Point,
+        cross, dot, express, time_derivative, outer, kinematic_equations,
+        get_motion_params, partial_velocity, dynamicsymbols, vprint,
+        vsstrrepr, vsprint, vpprint, vlatex, init_vprinting, curl, divergence,
+        gradient, is_conservative, is_solenoidal, scalar_potential,
+        scalar_potential_difference)
+
+from .kane import KanesMethod
+
+from .rigidbody import RigidBody
+
+from .functions import (linear_momentum, angular_momentum, kinetic_energy,
+                        potential_energy, Lagrangian, mechanics_printing,
+                        mprint, msprint, mpprint, mlatex, msubs,
+                        find_dynamicsymbols)
+
+from .inertia import inertia, inertia_of_point_mass, Inertia
+
+from .loads import Force, Torque
+
+from .particle import Particle
+
+from .lagrange import LagrangesMethod
+
+from .linearize import Linearizer
+
+from .body import Body
+
+from .system import SymbolicSystem, System
+
+from .jointsmethod import JointsMethod
+
+from .joint import (PinJoint, PrismaticJoint, CylindricalJoint, PlanarJoint,
+                    SphericalJoint, WeldJoint)
+
+from .wrapping_geometry import (WrappingCylinder, WrappingGeometryBase,
+                                WrappingSphere)
+
+from .pathway import (PathwayBase, LinearPathway, ObstacleSetPathway,
+                      WrappingPathway)
+
+from .actuator import (ActuatorBase, ForceActuator, LinearDamper, LinearSpring,
+                       TorqueActuator, DuffingSpring, CoulombKineticFriction)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/actuator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/actuator.py
new file mode 100644
index 0000000000000000000000000000000000000000..625b3e55019e7545c6dfed073d388acba91a324c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/actuator.py
@@ -0,0 +1,1147 @@
+"""Implementations of actuators for linked force and torque application."""
+
+from abc import ABC, abstractmethod
+
+from sympy import S, sympify, exp, sign
+from sympy.physics.mechanics.joint import PinJoint
+from sympy.physics.mechanics.loads import Torque
+from sympy.physics.mechanics.pathway import PathwayBase
+from sympy.physics.mechanics.rigidbody import RigidBody
+from sympy.physics.vector import ReferenceFrame, Vector
+
+
+__all__ = [
+    'ActuatorBase',
+    'ForceActuator',
+    'LinearDamper',
+    'LinearSpring',
+    'TorqueActuator',
+    'DuffingSpring',
+    'CoulombKineticFriction',
+]
+
+
+class ActuatorBase(ABC):
+    """Abstract base class for all actuator classes to inherit from.
+
+    Notes
+    =====
+
+    Instances of this class cannot be directly instantiated by users. However,
+    it can be used to created custom actuator types through subclassing.
+
+    """
+
+    def __init__(self):
+        """Initializer for ``ActuatorBase``."""
+        pass
+
+    @abstractmethod
+    def to_loads(self):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        """
+        pass
+
+    def __repr__(self):
+        """Default representation of an actuator."""
+        return f'{self.__class__.__name__}()'
+
+
+class ForceActuator(ActuatorBase):
+    """Force-producing actuator.
+
+    Explanation
+    ===========
+
+    A ``ForceActuator`` is an actuator that produces a (expansile) force along
+    its length.
+
+    A force actuator uses a pathway instance to determine the direction and
+    number of forces that it applies to a system. Consider the simplest case
+    where a ``LinearPathway`` instance is used. This pathway is made up of two
+    points that can move relative to each other, and results in a pair of equal
+    and opposite forces acting on the endpoints. If the positive time-varying
+    Euclidean distance between the two points is defined, then the "extension
+    velocity" is the time derivative of this distance. The extension velocity
+    is positive when the two points are moving away from each other and
+    negative when moving closer to each other. The direction for the force
+    acting on either point is determined by constructing a unit vector directed
+    from the other point to this point. This establishes a sign convention such
+    that a positive force magnitude tends to push the points apart, this is the
+    meaning of "expansile" in this context. The following diagram shows the
+    positive force sense and the distance between the points::
+
+       P           Q
+       o<--- F --->o
+       |           |
+       |<--l(t)--->|
+
+    Examples
+    ========
+
+    To construct an actuator, an expression (or symbol) must be supplied to
+    represent the force it can produce, alongside a pathway specifying its line
+    of action. Let's also create a global reference frame and spatially fix one
+    of the points in it while setting the other to be positioned such that it
+    can freely move in the frame's x direction specified by the coordinate
+    ``q``.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import (ForceActuator, LinearPathway,
+    ...     Point, ReferenceFrame)
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> N = ReferenceFrame('N')
+    >>> q = dynamicsymbols('q')
+    >>> force = symbols('F')
+    >>> pA, pB = Point('pA'), Point('pB')
+    >>> pA.set_vel(N, 0)
+    >>> pB.set_pos(pA, q*N.x)
+    >>> pB.pos_from(pA)
+    q(t)*N.x
+    >>> linear_pathway = LinearPathway(pA, pB)
+    >>> actuator = ForceActuator(force, linear_pathway)
+    >>> actuator
+    ForceActuator(F, LinearPathway(pA, pB))
+
+    Parameters
+    ==========
+
+    force : Expr
+        The scalar expression defining the (expansile) force that the actuator
+        produces.
+    pathway : PathwayBase
+        The pathway that the actuator follows. This must be an instance of a
+        concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+
+    """
+
+    def __init__(self, force, pathway):
+        """Initializer for ``ForceActuator``.
+
+        Parameters
+        ==========
+
+        force : Expr
+            The scalar expression defining the (expansile) force that the
+            actuator produces.
+        pathway : PathwayBase
+            The pathway that the actuator follows. This must be an instance of
+            a concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+
+        """
+        self.force = force
+        self.pathway = pathway
+
+    @property
+    def force(self):
+        """The magnitude of the force produced by the actuator."""
+        return self._force
+
+    @force.setter
+    def force(self, force):
+        if hasattr(self, '_force'):
+            msg = (
+                f'Can\'t set attribute `force` to {repr(force)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        self._force = sympify(force, strict=True)
+
+    @property
+    def pathway(self):
+        """The ``Pathway`` defining the actuator's line of action."""
+        return self._pathway
+
+    @pathway.setter
+    def pathway(self, pathway):
+        if hasattr(self, '_pathway'):
+            msg = (
+                f'Can\'t set attribute `pathway` to {repr(pathway)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        if not isinstance(pathway, PathwayBase):
+            msg = (
+                f'Value {repr(pathway)} passed to `pathway` was of type '
+                f'{type(pathway)}, must be {PathwayBase}.'
+            )
+            raise TypeError(msg)
+        self._pathway = pathway
+
+    def to_loads(self):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        Examples
+        ========
+
+        The below example shows how to generate the loads produced by a force
+        actuator that follows a linear pathway. In this example we'll assume
+        that the force actuator is being used to model a simple linear spring.
+        First, create a linear pathway between two points separated by the
+        coordinate ``q`` in the ``x`` direction of the global frame ``N``.
+
+        >>> from sympy.physics.mechanics import (LinearPathway, Point,
+        ...     ReferenceFrame)
+        >>> from sympy.physics.vector import dynamicsymbols
+        >>> q = dynamicsymbols('q')
+        >>> N = ReferenceFrame('N')
+        >>> pA, pB = Point('pA'), Point('pB')
+        >>> pB.set_pos(pA, q*N.x)
+        >>> pathway = LinearPathway(pA, pB)
+
+        Now create a symbol ``k`` to describe the spring's stiffness and
+        instantiate a force actuator that produces a (contractile) force
+        proportional to both the spring's stiffness and the pathway's length.
+        Note that actuator classes use the sign convention that expansile
+        forces are positive, so for a spring to produce a contractile force the
+        spring force needs to be calculated as the negative for the stiffness
+        multiplied by the length.
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import ForceActuator
+        >>> stiffness = symbols('k')
+        >>> spring_force = -stiffness*pathway.length
+        >>> spring = ForceActuator(spring_force, pathway)
+
+        The forces produced by the spring can be generated in the list of loads
+        form that ``KanesMethod`` (and other equations of motion methods)
+        requires by calling the ``to_loads`` method.
+
+        >>> spring.to_loads()
+        [(pA, k*q(t)*N.x), (pB, - k*q(t)*N.x)]
+
+        A simple linear damper can be modeled in a similar way. Create another
+        symbol ``c`` to describe the dampers damping coefficient. This time
+        instantiate a force actuator that produces a force proportional to both
+        the damper's damping coefficient and the pathway's extension velocity.
+        Note that the damping force is negative as it acts in the opposite
+        direction to which the damper is changing in length.
+
+        >>> damping_coefficient = symbols('c')
+        >>> damping_force = -damping_coefficient*pathway.extension_velocity
+        >>> damper = ForceActuator(damping_force, pathway)
+
+        Again, the forces produces by the damper can be generated by calling
+        the ``to_loads`` method.
+
+        >>> damper.to_loads()
+        [(pA, c*Derivative(q(t), t)*N.x), (pB, - c*Derivative(q(t), t)*N.x)]
+
+        """
+        return self.pathway.to_loads(self.force)
+
+    def __repr__(self):
+        """Representation of a ``ForceActuator``."""
+        return f'{self.__class__.__name__}({self.force}, {self.pathway})'
+
+
+class LinearSpring(ForceActuator):
+    """A spring with its spring force as a linear function of its length.
+
+    Explanation
+    ===========
+
+    Note that the "linear" in the name ``LinearSpring`` refers to the fact that
+    the spring force is a linear function of the springs length. I.e. for a
+    linear spring with stiffness ``k``, distance between its ends of ``x``, and
+    an equilibrium length of ``0``, the spring force will be ``-k*x``, which is
+    a linear function in ``x``. To create a spring that follows a linear, or
+    straight, pathway between its two ends, a ``LinearPathway`` instance needs
+    to be passed to the ``pathway`` parameter.
+
+    A ``LinearSpring`` is a subclass of ``ForceActuator`` and so follows the
+    same sign conventions for length, extension velocity, and the direction of
+    the forces it applies to its points of attachment on bodies. The sign
+    convention for the direction of forces is such that, for the case where a
+    linear spring is instantiated with a ``LinearPathway`` instance as its
+    pathway, they act to push the two ends of the spring away from one another.
+    Because springs produces a contractile force and acts to pull the two ends
+    together towards the equilibrium length when stretched, the scalar portion
+    of the forces on the endpoint are negative in order to flip the sign of the
+    forces on the endpoints when converted into vector quantities. The
+    following diagram shows the positive force sense and the distance between
+    the points::
+
+       P           Q
+       o<--- F --->o
+       |           |
+       |<--l(t)--->|
+
+    Examples
+    ========
+
+    To construct a linear spring, an expression (or symbol) must be supplied to
+    represent the stiffness (spring constant) of the spring, alongside a
+    pathway specifying its line of action. Let's also create a global reference
+    frame and spatially fix one of the points in it while setting the other to
+    be positioned such that it can freely move in the frame's x direction
+    specified by the coordinate ``q``.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import (LinearPathway, LinearSpring,
+    ...     Point, ReferenceFrame)
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> N = ReferenceFrame('N')
+    >>> q = dynamicsymbols('q')
+    >>> stiffness = symbols('k')
+    >>> pA, pB = Point('pA'), Point('pB')
+    >>> pA.set_vel(N, 0)
+    >>> pB.set_pos(pA, q*N.x)
+    >>> pB.pos_from(pA)
+    q(t)*N.x
+    >>> linear_pathway = LinearPathway(pA, pB)
+    >>> spring = LinearSpring(stiffness, linear_pathway)
+    >>> spring
+    LinearSpring(k, LinearPathway(pA, pB))
+
+    This spring will produce a force that is proportional to both its stiffness
+    and the pathway's length. Note that this force is negative as SymPy's sign
+    convention for actuators is that negative forces are contractile.
+
+    >>> spring.force
+    -k*sqrt(q(t)**2)
+
+    To create a linear spring with a non-zero equilibrium length, an expression
+    (or symbol) can be passed to the ``equilibrium_length`` parameter on
+    construction on a ``LinearSpring`` instance. Let's create a symbol ``l``
+    to denote a non-zero equilibrium length and create another linear spring.
+
+    >>> l = symbols('l')
+    >>> spring = LinearSpring(stiffness, linear_pathway, equilibrium_length=l)
+    >>> spring
+    LinearSpring(k, LinearPathway(pA, pB), equilibrium_length=l)
+
+    The spring force of this new spring is again proportional to both its
+    stiffness and the pathway's length. However, the spring will not produce
+    any force when ``q(t)`` equals ``l``. Note that the force will become
+    expansile when ``q(t)`` is less than ``l``, as expected.
+
+    >>> spring.force
+    -k*(-l + sqrt(q(t)**2))
+
+    Parameters
+    ==========
+
+    stiffness : Expr
+        The spring constant.
+    pathway : PathwayBase
+        The pathway that the actuator follows. This must be an instance of a
+        concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+    equilibrium_length : Expr, optional
+        The length at which the spring is in equilibrium, i.e. it produces no
+        force. The default value is 0, i.e. the spring force is a linear
+        function of the pathway's length with no constant offset.
+
+    See Also
+    ========
+
+    ForceActuator: force-producing actuator (superclass of ``LinearSpring``).
+    LinearPathway: straight-line pathway between a pair of points.
+
+    """
+
+    def __init__(self, stiffness, pathway, equilibrium_length=S.Zero):
+        """Initializer for ``LinearSpring``.
+
+        Parameters
+        ==========
+
+        stiffness : Expr
+            The spring constant.
+        pathway : PathwayBase
+            The pathway that the actuator follows. This must be an instance of
+            a concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+        equilibrium_length : Expr, optional
+            The length at which the spring is in equilibrium, i.e. it produces
+            no force. The default value is 0, i.e. the spring force is a linear
+            function of the pathway's length with no constant offset.
+
+        """
+        self.stiffness = stiffness
+        self.pathway = pathway
+        self.equilibrium_length = equilibrium_length
+
+    @property
+    def force(self):
+        """The spring force produced by the linear spring."""
+        return -self.stiffness*(self.pathway.length - self.equilibrium_length)
+
+    @force.setter
+    def force(self, force):
+        raise AttributeError('Can\'t set computed attribute `force`.')
+
+    @property
+    def stiffness(self):
+        """The spring constant for the linear spring."""
+        return self._stiffness
+
+    @stiffness.setter
+    def stiffness(self, stiffness):
+        if hasattr(self, '_stiffness'):
+            msg = (
+                f'Can\'t set attribute `stiffness` to {repr(stiffness)} as it '
+                f'is immutable.'
+            )
+            raise AttributeError(msg)
+        self._stiffness = sympify(stiffness, strict=True)
+
+    @property
+    def equilibrium_length(self):
+        """The length of the spring at which it produces no force."""
+        return self._equilibrium_length
+
+    @equilibrium_length.setter
+    def equilibrium_length(self, equilibrium_length):
+        if hasattr(self, '_equilibrium_length'):
+            msg = (
+                f'Can\'t set attribute `equilibrium_length` to '
+                f'{repr(equilibrium_length)} as it is immutable.'
+            )
+            raise AttributeError(msg)
+        self._equilibrium_length = sympify(equilibrium_length, strict=True)
+
+    def __repr__(self):
+        """Representation of a ``LinearSpring``."""
+        string = f'{self.__class__.__name__}({self.stiffness}, {self.pathway}'
+        if self.equilibrium_length == S.Zero:
+            string += ')'
+        else:
+            string += f', equilibrium_length={self.equilibrium_length})'
+        return string
+
+
+class LinearDamper(ForceActuator):
+    """A damper whose force is a linear function of its extension velocity.
+
+    Explanation
+    ===========
+
+    Note that the "linear" in the name ``LinearDamper`` refers to the fact that
+    the damping force is a linear function of the damper's rate of change in
+    its length. I.e. for a linear damper with damping ``c`` and extension
+    velocity ``v``, the damping force will be ``-c*v``, which is a linear
+    function in ``v``. To create a damper that follows a linear, or straight,
+    pathway between its two ends, a ``LinearPathway`` instance needs to be
+    passed to the ``pathway`` parameter.
+
+    A ``LinearDamper`` is a subclass of ``ForceActuator`` and so follows the
+    same sign conventions for length, extension velocity, and the direction of
+    the forces it applies to its points of attachment on bodies. The sign
+    convention for the direction of forces is such that, for the case where a
+    linear damper is instantiated with a ``LinearPathway`` instance as its
+    pathway, they act to push the two ends of the damper away from one another.
+    Because dampers produce a force that opposes the direction of change in
+    length, when extension velocity is positive the scalar portions of the
+    forces applied at the two endpoints are negative in order to flip the sign
+    of the forces on the endpoints wen converted into vector quantities. When
+    extension velocity is negative (i.e. when the damper is shortening), the
+    scalar portions of the fofces applied are also negative so that the signs
+    cancel producing forces on the endpoints that are in the same direction as
+    the positive sign convention for the forces at the endpoints of the pathway
+    (i.e. they act to push the endpoints away from one another). The following
+    diagram shows the positive force sense and the distance between the
+    points::
+
+       P           Q
+       o<--- F --->o
+       |           |
+       |<--l(t)--->|
+
+    Examples
+    ========
+
+    To construct a linear damper, an expression (or symbol) must be supplied to
+    represent the damping coefficient of the damper (we'll use the symbol
+    ``c``), alongside a pathway specifying its line of action. Let's also
+    create a global reference frame and spatially fix one of the points in it
+    while setting the other to be positioned such that it can freely move in
+    the frame's x direction specified by the coordinate ``q``. The velocity
+    that the two points move away from one another can be specified by the
+    coordinate ``u`` where ``u`` is the first time derivative of ``q``
+    (i.e., ``u = Derivative(q(t), t)``).
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import (LinearDamper, LinearPathway,
+    ...     Point, ReferenceFrame)
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> N = ReferenceFrame('N')
+    >>> q = dynamicsymbols('q')
+    >>> damping = symbols('c')
+    >>> pA, pB = Point('pA'), Point('pB')
+    >>> pA.set_vel(N, 0)
+    >>> pB.set_pos(pA, q*N.x)
+    >>> pB.pos_from(pA)
+    q(t)*N.x
+    >>> pB.vel(N)
+    Derivative(q(t), t)*N.x
+    >>> linear_pathway = LinearPathway(pA, pB)
+    >>> damper = LinearDamper(damping, linear_pathway)
+    >>> damper
+    LinearDamper(c, LinearPathway(pA, pB))
+
+    This damper will produce a force that is proportional to both its damping
+    coefficient and the pathway's extension length. Note that this force is
+    negative as SymPy's sign convention for actuators is that negative forces
+    are contractile and the damping force of the damper will oppose the
+    direction of length change.
+
+    >>> damper.force
+    -c*sqrt(q(t)**2)*Derivative(q(t), t)/q(t)
+
+    Parameters
+    ==========
+
+    damping : Expr
+        The damping constant.
+    pathway : PathwayBase
+        The pathway that the actuator follows. This must be an instance of a
+        concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+
+    See Also
+    ========
+
+    ForceActuator: force-producing actuator (superclass of ``LinearDamper``).
+    LinearPathway: straight-line pathway between a pair of points.
+
+    """
+
+    def __init__(self, damping, pathway):
+        """Initializer for ``LinearDamper``.
+
+        Parameters
+        ==========
+
+        damping : Expr
+            The damping constant.
+        pathway : PathwayBase
+            The pathway that the actuator follows. This must be an instance of
+            a concrete subclass of ``PathwayBase``, e.g. ``LinearPathway``.
+
+        """
+        self.damping = damping
+        self.pathway = pathway
+
+    @property
+    def force(self):
+        """The damping force produced by the linear damper."""
+        return -self.damping*self.pathway.extension_velocity
+
+    @force.setter
+    def force(self, force):
+        raise AttributeError('Can\'t set computed attribute `force`.')
+
+    @property
+    def damping(self):
+        """The damping constant for the linear damper."""
+        return self._damping
+
+    @damping.setter
+    def damping(self, damping):
+        if hasattr(self, '_damping'):
+            msg = (
+                f'Can\'t set attribute `damping` to {repr(damping)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        self._damping = sympify(damping, strict=True)
+
+    def __repr__(self):
+        """Representation of a ``LinearDamper``."""
+        return f'{self.__class__.__name__}({self.damping}, {self.pathway})'
+
+
+class TorqueActuator(ActuatorBase):
+    """Torque-producing actuator.
+
+    Explanation
+    ===========
+
+    A ``TorqueActuator`` is an actuator that produces a pair of equal and
+    opposite torques on a pair of bodies.
+
+    Examples
+    ========
+
+    To construct a torque actuator, an expression (or symbol) must be supplied
+    to represent the torque it can produce, alongside a vector specifying the
+    axis about which the torque will act, and a pair of frames on which the
+    torque will act.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import (ReferenceFrame, RigidBody,
+    ...     TorqueActuator)
+    >>> N = ReferenceFrame('N')
+    >>> A = ReferenceFrame('A')
+    >>> torque = symbols('T')
+    >>> axis = N.z
+    >>> parent = RigidBody('parent', frame=N)
+    >>> child = RigidBody('child', frame=A)
+    >>> bodies = (child, parent)
+    >>> actuator = TorqueActuator(torque, axis, *bodies)
+    >>> actuator
+    TorqueActuator(T, axis=N.z, target_frame=A, reaction_frame=N)
+
+    Note that because torques actually act on frames, not bodies,
+    ``TorqueActuator`` will extract the frame associated with a ``RigidBody``
+    when one is passed instead of a ``ReferenceFrame``.
+
+    Parameters
+    ==========
+
+    torque : Expr
+        The scalar expression defining the torque that the actuator produces.
+    axis : Vector
+        The axis about which the actuator applies torques.
+    target_frame : ReferenceFrame | RigidBody
+        The primary frame on which the actuator will apply the torque.
+    reaction_frame : ReferenceFrame | RigidBody | None
+        The secondary frame on which the actuator will apply the torque. Note
+        that the (equal and opposite) reaction torque is applied to this frame.
+
+    """
+
+    def __init__(self, torque, axis, target_frame, reaction_frame=None):
+        """Initializer for ``TorqueActuator``.
+
+        Parameters
+        ==========
+
+        torque : Expr
+            The scalar expression defining the torque that the actuator
+            produces.
+        axis : Vector
+            The axis about which the actuator applies torques.
+        target_frame : ReferenceFrame | RigidBody
+            The primary frame on which the actuator will apply the torque.
+        reaction_frame : ReferenceFrame | RigidBody | None
+           The secondary frame on which the actuator will apply the torque.
+           Note that the (equal and opposite) reaction torque is applied to
+           this frame.
+
+        """
+        self.torque = torque
+        self.axis = axis
+        self.target_frame = target_frame
+        self.reaction_frame = reaction_frame
+
+    @classmethod
+    def at_pin_joint(cls, torque, pin_joint):
+        """Alternate constructor to instantiate from a ``PinJoint`` instance.
+
+        Examples
+        ========
+
+        To create a pin joint the ``PinJoint`` class requires a name, parent
+        body, and child body to be passed to its constructor. It is also
+        possible to control the joint axis using the ``joint_axis`` keyword
+        argument. In this example let's use the parent body's reference frame's
+        z-axis as the joint axis.
+
+        >>> from sympy.physics.mechanics import (PinJoint, ReferenceFrame,
+        ...     RigidBody, TorqueActuator)
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> parent = RigidBody('parent', frame=N)
+        >>> child = RigidBody('child', frame=A)
+        >>> pin_joint = PinJoint(
+        ...     'pin',
+        ...     parent,
+        ...     child,
+        ...     joint_axis=N.z,
+        ... )
+
+        Let's also create a symbol ``T`` that will represent the torque applied
+        by the torque actuator.
+
+        >>> from sympy import symbols
+        >>> torque = symbols('T')
+
+        To create the torque actuator from the ``torque`` and ``pin_joint``
+        variables previously instantiated, these can be passed to the alternate
+        constructor class method ``at_pin_joint`` of the ``TorqueActuator``
+        class. It should be noted that a positive torque will cause a positive
+        displacement of the joint coordinate or that the torque is applied on
+        the child body with a reaction torque on the parent.
+
+        >>> actuator = TorqueActuator.at_pin_joint(torque, pin_joint)
+        >>> actuator
+        TorqueActuator(T, axis=N.z, target_frame=A, reaction_frame=N)
+
+        Parameters
+        ==========
+
+        torque : Expr
+            The scalar expression defining the torque that the actuator
+            produces.
+        pin_joint : PinJoint
+            The pin joint, and by association the parent and child bodies, on
+            which the torque actuator will act. The pair of bodies acted upon
+            by the torque actuator are the parent and child bodies of the pin
+            joint, with the child acting as the reaction body. The pin joint's
+            axis is used as the axis about which the torque actuator will apply
+            its torque.
+
+        """
+        if not isinstance(pin_joint, PinJoint):
+            msg = (
+                f'Value {repr(pin_joint)} passed to `pin_joint` was of type '
+                f'{type(pin_joint)}, must be {PinJoint}.'
+            )
+            raise TypeError(msg)
+        return cls(
+            torque,
+            pin_joint.joint_axis,
+            pin_joint.child_interframe,
+            pin_joint.parent_interframe,
+        )
+
+    @property
+    def torque(self):
+        """The magnitude of the torque produced by the actuator."""
+        return self._torque
+
+    @torque.setter
+    def torque(self, torque):
+        if hasattr(self, '_torque'):
+            msg = (
+                f'Can\'t set attribute `torque` to {repr(torque)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        self._torque = sympify(torque, strict=True)
+
+    @property
+    def axis(self):
+        """The axis about which the torque acts."""
+        return self._axis
+
+    @axis.setter
+    def axis(self, axis):
+        if hasattr(self, '_axis'):
+            msg = (
+                f'Can\'t set attribute `axis` to {repr(axis)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        if not isinstance(axis, Vector):
+            msg = (
+                f'Value {repr(axis)} passed to `axis` was of type '
+                f'{type(axis)}, must be {Vector}.'
+            )
+            raise TypeError(msg)
+        self._axis = axis
+
+    @property
+    def target_frame(self):
+        """The primary reference frames on which the torque will act."""
+        return self._target_frame
+
+    @target_frame.setter
+    def target_frame(self, target_frame):
+        if hasattr(self, '_target_frame'):
+            msg = (
+                f'Can\'t set attribute `target_frame` to {repr(target_frame)} '
+                f'as it is immutable.'
+            )
+            raise AttributeError(msg)
+        if isinstance(target_frame, RigidBody):
+            target_frame = target_frame.frame
+        elif not isinstance(target_frame, ReferenceFrame):
+            msg = (
+                f'Value {repr(target_frame)} passed to `target_frame` was of '
+                f'type {type(target_frame)}, must be {ReferenceFrame}.'
+            )
+            raise TypeError(msg)
+        self._target_frame = target_frame
+
+    @property
+    def reaction_frame(self):
+        """The primary reference frames on which the torque will act."""
+        return self._reaction_frame
+
+    @reaction_frame.setter
+    def reaction_frame(self, reaction_frame):
+        if hasattr(self, '_reaction_frame'):
+            msg = (
+                f'Can\'t set attribute `reaction_frame` to '
+                f'{repr(reaction_frame)} as it is immutable.'
+            )
+            raise AttributeError(msg)
+        if isinstance(reaction_frame, RigidBody):
+            reaction_frame = reaction_frame.frame
+        elif (
+            not isinstance(reaction_frame, ReferenceFrame)
+            and reaction_frame is not None
+        ):
+            msg = (
+                f'Value {repr(reaction_frame)} passed to `reaction_frame` was '
+                f'of type {type(reaction_frame)}, must be {ReferenceFrame}.'
+            )
+            raise TypeError(msg)
+        self._reaction_frame = reaction_frame
+
+    def to_loads(self):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        Examples
+        ========
+
+        The below example shows how to generate the loads produced by a torque
+        actuator that acts on a pair of bodies attached by a pin joint.
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import (PinJoint, ReferenceFrame,
+        ...     RigidBody, TorqueActuator)
+        >>> torque = symbols('T')
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> parent = RigidBody('parent', frame=N)
+        >>> child = RigidBody('child', frame=A)
+        >>> pin_joint = PinJoint(
+        ...     'pin',
+        ...     parent,
+        ...     child,
+        ...     joint_axis=N.z,
+        ... )
+        >>> actuator = TorqueActuator.at_pin_joint(torque, pin_joint)
+
+        The forces produces by the damper can be generated by calling the
+        ``to_loads`` method.
+
+        >>> actuator.to_loads()
+        [(A, T*N.z), (N, - T*N.z)]
+
+        Alternatively, if a torque actuator is created without a reaction frame
+        then the loads returned by the ``to_loads`` method will contain just
+        the single load acting on the target frame.
+
+        >>> actuator = TorqueActuator(torque, N.z, N)
+        >>> actuator.to_loads()
+        [(N, T*N.z)]
+
+        """
+        loads = [
+            Torque(self.target_frame, self.torque*self.axis),
+        ]
+        if self.reaction_frame is not None:
+            loads.append(Torque(self.reaction_frame, -self.torque*self.axis))
+        return loads
+
+    def __repr__(self):
+        """Representation of a ``TorqueActuator``."""
+        string = (
+            f'{self.__class__.__name__}({self.torque}, axis={self.axis}, '
+            f'target_frame={self.target_frame}'
+        )
+        if self.reaction_frame is not None:
+            string += f', reaction_frame={self.reaction_frame})'
+        else:
+            string += ')'
+        return string
+
+
+class DuffingSpring(ForceActuator):
+    """A nonlinear spring based on the Duffing equation.
+
+    Explanation
+    ===========
+
+    Here, ``DuffingSpring`` represents the force exerted by a nonlinear spring based on the Duffing equation:
+    F = -beta*x-alpha*x**3, where x is the displacement from the equilibrium position, beta is the linear spring constant,
+    and alpha is the coefficient for the nonlinear cubic term.
+
+    Parameters
+    ==========
+
+    linear_stiffness : Expr
+        The linear stiffness coefficient (beta).
+    nonlinear_stiffness : Expr
+        The nonlinear stiffness coefficient (alpha).
+    pathway : PathwayBase
+        The pathway that the actuator follows.
+    equilibrium_length : Expr, optional
+        The length at which the spring is in equilibrium (x).
+    """
+
+    def __init__(self, linear_stiffness, nonlinear_stiffness, pathway, equilibrium_length=S.Zero):
+        self.linear_stiffness = sympify(linear_stiffness, strict=True)
+        self.nonlinear_stiffness = sympify(nonlinear_stiffness, strict=True)
+        self.equilibrium_length = sympify(equilibrium_length, strict=True)
+
+        if not isinstance(pathway, PathwayBase):
+            raise TypeError("pathway must be an instance of PathwayBase.")
+        self._pathway = pathway
+
+    @property
+    def linear_stiffness(self):
+        return self._linear_stiffness
+
+    @linear_stiffness.setter
+    def linear_stiffness(self, linear_stiffness):
+        if hasattr(self, '_linear_stiffness'):
+            msg = (
+                f'Can\'t set attribute `linear_stiffness` to '
+                f'{repr(linear_stiffness)} as it is immutable.'
+            )
+            raise AttributeError(msg)
+        self._linear_stiffness = sympify(linear_stiffness, strict=True)
+
+    @property
+    def nonlinear_stiffness(self):
+        return self._nonlinear_stiffness
+
+    @nonlinear_stiffness.setter
+    def nonlinear_stiffness(self, nonlinear_stiffness):
+        if hasattr(self, '_nonlinear_stiffness'):
+            msg = (
+                f'Can\'t set attribute `nonlinear_stiffness` to '
+                f'{repr(nonlinear_stiffness)} as it is immutable.'
+            )
+            raise AttributeError(msg)
+        self._nonlinear_stiffness = sympify(nonlinear_stiffness, strict=True)
+
+    @property
+    def pathway(self):
+        return self._pathway
+
+    @pathway.setter
+    def pathway(self, pathway):
+        if hasattr(self, '_pathway'):
+            msg = (
+                f'Can\'t set attribute `pathway` to {repr(pathway)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        if not isinstance(pathway, PathwayBase):
+            msg = (
+                f'Value {repr(pathway)} passed to `pathway` was of type '
+                f'{type(pathway)}, must be {PathwayBase}.'
+            )
+            raise TypeError(msg)
+        self._pathway = pathway
+
+    @property
+    def equilibrium_length(self):
+        return self._equilibrium_length
+
+    @equilibrium_length.setter
+    def equilibrium_length(self, equilibrium_length):
+        if hasattr(self, '_equilibrium_length'):
+            msg = (
+                f'Can\'t set attribute `equilibrium_length` to '
+                f'{repr(equilibrium_length)} as it is immutable.'
+            )
+            raise AttributeError(msg)
+        self._equilibrium_length = sympify(equilibrium_length, strict=True)
+
+    @property
+    def force(self):
+        """The force produced by the Duffing spring."""
+        displacement = self.pathway.length - self.equilibrium_length
+        return -self.linear_stiffness * displacement - self.nonlinear_stiffness * displacement**3
+
+    @force.setter
+    def force(self, force):
+        if hasattr(self, '_force'):
+            msg = (
+                f'Can\'t set attribute `force` to {repr(force)} as it is '
+                f'immutable.'
+            )
+            raise AttributeError(msg)
+        self._force = sympify(force, strict=True)
+
+    def __repr__(self):
+        return (f"{self.__class__.__name__}("
+                f"{self.linear_stiffness}, {self.nonlinear_stiffness}, {self.pathway}, "
+                f"equilibrium_length={self.equilibrium_length})")
+
+class CoulombKineticFriction(ForceActuator):
+    r"""Coulomb kinetic friction with Stribeck and viscous effects.
+
+    Explanation
+    ===========
+
+    This represents a Coulomb kinetic friction with the Stribeck and viscous effect,
+    described by the function:
+
+    .. math::
+        F = (\mu_k f_n + (\mu_s - \mu_k) f_n e^{-(\frac{v}{v_s})^2}) \text{sign}(v) + \sigma  v
+
+    where :math:`\mu_k` is the coefficient of kinetic friction, :math:`\mu_s` is the
+    coefficient of static friction, :math:`f_n` is the normal force, :math:`v` is the
+    relative velocity, :math:`v_s` is the Stribeck friction coefficient, and
+    :math:`\sigma` is the viscous friction constant.
+
+    The default friction force is :math:`F = \mu_k f_n`.
+    When specified, the actuator includes:
+
+    - Stribeck effect: :math:`(\mu_s - \mu_k) f_n e^{-(\frac{v}{v_s})^2}`
+    - Viscous effect: :math:`\sigma v`
+
+    Notes
+    =====
+
+    The actuator makes the following assumptions:
+
+    - The actuator assumes relative motion is non-zero.
+    - The normal force is assumed to be a non-negative scalar.
+    - The resultant friction force is opposite to the velocity direction.
+    - Each point in the pathway is fixed within separate objects that are sliding relative to each other. In other words, these two points are fixed in the mutually sliding objects.
+
+    This actuator has been tested for straightforward motions, like a block sliding
+    on a surface.
+
+    The friction force is defined to always oppose the direction of relative velocity :math:`v`.
+    Specifically:
+
+    - The default Coulomb friction force :math:`\mu_k f_n \text{sign}(v)` is opposite to :math:`v`.
+    - The Stribeck effect :math:`(\mu_s - \mu_k) f_n e^{-(\frac{v}{v_s})^2} \text{sign}(v)` is also opposite to :math:`v`.
+    - The viscous friction term :math:`\sigma v` is opposite to :math:`v`.
+
+    Examples
+    ========
+
+    The below example shows how to generate the loads produced by a Coulomb kinetic
+    friction actuator in a mass-spring system with friction.
+
+    >>> import sympy as sm
+    >>> from sympy.physics.mechanics import (dynamicsymbols, ReferenceFrame, Point,
+    ...     LinearPathway, CoulombKineticFriction, LinearSpring, KanesMethod, Particle)
+
+    >>> x, v = dynamicsymbols('x, v', real=True)
+    >>> m, g, k, mu_k, mu_s, v_s, sigma = sm.symbols('m, g, k, mu_k, mu_s, v_s, sigma')
+
+    >>> N = ReferenceFrame('N')
+    >>> O, P = Point('O'), Point('P')
+    >>> O.set_vel(N, 0)
+    >>> P.set_pos(O, x*N.x)
+
+    >>> pathway = LinearPathway(O, P)
+    >>> friction = CoulombKineticFriction(mu_k, m*g, pathway, v_s=v_s, sigma=sigma, mu_s=mu_k)
+    >>> spring = LinearSpring(k, pathway)
+    >>> block = Particle('block', point=P, mass=m)
+
+    >>> kane = KanesMethod(N, (x,), (v,), kd_eqs=(x.diff() - v,))
+    >>> friction.to_loads()
+        [(O, (g*m*mu_k*sign(sign(x(t))*Derivative(x(t), t)) + sigma*sign(x(t))*Derivative(x(t), t))*x(t)/Abs(x(t))*N.x), (P, (-g*m*mu_k*sign(sign(x(t))*Derivative(x(t), t)) - sigma*sign(x(t))*Derivative(x(t), t))*x(t)/Abs(x(t))*N.x)]
+    >>> loads = friction.to_loads() + spring.to_loads()
+    >>> fr, frstar = kane.kanes_equations([block], loads)
+    >>> eom = fr + frstar
+    >>> eom
+        Matrix([[-k*x(t) - m*Derivative(v(t), t) + (-g*m*mu_k*sign(v(t)*sign(x(t))) - sigma*v(t)*sign(x(t)))*x(t)/Abs(x(t))]])
+
+    Parameters
+    ==========
+
+    f_n : sympifiable
+        The normal force between the surfaces. It should always be a non-negative scalar.
+    mu_k : sympifiable
+        The coefficient of kinetic friction.
+    pathway : PathwayBase
+        The pathway that the actuator follows.
+    v_s : sympifiable, optional
+        The Stribeck friction coefficient.
+    sigma : sympifiable, optional
+        The viscous friction coefficient.
+    mu_s : sympifiable, optional
+        The coefficient of static friction. Defaults to mu_k, meaning the Stribeck effect evaluates to 0 by default.
+
+    References
+    ==========
+
+    .. [Moore2022] https://moorepants.github.io/learn-multibody-dynamics/loads.html#friction.
+    .. [Flores2023] Paulo Flores, Jorge Ambrosio, Hamid M. Lankarani,
+            "Contact-impact events with friction in multibody dynamics: Back to basics",
+            Mechanism and Machine Theory, vol. 184, 2023. https://doi.org/10.1016/j.mechmachtheory.2023.105305.
+    .. [Rogner2017] I. Rogner, "Friction modelling for robotic applications with planar motion",
+            Chalmers University of Technology, Department of Electrical Engineering, 2017.
+
+    """
+
+    def __init__(self, mu_k, f_n, pathway, *, v_s=None, sigma=None, mu_s=None):
+        self._mu_k = sympify(mu_k, strict=True) if mu_k is not None else 1
+        self._mu_s = sympify(mu_s, strict=True) if mu_s is not None else self._mu_k
+        self._f_n = sympify(f_n, strict=True)
+        self._sigma = sympify(sigma, strict=True) if sigma is not None else 0
+        self._v_s = sympify(v_s, strict=True) if v_s is not None or v_s == 0 else 0.01
+        self.pathway = pathway
+
+    @property
+    def mu_k(self):
+        """The coefficient of kinetic friction."""
+        return self._mu_k
+
+    @property
+    def mu_s(self):
+        """The coefficient of static friction."""
+        return self._mu_s
+
+    @property
+    def f_n(self):
+        """The normal force between the surfaces."""
+        return self._f_n
+
+    @property
+    def sigma(self):
+        """The viscous friction coefficient."""
+        return self._sigma
+
+    @property
+    def v_s(self):
+        """The Stribeck friction coefficient."""
+        return self._v_s
+
+    @property
+    def force(self):
+        v = self.pathway.extension_velocity
+        f_c = self.mu_k * self.f_n
+        f_max = self.mu_s * self.f_n
+        stribeck_term = (f_max - f_c) * exp(-(v / self.v_s)**2) if self.v_s is not None else 0
+        viscous_term = self.sigma * v if self.sigma is not None else 0
+        return (f_c + stribeck_term) * -sign(v) - viscous_term
+
+    @force.setter
+    def force(self, force):
+        raise AttributeError('Can\'t set computed attribute `force`.')
+
+    def __repr__(self):
+        return (f'{self.__class__.__name__}({self._mu_k}, {self._mu_s} '
+                f'{self._f_n}, {self.pathway}, {self._v_s}, '
+                f'{self._sigma})')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/body.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/body.py
new file mode 100644
index 0000000000000000000000000000000000000000..efc367158bbf51e7d9929318ac9286ba5c3fb3ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/body.py
@@ -0,0 +1,710 @@
+from sympy import Symbol
+from sympy.physics.vector import Point, Vector, ReferenceFrame, Dyadic
+from sympy.physics.mechanics import RigidBody, Particle, Inertia
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+__all__ = ['Body']
+
+
+# XXX: We use type:ignore because the classes RigidBody and Particle have
+# inconsistent parallel axis methods that take different numbers of arguments.
+class Body(RigidBody, Particle):  # type: ignore
+    """
+    Body is a common representation of either a RigidBody or a Particle SymPy
+    object depending on what is passed in during initialization. If a mass is
+    passed in and central_inertia is left as None, the Particle object is
+    created. Otherwise a RigidBody object will be created.
+
+    .. deprecated:: 1.13
+        The Body class is deprecated. Its functionality is captured by
+        :class:`~.RigidBody` and :class:`~.Particle`.
+
+    Explanation
+    ===========
+
+    The attributes that Body possesses will be the same as a Particle instance
+    or a Rigid Body instance depending on which was created. Additional
+    attributes are listed below.
+
+    Attributes
+    ==========
+
+    name : string
+        The body's name
+    masscenter : Point
+        The point which represents the center of mass of the rigid body
+    frame : ReferenceFrame
+        The reference frame which the body is fixed in
+    mass : Sympifyable
+        The body's mass
+    inertia : (Dyadic, Point)
+        The body's inertia around its center of mass. This attribute is specific
+        to the rigid body form of Body and is left undefined for the Particle
+        form
+    loads : iterable
+        This list contains information on the different loads acting on the
+        Body. Forces are listed as a (point, vector) tuple and torques are
+        listed as (reference frame, vector) tuples.
+
+    Parameters
+    ==========
+
+    name : String
+        Defines the name of the body. It is used as the base for defining
+        body specific properties.
+    masscenter : Point, optional
+        A point that represents the center of mass of the body or particle.
+        If no point is given, a point is generated.
+    mass : Sympifyable, optional
+        A Sympifyable object which represents the mass of the body. If no
+        mass is passed, one is generated.
+    frame : ReferenceFrame, optional
+        The ReferenceFrame that represents the reference frame of the body.
+        If no frame is given, a frame is generated.
+    central_inertia : Dyadic, optional
+        Central inertia dyadic of the body. If none is passed while creating
+        RigidBody, a default inertia is generated.
+
+    Examples
+    ========
+
+    As Body has been deprecated, the following examples are for illustrative
+    purposes only. The functionality of Body is fully captured by
+    :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+    warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+
+    Default behaviour. This results in the creation of a RigidBody object for
+    which the mass, mass center, frame and inertia attributes are given default
+    values. ::
+
+        >>> from sympy.physics.mechanics import Body
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     body = Body('name_of_body')
+
+    This next example demonstrates the code required to specify all of the
+    values of the Body object. Note this will also create a RigidBody version of
+    the Body object. ::
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.mechanics import ReferenceFrame, Point, inertia
+        >>> from sympy.physics.mechanics import Body
+        >>> mass = Symbol('mass')
+        >>> masscenter = Point('masscenter')
+        >>> frame = ReferenceFrame('frame')
+        >>> ixx = Symbol('ixx')
+        >>> body_inertia = inertia(frame, ixx, 0, 0)
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     body = Body('name_of_body', masscenter, mass, frame, body_inertia)
+
+    The minimal code required to create a Particle version of the Body object
+    involves simply passing in a name and a mass. ::
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.mechanics import Body
+        >>> mass = Symbol('mass')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     body = Body('name_of_body', mass=mass)
+
+    The Particle version of the Body object can also receive a masscenter point
+    and a reference frame, just not an inertia.
+    """
+
+    def __init__(self, name, masscenter=None, mass=None, frame=None,
+                 central_inertia=None):
+        sympy_deprecation_warning(
+            """
+            Support for the Body class has been removed, as its functionality is
+            fully captured by RigidBody and Particle.
+            """,
+            deprecated_since_version="1.13",
+            active_deprecations_target="deprecated-mechanics-body-class"
+        )
+
+        self._loads = []
+
+        if frame is None:
+            frame = ReferenceFrame(name + '_frame')
+
+        if masscenter is None:
+            masscenter = Point(name + '_masscenter')
+
+        if central_inertia is None and mass is None:
+            ixx = Symbol(name + '_ixx')
+            iyy = Symbol(name + '_iyy')
+            izz = Symbol(name + '_izz')
+            izx = Symbol(name + '_izx')
+            ixy = Symbol(name + '_ixy')
+            iyz = Symbol(name + '_iyz')
+            _inertia = Inertia.from_inertia_scalars(masscenter, frame, ixx, iyy,
+                                                    izz, ixy, iyz, izx)
+        else:
+            _inertia = (central_inertia, masscenter)
+
+        if mass is None:
+            _mass = Symbol(name + '_mass')
+        else:
+            _mass = mass
+
+        masscenter.set_vel(frame, 0)
+
+        # If user passes masscenter and mass then a particle is created
+        # otherwise a rigidbody. As a result a body may or may not have inertia.
+        # Note: BodyBase.__init__ is used to prevent problems with super() calls in
+        # Particle and RigidBody arising due to multiple inheritance.
+        if central_inertia is None and mass is not None:
+            BodyBase.__init__(self, name, masscenter, _mass)
+            self.frame = frame
+            self._central_inertia = Dyadic(0)
+        else:
+            BodyBase.__init__(self, name, masscenter, _mass)
+            self.frame = frame
+            self.inertia = _inertia
+
+    def __repr__(self):
+        if self.is_rigidbody:
+            return RigidBody.__repr__(self)
+        return Particle.__repr__(self)
+
+    @property
+    def loads(self):
+        return self._loads
+
+    @property
+    def x(self):
+        """The basis Vector for the Body, in the x direction."""
+        return self.frame.x
+
+    @property
+    def y(self):
+        """The basis Vector for the Body, in the y direction."""
+        return self.frame.y
+
+    @property
+    def z(self):
+        """The basis Vector for the Body, in the z direction."""
+        return self.frame.z
+
+    @property
+    def inertia(self):
+        """The body's inertia about a point; stored as (Dyadic, Point)."""
+        if self.is_rigidbody:
+            return RigidBody.inertia.fget(self)
+        return (self.central_inertia, self.masscenter)
+
+    @inertia.setter
+    def inertia(self, I):
+        RigidBody.inertia.fset(self, I)
+
+    @property
+    def is_rigidbody(self):
+        if hasattr(self, '_inertia'):
+            return True
+        return False
+
+    def kinetic_energy(self, frame):
+        """Kinetic energy of the body.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame or Body
+            The Body's angular velocity and the velocity of it's mass
+            center are typically defined with respect to an inertial frame but
+            any relevant frame in which the velocities are known can be supplied.
+
+        Examples
+        ========
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body, ReferenceFrame, Point
+        >>> from sympy import symbols
+        >>> m, v, r, omega = symbols('m v r omega')
+        >>> N = ReferenceFrame('N')
+        >>> O = Point('O')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     P = Body('P', masscenter=O, mass=m)
+        >>> P.masscenter.set_vel(N, v * N.y)
+        >>> P.kinetic_energy(N)
+        m*v**2/2
+
+        >>> N = ReferenceFrame('N')
+        >>> b = ReferenceFrame('b')
+        >>> b.set_ang_vel(N, omega * b.x)
+        >>> P = Point('P')
+        >>> P.set_vel(N, v * N.x)
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B = Body('B', masscenter=P, frame=b)
+        >>> B.kinetic_energy(N)
+        B_ixx*omega**2/2 + B_mass*v**2/2
+
+        See Also
+        ========
+
+        sympy.physics.mechanics : Particle, RigidBody
+
+        """
+        if isinstance(frame, Body):
+            frame = Body.frame
+        if self.is_rigidbody:
+            return RigidBody(self.name, self.masscenter, self.frame, self.mass,
+                            (self.central_inertia, self.masscenter)).kinetic_energy(frame)
+        return Particle(self.name, self.masscenter, self.mass).kinetic_energy(frame)
+
+    def apply_force(self, force, point=None, reaction_body=None, reaction_point=None):
+        """Add force to the body(s).
+
+        Explanation
+        ===========
+
+        Applies the force on self or equal and opposite forces on
+        self and other body if both are given on the desired point on the bodies.
+        The force applied on other body is taken opposite of self, i.e, -force.
+
+        Parameters
+        ==========
+
+        force: Vector
+            The force to be applied.
+        point: Point, optional
+            The point on self on which force is applied.
+            By default self's masscenter.
+        reaction_body: Body, optional
+            Second body on which equal and opposite force
+            is to be applied.
+        reaction_point : Point, optional
+            The point on other body on which equal and opposite
+            force is applied. By default masscenter of other body.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import Body, Point, dynamicsymbols
+        >>> m, g = symbols('m g')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B = Body('B')
+        >>> force1 = m*g*B.z
+        >>> B.apply_force(force1) #Applying force on B's masscenter
+        >>> B.loads
+        [(B_masscenter, g*m*B_frame.z)]
+
+        We can also remove some part of force from any point on the body by
+        adding the opposite force to the body on that point.
+
+        >>> f1, f2 = dynamicsymbols('f1 f2')
+        >>> P = Point('P') #Considering point P on body B
+        >>> B.apply_force(f1*B.x + f2*B.y, P)
+        >>> B.loads
+        [(B_masscenter, g*m*B_frame.z), (P, f1(t)*B_frame.x + f2(t)*B_frame.y)]
+
+        Let's remove f1 from point P on body B.
+
+        >>> B.apply_force(-f1*B.x, P)
+        >>> B.loads
+        [(B_masscenter, g*m*B_frame.z), (P, f2(t)*B_frame.y)]
+
+        To further demonstrate the use of ``apply_force`` attribute,
+        consider two bodies connected through a spring.
+
+        >>> from sympy.physics.mechanics import Body, dynamicsymbols
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     N = Body('N') #Newtonion Frame
+        >>> x = dynamicsymbols('x')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B1 = Body('B1')
+        ...     B2 = Body('B2')
+        >>> spring_force = x*N.x
+
+        Now let's apply equal and opposite spring force to the bodies.
+
+        >>> P1 = Point('P1')
+        >>> P2 = Point('P2')
+        >>> B1.apply_force(spring_force, point=P1, reaction_body=B2, reaction_point=P2)
+
+        We can check the loads(forces) applied to bodies now.
+
+        >>> B1.loads
+        [(P1, x(t)*N_frame.x)]
+        >>> B2.loads
+        [(P2, - x(t)*N_frame.x)]
+
+        Notes
+        =====
+
+        If a new force is applied to a body on a point which already has some
+        force applied on it, then the new force is added to the already applied
+        force on that point.
+
+        """
+
+        if not isinstance(point, Point):
+            if point is None:
+                point = self.masscenter  # masscenter
+            else:
+                raise TypeError("Force must be applied to a point on the body.")
+        if not isinstance(force, Vector):
+            raise TypeError("Force must be a vector.")
+
+        if reaction_body is not None:
+            reaction_body.apply_force(-force, point=reaction_point)
+
+        for load in self._loads:
+            if point in load:
+                force += load[1]
+                self._loads.remove(load)
+                break
+
+        self._loads.append((point, force))
+
+    def apply_torque(self, torque, reaction_body=None):
+        """Add torque to the body(s).
+
+        Explanation
+        ===========
+
+        Applies the torque on self or equal and opposite torques on
+        self and other body if both are given.
+        The torque applied on other body is taken opposite of self,
+        i.e, -torque.
+
+        Parameters
+        ==========
+
+        torque: Vector
+            The torque to be applied.
+        reaction_body: Body, optional
+            Second body on which equal and opposite torque
+            is to be applied.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import Body, dynamicsymbols
+        >>> t = symbols('t')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B = Body('B')
+        >>> torque1 = t*B.z
+        >>> B.apply_torque(torque1)
+        >>> B.loads
+        [(B_frame, t*B_frame.z)]
+
+        We can also remove some part of torque from the body by
+        adding the opposite torque to the body.
+
+        >>> t1, t2 = dynamicsymbols('t1 t2')
+        >>> B.apply_torque(t1*B.x + t2*B.y)
+        >>> B.loads
+        [(B_frame, t1(t)*B_frame.x + t2(t)*B_frame.y + t*B_frame.z)]
+
+        Let's remove t1 from Body B.
+
+        >>> B.apply_torque(-t1*B.x)
+        >>> B.loads
+        [(B_frame, t2(t)*B_frame.y + t*B_frame.z)]
+
+        To further demonstrate the use, let us consider two bodies such that
+        a torque `T` is acting on one body, and `-T` on the other.
+
+        >>> from sympy.physics.mechanics import Body, dynamicsymbols
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     N = Body('N') #Newtonion frame
+        ...     B1 = Body('B1')
+        ...     B2 = Body('B2')
+        >>> v = dynamicsymbols('v')
+        >>> T = v*N.y #Torque
+
+        Now let's apply equal and opposite torque to the bodies.
+
+        >>> B1.apply_torque(T, B2)
+
+        We can check the loads (torques) applied to bodies now.
+
+        >>> B1.loads
+        [(B1_frame, v(t)*N_frame.y)]
+        >>> B2.loads
+        [(B2_frame, - v(t)*N_frame.y)]
+
+        Notes
+        =====
+
+        If a new torque is applied on body which already has some torque applied on it,
+        then the new torque is added to the previous torque about the body's frame.
+
+        """
+
+        if not isinstance(torque, Vector):
+            raise TypeError("A Vector must be supplied to add torque.")
+
+        if reaction_body is not None:
+            reaction_body.apply_torque(-torque)
+
+        for load in self._loads:
+            if self.frame in load:
+                torque += load[1]
+                self._loads.remove(load)
+                break
+        self._loads.append((self.frame, torque))
+
+    def clear_loads(self):
+        """
+        Clears the Body's loads list.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B = Body('B')
+        >>> force = B.x + B.y
+        >>> B.apply_force(force)
+        >>> B.loads
+        [(B_masscenter, B_frame.x + B_frame.y)]
+        >>> B.clear_loads()
+        >>> B.loads
+        []
+
+        """
+
+        self._loads = []
+
+    def remove_load(self, about=None):
+        """
+        Remove load about a point or frame.
+
+        Parameters
+        ==========
+
+        about : Point or ReferenceFrame, optional
+            The point about which force is applied,
+            and is to be removed.
+            If about is None, then the torque about
+            self's frame is removed.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body, Point
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B = Body('B')
+        >>> P = Point('P')
+        >>> f1 = B.x
+        >>> f2 = B.y
+        >>> B.apply_force(f1)
+        >>> B.apply_force(f2, P)
+        >>> B.loads
+        [(B_masscenter, B_frame.x), (P, B_frame.y)]
+
+        >>> B.remove_load(P)
+        >>> B.loads
+        [(B_masscenter, B_frame.x)]
+
+        """
+
+        if about is not None:
+            if not isinstance(about, Point):
+                raise TypeError('Load is applied about Point or ReferenceFrame.')
+        else:
+            about = self.frame
+
+        for load in self._loads:
+            if about in load:
+                self._loads.remove(load)
+                break
+
+    def masscenter_vel(self, body):
+        """
+        Returns the velocity of the mass center with respect to the provided
+        rigid body or reference frame.
+
+        Parameters
+        ==========
+
+        body: Body or ReferenceFrame
+            The rigid body or reference frame to calculate the velocity in.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     A = Body('A')
+        ...     B = Body('B')
+        >>> A.masscenter.set_vel(B.frame, 5*B.frame.x)
+        >>> A.masscenter_vel(B)
+        5*B_frame.x
+        >>> A.masscenter_vel(B.frame)
+        5*B_frame.x
+
+        """
+
+        if isinstance(body,  ReferenceFrame):
+            frame=body
+        elif isinstance(body, Body):
+            frame = body.frame
+        return self.masscenter.vel(frame)
+
+    def ang_vel_in(self, body):
+        """
+        Returns this body's angular velocity with respect to the provided
+        rigid body or reference frame.
+
+        Parameters
+        ==========
+
+        body: Body or ReferenceFrame
+            The rigid body or reference frame to calculate the angular velocity in.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body, ReferenceFrame
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     A = Body('A')
+        >>> N = ReferenceFrame('N')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     B = Body('B', frame=N)
+        >>> A.frame.set_ang_vel(N, 5*N.x)
+        >>> A.ang_vel_in(B)
+        5*N.x
+        >>> A.ang_vel_in(N)
+        5*N.x
+
+        """
+
+        if isinstance(body,  ReferenceFrame):
+            frame=body
+        elif isinstance(body, Body):
+            frame = body.frame
+        return self.frame.ang_vel_in(frame)
+
+    def dcm(self, body):
+        """
+        Returns the direction cosine matrix of this body relative to the
+        provided rigid body or reference frame.
+
+        Parameters
+        ==========
+
+        body: Body or ReferenceFrame
+            The rigid body or reference frame to calculate the dcm.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     A = Body('A')
+        ...     B = Body('B')
+        >>> A.frame.orient_axis(B.frame, B.frame.x, 5)
+        >>> A.dcm(B)
+        Matrix([
+        [1,       0,      0],
+        [0,  cos(5), sin(5)],
+        [0, -sin(5), cos(5)]])
+        >>> A.dcm(B.frame)
+        Matrix([
+        [1,       0,      0],
+        [0,  cos(5), sin(5)],
+        [0, -sin(5), cos(5)]])
+
+        """
+
+        if isinstance(body,  ReferenceFrame):
+            frame=body
+        elif isinstance(body, Body):
+            frame = body.frame
+        return self.frame.dcm(frame)
+
+    def parallel_axis(self, point, frame=None):
+        """Returns the inertia dyadic of the body with respect to another
+        point.
+
+        Parameters
+        ==========
+
+        point : sympy.physics.vector.Point
+            The point to express the inertia dyadic about.
+        frame : sympy.physics.vector.ReferenceFrame
+            The reference frame used to construct the dyadic.
+
+        Returns
+        =======
+
+        inertia : sympy.physics.vector.Dyadic
+            The inertia dyadic of the rigid body expressed about the provided
+            point.
+
+        Example
+        =======
+
+        As Body has been deprecated, the following examples are for illustrative
+        purposes only. The functionality of Body is fully captured by
+        :class:`~.RigidBody` and :class:`~.Particle`. To ignore the deprecation
+        warning we can use the ignore_warnings context manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+        >>> from sympy.physics.mechanics import Body
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     A = Body('A')
+        >>> P = A.masscenter.locatenew('point', 3 * A.x + 5 * A.y)
+        >>> A.parallel_axis(P).to_matrix(A.frame)
+        Matrix([
+        [A_ixx + 25*A_mass, A_ixy - 15*A_mass,             A_izx],
+        [A_ixy - 15*A_mass,  A_iyy + 9*A_mass,             A_iyz],
+        [            A_izx,             A_iyz, A_izz + 34*A_mass]])
+
+        """
+        if self.is_rigidbody:
+            return RigidBody.parallel_axis(self, point, frame)
+        return Particle.parallel_axis(self, point, frame)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/body_base.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/body_base.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2546faf685f579d2aea10ed7f139a4beced7dd0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/body_base.py
@@ -0,0 +1,94 @@
+from abc import ABC, abstractmethod
+from sympy import Symbol, sympify
+from sympy.physics.vector import Point
+
+__all__ = ['BodyBase']
+
+
+class BodyBase(ABC):
+    """Abstract class for body type objects."""
+    def __init__(self, name, masscenter=None, mass=None):
+        # Note: If frame=None, no auto-generated frame is created, because a
+        # Particle does not need to have a frame by default.
+        if not isinstance(name, str):
+            raise TypeError('Supply a valid name.')
+        self._name = name
+        if mass is None:
+            mass = Symbol(f'{name}_mass')
+        if masscenter is None:
+            masscenter = Point(f'{name}_masscenter')
+        self.mass = mass
+        self.masscenter = masscenter
+        self.potential_energy = 0
+        self.points = []
+
+    def __str__(self):
+        return self.name
+
+    def __repr__(self):
+        return (f'{self.__class__.__name__}({repr(self.name)}, masscenter='
+                f'{repr(self.masscenter)}, mass={repr(self.mass)})')
+
+    @property
+    def name(self):
+        """The name of the body."""
+        return self._name
+
+    @property
+    def masscenter(self):
+        """The body's center of mass."""
+        return self._masscenter
+
+    @masscenter.setter
+    def masscenter(self, point):
+        if not isinstance(point, Point):
+            raise TypeError("The body's center of mass must be a Point object.")
+        self._masscenter = point
+
+    @property
+    def mass(self):
+        """The body's mass."""
+        return self._mass
+
+    @mass.setter
+    def mass(self, mass):
+        self._mass = sympify(mass)
+
+    @property
+    def potential_energy(self):
+        """The potential energy of the body.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Particle, Point
+        >>> from sympy import symbols
+        >>> m, g, h = symbols('m g h')
+        >>> O = Point('O')
+        >>> P = Particle('P', O, m)
+        >>> P.potential_energy = m * g * h
+        >>> P.potential_energy
+        g*h*m
+
+        """
+        return self._potential_energy
+
+    @potential_energy.setter
+    def potential_energy(self, scalar):
+        self._potential_energy = sympify(scalar)
+
+    @abstractmethod
+    def kinetic_energy(self, frame):
+        pass
+
+    @abstractmethod
+    def linear_momentum(self, frame):
+        pass
+
+    @abstractmethod
+    def angular_momentum(self, point, frame):
+        pass
+
+    @abstractmethod
+    def parallel_axis(self, point, frame):
+        pass
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..42abe2b7fe608b4602cdab518f209b446b2dbe03
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/functions.py
@@ -0,0 +1,735 @@
+from sympy.utilities import dict_merge
+from sympy.utilities.iterables import iterable
+from sympy.physics.vector import (Dyadic, Vector, ReferenceFrame,
+                                  Point, dynamicsymbols)
+from sympy.physics.vector.printing import (vprint, vsprint, vpprint, vlatex,
+                                           init_vprinting)
+from sympy.physics.mechanics.particle import Particle
+from sympy.physics.mechanics.rigidbody import RigidBody
+from sympy.simplify.simplify import simplify
+from sympy import Matrix, Mul, Derivative, sin, cos, tan, S
+from sympy.core.function import AppliedUndef
+from sympy.physics.mechanics.inertia import (inertia as _inertia,
+    inertia_of_point_mass as _inertia_of_point_mass)
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+__all__ = ['linear_momentum',
+           'angular_momentum',
+           'kinetic_energy',
+           'potential_energy',
+           'Lagrangian',
+           'mechanics_printing',
+           'mprint',
+           'msprint',
+           'mpprint',
+           'mlatex',
+           'msubs',
+           'find_dynamicsymbols']
+
+# These are functions that we've moved and renamed during extracting the
+# basic vector calculus code from the mechanics packages.
+
+mprint = vprint
+msprint = vsprint
+mpprint = vpprint
+mlatex = vlatex
+
+
+def mechanics_printing(**kwargs):
+    """
+    Initializes time derivative printing for all SymPy objects in
+    mechanics module.
+    """
+
+    init_vprinting(**kwargs)
+
+mechanics_printing.__doc__ = init_vprinting.__doc__
+
+
+def inertia(frame, ixx, iyy, izz, ixy=0, iyz=0, izx=0):
+    sympy_deprecation_warning(
+        """
+        The inertia function has been moved.
+        Import it from "sympy.physics.mechanics".
+        """,
+        deprecated_since_version="1.13",
+        active_deprecations_target="moved-mechanics-functions"
+    )
+    return _inertia(frame, ixx, iyy, izz, ixy, iyz, izx)
+
+
+def inertia_of_point_mass(mass, pos_vec, frame):
+    sympy_deprecation_warning(
+        """
+        The inertia_of_point_mass function has been moved.
+        Import it from "sympy.physics.mechanics".
+        """,
+        deprecated_since_version="1.13",
+        active_deprecations_target="moved-mechanics-functions"
+    )
+    return _inertia_of_point_mass(mass, pos_vec, frame)
+
+
+def linear_momentum(frame, *body):
+    """Linear momentum of the system.
+
+    Explanation
+    ===========
+
+    This function returns the linear momentum of a system of Particle's and/or
+    RigidBody's. The linear momentum of a system is equal to the vector sum of
+    the linear momentum of its constituents. Consider a system, S, comprised of
+    a rigid body, A, and a particle, P. The linear momentum of the system, L,
+    is equal to the vector sum of the linear momentum of the particle, L1, and
+    the linear momentum of the rigid body, L2, i.e.
+
+    L = L1 + L2
+
+    Parameters
+    ==========
+
+    frame : ReferenceFrame
+        The frame in which linear momentum is desired.
+    body1, body2, body3... : Particle and/or RigidBody
+        The body (or bodies) whose linear momentum is required.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
+    >>> from sympy.physics.mechanics import RigidBody, outer, linear_momentum
+    >>> N = ReferenceFrame('N')
+    >>> P = Point('P')
+    >>> P.set_vel(N, 10 * N.x)
+    >>> Pa = Particle('Pa', P, 1)
+    >>> Ac = Point('Ac')
+    >>> Ac.set_vel(N, 25 * N.y)
+    >>> I = outer(N.x, N.x)
+    >>> A = RigidBody('A', Ac, N, 20, (I, Ac))
+    >>> linear_momentum(N, A, Pa)
+    10*N.x + 500*N.y
+
+    """
+
+    if not isinstance(frame, ReferenceFrame):
+        raise TypeError('Please specify a valid ReferenceFrame')
+    else:
+        linear_momentum_sys = Vector(0)
+        for e in body:
+            if isinstance(e, (RigidBody, Particle)):
+                linear_momentum_sys += e.linear_momentum(frame)
+            else:
+                raise TypeError('*body must have only Particle or RigidBody')
+    return linear_momentum_sys
+
+
+def angular_momentum(point, frame, *body):
+    """Angular momentum of a system.
+
+    Explanation
+    ===========
+
+    This function returns the angular momentum of a system of Particle's and/or
+    RigidBody's. The angular momentum of such a system is equal to the vector
+    sum of the angular momentum of its constituents. Consider a system, S,
+    comprised of a rigid body, A, and a particle, P. The angular momentum of
+    the system, H, is equal to the vector sum of the angular momentum of the
+    particle, H1, and the angular momentum of the rigid body, H2, i.e.
+
+    H = H1 + H2
+
+    Parameters
+    ==========
+
+    point : Point
+        The point about which angular momentum of the system is desired.
+    frame : ReferenceFrame
+        The frame in which angular momentum is desired.
+    body1, body2, body3... : Particle and/or RigidBody
+        The body (or bodies) whose angular momentum is required.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
+    >>> from sympy.physics.mechanics import RigidBody, outer, angular_momentum
+    >>> N = ReferenceFrame('N')
+    >>> O = Point('O')
+    >>> O.set_vel(N, 0 * N.x)
+    >>> P = O.locatenew('P', 1 * N.x)
+    >>> P.set_vel(N, 10 * N.x)
+    >>> Pa = Particle('Pa', P, 1)
+    >>> Ac = O.locatenew('Ac', 2 * N.y)
+    >>> Ac.set_vel(N, 5 * N.y)
+    >>> a = ReferenceFrame('a')
+    >>> a.set_ang_vel(N, 10 * N.z)
+    >>> I = outer(N.z, N.z)
+    >>> A = RigidBody('A', Ac, a, 20, (I, Ac))
+    >>> angular_momentum(O, N, Pa, A)
+    10*N.z
+
+    """
+
+    if not isinstance(frame, ReferenceFrame):
+        raise TypeError('Please enter a valid ReferenceFrame')
+    if not isinstance(point, Point):
+        raise TypeError('Please specify a valid Point')
+    else:
+        angular_momentum_sys = Vector(0)
+        for e in body:
+            if isinstance(e, (RigidBody, Particle)):
+                angular_momentum_sys += e.angular_momentum(point, frame)
+            else:
+                raise TypeError('*body must have only Particle or RigidBody')
+    return angular_momentum_sys
+
+
+def kinetic_energy(frame, *body):
+    """Kinetic energy of a multibody system.
+
+    Explanation
+    ===========
+
+    This function returns the kinetic energy of a system of Particle's and/or
+    RigidBody's. The kinetic energy of such a system is equal to the sum of
+    the kinetic energies of its constituents. Consider a system, S, comprising
+    a rigid body, A, and a particle, P. The kinetic energy of the system, T,
+    is equal to the vector sum of the kinetic energy of the particle, T1, and
+    the kinetic energy of the rigid body, T2, i.e.
+
+    T = T1 + T2
+
+    Kinetic energy is a scalar.
+
+    Parameters
+    ==========
+
+    frame : ReferenceFrame
+        The frame in which the velocity or angular velocity of the body is
+        defined.
+    body1, body2, body3... : Particle and/or RigidBody
+        The body (or bodies) whose kinetic energy is required.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
+    >>> from sympy.physics.mechanics import RigidBody, outer, kinetic_energy
+    >>> N = ReferenceFrame('N')
+    >>> O = Point('O')
+    >>> O.set_vel(N, 0 * N.x)
+    >>> P = O.locatenew('P', 1 * N.x)
+    >>> P.set_vel(N, 10 * N.x)
+    >>> Pa = Particle('Pa', P, 1)
+    >>> Ac = O.locatenew('Ac', 2 * N.y)
+    >>> Ac.set_vel(N, 5 * N.y)
+    >>> a = ReferenceFrame('a')
+    >>> a.set_ang_vel(N, 10 * N.z)
+    >>> I = outer(N.z, N.z)
+    >>> A = RigidBody('A', Ac, a, 20, (I, Ac))
+    >>> kinetic_energy(N, Pa, A)
+    350
+
+    """
+
+    if not isinstance(frame, ReferenceFrame):
+        raise TypeError('Please enter a valid ReferenceFrame')
+    ke_sys = S.Zero
+    for e in body:
+        if isinstance(e, (RigidBody, Particle)):
+            ke_sys += e.kinetic_energy(frame)
+        else:
+            raise TypeError('*body must have only Particle or RigidBody')
+    return ke_sys
+
+
+def potential_energy(*body):
+    """Potential energy of a multibody system.
+
+    Explanation
+    ===========
+
+    This function returns the potential energy of a system of Particle's and/or
+    RigidBody's. The potential energy of such a system is equal to the sum of
+    the potential energy of its constituents. Consider a system, S, comprising
+    a rigid body, A, and a particle, P. The potential energy of the system, V,
+    is equal to the vector sum of the potential energy of the particle, V1, and
+    the potential energy of the rigid body, V2, i.e.
+
+    V = V1 + V2
+
+    Potential energy is a scalar.
+
+    Parameters
+    ==========
+
+    body1, body2, body3... : Particle and/or RigidBody
+        The body (or bodies) whose potential energy is required.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
+    >>> from sympy.physics.mechanics import RigidBody, outer, potential_energy
+    >>> from sympy import symbols
+    >>> M, m, g, h = symbols('M m g h')
+    >>> N = ReferenceFrame('N')
+    >>> O = Point('O')
+    >>> O.set_vel(N, 0 * N.x)
+    >>> P = O.locatenew('P', 1 * N.x)
+    >>> Pa = Particle('Pa', P, m)
+    >>> Ac = O.locatenew('Ac', 2 * N.y)
+    >>> a = ReferenceFrame('a')
+    >>> I = outer(N.z, N.z)
+    >>> A = RigidBody('A', Ac, a, M, (I, Ac))
+    >>> Pa.potential_energy = m * g * h
+    >>> A.potential_energy = M * g * h
+    >>> potential_energy(Pa, A)
+    M*g*h + g*h*m
+
+    """
+
+    pe_sys = S.Zero
+    for e in body:
+        if isinstance(e, (RigidBody, Particle)):
+            pe_sys += e.potential_energy
+        else:
+            raise TypeError('*body must have only Particle or RigidBody')
+    return pe_sys
+
+
+def gravity(acceleration, *bodies):
+    from sympy.physics.mechanics.loads import gravity as _gravity
+    sympy_deprecation_warning(
+        """
+        The gravity function has been moved.
+        Import it from "sympy.physics.mechanics.loads".
+        """,
+        deprecated_since_version="1.13",
+        active_deprecations_target="moved-mechanics-functions"
+    )
+    return _gravity(acceleration, *bodies)
+
+
+def center_of_mass(point, *bodies):
+    """
+    Returns the position vector from the given point to the center of mass
+    of the given bodies(particles or rigidbodies).
+
+    Example
+    =======
+
+    >>> from sympy import symbols, S
+    >>> from sympy.physics.vector import Point
+    >>> from sympy.physics.mechanics import Particle, ReferenceFrame, RigidBody, outer
+    >>> from sympy.physics.mechanics.functions import center_of_mass
+    >>> a = ReferenceFrame('a')
+    >>> m = symbols('m', real=True)
+    >>> p1 = Particle('p1', Point('p1_pt'), S(1))
+    >>> p2 = Particle('p2', Point('p2_pt'), S(2))
+    >>> p3 = Particle('p3', Point('p3_pt'), S(3))
+    >>> p4 = Particle('p4', Point('p4_pt'), m)
+    >>> b_f = ReferenceFrame('b_f')
+    >>> b_cm = Point('b_cm')
+    >>> mb = symbols('mb')
+    >>> b = RigidBody('b', b_cm, b_f, mb, (outer(b_f.x, b_f.x), b_cm))
+    >>> p2.point.set_pos(p1.point, a.x)
+    >>> p3.point.set_pos(p1.point, a.x + a.y)
+    >>> p4.point.set_pos(p1.point, a.y)
+    >>> b.masscenter.set_pos(p1.point, a.y + a.z)
+    >>> point_o=Point('o')
+    >>> point_o.set_pos(p1.point, center_of_mass(p1.point, p1, p2, p3, p4, b))
+    >>> expr = 5/(m + mb + 6)*a.x + (m + mb + 3)/(m + mb + 6)*a.y + mb/(m + mb + 6)*a.z
+    >>> point_o.pos_from(p1.point)
+    5/(m + mb + 6)*a.x + (m + mb + 3)/(m + mb + 6)*a.y + mb/(m + mb + 6)*a.z
+
+    """
+    if not bodies:
+        raise TypeError("No bodies(instances of Particle or Rigidbody) were passed.")
+
+    total_mass = 0
+    vec = Vector(0)
+    for i in bodies:
+        total_mass += i.mass
+
+        masscenter = getattr(i, 'masscenter', None)
+        if masscenter is None:
+            masscenter = i.point
+        vec += i.mass*masscenter.pos_from(point)
+
+    return vec/total_mass
+
+
+def Lagrangian(frame, *body):
+    """Lagrangian of a multibody system.
+
+    Explanation
+    ===========
+
+    This function returns the Lagrangian of a system of Particle's and/or
+    RigidBody's. The Lagrangian of such a system is equal to the difference
+    between the kinetic energies and potential energies of its constituents. If
+    T and V are the kinetic and potential energies of a system then it's
+    Lagrangian, L, is defined as
+
+    L = T - V
+
+    The Lagrangian is a scalar.
+
+    Parameters
+    ==========
+
+    frame : ReferenceFrame
+        The frame in which the velocity or angular velocity of the body is
+        defined to determine the kinetic energy.
+
+    body1, body2, body3... : Particle and/or RigidBody
+        The body (or bodies) whose Lagrangian is required.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
+    >>> from sympy.physics.mechanics import RigidBody, outer, Lagrangian
+    >>> from sympy import symbols
+    >>> M, m, g, h = symbols('M m g h')
+    >>> N = ReferenceFrame('N')
+    >>> O = Point('O')
+    >>> O.set_vel(N, 0 * N.x)
+    >>> P = O.locatenew('P', 1 * N.x)
+    >>> P.set_vel(N, 10 * N.x)
+    >>> Pa = Particle('Pa', P, 1)
+    >>> Ac = O.locatenew('Ac', 2 * N.y)
+    >>> Ac.set_vel(N, 5 * N.y)
+    >>> a = ReferenceFrame('a')
+    >>> a.set_ang_vel(N, 10 * N.z)
+    >>> I = outer(N.z, N.z)
+    >>> A = RigidBody('A', Ac, a, 20, (I, Ac))
+    >>> Pa.potential_energy = m * g * h
+    >>> A.potential_energy = M * g * h
+    >>> Lagrangian(N, Pa, A)
+    -M*g*h - g*h*m + 350
+
+    """
+
+    if not isinstance(frame, ReferenceFrame):
+        raise TypeError('Please supply a valid ReferenceFrame')
+    for e in body:
+        if not isinstance(e, (RigidBody, Particle)):
+            raise TypeError('*body must have only Particle or RigidBody')
+    return kinetic_energy(frame, *body) - potential_energy(*body)
+
+
+def find_dynamicsymbols(expression, exclude=None, reference_frame=None):
+    """Find all dynamicsymbols in expression.
+
+    Explanation
+    ===========
+
+    If the optional ``exclude`` kwarg is used, only dynamicsymbols
+    not in the iterable ``exclude`` are returned.
+    If we intend to apply this function on a vector, the optional
+    ``reference_frame`` is also used to inform about the corresponding frame
+    with respect to which the dynamic symbols of the given vector is to be
+    determined.
+
+    Parameters
+    ==========
+
+    expression : SymPy expression
+
+    exclude : iterable of dynamicsymbols, optional
+
+    reference_frame : ReferenceFrame, optional
+        The frame with respect to which the dynamic symbols of the
+        given vector is to be determined.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import dynamicsymbols, find_dynamicsymbols
+    >>> from sympy.physics.mechanics import ReferenceFrame
+    >>> x, y = dynamicsymbols('x, y')
+    >>> expr = x + x.diff()*y
+    >>> find_dynamicsymbols(expr)
+    {x(t), y(t), Derivative(x(t), t)}
+    >>> find_dynamicsymbols(expr, exclude=[x, y])
+    {Derivative(x(t), t)}
+    >>> a, b, c = dynamicsymbols('a, b, c')
+    >>> A = ReferenceFrame('A')
+    >>> v = a * A.x + b * A.y + c * A.z
+    >>> find_dynamicsymbols(v, reference_frame=A)
+    {a(t), b(t), c(t)}
+
+    """
+    t_set = {dynamicsymbols._t}
+    if exclude:
+        if iterable(exclude):
+            exclude_set = set(exclude)
+        else:
+            raise TypeError("exclude kwarg must be iterable")
+    else:
+        exclude_set = set()
+    if isinstance(expression, Vector):
+        if reference_frame is None:
+            raise ValueError("You must provide reference_frame when passing a "
+                             "vector expression, got %s." % reference_frame)
+        else:
+            expression = expression.to_matrix(reference_frame)
+    return {i for i in expression.atoms(AppliedUndef, Derivative) if
+            i.free_symbols == t_set} - exclude_set
+
+
+def msubs(expr, *sub_dicts, smart=False, **kwargs):
+    """A custom subs for use on expressions derived in physics.mechanics.
+
+    Traverses the expression tree once, performing the subs found in sub_dicts.
+    Terms inside ``Derivative`` expressions are ignored:
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import dynamicsymbols, msubs
+    >>> x = dynamicsymbols('x')
+    >>> msubs(x.diff() + x, {x: 1})
+    Derivative(x(t), t) + 1
+
+    Note that sub_dicts can be a single dictionary, or several dictionaries:
+
+    >>> x, y, z = dynamicsymbols('x, y, z')
+    >>> sub1 = {x: 1, y: 2}
+    >>> sub2 = {z: 3, x.diff(): 4}
+    >>> msubs(x.diff() + x + y + z, sub1, sub2)
+    10
+
+    If smart=True (default False), also checks for conditions that may result
+    in ``nan``, but if simplified would yield a valid expression. For example:
+
+    >>> from sympy import sin, tan
+    >>> (sin(x)/tan(x)).subs(x, 0)
+    nan
+    >>> msubs(sin(x)/tan(x), {x: 0}, smart=True)
+    1
+
+    It does this by first replacing all ``tan`` with ``sin/cos``. Then each
+    node is traversed. If the node is a fraction, subs is first evaluated on
+    the denominator. If this results in 0, simplification of the entire
+    fraction is attempted. Using this selective simplification, only
+    subexpressions that result in 1/0 are targeted, resulting in faster
+    performance.
+
+    """
+
+    sub_dict = dict_merge(*sub_dicts)
+    if smart:
+        func = _smart_subs
+    elif hasattr(expr, 'msubs'):
+        return expr.msubs(sub_dict)
+    else:
+        func = lambda expr, sub_dict: _crawl(expr, _sub_func, sub_dict)
+    if isinstance(expr, (Matrix, Vector, Dyadic)):
+        return expr.applyfunc(lambda x: func(x, sub_dict))
+    else:
+        return func(expr, sub_dict)
+
+
+def _crawl(expr, func, *args, **kwargs):
+    """Crawl the expression tree, and apply func to every node."""
+    val = func(expr, *args, **kwargs)
+    if val is not None:
+        return val
+    new_args = (_crawl(arg, func, *args, **kwargs) for arg in expr.args)
+    return expr.func(*new_args)
+
+
+def _sub_func(expr, sub_dict):
+    """Perform direct matching substitution, ignoring derivatives."""
+    if expr in sub_dict:
+        return sub_dict[expr]
+    elif not expr.args or expr.is_Derivative:
+        return expr
+
+
+def _tan_repl_func(expr):
+    """Replace tan with sin/cos."""
+    if isinstance(expr, tan):
+        return sin(*expr.args) / cos(*expr.args)
+    elif not expr.args or expr.is_Derivative:
+        return expr
+
+
+def _smart_subs(expr, sub_dict):
+    """Performs subs, checking for conditions that may result in `nan` or
+    `oo`, and attempts to simplify them out.
+
+    The expression tree is traversed twice, and the following steps are
+    performed on each expression node:
+    - First traverse:
+        Replace all `tan` with `sin/cos`.
+    - Second traverse:
+        If node is a fraction, check if the denominator evaluates to 0.
+        If so, attempt to simplify it out. Then if node is in sub_dict,
+        sub in the corresponding value.
+
+    """
+    expr = _crawl(expr, _tan_repl_func)
+
+    def _recurser(expr, sub_dict):
+        # Decompose the expression into num, den
+        num, den = _fraction_decomp(expr)
+        if den != 1:
+            # If there is a non trivial denominator, we need to handle it
+            denom_subbed = _recurser(den, sub_dict)
+            if denom_subbed.evalf() == 0:
+                # If denom is 0 after this, attempt to simplify the bad expr
+                expr = simplify(expr)
+            else:
+                # Expression won't result in nan, find numerator
+                num_subbed = _recurser(num, sub_dict)
+                return num_subbed / denom_subbed
+        # We have to crawl the tree manually, because `expr` may have been
+        # modified in the simplify step. First, perform subs as normal:
+        val = _sub_func(expr, sub_dict)
+        if val is not None:
+            return val
+        new_args = (_recurser(arg, sub_dict) for arg in expr.args)
+        return expr.func(*new_args)
+    return _recurser(expr, sub_dict)
+
+
+def _fraction_decomp(expr):
+    """Return num, den such that expr = num/den."""
+    if not isinstance(expr, Mul):
+        return expr, 1
+    num = []
+    den = []
+    for a in expr.args:
+        if a.is_Pow and a.args[1] < 0:
+            den.append(1 / a)
+        else:
+            num.append(a)
+    if not den:
+        return expr, 1
+    num = Mul(*num)
+    den = Mul(*den)
+    return num, den
+
+
+def _f_list_parser(fl, ref_frame):
+    """Parses the provided forcelist composed of items
+    of the form (obj, force).
+    Returns a tuple containing:
+        vel_list: The velocity (ang_vel for Frames, vel for Points) in
+                the provided reference frame.
+        f_list: The forces.
+
+    Used internally in the KanesMethod and LagrangesMethod classes.
+
+    """
+    def flist_iter():
+        for pair in fl:
+            obj, force = pair
+            if isinstance(obj, ReferenceFrame):
+                yield obj.ang_vel_in(ref_frame), force
+            elif isinstance(obj, Point):
+                yield obj.vel(ref_frame), force
+            else:
+                raise TypeError('First entry in each forcelist pair must '
+                                'be a point or frame.')
+
+    if not fl:
+        vel_list, f_list = (), ()
+    else:
+        unzip = lambda l: list(zip(*l)) if l[0] else [(), ()]
+        vel_list, f_list = unzip(list(flist_iter()))
+    return vel_list, f_list
+
+
+def _validate_coordinates(coordinates=None, speeds=None, check_duplicates=True,
+                          is_dynamicsymbols=True, u_auxiliary=None):
+    """Validate the generalized coordinates and generalized speeds.
+
+    Parameters
+    ==========
+    coordinates : iterable, optional
+        Generalized coordinates to be validated.
+    speeds : iterable, optional
+        Generalized speeds to be validated.
+    check_duplicates : bool, optional
+        Checks if there are duplicates in the generalized coordinates and
+        generalized speeds. If so it will raise a ValueError. The default is
+        True.
+    is_dynamicsymbols : iterable, optional
+        Checks if all the generalized coordinates and generalized speeds are
+        dynamicsymbols. If any is not a dynamicsymbol, a ValueError will be
+        raised. The default is True.
+    u_auxiliary : iterable, optional
+        Auxiliary generalized speeds to be validated.
+
+    """
+    t_set = {dynamicsymbols._t}
+    # Convert input to iterables
+    if coordinates is None:
+        coordinates = []
+    elif not iterable(coordinates):
+        coordinates = [coordinates]
+    if speeds is None:
+        speeds = []
+    elif not iterable(speeds):
+        speeds = [speeds]
+    if u_auxiliary is None:
+        u_auxiliary = []
+    elif not iterable(u_auxiliary):
+        u_auxiliary = [u_auxiliary]
+
+    msgs = []
+    if check_duplicates:  # Check for duplicates
+        seen = set()
+        coord_duplicates = {x for x in coordinates if x in seen or seen.add(x)}
+        seen = set()
+        speed_duplicates = {x for x in speeds if x in seen or seen.add(x)}
+        seen = set()
+        aux_duplicates = {x for x in u_auxiliary if x in seen or seen.add(x)}
+        overlap_coords = set(coordinates).intersection(speeds)
+        overlap_aux = set(coordinates).union(speeds).intersection(u_auxiliary)
+        if coord_duplicates:
+            msgs.append(f'The generalized coordinates {coord_duplicates} are '
+                        f'duplicated, all generalized coordinates should be '
+                        f'unique.')
+        if speed_duplicates:
+            msgs.append(f'The generalized speeds {speed_duplicates} are '
+                        f'duplicated, all generalized speeds should be unique.')
+        if aux_duplicates:
+            msgs.append(f'The auxiliary speeds {aux_duplicates} are duplicated,'
+                        f' all auxiliary speeds should be unique.')
+        if overlap_coords:
+            msgs.append(f'{overlap_coords} are defined as both generalized '
+                        f'coordinates and generalized speeds.')
+        if overlap_aux:
+            msgs.append(f'The auxiliary speeds {overlap_aux} are also defined '
+                        f'as generalized coordinates or generalized speeds.')
+    if is_dynamicsymbols:  # Check whether all coordinates are dynamicsymbols
+        for coordinate in coordinates:
+            if not (isinstance(coordinate, (AppliedUndef, Derivative)) and
+                    coordinate.free_symbols == t_set):
+                msgs.append(f'Generalized coordinate "{coordinate}" is not a '
+                            f'dynamicsymbol.')
+        for speed in speeds:
+            if not (isinstance(speed, (AppliedUndef, Derivative)) and
+                    speed.free_symbols == t_set):
+                msgs.append(
+                    f'Generalized speed "{speed}" is not a dynamicsymbol.')
+        for aux in u_auxiliary:
+            if not (isinstance(aux, (AppliedUndef, Derivative)) and
+                    aux.free_symbols == t_set):
+                msgs.append(
+                    f'Auxiliary speed "{aux}" is not a dynamicsymbol.')
+    if msgs:
+        raise ValueError('\n'.join(msgs))
+
+
+def _parse_linear_solver(linear_solver):
+    """Helper function to retrieve a specified linear solver."""
+    if callable(linear_solver):
+        return linear_solver
+    return lambda A, b: Matrix.solve(A, b, method=linear_solver)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/inertia.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/inertia.py
new file mode 100644
index 0000000000000000000000000000000000000000..683c1f630f3cedb82d02a9c5ba2309ae438b7fff
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/inertia.py
@@ -0,0 +1,199 @@
+from sympy import sympify
+from sympy.physics.vector import Point, Dyadic, ReferenceFrame, outer
+from collections import namedtuple
+
+__all__ = ['inertia', 'inertia_of_point_mass', 'Inertia']
+
+
+def inertia(frame, ixx, iyy, izz, ixy=0, iyz=0, izx=0):
+    """Simple way to create inertia Dyadic object.
+
+    Explanation
+    ===========
+
+    Creates an inertia Dyadic based on the given tensor values and a body-fixed
+    reference frame.
+
+    Parameters
+    ==========
+
+    frame : ReferenceFrame
+        The frame the inertia is defined in.
+    ixx : Sympifyable
+        The xx element in the inertia dyadic.
+    iyy : Sympifyable
+        The yy element in the inertia dyadic.
+    izz : Sympifyable
+        The zz element in the inertia dyadic.
+    ixy : Sympifyable
+        The xy element in the inertia dyadic.
+    iyz : Sympifyable
+        The yz element in the inertia dyadic.
+    izx : Sympifyable
+        The zx element in the inertia dyadic.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import ReferenceFrame, inertia
+    >>> N = ReferenceFrame('N')
+    >>> inertia(N, 1, 2, 3)
+    (N.x|N.x) + 2*(N.y|N.y) + 3*(N.z|N.z)
+
+    """
+
+    if not isinstance(frame, ReferenceFrame):
+        raise TypeError('Need to define the inertia in a frame')
+    ixx, iyy, izz = sympify(ixx), sympify(iyy), sympify(izz)
+    ixy, iyz, izx = sympify(ixy), sympify(iyz), sympify(izx)
+    return (ixx*outer(frame.x, frame.x) + ixy*outer(frame.x, frame.y) +
+            izx*outer(frame.x, frame.z) + ixy*outer(frame.y, frame.x) +
+            iyy*outer(frame.y, frame.y) + iyz*outer(frame.y, frame.z) +
+            izx*outer(frame.z, frame.x) + iyz*outer(frame.z, frame.y) +
+            izz*outer(frame.z, frame.z))
+
+
+def inertia_of_point_mass(mass, pos_vec, frame):
+    """Inertia dyadic of a point mass relative to point O.
+
+    Parameters
+    ==========
+
+    mass : Sympifyable
+        Mass of the point mass
+    pos_vec : Vector
+        Position from point O to point mass
+    frame : ReferenceFrame
+        Reference frame to express the dyadic in
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import ReferenceFrame, inertia_of_point_mass
+    >>> N = ReferenceFrame('N')
+    >>> r, m = symbols('r m')
+    >>> px = r * N.x
+    >>> inertia_of_point_mass(m, px, N)
+    m*r**2*(N.y|N.y) + m*r**2*(N.z|N.z)
+
+    """
+
+    return mass*(
+        (outer(frame.x, frame.x) +
+         outer(frame.y, frame.y) +
+         outer(frame.z, frame.z)) *
+        (pos_vec.dot(pos_vec)) - outer(pos_vec, pos_vec))
+
+
+class Inertia(namedtuple('Inertia', ['dyadic', 'point'])):
+    """Inertia object consisting of a Dyadic and a Point of reference.
+
+    Explanation
+    ===========
+
+    This is a simple class to store the Point and Dyadic, belonging to an
+    inertia.
+
+    Attributes
+    ==========
+
+    dyadic : Dyadic
+        The dyadic of the inertia.
+    point : Point
+        The reference point of the inertia.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import ReferenceFrame, Point, Inertia
+    >>> N = ReferenceFrame('N')
+    >>> Po = Point('Po')
+    >>> Inertia(N.x.outer(N.x) + N.y.outer(N.y) + N.z.outer(N.z), Po)
+    ((N.x|N.x) + (N.y|N.y) + (N.z|N.z), Po)
+
+    In the example above the Dyadic was created manually, one can however also
+    use the ``inertia`` function for this or the class method ``from_tensor`` as
+    shown below.
+
+    >>> Inertia.from_inertia_scalars(Po, N, 1, 1, 1)
+    ((N.x|N.x) + (N.y|N.y) + (N.z|N.z), Po)
+
+    """
+    __slots__ = ()
+
+    def __new__(cls, dyadic, point):
+        # Switch order if given in the wrong order
+        if isinstance(dyadic, Point) and isinstance(point, Dyadic):
+            point, dyadic = dyadic, point
+        if not isinstance(point, Point):
+            raise TypeError('Reference point should be of type Point')
+        if not isinstance(dyadic, Dyadic):
+            raise TypeError('Inertia value should be expressed as a Dyadic')
+        return super().__new__(cls, dyadic, point)
+
+    @classmethod
+    def from_inertia_scalars(cls, point, frame, ixx, iyy, izz, ixy=0, iyz=0,
+                             izx=0):
+        """Simple way to create an Inertia object based on the tensor values.
+
+        Explanation
+        ===========
+
+        This class method uses the :func`~.inertia` to create the Dyadic based
+        on the tensor values.
+
+        Parameters
+        ==========
+
+        point : Point
+            The reference point of the inertia.
+        frame : ReferenceFrame
+            The frame the inertia is defined in.
+        ixx : Sympifyable
+            The xx element in the inertia dyadic.
+        iyy : Sympifyable
+            The yy element in the inertia dyadic.
+        izz : Sympifyable
+            The zz element in the inertia dyadic.
+        ixy : Sympifyable
+            The xy element in the inertia dyadic.
+        iyz : Sympifyable
+            The yz element in the inertia dyadic.
+        izx : Sympifyable
+            The zx element in the inertia dyadic.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import ReferenceFrame, Point, Inertia
+        >>> ixx, iyy, izz, ixy, iyz, izx = symbols('ixx iyy izz ixy iyz izx')
+        >>> N = ReferenceFrame('N')
+        >>> P = Point('P')
+        >>> I = Inertia.from_inertia_scalars(P, N, ixx, iyy, izz, ixy, iyz, izx)
+
+        The tensor values can easily be seen when converting the dyadic to a
+        matrix.
+
+        >>> I.dyadic.to_matrix(N)
+        Matrix([
+        [ixx, ixy, izx],
+        [ixy, iyy, iyz],
+        [izx, iyz, izz]])
+
+        """
+        return cls(inertia(frame, ixx, iyy, izz, ixy, iyz, izx), point)
+
+    def __add__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: "
+                        f"'{self.__class__.__name__}' and "
+                        f"'{other.__class__.__name__}'")
+
+    def __mul__(self, other):
+        raise TypeError(f"unsupported operand type(s) for *: "
+                        f"'{self.__class__.__name__}' and "
+                        f"'{other.__class__.__name__}'")
+
+    __radd__ = __add__
+    __rmul__ = __mul__
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/joint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/joint.py
new file mode 100644
index 0000000000000000000000000000000000000000..6f3fe661532cff6bf8dda4ab4383fc09f75e9e44
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/joint.py
@@ -0,0 +1,2188 @@
+# coding=utf-8
+
+from abc import ABC, abstractmethod
+
+from sympy import pi, Derivative, Matrix
+from sympy.core.function import AppliedUndef
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.physics.mechanics.functions import _validate_coordinates
+from sympy.physics.vector import (Vector, dynamicsymbols, cross, Point,
+                                  ReferenceFrame)
+from sympy.utilities.iterables import iterable
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+__all__ = ['Joint', 'PinJoint', 'PrismaticJoint', 'CylindricalJoint',
+           'PlanarJoint', 'SphericalJoint', 'WeldJoint']
+
+
+class Joint(ABC):
+    """Abstract base class for all specific joints.
+
+    Explanation
+    ===========
+
+    A joint subtracts degrees of freedom from a body. This is the base class
+    for all specific joints and holds all common methods acting as an interface
+    for all joints. Custom joint can be created by inheriting Joint class and
+    defining all abstract functions.
+
+    The abstract methods are:
+
+    - ``_generate_coordinates``
+    - ``_generate_speeds``
+    - ``_orient_frames``
+    - ``_set_angular_velocity``
+    - ``_set_linear_velocity``
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    coordinates : iterable of dynamicsymbols, optional
+        Generalized coordinates of the joint.
+    speeds : iterable of dynamicsymbols, optional
+        Generalized speeds of joint.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_axis : Vector, optional
+        .. deprecated:: 1.12
+            Axis fixed in the parent body which aligns with an axis fixed in the
+            child body. The default is the x axis of parent's reference frame.
+            For more information on this deprecation, see
+            :ref:`deprecated-mechanics-joint-axis`.
+    child_axis : Vector, optional
+        .. deprecated:: 1.12
+            Axis fixed in the child body which aligns with an axis fixed in the
+            parent body. The default is the x axis of child's reference frame.
+            For more information on this deprecation, see
+            :ref:`deprecated-mechanics-joint-axis`.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+    parent_joint_pos : Point or Vector, optional
+        .. deprecated:: 1.12
+            This argument is replaced by parent_point and will be removed in a
+            future version.
+            See :ref:`deprecated-mechanics-joint-pos` for more information.
+    child_joint_pos : Point or Vector, optional
+        .. deprecated:: 1.12
+            This argument is replaced by child_point and will be removed in a
+            future version.
+            See :ref:`deprecated-mechanics-joint-pos` for more information.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_axis : Vector
+        The axis fixed in the parent frame that represents the joint.
+    child_axis : Vector
+        The axis fixed in the child frame that represents the joint.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+
+    Notes
+    =====
+
+    When providing a vector as the intermediate frame, a new intermediate frame
+    is created which aligns its X axis with the provided vector. This is done
+    with a single fixed rotation about a rotation axis. This rotation axis is
+    determined by taking the cross product of the ``body.x`` axis with the
+    provided vector. In the case where the provided vector is in the ``-body.x``
+    direction, the rotation is done about the ``body.y`` axis.
+
+    """
+
+    def __init__(self, name, parent, child, coordinates=None, speeds=None,
+                 parent_point=None, child_point=None, parent_interframe=None,
+                 child_interframe=None, parent_axis=None, child_axis=None,
+                 parent_joint_pos=None, child_joint_pos=None):
+
+        if not isinstance(name, str):
+            raise TypeError('Supply a valid name.')
+        self._name = name
+
+        if not isinstance(parent, BodyBase):
+            raise TypeError('Parent must be a body.')
+        self._parent = parent
+
+        if not isinstance(child, BodyBase):
+            raise TypeError('Child must be a body.')
+        self._child = child
+
+        if parent_axis is not None or child_axis is not None:
+            sympy_deprecation_warning(
+                """
+                The parent_axis and child_axis arguments for the Joint classes
+                are deprecated. Instead use parent_interframe, child_interframe.
+                """,
+                deprecated_since_version="1.12",
+                active_deprecations_target="deprecated-mechanics-joint-axis",
+                stacklevel=4
+            )
+            if parent_interframe is None:
+                parent_interframe = parent_axis
+            if child_interframe is None:
+                child_interframe = child_axis
+
+        # Set parent and child frame attributes
+        if hasattr(self._parent, 'frame'):
+            self._parent_frame = self._parent.frame
+        else:
+            if isinstance(parent_interframe, ReferenceFrame):
+                self._parent_frame = parent_interframe
+            else:
+                self._parent_frame = ReferenceFrame(
+                    f'{self.name}_{self._parent.name}_frame')
+        if hasattr(self._child, 'frame'):
+            self._child_frame = self._child.frame
+        else:
+            if isinstance(child_interframe, ReferenceFrame):
+                self._child_frame = child_interframe
+            else:
+                self._child_frame = ReferenceFrame(
+                    f'{self.name}_{self._child.name}_frame')
+
+        self._parent_interframe = self._locate_joint_frame(
+            self._parent, parent_interframe, self._parent_frame)
+        self._child_interframe = self._locate_joint_frame(
+            self._child, child_interframe, self._child_frame)
+        self._parent_axis = self._axis(parent_axis, self._parent_frame)
+        self._child_axis = self._axis(child_axis, self._child_frame)
+
+        if parent_joint_pos is not None or child_joint_pos is not None:
+            sympy_deprecation_warning(
+                """
+                The parent_joint_pos and child_joint_pos arguments for the Joint
+                classes are deprecated. Instead use parent_point and child_point.
+                """,
+                deprecated_since_version="1.12",
+                active_deprecations_target="deprecated-mechanics-joint-pos",
+                stacklevel=4
+            )
+            if parent_point is None:
+                parent_point = parent_joint_pos
+            if child_point is None:
+                child_point = child_joint_pos
+        self._parent_point = self._locate_joint_pos(
+            self._parent, parent_point, self._parent_frame)
+        self._child_point = self._locate_joint_pos(
+            self._child, child_point, self._child_frame)
+
+        self._coordinates = self._generate_coordinates(coordinates)
+        self._speeds = self._generate_speeds(speeds)
+        _validate_coordinates(self.coordinates, self.speeds)
+        self._kdes = self._generate_kdes()
+
+        self._orient_frames()
+        self._set_angular_velocity()
+        self._set_linear_velocity()
+
+    def __str__(self):
+        return self.name
+
+    def __repr__(self):
+        return self.__str__()
+
+    @property
+    def name(self):
+        """Name of the joint."""
+        return self._name
+
+    @property
+    def parent(self):
+        """Parent body of Joint."""
+        return self._parent
+
+    @property
+    def child(self):
+        """Child body of Joint."""
+        return self._child
+
+    @property
+    def coordinates(self):
+        """Matrix of the joint's generalized coordinates."""
+        return self._coordinates
+
+    @property
+    def speeds(self):
+        """Matrix of the joint's generalized speeds."""
+        return self._speeds
+
+    @property
+    def kdes(self):
+        """Kinematical differential equations of the joint."""
+        return self._kdes
+
+    @property
+    def parent_axis(self):
+        """The axis of parent frame."""
+        # Will be removed with `deprecated-mechanics-joint-axis`
+        return self._parent_axis
+
+    @property
+    def child_axis(self):
+        """The axis of child frame."""
+        # Will be removed with `deprecated-mechanics-joint-axis`
+        return self._child_axis
+
+    @property
+    def parent_point(self):
+        """Attachment point where the joint is fixed to the parent body."""
+        return self._parent_point
+
+    @property
+    def child_point(self):
+        """Attachment point where the joint is fixed to the child body."""
+        return self._child_point
+
+    @property
+    def parent_interframe(self):
+        return self._parent_interframe
+
+    @property
+    def child_interframe(self):
+        return self._child_interframe
+
+    @abstractmethod
+    def _generate_coordinates(self, coordinates):
+        """Generate Matrix of the joint's generalized coordinates."""
+        pass
+
+    @abstractmethod
+    def _generate_speeds(self, speeds):
+        """Generate Matrix of the joint's generalized speeds."""
+        pass
+
+    @abstractmethod
+    def _orient_frames(self):
+        """Orient frames as per the joint."""
+        pass
+
+    @abstractmethod
+    def _set_angular_velocity(self):
+        """Set angular velocity of the joint related frames."""
+        pass
+
+    @abstractmethod
+    def _set_linear_velocity(self):
+        """Set velocity of related points to the joint."""
+        pass
+
+    @staticmethod
+    def _to_vector(matrix, frame):
+        """Converts a matrix to a vector in the given frame."""
+        return Vector([(matrix, frame)])
+
+    @staticmethod
+    def _axis(ax, *frames):
+        """Check whether an axis is fixed in one of the frames."""
+        if ax is None:
+            ax = frames[0].x
+            return ax
+        if not isinstance(ax, Vector):
+            raise TypeError("Axis must be a Vector.")
+        ref_frame = None  # Find a body in which the axis can be expressed
+        for frame in frames:
+            try:
+                ax.to_matrix(frame)
+            except ValueError:
+                pass
+            else:
+                ref_frame = frame
+                break
+        if ref_frame is None:
+            raise ValueError("Axis cannot be expressed in one of the body's "
+                             "frames.")
+        if not ax.dt(ref_frame) == 0:
+            raise ValueError('Axis cannot be time-varying when viewed from the '
+                             'associated body.')
+        return ax
+
+    @staticmethod
+    def _choose_rotation_axis(frame, axis):
+        components = axis.to_matrix(frame)
+        x, y, z = components[0], components[1], components[2]
+
+        if x != 0:
+            if y != 0:
+                if z != 0:
+                    return cross(axis, frame.x)
+            if z != 0:
+                return frame.y
+            return frame.z
+        else:
+            if y != 0:
+                return frame.x
+            return frame.y
+
+    @staticmethod
+    def _create_aligned_interframe(frame, align_axis, frame_axis=None,
+                                   frame_name=None):
+        """
+        Returns an intermediate frame, where the ``frame_axis`` defined in
+        ``frame`` is aligned with ``axis``. By default this means that the X
+        axis will be aligned with ``axis``.
+
+        Parameters
+        ==========
+
+        frame : BodyBase or ReferenceFrame
+            The body or reference frame with respect to which the intermediate
+            frame is oriented.
+        align_axis : Vector
+            The vector with respect to which the intermediate frame will be
+            aligned.
+        frame_axis : Vector
+            The vector of the frame which should get aligned with ``axis``. The
+            default is the X axis of the frame.
+        frame_name : string
+            Name of the to be created intermediate frame. The default adds
+            "_int_frame" to the name of ``frame``.
+
+        Example
+        =======
+
+        An intermediate frame, where the X axis of the parent becomes aligned
+        with ``parent.y + parent.z`` can be created as follows:
+
+        >>> from sympy.physics.mechanics.joint import Joint
+        >>> from sympy.physics.mechanics import RigidBody
+        >>> parent = RigidBody('parent')
+        >>> parent_interframe = Joint._create_aligned_interframe(
+        ...     parent, parent.y + parent.z)
+        >>> parent_interframe
+        parent_int_frame
+        >>> parent.frame.dcm(parent_interframe)
+        Matrix([
+        [        0, -sqrt(2)/2, -sqrt(2)/2],
+        [sqrt(2)/2,        1/2,       -1/2],
+        [sqrt(2)/2,       -1/2,        1/2]])
+        >>> (parent.y + parent.z).express(parent_interframe)
+        sqrt(2)*parent_int_frame.x
+
+        Notes
+        =====
+
+        The direction cosine matrix between the given frame and intermediate
+        frame is formed using a simple rotation about an axis that is normal to
+        both ``align_axis`` and ``frame_axis``. In general, the normal axis is
+        formed by crossing the ``frame_axis`` with the ``align_axis``. The
+        exception is if the axes are parallel with opposite directions, in which
+        case the rotation vector is chosen using the rules in the following
+        table with the vectors expressed in the given frame:
+
+        .. list-table::
+           :header-rows: 1
+
+           * - ``align_axis``
+             - ``frame_axis``
+             - ``rotation_axis``
+           * - ``-x``
+             - ``x``
+             - ``z``
+           * - ``-y``
+             - ``y``
+             - ``x``
+           * - ``-z``
+             - ``z``
+             - ``y``
+           * - ``-x-y``
+             - ``x+y``
+             - ``z``
+           * - ``-y-z``
+             - ``y+z``
+             - ``x``
+           * - ``-x-z``
+             - ``x+z``
+             - ``y``
+           * - ``-x-y-z``
+             - ``x+y+z``
+             - ``(x+y+z) × x``
+
+        """
+        if isinstance(frame, BodyBase):
+            frame = frame.frame
+        if frame_axis is None:
+            frame_axis = frame.x
+        if frame_name is None:
+            if frame.name[-6:] == '_frame':
+                frame_name = f'{frame.name[:-6]}_int_frame'
+            else:
+                frame_name = f'{frame.name}_int_frame'
+        angle = frame_axis.angle_between(align_axis)
+        rotation_axis = cross(frame_axis, align_axis)
+        if rotation_axis == Vector(0) and angle == 0:
+            return frame
+        if angle == pi:
+            rotation_axis = Joint._choose_rotation_axis(frame, align_axis)
+
+        int_frame = ReferenceFrame(frame_name)
+        int_frame.orient_axis(frame, rotation_axis, angle)
+        int_frame.set_ang_vel(frame, 0 * rotation_axis)
+        return int_frame
+
+    def _generate_kdes(self):
+        """Generate kinematical differential equations."""
+        kdes = []
+        t = dynamicsymbols._t
+        for i in range(len(self.coordinates)):
+            kdes.append(-self.coordinates[i].diff(t) + self.speeds[i])
+        return Matrix(kdes)
+
+    def _locate_joint_pos(self, body, joint_pos, body_frame=None):
+        """Returns the attachment point of a body."""
+        if body_frame is None:
+            body_frame = body.frame
+        if joint_pos is None:
+            return body.masscenter
+        if not isinstance(joint_pos, (Point, Vector)):
+            raise TypeError('Attachment point must be a Point or Vector.')
+        if isinstance(joint_pos, Vector):
+            point_name = f'{self.name}_{body.name}_joint'
+            joint_pos = body.masscenter.locatenew(point_name, joint_pos)
+        if not joint_pos.pos_from(body.masscenter).dt(body_frame) == 0:
+            raise ValueError('Attachment point must be fixed to the associated '
+                             'body.')
+        return joint_pos
+
+    def _locate_joint_frame(self, body, interframe, body_frame=None):
+        """Returns the attachment frame of a body."""
+        if body_frame is None:
+            body_frame = body.frame
+        if interframe is None:
+            return body_frame
+        if isinstance(interframe, Vector):
+            interframe = Joint._create_aligned_interframe(
+                body_frame, interframe,
+                frame_name=f'{self.name}_{body.name}_int_frame')
+        elif not isinstance(interframe, ReferenceFrame):
+            raise TypeError('Interframe must be a ReferenceFrame.')
+        if not interframe.ang_vel_in(body_frame) == 0:
+            raise ValueError(f'Interframe {interframe} is not fixed to body '
+                             f'{body}.')
+        body.masscenter.set_vel(interframe, 0)  # Fixate interframe to body
+        return interframe
+
+    def _fill_coordinate_list(self, coordinates, n_coords, label='q', offset=0,
+                              number_single=False):
+        """Helper method for _generate_coordinates and _generate_speeds.
+
+        Parameters
+        ==========
+
+        coordinates : iterable
+            Iterable of coordinates or speeds that have been provided.
+        n_coords : Integer
+            Number of coordinates that should be returned.
+        label : String, optional
+            Coordinate type either 'q' (coordinates) or 'u' (speeds). The
+            Default is 'q'.
+        offset : Integer
+            Count offset when creating new dynamicsymbols. The default is 0.
+        number_single : Boolean
+            Boolean whether if n_coords == 1, number should still be used. The
+            default is False.
+
+        """
+
+        def create_symbol(number):
+            if n_coords == 1 and not number_single:
+                return dynamicsymbols(f'{label}_{self.name}')
+            return dynamicsymbols(f'{label}{number}_{self.name}')
+
+        name = 'generalized coordinate' if label == 'q' else 'generalized speed'
+        generated_coordinates = []
+        if coordinates is None:
+            coordinates = []
+        elif not iterable(coordinates):
+            coordinates = [coordinates]
+        if not (len(coordinates) == 0 or len(coordinates) == n_coords):
+            raise ValueError(f'Expected {n_coords} {name}s, instead got '
+                             f'{len(coordinates)} {name}s.')
+        # Supports more iterables, also Matrix
+        for i, coord in enumerate(coordinates):
+            if coord is None:
+                generated_coordinates.append(create_symbol(i + offset))
+            elif isinstance(coord, (AppliedUndef, Derivative)):
+                generated_coordinates.append(coord)
+            else:
+                raise TypeError(f'The {name} {coord} should have been a '
+                                f'dynamicsymbol.')
+        for i in range(len(coordinates) + offset, n_coords + offset):
+            generated_coordinates.append(create_symbol(i))
+        return Matrix(generated_coordinates)
+
+
+class PinJoint(Joint):
+    """Pin (Revolute) Joint.
+
+    .. raw:: html
+        :file: ../../../doc/src/explanation/modules/physics/mechanics/PinJoint.svg
+
+    Explanation
+    ===========
+
+    A pin joint is defined such that the joint rotation axis is fixed in both
+    the child and parent and the location of the joint is relative to the mass
+    center of each body. The child rotates an angle, θ, from the parent about
+    the rotation axis and has a simple angular speed, ω, relative to the
+    parent. The direction cosine matrix between the child interframe and
+    parent interframe is formed using a simple rotation about the joint axis.
+    The page on the joints framework gives a more detailed explanation of the
+    intermediate frames.
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    coordinates : dynamicsymbol, optional
+        Generalized coordinates of the joint.
+    speeds : dynamicsymbol, optional
+        Generalized speeds of joint.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_axis : Vector, optional
+        .. deprecated:: 1.12
+            Axis fixed in the parent body which aligns with an axis fixed in the
+            child body. The default is the x axis of parent's reference frame.
+            For more information on this deprecation, see
+            :ref:`deprecated-mechanics-joint-axis`.
+    child_axis : Vector, optional
+        .. deprecated:: 1.12
+            Axis fixed in the child body which aligns with an axis fixed in the
+            parent body. The default is the x axis of child's reference frame.
+            For more information on this deprecation, see
+            :ref:`deprecated-mechanics-joint-axis`.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+    joint_axis : Vector
+        The axis about which the rotation occurs. Note that the components
+        of this axis are the same in the parent_interframe and child_interframe.
+    parent_joint_pos : Point or Vector, optional
+        .. deprecated:: 1.12
+            This argument is replaced by parent_point and will be removed in a
+            future version.
+            See :ref:`deprecated-mechanics-joint-pos` for more information.
+    child_joint_pos : Point or Vector, optional
+        .. deprecated:: 1.12
+            This argument is replaced by child_point and will be removed in a
+            future version.
+            See :ref:`deprecated-mechanics-joint-pos` for more information.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates. The default value is
+        ``dynamicsymbols(f'q_{joint.name}')``.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds. The default value is
+        ``dynamicsymbols(f'u_{joint.name}')``.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_axis : Vector
+        The axis fixed in the parent frame that represents the joint.
+    child_axis : Vector
+        The axis fixed in the child frame that represents the joint.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    joint_axis : Vector
+        The axis about which the rotation occurs. Note that the components of
+        this axis are the same in the parent_interframe and child_interframe.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+
+    Examples
+    =========
+
+    A single pin joint is created from two bodies and has the following basic
+    attributes:
+
+    >>> from sympy.physics.mechanics import RigidBody, PinJoint
+    >>> parent = RigidBody('P')
+    >>> parent
+    P
+    >>> child = RigidBody('C')
+    >>> child
+    C
+    >>> joint = PinJoint('PC', parent, child)
+    >>> joint
+    PinJoint: PC  parent: P  child: C
+    >>> joint.name
+    'PC'
+    >>> joint.parent
+    P
+    >>> joint.child
+    C
+    >>> joint.parent_point
+    P_masscenter
+    >>> joint.child_point
+    C_masscenter
+    >>> joint.parent_axis
+    P_frame.x
+    >>> joint.child_axis
+    C_frame.x
+    >>> joint.coordinates
+    Matrix([[q_PC(t)]])
+    >>> joint.speeds
+    Matrix([[u_PC(t)]])
+    >>> child.frame.ang_vel_in(parent.frame)
+    u_PC(t)*P_frame.x
+    >>> child.frame.dcm(parent.frame)
+    Matrix([
+    [1,             0,            0],
+    [0,  cos(q_PC(t)), sin(q_PC(t))],
+    [0, -sin(q_PC(t)), cos(q_PC(t))]])
+    >>> joint.child_point.pos_from(joint.parent_point)
+    0
+
+    To further demonstrate the use of the pin joint, the kinematics of simple
+    double pendulum that rotates about the Z axis of each connected body can be
+    created as follows.
+
+    >>> from sympy import symbols, trigsimp
+    >>> from sympy.physics.mechanics import RigidBody, PinJoint
+    >>> l1, l2 = symbols('l1 l2')
+
+    First create bodies to represent the fixed ceiling and one to represent
+    each pendulum bob.
+
+    >>> ceiling = RigidBody('C')
+    >>> upper_bob = RigidBody('U')
+    >>> lower_bob = RigidBody('L')
+
+    The first joint will connect the upper bob to the ceiling by a distance of
+    ``l1`` and the joint axis will be about the Z axis for each body.
+
+    >>> ceiling_joint = PinJoint('P1', ceiling, upper_bob,
+    ... child_point=-l1*upper_bob.frame.x,
+    ... joint_axis=ceiling.frame.z)
+
+    The second joint will connect the lower bob to the upper bob by a distance
+    of ``l2`` and the joint axis will also be about the Z axis for each body.
+
+    >>> pendulum_joint = PinJoint('P2', upper_bob, lower_bob,
+    ... child_point=-l2*lower_bob.frame.x,
+    ... joint_axis=upper_bob.frame.z)
+
+    Once the joints are established the kinematics of the connected bodies can
+    be accessed. First the direction cosine matrices of pendulum link relative
+    to the ceiling are found:
+
+    >>> upper_bob.frame.dcm(ceiling.frame)
+    Matrix([
+    [ cos(q_P1(t)), sin(q_P1(t)), 0],
+    [-sin(q_P1(t)), cos(q_P1(t)), 0],
+    [            0,            0, 1]])
+    >>> trigsimp(lower_bob.frame.dcm(ceiling.frame))
+    Matrix([
+    [ cos(q_P1(t) + q_P2(t)), sin(q_P1(t) + q_P2(t)), 0],
+    [-sin(q_P1(t) + q_P2(t)), cos(q_P1(t) + q_P2(t)), 0],
+    [                      0,                      0, 1]])
+
+    The position of the lower bob's masscenter is found with:
+
+    >>> lower_bob.masscenter.pos_from(ceiling.masscenter)
+    l1*U_frame.x + l2*L_frame.x
+
+    The angular velocities of the two pendulum links can be computed with
+    respect to the ceiling.
+
+    >>> upper_bob.frame.ang_vel_in(ceiling.frame)
+    u_P1(t)*C_frame.z
+    >>> lower_bob.frame.ang_vel_in(ceiling.frame)
+    u_P1(t)*C_frame.z + u_P2(t)*U_frame.z
+
+    And finally, the linear velocities of the two pendulum bobs can be computed
+    with respect to the ceiling.
+
+    >>> upper_bob.masscenter.vel(ceiling.frame)
+    l1*u_P1(t)*U_frame.y
+    >>> lower_bob.masscenter.vel(ceiling.frame)
+    l1*u_P1(t)*U_frame.y + l2*(u_P1(t) + u_P2(t))*L_frame.y
+
+    """
+
+    def __init__(self, name, parent, child, coordinates=None, speeds=None,
+                 parent_point=None, child_point=None, parent_interframe=None,
+                 child_interframe=None, parent_axis=None, child_axis=None,
+                 joint_axis=None, parent_joint_pos=None, child_joint_pos=None):
+
+        self._joint_axis = joint_axis
+        super().__init__(name, parent, child, coordinates, speeds, parent_point,
+                         child_point, parent_interframe, child_interframe,
+                         parent_axis, child_axis, parent_joint_pos,
+                         child_joint_pos)
+
+    def __str__(self):
+        return (f'PinJoint: {self.name}  parent: {self.parent}  '
+                f'child: {self.child}')
+
+    @property
+    def joint_axis(self):
+        """Axis about which the child rotates with respect to the parent."""
+        return self._joint_axis
+
+    def _generate_coordinates(self, coordinate):
+        return self._fill_coordinate_list(coordinate, 1, 'q')
+
+    def _generate_speeds(self, speed):
+        return self._fill_coordinate_list(speed, 1, 'u')
+
+    def _orient_frames(self):
+        self._joint_axis = self._axis(self.joint_axis, self.parent_interframe)
+        self.child_interframe.orient_axis(
+            self.parent_interframe, self.joint_axis, self.coordinates[0])
+
+    def _set_angular_velocity(self):
+        self.child_interframe.set_ang_vel(self.parent_interframe, self.speeds[
+            0] * self.joint_axis.normalize())
+
+    def _set_linear_velocity(self):
+        self.child_point.set_pos(self.parent_point, 0)
+        self.parent_point.set_vel(self._parent_frame, 0)
+        self.child_point.set_vel(self._child_frame, 0)
+        self.child.masscenter.v2pt_theory(self.parent_point,
+                                          self._parent_frame, self._child_frame)
+
+
+class PrismaticJoint(Joint):
+    """Prismatic (Sliding) Joint.
+
+    .. image:: PrismaticJoint.svg
+
+    Explanation
+    ===========
+
+    It is defined such that the child body translates with respect to the parent
+    body along the body-fixed joint axis. The location of the joint is defined
+    by two points, one in each body, which coincide when the generalized
+    coordinate is zero. The direction cosine matrix between the
+    parent_interframe and child_interframe is the identity matrix. Therefore,
+    the direction cosine matrix between the parent and child frames is fully
+    defined by the definition of the intermediate frames. The page on the joints
+    framework gives a more detailed explanation of the intermediate frames.
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    coordinates : dynamicsymbol, optional
+        Generalized coordinates of the joint. The default value is
+        ``dynamicsymbols(f'q_{joint.name}')``.
+    speeds : dynamicsymbol, optional
+        Generalized speeds of joint. The default value is
+        ``dynamicsymbols(f'u_{joint.name}')``.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_axis : Vector, optional
+        .. deprecated:: 1.12
+            Axis fixed in the parent body which aligns with an axis fixed in the
+            child body. The default is the x axis of parent's reference frame.
+            For more information on this deprecation, see
+            :ref:`deprecated-mechanics-joint-axis`.
+    child_axis : Vector, optional
+        .. deprecated:: 1.12
+            Axis fixed in the child body which aligns with an axis fixed in the
+            parent body. The default is the x axis of child's reference frame.
+            For more information on this deprecation, see
+            :ref:`deprecated-mechanics-joint-axis`.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+    joint_axis : Vector
+        The axis along which the translation occurs. Note that the components
+        of this axis are the same in the parent_interframe and child_interframe.
+    parent_joint_pos : Point or Vector, optional
+        .. deprecated:: 1.12
+            This argument is replaced by parent_point and will be removed in a
+            future version.
+            See :ref:`deprecated-mechanics-joint-pos` for more information.
+    child_joint_pos : Point or Vector, optional
+        .. deprecated:: 1.12
+            This argument is replaced by child_point and will be removed in a
+            future version.
+            See :ref:`deprecated-mechanics-joint-pos` for more information.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_axis : Vector
+        The axis fixed in the parent frame that represents the joint.
+    child_axis : Vector
+        The axis fixed in the child frame that represents the joint.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+
+    Examples
+    =========
+
+    A single prismatic joint is created from two bodies and has the following
+    basic attributes:
+
+    >>> from sympy.physics.mechanics import RigidBody, PrismaticJoint
+    >>> parent = RigidBody('P')
+    >>> parent
+    P
+    >>> child = RigidBody('C')
+    >>> child
+    C
+    >>> joint = PrismaticJoint('PC', parent, child)
+    >>> joint
+    PrismaticJoint: PC  parent: P  child: C
+    >>> joint.name
+    'PC'
+    >>> joint.parent
+    P
+    >>> joint.child
+    C
+    >>> joint.parent_point
+    P_masscenter
+    >>> joint.child_point
+    C_masscenter
+    >>> joint.parent_axis
+    P_frame.x
+    >>> joint.child_axis
+    C_frame.x
+    >>> joint.coordinates
+    Matrix([[q_PC(t)]])
+    >>> joint.speeds
+    Matrix([[u_PC(t)]])
+    >>> child.frame.ang_vel_in(parent.frame)
+    0
+    >>> child.frame.dcm(parent.frame)
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> joint.child_point.pos_from(joint.parent_point)
+    q_PC(t)*P_frame.x
+
+    To further demonstrate the use of the prismatic joint, the kinematics of two
+    masses sliding, one moving relative to a fixed body and the other relative
+    to the moving body. about the X axis of each connected body can be created
+    as follows.
+
+    >>> from sympy.physics.mechanics import PrismaticJoint, RigidBody
+
+    First create bodies to represent the fixed ceiling and one to represent
+    a particle.
+
+    >>> wall = RigidBody('W')
+    >>> Part1 = RigidBody('P1')
+    >>> Part2 = RigidBody('P2')
+
+    The first joint will connect the particle to the ceiling and the
+    joint axis will be about the X axis for each body.
+
+    >>> J1 = PrismaticJoint('J1', wall, Part1)
+
+    The second joint will connect the second particle to the first particle
+    and the joint axis will also be about the X axis for each body.
+
+    >>> J2 = PrismaticJoint('J2', Part1, Part2)
+
+    Once the joint is established the kinematics of the connected bodies can
+    be accessed. First the direction cosine matrices of Part relative
+    to the ceiling are found:
+
+    >>> Part1.frame.dcm(wall.frame)
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+
+    >>> Part2.frame.dcm(wall.frame)
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+
+    The position of the particles' masscenter is found with:
+
+    >>> Part1.masscenter.pos_from(wall.masscenter)
+    q_J1(t)*W_frame.x
+
+    >>> Part2.masscenter.pos_from(wall.masscenter)
+    q_J1(t)*W_frame.x + q_J2(t)*P1_frame.x
+
+    The angular velocities of the two particle links can be computed with
+    respect to the ceiling.
+
+    >>> Part1.frame.ang_vel_in(wall.frame)
+    0
+
+    >>> Part2.frame.ang_vel_in(wall.frame)
+    0
+
+    And finally, the linear velocities of the two particles can be computed
+    with respect to the ceiling.
+
+    >>> Part1.masscenter.vel(wall.frame)
+    u_J1(t)*W_frame.x
+
+    >>> Part2.masscenter.vel(wall.frame)
+    u_J1(t)*W_frame.x + Derivative(q_J2(t), t)*P1_frame.x
+
+    """
+
+    def __init__(self, name, parent, child, coordinates=None, speeds=None,
+                 parent_point=None, child_point=None, parent_interframe=None,
+                 child_interframe=None, parent_axis=None, child_axis=None,
+                 joint_axis=None, parent_joint_pos=None, child_joint_pos=None):
+
+        self._joint_axis = joint_axis
+        super().__init__(name, parent, child, coordinates, speeds, parent_point,
+                         child_point, parent_interframe, child_interframe,
+                         parent_axis, child_axis, parent_joint_pos,
+                         child_joint_pos)
+
+    def __str__(self):
+        return (f'PrismaticJoint: {self.name}  parent: {self.parent}  '
+                f'child: {self.child}')
+
+    @property
+    def joint_axis(self):
+        """Axis along which the child translates with respect to the parent."""
+        return self._joint_axis
+
+    def _generate_coordinates(self, coordinate):
+        return self._fill_coordinate_list(coordinate, 1, 'q')
+
+    def _generate_speeds(self, speed):
+        return self._fill_coordinate_list(speed, 1, 'u')
+
+    def _orient_frames(self):
+        self._joint_axis = self._axis(self.joint_axis, self.parent_interframe)
+        self.child_interframe.orient_axis(
+            self.parent_interframe, self.joint_axis, 0)
+
+    def _set_angular_velocity(self):
+        self.child_interframe.set_ang_vel(self.parent_interframe, 0)
+
+    def _set_linear_velocity(self):
+        axis = self.joint_axis.normalize()
+        self.child_point.set_pos(self.parent_point, self.coordinates[0] * axis)
+        self.parent_point.set_vel(self._parent_frame, 0)
+        self.child_point.set_vel(self._child_frame, 0)
+        self.child_point.set_vel(self._parent_frame, self.speeds[0] * axis)
+        self.child.masscenter.set_vel(self._parent_frame, self.speeds[0] * axis)
+
+
+class CylindricalJoint(Joint):
+    """Cylindrical Joint.
+
+    .. image:: CylindricalJoint.svg
+        :align: center
+        :width: 600
+
+    Explanation
+    ===========
+
+    A cylindrical joint is defined such that the child body both rotates about
+    and translates along the body-fixed joint axis with respect to the parent
+    body. The joint axis is both the rotation axis and translation axis. The
+    location of the joint is defined by two points, one in each body, which
+    coincide when the generalized coordinate corresponding to the translation is
+    zero. The direction cosine matrix between the child interframe and parent
+    interframe is formed using a simple rotation about the joint axis. The page
+    on the joints framework gives a more detailed explanation of the
+    intermediate frames.
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    rotation_coordinate : dynamicsymbol, optional
+        Generalized coordinate corresponding to the rotation angle. The default
+        value is ``dynamicsymbols(f'q0_{joint.name}')``.
+    translation_coordinate : dynamicsymbol, optional
+        Generalized coordinate corresponding to the translation distance. The
+        default value is ``dynamicsymbols(f'q1_{joint.name}')``.
+    rotation_speed : dynamicsymbol, optional
+        Generalized speed corresponding to the angular velocity. The default
+        value is ``dynamicsymbols(f'u0_{joint.name}')``.
+    translation_speed : dynamicsymbol, optional
+        Generalized speed corresponding to the translation velocity. The default
+        value is ``dynamicsymbols(f'u1_{joint.name}')``.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+    joint_axis : Vector, optional
+        The rotation as well as translation axis. Note that the components of
+        this axis are the same in the parent_interframe and child_interframe.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    rotation_coordinate : dynamicsymbol
+        Generalized coordinate corresponding to the rotation angle.
+    translation_coordinate : dynamicsymbol
+        Generalized coordinate corresponding to the translation distance.
+    rotation_speed : dynamicsymbol
+        Generalized speed corresponding to the angular velocity.
+    translation_speed : dynamicsymbol
+        Generalized speed corresponding to the translation velocity.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+    joint_axis : Vector
+        The axis of rotation and translation.
+
+    Examples
+    =========
+
+    A single cylindrical joint is created between two bodies and has the
+    following basic attributes:
+
+    >>> from sympy.physics.mechanics import RigidBody, CylindricalJoint
+    >>> parent = RigidBody('P')
+    >>> parent
+    P
+    >>> child = RigidBody('C')
+    >>> child
+    C
+    >>> joint = CylindricalJoint('PC', parent, child)
+    >>> joint
+    CylindricalJoint: PC  parent: P  child: C
+    >>> joint.name
+    'PC'
+    >>> joint.parent
+    P
+    >>> joint.child
+    C
+    >>> joint.parent_point
+    P_masscenter
+    >>> joint.child_point
+    C_masscenter
+    >>> joint.parent_axis
+    P_frame.x
+    >>> joint.child_axis
+    C_frame.x
+    >>> joint.coordinates
+    Matrix([
+    [q0_PC(t)],
+    [q1_PC(t)]])
+    >>> joint.speeds
+    Matrix([
+    [u0_PC(t)],
+    [u1_PC(t)]])
+    >>> child.frame.ang_vel_in(parent.frame)
+    u0_PC(t)*P_frame.x
+    >>> child.frame.dcm(parent.frame)
+    Matrix([
+    [1,              0,             0],
+    [0,  cos(q0_PC(t)), sin(q0_PC(t))],
+    [0, -sin(q0_PC(t)), cos(q0_PC(t))]])
+    >>> joint.child_point.pos_from(joint.parent_point)
+    q1_PC(t)*P_frame.x
+    >>> child.masscenter.vel(parent.frame)
+    u1_PC(t)*P_frame.x
+
+    To further demonstrate the use of the cylindrical joint, the kinematics of
+    two cylindrical joints perpendicular to each other can be created as follows.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import RigidBody, CylindricalJoint
+    >>> r, l, w = symbols('r l w')
+
+    First create bodies to represent the fixed floor with a fixed pole on it.
+    The second body represents a freely moving tube around that pole. The third
+    body represents a solid flag freely translating along and rotating around
+    the Y axis of the tube.
+
+    >>> floor = RigidBody('floor')
+    >>> tube = RigidBody('tube')
+    >>> flag = RigidBody('flag')
+
+    The first joint will connect the first tube to the floor with it translating
+    along and rotating around the Z axis of both bodies.
+
+    >>> floor_joint = CylindricalJoint('C1', floor, tube, joint_axis=floor.z)
+
+    The second joint will connect the tube perpendicular to the flag along the Y
+    axis of both the tube and the flag, with the joint located at a distance
+    ``r`` from the tube's center of mass and a combination of the distances
+    ``l`` and ``w`` from the flag's center of mass.
+
+    >>> flag_joint = CylindricalJoint('C2', tube, flag,
+    ...                               parent_point=r * tube.y,
+    ...                               child_point=-w * flag.y + l * flag.z,
+    ...                               joint_axis=tube.y)
+
+    Once the joints are established the kinematics of the connected bodies can
+    be accessed. First the direction cosine matrices of both the body and the
+    flag relative to the floor are found:
+
+    >>> tube.frame.dcm(floor.frame)
+    Matrix([
+    [ cos(q0_C1(t)), sin(q0_C1(t)), 0],
+    [-sin(q0_C1(t)), cos(q0_C1(t)), 0],
+    [             0,             0, 1]])
+    >>> flag.frame.dcm(floor.frame)
+    Matrix([
+    [cos(q0_C1(t))*cos(q0_C2(t)), sin(q0_C1(t))*cos(q0_C2(t)), -sin(q0_C2(t))],
+    [             -sin(q0_C1(t)),               cos(q0_C1(t)),              0],
+    [sin(q0_C2(t))*cos(q0_C1(t)), sin(q0_C1(t))*sin(q0_C2(t)),  cos(q0_C2(t))]])
+
+    The position of the flag's center of mass is found with:
+
+    >>> flag.masscenter.pos_from(floor.masscenter)
+    q1_C1(t)*floor_frame.z + (r + q1_C2(t))*tube_frame.y + w*flag_frame.y - l*flag_frame.z
+
+    The angular velocities of the two tubes can be computed with respect to the
+    floor.
+
+    >>> tube.frame.ang_vel_in(floor.frame)
+    u0_C1(t)*floor_frame.z
+    >>> flag.frame.ang_vel_in(floor.frame)
+    u0_C1(t)*floor_frame.z + u0_C2(t)*tube_frame.y
+
+    Finally, the linear velocities of the two tube centers of mass can be
+    computed with respect to the floor, while expressed in the tube's frame.
+
+    >>> tube.masscenter.vel(floor.frame).to_matrix(tube.frame)
+    Matrix([
+    [       0],
+    [       0],
+    [u1_C1(t)]])
+    >>> flag.masscenter.vel(floor.frame).to_matrix(tube.frame).simplify()
+    Matrix([
+    [-l*u0_C2(t)*cos(q0_C2(t)) - r*u0_C1(t) - w*u0_C1(t) - q1_C2(t)*u0_C1(t)],
+    [                    -l*u0_C1(t)*sin(q0_C2(t)) + Derivative(q1_C2(t), t)],
+    [                                    l*u0_C2(t)*sin(q0_C2(t)) + u1_C1(t)]])
+
+    """
+
+    def __init__(self, name, parent, child, rotation_coordinate=None,
+                 translation_coordinate=None, rotation_speed=None,
+                 translation_speed=None, parent_point=None, child_point=None,
+                 parent_interframe=None, child_interframe=None,
+                 joint_axis=None):
+        self._joint_axis = joint_axis
+        coordinates = (rotation_coordinate, translation_coordinate)
+        speeds = (rotation_speed, translation_speed)
+        super().__init__(name, parent, child, coordinates, speeds,
+                         parent_point, child_point,
+                         parent_interframe=parent_interframe,
+                         child_interframe=child_interframe)
+
+    def __str__(self):
+        return (f'CylindricalJoint: {self.name}  parent: {self.parent}  '
+                f'child: {self.child}')
+
+    @property
+    def joint_axis(self):
+        """Axis about and along which the rotation and translation occurs."""
+        return self._joint_axis
+
+    @property
+    def rotation_coordinate(self):
+        """Generalized coordinate corresponding to the rotation angle."""
+        return self.coordinates[0]
+
+    @property
+    def translation_coordinate(self):
+        """Generalized coordinate corresponding to the translation distance."""
+        return self.coordinates[1]
+
+    @property
+    def rotation_speed(self):
+        """Generalized speed corresponding to the angular velocity."""
+        return self.speeds[0]
+
+    @property
+    def translation_speed(self):
+        """Generalized speed corresponding to the translation velocity."""
+        return self.speeds[1]
+
+    def _generate_coordinates(self, coordinates):
+        return self._fill_coordinate_list(coordinates, 2, 'q')
+
+    def _generate_speeds(self, speeds):
+        return self._fill_coordinate_list(speeds, 2, 'u')
+
+    def _orient_frames(self):
+        self._joint_axis = self._axis(self.joint_axis, self.parent_interframe)
+        self.child_interframe.orient_axis(
+            self.parent_interframe, self.joint_axis, self.rotation_coordinate)
+
+    def _set_angular_velocity(self):
+        self.child_interframe.set_ang_vel(
+            self.parent_interframe,
+            self.rotation_speed * self.joint_axis.normalize())
+
+    def _set_linear_velocity(self):
+        self.child_point.set_pos(
+            self.parent_point,
+            self.translation_coordinate * self.joint_axis.normalize())
+        self.parent_point.set_vel(self._parent_frame, 0)
+        self.child_point.set_vel(self._child_frame, 0)
+        self.child_point.set_vel(
+            self._parent_frame,
+            self.translation_speed * self.joint_axis.normalize())
+        self.child.masscenter.v2pt_theory(self.child_point, self._parent_frame,
+                                          self.child_interframe)
+
+
+class PlanarJoint(Joint):
+    """Planar Joint.
+
+    .. raw:: html
+        :file: ../../../doc/src/modules/physics/mechanics/api/PlanarJoint.svg
+
+    Explanation
+    ===========
+
+    A planar joint is defined such that the child body translates over a fixed
+    plane of the parent body as well as rotate about the rotation axis, which
+    is perpendicular to that plane. The origin of this plane is the
+    ``parent_point`` and the plane is spanned by two nonparallel planar vectors.
+    The location of the ``child_point`` is based on the planar vectors
+    ($\\vec{v}_1$, $\\vec{v}_2$) and generalized coordinates ($q_1$, $q_2$),
+    i.e. $\\vec{r} = q_1 \\hat{v}_1 + q_2 \\hat{v}_2$. The direction cosine
+    matrix between the ``child_interframe`` and ``parent_interframe`` is formed
+    using a simple rotation ($q_0$) about the rotation axis.
+
+    In order to simplify the definition of the ``PlanarJoint``, the
+    ``rotation_axis`` and ``planar_vectors`` are set to be the unit vectors of
+    the ``parent_interframe`` according to the table below. This ensures that
+    you can only define these vectors by creating a separate frame and supplying
+    that as the interframe. If you however would only like to supply the normals
+    of the plane with respect to the parent and child bodies, then you can also
+    supply those to the ``parent_interframe`` and ``child_interframe``
+    arguments. An example of both of these cases is in the examples section
+    below and the page on the joints framework provides a more detailed
+    explanation of the intermediate frames.
+
+    .. list-table::
+
+        * - ``rotation_axis``
+          - ``parent_interframe.x``
+        * - ``planar_vectors[0]``
+          - ``parent_interframe.y``
+        * - ``planar_vectors[1]``
+          - ``parent_interframe.z``
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    rotation_coordinate : dynamicsymbol, optional
+        Generalized coordinate corresponding to the rotation angle. The default
+        value is ``dynamicsymbols(f'q0_{joint.name}')``.
+    planar_coordinates : iterable of dynamicsymbols, optional
+        Two generalized coordinates used for the planar translation. The default
+        value is ``dynamicsymbols(f'q1_{joint.name} q2_{joint.name}')``.
+    rotation_speed : dynamicsymbol, optional
+        Generalized speed corresponding to the angular velocity. The default
+        value is ``dynamicsymbols(f'u0_{joint.name}')``.
+    planar_speeds : dynamicsymbols, optional
+        Two generalized speeds used for the planar translation velocity. The
+        default value is ``dynamicsymbols(f'u1_{joint.name} u2_{joint.name}')``.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    rotation_coordinate : dynamicsymbol
+        Generalized coordinate corresponding to the rotation angle.
+    planar_coordinates : Matrix
+        Two generalized coordinates used for the planar translation.
+    rotation_speed : dynamicsymbol
+        Generalized speed corresponding to the angular velocity.
+    planar_speeds : Matrix
+        Two generalized speeds used for the planar translation velocity.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+    rotation_axis : Vector
+        The axis about which the rotation occurs.
+    planar_vectors : list
+        The vectors that describe the planar translation directions.
+
+    Examples
+    =========
+
+    A single planar joint is created between two bodies and has the following
+    basic attributes:
+
+    >>> from sympy.physics.mechanics import RigidBody, PlanarJoint
+    >>> parent = RigidBody('P')
+    >>> parent
+    P
+    >>> child = RigidBody('C')
+    >>> child
+    C
+    >>> joint = PlanarJoint('PC', parent, child)
+    >>> joint
+    PlanarJoint: PC  parent: P  child: C
+    >>> joint.name
+    'PC'
+    >>> joint.parent
+    P
+    >>> joint.child
+    C
+    >>> joint.parent_point
+    P_masscenter
+    >>> joint.child_point
+    C_masscenter
+    >>> joint.rotation_axis
+    P_frame.x
+    >>> joint.planar_vectors
+    [P_frame.y, P_frame.z]
+    >>> joint.rotation_coordinate
+    q0_PC(t)
+    >>> joint.planar_coordinates
+    Matrix([
+    [q1_PC(t)],
+    [q2_PC(t)]])
+    >>> joint.coordinates
+    Matrix([
+    [q0_PC(t)],
+    [q1_PC(t)],
+    [q2_PC(t)]])
+    >>> joint.rotation_speed
+    u0_PC(t)
+    >>> joint.planar_speeds
+    Matrix([
+    [u1_PC(t)],
+    [u2_PC(t)]])
+    >>> joint.speeds
+    Matrix([
+    [u0_PC(t)],
+    [u1_PC(t)],
+    [u2_PC(t)]])
+    >>> child.frame.ang_vel_in(parent.frame)
+    u0_PC(t)*P_frame.x
+    >>> child.frame.dcm(parent.frame)
+    Matrix([
+    [1,              0,             0],
+    [0,  cos(q0_PC(t)), sin(q0_PC(t))],
+    [0, -sin(q0_PC(t)), cos(q0_PC(t))]])
+    >>> joint.child_point.pos_from(joint.parent_point)
+    q1_PC(t)*P_frame.y + q2_PC(t)*P_frame.z
+    >>> child.masscenter.vel(parent.frame)
+    u1_PC(t)*P_frame.y + u2_PC(t)*P_frame.z
+
+    To further demonstrate the use of the planar joint, the kinematics of a
+    block sliding on a slope, can be created as follows.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import PlanarJoint, RigidBody, ReferenceFrame
+    >>> a, d, h = symbols('a d h')
+
+    First create bodies to represent the slope and the block.
+
+    >>> ground = RigidBody('G')
+    >>> block = RigidBody('B')
+
+    To define the slope you can either define the plane by specifying the
+    ``planar_vectors`` or/and the ``rotation_axis``. However it is advisable to
+    create a rotated intermediate frame, so that the ``parent_vectors`` and
+    ``rotation_axis`` will be the unit vectors of this intermediate frame.
+
+    >>> slope = ReferenceFrame('A')
+    >>> slope.orient_axis(ground.frame, ground.y, a)
+
+    The planar joint can be created using these bodies and intermediate frame.
+    We can specify the origin of the slope to be ``d`` above the slope's center
+    of mass and the block's center of mass to be a distance ``h`` above the
+    slope's surface. Note that we can specify the normal of the plane using the
+    rotation axis argument.
+
+    >>> joint = PlanarJoint('PC', ground, block, parent_point=d * ground.x,
+    ...                     child_point=-h * block.x, parent_interframe=slope)
+
+    Once the joint is established the kinematics of the bodies can be accessed.
+    First the ``rotation_axis``, which is normal to the plane and the
+    ``plane_vectors``, can be found.
+
+    >>> joint.rotation_axis
+    A.x
+    >>> joint.planar_vectors
+    [A.y, A.z]
+
+    The direction cosine matrix of the block with respect to the ground can be
+    found with:
+
+    >>> block.frame.dcm(ground.frame)
+    Matrix([
+    [              cos(a),              0,              -sin(a)],
+    [sin(a)*sin(q0_PC(t)),  cos(q0_PC(t)), sin(q0_PC(t))*cos(a)],
+    [sin(a)*cos(q0_PC(t)), -sin(q0_PC(t)), cos(a)*cos(q0_PC(t))]])
+
+    The angular velocity of the block can be computed with respect to the
+    ground.
+
+    >>> block.frame.ang_vel_in(ground.frame)
+    u0_PC(t)*A.x
+
+    The position of the block's center of mass can be found with:
+
+    >>> block.masscenter.pos_from(ground.masscenter)
+    d*G_frame.x + h*B_frame.x + q1_PC(t)*A.y + q2_PC(t)*A.z
+
+    Finally, the linear velocity of the block's center of mass can be
+    computed with respect to the ground.
+
+    >>> block.masscenter.vel(ground.frame)
+    u1_PC(t)*A.y + u2_PC(t)*A.z
+
+    In some cases it could be your preference to only define the normals of the
+    plane with respect to both bodies. This can most easily be done by supplying
+    vectors to the ``interframe`` arguments. What will happen in this case is
+    that an interframe will be created with its ``x`` axis aligned with the
+    provided vector. For a further explanation of how this is done see the notes
+    of the ``Joint`` class. In the code below, the above example (with the block
+    on the slope) is recreated by supplying vectors to the interframe arguments.
+    Note that the previously described option is however more computationally
+    efficient, because the algorithm now has to compute the rotation angle
+    between the provided vector and the 'x' axis.
+
+    >>> from sympy import symbols, cos, sin
+    >>> from sympy.physics.mechanics import PlanarJoint, RigidBody
+    >>> a, d, h = symbols('a d h')
+    >>> ground = RigidBody('G')
+    >>> block = RigidBody('B')
+    >>> joint = PlanarJoint(
+    ...     'PC', ground, block, parent_point=d * ground.x,
+    ...     child_point=-h * block.x, child_interframe=block.x,
+    ...     parent_interframe=cos(a) * ground.x + sin(a) * ground.z)
+    >>> block.frame.dcm(ground.frame).simplify()
+    Matrix([
+    [               cos(a),              0,               sin(a)],
+    [-sin(a)*sin(q0_PC(t)),  cos(q0_PC(t)), sin(q0_PC(t))*cos(a)],
+    [-sin(a)*cos(q0_PC(t)), -sin(q0_PC(t)), cos(a)*cos(q0_PC(t))]])
+
+    """
+
+    def __init__(self, name, parent, child, rotation_coordinate=None,
+                 planar_coordinates=None, rotation_speed=None,
+                 planar_speeds=None, parent_point=None, child_point=None,
+                 parent_interframe=None, child_interframe=None):
+        # A ready to merge implementation of setting the planar_vectors and
+        # rotation_axis was added and removed in PR #24046
+        coordinates = (rotation_coordinate, planar_coordinates)
+        speeds = (rotation_speed, planar_speeds)
+        super().__init__(name, parent, child, coordinates, speeds,
+                         parent_point, child_point,
+                         parent_interframe=parent_interframe,
+                         child_interframe=child_interframe)
+
+    def __str__(self):
+        return (f'PlanarJoint: {self.name}  parent: {self.parent}  '
+                f'child: {self.child}')
+
+    @property
+    def rotation_coordinate(self):
+        """Generalized coordinate corresponding to the rotation angle."""
+        return self.coordinates[0]
+
+    @property
+    def planar_coordinates(self):
+        """Two generalized coordinates used for the planar translation."""
+        return self.coordinates[1:, 0]
+
+    @property
+    def rotation_speed(self):
+        """Generalized speed corresponding to the angular velocity."""
+        return self.speeds[0]
+
+    @property
+    def planar_speeds(self):
+        """Two generalized speeds used for the planar translation velocity."""
+        return self.speeds[1:, 0]
+
+    @property
+    def rotation_axis(self):
+        """The axis about which the rotation occurs."""
+        return self.parent_interframe.x
+
+    @property
+    def planar_vectors(self):
+        """The vectors that describe the planar translation directions."""
+        return [self.parent_interframe.y, self.parent_interframe.z]
+
+    def _generate_coordinates(self, coordinates):
+        rotation_speed = self._fill_coordinate_list(coordinates[0], 1, 'q',
+                                                    number_single=True)
+        planar_speeds = self._fill_coordinate_list(coordinates[1], 2, 'q', 1)
+        return rotation_speed.col_join(planar_speeds)
+
+    def _generate_speeds(self, speeds):
+        rotation_speed = self._fill_coordinate_list(speeds[0], 1, 'u',
+                                                    number_single=True)
+        planar_speeds = self._fill_coordinate_list(speeds[1], 2, 'u', 1)
+        return rotation_speed.col_join(planar_speeds)
+
+    def _orient_frames(self):
+        self.child_interframe.orient_axis(
+            self.parent_interframe, self.rotation_axis,
+            self.rotation_coordinate)
+
+    def _set_angular_velocity(self):
+        self.child_interframe.set_ang_vel(
+            self.parent_interframe,
+            self.rotation_speed * self.rotation_axis)
+
+    def _set_linear_velocity(self):
+        self.child_point.set_pos(
+            self.parent_point,
+            self.planar_coordinates[0] * self.planar_vectors[0] +
+            self.planar_coordinates[1] * self.planar_vectors[1])
+        self.parent_point.set_vel(self.parent_interframe, 0)
+        self.child_point.set_vel(self.child_interframe, 0)
+        self.child_point.set_vel(
+            self._parent_frame, self.planar_speeds[0] * self.planar_vectors[0] +
+            self.planar_speeds[1] * self.planar_vectors[1])
+        self.child.masscenter.v2pt_theory(self.child_point, self._parent_frame,
+                                          self._child_frame)
+
+
+class SphericalJoint(Joint):
+    """Spherical (Ball-and-Socket) Joint.
+
+    .. image:: SphericalJoint.svg
+        :align: center
+        :width: 600
+
+    Explanation
+    ===========
+
+    A spherical joint is defined such that the child body is free to rotate in
+    any direction, without allowing a translation of the ``child_point``. As can
+    also be seen in the image, the ``parent_point`` and ``child_point`` are
+    fixed on top of each other, i.e. the ``joint_point``. This rotation is
+    defined using the :func:`parent_interframe.orient(child_interframe,
+    rot_type, amounts, rot_order)
+    ` method. The default
+    rotation consists of three relative rotations, i.e. body-fixed rotations.
+    Based on the direction cosine matrix following from these rotations, the
+    angular velocity is computed based on the generalized coordinates and
+    generalized speeds.
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    coordinates: iterable of dynamicsymbols, optional
+        Generalized coordinates of the joint.
+    speeds : iterable of dynamicsymbols, optional
+        Generalized speeds of joint.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+    rot_type : str, optional
+        The method used to generate the direction cosine matrix. Supported
+        methods are:
+
+        - ``'Body'``: three successive rotations about new intermediate axes,
+          also called "Euler and Tait-Bryan angles"
+        - ``'Space'``: three successive rotations about the parent frames' unit
+          vectors
+
+        The default method is ``'Body'``.
+    amounts :
+        Expressions defining the rotation angles or direction cosine matrix.
+        These must match the ``rot_type``. See examples below for details. The
+        input types are:
+
+        - ``'Body'``: 3-tuple of expressions, symbols, or functions
+        - ``'Space'``: 3-tuple of expressions, symbols, or functions
+
+        The default amounts are the given ``coordinates``.
+    rot_order : str or int, optional
+        If applicable, the order of the successive of rotations. The string
+        ``'123'`` and integer ``123`` are equivalent, for example. Required for
+        ``'Body'`` and ``'Space'``. The default value is ``123``.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+
+    Examples
+    =========
+
+    A single spherical joint is created from two bodies and has the following
+    basic attributes:
+
+    >>> from sympy.physics.mechanics import RigidBody, SphericalJoint
+    >>> parent = RigidBody('P')
+    >>> parent
+    P
+    >>> child = RigidBody('C')
+    >>> child
+    C
+    >>> joint = SphericalJoint('PC', parent, child)
+    >>> joint
+    SphericalJoint: PC  parent: P  child: C
+    >>> joint.name
+    'PC'
+    >>> joint.parent
+    P
+    >>> joint.child
+    C
+    >>> joint.parent_point
+    P_masscenter
+    >>> joint.child_point
+    C_masscenter
+    >>> joint.parent_interframe
+    P_frame
+    >>> joint.child_interframe
+    C_frame
+    >>> joint.coordinates
+    Matrix([
+    [q0_PC(t)],
+    [q1_PC(t)],
+    [q2_PC(t)]])
+    >>> joint.speeds
+    Matrix([
+    [u0_PC(t)],
+    [u1_PC(t)],
+    [u2_PC(t)]])
+    >>> child.frame.ang_vel_in(parent.frame).to_matrix(child.frame)
+    Matrix([
+    [ u0_PC(t)*cos(q1_PC(t))*cos(q2_PC(t)) + u1_PC(t)*sin(q2_PC(t))],
+    [-u0_PC(t)*sin(q2_PC(t))*cos(q1_PC(t)) + u1_PC(t)*cos(q2_PC(t))],
+    [                             u0_PC(t)*sin(q1_PC(t)) + u2_PC(t)]])
+    >>> child.frame.x.to_matrix(parent.frame)
+    Matrix([
+    [                                            cos(q1_PC(t))*cos(q2_PC(t))],
+    [sin(q0_PC(t))*sin(q1_PC(t))*cos(q2_PC(t)) + sin(q2_PC(t))*cos(q0_PC(t))],
+    [sin(q0_PC(t))*sin(q2_PC(t)) - sin(q1_PC(t))*cos(q0_PC(t))*cos(q2_PC(t))]])
+    >>> joint.child_point.pos_from(joint.parent_point)
+    0
+
+    To further demonstrate the use of the spherical joint, the kinematics of a
+    spherical joint with a ZXZ rotation can be created as follows.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import RigidBody, SphericalJoint
+    >>> l1 = symbols('l1')
+
+    First create bodies to represent the fixed floor and a pendulum bob.
+
+    >>> floor = RigidBody('F')
+    >>> bob = RigidBody('B')
+
+    The joint will connect the bob to the floor, with the joint located at a
+    distance of ``l1`` from the child's center of mass and the rotation set to a
+    body-fixed ZXZ rotation.
+
+    >>> joint = SphericalJoint('S', floor, bob, child_point=l1 * bob.y,
+    ...                        rot_type='body', rot_order='ZXZ')
+
+    Now that the joint is established, the kinematics of the connected body can
+    be accessed.
+
+    The position of the bob's masscenter is found with:
+
+    >>> bob.masscenter.pos_from(floor.masscenter)
+    - l1*B_frame.y
+
+    The angular velocities of the pendulum link can be computed with respect to
+    the floor.
+
+    >>> bob.frame.ang_vel_in(floor.frame).to_matrix(
+    ...     floor.frame).simplify()
+    Matrix([
+    [u1_S(t)*cos(q0_S(t)) + u2_S(t)*sin(q0_S(t))*sin(q1_S(t))],
+    [u1_S(t)*sin(q0_S(t)) - u2_S(t)*sin(q1_S(t))*cos(q0_S(t))],
+    [                          u0_S(t) + u2_S(t)*cos(q1_S(t))]])
+
+    Finally, the linear velocity of the bob's center of mass can be computed.
+
+    >>> bob.masscenter.vel(floor.frame).to_matrix(bob.frame)
+    Matrix([
+    [                           l1*(u0_S(t)*cos(q1_S(t)) + u2_S(t))],
+    [                                                             0],
+    [-l1*(u0_S(t)*sin(q1_S(t))*sin(q2_S(t)) + u1_S(t)*cos(q2_S(t)))]])
+
+    """
+    def __init__(self, name, parent, child, coordinates=None, speeds=None,
+                 parent_point=None, child_point=None, parent_interframe=None,
+                 child_interframe=None, rot_type='BODY', amounts=None,
+                 rot_order=123):
+        self._rot_type = rot_type
+        self._amounts = amounts
+        self._rot_order = rot_order
+        super().__init__(name, parent, child, coordinates, speeds,
+                         parent_point, child_point,
+                         parent_interframe=parent_interframe,
+                         child_interframe=child_interframe)
+
+    def __str__(self):
+        return (f'SphericalJoint: {self.name}  parent: {self.parent}  '
+                f'child: {self.child}')
+
+    def _generate_coordinates(self, coordinates):
+        return self._fill_coordinate_list(coordinates, 3, 'q')
+
+    def _generate_speeds(self, speeds):
+        return self._fill_coordinate_list(speeds, len(self.coordinates), 'u')
+
+    def _orient_frames(self):
+        supported_rot_types = ('BODY', 'SPACE')
+        if self._rot_type.upper() not in supported_rot_types:
+            raise NotImplementedError(
+                f'Rotation type "{self._rot_type}" is not implemented. '
+                f'Implemented rotation types are: {supported_rot_types}')
+        amounts = self.coordinates if self._amounts is None else self._amounts
+        self.child_interframe.orient(self.parent_interframe, self._rot_type,
+                                     amounts, self._rot_order)
+
+    def _set_angular_velocity(self):
+        t = dynamicsymbols._t
+        vel = self.child_interframe.ang_vel_in(self.parent_interframe).xreplace(
+            {q.diff(t): u for q, u in zip(self.coordinates, self.speeds)}
+        )
+        self.child_interframe.set_ang_vel(self.parent_interframe, vel)
+
+    def _set_linear_velocity(self):
+        self.child_point.set_pos(self.parent_point, 0)
+        self.parent_point.set_vel(self._parent_frame, 0)
+        self.child_point.set_vel(self._child_frame, 0)
+        self.child.masscenter.v2pt_theory(self.parent_point, self._parent_frame,
+                                          self._child_frame)
+
+
+class WeldJoint(Joint):
+    """Weld Joint.
+
+    .. raw:: html
+        :file: ../../../doc/src/modules/physics/mechanics/api/WeldJoint.svg
+
+    Explanation
+    ===========
+
+    A weld joint is defined such that there is no relative motion between the
+    child and parent bodies. The direction cosine matrix between the attachment
+    frame (``parent_interframe`` and ``child_interframe``) is the identity
+    matrix and the attachment points (``parent_point`` and ``child_point``) are
+    coincident. The page on the joints framework gives a more detailed
+    explanation of the intermediate frames.
+
+    Parameters
+    ==========
+
+    name : string
+        A unique name for the joint.
+    parent : Particle or RigidBody
+        The parent body of joint.
+    child : Particle or RigidBody
+        The child body of joint.
+    parent_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the parent body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the parent's mass
+        center.
+    child_point : Point or Vector, optional
+        Attachment point where the joint is fixed to the child body. If a
+        vector is provided, then the attachment point is computed by adding the
+        vector to the body's mass center. The default value is the child's mass
+        center.
+    parent_interframe : ReferenceFrame, optional
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the parent's own frame.
+    child_interframe : ReferenceFrame, optional
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated. If a Vector is provided then an interframe
+        is created which aligns its X axis with the given vector. The default
+        value is the child's own frame.
+
+    Attributes
+    ==========
+
+    name : string
+        The joint's name.
+    parent : Particle or RigidBody
+        The joint's parent body.
+    child : Particle or RigidBody
+        The joint's child body.
+    coordinates : Matrix
+        Matrix of the joint's generalized coordinates. The default value is
+        ``dynamicsymbols(f'q_{joint.name}')``.
+    speeds : Matrix
+        Matrix of the joint's generalized speeds. The default value is
+        ``dynamicsymbols(f'u_{joint.name}')``.
+    parent_point : Point
+        Attachment point where the joint is fixed to the parent body.
+    child_point : Point
+        Attachment point where the joint is fixed to the child body.
+    parent_interframe : ReferenceFrame
+        Intermediate frame of the parent body with respect to which the joint
+        transformation is formulated.
+    child_interframe : ReferenceFrame
+        Intermediate frame of the child body with respect to which the joint
+        transformation is formulated.
+    kdes : Matrix
+        Kinematical differential equations of the joint.
+
+    Examples
+    =========
+
+    A single weld joint is created from two bodies and has the following basic
+    attributes:
+
+    >>> from sympy.physics.mechanics import RigidBody, WeldJoint
+    >>> parent = RigidBody('P')
+    >>> parent
+    P
+    >>> child = RigidBody('C')
+    >>> child
+    C
+    >>> joint = WeldJoint('PC', parent, child)
+    >>> joint
+    WeldJoint: PC  parent: P  child: C
+    >>> joint.name
+    'PC'
+    >>> joint.parent
+    P
+    >>> joint.child
+    C
+    >>> joint.parent_point
+    P_masscenter
+    >>> joint.child_point
+    C_masscenter
+    >>> joint.coordinates
+    Matrix(0, 0, [])
+    >>> joint.speeds
+    Matrix(0, 0, [])
+    >>> child.frame.ang_vel_in(parent.frame)
+    0
+    >>> child.frame.dcm(parent.frame)
+    Matrix([
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1]])
+    >>> joint.child_point.pos_from(joint.parent_point)
+    0
+
+    To further demonstrate the use of the weld joint, two relatively-fixed
+    bodies rotated by a quarter turn about the Y axis can be created as follows:
+
+    >>> from sympy import symbols, pi
+    >>> from sympy.physics.mechanics import ReferenceFrame, RigidBody, WeldJoint
+    >>> l1, l2 = symbols('l1 l2')
+
+    First create the bodies to represent the parent and rotated child body.
+
+    >>> parent = RigidBody('P')
+    >>> child = RigidBody('C')
+
+    Next the intermediate frame specifying the fixed rotation with respect to
+    the parent can be created.
+
+    >>> rotated_frame = ReferenceFrame('Pr')
+    >>> rotated_frame.orient_axis(parent.frame, parent.y, pi / 2)
+
+    The weld between the parent body and child body is located at a distance
+    ``l1`` from the parent's center of mass in the X direction and ``l2`` from
+    the child's center of mass in the child's negative X direction.
+
+    >>> weld = WeldJoint('weld', parent, child, parent_point=l1 * parent.x,
+    ...                  child_point=-l2 * child.x,
+    ...                  parent_interframe=rotated_frame)
+
+    Now that the joint has been established, the kinematics of the bodies can be
+    accessed. The direction cosine matrix of the child body with respect to the
+    parent can be found:
+
+    >>> child.frame.dcm(parent.frame)
+    Matrix([
+    [0, 0, -1],
+    [0, 1,  0],
+    [1, 0,  0]])
+
+    As can also been seen from the direction cosine matrix, the parent X axis is
+    aligned with the child's Z axis:
+    >>> parent.x == child.z
+    True
+
+    The position of the child's center of mass with respect to the parent's
+    center of mass can be found with:
+
+    >>> child.masscenter.pos_from(parent.masscenter)
+    l1*P_frame.x + l2*C_frame.x
+
+    The angular velocity of the child with respect to the parent is 0 as one
+    would expect.
+
+    >>> child.frame.ang_vel_in(parent.frame)
+    0
+
+    """
+
+    def __init__(self, name, parent, child, parent_point=None, child_point=None,
+                 parent_interframe=None, child_interframe=None):
+        super().__init__(name, parent, child, [], [], parent_point,
+                         child_point, parent_interframe=parent_interframe,
+                         child_interframe=child_interframe)
+        self._kdes = Matrix(1, 0, []).T  # Removes stackability problems #10770
+
+    def __str__(self):
+        return (f'WeldJoint: {self.name}  parent: {self.parent}  '
+                f'child: {self.child}')
+
+    def _generate_coordinates(self, coordinate):
+        return Matrix()
+
+    def _generate_speeds(self, speed):
+        return Matrix()
+
+    def _orient_frames(self):
+        self.child_interframe.orient_axis(self.parent_interframe,
+                                          self.parent_interframe.x, 0)
+
+    def _set_angular_velocity(self):
+        self.child_interframe.set_ang_vel(self.parent_interframe, 0)
+
+    def _set_linear_velocity(self):
+        self.child_point.set_pos(self.parent_point, 0)
+        self.parent_point.set_vel(self._parent_frame, 0)
+        self.child_point.set_vel(self._child_frame, 0)
+        self.child.masscenter.set_vel(self._parent_frame, 0)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/jointsmethod.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/jointsmethod.py
new file mode 100644
index 0000000000000000000000000000000000000000..df7bd56360072feb57a65e5f78c2d116f0d4842d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/jointsmethod.py
@@ -0,0 +1,318 @@
+from sympy.physics.mechanics import (Body, Lagrangian, KanesMethod, LagrangesMethod,
+                                    RigidBody, Particle)
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.physics.mechanics.method import _Methods
+from sympy import Matrix
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+__all__ = ['JointsMethod']
+
+
+class JointsMethod(_Methods):
+    """Method for formulating the equations of motion using a set of interconnected bodies with joints.
+
+    .. deprecated:: 1.13
+        The JointsMethod class is deprecated. Its functionality has been
+        replaced by the new :class:`~.System` class.
+
+    Parameters
+    ==========
+
+    newtonion : Body or ReferenceFrame
+        The newtonion(inertial) frame.
+    *joints : Joint
+        The joints in the system
+
+    Attributes
+    ==========
+
+    q, u : iterable
+        Iterable of the generalized coordinates and speeds
+    bodies : iterable
+        Iterable of Body objects in the system.
+    loads : iterable
+        Iterable of (Point, vector) or (ReferenceFrame, vector) tuples
+        describing the forces on the system.
+    mass_matrix : Matrix, shape(n, n)
+        The system's mass matrix
+    forcing : Matrix, shape(n, 1)
+        The system's forcing vector
+    mass_matrix_full : Matrix, shape(2*n, 2*n)
+        The "mass matrix" for the u's and q's
+    forcing_full : Matrix, shape(2*n, 1)
+        The "forcing vector" for the u's and q's
+    method : KanesMethod or Lagrange's method
+        Method's object.
+    kdes : iterable
+        Iterable of kde in they system.
+
+    Examples
+    ========
+
+    As Body and JointsMethod have been deprecated, the following examples are
+    for illustrative purposes only. The functionality of Body is fully captured
+    by :class:`~.RigidBody` and :class:`~.Particle` and the functionality of
+    JointsMethod is fully captured by :class:`~.System`. To ignore the
+    deprecation warning we can use the ignore_warnings context manager.
+
+    >>> from sympy.utilities.exceptions import ignore_warnings
+
+    This is a simple example for a one degree of freedom translational
+    spring-mass-damper.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import Body, JointsMethod, PrismaticJoint
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> c, k = symbols('c k')
+    >>> x, v = dynamicsymbols('x v')
+    >>> with ignore_warnings(DeprecationWarning):
+    ...     wall = Body('W')
+    ...     body = Body('B')
+    >>> J = PrismaticJoint('J', wall, body, coordinates=x, speeds=v)
+    >>> wall.apply_force(c*v*wall.x, reaction_body=body)
+    >>> wall.apply_force(k*x*wall.x, reaction_body=body)
+    >>> with ignore_warnings(DeprecationWarning):
+    ...     method = JointsMethod(wall, J)
+    >>> method.form_eoms()
+    Matrix([[-B_mass*Derivative(v(t), t) - c*v(t) - k*x(t)]])
+    >>> M = method.mass_matrix_full
+    >>> F = method.forcing_full
+    >>> rhs = M.LUsolve(F)
+    >>> rhs
+    Matrix([
+    [                     v(t)],
+    [(-c*v(t) - k*x(t))/B_mass]])
+
+    Notes
+    =====
+
+    ``JointsMethod`` currently only works with systems that do not have any
+    configuration or motion constraints.
+
+    """
+
+    def __init__(self, newtonion, *joints):
+        sympy_deprecation_warning(
+            """
+            The JointsMethod class is deprecated.
+            Its functionality has been replaced by the new System class.
+            """,
+            deprecated_since_version="1.13",
+            active_deprecations_target="deprecated-mechanics-jointsmethod"
+        )
+        if isinstance(newtonion, BodyBase):
+            self.frame = newtonion.frame
+        else:
+            self.frame = newtonion
+
+        self._joints = joints
+        self._bodies = self._generate_bodylist()
+        self._loads = self._generate_loadlist()
+        self._q = self._generate_q()
+        self._u = self._generate_u()
+        self._kdes = self._generate_kdes()
+
+        self._method = None
+
+    @property
+    def bodies(self):
+        """List of bodies in they system."""
+        return self._bodies
+
+    @property
+    def loads(self):
+        """List of loads on the system."""
+        return self._loads
+
+    @property
+    def q(self):
+        """List of the generalized coordinates."""
+        return self._q
+
+    @property
+    def u(self):
+        """List of the generalized speeds."""
+        return self._u
+
+    @property
+    def kdes(self):
+        """List of the generalized coordinates."""
+        return self._kdes
+
+    @property
+    def forcing_full(self):
+        """The "forcing vector" for the u's and q's."""
+        return self.method.forcing_full
+
+    @property
+    def mass_matrix_full(self):
+        """The "mass matrix" for the u's and q's."""
+        return self.method.mass_matrix_full
+
+    @property
+    def mass_matrix(self):
+        """The system's mass matrix."""
+        return self.method.mass_matrix
+
+    @property
+    def forcing(self):
+        """The system's forcing vector."""
+        return self.method.forcing
+
+    @property
+    def method(self):
+        """Object of method used to form equations of systems."""
+        return self._method
+
+    def _generate_bodylist(self):
+        bodies = []
+        for joint in self._joints:
+            if joint.child not in bodies:
+                bodies.append(joint.child)
+            if joint.parent not in bodies:
+                bodies.append(joint.parent)
+        return bodies
+
+    def _generate_loadlist(self):
+        load_list = []
+        for body in self.bodies:
+            if isinstance(body, Body):
+                load_list.extend(body.loads)
+        return load_list
+
+    def _generate_q(self):
+        q_ind = []
+        for joint in self._joints:
+            for coordinate in joint.coordinates:
+                if coordinate in q_ind:
+                    raise ValueError('Coordinates of joints should be unique.')
+                q_ind.append(coordinate)
+        return Matrix(q_ind)
+
+    def _generate_u(self):
+        u_ind = []
+        for joint in self._joints:
+            for speed in joint.speeds:
+                if speed in u_ind:
+                    raise ValueError('Speeds of joints should be unique.')
+                u_ind.append(speed)
+        return Matrix(u_ind)
+
+    def _generate_kdes(self):
+        kd_ind = Matrix(1, 0, []).T
+        for joint in self._joints:
+            kd_ind = kd_ind.col_join(joint.kdes)
+        return kd_ind
+
+    def _convert_bodies(self):
+        # Convert `Body` to `Particle` and `RigidBody`
+        bodylist = []
+        for body in self.bodies:
+            if not isinstance(body, Body):
+                bodylist.append(body)
+                continue
+            if body.is_rigidbody:
+                rb = RigidBody(body.name, body.masscenter, body.frame, body.mass,
+                    (body.central_inertia, body.masscenter))
+                rb.potential_energy = body.potential_energy
+                bodylist.append(rb)
+            else:
+                part = Particle(body.name, body.masscenter, body.mass)
+                part.potential_energy = body.potential_energy
+                bodylist.append(part)
+        return bodylist
+
+    def form_eoms(self, method=KanesMethod):
+        """Method to form system's equation of motions.
+
+        Parameters
+        ==========
+
+        method : Class
+            Class name of method.
+
+        Returns
+        ========
+
+        Matrix
+            Vector of equations of motions.
+
+        Examples
+        ========
+
+        As Body and JointsMethod have been deprecated, the following examples
+        are for illustrative purposes only. The functionality of Body is fully
+        captured by :class:`~.RigidBody` and :class:`~.Particle` and the
+        functionality of JointsMethod is fully captured by :class:`~.System`. To
+        ignore the deprecation warning we can use the ignore_warnings context
+        manager.
+
+        >>> from sympy.utilities.exceptions import ignore_warnings
+
+        This is a simple example for a one degree of freedom translational
+        spring-mass-damper.
+
+        >>> from sympy import S, symbols
+        >>> from sympy.physics.mechanics import LagrangesMethod, dynamicsymbols, Body
+        >>> from sympy.physics.mechanics import PrismaticJoint, JointsMethod
+        >>> q = dynamicsymbols('q')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> m, k, b = symbols('m k b')
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     wall = Body('W')
+        ...     part = Body('P', mass=m)
+        >>> part.potential_energy = k * q**2 / S(2)
+        >>> J = PrismaticJoint('J', wall, part, coordinates=q, speeds=qd)
+        >>> wall.apply_force(b * qd * wall.x, reaction_body=part)
+        >>> with ignore_warnings(DeprecationWarning):
+        ...     method = JointsMethod(wall, J)
+        >>> method.form_eoms(LagrangesMethod)
+        Matrix([[b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]])
+
+        We can also solve for the states using the 'rhs' method.
+
+        >>> method.rhs()
+        Matrix([
+        [                Derivative(q(t), t)],
+        [(-b*Derivative(q(t), t) - k*q(t))/m]])
+
+        """
+
+        bodylist = self._convert_bodies()
+        if issubclass(method, LagrangesMethod): #LagrangesMethod or similar
+            L = Lagrangian(self.frame, *bodylist)
+            self._method = method(L, self.q, self.loads, bodylist, self.frame)
+        else: #KanesMethod or similar
+            self._method = method(self.frame, q_ind=self.q, u_ind=self.u, kd_eqs=self.kdes,
+                                    forcelist=self.loads, bodies=bodylist)
+        soln = self.method._form_eoms()
+        return soln
+
+    def rhs(self, inv_method=None):
+        """Returns equations that can be solved numerically.
+
+        Parameters
+        ==========
+
+        inv_method : str
+            The specific sympy inverse matrix calculation method to use. For a
+            list of valid methods, see
+            :meth:`~sympy.matrices.matrixbase.MatrixBase.inv`
+
+        Returns
+        ========
+
+        Matrix
+            Numerically solvable equations.
+
+        See Also
+        ========
+
+        sympy.physics.mechanics.kane.KanesMethod.rhs:
+            KanesMethod's rhs function.
+        sympy.physics.mechanics.lagrange.LagrangesMethod.rhs:
+            LagrangesMethod's rhs function.
+
+        """
+
+        return self.method.rhs(inv_method=inv_method)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/kane.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/kane.py
new file mode 100644
index 0000000000000000000000000000000000000000..805587a4fe9d7696f45c5815ee5406b103150698
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/kane.py
@@ -0,0 +1,859 @@
+from sympy import zeros, Matrix, diff, eye, linear_eq_to_matrix
+from sympy.core.sorting import default_sort_key
+from sympy.physics.vector import (ReferenceFrame, dynamicsymbols,
+                                  partial_velocity)
+from sympy.physics.mechanics.method import _Methods
+from sympy.physics.mechanics.particle import Particle
+from sympy.physics.mechanics.rigidbody import RigidBody
+from sympy.physics.mechanics.functions import (msubs, find_dynamicsymbols,
+                                               _f_list_parser,
+                                               _validate_coordinates,
+                                               _parse_linear_solver)
+from sympy.physics.mechanics.linearize import Linearizer
+from sympy.utilities.iterables import iterable
+
+
+__all__ = ['KanesMethod']
+
+
+class KanesMethod(_Methods):
+    r"""Kane's method object.
+
+    Explanation
+    ===========
+
+    This object is used to do the "book-keeping" as you go through and form
+    equations of motion in the way Kane presents in:
+    Kane, T., Levinson, D. Dynamics Theory and Applications. 1985 McGraw-Hill
+
+    The attributes are for equations in the form [M] udot = forcing.
+
+    Attributes
+    ==========
+
+    q, u : Matrix
+        Matrices of the generalized coordinates and speeds
+    bodies : iterable
+        Iterable of Particle and RigidBody objects in the system.
+    loads : iterable
+        Iterable of (Point, vector) or (ReferenceFrame, vector) tuples
+        describing the forces on the system.
+    auxiliary_eqs : Matrix
+        If applicable, the set of auxiliary Kane's
+        equations used to solve for non-contributing
+        forces.
+    mass_matrix : Matrix
+        The system's dynamics mass matrix: [k_d; k_dnh]
+    forcing : Matrix
+        The system's dynamics forcing vector: -[f_d; f_dnh]
+    mass_matrix_kin : Matrix
+        The "mass matrix" for kinematic differential equations: k_kqdot
+    forcing_kin : Matrix
+        The forcing vector for kinematic differential equations: -(k_ku*u + f_k)
+    mass_matrix_full : Matrix
+        The "mass matrix" for the u's and q's with dynamics and kinematics
+    forcing_full : Matrix
+        The "forcing vector" for the u's and q's with dynamics and kinematics
+
+    Parameters
+    ==========
+
+    frame : ReferenceFrame
+        The inertial reference frame for the system.
+    q_ind : iterable of dynamicsymbols
+        Independent generalized coordinates.
+    u_ind : iterable of dynamicsymbols
+        Independent generalized speeds.
+    kd_eqs : iterable of Expr, optional
+        Kinematic differential equations, which linearly relate the generalized
+        speeds to the time-derivatives of the generalized coordinates.
+    q_dependent : iterable of dynamicsymbols, optional
+        Dependent generalized coordinates.
+    configuration_constraints : iterable of Expr, optional
+        Constraints on the system's configuration, i.e. holonomic constraints.
+    u_dependent : iterable of dynamicsymbols, optional
+        Dependent generalized speeds.
+    velocity_constraints : iterable of Expr, optional
+        Constraints on the system's velocity, i.e. the combination of the
+        nonholonomic constraints and the time-derivative of the holonomic
+        constraints.
+    acceleration_constraints : iterable of Expr, optional
+        Constraints on the system's acceleration, by default these are the
+        time-derivative of the velocity constraints.
+    u_auxiliary : iterable of dynamicsymbols, optional
+        Auxiliary generalized speeds.
+    bodies : iterable of Particle and/or RigidBody, optional
+        The particles and rigid bodies in the system.
+    forcelist : iterable of tuple[Point | ReferenceFrame, Vector], optional
+        Forces and torques applied on the system.
+    explicit_kinematics : bool
+        Boolean whether the mass matrices and forcing vectors should use the
+        explicit form (default) or implicit form for kinematics.
+        See the notes for more details.
+    kd_eqs_solver : str, callable
+        Method used to solve the kinematic differential equations. If a string
+        is supplied, it should be a valid method that can be used with the
+        :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+        supplied, it should have the format ``f(A, rhs)``, where it solves the
+        equations and returns the solution. The default utilizes LU solve. See
+        the notes for more information.
+    constraint_solver : str, callable
+        Method used to solve the velocity constraints. If a string is
+        supplied, it should be a valid method that can be used with the
+        :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+        supplied, it should have the format ``f(A, rhs)``, where it solves the
+        equations and returns the solution. The default utilizes LU solve. See
+        the notes for more information.
+
+    Notes
+    =====
+
+    The mass matrices and forcing vectors related to kinematic equations
+    are given in the explicit form by default. In other words, the kinematic
+    mass matrix is $\mathbf{k_{k\dot{q}}} = \mathbf{I}$.
+    In order to get the implicit form of those matrices/vectors, you can set the
+    ``explicit_kinematics`` attribute to ``False``. So $\mathbf{k_{k\dot{q}}}$
+    is not necessarily an identity matrix. This can provide more compact
+    equations for non-simple kinematics.
+
+    Two linear solvers can be supplied to ``KanesMethod``: one for solving the
+    kinematic differential equations and one to solve the velocity constraints.
+    Both of these sets of equations can be expressed as a linear system ``Ax = rhs``,
+    which have to be solved in order to obtain the equations of motion.
+
+    The default solver ``'LU'``, which stands for LU solve, results relatively low
+    number of operations. The weakness of this method is that it can result in zero
+    division errors.
+
+    If zero divisions are encountered, a possible solver which may solve the problem
+    is ``"CRAMER"``. This method uses Cramer's rule to solve the system. This method
+    is slower and results in more operations than the default solver. However it only
+    uses a single division by default per entry of the solution.
+
+    While a valid list of solvers can be found at
+    :meth:`sympy.matrices.matrixbase.MatrixBase.solve`, it is also possible to supply a
+    `callable`. This way it is possible to use a different solver routine. If the
+    kinematic differential equations are not too complex it can be worth it to simplify
+    the solution by using ``lambda A, b: simplify(Matrix.LUsolve(A, b))``. Another
+    option solver one may use is :func:`sympy.solvers.solveset.linsolve`. This can be
+    done using `lambda A, b: tuple(linsolve((A, b)))[0]`, where we select the first
+    solution as our system should have only one unique solution.
+
+    Examples
+    ========
+
+    This is a simple example for a one degree of freedom translational
+    spring-mass-damper.
+
+    In this example, we first need to do the kinematics.
+    This involves creating generalized speeds and coordinates and their
+    derivatives.
+    Then we create a point and set its velocity in a frame.
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import dynamicsymbols, ReferenceFrame
+        >>> from sympy.physics.mechanics import Point, Particle, KanesMethod
+        >>> q, u = dynamicsymbols('q u')
+        >>> qd, ud = dynamicsymbols('q u', 1)
+        >>> m, c, k = symbols('m c k')
+        >>> N = ReferenceFrame('N')
+        >>> P = Point('P')
+        >>> P.set_vel(N, u * N.x)
+
+    Next we need to arrange/store information in the way that KanesMethod
+    requires. The kinematic differential equations should be an iterable of
+    expressions. A list of forces/torques must be constructed, where each entry
+    in the list is a (Point, Vector) or (ReferenceFrame, Vector) tuple, where
+    the Vectors represent the Force or Torque.
+    Next a particle needs to be created, and it needs to have a point and mass
+    assigned to it.
+    Finally, a list of all bodies and particles needs to be created.
+
+        >>> kd = [qd - u]
+        >>> FL = [(P, (-k * q - c * u) * N.x)]
+        >>> pa = Particle('pa', P, m)
+        >>> BL = [pa]
+
+    Finally we can generate the equations of motion.
+    First we create the KanesMethod object and supply an inertial frame,
+    coordinates, generalized speeds, and the kinematic differential equations.
+    Additional quantities such as configuration and motion constraints,
+    dependent coordinates and speeds, and auxiliary speeds are also supplied
+    here (see the online documentation).
+    Next we form FR* and FR to complete: Fr + Fr* = 0.
+    We have the equations of motion at this point.
+    It makes sense to rearrange them though, so we calculate the mass matrix and
+    the forcing terms, for E.o.M. in the form: [MM] udot = forcing, where MM is
+    the mass matrix, udot is a vector of the time derivatives of the
+    generalized speeds, and forcing is a vector representing "forcing" terms.
+
+        >>> KM = KanesMethod(N, q_ind=[q], u_ind=[u], kd_eqs=kd)
+        >>> (fr, frstar) = KM.kanes_equations(BL, FL)
+        >>> MM = KM.mass_matrix
+        >>> forcing = KM.forcing
+        >>> rhs = MM.inv() * forcing
+        >>> rhs
+        Matrix([[(-c*u(t) - k*q(t))/m]])
+        >>> KM.linearize(A_and_B=True)[0]
+        Matrix([
+        [   0,    1],
+        [-k/m, -c/m]])
+
+    Please look at the documentation pages for more information on how to
+    perform linearization and how to deal with dependent coordinates & speeds,
+    and how do deal with bringing non-contributing forces into evidence.
+
+    """
+
+    def __init__(self, frame, q_ind, u_ind, kd_eqs=None, q_dependent=None,
+                 configuration_constraints=None, u_dependent=None,
+                 velocity_constraints=None, acceleration_constraints=None,
+                 u_auxiliary=None, bodies=None, forcelist=None,
+                 explicit_kinematics=True, kd_eqs_solver='LU',
+                 constraint_solver='LU'):
+
+        """Please read the online documentation. """
+        if not q_ind:
+            q_ind = [dynamicsymbols('dummy_q')]
+            kd_eqs = [dynamicsymbols('dummy_kd')]
+
+        if not isinstance(frame, ReferenceFrame):
+            raise TypeError('An inertial ReferenceFrame must be supplied')
+        self._inertial = frame
+
+        self._fr = None
+        self._frstar = None
+
+        self._forcelist = forcelist
+        self._bodylist = bodies
+
+        self.explicit_kinematics = explicit_kinematics
+        self._constraint_solver = constraint_solver
+        self._initialize_vectors(q_ind, q_dependent, u_ind, u_dependent,
+                u_auxiliary)
+        _validate_coordinates(self.q, self.u)
+        self._initialize_kindiffeq_matrices(kd_eqs, kd_eqs_solver)
+        self._initialize_constraint_matrices(
+            configuration_constraints, velocity_constraints,
+            acceleration_constraints, constraint_solver)
+
+    def _initialize_vectors(self, q_ind, q_dep, u_ind, u_dep, u_aux):
+        """Initialize the coordinate and speed vectors."""
+
+        none_handler = lambda x: Matrix(x) if x else Matrix()
+
+        # Initialize generalized coordinates
+        q_dep = none_handler(q_dep)
+        if not iterable(q_ind):
+            raise TypeError('Generalized coordinates must be an iterable.')
+        if not iterable(q_dep):
+            raise TypeError('Dependent coordinates must be an iterable.')
+        q_ind = Matrix(q_ind)
+        self._qdep = q_dep
+        self._q = Matrix([q_ind, q_dep])
+        self._qdot = self.q.diff(dynamicsymbols._t)
+
+        # Initialize generalized speeds
+        u_dep = none_handler(u_dep)
+        if not iterable(u_ind):
+            raise TypeError('Generalized speeds must be an iterable.')
+        if not iterable(u_dep):
+            raise TypeError('Dependent speeds must be an iterable.')
+        u_ind = Matrix(u_ind)
+        self._udep = u_dep
+        self._u = Matrix([u_ind, u_dep])
+        self._udot = self.u.diff(dynamicsymbols._t)
+        self._uaux = none_handler(u_aux)
+
+    def _initialize_constraint_matrices(self, config, vel, acc, linear_solver='LU'):
+        """Initializes constraint matrices."""
+        linear_solver = _parse_linear_solver(linear_solver)
+        # Define vector dimensions
+        o = len(self.u)
+        m = len(self._udep)
+        p = o - m
+        none_handler = lambda x: Matrix(x) if x else Matrix()
+
+        # Initialize configuration constraints
+        config = none_handler(config)
+        if len(self._qdep) != len(config):
+            raise ValueError('There must be an equal number of dependent '
+                             'coordinates and configuration constraints.')
+        self._f_h = none_handler(config)
+
+        # Initialize velocity and acceleration constraints
+        vel = none_handler(vel)
+        acc = none_handler(acc)
+        if len(vel) != m:
+            raise ValueError('There must be an equal number of dependent '
+                             'speeds and velocity constraints.')
+        if acc and (len(acc) != m):
+            raise ValueError('There must be an equal number of dependent '
+                             'speeds and acceleration constraints.')
+        if vel:
+
+            # When calling kanes_equations, another class instance will be
+            # created if auxiliary u's are present. In this case, the
+            # computation of kinetic differential equation matrices will be
+            # skipped as this was computed during the original KanesMethod
+            # object, and the qd_u_map will not be available.
+            if self._qdot_u_map is not None:
+                vel = msubs(vel, self._qdot_u_map)
+            self._k_nh, f_nh_neg = linear_eq_to_matrix(vel, self.u[:])
+            self._f_nh = -f_nh_neg
+
+            # If no acceleration constraints given, calculate them.
+            if not acc:
+                _f_dnh = (self._k_nh.diff(dynamicsymbols._t) * self.u +
+                    self._f_nh.diff(dynamicsymbols._t))
+                if self._qdot_u_map is not None:
+                    _f_dnh = msubs(_f_dnh, self._qdot_u_map)
+                self._f_dnh = _f_dnh
+                self._k_dnh = self._k_nh
+            else:
+                if self._qdot_u_map is not None:
+                    acc = msubs(acc, self._qdot_u_map)
+
+                self._k_dnh, f_dnh_neg = linear_eq_to_matrix(acc, self._udot[:])
+                self._f_dnh = -f_dnh_neg
+            # Form of non-holonomic constraints is B*u + C = 0.
+            # We partition B into independent and dependent columns:
+            # Ars is then -B_dep.inv() * B_ind, and it relates dependent speeds
+            # to independent speeds as: udep = Ars*uind, neglecting the C term.
+            B_ind = self._k_nh[:, :p]
+            B_dep = self._k_nh[:, p:o]
+            self._Ars = -linear_solver(B_dep, B_ind)
+        else:
+            self._f_nh = Matrix()
+            self._k_nh = Matrix()
+            self._f_dnh = Matrix()
+            self._k_dnh = Matrix()
+            self._Ars = Matrix()
+
+    def _initialize_kindiffeq_matrices(self, kdeqs, linear_solver='LU'):
+        """Initialize the kinematic differential equation matrices.
+
+        Parameters
+        ==========
+        kdeqs : sequence of sympy expressions
+            Kinematic differential equations in the form of f(u,q',q,t) where
+            f() = 0. The equations have to be linear in the time-derivatives of
+            the generalized coordinates and in the generalized speeds.
+
+        """
+        linear_solver = _parse_linear_solver(linear_solver)
+        if kdeqs:
+            if len(self.q) != len(kdeqs):
+                raise ValueError('There must be an equal number of kinematic '
+                                 'differential equations and coordinates.')
+
+            u = self.u
+            qdot = self._qdot
+
+            kdeqs = Matrix(kdeqs)
+
+            u_zero = dict.fromkeys(u, 0)
+            uaux_zero = dict.fromkeys(self._uaux, 0)
+            qdot_zero = dict.fromkeys(qdot, 0)
+
+            # Extract the linear coefficient matrices as per the following
+            # equation:
+            #
+            # k_ku(q,t)*u(t) + k_kqdot(q,t)*q'(t) + f_k(q,t) = 0
+            #
+            k_ku = kdeqs.jacobian(u)
+            k_kqdot = kdeqs.jacobian(qdot)
+            f_k = kdeqs.xreplace(u_zero).xreplace(qdot_zero)
+
+            # The kinematic differential equations should be linear in both q'
+            # and u so check for u and q' in the components.
+            dy_syms = find_dynamicsymbols(k_ku.row_join(k_kqdot).row_join(f_k))
+            nonlin_vars = [vari for vari in u[:] + qdot[:] if vari in dy_syms]
+            if nonlin_vars:
+                msg = ('The provided kinematic differential equations are '
+                       'nonlinear in {}. They must be linear in the '
+                       'generalized speeds and derivatives of the generalized '
+                       'coordinates.')
+                raise ValueError(msg.format(nonlin_vars))
+
+            self._f_k_implicit = f_k.xreplace(uaux_zero)
+            self._k_ku_implicit = k_ku.xreplace(uaux_zero)
+            self._k_kqdot_implicit = k_kqdot
+
+            # Solve for q'(t) such that the coefficient matrices are now in
+            # this form:
+            #
+            # k_kqdot^-1*k_ku*u(t) + I*q'(t) + k_kqdot^-1*f_k = 0
+            #
+            # NOTE : Solving the kinematic differential equations here is not
+            # necessary and prevents the equations from being provided in fully
+            # implicit form.
+            f_k_explicit = linear_solver(k_kqdot, f_k)
+            k_ku_explicit = linear_solver(k_kqdot, k_ku)
+            self._qdot_u_map = dict(zip(qdot, -(k_ku_explicit*u + f_k_explicit)))
+
+            self._f_k = f_k_explicit.xreplace(uaux_zero)
+            self._k_ku = k_ku_explicit.xreplace(uaux_zero)
+            self._k_kqdot = eye(len(qdot))
+
+        else:
+            self._qdot_u_map = None
+            self._f_k_implicit = self._f_k = Matrix()
+            self._k_ku_implicit = self._k_ku = Matrix()
+            self._k_kqdot_implicit = self._k_kqdot = Matrix()
+
+    def _form_fr(self, fl):
+        """Form the generalized active force."""
+        if fl is not None and (len(fl) == 0 or not iterable(fl)):
+            raise ValueError('Force pairs must be supplied in an '
+                'non-empty iterable or None.')
+
+        N = self._inertial
+        # pull out relevant velocities for constructing partial velocities
+        vel_list, f_list = _f_list_parser(fl, N)
+        vel_list = [msubs(i, self._qdot_u_map) for i in vel_list]
+        f_list = [msubs(i, self._qdot_u_map) for i in f_list]
+
+        # Fill Fr with dot product of partial velocities and forces
+        o = len(self.u)
+        b = len(f_list)
+        FR = zeros(o, 1)
+        partials = partial_velocity(vel_list, self.u, N)
+        for i in range(o):
+            FR[i] = sum(partials[j][i].dot(f_list[j]) for j in range(b))
+
+        # In case there are dependent speeds
+        if self._udep:
+            p = o - len(self._udep)
+            FRtilde = FR[:p, 0]
+            FRold = FR[p:o, 0]
+            FRtilde += self._Ars.T * FRold
+            FR = FRtilde
+
+        self._forcelist = fl
+        self._fr = FR
+        return FR
+
+    def _form_frstar(self, bl):
+        """Form the generalized inertia force."""
+
+        if not iterable(bl):
+            raise TypeError('Bodies must be supplied in an iterable.')
+
+        t = dynamicsymbols._t
+        N = self._inertial
+        # Dicts setting things to zero
+        udot_zero = dict.fromkeys(self._udot, 0)
+        uaux_zero = dict.fromkeys(self._uaux, 0)
+        uauxdot = [diff(i, t) for i in self._uaux]
+        uauxdot_zero = dict.fromkeys(uauxdot, 0)
+        # Dictionary of q' and q'' to u and u'
+        q_ddot_u_map = {k.diff(t): v.diff(t).xreplace(
+            self._qdot_u_map) for (k, v) in self._qdot_u_map.items()}
+        q_ddot_u_map.update(self._qdot_u_map)
+
+        # Fill up the list of partials: format is a list with num elements
+        # equal to number of entries in body list. Each of these elements is a
+        # list - either of length 1 for the translational components of
+        # particles or of length 2 for the translational and rotational
+        # components of rigid bodies. The inner most list is the list of
+        # partial velocities.
+        def get_partial_velocity(body):
+            if isinstance(body, RigidBody):
+                vlist = [body.masscenter.vel(N), body.frame.ang_vel_in(N)]
+            elif isinstance(body, Particle):
+                vlist = [body.point.vel(N),]
+            else:
+                raise TypeError('The body list may only contain either '
+                                'RigidBody or Particle as list elements.')
+            v = [msubs(vel, self._qdot_u_map) for vel in vlist]
+            return partial_velocity(v, self.u, N)
+        partials = [get_partial_velocity(body) for body in bl]
+
+        # Compute fr_star in two components:
+        # fr_star = -(MM*u' + nonMM)
+        o = len(self.u)
+        MM = zeros(o, o)
+        nonMM = zeros(o, 1)
+        zero_uaux = lambda expr: msubs(expr, uaux_zero)
+        zero_udot_uaux = lambda expr: msubs(msubs(expr, udot_zero), uaux_zero)
+        for i, body in enumerate(bl):
+            if isinstance(body, RigidBody):
+                M = zero_uaux(body.mass)
+                I = zero_uaux(body.central_inertia)
+                vel = zero_uaux(body.masscenter.vel(N))
+                omega = zero_uaux(body.frame.ang_vel_in(N))
+                acc = zero_udot_uaux(body.masscenter.acc(N))
+                inertial_force = (M.diff(t) * vel + M * acc)
+                inertial_torque = zero_uaux((I.dt(body.frame).dot(omega)) +
+                    msubs(I.dot(body.frame.ang_acc_in(N)), udot_zero) +
+                    (omega.cross(I.dot(omega))))
+                for j in range(o):
+                    tmp_vel = zero_uaux(partials[i][0][j])
+                    tmp_ang = zero_uaux(I.dot(partials[i][1][j]))
+                    for k in range(o):
+                        # translational
+                        MM[j, k] += M*tmp_vel.dot(partials[i][0][k])
+                        # rotational
+                        MM[j, k] += tmp_ang.dot(partials[i][1][k])
+                    nonMM[j] += inertial_force.dot(partials[i][0][j])
+                    nonMM[j] += inertial_torque.dot(partials[i][1][j])
+            else:
+                M = zero_uaux(body.mass)
+                vel = zero_uaux(body.point.vel(N))
+                acc = zero_udot_uaux(body.point.acc(N))
+                inertial_force = (M.diff(t) * vel + M * acc)
+                for j in range(o):
+                    temp = zero_uaux(partials[i][0][j])
+                    for k in range(o):
+                        MM[j, k] += M*temp.dot(partials[i][0][k])
+                    nonMM[j] += inertial_force.dot(partials[i][0][j])
+        # Compose fr_star out of MM and nonMM
+        MM = zero_uaux(msubs(MM, q_ddot_u_map))
+        nonMM = msubs(msubs(nonMM, q_ddot_u_map),
+                udot_zero, uauxdot_zero, uaux_zero)
+        fr_star = -(MM * msubs(Matrix(self._udot), uauxdot_zero) + nonMM)
+
+        # If there are dependent speeds, we need to find fr_star_tilde
+        if self._udep:
+            p = o - len(self._udep)
+            fr_star_ind = fr_star[:p, 0]
+            fr_star_dep = fr_star[p:o, 0]
+            fr_star = fr_star_ind + (self._Ars.T * fr_star_dep)
+            # Apply the same to MM
+            MMi = MM[:p, :]
+            MMd = MM[p:o, :]
+            MM = MMi + (self._Ars.T * MMd)
+            # Apply the same to nonMM
+            nonMM = nonMM[:p, :] + (self._Ars.T * nonMM[p:o, :])
+
+        self._bodylist = bl
+        self._frstar = fr_star
+        self._k_d = MM
+        self._f_d = -(self._fr - nonMM)
+        return fr_star
+
+    def to_linearizer(self, linear_solver='LU'):
+        """Returns an instance of the Linearizer class, initiated from the
+        data in the KanesMethod class. This may be more desirable than using
+        the linearize class method, as the Linearizer object will allow more
+        efficient recalculation (i.e. about varying operating points).
+
+        Parameters
+        ==========
+        linear_solver : str, callable
+            Method used to solve the several symbolic linear systems of the
+            form ``A*x=b`` in the linearization process. If a string is
+            supplied, it should be a valid method that can be used with the
+            :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+            supplied, it should have the format ``x = f(A, b)``, where it
+            solves the equations and returns the solution. The default is
+            ``'LU'`` which corresponds to SymPy's ``A.LUsolve(b)``.
+            ``LUsolve()`` is fast to compute but will often result in
+            divide-by-zero and thus ``nan`` results.
+
+        Returns
+        =======
+        Linearizer
+            An instantiated
+            :class:`sympy.physics.mechanics.linearize.Linearizer`.
+
+        """
+
+        if (self._fr is None) or (self._frstar is None):
+            raise ValueError('Need to compute Fr, Fr* first.')
+
+        # Get required equation components. The Kane's method class breaks
+        # these into pieces. Need to reassemble
+        f_c = self._f_h
+        if self._f_nh and self._k_nh:
+            f_v = self._f_nh + self._k_nh*Matrix(self.u)
+        else:
+            f_v = Matrix()
+        if self._f_dnh and self._k_dnh:
+            f_a = self._f_dnh + self._k_dnh*Matrix(self._udot)
+        else:
+            f_a = Matrix()
+        # Dicts to sub to zero, for splitting up expressions
+        u_zero = dict.fromkeys(self.u, 0)
+        ud_zero = dict.fromkeys(self._udot, 0)
+        qd_zero = dict.fromkeys(self._qdot, 0)
+        qd_u_zero = dict.fromkeys(Matrix([self._qdot, self.u]), 0)
+        # Break the kinematic differential eqs apart into f_0 and f_1
+        f_0 = msubs(self._f_k, u_zero) + self._k_kqdot*Matrix(self._qdot)
+        f_1 = msubs(self._f_k, qd_zero) + self._k_ku*Matrix(self.u)
+        # Break the dynamic differential eqs into f_2 and f_3
+        f_2 = msubs(self._frstar, qd_u_zero)
+        f_3 = msubs(self._frstar, ud_zero) + self._fr
+        f_4 = zeros(len(f_2), 1)
+
+        # Get the required vector components
+        q = self.q
+        u = self.u
+        if self._qdep:
+            q_i = q[:-len(self._qdep)]
+        else:
+            q_i = q
+        q_d = self._qdep
+        if self._udep:
+            u_i = u[:-len(self._udep)]
+        else:
+            u_i = u
+        u_d = self._udep
+
+        # Form dictionary to set auxiliary speeds & their derivatives to 0.
+        uaux = self._uaux
+        uauxdot = uaux.diff(dynamicsymbols._t)
+        uaux_zero = dict.fromkeys(Matrix([uaux, uauxdot]), 0)
+
+        # Checking for dynamic symbols outside the dynamic differential
+        # equations; throws error if there is.
+        sym_list = set(Matrix([q, self._qdot, u, self._udot, uaux, uauxdot]))
+        if any(find_dynamicsymbols(i, sym_list) for i in [self._k_kqdot,
+                self._k_ku, self._f_k, self._k_dnh, self._f_dnh, self._k_d]):
+            raise ValueError('Cannot have dynamicsymbols outside dynamic \
+                             forcing vector.')
+
+        # Find all other dynamic symbols, forming the forcing vector r.
+        # Sort r to make it canonical.
+        r = list(find_dynamicsymbols(msubs(self._f_d, uaux_zero), sym_list))
+        r.sort(key=default_sort_key)
+
+        # Check for any derivatives of variables in r that are also found in r.
+        for i in r:
+            if diff(i, dynamicsymbols._t) in r:
+                raise ValueError('Cannot have derivatives of specified \
+                                 quantities when linearizing forcing terms.')
+        return Linearizer(f_0, f_1, f_2, f_3, f_4, f_c, f_v, f_a, q, u, q_i,
+                q_d, u_i, u_d, r, linear_solver=linear_solver)
+
+    # TODO : Remove `new_method` after 1.1 has been released.
+    def linearize(self, *, new_method=None, linear_solver='LU', **kwargs):
+        """ Linearize the equations of motion about a symbolic operating point.
+
+        Parameters
+        ==========
+        new_method
+            Deprecated, does nothing and will be removed.
+        linear_solver : str, callable
+            Method used to solve the several symbolic linear systems of the
+            form ``A*x=b`` in the linearization process. If a string is
+            supplied, it should be a valid method that can be used with the
+            :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+            supplied, it should have the format ``x = f(A, b)``, where it
+            solves the equations and returns the solution. The default is
+            ``'LU'`` which corresponds to SymPy's ``A.LUsolve(b)``.
+            ``LUsolve()`` is fast to compute but will often result in
+            divide-by-zero and thus ``nan`` results.
+        **kwargs
+            Extra keyword arguments are passed to
+            :meth:`sympy.physics.mechanics.linearize.Linearizer.linearize`.
+
+        Explanation
+        ===========
+
+        If kwarg A_and_B is False (default), returns M, A, B, r for the
+        linearized form, M*[q', u']^T = A*[q_ind, u_ind]^T + B*r.
+
+        If kwarg A_and_B is True, returns A, B, r for the linearized form
+        dx = A*x + B*r, where x = [q_ind, u_ind]^T. Note that this is
+        computationally intensive if there are many symbolic parameters. For
+        this reason, it may be more desirable to use the default A_and_B=False,
+        returning M, A, and B. Values may then be substituted in to these
+        matrices, and the state space form found as
+        A = P.T*M.inv()*A, B = P.T*M.inv()*B, where P = Linearizer.perm_mat.
+
+        In both cases, r is found as all dynamicsymbols in the equations of
+        motion that are not part of q, u, q', or u'. They are sorted in
+        canonical form.
+
+        The operating points may be also entered using the ``op_point`` kwarg.
+        This takes a dictionary of {symbol: value}, or a an iterable of such
+        dictionaries. The values may be numeric or symbolic. The more values
+        you can specify beforehand, the faster this computation will run.
+
+        For more documentation, please see the ``Linearizer`` class.
+
+        """
+
+        linearizer = self.to_linearizer(linear_solver=linear_solver)
+        result = linearizer.linearize(**kwargs)
+        return result + (linearizer.r,)
+
+    def kanes_equations(self, bodies=None, loads=None):
+        """ Method to form Kane's equations, Fr + Fr* = 0.
+
+        Explanation
+        ===========
+
+        Returns (Fr, Fr*). In the case where auxiliary generalized speeds are
+        present (say, s auxiliary speeds, o generalized speeds, and m motion
+        constraints) the length of the returned vectors will be o - m + s in
+        length. The first o - m equations will be the constrained Kane's
+        equations, then the s auxiliary Kane's equations. These auxiliary
+        equations can be accessed with the auxiliary_eqs property.
+
+        Parameters
+        ==========
+
+        bodies : iterable
+            An iterable of all RigidBody's and Particle's in the system.
+            A system must have at least one body.
+        loads : iterable
+            Takes in an iterable of (Particle, Vector) or (ReferenceFrame, Vector)
+            tuples which represent the force at a point or torque on a frame.
+            Must be either a non-empty iterable of tuples or None which corresponds
+            to a system with no constraints.
+        """
+        if bodies is None:
+            bodies = self.bodies
+        if  loads is None and self._forcelist is not None:
+            loads = self._forcelist
+        if loads == []:
+            loads = None
+        if not self._k_kqdot:
+            raise AttributeError('Create an instance of KanesMethod with '
+                    'kinematic differential equations to use this method.')
+        fr = self._form_fr(loads)
+        frstar = self._form_frstar(bodies)
+        if self._uaux:
+            if not self._udep:
+                km = KanesMethod(self._inertial, self.q, self._uaux,
+                             u_auxiliary=self._uaux, constraint_solver=self._constraint_solver)
+            else:
+                km = KanesMethod(self._inertial, self.q, self._uaux,
+                        u_auxiliary=self._uaux, u_dependent=self._udep,
+                        velocity_constraints=(self._k_nh * self.u +
+                        self._f_nh),
+                        acceleration_constraints=(self._k_dnh * self._udot +
+                        self._f_dnh),
+                        constraint_solver=self._constraint_solver
+                        )
+            km._qdot_u_map = self._qdot_u_map
+            self._km = km
+            fraux = km._form_fr(loads)
+            frstaraux = km._form_frstar(bodies)
+            self._aux_eq = fraux + frstaraux
+            self._fr = fr.col_join(fraux)
+            self._frstar = frstar.col_join(frstaraux)
+        return (self._fr, self._frstar)
+
+    def _form_eoms(self):
+        fr, frstar = self.kanes_equations(self.bodylist, self.forcelist)
+        return fr + frstar
+
+    def rhs(self, inv_method=None):
+        """Returns the system's equations of motion in first order form. The
+        output is the right hand side of::
+
+           x' = |q'| =: f(q, u, r, p, t)
+                |u'|
+
+        The right hand side is what is needed by most numerical ODE
+        integrators.
+
+        Parameters
+        ==========
+
+        inv_method : str
+            The specific sympy inverse matrix calculation method to use. For a
+            list of valid methods, see
+            :meth:`~sympy.matrices.matrixbase.MatrixBase.inv`
+
+        """
+        rhs = zeros(len(self.q) + len(self.u), 1)
+        kdes = self.kindiffdict()
+        for i, q_i in enumerate(self.q):
+            rhs[i] = kdes[q_i.diff()]
+
+        if inv_method is None:
+            rhs[len(self.q):, 0] = self.mass_matrix.LUsolve(self.forcing)
+        else:
+            rhs[len(self.q):, 0] = (self.mass_matrix.inv(inv_method,
+                                                         try_block_diag=True) *
+                                    self.forcing)
+
+        return rhs
+
+    def kindiffdict(self):
+        """Returns a dictionary mapping q' to u."""
+        if not self._qdot_u_map:
+            raise AttributeError('Create an instance of KanesMethod with '
+                    'kinematic differential equations to use this method.')
+        return self._qdot_u_map
+
+    @property
+    def auxiliary_eqs(self):
+        """A matrix containing the auxiliary equations."""
+        if not self._fr or not self._frstar:
+            raise ValueError('Need to compute Fr, Fr* first.')
+        if not self._uaux:
+            raise ValueError('No auxiliary speeds have been declared.')
+        return self._aux_eq
+
+    @property
+    def mass_matrix_kin(self):
+        r"""The kinematic "mass matrix" $\mathbf{k_{k\dot{q}}}$ of the system."""
+        return self._k_kqdot if self.explicit_kinematics else self._k_kqdot_implicit
+
+    @property
+    def forcing_kin(self):
+        """The kinematic "forcing vector" of the system."""
+        if self.explicit_kinematics:
+            return -(self._k_ku * Matrix(self.u) + self._f_k)
+        else:
+            return -(self._k_ku_implicit * Matrix(self.u) + self._f_k_implicit)
+
+    @property
+    def mass_matrix(self):
+        """The mass matrix of the system."""
+        if not self._fr or not self._frstar:
+            raise ValueError('Need to compute Fr, Fr* first.')
+        return Matrix([self._k_d, self._k_dnh])
+
+    @property
+    def forcing(self):
+        """The forcing vector of the system."""
+        if not self._fr or not self._frstar:
+            raise ValueError('Need to compute Fr, Fr* first.')
+        return -Matrix([self._f_d, self._f_dnh])
+
+    @property
+    def mass_matrix_full(self):
+        """The mass matrix of the system, augmented by the kinematic
+        differential equations in explicit or implicit form."""
+        if not self._fr or not self._frstar:
+            raise ValueError('Need to compute Fr, Fr* first.')
+        o, n = len(self.u), len(self.q)
+        return (self.mass_matrix_kin.row_join(zeros(n, o))).col_join(
+            zeros(o, n).row_join(self.mass_matrix))
+
+    @property
+    def forcing_full(self):
+        """The forcing vector of the system, augmented by the kinematic
+        differential equations in explicit or implicit form."""
+        return Matrix([self.forcing_kin, self.forcing])
+
+    @property
+    def q(self):
+        return self._q
+
+    @property
+    def u(self):
+        return self._u
+
+    @property
+    def bodylist(self):
+        return self._bodylist
+
+    @property
+    def forcelist(self):
+        return self._forcelist
+
+    @property
+    def bodies(self):
+        return self._bodylist
+
+    @property
+    def loads(self):
+        return self._forcelist
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/lagrange.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/lagrange.py
new file mode 100644
index 0000000000000000000000000000000000000000..282176a404f77762abc3ee8c6a575519b2de1f02
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/lagrange.py
@@ -0,0 +1,512 @@
+from sympy import diff, zeros, Matrix, eye, sympify
+from sympy.core.sorting import default_sort_key
+from sympy.physics.vector import dynamicsymbols, ReferenceFrame
+from sympy.physics.mechanics.method import _Methods
+from sympy.physics.mechanics.functions import (
+    find_dynamicsymbols, msubs, _f_list_parser, _validate_coordinates)
+from sympy.physics.mechanics.linearize import Linearizer
+from sympy.utilities.iterables import iterable
+
+__all__ = ['LagrangesMethod']
+
+
+class LagrangesMethod(_Methods):
+    """Lagrange's method object.
+
+    Explanation
+    ===========
+
+    This object generates the equations of motion in a two step procedure. The
+    first step involves the initialization of LagrangesMethod by supplying the
+    Lagrangian and the generalized coordinates, at the bare minimum. If there
+    are any constraint equations, they can be supplied as keyword arguments.
+    The Lagrange multipliers are automatically generated and are equal in
+    number to the constraint equations. Similarly any non-conservative forces
+    can be supplied in an iterable (as described below and also shown in the
+    example) along with a ReferenceFrame. This is also discussed further in the
+    __init__ method.
+
+    Attributes
+    ==========
+
+    q, u : Matrix
+        Matrices of the generalized coordinates and speeds
+    loads : iterable
+        Iterable of (Point, vector) or (ReferenceFrame, vector) tuples
+        describing the forces on the system.
+    bodies : iterable
+        Iterable containing the rigid bodies and particles of the system.
+    mass_matrix : Matrix
+        The system's mass matrix
+    forcing : Matrix
+        The system's forcing vector
+    mass_matrix_full : Matrix
+        The "mass matrix" for the qdot's, qdoubledot's, and the
+        lagrange multipliers (lam)
+    forcing_full : Matrix
+        The forcing vector for the qdot's, qdoubledot's and
+        lagrange multipliers (lam)
+
+    Examples
+    ========
+
+    This is a simple example for a one degree of freedom translational
+    spring-mass-damper.
+
+    In this example, we first need to do the kinematics.
+    This involves creating generalized coordinates and their derivatives.
+    Then we create a point and set its velocity in a frame.
+
+        >>> from sympy.physics.mechanics import LagrangesMethod, Lagrangian
+        >>> from sympy.physics.mechanics import ReferenceFrame, Particle, Point
+        >>> from sympy.physics.mechanics import dynamicsymbols
+        >>> from sympy import symbols
+        >>> q = dynamicsymbols('q')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> m, k, b = symbols('m k b')
+        >>> N = ReferenceFrame('N')
+        >>> P = Point('P')
+        >>> P.set_vel(N, qd * N.x)
+
+    We need to then prepare the information as required by LagrangesMethod to
+    generate equations of motion.
+    First we create the Particle, which has a point attached to it.
+    Following this the lagrangian is created from the kinetic and potential
+    energies.
+    Then, an iterable of nonconservative forces/torques must be constructed,
+    where each item is a (Point, Vector) or (ReferenceFrame, Vector) tuple,
+    with the Vectors representing the nonconservative forces or torques.
+
+        >>> Pa = Particle('Pa', P, m)
+        >>> Pa.potential_energy = k * q**2 / 2.0
+        >>> L = Lagrangian(N, Pa)
+        >>> fl = [(P, -b * qd * N.x)]
+
+    Finally we can generate the equations of motion.
+    First we create the LagrangesMethod object. To do this one must supply
+    the Lagrangian, and the generalized coordinates. The constraint equations,
+    the forcelist, and the inertial frame may also be provided, if relevant.
+    Next we generate Lagrange's equations of motion, such that:
+    Lagrange's equations of motion = 0.
+    We have the equations of motion at this point.
+
+        >>> l = LagrangesMethod(L, [q], forcelist = fl, frame = N)
+        >>> print(l.form_lagranges_equations())
+        Matrix([[b*Derivative(q(t), t) + 1.0*k*q(t) + m*Derivative(q(t), (t, 2))]])
+
+    We can also solve for the states using the 'rhs' method.
+
+        >>> print(l.rhs())
+        Matrix([[Derivative(q(t), t)], [(-b*Derivative(q(t), t) - 1.0*k*q(t))/m]])
+
+    Please refer to the docstrings on each method for more details.
+    """
+
+    def __init__(self, Lagrangian, qs, forcelist=None, bodies=None, frame=None,
+                 hol_coneqs=None, nonhol_coneqs=None):
+        """Supply the following for the initialization of LagrangesMethod.
+
+        Lagrangian : Sympifyable
+
+        qs : array_like
+            The generalized coordinates
+
+        hol_coneqs : array_like, optional
+            The holonomic constraint equations
+
+        nonhol_coneqs : array_like, optional
+            The nonholonomic constraint equations
+
+        forcelist : iterable, optional
+            Takes an iterable of (Point, Vector) or (ReferenceFrame, Vector)
+            tuples which represent the force at a point or torque on a frame.
+            This feature is primarily to account for the nonconservative forces
+            and/or moments.
+
+        bodies : iterable, optional
+            Takes an iterable containing the rigid bodies and particles of the
+            system.
+
+        frame : ReferenceFrame, optional
+            Supply the inertial frame. This is used to determine the
+            generalized forces due to non-conservative forces.
+        """
+
+        self._L = Matrix([sympify(Lagrangian)])
+        self.eom = None
+        self._m_cd = Matrix()           # Mass Matrix of differentiated coneqs
+        self._m_d = Matrix()            # Mass Matrix of dynamic equations
+        self._f_cd = Matrix()           # Forcing part of the diff coneqs
+        self._f_d = Matrix()            # Forcing part of the dynamic equations
+        self.lam_coeffs = Matrix()      # The coeffecients of the multipliers
+
+        forcelist = forcelist if forcelist else []
+        if not iterable(forcelist):
+            raise TypeError('Force pairs must be supplied in an iterable.')
+        self._forcelist = forcelist
+        if frame and not isinstance(frame, ReferenceFrame):
+            raise TypeError('frame must be a valid ReferenceFrame')
+        self._bodies = bodies
+        self.inertial = frame
+
+        self.lam_vec = Matrix()
+
+        self._term1 = Matrix()
+        self._term2 = Matrix()
+        self._term3 = Matrix()
+        self._term4 = Matrix()
+
+        # Creating the qs, qdots and qdoubledots
+        if not iterable(qs):
+            raise TypeError('Generalized coordinates must be an iterable')
+        self._q = Matrix(qs)
+        self._qdots = self.q.diff(dynamicsymbols._t)
+        self._qdoubledots = self._qdots.diff(dynamicsymbols._t)
+        _validate_coordinates(self.q)
+
+        mat_build = lambda x: Matrix(x) if x else Matrix()
+        hol_coneqs = mat_build(hol_coneqs)
+        nonhol_coneqs = mat_build(nonhol_coneqs)
+        self.coneqs = Matrix([hol_coneqs.diff(dynamicsymbols._t),
+                nonhol_coneqs])
+        self._hol_coneqs = hol_coneqs
+
+    def form_lagranges_equations(self):
+        """Method to form Lagrange's equations of motion.
+
+        Returns a vector of equations of motion using Lagrange's equations of
+        the second kind.
+        """
+
+        qds = self._qdots
+        qdd_zero = dict.fromkeys(self._qdoubledots, 0)
+        n = len(self.q)
+
+        # Internally we represent the EOM as four terms:
+        # EOM = term1 - term2 - term3 - term4 = 0
+
+        # First term
+        self._term1 = self._L.jacobian(qds)
+        self._term1 = self._term1.diff(dynamicsymbols._t).T
+
+        # Second term
+        self._term2 = self._L.jacobian(self.q).T
+
+        # Third term
+        if self.coneqs:
+            coneqs = self.coneqs
+            m = len(coneqs)
+            # Creating the multipliers
+            self.lam_vec = Matrix(dynamicsymbols('lam1:' + str(m + 1)))
+            self.lam_coeffs = -coneqs.jacobian(qds)
+            self._term3 = self.lam_coeffs.T * self.lam_vec
+            # Extracting the coeffecients of the qdds from the diff coneqs
+            diffconeqs = coneqs.diff(dynamicsymbols._t)
+            self._m_cd = diffconeqs.jacobian(self._qdoubledots)
+            # The remaining terms i.e. the 'forcing' terms in diff coneqs
+            self._f_cd = -diffconeqs.subs(qdd_zero)
+        else:
+            self._term3 = zeros(n, 1)
+
+        # Fourth term
+        if self.forcelist:
+            N = self.inertial
+            self._term4 = zeros(n, 1)
+            for i, qd in enumerate(qds):
+                flist = zip(*_f_list_parser(self.forcelist, N))
+                self._term4[i] = sum(v.diff(qd, N).dot(f) for (v, f) in flist)
+        else:
+            self._term4 = zeros(n, 1)
+
+        # Form the dynamic mass and forcing matrices
+        without_lam = self._term1 - self._term2 - self._term4
+        self._m_d = without_lam.jacobian(self._qdoubledots)
+        self._f_d = -without_lam.subs(qdd_zero)
+
+        # Form the EOM
+        self.eom = without_lam - self._term3
+        return self.eom
+
+    def _form_eoms(self):
+        return self.form_lagranges_equations()
+
+    @property
+    def mass_matrix(self):
+        """Returns the mass matrix, which is augmented by the Lagrange
+        multipliers, if necessary.
+
+        Explanation
+        ===========
+
+        If the system is described by 'n' generalized coordinates and there are
+        no constraint equations then an n X n matrix is returned.
+
+        If there are 'n' generalized coordinates and 'm' constraint equations
+        have been supplied during initialization then an n X (n+m) matrix is
+        returned. The (n + m - 1)th and (n + m)th columns contain the
+        coefficients of the Lagrange multipliers.
+        """
+
+        if self.eom is None:
+            raise ValueError('Need to compute the equations of motion first')
+        if self.coneqs:
+            return (self._m_d).row_join(self.lam_coeffs.T)
+        else:
+            return self._m_d
+
+    @property
+    def mass_matrix_full(self):
+        """Augments the coefficients of qdots to the mass_matrix."""
+
+        if self.eom is None:
+            raise ValueError('Need to compute the equations of motion first')
+        n = len(self.q)
+        m = len(self.coneqs)
+        row1 = eye(n).row_join(zeros(n, n + m))
+        row2 = zeros(n, n).row_join(self.mass_matrix)
+        if self.coneqs:
+            row3 = zeros(m, n).row_join(self._m_cd).row_join(zeros(m, m))
+            return row1.col_join(row2).col_join(row3)
+        else:
+            return row1.col_join(row2)
+
+    @property
+    def forcing(self):
+        """Returns the forcing vector from 'lagranges_equations' method."""
+
+        if self.eom is None:
+            raise ValueError('Need to compute the equations of motion first')
+        return self._f_d
+
+    @property
+    def forcing_full(self):
+        """Augments qdots to the forcing vector above."""
+
+        if self.eom is None:
+            raise ValueError('Need to compute the equations of motion first')
+        if self.coneqs:
+            return self._qdots.col_join(self.forcing).col_join(self._f_cd)
+        else:
+            return self._qdots.col_join(self.forcing)
+
+    def to_linearizer(self, q_ind=None, qd_ind=None, q_dep=None, qd_dep=None,
+                      linear_solver='LU'):
+        """Returns an instance of the Linearizer class, initiated from the data
+        in the LagrangesMethod class. This may be more desirable than using the
+        linearize class method, as the Linearizer object will allow more
+        efficient recalculation (i.e. about varying operating points).
+
+        Parameters
+        ==========
+
+        q_ind, qd_ind : array_like, optional
+            The independent generalized coordinates and speeds.
+        q_dep, qd_dep : array_like, optional
+            The dependent generalized coordinates and speeds.
+        linear_solver : str, callable
+            Method used to solve the several symbolic linear systems of the
+            form ``A*x=b`` in the linearization process. If a string is
+            supplied, it should be a valid method that can be used with the
+            :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+            supplied, it should have the format ``x = f(A, b)``, where it
+            solves the equations and returns the solution. The default is
+            ``'LU'`` which corresponds to SymPy's ``A.LUsolve(b)``.
+            ``LUsolve()`` is fast to compute but will often result in
+            divide-by-zero and thus ``nan`` results.
+
+        Returns
+        =======
+        Linearizer
+            An instantiated
+            :class:`sympy.physics.mechanics.linearize.Linearizer`.
+
+        """
+
+        # Compose vectors
+        t = dynamicsymbols._t
+        q = self.q
+        u = self._qdots
+        ud = u.diff(t)
+        # Get vector of lagrange multipliers
+        lams = self.lam_vec
+
+        mat_build = lambda x: Matrix(x) if x else Matrix()
+        q_i = mat_build(q_ind)
+        q_d = mat_build(q_dep)
+        u_i = mat_build(qd_ind)
+        u_d = mat_build(qd_dep)
+
+        # Compose general form equations
+        f_c = self._hol_coneqs
+        f_v = self.coneqs
+        f_a = f_v.diff(t)
+        f_0 = u
+        f_1 = -u
+        f_2 = self._term1
+        f_3 = -(self._term2 + self._term4)
+        f_4 = -self._term3
+
+        # Check that there are an appropriate number of independent and
+        # dependent coordinates
+        if len(q_d) != len(f_c) or len(u_d) != len(f_v):
+            raise ValueError(("Must supply {:} dependent coordinates, and " +
+                    "{:} dependent speeds").format(len(f_c), len(f_v)))
+        if set(Matrix([q_i, q_d])) != set(q):
+            raise ValueError("Must partition q into q_ind and q_dep, with " +
+                    "no extra or missing symbols.")
+        if set(Matrix([u_i, u_d])) != set(u):
+            raise ValueError("Must partition qd into qd_ind and qd_dep, " +
+                    "with no extra or missing symbols.")
+
+        # Find all other dynamic symbols, forming the forcing vector r.
+        # Sort r to make it canonical.
+        insyms = set(Matrix([q, u, ud, lams]))
+        r = list(find_dynamicsymbols(f_3, insyms))
+        r.sort(key=default_sort_key)
+        # Check for any derivatives of variables in r that are also found in r.
+        for i in r:
+            if diff(i, dynamicsymbols._t) in r:
+                raise ValueError('Cannot have derivatives of specified \
+                                 quantities when linearizing forcing terms.')
+
+        return Linearizer(f_0, f_1, f_2, f_3, f_4, f_c, f_v, f_a, q, u, q_i,
+                          q_d, u_i, u_d, r, lams, linear_solver=linear_solver)
+
+    def linearize(self, q_ind=None, qd_ind=None, q_dep=None, qd_dep=None,
+                  linear_solver='LU', **kwargs):
+        """Linearize the equations of motion about a symbolic operating point.
+
+        Parameters
+        ==========
+        linear_solver : str, callable
+            Method used to solve the several symbolic linear systems of the
+            form ``A*x=b`` in the linearization process. If a string is
+            supplied, it should be a valid method that can be used with the
+            :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+            supplied, it should have the format ``x = f(A, b)``, where it
+            solves the equations and returns the solution. The default is
+            ``'LU'`` which corresponds to SymPy's ``A.LUsolve(b)``.
+            ``LUsolve()`` is fast to compute but will often result in
+            divide-by-zero and thus ``nan`` results.
+        **kwargs
+            Extra keyword arguments are passed to
+            :meth:`sympy.physics.mechanics.linearize.Linearizer.linearize`.
+
+        Explanation
+        ===========
+
+        If kwarg A_and_B is False (default), returns M, A, B, r for the
+        linearized form, M*[q', u']^T = A*[q_ind, u_ind]^T + B*r.
+
+        If kwarg A_and_B is True, returns A, B, r for the linearized form
+        dx = A*x + B*r, where x = [q_ind, u_ind]^T. Note that this is
+        computationally intensive if there are many symbolic parameters. For
+        this reason, it may be more desirable to use the default A_and_B=False,
+        returning M, A, and B. Values may then be substituted in to these
+        matrices, and the state space form found as
+        A = P.T*M.inv()*A, B = P.T*M.inv()*B, where P = Linearizer.perm_mat.
+
+        In both cases, r is found as all dynamicsymbols in the equations of
+        motion that are not part of q, u, q', or u'. They are sorted in
+        canonical form.
+
+        The operating points may be also entered using the ``op_point`` kwarg.
+        This takes a dictionary of {symbol: value}, or a an iterable of such
+        dictionaries. The values may be numeric or symbolic. The more values
+        you can specify beforehand, the faster this computation will run.
+
+        For more documentation, please see the ``Linearizer`` class."""
+
+        linearizer = self.to_linearizer(q_ind, qd_ind, q_dep, qd_dep,
+                                        linear_solver=linear_solver)
+        result = linearizer.linearize(**kwargs)
+        return result + (linearizer.r,)
+
+    def solve_multipliers(self, op_point=None, sol_type='dict'):
+        """Solves for the values of the lagrange multipliers symbolically at
+        the specified operating point.
+
+        Parameters
+        ==========
+
+        op_point : dict or iterable of dicts, optional
+            Point at which to solve at. The operating point is specified as
+            a dictionary or iterable of dictionaries of {symbol: value}. The
+            value may be numeric or symbolic itself.
+
+        sol_type : str, optional
+            Solution return type. Valid options are:
+            - 'dict': A dict of {symbol : value} (default)
+            - 'Matrix': An ordered column matrix of the solution
+        """
+
+        # Determine number of multipliers
+        k = len(self.lam_vec)
+        if k == 0:
+            raise ValueError("System has no lagrange multipliers to solve for.")
+        # Compose dict of operating conditions
+        if isinstance(op_point, dict):
+            op_point_dict = op_point
+        elif iterable(op_point):
+            op_point_dict = {}
+            for op in op_point:
+                op_point_dict.update(op)
+        elif op_point is None:
+            op_point_dict = {}
+        else:
+            raise TypeError("op_point must be either a dictionary or an "
+                            "iterable of dictionaries.")
+        # Compose the system to be solved
+        mass_matrix = self.mass_matrix.col_join(-self.lam_coeffs.row_join(
+                zeros(k, k)))
+        force_matrix = self.forcing.col_join(self._f_cd)
+        # Sub in the operating point
+        mass_matrix = msubs(mass_matrix, op_point_dict)
+        force_matrix = msubs(force_matrix, op_point_dict)
+        # Solve for the multipliers
+        sol_list = mass_matrix.LUsolve(-force_matrix)[-k:]
+        if sol_type == 'dict':
+            return dict(zip(self.lam_vec, sol_list))
+        elif sol_type == 'Matrix':
+            return Matrix(sol_list)
+        else:
+            raise ValueError("Unknown sol_type {:}.".format(sol_type))
+
+    def rhs(self, inv_method=None, **kwargs):
+        """Returns equations that can be solved numerically.
+
+        Parameters
+        ==========
+
+        inv_method : str
+            The specific sympy inverse matrix calculation method to use. For a
+            list of valid methods, see
+            :meth:`~sympy.matrices.matrixbase.MatrixBase.inv`
+        """
+
+        if inv_method is None:
+            self._rhs = self.mass_matrix_full.LUsolve(self.forcing_full)
+        else:
+            self._rhs = (self.mass_matrix_full.inv(inv_method,
+                         try_block_diag=True) * self.forcing_full)
+        return self._rhs
+
+    @property
+    def q(self):
+        return self._q
+
+    @property
+    def u(self):
+        return self._qdots
+
+    @property
+    def bodies(self):
+        return self._bodies
+
+    @property
+    def forcelist(self):
+        return self._forcelist
+
+    @property
+    def loads(self):
+        return self._forcelist
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/linearize.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/linearize.py
new file mode 100644
index 0000000000000000000000000000000000000000..b94ddb865a7236a5ac6f1a41ba96679eb8b2cd8f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/linearize.py
@@ -0,0 +1,474 @@
+__all__ = ['Linearizer']
+
+from sympy import Matrix, eye, zeros
+from sympy.core.symbol import Dummy
+from sympy.utilities.iterables import flatten
+from sympy.physics.vector import dynamicsymbols
+from sympy.physics.mechanics.functions import msubs, _parse_linear_solver
+
+from collections import namedtuple
+from collections.abc import Iterable
+
+
+class Linearizer:
+    """This object holds the general model form for a dynamic system. This
+    model is used for computing the linearized form of the system, while
+    properly dealing with constraints leading to  dependent coordinates and
+    speeds. The notation and method is described in [1]_.
+
+    Attributes
+    ==========
+
+    f_0, f_1, f_2, f_3, f_4, f_c, f_v, f_a : Matrix
+        Matrices holding the general system form.
+    q, u, r : Matrix
+        Matrices holding the generalized coordinates, speeds, and
+        input vectors.
+    q_i, u_i : Matrix
+        Matrices of the independent generalized coordinates and speeds.
+    q_d, u_d : Matrix
+        Matrices of the dependent generalized coordinates and speeds.
+    perm_mat : Matrix
+        Permutation matrix such that [q_ind, u_ind]^T = perm_mat*[q, u]^T
+
+    References
+    ==========
+
+    .. [1] D. L. Peterson, G. Gede, and M. Hubbard, "Symbolic linearization of
+           equations of motion of constrained multibody systems," Multibody
+           Syst Dyn, vol. 33, no. 2, pp. 143-161, Feb. 2015, doi:
+           10.1007/s11044-014-9436-5.
+
+    """
+
+    def __init__(self, f_0, f_1, f_2, f_3, f_4, f_c, f_v, f_a, q, u, q_i=None,
+                 q_d=None, u_i=None, u_d=None, r=None, lams=None,
+                 linear_solver='LU'):
+        """
+        Parameters
+        ==========
+
+        f_0, f_1, f_2, f_3, f_4, f_c, f_v, f_a : array_like
+            System of equations holding the general system form.
+            Supply empty array or Matrix if the parameter
+            does not exist.
+        q : array_like
+            The generalized coordinates.
+        u : array_like
+            The generalized speeds
+        q_i, u_i : array_like, optional
+            The independent generalized coordinates and speeds.
+        q_d, u_d : array_like, optional
+            The dependent generalized coordinates and speeds.
+        r : array_like, optional
+            The input variables.
+        lams : array_like, optional
+            The lagrange multipliers
+        linear_solver : str, callable
+            Method used to solve the several symbolic linear systems of the
+            form ``A*x=b`` in the linearization process. If a string is
+            supplied, it should be a valid method that can be used with the
+            :meth:`sympy.matrices.matrixbase.MatrixBase.solve`. If a callable is
+            supplied, it should have the format ``x = f(A, b)``, where it
+            solves the equations and returns the solution. The default is
+            ``'LU'`` which corresponds to SymPy's ``A.LUsolve(b)``.
+            ``LUsolve()`` is fast to compute but will often result in
+            divide-by-zero and thus ``nan`` results.
+
+        """
+        self.linear_solver = _parse_linear_solver(linear_solver)
+
+        # Generalized equation form
+        self.f_0 = Matrix(f_0)
+        self.f_1 = Matrix(f_1)
+        self.f_2 = Matrix(f_2)
+        self.f_3 = Matrix(f_3)
+        self.f_4 = Matrix(f_4)
+        self.f_c = Matrix(f_c)
+        self.f_v = Matrix(f_v)
+        self.f_a = Matrix(f_a)
+
+        # Generalized equation variables
+        self.q = Matrix(q)
+        self.u = Matrix(u)
+        none_handler = lambda x: Matrix(x) if x else Matrix()
+        self.q_i = none_handler(q_i)
+        self.q_d = none_handler(q_d)
+        self.u_i = none_handler(u_i)
+        self.u_d = none_handler(u_d)
+        self.r = none_handler(r)
+        self.lams = none_handler(lams)
+
+        # Derivatives of generalized equation variables
+        self._qd = self.q.diff(dynamicsymbols._t)
+        self._ud = self.u.diff(dynamicsymbols._t)
+        # If the user doesn't actually use generalized variables, and the
+        # qd and u vectors have any intersecting variables, this can cause
+        # problems. We'll fix this with some hackery, and Dummy variables
+        dup_vars = set(self._qd).intersection(self.u)
+        self._qd_dup = Matrix([var if var not in dup_vars else Dummy() for var
+                               in self._qd])
+
+        # Derive dimension terms
+        l = len(self.f_c)
+        m = len(self.f_v)
+        n = len(self.q)
+        o = len(self.u)
+        s = len(self.r)
+        k = len(self.lams)
+        dims = namedtuple('dims', ['l', 'm', 'n', 'o', 's', 'k'])
+        self._dims = dims(l, m, n, o, s, k)
+
+        self._Pq = None
+        self._Pqi = None
+        self._Pqd = None
+        self._Pu = None
+        self._Pui = None
+        self._Pud = None
+        self._C_0 = None
+        self._C_1 = None
+        self._C_2 = None
+        self.perm_mat = None
+
+        self._setup_done = False
+
+    def _setup(self):
+        # Calculations here only need to be run once. They are moved out of
+        # the __init__ method to increase the speed of Linearizer creation.
+        self._form_permutation_matrices()
+        self._form_block_matrices()
+        self._form_coefficient_matrices()
+        self._setup_done = True
+
+    def _form_permutation_matrices(self):
+        """Form the permutation matrices Pq and Pu."""
+
+        # Extract dimension variables
+        l, m, n, o, s, k = self._dims
+        # Compute permutation matrices
+        if n != 0:
+            self._Pq = permutation_matrix(self.q, Matrix([self.q_i, self.q_d]))
+            if l > 0:
+                self._Pqi = self._Pq[:, :-l]
+                self._Pqd = self._Pq[:, -l:]
+            else:
+                self._Pqi = self._Pq
+                self._Pqd = Matrix()
+        if o != 0:
+            self._Pu = permutation_matrix(self.u, Matrix([self.u_i, self.u_d]))
+            if m > 0:
+                self._Pui = self._Pu[:, :-m]
+                self._Pud = self._Pu[:, -m:]
+            else:
+                self._Pui = self._Pu
+                self._Pud = Matrix()
+        # Compute combination permutation matrix for computing A and B
+        P_col1 = Matrix([self._Pqi, zeros(o + k, n - l)])
+        P_col2 = Matrix([zeros(n, o - m), self._Pui, zeros(k, o - m)])
+        if P_col1:
+            if P_col2:
+                self.perm_mat = P_col1.row_join(P_col2)
+            else:
+                self.perm_mat = P_col1
+        else:
+            self.perm_mat = P_col2
+
+    def _form_coefficient_matrices(self):
+        """Form the coefficient matrices C_0, C_1, and C_2."""
+
+        # Extract dimension variables
+        l, m, n, o, s, k = self._dims
+        # Build up the coefficient matrices C_0, C_1, and C_2
+        # If there are configuration constraints (l > 0), form C_0 as normal.
+        # If not, C_0 is I_(nxn). Note that this works even if n=0
+        if l > 0:
+            f_c_jac_q = self.f_c.jacobian(self.q)
+            self._C_0 = (eye(n) - self._Pqd *
+                         self.linear_solver(f_c_jac_q*self._Pqd,
+                                            f_c_jac_q))*self._Pqi
+        else:
+            self._C_0 = eye(n)
+        # If there are motion constraints (m > 0), form C_1 and C_2 as normal.
+        # If not, C_1 is 0, and C_2 is I_(oxo). Note that this works even if
+        # o = 0.
+        if m > 0:
+            f_v_jac_u = self.f_v.jacobian(self.u)
+            temp = f_v_jac_u * self._Pud
+            if n != 0:
+                f_v_jac_q = self.f_v.jacobian(self.q)
+                self._C_1 = -self._Pud * self.linear_solver(temp, f_v_jac_q)
+            else:
+                self._C_1 = zeros(o, n)
+            self._C_2 = (eye(o) - self._Pud *
+                         self.linear_solver(temp, f_v_jac_u))*self._Pui
+        else:
+            self._C_1 = zeros(o, n)
+            self._C_2 = eye(o)
+
+    def _form_block_matrices(self):
+        """Form the block matrices for composing M, A, and B."""
+
+        # Extract dimension variables
+        l, m, n, o, s, k = self._dims
+        # Block Matrix Definitions. These are only defined if under certain
+        # conditions. If undefined, an empty matrix is used instead
+        if n != 0:
+            self._M_qq = self.f_0.jacobian(self._qd)
+            self._A_qq = -(self.f_0 + self.f_1).jacobian(self.q)
+        else:
+            self._M_qq = Matrix()
+            self._A_qq = Matrix()
+        if n != 0 and m != 0:
+            self._M_uqc = self.f_a.jacobian(self._qd_dup)
+            self._A_uqc = -self.f_a.jacobian(self.q)
+        else:
+            self._M_uqc = Matrix()
+            self._A_uqc = Matrix()
+        if n != 0 and o - m + k != 0:
+            self._M_uqd = self.f_3.jacobian(self._qd_dup)
+            self._A_uqd = -(self.f_2 + self.f_3 + self.f_4).jacobian(self.q)
+        else:
+            self._M_uqd = Matrix()
+            self._A_uqd = Matrix()
+        if o != 0 and m != 0:
+            self._M_uuc = self.f_a.jacobian(self._ud)
+            self._A_uuc = -self.f_a.jacobian(self.u)
+        else:
+            self._M_uuc = Matrix()
+            self._A_uuc = Matrix()
+        if o != 0 and o - m + k != 0:
+            self._M_uud = self.f_2.jacobian(self._ud)
+            self._A_uud = -(self.f_2 + self.f_3).jacobian(self.u)
+        else:
+            self._M_uud = Matrix()
+            self._A_uud = Matrix()
+        if o != 0 and n != 0:
+            self._A_qu = -self.f_1.jacobian(self.u)
+        else:
+            self._A_qu = Matrix()
+        if k != 0 and o - m + k != 0:
+            self._M_uld = self.f_4.jacobian(self.lams)
+        else:
+            self._M_uld = Matrix()
+        if s != 0 and o - m + k != 0:
+            self._B_u = -self.f_3.jacobian(self.r)
+        else:
+            self._B_u = Matrix()
+
+    def linearize(self, op_point=None, A_and_B=False, simplify=False):
+        """Linearize the system about the operating point. Note that
+        q_op, u_op, qd_op, ud_op must satisfy the equations of motion.
+        These may be either symbolic or numeric.
+
+        Parameters
+        ==========
+        op_point : dict or iterable of dicts, optional
+            Dictionary or iterable of dictionaries containing the operating
+            point conditions for all or a subset of the generalized
+            coordinates, generalized speeds, and time derivatives of the
+            generalized speeds. These will be substituted into the linearized
+            system before the linearization is complete. Leave set to ``None``
+            if you want the operating point to be an arbitrary set of symbols.
+            Note that any reduction in symbols (whether substituted for numbers
+            or expressions with a common parameter) will result in faster
+            runtime.
+        A_and_B : bool, optional
+            If A_and_B=False (default), (M, A, B) is returned and of
+            A_and_B=True, (A, B) is returned. See below.
+        simplify : bool, optional
+            Determines if returned values are simplified before return.
+            For large expressions this may be time consuming. Default is False.
+
+        Returns
+        =======
+        M, A, B : Matrices, ``A_and_B=False``
+            Matrices from the implicit form:
+                ``[M]*[q', u']^T = [A]*[q_ind, u_ind]^T + [B]*r``
+        A, B : Matrices, ``A_and_B=True``
+            Matrices from the explicit form:
+                ``[q_ind', u_ind']^T = [A]*[q_ind, u_ind]^T + [B]*r``
+
+        Notes
+        =====
+
+        Note that the process of solving with A_and_B=True is computationally
+        intensive if there are many symbolic parameters. For this reason, it
+        may be more desirable to use the default A_and_B=False, returning M, A,
+        and B. More values may then be substituted in to these matrices later
+        on. The state space form can then be found as A = P.T*M.LUsolve(A), B =
+        P.T*M.LUsolve(B), where P = Linearizer.perm_mat.
+
+        """
+
+        # Run the setup if needed:
+        if not self._setup_done:
+            self._setup()
+
+        # Compose dict of operating conditions
+        if isinstance(op_point, dict):
+            op_point_dict = op_point
+        elif isinstance(op_point, Iterable):
+            op_point_dict = {}
+            for op in op_point:
+                op_point_dict.update(op)
+        else:
+            op_point_dict = {}
+
+        # Extract dimension variables
+        l, m, n, o, s, k = self._dims
+
+        # Rename terms to shorten expressions
+        M_qq = self._M_qq
+        M_uqc = self._M_uqc
+        M_uqd = self._M_uqd
+        M_uuc = self._M_uuc
+        M_uud = self._M_uud
+        M_uld = self._M_uld
+        A_qq = self._A_qq
+        A_uqc = self._A_uqc
+        A_uqd = self._A_uqd
+        A_qu = self._A_qu
+        A_uuc = self._A_uuc
+        A_uud = self._A_uud
+        B_u = self._B_u
+        C_0 = self._C_0
+        C_1 = self._C_1
+        C_2 = self._C_2
+
+        # Build up Mass Matrix
+        #     |M_qq    0_nxo   0_nxk|
+        # M = |M_uqc   M_uuc   0_mxk|
+        #     |M_uqd   M_uud   M_uld|
+        if o != 0:
+            col2 = Matrix([zeros(n, o), M_uuc, M_uud])
+        if k != 0:
+            col3 = Matrix([zeros(n + m, k), M_uld])
+        if n != 0:
+            col1 = Matrix([M_qq, M_uqc, M_uqd])
+            if o != 0 and k != 0:
+                M = col1.row_join(col2).row_join(col3)
+            elif o != 0:
+                M = col1.row_join(col2)
+            else:
+                M = col1
+        elif k != 0:
+            M = col2.row_join(col3)
+        else:
+            M = col2
+        M_eq = msubs(M, op_point_dict)
+
+        # Build up state coefficient matrix A
+        #     |(A_qq + A_qu*C_1)*C_0       A_qu*C_2|
+        # A = |(A_uqc + A_uuc*C_1)*C_0    A_uuc*C_2|
+        #     |(A_uqd + A_uud*C_1)*C_0    A_uud*C_2|
+        # Col 1 is only defined if n != 0
+        if n != 0:
+            r1c1 = A_qq
+            if o != 0:
+                r1c1 += (A_qu * C_1)
+            r1c1 = r1c1 * C_0
+            if m != 0:
+                r2c1 = A_uqc
+                if o != 0:
+                    r2c1 += (A_uuc * C_1)
+                r2c1 = r2c1 * C_0
+            else:
+                r2c1 = Matrix()
+            if o - m + k != 0:
+                r3c1 = A_uqd
+                if o != 0:
+                    r3c1 += (A_uud * C_1)
+                r3c1 = r3c1 * C_0
+            else:
+                r3c1 = Matrix()
+            col1 = Matrix([r1c1, r2c1, r3c1])
+        else:
+            col1 = Matrix()
+        # Col 2 is only defined if o != 0
+        if o != 0:
+            if n != 0:
+                r1c2 = A_qu * C_2
+            else:
+                r1c2 = Matrix()
+            if m != 0:
+                r2c2 = A_uuc * C_2
+            else:
+                r2c2 = Matrix()
+            if o - m + k != 0:
+                r3c2 = A_uud * C_2
+            else:
+                r3c2 = Matrix()
+            col2 = Matrix([r1c2, r2c2, r3c2])
+        else:
+            col2 = Matrix()
+        if col1:
+            if col2:
+                Amat = col1.row_join(col2)
+            else:
+                Amat = col1
+        else:
+            Amat = col2
+        Amat_eq = msubs(Amat, op_point_dict)
+
+        # Build up the B matrix if there are forcing variables
+        #     |0_(n + m)xs|
+        # B = |B_u        |
+        if s != 0 and o - m + k != 0:
+            Bmat = zeros(n + m, s).col_join(B_u)
+            Bmat_eq = msubs(Bmat, op_point_dict)
+        else:
+            Bmat_eq = Matrix()
+
+        # kwarg A_and_B indicates to return  A, B for forming the equation
+        # dx = [A]x + [B]r, where x = [q_indnd, u_indnd]^T,
+        if A_and_B:
+            A_cont = self.perm_mat.T * self.linear_solver(M_eq, Amat_eq)
+            if Bmat_eq:
+                B_cont = self.perm_mat.T * self.linear_solver(M_eq, Bmat_eq)
+            else:
+                # Bmat = Matrix([]), so no need to sub
+                B_cont = Bmat_eq
+            if simplify:
+                A_cont.simplify()
+                B_cont.simplify()
+            return A_cont, B_cont
+        # Otherwise return M, A, B for forming the equation
+        # [M]dx = [A]x + [B]r, where x = [q, u]^T
+        else:
+            if simplify:
+                M_eq.simplify()
+                Amat_eq.simplify()
+                Bmat_eq.simplify()
+            return M_eq, Amat_eq, Bmat_eq
+
+
+def permutation_matrix(orig_vec, per_vec):
+    """Compute the permutation matrix to change order of
+    orig_vec into order of per_vec.
+
+    Parameters
+    ==========
+
+    orig_vec : array_like
+        Symbols in original ordering.
+    per_vec : array_like
+        Symbols in new ordering.
+
+    Returns
+    =======
+
+    p_matrix : Matrix
+        Permutation matrix such that orig_vec == (p_matrix * per_vec).
+    """
+    if not isinstance(orig_vec, (list, tuple)):
+        orig_vec = flatten(orig_vec)
+    if not isinstance(per_vec, (list, tuple)):
+        per_vec = flatten(per_vec)
+    if set(orig_vec) != set(per_vec):
+        raise ValueError("orig_vec and per_vec must be the same length, "
+                         "and contain the same symbols.")
+    ind_list = [orig_vec.index(i) for i in per_vec]
+    p_matrix = zeros(len(orig_vec))
+    for i, j in enumerate(ind_list):
+        p_matrix[i, j] = 1
+    return p_matrix
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/loads.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/loads.py
new file mode 100644
index 0000000000000000000000000000000000000000..3b9db763ffd6f99905e9d17fdc07f4171de4801b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/loads.py
@@ -0,0 +1,177 @@
+from abc import ABC
+from collections import namedtuple
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.physics.vector import Vector, ReferenceFrame, Point
+
+__all__ = ['LoadBase', 'Force', 'Torque']
+
+
+class LoadBase(ABC, namedtuple('LoadBase', ['location', 'vector'])):
+    """Abstract base class for the various loading types."""
+
+    def __add__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: "
+                        f"'{self.__class__.__name__}' and "
+                        f"'{other.__class__.__name__}'")
+
+    def __mul__(self, other):
+        raise TypeError(f"unsupported operand type(s) for *: "
+                        f"'{self.__class__.__name__}' and "
+                        f"'{other.__class__.__name__}'")
+
+    __radd__ = __add__
+    __rmul__ = __mul__
+
+
+class Force(LoadBase):
+    """Force acting upon a point.
+
+    Explanation
+    ===========
+
+    A force is a vector that is bound to a line of action. This class stores
+    both a point, which lies on the line of action, and the vector. A tuple can
+    also be used, with the location as the first entry and the vector as second
+    entry.
+
+    Examples
+    ========
+
+    A force of magnitude 2 along N.x acting on a point Po can be created as
+    follows:
+
+    >>> from sympy.physics.mechanics import Point, ReferenceFrame, Force
+    >>> N = ReferenceFrame('N')
+    >>> Po = Point('Po')
+    >>> Force(Po, 2 * N.x)
+    (Po, 2*N.x)
+
+    If a body is supplied, then the center of mass of that body is used.
+
+    >>> from sympy.physics.mechanics import Particle
+    >>> P = Particle('P', point=Po)
+    >>> Force(P, 2 * N.x)
+    (Po, 2*N.x)
+
+    """
+
+    def __new__(cls, point, force):
+        if isinstance(point, BodyBase):
+            point = point.masscenter
+        if not isinstance(point, Point):
+            raise TypeError('Force location should be a Point.')
+        if not isinstance(force, Vector):
+            raise TypeError('Force vector should be a Vector.')
+        return super().__new__(cls, point, force)
+
+    def __repr__(self):
+        return (f'{self.__class__.__name__}(point={self.point}, '
+                f'force={self.force})')
+
+    @property
+    def point(self):
+        return self.location
+
+    @property
+    def force(self):
+        return self.vector
+
+
+class Torque(LoadBase):
+    """Torque acting upon a frame.
+
+    Explanation
+    ===========
+
+    A torque is a free vector that is acting on a reference frame, which is
+    associated with a rigid body. This class stores both the frame and the
+    vector. A tuple can also be used, with the location as the first item and
+    the vector as second item.
+
+    Examples
+    ========
+
+    A torque of magnitude 2 about N.x acting on a frame N can be created as
+    follows:
+
+    >>> from sympy.physics.mechanics import ReferenceFrame, Torque
+    >>> N = ReferenceFrame('N')
+    >>> Torque(N, 2 * N.x)
+    (N, 2*N.x)
+
+    If a body is supplied, then the frame fixed to that body is used.
+
+    >>> from sympy.physics.mechanics import RigidBody
+    >>> rb = RigidBody('rb', frame=N)
+    >>> Torque(rb, 2 * N.x)
+    (N, 2*N.x)
+
+    """
+
+    def __new__(cls, frame, torque):
+        if isinstance(frame, BodyBase):
+            frame = frame.frame
+        if not isinstance(frame, ReferenceFrame):
+            raise TypeError('Torque location should be a ReferenceFrame.')
+        if not isinstance(torque, Vector):
+            raise TypeError('Torque vector should be a Vector.')
+        return super().__new__(cls, frame, torque)
+
+    def __repr__(self):
+        return (f'{self.__class__.__name__}(frame={self.frame}, '
+                f'torque={self.torque})')
+
+    @property
+    def frame(self):
+        return self.location
+
+    @property
+    def torque(self):
+        return self.vector
+
+
+def gravity(acceleration, *bodies):
+    """
+    Returns a list of gravity forces given the acceleration
+    due to gravity and any number of particles or rigidbodies.
+
+    Example
+    =======
+
+    >>> from sympy.physics.mechanics import ReferenceFrame, Particle, RigidBody
+    >>> from sympy.physics.mechanics.loads import gravity
+    >>> from sympy import symbols
+    >>> N = ReferenceFrame('N')
+    >>> g = symbols('g')
+    >>> P = Particle('P')
+    >>> B = RigidBody('B')
+    >>> gravity(g*N.y, P, B)
+    [(P_masscenter, P_mass*g*N.y),
+     (B_masscenter, B_mass*g*N.y)]
+
+    """
+
+    gravity_force = []
+    for body in bodies:
+        if not isinstance(body, BodyBase):
+            raise TypeError(f'{type(body)} is not a body type')
+        gravity_force.append(Force(body.masscenter, body.mass * acceleration))
+    return gravity_force
+
+
+def _parse_load(load):
+    """Helper function to parse loads and convert tuples to load objects."""
+    if isinstance(load, LoadBase):
+        return load
+    elif isinstance(load, tuple):
+        if len(load) != 2:
+            raise ValueError(f'Load {load} should have a length of 2.')
+        if isinstance(load[0], Point):
+            return Force(load[0], load[1])
+        elif isinstance(load[0], ReferenceFrame):
+            return Torque(load[0], load[1])
+        else:
+            raise ValueError(f'Load not recognized. The load location {load[0]}'
+                             f' should either be a Point or a ReferenceFrame.')
+    raise TypeError(f'Load type {type(load)} not recognized as a load. It '
+                    f'should be a Force, Torque or tuple.')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/method.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/method.py
new file mode 100644
index 0000000000000000000000000000000000000000..5c2c4a5f388e56e37bd9ecdf6daffc08ffa51070
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/method.py
@@ -0,0 +1,39 @@
+from abc import ABC, abstractmethod
+
+class _Methods(ABC):
+    """Abstract Base Class for all methods."""
+
+    @abstractmethod
+    def q(self):
+        pass
+
+    @abstractmethod
+    def u(self):
+        pass
+
+    @abstractmethod
+    def bodies(self):
+        pass
+
+    @abstractmethod
+    def loads(self):
+        pass
+
+    @abstractmethod
+    def mass_matrix(self):
+        pass
+
+    @abstractmethod
+    def forcing(self):
+        pass
+
+    @abstractmethod
+    def mass_matrix_full(self):
+        pass
+
+    @abstractmethod
+    def forcing_full(self):
+        pass
+
+    def _form_eoms(self):
+        raise NotImplementedError("Subclasses must implement this.")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/models.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/models.py
new file mode 100644
index 0000000000000000000000000000000000000000..a89b929ffd540a07787f6f94714850b348c90781
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/models.py
@@ -0,0 +1,230 @@
+#!/usr/bin/env python
+"""This module contains some sample symbolic models used for testing and
+examples."""
+
+# Internal imports
+from sympy.core import backend as sm
+import sympy.physics.mechanics as me
+
+
+def multi_mass_spring_damper(n=1, apply_gravity=False,
+                             apply_external_forces=False):
+    r"""Returns a system containing the symbolic equations of motion and
+    associated variables for a simple multi-degree of freedom point mass,
+    spring, damper system with optional gravitational and external
+    specified forces. For example, a two mass system under the influence of
+    gravity and external forces looks like:
+
+    ::
+
+        ----------------
+         |     |     |   | g
+         \    | |    |   V
+      k0 /    --- c0 |
+         |     |     | x0, v0
+        ---------    V
+        |  m0   | -----
+        ---------    |
+         | |   |     |
+         \ v  | |    |
+      k1 / f0 --- c1 |
+         |     |     | x1, v1
+        ---------    V
+        |  m1   | -----
+        ---------
+           | f1
+           V
+
+    Parameters
+    ==========
+
+    n : integer
+        The number of masses in the serial chain.
+    apply_gravity : boolean
+        If true, gravity will be applied to each mass.
+    apply_external_forces : boolean
+        If true, a time varying external force will be applied to each mass.
+
+    Returns
+    =======
+
+    kane : sympy.physics.mechanics.kane.KanesMethod
+        A KanesMethod object.
+
+    """
+
+    mass = sm.symbols('m:{}'.format(n))
+    stiffness = sm.symbols('k:{}'.format(n))
+    damping = sm.symbols('c:{}'.format(n))
+
+    acceleration_due_to_gravity = sm.symbols('g')
+
+    coordinates = me.dynamicsymbols('x:{}'.format(n))
+    speeds = me.dynamicsymbols('v:{}'.format(n))
+    specifieds = me.dynamicsymbols('f:{}'.format(n))
+
+    ceiling = me.ReferenceFrame('N')
+    origin = me.Point('origin')
+    origin.set_vel(ceiling, 0)
+
+    points = [origin]
+    kinematic_equations = []
+    particles = []
+    forces = []
+
+    for i in range(n):
+
+        center = points[-1].locatenew('center{}'.format(i),
+                                      coordinates[i] * ceiling.x)
+        center.set_vel(ceiling, points[-1].vel(ceiling) +
+                       speeds[i] * ceiling.x)
+        points.append(center)
+
+        block = me.Particle('block{}'.format(i), center, mass[i])
+
+        kinematic_equations.append(speeds[i] - coordinates[i].diff())
+
+        total_force = (-stiffness[i] * coordinates[i] -
+                       damping[i] * speeds[i])
+        try:
+            total_force += (stiffness[i + 1] * coordinates[i + 1] +
+                            damping[i + 1] * speeds[i + 1])
+        except IndexError:  # no force from below on last mass
+            pass
+
+        if apply_gravity:
+            total_force += mass[i] * acceleration_due_to_gravity
+
+        if apply_external_forces:
+            total_force += specifieds[i]
+
+        forces.append((center, total_force * ceiling.x))
+
+        particles.append(block)
+
+    kane = me.KanesMethod(ceiling, q_ind=coordinates, u_ind=speeds,
+                          kd_eqs=kinematic_equations)
+    kane.kanes_equations(particles, forces)
+
+    return kane
+
+
+def n_link_pendulum_on_cart(n=1, cart_force=True, joint_torques=False):
+    r"""Returns the system containing the symbolic first order equations of
+    motion for a 2D n-link pendulum on a sliding cart under the influence of
+    gravity.
+
+    ::
+
+                  |
+         o    y   v
+          \ 0 ^   g
+           \  |
+          --\-|----
+          |  \|   |
+      F-> |   o --|---> x
+          |       |
+          ---------
+           o     o
+
+    Parameters
+    ==========
+
+    n : integer
+        The number of links in the pendulum.
+    cart_force : boolean, default=True
+        If true an external specified lateral force is applied to the cart.
+    joint_torques : boolean, default=False
+        If true joint torques will be added as specified inputs at each
+        joint.
+
+    Returns
+    =======
+
+    kane : sympy.physics.mechanics.kane.KanesMethod
+        A KanesMethod object.
+
+    Notes
+    =====
+
+    The degrees of freedom of the system are n + 1, i.e. one for each
+    pendulum link and one for the lateral motion of the cart.
+
+    M x' = F, where x = [u0, ..., un+1, q0, ..., qn+1]
+
+    The joint angles are all defined relative to the ground where the x axis
+    defines the ground line and the y axis points up. The joint torques are
+    applied between each adjacent link and the between the cart and the
+    lower link where a positive torque corresponds to positive angle.
+
+    """
+    if n <= 0:
+        raise ValueError('The number of links must be a positive integer.')
+
+    q = me.dynamicsymbols('q:{}'.format(n + 1))
+    u = me.dynamicsymbols('u:{}'.format(n + 1))
+
+    if joint_torques is True:
+        T = me.dynamicsymbols('T1:{}'.format(n + 1))
+
+    m = sm.symbols('m:{}'.format(n + 1))
+    l = sm.symbols('l:{}'.format(n))
+    g, t = sm.symbols('g t')
+
+    I = me.ReferenceFrame('I')
+    O = me.Point('O')
+    O.set_vel(I, 0)
+
+    P0 = me.Point('P0')
+    P0.set_pos(O, q[0] * I.x)
+    P0.set_vel(I, u[0] * I.x)
+    Pa0 = me.Particle('Pa0', P0, m[0])
+
+    frames = [I]
+    points = [P0]
+    particles = [Pa0]
+    forces = [(P0, -m[0] * g * I.y)]
+    kindiffs = [q[0].diff(t) - u[0]]
+
+    if cart_force is True or joint_torques is True:
+        specified = []
+    else:
+        specified = None
+
+    for i in range(n):
+        Bi = I.orientnew('B{}'.format(i), 'Axis', [q[i + 1], I.z])
+        Bi.set_ang_vel(I, u[i + 1] * I.z)
+        frames.append(Bi)
+
+        Pi = points[-1].locatenew('P{}'.format(i + 1), l[i] * Bi.y)
+        Pi.v2pt_theory(points[-1], I, Bi)
+        points.append(Pi)
+
+        Pai = me.Particle('Pa' + str(i + 1), Pi, m[i + 1])
+        particles.append(Pai)
+
+        forces.append((Pi, -m[i + 1] * g * I.y))
+
+        if joint_torques is True:
+
+            specified.append(T[i])
+
+            if i == 0:
+                forces.append((I, -T[i] * I.z))
+
+            if i == n - 1:
+                forces.append((Bi, T[i] * I.z))
+            else:
+                forces.append((Bi, T[i] * I.z - T[i + 1] * I.z))
+
+        kindiffs.append(q[i + 1].diff(t) - u[i + 1])
+
+    if cart_force is True:
+        F = me.dynamicsymbols('F')
+        forces.append((P0, F * I.x))
+        specified.append(F)
+
+    kane = me.KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kindiffs)
+    kane.kanes_equations(particles, forces)
+
+    return kane
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/particle.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/particle.py
new file mode 100644
index 0000000000000000000000000000000000000000..5d49d4f811b8d1c7fff16c71991f5e01da6ded02
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/particle.py
@@ -0,0 +1,209 @@
+from sympy import S
+from sympy.physics.vector import cross, dot
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.physics.mechanics.inertia import inertia_of_point_mass
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+__all__ = ['Particle']
+
+
+class Particle(BodyBase):
+    """A particle.
+
+    Explanation
+    ===========
+
+    Particles have a non-zero mass and lack spatial extension; they take up no
+    space.
+
+    Values need to be supplied on initialization, but can be changed later.
+
+    Parameters
+    ==========
+
+    name : str
+        Name of particle
+    point : Point
+        A physics/mechanics Point which represents the position, velocity, and
+        acceleration of this Particle
+    mass : Sympifyable
+        A SymPy expression representing the Particle's mass
+    potential_energy : Sympifyable
+        The potential energy of the Particle.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import Particle, Point
+    >>> from sympy import Symbol
+    >>> po = Point('po')
+    >>> m = Symbol('m')
+    >>> pa = Particle('pa', po, m)
+    >>> # Or you could change these later
+    >>> pa.mass = m
+    >>> pa.point = po
+
+    """
+    point = BodyBase.masscenter
+
+    def __init__(self, name, point=None, mass=None):
+        super().__init__(name, point, mass)
+
+    def linear_momentum(self, frame):
+        """Linear momentum of the particle.
+
+        Explanation
+        ===========
+
+        The linear momentum L, of a particle P, with respect to frame N is
+        given by:
+
+        L = m * v
+
+        where m is the mass of the particle, and v is the velocity of the
+        particle in the frame N.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame in which linear momentum is desired.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Particle, Point, ReferenceFrame
+        >>> from sympy.physics.mechanics import dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> m, v = dynamicsymbols('m v')
+        >>> N = ReferenceFrame('N')
+        >>> P = Point('P')
+        >>> A = Particle('A', P, m)
+        >>> P.set_vel(N, v * N.x)
+        >>> A.linear_momentum(N)
+        m*v*N.x
+
+        """
+
+        return self.mass * self.point.vel(frame)
+
+    def angular_momentum(self, point, frame):
+        """Angular momentum of the particle about the point.
+
+        Explanation
+        ===========
+
+        The angular momentum H, about some point O of a particle, P, is given
+        by:
+
+        ``H = cross(r, m * v)``
+
+        where r is the position vector from point O to the particle P, m is
+        the mass of the particle, and v is the velocity of the particle in
+        the inertial frame, N.
+
+        Parameters
+        ==========
+
+        point : Point
+            The point about which angular momentum of the particle is desired.
+
+        frame : ReferenceFrame
+            The frame in which angular momentum is desired.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Particle, Point, ReferenceFrame
+        >>> from sympy.physics.mechanics import dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> m, v, r = dynamicsymbols('m v r')
+        >>> N = ReferenceFrame('N')
+        >>> O = Point('O')
+        >>> A = O.locatenew('A', r * N.x)
+        >>> P = Particle('P', A, m)
+        >>> P.point.set_vel(N, v * N.y)
+        >>> P.angular_momentum(O, N)
+        m*r*v*N.z
+
+        """
+
+        return cross(self.point.pos_from(point),
+                     self.mass * self.point.vel(frame))
+
+    def kinetic_energy(self, frame):
+        """Kinetic energy of the particle.
+
+        Explanation
+        ===========
+
+        The kinetic energy, T, of a particle, P, is given by:
+
+        ``T = 1/2 (dot(m * v, v))``
+
+        where m is the mass of particle P, and v is the velocity of the
+        particle in the supplied ReferenceFrame.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The Particle's velocity is typically defined with respect to
+            an inertial frame but any relevant frame in which the velocity is
+            known can be supplied.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Particle, Point, ReferenceFrame
+        >>> from sympy import symbols
+        >>> m, v, r = symbols('m v r')
+        >>> N = ReferenceFrame('N')
+        >>> O = Point('O')
+        >>> P = Particle('P', O, m)
+        >>> P.point.set_vel(N, v * N.y)
+        >>> P.kinetic_energy(N)
+        m*v**2/2
+
+        """
+
+        return S.Half * self.mass * dot(self.point.vel(frame),
+                                        self.point.vel(frame))
+
+    def set_potential_energy(self, scalar):
+        sympy_deprecation_warning(
+            """
+The sympy.physics.mechanics.Particle.set_potential_energy()
+method is deprecated. Instead use
+
+    P.potential_energy = scalar
+            """,
+        deprecated_since_version="1.5",
+        active_deprecations_target="deprecated-set-potential-energy",
+        )
+        self.potential_energy = scalar
+
+    def parallel_axis(self, point, frame):
+        """Returns an inertia dyadic of the particle with respect to another
+        point and frame.
+
+        Parameters
+        ==========
+
+        point : sympy.physics.vector.Point
+            The point to express the inertia dyadic about.
+        frame : sympy.physics.vector.ReferenceFrame
+            The reference frame used to construct the dyadic.
+
+        Returns
+        =======
+
+        inertia : sympy.physics.vector.Dyadic
+            The inertia dyadic of the particle expressed about the provided
+            point and frame.
+
+        """
+        return inertia_of_point_mass(self.mass, self.point.pos_from(point),
+                                     frame)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/pathway.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/pathway.py
new file mode 100644
index 0000000000000000000000000000000000000000..b86ba85b1d9d1434c51de3fd7cc429442fdbedb0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/pathway.py
@@ -0,0 +1,688 @@
+"""Implementations of pathways for use by actuators."""
+
+from abc import ABC, abstractmethod
+
+from sympy.core.singleton import S
+from sympy.physics.mechanics.loads import Force
+from sympy.physics.mechanics.wrapping_geometry import WrappingGeometryBase
+from sympy.physics.vector import Point, dynamicsymbols
+
+
+__all__ = ['PathwayBase', 'LinearPathway', 'ObstacleSetPathway',
+           'WrappingPathway']
+
+
+class PathwayBase(ABC):
+    """Abstract base class for all pathway classes to inherit from.
+
+    Notes
+    =====
+
+    Instances of this class cannot be directly instantiated by users. However,
+    it can be used to created custom pathway types through subclassing.
+
+    """
+
+    def __init__(self, *attachments):
+        """Initializer for ``PathwayBase``."""
+        self.attachments = attachments
+
+    @property
+    def attachments(self):
+        """The pair of points defining a pathway's ends."""
+        return self._attachments
+
+    @attachments.setter
+    def attachments(self, attachments):
+        if hasattr(self, '_attachments'):
+            msg = (
+                f'Can\'t set attribute `attachments` to {repr(attachments)} '
+                f'as it is immutable.'
+            )
+            raise AttributeError(msg)
+        if len(attachments) != 2:
+            msg = (
+                f'Value {repr(attachments)} passed to `attachments` was an '
+                f'iterable of length {len(attachments)}, must be an iterable '
+                f'of length 2.'
+            )
+            raise ValueError(msg)
+        for i, point in enumerate(attachments):
+            if not isinstance(point, Point):
+                msg = (
+                    f'Value {repr(point)} passed to `attachments` at index '
+                    f'{i} was of type {type(point)}, must be {Point}.'
+                )
+                raise TypeError(msg)
+        self._attachments = tuple(attachments)
+
+    @property
+    @abstractmethod
+    def length(self):
+        """An expression representing the pathway's length."""
+        pass
+
+    @property
+    @abstractmethod
+    def extension_velocity(self):
+        """An expression representing the pathway's extension velocity."""
+        pass
+
+    @abstractmethod
+    def to_loads(self, force):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        """
+        pass
+
+    def __repr__(self):
+        """Default representation of a pathway."""
+        attachments = ', '.join(str(a) for a in self.attachments)
+        return f'{self.__class__.__name__}({attachments})'
+
+
+class LinearPathway(PathwayBase):
+    """Linear pathway between a pair of attachment points.
+
+    Explanation
+    ===========
+
+    A linear pathway forms a straight-line segment between two points and is
+    the simplest pathway that can be formed. It will not interact with any
+    other objects in the system, i.e. a ``LinearPathway`` will intersect other
+    objects to ensure that the path between its two ends (its attachments) is
+    the shortest possible.
+
+    A linear pathway is made up of two points that can move relative to each
+    other, and a pair of equal and opposite forces acting on the points. If the
+    positive time-varying Euclidean distance between the two points is defined,
+    then the "extension velocity" is the time derivative of this distance. The
+    extension velocity is positive when the two points are moving away from
+    each other and negative when moving closer to each other. The direction for
+    the force acting on either point is determined by constructing a unit
+    vector directed from the other point to this point. This establishes a sign
+    convention such that a positive force magnitude tends to push the points
+    apart. The following diagram shows the positive force sense and the
+    distance between the points::
+
+       P           Q
+       o<--- F --->o
+       |           |
+       |<--l(t)--->|
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import LinearPathway
+
+    To construct a pathway, two points are required to be passed to the
+    ``attachments`` parameter as a ``tuple``.
+
+    >>> from sympy.physics.mechanics import Point
+    >>> pA, pB = Point('pA'), Point('pB')
+    >>> linear_pathway = LinearPathway(pA, pB)
+    >>> linear_pathway
+    LinearPathway(pA, pB)
+
+    The pathway created above isn't very interesting without the positions and
+    velocities of its attachment points being described. Without this its not
+    possible to describe how the pathway moves, i.e. its length or its
+    extension velocity.
+
+    >>> from sympy.physics.mechanics import ReferenceFrame
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> N = ReferenceFrame('N')
+    >>> q = dynamicsymbols('q')
+    >>> pB.set_pos(pA, q*N.x)
+    >>> pB.pos_from(pA)
+    q(t)*N.x
+
+    A pathway's length can be accessed via its ``length`` attribute.
+
+    >>> linear_pathway.length
+    sqrt(q(t)**2)
+
+    Note how what appears to be an overly-complex expression is returned. This
+    is actually required as it ensures that a pathway's length is always
+    positive.
+
+    A pathway's extension velocity can be accessed similarly via its
+    ``extension_velocity`` attribute.
+
+    >>> linear_pathway.extension_velocity
+    sqrt(q(t)**2)*Derivative(q(t), t)/q(t)
+
+    Parameters
+    ==========
+
+    attachments : tuple[Point, Point]
+        Pair of ``Point`` objects between which the linear pathway spans.
+        Constructor expects two points to be passed, e.g.
+        ``LinearPathway(Point('pA'), Point('pB'))``. More or fewer points will
+        cause an error to be thrown.
+
+    """
+
+    def __init__(self, *attachments):
+        """Initializer for ``LinearPathway``.
+
+        Parameters
+        ==========
+
+        attachments : Point
+            Pair of ``Point`` objects between which the linear pathway spans.
+            Constructor expects two points to be passed, e.g.
+            ``LinearPathway(Point('pA'), Point('pB'))``. More or fewer points
+            will cause an error to be thrown.
+
+        """
+        super().__init__(*attachments)
+
+    @property
+    def length(self):
+        """Exact analytical expression for the pathway's length."""
+        return _point_pair_length(*self.attachments)
+
+    @property
+    def extension_velocity(self):
+        """Exact analytical expression for the pathway's extension velocity."""
+        return _point_pair_extension_velocity(*self.attachments)
+
+    def to_loads(self, force):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        Examples
+        ========
+
+        The below example shows how to generate the loads produced in a linear
+        actuator that produces an expansile force ``F``. First, create a linear
+        actuator between two points separated by the coordinate ``q`` in the
+        ``x`` direction of the global frame ``N``.
+
+        >>> from sympy.physics.mechanics import (LinearPathway, Point,
+        ...     ReferenceFrame)
+        >>> from sympy.physics.vector import dynamicsymbols
+        >>> q = dynamicsymbols('q')
+        >>> N = ReferenceFrame('N')
+        >>> pA, pB = Point('pA'), Point('pB')
+        >>> pB.set_pos(pA, q*N.x)
+        >>> linear_pathway = LinearPathway(pA, pB)
+
+        Now create a symbol ``F`` to describe the magnitude of the (expansile)
+        force that will be produced along the pathway. The list of loads that
+        ``KanesMethod`` requires can be produced by calling the pathway's
+        ``to_loads`` method with ``F`` passed as the only argument.
+
+        >>> from sympy import symbols
+        >>> F = symbols('F')
+        >>> linear_pathway.to_loads(F)
+        [(pA, - F*q(t)/sqrt(q(t)**2)*N.x), (pB, F*q(t)/sqrt(q(t)**2)*N.x)]
+
+        Parameters
+        ==========
+
+        force : Expr
+            Magnitude of the force acting along the length of the pathway. As
+            per the sign conventions for the pathway length, pathway extension
+            velocity, and pair of point forces, if this ``Expr`` is positive
+            then the force will act to push the pair of points away from one
+            another (it is expansile).
+
+        """
+        relative_position = _point_pair_relative_position(*self.attachments)
+        loads = [
+            Force(self.attachments[0], -force*relative_position/self.length),
+            Force(self.attachments[-1], force*relative_position/self.length),
+        ]
+        return loads
+
+
+class ObstacleSetPathway(PathwayBase):
+    """Obstacle-set pathway between a set of attachment points.
+
+    Explanation
+    ===========
+
+    An obstacle-set pathway forms a series of straight-line segment between
+    pairs of consecutive points in a set of points. It is similar to multiple
+    linear pathways joined end-to-end. It will not interact with any other
+    objects in the system, i.e. an ``ObstacleSetPathway`` will intersect other
+    objects to ensure that the path between its pairs of points (its
+    attachments) is the shortest possible.
+
+    Examples
+    ========
+
+    To construct an obstacle-set pathway, three or more points are required to
+    be passed to the ``attachments`` parameter as a ``tuple``.
+
+    >>> from sympy.physics.mechanics import ObstacleSetPathway, Point
+    >>> pA, pB, pC, pD = Point('pA'), Point('pB'), Point('pC'), Point('pD')
+    >>> obstacle_set_pathway = ObstacleSetPathway(pA, pB, pC, pD)
+    >>> obstacle_set_pathway
+    ObstacleSetPathway(pA, pB, pC, pD)
+
+    The pathway created above isn't very interesting without the positions and
+    velocities of its attachment points being described. Without this its not
+    possible to describe how the pathway moves, i.e. its length or its
+    extension velocity.
+
+    >>> from sympy import cos, sin
+    >>> from sympy.physics.mechanics import ReferenceFrame
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> N = ReferenceFrame('N')
+    >>> q = dynamicsymbols('q')
+    >>> pO = Point('pO')
+    >>> pA.set_pos(pO, N.y)
+    >>> pB.set_pos(pO, -N.x)
+    >>> pC.set_pos(pA, cos(q) * N.x - (sin(q) + 1) * N.y)
+    >>> pD.set_pos(pA, sin(q) * N.x + (cos(q) - 1) * N.y)
+    >>> pB.pos_from(pA)
+    - N.x - N.y
+    >>> pC.pos_from(pA)
+    cos(q(t))*N.x + (-sin(q(t)) - 1)*N.y
+    >>> pD.pos_from(pA)
+    sin(q(t))*N.x + (cos(q(t)) - 1)*N.y
+
+    A pathway's length can be accessed via its ``length`` attribute.
+
+    >>> obstacle_set_pathway.length.simplify()
+    sqrt(2)*(sqrt(cos(q(t)) + 1) + 2)
+
+    A pathway's extension velocity can be accessed similarly via its
+    ``extension_velocity`` attribute.
+
+    >>> obstacle_set_pathway.extension_velocity.simplify()
+    -sqrt(2)*sin(q(t))*Derivative(q(t), t)/(2*sqrt(cos(q(t)) + 1))
+
+    Parameters
+    ==========
+
+    attachments : tuple[Point, ...]
+        The set of ``Point`` objects that define the segmented obstacle-set
+        pathway.
+
+    """
+
+    def __init__(self, *attachments):
+        """Initializer for ``ObstacleSetPathway``.
+
+        Parameters
+        ==========
+
+        attachments : tuple[Point, ...]
+            The set of ``Point`` objects that define the segmented obstacle-set
+            pathway.
+
+        """
+        super().__init__(*attachments)
+
+    @property
+    def attachments(self):
+        """The set of points defining a pathway's segmented path."""
+        return self._attachments
+
+    @attachments.setter
+    def attachments(self, attachments):
+        if hasattr(self, '_attachments'):
+            msg = (
+                f'Can\'t set attribute `attachments` to {repr(attachments)} '
+                f'as it is immutable.'
+            )
+            raise AttributeError(msg)
+        if len(attachments) <= 2:
+            msg = (
+                f'Value {repr(attachments)} passed to `attachments` was an '
+                f'iterable of length {len(attachments)}, must be an iterable '
+                f'of length 3 or greater.'
+            )
+            raise ValueError(msg)
+        for i, point in enumerate(attachments):
+            if not isinstance(point, Point):
+                msg = (
+                    f'Value {repr(point)} passed to `attachments` at index '
+                    f'{i} was of type {type(point)}, must be {Point}.'
+                )
+                raise TypeError(msg)
+        self._attachments = tuple(attachments)
+
+    @property
+    def length(self):
+        """Exact analytical expression for the pathway's length."""
+        length = S.Zero
+        attachment_pairs = zip(self.attachments[:-1], self.attachments[1:])
+        for attachment_pair in attachment_pairs:
+            length += _point_pair_length(*attachment_pair)
+        return length
+
+    @property
+    def extension_velocity(self):
+        """Exact analytical expression for the pathway's extension velocity."""
+        extension_velocity = S.Zero
+        attachment_pairs = zip(self.attachments[:-1], self.attachments[1:])
+        for attachment_pair in attachment_pairs:
+            extension_velocity += _point_pair_extension_velocity(*attachment_pair)
+        return extension_velocity
+
+    def to_loads(self, force):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        Examples
+        ========
+
+        The below example shows how to generate the loads produced in an
+        actuator that follows an obstacle-set pathway between four points and
+        produces an expansile force ``F``. First, create a pair of reference
+        frames, ``A`` and ``B``, in which the four points ``pA``, ``pB``,
+        ``pC``, and ``pD`` will be located. The first two points in frame ``A``
+        and the second two in frame ``B``. Frame ``B`` will also be oriented
+        such that it relates to ``A`` via a rotation of ``q`` about an axis
+        ``N.z`` in a global frame (``N.z``, ``A.z``, and ``B.z`` are parallel).
+
+        >>> from sympy.physics.mechanics import (ObstacleSetPathway, Point,
+        ...     ReferenceFrame)
+        >>> from sympy.physics.vector import dynamicsymbols
+        >>> q = dynamicsymbols('q')
+        >>> N = ReferenceFrame('N')
+        >>> N = ReferenceFrame('N')
+        >>> A = N.orientnew('A', 'axis', (0, N.x))
+        >>> B = A.orientnew('B', 'axis', (q, N.z))
+        >>> pO = Point('pO')
+        >>> pA, pB, pC, pD = Point('pA'), Point('pB'), Point('pC'), Point('pD')
+        >>> pA.set_pos(pO, A.x)
+        >>> pB.set_pos(pO, -A.y)
+        >>> pC.set_pos(pO, B.y)
+        >>> pD.set_pos(pO, B.x)
+        >>> obstacle_set_pathway = ObstacleSetPathway(pA, pB, pC, pD)
+
+        Now create a symbol ``F`` to describe the magnitude of the (expansile)
+        force that will be produced along the pathway. The list of loads that
+        ``KanesMethod`` requires can be produced by calling the pathway's
+        ``to_loads`` method with ``F`` passed as the only argument.
+
+        >>> from sympy import Symbol
+        >>> F = Symbol('F')
+        >>> obstacle_set_pathway.to_loads(F)
+        [(pA, sqrt(2)*F/2*A.x + sqrt(2)*F/2*A.y),
+         (pB, - sqrt(2)*F/2*A.x - sqrt(2)*F/2*A.y),
+         (pB, - F/sqrt(2*cos(q(t)) + 2)*A.y - F/sqrt(2*cos(q(t)) + 2)*B.y),
+         (pC, F/sqrt(2*cos(q(t)) + 2)*A.y + F/sqrt(2*cos(q(t)) + 2)*B.y),
+         (pC, - sqrt(2)*F/2*B.x + sqrt(2)*F/2*B.y),
+         (pD, sqrt(2)*F/2*B.x - sqrt(2)*F/2*B.y)]
+
+        Parameters
+        ==========
+
+        force : Expr
+            The force acting along the length of the pathway. It is assumed
+            that this ``Expr`` represents an expansile force.
+
+        """
+        loads = []
+        attachment_pairs = zip(self.attachments[:-1], self.attachments[1:])
+        for attachment_pair in attachment_pairs:
+            relative_position = _point_pair_relative_position(*attachment_pair)
+            length = _point_pair_length(*attachment_pair)
+            loads.extend([
+                Force(attachment_pair[0], -force*relative_position/length),
+                Force(attachment_pair[1], force*relative_position/length),
+            ])
+        return loads
+
+
+class WrappingPathway(PathwayBase):
+    """Pathway that wraps a geometry object.
+
+    Explanation
+    ===========
+
+    A wrapping pathway interacts with a geometry object and forms a path that
+    wraps smoothly along its surface. The wrapping pathway along the geometry
+    object will be the geodesic that the geometry object defines based on the
+    two points. It will not interact with any other objects in the system, i.e.
+    a ``WrappingPathway`` will intersect other objects to ensure that the path
+    between its two ends (its attachments) is the shortest possible.
+
+    To explain the sign conventions used for pathway length, extension
+    velocity, and direction of applied forces, we can ignore the geometry with
+    which the wrapping pathway interacts. A wrapping pathway is made up of two
+    points that can move relative to each other, and a pair of equal and
+    opposite forces acting on the points. If the positive time-varying
+    Euclidean distance between the two points is defined, then the "extension
+    velocity" is the time derivative of this distance. The extension velocity
+    is positive when the two points are moving away from each other and
+    negative when moving closer to each other. The direction for the force
+    acting on either point is determined by constructing a unit vector directed
+    from the other point to this point. This establishes a sign convention such
+    that a positive force magnitude tends to push the points apart. The
+    following diagram shows the positive force sense and the distance between
+    the points::
+
+       P           Q
+       o<--- F --->o
+       |           |
+       |<--l(t)--->|
+
+    Examples
+    ========
+
+    >>> from sympy.physics.mechanics import WrappingPathway
+
+    To construct a wrapping pathway, like other pathways, a pair of points must
+    be passed, followed by an instance of a wrapping geometry class as a
+    keyword argument. We'll use a cylinder with radius ``r`` and its axis
+    parallel to ``N.x`` passing through a point ``pO``.
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import Point, ReferenceFrame, WrappingCylinder
+    >>> r = symbols('r')
+    >>> N = ReferenceFrame('N')
+    >>> pA, pB, pO = Point('pA'), Point('pB'), Point('pO')
+    >>> cylinder = WrappingCylinder(r, pO, N.x)
+    >>> wrapping_pathway = WrappingPathway(pA, pB, cylinder)
+    >>> wrapping_pathway
+    WrappingPathway(pA, pB, geometry=WrappingCylinder(radius=r, point=pO,
+        axis=N.x))
+
+    Parameters
+    ==========
+
+    attachment_1 : Point
+        First of the pair of ``Point`` objects between which the wrapping
+        pathway spans.
+    attachment_2 : Point
+        Second of the pair of ``Point`` objects between which the wrapping
+        pathway spans.
+    geometry : WrappingGeometryBase
+        Geometry about which the pathway wraps.
+
+    """
+
+    def __init__(self, attachment_1, attachment_2, geometry):
+        """Initializer for ``WrappingPathway``.
+
+        Parameters
+        ==========
+
+        attachment_1 : Point
+            First of the pair of ``Point`` objects between which the wrapping
+            pathway spans.
+        attachment_2 : Point
+            Second of the pair of ``Point`` objects between which the wrapping
+            pathway spans.
+        geometry : WrappingGeometryBase
+            Geometry about which the pathway wraps.
+            The geometry about which the pathway wraps.
+
+        """
+        super().__init__(attachment_1, attachment_2)
+        self.geometry = geometry
+
+    @property
+    def geometry(self):
+        """Geometry around which the pathway wraps."""
+        return self._geometry
+
+    @geometry.setter
+    def geometry(self, geometry):
+        if hasattr(self, '_geometry'):
+            msg = (
+                f'Can\'t set attribute `geometry` to {repr(geometry)} as it '
+                f'is immutable.'
+            )
+            raise AttributeError(msg)
+        if not isinstance(geometry, WrappingGeometryBase):
+            msg = (
+                f'Value {repr(geometry)} passed to `geometry` was of type '
+                f'{type(geometry)}, must be {WrappingGeometryBase}.'
+            )
+            raise TypeError(msg)
+        self._geometry = geometry
+
+    @property
+    def length(self):
+        """Exact analytical expression for the pathway's length."""
+        return self.geometry.geodesic_length(*self.attachments)
+
+    @property
+    def extension_velocity(self):
+        """Exact analytical expression for the pathway's extension velocity."""
+        return self.length.diff(dynamicsymbols._t)
+
+    def to_loads(self, force):
+        """Loads required by the equations of motion method classes.
+
+        Explanation
+        ===========
+
+        ``KanesMethod`` requires a list of ``Point``-``Vector`` tuples to be
+        passed to the ``loads`` parameters of its ``kanes_equations`` method
+        when constructing the equations of motion. This method acts as a
+        utility to produce the correctly-structred pairs of points and vectors
+        required so that these can be easily concatenated with other items in
+        the list of loads and passed to ``KanesMethod.kanes_equations``. These
+        loads are also in the correct form to also be passed to the other
+        equations of motion method classes, e.g. ``LagrangesMethod``.
+
+        Examples
+        ========
+
+        The below example shows how to generate the loads produced in an
+        actuator that produces an expansile force ``F`` while wrapping around a
+        cylinder. First, create a cylinder with radius ``r`` and an axis
+        parallel to the ``N.z`` direction of the global frame ``N`` that also
+        passes through a point ``pO``.
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import (Point, ReferenceFrame,
+        ...     WrappingCylinder)
+        >>> N = ReferenceFrame('N')
+        >>> r = symbols('r', positive=True)
+        >>> pO = Point('pO')
+        >>> cylinder = WrappingCylinder(r, pO, N.z)
+
+        Create the pathway of the actuator using the ``WrappingPathway`` class,
+        defined to span between two points ``pA`` and ``pB``. Both points lie
+        on the surface of the cylinder and the location of ``pB`` is defined
+        relative to ``pA`` by the dynamics symbol ``q``.
+
+        >>> from sympy import cos, sin
+        >>> from sympy.physics.mechanics import WrappingPathway, dynamicsymbols
+        >>> q = dynamicsymbols('q')
+        >>> pA = Point('pA')
+        >>> pB = Point('pB')
+        >>> pA.set_pos(pO, r*N.x)
+        >>> pB.set_pos(pO, r*(cos(q)*N.x + sin(q)*N.y))
+        >>> pB.pos_from(pA)
+        (r*cos(q(t)) - r)*N.x + r*sin(q(t))*N.y
+        >>> pathway = WrappingPathway(pA, pB, cylinder)
+
+        Now create a symbol ``F`` to describe the magnitude of the (expansile)
+        force that will be produced along the pathway. The list of loads that
+        ``KanesMethod`` requires can be produced by calling the pathway's
+        ``to_loads`` method with ``F`` passed as the only argument.
+
+        >>> F = symbols('F')
+        >>> loads = pathway.to_loads(F)
+        >>> [load.__class__(load.location, load.vector.simplify()) for load in loads]
+        [(pA, F*N.y), (pB, F*sin(q(t))*N.x - F*cos(q(t))*N.y),
+         (pO, - F*sin(q(t))*N.x + F*(cos(q(t)) - 1)*N.y)]
+
+        Parameters
+        ==========
+
+        force : Expr
+            Magnitude of the force acting along the length of the pathway. It
+            is assumed that this ``Expr`` represents an expansile force.
+
+        """
+        pA, pB = self.attachments
+        pO = self.geometry.point
+        pA_force, pB_force = self.geometry.geodesic_end_vectors(pA, pB)
+        pO_force = -(pA_force + pB_force)
+
+        loads = [
+            Force(pA, force * pA_force),
+            Force(pB, force * pB_force),
+            Force(pO, force * pO_force),
+        ]
+        return loads
+
+    def __repr__(self):
+        """Representation of a ``WrappingPathway``."""
+        attachments = ', '.join(str(a) for a in self.attachments)
+        return (
+            f'{self.__class__.__name__}({attachments}, '
+            f'geometry={self.geometry})'
+        )
+
+
+def _point_pair_relative_position(point_1, point_2):
+    """The relative position between a pair of points."""
+    return point_2.pos_from(point_1)
+
+
+def _point_pair_length(point_1, point_2):
+    """The length of the direct linear path between two points."""
+    return _point_pair_relative_position(point_1, point_2).magnitude()
+
+
+def _point_pair_extension_velocity(point_1, point_2):
+    """The extension velocity of the direct linear path between two points."""
+    return _point_pair_length(point_1, point_2).diff(dynamicsymbols._t)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/rigidbody.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/rigidbody.py
new file mode 100644
index 0000000000000000000000000000000000000000..7cc61ff468f7f26d98209a48ca59ffa12a570490
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/rigidbody.py
@@ -0,0 +1,314 @@
+from sympy import Symbol, S
+from sympy.physics.vector import ReferenceFrame, Dyadic, Point, dot
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.physics.mechanics.inertia import inertia_of_point_mass, Inertia
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+__all__ = ['RigidBody']
+
+
+class RigidBody(BodyBase):
+    """An idealized rigid body.
+
+    Explanation
+    ===========
+
+    This is essentially a container which holds the various components which
+    describe a rigid body: a name, mass, center of mass, reference frame, and
+    inertia.
+
+    All of these need to be supplied on creation, but can be changed
+    afterwards.
+
+    Attributes
+    ==========
+
+    name : string
+        The body's name.
+    masscenter : Point
+        The point which represents the center of mass of the rigid body.
+    frame : ReferenceFrame
+        The ReferenceFrame which the rigid body is fixed in.
+    mass : Sympifyable
+        The body's mass.
+    inertia : (Dyadic, Point)
+        The body's inertia about a point; stored in a tuple as shown above.
+    potential_energy : Sympifyable
+        The potential energy of the RigidBody.
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol
+    >>> from sympy.physics.mechanics import ReferenceFrame, Point, RigidBody
+    >>> from sympy.physics.mechanics import outer
+    >>> m = Symbol('m')
+    >>> A = ReferenceFrame('A')
+    >>> P = Point('P')
+    >>> I = outer (A.x, A.x)
+    >>> inertia_tuple = (I, P)
+    >>> B = RigidBody('B', P, A, m, inertia_tuple)
+    >>> # Or you could change them afterwards
+    >>> m2 = Symbol('m2')
+    >>> B.mass = m2
+
+    """
+
+    def __init__(self, name, masscenter=None, frame=None, mass=None,
+                 inertia=None):
+        super().__init__(name, masscenter, mass)
+        if frame is None:
+            frame = ReferenceFrame(f'{name}_frame')
+        self.frame = frame
+        if inertia is None:
+            ixx = Symbol(f'{name}_ixx')
+            iyy = Symbol(f'{name}_iyy')
+            izz = Symbol(f'{name}_izz')
+            izx = Symbol(f'{name}_izx')
+            ixy = Symbol(f'{name}_ixy')
+            iyz = Symbol(f'{name}_iyz')
+            inertia = Inertia.from_inertia_scalars(self.masscenter, self.frame,
+                                                   ixx, iyy, izz, ixy, iyz, izx)
+        self.inertia = inertia
+
+    def __repr__(self):
+        return (f'{self.__class__.__name__}({repr(self.name)}, masscenter='
+                f'{repr(self.masscenter)}, frame={repr(self.frame)}, mass='
+                f'{repr(self.mass)}, inertia={repr(self.inertia)})')
+
+    @property
+    def frame(self):
+        """The ReferenceFrame fixed to the body."""
+        return self._frame
+
+    @frame.setter
+    def frame(self, F):
+        if not isinstance(F, ReferenceFrame):
+            raise TypeError("RigidBody frame must be a ReferenceFrame object.")
+        self._frame = F
+
+    @property
+    def x(self):
+        """The basis Vector for the body, in the x direction. """
+        return self.frame.x
+
+    @property
+    def y(self):
+        """The basis Vector for the body, in the y direction. """
+        return self.frame.y
+
+    @property
+    def z(self):
+        """The basis Vector for the body, in the z direction. """
+        return self.frame.z
+
+    @property
+    def inertia(self):
+        """The body's inertia about a point; stored as (Dyadic, Point)."""
+        return self._inertia
+
+    @inertia.setter
+    def inertia(self, I):
+        # check if I is of the form (Dyadic, Point)
+        if len(I) != 2 or not isinstance(I[0], Dyadic) or not isinstance(I[1], Point):
+            raise TypeError("RigidBody inertia must be a tuple of the form (Dyadic, Point).")
+
+        self._inertia = Inertia(I[0], I[1])
+        # have I S/O, want I S/S*
+        # I S/O = I S/S* + I S*/O; I S/S* = I S/O - I S*/O
+        # I_S/S* = I_S/O - I_S*/O
+        I_Ss_O = inertia_of_point_mass(self.mass,
+                                       self.masscenter.pos_from(I[1]),
+                                       self.frame)
+        self._central_inertia = I[0] - I_Ss_O
+
+    @property
+    def central_inertia(self):
+        """The body's central inertia dyadic."""
+        return self._central_inertia
+
+    @central_inertia.setter
+    def central_inertia(self, I):
+        if not isinstance(I, Dyadic):
+            raise TypeError("RigidBody inertia must be a Dyadic object.")
+        self.inertia = Inertia(I, self.masscenter)
+
+    def linear_momentum(self, frame):
+        """ Linear momentum of the rigid body.
+
+        Explanation
+        ===========
+
+        The linear momentum L, of a rigid body B, with respect to frame N is
+        given by:
+
+        ``L = m * v``
+
+        where m is the mass of the rigid body, and v is the velocity of the mass
+        center of B in the frame N.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame in which linear momentum is desired.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Point, ReferenceFrame, outer
+        >>> from sympy.physics.mechanics import RigidBody, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> m, v = dynamicsymbols('m v')
+        >>> N = ReferenceFrame('N')
+        >>> P = Point('P')
+        >>> P.set_vel(N, v * N.x)
+        >>> I = outer (N.x, N.x)
+        >>> Inertia_tuple = (I, P)
+        >>> B = RigidBody('B', P, N, m, Inertia_tuple)
+        >>> B.linear_momentum(N)
+        m*v*N.x
+
+        """
+
+        return self.mass * self.masscenter.vel(frame)
+
+    def angular_momentum(self, point, frame):
+        """Returns the angular momentum of the rigid body about a point in the
+        given frame.
+
+        Explanation
+        ===========
+
+        The angular momentum H of a rigid body B about some point O in a frame N
+        is given by:
+
+        ``H = dot(I, w) + cross(r, m * v)``
+
+        where I and m are the central inertia dyadic and mass of rigid body B, w
+        is the angular velocity of body B in the frame N, r is the position
+        vector from point O to the mass center of B, and v is the velocity of
+        the mass center in the frame N.
+
+        Parameters
+        ==========
+
+        point : Point
+            The point about which angular momentum is desired.
+        frame : ReferenceFrame
+            The frame in which angular momentum is desired.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Point, ReferenceFrame, outer
+        >>> from sympy.physics.mechanics import RigidBody, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> m, v, r, omega = dynamicsymbols('m v r omega')
+        >>> N = ReferenceFrame('N')
+        >>> b = ReferenceFrame('b')
+        >>> b.set_ang_vel(N, omega * b.x)
+        >>> P = Point('P')
+        >>> P.set_vel(N, 1 * N.x)
+        >>> I = outer(b.x, b.x)
+        >>> B = RigidBody('B', P, b, m, (I, P))
+        >>> B.angular_momentum(P, N)
+        omega*b.x
+
+        """
+        I = self.central_inertia
+        w = self.frame.ang_vel_in(frame)
+        m = self.mass
+        r = self.masscenter.pos_from(point)
+        v = self.masscenter.vel(frame)
+
+        return I.dot(w) + r.cross(m * v)
+
+    def kinetic_energy(self, frame):
+        """Kinetic energy of the rigid body.
+
+        Explanation
+        ===========
+
+        The kinetic energy, T, of a rigid body, B, is given by:
+
+        ``T = 1/2 * (dot(dot(I, w), w) + dot(m * v, v))``
+
+        where I and m are the central inertia dyadic and mass of rigid body B
+        respectively, w is the body's angular velocity, and v is the velocity of
+        the body's mass center in the supplied ReferenceFrame.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The RigidBody's angular velocity and the velocity of it's mass
+            center are typically defined with respect to an inertial frame but
+            any relevant frame in which the velocities are known can be
+            supplied.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.mechanics import Point, ReferenceFrame, outer
+        >>> from sympy.physics.mechanics import RigidBody
+        >>> from sympy import symbols
+        >>> m, v, r, omega = symbols('m v r omega')
+        >>> N = ReferenceFrame('N')
+        >>> b = ReferenceFrame('b')
+        >>> b.set_ang_vel(N, omega * b.x)
+        >>> P = Point('P')
+        >>> P.set_vel(N, v * N.x)
+        >>> I = outer (b.x, b.x)
+        >>> inertia_tuple = (I, P)
+        >>> B = RigidBody('B', P, b, m, inertia_tuple)
+        >>> B.kinetic_energy(N)
+        m*v**2/2 + omega**2/2
+
+        """
+
+        rotational_KE = S.Half * dot(
+            self.frame.ang_vel_in(frame),
+            dot(self.central_inertia, self.frame.ang_vel_in(frame)))
+        translational_KE = S.Half * self.mass * dot(self.masscenter.vel(frame),
+                                                    self.masscenter.vel(frame))
+        return rotational_KE + translational_KE
+
+    def set_potential_energy(self, scalar):
+        sympy_deprecation_warning(
+            """
+The sympy.physics.mechanics.RigidBody.set_potential_energy()
+method is deprecated. Instead use
+
+    B.potential_energy = scalar
+            """,
+        deprecated_since_version="1.5",
+        active_deprecations_target="deprecated-set-potential-energy",
+        )
+        self.potential_energy = scalar
+
+    def parallel_axis(self, point, frame=None):
+        """Returns the inertia dyadic of the body with respect to another point.
+
+        Parameters
+        ==========
+
+        point : sympy.physics.vector.Point
+            The point to express the inertia dyadic about.
+        frame : sympy.physics.vector.ReferenceFrame
+            The reference frame used to construct the dyadic.
+
+        Returns
+        =======
+
+        inertia : sympy.physics.vector.Dyadic
+            The inertia dyadic of the rigid body expressed about the provided
+            point.
+
+        """
+        if frame is None:
+            frame = self.frame
+        return self.central_inertia + inertia_of_point_mass(
+            self.mass, self.masscenter.pos_from(point), frame)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/system.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/system.py
new file mode 100644
index 0000000000000000000000000000000000000000..c8e0657d7da54ca5aaad9b37b816235641968470
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/system.py
@@ -0,0 +1,1553 @@
+from functools import wraps
+
+from sympy.core.basic import Basic
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.matrices.dense import Matrix, eye, zeros
+from sympy.core.containers import OrderedSet
+from sympy.physics.mechanics.actuator import ActuatorBase
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.physics.mechanics.functions import (
+    Lagrangian, _validate_coordinates, find_dynamicsymbols)
+from sympy.physics.mechanics.joint import Joint
+from sympy.physics.mechanics.kane import KanesMethod
+from sympy.physics.mechanics.lagrange import LagrangesMethod
+from sympy.physics.mechanics.loads import _parse_load, gravity
+from sympy.physics.mechanics.method import _Methods
+from sympy.physics.mechanics.particle import Particle
+from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import filldedent
+
+__all__ = ['SymbolicSystem', 'System']
+
+
+def _reset_eom_method(method):
+    """Decorator to reset the eom_method if a property is changed."""
+
+    @wraps(method)
+    def wrapper(self, *args, **kwargs):
+        self._eom_method = None
+        return method(self, *args, **kwargs)
+
+    return wrapper
+
+
+class System(_Methods):
+    """Class to define a multibody system and form its equations of motion.
+
+    Explanation
+    ===========
+
+    A ``System`` instance stores the different objects associated with a model,
+    including bodies, joints, constraints, and other relevant information. With
+    all the relationships between components defined, the ``System`` can be used
+    to form the equations of motion using a backend, such as ``KanesMethod``.
+    The ``System`` has been designed to be compatible with third-party
+    libraries for greater flexibility and integration with other tools.
+
+    Attributes
+    ==========
+
+    frame : ReferenceFrame
+        Inertial reference frame of the system.
+    fixed_point : Point
+        A fixed point in the inertial reference frame.
+    x : Vector
+        Unit vector fixed in the inertial reference frame.
+    y : Vector
+        Unit vector fixed in the inertial reference frame.
+    z : Vector
+        Unit vector fixed in the inertial reference frame.
+    q : ImmutableMatrix
+        Matrix of all the generalized coordinates, i.e. the independent
+        generalized coordinates stacked upon the dependent.
+    u : ImmutableMatrix
+        Matrix of all the generalized speeds, i.e. the independent generealized
+        speeds stacked upon the dependent.
+    q_ind : ImmutableMatrix
+        Matrix of the independent generalized coordinates.
+    q_dep : ImmutableMatrix
+        Matrix of the dependent generalized coordinates.
+    u_ind : ImmutableMatrix
+        Matrix of the independent generalized speeds.
+    u_dep : ImmutableMatrix
+        Matrix of the dependent generalized speeds.
+    u_aux : ImmutableMatrix
+        Matrix of auxiliary generalized speeds.
+    kdes : ImmutableMatrix
+        Matrix of the kinematical differential equations as expressions equated
+        to the zero matrix.
+    bodies : tuple of BodyBase subclasses
+        Tuple of all bodies that make up the system.
+    joints : tuple of Joint
+        Tuple of all joints that connect bodies in the system.
+    loads : tuple of LoadBase subclasses
+        Tuple of all loads that have been applied to the system.
+    actuators : tuple of ActuatorBase subclasses
+        Tuple of all actuators present in the system.
+    holonomic_constraints : ImmutableMatrix
+        Matrix with the holonomic constraints as expressions equated to the zero
+        matrix.
+    nonholonomic_constraints : ImmutableMatrix
+        Matrix with the nonholonomic constraints as expressions equated to the
+        zero matrix.
+    velocity_constraints : ImmutableMatrix
+        Matrix with the velocity constraints as expressions equated to the zero
+        matrix. These are by default derived as the time derivatives of the
+        holonomic constraints extended with the nonholonomic constraints.
+    eom_method : subclass of KanesMethod or LagrangesMethod
+        Backend for forming the equations of motion.
+
+    Examples
+    ========
+
+    In the example below a cart with a pendulum is created. The cart moves along
+    the x axis of the rail and the pendulum rotates about the z axis. The length
+    of the pendulum is ``l`` with the pendulum represented as a particle. To
+    move the cart a time dependent force ``F`` is applied to the cart.
+
+    We first need to import some functions and create some of our variables.
+
+    >>> from sympy import symbols, simplify
+    >>> from sympy.physics.mechanics import (
+    ...     mechanics_printing, dynamicsymbols, RigidBody, Particle,
+    ...     ReferenceFrame, PrismaticJoint, PinJoint, System)
+    >>> mechanics_printing(pretty_print=False)
+    >>> g, l = symbols('g l')
+    >>> F = dynamicsymbols('F')
+
+    The next step is to create bodies. It is also useful to create a frame for
+    locating the particle with respect to the pin joint later on, as a particle
+    does not have a body-fixed frame.
+
+    >>> rail = RigidBody('rail')
+    >>> cart = RigidBody('cart')
+    >>> bob = Particle('bob')
+    >>> bob_frame = ReferenceFrame('bob_frame')
+
+    Initialize the system, with the rail as the Newtonian reference. The body is
+    also automatically added to the system.
+
+    >>> system = System.from_newtonian(rail)
+    >>> print(system.bodies[0])
+    rail
+
+    Create the joints, while immediately also adding them to the system.
+
+    >>> system.add_joints(
+    ...     PrismaticJoint('slider', rail, cart, joint_axis=rail.x),
+    ...     PinJoint('pin', cart, bob, joint_axis=cart.z,
+    ...              child_interframe=bob_frame,
+    ...              child_point=l * bob_frame.y)
+    ... )
+    >>> system.joints
+    (PrismaticJoint: slider  parent: rail  child: cart,
+    PinJoint: pin  parent: cart  child: bob)
+
+    While adding the joints, the associated generalized coordinates, generalized
+    speeds, kinematic differential equations and bodies are also added to the
+    system.
+
+    >>> system.q
+    Matrix([
+    [q_slider],
+    [   q_pin]])
+    >>> system.u
+    Matrix([
+    [u_slider],
+    [   u_pin]])
+    >>> system.kdes
+    Matrix([
+    [u_slider - q_slider'],
+    [      u_pin - q_pin']])
+    >>> [body.name for body in system.bodies]
+    ['rail', 'cart', 'bob']
+
+    With the kinematics established, we can now apply gravity and the cart force
+    ``F``.
+
+    >>> system.apply_uniform_gravity(-g * system.y)
+    >>> system.add_loads((cart.masscenter, F * rail.x))
+    >>> system.loads
+    ((rail_masscenter, - g*rail_mass*rail_frame.y),
+     (cart_masscenter, - cart_mass*g*rail_frame.y),
+     (bob_masscenter, - bob_mass*g*rail_frame.y),
+     (cart_masscenter, F*rail_frame.x))
+
+    With the entire system defined, we can now form the equations of motion.
+    Before forming the equations of motion, one can also run some checks that
+    will try to identify some common errors.
+
+    >>> system.validate_system()
+    >>> system.form_eoms()
+    Matrix([
+    [bob_mass*l*u_pin**2*sin(q_pin) - bob_mass*l*cos(q_pin)*u_pin'
+     - (bob_mass + cart_mass)*u_slider' + F],
+    [                   -bob_mass*g*l*sin(q_pin) - bob_mass*l**2*u_pin'
+     - bob_mass*l*cos(q_pin)*u_slider']])
+    >>> simplify(system.mass_matrix)
+    Matrix([
+    [ bob_mass + cart_mass, bob_mass*l*cos(q_pin)],
+    [bob_mass*l*cos(q_pin),         bob_mass*l**2]])
+    >>> system.forcing
+    Matrix([
+    [bob_mass*l*u_pin**2*sin(q_pin) + F],
+    [          -bob_mass*g*l*sin(q_pin)]])
+
+    The complexity of the above example can be increased if we add a constraint
+    to prevent the particle from moving in the horizontal (x) direction. This
+    can be done by adding a holonomic constraint. After which we should also
+    redefine what our (in)dependent generalized coordinates and speeds are.
+
+    >>> system.add_holonomic_constraints(
+    ...     bob.masscenter.pos_from(rail.masscenter).dot(system.x)
+    ... )
+    >>> system.q_ind = system.get_joint('pin').coordinates
+    >>> system.q_dep = system.get_joint('slider').coordinates
+    >>> system.u_ind = system.get_joint('pin').speeds
+    >>> system.u_dep = system.get_joint('slider').speeds
+
+    With the updated system the equations of motion can be formed again.
+
+    >>> system.validate_system()
+    >>> system.form_eoms()
+    Matrix([[-bob_mass*g*l*sin(q_pin)
+             - bob_mass*l**2*u_pin'
+             - bob_mass*l*cos(q_pin)*u_slider'
+             - l*(bob_mass*l*u_pin**2*sin(q_pin)
+             - bob_mass*l*cos(q_pin)*u_pin'
+             - (bob_mass + cart_mass)*u_slider')*cos(q_pin)
+             - l*F*cos(q_pin)]])
+    >>> simplify(system.mass_matrix)
+    Matrix([
+    [bob_mass*l**2*sin(q_pin)**2, -cart_mass*l*cos(q_pin)],
+    [               l*cos(q_pin),                       1]])
+    >>> simplify(system.forcing)
+    Matrix([
+    [-l*(bob_mass*g*sin(q_pin) + bob_mass*l*u_pin**2*sin(2*q_pin)/2
+     + F*cos(q_pin))],
+    [
+    l*u_pin**2*sin(q_pin)]])
+
+    """
+
+    def __init__(self, frame=None, fixed_point=None):
+        """Initialize the system.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame, optional
+            The inertial frame of the system. If none is supplied, a new frame
+            will be created.
+        fixed_point : Point, optional
+            A fixed point in the inertial reference frame. If none is supplied,
+            a new fixed_point will be created.
+
+        """
+        if frame is None:
+            frame = ReferenceFrame('inertial_frame')
+        elif not isinstance(frame, ReferenceFrame):
+            raise TypeError('Frame must be an instance of ReferenceFrame.')
+        self._frame = frame
+        if fixed_point is None:
+            fixed_point = Point('inertial_point')
+        elif not isinstance(fixed_point, Point):
+            raise TypeError('Fixed point must be an instance of Point.')
+        self._fixed_point = fixed_point
+        self._fixed_point.set_vel(self._frame, 0)
+        self._q_ind = ImmutableMatrix(1, 0, []).T
+        self._q_dep = ImmutableMatrix(1, 0, []).T
+        self._u_ind = ImmutableMatrix(1, 0, []).T
+        self._u_dep = ImmutableMatrix(1, 0, []).T
+        self._u_aux = ImmutableMatrix(1, 0, []).T
+        self._kdes = ImmutableMatrix(1, 0, []).T
+        self._hol_coneqs = ImmutableMatrix(1, 0, []).T
+        self._nonhol_coneqs = ImmutableMatrix(1, 0, []).T
+        self._vel_constrs = None
+        self._bodies = []
+        self._joints = []
+        self._loads = []
+        self._actuators = []
+        self._eom_method = None
+
+    @classmethod
+    def from_newtonian(cls, newtonian):
+        """Constructs the system with respect to a Newtonian body."""
+        if isinstance(newtonian, Particle):
+            raise TypeError('A Particle has no frame so cannot act as '
+                            'the Newtonian.')
+        system = cls(frame=newtonian.frame, fixed_point=newtonian.masscenter)
+        system.add_bodies(newtonian)
+        return system
+
+    @property
+    def fixed_point(self):
+        """Fixed point in the inertial reference frame."""
+        return self._fixed_point
+
+    @property
+    def frame(self):
+        """Inertial reference frame of the system."""
+        return self._frame
+
+    @property
+    def x(self):
+        """Unit vector fixed in the inertial reference frame."""
+        return self._frame.x
+
+    @property
+    def y(self):
+        """Unit vector fixed in the inertial reference frame."""
+        return self._frame.y
+
+    @property
+    def z(self):
+        """Unit vector fixed in the inertial reference frame."""
+        return self._frame.z
+
+    @property
+    def bodies(self):
+        """Tuple of all bodies that have been added to the system."""
+        return tuple(self._bodies)
+
+    @bodies.setter
+    @_reset_eom_method
+    def bodies(self, bodies):
+        bodies = self._objects_to_list(bodies)
+        self._check_objects(bodies, [], BodyBase, 'Bodies', 'bodies')
+        self._bodies = bodies
+
+    @property
+    def joints(self):
+        """Tuple of all joints that have been added to the system."""
+        return tuple(self._joints)
+
+    @joints.setter
+    @_reset_eom_method
+    def joints(self, joints):
+        joints = self._objects_to_list(joints)
+        self._check_objects(joints, [], Joint, 'Joints', 'joints')
+        self._joints = []
+        self.add_joints(*joints)
+
+    @property
+    def loads(self):
+        """Tuple of loads that have been applied on the system."""
+        return tuple(self._loads)
+
+    @loads.setter
+    @_reset_eom_method
+    def loads(self, loads):
+        loads = self._objects_to_list(loads)
+        self._loads = [_parse_load(load) for load in loads]
+
+    @property
+    def actuators(self):
+        """Tuple of actuators present in the system."""
+        return tuple(self._actuators)
+
+    @actuators.setter
+    @_reset_eom_method
+    def actuators(self, actuators):
+        actuators = self._objects_to_list(actuators)
+        self._check_objects(actuators, [], ActuatorBase, 'Actuators',
+                            'actuators')
+        self._actuators = actuators
+
+    @property
+    def q(self):
+        """Matrix of all the generalized coordinates with the independent
+        stacked upon the dependent."""
+        return self._q_ind.col_join(self._q_dep)
+
+    @property
+    def u(self):
+        """Matrix of all the generalized speeds with the independent stacked
+        upon the dependent."""
+        return self._u_ind.col_join(self._u_dep)
+
+    @property
+    def q_ind(self):
+        """Matrix of the independent generalized coordinates."""
+        return self._q_ind
+
+    @q_ind.setter
+    @_reset_eom_method
+    def q_ind(self, q_ind):
+        self._q_ind, self._q_dep = self._parse_coordinates(
+            self._objects_to_list(q_ind), True, [], self.q_dep, 'coordinates')
+
+    @property
+    def q_dep(self):
+        """Matrix of the dependent generalized coordinates."""
+        return self._q_dep
+
+    @q_dep.setter
+    @_reset_eom_method
+    def q_dep(self, q_dep):
+        self._q_ind, self._q_dep = self._parse_coordinates(
+            self._objects_to_list(q_dep), False, self.q_ind, [], 'coordinates')
+
+    @property
+    def u_ind(self):
+        """Matrix of the independent generalized speeds."""
+        return self._u_ind
+
+    @u_ind.setter
+    @_reset_eom_method
+    def u_ind(self, u_ind):
+        self._u_ind, self._u_dep = self._parse_coordinates(
+            self._objects_to_list(u_ind), True, [], self.u_dep, 'speeds')
+
+    @property
+    def u_dep(self):
+        """Matrix of the dependent generalized speeds."""
+        return self._u_dep
+
+    @u_dep.setter
+    @_reset_eom_method
+    def u_dep(self, u_dep):
+        self._u_ind, self._u_dep = self._parse_coordinates(
+            self._objects_to_list(u_dep), False, self.u_ind, [], 'speeds')
+
+    @property
+    def u_aux(self):
+        """Matrix of auxiliary generalized speeds."""
+        return self._u_aux
+
+    @u_aux.setter
+    @_reset_eom_method
+    def u_aux(self, u_aux):
+        self._u_aux = self._parse_coordinates(
+            self._objects_to_list(u_aux), True, [], [], 'u_auxiliary')[0]
+
+    @property
+    def kdes(self):
+        """Kinematical differential equations as expressions equated to the zero
+        matrix. These equations describe the coupling between the generalized
+        coordinates and the generalized speeds."""
+        return self._kdes
+
+    @kdes.setter
+    @_reset_eom_method
+    def kdes(self, kdes):
+        kdes = self._objects_to_list(kdes)
+        self._kdes = self._parse_expressions(
+            kdes, [], 'kinematic differential equations')
+
+    @property
+    def holonomic_constraints(self):
+        """Matrix with the holonomic constraints as expressions equated to the
+        zero matrix."""
+        return self._hol_coneqs
+
+    @holonomic_constraints.setter
+    @_reset_eom_method
+    def holonomic_constraints(self, constraints):
+        constraints = self._objects_to_list(constraints)
+        self._hol_coneqs = self._parse_expressions(
+            constraints, [], 'holonomic constraints')
+
+    @property
+    def nonholonomic_constraints(self):
+        """Matrix with the nonholonomic constraints as expressions equated to
+        the zero matrix."""
+        return self._nonhol_coneqs
+
+    @nonholonomic_constraints.setter
+    @_reset_eom_method
+    def nonholonomic_constraints(self, constraints):
+        constraints = self._objects_to_list(constraints)
+        self._nonhol_coneqs = self._parse_expressions(
+            constraints, [], 'nonholonomic constraints')
+
+    @property
+    def velocity_constraints(self):
+        """Matrix with the velocity constraints as expressions equated to the
+        zero matrix. The velocity constraints are by default derived from the
+        holonomic and nonholonomic constraints unless they are explicitly set.
+        """
+        if self._vel_constrs is None:
+            return self.holonomic_constraints.diff(dynamicsymbols._t).col_join(
+                self.nonholonomic_constraints)
+        return self._vel_constrs
+
+    @velocity_constraints.setter
+    @_reset_eom_method
+    def velocity_constraints(self, constraints):
+        if constraints is None:
+            self._vel_constrs = None
+            return
+        constraints = self._objects_to_list(constraints)
+        self._vel_constrs = self._parse_expressions(
+            constraints, [], 'velocity constraints')
+
+    @property
+    def eom_method(self):
+        """Backend for forming the equations of motion."""
+        return self._eom_method
+
+    @staticmethod
+    def _objects_to_list(lst):
+        """Helper to convert passed objects to a list."""
+        if not iterable(lst):  # Only one object
+            return [lst]
+        return list(lst[:])  # converts Matrix and tuple to flattened list
+
+    @staticmethod
+    def _check_objects(objects, obj_lst, expected_type, obj_name, type_name):
+        """Helper to check the objects that are being added to the system.
+
+        Explanation
+        ===========
+        This method checks that the objects that are being added to the system
+        are of the correct type and have not already been added. If any of the
+        objects are not of the correct type or have already been added, then
+        an error is raised.
+
+        Parameters
+        ==========
+        objects : iterable
+            The objects that would be added to the system.
+        obj_lst : list
+            The list of objects that are already in the system.
+        expected_type : type
+            The type that the objects should be.
+        obj_name : str
+            The name of the category of objects. This string is used to
+            formulate the error message for the user.
+        type_name : str
+            The name of the type that the objects should be. This string is used
+            to formulate the error message for the user.
+
+        """
+        seen = set(obj_lst)
+        duplicates = set()
+        wrong_types = set()
+        for obj in objects:
+            if not isinstance(obj, expected_type):
+                wrong_types.add(obj)
+            if obj in seen:
+                duplicates.add(obj)
+            else:
+                seen.add(obj)
+        if wrong_types:
+            raise TypeError(f'{obj_name} {wrong_types} are not {type_name}.')
+        if duplicates:
+            raise ValueError(f'{obj_name} {duplicates} have already been added '
+                             f'to the system.')
+
+    def _parse_coordinates(self, new_coords, independent, old_coords_ind,
+                           old_coords_dep, coord_type='coordinates'):
+        """Helper to parse coordinates and speeds."""
+        # Construct lists of the independent and dependent coordinates
+        coords_ind, coords_dep = old_coords_ind[:], old_coords_dep[:]
+        if not iterable(independent):
+            independent = [independent] * len(new_coords)
+        for coord, indep in zip(new_coords, independent):
+            if indep:
+                coords_ind.append(coord)
+            else:
+                coords_dep.append(coord)
+        # Check types and duplicates
+        current = {'coordinates': self.q_ind[:] + self.q_dep[:],
+                   'speeds': self.u_ind[:] + self.u_dep[:],
+                   'u_auxiliary': self._u_aux[:],
+                   coord_type: coords_ind + coords_dep}
+        _validate_coordinates(**current)
+        return (ImmutableMatrix(1, len(coords_ind), coords_ind).T,
+                ImmutableMatrix(1, len(coords_dep), coords_dep).T)
+
+    @staticmethod
+    def _parse_expressions(new_expressions, old_expressions, name,
+                           check_negatives=False):
+        """Helper to parse expressions like constraints."""
+        old_expressions = old_expressions[:]
+        new_expressions = list(new_expressions)  # Converts a possible tuple
+        if check_negatives:
+            check_exprs = old_expressions + [-expr for expr in old_expressions]
+        else:
+            check_exprs = old_expressions
+        System._check_objects(new_expressions, check_exprs, Basic, name,
+                              'expressions')
+        for expr in new_expressions:
+            if expr == 0:
+                raise ValueError(f'Parsed {name} are zero.')
+        return ImmutableMatrix(1, len(old_expressions) + len(new_expressions),
+                               old_expressions + new_expressions).T
+
+    @_reset_eom_method
+    def add_coordinates(self, *coordinates, independent=True):
+        """Add generalized coordinate(s) to the system.
+
+        Parameters
+        ==========
+
+        *coordinates : dynamicsymbols
+            One or more generalized coordinates to be added to the system.
+        independent : bool or list of bool, optional
+            Boolean whether a coordinate is dependent or independent. The
+            default is True, so the coordinates are added as independent by
+            default.
+
+        """
+        self._q_ind, self._q_dep = self._parse_coordinates(
+            coordinates, independent, self.q_ind, self.q_dep, 'coordinates')
+
+    @_reset_eom_method
+    def add_speeds(self, *speeds, independent=True):
+        """Add generalized speed(s) to the system.
+
+        Parameters
+        ==========
+
+        *speeds : dynamicsymbols
+            One or more generalized speeds to be added to the system.
+        independent : bool or list of bool, optional
+            Boolean whether a speed is dependent or independent. The default is
+            True, so the speeds are added as independent by default.
+
+        """
+        self._u_ind, self._u_dep = self._parse_coordinates(
+            speeds, independent, self.u_ind, self.u_dep, 'speeds')
+
+    @_reset_eom_method
+    def add_auxiliary_speeds(self, *speeds):
+        """Add auxiliary speed(s) to the system.
+
+        Parameters
+        ==========
+
+        *speeds : dynamicsymbols
+            One or more auxiliary speeds to be added to the system.
+
+        """
+        self._u_aux = self._parse_coordinates(
+            speeds, True, self._u_aux, [], 'u_auxiliary')[0]
+
+    @_reset_eom_method
+    def add_kdes(self, *kdes):
+        """Add kinematic differential equation(s) to the system.
+
+        Parameters
+        ==========
+
+        *kdes : Expr
+            One or more kinematic differential equations.
+
+        """
+        self._kdes = self._parse_expressions(
+            kdes, self.kdes, 'kinematic differential equations',
+            check_negatives=True)
+
+    @_reset_eom_method
+    def add_holonomic_constraints(self, *constraints):
+        """Add holonomic constraint(s) to the system.
+
+        Parameters
+        ==========
+
+        *constraints : Expr
+            One or more holonomic constraints, which are expressions that should
+            be zero.
+
+        """
+        self._hol_coneqs = self._parse_expressions(
+            constraints, self._hol_coneqs, 'holonomic constraints',
+            check_negatives=True)
+
+    @_reset_eom_method
+    def add_nonholonomic_constraints(self, *constraints):
+        """Add nonholonomic constraint(s) to the system.
+
+        Parameters
+        ==========
+
+        *constraints : Expr
+            One or more nonholonomic constraints, which are expressions that
+            should be zero.
+
+        """
+        self._nonhol_coneqs = self._parse_expressions(
+            constraints, self._nonhol_coneqs, 'nonholonomic constraints',
+            check_negatives=True)
+
+    @_reset_eom_method
+    def add_bodies(self, *bodies):
+        """Add body(ies) to the system.
+
+        Parameters
+        ==========
+
+        bodies : Particle or RigidBody
+            One or more bodies.
+
+        """
+        self._check_objects(bodies, self.bodies, BodyBase, 'Bodies', 'bodies')
+        self._bodies.extend(bodies)
+
+    @_reset_eom_method
+    def add_loads(self, *loads):
+        """Add load(s) to the system.
+
+        Parameters
+        ==========
+
+        *loads : Force or Torque
+            One or more loads.
+
+        """
+        loads = [_parse_load(load) for load in loads]  # Checks the loads
+        self._loads.extend(loads)
+
+    @_reset_eom_method
+    def apply_uniform_gravity(self, acceleration):
+        """Apply uniform gravity to all bodies in the system by adding loads.
+
+        Parameters
+        ==========
+
+        acceleration : Vector
+            The acceleration due to gravity.
+
+        """
+        self.add_loads(*gravity(acceleration, *self.bodies))
+
+    @_reset_eom_method
+    def add_actuators(self, *actuators):
+        """Add actuator(s) to the system.
+
+        Parameters
+        ==========
+
+        *actuators : subclass of ActuatorBase
+            One or more actuators.
+
+        """
+        self._check_objects(actuators, self.actuators, ActuatorBase,
+                            'Actuators', 'actuators')
+        self._actuators.extend(actuators)
+
+    @_reset_eom_method
+    def add_joints(self, *joints):
+        """Add joint(s) to the system.
+
+        Explanation
+        ===========
+
+        This methods adds one or more joints to the system including its
+        associated objects, i.e. generalized coordinates, generalized speeds,
+        kinematic differential equations and the bodies.
+
+        Parameters
+        ==========
+
+        *joints : subclass of Joint
+            One or more joints.
+
+        Notes
+        =====
+
+        For the generalized coordinates, generalized speeds and bodies it is
+        checked whether they are already known by the system instance. If they
+        are, then they are not added. The kinematic differential equations are
+        however always added to the system, so you should not also manually add
+        those on beforehand.
+
+        """
+        self._check_objects(joints, self.joints, Joint, 'Joints', 'joints')
+        self._joints.extend(joints)
+        coordinates, speeds, kdes, bodies = (OrderedSet() for _ in range(4))
+        for joint in joints:
+            coordinates.update(joint.coordinates)
+            speeds.update(joint.speeds)
+            kdes.update(joint.kdes)
+            bodies.update((joint.parent, joint.child))
+        coordinates = coordinates.difference(self.q)
+        speeds = speeds.difference(self.u)
+        kdes = kdes.difference(self.kdes[:] + (-self.kdes)[:])
+        bodies = bodies.difference(self.bodies)
+        self.add_coordinates(*tuple(coordinates))
+        self.add_speeds(*tuple(speeds))
+        self.add_kdes(*(kde for kde in tuple(kdes) if not kde == 0))
+        self.add_bodies(*tuple(bodies))
+
+    def get_body(self, name):
+        """Retrieve a body from the system by name.
+
+        Parameters
+        ==========
+
+        name : str
+            The name of the body to retrieve.
+
+        Returns
+        =======
+
+        RigidBody or Particle
+            The body with the given name, or None if no such body exists.
+
+        """
+        for body in self._bodies:
+            if body.name == name:
+                return body
+
+    def get_joint(self, name):
+        """Retrieve a joint from the system by name.
+
+        Parameters
+        ==========
+
+        name : str
+            The name of the joint to retrieve.
+
+        Returns
+        =======
+
+        subclass of Joint
+            The joint with the given name, or None if no such joint exists.
+
+        """
+        for joint in self._joints:
+            if joint.name == name:
+                return joint
+
+    def _form_eoms(self):
+        return self.form_eoms()
+
+    def form_eoms(self, eom_method=KanesMethod, **kwargs):
+        """Form the equations of motion of the system.
+
+        Parameters
+        ==========
+
+        eom_method : subclass of KanesMethod or LagrangesMethod
+            Backend class to be used for forming the equations of motion. The
+            default is ``KanesMethod``.
+
+        Returns
+        ========
+
+        ImmutableMatrix
+            Vector of equations of motions.
+
+        Examples
+        ========
+
+        This is a simple example for a one degree of freedom translational
+        spring-mass-damper.
+
+        >>> from sympy import S, symbols
+        >>> from sympy.physics.mechanics import (
+        ...     LagrangesMethod, dynamicsymbols, PrismaticJoint, Particle,
+        ...     RigidBody, System)
+        >>> q = dynamicsymbols('q')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> m, k, b = symbols('m k b')
+        >>> wall = RigidBody('W')
+        >>> system = System.from_newtonian(wall)
+        >>> bob = Particle('P', mass=m)
+        >>> bob.potential_energy = S.Half * k * q**2
+        >>> system.add_joints(PrismaticJoint('J', wall, bob, q, qd))
+        >>> system.add_loads((bob.masscenter, b * qd * system.x))
+        >>> system.form_eoms(LagrangesMethod)
+        Matrix([[-b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]])
+
+        We can also solve for the states using the 'rhs' method.
+
+        >>> system.rhs()
+        Matrix([
+        [               Derivative(q(t), t)],
+        [(b*Derivative(q(t), t) - k*q(t))/m]])
+
+        """
+        # KanesMethod does not accept empty iterables
+        loads = self.loads + tuple(
+            load for act in self.actuators for load in act.to_loads())
+        loads = loads if loads else None
+        if issubclass(eom_method, KanesMethod):
+            disallowed_kwargs = {
+                "frame", "q_ind", "u_ind", "kd_eqs", "q_dependent",
+                "u_dependent", "u_auxiliary", "configuration_constraints",
+                "velocity_constraints", "forcelist", "bodies"}
+            wrong_kwargs = disallowed_kwargs.intersection(kwargs)
+            if wrong_kwargs:
+                raise ValueError(
+                    f"The following keyword arguments are not allowed to be "
+                    f"overwritten in {eom_method.__name__}: {wrong_kwargs}.")
+            kwargs = {"frame": self.frame, "q_ind": self.q_ind,
+                      "u_ind": self.u_ind, "kd_eqs": self.kdes,
+                      "q_dependent": self.q_dep, "u_dependent": self.u_dep,
+                      "configuration_constraints": self.holonomic_constraints,
+                      "velocity_constraints": self.velocity_constraints,
+                      "u_auxiliary": self.u_aux,
+                      "forcelist": loads, "bodies": self.bodies,
+                      "explicit_kinematics": False, **kwargs}
+            self._eom_method = eom_method(**kwargs)
+        elif issubclass(eom_method, LagrangesMethod):
+            disallowed_kwargs = {
+                "frame", "qs", "forcelist", "bodies", "hol_coneqs",
+                "nonhol_coneqs", "Lagrangian"}
+            wrong_kwargs = disallowed_kwargs.intersection(kwargs)
+            if wrong_kwargs:
+                raise ValueError(
+                    f"The following keyword arguments are not allowed to be "
+                    f"overwritten in {eom_method.__name__}: {wrong_kwargs}.")
+            kwargs = {"frame": self.frame, "qs": self.q, "forcelist": loads,
+                      "bodies": self.bodies,
+                      "hol_coneqs": self.holonomic_constraints,
+                      "nonhol_coneqs": self.nonholonomic_constraints, **kwargs}
+            if "Lagrangian" not in kwargs:
+                kwargs["Lagrangian"] = Lagrangian(kwargs["frame"],
+                                                  *kwargs["bodies"])
+            self._eom_method = eom_method(**kwargs)
+        else:
+            raise NotImplementedError(f'{eom_method} has not been implemented.')
+        return self.eom_method._form_eoms()
+
+    def rhs(self, inv_method=None):
+        """Compute the equations of motion in the explicit form.
+
+        Parameters
+        ==========
+
+        inv_method : str
+            The specific sympy inverse matrix calculation method to use. For a
+            list of valid methods, see
+            :meth:`~sympy.matrices.matrixbase.MatrixBase.inv`
+
+        Returns
+        ========
+
+        ImmutableMatrix
+            Equations of motion in the explicit form.
+
+        See Also
+        ========
+
+        sympy.physics.mechanics.kane.KanesMethod.rhs:
+            KanesMethod's ``rhs`` function.
+        sympy.physics.mechanics.lagrange.LagrangesMethod.rhs:
+            LagrangesMethod's ``rhs`` function.
+
+        """
+        return self.eom_method.rhs(inv_method=inv_method)
+
+    @property
+    def mass_matrix(self):
+        r"""The mass matrix of the system.
+
+        Explanation
+        ===========
+
+        The mass matrix $M_d$ and the forcing vector $f_d$ of a system describe
+        the system's dynamics according to the following equations:
+
+        .. math::
+            M_d \dot{u} = f_d
+
+        where $\dot{u}$ is the time derivative of the generalized speeds.
+
+        """
+        return self.eom_method.mass_matrix
+
+    @property
+    def mass_matrix_full(self):
+        r"""The mass matrix of the system, augmented by the kinematic
+        differential equations in explicit or implicit form.
+
+        Explanation
+        ===========
+
+        The full mass matrix $M_m$ and the full forcing vector $f_m$ of a system
+        describe the dynamics and kinematics according to the following
+        equation:
+
+        .. math::
+            M_m \dot{x} = f_m
+
+        where $x$ is the state vector stacking $q$ and $u$.
+
+        """
+        return self.eom_method.mass_matrix_full
+
+    @property
+    def forcing(self):
+        """The forcing vector of the system."""
+        return self.eom_method.forcing
+
+    @property
+    def forcing_full(self):
+        """The forcing vector of the system, augmented by the kinematic
+        differential equations in explicit or implicit form."""
+        return self.eom_method.forcing_full
+
+    def validate_system(self, eom_method=KanesMethod, check_duplicates=False):
+        """Validates the system using some basic checks.
+
+        Explanation
+        ===========
+
+        This method validates the system based on the following checks:
+
+        - The number of dependent generalized coordinates should equal the
+          number of holonomic constraints.
+        - All generalized coordinates defined by the joints should also be known
+          to the system.
+        - If ``KanesMethod`` is used as a ``eom_method``:
+            - All generalized speeds and kinematic differential equations
+              defined by the joints should also be known to the system.
+            - The number of dependent generalized speeds should equal the number
+              of velocity constraints.
+            - The number of generalized coordinates should be less than or equal
+              to the number of generalized speeds.
+            - The number of generalized coordinates should equal the number of
+              kinematic differential equations.
+        - If ``LagrangesMethod`` is used as ``eom_method``:
+            - There should not be any generalized speeds that are not
+              derivatives of the generalized coordinates (this includes the
+              generalized speeds defined by the joints).
+
+        Parameters
+        ==========
+
+        eom_method : subclass of KanesMethod or LagrangesMethod
+            Backend class that will be used for forming the equations of motion.
+            There are different checks for the different backends. The default
+            is ``KanesMethod``.
+        check_duplicates : bool
+            Boolean whether the system should be checked for duplicate
+            definitions. The default is False, because duplicates are already
+            checked when adding objects to the system.
+
+        Notes
+        =====
+
+        This method is not guaranteed to be backwards compatible as it may
+        improve over time. The method can become both more and less strict in
+        certain areas. However a well-defined system should always pass all
+        these tests.
+
+        """
+        msgs = []
+        # Save some data in variables
+        n_hc = self.holonomic_constraints.shape[0]
+        n_vc = self.velocity_constraints.shape[0]
+        n_q_dep, n_u_dep = self.q_dep.shape[0], self.u_dep.shape[0]
+        q_set, u_set = set(self.q), set(self.u)
+        n_q, n_u = len(q_set), len(u_set)
+        # Check number of holonomic constraints
+        if n_q_dep != n_hc:
+            msgs.append(filldedent(f"""
+            The number of dependent generalized coordinates {n_q_dep} should be
+            equal to the number of holonomic constraints {n_hc}."""))
+        # Check if all joint coordinates and speeds are present
+        missing_q = set()
+        for joint in self.joints:
+            missing_q.update(set(joint.coordinates).difference(q_set))
+        if missing_q:
+            msgs.append(filldedent(f"""
+            The generalized coordinates {missing_q} used in joints are not added
+            to the system."""))
+        # Method dependent checks
+        if issubclass(eom_method, KanesMethod):
+            n_kdes = len(self.kdes)
+            missing_kdes, missing_u = set(), set()
+            for joint in self.joints:
+                missing_u.update(set(joint.speeds).difference(u_set))
+                missing_kdes.update(set(joint.kdes).difference(
+                    self.kdes[:] + (-self.kdes)[:]))
+            if missing_u:
+                msgs.append(filldedent(f"""
+                The generalized speeds {missing_u} used in joints are not added
+                to the system."""))
+            if missing_kdes:
+                msgs.append(filldedent(f"""
+                The kinematic differential equations {missing_kdes} used in
+                joints are not added to the system."""))
+            if n_u_dep != n_vc:
+                msgs.append(filldedent(f"""
+                The number of dependent generalized speeds {n_u_dep} should be
+                equal to the number of velocity constraints {n_vc}."""))
+            if n_q > n_u:
+                msgs.append(filldedent(f"""
+                The number of generalized coordinates {n_q} should be less than
+                or equal to the number of generalized speeds {n_u}."""))
+            if n_u != n_kdes:
+                msgs.append(filldedent(f"""
+                The number of generalized speeds {n_u} should be equal to the
+                number of kinematic differential equations {n_kdes}."""))
+        elif issubclass(eom_method, LagrangesMethod):
+            not_qdots = set(self.u).difference(self.q.diff(dynamicsymbols._t))
+            for joint in self.joints:
+                not_qdots.update(set(
+                    joint.speeds).difference(self.q.diff(dynamicsymbols._t)))
+            if not_qdots:
+                msgs.append(filldedent(f"""
+                The generalized speeds {not_qdots} are not supported by this
+                method. Only derivatives of the generalized coordinates are
+                supported. If these symbols are used in your expressions, then
+                this will result in wrong equations of motion."""))
+            if self.u_aux:
+                msgs.append(filldedent(f"""
+                This method does not support auxiliary speeds. If these symbols
+                are used in your expressions, then this will result in wrong
+                equations of motion. The auxiliary speeds are {self.u_aux}."""))
+        else:
+            raise NotImplementedError(f'{eom_method} has not been implemented.')
+        if check_duplicates:  # Should be redundant
+            duplicates_to_check = [('generalized coordinates', self.q),
+                                   ('generalized speeds', self.u),
+                                   ('auxiliary speeds', self.u_aux),
+                                   ('bodies', self.bodies),
+                                   ('joints', self.joints)]
+            for name, lst in duplicates_to_check:
+                seen = set()
+                duplicates = {x for x in lst if x in seen or seen.add(x)}
+                if duplicates:
+                    msgs.append(filldedent(f"""
+                    The {name} {duplicates} exist multiple times within the
+                    system."""))
+        if msgs:
+            raise ValueError('\n'.join(msgs))
+
+
+class SymbolicSystem:
+    """SymbolicSystem is a class that contains all the information about a
+    system in a symbolic format such as the equations of motions and the bodies
+    and loads in the system.
+
+    There are three ways that the equations of motion can be described for
+    Symbolic System:
+
+
+        [1] Explicit form where the kinematics and dynamics are combined
+            x' = F_1(x, t, r, p)
+
+        [2] Implicit form where the kinematics and dynamics are combined
+            M_2(x, p) x' = F_2(x, t, r, p)
+
+        [3] Implicit form where the kinematics and dynamics are separate
+            M_3(q, p) u' = F_3(q, u, t, r, p)
+            q' = G(q, u, t, r, p)
+
+    where
+
+    x : states, e.g. [q, u]
+    t : time
+    r : specified (exogenous) inputs
+    p : constants
+    q : generalized coordinates
+    u : generalized speeds
+    F_1 : right hand side of the combined equations in explicit form
+    F_2 : right hand side of the combined equations in implicit form
+    F_3 : right hand side of the dynamical equations in implicit form
+    M_2 : mass matrix of the combined equations in implicit form
+    M_3 : mass matrix of the dynamical equations in implicit form
+    G : right hand side of the kinematical differential equations
+
+        Parameters
+        ==========
+
+        coord_states : ordered iterable of functions of time
+            This input will either be a collection of the coordinates or states
+            of the system depending on whether or not the speeds are also
+            given. If speeds are specified this input will be assumed to
+            be the coordinates otherwise this input will be assumed to
+            be the states.
+
+        right_hand_side : Matrix
+            This variable is the right hand side of the equations of motion in
+            any of the forms. The specific form will be assumed depending on
+            whether a mass matrix or coordinate derivatives are given.
+
+        speeds : ordered iterable of functions of time, optional
+            This is a collection of the generalized speeds of the system. If
+            given it will be assumed that the first argument (coord_states)
+            will represent the generalized coordinates of the system.
+
+        mass_matrix : Matrix, optional
+            The matrix of the implicit forms of the equations of motion (forms
+            [2] and [3]). The distinction between the forms is determined by
+            whether or not the coordinate derivatives are passed in. If
+            they are given form [3] will be assumed otherwise form [2] is
+            assumed.
+
+        coordinate_derivatives : Matrix, optional
+            The right hand side of the kinematical equations in explicit form.
+            If given it will be assumed that the equations of motion are being
+            entered in form [3].
+
+        alg_con : Iterable, optional
+            The indexes of the rows in the equations of motion that contain
+            algebraic constraints instead of differential equations. If the
+            equations are input in form [3], it will be assumed the indexes are
+            referencing the mass_matrix/right_hand_side combination and not the
+            coordinate_derivatives.
+
+        output_eqns : Dictionary, optional
+            Any output equations that are desired to be tracked are stored in a
+            dictionary where the key corresponds to the name given for the
+            specific equation and the value is the equation itself in symbolic
+            form
+
+        coord_idxs : Iterable, optional
+            If coord_states corresponds to the states rather than the
+            coordinates this variable will tell SymbolicSystem which indexes of
+            the states correspond to generalized coordinates.
+
+        speed_idxs : Iterable, optional
+            If coord_states corresponds to the states rather than the
+            coordinates this variable will tell SymbolicSystem which indexes of
+            the states correspond to generalized speeds.
+
+        bodies : iterable of Body/Rigidbody objects, optional
+            Iterable containing the bodies of the system
+
+        loads : iterable of load instances (described below), optional
+            Iterable containing the loads of the system where forces are given
+            by (point of application, force vector) and torques are given by
+            (reference frame acting upon, torque vector). Ex [(point, force),
+            (ref_frame, torque)]
+
+    Attributes
+    ==========
+
+    coordinates : Matrix, shape(n, 1)
+        This is a matrix containing the generalized coordinates of the system
+
+    speeds : Matrix, shape(m, 1)
+        This is a matrix containing the generalized speeds of the system
+
+    states : Matrix, shape(o, 1)
+        This is a matrix containing the state variables of the system
+
+    alg_con : List
+        This list contains the indices of the algebraic constraints in the
+        combined equations of motion. The presence of these constraints
+        requires that a DAE solver be used instead of an ODE solver.
+        If the system is given in form [3] the alg_con variable will be
+        adjusted such that it is a representation of the combined kinematics
+        and dynamics thus make sure it always matches the mass matrix
+        entered.
+
+    dyn_implicit_mat : Matrix, shape(m, m)
+        This is the M matrix in form [3] of the equations of motion (the mass
+        matrix or generalized inertia matrix of the dynamical equations of
+        motion in implicit form).
+
+    dyn_implicit_rhs : Matrix, shape(m, 1)
+        This is the F vector in form [3] of the equations of motion (the right
+        hand side of the dynamical equations of motion in implicit form).
+
+    comb_implicit_mat : Matrix, shape(o, o)
+        This is the M matrix in form [2] of the equations of motion.
+        This matrix contains a block diagonal structure where the top
+        left block (the first rows) represent the matrix in the
+        implicit form of the kinematical equations and the bottom right
+        block (the last rows) represent the matrix in the implicit form
+        of the dynamical equations.
+
+    comb_implicit_rhs : Matrix, shape(o, 1)
+        This is the F vector in form [2] of the equations of motion. The top
+        part of the vector represents the right hand side of the implicit form
+        of the kinemaical equations and the bottom of the vector represents the
+        right hand side of the implicit form of the dynamical equations of
+        motion.
+
+    comb_explicit_rhs : Matrix, shape(o, 1)
+        This vector represents the right hand side of the combined equations of
+        motion in explicit form (form [1] from above).
+
+    kin_explicit_rhs : Matrix, shape(m, 1)
+        This is the right hand side of the explicit form of the kinematical
+        equations of motion as can be seen in form [3] (the G matrix).
+
+    output_eqns : Dictionary
+        If output equations were given they are stored in a dictionary where
+        the key corresponds to the name given for the specific equation and
+        the value is the equation itself in symbolic form
+
+    bodies : Tuple
+        If the bodies in the system were given they are stored in a tuple for
+        future access
+
+    loads : Tuple
+        If the loads in the system were given they are stored in a tuple for
+        future access. This includes forces and torques where forces are given
+        by (point of application, force vector) and torques are given by
+        (reference frame acted upon, torque vector).
+
+    Example
+    =======
+
+    As a simple example, the dynamics of a simple pendulum will be input into a
+    SymbolicSystem object manually. First some imports will be needed and then
+    symbols will be set up for the length of the pendulum (l), mass at the end
+    of the pendulum (m), and a constant for gravity (g). ::
+
+        >>> from sympy import Matrix, sin, symbols
+        >>> from sympy.physics.mechanics import dynamicsymbols, SymbolicSystem
+        >>> l, m, g = symbols('l m g')
+
+    The system will be defined by an angle of theta from the vertical and a
+    generalized speed of omega will be used where omega = theta_dot. ::
+
+        >>> theta, omega = dynamicsymbols('theta omega')
+
+    Now the equations of motion are ready to be formed and passed to the
+    SymbolicSystem object. ::
+
+        >>> kin_explicit_rhs = Matrix([omega])
+        >>> dyn_implicit_mat = Matrix([l**2 * m])
+        >>> dyn_implicit_rhs = Matrix([-g * l * m * sin(theta)])
+        >>> symsystem = SymbolicSystem([theta], dyn_implicit_rhs, [omega],
+        ...                            dyn_implicit_mat)
+
+    Notes
+    =====
+
+    m : number of generalized speeds
+    n : number of generalized coordinates
+    o : number of states
+
+    """
+
+    def __init__(self, coord_states, right_hand_side, speeds=None,
+                 mass_matrix=None, coordinate_derivatives=None, alg_con=None,
+                 output_eqns={}, coord_idxs=None, speed_idxs=None, bodies=None,
+                 loads=None):
+        """Initializes a SymbolicSystem object"""
+
+        # Extract information on speeds, coordinates and states
+        if speeds is None:
+            self._states = Matrix(coord_states)
+
+            if coord_idxs is None:
+                self._coordinates = None
+            else:
+                coords = [coord_states[i] for i in coord_idxs]
+                self._coordinates = Matrix(coords)
+
+            if speed_idxs is None:
+                self._speeds = None
+            else:
+                speeds_inter = [coord_states[i] for i in speed_idxs]
+                self._speeds = Matrix(speeds_inter)
+        else:
+            self._coordinates = Matrix(coord_states)
+            self._speeds = Matrix(speeds)
+            self._states = self._coordinates.col_join(self._speeds)
+
+        # Extract equations of motion form
+        if coordinate_derivatives is not None:
+            self._kin_explicit_rhs = coordinate_derivatives
+            self._dyn_implicit_rhs = right_hand_side
+            self._dyn_implicit_mat = mass_matrix
+            self._comb_implicit_rhs = None
+            self._comb_implicit_mat = None
+            self._comb_explicit_rhs = None
+        elif mass_matrix is not None:
+            self._kin_explicit_rhs = None
+            self._dyn_implicit_rhs = None
+            self._dyn_implicit_mat = None
+            self._comb_implicit_rhs = right_hand_side
+            self._comb_implicit_mat = mass_matrix
+            self._comb_explicit_rhs = None
+        else:
+            self._kin_explicit_rhs = None
+            self._dyn_implicit_rhs = None
+            self._dyn_implicit_mat = None
+            self._comb_implicit_rhs = None
+            self._comb_implicit_mat = None
+            self._comb_explicit_rhs = right_hand_side
+
+        # Set the remainder of the inputs as instance attributes
+        if alg_con is not None and coordinate_derivatives is not None:
+            alg_con = [i + len(coordinate_derivatives) for i in alg_con]
+        self._alg_con = alg_con
+        self.output_eqns = output_eqns
+
+        # Change the body and loads iterables to tuples if they are not tuples
+        # already
+        if not isinstance(bodies, tuple) and bodies is not None:
+            bodies = tuple(bodies)
+        if not isinstance(loads, tuple) and loads is not None:
+            loads = tuple(loads)
+        self._bodies = bodies
+        self._loads = loads
+
+    @property
+    def coordinates(self):
+        """Returns the column matrix of the generalized coordinates"""
+        if self._coordinates is None:
+            raise AttributeError("The coordinates were not specified.")
+        else:
+            return self._coordinates
+
+    @property
+    def speeds(self):
+        """Returns the column matrix of generalized speeds"""
+        if self._speeds is None:
+            raise AttributeError("The speeds were not specified.")
+        else:
+            return self._speeds
+
+    @property
+    def states(self):
+        """Returns the column matrix of the state variables"""
+        return self._states
+
+    @property
+    def alg_con(self):
+        """Returns a list with the indices of the rows containing algebraic
+        constraints in the combined form of the equations of motion"""
+        return self._alg_con
+
+    @property
+    def dyn_implicit_mat(self):
+        """Returns the matrix, M, corresponding to the dynamic equations in
+        implicit form, M x' = F, where the kinematical equations are not
+        included"""
+        if self._dyn_implicit_mat is None:
+            raise AttributeError("dyn_implicit_mat is not specified for "
+                                 "equations of motion form [1] or [2].")
+        else:
+            return self._dyn_implicit_mat
+
+    @property
+    def dyn_implicit_rhs(self):
+        """Returns the column matrix, F, corresponding to the dynamic equations
+        in implicit form, M x' = F, where the kinematical equations are not
+        included"""
+        if self._dyn_implicit_rhs is None:
+            raise AttributeError("dyn_implicit_rhs is not specified for "
+                                 "equations of motion form [1] or [2].")
+        else:
+            return self._dyn_implicit_rhs
+
+    @property
+    def comb_implicit_mat(self):
+        """Returns the matrix, M, corresponding to the equations of motion in
+        implicit form (form [2]), M x' = F, where the kinematical equations are
+        included"""
+        if self._comb_implicit_mat is None:
+            if self._dyn_implicit_mat is not None:
+                num_kin_eqns = len(self._kin_explicit_rhs)
+                num_dyn_eqns = len(self._dyn_implicit_rhs)
+                zeros1 = zeros(num_kin_eqns, num_dyn_eqns)
+                zeros2 = zeros(num_dyn_eqns, num_kin_eqns)
+                inter1 = eye(num_kin_eqns).row_join(zeros1)
+                inter2 = zeros2.row_join(self._dyn_implicit_mat)
+                self._comb_implicit_mat = inter1.col_join(inter2)
+                return self._comb_implicit_mat
+            else:
+                raise AttributeError("comb_implicit_mat is not specified for "
+                                     "equations of motion form [1].")
+        else:
+            return self._comb_implicit_mat
+
+    @property
+    def comb_implicit_rhs(self):
+        """Returns the column matrix, F, corresponding to the equations of
+        motion in implicit form (form [2]), M x' = F, where the kinematical
+        equations are included"""
+        if self._comb_implicit_rhs is None:
+            if self._dyn_implicit_rhs is not None:
+                kin_inter = self._kin_explicit_rhs
+                dyn_inter = self._dyn_implicit_rhs
+                self._comb_implicit_rhs = kin_inter.col_join(dyn_inter)
+                return self._comb_implicit_rhs
+            else:
+                raise AttributeError("comb_implicit_mat is not specified for "
+                                     "equations of motion in form [1].")
+        else:
+            return self._comb_implicit_rhs
+
+    def compute_explicit_form(self):
+        """If the explicit right hand side of the combined equations of motion
+        is to provided upon initialization, this method will calculate it. This
+        calculation can potentially take awhile to compute."""
+        if self._comb_explicit_rhs is not None:
+            raise AttributeError("comb_explicit_rhs is already formed.")
+
+        inter1 = getattr(self, 'kin_explicit_rhs', None)
+        if inter1 is not None:
+            inter2 = self._dyn_implicit_mat.LUsolve(self._dyn_implicit_rhs)
+            out = inter1.col_join(inter2)
+        else:
+            out = self._comb_implicit_mat.LUsolve(self._comb_implicit_rhs)
+
+        self._comb_explicit_rhs = out
+
+    @property
+    def comb_explicit_rhs(self):
+        """Returns the right hand side of the equations of motion in explicit
+        form, x' = F, where the kinematical equations are included"""
+        if self._comb_explicit_rhs is None:
+            raise AttributeError("Please run .combute_explicit_form before "
+                                 "attempting to access comb_explicit_rhs.")
+        else:
+            return self._comb_explicit_rhs
+
+    @property
+    def kin_explicit_rhs(self):
+        """Returns the right hand side of the kinematical equations in explicit
+        form, q' = G"""
+        if self._kin_explicit_rhs is None:
+            raise AttributeError("kin_explicit_rhs is not specified for "
+                                 "equations of motion form [1] or [2].")
+        else:
+            return self._kin_explicit_rhs
+
+    def dynamic_symbols(self):
+        """Returns a column matrix containing all of the symbols in the system
+        that depend on time"""
+        # Create a list of all of the expressions in the equations of motion
+        if self._comb_explicit_rhs is None:
+            eom_expressions = (self.comb_implicit_mat[:] +
+                               self.comb_implicit_rhs[:])
+        else:
+            eom_expressions = (self._comb_explicit_rhs[:])
+
+        functions_of_time = set()
+        for expr in eom_expressions:
+            functions_of_time = functions_of_time.union(
+                find_dynamicsymbols(expr))
+        functions_of_time = functions_of_time.union(self._states)
+
+        return tuple(functions_of_time)
+
+    def constant_symbols(self):
+        """Returns a column matrix containing all of the symbols in the system
+        that do not depend on time"""
+        # Create a list of all of the expressions in the equations of motion
+        if self._comb_explicit_rhs is None:
+            eom_expressions = (self.comb_implicit_mat[:] +
+                               self.comb_implicit_rhs[:])
+        else:
+            eom_expressions = (self._comb_explicit_rhs[:])
+
+        constants = set()
+        for expr in eom_expressions:
+            constants = constants.union(expr.free_symbols)
+        constants.remove(dynamicsymbols._t)
+
+        return tuple(constants)
+
+    @property
+    def bodies(self):
+        """Returns the bodies in the system"""
+        if self._bodies is None:
+            raise AttributeError("bodies were not specified for the system.")
+        else:
+            return self._bodies
+
+    @property
+    def loads(self):
+        """Returns the loads in the system"""
+        if self._loads is None:
+            raise AttributeError("loads were not specified for the system.")
+        else:
+            return self._loads
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_actuator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_actuator.py
new file mode 100644
index 0000000000000000000000000000000000000000..5d69bccfe7a86d7555242a64923d77cb52cade88
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_actuator.py
@@ -0,0 +1,1084 @@
+"""Tests for the ``sympy.physics.mechanics.actuator.py`` module."""
+
+import pytest
+
+from sympy import (
+    S,
+    Matrix,
+    Symbol,
+    SympifyError,
+    sqrt,
+    Abs,
+    symbols,
+    exp,
+    sign,
+)
+from sympy.physics.mechanics import (
+    ActuatorBase,
+    Force,
+    ForceActuator,
+    KanesMethod,
+    LinearDamper,
+    LinearPathway,
+    LinearSpring,
+    Particle,
+    PinJoint,
+    Point,
+    ReferenceFrame,
+    RigidBody,
+    TorqueActuator,
+    Vector,
+    dynamicsymbols,
+    DuffingSpring,
+    CoulombKineticFriction,
+)
+
+from sympy.core.expr import Expr as ExprType
+
+target = RigidBody('target')
+reaction = RigidBody('reaction')
+
+
+class TestForceActuator:
+
+    @pytest.fixture(autouse=True)
+    def _linear_pathway_fixture(self):
+        self.force = Symbol('F')
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.pathway = LinearPathway(self.pA, self.pB)
+        self.q1 = dynamicsymbols('q1')
+        self.q2 = dynamicsymbols('q2')
+        self.q3 = dynamicsymbols('q3')
+        self.q1d = dynamicsymbols('q1', 1)
+        self.q2d = dynamicsymbols('q2', 1)
+        self.q3d = dynamicsymbols('q3', 1)
+        self.N = ReferenceFrame('N')
+
+    def test_is_actuator_base_subclass(self):
+        assert issubclass(ForceActuator, ActuatorBase)
+
+    @pytest.mark.parametrize(
+        'force, expected_force',
+        [
+            (1, S.One),
+            (S.One, S.One),
+            (Symbol('F'), Symbol('F')),
+            (dynamicsymbols('F'), dynamicsymbols('F')),
+            (Symbol('F')**2 + Symbol('F'), Symbol('F')**2 + Symbol('F')),
+        ]
+    )
+    def test_valid_constructor_force(self, force, expected_force):
+        instance = ForceActuator(force, self.pathway)
+        assert isinstance(instance, ForceActuator)
+        assert hasattr(instance, 'force')
+        assert isinstance(instance.force, ExprType)
+        assert instance.force == expected_force
+
+    @pytest.mark.parametrize('force', [None, 'F'])
+    def test_invalid_constructor_force_not_sympifyable(self, force):
+        with pytest.raises(SympifyError):
+            _ = ForceActuator(force, self.pathway)
+
+    @pytest.mark.parametrize(
+        'pathway',
+        [
+            LinearPathway(Point('pA'), Point('pB')),
+        ]
+    )
+    def test_valid_constructor_pathway(self, pathway):
+        instance = ForceActuator(self.force, pathway)
+        assert isinstance(instance, ForceActuator)
+        assert hasattr(instance, 'pathway')
+        assert isinstance(instance.pathway, LinearPathway)
+        assert instance.pathway == pathway
+
+    def test_invalid_constructor_pathway_not_pathway_base(self):
+        with pytest.raises(TypeError):
+            _ = ForceActuator(self.force, None)
+
+    @pytest.mark.parametrize(
+        'property_name, fixture_attr_name',
+        [
+            ('force', 'force'),
+            ('pathway', 'pathway'),
+        ]
+    )
+    def test_properties_are_immutable(self, property_name, fixture_attr_name):
+        instance = ForceActuator(self.force, self.pathway)
+        value = getattr(self, fixture_attr_name)
+        with pytest.raises(AttributeError):
+            setattr(instance, property_name, value)
+
+    def test_repr(self):
+        actuator = ForceActuator(self.force, self.pathway)
+        expected = "ForceActuator(F, LinearPathway(pA, pB))"
+        assert repr(actuator) == expected
+
+    def test_to_loads_static_pathway(self):
+        self.pB.set_pos(self.pA, 2*self.N.x)
+        actuator = ForceActuator(self.force, self.pathway)
+        expected = [
+            (self.pA, - self.force*self.N.x),
+            (self.pB, self.force*self.N.x),
+        ]
+        assert actuator.to_loads() == expected
+
+    def test_to_loads_2D_pathway(self):
+        self.pB.set_pos(self.pA, 2*self.q1*self.N.x)
+        actuator = ForceActuator(self.force, self.pathway)
+        expected = [
+            (self.pA, - self.force*(self.q1/sqrt(self.q1**2))*self.N.x),
+            (self.pB, self.force*(self.q1/sqrt(self.q1**2))*self.N.x),
+        ]
+        assert actuator.to_loads() == expected
+
+    def test_to_loads_3D_pathway(self):
+        self.pB.set_pos(
+            self.pA,
+            self.q1*self.N.x - self.q2*self.N.y + 2*self.q3*self.N.z,
+        )
+        actuator = ForceActuator(self.force, self.pathway)
+        length = sqrt(self.q1**2 + self.q2**2 + 4*self.q3**2)
+        pO_force = (
+            - self.force*self.q1*self.N.x/length
+            + self.force*self.q2*self.N.y/length
+            - 2*self.force*self.q3*self.N.z/length
+        )
+        pI_force = (
+            self.force*self.q1*self.N.x/length
+            - self.force*self.q2*self.N.y/length
+            + 2*self.force*self.q3*self.N.z/length
+        )
+        expected = [
+            (self.pA, pO_force),
+            (self.pB, pI_force),
+        ]
+        assert actuator.to_loads() == expected
+
+
+class TestLinearSpring:
+
+    @pytest.fixture(autouse=True)
+    def _linear_spring_fixture(self):
+        self.stiffness = Symbol('k')
+        self.l = Symbol('l')
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.pathway = LinearPathway(self.pA, self.pB)
+        self.q = dynamicsymbols('q')
+        self.N = ReferenceFrame('N')
+
+    def test_is_force_actuator_subclass(self):
+        assert issubclass(LinearSpring, ForceActuator)
+
+    def test_is_actuator_base_subclass(self):
+        assert issubclass(LinearSpring, ActuatorBase)
+
+    @pytest.mark.parametrize(
+        (
+            'stiffness, '
+            'expected_stiffness, '
+            'equilibrium_length, '
+            'expected_equilibrium_length, '
+            'force'
+        ),
+        [
+            (
+                1,
+                S.One,
+                0,
+                S.Zero,
+                -sqrt(dynamicsymbols('q')**2),
+            ),
+            (
+                Symbol('k'),
+                Symbol('k'),
+                0,
+                S.Zero,
+                -Symbol('k')*sqrt(dynamicsymbols('q')**2),
+            ),
+            (
+                Symbol('k'),
+                Symbol('k'),
+                S.Zero,
+                S.Zero,
+                -Symbol('k')*sqrt(dynamicsymbols('q')**2),
+            ),
+            (
+                Symbol('k'),
+                Symbol('k'),
+                Symbol('l'),
+                Symbol('l'),
+                -Symbol('k')*(sqrt(dynamicsymbols('q')**2) - Symbol('l')),
+            ),
+        ]
+    )
+    def test_valid_constructor(
+        self,
+        stiffness,
+        expected_stiffness,
+        equilibrium_length,
+        expected_equilibrium_length,
+        force,
+    ):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        spring = LinearSpring(stiffness, self.pathway, equilibrium_length)
+
+        assert isinstance(spring, LinearSpring)
+
+        assert hasattr(spring, 'stiffness')
+        assert isinstance(spring.stiffness, ExprType)
+        assert spring.stiffness == expected_stiffness
+
+        assert hasattr(spring, 'pathway')
+        assert isinstance(spring.pathway, LinearPathway)
+        assert spring.pathway == self.pathway
+
+        assert hasattr(spring, 'equilibrium_length')
+        assert isinstance(spring.equilibrium_length, ExprType)
+        assert spring.equilibrium_length == expected_equilibrium_length
+
+        assert hasattr(spring, 'force')
+        assert isinstance(spring.force, ExprType)
+        assert spring.force == force
+
+    @pytest.mark.parametrize('stiffness', [None, 'k'])
+    def test_invalid_constructor_stiffness_not_sympifyable(self, stiffness):
+        with pytest.raises(SympifyError):
+            _ = LinearSpring(stiffness, self.pathway, self.l)
+
+    def test_invalid_constructor_pathway_not_pathway_base(self):
+        with pytest.raises(TypeError):
+            _ = LinearSpring(self.stiffness, None, self.l)
+
+    @pytest.mark.parametrize('equilibrium_length', [None, 'l'])
+    def test_invalid_constructor_equilibrium_length_not_sympifyable(
+        self,
+        equilibrium_length,
+    ):
+        with pytest.raises(SympifyError):
+            _ = LinearSpring(self.stiffness, self.pathway, equilibrium_length)
+
+    @pytest.mark.parametrize(
+        'property_name, fixture_attr_name',
+        [
+            ('stiffness', 'stiffness'),
+            ('pathway', 'pathway'),
+            ('equilibrium_length', 'l'),
+        ]
+    )
+    def test_properties_are_immutable(self, property_name, fixture_attr_name):
+        spring = LinearSpring(self.stiffness, self.pathway, self.l)
+        value = getattr(self, fixture_attr_name)
+        with pytest.raises(AttributeError):
+            setattr(spring, property_name, value)
+
+    @pytest.mark.parametrize(
+        'equilibrium_length, expected',
+        [
+            (S.Zero, 'LinearSpring(k, LinearPathway(pA, pB))'),
+            (
+                Symbol('l'),
+                'LinearSpring(k, LinearPathway(pA, pB), equilibrium_length=l)',
+            ),
+        ]
+    )
+    def test_repr(self, equilibrium_length, expected):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        spring = LinearSpring(self.stiffness, self.pathway, equilibrium_length)
+        assert repr(spring) == expected
+
+    def test_to_loads(self):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        spring = LinearSpring(self.stiffness, self.pathway, self.l)
+        normal = self.q/sqrt(self.q**2)*self.N.x
+        pA_force = self.stiffness*(sqrt(self.q**2) - self.l)*normal
+        pB_force = -self.stiffness*(sqrt(self.q**2) - self.l)*normal
+        expected = [Force(self.pA, pA_force), Force(self.pB, pB_force)]
+        loads = spring.to_loads()
+
+        for load, (point, vector) in zip(loads, expected):
+            assert isinstance(load, Force)
+            assert load.point == point
+            assert (load.vector - vector).simplify() == 0
+
+
+class TestLinearDamper:
+
+    @pytest.fixture(autouse=True)
+    def _linear_damper_fixture(self):
+        self.damping = Symbol('c')
+        self.l = Symbol('l')
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.pathway = LinearPathway(self.pA, self.pB)
+        self.q = dynamicsymbols('q')
+        self.dq = dynamicsymbols('q', 1)
+        self.u = dynamicsymbols('u')
+        self.N = ReferenceFrame('N')
+
+    def test_is_force_actuator_subclass(self):
+        assert issubclass(LinearDamper, ForceActuator)
+
+    def test_is_actuator_base_subclass(self):
+        assert issubclass(LinearDamper, ActuatorBase)
+
+    def test_valid_constructor(self):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        damper = LinearDamper(self.damping, self.pathway)
+
+        assert isinstance(damper, LinearDamper)
+
+        assert hasattr(damper, 'damping')
+        assert isinstance(damper.damping, ExprType)
+        assert damper.damping == self.damping
+
+        assert hasattr(damper, 'pathway')
+        assert isinstance(damper.pathway, LinearPathway)
+        assert damper.pathway == self.pathway
+
+    def test_valid_constructor_force(self):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        damper = LinearDamper(self.damping, self.pathway)
+
+        expected_force = -self.damping*sqrt(self.q**2)*self.dq/self.q
+        assert hasattr(damper, 'force')
+        assert isinstance(damper.force, ExprType)
+        assert damper.force == expected_force
+
+    @pytest.mark.parametrize('damping', [None, 'c'])
+    def test_invalid_constructor_damping_not_sympifyable(self, damping):
+        with pytest.raises(SympifyError):
+            _ = LinearDamper(damping, self.pathway)
+
+    def test_invalid_constructor_pathway_not_pathway_base(self):
+        with pytest.raises(TypeError):
+            _ = LinearDamper(self.damping, None)
+
+    @pytest.mark.parametrize(
+        'property_name, fixture_attr_name',
+        [
+            ('damping', 'damping'),
+            ('pathway', 'pathway'),
+        ]
+    )
+    def test_properties_are_immutable(self, property_name, fixture_attr_name):
+        damper = LinearDamper(self.damping, self.pathway)
+        value = getattr(self, fixture_attr_name)
+        with pytest.raises(AttributeError):
+            setattr(damper, property_name, value)
+
+    def test_repr(self):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        damper = LinearDamper(self.damping, self.pathway)
+        expected = 'LinearDamper(c, LinearPathway(pA, pB))'
+        assert repr(damper) == expected
+
+    def test_to_loads(self):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        damper = LinearDamper(self.damping, self.pathway)
+        direction = self.q**2/self.q**2*self.N.x
+        pA_force = self.damping*self.dq*direction
+        pB_force = -self.damping*self.dq*direction
+        expected = [Force(self.pA, pA_force), Force(self.pB, pB_force)]
+        assert damper.to_loads() == expected
+
+
+class TestForcedMassSpringDamperModel():
+    r"""A single degree of freedom translational forced mass-spring-damper.
+
+    Notes
+    =====
+
+    This system is well known to have the governing equation:
+
+    .. math::
+        m \ddot{x} = F - k x - c \dot{x}
+
+    where $F$ is an externally applied force, $m$ is the mass of the particle
+    to which the spring and damper are attached, $k$ is the spring's stiffness,
+    $c$ is the dampers damping coefficient, and $x$ is the generalized
+    coordinate representing the system's single (translational) degree of
+    freedom.
+
+    """
+
+    @pytest.fixture(autouse=True)
+    def _force_mass_spring_damper_model_fixture(self):
+        self.m = Symbol('m')
+        self.k = Symbol('k')
+        self.c = Symbol('c')
+        self.F = Symbol('F')
+
+        self.q = dynamicsymbols('q')
+        self.dq = dynamicsymbols('q', 1)
+        self.u = dynamicsymbols('u')
+
+        self.frame = ReferenceFrame('N')
+        self.origin = Point('pO')
+        self.origin.set_vel(self.frame, 0)
+
+        self.attachment = Point('pA')
+        self.attachment.set_pos(self.origin, self.q*self.frame.x)
+
+        self.mass = Particle('mass', self.attachment, self.m)
+        self.pathway = LinearPathway(self.origin, self.attachment)
+
+        self.kanes_method = KanesMethod(
+            self.frame,
+            q_ind=[self.q],
+            u_ind=[self.u],
+            kd_eqs=[self.dq - self.u],
+        )
+        self.bodies = [self.mass]
+
+        self.mass_matrix = Matrix([[self.m]])
+        self.forcing = Matrix([[self.F - self.c*self.u - self.k*self.q]])
+
+    def test_force_acuator(self):
+        stiffness = -self.k*self.pathway.length
+        spring = ForceActuator(stiffness, self.pathway)
+        damping = -self.c*self.pathway.extension_velocity
+        damper = ForceActuator(damping, self.pathway)
+
+        loads = [
+            (self.attachment, self.F*self.frame.x),
+            *spring.to_loads(),
+            *damper.to_loads(),
+        ]
+        self.kanes_method.kanes_equations(self.bodies, loads)
+
+        assert self.kanes_method.mass_matrix == self.mass_matrix
+        assert self.kanes_method.forcing == self.forcing
+
+    def test_linear_spring_linear_damper(self):
+        spring = LinearSpring(self.k, self.pathway)
+        damper = LinearDamper(self.c, self.pathway)
+
+        loads = [
+            (self.attachment, self.F*self.frame.x),
+            *spring.to_loads(),
+            *damper.to_loads(),
+        ]
+        self.kanes_method.kanes_equations(self.bodies, loads)
+
+        assert self.kanes_method.mass_matrix == self.mass_matrix
+        assert self.kanes_method.forcing == self.forcing
+
+
+class TestTorqueActuator:
+
+    @pytest.fixture(autouse=True)
+    def _torque_actuator_fixture(self):
+        self.torque = Symbol('T')
+        self.N = ReferenceFrame('N')
+        self.A = ReferenceFrame('A')
+        self.axis = self.N.z
+        self.target = RigidBody('target', frame=self.N)
+        self.reaction = RigidBody('reaction', frame=self.A)
+
+    def test_is_actuator_base_subclass(self):
+        assert issubclass(TorqueActuator, ActuatorBase)
+
+    @pytest.mark.parametrize(
+        'torque',
+        [
+            Symbol('T'),
+            dynamicsymbols('T'),
+            Symbol('T')**2 + Symbol('T'),
+        ]
+    )
+    @pytest.mark.parametrize(
+        'target_frame, reaction_frame',
+        [
+            (target.frame, reaction.frame),
+            (target, reaction.frame),
+            (target.frame, reaction),
+            (target, reaction),
+        ]
+    )
+    def test_valid_constructor_with_reaction(
+        self,
+        torque,
+        target_frame,
+        reaction_frame,
+    ):
+        instance = TorqueActuator(
+            torque,
+            self.axis,
+            target_frame,
+            reaction_frame,
+        )
+        assert isinstance(instance, TorqueActuator)
+
+        assert hasattr(instance, 'torque')
+        assert isinstance(instance.torque, ExprType)
+        assert instance.torque == torque
+
+        assert hasattr(instance, 'axis')
+        assert isinstance(instance.axis, Vector)
+        assert instance.axis == self.axis
+
+        assert hasattr(instance, 'target_frame')
+        assert isinstance(instance.target_frame, ReferenceFrame)
+        assert instance.target_frame == target.frame
+
+        assert hasattr(instance, 'reaction_frame')
+        assert isinstance(instance.reaction_frame, ReferenceFrame)
+        assert instance.reaction_frame == reaction.frame
+
+    @pytest.mark.parametrize(
+        'torque',
+        [
+            Symbol('T'),
+            dynamicsymbols('T'),
+            Symbol('T')**2 + Symbol('T'),
+        ]
+    )
+    @pytest.mark.parametrize('target_frame', [target.frame, target])
+    def test_valid_constructor_without_reaction(self, torque, target_frame):
+        instance = TorqueActuator(torque, self.axis, target_frame)
+        assert isinstance(instance, TorqueActuator)
+
+        assert hasattr(instance, 'torque')
+        assert isinstance(instance.torque, ExprType)
+        assert instance.torque == torque
+
+        assert hasattr(instance, 'axis')
+        assert isinstance(instance.axis, Vector)
+        assert instance.axis == self.axis
+
+        assert hasattr(instance, 'target_frame')
+        assert isinstance(instance.target_frame, ReferenceFrame)
+        assert instance.target_frame == target.frame
+
+        assert hasattr(instance, 'reaction_frame')
+        assert instance.reaction_frame is None
+
+    @pytest.mark.parametrize('torque', [None, 'T'])
+    def test_invalid_constructor_torque_not_sympifyable(self, torque):
+        with pytest.raises(SympifyError):
+            _ = TorqueActuator(torque, self.axis, self.target)
+
+    @pytest.mark.parametrize('axis', [Symbol('a'), dynamicsymbols('a')])
+    def test_invalid_constructor_axis_not_vector(self, axis):
+        with pytest.raises(TypeError):
+            _ = TorqueActuator(self.torque, axis, self.target, self.reaction)
+
+    @pytest.mark.parametrize(
+        'frames',
+        [
+            (None, ReferenceFrame('child')),
+            (ReferenceFrame('parent'), True),
+            (None, RigidBody('child')),
+            (RigidBody('parent'), True),
+        ]
+    )
+    def test_invalid_constructor_frames_not_frame(self, frames):
+        with pytest.raises(TypeError):
+            _ = TorqueActuator(self.torque, self.axis, *frames)
+
+    @pytest.mark.parametrize(
+        'property_name, fixture_attr_name',
+        [
+            ('torque', 'torque'),
+            ('axis', 'axis'),
+            ('target_frame', 'target'),
+            ('reaction_frame', 'reaction'),
+        ]
+    )
+    def test_properties_are_immutable(self, property_name, fixture_attr_name):
+        actuator = TorqueActuator(
+            self.torque,
+            self.axis,
+            self.target,
+            self.reaction,
+        )
+        value = getattr(self, fixture_attr_name)
+        with pytest.raises(AttributeError):
+            setattr(actuator, property_name, value)
+
+    def test_repr_without_reaction(self):
+        actuator = TorqueActuator(self.torque, self.axis, self.target)
+        expected = 'TorqueActuator(T, axis=N.z, target_frame=N)'
+        assert repr(actuator) == expected
+
+    def test_repr_with_reaction(self):
+        actuator = TorqueActuator(
+            self.torque,
+            self.axis,
+            self.target,
+            self.reaction,
+        )
+        expected = 'TorqueActuator(T, axis=N.z, target_frame=N, reaction_frame=A)'
+        assert repr(actuator) == expected
+
+    def test_at_pin_joint_constructor(self):
+        pin_joint = PinJoint(
+            'pin',
+            self.target,
+            self.reaction,
+            coordinates=dynamicsymbols('q'),
+            speeds=dynamicsymbols('u'),
+            parent_interframe=self.N,
+            joint_axis=self.axis,
+        )
+        instance = TorqueActuator.at_pin_joint(self.torque, pin_joint)
+        assert isinstance(instance, TorqueActuator)
+
+        assert hasattr(instance, 'torque')
+        assert isinstance(instance.torque, ExprType)
+        assert instance.torque == self.torque
+
+        assert hasattr(instance, 'axis')
+        assert isinstance(instance.axis, Vector)
+        assert instance.axis == self.axis
+
+        assert hasattr(instance, 'target_frame')
+        assert isinstance(instance.target_frame, ReferenceFrame)
+        assert instance.target_frame == self.A
+
+        assert hasattr(instance, 'reaction_frame')
+        assert isinstance(instance.reaction_frame, ReferenceFrame)
+        assert instance.reaction_frame == self.N
+
+    def test_at_pin_joint_pin_joint_not_pin_joint_invalid(self):
+        with pytest.raises(TypeError):
+            _ = TorqueActuator.at_pin_joint(self.torque, Symbol('pin'))
+
+    def test_to_loads_without_reaction(self):
+        actuator = TorqueActuator(self.torque, self.axis, self.target)
+        expected = [
+            (self.N, self.torque*self.axis),
+        ]
+        assert actuator.to_loads() == expected
+
+    def test_to_loads_with_reaction(self):
+        actuator = TorqueActuator(
+            self.torque,
+            self.axis,
+            self.target,
+            self.reaction,
+        )
+        expected = [
+            (self.N, self.torque*self.axis),
+            (self.A, - self.torque*self.axis),
+        ]
+        assert actuator.to_loads() == expected
+
+
+class NonSympifyable:
+    pass
+
+
+class TestDuffingSpring:
+    @pytest.fixture(autouse=True)
+    # Set up common variables that will be used in multiple tests
+    def _duffing_spring_fixture(self):
+        self.linear_stiffness = Symbol('beta')
+        self.nonlinear_stiffness = Symbol('alpha')
+        self.equilibrium_length = Symbol('l')
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.pathway = LinearPathway(self.pA, self.pB)
+        self.q = dynamicsymbols('q')
+        self.N = ReferenceFrame('N')
+
+    # Simples tests to check that DuffingSpring is a subclass of ForceActuator and ActuatorBase
+    def test_is_force_actuator_subclass(self):
+        assert issubclass(DuffingSpring, ForceActuator)
+
+    def test_is_actuator_base_subclass(self):
+        assert issubclass(DuffingSpring, ActuatorBase)
+
+    @pytest.mark.parametrize(
+    # Create parametrized tests that allows running the same test function multiple times with different sets of arguments
+    (
+        'linear_stiffness,  '
+        'expected_linear_stiffness,  '
+        'nonlinear_stiffness,   '
+        'expected_nonlinear_stiffness,  '
+        'equilibrium_length,    '
+        'expected_equilibrium_length,   '
+        'force'
+    ),
+    [
+            (
+                1,
+                S.One,
+                1,
+                S.One,
+                0,
+                S.Zero,
+                -sqrt(dynamicsymbols('q')**2)-(sqrt(dynamicsymbols('q')**2))**3,
+            ),
+            (
+                Symbol('beta'),
+                Symbol('beta'),
+                Symbol('alpha'),
+                Symbol('alpha'),
+                0,
+                S.Zero,
+                -Symbol('beta')*sqrt(dynamicsymbols('q')**2)-Symbol('alpha')*(sqrt(dynamicsymbols('q')**2))**3,
+            ),
+            (
+                Symbol('beta'),
+                Symbol('beta'),
+                Symbol('alpha'),
+                Symbol('alpha'),
+                S.Zero,
+                S.Zero,
+                -Symbol('beta')*sqrt(dynamicsymbols('q')**2)-Symbol('alpha')*(sqrt(dynamicsymbols('q')**2))**3,
+            ),
+            (
+                Symbol('beta'),
+                Symbol('beta'),
+                Symbol('alpha'),
+                Symbol('alpha'),
+                Symbol('l'),
+                Symbol('l'),
+                -Symbol('beta') * (sqrt(dynamicsymbols('q')**2) - Symbol('l')) - Symbol('alpha') * (sqrt(dynamicsymbols('q')**2) - Symbol('l'))**3,
+            ),
+        ]
+    )
+
+    # Check if DuffingSpring correctly initializes its attributes
+    # It tests various combinations of linear & nonlinear stiffness, equilibriun length, and the resulting force expression
+    def test_valid_constructor(
+        self,
+        linear_stiffness,
+        expected_linear_stiffness,
+        nonlinear_stiffness,
+        expected_nonlinear_stiffness,
+        equilibrium_length,
+        expected_equilibrium_length,
+        force,
+    ):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        spring = DuffingSpring(linear_stiffness, nonlinear_stiffness, self.pathway, equilibrium_length)
+
+        assert isinstance(spring, DuffingSpring)
+
+        assert hasattr(spring, 'linear_stiffness')
+        assert isinstance(spring.linear_stiffness, ExprType)
+        assert spring.linear_stiffness == expected_linear_stiffness
+
+        assert hasattr(spring, 'nonlinear_stiffness')
+        assert isinstance(spring.nonlinear_stiffness, ExprType)
+        assert spring.nonlinear_stiffness == expected_nonlinear_stiffness
+
+        assert hasattr(spring, 'pathway')
+        assert isinstance(spring.pathway, LinearPathway)
+        assert spring.pathway == self.pathway
+
+        assert hasattr(spring, 'equilibrium_length')
+        assert isinstance(spring.equilibrium_length, ExprType)
+        assert spring.equilibrium_length == expected_equilibrium_length
+
+        assert hasattr(spring, 'force')
+        assert isinstance(spring.force, ExprType)
+        assert spring.force == force
+
+    @pytest.mark.parametrize('linear_stiffness', [None, NonSympifyable()])
+    def test_invalid_constructor_linear_stiffness_not_sympifyable(self, linear_stiffness):
+        with pytest.raises(SympifyError):
+            _ = DuffingSpring(linear_stiffness, self.nonlinear_stiffness, self.pathway, self.equilibrium_length)
+
+    @pytest.mark.parametrize('nonlinear_stiffness', [None, NonSympifyable()])
+    def test_invalid_constructor_nonlinear_stiffness_not_sympifyable(self, nonlinear_stiffness):
+        with pytest.raises(SympifyError):
+            _ = DuffingSpring(self.linear_stiffness, nonlinear_stiffness, self.pathway, self.equilibrium_length)
+
+    def test_invalid_constructor_pathway_not_pathway_base(self):
+        with pytest.raises(TypeError):
+            _ = DuffingSpring(self.linear_stiffness, self.nonlinear_stiffness, NonSympifyable(), self.equilibrium_length)
+
+    @pytest.mark.parametrize('equilibrium_length', [None, NonSympifyable()])
+    def test_invalid_constructor_equilibrium_length_not_sympifyable(self, equilibrium_length):
+        with pytest.raises(SympifyError):
+            _ = DuffingSpring(self.linear_stiffness, self.nonlinear_stiffness, self.pathway, equilibrium_length)
+
+    @pytest.mark.parametrize(
+        'property_name, fixture_attr_name',
+        [
+            ('linear_stiffness', 'linear_stiffness'),
+            ('nonlinear_stiffness', 'nonlinear_stiffness'),
+            ('pathway', 'pathway'),
+            ('equilibrium_length', 'equilibrium_length')
+        ]
+    )
+    # Check if certain properties of DuffingSpring object are immutable after initialization
+    # Ensure that once DuffingSpring is created, its key properties cannot be changed
+    def test_properties_are_immutable(self, property_name, fixture_attr_name):
+        spring = DuffingSpring(self.linear_stiffness, self.nonlinear_stiffness, self.pathway, self.equilibrium_length)
+        with pytest.raises(AttributeError):
+            setattr(spring, property_name, getattr(self, fixture_attr_name))
+
+    @pytest.mark.parametrize(
+        'equilibrium_length, expected',
+        [
+            (0, 'DuffingSpring(beta, alpha, LinearPathway(pA, pB), equilibrium_length=0)'),
+            (Symbol('l'), 'DuffingSpring(beta, alpha, LinearPathway(pA, pB), equilibrium_length=l)'),
+        ]
+    )
+    # Check the __repr__ method of DuffingSpring class
+    # Check if the actual string representation of DuffingSpring instance matches the expected string for each provided parameter values
+    def test_repr(self, equilibrium_length, expected):
+        spring = DuffingSpring(self.linear_stiffness, self.nonlinear_stiffness, self.pathway, equilibrium_length)
+        assert repr(spring) == expected
+
+    def test_to_loads(self):
+        self.pB.set_pos(self.pA, self.q*self.N.x)
+        spring = DuffingSpring(self.linear_stiffness, self.nonlinear_stiffness, self.pathway, self.equilibrium_length)
+
+        # Calculate the displacement from the equilibrium length
+        displacement = self.q - self.equilibrium_length
+
+        # Make sure this matches the computation in DuffingSpring class
+        force = -self.linear_stiffness * displacement - self.nonlinear_stiffness * displacement**3
+
+        # The expected loads on pA and pB due to the spring
+        expected_loads = [Force(self.pA, force * self.N.x), Force(self.pB, -force * self.N.x)]
+
+        # Compare expected loads to what is returned from DuffingSpring.to_loads()
+        calculated_loads = spring.to_loads()
+        for calculated, expected in zip(calculated_loads, expected_loads):
+            assert calculated.point == expected.point
+            for dim in self.N:  # Assuming self.N is the reference frame
+                calculated_component = calculated.vector.dot(dim)
+                expected_component = expected.vector.dot(dim)
+                # Substitute all symbols with numeric values
+                substitutions = {self.q: 1, Symbol('l'): 1, Symbol('alpha'): 1, Symbol('beta'): 1}  # Add other necessary symbols as needed
+                diff = (calculated_component - expected_component).subs(substitutions).evalf()
+                # Check if the absolute value of the difference is below a threshold
+                assert Abs(diff) < 1e-9, f"The forces do not match. Difference: {diff}"
+
+class TestCoulombKineticFriction:
+    @pytest.fixture(autouse=True)
+    def _block_on_surface(self):
+        """A block sliding on a surface.
+
+        Notes
+        =====
+        This test validates the correctness of the CoulombKineticFriction by simulating
+        a block sliding on a surface with the Coulomb kinetic friction force.
+        The test covers scenarios with both positive and negative velocities.
+
+        """
+
+        # Mass, gravity constant, friction coefficient, coefficient of Stribeck friction, viscous_coefficient
+        self.m, self.g, self.mu_k, self.mu_s, self.v_s, self.sigma, self.F = symbols('m g mu_k mu_s v_s sigma F', real=True)
+
+    def test_block_on_surface_default(self):
+        # General Case
+        q = dynamicsymbols('q')
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway)
+        expected_general = [Force(point=O, force=self.g * self.m * self.mu_k * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2) * N.x),
+                            Force(point=P, force=-self.g * self.m * self.mu_k * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_general
+
+        # Positive
+        q = dynamicsymbols('q', positive=True)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway)
+        expected_positive = [Force(point=O, force=self.g * self.m * self.mu_k * sign(q.diff()) * N.x),
+                             Force(point=P, force=-self.g * self.m * self.mu_k * sign(q.diff()) * N.x)]
+
+        assert friction.to_loads() == expected_positive
+
+        # Negative
+        q = dynamicsymbols('q', positive=False)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway)
+        expected_negative = [Force(point=O, force=self.g * self.m * self.mu_k * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2)*N.x),
+                             Force(point=P, force=-self.g * self.m * self.mu_k * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2)*N.x)]
+
+        assert friction.to_loads() == expected_negative
+
+    def test_block_on_surface_viscous(self):
+        # General Case
+        q = dynamicsymbols('q')
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, sigma=self.sigma)
+        expected_general = [Force(point=O, force=(self.g * self.m * self.mu_k * sign(sqrt(q**2) * q.diff()/q) + self.sigma * sqrt(q**2) * q.diff()/q) * q/sqrt(q**2) * N.x),
+                            Force(point=P, force=(-self.g * self.m * self.mu_k * sign(sqrt(q**2) * q.diff()/q) - self.sigma * sqrt(q**2) * q.diff()/q) * q/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_general
+
+        # Positive
+        q = dynamicsymbols('q', positive=True)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, sigma=self.sigma)
+        expected_positive = [Force(point=O, force=(self.g * self.m * self.mu_k * sign(q.diff()) + self.sigma * q.diff()) * N.x),
+                             Force(point=P, force=(-self.g * self.m * self.mu_k * sign(q.diff()) - self.sigma * q.diff()) * N.x)]
+
+        assert friction.to_loads() == expected_positive
+
+        # Negative
+        q = dynamicsymbols('q', positive=False)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, sigma=self.sigma)
+        expected_negative = [Force(point=O, force=(self.g * self.m * self.mu_k * sign(sqrt(q**2) * q.diff()/q) + self.sigma * sqrt(q**2) * q.diff()/q) * q/sqrt(q**2) * N.x),
+                             Force(point=P, force=(-self.g * self.m * self.mu_k * sign(sqrt(q**2) * q.diff()/q) - self.sigma * sqrt(q**2) * q.diff()/q) * q/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_negative
+
+    def test_block_on_surface_stribeck(self):
+        # General Case
+        q = dynamicsymbols('q')
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, v_s=self.v_s, mu_s=self.mu_s)
+        expected_general = [Force(point=O, force=(self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2) * N.x),
+                            Force(point=P, force=- (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_general
+
+        # Positive
+        q = dynamicsymbols('q', positive=True)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, v_s=self.v_s, mu_s=self.mu_s)
+        expected_positive = [Force(point=O, force=(self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(q.diff()) * N.x),
+                             Force(point=P, force=- (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(q.diff()) * N.x)]
+
+        assert friction.to_loads() == expected_positive
+
+        # Negative
+        q = dynamicsymbols('q', positive=False)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, v_s=self.v_s, mu_s=self.mu_s)
+        expected_negative = [Force(point=O, force=(self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2) * N.x),
+                             Force(point=P, force=- (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * q * sign(sqrt(q**2) * q.diff()/q)/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_negative
+
+    def test_block_on_surface_all(self):
+        # General Case
+        q = dynamicsymbols('q')
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, v_s=self.v_s, sigma=self.sigma, mu_s=self.mu_s)
+        expected_general = [Force(point=O, force=(self.sigma * sqrt(q**2) * q.diff()/q + (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(sqrt(q**2) * q.diff()/q)) * q/sqrt(q**2) * N.x),
+                            Force(point=P, force=(-self.sigma * sqrt(q**2) * q.diff()/q - (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(sqrt(q**2) * q.diff()/q)) * q/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_general
+
+        # Positive
+        q = dynamicsymbols('q', positive=True)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, v_s=self.v_s, sigma=self.sigma, mu_s=self.mu_s)
+        expected_positive = [Force(point=O, force=(self.sigma * q.diff() + (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(q.diff())) * N.x),
+                             Force(point=P, force=(-self.sigma * q.diff() - (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(q.diff())) * N.x)]
+
+        assert friction.to_loads() == expected_positive
+
+        # Negative
+        q = dynamicsymbols('q', positive=False)
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(self.mu_k, self.m * self.g, pathway, v_s=self.v_s, sigma=self.sigma, mu_s=self.mu_s)
+        expected_negative = [Force(point=O, force=(self.sigma * sqrt(q**2) * q.diff()/q + (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(sqrt(q**2) * q.diff()/q)) * q/sqrt(q**2) * N.x),
+                             Force(point=P, force=(-self.sigma * sqrt(q**2) * q.diff()/q - (self.g * self.m * self.mu_k + (-self.g * self.m * self.mu_k + self.g * self.m * self.mu_s) * exp(-q.diff()**2/self.v_s**2)) * sign(sqrt(q**2) * q.diff()/q)) * q/sqrt(q**2) * N.x)]
+
+        assert friction.to_loads() == expected_negative
+
+    def test_normal_force_zero(self):
+        q = dynamicsymbols('q')
+
+        N = ReferenceFrame('N')
+        O = Point('O')
+        P = O.locatenew('P', q * N.x)
+        O.set_vel(N, 0)
+        P.set_vel(N, q.diff() * N.x)
+
+        pathway = LinearPathway(O, P)
+        friction = CoulombKineticFriction(
+            self.mu_k,
+            0,
+            pathway
+        )
+        assert friction.force == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_body.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_body.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d59d747400652a0cbb081f4afc5ae4ebaa4db85
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_body.py
@@ -0,0 +1,340 @@
+from sympy import (Symbol, symbols, sin, cos, Matrix, zeros,
+                                simplify)
+from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols, Dyadic
+from sympy.physics.mechanics import inertia, Body
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+def test_default():
+    with warns_deprecated_sympy():
+        body = Body('body')
+    assert body.name == 'body'
+    assert body.loads == []
+    point = Point('body_masscenter')
+    point.set_vel(body.frame, 0)
+    com = body.masscenter
+    frame = body.frame
+    assert com.vel(frame) == point.vel(frame)
+    assert body.mass == Symbol('body_mass')
+    ixx, iyy, izz = symbols('body_ixx body_iyy body_izz')
+    ixy, iyz, izx = symbols('body_ixy body_iyz body_izx')
+    assert body.inertia == (inertia(body.frame, ixx, iyy, izz, ixy, iyz, izx),
+                            body.masscenter)
+
+
+def test_custom_rigid_body():
+    # Body with RigidBody.
+    rigidbody_masscenter = Point('rigidbody_masscenter')
+    rigidbody_mass = Symbol('rigidbody_mass')
+    rigidbody_frame = ReferenceFrame('rigidbody_frame')
+    body_inertia = inertia(rigidbody_frame, 1, 0, 0)
+    with warns_deprecated_sympy():
+        rigid_body = Body('rigidbody_body', rigidbody_masscenter,
+                          rigidbody_mass, rigidbody_frame, body_inertia)
+    com = rigid_body.masscenter
+    frame = rigid_body.frame
+    rigidbody_masscenter.set_vel(rigidbody_frame, 0)
+    assert com.vel(frame) == rigidbody_masscenter.vel(frame)
+    assert com.pos_from(com) == rigidbody_masscenter.pos_from(com)
+
+    assert rigid_body.mass == rigidbody_mass
+    assert rigid_body.inertia == (body_inertia, rigidbody_masscenter)
+
+    assert rigid_body.is_rigidbody
+
+    assert hasattr(rigid_body, 'masscenter')
+    assert hasattr(rigid_body, 'mass')
+    assert hasattr(rigid_body, 'frame')
+    assert hasattr(rigid_body, 'inertia')
+
+
+def test_particle_body():
+    #  Body with Particle
+    particle_masscenter = Point('particle_masscenter')
+    particle_mass = Symbol('particle_mass')
+    particle_frame = ReferenceFrame('particle_frame')
+    with warns_deprecated_sympy():
+        particle_body = Body('particle_body', particle_masscenter,
+                             particle_mass, particle_frame)
+    com = particle_body.masscenter
+    frame = particle_body.frame
+    particle_masscenter.set_vel(particle_frame, 0)
+    assert com.vel(frame) == particle_masscenter.vel(frame)
+    assert com.pos_from(com) == particle_masscenter.pos_from(com)
+
+    assert particle_body.mass == particle_mass
+    assert not hasattr(particle_body, "_inertia")
+    assert hasattr(particle_body, 'frame')
+    assert hasattr(particle_body, 'masscenter')
+    assert hasattr(particle_body, 'mass')
+    assert particle_body.inertia == (Dyadic(0), particle_body.masscenter)
+    assert particle_body.central_inertia == Dyadic(0)
+    assert not particle_body.is_rigidbody
+
+    particle_body.central_inertia = inertia(particle_frame, 1, 1, 1)
+    assert particle_body.central_inertia == inertia(particle_frame, 1, 1, 1)
+    assert particle_body.is_rigidbody
+
+    with warns_deprecated_sympy():
+        particle_body = Body('particle_body', mass=particle_mass)
+    assert not particle_body.is_rigidbody
+    point = particle_body.masscenter.locatenew('point', particle_body.x)
+    point_inertia = particle_mass * inertia(particle_body.frame, 0, 1, 1)
+    particle_body.inertia = (point_inertia, point)
+    assert particle_body.inertia == (point_inertia, point)
+    assert particle_body.central_inertia == Dyadic(0)
+    assert particle_body.is_rigidbody
+
+
+def test_particle_body_add_force():
+    #  Body with Particle
+    particle_masscenter = Point('particle_masscenter')
+    particle_mass = Symbol('particle_mass')
+    particle_frame = ReferenceFrame('particle_frame')
+    with warns_deprecated_sympy():
+        particle_body = Body('particle_body', particle_masscenter,
+                             particle_mass, particle_frame)
+
+    a = Symbol('a')
+    force_vector = a * particle_body.frame.x
+    particle_body.apply_force(force_vector, particle_body.masscenter)
+    assert len(particle_body.loads) == 1
+    point = particle_body.masscenter.locatenew(
+        particle_body._name + '_point0', 0)
+    point.set_vel(particle_body.frame, 0)
+    force_point = particle_body.loads[0][0]
+
+    frame = particle_body.frame
+    assert force_point.vel(frame) == point.vel(frame)
+    assert force_point.pos_from(force_point) == point.pos_from(force_point)
+
+    assert particle_body.loads[0][1] == force_vector
+
+
+def test_body_add_force():
+    # Body with RigidBody.
+    rigidbody_masscenter = Point('rigidbody_masscenter')
+    rigidbody_mass = Symbol('rigidbody_mass')
+    rigidbody_frame = ReferenceFrame('rigidbody_frame')
+    body_inertia = inertia(rigidbody_frame, 1, 0, 0)
+    with warns_deprecated_sympy():
+        rigid_body = Body('rigidbody_body', rigidbody_masscenter,
+                          rigidbody_mass, rigidbody_frame, body_inertia)
+
+    l = Symbol('l')
+    Fa = Symbol('Fa')
+    point = rigid_body.masscenter.locatenew(
+        'rigidbody_body_point0',
+        l * rigid_body.frame.x)
+    point.set_vel(rigid_body.frame, 0)
+    force_vector = Fa * rigid_body.frame.z
+    # apply_force with point
+    rigid_body.apply_force(force_vector, point)
+    assert len(rigid_body.loads) == 1
+    force_point = rigid_body.loads[0][0]
+    frame = rigid_body.frame
+    assert force_point.vel(frame) == point.vel(frame)
+    assert force_point.pos_from(force_point) == point.pos_from(force_point)
+    assert rigid_body.loads[0][1] == force_vector
+    # apply_force without point
+    rigid_body.apply_force(force_vector)
+    assert len(rigid_body.loads) == 2
+    assert rigid_body.loads[1][1] == force_vector
+    # passing something else than point
+    raises(TypeError, lambda: rigid_body.apply_force(force_vector,  0))
+    raises(TypeError, lambda: rigid_body.apply_force(0))
+
+def test_body_add_torque():
+    with warns_deprecated_sympy():
+        body = Body('body')
+    torque_vector = body.frame.x
+    body.apply_torque(torque_vector)
+
+    assert len(body.loads) == 1
+    assert body.loads[0] == (body.frame, torque_vector)
+    raises(TypeError, lambda: body.apply_torque(0))
+
+def test_body_masscenter_vel():
+    with warns_deprecated_sympy():
+        A = Body('A')
+    N = ReferenceFrame('N')
+    with warns_deprecated_sympy():
+        B = Body('B', frame=N)
+    A.masscenter.set_vel(N, N.z)
+    assert A.masscenter_vel(B) == N.z
+    assert A.masscenter_vel(N) == N.z
+
+def test_body_ang_vel():
+    with warns_deprecated_sympy():
+        A = Body('A')
+    N = ReferenceFrame('N')
+    with warns_deprecated_sympy():
+        B = Body('B', frame=N)
+    A.frame.set_ang_vel(N, N.y)
+    assert A.ang_vel_in(B) == N.y
+    assert B.ang_vel_in(A) == -N.y
+    assert A.ang_vel_in(N) == N.y
+
+def test_body_dcm():
+    with warns_deprecated_sympy():
+        A = Body('A')
+        B = Body('B')
+    A.frame.orient_axis(B.frame, B.frame.z, 10)
+    assert A.dcm(B) == Matrix([[cos(10), sin(10), 0], [-sin(10), cos(10), 0], [0, 0, 1]])
+    assert A.dcm(B.frame) == Matrix([[cos(10), sin(10), 0], [-sin(10), cos(10), 0], [0, 0, 1]])
+
+def test_body_axis():
+    N = ReferenceFrame('N')
+    with warns_deprecated_sympy():
+        B = Body('B', frame=N)
+    assert B.x == N.x
+    assert B.y == N.y
+    assert B.z == N.z
+
+def test_apply_force_multiple_one_point():
+    a, b = symbols('a b')
+    P = Point('P')
+    with warns_deprecated_sympy():
+        B = Body('B')
+    f1 = a*B.x
+    f2 = b*B.y
+    B.apply_force(f1, P)
+    assert B.loads == [(P, f1)]
+    B.apply_force(f2, P)
+    assert B.loads == [(P, f1+f2)]
+
+def test_apply_force():
+    f, g = symbols('f g')
+    q, x, v1, v2 = dynamicsymbols('q x v1 v2')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    with warns_deprecated_sympy():
+        B1 = Body('B1')
+        B2 = Body('B2')
+    N = ReferenceFrame('N')
+
+    P1.set_vel(B1.frame, v1*B1.x)
+    P2.set_vel(B2.frame, v2*B2.x)
+    force = f*q*N.z # time varying force
+
+    B1.apply_force(force, P1, B2, P2) #applying equal and opposite force on moving points
+    assert B1.loads == [(P1, force)]
+    assert B2.loads == [(P2, -force)]
+
+    g1 = B1.mass*g*N.y
+    g2 = B2.mass*g*N.y
+
+    B1.apply_force(g1) #applying gravity on B1 masscenter
+    B2.apply_force(g2) #applying gravity on B2 masscenter
+
+    assert B1.loads == [(P1,force), (B1.masscenter, g1)]
+    assert B2.loads == [(P2, -force), (B2.masscenter, g2)]
+
+    force2 = x*N.x
+
+    B1.apply_force(force2, reaction_body=B2) #Applying time varying force on masscenter
+
+    assert B1.loads == [(P1, force), (B1.masscenter, force2+g1)]
+    assert B2.loads == [(P2, -force), (B2.masscenter, -force2+g2)]
+
+def test_apply_torque():
+    t = symbols('t')
+    q = dynamicsymbols('q')
+    with warns_deprecated_sympy():
+        B1 = Body('B1')
+        B2 = Body('B2')
+    N = ReferenceFrame('N')
+    torque = t*q*N.x
+
+    B1.apply_torque(torque, B2) #Applying equal and opposite torque
+    assert B1.loads == [(B1.frame, torque)]
+    assert B2.loads == [(B2.frame, -torque)]
+
+    torque2 = t*N.y
+    B1.apply_torque(torque2)
+    assert B1.loads == [(B1.frame, torque+torque2)]
+
+def test_clear_load():
+    a = symbols('a')
+    P = Point('P')
+    with warns_deprecated_sympy():
+        B = Body('B')
+    force = a*B.z
+    B.apply_force(force, P)
+    assert B.loads == [(P, force)]
+    B.clear_loads()
+    assert B.loads == []
+
+def test_remove_load():
+    P1 = Point('P1')
+    P2 = Point('P2')
+    with warns_deprecated_sympy():
+        B = Body('B')
+    f1 = B.x
+    f2 = B.y
+    B.apply_force(f1, P1)
+    B.apply_force(f2, P2)
+    assert B.loads == [(P1, f1), (P2, f2)]
+    B.remove_load(P2)
+    assert B.loads == [(P1, f1)]
+    B.apply_torque(f1.cross(f2))
+    assert B.loads == [(P1, f1), (B.frame, f1.cross(f2))]
+    B.remove_load()
+    assert B.loads == [(P1, f1)]
+
+def test_apply_loads_on_multi_degree_freedom_holonomic_system():
+    """Example based on: https://pydy.readthedocs.io/en/latest/examples/multidof-holonomic.html"""
+    with warns_deprecated_sympy():
+        W = Body('W') #Wall
+        B = Body('B') #Block
+        P = Body('P') #Pendulum
+        b = Body('b') #bob
+    q1, q2 = dynamicsymbols('q1 q2') #generalized coordinates
+    k, c, g, kT = symbols('k c g kT') #constants
+    F, T = dynamicsymbols('F T') #Specified forces
+
+    #Applying forces
+    B.apply_force(F*W.x)
+    W.apply_force(k*q1*W.x, reaction_body=B) #Spring force
+    W.apply_force(c*q1.diff()*W.x, reaction_body=B) #dampner
+    P.apply_force(P.mass*g*W.y)
+    b.apply_force(b.mass*g*W.y)
+
+    #Applying torques
+    P.apply_torque(kT*q2*W.z, reaction_body=b)
+    P.apply_torque(T*W.z)
+
+    assert B.loads == [(B.masscenter, (F - k*q1 - c*q1.diff())*W.x)]
+    assert P.loads == [(P.masscenter, P.mass*g*W.y), (P.frame, (T + kT*q2)*W.z)]
+    assert b.loads == [(b.masscenter, b.mass*g*W.y), (b.frame, -kT*q2*W.z)]
+    assert W.loads == [(W.masscenter, (c*q1.diff() + k*q1)*W.x)]
+
+
+def test_parallel_axis():
+    N = ReferenceFrame('N')
+    m, Ix, Iy, Iz, a, b = symbols('m, I_x, I_y, I_z, a, b')
+    Io = inertia(N, Ix, Iy, Iz)
+    # Test RigidBody
+    o = Point('o')
+    p = o.locatenew('p', a * N.x + b * N.y)
+    with warns_deprecated_sympy():
+        R = Body('R', masscenter=o, frame=N, mass=m, central_inertia=Io)
+    Ip = R.parallel_axis(p)
+    Ip_expected = inertia(N, Ix + m * b**2, Iy + m * a**2,
+                          Iz + m * (a**2 + b**2), ixy=-m * a * b)
+    assert Ip == Ip_expected
+    # Reference frame from which the parallel axis is viewed should not matter
+    A = ReferenceFrame('A')
+    A.orient_axis(N, N.z, 1)
+    assert simplify(
+        (R.parallel_axis(p, A) - Ip_expected).to_matrix(A)) == zeros(3, 3)
+    # Test Particle
+    o = Point('o')
+    p = o.locatenew('p', a * N.x + b * N.y)
+    with warns_deprecated_sympy():
+        P = Body('P', masscenter=o, mass=m, frame=N)
+    Ip = P.parallel_axis(p, N)
+    Ip_expected = inertia(N, m * b ** 2, m * a ** 2, m * (a ** 2 + b ** 2),
+                          ixy=-m * a * b)
+    assert not P.is_rigidbody
+    assert Ip == Ip_expected
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_functions.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..bae6b19b2807dca1632942bd3717e29d214eb269
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_functions.py
@@ -0,0 +1,262 @@
+from sympy import sin, cos, tan, pi, symbols, Matrix, S, Function
+from sympy.physics.mechanics import (Particle, Point, ReferenceFrame,
+                                     RigidBody)
+from sympy.physics.mechanics import (angular_momentum, dynamicsymbols,
+                                     kinetic_energy, linear_momentum,
+                                     outer, potential_energy, msubs,
+                                     find_dynamicsymbols, Lagrangian)
+
+from sympy.physics.mechanics.functions import (
+    center_of_mass, _validate_coordinates, _parse_linear_solver)
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+q1, q2, q3, q4, q5 = symbols('q1 q2 q3 q4 q5')
+N = ReferenceFrame('N')
+A = N.orientnew('A', 'Axis', [q1, N.z])
+B = A.orientnew('B', 'Axis', [q2, A.x])
+C = B.orientnew('C', 'Axis', [q3, B.y])
+
+
+def test_linear_momentum():
+    N = ReferenceFrame('N')
+    Ac = Point('Ac')
+    Ac.set_vel(N, 25 * N.y)
+    I = outer(N.x, N.x)
+    A = RigidBody('A', Ac, N, 20, (I, Ac))
+    P = Point('P')
+    Pa = Particle('Pa', P, 1)
+    Pa.point.set_vel(N, 10 * N.x)
+    raises(TypeError, lambda: linear_momentum(A, A, Pa))
+    raises(TypeError, lambda: linear_momentum(N, N, Pa))
+    assert linear_momentum(N, A, Pa) == 10 * N.x + 500 * N.y
+
+
+def test_angular_momentum_and_linear_momentum():
+    """A rod with length 2l, centroidal inertia I, and mass M along with a
+    particle of mass m fixed to the end of the rod rotate with an angular rate
+    of omega about point O which is fixed to the non-particle end of the rod.
+    The rod's reference frame is A and the inertial frame is N."""
+    m, M, l, I = symbols('m, M, l, I')
+    omega = dynamicsymbols('omega')
+    N = ReferenceFrame('N')
+    a = ReferenceFrame('a')
+    O = Point('O')
+    Ac = O.locatenew('Ac', l * N.x)
+    P = Ac.locatenew('P', l * N.x)
+    O.set_vel(N, 0 * N.x)
+    a.set_ang_vel(N, omega * N.z)
+    Ac.v2pt_theory(O, N, a)
+    P.v2pt_theory(O, N, a)
+    Pa = Particle('Pa', P, m)
+    A = RigidBody('A', Ac, a, M, (I * outer(N.z, N.z), Ac))
+    expected = 2 * m * omega * l * N.y + M * l * omega * N.y
+    assert linear_momentum(N, A, Pa) == expected
+    raises(TypeError, lambda: angular_momentum(N, N, A, Pa))
+    raises(TypeError, lambda: angular_momentum(O, O, A, Pa))
+    raises(TypeError, lambda: angular_momentum(O, N, O, Pa))
+    expected = (I + M * l**2 + 4 * m * l**2) * omega * N.z
+    assert angular_momentum(O, N, A, Pa) == expected
+
+
+def test_kinetic_energy():
+    m, M, l1 = symbols('m M l1')
+    omega = dynamicsymbols('omega')
+    N = ReferenceFrame('N')
+    O = Point('O')
+    O.set_vel(N, 0 * N.x)
+    Ac = O.locatenew('Ac', l1 * N.x)
+    P = Ac.locatenew('P', l1 * N.x)
+    a = ReferenceFrame('a')
+    a.set_ang_vel(N, omega * N.z)
+    Ac.v2pt_theory(O, N, a)
+    P.v2pt_theory(O, N, a)
+    Pa = Particle('Pa', P, m)
+    I = outer(N.z, N.z)
+    A = RigidBody('A', Ac, a, M, (I, Ac))
+    raises(TypeError, lambda: kinetic_energy(Pa, Pa, A))
+    raises(TypeError, lambda: kinetic_energy(N, N, A))
+    assert 0 == (kinetic_energy(N, Pa, A) - (M*l1**2*omega**2/2
+            + 2*l1**2*m*omega**2 + omega**2/2)).expand()
+
+
+def test_potential_energy():
+    m, M, l1, g, h, H = symbols('m M l1 g h H')
+    omega = dynamicsymbols('omega')
+    N = ReferenceFrame('N')
+    O = Point('O')
+    O.set_vel(N, 0 * N.x)
+    Ac = O.locatenew('Ac', l1 * N.x)
+    P = Ac.locatenew('P', l1 * N.x)
+    a = ReferenceFrame('a')
+    a.set_ang_vel(N, omega * N.z)
+    Ac.v2pt_theory(O, N, a)
+    P.v2pt_theory(O, N, a)
+    Pa = Particle('Pa', P, m)
+    I = outer(N.z, N.z)
+    A = RigidBody('A', Ac, a, M, (I, Ac))
+    Pa.potential_energy = m * g * h
+    A.potential_energy = M * g * H
+    assert potential_energy(A, Pa) == m * g * h + M * g * H
+
+
+def test_Lagrangian():
+    M, m, g, h = symbols('M m g h')
+    N = ReferenceFrame('N')
+    O = Point('O')
+    O.set_vel(N, 0 * N.x)
+    P = O.locatenew('P', 1 * N.x)
+    P.set_vel(N, 10 * N.x)
+    Pa = Particle('Pa', P, 1)
+    Ac = O.locatenew('Ac', 2 * N.y)
+    Ac.set_vel(N, 5 * N.y)
+    a = ReferenceFrame('a')
+    a.set_ang_vel(N, 10 * N.z)
+    I = outer(N.z, N.z)
+    A = RigidBody('A', Ac, a, 20, (I, Ac))
+    Pa.potential_energy = m * g * h
+    A.potential_energy = M * g * h
+    raises(TypeError, lambda: Lagrangian(A, A, Pa))
+    raises(TypeError, lambda: Lagrangian(N, N, Pa))
+
+
+def test_msubs():
+    a, b = symbols('a, b')
+    x, y, z = dynamicsymbols('x, y, z')
+    # Test simple substitution
+    expr = Matrix([[a*x + b, x*y.diff() + y],
+                   [x.diff().diff(), z + sin(z.diff())]])
+    sol = Matrix([[a + b, y],
+                  [x.diff().diff(), 1]])
+    sd = {x: 1, z: 1, z.diff(): 0, y.diff(): 0}
+    assert msubs(expr, sd) == sol
+    # Test smart substitution
+    expr = cos(x + y)*tan(x + y) + b*x.diff()
+    sd = {x: 0, y: pi/2, x.diff(): 1}
+    assert msubs(expr, sd, smart=True) == b + 1
+    N = ReferenceFrame('N')
+    v = x*N.x + y*N.y
+    d = x*(N.x|N.x) + y*(N.y|N.y)
+    v_sol = 1*N.y
+    d_sol = 1*(N.y|N.y)
+    sd = {x: 0, y: 1}
+    assert msubs(v, sd) == v_sol
+    assert msubs(d, sd) == d_sol
+
+
+def test_find_dynamicsymbols():
+    a, b = symbols('a, b')
+    x, y, z = dynamicsymbols('x, y, z')
+    expr = Matrix([[a*x + b, x*y.diff() + y],
+                   [x.diff().diff(), z + sin(z.diff())]])
+    # Test finding all dynamicsymbols
+    sol = {x, y.diff(), y, x.diff().diff(), z, z.diff()}
+    assert find_dynamicsymbols(expr) == sol
+    # Test finding all but those in sym_list
+    exclude_list = [x, y, z]
+    sol = {y.diff(), x.diff().diff(), z.diff()}
+    assert find_dynamicsymbols(expr, exclude=exclude_list) == sol
+    # Test finding all dynamicsymbols in a vector with a given reference frame
+    d, e, f = dynamicsymbols('d, e, f')
+    A = ReferenceFrame('A')
+    v = d * A.x + e * A.y + f * A.z
+    sol = {d, e, f}
+    assert find_dynamicsymbols(v, reference_frame=A) == sol
+    # Test if a ValueError is raised on supplying only a vector as input
+    raises(ValueError, lambda: find_dynamicsymbols(v))
+
+
+# This function tests the center_of_mass() function
+# that was added in PR #14758 to compute the center of
+# mass of a system of bodies.
+def test_center_of_mass():
+    a = ReferenceFrame('a')
+    m = symbols('m', real=True)
+    p1 = Particle('p1', Point('p1_pt'), S.One)
+    p2 = Particle('p2', Point('p2_pt'), S(2))
+    p3 = Particle('p3', Point('p3_pt'), S(3))
+    p4 = Particle('p4', Point('p4_pt'), m)
+    b_f = ReferenceFrame('b_f')
+    b_cm = Point('b_cm')
+    mb = symbols('mb')
+    b = RigidBody('b', b_cm, b_f, mb, (outer(b_f.x, b_f.x), b_cm))
+    p2.point.set_pos(p1.point, a.x)
+    p3.point.set_pos(p1.point, a.x + a.y)
+    p4.point.set_pos(p1.point, a.y)
+    b.masscenter.set_pos(p1.point, a.y + a.z)
+    point_o=Point('o')
+    point_o.set_pos(p1.point, center_of_mass(p1.point, p1, p2, p3, p4, b))
+    expr = 5/(m + mb + 6)*a.x + (m + mb + 3)/(m + mb + 6)*a.y + mb/(m + mb + 6)*a.z
+    assert point_o.pos_from(p1.point)-expr == 0
+
+
+def test_validate_coordinates():
+    q1, q2, q3, u1, u2, u3, ua1, ua2, ua3 = dynamicsymbols('q1:4 u1:4 ua1:4')
+    s1, s2, s3 = symbols('s1:4')
+    # Test normal
+    _validate_coordinates([q1, q2, q3], [u1, u2, u3],
+                          u_auxiliary=[ua1, ua2, ua3])
+    # Test not equal number of coordinates and speeds
+    _validate_coordinates([q1, q2])
+    _validate_coordinates([q1, q2], [u1])
+    _validate_coordinates(speeds=[u1, u2])
+    # Test duplicate
+    _validate_coordinates([q1, q2, q2], [u1, u2, u3], check_duplicates=False)
+    raises(ValueError, lambda: _validate_coordinates(
+        [q1, q2, q2], [u1, u2, u3]))
+    _validate_coordinates([q1, q2, q3], [u1, u2, u2], check_duplicates=False)
+    raises(ValueError, lambda: _validate_coordinates(
+        [q1, q2, q3], [u1, u2, u2], check_duplicates=True))
+    raises(ValueError, lambda: _validate_coordinates(
+        [q1, q2, q3], [q1, u2, u3], check_duplicates=True))
+    _validate_coordinates([q1, q2, q3], [u1, u2, u3], check_duplicates=False,
+                          u_auxiliary=[u1, ua2, ua2])
+    raises(ValueError, lambda: _validate_coordinates(
+        [q1, q2, q3], [u1, u2, u3], u_auxiliary=[u1, ua2, ua3]))
+    raises(ValueError, lambda: _validate_coordinates(
+        [q1, q2, q3], [u1, u2, u3], u_auxiliary=[q1, ua2, ua3]))
+    raises(ValueError, lambda: _validate_coordinates(
+        [q1, q2, q3], [u1, u2, u3], u_auxiliary=[ua1, ua2, ua2]))
+    # Test is_dynamicsymbols
+    _validate_coordinates([q1 + q2, q3], is_dynamicsymbols=False)
+    raises(ValueError, lambda: _validate_coordinates([q1 + q2, q3]))
+    _validate_coordinates([s1, q1, q2], [0, u1, u2], is_dynamicsymbols=False)
+    raises(ValueError, lambda: _validate_coordinates(
+        [s1, q1, q2], [0, u1, u2], is_dynamicsymbols=True))
+    _validate_coordinates([s1 + s2 + s3, q1], [0, u1], is_dynamicsymbols=False)
+    raises(ValueError, lambda: _validate_coordinates(
+        [s1 + s2 + s3, q1], [0, u1], is_dynamicsymbols=True))
+    _validate_coordinates(u_auxiliary=[s1, ua1], is_dynamicsymbols=False)
+    raises(ValueError, lambda: _validate_coordinates(u_auxiliary=[s1, ua1]))
+    # Test normal function
+    t = dynamicsymbols._t
+    a = symbols('a')
+    f1, f2 = symbols('f1:3', cls=Function)
+    _validate_coordinates([f1(a), f2(a)], is_dynamicsymbols=False)
+    raises(ValueError, lambda: _validate_coordinates([f1(a), f2(a)]))
+    raises(ValueError, lambda: _validate_coordinates(speeds=[f1(a), f2(a)]))
+    dynamicsymbols._t = a
+    _validate_coordinates([f1(a), f2(a)])
+    raises(ValueError, lambda: _validate_coordinates([f1(t), f2(t)]))
+    dynamicsymbols._t = t
+
+
+def test_parse_linear_solver():
+    A, b = Matrix(3, 3, symbols('a:9')), Matrix(3, 2, symbols('b:6'))
+    assert _parse_linear_solver(Matrix.LUsolve) == Matrix.LUsolve  # Test callable
+    assert _parse_linear_solver('LU')(A, b) == Matrix.LUsolve(A, b)
+
+
+def test_deprecated_moved_functions():
+    from sympy.physics.mechanics.functions import (
+        inertia, inertia_of_point_mass, gravity)
+    N = ReferenceFrame('N')
+    with warns_deprecated_sympy():
+        assert inertia(N, 0, 1, 0, 1) == (N.x | N.y) + (N.y | N.x) + (N.y | N.y)
+    with warns_deprecated_sympy():
+        assert inertia_of_point_mass(1, N.x + N.y, N) == (
+            (N.x | N.x) + (N.y | N.y) + 2 * (N.z | N.z) -
+            (N.x | N.y) - (N.y | N.x))
+    p = Particle('P')
+    with warns_deprecated_sympy():
+        assert gravity(-2 * N.z, p) == [(p.masscenter, -2 * p.mass * N.z)]
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_inertia.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_inertia.py
new file mode 100644
index 0000000000000000000000000000000000000000..8d29e5f31868e539c4b50575af5180e5eb96f2cd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_inertia.py
@@ -0,0 +1,71 @@
+from sympy import symbols
+from sympy.testing.pytest import raises
+from sympy.physics.mechanics import (inertia, inertia_of_point_mass,
+                                     Inertia, ReferenceFrame, Point)
+
+
+def test_inertia_dyadic():
+    N = ReferenceFrame('N')
+    ixx, iyy, izz = symbols('ixx iyy izz')
+    ixy, iyz, izx = symbols('ixy iyz izx')
+    assert inertia(N, ixx, iyy, izz) == (ixx * (N.x | N.x) + iyy *
+            (N.y | N.y) + izz * (N.z | N.z))
+    assert inertia(N, 0, 0, 0) == 0 * (N.x | N.x)
+    raises(TypeError, lambda: inertia(0, 0, 0, 0))
+    assert inertia(N, ixx, iyy, izz, ixy, iyz, izx) == (ixx * (N.x | N.x) +
+            ixy * (N.x | N.y) + izx * (N.x | N.z) + ixy * (N.y | N.x) + iyy *
+        (N.y | N.y) + iyz * (N.y | N.z) + izx * (N.z | N.x) + iyz * (N.z |
+            N.y) + izz * (N.z | N.z))
+
+
+def test_inertia_of_point_mass():
+    r, s, t, m = symbols('r s t m')
+    N = ReferenceFrame('N')
+
+    px = r * N.x
+    I = inertia_of_point_mass(m, px, N)
+    assert I == m * r**2 * (N.y | N.y) + m * r**2 * (N.z | N.z)
+
+    py = s * N.y
+    I = inertia_of_point_mass(m, py, N)
+    assert I == m * s**2 * (N.x | N.x) + m * s**2 * (N.z | N.z)
+
+    pz = t * N.z
+    I = inertia_of_point_mass(m, pz, N)
+    assert I == m * t**2 * (N.x | N.x) + m * t**2 * (N.y | N.y)
+
+    p = px + py + pz
+    I = inertia_of_point_mass(m, p, N)
+    assert I == (m * (s**2 + t**2) * (N.x | N.x) -
+                 m * r * s * (N.x | N.y) -
+                 m * r * t * (N.x | N.z) -
+                 m * r * s * (N.y | N.x) +
+                 m * (r**2 + t**2) * (N.y | N.y) -
+                 m * s * t * (N.y | N.z) -
+                 m * r * t * (N.z | N.x) -
+                 m * s * t * (N.z | N.y) +
+                 m * (r**2 + s**2) * (N.z | N.z))
+
+
+def test_inertia_object():
+    N = ReferenceFrame('N')
+    O = Point('O')
+    ixx, iyy, izz = symbols('ixx iyy izz')
+    I_dyadic = ixx * (N.x | N.x) + iyy * (N.y | N.y) + izz * (N.z | N.z)
+    I = Inertia(inertia(N, ixx, iyy, izz), O)
+    assert isinstance(I, tuple)
+    assert I.__repr__() == ('Inertia(dyadic=ixx*(N.x|N.x) + iyy*(N.y|N.y) + '
+                            'izz*(N.z|N.z), point=O)')
+    assert I.dyadic == I_dyadic
+    assert I.point == O
+    assert I[0] == I_dyadic
+    assert I[1] == O
+    assert I == (I_dyadic, O)  # Test tuple equal
+    raises(TypeError, lambda: I != (O, I_dyadic))  # Incorrect tuple order
+    assert I == Inertia(O, I_dyadic)  # Parse changed argument order
+    assert I == Inertia.from_inertia_scalars(O, N, ixx, iyy, izz)
+    # Test invalid tuple operations
+    raises(TypeError, lambda: I + (1, 2))
+    raises(TypeError, lambda: (1, 2) + I)
+    raises(TypeError, lambda: I * 2)
+    raises(TypeError, lambda: 2 * I)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_joint.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_joint.py
new file mode 100644
index 0000000000000000000000000000000000000000..271801b5b7290a4479ee61e1414741e4c4d6f966
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_joint.py
@@ -0,0 +1,1240 @@
+from sympy.core.function import expand_mul
+from sympy.core.numbers import pi
+from sympy.core.singleton import S
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy import Matrix, simplify, eye, zeros
+from sympy.core.symbol import symbols
+from sympy.physics.mechanics import (
+    dynamicsymbols, RigidBody, Particle, JointsMethod, PinJoint, PrismaticJoint,
+    CylindricalJoint, PlanarJoint, SphericalJoint, WeldJoint, Body)
+from sympy.physics.mechanics.joint import Joint
+from sympy.physics.vector import Vector, ReferenceFrame, Point
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+t = dynamicsymbols._t # type: ignore
+
+
+def _generate_body(interframe=False):
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    P = RigidBody('P', frame=N)
+    C = RigidBody('C', frame=A)
+    if interframe:
+        Pint, Cint = ReferenceFrame('P_int'), ReferenceFrame('C_int')
+        Pint.orient_axis(N, N.x, pi)
+        Cint.orient_axis(A, A.y, -pi / 2)
+        return N, A, P, C, Pint, Cint
+    return N, A, P, C
+
+
+def test_Joint():
+    parent = RigidBody('parent')
+    child = RigidBody('child')
+    raises(TypeError, lambda: Joint('J', parent, child))
+
+
+def test_coordinate_generation():
+    q, u, qj, uj = dynamicsymbols('q u q_J u_J')
+    q0j, q1j, q2j, q3j, u0j, u1j, u2j, u3j = dynamicsymbols('q0:4_J u0:4_J')
+    q0, q1, q2, q3, u0, u1, u2, u3 = dynamicsymbols('q0:4 u0:4')
+    _, _, P, C = _generate_body()
+    # Using PinJoint to access Joint's coordinate generation method
+    J = PinJoint('J', P, C)
+    # Test single given
+    assert J._fill_coordinate_list(q, 1) == Matrix([q])
+    assert J._fill_coordinate_list([u], 1) == Matrix([u])
+    assert J._fill_coordinate_list([u], 1, offset=2) == Matrix([u])
+    # Test None
+    assert J._fill_coordinate_list(None, 1) == Matrix([qj])
+    assert J._fill_coordinate_list([None], 1) == Matrix([qj])
+    assert J._fill_coordinate_list([q0, None, None], 3) == Matrix(
+        [q0, q1j, q2j])
+    # Test autofill
+    assert J._fill_coordinate_list(None, 3) == Matrix([q0j, q1j, q2j])
+    assert J._fill_coordinate_list([], 3) == Matrix([q0j, q1j, q2j])
+    # Test offset
+    assert J._fill_coordinate_list([], 3, offset=1) == Matrix([q1j, q2j, q3j])
+    assert J._fill_coordinate_list([q1, None, q3], 3, offset=1) == Matrix(
+        [q1, q2j, q3])
+    assert J._fill_coordinate_list(None, 2, offset=2) == Matrix([q2j, q3j])
+    # Test label
+    assert J._fill_coordinate_list(None, 1, 'u') == Matrix([uj])
+    assert J._fill_coordinate_list([], 3, 'u') == Matrix([u0j, u1j, u2j])
+    # Test single numbering
+    assert J._fill_coordinate_list(None, 1, number_single=True) == Matrix([q0j])
+    assert J._fill_coordinate_list([], 1, 'u', 2, True) == Matrix([u2j])
+    assert J._fill_coordinate_list([], 3, 'q') == Matrix([q0j, q1j, q2j])
+    # Test invalid number of coordinates supplied
+    raises(ValueError, lambda: J._fill_coordinate_list([q0, q1], 1))
+    raises(ValueError, lambda: J._fill_coordinate_list([u0, u1, None], 2, 'u'))
+    raises(ValueError, lambda: J._fill_coordinate_list([q0, q1], 3))
+    # Test incorrect coordinate type
+    raises(TypeError, lambda: J._fill_coordinate_list([q0, symbols('q1')], 2))
+    raises(TypeError, lambda: J._fill_coordinate_list([q0 + q1, q1], 2))
+    # Test if derivative as generalized speed is allowed
+    _, _, P, C = _generate_body()
+    PinJoint('J', P, C, q1, q1.diff(t))
+    # Test duplicate coordinates
+    _, _, P, C = _generate_body()
+    raises(ValueError, lambda: SphericalJoint('J', P, C, [q1j, None, None]))
+    raises(ValueError, lambda: SphericalJoint('J', P, C, speeds=[u0, u0, u1]))
+
+
+def test_pin_joint():
+    P = RigidBody('P')
+    C = RigidBody('C')
+    l, m = symbols('l m')
+    q, u = dynamicsymbols('q_J, u_J')
+    Pj = PinJoint('J', P, C)
+    assert Pj.name == 'J'
+    assert Pj.parent == P
+    assert Pj.child == C
+    assert Pj.coordinates == Matrix([q])
+    assert Pj.speeds == Matrix([u])
+    assert Pj.kdes == Matrix([u - q.diff(t)])
+    assert Pj.joint_axis == P.frame.x
+    assert Pj.child_point.pos_from(C.masscenter) == Vector(0)
+    assert Pj.parent_point.pos_from(P.masscenter) == Vector(0)
+    assert Pj.parent_point.pos_from(Pj._child_point) == Vector(0)
+    assert C.masscenter.pos_from(P.masscenter) == Vector(0)
+    assert Pj.parent_interframe == P.frame
+    assert Pj.child_interframe == C.frame
+    assert Pj.__str__() == 'PinJoint: J  parent: P  child: C'
+
+    P1 = RigidBody('P1')
+    C1 = RigidBody('C1')
+    Pint = ReferenceFrame('P_int')
+    Pint.orient_axis(P1.frame, P1.y, pi / 2)
+    J1 = PinJoint('J1', P1, C1, parent_point=l*P1.frame.x,
+                  child_point=m*C1.frame.y, joint_axis=P1.frame.z,
+                  parent_interframe=Pint)
+    assert J1._joint_axis == P1.frame.z
+    assert J1._child_point.pos_from(C1.masscenter) == m * C1.frame.y
+    assert J1._parent_point.pos_from(P1.masscenter) == l * P1.frame.x
+    assert J1._parent_point.pos_from(J1._child_point) == Vector(0)
+    assert (P1.masscenter.pos_from(C1.masscenter) ==
+            -l*P1.frame.x + m*C1.frame.y)
+    assert J1.parent_interframe == Pint
+    assert J1.child_interframe == C1.frame
+
+    q, u = dynamicsymbols('q, u')
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    parent_point = P.masscenter.locatenew('parent_point', N.x + N.y)
+    child_point = C.masscenter.locatenew('child_point', C.y + C.z)
+    J = PinJoint('J', P, C, q, u, parent_point=parent_point,
+                 child_point=child_point, parent_interframe=Pint,
+                 child_interframe=Cint, joint_axis=N.z)
+    assert J.joint_axis == N.z
+    assert J.parent_point.vel(N) == 0
+    assert J.parent_point == parent_point
+    assert J.child_point == child_point
+    assert J.child_point.pos_from(P.masscenter) == N.x + N.y
+    assert J.parent_point.pos_from(C.masscenter) == C.y + C.z
+    assert C.masscenter.pos_from(P.masscenter) == N.x + N.y - C.y - C.z
+    assert C.masscenter.vel(N).express(N) == (u * sin(q) - u * cos(q)) * N.x + (
+            -u * sin(q) - u * cos(q)) * N.y
+    assert J.parent_interframe == Pint
+    assert J.child_interframe == Cint
+
+
+def test_particle_compatibility():
+    m, l = symbols('m l')
+    C_frame = ReferenceFrame('C')
+    P = Particle('P')
+    C = Particle('C', mass=m)
+    q, u = dynamicsymbols('q, u')
+    J = PinJoint('J', P, C, q, u, child_interframe=C_frame,
+                 child_point=l * C_frame.y)
+    assert J.child_interframe == C_frame
+    assert J.parent_interframe.name == 'J_P_frame'
+    assert C.masscenter.pos_from(P.masscenter) == -l * C_frame.y
+    assert C_frame.dcm(J.parent_interframe) == Matrix([[1, 0, 0],
+                                                       [0, cos(q), sin(q)],
+                                                       [0, -sin(q), cos(q)]])
+    assert C.masscenter.vel(J.parent_interframe) == -l * u * C_frame.z
+    # Test with specified joint axis
+    P_frame = ReferenceFrame('P')
+    C_frame = ReferenceFrame('C')
+    P = Particle('P')
+    C = Particle('C', mass=m)
+    q, u = dynamicsymbols('q, u')
+    J = PinJoint('J', P, C, q, u, parent_interframe=P_frame,
+                 child_interframe=C_frame, child_point=l * C_frame.y,
+                 joint_axis=P_frame.z)
+    assert J.joint_axis == J.parent_interframe.z
+    assert C_frame.dcm(J.parent_interframe) == Matrix([[cos(q), sin(q), 0],
+                                                       [-sin(q), cos(q), 0],
+                                                       [0, 0, 1]])
+    assert P.masscenter.vel(J.parent_interframe) == 0
+    assert C.masscenter.vel(J.parent_interframe) == l * u * C_frame.x
+    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1:4 u1:4')
+    qdot_to_u = {qi.diff(t): ui for qi, ui in ((q1, u1), (q2, u2), (q3, u3))}
+    # Test compatibility for prismatic joint
+    P, C = Particle('P'), Particle('C')
+    J = PrismaticJoint('J', P, C, q, u)
+    assert J.parent_interframe.dcm(J.child_interframe) == eye(3)
+    assert C.masscenter.pos_from(P.masscenter) == q * J.parent_interframe.x
+    assert P.masscenter.vel(J.parent_interframe) == 0
+    assert C.masscenter.vel(J.parent_interframe) == u * J.parent_interframe.x
+    # Test compatibility for cylindrical joint
+    P, C = Particle('P'), Particle('C')
+    P_frame = ReferenceFrame('P_frame')
+    J = CylindricalJoint('J', P, C, q1, q2, u1, u2, parent_interframe=P_frame,
+                         parent_point=l * P_frame.x, joint_axis=P_frame.y)
+    assert J.parent_interframe.dcm(J.child_interframe) == Matrix([
+        [cos(q1), 0, sin(q1)], [0, 1, 0], [-sin(q1), 0, cos(q1)]])
+    assert C.masscenter.pos_from(P.masscenter) == l * P_frame.x + q2 * P_frame.y
+    assert C.masscenter.vel(J.parent_interframe) == u2 * P_frame.y
+    assert P.masscenter.vel(J.child_interframe).xreplace(qdot_to_u) == (
+        -u2 * P_frame.y - l * u1 * P_frame.z)
+    # Test compatibility for planar joint
+    P, C = Particle('P'), Particle('C')
+    C_frame = ReferenceFrame('C_frame')
+    J = PlanarJoint('J', P, C, q1, [q2, q3], u1, [u2, u3],
+                    child_interframe=C_frame, child_point=l * C_frame.z)
+    P_frame = J.parent_interframe
+    assert J.parent_interframe.dcm(J.child_interframe) == Matrix([
+        [1, 0, 0], [0, cos(q1), -sin(q1)], [0, sin(q1), cos(q1)]])
+    assert C.masscenter.pos_from(P.masscenter) == (
+        -l * C_frame.z + q2 * P_frame.y + q3 * P_frame.z)
+    assert C.masscenter.vel(J.parent_interframe) == (
+        l * u1 * C_frame.y + u2 * P_frame.y + u3 * P_frame.z)
+    # Test compatibility for weld joint
+    P, C = Particle('P'), Particle('C')
+    C_frame, P_frame = ReferenceFrame('C_frame'), ReferenceFrame('P_frame')
+    J = WeldJoint('J', P, C, parent_interframe=P_frame,
+                  child_interframe=C_frame, parent_point=l * P_frame.x,
+                  child_point=l * C_frame.y)
+    assert P_frame.dcm(C_frame) == eye(3)
+    assert C.masscenter.pos_from(P.masscenter) == l * P_frame.x - l * C_frame.y
+    assert C.masscenter.vel(J.parent_interframe) == 0
+
+
+def test_body_compatibility():
+    m, l = symbols('m l')
+    C_frame = ReferenceFrame('C')
+    with warns_deprecated_sympy():
+        P = Body('P')
+        C = Body('C', mass=m, frame=C_frame)
+    q, u = dynamicsymbols('q, u')
+    PinJoint('J', P, C, q, u, child_point=l * C_frame.y)
+    assert C.frame == C_frame
+    assert P.frame.name == 'P_frame'
+    assert C.masscenter.pos_from(P.masscenter) == -l * C.y
+    assert C.frame.dcm(P.frame) == Matrix([[1, 0, 0],
+                                           [0, cos(q), sin(q)],
+                                           [0, -sin(q), cos(q)]])
+    assert C.masscenter.vel(P.frame) == -l * u * C.z
+
+
+def test_pin_joint_double_pendulum():
+    q1, q2 = dynamicsymbols('q1 q2')
+    u1, u2 = dynamicsymbols('u1 u2')
+    m, l = symbols('m l')
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = RigidBody('C', frame=N)  # ceiling
+    PartP = RigidBody('P', frame=A, mass=m)
+    PartR = RigidBody('R', frame=B, mass=m)
+
+    J1 = PinJoint('J1', C, PartP, speeds=u1, coordinates=q1,
+                  child_point=-l*A.x, joint_axis=C.frame.z)
+    J2 = PinJoint('J2', PartP, PartR, speeds=u2, coordinates=q2,
+                  child_point=-l*B.x, joint_axis=PartP.frame.z)
+
+    # Check orientation
+    assert N.dcm(A) == Matrix([[cos(q1), -sin(q1), 0],
+                               [sin(q1), cos(q1), 0], [0, 0, 1]])
+    assert A.dcm(B) == Matrix([[cos(q2), -sin(q2), 0],
+                               [sin(q2), cos(q2), 0], [0, 0, 1]])
+    assert simplify(N.dcm(B)) == Matrix([[cos(q1 + q2), -sin(q1 + q2), 0],
+                                                 [sin(q1 + q2), cos(q1 + q2), 0],
+                                                 [0, 0, 1]])
+
+    # Check Angular Velocity
+    assert A.ang_vel_in(N) == u1 * N.z
+    assert B.ang_vel_in(A) == u2 * A.z
+    assert B.ang_vel_in(N) == u1 * N.z + u2 * A.z
+
+    # Check kde
+    assert J1.kdes == Matrix([u1 - q1.diff(t)])
+    assert J2.kdes == Matrix([u2 - q2.diff(t)])
+
+    # Check Linear Velocity
+    assert PartP.masscenter.vel(N) == l*u1*A.y
+    assert PartR.masscenter.vel(A) == l*u2*B.y
+    assert PartR.masscenter.vel(N) == l*u1*A.y + l*(u1 + u2)*B.y
+
+
+def test_pin_joint_chaos_pendulum():
+    mA, mB, lA, lB, h = symbols('mA, mB, lA, lB, h')
+    theta, phi, omega, alpha = dynamicsymbols('theta phi omega alpha')
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    lA = (lB - h / 2) / 2
+    lC = (lB/2 + h/4)
+    rod = RigidBody('rod', frame=A, mass=mA)
+    plate = RigidBody('plate', mass=mB, frame=B)
+    C = RigidBody('C', frame=N)
+    J1 = PinJoint('J1', C, rod, coordinates=theta, speeds=omega,
+                  child_point=lA*A.z, joint_axis=N.y)
+    J2 = PinJoint('J2', rod, plate, coordinates=phi, speeds=alpha,
+                  parent_point=lC*A.z, joint_axis=A.z)
+
+    # Check orientation
+    assert A.dcm(N) == Matrix([[cos(theta), 0, -sin(theta)],
+                               [0, 1, 0],
+                               [sin(theta), 0, cos(theta)]])
+    assert A.dcm(B) == Matrix([[cos(phi), -sin(phi), 0],
+                               [sin(phi), cos(phi), 0],
+                               [0, 0, 1]])
+    assert B.dcm(N) == Matrix([
+        [cos(phi)*cos(theta), sin(phi), -sin(theta)*cos(phi)],
+        [-sin(phi)*cos(theta), cos(phi), sin(phi)*sin(theta)],
+        [sin(theta), 0, cos(theta)]])
+
+    # Check Angular Velocity
+    assert A.ang_vel_in(N) == omega*N.y
+    assert A.ang_vel_in(B) == -alpha*A.z
+    assert N.ang_vel_in(B) == -omega*N.y - alpha*A.z
+
+    # Check kde
+    assert J1.kdes == Matrix([omega - theta.diff(t)])
+    assert J2.kdes == Matrix([alpha - phi.diff(t)])
+
+    # Check pos of masscenters
+    assert C.masscenter.pos_from(rod.masscenter) == lA*A.z
+    assert rod.masscenter.pos_from(plate.masscenter) == - lC * A.z
+
+    # Check Linear Velocities
+    assert rod.masscenter.vel(N) == (h/4 - lB/2)*omega*A.x
+    assert plate.masscenter.vel(N) == ((h/4 - lB/2)*omega +
+                                       (h/4 + lB/2)*omega)*A.x
+
+
+def test_pin_joint_interframe():
+    q, u = dynamicsymbols('q, u')
+    # Check not connected
+    N, A, P, C = _generate_body()
+    Pint, Cint = ReferenceFrame('Pint'), ReferenceFrame('Cint')
+    raises(ValueError, lambda: PinJoint('J', P, C, parent_interframe=Pint))
+    raises(ValueError, lambda: PinJoint('J', P, C, child_interframe=Cint))
+    # Check not fixed interframe
+    Pint.orient_axis(N, N.z, q)
+    Cint.orient_axis(A, A.z, q)
+    raises(ValueError, lambda: PinJoint('J', P, C, parent_interframe=Pint))
+    raises(ValueError, lambda: PinJoint('J', P, C, child_interframe=Cint))
+    # Check only parent_interframe
+    N, A, P, C = _generate_body()
+    Pint = ReferenceFrame('Pint')
+    Pint.orient_body_fixed(N, (pi / 4, pi, pi / 3), 'xyz')
+    PinJoint('J', P, C, q, u, parent_point=N.x, child_point=-C.y,
+             parent_interframe=Pint, joint_axis=Pint.x)
+    assert simplify(N.dcm(A)) - Matrix([
+        [-1 / 2, sqrt(3) * cos(q) / 2, -sqrt(3) * sin(q) / 2],
+        [sqrt(6) / 4, sqrt(2) * (2 * sin(q) + cos(q)) / 4,
+         sqrt(2) * (-sin(q) + 2 * cos(q)) / 4],
+        [sqrt(6) / 4, sqrt(2) * (-2 * sin(q) + cos(q)) / 4,
+         -sqrt(2) * (sin(q) + 2 * cos(q)) / 4]]) == zeros(3)
+    assert A.ang_vel_in(N) == u * Pint.x
+    assert C.masscenter.pos_from(P.masscenter) == N.x + A.y
+    assert C.masscenter.vel(N) == u * A.z
+    assert P.masscenter.vel(Pint) == Vector(0)
+    assert C.masscenter.vel(Pint) == u * A.z
+    # Check only child_interframe
+    N, A, P, C = _generate_body()
+    Cint = ReferenceFrame('Cint')
+    Cint.orient_body_fixed(A, (2 * pi / 3, -pi, pi / 2), 'xyz')
+    PinJoint('J', P, C, q, u, parent_point=-N.z, child_point=C.x,
+             child_interframe=Cint, joint_axis=P.x + P.z)
+    assert simplify(N.dcm(A)) == Matrix([
+        [-sqrt(2) * sin(q) / 2,
+         -sqrt(3) * (cos(q) - 1) / 4 - cos(q) / 4 - S(1) / 4,
+         sqrt(3) * (cos(q) + 1) / 4 - cos(q) / 4 + S(1) / 4],
+        [cos(q), (sqrt(2) + sqrt(6)) * -sin(q) / 4,
+         (-sqrt(2) + sqrt(6)) * sin(q) / 4],
+        [sqrt(2) * sin(q) / 2,
+         sqrt(3) * (cos(q) + 1) / 4 + cos(q) / 4 - S(1) / 4,
+         sqrt(3) * (1 - cos(q)) / 4 + cos(q) / 4 + S(1) / 4]])
+    assert A.ang_vel_in(N) == sqrt(2) * u / 2 * N.x + sqrt(2) * u / 2 * N.z
+    assert C.masscenter.pos_from(P.masscenter) == - N.z - A.x
+    assert C.masscenter.vel(N).simplify() == (
+        -sqrt(6) - sqrt(2)) * u / 4 * A.y + (
+               -sqrt(2) + sqrt(6)) * u / 4 * A.z
+    assert C.masscenter.vel(Cint) == Vector(0)
+    # Check combination
+    N, A, P, C = _generate_body()
+    Pint, Cint = ReferenceFrame('Pint'), ReferenceFrame('Cint')
+    Pint.orient_body_fixed(N, (-pi / 2, pi, pi / 2), 'xyz')
+    Cint.orient_body_fixed(A, (2 * pi / 3, -pi, pi / 2), 'xyz')
+    PinJoint('J', P, C, q, u, parent_point=N.x - N.y, child_point=-C.z,
+             parent_interframe=Pint, child_interframe=Cint,
+             joint_axis=Pint.x + Pint.z)
+    assert simplify(N.dcm(A)) == Matrix([
+        [cos(q), (sqrt(2) + sqrt(6)) * -sin(q) / 4,
+         (-sqrt(2) + sqrt(6)) * sin(q) / 4],
+        [-sqrt(2) * sin(q) / 2,
+         -sqrt(3) * (cos(q) + 1) / 4 - cos(q) / 4 + S(1) / 4,
+         sqrt(3) * (cos(q) - 1) / 4 - cos(q) / 4 - S(1) / 4],
+        [sqrt(2) * sin(q) / 2,
+         sqrt(3) * (cos(q) - 1) / 4 + cos(q) / 4 + S(1) / 4,
+         -sqrt(3) * (cos(q) + 1) / 4 + cos(q) / 4 - S(1) / 4]])
+    assert A.ang_vel_in(N) == sqrt(2) * u / 2 * Pint.x + sqrt(
+        2) * u / 2 * Pint.z
+    assert C.masscenter.pos_from(P.masscenter) == N.x - N.y + A.z
+    N_v_C = (-sqrt(2) + sqrt(6)) * u / 4 * A.x
+    assert C.masscenter.vel(N).simplify() == N_v_C
+    assert C.masscenter.vel(Pint).simplify() == N_v_C
+    assert C.masscenter.vel(Cint) == Vector(0)
+
+
+def test_pin_joint_joint_axis():
+    q, u = dynamicsymbols('q, u')
+    # Check parent as reference
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    pin = PinJoint('J', P, C, q, u, parent_interframe=Pint,
+                   child_interframe=Cint, joint_axis=P.y)
+    assert pin.joint_axis == P.y
+    assert N.dcm(A) == Matrix([[sin(q), 0, cos(q)], [0, -1, 0],
+                               [cos(q), 0, -sin(q)]])
+    # Check parent_interframe as reference
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    pin = PinJoint('J', P, C, q, u, parent_interframe=Pint,
+                   child_interframe=Cint, joint_axis=Pint.y)
+    assert pin.joint_axis == Pint.y
+    assert N.dcm(A) == Matrix([[-sin(q), 0, cos(q)], [0, -1, 0],
+                               [cos(q), 0, sin(q)]])
+    # Check combination of joint_axis with interframes supplied as vectors (2x)
+    N, A, P, C = _generate_body()
+    pin = PinJoint('J', P, C, q, u, parent_interframe=N.z,
+                   child_interframe=-C.z, joint_axis=N.z)
+    assert pin.joint_axis == N.z
+    assert N.dcm(A) == Matrix([[-cos(q), -sin(q), 0], [-sin(q), cos(q), 0],
+                               [0, 0, -1]])
+    N, A, P, C = _generate_body()
+    pin = PinJoint('J', P, C, q, u, parent_interframe=N.z,
+                   child_interframe=-C.z, joint_axis=N.x)
+    assert pin.joint_axis == N.x
+    assert N.dcm(A) == Matrix([[-1, 0, 0], [0, cos(q), sin(q)],
+                               [0, sin(q), -cos(q)]])
+    # Check time varying axis
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    raises(ValueError, lambda: PinJoint('J', P, C,
+                                        joint_axis=cos(q) * N.x + sin(q) * N.y))
+    # Check joint_axis provided in child frame
+    raises(ValueError, lambda: PinJoint('J', P, C, joint_axis=C.x))
+    # Check some invalid combinations
+    raises(ValueError, lambda: PinJoint('J', P, C, joint_axis=P.x + C.y))
+    raises(ValueError, lambda: PinJoint(
+        'J', P, C, parent_interframe=Pint, child_interframe=Cint,
+        joint_axis=Pint.x + C.y))
+    raises(ValueError, lambda: PinJoint(
+        'J', P, C, parent_interframe=Pint, child_interframe=Cint,
+        joint_axis=P.x + Cint.y))
+    # Check valid special combination
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    PinJoint('J', P, C, parent_interframe=Pint, child_interframe=Cint,
+             joint_axis=Pint.x + P.y)
+    # Check invalid zero vector
+    raises(Exception, lambda: PinJoint(
+        'J', P, C, parent_interframe=Pint, child_interframe=Cint,
+        joint_axis=Vector(0)))
+    raises(Exception, lambda: PinJoint(
+        'J', P, C, parent_interframe=Pint, child_interframe=Cint,
+        joint_axis=P.y + Pint.y))
+
+
+def test_pin_joint_arbitrary_axis():
+    q, u = dynamicsymbols('q_J, u_J')
+
+    # When the bodies are attached though masscenters but axes are opposite.
+    N, A, P, C = _generate_body()
+    PinJoint('J', P, C, child_interframe=-A.x)
+
+    assert (-A.x).angle_between(N.x) == 0
+    assert -A.x.express(N) == N.x
+    assert A.dcm(N) == Matrix([[-1, 0, 0],
+                               [0, -cos(q), -sin(q)],
+                               [0, -sin(q), cos(q)]])
+    assert A.ang_vel_in(N) == u*N.x
+    assert A.ang_vel_in(N).magnitude() == sqrt(u**2)
+    assert C.masscenter.pos_from(P.masscenter) == 0
+    assert C.masscenter.pos_from(P.masscenter).express(N).simplify() == 0
+    assert C.masscenter.vel(N) == 0
+
+    # When axes are different and parent joint is at masscenter but child joint
+    # is at a unit vector from child masscenter.
+    N, A, P, C = _generate_body()
+    PinJoint('J', P, C, child_interframe=A.y, child_point=A.x)
+
+    assert A.y.angle_between(N.x) == 0  # Axis are aligned
+    assert A.y.express(N) == N.x
+    assert A.dcm(N) == Matrix([[0, -cos(q), -sin(q)],
+                               [1, 0, 0],
+                               [0, -sin(q), cos(q)]])
+    assert A.ang_vel_in(N) == u*N.x
+    assert A.ang_vel_in(N).express(A) == u * A.y
+    assert A.ang_vel_in(N).magnitude() == sqrt(u**2)
+    assert A.ang_vel_in(N).cross(A.y) == 0
+    assert C.masscenter.vel(N) == u*A.z
+    assert C.masscenter.pos_from(P.masscenter) == -A.x
+    assert (C.masscenter.pos_from(P.masscenter).express(N).simplify() ==
+            cos(q)*N.y + sin(q)*N.z)
+    assert C.masscenter.vel(N).angle_between(A.x) == pi/2
+
+    # Similar to previous case but wrt parent body
+    N, A, P, C = _generate_body()
+    PinJoint('J', P, C, parent_interframe=N.y, parent_point=N.x)
+
+    assert N.y.angle_between(A.x) == 0  # Axis are aligned
+    assert N.y.express(A) == A.x
+    assert A.dcm(N) == Matrix([[0, 1, 0],
+                               [-cos(q), 0, sin(q)],
+                               [sin(q), 0, cos(q)]])
+    assert A.ang_vel_in(N) == u*N.y
+    assert A.ang_vel_in(N).express(A) == u*A.x
+    assert A.ang_vel_in(N).magnitude() == sqrt(u**2)
+    angle = A.ang_vel_in(N).angle_between(A.x)
+    assert angle.xreplace({u: 1}) == 0
+    assert C.masscenter.vel(N) == 0
+    assert C.masscenter.pos_from(P.masscenter) == N.x
+
+    # Both joint pos id defined but different axes
+    N, A, P, C = _generate_body()
+    PinJoint('J', P, C, parent_point=N.x, child_point=A.x,
+             child_interframe=A.x + A.y)
+    assert expand_mul(N.x.angle_between(A.x + A.y)) == 0  # Axis are aligned
+    assert (A.x + A.y).express(N).simplify() == sqrt(2)*N.x
+    assert simplify(A.dcm(N)) == Matrix([
+        [sqrt(2)/2, -sqrt(2)*cos(q)/2, -sqrt(2)*sin(q)/2],
+        [sqrt(2)/2, sqrt(2)*cos(q)/2, sqrt(2)*sin(q)/2],
+        [0, -sin(q), cos(q)]])
+    assert A.ang_vel_in(N) == u*N.x
+    assert (A.ang_vel_in(N).express(A).simplify() ==
+            (u*A.x + u*A.y)/sqrt(2))
+    assert A.ang_vel_in(N).magnitude() == sqrt(u**2)
+    angle = A.ang_vel_in(N).angle_between(A.x + A.y)
+    assert angle.xreplace({u: 1}) == 0
+    assert C.masscenter.vel(N).simplify() == (u * A.z)/sqrt(2)
+    assert C.masscenter.pos_from(P.masscenter) == N.x - A.x
+    assert (C.masscenter.pos_from(P.masscenter).express(N).simplify() ==
+            (1 - sqrt(2)/2)*N.x + sqrt(2)*cos(q)/2*N.y +
+            sqrt(2)*sin(q)/2*N.z)
+    assert (C.masscenter.vel(N).express(N).simplify() ==
+            -sqrt(2)*u*sin(q)/2*N.y + sqrt(2)*u*cos(q)/2*N.z)
+    assert C.masscenter.vel(N).angle_between(A.x) == pi/2
+
+    N, A, P, C = _generate_body()
+    PinJoint('J', P, C, parent_point=N.x, child_point=A.x,
+             child_interframe=A.x + A.y - A.z)
+    assert expand_mul(N.x.angle_between(A.x + A.y - A.z)) == 0  # Axis aligned
+    assert (A.x + A.y - A.z).express(N).simplify() == sqrt(3)*N.x
+    assert simplify(A.dcm(N)) == Matrix([
+        [sqrt(3)/3, -sqrt(6)*sin(q + pi/4)/3,
+         sqrt(6)*cos(q + pi/4)/3],
+        [sqrt(3)/3, sqrt(6)*cos(q + pi/12)/3,
+         sqrt(6)*sin(q + pi/12)/3],
+        [-sqrt(3)/3, sqrt(6)*cos(q + 5*pi/12)/3,
+         sqrt(6)*sin(q + 5*pi/12)/3]])
+    assert A.ang_vel_in(N) == u*N.x
+    assert A.ang_vel_in(N).express(A).simplify() == (u*A.x + u*A.y -
+                                                     u*A.z)/sqrt(3)
+    assert A.ang_vel_in(N).magnitude() == sqrt(u**2)
+    angle = A.ang_vel_in(N).angle_between(A.x + A.y-A.z)
+    assert angle.xreplace({u: 1}).simplify() == 0
+    assert C.masscenter.vel(N).simplify() == (u*A.y + u*A.z)/sqrt(3)
+    assert C.masscenter.pos_from(P.masscenter) == N.x - A.x
+    assert (C.masscenter.pos_from(P.masscenter).express(N).simplify() ==
+            (1 - sqrt(3)/3)*N.x + sqrt(6)*sin(q + pi/4)/3*N.y -
+            sqrt(6)*cos(q + pi/4)/3*N.z)
+    assert (C.masscenter.vel(N).express(N).simplify() ==
+            sqrt(6)*u*cos(q + pi/4)/3*N.y +
+            sqrt(6)*u*sin(q + pi/4)/3*N.z)
+    assert C.masscenter.vel(N).angle_between(A.x) == pi/2
+
+    N, A, P, C = _generate_body()
+    m, n = symbols('m n')
+    PinJoint('J', P, C, parent_point=m * N.x, child_point=n * A.x,
+             child_interframe=A.x + A.y - A.z,
+             parent_interframe=N.x - N.y + N.z)
+    angle = (N.x - N.y + N.z).angle_between(A.x + A.y - A.z)
+    assert expand_mul(angle) == 0  # Axis are aligned
+    assert ((A.x-A.y+A.z).express(N).simplify() ==
+            (-4*cos(q)/3 - S(1)/3)*N.x + (S(1)/3 - 4*sin(q + pi/6)/3)*N.y +
+            (4*cos(q + pi/3)/3 - S(1)/3)*N.z)
+    assert simplify(A.dcm(N)) == Matrix([
+        [S(1)/3 - 2*cos(q)/3, -2*sin(q + pi/6)/3 - S(1)/3,
+         2*cos(q + pi/3)/3 + S(1)/3],
+        [2*cos(q + pi/3)/3 + S(1)/3, 2*cos(q)/3 - S(1)/3,
+         2*sin(q + pi/6)/3 + S(1)/3],
+        [-2*sin(q + pi/6)/3 - S(1)/3, 2*cos(q + pi/3)/3 + S(1)/3,
+         2*cos(q)/3 - S(1)/3]])
+    assert (A.ang_vel_in(N) - (u*N.x - u*N.y + u*N.z)/sqrt(3)).simplify()
+    assert A.ang_vel_in(N).express(A).simplify() == (u*A.x + u*A.y -
+                                                     u*A.z)/sqrt(3)
+    assert A.ang_vel_in(N).magnitude() == sqrt(u**2)
+    angle = A.ang_vel_in(N).angle_between(A.x+A.y-A.z)
+    assert angle.xreplace({u: 1}).simplify() == 0
+    assert (C.masscenter.vel(N).simplify() ==
+            sqrt(3)*n*u/3*A.y + sqrt(3)*n*u/3*A.z)
+    assert C.masscenter.pos_from(P.masscenter) == m*N.x - n*A.x
+    assert (C.masscenter.pos_from(P.masscenter).express(N).simplify() ==
+            (m + n*(2*cos(q) - 1)/3)*N.x + n*(2*sin(q + pi/6) +
+            1)/3*N.y - n*(2*cos(q + pi/3) + 1)/3*N.z)
+    assert (C.masscenter.vel(N).express(N).simplify() ==
+            - 2*n*u*sin(q)/3*N.x + 2*n*u*cos(q + pi/6)/3*N.y +
+            2*n*u*sin(q + pi/3)/3*N.z)
+    assert C.masscenter.vel(N).dot(N.x - N.y + N.z).simplify() == 0
+
+
+def test_create_aligned_frame_pi():
+    N, A, P, C = _generate_body()
+    f = Joint._create_aligned_interframe(P, -P.x, P.x)
+    assert f.z == P.z
+    f = Joint._create_aligned_interframe(P, -P.y, P.y)
+    assert f.x == P.x
+    f = Joint._create_aligned_interframe(P, -P.z, P.z)
+    assert f.y == P.y
+    f = Joint._create_aligned_interframe(P, -P.x - P.y, P.x + P.y)
+    assert f.z == P.z
+    f = Joint._create_aligned_interframe(P, -P.y - P.z, P.y + P.z)
+    assert f.x == P.x
+    f = Joint._create_aligned_interframe(P, -P.x - P.z, P.x + P.z)
+    assert f.y == P.y
+    f = Joint._create_aligned_interframe(P, -P.x - P.y - P.z, P.x + P.y + P.z)
+    assert f.y - f.z == P.y - P.z
+
+
+def test_pin_joint_axis():
+    q, u = dynamicsymbols('q u')
+    # Test default joint axis
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    J = PinJoint('J', P, C, q, u, parent_interframe=Pint, child_interframe=Cint)
+    assert J.joint_axis == Pint.x
+    # Test for the same joint axis expressed in different frames
+    N_R_A = Matrix([[0, sin(q), cos(q)],
+                    [0, -cos(q), sin(q)],
+                    [1, 0, 0]])
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    PinJoint('J', P, C, q, u, parent_interframe=Pint, child_interframe=Cint,
+             joint_axis=N.z)
+    assert N.dcm(A) == N_R_A
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    PinJoint('J', P, C, q, u, parent_interframe=Pint, child_interframe=Cint,
+             joint_axis=-Pint.z)
+    assert N.dcm(A) == N_R_A
+    # Test time varying joint axis
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    raises(ValueError, lambda: PinJoint('J', P, C, joint_axis=q * N.z))
+
+
+def test_locate_joint_pos():
+    # Test Vector and default
+    N, A, P, C = _generate_body()
+    joint = PinJoint('J', P, C, parent_point=N.y + N.z)
+    assert joint.parent_point.name == 'J_P_joint'
+    assert joint.parent_point.pos_from(P.masscenter) == N.y + N.z
+    assert joint.child_point == C.masscenter
+    # Test Point objects
+    N, A, P, C = _generate_body()
+    parent_point = P.masscenter.locatenew('p', N.y + N.z)
+    joint = PinJoint('J', P, C, parent_point=parent_point,
+                     child_point=C.masscenter)
+    assert joint.parent_point == parent_point
+    assert joint.child_point == C.masscenter
+    # Check invalid type
+    N, A, P, C = _generate_body()
+    raises(TypeError,
+           lambda: PinJoint('J', P, C, parent_point=N.x.to_matrix(N)))
+    # Test time varying positions
+    q = dynamicsymbols('q')
+    N, A, P, C = _generate_body()
+    raises(ValueError, lambda: PinJoint('J', P, C, parent_point=q * N.x))
+    N, A, P, C = _generate_body()
+    child_point = C.masscenter.locatenew('p', q * A.y)
+    raises(ValueError, lambda: PinJoint('J', P, C, child_point=child_point))
+    # Test undefined position
+    child_point = Point('p')
+    raises(ValueError, lambda: PinJoint('J', P, C, child_point=child_point))
+
+
+def test_locate_joint_frame():
+    # Test rotated frame and default
+    N, A, P, C = _generate_body()
+    parent_interframe = ReferenceFrame('int_frame')
+    parent_interframe.orient_axis(N, N.z, 1)
+    joint = PinJoint('J', P, C, parent_interframe=parent_interframe)
+    assert joint.parent_interframe == parent_interframe
+    assert joint.parent_interframe.ang_vel_in(N) == 0
+    assert joint.child_interframe == A
+    # Test time varying orientations
+    q = dynamicsymbols('q')
+    N, A, P, C = _generate_body()
+    parent_interframe = ReferenceFrame('int_frame')
+    parent_interframe.orient_axis(N, N.z, q)
+    raises(ValueError,
+           lambda: PinJoint('J', P, C, parent_interframe=parent_interframe))
+    # Test undefined frame
+    N, A, P, C = _generate_body()
+    child_interframe = ReferenceFrame('int_frame')
+    child_interframe.orient_axis(N, N.z, 1)  # Defined with respect to parent
+    raises(ValueError,
+           lambda: PinJoint('J', P, C, child_interframe=child_interframe))
+
+
+def test_prismatic_joint():
+    _, _, P, C = _generate_body()
+    q, u = dynamicsymbols('q_S, u_S')
+    S = PrismaticJoint('S', P, C)
+    assert S.name == 'S'
+    assert S.parent == P
+    assert S.child == C
+    assert S.coordinates == Matrix([q])
+    assert S.speeds == Matrix([u])
+    assert S.kdes == Matrix([u - q.diff(t)])
+    assert S.joint_axis == P.frame.x
+    assert S.child_point.pos_from(C.masscenter) == Vector(0)
+    assert S.parent_point.pos_from(P.masscenter) == Vector(0)
+    assert S.parent_point.pos_from(S.child_point) == - q * P.frame.x
+    assert P.masscenter.pos_from(C.masscenter) == - q * P.frame.x
+    assert C.masscenter.vel(P.frame) == u * P.frame.x
+    assert P.frame.ang_vel_in(C.frame) == 0
+    assert C.frame.ang_vel_in(P.frame) == 0
+    assert S.__str__() == 'PrismaticJoint: S  parent: P  child: C'
+
+    N, A, P, C = _generate_body()
+    l, m = symbols('l m')
+    Pint = ReferenceFrame('P_int')
+    Pint.orient_axis(P.frame, P.y, pi / 2)
+    S = PrismaticJoint('S', P, C, parent_point=l * P.frame.x,
+                       child_point=m * C.frame.y, joint_axis=P.frame.z,
+                       parent_interframe=Pint)
+
+    assert S.joint_axis == P.frame.z
+    assert S.child_point.pos_from(C.masscenter) == m * C.frame.y
+    assert S.parent_point.pos_from(P.masscenter) == l * P.frame.x
+    assert S.parent_point.pos_from(S.child_point) == - q * P.frame.z
+    assert P.masscenter.pos_from(C.masscenter) == - l * N.x - q * N.z + m * A.y
+    assert C.masscenter.vel(P.frame) == u * P.frame.z
+    assert P.masscenter.vel(Pint) == Vector(0)
+    assert C.frame.ang_vel_in(P.frame) == 0
+    assert P.frame.ang_vel_in(C.frame) == 0
+
+    _, _, P, C = _generate_body()
+    Pint = ReferenceFrame('P_int')
+    Pint.orient_axis(P.frame, P.y, pi / 2)
+    S = PrismaticJoint('S', P, C, parent_point=l * P.frame.z,
+                       child_point=m * C.frame.x, joint_axis=P.frame.z,
+                       parent_interframe=Pint)
+    assert S.joint_axis == P.frame.z
+    assert S.child_point.pos_from(C.masscenter) == m * C.frame.x
+    assert S.parent_point.pos_from(P.masscenter) == l * P.frame.z
+    assert S.parent_point.pos_from(S.child_point) == - q * P.frame.z
+    assert P.masscenter.pos_from(C.masscenter) == (-l - q)*P.frame.z + m*C.frame.x
+    assert C.masscenter.vel(P.frame) == u * P.frame.z
+    assert C.frame.ang_vel_in(P.frame) == 0
+    assert P.frame.ang_vel_in(C.frame) == 0
+
+
+def test_prismatic_joint_arbitrary_axis():
+    q, u = dynamicsymbols('q_S, u_S')
+
+    N, A, P, C = _generate_body()
+    PrismaticJoint('S', P, C, child_interframe=-A.x)
+
+    assert (-A.x).angle_between(N.x) == 0
+    assert -A.x.express(N) == N.x
+    assert A.dcm(N) == Matrix([[-1, 0, 0], [0, -1, 0], [0, 0, 1]])
+    assert C.masscenter.pos_from(P.masscenter) == q * N.x
+    assert C.masscenter.pos_from(P.masscenter).express(A).simplify() == -q * A.x
+    assert C.masscenter.vel(N) == u * N.x
+    assert C.masscenter.vel(N).express(A) == -u * A.x
+    assert A.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == 0
+
+    #When axes are different and parent joint is at masscenter but child joint is at a unit vector from
+    #child masscenter.
+    N, A, P, C = _generate_body()
+    PrismaticJoint('S', P, C, child_interframe=A.y, child_point=A.x)
+
+    assert A.y.angle_between(N.x) == 0 #Axis are aligned
+    assert A.y.express(N) == N.x
+    assert A.dcm(N) == Matrix([[0, -1, 0], [1, 0, 0], [0, 0, 1]])
+    assert C.masscenter.vel(N) == u * N.x
+    assert C.masscenter.vel(N).express(A) == u * A.y
+    assert C.masscenter.pos_from(P.masscenter) == q*N.x - A.x
+    assert C.masscenter.pos_from(P.masscenter).express(N).simplify() == q*N.x + N.y
+    assert A.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == 0
+
+    #Similar to previous case but wrt parent body
+    N, A, P, C = _generate_body()
+    PrismaticJoint('S', P, C, parent_interframe=N.y, parent_point=N.x)
+
+    assert N.y.angle_between(A.x) == 0 #Axis are aligned
+    assert N.y.express(A) ==  A.x
+    assert A.dcm(N) == Matrix([[0, 1, 0], [-1, 0, 0], [0, 0, 1]])
+    assert C.masscenter.vel(N) == u * N.y
+    assert C.masscenter.vel(N).express(A) == u * A.x
+    assert C.masscenter.pos_from(P.masscenter) == N.x + q*N.y
+    assert A.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == 0
+
+    #Both joint pos is defined but different axes
+    N, A, P, C = _generate_body()
+    PrismaticJoint('S', P, C, parent_point=N.x, child_point=A.x,
+                   child_interframe=A.x + A.y)
+    assert N.x.angle_between(A.x + A.y) == 0 #Axis are aligned
+    assert (A.x + A.y).express(N) == sqrt(2)*N.x
+    assert A.dcm(N) == Matrix([[sqrt(2)/2, -sqrt(2)/2, 0], [sqrt(2)/2, sqrt(2)/2, 0], [0, 0, 1]])
+    assert C.masscenter.pos_from(P.masscenter) == (q + 1)*N.x - A.x
+    assert C.masscenter.pos_from(P.masscenter).express(N) == (q - sqrt(2)/2 + 1)*N.x + sqrt(2)/2*N.y
+    assert C.masscenter.vel(N).express(A) == u * (A.x + A.y)/sqrt(2)
+    assert C.masscenter.vel(N) == u*N.x
+    assert A.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == 0
+
+    N, A, P, C = _generate_body()
+    PrismaticJoint('S', P, C, parent_point=N.x, child_point=A.x,
+                   child_interframe=A.x + A.y - A.z)
+    assert N.x.angle_between(A.x + A.y - A.z).simplify() == 0 #Axis are aligned
+    assert ((A.x + A.y - A.z).express(N) - sqrt(3)*N.x).simplify() == 0
+    assert simplify(A.dcm(N)) == Matrix([[sqrt(3)/3, -sqrt(3)/3, sqrt(3)/3],
+                                                 [sqrt(3)/3, sqrt(3)/6 + S(1)/2, S(1)/2 - sqrt(3)/6],
+                                                 [-sqrt(3)/3, S(1)/2 - sqrt(3)/6, sqrt(3)/6 + S(1)/2]])
+    assert C.masscenter.pos_from(P.masscenter) == (q + 1)*N.x - A.x
+    assert (C.masscenter.pos_from(P.masscenter).express(N) -
+        ((q - sqrt(3)/3 + 1)*N.x + sqrt(3)/3*N.y - sqrt(3)/3*N.z)).simplify() == 0
+    assert C.masscenter.vel(N) == u*N.x
+    assert (C.masscenter.vel(N).express(A) - (
+        sqrt(3)*u/3*A.x + sqrt(3)*u/3*A.y - sqrt(3)*u/3*A.z)).simplify()
+    assert A.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == 0
+
+    N, A, P, C = _generate_body()
+    m, n = symbols('m n')
+    PrismaticJoint('S', P, C, parent_point=m*N.x, child_point=n*A.x,
+                   child_interframe=A.x + A.y - A.z,
+                   parent_interframe=N.x - N.y + N.z)
+    # 0 angle means that the axis are aligned
+    assert (N.x-N.y+N.z).angle_between(A.x+A.y-A.z).simplify() == 0
+    assert ((A.x+A.y-A.z).express(N) - (N.x - N.y + N.z)).simplify() == 0
+    assert simplify(A.dcm(N)) == Matrix([[-S(1)/3, -S(2)/3, S(2)/3],
+                                                 [S(2)/3, S(1)/3, S(2)/3],
+                                                 [-S(2)/3, S(2)/3, S(1)/3]])
+    assert (C.masscenter.pos_from(P.masscenter) - (
+        (m + sqrt(3)*q/3)*N.x - sqrt(3)*q/3*N.y + sqrt(3)*q/3*N.z - n*A.x)
+            ).express(N).simplify() == 0
+    assert (C.masscenter.pos_from(P.masscenter).express(N) - (
+        (m + n/3 + sqrt(3)*q/3)*N.x + (2*n/3 - sqrt(3)*q/3)*N.y +
+        (-2*n/3 + sqrt(3)*q/3)*N.z)).simplify() == 0
+    assert (C.masscenter.vel(N).express(N) - (
+        sqrt(3)*u/3*N.x - sqrt(3)*u/3*N.y + sqrt(3)*u/3*N.z)).simplify() == 0
+    assert (C.masscenter.vel(N).express(A) -
+            (sqrt(3)*u/3*A.x + sqrt(3)*u/3*A.y - sqrt(3)*u/3*A.z)).simplify() == 0
+    assert A.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == 0
+
+
+def test_cylindrical_joint():
+    N, A, P, C = _generate_body()
+    q0_def, q1_def, u0_def, u1_def = dynamicsymbols('q0:2_J, u0:2_J')
+    Cj = CylindricalJoint('J', P, C)
+    assert Cj.name == 'J'
+    assert Cj.parent == P
+    assert Cj.child == C
+    assert Cj.coordinates == Matrix([q0_def, q1_def])
+    assert Cj.speeds == Matrix([u0_def, u1_def])
+    assert Cj.rotation_coordinate == q0_def
+    assert Cj.translation_coordinate == q1_def
+    assert Cj.rotation_speed == u0_def
+    assert Cj.translation_speed == u1_def
+    assert Cj.kdes == Matrix([u0_def - q0_def.diff(t), u1_def - q1_def.diff(t)])
+    assert Cj.joint_axis == N.x
+    assert Cj.child_point.pos_from(C.masscenter) == Vector(0)
+    assert Cj.parent_point.pos_from(P.masscenter) == Vector(0)
+    assert Cj.parent_point.pos_from(Cj._child_point) == -q1_def * N.x
+    assert C.masscenter.pos_from(P.masscenter) == q1_def * N.x
+    assert Cj.child_point.vel(N) == u1_def * N.x
+    assert A.ang_vel_in(N) == u0_def * N.x
+    assert Cj.parent_interframe == N
+    assert Cj.child_interframe == A
+    assert Cj.__str__() == 'CylindricalJoint: J  parent: P  child: C'
+
+    q0, q1, u0, u1 = dynamicsymbols('q0:2, u0:2')
+    l, m = symbols('l, m')
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    Cj = CylindricalJoint('J', P, C, rotation_coordinate=q0, rotation_speed=u0,
+                          translation_speed=u1, parent_point=m * N.x,
+                          child_point=l * A.y, parent_interframe=Pint,
+                          child_interframe=Cint, joint_axis=2 * N.z)
+    assert Cj.coordinates == Matrix([q0, q1_def])
+    assert Cj.speeds == Matrix([u0, u1])
+    assert Cj.rotation_coordinate == q0
+    assert Cj.translation_coordinate == q1_def
+    assert Cj.rotation_speed == u0
+    assert Cj.translation_speed == u1
+    assert Cj.kdes == Matrix([u0 - q0.diff(t), u1 - q1_def.diff(t)])
+    assert Cj.joint_axis == 2 * N.z
+    assert Cj.child_point.pos_from(C.masscenter) == l * A.y
+    assert Cj.parent_point.pos_from(P.masscenter) == m * N.x
+    assert Cj.parent_point.pos_from(Cj._child_point) == -q1_def * N.z
+    assert C.masscenter.pos_from(
+        P.masscenter) == m * N.x + q1_def * N.z - l * A.y
+    assert C.masscenter.vel(N) == u1 * N.z - u0 * l * A.z
+    assert A.ang_vel_in(N) == u0 * N.z
+
+
+def test_planar_joint():
+    N, A, P, C = _generate_body()
+    q0_def, q1_def, q2_def = dynamicsymbols('q0:3_J')
+    u0_def, u1_def, u2_def = dynamicsymbols('u0:3_J')
+    Cj = PlanarJoint('J', P, C)
+    assert Cj.name == 'J'
+    assert Cj.parent == P
+    assert Cj.child == C
+    assert Cj.coordinates == Matrix([q0_def, q1_def, q2_def])
+    assert Cj.speeds == Matrix([u0_def, u1_def, u2_def])
+    assert Cj.rotation_coordinate == q0_def
+    assert Cj.planar_coordinates == Matrix([q1_def, q2_def])
+    assert Cj.rotation_speed == u0_def
+    assert Cj.planar_speeds == Matrix([u1_def, u2_def])
+    assert Cj.kdes == Matrix([u0_def - q0_def.diff(t), u1_def - q1_def.diff(t),
+                              u2_def - q2_def.diff(t)])
+    assert Cj.rotation_axis == N.x
+    assert Cj.planar_vectors == [N.y, N.z]
+    assert Cj.child_point.pos_from(C.masscenter) == Vector(0)
+    assert Cj.parent_point.pos_from(P.masscenter) == Vector(0)
+    r_P_C = q1_def * N.y + q2_def * N.z
+    assert Cj.parent_point.pos_from(Cj.child_point) == -r_P_C
+    assert C.masscenter.pos_from(P.masscenter) == r_P_C
+    assert Cj.child_point.vel(N) == u1_def * N.y + u2_def * N.z
+    assert A.ang_vel_in(N) == u0_def * N.x
+    assert Cj.parent_interframe == N
+    assert Cj.child_interframe == A
+    assert Cj.__str__() == 'PlanarJoint: J  parent: P  child: C'
+
+    q0, q1, q2, u0, u1, u2 = dynamicsymbols('q0:3, u0:3')
+    l, m = symbols('l, m')
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    Cj = PlanarJoint('J', P, C, rotation_coordinate=q0,
+                     planar_coordinates=[q1, q2], planar_speeds=[u1, u2],
+                     parent_point=m * N.x, child_point=l * A.y,
+                     parent_interframe=Pint, child_interframe=Cint)
+    assert Cj.coordinates == Matrix([q0, q1, q2])
+    assert Cj.speeds == Matrix([u0_def, u1, u2])
+    assert Cj.rotation_coordinate == q0
+    assert Cj.planar_coordinates == Matrix([q1, q2])
+    assert Cj.rotation_speed == u0_def
+    assert Cj.planar_speeds == Matrix([u1, u2])
+    assert Cj.kdes == Matrix([u0_def - q0.diff(t), u1 - q1.diff(t),
+                              u2 - q2.diff(t)])
+    assert Cj.rotation_axis == Pint.x
+    assert Cj.planar_vectors == [Pint.y, Pint.z]
+    assert Cj.child_point.pos_from(C.masscenter) == l * A.y
+    assert Cj.parent_point.pos_from(P.masscenter) == m * N.x
+    assert Cj.parent_point.pos_from(Cj.child_point) == q1 * N.y + q2 * N.z
+    assert C.masscenter.pos_from(
+        P.masscenter) == m * N.x - q1 * N.y - q2 * N.z - l * A.y
+    assert C.masscenter.vel(N) == -u1 * N.y - u2 * N.z + u0_def * l * A.x
+    assert A.ang_vel_in(N) == u0_def * N.x
+
+
+def test_planar_joint_advanced():
+    # Tests whether someone is able to just specify two normals, which will form
+    # the rotation axis seen from the parent and child body.
+    # This specific example is a block on a slope, which has that same slope of
+    # 30 degrees, so in the zero configuration the frames of the parent and
+    # child are actually aligned.
+    q0, q1, q2, u0, u1, u2 = dynamicsymbols('q0:3, u0:3')
+    l1, l2 = symbols('l1:3')
+    N, A, P, C = _generate_body()
+    J = PlanarJoint('J', P, C, q0, [q1, q2], u0, [u1, u2],
+                    parent_point=l1 * N.z,
+                    child_point=-l2 * C.z,
+                    parent_interframe=N.z + N.y / sqrt(3),
+                    child_interframe=A.z + A.y / sqrt(3))
+    assert J.rotation_axis.express(N) == (N.z + N.y / sqrt(3)).normalize()
+    assert J.rotation_axis.express(A) == (A.z + A.y / sqrt(3)).normalize()
+    assert J.rotation_axis.angle_between(N.z) == pi / 6
+    assert N.dcm(A).xreplace({q0: 0, q1: 0, q2: 0}) == eye(3)
+    N_R_A = Matrix([
+        [cos(q0), -sqrt(3) * sin(q0) / 2, sin(q0) / 2],
+        [sqrt(3) * sin(q0) / 2, 3 * cos(q0) / 4 + 1 / 4,
+         sqrt(3) * (1 - cos(q0)) / 4],
+        [-sin(q0) / 2, sqrt(3) * (1 - cos(q0)) / 4, cos(q0) / 4 + 3 / 4]])
+    # N.dcm(A) == N_R_A did not work
+    assert simplify(N.dcm(A) - N_R_A) == zeros(3)
+
+
+def test_spherical_joint():
+    N, A, P, C = _generate_body()
+    q0, q1, q2, u0, u1, u2 = dynamicsymbols('q0:3_S, u0:3_S')
+    S = SphericalJoint('S', P, C)
+    assert S.name == 'S'
+    assert S.parent == P
+    assert S.child == C
+    assert S.coordinates == Matrix([q0, q1, q2])
+    assert S.speeds == Matrix([u0, u1, u2])
+    assert S.kdes == Matrix([u0 - q0.diff(t), u1 - q1.diff(t), u2 - q2.diff(t)])
+    assert S.child_point.pos_from(C.masscenter) == Vector(0)
+    assert S.parent_point.pos_from(P.masscenter) == Vector(0)
+    assert S.parent_point.pos_from(S.child_point) == Vector(0)
+    assert P.masscenter.pos_from(C.masscenter) == Vector(0)
+    assert C.masscenter.vel(N) == Vector(0)
+    assert N.ang_vel_in(A) == (-u0 * cos(q1) * cos(q2) - u1 * sin(q2)) * A.x + (
+            u0 * sin(q2) * cos(q1) - u1 * cos(q2)) * A.y + (
+                   -u0 * sin(q1) - u2) * A.z
+    assert A.ang_vel_in(N) == (u0 * cos(q1) * cos(q2) + u1 * sin(q2)) * A.x + (
+            -u0 * sin(q2) * cos(q1) + u1 * cos(q2)) * A.y + (
+                   u0 * sin(q1) + u2) * A.z
+    assert S.__str__() == 'SphericalJoint: S  parent: P  child: C'
+    assert S._rot_type == 'BODY'
+    assert S._rot_order == 123
+    assert S._amounts is None
+
+
+def test_spherical_joint_speeds_as_derivative_terms():
+    # This tests checks whether the system remains valid if the user chooses to
+    # pass the derivative of the generalized coordinates as generalized speeds
+    q0, q1, q2 = dynamicsymbols('q0:3')
+    u0, u1, u2 = dynamicsymbols('q0:3', 1)
+    N, A, P, C = _generate_body()
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2])
+    assert S.coordinates == Matrix([q0, q1, q2])
+    assert S.speeds == Matrix([u0, u1, u2])
+    assert S.kdes == Matrix([0, 0, 0])
+    assert N.ang_vel_in(A) == (-u0 * cos(q1) * cos(q2) - u1 * sin(q2)) * A.x + (
+        u0 * sin(q2) * cos(q1) - u1 * cos(q2)) * A.y + (
+               -u0 * sin(q1) - u2) * A.z
+
+
+def test_spherical_joint_coords():
+    q0s, q1s, q2s, u0s, u1s, u2s = dynamicsymbols('q0:3_S, u0:3_S')
+    q0, q1, q2, q3, u0, u1, u2, u4 = dynamicsymbols('q0:4, u0:4')
+    # Test coordinates as list
+    N, A, P, C = _generate_body()
+    S = SphericalJoint('S', P, C, [q0, q1, q2], [u0, u1, u2])
+    assert S.coordinates == Matrix([q0, q1, q2])
+    assert S.speeds == Matrix([u0, u1, u2])
+    # Test coordinates as Matrix
+    N, A, P, C = _generate_body()
+    S = SphericalJoint('S', P, C, Matrix([q0, q1, q2]),
+                       Matrix([u0, u1, u2]))
+    assert S.coordinates == Matrix([q0, q1, q2])
+    assert S.speeds == Matrix([u0, u1, u2])
+    # Test too few generalized coordinates
+    N, A, P, C = _generate_body()
+    raises(ValueError,
+           lambda: SphericalJoint('S', P, C, Matrix([q0, q1]), Matrix([u0])))
+    # Test too many generalized coordinates
+    raises(ValueError, lambda: SphericalJoint(
+        'S', P, C, Matrix([q0, q1, q2, q3]), Matrix([u0, u1, u2])))
+    raises(ValueError, lambda: SphericalJoint(
+        'S', P, C, Matrix([q0, q1, q2]), Matrix([u0, u1, u2, u4])))
+
+
+def test_spherical_joint_orient_body():
+    q0, q1, q2, u0, u1, u2 = dynamicsymbols('q0:3, u0:3')
+    N_R_A = Matrix([
+        [-sin(q1), -sin(q2) * cos(q1), cos(q1) * cos(q2)],
+        [-sin(q0) * cos(q1), sin(q0) * sin(q1) * sin(q2) - cos(q0) * cos(q2),
+         -sin(q0) * sin(q1) * cos(q2) - sin(q2) * cos(q0)],
+        [cos(q0) * cos(q1), -sin(q0) * cos(q2) - sin(q1) * sin(q2) * cos(q0),
+         -sin(q0) * sin(q2) + sin(q1) * cos(q0) * cos(q2)]])
+    N_w_A = Matrix([[-u0 * sin(q1) - u2],
+                    [-u0 * sin(q2) * cos(q1) + u1 * cos(q2)],
+                    [u0 * cos(q1) * cos(q2) + u1 * sin(q2)]])
+    N_v_Co = Matrix([
+        [-sqrt(2) * (u0 * cos(q2 + pi / 4) * cos(q1) + u1 * sin(q2 + pi / 4))],
+        [-u0 * sin(q1) - u2], [-u0 * sin(q1) - u2]])
+    # Test default rot_type='BODY', rot_order=123
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2],
+                       parent_point=N.x + N.y, child_point=-A.y + A.z,
+                       parent_interframe=Pint, child_interframe=Cint,
+                       rot_type='body', rot_order=123)
+    assert S._rot_type.upper() == 'BODY'
+    assert S._rot_order == 123
+    assert simplify(N.dcm(A) - N_R_A) == zeros(3)
+    assert simplify(A.ang_vel_in(N).to_matrix(A) - N_w_A) == zeros(3, 1)
+    assert simplify(C.masscenter.vel(N).to_matrix(A)) == N_v_Co
+    # Test change of amounts
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2],
+                       parent_point=N.x + N.y, child_point=-A.y + A.z,
+                       parent_interframe=Pint, child_interframe=Cint,
+                       rot_type='BODY', amounts=(q1, q0, q2), rot_order=123)
+    switch_order = lambda expr: expr.xreplace(
+        {q0: q1, q1: q0, q2: q2, u0: u1, u1: u0, u2: u2})
+    assert S._rot_type.upper() == 'BODY'
+    assert S._rot_order == 123
+    assert simplify(N.dcm(A) - switch_order(N_R_A)) == zeros(3)
+    assert simplify(A.ang_vel_in(N).to_matrix(A) - switch_order(N_w_A)
+                            ) == zeros(3, 1)
+    assert simplify(C.masscenter.vel(N).to_matrix(A)) == switch_order(N_v_Co)
+    # Test different rot_order
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2],
+                       parent_point=N.x + N.y, child_point=-A.y + A.z,
+                       parent_interframe=Pint, child_interframe=Cint,
+                       rot_type='BodY', rot_order='yxz')
+    assert S._rot_type.upper() == 'BODY'
+    assert S._rot_order == 'yxz'
+    assert simplify(N.dcm(A) - Matrix([
+        [-sin(q0) * cos(q1), sin(q0) * sin(q1) * cos(q2) - sin(q2) * cos(q0),
+         sin(q0) * sin(q1) * sin(q2) + cos(q0) * cos(q2)],
+        [-sin(q1), -cos(q1) * cos(q2), -sin(q2) * cos(q1)],
+        [cos(q0) * cos(q1), -sin(q0) * sin(q2) - sin(q1) * cos(q0) * cos(q2),
+         sin(q0) * cos(q2) - sin(q1) * sin(q2) * cos(q0)]])) == zeros(3)
+    assert simplify(A.ang_vel_in(N).to_matrix(A) - Matrix([
+        [u0 * sin(q1) - u2], [u0 * cos(q1) * cos(q2) - u1 * sin(q2)],
+        [u0 * sin(q2) * cos(q1) + u1 * cos(q2)]])) == zeros(3, 1)
+    assert simplify(C.masscenter.vel(N).to_matrix(A)) == Matrix([
+        [-sqrt(2) * (u0 * sin(q2 + pi / 4) * cos(q1) + u1 * cos(q2 + pi / 4))],
+        [u0 * sin(q1) - u2], [u0 * sin(q1) - u2]])
+
+
+def test_spherical_joint_orient_space():
+    q0, q1, q2, u0, u1, u2 = dynamicsymbols('q0:3, u0:3')
+    N_R_A = Matrix([
+        [-sin(q0) * sin(q2) - sin(q1) * cos(q0) * cos(q2),
+         sin(q0) * sin(q1) * cos(q2) - sin(q2) * cos(q0), cos(q1) * cos(q2)],
+        [-sin(q0) * cos(q2) + sin(q1) * sin(q2) * cos(q0),
+         -sin(q0) * sin(q1) * sin(q2) - cos(q0) * cos(q2), -sin(q2) * cos(q1)],
+        [cos(q0) * cos(q1), -sin(q0) * cos(q1), sin(q1)]])
+    N_w_A = Matrix([
+        [u1 * sin(q0) - u2 * cos(q0) * cos(q1)],
+        [u1 * cos(q0) + u2 * sin(q0) * cos(q1)], [u0 - u2 * sin(q1)]])
+    N_v_Co = Matrix([
+        [u0 - u2 * sin(q1)], [u0 - u2 * sin(q1)],
+        [sqrt(2) * (-u1 * sin(q0 + pi / 4) + u2 * cos(q0 + pi / 4) * cos(q1))]])
+    # Test default rot_type='BODY', rot_order=123
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2],
+                       parent_point=N.x + N.z, child_point=-A.x + A.y,
+                       parent_interframe=Pint, child_interframe=Cint,
+                       rot_type='space', rot_order=123)
+    assert S._rot_type.upper() == 'SPACE'
+    assert S._rot_order == 123
+    assert simplify(N.dcm(A) - N_R_A) == zeros(3)
+    assert simplify(A.ang_vel_in(N).to_matrix(A)) == N_w_A
+    assert simplify(C.masscenter.vel(N).to_matrix(A)) == N_v_Co
+    # Test change of amounts
+    switch_order = lambda expr: expr.xreplace(
+        {q0: q1, q1: q0, q2: q2, u0: u1, u1: u0, u2: u2})
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2],
+                       parent_point=N.x + N.z, child_point=-A.x + A.y,
+                       parent_interframe=Pint, child_interframe=Cint,
+                       rot_type='SPACE', amounts=(q1, q0, q2), rot_order=123)
+    assert S._rot_type.upper() == 'SPACE'
+    assert S._rot_order == 123
+    assert simplify(N.dcm(A) - switch_order(N_R_A)) == zeros(3)
+    assert simplify(A.ang_vel_in(N).to_matrix(A)) == switch_order(N_w_A)
+    assert simplify(C.masscenter.vel(N).to_matrix(A)) == switch_order(N_v_Co)
+    # Test different rot_order
+    N, A, P, C, Pint, Cint = _generate_body(True)
+    S = SphericalJoint('S', P, C, coordinates=[q0, q1, q2], speeds=[u0, u1, u2],
+                       parent_point=N.x + N.z, child_point=-A.x + A.y,
+                       parent_interframe=Pint, child_interframe=Cint,
+                       rot_type='SPaCe', rot_order='zxy')
+    assert S._rot_type.upper() == 'SPACE'
+    assert S._rot_order == 'zxy'
+    assert simplify(N.dcm(A) - Matrix([
+        [-sin(q2) * cos(q1), -sin(q0) * cos(q2) + sin(q1) * sin(q2) * cos(q0),
+         sin(q0) * sin(q1) * sin(q2) + cos(q0) * cos(q2)],
+        [-sin(q1), -cos(q0) * cos(q1), -sin(q0) * cos(q1)],
+        [cos(q1) * cos(q2), -sin(q0) * sin(q2) - sin(q1) * cos(q0) * cos(q2),
+         -sin(q0) * sin(q1) * cos(q2) + sin(q2) * cos(q0)]]))
+    assert simplify(A.ang_vel_in(N).to_matrix(A) - Matrix([
+        [-u0 + u2 * sin(q1)], [-u1 * sin(q0) + u2 * cos(q0) * cos(q1)],
+        [u1 * cos(q0) + u2 * sin(q0) * cos(q1)]])) == zeros(3, 1)
+    assert simplify(C.masscenter.vel(N).to_matrix(A) - Matrix([
+        [u1 * cos(q0) + u2 * sin(q0) * cos(q1)],
+        [u1 * cos(q0) + u2 * sin(q0) * cos(q1)],
+        [u0 + u1 * sin(q0) - u2 * sin(q1) -
+         u2 * cos(q0) * cos(q1)]])) == zeros(3, 1)
+
+
+def test_weld_joint():
+    _, _, P, C = _generate_body()
+    W = WeldJoint('W', P, C)
+    assert W.name == 'W'
+    assert W.parent == P
+    assert W.child == C
+    assert W.coordinates == Matrix()
+    assert W.speeds == Matrix()
+    assert W.kdes == Matrix(1, 0, []).T
+    assert P.frame.dcm(C.frame) == eye(3)
+    assert W.child_point.pos_from(C.masscenter) == Vector(0)
+    assert W.parent_point.pos_from(P.masscenter) == Vector(0)
+    assert W.parent_point.pos_from(W.child_point) == Vector(0)
+    assert P.masscenter.pos_from(C.masscenter) == Vector(0)
+    assert C.masscenter.vel(P.frame) == Vector(0)
+    assert P.frame.ang_vel_in(C.frame) == 0
+    assert C.frame.ang_vel_in(P.frame) == 0
+    assert W.__str__() == 'WeldJoint: W  parent: P  child: C'
+
+    N, A, P, C = _generate_body()
+    l, m = symbols('l m')
+    Pint = ReferenceFrame('P_int')
+    Pint.orient_axis(P.frame, P.y, pi / 2)
+    W = WeldJoint('W', P, C, parent_point=l * P.frame.x,
+                  child_point=m * C.frame.y, parent_interframe=Pint)
+
+    assert W.child_point.pos_from(C.masscenter) == m * C.frame.y
+    assert W.parent_point.pos_from(P.masscenter) == l * P.frame.x
+    assert W.parent_point.pos_from(W.child_point) == Vector(0)
+    assert P.masscenter.pos_from(C.masscenter) == - l * N.x + m * A.y
+    assert C.masscenter.vel(P.frame) == Vector(0)
+    assert P.masscenter.vel(Pint) == Vector(0)
+    assert C.frame.ang_vel_in(P.frame) == 0
+    assert P.frame.ang_vel_in(C.frame) == 0
+    assert P.x == A.z
+
+    with warns_deprecated_sympy():
+        JointsMethod(P, W)  # Tests #10770
+
+
+def test_deprecated_parent_child_axis():
+    q, u = dynamicsymbols('q_J, u_J')
+    N, A, P, C = _generate_body()
+    with warns_deprecated_sympy():
+        PinJoint('J', P, C, child_axis=-A.x)
+    assert (-A.x).angle_between(N.x) == 0
+    assert -A.x.express(N) == N.x
+    assert A.dcm(N) == Matrix([[-1, 0, 0],
+                               [0, -cos(q), -sin(q)],
+                               [0, -sin(q), cos(q)]])
+    assert A.ang_vel_in(N) == u * N.x
+    assert A.ang_vel_in(N).magnitude() == sqrt(u ** 2)
+
+    N, A, P, C = _generate_body()
+    with warns_deprecated_sympy():
+        PrismaticJoint('J', P, C, parent_axis=P.x + P.y)
+    assert (A.x).angle_between(N.x + N.y) == 0
+    assert A.x.express(N) == (N.x + N.y) / sqrt(2)
+    assert A.dcm(N) == Matrix([[sqrt(2) / 2, sqrt(2) / 2, 0],
+                               [-sqrt(2) / 2, sqrt(2) / 2, 0], [0, 0, 1]])
+    assert A.ang_vel_in(N) == Vector(0)
+
+
+def test_deprecated_joint_pos():
+    N, A, P, C = _generate_body()
+    with warns_deprecated_sympy():
+        pin = PinJoint('J', P, C, parent_joint_pos=N.x + N.y,
+                       child_joint_pos=C.y - C.z)
+    assert pin.parent_point.pos_from(P.masscenter) == N.x + N.y
+    assert pin.child_point.pos_from(C.masscenter) == C.y - C.z
+
+    N, A, P, C = _generate_body()
+    with warns_deprecated_sympy():
+        slider = PrismaticJoint('J', P, C, parent_joint_pos=N.z + N.y,
+                                child_joint_pos=C.y - C.x)
+    assert slider.parent_point.pos_from(P.masscenter) == N.z + N.y
+    assert slider.child_point.pos_from(C.masscenter) == C.y - C.x
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_jointsmethod.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_jointsmethod.py
new file mode 100644
index 0000000000000000000000000000000000000000..1b48eae06dadc627442fd4e42445450be0393e33
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_jointsmethod.py
@@ -0,0 +1,249 @@
+from sympy.core.function import expand
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.matrices.dense import Matrix
+from sympy.simplify.trigsimp import trigsimp
+from sympy.physics.mechanics import (
+    PinJoint, JointsMethod, RigidBody, Particle, Body, KanesMethod,
+    PrismaticJoint, LagrangesMethod, inertia)
+from sympy.physics.vector import dynamicsymbols, ReferenceFrame
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+from sympy import zeros
+from sympy.utilities.lambdify import lambdify
+from sympy.solvers.solvers import solve
+
+
+t = dynamicsymbols._t # type: ignore
+
+
+def test_jointsmethod():
+    with warns_deprecated_sympy():
+        P = Body('P')
+        C = Body('C')
+    Pin = PinJoint('P1', P, C)
+    C_ixx, g = symbols('C_ixx g')
+    q, u = dynamicsymbols('q_P1, u_P1')
+    P.apply_force(g*P.y)
+    with warns_deprecated_sympy():
+        method = JointsMethod(P, Pin)
+    assert method.frame == P.frame
+    assert method.bodies == [C, P]
+    assert method.loads == [(P.masscenter, g*P.frame.y)]
+    assert method.q == Matrix([q])
+    assert method.u == Matrix([u])
+    assert method.kdes == Matrix([u - q.diff()])
+    soln = method.form_eoms()
+    assert soln == Matrix([[-C_ixx*u.diff()]])
+    assert method.forcing_full == Matrix([[u], [0]])
+    assert method.mass_matrix_full == Matrix([[1, 0], [0, C_ixx]])
+    assert isinstance(method.method, KanesMethod)
+
+
+def test_rigid_body_particle_compatibility():
+    l, m, g = symbols('l m g')
+    C = RigidBody('C')
+    b = Particle('b', mass=m)
+    b_frame = ReferenceFrame('b_frame')
+    q, u = dynamicsymbols('q u')
+    P = PinJoint('P', C, b, coordinates=q, speeds=u, child_interframe=b_frame,
+                 child_point=-l * b_frame.x, joint_axis=C.z)
+    with warns_deprecated_sympy():
+        method = JointsMethod(C, P)
+    method.loads.append((b.masscenter, m * g * C.x))
+    method.form_eoms()
+    rhs = method.rhs()
+    assert rhs[1] == -g*sin(q)/l
+
+
+def test_jointmethod_duplicate_coordinates_speeds():
+    with warns_deprecated_sympy():
+        P = Body('P')
+        C = Body('C')
+        T = Body('T')
+    q, u = dynamicsymbols('q u')
+    P1 = PinJoint('P1', P, C, q)
+    P2 = PrismaticJoint('P2', C, T, q)
+    with warns_deprecated_sympy():
+        raises(ValueError, lambda: JointsMethod(P, P1, P2))
+
+    P1 = PinJoint('P1', P, C, speeds=u)
+    P2 = PrismaticJoint('P2', C, T, speeds=u)
+    with warns_deprecated_sympy():
+        raises(ValueError, lambda: JointsMethod(P, P1, P2))
+
+    P1 = PinJoint('P1', P, C, q, u)
+    P2 = PrismaticJoint('P2', C, T, q, u)
+    with warns_deprecated_sympy():
+        raises(ValueError, lambda: JointsMethod(P, P1, P2))
+
+def test_complete_simple_double_pendulum():
+    q1, q2 = dynamicsymbols('q1 q2')
+    u1, u2 = dynamicsymbols('u1 u2')
+    m, l, g = symbols('m l g')
+    with warns_deprecated_sympy():
+        C = Body('C')  # ceiling
+        PartP = Body('P', mass=m)
+        PartR = Body('R', mass=m)
+    J1 = PinJoint('J1', C, PartP, speeds=u1, coordinates=q1,
+                  child_point=-l*PartP.x, joint_axis=C.z)
+    J2 = PinJoint('J2', PartP, PartR, speeds=u2, coordinates=q2,
+                  child_point=-l*PartR.x, joint_axis=PartP.z)
+
+    PartP.apply_force(m*g*C.x)
+    PartR.apply_force(m*g*C.x)
+
+    with warns_deprecated_sympy():
+        method = JointsMethod(C, J1, J2)
+    method.form_eoms()
+
+    assert expand(method.mass_matrix_full) == Matrix([[1, 0, 0, 0],
+                                                      [0, 1, 0, 0],
+                                                      [0, 0, 2*l**2*m*cos(q2) + 3*l**2*m, l**2*m*cos(q2) + l**2*m],
+                                                      [0, 0, l**2*m*cos(q2) + l**2*m, l**2*m]])
+    assert trigsimp(method.forcing_full) == trigsimp(Matrix([[u1], [u2], [-g*l*m*(sin(q1 + q2) + sin(q1)) -
+                                           g*l*m*sin(q1) + l**2*m*(2*u1 + u2)*u2*sin(q2)],
+                                          [-g*l*m*sin(q1 + q2) - l**2*m*u1**2*sin(q2)]]))
+
+def test_two_dof_joints():
+    q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
+    m, c1, c2, k1, k2 = symbols('m c1 c2 k1 k2')
+    with warns_deprecated_sympy():
+        W = Body('W')
+        B1 = Body('B1', mass=m)
+        B2 = Body('B2', mass=m)
+    J1 = PrismaticJoint('J1', W, B1, coordinates=q1, speeds=u1)
+    J2 = PrismaticJoint('J2', B1, B2, coordinates=q2, speeds=u2)
+    W.apply_force(k1*q1*W.x, reaction_body=B1)
+    W.apply_force(c1*u1*W.x, reaction_body=B1)
+    B1.apply_force(k2*q2*W.x, reaction_body=B2)
+    B1.apply_force(c2*u2*W.x, reaction_body=B2)
+    with warns_deprecated_sympy():
+        method = JointsMethod(W, J1, J2)
+    method.form_eoms()
+    MM = method.mass_matrix
+    forcing = method.forcing
+    rhs = MM.LUsolve(forcing)
+    assert expand(rhs[0]) == expand((-k1 * q1 - c1 * u1 + k2 * q2 + c2 * u2)/m)
+    assert expand(rhs[1]) == expand((k1 * q1 + c1 * u1 - 2 * k2 * q2 - 2 *
+                                    c2 * u2) / m)
+
+def test_simple_pedulum():
+    l, m, g = symbols('l m g')
+    with warns_deprecated_sympy():
+        C = Body('C')
+        b = Body('b', mass=m)
+    q = dynamicsymbols('q')
+    P = PinJoint('P', C, b, speeds=q.diff(t), coordinates=q,
+                 child_point=-l * b.x, joint_axis=C.z)
+    b.potential_energy = - m * g * l * cos(q)
+    with warns_deprecated_sympy():
+        method = JointsMethod(C, P)
+    method.form_eoms(LagrangesMethod)
+    rhs = method.rhs()
+    assert rhs[1] == -g*sin(q)/l
+
+def test_chaos_pendulum():
+    #https://www.pydy.org/examples/chaos_pendulum.html
+    mA, mB, lA, lB, IAxx, IBxx, IByy, IBzz, g = symbols('mA, mB, lA, lB, IAxx, IBxx, IByy, IBzz, g')
+    theta, phi, omega, alpha = dynamicsymbols('theta phi omega alpha')
+
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+
+    with warns_deprecated_sympy():
+        rod = Body('rod', mass=mA, frame=A,
+                   central_inertia=inertia(A, IAxx, IAxx, 0))
+        plate = Body('plate', mass=mB, frame=B,
+                     central_inertia=inertia(B, IBxx, IByy, IBzz))
+        C = Body('C')
+    J1 = PinJoint('J1', C, rod, coordinates=theta, speeds=omega,
+                  child_point=-lA * rod.z, joint_axis=C.y)
+    J2 = PinJoint('J2', rod, plate, coordinates=phi, speeds=alpha,
+                  parent_point=(lB - lA) * rod.z, joint_axis=rod.z)
+
+    rod.apply_force(mA*g*C.z)
+    plate.apply_force(mB*g*C.z)
+
+    with warns_deprecated_sympy():
+        method = JointsMethod(C, J1, J2)
+    method.form_eoms()
+
+    MM = method.mass_matrix
+    forcing = method.forcing
+    rhs = MM.LUsolve(forcing)
+    xd = (-2 * IBxx * alpha * omega * sin(phi) * cos(phi) + 2 * IByy * alpha * omega * sin(phi) *
+            cos(phi) - g * lA * mA * sin(theta) - g * lB * mB * sin(theta)) / (IAxx + IBxx *
+                sin(phi)**2 + IByy * cos(phi)**2 + lA**2 * mA + lB**2 * mB)
+    assert (rhs[0] - xd).simplify() == 0
+    xd = (IBxx - IByy) * omega**2 * sin(phi) * cos(phi) / IBzz
+    assert (rhs[1] - xd).simplify() == 0
+
+def test_four_bar_linkage_with_manual_constraints():
+    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1:4, u1:4')
+    l1, l2, l3, l4, rho = symbols('l1:5, rho')
+
+    N = ReferenceFrame('N')
+    inertias = [inertia(N, 0, 0, rho * l ** 3 / 12) for l in (l1, l2, l3, l4)]
+    with warns_deprecated_sympy():
+        link1 = Body('Link1', frame=N, mass=rho * l1,
+                     central_inertia=inertias[0])
+        link2 = Body('Link2', mass=rho * l2, central_inertia=inertias[1])
+        link3 = Body('Link3', mass=rho * l3, central_inertia=inertias[2])
+        link4 = Body('Link4', mass=rho * l4, central_inertia=inertias[3])
+
+    joint1 = PinJoint(
+        'J1', link1, link2, coordinates=q1, speeds=u1, joint_axis=link1.z,
+        parent_point=l1 / 2 * link1.x, child_point=-l2 / 2 * link2.x)
+    joint2 = PinJoint(
+        'J2', link2, link3, coordinates=q2, speeds=u2, joint_axis=link2.z,
+        parent_point=l2 / 2 * link2.x, child_point=-l3 / 2 * link3.x)
+    joint3 = PinJoint(
+        'J3', link3, link4, coordinates=q3, speeds=u3, joint_axis=link3.z,
+        parent_point=l3 / 2 * link3.x, child_point=-l4 / 2 * link4.x)
+
+    loop = link4.masscenter.pos_from(link1.masscenter) \
+           + l1 / 2 * link1.x + l4 / 2 * link4.x
+
+    fh = Matrix([loop.dot(link1.x), loop.dot(link1.y)])
+
+    with warns_deprecated_sympy():
+        method = JointsMethod(link1, joint1, joint2, joint3)
+
+    t = dynamicsymbols._t
+    qdots = solve(method.kdes, [q1.diff(t), q2.diff(t), q3.diff(t)])
+    fhd = fh.diff(t).subs(qdots)
+
+    kane = KanesMethod(method.frame, q_ind=[q1], u_ind=[u1],
+                       q_dependent=[q2, q3], u_dependent=[u2, u3],
+                       kd_eqs=method.kdes, configuration_constraints=fh,
+                       velocity_constraints=fhd, forcelist=method.loads,
+                       bodies=method.bodies)
+    fr, frs = kane.kanes_equations()
+    assert fr == zeros(1)
+
+    # Numerically check the mass- and forcing-matrix
+    p = Matrix([l1, l2, l3, l4, rho])
+    q = Matrix([q1, q2, q3])
+    u = Matrix([u1, u2, u3])
+    eval_m = lambdify((q, p), kane.mass_matrix)
+    eval_f = lambdify((q, u, p), kane.forcing)
+    eval_fhd = lambdify((q, u, p), fhd)
+
+    p_vals = [0.13, 0.24, 0.21, 0.34, 997]
+    q_vals = [2.1, 0.6655470375077588, 2.527408138024188]  # Satisfies fh
+    u_vals = [0.2, -0.17963733938852067, 0.1309060540601612]  # Satisfies fhd
+    mass_check = Matrix([[3.452709815256506e+01, 7.003948798374735e+00,
+                          -4.939690970641498e+00],
+                         [-2.203792703880936e-14, 2.071702479957077e-01,
+                          2.842917573033711e-01],
+                         [-1.300000000000123e-01, -8.836934896046506e-03,
+                          1.864891330060847e-01]])
+    forcing_check = Matrix([[-0.031211821321648],
+                            [-0.00066022608181],
+                            [0.001813559741243]])
+    eps = 1e-10
+    assert all(abs(x) < eps for x in eval_fhd(q_vals, u_vals, p_vals))
+    assert all(abs(x) < eps for x in
+               (Matrix(eval_m(q_vals, p_vals)) - mass_check))
+    assert all(abs(x) < eps for x in
+               (Matrix(eval_f(q_vals, u_vals, p_vals)) - forcing_check))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane.py
new file mode 100644
index 0000000000000000000000000000000000000000..5f9310aae6d720c32615a86df5e488f46a513c76
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane.py
@@ -0,0 +1,553 @@
+from sympy import solve
+from sympy import (cos, expand, Matrix, sin, symbols, tan, sqrt, S,
+                                zeros, eye)
+from sympy.simplify.simplify import simplify
+from sympy.physics.mechanics import (dynamicsymbols, ReferenceFrame, Point,
+                                     RigidBody, KanesMethod, inertia, Particle,
+                                     dot, find_dynamicsymbols)
+from sympy.testing.pytest import raises
+
+
+def test_invalid_coordinates():
+    # Simple pendulum, but use symbols instead of dynamicsymbols
+    l, m, g = symbols('l m g')
+    q, u = symbols('q u')  # Generalized coordinate
+    kd = [q.diff(dynamicsymbols._t) - u]
+    N, O = ReferenceFrame('N'), Point('O')
+    O.set_vel(N, 0)
+    P = Particle('P', Point('P'), m)
+    P.point.set_pos(O, l * (sin(q) * N.x - cos(q) * N.y))
+    F = (P.point, -m * g * N.y)
+    raises(ValueError, lambda: KanesMethod(N, [q], [u], kd, bodies=[P],
+                                           forcelist=[F]))
+
+
+def test_one_dof():
+    # This is for a 1 dof spring-mass-damper case.
+    # It is described in more detail in the KanesMethod docstring.
+    q, u = dynamicsymbols('q u')
+    qd, ud = dynamicsymbols('q u', 1)
+    m, c, k = symbols('m c k')
+    N = ReferenceFrame('N')
+    P = Point('P')
+    P.set_vel(N, u * N.x)
+
+    kd = [qd - u]
+    FL = [(P, (-k * q - c * u) * N.x)]
+    pa = Particle('pa', P, m)
+    BL = [pa]
+
+    KM = KanesMethod(N, [q], [u], kd)
+    KM.kanes_equations(BL, FL)
+
+    assert KM.bodies == BL
+    assert KM.loads == FL
+
+    MM = KM.mass_matrix
+    forcing = KM.forcing
+    rhs = MM.inv() * forcing
+    assert expand(rhs[0]) == expand(-(q * k + u * c) / m)
+
+    assert simplify(KM.rhs() -
+                    KM.mass_matrix_full.LUsolve(KM.forcing_full)) == zeros(2, 1)
+
+    assert (KM.linearize(A_and_B=True, )[0] == Matrix([[0, 1], [-k/m, -c/m]]))
+
+
+def test_two_dof():
+    # This is for a 2 d.o.f., 2 particle spring-mass-damper.
+    # The first coordinate is the displacement of the first particle, and the
+    # second is the relative displacement between the first and second
+    # particles. Speeds are defined as the time derivatives of the particles.
+    q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
+    q1d, q2d, u1d, u2d = dynamicsymbols('q1 q2 u1 u2', 1)
+    m, c1, c2, k1, k2 = symbols('m c1 c2 k1 k2')
+    N = ReferenceFrame('N')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    P1.set_vel(N, u1 * N.x)
+    P2.set_vel(N, (u1 + u2) * N.x)
+    # Note we multiply the kinematic equation by an arbitrary factor
+    # to test the implicit vs explicit kinematics attribute
+    kd = [q1d/2 - u1/2, 2*q2d - 2*u2]
+
+    # Now we create the list of forces, then assign properties to each
+    # particle, then create a list of all particles.
+    FL = [(P1, (-k1 * q1 - c1 * u1 + k2 * q2 + c2 * u2) * N.x), (P2, (-k2 *
+        q2 - c2 * u2) * N.x)]
+    pa1 = Particle('pa1', P1, m)
+    pa2 = Particle('pa2', P2, m)
+    BL = [pa1, pa2]
+
+    # Finally we create the KanesMethod object, specify the inertial frame,
+    # pass relevant information, and form Fr & Fr*. Then we calculate the mass
+    # matrix and forcing terms, and finally solve for the udots.
+    KM = KanesMethod(N, q_ind=[q1, q2], u_ind=[u1, u2], kd_eqs=kd)
+    KM.kanes_equations(BL, FL)
+    MM = KM.mass_matrix
+    forcing = KM.forcing
+    rhs = MM.inv() * forcing
+    assert expand(rhs[0]) == expand((-k1 * q1 - c1 * u1 + k2 * q2 + c2 * u2)/m)
+    assert expand(rhs[1]) == expand((k1 * q1 + c1 * u1 - 2 * k2 * q2 - 2 *
+                                    c2 * u2) / m)
+
+    # Check that the explicit form is the default and kinematic mass matrix is identity
+    assert KM.explicit_kinematics
+    assert KM.mass_matrix_kin == eye(2)
+
+    # Check that for the implicit form the mass matrix is not identity
+    KM.explicit_kinematics = False
+    assert KM.mass_matrix_kin == Matrix([[S(1)/2, 0], [0, 2]])
+
+    # Check that whether using implicit or explicit kinematics the RHS
+    # equations are consistent with the matrix form
+    for explicit_kinematics in [False, True]:
+        KM.explicit_kinematics = explicit_kinematics
+        assert simplify(KM.rhs() -
+                        KM.mass_matrix_full.LUsolve(KM.forcing_full)) == zeros(4, 1)
+
+    # Make sure an error is raised if nonlinear kinematic differential
+    # equations are supplied.
+    kd = [q1d - u1**2, sin(q2d) - cos(u2)]
+    raises(ValueError, lambda: KanesMethod(N, q_ind=[q1, q2],
+                                           u_ind=[u1, u2], kd_eqs=kd))
+
+def test_pend():
+    q, u = dynamicsymbols('q u')
+    qd, ud = dynamicsymbols('q u', 1)
+    m, l, g = symbols('m l g')
+    N = ReferenceFrame('N')
+    P = Point('P')
+    P.set_vel(N, -l * u * sin(q) * N.x + l * u * cos(q) * N.y)
+    kd = [qd - u]
+
+    FL = [(P, m * g * N.x)]
+    pa = Particle('pa', P, m)
+    BL = [pa]
+
+    KM = KanesMethod(N, [q], [u], kd)
+    KM.kanes_equations(BL, FL)
+    MM = KM.mass_matrix
+    forcing = KM.forcing
+    rhs = MM.inv() * forcing
+    rhs.simplify()
+    assert expand(rhs[0]) == expand(-g / l * sin(q))
+    assert simplify(KM.rhs() -
+                    KM.mass_matrix_full.LUsolve(KM.forcing_full)) == zeros(2, 1)
+
+
+def test_rolling_disc():
+    # Rolling Disc Example
+    # Here the rolling disc is formed from the contact point up, removing the
+    # need to introduce generalized speeds. Only 3 configuration and three
+    # speed variables are need to describe this system, along with the disc's
+    # mass and radius, and the local gravity (note that mass will drop out).
+    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
+    q1d, q2d, q3d, u1d, u2d, u3d = dynamicsymbols('q1 q2 q3 u1 u2 u3', 1)
+    r, m, g = symbols('r m g')
+
+    # The kinematics are formed by a series of simple rotations. Each simple
+    # rotation creates a new frame, and the next rotation is defined by the new
+    # frame's basis vectors. This example uses a 3-1-2 series of rotations, or
+    # Z, X, Y series of rotations. Angular velocity for this is defined using
+    # the second frame's basis (the lean frame).
+    N = ReferenceFrame('N')
+    Y = N.orientnew('Y', 'Axis', [q1, N.z])
+    L = Y.orientnew('L', 'Axis', [q2, Y.x])
+    R = L.orientnew('R', 'Axis', [q3, L.y])
+    w_R_N_qd = R.ang_vel_in(N)
+    R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
+
+    # This is the translational kinematics. We create a point with no velocity
+    # in N; this is the contact point between the disc and ground. Next we form
+    # the position vector from the contact point to the disc's center of mass.
+    # Finally we form the velocity and acceleration of the disc.
+    C = Point('C')
+    C.set_vel(N, 0)
+    Dmc = C.locatenew('Dmc', r * L.z)
+    Dmc.v2pt_theory(C, N, R)
+
+    # This is a simple way to form the inertia dyadic.
+    I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)
+
+    # Kinematic differential equations; how the generalized coordinate time
+    # derivatives relate to generalized speeds.
+    kd = [dot(R.ang_vel_in(N) - w_R_N_qd, uv) for uv in L]
+
+    # Creation of the force list; it is the gravitational force at the mass
+    # center of the disc. Then we create the disc by assigning a Point to the
+    # center of mass attribute, a ReferenceFrame to the frame attribute, and mass
+    # and inertia. Then we form the body list.
+    ForceList = [(Dmc, - m * g * Y.z)]
+    BodyD = RigidBody('BodyD', Dmc, R, m, (I, Dmc))
+    BodyList = [BodyD]
+
+    # Finally we form the equations of motion, using the same steps we did
+    # before. Specify inertial frame, supply generalized speeds, supply
+    # kinematic differential equation dictionary, compute Fr from the force
+    # list and Fr* from the body list, compute the mass matrix and forcing
+    # terms, then solve for the u dots (time derivatives of the generalized
+    # speeds).
+    KM = KanesMethod(N, q_ind=[q1, q2, q3], u_ind=[u1, u2, u3], kd_eqs=kd)
+    KM.kanes_equations(BodyList, ForceList)
+    MM = KM.mass_matrix
+    forcing = KM.forcing
+    rhs = MM.inv() * forcing
+    kdd = KM.kindiffdict()
+    rhs = rhs.subs(kdd)
+    rhs.simplify()
+    assert rhs.expand() == Matrix([(6*u2*u3*r - u3**2*r*tan(q2) +
+        4*g*sin(q2))/(5*r), -2*u1*u3/3, u1*(-2*u2 + u3*tan(q2))]).expand()
+    assert simplify(KM.rhs() -
+                    KM.mass_matrix_full.LUsolve(KM.forcing_full)) == zeros(6, 1)
+
+    # This code tests our output vs. benchmark values. When r=g=m=1, the
+    # critical speed (where all eigenvalues of the linearized equations are 0)
+    # is 1 / sqrt(3) for the upright case.
+    A = KM.linearize(A_and_B=True)[0]
+    A_upright = A.subs({r: 1, g: 1, m: 1}).subs({q1: 0, q2: 0, q3: 0, u1: 0, u3: 0})
+    import sympy
+    assert sympy.sympify(A_upright.subs({u2: 1 / sqrt(3)})).eigenvals() == {S.Zero: 6}
+
+
+def test_aux():
+    # Same as above, except we have 2 auxiliary speeds for the ground contact
+    # point, which is known to be zero. In one case, we go through then
+    # substitute the aux. speeds in at the end (they are zero, as well as their
+    # derivative), in the other case, we use the built-in auxiliary speed part
+    # of KanesMethod. The equations from each should be the same.
+    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
+    q1d, q2d, q3d, u1d, u2d, u3d = dynamicsymbols('q1 q2 q3 u1 u2 u3', 1)
+    u4, u5, f1, f2 = dynamicsymbols('u4, u5, f1, f2')
+    u4d, u5d = dynamicsymbols('u4, u5', 1)
+    r, m, g = symbols('r m g')
+
+    N = ReferenceFrame('N')
+    Y = N.orientnew('Y', 'Axis', [q1, N.z])
+    L = Y.orientnew('L', 'Axis', [q2, Y.x])
+    R = L.orientnew('R', 'Axis', [q3, L.y])
+    w_R_N_qd = R.ang_vel_in(N)
+    R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
+
+    C = Point('C')
+    C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
+    Dmc = C.locatenew('Dmc', r * L.z)
+    Dmc.v2pt_theory(C, N, R)
+    Dmc.a2pt_theory(C, N, R)
+
+    I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)
+
+    kd = [dot(R.ang_vel_in(N) - w_R_N_qd, uv) for uv in L]
+
+    ForceList = [(Dmc, - m * g * Y.z), (C, f1 * L.x + f2 * (Y.z ^ L.x))]
+    BodyD = RigidBody('BodyD', Dmc, R, m, (I, Dmc))
+    BodyList = [BodyD]
+
+    KM = KanesMethod(N, q_ind=[q1, q2, q3], u_ind=[u1, u2, u3, u4, u5],
+                     kd_eqs=kd)
+    (fr, frstar) = KM.kanes_equations(BodyList, ForceList)
+    fr = fr.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5: 0})
+    frstar = frstar.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5: 0})
+
+    KM2 = KanesMethod(N, q_ind=[q1, q2, q3], u_ind=[u1, u2, u3], kd_eqs=kd,
+                      u_auxiliary=[u4, u5])
+    (fr2, frstar2) = KM2.kanes_equations(BodyList, ForceList)
+    fr2 = fr2.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5: 0})
+    frstar2 = frstar2.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5: 0})
+
+    frstar.simplify()
+    frstar2.simplify()
+
+    assert (fr - fr2).expand() == Matrix([0, 0, 0, 0, 0])
+    assert (frstar - frstar2).expand() == Matrix([0, 0, 0, 0, 0])
+
+
+def test_parallel_axis():
+    # This is for a 2 dof inverted pendulum on a cart.
+    # This tests the parallel axis code in KanesMethod. The inertia of the
+    # pendulum is defined about the hinge, not about the center of mass.
+
+    # Defining the constants and knowns of the system
+    gravity = symbols('g')
+    k, ls = symbols('k ls')
+    a, mA, mC = symbols('a mA mC')
+    F = dynamicsymbols('F')
+    Ix, Iy, Iz = symbols('Ix Iy Iz')
+
+    # Declaring the Generalized coordinates and speeds
+    q1, q2 = dynamicsymbols('q1 q2')
+    q1d, q2d = dynamicsymbols('q1 q2', 1)
+    u1, u2 = dynamicsymbols('u1 u2')
+    u1d, u2d = dynamicsymbols('u1 u2', 1)
+
+    # Creating reference frames
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+
+    A.orient(N, 'Axis', [-q2, N.z])
+    A.set_ang_vel(N, -u2 * N.z)
+
+    # Origin of Newtonian reference frame
+    O = Point('O')
+
+    # Creating and Locating the positions of the cart, C, and the
+    # center of mass of the pendulum, A
+    C = O.locatenew('C', q1 * N.x)
+    Ao = C.locatenew('Ao', a * A.y)
+
+    # Defining velocities of the points
+    O.set_vel(N, 0)
+    C.set_vel(N, u1 * N.x)
+    Ao.v2pt_theory(C, N, A)
+    Cart = Particle('Cart', C, mC)
+    Pendulum = RigidBody('Pendulum', Ao, A, mA, (inertia(A, Ix, Iy, Iz), C))
+
+    # kinematical differential equations
+
+    kindiffs = [q1d - u1, q2d - u2]
+
+    bodyList = [Cart, Pendulum]
+
+    forceList = [(Ao, -N.y * gravity * mA),
+                 (C, -N.y * gravity * mC),
+                 (C, -N.x * k * (q1 - ls)),
+                 (C, N.x * F)]
+
+    km = KanesMethod(N, [q1, q2], [u1, u2], kindiffs)
+    (fr, frstar) = km.kanes_equations(bodyList, forceList)
+    mm = km.mass_matrix_full
+    assert mm[3, 3] == Iz
+
+def test_input_format():
+    # 1 dof problem from test_one_dof
+    q, u = dynamicsymbols('q u')
+    qd, ud = dynamicsymbols('q u', 1)
+    m, c, k = symbols('m c k')
+    N = ReferenceFrame('N')
+    P = Point('P')
+    P.set_vel(N, u * N.x)
+
+    kd = [qd - u]
+    FL = [(P, (-k * q - c * u) * N.x)]
+    pa = Particle('pa', P, m)
+    BL = [pa]
+
+    KM = KanesMethod(N, [q], [u], kd)
+    # test for input format kane.kanes_equations((body1, body2, particle1))
+    assert KM.kanes_equations(BL)[0] == Matrix([0])
+    # test for input format kane.kanes_equations(bodies=(body1, body 2), loads=(load1,load2))
+    assert KM.kanes_equations(bodies=BL, loads=None)[0] == Matrix([0])
+    # test for input format kane.kanes_equations(bodies=(body1, body 2), loads=None)
+    assert KM.kanes_equations(BL, loads=None)[0] == Matrix([0])
+    # test for input format kane.kanes_equations(bodies=(body1, body 2))
+    assert KM.kanes_equations(BL)[0] == Matrix([0])
+    # test for input format kane.kanes_equations(bodies=(body1, body2), loads=[])
+    assert KM.kanes_equations(BL, [])[0] == Matrix([0])
+    # test for error raised when a wrong force list (in this case a string) is provided
+    raises(ValueError, lambda: KM._form_fr('bad input'))
+
+    # 1 dof problem from test_one_dof with FL & BL in instance
+    KM = KanesMethod(N, [q], [u], kd, bodies=BL, forcelist=FL)
+    assert KM.kanes_equations()[0] == Matrix([-c*u - k*q])
+
+    # 2 dof problem from test_two_dof
+    q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
+    q1d, q2d, u1d, u2d = dynamicsymbols('q1 q2 u1 u2', 1)
+    m, c1, c2, k1, k2 = symbols('m c1 c2 k1 k2')
+    N = ReferenceFrame('N')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    P1.set_vel(N, u1 * N.x)
+    P2.set_vel(N, (u1 + u2) * N.x)
+    kd = [q1d - u1, q2d - u2]
+
+    FL = ((P1, (-k1 * q1 - c1 * u1 + k2 * q2 + c2 * u2) * N.x), (P2, (-k2 *
+        q2 - c2 * u2) * N.x))
+    pa1 = Particle('pa1', P1, m)
+    pa2 = Particle('pa2', P2, m)
+    BL = (pa1, pa2)
+
+    KM = KanesMethod(N, q_ind=[q1, q2], u_ind=[u1, u2], kd_eqs=kd)
+    # test for input format
+    # kane.kanes_equations((body1, body2), (load1, load2))
+    KM.kanes_equations(BL, FL)
+    MM = KM.mass_matrix
+    forcing = KM.forcing
+    rhs = MM.inv() * forcing
+    assert expand(rhs[0]) == expand((-k1 * q1 - c1 * u1 + k2 * q2 + c2 * u2)/m)
+    assert expand(rhs[1]) == expand((k1 * q1 + c1 * u1 - 2 * k2 * q2 - 2 *
+                                    c2 * u2) / m)
+
+
+def test_implicit_kinematics():
+    # Test that implicit kinematics can handle complicated
+    # equations that explicit form struggles with
+    # See https://github.com/sympy/sympy/issues/22626
+
+    # Inertial frame
+    NED = ReferenceFrame('NED')
+    NED_o = Point('NED_o')
+    NED_o.set_vel(NED, 0)
+
+    # body frame
+    q_att = dynamicsymbols('lambda_0:4', real=True)
+    B = NED.orientnew('B', 'Quaternion', q_att)
+
+    # Generalized coordinates
+    q_pos = dynamicsymbols('B_x:z')
+    B_cm = NED_o.locatenew('B_cm', q_pos[0]*B.x + q_pos[1]*B.y + q_pos[2]*B.z)
+
+    q_ind = q_att[1:] + q_pos
+    q_dep = [q_att[0]]
+
+    kinematic_eqs = []
+
+    # Generalized velocities
+    B_ang_vel = B.ang_vel_in(NED)
+    P, Q, R = dynamicsymbols('P Q R')
+    B.set_ang_vel(NED, P*B.x + Q*B.y + R*B.z)
+
+    B_ang_vel_kd = (B.ang_vel_in(NED) - B_ang_vel).simplify()
+
+    # Equating the two gives us the kinematic equation
+    kinematic_eqs += [
+        B_ang_vel_kd & B.x,
+        B_ang_vel_kd & B.y,
+        B_ang_vel_kd & B.z
+    ]
+
+    B_cm_vel = B_cm.vel(NED)
+    U, V, W = dynamicsymbols('U V W')
+    B_cm.set_vel(NED, U*B.x + V*B.y + W*B.z)
+
+    # Compute the velocity of the point using the two methods
+    B_ref_vel_kd = (B_cm.vel(NED) - B_cm_vel)
+
+    # taking dot product with unit vectors to get kinematic equations
+    # relating body coordinates and velocities
+
+    # Note, there is a choice to dot with NED.xyz here. That makes
+    # the implicit form have some bigger terms but is still fine, the
+    # explicit form still struggles though
+    kinematic_eqs += [
+                      B_ref_vel_kd & B.x,
+                      B_ref_vel_kd & B.y,
+                      B_ref_vel_kd & B.z,
+                     ]
+
+    u_ind = [U, V, W, P, Q, R]
+
+    # constraints
+    q_att_vec = Matrix(q_att)
+    config_cons = [(q_att_vec.T*q_att_vec)[0] - 1] #unit norm
+    kinematic_eqs = kinematic_eqs + [(q_att_vec.T * q_att_vec.diff())[0]]
+
+    try:
+        KM = KanesMethod(NED, q_ind, u_ind,
+          q_dependent= q_dep,
+          kd_eqs = kinematic_eqs,
+          configuration_constraints = config_cons,
+          velocity_constraints= [],
+          u_dependent= [], #no dependent speeds
+          u_auxiliary = [], # No auxiliary speeds
+          explicit_kinematics = False # implicit kinematics
+        )
+    except Exception as e:
+        raise e
+
+    # mass and inertia dyadic relative to CM
+    M_B = symbols('M_B')
+    J_B = inertia(B, *[S(f'J_B_{ax}')*(1 if ax[0] == ax[1] else -1)
+            for ax in ['xx', 'yy', 'zz', 'xy', 'yz', 'xz']])
+    J_B = J_B.subs({S('J_B_xy'): 0, S('J_B_yz'): 0})
+    RB = RigidBody('RB', B_cm, B, M_B, (J_B, B_cm))
+
+    rigid_bodies = [RB]
+    # Forces
+    force_list = [
+        #gravity pointing down
+        (RB.masscenter, RB.mass*S('g')*NED.z),
+        #generic forces and torques in body frame(inputs)
+        (RB.frame, dynamicsymbols('T_z')*B.z),
+        (RB.masscenter, dynamicsymbols('F_z')*B.z)
+    ]
+
+    KM.kanes_equations(rigid_bodies, force_list)
+
+    # Expecting implicit form to be less than 5% of the flops
+    n_ops_implicit = sum(
+        [x.count_ops() for x in KM.forcing_full] +
+        [x.count_ops() for x in KM.mass_matrix_full]
+    )
+    # Save implicit kinematic matrices to use later
+    mass_matrix_kin_implicit = KM.mass_matrix_kin
+    forcing_kin_implicit = KM.forcing_kin
+
+    KM.explicit_kinematics = True
+    n_ops_explicit = sum(
+        [x.count_ops() for x in KM.forcing_full] +
+        [x.count_ops() for x in KM.mass_matrix_full]
+    )
+    forcing_kin_explicit = KM.forcing_kin
+
+    assert n_ops_implicit / n_ops_explicit < .05
+
+    # Ideally we would check that implicit and explicit equations give the same result as done in test_one_dof
+    # But the whole raison-d'etre of the implicit equations is to deal with problems such
+    # as this one where the explicit form is too complicated to handle, especially the angular part
+    # (i.e. tests would be too slow)
+    # Instead, we check that the kinematic equations are correct using more fundamental tests:
+    #
+    # (1) that we recover the kinematic equations we have provided
+    assert (mass_matrix_kin_implicit * KM.q.diff() - forcing_kin_implicit) == Matrix(kinematic_eqs)
+
+    # (2) that rate of quaternions matches what 'textbook' solutions give
+    # Note that we just use the explicit kinematics for the linear velocities
+    # as they are not as complicated as the angular ones
+    qdot_candidate = forcing_kin_explicit
+
+    quat_dot_textbook = Matrix([
+        [0, -P, -Q, -R],
+        [P,  0,  R, -Q],
+        [Q, -R,  0,  P],
+        [R,  Q, -P,  0],
+    ]) * q_att_vec / 2
+
+    # Again, if we don't use this "textbook" solution
+    # sympy will struggle to deal with the terms related to quaternion rates
+    # due to the number of operations involved
+    qdot_candidate[-1] = quat_dot_textbook[0] # lambda_0, note the [-1] as sympy's Kane puts the dependent coordinate last
+    qdot_candidate[0]  = quat_dot_textbook[1] # lambda_1
+    qdot_candidate[1]  = quat_dot_textbook[2] # lambda_2
+    qdot_candidate[2]  = quat_dot_textbook[3] # lambda_3
+
+    # sub the config constraint in the candidate solution and compare to the implicit rhs
+    lambda_0_sol = solve(config_cons[0], q_att_vec[0])[1]
+    lhs_candidate = simplify(mass_matrix_kin_implicit * qdot_candidate).subs({q_att_vec[0]: lambda_0_sol})
+    assert lhs_candidate == forcing_kin_implicit
+
+def test_issue_24887():
+    # Spherical pendulum
+    g, l, m, c = symbols('g l m c')
+    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1:4 u1:4')
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    A.orient_body_fixed(N, (q1, q2, q3), 'zxy')
+    N_w_A = A.ang_vel_in(N)
+    # A.set_ang_vel(N, u1 * A.x + u2 * A.y + u3 * A.z)
+    kdes = [N_w_A.dot(A.x) - u1, N_w_A.dot(A.y) - u2, N_w_A.dot(A.z) - u3]
+    O = Point('O')
+    O.set_vel(N, 0)
+    Po = O.locatenew('Po', -l * A.y)
+    Po.set_vel(A, 0)
+    P = Particle('P', Po, m)
+    kane = KanesMethod(N, [q1, q2, q3], [u1, u2, u3], kdes, bodies=[P],
+                       forcelist=[(Po, -m * g * N.y)])
+    kane.kanes_equations()
+    expected_md = m * l ** 2 * Matrix([[1, 0, 0], [0, 0, 0], [0, 0, 1]])
+    expected_fd = Matrix([
+        [l*m*(g*(sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3)) - l*u2*u3)],
+        [0], [l*m*(-g*(sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)) + l*u1*u2)]])
+    assert find_dynamicsymbols(kane.forcing).issubset({q1, q2, q3, u1, u2, u3})
+    assert simplify(kane.mass_matrix - expected_md) == zeros(3, 3)
+    assert simplify(kane.forcing - expected_fd) == zeros(3, 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane2.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane2.py
new file mode 100644
index 0000000000000000000000000000000000000000..e55866672aec0adcd951e772964a4ed205b56405
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane2.py
@@ -0,0 +1,464 @@
+from sympy import cos, Matrix, sin, zeros, tan, pi, symbols
+from sympy.simplify.simplify import simplify
+from sympy.simplify.trigsimp import trigsimp
+from sympy.solvers.solvers import solve
+from sympy.physics.mechanics import (cross, dot, dynamicsymbols,
+                                     find_dynamicsymbols, KanesMethod, inertia,
+                                     inertia_of_point_mass, Point,
+                                     ReferenceFrame, RigidBody)
+
+
+def test_aux_dep():
+    # This test is about rolling disc dynamics, comparing the results found
+    # with KanesMethod to those found when deriving the equations "manually"
+    # with SymPy.
+    # The terms Fr, Fr*, and Fr*_steady are all compared between the two
+    # methods. Here, Fr*_steady refers to the generalized inertia forces for an
+    # equilibrium configuration.
+    # Note: comparing to the test of test_rolling_disc() in test_kane.py, this
+    # test also tests auxiliary speeds and configuration and motion constraints
+    #, seen in  the generalized dependent coordinates q[3], and depend speeds
+    # u[3], u[4] and u[5].
+
+
+    # First, manual derivation of Fr, Fr_star, Fr_star_steady.
+
+    # Symbols for time and constant parameters.
+    # Symbols for contact forces: Fx, Fy, Fz.
+    t, r, m, g, I, J = symbols('t r m g I J')
+    Fx, Fy, Fz = symbols('Fx Fy Fz')
+
+    # Configuration variables and their time derivatives:
+    # q[0] -- yaw
+    # q[1] -- lean
+    # q[2] -- spin
+    # q[3] -- dot(-r*B.z, A.z) -- distance from ground plane to disc center in
+    #         A.z direction
+    # Generalized speeds and their time derivatives:
+    # u[0] -- disc angular velocity component, disc fixed x direction
+    # u[1] -- disc angular velocity component, disc fixed y direction
+    # u[2] -- disc angular velocity component, disc fixed z direction
+    # u[3] -- disc velocity component, A.x direction
+    # u[4] -- disc velocity component, A.y direction
+    # u[5] -- disc velocity component, A.z direction
+    # Auxiliary generalized speeds:
+    # ua[0] -- contact point auxiliary generalized speed, A.x direction
+    # ua[1] -- contact point auxiliary generalized speed, A.y direction
+    # ua[2] -- contact point auxiliary generalized speed, A.z direction
+    q = dynamicsymbols('q:4')
+    qd = [qi.diff(t) for qi in q]
+    u = dynamicsymbols('u:6')
+    ud = [ui.diff(t) for ui in u]
+    ud_zero = dict(zip(ud, [0.]*len(ud)))
+    ua = dynamicsymbols('ua:3')
+    ua_zero = dict(zip(ua, [0.]*len(ua))) # noqa:F841
+
+    # Reference frames:
+    # Yaw intermediate frame: A.
+    # Lean intermediate frame: B.
+    # Disc fixed frame: C.
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [q[0], N.z])
+    B = A.orientnew('B', 'Axis', [q[1], A.x])
+    C = B.orientnew('C', 'Axis', [q[2], B.y])
+
+    # Angular velocity and angular acceleration of disc fixed frame
+    # u[0], u[1] and u[2] are generalized independent speeds.
+    C.set_ang_vel(N, u[0]*B.x + u[1]*B.y + u[2]*B.z)
+    C.set_ang_acc(N, C.ang_vel_in(N).diff(t, B)
+                   + cross(B.ang_vel_in(N), C.ang_vel_in(N)))
+
+    # Velocity and acceleration of points:
+    # Disc-ground contact point: P.
+    # Center of disc: O, defined from point P with depend coordinate: q[3]
+    # u[3], u[4] and u[5] are generalized dependent speeds.
+    P = Point('P')
+    P.set_vel(N, ua[0]*A.x + ua[1]*A.y + ua[2]*A.z)
+    O = P.locatenew('O', q[3]*A.z + r*sin(q[1])*A.y)
+    O.set_vel(N, u[3]*A.x + u[4]*A.y + u[5]*A.z)
+    O.set_acc(N, O.vel(N).diff(t, A) + cross(A.ang_vel_in(N), O.vel(N)))
+
+    # Kinematic differential equations:
+    # Two equalities: one is w_c_n_qd = C.ang_vel_in(N) in three coordinates
+    #                 directions of B, for qd0, qd1 and qd2.
+    #                 the other is v_o_n_qd = O.vel(N) in A.z direction for qd3.
+    # Then, solve for dq/dt's in terms of u's: qd_kd.
+    w_c_n_qd = qd[0]*A.z + qd[1]*B.x + qd[2]*B.y
+    v_o_n_qd = O.pos_from(P).diff(t, A) + cross(A.ang_vel_in(N), O.pos_from(P))
+    kindiffs = Matrix([dot(w_c_n_qd - C.ang_vel_in(N), uv) for uv in B] +
+                      [dot(v_o_n_qd - O.vel(N), A.z)])
+    qd_kd = solve(kindiffs, qd) # noqa:F841
+
+    # Values of generalized speeds during a steady turn for later substitution
+    # into the Fr_star_steady.
+    steady_conditions = solve(kindiffs.subs({qd[1] : 0, qd[3] : 0}), u)
+    steady_conditions.update({qd[1] : 0, qd[3] : 0})
+
+    # Partial angular velocities and velocities.
+    partial_w_C = [C.ang_vel_in(N).diff(ui, N) for ui in u + ua]
+    partial_v_O = [O.vel(N).diff(ui, N) for ui in u + ua]
+    partial_v_P = [P.vel(N).diff(ui, N) for ui in u + ua]
+
+    # Configuration constraint: f_c, the projection of radius r in A.z direction
+    #                                is q[3].
+    # Velocity constraints: f_v, for u3, u4 and u5.
+    # Acceleration constraints: f_a.
+    f_c = Matrix([dot(-r*B.z, A.z) - q[3]])
+    f_v = Matrix([dot(O.vel(N) - (P.vel(N) + cross(C.ang_vel_in(N),
+        O.pos_from(P))), ai).expand() for ai in A])
+    v_o_n = cross(C.ang_vel_in(N), O.pos_from(P))
+    a_o_n = v_o_n.diff(t, A) + cross(A.ang_vel_in(N), v_o_n)
+    f_a = Matrix([dot(O.acc(N) - a_o_n, ai) for ai in A]) # noqa:F841
+
+    # Solve for constraint equations in the form of
+    #                           u_dependent = A_rs * [u_i; u_aux].
+    # First, obtain constraint coefficient matrix:  M_v * [u; ua] = 0;
+    # Second, taking u[0], u[1], u[2] as independent,
+    #         taking u[3], u[4], u[5] as dependent,
+    #         rearranging the matrix of M_v to be A_rs for u_dependent.
+    # Third, u_aux ==0 for u_dep, and resulting dictionary of u_dep_dict.
+    M_v = zeros(3, 9)
+    for i in range(3):
+        for j, ui in enumerate(u + ua):
+            M_v[i, j] = f_v[i].diff(ui)
+
+    M_v_i = M_v[:, :3]
+    M_v_d = M_v[:, 3:6]
+    M_v_aux = M_v[:, 6:]
+    M_v_i_aux = M_v_i.row_join(M_v_aux)
+    A_rs = - M_v_d.inv() * M_v_i_aux
+
+    u_dep = A_rs[:, :3] * Matrix(u[:3])
+    u_dep_dict = dict(zip(u[3:], u_dep))
+
+    # Active forces: F_O acting on point O; F_P acting on point P.
+    # Generalized active forces (unconstrained): Fr_u = F_point * pv_point.
+    F_O = m*g*A.z
+    F_P = Fx * A.x + Fy * A.y + Fz * A.z
+    Fr_u = Matrix([dot(F_O, pv_o) + dot(F_P, pv_p) for pv_o, pv_p in
+            zip(partial_v_O, partial_v_P)])
+
+    # Inertia force: R_star_O.
+    # Inertia of disc: I_C_O, where J is a inertia component about principal axis.
+    # Inertia torque: T_star_C.
+    # Generalized inertia forces (unconstrained): Fr_star_u.
+    R_star_O = -m*O.acc(N)
+    I_C_O = inertia(B, I, J, I)
+    T_star_C = -(dot(I_C_O, C.ang_acc_in(N)) \
+                 + cross(C.ang_vel_in(N), dot(I_C_O, C.ang_vel_in(N))))
+    Fr_star_u = Matrix([dot(R_star_O, pv) + dot(T_star_C, pav) for pv, pav in
+                        zip(partial_v_O, partial_w_C)])
+
+    # Form nonholonomic Fr: Fr_c, and nonholonomic Fr_star: Fr_star_c.
+    # Also, nonholonomic Fr_star in steady turning condition: Fr_star_steady.
+    Fr_c = Fr_u[:3, :].col_join(Fr_u[6:, :]) + A_rs.T * Fr_u[3:6, :]
+    Fr_star_c = Fr_star_u[:3, :].col_join(Fr_star_u[6:, :])\
+                + A_rs.T * Fr_star_u[3:6, :]
+    Fr_star_steady = Fr_star_c.subs(ud_zero).subs(u_dep_dict)\
+            .subs(steady_conditions).subs({q[3]: -r*cos(q[1])}).expand()
+
+
+    # Second, using KaneMethod in mechanics for fr, frstar and frstar_steady.
+
+    # Rigid Bodies: disc, with inertia I_C_O.
+    iner_tuple = (I_C_O, O)
+    disc = RigidBody('disc', O, C, m, iner_tuple)
+    bodyList = [disc]
+
+    # Generalized forces: Gravity: F_o; Auxiliary forces: F_p.
+    F_o = (O, F_O)
+    F_p = (P, F_P)
+    forceList = [F_o,  F_p]
+
+    # KanesMethod.
+    kane = KanesMethod(
+        N, q_ind= q[:3], u_ind= u[:3], kd_eqs=kindiffs,
+        q_dependent=q[3:], configuration_constraints = f_c,
+        u_dependent=u[3:], velocity_constraints= f_v,
+        u_auxiliary=ua
+        )
+
+    # fr, frstar, frstar_steady and kdd(kinematic differential equations).
+    (fr, frstar)= kane.kanes_equations(bodyList, forceList)
+    frstar_steady = frstar.subs(ud_zero).subs(u_dep_dict).subs(steady_conditions)\
+                    .subs({q[3]: -r*cos(q[1])}).expand()
+    kdd = kane.kindiffdict()
+
+    assert Matrix(Fr_c).expand() == fr.expand()
+    assert Matrix(Fr_star_c.subs(kdd)).expand() == frstar.expand()
+    # These Matrices have some Integer(0) and some Float(0). Running under
+    # SymEngine gives different types of zero.
+    assert (simplify(Matrix(Fr_star_steady).expand()).xreplace({0:0.0}) ==
+            simplify(frstar_steady.expand()).xreplace({0:0.0}))
+
+    syms_in_forcing = find_dynamicsymbols(kane.forcing)
+    for qdi in qd:
+        assert qdi not in syms_in_forcing
+
+
+def test_non_central_inertia():
+    # This tests that the calculation of Fr* does not depend the point
+    # about which the inertia of a rigid body is defined. This test solves
+    # exercises 8.12, 8.17 from Kane 1985.
+
+    # Declare symbols
+    q1, q2, q3 = dynamicsymbols('q1:4')
+    q1d, q2d, q3d = dynamicsymbols('q1:4', level=1)
+    u1, u2, u3, u4, u5 = dynamicsymbols('u1:6')
+    u_prime, R, M, g, e, f, theta = symbols('u\' R, M, g, e, f, theta')
+    a, b, mA, mB, IA, J, K, t = symbols('a b mA mB IA J K t')
+    Q1, Q2, Q3 = symbols('Q1, Q2 Q3')
+    IA22, IA23, IA33 = symbols('IA22 IA23 IA33')
+
+    # Reference Frames
+    F = ReferenceFrame('F')
+    P = F.orientnew('P', 'axis', [-theta, F.y])
+    A = P.orientnew('A', 'axis', [q1, P.x])
+    A.set_ang_vel(F, u1*A.x + u3*A.z)
+    # define frames for wheels
+    B = A.orientnew('B', 'axis', [q2, A.z])
+    C = A.orientnew('C', 'axis', [q3, A.z])
+    B.set_ang_vel(A, u4 * A.z)
+    C.set_ang_vel(A, u5 * A.z)
+
+    # define points D, S*, Q on frame A and their velocities
+    pD = Point('D')
+    pD.set_vel(A, 0)
+    # u3 will not change v_D_F since wheels are still assumed to roll without slip.
+    pD.set_vel(F, u2 * A.y)
+
+    pS_star = pD.locatenew('S*', e*A.y)
+    pQ = pD.locatenew('Q', f*A.y - R*A.x)
+    for p in [pS_star, pQ]:
+        p.v2pt_theory(pD, F, A)
+
+    # masscenters of bodies A, B, C
+    pA_star = pD.locatenew('A*', a*A.y)
+    pB_star = pD.locatenew('B*', b*A.z)
+    pC_star = pD.locatenew('C*', -b*A.z)
+    for p in [pA_star, pB_star, pC_star]:
+        p.v2pt_theory(pD, F, A)
+
+    # points of B, C touching the plane P
+    pB_hat = pB_star.locatenew('B^', -R*A.x)
+    pC_hat = pC_star.locatenew('C^', -R*A.x)
+    pB_hat.v2pt_theory(pB_star, F, B)
+    pC_hat.v2pt_theory(pC_star, F, C)
+
+    # the velocities of B^, C^ are zero since B, C are assumed to roll without slip
+    kde = [q1d - u1, q2d - u4, q3d - u5]
+    vc = [dot(p.vel(F), A.y) for p in [pB_hat, pC_hat]]
+
+    # inertias of bodies A, B, C
+    # IA22, IA23, IA33 are not specified in the problem statement, but are
+    # necessary to define an inertia object. Although the values of
+    # IA22, IA23, IA33 are not known in terms of the variables given in the
+    # problem statement, they do not appear in the general inertia terms.
+    inertia_A = inertia(A, IA, IA22, IA33, 0, IA23, 0)
+    inertia_B = inertia(B, K, K, J)
+    inertia_C = inertia(C, K, K, J)
+
+    # define the rigid bodies A, B, C
+    rbA = RigidBody('rbA', pA_star, A, mA, (inertia_A, pA_star))
+    rbB = RigidBody('rbB', pB_star, B, mB, (inertia_B, pB_star))
+    rbC = RigidBody('rbC', pC_star, C, mB, (inertia_C, pC_star))
+
+    km = KanesMethod(F, q_ind=[q1, q2, q3], u_ind=[u1, u2], kd_eqs=kde,
+                     u_dependent=[u4, u5], velocity_constraints=vc,
+                     u_auxiliary=[u3])
+
+    forces = [(pS_star, -M*g*F.x), (pQ, Q1*A.x + Q2*A.y + Q3*A.z)]
+    bodies = [rbA, rbB, rbC]
+    fr, fr_star = km.kanes_equations(bodies, forces)
+    vc_map = solve(vc, [u4, u5])
+
+    # KanesMethod returns the negative of Fr, Fr* as defined in Kane1985.
+    fr_star_expected = Matrix([
+            -(IA + 2*J*b**2/R**2 + 2*K +
+              mA*a**2 + 2*mB*b**2) * u1.diff(t) - mA*a*u1*u2,
+            -(mA + 2*mB +2*J/R**2) * u2.diff(t) + mA*a*u1**2,
+            0])
+    t = trigsimp(fr_star.subs(vc_map).subs({u3: 0})).doit().expand()
+    assert ((fr_star_expected - t).expand() == zeros(3, 1))
+
+    # define inertias of rigid bodies A, B, C about point D
+    # I_S/O = I_S/S* + I_S*/O
+    bodies2 = []
+    for rb, I_star in zip([rbA, rbB, rbC], [inertia_A, inertia_B, inertia_C]):
+        I = I_star + inertia_of_point_mass(rb.mass,
+                                           rb.masscenter.pos_from(pD),
+                                           rb.frame)
+        bodies2.append(RigidBody('', rb.masscenter, rb.frame, rb.mass,
+                                 (I, pD)))
+    fr2, fr_star2 = km.kanes_equations(bodies2, forces)
+
+    t = trigsimp(fr_star2.subs(vc_map).subs({u3: 0})).doit()
+    assert (fr_star_expected - t).expand() == zeros(3, 1)
+
+def test_sub_qdot():
+    # This test solves exercises 8.12, 8.17 from Kane 1985 and defines
+    # some velocities in terms of q, qdot.
+
+    ## --- Declare symbols ---
+    q1, q2, q3 = dynamicsymbols('q1:4')
+    q1d, q2d, q3d = dynamicsymbols('q1:4', level=1)
+    u1, u2, u3 = dynamicsymbols('u1:4')
+    u_prime, R, M, g, e, f, theta = symbols('u\' R, M, g, e, f, theta')
+    a, b, mA, mB, IA, J, K, t = symbols('a b mA mB IA J K t')
+    IA22, IA23, IA33 = symbols('IA22 IA23 IA33')
+    Q1, Q2, Q3 = symbols('Q1 Q2 Q3')
+
+    # --- Reference Frames ---
+    F = ReferenceFrame('F')
+    P = F.orientnew('P', 'axis', [-theta, F.y])
+    A = P.orientnew('A', 'axis', [q1, P.x])
+    A.set_ang_vel(F, u1*A.x + u3*A.z)
+    # define frames for wheels
+    B = A.orientnew('B', 'axis', [q2, A.z])
+    C = A.orientnew('C', 'axis', [q3, A.z])
+
+    ## --- define points D, S*, Q on frame A and their velocities ---
+    pD = Point('D')
+    pD.set_vel(A, 0)
+    # u3 will not change v_D_F since wheels are still assumed to roll w/o slip
+    pD.set_vel(F, u2 * A.y)
+
+    pS_star = pD.locatenew('S*', e*A.y)
+    pQ = pD.locatenew('Q', f*A.y - R*A.x)
+    # masscenters of bodies A, B, C
+    pA_star = pD.locatenew('A*', a*A.y)
+    pB_star = pD.locatenew('B*', b*A.z)
+    pC_star = pD.locatenew('C*', -b*A.z)
+    for p in [pS_star, pQ, pA_star, pB_star, pC_star]:
+        p.v2pt_theory(pD, F, A)
+
+    # points of B, C touching the plane P
+    pB_hat = pB_star.locatenew('B^', -R*A.x)
+    pC_hat = pC_star.locatenew('C^', -R*A.x)
+    pB_hat.v2pt_theory(pB_star, F, B)
+    pC_hat.v2pt_theory(pC_star, F, C)
+
+    # --- relate qdot, u ---
+    # the velocities of B^, C^ are zero since B, C are assumed to roll w/o slip
+    kde = [dot(p.vel(F), A.y) for p in [pB_hat, pC_hat]]
+    kde += [u1 - q1d]
+    kde_map = solve(kde, [q1d, q2d, q3d])
+    for k, v in list(kde_map.items()):
+        kde_map[k.diff(t)] = v.diff(t)
+
+    # inertias of bodies A, B, C
+    # IA22, IA23, IA33 are not specified in the problem statement, but are
+    # necessary to define an inertia object. Although the values of
+    # IA22, IA23, IA33 are not known in terms of the variables given in the
+    # problem statement, they do not appear in the general inertia terms.
+    inertia_A = inertia(A, IA, IA22, IA33, 0, IA23, 0)
+    inertia_B = inertia(B, K, K, J)
+    inertia_C = inertia(C, K, K, J)
+
+    # define the rigid bodies A, B, C
+    rbA = RigidBody('rbA', pA_star, A, mA, (inertia_A, pA_star))
+    rbB = RigidBody('rbB', pB_star, B, mB, (inertia_B, pB_star))
+    rbC = RigidBody('rbC', pC_star, C, mB, (inertia_C, pC_star))
+
+    ## --- use kanes method ---
+    km = KanesMethod(F, [q1, q2, q3], [u1, u2], kd_eqs=kde, u_auxiliary=[u3])
+
+    forces = [(pS_star, -M*g*F.x), (pQ, Q1*A.x + Q2*A.y + Q3*A.z)]
+    bodies = [rbA, rbB, rbC]
+
+    # Q2 = -u_prime * u2 * Q1 / sqrt(u2**2 + f**2 * u1**2)
+    # -u_prime * R * u2 / sqrt(u2**2 + f**2 * u1**2) = R / Q1 * Q2
+    fr_expected = Matrix([
+            f*Q3 + M*g*e*sin(theta)*cos(q1),
+            Q2 + M*g*sin(theta)*sin(q1),
+            e*M*g*cos(theta) - Q1*f - Q2*R])
+             #Q1 * (f - u_prime * R * u2 / sqrt(u2**2 + f**2 * u1**2)))])
+    fr_star_expected = Matrix([
+            -(IA + 2*J*b**2/R**2 + 2*K +
+              mA*a**2 + 2*mB*b**2) * u1.diff(t) - mA*a*u1*u2,
+            -(mA + 2*mB +2*J/R**2) * u2.diff(t) + mA*a*u1**2,
+            0])
+
+    fr, fr_star = km.kanes_equations(bodies, forces)
+    assert (fr.expand() == fr_expected.expand())
+    assert ((fr_star_expected - trigsimp(fr_star)).expand() == zeros(3, 1))
+
+def test_sub_qdot2():
+    # This test solves exercises 8.3 from Kane 1985 and defines
+    # all velocities in terms of q, qdot. We check that the generalized active
+    # forces are correctly computed if u terms are only defined in the
+    # kinematic differential equations.
+    #
+    # This functionality was added in PR 8948. Without qdot/u substitution, the
+    # KanesMethod constructor will fail during the constraint initialization as
+    # the B matrix will be poorly formed and inversion of the dependent part
+    # will fail.
+
+    g, m, Px, Py, Pz, R, t = symbols('g m Px Py Pz R t')
+    q = dynamicsymbols('q:5')
+    qd = dynamicsymbols('q:5', level=1)
+    u = dynamicsymbols('u:5')
+
+    ## Define inertial, intermediate, and rigid body reference frames
+    A = ReferenceFrame('A')
+    B_prime = A.orientnew('B_prime', 'Axis', [q[0], A.z])
+    B = B_prime.orientnew('B', 'Axis', [pi/2 - q[1], B_prime.x])
+    C = B.orientnew('C', 'Axis', [q[2], B.z])
+
+    ## Define points of interest and their velocities
+    pO = Point('O')
+    pO.set_vel(A, 0)
+
+    # R is the point in plane H that comes into contact with disk C.
+    pR = pO.locatenew('R', q[3]*A.x + q[4]*A.y)
+    pR.set_vel(A, pR.pos_from(pO).diff(t, A))
+    pR.set_vel(B, 0)
+
+    # C^ is the point in disk C that comes into contact with plane H.
+    pC_hat = pR.locatenew('C^', 0)
+    pC_hat.set_vel(C, 0)
+
+    # C* is the point at the center of disk C.
+    pCs = pC_hat.locatenew('C*', R*B.y)
+    pCs.set_vel(C, 0)
+    pCs.set_vel(B, 0)
+
+    # calculate velocites of points C* and C^ in frame A
+    pCs.v2pt_theory(pR, A, B) # points C* and R are fixed in frame B
+    pC_hat.v2pt_theory(pCs, A, C) # points C* and C^ are fixed in frame C
+
+    ## Define forces on each point of the system
+    R_C_hat = Px*A.x + Py*A.y + Pz*A.z
+    R_Cs = -m*g*A.z
+    forces = [(pC_hat, R_C_hat), (pCs, R_Cs)]
+
+    ## Define kinematic differential equations
+    # let ui = omega_C_A & bi (i = 1, 2, 3)
+    # u4 = qd4, u5 = qd5
+    u_expr = [C.ang_vel_in(A) & uv for uv in B]
+    u_expr += qd[3:]
+    kde = [ui - e for ui, e in zip(u, u_expr)]
+    km1 = KanesMethod(A, q, u, kde)
+    fr1, _ = km1.kanes_equations([], forces)
+
+    ## Calculate generalized active forces if we impose the condition that the
+    # disk C is rolling without slipping
+    u_indep = u[:3]
+    u_dep = list(set(u) - set(u_indep))
+    vc = [pC_hat.vel(A) & uv for uv in [A.x, A.y]]
+    km2 = KanesMethod(A, q, u_indep, kde,
+                      u_dependent=u_dep, velocity_constraints=vc)
+    fr2, _ = km2.kanes_equations([], forces)
+
+    fr1_expected = Matrix([
+        -R*g*m*sin(q[1]),
+        -R*(Px*cos(q[0]) + Py*sin(q[0]))*tan(q[1]),
+        R*(Px*cos(q[0]) + Py*sin(q[0])),
+        Px,
+        Py])
+    fr2_expected = Matrix([
+        -R*g*m*sin(q[1]),
+        0,
+        0])
+    assert (trigsimp(fr1.expand()) == trigsimp(fr1_expected.expand()))
+    assert (trigsimp(fr2.expand()) == trigsimp(fr2_expected.expand()))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane3.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane3.py
new file mode 100644
index 0000000000000000000000000000000000000000..438759451cfb142c488b9b5c67ac269b668cac68
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane3.py
@@ -0,0 +1,315 @@
+from sympy.core.numbers import pi
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import acos, sin, cos
+from sympy.matrices.dense import Matrix
+from sympy.physics.mechanics import (ReferenceFrame, dynamicsymbols,
+                                     KanesMethod, inertia, Point, RigidBody,
+                                     dot)
+from sympy.testing.pytest import slow
+
+
+@slow
+def test_bicycle():
+    # Code to get equations of motion for a bicycle modeled as in:
+    # J.P Meijaard, Jim M Papadopoulos, Andy Ruina and A.L Schwab. Linearized
+    # dynamics equations for the balance and steer of a bicycle: a benchmark
+    # and review. Proceedings of The Royal Society (2007) 463, 1955-1982
+    # doi: 10.1098/rspa.2007.1857
+
+    # Note that this code has been crudely ported from Autolev, which is the
+    # reason for some of the unusual naming conventions. It was purposefully as
+    # similar as possible in order to aide debugging.
+
+    # Declare Coordinates & Speeds
+    # Simple definitions for qdots - qd = u
+    # Speeds are:
+    # - u1: yaw frame ang. rate
+    # - u2: roll frame ang. rate
+    # - u3: rear wheel frame ang. rate (spinning motion)
+    # - u4: frame ang. rate (pitching motion)
+    # - u5: steering frame ang. rate
+    # - u6: front wheel ang. rate (spinning motion)
+    # Wheel positions are ignorable coordinates, so they are not introduced.
+    q1, q2, q4, q5 = dynamicsymbols('q1 q2 q4 q5')
+    q1d, q2d, q4d, q5d = dynamicsymbols('q1 q2 q4 q5', 1)
+    u1, u2, u3, u4, u5, u6 = dynamicsymbols('u1 u2 u3 u4 u5 u6')
+    u1d, u2d, u3d, u4d, u5d, u6d = dynamicsymbols('u1 u2 u3 u4 u5 u6', 1)
+
+    # Declare System's Parameters
+    WFrad, WRrad, htangle, forkoffset = symbols('WFrad WRrad htangle forkoffset')
+    forklength, framelength, forkcg1 = symbols('forklength framelength forkcg1')
+    forkcg3, framecg1, framecg3, Iwr11 = symbols('forkcg3 framecg1 framecg3 Iwr11')
+    Iwr22, Iwf11, Iwf22, Iframe11 = symbols('Iwr22 Iwf11 Iwf22 Iframe11')
+    Iframe22, Iframe33, Iframe31, Ifork11 = symbols('Iframe22 Iframe33 Iframe31 Ifork11')
+    Ifork22, Ifork33, Ifork31, g = symbols('Ifork22 Ifork33 Ifork31 g')
+    mframe, mfork, mwf, mwr = symbols('mframe mfork mwf mwr')
+
+    # Set up reference frames for the system
+    # N - inertial
+    # Y - yaw
+    # R - roll
+    # WR - rear wheel, rotation angle is ignorable coordinate so not oriented
+    # Frame - bicycle frame
+    # TempFrame - statically rotated frame for easier reference inertia definition
+    # Fork - bicycle fork
+    # TempFork - statically rotated frame for easier reference inertia definition
+    # WF - front wheel, again posses a ignorable coordinate
+    N = ReferenceFrame('N')
+    Y = N.orientnew('Y', 'Axis', [q1, N.z])
+    R = Y.orientnew('R', 'Axis', [q2, Y.x])
+    Frame = R.orientnew('Frame', 'Axis', [q4 + htangle, R.y])
+    WR = ReferenceFrame('WR')
+    TempFrame = Frame.orientnew('TempFrame', 'Axis', [-htangle, Frame.y])
+    Fork = Frame.orientnew('Fork', 'Axis', [q5, Frame.x])
+    TempFork = Fork.orientnew('TempFork', 'Axis', [-htangle, Fork.y])
+    WF = ReferenceFrame('WF')
+
+    # Kinematics of the Bicycle First block of code is forming the positions of
+    # the relevant points
+    # rear wheel contact -> rear wheel mass center -> frame mass center +
+    # frame/fork connection -> fork mass center + front wheel mass center ->
+    # front wheel contact point
+    WR_cont = Point('WR_cont')
+    WR_mc = WR_cont.locatenew('WR_mc', WRrad * R.z)
+    Steer = WR_mc.locatenew('Steer', framelength * Frame.z)
+    Frame_mc = WR_mc.locatenew('Frame_mc', - framecg1 * Frame.x
+                                           + framecg3 * Frame.z)
+    Fork_mc = Steer.locatenew('Fork_mc', - forkcg1 * Fork.x
+                                         + forkcg3 * Fork.z)
+    WF_mc = Steer.locatenew('WF_mc', forklength * Fork.x + forkoffset * Fork.z)
+    WF_cont = WF_mc.locatenew('WF_cont', WFrad * (dot(Fork.y, Y.z) * Fork.y -
+                                                  Y.z).normalize())
+
+    # Set the angular velocity of each frame.
+    # Angular accelerations end up being calculated automatically by
+    # differentiating the angular velocities when first needed.
+    # u1 is yaw rate
+    # u2 is roll rate
+    # u3 is rear wheel rate
+    # u4 is frame pitch rate
+    # u5 is fork steer rate
+    # u6 is front wheel rate
+    Y.set_ang_vel(N, u1 * Y.z)
+    R.set_ang_vel(Y, u2 * R.x)
+    WR.set_ang_vel(Frame, u3 * Frame.y)
+    Frame.set_ang_vel(R, u4 * Frame.y)
+    Fork.set_ang_vel(Frame, u5 * Fork.x)
+    WF.set_ang_vel(Fork, u6 * Fork.y)
+
+    # Form the velocities of the previously defined points, using the 2 - point
+    # theorem (written out by hand here).  Accelerations again are calculated
+    # automatically when first needed.
+    WR_cont.set_vel(N, 0)
+    WR_mc.v2pt_theory(WR_cont, N, WR)
+    Steer.v2pt_theory(WR_mc, N, Frame)
+    Frame_mc.v2pt_theory(WR_mc, N, Frame)
+    Fork_mc.v2pt_theory(Steer, N, Fork)
+    WF_mc.v2pt_theory(Steer, N, Fork)
+    WF_cont.v2pt_theory(WF_mc, N, WF)
+
+    # Sets the inertias of each body. Uses the inertia frame to construct the
+    # inertia dyadics. Wheel inertias are only defined by principle moments of
+    # inertia, and are in fact constant in the frame and fork reference frames;
+    # it is for this reason that the orientations of the wheels does not need
+    # to be defined. The frame and fork inertias are defined in the 'Temp'
+    # frames which are fixed to the appropriate body frames; this is to allow
+    # easier input of the reference values of the benchmark paper. Note that
+    # due to slightly different orientations, the products of inertia need to
+    # have their signs flipped; this is done later when entering the numerical
+    # value.
+
+    Frame_I = (inertia(TempFrame, Iframe11, Iframe22, Iframe33, 0, 0, Iframe31), Frame_mc)
+    Fork_I = (inertia(TempFork, Ifork11, Ifork22, Ifork33, 0, 0, Ifork31), Fork_mc)
+    WR_I = (inertia(Frame, Iwr11, Iwr22, Iwr11), WR_mc)
+    WF_I = (inertia(Fork, Iwf11, Iwf22, Iwf11), WF_mc)
+
+    # Declaration of the RigidBody containers. ::
+
+    BodyFrame = RigidBody('BodyFrame', Frame_mc, Frame, mframe, Frame_I)
+    BodyFork = RigidBody('BodyFork', Fork_mc, Fork, mfork, Fork_I)
+    BodyWR = RigidBody('BodyWR', WR_mc, WR, mwr, WR_I)
+    BodyWF = RigidBody('BodyWF', WF_mc, WF, mwf, WF_I)
+
+    # The kinematic differential equations; they are defined quite simply. Each
+    # entry in this list is equal to zero.
+    kd = [q1d - u1, q2d - u2, q4d - u4, q5d - u5]
+
+    # The nonholonomic constraints are the velocity of the front wheel contact
+    # point dotted into the X, Y, and Z directions; the yaw frame is used as it
+    # is "closer" to the front wheel (1 less DCM connecting them). These
+    # constraints force the velocity of the front wheel contact point to be 0
+    # in the inertial frame; the X and Y direction constraints enforce a
+    # "no-slip" condition, and the Z direction constraint forces the front
+    # wheel contact point to not move away from the ground frame, essentially
+    # replicating the holonomic constraint which does not allow the frame pitch
+    # to change in an invalid fashion.
+
+    conlist_speed = [WF_cont.vel(N) & Y.x, WF_cont.vel(N) & Y.y, WF_cont.vel(N) & Y.z]
+
+    # The holonomic constraint is that the position from the rear wheel contact
+    # point to the front wheel contact point when dotted into the
+    # normal-to-ground plane direction must be zero; effectively that the front
+    # and rear wheel contact points are always touching the ground plane. This
+    # is actually not part of the dynamic equations, but instead is necessary
+    # for the lineraization process.
+
+    conlist_coord = [WF_cont.pos_from(WR_cont) & Y.z]
+
+    # The force list; each body has the appropriate gravitational force applied
+    # at its mass center.
+    FL = [(Frame_mc, -mframe * g * Y.z),
+        (Fork_mc, -mfork * g * Y.z),
+        (WF_mc, -mwf * g * Y.z),
+        (WR_mc, -mwr * g * Y.z)]
+    BL = [BodyFrame, BodyFork, BodyWR, BodyWF]
+
+
+    # The N frame is the inertial frame, coordinates are supplied in the order
+    # of independent, dependent coordinates, as are the speeds. The kinematic
+    # differential equation are also entered here.  Here the dependent speeds
+    # are specified, in the same order they were provided in earlier, along
+    # with the non-holonomic constraints.  The dependent coordinate is also
+    # provided, with the holonomic constraint.  Again, this is only provided
+    # for the linearization process.
+
+    KM = KanesMethod(N, q_ind=[q1, q2, q5],
+            q_dependent=[q4], configuration_constraints=conlist_coord,
+            u_ind=[u2, u3, u5],
+            u_dependent=[u1, u4, u6], velocity_constraints=conlist_speed,
+            kd_eqs=kd,
+            constraint_solver="CRAMER")
+    (fr, frstar) = KM.kanes_equations(BL, FL)
+
+    # This is the start of entering in the numerical values from the benchmark
+    # paper to validate the eigen values of the linearized equations from this
+    # model to the reference eigen values. Look at the aforementioned paper for
+    # more information. Some of these are intermediate values, used to
+    # transform values from the paper into the coordinate systems used in this
+    # model.
+    PaperRadRear                    =  0.3
+    PaperRadFront                   =  0.35
+    HTA                             =  (pi / 2 - pi / 10).evalf()
+    TrailPaper                      =  0.08
+    rake                            =  (-(TrailPaper*sin(HTA)-(PaperRadFront*cos(HTA)))).evalf()
+    PaperWb                         =  1.02
+    PaperFrameCgX                   =  0.3
+    PaperFrameCgZ                   =  0.9
+    PaperForkCgX                    =  0.9
+    PaperForkCgZ                    =  0.7
+    FrameLength                     =  (PaperWb*sin(HTA)-(rake-(PaperRadFront-PaperRadRear)*cos(HTA))).evalf()
+    FrameCGNorm                     =  ((PaperFrameCgZ - PaperRadRear-(PaperFrameCgX/sin(HTA))*cos(HTA))*sin(HTA)).evalf()
+    FrameCGPar                      =  (PaperFrameCgX / sin(HTA) + (PaperFrameCgZ - PaperRadRear - PaperFrameCgX / sin(HTA) * cos(HTA)) * cos(HTA)).evalf()
+    tempa                           =  (PaperForkCgZ - PaperRadFront)
+    tempb                           =  (PaperWb-PaperForkCgX)
+    tempc                           =  (sqrt(tempa**2+tempb**2)).evalf()
+    PaperForkL                      =  (PaperWb*cos(HTA)-(PaperRadFront-PaperRadRear)*sin(HTA)).evalf()
+    ForkCGNorm                      =  (rake+(tempc * sin(pi/2-HTA-acos(tempa/tempc)))).evalf()
+    ForkCGPar                       =  (tempc * cos((pi/2-HTA)-acos(tempa/tempc))-PaperForkL).evalf()
+
+    # Here is the final assembly of the numerical values. The symbol 'v' is the
+    # forward speed of the bicycle (a concept which only makes sense in the
+    # upright, static equilibrium case?). These are in a dictionary which will
+    # later be substituted in. Again the sign on the *product* of inertia
+    # values is flipped here, due to different orientations of coordinate
+    # systems.
+    v = symbols('v')
+    val_dict = {WFrad: PaperRadFront,
+                WRrad: PaperRadRear,
+                htangle: HTA,
+                forkoffset: rake,
+                forklength: PaperForkL,
+                framelength: FrameLength,
+                forkcg1: ForkCGPar,
+                forkcg3: ForkCGNorm,
+                framecg1: FrameCGNorm,
+                framecg3: FrameCGPar,
+                Iwr11: 0.0603,
+                Iwr22: 0.12,
+                Iwf11: 0.1405,
+                Iwf22: 0.28,
+                Ifork11: 0.05892,
+                Ifork22: 0.06,
+                Ifork33: 0.00708,
+                Ifork31: 0.00756,
+                Iframe11: 9.2,
+                Iframe22: 11,
+                Iframe33: 2.8,
+                Iframe31: -2.4,
+                mfork: 4,
+                mframe: 85,
+                mwf: 3,
+                mwr: 2,
+                g: 9.81,
+                q1: 0,
+                q2: 0,
+                q4: 0,
+                q5: 0,
+                u1: 0,
+                u2: 0,
+                u3: v / PaperRadRear,
+                u4: 0,
+                u5: 0,
+                u6: v / PaperRadFront}
+
+    # Linearizes the forcing vector; the equations are set up as MM udot =
+    # forcing, where MM is the mass matrix, udot is the vector representing the
+    # time derivatives of the generalized speeds, and forcing is a vector which
+    # contains both external forcing terms and internal forcing terms, such as
+    # centripital or coriolis forces.  This actually returns a matrix with as
+    # many rows as *total* coordinates and speeds, but only as many columns as
+    # independent coordinates and speeds.
+
+    A, B, _ = KM.linearize(
+        A_and_B=True,
+        op_point={
+            # Operating points for the accelerations are required for the
+            # linearizer to eliminate u' terms showing up in the coefficient
+            # matrices.
+            u1.diff(): 0,
+            u2.diff(): 0,
+            u3.diff(): 0,
+            u4.diff(): 0,
+            u5.diff(): 0,
+            u6.diff(): 0,
+            u1: 0,
+            u2: 0,
+            u3: v / PaperRadRear,
+            u4: 0,
+            u5: 0,
+            u6: v / PaperRadFront,
+            q1: 0,
+            q2: 0,
+            q4: 0,
+            q5: 0,
+        },
+        linear_solver="CRAMER",
+    )
+    # As mentioned above, the size of the linearized forcing terms is expanded
+    # to include both q's and u's, so the mass matrix must have this done as
+    # well.  This will likely be changed to be part of the linearized process,
+    # for future reference.
+    A_s = A.xreplace(val_dict)
+    B_s = B.xreplace(val_dict)
+
+    A_s = A_s.evalf()
+    B_s = B_s.evalf()
+
+    # Finally, we construct an "A" matrix for the form xdot = A x (x being the
+    # state vector, although in this case, the sizes are a little off). The
+    # following line extracts only the minimum entries required for eigenvalue
+    # analysis, which correspond to rows and columns for lean, steer, lean
+    # rate, and steer rate.
+    A = A_s.extract([1, 2, 3, 5], [1, 2, 3, 5])
+
+    # Precomputed for comparison
+    Res = Matrix([[               0,                                           0,                  1.0,                    0],
+                  [               0,                                           0,                    0,                  1.0],
+                  [9.48977444677355, -0.891197738059089*v**2 - 0.571523173729245, -0.105522449805691*v, -0.330515398992311*v],
+                  [11.7194768719633,   -1.97171508499972*v**2 + 30.9087533932407,   3.67680523332152*v,  -3.08486552743311*v]])
+
+    # Actual eigenvalue comparison
+    eps = 1.e-12
+    for i in range(6):
+        error = Res.subs(v, i) - A.subs(v, i)
+        assert all(abs(x) < eps for x in error)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane4.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane4.py
new file mode 100644
index 0000000000000000000000000000000000000000..a44dd2d407056ea36669268d478780fc581def51
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane4.py
@@ -0,0 +1,115 @@
+from sympy import (cos, sin, Matrix, symbols)
+from sympy.physics.mechanics import (dynamicsymbols, ReferenceFrame, Point,
+                                        KanesMethod, Particle)
+
+def test_replace_qdots_in_force():
+    # Test PR 16700 "Replaces qdots with us in force-list in kanes.py"
+    # The new functionality allows one to specify forces in qdots which will
+    # automatically be replaced with u:s which are defined by the kde supplied
+    # to KanesMethod. The test case is the double pendulum with interacting
+    # forces in the example of chapter 4.7 "CONTRIBUTING INTERACTION FORCES"
+    # in Ref. [1]. Reference list at end test function.
+
+    q1, q2 = dynamicsymbols('q1, q2')
+    qd1, qd2 = dynamicsymbols('q1, q2', level=1)
+    u1, u2 = dynamicsymbols('u1, u2')
+
+    l, m = symbols('l, m')
+
+    N = ReferenceFrame('N') # Inertial frame
+    A = N.orientnew('A', 'Axis', (q1, N.z)) # Rod A frame
+    B = A.orientnew('B', 'Axis', (q2, N.z)) # Rod B frame
+
+    O = Point('O') # Origo
+    O.set_vel(N, 0)
+
+    P = O.locatenew('P', ( l * A.x )) # Point @ end of rod A
+    P.v2pt_theory(O, N, A)
+
+    Q = P.locatenew('Q', ( l * B.x )) # Point @ end of rod B
+    Q.v2pt_theory(P, N, B)
+
+    Ap = Particle('Ap', P, m)
+    Bp = Particle('Bp', Q, m)
+
+    # The forces are specified below. sigma is the torsional spring stiffness
+    # and delta is the viscous damping coefficient acting between the two
+    # bodies. Here, we specify the viscous damper as function of qdots prior
+    # forming the kde. In more complex systems it not might be obvious which
+    # kde is most efficient, why it is convenient to specify viscous forces in
+    # qdots independently of the kde.
+    sig, delta = symbols('sigma, delta')
+    Ta = (sig * q2 + delta * qd2) * N.z
+    forces = [(A, Ta), (B, -Ta)]
+
+    # Try different kdes.
+    kde1 = [u1 - qd1, u2 - qd2]
+    kde2 = [u1 - qd1, u2 - (qd1 + qd2)]
+
+    KM1 = KanesMethod(N, [q1, q2], [u1, u2], kd_eqs=kde1)
+    fr1, fstar1 = KM1.kanes_equations([Ap, Bp], forces)
+
+    KM2 = KanesMethod(N, [q1, q2], [u1, u2], kd_eqs=kde2)
+    fr2, fstar2 = KM2.kanes_equations([Ap, Bp], forces)
+
+    # Check EOM for KM2:
+    # Mass and force matrix from p.6 in Ref. [2] with added forces from
+    # example of chapter 4.7 in [1] and without gravity.
+    forcing_matrix_expected = Matrix( [ [ m * l**2 * sin(q2) * u2**2 + sig * q2
+                                        + delta * (u2 - u1)],
+                                        [ m * l**2 * sin(q2) * -u1**2 - sig * q2
+                                        - delta * (u2 - u1)] ] )
+    mass_matrix_expected = Matrix( [ [ 2 * m * l**2, m * l**2 * cos(q2) ],
+                                    [ m * l**2 * cos(q2), m * l**2 ] ] )
+
+    assert (KM2.mass_matrix.expand() == mass_matrix_expected.expand())
+    assert (KM2.forcing.expand() == forcing_matrix_expected.expand())
+
+    # Check fr1 with reference fr_expected from [1] with u:s instead of qdots.
+    fr1_expected = Matrix([ 0, -(sig*q2 + delta * u2) ])
+    assert fr1.expand() == fr1_expected.expand()
+
+    # Check fr2
+    fr2_expected = Matrix([sig * q2 + delta * (u2 - u1),
+                            - sig * q2 - delta * (u2 - u1)])
+    assert fr2.expand() == fr2_expected.expand()
+
+    # Specifying forces in u:s should stay the same:
+    Ta = (sig * q2 + delta * u2) * N.z
+    forces = [(A, Ta), (B, -Ta)]
+    KM1 = KanesMethod(N, [q1, q2], [u1, u2], kd_eqs=kde1)
+    fr1, fstar1 = KM1.kanes_equations([Ap, Bp], forces)
+
+    assert fr1.expand() == fr1_expected.expand()
+
+    Ta = (sig * q2 + delta * (u2-u1)) * N.z
+    forces = [(A, Ta), (B, -Ta)]
+    KM2 = KanesMethod(N, [q1, q2], [u1, u2], kd_eqs=kde2)
+    fr2, fstar2 = KM2.kanes_equations([Ap, Bp], forces)
+
+    assert fr2.expand() == fr2_expected.expand()
+
+    # Test if we have a qubic qdot force:
+    Ta = (sig * q2 + delta * qd2**3) * N.z
+    forces = [(A, Ta), (B, -Ta)]
+
+    KM1 = KanesMethod(N, [q1, q2], [u1, u2], kd_eqs=kde1)
+    fr1, fstar1 = KM1.kanes_equations([Ap, Bp], forces)
+
+    fr1_cubic_expected = Matrix([ 0, -(sig*q2 + delta * u2**3) ])
+
+    assert fr1.expand() == fr1_cubic_expected.expand()
+
+    KM2 = KanesMethod(N, [q1, q2], [u1, u2], kd_eqs=kde2)
+    fr2, fstar2 = KM2.kanes_equations([Ap, Bp], forces)
+
+    fr2_cubic_expected = Matrix([sig * q2 + delta * (u2 - u1)**3,
+                            - sig * q2 - delta * (u2 - u1)**3])
+
+    assert fr2.expand() == fr2_cubic_expected.expand()
+
+    # References:
+    # [1] T.R. Kane, D. a Levinson, Dynamics Theory and Applications, 2005.
+    # [2] Arun K Banerjee, Flexible Multibody Dynamics:Efficient Formulations
+    #     and Applications, John Wiley and Sons, Ltd, 2016.
+    #     doi:http://dx.doi.org/10.1002/9781119015635.
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane5.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane5.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d0f863e8fa0f46bcd8ae729a1a8852b702bdafa
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_kane5.py
@@ -0,0 +1,128 @@
+from sympy import (zeros, Matrix, symbols, lambdify, sqrt, pi,
+                                simplify)
+from sympy.physics.mechanics import (dynamicsymbols, cross, inertia, RigidBody,
+                                     ReferenceFrame, KanesMethod)
+
+
+def _create_rolling_disc():
+    # Define symbols and coordinates
+    t = dynamicsymbols._t
+    q1, q2, q3, q4, q5, u1, u2, u3, u4, u5 = dynamicsymbols('q1:6 u1:6')
+    g, r, m = symbols('g r m')
+    # Define bodies and frames
+    ground = RigidBody('ground')
+    disc = RigidBody('disk', mass=m)
+    disc.inertia = (m * r ** 2 / 4 * inertia(disc.frame, 1, 2, 1),
+                    disc.masscenter)
+    ground.masscenter.set_vel(ground.frame, 0)
+    disc.masscenter.set_vel(disc.frame, 0)
+    int_frame = ReferenceFrame('int_frame')
+    # Orient frames
+    int_frame.orient_body_fixed(ground.frame, (q1, q2, 0), 'zxy')
+    disc.frame.orient_axis(int_frame, int_frame.y, q3)
+    g_w_d = disc.frame.ang_vel_in(ground.frame)
+    disc.frame.set_ang_vel(ground.frame,
+                           u1 * disc.x + u2 * disc.y + u3 * disc.z)
+    # Define points
+    cp = ground.masscenter.locatenew('contact_point',
+                                     q4 * ground.x + q5 * ground.y)
+    cp.set_vel(ground.frame, u4 * ground.x + u5 * ground.y)
+    disc.masscenter.set_pos(cp, r * int_frame.z)
+    disc.masscenter.set_vel(ground.frame, cross(
+        disc.frame.ang_vel_in(ground.frame), disc.masscenter.pos_from(cp)))
+    # Define kinematic differential equations
+    kdes = [g_w_d.dot(disc.x) - u1, g_w_d.dot(disc.y) - u2,
+            g_w_d.dot(disc.z) - u3, q4.diff(t) - u4, q5.diff(t) - u5]
+    # Define nonholonomic constraints
+    v0 = cp.vel(ground.frame) + cross(
+        disc.frame.ang_vel_in(int_frame), cp.pos_from(disc.masscenter))
+    fnh = [v0.dot(ground.x), v0.dot(ground.y)]
+    # Define loads
+    loads = [(disc.masscenter, -disc.mass * g * ground.z)]
+    bodies = [disc]
+    return {
+        'frame': ground.frame,
+        'q_ind': [q1, q2, q3, q4, q5],
+        'u_ind': [u1, u2, u3],
+        'u_dep': [u4, u5],
+        'kdes': kdes,
+        'fnh': fnh,
+        'bodies': bodies,
+        'loads': loads
+    }
+
+
+def _verify_rolling_disc_numerically(kane, all_zero=False):
+    q, u, p = dynamicsymbols('q1:6'), dynamicsymbols('u1:6'), symbols('g r m')
+    eval_sys = lambdify((q, u, p), (kane.mass_matrix_full, kane.forcing_full),
+                        cse=True)
+    solve_sys = lambda q, u, p: Matrix.LUsolve(
+        *(Matrix(mat) for mat in eval_sys(q, u, p)))
+    solve_u_dep = lambdify((q, u[:3], p), kane._Ars * Matrix(u[:3]), cse=True)
+    eps = 1e-10
+    p_vals = (9.81, 0.26, 3.43)
+    # First numeric test
+    q_vals = (0.3, 0.1, 1.97, -0.35, 2.27)
+    u_vals = [-0.2, 1.3, 0.15]
+    u_vals.extend(solve_u_dep(q_vals, u_vals, p_vals)[:2, 0])
+    expected = Matrix([
+        0.126603940595934, 0.215942571601660, 1.28736069604936,
+        0.319764288376543, 0.0989146857254898, -0.925848952664489,
+        -0.0181350656532944, 2.91695398184589, -0.00992793421754526,
+        0.0412861634829171])
+    assert all(abs(x) < eps for x in
+               (solve_sys(q_vals, u_vals, p_vals) - expected))
+    # Second numeric test
+    q_vals = (3.97, -0.28, 8.2, -0.35, 2.27)
+    u_vals = [-0.25, -2.2, 0.62]
+    u_vals.extend(solve_u_dep(q_vals, u_vals, p_vals)[:2, 0])
+    expected = Matrix([
+        0.0259159090798597, 0.668041660387416, -2.19283799213811,
+        0.385441810852219, 0.420109283790573, 1.45030568179066,
+        -0.0110924422400793, -8.35617840186040, -0.154098542632173,
+        -0.146102664410010])
+    assert all(abs(x) < eps for x in
+               (solve_sys(q_vals, u_vals, p_vals) - expected))
+    if all_zero:
+        q_vals = (0, 0, 0, 0, 0)
+        u_vals = (0, 0, 0, 0, 0)
+        assert solve_sys(q_vals, u_vals, p_vals) == zeros(10, 1)
+
+
+def test_kane_rolling_disc_lu():
+    props = _create_rolling_disc()
+    kane = KanesMethod(props['frame'], props['q_ind'], props['u_ind'],
+                       props['kdes'], u_dependent=props['u_dep'],
+                       velocity_constraints=props['fnh'],
+                       bodies=props['bodies'], forcelist=props['loads'],
+                       explicit_kinematics=False, constraint_solver='LU')
+    kane.kanes_equations()
+    _verify_rolling_disc_numerically(kane)
+
+
+def test_kane_rolling_disc_kdes_callable():
+    props = _create_rolling_disc()
+    kane = KanesMethod(
+        props['frame'], props['q_ind'], props['u_ind'], props['kdes'],
+        u_dependent=props['u_dep'], velocity_constraints=props['fnh'],
+        bodies=props['bodies'], forcelist=props['loads'],
+        explicit_kinematics=False,
+        kd_eqs_solver=lambda A, b: simplify(A.LUsolve(b)))
+    q, u, p = dynamicsymbols('q1:6'), dynamicsymbols('u1:6'), symbols('g r m')
+    qd = dynamicsymbols('q1:6', 1)
+    eval_kdes = lambdify((q, qd, u, p), tuple(kane.kindiffdict().items()))
+    eps = 1e-10
+    # Test with only zeros. If 'LU' would be used this would result in nan.
+    p_vals = (9.81, 0.25, 3.5)
+    zero_vals = (0, 0, 0, 0, 0)
+    assert all(abs(qdi - fui) < eps for qdi, fui in
+               eval_kdes(zero_vals, zero_vals, zero_vals, p_vals))
+    # Test with some arbitrary values
+    q_vals = tuple(map(float, (pi / 6, pi / 3, pi / 2, 0.42, 0.62)))
+    qd_vals = tuple(map(float, (4, 1 / 3, 4 - 2 * sqrt(3),
+                                0.25 * (2 * sqrt(3) - 3),
+                                0.25 * (2 - sqrt(3)))))
+    u_vals = tuple(map(float, (-2, 4, 1 / 3, 0.25 * (-3 + 2 * sqrt(3)),
+                               0.25 * (-sqrt(3) + 2))))
+    assert all(abs(qdi - fui) < eps for qdi, fui in
+               eval_kdes(q_vals, qd_vals, u_vals, p_vals))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_lagrange.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_lagrange.py
new file mode 100644
index 0000000000000000000000000000000000000000..81552bc7a4d0f6766dc46dcd47b7c7b1b0151b3f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_lagrange.py
@@ -0,0 +1,247 @@
+from sympy.physics.mechanics import (dynamicsymbols, ReferenceFrame, Point,
+                                    RigidBody, LagrangesMethod, Particle,
+                                    inertia, Lagrangian)
+from sympy.core.function import (Derivative, Function)
+from sympy.core.numbers import pi
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.matrices.dense import Matrix
+from sympy.simplify.simplify import simplify
+from sympy.testing.pytest import raises
+
+
+def test_invalid_coordinates():
+    # Simple pendulum, but use symbol instead of dynamicsymbol
+    l, m, g = symbols('l m g')
+    q = symbols('q')  # Generalized coordinate
+    N, O = ReferenceFrame('N'), Point('O')
+    O.set_vel(N, 0)
+    P = Particle('P', Point('P'), m)
+    P.point.set_pos(O, l * (sin(q) * N.x - cos(q) * N.y))
+    P.potential_energy = m * g * P.point.pos_from(O).dot(N.y)
+    L = Lagrangian(N, P)
+    raises(ValueError, lambda: LagrangesMethod(L, [q], bodies=P))
+
+
+def test_disc_on_an_incline_plane():
+    # Disc rolling on an inclined plane
+    # First the generalized coordinates are created. The mass center of the
+    # disc is located from top vertex of the inclined plane by the generalized
+    # coordinate 'y'. The orientation of the disc is defined by the angle
+    # 'theta'. The mass of the disc is 'm' and its radius is 'R'. The length of
+    # the inclined path is 'l', the angle of inclination is 'alpha'. 'g' is the
+    # gravitational constant.
+    y, theta = dynamicsymbols('y theta')
+    yd, thetad = dynamicsymbols('y theta', 1)
+    m, g, R, l, alpha = symbols('m g R l alpha')
+
+    # Next, we create the inertial reference frame 'N'. A reference frame 'A'
+    # is attached to the inclined plane. Finally a frame is created which is attached to the disk.
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [pi/2 - alpha, N.z])
+    B = A.orientnew('B', 'Axis', [-theta, A.z])
+
+    # Creating the disc 'D'; we create the point that represents the mass
+    # center of the disc and set its velocity. The inertia dyadic of the disc
+    # is created. Finally, we create the disc.
+    Do = Point('Do')
+    Do.set_vel(N, yd * A.x)
+    I = m * R**2/2 * B.z | B.z
+    D = RigidBody('D', Do, B, m, (I, Do))
+
+    # To construct the Lagrangian, 'L', of the disc, we determine its kinetic
+    # and potential energies, T and U, respectively. L is defined as the
+    # difference between T and U.
+    D.potential_energy = m * g * (l - y) * sin(alpha)
+    L = Lagrangian(N, D)
+
+    # We then create the list of generalized coordinates and constraint
+    # equations. The constraint arises due to the disc rolling without slip on
+    # on the inclined path. We then invoke the 'LagrangesMethod' class and
+    # supply it the necessary arguments and generate the equations of motion.
+    # The'rhs' method solves for the q_double_dots (i.e. the second derivative
+    # with respect to time  of the generalized coordinates and the lagrange
+    # multipliers.
+    q = [y, theta]
+    hol_coneqs = [y - R * theta]
+    m = LagrangesMethod(L, q, hol_coneqs=hol_coneqs)
+    m.form_lagranges_equations()
+    rhs = m.rhs()
+    rhs.simplify()
+    assert rhs[2] == 2*g*sin(alpha)/3
+
+
+def test_simp_pen():
+    # This tests that the equations generated by LagrangesMethod are identical
+    # to those obtained by hand calculations. The system under consideration is
+    # the simple pendulum.
+    # We begin by creating the generalized coordinates as per the requirements
+    # of LagrangesMethod. Also we created the associate symbols
+    # that characterize the system: 'm' is the mass of the bob, l is the length
+    # of the massless rigid rod connecting the bob to a point O fixed in the
+    # inertial frame.
+    q, u = dynamicsymbols('q u')
+    qd, ud = dynamicsymbols('q u ', 1)
+    l, m, g = symbols('l m g')
+
+    # We then create the inertial frame and a frame attached to the massless
+    # string following which we define the inertial angular velocity of the
+    # string.
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [q, N.z])
+    A.set_ang_vel(N, qd * N.z)
+
+    # Next, we create the point O and fix it in the inertial frame. We then
+    # locate the point P to which the bob is attached. Its corresponding
+    # velocity is then determined by the 'two point formula'.
+    O = Point('O')
+    O.set_vel(N, 0)
+    P = O.locatenew('P', l * A.x)
+    P.v2pt_theory(O, N, A)
+
+    # The 'Particle' which represents the bob is then created and its
+    # Lagrangian generated.
+    Pa = Particle('Pa', P, m)
+    Pa.potential_energy = - m * g * l * cos(q)
+    L = Lagrangian(N, Pa)
+
+    # The 'LagrangesMethod' class is invoked to obtain equations of motion.
+    lm = LagrangesMethod(L, [q])
+    lm.form_lagranges_equations()
+    RHS = lm.rhs()
+    assert RHS[1] == -g*sin(q)/l
+
+
+def test_nonminimal_pendulum():
+    q1, q2 = dynamicsymbols('q1:3')
+    q1d, q2d = dynamicsymbols('q1:3', level=1)
+    L, m, t = symbols('L, m, t')
+    g = 9.8
+    # Compose World Frame
+    N = ReferenceFrame('N')
+    pN = Point('N*')
+    pN.set_vel(N, 0)
+    # Create point P, the pendulum mass
+    P = pN.locatenew('P1', q1*N.x + q2*N.y)
+    P.set_vel(N, P.pos_from(pN).dt(N))
+    pP = Particle('pP', P, m)
+    # Constraint Equations
+    f_c = Matrix([q1**2 + q2**2 - L**2])
+    # Calculate the lagrangian, and form the equations of motion
+    Lag = Lagrangian(N, pP)
+    LM = LagrangesMethod(Lag, [q1, q2], hol_coneqs=f_c,
+            forcelist=[(P, m*g*N.x)], frame=N)
+    LM.form_lagranges_equations()
+    # Check solution
+    lam1 = LM.lam_vec[0, 0]
+    eom_sol = Matrix([[m*Derivative(q1, t, t) - 9.8*m + 2*lam1*q1],
+                      [m*Derivative(q2, t, t) + 2*lam1*q2]])
+    assert LM.eom == eom_sol
+    # Check multiplier solution
+    lam_sol = Matrix([(19.6*q1 + 2*q1d**2 + 2*q2d**2)/(4*q1**2/m + 4*q2**2/m)])
+    assert simplify(LM.solve_multipliers(sol_type='Matrix')) == simplify(lam_sol)
+
+
+def test_dub_pen():
+
+    # The system considered is the double pendulum. Like in the
+    # test of the simple pendulum above, we begin by creating the generalized
+    # coordinates and the simple generalized speeds and accelerations which
+    # will be used later. Following this we create frames and points necessary
+    # for the kinematics. The procedure isn't explicitly explained as this is
+    # similar to the simple  pendulum. Also this is documented on the pydy.org
+    # website.
+    q1, q2 = dynamicsymbols('q1 q2')
+    q1d, q2d = dynamicsymbols('q1 q2', 1)
+    q1dd, q2dd = dynamicsymbols('q1 q2', 2)
+    u1, u2 = dynamicsymbols('u1 u2')
+    u1d, u2d = dynamicsymbols('u1 u2', 1)
+    l, m, g = symbols('l m g')
+
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [q1, N.z])
+    B = N.orientnew('B', 'Axis', [q2, N.z])
+
+    A.set_ang_vel(N, q1d * A.z)
+    B.set_ang_vel(N, q2d * A.z)
+
+    O = Point('O')
+    P = O.locatenew('P', l * A.x)
+    R = P.locatenew('R', l * B.x)
+
+    O.set_vel(N, 0)
+    P.v2pt_theory(O, N, A)
+    R.v2pt_theory(P, N, B)
+
+    ParP = Particle('ParP', P, m)
+    ParR = Particle('ParR', R, m)
+
+    ParP.potential_energy = - m * g * l * cos(q1)
+    ParR.potential_energy = - m * g * l * cos(q1) - m * g * l * cos(q2)
+    L = Lagrangian(N, ParP, ParR)
+    lm = LagrangesMethod(L, [q1, q2], bodies=[ParP, ParR])
+    lm.form_lagranges_equations()
+
+    assert simplify(l*m*(2*g*sin(q1) + l*sin(q1)*sin(q2)*q2dd
+        + l*sin(q1)*cos(q2)*q2d**2 - l*sin(q2)*cos(q1)*q2d**2
+        + l*cos(q1)*cos(q2)*q2dd + 2*l*q1dd) - lm.eom[0]) == 0
+    assert simplify(l*m*(g*sin(q2) + l*sin(q1)*sin(q2)*q1dd
+        - l*sin(q1)*cos(q2)*q1d**2 + l*sin(q2)*cos(q1)*q1d**2
+        + l*cos(q1)*cos(q2)*q1dd + l*q2dd) - lm.eom[1]) == 0
+    assert lm.bodies == [ParP, ParR]
+
+
+def test_rolling_disc():
+    # Rolling Disc Example
+    # Here the rolling disc is formed from the contact point up, removing the
+    # need to introduce generalized speeds. Only 3 configuration and 3
+    # speed variables are need to describe this system, along with the
+    # disc's mass and radius, and the local gravity.
+    q1, q2, q3 = dynamicsymbols('q1 q2 q3')
+    q1d, q2d, q3d = dynamicsymbols('q1 q2 q3', 1)
+    r, m, g = symbols('r m g')
+
+    # The kinematics are formed by a series of simple rotations. Each simple
+    # rotation creates a new frame, and the next rotation is defined by the new
+    # frame's basis vectors. This example uses a 3-1-2 series of rotations, or
+    # Z, X, Y series of rotations. Angular velocity for this is defined using
+    # the second frame's basis (the lean frame).
+    N = ReferenceFrame('N')
+    Y = N.orientnew('Y', 'Axis', [q1, N.z])
+    L = Y.orientnew('L', 'Axis', [q2, Y.x])
+    R = L.orientnew('R', 'Axis', [q3, L.y])
+
+    # This is the translational kinematics. We create a point with no velocity
+    # in N; this is the contact point between the disc and ground. Next we form
+    # the position vector from the contact point to the disc's center of mass.
+    # Finally we form the velocity and acceleration of the disc.
+    C = Point('C')
+    C.set_vel(N, 0)
+    Dmc = C.locatenew('Dmc', r * L.z)
+    Dmc.v2pt_theory(C, N, R)
+
+    # Forming the inertia dyadic.
+    I = inertia(L, m/4 * r**2, m/2 * r**2, m/4 * r**2)
+    BodyD = RigidBody('BodyD', Dmc, R, m, (I, Dmc))
+
+    # Finally we form the equations of motion, using the same steps we did
+    # before. Supply the Lagrangian, the generalized speeds.
+    BodyD.potential_energy = - m * g * r * cos(q2)
+    Lag = Lagrangian(N, BodyD)
+    q = [q1, q2, q3]
+    q1 = Function('q1')
+    q2 = Function('q2')
+    q3 = Function('q3')
+    l = LagrangesMethod(Lag, q)
+    l.form_lagranges_equations()
+    RHS = l.rhs()
+    RHS.simplify()
+    t = symbols('t')
+
+    assert (l.mass_matrix[3:6] == [0, 5*m*r**2/4, 0])
+    assert RHS[4].simplify() == (
+        (-8*g*sin(q2(t)) + r*(5*sin(2*q2(t))*Derivative(q1(t), t) +
+        12*cos(q2(t))*Derivative(q3(t), t))*Derivative(q1(t), t))/(10*r))
+    assert RHS[5] == (-5*cos(q2(t))*Derivative(q1(t), t) + 6*tan(q2(t)
+        )*Derivative(q3(t), t) + 4*Derivative(q1(t), t)/cos(q2(t))
+        )*Derivative(q2(t), t)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_lagrange2.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_lagrange2.py
new file mode 100644
index 0000000000000000000000000000000000000000..7602df157e9beb13db1dbb68a2980765cdc49bf2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_lagrange2.py
@@ -0,0 +1,46 @@
+from sympy import symbols
+from sympy.physics.mechanics import dynamicsymbols
+from sympy.physics.mechanics import ReferenceFrame, Point, Particle
+from sympy.physics.mechanics import LagrangesMethod, Lagrangian
+
+### This test asserts that a system with more than one external forces
+### is accurately formed with Lagrange method (see issue #8626)
+
+def test_lagrange_2forces():
+    ### Equations for two damped springs in series with two forces
+
+    ### generalized coordinates
+    q1, q2 = dynamicsymbols('q1, q2')
+    ### generalized speeds
+    q1d, q2d = dynamicsymbols('q1, q2', 1)
+
+    ### Mass, spring strength, friction coefficient
+    m, k, nu = symbols('m, k, nu')
+
+    N = ReferenceFrame('N')
+    O = Point('O')
+
+    ### Two points
+    P1 = O.locatenew('P1', q1 * N.x)
+    P1.set_vel(N, q1d * N.x)
+    P2 = O.locatenew('P1', q2 * N.x)
+    P2.set_vel(N, q2d * N.x)
+
+    pP1 = Particle('pP1', P1, m)
+    pP1.potential_energy = k * q1**2 / 2
+
+    pP2 = Particle('pP2', P2, m)
+    pP2.potential_energy = k * (q1 - q2)**2 / 2
+
+    #### Friction forces
+    forcelist = [(P1, - nu * q1d * N.x),
+                 (P2, - nu * q2d * N.x)]
+    lag = Lagrangian(N, pP1, pP2)
+
+    l_method = LagrangesMethod(lag, (q1, q2), forcelist=forcelist, frame=N)
+    l_method.form_lagranges_equations()
+
+    eq1 = l_method.eom[0]
+    assert eq1.diff(q1d) == nu
+    eq2 = l_method.eom[1]
+    assert eq2.diff(q2d) == nu
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearity_of_velocity_constraints.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearity_of_velocity_constraints.py
new file mode 100644
index 0000000000000000000000000000000000000000..33c9e7ec070a3e6db2a6e26697d670964b0a32b9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearity_of_velocity_constraints.py
@@ -0,0 +1,41 @@
+from sympy import symbols, sin, cos
+from sympy.physics.mechanics import (dynamicsymbols, ReferenceFrame, Point,
+            KanesMethod)
+from sympy.testing import pytest
+from sympy.solvers.solveset import NonlinearError
+
+def test_linearity_of_motion_constraints():
+    # Test that an error is raised by KanesMethod if nonlinear velocity
+    # constraints are supplied.
+    # It is a simple pendulum.
+    t = dynamicsymbols._t
+    N, A = ReferenceFrame('N'), ReferenceFrame('A')
+    O, P = Point('O'), Point('P')
+    O.set_vel(N, 0)
+
+    l = symbols('l')
+    q, x, y, u, ux, uy = dynamicsymbols('q x y u ux uy')
+
+    A.orient_axis(N, q, N.z)
+    A.set_ang_vel(N, u * N.z)
+    P.set_pos(O, -l * A.y)
+    P.v2pt_theory(O, N, A)
+
+    kd = [u - q.diff(t), ux - x.diff(t), uy - y.diff(t)]
+    config_constr = [x - l * sin(q), y - l * cos(q)]
+
+    q_ind = [q]
+    q_dep = [x, y]
+    u_ind = [u]
+    u_dep = [ux, uy]
+
+    # Make sure an error is raised if nonlinear velocity constraints are
+    # supplied.
+    speed_constr = [ux - l * q.diff(t) * cos(q), sin(uy) +
+        l * q.diff(t) * sin(q)]
+
+    with pytest.raises(NonlinearError):
+        KanesMethod(N, q_ind=q_ind, q_dependent=q_dep, u_ind=u_ind,
+            u_dependent=u_dep, kd_eqs=kd,
+            configuration_constraints=config_constr,
+            velocity_constraints=speed_constr)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearize.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearize.py
new file mode 100644
index 0000000000000000000000000000000000000000..ec62b960b71d7fce5a5504478431ca23eb371fe0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearize.py
@@ -0,0 +1,372 @@
+from sympy import symbols, Matrix, cos, sin, atan, sqrt, Rational
+from sympy.core.sympify import sympify
+from sympy.simplify.simplify import simplify
+from sympy.solvers.solvers import solve
+from sympy.physics.mechanics import dynamicsymbols, ReferenceFrame, Point,\
+    dot, cross, inertia, KanesMethod, Particle, RigidBody, Lagrangian,\
+    LagrangesMethod
+from sympy.testing.pytest import slow
+
+
+@slow
+def test_linearize_rolling_disc_kane():
+    # Symbols for time and constant parameters
+    t, r, m, g, v = symbols('t r m g v')
+
+    # Configuration variables and their time derivatives
+    q1, q2, q3, q4, q5, q6 = q = dynamicsymbols('q1:7')
+    q1d, q2d, q3d, q4d, q5d, q6d = qd = [qi.diff(t) for qi in q]
+
+    # Generalized speeds and their time derivatives
+    u = dynamicsymbols('u:6')
+    u1, u2, u3, u4, u5, u6 = u = dynamicsymbols('u1:7')
+    u1d, u2d, u3d, u4d, u5d, u6d = [ui.diff(t) for ui in u]
+
+    # Reference frames
+    N = ReferenceFrame('N')                   # Inertial frame
+    NO = Point('NO')                          # Inertial origin
+    A = N.orientnew('A', 'Axis', [q1, N.z])   # Yaw intermediate frame
+    B = A.orientnew('B', 'Axis', [q2, A.x])   # Lean intermediate frame
+    C = B.orientnew('C', 'Axis', [q3, B.y])   # Disc fixed frame
+    CO = NO.locatenew('CO', q4*N.x + q5*N.y + q6*N.z)      # Disc center
+
+    # Disc angular velocity in N expressed using time derivatives of coordinates
+    w_c_n_qd = C.ang_vel_in(N)
+    w_b_n_qd = B.ang_vel_in(N)
+
+    # Inertial angular velocity and angular acceleration of disc fixed frame
+    C.set_ang_vel(N, u1*B.x + u2*B.y + u3*B.z)
+
+    # Disc center velocity in N expressed using time derivatives of coordinates
+    v_co_n_qd = CO.pos_from(NO).dt(N)
+
+    # Disc center velocity in N expressed using generalized speeds
+    CO.set_vel(N, u4*C.x + u5*C.y + u6*C.z)
+
+    # Disc Ground Contact Point
+    P = CO.locatenew('P', r*B.z)
+    P.v2pt_theory(CO, N, C)
+
+    # Configuration constraint
+    f_c = Matrix([q6 - dot(CO.pos_from(P), N.z)])
+
+    # Velocity level constraints
+    f_v = Matrix([dot(P.vel(N), uv) for uv in C])
+
+    # Kinematic differential equations
+    kindiffs = Matrix([dot(w_c_n_qd - C.ang_vel_in(N), uv) for uv in B] +
+                        [dot(v_co_n_qd - CO.vel(N), uv) for uv in N])
+    qdots = solve(kindiffs, qd)
+
+    # Set angular velocity of remaining frames
+    B.set_ang_vel(N, w_b_n_qd.subs(qdots))
+    C.set_ang_acc(N, C.ang_vel_in(N).dt(B) + cross(B.ang_vel_in(N), C.ang_vel_in(N)))
+
+    # Active forces
+    F_CO = m*g*A.z
+
+    # Create inertia dyadic of disc C about point CO
+    I = (m * r**2) / 4
+    J = (m * r**2) / 2
+    I_C_CO = inertia(C, I, J, I)
+
+    Disc = RigidBody('Disc', CO, C, m, (I_C_CO, CO))
+    BL = [Disc]
+    FL = [(CO, F_CO)]
+    KM = KanesMethod(N, [q1, q2, q3, q4, q5], [u1, u2, u3], kd_eqs=kindiffs,
+            q_dependent=[q6], configuration_constraints=f_c,
+            u_dependent=[u4, u5, u6], velocity_constraints=f_v)
+    (fr, fr_star) = KM.kanes_equations(BL, FL)
+
+    # Test generalized form equations
+    linearizer = KM.to_linearizer()
+    assert linearizer.f_c == f_c
+    assert linearizer.f_v == f_v
+    assert linearizer.f_a == f_v.diff(t).subs(KM.kindiffdict())
+    sol = solve(linearizer.f_0 + linearizer.f_1, qd)
+    for qi in qdots.keys():
+        assert sol[qi] == qdots[qi]
+    assert simplify(linearizer.f_2 + linearizer.f_3 - fr - fr_star) == Matrix([0, 0, 0])
+
+    # Perform the linearization
+    # Precomputed operating point
+    q_op = {q6: -r*cos(q2)}
+    u_op = {u1: 0,
+            u2: sin(q2)*q1d + q3d,
+            u3: cos(q2)*q1d,
+            u4: -r*(sin(q2)*q1d + q3d)*cos(q3),
+            u5: 0,
+            u6: -r*(sin(q2)*q1d + q3d)*sin(q3)}
+    qd_op = {q2d: 0,
+             q4d: -r*(sin(q2)*q1d + q3d)*cos(q1),
+             q5d: -r*(sin(q2)*q1d + q3d)*sin(q1),
+             q6d: 0}
+    ud_op = {u1d: 4*g*sin(q2)/(5*r) + sin(2*q2)*q1d**2/2 + 6*cos(q2)*q1d*q3d/5,
+             u2d: 0,
+             u3d: 0,
+             u4d: r*(sin(q2)*sin(q3)*q1d*q3d + sin(q3)*q3d**2),
+             u5d: r*(4*g*sin(q2)/(5*r) + sin(2*q2)*q1d**2/2 + 6*cos(q2)*q1d*q3d/5),
+             u6d: -r*(sin(q2)*cos(q3)*q1d*q3d + cos(q3)*q3d**2)}
+
+    A, B = linearizer.linearize(op_point=[q_op, u_op, qd_op, ud_op], A_and_B=True, simplify=True)
+
+    upright_nominal = {q1d: 0, q2: 0, m: 1, r: 1, g: 1}
+
+    # Precomputed solution
+    A_sol = Matrix([[0, 0, 0, 0, 0, 0, 0, 1],
+                    [0, 0, 0, 0, 0, 1, 0, 0],
+                    [0, 0, 0, 0, 0, 0, 1, 0],
+                    [sin(q1)*q3d, 0, 0, 0, 0, -sin(q1), -cos(q1), 0],
+                    [-cos(q1)*q3d, 0, 0, 0, 0, cos(q1), -sin(q1), 0],
+                    [0, Rational(4, 5), 0, 0, 0, 0, 0, 6*q3d/5],
+                    [0, 0, 0, 0, 0, 0, 0, 0],
+                    [0, 0, 0, 0, 0, -2*q3d, 0, 0]])
+    B_sol = Matrix([])
+
+    # Check that linearization is correct
+    assert A.subs(upright_nominal) == A_sol
+    assert B.subs(upright_nominal) == B_sol
+
+    # Check eigenvalues at critical speed are all zero:
+    assert sympify(A.subs(upright_nominal).subs(q3d, 1/sqrt(3))).eigenvals() == {0: 8}
+
+    # Check whether alternative solvers work
+    # symengine doesn't support method='GJ'
+    linearizer = KM.to_linearizer(linear_solver='GJ')
+    A, B = linearizer.linearize(op_point=[q_op, u_op, qd_op, ud_op],
+                                A_and_B=True, simplify=True)
+    assert A.subs(upright_nominal) == A_sol
+    assert B.subs(upright_nominal) == B_sol
+
+def test_linearize_pendulum_kane_minimal():
+    q1 = dynamicsymbols('q1')                     # angle of pendulum
+    u1 = dynamicsymbols('u1')                     # Angular velocity
+    q1d = dynamicsymbols('q1', 1)                 # Angular velocity
+    L, m, t = symbols('L, m, t')
+    g = 9.8
+
+    # Compose world frame
+    N = ReferenceFrame('N')
+    pN = Point('N*')
+    pN.set_vel(N, 0)
+
+    # A.x is along the pendulum
+    A = N.orientnew('A', 'axis', [q1, N.z])
+    A.set_ang_vel(N, u1*N.z)
+
+    # Locate point P relative to the origin N*
+    P = pN.locatenew('P', L*A.x)
+    P.v2pt_theory(pN, N, A)
+    pP = Particle('pP', P, m)
+
+    # Create Kinematic Differential Equations
+    kde = Matrix([q1d - u1])
+
+    # Input the force resultant at P
+    R = m*g*N.x
+
+    # Solve for eom with kanes method
+    KM = KanesMethod(N, q_ind=[q1], u_ind=[u1], kd_eqs=kde)
+    (fr, frstar) = KM.kanes_equations([pP], [(P, R)])
+
+    # Linearize
+    A, B, inp_vec = KM.linearize(A_and_B=True, simplify=True)
+
+    assert A == Matrix([[0, 1], [-9.8*cos(q1)/L, 0]])
+    assert B == Matrix([])
+
+def test_linearize_pendulum_kane_nonminimal():
+    # Create generalized coordinates and speeds for this non-minimal realization
+    # q1, q2 = N.x and N.y coordinates of pendulum
+    # u1, u2 = N.x and N.y velocities of pendulum
+    q1, q2 = dynamicsymbols('q1:3')
+    q1d, q2d = dynamicsymbols('q1:3', level=1)
+    u1, u2 = dynamicsymbols('u1:3')
+    u1d, u2d = dynamicsymbols('u1:3', level=1)
+    L, m, t = symbols('L, m, t')
+    g = 9.8
+
+    # Compose world frame
+    N = ReferenceFrame('N')
+    pN = Point('N*')
+    pN.set_vel(N, 0)
+
+    # A.x is along the pendulum
+    theta1 = atan(q2/q1)
+    A = N.orientnew('A', 'axis', [theta1, N.z])
+
+    # Locate the pendulum mass
+    P = pN.locatenew('P1', q1*N.x + q2*N.y)
+    pP = Particle('pP', P, m)
+
+    # Calculate the kinematic differential equations
+    kde = Matrix([q1d - u1,
+                  q2d - u2])
+    dq_dict = solve(kde, [q1d, q2d])
+
+    # Set velocity of point P
+    P.set_vel(N, P.pos_from(pN).dt(N).subs(dq_dict))
+
+    # Configuration constraint is length of pendulum
+    f_c = Matrix([P.pos_from(pN).magnitude() - L])
+
+    # Velocity constraint is that the velocity in the A.x direction is
+    # always zero (the pendulum is never getting longer).
+    f_v = Matrix([P.vel(N).express(A).dot(A.x)])
+    f_v.simplify()
+
+    # Acceleration constraints is the time derivative of the velocity constraint
+    f_a = f_v.diff(t)
+    f_a.simplify()
+
+    # Input the force resultant at P
+    R = m*g*N.x
+
+    # Derive the equations of motion using the KanesMethod class.
+    KM = KanesMethod(N, q_ind=[q2], u_ind=[u2], q_dependent=[q1],
+            u_dependent=[u1], configuration_constraints=f_c,
+            velocity_constraints=f_v, acceleration_constraints=f_a, kd_eqs=kde)
+    (fr, frstar) = KM.kanes_equations([pP], [(P, R)])
+
+    # Set the operating point to be straight down, and non-moving
+    q_op = {q1: L, q2: 0}
+    u_op = {u1: 0, u2: 0}
+    ud_op = {u1d: 0, u2d: 0}
+
+    A, B, inp_vec = KM.linearize(op_point=[q_op, u_op, ud_op], A_and_B=True,
+                                 simplify=True)
+
+    assert A.expand() == Matrix([[0, 1], [-9.8/L, 0]])
+    assert B == Matrix([])
+
+
+    # symengine doesn't support method='GJ'
+    A, B, inp_vec = KM.linearize(op_point=[q_op, u_op, ud_op], A_and_B=True,
+                                simplify=True, linear_solver='GJ')
+
+    assert A.expand() == Matrix([[0, 1], [-9.8/L, 0]])
+    assert B == Matrix([])
+
+    A, B, inp_vec = KM.linearize(op_point=[q_op, u_op, ud_op],
+                                 A_and_B=True,
+                                 simplify=True,
+                                 linear_solver=lambda A, b: A.LUsolve(b))
+
+    assert A.expand() == Matrix([[0, 1], [-9.8/L, 0]])
+    assert B == Matrix([])
+
+
+def test_linearize_pendulum_lagrange_minimal():
+    q1 = dynamicsymbols('q1')                     # angle of pendulum
+    q1d = dynamicsymbols('q1', 1)                 # Angular velocity
+    L, m, t = symbols('L, m, t')
+    g = 9.8
+
+    # Compose world frame
+    N = ReferenceFrame('N')
+    pN = Point('N*')
+    pN.set_vel(N, 0)
+
+    # A.x is along the pendulum
+    A = N.orientnew('A', 'axis', [q1, N.z])
+    A.set_ang_vel(N, q1d*N.z)
+
+    # Locate point P relative to the origin N*
+    P = pN.locatenew('P', L*A.x)
+    P.v2pt_theory(pN, N, A)
+    pP = Particle('pP', P, m)
+
+    # Solve for eom with Lagranges method
+    Lag = Lagrangian(N, pP)
+    LM = LagrangesMethod(Lag, [q1], forcelist=[(P, m*g*N.x)], frame=N)
+    LM.form_lagranges_equations()
+
+    # Linearize
+    A, B, inp_vec = LM.linearize([q1], [q1d], A_and_B=True)
+
+    assert simplify(A) == Matrix([[0, 1], [-9.8*cos(q1)/L, 0]])
+    assert B == Matrix([])
+
+    # Check an alternative solver
+    A, B, inp_vec = LM.linearize([q1], [q1d], A_and_B=True, linear_solver='GJ')
+
+    assert simplify(A) == Matrix([[0, 1], [-9.8*cos(q1)/L, 0]])
+    assert B == Matrix([])
+
+
+def test_linearize_pendulum_lagrange_nonminimal():
+    q1, q2 = dynamicsymbols('q1:3')
+    q1d, q2d = dynamicsymbols('q1:3', level=1)
+    L, m, t = symbols('L, m, t')
+    g = 9.8
+    # Compose World Frame
+    N = ReferenceFrame('N')
+    pN = Point('N*')
+    pN.set_vel(N, 0)
+    # A.x is along the pendulum
+    theta1 = atan(q2/q1)
+    A = N.orientnew('A', 'axis', [theta1, N.z])
+    # Create point P, the pendulum mass
+    P = pN.locatenew('P1', q1*N.x + q2*N.y)
+    P.set_vel(N, P.pos_from(pN).dt(N))
+    pP = Particle('pP', P, m)
+    # Constraint Equations
+    f_c = Matrix([q1**2 + q2**2 - L**2])
+    # Calculate the lagrangian, and form the equations of motion
+    Lag = Lagrangian(N, pP)
+    LM = LagrangesMethod(Lag, [q1, q2], hol_coneqs=f_c, forcelist=[(P, m*g*N.x)], frame=N)
+    LM.form_lagranges_equations()
+    # Compose operating point
+    op_point = {q1: L, q2: 0, q1d: 0, q2d: 0, q1d.diff(t): 0, q2d.diff(t): 0}
+    # Solve for multiplier operating point
+    lam_op = LM.solve_multipliers(op_point=op_point)
+    op_point.update(lam_op)
+    # Perform the Linearization
+    A, B, inp_vec = LM.linearize([q2], [q2d], [q1], [q1d],
+            op_point=op_point, A_and_B=True)
+    assert simplify(A) == Matrix([[0, 1], [-9.8/L, 0]])
+    assert B == Matrix([])
+
+    # Check if passing a function to linear_solver works
+    A, B, inp_vec = LM.linearize([q2], [q2d], [q1], [q1d], op_point=op_point,
+                                 A_and_B=True, linear_solver=lambda A, b:
+                                 A.LUsolve(b))
+    assert simplify(A) == Matrix([[0, 1], [-9.8/L, 0]])
+    assert B == Matrix([])
+
+def test_linearize_rolling_disc_lagrange():
+    q1, q2, q3 = q = dynamicsymbols('q1 q2 q3')
+    q1d, q2d, q3d = qd = dynamicsymbols('q1 q2 q3', 1)
+    r, m, g = symbols('r m g')
+
+    N = ReferenceFrame('N')
+    Y = N.orientnew('Y', 'Axis', [q1, N.z])
+    L = Y.orientnew('L', 'Axis', [q2, Y.x])
+    R = L.orientnew('R', 'Axis', [q3, L.y])
+
+    C = Point('C')
+    C.set_vel(N, 0)
+    Dmc = C.locatenew('Dmc', r * L.z)
+    Dmc.v2pt_theory(C, N, R)
+
+    I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)
+    BodyD = RigidBody('BodyD', Dmc, R, m, (I, Dmc))
+    BodyD.potential_energy = - m * g * r * cos(q2)
+
+    Lag = Lagrangian(N, BodyD)
+    l = LagrangesMethod(Lag, q)
+    l.form_lagranges_equations()
+
+    # Linearize about steady-state upright rolling
+    op_point = {q1: 0, q2: 0, q3: 0,
+                q1d: 0, q2d: 0,
+                q1d.diff(): 0, q2d.diff(): 0, q3d.diff(): 0}
+    A = l.linearize(q_ind=q, qd_ind=qd, op_point=op_point, A_and_B=True)[0]
+    sol = Matrix([[0, 0, 0, 1, 0, 0],
+                  [0, 0, 0, 0, 1, 0],
+                  [0, 0, 0, 0, 0, 1],
+                  [0, 0, 0, 0, -6*q3d, 0],
+                  [0, -4*g/(5*r), 0, 6*q3d/5, 0, 0],
+                  [0, 0, 0, 0, 0, 0]])
+
+    assert A == sol
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_loads.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_loads.py
new file mode 100644
index 0000000000000000000000000000000000000000..8aa0cec14887f0778fc1e60e7ff33830ceef72d3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_loads.py
@@ -0,0 +1,86 @@
+from pytest import raises
+
+from sympy import symbols
+from sympy.physics.mechanics import (RigidBody, Particle, ReferenceFrame, Point,
+                                     outer, dynamicsymbols, Force, Torque)
+from sympy.physics.mechanics.loads import gravity, _parse_load
+
+
+def test_force_default():
+    N = ReferenceFrame('N')
+    Po = Point('Po')
+    f1 = Force(Po, N.x)
+    assert f1.point == Po
+    assert f1.force == N.x
+    assert f1.__repr__() == 'Force(point=Po, force=N.x)'
+    # Test tuple behaviour
+    assert isinstance(f1, tuple)
+    assert f1[0] == Po
+    assert f1[1] == N.x
+    assert f1 == (Po, N.x)
+    assert f1 != (N.x, Po)
+    assert f1 != (Po, N.x + N.y)
+    assert f1 != (Point('Co'), N.x)
+    # Test body as input
+    P = Particle('P', Po)
+    f2 = Force(P, N.x)
+    assert f1 == f2
+
+
+def test_torque_default():
+    N = ReferenceFrame('N')
+    f1 = Torque(N, N.x)
+    assert f1.frame == N
+    assert f1.torque == N.x
+    assert f1.__repr__() == 'Torque(frame=N, torque=N.x)'
+    # Test tuple behaviour
+    assert isinstance(f1, tuple)
+    assert f1[0] == N
+    assert f1[1] == N.x
+    assert f1 == (N, N.x)
+    assert f1 != (N.x, N)
+    assert f1 != (N, N.x + N.y)
+    assert f1 != (ReferenceFrame('A'), N.x)
+    # Test body as input
+    rb = RigidBody('P', frame=N)
+    f2 = Torque(rb, N.x)
+    assert f1 == f2
+
+
+def test_gravity():
+    N = ReferenceFrame('N')
+    m, M, g = symbols('m M g')
+    F1, F2 = dynamicsymbols('F1 F2')
+    po = Point('po')
+    pa = Particle('pa', po, m)
+    A = ReferenceFrame('A')
+    P = Point('P')
+    I = outer(A.x, A.x)
+    B = RigidBody('B', P, A, M, (I, P))
+    forceList = [(po, F1), (P, F2)]
+    forceList.extend(gravity(g * N.y, pa, B))
+    l = [(po, F1), (P, F2), (po, g * m * N.y), (P, g * M * N.y)]
+
+    for i in range(len(l)):
+        for j in range(len(l[i])):
+            assert forceList[i][j] == l[i][j]
+
+
+def test_parse_loads():
+    N = ReferenceFrame('N')
+    po = Point('po')
+    assert _parse_load(Force(po, N.z)) == (po, N.z)
+    assert _parse_load(Torque(N, N.x)) == (N, N.x)
+    f1 = _parse_load((po, N.x))  # Test whether a force is recognized
+    assert isinstance(f1, Force)
+    assert f1 == Force(po, N.x)
+    t1 = _parse_load((N, N.y))  # Test whether a torque is recognized
+    assert isinstance(t1, Torque)
+    assert t1 == Torque(N, N.y)
+    # Bodies should be undetermined (even in case of a Particle)
+    raises(ValueError, lambda: _parse_load((Particle('pa', po), N.x)))
+    raises(ValueError, lambda: _parse_load((RigidBody('pa', po, N), N.x)))
+    # Invalid tuple length
+    raises(ValueError, lambda: _parse_load((po, N.x, po, N.x)))
+    # Invalid type
+    raises(TypeError, lambda: _parse_load([po, N.x]))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_method.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_method.py
new file mode 100644
index 0000000000000000000000000000000000000000..4a8fd5fb50c3178f5a5cdab1e80423df8b52f525
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_method.py
@@ -0,0 +1,5 @@
+from sympy.physics.mechanics.method import _Methods
+from sympy.testing.pytest import raises
+
+def test_method():
+    raises(TypeError, lambda: _Methods())
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_models.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_models.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b3d3ae89b44d774ead1a3ea641a8274ba951638
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_models.py
@@ -0,0 +1,117 @@
+import sympy.physics.mechanics.models as models
+from sympy import (cos, sin, Matrix, symbols, zeros)
+from sympy.simplify.simplify import simplify
+from sympy.physics.mechanics import (dynamicsymbols)
+
+
+def test_multi_mass_spring_damper_inputs():
+
+    c0, k0, m0 = symbols("c0 k0 m0")
+    g = symbols("g")
+    v0, x0, f0 = dynamicsymbols("v0 x0 f0")
+
+    kane1 = models.multi_mass_spring_damper(1)
+    massmatrix1 = Matrix([[m0]])
+    forcing1 = Matrix([[-c0*v0 - k0*x0]])
+    assert simplify(massmatrix1 - kane1.mass_matrix) == Matrix([0])
+    assert simplify(forcing1 - kane1.forcing) == Matrix([0])
+
+    kane2 = models.multi_mass_spring_damper(1, True)
+    massmatrix2 = Matrix([[m0]])
+    forcing2 = Matrix([[-c0*v0 + g*m0 - k0*x0]])
+    assert simplify(massmatrix2 - kane2.mass_matrix) == Matrix([0])
+    assert simplify(forcing2 - kane2.forcing) == Matrix([0])
+
+    kane3 = models.multi_mass_spring_damper(1, True, True)
+    massmatrix3 = Matrix([[m0]])
+    forcing3 = Matrix([[-c0*v0 + g*m0 - k0*x0 + f0]])
+    assert simplify(massmatrix3 - kane3.mass_matrix) == Matrix([0])
+    assert simplify(forcing3 - kane3.forcing) == Matrix([0])
+
+    kane4 = models.multi_mass_spring_damper(1, False, True)
+    massmatrix4 = Matrix([[m0]])
+    forcing4 = Matrix([[-c0*v0 - k0*x0 + f0]])
+    assert simplify(massmatrix4 - kane4.mass_matrix) == Matrix([0])
+    assert simplify(forcing4 - kane4.forcing) == Matrix([0])
+
+
+def test_multi_mass_spring_damper_higher_order():
+    c0, k0, m0 = symbols("c0 k0 m0")
+    c1, k1, m1 = symbols("c1 k1 m1")
+    c2, k2, m2 = symbols("c2 k2 m2")
+    v0, x0 = dynamicsymbols("v0 x0")
+    v1, x1 = dynamicsymbols("v1 x1")
+    v2, x2 = dynamicsymbols("v2 x2")
+
+    kane1 = models.multi_mass_spring_damper(3)
+    massmatrix1 = Matrix([[m0 + m1 + m2, m1 + m2, m2],
+                          [m1 + m2, m1 + m2, m2],
+                          [m2, m2, m2]])
+    forcing1 = Matrix([[-c0*v0 - k0*x0],
+                       [-c1*v1 - k1*x1],
+                       [-c2*v2 - k2*x2]])
+    assert simplify(massmatrix1 - kane1.mass_matrix) == zeros(3)
+    assert simplify(forcing1 - kane1.forcing) == Matrix([0, 0, 0])
+
+
+def test_n_link_pendulum_on_cart_inputs():
+    l0, m0 = symbols("l0 m0")
+    m1 = symbols("m1")
+    g = symbols("g")
+    q0, q1, F, T1 = dynamicsymbols("q0 q1 F T1")
+    u0, u1 = dynamicsymbols("u0 u1")
+
+    kane1 = models.n_link_pendulum_on_cart(1)
+    massmatrix1 = Matrix([[m0 + m1, -l0*m1*cos(q1)],
+                          [-l0*m1*cos(q1), l0**2*m1]])
+    forcing1 = Matrix([[-l0*m1*u1**2*sin(q1) + F], [g*l0*m1*sin(q1)]])
+    assert simplify(massmatrix1 - kane1.mass_matrix) == zeros(2)
+    assert simplify(forcing1 - kane1.forcing) == Matrix([0, 0])
+
+    kane2 = models.n_link_pendulum_on_cart(1, False)
+    massmatrix2 = Matrix([[m0 + m1, -l0*m1*cos(q1)],
+                          [-l0*m1*cos(q1), l0**2*m1]])
+    forcing2 = Matrix([[-l0*m1*u1**2*sin(q1)], [g*l0*m1*sin(q1)]])
+    assert simplify(massmatrix2 - kane2.mass_matrix) == zeros(2)
+    assert simplify(forcing2 - kane2.forcing) == Matrix([0, 0])
+
+    kane3 = models.n_link_pendulum_on_cart(1, False, True)
+    massmatrix3 = Matrix([[m0 + m1, -l0*m1*cos(q1)],
+                          [-l0*m1*cos(q1), l0**2*m1]])
+    forcing3 = Matrix([[-l0*m1*u1**2*sin(q1)], [g*l0*m1*sin(q1) + T1]])
+    assert simplify(massmatrix3 - kane3.mass_matrix) == zeros(2)
+    assert simplify(forcing3 - kane3.forcing) == Matrix([0, 0])
+
+    kane4 = models.n_link_pendulum_on_cart(1, True, False)
+    massmatrix4 = Matrix([[m0 + m1, -l0*m1*cos(q1)],
+                          [-l0*m1*cos(q1), l0**2*m1]])
+    forcing4 = Matrix([[-l0*m1*u1**2*sin(q1) + F], [g*l0*m1*sin(q1)]])
+    assert simplify(massmatrix4 - kane4.mass_matrix) == zeros(2)
+    assert simplify(forcing4 - kane4.forcing) == Matrix([0, 0])
+
+
+def test_n_link_pendulum_on_cart_higher_order():
+    l0, m0 = symbols("l0 m0")
+    l1, m1 = symbols("l1 m1")
+    m2 = symbols("m2")
+    g = symbols("g")
+    q0, q1, q2 = dynamicsymbols("q0 q1 q2")
+    u0, u1, u2 = dynamicsymbols("u0 u1 u2")
+    F, T1 = dynamicsymbols("F T1")
+
+    kane1 = models.n_link_pendulum_on_cart(2)
+    massmatrix1 = Matrix([[m0 + m1 + m2, -l0*m1*cos(q1) - l0*m2*cos(q1),
+                           -l1*m2*cos(q2)],
+                          [-l0*m1*cos(q1) - l0*m2*cos(q1), l0**2*m1 + l0**2*m2,
+                           l0*l1*m2*(sin(q1)*sin(q2) + cos(q1)*cos(q2))],
+                          [-l1*m2*cos(q2),
+                           l0*l1*m2*(sin(q1)*sin(q2) + cos(q1)*cos(q2)),
+                           l1**2*m2]])
+    forcing1 = Matrix([[-l0*m1*u1**2*sin(q1) - l0*m2*u1**2*sin(q1) -
+                        l1*m2*u2**2*sin(q2) + F],
+                       [g*l0*m1*sin(q1) + g*l0*m2*sin(q1) -
+                        l0*l1*m2*(sin(q1)*cos(q2) - sin(q2)*cos(q1))*u2**2],
+                       [g*l1*m2*sin(q2) - l0*l1*m2*(-sin(q1)*cos(q2) +
+                                                    sin(q2)*cos(q1))*u1**2]])
+    assert simplify(massmatrix1 - kane1.mass_matrix) == zeros(3)
+    assert simplify(forcing1 - kane1.forcing) == Matrix([0, 0, 0])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_particle.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_particle.py
new file mode 100644
index 0000000000000000000000000000000000000000..8eec80275b532055eacaf2339a276c0fd19b330a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_particle.py
@@ -0,0 +1,78 @@
+from sympy import symbols
+from sympy.physics.mechanics import Point, Particle, ReferenceFrame, inertia
+from sympy.physics.mechanics.body_base import BodyBase
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+def test_particle_default():
+    # Test default
+    p = Particle('P')
+    assert p.name == 'P'
+    assert p.mass == symbols('P_mass')
+    assert p.masscenter.name == 'P_masscenter'
+    assert p.potential_energy == 0
+    assert p.__str__() == 'P'
+    assert p.__repr__() == ("Particle('P', masscenter=P_masscenter, "
+                            "mass=P_mass)")
+    raises(AttributeError, lambda: p.frame)
+
+
+def test_particle():
+    # Test initializing with parameters
+    m, m2, v1, v2, v3, r, g, h = symbols('m m2 v1 v2 v3 r g h')
+    P = Point('P')
+    P2 = Point('P2')
+    p = Particle('pa', P, m)
+    assert isinstance(p, BodyBase)
+    assert p.mass == m
+    assert p.point == P
+    # Test the mass setter
+    p.mass = m2
+    assert p.mass == m2
+    # Test the point setter
+    p.point = P2
+    assert p.point == P2
+    # Test the linear momentum function
+    N = ReferenceFrame('N')
+    O = Point('O')
+    P2.set_pos(O, r * N.y)
+    P2.set_vel(N, v1 * N.x)
+    raises(TypeError, lambda: Particle(P, P, m))
+    raises(TypeError, lambda: Particle('pa', m, m))
+    assert p.linear_momentum(N) == m2 * v1 * N.x
+    assert p.angular_momentum(O, N) == -m2 * r * v1 * N.z
+    P2.set_vel(N, v2 * N.y)
+    assert p.linear_momentum(N) == m2 * v2 * N.y
+    assert p.angular_momentum(O, N) == 0
+    P2.set_vel(N, v3 * N.z)
+    assert p.linear_momentum(N) == m2 * v3 * N.z
+    assert p.angular_momentum(O, N) == m2 * r * v3 * N.x
+    P2.set_vel(N, v1 * N.x + v2 * N.y + v3 * N.z)
+    assert p.linear_momentum(N) == m2 * (v1 * N.x + v2 * N.y + v3 * N.z)
+    assert p.angular_momentum(O, N) == m2 * r * (v3 * N.x - v1 * N.z)
+    p.potential_energy = m * g * h
+    assert p.potential_energy == m * g * h
+    # TODO make the result not be system-dependent
+    assert p.kinetic_energy(
+        N) in [m2 * (v1 ** 2 + v2 ** 2 + v3 ** 2) / 2,
+               m2 * v1 ** 2 / 2 + m2 * v2 ** 2 / 2 + m2 * v3 ** 2 / 2]
+
+
+def test_parallel_axis():
+    N = ReferenceFrame('N')
+    m, a, b = symbols('m, a, b')
+    o = Point('o')
+    p = o.locatenew('p', a * N.x + b * N.y)
+    P = Particle('P', o, m)
+    Ip = P.parallel_axis(p, N)
+    Ip_expected = inertia(N, m * b ** 2, m * a ** 2, m * (a ** 2 + b ** 2),
+                          ixy=-m * a * b)
+    assert Ip == Ip_expected
+
+
+def test_deprecated_set_potential_energy():
+    m, g, h = symbols('m g h')
+    P = Point('P')
+    p = Particle('pa', P, m)
+    with warns_deprecated_sympy():
+        p.set_potential_energy(m * g * h)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_pathway.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_pathway.py
new file mode 100644
index 0000000000000000000000000000000000000000..49dc4bd4d61300745833f9d32f3a91d9054c4839
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_pathway.py
@@ -0,0 +1,691 @@
+"""Tests for the ``sympy.physics.mechanics.pathway.py`` module."""
+
+import pytest
+
+from sympy import (
+    Rational,
+    Symbol,
+    cos,
+    pi,
+    sin,
+    sqrt,
+)
+from sympy.physics.mechanics import (
+    Force,
+    LinearPathway,
+    ObstacleSetPathway,
+    PathwayBase,
+    Point,
+    ReferenceFrame,
+    WrappingCylinder,
+    WrappingGeometryBase,
+    WrappingPathway,
+    WrappingSphere,
+    dynamicsymbols,
+)
+from sympy.simplify.simplify import simplify
+
+
+def _simplify_loads(loads):
+    return [
+        load.__class__(load.location, load.vector.simplify())
+        for load in loads
+    ]
+
+
+class TestLinearPathway:
+
+    def test_is_pathway_base_subclass(self):
+        assert issubclass(LinearPathway, PathwayBase)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'args, kwargs',
+        [
+            ((Point('pA'), Point('pB')), {}),
+        ]
+    )
+    def test_valid_constructor(args, kwargs):
+        pointA, pointB = args
+        instance = LinearPathway(*args, **kwargs)
+        assert isinstance(instance, LinearPathway)
+        assert hasattr(instance, 'attachments')
+        assert len(instance.attachments) == 2
+        assert instance.attachments[0] is pointA
+        assert instance.attachments[1] is pointB
+        assert isinstance(instance.attachments[0], Point)
+        assert instance.attachments[0].name == 'pA'
+        assert isinstance(instance.attachments[1], Point)
+        assert instance.attachments[1].name == 'pB'
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'attachments',
+        [
+            (Point('pA'), ),
+            (Point('pA'), Point('pB'), Point('pZ')),
+        ]
+    )
+    def test_invalid_attachments_incorrect_number(attachments):
+        with pytest.raises(ValueError):
+            _ = LinearPathway(*attachments)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'attachments',
+        [
+            (None, Point('pB')),
+            (Point('pA'), None),
+        ]
+    )
+    def test_invalid_attachments_not_point(attachments):
+        with pytest.raises(TypeError):
+            _ = LinearPathway(*attachments)
+
+    @pytest.fixture(autouse=True)
+    def _linear_pathway_fixture(self):
+        self.N = ReferenceFrame('N')
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.pathway = LinearPathway(self.pA, self.pB)
+        self.q1 = dynamicsymbols('q1')
+        self.q2 = dynamicsymbols('q2')
+        self.q3 = dynamicsymbols('q3')
+        self.q1d = dynamicsymbols('q1', 1)
+        self.q2d = dynamicsymbols('q2', 1)
+        self.q3d = dynamicsymbols('q3', 1)
+        self.F = Symbol('F')
+
+    def test_properties_are_immutable(self):
+        instance = LinearPathway(self.pA, self.pB)
+        with pytest.raises(AttributeError):
+            instance.attachments = None
+        with pytest.raises(TypeError):
+            instance.attachments[0] = None
+        with pytest.raises(TypeError):
+            instance.attachments[1] = None
+
+    def test_repr(self):
+        pathway = LinearPathway(self.pA, self.pB)
+        expected = 'LinearPathway(pA, pB)'
+        assert repr(pathway) == expected
+
+    def test_static_pathway_length(self):
+        self.pB.set_pos(self.pA, 2*self.N.x)
+        assert self.pathway.length == 2
+
+    def test_static_pathway_extension_velocity(self):
+        self.pB.set_pos(self.pA, 2*self.N.x)
+        assert self.pathway.extension_velocity == 0
+
+    def test_static_pathway_to_loads(self):
+        self.pB.set_pos(self.pA, 2*self.N.x)
+        expected = [
+            (self.pA, - self.F*self.N.x),
+            (self.pB, self.F*self.N.x),
+        ]
+        assert self.pathway.to_loads(self.F) == expected
+
+    def test_2D_pathway_length(self):
+        self.pB.set_pos(self.pA, 2*self.q1*self.N.x)
+        expected = 2*sqrt(self.q1**2)
+        assert self.pathway.length == expected
+
+    def test_2D_pathway_extension_velocity(self):
+        self.pB.set_pos(self.pA, 2*self.q1*self.N.x)
+        expected = 2*sqrt(self.q1**2)*self.q1d/self.q1
+        assert self.pathway.extension_velocity == expected
+
+    def test_2D_pathway_to_loads(self):
+        self.pB.set_pos(self.pA, 2*self.q1*self.N.x)
+        expected = [
+            (self.pA, - self.F*(self.q1 / sqrt(self.q1**2))*self.N.x),
+            (self.pB, self.F*(self.q1 / sqrt(self.q1**2))*self.N.x),
+        ]
+        assert self.pathway.to_loads(self.F) == expected
+
+    def test_3D_pathway_length(self):
+        self.pB.set_pos(
+            self.pA,
+            self.q1*self.N.x - self.q2*self.N.y + 2*self.q3*self.N.z,
+        )
+        expected = sqrt(self.q1**2 + self.q2**2 + 4*self.q3**2)
+        assert simplify(self.pathway.length - expected) == 0
+
+    def test_3D_pathway_extension_velocity(self):
+        self.pB.set_pos(
+            self.pA,
+            self.q1*self.N.x - self.q2*self.N.y + 2*self.q3*self.N.z,
+        )
+        length = sqrt(self.q1**2 + self.q2**2 + 4*self.q3**2)
+        expected = (
+            self.q1*self.q1d/length
+            + self.q2*self.q2d/length
+            + 4*self.q3*self.q3d/length
+        )
+        assert simplify(self.pathway.extension_velocity - expected) == 0
+
+    def test_3D_pathway_to_loads(self):
+        self.pB.set_pos(
+            self.pA,
+            self.q1*self.N.x - self.q2*self.N.y + 2*self.q3*self.N.z,
+        )
+        length = sqrt(self.q1**2 + self.q2**2 + 4*self.q3**2)
+        pO_force = (
+            - self.F*self.q1*self.N.x/length
+            + self.F*self.q2*self.N.y/length
+            - 2*self.F*self.q3*self.N.z/length
+        )
+        pI_force = (
+            self.F*self.q1*self.N.x/length
+            - self.F*self.q2*self.N.y/length
+            + 2*self.F*self.q3*self.N.z/length
+        )
+        expected = [
+            (self.pA, pO_force),
+            (self.pB, pI_force),
+        ]
+        assert self.pathway.to_loads(self.F) == expected
+
+
+class TestObstacleSetPathway:
+
+    def test_is_pathway_base_subclass(self):
+        assert issubclass(ObstacleSetPathway, PathwayBase)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'num_attachments, attachments',
+        [
+            (3, [Point(name) for name in ('pO', 'pA', 'pI')]),
+            (4, [Point(name) for name in ('pO', 'pA', 'pB', 'pI')]),
+            (5, [Point(name) for name in ('pO', 'pA', 'pB', 'pC', 'pI')]),
+            (6, [Point(name) for name in ('pO', 'pA', 'pB', 'pC', 'pD', 'pI')]),
+        ]
+    )
+    def test_valid_constructor(num_attachments, attachments):
+        instance = ObstacleSetPathway(*attachments)
+        assert isinstance(instance, ObstacleSetPathway)
+        assert hasattr(instance, 'attachments')
+        assert len(instance.attachments) == num_attachments
+        for attachment in instance.attachments:
+            assert isinstance(attachment, Point)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'attachments',
+        [[Point('pO')], [Point('pO'), Point('pI')]],
+    )
+    def test_invalid_constructor_attachments_incorrect_number(attachments):
+        with pytest.raises(ValueError):
+            _ = ObstacleSetPathway(*attachments)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'attachments',
+        [
+            (None, Point('pA'), Point('pI')),
+            (Point('pO'), None, Point('pI')),
+            (Point('pO'), Point('pA'), None),
+        ]
+    )
+    def test_invalid_constructor_attachments_not_point(attachments):
+        with pytest.raises(TypeError):
+            _ = WrappingPathway(*attachments)  # type: ignore
+
+    def test_properties_are_immutable(self):
+        pathway = ObstacleSetPathway(Point('pO'), Point('pA'), Point('pI'))
+        with pytest.raises(AttributeError):
+            pathway.attachments = None  # type: ignore
+        with pytest.raises(TypeError):
+            pathway.attachments[0] = None  # type: ignore
+        with pytest.raises(TypeError):
+            pathway.attachments[1] = None  # type: ignore
+        with pytest.raises(TypeError):
+            pathway.attachments[-1] = None  # type: ignore
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'attachments, expected',
+        [
+            (
+                [Point(name) for name in ('pO', 'pA', 'pI')],
+                'ObstacleSetPathway(pO, pA, pI)'
+            ),
+            (
+                [Point(name) for name in ('pO', 'pA', 'pB', 'pI')],
+                'ObstacleSetPathway(pO, pA, pB, pI)'
+            ),
+            (
+                [Point(name) for name in ('pO', 'pA', 'pB', 'pC', 'pI')],
+                'ObstacleSetPathway(pO, pA, pB, pC, pI)'
+            ),
+        ]
+    )
+    def test_repr(attachments, expected):
+        pathway = ObstacleSetPathway(*attachments)
+        assert repr(pathway) == expected
+
+    @pytest.fixture(autouse=True)
+    def _obstacle_set_pathway_fixture(self):
+        self.N = ReferenceFrame('N')
+        self.pO = Point('pO')
+        self.pI = Point('pI')
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.q = dynamicsymbols('q')
+        self.qd = dynamicsymbols('q', 1)
+        self.F = Symbol('F')
+
+    def test_static_pathway_length(self):
+        self.pA.set_pos(self.pO, self.N.x)
+        self.pB.set_pos(self.pO, self.N.y)
+        self.pI.set_pos(self.pO, self.N.z)
+        pathway = ObstacleSetPathway(self.pO, self.pA, self.pB, self.pI)
+        assert pathway.length == 1 + 2 * sqrt(2)
+
+    def test_static_pathway_extension_velocity(self):
+        self.pA.set_pos(self.pO, self.N.x)
+        self.pB.set_pos(self.pO, self.N.y)
+        self.pI.set_pos(self.pO, self.N.z)
+        pathway = ObstacleSetPathway(self.pO, self.pA, self.pB, self.pI)
+        assert pathway.extension_velocity == 0
+
+    def test_static_pathway_to_loads(self):
+        self.pA.set_pos(self.pO, self.N.x)
+        self.pB.set_pos(self.pO, self.N.y)
+        self.pI.set_pos(self.pO, self.N.z)
+        pathway = ObstacleSetPathway(self.pO, self.pA, self.pB, self.pI)
+        expected = [
+            Force(self.pO, -self.F * self.N.x),
+            Force(self.pA, self.F * self.N.x),
+            Force(self.pA, self.F * sqrt(2) / 2 * (self.N.x - self.N.y)),
+            Force(self.pB, self.F * sqrt(2) / 2 * (self.N.y - self.N.x)),
+            Force(self.pB, self.F * sqrt(2) / 2 * (self.N.y - self.N.z)),
+            Force(self.pI, self.F * sqrt(2) / 2 * (self.N.z - self.N.y)),
+        ]
+        assert pathway.to_loads(self.F) == expected
+
+    def test_2D_pathway_length(self):
+        self.pA.set_pos(self.pO, -(self.N.x + self.N.y))
+        self.pB.set_pos(
+            self.pO, cos(self.q) * self.N.x - (sin(self.q) + 1) * self.N.y
+        )
+        self.pI.set_pos(
+            self.pO, sin(self.q) * self.N.x + (cos(self.q) - 1) * self.N.y
+        )
+        pathway = ObstacleSetPathway(self.pO, self.pA, self.pB, self.pI)
+        expected = 2 * sqrt(2) + sqrt(2 + 2*cos(self.q))
+        assert (pathway.length - expected).simplify() == 0
+
+    def test_2D_pathway_extension_velocity(self):
+        self.pA.set_pos(self.pO, -(self.N.x + self.N.y))
+        self.pB.set_pos(
+            self.pO, cos(self.q) * self.N.x - (sin(self.q) + 1) * self.N.y
+        )
+        self.pI.set_pos(
+            self.pO, sin(self.q) * self.N.x + (cos(self.q) - 1) * self.N.y
+        )
+        pathway = ObstacleSetPathway(self.pO, self.pA, self.pB, self.pI)
+        expected = - (sqrt(2) * sin(self.q) * self.qd) / (2 * sqrt(cos(self.q) + 1))
+        assert (pathway.extension_velocity - expected).simplify() == 0
+
+    def test_2D_pathway_to_loads(self):
+        self.pA.set_pos(self.pO, -(self.N.x + self.N.y))
+        self.pB.set_pos(
+            self.pO, cos(self.q) * self.N.x - (sin(self.q) + 1) * self.N.y
+        )
+        self.pI.set_pos(
+            self.pO, sin(self.q) * self.N.x + (cos(self.q) - 1) * self.N.y
+        )
+        pathway = ObstacleSetPathway(self.pO, self.pA, self.pB, self.pI)
+        pO_pA_force_vec = sqrt(2) / 2 * (self.N.x + self.N.y)
+        pA_pB_force_vec = (
+            - sqrt(2 * cos(self.q) + 2) / 2 * self.N.x
+            + sqrt(2) * sin(self.q) / (2 * sqrt(cos(self.q) + 1)) * self.N.y
+        )
+        pB_pI_force_vec = cos(self.q + pi/4) * self.N.x - sin(self.q + pi/4) * self.N.y
+        expected = [
+            Force(self.pO, self.F * pO_pA_force_vec),
+            Force(self.pA, -self.F * pO_pA_force_vec),
+            Force(self.pA, self.F * pA_pB_force_vec),
+            Force(self.pB, -self.F * pA_pB_force_vec),
+            Force(self.pB, self.F * pB_pI_force_vec),
+            Force(self.pI, -self.F * pB_pI_force_vec),
+        ]
+        assert _simplify_loads(pathway.to_loads(self.F)) == expected
+
+
+class TestWrappingPathway:
+
+    def test_is_pathway_base_subclass(self):
+        assert issubclass(WrappingPathway, PathwayBase)
+
+    @pytest.fixture(autouse=True)
+    def _wrapping_pathway_fixture(self):
+        self.pA = Point('pA')
+        self.pB = Point('pB')
+        self.r = Symbol('r', positive=True)
+        self.pO = Point('pO')
+        self.N = ReferenceFrame('N')
+        self.ax = self.N.z
+        self.sphere = WrappingSphere(self.r, self.pO)
+        self.cylinder = WrappingCylinder(self.r, self.pO, self.ax)
+        self.pathway = WrappingPathway(self.pA, self.pB, self.cylinder)
+        self.F = Symbol('F')
+
+    def test_valid_constructor(self):
+        instance = WrappingPathway(self.pA, self.pB, self.cylinder)
+        assert isinstance(instance, WrappingPathway)
+        assert hasattr(instance, 'attachments')
+        assert len(instance.attachments) == 2
+        assert isinstance(instance.attachments[0], Point)
+        assert instance.attachments[0] == self.pA
+        assert isinstance(instance.attachments[1], Point)
+        assert instance.attachments[1] == self.pB
+        assert hasattr(instance, 'geometry')
+        assert isinstance(instance.geometry, WrappingGeometryBase)
+        assert instance.geometry == self.cylinder
+
+    @pytest.mark.parametrize(
+        'attachments',
+        [
+            (Point('pA'), ),
+            (Point('pA'), Point('pB'), Point('pZ')),
+        ]
+    )
+    def test_invalid_constructor_attachments_incorrect_number(self, attachments):
+        with pytest.raises(TypeError):
+            _ = WrappingPathway(*attachments, self.cylinder)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'attachments',
+        [
+            (None, Point('pB')),
+            (Point('pA'), None),
+        ]
+    )
+    def test_invalid_constructor_attachments_not_point(attachments):
+        with pytest.raises(TypeError):
+            _ = WrappingPathway(*attachments)
+
+    def test_invalid_constructor_geometry_is_not_supplied(self):
+        with pytest.raises(TypeError):
+            _ = WrappingPathway(self.pA, self.pB)
+
+    @pytest.mark.parametrize(
+        'geometry',
+        [
+            Symbol('r'),
+            dynamicsymbols('q'),
+            ReferenceFrame('N'),
+            ReferenceFrame('N').x,
+        ]
+    )
+    def test_invalid_geometry_not_geometry(self, geometry):
+        with pytest.raises(TypeError):
+            _ = WrappingPathway(self.pA, self.pB, geometry)
+
+    def test_attachments_property_is_immutable(self):
+        with pytest.raises(TypeError):
+            self.pathway.attachments[0] = self.pB
+        with pytest.raises(TypeError):
+            self.pathway.attachments[1] = self.pA
+
+    def test_geometry_property_is_immutable(self):
+        with pytest.raises(AttributeError):
+            self.pathway.geometry = None
+
+    def test_repr(self):
+        expected = (
+            f'WrappingPathway(pA, pB, '
+            f'geometry={self.cylinder!r})'
+        )
+        assert repr(self.pathway) == expected
+
+    @staticmethod
+    def _expand_pos_to_vec(pos, frame):
+        return sum(mag*unit for (mag, unit) in zip(pos, frame))
+
+    @pytest.mark.parametrize(
+        'pA_vec, pB_vec, factor',
+        [
+            ((1, 0, 0), (0, 1, 0), pi/2),
+            ((0, 1, 0), (sqrt(2)/2, -sqrt(2)/2, 0), 3*pi/4),
+            ((1, 0, 0), (Rational(1, 2), sqrt(3)/2, 0), pi/3),
+        ]
+    )
+    def test_static_pathway_on_sphere_length(self, pA_vec, pB_vec, factor):
+        pA_vec = self._expand_pos_to_vec(pA_vec, self.N)
+        pB_vec = self._expand_pos_to_vec(pB_vec, self.N)
+        self.pA.set_pos(self.pO, self.r*pA_vec)
+        self.pB.set_pos(self.pO, self.r*pB_vec)
+        pathway = WrappingPathway(self.pA, self.pB, self.sphere)
+        expected = factor*self.r
+        assert simplify(pathway.length - expected) == 0
+
+    @pytest.mark.parametrize(
+        'pA_vec, pB_vec, factor',
+        [
+            ((1, 0, 0), (0, 1, 0), Rational(1, 2)*pi),
+            ((1, 0, 0), (-1, 0, 0), pi),
+            ((-1, 0, 0), (1, 0, 0), pi),
+            ((0, 1, 0), (sqrt(2)/2, -sqrt(2)/2, 0), 5*pi/4),
+            ((1, 0, 0), (Rational(1, 2), sqrt(3)/2, 0), pi/3),
+            (
+                (0, 1, 0),
+                (sqrt(2)*Rational(1, 2), -sqrt(2)*Rational(1, 2), 1),
+                sqrt(1 + (Rational(5, 4)*pi)**2),
+            ),
+            (
+                (1, 0, 0),
+                (Rational(1, 2), sqrt(3)*Rational(1, 2), 1),
+                sqrt(1 + (Rational(1, 3)*pi)**2),
+            ),
+        ]
+    )
+    def test_static_pathway_on_cylinder_length(self, pA_vec, pB_vec, factor):
+        pA_vec = self._expand_pos_to_vec(pA_vec, self.N)
+        pB_vec = self._expand_pos_to_vec(pB_vec, self.N)
+        self.pA.set_pos(self.pO, self.r*pA_vec)
+        self.pB.set_pos(self.pO, self.r*pB_vec)
+        pathway = WrappingPathway(self.pA, self.pB, self.cylinder)
+        expected = factor*sqrt(self.r**2)
+        assert simplify(pathway.length - expected) == 0
+
+    @pytest.mark.parametrize(
+        'pA_vec, pB_vec',
+        [
+            ((1, 0, 0), (0, 1, 0)),
+            ((0, 1, 0), (sqrt(2)*Rational(1, 2), -sqrt(2)*Rational(1, 2), 0)),
+            ((1, 0, 0), (Rational(1, 2), sqrt(3)*Rational(1, 2), 0)),
+        ]
+    )
+    def test_static_pathway_on_sphere_extension_velocity(self, pA_vec, pB_vec):
+        pA_vec = self._expand_pos_to_vec(pA_vec, self.N)
+        pB_vec = self._expand_pos_to_vec(pB_vec, self.N)
+        self.pA.set_pos(self.pO, self.r*pA_vec)
+        self.pB.set_pos(self.pO, self.r*pB_vec)
+        pathway = WrappingPathway(self.pA, self.pB, self.sphere)
+        assert pathway.extension_velocity == 0
+
+    @pytest.mark.parametrize(
+        'pA_vec, pB_vec',
+        [
+            ((1, 0, 0), (0, 1, 0)),
+            ((1, 0, 0), (-1, 0, 0)),
+            ((-1, 0, 0), (1, 0, 0)),
+            ((0, 1, 0), (sqrt(2)/2, -sqrt(2)/2, 0)),
+            ((1, 0, 0), (Rational(1, 2), sqrt(3)/2, 0)),
+            ((0, 1, 0), (sqrt(2)*Rational(1, 2), -sqrt(2)/2, 1)),
+            ((1, 0, 0), (Rational(1, 2), sqrt(3)/2, 1)),
+        ]
+    )
+    def test_static_pathway_on_cylinder_extension_velocity(self, pA_vec, pB_vec):
+        pA_vec = self._expand_pos_to_vec(pA_vec, self.N)
+        pB_vec = self._expand_pos_to_vec(pB_vec, self.N)
+        self.pA.set_pos(self.pO, self.r*pA_vec)
+        self.pB.set_pos(self.pO, self.r*pB_vec)
+        pathway = WrappingPathway(self.pA, self.pB, self.cylinder)
+        assert pathway.extension_velocity == 0
+
+    @pytest.mark.parametrize(
+        'pA_vec, pB_vec, pA_vec_expected, pB_vec_expected, pO_vec_expected',
+        (
+            ((1, 0, 0), (0, 1, 0), (0, 1, 0), (1, 0, 0), (-1, -1, 0)),
+            (
+                (0, 1, 0),
+                (sqrt(2)/2, -sqrt(2)/2, 0),
+                (1, 0, 0),
+                (sqrt(2)/2, sqrt(2)/2, 0),
+                (-1 - sqrt(2)/2, -sqrt(2)/2, 0)
+            ),
+            (
+                (1, 0, 0),
+                (Rational(1, 2), sqrt(3)/2, 0),
+                (0, 1, 0),
+                (sqrt(3)/2, -Rational(1, 2), 0),
+                (-sqrt(3)/2, Rational(1, 2) - 1, 0),
+            ),
+        )
+    )
+    def test_static_pathway_on_sphere_to_loads(
+        self,
+        pA_vec,
+        pB_vec,
+        pA_vec_expected,
+        pB_vec_expected,
+        pO_vec_expected,
+    ):
+        pA_vec = self._expand_pos_to_vec(pA_vec, self.N)
+        pB_vec = self._expand_pos_to_vec(pB_vec, self.N)
+        self.pA.set_pos(self.pO, self.r*pA_vec)
+        self.pB.set_pos(self.pO, self.r*pB_vec)
+        pathway = WrappingPathway(self.pA, self.pB, self.sphere)
+
+        pA_vec_expected = sum(
+            mag*unit for (mag, unit) in zip(pA_vec_expected, self.N)
+        )
+        pB_vec_expected = sum(
+            mag*unit for (mag, unit) in zip(pB_vec_expected, self.N)
+        )
+        pO_vec_expected = sum(
+            mag*unit for (mag, unit) in zip(pO_vec_expected, self.N)
+        )
+        expected = [
+            Force(self.pA, self.F*(self.r**3/sqrt(self.r**6))*pA_vec_expected),
+            Force(self.pB, self.F*(self.r**3/sqrt(self.r**6))*pB_vec_expected),
+            Force(self.pO, self.F*(self.r**3/sqrt(self.r**6))*pO_vec_expected),
+        ]
+        assert pathway.to_loads(self.F) == expected
+
+    @pytest.mark.parametrize(
+        'pA_vec, pB_vec, pA_vec_expected, pB_vec_expected, pO_vec_expected',
+        (
+            ((1, 0, 0), (0, 1, 0), (0, 1, 0), (1, 0, 0), (-1, -1, 0)),
+            ((1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, 1, 0), (0, -2, 0)),
+            ((-1, 0, 0), (1, 0, 0), (0, -1, 0), (0, -1, 0), (0, 2, 0)),
+            (
+                (0, 1, 0),
+                (sqrt(2)/2, -sqrt(2)/2, 0),
+                (-1, 0, 0),
+                (-sqrt(2)/2, -sqrt(2)/2, 0),
+                (1 + sqrt(2)/2, sqrt(2)/2, 0)
+            ),
+            (
+                (1, 0, 0),
+                (Rational(1, 2), sqrt(3)/2, 0),
+                (0, 1, 0),
+                (sqrt(3)/2, -Rational(1, 2), 0),
+                (-sqrt(3)/2, Rational(1, 2) - 1, 0),
+            ),
+            (
+                (1, 0, 0),
+                (sqrt(2)/2, sqrt(2)/2, 0),
+                (0, 1, 0),
+                (sqrt(2)/2, -sqrt(2)/2, 0),
+                (-sqrt(2)/2, sqrt(2)/2 - 1, 0),
+            ),
+            ((0, 1, 0), (0, 1, 1), (0, 0, 1), (0, 0, -1), (0, 0, 0)),
+            (
+                (0, 1, 0),
+                (sqrt(2)/2, -sqrt(2)/2, 1),
+                (-5*pi/sqrt(16 + 25*pi**2), 0, 4/sqrt(16 + 25*pi**2)),
+                (
+                    -5*sqrt(2)*pi/(2*sqrt(16 + 25*pi**2)),
+                    -5*sqrt(2)*pi/(2*sqrt(16 + 25*pi**2)),
+                    -4/sqrt(16 + 25*pi**2),
+                ),
+                (
+                    5*(sqrt(2) + 2)*pi/(2*sqrt(16 + 25*pi**2)),
+                    5*sqrt(2)*pi/(2*sqrt(16 + 25*pi**2)),
+                    0,
+                ),
+            ),
+        )
+    )
+    def test_static_pathway_on_cylinder_to_loads(
+        self,
+        pA_vec,
+        pB_vec,
+        pA_vec_expected,
+        pB_vec_expected,
+        pO_vec_expected,
+    ):
+        pA_vec = self._expand_pos_to_vec(pA_vec, self.N)
+        pB_vec = self._expand_pos_to_vec(pB_vec, self.N)
+        self.pA.set_pos(self.pO, self.r*pA_vec)
+        self.pB.set_pos(self.pO, self.r*pB_vec)
+        pathway = WrappingPathway(self.pA, self.pB, self.cylinder)
+
+        pA_force_expected = self.F*self._expand_pos_to_vec(pA_vec_expected,
+                                                           self.N)
+        pB_force_expected = self.F*self._expand_pos_to_vec(pB_vec_expected,
+                                                           self.N)
+        pO_force_expected = self.F*self._expand_pos_to_vec(pO_vec_expected,
+                                                           self.N)
+        expected = [
+            Force(self.pA, pA_force_expected),
+            Force(self.pB, pB_force_expected),
+            Force(self.pO, pO_force_expected),
+        ]
+        assert _simplify_loads(pathway.to_loads(self.F)) == expected
+
+    def test_2D_pathway_on_cylinder_length(self):
+        q = dynamicsymbols('q')
+        pA_pos = self.r*self.N.x
+        pB_pos = self.r*(cos(q)*self.N.x + sin(q)*self.N.y)
+        self.pA.set_pos(self.pO, pA_pos)
+        self.pB.set_pos(self.pO, pB_pos)
+        expected = self.r*sqrt(q**2)
+        assert simplify(self.pathway.length - expected) == 0
+
+    def test_2D_pathway_on_cylinder_extension_velocity(self):
+        q = dynamicsymbols('q')
+        qd = dynamicsymbols('q', 1)
+        pA_pos = self.r*self.N.x
+        pB_pos = self.r*(cos(q)*self.N.x + sin(q)*self.N.y)
+        self.pA.set_pos(self.pO, pA_pos)
+        self.pB.set_pos(self.pO, pB_pos)
+        expected = self.r*(sqrt(q**2)/q)*qd
+        assert simplify(self.pathway.extension_velocity - expected) == 0
+
+    def test_2D_pathway_on_cylinder_to_loads(self):
+        q = dynamicsymbols('q')
+        pA_pos = self.r*self.N.x
+        pB_pos = self.r*(cos(q)*self.N.x + sin(q)*self.N.y)
+        self.pA.set_pos(self.pO, pA_pos)
+        self.pB.set_pos(self.pO, pB_pos)
+
+        pA_force = self.F*self.N.y
+        pB_force = self.F*(sin(q)*self.N.x - cos(q)*self.N.y)
+        pO_force = self.F*(-sin(q)*self.N.x + (cos(q) - 1)*self.N.y)
+        expected = [
+            Force(self.pA, pA_force),
+            Force(self.pB, pB_force),
+            Force(self.pO, pO_force),
+        ]
+
+        loads = _simplify_loads(self.pathway.to_loads(self.F))
+        assert loads == expected
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_rigidbody.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_rigidbody.py
new file mode 100644
index 0000000000000000000000000000000000000000..78161e0c9fc33be6e3d274034b67278c8ceee8fd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_rigidbody.py
@@ -0,0 +1,184 @@
+from sympy.physics.mechanics import Point, ReferenceFrame, Dyadic, RigidBody
+from sympy.physics.mechanics import dynamicsymbols, outer, inertia, Inertia
+from sympy.physics.mechanics import inertia_of_point_mass
+from sympy import expand, zeros, simplify, symbols
+from sympy.testing.pytest import raises, warns_deprecated_sympy
+
+
+def test_rigidbody_default():
+    # Test default
+    b = RigidBody('B')
+    I = inertia(b.frame, *symbols('B_ixx B_iyy B_izz B_ixy B_iyz B_izx'))
+    assert b.name == 'B'
+    assert b.mass == symbols('B_mass')
+    assert b.masscenter.name == 'B_masscenter'
+    assert b.inertia == (I, b.masscenter)
+    assert b.central_inertia == I
+    assert b.frame.name == 'B_frame'
+    assert b.__str__() == 'B'
+    assert b.__repr__() == (
+        "RigidBody('B', masscenter=B_masscenter, frame=B_frame, mass=B_mass, "
+        "inertia=Inertia(dyadic=B_ixx*(B_frame.x|B_frame.x) + "
+        "B_ixy*(B_frame.x|B_frame.y) + B_izx*(B_frame.x|B_frame.z) + "
+        "B_ixy*(B_frame.y|B_frame.x) + B_iyy*(B_frame.y|B_frame.y) + "
+        "B_iyz*(B_frame.y|B_frame.z) + B_izx*(B_frame.z|B_frame.x) + "
+        "B_iyz*(B_frame.z|B_frame.y) + B_izz*(B_frame.z|B_frame.z), "
+        "point=B_masscenter))")
+
+
+def test_rigidbody():
+    m, m2, v1, v2, v3, omega = symbols('m m2 v1 v2 v3 omega')
+    A = ReferenceFrame('A')
+    A2 = ReferenceFrame('A2')
+    P = Point('P')
+    P2 = Point('P2')
+    I = Dyadic(0)
+    I2 = Dyadic(0)
+    B = RigidBody('B', P, A, m, (I, P))
+    assert B.mass == m
+    assert B.frame == A
+    assert B.masscenter == P
+    assert B.inertia == (I, B.masscenter)
+
+    B.mass = m2
+    B.frame = A2
+    B.masscenter = P2
+    B.inertia = (I2, B.masscenter)
+    raises(TypeError, lambda: RigidBody(P, P, A, m, (I, P)))
+    raises(TypeError, lambda: RigidBody('B', P, P, m, (I, P)))
+    raises(TypeError, lambda: RigidBody('B', P, A, m, (P, P)))
+    raises(TypeError, lambda: RigidBody('B', P, A, m, (I, I)))
+    assert B.__str__() == 'B'
+    assert B.mass == m2
+    assert B.frame == A2
+    assert B.masscenter == P2
+    assert B.inertia == (I2, B.masscenter)
+    assert isinstance(B.inertia, Inertia)
+
+    # Testing linear momentum function assuming A2 is the inertial frame
+    N = ReferenceFrame('N')
+    P2.set_vel(N, v1 * N.x + v2 * N.y + v3 * N.z)
+    assert B.linear_momentum(N) == m2 * (v1 * N.x + v2 * N.y + v3 * N.z)
+
+
+def test_rigidbody2():
+    M, v, r, omega, g, h = dynamicsymbols('M v r omega g h')
+    N = ReferenceFrame('N')
+    b = ReferenceFrame('b')
+    b.set_ang_vel(N, omega * b.x)
+    P = Point('P')
+    I = outer(b.x, b.x)
+    Inertia_tuple = (I, P)
+    B = RigidBody('B', P, b, M, Inertia_tuple)
+    P.set_vel(N, v * b.x)
+    assert B.angular_momentum(P, N) == omega * b.x
+    O = Point('O')
+    O.set_vel(N, v * b.x)
+    P.set_pos(O, r * b.y)
+    assert B.angular_momentum(O, N) == omega * b.x - M*v*r*b.z
+    B.potential_energy = M * g * h
+    assert B.potential_energy == M * g * h
+    assert expand(2 * B.kinetic_energy(N)) == omega**2 + M * v**2
+
+
+def test_rigidbody3():
+    q1, q2, q3, q4 = dynamicsymbols('q1:5')
+    p1, p2, p3 = symbols('p1:4')
+    m = symbols('m')
+
+    A = ReferenceFrame('A')
+    B = A.orientnew('B', 'axis', [q1, A.x])
+    O = Point('O')
+    O.set_vel(A, q2*A.x + q3*A.y + q4*A.z)
+    P = O.locatenew('P', p1*B.x + p2*B.y + p3*B.z)
+    P.v2pt_theory(O, A, B)
+    I = outer(B.x, B.x)
+
+    rb1 = RigidBody('rb1', P, B, m, (I, P))
+    # I_S/O = I_S/S* + I_S*/O
+    rb2 = RigidBody('rb2', P, B, m,
+                    (I + inertia_of_point_mass(m, P.pos_from(O), B), O))
+
+    assert rb1.central_inertia == rb2.central_inertia
+    assert rb1.angular_momentum(O, A) == rb2.angular_momentum(O, A)
+
+
+def test_pendulum_angular_momentum():
+    """Consider a pendulum of length OA = 2a, of mass m as a rigid body of
+    center of mass G (OG = a) which turn around (O,z). The angle between the
+    reference frame R and the rod is q.  The inertia of the body is I =
+    (G,0,ma^2/3,ma^2/3). """
+
+    m, a = symbols('m, a')
+    q = dynamicsymbols('q')
+
+    R = ReferenceFrame('R')
+    R1 = R.orientnew('R1', 'Axis', [q, R.z])
+    R1.set_ang_vel(R, q.diff() * R.z)
+
+    I = inertia(R1, 0, m * a**2 / 3, m * a**2 / 3)
+
+    O = Point('O')
+
+    A = O.locatenew('A', 2*a * R1.x)
+    G = O.locatenew('G', a * R1.x)
+
+    S = RigidBody('S', G, R1, m, (I, G))
+
+    O.set_vel(R, 0)
+    A.v2pt_theory(O, R, R1)
+    G.v2pt_theory(O, R, R1)
+
+    assert (4 * m * a**2 / 3 * q.diff() * R.z -
+            S.angular_momentum(O, R).express(R)) == 0
+
+
+def test_rigidbody_inertia():
+    N = ReferenceFrame('N')
+    m, Ix, Iy, Iz, a, b = symbols('m, I_x, I_y, I_z, a, b')
+    Io = inertia(N, Ix, Iy, Iz)
+    o = Point('o')
+    p = o.locatenew('p', a * N.x + b * N.y)
+    R = RigidBody('R', o, N, m, (Io, p))
+    I_check = inertia(N, Ix - b ** 2 * m, Iy - a ** 2 * m,
+                      Iz - m * (a ** 2 + b ** 2), m * a * b)
+    assert isinstance(R.inertia, Inertia)
+    assert R.inertia == (Io, p)
+    assert R.central_inertia == I_check
+    R.central_inertia = Io
+    assert R.inertia == (Io, o)
+    assert R.central_inertia == Io
+    R.inertia = (Io, p)
+    assert R.inertia == (Io, p)
+    assert R.central_inertia == I_check
+    # parse Inertia object
+    R.inertia = Inertia(Io, o)
+    assert R.inertia == (Io, o)
+
+
+def test_parallel_axis():
+    N = ReferenceFrame('N')
+    m, Ix, Iy, Iz, a, b = symbols('m, I_x, I_y, I_z, a, b')
+    Io = inertia(N, Ix, Iy, Iz)
+    o = Point('o')
+    p = o.locatenew('p', a * N.x + b * N.y)
+    R = RigidBody('R', o, N, m, (Io, o))
+    Ip = R.parallel_axis(p)
+    Ip_expected = inertia(N, Ix + m * b**2, Iy + m * a**2,
+                          Iz + m * (a**2 + b**2), ixy=-m * a * b)
+    assert Ip == Ip_expected
+    # Reference frame from which the parallel axis is viewed should not matter
+    A = ReferenceFrame('A')
+    A.orient_axis(N, N.z, 1)
+    assert simplify(
+        (R.parallel_axis(p, A) - Ip_expected).to_matrix(A)) == zeros(3, 3)
+
+
+def test_deprecated_set_potential_energy():
+    m, g, h = symbols('m g h')
+    A = ReferenceFrame('A')
+    P = Point('P')
+    I = Dyadic(0)
+    B = RigidBody('B', P, A, m, (I, P))
+    with warns_deprecated_sympy():
+        B.set_potential_energy(m*g*h)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_system.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_system.py
new file mode 100644
index 0000000000000000000000000000000000000000..6fdac1ea10e9f71f8cf999cc5069da7567f67adf
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_system.py
@@ -0,0 +1,245 @@
+from sympy import symbols, Matrix, atan, zeros
+from sympy.simplify.simplify import simplify
+from sympy.physics.mechanics import (dynamicsymbols, Particle, Point,
+                                     ReferenceFrame, SymbolicSystem)
+from sympy.testing.pytest import raises
+
+# This class is going to be tested using a simple pendulum set up in x and y
+# coordinates
+x, y, u, v, lam = dynamicsymbols('x y u v lambda')
+m, l, g = symbols('m l g')
+
+# Set up the different forms the equations can take
+#       [1] Explicit form where the kinematics and dynamics are combined
+#           x' = F(x, t, r, p)
+#
+#       [2] Implicit form where the kinematics and dynamics are combined
+#           M(x, p) x' = F(x, t, r, p)
+#
+#       [3] Implicit form where the kinematics and dynamics are separate
+#           M(q, p) u' = F(q, u, t, r, p)
+#           q' = G(q, u, t, r, p)
+dyn_implicit_mat = Matrix([[1, 0, -x/m],
+                           [0, 1, -y/m],
+                           [0, 0, l**2/m]])
+
+dyn_implicit_rhs = Matrix([0, 0, u**2 + v**2 - g*y])
+
+comb_implicit_mat = Matrix([[1, 0, 0, 0, 0],
+                            [0, 1, 0, 0, 0],
+                            [0, 0, 1, 0, -x/m],
+                            [0, 0, 0, 1, -y/m],
+                            [0, 0, 0, 0, l**2/m]])
+
+comb_implicit_rhs = Matrix([u, v, 0, 0, u**2 + v**2 - g*y])
+
+kin_explicit_rhs = Matrix([u, v])
+
+comb_explicit_rhs = comb_implicit_mat.LUsolve(comb_implicit_rhs)
+
+# Set up a body and load to pass into the system
+theta = atan(x/y)
+N = ReferenceFrame('N')
+A = N.orientnew('A', 'Axis', [theta, N.z])
+O = Point('O')
+P = O.locatenew('P', l * A.x)
+
+Pa = Particle('Pa', P, m)
+
+bodies = [Pa]
+loads = [(P, g * m * N.x)]
+
+# Set up some output equations to be given to SymbolicSystem
+# Change to make these fit the pendulum
+PE = symbols("PE")
+out_eqns = {PE: m*g*(l+y)}
+
+# Set up remaining arguments that can be passed to SymbolicSystem
+alg_con = [2]
+alg_con_full = [4]
+coordinates = (x, y, lam)
+speeds = (u, v)
+states = (x, y, u, v, lam)
+coord_idxs = (0, 1)
+speed_idxs = (2, 3)
+
+
+def test_form_1():
+    symsystem1 = SymbolicSystem(states, comb_explicit_rhs,
+                                alg_con=alg_con_full, output_eqns=out_eqns,
+                                coord_idxs=coord_idxs, speed_idxs=speed_idxs,
+                                bodies=bodies, loads=loads)
+
+    assert symsystem1.coordinates == Matrix([x, y])
+    assert symsystem1.speeds == Matrix([u, v])
+    assert symsystem1.states == Matrix([x, y, u, v, lam])
+
+    assert symsystem1.alg_con == [4]
+
+    inter = comb_explicit_rhs
+    assert simplify(symsystem1.comb_explicit_rhs - inter) == zeros(5, 1)
+
+    assert set(symsystem1.dynamic_symbols()) == {y, v, lam, u, x}
+    assert type(symsystem1.dynamic_symbols()) == tuple
+    assert set(symsystem1.constant_symbols()) == {l, g, m}
+    assert type(symsystem1.constant_symbols()) == tuple
+
+    assert symsystem1.output_eqns == out_eqns
+
+    assert symsystem1.bodies == (Pa,)
+    assert symsystem1.loads == ((P, g * m * N.x),)
+
+
+def test_form_2():
+    symsystem2 = SymbolicSystem(coordinates, comb_implicit_rhs, speeds=speeds,
+                                mass_matrix=comb_implicit_mat,
+                                alg_con=alg_con_full, output_eqns=out_eqns,
+                                bodies=bodies, loads=loads)
+
+    assert symsystem2.coordinates == Matrix([x, y, lam])
+    assert symsystem2.speeds == Matrix([u, v])
+    assert symsystem2.states == Matrix([x, y, lam, u, v])
+
+    assert symsystem2.alg_con == [4]
+
+    inter = comb_implicit_rhs
+    assert simplify(symsystem2.comb_implicit_rhs - inter) == zeros(5, 1)
+    assert simplify(symsystem2.comb_implicit_mat-comb_implicit_mat) == zeros(5)
+
+    assert set(symsystem2.dynamic_symbols()) == {y, v, lam, u, x}
+    assert type(symsystem2.dynamic_symbols()) == tuple
+    assert set(symsystem2.constant_symbols()) == {l, g, m}
+    assert type(symsystem2.constant_symbols()) == tuple
+
+    inter = comb_explicit_rhs
+    symsystem2.compute_explicit_form()
+    assert simplify(symsystem2.comb_explicit_rhs - inter) == zeros(5, 1)
+
+
+    assert symsystem2.output_eqns == out_eqns
+
+    assert symsystem2.bodies == (Pa,)
+    assert symsystem2.loads == ((P, g * m * N.x),)
+
+
+def test_form_3():
+    symsystem3 = SymbolicSystem(states, dyn_implicit_rhs,
+                                mass_matrix=dyn_implicit_mat,
+                                coordinate_derivatives=kin_explicit_rhs,
+                                alg_con=alg_con, coord_idxs=coord_idxs,
+                                speed_idxs=speed_idxs, bodies=bodies,
+                                loads=loads)
+
+    assert symsystem3.coordinates == Matrix([x, y])
+    assert symsystem3.speeds == Matrix([u, v])
+    assert symsystem3.states == Matrix([x, y, u, v, lam])
+
+    assert symsystem3.alg_con == [4]
+
+    inter1 = kin_explicit_rhs
+    inter2 = dyn_implicit_rhs
+    assert simplify(symsystem3.kin_explicit_rhs - inter1) == zeros(2, 1)
+    assert simplify(symsystem3.dyn_implicit_mat - dyn_implicit_mat) == zeros(3)
+    assert simplify(symsystem3.dyn_implicit_rhs - inter2) == zeros(3, 1)
+
+    inter = comb_implicit_rhs
+    assert simplify(symsystem3.comb_implicit_rhs - inter) == zeros(5, 1)
+    assert simplify(symsystem3.comb_implicit_mat-comb_implicit_mat) == zeros(5)
+
+    inter = comb_explicit_rhs
+    symsystem3.compute_explicit_form()
+    assert simplify(symsystem3.comb_explicit_rhs - inter) == zeros(5, 1)
+
+    assert set(symsystem3.dynamic_symbols()) == {y, v, lam, u, x}
+    assert type(symsystem3.dynamic_symbols()) == tuple
+    assert set(symsystem3.constant_symbols()) == {l, g, m}
+    assert type(symsystem3.constant_symbols()) == tuple
+
+    assert symsystem3.output_eqns == {}
+
+    assert symsystem3.bodies == (Pa,)
+    assert symsystem3.loads == ((P, g * m * N.x),)
+
+
+def test_property_attributes():
+    symsystem = SymbolicSystem(states, comb_explicit_rhs,
+                               alg_con=alg_con_full, output_eqns=out_eqns,
+                               coord_idxs=coord_idxs, speed_idxs=speed_idxs,
+                               bodies=bodies, loads=loads)
+
+    with raises(AttributeError):
+        symsystem.bodies = 42
+    with raises(AttributeError):
+        symsystem.coordinates = 42
+    with raises(AttributeError):
+        symsystem.dyn_implicit_rhs = 42
+    with raises(AttributeError):
+        symsystem.comb_implicit_rhs = 42
+    with raises(AttributeError):
+        symsystem.loads = 42
+    with raises(AttributeError):
+        symsystem.dyn_implicit_mat = 42
+    with raises(AttributeError):
+        symsystem.comb_implicit_mat = 42
+    with raises(AttributeError):
+        symsystem.kin_explicit_rhs = 42
+    with raises(AttributeError):
+        symsystem.comb_explicit_rhs = 42
+    with raises(AttributeError):
+        symsystem.speeds = 42
+    with raises(AttributeError):
+        symsystem.states = 42
+    with raises(AttributeError):
+        symsystem.alg_con = 42
+
+
+def test_not_specified_errors():
+    """This test will cover errors that arise from trying to access attributes
+    that were not specified upon object creation or were specified on creation
+    and the user tries to recalculate them."""
+    # Trying to access form 2 when form 1 given
+    # Trying to access form 3 when form 2 given
+
+    symsystem1 = SymbolicSystem(states, comb_explicit_rhs)
+
+    with raises(AttributeError):
+        symsystem1.comb_implicit_mat
+    with raises(AttributeError):
+        symsystem1.comb_implicit_rhs
+    with raises(AttributeError):
+        symsystem1.dyn_implicit_mat
+    with raises(AttributeError):
+        symsystem1.dyn_implicit_rhs
+    with raises(AttributeError):
+        symsystem1.kin_explicit_rhs
+    with raises(AttributeError):
+        symsystem1.compute_explicit_form()
+
+    symsystem2 = SymbolicSystem(coordinates, comb_implicit_rhs, speeds=speeds,
+                                mass_matrix=comb_implicit_mat)
+
+    with raises(AttributeError):
+        symsystem2.dyn_implicit_mat
+    with raises(AttributeError):
+        symsystem2.dyn_implicit_rhs
+    with raises(AttributeError):
+        symsystem2.kin_explicit_rhs
+
+    # Attribute error when trying to access coordinates and speeds when only the
+    # states were given.
+    with raises(AttributeError):
+        symsystem1.coordinates
+    with raises(AttributeError):
+        symsystem1.speeds
+
+    # Attribute error when trying to access bodies and loads when they are not
+    # given
+    with raises(AttributeError):
+        symsystem1.bodies
+    with raises(AttributeError):
+        symsystem1.loads
+
+    # Attribute error when trying to access comb_explicit_rhs before it was
+    # calculated
+    with raises(AttributeError):
+        symsystem2.comb_explicit_rhs
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_system_class.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_system_class.py
new file mode 100644
index 0000000000000000000000000000000000000000..924cb8272c27c4f978aa4c3b1999f6ac56e47335
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_system_class.py
@@ -0,0 +1,831 @@
+import pytest
+
+from sympy.core.symbol import symbols
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.trigonometric import cos, sin
+from sympy.matrices.dense import eye, zeros
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.physics.mechanics import (
+    Force, KanesMethod, LagrangesMethod, Particle, PinJoint, Point,
+    PrismaticJoint, ReferenceFrame, RigidBody, Torque, TorqueActuator, System,
+    dynamicsymbols)
+from sympy.simplify.simplify import simplify
+from sympy.solvers.solvers import solve
+
+t = dynamicsymbols._t  # type: ignore
+q = dynamicsymbols('q:6')  # type: ignore
+qd = dynamicsymbols('q:6', 1)  # type: ignore
+u = dynamicsymbols('u:6')  # type: ignore
+ua = dynamicsymbols('ua:3')  # type: ignore
+
+
+class TestSystemBase:
+    @pytest.fixture()
+    def _empty_system_setup(self):
+        self.system = System(ReferenceFrame('frame'), Point('fixed_point'))
+
+    def _empty_system_check(self, exclude=()):
+        matrices = ('q_ind', 'q_dep', 'q', 'u_ind', 'u_dep', 'u', 'u_aux',
+                    'kdes', 'holonomic_constraints', 'nonholonomic_constraints')
+        tuples = ('loads', 'bodies', 'joints', 'actuators')
+        for attr in matrices:
+            if attr not in exclude:
+                assert getattr(self.system, attr)[:] == []
+        for attr in tuples:
+            if attr not in exclude:
+                assert getattr(self.system, attr) == ()
+        if 'eom_method' not in exclude:
+            assert self.system.eom_method is None
+
+    def _create_filled_system(self, with_speeds=True):
+        self.system = System(ReferenceFrame('frame'), Point('fixed_point'))
+        u = dynamicsymbols('u:6') if with_speeds else qd
+        self.bodies = symbols('rb1:5', cls=RigidBody)
+        self.joints = (
+            PinJoint('J1', self.bodies[0], self.bodies[1], q[0], u[0]),
+            PrismaticJoint('J2', self.bodies[1], self.bodies[2], q[1], u[1]),
+            PinJoint('J3', self.bodies[2], self.bodies[3], q[2], u[2])
+        )
+        self.system.add_joints(*self.joints)
+        self.system.add_coordinates(q[3], independent=[False])
+        self.system.add_speeds(u[3], independent=False)
+        if with_speeds:
+            self.system.add_kdes(u[3] - qd[3])
+            self.system.add_auxiliary_speeds(ua[0], ua[1])
+        self.system.add_holonomic_constraints(q[2] - q[0] + q[1])
+        self.system.add_nonholonomic_constraints(u[3] - qd[1] + u[2])
+        self.system.u_ind = u[:2]
+        self.system.u_dep = u[2:4]
+        self.q_ind, self.q_dep = self.system.q_ind[:], self.system.q_dep[:]
+        self.u_ind, self.u_dep = self.system.u_ind[:], self.system.u_dep[:]
+        self.kdes = self.system.kdes[:]
+        self.hc = self.system.holonomic_constraints[:]
+        self.vc = self.system.velocity_constraints[:]
+        self.nhc = self.system.nonholonomic_constraints[:]
+
+    @pytest.fixture()
+    def _filled_system_setup(self):
+        self._create_filled_system(with_speeds=True)
+
+    @pytest.fixture()
+    def _filled_system_setup_no_speeds(self):
+        self._create_filled_system(with_speeds=False)
+
+    def _filled_system_check(self, exclude=()):
+        assert 'q_ind' in exclude or self.system.q_ind[:] == q[:3]
+        assert 'q_dep' in exclude or self.system.q_dep[:] == [q[3]]
+        assert 'q' in exclude or self.system.q[:] == q[:4]
+        assert 'u_ind' in exclude or self.system.u_ind[:] == u[:2]
+        assert 'u_dep' in exclude or self.system.u_dep[:] == u[2:4]
+        assert 'u' in exclude or self.system.u[:] == u[:4]
+        assert 'u_aux' in exclude or self.system.u_aux[:] == ua[:2]
+        assert 'kdes' in exclude or self.system.kdes[:] == [
+            ui - qdi for ui, qdi in zip(u[:4], qd[:4])]
+        assert ('holonomic_constraints' in exclude or
+                self.system.holonomic_constraints[:] == [q[2] - q[0] + q[1]])
+        assert ('nonholonomic_constraints' in exclude or
+                self.system.nonholonomic_constraints[:] == [u[3] - qd[1] + u[2]]
+                )
+        assert ('velocity_constraints' in exclude or
+                self.system.velocity_constraints[:] == [
+                    qd[2] - qd[0] + qd[1], u[3] - qd[1] + u[2]])
+        assert ('bodies' in exclude or
+                self.system.bodies == tuple(self.bodies))
+        assert ('joints' in exclude or
+                self.system.joints == tuple(self.joints))
+
+    @pytest.fixture()
+    def _moving_point_mass(self, _empty_system_setup):
+        self.system.q_ind = q[0]
+        self.system.u_ind = u[0]
+        self.system.kdes = u[0] - q[0].diff(t)
+        p = Particle('p', mass=symbols('m'))
+        self.system.add_bodies(p)
+        p.masscenter.set_pos(self.system.fixed_point, q[0] * self.system.x)
+
+
+class TestSystem(TestSystemBase):
+    def test_empty_system(self, _empty_system_setup):
+        self._empty_system_check()
+        self.system.validate_system()
+
+    def test_filled_system(self, _filled_system_setup):
+        self._filled_system_check()
+        self.system.validate_system()
+
+    @pytest.mark.parametrize('frame', [None, ReferenceFrame('frame')])
+    @pytest.mark.parametrize('fixed_point', [None, Point('fixed_point')])
+    def test_init(self, frame, fixed_point):
+        if fixed_point is None and frame is None:
+            self.system = System()
+        else:
+            self.system = System(frame, fixed_point)
+        if fixed_point is None:
+            assert self.system.fixed_point.name == 'inertial_point'
+        else:
+            assert self.system.fixed_point == fixed_point
+        if frame is None:
+            assert self.system.frame.name == 'inertial_frame'
+        else:
+            assert self.system.frame == frame
+        self._empty_system_check()
+        assert isinstance(self.system.q_ind, ImmutableMatrix)
+        assert isinstance(self.system.q_dep, ImmutableMatrix)
+        assert isinstance(self.system.q, ImmutableMatrix)
+        assert isinstance(self.system.u_ind, ImmutableMatrix)
+        assert isinstance(self.system.u_dep, ImmutableMatrix)
+        assert isinstance(self.system.u, ImmutableMatrix)
+        assert isinstance(self.system.kdes, ImmutableMatrix)
+        assert isinstance(self.system.holonomic_constraints, ImmutableMatrix)
+        assert isinstance(self.system.nonholonomic_constraints, ImmutableMatrix)
+
+    def test_from_newtonian_rigid_body(self):
+        rb = RigidBody('body')
+        self.system = System.from_newtonian(rb)
+        assert self.system.fixed_point == rb.masscenter
+        assert self.system.frame == rb.frame
+        self._empty_system_check(exclude=('bodies',))
+        self.system.bodies = (rb,)
+
+    def test_from_newtonian_particle(self):
+        pt = Particle('particle')
+        with pytest.raises(TypeError):
+            System.from_newtonian(pt)
+
+    @pytest.mark.parametrize('args, kwargs, exp_q_ind, exp_q_dep, exp_q', [
+        (q[:3], {}, q[:3], [], q[:3]),
+        (q[:3], {'independent': True}, q[:3], [], q[:3]),
+        (q[:3], {'independent': False}, [], q[:3], q[:3]),
+        (q[:3], {'independent': [True, False, True]}, [q[0], q[2]], [q[1]],
+         [q[0], q[2], q[1]]),
+    ])
+    def test_coordinates(self, _empty_system_setup, args, kwargs,
+                         exp_q_ind, exp_q_dep, exp_q):
+        # Test add_coordinates
+        self.system.add_coordinates(*args, **kwargs)
+        assert self.system.q_ind[:] == exp_q_ind
+        assert self.system.q_dep[:] == exp_q_dep
+        assert self.system.q[:] == exp_q
+        self._empty_system_check(exclude=('q_ind', 'q_dep', 'q'))
+        # Test setter for q_ind and q_dep
+        self.system.q_ind = exp_q_ind
+        self.system.q_dep = exp_q_dep
+        assert self.system.q_ind[:] == exp_q_ind
+        assert self.system.q_dep[:] == exp_q_dep
+        assert self.system.q[:] == exp_q
+        self._empty_system_check(exclude=('q_ind', 'q_dep', 'q'))
+
+    @pytest.mark.parametrize('func', ['add_coordinates', 'add_speeds'])
+    @pytest.mark.parametrize('args, kwargs', [
+        ((q[0], q[5]), {}),
+        ((u[0], u[5]), {}),
+        ((q[0],), {'independent': False}),
+        ((u[0],), {'independent': False}),
+        ((u[0], q[5]), {}),
+        ((symbols('a'), q[5]), {}),
+    ])
+    def test_coordinates_speeds_invalid(self, _filled_system_setup, func, args,
+                                        kwargs):
+        with pytest.raises(ValueError):
+            getattr(self.system, func)(*args, **kwargs)
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('args, kwargs, exp_u_ind, exp_u_dep, exp_u', [
+        (u[:3], {}, u[:3], [], u[:3]),
+        (u[:3], {'independent': True}, u[:3], [], u[:3]),
+        (u[:3], {'independent': False}, [], u[:3], u[:3]),
+        (u[:3], {'independent': [True, False, True]}, [u[0], u[2]], [u[1]],
+         [u[0], u[2], u[1]]),
+    ])
+    def test_speeds(self, _empty_system_setup, args, kwargs, exp_u_ind,
+                    exp_u_dep, exp_u):
+        # Test add_speeds
+        self.system.add_speeds(*args, **kwargs)
+        assert self.system.u_ind[:] == exp_u_ind
+        assert self.system.u_dep[:] == exp_u_dep
+        assert self.system.u[:] == exp_u
+        self._empty_system_check(exclude=('u_ind', 'u_dep', 'u'))
+        # Test setter for u_ind and u_dep
+        self.system.u_ind = exp_u_ind
+        self.system.u_dep = exp_u_dep
+        assert self.system.u_ind[:] == exp_u_ind
+        assert self.system.u_dep[:] == exp_u_dep
+        assert self.system.u[:] == exp_u
+        self._empty_system_check(exclude=('u_ind', 'u_dep', 'u'))
+
+    @pytest.mark.parametrize('args, kwargs, exp_u_aux', [
+        (ua[:3], {}, ua[:3]),
+    ])
+    def test_auxiliary_speeds(self, _empty_system_setup, args, kwargs,
+                              exp_u_aux):
+        # Test add_speeds
+        self.system.add_auxiliary_speeds(*args, **kwargs)
+        assert self.system.u_aux[:] == exp_u_aux
+        self._empty_system_check(exclude=('u_aux',))
+        # Test setter for u_ind and u_dep
+        self.system.u_aux = exp_u_aux
+        assert self.system.u_aux[:] == exp_u_aux
+        self._empty_system_check(exclude=('u_aux',))
+
+    @pytest.mark.parametrize('args, kwargs', [
+        ((ua[2], q[0]), {}),
+        ((ua[2], u[1]), {}),
+        ((ua[0], ua[2]), {}),
+        ((symbols('a'), ua[2]), {}),
+    ])
+    def test_auxiliary_invalid(self, _filled_system_setup, args, kwargs):
+        with pytest.raises(ValueError):
+            self.system.add_auxiliary_speeds(*args, **kwargs)
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('prop, add_func, args, kwargs', [
+        ('q_ind', 'add_coordinates', (q[0],), {}),
+        ('q_dep', 'add_coordinates', (q[3],), {'independent': False}),
+        ('u_ind', 'add_speeds', (u[0],), {}),
+        ('u_dep', 'add_speeds', (u[3],), {'independent': False}),
+        ('u_aux', 'add_auxiliary_speeds', (ua[2],), {}),
+        ('kdes', 'add_kdes', (qd[0] - u[0],), {}),
+        ('holonomic_constraints', 'add_holonomic_constraints',
+         (q[0] - q[1],), {}),
+        ('nonholonomic_constraints', 'add_nonholonomic_constraints',
+         (u[0] - u[1],), {}),
+        ('bodies', 'add_bodies', (RigidBody('body'),), {}),
+        ('loads', 'add_loads', (Force(Point('P'), ReferenceFrame('N').x),), {}),
+        ('actuators', 'add_actuators', (TorqueActuator(
+            symbols('T'), ReferenceFrame('N').x, ReferenceFrame('A')),), {}),
+    ])
+    def test_add_after_reset(self, _filled_system_setup, prop, add_func, args,
+                             kwargs):
+        setattr(self.system, prop, ())
+        exclude = (prop, 'q', 'u')
+        if prop in ('holonomic_constraints', 'nonholonomic_constraints'):
+            exclude += ('velocity_constraints',)
+        self._filled_system_check(exclude=exclude)
+        assert list(getattr(self.system, prop)[:]) == []
+        getattr(self.system, add_func)(*args, **kwargs)
+        assert list(getattr(self.system, prop)[:]) == list(args)
+
+    @pytest.mark.parametrize('prop, add_func, value, error', [
+        ('q_ind', 'add_coordinates', symbols('a'), ValueError),
+        ('q_dep', 'add_coordinates', symbols('a'), ValueError),
+        ('u_ind', 'add_speeds', symbols('a'), ValueError),
+        ('u_dep', 'add_speeds', symbols('a'), ValueError),
+        ('u_aux', 'add_auxiliary_speeds', symbols('a'), ValueError),
+        ('kdes', 'add_kdes', 7, TypeError),
+        ('holonomic_constraints', 'add_holonomic_constraints', 7, TypeError),
+        ('nonholonomic_constraints', 'add_nonholonomic_constraints', 7,
+         TypeError),
+        ('bodies', 'add_bodies', symbols('a'), TypeError),
+        ('loads', 'add_loads', symbols('a'), TypeError),
+        ('actuators', 'add_actuators', symbols('a'), TypeError),
+    ])
+    def test_type_error(self, _filled_system_setup, prop, add_func, value,
+                        error):
+        with pytest.raises(error):
+            getattr(self.system, add_func)(value)
+        with pytest.raises(error):
+            setattr(self.system, prop, value)
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('args, kwargs, exp_kdes', [
+        ((), {}, [ui - qdi for ui, qdi in zip(u[:4], qd[:4])]),
+        ((u[4] - qd[4], u[5] - qd[5]), {},
+         [ui - qdi for ui, qdi in zip(u[:6], qd[:6])]),
+    ])
+    def test_kdes(self, _filled_system_setup, args, kwargs, exp_kdes):
+        # Test add_speeds
+        self.system.add_kdes(*args, **kwargs)
+        self._filled_system_check(exclude=('kdes',))
+        assert self.system.kdes[:] == exp_kdes
+        # Test setter for kdes
+        self.system.kdes = exp_kdes
+        self._filled_system_check(exclude=('kdes',))
+        assert self.system.kdes[:] == exp_kdes
+
+    @pytest.mark.parametrize('args, kwargs', [
+        ((u[0] - qd[0], u[4] - qd[4]), {}),
+        ((-(u[0] - qd[0]), u[4] - qd[4]), {}),
+        (([u[0] - u[0], u[4] - qd[4]]), {}),
+    ])
+    def test_kdes_invalid(self, _filled_system_setup, args, kwargs):
+        with pytest.raises(ValueError):
+            self.system.add_kdes(*args, **kwargs)
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('args, kwargs, exp_con', [
+        ((), {}, [q[2] - q[0] + q[1]]),
+        ((q[4] - q[5], q[5] + q[3]), {},
+         [q[2] - q[0] + q[1], q[4] - q[5], q[5] + q[3]]),
+    ])
+    def test_holonomic_constraints(self, _filled_system_setup, args, kwargs,
+                                   exp_con):
+        exclude = ('holonomic_constraints', 'velocity_constraints')
+        exp_vel_con = [c.diff(t) for c in exp_con] + self.nhc
+        # Test add_holonomic_constraints
+        self.system.add_holonomic_constraints(*args, **kwargs)
+        self._filled_system_check(exclude=exclude)
+        assert self.system.holonomic_constraints[:] == exp_con
+        assert self.system.velocity_constraints[:] == exp_vel_con
+        # Test setter for holonomic_constraints
+        self.system.holonomic_constraints = exp_con
+        self._filled_system_check(exclude=exclude)
+        assert self.system.holonomic_constraints[:] == exp_con
+        assert self.system.velocity_constraints[:] == exp_vel_con
+
+    @pytest.mark.parametrize('args, kwargs', [
+        ((q[2] - q[0] + q[1], q[4] - q[3]), {}),
+        ((-(q[2] - q[0] + q[1]), q[4] - q[3]), {}),
+        ((q[0] - q[0], q[4] - q[3]), {}),
+    ])
+    def test_holonomic_constraints_invalid(self, _filled_system_setup, args,
+                                           kwargs):
+        with pytest.raises(ValueError):
+            self.system.add_holonomic_constraints(*args, **kwargs)
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('args, kwargs, exp_con', [
+        ((), {}, [u[3] - qd[1] + u[2]]),
+        ((u[4] - u[5], u[5] + u[3]), {},
+         [u[3] - qd[1] + u[2], u[4] - u[5], u[5] + u[3]]),
+    ])
+    def test_nonholonomic_constraints(self, _filled_system_setup, args, kwargs,
+                                      exp_con):
+        exclude = ('nonholonomic_constraints', 'velocity_constraints')
+        exp_vel_con = self.vc[:len(self.hc)] + exp_con
+        # Test add_nonholonomic_constraints
+        self.system.add_nonholonomic_constraints(*args, **kwargs)
+        self._filled_system_check(exclude=exclude)
+        assert self.system.nonholonomic_constraints[:] == exp_con
+        assert self.system.velocity_constraints[:] == exp_vel_con
+        # Test setter for nonholonomic_constraints
+        self.system.nonholonomic_constraints = exp_con
+        self._filled_system_check(exclude=exclude)
+        assert self.system.nonholonomic_constraints[:] == exp_con
+        assert self.system.velocity_constraints[:] == exp_vel_con
+
+    @pytest.mark.parametrize('args, kwargs', [
+        ((u[3] - qd[1] + u[2], u[4] - u[3]), {}),
+        ((-(u[3] - qd[1] + u[2]), u[4] - u[3]), {}),
+        ((u[0] - u[0], u[4] - u[3]), {}),
+        (([u[0] - u[0], u[4] - u[3]]), {}),
+    ])
+    def test_nonholonomic_constraints_invalid(self, _filled_system_setup, args,
+                                              kwargs):
+        with pytest.raises(ValueError):
+            self.system.add_nonholonomic_constraints(*args, **kwargs)
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('constraints, expected', [
+        ([], []),
+        (qd[2] - qd[0] + qd[1], [qd[2] - qd[0] + qd[1]]),
+        ([qd[2] + qd[1], u[2] - u[1]], [qd[2] + qd[1], u[2] - u[1]]),
+    ])
+    def test_velocity_constraints_overwrite(self, _filled_system_setup,
+                                            constraints, expected):
+        self.system.velocity_constraints = constraints
+        self._filled_system_check(exclude=('velocity_constraints',))
+        assert self.system.velocity_constraints[:] == expected
+
+    def test_velocity_constraints_back_to_auto(self, _filled_system_setup):
+        self.system.velocity_constraints = qd[3] - qd[2]
+        self._filled_system_check(exclude=('velocity_constraints',))
+        assert self.system.velocity_constraints[:] == [qd[3] - qd[2]]
+        self.system.velocity_constraints = None
+        self._filled_system_check()
+
+    def test_bodies(self, _filled_system_setup):
+        rb1, rb2 = RigidBody('rb1'), RigidBody('rb2')
+        p1, p2 = Particle('p1'), Particle('p2')
+        self.system.add_bodies(rb1, p1)
+        assert self.system.bodies == (*self.bodies, rb1, p1)
+        self.system.add_bodies(p2)
+        assert self.system.bodies == (*self.bodies, rb1, p1, p2)
+        self.system.bodies = []
+        assert self.system.bodies == ()
+        self.system.bodies = p2
+        assert self.system.bodies == (p2,)
+        symb = symbols('symb')
+        pytest.raises(TypeError, lambda: self.system.add_bodies(symb))
+        pytest.raises(ValueError, lambda: self.system.add_bodies(p2))
+        with pytest.raises(TypeError):
+            self.system.bodies = (rb1, rb2, p1, p2, symb)
+        assert self.system.bodies == (p2,)
+
+    def test_add_loads(self):
+        system = System()
+        N, A = ReferenceFrame('N'), ReferenceFrame('A')
+        rb1 = RigidBody('rb1', frame=N)
+        mc1 = Point('mc1')
+        p1 = Particle('p1', mc1)
+        system.add_loads(Torque(rb1, N.x), (mc1, A.x), Force(p1, A.x))
+        assert system.loads == ((N, N.x), (mc1, A.x), (mc1, A.x))
+        system.loads = [(A, A.x)]
+        assert system.loads == ((A, A.x),)
+        pytest.raises(ValueError, lambda: system.add_loads((N, N.x, N.y)))
+        with pytest.raises(TypeError):
+            system.loads = (N, N.x)
+        assert system.loads == ((A, A.x),)
+
+    def test_add_actuators(self):
+        system = System()
+        N, A = ReferenceFrame('N'), ReferenceFrame('A')
+        act1 = TorqueActuator(symbols('T1'), N.x, N)
+        act2 = TorqueActuator(symbols('T2'), N.y, N, A)
+        system.add_actuators(act1)
+        assert system.actuators == (act1,)
+        assert system.loads == ()
+        system.actuators = (act2,)
+        assert system.actuators == (act2,)
+
+    def test_add_joints(self):
+        q1, q2, q3, q4, u1, u2, u3 = dynamicsymbols('q1:5 u1:4')
+        rb1, rb2, rb3, rb4, rb5 = symbols('rb1:6', cls=RigidBody)
+        J1 = PinJoint('J1', rb1, rb2, q1, u1)
+        J2 = PrismaticJoint('J2', rb2, rb3, q2, u2)
+        J3 = PinJoint('J3', rb3, rb4, q3, u3)
+        J_lag = PinJoint('J_lag', rb4, rb5, q4, q4.diff(t))
+        system = System()
+        system.add_joints(J1)
+        assert system.joints == (J1,)
+        assert system.bodies == (rb1, rb2)
+        assert system.q_ind == ImmutableMatrix([q1])
+        assert system.u_ind == ImmutableMatrix([u1])
+        assert system.kdes == ImmutableMatrix([u1 - q1.diff(t)])
+        system.add_bodies(rb4)
+        system.add_coordinates(q3)
+        system.add_kdes(u3 - q3.diff(t))
+        system.add_joints(J3)
+        assert system.joints == (J1, J3)
+        assert system.bodies == (rb1, rb2, rb4, rb3)
+        assert system.q_ind == ImmutableMatrix([q1, q3])
+        assert system.u_ind == ImmutableMatrix([u1, u3])
+        assert system.kdes == ImmutableMatrix(
+            [u1 - q1.diff(t), u3 - q3.diff(t)])
+        system.add_kdes(-(u2 - q2.diff(t)))
+        system.add_joints(J2)
+        assert system.joints == (J1, J3, J2)
+        assert system.bodies == (rb1, rb2, rb4, rb3)
+        assert system.q_ind == ImmutableMatrix([q1, q3, q2])
+        assert system.u_ind == ImmutableMatrix([u1, u3, u2])
+        assert system.kdes == ImmutableMatrix([u1 - q1.diff(t), u3 - q3.diff(t),
+                                               -(u2 - q2.diff(t))])
+        system.add_joints(J_lag)
+        assert system.joints == (J1, J3, J2, J_lag)
+        assert system.bodies == (rb1, rb2, rb4, rb3, rb5)
+        assert system.q_ind == ImmutableMatrix([q1, q3, q2, q4])
+        assert system.u_ind == ImmutableMatrix([u1, u3, u2, q4.diff(t)])
+        assert system.kdes == ImmutableMatrix([u1 - q1.diff(t), u3 - q3.diff(t),
+                                               -(u2 - q2.diff(t))])
+        assert system.q_dep[:] == []
+        assert system.u_dep[:] == []
+        pytest.raises(ValueError, lambda: system.add_joints(J2))
+        pytest.raises(TypeError, lambda: system.add_joints(rb1))
+
+    def test_joints_setter(self, _filled_system_setup):
+        self.system.joints = self.joints[1:]
+        assert self.system.joints == self.joints[1:]
+        self._filled_system_check(exclude=('joints',))
+        self.system.q_ind = ()
+        self.system.u_ind = ()
+        self.system.joints = self.joints
+        self._filled_system_check()
+
+    @pytest.mark.parametrize('name, joint_index', [
+        ('J1', 0),
+        ('J2', 1),
+        ('not_existing', None),
+    ])
+    def test_get_joint(self, _filled_system_setup, name, joint_index):
+        joint = self.system.get_joint(name)
+        if joint_index is None:
+            assert joint is None
+        else:
+            assert joint == self.joints[joint_index]
+
+    @pytest.mark.parametrize('name, body_index', [
+        ('rb1', 0),
+        ('rb3', 2),
+        ('not_existing', None),
+    ])
+    def test_get_body(self, _filled_system_setup, name, body_index):
+        body = self.system.get_body(name)
+        if body_index is None:
+            assert body is None
+        else:
+            assert body == self.bodies[body_index]
+
+    @pytest.mark.parametrize('eom_method', [KanesMethod, LagrangesMethod])
+    def test_form_eoms_calls_subclass(self, _moving_point_mass, eom_method):
+        class MyMethod(eom_method):
+            pass
+
+        self.system.form_eoms(eom_method=MyMethod)
+        assert isinstance(self.system.eom_method, MyMethod)
+
+    @pytest.mark.parametrize('kwargs, expected', [
+        ({}, ImmutableMatrix([[-1, 0], [0, symbols('m')]])),
+        ({'explicit_kinematics': True}, ImmutableMatrix([[1, 0],
+                                                         [0, symbols('m')]])),
+    ])
+    def test_system_kane_form_eoms_kwargs(self, _moving_point_mass, kwargs,
+                                          expected):
+        self.system.form_eoms(**kwargs)
+        assert self.system.mass_matrix_full == expected
+
+    @pytest.mark.parametrize('kwargs, mm, gm', [
+        ({}, ImmutableMatrix([[1, 0], [0, symbols('m')]]),
+         ImmutableMatrix([q[0].diff(t), 0])),
+    ])
+    def test_system_lagrange_form_eoms_kwargs(self, _moving_point_mass, kwargs,
+                                              mm, gm):
+        self.system.form_eoms(eom_method=LagrangesMethod, **kwargs)
+        assert self.system.mass_matrix_full == mm
+        assert self.system.forcing_full == gm
+
+    @pytest.mark.parametrize('eom_method, kwargs, error', [
+        (KanesMethod, {'non_existing_kwarg': 1}, TypeError),
+        (LagrangesMethod, {'non_existing_kwarg': 1}, TypeError),
+        (KanesMethod, {'bodies': []}, ValueError),
+        (KanesMethod, {'kd_eqs': []}, ValueError),
+        (LagrangesMethod, {'bodies': []}, ValueError),
+        (LagrangesMethod, {'Lagrangian': 1}, ValueError),
+    ])
+    def test_form_eoms_kwargs_errors(self, _empty_system_setup, eom_method,
+                                     kwargs, error):
+        self.system.q_ind = q[0]
+        p = Particle('p', mass=symbols('m'))
+        self.system.add_bodies(p)
+        p.masscenter.set_pos(self.system.fixed_point, q[0] * self.system.x)
+        with pytest.raises(error):
+            self.system.form_eoms(eom_method=eom_method, **kwargs)
+
+
+class TestValidateSystem(TestSystemBase):
+    @pytest.mark.parametrize('valid_method, invalid_method, with_speeds', [
+        (KanesMethod, LagrangesMethod, True),
+        (LagrangesMethod, KanesMethod, False)
+    ])
+    def test_only_valid(self, valid_method, invalid_method, with_speeds):
+        self._create_filled_system(with_speeds=with_speeds)
+        self.system.validate_system(valid_method)
+        # Test Lagrange should fail due to the usage of generalized speeds
+        with pytest.raises(ValueError):
+            self.system.validate_system(invalid_method)
+
+    @pytest.mark.parametrize('method, with_speeds', [
+        (KanesMethod, True), (LagrangesMethod, False)])
+    def test_missing_joint_coordinate(self, method, with_speeds):
+        self._create_filled_system(with_speeds=with_speeds)
+        self.system.q_ind = self.q_ind[1:]
+        self.system.u_ind = self.u_ind[:-1]
+        self.system.kdes = self.kdes[:-1]
+        pytest.raises(ValueError, lambda: self.system.validate_system(method))
+
+    def test_missing_joint_speed(self, _filled_system_setup):
+        self.system.q_ind = self.q_ind[:-1]
+        self.system.u_ind = self.u_ind[1:]
+        self.system.kdes = self.kdes[:-1]
+        pytest.raises(ValueError, lambda: self.system.validate_system())
+
+    def test_missing_joint_kdes(self, _filled_system_setup):
+        self.system.kdes = self.kdes[1:]
+        pytest.raises(ValueError, lambda: self.system.validate_system())
+
+    def test_negative_joint_kdes(self, _filled_system_setup):
+        self.system.kdes = [-self.kdes[0]] + self.kdes[1:]
+        self.system.validate_system()
+
+    @pytest.mark.parametrize('method, with_speeds', [
+        (KanesMethod, True), (LagrangesMethod, False)])
+    def test_missing_holonomic_constraint(self, method, with_speeds):
+        self._create_filled_system(with_speeds=with_speeds)
+        self.system.holonomic_constraints = []
+        self.system.nonholonomic_constraints = self.nhc + [
+            self.u_ind[1] - self.u_dep[0] + self.u_ind[0]]
+        pytest.raises(ValueError, lambda: self.system.validate_system(method))
+        self.system.q_dep = []
+        self.system.q_ind = self.q_ind + self.q_dep
+        self.system.validate_system(method)
+
+    def test_missing_nonholonomic_constraint(self, _filled_system_setup):
+        self.system.nonholonomic_constraints = []
+        pytest.raises(ValueError, lambda: self.system.validate_system())
+        self.system.u_dep = self.u_dep[1]
+        self.system.u_ind = self.u_ind + [self.u_dep[0]]
+        self.system.validate_system()
+
+    def test_number_of_coordinates_speeds(self, _filled_system_setup):
+        # Test more speeds than coordinates
+        self.system.u_ind = self.u_ind + [u[5]]
+        self.system.kdes = self.kdes + [u[5] - qd[5]]
+        self.system.validate_system()
+        # Test more coordinates than speeds
+        self.system.q_ind = self.q_ind
+        self.system.u_ind = self.u_ind[:-1]
+        self.system.kdes = self.kdes[:-1]
+        pytest.raises(ValueError, lambda: self.system.validate_system())
+
+    def test_number_of_kdes(self, _filled_system_setup):
+        # Test wrong number of kdes
+        self.system.kdes = self.kdes[:-1]
+        pytest.raises(ValueError, lambda: self.system.validate_system())
+        self.system.kdes = self.kdes + [u[2] + u[1] - qd[2]]
+        pytest.raises(ValueError, lambda: self.system.validate_system())
+
+    def test_duplicates(self, _filled_system_setup):
+        # This is basically a redundant feature, which should never fail
+        self.system.validate_system(check_duplicates=True)
+
+    def test_speeds_in_lagrange(self, _filled_system_setup_no_speeds):
+        self.system.u_ind = u[:len(self.u_ind)]
+        with pytest.raises(ValueError):
+            self.system.validate_system(LagrangesMethod)
+        self.system.u_ind = []
+        self.system.validate_system(LagrangesMethod)
+        self.system.u_aux = ua
+        with pytest.raises(ValueError):
+            self.system.validate_system(LagrangesMethod)
+        self.system.u_aux = []
+        self.system.validate_system(LagrangesMethod)
+        self.system.add_joints(
+            PinJoint('Ju', RigidBody('rbu1'), RigidBody('rbu2')))
+        self.system.u_ind = []
+        with pytest.raises(ValueError):
+            self.system.validate_system(LagrangesMethod)
+
+
+class TestSystemExamples:
+    def test_cart_pendulum_kanes(self):
+        # This example is the same as in the top documentation of System
+        # Added a spring to the cart
+        g, l, mc, mp, k = symbols('g l mc mp k')
+        F, qp, qc, up, uc = dynamicsymbols('F qp qc up uc')
+        rail = RigidBody('rail')
+        cart = RigidBody('cart', mass=mc)
+        bob = Particle('bob', mass=mp)
+        bob_frame = ReferenceFrame('bob_frame')
+        system = System.from_newtonian(rail)
+        assert system.bodies == (rail,)
+        assert system.frame == rail.frame
+        assert system.fixed_point == rail.masscenter
+        slider = PrismaticJoint('slider', rail, cart, qc, uc, joint_axis=rail.x)
+        pin = PinJoint('pin', cart, bob, qp, up, joint_axis=cart.z,
+                       child_interframe=bob_frame, child_point=l * bob_frame.y)
+        system.add_joints(slider, pin)
+        assert system.joints == (slider, pin)
+        assert system.get_joint('slider') == slider
+        assert system.get_body('bob') == bob
+        system.apply_uniform_gravity(-g * system.y)
+        system.add_loads((cart.masscenter, F * rail.x))
+        system.add_actuators(TorqueActuator(k * qp, cart.z, bob_frame, cart))
+        system.validate_system()
+        system.form_eoms()
+        assert isinstance(system.eom_method, KanesMethod)
+        assert (simplify(system.mass_matrix - ImmutableMatrix(
+            [[mp + mc, mp * l * cos(qp)], [mp * l * cos(qp), mp * l ** 2]]))
+                == zeros(2, 2))
+        assert (simplify(system.forcing - ImmutableMatrix([
+            [mp * l * up ** 2 * sin(qp) + F],
+            [-mp * g * l * sin(qp) + k * qp]])) == zeros(2, 1))
+
+        system.add_holonomic_constraints(
+            sympify(bob.masscenter.pos_from(rail.masscenter).dot(system.x)))
+        assert system.eom_method is None
+        system.q_ind, system.q_dep = qp, qc
+        system.u_ind, system.u_dep = up, uc
+        system.validate_system()
+
+        # Computed solution based on manually solving the constraints
+        subs = {qc: -l * sin(qp),
+                uc: -l * cos(qp) * up,
+                uc.diff(t): l * (up ** 2 * sin(qp) - up.diff(t) * cos(qp))}
+        upd_expected = (
+            (-g * mp * sin(qp) + k * qp / l + l * mc * sin(2 * qp) * up ** 2 / 2
+             - l * mp * sin(2 * qp) * up ** 2 / 2 - F * cos(qp)) /
+            (l * (mc * cos(qp) ** 2 + mp * sin(qp) ** 2)))
+        upd_sol = tuple(solve(system.form_eoms().xreplace(subs),
+                              up.diff(t)).values())[0]
+        assert simplify(upd_sol - upd_expected) == 0
+        assert isinstance(system.eom_method, KanesMethod)
+
+        # Test other output
+        Mk = -ImmutableMatrix([[0, 1], [1, 0]])
+        gk = -ImmutableMatrix([uc, up])
+        Md = ImmutableMatrix([[-l ** 2 * mp * cos(qp) ** 2 + l ** 2 * mp,
+                               l * mp * cos(qp) - l * (mc + mp) * cos(qp)],
+                              [l * cos(qp), 1]])
+        gd = ImmutableMatrix(
+            [[-g * l * mp * sin(qp) + k * qp - l ** 2 * mp * up ** 2 * sin(qp) *
+              cos(qp) - l * F * cos(qp)], [l * up ** 2 * sin(qp)]])
+        Mm = (Mk.row_join(zeros(2, 2))).col_join(zeros(2, 2).row_join(Md))
+        gm = gk.col_join(gd)
+        assert simplify(system.mass_matrix - Md) == zeros(2, 2)
+        assert simplify(system.forcing - gd) == zeros(2, 1)
+        assert simplify(system.mass_matrix_full - Mm) == zeros(4, 4)
+        assert simplify(system.forcing_full - gm) == zeros(4, 1)
+
+    def test_cart_pendulum_lagrange(self):
+        # Lagrange version of test_cart_pendulus_kanes
+        # Added a spring to the cart
+        g, l, mc, mp, k = symbols('g l mc mp k')
+        F, qp, qc = dynamicsymbols('F qp qc')
+        qpd, qcd = dynamicsymbols('qp qc', 1)
+        rail = RigidBody('rail')
+        cart = RigidBody('cart', mass=mc)
+        bob = Particle('bob', mass=mp)
+        bob_frame = ReferenceFrame('bob_frame')
+        system = System.from_newtonian(rail)
+        assert system.bodies == (rail,)
+        assert system.frame == rail.frame
+        assert system.fixed_point == rail.masscenter
+        slider = PrismaticJoint('slider', rail, cart, qc, qcd,
+                                joint_axis=rail.x)
+        pin = PinJoint('pin', cart, bob, qp, qpd, joint_axis=cart.z,
+                       child_interframe=bob_frame, child_point=l * bob_frame.y)
+        system.add_joints(slider, pin)
+        assert system.joints == (slider, pin)
+        assert system.get_joint('slider') == slider
+        assert system.get_body('bob') == bob
+        for body in system.bodies:
+            body.potential_energy = body.mass * g * body.masscenter.pos_from(
+                system.fixed_point).dot(system.y)
+        system.add_loads((cart.masscenter, F * rail.x))
+        system.add_actuators(TorqueActuator(k * qp, cart.z, bob_frame, cart))
+        system.validate_system(LagrangesMethod)
+        system.form_eoms(LagrangesMethod)
+        assert (simplify(system.mass_matrix - ImmutableMatrix(
+            [[mp + mc, mp * l * cos(qp)], [mp * l * cos(qp), mp * l ** 2]]))
+                == zeros(2, 2))
+        assert (simplify(system.forcing - ImmutableMatrix([
+            [mp * l * qpd ** 2 * sin(qp) + F], [-mp * g * l * sin(qp) + k * qp]]
+        )) == zeros(2, 1))
+
+        system.add_holonomic_constraints(
+            sympify(bob.masscenter.pos_from(rail.masscenter).dot(system.x)))
+        assert system.eom_method is None
+        system.q_ind, system.q_dep = qp, qc
+
+        # Computed solution based on manually solving the constraints
+        subs = {qc: -l * sin(qp),
+                qcd: -l * cos(qp) * qpd,
+                qcd.diff(t): l * (qpd ** 2 * sin(qp) - qpd.diff(t) * cos(qp))}
+        qpdd_expected = (
+            (-g * mp * sin(qp) + k * qp / l + l * mc * sin(2 * qp) * qpd ** 2 /
+             2 - l * mp * sin(2 * qp) * qpd ** 2 / 2 - F * cos(qp)) /
+            (l * (mc * cos(qp) ** 2 + mp * sin(qp) ** 2)))
+        eoms = system.form_eoms(LagrangesMethod)
+        lam1 = system.eom_method.lam_vec[0]
+        lam1_sol = system.eom_method.solve_multipliers()[lam1]
+        qpdd_sol = solve(eoms[0].xreplace({lam1: lam1_sol}).xreplace(subs),
+                         qpd.diff(t))[0]
+        assert simplify(qpdd_sol - qpdd_expected) == 0
+        assert isinstance(system.eom_method, LagrangesMethod)
+
+        # Test other output
+        Md = ImmutableMatrix([[l ** 2 * mp, l * mp * cos(qp), -l * cos(qp)],
+                              [l * mp * cos(qp), mc + mp, -1]])
+        gd = ImmutableMatrix(
+            [[-g * l * mp * sin(qp) + k * qp],
+             [l * mp * sin(qp) * qpd ** 2 + F]])
+        Mm = (eye(2).row_join(zeros(2, 3))).col_join(zeros(3, 2).row_join(
+            Md.col_join(ImmutableMatrix([l * cos(qp), 1, 0]).T)))
+        gm = ImmutableMatrix([qpd, qcd] + gd[:] + [l * sin(qp) * qpd ** 2])
+        assert simplify(system.mass_matrix - Md) == zeros(2, 3)
+        assert simplify(system.forcing - gd) == zeros(2, 1)
+        assert simplify(system.mass_matrix_full - Mm) == zeros(5, 5)
+        assert simplify(system.forcing_full - gm) == zeros(5, 1)
+
+    def test_box_on_ground(self):
+        # Particle sliding on ground with friction. The applied force is assumed
+        # to be positive and to be higher than the friction force.
+        g, m, mu = symbols('g m mu')
+        q, u, ua = dynamicsymbols('q u ua')
+        N, F = dynamicsymbols('N F', positive=True)
+        P = Particle("P", mass=m)
+        system = System()
+        system.add_bodies(P)
+        P.masscenter.set_pos(system.fixed_point, q * system.x)
+        P.masscenter.set_vel(system.frame, u * system.x + ua * system.y)
+        system.q_ind, system.u_ind, system.u_aux = [q], [u], [ua]
+        system.kdes = [q.diff(t) - u]
+        system.apply_uniform_gravity(-g * system.y)
+        system.add_loads(
+            Force(P, N * system.y),
+            Force(P, F * system.x - mu * N * system.x))
+        system.validate_system()
+        system.form_eoms()
+
+        # Test other output
+        Mk = ImmutableMatrix([1])
+        gk = ImmutableMatrix([u])
+        Md = ImmutableMatrix([m])
+        gd = ImmutableMatrix([F - mu * N])
+        Mm = (Mk.row_join(zeros(1, 1))).col_join(zeros(1, 1).row_join(Md))
+        gm = gk.col_join(gd)
+        aux_eqs = ImmutableMatrix([N - m * g])
+        assert simplify(system.mass_matrix - Md) == zeros(1, 1)
+        assert simplify(system.forcing - gd) == zeros(1, 1)
+        assert simplify(system.mass_matrix_full - Mm) == zeros(2, 2)
+        assert simplify(system.forcing_full - gm) == zeros(2, 1)
+        assert simplify(system.eom_method.auxiliary_eqs - aux_eqs
+                        ) == zeros(1, 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_wrapping_geometry.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_wrapping_geometry.py
new file mode 100644
index 0000000000000000000000000000000000000000..30c3ae71db5da75238ebb3d4cc53e11a29a72e5d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/tests/test_wrapping_geometry.py
@@ -0,0 +1,363 @@
+"""Tests for the ``sympy.physics.mechanics.wrapping_geometry.py`` module."""
+
+import pytest
+
+from sympy import (
+    Integer,
+    Rational,
+    S,
+    Symbol,
+    acos,
+    cos,
+    pi,
+    sin,
+    sqrt,
+)
+from sympy.core.relational import Eq
+from sympy.physics.mechanics import (
+    Point,
+    ReferenceFrame,
+    WrappingCylinder,
+    WrappingSphere,
+    dynamicsymbols,
+)
+from sympy.simplify.simplify import simplify
+
+
+r = Symbol('r', positive=True)
+x = Symbol('x')
+q = dynamicsymbols('q')
+N = ReferenceFrame('N')
+
+
+class TestWrappingSphere:
+
+    @staticmethod
+    def test_valid_constructor():
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        sphere = WrappingSphere(r, pO)
+        assert isinstance(sphere, WrappingSphere)
+        assert hasattr(sphere, 'radius')
+        assert sphere.radius == r
+        assert hasattr(sphere, 'point')
+        assert sphere.point == pO
+
+    @staticmethod
+    @pytest.mark.parametrize('position', [S.Zero, Integer(2)*r*N.x])
+    def test_geodesic_length_point_not_on_surface_invalid(position):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        sphere = WrappingSphere(r, pO)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position)
+        p2 = Point('p2')
+        p2.set_pos(pO, position)
+
+        error_msg = r'point .* does not lie on the surface of'
+        with pytest.raises(ValueError, match=error_msg):
+            sphere.geodesic_length(p1, p2)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'position_1, position_2, expected',
+        [
+            (r*N.x, r*N.x, S.Zero),
+            (r*N.x, r*N.y, S.Half*pi*r),
+            (r*N.x, r*-N.x, pi*r),
+            (r*-N.x, r*N.x, pi*r),
+            (r*N.x, r*sqrt(2)*S.Half*(N.x + N.y), Rational(1, 4)*pi*r),
+            (
+                r*sqrt(2)*S.Half*(N.x + N.y),
+                r*sqrt(3)*Rational(1, 3)*(N.x + N.y + N.z),
+                r*acos(sqrt(6)*Rational(1, 3)),
+            ),
+        ]
+    )
+    def test_geodesic_length(position_1, position_2, expected):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        sphere = WrappingSphere(r, pO)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position_1)
+        p2 = Point('p2')
+        p2.set_pos(pO, position_2)
+
+        assert simplify(Eq(sphere.geodesic_length(p1, p2), expected))
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'position_1, position_2, vector_1, vector_2',
+        [
+            (r * N.x, r * N.y, N.y, N.x),
+            (r * N.x, -r * N.y, -N.y, N.x),
+            (
+                r * N.y,
+                sqrt(2)/2 * r * N.x - sqrt(2)/2 * r * N.y,
+                N.x,
+                sqrt(2)/2 * N.x + sqrt(2)/2 * N.y,
+            ),
+            (
+                r * N.x,
+                r / 2 * N.x + sqrt(3)/2 * r * N.y,
+                N.y,
+                sqrt(3)/2 * N.x - 1/2 * N.y,
+            ),
+            (
+                r * N.x,
+                sqrt(2)/2 * r * N.x + sqrt(2)/2 * r * N.y,
+                N.y,
+                sqrt(2)/2 * N.x - sqrt(2)/2 * N.y,
+            ),
+        ]
+    )
+    def test_geodesic_end_vectors(position_1, position_2, vector_1, vector_2):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        sphere = WrappingSphere(r, pO)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position_1)
+        p2 = Point('p2')
+        p2.set_pos(pO, position_2)
+
+        expected = (vector_1, vector_2)
+
+        assert sphere.geodesic_end_vectors(p1, p2) == expected
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'position',
+        [r * N.x, r * cos(q) * N.x + r * sin(q) * N.y]
+    )
+    def test_geodesic_end_vectors_invalid_coincident(position):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        sphere = WrappingSphere(r, pO)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position)
+        p2 = Point('p2')
+        p2.set_pos(pO, position)
+
+        with pytest.raises(ValueError):
+            _ = sphere.geodesic_end_vectors(p1, p2)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'position_1, position_2',
+        [
+            (r * N.x, -r * N.x),
+            (-r * N.y, r * N.y),
+            (
+                r * cos(q) * N.x + r * sin(q) * N.y,
+                -r * cos(q) * N.x - r * sin(q) * N.y,
+            )
+        ]
+    )
+    def test_geodesic_end_vectors_invalid_diametrically_opposite(
+        position_1,
+        position_2,
+    ):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        sphere = WrappingSphere(r, pO)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position_1)
+        p2 = Point('p2')
+        p2.set_pos(pO, position_2)
+
+        with pytest.raises(ValueError):
+            _ = sphere.geodesic_end_vectors(p1, p2)
+
+
+class TestWrappingCylinder:
+
+    @staticmethod
+    def test_valid_constructor():
+        N = ReferenceFrame('N')
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        cylinder = WrappingCylinder(r, pO, N.x)
+        assert isinstance(cylinder, WrappingCylinder)
+        assert hasattr(cylinder, 'radius')
+        assert cylinder.radius == r
+        assert hasattr(cylinder, 'point')
+        assert cylinder.point == pO
+        assert hasattr(cylinder, 'axis')
+        assert cylinder.axis == N.x
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'position, expected',
+        [
+            (S.Zero, False),
+            (r*N.y, True),
+            (r*N.z, True),
+            (r*(N.y + N.z).normalize(), True),
+            (Integer(2)*r*N.y, False),
+            (r*(N.x + N.y), True),
+            (r*(Integer(2)*N.x + N.y), True),
+            (Integer(2)*N.x + r*(Integer(2)*N.y + N.z).normalize(), True),
+            (r*(cos(q)*N.y + sin(q)*N.z), True)
+        ]
+    )
+    def test_point_is_on_surface(position, expected):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        cylinder = WrappingCylinder(r, pO, N.x)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position)
+
+        assert cylinder.point_on_surface(p1) is expected
+
+    @staticmethod
+    @pytest.mark.parametrize('position', [S.Zero, Integer(2)*r*N.y])
+    def test_geodesic_length_point_not_on_surface_invalid(position):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        cylinder = WrappingCylinder(r, pO, N.x)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position)
+        p2 = Point('p2')
+        p2.set_pos(pO, position)
+
+        error_msg = r'point .* does not lie on the surface of'
+        with pytest.raises(ValueError, match=error_msg):
+            cylinder.geodesic_length(p1, p2)
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'axis, position_1, position_2, expected',
+        [
+            (N.x, r*N.y, r*N.y, S.Zero),
+            (N.x, r*N.y, N.x + r*N.y, S.One),
+            (N.x, r*N.y, -x*N.x + r*N.y, sqrt(x**2)),
+            (-N.x, r*N.y, x*N.x + r*N.y, sqrt(x**2)),
+            (N.x, r*N.y, r*N.z, S.Half*pi*sqrt(r**2)),
+            (-N.x, r*N.y, r*N.z, Integer(3)*S.Half*pi*sqrt(r**2)),
+            (N.x, r*N.z, r*N.y, Integer(3)*S.Half*pi*sqrt(r**2)),
+            (-N.x, r*N.z, r*N.y, S.Half*pi*sqrt(r**2)),
+            (N.x, r*N.y, r*(cos(q)*N.y + sin(q)*N.z), sqrt(r**2*q**2)),
+            (
+                -N.x, r*N.y,
+                r*(cos(q)*N.y + sin(q)*N.z),
+                sqrt(r**2*(Integer(2)*pi - q)**2),
+            ),
+        ]
+    )
+    def test_geodesic_length(axis, position_1, position_2, expected):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        cylinder = WrappingCylinder(r, pO, axis)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position_1)
+        p2 = Point('p2')
+        p2.set_pos(pO, position_2)
+
+        assert simplify(Eq(cylinder.geodesic_length(p1, p2), expected))
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'axis, position_1, position_2, vector_1, vector_2',
+        [
+            (N.z, r * N.x, r * N.y, N.y, N.x),
+            (N.z, r * N.x, -r * N.x, N.y, N.y),
+            (N.z, -r * N.x, r * N.x, -N.y, -N.y),
+            (-N.z, r * N.x, -r * N.x, -N.y, -N.y),
+            (-N.z, -r * N.x, r * N.x, N.y, N.y),
+            (N.z, r * N.x, -r * N.y, N.y, -N.x),
+            (
+                N.z,
+                r * N.y,
+                sqrt(2)/2 * r * N.x - sqrt(2)/2 * r * N.y,
+                - N.x,
+                - sqrt(2)/2 * N.x - sqrt(2)/2 * N.y,
+            ),
+            (
+                N.z,
+                r * N.x,
+                r / 2 * N.x + sqrt(3)/2 * r * N.y,
+                N.y,
+                sqrt(3)/2 * N.x - 1/2 * N.y,
+            ),
+            (
+                N.z,
+                r * N.x,
+                sqrt(2)/2 * r * N.x + sqrt(2)/2 * r * N.y,
+                N.y,
+                sqrt(2)/2 * N.x - sqrt(2)/2 * N.y,
+            ),
+            (
+                N.z,
+                r * N.x,
+                r * N.x + N.z,
+                N.z,
+                -N.z,
+            ),
+            (
+                N.z,
+                r * N.x,
+                r * N.y + pi/2 * r * N.z,
+                sqrt(2)/2 * N.y + sqrt(2)/2 * N.z,
+                sqrt(2)/2 * N.x - sqrt(2)/2 * N.z,
+            ),
+            (
+                N.z,
+                r * N.x,
+                r * cos(q) * N.x + r * sin(q) * N.y,
+                N.y,
+                sin(q) * N.x - cos(q) * N.y,
+            ),
+        ]
+    )
+    def test_geodesic_end_vectors(
+        axis,
+        position_1,
+        position_2,
+        vector_1,
+        vector_2,
+    ):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        cylinder = WrappingCylinder(r, pO, axis)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position_1)
+        p2 = Point('p2')
+        p2.set_pos(pO, position_2)
+
+        expected = (vector_1, vector_2)
+        end_vectors = tuple(
+            end_vector.simplify()
+            for end_vector in cylinder.geodesic_end_vectors(p1, p2)
+        )
+
+        assert end_vectors == expected
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        'axis, position',
+        [
+            (N.z, r * N.x),
+            (N.z, r * cos(q) * N.x + r * sin(q) * N.y + N.z),
+        ]
+    )
+    def test_geodesic_end_vectors_invalid_coincident(axis, position):
+        r = Symbol('r', positive=True)
+        pO = Point('pO')
+        cylinder = WrappingCylinder(r, pO, axis)
+
+        p1 = Point('p1')
+        p1.set_pos(pO, position)
+        p2 = Point('p2')
+        p2.set_pos(pO, position)
+
+        with pytest.raises(ValueError):
+            _ = cylinder.geodesic_end_vectors(p1, p2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/wrapping_geometry.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/wrapping_geometry.py
new file mode 100644
index 0000000000000000000000000000000000000000..47ed3c1c463499b024afb9e31cfa2ecd77534132
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/mechanics/wrapping_geometry.py
@@ -0,0 +1,641 @@
+"""Geometry objects for use by wrapping pathways."""
+
+from abc import ABC, abstractmethod
+
+from sympy import Integer, acos, pi, sqrt, sympify, tan
+from sympy.core.relational import Eq
+from sympy.functions.elementary.trigonometric import atan2
+from sympy.polys.polytools import cancel
+from sympy.physics.vector import Vector, dot
+from sympy.simplify.simplify import trigsimp
+
+
+__all__ = [
+    'WrappingGeometryBase',
+    'WrappingCylinder',
+    'WrappingSphere',
+]
+
+
+class WrappingGeometryBase(ABC):
+    """Abstract base class for all geometry classes to inherit from.
+
+    Notes
+    =====
+
+    Instances of this class cannot be directly instantiated by users. However,
+    it can be used to created custom geometry types through subclassing.
+
+    """
+
+    @property
+    @abstractmethod
+    def point(cls):
+        """The point with which the geometry is associated."""
+        pass
+
+    @abstractmethod
+    def point_on_surface(self, point):
+        """Returns ``True`` if a point is on the geometry's surface.
+
+        Parameters
+        ==========
+        point : Point
+            The point for which it's to be ascertained if it's on the
+            geometry's surface or not.
+
+        """
+        pass
+
+    @abstractmethod
+    def geodesic_length(self, point_1, point_2):
+        """Returns the shortest distance between two points on a geometry's
+        surface.
+
+        Parameters
+        ==========
+
+        point_1 : Point
+            The point from which the geodesic length should be calculated.
+        point_2 : Point
+            The point to which the geodesic length should be calculated.
+
+        """
+        pass
+
+    @abstractmethod
+    def geodesic_end_vectors(self, point_1, point_2):
+        """The vectors parallel to the geodesic at the two end points.
+
+        Parameters
+        ==========
+
+        point_1 : Point
+            The point from which the geodesic originates.
+        point_2 : Point
+            The point at which the geodesic terminates.
+
+        """
+        pass
+
+    def __repr__(self):
+        """Default representation of a geometry object."""
+        return f'{self.__class__.__name__}()'
+
+
+class WrappingSphere(WrappingGeometryBase):
+    """A solid spherical object.
+
+    Explanation
+    ===========
+
+    A wrapping geometry that allows for circular arcs to be defined between
+    pairs of points. These paths are always geodetic (the shortest possible).
+
+    Examples
+    ========
+
+    To create a ``WrappingSphere`` instance, a ``Symbol`` denoting its radius
+    and ``Point`` at which its center will be located are needed:
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import Point, WrappingSphere
+    >>> r = symbols('r')
+    >>> pO = Point('pO')
+
+    A sphere with radius ``r`` centered on ``pO`` can be instantiated with:
+
+    >>> WrappingSphere(r, pO)
+    WrappingSphere(radius=r, point=pO)
+
+    Parameters
+    ==========
+
+    radius : Symbol
+        Radius of the sphere. This symbol must represent a value that is
+        positive and constant, i.e. it cannot be a dynamic symbol, nor can it
+        be an expression.
+    point : Point
+        A point at which the sphere is centered.
+
+    See Also
+    ========
+
+    WrappingCylinder: Cylindrical geometry where the wrapping direction can be
+        defined.
+
+    """
+
+    def __init__(self, radius, point):
+        """Initializer for ``WrappingSphere``.
+
+        Parameters
+        ==========
+
+        radius : Symbol
+            The radius of the sphere.
+        point : Point
+            A point on which the sphere is centered.
+
+        """
+        self.radius = radius
+        self.point = point
+
+    @property
+    def radius(self):
+        """Radius of the sphere."""
+        return self._radius
+
+    @radius.setter
+    def radius(self, radius):
+        self._radius = radius
+
+    @property
+    def point(self):
+        """A point on which the sphere is centered."""
+        return self._point
+
+    @point.setter
+    def point(self, point):
+        self._point = point
+
+    def point_on_surface(self, point):
+        """Returns ``True`` if a point is on the sphere's surface.
+
+        Parameters
+        ==========
+
+        point : Point
+            The point for which it's to be ascertained if it's on the sphere's
+            surface or not. This point's position relative to the sphere's
+            center must be a simple expression involving the radius of the
+            sphere, otherwise this check will likely not work.
+
+        """
+        point_vector = point.pos_from(self.point)
+        if isinstance(point_vector, Vector):
+            point_radius_squared = dot(point_vector, point_vector)
+        else:
+            point_radius_squared = point_vector**2
+        return Eq(point_radius_squared, self.radius**2) == True
+
+    def geodesic_length(self, point_1, point_2):
+        r"""Returns the shortest distance between two points on the sphere's
+        surface.
+
+        Explanation
+        ===========
+
+        The geodesic length, i.e. the shortest arc along the surface of a
+        sphere, connecting two points can be calculated using the formula:
+
+        .. math::
+
+           l = \arccos\left(\mathbf{v}_1 \cdot \mathbf{v}_2\right)
+
+        where $\mathbf{v}_1$ and $\mathbf{v}_2$ are the unit vectors from the
+        sphere's center to the first and second points on the sphere's surface
+        respectively. Note that the actual path that the geodesic will take is
+        undefined when the two points are directly opposite one another.
+
+        Examples
+        ========
+
+        A geodesic length can only be calculated between two points on the
+        sphere's surface. Firstly, a ``WrappingSphere`` instance must be
+        created along with two points that will lie on its surface:
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.mechanics import (Point, ReferenceFrame,
+        ...     WrappingSphere)
+        >>> N = ReferenceFrame('N')
+        >>> r = symbols('r')
+        >>> pO = Point('pO')
+        >>> pO.set_vel(N, 0)
+        >>> sphere = WrappingSphere(r, pO)
+        >>> p1 = Point('p1')
+        >>> p2 = Point('p2')
+
+        Let's assume that ``p1`` lies at a distance of ``r`` in the ``N.x``
+        direction from ``pO`` and that ``p2`` is located on the sphere's
+        surface in the ``N.y + N.z`` direction from ``pO``. These positions can
+        be set with:
+
+        >>> p1.set_pos(pO, r*N.x)
+        >>> p1.pos_from(pO)
+        r*N.x
+        >>> p2.set_pos(pO, r*(N.y + N.z).normalize())
+        >>> p2.pos_from(pO)
+        sqrt(2)*r/2*N.y + sqrt(2)*r/2*N.z
+
+        The geodesic length, which is in this case is a quarter of the sphere's
+        circumference, can be calculated using the ``geodesic_length`` method:
+
+        >>> sphere.geodesic_length(p1, p2)
+        pi*r/2
+
+        If the ``geodesic_length`` method is passed an argument, the ``Point``
+        that doesn't lie on the sphere's surface then a ``ValueError`` is
+        raised because it's not possible to calculate a value in this case.
+
+        Parameters
+        ==========
+
+        point_1 : Point
+            Point from which the geodesic length should be calculated.
+        point_2 : Point
+            Point to which the geodesic length should be calculated.
+
+        """
+        for point in (point_1, point_2):
+            if not self.point_on_surface(point):
+                msg = (
+                    f'Geodesic length cannot be calculated as point {point} '
+                    f'with radius {point.pos_from(self.point).magnitude()} '
+                    f'from the sphere\'s center {self.point} does not lie on '
+                    f'the surface of {self} with radius {self.radius}.'
+                )
+                raise ValueError(msg)
+        point_1_vector = point_1.pos_from(self.point).normalize()
+        point_2_vector = point_2.pos_from(self.point).normalize()
+        central_angle = acos(point_2_vector.dot(point_1_vector))
+        geodesic_length = self.radius*central_angle
+        return geodesic_length
+
+    def geodesic_end_vectors(self, point_1, point_2):
+        """The vectors parallel to the geodesic at the two end points.
+
+        Parameters
+        ==========
+
+        point_1 : Point
+            The point from which the geodesic originates.
+        point_2 : Point
+            The point at which the geodesic terminates.
+
+        """
+        pA, pB = point_1, point_2
+        pO = self.point
+        pA_vec = pA.pos_from(pO)
+        pB_vec = pB.pos_from(pO)
+
+        if pA_vec.cross(pB_vec) == 0:
+            msg = (
+                f'Can\'t compute geodesic end vectors for the pair of points '
+                f'{pA} and {pB} on a sphere {self} as they are diametrically '
+                f'opposed, thus the geodesic is not defined.'
+            )
+            raise ValueError(msg)
+
+        return (
+            pA_vec.cross(pB.pos_from(pA)).cross(pA_vec).normalize(),
+            pB_vec.cross(pA.pos_from(pB)).cross(pB_vec).normalize(),
+        )
+
+    def __repr__(self):
+        """Representation of a ``WrappingSphere``."""
+        return (
+            f'{self.__class__.__name__}(radius={self.radius}, '
+            f'point={self.point})'
+        )
+
+
+class WrappingCylinder(WrappingGeometryBase):
+    """A solid (infinite) cylindrical object.
+
+    Explanation
+    ===========
+
+    A wrapping geometry that allows for circular arcs to be defined between
+    pairs of points. These paths are always geodetic (the shortest possible) in
+    the sense that they will be a straight line on the unwrapped cylinder's
+    surface. However, it is also possible for a direction to be specified, i.e.
+    paths can be influenced such that they either wrap along the shortest side
+    or the longest side of the cylinder. To define these directions, rotations
+    are in the positive direction following the right-hand rule.
+
+    Examples
+    ========
+
+    To create a ``WrappingCylinder`` instance, a ``Symbol`` denoting its
+    radius, a ``Vector`` defining its axis, and a ``Point`` through which its
+    axis passes are needed:
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.mechanics import (Point, ReferenceFrame,
+    ...     WrappingCylinder)
+    >>> N = ReferenceFrame('N')
+    >>> r = symbols('r')
+    >>> pO = Point('pO')
+    >>> ax = N.x
+
+    A cylinder with radius ``r``, and axis parallel to ``N.x`` passing through
+    ``pO`` can be instantiated with:
+
+    >>> WrappingCylinder(r, pO, ax)
+    WrappingCylinder(radius=r, point=pO, axis=N.x)
+
+    Parameters
+    ==========
+
+    radius : Symbol
+        The radius of the cylinder.
+    point : Point
+        A point through which the cylinder's axis passes.
+    axis : Vector
+        The axis along which the cylinder is aligned.
+
+    See Also
+    ========
+
+    WrappingSphere: Spherical geometry where the wrapping direction is always
+        geodetic.
+
+    """
+
+    def __init__(self, radius, point, axis):
+        """Initializer for ``WrappingCylinder``.
+
+        Parameters
+        ==========
+
+        radius : Symbol
+            The radius of the cylinder. This symbol must represent a value that
+            is positive and constant, i.e. it cannot be a dynamic symbol.
+        point : Point
+            A point through which the cylinder's axis passes.
+        axis : Vector
+            The axis along which the cylinder is aligned.
+
+        """
+        self.radius = radius
+        self.point = point
+        self.axis = axis
+
+    @property
+    def radius(self):
+        """Radius of the cylinder."""
+        return self._radius
+
+    @radius.setter
+    def radius(self, radius):
+        self._radius = radius
+
+    @property
+    def point(self):
+        """A point through which the cylinder's axis passes."""
+        return self._point
+
+    @point.setter
+    def point(self, point):
+        self._point = point
+
+    @property
+    def axis(self):
+        """Axis along which the cylinder is aligned."""
+        return self._axis
+
+    @axis.setter
+    def axis(self, axis):
+        self._axis = axis.normalize()
+
+    def point_on_surface(self, point):
+        """Returns ``True`` if a point is on the cylinder's surface.
+
+        Parameters
+        ==========
+
+        point : Point
+            The point for which it's to be ascertained if it's on the
+            cylinder's surface or not. This point's position relative to the
+            cylinder's axis must be a simple expression involving the radius of
+            the sphere, otherwise this check will likely not work.
+
+        """
+        relative_position = point.pos_from(self.point)
+        parallel = relative_position.dot(self.axis) * self.axis
+        point_vector = relative_position - parallel
+        if isinstance(point_vector, Vector):
+            point_radius_squared = dot(point_vector, point_vector)
+        else:
+            point_radius_squared = point_vector**2
+        return Eq(trigsimp(point_radius_squared), self.radius**2) == True
+
+    def geodesic_length(self, point_1, point_2):
+        """The shortest distance between two points on a geometry's surface.
+
+        Explanation
+        ===========
+
+        The geodesic length, i.e. the shortest arc along the surface of a
+        cylinder, connecting two points. It can be calculated using Pythagoras'
+        theorem. The first short side is the distance between the two points on
+        the cylinder's surface parallel to the cylinder's axis. The second
+        short side is the arc of a circle between the two points of the
+        cylinder's surface perpendicular to the cylinder's axis. The resulting
+        hypotenuse is the geodesic length.
+
+        Examples
+        ========
+
+        A geodesic length can only be calculated between two points on the
+        cylinder's surface. Firstly, a ``WrappingCylinder`` instance must be
+        created along with two points that will lie on its surface:
+
+        >>> from sympy import symbols, cos, sin
+        >>> from sympy.physics.mechanics import (Point, ReferenceFrame,
+        ...     WrappingCylinder, dynamicsymbols)
+        >>> N = ReferenceFrame('N')
+        >>> r = symbols('r')
+        >>> pO = Point('pO')
+        >>> pO.set_vel(N, 0)
+        >>> cylinder = WrappingCylinder(r, pO, N.x)
+        >>> p1 = Point('p1')
+        >>> p2 = Point('p2')
+
+        Let's assume that ``p1`` is located at ``N.x + r*N.y`` relative to
+        ``pO`` and that ``p2`` is located at ``r*(cos(q)*N.y + sin(q)*N.z)``
+        relative to ``pO``, where ``q(t)`` is a generalized coordinate
+        specifying the angle rotated around the ``N.x`` axis according to the
+        right-hand rule where ``N.y`` is zero. These positions can be set with:
+
+        >>> q = dynamicsymbols('q')
+        >>> p1.set_pos(pO, N.x + r*N.y)
+        >>> p1.pos_from(pO)
+        N.x + r*N.y
+        >>> p2.set_pos(pO, r*(cos(q)*N.y + sin(q)*N.z).normalize())
+        >>> p2.pos_from(pO).simplify()
+        r*cos(q(t))*N.y + r*sin(q(t))*N.z
+
+        The geodesic length, which is in this case a is the hypotenuse of a
+        right triangle where the other two side lengths are ``1`` (parallel to
+        the cylinder's axis) and ``r*q(t)`` (parallel to the cylinder's cross
+        section), can be calculated using the ``geodesic_length`` method:
+
+        >>> cylinder.geodesic_length(p1, p2).simplify()
+        sqrt(r**2*q(t)**2 + 1)
+
+        If the ``geodesic_length`` method is passed an argument ``Point`` that
+        doesn't lie on the sphere's surface then a ``ValueError`` is raised
+        because it's not possible to calculate a value in this case.
+
+        Parameters
+        ==========
+
+        point_1 : Point
+            Point from which the geodesic length should be calculated.
+        point_2 : Point
+            Point to which the geodesic length should be calculated.
+
+        """
+        for point in (point_1, point_2):
+            if not self.point_on_surface(point):
+                msg = (
+                    f'Geodesic length cannot be calculated as point {point} '
+                    f'with radius {point.pos_from(self.point).magnitude()} '
+                    f'from the cylinder\'s center {self.point} does not lie on '
+                    f'the surface of {self} with radius {self.radius} and axis '
+                    f'{self.axis}.'
+                )
+                raise ValueError(msg)
+
+        relative_position = point_2.pos_from(point_1)
+        parallel_length = relative_position.dot(self.axis)
+
+        point_1_relative_position = point_1.pos_from(self.point)
+        point_1_perpendicular_vector = (
+            point_1_relative_position
+            - point_1_relative_position.dot(self.axis)*self.axis
+        ).normalize()
+
+        point_2_relative_position = point_2.pos_from(self.point)
+        point_2_perpendicular_vector = (
+            point_2_relative_position
+            - point_2_relative_position.dot(self.axis)*self.axis
+        ).normalize()
+
+        central_angle = _directional_atan(
+            cancel(point_1_perpendicular_vector
+                .cross(point_2_perpendicular_vector)
+                .dot(self.axis)),
+            cancel(point_1_perpendicular_vector.dot(point_2_perpendicular_vector)),
+        )
+
+        planar_arc_length = self.radius*central_angle
+        geodesic_length = sqrt(parallel_length**2 + planar_arc_length**2)
+        return geodesic_length
+
+    def geodesic_end_vectors(self, point_1, point_2):
+        """The vectors parallel to the geodesic at the two end points.
+
+        Parameters
+        ==========
+
+        point_1 : Point
+            The point from which the geodesic originates.
+        point_2 : Point
+            The point at which the geodesic terminates.
+
+        """
+        point_1_from_origin_point = point_1.pos_from(self.point)
+        point_2_from_origin_point = point_2.pos_from(self.point)
+
+        if point_1_from_origin_point == point_2_from_origin_point:
+            msg = (
+                f'Cannot compute geodesic end vectors for coincident points '
+                f'{point_1} and {point_2} as no geodesic exists.'
+            )
+            raise ValueError(msg)
+
+        point_1_parallel = point_1_from_origin_point.dot(self.axis) * self.axis
+        point_2_parallel = point_2_from_origin_point.dot(self.axis) * self.axis
+        point_1_normal = (point_1_from_origin_point - point_1_parallel)
+        point_2_normal = (point_2_from_origin_point - point_2_parallel)
+
+        if point_1_normal == point_2_normal:
+            point_1_perpendicular = Vector(0)
+            point_2_perpendicular = Vector(0)
+        else:
+            point_1_perpendicular = self.axis.cross(point_1_normal).normalize()
+            point_2_perpendicular = -self.axis.cross(point_2_normal).normalize()
+
+        geodesic_length = self.geodesic_length(point_1, point_2)
+        relative_position = point_2.pos_from(point_1)
+        parallel_length = relative_position.dot(self.axis)
+        planar_arc_length = sqrt(geodesic_length**2 - parallel_length**2)
+
+        point_1_vector = (
+            planar_arc_length * point_1_perpendicular
+            + parallel_length * self.axis
+        ).normalize()
+        point_2_vector = (
+            planar_arc_length * point_2_perpendicular
+            - parallel_length * self.axis
+        ).normalize()
+
+        return (point_1_vector, point_2_vector)
+
+    def __repr__(self):
+        """Representation of a ``WrappingCylinder``."""
+        return (
+            f'{self.__class__.__name__}(radius={self.radius}, '
+            f'point={self.point}, axis={self.axis})'
+        )
+
+
+def _directional_atan(numerator, denominator):
+    """Compute atan in a directional sense as required for geodesics.
+
+    Explanation
+    ===========
+
+    To be able to control the direction of the geodesic length along the
+    surface of a cylinder a dedicated arctangent function is needed that
+    properly handles the directionality of different case. This function
+    ensures that the central angle is always positive but shifting the case
+    where ``atan2`` would return a negative angle to be centered around
+    ``2*pi``.
+
+    Notes
+    =====
+
+    This function only handles very specific cases, i.e. the ones that are
+    expected to be encountered when calculating symbolic geodesics on uniformly
+    curved surfaces. As such, ``NotImplemented`` errors can be raised in many
+    cases. This function is named with a leader underscore to indicate that it
+    only aims to provide very specific functionality within the private scope
+    of this module.
+
+    """
+
+    if numerator.is_number and denominator.is_number:
+        angle = atan2(numerator, denominator)
+        if angle < 0:
+            angle += 2 * pi
+    elif numerator.is_number:
+        msg = (
+            f'Cannot compute a directional atan when the numerator {numerator} '
+            f'is numeric and the denominator {denominator} is symbolic.'
+        )
+        raise NotImplementedError(msg)
+    elif denominator.is_number:
+        msg = (
+            f'Cannot compute a directional atan when the numerator {numerator} '
+            f'is symbolic and the denominator {denominator} is numeric.'
+        )
+        raise NotImplementedError(msg)
+    else:
+        ratio = sympify(trigsimp(numerator / denominator))
+        if isinstance(ratio, tan):
+            angle = ratio.args[0]
+        elif (
+            ratio.is_Mul
+            and ratio.args[0] == Integer(-1)
+            and isinstance(ratio.args[1], tan)
+        ):
+            angle = 2 * pi - ratio.args[1].args[0]
+        else:
+            msg = f'Cannot compute a directional atan for the value {ratio}.'
+            raise NotImplementedError(msg)
+
+    return angle
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2d83d452fd30e718546c0eac26fe03bbef59c06
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/__init__.py
@@ -0,0 +1,38 @@
+__all__ = [
+    'TWave',
+
+    'RayTransferMatrix', 'FreeSpace', 'FlatRefraction', 'CurvedRefraction',
+    'FlatMirror', 'CurvedMirror', 'ThinLens', 'GeometricRay', 'BeamParameter',
+    'waist2rayleigh', 'rayleigh2waist', 'geometric_conj_ab',
+    'geometric_conj_af', 'geometric_conj_bf', 'gaussian_conj',
+    'conjugate_gauss_beams',
+
+    'Medium',
+
+    'refraction_angle', 'deviation', 'fresnel_coefficients', 'brewster_angle',
+    'critical_angle', 'lens_makers_formula', 'mirror_formula', 'lens_formula',
+    'hyperfocal_distance', 'transverse_magnification',
+
+    'jones_vector', 'stokes_vector', 'jones_2_stokes', 'linear_polarizer',
+    'phase_retarder', 'half_wave_retarder', 'quarter_wave_retarder',
+    'transmissive_filter', 'reflective_filter', 'mueller_matrix',
+    'polarizing_beam_splitter',
+]
+from .waves import TWave
+
+from .gaussopt import (RayTransferMatrix, FreeSpace, FlatRefraction,
+        CurvedRefraction, FlatMirror, CurvedMirror, ThinLens, GeometricRay,
+        BeamParameter, waist2rayleigh, rayleigh2waist, geometric_conj_ab,
+        geometric_conj_af, geometric_conj_bf, gaussian_conj,
+        conjugate_gauss_beams)
+
+from .medium import Medium
+
+from .utils import (refraction_angle, deviation, fresnel_coefficients,
+        brewster_angle, critical_angle, lens_makers_formula, mirror_formula,
+        lens_formula, hyperfocal_distance, transverse_magnification)
+
+from .polarization import (jones_vector, stokes_vector, jones_2_stokes,
+        linear_polarizer, phase_retarder, half_wave_retarder,
+        quarter_wave_retarder, transmissive_filter, reflective_filter,
+        mueller_matrix, polarizing_beam_splitter)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/gaussopt.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/gaussopt.py
new file mode 100644
index 0000000000000000000000000000000000000000..d9e8ef555d60e3204341cdc65cdd05fb02b2f196
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/gaussopt.py
@@ -0,0 +1,923 @@
+"""
+Gaussian optics.
+
+The module implements:
+
+- Ray transfer matrices for geometrical and gaussian optics.
+
+  See RayTransferMatrix, GeometricRay and BeamParameter
+
+- Conjugation relations for geometrical and gaussian optics.
+
+  See geometric_conj*, gauss_conj and conjugate_gauss_beams
+
+The conventions for the distances are as follows:
+
+focal distance
+    positive for convergent lenses
+object distance
+    positive for real objects
+image distance
+    positive for real images
+"""
+
+__all__ = [
+    'RayTransferMatrix',
+    'FreeSpace',
+    'FlatRefraction',
+    'CurvedRefraction',
+    'FlatMirror',
+    'CurvedMirror',
+    'ThinLens',
+    'GeometricRay',
+    'BeamParameter',
+    'waist2rayleigh',
+    'rayleigh2waist',
+    'geometric_conj_ab',
+    'geometric_conj_af',
+    'geometric_conj_bf',
+    'gaussian_conj',
+    'conjugate_gauss_beams',
+]
+
+
+from sympy.core.expr import Expr
+from sympy.core.numbers import (I, pi)
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.complexes import (im, re)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import atan2
+from sympy.matrices.dense import Matrix, MutableDenseMatrix
+from sympy.polys.rationaltools import together
+from sympy.utilities.misc import filldedent
+
+###
+# A, B, C, D matrices
+###
+
+
+class RayTransferMatrix(MutableDenseMatrix):
+    """
+    Base class for a Ray Transfer Matrix.
+
+    It should be used if there is not already a more specific subclass mentioned
+    in See Also.
+
+    Parameters
+    ==========
+
+    parameters :
+        A, B, C and D or 2x2 matrix (Matrix(2, 2, [A, B, C, D]))
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import RayTransferMatrix, ThinLens
+    >>> from sympy import Symbol, Matrix
+
+    >>> mat = RayTransferMatrix(1, 2, 3, 4)
+    >>> mat
+    Matrix([
+    [1, 2],
+    [3, 4]])
+
+    >>> RayTransferMatrix(Matrix([[1, 2], [3, 4]]))
+    Matrix([
+    [1, 2],
+    [3, 4]])
+
+    >>> mat.A
+    1
+
+    >>> f = Symbol('f')
+    >>> lens = ThinLens(f)
+    >>> lens
+    Matrix([
+    [   1, 0],
+    [-1/f, 1]])
+
+    >>> lens.C
+    -1/f
+
+    See Also
+    ========
+
+    GeometricRay, BeamParameter,
+    FreeSpace, FlatRefraction, CurvedRefraction,
+    FlatMirror, CurvedMirror, ThinLens
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis
+    """
+
+    def __new__(cls, *args):
+
+        if len(args) == 4:
+            temp = ((args[0], args[1]), (args[2], args[3]))
+        elif len(args) == 1 \
+            and isinstance(args[0], Matrix) \
+                and args[0].shape == (2, 2):
+            temp = args[0]
+        else:
+            raise ValueError(filldedent('''
+                Expecting 2x2 Matrix or the 4 elements of
+                the Matrix but got %s''' % str(args)))
+        return Matrix.__new__(cls, temp)
+
+    def __mul__(self, other):
+        if isinstance(other, RayTransferMatrix):
+            return RayTransferMatrix(Matrix(self)*Matrix(other))
+        elif isinstance(other, GeometricRay):
+            return GeometricRay(Matrix(self)*Matrix(other))
+        elif isinstance(other, BeamParameter):
+            temp = Matrix(self)*Matrix(((other.q,), (1,)))
+            q = (temp[0]/temp[1]).expand(complex=True)
+            return BeamParameter(other.wavelen,
+                                 together(re(q)),
+                                 z_r=together(im(q)))
+        else:
+            return Matrix.__mul__(self, other)
+
+    @property
+    def A(self):
+        """
+        The A parameter of the Matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import RayTransferMatrix
+        >>> mat = RayTransferMatrix(1, 2, 3, 4)
+        >>> mat.A
+        1
+        """
+        return self[0, 0]
+
+    @property
+    def B(self):
+        """
+        The B parameter of the Matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import RayTransferMatrix
+        >>> mat = RayTransferMatrix(1, 2, 3, 4)
+        >>> mat.B
+        2
+        """
+        return self[0, 1]
+
+    @property
+    def C(self):
+        """
+        The C parameter of the Matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import RayTransferMatrix
+        >>> mat = RayTransferMatrix(1, 2, 3, 4)
+        >>> mat.C
+        3
+        """
+        return self[1, 0]
+
+    @property
+    def D(self):
+        """
+        The D parameter of the Matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import RayTransferMatrix
+        >>> mat = RayTransferMatrix(1, 2, 3, 4)
+        >>> mat.D
+        4
+        """
+        return self[1, 1]
+
+
+class FreeSpace(RayTransferMatrix):
+    """
+    Ray Transfer Matrix for free space.
+
+    Parameters
+    ==========
+
+    distance
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import FreeSpace
+    >>> from sympy import symbols
+    >>> d = symbols('d')
+    >>> FreeSpace(d)
+    Matrix([
+    [1, d],
+    [0, 1]])
+    """
+    def __new__(cls, d):
+        return RayTransferMatrix.__new__(cls, 1, d, 0, 1)
+
+
+class FlatRefraction(RayTransferMatrix):
+    """
+    Ray Transfer Matrix for refraction.
+
+    Parameters
+    ==========
+
+    n1 :
+        Refractive index of one medium.
+    n2 :
+        Refractive index of other medium.
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import FlatRefraction
+    >>> from sympy import symbols
+    >>> n1, n2 = symbols('n1 n2')
+    >>> FlatRefraction(n1, n2)
+    Matrix([
+    [1,     0],
+    [0, n1/n2]])
+    """
+    def __new__(cls, n1, n2):
+        n1, n2 = map(sympify, (n1, n2))
+        return RayTransferMatrix.__new__(cls, 1, 0, 0, n1/n2)
+
+
+class CurvedRefraction(RayTransferMatrix):
+    """
+    Ray Transfer Matrix for refraction on curved interface.
+
+    Parameters
+    ==========
+
+    R :
+        Radius of curvature (positive for concave).
+    n1 :
+        Refractive index of one medium.
+    n2 :
+        Refractive index of other medium.
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import CurvedRefraction
+    >>> from sympy import symbols
+    >>> R, n1, n2 = symbols('R n1 n2')
+    >>> CurvedRefraction(R, n1, n2)
+    Matrix([
+    [               1,     0],
+    [(n1 - n2)/(R*n2), n1/n2]])
+    """
+    def __new__(cls, R, n1, n2):
+        R, n1, n2 = map(sympify, (R, n1, n2))
+        return RayTransferMatrix.__new__(cls, 1, 0, (n1 - n2)/R/n2, n1/n2)
+
+
+class FlatMirror(RayTransferMatrix):
+    """
+    Ray Transfer Matrix for reflection.
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import FlatMirror
+    >>> FlatMirror()
+    Matrix([
+    [1, 0],
+    [0, 1]])
+    """
+    def __new__(cls):
+        return RayTransferMatrix.__new__(cls, 1, 0, 0, 1)
+
+
+class CurvedMirror(RayTransferMatrix):
+    """
+    Ray Transfer Matrix for reflection from curved surface.
+
+    Parameters
+    ==========
+
+    R : radius of curvature (positive for concave)
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import CurvedMirror
+    >>> from sympy import symbols
+    >>> R = symbols('R')
+    >>> CurvedMirror(R)
+    Matrix([
+    [   1, 0],
+    [-2/R, 1]])
+    """
+    def __new__(cls, R):
+        R = sympify(R)
+        return RayTransferMatrix.__new__(cls, 1, 0, -2/R, 1)
+
+
+class ThinLens(RayTransferMatrix):
+    """
+    Ray Transfer Matrix for a thin lens.
+
+    Parameters
+    ==========
+
+    f :
+        The focal distance.
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import ThinLens
+    >>> from sympy import symbols
+    >>> f = symbols('f')
+    >>> ThinLens(f)
+    Matrix([
+    [   1, 0],
+    [-1/f, 1]])
+    """
+    def __new__(cls, f):
+        f = sympify(f)
+        return RayTransferMatrix.__new__(cls, 1, 0, -1/f, 1)
+
+
+###
+# Representation for geometric ray
+###
+
+class GeometricRay(MutableDenseMatrix):
+    """
+    Representation for a geometric ray in the Ray Transfer Matrix formalism.
+
+    Parameters
+    ==========
+
+    h : height, and
+    angle : angle, or
+    matrix : a 2x1 matrix (Matrix(2, 1, [height, angle]))
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import GeometricRay, FreeSpace
+    >>> from sympy import symbols, Matrix
+    >>> d, h, angle = symbols('d, h, angle')
+
+    >>> GeometricRay(h, angle)
+    Matrix([
+    [    h],
+    [angle]])
+
+    >>> FreeSpace(d)*GeometricRay(h, angle)
+    Matrix([
+    [angle*d + h],
+    [      angle]])
+
+    >>> GeometricRay( Matrix( ((h,), (angle,)) ) )
+    Matrix([
+    [    h],
+    [angle]])
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    """
+
+    def __new__(cls, *args):
+        if len(args) == 1 and isinstance(args[0], Matrix) \
+                and args[0].shape == (2, 1):
+            temp = args[0]
+        elif len(args) == 2:
+            temp = ((args[0],), (args[1],))
+        else:
+            raise ValueError(filldedent('''
+                Expecting 2x1 Matrix or the 2 elements of
+                the Matrix but got %s''' % str(args)))
+        return Matrix.__new__(cls, temp)
+
+    @property
+    def height(self):
+        """
+        The distance from the optical axis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import GeometricRay
+        >>> from sympy import symbols
+        >>> h, angle = symbols('h, angle')
+        >>> gRay = GeometricRay(h, angle)
+        >>> gRay.height
+        h
+        """
+        return self[0]
+
+    @property
+    def angle(self):
+        """
+        The angle with the optical axis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import GeometricRay
+        >>> from sympy import symbols
+        >>> h, angle = symbols('h, angle')
+        >>> gRay = GeometricRay(h, angle)
+        >>> gRay.angle
+        angle
+        """
+        return self[1]
+
+
+###
+# Representation for gauss beam
+###
+
+class BeamParameter(Expr):
+    """
+    Representation for a gaussian ray in the Ray Transfer Matrix formalism.
+
+    Parameters
+    ==========
+
+    wavelen : the wavelength,
+    z : the distance to waist, and
+    w : the waist, or
+    z_r : the rayleigh range.
+    n : the refractive index of medium.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import BeamParameter
+    >>> p = BeamParameter(530e-9, 1, w=1e-3)
+    >>> p.q
+    1 + 1.88679245283019*I*pi
+
+    >>> p.q.n()
+    1.0 + 5.92753330865999*I
+    >>> p.w_0.n()
+    0.00100000000000000
+    >>> p.z_r.n()
+    5.92753330865999
+
+    >>> from sympy.physics.optics import FreeSpace
+    >>> fs = FreeSpace(10)
+    >>> p1 = fs*p
+    >>> p.w.n()
+    0.00101413072159615
+    >>> p1.w.n()
+    0.00210803120913829
+
+    See Also
+    ========
+
+    RayTransferMatrix
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Complex_beam_parameter
+    .. [2] https://en.wikipedia.org/wiki/Gaussian_beam
+    """
+    #TODO A class Complex may be implemented. The BeamParameter may
+    # subclass it. See:
+    # https://groups.google.com/d/topic/sympy/7XkU07NRBEs/discussion
+
+    def __new__(cls, wavelen, z, z_r=None, w=None, n=1):
+        wavelen = sympify(wavelen)
+        z = sympify(z)
+        n = sympify(n)
+
+        if z_r is not None and w is None:
+            z_r = sympify(z_r)
+        elif w is not None and z_r is None:
+            z_r = waist2rayleigh(sympify(w), wavelen, n)
+        elif z_r is None and w is None:
+            raise ValueError('Must specify one of w and z_r.')
+
+        return Expr.__new__(cls, wavelen, z, z_r, n)
+
+    @property
+    def wavelen(self):
+        return self.args[0]
+
+    @property
+    def z(self):
+        return self.args[1]
+
+    @property
+    def z_r(self):
+        return self.args[2]
+
+    @property
+    def n(self):
+        return self.args[3]
+
+    @property
+    def q(self):
+        """
+        The complex parameter representing the beam.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.q
+        1 + 1.88679245283019*I*pi
+        """
+        return self.z + I*self.z_r
+
+    @property
+    def radius(self):
+        """
+        The radius of curvature of the phase front.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.radius
+        1 + 3.55998576005696*pi**2
+        """
+        return self.z*(1 + (self.z_r/self.z)**2)
+
+    @property
+    def w(self):
+        """
+        The radius of the beam w(z), at any position z along the beam.
+        The beam radius at `1/e^2` intensity (axial value).
+
+        See Also
+        ========
+
+        w_0 :
+            The minimal radius of beam.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.w
+        0.001*sqrt(0.2809/pi**2 + 1)
+        """
+        return self.w_0*sqrt(1 + (self.z/self.z_r)**2)
+
+    @property
+    def w_0(self):
+        """
+         The minimal radius of beam at `1/e^2` intensity (peak value).
+
+        See Also
+        ========
+
+        w : the beam radius at `1/e^2` intensity (axial value).
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.w_0
+        0.00100000000000000
+        """
+        return sqrt(self.z_r/(pi*self.n)*self.wavelen)
+
+    @property
+    def divergence(self):
+        """
+        Half of the total angular spread.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.divergence
+        0.00053/pi
+        """
+        return self.wavelen/pi/self.w_0
+
+    @property
+    def gouy(self):
+        """
+        The Gouy phase.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.gouy
+        atan(0.53/pi)
+        """
+        return atan2(self.z, self.z_r)
+
+    @property
+    def waist_approximation_limit(self):
+        """
+        The minimal waist for which the gauss beam approximation is valid.
+
+        Explanation
+        ===========
+
+        The gauss beam is a solution to the paraxial equation. For curvatures
+        that are too great it is not a valid approximation.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import BeamParameter
+        >>> p = BeamParameter(530e-9, 1, w=1e-3)
+        >>> p.waist_approximation_limit
+        1.06e-6/pi
+        """
+        return 2*self.wavelen/pi
+
+
+###
+# Utilities
+###
+
+def waist2rayleigh(w, wavelen, n=1):
+    """
+    Calculate the rayleigh range from the waist of a gaussian beam.
+
+    See Also
+    ========
+
+    rayleigh2waist, BeamParameter
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import waist2rayleigh
+    >>> from sympy import symbols
+    >>> w, wavelen = symbols('w wavelen')
+    >>> waist2rayleigh(w, wavelen)
+    pi*w**2/wavelen
+    """
+    w, wavelen = map(sympify, (w, wavelen))
+    return w**2*n*pi/wavelen
+
+
+def rayleigh2waist(z_r, wavelen):
+    """Calculate the waist from the rayleigh range of a gaussian beam.
+
+    See Also
+    ========
+
+    waist2rayleigh, BeamParameter
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import rayleigh2waist
+    >>> from sympy import symbols
+    >>> z_r, wavelen = symbols('z_r wavelen')
+    >>> rayleigh2waist(z_r, wavelen)
+    sqrt(wavelen*z_r)/sqrt(pi)
+    """
+    z_r, wavelen = map(sympify, (z_r, wavelen))
+    return sqrt(z_r/pi*wavelen)
+
+
+def geometric_conj_ab(a, b):
+    """
+    Conjugation relation for geometrical beams under paraxial conditions.
+
+    Explanation
+    ===========
+
+    Takes the distances to the optical element and returns the needed
+    focal distance.
+
+    See Also
+    ========
+
+    geometric_conj_af, geometric_conj_bf
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import geometric_conj_ab
+    >>> from sympy import symbols
+    >>> a, b = symbols('a b')
+    >>> geometric_conj_ab(a, b)
+    a*b/(a + b)
+    """
+    a, b = map(sympify, (a, b))
+    if a.is_infinite or b.is_infinite:
+        return a if b.is_infinite else b
+    else:
+        return a*b/(a + b)
+
+
+def geometric_conj_af(a, f):
+    """
+    Conjugation relation for geometrical beams under paraxial conditions.
+
+    Explanation
+    ===========
+
+    Takes the object distance (for geometric_conj_af) or the image distance
+    (for geometric_conj_bf) to the optical element and the focal distance.
+    Then it returns the other distance needed for conjugation.
+
+    See Also
+    ========
+
+    geometric_conj_ab
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics.gaussopt import geometric_conj_af, geometric_conj_bf
+    >>> from sympy import symbols
+    >>> a, b, f = symbols('a b f')
+    >>> geometric_conj_af(a, f)
+    a*f/(a - f)
+    >>> geometric_conj_bf(b, f)
+    b*f/(b - f)
+    """
+    a, f = map(sympify, (a, f))
+    return -geometric_conj_ab(a, -f)
+
+geometric_conj_bf = geometric_conj_af
+
+
+def gaussian_conj(s_in, z_r_in, f):
+    """
+    Conjugation relation for gaussian beams.
+
+    Parameters
+    ==========
+
+    s_in :
+        The distance to optical element from the waist.
+    z_r_in :
+        The rayleigh range of the incident beam.
+    f :
+        The focal length of the optical element.
+
+    Returns
+    =======
+
+    a tuple containing (s_out, z_r_out, m)
+    s_out :
+        The distance between the new waist and the optical element.
+    z_r_out :
+        The rayleigh range of the emergent beam.
+    m :
+        The ration between the new and the old waists.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import gaussian_conj
+    >>> from sympy import symbols
+    >>> s_in, z_r_in, f = symbols('s_in z_r_in f')
+
+    >>> gaussian_conj(s_in, z_r_in, f)[0]
+    1/(-1/(s_in + z_r_in**2/(-f + s_in)) + 1/f)
+
+    >>> gaussian_conj(s_in, z_r_in, f)[1]
+    z_r_in/(1 - s_in**2/f**2 + z_r_in**2/f**2)
+
+    >>> gaussian_conj(s_in, z_r_in, f)[2]
+    1/sqrt(1 - s_in**2/f**2 + z_r_in**2/f**2)
+    """
+    s_in, z_r_in, f = map(sympify, (s_in, z_r_in, f))
+    s_out = 1 / ( -1/(s_in + z_r_in**2/(s_in - f)) + 1/f )
+    m = 1/sqrt((1 - (s_in/f)**2) + (z_r_in/f)**2)
+    z_r_out = z_r_in / ((1 - (s_in/f)**2) + (z_r_in/f)**2)
+    return (s_out, z_r_out, m)
+
+
+def conjugate_gauss_beams(wavelen, waist_in, waist_out, **kwargs):
+    """
+    Find the optical setup conjugating the object/image waists.
+
+    Parameters
+    ==========
+
+    wavelen :
+        The wavelength of the beam.
+    waist_in and waist_out :
+        The waists to be conjugated.
+    f :
+        The focal distance of the element used in the conjugation.
+
+    Returns
+    =======
+
+    a tuple containing (s_in, s_out, f)
+    s_in :
+        The distance before the optical element.
+    s_out :
+        The distance after the optical element.
+    f :
+        The focal distance of the optical element.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import conjugate_gauss_beams
+    >>> from sympy import symbols, factor
+    >>> l, w_i, w_o, f = symbols('l w_i w_o f')
+
+    >>> conjugate_gauss_beams(l, w_i, w_o, f=f)[0]
+    f*(1 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)))
+
+    >>> factor(conjugate_gauss_beams(l, w_i, w_o, f=f)[1])
+    f*w_o**2*(w_i**2/w_o**2 - sqrt(w_i**2/w_o**2 -
+              pi**2*w_i**4/(f**2*l**2)))/w_i**2
+
+    >>> conjugate_gauss_beams(l, w_i, w_o, f=f)[2]
+    f
+    """
+    #TODO add the other possible arguments
+    wavelen, waist_in, waist_out = map(sympify, (wavelen, waist_in, waist_out))
+    m = waist_out / waist_in
+    z = waist2rayleigh(waist_in, wavelen)
+    if len(kwargs) != 1:
+        raise ValueError("The function expects only one named argument")
+    elif 'dist' in kwargs:
+        raise NotImplementedError(filldedent('''
+            Currently only focal length is supported as a parameter'''))
+    elif 'f' in kwargs:
+        f = sympify(kwargs['f'])
+        s_in = f * (1 - sqrt(1/m**2 - z**2/f**2))
+        s_out = gaussian_conj(s_in, z, f)[0]
+    elif 's_in' in kwargs:
+        raise NotImplementedError(filldedent('''
+            Currently only focal length is supported as a parameter'''))
+    else:
+        raise ValueError(filldedent('''
+            The functions expects the focal length as a named argument'''))
+    return (s_in, s_out, f)
+
+#TODO
+#def plot_beam():
+#    """Plot the beam radius as it propagates in space."""
+#    pass
+
+#TODO
+#def plot_beam_conjugation():
+#    """
+#    Plot the intersection of two beams.
+#
+#    Represents the conjugation relation.
+#
+#    See Also
+#    ========
+#
+#    conjugate_gauss_beams
+#    """
+#    pass
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/medium.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/medium.py
new file mode 100644
index 0000000000000000000000000000000000000000..764b68caad5865b8f3cee028a14cfa304796b4c0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/medium.py
@@ -0,0 +1,253 @@
+"""
+**Contains**
+
+* Medium
+"""
+from sympy.physics.units import second, meter, kilogram, ampere
+
+__all__ = ['Medium']
+
+from sympy.core.basic import Basic
+from sympy.core.symbol import Str
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.units import speed_of_light, u0, e0
+
+
+c = speed_of_light.convert_to(meter/second)
+_e0mksa = e0.convert_to(ampere**2*second**4/(kilogram*meter**3))
+_u0mksa = u0.convert_to(meter*kilogram/(ampere**2*second**2))
+
+
+class Medium(Basic):
+
+    """
+    This class represents an optical medium. The prime reason to implement this is
+    to facilitate refraction, Fermat's principle, etc.
+
+    Explanation
+    ===========
+
+    An optical medium is a material through which electromagnetic waves propagate.
+    The permittivity and permeability of the medium define how electromagnetic
+    waves propagate in it.
+
+
+    Parameters
+    ==========
+
+    name: string
+        The display name of the Medium.
+
+    permittivity: Sympifyable
+        Electric permittivity of the space.
+
+    permeability: Sympifyable
+        Magnetic permeability of the space.
+
+    n: Sympifyable
+        Index of refraction of the medium.
+
+
+    Examples
+    ========
+
+    >>> from sympy.abc import epsilon, mu
+    >>> from sympy.physics.optics import Medium
+    >>> m1 = Medium('m1')
+    >>> m2 = Medium('m2', epsilon, mu)
+    >>> m1.intrinsic_impedance
+    149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3)
+    >>> m2.refractive_index
+    299792458*meter*sqrt(epsilon*mu)/second
+
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Optical_medium
+
+    """
+
+    def __new__(cls, name, permittivity=None, permeability=None, n=None):
+        if not isinstance(name, Str):
+            name = Str(name)
+
+        permittivity = _sympify(permittivity) if permittivity is not None else permittivity
+        permeability = _sympify(permeability) if permeability is not None else permeability
+        n = _sympify(n) if n is not None else n
+
+        if n is not None:
+            if permittivity is not None and permeability is None:
+                permeability = n**2/(c**2*permittivity)
+                return MediumPP(name, permittivity, permeability)
+            elif permeability is not None and permittivity is None:
+                permittivity = n**2/(c**2*permeability)
+                return MediumPP(name, permittivity, permeability)
+            elif permittivity is not None and permittivity is not None:
+                raise ValueError("Specifying all of permittivity, permeability, and n is not allowed")
+            else:
+                return MediumN(name, n)
+        elif permittivity is not None and permeability is not None:
+            return MediumPP(name, permittivity, permeability)
+        elif permittivity is None and permeability is None:
+            return MediumPP(name, _e0mksa, _u0mksa)
+        else:
+            raise ValueError("Arguments are underspecified. Either specify n or any two of permittivity, "
+                             "permeability, and n")
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def speed(self):
+        """
+        Returns speed of the electromagnetic wave travelling in the medium.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import Medium
+        >>> m = Medium('m')
+        >>> m.speed
+        299792458*meter/second
+        >>> m2 = Medium('m2', n=1)
+        >>> m.speed == m2.speed
+        True
+
+        """
+        return c / self.n
+
+    @property
+    def refractive_index(self):
+        """
+        Returns refractive index of the medium.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import Medium
+        >>> m = Medium('m')
+        >>> m.refractive_index
+        1
+
+        """
+        return (c/self.speed)
+
+
+class MediumN(Medium):
+
+    """
+    Represents an optical medium for which only the refractive index is known.
+    Useful for simple ray optics.
+
+    This class should never be instantiated directly.
+    Instead it should be instantiated indirectly by instantiating Medium with
+    only n specified.
+
+    Examples
+    ========
+    >>> from sympy.physics.optics import Medium
+    >>> m = Medium('m', n=2)
+    >>> m
+    MediumN(Str('m'), 2)
+    """
+
+    def __new__(cls, name, n):
+        obj = super(Medium, cls).__new__(cls, name, n)
+        return obj
+
+    @property
+    def n(self):
+        return self.args[1]
+
+
+class MediumPP(Medium):
+    """
+    Represents an optical medium for which the permittivity and permeability are known.
+
+    This class should never be instantiated directly. Instead it should be
+    instantiated indirectly by instantiating Medium with any two of
+    permittivity, permeability, and n specified, or by not specifying any
+    of permittivity, permeability, or n, in which case default values for
+    permittivity and permeability will be used.
+
+    Examples
+    ========
+    >>> from sympy.physics.optics import Medium
+    >>> from sympy.abc import epsilon, mu
+    >>> m1 = Medium('m1', permittivity=epsilon, permeability=mu)
+    >>> m1
+    MediumPP(Str('m1'), epsilon, mu)
+    >>> m2 = Medium('m2')
+    >>> m2
+    MediumPP(Str('m2'), 625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3), pi*kilogram*meter/(2500000*ampere**2*second**2))
+    """
+
+
+    def __new__(cls, name, permittivity, permeability):
+        obj = super(Medium, cls).__new__(cls, name, permittivity, permeability)
+        return obj
+
+    @property
+    def intrinsic_impedance(self):
+        """
+        Returns intrinsic impedance of the medium.
+
+        Explanation
+        ===========
+
+        The intrinsic impedance of a medium is the ratio of the
+        transverse components of the electric and magnetic fields
+        of the electromagnetic wave travelling in the medium.
+        In a region with no electrical conductivity it simplifies
+        to the square root of ratio of magnetic permeability to
+        electric permittivity.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import Medium
+        >>> m = Medium('m')
+        >>> m.intrinsic_impedance
+        149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3)
+
+        """
+        return sqrt(self.permeability / self.permittivity)
+
+    @property
+    def permittivity(self):
+        """
+        Returns electric permittivity of the medium.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import Medium
+        >>> m = Medium('m')
+        >>> m.permittivity
+        625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3)
+
+        """
+        return self.args[1]
+
+    @property
+    def permeability(self):
+        """
+        Returns magnetic permeability of the medium.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.optics import Medium
+        >>> m = Medium('m')
+        >>> m.permeability
+        pi*kilogram*meter/(2500000*ampere**2*second**2)
+
+        """
+        return self.args[2]
+
+    @property
+    def n(self):
+        return c*sqrt(self.permittivity*self.permeability)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/polarization.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/polarization.py
new file mode 100644
index 0000000000000000000000000000000000000000..0bdb546548ad082ef38f5f0c159d7eadd38f6d30
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/polarization.py
@@ -0,0 +1,732 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""
+The module implements routines to model the polarization of optical fields
+and can be used to calculate the effects of polarization optical elements on
+the fields.
+
+- Jones vectors.
+
+- Stokes vectors.
+
+- Jones matrices.
+
+- Mueller matrices.
+
+Examples
+========
+
+We calculate a generic Jones vector:
+
+>>> from sympy import symbols, pprint, zeros, simplify
+>>> from sympy.physics.optics.polarization import (jones_vector, stokes_vector,
+...     half_wave_retarder, polarizing_beam_splitter, jones_2_stokes)
+
+>>> psi, chi, p, I0 = symbols("psi, chi, p, I0", real=True)
+>>> x0 = jones_vector(psi, chi)
+>>> pprint(x0, use_unicode=True)
+⎡-ⅈ⋅sin(χ)⋅sin(ψ) + cos(χ)⋅cos(ψ)⎤
+⎢                                ⎥
+⎣ⅈ⋅sin(χ)⋅cos(ψ) + sin(ψ)⋅cos(χ) ⎦
+
+And the more general Stokes vector:
+
+>>> s0 = stokes_vector(psi, chi, p, I0)
+>>> pprint(s0, use_unicode=True)
+⎡          I₀          ⎤
+⎢                      ⎥
+⎢I₀⋅p⋅cos(2⋅χ)⋅cos(2⋅ψ)⎥
+⎢                      ⎥
+⎢I₀⋅p⋅sin(2⋅ψ)⋅cos(2⋅χ)⎥
+⎢                      ⎥
+⎣    I₀⋅p⋅sin(2⋅χ)     ⎦
+
+We calculate how the Jones vector is modified by a half-wave plate:
+
+>>> alpha = symbols("alpha", real=True)
+>>> HWP = half_wave_retarder(alpha)
+>>> x1 = simplify(HWP*x0)
+
+We calculate the very common operation of passing a beam through a half-wave
+plate and then through a polarizing beam-splitter. We do this by putting this
+Jones vector as the first entry of a two-Jones-vector state that is transformed
+by a 4x4 Jones matrix modelling the polarizing beam-splitter to get the
+transmitted and reflected Jones vectors:
+
+>>> PBS = polarizing_beam_splitter()
+>>> X1 = zeros(4, 1)
+>>> X1[:2, :] = x1
+>>> X2 = PBS*X1
+>>> transmitted_port = X2[:2, :]
+>>> reflected_port = X2[2:, :]
+
+This allows us to calculate how the power in both ports depends on the initial
+polarization:
+
+>>> transmitted_power = jones_2_stokes(transmitted_port)[0]
+>>> reflected_power = jones_2_stokes(reflected_port)[0]
+>>> print(transmitted_power)
+cos(-2*alpha + chi + psi)**2/2 + cos(2*alpha + chi - psi)**2/2
+
+
+>>> print(reflected_power)
+sin(-2*alpha + chi + psi)**2/2 + sin(2*alpha + chi - psi)**2/2
+
+Please see the description of the individual functions for further
+details and examples.
+
+References
+==========
+
+.. [1] https://en.wikipedia.org/wiki/Jones_calculus
+.. [2] https://en.wikipedia.org/wiki/Mueller_calculus
+.. [3] https://en.wikipedia.org/wiki/Stokes_parameters
+
+"""
+
+from sympy.core.numbers import (I, pi)
+from sympy.functions.elementary.complexes import (Abs, im, re)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.matrices.dense import Matrix
+from sympy.simplify.simplify import simplify
+from sympy.physics.quantum import TensorProduct
+
+
+def jones_vector(psi, chi):
+    """A Jones vector corresponding to a polarization ellipse with `psi` tilt,
+    and `chi` circularity.
+
+    Parameters
+    ==========
+
+    psi : numeric type or SymPy Symbol
+        The tilt of the polarization relative to the `x` axis.
+
+    chi : numeric type or SymPy Symbol
+        The angle adjacent to the mayor axis of the polarization ellipse.
+
+
+    Returns
+    =======
+
+    Matrix :
+        A Jones vector.
+
+    Examples
+    ========
+
+    The axes on the Poincaré sphere.
+
+    >>> from sympy import pprint, symbols, pi
+    >>> from sympy.physics.optics.polarization import jones_vector
+    >>> psi, chi = symbols("psi, chi", real=True)
+
+    A general Jones vector.
+
+    >>> pprint(jones_vector(psi, chi), use_unicode=True)
+    ⎡-ⅈ⋅sin(χ)⋅sin(ψ) + cos(χ)⋅cos(ψ)⎤
+    ⎢                                ⎥
+    ⎣ⅈ⋅sin(χ)⋅cos(ψ) + sin(ψ)⋅cos(χ) ⎦
+
+    Horizontal polarization.
+
+    >>> pprint(jones_vector(0, 0), use_unicode=True)
+    ⎡1⎤
+    ⎢ ⎥
+    ⎣0⎦
+
+    Vertical polarization.
+
+    >>> pprint(jones_vector(pi/2, 0), use_unicode=True)
+    ⎡0⎤
+    ⎢ ⎥
+    ⎣1⎦
+
+    Diagonal polarization.
+
+    >>> pprint(jones_vector(pi/4, 0), use_unicode=True)
+    ⎡√2⎤
+    ⎢──⎥
+    ⎢2 ⎥
+    ⎢  ⎥
+    ⎢√2⎥
+    ⎢──⎥
+    ⎣2 ⎦
+
+    Anti-diagonal polarization.
+
+    >>> pprint(jones_vector(-pi/4, 0), use_unicode=True)
+    ⎡ √2 ⎤
+    ⎢ ── ⎥
+    ⎢ 2  ⎥
+    ⎢    ⎥
+    ⎢-√2 ⎥
+    ⎢────⎥
+    ⎣ 2  ⎦
+
+    Right-hand circular polarization.
+
+    >>> pprint(jones_vector(0, pi/4), use_unicode=True)
+    ⎡ √2 ⎤
+    ⎢ ── ⎥
+    ⎢ 2  ⎥
+    ⎢    ⎥
+    ⎢√2⋅ⅈ⎥
+    ⎢────⎥
+    ⎣ 2  ⎦
+
+    Left-hand circular polarization.
+
+    >>> pprint(jones_vector(0, -pi/4), use_unicode=True)
+    ⎡  √2  ⎤
+    ⎢  ──  ⎥
+    ⎢  2   ⎥
+    ⎢      ⎥
+    ⎢-√2⋅ⅈ ⎥
+    ⎢──────⎥
+    ⎣  2   ⎦
+
+    """
+    return Matrix([-I*sin(chi)*sin(psi) + cos(chi)*cos(psi),
+                   I*sin(chi)*cos(psi) + sin(psi)*cos(chi)])
+
+
+def stokes_vector(psi, chi, p=1, I=1):
+    """A Stokes vector corresponding to a polarization ellipse with ``psi``
+    tilt, and ``chi`` circularity.
+
+    Parameters
+    ==========
+
+    psi : numeric type or SymPy Symbol
+        The tilt of the polarization relative to the ``x`` axis.
+    chi : numeric type or SymPy Symbol
+        The angle adjacent to the mayor axis of the polarization ellipse.
+    p : numeric type or SymPy Symbol
+        The degree of polarization.
+    I : numeric type or SymPy Symbol
+        The intensity of the field.
+
+
+    Returns
+    =======
+
+    Matrix :
+        A Stokes vector.
+
+    Examples
+    ========
+
+    The axes on the Poincaré sphere.
+
+    >>> from sympy import pprint, symbols, pi
+    >>> from sympy.physics.optics.polarization import stokes_vector
+    >>> psi, chi, p, I = symbols("psi, chi, p, I", real=True)
+    >>> pprint(stokes_vector(psi, chi, p, I), use_unicode=True)
+    ⎡          I          ⎤
+    ⎢                     ⎥
+    ⎢I⋅p⋅cos(2⋅χ)⋅cos(2⋅ψ)⎥
+    ⎢                     ⎥
+    ⎢I⋅p⋅sin(2⋅ψ)⋅cos(2⋅χ)⎥
+    ⎢                     ⎥
+    ⎣    I⋅p⋅sin(2⋅χ)     ⎦
+
+
+    Horizontal polarization
+
+    >>> pprint(stokes_vector(0, 0), use_unicode=True)
+    ⎡1⎤
+    ⎢ ⎥
+    ⎢1⎥
+    ⎢ ⎥
+    ⎢0⎥
+    ⎢ ⎥
+    ⎣0⎦
+
+    Vertical polarization
+
+    >>> pprint(stokes_vector(pi/2, 0), use_unicode=True)
+    ⎡1 ⎤
+    ⎢  ⎥
+    ⎢-1⎥
+    ⎢  ⎥
+    ⎢0 ⎥
+    ⎢  ⎥
+    ⎣0 ⎦
+
+    Diagonal polarization
+
+    >>> pprint(stokes_vector(pi/4, 0), use_unicode=True)
+    ⎡1⎤
+    ⎢ ⎥
+    ⎢0⎥
+    ⎢ ⎥
+    ⎢1⎥
+    ⎢ ⎥
+    ⎣0⎦
+
+    Anti-diagonal polarization
+
+    >>> pprint(stokes_vector(-pi/4, 0), use_unicode=True)
+    ⎡1 ⎤
+    ⎢  ⎥
+    ⎢0 ⎥
+    ⎢  ⎥
+    ⎢-1⎥
+    ⎢  ⎥
+    ⎣0 ⎦
+
+    Right-hand circular polarization
+
+    >>> pprint(stokes_vector(0, pi/4), use_unicode=True)
+    ⎡1⎤
+    ⎢ ⎥
+    ⎢0⎥
+    ⎢ ⎥
+    ⎢0⎥
+    ⎢ ⎥
+    ⎣1⎦
+
+    Left-hand circular polarization
+
+    >>> pprint(stokes_vector(0, -pi/4), use_unicode=True)
+    ⎡1 ⎤
+    ⎢  ⎥
+    ⎢0 ⎥
+    ⎢  ⎥
+    ⎢0 ⎥
+    ⎢  ⎥
+    ⎣-1⎦
+
+    Unpolarized light
+
+    >>> pprint(stokes_vector(0, 0, 0), use_unicode=True)
+    ⎡1⎤
+    ⎢ ⎥
+    ⎢0⎥
+    ⎢ ⎥
+    ⎢0⎥
+    ⎢ ⎥
+    ⎣0⎦
+
+    """
+    S0 = I
+    S1 = I*p*cos(2*psi)*cos(2*chi)
+    S2 = I*p*sin(2*psi)*cos(2*chi)
+    S3 = I*p*sin(2*chi)
+    return Matrix([S0, S1, S2, S3])
+
+
+def jones_2_stokes(e):
+    """Return the Stokes vector for a Jones vector ``e``.
+
+    Parameters
+    ==========
+
+    e : SymPy Matrix
+        A Jones vector.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A Jones vector.
+
+    Examples
+    ========
+
+    The axes on the Poincaré sphere.
+
+    >>> from sympy import pprint, pi
+    >>> from sympy.physics.optics.polarization import jones_vector
+    >>> from sympy.physics.optics.polarization import jones_2_stokes
+    >>> H = jones_vector(0, 0)
+    >>> V = jones_vector(pi/2, 0)
+    >>> D = jones_vector(pi/4, 0)
+    >>> A = jones_vector(-pi/4, 0)
+    >>> R = jones_vector(0, pi/4)
+    >>> L = jones_vector(0, -pi/4)
+    >>> pprint([jones_2_stokes(e) for e in [H, V, D, A, R, L]],
+    ...         use_unicode=True)
+    ⎡⎡1⎤  ⎡1 ⎤  ⎡1⎤  ⎡1 ⎤  ⎡1⎤  ⎡1 ⎤⎤
+    ⎢⎢ ⎥  ⎢  ⎥  ⎢ ⎥  ⎢  ⎥  ⎢ ⎥  ⎢  ⎥⎥
+    ⎢⎢1⎥  ⎢-1⎥  ⎢0⎥  ⎢0 ⎥  ⎢0⎥  ⎢0 ⎥⎥
+    ⎢⎢ ⎥, ⎢  ⎥, ⎢ ⎥, ⎢  ⎥, ⎢ ⎥, ⎢  ⎥⎥
+    ⎢⎢0⎥  ⎢0 ⎥  ⎢1⎥  ⎢-1⎥  ⎢0⎥  ⎢0 ⎥⎥
+    ⎢⎢ ⎥  ⎢  ⎥  ⎢ ⎥  ⎢  ⎥  ⎢ ⎥  ⎢  ⎥⎥
+    ⎣⎣0⎦  ⎣0 ⎦  ⎣0⎦  ⎣0 ⎦  ⎣1⎦  ⎣-1⎦⎦
+
+    """
+    ex, ey = e
+    return Matrix([Abs(ex)**2 + Abs(ey)**2,
+                   Abs(ex)**2 - Abs(ey)**2,
+                   2*re(ex*ey.conjugate()),
+                   -2*im(ex*ey.conjugate())])
+
+
+def linear_polarizer(theta=0):
+    """A linear polarizer Jones matrix with transmission axis at
+    an angle ``theta``.
+
+    Parameters
+    ==========
+
+    theta : numeric type or SymPy Symbol
+        The angle of the transmission axis relative to the horizontal plane.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A Jones matrix representing the polarizer.
+
+    Examples
+    ========
+
+    A generic polarizer.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import linear_polarizer
+    >>> theta = symbols("theta", real=True)
+    >>> J = linear_polarizer(theta)
+    >>> pprint(J, use_unicode=True)
+    ⎡      2                     ⎤
+    ⎢   cos (θ)     sin(θ)⋅cos(θ)⎥
+    ⎢                            ⎥
+    ⎢                     2      ⎥
+    ⎣sin(θ)⋅cos(θ)     sin (θ)   ⎦
+
+
+    """
+    M = Matrix([[cos(theta)**2, sin(theta)*cos(theta)],
+                [sin(theta)*cos(theta), sin(theta)**2]])
+    return M
+
+
+def phase_retarder(theta=0, delta=0):
+    """A phase retarder Jones matrix with retardance ``delta`` at angle ``theta``.
+
+    Parameters
+    ==========
+
+    theta : numeric type or SymPy Symbol
+        The angle of the fast axis relative to the horizontal plane.
+    delta : numeric type or SymPy Symbol
+        The phase difference between the fast and slow axes of the
+        transmitted light.
+
+    Returns
+    =======
+
+    SymPy Matrix :
+        A Jones matrix representing the retarder.
+
+    Examples
+    ========
+
+    A generic retarder.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import phase_retarder
+    >>> theta, delta = symbols("theta, delta", real=True)
+    >>> R = phase_retarder(theta, delta)
+    >>> pprint(R, use_unicode=True)
+    ⎡                          -ⅈ⋅δ               -ⅈ⋅δ               ⎤
+    ⎢                          ─────              ─────              ⎥
+    ⎢⎛ ⅈ⋅δ    2         2   ⎞    2    ⎛     ⅈ⋅δ⎞    2                ⎥
+    ⎢⎝ℯ   ⋅sin (θ) + cos (θ)⎠⋅ℯ       ⎝1 - ℯ   ⎠⋅ℯ     ⋅sin(θ)⋅cos(θ)⎥
+    ⎢                                                                ⎥
+    ⎢            -ⅈ⋅δ                                           -ⅈ⋅δ ⎥
+    ⎢            ─────                                          ─────⎥
+    ⎢⎛     ⅈ⋅δ⎞    2                  ⎛ ⅈ⋅δ    2         2   ⎞    2  ⎥
+    ⎣⎝1 - ℯ   ⎠⋅ℯ     ⋅sin(θ)⋅cos(θ)  ⎝ℯ   ⋅cos (θ) + sin (θ)⎠⋅ℯ     ⎦
+
+    """
+    R = Matrix([[cos(theta)**2 + exp(I*delta)*sin(theta)**2,
+                (1-exp(I*delta))*cos(theta)*sin(theta)],
+                [(1-exp(I*delta))*cos(theta)*sin(theta),
+                sin(theta)**2 + exp(I*delta)*cos(theta)**2]])
+    return R*exp(-I*delta/2)
+
+
+def half_wave_retarder(theta):
+    """A half-wave retarder Jones matrix at angle ``theta``.
+
+    Parameters
+    ==========
+
+    theta : numeric type or SymPy Symbol
+        The angle of the fast axis relative to the horizontal plane.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A Jones matrix representing the retarder.
+
+    Examples
+    ========
+
+    A generic half-wave plate.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import half_wave_retarder
+    >>> theta= symbols("theta", real=True)
+    >>> HWP = half_wave_retarder(theta)
+    >>> pprint(HWP, use_unicode=True)
+    ⎡   ⎛     2         2   ⎞                        ⎤
+    ⎢-ⅈ⋅⎝- sin (θ) + cos (θ)⎠    -2⋅ⅈ⋅sin(θ)⋅cos(θ)  ⎥
+    ⎢                                                ⎥
+    ⎢                             ⎛   2         2   ⎞⎥
+    ⎣   -2⋅ⅈ⋅sin(θ)⋅cos(θ)     -ⅈ⋅⎝sin (θ) - cos (θ)⎠⎦
+
+    """
+    return phase_retarder(theta, pi)
+
+
+def quarter_wave_retarder(theta):
+    """A quarter-wave retarder Jones matrix at angle ``theta``.
+
+    Parameters
+    ==========
+
+    theta : numeric type or SymPy Symbol
+        The angle of the fast axis relative to the horizontal plane.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A Jones matrix representing the retarder.
+
+    Examples
+    ========
+
+    A generic quarter-wave plate.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import quarter_wave_retarder
+    >>> theta= symbols("theta", real=True)
+    >>> QWP = quarter_wave_retarder(theta)
+    >>> pprint(QWP, use_unicode=True)
+    ⎡                       -ⅈ⋅π            -ⅈ⋅π               ⎤
+    ⎢                       ─────           ─────              ⎥
+    ⎢⎛     2         2   ⎞    4               4                ⎥
+    ⎢⎝ⅈ⋅sin (θ) + cos (θ)⎠⋅ℯ       (1 - ⅈ)⋅ℯ     ⋅sin(θ)⋅cos(θ)⎥
+    ⎢                                                          ⎥
+    ⎢         -ⅈ⋅π                                        -ⅈ⋅π ⎥
+    ⎢         ─────                                       ─────⎥
+    ⎢           4                  ⎛   2           2   ⎞    4  ⎥
+    ⎣(1 - ⅈ)⋅ℯ     ⋅sin(θ)⋅cos(θ)  ⎝sin (θ) + ⅈ⋅cos (θ)⎠⋅ℯ     ⎦
+
+    """
+    return phase_retarder(theta, pi/2)
+
+
+def transmissive_filter(T):
+    """An attenuator Jones matrix with transmittance ``T``.
+
+    Parameters
+    ==========
+
+    T : numeric type or SymPy Symbol
+        The transmittance of the attenuator.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A Jones matrix representing the filter.
+
+    Examples
+    ========
+
+    A generic filter.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import transmissive_filter
+    >>> T = symbols("T", real=True)
+    >>> NDF = transmissive_filter(T)
+    >>> pprint(NDF, use_unicode=True)
+    ⎡√T  0 ⎤
+    ⎢      ⎥
+    ⎣0   √T⎦
+
+    """
+    return Matrix([[sqrt(T), 0], [0, sqrt(T)]])
+
+
+def reflective_filter(R):
+    """A reflective filter Jones matrix with reflectance ``R``.
+
+    Parameters
+    ==========
+
+    R : numeric type or SymPy Symbol
+        The reflectance of the filter.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A Jones matrix representing the filter.
+
+    Examples
+    ========
+
+    A generic filter.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import reflective_filter
+    >>> R = symbols("R", real=True)
+    >>> pprint(reflective_filter(R), use_unicode=True)
+    ⎡√R   0 ⎤
+    ⎢       ⎥
+    ⎣0   -√R⎦
+
+    """
+    return Matrix([[sqrt(R), 0], [0, -sqrt(R)]])
+
+
+def mueller_matrix(J):
+    """The Mueller matrix corresponding to Jones matrix `J`.
+
+    Parameters
+    ==========
+
+    J : SymPy Matrix
+        A Jones matrix.
+
+    Returns
+    =======
+
+    SymPy Matrix
+        The corresponding Mueller matrix.
+
+    Examples
+    ========
+
+    Generic optical components.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import (mueller_matrix,
+    ...     linear_polarizer, half_wave_retarder, quarter_wave_retarder)
+    >>> theta = symbols("theta", real=True)
+
+    A linear_polarizer
+
+    >>> pprint(mueller_matrix(linear_polarizer(theta)), use_unicode=True)
+    ⎡            cos(2⋅θ)      sin(2⋅θ)     ⎤
+    ⎢  1/2       ────────      ────────    0⎥
+    ⎢               2             2         ⎥
+    ⎢                                       ⎥
+    ⎢cos(2⋅θ)  cos(4⋅θ)   1    sin(4⋅θ)     ⎥
+    ⎢────────  ──────── + ─    ────────    0⎥
+    ⎢   2         4       4       4         ⎥
+    ⎢                                       ⎥
+    ⎢sin(2⋅θ)    sin(4⋅θ)    1   cos(4⋅θ)   ⎥
+    ⎢────────    ────────    ─ - ────────  0⎥
+    ⎢   2           4        4      4       ⎥
+    ⎢                                       ⎥
+    ⎣   0           0             0        0⎦
+
+    A half-wave plate
+
+    >>> pprint(mueller_matrix(half_wave_retarder(theta)), use_unicode=True)
+    ⎡1              0                           0               0 ⎤
+    ⎢                                                             ⎥
+    ⎢        4           2                                        ⎥
+    ⎢0  8⋅sin (θ) - 8⋅sin (θ) + 1           sin(4⋅θ)            0 ⎥
+    ⎢                                                             ⎥
+    ⎢                                     4           2           ⎥
+    ⎢0          sin(4⋅θ)           - 8⋅sin (θ) + 8⋅sin (θ) - 1  0 ⎥
+    ⎢                                                             ⎥
+    ⎣0              0                           0               -1⎦
+
+    A quarter-wave plate
+
+    >>> pprint(mueller_matrix(quarter_wave_retarder(theta)), use_unicode=True)
+    ⎡1       0             0            0    ⎤
+    ⎢                                        ⎥
+    ⎢   cos(4⋅θ)   1    sin(4⋅θ)             ⎥
+    ⎢0  ──────── + ─    ────────    -sin(2⋅θ)⎥
+    ⎢      2       2       2                 ⎥
+    ⎢                                        ⎥
+    ⎢     sin(4⋅θ)    1   cos(4⋅θ)           ⎥
+    ⎢0    ────────    ─ - ────────  cos(2⋅θ) ⎥
+    ⎢        2        2      2               ⎥
+    ⎢                                        ⎥
+    ⎣0    sin(2⋅θ)     -cos(2⋅θ)        0    ⎦
+
+    """
+    A = Matrix([[1, 0, 0, 1],
+                [1, 0, 0, -1],
+                [0, 1, 1, 0],
+                [0, -I, I, 0]])
+
+    return simplify(A*TensorProduct(J, J.conjugate())*A.inv())
+
+
+def polarizing_beam_splitter(Tp=1, Rs=1, Ts=0, Rp=0, phia=0, phib=0):
+    r"""A polarizing beam splitter Jones matrix at angle `theta`.
+
+    Parameters
+    ==========
+
+    J : SymPy Matrix
+        A Jones matrix.
+    Tp : numeric type or SymPy Symbol
+        The transmissivity of the P-polarized component.
+    Rs : numeric type or SymPy Symbol
+        The reflectivity of the S-polarized component.
+    Ts : numeric type or SymPy Symbol
+        The transmissivity of the S-polarized component.
+    Rp : numeric type or SymPy Symbol
+        The reflectivity of the P-polarized component.
+    phia : numeric type or SymPy Symbol
+        The phase difference between transmitted and reflected component for
+        output mode a.
+    phib : numeric type or SymPy Symbol
+        The phase difference between transmitted and reflected component for
+        output mode b.
+
+
+    Returns
+    =======
+
+    SymPy Matrix
+        A 4x4 matrix representing the PBS. This matrix acts on a 4x1 vector
+        whose first two entries are the Jones vector on one of the PBS ports,
+        and the last two entries the Jones vector on the other port.
+
+    Examples
+    ========
+
+    Generic polarizing beam-splitter.
+
+    >>> from sympy import pprint, symbols
+    >>> from sympy.physics.optics.polarization import polarizing_beam_splitter
+    >>> Ts, Rs, Tp, Rp = symbols(r"Ts, Rs, Tp, Rp", positive=True)
+    >>> phia, phib = symbols("phi_a, phi_b", real=True)
+    >>> PBS = polarizing_beam_splitter(Tp, Rs, Ts, Rp, phia, phib)
+    >>> pprint(PBS, use_unicode=False)
+    [   ____                           ____                    ]
+    [ \/ Tp            0           I*\/ Rp           0         ]
+    [                                                          ]
+    [                  ____                       ____  I*phi_a]
+    [   0            \/ Ts            0      -I*\/ Rs *e       ]
+    [                                                          ]
+    [    ____                         ____                     ]
+    [I*\/ Rp           0            \/ Tp            0         ]
+    [                                                          ]
+    [               ____  I*phi_b                    ____      ]
+    [   0      -I*\/ Rs *e            0            \/ Ts       ]
+
+    """
+    PBS = Matrix([[sqrt(Tp), 0, I*sqrt(Rp), 0],
+                  [0, sqrt(Ts), 0, -I*sqrt(Rs)*exp(I*phia)],
+                  [I*sqrt(Rp), 0, sqrt(Tp), 0],
+                  [0, -I*sqrt(Rs)*exp(I*phib), 0, sqrt(Ts)]])
+    return PBS
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_gaussopt.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_gaussopt.py
new file mode 100644
index 0000000000000000000000000000000000000000..5271f3cbb69cf5de861ff332d36418b79daeb1b5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_gaussopt.py
@@ -0,0 +1,102 @@
+from sympy.core.evalf import N
+from sympy.core.numbers import (Float, I, oo, pi)
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import atan2
+from sympy.matrices.dense import Matrix
+from sympy.polys.polytools import factor
+
+from sympy.physics.optics import (BeamParameter, CurvedMirror,
+  CurvedRefraction, FlatMirror, FlatRefraction, FreeSpace, GeometricRay,
+  RayTransferMatrix, ThinLens, conjugate_gauss_beams,
+  gaussian_conj, geometric_conj_ab, geometric_conj_af, geometric_conj_bf,
+  rayleigh2waist, waist2rayleigh)
+
+
+def streq(a, b):
+    return str(a) == str(b)
+
+
+def test_gauss_opt():
+    mat = RayTransferMatrix(1, 2, 3, 4)
+    assert mat == Matrix([[1, 2], [3, 4]])
+    assert mat == RayTransferMatrix( Matrix([[1, 2], [3, 4]]) )
+    assert [mat.A, mat.B, mat.C, mat.D] == [1, 2, 3, 4]
+
+    d, f, h, n1, n2, R = symbols('d f h n1 n2 R')
+    lens = ThinLens(f)
+    assert lens == Matrix([[   1, 0], [-1/f, 1]])
+    assert lens.C == -1/f
+    assert FreeSpace(d) == Matrix([[ 1, d], [0, 1]])
+    assert FlatRefraction(n1, n2) == Matrix([[1, 0], [0, n1/n2]])
+    assert CurvedRefraction(
+        R, n1, n2) == Matrix([[1, 0], [(n1 - n2)/(R*n2), n1/n2]])
+    assert FlatMirror() == Matrix([[1, 0], [0, 1]])
+    assert CurvedMirror(R) == Matrix([[   1, 0], [-2/R, 1]])
+    assert ThinLens(f) == Matrix([[   1, 0], [-1/f, 1]])
+
+    mul = CurvedMirror(R)*FreeSpace(d)
+    mul_mat = Matrix([[   1, 0], [-2/R, 1]])*Matrix([[ 1, d], [0, 1]])
+    assert mul.A == mul_mat[0, 0]
+    assert mul.B == mul_mat[0, 1]
+    assert mul.C == mul_mat[1, 0]
+    assert mul.D == mul_mat[1, 1]
+
+    angle = symbols('angle')
+    assert GeometricRay(h, angle) == Matrix([[    h], [angle]])
+    assert FreeSpace(
+        d)*GeometricRay(h, angle) == Matrix([[angle*d + h], [angle]])
+    assert GeometricRay( Matrix( ((h,), (angle,)) ) ) == Matrix([[h], [angle]])
+    assert (FreeSpace(d)*GeometricRay(h, angle)).height == angle*d + h
+    assert (FreeSpace(d)*GeometricRay(h, angle)).angle == angle
+
+    p = BeamParameter(530e-9, 1, w=1e-3)
+    assert streq(p.q, 1 + 1.88679245283019*I*pi)
+    assert streq(N(p.q), 1.0 + 5.92753330865999*I)
+    assert streq(N(p.w_0), Float(0.00100000000000000))
+    assert streq(N(p.z_r), Float(5.92753330865999))
+    fs = FreeSpace(10)
+    p1 = fs*p
+    assert streq(N(p.w), Float(0.00101413072159615))
+    assert streq(N(p1.w), Float(0.00210803120913829))
+
+    w, wavelen = symbols('w wavelen')
+    assert waist2rayleigh(w, wavelen) == pi*w**2/wavelen
+    z_r, wavelen = symbols('z_r wavelen')
+    assert rayleigh2waist(z_r, wavelen) == sqrt(wavelen*z_r)/sqrt(pi)
+
+    a, b, f = symbols('a b f')
+    assert geometric_conj_ab(a, b) == a*b/(a + b)
+    assert geometric_conj_af(a, f) == a*f/(a - f)
+    assert geometric_conj_bf(b, f) == b*f/(b - f)
+    assert geometric_conj_ab(oo, b) == b
+    assert geometric_conj_ab(a, oo) == a
+
+    s_in, z_r_in, f = symbols('s_in z_r_in f')
+    assert gaussian_conj(
+        s_in, z_r_in, f)[0] == 1/(-1/(s_in + z_r_in**2/(-f + s_in)) + 1/f)
+    assert gaussian_conj(
+        s_in, z_r_in, f)[1] == z_r_in/(1 - s_in**2/f**2 + z_r_in**2/f**2)
+    assert gaussian_conj(
+        s_in, z_r_in, f)[2] == 1/sqrt(1 - s_in**2/f**2 + z_r_in**2/f**2)
+
+    l, w_i, w_o, f = symbols('l w_i w_o f')
+    assert conjugate_gauss_beams(l, w_i, w_o, f=f)[0] == f*(
+        -sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)) + 1)
+    assert factor(conjugate_gauss_beams(l, w_i, w_o, f=f)[1]) == f*w_o**2*(
+        w_i**2/w_o**2 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)))/w_i**2
+    assert conjugate_gauss_beams(l, w_i, w_o, f=f)[2] == f
+
+    z, l, w_0 = symbols('z l w_0', positive=True)
+    p = BeamParameter(l, z, w=w_0)
+    assert p.radius == z*(pi**2*w_0**4/(l**2*z**2) + 1)
+    assert p.w == w_0*sqrt(l**2*z**2/(pi**2*w_0**4) + 1)
+    assert p.w_0 == w_0
+    assert p.divergence == l/(pi*w_0)
+    assert p.gouy == atan2(z, pi*w_0**2/l)
+    assert p.waist_approximation_limit == 2*l/pi
+
+    p = BeamParameter(530e-9, 1, w=1e-3, n=2)
+    assert streq(p.q, 1 + 3.77358490566038*I*pi)
+    assert streq(N(p.z_r), Float(11.8550666173200))
+    assert streq(N(p.w_0), Float(0.00100000000000000))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_medium.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_medium.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfbb485f5b8e401f38c7f1cfa573f960a2479d7b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_medium.py
@@ -0,0 +1,48 @@
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.optics import Medium
+from sympy.abc import epsilon, mu, n
+from sympy.physics.units import speed_of_light, u0, e0, m, kg, s, A
+
+from sympy.testing.pytest import raises
+
+c = speed_of_light.convert_to(m/s)
+e0 = e0.convert_to(A**2*s**4/(kg*m**3))
+u0 = u0.convert_to(m*kg/(A**2*s**2))
+
+
+def test_medium():
+    m1 = Medium('m1')
+    assert m1.intrinsic_impedance == sqrt(u0/e0)
+    assert m1.speed == 1/sqrt(e0*u0)
+    assert m1.refractive_index == c*sqrt(e0*u0)
+    assert m1.permittivity == e0
+    assert m1.permeability == u0
+    m2 = Medium('m2', epsilon, mu)
+    assert m2.intrinsic_impedance == sqrt(mu/epsilon)
+    assert m2.speed == 1/sqrt(epsilon*mu)
+    assert m2.refractive_index == c*sqrt(epsilon*mu)
+    assert m2.permittivity == epsilon
+    assert m2.permeability == mu
+    # Increasing electric permittivity and magnetic permeability
+    # by small amount from its value in vacuum.
+    m3 = Medium('m3', 9.0*10**(-12)*s**4*A**2/(m**3*kg), 1.45*10**(-6)*kg*m/(A**2*s**2))
+    assert m3.refractive_index > m1.refractive_index
+    assert m3 != m1
+    # Decreasing electric permittivity and magnetic permeability
+    # by small amount from its value in vacuum.
+    m4 = Medium('m4', 7.0*10**(-12)*s**4*A**2/(m**3*kg), 1.15*10**(-6)*kg*m/(A**2*s**2))
+    assert m4.refractive_index < m1.refractive_index
+    m5 = Medium('m5', permittivity=710*10**(-12)*s**4*A**2/(m**3*kg), n=1.33)
+    assert abs(m5.intrinsic_impedance - 6.24845417765552*kg*m**2/(A**2*s**3)) \
+                < 1e-12*kg*m**2/(A**2*s**3)
+    assert abs(m5.speed - 225407863.157895*m/s) < 1e-6*m/s
+    assert abs(m5.refractive_index - 1.33000000000000) < 1e-12
+    assert abs(m5.permittivity - 7.1e-10*A**2*s**4/(kg*m**3)) \
+                < 1e-20*A**2*s**4/(kg*m**3)
+    assert abs(m5.permeability - 2.77206575232851e-8*kg*m/(A**2*s**2)) \
+                < 1e-20*kg*m/(A**2*s**2)
+    m6 = Medium('m6', None, mu, n)
+    assert m6.permittivity == n**2/(c**2*mu)
+    # test for equality of refractive indices
+    assert Medium('m7').refractive_index == Medium('m8', e0, u0).refractive_index
+    raises(ValueError, lambda:Medium('m9', e0, u0, 2))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_polarization.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_polarization.py
new file mode 100644
index 0000000000000000000000000000000000000000..99c595d82a4a296066d5075f6182895a8de54d91
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_polarization.py
@@ -0,0 +1,57 @@
+from sympy.physics.optics.polarization import (jones_vector, stokes_vector,
+    jones_2_stokes, linear_polarizer, phase_retarder, half_wave_retarder,
+    quarter_wave_retarder, transmissive_filter, reflective_filter,
+    mueller_matrix, polarizing_beam_splitter)
+from sympy.core.numbers import (I, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.matrices.dense import Matrix
+
+
+def test_polarization():
+    assert jones_vector(0, 0) == Matrix([1, 0])
+    assert jones_vector(pi/2, 0) == Matrix([0, 1])
+    #################################################################
+    assert stokes_vector(0, 0) == Matrix([1, 1, 0, 0])
+    assert stokes_vector(pi/2, 0) == Matrix([1, -1, 0, 0])
+    #################################################################
+    H = jones_vector(0, 0)
+    V = jones_vector(pi/2, 0)
+    D = jones_vector(pi/4, 0)
+    A = jones_vector(-pi/4, 0)
+    R = jones_vector(0, pi/4)
+    L = jones_vector(0, -pi/4)
+
+    res = [Matrix([1, 1, 0, 0]),
+           Matrix([1, -1, 0, 0]),
+           Matrix([1, 0, 1, 0]),
+           Matrix([1, 0, -1, 0]),
+           Matrix([1, 0, 0, 1]),
+           Matrix([1, 0, 0, -1])]
+
+    assert [jones_2_stokes(e) for e in [H, V, D, A, R, L]] == res
+    #################################################################
+    assert linear_polarizer(0) == Matrix([[1, 0], [0, 0]])
+    #################################################################
+    delta = symbols("delta", real=True)
+    res = Matrix([[exp(-I*delta/2), 0], [0, exp(I*delta/2)]])
+    assert phase_retarder(0, delta) == res
+    #################################################################
+    assert half_wave_retarder(0) == Matrix([[-I, 0], [0, I]])
+    #################################################################
+    res = Matrix([[exp(-I*pi/4), 0], [0, I*exp(-I*pi/4)]])
+    assert quarter_wave_retarder(0) == res
+    #################################################################
+    assert transmissive_filter(1) == Matrix([[1, 0], [0, 1]])
+    #################################################################
+    assert reflective_filter(1) == Matrix([[1, 0], [0, -1]])
+
+    res = Matrix([[S(1)/2, S(1)/2, 0, 0],
+                  [S(1)/2, S(1)/2, 0, 0],
+                  [0, 0, 0, 0],
+                  [0, 0, 0, 0]])
+    assert mueller_matrix(linear_polarizer(0)) == res
+    #################################################################
+    res = Matrix([[1, 0, 0, 0], [0, 0, 0, -I], [0, 0, 1, 0], [0, -I, 0, 0]])
+    assert polarizing_beam_splitter() == res
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_utils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..6c93883a081d3614a604aeadc8a4b617181de669
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_utils.py
@@ -0,0 +1,202 @@
+from sympy.core.numbers import comp, Rational
+from sympy.physics.optics.utils import (refraction_angle, fresnel_coefficients,
+        deviation, brewster_angle, critical_angle, lens_makers_formula,
+        mirror_formula, lens_formula, hyperfocal_distance,
+        transverse_magnification)
+from sympy.physics.optics.medium import Medium
+from sympy.physics.units import e0
+
+from sympy.core.numbers import oo
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import Matrix
+from sympy.geometry.point import Point3D
+from sympy.geometry.line import Ray3D
+from sympy.geometry.plane import Plane
+
+from sympy.testing.pytest import raises
+
+
+ae = lambda a, b, n: comp(a, b, 10**-n)
+
+
+def test_refraction_angle():
+    n1, n2 = symbols('n1, n2')
+    m1 = Medium('m1')
+    m2 = Medium('m2')
+    r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
+    i = Matrix([1, 1, 1])
+    n = Matrix([0, 0, 1])
+    normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1))
+    P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
+    assert refraction_angle(r1, 1, 1, n) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle([1, 1, 1], 1, 1, n) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle((1, 1, 1), 1, 1, n) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle(i, 1, 1, [0, 0, 1]) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle(i, 1, 1, (0, 0, 1)) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle(i, 1, 1, normal_ray) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle(i, 1, 1, plane=P) == Matrix([
+                                            [ 1],
+                                            [ 1],
+                                            [-1]])
+    assert refraction_angle(r1, 1, 1, plane=P) == \
+        Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
+    assert refraction_angle(r1, m1, 1.33, plane=P) == \
+        Ray3D(Point3D(0, 0, 0), Point3D(Rational(100, 133), Rational(100, 133), -789378201649271*sqrt(3)/1000000000000000))
+    assert refraction_angle(r1, 1, m2, plane=P) == \
+        Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
+    assert refraction_angle(r1, n1, n2, plane=P) == \
+        Ray3D(Point3D(0, 0, 0), Point3D(n1/n2, n1/n2, -sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)))
+    assert refraction_angle(r1, 1.33, 1, plane=P) == 0  # TIR
+    assert refraction_angle(r1, 1, 1, normal_ray) == \
+        Ray3D(Point3D(0, 0, 0), direction_ratio=[1, 1, -1])
+    assert ae(refraction_angle(0.5, 1, 2), 0.24207, 5)
+    assert ae(refraction_angle(0.5, 2, 1), 1.28293, 5)
+    raises(ValueError, lambda: refraction_angle(r1, m1, m2, normal_ray, P))
+    raises(TypeError, lambda: refraction_angle(m1, m1, m2)) # can add other values for arg[0]
+    raises(TypeError, lambda: refraction_angle(r1, m1, m2, None, i))
+    raises(TypeError, lambda: refraction_angle(r1, m1, m2, m2))
+
+
+def test_fresnel_coefficients():
+    assert all(ae(i, j, 5) for i, j in zip(
+        fresnel_coefficients(0.5, 1, 1.33),
+        [0.11163, -0.17138, 0.83581, 0.82862]))
+    assert all(ae(i, j, 5) for i, j in zip(
+        fresnel_coefficients(0.5, 1.33, 1),
+        [-0.07726, 0.20482, 1.22724, 1.20482]))
+    m1 = Medium('m1')
+    m2 = Medium('m2', n=2)
+    assert all(ae(i, j, 5) for i, j in zip(
+        fresnel_coefficients(0.3, m1, m2),
+        [0.31784, -0.34865, 0.65892, 0.65135]))
+    ans = [[-0.23563, -0.97184], [0.81648, -0.57738]]
+    got = fresnel_coefficients(0.6, m2, m1)
+    for i, j in zip(got, ans):
+        for a, b in zip(i.as_real_imag(), j):
+            assert ae(a, b, 5)
+
+
+def test_deviation():
+    n1, n2 = symbols('n1, n2')
+    r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
+    n = Matrix([0, 0, 1])
+    i = Matrix([-1, -1, -1])
+    normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1))
+    P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
+    assert deviation(r1, 1, 1, normal=n) == 0
+    assert deviation(r1, 1, 1, plane=P) == 0
+    assert deviation(r1, 1, 1.1, plane=P).evalf(3) + 0.119 < 1e-3
+    assert deviation(i, 1, 1.1, normal=normal_ray).evalf(3) + 0.119 < 1e-3
+    assert deviation(r1, 1.33, 1, plane=P) is None  # TIR
+    assert deviation(r1, 1, 1, normal=[0, 0, 1]) == 0
+    assert deviation([-1, -1, -1], 1, 1, normal=[0, 0, 1]) == 0
+    assert ae(deviation(0.5, 1, 2), -0.25793, 5)
+    assert ae(deviation(0.5, 2, 1), 0.78293, 5)
+
+
+def test_brewster_angle():
+    m1 = Medium('m1', n=1)
+    m2 = Medium('m2', n=1.33)
+    assert ae(brewster_angle(m1, m2), 0.93, 2)
+    m1 = Medium('m1', permittivity=e0, n=1)
+    m2 = Medium('m2', permittivity=e0, n=1.33)
+    assert ae(brewster_angle(m1, m2), 0.93, 2)
+    assert ae(brewster_angle(1, 1.33), 0.93, 2)
+
+
+def test_critical_angle():
+    m1 = Medium('m1', n=1)
+    m2 = Medium('m2', n=1.33)
+    assert ae(critical_angle(m2, m1), 0.85, 2)
+
+
+def test_lens_makers_formula():
+    n1, n2 = symbols('n1, n2')
+    m1 = Medium('m1', permittivity=e0, n=1)
+    m2 = Medium('m2', permittivity=e0, n=1.33)
+    assert lens_makers_formula(n1, n2, 10, -10) == 5.0*n2/(n1 - n2)
+    assert ae(lens_makers_formula(m1, m2, 10, -10), -20.15, 2)
+    assert ae(lens_makers_formula(1.33, 1, 10, -10),  15.15, 2)
+
+
+def test_mirror_formula():
+    u, v, f = symbols('u, v, f')
+    assert mirror_formula(focal_length=f, u=u) == f*u/(-f + u)
+    assert mirror_formula(focal_length=f, v=v) == f*v/(-f + v)
+    assert mirror_formula(u=u, v=v) == u*v/(u + v)
+    assert mirror_formula(u=oo, v=v) == v
+    assert mirror_formula(u=oo, v=oo) is oo
+    assert mirror_formula(focal_length=oo, u=u) == -u
+    assert mirror_formula(u=u, v=oo) == u
+    assert mirror_formula(focal_length=oo, v=oo) is oo
+    assert mirror_formula(focal_length=f, v=oo) == f
+    assert mirror_formula(focal_length=oo, v=v) == -v
+    assert mirror_formula(focal_length=oo, u=oo) is oo
+    assert mirror_formula(focal_length=f, u=oo) == f
+    assert mirror_formula(focal_length=oo, u=u) == -u
+    raises(ValueError, lambda: mirror_formula(focal_length=f, u=u, v=v))
+
+
+def test_lens_formula():
+    u, v, f = symbols('u, v, f')
+    assert lens_formula(focal_length=f, u=u) == f*u/(f + u)
+    assert lens_formula(focal_length=f, v=v) == f*v/(f - v)
+    assert lens_formula(u=u, v=v) == u*v/(u - v)
+    assert lens_formula(u=oo, v=v) == v
+    assert lens_formula(u=oo, v=oo) is oo
+    assert lens_formula(focal_length=oo, u=u) == u
+    assert lens_formula(u=u, v=oo) == -u
+    assert lens_formula(focal_length=oo, v=oo) is -oo
+    assert lens_formula(focal_length=oo, v=v) == v
+    assert lens_formula(focal_length=f, v=oo) == -f
+    assert lens_formula(focal_length=oo, u=oo) is oo
+    assert lens_formula(focal_length=oo, u=u) == u
+    assert lens_formula(focal_length=f, u=oo) == f
+    raises(ValueError, lambda: lens_formula(focal_length=f, u=u, v=v))
+
+
+def test_hyperfocal_distance():
+    f, N, c = symbols('f, N, c')
+    assert hyperfocal_distance(f=f, N=N, c=c) == f**2/(N*c)
+    assert ae(hyperfocal_distance(f=0.5, N=8, c=0.0033), 9.47, 2)
+
+
+def test_transverse_magnification():
+    si, so = symbols('si, so')
+    assert transverse_magnification(si, so) == -si/so
+    assert transverse_magnification(30, 15) == -2
+
+
+def test_lens_makers_formula_thick_lens():
+    n1, n2 = symbols('n1, n2')
+    m1 = Medium('m1', permittivity=e0, n=1)
+    m2 = Medium('m2', permittivity=e0, n=1.33)
+    assert ae(lens_makers_formula(m1, m2, 10, -10, d=1), -19.82, 2)
+    assert lens_makers_formula(n1, n2, 1, -1, d=0.1) == n2/((2.0 - (0.1*n1 - 0.1*n2)/n1)*(n1 - n2))
+
+
+def test_lens_makers_formula_plano_lens():
+    n1, n2 = symbols('n1, n2')
+    m1 = Medium('m1', permittivity=e0, n=1)
+    m2 = Medium('m2', permittivity=e0, n=1.33)
+    assert ae(lens_makers_formula(m1, m2, 10, oo), -40.30, 2)
+    assert lens_makers_formula(n1, n2, 10, oo) == 10.0*n2/(n1 - n2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_waves.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_waves.py
new file mode 100644
index 0000000000000000000000000000000000000000..3cb8f804fb5be86d6174cb7c7b15fd8979c85ff8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/tests/test_waves.py
@@ -0,0 +1,82 @@
+from sympy.core.function import (Derivative, Function)
+from sympy.core.numbers import (I, pi)
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (atan2, cos, sin)
+from sympy.simplify.simplify import simplify
+from sympy.abc import epsilon, mu
+from sympy.functions.elementary.exponential import exp
+from sympy.physics.units import speed_of_light, m, s
+from sympy.physics.optics import TWave
+
+from sympy.testing.pytest import raises
+
+c = speed_of_light.convert_to(m/s)
+
+def test_twave():
+    A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
+    n = Symbol('n')  # Refractive index
+    t = Symbol('t')  # Time
+    x = Symbol('x')  # Spatial variable
+    E = Function('E')
+    w1 = TWave(A1, f, phi1)
+    w2 = TWave(A2, f, phi2)
+    assert w1.amplitude == A1
+    assert w1.frequency == f
+    assert w1.phase == phi1
+    assert w1.wavelength == c/(f*n)
+    assert w1.time_period == 1/f
+    assert w1.angular_velocity == 2*pi*f
+    assert w1.wavenumber == 2*pi*f*n/c
+    assert w1.speed == c/n
+
+    w3 = w1 + w2
+    assert w3.amplitude == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2)
+    assert w3.frequency == f
+    assert w3.phase == atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2))
+    assert w3.wavelength == c/(f*n)
+    assert w3.time_period == 1/f
+    assert w3.angular_velocity == 2*pi*f
+    assert w3.wavenumber == 2*pi*f*n/c
+    assert w3.speed == c/n
+    assert simplify(w3.rewrite(sin) - w2.rewrite(sin) - w1.rewrite(sin)) == 0
+    assert w3.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x)
+    assert w3.rewrite(cos) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
+        + A2**2)*cos(pi*f*n*x*s/(149896229*m) - 2*pi*f*t + atan2(A1*sin(phi1)
+        + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)))
+    assert w3.rewrite(exp) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
+        + A2**2)*exp(I*(-2*pi*f*t + atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1)
+        + A2*cos(phi2)) + pi*s*f*n*x/(149896229*m)))
+
+    w4 = TWave(A1, None, 0, 1/f)
+    assert w4.frequency == f
+
+    w5 = w1 - w2
+    assert w5.amplitude == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2) + A2**2)
+    assert w5.frequency == f
+    assert w5.phase == atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1) - A2*cos(phi2))
+    assert w5.wavelength == c/(f*n)
+    assert w5.time_period == 1/f
+    assert w5.angular_velocity == 2*pi*f
+    assert w5.wavenumber == 2*pi*f*n/c
+    assert w5.speed == c/n
+    assert simplify(w5.rewrite(sin) - w1.rewrite(sin) + w2.rewrite(sin)) == 0
+    assert w5.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x)
+    assert w5.rewrite(cos) == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2)
+        + A2**2)*cos(-2*pi*f*t + atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1)
+        - A2*cos(phi2)) + pi*s*f*n*x/(149896229*m))
+    assert w5.rewrite(exp) == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2)
+        + A2**2)*exp(I*(-2*pi*f*t + atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1)
+        - A2*cos(phi2)) + pi*s*f*n*x/(149896229*m)))
+
+    w6 = 2*w1
+    assert w6.amplitude == 2*A1
+    assert w6.frequency == f
+    assert w6.phase == phi1
+    w7 = -w6
+    assert w7.amplitude == -2*A1
+    assert w7.frequency == f
+    assert w7.phase == phi1
+
+    raises(ValueError, lambda:TWave(A1))
+    raises(ValueError, lambda:TWave(A1, f, phi1, t))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/utils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..72c3b78bd4b09eb069757fb3f8d3632f09ec4b80
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/utils.py
@@ -0,0 +1,698 @@
+"""
+**Contains**
+
+* refraction_angle
+* fresnel_coefficients
+* deviation
+* brewster_angle
+* critical_angle
+* lens_makers_formula
+* mirror_formula
+* lens_formula
+* hyperfocal_distance
+* transverse_magnification
+"""
+
+__all__ = ['refraction_angle',
+           'deviation',
+           'fresnel_coefficients',
+           'brewster_angle',
+           'critical_angle',
+           'lens_makers_formula',
+           'mirror_formula',
+           'lens_formula',
+           'hyperfocal_distance',
+           'transverse_magnification'
+           ]
+
+from sympy.core.numbers import (Float, I, oo, pi, zoo)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (acos, asin, atan2, cos, sin, tan)
+from sympy.matrices.dense import Matrix
+from sympy.polys.polytools import cancel
+from sympy.series.limits import Limit
+from sympy.geometry.line import Ray3D
+from sympy.geometry.util import intersection
+from sympy.geometry.plane import Plane
+from sympy.utilities.iterables import is_sequence
+from .medium import Medium
+
+
+def refractive_index_of_medium(medium):
+    """
+    Helper function that returns refractive index, given a medium
+    """
+    if isinstance(medium, Medium):
+        n = medium.refractive_index
+    else:
+        n = sympify(medium)
+    return n
+
+
+def refraction_angle(incident, medium1, medium2, normal=None, plane=None):
+    """
+    This function calculates transmitted vector after refraction at planar
+    surface. ``medium1`` and ``medium2`` can be ``Medium`` or any sympifiable object.
+    If ``incident`` is a number then treated as angle of incidence (in radians)
+    in which case refraction angle is returned.
+
+    If ``incident`` is an object of `Ray3D`, `normal` also has to be an instance
+    of `Ray3D` in order to get the output as a `Ray3D`. Please note that if
+    plane of separation is not provided and normal is an instance of `Ray3D`,
+    ``normal`` will be assumed to be intersecting incident ray at the plane of
+    separation. This will not be the case when `normal` is a `Matrix` or
+    any other sequence.
+    If ``incident`` is an instance of `Ray3D` and `plane` has not been provided
+    and ``normal`` is not `Ray3D`, output will be a `Matrix`.
+
+    Parameters
+    ==========
+
+    incident : Matrix, Ray3D, sequence or a number
+        Incident vector or angle of incidence
+    medium1 : sympy.physics.optics.medium.Medium or sympifiable
+        Medium 1 or its refractive index
+    medium2 : sympy.physics.optics.medium.Medium or sympifiable
+        Medium 2 or its refractive index
+    normal : Matrix, Ray3D, or sequence
+        Normal vector
+    plane : Plane
+        Plane of separation of the two media.
+
+    Returns
+    =======
+
+    Returns an angle of refraction or a refracted ray depending on inputs.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import refraction_angle
+    >>> from sympy.geometry import Point3D, Ray3D, Plane
+    >>> from sympy.matrices import Matrix
+    >>> from sympy import symbols, pi
+    >>> n = Matrix([0, 0, 1])
+    >>> P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
+    >>> r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
+    >>> refraction_angle(r1, 1, 1, n)
+    Matrix([
+    [ 1],
+    [ 1],
+    [-1]])
+    >>> refraction_angle(r1, 1, 1, plane=P)
+    Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
+
+    With different index of refraction of the two media
+
+    >>> n1, n2 = symbols('n1, n2')
+    >>> refraction_angle(r1, n1, n2, n)
+    Matrix([
+    [                                n1/n2],
+    [                                n1/n2],
+    [-sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)]])
+    >>> refraction_angle(r1, n1, n2, plane=P)
+    Ray3D(Point3D(0, 0, 0), Point3D(n1/n2, n1/n2, -sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)))
+    >>> round(refraction_angle(pi/6, 1.2, 1.5), 5)
+    0.41152
+    """
+
+    n1 = refractive_index_of_medium(medium1)
+    n2 = refractive_index_of_medium(medium2)
+
+    # check if an incidence angle was supplied instead of a ray
+    try:
+        angle_of_incidence = float(incident)
+    except TypeError:
+        angle_of_incidence = None
+
+    try:
+        critical_angle_ = critical_angle(medium1, medium2)
+    except (ValueError, TypeError):
+        critical_angle_ = None
+
+    if angle_of_incidence is not None:
+        if normal is not None or plane is not None:
+            raise ValueError('Normal/plane not allowed if incident is an angle')
+
+        if not 0.0 <= angle_of_incidence < pi*0.5:
+            raise ValueError('Angle of incidence not in range [0:pi/2)')
+
+        if critical_angle_ and angle_of_incidence > critical_angle_:
+            raise ValueError('Ray undergoes total internal reflection')
+        return asin(n1*sin(angle_of_incidence)/n2)
+
+    # Treat the incident as ray below
+    # A flag to check whether to return Ray3D or not
+    return_ray = False
+
+    if plane is not None and normal is not None:
+        raise ValueError("Either plane or normal is acceptable.")
+
+    if not isinstance(incident, Matrix):
+        if is_sequence(incident):
+            _incident = Matrix(incident)
+        elif isinstance(incident, Ray3D):
+            _incident = Matrix(incident.direction_ratio)
+        else:
+            raise TypeError(
+                "incident should be a Matrix, Ray3D, or sequence")
+    else:
+        _incident = incident
+
+    # If plane is provided, get direction ratios of the normal
+    # to the plane from the plane else go with `normal` param.
+    if plane is not None:
+        if not isinstance(plane, Plane):
+            raise TypeError("plane should be an instance of geometry.plane.Plane")
+        # If we have the plane, we can get the intersection
+        # point of incident ray and the plane and thus return
+        # an instance of Ray3D.
+        if isinstance(incident, Ray3D):
+            return_ray = True
+            intersection_pt = plane.intersection(incident)[0]
+        _normal = Matrix(plane.normal_vector)
+    else:
+        if not isinstance(normal, Matrix):
+            if is_sequence(normal):
+                _normal = Matrix(normal)
+            elif isinstance(normal, Ray3D):
+                _normal = Matrix(normal.direction_ratio)
+                if isinstance(incident, Ray3D):
+                    intersection_pt = intersection(incident, normal)
+                    if len(intersection_pt) == 0:
+                        raise ValueError(
+                            "Normal isn't concurrent with the incident ray.")
+                    else:
+                        return_ray = True
+                        intersection_pt = intersection_pt[0]
+            else:
+                raise TypeError(
+                    "Normal should be a Matrix, Ray3D, or sequence")
+        else:
+            _normal = normal
+
+    eta = n1/n2  # Relative index of refraction
+    # Calculating magnitude of the vectors
+    mag_incident = sqrt(sum(i**2 for i in _incident))
+    mag_normal = sqrt(sum(i**2 for i in _normal))
+    # Converting vectors to unit vectors by dividing
+    # them with their magnitudes
+    _incident /= mag_incident
+    _normal /= mag_normal
+    c1 = -_incident.dot(_normal)  # cos(angle_of_incidence)
+    cs2 = 1 - eta**2*(1 - c1**2)  # cos(angle_of_refraction)**2
+    if cs2.is_negative:  # This is the case of total internal reflection(TIR).
+        return S.Zero
+    drs = eta*_incident + (eta*c1 - sqrt(cs2))*_normal
+    # Multiplying unit vector by its magnitude
+    drs = drs*mag_incident
+    if not return_ray:
+        return drs
+    else:
+        return Ray3D(intersection_pt, direction_ratio=drs)
+
+
+def fresnel_coefficients(angle_of_incidence, medium1, medium2):
+    """
+    This function uses Fresnel equations to calculate reflection and
+    transmission coefficients. Those are obtained for both polarisations
+    when the electric field vector is in the plane of incidence (labelled 'p')
+    and when the electric field vector is perpendicular to the plane of
+    incidence (labelled 's'). There are four real coefficients unless the
+    incident ray reflects in total internal in which case there are two complex
+    ones. Angle of incidence is the angle between the incident ray and the
+    surface normal. ``medium1`` and ``medium2`` can be ``Medium`` or any
+    sympifiable object.
+
+    Parameters
+    ==========
+
+    angle_of_incidence : sympifiable
+
+    medium1 : Medium or sympifiable
+        Medium 1 or its refractive index
+
+    medium2 : Medium or sympifiable
+        Medium 2 or its refractive index
+
+    Returns
+    =======
+
+    Returns a list with four real Fresnel coefficients:
+    [reflection p (TM), reflection s (TE),
+    transmission p (TM), transmission s (TE)]
+    If the ray is undergoes total internal reflection then returns a
+    list of two complex Fresnel coefficients:
+    [reflection p (TM), reflection s (TE)]
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import fresnel_coefficients
+    >>> fresnel_coefficients(0.3, 1, 2)
+    [0.317843553417859, -0.348645229818821,
+            0.658921776708929, 0.651354770181179]
+    >>> fresnel_coefficients(0.6, 2, 1)
+    [-0.235625382192159 - 0.971843958291041*I,
+             0.816477005968898 - 0.577377951366403*I]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fresnel_equations
+    """
+    if not 0 <= 2*angle_of_incidence < pi:
+        raise ValueError('Angle of incidence not in range [0:pi/2)')
+
+    n1 = refractive_index_of_medium(medium1)
+    n2 = refractive_index_of_medium(medium2)
+
+    angle_of_refraction = asin(n1*sin(angle_of_incidence)/n2)
+    try:
+        angle_of_total_internal_reflection_onset = critical_angle(n1, n2)
+    except ValueError:
+        angle_of_total_internal_reflection_onset = None
+
+    if angle_of_total_internal_reflection_onset is None or\
+    angle_of_total_internal_reflection_onset > angle_of_incidence:
+        R_s = -sin(angle_of_incidence - angle_of_refraction)\
+                /sin(angle_of_incidence + angle_of_refraction)
+        R_p = tan(angle_of_incidence - angle_of_refraction)\
+                /tan(angle_of_incidence + angle_of_refraction)
+        T_s = 2*sin(angle_of_refraction)*cos(angle_of_incidence)\
+                /sin(angle_of_incidence + angle_of_refraction)
+        T_p = 2*sin(angle_of_refraction)*cos(angle_of_incidence)\
+                /(sin(angle_of_incidence + angle_of_refraction)\
+                *cos(angle_of_incidence - angle_of_refraction))
+        return [R_p, R_s, T_p, T_s]
+    else:
+        n = n2/n1
+        R_s = cancel((cos(angle_of_incidence)-\
+                I*sqrt(sin(angle_of_incidence)**2 - n**2))\
+                /(cos(angle_of_incidence)+\
+                I*sqrt(sin(angle_of_incidence)**2 - n**2)))
+        R_p = cancel((n**2*cos(angle_of_incidence)-\
+                I*sqrt(sin(angle_of_incidence)**2 - n**2))\
+                /(n**2*cos(angle_of_incidence)+\
+                I*sqrt(sin(angle_of_incidence)**2 - n**2)))
+        return [R_p, R_s]
+
+
+def deviation(incident, medium1, medium2, normal=None, plane=None):
+    """
+    This function calculates the angle of deviation of a ray
+    due to refraction at planar surface.
+
+    Parameters
+    ==========
+
+    incident : Matrix, Ray3D, sequence or float
+        Incident vector or angle of incidence
+    medium1 : sympy.physics.optics.medium.Medium or sympifiable
+        Medium 1 or its refractive index
+    medium2 : sympy.physics.optics.medium.Medium or sympifiable
+        Medium 2 or its refractive index
+    normal : Matrix, Ray3D, or sequence
+        Normal vector
+    plane : Plane
+        Plane of separation of the two media.
+
+    Returns angular deviation between incident and refracted rays
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import deviation
+    >>> from sympy.geometry import Point3D, Ray3D, Plane
+    >>> from sympy.matrices import Matrix
+    >>> from sympy import symbols
+    >>> n1, n2 = symbols('n1, n2')
+    >>> n = Matrix([0, 0, 1])
+    >>> P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
+    >>> r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
+    >>> deviation(r1, 1, 1, n)
+    0
+    >>> deviation(r1, n1, n2, plane=P)
+    -acos(-sqrt(-2*n1**2/(3*n2**2) + 1)) + acos(-sqrt(3)/3)
+    >>> round(deviation(0.1, 1.2, 1.5), 5)
+    -0.02005
+    """
+    refracted = refraction_angle(incident,
+                                 medium1,
+                                 medium2,
+                                 normal=normal,
+                                 plane=plane)
+    try:
+        angle_of_incidence = Float(incident)
+    except TypeError:
+        angle_of_incidence = None
+
+    if angle_of_incidence is not None:
+        return float(refracted) - angle_of_incidence
+
+    if refracted != 0:
+        if isinstance(refracted, Ray3D):
+            refracted = Matrix(refracted.direction_ratio)
+
+        if not isinstance(incident, Matrix):
+            if is_sequence(incident):
+                _incident = Matrix(incident)
+            elif isinstance(incident, Ray3D):
+                _incident = Matrix(incident.direction_ratio)
+            else:
+                raise TypeError(
+                    "incident should be a Matrix, Ray3D, or sequence")
+        else:
+            _incident = incident
+
+        if plane is None:
+            if not isinstance(normal, Matrix):
+                if is_sequence(normal):
+                    _normal = Matrix(normal)
+                elif isinstance(normal, Ray3D):
+                    _normal = Matrix(normal.direction_ratio)
+                else:
+                    raise TypeError(
+                        "normal should be a Matrix, Ray3D, or sequence")
+            else:
+                _normal = normal
+        else:
+            _normal = Matrix(plane.normal_vector)
+
+        mag_incident = sqrt(sum(i**2 for i in _incident))
+        mag_normal = sqrt(sum(i**2 for i in _normal))
+        mag_refracted = sqrt(sum(i**2 for i in refracted))
+        _incident /= mag_incident
+        _normal /= mag_normal
+        refracted /= mag_refracted
+        i = acos(_incident.dot(_normal))
+        r = acos(refracted.dot(_normal))
+        return i - r
+
+
+def brewster_angle(medium1, medium2):
+    """
+    This function calculates the Brewster's angle of incidence to Medium 2 from
+    Medium 1 in radians.
+
+    Parameters
+    ==========
+
+    medium 1 : Medium or sympifiable
+        Refractive index of Medium 1
+    medium 2 : Medium or sympifiable
+        Refractive index of Medium 1
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import brewster_angle
+    >>> brewster_angle(1, 1.33)
+    0.926093295503462
+
+    """
+
+    n1 = refractive_index_of_medium(medium1)
+    n2 = refractive_index_of_medium(medium2)
+
+    return atan2(n2, n1)
+
+def critical_angle(medium1, medium2):
+    """
+    This function calculates the critical angle of incidence (marking the onset
+    of total internal) to Medium 2 from Medium 1 in radians.
+
+    Parameters
+    ==========
+
+    medium 1 : Medium or sympifiable
+        Refractive index of Medium 1.
+    medium 2 : Medium or sympifiable
+        Refractive index of Medium 1.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import critical_angle
+    >>> critical_angle(1.33, 1)
+    0.850908514477849
+
+    """
+
+    n1 = refractive_index_of_medium(medium1)
+    n2 = refractive_index_of_medium(medium2)
+
+    if n2 > n1:
+        raise ValueError('Total internal reflection impossible for n1 < n2')
+    else:
+        return asin(n2/n1)
+
+
+
+def lens_makers_formula(n_lens, n_surr, r1, r2, d=0):
+    """
+    This function calculates focal length of a lens.
+    It follows cartesian sign convention.
+
+    Parameters
+    ==========
+
+    n_lens : Medium or sympifiable
+        Index of refraction of lens.
+    n_surr : Medium or sympifiable
+        Index of reflection of surrounding.
+    r1 : sympifiable
+        Radius of curvature of first surface.
+    r2 : sympifiable
+        Radius of curvature of second surface.
+    d : sympifiable, optional
+        Thickness of lens, default value is 0.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import lens_makers_formula
+    >>> from sympy import S
+    >>> lens_makers_formula(1.33, 1, 10, -10)
+    15.1515151515151
+    >>> lens_makers_formula(1.2, 1, 10, S.Infinity)
+    50.0000000000000
+    >>> lens_makers_formula(1.33, 1, 10, -10, d=1)
+    15.3418463277618
+
+    """
+
+    if isinstance(n_lens, Medium):
+        n_lens = n_lens.refractive_index
+    else:
+        n_lens = sympify(n_lens)
+    if isinstance(n_surr, Medium):
+        n_surr = n_surr.refractive_index
+    else:
+        n_surr = sympify(n_surr)
+    d = sympify(d)
+
+    focal_length = 1/((n_lens - n_surr) / n_surr*(1/r1 - 1/r2 + (((n_lens - n_surr) * d) / (n_lens * r1 * r2))))
+
+    if focal_length == zoo:
+        return S.Infinity
+    return focal_length
+
+
+def mirror_formula(focal_length=None, u=None, v=None):
+    """
+    This function provides one of the three parameters
+    when two of them are supplied.
+    This is valid only for paraxial rays.
+
+    Parameters
+    ==========
+
+    focal_length : sympifiable
+        Focal length of the mirror.
+    u : sympifiable
+        Distance of object from the pole on
+        the principal axis.
+    v : sympifiable
+        Distance of the image from the pole
+        on the principal axis.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import mirror_formula
+    >>> from sympy.abc import f, u, v
+    >>> mirror_formula(focal_length=f, u=u)
+    f*u/(-f + u)
+    >>> mirror_formula(focal_length=f, v=v)
+    f*v/(-f + v)
+    >>> mirror_formula(u=u, v=v)
+    u*v/(u + v)
+
+    """
+    if focal_length and u and v:
+        raise ValueError("Please provide only two parameters")
+
+    focal_length = sympify(focal_length)
+    u = sympify(u)
+    v = sympify(v)
+    if u is oo:
+        _u = Symbol('u')
+    if v is oo:
+        _v = Symbol('v')
+    if focal_length is oo:
+        _f = Symbol('f')
+    if focal_length is None:
+        if u is oo and v is oo:
+            return Limit(Limit(_v*_u/(_v + _u), _u, oo), _v, oo).doit()
+        if u is oo:
+            return Limit(v*_u/(v + _u), _u, oo).doit()
+        if v is oo:
+            return Limit(_v*u/(_v + u), _v, oo).doit()
+        return v*u/(v + u)
+    if u is None:
+        if v is oo and focal_length is oo:
+            return Limit(Limit(_v*_f/(_v - _f), _v, oo), _f, oo).doit()
+        if v is oo:
+            return Limit(_v*focal_length/(_v - focal_length), _v, oo).doit()
+        if focal_length is oo:
+            return Limit(v*_f/(v - _f), _f, oo).doit()
+        return v*focal_length/(v - focal_length)
+    if v is None:
+        if u is oo and focal_length is oo:
+            return Limit(Limit(_u*_f/(_u - _f), _u, oo), _f, oo).doit()
+        if u is oo:
+            return Limit(_u*focal_length/(_u - focal_length), _u, oo).doit()
+        if focal_length is oo:
+            return Limit(u*_f/(u - _f), _f, oo).doit()
+        return u*focal_length/(u - focal_length)
+
+
+def lens_formula(focal_length=None, u=None, v=None):
+    """
+    This function provides one of the three parameters
+    when two of them are supplied.
+    This is valid only for paraxial rays.
+
+    Parameters
+    ==========
+
+    focal_length : sympifiable
+        Focal length of the mirror.
+    u : sympifiable
+        Distance of object from the optical center on
+        the principal axis.
+    v : sympifiable
+        Distance of the image from the optical center
+        on the principal axis.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.optics import lens_formula
+    >>> from sympy.abc import f, u, v
+    >>> lens_formula(focal_length=f, u=u)
+    f*u/(f + u)
+    >>> lens_formula(focal_length=f, v=v)
+    f*v/(f - v)
+    >>> lens_formula(u=u, v=v)
+    u*v/(u - v)
+
+    """
+    if focal_length and u and v:
+        raise ValueError("Please provide only two parameters")
+
+    focal_length = sympify(focal_length)
+    u = sympify(u)
+    v = sympify(v)
+    if u is oo:
+        _u = Symbol('u')
+    if v is oo:
+        _v = Symbol('v')
+    if focal_length is oo:
+        _f = Symbol('f')
+    if focal_length is None:
+        if u is oo and v is oo:
+            return Limit(Limit(_v*_u/(_u - _v), _u, oo), _v, oo).doit()
+        if u is oo:
+            return Limit(v*_u/(_u - v), _u, oo).doit()
+        if v is oo:
+            return Limit(_v*u/(u - _v), _v, oo).doit()
+        return v*u/(u - v)
+    if u is None:
+        if v is oo and focal_length is oo:
+            return Limit(Limit(_v*_f/(_f - _v), _v, oo), _f, oo).doit()
+        if v is oo:
+            return Limit(_v*focal_length/(focal_length - _v), _v, oo).doit()
+        if focal_length is oo:
+            return Limit(v*_f/(_f - v), _f, oo).doit()
+        return v*focal_length/(focal_length - v)
+    if v is None:
+        if u is oo and focal_length is oo:
+            return Limit(Limit(_u*_f/(_u + _f), _u, oo), _f, oo).doit()
+        if u is oo:
+            return Limit(_u*focal_length/(_u + focal_length), _u, oo).doit()
+        if focal_length is oo:
+            return Limit(u*_f/(u + _f), _f, oo).doit()
+        return u*focal_length/(u + focal_length)
+
+def hyperfocal_distance(f, N, c):
+    """
+
+    Parameters
+    ==========
+
+    f: sympifiable
+        Focal length of a given lens.
+
+    N: sympifiable
+        F-number of a given lens.
+
+    c: sympifiable
+        Circle of Confusion (CoC) of a given image format.
+
+    Example
+    =======
+
+    >>> from sympy.physics.optics import hyperfocal_distance
+    >>> round(hyperfocal_distance(f = 0.5, N = 8, c = 0.0033), 2)
+    9.47
+    """
+
+    f = sympify(f)
+    N = sympify(N)
+    c = sympify(c)
+
+    return (1/(N * c))*(f**2)
+
+def transverse_magnification(si, so):
+    """
+
+    Calculates the transverse magnification upon reflection in a mirror,
+    which is the ratio of the image size to the object size.
+
+    Parameters
+    ==========
+
+    so: sympifiable
+        Lens-object distance.
+
+    si: sympifiable
+        Lens-image distance.
+
+    Example
+    =======
+
+    >>> from sympy.physics.optics import transverse_magnification
+    >>> transverse_magnification(30, 15)
+    -2
+
+    """
+
+    si = sympify(si)
+    so = sympify(so)
+
+    return (-(si/so))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/waves.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/waves.py
new file mode 100644
index 0000000000000000000000000000000000000000..61e2ff4db578543f9f2694f239f03439bfab2c41
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/optics/waves.py
@@ -0,0 +1,340 @@
+"""
+This module has all the classes and functions related to waves in optics.
+
+**Contains**
+
+* TWave
+"""
+
+__all__ = ['TWave']
+
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.function import Derivative, Function
+from sympy.core.numbers import (Number, pi, I)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import _sympify, sympify
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (atan2, cos, sin)
+from sympy.physics.units import speed_of_light, meter, second
+
+
+c = speed_of_light.convert_to(meter/second)
+
+
+class TWave(Expr):
+
+    r"""
+    This is a simple transverse sine wave travelling in a one-dimensional space.
+    Basic properties are required at the time of creation of the object,
+    but they can be changed later with respective methods provided.
+
+    Explanation
+    ===========
+
+    It is represented as :math:`A \times cos(k*x - \omega \times t + \phi )`,
+    where :math:`A` is the amplitude, :math:`\omega` is the angular frequency,
+    :math:`k` is the wavenumber (spatial frequency), :math:`x` is a spatial variable
+    to represent the position on the dimension on which the wave propagates,
+    and :math:`\phi` is the phase angle of the wave.
+
+
+    Arguments
+    =========
+
+    amplitude : Sympifyable
+        Amplitude of the wave.
+    frequency : Sympifyable
+        Frequency of the wave.
+    phase : Sympifyable
+        Phase angle of the wave.
+    time_period : Sympifyable
+        Time period of the wave.
+    n : Sympifyable
+        Refractive index of the medium.
+
+    Raises
+    =======
+
+    ValueError : When neither frequency nor time period is provided
+        or they are not consistent.
+    TypeError : When anything other than TWave objects is added.
+
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.optics import TWave
+    >>> A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
+    >>> w1 = TWave(A1, f, phi1)
+    >>> w2 = TWave(A2, f, phi2)
+    >>> w3 = w1 + w2  # Superposition of two waves
+    >>> w3
+    TWave(sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2), f,
+        atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)), 1/f, n)
+    >>> w3.amplitude
+    sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2)
+    >>> w3.phase
+    atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2))
+    >>> w3.speed
+    299792458*meter/(second*n)
+    >>> w3.angular_velocity
+    2*pi*f
+
+    """
+
+    def __new__(
+            cls,
+            amplitude,
+            frequency=None,
+            phase=S.Zero,
+            time_period=None,
+            n=Symbol('n')):
+        if time_period is not None:
+            time_period = _sympify(time_period)
+            _frequency = S.One/time_period
+        if frequency is not None:
+            frequency = _sympify(frequency)
+            _time_period = S.One/frequency
+            if time_period is not None:
+                if frequency != S.One/time_period:
+                    raise ValueError("frequency and time_period should be consistent.")
+        if frequency is None and time_period is None:
+            raise ValueError("Either frequency or time period is needed.")
+        if frequency is None:
+            frequency = _frequency
+        if time_period is None:
+            time_period = _time_period
+
+        amplitude = _sympify(amplitude)
+        phase = _sympify(phase)
+        n = sympify(n)
+        obj = Basic.__new__(cls, amplitude, frequency, phase, time_period, n)
+        return obj
+
+    @property
+    def amplitude(self):
+        """
+        Returns the amplitude of the wave.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.amplitude
+        A
+        """
+        return self.args[0]
+
+    @property
+    def frequency(self):
+        """
+        Returns the frequency of the wave,
+        in cycles per second.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.frequency
+        f
+        """
+        return self.args[1]
+
+    @property
+    def phase(self):
+        """
+        Returns the phase angle of the wave,
+        in radians.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.phase
+        phi
+        """
+        return self.args[2]
+
+    @property
+    def time_period(self):
+        """
+        Returns the temporal period of the wave,
+        in seconds per cycle.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.time_period
+        1/f
+        """
+        return self.args[3]
+
+    @property
+    def n(self):
+        """
+        Returns the refractive index of the medium
+        """
+        return self.args[4]
+
+    @property
+    def wavelength(self):
+        """
+        Returns the wavelength (spatial period) of the wave,
+        in meters per cycle.
+        It depends on the medium of the wave.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.wavelength
+        299792458*meter/(second*f*n)
+        """
+        return c/(self.frequency*self.n)
+
+
+    @property
+    def speed(self):
+        """
+        Returns the propagation speed of the wave,
+        in meters per second.
+        It is dependent on the propagation medium.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.speed
+        299792458*meter/(second*n)
+        """
+        return self.wavelength*self.frequency
+
+    @property
+    def angular_velocity(self):
+        """
+        Returns the angular velocity of the wave,
+        in radians per second.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.angular_velocity
+        2*pi*f
+        """
+        return 2*pi*self.frequency
+
+    @property
+    def wavenumber(self):
+        """
+        Returns the wavenumber of the wave,
+        in radians per meter.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.optics import TWave
+        >>> A, phi, f = symbols('A, phi, f')
+        >>> w = TWave(A, f, phi)
+        >>> w.wavenumber
+        pi*second*f*n/(149896229*meter)
+        """
+        return 2*pi/self.wavelength
+
+    def __str__(self):
+        """String representation of a TWave."""
+        from sympy.printing import sstr
+        return type(self).__name__ + sstr(self.args)
+
+    __repr__ = __str__
+
+    def __add__(self, other):
+        """
+        Addition of two waves will result in their superposition.
+        The type of interference will depend on their phase angles.
+        """
+        if isinstance(other, TWave):
+            if self.frequency == other.frequency and self.wavelength == other.wavelength:
+                return TWave(sqrt(self.amplitude**2 + other.amplitude**2 + 2 *
+                                  self.amplitude*other.amplitude*cos(
+                                      self.phase - other.phase)),
+                             self.frequency,
+                             atan2(self.amplitude*sin(self.phase)
+                             + other.amplitude*sin(other.phase),
+                             self.amplitude*cos(self.phase)
+                             + other.amplitude*cos(other.phase))
+                             )
+            else:
+                raise NotImplementedError("Interference of waves with different frequencies"
+                    " has not been implemented.")
+        else:
+            raise TypeError(type(other).__name__ + " and TWave objects cannot be added.")
+
+    def __mul__(self, other):
+        """
+        Multiplying a wave by a scalar rescales the amplitude of the wave.
+        """
+        other = sympify(other)
+        if isinstance(other, Number):
+            return TWave(self.amplitude*other, *self.args[1:])
+        else:
+            raise TypeError(type(other).__name__ + " and TWave objects cannot be multiplied.")
+
+    def __sub__(self, other):
+        return self.__add__(-1*other)
+
+    def __neg__(self):
+        return self.__mul__(-1)
+
+    def __radd__(self, other):
+        return self.__add__(other)
+
+    def __rmul__(self, other):
+        return self.__mul__(other)
+
+    def __rsub__(self, other):
+        return (-self).__radd__(other)
+
+    def _eval_rewrite_as_sin(self, *args, **kwargs):
+        return self.amplitude*sin(self.wavenumber*Symbol('x')
+            - self.angular_velocity*Symbol('t') + self.phase + pi/2, evaluate=False)
+
+    def _eval_rewrite_as_cos(self, *args, **kwargs):
+        return self.amplitude*cos(self.wavenumber*Symbol('x')
+            - self.angular_velocity*Symbol('t') + self.phase)
+
+    def _eval_rewrite_as_pde(self, *args, **kwargs):
+        mu, epsilon, x, t = symbols('mu, epsilon, x, t')
+        E = Function('E')
+        return Derivative(E(x, t), x, 2) + mu*epsilon*Derivative(E(x, t), t, 2)
+
+    def _eval_rewrite_as_exp(self, *args, **kwargs):
+        return self.amplitude*exp(I*(self.wavenumber*Symbol('x')
+            - self.angular_velocity*Symbol('t') + self.phase))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/paulialgebra.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/paulialgebra.py
new file mode 100644
index 0000000000000000000000000000000000000000..300957354ff34907035aa1d1a48b00276230a1e5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/paulialgebra.py
@@ -0,0 +1,231 @@
+"""
+This module implements Pauli algebra by subclassing Symbol. Only algebraic
+properties of Pauli matrices are used (we do not use the Matrix class).
+
+See the documentation to the class Pauli for examples.
+
+References
+==========
+
+.. [1] https://en.wikipedia.org/wiki/Pauli_matrices
+"""
+
+from sympy.core.add import Add
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.core.symbol import Symbol
+from sympy.physics.quantum import TensorProduct
+
+__all__ = ['evaluate_pauli_product']
+
+
+def delta(i, j):
+    """
+    Returns 1 if ``i == j``, else 0.
+
+    This is used in the multiplication of Pauli matrices.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import delta
+    >>> delta(1, 1)
+    1
+    >>> delta(2, 3)
+    0
+    """
+    if i == j:
+        return 1
+    else:
+        return 0
+
+
+def epsilon(i, j, k):
+    """
+    Return 1 if i,j,k is equal to (1,2,3), (2,3,1), or (3,1,2);
+    -1 if ``i``,``j``,``k`` is equal to (1,3,2), (3,2,1), or (2,1,3);
+    else return 0.
+
+    This is used in the multiplication of Pauli matrices.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import epsilon
+    >>> epsilon(1, 2, 3)
+    1
+    >>> epsilon(1, 3, 2)
+    -1
+    """
+    if (i, j, k) in ((1, 2, 3), (2, 3, 1), (3, 1, 2)):
+        return 1
+    elif (i, j, k) in ((1, 3, 2), (3, 2, 1), (2, 1, 3)):
+        return -1
+    else:
+        return 0
+
+
+class Pauli(Symbol):
+    """
+    The class representing algebraic properties of Pauli matrices.
+
+    Explanation
+    ===========
+
+    The symbol used to display the Pauli matrices can be changed with an
+    optional parameter ``label="sigma"``. Pauli matrices with different
+    ``label`` attributes cannot multiply together.
+
+    If the left multiplication of symbol or number with Pauli matrix is needed,
+    please use parentheses  to separate Pauli and symbolic multiplication
+    (for example: 2*I*(Pauli(3)*Pauli(2))).
+
+    Another variant is to use evaluate_pauli_product function to evaluate
+    the product of Pauli matrices and other symbols (with commutative
+    multiply rules).
+
+    See Also
+    ========
+
+    evaluate_pauli_product
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import Pauli
+    >>> Pauli(1)
+    sigma1
+    >>> Pauli(1)*Pauli(2)
+    I*sigma3
+    >>> Pauli(1)*Pauli(1)
+    1
+    >>> Pauli(3)**4
+    1
+    >>> Pauli(1)*Pauli(2)*Pauli(3)
+    I
+
+    >>> from sympy.physics.paulialgebra import Pauli
+    >>> Pauli(1, label="tau")
+    tau1
+    >>> Pauli(1)*Pauli(2, label="tau")
+    sigma1*tau2
+    >>> Pauli(1, label="tau")*Pauli(2, label="tau")
+    I*tau3
+
+    >>> from sympy import I
+    >>> I*(Pauli(2)*Pauli(3))
+    -sigma1
+
+    >>> from sympy.physics.paulialgebra import evaluate_pauli_product
+    >>> f = I*Pauli(2)*Pauli(3)
+    >>> f
+    I*sigma2*sigma3
+    >>> evaluate_pauli_product(f)
+    -sigma1
+    """
+
+    __slots__ = ("i", "label")
+
+    def __new__(cls, i, label="sigma"):
+        if i not in [1, 2, 3]:
+            raise IndexError("Invalid Pauli index")
+        obj = Symbol.__new__(cls, "%s%d" %(label,i), commutative=False, hermitian=True)
+        obj.i = i
+        obj.label = label
+        return obj
+
+    def __getnewargs_ex__(self):
+        return (self.i, self.label), {}
+
+    def _hashable_content(self):
+        return (self.i, self.label)
+
+    # FIXME don't work for -I*Pauli(2)*Pauli(3)
+    def __mul__(self, other):
+        if isinstance(other, Pauli):
+            j = self.i
+            k = other.i
+            jlab = self.label
+            klab = other.label
+
+            if jlab == klab:
+                return delta(j, k) \
+                    + I*epsilon(j, k, 1)*Pauli(1,jlab) \
+                    + I*epsilon(j, k, 2)*Pauli(2,jlab) \
+                    + I*epsilon(j, k, 3)*Pauli(3,jlab)
+        return super().__mul__(other)
+
+    def _eval_power(b, e):
+        if e.is_Integer and e.is_positive:
+            return super().__pow__(int(e) % 2)
+
+
+def evaluate_pauli_product(arg):
+    '''Help function to evaluate Pauli matrices product
+    with symbolic objects.
+
+    Parameters
+    ==========
+
+    arg: symbolic expression that contains Paulimatrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import Pauli, evaluate_pauli_product
+    >>> from sympy import I
+    >>> evaluate_pauli_product(I*Pauli(1)*Pauli(2))
+    -sigma3
+
+    >>> from sympy.abc import x
+    >>> evaluate_pauli_product(x**2*Pauli(2)*Pauli(1))
+    -I*x**2*sigma3
+    '''
+    start = arg
+    end = arg
+
+    if isinstance(arg, Pow) and isinstance(arg.args[0], Pauli):
+        if arg.args[1].is_odd:
+            return arg.args[0]
+        else:
+            return 1
+
+    if isinstance(arg, Add):
+        return Add(*[evaluate_pauli_product(part) for part in arg.args])
+
+    if isinstance(arg, TensorProduct):
+        return TensorProduct(*[evaluate_pauli_product(part) for part in arg.args])
+
+    elif not(isinstance(arg, Mul)):
+        return arg
+
+    while not start == end or start == arg and end == arg:
+        start = end
+
+        tmp = start.as_coeff_mul()
+        sigma_product = 1
+        com_product = 1
+        keeper = 1
+
+        for el in tmp[1]:
+            if isinstance(el, Pauli):
+                sigma_product *= el
+            elif not el.is_commutative:
+                if isinstance(el, Pow) and isinstance(el.args[0], Pauli):
+                    if el.args[1].is_odd:
+                        sigma_product *= el.args[0]
+                elif isinstance(el, TensorProduct):
+                    keeper = keeper*sigma_product*\
+                        TensorProduct(
+                            *[evaluate_pauli_product(part) for part in el.args]
+                        )
+                    sigma_product = 1
+                else:
+                    keeper = keeper*sigma_product*el
+                    sigma_product = 1
+            else:
+                com_product *= el
+        end = tmp[0]*keeper*sigma_product*com_product
+        if end == arg: break
+    return end
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/pring.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/pring.py
new file mode 100644
index 0000000000000000000000000000000000000000..325f4ff98a8c9fc428b4e332153af533f4d199ca
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/pring.py
@@ -0,0 +1,94 @@
+from sympy.core.numbers import (I, pi)
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum.constants import hbar
+
+
+def wavefunction(n, x):
+    """
+    Returns the wavefunction for particle on ring.
+
+    Parameters
+    ==========
+
+    n : The quantum number.
+        Here ``n`` can be positive as well as negative
+        which can be used to describe the direction of motion of particle.
+    x :
+        The angle.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.pring import wavefunction
+    >>> from sympy import Symbol, integrate, pi
+    >>> x=Symbol("x")
+    >>> wavefunction(1, x)
+    sqrt(2)*exp(I*x)/(2*sqrt(pi))
+    >>> wavefunction(2, x)
+    sqrt(2)*exp(2*I*x)/(2*sqrt(pi))
+    >>> wavefunction(3, x)
+    sqrt(2)*exp(3*I*x)/(2*sqrt(pi))
+
+    The normalization of the wavefunction is:
+
+    >>> integrate(wavefunction(2, x)*wavefunction(-2, x), (x, 0, 2*pi))
+    1
+    >>> integrate(wavefunction(4, x)*wavefunction(-4, x), (x, 0, 2*pi))
+    1
+
+    References
+    ==========
+
+    .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum
+           Mechanics (4th ed.).  Pages 71-73.
+
+    """
+    # sympify arguments
+    n, x = S(n), S(x)
+    return exp(n * I * x) / sqrt(2 * pi)
+
+
+def energy(n, m, r):
+    """
+    Returns the energy of the state corresponding to quantum number ``n``.
+
+    E=(n**2 * (hcross)**2) / (2 * m * r**2)
+
+    Parameters
+    ==========
+
+    n :
+        The quantum number.
+    m :
+        Mass of the particle.
+    r :
+        Radius of circle.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.pring import energy
+    >>> from sympy import Symbol
+    >>> m=Symbol("m")
+    >>> r=Symbol("r")
+    >>> energy(1, m, r)
+    hbar**2/(2*m*r**2)
+    >>> energy(2, m, r)
+    2*hbar**2/(m*r**2)
+    >>> energy(-2, 2.0, 3.0)
+    0.111111111111111*hbar**2
+
+    References
+    ==========
+
+    .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum
+           Mechanics (4th ed.).  Pages 71-73.
+
+    """
+    n, m, r = S(n), S(m), S(r)
+    if n.is_integer:
+        return (n**2 * hbar**2) / (2 * m * r**2)
+    else:
+        raise ValueError("'n' must be integer")
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/qho_1d.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/qho_1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..f418e0e954656923fbfa64cea2145581ddf65aea
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/qho_1d.py
@@ -0,0 +1,88 @@
+from sympy.core import S, pi, Rational
+from sympy.functions import hermite, sqrt, exp, factorial, Abs
+from sympy.physics.quantum.constants import hbar
+
+
+def psi_n(n, x, m, omega):
+    """
+    Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        the "nodal" quantum number.  Corresponds to the number of nodes in the
+        wavefunction.  ``n >= 0``
+    x :
+        x coordinate.
+    m :
+        Mass of the particle.
+    omega :
+        Angular frequency of the oscillator.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.qho_1d import psi_n
+    >>> from sympy.abc import m, x, omega
+    >>> psi_n(0, x, m, omega)
+    (m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4))
+
+    """
+
+    # sympify arguments
+    n, x, m, omega = map(S, [n, x, m, omega])
+    nu = m * omega / hbar
+    # normalization coefficient
+    C = (nu/pi)**Rational(1, 4) * sqrt(1/(2**n*factorial(n)))
+
+    return C * exp(-nu* x**2 /2) * hermite(n, sqrt(nu)*x)
+
+
+def E_n(n, omega):
+    """
+    Returns the Energy of the One-dimensional harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    omega :
+        The harmonic oscillator angular frequency.
+
+    Notes
+    =====
+
+    The unit of the returned value matches the unit of hw, since the energy is
+    calculated as:
+
+        E_n = hbar * omega*(n + 1/2)
+
+    Examples
+    ========
+
+    >>> from sympy.physics.qho_1d import E_n
+    >>> from sympy.abc import x, omega
+    >>> E_n(x, omega)
+    hbar*omega*(x + 1/2)
+    """
+
+    return hbar * omega * (n + S.Half)
+
+
+def coherent_state(n, alpha):
+    """
+    Returns  for the coherent states of 1D harmonic oscillator.
+    See https://en.wikipedia.org/wiki/Coherent_states
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    alpha :
+        The eigen value of annihilation operator.
+    """
+
+    return exp(- Abs(alpha)**2/2)*(alpha**n)/sqrt(factorial(n))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..36203f1a48c4c53832ce44942878ddc7b89f8091
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/__init__.py
@@ -0,0 +1,65 @@
+# Names exposed by 'from sympy.physics.quantum import *'
+
+__all__ = [
+    'AntiCommutator',
+
+    'qapply',
+
+    'Commutator',
+
+    'Dagger',
+
+    'HilbertSpaceError', 'HilbertSpace', 'TensorProductHilbertSpace',
+    'TensorPowerHilbertSpace', 'DirectSumHilbertSpace', 'ComplexSpace', 'L2',
+    'FockSpace',
+
+    'InnerProduct',
+
+    'Operator', 'HermitianOperator', 'UnitaryOperator', 'IdentityOperator',
+    'OuterProduct', 'DifferentialOperator',
+
+    'represent', 'rep_innerproduct', 'rep_expectation', 'integrate_result',
+    'get_basis', 'enumerate_states',
+
+    'KetBase', 'BraBase', 'StateBase', 'State', 'Ket', 'Bra', 'TimeDepState',
+    'TimeDepBra', 'TimeDepKet', 'OrthogonalKet', 'OrthogonalBra',
+    'OrthogonalState', 'Wavefunction',
+
+    'TensorProduct', 'tensor_product_simp',
+
+    'hbar', 'HBar',
+
+    '_postprocess_state_mul', '_postprocess_state_pow'
+]
+
+from .anticommutator import AntiCommutator
+
+from .qapply import qapply
+
+from .commutator import Commutator
+
+from .dagger import Dagger
+
+from .hilbert import (HilbertSpaceError, HilbertSpace,
+        TensorProductHilbertSpace, TensorPowerHilbertSpace,
+        DirectSumHilbertSpace, ComplexSpace, L2, FockSpace)
+
+from .innerproduct import InnerProduct
+
+from .operator import (Operator, HermitianOperator, UnitaryOperator,
+        IdentityOperator, OuterProduct, DifferentialOperator)
+
+from .represent import (represent, rep_innerproduct, rep_expectation,
+        integrate_result, get_basis, enumerate_states)
+
+from .state import (KetBase, BraBase, StateBase, State, Ket, Bra,
+        TimeDepState, TimeDepBra, TimeDepKet, OrthogonalKet,
+        OrthogonalBra, OrthogonalState, Wavefunction)
+
+from .tensorproduct import TensorProduct, tensor_product_simp
+
+from .constants import hbar, HBar
+
+# These are private, but need to be imported so they are registered
+# as postprocessing transformers with Mul and Pow.
+from .transforms import _postprocess_state_mul, _postprocess_state_pow
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/anticommutator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/anticommutator.py
new file mode 100644
index 0000000000000000000000000000000000000000..cbd26eade640b60a48eaac8c8b0abaf236478ca9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/anticommutator.py
@@ -0,0 +1,166 @@
+"""The anti-commutator: ``{A,B} = A*B + B*A``."""
+
+from sympy.core.expr import Expr
+from sympy.core.kind import KindDispatcher
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+from sympy.printing.pretty.stringpict import prettyForm
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.kind import _OperatorKind, OperatorKind
+
+__all__ = [
+    'AntiCommutator'
+]
+
+#-----------------------------------------------------------------------------
+# Anti-commutator
+#-----------------------------------------------------------------------------
+
+
+class AntiCommutator(Expr):
+    """The standard anticommutator, in an unevaluated state.
+
+    Explanation
+    ===========
+
+    Evaluating an anticommutator is defined [1]_ as: ``{A, B} = A*B + B*A``.
+    This class returns the anticommutator in an unevaluated form.  To evaluate
+    the anticommutator, use the ``.doit()`` method.
+
+    Canonical ordering of an anticommutator is ``{A, B}`` for ``A < B``. The
+    arguments of the anticommutator are put into canonical order using
+    ``__cmp__``. If ``B < A``, then ``{A, B}`` is returned as ``{B, A}``.
+
+    Parameters
+    ==========
+
+    A : Expr
+        The first argument of the anticommutator {A,B}.
+    B : Expr
+        The second argument of the anticommutator {A,B}.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.quantum import AntiCommutator
+    >>> from sympy.physics.quantum import Operator, Dagger
+    >>> x, y = symbols('x,y')
+    >>> A = Operator('A')
+    >>> B = Operator('B')
+
+    Create an anticommutator and use ``doit()`` to multiply them out.
+
+    >>> ac = AntiCommutator(A,B); ac
+    {A,B}
+    >>> ac.doit()
+    A*B + B*A
+
+    The commutator orders it arguments in canonical order:
+
+    >>> ac = AntiCommutator(B,A); ac
+    {A,B}
+
+    Commutative constants are factored out:
+
+    >>> AntiCommutator(3*x*A,x*y*B)
+    3*x**2*y*{A,B}
+
+    Adjoint operations applied to the anticommutator are properly applied to
+    the arguments:
+
+    >>> Dagger(AntiCommutator(A,B))
+    {Dagger(A),Dagger(B)}
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Commutator
+    """
+    is_commutative = False
+
+    _kind_dispatcher = KindDispatcher("AntiCommutator_kind_dispatcher", commutative=True)
+
+    @property
+    def kind(self):
+        arg_kinds = (a.kind for a in self.args)
+        return self._kind_dispatcher(*arg_kinds)
+
+    def __new__(cls, A, B):
+        r = cls.eval(A, B)
+        if r is not None:
+            return r
+        obj = Expr.__new__(cls, A, B)
+        return obj
+
+    @classmethod
+    def eval(cls, a, b):
+        if not (a and b):
+            return S.Zero
+        if a == b:
+            return Integer(2)*a**2
+        if a.is_commutative or b.is_commutative:
+            return Integer(2)*a*b
+
+        # [xA,yB]  ->  xy*[A,B]
+        ca, nca = a.args_cnc()
+        cb, ncb = b.args_cnc()
+        c_part = ca + cb
+        if c_part:
+            return Mul(Mul(*c_part), cls(Mul._from_args(nca), Mul._from_args(ncb)))
+
+        # Canonical ordering of arguments
+        #The Commutator [A,B] is on canonical form if A < B.
+        if a.compare(b) == 1:
+            return cls(b, a)
+
+    def doit(self, **hints):
+        """ Evaluate anticommutator """
+        # Keep the import of Operator here to avoid problems with
+        # circular imports.
+        from sympy.physics.quantum.operator import Operator
+        A = self.args[0]
+        B = self.args[1]
+        if isinstance(A, Operator) and isinstance(B, Operator):
+            try:
+                comm = A._eval_anticommutator(B, **hints)
+            except NotImplementedError:
+                try:
+                    comm = B._eval_anticommutator(A, **hints)
+                except NotImplementedError:
+                    comm = None
+            if comm is not None:
+                return comm.doit(**hints)
+        return (A*B + B*A).doit(**hints)
+
+    def _eval_adjoint(self):
+        return AntiCommutator(Dagger(self.args[0]), Dagger(self.args[1]))
+
+    def _sympyrepr(self, printer, *args):
+        return "%s(%s,%s)" % (
+            self.__class__.__name__, printer._print(
+                self.args[0]), printer._print(self.args[1])
+        )
+
+    def _sympystr(self, printer, *args):
+        return "{%s,%s}" % (
+            printer._print(self.args[0]), printer._print(self.args[1]))
+
+    def _pretty(self, printer, *args):
+        pform = printer._print(self.args[0], *args)
+        pform = prettyForm(*pform.right(prettyForm(',')))
+        pform = prettyForm(*pform.right(printer._print(self.args[1], *args)))
+        pform = prettyForm(*pform.parens(left='{', right='}'))
+        return pform
+
+    def _latex(self, printer, *args):
+        return "\\left\\{%s,%s\\right\\}" % tuple([
+            printer._print(arg, *args) for arg in self.args])
+
+
+@AntiCommutator._kind_dispatcher.register(_OperatorKind, _OperatorKind)
+def find_op_kind(e1, e2):
+    """Find the kind of an anticommutator of two OperatorKinds."""
+    return OperatorKind
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/boson.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/boson.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f24cae2a7ad2f438234fcf00dadb2a4a9d76fe8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/boson.py
@@ -0,0 +1,243 @@
+"""Bosonic quantum operators."""
+
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum import Operator
+from sympy.physics.quantum import HilbertSpace, FockSpace, Ket, Bra
+from sympy.functions.special.tensor_functions import KroneckerDelta
+
+
+__all__ = [
+    'BosonOp',
+    'BosonFockKet',
+    'BosonFockBra',
+    'BosonCoherentKet',
+    'BosonCoherentBra'
+]
+
+
+class BosonOp(Operator):
+    """A bosonic operator that satisfies [a, Dagger(a)] == 1.
+
+    Parameters
+    ==========
+
+    name : str
+        A string that labels the bosonic mode.
+
+    annihilation : bool
+        A bool that indicates if the bosonic operator is an annihilation (True,
+        default value) or creation operator (False)
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Dagger, Commutator
+    >>> from sympy.physics.quantum.boson import BosonOp
+    >>> a = BosonOp("a")
+    >>> Commutator(a, Dagger(a)).doit()
+    1
+    """
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def is_annihilation(self):
+        return bool(self.args[1])
+
+    @classmethod
+    def default_args(self):
+        return ("a", True)
+
+    def __new__(cls, *args, **hints):
+        if not len(args) in [1, 2]:
+            raise ValueError('1 or 2 parameters expected, got %s' % args)
+
+        if len(args) == 1:
+            args = (args[0], S.One)
+
+        if len(args) == 2:
+            args = (args[0], Integer(args[1]))
+
+        return Operator.__new__(cls, *args)
+
+    def _eval_commutator_BosonOp(self, other, **hints):
+        if self.name == other.name:
+            # [a^\dagger, a] = -1
+            if not self.is_annihilation and other.is_annihilation:
+                return S.NegativeOne
+
+        elif 'independent' in hints and hints['independent']:
+            # [a, b] = 0
+            return S.Zero
+
+        return None
+
+    def _eval_commutator_FermionOp(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_BosonOp(self, other, **hints):
+        if 'independent' in hints and hints['independent']:
+            # {a, b} = 2 * a * b, because [a, b] = 0
+            return 2 * self * other
+
+        return None
+
+    def _eval_adjoint(self):
+        return BosonOp(str(self.name), not self.is_annihilation)
+
+    def _print_contents_latex(self, printer, *args):
+        if self.is_annihilation:
+            return r'{%s}' % str(self.name)
+        else:
+            return r'{{%s}^\dagger}' % str(self.name)
+
+    def _print_contents(self, printer, *args):
+        if self.is_annihilation:
+            return r'%s' % str(self.name)
+        else:
+            return r'Dagger(%s)' % str(self.name)
+
+    def _print_contents_pretty(self, printer, *args):
+        from sympy.printing.pretty.stringpict import prettyForm
+        pform = printer._print(self.args[0], *args)
+        if self.is_annihilation:
+            return pform
+        else:
+            return pform**prettyForm('\N{DAGGER}')
+
+
+class BosonFockKet(Ket):
+    """Fock state ket for a bosonic mode.
+
+    Parameters
+    ==========
+
+    n : Number
+        The Fock state number.
+
+    """
+
+    def __new__(cls, n):
+        return Ket.__new__(cls, n)
+
+    @property
+    def n(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return BosonFockBra
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return FockSpace()
+
+    def _eval_innerproduct_BosonFockBra(self, bra, **hints):
+        return KroneckerDelta(self.n, bra.n)
+
+    def _apply_from_right_to_BosonOp(self, op, **options):
+        if op.is_annihilation:
+            return sqrt(self.n) * BosonFockKet(self.n - 1)
+        else:
+            return sqrt(self.n + 1) * BosonFockKet(self.n + 1)
+
+
+class BosonFockBra(Bra):
+    """Fock state bra for a bosonic mode.
+
+    Parameters
+    ==========
+
+    n : Number
+        The Fock state number.
+
+    """
+
+    def __new__(cls, n):
+        return Bra.__new__(cls, n)
+
+    @property
+    def n(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return BosonFockKet
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return FockSpace()
+
+
+class BosonCoherentKet(Ket):
+    """Coherent state ket for a bosonic mode.
+
+    Parameters
+    ==========
+
+    alpha : Number, Symbol
+        The complex amplitude of the coherent state.
+
+    """
+
+    def __new__(cls, alpha):
+        return Ket.__new__(cls, alpha)
+
+    @property
+    def alpha(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return BosonCoherentBra
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return HilbertSpace()
+
+    def _eval_innerproduct_BosonCoherentBra(self, bra, **hints):
+        if self.alpha == bra.alpha:
+            return S.One
+        else:
+            return exp(-(abs(self.alpha)**2 + abs(bra.alpha)**2 - 2 * conjugate(bra.alpha) * self.alpha)/2)
+
+    def _apply_from_right_to_BosonOp(self, op, **options):
+        if op.is_annihilation:
+            return self.alpha * self
+        else:
+            return None
+
+
+class BosonCoherentBra(Bra):
+    """Coherent state bra for a bosonic mode.
+
+    Parameters
+    ==========
+
+    alpha : Number, Symbol
+        The complex amplitude of the coherent state.
+
+    """
+
+    def __new__(cls, alpha):
+        return Bra.__new__(cls, alpha)
+
+    @property
+    def alpha(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return BosonCoherentKet
+
+    def _apply_operator_BosonOp(self, op, **options):
+        if not op.is_annihilation:
+            return self.alpha * self
+        else:
+            return None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/cartesian.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/cartesian.py
new file mode 100644
index 0000000000000000000000000000000000000000..f3af1856f22c8fe4535b24be30bf99d0b3541a50
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/cartesian.py
@@ -0,0 +1,341 @@
+"""Operators and states for 1D cartesian position and momentum.
+
+TODO:
+
+* Add 3D classes to mappings in operatorset.py
+
+"""
+
+from sympy.core.numbers import (I, pi)
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.delta_functions import DiracDelta
+from sympy.sets.sets import Interval
+
+from sympy.physics.quantum.constants import hbar
+from sympy.physics.quantum.hilbert import L2
+from sympy.physics.quantum.operator import DifferentialOperator, HermitianOperator
+from sympy.physics.quantum.state import Ket, Bra, State
+
+__all__ = [
+    'XOp',
+    'YOp',
+    'ZOp',
+    'PxOp',
+    'X',
+    'Y',
+    'Z',
+    'Px',
+    'XKet',
+    'XBra',
+    'PxKet',
+    'PxBra',
+    'PositionState3D',
+    'PositionKet3D',
+    'PositionBra3D'
+]
+
+#-------------------------------------------------------------------------
+# Position operators
+#-------------------------------------------------------------------------
+
+
+class XOp(HermitianOperator):
+    """1D cartesian position operator."""
+
+    @classmethod
+    def default_args(self):
+        return ("X",)
+
+    @classmethod
+    def _eval_hilbert_space(self, args):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    def _eval_commutator_PxOp(self, other):
+        return I*hbar
+
+    def _apply_operator_XKet(self, ket, **options):
+        return ket.position*ket
+
+    def _apply_operator_PositionKet3D(self, ket, **options):
+        return ket.position_x*ket
+
+    def _represent_PxKet(self, basis, *, index=1, **options):
+        states = basis._enumerate_state(2, start_index=index)
+        coord1 = states[0].momentum
+        coord2 = states[1].momentum
+        d = DifferentialOperator(coord1)
+        delta = DiracDelta(coord1 - coord2)
+
+        return I*hbar*(d*delta)
+
+
+class YOp(HermitianOperator):
+    """ Y cartesian coordinate operator (for 2D or 3D systems) """
+
+    @classmethod
+    def default_args(self):
+        return ("Y",)
+
+    @classmethod
+    def _eval_hilbert_space(self, args):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    def _apply_operator_PositionKet3D(self, ket, **options):
+        return ket.position_y*ket
+
+
+class ZOp(HermitianOperator):
+    """ Z cartesian coordinate operator (for 3D systems) """
+
+    @classmethod
+    def default_args(self):
+        return ("Z",)
+
+    @classmethod
+    def _eval_hilbert_space(self, args):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    def _apply_operator_PositionKet3D(self, ket, **options):
+        return ket.position_z*ket
+
+#-------------------------------------------------------------------------
+# Momentum operators
+#-------------------------------------------------------------------------
+
+
+class PxOp(HermitianOperator):
+    """1D cartesian momentum operator."""
+
+    @classmethod
+    def default_args(self):
+        return ("Px",)
+
+    @classmethod
+    def _eval_hilbert_space(self, args):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    def _apply_operator_PxKet(self, ket, **options):
+        return ket.momentum*ket
+
+    def _represent_XKet(self, basis, *, index=1, **options):
+        states = basis._enumerate_state(2, start_index=index)
+        coord1 = states[0].position
+        coord2 = states[1].position
+        d = DifferentialOperator(coord1)
+        delta = DiracDelta(coord1 - coord2)
+
+        return -I*hbar*(d*delta)
+
+X = XOp('X')
+Y = YOp('Y')
+Z = ZOp('Z')
+Px = PxOp('Px')
+
+#-------------------------------------------------------------------------
+# Position eigenstates
+#-------------------------------------------------------------------------
+
+
+class XKet(Ket):
+    """1D cartesian position eigenket."""
+
+    @classmethod
+    def _operators_to_state(self, op, **options):
+        return self.__new__(self, *_lowercase_labels(op), **options)
+
+    def _state_to_operators(self, op_class, **options):
+        return op_class.__new__(op_class,
+                                *_uppercase_labels(self), **options)
+
+    @classmethod
+    def default_args(self):
+        return ("x",)
+
+    @classmethod
+    def dual_class(self):
+        return XBra
+
+    @property
+    def position(self):
+        """The position of the state."""
+        return self.label[0]
+
+    def _enumerate_state(self, num_states, **options):
+        return _enumerate_continuous_1D(self, num_states, **options)
+
+    def _eval_innerproduct_XBra(self, bra, **hints):
+        return DiracDelta(self.position - bra.position)
+
+    def _eval_innerproduct_PxBra(self, bra, **hints):
+        return exp(-I*self.position*bra.momentum/hbar)/sqrt(2*pi*hbar)
+
+
+class XBra(Bra):
+    """1D cartesian position eigenbra."""
+
+    @classmethod
+    def default_args(self):
+        return ("x",)
+
+    @classmethod
+    def dual_class(self):
+        return XKet
+
+    @property
+    def position(self):
+        """The position of the state."""
+        return self.label[0]
+
+
+class PositionState3D(State):
+    """ Base class for 3D cartesian position eigenstates """
+
+    @classmethod
+    def _operators_to_state(self, op, **options):
+        return self.__new__(self, *_lowercase_labels(op), **options)
+
+    def _state_to_operators(self, op_class, **options):
+        return op_class.__new__(op_class,
+                                *_uppercase_labels(self), **options)
+
+    @classmethod
+    def default_args(self):
+        return ("x", "y", "z")
+
+    @property
+    def position_x(self):
+        """ The x coordinate of the state """
+        return self.label[0]
+
+    @property
+    def position_y(self):
+        """ The y coordinate of the state """
+        return self.label[1]
+
+    @property
+    def position_z(self):
+        """ The z coordinate of the state """
+        return self.label[2]
+
+
+class PositionKet3D(Ket, PositionState3D):
+    """ 3D cartesian position eigenket """
+
+    def _eval_innerproduct_PositionBra3D(self, bra, **options):
+        x_diff = self.position_x - bra.position_x
+        y_diff = self.position_y - bra.position_y
+        z_diff = self.position_z - bra.position_z
+
+        return DiracDelta(x_diff)*DiracDelta(y_diff)*DiracDelta(z_diff)
+
+    @classmethod
+    def dual_class(self):
+        return PositionBra3D
+
+
+# XXX: The type:ignore here is because mypy gives Definition of
+# "_state_to_operators" in base class "PositionState3D" is incompatible with
+# definition in base class "BraBase"
+class PositionBra3D(Bra, PositionState3D):  # type: ignore
+    """ 3D cartesian position eigenbra """
+
+    @classmethod
+    def dual_class(self):
+        return PositionKet3D
+
+#-------------------------------------------------------------------------
+# Momentum eigenstates
+#-------------------------------------------------------------------------
+
+
+class PxKet(Ket):
+    """1D cartesian momentum eigenket."""
+
+    @classmethod
+    def _operators_to_state(self, op, **options):
+        return self.__new__(self, *_lowercase_labels(op), **options)
+
+    def _state_to_operators(self, op_class, **options):
+        return op_class.__new__(op_class,
+                                *_uppercase_labels(self), **options)
+
+    @classmethod
+    def default_args(self):
+        return ("px",)
+
+    @classmethod
+    def dual_class(self):
+        return PxBra
+
+    @property
+    def momentum(self):
+        """The momentum of the state."""
+        return self.label[0]
+
+    def _enumerate_state(self, *args, **options):
+        return _enumerate_continuous_1D(self, *args, **options)
+
+    def _eval_innerproduct_XBra(self, bra, **hints):
+        return exp(I*self.momentum*bra.position/hbar)/sqrt(2*pi*hbar)
+
+    def _eval_innerproduct_PxBra(self, bra, **hints):
+        return DiracDelta(self.momentum - bra.momentum)
+
+
+class PxBra(Bra):
+    """1D cartesian momentum eigenbra."""
+
+    @classmethod
+    def default_args(self):
+        return ("px",)
+
+    @classmethod
+    def dual_class(self):
+        return PxKet
+
+    @property
+    def momentum(self):
+        """The momentum of the state."""
+        return self.label[0]
+
+#-------------------------------------------------------------------------
+# Global helper functions
+#-------------------------------------------------------------------------
+
+
+def _enumerate_continuous_1D(*args, **options):
+    state = args[0]
+    num_states = args[1]
+    state_class = state.__class__
+    index_list = options.pop('index_list', [])
+
+    if len(index_list) == 0:
+        start_index = options.pop('start_index', 1)
+        index_list = list(range(start_index, start_index + num_states))
+
+    enum_states = [0 for i in range(len(index_list))]
+
+    for i, ind in enumerate(index_list):
+        label = state.args[0]
+        enum_states[i] = state_class(str(label) + "_" + str(ind), **options)
+
+    return enum_states
+
+
+def _lowercase_labels(ops):
+    if not isinstance(ops, set):
+        ops = [ops]
+
+    return [str(arg.label[0]).lower() for arg in ops]
+
+
+def _uppercase_labels(ops):
+    if not isinstance(ops, set):
+        ops = [ops]
+
+    new_args = [str(arg.label[0])[0].upper() +
+                str(arg.label[0])[1:] for arg in ops]
+
+    return new_args
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/cg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/cg.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f285cd39413a953246777c42fb6763c22a5716b
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/cg.py
@@ -0,0 +1,754 @@
+#TODO:
+# -Implement Clebsch-Gordan symmetries
+# -Improve simplification method
+# -Implement new simplifications
+"""Clebsch-Gordon Coefficients."""
+
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.function import expand
+from sympy.core.mul import Mul
+from sympy.core.power import Pow
+from sympy.core.relational import Eq
+from sympy.core.singleton import S
+from sympy.core.symbol import (Wild, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.printing.pretty.stringpict import prettyForm, stringPict
+
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.physics.wigner import clebsch_gordan, wigner_3j, wigner_6j, wigner_9j
+from sympy.printing.precedence import PRECEDENCE
+
+__all__ = [
+    'CG',
+    'Wigner3j',
+    'Wigner6j',
+    'Wigner9j',
+    'cg_simp'
+]
+
+#-----------------------------------------------------------------------------
+# CG Coefficients
+#-----------------------------------------------------------------------------
+
+
+class Wigner3j(Expr):
+    """Class for the Wigner-3j symbols.
+
+    Explanation
+    ===========
+
+    Wigner 3j-symbols are coefficients determined by the coupling of
+    two angular momenta. When created, they are expressed as symbolic
+    quantities that, for numerical parameters, can be evaluated using the
+    ``.doit()`` method [1]_.
+
+    Parameters
+    ==========
+
+    j1, m1, j2, m2, j3, m3 : Number, Symbol
+        Terms determining the angular momentum of coupled angular momentum
+        systems.
+
+    Examples
+    ========
+
+    Declare a Wigner-3j coefficient and calculate its value
+
+        >>> from sympy.physics.quantum.cg import Wigner3j
+        >>> w3j = Wigner3j(6,0,4,0,2,0)
+        >>> w3j
+        Wigner3j(6, 0, 4, 0, 2, 0)
+        >>> w3j.doit()
+        sqrt(715)/143
+
+    See Also
+    ========
+
+    CG: Clebsch-Gordan coefficients
+
+    References
+    ==========
+
+    .. [1] Varshalovich, D A, Quantum Theory of Angular Momentum. 1988.
+    """
+
+    is_commutative = True
+
+    def __new__(cls, j1, m1, j2, m2, j3, m3):
+        args = map(sympify, (j1, m1, j2, m2, j3, m3))
+        return Expr.__new__(cls, *args)
+
+    @property
+    def j1(self):
+        return self.args[0]
+
+    @property
+    def m1(self):
+        return self.args[1]
+
+    @property
+    def j2(self):
+        return self.args[2]
+
+    @property
+    def m2(self):
+        return self.args[3]
+
+    @property
+    def j3(self):
+        return self.args[4]
+
+    @property
+    def m3(self):
+        return self.args[5]
+
+    @property
+    def is_symbolic(self):
+        return not all(arg.is_number for arg in self.args)
+
+    # This is modified from the _print_Matrix method
+    def _pretty(self, printer, *args):
+        m = ((printer._print(self.j1), printer._print(self.m1)),
+            (printer._print(self.j2), printer._print(self.m2)),
+            (printer._print(self.j3), printer._print(self.m3)))
+        hsep = 2
+        vsep = 1
+        maxw = [-1]*3
+        for j in range(3):
+            maxw[j] = max(m[j][i].width() for i in range(2))
+        D = None
+        for i in range(2):
+            D_row = None
+            for j in range(3):
+                s = m[j][i]
+                wdelta = maxw[j] - s.width()
+                wleft = wdelta //2
+                wright = wdelta - wleft
+
+                s = prettyForm(*s.right(' '*wright))
+                s = prettyForm(*s.left(' '*wleft))
+
+                if D_row is None:
+                    D_row = s
+                    continue
+                D_row = prettyForm(*D_row.right(' '*hsep))
+                D_row = prettyForm(*D_row.right(s))
+            if D is None:
+                D = D_row
+                continue
+            for _ in range(vsep):
+                D = prettyForm(*D.below(' '))
+            D = prettyForm(*D.below(D_row))
+        D = prettyForm(*D.parens())
+        return D
+
+    def _latex(self, printer, *args):
+        label = map(printer._print, (self.j1, self.j2, self.j3,
+                    self.m1, self.m2, self.m3))
+        return r'\left(\begin{array}{ccc} %s & %s & %s \\ %s & %s & %s \end{array}\right)' % \
+            tuple(label)
+
+    def doit(self, **hints):
+        if self.is_symbolic:
+            raise ValueError("Coefficients must be numerical")
+        return wigner_3j(self.j1, self.j2, self.j3, self.m1, self.m2, self.m3)
+
+
+class CG(Wigner3j):
+    r"""Class for Clebsch-Gordan coefficient.
+
+    Explanation
+    ===========
+
+    Clebsch-Gordan coefficients describe the angular momentum coupling between
+    two systems. The coefficients give the expansion of a coupled total angular
+    momentum state and an uncoupled tensor product state. The Clebsch-Gordan
+    coefficients are defined as [1]_:
+
+    .. math ::
+        C^{j_3,m_3}_{j_1,m_1,j_2,m_2} = \left\langle j_1,m_1;j_2,m_2 | j_3,m_3\right\rangle
+
+    Parameters
+    ==========
+
+    j1, m1, j2, m2 : Number, Symbol
+        Angular momenta of states 1 and 2.
+
+    j3, m3: Number, Symbol
+        Total angular momentum of the coupled system.
+
+    Examples
+    ========
+
+    Define a Clebsch-Gordan coefficient and evaluate its value
+
+        >>> from sympy.physics.quantum.cg import CG
+        >>> from sympy import S
+        >>> cg = CG(S(3)/2, S(3)/2, S(1)/2, -S(1)/2, 1, 1)
+        >>> cg
+        CG(3/2, 3/2, 1/2, -1/2, 1, 1)
+        >>> cg.doit()
+        sqrt(3)/2
+        >>> CG(j1=S(1)/2, m1=-S(1)/2, j2=S(1)/2, m2=+S(1)/2, j3=1, m3=0).doit()
+        sqrt(2)/2
+
+
+    Compare [2]_.
+
+    See Also
+    ========
+
+    Wigner3j: Wigner-3j symbols
+
+    References
+    ==========
+
+    .. [1] Varshalovich, D A, Quantum Theory of Angular Momentum. 1988.
+    .. [2] `Clebsch-Gordan Coefficients, Spherical Harmonics, and d Functions
+        `_
+        in P.A. Zyla *et al.* (Particle Data Group), Prog. Theor. Exp. Phys.
+        2020, 083C01 (2020).
+    """
+    precedence = PRECEDENCE["Pow"] - 1
+
+    def doit(self, **hints):
+        if self.is_symbolic:
+            raise ValueError("Coefficients must be numerical")
+        return clebsch_gordan(self.j1, self.j2, self.j3, self.m1, self.m2, self.m3)
+
+    def _pretty(self, printer, *args):
+        bot = printer._print_seq(
+            (self.j1, self.m1, self.j2, self.m2), delimiter=',')
+        top = printer._print_seq((self.j3, self.m3), delimiter=',')
+
+        pad = max(top.width(), bot.width())
+        bot = prettyForm(*bot.left(' '))
+        top = prettyForm(*top.left(' '))
+
+        if not pad == bot.width():
+            bot = prettyForm(*bot.right(' '*(pad - bot.width())))
+        if not pad == top.width():
+            top = prettyForm(*top.right(' '*(pad - top.width())))
+        s = stringPict('C' + ' '*pad)
+        s = prettyForm(*s.below(bot))
+        s = prettyForm(*s.above(top))
+        return s
+
+    def _latex(self, printer, *args):
+        label = map(printer._print, (self.j3, self.m3, self.j1,
+                    self.m1, self.j2, self.m2))
+        return r'C^{%s,%s}_{%s,%s,%s,%s}' % tuple(label)
+
+
+class Wigner6j(Expr):
+    """Class for the Wigner-6j symbols
+
+    See Also
+    ========
+
+    Wigner3j: Wigner-3j symbols
+
+    """
+    def __new__(cls, j1, j2, j12, j3, j, j23):
+        args = map(sympify, (j1, j2, j12, j3, j, j23))
+        return Expr.__new__(cls, *args)
+
+    @property
+    def j1(self):
+        return self.args[0]
+
+    @property
+    def j2(self):
+        return self.args[1]
+
+    @property
+    def j12(self):
+        return self.args[2]
+
+    @property
+    def j3(self):
+        return self.args[3]
+
+    @property
+    def j(self):
+        return self.args[4]
+
+    @property
+    def j23(self):
+        return self.args[5]
+
+    @property
+    def is_symbolic(self):
+        return not all(arg.is_number for arg in self.args)
+
+    # This is modified from the _print_Matrix method
+    def _pretty(self, printer, *args):
+        m = ((printer._print(self.j1), printer._print(self.j3)),
+            (printer._print(self.j2), printer._print(self.j)),
+            (printer._print(self.j12), printer._print(self.j23)))
+        hsep = 2
+        vsep = 1
+        maxw = [-1]*3
+        for j in range(3):
+            maxw[j] = max(m[j][i].width() for i in range(2))
+        D = None
+        for i in range(2):
+            D_row = None
+            for j in range(3):
+                s = m[j][i]
+                wdelta = maxw[j] - s.width()
+                wleft = wdelta //2
+                wright = wdelta - wleft
+
+                s = prettyForm(*s.right(' '*wright))
+                s = prettyForm(*s.left(' '*wleft))
+
+                if D_row is None:
+                    D_row = s
+                    continue
+                D_row = prettyForm(*D_row.right(' '*hsep))
+                D_row = prettyForm(*D_row.right(s))
+            if D is None:
+                D = D_row
+                continue
+            for _ in range(vsep):
+                D = prettyForm(*D.below(' '))
+            D = prettyForm(*D.below(D_row))
+        D = prettyForm(*D.parens(left='{', right='}'))
+        return D
+
+    def _latex(self, printer, *args):
+        label = map(printer._print, (self.j1, self.j2, self.j12,
+                    self.j3, self.j, self.j23))
+        return r'\left\{\begin{array}{ccc} %s & %s & %s \\ %s & %s & %s \end{array}\right\}' % \
+            tuple(label)
+
+    def doit(self, **hints):
+        if self.is_symbolic:
+            raise ValueError("Coefficients must be numerical")
+        return wigner_6j(self.j1, self.j2, self.j12, self.j3, self.j, self.j23)
+
+
+class Wigner9j(Expr):
+    """Class for the Wigner-9j symbols
+
+    See Also
+    ========
+
+    Wigner3j: Wigner-3j symbols
+
+    """
+    def __new__(cls, j1, j2, j12, j3, j4, j34, j13, j24, j):
+        args = map(sympify, (j1, j2, j12, j3, j4, j34, j13, j24, j))
+        return Expr.__new__(cls, *args)
+
+    @property
+    def j1(self):
+        return self.args[0]
+
+    @property
+    def j2(self):
+        return self.args[1]
+
+    @property
+    def j12(self):
+        return self.args[2]
+
+    @property
+    def j3(self):
+        return self.args[3]
+
+    @property
+    def j4(self):
+        return self.args[4]
+
+    @property
+    def j34(self):
+        return self.args[5]
+
+    @property
+    def j13(self):
+        return self.args[6]
+
+    @property
+    def j24(self):
+        return self.args[7]
+
+    @property
+    def j(self):
+        return self.args[8]
+
+    @property
+    def is_symbolic(self):
+        return not all(arg.is_number for arg in self.args)
+
+    # This is modified from the _print_Matrix method
+    def _pretty(self, printer, *args):
+        m = (
+            (printer._print(
+                self.j1), printer._print(self.j3), printer._print(self.j13)),
+            (printer._print(
+                self.j2), printer._print(self.j4), printer._print(self.j24)),
+            (printer._print(self.j12), printer._print(self.j34), printer._print(self.j)))
+        hsep = 2
+        vsep = 1
+        maxw = [-1]*3
+        for j in range(3):
+            maxw[j] = max(m[j][i].width() for i in range(3))
+        D = None
+        for i in range(3):
+            D_row = None
+            for j in range(3):
+                s = m[j][i]
+                wdelta = maxw[j] - s.width()
+                wleft = wdelta //2
+                wright = wdelta - wleft
+
+                s = prettyForm(*s.right(' '*wright))
+                s = prettyForm(*s.left(' '*wleft))
+
+                if D_row is None:
+                    D_row = s
+                    continue
+                D_row = prettyForm(*D_row.right(' '*hsep))
+                D_row = prettyForm(*D_row.right(s))
+            if D is None:
+                D = D_row
+                continue
+            for _ in range(vsep):
+                D = prettyForm(*D.below(' '))
+            D = prettyForm(*D.below(D_row))
+        D = prettyForm(*D.parens(left='{', right='}'))
+        return D
+
+    def _latex(self, printer, *args):
+        label = map(printer._print, (self.j1, self.j2, self.j12, self.j3,
+                self.j4, self.j34, self.j13, self.j24, self.j))
+        return r'\left\{\begin{array}{ccc} %s & %s & %s \\ %s & %s & %s \\ %s & %s & %s \end{array}\right\}' % \
+            tuple(label)
+
+    def doit(self, **hints):
+        if self.is_symbolic:
+            raise ValueError("Coefficients must be numerical")
+        return wigner_9j(self.j1, self.j2, self.j12, self.j3, self.j4, self.j34, self.j13, self.j24, self.j)
+
+
+def cg_simp(e):
+    """Simplify and combine CG coefficients.
+
+    Explanation
+    ===========
+
+    This function uses various symmetry and properties of sums and
+    products of Clebsch-Gordan coefficients to simplify statements
+    involving these terms [1]_.
+
+    Examples
+    ========
+
+    Simplify the sum over CG(a,alpha,0,0,a,alpha) for all alpha to
+    2*a+1
+
+        >>> from sympy.physics.quantum.cg import CG, cg_simp
+        >>> a = CG(1,1,0,0,1,1)
+        >>> b = CG(1,0,0,0,1,0)
+        >>> c = CG(1,-1,0,0,1,-1)
+        >>> cg_simp(a+b+c)
+        3
+
+    See Also
+    ========
+
+    CG: Clebsh-Gordan coefficients
+
+    References
+    ==========
+
+    .. [1] Varshalovich, D A, Quantum Theory of Angular Momentum. 1988.
+    """
+    if isinstance(e, Add):
+        return _cg_simp_add(e)
+    elif isinstance(e, Sum):
+        return _cg_simp_sum(e)
+    elif isinstance(e, Mul):
+        return Mul(*[cg_simp(arg) for arg in e.args])
+    elif isinstance(e, Pow):
+        return Pow(cg_simp(e.base), e.exp)
+    else:
+        return e
+
+
+def _cg_simp_add(e):
+    #TODO: Improve simplification method
+    """Takes a sum of terms involving Clebsch-Gordan coefficients and
+    simplifies the terms.
+
+    Explanation
+    ===========
+
+    First, we create two lists, cg_part, which is all the terms involving CG
+    coefficients, and other_part, which is all other terms. The cg_part list
+    is then passed to the simplification methods, which return the new cg_part
+    and any additional terms that are added to other_part
+    """
+    cg_part = []
+    other_part = []
+
+    e = expand(e)
+    for arg in e.args:
+        if arg.has(CG):
+            if isinstance(arg, Sum):
+                other_part.append(_cg_simp_sum(arg))
+            elif isinstance(arg, Mul):
+                terms = 1
+                for term in arg.args:
+                    if isinstance(term, Sum):
+                        terms *= _cg_simp_sum(term)
+                    else:
+                        terms *= term
+                if terms.has(CG):
+                    cg_part.append(terms)
+                else:
+                    other_part.append(terms)
+            else:
+                cg_part.append(arg)
+        else:
+            other_part.append(arg)
+
+    cg_part, other = _check_varsh_871_1(cg_part)
+    other_part.append(other)
+    cg_part, other = _check_varsh_871_2(cg_part)
+    other_part.append(other)
+    cg_part, other = _check_varsh_872_9(cg_part)
+    other_part.append(other)
+    return Add(*cg_part) + Add(*other_part)
+
+
+def _check_varsh_871_1(term_list):
+    # Sum( CG(a,alpha,b,0,a,alpha), (alpha, -a, a)) == KroneckerDelta(b,0)
+    a, alpha, b, lt = map(Wild, ('a', 'alpha', 'b', 'lt'))
+    expr = lt*CG(a, alpha, b, 0, a, alpha)
+    simp = (2*a + 1)*KroneckerDelta(b, 0)
+    sign = lt/abs(lt)
+    build_expr = 2*a + 1
+    index_expr = a + alpha
+    return _check_cg_simp(expr, simp, sign, lt, term_list, (a, alpha, b, lt), (a, b), build_expr, index_expr)
+
+
+def _check_varsh_871_2(term_list):
+    # Sum((-1)**(a-alpha)*CG(a,alpha,a,-alpha,c,0),(alpha,-a,a))
+    a, alpha, c, lt = map(Wild, ('a', 'alpha', 'c', 'lt'))
+    expr = lt*CG(a, alpha, a, -alpha, c, 0)
+    simp = sqrt(2*a + 1)*KroneckerDelta(c, 0)
+    sign = (-1)**(a - alpha)*lt/abs(lt)
+    build_expr = 2*a + 1
+    index_expr = a + alpha
+    return _check_cg_simp(expr, simp, sign, lt, term_list, (a, alpha, c, lt), (a, c), build_expr, index_expr)
+
+
+def _check_varsh_872_9(term_list):
+    # Sum( CG(a,alpha,b,beta,c,gamma)*CG(a,alpha',b,beta',c,gamma), (gamma, -c, c), (c, abs(a-b), a+b))
+    a, alpha, alphap, b, beta, betap, c, gamma, lt = map(Wild, (
+        'a', 'alpha', 'alphap', 'b', 'beta', 'betap', 'c', 'gamma', 'lt'))
+    # Case alpha==alphap, beta==betap
+
+    # For numerical alpha,beta
+    expr = lt*CG(a, alpha, b, beta, c, gamma)**2
+    simp = S.One
+    sign = lt/abs(lt)
+    x = abs(a - b)
+    y = abs(alpha + beta)
+    build_expr = a + b + 1 - Piecewise((x, x > y), (0, Eq(x, y)), (y, y > x))
+    index_expr = a + b - c
+    term_list, other1 = _check_cg_simp(expr, simp, sign, lt, term_list, (a, alpha, b, beta, c, gamma, lt), (a, alpha, b, beta), build_expr, index_expr)
+
+    # For symbolic alpha,beta
+    x = abs(a - b)
+    y = a + b
+    build_expr = (y + 1 - x)*(x + y + 1)
+    index_expr = (c - x)*(x + c) + c + gamma
+    term_list, other2 = _check_cg_simp(expr, simp, sign, lt, term_list, (a, alpha, b, beta, c, gamma, lt), (a, alpha, b, beta), build_expr, index_expr)
+
+    # Case alpha!=alphap or beta!=betap
+    # Note: this only works with leading term of 1, pattern matching is unable to match when there is a Wild leading term
+    # For numerical alpha,alphap,beta,betap
+    expr = CG(a, alpha, b, beta, c, gamma)*CG(a, alphap, b, betap, c, gamma)
+    simp = KroneckerDelta(alpha, alphap)*KroneckerDelta(beta, betap)
+    sign = S.One
+    x = abs(a - b)
+    y = abs(alpha + beta)
+    build_expr = a + b + 1 - Piecewise((x, x > y), (0, Eq(x, y)), (y, y > x))
+    index_expr = a + b - c
+    term_list, other3 = _check_cg_simp(expr, simp, sign, S.One, term_list, (a, alpha, alphap, b, beta, betap, c, gamma), (a, alpha, alphap, b, beta, betap), build_expr, index_expr)
+
+    # For symbolic alpha,alphap,beta,betap
+    x = abs(a - b)
+    y = a + b
+    build_expr = (y + 1 - x)*(x + y + 1)
+    index_expr = (c - x)*(x + c) + c + gamma
+    term_list, other4 = _check_cg_simp(expr, simp, sign, S.One, term_list, (a, alpha, alphap, b, beta, betap, c, gamma), (a, alpha, alphap, b, beta, betap), build_expr, index_expr)
+
+    return term_list, other1 + other2 + other4
+
+
+def _check_cg_simp(expr, simp, sign, lt, term_list, variables, dep_variables, build_index_expr, index_expr):
+    """ Checks for simplifications that can be made, returning a tuple of the
+    simplified list of terms and any terms generated by simplification.
+
+    Parameters
+    ==========
+
+    expr: expression
+        The expression with Wild terms that will be matched to the terms in
+        the sum
+
+    simp: expression
+        The expression with Wild terms that is substituted in place of the CG
+        terms in the case of simplification
+
+    sign: expression
+        The expression with Wild terms denoting the sign that is on expr that
+        must match
+
+    lt: expression
+        The expression with Wild terms that gives the leading term of the
+        matched expr
+
+    term_list: list
+        A list of all of the terms is the sum to be simplified
+
+    variables: list
+        A list of all the variables that appears in expr
+
+    dep_variables: list
+        A list of the variables that must match for all the terms in the sum,
+        i.e. the dependent variables
+
+    build_index_expr: expression
+        Expression with Wild terms giving the number of elements in cg_index
+
+    index_expr: expression
+        Expression with Wild terms giving the index terms have when storing
+        them to cg_index
+
+    """
+    other_part = 0
+    i = 0
+    while i < len(term_list):
+        sub_1 = _check_cg(term_list[i], expr, len(variables))
+        if sub_1 is None:
+            i += 1
+            continue
+        if not build_index_expr.subs(sub_1).is_number:
+            i += 1
+            continue
+        sub_dep = [(x, sub_1[x]) for x in dep_variables]
+        cg_index = [None]*build_index_expr.subs(sub_1)
+        for j in range(i, len(term_list)):
+            sub_2 = _check_cg(term_list[j], expr.subs(sub_dep), len(variables) - len(dep_variables), sign=(sign.subs(sub_1), sign.subs(sub_dep)))
+            if sub_2 is None:
+                continue
+            if not index_expr.subs(sub_dep).subs(sub_2).is_number:
+                continue
+            cg_index[index_expr.subs(sub_dep).subs(sub_2)] = j, expr.subs(lt, 1).subs(sub_dep).subs(sub_2), lt.subs(sub_2), sign.subs(sub_dep).subs(sub_2)
+        if not any(i is None for i in cg_index):
+            min_lt = min(*[ abs(term[2]) for term in cg_index ])
+            indices = [ term[0] for term in cg_index]
+            indices.sort()
+            indices.reverse()
+            [ term_list.pop(j) for j in indices ]
+            for term in cg_index:
+                if abs(term[2]) > min_lt:
+                    term_list.append( (term[2] - min_lt*term[3])*term[1] )
+            other_part += min_lt*(sign*simp).subs(sub_1)
+        else:
+            i += 1
+    return term_list, other_part
+
+
+def _check_cg(cg_term, expr, length, sign=None):
+    """Checks whether a term matches the given expression"""
+    # TODO: Check for symmetries
+    matches = cg_term.match(expr)
+    if matches is None:
+        return
+    if sign is not None:
+        if not isinstance(sign, tuple):
+            raise TypeError('sign must be a tuple')
+        if not sign[0] == (sign[1]).subs(matches):
+            return
+    if len(matches) == length:
+        return matches
+
+
+def _cg_simp_sum(e):
+    e = _check_varsh_sum_871_1(e)
+    e = _check_varsh_sum_871_2(e)
+    e = _check_varsh_sum_872_4(e)
+    return e
+
+
+def _check_varsh_sum_871_1(e):
+    a = Wild('a')
+    alpha = symbols('alpha')
+    b = Wild('b')
+    match = e.match(Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)))
+    if match is not None and len(match) == 2:
+        return ((2*a + 1)*KroneckerDelta(b, 0)).subs(match)
+    return e
+
+
+def _check_varsh_sum_871_2(e):
+    a = Wild('a')
+    alpha = symbols('alpha')
+    c = Wild('c')
+    match = e.match(
+        Sum((-1)**(a - alpha)*CG(a, alpha, a, -alpha, c, 0), (alpha, -a, a)))
+    if match is not None and len(match) == 2:
+        return (sqrt(2*a + 1)*KroneckerDelta(c, 0)).subs(match)
+    return e
+
+
+def _check_varsh_sum_872_4(e):
+    alpha = symbols('alpha')
+    beta = symbols('beta')
+    a = Wild('a')
+    b = Wild('b')
+    c = Wild('c')
+    cp = Wild('cp')
+    gamma = Wild('gamma')
+    gammap = Wild('gammap')
+    cg1 = CG(a, alpha, b, beta, c, gamma)
+    cg2 = CG(a, alpha, b, beta, cp, gammap)
+    match1 = e.match(Sum(cg1*cg2, (alpha, -a, a), (beta, -b, b)))
+    if match1 is not None and len(match1) == 6:
+        return (KroneckerDelta(c, cp)*KroneckerDelta(gamma, gammap)).subs(match1)
+    match2 = e.match(Sum(cg1**2, (alpha, -a, a), (beta, -b, b)))
+    if match2 is not None and len(match2) == 4:
+        return S.One
+    return e
+
+
+def _cg_list(term):
+    if isinstance(term, CG):
+        return (term,), 1, 1
+    cg = []
+    coeff = 1
+    if not isinstance(term, (Mul, Pow)):
+        raise NotImplementedError('term must be CG, Add, Mul or Pow')
+    if isinstance(term, Pow) and term.exp.is_number:
+        if term.exp.is_number:
+            [ cg.append(term.base) for _ in range(term.exp) ]
+        else:
+            return (term,), 1, 1
+    if isinstance(term, Mul):
+        for arg in term.args:
+            if isinstance(arg, CG):
+                cg.append(arg)
+            else:
+                coeff *= arg
+        return cg, coeff, coeff/abs(coeff)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/circuitplot.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/circuitplot.py
new file mode 100644
index 0000000000000000000000000000000000000000..316a4be613b2e275565999130c06ea678acd8b96
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/circuitplot.py
@@ -0,0 +1,370 @@
+"""Matplotlib based plotting of quantum circuits.
+
+Todo:
+
+* Optimize printing of large circuits.
+* Get this to work with single gates.
+* Do a better job checking the form of circuits to make sure it is a Mul of
+  Gates.
+* Get multi-target gates plotting.
+* Get initial and final states to plot.
+* Get measurements to plot. Might need to rethink measurement as a gate
+  issue.
+* Get scale and figsize to be handled in a better way.
+* Write some tests/examples!
+"""
+
+from __future__ import annotations
+
+from sympy.core.mul import Mul
+from sympy.external import import_module
+from sympy.physics.quantum.gate import Gate, OneQubitGate, CGate, CGateS
+
+
+__all__ = [
+    'CircuitPlot',
+    'circuit_plot',
+    'labeller',
+    'Mz',
+    'Mx',
+    'CreateOneQubitGate',
+    'CreateCGate',
+]
+
+np = import_module('numpy')
+matplotlib = import_module(
+    'matplotlib', import_kwargs={'fromlist': ['pyplot']},
+    catch=(RuntimeError,))  # This is raised in environments that have no display.
+
+if np and matplotlib:
+    pyplot = matplotlib.pyplot
+    Line2D = matplotlib.lines.Line2D
+    Circle = matplotlib.patches.Circle
+
+#from matplotlib import rc
+#rc('text',usetex=True)
+
+class CircuitPlot:
+    """A class for managing a circuit plot."""
+
+    scale = 1.0
+    fontsize = 20.0
+    linewidth = 1.0
+    control_radius = 0.05
+    not_radius = 0.15
+    swap_delta = 0.05
+    labels: list[str] = []
+    inits: dict[str, str] = {}
+    label_buffer = 0.5
+
+    def __init__(self, c, nqubits, **kwargs):
+        if not np or not matplotlib:
+            raise ImportError('numpy or matplotlib not available.')
+        self.circuit = c
+        self.ngates = len(self.circuit.args)
+        self.nqubits = nqubits
+        self.update(kwargs)
+        self._create_grid()
+        self._create_figure()
+        self._plot_wires()
+        self._plot_gates()
+        self._finish()
+
+    def update(self, kwargs):
+        """Load the kwargs into the instance dict."""
+        self.__dict__.update(kwargs)
+
+    def _create_grid(self):
+        """Create the grid of wires."""
+        scale = self.scale
+        wire_grid = np.arange(0.0, self.nqubits*scale, scale, dtype=float)
+        gate_grid = np.arange(0.0, self.ngates*scale, scale, dtype=float)
+        self._wire_grid = wire_grid
+        self._gate_grid = gate_grid
+
+    def _create_figure(self):
+        """Create the main matplotlib figure."""
+        self._figure = pyplot.figure(
+            figsize=(self.ngates*self.scale, self.nqubits*self.scale),
+            facecolor='w',
+            edgecolor='w'
+        )
+        ax = self._figure.add_subplot(
+            1, 1, 1,
+            frameon=True
+        )
+        ax.set_axis_off()
+        offset = 0.5*self.scale
+        ax.set_xlim(self._gate_grid[0] - offset, self._gate_grid[-1] + offset)
+        ax.set_ylim(self._wire_grid[0] - offset, self._wire_grid[-1] + offset)
+        ax.set_aspect('equal')
+        self._axes = ax
+
+    def _plot_wires(self):
+        """Plot the wires of the circuit diagram."""
+        xstart = self._gate_grid[0]
+        xstop = self._gate_grid[-1]
+        xdata = (xstart - self.scale, xstop + self.scale)
+        for i in range(self.nqubits):
+            ydata = (self._wire_grid[i], self._wire_grid[i])
+            line = Line2D(
+                xdata, ydata,
+                color='k',
+                lw=self.linewidth
+            )
+            self._axes.add_line(line)
+            if self.labels:
+                init_label_buffer = 0
+                if self.inits.get(self.labels[i]): init_label_buffer = 0.25
+                self._axes.text(
+                    xdata[0]-self.label_buffer-init_label_buffer,ydata[0],
+                    render_label(self.labels[i],self.inits),
+                    size=self.fontsize,
+                    color='k',ha='center',va='center')
+        self._plot_measured_wires()
+
+    def _plot_measured_wires(self):
+        ismeasured = self._measurements()
+        xstop = self._gate_grid[-1]
+        dy = 0.04 # amount to shift wires when doubled
+        # Plot doubled wires after they are measured
+        for im in ismeasured:
+            xdata = (self._gate_grid[ismeasured[im]],xstop+self.scale)
+            ydata = (self._wire_grid[im]+dy,self._wire_grid[im]+dy)
+            line = Line2D(
+                xdata, ydata,
+                color='k',
+                lw=self.linewidth
+            )
+            self._axes.add_line(line)
+        # Also double any controlled lines off these wires
+        for i,g in enumerate(self._gates()):
+            if isinstance(g, (CGate, CGateS)):
+                wires = g.controls + g.targets
+                for wire in wires:
+                    if wire in ismeasured and \
+                           self._gate_grid[i] > self._gate_grid[ismeasured[wire]]:
+                        ydata = min(wires), max(wires)
+                        xdata = self._gate_grid[i]-dy, self._gate_grid[i]-dy
+                        line = Line2D(
+                            xdata, ydata,
+                            color='k',
+                            lw=self.linewidth
+                            )
+                        self._axes.add_line(line)
+    def _gates(self):
+        """Create a list of all gates in the circuit plot."""
+        gates = []
+        if isinstance(self.circuit, Mul):
+            for g in reversed(self.circuit.args):
+                if isinstance(g, Gate):
+                    gates.append(g)
+        elif isinstance(self.circuit, Gate):
+            gates.append(self.circuit)
+        return gates
+
+    def _plot_gates(self):
+        """Iterate through the gates and plot each of them."""
+        for i, gate in enumerate(self._gates()):
+            gate.plot_gate(self, i)
+
+    def _measurements(self):
+        """Return a dict ``{i:j}`` where i is the index of the wire that has
+        been measured, and j is the gate where the wire is measured.
+        """
+        ismeasured = {}
+        for i,g in enumerate(self._gates()):
+            if getattr(g,'measurement',False):
+                for target in g.targets:
+                    if target in ismeasured:
+                        if ismeasured[target] > i:
+                            ismeasured[target] = i
+                    else:
+                        ismeasured[target] = i
+        return ismeasured
+
+    def _finish(self):
+        # Disable clipping to make panning work well for large circuits.
+        for o in self._figure.findobj():
+            o.set_clip_on(False)
+
+    def one_qubit_box(self, t, gate_idx, wire_idx):
+        """Draw a box for a single qubit gate."""
+        x = self._gate_grid[gate_idx]
+        y = self._wire_grid[wire_idx]
+        self._axes.text(
+            x, y, t,
+            color='k',
+            ha='center',
+            va='center',
+            bbox={"ec": 'k', "fc": 'w', "fill": True, "lw": self.linewidth},
+            size=self.fontsize
+        )
+
+    def two_qubit_box(self, t, gate_idx, wire_idx):
+        """Draw a box for a two qubit gate. Does not work yet.
+        """
+        # x = self._gate_grid[gate_idx]
+        # y = self._wire_grid[wire_idx]+0.5
+        print(self._gate_grid)
+        print(self._wire_grid)
+        # unused:
+        # obj = self._axes.text(
+        #     x, y, t,
+        #     color='k',
+        #     ha='center',
+        #     va='center',
+        #     bbox=dict(ec='k', fc='w', fill=True, lw=self.linewidth),
+        #     size=self.fontsize
+        # )
+
+    def control_line(self, gate_idx, min_wire, max_wire):
+        """Draw a vertical control line."""
+        xdata = (self._gate_grid[gate_idx], self._gate_grid[gate_idx])
+        ydata = (self._wire_grid[min_wire], self._wire_grid[max_wire])
+        line = Line2D(
+            xdata, ydata,
+            color='k',
+            lw=self.linewidth
+        )
+        self._axes.add_line(line)
+
+    def control_point(self, gate_idx, wire_idx):
+        """Draw a control point."""
+        x = self._gate_grid[gate_idx]
+        y = self._wire_grid[wire_idx]
+        radius = self.control_radius
+        c = Circle(
+            (x, y),
+            radius*self.scale,
+            ec='k',
+            fc='k',
+            fill=True,
+            lw=self.linewidth
+        )
+        self._axes.add_patch(c)
+
+    def not_point(self, gate_idx, wire_idx):
+        """Draw a NOT gates as the circle with plus in the middle."""
+        x = self._gate_grid[gate_idx]
+        y = self._wire_grid[wire_idx]
+        radius = self.not_radius
+        c = Circle(
+            (x, y),
+            radius,
+            ec='k',
+            fc='w',
+            fill=False,
+            lw=self.linewidth
+        )
+        self._axes.add_patch(c)
+        l = Line2D(
+            (x, x), (y - radius, y + radius),
+            color='k',
+            lw=self.linewidth
+        )
+        self._axes.add_line(l)
+
+    def swap_point(self, gate_idx, wire_idx):
+        """Draw a swap point as a cross."""
+        x = self._gate_grid[gate_idx]
+        y = self._wire_grid[wire_idx]
+        d = self.swap_delta
+        l1 = Line2D(
+            (x - d, x + d),
+            (y - d, y + d),
+            color='k',
+            lw=self.linewidth
+        )
+        l2 = Line2D(
+            (x - d, x + d),
+            (y + d, y - d),
+            color='k',
+            lw=self.linewidth
+        )
+        self._axes.add_line(l1)
+        self._axes.add_line(l2)
+
+def circuit_plot(c, nqubits, **kwargs):
+    """Draw the circuit diagram for the circuit with nqubits.
+
+    Parameters
+    ==========
+
+    c : circuit
+        The circuit to plot. Should be a product of Gate instances.
+    nqubits : int
+        The number of qubits to include in the circuit. Must be at least
+        as big as the largest ``min_qubits`` of the gates.
+    """
+    return CircuitPlot(c, nqubits, **kwargs)
+
+def render_label(label, inits={}):
+    """Slightly more flexible way to render labels.
+
+    >>> from sympy.physics.quantum.circuitplot import render_label
+    >>> render_label('q0')
+    '$\\\\left|q0\\\\right\\\\rangle$'
+    >>> render_label('q0', {'q0':'0'})
+    '$\\\\left|q0\\\\right\\\\rangle=\\\\left|0\\\\right\\\\rangle$'
+    """
+    init = inits.get(label)
+    if init:
+        return r'$\left|%s\right\rangle=\left|%s\right\rangle$' % (label, init)
+    return r'$\left|%s\right\rangle$' % label
+
+def labeller(n, symbol='q'):
+    """Autogenerate labels for wires of quantum circuits.
+
+    Parameters
+    ==========
+
+    n : int
+        number of qubits in the circuit.
+    symbol : string
+        A character string to precede all gate labels. E.g. 'q_0', 'q_1', etc.
+
+    >>> from sympy.physics.quantum.circuitplot import labeller
+    >>> labeller(2)
+    ['q_1', 'q_0']
+    >>> labeller(3,'j')
+    ['j_2', 'j_1', 'j_0']
+    """
+    return ['%s_%d' % (symbol,n-i-1) for i in range(n)]
+
+class Mz(OneQubitGate):
+    """Mock-up of a z measurement gate.
+
+    This is in circuitplot rather than gate.py because it's not a real
+    gate, it just draws one.
+    """
+    measurement = True
+    gate_name='Mz'
+    gate_name_latex='M_z'
+
+class Mx(OneQubitGate):
+    """Mock-up of an x measurement gate.
+
+    This is in circuitplot rather than gate.py because it's not a real
+    gate, it just draws one.
+    """
+    measurement = True
+    gate_name='Mx'
+    gate_name_latex='M_x'
+
+class CreateOneQubitGate(type):
+    def __new__(mcl, name, latexname=None):
+        if not latexname:
+            latexname = name
+        return type(name + "Gate", (OneQubitGate,),
+            {'gate_name': name, 'gate_name_latex': latexname})
+
+def CreateCGate(name, latexname=None):
+    """Use a lexical closure to make a controlled gate.
+    """
+    if not latexname:
+        latexname = name
+    onequbitgate = CreateOneQubitGate(name, latexname)
+    def ControlledGate(ctrls,target):
+        return CGate(tuple(ctrls),onequbitgate(target))
+    return ControlledGate
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/circuitutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/circuitutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..84955d3d724a2658f2dc3b26738133bd46f1aa57
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/circuitutils.py
@@ -0,0 +1,488 @@
+"""Primitive circuit operations on quantum circuits."""
+
+from functools import reduce
+
+from sympy.core.sorting import default_sort_key
+from sympy.core.containers import Tuple
+from sympy.core.mul import Mul
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.utilities import numbered_symbols
+from sympy.physics.quantum.gate import Gate
+
+__all__ = [
+    'kmp_table',
+    'find_subcircuit',
+    'replace_subcircuit',
+    'convert_to_symbolic_indices',
+    'convert_to_real_indices',
+    'random_reduce',
+    'random_insert'
+]
+
+
+def kmp_table(word):
+    """Build the 'partial match' table of the Knuth-Morris-Pratt algorithm.
+
+    Note: This is applicable to strings or
+    quantum circuits represented as tuples.
+    """
+
+    # Current position in subcircuit
+    pos = 2
+    # Beginning position of candidate substring that
+    # may reappear later in word
+    cnd = 0
+    # The 'partial match' table that helps one determine
+    # the next location to start substring search
+    table = []
+    table.append(-1)
+    table.append(0)
+
+    while pos < len(word):
+        if word[pos - 1] == word[cnd]:
+            cnd = cnd + 1
+            table.append(cnd)
+            pos = pos + 1
+        elif cnd > 0:
+            cnd = table[cnd]
+        else:
+            table.append(0)
+            pos = pos + 1
+
+    return table
+
+
+def find_subcircuit(circuit, subcircuit, start=0, end=0):
+    """Finds the subcircuit in circuit, if it exists.
+
+    Explanation
+    ===========
+
+    If the subcircuit exists, the index of the start of
+    the subcircuit in circuit is returned; otherwise,
+    -1 is returned.  The algorithm that is implemented
+    is the Knuth-Morris-Pratt algorithm.
+
+    Parameters
+    ==========
+
+    circuit : tuple, Gate or Mul
+        A tuple of Gates or Mul representing a quantum circuit
+    subcircuit : tuple, Gate or Mul
+        A tuple of Gates or Mul to find in circuit
+    start : int
+        The location to start looking for subcircuit.
+        If start is the same or past end, -1 is returned.
+    end : int
+        The last place to look for a subcircuit.  If end
+        is less than 1 (one), then the length of circuit
+        is taken to be end.
+
+    Examples
+    ========
+
+    Find the first instance of a subcircuit:
+
+    >>> from sympy.physics.quantum.circuitutils import find_subcircuit
+    >>> from sympy.physics.quantum.gate import X, Y, Z, H
+    >>> circuit = X(0)*Z(0)*Y(0)*H(0)
+    >>> subcircuit = Z(0)*Y(0)
+    >>> find_subcircuit(circuit, subcircuit)
+    1
+
+    Find the first instance starting at a specific position:
+
+    >>> find_subcircuit(circuit, subcircuit, start=1)
+    1
+
+    >>> find_subcircuit(circuit, subcircuit, start=2)
+    -1
+
+    >>> circuit = circuit*subcircuit
+    >>> find_subcircuit(circuit, subcircuit, start=2)
+    4
+
+    Find the subcircuit within some interval:
+
+    >>> find_subcircuit(circuit, subcircuit, start=2, end=2)
+    -1
+    """
+
+    if isinstance(circuit, Mul):
+        circuit = circuit.args
+
+    if isinstance(subcircuit, Mul):
+        subcircuit = subcircuit.args
+
+    if len(subcircuit) == 0 or len(subcircuit) > len(circuit):
+        return -1
+
+    if end < 1:
+        end = len(circuit)
+
+    # Location in circuit
+    pos = start
+    # Location in the subcircuit
+    index = 0
+    # 'Partial match' table
+    table = kmp_table(subcircuit)
+
+    while (pos + index) < end:
+        if subcircuit[index] == circuit[pos + index]:
+            index = index + 1
+        else:
+            pos = pos + index - table[index]
+            index = table[index] if table[index] > -1 else 0
+
+        if index == len(subcircuit):
+            return pos
+
+    return -1
+
+
+def replace_subcircuit(circuit, subcircuit, replace=None, pos=0):
+    """Replaces a subcircuit with another subcircuit in circuit,
+    if it exists.
+
+    Explanation
+    ===========
+
+    If multiple instances of subcircuit exists, the first instance is
+    replaced.  The position to being searching from (if different from
+    0) may be optionally given.  If subcircuit cannot be found, circuit
+    is returned.
+
+    Parameters
+    ==========
+
+    circuit : tuple, Gate or Mul
+        A quantum circuit.
+    subcircuit : tuple, Gate or Mul
+        The circuit to be replaced.
+    replace : tuple, Gate or Mul
+        The replacement circuit.
+    pos : int
+        The location to start search and replace
+        subcircuit, if it exists.  This may be used
+        if it is known beforehand that multiple
+        instances exist, and it is desirable to
+        replace a specific instance.  If a negative number
+        is given, pos will be defaulted to 0.
+
+    Examples
+    ========
+
+    Find and remove the subcircuit:
+
+    >>> from sympy.physics.quantum.circuitutils import replace_subcircuit
+    >>> from sympy.physics.quantum.gate import X, Y, Z, H
+    >>> circuit = X(0)*Z(0)*Y(0)*H(0)*X(0)*H(0)*Y(0)
+    >>> subcircuit = Z(0)*Y(0)
+    >>> replace_subcircuit(circuit, subcircuit)
+    (X(0), H(0), X(0), H(0), Y(0))
+
+    Remove the subcircuit given a starting search point:
+
+    >>> replace_subcircuit(circuit, subcircuit, pos=1)
+    (X(0), H(0), X(0), H(0), Y(0))
+
+    >>> replace_subcircuit(circuit, subcircuit, pos=2)
+    (X(0), Z(0), Y(0), H(0), X(0), H(0), Y(0))
+
+    Replace the subcircuit:
+
+    >>> replacement = H(0)*Z(0)
+    >>> replace_subcircuit(circuit, subcircuit, replace=replacement)
+    (X(0), H(0), Z(0), H(0), X(0), H(0), Y(0))
+    """
+
+    if pos < 0:
+        pos = 0
+
+    if isinstance(circuit, Mul):
+        circuit = circuit.args
+
+    if isinstance(subcircuit, Mul):
+        subcircuit = subcircuit.args
+
+    if isinstance(replace, Mul):
+        replace = replace.args
+    elif replace is None:
+        replace = ()
+
+    # Look for the subcircuit starting at pos
+    loc = find_subcircuit(circuit, subcircuit, start=pos)
+
+    # If subcircuit was found
+    if loc > -1:
+        # Get the gates to the left of subcircuit
+        left = circuit[0:loc]
+        # Get the gates to the right of subcircuit
+        right = circuit[loc + len(subcircuit):len(circuit)]
+        # Recombine the left and right side gates into a circuit
+        circuit = left + replace + right
+
+    return circuit
+
+
+def _sympify_qubit_map(mapping):
+    new_map = {}
+    for key in mapping:
+        new_map[key] = sympify(mapping[key])
+    return new_map
+
+
+def convert_to_symbolic_indices(seq, start=None, gen=None, qubit_map=None):
+    """Returns the circuit with symbolic indices and the
+    dictionary mapping symbolic indices to real indices.
+
+    The mapping is 1 to 1 and onto (bijective).
+
+    Parameters
+    ==========
+
+    seq : tuple, Gate/Integer/tuple or Mul
+        A tuple of Gate, Integer, or tuple objects, or a Mul
+    start : Symbol
+        An optional starting symbolic index
+    gen : object
+        An optional numbered symbol generator
+    qubit_map : dict
+        An existing mapping of symbolic indices to real indices
+
+    All symbolic indices have the format 'i#', where # is
+    some number >= 0.
+    """
+
+    if isinstance(seq, Mul):
+        seq = seq.args
+
+    # A numbered symbol generator
+    index_gen = numbered_symbols(prefix='i', start=-1)
+    cur_ndx = next(index_gen)
+
+    # keys are symbolic indices; values are real indices
+    ndx_map = {}
+
+    def create_inverse_map(symb_to_real_map):
+        rev_items = lambda item: (item[1], item[0])
+        return dict(map(rev_items, symb_to_real_map.items()))
+
+    if start is not None:
+        if not isinstance(start, Symbol):
+            msg = 'Expected Symbol for starting index, got %r.' % start
+            raise TypeError(msg)
+        cur_ndx = start
+
+    if gen is not None:
+        if not isinstance(gen, numbered_symbols().__class__):
+            msg = 'Expected a generator, got %r.' % gen
+            raise TypeError(msg)
+        index_gen = gen
+
+    if qubit_map is not None:
+        if not isinstance(qubit_map, dict):
+            msg = ('Expected dict for existing map, got ' +
+                   '%r.' % qubit_map)
+            raise TypeError(msg)
+        ndx_map = qubit_map
+
+    ndx_map = _sympify_qubit_map(ndx_map)
+    # keys are real indices; keys are symbolic indices
+    inv_map = create_inverse_map(ndx_map)
+
+    sym_seq = ()
+    for item in seq:
+        # Nested items, so recurse
+        if isinstance(item, Gate):
+            result = convert_to_symbolic_indices(item.args,
+                                                 qubit_map=ndx_map,
+                                                 start=cur_ndx,
+                                                 gen=index_gen)
+            sym_item, new_map, cur_ndx, index_gen = result
+            ndx_map.update(new_map)
+            inv_map = create_inverse_map(ndx_map)
+
+        elif isinstance(item, (tuple, Tuple)):
+            result = convert_to_symbolic_indices(item,
+                                                 qubit_map=ndx_map,
+                                                 start=cur_ndx,
+                                                 gen=index_gen)
+            sym_item, new_map, cur_ndx, index_gen = result
+            ndx_map.update(new_map)
+            inv_map = create_inverse_map(ndx_map)
+
+        elif item in inv_map:
+            sym_item = inv_map[item]
+
+        else:
+            cur_ndx = next(gen)
+            ndx_map[cur_ndx] = item
+            inv_map[item] = cur_ndx
+            sym_item = cur_ndx
+
+        if isinstance(item, Gate):
+            sym_item = item.__class__(*sym_item)
+
+        sym_seq = sym_seq + (sym_item,)
+
+    return sym_seq, ndx_map, cur_ndx, index_gen
+
+
+def convert_to_real_indices(seq, qubit_map):
+    """Returns the circuit with real indices.
+
+    Parameters
+    ==========
+
+    seq : tuple, Gate/Integer/tuple or Mul
+        A tuple of Gate, Integer, or tuple objects or a Mul
+    qubit_map : dict
+        A dictionary mapping symbolic indices to real indices.
+
+    Examples
+    ========
+
+    Change the symbolic indices to real integers:
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.quantum.circuitutils import convert_to_real_indices
+    >>> from sympy.physics.quantum.gate import X, Y, H
+    >>> i0, i1 = symbols('i:2')
+    >>> index_map = {i0 : 0, i1 : 1}
+    >>> convert_to_real_indices(X(i0)*Y(i1)*H(i0)*X(i1), index_map)
+    (X(0), Y(1), H(0), X(1))
+    """
+
+    if isinstance(seq, Mul):
+        seq = seq.args
+
+    if not isinstance(qubit_map, dict):
+        msg = 'Expected dict for qubit_map, got %r.' % qubit_map
+        raise TypeError(msg)
+
+    qubit_map = _sympify_qubit_map(qubit_map)
+    real_seq = ()
+    for item in seq:
+        # Nested items, so recurse
+        if isinstance(item, Gate):
+            real_item = convert_to_real_indices(item.args, qubit_map)
+
+        elif isinstance(item, (tuple, Tuple)):
+            real_item = convert_to_real_indices(item, qubit_map)
+
+        else:
+            real_item = qubit_map[item]
+
+        if isinstance(item, Gate):
+            real_item = item.__class__(*real_item)
+
+        real_seq = real_seq + (real_item,)
+
+    return real_seq
+
+
+def random_reduce(circuit, gate_ids, seed=None):
+    """Shorten the length of a quantum circuit.
+
+    Explanation
+    ===========
+
+    random_reduce looks for circuit identities in circuit, randomly chooses
+    one to remove, and returns a shorter yet equivalent circuit.  If no
+    identities are found, the same circuit is returned.
+
+    Parameters
+    ==========
+
+    circuit : Gate tuple of Mul
+        A tuple of Gates representing a quantum circuit
+    gate_ids : list, GateIdentity
+        List of gate identities to find in circuit
+    seed : int or list
+        seed used for _randrange; to override the random selection, provide a
+        list of integers: the elements of gate_ids will be tested in the order
+        given by the list
+
+    """
+    from sympy.core.random import _randrange
+
+    if not gate_ids:
+        return circuit
+
+    if isinstance(circuit, Mul):
+        circuit = circuit.args
+
+    ids = flatten_ids(gate_ids)
+
+    # Create the random integer generator with the seed
+    randrange = _randrange(seed)
+
+    # Look for an identity in the circuit
+    while ids:
+        i = randrange(len(ids))
+        id = ids.pop(i)
+        if find_subcircuit(circuit, id) != -1:
+            break
+    else:
+        # no identity was found
+        return circuit
+
+    # return circuit with the identity removed
+    return replace_subcircuit(circuit, id)
+
+
+def random_insert(circuit, choices, seed=None):
+    """Insert a circuit into another quantum circuit.
+
+    Explanation
+    ===========
+
+    random_insert randomly chooses a location in the circuit to insert
+    a randomly selected circuit from amongst the given choices.
+
+    Parameters
+    ==========
+
+    circuit : Gate tuple or Mul
+        A tuple or Mul of Gates representing a quantum circuit
+    choices : list
+        Set of circuit choices
+    seed : int or list
+        seed used for _randrange; to override the random selections, give
+        a list two integers, [i, j] where i is the circuit location where
+        choice[j] will be inserted.
+
+    Notes
+    =====
+
+    Indices for insertion should be [0, n] if n is the length of the
+    circuit.
+    """
+    from sympy.core.random import _randrange
+
+    if not choices:
+        return circuit
+
+    if isinstance(circuit, Mul):
+        circuit = circuit.args
+
+    # get the location in the circuit and the element to insert from choices
+    randrange = _randrange(seed)
+    loc = randrange(len(circuit) + 1)
+    choice = choices[randrange(len(choices))]
+
+    circuit = list(circuit)
+    circuit[loc: loc] = choice
+    return tuple(circuit)
+
+# Flatten the GateIdentity objects (with gate rules) into one single list
+
+
+def flatten_ids(ids):
+    collapse = lambda acc, an_id: acc + sorted(an_id.equivalent_ids,
+                                        key=default_sort_key)
+    ids = reduce(collapse, ids, [])
+    ids.sort(key=default_sort_key)
+    return ids
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/commutator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/commutator.py
new file mode 100644
index 0000000000000000000000000000000000000000..a2d97a679e27387077429a9973de21ad868e84ac
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/commutator.py
@@ -0,0 +1,256 @@
+"""The commutator: [A,B] = A*B - B*A."""
+
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.kind import KindDispatcher
+from sympy.core.mul import Mul
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.printing.pretty.stringpict import prettyForm
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.kind import _OperatorKind, OperatorKind
+
+
+__all__ = [
+    'Commutator'
+]
+
+#-----------------------------------------------------------------------------
+# Commutator
+#-----------------------------------------------------------------------------
+
+
+class Commutator(Expr):
+    """The standard commutator, in an unevaluated state.
+
+    Explanation
+    ===========
+
+    Evaluating a commutator is defined [1]_ as: ``[A, B] = A*B - B*A``. This
+    class returns the commutator in an unevaluated form. To evaluate the
+    commutator, use the ``.doit()`` method.
+
+    Canonical ordering of a commutator is ``[A, B]`` for ``A < B``. The
+    arguments of the commutator are put into canonical order using ``__cmp__``.
+    If ``B < A``, then ``[B, A]`` is returned as ``-[A, B]``.
+
+    Parameters
+    ==========
+
+    A : Expr
+        The first argument of the commutator [A,B].
+    B : Expr
+        The second argument of the commutator [A,B].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Commutator, Dagger, Operator
+    >>> from sympy.abc import x, y
+    >>> A = Operator('A')
+    >>> B = Operator('B')
+    >>> C = Operator('C')
+
+    Create a commutator and use ``.doit()`` to evaluate it:
+
+    >>> comm = Commutator(A, B)
+    >>> comm
+    [A,B]
+    >>> comm.doit()
+    A*B - B*A
+
+    The commutator orders it arguments in canonical order:
+
+    >>> comm = Commutator(B, A); comm
+    -[A,B]
+
+    Commutative constants are factored out:
+
+    >>> Commutator(3*x*A, x*y*B)
+    3*x**2*y*[A,B]
+
+    Using ``.expand(commutator=True)``, the standard commutator expansion rules
+    can be applied:
+
+    >>> Commutator(A+B, C).expand(commutator=True)
+    [A,C] + [B,C]
+    >>> Commutator(A, B+C).expand(commutator=True)
+    [A,B] + [A,C]
+    >>> Commutator(A*B, C).expand(commutator=True)
+    [A,C]*B + A*[B,C]
+    >>> Commutator(A, B*C).expand(commutator=True)
+    [A,B]*C + B*[A,C]
+
+    Adjoint operations applied to the commutator are properly applied to the
+    arguments:
+
+    >>> Dagger(Commutator(A, B))
+    -[Dagger(A),Dagger(B)]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Commutator
+    """
+    is_commutative = False
+
+    _kind_dispatcher = KindDispatcher("Commutator_kind_dispatcher", commutative=True)
+
+    @property
+    def kind(self):
+        arg_kinds = (a.kind for a in self.args)
+        return self._kind_dispatcher(*arg_kinds)
+
+    def __new__(cls, A, B):
+        r = cls.eval(A, B)
+        if r is not None:
+            return r
+        obj = Expr.__new__(cls, A, B)
+        return obj
+
+    @classmethod
+    def eval(cls, a, b):
+        if not (a and b):
+            return S.Zero
+        if a == b:
+            return S.Zero
+        if a.is_commutative or b.is_commutative:
+            return S.Zero
+
+        # [xA,yB]  ->  xy*[A,B]
+        ca, nca = a.args_cnc()
+        cb, ncb = b.args_cnc()
+        c_part = ca + cb
+        if c_part:
+            return Mul(Mul(*c_part), cls(Mul._from_args(nca), Mul._from_args(ncb)))
+
+        # Canonical ordering of arguments
+        # The Commutator [A, B] is in canonical form if A < B.
+        if a.compare(b) == 1:
+            return S.NegativeOne*cls(b, a)
+
+    def _expand_pow(self, A, B, sign):
+        exp = A.exp
+        if not exp.is_integer or not exp.is_constant() or abs(exp) <= 1:
+            # nothing to do
+            return self
+        base = A.base
+        if exp.is_negative:
+            base = A.base**-1
+            exp = -exp
+        comm = Commutator(base, B).expand(commutator=True)
+
+        result = base**(exp - 1) * comm
+        for i in range(1, exp):
+            result += base**(exp - 1 - i) * comm * base**i
+        return sign*result.expand()
+
+    def _eval_expand_commutator(self, **hints):
+        A = self.args[0]
+        B = self.args[1]
+
+        if isinstance(A, Add):
+            # [A + B, C]  ->  [A, C] + [B, C]
+            sargs = []
+            for term in A.args:
+                comm = Commutator(term, B)
+                if isinstance(comm, Commutator):
+                    comm = comm._eval_expand_commutator()
+                sargs.append(comm)
+            return Add(*sargs)
+        elif isinstance(B, Add):
+            # [A, B + C]  ->  [A, B] + [A, C]
+            sargs = []
+            for term in B.args:
+                comm = Commutator(A, term)
+                if isinstance(comm, Commutator):
+                    comm = comm._eval_expand_commutator()
+                sargs.append(comm)
+            return Add(*sargs)
+        elif isinstance(A, Mul):
+            # [A*B, C] -> A*[B, C] + [A, C]*B
+            a = A.args[0]
+            b = Mul(*A.args[1:])
+            c = B
+            comm1 = Commutator(b, c)
+            comm2 = Commutator(a, c)
+            if isinstance(comm1, Commutator):
+                comm1 = comm1._eval_expand_commutator()
+            if isinstance(comm2, Commutator):
+                comm2 = comm2._eval_expand_commutator()
+            first = Mul(a, comm1)
+            second = Mul(comm2, b)
+            return Add(first, second)
+        elif isinstance(B, Mul):
+            # [A, B*C] -> [A, B]*C + B*[A, C]
+            a = A
+            b = B.args[0]
+            c = Mul(*B.args[1:])
+            comm1 = Commutator(a, b)
+            comm2 = Commutator(a, c)
+            if isinstance(comm1, Commutator):
+                comm1 = comm1._eval_expand_commutator()
+            if isinstance(comm2, Commutator):
+                comm2 = comm2._eval_expand_commutator()
+            first = Mul(comm1, c)
+            second = Mul(b, comm2)
+            return Add(first, second)
+        elif isinstance(A, Pow):
+            # [A**n, C] -> A**(n - 1)*[A, C] + A**(n - 2)*[A, C]*A + ... + [A, C]*A**(n-1)
+            return self._expand_pow(A, B, 1)
+        elif isinstance(B, Pow):
+            # [A, C**n] -> C**(n - 1)*[C, A] + C**(n - 2)*[C, A]*C + ... + [C, A]*C**(n-1)
+            return self._expand_pow(B, A, -1)
+
+        # No changes, so return self
+        return self
+
+    def doit(self, **hints):
+        """ Evaluate commutator """
+        # Keep the import of Operator here to avoid problems with
+        # circular imports.
+        from sympy.physics.quantum.operator import Operator
+        A = self.args[0]
+        B = self.args[1]
+        if isinstance(A, Operator) and isinstance(B, Operator):
+            try:
+                comm = A._eval_commutator(B, **hints)
+            except NotImplementedError:
+                try:
+                    comm = -1*B._eval_commutator(A, **hints)
+                except NotImplementedError:
+                    comm = None
+            if comm is not None:
+                return comm.doit(**hints)
+        return (A*B - B*A).doit(**hints)
+
+    def _eval_adjoint(self):
+        return Commutator(Dagger(self.args[1]), Dagger(self.args[0]))
+
+    def _sympyrepr(self, printer, *args):
+        return "%s(%s,%s)" % (
+            self.__class__.__name__, printer._print(
+                self.args[0]), printer._print(self.args[1])
+        )
+
+    def _sympystr(self, printer, *args):
+        return "[%s,%s]" % (
+            printer._print(self.args[0]), printer._print(self.args[1]))
+
+    def _pretty(self, printer, *args):
+        pform = printer._print(self.args[0], *args)
+        pform = prettyForm(*pform.right(prettyForm(',')))
+        pform = prettyForm(*pform.right(printer._print(self.args[1], *args)))
+        pform = prettyForm(*pform.parens(left='[', right=']'))
+        return pform
+
+    def _latex(self, printer, *args):
+        return "\\left[%s,%s\\right]" % tuple([
+            printer._print(arg, *args) for arg in self.args])
+
+
+@Commutator._kind_dispatcher.register(_OperatorKind, _OperatorKind)
+def find_op_kind(e1, e2):
+    """Find the kind of an anticommutator of two OperatorKinds."""
+    return OperatorKind
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/constants.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/constants.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e848bf24e95e3bd612169128a1845202066c6e9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/constants.py
@@ -0,0 +1,59 @@
+"""Constants (like hbar) related to quantum mechanics."""
+
+from sympy.core.numbers import NumberSymbol
+from sympy.core.singleton import Singleton
+from sympy.printing.pretty.stringpict import prettyForm
+import mpmath.libmp as mlib
+
+#-----------------------------------------------------------------------------
+# Constants
+#-----------------------------------------------------------------------------
+
+__all__ = [
+    'hbar',
+    'HBar',
+]
+
+
+class HBar(NumberSymbol, metaclass=Singleton):
+    """Reduced Plank's constant in numerical and symbolic form [1]_.
+
+    Examples
+    ========
+
+        >>> from sympy.physics.quantum.constants import hbar
+        >>> hbar.evalf()
+        1.05457162000000e-34
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Planck_constant
+    """
+
+    is_real = True
+    is_positive = True
+    is_negative = False
+    is_irrational = True
+
+    __slots__ = ()
+
+    def _as_mpf_val(self, prec):
+        return mlib.from_float(1.05457162e-34, prec)
+
+    def _sympyrepr(self, printer, *args):
+        return 'HBar()'
+
+    def _sympystr(self, printer, *args):
+        return 'hbar'
+
+    def _pretty(self, printer, *args):
+        if printer._use_unicode:
+            return prettyForm('\N{PLANCK CONSTANT OVER TWO PI}')
+        return prettyForm('hbar')
+
+    def _latex(self, printer, *args):
+        return r'\hbar'
+
+# Create an instance for everyone to use.
+hbar = HBar()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/dagger.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/dagger.py
new file mode 100644
index 0000000000000000000000000000000000000000..f96f01e3b9ac86ae30b03e3b97293bbafceaed8a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/dagger.py
@@ -0,0 +1,95 @@
+"""Hermitian conjugation."""
+
+from sympy.core import Expr, sympify
+from sympy.functions.elementary.complexes import adjoint
+
+__all__ = [
+    'Dagger'
+]
+
+
+class Dagger(adjoint):
+    """General Hermitian conjugate operation.
+
+    Explanation
+    ===========
+
+    Take the Hermetian conjugate of an argument [1]_. For matrices this
+    operation is equivalent to transpose and complex conjugate [2]_.
+
+    Parameters
+    ==========
+
+    arg : Expr
+        The SymPy expression that we want to take the dagger of.
+    evaluate : bool
+        Whether the resulting expression should be directly evaluated.
+
+    Examples
+    ========
+
+    Daggering various quantum objects:
+
+        >>> from sympy.physics.quantum.dagger import Dagger
+        >>> from sympy.physics.quantum.state import Ket, Bra
+        >>> from sympy.physics.quantum.operator import Operator
+        >>> Dagger(Ket('psi'))
+        >> Dagger(Bra('phi'))
+        |phi>
+        >>> Dagger(Operator('A'))
+        Dagger(A)
+
+    Inner and outer products::
+
+        >>> from sympy.physics.quantum import InnerProduct, OuterProduct
+        >>> Dagger(InnerProduct(Bra('a'), Ket('b')))
+        
+        >>> Dagger(OuterProduct(Ket('a'), Bra('b')))
+        |b>>> A = Operator('A')
+        >>> B = Operator('B')
+        >>> Dagger(A*B)
+        Dagger(B)*Dagger(A)
+        >>> Dagger(A+B)
+        Dagger(A) + Dagger(B)
+        >>> Dagger(A**2)
+        Dagger(A)**2
+
+    Dagger also seamlessly handles complex numbers and matrices::
+
+        >>> from sympy import Matrix, I
+        >>> m = Matrix([[1,I],[2,I]])
+        >>> m
+        Matrix([
+        [1, I],
+        [2, I]])
+        >>> Dagger(m)
+        Matrix([
+        [ 1,  2],
+        [-I, -I]])
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hermitian_adjoint
+    .. [2] https://en.wikipedia.org/wiki/Hermitian_transpose
+    """
+
+    @property
+    def kind(self):
+        """Find the kind of a dagger of something (just the kind of the something)."""
+        return self.args[0].kind
+
+    def __new__(cls, arg, evaluate=True):
+        if hasattr(arg, 'adjoint') and evaluate:
+            return arg.adjoint()
+        elif hasattr(arg, 'conjugate') and hasattr(arg, 'transpose') and evaluate:
+            return arg.conjugate().transpose()
+        return Expr.__new__(cls, sympify(arg))
+
+adjoint.__name__ = "Dagger"
+adjoint._sympyrepr = lambda a, b: "Dagger(%s)" % b._print(a.args[0])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/density.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/density.py
new file mode 100644
index 0000000000000000000000000000000000000000..941373e8105dd0c725626396dfd9cd794b19d3f5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/density.py
@@ -0,0 +1,315 @@
+from itertools import product
+
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.function import expand
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import log
+from sympy.matrices.dense import MutableDenseMatrix as Matrix
+from sympy.printing.pretty.stringpict import prettyForm
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.operator import HermitianOperator
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.matrixutils import numpy_ndarray, scipy_sparse_matrix, to_numpy
+from sympy.physics.quantum.trace import Tr
+
+
+class Density(HermitianOperator):
+    """Density operator for representing mixed states.
+
+    TODO: Density operator support for Qubits
+
+    Parameters
+    ==========
+
+    values : tuples/lists
+    Each tuple/list should be of form (state, prob) or [state,prob]
+
+    Examples
+    ========
+
+    Create a density operator with 2 states represented by Kets.
+
+    >>> from sympy.physics.quantum.state import Ket
+    >>> from sympy.physics.quantum.density import Density
+    >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+    >>> d
+    Density((|0>, 0.5),(|1>, 0.5))
+
+    """
+    @classmethod
+    def _eval_args(cls, args):
+        # call this to qsympify the args
+        args = super()._eval_args(args)
+
+        for arg in args:
+            # Check if arg is a tuple
+            if not (isinstance(arg, Tuple) and len(arg) == 2):
+                raise ValueError("Each argument should be of form [state,prob]"
+                                 " or ( state, prob )")
+
+        return args
+
+    def states(self):
+        """Return list of all states.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.state import Ket
+        >>> from sympy.physics.quantum.density import Density
+        >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+        >>> d.states()
+        (|0>, |1>)
+
+        """
+        return Tuple(*[arg[0] for arg in self.args])
+
+    def probs(self):
+        """Return list of all probabilities.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.state import Ket
+        >>> from sympy.physics.quantum.density import Density
+        >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+        >>> d.probs()
+        (0.5, 0.5)
+
+        """
+        return Tuple(*[arg[1] for arg in self.args])
+
+    def get_state(self, index):
+        """Return specific state by index.
+
+        Parameters
+        ==========
+
+        index : index of state to be returned
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.state import Ket
+        >>> from sympy.physics.quantum.density import Density
+        >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+        >>> d.states()[1]
+        |1>
+
+        """
+        state = self.args[index][0]
+        return state
+
+    def get_prob(self, index):
+        """Return probability of specific state by index.
+
+        Parameters
+        ===========
+
+        index : index of states whose probability is returned.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.state import Ket
+        >>> from sympy.physics.quantum.density import Density
+        >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+        >>> d.probs()[1]
+        0.500000000000000
+
+        """
+        prob = self.args[index][1]
+        return prob
+
+    def apply_op(self, op):
+        """op will operate on each individual state.
+
+        Parameters
+        ==========
+
+        op : Operator
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.state import Ket
+        >>> from sympy.physics.quantum.density import Density
+        >>> from sympy.physics.quantum.operator import Operator
+        >>> A = Operator('A')
+        >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+        >>> d.apply_op(A)
+        Density((A*|0>, 0.5),(A*|1>, 0.5))
+
+        """
+        new_args = [(op*state, prob) for (state, prob) in self.args]
+        return Density(*new_args)
+
+    def doit(self, **hints):
+        """Expand the density operator into an outer product format.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.state import Ket
+        >>> from sympy.physics.quantum.density import Density
+        >>> from sympy.physics.quantum.operator import Operator
+        >>> A = Operator('A')
+        >>> d = Density([Ket(0), 0.5], [Ket(1),0.5])
+        >>> d.doit()
+        0.5*|0><0| + 0.5*|1><1|
+
+        """
+
+        terms = []
+        for (state, prob) in self.args:
+            state = state.expand()  # needed to break up (a+b)*c
+            if (isinstance(state, Add)):
+                for arg in product(state.args, repeat=2):
+                    terms.append(prob*self._generate_outer_prod(arg[0],
+                                                                arg[1]))
+            else:
+                terms.append(prob*self._generate_outer_prod(state, state))
+
+        return Add(*terms)
+
+    def _generate_outer_prod(self, arg1, arg2):
+        c_part1, nc_part1 = arg1.args_cnc()
+        c_part2, nc_part2 = arg2.args_cnc()
+
+        if (len(nc_part1) == 0 or len(nc_part2) == 0):
+            raise ValueError('Atleast one-pair of'
+                             ' Non-commutative instance required'
+                             ' for outer product.')
+
+        # We were able to remove some tensor product simplifications that
+        # used to be here as those transformations are not automatically
+        # applied by transforms.py.
+        op = Mul(*nc_part1)*Dagger(Mul(*nc_part2))
+
+        return Mul(*c_part1)*Mul(*c_part2) * op
+
+    def _represent(self, **options):
+        return represent(self.doit(), **options)
+
+    def _print_operator_name_latex(self, printer, *args):
+        return r'\rho'
+
+    def _print_operator_name_pretty(self, printer, *args):
+        return prettyForm('\N{GREEK SMALL LETTER RHO}')
+
+    def _eval_trace(self, **kwargs):
+        indices = kwargs.get('indices', [])
+        return Tr(self.doit(), indices).doit()
+
+    def entropy(self):
+        """ Compute the entropy of a density matrix.
+
+        Refer to density.entropy() method  for examples.
+        """
+        return entropy(self)
+
+
+def entropy(density):
+    """Compute the entropy of a matrix/density object.
+
+    This computes -Tr(density*ln(density)) using the eigenvalue decomposition
+    of density, which is given as either a Density instance or a matrix
+    (numpy.ndarray, sympy.Matrix or scipy.sparse).
+
+    Parameters
+    ==========
+
+    density : density matrix of type Density, SymPy matrix,
+    scipy.sparse or numpy.ndarray
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.density import Density, entropy
+    >>> from sympy.physics.quantum.spin import JzKet
+    >>> from sympy import S
+    >>> up = JzKet(S(1)/2,S(1)/2)
+    >>> down = JzKet(S(1)/2,-S(1)/2)
+    >>> d = Density((up,S(1)/2),(down,S(1)/2))
+    >>> entropy(d)
+    log(2)/2
+
+    """
+    if isinstance(density, Density):
+        density = represent(density)  # represent in Matrix
+
+    if isinstance(density, scipy_sparse_matrix):
+        density = to_numpy(density)
+
+    if isinstance(density, Matrix):
+        eigvals = density.eigenvals().keys()
+        return expand(-sum(e*log(e) for e in eigvals))
+    elif isinstance(density, numpy_ndarray):
+        import numpy as np
+        eigvals = np.linalg.eigvals(density)
+        return -np.sum(eigvals*np.log(eigvals))
+    else:
+        raise ValueError(
+            "numpy.ndarray, scipy.sparse or SymPy matrix expected")
+
+
+def fidelity(state1, state2):
+    """ Computes the fidelity [1]_ between two quantum states
+
+    The arguments provided to this function should be a square matrix or a
+    Density object. If it is a square matrix, it is assumed to be diagonalizable.
+
+    Parameters
+    ==========
+
+    state1, state2 : a density matrix or Matrix
+
+
+    Examples
+    ========
+
+    >>> from sympy import S, sqrt
+    >>> from sympy.physics.quantum.dagger import Dagger
+    >>> from sympy.physics.quantum.spin import JzKet
+    >>> from sympy.physics.quantum.density import fidelity
+    >>> from sympy.physics.quantum.represent import represent
+    >>>
+    >>> up = JzKet(S(1)/2,S(1)/2)
+    >>> down = JzKet(S(1)/2,-S(1)/2)
+    >>> amp = 1/sqrt(2)
+    >>> updown = (amp*up) + (amp*down)
+    >>>
+    >>> # represent turns Kets into matrices
+    >>> up_dm = represent(up*Dagger(up))
+    >>> down_dm = represent(down*Dagger(down))
+    >>> updown_dm = represent(updown*Dagger(updown))
+    >>>
+    >>> fidelity(up_dm, up_dm)
+    1
+    >>> fidelity(up_dm, down_dm) #orthogonal states
+    0
+    >>> fidelity(up_dm, updown_dm).evalf().round(3)
+    0.707
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fidelity_of_quantum_states
+
+    """
+    state1 = represent(state1) if isinstance(state1, Density) else state1
+    state2 = represent(state2) if isinstance(state2, Density) else state2
+
+    if not isinstance(state1, Matrix) or not isinstance(state2, Matrix):
+        raise ValueError("state1 and state2 must be of type Density or Matrix "
+                         "received type=%s for state1 and type=%s for state2" %
+                         (type(state1), type(state2)))
+
+    if state1.shape != state2.shape and state1.is_square:
+        raise ValueError("The dimensions of both args should be equal and the "
+                         "matrix obtained should be a square matrix")
+
+    sqrt_state1 = state1**S.Half
+    return Tr((sqrt_state1*state2*sqrt_state1)**S.Half).doit()
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/fermion.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/fermion.py
new file mode 100644
index 0000000000000000000000000000000000000000..8080bd3b0904b837652fdae7be0bd526da2d508f
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/fermion.py
@@ -0,0 +1,191 @@
+"""Fermionic quantum operators."""
+
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+from sympy.physics.quantum import Operator
+from sympy.physics.quantum import HilbertSpace, Ket, Bra
+from sympy.functions.special.tensor_functions import KroneckerDelta
+
+
+__all__ = [
+    'FermionOp',
+    'FermionFockKet',
+    'FermionFockBra'
+]
+
+
+class FermionOp(Operator):
+    """A fermionic operator that satisfies {c, Dagger(c)} == 1.
+
+    Parameters
+    ==========
+
+    name : str
+        A string that labels the fermionic mode.
+
+    annihilation : bool
+        A bool that indicates if the fermionic operator is an annihilation
+        (True, default value) or creation operator (False)
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Dagger, AntiCommutator
+    >>> from sympy.physics.quantum.fermion import FermionOp
+    >>> c = FermionOp("c")
+    >>> AntiCommutator(c, Dagger(c)).doit()
+    1
+    """
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def is_annihilation(self):
+        return bool(self.args[1])
+
+    @classmethod
+    def default_args(self):
+        return ("c", True)
+
+    def __new__(cls, *args, **hints):
+        if not len(args) in [1, 2]:
+            raise ValueError('1 or 2 parameters expected, got %s' % args)
+
+        if len(args) == 1:
+            args = (args[0], S.One)
+
+        if len(args) == 2:
+            args = (args[0], Integer(args[1]))
+
+        return Operator.__new__(cls, *args)
+
+    def _eval_commutator_FermionOp(self, other, **hints):
+        if 'independent' in hints and hints['independent']:
+            # [c, d] = 0
+            return S.Zero
+
+        return None
+
+    def _eval_anticommutator_FermionOp(self, other, **hints):
+        if self.name == other.name:
+            # {a^\dagger, a} = 1
+            if not self.is_annihilation and other.is_annihilation:
+                return S.One
+
+        elif 'independent' in hints and hints['independent']:
+            # {c, d} = 2 * c * d, because [c, d] = 0 for independent operators
+            return 2 * self * other
+
+        return None
+
+    def _eval_anticommutator_BosonOp(self, other, **hints):
+        # because fermions and bosons commute
+        return 2 * self * other
+
+    def _eval_commutator_BosonOp(self, other, **hints):
+        return S.Zero
+
+    def _eval_adjoint(self):
+        return FermionOp(str(self.name), not self.is_annihilation)
+
+    def _print_contents_latex(self, printer, *args):
+        if self.is_annihilation:
+            return r'{%s}' % str(self.name)
+        else:
+            return r'{{%s}^\dagger}' % str(self.name)
+
+    def _print_contents(self, printer, *args):
+        if self.is_annihilation:
+            return r'%s' % str(self.name)
+        else:
+            return r'Dagger(%s)' % str(self.name)
+
+    def _print_contents_pretty(self, printer, *args):
+        from sympy.printing.pretty.stringpict import prettyForm
+        pform = printer._print(self.args[0], *args)
+        if self.is_annihilation:
+            return pform
+        else:
+            return pform**prettyForm('\N{DAGGER}')
+
+    def _eval_power(self, exp):
+        from sympy.core.singleton import S
+        if exp == 0:
+            return S.One
+        elif exp == 1:
+            return self
+        elif (exp > 1) == True and exp.is_integer == True:
+            return S.Zero
+        elif (exp < 0) == True or exp.is_integer == False:
+            raise ValueError("Fermionic operators can only be raised to a"
+                " positive integer power")
+        return Operator._eval_power(self, exp)
+
+class FermionFockKet(Ket):
+    """Fock state ket for a fermionic mode.
+
+    Parameters
+    ==========
+
+    n : Number
+        The Fock state number.
+
+    """
+
+    def __new__(cls, n):
+        if n not in (0, 1):
+            raise ValueError("n must be 0 or 1")
+        return Ket.__new__(cls, n)
+
+    @property
+    def n(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return FermionFockBra
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return HilbertSpace()
+
+    def _eval_innerproduct_FermionFockBra(self, bra, **hints):
+        return KroneckerDelta(self.n, bra.n)
+
+    def _apply_from_right_to_FermionOp(self, op, **options):
+        if op.is_annihilation:
+            if self.n == 1:
+                return FermionFockKet(0)
+            else:
+                return S.Zero
+        else:
+            if self.n == 0:
+                return FermionFockKet(1)
+            else:
+                return S.Zero
+
+
+class FermionFockBra(Bra):
+    """Fock state bra for a fermionic mode.
+
+    Parameters
+    ==========
+
+    n : Number
+        The Fock state number.
+
+    """
+
+    def __new__(cls, n):
+        if n not in (0, 1):
+            raise ValueError("n must be 0 or 1")
+        return Bra.__new__(cls, n)
+
+    @property
+    def n(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return FermionFockKet
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/gate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/gate.py
new file mode 100644
index 0000000000000000000000000000000000000000..f8bcf5cd3611173cd9ebd6308dbbc896f5257f20
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/gate.py
@@ -0,0 +1,1309 @@
+"""An implementation of gates that act on qubits.
+
+Gates are unitary operators that act on the space of qubits.
+
+Medium Term Todo:
+
+* Optimize Gate._apply_operators_Qubit to remove the creation of many
+  intermediate Qubit objects.
+* Add commutation relationships to all operators and use this in gate_sort.
+* Fix gate_sort and gate_simp.
+* Get multi-target UGates plotting properly.
+* Get UGate to work with either sympy/numpy matrices and output either
+  format. This should also use the matrix slots.
+"""
+
+from itertools import chain
+import random
+
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer)
+from sympy.core.power import Pow
+from sympy.core.numbers import Number
+from sympy.core.singleton import S as _S
+from sympy.core.sorting import default_sort_key
+from sympy.core.sympify import _sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.printing.pretty.stringpict import prettyForm, stringPict
+
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.qexpr import QuantumError
+from sympy.physics.quantum.hilbert import ComplexSpace
+from sympy.physics.quantum.operator import (UnitaryOperator, Operator,
+                                            HermitianOperator)
+from sympy.physics.quantum.matrixutils import matrix_tensor_product, matrix_eye
+from sympy.physics.quantum.matrixcache import matrix_cache
+
+from sympy.matrices.matrixbase import MatrixBase
+
+from sympy.utilities.iterables import is_sequence
+
+__all__ = [
+    'Gate',
+    'CGate',
+    'UGate',
+    'OneQubitGate',
+    'TwoQubitGate',
+    'IdentityGate',
+    'HadamardGate',
+    'XGate',
+    'YGate',
+    'ZGate',
+    'TGate',
+    'PhaseGate',
+    'SwapGate',
+    'CNotGate',
+    # Aliased gate names
+    'CNOT',
+    'SWAP',
+    'H',
+    'X',
+    'Y',
+    'Z',
+    'T',
+    'S',
+    'Phase',
+    'normalized',
+    'gate_sort',
+    'gate_simp',
+    'random_circuit',
+    'CPHASE',
+    'CGateS',
+]
+
+#-----------------------------------------------------------------------------
+# Gate Super-Classes
+#-----------------------------------------------------------------------------
+
+_normalized = True
+
+
+def _max(*args, **kwargs):
+    if "key" not in kwargs:
+        kwargs["key"] = default_sort_key
+    return max(*args, **kwargs)
+
+
+def _min(*args, **kwargs):
+    if "key" not in kwargs:
+        kwargs["key"] = default_sort_key
+    return min(*args, **kwargs)
+
+
+def normalized(normalize):
+    r"""Set flag controlling normalization of Hadamard gates by `1/\sqrt{2}`.
+
+    This is a global setting that can be used to simplify the look of various
+    expressions, by leaving off the leading `1/\sqrt{2}` of the Hadamard gate.
+
+    Parameters
+    ----------
+    normalize : bool
+        Should the Hadamard gate include the `1/\sqrt{2}` normalization factor?
+        When True, the Hadamard gate will have the `1/\sqrt{2}`. When False, the
+        Hadamard gate will not have this factor.
+    """
+    global _normalized
+    _normalized = normalize
+
+
+def _validate_targets_controls(tandc):
+    tandc = list(tandc)
+    # Check for integers
+    for bit in tandc:
+        if not bit.is_Integer and not bit.is_Symbol:
+            raise TypeError('Integer expected, got: %r' % tandc[bit])
+    # Detect duplicates
+    if len(set(tandc)) != len(tandc):
+        raise QuantumError(
+            'Target/control qubits in a gate cannot be duplicated'
+        )
+
+
+class Gate(UnitaryOperator):
+    """Non-controlled unitary gate operator that acts on qubits.
+
+    This is a general abstract gate that needs to be subclassed to do anything
+    useful.
+
+    Parameters
+    ----------
+    label : tuple, int
+        A list of the target qubits (as ints) that the gate will apply to.
+
+    Examples
+    ========
+
+
+    """
+
+    _label_separator = ','
+
+    gate_name = 'G'
+    gate_name_latex = 'G'
+
+    #-------------------------------------------------------------------------
+    # Initialization/creation
+    #-------------------------------------------------------------------------
+
+    @classmethod
+    def _eval_args(cls, args):
+        args = Tuple(*UnitaryOperator._eval_args(args))
+        _validate_targets_controls(args)
+        return args
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        """This returns the smallest possible Hilbert space."""
+        return ComplexSpace(2)**(_max(args) + 1)
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def nqubits(self):
+        """The total number of qubits this gate acts on.
+
+        For controlled gate subclasses this includes both target and control
+        qubits, so that, for examples the CNOT gate acts on 2 qubits.
+        """
+        return len(self.targets)
+
+    @property
+    def min_qubits(self):
+        """The minimum number of qubits this gate needs to act on."""
+        return _max(self.targets) + 1
+
+    @property
+    def targets(self):
+        """A tuple of target qubits."""
+        return self.label
+
+    @property
+    def gate_name_plot(self):
+        return r'$%s$' % self.gate_name_latex
+
+    #-------------------------------------------------------------------------
+    # Gate methods
+    #-------------------------------------------------------------------------
+
+    def get_target_matrix(self, format='sympy'):
+        """The matrix representation of the target part of the gate.
+
+        Parameters
+        ----------
+        format : str
+            The format string ('sympy','numpy', etc.)
+        """
+        raise NotImplementedError(
+            'get_target_matrix is not implemented in Gate.')
+
+    #-------------------------------------------------------------------------
+    # Apply
+    #-------------------------------------------------------------------------
+
+    def _apply_operator_IntQubit(self, qubits, **options):
+        """Redirect an apply from IntQubit to Qubit"""
+        return self._apply_operator_Qubit(qubits, **options)
+
+    def _apply_operator_Qubit(self, qubits, **options):
+        """Apply this gate to a Qubit."""
+
+        # Check number of qubits this gate acts on.
+        if qubits.nqubits < self.min_qubits:
+            raise QuantumError(
+                'Gate needs a minimum of %r qubits to act on, got: %r' %
+                (self.min_qubits, qubits.nqubits)
+            )
+
+        # If the controls are not met, just return
+        if isinstance(self, CGate):
+            if not self.eval_controls(qubits):
+                return qubits
+
+        targets = self.targets
+        target_matrix = self.get_target_matrix(format='sympy')
+
+        # Find which column of the target matrix this applies to.
+        column_index = 0
+        n = 1
+        for target in targets:
+            column_index += n*qubits[target]
+            n = n << 1
+        column = target_matrix[:, int(column_index)]
+
+        # Now apply each column element to the qubit.
+        result = 0
+        for index in range(column.rows):
+            # TODO: This can be optimized to reduce the number of Qubit
+            # creations. We should simply manipulate the raw list of qubit
+            # values and then build the new Qubit object once.
+            # Make a copy of the incoming qubits.
+            new_qubit = qubits.__class__(*qubits.args)
+            # Flip the bits that need to be flipped.
+            for bit, target in enumerate(targets):
+                if new_qubit[target] != (index >> bit) & 1:
+                    new_qubit = new_qubit.flip(target)
+            # The value in that row and column times the flipped-bit qubit
+            # is the result for that part.
+            result += column[index]*new_qubit
+        return result
+
+    #-------------------------------------------------------------------------
+    # Represent
+    #-------------------------------------------------------------------------
+
+    def _represent_default_basis(self, **options):
+        return self._represent_ZGate(None, **options)
+
+    def _represent_ZGate(self, basis, **options):
+        format = options.get('format', 'sympy')
+        nqubits = options.get('nqubits', 0)
+        if nqubits == 0:
+            raise QuantumError(
+                'The number of qubits must be given as nqubits.')
+
+        # Make sure we have enough qubits for the gate.
+        if nqubits < self.min_qubits:
+            raise QuantumError(
+                'The number of qubits %r is too small for the gate.' % nqubits
+            )
+
+        target_matrix = self.get_target_matrix(format)
+        targets = self.targets
+        if isinstance(self, CGate):
+            controls = self.controls
+        else:
+            controls = []
+        m = represent_zbasis(
+            controls, targets, target_matrix, nqubits, format
+        )
+        return m
+
+    #-------------------------------------------------------------------------
+    # Print methods
+    #-------------------------------------------------------------------------
+
+    def _sympystr(self, printer, *args):
+        label = self._print_label(printer, *args)
+        return '%s(%s)' % (self.gate_name, label)
+
+    def _pretty(self, printer, *args):
+        a = stringPict(self.gate_name)
+        b = self._print_label_pretty(printer, *args)
+        return self._print_subscript_pretty(a, b)
+
+    def _latex(self, printer, *args):
+        label = self._print_label(printer, *args)
+        return '%s_{%s}' % (self.gate_name_latex, label)
+
+    def plot_gate(self, axes, gate_idx, gate_grid, wire_grid):
+        raise NotImplementedError('plot_gate is not implemented.')
+
+
+class CGate(Gate):
+    """A general unitary gate with control qubits.
+
+    A general control gate applies a target gate to a set of targets if all
+    of the control qubits have a particular values (set by
+    ``CGate.control_value``).
+
+    Parameters
+    ----------
+    label : tuple
+        The label in this case has the form (controls, gate), where controls
+        is a tuple/list of control qubits (as ints) and gate is a ``Gate``
+        instance that is the target operator.
+
+    Examples
+    ========
+
+    """
+
+    gate_name = 'C'
+    gate_name_latex = 'C'
+
+    # The values this class controls for.
+    control_value = _S.One
+
+    simplify_cgate = False
+
+    #-------------------------------------------------------------------------
+    # Initialization
+    #-------------------------------------------------------------------------
+
+    @classmethod
+    def _eval_args(cls, args):
+        # _eval_args has the right logic for the controls argument.
+        controls = args[0]
+        gate = args[1]
+        if not is_sequence(controls):
+            controls = (controls,)
+        controls = UnitaryOperator._eval_args(controls)
+        _validate_targets_controls(chain(controls, gate.targets))
+        return (Tuple(*controls), gate)
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        """This returns the smallest possible Hilbert space."""
+        return ComplexSpace(2)**_max(_max(args[0]) + 1, args[1].min_qubits)
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def nqubits(self):
+        """The total number of qubits this gate acts on.
+
+        For controlled gate subclasses this includes both target and control
+        qubits, so that, for examples the CNOT gate acts on 2 qubits.
+        """
+        return len(self.targets) + len(self.controls)
+
+    @property
+    def min_qubits(self):
+        """The minimum number of qubits this gate needs to act on."""
+        return _max(_max(self.controls), _max(self.targets)) + 1
+
+    @property
+    def targets(self):
+        """A tuple of target qubits."""
+        return self.gate.targets
+
+    @property
+    def controls(self):
+        """A tuple of control qubits."""
+        return tuple(self.label[0])
+
+    @property
+    def gate(self):
+        """The non-controlled gate that will be applied to the targets."""
+        return self.label[1]
+
+    #-------------------------------------------------------------------------
+    # Gate methods
+    #-------------------------------------------------------------------------
+
+    def get_target_matrix(self, format='sympy'):
+        return self.gate.get_target_matrix(format)
+
+    def eval_controls(self, qubit):
+        """Return True/False to indicate if the controls are satisfied."""
+        return all(qubit[bit] == self.control_value for bit in self.controls)
+
+    def decompose(self, **options):
+        """Decompose the controlled gate into CNOT and single qubits gates."""
+        if len(self.controls) == 1:
+            c = self.controls[0]
+            t = self.gate.targets[0]
+            if isinstance(self.gate, YGate):
+                g1 = PhaseGate(t)
+                g2 = CNotGate(c, t)
+                g3 = PhaseGate(t)
+                g4 = ZGate(t)
+                return g1*g2*g3*g4
+            if isinstance(self.gate, ZGate):
+                g1 = HadamardGate(t)
+                g2 = CNotGate(c, t)
+                g3 = HadamardGate(t)
+                return g1*g2*g3
+        else:
+            return self
+
+    #-------------------------------------------------------------------------
+    # Print methods
+    #-------------------------------------------------------------------------
+
+    def _print_label(self, printer, *args):
+        controls = self._print_sequence(self.controls, ',', printer, *args)
+        gate = printer._print(self.gate, *args)
+        return '(%s),%s' % (controls, gate)
+
+    def _pretty(self, printer, *args):
+        controls = self._print_sequence_pretty(
+            self.controls, ',', printer, *args)
+        gate = printer._print(self.gate)
+        gate_name = stringPict(self.gate_name)
+        first = self._print_subscript_pretty(gate_name, controls)
+        gate = self._print_parens_pretty(gate)
+        final = prettyForm(*first.right(gate))
+        return final
+
+    def _latex(self, printer, *args):
+        controls = self._print_sequence(self.controls, ',', printer, *args)
+        gate = printer._print(self.gate, *args)
+        return r'%s_{%s}{\left(%s\right)}' % \
+            (self.gate_name_latex, controls, gate)
+
+    def plot_gate(self, circ_plot, gate_idx):
+        """
+        Plot the controlled gate. If *simplify_cgate* is true, simplify
+        C-X and C-Z gates into their more familiar forms.
+        """
+        min_wire = int(_min(chain(self.controls, self.targets)))
+        max_wire = int(_max(chain(self.controls, self.targets)))
+        circ_plot.control_line(gate_idx, min_wire, max_wire)
+        for c in self.controls:
+            circ_plot.control_point(gate_idx, int(c))
+        if self.simplify_cgate:
+            if self.gate.gate_name == 'X':
+                self.gate.plot_gate_plus(circ_plot, gate_idx)
+            elif self.gate.gate_name == 'Z':
+                circ_plot.control_point(gate_idx, self.targets[0])
+            else:
+                self.gate.plot_gate(circ_plot, gate_idx)
+        else:
+            self.gate.plot_gate(circ_plot, gate_idx)
+
+    #-------------------------------------------------------------------------
+    # Miscellaneous
+    #-------------------------------------------------------------------------
+
+    def _eval_dagger(self):
+        if isinstance(self.gate, HermitianOperator):
+            return self
+        else:
+            return Gate._eval_dagger(self)
+
+    def _eval_inverse(self):
+        if isinstance(self.gate, HermitianOperator):
+            return self
+        else:
+            return Gate._eval_inverse(self)
+
+    def _eval_power(self, exp):
+        if isinstance(self.gate, HermitianOperator):
+            if exp == -1:
+                return Gate._eval_power(self, exp)
+            elif abs(exp) % 2 == 0:
+                return self*(Gate._eval_inverse(self))
+            else:
+                return self
+        else:
+            return Gate._eval_power(self, exp)
+
+class CGateS(CGate):
+    """Version of CGate that allows gate simplifications.
+    I.e. cnot looks like an oplus, cphase has dots, etc.
+    """
+    simplify_cgate=True
+
+
+class UGate(Gate):
+    """General gate specified by a set of targets and a target matrix.
+
+    Parameters
+    ----------
+    label : tuple
+        A tuple of the form (targets, U), where targets is a tuple of the
+        target qubits and U is a unitary matrix with dimension of
+        len(targets).
+    """
+    gate_name = 'U'
+    gate_name_latex = 'U'
+
+    #-------------------------------------------------------------------------
+    # Initialization
+    #-------------------------------------------------------------------------
+
+    @classmethod
+    def _eval_args(cls, args):
+        targets = args[0]
+        if not is_sequence(targets):
+            targets = (targets,)
+        targets = Gate._eval_args(targets)
+        _validate_targets_controls(targets)
+        mat = args[1]
+        if not isinstance(mat, MatrixBase):
+            raise TypeError('Matrix expected, got: %r' % mat)
+        #make sure this matrix is of a Basic type
+        mat = _sympify(mat)
+        dim = 2**len(targets)
+        if not all(dim == shape for shape in mat.shape):
+            raise IndexError(
+                'Number of targets must match the matrix size: %r %r' %
+                (targets, mat)
+            )
+        return (targets, mat)
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        """This returns the smallest possible Hilbert space."""
+        return ComplexSpace(2)**(_max(args[0]) + 1)
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def targets(self):
+        """A tuple of target qubits."""
+        return tuple(self.label[0])
+
+    #-------------------------------------------------------------------------
+    # Gate methods
+    #-------------------------------------------------------------------------
+
+    def get_target_matrix(self, format='sympy'):
+        """The matrix rep. of the target part of the gate.
+
+        Parameters
+        ----------
+        format : str
+            The format string ('sympy','numpy', etc.)
+        """
+        return self.label[1]
+
+    #-------------------------------------------------------------------------
+    # Print methods
+    #-------------------------------------------------------------------------
+    def _pretty(self, printer, *args):
+        targets = self._print_sequence_pretty(
+            self.targets, ',', printer, *args)
+        gate_name = stringPict(self.gate_name)
+        return self._print_subscript_pretty(gate_name, targets)
+
+    def _latex(self, printer, *args):
+        targets = self._print_sequence(self.targets, ',', printer, *args)
+        return r'%s_{%s}' % (self.gate_name_latex, targets)
+
+    def plot_gate(self, circ_plot, gate_idx):
+        circ_plot.one_qubit_box(
+            self.gate_name_plot,
+            gate_idx, int(self.targets[0])
+        )
+
+
+class OneQubitGate(Gate):
+    """A single qubit unitary gate base class."""
+
+    nqubits = _S.One
+
+    def plot_gate(self, circ_plot, gate_idx):
+        circ_plot.one_qubit_box(
+            self.gate_name_plot,
+            gate_idx, int(self.targets[0])
+        )
+
+    def _eval_commutator(self, other, **hints):
+        if isinstance(other, OneQubitGate):
+            if self.targets != other.targets or self.__class__ == other.__class__:
+                return _S.Zero
+        return Operator._eval_commutator(self, other, **hints)
+
+    def _eval_anticommutator(self, other, **hints):
+        if isinstance(other, OneQubitGate):
+            if self.targets != other.targets or self.__class__ == other.__class__:
+                return Integer(2)*self*other
+        return Operator._eval_anticommutator(self, other, **hints)
+
+
+class TwoQubitGate(Gate):
+    """A two qubit unitary gate base class."""
+
+    nqubits = Integer(2)
+
+#-----------------------------------------------------------------------------
+# Single Qubit Gates
+#-----------------------------------------------------------------------------
+
+
+class IdentityGate(OneQubitGate):
+    """The single qubit identity gate.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    """
+    is_hermitian = True
+    gate_name = '1'
+    gate_name_latex = '1'
+
+    # Short cut version of gate._apply_operator_Qubit
+    def _apply_operator_Qubit(self, qubits, **options):
+        # Check number of qubits this gate acts on (see gate._apply_operator_Qubit)
+        if qubits.nqubits < self.min_qubits:
+            raise QuantumError(
+                'Gate needs a minimum of %r qubits to act on, got: %r' %
+                (self.min_qubits, qubits.nqubits)
+            )
+        return qubits # no computation required for IdentityGate
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('eye2', format)
+
+    def _eval_commutator(self, other, **hints):
+        return _S.Zero
+
+    def _eval_anticommutator(self, other, **hints):
+        return Integer(2)*other
+
+
+class HadamardGate(HermitianOperator, OneQubitGate):
+    """The single qubit Hadamard gate.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    >>> from sympy import sqrt
+    >>> from sympy.physics.quantum.qubit import Qubit
+    >>> from sympy.physics.quantum.gate import HadamardGate
+    >>> from sympy.physics.quantum.qapply import qapply
+    >>> qapply(HadamardGate(0)*Qubit('1'))
+    sqrt(2)*|0>/2 - sqrt(2)*|1>/2
+    >>> # Hadamard on bell state, applied on 2 qubits.
+    >>> psi = 1/sqrt(2)*(Qubit('00')+Qubit('11'))
+    >>> qapply(HadamardGate(0)*HadamardGate(1)*psi)
+    sqrt(2)*|00>/2 + sqrt(2)*|11>/2
+
+    """
+    gate_name = 'H'
+    gate_name_latex = 'H'
+
+    def get_target_matrix(self, format='sympy'):
+        if _normalized:
+            return matrix_cache.get_matrix('H', format)
+        else:
+            return matrix_cache.get_matrix('Hsqrt2', format)
+
+    def _eval_commutator_XGate(self, other, **hints):
+        return I*sqrt(2)*YGate(self.targets[0])
+
+    def _eval_commutator_YGate(self, other, **hints):
+        return I*sqrt(2)*(ZGate(self.targets[0]) - XGate(self.targets[0]))
+
+    def _eval_commutator_ZGate(self, other, **hints):
+        return -I*sqrt(2)*YGate(self.targets[0])
+
+    def _eval_anticommutator_XGate(self, other, **hints):
+        return sqrt(2)*IdentityGate(self.targets[0])
+
+    def _eval_anticommutator_YGate(self, other, **hints):
+        return _S.Zero
+
+    def _eval_anticommutator_ZGate(self, other, **hints):
+        return sqrt(2)*IdentityGate(self.targets[0])
+
+
+class XGate(HermitianOperator, OneQubitGate):
+    """The single qubit X, or NOT, gate.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    """
+    gate_name = 'X'
+    gate_name_latex = 'X'
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('X', format)
+
+    def plot_gate(self, circ_plot, gate_idx):
+        OneQubitGate.plot_gate(self,circ_plot,gate_idx)
+
+    def plot_gate_plus(self, circ_plot, gate_idx):
+        circ_plot.not_point(
+            gate_idx, int(self.label[0])
+        )
+
+    def _eval_commutator_YGate(self, other, **hints):
+        return Integer(2)*I*ZGate(self.targets[0])
+
+    def _eval_anticommutator_XGate(self, other, **hints):
+        return Integer(2)*IdentityGate(self.targets[0])
+
+    def _eval_anticommutator_YGate(self, other, **hints):
+        return _S.Zero
+
+    def _eval_anticommutator_ZGate(self, other, **hints):
+        return _S.Zero
+
+
+class YGate(HermitianOperator, OneQubitGate):
+    """The single qubit Y gate.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    """
+    gate_name = 'Y'
+    gate_name_latex = 'Y'
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('Y', format)
+
+    def _eval_commutator_ZGate(self, other, **hints):
+        return Integer(2)*I*XGate(self.targets[0])
+
+    def _eval_anticommutator_YGate(self, other, **hints):
+        return Integer(2)*IdentityGate(self.targets[0])
+
+    def _eval_anticommutator_ZGate(self, other, **hints):
+        return _S.Zero
+
+
+class ZGate(HermitianOperator, OneQubitGate):
+    """The single qubit Z gate.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    """
+    gate_name = 'Z'
+    gate_name_latex = 'Z'
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('Z', format)
+
+    def _eval_commutator_XGate(self, other, **hints):
+        return Integer(2)*I*YGate(self.targets[0])
+
+    def _eval_anticommutator_YGate(self, other, **hints):
+        return _S.Zero
+
+
+class PhaseGate(OneQubitGate):
+    """The single qubit phase, or S, gate.
+
+    This gate rotates the phase of the state by pi/2 if the state is ``|1>`` and
+    does nothing if the state is ``|0>``.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    """
+    is_hermitian =  False
+    gate_name = 'S'
+    gate_name_latex = 'S'
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('S', format)
+
+    def _eval_commutator_ZGate(self, other, **hints):
+        return _S.Zero
+
+    def _eval_commutator_TGate(self, other, **hints):
+        return _S.Zero
+
+
+class TGate(OneQubitGate):
+    """The single qubit pi/8 gate.
+
+    This gate rotates the phase of the state by pi/4 if the state is ``|1>`` and
+    does nothing if the state is ``|0>``.
+
+    Parameters
+    ----------
+    target : int
+        The target qubit this gate will apply to.
+
+    Examples
+    ========
+
+    """
+    is_hermitian = False
+    gate_name = 'T'
+    gate_name_latex = 'T'
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('T', format)
+
+    def _eval_commutator_ZGate(self, other, **hints):
+        return _S.Zero
+
+    def _eval_commutator_PhaseGate(self, other, **hints):
+        return _S.Zero
+
+
+# Aliases for gate names.
+H = HadamardGate
+X = XGate
+Y = YGate
+Z = ZGate
+T = TGate
+Phase = S = PhaseGate
+
+
+#-----------------------------------------------------------------------------
+# 2 Qubit Gates
+#-----------------------------------------------------------------------------
+
+
+class CNotGate(HermitianOperator, CGate, TwoQubitGate):
+    """Two qubit controlled-NOT.
+
+    This gate performs the NOT or X gate on the target qubit if the control
+    qubits all have the value 1.
+
+    Parameters
+    ----------
+    label : tuple
+        A tuple of the form (control, target).
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.gate import CNOT
+    >>> from sympy.physics.quantum.qapply import qapply
+    >>> from sympy.physics.quantum.qubit import Qubit
+    >>> c = CNOT(1,0)
+    >>> qapply(c*Qubit('10')) # note that qubits are indexed from right to left
+    |11>
+
+    """
+    gate_name = 'CNOT'
+    gate_name_latex = r'\text{CNOT}'
+    simplify_cgate = True
+
+    #-------------------------------------------------------------------------
+    # Initialization
+    #-------------------------------------------------------------------------
+
+    @classmethod
+    def _eval_args(cls, args):
+        args = Gate._eval_args(args)
+        return args
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        """This returns the smallest possible Hilbert space."""
+        return ComplexSpace(2)**(_max(args) + 1)
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def min_qubits(self):
+        """The minimum number of qubits this gate needs to act on."""
+        return _max(self.label) + 1
+
+    @property
+    def targets(self):
+        """A tuple of target qubits."""
+        return (self.label[1],)
+
+    @property
+    def controls(self):
+        """A tuple of control qubits."""
+        return (self.label[0],)
+
+    @property
+    def gate(self):
+        """The non-controlled gate that will be applied to the targets."""
+        return XGate(self.label[1])
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    # The default printing of Gate works better than those of CGate, so we
+    # go around the overridden methods in CGate.
+
+    def _print_label(self, printer, *args):
+        return Gate._print_label(self, printer, *args)
+
+    def _pretty(self, printer, *args):
+        return Gate._pretty(self, printer, *args)
+
+    def _latex(self, printer, *args):
+        return Gate._latex(self, printer, *args)
+
+    #-------------------------------------------------------------------------
+    # Commutator/AntiCommutator
+    #-------------------------------------------------------------------------
+
+    def _eval_commutator_ZGate(self, other, **hints):
+        """[CNOT(i, j), Z(i)] == 0."""
+        if self.controls[0] == other.targets[0]:
+            return _S.Zero
+        else:
+            raise NotImplementedError('Commutator not implemented: %r' % other)
+
+    def _eval_commutator_TGate(self, other, **hints):
+        """[CNOT(i, j), T(i)] == 0."""
+        return self._eval_commutator_ZGate(other, **hints)
+
+    def _eval_commutator_PhaseGate(self, other, **hints):
+        """[CNOT(i, j), S(i)] == 0."""
+        return self._eval_commutator_ZGate(other, **hints)
+
+    def _eval_commutator_XGate(self, other, **hints):
+        """[CNOT(i, j), X(j)] == 0."""
+        if self.targets[0] == other.targets[0]:
+            return _S.Zero
+        else:
+            raise NotImplementedError('Commutator not implemented: %r' % other)
+
+    def _eval_commutator_CNotGate(self, other, **hints):
+        """[CNOT(i, j), CNOT(i,k)] == 0."""
+        if self.controls[0] == other.controls[0]:
+            return _S.Zero
+        else:
+            raise NotImplementedError('Commutator not implemented: %r' % other)
+
+
+class SwapGate(TwoQubitGate):
+    """Two qubit SWAP gate.
+
+    This gate swap the values of the two qubits.
+
+    Parameters
+    ----------
+    label : tuple
+        A tuple of the form (target1, target2).
+
+    Examples
+    ========
+
+    """
+    is_hermitian = True
+    gate_name = 'SWAP'
+    gate_name_latex = r'\text{SWAP}'
+
+    def get_target_matrix(self, format='sympy'):
+        return matrix_cache.get_matrix('SWAP', format)
+
+    def decompose(self, **options):
+        """Decompose the SWAP gate into CNOT gates."""
+        i, j = self.targets[0], self.targets[1]
+        g1 = CNotGate(i, j)
+        g2 = CNotGate(j, i)
+        return g1*g2*g1
+
+    def plot_gate(self, circ_plot, gate_idx):
+        min_wire = int(_min(self.targets))
+        max_wire = int(_max(self.targets))
+        circ_plot.control_line(gate_idx, min_wire, max_wire)
+        circ_plot.swap_point(gate_idx, min_wire)
+        circ_plot.swap_point(gate_idx, max_wire)
+
+    def _represent_ZGate(self, basis, **options):
+        """Represent the SWAP gate in the computational basis.
+
+        The following representation is used to compute this:
+
+        SWAP = |1><1|x|1><1| + |0><0|x|0><0| + |1><0|x|0><1| + |0><1|x|1><0|
+        """
+        format = options.get('format', 'sympy')
+        targets = [int(t) for t in self.targets]
+        min_target = _min(targets)
+        max_target = _max(targets)
+        nqubits = options.get('nqubits', self.min_qubits)
+
+        op01 = matrix_cache.get_matrix('op01', format)
+        op10 = matrix_cache.get_matrix('op10', format)
+        op11 = matrix_cache.get_matrix('op11', format)
+        op00 = matrix_cache.get_matrix('op00', format)
+        eye2 = matrix_cache.get_matrix('eye2', format)
+
+        result = None
+        for i, j in ((op01, op10), (op10, op01), (op00, op00), (op11, op11)):
+            product = nqubits*[eye2]
+            product[nqubits - min_target - 1] = i
+            product[nqubits - max_target - 1] = j
+            new_result = matrix_tensor_product(*product)
+            if result is None:
+                result = new_result
+            else:
+                result = result + new_result
+
+        return result
+
+
+# Aliases for gate names.
+CNOT = CNotGate
+SWAP = SwapGate
+def CPHASE(a,b): return CGateS((a,),Z(b))
+
+
+#-----------------------------------------------------------------------------
+# Represent
+#-----------------------------------------------------------------------------
+
+
+def represent_zbasis(controls, targets, target_matrix, nqubits, format='sympy'):
+    """Represent a gate with controls, targets and target_matrix.
+
+    This function does the low-level work of representing gates as matrices
+    in the standard computational basis (ZGate). Currently, we support two
+    main cases:
+
+    1. One target qubit and no control qubits.
+    2. One target qubits and multiple control qubits.
+
+    For the base of multiple controls, we use the following expression [1]:
+
+    1_{2**n} + (|1><1|)^{(n-1)} x (target-matrix - 1_{2})
+
+    Parameters
+    ----------
+    controls : list, tuple
+        A sequence of control qubits.
+    targets : list, tuple
+        A sequence of target qubits.
+    target_matrix : sympy.Matrix, numpy.matrix, scipy.sparse
+        The matrix form of the transformation to be performed on the target
+        qubits.  The format of this matrix must match that passed into
+        the `format` argument.
+    nqubits : int
+        The total number of qubits used for the representation.
+    format : str
+        The format of the final matrix ('sympy', 'numpy', 'scipy.sparse').
+
+    Examples
+    ========
+
+    References
+    ----------
+    [1] http://www.johnlapeyre.com/qinf/qinf_html/node6.html.
+    """
+    controls = [int(x) for x in controls]
+    targets = [int(x) for x in targets]
+    nqubits = int(nqubits)
+
+    # This checks for the format as well.
+    op11 = matrix_cache.get_matrix('op11', format)
+    eye2 = matrix_cache.get_matrix('eye2', format)
+
+    # Plain single qubit case
+    if len(controls) == 0 and len(targets) == 1:
+        product = []
+        bit = targets[0]
+        # Fill product with [I1,Gate,I2] such that the unitaries,
+        # I, cause the gate to be applied to the correct Qubit
+        if bit != nqubits - 1:
+            product.append(matrix_eye(2**(nqubits - bit - 1), format=format))
+        product.append(target_matrix)
+        if bit != 0:
+            product.append(matrix_eye(2**bit, format=format))
+        return matrix_tensor_product(*product)
+
+    # Single target, multiple controls.
+    elif len(targets) == 1 and len(controls) >= 1:
+        target = targets[0]
+
+        # Build the non-trivial part.
+        product2 = []
+        for i in range(nqubits):
+            product2.append(matrix_eye(2, format=format))
+        for control in controls:
+            product2[nqubits - 1 - control] = op11
+        product2[nqubits - 1 - target] = target_matrix - eye2
+
+        return matrix_eye(2**nqubits, format=format) + \
+            matrix_tensor_product(*product2)
+
+    # Multi-target, multi-control is not yet implemented.
+    else:
+        raise NotImplementedError(
+            'The representation of multi-target, multi-control gates '
+            'is not implemented.'
+        )
+
+
+#-----------------------------------------------------------------------------
+# Gate manipulation functions.
+#-----------------------------------------------------------------------------
+
+
+def gate_simp(circuit):
+    """Simplifies gates symbolically
+
+    It first sorts gates using gate_sort. It then applies basic
+    simplification rules to the circuit, e.g., XGate**2 = Identity
+    """
+
+    # Bubble sort out gates that commute.
+    circuit = gate_sort(circuit)
+
+    # Do simplifications by subing a simplification into the first element
+    # which can be simplified. We recursively call gate_simp with new circuit
+    # as input more simplifications exist.
+    if isinstance(circuit, Add):
+        return sum(gate_simp(t) for t in circuit.args)
+    elif isinstance(circuit, Mul):
+        circuit_args = circuit.args
+    elif isinstance(circuit, Pow):
+        b, e = circuit.as_base_exp()
+        circuit_args = (gate_simp(b)**e,)
+    else:
+        return circuit
+
+    # Iterate through each element in circuit, simplify if possible.
+    for i in range(len(circuit_args)):
+        # H,X,Y or Z squared is 1.
+        # T**2 = S, S**2 = Z
+        if isinstance(circuit_args[i], Pow):
+            if isinstance(circuit_args[i].base,
+                (HadamardGate, XGate, YGate, ZGate)) \
+                    and isinstance(circuit_args[i].exp, Number):
+                # Build a new circuit taking replacing the
+                # H,X,Y,Z squared with one.
+                newargs = (circuit_args[:i] +
+                          (circuit_args[i].base**(circuit_args[i].exp % 2),) +
+                           circuit_args[i + 1:])
+                # Recursively simplify the new circuit.
+                circuit = gate_simp(Mul(*newargs))
+                break
+            elif isinstance(circuit_args[i].base, PhaseGate):
+                # Build a new circuit taking old circuit but splicing
+                # in simplification.
+                newargs = circuit_args[:i]
+                # Replace PhaseGate**2 with ZGate.
+                newargs = newargs + (ZGate(circuit_args[i].base.args[0])**
+                (Integer(circuit_args[i].exp/2)), circuit_args[i].base**
+                (circuit_args[i].exp % 2))
+                # Append the last elements.
+                newargs = newargs + circuit_args[i + 1:]
+                # Recursively simplify the new circuit.
+                circuit = gate_simp(Mul(*newargs))
+                break
+            elif isinstance(circuit_args[i].base, TGate):
+                # Build a new circuit taking all the old elements.
+                newargs = circuit_args[:i]
+
+                # Put an Phasegate in place of any TGate**2.
+                newargs = newargs + (PhaseGate(circuit_args[i].base.args[0])**
+                Integer(circuit_args[i].exp/2), circuit_args[i].base**
+                    (circuit_args[i].exp % 2))
+
+                # Append the last elements.
+                newargs = newargs + circuit_args[i + 1:]
+                # Recursively simplify the new circuit.
+                circuit = gate_simp(Mul(*newargs))
+                break
+    return circuit
+
+
+def gate_sort(circuit):
+    """Sorts the gates while keeping track of commutation relations
+
+    This function uses a bubble sort to rearrange the order of gate
+    application. Keeps track of Quantum computations special commutation
+    relations (e.g. things that apply to the same Qubit do not commute with
+    each other)
+
+    circuit is the Mul of gates that are to be sorted.
+    """
+    # Make sure we have an Add or Mul.
+    if isinstance(circuit, Add):
+        return sum(gate_sort(t) for t in circuit.args)
+    if isinstance(circuit, Pow):
+        return gate_sort(circuit.base)**circuit.exp
+    elif isinstance(circuit, Gate):
+        return circuit
+    if not isinstance(circuit, Mul):
+        return circuit
+
+    changes = True
+    while changes:
+        changes = False
+        circ_array = circuit.args
+        for i in range(len(circ_array) - 1):
+            # Go through each element and switch ones that are in wrong order
+            if isinstance(circ_array[i], (Gate, Pow)) and \
+                    isinstance(circ_array[i + 1], (Gate, Pow)):
+                # If we have a Pow object, look at only the base
+                first_base, first_exp = circ_array[i].as_base_exp()
+                second_base, second_exp = circ_array[i + 1].as_base_exp()
+
+                # Use SymPy's hash based sorting. This is not mathematical
+                # sorting, but is rather based on comparing hashes of objects.
+                # See Basic.compare for details.
+                if first_base.compare(second_base) > 0:
+                    if Commutator(first_base, second_base).doit() == 0:
+                        new_args = (circuit.args[:i] + (circuit.args[i + 1],) +
+                                   (circuit.args[i],) + circuit.args[i + 2:])
+                        circuit = Mul(*new_args)
+                        changes = True
+                        break
+                    if AntiCommutator(first_base, second_base).doit() == 0:
+                        new_args = (circuit.args[:i] + (circuit.args[i + 1],) +
+                                   (circuit.args[i],) + circuit.args[i + 2:])
+                        sign = _S.NegativeOne**(first_exp*second_exp)
+                        circuit = sign*Mul(*new_args)
+                        changes = True
+                        break
+    return circuit
+
+
+#-----------------------------------------------------------------------------
+# Utility functions
+#-----------------------------------------------------------------------------
+
+
+def random_circuit(ngates, nqubits, gate_space=(X, Y, Z, S, T, H, CNOT, SWAP)):
+    """Return a random circuit of ngates and nqubits.
+
+    This uses an equally weighted sample of (X, Y, Z, S, T, H, CNOT, SWAP)
+    gates.
+
+    Parameters
+    ----------
+    ngates : int
+        The number of gates in the circuit.
+    nqubits : int
+        The number of qubits in the circuit.
+    gate_space : tuple
+        A tuple of the gate classes that will be used in the circuit.
+        Repeating gate classes multiple times in this tuple will increase
+        the frequency they appear in the random circuit.
+    """
+    qubit_space = range(nqubits)
+    result = []
+    for i in range(ngates):
+        g = random.choice(gate_space)
+        if g == CNotGate or g == SwapGate:
+            qubits = random.sample(qubit_space, 2)
+            g = g(*qubits)
+        else:
+            qubit = random.choice(qubit_space)
+            g = g(qubit)
+        result.append(g)
+    return Mul(*result)
+
+
+def zx_basis_transform(self, format='sympy'):
+    """Transformation matrix from Z to X basis."""
+    return matrix_cache.get_matrix('ZX', format)
+
+
+def zy_basis_transform(self, format='sympy'):
+    """Transformation matrix from Z to Y basis."""
+    return matrix_cache.get_matrix('ZY', format)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/grover.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/grover.py
new file mode 100644
index 0000000000000000000000000000000000000000..a03bd3a61a6e0960ab66d55bcc0fc7f25936199e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/grover.py
@@ -0,0 +1,345 @@
+"""Grover's algorithm and helper functions.
+
+Todo:
+
+* W gate construction (or perhaps -W gate based on Mermin's book)
+* Generalize the algorithm for an unknown function that returns 1 on multiple
+  qubit states, not just one.
+* Implement _represent_ZGate in OracleGate
+"""
+
+from sympy.core.numbers import pi
+from sympy.core.sympify import sympify
+from sympy.core.basic import Atom
+from sympy.functions.elementary.integers import floor
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import eye
+from sympy.core.numbers import NegativeOne
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qexpr import QuantumError
+from sympy.physics.quantum.hilbert import ComplexSpace
+from sympy.physics.quantum.operator import UnitaryOperator
+from sympy.physics.quantum.gate import Gate
+from sympy.physics.quantum.qubit import IntQubit
+
+__all__ = [
+    'OracleGate',
+    'WGate',
+    'superposition_basis',
+    'grover_iteration',
+    'apply_grover'
+]
+
+
+def superposition_basis(nqubits):
+    """Creates an equal superposition of the computational basis.
+
+    Parameters
+    ==========
+
+    nqubits : int
+        The number of qubits.
+
+    Returns
+    =======
+
+    state : Qubit
+        An equal superposition of the computational basis with nqubits.
+
+    Examples
+    ========
+
+    Create an equal superposition of 2 qubits::
+
+        >>> from sympy.physics.quantum.grover import superposition_basis
+        >>> superposition_basis(2)
+        |0>/2 + |1>/2 + |2>/2 + |3>/2
+    """
+
+    amp = 1/sqrt(2**nqubits)
+    return sum(amp*IntQubit(n, nqubits=nqubits) for n in range(2**nqubits))
+
+class OracleGateFunction(Atom):
+    """Wrapper for python functions used in `OracleGate`s"""
+
+    def __new__(cls, function):
+        if not callable(function):
+            raise TypeError('Callable expected, got: %r' % function)
+        obj = Atom.__new__(cls)
+        obj.function = function
+        return obj
+
+    def _hashable_content(self):
+        return type(self), self.function
+
+    def __call__(self, *args):
+        return self.function(*args)
+
+
+class OracleGate(Gate):
+    """A black box gate.
+
+    The gate marks the desired qubits of an unknown function by flipping
+    the sign of the qubits.  The unknown function returns true when it
+    finds its desired qubits and false otherwise.
+
+    Parameters
+    ==========
+
+    qubits : int
+        Number of qubits.
+
+    oracle : callable
+        A callable function that returns a boolean on a computational basis.
+
+    Examples
+    ========
+
+    Apply an Oracle gate that flips the sign of ``|2>`` on different qubits::
+
+        >>> from sympy.physics.quantum.qubit import IntQubit
+        >>> from sympy.physics.quantum.qapply import qapply
+        >>> from sympy.physics.quantum.grover import OracleGate
+        >>> f = lambda qubits: qubits == IntQubit(2)
+        >>> v = OracleGate(2, f)
+        >>> qapply(v*IntQubit(2))
+        -|2>
+        >>> qapply(v*IntQubit(3))
+        |3>
+    """
+
+    gate_name = 'V'
+    gate_name_latex = 'V'
+
+    #-------------------------------------------------------------------------
+    # Initialization/creation
+    #-------------------------------------------------------------------------
+
+    @classmethod
+    def _eval_args(cls, args):
+        if len(args) != 2:
+            raise QuantumError(
+                'Insufficient/excessive arguments to Oracle.  Please ' +
+                'supply the number of qubits and an unknown function.'
+            )
+        sub_args = (args[0],)
+        sub_args = UnitaryOperator._eval_args(sub_args)
+        if not sub_args[0].is_Integer:
+            raise TypeError('Integer expected, got: %r' % sub_args[0])
+
+        function = args[1]
+        if not isinstance(function, OracleGateFunction):
+            function = OracleGateFunction(function)
+
+        return (sub_args[0], function)
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        """This returns the smallest possible Hilbert space."""
+        return ComplexSpace(2)**args[0]
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def search_function(self):
+        """The unknown function that helps find the sought after qubits."""
+        return self.label[1]
+
+    @property
+    def targets(self):
+        """A tuple of target qubits."""
+        return sympify(tuple(range(self.args[0])))
+
+    #-------------------------------------------------------------------------
+    # Apply
+    #-------------------------------------------------------------------------
+
+    def _apply_operator_Qubit(self, qubits, **options):
+        """Apply this operator to a Qubit subclass.
+
+        Parameters
+        ==========
+
+        qubits : Qubit
+            The qubit subclass to apply this operator to.
+
+        Returns
+        =======
+
+        state : Expr
+            The resulting quantum state.
+        """
+        if qubits.nqubits != self.nqubits:
+            raise QuantumError(
+                'OracleGate operates on %r qubits, got: %r'
+                % (self.nqubits, qubits.nqubits)
+            )
+        # If function returns 1 on qubits
+            # return the negative of the qubits (flip the sign)
+        if self.search_function(qubits):
+            return -qubits
+        else:
+            return qubits
+
+    #-------------------------------------------------------------------------
+    # Represent
+    #-------------------------------------------------------------------------
+
+    def _represent_ZGate(self, basis, **options):
+        """
+        Represent the OracleGate in the computational basis.
+        """
+        nbasis = 2**self.nqubits  # compute it only once
+        matrixOracle = eye(nbasis)
+        # Flip the sign given the output of the oracle function
+        for i in range(nbasis):
+            if self.search_function(IntQubit(i, nqubits=self.nqubits)):
+                matrixOracle[i, i] = NegativeOne()
+        return matrixOracle
+
+
+class WGate(Gate):
+    """General n qubit W Gate in Grover's algorithm.
+
+    The gate performs the operation ``2|phi> = (tensor product of n Hadamards)*(|0> with n qubits)``
+
+    Parameters
+    ==========
+
+    nqubits : int
+        The number of qubits to operate on
+
+    """
+
+    gate_name = 'W'
+    gate_name_latex = 'W'
+
+    @classmethod
+    def _eval_args(cls, args):
+        if len(args) != 1:
+            raise QuantumError(
+                'Insufficient/excessive arguments to W gate.  Please ' +
+                'supply the number of qubits to operate on.'
+            )
+        args = UnitaryOperator._eval_args(args)
+        if not args[0].is_Integer:
+            raise TypeError('Integer expected, got: %r' % args[0])
+        return args
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def targets(self):
+        return sympify(tuple(reversed(range(self.args[0]))))
+
+    #-------------------------------------------------------------------------
+    # Apply
+    #-------------------------------------------------------------------------
+
+    def _apply_operator_Qubit(self, qubits, **options):
+        """
+        qubits: a set of qubits (Qubit)
+        Returns: quantum object (quantum expression - QExpr)
+        """
+        if qubits.nqubits != self.nqubits:
+            raise QuantumError(
+                'WGate operates on %r qubits, got: %r'
+                % (self.nqubits, qubits.nqubits)
+            )
+
+        # See 'Quantum Computer Science' by David Mermin p.92 -> W|a> result
+        # Return (2/(sqrt(2^n)))|phi> - |a> where |a> is the current basis
+        # state and phi is the superposition of basis states (see function
+        # create_computational_basis above)
+        basis_states = superposition_basis(self.nqubits)
+        change_to_basis = (2/sqrt(2**self.nqubits))*basis_states
+        return change_to_basis - qubits
+
+
+def grover_iteration(qstate, oracle):
+    """Applies one application of the Oracle and W Gate, WV.
+
+    Parameters
+    ==========
+
+    qstate : Qubit
+        A superposition of qubits.
+    oracle : OracleGate
+        The black box operator that flips the sign of the desired basis qubits.
+
+    Returns
+    =======
+
+    Qubit : The qubits after applying the Oracle and W gate.
+
+    Examples
+    ========
+
+    Perform one iteration of grover's algorithm to see a phase change::
+
+        >>> from sympy.physics.quantum.qapply import qapply
+        >>> from sympy.physics.quantum.qubit import IntQubit
+        >>> from sympy.physics.quantum.grover import OracleGate
+        >>> from sympy.physics.quantum.grover import superposition_basis
+        >>> from sympy.physics.quantum.grover import grover_iteration
+        >>> numqubits = 2
+        >>> basis_states = superposition_basis(numqubits)
+        >>> f = lambda qubits: qubits == IntQubit(2)
+        >>> v = OracleGate(numqubits, f)
+        >>> qapply(grover_iteration(basis_states, v))
+        |2>
+
+    """
+    wgate = WGate(oracle.nqubits)
+    return wgate*oracle*qstate
+
+
+def apply_grover(oracle, nqubits, iterations=None):
+    """Applies grover's algorithm.
+
+    Parameters
+    ==========
+
+    oracle : callable
+        The unknown callable function that returns true when applied to the
+        desired qubits and false otherwise.
+
+    Returns
+    =======
+
+    state : Expr
+        The resulting state after Grover's algorithm has been iterated.
+
+    Examples
+    ========
+
+    Apply grover's algorithm to an even superposition of 2 qubits::
+
+        >>> from sympy.physics.quantum.qapply import qapply
+        >>> from sympy.physics.quantum.qubit import IntQubit
+        >>> from sympy.physics.quantum.grover import apply_grover
+        >>> f = lambda qubits: qubits == IntQubit(2)
+        >>> qapply(apply_grover(f, 2))
+        |2>
+
+    """
+    if nqubits <= 0:
+        raise QuantumError(
+            'Grover\'s algorithm needs nqubits > 0, received %r qubits'
+            % nqubits
+        )
+    if iterations is None:
+        iterations = floor(sqrt(2**nqubits)*(pi/4))
+
+    v = OracleGate(nqubits, oracle)
+    iterated = superposition_basis(nqubits)
+    for iter in range(iterations):
+        iterated = grover_iteration(iterated, v)
+        iterated = qapply(iterated)
+
+    return iterated
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/hilbert.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/hilbert.py
new file mode 100644
index 0000000000000000000000000000000000000000..f475a9e83a6ccc93e9e2dbb9873ad111c1d05f93
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/hilbert.py
@@ -0,0 +1,653 @@
+"""Hilbert spaces for quantum mechanics.
+
+Authors:
+* Brian Granger
+* Matt Curry
+"""
+
+from functools import reduce
+
+from sympy.core.basic import Basic
+from sympy.core.singleton import S
+from sympy.core.sympify import sympify
+from sympy.sets.sets import Interval
+from sympy.printing.pretty.stringpict import prettyForm
+from sympy.physics.quantum.qexpr import QuantumError
+
+
+__all__ = [
+    'HilbertSpaceError',
+    'HilbertSpace',
+    'TensorProductHilbertSpace',
+    'TensorPowerHilbertSpace',
+    'DirectSumHilbertSpace',
+    'ComplexSpace',
+    'L2',
+    'FockSpace'
+]
+
+#-----------------------------------------------------------------------------
+# Main objects
+#-----------------------------------------------------------------------------
+
+
+class HilbertSpaceError(QuantumError):
+    pass
+
+#-----------------------------------------------------------------------------
+# Main objects
+#-----------------------------------------------------------------------------
+
+
+class HilbertSpace(Basic):
+    """An abstract Hilbert space for quantum mechanics.
+
+    In short, a Hilbert space is an abstract vector space that is complete
+    with inner products defined [1]_.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.hilbert import HilbertSpace
+    >>> hs = HilbertSpace()
+    >>> hs
+    H
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hilbert_space
+    """
+
+    def __new__(cls):
+        obj = Basic.__new__(cls)
+        return obj
+
+    @property
+    def dimension(self):
+        """Return the Hilbert dimension of the space."""
+        raise NotImplementedError('This Hilbert space has no dimension.')
+
+    def __add__(self, other):
+        return DirectSumHilbertSpace(self, other)
+
+    def __radd__(self, other):
+        return DirectSumHilbertSpace(other, self)
+
+    def __mul__(self, other):
+        return TensorProductHilbertSpace(self, other)
+
+    def __rmul__(self, other):
+        return TensorProductHilbertSpace(other, self)
+
+    def __pow__(self, other, mod=None):
+        if mod is not None:
+            raise ValueError('The third argument to __pow__ is not supported \
+            for Hilbert spaces.')
+        return TensorPowerHilbertSpace(self, other)
+
+    def __contains__(self, other):
+        """Is the operator or state in this Hilbert space.
+
+        This is checked by comparing the classes of the Hilbert spaces, not
+        the instances. This is to allow Hilbert Spaces with symbolic
+        dimensions.
+        """
+        if other.hilbert_space.__class__ == self.__class__:
+            return True
+        else:
+            return False
+
+    def _sympystr(self, printer, *args):
+        return 'H'
+
+    def _pretty(self, printer, *args):
+        ustr = '\N{LATIN CAPITAL LETTER H}'
+        return prettyForm(ustr)
+
+    def _latex(self, printer, *args):
+        return r'\mathcal{H}'
+
+
+class ComplexSpace(HilbertSpace):
+    """Finite dimensional Hilbert space of complex vectors.
+
+    The elements of this Hilbert space are n-dimensional complex valued
+    vectors with the usual inner product that takes the complex conjugate
+    of the vector on the right.
+
+    A classic example of this type of Hilbert space is spin-1/2, which is
+    ``ComplexSpace(2)``. Generalizing to spin-s, the space is
+    ``ComplexSpace(2*s+1)``.  Quantum computing with N qubits is done with the
+    direct product space ``ComplexSpace(2)**N``.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.quantum.hilbert import ComplexSpace
+    >>> c1 = ComplexSpace(2)
+    >>> c1
+    C(2)
+    >>> c1.dimension
+    2
+
+    >>> n = symbols('n')
+    >>> c2 = ComplexSpace(n)
+    >>> c2
+    C(n)
+    >>> c2.dimension
+    n
+
+    """
+
+    def __new__(cls, dimension):
+        dimension = sympify(dimension)
+        r = cls.eval(dimension)
+        if isinstance(r, Basic):
+            return r
+        obj = Basic.__new__(cls, dimension)
+        return obj
+
+    @classmethod
+    def eval(cls, dimension):
+        if len(dimension.atoms()) == 1:
+            if not (dimension.is_Integer and dimension > 0 or dimension is S.Infinity
+            or dimension.is_Symbol):
+                raise TypeError('The dimension of a ComplexSpace can only'
+                                'be a positive integer, oo, or a Symbol: %r'
+                                % dimension)
+        else:
+            for dim in dimension.atoms():
+                if not (dim.is_Integer or dim is S.Infinity or dim.is_Symbol):
+                    raise TypeError('The dimension of a ComplexSpace can only'
+                                    ' contain integers, oo, or a Symbol: %r'
+                                    % dim)
+
+    @property
+    def dimension(self):
+        return self.args[0]
+
+    def _sympyrepr(self, printer, *args):
+        return "%s(%s)" % (self.__class__.__name__,
+                           printer._print(self.dimension, *args))
+
+    def _sympystr(self, printer, *args):
+        return "C(%s)" % printer._print(self.dimension, *args)
+
+    def _pretty(self, printer, *args):
+        ustr = '\N{LATIN CAPITAL LETTER C}'
+        pform_exp = printer._print(self.dimension, *args)
+        pform_base = prettyForm(ustr)
+        return pform_base**pform_exp
+
+    def _latex(self, printer, *args):
+        return r'\mathcal{C}^{%s}' % printer._print(self.dimension, *args)
+
+
+class L2(HilbertSpace):
+    """The Hilbert space of square integrable functions on an interval.
+
+    An L2 object takes in a single SymPy Interval argument which represents
+    the interval its functions (vectors) are defined on.
+
+    Examples
+    ========
+
+    >>> from sympy import Interval, oo
+    >>> from sympy.physics.quantum.hilbert import L2
+    >>> hs = L2(Interval(0,oo))
+    >>> hs
+    L2(Interval(0, oo))
+    >>> hs.dimension
+    oo
+    >>> hs.interval
+    Interval(0, oo)
+
+    """
+
+    def __new__(cls, interval):
+        if not isinstance(interval, Interval):
+            raise TypeError('L2 interval must be an Interval instance: %r'
+            % interval)
+        obj = Basic.__new__(cls, interval)
+        return obj
+
+    @property
+    def dimension(self):
+        return S.Infinity
+
+    @property
+    def interval(self):
+        return self.args[0]
+
+    def _sympyrepr(self, printer, *args):
+        return "L2(%s)" % printer._print(self.interval, *args)
+
+    def _sympystr(self, printer, *args):
+        return "L2(%s)" % printer._print(self.interval, *args)
+
+    def _pretty(self, printer, *args):
+        pform_exp = prettyForm('2')
+        pform_base = prettyForm('L')
+        return pform_base**pform_exp
+
+    def _latex(self, printer, *args):
+        interval = printer._print(self.interval, *args)
+        return r'{\mathcal{L}^2}\left( %s \right)' % interval
+
+
+class FockSpace(HilbertSpace):
+    """The Hilbert space for second quantization.
+
+    Technically, this Hilbert space is a infinite direct sum of direct
+    products of single particle Hilbert spaces [1]_. This is a mess, so we have
+    a class to represent it directly.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.hilbert import FockSpace
+    >>> hs = FockSpace()
+    >>> hs
+    F
+    >>> hs.dimension
+    oo
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Fock_space
+    """
+
+    def __new__(cls):
+        obj = Basic.__new__(cls)
+        return obj
+
+    @property
+    def dimension(self):
+        return S.Infinity
+
+    def _sympyrepr(self, printer, *args):
+        return "FockSpace()"
+
+    def _sympystr(self, printer, *args):
+        return "F"
+
+    def _pretty(self, printer, *args):
+        ustr = '\N{LATIN CAPITAL LETTER F}'
+        return prettyForm(ustr)
+
+    def _latex(self, printer, *args):
+        return r'\mathcal{F}'
+
+
+class TensorProductHilbertSpace(HilbertSpace):
+    """A tensor product of Hilbert spaces [1]_.
+
+    The tensor product between Hilbert spaces is represented by the
+    operator ``*`` Products of the same Hilbert space will be combined into
+    tensor powers.
+
+    A ``TensorProductHilbertSpace`` object takes in an arbitrary number of
+    ``HilbertSpace`` objects as its arguments. In addition, multiplication of
+    ``HilbertSpace`` objects will automatically return this tensor product
+    object.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.hilbert import ComplexSpace, FockSpace
+    >>> from sympy import symbols
+
+    >>> c = ComplexSpace(2)
+    >>> f = FockSpace()
+    >>> hs = c*f
+    >>> hs
+    C(2)*F
+    >>> hs.dimension
+    oo
+    >>> hs.spaces
+    (C(2), F)
+
+    >>> c1 = ComplexSpace(2)
+    >>> n = symbols('n')
+    >>> c2 = ComplexSpace(n)
+    >>> hs = c1*c2
+    >>> hs
+    C(2)*C(n)
+    >>> hs.dimension
+    2*n
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hilbert_space#Tensor_products
+    """
+
+    def __new__(cls, *args):
+        r = cls.eval(args)
+        if isinstance(r, Basic):
+            return r
+        obj = Basic.__new__(cls, *args)
+        return obj
+
+    @classmethod
+    def eval(cls, args):
+        """Evaluates the direct product."""
+        new_args = []
+        recall = False
+        #flatten arguments
+        for arg in args:
+            if isinstance(arg, TensorProductHilbertSpace):
+                new_args.extend(arg.args)
+                recall = True
+            elif isinstance(arg, (HilbertSpace, TensorPowerHilbertSpace)):
+                new_args.append(arg)
+            else:
+                raise TypeError('Hilbert spaces can only be multiplied by \
+                other Hilbert spaces: %r' % arg)
+        #combine like arguments into direct powers
+        comb_args = []
+        prev_arg = None
+        for new_arg in new_args:
+            if prev_arg is not None:
+                if isinstance(new_arg, TensorPowerHilbertSpace) and \
+                    isinstance(prev_arg, TensorPowerHilbertSpace) and \
+                        new_arg.base == prev_arg.base:
+                    prev_arg = new_arg.base**(new_arg.exp + prev_arg.exp)
+                elif isinstance(new_arg, TensorPowerHilbertSpace) and \
+                        new_arg.base == prev_arg:
+                    prev_arg = prev_arg**(new_arg.exp + 1)
+                elif isinstance(prev_arg, TensorPowerHilbertSpace) and \
+                        new_arg == prev_arg.base:
+                    prev_arg = new_arg**(prev_arg.exp + 1)
+                elif new_arg == prev_arg:
+                    prev_arg = new_arg**2
+                else:
+                    comb_args.append(prev_arg)
+                    prev_arg = new_arg
+            elif prev_arg is None:
+                prev_arg = new_arg
+        comb_args.append(prev_arg)
+        if recall:
+            return TensorProductHilbertSpace(*comb_args)
+        elif len(comb_args) == 1:
+            return TensorPowerHilbertSpace(comb_args[0].base, comb_args[0].exp)
+        else:
+            return None
+
+    @property
+    def dimension(self):
+        arg_list = [arg.dimension for arg in self.args]
+        if S.Infinity in arg_list:
+            return S.Infinity
+        else:
+            return reduce(lambda x, y: x*y, arg_list)
+
+    @property
+    def spaces(self):
+        """A tuple of the Hilbert spaces in this tensor product."""
+        return self.args
+
+    def _spaces_printer(self, printer, *args):
+        spaces_strs = []
+        for arg in self.args:
+            s = printer._print(arg, *args)
+            if isinstance(arg, DirectSumHilbertSpace):
+                s = '(%s)' % s
+            spaces_strs.append(s)
+        return spaces_strs
+
+    def _sympyrepr(self, printer, *args):
+        spaces_reprs = self._spaces_printer(printer, *args)
+        return "TensorProductHilbertSpace(%s)" % ','.join(spaces_reprs)
+
+    def _sympystr(self, printer, *args):
+        spaces_strs = self._spaces_printer(printer, *args)
+        return '*'.join(spaces_strs)
+
+    def _pretty(self, printer, *args):
+        length = len(self.args)
+        pform = printer._print('', *args)
+        for i in range(length):
+            next_pform = printer._print(self.args[i], *args)
+            if isinstance(self.args[i], (DirectSumHilbertSpace,
+                          TensorProductHilbertSpace)):
+                next_pform = prettyForm(
+                    *next_pform.parens(left='(', right=')')
+                )
+            pform = prettyForm(*pform.right(next_pform))
+            if i != length - 1:
+                if printer._use_unicode:
+                    pform = prettyForm(*pform.right(' ' + '\N{N-ARY CIRCLED TIMES OPERATOR}' + ' '))
+                else:
+                    pform = prettyForm(*pform.right(' x '))
+        return pform
+
+    def _latex(self, printer, *args):
+        length = len(self.args)
+        s = ''
+        for i in range(length):
+            arg_s = printer._print(self.args[i], *args)
+            if isinstance(self.args[i], (DirectSumHilbertSpace,
+                 TensorProductHilbertSpace)):
+                arg_s = r'\left(%s\right)' % arg_s
+            s = s + arg_s
+            if i != length - 1:
+                s = s + r'\otimes '
+        return s
+
+
+class DirectSumHilbertSpace(HilbertSpace):
+    """A direct sum of Hilbert spaces [1]_.
+
+    This class uses the ``+`` operator to represent direct sums between
+    different Hilbert spaces.
+
+    A ``DirectSumHilbertSpace`` object takes in an arbitrary number of
+    ``HilbertSpace`` objects as its arguments. Also, addition of
+    ``HilbertSpace`` objects will automatically return a direct sum object.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.hilbert import ComplexSpace, FockSpace
+
+    >>> c = ComplexSpace(2)
+    >>> f = FockSpace()
+    >>> hs = c+f
+    >>> hs
+    C(2)+F
+    >>> hs.dimension
+    oo
+    >>> list(hs.spaces)
+    [C(2), F]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hilbert_space#Direct_sums
+    """
+    def __new__(cls, *args):
+        r = cls.eval(args)
+        if isinstance(r, Basic):
+            return r
+        obj = Basic.__new__(cls, *args)
+        return obj
+
+    @classmethod
+    def eval(cls, args):
+        """Evaluates the direct product."""
+        new_args = []
+        recall = False
+        #flatten arguments
+        for arg in args:
+            if isinstance(arg, DirectSumHilbertSpace):
+                new_args.extend(arg.args)
+                recall = True
+            elif isinstance(arg, HilbertSpace):
+                new_args.append(arg)
+            else:
+                raise TypeError('Hilbert spaces can only be summed with other \
+                Hilbert spaces: %r' % arg)
+        if recall:
+            return DirectSumHilbertSpace(*new_args)
+        else:
+            return None
+
+    @property
+    def dimension(self):
+        arg_list = [arg.dimension for arg in self.args]
+        if S.Infinity in arg_list:
+            return S.Infinity
+        else:
+            return reduce(lambda x, y: x + y, arg_list)
+
+    @property
+    def spaces(self):
+        """A tuple of the Hilbert spaces in this direct sum."""
+        return self.args
+
+    def _sympyrepr(self, printer, *args):
+        spaces_reprs = [printer._print(arg, *args) for arg in self.args]
+        return "DirectSumHilbertSpace(%s)" % ','.join(spaces_reprs)
+
+    def _sympystr(self, printer, *args):
+        spaces_strs = [printer._print(arg, *args) for arg in self.args]
+        return '+'.join(spaces_strs)
+
+    def _pretty(self, printer, *args):
+        length = len(self.args)
+        pform = printer._print('', *args)
+        for i in range(length):
+            next_pform = printer._print(self.args[i], *args)
+            if isinstance(self.args[i], (DirectSumHilbertSpace,
+                          TensorProductHilbertSpace)):
+                next_pform = prettyForm(
+                    *next_pform.parens(left='(', right=')')
+                )
+            pform = prettyForm(*pform.right(next_pform))
+            if i != length - 1:
+                if printer._use_unicode:
+                    pform = prettyForm(*pform.right(' \N{CIRCLED PLUS} '))
+                else:
+                    pform = prettyForm(*pform.right(' + '))
+        return pform
+
+    def _latex(self, printer, *args):
+        length = len(self.args)
+        s = ''
+        for i in range(length):
+            arg_s = printer._print(self.args[i], *args)
+            if isinstance(self.args[i], (DirectSumHilbertSpace,
+                 TensorProductHilbertSpace)):
+                arg_s = r'\left(%s\right)' % arg_s
+            s = s + arg_s
+            if i != length - 1:
+                s = s + r'\oplus '
+        return s
+
+
+class TensorPowerHilbertSpace(HilbertSpace):
+    """An exponentiated Hilbert space [1]_.
+
+    Tensor powers (repeated tensor products) are represented by the
+    operator ``**`` Identical Hilbert spaces that are multiplied together
+    will be automatically combined into a single tensor power object.
+
+    Any Hilbert space, product, or sum may be raised to a tensor power. The
+    ``TensorPowerHilbertSpace`` takes two arguments: the Hilbert space; and the
+    tensor power (number).
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.hilbert import ComplexSpace, FockSpace
+    >>> from sympy import symbols
+
+    >>> n = symbols('n')
+    >>> c = ComplexSpace(2)
+    >>> hs = c**n
+    >>> hs
+    C(2)**n
+    >>> hs.dimension
+    2**n
+
+    >>> c = ComplexSpace(2)
+    >>> c*c
+    C(2)**2
+    >>> f = FockSpace()
+    >>> c*f*f
+    C(2)*F**2
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Hilbert_space#Tensor_products
+    """
+
+    def __new__(cls, *args):
+        r = cls.eval(args)
+        if isinstance(r, Basic):
+            return r
+        return Basic.__new__(cls, *r)
+
+    @classmethod
+    def eval(cls, args):
+        new_args = args[0], sympify(args[1])
+        exp = new_args[1]
+        #simplify hs**1 -> hs
+        if exp is S.One:
+            return args[0]
+        #simplify hs**0 -> 1
+        if exp is S.Zero:
+            return S.One
+        #check (and allow) for hs**(x+42+y...) case
+        if len(exp.atoms()) == 1:
+            if not (exp.is_Integer and exp >= 0 or exp.is_Symbol):
+                raise ValueError('Hilbert spaces can only be raised to \
+                positive integers or Symbols: %r' % exp)
+        else:
+            for power in exp.atoms():
+                if not (power.is_Integer or power.is_Symbol):
+                    raise ValueError('Tensor powers can only contain integers \
+                    or Symbols: %r' % power)
+        return new_args
+
+    @property
+    def base(self):
+        return self.args[0]
+
+    @property
+    def exp(self):
+        return self.args[1]
+
+    @property
+    def dimension(self):
+        if self.base.dimension is S.Infinity:
+            return S.Infinity
+        else:
+            return self.base.dimension**self.exp
+
+    def _sympyrepr(self, printer, *args):
+        return "TensorPowerHilbertSpace(%s,%s)" % (printer._print(self.base,
+        *args), printer._print(self.exp, *args))
+
+    def _sympystr(self, printer, *args):
+        return "%s**%s" % (printer._print(self.base, *args),
+        printer._print(self.exp, *args))
+
+    def _pretty(self, printer, *args):
+        pform_exp = printer._print(self.exp, *args)
+        if printer._use_unicode:
+            pform_exp = prettyForm(*pform_exp.left(prettyForm('\N{N-ARY CIRCLED TIMES OPERATOR}')))
+        else:
+            pform_exp = prettyForm(*pform_exp.left(prettyForm('x')))
+        pform_base = printer._print(self.base, *args)
+        return pform_base**pform_exp
+
+    def _latex(self, printer, *args):
+        base = printer._print(self.base, *args)
+        exp = printer._print(self.exp, *args)
+        return r'{%s}^{\otimes %s}' % (base, exp)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/identitysearch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/identitysearch.py
new file mode 100644
index 0000000000000000000000000000000000000000..9a178e9b808450b7ce91175600d6b393fc9797d6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/identitysearch.py
@@ -0,0 +1,853 @@
+from collections import deque
+from sympy.core.random import randint
+
+from sympy.external import import_module
+from sympy.core.basic import Basic
+from sympy.core.mul import Mul
+from sympy.core.numbers import Number, equal_valued
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.dagger import Dagger
+
+__all__ = [
+    # Public interfaces
+    'generate_gate_rules',
+    'generate_equivalent_ids',
+    'GateIdentity',
+    'bfs_identity_search',
+    'random_identity_search',
+
+    # "Private" functions
+    'is_scalar_sparse_matrix',
+    'is_scalar_nonsparse_matrix',
+    'is_degenerate',
+    'is_reducible',
+]
+
+np = import_module('numpy')
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+
+def is_scalar_sparse_matrix(circuit, nqubits, identity_only, eps=1e-11):
+    """Checks if a given scipy.sparse matrix is a scalar matrix.
+
+    A scalar matrix is such that B = bI, where B is the scalar
+    matrix, b is some scalar multiple, and I is the identity
+    matrix.  A scalar matrix would have only the element b along
+    it's main diagonal and zeroes elsewhere.
+
+    Parameters
+    ==========
+
+    circuit : Gate tuple
+        Sequence of quantum gates representing a quantum circuit
+    nqubits : int
+        Number of qubits in the circuit
+    identity_only : bool
+        Check for only identity matrices
+    eps : number
+        The tolerance value for zeroing out elements in the matrix.
+        Values in the range [-eps, +eps] will be changed to a zero.
+    """
+
+    if not np or not scipy:
+        pass
+
+    matrix = represent(Mul(*circuit), nqubits=nqubits,
+                       format='scipy.sparse')
+
+    # In some cases, represent returns a 1D scalar value in place
+    # of a multi-dimensional scalar matrix
+    if (isinstance(matrix, int)):
+        return matrix == 1 if identity_only else True
+
+    # If represent returns a matrix, check if the matrix is diagonal
+    # and if every item along the diagonal is the same
+    else:
+        # Due to floating pointing operations, must zero out
+        # elements that are "very" small in the dense matrix
+        # See parameter for default value.
+
+        # Get the ndarray version of the dense matrix
+        dense_matrix = matrix.todense().getA()
+        # Since complex values can't be compared, must split
+        # the matrix into real and imaginary components
+        # Find the real values in between -eps and eps
+        bool_real = np.logical_and(dense_matrix.real > -eps,
+                                   dense_matrix.real < eps)
+        # Find the imaginary values between -eps and eps
+        bool_imag = np.logical_and(dense_matrix.imag > -eps,
+                                   dense_matrix.imag < eps)
+        # Replaces values between -eps and eps with 0
+        corrected_real = np.where(bool_real, 0.0, dense_matrix.real)
+        corrected_imag = np.where(bool_imag, 0.0, dense_matrix.imag)
+        # Convert the matrix with real values into imaginary values
+        corrected_imag = corrected_imag * complex(1j)
+        # Recombine the real and imaginary components
+        corrected_dense = corrected_real + corrected_imag
+
+        # Check if it's diagonal
+        row_indices = corrected_dense.nonzero()[0]
+        col_indices = corrected_dense.nonzero()[1]
+        # Check if the rows indices and columns indices are the same
+        # If they match, then matrix only contains elements along diagonal
+        bool_indices = row_indices == col_indices
+        is_diagonal = bool_indices.all()
+
+        first_element = corrected_dense[0][0]
+        # If the first element is a zero, then can't rescale matrix
+        # and definitely not diagonal
+        if (first_element == 0.0 + 0.0j):
+            return False
+
+        # The dimensions of the dense matrix should still
+        # be 2^nqubits if there are elements all along the
+        # the main diagonal
+        trace_of_corrected = (corrected_dense/first_element).trace()
+        expected_trace = pow(2, nqubits)
+        has_correct_trace = trace_of_corrected == expected_trace
+
+        # If only looking for identity matrices
+        # first element must be a 1
+        real_is_one = abs(first_element.real - 1.0) < eps
+        imag_is_zero = abs(first_element.imag) < eps
+        is_one = real_is_one and imag_is_zero
+        is_identity = is_one if identity_only else True
+        return bool(is_diagonal and has_correct_trace and is_identity)
+
+
+def is_scalar_nonsparse_matrix(circuit, nqubits, identity_only, eps=None):
+    """Checks if a given circuit, in matrix form, is equivalent to
+    a scalar value.
+
+    Parameters
+    ==========
+
+    circuit : Gate tuple
+        Sequence of quantum gates representing a quantum circuit
+    nqubits : int
+        Number of qubits in the circuit
+    identity_only : bool
+        Check for only identity matrices
+    eps : number
+        This argument is ignored. It is just for signature compatibility with
+        is_scalar_sparse_matrix.
+
+    Note: Used in situations when is_scalar_sparse_matrix has bugs
+    """
+
+    matrix = represent(Mul(*circuit), nqubits=nqubits)
+
+    # In some cases, represent returns a 1D scalar value in place
+    # of a multi-dimensional scalar matrix
+    if (isinstance(matrix, Number)):
+        return matrix == 1 if identity_only else True
+
+    # If represent returns a matrix, check if the matrix is diagonal
+    # and if every item along the diagonal is the same
+    else:
+        # Added up the diagonal elements
+        matrix_trace = matrix.trace()
+        # Divide the trace by the first element in the matrix
+        # if matrix is not required to be the identity matrix
+        adjusted_matrix_trace = (matrix_trace/matrix[0]
+                                 if not identity_only
+                                 else matrix_trace)
+
+        is_identity = equal_valued(matrix[0], 1) if identity_only else True
+
+        has_correct_trace = adjusted_matrix_trace == pow(2, nqubits)
+
+        # The matrix is scalar if it's diagonal and the adjusted trace
+        # value is equal to 2^nqubits
+        return bool(
+            matrix.is_diagonal() and has_correct_trace and is_identity)
+
+if np and scipy:
+    is_scalar_matrix = is_scalar_sparse_matrix
+else:
+    is_scalar_matrix = is_scalar_nonsparse_matrix
+
+
+def _get_min_qubits(a_gate):
+    if isinstance(a_gate, Pow):
+        return a_gate.base.min_qubits
+    else:
+        return a_gate.min_qubits
+
+
+def ll_op(left, right):
+    """Perform a LL operation.
+
+    A LL operation multiplies both left and right circuits
+    with the dagger of the left circuit's leftmost gate, and
+    the dagger is multiplied on the left side of both circuits.
+
+    If a LL is possible, it returns the new gate rule as a
+    2-tuple (LHS, RHS), where LHS is the left circuit and
+    and RHS is the right circuit of the new rule.
+    If a LL is not possible, None is returned.
+
+    Parameters
+    ==========
+
+    left : Gate tuple
+        The left circuit of a gate rule expression.
+    right : Gate tuple
+        The right circuit of a gate rule expression.
+
+    Examples
+    ========
+
+    Generate a new gate rule using a LL operation:
+
+    >>> from sympy.physics.quantum.identitysearch import ll_op
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> ll_op((x, y, z), ())
+    ((Y(0), Z(0)), (X(0),))
+
+    >>> ll_op((y, z), (x,))
+    ((Z(0),), (Y(0), X(0)))
+    """
+
+    if (len(left) > 0):
+        ll_gate = left[0]
+        ll_gate_is_unitary = is_scalar_matrix(
+            (Dagger(ll_gate), ll_gate), _get_min_qubits(ll_gate), True)
+
+    if (len(left) > 0 and ll_gate_is_unitary):
+        # Get the new left side w/o the leftmost gate
+        new_left = left[1:len(left)]
+        # Add the leftmost gate to the left position on the right side
+        new_right = (Dagger(ll_gate),) + right
+        # Return the new gate rule
+        return (new_left, new_right)
+
+    return None
+
+
+def lr_op(left, right):
+    """Perform a LR operation.
+
+    A LR operation multiplies both left and right circuits
+    with the dagger of the left circuit's rightmost gate, and
+    the dagger is multiplied on the right side of both circuits.
+
+    If a LR is possible, it returns the new gate rule as a
+    2-tuple (LHS, RHS), where LHS is the left circuit and
+    and RHS is the right circuit of the new rule.
+    If a LR is not possible, None is returned.
+
+    Parameters
+    ==========
+
+    left : Gate tuple
+        The left circuit of a gate rule expression.
+    right : Gate tuple
+        The right circuit of a gate rule expression.
+
+    Examples
+    ========
+
+    Generate a new gate rule using a LR operation:
+
+    >>> from sympy.physics.quantum.identitysearch import lr_op
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> lr_op((x, y, z), ())
+    ((X(0), Y(0)), (Z(0),))
+
+    >>> lr_op((x, y), (z,))
+    ((X(0),), (Z(0), Y(0)))
+    """
+
+    if (len(left) > 0):
+        lr_gate = left[len(left) - 1]
+        lr_gate_is_unitary = is_scalar_matrix(
+            (Dagger(lr_gate), lr_gate), _get_min_qubits(lr_gate), True)
+
+    if (len(left) > 0 and lr_gate_is_unitary):
+        # Get the new left side w/o the rightmost gate
+        new_left = left[0:len(left) - 1]
+        # Add the rightmost gate to the right position on the right side
+        new_right = right + (Dagger(lr_gate),)
+        # Return the new gate rule
+        return (new_left, new_right)
+
+    return None
+
+
+def rl_op(left, right):
+    """Perform a RL operation.
+
+    A RL operation multiplies both left and right circuits
+    with the dagger of the right circuit's leftmost gate, and
+    the dagger is multiplied on the left side of both circuits.
+
+    If a RL is possible, it returns the new gate rule as a
+    2-tuple (LHS, RHS), where LHS is the left circuit and
+    and RHS is the right circuit of the new rule.
+    If a RL is not possible, None is returned.
+
+    Parameters
+    ==========
+
+    left : Gate tuple
+        The left circuit of a gate rule expression.
+    right : Gate tuple
+        The right circuit of a gate rule expression.
+
+    Examples
+    ========
+
+    Generate a new gate rule using a RL operation:
+
+    >>> from sympy.physics.quantum.identitysearch import rl_op
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> rl_op((x,), (y, z))
+    ((Y(0), X(0)), (Z(0),))
+
+    >>> rl_op((x, y), (z,))
+    ((Z(0), X(0), Y(0)), ())
+    """
+
+    if (len(right) > 0):
+        rl_gate = right[0]
+        rl_gate_is_unitary = is_scalar_matrix(
+            (Dagger(rl_gate), rl_gate), _get_min_qubits(rl_gate), True)
+
+    if (len(right) > 0 and rl_gate_is_unitary):
+        # Get the new right side w/o the leftmost gate
+        new_right = right[1:len(right)]
+        # Add the leftmost gate to the left position on the left side
+        new_left = (Dagger(rl_gate),) + left
+        # Return the new gate rule
+        return (new_left, new_right)
+
+    return None
+
+
+def rr_op(left, right):
+    """Perform a RR operation.
+
+    A RR operation multiplies both left and right circuits
+    with the dagger of the right circuit's rightmost gate, and
+    the dagger is multiplied on the right side of both circuits.
+
+    If a RR is possible, it returns the new gate rule as a
+    2-tuple (LHS, RHS), where LHS is the left circuit and
+    and RHS is the right circuit of the new rule.
+    If a RR is not possible, None is returned.
+
+    Parameters
+    ==========
+
+    left : Gate tuple
+        The left circuit of a gate rule expression.
+    right : Gate tuple
+        The right circuit of a gate rule expression.
+
+    Examples
+    ========
+
+    Generate a new gate rule using a RR operation:
+
+    >>> from sympy.physics.quantum.identitysearch import rr_op
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> rr_op((x, y), (z,))
+    ((X(0), Y(0), Z(0)), ())
+
+    >>> rr_op((x,), (y, z))
+    ((X(0), Z(0)), (Y(0),))
+    """
+
+    if (len(right) > 0):
+        rr_gate = right[len(right) - 1]
+        rr_gate_is_unitary = is_scalar_matrix(
+            (Dagger(rr_gate), rr_gate), _get_min_qubits(rr_gate), True)
+
+    if (len(right) > 0 and rr_gate_is_unitary):
+        # Get the new right side w/o the rightmost gate
+        new_right = right[0:len(right) - 1]
+        # Add the rightmost gate to the right position on the right side
+        new_left = left + (Dagger(rr_gate),)
+        # Return the new gate rule
+        return (new_left, new_right)
+
+    return None
+
+
+def generate_gate_rules(gate_seq, return_as_muls=False):
+    """Returns a set of gate rules.  Each gate rules is represented
+    as a 2-tuple of tuples or Muls.  An empty tuple represents an arbitrary
+    scalar value.
+
+    This function uses the four operations (LL, LR, RL, RR)
+    to generate the gate rules.
+
+    A gate rule is an expression such as ABC = D or AB = CD, where
+    A, B, C, and D are gates.  Each value on either side of the
+    equal sign represents a circuit.  The four operations allow
+    one to find a set of equivalent circuits from a gate identity.
+    The letters denoting the operation tell the user what
+    activities to perform on each expression.  The first letter
+    indicates which side of the equal sign to focus on.  The
+    second letter indicates which gate to focus on given the
+    side.  Once this information is determined, the inverse
+    of the gate is multiplied on both circuits to create a new
+    gate rule.
+
+    For example, given the identity, ABCD = 1, a LL operation
+    means look at the left value and multiply both left sides by the
+    inverse of the leftmost gate A.  If A is Hermitian, the inverse
+    of A is still A.  The resulting new rule is BCD = A.
+
+    The following is a summary of the four operations.  Assume
+    that in the examples, all gates are Hermitian.
+
+        LL : left circuit, left multiply
+             ABCD = E -> AABCD = AE -> BCD = AE
+        LR : left circuit, right multiply
+             ABCD = E -> ABCDD = ED -> ABC = ED
+        RL : right circuit, left multiply
+             ABC = ED -> EABC = EED -> EABC = D
+        RR : right circuit, right multiply
+             AB = CD -> ABD = CDD -> ABD = C
+
+    The number of gate rules generated is n*(n+1), where n
+    is the number of gates in the sequence (unproven).
+
+    Parameters
+    ==========
+
+    gate_seq : Gate tuple, Mul, or Number
+        A variable length tuple or Mul of Gates whose product is equal to
+        a scalar matrix
+    return_as_muls : bool
+        True to return a set of Muls; False to return a set of tuples
+
+    Examples
+    ========
+
+    Find the gate rules of the current circuit using tuples:
+
+    >>> from sympy.physics.quantum.identitysearch import generate_gate_rules
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> generate_gate_rules((x, x))
+    {((X(0),), (X(0),)), ((X(0), X(0)), ())}
+
+    >>> generate_gate_rules((x, y, z))
+    {((), (X(0), Z(0), Y(0))), ((), (Y(0), X(0), Z(0))),
+     ((), (Z(0), Y(0), X(0))), ((X(0),), (Z(0), Y(0))),
+     ((Y(0),), (X(0), Z(0))), ((Z(0),), (Y(0), X(0))),
+     ((X(0), Y(0)), (Z(0),)), ((Y(0), Z(0)), (X(0),)),
+     ((Z(0), X(0)), (Y(0),)), ((X(0), Y(0), Z(0)), ()),
+     ((Y(0), Z(0), X(0)), ()), ((Z(0), X(0), Y(0)), ())}
+
+    Find the gate rules of the current circuit using Muls:
+
+    >>> generate_gate_rules(x*x, return_as_muls=True)
+    {(1, 1)}
+
+    >>> generate_gate_rules(x*y*z, return_as_muls=True)
+    {(1, X(0)*Z(0)*Y(0)), (1, Y(0)*X(0)*Z(0)),
+     (1, Z(0)*Y(0)*X(0)), (X(0)*Y(0), Z(0)),
+     (Y(0)*Z(0), X(0)), (Z(0)*X(0), Y(0)),
+     (X(0)*Y(0)*Z(0), 1), (Y(0)*Z(0)*X(0), 1),
+     (Z(0)*X(0)*Y(0), 1), (X(0), Z(0)*Y(0)),
+     (Y(0), X(0)*Z(0)), (Z(0), Y(0)*X(0))}
+    """
+
+    if isinstance(gate_seq, Number):
+        if return_as_muls:
+            return {(S.One, S.One)}
+        else:
+            return {((), ())}
+
+    elif isinstance(gate_seq, Mul):
+        gate_seq = gate_seq.args
+
+    # Each item in queue is a 3-tuple:
+    #     i)   first item is the left side of an equality
+    #    ii)   second item is the right side of an equality
+    #   iii)   third item is the number of operations performed
+    # The argument, gate_seq, will start on the left side, and
+    # the right side will be empty, implying the presence of an
+    # identity.
+    queue = deque()
+    # A set of gate rules
+    rules = set()
+    # Maximum number of operations to perform
+    max_ops = len(gate_seq)
+
+    def process_new_rule(new_rule, ops):
+        if new_rule is not None:
+            new_left, new_right = new_rule
+
+            if new_rule not in rules and (new_right, new_left) not in rules:
+                rules.add(new_rule)
+            # If haven't reached the max limit on operations
+            if ops + 1 < max_ops:
+                queue.append(new_rule + (ops + 1,))
+
+    queue.append((gate_seq, (), 0))
+    rules.add((gate_seq, ()))
+
+    while len(queue) > 0:
+        left, right, ops = queue.popleft()
+
+        # Do a LL
+        new_rule = ll_op(left, right)
+        process_new_rule(new_rule, ops)
+        # Do a LR
+        new_rule = lr_op(left, right)
+        process_new_rule(new_rule, ops)
+        # Do a RL
+        new_rule = rl_op(left, right)
+        process_new_rule(new_rule, ops)
+        # Do a RR
+        new_rule = rr_op(left, right)
+        process_new_rule(new_rule, ops)
+
+    if return_as_muls:
+        # Convert each rule as tuples into a rule as muls
+        mul_rules = set()
+        for rule in rules:
+            left, right = rule
+            mul_rules.add((Mul(*left), Mul(*right)))
+
+        rules = mul_rules
+
+    return rules
+
+
+def generate_equivalent_ids(gate_seq, return_as_muls=False):
+    """Returns a set of equivalent gate identities.
+
+    A gate identity is a quantum circuit such that the product
+    of the gates in the circuit is equal to a scalar value.
+    For example, XYZ = i, where X, Y, Z are the Pauli gates and
+    i is the imaginary value, is considered a gate identity.
+
+    This function uses the four operations (LL, LR, RL, RR)
+    to generate the gate rules and, subsequently, to locate equivalent
+    gate identities.
+
+    Note that all equivalent identities are reachable in n operations
+    from the starting gate identity, where n is the number of gates
+    in the sequence.
+
+    The max number of gate identities is 2n, where n is the number
+    of gates in the sequence (unproven).
+
+    Parameters
+    ==========
+
+    gate_seq : Gate tuple, Mul, or Number
+        A variable length tuple or Mul of Gates whose product is equal to
+        a scalar matrix.
+    return_as_muls: bool
+        True to return as Muls; False to return as tuples
+
+    Examples
+    ========
+
+    Find equivalent gate identities from the current circuit with tuples:
+
+    >>> from sympy.physics.quantum.identitysearch import generate_equivalent_ids
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> generate_equivalent_ids((x, x))
+    {(X(0), X(0))}
+
+    >>> generate_equivalent_ids((x, y, z))
+    {(X(0), Y(0), Z(0)), (X(0), Z(0), Y(0)), (Y(0), X(0), Z(0)),
+     (Y(0), Z(0), X(0)), (Z(0), X(0), Y(0)), (Z(0), Y(0), X(0))}
+
+    Find equivalent gate identities from the current circuit with Muls:
+
+    >>> generate_equivalent_ids(x*x, return_as_muls=True)
+    {1}
+
+    >>> generate_equivalent_ids(x*y*z, return_as_muls=True)
+    {X(0)*Y(0)*Z(0), X(0)*Z(0)*Y(0), Y(0)*X(0)*Z(0),
+     Y(0)*Z(0)*X(0), Z(0)*X(0)*Y(0), Z(0)*Y(0)*X(0)}
+    """
+
+    if isinstance(gate_seq, Number):
+        return {S.One}
+    elif isinstance(gate_seq, Mul):
+        gate_seq = gate_seq.args
+
+    # Filter through the gate rules and keep the rules
+    # with an empty tuple either on the left or right side
+
+    # A set of equivalent gate identities
+    eq_ids = set()
+
+    gate_rules = generate_gate_rules(gate_seq)
+    for rule in gate_rules:
+        l, r = rule
+        if l == ():
+            eq_ids.add(r)
+        elif r == ():
+            eq_ids.add(l)
+
+    if return_as_muls:
+        convert_to_mul = lambda id_seq: Mul(*id_seq)
+        eq_ids = set(map(convert_to_mul, eq_ids))
+
+    return eq_ids
+
+
+class GateIdentity(Basic):
+    """Wrapper class for circuits that reduce to a scalar value.
+
+    A gate identity is a quantum circuit such that the product
+    of the gates in the circuit is equal to a scalar value.
+    For example, XYZ = i, where X, Y, Z are the Pauli gates and
+    i is the imaginary value, is considered a gate identity.
+
+    Parameters
+    ==========
+
+    args : Gate tuple
+        A variable length tuple of Gates that form an identity.
+
+    Examples
+    ========
+
+    Create a GateIdentity and look at its attributes:
+
+    >>> from sympy.physics.quantum.identitysearch import GateIdentity
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> an_identity = GateIdentity(x, y, z)
+    >>> an_identity.circuit
+    X(0)*Y(0)*Z(0)
+
+    >>> an_identity.equivalent_ids
+    {(X(0), Y(0), Z(0)), (X(0), Z(0), Y(0)), (Y(0), X(0), Z(0)),
+     (Y(0), Z(0), X(0)), (Z(0), X(0), Y(0)), (Z(0), Y(0), X(0))}
+    """
+
+    def __new__(cls, *args):
+        # args should be a tuple - a variable length argument list
+        obj = Basic.__new__(cls, *args)
+        obj._circuit = Mul(*args)
+        obj._rules = generate_gate_rules(args)
+        obj._eq_ids = generate_equivalent_ids(args)
+
+        return obj
+
+    @property
+    def circuit(self):
+        return self._circuit
+
+    @property
+    def gate_rules(self):
+        return self._rules
+
+    @property
+    def equivalent_ids(self):
+        return self._eq_ids
+
+    @property
+    def sequence(self):
+        return self.args
+
+    def __str__(self):
+        """Returns the string of gates in a tuple."""
+        return str(self.circuit)
+
+
+def is_degenerate(identity_set, gate_identity):
+    """Checks if a gate identity is a permutation of another identity.
+
+    Parameters
+    ==========
+
+    identity_set : set
+        A Python set with GateIdentity objects.
+    gate_identity : GateIdentity
+        The GateIdentity to check for existence in the set.
+
+    Examples
+    ========
+
+    Check if the identity is a permutation of another identity:
+
+    >>> from sympy.physics.quantum.identitysearch import (
+    ...     GateIdentity, is_degenerate)
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> an_identity = GateIdentity(x, y, z)
+    >>> id_set = {an_identity}
+    >>> another_id = (y, z, x)
+    >>> is_degenerate(id_set, another_id)
+    True
+
+    >>> another_id = (x, x)
+    >>> is_degenerate(id_set, another_id)
+    False
+    """
+
+    # For now, just iteratively go through the set and check if the current
+    # gate_identity is a permutation of an identity in the set
+    for an_id in identity_set:
+        if (gate_identity in an_id.equivalent_ids):
+            return True
+    return False
+
+
+def is_reducible(circuit, nqubits, begin, end):
+    """Determines if a circuit is reducible by checking
+    if its subcircuits are scalar values.
+
+    Parameters
+    ==========
+
+    circuit : Gate tuple
+        A tuple of Gates representing a circuit.  The circuit to check
+        if a gate identity is contained in a subcircuit.
+    nqubits : int
+        The number of qubits the circuit operates on.
+    begin : int
+        The leftmost gate in the circuit to include in a subcircuit.
+    end : int
+        The rightmost gate in the circuit to include in a subcircuit.
+
+    Examples
+    ========
+
+    Check if the circuit can be reduced:
+
+    >>> from sympy.physics.quantum.identitysearch import is_reducible
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> is_reducible((x, y, z), 1, 0, 3)
+    True
+
+    Check if an interval in the circuit can be reduced:
+
+    >>> is_reducible((x, y, z), 1, 1, 3)
+    False
+
+    >>> is_reducible((x, y, y), 1, 1, 3)
+    True
+    """
+
+    current_circuit = ()
+    # Start from the gate at "end" and go down to almost the gate at "begin"
+    for ndx in reversed(range(begin, end)):
+        next_gate = circuit[ndx]
+        current_circuit = (next_gate,) + current_circuit
+
+        # If a circuit as a matrix is equivalent to a scalar value
+        if (is_scalar_matrix(current_circuit, nqubits, False)):
+            return True
+
+    return False
+
+
+def bfs_identity_search(gate_list, nqubits, max_depth=None,
+       identity_only=False):
+    """Constructs a set of gate identities from the list of possible gates.
+
+    Performs a breadth first search over the space of gate identities.
+    This allows the finding of the shortest gate identities first.
+
+    Parameters
+    ==========
+
+    gate_list : list, Gate
+        A list of Gates from which to search for gate identities.
+    nqubits : int
+        The number of qubits the quantum circuit operates on.
+    max_depth : int
+        The longest quantum circuit to construct from gate_list.
+    identity_only : bool
+        True to search for gate identities that reduce to identity;
+        False to search for gate identities that reduce to a scalar.
+
+    Examples
+    ========
+
+    Find a list of gate identities:
+
+    >>> from sympy.physics.quantum.identitysearch import bfs_identity_search
+    >>> from sympy.physics.quantum.gate import X, Y, Z
+    >>> x = X(0); y = Y(0); z = Z(0)
+    >>> bfs_identity_search([x], 1, max_depth=2)
+    {GateIdentity(X(0), X(0))}
+
+    >>> bfs_identity_search([x, y, z], 1)
+    {GateIdentity(X(0), X(0)), GateIdentity(Y(0), Y(0)),
+     GateIdentity(Z(0), Z(0)), GateIdentity(X(0), Y(0), Z(0))}
+
+    Find a list of identities that only equal to 1:
+
+    >>> bfs_identity_search([x, y, z], 1, identity_only=True)
+    {GateIdentity(X(0), X(0)), GateIdentity(Y(0), Y(0)),
+     GateIdentity(Z(0), Z(0))}
+    """
+
+    if max_depth is None or max_depth <= 0:
+        max_depth = len(gate_list)
+
+    id_only = identity_only
+
+    # Start with an empty sequence (implicitly contains an IdentityGate)
+    queue = deque([()])
+
+    # Create an empty set of gate identities
+    ids = set()
+
+    # Begin searching for gate identities in given space.
+    while (len(queue) > 0):
+        current_circuit = queue.popleft()
+
+        for next_gate in gate_list:
+            new_circuit = current_circuit + (next_gate,)
+
+            # Determines if a (strict) subcircuit is a scalar matrix
+            circuit_reducible = is_reducible(new_circuit, nqubits,
+                                             1, len(new_circuit))
+
+            # In many cases when the matrix is a scalar value,
+            # the evaluated matrix will actually be an integer
+            if (is_scalar_matrix(new_circuit, nqubits, id_only) and
+                not is_degenerate(ids, new_circuit) and
+                    not circuit_reducible):
+                ids.add(GateIdentity(*new_circuit))
+
+            elif (len(new_circuit) < max_depth and
+                  not circuit_reducible):
+                queue.append(new_circuit)
+
+    return ids
+
+
+def random_identity_search(gate_list, numgates, nqubits):
+    """Randomly selects numgates from gate_list and checks if it is
+    a gate identity.
+
+    If the circuit is a gate identity, the circuit is returned;
+    Otherwise, None is returned.
+    """
+
+    gate_size = len(gate_list)
+    circuit = ()
+
+    for i in range(numgates):
+        next_gate = gate_list[randint(0, gate_size - 1)]
+        circuit = circuit + (next_gate,)
+
+    is_scalar = is_scalar_matrix(circuit, nqubits, False)
+
+    return circuit if is_scalar else None
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/innerproduct.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/innerproduct.py
new file mode 100644
index 0000000000000000000000000000000000000000..11fed882b6068a4df5a787ff90eee5392f97447a
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/innerproduct.py
@@ -0,0 +1,138 @@
+"""Symbolic inner product."""
+
+from sympy.core.expr import Expr
+from sympy.core.kind import NumberKind
+from sympy.functions.elementary.complexes import conjugate
+from sympy.printing.pretty.stringpict import prettyForm
+from sympy.physics.quantum.dagger import Dagger
+
+
+__all__ = [
+    'InnerProduct'
+]
+
+
+# InnerProduct is not an QExpr because it is really just a regular commutative
+# number. We have gone back and forth about this, but we gain a lot by having
+# it subclass Expr. The main challenges were getting Dagger to work
+# (we use _eval_conjugate) and represent (we can use atoms and subs). Having
+# it be an Expr, mean that there are no commutative QExpr subclasses,
+# which simplifies the design of everything.
+
+class InnerProduct(Expr):
+    """An unevaluated inner product between a Bra and a Ket [1].
+
+    Parameters
+    ==========
+
+    bra : BraBase or subclass
+        The bra on the left side of the inner product.
+    ket : KetBase or subclass
+        The ket on the right side of the inner product.
+
+    Examples
+    ========
+
+    Create an InnerProduct and check its properties:
+
+        >>> from sympy.physics.quantum import Bra, Ket
+        >>> b = Bra('b')
+        >>> k = Ket('k')
+        >>> ip = b*k
+        >>> ip
+        
+        >>> ip.bra
+        >> ip.ket
+        |k>
+
+    In quantum expressions, inner products will be automatically
+    identified and created::
+
+        >>> b*k
+        
+
+    In more complex expressions, where there is ambiguity in whether inner or
+    outer products should be created, inner products have high priority::
+
+        >>> k*b*k*b
+        *|k> moved to the left of the expression
+    because inner products are commutative complex numbers.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Inner_product
+    """
+
+    kind = NumberKind
+
+    is_complex = True
+
+    def __new__(cls, bra, ket):
+        # Keep the import of BraBase and KetBase here to avoid problems
+        # with circular imports.
+        from sympy.physics.quantum.state import KetBase, BraBase
+        if not isinstance(ket, KetBase):
+            raise TypeError('KetBase subclass expected, got: %r' % ket)
+        if not isinstance(bra, BraBase):
+            raise TypeError('BraBase subclass expected, got: %r' % ket)
+        obj = Expr.__new__(cls, bra, ket)
+        return obj
+
+    @property
+    def bra(self):
+        return self.args[0]
+
+    @property
+    def ket(self):
+        return self.args[1]
+
+    def _eval_conjugate(self):
+        return InnerProduct(Dagger(self.ket), Dagger(self.bra))
+
+    def _sympyrepr(self, printer, *args):
+        return '%s(%s,%s)' % (self.__class__.__name__,
+            printer._print(self.bra, *args), printer._print(self.ket, *args))
+
+    def _sympystr(self, printer, *args):
+        sbra = printer._print(self.bra)
+        sket = printer._print(self.ket)
+        return '%s|%s' % (sbra[:-1], sket[1:])
+
+    def _pretty(self, printer, *args):
+        # Print state contents
+        bra = self.bra._print_contents_pretty(printer, *args)
+        ket = self.ket._print_contents_pretty(printer, *args)
+        # Print brackets
+        height = max(bra.height(), ket.height())
+        use_unicode = printer._use_unicode
+        lbracket, _ = self.bra._pretty_brackets(height, use_unicode)
+        cbracket, rbracket = self.ket._pretty_brackets(height, use_unicode)
+        # Build innerproduct
+        pform = prettyForm(*bra.left(lbracket))
+        pform = prettyForm(*pform.right(cbracket))
+        pform = prettyForm(*pform.right(ket))
+        pform = prettyForm(*pform.right(rbracket))
+        return pform
+
+    def _latex(self, printer, *args):
+        bra_label = self.bra._print_contents_latex(printer, *args)
+        ket = printer._print(self.ket, *args)
+        return r'\left\langle %s \right. %s' % (bra_label, ket)
+
+    def doit(self, **hints):
+        try:
+            r = self.ket._eval_innerproduct(self.bra, **hints)
+        except NotImplementedError:
+            try:
+                r = conjugate(
+                    self.bra.dual._eval_innerproduct(self.ket.dual, **hints)
+                )
+            except NotImplementedError:
+                r = None
+        if r is not None:
+            return r
+        return self
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/kind.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/kind.py
new file mode 100644
index 0000000000000000000000000000000000000000..14b5bd2c7b0c87f49dc7e6dc9c1b492fbfad6d56
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/kind.py
@@ -0,0 +1,103 @@
+"""Kinds for Operators, Bras, and Kets.
+
+This module defines kinds for operators, bras, and kets. These are useful
+in various places in ``sympy.physics.quantum`` as you often want to know
+what the kind is of a compound expression. For example, if you multiply
+an operator, bra, or ket by a number, you get back another operator, bra,
+or ket - even though if you did an ``isinstance`` check you would find that
+you have a ``Mul`` instead. The kind system is meant to give you a quick
+way of determining how a compound expression behaves in terms of lower
+level kinds.
+
+The resolution calculation of kinds for compound expressions can be found
+either in container classes or in functions that are registered with
+kind dispatchers.
+"""
+
+from sympy.core.mul import Mul
+from sympy.core.kind import Kind, _NumberKind
+
+
+__all__ = [
+    '_KetKind',
+    'KetKind',
+    '_BraKind',
+    'BraKind',
+    '_OperatorKind',
+    'OperatorKind',
+]
+
+
+class _KetKind(Kind):
+    """A kind for quantum kets."""
+
+    def __new__(cls):
+        obj = super().__new__(cls)
+        return obj
+
+    def __repr__(self):
+        return "KetKind"
+
+# Create an instance as many situations need this.
+KetKind = _KetKind()
+
+
+class _BraKind(Kind):
+    """A kind for quantum bras."""
+
+    def __new__(cls):
+        obj = super().__new__(cls)
+        return obj
+
+    def __repr__(self):
+        return "BraKind"
+
+# Create an instance as many situations need this.
+BraKind = _BraKind()
+
+
+from sympy.core.kind import Kind
+
+class _OperatorKind(Kind):
+    """A kind for quantum operators."""
+
+    def __new__(cls):
+        obj = super().__new__(cls)
+        return obj
+
+    def __repr__(self):
+        return "OperatorKind"
+
+# Create an instance as many situations need this.
+OperatorKind = _OperatorKind()
+
+
+#-----------------------------------------------------------------------------
+# Kind resolution.
+#-----------------------------------------------------------------------------
+
+# Note: We can't currently add kind dispatchers for the following combinations
+#       as the Mul._kind_dispatcher is set to commutative and will also
+#       register the opposite order, which isn't correct for these pairs:
+#
+# 1. (_OperatorKind, _KetKind)
+# 2. (_BraKind, _OperatorKind)
+# 3. (_BraKind, _KetKind)
+
+
+@Mul._kind_dispatcher.register(_NumberKind, _KetKind)
+def _mul_number_ket_kind(lhs, rhs):
+    """Perform the kind calculation of NumberKind*KetKind -> KetKind."""
+    return KetKind
+
+
+@Mul._kind_dispatcher.register(_NumberKind, _BraKind)
+def _mul_number_bra_kind(lhs, rhs):
+    """Perform the kind calculation of NumberKind*BraKind -> BraKind."""
+    return BraKind
+
+
+@Mul._kind_dispatcher.register(_NumberKind, _OperatorKind)
+def _mul_operator_kind(lhs, rhs):
+    """Perform the kind calculation of NumberKind*OperatorKind -> OperatorKind."""
+    return OperatorKind
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/matrixcache.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/matrixcache.py
new file mode 100644
index 0000000000000000000000000000000000000000..3cfab3c3490c909966d8a56af395ffa578724ea7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/matrixcache.py
@@ -0,0 +1,103 @@
+"""A cache for storing small matrices in multiple formats."""
+
+from sympy.core.numbers import (I, Rational, pi)
+from sympy.core.power import Pow
+from sympy.functions.elementary.exponential import exp
+from sympy.matrices.dense import Matrix
+
+from sympy.physics.quantum.matrixutils import (
+    to_sympy, to_numpy, to_scipy_sparse
+)
+
+
+class MatrixCache:
+    """A cache for small matrices in different formats.
+
+    This class takes small matrices in the standard ``sympy.Matrix`` format,
+    and then converts these to both ``numpy.matrix`` and
+    ``scipy.sparse.csr_matrix`` matrices. These matrices are then stored for
+    future recovery.
+    """
+
+    def __init__(self, dtype='complex'):
+        self._cache = {}
+        self.dtype = dtype
+
+    def cache_matrix(self, name, m):
+        """Cache a matrix by its name.
+
+        Parameters
+        ----------
+        name : str
+            A descriptive name for the matrix, like "identity2".
+        m : list of lists
+            The raw matrix data as a SymPy Matrix.
+        """
+        try:
+            self._sympy_matrix(name, m)
+        except ImportError:
+            pass
+        try:
+            self._numpy_matrix(name, m)
+        except ImportError:
+            pass
+        try:
+            self._scipy_sparse_matrix(name, m)
+        except ImportError:
+            pass
+
+    def get_matrix(self, name, format):
+        """Get a cached matrix by name and format.
+
+        Parameters
+        ----------
+        name : str
+            A descriptive name for the matrix, like "identity2".
+        format : str
+            The format desired ('sympy', 'numpy', 'scipy.sparse')
+        """
+        m = self._cache.get((name, format))
+        if m is not None:
+            return m
+        raise NotImplementedError(
+            'Matrix with name %s and format %s is not available.' %
+            (name, format)
+        )
+
+    def _store_matrix(self, name, format, m):
+        self._cache[(name, format)] = m
+
+    def _sympy_matrix(self, name, m):
+        self._store_matrix(name, 'sympy', to_sympy(m))
+
+    def _numpy_matrix(self, name, m):
+        m = to_numpy(m, dtype=self.dtype)
+        self._store_matrix(name, 'numpy', m)
+
+    def _scipy_sparse_matrix(self, name, m):
+        # TODO: explore different sparse formats. But sparse.kron will use
+        # coo in most cases, so we use that here.
+        m = to_scipy_sparse(m, dtype=self.dtype)
+        self._store_matrix(name, 'scipy.sparse', m)
+
+
+sqrt2_inv = Pow(2, Rational(-1, 2), evaluate=False)
+
+# Save the common matrices that we will need
+matrix_cache = MatrixCache()
+matrix_cache.cache_matrix('eye2', Matrix([[1, 0], [0, 1]]))
+matrix_cache.cache_matrix('op11', Matrix([[0, 0], [0, 1]]))  # |1><1|
+matrix_cache.cache_matrix('op00', Matrix([[1, 0], [0, 0]]))  # |0><0|
+matrix_cache.cache_matrix('op10', Matrix([[0, 0], [1, 0]]))  # |1><0|
+matrix_cache.cache_matrix('op01', Matrix([[0, 1], [0, 0]]))  # |0><1|
+matrix_cache.cache_matrix('X', Matrix([[0, 1], [1, 0]]))
+matrix_cache.cache_matrix('Y', Matrix([[0, -I], [I, 0]]))
+matrix_cache.cache_matrix('Z', Matrix([[1, 0], [0, -1]]))
+matrix_cache.cache_matrix('S', Matrix([[1, 0], [0, I]]))
+matrix_cache.cache_matrix('T', Matrix([[1, 0], [0, exp(I*pi/4)]]))
+matrix_cache.cache_matrix('H', sqrt2_inv*Matrix([[1, 1], [1, -1]]))
+matrix_cache.cache_matrix('Hsqrt2', Matrix([[1, 1], [1, -1]]))
+matrix_cache.cache_matrix(
+    'SWAP', Matrix([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]))
+matrix_cache.cache_matrix('ZX', sqrt2_inv*Matrix([[1, 1], [1, -1]]))
+matrix_cache.cache_matrix('ZY', Matrix([[I, 0], [0, -I]]))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/matrixutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/matrixutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..1082ea326b68256dac96030e36d72efa664495d2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/matrixutils.py
@@ -0,0 +1,272 @@
+"""Utilities to deal with sympy.Matrix, numpy and scipy.sparse."""
+
+from sympy.core.expr import Expr
+from sympy.core.numbers import I
+from sympy.core.singleton import S
+from sympy.matrices.matrixbase import MatrixBase
+from sympy.matrices import eye, zeros
+from sympy.external import import_module
+
+__all__ = [
+    'numpy_ndarray',
+    'scipy_sparse_matrix',
+    'sympy_to_numpy',
+    'sympy_to_scipy_sparse',
+    'numpy_to_sympy',
+    'scipy_sparse_to_sympy',
+    'flatten_scalar',
+    'matrix_dagger',
+    'to_sympy',
+    'to_numpy',
+    'to_scipy_sparse',
+    'matrix_tensor_product',
+    'matrix_zeros'
+]
+
+# Conditionally define the base classes for numpy and scipy.sparse arrays
+# for use in isinstance tests.
+
+np = import_module('numpy')
+if not np:
+    class numpy_ndarray:
+        pass
+else:
+    numpy_ndarray = np.ndarray  # type: ignore
+
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+if not scipy:
+    class scipy_sparse_matrix:
+        pass
+    sparse = None
+else:
+    sparse = scipy.sparse
+    scipy_sparse_matrix = sparse.spmatrix # type: ignore
+
+
+def sympy_to_numpy(m, **options):
+    """Convert a SymPy Matrix/complex number to a numpy matrix or scalar."""
+    if not np:
+        raise ImportError
+    dtype = options.get('dtype', 'complex')
+    if isinstance(m, MatrixBase):
+        return np.array(m.tolist(), dtype=dtype)
+    elif isinstance(m, Expr):
+        if m.is_Number or m.is_NumberSymbol or m == I:
+            return complex(m)
+    raise TypeError('Expected MatrixBase or complex scalar, got: %r' % m)
+
+
+def sympy_to_scipy_sparse(m, **options):
+    """Convert a SymPy Matrix/complex number to a numpy matrix or scalar."""
+    if not np or not sparse:
+        raise ImportError
+    dtype = options.get('dtype', 'complex')
+    if isinstance(m, MatrixBase):
+        return sparse.csr_matrix(np.array(m.tolist(), dtype=dtype))
+    elif isinstance(m, Expr):
+        if m.is_Number or m.is_NumberSymbol or m == I:
+            return complex(m)
+    raise TypeError('Expected MatrixBase or complex scalar, got: %r' % m)
+
+
+def scipy_sparse_to_sympy(m, **options):
+    """Convert a scipy.sparse matrix to a SymPy matrix."""
+    return MatrixBase(m.todense())
+
+
+def numpy_to_sympy(m, **options):
+    """Convert a numpy matrix to a SymPy matrix."""
+    return MatrixBase(m)
+
+
+def to_sympy(m, **options):
+    """Convert a numpy/scipy.sparse matrix to a SymPy matrix."""
+    if isinstance(m, MatrixBase):
+        return m
+    elif isinstance(m, numpy_ndarray):
+        return numpy_to_sympy(m)
+    elif isinstance(m, scipy_sparse_matrix):
+        return scipy_sparse_to_sympy(m)
+    elif isinstance(m, Expr):
+        return m
+    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)
+
+
+def to_numpy(m, **options):
+    """Convert a sympy/scipy.sparse matrix to a numpy matrix."""
+    dtype = options.get('dtype', 'complex')
+    if isinstance(m, (MatrixBase, Expr)):
+        return sympy_to_numpy(m, dtype=dtype)
+    elif isinstance(m, numpy_ndarray):
+        return m
+    elif isinstance(m, scipy_sparse_matrix):
+        return m.todense()
+    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)
+
+
+def to_scipy_sparse(m, **options):
+    """Convert a sympy/numpy matrix to a scipy.sparse matrix."""
+    dtype = options.get('dtype', 'complex')
+    if isinstance(m, (MatrixBase, Expr)):
+        return sympy_to_scipy_sparse(m, dtype=dtype)
+    elif isinstance(m, numpy_ndarray):
+        if not sparse:
+            raise ImportError
+        return sparse.csr_matrix(m)
+    elif isinstance(m, scipy_sparse_matrix):
+        return m
+    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)
+
+
+def flatten_scalar(e):
+    """Flatten a 1x1 matrix to a scalar, return larger matrices unchanged."""
+    if isinstance(e, MatrixBase):
+        if e.shape == (1, 1):
+            e = e[0]
+    if isinstance(e, (numpy_ndarray, scipy_sparse_matrix)):
+        if e.shape == (1, 1):
+            e = complex(e[0, 0])
+    return e
+
+
+def matrix_dagger(e):
+    """Return the dagger of a sympy/numpy/scipy.sparse matrix."""
+    if isinstance(e, MatrixBase):
+        return e.H
+    elif isinstance(e, (numpy_ndarray, scipy_sparse_matrix)):
+        return e.conjugate().transpose()
+    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % e)
+
+
+# TODO: Move this into sympy.matrices.
+def _sympy_tensor_product(*matrices):
+    """Compute the kronecker product of a sequence of SymPy Matrices.
+    """
+    from sympy.matrices.expressions.kronecker import matrix_kronecker_product
+
+    return matrix_kronecker_product(*matrices)
+
+
+def _numpy_tensor_product(*product):
+    """numpy version of tensor product of multiple arguments."""
+    if not np:
+        raise ImportError
+    answer = product[0]
+    for item in product[1:]:
+        answer = np.kron(answer, item)
+    return answer
+
+
+def _scipy_sparse_tensor_product(*product):
+    """scipy.sparse version of tensor product of multiple arguments."""
+    if not sparse:
+        raise ImportError
+    answer = product[0]
+    for item in product[1:]:
+        answer = sparse.kron(answer, item)
+    # The final matrices will just be multiplied, so csr is a good final
+    # sparse format.
+    return sparse.csr_matrix(answer)
+
+
+def matrix_tensor_product(*product):
+    """Compute the matrix tensor product of sympy/numpy/scipy.sparse matrices."""
+    if isinstance(product[0], MatrixBase):
+        return _sympy_tensor_product(*product)
+    elif isinstance(product[0], numpy_ndarray):
+        return _numpy_tensor_product(*product)
+    elif isinstance(product[0], scipy_sparse_matrix):
+        return _scipy_sparse_tensor_product(*product)
+
+
+def _numpy_eye(n):
+    """numpy version of complex eye."""
+    if not np:
+        raise ImportError
+    return np.array(np.eye(n, dtype='complex'))
+
+
+def _scipy_sparse_eye(n):
+    """scipy.sparse version of complex eye."""
+    if not sparse:
+        raise ImportError
+    return sparse.eye(n, n, dtype='complex')
+
+
+def matrix_eye(n, **options):
+    """Get the version of eye and tensor_product for a given format."""
+    format = options.get('format', 'sympy')
+    if format == 'sympy':
+        return eye(n)
+    elif format == 'numpy':
+        return _numpy_eye(n)
+    elif format == 'scipy.sparse':
+        return _scipy_sparse_eye(n)
+    raise NotImplementedError('Invalid format: %r' % format)
+
+
+def _numpy_zeros(m, n, **options):
+    """numpy version of zeros."""
+    dtype = options.get('dtype', 'float64')
+    if not np:
+        raise ImportError
+    return np.zeros((m, n), dtype=dtype)
+
+
+def _scipy_sparse_zeros(m, n, **options):
+    """scipy.sparse version of zeros."""
+    spmatrix = options.get('spmatrix', 'csr')
+    dtype = options.get('dtype', 'float64')
+    if not sparse:
+        raise ImportError
+    if spmatrix == 'lil':
+        return sparse.lil_matrix((m, n), dtype=dtype)
+    elif spmatrix == 'csr':
+        return sparse.csr_matrix((m, n), dtype=dtype)
+
+
+def matrix_zeros(m, n, **options):
+    """"Get a zeros matrix for a given format."""
+    format = options.get('format', 'sympy')
+    if format == 'sympy':
+        return zeros(m, n)
+    elif format == 'numpy':
+        return _numpy_zeros(m, n, **options)
+    elif format == 'scipy.sparse':
+        return _scipy_sparse_zeros(m, n, **options)
+    raise NotImplementedError('Invaild format: %r' % format)
+
+
+def _numpy_matrix_to_zero(e):
+    """Convert a numpy zero matrix to the zero scalar."""
+    if not np:
+        raise ImportError
+    test = np.zeros_like(e)
+    if np.allclose(e, test):
+        return 0.0
+    else:
+        return e
+
+
+def _scipy_sparse_matrix_to_zero(e):
+    """Convert a scipy.sparse zero matrix to the zero scalar."""
+    if not np:
+        raise ImportError
+    edense = e.todense()
+    test = np.zeros_like(edense)
+    if np.allclose(edense, test):
+        return 0.0
+    else:
+        return e
+
+
+def matrix_to_zero(e):
+    """Convert a zero matrix to the scalar zero."""
+    if isinstance(e, MatrixBase):
+        if zeros(*e.shape) == e:
+            e = S.Zero
+    elif isinstance(e, numpy_ndarray):
+        e = _numpy_matrix_to_zero(e)
+    elif isinstance(e, scipy_sparse_matrix):
+        e = _scipy_sparse_matrix_to_zero(e)
+    return e
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operator.py
new file mode 100644
index 0000000000000000000000000000000000000000..b44617e15c19e8b30b76f011630430787233e724
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operator.py
@@ -0,0 +1,653 @@
+"""Quantum mechanical operators.
+
+TODO:
+
+* Fix early 0 in apply_operators.
+* Debug and test apply_operators.
+* Get cse working with classes in this file.
+* Doctests and documentation of special methods for InnerProduct, Commutator,
+  AntiCommutator, represent, apply_operators.
+"""
+from typing import Optional
+
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.function import (Derivative, expand)
+from sympy.core.mul import Mul
+from sympy.core.numbers import oo
+from sympy.core.singleton import S
+from sympy.printing.pretty.stringpict import prettyForm
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.kind import OperatorKind
+from sympy.physics.quantum.qexpr import QExpr, dispatch_method
+from sympy.matrices import eye
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+
+
+__all__ = [
+    'Operator',
+    'HermitianOperator',
+    'UnitaryOperator',
+    'IdentityOperator',
+    'OuterProduct',
+    'DifferentialOperator'
+]
+
+#-----------------------------------------------------------------------------
+# Operators and outer products
+#-----------------------------------------------------------------------------
+
+
+class Operator(QExpr):
+    """Base class for non-commuting quantum operators.
+
+    An operator maps between quantum states [1]_. In quantum mechanics,
+    observables (including, but not limited to, measured physical values) are
+    represented as Hermitian operators [2]_.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        operator. For time-dependent operators, this will include the time.
+
+    Examples
+    ========
+
+    Create an operator and examine its attributes::
+
+        >>> from sympy.physics.quantum import Operator
+        >>> from sympy import I
+        >>> A = Operator('A')
+        >>> A
+        A
+        >>> A.hilbert_space
+        H
+        >>> A.label
+        (A,)
+        >>> A.is_commutative
+        False
+
+    Create another operator and do some arithmetic operations::
+
+        >>> B = Operator('B')
+        >>> C = 2*A*A + I*B
+        >>> C
+        2*A**2 + I*B
+
+    Operators do not commute::
+
+        >>> A.is_commutative
+        False
+        >>> B.is_commutative
+        False
+        >>> A*B == B*A
+        False
+
+    Polymonials of operators respect the commutation properties::
+
+        >>> e = (A+B)**3
+        >>> e.expand()
+        A*B*A + A*B**2 + A**2*B + A**3 + B*A*B + B*A**2 + B**2*A + B**3
+
+    Operator inverses are handle symbolically::
+
+        >>> A.inv()
+        A**(-1)
+        >>> A*A.inv()
+        1
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Operator_%28physics%29
+    .. [2] https://en.wikipedia.org/wiki/Observable
+    """
+    is_hermitian: Optional[bool] = None
+    is_unitary: Optional[bool] = None
+    @classmethod
+    def default_args(self):
+        return ("O",)
+
+    kind = OperatorKind
+
+    #-------------------------------------------------------------------------
+    # Printing
+    #-------------------------------------------------------------------------
+
+    _label_separator = ','
+
+    def _print_operator_name(self, printer, *args):
+        return self.__class__.__name__
+
+    _print_operator_name_latex = _print_operator_name
+
+    def _print_operator_name_pretty(self, printer, *args):
+        return prettyForm(self.__class__.__name__)
+
+    def _print_contents(self, printer, *args):
+        if len(self.label) == 1:
+            return self._print_label(printer, *args)
+        else:
+            return '%s(%s)' % (
+                self._print_operator_name(printer, *args),
+                self._print_label(printer, *args)
+            )
+
+    def _print_contents_pretty(self, printer, *args):
+        if len(self.label) == 1:
+            return self._print_label_pretty(printer, *args)
+        else:
+            pform = self._print_operator_name_pretty(printer, *args)
+            label_pform = self._print_label_pretty(printer, *args)
+            label_pform = prettyForm(
+                *label_pform.parens(left='(', right=')')
+            )
+            pform = prettyForm(*pform.right(label_pform))
+            return pform
+
+    def _print_contents_latex(self, printer, *args):
+        if len(self.label) == 1:
+            return self._print_label_latex(printer, *args)
+        else:
+            return r'%s\left(%s\right)' % (
+                self._print_operator_name_latex(printer, *args),
+                self._print_label_latex(printer, *args)
+            )
+
+    #-------------------------------------------------------------------------
+    # _eval_* methods
+    #-------------------------------------------------------------------------
+
+    def _eval_commutator(self, other, **options):
+        """Evaluate [self, other] if known, return None if not known."""
+        return dispatch_method(self, '_eval_commutator', other, **options)
+
+    def _eval_anticommutator(self, other, **options):
+        """Evaluate [self, other] if known."""
+        return dispatch_method(self, '_eval_anticommutator', other, **options)
+
+    #-------------------------------------------------------------------------
+    # Operator application
+    #-------------------------------------------------------------------------
+
+    def _apply_operator(self, ket, **options):
+        return dispatch_method(self, '_apply_operator', ket, **options)
+
+    def _apply_from_right_to(self, bra, **options):
+        return None
+
+    def matrix_element(self, *args):
+        raise NotImplementedError('matrix_elements is not defined')
+
+    def inverse(self):
+        return self._eval_inverse()
+
+    inv = inverse
+
+    def _eval_inverse(self):
+        return self**(-1)
+
+
+class HermitianOperator(Operator):
+    """A Hermitian operator that satisfies H == Dagger(H).
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        operator. For time-dependent operators, this will include the time.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Dagger, HermitianOperator
+    >>> H = HermitianOperator('H')
+    >>> Dagger(H)
+    H
+    """
+
+    is_hermitian = True
+
+    def _eval_inverse(self):
+        if isinstance(self, UnitaryOperator):
+            return self
+        else:
+            return Operator._eval_inverse(self)
+
+    def _eval_power(self, exp):
+        if isinstance(self, UnitaryOperator):
+            # so all eigenvalues of self are 1 or -1
+            if exp.is_even:
+                from sympy.core.singleton import S
+                return S.One # is identity, see Issue 24153.
+            elif exp.is_odd:
+                return self
+        # No simplification in all other cases
+        return Operator._eval_power(self, exp)
+
+
+class UnitaryOperator(Operator):
+    """A unitary operator that satisfies U*Dagger(U) == 1.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        operator. For time-dependent operators, this will include the time.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Dagger, UnitaryOperator
+    >>> U = UnitaryOperator('U')
+    >>> U*Dagger(U)
+    1
+    """
+    is_unitary = True
+    def _eval_adjoint(self):
+        return self._eval_inverse()
+
+
+class IdentityOperator(Operator):
+    """An identity operator I that satisfies op * I == I * op == op for any
+    operator op.
+
+    .. deprecated:: 1.14.
+        Use the scalar S.One instead as the multiplicative identity for
+        operators and states.
+
+    Parameters
+    ==========
+
+    N : Integer
+        Optional parameter that specifies the dimension of the Hilbert space
+        of operator. This is used when generating a matrix representation.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import IdentityOperator
+    >>> IdentityOperator() # doctest: +SKIP
+    I
+    """
+    is_hermitian = True
+    is_unitary = True
+    @property
+    def dimension(self):
+        return self.N
+
+    @classmethod
+    def default_args(self):
+        return (oo,)
+
+    def __init__(self, *args, **hints):
+        sympy_deprecation_warning(
+            """
+            IdentityOperator has been deprecated. In the future, please use
+            S.One as the identity for quantum operators and states.
+            """,
+            deprecated_since_version="1.14",
+            active_deprecations_target='deprecated-operator-identity',
+        )
+        if not len(args) in (0, 1):
+            raise ValueError('0 or 1 parameters expected, got %s' % args)
+
+        self.N = args[0] if (len(args) == 1 and args[0]) else oo
+
+    def _eval_commutator(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator(self, other, **hints):
+        return 2 * other
+
+    def _eval_inverse(self):
+        return self
+
+    def _eval_adjoint(self):
+        return self
+
+    def _apply_operator(self, ket, **options):
+        return ket
+
+    def _apply_from_right_to(self, bra, **options):
+        return bra
+
+    def _eval_power(self, exp):
+        return self
+
+    def _print_contents(self, printer, *args):
+        return 'I'
+
+    def _print_contents_pretty(self, printer, *args):
+        return prettyForm('I')
+
+    def _print_contents_latex(self, printer, *args):
+        return r'{\mathcal{I}}'
+
+    def _represent_default_basis(self, **options):
+        if not self.N or self.N == oo:
+            raise NotImplementedError('Cannot represent infinite dimensional' +
+                                      ' identity operator as a matrix')
+
+        format = options.get('format', 'sympy')
+        if format != 'sympy':
+            raise NotImplementedError('Representation in format ' +
+                                      '%s not implemented.' % format)
+
+        return eye(self.N)
+
+
+class OuterProduct(Operator):
+    """An unevaluated outer product between a ket and bra.
+
+    This constructs an outer product between any subclass of ``KetBase`` and
+    ``BraBase`` as ``|a>>> from sympy.physics.quantum import Ket, Bra, OuterProduct, Dagger
+
+        >>> k = Ket('k')
+        >>> b = Bra('b')
+        >>> op = OuterProduct(k, b)
+        >>> op
+        |k>>> op.hilbert_space
+        H
+        >>> op.ket
+        |k>
+        >>> op.bra
+        >> Dagger(op)
+        |b>>> k*b
+        |k>>> b*k*b
+        *>> from sympy import Derivative, Function, Symbol
+    >>> from sympy.physics.quantum.operator import DifferentialOperator
+    >>> from sympy.physics.quantum.state import Wavefunction
+    >>> from sympy.physics.quantum.qapply import qapply
+    >>> f = Function('f')
+    >>> x = Symbol('x')
+    >>> d = DifferentialOperator(1/x*Derivative(f(x), x), f(x))
+    >>> w = Wavefunction(x**2, x)
+    >>> d.function
+    f(x)
+    >>> d.variables
+    (x,)
+    >>> qapply(d*w)
+    Wavefunction(2, x)
+
+    """
+
+    @property
+    def variables(self):
+        """
+        Returns the variables with which the function in the specified
+        arbitrary expression is evaluated
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.operator import DifferentialOperator
+        >>> from sympy import Symbol, Function, Derivative
+        >>> x = Symbol('x')
+        >>> f = Function('f')
+        >>> d = DifferentialOperator(1/x*Derivative(f(x), x), f(x))
+        >>> d.variables
+        (x,)
+        >>> y = Symbol('y')
+        >>> d = DifferentialOperator(Derivative(f(x, y), x) +
+        ...                          Derivative(f(x, y), y), f(x, y))
+        >>> d.variables
+        (x, y)
+        """
+
+        return self.args[-1].args
+
+    @property
+    def function(self):
+        """
+        Returns the function which is to be replaced with the Wavefunction
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.operator import DifferentialOperator
+        >>> from sympy import Function, Symbol, Derivative
+        >>> x = Symbol('x')
+        >>> f = Function('f')
+        >>> d = DifferentialOperator(Derivative(f(x), x), f(x))
+        >>> d.function
+        f(x)
+        >>> y = Symbol('y')
+        >>> d = DifferentialOperator(Derivative(f(x, y), x) +
+        ...                          Derivative(f(x, y), y), f(x, y))
+        >>> d.function
+        f(x, y)
+        """
+
+        return self.args[-1]
+
+    @property
+    def expr(self):
+        """
+        Returns the arbitrary expression which is to have the Wavefunction
+        substituted into it
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.operator import DifferentialOperator
+        >>> from sympy import Function, Symbol, Derivative
+        >>> x = Symbol('x')
+        >>> f = Function('f')
+        >>> d = DifferentialOperator(Derivative(f(x), x), f(x))
+        >>> d.expr
+        Derivative(f(x), x)
+        >>> y = Symbol('y')
+        >>> d = DifferentialOperator(Derivative(f(x, y), x) +
+        ...                          Derivative(f(x, y), y), f(x, y))
+        >>> d.expr
+        Derivative(f(x, y), x) + Derivative(f(x, y), y)
+        """
+
+        return self.args[0]
+
+    @property
+    def free_symbols(self):
+        """
+        Return the free symbols of the expression.
+        """
+
+        return self.expr.free_symbols
+
+    def _apply_operator_Wavefunction(self, func, **options):
+        from sympy.physics.quantum.state import Wavefunction
+        var = self.variables
+        wf_vars = func.args[1:]
+
+        f = self.function
+        new_expr = self.expr.subs(f, func(*var))
+        new_expr = new_expr.doit()
+
+        return Wavefunction(new_expr, *wf_vars)
+
+    def _eval_derivative(self, symbol):
+        new_expr = Derivative(self.expr, symbol)
+        return DifferentialOperator(new_expr, self.args[-1])
+
+    #-------------------------------------------------------------------------
+    # Printing
+    #-------------------------------------------------------------------------
+
+    def _print(self, printer, *args):
+        return '%s(%s)' % (
+            self._print_operator_name(printer, *args),
+            self._print_label(printer, *args)
+        )
+
+    def _print_pretty(self, printer, *args):
+        pform = self._print_operator_name_pretty(printer, *args)
+        label_pform = self._print_label_pretty(printer, *args)
+        label_pform = prettyForm(
+            *label_pform.parens(left='(', right=')')
+        )
+        pform = prettyForm(*pform.right(label_pform))
+        return pform
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operatorordering.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operatorordering.py
new file mode 100644
index 0000000000000000000000000000000000000000..d6ba3dd83b4b79b773793b0094e636cc8a901f44
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operatorordering.py
@@ -0,0 +1,290 @@
+"""Functions for reordering operator expressions."""
+
+import warnings
+
+from sympy.core.add import Add
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.core.power import Pow
+from sympy.physics.quantum import Commutator, AntiCommutator
+from sympy.physics.quantum.boson import BosonOp
+from sympy.physics.quantum.fermion import FermionOp
+
+__all__ = [
+    'normal_order',
+    'normal_ordered_form'
+]
+
+
+def _expand_powers(factors):
+    """
+    Helper function for normal_ordered_form and normal_order: Expand a
+    power expression to a multiplication expression so that that the
+    expression can be handled by the normal ordering functions.
+    """
+
+    new_factors = []
+    for factor in factors.args:
+        if (isinstance(factor, Pow)
+                and isinstance(factor.args[1], Integer)
+                and factor.args[1] > 0):
+            for n in range(factor.args[1]):
+                new_factors.append(factor.args[0])
+        else:
+            new_factors.append(factor)
+
+    return new_factors
+
+def _normal_ordered_form_factor(product, independent=False, recursive_limit=10,
+                                _recursive_depth=0):
+    """
+    Helper function for normal_ordered_form_factor: Write multiplication
+    expression with bosonic or fermionic operators on normally ordered form,
+    using the bosonic and fermionic commutation relations. The resulting
+    operator expression is equivalent to the argument, but will in general be
+    a sum of operator products instead of a simple product.
+    """
+
+    factors = _expand_powers(product)
+
+    new_factors = []
+    n = 0
+    while n < len(factors) - 1:
+        current, next = factors[n], factors[n + 1]
+        if any(not isinstance(f, (FermionOp, BosonOp)) for f in (current, next)):
+            new_factors.append(current)
+            n += 1
+            continue
+
+        key_1 = (current.is_annihilation, str(current.name))
+        key_2 = (next.is_annihilation, str(next.name))
+
+        if key_1 <= key_2:
+            new_factors.append(current)
+            n += 1
+            continue
+
+        n += 2
+        if current.is_annihilation and not next.is_annihilation:
+            if isinstance(current, BosonOp) and isinstance(next, BosonOp):
+                if current.args[0] != next.args[0]:
+                    if independent:
+                        c = 0
+                    else:
+                        c = Commutator(current, next)
+                    new_factors.append(next * current + c)
+                else:
+                    new_factors.append(next * current + 1)
+            elif isinstance(current, FermionOp) and isinstance(next, FermionOp):
+                if current.args[0] != next.args[0]:
+                    if independent:
+                        c = 0
+                    else:
+                        c = AntiCommutator(current, next)
+                    new_factors.append(-next * current + c)
+                else:
+                    new_factors.append(-next * current + 1)
+        elif (current.is_annihilation == next.is_annihilation and
+            isinstance(current, FermionOp) and isinstance(next, FermionOp)):
+            new_factors.append(-next * current)
+        else:
+            new_factors.append(next * current)
+
+    if n == len(factors) - 1:
+        new_factors.append(factors[-1])
+
+    if new_factors == factors:
+        return product
+    else:
+        expr = Mul(*new_factors).expand()
+        return normal_ordered_form(expr,
+                                   recursive_limit=recursive_limit,
+                                   _recursive_depth=_recursive_depth + 1,
+                                   independent=independent)
+
+
+def _normal_ordered_form_terms(expr, independent=False, recursive_limit=10,
+                               _recursive_depth=0):
+    """
+    Helper function for normal_ordered_form: loop through each term in an
+    addition expression and call _normal_ordered_form_factor to perform the
+    factor to an normally ordered expression.
+    """
+
+    new_terms = []
+    for term in expr.args:
+        if isinstance(term, Mul):
+            new_term = _normal_ordered_form_factor(
+                term, recursive_limit=recursive_limit,
+                _recursive_depth=_recursive_depth, independent=independent)
+            new_terms.append(new_term)
+        else:
+            new_terms.append(term)
+
+    return Add(*new_terms)
+
+
+def normal_ordered_form(expr, independent=False, recursive_limit=10,
+                        _recursive_depth=0):
+    """Write an expression with bosonic or fermionic operators on normal
+    ordered form, where each term is normally ordered. Note that this
+    normal ordered form is equivalent to the original expression.
+
+    Parameters
+    ==========
+
+    expr : expression
+        The expression write on normal ordered form.
+    independent : bool (default False)
+        Whether to consider operator with different names as operating in
+        different Hilbert spaces. If False, the (anti-)commutation is left
+        explicit.
+    recursive_limit : int (default 10)
+        The number of allowed recursive applications of the function.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Dagger
+    >>> from sympy.physics.quantum.boson import BosonOp
+    >>> from sympy.physics.quantum.operatorordering import normal_ordered_form
+    >>> a = BosonOp("a")
+    >>> normal_ordered_form(a * Dagger(a))
+    1 + Dagger(a)*a
+    """
+
+    if _recursive_depth > recursive_limit:
+        warnings.warn("Too many recursions, aborting")
+        return expr
+
+    if isinstance(expr, Add):
+        return _normal_ordered_form_terms(expr,
+                                          recursive_limit=recursive_limit,
+                                          _recursive_depth=_recursive_depth,
+                                          independent=independent)
+    elif isinstance(expr, Mul):
+        return _normal_ordered_form_factor(expr,
+                                           recursive_limit=recursive_limit,
+                                           _recursive_depth=_recursive_depth,
+                                           independent=independent)
+    else:
+        return expr
+
+
+def _normal_order_factor(product, recursive_limit=10, _recursive_depth=0):
+    """
+    Helper function for normal_order: Normal order a multiplication expression
+    with bosonic or fermionic operators. In general the resulting operator
+    expression will not be equivalent to original product.
+    """
+
+    factors = _expand_powers(product)
+
+    n = 0
+    new_factors = []
+    while n < len(factors) - 1:
+
+        if (isinstance(factors[n], BosonOp) and
+                factors[n].is_annihilation):
+            # boson
+            if not isinstance(factors[n + 1], BosonOp):
+                new_factors.append(factors[n])
+            else:
+                if factors[n + 1].is_annihilation:
+                    new_factors.append(factors[n])
+                else:
+                    if factors[n].args[0] != factors[n + 1].args[0]:
+                        new_factors.append(factors[n + 1] * factors[n])
+                    else:
+                        new_factors.append(factors[n + 1] * factors[n])
+                    n += 1
+
+        elif (isinstance(factors[n], FermionOp) and
+              factors[n].is_annihilation):
+            # fermion
+            if not isinstance(factors[n + 1], FermionOp):
+                new_factors.append(factors[n])
+            else:
+                if factors[n + 1].is_annihilation:
+                    new_factors.append(factors[n])
+                else:
+                    if factors[n].args[0] != factors[n + 1].args[0]:
+                        new_factors.append(-factors[n + 1] * factors[n])
+                    else:
+                        new_factors.append(-factors[n + 1] * factors[n])
+                    n += 1
+
+        else:
+            new_factors.append(factors[n])
+
+        n += 1
+
+    if n == len(factors) - 1:
+        new_factors.append(factors[-1])
+
+    if new_factors == factors:
+        return product
+    else:
+        expr = Mul(*new_factors).expand()
+        return normal_order(expr,
+                            recursive_limit=recursive_limit,
+                            _recursive_depth=_recursive_depth + 1)
+
+
+def _normal_order_terms(expr, recursive_limit=10, _recursive_depth=0):
+    """
+    Helper function for normal_order: look through each term in an addition
+    expression and call _normal_order_factor to perform the normal ordering
+    on the factors.
+    """
+
+    new_terms = []
+    for term in expr.args:
+        if isinstance(term, Mul):
+            new_term = _normal_order_factor(term,
+                                            recursive_limit=recursive_limit,
+                                            _recursive_depth=_recursive_depth)
+            new_terms.append(new_term)
+        else:
+            new_terms.append(term)
+
+    return Add(*new_terms)
+
+
+def normal_order(expr, recursive_limit=10, _recursive_depth=0):
+    """Normal order an expression with bosonic or fermionic operators. Note
+    that this normal order is not equivalent to the original expression, but
+    the creation and annihilation operators in each term in expr is reordered
+    so that the expression becomes normal ordered.
+
+    Parameters
+    ==========
+
+    expr : expression
+        The expression to normal order.
+
+    recursive_limit : int (default 10)
+        The number of allowed recursive applications of the function.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import Dagger
+    >>> from sympy.physics.quantum.boson import BosonOp
+    >>> from sympy.physics.quantum.operatorordering import normal_order
+    >>> a = BosonOp("a")
+    >>> normal_order(a * Dagger(a))
+    Dagger(a)*a
+    """
+    if _recursive_depth > recursive_limit:
+        warnings.warn("Too many recursions, aborting")
+        return expr
+
+    if isinstance(expr, Add):
+        return _normal_order_terms(expr, recursive_limit=recursive_limit,
+                                   _recursive_depth=_recursive_depth)
+    elif isinstance(expr, Mul):
+        return _normal_order_factor(expr, recursive_limit=recursive_limit,
+                                    _recursive_depth=_recursive_depth)
+    else:
+        return expr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operatorset.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operatorset.py
new file mode 100644
index 0000000000000000000000000000000000000000..bf32bcabbe5d33381dff0b94a9b130375032adef
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/operatorset.py
@@ -0,0 +1,279 @@
+""" A module for mapping operators to their corresponding eigenstates
+and vice versa
+
+It contains a global dictionary with eigenstate-operator pairings.
+If a new state-operator pair is created, this dictionary should be
+updated as well.
+
+It also contains functions operators_to_state and state_to_operators
+for mapping between the two. These can handle both classes and
+instances of operators and states. See the individual function
+descriptions for details.
+
+TODO List:
+- Update the dictionary with a complete list of state-operator pairs
+"""
+
+from sympy.physics.quantum.cartesian import (XOp, YOp, ZOp, XKet, PxOp, PxKet,
+                                             PositionKet3D)
+from sympy.physics.quantum.operator import Operator
+from sympy.physics.quantum.state import StateBase, BraBase, Ket
+from sympy.physics.quantum.spin import (JxOp, JyOp, JzOp, J2Op, JxKet, JyKet,
+                                        JzKet)
+
+__all__ = [
+    'operators_to_state',
+    'state_to_operators'
+]
+
+#state_mapping stores the mappings between states and their associated
+#operators or tuples of operators. This should be updated when new
+#classes are written! Entries are of the form PxKet : PxOp or
+#something like 3DKet : (ROp, ThetaOp, PhiOp)
+
+#frozenset is used so that the reverse mapping can be made
+#(regular sets are not hashable because they are mutable
+state_mapping = { JxKet: frozenset((J2Op, JxOp)),
+                  JyKet: frozenset((J2Op, JyOp)),
+                  JzKet: frozenset((J2Op, JzOp)),
+                  Ket: Operator,
+                  PositionKet3D: frozenset((XOp, YOp, ZOp)),
+                  PxKet: PxOp,
+                  XKet: XOp }
+
+op_mapping = {v: k for k, v in state_mapping.items()}
+
+
+def operators_to_state(operators, **options):
+    """ Returns the eigenstate of the given operator or set of operators
+
+    A global function for mapping operator classes to their associated
+    states. It takes either an Operator or a set of operators and
+    returns the state associated with these.
+
+    This function can handle both instances of a given operator or
+    just the class itself (i.e. both XOp() and XOp)
+
+    There are multiple use cases to consider:
+
+    1) A class or set of classes is passed: First, we try to
+    instantiate default instances for these operators. If this fails,
+    then the class is simply returned. If we succeed in instantiating
+    default instances, then we try to call state._operators_to_state
+    on the operator instances. If this fails, the class is returned.
+    Otherwise, the instance returned by _operators_to_state is returned.
+
+    2) An instance or set of instances is passed: In this case,
+    state._operators_to_state is called on the instances passed. If
+    this fails, a state class is returned. If the method returns an
+    instance, that instance is returned.
+
+    In both cases, if the operator class or set does not exist in the
+    state_mapping dictionary, None is returned.
+
+    Parameters
+    ==========
+
+    arg: Operator or set
+         The class or instance of the operator or set of operators
+         to be mapped to a state
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.cartesian import XOp, PxOp
+    >>> from sympy.physics.quantum.operatorset import operators_to_state
+    >>> from sympy.physics.quantum.operator import Operator
+    >>> operators_to_state(XOp)
+    |x>
+    >>> operators_to_state(XOp())
+    |x>
+    >>> operators_to_state(PxOp)
+    |px>
+    >>> operators_to_state(PxOp())
+    |px>
+    >>> operators_to_state(Operator)
+    |psi>
+    >>> operators_to_state(Operator())
+    |psi>
+    """
+
+    if not (isinstance(operators, (Operator, set)) or issubclass(operators, Operator)):
+        raise NotImplementedError("Argument is not an Operator or a set!")
+
+    if isinstance(operators, set):
+        for s in operators:
+            if not (isinstance(s, Operator)
+                   or issubclass(s, Operator)):
+                raise NotImplementedError("Set is not all Operators!")
+
+        ops = frozenset(operators)
+
+        if ops in op_mapping:  # ops is a list of classes in this case
+            #Try to get an object from default instances of the
+            #operators...if this fails, return the class
+            try:
+                op_instances = [op() for op in ops]
+                ret = _get_state(op_mapping[ops], set(op_instances), **options)
+            except NotImplementedError:
+                ret = op_mapping[ops]
+
+            return ret
+        else:
+            tmp = [type(o) for o in ops]
+            classes = frozenset(tmp)
+
+            if classes in op_mapping:
+                ret = _get_state(op_mapping[classes], ops, **options)
+            else:
+                ret = None
+
+            return ret
+    else:
+        if operators in op_mapping:
+            try:
+                op_instance = operators()
+                ret = _get_state(op_mapping[operators], op_instance, **options)
+            except NotImplementedError:
+                ret = op_mapping[operators]
+
+            return ret
+        elif type(operators) in op_mapping:
+            return _get_state(op_mapping[type(operators)], operators, **options)
+        else:
+            return None
+
+
+def state_to_operators(state, **options):
+    """ Returns the operator or set of operators corresponding to the
+    given eigenstate
+
+    A global function for mapping state classes to their associated
+    operators or sets of operators. It takes either a state class
+    or instance.
+
+    This function can handle both instances of a given state or just
+    the class itself (i.e. both XKet() and XKet)
+
+    There are multiple use cases to consider:
+
+    1) A state class is passed: In this case, we first try
+    instantiating a default instance of the class. If this succeeds,
+    then we try to call state._state_to_operators on that instance.
+    If the creation of the default instance or if the calling of
+    _state_to_operators fails, then either an operator class or set of
+    operator classes is returned. Otherwise, the appropriate
+    operator instances are returned.
+
+    2) A state instance is returned: Here, state._state_to_operators
+    is called for the instance. If this fails, then a class or set of
+    operator classes is returned. Otherwise, the instances are returned.
+
+    In either case, if the state's class does not exist in
+    state_mapping, None is returned.
+
+    Parameters
+    ==========
+
+    arg: StateBase class or instance (or subclasses)
+         The class or instance of the state to be mapped to an
+         operator or set of operators
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.cartesian import XKet, PxKet, XBra, PxBra
+    >>> from sympy.physics.quantum.operatorset import state_to_operators
+    >>> from sympy.physics.quantum.state import Ket, Bra
+    >>> state_to_operators(XKet)
+    X
+    >>> state_to_operators(XKet())
+    X
+    >>> state_to_operators(PxKet)
+    Px
+    >>> state_to_operators(PxKet())
+    Px
+    >>> state_to_operators(PxBra)
+    Px
+    >>> state_to_operators(XBra)
+    X
+    >>> state_to_operators(Ket)
+    O
+    >>> state_to_operators(Bra)
+    O
+    """
+
+    if not (isinstance(state, StateBase) or issubclass(state, StateBase)):
+        raise NotImplementedError("Argument is not a state!")
+
+    if state in state_mapping:  # state is a class
+        state_inst = _make_default(state)
+        try:
+            ret = _get_ops(state_inst,
+                           _make_set(state_mapping[state]), **options)
+        except (NotImplementedError, TypeError):
+            ret = state_mapping[state]
+    elif type(state) in state_mapping:
+        ret = _get_ops(state,
+                       _make_set(state_mapping[type(state)]), **options)
+    elif isinstance(state, BraBase) and state.dual_class() in state_mapping:
+        ret = _get_ops(state,
+                       _make_set(state_mapping[state.dual_class()]))
+    elif issubclass(state, BraBase) and state.dual_class() in state_mapping:
+        state_inst = _make_default(state)
+        try:
+            ret = _get_ops(state_inst,
+                           _make_set(state_mapping[state.dual_class()]))
+        except (NotImplementedError, TypeError):
+            ret = state_mapping[state.dual_class()]
+    else:
+        ret = None
+
+    return _make_set(ret)
+
+
+def _make_default(expr):
+    # XXX: Catching TypeError like this is a bad way of distinguishing between
+    # classes and instances. The logic using this function should be rewritten
+    # somehow.
+    try:
+        ret = expr()
+    except TypeError:
+        ret = expr
+
+    return ret
+
+
+def _get_state(state_class, ops, **options):
+    # Try to get a state instance from the operator INSTANCES.
+    # If this fails, get the class
+    try:
+        ret = state_class._operators_to_state(ops, **options)
+    except NotImplementedError:
+        ret = _make_default(state_class)
+
+    return ret
+
+
+def _get_ops(state_inst, op_classes, **options):
+    # Try to get operator instances from the state INSTANCE.
+    # If this fails, just return the classes
+    try:
+        ret = state_inst._state_to_operators(op_classes, **options)
+    except NotImplementedError:
+        if isinstance(op_classes, (set, tuple, frozenset)):
+            ret = tuple(_make_default(x) for x in op_classes)
+        else:
+            ret = _make_default(op_classes)
+
+    if isinstance(ret, set) and len(ret) == 1:
+        return ret[0]
+
+    return ret
+
+
+def _make_set(ops):
+    if isinstance(ops, (tuple, list, frozenset)):
+        return set(ops)
+    else:
+        return ops
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/pauli.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/pauli.py
new file mode 100644
index 0000000000000000000000000000000000000000..89762ed2b38e1c5df3775714ee08d3700df0fa65
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/pauli.py
@@ -0,0 +1,675 @@
+"""Pauli operators and states"""
+
+from sympy.core.add import Add
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.physics.quantum import Operator, Ket, Bra
+from sympy.physics.quantum import ComplexSpace
+from sympy.matrices import Matrix
+from sympy.functions.special.tensor_functions import KroneckerDelta
+
+__all__ = [
+    'SigmaX', 'SigmaY', 'SigmaZ', 'SigmaMinus', 'SigmaPlus', 'SigmaZKet',
+    'SigmaZBra', 'qsimplify_pauli'
+]
+
+
+class SigmaOpBase(Operator):
+    """Pauli sigma operator, base class"""
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    @property
+    def use_name(self):
+        return bool(self.args[0]) is not False
+
+    @classmethod
+    def default_args(self):
+        return (False,)
+
+    def __new__(cls, *args, **hints):
+        return Operator.__new__(cls, *args, **hints)
+
+    def _eval_commutator_BosonOp(self, other, **hints):
+        return S.Zero
+
+
+class SigmaX(SigmaOpBase):
+    """Pauli sigma x operator
+
+    Parameters
+    ==========
+
+    name : str
+        An optional string that labels the operator. Pauli operators with
+        different names commute.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import represent
+    >>> from sympy.physics.quantum.pauli import SigmaX
+    >>> sx = SigmaX()
+    >>> sx
+    SigmaX()
+    >>> represent(sx)
+    Matrix([
+    [0, 1],
+    [1, 0]])
+    """
+
+    def __new__(cls, *args, **hints):
+        return SigmaOpBase.__new__(cls, *args, **hints)
+
+    def _eval_commutator_SigmaY(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return 2 * I * SigmaZ(self.name)
+
+    def _eval_commutator_SigmaZ(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return - 2 * I * SigmaY(self.name)
+
+    def _eval_commutator_BosonOp(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_SigmaY(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_SigmaZ(self, other, **hints):
+        return S.Zero
+
+    def _eval_adjoint(self):
+        return self
+
+    def _print_contents_latex(self, printer, *args):
+        if self.use_name:
+            return r'{\sigma_x^{(%s)}}' % str(self.name)
+        else:
+            return r'{\sigma_x}'
+
+    def _print_contents(self, printer, *args):
+        return 'SigmaX()'
+
+    def _eval_power(self, e):
+        if e.is_Integer and e.is_positive:
+            return SigmaX(self.name).__pow__(int(e) % 2)
+
+    def _represent_default_basis(self, **options):
+        format = options.get('format', 'sympy')
+        if format == 'sympy':
+            return Matrix([[0, 1], [1, 0]])
+        else:
+            raise NotImplementedError('Representation in format ' +
+                                      format + ' not implemented.')
+
+
+class SigmaY(SigmaOpBase):
+    """Pauli sigma y operator
+
+    Parameters
+    ==========
+
+    name : str
+        An optional string that labels the operator. Pauli operators with
+        different names commute.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import represent
+    >>> from sympy.physics.quantum.pauli import SigmaY
+    >>> sy = SigmaY()
+    >>> sy
+    SigmaY()
+    >>> represent(sy)
+    Matrix([
+    [0, -I],
+    [I,  0]])
+    """
+
+    def __new__(cls, *args, **hints):
+        return SigmaOpBase.__new__(cls, *args)
+
+    def _eval_commutator_SigmaZ(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return 2 * I * SigmaX(self.name)
+
+    def _eval_commutator_SigmaX(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return - 2 * I * SigmaZ(self.name)
+
+    def _eval_anticommutator_SigmaX(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_SigmaZ(self, other, **hints):
+        return S.Zero
+
+    def _eval_adjoint(self):
+        return self
+
+    def _print_contents_latex(self, printer, *args):
+        if self.use_name:
+            return r'{\sigma_y^{(%s)}}' % str(self.name)
+        else:
+            return r'{\sigma_y}'
+
+    def _print_contents(self, printer, *args):
+        return 'SigmaY()'
+
+    def _eval_power(self, e):
+        if e.is_Integer and e.is_positive:
+            return SigmaY(self.name).__pow__(int(e) % 2)
+
+    def _represent_default_basis(self, **options):
+        format = options.get('format', 'sympy')
+        if format == 'sympy':
+            return Matrix([[0, -I], [I, 0]])
+        else:
+            raise NotImplementedError('Representation in format ' +
+                                      format + ' not implemented.')
+
+
+class SigmaZ(SigmaOpBase):
+    """Pauli sigma z operator
+
+    Parameters
+    ==========
+
+    name : str
+        An optional string that labels the operator. Pauli operators with
+        different names commute.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import represent
+    >>> from sympy.physics.quantum.pauli import SigmaZ
+    >>> sz = SigmaZ()
+    >>> sz ** 3
+    SigmaZ()
+    >>> represent(sz)
+    Matrix([
+    [1,  0],
+    [0, -1]])
+    """
+
+    def __new__(cls, *args, **hints):
+        return SigmaOpBase.__new__(cls, *args)
+
+    def _eval_commutator_SigmaX(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return 2 * I * SigmaY(self.name)
+
+    def _eval_commutator_SigmaY(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return - 2 * I * SigmaX(self.name)
+
+    def _eval_anticommutator_SigmaX(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_SigmaY(self, other, **hints):
+        return S.Zero
+
+    def _eval_adjoint(self):
+        return self
+
+    def _print_contents_latex(self, printer, *args):
+        if self.use_name:
+            return r'{\sigma_z^{(%s)}}' % str(self.name)
+        else:
+            return r'{\sigma_z}'
+
+    def _print_contents(self, printer, *args):
+        return 'SigmaZ()'
+
+    def _eval_power(self, e):
+        if e.is_Integer and e.is_positive:
+            return SigmaZ(self.name).__pow__(int(e) % 2)
+
+    def _represent_default_basis(self, **options):
+        format = options.get('format', 'sympy')
+        if format == 'sympy':
+            return Matrix([[1, 0], [0, -1]])
+        else:
+            raise NotImplementedError('Representation in format ' +
+                                      format + ' not implemented.')
+
+
+class SigmaMinus(SigmaOpBase):
+    """Pauli sigma minus operator
+
+    Parameters
+    ==========
+
+    name : str
+        An optional string that labels the operator. Pauli operators with
+        different names commute.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import represent, Dagger
+    >>> from sympy.physics.quantum.pauli import SigmaMinus
+    >>> sm = SigmaMinus()
+    >>> sm
+    SigmaMinus()
+    >>> Dagger(sm)
+    SigmaPlus()
+    >>> represent(sm)
+    Matrix([
+    [0, 0],
+    [1, 0]])
+    """
+
+    def __new__(cls, *args, **hints):
+        return SigmaOpBase.__new__(cls, *args)
+
+    def _eval_commutator_SigmaX(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return -SigmaZ(self.name)
+
+    def _eval_commutator_SigmaY(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return I * SigmaZ(self.name)
+
+    def _eval_commutator_SigmaZ(self, other, **hints):
+        return 2 * self
+
+    def _eval_commutator_SigmaMinus(self, other, **hints):
+        return SigmaZ(self.name)
+
+    def _eval_anticommutator_SigmaZ(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_SigmaX(self, other, **hints):
+        return S.One
+
+    def _eval_anticommutator_SigmaY(self, other, **hints):
+        return I * S.NegativeOne
+
+    def _eval_anticommutator_SigmaPlus(self, other, **hints):
+        return S.One
+
+    def _eval_adjoint(self):
+        return SigmaPlus(self.name)
+
+    def _eval_power(self, e):
+        if e.is_Integer and e.is_positive:
+            return S.Zero
+
+    def _print_contents_latex(self, printer, *args):
+        if self.use_name:
+            return r'{\sigma_-^{(%s)}}' % str(self.name)
+        else:
+            return r'{\sigma_-}'
+
+    def _print_contents(self, printer, *args):
+        return 'SigmaMinus()'
+
+    def _represent_default_basis(self, **options):
+        format = options.get('format', 'sympy')
+        if format == 'sympy':
+            return Matrix([[0, 0], [1, 0]])
+        else:
+            raise NotImplementedError('Representation in format ' +
+                                      format + ' not implemented.')
+
+
+class SigmaPlus(SigmaOpBase):
+    """Pauli sigma plus operator
+
+    Parameters
+    ==========
+
+    name : str
+        An optional string that labels the operator. Pauli operators with
+        different names commute.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum import represent, Dagger
+    >>> from sympy.physics.quantum.pauli import SigmaPlus
+    >>> sp = SigmaPlus()
+    >>> sp
+    SigmaPlus()
+    >>> Dagger(sp)
+    SigmaMinus()
+    >>> represent(sp)
+    Matrix([
+    [0, 1],
+    [0, 0]])
+    """
+
+    def __new__(cls, *args, **hints):
+        return SigmaOpBase.__new__(cls, *args)
+
+    def _eval_commutator_SigmaX(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return SigmaZ(self.name)
+
+    def _eval_commutator_SigmaY(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return I * SigmaZ(self.name)
+
+    def _eval_commutator_SigmaZ(self, other, **hints):
+        if self.name != other.name:
+            return S.Zero
+        else:
+            return -2 * self
+
+    def _eval_commutator_SigmaMinus(self, other, **hints):
+        return SigmaZ(self.name)
+
+    def _eval_anticommutator_SigmaZ(self, other, **hints):
+        return S.Zero
+
+    def _eval_anticommutator_SigmaX(self, other, **hints):
+        return S.One
+
+    def _eval_anticommutator_SigmaY(self, other, **hints):
+        return I
+
+    def _eval_anticommutator_SigmaMinus(self, other, **hints):
+        return S.One
+
+    def _eval_adjoint(self):
+        return SigmaMinus(self.name)
+
+    def _eval_mul(self, other):
+        return self * other
+
+    def _eval_power(self, e):
+        if e.is_Integer and e.is_positive:
+            return S.Zero
+
+    def _print_contents_latex(self, printer, *args):
+        if self.use_name:
+            return r'{\sigma_+^{(%s)}}' % str(self.name)
+        else:
+            return r'{\sigma_+}'
+
+    def _print_contents(self, printer, *args):
+        return 'SigmaPlus()'
+
+    def _represent_default_basis(self, **options):
+        format = options.get('format', 'sympy')
+        if format == 'sympy':
+            return Matrix([[0, 1], [0, 0]])
+        else:
+            raise NotImplementedError('Representation in format ' +
+                                      format + ' not implemented.')
+
+
+class SigmaZKet(Ket):
+    """Ket for a two-level system quantum system.
+
+    Parameters
+    ==========
+
+    n : Number
+        The state number (0 or 1).
+
+    """
+
+    def __new__(cls, n):
+        if n not in (0, 1):
+            raise ValueError("n must be 0 or 1")
+        return Ket.__new__(cls, n)
+
+    @property
+    def n(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return SigmaZBra
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return ComplexSpace(2)
+
+    def _eval_innerproduct_SigmaZBra(self, bra, **hints):
+        return KroneckerDelta(self.n, bra.n)
+
+    def _apply_from_right_to_SigmaZ(self, op, **options):
+        if self.n == 0:
+            return self
+        else:
+            return S.NegativeOne * self
+
+    def _apply_from_right_to_SigmaX(self, op, **options):
+        return SigmaZKet(1) if self.n == 0 else SigmaZKet(0)
+
+    def _apply_from_right_to_SigmaY(self, op, **options):
+        return I * SigmaZKet(1) if self.n == 0 else (-I) * SigmaZKet(0)
+
+    def _apply_from_right_to_SigmaMinus(self, op, **options):
+        if self.n == 0:
+            return SigmaZKet(1)
+        else:
+            return S.Zero
+
+    def _apply_from_right_to_SigmaPlus(self, op, **options):
+        if self.n == 0:
+            return S.Zero
+        else:
+            return SigmaZKet(0)
+
+    def _represent_default_basis(self, **options):
+        format = options.get('format', 'sympy')
+        if format == 'sympy':
+            return Matrix([[1], [0]]) if self.n == 0 else Matrix([[0], [1]])
+        else:
+            raise NotImplementedError('Representation in format ' +
+                                      format + ' not implemented.')
+
+
+class SigmaZBra(Bra):
+    """Bra for a two-level quantum system.
+
+    Parameters
+    ==========
+
+    n : Number
+        The state number (0 or 1).
+
+    """
+
+    def __new__(cls, n):
+        if n not in (0, 1):
+            raise ValueError("n must be 0 or 1")
+        return Bra.__new__(cls, n)
+
+    @property
+    def n(self):
+        return self.label[0]
+
+    @classmethod
+    def dual_class(self):
+        return SigmaZKet
+
+
+def _qsimplify_pauli_product(a, b):
+    """
+    Internal helper function for simplifying products of Pauli operators.
+    """
+    if not (isinstance(a, SigmaOpBase) and isinstance(b, SigmaOpBase)):
+        return Mul(a, b)
+
+    if a.name != b.name:
+        # Pauli matrices with different labels commute; sort by name
+        if a.name < b.name:
+            return Mul(a, b)
+        else:
+            return Mul(b, a)
+
+    elif isinstance(a, SigmaX):
+
+        if isinstance(b, SigmaX):
+            return S.One
+
+        if isinstance(b, SigmaY):
+            return I * SigmaZ(a.name)
+
+        if isinstance(b, SigmaZ):
+            return - I * SigmaY(a.name)
+
+        if isinstance(b, SigmaMinus):
+            return (S.Half + SigmaZ(a.name)/2)
+
+        if isinstance(b, SigmaPlus):
+            return (S.Half - SigmaZ(a.name)/2)
+
+    elif isinstance(a, SigmaY):
+
+        if isinstance(b, SigmaX):
+            return - I * SigmaZ(a.name)
+
+        if isinstance(b, SigmaY):
+            return S.One
+
+        if isinstance(b, SigmaZ):
+            return I * SigmaX(a.name)
+
+        if isinstance(b, SigmaMinus):
+            return -I * (S.One + SigmaZ(a.name))/2
+
+        if isinstance(b, SigmaPlus):
+            return I * (S.One - SigmaZ(a.name))/2
+
+    elif isinstance(a, SigmaZ):
+
+        if isinstance(b, SigmaX):
+            return I * SigmaY(a.name)
+
+        if isinstance(b, SigmaY):
+            return - I * SigmaX(a.name)
+
+        if isinstance(b, SigmaZ):
+            return S.One
+
+        if isinstance(b, SigmaMinus):
+            return - SigmaMinus(a.name)
+
+        if isinstance(b, SigmaPlus):
+            return SigmaPlus(a.name)
+
+    elif isinstance(a, SigmaMinus):
+
+        if isinstance(b, SigmaX):
+            return (S.One - SigmaZ(a.name))/2
+
+        if isinstance(b, SigmaY):
+            return - I * (S.One - SigmaZ(a.name))/2
+
+        if isinstance(b, SigmaZ):
+            # (SigmaX(a.name) - I * SigmaY(a.name))/2
+            return SigmaMinus(b.name)
+
+        if isinstance(b, SigmaMinus):
+            return S.Zero
+
+        if isinstance(b, SigmaPlus):
+            return S.Half - SigmaZ(a.name)/2
+
+    elif isinstance(a, SigmaPlus):
+
+        if isinstance(b, SigmaX):
+            return (S.One + SigmaZ(a.name))/2
+
+        if isinstance(b, SigmaY):
+            return I * (S.One + SigmaZ(a.name))/2
+
+        if isinstance(b, SigmaZ):
+            #-(SigmaX(a.name) + I * SigmaY(a.name))/2
+            return -SigmaPlus(a.name)
+
+        if isinstance(b, SigmaMinus):
+            return (S.One + SigmaZ(a.name))/2
+
+        if isinstance(b, SigmaPlus):
+            return S.Zero
+
+    else:
+        return a * b
+
+
+def qsimplify_pauli(e):
+    """
+    Simplify an expression that includes products of pauli operators.
+
+    Parameters
+    ==========
+
+    e : expression
+        An expression that contains products of Pauli operators that is
+        to be simplified.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.pauli import SigmaX, SigmaY
+    >>> from sympy.physics.quantum.pauli import qsimplify_pauli
+    >>> sx, sy = SigmaX(), SigmaY()
+    >>> sx * sy
+    SigmaX()*SigmaY()
+    >>> qsimplify_pauli(sx * sy)
+    I*SigmaZ()
+    """
+    if isinstance(e, Operator):
+        return e
+
+    if isinstance(e, (Add, Pow, exp)):
+        t = type(e)
+        return t(*(qsimplify_pauli(arg) for arg in e.args))
+
+    if isinstance(e, Mul):
+
+        c, nc = e.args_cnc()
+
+        nc_s = []
+        while nc:
+            curr = nc.pop(0)
+
+            while (len(nc) and
+                   isinstance(curr, SigmaOpBase) and
+                   isinstance(nc[0], SigmaOpBase) and
+                   curr.name == nc[0].name):
+
+                x = nc.pop(0)
+                y = _qsimplify_pauli_product(curr, x)
+                c1, nc1 = y.args_cnc()
+                curr = Mul(*nc1)
+                c = c + c1
+
+            nc_s.append(curr)
+
+        return Mul(*c) * Mul(*nc_s)
+
+    return e
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/piab.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/piab.py
new file mode 100644
index 0000000000000000000000000000000000000000..f8ac8135ee03e640f745070602c7dd8ca20f2767
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/piab.py
@@ -0,0 +1,72 @@
+"""1D quantum particle in a box."""
+
+from sympy.core.numbers import pi
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+from sympy.sets.sets import Interval
+
+from sympy.physics.quantum.operator import HermitianOperator
+from sympy.physics.quantum.state import Ket, Bra
+from sympy.physics.quantum.constants import hbar
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.physics.quantum.hilbert import L2
+
+m = Symbol('m')
+L = Symbol('L')
+
+
+__all__ = [
+    'PIABHamiltonian',
+    'PIABKet',
+    'PIABBra'
+]
+
+
+class PIABHamiltonian(HermitianOperator):
+    """Particle in a box Hamiltonian operator."""
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    def _apply_operator_PIABKet(self, ket, **options):
+        n = ket.label[0]
+        return (n**2*pi**2*hbar**2)/(2*m*L**2)*ket
+
+
+class PIABKet(Ket):
+    """Particle in a box eigenket."""
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    @classmethod
+    def dual_class(self):
+        return PIABBra
+
+    def _represent_default_basis(self, **options):
+        return self._represent_XOp(None, **options)
+
+    def _represent_XOp(self, basis, **options):
+        x = Symbol('x')
+        n = Symbol('n')
+        subs_info = options.get('subs', {})
+        return sqrt(2/L)*sin(n*pi*x/L).subs(subs_info)
+
+    def _eval_innerproduct_PIABBra(self, bra):
+        return KroneckerDelta(bra.label[0], self.label[0])
+
+
+class PIABBra(Bra):
+    """Particle in a box eigenbra."""
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    @classmethod
+    def dual_class(self):
+        return PIABKet
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qapply.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qapply.py
new file mode 100644
index 0000000000000000000000000000000000000000..a2d8c92e51552c8114d65a1304fcd1925ae752f4
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qapply.py
@@ -0,0 +1,263 @@
+"""Logic for applying operators to states.
+
+Todo:
+* Sometimes the final result needs to be expanded, we should do this by hand.
+"""
+
+from sympy.concrete import Sum
+from sympy.core.add import Add
+from sympy.core.kind import NumberKind
+from sympy.core.mul import Mul
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.sympify import sympify, _sympify
+
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.operator import OuterProduct, Operator
+from sympy.physics.quantum.state import State, KetBase, BraBase, Wavefunction
+from sympy.physics.quantum.tensorproduct import TensorProduct
+
+__all__ = [
+    'qapply'
+]
+
+
+#-----------------------------------------------------------------------------
+# Main code
+#-----------------------------------------------------------------------------
+
+
+def ip_doit_func(e):
+    """Transform the inner products in an expression by calling ``.doit()``."""
+    return e.replace(InnerProduct, lambda *args: InnerProduct(*args).doit())
+
+
+def sum_doit_func(e):
+    """Transform the sums in an expression by calling ``.doit()``."""
+    return e.replace(Sum, lambda *args: Sum(*args).doit())
+
+
+def qapply(e, **options):
+    """Apply operators to states in a quantum expression.
+
+    Parameters
+    ==========
+
+    e : Expr
+        The expression containing operators and states. This expression tree
+        will be walked to find operators acting on states symbolically.
+    options : dict
+        A dict of key/value pairs that determine how the operator actions
+        are carried out.
+
+        The following options are valid:
+
+        * ``dagger``: try to apply Dagger operators to the left
+          (default: False).
+        * ``ip_doit``: call ``.doit()`` in inner products when they are
+          encountered (default: True).
+        * ``sum_doit``: call ``.doit()`` on sums when they are encountered
+          (default: False). This is helpful for collapsing sums over Kronecker
+          delta's that are created when calling ``qapply``.
+
+    Returns
+    =======
+
+    e : Expr
+        The original expression, but with the operators applied to states.
+
+    Examples
+    ========
+
+        >>> from sympy.physics.quantum import qapply, Ket, Bra
+        >>> b = Bra('b')
+        >>> k = Ket('k')
+        >>> A = k * b
+        >>> A
+        |k>>> qapply(A * b.dual / (b * b.dual))
+        |k>
+        >>> qapply(k.dual * A / (k.dual * k))
+         and A*(|a>+|b>) and all Commutators and
+    # TensorProducts. The only problem with this is that if we can't apply
+    # all the Operators, we have just expanded everything.
+    # TODO: don't expand the scalars in front of each Mul.
+    e = e.expand(commutator=True, tensorproduct=True)
+
+    # If we just have a raw ket, return it.
+    if isinstance(e, KetBase):
+        return e
+
+    # We have an Add(a, b, c, ...) and compute
+    # Add(qapply(a), qapply(b), ...)
+    elif isinstance(e, Add):
+        result = 0
+        for arg in e.args:
+            result += qapply(arg, **options)
+        return result.expand()
+
+    # For a Density operator call qapply on its state
+    elif isinstance(e, Density):
+        new_args = [(qapply(state, **options), prob) for (state,
+                     prob) in e.args]
+        return Density(*new_args)
+
+    # For a raw TensorProduct, call qapply on its args.
+    elif isinstance(e, TensorProduct):
+        return TensorProduct(*[qapply(t, **options) for t in e.args])
+
+    # For a Sum, call qapply on its function.
+    elif isinstance(e, Sum):
+        result = Sum(qapply(e.function, **options), *e.limits)
+        result = sum_doit_func(result) if sum_doit else result
+        return result
+
+    # For a Pow, call qapply on its base.
+    elif isinstance(e, Pow):
+        return qapply(e.base, **options)**e.exp
+
+    # We have a Mul where there might be actual operators to apply to kets.
+    elif isinstance(e, Mul):
+        c_part, nc_part = e.args_cnc()
+        c_mul = Mul(*c_part)
+        nc_mul = Mul(*nc_part)
+        if not nc_part: # If we only have a commuting part, just return it.
+            result = c_mul
+        elif isinstance(nc_mul, Mul):
+            result = c_mul*qapply_Mul(nc_mul, **options)
+        else:
+            result = c_mul*qapply(nc_mul, **options)
+        if result == e and dagger:
+            result = Dagger(qapply_Mul(Dagger(e), **options))
+        result = ip_doit_func(result) if ip_doit else result
+        result = sum_doit_func(result) if sum_doit else result
+        return result
+
+    # In all other cases (State, Operator, Pow, Commutator, InnerProduct,
+    # OuterProduct) we won't ever have operators to apply to kets.
+    else:
+        return e
+
+
+def qapply_Mul(e, **options):
+
+    args = list(e.args)
+    extra = S.One
+    result = None
+
+    # If we only have 0 or 1 args, we have nothing to do and return.
+    if len(args) <= 1 or not isinstance(e, Mul):
+        return e
+    rhs = args.pop()
+    lhs = args.pop()
+
+    # Make sure we have two non-commutative objects before proceeding.
+    if (not isinstance(rhs, Wavefunction) and sympify(rhs).is_commutative) or \
+            (not isinstance(lhs, Wavefunction) and sympify(lhs).is_commutative):
+        return e
+
+    # For a Pow with an integer exponent, apply one of them and reduce the
+    # exponent by one.
+    if isinstance(lhs, Pow) and lhs.exp.is_Integer:
+        args.append(lhs.base**(lhs.exp - 1))
+        lhs = lhs.base
+
+    # Pull OuterProduct apart
+    if isinstance(lhs, OuterProduct):
+        args.append(lhs.ket)
+        lhs = lhs.bra
+
+    if isinstance(rhs, OuterProduct):
+        extra = rhs.bra # Append to the right of the result
+        rhs = rhs.ket
+
+    # Call .doit() on Commutator/AntiCommutator.
+    if isinstance(lhs, (Commutator, AntiCommutator)):
+        comm = lhs.doit()
+        if isinstance(comm, Add):
+            return qapply(
+                e.func(*(args + [comm.args[0], rhs])) +
+                e.func(*(args + [comm.args[1], rhs])),
+                **options
+            )*extra
+        else:
+            return qapply(e.func(*args)*comm*rhs, **options)*extra
+
+    # Apply tensor products of operators to states
+    if isinstance(lhs, TensorProduct) and all(isinstance(arg, (Operator, State, Mul, Pow)) or arg == 1 for arg in lhs.args) and \
+            isinstance(rhs, TensorProduct) and all(isinstance(arg, (Operator, State, Mul, Pow)) or arg == 1 for arg in rhs.args) and \
+            len(lhs.args) == len(rhs.args):
+        result = TensorProduct(*[qapply(lhs.args[n]*rhs.args[n], **options) for n in range(len(lhs.args))]).expand(tensorproduct=True)
+        return qapply_Mul(e.func(*args), **options)*result*extra
+
+    # For Sums, move the Sum to the right.
+    if isinstance(rhs, Sum):
+        if isinstance(lhs, Sum):
+            if set(lhs.variables).intersection(set(rhs.variables)):
+                raise ValueError('Duplicated dummy indices in separate sums in qapply.')
+            limits = lhs.limits + rhs.limits
+            result = Sum(qapply(lhs.function*rhs.function, **options), *limits)
+            return qapply_Mul(e.func(*args)*result, **options)
+        else:
+            result = Sum(qapply(lhs*rhs.function, **options), *rhs.limits)
+            return qapply_Mul(e.func(*args)*result, **options)
+
+    if isinstance(lhs, Sum):
+        result = Sum(qapply(lhs.function*rhs, **options), *lhs.limits)
+        return qapply_Mul(e.func(*args)*result, **options)
+
+    # Now try to actually apply the operator and build an inner product.
+    _apply = getattr(lhs, '_apply_operator', None)
+    if _apply is not None:
+        try:
+            result = _apply(rhs, **options)
+        except NotImplementedError:
+            result = None
+    else:
+        result = None
+
+    if result is None:
+        _apply_right = getattr(rhs, '_apply_from_right_to', None)
+        if _apply_right is not None:
+            try:
+                result = _apply_right(lhs, **options)
+            except NotImplementedError:
+                result = None
+
+    if result is None:
+        if isinstance(lhs, BraBase) and isinstance(rhs, KetBase):
+            result = InnerProduct(lhs, rhs)
+
+    # TODO: I may need to expand before returning the final result.
+    if isinstance(result, (int, complex, float)):
+        return _sympify(result)
+    elif result is None:
+        if len(args) == 0:
+            # We had two args to begin with so args=[].
+            return e
+        else:
+            return qapply_Mul(e.func(*(args + [lhs])), **options)*rhs*extra
+    elif isinstance(result, InnerProduct):
+        return result*qapply_Mul(e.func(*args), **options)*extra
+    else:  # result is a scalar times a Mul, Add or TensorProduct
+        return qapply(e.func(*args)*result, **options)*extra
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qasm.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qasm.py
new file mode 100644
index 0000000000000000000000000000000000000000..39b49d9a67399114e7d03f12148854b2e41b0b26
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qasm.py
@@ -0,0 +1,224 @@
+"""
+
+qasm.py - Functions to parse a set of qasm commands into a SymPy Circuit.
+
+Examples taken from Chuang's page: https://web.archive.org/web/20220120121541/https://www.media.mit.edu/quanta/qasm2circ/
+
+The code returns a circuit and an associated list of labels.
+
+>>> from sympy.physics.quantum.qasm import Qasm
+>>> q = Qasm('qubit q0', 'qubit q1', 'h q0', 'cnot q0,q1')
+>>> q.get_circuit()
+CNOT(1,0)*H(1)
+
+>>> q = Qasm('qubit q0', 'qubit q1', 'cnot q0,q1', 'cnot q1,q0', 'cnot q0,q1')
+>>> q.get_circuit()
+CNOT(1,0)*CNOT(0,1)*CNOT(1,0)
+"""
+
+__all__ = [
+    'Qasm',
+    ]
+
+from math import prod
+
+from sympy.physics.quantum.gate import H, CNOT, X, Z, CGate, CGateS, SWAP, S, T,CPHASE
+from sympy.physics.quantum.circuitplot import Mz
+
+def read_qasm(lines):
+    return Qasm(*lines.splitlines())
+
+def read_qasm_file(filename):
+    return Qasm(*open(filename).readlines())
+
+def flip_index(i, n):
+    """Reorder qubit indices from largest to smallest.
+
+    >>> from sympy.physics.quantum.qasm import flip_index
+    >>> flip_index(0, 2)
+    1
+    >>> flip_index(1, 2)
+    0
+    """
+    return n-i-1
+
+def trim(line):
+    """Remove everything following comment # characters in line.
+
+    >>> from sympy.physics.quantum.qasm import trim
+    >>> trim('nothing happens here')
+    'nothing happens here'
+    >>> trim('something #happens here')
+    'something '
+    """
+    if '#' not in line:
+        return line
+    return line.split('#')[0]
+
+def get_index(target, labels):
+    """Get qubit labels from the rest of the line,and return indices
+
+    >>> from sympy.physics.quantum.qasm import get_index
+    >>> get_index('q0', ['q0', 'q1'])
+    1
+    >>> get_index('q1', ['q0', 'q1'])
+    0
+    """
+    nq = len(labels)
+    return flip_index(labels.index(target), nq)
+
+def get_indices(targets, labels):
+    return [get_index(t, labels) for t in targets]
+
+def nonblank(args):
+    for line in args:
+        line = trim(line)
+        if line.isspace():
+            continue
+        yield line
+    return
+
+def fullsplit(line):
+    words = line.split()
+    rest = ' '.join(words[1:])
+    return fixcommand(words[0]), [s.strip() for s in rest.split(',')]
+
+def fixcommand(c):
+    """Fix Qasm command names.
+
+    Remove all of forbidden characters from command c, and
+    replace 'def' with 'qdef'.
+    """
+    forbidden_characters = ['-']
+    c = c.lower()
+    for char in forbidden_characters:
+        c = c.replace(char, '')
+    if c == 'def':
+        return 'qdef'
+    return c
+
+def stripquotes(s):
+    """Replace explicit quotes in a string.
+
+    >>> from sympy.physics.quantum.qasm import stripquotes
+    >>> stripquotes("'S'") == 'S'
+    True
+    >>> stripquotes('"S"') == 'S'
+    True
+    >>> stripquotes('S') == 'S'
+    True
+    """
+    s = s.replace('"', '') # Remove second set of quotes?
+    s = s.replace("'", '')
+    return s
+
+class Qasm:
+    """Class to form objects from Qasm lines
+
+    >>> from sympy.physics.quantum.qasm import Qasm
+    >>> q = Qasm('qubit q0', 'qubit q1', 'h q0', 'cnot q0,q1')
+    >>> q.get_circuit()
+    CNOT(1,0)*H(1)
+    >>> q = Qasm('qubit q0', 'qubit q1', 'cnot q0,q1', 'cnot q1,q0', 'cnot q0,q1')
+    >>> q.get_circuit()
+    CNOT(1,0)*CNOT(0,1)*CNOT(1,0)
+    """
+    def __init__(self, *args, **kwargs):
+        self.defs = {}
+        self.circuit = []
+        self.labels = []
+        self.inits = {}
+        self.add(*args)
+        self.kwargs = kwargs
+
+    def add(self, *lines):
+        for line in nonblank(lines):
+            command, rest = fullsplit(line)
+            if self.defs.get(command): #defs come first, since you can override built-in
+                function = self.defs.get(command)
+                indices = self.indices(rest)
+                if len(indices) == 1:
+                    self.circuit.append(function(indices[0]))
+                else:
+                    self.circuit.append(function(indices[:-1], indices[-1]))
+            elif hasattr(self, command):
+                function = getattr(self, command)
+                function(*rest)
+            else:
+                print("Function %s not defined. Skipping" % command)
+
+    def get_circuit(self):
+        return prod(reversed(self.circuit))
+
+    def get_labels(self):
+        return list(reversed(self.labels))
+
+    def plot(self):
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+        circuit, labels = self.get_circuit(), self.get_labels()
+        CircuitPlot(circuit, len(labels), labels=labels, inits=self.inits)
+
+    def qubit(self, arg, init=None):
+        self.labels.append(arg)
+        if init: self.inits[arg] = init
+
+    def indices(self, args):
+        return get_indices(args, self.labels)
+
+    def index(self, arg):
+        return get_index(arg, self.labels)
+
+    def nop(self, *args):
+        pass
+
+    def x(self, arg):
+        self.circuit.append(X(self.index(arg)))
+
+    def z(self, arg):
+        self.circuit.append(Z(self.index(arg)))
+
+    def h(self, arg):
+        self.circuit.append(H(self.index(arg)))
+
+    def s(self, arg):
+        self.circuit.append(S(self.index(arg)))
+
+    def t(self, arg):
+        self.circuit.append(T(self.index(arg)))
+
+    def measure(self, arg):
+        self.circuit.append(Mz(self.index(arg)))
+
+    def cnot(self, a1, a2):
+        self.circuit.append(CNOT(*self.indices([a1, a2])))
+
+    def swap(self, a1, a2):
+        self.circuit.append(SWAP(*self.indices([a1, a2])))
+
+    def cphase(self, a1, a2):
+        self.circuit.append(CPHASE(*self.indices([a1, a2])))
+
+    def toffoli(self, a1, a2, a3):
+        i1, i2, i3 = self.indices([a1, a2, a3])
+        self.circuit.append(CGateS((i1, i2), X(i3)))
+
+    def cx(self, a1, a2):
+        fi, fj = self.indices([a1, a2])
+        self.circuit.append(CGate(fi, X(fj)))
+
+    def cz(self, a1, a2):
+        fi, fj = self.indices([a1, a2])
+        self.circuit.append(CGate(fi, Z(fj)))
+
+    def defbox(self, *args):
+        print("defbox not supported yet. Skipping: ", args)
+
+    def qdef(self, name, ncontrols, symbol):
+        from sympy.physics.quantum.circuitplot import CreateOneQubitGate, CreateCGate
+        ncontrols = int(ncontrols)
+        command = fixcommand(name)
+        symbol = stripquotes(symbol)
+        if ncontrols > 0:
+            self.defs[command] = CreateCGate(symbol)
+        else:
+            self.defs[command] = CreateOneQubitGate(symbol)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qexpr.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qexpr.py
new file mode 100644
index 0000000000000000000000000000000000000000..64f7e2a200fa7d89b35db1da551bcbd25492f2d9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qexpr.py
@@ -0,0 +1,409 @@
+from sympy.core.expr import Expr
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.matrices.dense import Matrix
+from sympy.printing.pretty.stringpict import prettyForm
+from sympy.core.containers import Tuple
+from sympy.utilities.iterables import is_sequence
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.matrixutils import (
+    numpy_ndarray, scipy_sparse_matrix,
+    to_sympy, to_numpy, to_scipy_sparse
+)
+
+__all__ = [
+    'QuantumError',
+    'QExpr'
+]
+
+
+#-----------------------------------------------------------------------------
+# Error handling
+#-----------------------------------------------------------------------------
+
+class QuantumError(Exception):
+    pass
+
+
+def _qsympify_sequence(seq):
+    """Convert elements of a sequence to standard form.
+
+    This is like sympify, but it performs special logic for arguments passed
+    to QExpr. The following conversions are done:
+
+    * (list, tuple, Tuple) => _qsympify_sequence each element and convert
+      sequence to a Tuple.
+    * basestring => Symbol
+    * Matrix => Matrix
+    * other => sympify
+
+    Strings are passed to Symbol, not sympify to make sure that variables like
+    'pi' are kept as Symbols, not the SymPy built-in number subclasses.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.qexpr import _qsympify_sequence
+    >>> _qsympify_sequence((1,2,[3,4,[1,]]))
+    (1, 2, (3, 4, (1,)))
+
+    """
+
+    return tuple(__qsympify_sequence_helper(seq))
+
+
+def __qsympify_sequence_helper(seq):
+    """
+       Helper function for _qsympify_sequence
+       This function does the actual work.
+    """
+    #base case. If not a list, do Sympification
+    if not is_sequence(seq):
+        if isinstance(seq, Matrix):
+            return seq
+        elif isinstance(seq, str):
+            return Symbol(seq)
+        else:
+            return sympify(seq)
+
+    # base condition, when seq is QExpr and also
+    # is iterable.
+    if isinstance(seq, QExpr):
+        return seq
+
+    #if list, recurse on each item in the list
+    result = [__qsympify_sequence_helper(item) for item in seq]
+
+    return Tuple(*result)
+
+
+#-----------------------------------------------------------------------------
+# Basic Quantum Expression from which all objects descend
+#-----------------------------------------------------------------------------
+
+class QExpr(Expr):
+    """A base class for all quantum object like operators and states."""
+
+    # In sympy, slots are for instance attributes that are computed
+    # dynamically by the __new__ method. They are not part of args, but they
+    # derive from args.
+
+    # The Hilbert space a quantum Object belongs to.
+    __slots__ = ('hilbert_space', )
+
+    is_commutative = False
+
+    # The separator used in printing the label.
+    _label_separator = ''
+
+    def __new__(cls, *args, **kwargs):
+        """Construct a new quantum object.
+
+        Parameters
+        ==========
+
+        args : tuple
+            The list of numbers or parameters that uniquely specify the
+            quantum object. For a state, this will be its symbol or its
+            set of quantum numbers.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.qexpr import QExpr
+        >>> q = QExpr(0)
+        >>> q
+        0
+        >>> q.label
+        (0,)
+        >>> q.hilbert_space
+        H
+        >>> q.args
+        (0,)
+        >>> q.is_commutative
+        False
+        """
+
+        # First compute args and call Expr.__new__ to create the instance
+        args = cls._eval_args(args, **kwargs)
+        if len(args) == 0:
+            args = cls._eval_args(tuple(cls.default_args()), **kwargs)
+        inst = Expr.__new__(cls, *args)
+        # Now set the slots on the instance
+        inst.hilbert_space = cls._eval_hilbert_space(args)
+        return inst
+
+    @classmethod
+    def _new_rawargs(cls, hilbert_space, *args, **old_assumptions):
+        """Create new instance of this class with hilbert_space and args.
+
+        This is used to bypass the more complex logic in the ``__new__``
+        method in cases where you already have the exact ``hilbert_space``
+        and ``args``. This should be used when you are positive these
+        arguments are valid, in their final, proper form and want to optimize
+        the creation of the object.
+        """
+
+        obj = Expr.__new__(cls, *args, **old_assumptions)
+        obj.hilbert_space = hilbert_space
+        return obj
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def label(self):
+        """The label is the unique set of identifiers for the object.
+
+        Usually, this will include all of the information about the state
+        *except* the time (in the case of time-dependent objects).
+
+        This must be a tuple, rather than a Tuple.
+        """
+        if len(self.args) == 0:  # If there is no label specified, return the default
+            return self._eval_args(list(self.default_args()))
+        else:
+            return self.args
+
+    @property
+    def is_symbolic(self):
+        return True
+
+    @classmethod
+    def default_args(self):
+        """If no arguments are specified, then this will return a default set
+        of arguments to be run through the constructor.
+
+        NOTE: Any classes that override this MUST return a tuple of arguments.
+        Should be overridden by subclasses to specify the default arguments for kets and operators
+        """
+        raise NotImplementedError("No default arguments for this class!")
+
+    #-------------------------------------------------------------------------
+    # _eval_* methods
+    #-------------------------------------------------------------------------
+
+    def _eval_adjoint(self):
+        obj = Expr._eval_adjoint(self)
+        if obj is None:
+            obj = Expr.__new__(Dagger, self)
+        if isinstance(obj, QExpr):
+            obj.hilbert_space = self.hilbert_space
+        return obj
+
+    @classmethod
+    def _eval_args(cls, args):
+        """Process the args passed to the __new__ method.
+
+        This simply runs args through _qsympify_sequence.
+        """
+        return _qsympify_sequence(args)
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        """Compute the Hilbert space instance from the args.
+        """
+        from sympy.physics.quantum.hilbert import HilbertSpace
+        return HilbertSpace()
+
+    #-------------------------------------------------------------------------
+    # Printing
+    #-------------------------------------------------------------------------
+
+    # Utilities for printing: these operate on raw SymPy objects
+
+    def _print_sequence(self, seq, sep, printer, *args):
+        result = []
+        for item in seq:
+            result.append(printer._print(item, *args))
+        return sep.join(result)
+
+    def _print_sequence_pretty(self, seq, sep, printer, *args):
+        pform = printer._print(seq[0], *args)
+        for item in seq[1:]:
+            pform = prettyForm(*pform.right(sep))
+            pform = prettyForm(*pform.right(printer._print(item, *args)))
+        return pform
+
+    # Utilities for printing: these operate prettyForm objects
+
+    def _print_subscript_pretty(self, a, b):
+        top = prettyForm(*b.left(' '*a.width()))
+        bot = prettyForm(*a.right(' '*b.width()))
+        return prettyForm(binding=prettyForm.POW, *bot.below(top))
+
+    def _print_superscript_pretty(self, a, b):
+        return a**b
+
+    def _print_parens_pretty(self, pform, left='(', right=')'):
+        return prettyForm(*pform.parens(left=left, right=right))
+
+    # Printing of labels (i.e. args)
+
+    def _print_label(self, printer, *args):
+        """Prints the label of the QExpr
+
+        This method prints self.label, using self._label_separator to separate
+        the elements. This method should not be overridden, instead, override
+        _print_contents to change printing behavior.
+        """
+        return self._print_sequence(
+            self.label, self._label_separator, printer, *args
+        )
+
+    def _print_label_repr(self, printer, *args):
+        return self._print_sequence(
+            self.label, ',', printer, *args
+        )
+
+    def _print_label_pretty(self, printer, *args):
+        return self._print_sequence_pretty(
+            self.label, self._label_separator, printer, *args
+        )
+
+    def _print_label_latex(self, printer, *args):
+        return self._print_sequence(
+            self.label, self._label_separator, printer, *args
+        )
+
+    # Printing of contents (default to label)
+
+    def _print_contents(self, printer, *args):
+        """Printer for contents of QExpr
+
+        Handles the printing of any unique identifying contents of a QExpr to
+        print as its contents, such as any variables or quantum numbers. The
+        default is to print the label, which is almost always the args. This
+        should not include printing of any brackets or parentheses.
+        """
+        return self._print_label(printer, *args)
+
+    def _print_contents_pretty(self, printer, *args):
+        return self._print_label_pretty(printer, *args)
+
+    def _print_contents_latex(self, printer, *args):
+        return self._print_label_latex(printer, *args)
+
+    # Main printing methods
+
+    def _sympystr(self, printer, *args):
+        """Default printing behavior of QExpr objects
+
+        Handles the default printing of a QExpr. To add other things to the
+        printing of the object, such as an operator name to operators or
+        brackets to states, the class should override the _print/_pretty/_latex
+        functions directly and make calls to _print_contents where appropriate.
+        This allows things like InnerProduct to easily control its printing the
+        printing of contents.
+        """
+        return self._print_contents(printer, *args)
+
+    def _sympyrepr(self, printer, *args):
+        classname = self.__class__.__name__
+        label = self._print_label_repr(printer, *args)
+        return '%s(%s)' % (classname, label)
+
+    def _pretty(self, printer, *args):
+        pform = self._print_contents_pretty(printer, *args)
+        return pform
+
+    def _latex(self, printer, *args):
+        return self._print_contents_latex(printer, *args)
+
+    #-------------------------------------------------------------------------
+    # Represent
+    #-------------------------------------------------------------------------
+
+    def _represent_default_basis(self, **options):
+        raise NotImplementedError('This object does not have a default basis')
+
+    def _represent(self, *, basis=None, **options):
+        """Represent this object in a given basis.
+
+        This method dispatches to the actual methods that perform the
+        representation. Subclases of QExpr should define various methods to
+        determine how the object will be represented in various bases. The
+        format of these methods is::
+
+            def _represent_BasisName(self, basis, **options):
+
+        Thus to define how a quantum object is represented in the basis of
+        the operator Position, you would define::
+
+            def _represent_Position(self, basis, **options):
+
+        Usually, basis object will be instances of Operator subclasses, but
+        there is a chance we will relax this in the future to accommodate other
+        types of basis sets that are not associated with an operator.
+
+        If the ``format`` option is given it can be ("sympy", "numpy",
+        "scipy.sparse"). This will ensure that any matrices that result from
+        representing the object are returned in the appropriate matrix format.
+
+        Parameters
+        ==========
+
+        basis : Operator
+            The Operator whose basis functions will be used as the basis for
+            representation.
+        options : dict
+            A dictionary of key/value pairs that give options and hints for
+            the representation, such as the number of basis functions to
+            be used.
+        """
+        if basis is None:
+            result = self._represent_default_basis(**options)
+        else:
+            result = dispatch_method(self, '_represent', basis, **options)
+
+        # If we get a matrix representation, convert it to the right format.
+        format = options.get('format', 'sympy')
+        result = self._format_represent(result, format)
+        return result
+
+    def _format_represent(self, result, format):
+        if format == 'sympy' and not isinstance(result, Matrix):
+            return to_sympy(result)
+        elif format == 'numpy' and not isinstance(result, numpy_ndarray):
+            return to_numpy(result)
+        elif format == 'scipy.sparse' and \
+                not isinstance(result, scipy_sparse_matrix):
+            return to_scipy_sparse(result)
+
+        return result
+
+
+def split_commutative_parts(e):
+    """Split into commutative and non-commutative parts."""
+    c_part, nc_part = e.args_cnc()
+    c_part = list(c_part)
+    return c_part, nc_part
+
+
+def split_qexpr_parts(e):
+    """Split an expression into Expr and noncommutative QExpr parts."""
+    expr_part = []
+    qexpr_part = []
+    for arg in e.args:
+        if not isinstance(arg, QExpr):
+            expr_part.append(arg)
+        else:
+            qexpr_part.append(arg)
+    return expr_part, qexpr_part
+
+
+def dispatch_method(self, basename, arg, **options):
+    """Dispatch a method to the proper handlers."""
+    method_name = '%s_%s' % (basename, arg.__class__.__name__)
+    if hasattr(self, method_name):
+        f = getattr(self, method_name)
+        # This can raise and we will allow it to propagate.
+        result = f(arg, **options)
+        if result is not None:
+            return result
+    raise NotImplementedError(
+        "%s.%s cannot handle: %r" %
+        (self.__class__.__name__, basename, arg)
+    )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qft.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qft.py
new file mode 100644
index 0000000000000000000000000000000000000000..c6a3fa4539267f7bb6cf015521007e292b3d4cfd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qft.py
@@ -0,0 +1,215 @@
+"""An implementation of qubits and gates acting on them.
+
+Todo:
+
+* Update docstrings.
+* Update tests.
+* Implement apply using decompose.
+* Implement represent using decompose or something smarter. For this to
+  work we first have to implement represent for SWAP.
+* Decide if we want upper index to be inclusive in the constructor.
+* Fix the printing of Rk gates in plotting.
+"""
+
+from sympy.core.expr import Expr
+from sympy.core.numbers import (I, Integer, pi)
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import exp
+from sympy.matrices.dense import Matrix
+from sympy.functions import sqrt
+
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qexpr import QuantumError, QExpr
+from sympy.matrices import eye
+from sympy.physics.quantum.tensorproduct import matrix_tensor_product
+
+from sympy.physics.quantum.gate import (
+    Gate, HadamardGate, SwapGate, OneQubitGate, CGate, PhaseGate, TGate, ZGate
+)
+
+from sympy.functions.elementary.complexes import sign
+
+__all__ = [
+    'QFT',
+    'IQFT',
+    'RkGate',
+    'Rk'
+]
+
+#-----------------------------------------------------------------------------
+# Fourier stuff
+#-----------------------------------------------------------------------------
+
+
+class RkGate(OneQubitGate):
+    """This is the R_k gate of the QTF."""
+    gate_name = 'Rk'
+    gate_name_latex = 'R'
+
+    def __new__(cls, *args):
+        if len(args) != 2:
+            raise QuantumError(
+                'Rk gates only take two arguments, got: %r' % args
+            )
+        # For small k, Rk gates simplify to other gates, using these
+        # substitutions give us familiar results for the QFT for small numbers
+        # of qubits.
+        target = args[0]
+        k = args[1]
+        if k == 1:
+            return ZGate(target)
+        elif k == 2:
+            return PhaseGate(target)
+        elif k == 3:
+            return TGate(target)
+        args = cls._eval_args(args)
+        inst = Expr.__new__(cls, *args)
+        inst.hilbert_space = cls._eval_hilbert_space(args)
+        return inst
+
+    @classmethod
+    def _eval_args(cls, args):
+        # Fall back to this, because Gate._eval_args assumes that args is
+        # all targets and can't contain duplicates.
+        return QExpr._eval_args(args)
+
+    @property
+    def k(self):
+        return self.label[1]
+
+    @property
+    def targets(self):
+        return self.label[:1]
+
+    @property
+    def gate_name_plot(self):
+        return r'$%s_%s$' % (self.gate_name_latex, str(self.k))
+
+    def get_target_matrix(self, format='sympy'):
+        if format == 'sympy':
+            return Matrix([[1, 0], [0, exp(sign(self.k)*Integer(2)*pi*I/(Integer(2)**abs(self.k)))]])
+        raise NotImplementedError(
+            'Invalid format for the R_k gate: %r' % format)
+
+
+Rk = RkGate
+
+
+class Fourier(Gate):
+    """Superclass of Quantum Fourier and Inverse Quantum Fourier Gates."""
+
+    @classmethod
+    def _eval_args(self, args):
+        if len(args) != 2:
+            raise QuantumError(
+                'QFT/IQFT only takes two arguments, got: %r' % args
+            )
+        if args[0] >= args[1]:
+            raise QuantumError("Start must be smaller than finish")
+        return Gate._eval_args(args)
+
+    def _represent_default_basis(self, **options):
+        return self._represent_ZGate(None, **options)
+
+    def _represent_ZGate(self, basis, **options):
+        """
+            Represents the (I)QFT In the Z Basis
+        """
+        nqubits = options.get('nqubits', 0)
+        if nqubits == 0:
+            raise QuantumError(
+                'The number of qubits must be given as nqubits.')
+        if nqubits < self.min_qubits:
+            raise QuantumError(
+                'The number of qubits %r is too small for the gate.' % nqubits
+            )
+        size = self.size
+        omega = self.omega
+
+        #Make a matrix that has the basic Fourier Transform Matrix
+        arrayFT = [[omega**(
+            i*j % size)/sqrt(size) for i in range(size)] for j in range(size)]
+        matrixFT = Matrix(arrayFT)
+
+        #Embed the FT Matrix in a higher space, if necessary
+        if self.label[0] != 0:
+            matrixFT = matrix_tensor_product(eye(2**self.label[0]), matrixFT)
+        if self.min_qubits < nqubits:
+            matrixFT = matrix_tensor_product(
+                matrixFT, eye(2**(nqubits - self.min_qubits)))
+
+        return matrixFT
+
+    @property
+    def targets(self):
+        return range(self.label[0], self.label[1])
+
+    @property
+    def min_qubits(self):
+        return self.label[1]
+
+    @property
+    def size(self):
+        """Size is the size of the QFT matrix"""
+        return 2**(self.label[1] - self.label[0])
+
+    @property
+    def omega(self):
+        return Symbol('omega')
+
+
+class QFT(Fourier):
+    """The forward quantum Fourier transform."""
+
+    gate_name = 'QFT'
+    gate_name_latex = 'QFT'
+
+    def decompose(self):
+        """Decomposes QFT into elementary gates."""
+        start = self.label[0]
+        finish = self.label[1]
+        circuit = 1
+        for level in reversed(range(start, finish)):
+            circuit = HadamardGate(level)*circuit
+            for i in range(level - start):
+                circuit = CGate(level - i - 1, RkGate(level, i + 2))*circuit
+        for i in range((finish - start)//2):
+            circuit = SwapGate(i + start, finish - i - 1)*circuit
+        return circuit
+
+    def _apply_operator_Qubit(self, qubits, **options):
+        return qapply(self.decompose()*qubits)
+
+    def _eval_inverse(self):
+        return IQFT(*self.args)
+
+    @property
+    def omega(self):
+        return exp(2*pi*I/self.size)
+
+
+class IQFT(Fourier):
+    """The inverse quantum Fourier transform."""
+
+    gate_name = 'IQFT'
+    gate_name_latex = '{QFT^{-1}}'
+
+    def decompose(self):
+        """Decomposes IQFT into elementary gates."""
+        start = self.args[0]
+        finish = self.args[1]
+        circuit = 1
+        for i in range((finish - start)//2):
+            circuit = SwapGate(i + start, finish - i - 1)*circuit
+        for level in range(start, finish):
+            for i in reversed(range(level - start)):
+                circuit = CGate(level - i - 1, RkGate(level, -i - 2))*circuit
+            circuit = HadamardGate(level)*circuit
+        return circuit
+
+    def _eval_inverse(self):
+        return QFT(*self.args)
+
+    @property
+    def omega(self):
+        return exp(-2*pi*I/self.size)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qubit.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qubit.py
new file mode 100644
index 0000000000000000000000000000000000000000..71d1dbc01e3a16e2a4b64eec3c3800b7218b2636
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/qubit.py
@@ -0,0 +1,811 @@
+"""Qubits for quantum computing.
+
+Todo:
+* Finish implementing measurement logic. This should include POVM.
+* Update docstrings.
+* Update tests.
+"""
+
+
+import math
+
+from sympy.core.add import Add
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.exponential import log
+from sympy.core.basic import _sympify
+from sympy.external.gmpy import SYMPY_INTS
+from sympy.matrices import Matrix, zeros
+from sympy.printing.pretty.stringpict import prettyForm
+
+from sympy.physics.quantum.hilbert import ComplexSpace
+from sympy.physics.quantum.state import Ket, Bra, State
+
+from sympy.physics.quantum.qexpr import QuantumError
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.matrixutils import (
+    numpy_ndarray, scipy_sparse_matrix
+)
+from mpmath.libmp.libintmath import bitcount
+
+__all__ = [
+    'Qubit',
+    'QubitBra',
+    'IntQubit',
+    'IntQubitBra',
+    'qubit_to_matrix',
+    'matrix_to_qubit',
+    'matrix_to_density',
+    'measure_all',
+    'measure_partial',
+    'measure_partial_oneshot',
+    'measure_all_oneshot'
+]
+
+#-----------------------------------------------------------------------------
+# Qubit Classes
+#-----------------------------------------------------------------------------
+
+
+class QubitState(State):
+    """Base class for Qubit and QubitBra."""
+
+    #-------------------------------------------------------------------------
+    # Initialization/creation
+    #-------------------------------------------------------------------------
+
+    @classmethod
+    def _eval_args(cls, args):
+        # If we are passed a QubitState or subclass, we just take its qubit
+        # values directly.
+        if len(args) == 1 and isinstance(args[0], QubitState):
+            return args[0].qubit_values
+
+        # Turn strings into tuple of strings
+        if len(args) == 1 and isinstance(args[0], str):
+            args = tuple( S.Zero if qb == "0" else S.One for qb in args[0])
+        else:
+            args = tuple( S.Zero if qb == "0" else S.One if qb == "1" else qb for qb in args)
+        args = tuple(_sympify(arg) for arg in args)
+
+        # Validate input (must have 0 or 1 input)
+        for element in args:
+            if element not in (S.Zero, S.One):
+                raise ValueError(
+                    "Qubit values must be 0 or 1, got: %r" % element)
+        return args
+
+    @classmethod
+    def _eval_hilbert_space(cls, args):
+        return ComplexSpace(2)**len(args)
+
+    #-------------------------------------------------------------------------
+    # Properties
+    #-------------------------------------------------------------------------
+
+    @property
+    def dimension(self):
+        """The number of Qubits in the state."""
+        return len(self.qubit_values)
+
+    @property
+    def nqubits(self):
+        return self.dimension
+
+    @property
+    def qubit_values(self):
+        """Returns the values of the qubits as a tuple."""
+        return self.label
+
+    #-------------------------------------------------------------------------
+    # Special methods
+    #-------------------------------------------------------------------------
+
+    def __len__(self):
+        return self.dimension
+
+    def __getitem__(self, bit):
+        return self.qubit_values[int(self.dimension - bit - 1)]
+
+    #-------------------------------------------------------------------------
+    # Utility methods
+    #-------------------------------------------------------------------------
+
+    def flip(self, *bits):
+        """Flip the bit(s) given."""
+        newargs = list(self.qubit_values)
+        for i in bits:
+            bit = int(self.dimension - i - 1)
+            if newargs[bit] == 1:
+                newargs[bit] = 0
+            else:
+                newargs[bit] = 1
+        return self.__class__(*tuple(newargs))
+
+
+class Qubit(QubitState, Ket):
+    """A multi-qubit ket in the computational (z) basis.
+
+    We use the normal convention that the least significant qubit is on the
+    right, so ``|00001>`` has a 1 in the least significant qubit.
+
+    Parameters
+    ==========
+
+    values : list, str
+        The qubit values as a list of ints ([0,0,0,1,1,]) or a string ('011').
+
+    Examples
+    ========
+
+    Create a qubit in a couple of different ways and look at their attributes:
+
+        >>> from sympy.physics.quantum.qubit import Qubit
+        >>> Qubit(0,0,0)
+        |000>
+        >>> q = Qubit('0101')
+        >>> q
+        |0101>
+
+        >>> q.nqubits
+        4
+        >>> len(q)
+        4
+        >>> q.dimension
+        4
+        >>> q.qubit_values
+        (0, 1, 0, 1)
+
+    We can flip the value of an individual qubit:
+
+        >>> q.flip(1)
+        |0111>
+
+    We can take the dagger of a Qubit to get a bra:
+
+        >>> from sympy.physics.quantum.dagger import Dagger
+        >>> Dagger(q)
+        <0101|
+        >>> type(Dagger(q))
+        
+
+    Inner products work as expected:
+
+        >>> ip = Dagger(q)*q
+        >>> ip
+        <0101|0101>
+        >>> ip.doit()
+        1
+    """
+
+    @classmethod
+    def dual_class(self):
+        return QubitBra
+
+    def _eval_innerproduct_QubitBra(self, bra, **hints):
+        if self.label == bra.label:
+            return S.One
+        else:
+            return S.Zero
+
+    def _represent_default_basis(self, **options):
+        return self._represent_ZGate(None, **options)
+
+    def _represent_ZGate(self, basis, **options):
+        """Represent this qubits in the computational basis (ZGate).
+        """
+        _format = options.get('format', 'sympy')
+        n = 1
+        definite_state = 0
+        for it in reversed(self.qubit_values):
+            definite_state += n*it
+            n = n*2
+        result = [0]*(2**self.dimension)
+        result[int(definite_state)] = 1
+        if _format == 'sympy':
+            return Matrix(result)
+        elif _format == 'numpy':
+            import numpy as np
+            return np.array(result, dtype='complex').transpose()
+        elif _format == 'scipy.sparse':
+            from scipy import sparse
+            return sparse.csr_matrix(result, dtype='complex').transpose()
+
+    def _eval_trace(self, bra, **kwargs):
+        indices = kwargs.get('indices', [])
+
+        #sort index list to begin trace from most-significant
+        #qubit
+        sorted_idx = list(indices)
+        if len(sorted_idx) == 0:
+            sorted_idx = list(range(0, self.nqubits))
+        sorted_idx.sort()
+
+        #trace out for each of index
+        new_mat = self*bra
+        for i in range(len(sorted_idx) - 1, -1, -1):
+            # start from tracing out from leftmost qubit
+            new_mat = self._reduced_density(new_mat, int(sorted_idx[i]))
+
+        if (len(sorted_idx) == self.nqubits):
+            #in case full trace was requested
+            return new_mat[0]
+        else:
+            return matrix_to_density(new_mat)
+
+    def _reduced_density(self, matrix, qubit, **options):
+        """Compute the reduced density matrix by tracing out one qubit.
+           The qubit argument should be of type Python int, since it is used
+           in bit operations
+        """
+        def find_index_that_is_projected(j, k, qubit):
+            bit_mask = 2**qubit - 1
+            return ((j >> qubit) << (1 + qubit)) + (j & bit_mask) + (k << qubit)
+
+        old_matrix = represent(matrix, **options)
+        old_size = old_matrix.cols
+        #we expect the old_size to be even
+        new_size = old_size//2
+        new_matrix = Matrix().zeros(new_size)
+
+        for i in range(new_size):
+            for j in range(new_size):
+                for k in range(2):
+                    col = find_index_that_is_projected(j, k, qubit)
+                    row = find_index_that_is_projected(i, k, qubit)
+                    new_matrix[i, j] += old_matrix[row, col]
+
+        return new_matrix
+
+
+class QubitBra(QubitState, Bra):
+    """A multi-qubit bra in the computational (z) basis.
+
+    We use the normal convention that the least significant qubit is on the
+    right, so ``|00001>`` has a 1 in the least significant qubit.
+
+    Parameters
+    ==========
+
+    values : list, str
+        The qubit values as a list of ints ([0,0,0,1,1,]) or a string ('011').
+
+    See also
+    ========
+
+    Qubit: Examples using qubits
+
+    """
+    @classmethod
+    def dual_class(self):
+        return Qubit
+
+
+class IntQubitState(QubitState):
+    """A base class for qubits that work with binary representations."""
+
+    @classmethod
+    def _eval_args(cls, args, nqubits=None):
+        # The case of a QubitState instance
+        if len(args) == 1 and isinstance(args[0], QubitState):
+            return QubitState._eval_args(args)
+        # otherwise, args should be integer
+        elif not all(isinstance(a, (int, Integer)) for a in args):
+            raise ValueError('values must be integers, got (%s)' % (tuple(type(a) for a in args),))
+        # use nqubits if specified
+        if nqubits is not None:
+            if not isinstance(nqubits, (int, Integer)):
+                raise ValueError('nqubits must be an integer, got (%s)' % type(nqubits))
+            if len(args) != 1:
+                raise ValueError(
+                    'too many positional arguments (%s). should be (number, nqubits=n)' % (args,))
+            return cls._eval_args_with_nqubits(args[0], nqubits)
+        # For a single argument, we construct the binary representation of
+        # that integer with the minimal number of bits.
+        if len(args) == 1 and args[0] > 1:
+            #rvalues is the minimum number of bits needed to express the number
+            rvalues = reversed(range(bitcount(abs(args[0]))))
+            qubit_values = [(args[0] >> i) & 1 for i in rvalues]
+            return QubitState._eval_args(qubit_values)
+        # For two numbers, the second number is the number of bits
+        # on which it is expressed, so IntQubit(0,5) == |00000>.
+        elif len(args) == 2 and args[1] > 1:
+            return cls._eval_args_with_nqubits(args[0], args[1])
+        else:
+            return QubitState._eval_args(args)
+
+    @classmethod
+    def _eval_args_with_nqubits(cls, number, nqubits):
+        need = bitcount(abs(number))
+        if nqubits < need:
+            raise ValueError(
+                'cannot represent %s with %s bits' % (number, nqubits))
+        qubit_values = [(number >> i) & 1 for i in reversed(range(nqubits))]
+        return QubitState._eval_args(qubit_values)
+
+    def as_int(self):
+        """Return the numerical value of the qubit."""
+        number = 0
+        n = 1
+        for i in reversed(self.qubit_values):
+            number += n*i
+            n = n << 1
+        return number
+
+    def _print_label(self, printer, *args):
+        return str(self.as_int())
+
+    def _print_label_pretty(self, printer, *args):
+        label = self._print_label(printer, *args)
+        return prettyForm(label)
+
+    _print_label_repr = _print_label
+    _print_label_latex = _print_label
+
+
+class IntQubit(IntQubitState, Qubit):
+    """A qubit ket that store integers as binary numbers in qubit values.
+
+    The differences between this class and ``Qubit`` are:
+
+    * The form of the constructor.
+    * The qubit values are printed as their corresponding integer, rather
+      than the raw qubit values. The internal storage format of the qubit
+      values in the same as ``Qubit``.
+
+    Parameters
+    ==========
+
+    values : int, tuple
+        If a single argument, the integer we want to represent in the qubit
+        values. This integer will be represented using the fewest possible
+        number of qubits.
+        If a pair of integers and the second value is more than one, the first
+        integer gives the integer to represent in binary form and the second
+        integer gives the number of qubits to use.
+        List of zeros and ones is also accepted to generate qubit by bit pattern.
+
+    nqubits : int
+        The integer that represents the number of qubits.
+        This number should be passed with keyword ``nqubits=N``.
+        You can use this in order to avoid ambiguity of Qubit-style tuple of bits.
+        Please see the example below for more details.
+
+    Examples
+    ========
+
+    Create a qubit for the integer 5:
+
+        >>> from sympy.physics.quantum.qubit import IntQubit
+        >>> from sympy.physics.quantum.qubit import Qubit
+        >>> q = IntQubit(5)
+        >>> q
+        |5>
+
+    We can also create an ``IntQubit`` by passing a ``Qubit`` instance.
+
+        >>> q = IntQubit(Qubit('101'))
+        >>> q
+        |5>
+        >>> q.as_int()
+        5
+        >>> q.nqubits
+        3
+        >>> q.qubit_values
+        (1, 0, 1)
+
+    We can go back to the regular qubit form.
+
+        >>> Qubit(q)
+        |101>
+
+    Please note that ``IntQubit`` also accepts a ``Qubit``-style list of bits.
+    So, the code below yields qubits 3, not a single bit ``1``.
+
+        >>> IntQubit(1, 1)
+        |3>
+
+    To avoid ambiguity, use ``nqubits`` parameter.
+    Use of this keyword is recommended especially when you provide the values by variables.
+
+        >>> IntQubit(1, nqubits=1)
+        |1>
+        >>> a = 1
+        >>> IntQubit(a, nqubits=1)
+        |1>
+    """
+    @classmethod
+    def dual_class(self):
+        return IntQubitBra
+
+    def _eval_innerproduct_IntQubitBra(self, bra, **hints):
+        return Qubit._eval_innerproduct_QubitBra(self, bra)
+
+class IntQubitBra(IntQubitState, QubitBra):
+    """A qubit bra that store integers as binary numbers in qubit values."""
+
+    @classmethod
+    def dual_class(self):
+        return IntQubit
+
+
+#-----------------------------------------------------------------------------
+# Qubit <---> Matrix conversion functions
+#-----------------------------------------------------------------------------
+
+
+def matrix_to_qubit(matrix):
+    """Convert from the matrix repr. to a sum of Qubit objects.
+
+    Parameters
+    ----------
+    matrix : Matrix, numpy.matrix, scipy.sparse
+        The matrix to build the Qubit representation of. This works with
+        SymPy matrices, numpy matrices and scipy.sparse sparse matrices.
+
+    Examples
+    ========
+
+    Represent a state and then go back to its qubit form:
+
+        >>> from sympy.physics.quantum.qubit import matrix_to_qubit, Qubit
+        >>> from sympy.physics.quantum.represent import represent
+        >>> q = Qubit('01')
+        >>> matrix_to_qubit(represent(q))
+        |01>
+    """
+    # Determine the format based on the type of the input matrix
+    format = 'sympy'
+    if isinstance(matrix, numpy_ndarray):
+        format = 'numpy'
+    if isinstance(matrix, scipy_sparse_matrix):
+        format = 'scipy.sparse'
+
+    # Make sure it is of correct dimensions for a Qubit-matrix representation.
+    # This logic should work with sympy, numpy or scipy.sparse matrices.
+    if matrix.shape[0] == 1:
+        mlistlen = matrix.shape[1]
+        nqubits = log(mlistlen, 2)
+        ket = False
+        cls = QubitBra
+    elif matrix.shape[1] == 1:
+        mlistlen = matrix.shape[0]
+        nqubits = log(mlistlen, 2)
+        ket = True
+        cls = Qubit
+    else:
+        raise QuantumError(
+            'Matrix must be a row/column vector, got %r' % matrix
+        )
+    if not isinstance(nqubits, Integer):
+        raise QuantumError('Matrix must be a row/column vector of size '
+                           '2**nqubits, got: %r' % matrix)
+    # Go through each item in matrix, if element is non-zero, make it into a
+    # Qubit item times the element.
+    result = 0
+    for i in range(mlistlen):
+        if ket:
+            element = matrix[i, 0]
+        else:
+            element = matrix[0, i]
+        if format in ('numpy', 'scipy.sparse'):
+            element = complex(element)
+        if element:
+            # Form Qubit array; 0 in bit-locations where i is 0, 1 in
+            # bit-locations where i is 1
+            qubit_array = [int(i & (1 << x) != 0) for x in range(nqubits)]
+            qubit_array.reverse()
+            result = result + element*cls(*qubit_array)
+
+    # If SymPy simplified by pulling out a constant coefficient, undo that.
+    if isinstance(result, (Mul, Add, Pow)):
+        result = result.expand()
+
+    return result
+
+
+def matrix_to_density(mat):
+    """
+    Works by finding the eigenvectors and eigenvalues of the matrix.
+    We know we can decompose rho by doing:
+    sum(EigenVal*|Eigenvect>>> from sympy.physics.quantum.qubit import Qubit, measure_all
+        >>> from sympy.physics.quantum.gate import H
+        >>> from sympy.physics.quantum.qapply import qapply
+
+        >>> c = H(0)*H(1)*Qubit('00')
+        >>> c
+        H(0)*H(1)*|00>
+        >>> q = qapply(c)
+        >>> measure_all(q)
+        [(|00>, 1/4), (|01>, 1/4), (|10>, 1/4), (|11>, 1/4)]
+    """
+    m = qubit_to_matrix(qubit, format)
+
+    if format == 'sympy':
+        results = []
+
+        if normalize:
+            m = m.normalized()
+
+        size = max(m.shape)  # Max of shape to account for bra or ket
+        nqubits = int(math.log(size)/math.log(2))
+        for i in range(size):
+            if m[i]:
+                results.append(
+                    (Qubit(IntQubit(i, nqubits=nqubits)), m[i]*conjugate(m[i]))
+                )
+        return results
+    else:
+        raise NotImplementedError(
+            "This function cannot handle non-SymPy matrix formats yet"
+        )
+
+
+def measure_partial(qubit, bits, format='sympy', normalize=True):
+    """Perform a partial ensemble measure on the specified qubits.
+
+    Parameters
+    ==========
+
+    qubits : Qubit
+        The qubit to measure.  This can be any Qubit or a linear combination
+        of them.
+    bits : tuple
+        The qubits to measure.
+    format : str
+        The format of the intermediate matrices to use. Possible values are
+        ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is
+        implemented.
+
+    Returns
+    =======
+
+    result : list
+        A list that consists of primitive states and their probabilities.
+
+    Examples
+    ========
+
+        >>> from sympy.physics.quantum.qubit import Qubit, measure_partial
+        >>> from sympy.physics.quantum.gate import H
+        >>> from sympy.physics.quantum.qapply import qapply
+
+        >>> c = H(0)*H(1)*Qubit('00')
+        >>> c
+        H(0)*H(1)*|00>
+        >>> q = qapply(c)
+        >>> measure_partial(q, (0,))
+        [(sqrt(2)*|00>/2 + sqrt(2)*|10>/2, 1/2), (sqrt(2)*|01>/2 + sqrt(2)*|11>/2, 1/2)]
+    """
+    m = qubit_to_matrix(qubit, format)
+
+    if isinstance(bits, (SYMPY_INTS, Integer)):
+        bits = (int(bits),)
+
+    if format == 'sympy':
+        if normalize:
+            m = m.normalized()
+
+        possible_outcomes = _get_possible_outcomes(m, bits)
+
+        # Form output from function.
+        output = []
+        for outcome in possible_outcomes:
+            # Calculate probability of finding the specified bits with
+            # given values.
+            prob_of_outcome = 0
+            prob_of_outcome += (outcome.H*outcome)[0]
+
+            # If the output has a chance, append it to output with found
+            # probability.
+            if prob_of_outcome != 0:
+                if normalize:
+                    next_matrix = matrix_to_qubit(outcome.normalized())
+                else:
+                    next_matrix = matrix_to_qubit(outcome)
+
+                output.append((
+                    next_matrix,
+                    prob_of_outcome
+                ))
+
+        return output
+    else:
+        raise NotImplementedError(
+            "This function cannot handle non-SymPy matrix formats yet"
+        )
+
+
+def measure_partial_oneshot(qubit, bits, format='sympy'):
+    """Perform a partial oneshot measurement on the specified qubits.
+
+    A oneshot measurement is equivalent to performing a measurement on a
+    quantum system. This type of measurement does not return the probabilities
+    like an ensemble measurement does, but rather returns *one* of the
+    possible resulting states. The exact state that is returned is determined
+    by picking a state randomly according to the ensemble probabilities.
+
+    Parameters
+    ----------
+    qubits : Qubit
+        The qubit to measure.  This can be any Qubit or a linear combination
+        of them.
+    bits : tuple
+        The qubits to measure.
+    format : str
+        The format of the intermediate matrices to use. Possible values are
+        ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is
+        implemented.
+
+    Returns
+    -------
+    result : Qubit
+        The qubit that the system collapsed to upon measurement.
+    """
+    import random
+    m = qubit_to_matrix(qubit, format)
+
+    if format == 'sympy':
+        m = m.normalized()
+        possible_outcomes = _get_possible_outcomes(m, bits)
+
+        # Form output from function
+        random_number = random.random()
+        total_prob = 0
+        for outcome in possible_outcomes:
+            # Calculate probability of finding the specified bits
+            # with given values
+            total_prob += (outcome.H*outcome)[0]
+            if total_prob >= random_number:
+                return matrix_to_qubit(outcome.normalized())
+    else:
+        raise NotImplementedError(
+            "This function cannot handle non-SymPy matrix formats yet"
+        )
+
+
+def _get_possible_outcomes(m, bits):
+    """Get the possible states that can be produced in a measurement.
+
+    Parameters
+    ----------
+    m : Matrix
+        The matrix representing the state of the system.
+    bits : tuple, list
+        Which bits will be measured.
+
+    Returns
+    -------
+    result : list
+        The list of possible states which can occur given this measurement.
+        These are un-normalized so we can derive the probability of finding
+        this state by taking the inner product with itself
+    """
+
+    # This is filled with loads of dirty binary tricks...You have been warned
+
+    size = max(m.shape)  # Max of shape to account for bra or ket
+    nqubits = int(math.log2(size) + .1)  # Number of qubits possible
+
+    # Make the output states and put in output_matrices, nothing in them now.
+    # Each state will represent a possible outcome of the measurement
+    # Thus, output_matrices[0] is the matrix which we get when all measured
+    # bits return 0. and output_matrices[1] is the matrix for only the 0th
+    # bit being true
+    output_matrices = []
+    for i in range(1 << len(bits)):
+        output_matrices.append(zeros(2**nqubits, 1))
+
+    # Bitmasks will help sort how to determine possible outcomes.
+    # When the bit mask is and-ed with a matrix-index,
+    # it will determine which state that index belongs to
+    bit_masks = []
+    for bit in bits:
+        bit_masks.append(1 << bit)
+
+    # Make possible outcome states
+    for i in range(2**nqubits):
+        trueness = 0  # This tells us to which output_matrix this value belongs
+        # Find trueness
+        for j in range(len(bit_masks)):
+            if i & bit_masks[j]:
+                trueness += j + 1
+        # Put the value in the correct output matrix
+        output_matrices[trueness][i] = m[i]
+    return output_matrices
+
+
+def measure_all_oneshot(qubit, format='sympy'):
+    """Perform a oneshot ensemble measurement on all qubits.
+
+    A oneshot measurement is equivalent to performing a measurement on a
+    quantum system. This type of measurement does not return the probabilities
+    like an ensemble measurement does, but rather returns *one* of the
+    possible resulting states. The exact state that is returned is determined
+    by picking a state randomly according to the ensemble probabilities.
+
+    Parameters
+    ----------
+    qubits : Qubit
+        The qubit to measure.  This can be any Qubit or a linear combination
+        of them.
+    format : str
+        The format of the intermediate matrices to use. Possible values are
+        ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is
+        implemented.
+
+    Returns
+    -------
+    result : Qubit
+        The qubit that the system collapsed to upon measurement.
+    """
+    import random
+    m = qubit_to_matrix(qubit)
+
+    if format == 'sympy':
+        m = m.normalized()
+        random_number = random.random()
+        total = 0
+        result = 0
+        for i in m:
+            total += i*i.conjugate()
+            if total > random_number:
+                break
+            result += 1
+        return Qubit(IntQubit(result, nqubits=int(math.log2(max(m.shape)) + .1)))
+    else:
+        raise NotImplementedError(
+            "This function cannot handle non-SymPy matrix formats yet"
+        )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/represent.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/represent.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a1ada80aa6a3dd2caad43ec132fb9a148947106
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/represent.py
@@ -0,0 +1,574 @@
+"""Logic for representing operators in state in various bases.
+
+TODO:
+
+* Get represent working with continuous hilbert spaces.
+* Document default basis functionality.
+"""
+
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.integrals.integrals import integrate
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.qexpr import QExpr
+from sympy.physics.quantum.tensorproduct import TensorProduct
+from sympy.physics.quantum.matrixutils import flatten_scalar
+from sympy.physics.quantum.state import KetBase, BraBase, StateBase
+from sympy.physics.quantum.operator import Operator, OuterProduct
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.operatorset import operators_to_state, state_to_operators
+
+
+__all__ = [
+    'represent',
+    'rep_innerproduct',
+    'rep_expectation',
+    'integrate_result',
+    'get_basis',
+    'enumerate_states'
+]
+
+#-----------------------------------------------------------------------------
+# Represent
+#-----------------------------------------------------------------------------
+
+
+def _sympy_to_scalar(e):
+    """Convert from a SymPy scalar to a Python scalar."""
+    if isinstance(e, Expr):
+        if e.is_Integer:
+            return int(e)
+        elif e.is_Float:
+            return float(e)
+        elif e.is_Rational:
+            return float(e)
+        elif e.is_Number or e.is_NumberSymbol or e == I:
+            return complex(e)
+    raise TypeError('Expected number, got: %r' % e)
+
+
+def represent(expr, **options):
+    """Represent the quantum expression in the given basis.
+
+    In quantum mechanics abstract states and operators can be represented in
+    various basis sets. Under this operation the follow transforms happen:
+
+    * Ket -> column vector or function
+    * Bra -> row vector of function
+    * Operator -> matrix or differential operator
+
+    This function is the top-level interface for this action.
+
+    This function walks the SymPy expression tree looking for ``QExpr``
+    instances that have a ``_represent`` method. This method is then called
+    and the object is replaced by the representation returned by this method.
+    By default, the ``_represent`` method will dispatch to other methods
+    that handle the representation logic for a particular basis set. The
+    naming convention for these methods is the following::
+
+        def _represent_FooBasis(self, e, basis, **options)
+
+    This function will have the logic for representing instances of its class
+    in the basis set having a class named ``FooBasis``.
+
+    Parameters
+    ==========
+
+    expr  : Expr
+        The expression to represent.
+    basis : Operator, basis set
+        An object that contains the information about the basis set. If an
+        operator is used, the basis is assumed to be the orthonormal
+        eigenvectors of that operator. In general though, the basis argument
+        can be any object that contains the basis set information.
+    options : dict
+        Key/value pairs of options that are passed to the underlying method
+        that finds the representation. These options can be used to
+        control how the representation is done. For example, this is where
+        the size of the basis set would be set.
+
+    Returns
+    =======
+
+    e : Expr
+        The SymPy expression of the represented quantum expression.
+
+    Examples
+    ========
+
+    Here we subclass ``Operator`` and ``Ket`` to create the z-spin operator
+    and its spin 1/2 up eigenstate. By defining the ``_represent_SzOp``
+    method, the ket can be represented in the z-spin basis.
+
+    >>> from sympy.physics.quantum import Operator, represent, Ket
+    >>> from sympy import Matrix
+
+    >>> class SzUpKet(Ket):
+    ...     def _represent_SzOp(self, basis, **options):
+    ...         return Matrix([1,0])
+    ...
+    >>> class SzOp(Operator):
+    ...     pass
+    ...
+    >>> sz = SzOp('Sz')
+    >>> up = SzUpKet('up')
+    >>> represent(up, basis=sz)
+    Matrix([
+    [1],
+    [0]])
+
+    Here we see an example of representations in a continuous
+    basis. We see that the result of representing various combinations
+    of cartesian position operators and kets give us continuous
+    expressions involving DiracDelta functions.
+
+    >>> from sympy.physics.quantum.cartesian import XOp, XKet, XBra
+    >>> X = XOp()
+    >>> x = XKet()
+    >>> y = XBra('y')
+    >>> represent(X*x)
+    x*DiracDelta(x - x_2)
+    """
+
+    format = options.get('format', 'sympy')
+    if format == 'numpy':
+        import numpy as np
+    if isinstance(expr, QExpr) and not isinstance(expr, OuterProduct):
+        options['replace_none'] = False
+        temp_basis = get_basis(expr, **options)
+        if temp_basis is not None:
+            options['basis'] = temp_basis
+        try:
+            return expr._represent(**options)
+        except NotImplementedError as strerr:
+            #If no _represent_FOO method exists, map to the
+            #appropriate basis state and try
+            #the other methods of representation
+            options['replace_none'] = True
+
+            if isinstance(expr, (KetBase, BraBase)):
+                try:
+                    return rep_innerproduct(expr, **options)
+                except NotImplementedError:
+                    raise NotImplementedError(strerr)
+            elif isinstance(expr, Operator):
+                try:
+                    return rep_expectation(expr, **options)
+                except NotImplementedError:
+                    raise NotImplementedError(strerr)
+            else:
+                raise NotImplementedError(strerr)
+    elif isinstance(expr, Add):
+        result = represent(expr.args[0], **options)
+        for args in expr.args[1:]:
+            # scipy.sparse doesn't support += so we use plain = here.
+            result = result + represent(args, **options)
+        return result
+    elif isinstance(expr, Pow):
+        base, exp = expr.as_base_exp()
+        if format in ('numpy', 'scipy.sparse'):
+            exp = _sympy_to_scalar(exp)
+        base = represent(base, **options)
+        # scipy.sparse doesn't support negative exponents
+        # and warns when inverting a matrix in csr format.
+        if format == 'scipy.sparse' and exp < 0:
+            from scipy.sparse.linalg import inv
+            exp = - exp
+            base = inv(base.tocsc()).tocsr()
+        if format == 'numpy':
+            return np.linalg.matrix_power(base, exp)
+        return base ** exp
+    elif isinstance(expr, TensorProduct):
+        new_args = [represent(arg, **options) for arg in expr.args]
+        return TensorProduct(*new_args)
+    elif isinstance(expr, Dagger):
+        return Dagger(represent(expr.args[0], **options))
+    elif isinstance(expr, Commutator):
+        A = expr.args[0]
+        B = expr.args[1]
+        return represent(Mul(A, B) - Mul(B, A), **options)
+    elif isinstance(expr, AntiCommutator):
+        A = expr.args[0]
+        B = expr.args[1]
+        return represent(Mul(A, B) + Mul(B, A), **options)
+    elif not isinstance(expr, (Mul, OuterProduct, InnerProduct)):
+        # We have removed special handling of inner products that used to be
+        # required (before automatic transforms).
+        # For numpy and scipy.sparse, we can only handle numerical prefactors.
+        if format in ('numpy', 'scipy.sparse'):
+            return _sympy_to_scalar(expr)
+        return expr
+
+    if not isinstance(expr, (Mul, OuterProduct, InnerProduct)):
+        raise TypeError('Mul expected, got: %r' % expr)
+
+    if "index" in options:
+        options["index"] += 1
+    else:
+        options["index"] = 1
+
+    if "unities" not in options:
+        options["unities"] = []
+
+    result = represent(expr.args[-1], **options)
+    last_arg = expr.args[-1]
+
+    for arg in reversed(expr.args[:-1]):
+        if isinstance(last_arg, Operator):
+            options["index"] += 1
+            options["unities"].append(options["index"])
+        elif isinstance(last_arg, BraBase) and isinstance(arg, KetBase):
+            options["index"] += 1
+        elif isinstance(last_arg, KetBase) and isinstance(arg, Operator):
+            options["unities"].append(options["index"])
+        elif isinstance(last_arg, KetBase) and isinstance(arg, BraBase):
+            options["unities"].append(options["index"])
+
+        next_arg = represent(arg, **options)
+        if format == 'numpy' and isinstance(next_arg, np.ndarray):
+            # Must use np.matmult to "matrix multiply" two np.ndarray
+            result = np.matmul(next_arg, result)
+        else:
+            result = next_arg*result
+        last_arg = arg
+
+    # All three matrix formats create 1 by 1 matrices when inner products of
+    # vectors are taken. In these cases, we simply return a scalar.
+    result = flatten_scalar(result)
+
+    result = integrate_result(expr, result, **options)
+
+    return result
+
+
+def rep_innerproduct(expr, **options):
+    """
+    Returns an innerproduct like representation (e.g. ````) for the
+    given state.
+
+    Attempts to calculate inner product with a bra from the specified
+    basis. Should only be passed an instance of KetBase or BraBase
+
+    Parameters
+    ==========
+
+    expr : KetBase or BraBase
+        The expression to be represented
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.represent import rep_innerproduct
+    >>> from sympy.physics.quantum.cartesian import XOp, XKet, PxOp, PxKet
+    >>> rep_innerproduct(XKet())
+    DiracDelta(x - x_1)
+    >>> rep_innerproduct(XKet(), basis=PxOp())
+    sqrt(2)*exp(-I*px_1*x/hbar)/(2*sqrt(hbar)*sqrt(pi))
+    >>> rep_innerproduct(PxKet(), basis=XOp())
+    sqrt(2)*exp(I*px*x_1/hbar)/(2*sqrt(hbar)*sqrt(pi))
+
+    """
+
+    if not isinstance(expr, (KetBase, BraBase)):
+        raise TypeError("expr passed is not a Bra or Ket")
+
+    basis = get_basis(expr, **options)
+
+    if not isinstance(basis, StateBase):
+        raise NotImplementedError("Can't form this representation!")
+
+    if "index" not in options:
+        options["index"] = 1
+
+    basis_kets = enumerate_states(basis, options["index"], 2)
+
+    if isinstance(expr, BraBase):
+        bra = expr
+        ket = (basis_kets[1] if basis_kets[0].dual == expr else basis_kets[0])
+    else:
+        bra = (basis_kets[1].dual if basis_kets[0]
+               == expr else basis_kets[0].dual)
+        ket = expr
+
+    prod = InnerProduct(bra, ket)
+    result = prod.doit()
+
+    format = options.get('format', 'sympy')
+    result = expr._format_represent(result, format)
+    return result
+
+
+def rep_expectation(expr, **options):
+    """
+    Returns an ```` type representation for the given operator.
+
+    Parameters
+    ==========
+
+    expr : Operator
+        Operator to be represented in the specified basis
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.cartesian import XOp, PxOp, PxKet
+    >>> from sympy.physics.quantum.represent import rep_expectation
+    >>> rep_expectation(XOp())
+    x_1*DiracDelta(x_1 - x_2)
+    >>> rep_expectation(XOp(), basis=PxOp())
+    
+    >>> rep_expectation(XOp(), basis=PxKet())
+    
+
+    """
+
+    if "index" not in options:
+        options["index"] = 1
+
+    if not isinstance(expr, Operator):
+        raise TypeError("The passed expression is not an operator")
+
+    basis_state = get_basis(expr, **options)
+
+    if basis_state is None or not isinstance(basis_state, StateBase):
+        raise NotImplementedError("Could not get basis kets for this operator")
+
+    basis_kets = enumerate_states(basis_state, options["index"], 2)
+
+    bra = basis_kets[1].dual
+    ket = basis_kets[0]
+
+    result = qapply(bra*expr*ket)
+    return result
+
+
+def integrate_result(orig_expr, result, **options):
+    """
+    Returns the result of integrating over any unities ``(|x>>> from sympy import symbols, DiracDelta
+    >>> from sympy.physics.quantum.represent import integrate_result
+    >>> from sympy.physics.quantum.cartesian import XOp, XKet
+    >>> x_ket = XKet()
+    >>> X_op = XOp()
+    >>> x, x_1, x_2 = symbols('x, x_1, x_2')
+    >>> integrate_result(X_op*x_ket, x*DiracDelta(x-x_1)*DiracDelta(x_1-x_2))
+    x*DiracDelta(x - x_1)*DiracDelta(x_1 - x_2)
+    >>> integrate_result(X_op*x_ket, x*DiracDelta(x-x_1)*DiracDelta(x_1-x_2),
+    ...     unities=[1])
+    x*DiracDelta(x - x_2)
+
+    """
+    if not isinstance(result, Expr):
+        return result
+
+    options['replace_none'] = True
+    if "basis" not in options:
+        arg = orig_expr.args[-1]
+        options["basis"] = get_basis(arg, **options)
+    elif not isinstance(options["basis"], StateBase):
+        options["basis"] = get_basis(orig_expr, **options)
+
+    basis = options.pop("basis", None)
+
+    if basis is None:
+        return result
+
+    unities = options.pop("unities", [])
+
+    if len(unities) == 0:
+        return result
+
+    kets = enumerate_states(basis, unities)
+    coords = [k.label[0] for k in kets]
+
+    for coord in coords:
+        if coord in result.free_symbols:
+            #TODO: Add support for sets of operators
+            basis_op = state_to_operators(basis)
+            start = basis_op.hilbert_space.interval.start
+            end = basis_op.hilbert_space.interval.end
+            result = integrate(result, (coord, start, end))
+
+    return result
+
+
+def get_basis(expr, *, basis=None, replace_none=True, **options):
+    """
+    Returns a basis state instance corresponding to the basis specified in
+    options=s. If no basis is specified, the function tries to form a default
+    basis state of the given expression.
+
+    There are three behaviors:
+
+    1. The basis specified in options is already an instance of StateBase. If
+       this is the case, it is simply returned. If the class is specified but
+       not an instance, a default instance is returned.
+
+    2. The basis specified is an operator or set of operators. If this
+       is the case, the operator_to_state mapping method is used.
+
+    3. No basis is specified. If expr is a state, then a default instance of
+       its class is returned.  If expr is an operator, then it is mapped to the
+       corresponding state.  If it is neither, then we cannot obtain the basis
+       state.
+
+    If the basis cannot be mapped, then it is not changed.
+
+    This will be called from within represent, and represent will
+    only pass QExpr's.
+
+    TODO (?): Support for Muls and other types of expressions?
+
+    Parameters
+    ==========
+
+    expr : Operator or StateBase
+        Expression whose basis is sought
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.represent import get_basis
+    >>> from sympy.physics.quantum.cartesian import XOp, XKet, PxOp, PxKet
+    >>> x = XKet()
+    >>> X = XOp()
+    >>> get_basis(x)
+    |x>
+    >>> get_basis(X)
+    |x>
+    >>> get_basis(x, basis=PxOp())
+    |px>
+    >>> get_basis(x, basis=PxKet)
+    |px>
+
+    """
+
+    if basis is None and not replace_none:
+        return None
+
+    if basis is None:
+        if isinstance(expr, KetBase):
+            return _make_default(expr.__class__)
+        elif isinstance(expr, BraBase):
+            return _make_default(expr.dual_class())
+        elif isinstance(expr, Operator):
+            state_inst = operators_to_state(expr)
+            return (state_inst if state_inst is not None else None)
+        else:
+            return None
+    elif (isinstance(basis, Operator) or
+          (not isinstance(basis, StateBase) and issubclass(basis, Operator))):
+        state = operators_to_state(basis)
+        if state is None:
+            return None
+        elif isinstance(state, StateBase):
+            return state
+        else:
+            return _make_default(state)
+    elif isinstance(basis, StateBase):
+        return basis
+    elif issubclass(basis, StateBase):
+        return _make_default(basis)
+    else:
+        return None
+
+
+def _make_default(expr):
+    # XXX: Catching TypeError like this is a bad way of distinguishing
+    # instances from classes. The logic using this function should be
+    # rewritten somehow.
+    try:
+        expr = expr()
+    except TypeError:
+        return expr
+
+    return expr
+
+
+def enumerate_states(*args, **options):
+    """
+    Returns instances of the given state with dummy indices appended
+
+    Operates in two different modes:
+
+    1. Two arguments are passed to it. The first is the base state which is to
+       be indexed, and the second argument is a list of indices to append.
+
+    2. Three arguments are passed. The first is again the base state to be
+       indexed. The second is the start index for counting.  The final argument
+       is the number of kets you wish to receive.
+
+    Tries to call state._enumerate_state. If this fails, returns an empty list
+
+    Parameters
+    ==========
+
+    args : list
+        See list of operation modes above for explanation
+
+    Examples
+    ========
+
+    >>> from sympy.physics.quantum.cartesian import XBra, XKet
+    >>> from sympy.physics.quantum.represent import enumerate_states
+    >>> test = XKet('foo')
+    >>> enumerate_states(test, 1, 3)
+    [|foo_1>, |foo_2>, |foo_3>]
+    >>> test2 = XBra('bar')
+    >>> enumerate_states(test2, [4, 5, 10])
+    [>> from sympy.physics.quantum.sho1d import RaisingOp
+        >>> from sympy.physics.quantum import Dagger
+
+        >>> ad = RaisingOp('a')
+        >>> ad.rewrite('xp').doit()
+        sqrt(2)*(m*omega*X - I*Px)/(2*sqrt(hbar)*sqrt(m*omega))
+
+        >>> Dagger(ad)
+        a
+
+    Taking the commutator of a^dagger with other Operators:
+
+        >>> from sympy.physics.quantum import Commutator
+        >>> from sympy.physics.quantum.sho1d import RaisingOp, LoweringOp
+        >>> from sympy.physics.quantum.sho1d import NumberOp
+
+        >>> ad = RaisingOp('a')
+        >>> a = LoweringOp('a')
+        >>> N = NumberOp('N')
+        >>> Commutator(ad, a).doit()
+        -1
+        >>> Commutator(ad, N).doit()
+        -RaisingOp(a)
+
+    Apply a^dagger to a state:
+
+        >>> from sympy.physics.quantum import qapply
+        >>> from sympy.physics.quantum.sho1d import RaisingOp, SHOKet
+
+        >>> ad = RaisingOp('a')
+        >>> k = SHOKet('k')
+        >>> qapply(ad*k)
+        sqrt(k + 1)*|k + 1>
+
+    Matrix Representation
+
+        >>> from sympy.physics.quantum.sho1d import RaisingOp
+        >>> from sympy.physics.quantum.represent import represent
+        >>> ad = RaisingOp('a')
+        >>> represent(ad, basis=N, ndim=4, format='sympy')
+        Matrix([
+        [0,       0,       0, 0],
+        [1,       0,       0, 0],
+        [0, sqrt(2),       0, 0],
+        [0,       0, sqrt(3), 0]])
+
+    """
+
+    def _eval_rewrite_as_xp(self, *args, **kwargs):
+        return (S.One/sqrt(Integer(2)*hbar*m*omega))*(
+            S.NegativeOne*I*Px + m*omega*X)
+
+    def _eval_adjoint(self):
+        return LoweringOp(*self.args)
+
+    def _eval_commutator_LoweringOp(self, other):
+        return S.NegativeOne
+
+    def _eval_commutator_NumberOp(self, other):
+        return S.NegativeOne*self
+
+    def _apply_operator_SHOKet(self, ket, **options):
+        temp = ket.n + S.One
+        return sqrt(temp)*SHOKet(temp)
+
+    def _represent_default_basis(self, **options):
+        return self._represent_NumberOp(None, **options)
+
+    def _represent_XOp(self, basis, **options):
+        # This logic is good but the underlying position
+        # representation logic is broken.
+        # temp = self.rewrite('xp').doit()
+        # result = represent(temp, basis=X)
+        # return result
+        raise NotImplementedError('Position representation is not implemented')
+
+    def _represent_NumberOp(self, basis, **options):
+        ndim_info = options.get('ndim', 4)
+        format = options.get('format','sympy')
+        matrix = matrix_zeros(ndim_info, ndim_info, **options)
+        for i in range(ndim_info - 1):
+            value = sqrt(i + 1)
+            if format == 'scipy.sparse':
+                value = float(value)
+            matrix[i + 1, i] = value
+        if format == 'scipy.sparse':
+            matrix = matrix.tocsr()
+        return matrix
+
+    #--------------------------------------------------------------------------
+    # Printing Methods
+    #--------------------------------------------------------------------------
+
+    def _print_contents(self, printer, *args):
+        arg0 = printer._print(self.args[0], *args)
+        return '%s(%s)' % (self.__class__.__name__, arg0)
+
+    def _print_contents_pretty(self, printer, *args):
+        from sympy.printing.pretty.stringpict import prettyForm
+        pform = printer._print(self.args[0], *args)
+        pform = pform**prettyForm('\N{DAGGER}')
+        return pform
+
+    def _print_contents_latex(self, printer, *args):
+        arg = printer._print(self.args[0])
+        return '%s^{\\dagger}' % arg
+
+class LoweringOp(SHOOp):
+    """The Lowering Operator or 'a'.
+
+    When 'a' acts on a state it lowers the state up by one. Taking
+    the adjoint of 'a' returns a^dagger, the Raising Operator. 'a'
+    can be rewritten in terms of position and momentum. We can
+    represent 'a' as a matrix, which will be its default basis.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        operator.
+
+    Examples
+    ========
+
+    Create a Lowering Operator and rewrite it in terms of position and
+    momentum, and show that taking its adjoint returns a^dagger:
+
+        >>> from sympy.physics.quantum.sho1d import LoweringOp
+        >>> from sympy.physics.quantum import Dagger
+
+        >>> a = LoweringOp('a')
+        >>> a.rewrite('xp').doit()
+        sqrt(2)*(m*omega*X + I*Px)/(2*sqrt(hbar)*sqrt(m*omega))
+
+        >>> Dagger(a)
+        RaisingOp(a)
+
+    Taking the commutator of 'a' with other Operators:
+
+        >>> from sympy.physics.quantum import Commutator
+        >>> from sympy.physics.quantum.sho1d import LoweringOp, RaisingOp
+        >>> from sympy.physics.quantum.sho1d import NumberOp
+
+        >>> a = LoweringOp('a')
+        >>> ad = RaisingOp('a')
+        >>> N = NumberOp('N')
+        >>> Commutator(a, ad).doit()
+        1
+        >>> Commutator(a, N).doit()
+        a
+
+    Apply 'a' to a state:
+
+        >>> from sympy.physics.quantum import qapply
+        >>> from sympy.physics.quantum.sho1d import LoweringOp, SHOKet
+
+        >>> a = LoweringOp('a')
+        >>> k = SHOKet('k')
+        >>> qapply(a*k)
+        sqrt(k)*|k - 1>
+
+    Taking 'a' of the lowest state will return 0:
+
+        >>> from sympy.physics.quantum import qapply
+        >>> from sympy.physics.quantum.sho1d import LoweringOp, SHOKet
+
+        >>> a = LoweringOp('a')
+        >>> k = SHOKet(0)
+        >>> qapply(a*k)
+        0
+
+    Matrix Representation
+
+        >>> from sympy.physics.quantum.sho1d import LoweringOp
+        >>> from sympy.physics.quantum.represent import represent
+        >>> a = LoweringOp('a')
+        >>> represent(a, basis=N, ndim=4, format='sympy')
+        Matrix([
+        [0, 1,       0,       0],
+        [0, 0, sqrt(2),       0],
+        [0, 0,       0, sqrt(3)],
+        [0, 0,       0,       0]])
+
+    """
+
+    def _eval_rewrite_as_xp(self, *args, **kwargs):
+        return (S.One/sqrt(Integer(2)*hbar*m*omega))*(
+            I*Px + m*omega*X)
+
+    def _eval_adjoint(self):
+        return RaisingOp(*self.args)
+
+    def _eval_commutator_RaisingOp(self, other):
+        return S.One
+
+    def _eval_commutator_NumberOp(self, other):
+        return self
+
+    def _apply_operator_SHOKet(self, ket, **options):
+        temp = ket.n - Integer(1)
+        if ket.n is S.Zero:
+            return S.Zero
+        else:
+            return sqrt(ket.n)*SHOKet(temp)
+
+    def _represent_default_basis(self, **options):
+        return self._represent_NumberOp(None, **options)
+
+    def _represent_XOp(self, basis, **options):
+        # This logic is good but the underlying position
+        # representation logic is broken.
+        # temp = self.rewrite('xp').doit()
+        # result = represent(temp, basis=X)
+        # return result
+        raise NotImplementedError('Position representation is not implemented')
+
+    def _represent_NumberOp(self, basis, **options):
+        ndim_info = options.get('ndim', 4)
+        format = options.get('format', 'sympy')
+        matrix = matrix_zeros(ndim_info, ndim_info, **options)
+        for i in range(ndim_info - 1):
+            value = sqrt(i + 1)
+            if format == 'scipy.sparse':
+                value = float(value)
+            matrix[i,i + 1] = value
+        if format == 'scipy.sparse':
+            matrix = matrix.tocsr()
+        return matrix
+
+
+class NumberOp(SHOOp):
+    """The Number Operator is simply a^dagger*a
+
+    It is often useful to write a^dagger*a as simply the Number Operator
+    because the Number Operator commutes with the Hamiltonian. And can be
+    expressed using the Number Operator. Also the Number Operator can be
+    applied to states. We can represent the Number Operator as a matrix,
+    which will be its default basis.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        operator.
+
+    Examples
+    ========
+
+    Create a Number Operator and rewrite it in terms of the ladder
+    operators, position and momentum operators, and Hamiltonian:
+
+        >>> from sympy.physics.quantum.sho1d import NumberOp
+
+        >>> N = NumberOp('N')
+        >>> N.rewrite('a').doit()
+        RaisingOp(a)*a
+        >>> N.rewrite('xp').doit()
+        -1/2 + (m**2*omega**2*X**2 + Px**2)/(2*hbar*m*omega)
+        >>> N.rewrite('H').doit()
+        -1/2 + H/(hbar*omega)
+
+    Take the Commutator of the Number Operator with other Operators:
+
+        >>> from sympy.physics.quantum import Commutator
+        >>> from sympy.physics.quantum.sho1d import NumberOp, Hamiltonian
+        >>> from sympy.physics.quantum.sho1d import RaisingOp, LoweringOp
+
+        >>> N = NumberOp('N')
+        >>> H = Hamiltonian('H')
+        >>> ad = RaisingOp('a')
+        >>> a = LoweringOp('a')
+        >>> Commutator(N,H).doit()
+        0
+        >>> Commutator(N,ad).doit()
+        RaisingOp(a)
+        >>> Commutator(N,a).doit()
+        -a
+
+    Apply the Number Operator to a state:
+
+        >>> from sympy.physics.quantum import qapply
+        >>> from sympy.physics.quantum.sho1d import NumberOp, SHOKet
+
+        >>> N = NumberOp('N')
+        >>> k = SHOKet('k')
+        >>> qapply(N*k)
+        k*|k>
+
+    Matrix Representation
+
+        >>> from sympy.physics.quantum.sho1d import NumberOp
+        >>> from sympy.physics.quantum.represent import represent
+        >>> N = NumberOp('N')
+        >>> represent(N, basis=N, ndim=4, format='sympy')
+        Matrix([
+        [0, 0, 0, 0],
+        [0, 1, 0, 0],
+        [0, 0, 2, 0],
+        [0, 0, 0, 3]])
+
+    """
+
+    def _eval_rewrite_as_a(self, *args, **kwargs):
+        return ad*a
+
+    def _eval_rewrite_as_xp(self, *args, **kwargs):
+        return (S.One/(Integer(2)*m*hbar*omega))*(Px**2 + (
+            m*omega*X)**2) - S.Half
+
+    def _eval_rewrite_as_H(self, *args, **kwargs):
+        return H/(hbar*omega) - S.Half
+
+    def _apply_operator_SHOKet(self, ket, **options):
+        return ket.n*ket
+
+    def _eval_commutator_Hamiltonian(self, other):
+        return S.Zero
+
+    def _eval_commutator_RaisingOp(self, other):
+        return other
+
+    def _eval_commutator_LoweringOp(self, other):
+        return S.NegativeOne*other
+
+    def _represent_default_basis(self, **options):
+        return self._represent_NumberOp(None, **options)
+
+    def _represent_XOp(self, basis, **options):
+        # This logic is good but the underlying position
+        # representation logic is broken.
+        # temp = self.rewrite('xp').doit()
+        # result = represent(temp, basis=X)
+        # return result
+        raise NotImplementedError('Position representation is not implemented')
+
+    def _represent_NumberOp(self, basis, **options):
+        ndim_info = options.get('ndim', 4)
+        format = options.get('format', 'sympy')
+        matrix = matrix_zeros(ndim_info, ndim_info, **options)
+        for i in range(ndim_info):
+            value = i
+            if format == 'scipy.sparse':
+                value = float(value)
+            matrix[i,i] = value
+        if format == 'scipy.sparse':
+            matrix = matrix.tocsr()
+        return matrix
+
+
+class Hamiltonian(SHOOp):
+    """The Hamiltonian Operator.
+
+    The Hamiltonian is used to solve the time-independent Schrodinger
+    equation. The Hamiltonian can be expressed using the ladder operators,
+    as well as by position and momentum. We can represent the Hamiltonian
+    Operator as a matrix, which will be its default basis.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        operator.
+
+    Examples
+    ========
+
+    Create a Hamiltonian Operator and rewrite it in terms of the ladder
+    operators, position and momentum, and the Number Operator:
+
+        >>> from sympy.physics.quantum.sho1d import Hamiltonian
+
+        >>> H = Hamiltonian('H')
+        >>> H.rewrite('a').doit()
+        hbar*omega*(1/2 + RaisingOp(a)*a)
+        >>> H.rewrite('xp').doit()
+        (m**2*omega**2*X**2 + Px**2)/(2*m)
+        >>> H.rewrite('N').doit()
+        hbar*omega*(1/2 + N)
+
+    Take the Commutator of the Hamiltonian and the Number Operator:
+
+        >>> from sympy.physics.quantum import Commutator
+        >>> from sympy.physics.quantum.sho1d import Hamiltonian, NumberOp
+
+        >>> H = Hamiltonian('H')
+        >>> N = NumberOp('N')
+        >>> Commutator(H,N).doit()
+        0
+
+    Apply the Hamiltonian Operator to a state:
+
+        >>> from sympy.physics.quantum import qapply
+        >>> from sympy.physics.quantum.sho1d import Hamiltonian, SHOKet
+
+        >>> H = Hamiltonian('H')
+        >>> k = SHOKet('k')
+        >>> qapply(H*k)
+        hbar*k*omega*|k> + hbar*omega*|k>/2
+
+    Matrix Representation
+
+        >>> from sympy.physics.quantum.sho1d import Hamiltonian
+        >>> from sympy.physics.quantum.represent import represent
+
+        >>> H = Hamiltonian('H')
+        >>> represent(H, basis=N, ndim=4, format='sympy')
+        Matrix([
+        [hbar*omega/2,              0,              0,              0],
+        [           0, 3*hbar*omega/2,              0,              0],
+        [           0,              0, 5*hbar*omega/2,              0],
+        [           0,              0,              0, 7*hbar*omega/2]])
+
+    """
+
+    def _eval_rewrite_as_a(self, *args, **kwargs):
+        return hbar*omega*(ad*a + S.Half)
+
+    def _eval_rewrite_as_xp(self, *args, **kwargs):
+        return (S.One/(Integer(2)*m))*(Px**2 + (m*omega*X)**2)
+
+    def _eval_rewrite_as_N(self, *args, **kwargs):
+        return hbar*omega*(N + S.Half)
+
+    def _apply_operator_SHOKet(self, ket, **options):
+        return (hbar*omega*(ket.n + S.Half))*ket
+
+    def _eval_commutator_NumberOp(self, other):
+        return S.Zero
+
+    def _represent_default_basis(self, **options):
+        return self._represent_NumberOp(None, **options)
+
+    def _represent_XOp(self, basis, **options):
+        # This logic is good but the underlying position
+        # representation logic is broken.
+        # temp = self.rewrite('xp').doit()
+        # result = represent(temp, basis=X)
+        # return result
+        raise NotImplementedError('Position representation is not implemented')
+
+    def _represent_NumberOp(self, basis, **options):
+        ndim_info = options.get('ndim', 4)
+        format = options.get('format', 'sympy')
+        matrix = matrix_zeros(ndim_info, ndim_info, **options)
+        for i in range(ndim_info):
+            value = i + S.Half
+            if format == 'scipy.sparse':
+                value = float(value)
+            matrix[i,i] = value
+        if format == 'scipy.sparse':
+            matrix = matrix.tocsr()
+        return hbar*omega*matrix
+
+#------------------------------------------------------------------------------
+
+class SHOState(State):
+    """State class for SHO states"""
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return ComplexSpace(S.Infinity)
+
+    @property
+    def n(self):
+        return self.args[0]
+
+
+class SHOKet(SHOState, Ket):
+    """1D eigenket.
+
+    Inherits from SHOState and Ket.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the ket
+        This is usually its quantum numbers or its symbol.
+
+    Examples
+    ========
+
+    Ket's know about their associated bra:
+
+        >>> from sympy.physics.quantum.sho1d import SHOKet
+
+        >>> k = SHOKet('k')
+        >>> k.dual
+        >> k.dual_class()
+        
+
+    Take the Inner Product with a bra:
+
+        >>> from sympy.physics.quantum import InnerProduct
+        >>> from sympy.physics.quantum.sho1d import SHOKet, SHOBra
+
+        >>> k = SHOKet('k')
+        >>> b = SHOBra('b')
+        >>> InnerProduct(b,k).doit()
+        KroneckerDelta(b, k)
+
+    Vector representation of a numerical state ket:
+
+        >>> from sympy.physics.quantum.sho1d import SHOKet, NumberOp
+        >>> from sympy.physics.quantum.represent import represent
+
+        >>> k = SHOKet(3)
+        >>> N = NumberOp('N')
+        >>> represent(k, basis=N, ndim=4)
+        Matrix([
+        [0],
+        [0],
+        [0],
+        [1]])
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return SHOBra
+
+    def _eval_innerproduct_SHOBra(self, bra, **hints):
+        result = KroneckerDelta(self.n, bra.n)
+        return result
+
+    def _represent_default_basis(self, **options):
+        return self._represent_NumberOp(None, **options)
+
+    def _represent_NumberOp(self, basis, **options):
+        ndim_info = options.get('ndim', 4)
+        format = options.get('format', 'sympy')
+        options['spmatrix'] = 'lil'
+        vector = matrix_zeros(ndim_info, 1, **options)
+        if isinstance(self.n, Integer):
+            if self.n >= ndim_info:
+                return ValueError("N-Dimension too small")
+            if format == 'scipy.sparse':
+                vector[int(self.n), 0] = 1.0
+                vector = vector.tocsr()
+            elif format == 'numpy':
+                vector[int(self.n), 0] = 1.0
+            else:
+                vector[self.n, 0] = S.One
+            return vector
+        else:
+            return ValueError("Not Numerical State")
+
+
+class SHOBra(SHOState, Bra):
+    """A time-independent Bra in SHO.
+
+    Inherits from SHOState and Bra.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the ket
+        This is usually its quantum numbers or its symbol.
+
+    Examples
+    ========
+
+    Bra's know about their associated ket:
+
+        >>> from sympy.physics.quantum.sho1d import SHOBra
+
+        >>> b = SHOBra('b')
+        >>> b.dual
+        |b>
+        >>> b.dual_class()
+        
+
+    Vector representation of a numerical state bra:
+
+        >>> from sympy.physics.quantum.sho1d import SHOBra, NumberOp
+        >>> from sympy.physics.quantum.represent import represent
+
+        >>> b = SHOBra(3)
+        >>> N = NumberOp('N')
+        >>> represent(b, basis=N, ndim=4)
+        Matrix([[0, 0, 0, 1]])
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return SHOKet
+
+    def _represent_default_basis(self, **options):
+        return self._represent_NumberOp(None, **options)
+
+    def _represent_NumberOp(self, basis, **options):
+        ndim_info = options.get('ndim', 4)
+        format = options.get('format', 'sympy')
+        options['spmatrix'] = 'lil'
+        vector = matrix_zeros(1, ndim_info, **options)
+        if isinstance(self.n, Integer):
+            if self.n >= ndim_info:
+                return ValueError("N-Dimension too small")
+            if format == 'scipy.sparse':
+                vector[0, int(self.n)] = 1.0
+                vector = vector.tocsr()
+            elif format == 'numpy':
+                vector[0, int(self.n)] = 1.0
+            else:
+                vector[0, self.n] = S.One
+            return vector
+        else:
+            return ValueError("Not Numerical State")
+
+
+ad = RaisingOp('a')
+a = LoweringOp('a')
+H = Hamiltonian('H')
+N = NumberOp('N')
+omega = Symbol('omega')
+m = Symbol('m')
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/shor.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/shor.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc9e55229d74634bdb82efc03c2d1649e088efb3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/shor.py
@@ -0,0 +1,173 @@
+"""Shor's algorithm and helper functions.
+
+Todo:
+
+* Get the CMod gate working again using the new Gate API.
+* Fix everything.
+* Update docstrings and reformat.
+"""
+
+import math
+import random
+
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.core.intfunc import igcd
+from sympy.ntheory import continued_fraction_periodic as continued_fraction
+from sympy.utilities.iterables import variations
+
+from sympy.physics.quantum.gate import Gate
+from sympy.physics.quantum.qubit import Qubit, measure_partial_oneshot
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qft import QFT
+from sympy.physics.quantum.qexpr import QuantumError
+
+
+class OrderFindingException(QuantumError):
+    pass
+
+
+class CMod(Gate):
+    """A controlled mod gate.
+
+    This is black box controlled Mod function for use by shor's algorithm.
+    TODO: implement a decompose property that returns how to do this in terms
+    of elementary gates
+    """
+
+    @classmethod
+    def _eval_args(cls, args):
+        # t = args[0]
+        # a = args[1]
+        # N = args[2]
+        raise NotImplementedError('The CMod gate has not been completed.')
+
+    @property
+    def t(self):
+        """Size of 1/2 input register.  First 1/2 holds output."""
+        return self.label[0]
+
+    @property
+    def a(self):
+        """Base of the controlled mod function."""
+        return self.label[1]
+
+    @property
+    def N(self):
+        """N is the type of modular arithmetic we are doing."""
+        return self.label[2]
+
+    def _apply_operator_Qubit(self, qubits, **options):
+        """
+            This directly calculates the controlled mod of the second half of
+            the register and puts it in the second
+            This will look pretty when we get Tensor Symbolically working
+        """
+        n = 1
+        k = 0
+        # Determine the value stored in high memory.
+        for i in range(self.t):
+            k += n*qubits[self.t + i]
+            n *= 2
+
+        # The value to go in low memory will be out.
+        out = int(self.a**k % self.N)
+
+        # Create array for new qbit-ket which will have high memory unaffected
+        outarray = list(qubits.args[0][:self.t])
+
+        # Place out in low memory
+        for i in reversed(range(self.t)):
+            outarray.append((out >> i) & 1)
+
+        return Qubit(*outarray)
+
+
+def shor(N):
+    """This function implements Shor's factoring algorithm on the Integer N
+
+    The algorithm starts by picking a random number (a) and seeing if it is
+    coprime with N. If it is not, then the gcd of the two numbers is a factor
+    and we are done. Otherwise, it begins the period_finding subroutine which
+    finds the period of a in modulo N arithmetic. This period, if even, can
+    be used to calculate factors by taking a**(r/2)-1 and a**(r/2)+1.
+    These values are returned.
+    """
+    a = random.randrange(N - 2) + 2
+    if igcd(N, a) != 1:
+        return igcd(N, a)
+    r = period_find(a, N)
+    if r % 2 == 1:
+        shor(N)
+    answer = (igcd(a**(r/2) - 1, N), igcd(a**(r/2) + 1, N))
+    return answer
+
+
+def getr(x, y, N):
+    fraction = continued_fraction(x, y)
+    # Now convert into r
+    total = ratioize(fraction, N)
+    return total
+
+
+def ratioize(list, N):
+    if list[0] > N:
+        return S.Zero
+    if len(list) == 1:
+        return list[0]
+    return list[0] + ratioize(list[1:], N)
+
+
+def period_find(a, N):
+    """Finds the period of a in modulo N arithmetic
+
+    This is quantum part of Shor's algorithm. It takes two registers,
+    puts first in superposition of states with Hadamards so: ``|k>|0>``
+    with k being all possible choices. It then does a controlled mod and
+    a QFT to determine the order of a.
+    """
+    epsilon = .5
+    # picks out t's such that maintains accuracy within epsilon
+    t = int(2*math.ceil(log(N, 2)))
+    # make the first half of register be 0's |000...000>
+    start = [0 for x in range(t)]
+    # Put second half into superposition of states so we have |1>x|0> + |2>x|0> + ... |k>x>|0> + ... + |2**n-1>x|0>
+    factor = 1/sqrt(2**t)
+    qubits = 0
+    for arr in variations(range(2), t, repetition=True):
+        qbitArray = list(arr) + start
+        qubits = qubits + Qubit(*qbitArray)
+    circuit = (factor*qubits).expand()
+    # Controlled second half of register so that we have:
+    # |1>x|a**1 %N> + |2>x|a**2 %N> + ... + |k>x|a**k %N >+ ... + |2**n-1=k>x|a**k % n>
+    circuit = CMod(t, a, N)*circuit
+    # will measure first half of register giving one of the a**k%N's
+
+    circuit = qapply(circuit)
+    for i in range(t):
+        circuit = measure_partial_oneshot(circuit, i)
+    # Now apply Inverse Quantum Fourier Transform on the second half of the register
+
+    circuit = qapply(QFT(t, t*2).decompose()*circuit, floatingPoint=True)
+    for i in range(t):
+        circuit = measure_partial_oneshot(circuit, i + t)
+    if isinstance(circuit, Qubit):
+        register = circuit
+    elif isinstance(circuit, Mul):
+        register = circuit.args[-1]
+    else:
+        register = circuit.args[-1].args[-1]
+
+    n = 1
+    answer = 0
+    for i in range(len(register)/2):
+        answer += n*register[i + t]
+        n = n << 1
+    if answer == 0:
+        raise OrderFindingException(
+            "Order finder returned 0. Happens with chance %f" % epsilon)
+    #turn answer into r using continued fractions
+    g = getr(answer, 2**t, N)
+    return g
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/spin.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/spin.py
new file mode 100644
index 0000000000000000000000000000000000000000..6be53d01711adbed8c078fffca1d618c1aa3c6e6
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/spin.py
@@ -0,0 +1,2150 @@
+"""Quantum mechanical angular momentum."""
+
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.numbers import int_valued
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer, Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Dummy, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import (binomial, factorial)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.simplify.simplify import simplify
+from sympy.matrices import zeros
+from sympy.printing.pretty.stringpict import prettyForm, stringPict
+from sympy.printing.pretty.pretty_symbology import pretty_symbol
+
+from sympy.physics.quantum.qexpr import QExpr
+from sympy.physics.quantum.operator import (HermitianOperator, Operator,
+                                            UnitaryOperator)
+from sympy.physics.quantum.state import Bra, Ket, State
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.physics.quantum.constants import hbar
+from sympy.physics.quantum.hilbert import ComplexSpace, DirectSumHilbertSpace
+from sympy.physics.quantum.tensorproduct import TensorProduct
+from sympy.physics.quantum.cg import CG
+from sympy.physics.quantum.qapply import qapply
+
+
+__all__ = [
+    'm_values',
+    'Jplus',
+    'Jminus',
+    'Jx',
+    'Jy',
+    'Jz',
+    'J2',
+    'Rotation',
+    'WignerD',
+    'JxKet',
+    'JxBra',
+    'JyKet',
+    'JyBra',
+    'JzKet',
+    'JzBra',
+    'JzOp',
+    'J2Op',
+    'JxKetCoupled',
+    'JxBraCoupled',
+    'JyKetCoupled',
+    'JyBraCoupled',
+    'JzKetCoupled',
+    'JzBraCoupled',
+    'couple',
+    'uncouple'
+]
+
+
+def m_values(j):
+    j = sympify(j)
+    size = 2*j + 1
+    if not size.is_Integer or not size > 0:
+        raise ValueError(
+            'Only integer or half-integer values allowed for j, got: : %r' % j
+        )
+    return size, [j - i for i in range(int(2*j + 1))]
+
+
+#-----------------------------------------------------------------------------
+# Spin Operators
+#-----------------------------------------------------------------------------
+
+
+class SpinOpBase:
+    """Base class for spin operators."""
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        # We consider all j values so our space is infinite.
+        return ComplexSpace(S.Infinity)
+
+    @property
+    def name(self):
+        return self.args[0]
+
+    def _print_contents(self, printer, *args):
+        return '%s%s' % (self.name, self._coord)
+
+    def _print_contents_pretty(self, printer, *args):
+        a = stringPict(str(self.name))
+        b = stringPict(self._coord)
+        return self._print_subscript_pretty(a, b)
+
+    def _print_contents_latex(self, printer, *args):
+        return r'%s_%s' % ((self.name, self._coord))
+
+    def _represent_base(self, basis, **options):
+        j = options.get('j', S.Half)
+        size, mvals = m_values(j)
+        result = zeros(size, size)
+        for p in range(size):
+            for q in range(size):
+                me = self.matrix_element(j, mvals[p], j, mvals[q])
+                result[p, q] = me
+        return result
+
+    def _apply_op(self, ket, orig_basis, **options):
+        state = ket.rewrite(self.basis)
+        # If the state has only one term
+        if isinstance(state, State):
+            ret = (hbar*state.m)*state
+        # state is a linear combination of states
+        elif isinstance(state, Sum):
+            ret = self._apply_operator_Sum(state, **options)
+        else:
+            ret = qapply(self*state)
+        if ret == self*state:
+            raise NotImplementedError
+        return ret.rewrite(orig_basis)
+
+    def _apply_operator_JxKet(self, ket, **options):
+        return self._apply_op(ket, 'Jx', **options)
+
+    def _apply_operator_JxKetCoupled(self, ket, **options):
+        return self._apply_op(ket, 'Jx', **options)
+
+    def _apply_operator_JyKet(self, ket, **options):
+        return self._apply_op(ket, 'Jy', **options)
+
+    def _apply_operator_JyKetCoupled(self, ket, **options):
+        return self._apply_op(ket, 'Jy', **options)
+
+    def _apply_operator_JzKet(self, ket, **options):
+        return self._apply_op(ket, 'Jz', **options)
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        return self._apply_op(ket, 'Jz', **options)
+
+    def _apply_operator_TensorProduct(self, tp, **options):
+        # Uncoupling operator is only easily found for coordinate basis spin operators
+        # TODO: add methods for uncoupling operators
+        if not isinstance(self, (JxOp, JyOp, JzOp)):
+            raise NotImplementedError
+        result = []
+        for n in range(len(tp.args)):
+            arg = []
+            arg.extend(tp.args[:n])
+            arg.append(self._apply_operator(tp.args[n]))
+            arg.extend(tp.args[n + 1:])
+            result.append(tp.__class__(*arg))
+        return Add(*result).expand()
+
+    # TODO: move this to qapply_Mul
+    def _apply_operator_Sum(self, s, **options):
+        new_func = qapply(self*s.function)
+        if new_func == self*s.function:
+            raise NotImplementedError
+        return Sum(new_func, *s.limits)
+
+    def _eval_trace(self, **options):
+        #TODO: use options to use different j values
+        #For now eval at default basis
+
+        # is it efficient to represent each time
+        # to do a trace?
+        return self._represent_default_basis().trace()
+
+
+class JplusOp(SpinOpBase, Operator):
+    """The J+ operator."""
+
+    _coord = '+'
+
+    basis = 'Jz'
+
+    def _eval_commutator_JminusOp(self, other):
+        return 2*hbar*JzOp(self.name)
+
+    def _apply_operator_JzKet(self, ket, **options):
+        j = ket.j
+        m = ket.m
+        if m.is_Number and j.is_Number:
+            if m >= j:
+                return S.Zero
+        return hbar*sqrt(j*(j + S.One) - m*(m + S.One))*JzKet(j, m + S.One)
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        j = ket.j
+        m = ket.m
+        jn = ket.jn
+        coupling = ket.coupling
+        if m.is_Number and j.is_Number:
+            if m >= j:
+                return S.Zero
+        return hbar*sqrt(j*(j + S.One) - m*(m + S.One))*JzKetCoupled(j, m + S.One, jn, coupling)
+
+    def matrix_element(self, j, m, jp, mp):
+        result = hbar*sqrt(j*(j + S.One) - mp*(mp + S.One))
+        result *= KroneckerDelta(m, mp + 1)
+        result *= KroneckerDelta(j, jp)
+        return result
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_base(basis, **options)
+
+    def _eval_rewrite_as_xyz(self, *args, **kwargs):
+        return JxOp(args[0]) + I*JyOp(args[0])
+
+
+class JminusOp(SpinOpBase, Operator):
+    """The J- operator."""
+
+    _coord = '-'
+
+    basis = 'Jz'
+
+    def _apply_operator_JzKet(self, ket, **options):
+        j = ket.j
+        m = ket.m
+        if m.is_Number and j.is_Number:
+            if m <= -j:
+                return S.Zero
+        return hbar*sqrt(j*(j + S.One) - m*(m - S.One))*JzKet(j, m - S.One)
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        j = ket.j
+        m = ket.m
+        jn = ket.jn
+        coupling = ket.coupling
+        if m.is_Number and j.is_Number:
+            if m <= -j:
+                return S.Zero
+        return hbar*sqrt(j*(j + S.One) - m*(m - S.One))*JzKetCoupled(j, m - S.One, jn, coupling)
+
+    def matrix_element(self, j, m, jp, mp):
+        result = hbar*sqrt(j*(j + S.One) - mp*(mp - S.One))
+        result *= KroneckerDelta(m, mp - 1)
+        result *= KroneckerDelta(j, jp)
+        return result
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_base(basis, **options)
+
+    def _eval_rewrite_as_xyz(self, *args, **kwargs):
+        return JxOp(args[0]) - I*JyOp(args[0])
+
+
+class JxOp(SpinOpBase, HermitianOperator):
+    """The Jx operator."""
+
+    _coord = 'x'
+
+    basis = 'Jx'
+
+    def _eval_commutator_JyOp(self, other):
+        return I*hbar*JzOp(self.name)
+
+    def _eval_commutator_JzOp(self, other):
+        return -I*hbar*JyOp(self.name)
+
+    def _apply_operator_JzKet(self, ket, **options):
+        jp = JplusOp(self.name)._apply_operator_JzKet(ket, **options)
+        jm = JminusOp(self.name)._apply_operator_JzKet(ket, **options)
+        return (jp + jm)/Integer(2)
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        jp = JplusOp(self.name)._apply_operator_JzKetCoupled(ket, **options)
+        jm = JminusOp(self.name)._apply_operator_JzKetCoupled(ket, **options)
+        return (jp + jm)/Integer(2)
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        jp = JplusOp(self.name)._represent_JzOp(basis, **options)
+        jm = JminusOp(self.name)._represent_JzOp(basis, **options)
+        return (jp + jm)/Integer(2)
+
+    def _eval_rewrite_as_plusminus(self, *args, **kwargs):
+        return (JplusOp(args[0]) + JminusOp(args[0]))/2
+
+
+class JyOp(SpinOpBase, HermitianOperator):
+    """The Jy operator."""
+
+    _coord = 'y'
+
+    basis = 'Jy'
+
+    def _eval_commutator_JzOp(self, other):
+        return I*hbar*JxOp(self.name)
+
+    def _eval_commutator_JxOp(self, other):
+        return -I*hbar*J2Op(self.name)
+
+    def _apply_operator_JzKet(self, ket, **options):
+        jp = JplusOp(self.name)._apply_operator_JzKet(ket, **options)
+        jm = JminusOp(self.name)._apply_operator_JzKet(ket, **options)
+        return (jp - jm)/(Integer(2)*I)
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        jp = JplusOp(self.name)._apply_operator_JzKetCoupled(ket, **options)
+        jm = JminusOp(self.name)._apply_operator_JzKetCoupled(ket, **options)
+        return (jp - jm)/(Integer(2)*I)
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        jp = JplusOp(self.name)._represent_JzOp(basis, **options)
+        jm = JminusOp(self.name)._represent_JzOp(basis, **options)
+        return (jp - jm)/(Integer(2)*I)
+
+    def _eval_rewrite_as_plusminus(self, *args, **kwargs):
+        return (JplusOp(args[0]) - JminusOp(args[0]))/(2*I)
+
+
+class JzOp(SpinOpBase, HermitianOperator):
+    """The Jz operator."""
+
+    _coord = 'z'
+
+    basis = 'Jz'
+
+    def _eval_commutator_JxOp(self, other):
+        return I*hbar*JyOp(self.name)
+
+    def _eval_commutator_JyOp(self, other):
+        return -I*hbar*JxOp(self.name)
+
+    def _eval_commutator_JplusOp(self, other):
+        return hbar*JplusOp(self.name)
+
+    def _eval_commutator_JminusOp(self, other):
+        return -hbar*JminusOp(self.name)
+
+    def matrix_element(self, j, m, jp, mp):
+        result = hbar*mp
+        result *= KroneckerDelta(m, mp)
+        result *= KroneckerDelta(j, jp)
+        return result
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_base(basis, **options)
+
+
+class J2Op(SpinOpBase, HermitianOperator):
+    """The J^2 operator."""
+
+    _coord = '2'
+
+    def _eval_commutator_JxOp(self, other):
+        return S.Zero
+
+    def _eval_commutator_JyOp(self, other):
+        return S.Zero
+
+    def _eval_commutator_JzOp(self, other):
+        return S.Zero
+
+    def _eval_commutator_JplusOp(self, other):
+        return S.Zero
+
+    def _eval_commutator_JminusOp(self, other):
+        return S.Zero
+
+    def _apply_operator_JxKet(self, ket, **options):
+        j = ket.j
+        return hbar**2*j*(j + 1)*ket
+
+    def _apply_operator_JxKetCoupled(self, ket, **options):
+        j = ket.j
+        return hbar**2*j*(j + 1)*ket
+
+    def _apply_operator_JyKet(self, ket, **options):
+        j = ket.j
+        return hbar**2*j*(j + 1)*ket
+
+    def _apply_operator_JyKetCoupled(self, ket, **options):
+        j = ket.j
+        return hbar**2*j*(j + 1)*ket
+
+    def _apply_operator_JzKet(self, ket, **options):
+        j = ket.j
+        return hbar**2*j*(j + 1)*ket
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        j = ket.j
+        return hbar**2*j*(j + 1)*ket
+
+    def matrix_element(self, j, m, jp, mp):
+        result = (hbar**2)*j*(j + 1)
+        result *= KroneckerDelta(m, mp)
+        result *= KroneckerDelta(j, jp)
+        return result
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_base(basis, **options)
+
+    def _print_contents_pretty(self, printer, *args):
+        a = prettyForm(str(self.name))
+        b = prettyForm('2')
+        return a**b
+
+    def _print_contents_latex(self, printer, *args):
+        return r'%s^2' % str(self.name)
+
+    def _eval_rewrite_as_xyz(self, *args, **kwargs):
+        return JxOp(args[0])**2 + JyOp(args[0])**2 + JzOp(args[0])**2
+
+    def _eval_rewrite_as_plusminus(self, *args, **kwargs):
+        a = args[0]
+        return JzOp(a)**2 + \
+            S.Half*(JplusOp(a)*JminusOp(a) + JminusOp(a)*JplusOp(a))
+
+
+class Rotation(UnitaryOperator):
+    """Wigner D operator in terms of Euler angles.
+
+    Defines the rotation operator in terms of the Euler angles defined by
+    the z-y-z convention for a passive transformation. That is the coordinate
+    axes are rotated first about the z-axis, giving the new x'-y'-z' axes. Then
+    this new coordinate system is rotated about the new y'-axis, giving new
+    x''-y''-z'' axes. Then this new coordinate system is rotated about the
+    z''-axis. Conventions follow those laid out in [1]_.
+
+    Parameters
+    ==========
+
+    alpha : Number, Symbol
+        First Euler Angle
+    beta : Number, Symbol
+        Second Euler angle
+    gamma : Number, Symbol
+        Third Euler angle
+
+    Examples
+    ========
+
+    A simple example rotation operator:
+
+        >>> from sympy import pi
+        >>> from sympy.physics.quantum.spin import Rotation
+        >>> Rotation(pi, 0, pi/2)
+        R(pi,0,pi/2)
+
+    With symbolic Euler angles and calculating the inverse rotation operator:
+
+        >>> from sympy import symbols
+        >>> a, b, c = symbols('a b c')
+        >>> Rotation(a, b, c)
+        R(a,b,c)
+        >>> Rotation(a, b, c).inverse()
+        R(-c,-b,-a)
+
+    See Also
+    ========
+
+    WignerD: Symbolic Wigner-D function
+    D: Wigner-D function
+    d: Wigner small-d function
+
+    References
+    ==========
+
+    .. [1] Varshalovich, D A, Quantum Theory of Angular Momentum. 1988.
+    """
+
+    @classmethod
+    def _eval_args(cls, args):
+        args = QExpr._eval_args(args)
+        if len(args) != 3:
+            raise ValueError('3 Euler angles required, got: %r' % args)
+        return args
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        # We consider all j values so our space is infinite.
+        return ComplexSpace(S.Infinity)
+
+    @property
+    def alpha(self):
+        return self.label[0]
+
+    @property
+    def beta(self):
+        return self.label[1]
+
+    @property
+    def gamma(self):
+        return self.label[2]
+
+    def _print_operator_name(self, printer, *args):
+        return 'R'
+
+    def _print_operator_name_pretty(self, printer, *args):
+        if printer._use_unicode:
+            return prettyForm('\N{SCRIPT CAPITAL R}' + ' ')
+        else:
+            return prettyForm("R ")
+
+    def _print_operator_name_latex(self, printer, *args):
+        return r'\mathcal{R}'
+
+    def _eval_inverse(self):
+        return Rotation(-self.gamma, -self.beta, -self.alpha)
+
+    @classmethod
+    def D(cls, j, m, mp, alpha, beta, gamma):
+        """Wigner D-function.
+
+        Returns an instance of the WignerD class corresponding to the Wigner-D
+        function specified by the parameters.
+
+        Parameters
+        ===========
+
+        j : Number
+            Total angular momentum
+        m : Number
+            Eigenvalue of angular momentum along axis after rotation
+        mp : Number
+            Eigenvalue of angular momentum along rotated axis
+        alpha : Number, Symbol
+            First Euler angle of rotation
+        beta : Number, Symbol
+            Second Euler angle of rotation
+        gamma : Number, Symbol
+            Third Euler angle of rotation
+
+        Examples
+        ========
+
+        Return the Wigner-D matrix element for a defined rotation, both
+        numerical and symbolic:
+
+            >>> from sympy.physics.quantum.spin import Rotation
+            >>> from sympy import pi, symbols
+            >>> alpha, beta, gamma = symbols('alpha beta gamma')
+            >>> Rotation.D(1, 1, 0,pi, pi/2,-pi)
+            WignerD(1, 1, 0, pi, pi/2, -pi)
+
+        See Also
+        ========
+
+        WignerD: Symbolic Wigner-D function
+
+        """
+        return WignerD(j, m, mp, alpha, beta, gamma)
+
+    @classmethod
+    def d(cls, j, m, mp, beta):
+        """Wigner small-d function.
+
+        Returns an instance of the WignerD class corresponding to the Wigner-D
+        function specified by the parameters with the alpha and gamma angles
+        given as 0.
+
+        Parameters
+        ===========
+
+        j : Number
+            Total angular momentum
+        m : Number
+            Eigenvalue of angular momentum along axis after rotation
+        mp : Number
+            Eigenvalue of angular momentum along rotated axis
+        beta : Number, Symbol
+            Second Euler angle of rotation
+
+        Examples
+        ========
+
+        Return the Wigner-D matrix element for a defined rotation, both
+        numerical and symbolic:
+
+            >>> from sympy.physics.quantum.spin import Rotation
+            >>> from sympy import pi, symbols
+            >>> beta = symbols('beta')
+            >>> Rotation.d(1, 1, 0, pi/2)
+            WignerD(1, 1, 0, 0, pi/2, 0)
+
+        See Also
+        ========
+
+        WignerD: Symbolic Wigner-D function
+
+        """
+        return WignerD(j, m, mp, 0, beta, 0)
+
+    def matrix_element(self, j, m, jp, mp):
+        result = self.__class__.D(
+            jp, m, mp, self.alpha, self.beta, self.gamma
+        )
+        result *= KroneckerDelta(j, jp)
+        return result
+
+    def _represent_base(self, basis, **options):
+        j = sympify(options.get('j', S.Half))
+        # TODO: move evaluation up to represent function/implement elsewhere
+        evaluate = sympify(options.get('doit'))
+        size, mvals = m_values(j)
+        result = zeros(size, size)
+        for p in range(size):
+            for q in range(size):
+                me = self.matrix_element(j, mvals[p], j, mvals[q])
+                if evaluate:
+                    result[p, q] = me.doit()
+                else:
+                    result[p, q] = me
+        return result
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_base(basis, **options)
+
+    def _apply_operator_uncoupled(self, state, ket, *, dummy=True, **options):
+        a = self.alpha
+        b = self.beta
+        g = self.gamma
+        j = ket.j
+        m = ket.m
+        if j.is_number:
+            s = []
+            size = m_values(j)
+            sz = size[1]
+            for mp in sz:
+                r = Rotation.D(j, m, mp, a, b, g)
+                z = r.doit()
+                s.append(z*state(j, mp))
+            return Add(*s)
+        else:
+            if dummy:
+                mp = Dummy('mp')
+            else:
+                mp = symbols('mp')
+            return Sum(Rotation.D(j, m, mp, a, b, g)*state(j, mp), (mp, -j, j))
+
+    def _apply_operator_JxKet(self, ket, **options):
+        return self._apply_operator_uncoupled(JxKet, ket, **options)
+
+    def _apply_operator_JyKet(self, ket, **options):
+        return self._apply_operator_uncoupled(JyKet, ket, **options)
+
+    def _apply_operator_JzKet(self, ket, **options):
+        return self._apply_operator_uncoupled(JzKet, ket, **options)
+
+    def _apply_operator_coupled(self, state, ket, *, dummy=True, **options):
+        a = self.alpha
+        b = self.beta
+        g = self.gamma
+        j = ket.j
+        m = ket.m
+        jn = ket.jn
+        coupling = ket.coupling
+        if j.is_number:
+            s = []
+            size = m_values(j)
+            sz = size[1]
+            for mp in sz:
+                r = Rotation.D(j, m, mp, a, b, g)
+                z = r.doit()
+                s.append(z*state(j, mp, jn, coupling))
+            return Add(*s)
+        else:
+            if dummy:
+                mp = Dummy('mp')
+            else:
+                mp = symbols('mp')
+            return Sum(Rotation.D(j, m, mp, a, b, g)*state(
+                j, mp, jn, coupling), (mp, -j, j))
+
+    def _apply_operator_JxKetCoupled(self, ket, **options):
+        return self._apply_operator_coupled(JxKetCoupled, ket, **options)
+
+    def _apply_operator_JyKetCoupled(self, ket, **options):
+        return self._apply_operator_coupled(JyKetCoupled, ket, **options)
+
+    def _apply_operator_JzKetCoupled(self, ket, **options):
+        return self._apply_operator_coupled(JzKetCoupled, ket, **options)
+
+class WignerD(Expr):
+    r"""Wigner-D function
+
+    The Wigner D-function gives the matrix elements of the rotation
+    operator in the jm-representation. For the Euler angles `\alpha`,
+    `\beta`, `\gamma`, the D-function is defined such that:
+
+    .. math ::
+         = \delta_{jj'} D(j, m, m', \alpha, \beta, \gamma)
+
+    Where the rotation operator is as defined by the Rotation class [1]_.
+
+    The Wigner D-function defined in this way gives:
+
+    .. math ::
+        D(j, m, m', \alpha, \beta, \gamma) = e^{-i m \alpha} d(j, m, m', \beta) e^{-i m' \gamma}
+
+    Where d is the Wigner small-d function, which is given by Rotation.d.
+
+    The Wigner small-d function gives the component of the Wigner
+    D-function that is determined by the second Euler angle. That is the
+    Wigner D-function is:
+
+    .. math ::
+        D(j, m, m', \alpha, \beta, \gamma) = e^{-i m \alpha} d(j, m, m', \beta) e^{-i m' \gamma}
+
+    Where d is the small-d function. The Wigner D-function is given by
+    Rotation.D.
+
+    Note that to evaluate the D-function, the j, m and mp parameters must
+    be integer or half integer numbers.
+
+    Parameters
+    ==========
+
+    j : Number
+        Total angular momentum
+    m : Number
+        Eigenvalue of angular momentum along axis after rotation
+    mp : Number
+        Eigenvalue of angular momentum along rotated axis
+    alpha : Number, Symbol
+        First Euler angle of rotation
+    beta : Number, Symbol
+        Second Euler angle of rotation
+    gamma : Number, Symbol
+        Third Euler angle of rotation
+
+    Examples
+    ========
+
+    Evaluate the Wigner-D matrix elements of a simple rotation:
+
+        >>> from sympy.physics.quantum.spin import Rotation
+        >>> from sympy import pi
+        >>> rot = Rotation.D(1, 1, 0, pi, pi/2, 0)
+        >>> rot
+        WignerD(1, 1, 0, pi, pi/2, 0)
+        >>> rot.doit()
+        sqrt(2)/2
+
+    Evaluate the Wigner-d matrix elements of a simple rotation
+
+        >>> rot = Rotation.d(1, 1, 0, pi/2)
+        >>> rot
+        WignerD(1, 1, 0, 0, pi/2, 0)
+        >>> rot.doit()
+        -sqrt(2)/2
+
+    See Also
+    ========
+
+    Rotation: Rotation operator
+
+    References
+    ==========
+
+    .. [1] Varshalovich, D A, Quantum Theory of Angular Momentum. 1988.
+    """
+
+    is_commutative = True
+
+    def __new__(cls, *args, **hints):
+        if not len(args) == 6:
+            raise ValueError('6 parameters expected, got %s' % args)
+        args = sympify(args)
+        evaluate = hints.get('evaluate', False)
+        if evaluate:
+            return Expr.__new__(cls, *args)._eval_wignerd()
+        return Expr.__new__(cls, *args)
+
+    @property
+    def j(self):
+        return self.args[0]
+
+    @property
+    def m(self):
+        return self.args[1]
+
+    @property
+    def mp(self):
+        return self.args[2]
+
+    @property
+    def alpha(self):
+        return self.args[3]
+
+    @property
+    def beta(self):
+        return self.args[4]
+
+    @property
+    def gamma(self):
+        return self.args[5]
+
+    def _latex(self, printer, *args):
+        if self.alpha == 0 and self.gamma == 0:
+            return r'd^{%s}_{%s,%s}\left(%s\right)' % \
+                (
+                    printer._print(self.j), printer._print(
+                        self.m), printer._print(self.mp),
+                    printer._print(self.beta) )
+        return r'D^{%s}_{%s,%s}\left(%s,%s,%s\right)' % \
+            (
+                printer._print(
+                    self.j), printer._print(self.m), printer._print(self.mp),
+                printer._print(self.alpha), printer._print(self.beta), printer._print(self.gamma) )
+
+    def _pretty(self, printer, *args):
+        top = printer._print(self.j)
+
+        bot = printer._print(self.m)
+        bot = prettyForm(*bot.right(','))
+        bot = prettyForm(*bot.right(printer._print(self.mp)))
+
+        pad = max(top.width(), bot.width())
+        top = prettyForm(*top.left(' '))
+        bot = prettyForm(*bot.left(' '))
+        if pad > top.width():
+            top = prettyForm(*top.right(' '*(pad - top.width())))
+        if pad > bot.width():
+            bot = prettyForm(*bot.right(' '*(pad - bot.width())))
+        if self.alpha == 0 and self.gamma == 0:
+            args = printer._print(self.beta)
+            s = stringPict('d' + ' '*pad)
+        else:
+            args = printer._print(self.alpha)
+            args = prettyForm(*args.right(','))
+            args = prettyForm(*args.right(printer._print(self.beta)))
+            args = prettyForm(*args.right(','))
+            args = prettyForm(*args.right(printer._print(self.gamma)))
+
+            s = stringPict('D' + ' '*pad)
+
+        args = prettyForm(*args.parens())
+        s = prettyForm(*s.above(top))
+        s = prettyForm(*s.below(bot))
+        s = prettyForm(*s.right(args))
+        return s
+
+    def doit(self, **hints):
+        hints['evaluate'] = True
+        return WignerD(*self.args, **hints)
+
+    def _eval_wignerd(self):
+        j = self.j
+        m = self.m
+        mp = self.mp
+        alpha = self.alpha
+        beta = self.beta
+        gamma = self.gamma
+        if alpha == 0 and beta == 0 and gamma == 0:
+            return KroneckerDelta(m, mp)
+        if not j.is_number:
+            raise ValueError(
+                'j parameter must be numerical to evaluate, got %s' % j)
+        r = 0
+        if beta == pi/2:
+            # Varshalovich Equation (5), Section 4.16, page 113, setting
+            # alpha=gamma=0.
+            for k in range(2*j + 1):
+                if k > j + mp or k > j - m or k < mp - m:
+                    continue
+                r += (S.NegativeOne)**k*binomial(j + mp, k)*binomial(j - mp, k + m - mp)
+            r *= (S.NegativeOne)**(m - mp) / 2**j*sqrt(factorial(j + m) *
+                    factorial(j - m) / (factorial(j + mp)*factorial(j - mp)))
+        else:
+            # Varshalovich Equation(5), Section 4.7.2, page 87, where we set
+            # beta1=beta2=pi/2, and we get alpha=gamma=pi/2 and beta=phi+pi,
+            # then we use the Eq. (1), Section 4.4. page 79, to simplify:
+            # d(j, m, mp, beta+pi) = (-1)**(j-mp)*d(j, m, -mp, beta)
+            # This happens to be almost the same as in Eq.(10), Section 4.16,
+            # except that we need to substitute -mp for mp.
+            size, mvals = m_values(j)
+            for mpp in mvals:
+                r += Rotation.d(j, m, mpp, pi/2).doit()*(cos(-mpp*beta) + I*sin(-mpp*beta))*\
+                    Rotation.d(j, mpp, -mp, pi/2).doit()
+            # Empirical normalization factor so results match Varshalovich
+            # Tables 4.3-4.12
+            # Note that this exact normalization does not follow from the
+            # above equations
+            r = r*I**(2*j - m - mp)*(-1)**(2*m)
+            # Finally, simplify the whole expression
+            r = simplify(r)
+        r *= exp(-I*m*alpha)*exp(-I*mp*gamma)
+        return r
+
+
+Jx = JxOp('J')
+Jy = JyOp('J')
+Jz = JzOp('J')
+J2 = J2Op('J')
+Jplus = JplusOp('J')
+Jminus = JminusOp('J')
+
+
+#-----------------------------------------------------------------------------
+# Spin States
+#-----------------------------------------------------------------------------
+
+
+class SpinState(State):
+    """Base class for angular momentum states."""
+
+    _label_separator = ','
+
+    def __new__(cls, j, m):
+        j = sympify(j)
+        m = sympify(m)
+        if j.is_number:
+            if 2*j != int(2*j):
+                raise ValueError(
+                    'j must be integer or half-integer, got: %s' % j)
+            if j < 0:
+                raise ValueError('j must be >= 0, got: %s' % j)
+        if m.is_number:
+            if 2*m != int(2*m):
+                raise ValueError(
+                    'm must be integer or half-integer, got: %s' % m)
+        if j.is_number and m.is_number:
+            if abs(m) > j:
+                raise ValueError('Allowed values for m are -j <= m <= j, got j, m: %s, %s' % (j, m))
+            if int(j - m) != j - m:
+                raise ValueError('Both j and m must be integer or half-integer, got j, m: %s, %s' % (j, m))
+        return State.__new__(cls, j, m)
+
+    @property
+    def j(self):
+        return self.label[0]
+
+    @property
+    def m(self):
+        return self.label[1]
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        return ComplexSpace(2*label[0] + 1)
+
+    def _represent_base(self, **options):
+        j = self.j
+        m = self.m
+        alpha = sympify(options.get('alpha', 0))
+        beta = sympify(options.get('beta', 0))
+        gamma = sympify(options.get('gamma', 0))
+        size, mvals = m_values(j)
+        result = zeros(size, 1)
+        # breaks finding angles on L930
+        for p, mval in enumerate(mvals):
+            if m.is_number:
+                result[p, 0] = Rotation.D(
+                    self.j, mval, self.m, alpha, beta, gamma).doit()
+            else:
+                result[p, 0] = Rotation.D(self.j, mval,
+                                          self.m, alpha, beta, gamma)
+        return result
+
+    def _eval_rewrite_as_Jx(self, *args, **options):
+        if isinstance(self, Bra):
+            return self._rewrite_basis(Jx, JxBra, **options)
+        return self._rewrite_basis(Jx, JxKet, **options)
+
+    def _eval_rewrite_as_Jy(self, *args, **options):
+        if isinstance(self, Bra):
+            return self._rewrite_basis(Jy, JyBra, **options)
+        return self._rewrite_basis(Jy, JyKet, **options)
+
+    def _eval_rewrite_as_Jz(self, *args, **options):
+        if isinstance(self, Bra):
+            return self._rewrite_basis(Jz, JzBra, **options)
+        return self._rewrite_basis(Jz, JzKet, **options)
+
+    def _rewrite_basis(self, basis, evect, **options):
+        from sympy.physics.quantum.represent import represent
+        j = self.j
+        args = self.args[2:]
+        if j.is_number:
+            if isinstance(self, CoupledSpinState):
+                if j == int(j):
+                    start = j**2
+                else:
+                    start = (2*j - 1)*(2*j + 1)/4
+            else:
+                start = 0
+            vect = represent(self, basis=basis, **options)
+            result = Add(
+                *[vect[start + i]*evect(j, j - i, *args) for i in range(2*j + 1)])
+            if isinstance(self, CoupledSpinState) and options.get('coupled') is False:
+                return uncouple(result)
+            return result
+        else:
+            i = 0
+            mi = symbols('mi')
+            # make sure not to introduce a symbol already in the state
+            while self.subs(mi, 0) != self:
+                i += 1
+                mi = symbols('mi%d' % i)
+                break
+            # TODO: better way to get angles of rotation
+            if isinstance(self, CoupledSpinState):
+                test_args = (0, mi, (0, 0))
+            else:
+                test_args = (0, mi)
+            if isinstance(self, Ket):
+                angles = represent(
+                    self.__class__(*test_args), basis=basis)[0].args[3:6]
+            else:
+                angles = represent(self.__class__(
+                    *test_args), basis=basis)[0].args[0].args[3:6]
+            if angles == (0, 0, 0):
+                return self
+            else:
+                state = evect(j, mi, *args)
+                lt = Rotation.D(j, mi, self.m, *angles)
+                return Sum(lt*state, (mi, -j, j))
+
+    def _eval_innerproduct_JxBra(self, bra, **hints):
+        result = KroneckerDelta(self.j, bra.j)
+        if bra.dual_class() is not self.__class__:
+            result *= self._represent_JxOp(None)[bra.j - bra.m]
+        else:
+            result *= KroneckerDelta(
+                self.j, bra.j)*KroneckerDelta(self.m, bra.m)
+        return result
+
+    def _eval_innerproduct_JyBra(self, bra, **hints):
+        result = KroneckerDelta(self.j, bra.j)
+        if bra.dual_class() is not self.__class__:
+            result *= self._represent_JyOp(None)[bra.j - bra.m]
+        else:
+            result *= KroneckerDelta(
+                self.j, bra.j)*KroneckerDelta(self.m, bra.m)
+        return result
+
+    def _eval_innerproduct_JzBra(self, bra, **hints):
+        result = KroneckerDelta(self.j, bra.j)
+        if bra.dual_class() is not self.__class__:
+            result *= self._represent_JzOp(None)[bra.j - bra.m]
+        else:
+            result *= KroneckerDelta(
+                self.j, bra.j)*KroneckerDelta(self.m, bra.m)
+        return result
+
+    def _eval_trace(self, bra, **hints):
+
+        # One way to implement this method is to assume the basis set k is
+        # passed.
+        # Then we can apply the discrete form of Trace formula here
+        # Tr(|i>
+        #then we do qapply() on each each inner product and sum over them.
+
+        # OR
+
+        # Inner product of |i>>> from sympy.physics.quantum.spin import JzKet, JxKet
+        >>> from sympy import symbols
+        >>> JzKet(1, 0)
+        |1,0>
+        >>> j, m = symbols('j m')
+        >>> JzKet(j, m)
+        |j,m>
+
+    Rewriting the JzKet in terms of eigenkets of the Jx operator:
+    Note: that the resulting eigenstates are JxKet's
+
+        >>> JzKet(1,1).rewrite("Jx")
+        |1,-1>/2 - sqrt(2)*|1,0>/2 + |1,1>/2
+
+    Get the vector representation of a state in terms of the basis elements
+    of the Jx operator:
+
+        >>> from sympy.physics.quantum.represent import represent
+        >>> from sympy.physics.quantum.spin import Jx, Jz
+        >>> represent(JzKet(1,-1), basis=Jx)
+        Matrix([
+        [      1/2],
+        [sqrt(2)/2],
+        [      1/2]])
+
+    Apply innerproducts between states:
+
+        >>> from sympy.physics.quantum.innerproduct import InnerProduct
+        >>> from sympy.physics.quantum.spin import JxBra
+        >>> i = InnerProduct(JxBra(1,1), JzKet(1,1))
+        >>> i
+        <1,1|1,1>
+        >>> i.doit()
+        1/2
+
+    *Uncoupled States:*
+
+    Define an uncoupled state as a TensorProduct between two Jz eigenkets:
+
+        >>> from sympy.physics.quantum.tensorproduct import TensorProduct
+        >>> j1,m1,j2,m2 = symbols('j1 m1 j2 m2')
+        >>> TensorProduct(JzKet(1,0), JzKet(1,1))
+        |1,0>x|1,1>
+        >>> TensorProduct(JzKet(j1,m1), JzKet(j2,m2))
+        |j1,m1>x|j2,m2>
+
+    A TensorProduct can be rewritten, in which case the eigenstates that make
+    up the tensor product is rewritten to the new basis:
+
+        >>> TensorProduct(JzKet(1,1),JxKet(1,1)).rewrite('Jz')
+        |1,1>x|1,-1>/2 + sqrt(2)*|1,1>x|1,0>/2 + |1,1>x|1,1>/2
+
+    The represent method for TensorProduct's gives the vector representation of
+    the state. Note that the state in the product basis is the equivalent of the
+    tensor product of the vector representation of the component eigenstates:
+
+        >>> represent(TensorProduct(JzKet(1,0),JzKet(1,1)))
+        Matrix([
+        [0],
+        [0],
+        [0],
+        [1],
+        [0],
+        [0],
+        [0],
+        [0],
+        [0]])
+        >>> represent(TensorProduct(JzKet(1,1),JxKet(1,1)), basis=Jz)
+        Matrix([
+        [      1/2],
+        [sqrt(2)/2],
+        [      1/2],
+        [        0],
+        [        0],
+        [        0],
+        [        0],
+        [        0],
+        [        0]])
+
+    See Also
+    ========
+
+    JzKetCoupled: Coupled eigenstates
+    sympy.physics.quantum.tensorproduct.TensorProduct: Used to specify uncoupled states
+    uncouple: Uncouples states given coupling parameters
+    couple: Couples uncoupled states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JzBra
+
+    @classmethod
+    def coupled_class(self):
+        return JzKetCoupled
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JxOp(self, basis, **options):
+        return self._represent_base(beta=pi*Rational(3, 2), **options)
+
+    def _represent_JyOp(self, basis, **options):
+        return self._represent_base(alpha=pi*Rational(3, 2), beta=pi/2, gamma=pi/2, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_base(**options)
+
+
+class JzBra(SpinState, Bra):
+    """Eigenbra of Jz.
+
+    See the JzKet for the usage of spin eigenstates.
+
+    See Also
+    ========
+
+    JzKet: Usage of spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JzKet
+
+    @classmethod
+    def coupled_class(self):
+        return JzBraCoupled
+
+
+# Method used primarily to create coupled_n and coupled_jn by __new__ in
+# CoupledSpinState
+# This same method is also used by the uncouple method, and is separated from
+# the CoupledSpinState class to maintain consistency in defining coupling
+def _build_coupled(jcoupling, length):
+    n_list = [ [n + 1] for n in range(length) ]
+    coupled_jn = []
+    coupled_n = []
+    for n1, n2, j_new in jcoupling:
+        coupled_jn.append(j_new)
+        coupled_n.append( (n_list[n1 - 1], n_list[n2 - 1]) )
+        n_sort = sorted(n_list[n1 - 1] + n_list[n2 - 1])
+        n_list[n_sort[0] - 1] = n_sort
+    return coupled_n, coupled_jn
+
+
+class CoupledSpinState(SpinState):
+    """Base class for coupled angular momentum states."""
+
+    def __new__(cls, j, m, jn, *jcoupling):
+        # Check j and m values using SpinState
+        SpinState(j, m)
+        # Build and check coupling scheme from arguments
+        if len(jcoupling) == 0:
+            # Use default coupling scheme
+            jcoupling = []
+            for n in range(2, len(jn)):
+                jcoupling.append( (1, n, Add(*[jn[i] for i in range(n)])) )
+            jcoupling.append( (1, len(jn), j) )
+        elif len(jcoupling) == 1:
+            # Use specified coupling scheme
+            jcoupling = jcoupling[0]
+        else:
+            raise TypeError("CoupledSpinState only takes 3 or 4 arguments, got: %s" % (len(jcoupling) + 3) )
+        # Check arguments have correct form
+        if not isinstance(jn, (list, tuple, Tuple)):
+            raise TypeError('jn must be Tuple, list or tuple, got %s' %
+                            jn.__class__.__name__)
+        if not isinstance(jcoupling, (list, tuple, Tuple)):
+            raise TypeError('jcoupling must be Tuple, list or tuple, got %s' %
+                            jcoupling.__class__.__name__)
+        if not all(isinstance(term, (list, tuple, Tuple)) for term in jcoupling):
+            raise TypeError(
+                'All elements of jcoupling must be list, tuple or Tuple')
+        if not len(jn) - 1 == len(jcoupling):
+            raise ValueError('jcoupling must have length of %d, got %d' %
+                             (len(jn) - 1, len(jcoupling)))
+        if not all(len(x) == 3 for x in jcoupling):
+            raise ValueError('All elements of jcoupling must have length 3')
+        # Build sympified args
+        j = sympify(j)
+        m = sympify(m)
+        jn = Tuple( *[sympify(ji) for ji in jn] )
+        jcoupling = Tuple( *[Tuple(sympify(
+            n1), sympify(n2), sympify(ji)) for (n1, n2, ji) in jcoupling] )
+        # Check values in coupling scheme give physical state
+        if any(2*ji != int(2*ji) for ji in jn if ji.is_number):
+            raise ValueError('All elements of jn must be integer or half-integer, got: %s' % jn)
+        if any(n1 != int(n1) or n2 != int(n2) for (n1, n2, _) in jcoupling):
+            raise ValueError('Indices in jcoupling must be integers')
+        if any(n1 < 1 or n2 < 1 or n1 > len(jn) or n2 > len(jn) for (n1, n2, _) in jcoupling):
+            raise ValueError('Indices must be between 1 and the number of coupled spin spaces')
+        if any(2*ji != int(2*ji) for (_, _, ji) in jcoupling if ji.is_number):
+            raise ValueError('All coupled j values in coupling scheme must be integer or half-integer')
+        coupled_n, coupled_jn = _build_coupled(jcoupling, len(jn))
+        jvals = list(jn)
+        for n, (n1, n2) in enumerate(coupled_n):
+            j1 = jvals[min(n1) - 1]
+            j2 = jvals[min(n2) - 1]
+            j3 = coupled_jn[n]
+            if sympify(j1).is_number and sympify(j2).is_number and sympify(j3).is_number:
+                if j1 + j2 < j3:
+                    raise ValueError('All couplings must have j1+j2 >= j3, '
+                        'in coupling number %d got j1,j2,j3: %d,%d,%d' % (n + 1, j1, j2, j3))
+                if abs(j1 - j2) > j3:
+                    raise ValueError("All couplings must have |j1+j2| <= j3, "
+                        "in coupling number %d got j1,j2,j3: %d,%d,%d" % (n + 1, j1, j2, j3))
+                if int_valued(j1 + j2):
+                    pass
+            jvals[min(n1 + n2) - 1] = j3
+        if len(jcoupling) > 0 and jcoupling[-1][2] != j:
+            raise ValueError('Last j value coupled together must be the final j of the state')
+        # Return state
+        return State.__new__(cls, j, m, jn, jcoupling)
+
+    def _print_label(self, printer, *args):
+        label = [printer._print(self.j), printer._print(self.m)]
+        for i, ji in enumerate(self.jn, start=1):
+            label.append('j%d=%s' % (
+                i, printer._print(ji)
+            ))
+        for jn, (n1, n2) in zip(self.coupled_jn[:-1], self.coupled_n[:-1]):
+            label.append('j(%s)=%s' % (
+                ','.join(str(i) for i in sorted(n1 + n2)), printer._print(jn)
+            ))
+        return ','.join(label)
+
+    def _print_label_pretty(self, printer, *args):
+        label = [self.j, self.m]
+        for i, ji in enumerate(self.jn, start=1):
+            symb = 'j%d' % i
+            symb = pretty_symbol(symb)
+            symb = prettyForm(symb + '=')
+            item = prettyForm(*symb.right(printer._print(ji)))
+            label.append(item)
+        for jn, (n1, n2) in zip(self.coupled_jn[:-1], self.coupled_n[:-1]):
+            n = ','.join(pretty_symbol("j%d" % i)[-1] for i in sorted(n1 + n2))
+            symb = prettyForm('j' + n + '=')
+            item = prettyForm(*symb.right(printer._print(jn)))
+            label.append(item)
+        return self._print_sequence_pretty(
+            label, self._label_separator, printer, *args
+        )
+
+    def _print_label_latex(self, printer, *args):
+        label = [
+            printer._print(self.j, *args),
+            printer._print(self.m, *args)
+        ]
+        for i, ji in enumerate(self.jn, start=1):
+            label.append('j_{%d}=%s' % (i, printer._print(ji, *args)) )
+        for jn, (n1, n2) in zip(self.coupled_jn[:-1], self.coupled_n[:-1]):
+            n = ','.join(str(i) for i in sorted(n1 + n2))
+            label.append('j_{%s}=%s' % (n, printer._print(jn, *args)) )
+        return self._label_separator.join(label)
+
+    @property
+    def jn(self):
+        return self.label[2]
+
+    @property
+    def coupling(self):
+        return self.label[3]
+
+    @property
+    def coupled_jn(self):
+        return _build_coupled(self.label[3], len(self.label[2]))[1]
+
+    @property
+    def coupled_n(self):
+        return _build_coupled(self.label[3], len(self.label[2]))[0]
+
+    @classmethod
+    def _eval_hilbert_space(cls, label):
+        j = Add(*label[2])
+        if j.is_number:
+            return DirectSumHilbertSpace(*[ ComplexSpace(x) for x in range(int(2*j + 1), 0, -2) ])
+        else:
+            # TODO: Need hilbert space fix, see issue 5732
+            # Desired behavior:
+            #ji = symbols('ji')
+            #ret = Sum(ComplexSpace(2*ji + 1), (ji, 0, j))
+            # Temporary fix:
+            return ComplexSpace(2*j + 1)
+
+    def _represent_coupled_base(self, **options):
+        evect = self.uncoupled_class()
+        if not self.j.is_number:
+            raise ValueError(
+                'State must not have symbolic j value to represent')
+        if not self.hilbert_space.dimension.is_number:
+            raise ValueError(
+                'State must not have symbolic j values to represent')
+        result = zeros(self.hilbert_space.dimension, 1)
+        if self.j == int(self.j):
+            start = self.j**2
+        else:
+            start = (2*self.j - 1)*(1 + 2*self.j)/4
+        result[start:start + 2*self.j + 1, 0] = evect(
+            self.j, self.m)._represent_base(**options)
+        return result
+
+    def _eval_rewrite_as_Jx(self, *args, **options):
+        if isinstance(self, Bra):
+            return self._rewrite_basis(Jx, JxBraCoupled, **options)
+        return self._rewrite_basis(Jx, JxKetCoupled, **options)
+
+    def _eval_rewrite_as_Jy(self, *args, **options):
+        if isinstance(self, Bra):
+            return self._rewrite_basis(Jy, JyBraCoupled, **options)
+        return self._rewrite_basis(Jy, JyKetCoupled, **options)
+
+    def _eval_rewrite_as_Jz(self, *args, **options):
+        if isinstance(self, Bra):
+            return self._rewrite_basis(Jz, JzBraCoupled, **options)
+        return self._rewrite_basis(Jz, JzKetCoupled, **options)
+
+
+class JxKetCoupled(CoupledSpinState, Ket):
+    """Coupled eigenket of Jx.
+
+    See JzKetCoupled for the usage of coupled spin eigenstates.
+
+    See Also
+    ========
+
+    JzKetCoupled: Usage of coupled spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JxBraCoupled
+
+    @classmethod
+    def uncoupled_class(self):
+        return JxKet
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JxOp(self, basis, **options):
+        return self._represent_coupled_base(**options)
+
+    def _represent_JyOp(self, basis, **options):
+        return self._represent_coupled_base(alpha=pi*Rational(3, 2), **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_coupled_base(beta=pi/2, **options)
+
+
+class JxBraCoupled(CoupledSpinState, Bra):
+    """Coupled eigenbra of Jx.
+
+    See JzKetCoupled for the usage of coupled spin eigenstates.
+
+    See Also
+    ========
+
+    JzKetCoupled: Usage of coupled spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JxKetCoupled
+
+    @classmethod
+    def uncoupled_class(self):
+        return JxBra
+
+
+class JyKetCoupled(CoupledSpinState, Ket):
+    """Coupled eigenket of Jy.
+
+    See JzKetCoupled for the usage of coupled spin eigenstates.
+
+    See Also
+    ========
+
+    JzKetCoupled: Usage of coupled spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JyBraCoupled
+
+    @classmethod
+    def uncoupled_class(self):
+        return JyKet
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JxOp(self, basis, **options):
+        return self._represent_coupled_base(gamma=pi/2, **options)
+
+    def _represent_JyOp(self, basis, **options):
+        return self._represent_coupled_base(**options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_coupled_base(alpha=pi*Rational(3, 2), beta=-pi/2, gamma=pi/2, **options)
+
+
+class JyBraCoupled(CoupledSpinState, Bra):
+    """Coupled eigenbra of Jy.
+
+    See JzKetCoupled for the usage of coupled spin eigenstates.
+
+    See Also
+    ========
+
+    JzKetCoupled: Usage of coupled spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JyKetCoupled
+
+    @classmethod
+    def uncoupled_class(self):
+        return JyBra
+
+
+class JzKetCoupled(CoupledSpinState, Ket):
+    r"""Coupled eigenket of Jz
+
+    Spin state that is an eigenket of Jz which represents the coupling of
+    separate spin spaces.
+
+    The arguments for creating instances of JzKetCoupled are ``j``, ``m``,
+    ``jn`` and an optional ``jcoupling`` argument. The ``j`` and ``m`` options
+    are the total angular momentum quantum numbers, as used for normal states
+    (e.g. JzKet).
+
+    The other required parameter in ``jn``, which is a tuple defining the `j_n`
+    angular momentum quantum numbers of the product spaces. So for example, if
+    a state represented the coupling of the product basis state
+    `\left|j_1,m_1\right\rangle\times\left|j_2,m_2\right\rangle`, the ``jn``
+    for this state would be ``(j1,j2)``.
+
+    The final option is ``jcoupling``, which is used to define how the spaces
+    specified by ``jn`` are coupled, which includes both the order these spaces
+    are coupled together and the quantum numbers that arise from these
+    couplings. The ``jcoupling`` parameter itself is a list of lists, such that
+    each of the sublists defines a single coupling between the spin spaces. If
+    there are N coupled angular momentum spaces, that is ``jn`` has N elements,
+    then there must be N-1 sublists. Each of these sublists making up the
+    ``jcoupling`` parameter have length 3. The first two elements are the
+    indices of the product spaces that are considered to be coupled together.
+    For example, if we want to couple `j_1` and `j_4`, the indices would be 1
+    and 4. If a state has already been coupled, it is referenced by the
+    smallest index that is coupled, so if `j_2` and `j_4` has already been
+    coupled to some `j_{24}`, then this value can be coupled by referencing it
+    with index 2. The final element of the sublist is the quantum number of the
+    coupled state. So putting everything together, into a valid sublist for
+    ``jcoupling``, if `j_1` and `j_2` are coupled to an angular momentum space
+    with quantum number `j_{12}` with the value ``j12``, the sublist would be
+    ``(1,2,j12)``, N-1 of these sublists are used in the list for
+    ``jcoupling``.
+
+    Note the ``jcoupling`` parameter is optional, if it is not specified, the
+    default coupling is taken. This default value is to coupled the spaces in
+    order and take the quantum number of the coupling to be the maximum value.
+    For example, if the spin spaces are `j_1`, `j_2`, `j_3`, `j_4`, then the
+    default coupling couples `j_1` and `j_2` to `j_{12}=j_1+j_2`, then,
+    `j_{12}` and `j_3` are coupled to `j_{123}=j_{12}+j_3`, and finally
+    `j_{123}` and `j_4` to `j=j_{123}+j_4`. The jcoupling value that would
+    correspond to this is:
+
+        ``((1,2,j1+j2),(1,3,j1+j2+j3))``
+
+    Parameters
+    ==========
+
+    args : tuple
+        The arguments that must be passed are ``j``, ``m``, ``jn``, and
+        ``jcoupling``. The ``j`` value is the total angular momentum. The ``m``
+        value is the eigenvalue of the Jz spin operator. The ``jn`` list are
+        the j values of argular momentum spaces coupled together. The
+        ``jcoupling`` parameter is an optional parameter defining how the spaces
+        are coupled together. See the above description for how these coupling
+        parameters are defined.
+
+    Examples
+    ========
+
+    Defining simple spin states, both numerical and symbolic:
+
+        >>> from sympy.physics.quantum.spin import JzKetCoupled
+        >>> from sympy import symbols
+        >>> JzKetCoupled(1, 0, (1, 1))
+        |1,0,j1=1,j2=1>
+        >>> j, m, j1, j2 = symbols('j m j1 j2')
+        >>> JzKetCoupled(j, m, (j1, j2))
+        |j,m,j1=j1,j2=j2>
+
+    Defining coupled spin states for more than 2 coupled spaces with various
+    coupling parameters:
+
+        >>> JzKetCoupled(2, 1, (1, 1, 1))
+        |2,1,j1=1,j2=1,j3=1,j(1,2)=2>
+        >>> JzKetCoupled(2, 1, (1, 1, 1), ((1,2,2),(1,3,2)) )
+        |2,1,j1=1,j2=1,j3=1,j(1,2)=2>
+        >>> JzKetCoupled(2, 1, (1, 1, 1), ((2,3,1),(1,2,2)) )
+        |2,1,j1=1,j2=1,j3=1,j(2,3)=1>
+
+    Rewriting the JzKetCoupled in terms of eigenkets of the Jx operator:
+    Note: that the resulting eigenstates are JxKetCoupled
+
+        >>> JzKetCoupled(1,1,(1,1)).rewrite("Jx")
+        |1,-1,j1=1,j2=1>/2 - sqrt(2)*|1,0,j1=1,j2=1>/2 + |1,1,j1=1,j2=1>/2
+
+    The rewrite method can be used to convert a coupled state to an uncoupled
+    state. This is done by passing coupled=False to the rewrite function:
+
+        >>> JzKetCoupled(1, 0, (1, 1)).rewrite('Jz', coupled=False)
+        -sqrt(2)*|1,-1>x|1,1>/2 + sqrt(2)*|1,1>x|1,-1>/2
+
+    Get the vector representation of a state in terms of the basis elements
+    of the Jx operator:
+
+        >>> from sympy.physics.quantum.represent import represent
+        >>> from sympy.physics.quantum.spin import Jx
+        >>> from sympy import S
+        >>> represent(JzKetCoupled(1,-1,(S(1)/2,S(1)/2)), basis=Jx)
+        Matrix([
+        [        0],
+        [      1/2],
+        [sqrt(2)/2],
+        [      1/2]])
+
+    See Also
+    ========
+
+    JzKet: Normal spin eigenstates
+    uncouple: Uncoupling of coupling spin states
+    couple: Coupling of uncoupled spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JzBraCoupled
+
+    @classmethod
+    def uncoupled_class(self):
+        return JzKet
+
+    def _represent_default_basis(self, **options):
+        return self._represent_JzOp(None, **options)
+
+    def _represent_JxOp(self, basis, **options):
+        return self._represent_coupled_base(beta=pi*Rational(3, 2), **options)
+
+    def _represent_JyOp(self, basis, **options):
+        return self._represent_coupled_base(alpha=pi*Rational(3, 2), beta=pi/2, gamma=pi/2, **options)
+
+    def _represent_JzOp(self, basis, **options):
+        return self._represent_coupled_base(**options)
+
+
+class JzBraCoupled(CoupledSpinState, Bra):
+    """Coupled eigenbra of Jz.
+
+    See the JzKetCoupled for the usage of coupled spin eigenstates.
+
+    See Also
+    ========
+
+    JzKetCoupled: Usage of coupled spin states
+
+    """
+
+    @classmethod
+    def dual_class(self):
+        return JzKetCoupled
+
+    @classmethod
+    def uncoupled_class(self):
+        return JzBra
+
+#-----------------------------------------------------------------------------
+# Coupling/uncoupling
+#-----------------------------------------------------------------------------
+
+
+def couple(expr, jcoupling_list=None):
+    """ Couple a tensor product of spin states
+
+    This function can be used to couple an uncoupled tensor product of spin
+    states. All of the eigenstates to be coupled must be of the same class. It
+    will return a linear combination of eigenstates that are subclasses of
+    CoupledSpinState determined by Clebsch-Gordan angular momentum coupling
+    coefficients.
+
+    Parameters
+    ==========
+
+    expr : Expr
+        An expression involving TensorProducts of spin states to be coupled.
+        Each state must be a subclass of SpinState and they all must be the
+        same class.
+
+    jcoupling_list : list or tuple
+        Elements of this list are sub-lists of length 2 specifying the order of
+        the coupling of the spin spaces. The length of this must be N-1, where N
+        is the number of states in the tensor product to be coupled. The
+        elements of this sublist are the same as the first two elements of each
+        sublist in the ``jcoupling`` parameter defined for JzKetCoupled. If this
+        parameter is not specified, the default value is taken, which couples
+        the first and second product basis spaces, then couples this new coupled
+        space to the third product space, etc
+
+    Examples
+    ========
+
+    Couple a tensor product of numerical states for two spaces:
+
+        >>> from sympy.physics.quantum.spin import JzKet, couple
+        >>> from sympy.physics.quantum.tensorproduct import TensorProduct
+        >>> couple(TensorProduct(JzKet(1,0), JzKet(1,1)))
+        -sqrt(2)*|1,1,j1=1,j2=1>/2 + sqrt(2)*|2,1,j1=1,j2=1>/2
+
+
+    Numerical coupling of three spaces using the default coupling method, i.e.
+    first and second spaces couple, then this couples to the third space:
+
+        >>> couple(TensorProduct(JzKet(1,1), JzKet(1,1), JzKet(1,0)))
+        sqrt(6)*|2,2,j1=1,j2=1,j3=1,j(1,2)=2>/3 + sqrt(3)*|3,2,j1=1,j2=1,j3=1,j(1,2)=2>/3
+
+    Perform this same coupling, but we define the coupling to first couple
+    the first and third spaces:
+
+        >>> couple(TensorProduct(JzKet(1,1), JzKet(1,1), JzKet(1,0)), ((1,3),(1,2)) )
+        sqrt(2)*|2,2,j1=1,j2=1,j3=1,j(1,3)=1>/2 - sqrt(6)*|2,2,j1=1,j2=1,j3=1,j(1,3)=2>/6 + sqrt(3)*|3,2,j1=1,j2=1,j3=1,j(1,3)=2>/3
+
+    Couple a tensor product of symbolic states:
+
+        >>> from sympy import symbols
+        >>> j1,m1,j2,m2 = symbols('j1 m1 j2 m2')
+        >>> couple(TensorProduct(JzKet(j1,m1), JzKet(j2,m2)))
+        Sum(CG(j1, m1, j2, m2, j, m1 + m2)*|j,m1 + m2,j1=j1,j2=j2>, (j, m1 + m2, j1 + j2))
+
+    """
+    a = expr.atoms(TensorProduct)
+    for tp in a:
+        # Allow other tensor products to be in expression
+        if not all(isinstance(state, SpinState) for state in tp.args):
+            continue
+        # If tensor product has all spin states, raise error for invalid tensor product state
+        if not all(state.__class__ is tp.args[0].__class__ for state in tp.args):
+            raise TypeError('All states must be the same basis')
+        expr = expr.subs(tp, _couple(tp, jcoupling_list))
+    return expr
+
+
+def _couple(tp, jcoupling_list):
+    states = tp.args
+    coupled_evect = states[0].coupled_class()
+
+    # Define default coupling if none is specified
+    if jcoupling_list is None:
+        jcoupling_list = []
+        for n in range(1, len(states)):
+            jcoupling_list.append( (1, n + 1) )
+
+    # Check jcoupling_list valid
+    if not len(jcoupling_list) == len(states) - 1:
+        raise TypeError('jcoupling_list must be length %d, got %d' %
+                        (len(states) - 1, len(jcoupling_list)))
+    if not all( len(coupling) == 2 for coupling in jcoupling_list):
+        raise ValueError('Each coupling must define 2 spaces')
+    if any(n1 == n2 for n1, n2 in jcoupling_list):
+        raise ValueError('Spin spaces cannot couple to themselves')
+    if all(sympify(n1).is_number and sympify(n2).is_number for n1, n2 in jcoupling_list):
+        j_test = [0]*len(states)
+        for n1, n2 in jcoupling_list:
+            if j_test[n1 - 1] == -1 or j_test[n2 - 1] == -1:
+                raise ValueError('Spaces coupling j_n\'s are referenced by smallest n value')
+            j_test[max(n1, n2) - 1] = -1
+
+    # j values of states to be coupled together
+    jn = [state.j for state in states]
+    mn = [state.m for state in states]
+
+    # Create coupling_list, which defines all the couplings between all
+    # the spaces from jcoupling_list
+    coupling_list = []
+    n_list = [ [i + 1] for i in range(len(states)) ]
+    for j_coupling in jcoupling_list:
+        # Least n for all j_n which is coupled as first and second spaces
+        n1, n2 = j_coupling
+        # List of all n's coupled in first and second spaces
+        j1_n = list(n_list[n1 - 1])
+        j2_n = list(n_list[n2 - 1])
+        coupling_list.append( (j1_n, j2_n) )
+        # Set new j_n to be coupling of all j_n in both first and second spaces
+        n_list[ min(n1, n2) - 1 ] = sorted(j1_n + j2_n)
+
+    if all(state.j.is_number and state.m.is_number for state in states):
+        # Numerical coupling
+        # Iterate over difference between maximum possible j value of each coupling and the actual value
+        diff_max = [ Add( *[ jn[n - 1] - mn[n - 1] for n in coupling[0] +
+                         coupling[1] ] ) for coupling in coupling_list ]
+        result = []
+        for diff in range(diff_max[-1] + 1):
+            # Determine available configurations
+            n = len(coupling_list)
+            tot = binomial(diff + n - 1, diff)
+
+            for config_num in range(tot):
+                diff_list = _confignum_to_difflist(config_num, diff, n)
+
+                # Skip the configuration if non-physical
+                # This is a lazy check for physical states given the loose restrictions of diff_max
+                if any(d > m for d, m in zip(diff_list, diff_max)):
+                    continue
+
+                # Determine term
+                cg_terms = []
+                coupled_j = list(jn)
+                jcoupling = []
+                for (j1_n, j2_n), coupling_diff in zip(coupling_list, diff_list):
+                    j1 = coupled_j[ min(j1_n) - 1 ]
+                    j2 = coupled_j[ min(j2_n) - 1 ]
+                    j3 = j1 + j2 - coupling_diff
+                    coupled_j[ min(j1_n + j2_n) - 1 ] = j3
+                    m1 = Add( *[ mn[x - 1] for x in j1_n] )
+                    m2 = Add( *[ mn[x - 1] for x in j2_n] )
+                    m3 = m1 + m2
+                    cg_terms.append( (j1, m1, j2, m2, j3, m3) )
+                    jcoupling.append( (min(j1_n), min(j2_n), j3) )
+                # Better checks that state is physical
+                if any(abs(term[5]) > term[4] for term in cg_terms):
+                    continue
+                if any(term[0] + term[2] < term[4] for term in cg_terms):
+                    continue
+                if any(abs(term[0] - term[2]) > term[4] for term in cg_terms):
+                    continue
+                coeff = Mul( *[ CG(*term).doit() for term in cg_terms] )
+                state = coupled_evect(j3, m3, jn, jcoupling)
+                result.append(coeff*state)
+        return Add(*result)
+    else:
+        # Symbolic coupling
+        cg_terms = []
+        jcoupling = []
+        sum_terms = []
+        coupled_j = list(jn)
+        for j1_n, j2_n in coupling_list:
+            j1 = coupled_j[ min(j1_n) - 1 ]
+            j2 = coupled_j[ min(j2_n) - 1 ]
+            if len(j1_n + j2_n) == len(states):
+                j3 = symbols('j')
+            else:
+                j3_name = 'j' + ''.join(["%s" % n for n in j1_n + j2_n])
+                j3 = symbols(j3_name)
+            coupled_j[ min(j1_n + j2_n) - 1 ] = j3
+            m1 = Add( *[ mn[x - 1] for x in j1_n] )
+            m2 = Add( *[ mn[x - 1] for x in j2_n] )
+            m3 = m1 + m2
+            cg_terms.append( (j1, m1, j2, m2, j3, m3) )
+            jcoupling.append( (min(j1_n), min(j2_n), j3) )
+            sum_terms.append((j3, m3, j1 + j2))
+        coeff = Mul( *[ CG(*term) for term in cg_terms] )
+        state = coupled_evect(j3, m3, jn, jcoupling)
+        return Sum(coeff*state, *sum_terms)
+
+
+def uncouple(expr, jn=None, jcoupling_list=None):
+    """ Uncouple a coupled spin state
+
+    Gives the uncoupled representation of a coupled spin state. Arguments must
+    be either a spin state that is a subclass of CoupledSpinState or a spin
+    state that is a subclass of SpinState and an array giving the j values
+    of the spaces that are to be coupled
+
+    Parameters
+    ==========
+
+    expr : Expr
+        The expression containing states that are to be coupled. If the states
+        are a subclass of SpinState, the ``jn`` and ``jcoupling`` parameters
+        must be defined. If the states are a subclass of CoupledSpinState,
+        ``jn`` and ``jcoupling`` will be taken from the state.
+
+    jn : list or tuple
+        The list of the j-values that are coupled. If state is a
+        CoupledSpinState, this parameter is ignored. This must be defined if
+        state is not a subclass of CoupledSpinState. The syntax of this
+        parameter is the same as the ``jn`` parameter of JzKetCoupled.
+
+    jcoupling_list : list or tuple
+        The list defining how the j-values are coupled together. If state is a
+        CoupledSpinState, this parameter is ignored. This must be defined if
+        state is not a subclass of CoupledSpinState. The syntax of this
+        parameter is the same as the ``jcoupling`` parameter of JzKetCoupled.
+
+    Examples
+    ========
+
+    Uncouple a numerical state using a CoupledSpinState state:
+
+        >>> from sympy.physics.quantum.spin import JzKetCoupled, uncouple
+        >>> from sympy import S
+        >>> uncouple(JzKetCoupled(1, 0, (S(1)/2, S(1)/2)))
+        sqrt(2)*|1/2,-1/2>x|1/2,1/2>/2 + sqrt(2)*|1/2,1/2>x|1/2,-1/2>/2
+
+    Perform the same calculation using a SpinState state:
+
+        >>> from sympy.physics.quantum.spin import JzKet
+        >>> uncouple(JzKet(1, 0), (S(1)/2, S(1)/2))
+        sqrt(2)*|1/2,-1/2>x|1/2,1/2>/2 + sqrt(2)*|1/2,1/2>x|1/2,-1/2>/2
+
+    Uncouple a numerical state of three coupled spaces using a CoupledSpinState state:
+
+        >>> uncouple(JzKetCoupled(1, 1, (1, 1, 1), ((1,3,1),(1,2,1)) ))
+        |1,-1>x|1,1>x|1,1>/2 - |1,0>x|1,0>x|1,1>/2 + |1,1>x|1,0>x|1,0>/2 - |1,1>x|1,1>x|1,-1>/2
+
+    Perform the same calculation using a SpinState state:
+
+        >>> uncouple(JzKet(1, 1), (1, 1, 1), ((1,3,1),(1,2,1)) )
+        |1,-1>x|1,1>x|1,1>/2 - |1,0>x|1,0>x|1,1>/2 + |1,1>x|1,0>x|1,0>/2 - |1,1>x|1,1>x|1,-1>/2
+
+    Uncouple a symbolic state using a CoupledSpinState state:
+
+        >>> from sympy import symbols
+        >>> j,m,j1,j2 = symbols('j m j1 j2')
+        >>> uncouple(JzKetCoupled(j, m, (j1, j2)))
+        Sum(CG(j1, m1, j2, m2, j, m)*|j1,m1>x|j2,m2>, (m1, -j1, j1), (m2, -j2, j2))
+
+    Perform the same calculation using a SpinState state
+
+        >>> uncouple(JzKet(j, m), (j1, j2))
+        Sum(CG(j1, m1, j2, m2, j, m)*|j1,m1>x|j2,m2>, (m1, -j1, j1), (m2, -j2, j2))
+
+    """
+    a = expr.atoms(SpinState)
+    for state in a:
+        expr = expr.subs(state, _uncouple(state, jn, jcoupling_list))
+    return expr
+
+
+def _uncouple(state, jn, jcoupling_list):
+    if isinstance(state, CoupledSpinState):
+        jn = state.jn
+        coupled_n = state.coupled_n
+        coupled_jn = state.coupled_jn
+        evect = state.uncoupled_class()
+    elif isinstance(state, SpinState):
+        if jn is None:
+            raise ValueError("Must specify j-values for coupled state")
+        if not isinstance(jn, (list, tuple)):
+            raise TypeError("jn must be list or tuple")
+        if jcoupling_list is None:
+            # Use default
+            jcoupling_list = []
+            for i in range(1, len(jn)):
+                jcoupling_list.append(
+                    (1, 1 + i, Add(*[jn[j] for j in range(i + 1)])) )
+        if not isinstance(jcoupling_list, (list, tuple)):
+            raise TypeError("jcoupling must be a list or tuple")
+        if not len(jcoupling_list) == len(jn) - 1:
+            raise ValueError("Must specify 2 fewer coupling terms than the number of j values")
+        coupled_n, coupled_jn = _build_coupled(jcoupling_list, len(jn))
+        evect = state.__class__
+    else:
+        raise TypeError("state must be a spin state")
+    j = state.j
+    m = state.m
+    coupling_list = []
+    j_list = list(jn)
+
+    # Create coupling, which defines all the couplings between all the spaces
+    for j3, (n1, n2) in zip(coupled_jn, coupled_n):
+        # j's which are coupled as first and second spaces
+        j1 = j_list[n1[0] - 1]
+        j2 = j_list[n2[0] - 1]
+        # Build coupling list
+        coupling_list.append( (n1, n2, j1, j2, j3) )
+        # Set new value in j_list
+        j_list[min(n1 + n2) - 1] = j3
+
+    if j.is_number and m.is_number:
+        diff_max = [ 2*x for x in jn ]
+        diff = Add(*jn) - m
+
+        n = len(jn)
+        tot = binomial(diff + n - 1, diff)
+
+        result = []
+        for config_num in range(tot):
+            diff_list = _confignum_to_difflist(config_num, diff, n)
+            if any(d > p for d, p in zip(diff_list, diff_max)):
+                continue
+
+            cg_terms = []
+            for coupling in coupling_list:
+                j1_n, j2_n, j1, j2, j3 = coupling
+                m1 = Add( *[ jn[x - 1] - diff_list[x - 1] for x in j1_n ] )
+                m2 = Add( *[ jn[x - 1] - diff_list[x - 1] for x in j2_n ] )
+                m3 = m1 + m2
+                cg_terms.append( (j1, m1, j2, m2, j3, m3) )
+            coeff = Mul( *[ CG(*term).doit() for term in cg_terms ] )
+            state = TensorProduct(
+                *[ evect(j, j - d) for j, d in zip(jn, diff_list) ] )
+            result.append(coeff*state)
+        return Add(*result)
+    else:
+        # Symbolic coupling
+        m_str = "m1:%d" % (len(jn) + 1)
+        mvals = symbols(m_str)
+        cg_terms = [(j1, Add(*[mvals[n - 1] for n in j1_n]),
+                     j2, Add(*[mvals[n - 1] for n in j2_n]),
+                     j3, Add(*[mvals[n - 1] for n in j1_n + j2_n])) for j1_n, j2_n, j1, j2, j3 in coupling_list[:-1] ]
+        cg_terms.append(*[(j1, Add(*[mvals[n - 1] for n in j1_n]),
+                           j2, Add(*[mvals[n - 1] for n in j2_n]),
+                           j, m) for j1_n, j2_n, j1, j2, j3 in [coupling_list[-1]] ])
+        cg_coeff = Mul(*[CG(*cg_term) for cg_term in cg_terms])
+        sum_terms = [ (m, -j, j) for j, m in zip(jn, mvals) ]
+        state = TensorProduct( *[ evect(j, m) for j, m in zip(jn, mvals) ] )
+        return Sum(cg_coeff*state, *sum_terms)
+
+
+def _confignum_to_difflist(config_num, diff, list_len):
+    # Determines configuration of diffs into list_len number of slots
+    diff_list = []
+    for n in range(list_len):
+        prev_diff = diff
+        # Number of spots after current one
+        rem_spots = list_len - n - 1
+        # Number of configurations of distributing diff among the remaining spots
+        rem_configs = binomial(diff + rem_spots - 1, diff)
+        while config_num >= rem_configs:
+            config_num -= rem_configs
+            diff -= 1
+            rem_configs = binomial(diff + rem_spots - 1, diff)
+        diff_list.append(prev_diff - diff)
+    return diff_list
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/state.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/state.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ccd1ce9b9875b59a5d1293ab3026808bdc85b27
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/state.py
@@ -0,0 +1,987 @@
+"""Dirac notation for states."""
+
+from sympy.core.cache import cacheit
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import Function
+from sympy.core.numbers import oo, equal_valued
+from sympy.core.singleton import S
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.integrals.integrals import integrate
+from sympy.printing.pretty.stringpict import stringPict
+from sympy.physics.quantum.qexpr import QExpr, dispatch_method
+from sympy.physics.quantum.kind import KetKind, BraKind
+
+
+__all__ = [
+    'KetBase',
+    'BraBase',
+    'StateBase',
+    'State',
+    'Ket',
+    'Bra',
+    'TimeDepState',
+    'TimeDepBra',
+    'TimeDepKet',
+    'OrthogonalKet',
+    'OrthogonalBra',
+    'OrthogonalState',
+    'Wavefunction'
+]
+
+
+#-----------------------------------------------------------------------------
+# States, bras and kets.
+#-----------------------------------------------------------------------------
+
+# ASCII brackets
+_lbracket = "<"
+_rbracket = ">"
+_straight_bracket = "|"
+
+
+# Unicode brackets
+# MATHEMATICAL ANGLE BRACKETS
+_lbracket_ucode = "\N{MATHEMATICAL LEFT ANGLE BRACKET}"
+_rbracket_ucode = "\N{MATHEMATICAL RIGHT ANGLE BRACKET}"
+# LIGHT VERTICAL BAR
+_straight_bracket_ucode = "\N{LIGHT VERTICAL BAR}"
+
+# Other options for unicode printing of <, > and | for Dirac notation.
+
+# LEFT-POINTING ANGLE BRACKET
+# _lbracket = "\u2329"
+# _rbracket = "\u232A"
+
+# LEFT ANGLE BRACKET
+# _lbracket = "\u3008"
+# _rbracket = "\u3009"
+
+# VERTICAL LINE
+# _straight_bracket = "\u007C"
+
+
+class StateBase(QExpr):
+    """Abstract base class for general abstract states in quantum mechanics.
+
+    All other state classes defined will need to inherit from this class. It
+    carries the basic structure for all other states such as dual, _eval_adjoint
+    and label.
+
+    This is an abstract base class and you should not instantiate it directly,
+    instead use State.
+    """
+
+    @classmethod
+    def _operators_to_state(self, ops, **options):
+        """ Returns the eigenstate instance for the passed operators.
+
+        This method should be overridden in subclasses. It will handle being
+        passed either an Operator instance or set of Operator instances. It
+        should return the corresponding state INSTANCE or simply raise a
+        NotImplementedError. See cartesian.py for an example.
+        """
+
+        raise NotImplementedError("Cannot map operators to states in this class. Method not implemented!")
+
+    def _state_to_operators(self, op_classes, **options):
+        """ Returns the operators which this state instance is an eigenstate
+        of.
+
+        This method should be overridden in subclasses. It will be called on
+        state instances and be passed the operator classes that we wish to make
+        into instances. The state instance will then transform the classes
+        appropriately, or raise a NotImplementedError if it cannot return
+        operator instances. See cartesian.py for examples,
+        """
+
+        raise NotImplementedError(
+            "Cannot map this state to operators. Method not implemented!")
+
+    @property
+    def operators(self):
+        """Return the operator(s) that this state is an eigenstate of"""
+        from .operatorset import state_to_operators  # import internally to avoid circular import errors
+        return state_to_operators(self)
+
+    def _enumerate_state(self, num_states, **options):
+        raise NotImplementedError("Cannot enumerate this state!")
+
+    def _represent_default_basis(self, **options):
+        return self._represent(basis=self.operators)
+
+    def _apply_operator(self, op, **options):
+        return None
+
+    #-------------------------------------------------------------------------
+    # Dagger/dual
+    #-------------------------------------------------------------------------
+
+    @property
+    def dual(self):
+        """Return the dual state of this one."""
+        return self.dual_class()._new_rawargs(self.hilbert_space, *self.args)
+
+    @classmethod
+    def dual_class(self):
+        """Return the class used to construct the dual."""
+        raise NotImplementedError(
+            'dual_class must be implemented in a subclass'
+        )
+
+    def _eval_adjoint(self):
+        """Compute the dagger of this state using the dual."""
+        return self.dual
+
+    #-------------------------------------------------------------------------
+    # Printing
+    #-------------------------------------------------------------------------
+
+    def _pretty_brackets(self, height, use_unicode=True):
+        # Return pretty printed brackets for the state
+        # Ideally, this could be done by pform.parens but it does not support the angled < and >
+
+        # Setup for unicode vs ascii
+        if use_unicode:
+            lbracket, rbracket = getattr(self, 'lbracket_ucode', ""), getattr(self, 'rbracket_ucode', "")
+            slash, bslash, vert = '\N{BOX DRAWINGS LIGHT DIAGONAL UPPER RIGHT TO LOWER LEFT}', \
+                                  '\N{BOX DRAWINGS LIGHT DIAGONAL UPPER LEFT TO LOWER RIGHT}', \
+                                  '\N{BOX DRAWINGS LIGHT VERTICAL}'
+        else:
+            lbracket, rbracket = getattr(self, 'lbracket', ""), getattr(self, 'rbracket', "")
+            slash, bslash, vert = '/', '\\', '|'
+
+        # If height is 1, just return brackets
+        if height == 1:
+            return stringPict(lbracket), stringPict(rbracket)
+        # Make height even
+        height += (height % 2)
+
+        brackets = []
+        for bracket in lbracket, rbracket:
+            # Create left bracket
+            if bracket in {_lbracket, _lbracket_ucode}:
+                bracket_args = [ ' ' * (height//2 - i - 1) +
+                                 slash for i in range(height // 2)]
+                bracket_args.extend(
+                    [' ' * i + bslash for i in range(height // 2)])
+            # Create right bracket
+            elif bracket in {_rbracket, _rbracket_ucode}:
+                bracket_args = [ ' ' * i + bslash for i in range(height // 2)]
+                bracket_args.extend([ ' ' * (
+                    height//2 - i - 1) + slash for i in range(height // 2)])
+            # Create straight bracket
+            elif bracket in {_straight_bracket, _straight_bracket_ucode}:
+                bracket_args = [vert] * height
+            else:
+                raise ValueError(bracket)
+            brackets.append(
+                stringPict('\n'.join(bracket_args), baseline=height//2))
+        return brackets
+
+    def _sympystr(self, printer, *args):
+        contents = self._print_contents(printer, *args)
+        return '%s%s%s' % (getattr(self, 'lbracket', ""), contents, getattr(self, 'rbracket', ""))
+
+    def _pretty(self, printer, *args):
+        from sympy.printing.pretty.stringpict import prettyForm
+        # Get brackets
+        pform = self._print_contents_pretty(printer, *args)
+        lbracket, rbracket = self._pretty_brackets(
+            pform.height(), printer._use_unicode)
+        # Put together state
+        pform = prettyForm(*pform.left(lbracket))
+        pform = prettyForm(*pform.right(rbracket))
+        return pform
+
+    def _latex(self, printer, *args):
+        contents = self._print_contents_latex(printer, *args)
+        # The extra {} brackets are needed to get matplotlib's latex
+        # rendered to render this properly.
+        return '{%s%s%s}' % (getattr(self, 'lbracket_latex', ""), contents, getattr(self, 'rbracket_latex', ""))
+
+
+class KetBase(StateBase):
+    """Base class for Kets.
+
+    This class defines the dual property and the brackets for printing. This is
+    an abstract base class and you should not instantiate it directly, instead
+    use Ket.
+    """
+
+    kind = KetKind
+
+    lbracket = _straight_bracket
+    rbracket = _rbracket
+    lbracket_ucode = _straight_bracket_ucode
+    rbracket_ucode = _rbracket_ucode
+    lbracket_latex = r'\left|'
+    rbracket_latex = r'\right\rangle '
+
+    @classmethod
+    def default_args(self):
+        return ("psi",)
+
+    @classmethod
+    def dual_class(self):
+        return BraBase
+
+    #-------------------------------------------------------------------------
+    # _eval_* methods
+    #-------------------------------------------------------------------------
+
+    def _eval_innerproduct(self, bra, **hints):
+        """Evaluate the inner product between this ket and a bra.
+
+        This is called to compute , where the ket is ``self``.
+
+        This method will dispatch to sub-methods having the format::
+
+            ``def _eval_innerproduct_BraClass(self, **hints):``
+
+        Subclasses should define these methods (one for each BraClass) to
+        teach the ket how to take inner products with bras.
+        """
+        return dispatch_method(self, '_eval_innerproduct', bra, **hints)
+
+    def _apply_from_right_to(self, op, **options):
+        """Apply an Operator to this Ket as Operator*Ket
+
+        This method will dispatch to methods having the format::
+
+            ``def _apply_from_right_to_OperatorName(op, **options):``
+
+        Subclasses should define these methods (one for each OperatorName) to
+        teach the Ket how to implement OperatorName*Ket
+
+        Parameters
+        ==========
+
+        op : Operator
+            The Operator that is acting on the Ket as op*Ket
+        options : dict
+            A dict of key/value pairs that control how the operator is applied
+            to the Ket.
+        """
+        return dispatch_method(self, '_apply_from_right_to', op, **options)
+
+
+class BraBase(StateBase):
+    """Base class for Bras.
+
+    This class defines the dual property and the brackets for printing. This
+    is an abstract base class and you should not instantiate it directly,
+    instead use Bra.
+    """
+
+    kind = BraKind
+
+    lbracket = _lbracket
+    rbracket = _straight_bracket
+    lbracket_ucode = _lbracket_ucode
+    rbracket_ucode = _straight_bracket_ucode
+    lbracket_latex = r'\left\langle '
+    rbracket_latex = r'\right|'
+
+    @classmethod
+    def _operators_to_state(self, ops, **options):
+        state = self.dual_class()._operators_to_state(ops, **options)
+        return state.dual
+
+    def _state_to_operators(self, op_classes, **options):
+        return self.dual._state_to_operators(op_classes, **options)
+
+    def _enumerate_state(self, num_states, **options):
+        dual_states = self.dual._enumerate_state(num_states, **options)
+        return [x.dual for x in dual_states]
+
+    @classmethod
+    def default_args(self):
+        return self.dual_class().default_args()
+
+    @classmethod
+    def dual_class(self):
+        return KetBase
+
+    def _represent(self, **options):
+        """A default represent that uses the Ket's version."""
+        from sympy.physics.quantum.dagger import Dagger
+        return Dagger(self.dual._represent(**options))
+
+
+class State(StateBase):
+    """General abstract quantum state used as a base class for Ket and Bra."""
+    pass
+
+
+class Ket(State, KetBase):
+    """A general time-independent Ket in quantum mechanics.
+
+    Inherits from State and KetBase. This class should be used as the base
+    class for all physical, time-independent Kets in a system. This class
+    and its subclasses will be the main classes that users will use for
+    expressing Kets in Dirac notation [1]_.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        ket. This will usually be its symbol or its quantum numbers. For
+        time-dependent state, this will include the time.
+
+    Examples
+    ========
+
+    Create a simple Ket and looking at its properties::
+
+        >>> from sympy.physics.quantum import Ket
+        >>> from sympy import symbols, I
+        >>> k = Ket('psi')
+        >>> k
+        |psi>
+        >>> k.hilbert_space
+        H
+        >>> k.is_commutative
+        False
+        >>> k.label
+        (psi,)
+
+    Ket's know about their associated bra::
+
+        >>> k.dual
+        >> k.dual_class()
+        
+
+    Take a linear combination of two kets::
+
+        >>> k0 = Ket(0)
+        >>> k1 = Ket(1)
+        >>> 2*I*k0 - 4*k1
+        2*I*|0> - 4*|1>
+
+    Compound labels are passed as tuples::
+
+        >>> n, m = symbols('n,m')
+        >>> k = Ket(n,m)
+        >>> k
+        |nm>
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Bra-ket_notation
+    """
+
+    @classmethod
+    def dual_class(self):
+        return Bra
+
+
+class Bra(State, BraBase):
+    """A general time-independent Bra in quantum mechanics.
+
+    Inherits from State and BraBase. A Bra is the dual of a Ket [1]_. This
+    class and its subclasses will be the main classes that users will use for
+    expressing Bras in Dirac notation.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the
+        ket. This will usually be its symbol or its quantum numbers. For
+        time-dependent state, this will include the time.
+
+    Examples
+    ========
+
+    Create a simple Bra and look at its properties::
+
+        >>> from sympy.physics.quantum import Bra
+        >>> from sympy import symbols, I
+        >>> b = Bra('psi')
+        >>> b
+        >> b.hilbert_space
+        H
+        >>> b.is_commutative
+        False
+
+    Bra's know about their dual Ket's::
+
+        >>> b.dual
+        |psi>
+        >>> b.dual_class()
+        
+
+    Like Kets, Bras can have compound labels and be manipulated in a similar
+    manner::
+
+        >>> n, m = symbols('n,m')
+        >>> b = Bra(n,m) - I*Bra(m,n)
+        >>> b
+        -I*>> b.subs(n,m)
+        >> from sympy.physics.quantum import TimeDepKet
+        >>> k = TimeDepKet('psi', 't')
+        >>> k
+        |psi;t>
+        >>> k.time
+        t
+        >>> k.label
+        (psi,)
+        >>> k.hilbert_space
+        H
+
+    TimeDepKets know about their dual bra::
+
+        >>> k.dual
+        >> k.dual_class()
+        
+    """
+
+    @classmethod
+    def dual_class(self):
+        return TimeDepBra
+
+
+class TimeDepBra(TimeDepState, BraBase):
+    """General time-dependent Bra in quantum mechanics.
+
+    This inherits from TimeDepState and BraBase and is the main class that
+    should be used for Bras that vary with time. Its dual is a TimeDepBra.
+
+    Parameters
+    ==========
+
+    args : tuple
+        The list of numbers or parameters that uniquely specify the ket. This
+        will usually be its symbol or its quantum numbers. For time-dependent
+        state, this will include the time as the final argument.
+
+    Examples
+    ========
+
+        >>> from sympy.physics.quantum import TimeDepBra
+        >>> b = TimeDepBra('psi', 't')
+        >>> b
+        >> b.time
+        t
+        >>> b.label
+        (psi,)
+        >>> b.hilbert_space
+        H
+        >>> b.dual
+        |psi;t>
+    """
+
+    @classmethod
+    def dual_class(self):
+        return TimeDepKet
+
+
+class OrthogonalState(State):
+    """General abstract quantum state used as a base class for Ket and Bra."""
+    pass
+
+class OrthogonalKet(OrthogonalState, KetBase):
+    """Orthogonal Ket in quantum mechanics.
+
+    The inner product of two states with different labels will give zero,
+    states with the same label will give one.
+
+        >>> from sympy.physics.quantum import OrthogonalBra, OrthogonalKet
+        >>> from sympy.abc import m, n
+        >>> (OrthogonalBra(n)*OrthogonalKet(n)).doit()
+        1
+        >>> (OrthogonalBra(n)*OrthogonalKet(n+1)).doit()
+        0
+        >>> (OrthogonalBra(n)*OrthogonalKet(m)).doit()
+        
+    """
+
+    @classmethod
+    def dual_class(self):
+        return OrthogonalBra
+
+    def _eval_innerproduct(self, bra, **hints):
+
+        if len(self.args) != len(bra.args):
+            raise ValueError('Cannot multiply a ket that has a different number of labels.')
+
+        for arg, bra_arg in zip(self.args, bra.args):
+            diff = arg - bra_arg
+            diff = diff.expand()
+
+            is_zero = diff.is_zero
+
+            if is_zero is False:
+                return S.Zero # i.e. Integer(0)
+
+            if is_zero is None:
+                return None
+
+        return S.One # i.e. Integer(1)
+
+
+class OrthogonalBra(OrthogonalState, BraBase):
+    """Orthogonal Bra in quantum mechanics.
+    """
+
+    @classmethod
+    def dual_class(self):
+        return OrthogonalKet
+
+
+class Wavefunction(Function):
+    """Class for representations in continuous bases
+
+    This class takes an expression and coordinates in its constructor. It can
+    be used to easily calculate normalizations and probabilities.
+
+    Parameters
+    ==========
+
+    expr : Expr
+           The expression representing the functional form of the w.f.
+
+    coords : Symbol or tuple
+           The coordinates to be integrated over, and their bounds
+
+    Examples
+    ========
+
+    Particle in a box, specifying bounds in the more primitive way of using
+    Piecewise:
+
+        >>> from sympy import Symbol, Piecewise, pi, N
+        >>> from sympy.functions import sqrt, sin
+        >>> from sympy.physics.quantum.state import Wavefunction
+        >>> x = Symbol('x', real=True)
+        >>> n = 1
+        >>> L = 1
+        >>> g = Piecewise((0, x < 0), (0, x > L), (sqrt(2//L)*sin(n*pi*x/L), True))
+        >>> f = Wavefunction(g, x)
+        >>> f.norm
+        1
+        >>> f.is_normalized
+        True
+        >>> p = f.prob()
+        >>> p(0)
+        0
+        >>> p(L)
+        0
+        >>> p(0.5)
+        2
+        >>> p(0.85*L)
+        2*sin(0.85*pi)**2
+        >>> N(p(0.85*L))
+        0.412214747707527
+
+    Additionally, you can specify the bounds of the function and the indices in
+    a more compact way:
+
+        >>> from sympy import symbols, pi, diff
+        >>> from sympy.functions import sqrt, sin
+        >>> from sympy.physics.quantum.state import Wavefunction
+        >>> x, L = symbols('x,L', positive=True)
+        >>> n = symbols('n', integer=True, positive=True)
+        >>> g = sqrt(2/L)*sin(n*pi*x/L)
+        >>> f = Wavefunction(g, (x, 0, L))
+        >>> f.norm
+        1
+        >>> f(L+1)
+        0
+        >>> f(L-1)
+        sqrt(2)*sin(pi*n*(L - 1)/L)/sqrt(L)
+        >>> f(-1)
+        0
+        >>> f(0.85)
+        sqrt(2)*sin(0.85*pi*n/L)/sqrt(L)
+        >>> f(0.85, n=1, L=1)
+        sqrt(2)*sin(0.85*pi)
+        >>> f.is_commutative
+        False
+
+    All arguments are automatically sympified, so you can define the variables
+    as strings rather than symbols:
+
+        >>> expr = x**2
+        >>> f = Wavefunction(expr, 'x')
+        >>> type(f.variables[0])
+        
+
+    Derivatives of Wavefunctions will return Wavefunctions:
+
+        >>> diff(f, x)
+        Wavefunction(2*x, x)
+
+    """
+
+    #Any passed tuples for coordinates and their bounds need to be
+    #converted to Tuples before Function's constructor is called, to
+    #avoid errors from calling is_Float in the constructor
+    def __new__(cls, *args, **options):
+        new_args = [None for i in args]
+        ct = 0
+        for arg in args:
+            if isinstance(arg, tuple):
+                new_args[ct] = Tuple(*arg)
+            else:
+                new_args[ct] = arg
+            ct += 1
+
+        return super().__new__(cls, *new_args, **options)
+
+    def __call__(self, *args, **options):
+        var = self.variables
+
+        if len(args) != len(var):
+            raise NotImplementedError(
+                "Incorrect number of arguments to function!")
+
+        ct = 0
+        #If the passed value is outside the specified bounds, return 0
+        for v in var:
+            lower, upper = self.limits[v]
+
+            #Do the comparison to limits only if the passed symbol is actually
+            #a symbol present in the limits;
+            #Had problems with a comparison of x > L
+            if isinstance(args[ct], Expr) and \
+                not (lower in args[ct].free_symbols
+                     or upper in args[ct].free_symbols):
+                continue
+
+            if (args[ct] < lower) == True or (args[ct] > upper) == True:
+                return S.Zero
+
+            ct += 1
+
+        expr = self.expr
+
+        #Allows user to make a call like f(2, 4, m=1, n=1)
+        for symbol in list(expr.free_symbols):
+            if str(symbol) in options.keys():
+                val = options[str(symbol)]
+                expr = expr.subs(symbol, val)
+
+        return expr.subs(zip(var, args))
+
+    def _eval_derivative(self, symbol):
+        expr = self.expr
+        deriv = expr._eval_derivative(symbol)
+
+        return Wavefunction(deriv, *self.args[1:])
+
+    def _eval_conjugate(self):
+        return Wavefunction(conjugate(self.expr), *self.args[1:])
+
+    def _eval_transpose(self):
+        return self
+
+    @property
+    def is_commutative(self):
+        """
+        Override Function's is_commutative so that order is preserved in
+        represented expressions
+        """
+        return False
+
+    @classmethod
+    def eval(self, *args):
+        return None
+
+    @property
+    def variables(self):
+        """
+        Return the coordinates which the wavefunction depends on
+
+        Examples
+        ========
+
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> from sympy import symbols
+            >>> x,y = symbols('x,y')
+            >>> f = Wavefunction(x*y, x, y)
+            >>> f.variables
+            (x, y)
+            >>> g = Wavefunction(x*y, x)
+            >>> g.variables
+            (x,)
+
+        """
+        var = [g[0] if isinstance(g, Tuple) else g for g in self._args[1:]]
+        return tuple(var)
+
+    @property
+    def limits(self):
+        """
+        Return the limits of the coordinates which the w.f. depends on If no
+        limits are specified, defaults to ``(-oo, oo)``.
+
+        Examples
+        ========
+
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> from sympy import symbols
+            >>> x, y = symbols('x, y')
+            >>> f = Wavefunction(x**2, (x, 0, 1))
+            >>> f.limits
+            {x: (0, 1)}
+            >>> f = Wavefunction(x**2, x)
+            >>> f.limits
+            {x: (-oo, oo)}
+            >>> f = Wavefunction(x**2 + y**2, x, (y, -1, 2))
+            >>> f.limits
+            {x: (-oo, oo), y: (-1, 2)}
+
+        """
+        limits = [(g[1], g[2]) if isinstance(g, Tuple) else (-oo, oo)
+                  for g in self._args[1:]]
+        return dict(zip(self.variables, tuple(limits)))
+
+    @property
+    def expr(self):
+        """
+        Return the expression which is the functional form of the Wavefunction
+
+        Examples
+        ========
+
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> from sympy import symbols
+            >>> x, y = symbols('x, y')
+            >>> f = Wavefunction(x**2, x)
+            >>> f.expr
+            x**2
+
+        """
+        return self._args[0]
+
+    @property
+    def is_normalized(self):
+        """
+        Returns true if the Wavefunction is properly normalized
+
+        Examples
+        ========
+
+            >>> from sympy import symbols, pi
+            >>> from sympy.functions import sqrt, sin
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> x, L = symbols('x,L', positive=True)
+            >>> n = symbols('n', integer=True, positive=True)
+            >>> g = sqrt(2/L)*sin(n*pi*x/L)
+            >>> f = Wavefunction(g, (x, 0, L))
+            >>> f.is_normalized
+            True
+
+        """
+
+        return equal_valued(self.norm, 1)
+
+    @property  # type: ignore
+    @cacheit
+    def norm(self):
+        """
+        Return the normalization of the specified functional form.
+
+        This function integrates over the coordinates of the Wavefunction, with
+        the bounds specified.
+
+        Examples
+        ========
+
+            >>> from sympy import symbols, pi
+            >>> from sympy.functions import sqrt, sin
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> x, L = symbols('x,L', positive=True)
+            >>> n = symbols('n', integer=True, positive=True)
+            >>> g = sqrt(2/L)*sin(n*pi*x/L)
+            >>> f = Wavefunction(g, (x, 0, L))
+            >>> f.norm
+            1
+            >>> g = sin(n*pi*x/L)
+            >>> f = Wavefunction(g, (x, 0, L))
+            >>> f.norm
+            sqrt(2)*sqrt(L)/2
+
+        """
+
+        exp = self.expr*conjugate(self.expr)
+        var = self.variables
+        limits = self.limits
+
+        for v in var:
+            curr_limits = limits[v]
+            exp = integrate(exp, (v, curr_limits[0], curr_limits[1]))
+
+        return sqrt(exp)
+
+    def normalize(self):
+        """
+        Return a normalized version of the Wavefunction
+
+        Examples
+        ========
+
+            >>> from sympy import symbols, pi
+            >>> from sympy.functions import sin
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> x = symbols('x', real=True)
+            >>> L = symbols('L', positive=True)
+            >>> n = symbols('n', integer=True, positive=True)
+            >>> g = sin(n*pi*x/L)
+            >>> f = Wavefunction(g, (x, 0, L))
+            >>> f.normalize()
+            Wavefunction(sqrt(2)*sin(pi*n*x/L)/sqrt(L), (x, 0, L))
+
+        """
+        const = self.norm
+
+        if const is oo:
+            raise NotImplementedError("The function is not normalizable!")
+        else:
+            return Wavefunction((const)**(-1)*self.expr, *self.args[1:])
+
+    def prob(self):
+        r"""
+        Return the absolute magnitude of the w.f., `|\psi(x)|^2`
+
+        Examples
+        ========
+
+            >>> from sympy import symbols, pi
+            >>> from sympy.functions import sin
+            >>> from sympy.physics.quantum.state import Wavefunction
+            >>> x, L = symbols('x,L', real=True)
+            >>> n = symbols('n', integer=True)
+            >>> g = sin(n*pi*x/L)
+            >>> f = Wavefunction(g, (x, 0, L))
+            >>> f.prob()
+            Wavefunction(sin(pi*n*x/L)**2, x)
+
+        """
+
+        return Wavefunction(self.expr*conjugate(self.expr), *self.variables)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tensorproduct.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tensorproduct.py
new file mode 100644
index 0000000000000000000000000000000000000000..058b3459227e5a020e2d0397fc66f56a2f917293
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tensorproduct.py
@@ -0,0 +1,363 @@
+"""Abstract tensor product."""
+
+from sympy.core.add import Add
+from sympy.core.expr import Expr
+from sympy.core.kind import KindDispatcher
+from sympy.core.mul import Mul
+from sympy.core.power import Pow
+from sympy.core.sympify import sympify
+from sympy.matrices.dense import DenseMatrix as Matrix
+from sympy.matrices.immutable import ImmutableDenseMatrix as ImmutableMatrix
+from sympy.printing.pretty.stringpict import prettyForm
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.kind import (
+    KetKind, _KetKind,
+    BraKind, _BraKind,
+    OperatorKind, _OperatorKind
+)
+from sympy.physics.quantum.matrixutils import (
+    numpy_ndarray,
+    scipy_sparse_matrix,
+    matrix_tensor_product
+)
+from sympy.physics.quantum.state import Ket, Bra
+from sympy.physics.quantum.trace import Tr
+
+
+__all__ = [
+    'TensorProduct',
+    'tensor_product_simp'
+]
+
+#-----------------------------------------------------------------------------
+# Tensor product
+#-----------------------------------------------------------------------------
+
+_combined_printing = False
+
+
+def combined_tensor_printing(combined):
+    """Set flag controlling whether tensor products of states should be
+    printed as a combined bra/ket or as an explicit tensor product of different
+    bra/kets. This is a global setting for all TensorProduct class instances.
+
+    Parameters
+    ----------
+    combine : bool
+        When true, tensor product states are combined into one ket/bra, and
+        when false explicit tensor product notation is used between each
+        ket/bra.
+    """
+    global _combined_printing
+    _combined_printing = combined
+
+
+class TensorProduct(Expr):
+    """The tensor product of two or more arguments.
+
+    For matrices, this uses ``matrix_tensor_product`` to compute the Kronecker
+    or tensor product matrix. For other objects a symbolic ``TensorProduct``
+    instance is returned. The tensor product is a non-commutative
+    multiplication that is used primarily with operators and states in quantum
+    mechanics.
+
+    Currently, the tensor product distinguishes between commutative and
+    non-commutative arguments.  Commutative arguments are assumed to be scalars
+    and are pulled out in front of the ``TensorProduct``. Non-commutative
+    arguments remain in the resulting ``TensorProduct``.
+
+    Parameters
+    ==========
+
+    args : tuple
+        A sequence of the objects to take the tensor product of.
+
+    Examples
+    ========
+
+    Start with a simple tensor product of SymPy matrices::
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.quantum import TensorProduct
+
+        >>> m1 = Matrix([[1,2],[3,4]])
+        >>> m2 = Matrix([[1,0],[0,1]])
+        >>> TensorProduct(m1, m2)
+        Matrix([
+        [1, 0, 2, 0],
+        [0, 1, 0, 2],
+        [3, 0, 4, 0],
+        [0, 3, 0, 4]])
+        >>> TensorProduct(m2, m1)
+        Matrix([
+        [1, 2, 0, 0],
+        [3, 4, 0, 0],
+        [0, 0, 1, 2],
+        [0, 0, 3, 4]])
+
+    We can also construct tensor products of non-commutative symbols:
+
+        >>> from sympy import Symbol
+        >>> A = Symbol('A',commutative=False)
+        >>> B = Symbol('B',commutative=False)
+        >>> tp = TensorProduct(A, B)
+        >>> tp
+        AxB
+
+    We can take the dagger of a tensor product (note the order does NOT reverse
+    like the dagger of a normal product):
+
+        >>> from sympy.physics.quantum import Dagger
+        >>> Dagger(tp)
+        Dagger(A)xDagger(B)
+
+    Expand can be used to distribute a tensor product across addition:
+
+        >>> C = Symbol('C',commutative=False)
+        >>> tp = TensorProduct(A+B,C)
+        >>> tp
+        (A + B)xC
+        >>> tp.expand(tensorproduct=True)
+        AxC + BxC
+    """
+    is_commutative = False
+
+    _kind_dispatcher = KindDispatcher("TensorProduct_kind_dispatcher", commutative=True)
+
+    @property
+    def kind(self):
+        """Calculate the kind of a tensor product by looking at its children."""
+        arg_kinds = (a.kind for a in self.args)
+        return self._kind_dispatcher(*arg_kinds)
+
+    def __new__(cls, *args):
+        if isinstance(args[0], (Matrix, ImmutableMatrix, numpy_ndarray,
+                                                    scipy_sparse_matrix)):
+            return matrix_tensor_product(*args)
+        c_part, new_args = cls.flatten(sympify(args))
+        c_part = Mul(*c_part)
+        if len(new_args) == 0:
+            return c_part
+        elif len(new_args) == 1:
+            return c_part * new_args[0]
+        else:
+            tp = Expr.__new__(cls, *new_args)
+            return c_part * tp
+
+    @classmethod
+    def flatten(cls, args):
+        # TODO: disallow nested TensorProducts.
+        c_part = []
+        nc_parts = []
+        for arg in args:
+            cp, ncp = arg.args_cnc()
+            c_part.extend(list(cp))
+            nc_parts.append(Mul._from_args(ncp))
+        return c_part, nc_parts
+
+    def _eval_adjoint(self):
+        return TensorProduct(*[Dagger(i) for i in self.args])
+
+    def _eval_rewrite(self, rule, args, **hints):
+        return TensorProduct(*args).expand(tensorproduct=True)
+
+    def _sympystr(self, printer, *args):
+        length = len(self.args)
+        s = ''
+        for i in range(length):
+            if isinstance(self.args[i], (Add, Pow, Mul)):
+                s = s + '('
+            s = s + printer._print(self.args[i])
+            if isinstance(self.args[i], (Add, Pow, Mul)):
+                s = s + ')'
+            if i != length - 1:
+                s = s + 'x'
+        return s
+
+    def _pretty(self, printer, *args):
+
+        if (_combined_printing and
+                (all(isinstance(arg, Ket) for arg in self.args) or
+                 all(isinstance(arg, Bra) for arg in self.args))):
+
+            length = len(self.args)
+            pform = printer._print('', *args)
+            for i in range(length):
+                next_pform = printer._print('', *args)
+                length_i = len(self.args[i].args)
+                for j in range(length_i):
+                    part_pform = printer._print(self.args[i].args[j], *args)
+                    next_pform = prettyForm(*next_pform.right(part_pform))
+                    if j != length_i - 1:
+                        next_pform = prettyForm(*next_pform.right(', '))
+
+                if len(self.args[i].args) > 1:
+                    next_pform = prettyForm(
+                        *next_pform.parens(left='{', right='}'))
+                pform = prettyForm(*pform.right(next_pform))
+                if i != length - 1:
+                    pform = prettyForm(*pform.right(',' + ' '))
+
+            pform = prettyForm(*pform.left(self.args[0].lbracket))
+            pform = prettyForm(*pform.right(self.args[0].rbracket))
+            return pform
+
+        length = len(self.args)
+        pform = printer._print('', *args)
+        for i in range(length):
+            next_pform = printer._print(self.args[i], *args)
+            if isinstance(self.args[i], (Add, Mul)):
+                next_pform = prettyForm(
+                    *next_pform.parens(left='(', right=')')
+                )
+            pform = prettyForm(*pform.right(next_pform))
+            if i != length - 1:
+                if printer._use_unicode:
+                    pform = prettyForm(*pform.right('\N{N-ARY CIRCLED TIMES OPERATOR}' + ' '))
+                else:
+                    pform = prettyForm(*pform.right('x' + ' '))
+        return pform
+
+    def _latex(self, printer, *args):
+
+        if (_combined_printing and
+                (all(isinstance(arg, Ket) for arg in self.args) or
+                 all(isinstance(arg, Bra) for arg in self.args))):
+
+            def _label_wrap(label, nlabels):
+                return label if nlabels == 1 else r"\left\{%s\right\}" % label
+
+            s = r", ".join([_label_wrap(arg._print_label_latex(printer, *args),
+                                        len(arg.args)) for arg in self.args])
+
+            return r"{%s%s%s}" % (self.args[0].lbracket_latex, s,
+                                  self.args[0].rbracket_latex)
+
+        length = len(self.args)
+        s = ''
+        for i in range(length):
+            if isinstance(self.args[i], (Add, Mul)):
+                s = s + '\\left('
+            # The extra {} brackets are needed to get matplotlib's latex
+            # rendered to render this properly.
+            s = s + '{' + printer._print(self.args[i], *args) + '}'
+            if isinstance(self.args[i], (Add, Mul)):
+                s = s + '\\right)'
+            if i != length - 1:
+                s = s + '\\otimes '
+        return s
+
+    def doit(self, **hints):
+        return TensorProduct(*[item.doit(**hints) for item in self.args])
+
+    def _eval_expand_tensorproduct(self, **hints):
+        """Distribute TensorProducts across addition."""
+        args = self.args
+        add_args = []
+        for i in range(len(args)):
+            if isinstance(args[i], Add):
+                for aa in args[i].args:
+                    tp = TensorProduct(*args[:i] + (aa,) + args[i + 1:])
+                    c_part, nc_part = tp.args_cnc()
+                    # Check for TensorProduct object: is the one object in nc_part, if any:
+                    # (Note: any other object type to be expanded must be added here)
+                    if len(nc_part) == 1 and isinstance(nc_part[0], TensorProduct):
+                        nc_part = (nc_part[0]._eval_expand_tensorproduct(), )
+                    add_args.append(Mul(*c_part)*Mul(*nc_part))
+                break
+
+        if add_args:
+            return Add(*add_args)
+        else:
+            return self
+
+    def _eval_trace(self, **kwargs):
+        indices = kwargs.get('indices', None)
+        exp = self
+
+        if indices is None or len(indices) == 0:
+            return Mul(*[Tr(arg).doit() for arg in exp.args])
+        else:
+            return Mul(*[Tr(value).doit() if idx in indices else value
+                         for idx, value in enumerate(exp.args)])
+
+
+def tensor_product_simp_Mul(e):
+    """Simplify a Mul with tensor products.
+
+    .. deprecated:: 1.14.
+        The transformations applied by this function are not done automatically
+        when tensor products are combined.
+
+    Originally, the main use of this function is to simplify a ``Mul`` of
+    ``TensorProduct``s to a ``TensorProduct`` of ``Muls``.
+    """
+    sympy_deprecation_warning(
+        """
+        tensor_product_simp_Mul has been deprecated. The transformations
+        performed by this function are now done automatically when
+        tensor products are multiplied.
+        """,
+        deprecated_since_version="1.14",
+        active_deprecations_target='deprecated-tensorproduct-simp'
+    )
+    return e
+
+def tensor_product_simp_Pow(e):
+    """Evaluates ``Pow`` expressions whose base is ``TensorProduct``
+
+    .. deprecated:: 1.14.
+        The transformations applied by this function are not done automatically
+        when tensor products are combined.
+    """
+    sympy_deprecation_warning(
+        """
+        tensor_product_simp_Pow has been deprecated. The transformations
+        performed by this function are now done automatically when
+        tensor products are exponentiated.
+        """,
+        deprecated_since_version="1.14",
+        active_deprecations_target='deprecated-tensorproduct-simp'
+    )
+    return e
+
+
+def tensor_product_simp(e, **hints):
+    """Try to simplify and combine tensor products.
+
+    .. deprecated:: 1.14.
+        The transformations applied by this function are not done automatically
+        when tensor products are combined.
+
+    Originally, this function tried to pull expressions inside of ``TensorProducts``.
+    It only worked for relatively simple cases where the products have
+    only scalars, raw ``TensorProducts``, not ``Add``, ``Pow``, ``Commutators``
+    of ``TensorProducts``.
+    """
+    sympy_deprecation_warning(
+        """
+        tensor_product_simp has been deprecated. The transformations
+        performed by this function are now done automatically when
+        tensor products are combined.
+        """,
+        deprecated_since_version="1.14",
+        active_deprecations_target='deprecated-tensorproduct-simp'
+    )
+    return e
+
+
+@TensorProduct._kind_dispatcher.register(_OperatorKind, _OperatorKind)
+def find_op_kind(e1, e2):
+    return OperatorKind
+
+
+@TensorProduct._kind_dispatcher.register(_KetKind, _KetKind)
+def find_ket_kind(e1, e2):
+    return KetKind
+
+
+@TensorProduct._kind_dispatcher.register(_BraKind, _BraKind)
+def find_bra_kind(e1, e2):
+    return BraKind
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/__init__.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_anticommutator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_anticommutator.py
new file mode 100644
index 0000000000000000000000000000000000000000..0e6b6cbc50651742fcbbbe6adce3f20dfadc2ec5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_anticommutator.py
@@ -0,0 +1,56 @@
+from sympy.core.numbers import Integer
+from sympy.core.symbol import symbols
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.anticommutator import AntiCommutator as AComm
+from sympy.physics.quantum.operator import Operator
+
+
+a, b, c = symbols('a,b,c')
+A, B, C, D = symbols('A,B,C,D', commutative=False)
+
+
+def test_anticommutator():
+    ac = AComm(A, B)
+    assert isinstance(ac, AComm)
+    assert ac.is_commutative is False
+    assert ac.subs(A, C) == AComm(C, B)
+
+
+def test_commutator_identities():
+    assert AComm(a*A, b*B) == a*b*AComm(A, B)
+    assert AComm(A, A) == 2*A**2
+    assert AComm(A, B) == AComm(B, A)
+    assert AComm(a, b) == 2*a*b
+    assert AComm(A, B).doit() == A*B + B*A
+
+
+def test_anticommutator_dagger():
+    assert Dagger(AComm(A, B)) == AComm(Dagger(A), Dagger(B))
+
+
+class Foo(Operator):
+
+    def _eval_anticommutator_Bar(self, bar):
+        return Integer(0)
+
+
+class Bar(Operator):
+    pass
+
+
+class Tam(Operator):
+
+    def _eval_anticommutator_Foo(self, foo):
+        return Integer(1)
+
+
+def test_eval_commutator():
+    F = Foo('F')
+    B = Bar('B')
+    T = Tam('T')
+    assert AComm(F, B).doit() == 0
+    assert AComm(B, F).doit() == 0
+    assert AComm(F, T).doit() == 1
+    assert AComm(T, F).doit() == 1
+    assert AComm(B, T).doit() == B*T + T*B
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_boson.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_boson.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd8dab745bede8b1c70303917dae81146fc03395
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_boson.py
@@ -0,0 +1,50 @@
+from math import prod
+
+from sympy.core.numbers import Rational
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum import Dagger, Commutator, qapply
+from sympy.physics.quantum.boson import BosonOp
+from sympy.physics.quantum.boson import (
+    BosonFockKet, BosonFockBra, BosonCoherentKet, BosonCoherentBra)
+
+
+def test_bosonoperator():
+    a = BosonOp('a')
+    b = BosonOp('b')
+
+    assert isinstance(a, BosonOp)
+    assert isinstance(Dagger(a), BosonOp)
+
+    assert a.is_annihilation
+    assert not Dagger(a).is_annihilation
+
+    assert BosonOp("a") == BosonOp("a", True)
+    assert BosonOp("a") != BosonOp("c")
+    assert BosonOp("a", True) != BosonOp("a", False)
+
+    assert Commutator(a, Dagger(a)).doit() == 1
+
+    assert Commutator(a, Dagger(b)).doit() == a * Dagger(b) - Dagger(b) * a
+
+    assert Dagger(exp(a)) == exp(Dagger(a))
+
+
+def test_boson_states():
+    a = BosonOp("a")
+
+    # Fock states
+    n = 3
+    assert (BosonFockBra(0) * BosonFockKet(1)).doit() == 0
+    assert (BosonFockBra(1) * BosonFockKet(1)).doit() == 1
+    assert qapply(BosonFockBra(n) * Dagger(a)**n * BosonFockKet(0)) \
+        == sqrt(prod(range(1, n+1)))
+
+    # Coherent states
+    alpha1, alpha2 = 1.2, 4.3
+    assert (BosonCoherentBra(alpha1) * BosonCoherentKet(alpha1)).doit() == 1
+    assert (BosonCoherentBra(alpha2) * BosonCoherentKet(alpha2)).doit() == 1
+    assert abs((BosonCoherentBra(alpha1) * BosonCoherentKet(alpha2)).doit() -
+               exp((alpha1 - alpha2) ** 2 * Rational(-1, 2))) < 1e-12
+    assert qapply(a * BosonCoherentKet(alpha1)) == \
+        alpha1 * BosonCoherentKet(alpha1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_cartesian.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_cartesian.py
new file mode 100644
index 0000000000000000000000000000000000000000..f1dd435fab68c9c71ac3602bc4c53847cbe39d57
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_cartesian.py
@@ -0,0 +1,113 @@
+"""Tests for cartesian.py"""
+
+from sympy.core.numbers import (I, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.delta_functions import DiracDelta
+from sympy.sets.sets import Interval
+from sympy.testing.pytest import XFAIL
+
+from sympy.physics.quantum import qapply, represent, L2, Dagger
+from sympy.physics.quantum import Commutator, hbar
+from sympy.physics.quantum.cartesian import (
+    XOp, YOp, ZOp, PxOp, X, Y, Z, Px, XKet, XBra, PxKet, PxBra,
+    PositionKet3D, PositionBra3D
+)
+from sympy.physics.quantum.operator import DifferentialOperator
+
+x, y, z, x_1, x_2, x_3, y_1, z_1 = symbols('x,y,z,x_1,x_2,x_3,y_1,z_1')
+px, py, px_1, px_2 = symbols('px py px_1 px_2')
+
+
+def test_x():
+    assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert Commutator(X, Px).doit() == I*hbar
+    assert qapply(X*XKet(x)) == x*XKet(x)
+    assert XKet(x).dual_class() == XBra
+    assert XBra(x).dual_class() == XKet
+    assert (Dagger(XKet(y))*XKet(x)).doit() == DiracDelta(x - y)
+    assert (PxBra(px)*XKet(x)).doit() == \
+        exp(-I*x*px/hbar)/sqrt(2*pi*hbar)
+    assert represent(XKet(x)) == DiracDelta(x - x_1)
+    assert represent(XBra(x)) == DiracDelta(-x + x_1)
+    assert XBra(x).position == x
+    assert represent(XOp()*XKet()) == x*DiracDelta(x - x_2)
+    assert represent(XBra("y")*XKet()) == DiracDelta(x - y)
+    assert represent(
+        XKet()*XBra()) == DiracDelta(x - x_2) * DiracDelta(x_1 - x)
+
+    rep_p = represent(XOp(), basis=PxOp)
+    assert rep_p == hbar*I*DiracDelta(px_1 - px_2)*DifferentialOperator(px_1)
+    assert rep_p == represent(XOp(), basis=PxOp())
+    assert rep_p == represent(XOp(), basis=PxKet)
+    assert rep_p == represent(XOp(), basis=PxKet())
+
+    assert represent(XOp()*PxKet(), basis=PxKet) == \
+        hbar*I*DiracDelta(px - px_2)*DifferentialOperator(px)
+
+
+@XFAIL
+def _text_x_broken():
+    # represent has some broken logic that is relying in particular
+    # forms of input, rather than a full and proper handling of
+    # all valid quantum expressions. Marking this test as XFAIL until
+    # we can refactor represent.
+    assert represent(XOp()*XKet()*XBra('y')) == \
+        x*DiracDelta(x - x_3)*DiracDelta(x_1 - y)
+
+
+def test_p():
+    assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert qapply(Px*PxKet(px)) == px*PxKet(px)
+    assert PxKet(px).dual_class() == PxBra
+    assert PxBra(x).dual_class() == PxKet
+    assert (Dagger(PxKet(py))*PxKet(px)).doit() == DiracDelta(px - py)
+    assert (XBra(x)*PxKet(px)).doit() == \
+        exp(I*x*px/hbar)/sqrt(2*pi*hbar)
+    assert represent(PxKet(px)) == DiracDelta(px - px_1)
+
+    rep_x = represent(PxOp(), basis=XOp)
+    assert rep_x == -hbar*I*DiracDelta(x_1 - x_2)*DifferentialOperator(x_1)
+    assert rep_x == represent(PxOp(), basis=XOp())
+    assert rep_x == represent(PxOp(), basis=XKet)
+    assert rep_x == represent(PxOp(), basis=XKet())
+
+    assert represent(PxOp()*XKet(), basis=XKet) == \
+        -hbar*I*DiracDelta(x - x_2)*DifferentialOperator(x)
+    assert represent(XBra("y")*PxOp()*XKet(), basis=XKet) == \
+        -hbar*I*DiracDelta(x - y)*DifferentialOperator(x)
+
+
+def test_3dpos():
+    assert Y.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+    assert Z.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
+
+    test_ket = PositionKet3D(x, y, z)
+    assert qapply(X*test_ket) == x*test_ket
+    assert qapply(Y*test_ket) == y*test_ket
+    assert qapply(Z*test_ket) == z*test_ket
+    assert qapply(X*Y*test_ket) == x*y*test_ket
+    assert qapply(X*Y*Z*test_ket) == x*y*z*test_ket
+    assert qapply(Y*Z*test_ket) == y*z*test_ket
+
+    assert PositionKet3D() == test_ket
+    assert YOp() == Y
+    assert ZOp() == Z
+
+    assert PositionKet3D.dual_class() == PositionBra3D
+    assert PositionBra3D.dual_class() == PositionKet3D
+
+    other_ket = PositionKet3D(x_1, y_1, z_1)
+    assert (Dagger(other_ket)*test_ket).doit() == \
+        DiracDelta(x - x_1)*DiracDelta(y - y_1)*DiracDelta(z - z_1)
+
+    assert test_ket.position_x == x
+    assert test_ket.position_y == y
+    assert test_ket.position_z == z
+    assert other_ket.position_x == x_1
+    assert other_ket.position_y == y_1
+    assert other_ket.position_z == z_1
+
+    # TODO: Add tests for representations
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_cg.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_cg.py
new file mode 100644
index 0000000000000000000000000000000000000000..384512aaac7a8d984ff2a733e6349161dc9414a0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_cg.py
@@ -0,0 +1,183 @@
+from sympy.concrete.summations import Sum
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum.cg import Wigner3j, Wigner6j, Wigner9j, CG, cg_simp
+from sympy.functions.special.tensor_functions import KroneckerDelta
+
+
+def test_cg_simp_add():
+    j, m1, m1p, m2, m2p = symbols('j m1 m1p m2 m2p')
+    # Test Varshalovich 8.7.1 Eq 1
+    a = CG(S.Half, S.Half, 0, 0, S.Half, S.Half)
+    b = CG(S.Half, Rational(-1, 2), 0, 0, S.Half, Rational(-1, 2))
+    c = CG(1, 1, 0, 0, 1, 1)
+    d = CG(1, 0, 0, 0, 1, 0)
+    e = CG(1, -1, 0, 0, 1, -1)
+    assert cg_simp(a + b) == 2
+    assert cg_simp(c + d + e) == 3
+    assert cg_simp(a + b + c + d + e) == 5
+    assert cg_simp(a + b + c) == 2 + c
+    assert cg_simp(2*a + b) == 2 + a
+    assert cg_simp(2*c + d + e) == 3 + c
+    assert cg_simp(5*a + 5*b) == 10
+    assert cg_simp(5*c + 5*d + 5*e) == 15
+    assert cg_simp(-a - b) == -2
+    assert cg_simp(-c - d - e) == -3
+    assert cg_simp(-6*a - 6*b) == -12
+    assert cg_simp(-4*c - 4*d - 4*e) == -12
+    a = CG(S.Half, S.Half, j, 0, S.Half, S.Half)
+    b = CG(S.Half, Rational(-1, 2), j, 0, S.Half, Rational(-1, 2))
+    c = CG(1, 1, j, 0, 1, 1)
+    d = CG(1, 0, j, 0, 1, 0)
+    e = CG(1, -1, j, 0, 1, -1)
+    assert cg_simp(a + b) == 2*KroneckerDelta(j, 0)
+    assert cg_simp(c + d + e) == 3*KroneckerDelta(j, 0)
+    assert cg_simp(a + b + c + d + e) == 5*KroneckerDelta(j, 0)
+    assert cg_simp(a + b + c) == 2*KroneckerDelta(j, 0) + c
+    assert cg_simp(2*a + b) == 2*KroneckerDelta(j, 0) + a
+    assert cg_simp(2*c + d + e) == 3*KroneckerDelta(j, 0) + c
+    assert cg_simp(5*a + 5*b) == 10*KroneckerDelta(j, 0)
+    assert cg_simp(5*c + 5*d + 5*e) == 15*KroneckerDelta(j, 0)
+    assert cg_simp(-a - b) == -2*KroneckerDelta(j, 0)
+    assert cg_simp(-c - d - e) == -3*KroneckerDelta(j, 0)
+    assert cg_simp(-6*a - 6*b) == -12*KroneckerDelta(j, 0)
+    assert cg_simp(-4*c - 4*d - 4*e) == -12*KroneckerDelta(j, 0)
+    # Test Varshalovich 8.7.1 Eq 2
+    a = CG(S.Half, S.Half, S.Half, Rational(-1, 2), 0, 0)
+    b = CG(S.Half, Rational(-1, 2), S.Half, S.Half, 0, 0)
+    c = CG(1, 1, 1, -1, 0, 0)
+    d = CG(1, 0, 1, 0, 0, 0)
+    e = CG(1, -1, 1, 1, 0, 0)
+    assert cg_simp(a - b) == sqrt(2)
+    assert cg_simp(c - d + e) == sqrt(3)
+    assert cg_simp(a - b + c - d + e) == sqrt(2) + sqrt(3)
+    assert cg_simp(a - b + c) == sqrt(2) + c
+    assert cg_simp(2*a - b) == sqrt(2) + a
+    assert cg_simp(2*c - d + e) == sqrt(3) + c
+    assert cg_simp(5*a - 5*b) == 5*sqrt(2)
+    assert cg_simp(5*c - 5*d + 5*e) == 5*sqrt(3)
+    assert cg_simp(-a + b) == -sqrt(2)
+    assert cg_simp(-c + d - e) == -sqrt(3)
+    assert cg_simp(-6*a + 6*b) == -6*sqrt(2)
+    assert cg_simp(-4*c + 4*d - 4*e) == -4*sqrt(3)
+    a = CG(S.Half, S.Half, S.Half, Rational(-1, 2), j, 0)
+    b = CG(S.Half, Rational(-1, 2), S.Half, S.Half, j, 0)
+    c = CG(1, 1, 1, -1, j, 0)
+    d = CG(1, 0, 1, 0, j, 0)
+    e = CG(1, -1, 1, 1, j, 0)
+    assert cg_simp(a - b) == sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(c - d + e) == sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(a - b + c - d + e) == sqrt(
+        2)*KroneckerDelta(j, 0) + sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(a - b + c) == sqrt(2)*KroneckerDelta(j, 0) + c
+    assert cg_simp(2*a - b) == sqrt(2)*KroneckerDelta(j, 0) + a
+    assert cg_simp(2*c - d + e) == sqrt(3)*KroneckerDelta(j, 0) + c
+    assert cg_simp(5*a - 5*b) == 5*sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(5*c - 5*d + 5*e) == 5*sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(-a + b) == -sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(-c + d - e) == -sqrt(3)*KroneckerDelta(j, 0)
+    assert cg_simp(-6*a + 6*b) == -6*sqrt(2)*KroneckerDelta(j, 0)
+    assert cg_simp(-4*c + 4*d - 4*e) == -4*sqrt(3)*KroneckerDelta(j, 0)
+    # Test Varshalovich 8.7.2 Eq 9
+    # alpha=alphap,beta=betap case
+    # numerical
+    a = CG(S.Half, S.Half, S.Half, Rational(-1, 2), 1, 0)**2
+    b = CG(S.Half, S.Half, S.Half, Rational(-1, 2), 0, 0)**2
+    c = CG(1, 0, 1, 1, 1, 1)**2
+    d = CG(1, 0, 1, 1, 2, 1)**2
+    assert cg_simp(a + b) == 1
+    assert cg_simp(c + d) == 1
+    assert cg_simp(a + b + c + d) == 2
+    assert cg_simp(4*a + 4*b) == 4
+    assert cg_simp(4*c + 4*d) == 4
+    assert cg_simp(5*a + 3*b) == 3 + 2*a
+    assert cg_simp(5*c + 3*d) == 3 + 2*c
+    assert cg_simp(-a - b) == -1
+    assert cg_simp(-c - d) == -1
+    # symbolic
+    a = CG(S.Half, m1, S.Half, m2, 1, 1)**2
+    b = CG(S.Half, m1, S.Half, m2, 1, 0)**2
+    c = CG(S.Half, m1, S.Half, m2, 1, -1)**2
+    d = CG(S.Half, m1, S.Half, m2, 0, 0)**2
+    assert cg_simp(a + b + c + d) == 1
+    assert cg_simp(4*a + 4*b + 4*c + 4*d) == 4
+    assert cg_simp(3*a + 5*b + 3*c + 4*d) == 3 + 2*b + d
+    assert cg_simp(-a - b - c - d) == -1
+    a = CG(1, m1, 1, m2, 2, 2)**2
+    b = CG(1, m1, 1, m2, 2, 1)**2
+    c = CG(1, m1, 1, m2, 2, 0)**2
+    d = CG(1, m1, 1, m2, 2, -1)**2
+    e = CG(1, m1, 1, m2, 2, -2)**2
+    f = CG(1, m1, 1, m2, 1, 1)**2
+    g = CG(1, m1, 1, m2, 1, 0)**2
+    h = CG(1, m1, 1, m2, 1, -1)**2
+    i = CG(1, m1, 1, m2, 0, 0)**2
+    assert cg_simp(a + b + c + d + e + f + g + h + i) == 1
+    assert cg_simp(4*(a + b + c + d + e + f + g + h + i)) == 4
+    assert cg_simp(a + b + 2*c + d + 4*e + f + g + h + i) == 1 + c + 3*e
+    assert cg_simp(-a - b - c - d - e - f - g - h - i) == -1
+    # alpha!=alphap or beta!=betap case
+    # numerical
+    a = CG(S.Half, S(
+        1)/2, S.Half, Rational(-1, 2), 1, 0)*CG(S.Half, Rational(-1, 2), S.Half, S.Half, 1, 0)
+    b = CG(S.Half, S(
+        1)/2, S.Half, Rational(-1, 2), 0, 0)*CG(S.Half, Rational(-1, 2), S.Half, S.Half, 0, 0)
+    c = CG(1, 1, 1, 0, 2, 1)*CG(1, 0, 1, 1, 2, 1)
+    d = CG(1, 1, 1, 0, 1, 1)*CG(1, 0, 1, 1, 1, 1)
+    assert cg_simp(a + b) == 0
+    assert cg_simp(c + d) == 0
+    # symbolic
+    a = CG(S.Half, m1, S.Half, m2, 1, 1)*CG(S.Half, m1p, S.Half, m2p, 1, 1)
+    b = CG(S.Half, m1, S.Half, m2, 1, 0)*CG(S.Half, m1p, S.Half, m2p, 1, 0)
+    c = CG(S.Half, m1, S.Half, m2, 1, -1)*CG(S.Half, m1p, S.Half, m2p, 1, -1)
+    d = CG(S.Half, m1, S.Half, m2, 0, 0)*CG(S.Half, m1p, S.Half, m2p, 0, 0)
+    assert cg_simp(a + b + c + d) == KroneckerDelta(m1, m1p)*KroneckerDelta(m2, m2p)
+    a = CG(1, m1, 1, m2, 2, 2)*CG(1, m1p, 1, m2p, 2, 2)
+    b = CG(1, m1, 1, m2, 2, 1)*CG(1, m1p, 1, m2p, 2, 1)
+    c = CG(1, m1, 1, m2, 2, 0)*CG(1, m1p, 1, m2p, 2, 0)
+    d = CG(1, m1, 1, m2, 2, -1)*CG(1, m1p, 1, m2p, 2, -1)
+    e = CG(1, m1, 1, m2, 2, -2)*CG(1, m1p, 1, m2p, 2, -2)
+    f = CG(1, m1, 1, m2, 1, 1)*CG(1, m1p, 1, m2p, 1, 1)
+    g = CG(1, m1, 1, m2, 1, 0)*CG(1, m1p, 1, m2p, 1, 0)
+    h = CG(1, m1, 1, m2, 1, -1)*CG(1, m1p, 1, m2p, 1, -1)
+    i = CG(1, m1, 1, m2, 0, 0)*CG(1, m1p, 1, m2p, 0, 0)
+    assert cg_simp(
+        a + b + c + d + e + f + g + h + i) == KroneckerDelta(m1, m1p)*KroneckerDelta(m2, m2p)
+
+
+def test_cg_simp_sum():
+    x, a, b, c, cp, alpha, beta, gamma, gammap = symbols(
+        'x a b c cp alpha beta gamma gammap')
+    # Varshalovich 8.7.1 Eq 1
+    assert cg_simp(x * Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)
+                   )) == x*(2*a + 1)*KroneckerDelta(b, 0)
+    assert cg_simp(x * Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)) + CG(1, 0, 1, 0, 1, 0)) == x*(2*a + 1)*KroneckerDelta(b, 0) + CG(1, 0, 1, 0, 1, 0)
+    assert cg_simp(2 * Sum(CG(1, alpha, 0, 0, 1, alpha), (alpha, -1, 1))) == 6
+    # Varshalovich 8.7.1 Eq 2
+    assert cg_simp(x*Sum((-1)**(a - alpha) * CG(a, alpha, a, -alpha, c,
+                   0), (alpha, -a, a))) == x*sqrt(2*a + 1)*KroneckerDelta(c, 0)
+    assert cg_simp(3*Sum((-1)**(2 - alpha) * CG(
+        2, alpha, 2, -alpha, 0, 0), (alpha, -2, 2))) == 3*sqrt(5)
+    # Varshalovich 8.7.2 Eq 4
+    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, cp, gammap), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(c, cp)*KroneckerDelta(gamma, gammap)
+    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, c, gammap), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(gamma, gammap)
+    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, cp, gamma), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(c, cp)
+    assert cg_simp(Sum(CG(
+        a, alpha, b, beta, c, gamma)**2, (alpha, -a, a), (beta, -b, b))) == 1
+    assert cg_simp(Sum(CG(2, alpha, 1, beta, 2, gamma)*CG(2, alpha, 1, beta, 2, gammap), (alpha, -2, 2), (beta, -1, 1))) == KroneckerDelta(gamma, gammap)
+
+
+def test_doit():
+    assert Wigner3j(S.Half, Rational(-1, 2), S.Half, S.Half, 0, 0).doit() == -sqrt(2)/2
+    assert Wigner3j(1/2,1/2,1/2,1/2,1/2,1/2).doit() == 0
+    assert Wigner3j(9/2,9/2,9/2,9/2,9/2,9/2).doit() ==  0
+    assert Wigner6j(1, 2, 3, 2, 1, 2).doit() == sqrt(21)/105
+    assert Wigner6j(3, 1, 2, 2, 2, 1).doit() == sqrt(21) / 105
+    assert Wigner9j(
+        2, 1, 1, Rational(3, 2), S.Half, 1, S.Half, S.Half, 0).doit() == sqrt(2)/12
+    assert CG(S.Half, S.Half, S.Half, Rational(-1, 2), 1, 0).doit() == sqrt(2)/2
+    # J minus M is not integer
+    assert Wigner3j(1, -1, S.Half, S.Half, 1, S.Half).doit() == 0
+    assert CG(4, -1, S.Half, S.Half, 4, Rational(-1, 2)).doit() == 0
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_circuitplot.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_circuitplot.py
new file mode 100644
index 0000000000000000000000000000000000000000..fcc89f77047450ad3f8663f371f483654dc70ea9
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_circuitplot.py
@@ -0,0 +1,69 @@
+from sympy.physics.quantum.circuitplot import labeller, render_label, Mz, CreateOneQubitGate,\
+     CreateCGate
+from sympy.physics.quantum.gate import CNOT, H, SWAP, CGate, S, T
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+
+mpl = import_module('matplotlib')
+
+def test_render_label():
+    assert render_label('q0') == r'$\left|q0\right\rangle$'
+    assert render_label('q0', {'q0': '0'}) == r'$\left|q0\right\rangle=\left|0\right\rangle$'
+
+def test_Mz():
+    assert str(Mz(0)) == 'Mz(0)'
+
+def test_create1():
+    Qgate = CreateOneQubitGate('Q')
+    assert str(Qgate(0)) == 'Q(0)'
+
+def test_createc():
+    Qgate = CreateCGate('Q')
+    assert str(Qgate([1],0)) == 'C((1),Q(0))'
+
+def test_labeller():
+    """Test the labeller utility"""
+    assert labeller(2) == ['q_1', 'q_0']
+    assert labeller(3,'j') == ['j_2', 'j_1', 'j_0']
+
+def test_cnot():
+    """Test a simple cnot circuit. Right now this only makes sure the code doesn't
+    raise an exception, and some simple properties
+    """
+    if not mpl:
+        skip("matplotlib not installed")
+    else:
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+
+    c = CircuitPlot(CNOT(1,0),2,labels=labeller(2))
+    assert c.ngates == 2
+    assert c.nqubits == 2
+    assert c.labels == ['q_1', 'q_0']
+
+    c = CircuitPlot(CNOT(1,0),2)
+    assert c.ngates == 2
+    assert c.nqubits == 2
+    assert c.labels == []
+
+def test_ex1():
+    if not mpl:
+        skip("matplotlib not installed")
+    else:
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+
+    c = CircuitPlot(CNOT(1,0)*H(1),2,labels=labeller(2))
+    assert c.ngates == 2
+    assert c.nqubits == 2
+    assert c.labels == ['q_1', 'q_0']
+
+def test_ex4():
+    if not mpl:
+        skip("matplotlib not installed")
+    else:
+        from sympy.physics.quantum.circuitplot import CircuitPlot
+
+    c = CircuitPlot(SWAP(0,2)*H(0)* CGate((0,),S(1)) *H(1)*CGate((0,),T(2))\
+                    *CGate((1,),S(2))*H(2),3,labels=labeller(3,'j'))
+    assert c.ngates == 7
+    assert c.nqubits == 3
+    assert c.labels == ['j_2', 'j_1', 'j_0']
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_circuitutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_circuitutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..8ea7232320417db8bf745871cff0e77aaf1901e7
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_circuitutils.py
@@ -0,0 +1,402 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.core.symbol import Symbol
+from sympy.utilities import numbered_symbols
+from sympy.physics.quantum.gate import X, Y, Z, H, CNOT, CGate
+from sympy.physics.quantum.identitysearch import bfs_identity_search
+from sympy.physics.quantum.circuitutils import (kmp_table, find_subcircuit,
+        replace_subcircuit, convert_to_symbolic_indices,
+        convert_to_real_indices, random_reduce, random_insert,
+        flatten_ids)
+from sympy.testing.pytest import slow
+
+
+def create_gate_sequence(qubit=0):
+    gates = (X(qubit), Y(qubit), Z(qubit), H(qubit))
+    return gates
+
+
+def test_kmp_table():
+    word = ('a', 'b', 'c', 'd', 'a', 'b', 'd')
+    expected_table = [-1, 0, 0, 0, 0, 1, 2]
+    assert expected_table == kmp_table(word)
+
+    word = ('P', 'A', 'R', 'T', 'I', 'C', 'I', 'P', 'A', 'T', 'E', ' ',
+            'I', 'N', ' ', 'P', 'A', 'R', 'A', 'C', 'H', 'U', 'T', 'E')
+    expected_table = [-1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0,
+                      0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0]
+    assert expected_table == kmp_table(word)
+
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    word = (x, y, y, x, z)
+    expected_table = [-1, 0, 0, 0, 1]
+    assert expected_table == kmp_table(word)
+
+    word = (x, x, y, h, z)
+    expected_table = [-1, 0, 1, 0, 0]
+    assert expected_table == kmp_table(word)
+
+
+def test_find_subcircuit():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    x1 = X(1)
+    y1 = Y(1)
+
+    i0 = Symbol('i0')
+    x_i0 = X(i0)
+    y_i0 = Y(i0)
+    z_i0 = Z(i0)
+    h_i0 = H(i0)
+
+    circuit = (x, y, z)
+
+    assert find_subcircuit(circuit, (x,)) == 0
+    assert find_subcircuit(circuit, (x1,)) == -1
+    assert find_subcircuit(circuit, (y,)) == 1
+    assert find_subcircuit(circuit, (h,)) == -1
+    assert find_subcircuit(circuit, Mul(x, h)) == -1
+    assert find_subcircuit(circuit, Mul(x, y, z)) == 0
+    assert find_subcircuit(circuit, Mul(y, z)) == 1
+    assert find_subcircuit(Mul(*circuit), (x, y, z, h)) == -1
+    assert find_subcircuit(Mul(*circuit), (z, y, x)) == -1
+    assert find_subcircuit(circuit, (x,), start=2, end=1) == -1
+
+    circuit = (x, y, x, y, z)
+    assert find_subcircuit(Mul(*circuit), Mul(x, y, z)) == 2
+    assert find_subcircuit(circuit, (x,), start=1) == 2
+    assert find_subcircuit(circuit, (x, y), start=1, end=2) == -1
+    assert find_subcircuit(Mul(*circuit), (x, y), start=1, end=3) == -1
+    assert find_subcircuit(circuit, (x, y), start=1, end=4) == 2
+    assert find_subcircuit(circuit, (x, y), start=2, end=4) == 2
+
+    circuit = (x, y, z, x1, x, y, z, h, x, y, x1,
+               x, y, z, h, y1, h)
+    assert find_subcircuit(circuit, (x, y, z, h, y1)) == 11
+
+    circuit = (x, y, x_i0, y_i0, z_i0, z)
+    assert find_subcircuit(circuit, (x_i0, y_i0, z_i0)) == 2
+
+    circuit = (x_i0, y_i0, z_i0, x_i0, y_i0, h_i0)
+    subcircuit = (x_i0, y_i0, z_i0)
+    result = find_subcircuit(circuit, subcircuit)
+    assert result == 0
+
+
+def test_replace_subcircuit():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+
+    # Standard cases
+    circuit = (z, y, x, x)
+    remove = (z, y, x)
+    assert replace_subcircuit(circuit, Mul(*remove)) == (x,)
+    assert replace_subcircuit(circuit, remove + (x,)) == ()
+    assert replace_subcircuit(circuit, remove, pos=1) == circuit
+    assert replace_subcircuit(circuit, remove, pos=0) == (x,)
+    assert replace_subcircuit(circuit, (x, x), pos=2) == (z, y)
+    assert replace_subcircuit(circuit, (h,)) == circuit
+
+    circuit = (x, y, x, y, z)
+    remove = (x, y, z)
+    assert replace_subcircuit(Mul(*circuit), Mul(*remove)) == (x, y)
+    remove = (x, y, x, y)
+    assert replace_subcircuit(circuit, remove) == (z,)
+
+    circuit = (x, h, cgate_z, h, cnot)
+    remove = (x, h, cgate_z)
+    assert replace_subcircuit(circuit, Mul(*remove), pos=-1) == (h, cnot)
+    assert replace_subcircuit(circuit, remove, pos=1) == circuit
+    remove = (h, h)
+    assert replace_subcircuit(circuit, remove) == circuit
+    remove = (h, cgate_z, h, cnot)
+    assert replace_subcircuit(circuit, remove) == (x,)
+
+    replace = (h, x)
+    actual = replace_subcircuit(circuit, remove,
+                     replace=replace)
+    assert actual == (x, h, x)
+
+    circuit = (x, y, h, x, y, z)
+    remove = (x, y)
+    replace = (cnot, cgate_z)
+    actual = replace_subcircuit(circuit, remove,
+                     replace=Mul(*replace))
+    assert actual == (cnot, cgate_z, h, x, y, z)
+
+    actual = replace_subcircuit(circuit, remove,
+                     replace=replace, pos=1)
+    assert actual == (x, y, h, cnot, cgate_z, z)
+
+
+def test_convert_to_symbolic_indices():
+    (x, y, z, h) = create_gate_sequence()
+
+    i0 = Symbol('i0')
+    exp_map = {i0: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x,))
+    assert actual == (X(i0),)
+    assert act_map == exp_map
+
+    expected = (X(i0), Y(i0), Z(i0), H(i0))
+    exp_map = {i0: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x, y, z, h))
+    assert actual == expected
+    assert exp_map == act_map
+
+    (x1, y1, z1, h1) = create_gate_sequence(1)
+    i1 = Symbol('i1')
+
+    expected = (X(i0), Y(i0), Z(i0), H(i0))
+    exp_map = {i0: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x1, y1, z1, h1))
+    assert actual == expected
+    assert act_map == exp_map
+
+    expected = (X(i0), Y(i0), Z(i0), H(i0), X(i1), Y(i1), Z(i1), H(i1))
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x, y, z, h,
+                                         x1, y1, z1, h1))
+    assert actual == expected
+    assert act_map == exp_map
+
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(Mul(x1, y1,
+                                         z1, h1, x, y, z, h))
+    assert actual == expected
+    assert act_map == exp_map
+
+    expected = (X(i0), X(i1), Y(i0), Y(i1), Z(i0), Z(i1), H(i0), H(i1))
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(Mul(x, x1,
+                                         y, y1, z, z1, h, h1))
+    assert actual == expected
+    assert act_map == exp_map
+
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices((x1, x, y1, y,
+                                         z1, z, h1, h))
+    assert actual == expected
+    assert act_map == exp_map
+
+    cnot_10 = CNOT(1, 0)
+    cnot_01 = CNOT(0, 1)
+    cgate_z_10 = CGate(1, Z(0))
+    cgate_z_01 = CGate(0, Z(1))
+
+    expected = (X(i0), X(i1), Y(i0), Y(i1), Z(i0), Z(i1),
+                H(i0), H(i1), CNOT(i1, i0), CNOT(i0, i1),
+                CGate(i1, Z(i0)), CGate(i0, Z(i1)))
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    args = (x, x1, y, y1, z, z1, h, h1, cnot_10, cnot_01,
+            cgate_z_10, cgate_z_01)
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (x1, x, y1, y, z1, z, h1, h, cnot_10, cnot_01,
+            cgate_z_10, cgate_z_01)
+    expected = (X(i0), X(i1), Y(i0), Y(i1), Z(i0), Z(i1),
+                H(i0), H(i1), CNOT(i0, i1), CNOT(i1, i0),
+                CGate(i0, Z(i1)), CGate(i1, Z(i0)))
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (cnot_10, h, cgate_z_01, h)
+    expected = (CNOT(i0, i1), H(i1), CGate(i1, Z(i0)), H(i1))
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (cnot_01, h1, cgate_z_10, h1)
+    exp_map = {i0: Integer(0), i1: Integer(1)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    args = (cnot_10, h1, cgate_z_01, h1)
+    expected = (CNOT(i0, i1), H(i0), CGate(i1, Z(i0)), H(i0))
+    exp_map = {i0: Integer(1), i1: Integer(0)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    i2 = Symbol('i2')
+    ccgate_z = CGate(0, CGate(1, Z(2)))
+    ccgate_x = CGate(1, CGate(2, X(0)))
+    args = (ccgate_z, ccgate_x)
+
+    expected = (CGate(i0, CGate(i1, Z(i2))), CGate(i1, CGate(i2, X(i0))))
+    exp_map = {i0: Integer(0), i1: Integer(1), i2: Integer(2)}
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+    ndx_map = {i0: Integer(0)}
+    index_gen = numbered_symbols(prefix='i', start=1)
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args,
+                                         qubit_map=ndx_map,
+                                         start=i0,
+                                         gen=index_gen)
+    assert actual == expected
+    assert act_map == exp_map
+
+    i3 = Symbol('i3')
+    cgate_x0_c321 = CGate((3, 2, 1), X(0))
+    exp_map = {i0: Integer(3), i1: Integer(2),
+               i2: Integer(1), i3: Integer(0)}
+    expected = (CGate((i0, i1, i2), X(i3)),)
+    args = (cgate_x0_c321,)
+    actual, act_map, sndx, gen = convert_to_symbolic_indices(args)
+    assert actual == expected
+    assert act_map == exp_map
+
+
+def test_convert_to_real_indices():
+    i0 = Symbol('i0')
+    i1 = Symbol('i1')
+
+    (x, y, z, h) = create_gate_sequence()
+
+    x_i0 = X(i0)
+    y_i0 = Y(i0)
+    z_i0 = Z(i0)
+
+    qubit_map = {i0: 0}
+    args = (z_i0, y_i0, x_i0)
+    expected = (z, y, x)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    cnot_10 = CNOT(1, 0)
+    cnot_01 = CNOT(0, 1)
+    cgate_z_10 = CGate(1, Z(0))
+    cgate_z_01 = CGate(0, Z(1))
+
+    cnot_i1_i0 = CNOT(i1, i0)
+    cnot_i0_i1 = CNOT(i0, i1)
+    cgate_z_i1_i0 = CGate(i1, Z(i0))
+
+    qubit_map = {i0: 0, i1: 1}
+    args = (cnot_i1_i0,)
+    expected = (cnot_10,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    args = (cgate_z_i1_i0,)
+    expected = (cgate_z_10,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    args = (cnot_i0_i1,)
+    expected = (cnot_01,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    qubit_map = {i0: 1, i1: 0}
+    args = (cgate_z_i1_i0,)
+    expected = (cgate_z_01,)
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+    i2 = Symbol('i2')
+    ccgate_z = CGate(i0, CGate(i1, Z(i2)))
+    ccgate_x = CGate(i1, CGate(i2, X(i0)))
+
+    qubit_map = {i0: 0, i1: 1, i2: 2}
+    args = (ccgate_z, ccgate_x)
+    expected = (CGate(0, CGate(1, Z(2))), CGate(1, CGate(2, X(0))))
+    actual = convert_to_real_indices(Mul(*args), qubit_map)
+    assert actual == expected
+
+    qubit_map = {i0: 1, i2: 0, i1: 2}
+    args = (ccgate_x, ccgate_z)
+    expected = (CGate(2, CGate(0, X(1))), CGate(1, CGate(2, Z(0))))
+    actual = convert_to_real_indices(args, qubit_map)
+    assert actual == expected
+
+
+@slow
+def test_random_reduce():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+
+    gate_list = [x, y, z]
+    ids = list(bfs_identity_search(gate_list, 1, max_depth=4))
+
+    circuit = (x, y, h, z, cnot)
+    assert random_reduce(circuit, []) == circuit
+    assert random_reduce(circuit, ids) == circuit
+
+    seq = [2, 11, 9, 3, 5]
+    circuit = (x, y, z, x, y, h)
+    assert random_reduce(circuit, ids, seed=seq) == (x, y, h)
+
+    circuit = (x, x, y, y, z, z)
+    assert random_reduce(circuit, ids, seed=seq) == (x, x, y, y)
+
+    seq = [14, 13, 0]
+    assert random_reduce(circuit, ids, seed=seq) == (y, y, z, z)
+
+    gate_list = [x, y, z, h, cnot, cgate_z]
+    ids = list(bfs_identity_search(gate_list, 2, max_depth=4))
+
+    seq = [25]
+    circuit = (x, y, z, y, h, y, h, cgate_z, h, cnot)
+    expected = (x, y, z, cgate_z, h, cnot)
+    assert random_reduce(circuit, ids, seed=seq) == expected
+    circuit = Mul(*circuit)
+    assert random_reduce(circuit, ids, seed=seq) == expected
+
+
+@slow
+def test_random_insert():
+    x = X(0)
+    y = Y(0)
+    z = Z(0)
+    h = H(0)
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+
+    choices = [(x, x)]
+    circuit = (y, y)
+    loc, choice = 0, 0
+    actual = random_insert(circuit, choices, seed=[loc, choice])
+    assert actual == (x, x, y, y)
+
+    circuit = (x, y, z, h)
+    choices = [(h, h), (x, y, z)]
+    expected = (x, x, y, z, y, z, h)
+    loc, choice = 1, 1
+    actual = random_insert(circuit, choices, seed=[loc, choice])
+    assert actual == expected
+
+    gate_list = [x, y, z, h, cnot, cgate_z]
+    ids = list(bfs_identity_search(gate_list, 2, max_depth=4))
+
+    eq_ids = flatten_ids(ids)
+
+    circuit = (x, y, h, cnot, cgate_z)
+    expected = (x, z, x, z, x, y, h, cnot, cgate_z)
+    loc, choice = 1, 30
+    actual = random_insert(circuit, eq_ids, seed=[loc, choice])
+    assert actual == expected
+    circuit = Mul(*circuit)
+    actual = random_insert(circuit, eq_ids, seed=[loc, choice])
+    assert actual == expected
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_commutator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_commutator.py
new file mode 100644
index 0000000000000000000000000000000000000000..04f45feddaca63d7306363a9235c63f534d11430
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_commutator.py
@@ -0,0 +1,81 @@
+from sympy.core.numbers import Integer
+from sympy.core.symbol import symbols
+
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.commutator import Commutator as Comm
+from sympy.physics.quantum.operator import Operator
+
+
+a, b, c = symbols('a,b,c')
+n = symbols('n', integer=True)
+A, B, C, D = symbols('A,B,C,D', commutative=False)
+
+
+def test_commutator():
+    c = Comm(A, B)
+    assert c.is_commutative is False
+    assert isinstance(c, Comm)
+    assert c.subs(A, C) == Comm(C, B)
+
+
+def test_commutator_identities():
+    assert Comm(a*A, b*B) == a*b*Comm(A, B)
+    assert Comm(A, A) == 0
+    assert Comm(a, b) == 0
+    assert Comm(A, B) == -Comm(B, A)
+    assert Comm(A, B).doit() == A*B - B*A
+    assert Comm(A, B*C).expand(commutator=True) == Comm(A, B)*C + B*Comm(A, C)
+    assert Comm(A*B, C*D).expand(commutator=True) == \
+        A*C*Comm(B, D) + A*Comm(B, C)*D + C*Comm(A, D)*B + Comm(A, C)*D*B
+    assert Comm(A, B**2).expand(commutator=True) == Comm(A, B)*B + B*Comm(A, B)
+    assert Comm(A**2, C**2).expand(commutator=True) == \
+        Comm(A*B, C*D).expand(commutator=True).replace(B, A).replace(D, C) == \
+        A*C*Comm(A, C) + A*Comm(A, C)*C + C*Comm(A, C)*A + Comm(A, C)*C*A
+    assert Comm(A, C**-2).expand(commutator=True) == \
+        Comm(A, (1/C)*(1/D)).expand(commutator=True).replace(D, C)
+    assert Comm(A + B, C + D).expand(commutator=True) == \
+        Comm(A, C) + Comm(A, D) + Comm(B, C) + Comm(B, D)
+    assert Comm(A, B + C).expand(commutator=True) == Comm(A, B) + Comm(A, C)
+    assert Comm(A**n, B).expand(commutator=True) == Comm(A**n, B)
+
+    e = Comm(A, Comm(B, C)) + Comm(B, Comm(C, A)) + Comm(C, Comm(A, B))
+    assert e.doit().expand() == 0
+
+
+def test_commutator_dagger():
+    comm = Comm(A*B, C)
+    assert Dagger(comm).expand(commutator=True) == \
+        - Comm(Dagger(B), Dagger(C))*Dagger(A) - \
+        Dagger(B)*Comm(Dagger(A), Dagger(C))
+
+
+class Foo(Operator):
+
+    def _eval_commutator_Bar(self, bar):
+        return Integer(0)
+
+
+class Bar(Operator):
+    pass
+
+
+class Tam(Operator):
+
+    def _eval_commutator_Foo(self, foo):
+        return Integer(1)
+
+
+def test_eval_commutator():
+    F = Foo('F')
+    B = Bar('B')
+    T = Tam('T')
+    assert Comm(F, B).doit() == 0
+    assert Comm(B, F).doit() == 0
+    assert Comm(F, T).doit() == -1
+    assert Comm(T, F).doit() == 1
+    assert Comm(B, T).doit() == B*T - T*B
+    assert Comm(F**2, B).expand(commutator=True).doit() == 0
+    assert Comm(F**2, T).expand(commutator=True).doit() == -2*F
+    assert Comm(F, T**2).expand(commutator=True).doit() == -2*T
+    assert Comm(T**2, F).expand(commutator=True).doit() == 2*T
+    assert Comm(T**2, F**3).expand(commutator=True).doit() == 2*F*T*F + 2*F**2*T + 2*T*F**2
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_constants.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_constants.py
new file mode 100644
index 0000000000000000000000000000000000000000..48a773ea6b5afbaf956143b50b16b3b18aaf5beb
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_constants.py
@@ -0,0 +1,13 @@
+from sympy.core.numbers import Float
+
+from sympy.physics.quantum.constants import hbar
+
+
+def test_hbar():
+    assert hbar.is_commutative is True
+    assert hbar.is_real is True
+    assert hbar.is_positive is True
+    assert hbar.is_negative is False
+    assert hbar.is_irrational is True
+
+    assert hbar.evalf() == Float(1.05457162e-34)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_dagger.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_dagger.py
new file mode 100644
index 0000000000000000000000000000000000000000..1357c9320a20afa2ba905a117d90ed1ac2e9642c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_dagger.py
@@ -0,0 +1,103 @@
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer)
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.complexes import conjugate
+from sympy.matrices.dense import Matrix
+
+from sympy.physics.quantum.dagger import adjoint, Dagger
+from sympy.external import import_module
+from sympy.testing.pytest import skip, warns_deprecated_sympy
+from sympy.physics.quantum.operator import Operator, IdentityOperator
+
+
+def test_scalars():
+    x = symbols('x', complex=True)
+    assert Dagger(x) == conjugate(x)
+    assert Dagger(I*x) == -I*conjugate(x)
+
+    i = symbols('i', real=True)
+    assert Dagger(i) == i
+
+    p = symbols('p')
+    assert isinstance(Dagger(p), conjugate)
+
+    i = Integer(3)
+    assert Dagger(i) == i
+
+    A = symbols('A', commutative=False)
+    assert Dagger(A).is_commutative is False
+
+
+def test_matrix():
+    x = symbols('x')
+    m = Matrix([[I, x*I], [2, 4]])
+    assert Dagger(m) == m.H
+
+
+def test_dagger_mul():
+    O = Operator('O')
+    assert Dagger(O)*O == Dagger(O)*O
+    with warns_deprecated_sympy():
+        I = IdentityOperator()
+        assert Dagger(O)*O*I == Mul(Dagger(O), O)*I
+    assert Dagger(O)*Dagger(O) == Dagger(O)**2
+    assert Dagger(O)*Dagger(I) == Dagger(O)
+
+
+class Foo(Expr):
+
+    def _eval_adjoint(self):
+        return I
+
+
+def test_eval_adjoint():
+    f = Foo()
+    d = Dagger(f)
+    assert d == I
+
+np = import_module('numpy')
+
+
+def test_numpy_dagger():
+    if not np:
+        skip("numpy not installed.")
+
+    a = np.array([[1.0, 2.0j], [-1.0j, 2.0]])
+    adag = a.copy().transpose().conjugate()
+    assert (Dagger(a) == adag).all()
+
+
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+
+def test_scipy_sparse_dagger():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+    else:
+        sparse = scipy.sparse
+
+    a = sparse.csr_matrix([[1.0 + 0.0j, 2.0j], [-1.0j, 2.0 + 0.0j]])
+    adag = a.copy().transpose().conjugate()
+    assert np.linalg.norm((Dagger(a) - adag).todense()) == 0.0
+
+
+def test_unknown():
+    """Check treatment of unknown objects.
+    Objects without adjoint or conjugate/transpose methods
+    are sympified and wrapped in dagger.
+    """
+    x = symbols("x", commutative=False)
+    result = Dagger(x)
+    assert result.args == (x,) and isinstance(result, adjoint)
+
+
+def test_unevaluated():
+    """Check that evaluate=False returns unevaluated Dagger.
+    """
+    x = symbols("x", real=True)
+    assert Dagger(x) == x
+    result = Dagger(x, evaluate=False)
+    assert result.args == (x,) and isinstance(result, adjoint)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_density.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_density.py
new file mode 100644
index 0000000000000000000000000000000000000000..399acce6e201b39f65ea674048198fd2f087b4d0
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_density.py
@@ -0,0 +1,289 @@
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import log
+from sympy.external import import_module
+from sympy.physics.quantum.density import Density, entropy, fidelity
+from sympy.physics.quantum.state import Ket, TimeDepKet
+from sympy.physics.quantum.qubit import Qubit
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.cartesian import XKet, PxKet, PxOp, XOp
+from sympy.physics.quantum.spin import JzKet
+from sympy.physics.quantum.operator import OuterProduct
+from sympy.physics.quantum.trace import Tr
+from sympy.functions import sqrt
+from sympy.testing.pytest import raises
+from sympy.physics.quantum.matrixutils import scipy_sparse_matrix
+from sympy.physics.quantum.tensorproduct import TensorProduct
+
+
+def test_eval_args():
+    # check instance created
+    assert isinstance(Density([Ket(0), 0.5], [Ket(1), 0.5]), Density)
+    assert isinstance(Density([Qubit('00'), 1/sqrt(2)],
+                              [Qubit('11'), 1/sqrt(2)]), Density)
+
+    #test if Qubit object type preserved
+    d = Density([Qubit('00'), 1/sqrt(2)], [Qubit('11'), 1/sqrt(2)])
+    for (state, prob) in d.args:
+        assert isinstance(state, Qubit)
+
+    # check for value error, when prob is not provided
+    raises(ValueError, lambda: Density([Ket(0)], [Ket(1)]))
+
+
+def test_doit():
+
+    x, y = symbols('x y')
+    A, B, C, D, E, F = symbols('A B C D E F', commutative=False)
+    d = Density([XKet(), 0.5], [PxKet(), 0.5])
+    assert (0.5*(PxKet()*Dagger(PxKet())) +
+            0.5*(XKet()*Dagger(XKet()))) == d.doit()
+
+    # check for kets with expr in them
+    d_with_sym = Density([XKet(x*y), 0.5], [PxKet(x*y), 0.5])
+    assert (0.5*(PxKet(x*y)*Dagger(PxKet(x*y))) +
+            0.5*(XKet(x*y)*Dagger(XKet(x*y)))) == d_with_sym.doit()
+
+    d = Density([(A + B)*C, 1.0])
+    assert d.doit() == (1.0*A*C*Dagger(C)*Dagger(A) +
+                        1.0*A*C*Dagger(C)*Dagger(B) +
+                        1.0*B*C*Dagger(C)*Dagger(A) +
+                        1.0*B*C*Dagger(C)*Dagger(B))
+
+    #  With TensorProducts as args
+    # Density with simple tensor products as args
+    t = TensorProduct(A, B, C)
+    d = Density([t, 1.0])
+    assert d.doit() == \
+        1.0 * TensorProduct(A*Dagger(A), B*Dagger(B), C*Dagger(C))
+
+    # Density with multiple Tensorproducts as states
+    t2 = TensorProduct(A, B)
+    t3 = TensorProduct(C, D)
+
+    d = Density([t2, 0.5], [t3, 0.5])
+    assert d.doit() == (0.5 * TensorProduct(A*Dagger(A), B*Dagger(B)) +
+                        0.5 * TensorProduct(C*Dagger(C), D*Dagger(D)))
+
+    #Density with mixed states
+    d = Density([t2 + t3, 1.0])
+    assert d.doit() == (1.0 * TensorProduct(A*Dagger(A), B*Dagger(B)) +
+                        1.0 * TensorProduct(A*Dagger(C), B*Dagger(D)) +
+                        1.0 * TensorProduct(C*Dagger(A), D*Dagger(B)) +
+                        1.0 * TensorProduct(C*Dagger(C), D*Dagger(D)))
+
+    #Density operators with spin states
+    tp1 = TensorProduct(JzKet(1, 1), JzKet(1, -1))
+    d = Density([tp1, 1])
+
+    # full trace
+    t = Tr(d)
+    assert t.doit() == 1
+
+    #Partial trace on density operators with spin states
+    t = Tr(d, [0])
+    assert t.doit() == JzKet(1, -1) * Dagger(JzKet(1, -1))
+    t = Tr(d, [1])
+    assert t.doit() == JzKet(1, 1) * Dagger(JzKet(1, 1))
+
+    # with another spin state
+    tp2 = TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))
+    d = Density([tp2, 1])
+
+    #full trace
+    t = Tr(d)
+    assert t.doit() == 1
+
+    #Partial trace on density operators with spin states
+    t = Tr(d, [0])
+    assert t.doit() == JzKet(S.Half, Rational(-1, 2)) * Dagger(JzKet(S.Half, Rational(-1, 2)))
+    t = Tr(d, [1])
+    assert t.doit() == JzKet(S.Half, S.Half) * Dagger(JzKet(S.Half, S.Half))
+
+
+def test_apply_op():
+    d = Density([Ket(0), 0.5], [Ket(1), 0.5])
+    assert d.apply_op(XOp()) == Density([XOp()*Ket(0), 0.5],
+                                        [XOp()*Ket(1), 0.5])
+
+
+def test_represent():
+    x, y = symbols('x y')
+    d = Density([XKet(), 0.5], [PxKet(), 0.5])
+    assert (represent(0.5*(PxKet()*Dagger(PxKet()))) +
+            represent(0.5*(XKet()*Dagger(XKet())))) == represent(d)
+
+    # check for kets with expr in them
+    d_with_sym = Density([XKet(x*y), 0.5], [PxKet(x*y), 0.5])
+    assert (represent(0.5*(PxKet(x*y)*Dagger(PxKet(x*y)))) +
+            represent(0.5*(XKet(x*y)*Dagger(XKet(x*y))))) == \
+        represent(d_with_sym)
+
+    # check when given explicit basis
+    assert (represent(0.5*(XKet()*Dagger(XKet())), basis=PxOp()) +
+            represent(0.5*(PxKet()*Dagger(PxKet())), basis=PxOp())) == \
+        represent(d, basis=PxOp())
+
+
+def test_states():
+    d = Density([Ket(0), 0.5], [Ket(1), 0.5])
+    states = d.states()
+    assert states[0] == Ket(0) and states[1] == Ket(1)
+
+
+def test_probs():
+    d = Density([Ket(0), .75], [Ket(1), 0.25])
+    probs = d.probs()
+    assert probs[0] == 0.75 and probs[1] == 0.25
+
+    #probs can be symbols
+    x, y = symbols('x y')
+    d = Density([Ket(0), x], [Ket(1), y])
+    probs = d.probs()
+    assert probs[0] == x and probs[1] == y
+
+
+def test_get_state():
+    x, y = symbols('x y')
+    d = Density([Ket(0), x], [Ket(1), y])
+    states = (d.get_state(0), d.get_state(1))
+    assert states[0] == Ket(0) and states[1] == Ket(1)
+
+
+def test_get_prob():
+    x, y = symbols('x y')
+    d = Density([Ket(0), x], [Ket(1), y])
+    probs = (d.get_prob(0), d.get_prob(1))
+    assert probs[0] == x and probs[1] == y
+
+
+def test_entropy():
+    up = JzKet(S.Half, S.Half)
+    down = JzKet(S.Half, Rational(-1, 2))
+    d = Density((up, S.Half), (down, S.Half))
+
+    # test for density object
+    ent = entropy(d)
+    assert entropy(d) == log(2)/2
+    assert d.entropy() == log(2)/2
+
+    np = import_module('numpy', min_module_version='1.4.0')
+    if np:
+        #do this test only if 'numpy' is available on test machine
+        np_mat = represent(d, format='numpy')
+        ent = entropy(np_mat)
+        assert isinstance(np_mat, np.ndarray)
+        assert ent.real == 0.69314718055994529
+        assert ent.imag == 0
+
+    scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+    if scipy and np:
+        #do this test only if numpy and scipy are available
+        mat = represent(d, format="scipy.sparse")
+        assert isinstance(mat, scipy_sparse_matrix)
+        assert ent.real == 0.69314718055994529
+        assert ent.imag == 0
+
+
+def test_eval_trace():
+    up = JzKet(S.Half, S.Half)
+    down = JzKet(S.Half, Rational(-1, 2))
+    d = Density((up, 0.5), (down, 0.5))
+
+    t = Tr(d)
+    assert t.doit() == 1.0
+
+    #test dummy time dependent states
+    class TestTimeDepKet(TimeDepKet):
+        def _eval_trace(self, bra, **options):
+            return 1
+
+    x, t = symbols('x t')
+    k1 = TestTimeDepKet(0, 0.5)
+    k2 = TestTimeDepKet(0, 1)
+    d = Density([k1, 0.5], [k2, 0.5])
+    assert d.doit() == (0.5 * OuterProduct(k1, k1.dual) +
+                        0.5 * OuterProduct(k2, k2.dual))
+
+    t = Tr(d)
+    assert t.doit() == 1.0
+
+
+def test_fidelity():
+    #test with kets
+    up = JzKet(S.Half, S.Half)
+    down = JzKet(S.Half, Rational(-1, 2))
+    updown = (S.One/sqrt(2))*up + (S.One/sqrt(2))*down
+
+    #check with matrices
+    up_dm = represent(up * Dagger(up))
+    down_dm = represent(down * Dagger(down))
+    updown_dm = represent(updown * Dagger(updown))
+
+    assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
+    assert fidelity(up_dm, down_dm) < 1e-3
+    assert abs(fidelity(up_dm, updown_dm) - (S.One/sqrt(2))) < 1e-3
+    assert abs(fidelity(updown_dm, down_dm) - (S.One/sqrt(2))) < 1e-3
+
+    #check with density
+    up_dm = Density([up, 1.0])
+    down_dm = Density([down, 1.0])
+    updown_dm = Density([updown, 1.0])
+
+    assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
+    assert abs(fidelity(up_dm, down_dm)) < 1e-3
+    assert abs(fidelity(up_dm, updown_dm) - (S.One/sqrt(2))) < 1e-3
+    assert abs(fidelity(updown_dm, down_dm) - (S.One/sqrt(2))) < 1e-3
+
+    #check mixed states with density
+    updown2 = sqrt(3)/2*up + S.Half*down
+    d1 = Density([updown, 0.25], [updown2, 0.75])
+    d2 = Density([updown, 0.75], [updown2, 0.25])
+    assert abs(fidelity(d1, d2) - 0.991) < 1e-3
+    assert abs(fidelity(d2, d1) - fidelity(d1, d2)) < 1e-3
+
+    #using qubits/density(pure states)
+    state1 = Qubit('0')
+    state2 = Qubit('1')
+    state3 = S.One/sqrt(2)*state1 + S.One/sqrt(2)*state2
+    state4 = sqrt(Rational(2, 3))*state1 + S.One/sqrt(3)*state2
+
+    state1_dm = Density([state1, 1])
+    state2_dm = Density([state2, 1])
+    state3_dm = Density([state3, 1])
+
+    assert fidelity(state1_dm, state1_dm) == 1
+    assert fidelity(state1_dm, state2_dm) == 0
+    assert abs(fidelity(state1_dm, state3_dm) - 1/sqrt(2)) < 1e-3
+    assert abs(fidelity(state3_dm, state2_dm) - 1/sqrt(2)) < 1e-3
+
+    #using qubits/density(mixed states)
+    d1 = Density([state3, 0.70], [state4, 0.30])
+    d2 = Density([state3, 0.20], [state4, 0.80])
+    assert abs(fidelity(d1, d1) - 1) < 1e-3
+    assert abs(fidelity(d1, d2) - 0.996) < 1e-3
+    assert abs(fidelity(d1, d2) - fidelity(d2, d1)) < 1e-3
+
+    #TODO: test for invalid arguments
+    # non-square matrix
+    mat1 = [[0, 0],
+            [0, 0],
+            [0, 0]]
+
+    mat2 = [[0, 0],
+            [0, 0]]
+    raises(ValueError, lambda: fidelity(mat1, mat2))
+
+    # unequal dimensions
+    mat1 = [[0, 0],
+            [0, 0]]
+    mat2 = [[0, 0, 0],
+            [0, 0, 0],
+            [0, 0, 0]]
+    raises(ValueError, lambda: fidelity(mat1, mat2))
+
+    # unsupported data-type
+    x, y = 1, 2  # random values that is not a matrix
+    raises(ValueError, lambda: fidelity(x, y))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_fermion.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_fermion.py
new file mode 100644
index 0000000000000000000000000000000000000000..061648c2d5578481196949c38e90ff169fcea972
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_fermion.py
@@ -0,0 +1,62 @@
+from pytest import raises
+
+import sympy
+from sympy.physics.quantum import Dagger, AntiCommutator, qapply
+from sympy.physics.quantum.fermion import FermionOp
+from sympy.physics.quantum.fermion import FermionFockKet, FermionFockBra
+from sympy import Symbol
+
+
+def test_fermionoperator():
+    c = FermionOp('c')
+    d = FermionOp('d')
+
+    assert isinstance(c, FermionOp)
+    assert isinstance(Dagger(c), FermionOp)
+
+    assert c.is_annihilation
+    assert not Dagger(c).is_annihilation
+
+    assert FermionOp("c") == FermionOp("c", True)
+    assert FermionOp("c") != FermionOp("d")
+    assert FermionOp("c", True) != FermionOp("c", False)
+
+    assert AntiCommutator(c, Dagger(c)).doit() == 1
+
+    assert AntiCommutator(c, Dagger(d)).doit() == c * Dagger(d) + Dagger(d) * c
+
+
+def test_fermion_states():
+    c = FermionOp("c")
+
+    # Fock states
+    assert (FermionFockBra(0) * FermionFockKet(1)).doit() == 0
+    assert (FermionFockBra(1) * FermionFockKet(1)).doit() == 1
+
+    assert qapply(c * FermionFockKet(1)) == FermionFockKet(0)
+    assert qapply(c * FermionFockKet(0)) == 0
+
+    assert qapply(Dagger(c) * FermionFockKet(0)) == FermionFockKet(1)
+    assert qapply(Dagger(c) * FermionFockKet(1)) == 0
+
+
+def test_power():
+    c = FermionOp("c")
+    assert c**0 == 1
+    assert c**1 == c
+    assert c**2 == 0
+    assert c**3 == 0
+    assert Dagger(c)**1 == Dagger(c)
+    assert Dagger(c)**2 == 0
+
+    assert (c**Symbol('a')).func == sympy.core.power.Pow
+    assert (c**Symbol('a')).args == (c, Symbol('a'))
+
+    with raises(ValueError):
+        c**-1
+
+    with raises(ValueError):
+        c**3.2
+
+    with raises(TypeError):
+        c**1j
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_gate.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_gate.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d7bf1d624faca8afe4b10699d23acc161ca0cdd
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_gate.py
@@ -0,0 +1,360 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, Integer, Rational, pi)
+from sympy.core.symbol import (Wild, symbols)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices import Matrix, ImmutableMatrix
+
+from sympy.physics.quantum.gate import (XGate, YGate, ZGate, random_circuit,
+        CNOT, IdentityGate, H, X, Y, S, T, Z, SwapGate, gate_simp, gate_sort,
+        CNotGate, TGate, HadamardGate, PhaseGate, UGate, CGate)
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qubit import Qubit, IntQubit, qubit_to_matrix, \
+    matrix_to_qubit
+from sympy.physics.quantum.matrixutils import matrix_to_zero
+from sympy.physics.quantum.matrixcache import sqrt2_inv
+from sympy.physics.quantum import Dagger
+
+
+def test_gate():
+    """Test a basic gate."""
+    h = HadamardGate(1)
+    assert h.min_qubits == 2
+    assert h.nqubits == 1
+
+    i0 = Wild('i0')
+    i1 = Wild('i1')
+    h0_w1 = HadamardGate(i0)
+    h0_w2 = HadamardGate(i0)
+    h1_w1 = HadamardGate(i1)
+
+    assert h0_w1 == h0_w2
+    assert h0_w1 != h1_w1
+    assert h1_w1 != h0_w2
+
+    cnot_10_w1 = CNOT(i1, i0)
+    cnot_10_w2 = CNOT(i1, i0)
+    cnot_01_w1 = CNOT(i0, i1)
+
+    assert cnot_10_w1 == cnot_10_w2
+    assert cnot_10_w1 != cnot_01_w1
+    assert cnot_10_w2 != cnot_01_w1
+
+
+def test_UGate():
+    a, b, c, d = symbols('a,b,c,d')
+    uMat = Matrix([[a, b], [c, d]])
+
+    # Test basic case where gate exists in 1-qubit space
+    u1 = UGate((0,), uMat)
+    assert represent(u1, nqubits=1) == uMat
+    assert qapply(u1*Qubit('0')) == a*Qubit('0') + c*Qubit('1')
+    assert qapply(u1*Qubit('1')) == b*Qubit('0') + d*Qubit('1')
+
+    # Test case where gate exists in a larger space
+    u2 = UGate((1,), uMat)
+    u2Rep = represent(u2, nqubits=2)
+    for i in range(4):
+        assert u2Rep*qubit_to_matrix(IntQubit(i, 2)) == \
+            qubit_to_matrix(qapply(u2*IntQubit(i, 2)))
+
+
+def test_cgate():
+    """Test the general CGate."""
+    # Test single control functionality
+    CNOTMatrix = Matrix(
+        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
+    assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix
+
+    # Test multiple control bit functionality
+    ToffoliGate = CGate((1, 2), XGate(0))
+    assert represent(ToffoliGate, nqubits=3) == \
+        Matrix(
+            [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0],
+    [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0,
+        1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1],
+    [0, 0, 0, 0, 0, 0, 1, 0]])
+
+    ToffoliGate = CGate((3, 0), XGate(1))
+    assert qapply(ToffoliGate*Qubit('1001')) == \
+        matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4))
+    assert qapply(ToffoliGate*Qubit('0000')) == \
+        matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4))
+
+    CYGate = CGate(1, YGate(0))
+    CYGate_matrix = Matrix(
+        ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, -I), (0, 0, I, 0)))
+    # Test 2 qubit controlled-Y gate decompose method.
+    assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix
+
+    CZGate = CGate(0, ZGate(1))
+    CZGate_matrix = Matrix(
+        ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, -1)))
+    assert qapply(CZGate*Qubit('11')) == -Qubit('11')
+    assert matrix_to_qubit(represent(CZGate*Qubit('11'), nqubits=2)) == \
+        -Qubit('11')
+    # Test 2 qubit controlled-Z gate decompose method.
+    assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix
+
+    CPhaseGate = CGate(0, PhaseGate(1))
+    assert qapply(CPhaseGate*Qubit('11')) == \
+        I*Qubit('11')
+    assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \
+        I*Qubit('11')
+
+    # Test that the dagger, inverse, and power of CGate is evaluated properly
+    assert Dagger(CZGate) == CZGate
+    assert pow(CZGate, 1) == Dagger(CZGate)
+    assert Dagger(CZGate) == CZGate.inverse()
+    assert Dagger(CPhaseGate) != CPhaseGate
+    assert Dagger(CPhaseGate) == CPhaseGate.inverse()
+    assert Dagger(CPhaseGate) == pow(CPhaseGate, -1)
+    assert pow(CPhaseGate, -1) == CPhaseGate.inverse()
+
+
+def test_UGate_CGate_combo():
+    a, b, c, d = symbols('a,b,c,d')
+    uMat = Matrix([[a, b], [c, d]])
+    cMat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, a, b], [0, 0, c, d]])
+
+    # Test basic case where gate exists in 1-qubit space.
+    u1 = UGate((0,), uMat)
+    cu1 = CGate(1, u1)
+    assert represent(cu1, nqubits=2) == cMat
+    assert qapply(cu1*Qubit('10')) == a*Qubit('10') + c*Qubit('11')
+    assert qapply(cu1*Qubit('11')) == b*Qubit('10') + d*Qubit('11')
+    assert qapply(cu1*Qubit('01')) == Qubit('01')
+    assert qapply(cu1*Qubit('00')) == Qubit('00')
+
+    # Test case where gate exists in a larger space.
+    u2 = UGate((1,), uMat)
+    u2Rep = represent(u2, nqubits=2)
+    for i in range(4):
+        assert u2Rep*qubit_to_matrix(IntQubit(i, 2)) == \
+            qubit_to_matrix(qapply(u2*IntQubit(i, 2)))
+
+def test_UGate_OneQubitGate_combo():
+    v, w, f, g = symbols('v w f g')
+    uMat1 = ImmutableMatrix([[v, w], [f, g]])
+    cMat1 = Matrix([[v, w + 1, 0, 0], [f + 1, g, 0, 0], [0, 0, v, w + 1], [0, 0, f + 1, g]])
+    u1 = X(0) + UGate(0, uMat1)
+    assert represent(u1, nqubits=2) == cMat1
+
+    uMat2 = ImmutableMatrix([[1/sqrt(2), 1/sqrt(2)], [I/sqrt(2), -I/sqrt(2)]])
+    cMat2_1 = Matrix([[Rational(1, 2) + I/2, Rational(1, 2) - I/2],
+                      [Rational(1, 2) - I/2, Rational(1, 2) + I/2]])
+    cMat2_2 = Matrix([[1, 0], [0, I]])
+    u2 = UGate(0, uMat2)
+    assert represent(H(0)*u2, nqubits=1) == cMat2_1
+    assert represent(u2*H(0), nqubits=1) == cMat2_2
+
+def test_represent_hadamard():
+    """Test the representation of the hadamard gate."""
+    circuit = HadamardGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    # Check that the answers are same to within an epsilon.
+    assert answer == Matrix([sqrt2_inv, sqrt2_inv, 0, 0])
+
+
+def test_represent_xgate():
+    """Test the representation of the X gate."""
+    circuit = XGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([0, 1, 0, 0]) == answer
+
+
+def test_represent_ygate():
+    """Test the representation of the Y gate."""
+    circuit = YGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert answer[0] == 0 and answer[1] == I and \
+        answer[2] == 0 and answer[3] == 0
+
+
+def test_represent_zgate():
+    """Test the representation of the Z gate."""
+    circuit = ZGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([1, 0, 0, 0]) == answer
+
+
+def test_represent_phasegate():
+    """Test the representation of the S gate."""
+    circuit = PhaseGate(0)*Qubit('01')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([0, I, 0, 0]) == answer
+
+
+def test_represent_tgate():
+    """Test the representation of the T gate."""
+    circuit = TGate(0)*Qubit('01')
+    assert Matrix([0, exp(I*pi/4), 0, 0]) == represent(circuit, nqubits=2)
+
+
+def test_compound_gates():
+    """Test a compound gate representation."""
+    circuit = YGate(0)*ZGate(0)*XGate(0)*HadamardGate(0)*Qubit('00')
+    answer = represent(circuit, nqubits=2)
+    assert Matrix([I/sqrt(2), I/sqrt(2), 0, 0]) == answer
+
+
+def test_cnot_gate():
+    """Test the CNOT gate."""
+    circuit = CNotGate(1, 0)
+    assert represent(circuit, nqubits=2) == \
+        Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
+    circuit = circuit*Qubit('111')
+    assert matrix_to_qubit(represent(circuit, nqubits=3)) == \
+        qapply(circuit)
+
+    circuit = CNotGate(1, 0)
+    assert Dagger(circuit) == circuit
+    assert Dagger(Dagger(circuit)) == circuit
+    assert circuit*circuit == 1
+
+
+def test_gate_sort():
+    """Test gate_sort."""
+    for g in (X, Y, Z, H, S, T):
+        assert gate_sort(g(2)*g(1)*g(0)) == g(0)*g(1)*g(2)
+    e = gate_sort(X(1)*H(0)**2*CNOT(0, 1)*X(1)*X(0))
+    assert e == H(0)**2*CNOT(0, 1)*X(0)*X(1)**2
+    assert gate_sort(Z(0)*X(0)) == -X(0)*Z(0)
+    assert gate_sort(Z(0)*X(0)**2) == X(0)**2*Z(0)
+    assert gate_sort(Y(0)*H(0)) == -H(0)*Y(0)
+    assert gate_sort(Y(0)*X(0)) == -X(0)*Y(0)
+    assert gate_sort(Z(0)*Y(0)) == -Y(0)*Z(0)
+    assert gate_sort(T(0)*S(0)) == S(0)*T(0)
+    assert gate_sort(Z(0)*S(0)) == S(0)*Z(0)
+    assert gate_sort(Z(0)*T(0)) == T(0)*Z(0)
+    assert gate_sort(Z(0)*CNOT(0, 1)) == CNOT(0, 1)*Z(0)
+    assert gate_sort(S(0)*CNOT(0, 1)) == CNOT(0, 1)*S(0)
+    assert gate_sort(T(0)*CNOT(0, 1)) == CNOT(0, 1)*T(0)
+    assert gate_sort(X(1)*CNOT(0, 1)) == CNOT(0, 1)*X(1)
+    # This takes a long time and should only be uncommented once in a while.
+    # nqubits = 5
+    # ngates = 10
+    # trials = 10
+    # for i in range(trials):
+    #     c = random_circuit(ngates, nqubits)
+    #     assert represent(c, nqubits=nqubits) == \
+    #            represent(gate_sort(c), nqubits=nqubits)
+
+
+def test_gate_simp():
+    """Test gate_simp."""
+    e = H(0)*X(1)*H(0)**2*CNOT(0, 1)*X(1)**3*X(0)*Z(3)**2*S(4)**3
+    assert gate_simp(e) == H(0)*CNOT(0, 1)*S(4)*X(0)*Z(4)
+    assert gate_simp(X(0)*X(0)) == 1
+    assert gate_simp(Y(0)*Y(0)) == 1
+    assert gate_simp(Z(0)*Z(0)) == 1
+    assert gate_simp(H(0)*H(0)) == 1
+    assert gate_simp(T(0)*T(0)) == S(0)
+    assert gate_simp(S(0)*S(0)) == Z(0)
+    assert gate_simp(Integer(1)) == Integer(1)
+    assert gate_simp(X(0)**2 + Y(0)**2) == Integer(2)
+
+
+def test_swap_gate():
+    """Test the SWAP gate."""
+    swap_gate_matrix = Matrix(
+        ((1, 0, 0, 0), (0, 0, 1, 0), (0, 1, 0, 0), (0, 0, 0, 1)))
+    assert represent(SwapGate(1, 0).decompose(), nqubits=2) == swap_gate_matrix
+    assert qapply(SwapGate(1, 3)*Qubit('0010')) == Qubit('1000')
+    nqubits = 4
+    for i in range(nqubits):
+        for j in range(i):
+            assert represent(SwapGate(i, j), nqubits=nqubits) == \
+                represent(SwapGate(i, j).decompose(), nqubits=nqubits)
+
+
+def test_one_qubit_commutators():
+    """Test single qubit gate commutation relations."""
+    for g1 in (IdentityGate, X, Y, Z, H, T, S):
+        for g2 in (IdentityGate, X, Y, Z, H, T, S):
+            e = Commutator(g1(0), g2(0))
+            a = matrix_to_zero(represent(e, nqubits=1, format='sympy'))
+            b = matrix_to_zero(represent(e.doit(), nqubits=1, format='sympy'))
+            assert a == b
+
+            e = Commutator(g1(0), g2(1))
+            assert e.doit() == 0
+
+
+def test_one_qubit_anticommutators():
+    """Test single qubit gate anticommutation relations."""
+    for g1 in (IdentityGate, X, Y, Z, H):
+        for g2 in (IdentityGate, X, Y, Z, H):
+            e = AntiCommutator(g1(0), g2(0))
+            a = matrix_to_zero(represent(e, nqubits=1, format='sympy'))
+            b = matrix_to_zero(represent(e.doit(), nqubits=1, format='sympy'))
+            assert a == b
+            e = AntiCommutator(g1(0), g2(1))
+            a = matrix_to_zero(represent(e, nqubits=2, format='sympy'))
+            b = matrix_to_zero(represent(e.doit(), nqubits=2, format='sympy'))
+            assert a == b
+
+
+def test_cnot_commutators():
+    """Test commutators of involving CNOT gates."""
+    assert Commutator(CNOT(0, 1), Z(0)).doit() == 0
+    assert Commutator(CNOT(0, 1), T(0)).doit() == 0
+    assert Commutator(CNOT(0, 1), S(0)).doit() == 0
+    assert Commutator(CNOT(0, 1), X(1)).doit() == 0
+    assert Commutator(CNOT(0, 1), CNOT(0, 1)).doit() == 0
+    assert Commutator(CNOT(0, 1), CNOT(0, 2)).doit() == 0
+    assert Commutator(CNOT(0, 2), CNOT(0, 1)).doit() == 0
+    assert Commutator(CNOT(1, 2), CNOT(1, 0)).doit() == 0
+
+
+def test_random_circuit():
+    c = random_circuit(10, 3)
+    assert isinstance(c, Mul)
+    m = represent(c, nqubits=3)
+    assert m.shape == (8, 8)
+    assert isinstance(m, Matrix)
+
+
+def test_hermitian_XGate():
+    x = XGate(1, 2)
+    x_dagger = Dagger(x)
+
+    assert (x == x_dagger)
+
+
+def test_hermitian_YGate():
+    y = YGate(1, 2)
+    y_dagger = Dagger(y)
+
+    assert (y == y_dagger)
+
+
+def test_hermitian_ZGate():
+    z = ZGate(1, 2)
+    z_dagger = Dagger(z)
+
+    assert (z == z_dagger)
+
+
+def test_unitary_XGate():
+    x = XGate(1, 2)
+    x_dagger = Dagger(x)
+
+    assert (x*x_dagger == 1)
+
+
+def test_unitary_YGate():
+    y = YGate(1, 2)
+    y_dagger = Dagger(y)
+
+    assert (y*y_dagger == 1)
+
+
+def test_unitary_ZGate():
+    z = ZGate(1, 2)
+    z_dagger = Dagger(z)
+
+    assert (z*z_dagger == 1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_grover.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_grover.py
new file mode 100644
index 0000000000000000000000000000000000000000..b93a5bc5e59380a993dc34e4a160e75f799b3493
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_grover.py
@@ -0,0 +1,92 @@
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import Matrix
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.qubit import IntQubit
+from sympy.physics.quantum.grover import (apply_grover, superposition_basis,
+        OracleGate, grover_iteration, WGate)
+
+
+def return_one_on_two(qubits):
+    return qubits == IntQubit(2, qubits.nqubits)
+
+
+def return_one_on_one(qubits):
+    return qubits == IntQubit(1, nqubits=qubits.nqubits)
+
+
+def test_superposition_basis():
+    nbits = 2
+    first_half_state = IntQubit(0, nqubits=nbits)/2 + IntQubit(1, nqubits=nbits)/2
+    second_half_state = IntQubit(2, nbits)/2 + IntQubit(3, nbits)/2
+    assert first_half_state + second_half_state == superposition_basis(nbits)
+
+    nbits = 3
+    firstq = (1/sqrt(8))*IntQubit(0, nqubits=nbits) + (1/sqrt(8))*IntQubit(1, nqubits=nbits)
+    secondq = (1/sqrt(8))*IntQubit(2, nbits) + (1/sqrt(8))*IntQubit(3, nbits)
+    thirdq = (1/sqrt(8))*IntQubit(4, nbits) + (1/sqrt(8))*IntQubit(5, nbits)
+    fourthq = (1/sqrt(8))*IntQubit(6, nbits) + (1/sqrt(8))*IntQubit(7, nbits)
+    assert firstq + secondq + thirdq + fourthq == superposition_basis(nbits)
+
+
+def test_OracleGate():
+    v = OracleGate(1, lambda qubits: qubits == IntQubit(0))
+    assert qapply(v*IntQubit(0)) == -IntQubit(0)
+    assert qapply(v*IntQubit(1)) == IntQubit(1)
+
+    nbits = 2
+    v = OracleGate(2, return_one_on_two)
+    assert qapply(v*IntQubit(0, nbits)) == IntQubit(0, nqubits=nbits)
+    assert qapply(v*IntQubit(1, nbits)) == IntQubit(1, nqubits=nbits)
+    assert qapply(v*IntQubit(2, nbits)) == -IntQubit(2, nbits)
+    assert qapply(v*IntQubit(3, nbits)) == IntQubit(3, nbits)
+
+    assert represent(OracleGate(1, lambda qubits: qubits == IntQubit(0)), nqubits=1) == \
+           Matrix([[-1, 0], [0, 1]])
+    assert represent(v, nqubits=2) == Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]])
+
+
+def test_WGate():
+    nqubits = 2
+    basis_states = superposition_basis(nqubits)
+    assert qapply(WGate(nqubits)*basis_states) == basis_states
+
+    expected = ((2/sqrt(pow(2, nqubits)))*basis_states) - IntQubit(1, nqubits=nqubits)
+    assert qapply(WGate(nqubits)*IntQubit(1, nqubits=nqubits)) == expected
+
+
+def test_grover_iteration_1():
+    numqubits = 2
+    basis_states = superposition_basis(numqubits)
+    v = OracleGate(numqubits, return_one_on_one)
+    expected = IntQubit(1, nqubits=numqubits)
+    assert qapply(grover_iteration(basis_states, v)) == expected
+
+
+def test_grover_iteration_2():
+    numqubits = 4
+    basis_states = superposition_basis(numqubits)
+    v = OracleGate(numqubits, return_one_on_two)
+    # After (pi/4)sqrt(pow(2, n)), IntQubit(2) should have highest prob
+    # In this case, after around pi times (3 or 4)
+    iterated = grover_iteration(basis_states, v)
+    iterated = qapply(iterated)
+    iterated = grover_iteration(iterated, v)
+    iterated = qapply(iterated)
+    iterated = grover_iteration(iterated, v)
+    iterated = qapply(iterated)
+    # In this case, probability was highest after 3 iterations
+    # Probability of Qubit('0010') was 251/256 (3) vs 781/1024 (4)
+    # Ask about measurement
+    expected = (-13*basis_states)/64 + 264*IntQubit(2, numqubits)/256
+    assert qapply(expected) == iterated
+
+
+def test_grover():
+    nqubits = 2
+    assert apply_grover(return_one_on_one, nqubits) == IntQubit(1, nqubits=nqubits)
+
+    nqubits = 4
+    basis_states = superposition_basis(nqubits)
+    expected = (-13*basis_states)/64 + 264*IntQubit(2, nqubits)/256
+    assert apply_grover(return_one_on_two, 4) == qapply(expected)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_hilbert.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_hilbert.py
new file mode 100644
index 0000000000000000000000000000000000000000..9a0e5c4187c6c62e14505efb1597a5cd63c23fea
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_hilbert.py
@@ -0,0 +1,110 @@
+from sympy.physics.quantum.hilbert import (
+    HilbertSpace, ComplexSpace, L2, FockSpace, TensorProductHilbertSpace,
+    DirectSumHilbertSpace, TensorPowerHilbertSpace
+)
+
+from sympy.core.numbers import oo
+from sympy.core.symbol import Symbol
+from sympy.printing.repr import srepr
+from sympy.printing.str import sstr
+from sympy.sets.sets import Interval
+
+
+def test_hilbert_space():
+    hs = HilbertSpace()
+    assert isinstance(hs, HilbertSpace)
+    assert sstr(hs) == 'H'
+    assert srepr(hs) == 'HilbertSpace()'
+
+
+def test_complex_space():
+    c1 = ComplexSpace(2)
+    assert isinstance(c1, ComplexSpace)
+    assert c1.dimension == 2
+    assert sstr(c1) == 'C(2)'
+    assert srepr(c1) == 'ComplexSpace(Integer(2))'
+
+    n = Symbol('n')
+    c2 = ComplexSpace(n)
+    assert isinstance(c2, ComplexSpace)
+    assert c2.dimension == n
+    assert sstr(c2) == 'C(n)'
+    assert srepr(c2) == "ComplexSpace(Symbol('n'))"
+    assert c2.subs(n, 2) == ComplexSpace(2)
+
+
+def test_L2():
+    b1 = L2(Interval(-oo, 1))
+    assert isinstance(b1, L2)
+    assert b1.dimension is oo
+    assert b1.interval == Interval(-oo, 1)
+
+    x = Symbol('x', real=True)
+    y = Symbol('y', real=True)
+    b2 = L2(Interval(x, y))
+    assert b2.dimension is oo
+    assert b2.interval == Interval(x, y)
+    assert b2.subs(x, -1) == L2(Interval(-1, y))
+
+
+def test_fock_space():
+    f1 = FockSpace()
+    f2 = FockSpace()
+    assert isinstance(f1, FockSpace)
+    assert f1.dimension is oo
+    assert f1 == f2
+
+
+def test_tensor_product():
+    n = Symbol('n')
+    hs1 = ComplexSpace(2)
+    hs2 = ComplexSpace(n)
+
+    h = hs1*hs2
+    assert isinstance(h, TensorProductHilbertSpace)
+    assert h.dimension == 2*n
+    assert h.spaces == (hs1, hs2)
+
+    h = hs2*hs2
+    assert isinstance(h, TensorPowerHilbertSpace)
+    assert h.base == hs2
+    assert h.exp == 2
+    assert h.dimension == n**2
+
+    f = FockSpace()
+    h = hs1*hs2*f
+    assert h.dimension is oo
+
+
+def test_tensor_power():
+    n = Symbol('n')
+    hs1 = ComplexSpace(2)
+    hs2 = ComplexSpace(n)
+
+    h = hs1**2
+    assert isinstance(h, TensorPowerHilbertSpace)
+    assert h.base == hs1
+    assert h.exp == 2
+    assert h.dimension == 4
+
+    h = hs2**3
+    assert isinstance(h, TensorPowerHilbertSpace)
+    assert h.base == hs2
+    assert h.exp == 3
+    assert h.dimension == n**3
+
+
+def test_direct_sum():
+    n = Symbol('n')
+    hs1 = ComplexSpace(2)
+    hs2 = ComplexSpace(n)
+
+    h = hs1 + hs2
+    assert isinstance(h, DirectSumHilbertSpace)
+    assert h.dimension == 2 + n
+    assert h.spaces == (hs1, hs2)
+
+    f = FockSpace()
+    h = hs1 + f + hs2
+    assert h.dimension is oo
+    assert h.spaces == (hs1, f, hs2)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_identitysearch.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_identitysearch.py
new file mode 100644
index 0000000000000000000000000000000000000000..8747b1f9d9630e699695f67734333f9d61581fb8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_identitysearch.py
@@ -0,0 +1,492 @@
+from sympy.external import import_module
+from sympy.core.mul import Mul
+from sympy.core.numbers import Integer
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.gate import (X, Y, Z, H, CNOT,
+        IdentityGate, CGate, PhaseGate, TGate)
+from sympy.physics.quantum.identitysearch import (generate_gate_rules,
+        generate_equivalent_ids, GateIdentity, bfs_identity_search,
+        is_scalar_sparse_matrix,
+        is_scalar_nonsparse_matrix, is_degenerate, is_reducible)
+from sympy.testing.pytest import skip
+
+
+def create_gate_sequence(qubit=0):
+    gates = (X(qubit), Y(qubit), Z(qubit), H(qubit))
+    return gates
+
+
+def test_generate_gate_rules_1():
+    # Test with tuples
+    (x, y, z, h) = create_gate_sequence()
+    ph = PhaseGate(0)
+    cgate_t = CGate(0, TGate(1))
+
+    assert generate_gate_rules((x,)) == {((x,), ())}
+
+    gate_rules = {((x, x), ()),
+                      ((x,), (x,))}
+    assert generate_gate_rules((x, x)) == gate_rules
+
+    gate_rules = {((x, y, x), ()),
+                      ((y, x, x), ()),
+                      ((x, x, y), ()),
+                      ((y, x), (x,)),
+                      ((x, y), (x,)),
+                      ((y,), (x, x))}
+    assert generate_gate_rules((x, y, x)) == gate_rules
+
+    gate_rules = {((x, y, z), ()), ((y, z, x), ()), ((z, x, y), ()),
+                      ((), (x, z, y)), ((), (y, x, z)), ((), (z, y, x)),
+                      ((x,), (z, y)), ((y, z), (x,)), ((y,), (x, z)),
+                      ((z, x), (y,)), ((z,), (y, x)), ((x, y), (z,))}
+    actual = generate_gate_rules((x, y, z))
+    assert actual == gate_rules
+
+    gate_rules = {
+        ((), (h, z, y, x)), ((), (x, h, z, y)), ((), (y, x, h, z)),
+         ((), (z, y, x, h)), ((h,), (z, y, x)), ((x,), (h, z, y)),
+         ((y,), (x, h, z)), ((z,), (y, x, h)), ((h, x), (z, y)),
+         ((x, y), (h, z)), ((y, z), (x, h)), ((z, h), (y, x)),
+         ((h, x, y), (z,)), ((x, y, z), (h,)), ((y, z, h), (x,)),
+         ((z, h, x), (y,)), ((h, x, y, z), ()), ((x, y, z, h), ()),
+         ((y, z, h, x), ()), ((z, h, x, y), ())}
+    actual = generate_gate_rules((x, y, z, h))
+    assert actual == gate_rules
+
+    gate_rules = {((), (cgate_t**(-1), ph**(-1), x)),
+                      ((), (ph**(-1), x, cgate_t**(-1))),
+                      ((), (x, cgate_t**(-1), ph**(-1))),
+                      ((cgate_t,), (ph**(-1), x)),
+                      ((ph,), (x, cgate_t**(-1))),
+                      ((x,), (cgate_t**(-1), ph**(-1))),
+                      ((cgate_t, x), (ph**(-1),)),
+                      ((ph, cgate_t), (x,)),
+                      ((x, ph), (cgate_t**(-1),)),
+                      ((cgate_t, x, ph), ()),
+                      ((ph, cgate_t, x), ()),
+                      ((x, ph, cgate_t), ())}
+    actual = generate_gate_rules((x, ph, cgate_t))
+    assert actual == gate_rules
+
+    gate_rules = {(Integer(1), cgate_t**(-1)*ph**(-1)*x),
+                      (Integer(1), ph**(-1)*x*cgate_t**(-1)),
+                      (Integer(1), x*cgate_t**(-1)*ph**(-1)),
+                      (cgate_t, ph**(-1)*x),
+                      (ph, x*cgate_t**(-1)),
+                      (x, cgate_t**(-1)*ph**(-1)),
+                      (cgate_t*x, ph**(-1)),
+                      (ph*cgate_t, x),
+                      (x*ph, cgate_t**(-1)),
+                      (cgate_t*x*ph, Integer(1)),
+                      (ph*cgate_t*x, Integer(1)),
+                      (x*ph*cgate_t, Integer(1))}
+    actual = generate_gate_rules((x, ph, cgate_t), return_as_muls=True)
+    assert actual == gate_rules
+
+
+def test_generate_gate_rules_2():
+    # Test with Muls
+    (x, y, z, h) = create_gate_sequence()
+    ph = PhaseGate(0)
+    cgate_t = CGate(0, TGate(1))
+
+    # Note: 1 (type int) is not the same as 1 (type One)
+    expected = {(x, Integer(1))}
+    assert generate_gate_rules((x,), return_as_muls=True) == expected
+
+    expected = {(Integer(1), Integer(1))}
+    assert generate_gate_rules(x*x, return_as_muls=True) == expected
+
+    expected = {((), ())}
+    assert generate_gate_rules(x*x, return_as_muls=False) == expected
+
+    gate_rules = {(x*y*x, Integer(1)),
+                      (y, Integer(1)),
+                      (y*x, x),
+                      (x*y, x)}
+    assert generate_gate_rules(x*y*x, return_as_muls=True) == gate_rules
+
+    gate_rules = {(x*y*z, Integer(1)),
+                      (y*z*x, Integer(1)),
+                      (z*x*y, Integer(1)),
+                      (Integer(1), x*z*y),
+                      (Integer(1), y*x*z),
+                      (Integer(1), z*y*x),
+                      (x, z*y),
+                      (y*z, x),
+                      (y, x*z),
+                      (z*x, y),
+                      (z, y*x),
+                      (x*y, z)}
+    actual = generate_gate_rules(x*y*z, return_as_muls=True)
+    assert actual == gate_rules
+
+    gate_rules = {(Integer(1), h*z*y*x),
+                      (Integer(1), x*h*z*y),
+                      (Integer(1), y*x*h*z),
+                      (Integer(1), z*y*x*h),
+                      (h, z*y*x), (x, h*z*y),
+                      (y, x*h*z), (z, y*x*h),
+                      (h*x, z*y), (z*h, y*x),
+                      (x*y, h*z), (y*z, x*h),
+                      (h*x*y, z), (x*y*z, h),
+                      (y*z*h, x), (z*h*x, y),
+                      (h*x*y*z, Integer(1)),
+                      (x*y*z*h, Integer(1)),
+                      (y*z*h*x, Integer(1)),
+                      (z*h*x*y, Integer(1))}
+    actual = generate_gate_rules(x*y*z*h, return_as_muls=True)
+    assert actual == gate_rules
+
+    gate_rules = {(Integer(1), cgate_t**(-1)*ph**(-1)*x),
+                      (Integer(1), ph**(-1)*x*cgate_t**(-1)),
+                      (Integer(1), x*cgate_t**(-1)*ph**(-1)),
+                      (cgate_t, ph**(-1)*x),
+                      (ph, x*cgate_t**(-1)),
+                      (x, cgate_t**(-1)*ph**(-1)),
+                      (cgate_t*x, ph**(-1)),
+                      (ph*cgate_t, x),
+                      (x*ph, cgate_t**(-1)),
+                      (cgate_t*x*ph, Integer(1)),
+                      (ph*cgate_t*x, Integer(1)),
+                      (x*ph*cgate_t, Integer(1))}
+    actual = generate_gate_rules(x*ph*cgate_t, return_as_muls=True)
+    assert actual == gate_rules
+
+    gate_rules = {((), (cgate_t**(-1), ph**(-1), x)),
+                      ((), (ph**(-1), x, cgate_t**(-1))),
+                      ((), (x, cgate_t**(-1), ph**(-1))),
+                      ((cgate_t,), (ph**(-1), x)),
+                      ((ph,), (x, cgate_t**(-1))),
+                      ((x,), (cgate_t**(-1), ph**(-1))),
+                      ((cgate_t, x), (ph**(-1),)),
+                      ((ph, cgate_t), (x,)),
+                      ((x, ph), (cgate_t**(-1),)),
+                      ((cgate_t, x, ph), ()),
+                      ((ph, cgate_t, x), ()),
+                      ((x, ph, cgate_t), ())}
+    actual = generate_gate_rules(x*ph*cgate_t)
+    assert actual == gate_rules
+
+
+def test_generate_equivalent_ids_1():
+    # Test with tuples
+    (x, y, z, h) = create_gate_sequence()
+
+    assert generate_equivalent_ids((x,)) == {(x,)}
+    assert generate_equivalent_ids((x, x)) == {(x, x)}
+    assert generate_equivalent_ids((x, y)) == {(x, y), (y, x)}
+
+    gate_seq = (x, y, z)
+    gate_ids = {(x, y, z), (y, z, x), (z, x, y), (z, y, x),
+                    (y, x, z), (x, z, y)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    gate_ids = {Mul(x, y, z), Mul(y, z, x), Mul(z, x, y),
+                    Mul(z, y, x), Mul(y, x, z), Mul(x, z, y)}
+    assert generate_equivalent_ids(gate_seq, return_as_muls=True) == gate_ids
+
+    gate_seq = (x, y, z, h)
+    gate_ids = {(x, y, z, h), (y, z, h, x),
+                    (h, x, y, z), (h, z, y, x),
+                    (z, y, x, h), (y, x, h, z),
+                    (z, h, x, y), (x, h, z, y)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    gate_seq = (x, y, x, y)
+    gate_ids = {(x, y, x, y), (y, x, y, x)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    cgate_y = CGate((1,), y)
+    gate_seq = (y, cgate_y, y, cgate_y)
+    gate_ids = {(y, cgate_y, y, cgate_y), (cgate_y, y, cgate_y, y)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+    gate_seq = (cnot, h, cgate_z, h)
+    gate_ids = {(cnot, h, cgate_z, h), (h, cgate_z, h, cnot),
+                    (h, cnot, h, cgate_z), (cgate_z, h, cnot, h)}
+    assert generate_equivalent_ids(gate_seq) == gate_ids
+
+
+def test_generate_equivalent_ids_2():
+    # Test with Muls
+    (x, y, z, h) = create_gate_sequence()
+
+    assert generate_equivalent_ids((x,), return_as_muls=True) == {x}
+
+    gate_ids = {Integer(1)}
+    assert generate_equivalent_ids(x*x, return_as_muls=True) == gate_ids
+
+    gate_ids = {x*y, y*x}
+    assert generate_equivalent_ids(x*y, return_as_muls=True) == gate_ids
+
+    gate_ids = {(x, y), (y, x)}
+    assert generate_equivalent_ids(x*y) == gate_ids
+
+    circuit = Mul(*(x, y, z))
+    gate_ids = {x*y*z, y*z*x, z*x*y, z*y*x,
+                    y*x*z, x*z*y}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    circuit = Mul(*(x, y, z, h))
+    gate_ids = {x*y*z*h, y*z*h*x,
+                    h*x*y*z, h*z*y*x,
+                    z*y*x*h, y*x*h*z,
+                    z*h*x*y, x*h*z*y}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    circuit = Mul(*(x, y, x, y))
+    gate_ids = {x*y*x*y, y*x*y*x}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    cgate_y = CGate((1,), y)
+    circuit = Mul(*(y, cgate_y, y, cgate_y))
+    gate_ids = {y*cgate_y*y*cgate_y, cgate_y*y*cgate_y*y}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+    cnot = CNOT(1, 0)
+    cgate_z = CGate((0,), Z(1))
+    circuit = Mul(*(cnot, h, cgate_z, h))
+    gate_ids = {cnot*h*cgate_z*h, h*cgate_z*h*cnot,
+                    h*cnot*h*cgate_z, cgate_z*h*cnot*h}
+    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids
+
+
+def test_is_scalar_nonsparse_matrix():
+    numqubits = 2
+    id_only = False
+
+    id_gate = (IdentityGate(1),)
+    actual = is_scalar_nonsparse_matrix(id_gate, numqubits, id_only)
+    assert actual is True
+
+    x0 = X(0)
+    xx_circuit = (x0, x0)
+    actual = is_scalar_nonsparse_matrix(xx_circuit, numqubits, id_only)
+    assert actual is True
+
+    x1 = X(1)
+    y1 = Y(1)
+    xy_circuit = (x1, y1)
+    actual = is_scalar_nonsparse_matrix(xy_circuit, numqubits, id_only)
+    assert actual is False
+
+    z1 = Z(1)
+    xyz_circuit = (x1, y1, z1)
+    actual = is_scalar_nonsparse_matrix(xyz_circuit, numqubits, id_only)
+    assert actual is True
+
+    cnot = CNOT(1, 0)
+    cnot_circuit = (cnot, cnot)
+    actual = is_scalar_nonsparse_matrix(cnot_circuit, numqubits, id_only)
+    assert actual is True
+
+    h = H(0)
+    hh_circuit = (h, h)
+    actual = is_scalar_nonsparse_matrix(hh_circuit, numqubits, id_only)
+    assert actual is True
+
+    h1 = H(1)
+    xhzh_circuit = (x1, h1, z1, h1)
+    actual = is_scalar_nonsparse_matrix(xhzh_circuit, numqubits, id_only)
+    assert actual is True
+
+    id_only = True
+    actual = is_scalar_nonsparse_matrix(xhzh_circuit, numqubits, id_only)
+    assert actual is True
+    actual = is_scalar_nonsparse_matrix(xyz_circuit, numqubits, id_only)
+    assert actual is False
+    actual = is_scalar_nonsparse_matrix(cnot_circuit, numqubits, id_only)
+    assert actual is True
+    actual = is_scalar_nonsparse_matrix(hh_circuit, numqubits, id_only)
+    assert actual is True
+
+
+def test_is_scalar_sparse_matrix():
+    np = import_module('numpy')
+    if not np:
+        skip("numpy not installed.")
+
+    scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+    if not scipy:
+        skip("scipy not installed.")
+
+    numqubits = 2
+    id_only = False
+
+    id_gate = (IdentityGate(1),)
+    assert is_scalar_sparse_matrix(id_gate, numqubits, id_only) is True
+
+    x0 = X(0)
+    xx_circuit = (x0, x0)
+    assert is_scalar_sparse_matrix(xx_circuit, numqubits, id_only) is True
+
+    x1 = X(1)
+    y1 = Y(1)
+    xy_circuit = (x1, y1)
+    assert is_scalar_sparse_matrix(xy_circuit, numqubits, id_only) is False
+
+    z1 = Z(1)
+    xyz_circuit = (x1, y1, z1)
+    assert is_scalar_sparse_matrix(xyz_circuit, numqubits, id_only) is True
+
+    cnot = CNOT(1, 0)
+    cnot_circuit = (cnot, cnot)
+    assert is_scalar_sparse_matrix(cnot_circuit, numqubits, id_only) is True
+
+    h = H(0)
+    hh_circuit = (h, h)
+    assert is_scalar_sparse_matrix(hh_circuit, numqubits, id_only) is True
+
+    # NOTE:
+    # The elements of the sparse matrix for the following circuit
+    # is actually 1.0000000000000002+0.0j.
+    h1 = H(1)
+    xhzh_circuit = (x1, h1, z1, h1)
+    assert is_scalar_sparse_matrix(xhzh_circuit, numqubits, id_only) is True
+
+    id_only = True
+    assert is_scalar_sparse_matrix(xhzh_circuit, numqubits, id_only) is True
+    assert is_scalar_sparse_matrix(xyz_circuit, numqubits, id_only) is False
+    assert is_scalar_sparse_matrix(cnot_circuit, numqubits, id_only) is True
+    assert is_scalar_sparse_matrix(hh_circuit, numqubits, id_only) is True
+
+
+def test_is_degenerate():
+    (x, y, z, h) = create_gate_sequence()
+
+    gate_id = GateIdentity(x, y, z)
+    ids = {gate_id}
+
+    another_id = (z, y, x)
+    assert is_degenerate(ids, another_id) is True
+
+
+def test_is_reducible():
+    nqubits = 2
+    (x, y, z, h) = create_gate_sequence()
+
+    circuit = (x, y, y)
+    assert is_reducible(circuit, nqubits, 1, 3) is True
+
+    circuit = (x, y, x)
+    assert is_reducible(circuit, nqubits, 1, 3) is False
+
+    circuit = (x, y, y, x)
+    assert is_reducible(circuit, nqubits, 0, 4) is True
+
+    circuit = (x, y, y, x)
+    assert is_reducible(circuit, nqubits, 1, 3) is True
+
+    circuit = (x, y, z, y, y)
+    assert is_reducible(circuit, nqubits, 1, 5) is True
+
+
+def test_bfs_identity_search():
+    assert bfs_identity_search([], 1) == set()
+
+    (x, y, z, h) = create_gate_sequence()
+
+    gate_list = [x]
+    id_set = {GateIdentity(x, x)}
+    assert bfs_identity_search(gate_list, 1, max_depth=2) == id_set
+
+    # Set should not contain degenerate quantum circuits
+    gate_list = [x, y, z]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(x, y, z)}
+    assert bfs_identity_search(gate_list, 1) == id_set
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(x, y, z),
+                  GateIdentity(x, y, x, y),
+                  GateIdentity(x, z, x, z),
+                  GateIdentity(y, z, y, z)}
+    assert bfs_identity_search(gate_list, 1, max_depth=4) == id_set
+    assert bfs_identity_search(gate_list, 1, max_depth=5) == id_set
+
+    gate_list = [x, y, z, h]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h),
+                  GateIdentity(x, y, z),
+                  GateIdentity(x, y, x, y),
+                  GateIdentity(x, z, x, z),
+                  GateIdentity(x, h, z, h),
+                  GateIdentity(y, z, y, z),
+                  GateIdentity(y, h, y, h)}
+    assert bfs_identity_search(gate_list, 1) == id_set
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h)}
+    assert id_set == bfs_identity_search(gate_list, 1, max_depth=3,
+                                         identity_only=True)
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h),
+                  GateIdentity(x, y, z),
+                  GateIdentity(x, y, x, y),
+                  GateIdentity(x, z, x, z),
+                  GateIdentity(x, h, z, h),
+                  GateIdentity(y, z, y, z),
+                  GateIdentity(y, h, y, h),
+                  GateIdentity(x, y, h, x, h),
+                  GateIdentity(x, z, h, y, h),
+                  GateIdentity(y, z, h, z, h)}
+    assert bfs_identity_search(gate_list, 1, max_depth=5) == id_set
+
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(y, y),
+                  GateIdentity(z, z),
+                  GateIdentity(h, h),
+                  GateIdentity(x, h, z, h)}
+    assert id_set == bfs_identity_search(gate_list, 1, max_depth=4,
+                                         identity_only=True)
+
+    cnot = CNOT(1, 0)
+    gate_list = [x, cnot]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(cnot, cnot),
+                  GateIdentity(x, cnot, x, cnot)}
+    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set
+
+    cgate_x = CGate((1,), x)
+    gate_list = [x, cgate_x]
+    id_set = {GateIdentity(x, x),
+                  GateIdentity(cgate_x, cgate_x),
+                  GateIdentity(x, cgate_x, x, cgate_x)}
+    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set
+
+    cgate_z = CGate((0,), Z(1))
+    gate_list = [cnot, cgate_z, h]
+    id_set = {GateIdentity(h, h),
+                  GateIdentity(cgate_z, cgate_z),
+                  GateIdentity(cnot, cnot),
+                  GateIdentity(cnot, h, cgate_z, h)}
+    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set
+
+    s = PhaseGate(0)
+    t = TGate(0)
+    gate_list = [s, t]
+    id_set = {GateIdentity(s, s, s, s)}
+    assert bfs_identity_search(gate_list, 1, max_depth=4) == id_set
+
+
+def test_bfs_identity_search_xfail():
+    s = PhaseGate(0)
+    t = TGate(0)
+    gate_list = [Dagger(s), t]
+    id_set = {GateIdentity(Dagger(s), t, t)}
+    assert bfs_identity_search(gate_list, 1, max_depth=3) == id_set
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_innerproduct.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_innerproduct.py
new file mode 100644
index 0000000000000000000000000000000000000000..2632031f8a9a9ec65dfab6d834eb704a00b621d3
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_innerproduct.py
@@ -0,0 +1,71 @@
+from sympy.core.numbers import (I, Integer)
+
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.state import Bra, Ket, StateBase
+
+
+def test_innerproduct():
+    k = Ket('k')
+    b = Bra('b')
+    ip = InnerProduct(b, k)
+    assert isinstance(ip, InnerProduct)
+    assert ip.bra == b
+    assert ip.ket == k
+    assert b*k == InnerProduct(b, k)
+    assert k*(b*k)*b == k*InnerProduct(b, k)*b
+    assert InnerProduct(b, k).subs(b, Dagger(k)) == Dagger(k)*k
+
+
+def test_innerproduct_dagger():
+    k = Ket('k')
+    b = Bra('b')
+    ip = b*k
+    assert Dagger(ip) == Dagger(k)*Dagger(b)
+
+
+class FooState(StateBase):
+    pass
+
+
+class FooKet(Ket, FooState):
+
+    @classmethod
+    def dual_class(self):
+        return FooBra
+
+    def _eval_innerproduct_FooBra(self, bra):
+        return Integer(1)
+
+    def _eval_innerproduct_BarBra(self, bra):
+        return I
+
+
+class FooBra(Bra, FooState):
+    @classmethod
+    def dual_class(self):
+        return FooKet
+
+
+class BarState(StateBase):
+    pass
+
+
+class BarKet(Ket, BarState):
+    @classmethod
+    def dual_class(self):
+        return BarBra
+
+
+class BarBra(Bra, BarState):
+    @classmethod
+    def dual_class(self):
+        return BarKet
+
+
+def test_doit():
+    f = FooKet('foo')
+    b = BarBra('bar')
+    assert InnerProduct(b, f).doit() == I
+    assert InnerProduct(Dagger(f), Dagger(b)).doit() == -I
+    assert InnerProduct(Dagger(f), f).doit() == Integer(1)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_kind.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_kind.py
new file mode 100644
index 0000000000000000000000000000000000000000..e50467db4c2d9bd8e19f4ea883c26bd5ac5bc8d8
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_kind.py
@@ -0,0 +1,75 @@
+"""Tests for sympy.physics.quantum.kind."""
+
+from sympy.core.kind import NumberKind, UndefinedKind
+from sympy.core.symbol import symbols
+
+from sympy.physics.quantum.kind import (
+    OperatorKind, KetKind, BraKind
+)
+from sympy.physics.quantum.anticommutator import AntiCommutator
+from sympy.physics.quantum.commutator import Commutator
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.operator import Operator
+from sympy.physics.quantum.state import Ket, Bra
+from sympy.physics.quantum.tensorproduct import TensorProduct
+
+k = Ket('k')
+b = Bra('k')
+A = Operator('A')
+B = Operator('B')
+x, y, z = symbols('x y z', integer=True)
+
+def test_bra_ket():
+    assert k.kind == KetKind
+    assert b.kind == BraKind
+    assert (b*k).kind == NumberKind # inner product
+    assert (x*k).kind == KetKind
+    assert (x*b).kind == BraKind
+
+
+def test_operator_kind():
+    assert A.kind == OperatorKind
+    assert (A*B).kind == OperatorKind
+    assert (x*A).kind == OperatorKind
+    assert (x*A*B).kind == OperatorKind
+    assert (x*k*b).kind == OperatorKind # outer product
+
+
+def test_undefind_kind():
+    # Because of limitations in the kind dispatcher API, we are currently
+    # unable to have OperatorKind*KetKind -> KetKind (and similar for bras).
+    assert (A*k).kind == UndefinedKind
+    assert (b*A).kind == UndefinedKind
+    assert (x*b*A*k).kind == UndefinedKind
+
+
+def test_dagger_kind():
+    assert Dagger(k).kind == BraKind
+    assert Dagger(b).kind == KetKind
+    assert Dagger(A).kind == OperatorKind
+
+
+def test_commutator_kind():
+    assert Commutator(A, B).kind == OperatorKind
+    assert Commutator(A, x*B).kind == OperatorKind
+    assert Commutator(x*A, B).kind == OperatorKind
+    assert Commutator(x*A, x*B).kind == OperatorKind
+
+
+def test_anticommutator_kind():
+    assert AntiCommutator(A, B).kind == OperatorKind
+    assert AntiCommutator(A, x*B).kind == OperatorKind
+    assert AntiCommutator(x*A, B).kind == OperatorKind
+    assert AntiCommutator(x*A, x*B).kind == OperatorKind
+
+
+def test_tensorproduct_kind():
+    assert TensorProduct(k,k).kind == KetKind
+    assert TensorProduct(b,b).kind == BraKind
+    assert TensorProduct(x*k,y*k).kind == KetKind
+    assert TensorProduct(x*b,y*b).kind == BraKind
+    assert TensorProduct(x*b*k, y*b*k).kind == NumberKind
+    assert TensorProduct(x*k*b, y*k*b).kind == OperatorKind
+    assert TensorProduct(A, B).kind == OperatorKind
+    assert TensorProduct(A, x*B).kind == OperatorKind
+    assert TensorProduct(x*A, B).kind == OperatorKind
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_matrixutils.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_matrixutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d4fa8a0a2a4374d200473fa03c68fc453262a4c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_matrixutils.py
@@ -0,0 +1,136 @@
+from sympy.core.random import randint
+
+from sympy.core.numbers import Integer
+from sympy.matrices.dense import (Matrix, ones, zeros)
+
+from sympy.physics.quantum.matrixutils import (
+    to_sympy, to_numpy, to_scipy_sparse, matrix_tensor_product,
+    matrix_to_zero, matrix_zeros, numpy_ndarray, scipy_sparse_matrix
+)
+
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+
+m = Matrix([[1, 2], [3, 4]])
+
+
+def test_sympy_to_sympy():
+    assert to_sympy(m) == m
+
+
+def test_matrix_to_zero():
+    assert matrix_to_zero(m) == m
+    assert matrix_to_zero(Matrix([[0, 0], [0, 0]])) == Integer(0)
+
+np = import_module('numpy')
+
+
+def test_to_numpy():
+    if not np:
+        skip("numpy not installed.")
+
+    result = np.array([[1, 2], [3, 4]], dtype='complex')
+    assert (to_numpy(m) == result).all()
+
+
+def test_matrix_tensor_product():
+    if not np:
+        skip("numpy not installed.")
+
+    l1 = zeros(4)
+    for i in range(16):
+        l1[i] = 2**i
+    l2 = zeros(4)
+    for i in range(16):
+        l2[i] = i
+    l3 = zeros(2)
+    for i in range(4):
+        l3[i] = i
+    vec = Matrix([1, 2, 3])
+
+    #test for Matrix known 4x4 matrices
+    numpyl1 = np.array(l1.tolist())
+    numpyl2 = np.array(l2.tolist())
+    numpy_product = np.kron(numpyl1, numpyl2)
+    args = [l1, l2]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+    numpy_product = np.kron(numpyl2, numpyl1)
+    args = [l2, l1]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+    #test for other known matrix of different dimensions
+    numpyl2 = np.array(l3.tolist())
+    numpy_product = np.kron(numpyl1, numpyl2)
+    args = [l1, l3]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+    numpy_product = np.kron(numpyl2, numpyl1)
+    args = [l3, l1]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+    #test for non square matrix
+    numpyl2 = np.array(vec.tolist())
+    numpy_product = np.kron(numpyl1, numpyl2)
+    args = [l1, vec]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+    numpy_product = np.kron(numpyl2, numpyl1)
+    args = [vec, l1]
+    sympy_product = matrix_tensor_product(*args)
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+    #test for random matrix with random values that are floats
+    random_matrix1 = np.random.rand(randint(1, 5), randint(1, 5))
+    random_matrix2 = np.random.rand(randint(1, 5), randint(1, 5))
+    numpy_product = np.kron(random_matrix1, random_matrix2)
+    args = [Matrix(random_matrix1.tolist()), Matrix(random_matrix2.tolist())]
+    sympy_product = matrix_tensor_product(*args)
+    assert not (sympy_product - Matrix(numpy_product.tolist())).tolist() > \
+        (ones(sympy_product.rows, sympy_product.cols)*epsilon).tolist()
+
+    #test for three matrix kronecker
+    sympy_product = matrix_tensor_product(l1, vec, l2)
+
+    numpy_product = np.kron(l1, np.kron(vec, l2))
+    assert numpy_product.tolist() == sympy_product.tolist()
+
+
+scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
+
+
+def test_to_scipy_sparse():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+    else:
+        sparse = scipy.sparse
+
+    result = sparse.csr_matrix([[1, 2], [3, 4]], dtype='complex')
+    assert np.linalg.norm((to_scipy_sparse(m) - result).todense()) == 0.0
+
+epsilon = .000001
+
+
+def test_matrix_zeros_sympy():
+    sym = matrix_zeros(4, 4, format='sympy')
+    assert isinstance(sym, Matrix)
+
+def test_matrix_zeros_numpy():
+    if not np:
+        skip("numpy not installed.")
+
+    num = matrix_zeros(4, 4, format='numpy')
+    assert isinstance(num, numpy_ndarray)
+
+def test_matrix_zeros_scipy():
+    if not np:
+        skip("numpy not installed.")
+    if not scipy:
+        skip("scipy not installed.")
+
+    sci = matrix_zeros(4, 4, format='scipy.sparse')
+    assert isinstance(sci, scipy_sparse_matrix)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operator.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operator.py
new file mode 100644
index 0000000000000000000000000000000000000000..100cacd9a800f7c4435b93672ef77877a3a99e5e
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operator.py
@@ -0,0 +1,269 @@
+from sympy.core.function import (Derivative, Function, diff)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (Integer, pi)
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.trigonometric import sin
+from sympy.physics.quantum.qexpr import QExpr
+from sympy.physics.quantum.dagger import Dagger
+from sympy.physics.quantum.hilbert import HilbertSpace
+from sympy.physics.quantum.operator import (Operator, UnitaryOperator,
+                                            HermitianOperator, OuterProduct,
+                                            DifferentialOperator,
+                                            IdentityOperator)
+from sympy.physics.quantum.state import Ket, Bra, Wavefunction
+from sympy.physics.quantum.qapply import qapply
+from sympy.physics.quantum.represent import represent
+from sympy.physics.quantum.spin import JzKet, JzBra
+from sympy.physics.quantum.trace import Tr
+from sympy.matrices import eye
+
+from sympy.testing.pytest import warns_deprecated_sympy
+
+
+class CustomKet(Ket):
+    @classmethod
+    def default_args(self):
+        return ("t",)
+
+
+class CustomOp(HermitianOperator):
+    @classmethod
+    def default_args(self):
+        return ("T",)
+
+t_ket = CustomKet()
+t_op = CustomOp()
+
+
+def test_operator():
+    A = Operator('A')
+    B = Operator('B')
+    C = Operator('C')
+
+    assert isinstance(A, Operator)
+    assert isinstance(A, QExpr)
+
+    assert A.label == (Symbol('A'),)
+    assert A.is_commutative is False
+    assert A.hilbert_space == HilbertSpace()
+
+    assert A*B != B*A
+
+    assert (A*(B + C)).expand() == A*B + A*C
+    assert ((A + B)**2).expand() == A**2 + A*B + B*A + B**2
+
+    assert t_op.label[0] == Symbol(t_op.default_args()[0])
+
+    assert Operator() == Operator("O")
+    with warns_deprecated_sympy():
+        assert A*IdentityOperator() == A
+
+
+def test_operator_inv():
+    A = Operator('A')
+    assert A*A.inv() == 1
+    assert A.inv()*A == 1
+
+
+def test_hermitian():
+    H = HermitianOperator('H')
+
+    assert isinstance(H, HermitianOperator)
+    assert isinstance(H, Operator)
+
+    assert Dagger(H) == H
+    assert H.inv() != H
+    assert H.is_commutative is False
+    assert Dagger(H).is_commutative is False
+
+
+def test_unitary():
+    U = UnitaryOperator('U')
+
+    assert isinstance(U, UnitaryOperator)
+    assert isinstance(U, Operator)
+
+    assert U.inv() == Dagger(U)
+    assert U*Dagger(U) == 1
+    assert Dagger(U)*U == 1
+    assert U.is_commutative is False
+    assert Dagger(U).is_commutative is False
+
+
+def test_identity():
+    with warns_deprecated_sympy():
+        I = IdentityOperator()
+        O = Operator('O')
+        x = Symbol("x")
+        three = sympify(3)
+
+        assert isinstance(I, IdentityOperator)
+        assert isinstance(I, Operator)
+
+        assert I * O == O
+        assert O * I == O
+        assert I * Dagger(O) == Dagger(O)
+        assert Dagger(O) * I == Dagger(O)
+        assert isinstance(I * I, IdentityOperator)
+        assert three * I == three
+        assert I * x == x
+        assert I.inv() == I
+        assert Dagger(I) == I
+        assert qapply(I * O) == O
+        assert qapply(O * I) == O
+
+        for n in [2, 3, 5]:
+            assert represent(IdentityOperator(n)) == eye(n)
+
+
+def test_outer_product():
+    k = Ket('k')
+    b = Bra('b')
+    op = OuterProduct(k, b)
+
+    assert isinstance(op, OuterProduct)
+    assert isinstance(op, Operator)
+
+    assert op.ket == k
+    assert op.bra == b
+    assert op.label == (k, b)
+    assert op.is_commutative is False
+
+    op = k*b
+
+    assert isinstance(op, OuterProduct)
+    assert isinstance(op, Operator)
+
+    assert op.ket == k
+    assert op.bra == b
+    assert op.label == (k, b)
+    assert op.is_commutative is False
+
+    op = 2*k*b
+
+    assert op == Mul(Integer(2), k, b)
+
+    op = 2*(k*b)
+
+    assert op == Mul(Integer(2), OuterProduct(k, b))
+
+    assert Dagger(k*b) == OuterProduct(Dagger(b), Dagger(k))
+    assert Dagger(k*b).is_commutative is False
+
+    #test the _eval_trace
+    assert Tr(OuterProduct(JzKet(1, 1), JzBra(1, 1))).doit() == 1
+
+    # test scaled kets and bras
+    assert OuterProduct(2 * k, b) == 2 * OuterProduct(k, b)
+    assert OuterProduct(k, 2 * b) == 2 * OuterProduct(k, b)
+
+    # test sums of kets and bras
+    k1, k2 = Ket('k1'), Ket('k2')
+    b1, b2 = Bra('b1'), Bra('b2')
+    assert (OuterProduct(k1 + k2, b1) ==
+            OuterProduct(k1, b1) + OuterProduct(k2, b1))
+    assert (OuterProduct(k1, b1 + b2) ==
+            OuterProduct(k1, b1) + OuterProduct(k1, b2))
+    assert (OuterProduct(1 * k1 + 2 * k2, 3 * b1 + 4 * b2) ==
+            3 * OuterProduct(k1, b1) +
+            4 * OuterProduct(k1, b2) +
+            6 * OuterProduct(k2, b1) +
+            8 * OuterProduct(k2, b2))
+
+
+def test_operator_dagger():
+    A = Operator('A')
+    B = Operator('B')
+    assert Dagger(A*B) == Dagger(B)*Dagger(A)
+    assert Dagger(A + B) == Dagger(A) + Dagger(B)
+    assert Dagger(A**2) == Dagger(A)**2
+
+
+def test_differential_operator():
+    x = Symbol('x')
+    f = Function('f')
+    d = DifferentialOperator(Derivative(f(x), x), f(x))
+    g = Wavefunction(x**2, x)
+    assert qapply(d*g) == Wavefunction(2*x, x)
+    assert d.expr == Derivative(f(x), x)
+    assert d.function == f(x)
+    assert d.variables == (x,)
+    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 2), f(x))
+
+    d = DifferentialOperator(Derivative(f(x), x, 2), f(x))
+    g = Wavefunction(x**3, x)
+    assert qapply(d*g) == Wavefunction(6*x, x)
+    assert d.expr == Derivative(f(x), x, 2)
+    assert d.function == f(x)
+    assert d.variables == (x,)
+    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 3), f(x))
+
+    d = DifferentialOperator(1/x*Derivative(f(x), x), f(x))
+    assert d.expr == 1/x*Derivative(f(x), x)
+    assert d.function == f(x)
+    assert d.variables == (x,)
+    assert diff(d, x) == \
+        DifferentialOperator(Derivative(1/x*Derivative(f(x), x), x), f(x))
+    assert qapply(d*g) == Wavefunction(3*x, x)
+
+    # 2D cartesian Laplacian
+    y = Symbol('y')
+    d = DifferentialOperator(Derivative(f(x, y), x, 2) +
+                             Derivative(f(x, y), y, 2), f(x, y))
+    w = Wavefunction(x**3*y**2 + y**3*x**2, x, y)
+    assert d.expr == Derivative(f(x, y), x, 2) + Derivative(f(x, y), y, 2)
+    assert d.function == f(x, y)
+    assert d.variables == (x, y)
+    assert diff(d, x) == \
+        DifferentialOperator(Derivative(d.expr, x), f(x, y))
+    assert diff(d, y) == \
+        DifferentialOperator(Derivative(d.expr, y), f(x, y))
+    assert qapply(d*w) == Wavefunction(2*x**3 + 6*x*y**2 + 6*x**2*y + 2*y**3,
+                                       x, y)
+
+    # 2D polar Laplacian (th = theta)
+    r, th = symbols('r th')
+    d = DifferentialOperator(1/r*Derivative(r*Derivative(f(r, th), r), r) +
+                             1/(r**2)*Derivative(f(r, th), th, 2), f(r, th))
+    w = Wavefunction(r**2*sin(th), r, (th, 0, pi))
+    assert d.expr == \
+        1/r*Derivative(r*Derivative(f(r, th), r), r) + \
+        1/(r**2)*Derivative(f(r, th), th, 2)
+    assert d.function == f(r, th)
+    assert d.variables == (r, th)
+    assert diff(d, r) == \
+        DifferentialOperator(Derivative(d.expr, r), f(r, th))
+    assert diff(d, th) == \
+        DifferentialOperator(Derivative(d.expr, th), f(r, th))
+    assert qapply(d*w) == Wavefunction(3*sin(th), r, (th, 0, pi))
+
+
+def test_eval_power():
+    from sympy.core import Pow
+    from sympy.core.expr import unchanged
+    O = Operator('O')
+    U = UnitaryOperator('U')
+    H = HermitianOperator('H')
+    assert O**-1 == O.inv() # same as doc test
+    assert U**-1 == U.inv()
+    assert H**-1 == H.inv()
+    x = symbols("x", commutative = True)
+    assert unchanged(Pow, H, x) # verify Pow(H,x)=="X^n"
+    assert H**x == Pow(H, x)
+    assert Pow(H,x) == Pow(H, x, evaluate=False) # Just check
+    from sympy.physics.quantum.gate import XGate
+    X = XGate(0) # is hermitian and unitary
+    assert unchanged(Pow, X, x) # verify Pow(X,x)=="X^x"
+    assert X**x == Pow(X, x)
+    assert Pow(X, x, evaluate=False) == Pow(X, x) # Just check
+    n = symbols("n", integer=True, even=True)
+    assert X**n == 1
+    n = symbols("n", integer=True, odd=True)
+    assert X**n == X
+    n = symbols("n", integer=True)
+    assert unchanged(Pow, X, n) # verify Pow(X,n)=="X^n"
+    assert X**n == Pow(X, n)
+    assert Pow(X, n, evaluate=False)==Pow(X, n) # Just check
+    assert X**4 == 1
+    assert X**7 == X
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operatorordering.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operatorordering.py
new file mode 100644
index 0000000000000000000000000000000000000000..f5255d555d1582b694dfe4ed681d894136ea0b70
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operatorordering.py
@@ -0,0 +1,50 @@
+from sympy.physics.quantum import Dagger
+from sympy.physics.quantum.boson import BosonOp
+from sympy.physics.quantum.fermion import FermionOp
+from sympy.physics.quantum.operatorordering import (normal_order,
+                                                 normal_ordered_form)
+
+
+def test_normal_order():
+    a = BosonOp('a')
+
+    c = FermionOp('c')
+
+    assert normal_order(a * Dagger(a)) == Dagger(a) * a
+    assert normal_order(Dagger(a) * a) == Dagger(a) * a
+    assert normal_order(a * Dagger(a) ** 2) == Dagger(a) ** 2 * a
+
+    assert normal_order(c * Dagger(c)) == - Dagger(c) * c
+    assert normal_order(Dagger(c) * c) == Dagger(c) * c
+    assert normal_order(c * Dagger(c) ** 2) == Dagger(c) ** 2 * c
+
+
+def test_normal_ordered_form():
+    a = BosonOp('a')
+    b = BosonOp('b')
+
+    c = FermionOp('c')
+    d = FermionOp('d')
+
+    assert normal_ordered_form(Dagger(a) * a) == Dagger(a) * a
+    assert normal_ordered_form(a * Dagger(a)) == 1 + Dagger(a) * a
+    assert normal_ordered_form(a ** 2 * Dagger(a)) == \
+        2 * a + Dagger(a) * a ** 2
+    assert normal_ordered_form(a ** 3 * Dagger(a)) == \
+        3 * a ** 2 + Dagger(a) * a ** 3
+
+    assert normal_ordered_form(Dagger(c) * c) == Dagger(c) * c
+    assert normal_ordered_form(c * Dagger(c)) == 1 - Dagger(c) * c
+    assert normal_ordered_form(c ** 2 * Dagger(c)) == Dagger(c) * c ** 2
+    assert normal_ordered_form(c ** 3 * Dagger(c)) == \
+        c ** 2 - Dagger(c) * c ** 3
+
+    assert normal_ordered_form(a * Dagger(b), True) == Dagger(b) * a
+    assert normal_ordered_form(Dagger(a) * b, True) == Dagger(a) * b
+    assert normal_ordered_form(b * a, True) == a * b
+    assert normal_ordered_form(Dagger(b) * Dagger(a), True) == Dagger(a) * Dagger(b)
+
+    assert normal_ordered_form(c * Dagger(d), True) == -Dagger(d) * c
+    assert normal_ordered_form(Dagger(c) * d, True) == Dagger(c) * d
+    assert normal_ordered_form(d * c, True) == -c * d
+    assert normal_ordered_form(Dagger(d) * Dagger(c), True) == -Dagger(c) * Dagger(d)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operatorset.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operatorset.py
new file mode 100644
index 0000000000000000000000000000000000000000..fff038bb12a7e6aa100ac00b0e145dc323a77e4d
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_operatorset.py
@@ -0,0 +1,68 @@
+from sympy.core.singleton import S
+
+from sympy.physics.quantum.operatorset import (
+    operators_to_state, state_to_operators
+)
+
+from sympy.physics.quantum.cartesian import (
+    XOp, XKet, PxOp, PxKet, XBra, PxBra
+)
+
+from sympy.physics.quantum.state import Ket, Bra
+from sympy.physics.quantum.operator import Operator
+from sympy.physics.quantum.spin import (
+    JxKet, JyKet, JzKet, JxBra, JyBra, JzBra,
+    JxOp, JyOp, JzOp, J2Op
+)
+
+from sympy.testing.pytest import raises
+
+
+def test_spin():
+    assert operators_to_state({J2Op, JxOp}) == JxKet
+    assert operators_to_state({J2Op, JyOp}) == JyKet
+    assert operators_to_state({J2Op, JzOp}) == JzKet
+    assert operators_to_state({J2Op(), JxOp()}) == JxKet
+    assert operators_to_state({J2Op(), JyOp()}) == JyKet
+    assert operators_to_state({J2Op(), JzOp()}) == JzKet
+
+    assert state_to_operators(JxKet) == {J2Op, JxOp}
+    assert state_to_operators(JyKet) == {J2Op, JyOp}
+    assert state_to_operators(JzKet) == {J2Op, JzOp}
+    assert state_to_operators(JxBra) == {J2Op, JxOp}
+    assert state_to_operators(JyBra) == {J2Op, JyOp}
+    assert state_to_operators(JzBra) == {J2Op, JzOp}
+
+    assert state_to_operators(JxKet(S.Half, S.Half)) == {J2Op(), JxOp()}
+    assert state_to_operators(JyKet(S.Half, S.Half)) == {J2Op(), JyOp()}
+    assert state_to_operators(JzKet(S.Half, S.Half)) == {J2Op(), JzOp()}
+    assert state_to_operators(JxBra(S.Half, S.Half)) == {J2Op(), JxOp()}
+    assert state_to_operators(JyBra(S.Half, S.Half)) == {J2Op(), JyOp()}
+    assert state_to_operators(JzBra(S.Half, S.Half)) == {J2Op(), JzOp()}
+
+
+def test_op_to_state():
+    assert operators_to_state(XOp) == XKet()
+    assert operators_to_state(PxOp) == PxKet()
+    assert operators_to_state(Operator) == Ket()
+
+    assert state_to_operators(operators_to_state(XOp("Q"))) == XOp("Q")
+    assert state_to_operators(operators_to_state(XOp())) == XOp()
+
+    raises(NotImplementedError, lambda: operators_to_state(XKet))
+
+
+def test_state_to_op():
+    assert state_to_operators(XKet) == XOp()
+    assert state_to_operators(PxKet) == PxOp()
+    assert state_to_operators(XBra) == XOp()
+    assert state_to_operators(PxBra) == PxOp()
+    assert state_to_operators(Ket) == Operator()
+    assert state_to_operators(Bra) == Operator()
+
+    assert operators_to_state(state_to_operators(XKet("test"))) == XKet("test")
+    assert operators_to_state(state_to_operators(XBra("test"))) == XKet("test")
+    assert operators_to_state(state_to_operators(XKet())) == XKet()
+    assert operators_to_state(state_to_operators(XBra())) == XKet()
+
+    raises(NotImplementedError, lambda: state_to_operators(XOp))
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_pauli.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_pauli.py
new file mode 100644
index 0000000000000000000000000000000000000000..77bbed93ac5b4b49680be01aefa2f779b62fc7ee
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/tests/test_pauli.py
@@ -0,0 +1,159 @@
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.matrices.dense import Matrix
+from sympy.printing.latex import latex
+from sympy.physics.quantum import (Dagger, Commutator, AntiCommutator, qapply,
+                                   Operator, represent)
+from sympy.physics.quantum.pauli import (SigmaOpBase, SigmaX, SigmaY, SigmaZ,
+                                         SigmaMinus, SigmaPlus,
+                                         qsimplify_pauli)
+from sympy.physics.quantum.pauli import SigmaZKet, SigmaZBra
+from sympy.testing.pytest import raises
+
+
+sx, sy, sz = SigmaX(), SigmaY(), SigmaZ()
+sx1, sy1, sz1 = SigmaX(1), SigmaY(1), SigmaZ(1)
+sx2, sy2, sz2 = SigmaX(2), SigmaY(2), SigmaZ(2)
+
+sm, sp = SigmaMinus(), SigmaPlus()
+sm1, sp1 = SigmaMinus(1), SigmaPlus(1)
+A, B = Operator("A"), Operator("B")
+
+
+def test_pauli_operators_types():
+
+    assert isinstance(sx, SigmaOpBase) and isinstance(sx, SigmaX)
+    assert isinstance(sy, SigmaOpBase) and isinstance(sy, SigmaY)
+    assert isinstance(sz, SigmaOpBase) and isinstance(sz, SigmaZ)
+    assert isinstance(sm, SigmaOpBase) and isinstance(sm, SigmaMinus)
+    assert isinstance(sp, SigmaOpBase) and isinstance(sp, SigmaPlus)
+
+
+def test_pauli_operators_commutator():
+
+    assert Commutator(sx, sy).doit() == 2 * I * sz
+    assert Commutator(sy, sz).doit() == 2 * I * sx
+    assert Commutator(sz, sx).doit() == 2 * I * sy
+
+
+def test_pauli_operators_commutator_with_labels():
+
+    assert Commutator(sx1, sy1).doit() == 2 * I * sz1
+    assert Commutator(sy1, sz1).doit() == 2 * I * sx1
+    assert Commutator(sz1, sx1).doit() == 2 * I * sy1
+
+    assert Commutator(sx2, sy2).doit() == 2 * I * sz2
+    assert Commutator(sy2, sz2).doit() == 2 * I * sx2
+    assert Commutator(sz2, sx2).doit() == 2 * I * sy2
+
+    assert Commutator(sx1, sy2).doit() == 0
+    assert Commutator(sy1, sz2).doit() == 0
+    assert Commutator(sz1, sx2).doit() == 0
+
+
+def test_pauli_operators_anticommutator():
+
+    assert AntiCommutator(sy, sz).doit() == 0
+    assert AntiCommutator(sz, sx).doit() == 0
+    assert AntiCommutator(sx, sm).doit() == 1
+    assert AntiCommutator(sx, sp).doit() == 1
+
+
+def test_pauli_operators_adjoint():
+
+    assert Dagger(sx) == sx
+    assert Dagger(sy) == sy
+    assert Dagger(sz) == sz
+
+
+def test_pauli_operators_adjoint_with_labels():
+
+    assert Dagger(sx1) == sx1
+    assert Dagger(sy1) == sy1
+    assert Dagger(sz1) == sz1
+
+    assert Dagger(sx1) != sx2
+    assert Dagger(sy1) != sy2
+    assert Dagger(sz1) != sz2
+
+
+def test_pauli_operators_multiplication():
+
+    assert qsimplify_pauli(sx * sx) == 1
+    assert qsimplify_pauli(sy * sy) == 1
+    assert qsimplify_pauli(sz * sz) == 1
+
+    assert qsimplify_pauli(sx * sy) == I * sz
+    assert qsimplify_pauli(sy * sz) == I * sx
+    assert qsimplify_pauli(sz * sx) == I * sy
+
+    assert qsimplify_pauli(sy * sx) == - I * sz
+    assert qsimplify_pauli(sz * sy) == - I * sx
+    assert qsimplify_pauli(sx * sz) == - I * sy
+
+
+def test_pauli_operators_multiplication_with_labels():
+
+    assert qsimplify_pauli(sx1 * sx1) == 1
+    assert qsimplify_pauli(sy1 * sy1) == 1
+    assert qsimplify_pauli(sz1 * sz1) == 1
+
+    assert isinstance(sx1 * sx2, Mul)
+    assert isinstance(sy1 * sy2, Mul)
+    assert isinstance(sz1 * sz2, Mul)
+
+    assert qsimplify_pauli(sx1 * sy1 * sx2 * sy2) == - sz1 * sz2
+    assert qsimplify_pauli(sy1 * sz1 * sz2 * sx2) == - sx1 * sy2
+
+
+def test_pauli_states():
+    sx, sz = SigmaX(), SigmaZ()
+
+    up = SigmaZKet(0)
+    down = SigmaZKet(1)
+
+    assert qapply(sx * up) == down
+    assert qapply(sx * down) == up
+    assert qapply(sz * up) == up
+    assert qapply(sz * down) == - down
+
+    up = SigmaZBra(0)
+    down = SigmaZBra(1)
+
+    assert qapply(up * sx, dagger=True) == down
+    assert qapply(down * sx, dagger=True) == up
+    assert qapply(up * sz, dagger=True) == up
+    assert qapply(down * sz, dagger=True) == - down
+
+    assert Dagger(SigmaZKet(0)) == SigmaZBra(0)
+    assert Dagger(SigmaZBra(1)) == SigmaZKet(1)
+    raises(ValueError, lambda: SigmaZBra(2))
+    raises(ValueError, lambda: SigmaZKet(2))
+
+
+def test_use_name():
+    assert sm.use_name is False
+    assert sm1.use_name is True
+    assert sx.use_name is False
+    assert sx1.use_name is True
+
+
+def test_printing():
+    assert latex(sx) == r'{\sigma_x}'
+    assert latex(sx1) == r'{\sigma_x^{(1)}}'
+    assert latex(sy) == r'{\sigma_y}'
+    assert latex(sy1) == r'{\sigma_y^{(1)}}'
+    assert latex(sz) == r'{\sigma_z}'
+    assert latex(sz1) == r'{\sigma_z^{(1)}}'
+    assert latex(sm) == r'{\sigma_-}'
+    assert latex(sm1) == r'{\sigma_-^{(1)}}'
+    assert latex(sp) == r'{\sigma_+}'
+    assert latex(sp1) == r'{\sigma_+^{(1)}}'
+
+
+def test_represent():
+    assert represent(sx) == Matrix([[0, 1], [1, 0]])
+    assert represent(sy) == Matrix([[0, -I], [I, 0]])
+    assert represent(sz) == Matrix([[1, 0], [0, -1]])
+    assert represent(sm) == Matrix([[0, 0], [1, 0]])
+    assert represent(sp) == Matrix([[0, 1], [0, 0]])
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/trace.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/trace.py
new file mode 100644
index 0000000000000000000000000000000000000000..03ab18f78a1bfcf5bfcd679f00eac8685144fd8c
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/trace.py
@@ -0,0 +1,230 @@
+from sympy.core.add import Add
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.power import Pow
+from sympy.core.sorting import default_sort_key
+from sympy.core.sympify import sympify
+from sympy.matrices import Matrix
+
+
+def _is_scalar(e):
+    """ Helper method used in Tr"""
+
+    # sympify to set proper attributes
+    e = sympify(e)
+    if isinstance(e, Expr):
+        if (e.is_Integer or e.is_Float or
+            e.is_Rational or e.is_Number or
+            (e.is_Symbol and e.is_commutative)
+                ):
+            return True
+
+    return False
+
+
+def _cycle_permute(l):
+    """ Cyclic permutations based on canonical ordering
+
+    Explanation
+    ===========
+
+    This method does the sort based ascii values while
+    a better approach would be to used lexicographic sort.
+
+    TODO: Handle condition such as symbols have subscripts/superscripts
+    in case of lexicographic sort
+
+    """
+
+    if len(l) == 1:
+        return l
+
+    min_item = min(l, key=default_sort_key)
+    indices = [i for i, x in enumerate(l) if x == min_item]
+
+    le = list(l)
+    le.extend(l)  # duplicate and extend string for easy processing
+
+    # adding the first min_item index back for easier looping
+    indices.append(len(l) + indices[0])
+
+    # create sublist of items with first item as min_item and last_item
+    # in each of the sublist is item just before the next occurrence of
+    # minitem in the cycle formed.
+    sublist = [[le[indices[i]:indices[i + 1]]] for i in
+               range(len(indices) - 1)]
+
+    # we do comparison of strings by comparing elements
+    # in each sublist
+    idx = sublist.index(min(sublist))
+    ordered_l = le[indices[idx]:indices[idx] + len(l)]
+
+    return ordered_l
+
+
+def _rearrange_args(l):
+    """ this just moves the last arg to first position
+     to enable expansion of args
+     A,B,A ==> A**2,B
+    """
+    if len(l) == 1:
+        return l
+
+    x = list(l[-1:])
+    x.extend(l[0:-1])
+    return Mul(*x).args
+
+
+class Tr(Expr):
+    """ Generic Trace operation than can trace over:
+
+    a) SymPy matrix
+    b) operators
+    c) outer products
+
+    Parameters
+    ==========
+    o : operator, matrix, expr
+    i : tuple/list indices (optional)
+
+    Examples
+    ========
+
+    # TODO: Need to handle printing
+
+    a) Trace(A+B) = Tr(A) + Tr(B)
+    b) Trace(scalar*Operator) = scalar*Trace(Operator)
+
+    >>> from sympy.physics.quantum.trace import Tr
+    >>> from sympy import symbols, Matrix
+    >>> a, b = symbols('a b', commutative=True)
+    >>> A, B = symbols('A B', commutative=False)
+    >>> Tr(a*A,[2])
+    a*Tr(A)
+    >>> m = Matrix([[1,2],[1,1]])
+    >>> Tr(m)
+    2
+
+    """
+    def __new__(cls, *args):
+        """ Construct a Trace object.
+
+        Parameters
+        ==========
+        args = SymPy expression
+        indices = tuple/list if indices, optional
+
+        """
+
+        # expect no indices,int or a tuple/list/Tuple
+        if (len(args) == 2):
+            if not isinstance(args[1], (list, Tuple, tuple)):
+                indices = Tuple(args[1])
+            else:
+                indices = Tuple(*args[1])
+
+            expr = args[0]
+        elif (len(args) == 1):
+            indices = Tuple()
+            expr = args[0]
+        else:
+            raise ValueError("Arguments to Tr should be of form "
+                             "(expr[, [indices]])")
+
+        if isinstance(expr, Matrix):
+            return expr.trace()
+        elif hasattr(expr, 'trace') and callable(expr.trace):
+            #for any objects that have trace() defined e.g numpy
+            return expr.trace()
+        elif isinstance(expr, Add):
+            return Add(*[Tr(arg, indices) for arg in expr.args])
+        elif isinstance(expr, Mul):
+            c_part, nc_part = expr.args_cnc()
+            if len(nc_part) == 0:
+                return Mul(*c_part)
+            else:
+                obj = Expr.__new__(cls, Mul(*nc_part), indices )
+                #this check is needed to prevent cached instances
+                #being returned even if len(c_part)==0
+                return Mul(*c_part)*obj if len(c_part) > 0 else obj
+        elif isinstance(expr, Pow):
+            if (_is_scalar(expr.args[0]) and
+                    _is_scalar(expr.args[1])):
+                return expr
+            else:
+                return Expr.__new__(cls, expr, indices)
+        else:
+            if (_is_scalar(expr)):
+                return expr
+
+            return Expr.__new__(cls, expr, indices)
+
+    @property
+    def kind(self):
+        expr = self.args[0]
+        expr_kind = expr.kind
+        return expr_kind.element_kind
+
+    def doit(self, **hints):
+        """ Perform the trace operation.
+
+        #TODO: Current version ignores the indices set for partial trace.
+
+        >>> from sympy.physics.quantum.trace import Tr
+        >>> from sympy.physics.quantum.operator import OuterProduct
+        >>> from sympy.physics.quantum.spin import JzKet, JzBra
+        >>> t = Tr(OuterProduct(JzKet(1,1), JzBra(1,1)))
+        >>> t.doit()
+        1
+
+        """
+        if hasattr(self.args[0], '_eval_trace'):
+            return self.args[0]._eval_trace(indices=self.args[1])
+
+        return self
+
+    @property
+    def is_number(self):
+        # TODO : improve this implementation
+        return True
+
+    #TODO: Review if the permute method is needed
+    # and if it needs to return a new instance
+    def permute(self, pos):
+        """ Permute the arguments cyclically.
+
+        Parameters
+        ==========
+
+        pos : integer, if positive, shift-right, else shift-left
+
+        Examples
+        ========
+
+        >>> from sympy.physics.quantum.trace import Tr
+        >>> from sympy import symbols
+        >>> A, B, C, D = symbols('A B C D', commutative=False)
+        >>> t = Tr(A*B*C*D)
+        >>> t.permute(2)
+        Tr(C*D*A*B)
+        >>> t.permute(-2)
+        Tr(C*D*A*B)
+
+        """
+        if pos > 0:
+            pos = pos % len(self.args[0].args)
+        else:
+            pos = -(abs(pos) % len(self.args[0].args))
+
+        args = list(self.args[0].args[-pos:] + self.args[0].args[0:-pos])
+
+        return Tr(Mul(*(args)))
+
+    def _hashable_content(self):
+        if isinstance(self.args[0], Mul):
+            args = _cycle_permute(_rearrange_args(self.args[0].args))
+        else:
+            args = [self.args[0]]
+
+        return tuple(args) + (self.args[1], )
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/transforms.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..dcbbcd9040b4f8f987375c2f903031610d6f9061
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/quantum/transforms.py
@@ -0,0 +1,291 @@
+"""Transforms that are always applied to quantum expressions.
+
+This module uses the kind and _constructor_postprocessor_mapping APIs
+to transform different combinations of Operators, Bras, and Kets into
+Inner/Outer/TensorProducts. These transformations are registered
+with the postprocessing API of core classes like `Mul` and `Pow` and
+are always applied to any expression involving Bras, Kets, and
+Operators. This API replaces the custom `__mul__` and `__pow__`
+methods of the quantum classes, which were found to be inconsistent.
+
+THIS IS EXPERIMENTAL.
+"""
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.multipledispatch.dispatcher import (
+    Dispatcher, ambiguity_register_error_ignore_dup
+)
+from sympy.utilities.misc import debug
+
+from sympy.physics.quantum.innerproduct import InnerProduct
+from sympy.physics.quantum.kind import KetKind, BraKind, OperatorKind
+from sympy.physics.quantum.operator import (
+    OuterProduct, IdentityOperator, Operator
+)
+from sympy.physics.quantum.state import BraBase, KetBase, StateBase
+from sympy.physics.quantum.tensorproduct import TensorProduct
+
+
+#-----------------------------------------------------------------------------
+# Multipledispatch based transformed for Mul and Pow
+#-----------------------------------------------------------------------------
+
+_transform_state_pair = Dispatcher('_transform_state_pair')
+"""Transform a pair of expression in a Mul to their canonical form.
+
+All functions that are registered with this dispatcher need to take
+two inputs and return either tuple of transformed outputs, or None if no
+transform is applied. The output tuple is inserted into the right place
+of the ``Mul`` that is being put into canonical form. It works something like
+the following:
+
+``Mul(a, b, c, d, e, f) -> Mul(*(_transform_state_pair(a, b) + (c, d, e, f))))``
+
+The transforms here are always applied when quantum objects are multiplied.
+
+THIS IS EXPERIMENTAL.
+
+However, users of ``sympy.physics.quantum`` can import this dispatcher and
+register their own transforms to control the canonical form of products
+of quantum expressions.
+"""
+
+@_transform_state_pair.register(Expr, Expr)
+def _transform_expr(a, b):
+    """Default transformer that does nothing for base types."""
+    return None
+
+
+# The identity times anything is the anything.
+_transform_state_pair.add(
+    (IdentityOperator, Expr),
+    lambda x, y: (y,),
+    on_ambiguity=ambiguity_register_error_ignore_dup
+)
+_transform_state_pair.add(
+    (Expr, IdentityOperator),
+    lambda x, y: (x,),
+    on_ambiguity=ambiguity_register_error_ignore_dup
+)
+_transform_state_pair.add(
+    (IdentityOperator, IdentityOperator),
+    lambda x, y: S.One,
+    on_ambiguity=ambiguity_register_error_ignore_dup
+)
+
+@_transform_state_pair.register(BraBase, KetBase)
+def _transform_bra_ket(a, b):
+    """Transform a bra*ket -> InnerProduct(bra, ket)."""
+    return (InnerProduct(a, b),)
+
+@_transform_state_pair.register(KetBase, BraBase)
+def _transform_ket_bra(a, b):
+    """Transform a keT*bra -> OuterProduct(ket, bra)."""
+    return (OuterProduct(a, b),)
+
+@_transform_state_pair.register(KetBase, KetBase)
+def _transform_ket_ket(a, b):
+    """Raise a TypeError if a user tries to multiply two kets.
+
+    Multiplication based on `*` is not a shorthand for tensor products.
+    """
+    raise TypeError(
+        'Multiplication of two kets is not allowed. Use TensorProduct instead.'
+    )
+
+@_transform_state_pair.register(BraBase, BraBase)
+def _transform_bra_bra(a, b):
+    """Raise a TypeError if a user tries to multiply two bras.
+
+    Multiplication based on `*` is not a shorthand for tensor products.
+    """
+    raise TypeError(
+        'Multiplication of two bras is not allowed. Use TensorProduct instead.'
+    )
+
+@_transform_state_pair.register(OuterProduct, KetBase)
+def _transform_op_ket(a, b):
+    return (InnerProduct(a.bra, b), a.ket)
+
+@_transform_state_pair.register(BraBase, OuterProduct)
+def _transform_bra_op(a, b):
+    return (InnerProduct(a, b.ket), b.bra)
+
+@_transform_state_pair.register(TensorProduct, KetBase)
+def _transform_tp_ket(a, b):
+    """Raise a TypeError if a user tries to multiply TensorProduct(*kets)*ket.
+
+    Multiplication based on `*` is not a shorthand for tensor products.
+    """
+    if a.kind == KetKind:
+        raise TypeError(
+            'Multiplication of TensorProduct(*kets)*ket is invalid.'
+        )
+
+@_transform_state_pair.register(KetBase, TensorProduct)
+def _transform_ket_tp(a, b):
+    """Raise a TypeError if a user tries to multiply ket*TensorProduct(*kets).
+
+    Multiplication based on `*` is not a shorthand for tensor products.
+    """
+    if b.kind == KetKind:
+        raise TypeError(
+            'Multiplication of ket*TensorProduct(*kets) is invalid.'
+        )
+
+@_transform_state_pair.register(TensorProduct, BraBase)
+def _transform_tp_bra(a, b):
+    """Raise a TypeError if a user tries to multiply TensorProduct(*bras)*bra.
+
+    Multiplication based on `*` is not a shorthand for tensor products.
+    """
+    if a.kind == BraKind:
+        raise TypeError(
+            'Multiplication of TensorProduct(*bras)*bra is invalid.'
+        )
+
+@_transform_state_pair.register(BraBase, TensorProduct)
+def _transform_bra_tp(a, b):
+    """Raise a TypeError if a user tries to multiply bra*TensorProduct(*bras).
+
+    Multiplication based on `*` is not a shorthand for tensor products.
+    """
+    if b.kind == BraKind:
+        raise TypeError(
+            'Multiplication of bra*TensorProduct(*bras) is invalid.'
+        )
+
+@_transform_state_pair.register(TensorProduct, TensorProduct)
+def _transform_tp_tp(a, b):
+    """Combine a product of tensor products if their number of args matches."""
+    debug('_transform_tp_tp', a, b)
+    if len(a.args) == len(b.args):
+        if a.kind == BraKind and b.kind == KetKind:
+            return tuple([InnerProduct(i, j) for (i, j) in zip(a.args, b.args)])
+        else:
+            return (TensorProduct(*(i*j for (i, j) in zip(a.args, b.args))), )
+
+@_transform_state_pair.register(OuterProduct, OuterProduct)
+def _transform_op_op(a, b):
+    """Extract an inner produt from a product of outer products."""
+    return (InnerProduct(a.bra, b.ket), OuterProduct(a.ket, b.bra))
+
+
+#-----------------------------------------------------------------------------
+# Postprocessing transforms for Mul and Pow
+#-----------------------------------------------------------------------------
+
+
+def _postprocess_state_mul(expr):
+    """Transform a ``Mul`` of quantum expressions into canonical form.
+
+    This function is registered ``_constructor_postprocessor_mapping`` as a
+    transformer for ``Mul``. This means that every time a quantum expression
+    is multiplied, this function will be called to transform it into canonical
+    form as defined by the binary functions registered with
+    ``_transform_state_pair``.
+
+    The algorithm of this function is as follows. It walks the args
+    of the input ``Mul`` from left to right and calls ``_transform_state_pair``
+    on every overlapping pair of args. Each time ``_transform_state_pair``
+    is called it can return a tuple of items or None. If None, the pair isn't
+    transformed. If a tuple, then the last element of the tuple goes back into
+    the args to be transformed again and the others are extended onto the result
+    args list.
+
+    The algorithm can be visualized in the following table:
+
+    step   result                                 args
+    ============================================================================
+    #0     []                                     [a, b, c, d, e, f]
+    #1     []                                     [T(a,b), c, d, e, f]
+    #2     [T(a,b)[:-1]]                          [T(a,b)[-1], c, d, e, f]
+    #3     [T(a,b)[:-1]]                          [T(T(a,b)[-1], c), d, e, f]
+    #4     [T(a,b)[:-1], T(T(a,b)[-1], c)[:-1]]   [T(T(T(a,b)[-1], c)[-1], d), e, f]
+    #5     ...
+
+    One limitation of the current implementation is that we assume that only the
+    last item of the transformed tuple goes back into the args to be transformed
+    again. These seems to handle the cases needed for Mul. However, we may need
+    to extend the algorithm to have the entire tuple go back into the args for
+    further transformation.
+    """
+    args = list(expr.args)
+    result = []
+
+    # Continue as long as we have at least 2 elements
+    while len(args) > 1:
+        # Get first two elements
+        first = args.pop(0)
+        second = args[0]  # Look at second element without popping yet
+
+        transformed = _transform_state_pair(first, second)
+
+        if transformed is None:
+            # If transform returns None, append first element
+            result.append(first)
+        else:
+            # This item was transformed, pop and discard
+            args.pop(0)
+            # The last item goes back to be transformed again
+            args.insert(0, transformed[-1])
+            # All other items go directly into the result
+            result.extend(transformed[:-1])
+
+    # Append any remaining element
+    if args:
+        result.append(args[0])
+
+    return Mul._from_args(result, is_commutative=False)
+
+
+def _postprocess_state_pow(expr):
+    """Handle bras and kets raised to powers.
+
+    Under ``*`` multiplication this is invalid. Users should use a
+    TensorProduct instead.
+    """
+    base, exp = expr.as_base_exp()
+    if base.kind == KetKind or base.kind == BraKind:
+        raise TypeError(
+            'A bra or ket to a power is invalid, use TensorProduct instead.'
+        )
+
+
+def _postprocess_tp_pow(expr):
+    """Handle TensorProduct(*operators)**(positive integer).
+
+    This handles a tensor product of operators, to an integer power.
+    The power here is interpreted as regular multiplication, not
+    tensor product exponentiation. The form of exponentiation performed
+    here leaves the space and dimension of the object the same.
+
+    This operation does not make sense for tensor product's of states.
+    """
+    base, exp = expr.as_base_exp()
+    debug('_postprocess_tp_pow: ', base, exp, expr.args)
+    if isinstance(base, TensorProduct) and exp.is_integer and exp.is_positive and base.kind == OperatorKind:
+        new_args = [a**exp for a in base.args]
+        return TensorProduct(*new_args)
+
+
+#-----------------------------------------------------------------------------
+# Register the transformers with Basic._constructor_postprocessor_mapping
+#-----------------------------------------------------------------------------
+
+
+Basic._constructor_postprocessor_mapping[StateBase] = {
+    "Mul": [_postprocess_state_mul],
+    "Pow": [_postprocess_state_pow]
+}
+
+Basic._constructor_postprocessor_mapping[TensorProduct] = {
+    "Mul": [_postprocess_state_mul],
+    "Pow": [_postprocess_tp_pow]
+}
+
+Basic._constructor_postprocessor_mapping[Operator] = {
+    "Mul": [_postprocess_state_mul]
+}
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/secondquant.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/secondquant.py
new file mode 100644
index 0000000000000000000000000000000000000000..189e8e8b50c785759b03f19f28285f7988cfca75
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/secondquant.py
@@ -0,0 +1,3125 @@
+"""
+Second quantization operators and states for bosons.
+
+This follow the formulation of Fetter and Welecka, "Quantum Theory
+of Many-Particle Systems."
+"""
+from collections import defaultdict
+
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.cache import cacheit
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import Function
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import Dummy, Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.complexes import conjugate
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import zeros
+from sympy.printing.str import StrPrinter
+from sympy.utilities.iterables import has_dups
+
+__all__ = [
+    'Dagger',
+    'KroneckerDelta',
+    'BosonicOperator',
+    'AnnihilateBoson',
+    'CreateBoson',
+    'AnnihilateFermion',
+    'CreateFermion',
+    'FockState',
+    'FockStateBra',
+    'FockStateKet',
+    'FockStateBosonKet',
+    'FockStateBosonBra',
+    'FockStateFermionKet',
+    'FockStateFermionBra',
+    'BBra',
+    'BKet',
+    'FBra',
+    'FKet',
+    'F',
+    'Fd',
+    'B',
+    'Bd',
+    'apply_operators',
+    'InnerProduct',
+    'BosonicBasis',
+    'VarBosonicBasis',
+    'FixedBosonicBasis',
+    'Commutator',
+    'matrix_rep',
+    'contraction',
+    'wicks',
+    'NO',
+    'evaluate_deltas',
+    'AntiSymmetricTensor',
+    'substitute_dummies',
+    'PermutationOperator',
+    'simplify_index_permutations',
+]
+
+
+class SecondQuantizationError(Exception):
+    pass
+
+
+class AppliesOnlyToSymbolicIndex(SecondQuantizationError):
+    pass
+
+
+class ContractionAppliesOnlyToFermions(SecondQuantizationError):
+    pass
+
+
+class ViolationOfPauliPrinciple(SecondQuantizationError):
+    pass
+
+
+class SubstitutionOfAmbigousOperatorFailed(SecondQuantizationError):
+    pass
+
+
+class WicksTheoremDoesNotApply(SecondQuantizationError):
+    pass
+
+
+class Dagger(Expr):
+    """
+    Hermitian conjugate of creation/annihilation operators.
+
+    Examples
+    ========
+
+    >>> from sympy import I
+    >>> from sympy.physics.secondquant import Dagger, B, Bd
+    >>> Dagger(2*I)
+    -2*I
+    >>> Dagger(B(0))
+    CreateBoson(0)
+    >>> Dagger(Bd(0))
+    AnnihilateBoson(0)
+
+    """
+
+    def __new__(cls, arg):
+        arg = sympify(arg)
+        r = cls.eval(arg)
+        if isinstance(r, Basic):
+            return r
+        obj = Basic.__new__(cls, arg)
+        return obj
+
+    @classmethod
+    def eval(cls, arg):
+        """
+        Evaluates the Dagger instance.
+
+        Examples
+        ========
+
+        >>> from sympy import I
+        >>> from sympy.physics.secondquant import Dagger, B, Bd
+        >>> Dagger(2*I)
+        -2*I
+        >>> Dagger(B(0))
+        CreateBoson(0)
+        >>> Dagger(Bd(0))
+        AnnihilateBoson(0)
+
+        The eval() method is called automatically.
+
+        """
+        dagger = getattr(arg, '_dagger_', None)
+        if dagger is not None:
+            return dagger()
+        if isinstance(arg, Symbol) and arg.is_commutative:
+            return conjugate(arg)
+        if isinstance(arg, Basic):
+            if arg.is_Add:
+                return Add(*tuple(map(Dagger, arg.args)))
+            if arg.is_Mul:
+                return Mul(*tuple(map(Dagger, reversed(arg.args))))
+            if arg.is_Number:
+                return arg
+            if arg.is_Pow:
+                return Pow(Dagger(arg.args[0]), arg.args[1])
+            if arg == I:
+                return -arg
+        if isinstance(arg, Function):
+            if all(a.is_commutative for a in arg.args):
+                return arg.func(*[Dagger(a) for a in arg.args])
+        else:
+            return None
+
+    def _dagger_(self):
+        return self.args[0]
+
+
+class TensorSymbol(Expr):
+
+    is_commutative = True
+
+
+class AntiSymmetricTensor(TensorSymbol):
+    """Stores upper and lower indices in separate Tuple's.
+
+    Each group of indices is assumed to be antisymmetric.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import AntiSymmetricTensor
+    >>> i, j = symbols('i j', below_fermi=True)
+    >>> a, b = symbols('a b', above_fermi=True)
+    >>> AntiSymmetricTensor('v', (a, i), (b, j))
+    AntiSymmetricTensor(v, (a, i), (b, j))
+    >>> AntiSymmetricTensor('v', (i, a), (b, j))
+    -AntiSymmetricTensor(v, (a, i), (b, j))
+
+    As you can see, the indices are automatically sorted to a canonical form.
+
+    """
+
+    def __new__(cls, symbol, upper, lower):
+
+        try:
+            upper, signu = _sort_anticommuting_fermions(
+                upper, key=_sqkey_index)
+            lower, signl = _sort_anticommuting_fermions(
+                lower, key=_sqkey_index)
+
+        except ViolationOfPauliPrinciple:
+            return S.Zero
+
+        symbol = sympify(symbol)
+        upper = Tuple(*upper)
+        lower = Tuple(*lower)
+
+        if (signu + signl) % 2:
+            return -TensorSymbol.__new__(cls, symbol, upper, lower)
+        else:
+
+            return TensorSymbol.__new__(cls, symbol, upper, lower)
+
+    def _latex(self, printer):
+        return "{%s^{%s}_{%s}}" % (
+            self.symbol,
+            "".join([ printer._print(i) for i in self.args[1]]),
+            "".join([ printer._print(i) for i in self.args[2]])
+        )
+
+    @property
+    def symbol(self):
+        """
+        Returns the symbol of the tensor.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import AntiSymmetricTensor
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> AntiSymmetricTensor('v', (a, i), (b, j))
+        AntiSymmetricTensor(v, (a, i), (b, j))
+        >>> AntiSymmetricTensor('v', (a, i), (b, j)).symbol
+        v
+
+        """
+        return self.args[0]
+
+    @property
+    def upper(self):
+        """
+        Returns the upper indices.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import AntiSymmetricTensor
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> AntiSymmetricTensor('v', (a, i), (b, j))
+        AntiSymmetricTensor(v, (a, i), (b, j))
+        >>> AntiSymmetricTensor('v', (a, i), (b, j)).upper
+        (a, i)
+
+
+        """
+        return self.args[1]
+
+    @property
+    def lower(self):
+        """
+        Returns the lower indices.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import AntiSymmetricTensor
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> AntiSymmetricTensor('v', (a, i), (b, j))
+        AntiSymmetricTensor(v, (a, i), (b, j))
+        >>> AntiSymmetricTensor('v', (a, i), (b, j)).lower
+        (b, j)
+
+        """
+        return self.args[2]
+
+    def __str__(self):
+        return "%s(%s,%s)" % self.args
+
+
+class SqOperator(Expr):
+    """
+    Base class for Second Quantization operators.
+    """
+
+    op_symbol = 'sq'
+
+    is_commutative = False
+
+    def __new__(cls, k):
+        obj = Basic.__new__(cls, sympify(k))
+        return obj
+
+    @property
+    def state(self):
+        """
+        Returns the state index related to this operator.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F, Fd, B, Bd
+        >>> p = Symbol('p')
+        >>> F(p).state
+        p
+        >>> Fd(p).state
+        p
+        >>> B(p).state
+        p
+        >>> Bd(p).state
+        p
+
+        """
+        return self.args[0]
+
+    @property
+    def is_symbolic(self):
+        """
+        Returns True if the state is a symbol (as opposed to a number).
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> p = Symbol('p')
+        >>> F(p).is_symbolic
+        True
+        >>> F(1).is_symbolic
+        False
+
+        """
+        if self.state.is_Integer:
+            return False
+        else:
+            return True
+
+    def __repr__(self):
+        return NotImplemented
+
+    def __str__(self):
+        return "%s(%r)" % (self.op_symbol, self.state)
+
+    def apply_operator(self, state):
+        """
+        Applies an operator to itself.
+        """
+        raise NotImplementedError('implement apply_operator in a subclass')
+
+
+class BosonicOperator(SqOperator):
+    pass
+
+
+class Annihilator(SqOperator):
+    pass
+
+
+class Creator(SqOperator):
+    pass
+
+
+class AnnihilateBoson(BosonicOperator, Annihilator):
+    """
+    Bosonic annihilation operator.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import B
+    >>> from sympy.abc import x
+    >>> B(x)
+    AnnihilateBoson(x)
+    """
+
+    op_symbol = 'b'
+
+    def _dagger_(self):
+        return CreateBoson(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, BKet
+        >>> from sympy.abc import x, y, n
+        >>> B(x).apply_operator(y)
+        y*AnnihilateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+
+        """
+        if not self.is_symbolic and isinstance(state, FockStateKet):
+            element = self.state
+            amp = sqrt(state[element])
+            return amp*state.down(element)
+        else:
+            return Mul(self, state)
+
+    def __repr__(self):
+        return "AnnihilateBoson(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "b_{0}"
+        else:
+            return "b_{%s}" % printer._print(self.state)
+
+class CreateBoson(BosonicOperator, Creator):
+    """
+    Bosonic creation operator.
+    """
+
+    op_symbol = 'b+'
+
+    def _dagger_(self):
+        return AnnihilateBoson(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, Dagger, BKet
+        >>> from sympy.abc import x, y, n
+        >>> Dagger(B(x)).apply_operator(y)
+        y*CreateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+        """
+        if not self.is_symbolic and isinstance(state, FockStateKet):
+            element = self.state
+            amp = sqrt(state[element] + 1)
+            return amp*state.up(element)
+        else:
+            return Mul(self, state)
+
+    def __repr__(self):
+        return "CreateBoson(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "{b^\\dagger_{0}}"
+        else:
+            return "{b^\\dagger_{%s}}" % printer._print(self.state)
+
+B = AnnihilateBoson
+Bd = CreateBoson
+
+
+class FermionicOperator(SqOperator):
+
+    @property
+    def is_restricted(self):
+        """
+        Is this FermionicOperator restricted with respect to fermi level?
+
+        Returns
+        =======
+
+        1  : restricted to orbits above fermi
+        0  : no restriction
+        -1 : restricted to orbits below fermi
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F, Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_restricted
+        1
+        >>> Fd(a).is_restricted
+        1
+        >>> F(i).is_restricted
+        -1
+        >>> Fd(i).is_restricted
+        -1
+        >>> F(p).is_restricted
+        0
+        >>> Fd(p).is_restricted
+        0
+
+        """
+        ass = self.args[0].assumptions0
+        if ass.get("below_fermi"):
+            return -1
+        if ass.get("above_fermi"):
+            return 1
+        return 0
+
+    @property
+    def is_above_fermi(self):
+        """
+        Does the index of this FermionicOperator allow values above fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_above_fermi
+        True
+        >>> F(i).is_above_fermi
+        False
+        >>> F(p).is_above_fermi
+        True
+
+        Note
+        ====
+
+        The same applies to creation operators Fd
+
+        """
+        return not self.args[0].assumptions0.get("below_fermi")
+
+    @property
+    def is_below_fermi(self):
+        """
+        Does the index of this FermionicOperator allow values below fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_below_fermi
+        False
+        >>> F(i).is_below_fermi
+        True
+        >>> F(p).is_below_fermi
+        True
+
+        The same applies to creation operators Fd
+
+        """
+        return not self.args[0].assumptions0.get("above_fermi")
+
+    @property
+    def is_only_below_fermi(self):
+        """
+        Is the index of this FermionicOperator restricted to values below fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_below_fermi
+        False
+        >>> F(i).is_only_below_fermi
+        True
+        >>> F(p).is_only_below_fermi
+        False
+
+        The same applies to creation operators Fd
+        """
+        return self.is_below_fermi and not self.is_above_fermi
+
+    @property
+    def is_only_above_fermi(self):
+        """
+        Is the index of this FermionicOperator restricted to values above fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_above_fermi
+        True
+        >>> F(i).is_only_above_fermi
+        False
+        >>> F(p).is_only_above_fermi
+        False
+
+        The same applies to creation operators Fd
+        """
+        return self.is_above_fermi and not self.is_below_fermi
+
+    def _sortkey(self):
+        h = hash(self)
+        label = str(self.args[0])
+
+        if self.is_only_q_creator:
+            return 1, label, h
+        if self.is_only_q_annihilator:
+            return 4, label, h
+        if isinstance(self, Annihilator):
+            return 3, label, h
+        if isinstance(self, Creator):
+            return 2, label, h
+
+
+class AnnihilateFermion(FermionicOperator, Annihilator):
+    """
+    Fermionic annihilation operator.
+    """
+
+    op_symbol = 'f'
+
+    def _dagger_(self):
+        return CreateFermion(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, Dagger, BKet
+        >>> from sympy.abc import x, y, n
+        >>> Dagger(B(x)).apply_operator(y)
+        y*CreateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+        """
+        if isinstance(state, FockStateFermionKet):
+            element = self.state
+            return state.down(element)
+
+        elif isinstance(state, Mul):
+            c_part, nc_part = state.args_cnc()
+            if isinstance(nc_part[0], FockStateFermionKet):
+                element = self.state
+                return Mul(*(c_part + [nc_part[0].down(element)] + nc_part[1:]))
+            else:
+                return Mul(self, state)
+
+        else:
+            return Mul(self, state)
+
+    @property
+    def is_q_creator(self):
+        """
+        Can we create a quasi-particle?  (create hole or create particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_q_creator
+        0
+        >>> F(i).is_q_creator
+        -1
+        >>> F(p).is_q_creator
+        -1
+
+        """
+        if self.is_below_fermi:
+            return -1
+        return 0
+
+    @property
+    def is_q_annihilator(self):
+        """
+        Can we destroy a quasi-particle?  (annihilate hole or annihilate particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=1)
+        >>> i = Symbol('i', below_fermi=1)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_q_annihilator
+        1
+        >>> F(i).is_q_annihilator
+        0
+        >>> F(p).is_q_annihilator
+        1
+
+        """
+        if self.is_above_fermi:
+            return 1
+        return 0
+
+    @property
+    def is_only_q_creator(self):
+        """
+        Always create a quasi-particle?  (create hole or create particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_q_creator
+        False
+        >>> F(i).is_only_q_creator
+        True
+        >>> F(p).is_only_q_creator
+        False
+
+        """
+        return self.is_only_below_fermi
+
+    @property
+    def is_only_q_annihilator(self):
+        """
+        Always destroy a quasi-particle?  (annihilate hole or annihilate particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_q_annihilator
+        True
+        >>> F(i).is_only_q_annihilator
+        False
+        >>> F(p).is_only_q_annihilator
+        False
+
+        """
+        return self.is_only_above_fermi
+
+    def __repr__(self):
+        return "AnnihilateFermion(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "a_{0}"
+        else:
+            return "a_{%s}" % printer._print(self.state)
+
+
+class CreateFermion(FermionicOperator, Creator):
+    """
+    Fermionic creation operator.
+    """
+
+    op_symbol = 'f+'
+
+    def _dagger_(self):
+        return AnnihilateFermion(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, Dagger, BKet
+        >>> from sympy.abc import x, y, n
+        >>> Dagger(B(x)).apply_operator(y)
+        y*CreateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+        """
+        if isinstance(state, FockStateFermionKet):
+            element = self.state
+            return state.up(element)
+
+        elif isinstance(state, Mul):
+            c_part, nc_part = state.args_cnc()
+            if isinstance(nc_part[0], FockStateFermionKet):
+                element = self.state
+                return Mul(*(c_part + [nc_part[0].up(element)] + nc_part[1:]))
+
+        return Mul(self, state)
+
+    @property
+    def is_q_creator(self):
+        """
+        Can we create a quasi-particle?  (create hole or create particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_q_creator
+        1
+        >>> Fd(i).is_q_creator
+        0
+        >>> Fd(p).is_q_creator
+        1
+
+        """
+        if self.is_above_fermi:
+            return 1
+        return 0
+
+    @property
+    def is_q_annihilator(self):
+        """
+        Can we destroy a quasi-particle?  (annihilate hole or annihilate particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=1)
+        >>> i = Symbol('i', below_fermi=1)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_q_annihilator
+        0
+        >>> Fd(i).is_q_annihilator
+        -1
+        >>> Fd(p).is_q_annihilator
+        -1
+
+        """
+        if self.is_below_fermi:
+            return -1
+        return 0
+
+    @property
+    def is_only_q_creator(self):
+        """
+        Always create a quasi-particle?  (create hole or create particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_only_q_creator
+        True
+        >>> Fd(i).is_only_q_creator
+        False
+        >>> Fd(p).is_only_q_creator
+        False
+
+        """
+        return self.is_only_above_fermi
+
+    @property
+    def is_only_q_annihilator(self):
+        """
+        Always destroy a quasi-particle?  (annihilate hole or annihilate particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_only_q_annihilator
+        False
+        >>> Fd(i).is_only_q_annihilator
+        True
+        >>> Fd(p).is_only_q_annihilator
+        False
+
+        """
+        return self.is_only_below_fermi
+
+    def __repr__(self):
+        return "CreateFermion(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "{a^\\dagger_{0}}"
+        else:
+            return "{a^\\dagger_{%s}}" % printer._print(self.state)
+
+Fd = CreateFermion
+F = AnnihilateFermion
+
+
+class FockState(Expr):
+    """
+    Many particle Fock state with a sequence of occupation numbers.
+
+    Anywhere you can have a FockState, you can also have S.Zero.
+    All code must check for this!
+
+    Base class to represent FockStates.
+    """
+    is_commutative = False
+
+    def __new__(cls, occupations):
+        """
+        occupations is a list with two possible meanings:
+
+        - For bosons it is a list of occupation numbers.
+          Element i is the number of particles in state i.
+
+        - For fermions it is a list of occupied orbits.
+          Element 0 is the state that was occupied first, element i
+          is the i'th occupied state.
+        """
+        occupations = list(map(sympify, occupations))
+        obj = Basic.__new__(cls, Tuple(*occupations))
+        return obj
+
+    def __getitem__(self, i):
+        i = int(i)
+        return self.args[0][i]
+
+    def __repr__(self):
+        return ("FockState(%r)") % (self.args)
+
+    def __str__(self):
+        return "%s%r%s" % (getattr(self, 'lbracket', ""), self._labels(), getattr(self, 'rbracket', ""))
+
+    def _labels(self):
+        return self.args[0]
+
+    def __len__(self):
+        return len(self.args[0])
+
+    def _latex(self, printer):
+        return "%s%s%s" % (getattr(self, 'lbracket_latex', ""), printer._print(self._labels()), getattr(self, 'rbracket_latex', ""))
+
+
+class BosonState(FockState):
+    """
+    Base class for FockStateBoson(Ket/Bra).
+    """
+
+    def up(self, i):
+        """
+        Performs the action of a creation operator.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import BBra
+        >>> b = BBra([1, 2])
+        >>> b
+        FockStateBosonBra((1, 2))
+        >>> b.up(1)
+        FockStateBosonBra((1, 3))
+        """
+        i = int(i)
+        new_occs = list(self.args[0])
+        new_occs[i] = new_occs[i] + S.One
+        return self.__class__(new_occs)
+
+    def down(self, i):
+        """
+        Performs the action of an annihilation operator.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import BBra
+        >>> b = BBra([1, 2])
+        >>> b
+        FockStateBosonBra((1, 2))
+        >>> b.down(1)
+        FockStateBosonBra((1, 1))
+        """
+        i = int(i)
+        new_occs = list(self.args[0])
+        if new_occs[i] == S.Zero:
+            return S.Zero
+        else:
+            new_occs[i] = new_occs[i] - S.One
+            return self.__class__(new_occs)
+
+
+class FermionState(FockState):
+    """
+    Base class for FockStateFermion(Ket/Bra).
+    """
+
+    fermi_level = 0
+
+    def __new__(cls, occupations, fermi_level=0):
+        occupations = list(map(sympify, occupations))
+        if len(occupations) > 1:
+            try:
+                (occupations, sign) = _sort_anticommuting_fermions(
+                    occupations, key=_sqkey_index)
+            except ViolationOfPauliPrinciple:
+                return S.Zero
+        else:
+            sign = 0
+
+        cls.fermi_level = fermi_level
+
+        if cls._count_holes(occupations) > fermi_level:
+            return S.Zero
+
+        if sign % 2:
+            return S.NegativeOne*FockState.__new__(cls, occupations)
+        else:
+            return FockState.__new__(cls, occupations)
+
+    def up(self, i):
+        """
+        Performs the action of a creation operator.
+
+        Explanation
+        ===========
+
+        If below fermi we try to remove a hole,
+        if above fermi we try to create a particle.
+
+        If general index p we return ``Kronecker(p,i)*self``
+        where ``i`` is a new symbol with restriction above or below.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import FKet
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> FKet([]).up(a)
+        FockStateFermionKet((a,))
+
+        A creator acting on vacuum below fermi vanishes
+
+        >>> FKet([]).up(i)
+        0
+
+
+        """
+        present = i in self.args[0]
+
+        if self._only_above_fermi(i):
+            if present:
+                return S.Zero
+            else:
+                return self._add_orbit(i)
+        elif self._only_below_fermi(i):
+            if present:
+                return self._remove_orbit(i)
+            else:
+                return S.Zero
+        else:
+            if present:
+                hole = Dummy("i", below_fermi=True)
+                return KroneckerDelta(i, hole)*self._remove_orbit(i)
+            else:
+                particle = Dummy("a", above_fermi=True)
+                return KroneckerDelta(i, particle)*self._add_orbit(i)
+
+    def down(self, i):
+        """
+        Performs the action of an annihilation operator.
+
+        Explanation
+        ===========
+
+        If below fermi we try to create a hole,
+        If above fermi we try to remove a particle.
+
+        If general index p we return ``Kronecker(p,i)*self``
+        where ``i`` is a new symbol with restriction above or below.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import FKet
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        An annihilator acting on vacuum above fermi vanishes
+
+        >>> FKet([]).down(a)
+        0
+
+        Also below fermi, it vanishes, unless we specify a fermi level > 0
+
+        >>> FKet([]).down(i)
+        0
+        >>> FKet([],4).down(i)
+        FockStateFermionKet((i,))
+
+        """
+        present = i in self.args[0]
+
+        if self._only_above_fermi(i):
+            if present:
+                return self._remove_orbit(i)
+            else:
+                return S.Zero
+
+        elif self._only_below_fermi(i):
+            if present:
+                return S.Zero
+            else:
+                return self._add_orbit(i)
+        else:
+            if present:
+                hole = Dummy("i", below_fermi=True)
+                return KroneckerDelta(i, hole)*self._add_orbit(i)
+            else:
+                particle = Dummy("a", above_fermi=True)
+                return KroneckerDelta(i, particle)*self._remove_orbit(i)
+
+    @classmethod
+    def _only_below_fermi(cls, i):
+        """
+        Tests if given orbit is only below fermi surface.
+
+        If nothing can be concluded we return a conservative False.
+        """
+        if i.is_number:
+            return i <= cls.fermi_level
+        if i.assumptions0.get('below_fermi'):
+            return True
+        return False
+
+    @classmethod
+    def _only_above_fermi(cls, i):
+        """
+        Tests if given orbit is only above fermi surface.
+
+        If fermi level has not been set we return True.
+        If nothing can be concluded we return a conservative False.
+        """
+        if i.is_number:
+            return i > cls.fermi_level
+        if i.assumptions0.get('above_fermi'):
+            return True
+        return not cls.fermi_level
+
+    def _remove_orbit(self, i):
+        """
+        Removes particle/fills hole in orbit i. No input tests performed here.
+        """
+        new_occs = list(self.args[0])
+        pos = new_occs.index(i)
+        del new_occs[pos]
+        if (pos) % 2:
+            return S.NegativeOne*self.__class__(new_occs, self.fermi_level)
+        else:
+            return self.__class__(new_occs, self.fermi_level)
+
+    def _add_orbit(self, i):
+        """
+        Adds particle/creates hole in orbit i. No input tests performed here.
+        """
+        return self.__class__((i,) + self.args[0], self.fermi_level)
+
+    @classmethod
+    def _count_holes(cls, occupations):
+        """
+        Returns the number of identified hole states in occupations list.
+        """
+        return len([i for i in occupations if cls._only_below_fermi(i)])
+
+    def _negate_holes(self, occupations):
+        """
+        Returns the occupations list where states below the fermi level have negative labels.
+
+        For symbolic state labels, no sign is included.
+        """
+        return tuple([-i if self._only_below_fermi(i) and i.is_number else i for i in occupations])
+
+    def __repr__(self):
+        if self.fermi_level:
+            return "FockStateKet(%r, fermi_level=%s)" % (self.args[0], self.fermi_level)
+        else:
+            return "FockStateKet(%r)" % (self.args[0],)
+
+    def _labels(self):
+        return self._negate_holes(self.args[0])
+
+
+class FockStateKet(FockState):
+    """
+    Representation of a ket.
+    """
+    lbracket = '|'
+    rbracket = '>'
+    lbracket_latex = r'\left|'
+    rbracket_latex = r'\right\rangle'
+
+
+class FockStateBra(FockState):
+    """
+    Representation of a bra.
+    """
+    lbracket = '<'
+    rbracket = '|'
+    lbracket_latex = r'\left\langle'
+    rbracket_latex = r'\right|'
+
+    def __mul__(self, other):
+        if isinstance(other, FockStateKet):
+            return InnerProduct(self, other)
+        else:
+            return Expr.__mul__(self, other)
+
+
+class FockStateBosonKet(BosonState, FockStateKet):
+    """
+    Many particle Fock state with a sequence of occupation numbers.
+
+    Occupation numbers can be any integer >= 0.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import BKet
+    >>> BKet([1, 2])
+    FockStateBosonKet((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateBosonBra(*self.args)
+
+
+class FockStateBosonBra(BosonState, FockStateBra):
+    """
+    Describes a collection of BosonBra particles.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import BBra
+    >>> BBra([1, 2])
+    FockStateBosonBra((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateBosonKet(*self.args)
+
+
+class FockStateFermionKet(FermionState, FockStateKet):
+    """
+    Many-particle Fock state with a sequence of occupied orbits.
+
+    Explanation
+    ===========
+
+    Each state can only have one particle, so we choose to store a list of
+    occupied orbits rather than a tuple with occupation numbers (zeros and ones).
+
+    states below fermi level are holes, and are represented by negative labels
+    in the occupation list.
+
+    For symbolic state labels, the fermi_level caps the number of allowed hole-
+    states.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import FKet
+    >>> FKet([1, 2])
+    FockStateFermionKet((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateFermionBra(*self.args)
+
+
+class FockStateFermionBra(FermionState, FockStateBra):
+    """
+    See Also
+    ========
+
+    FockStateFermionKet
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import FBra
+    >>> FBra([1, 2])
+    FockStateFermionBra((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateFermionKet(*self.args)
+
+BBra = FockStateBosonBra
+BKet = FockStateBosonKet
+FBra = FockStateFermionBra
+FKet = FockStateFermionKet
+
+
+def _apply_Mul(m):
+    """
+    Take a Mul instance with operators and apply them to states.
+
+    Explanation
+    ===========
+
+    This method applies all operators with integer state labels
+    to the actual states.  For symbolic state labels, nothing is done.
+    When inner products of FockStates are encountered (like ),
+    they are converted to instances of InnerProduct.
+
+    This does not currently work on double inner products like,
+    .
+
+    If the argument is not a Mul, it is simply returned as is.
+    """
+    if not isinstance(m, Mul):
+        return m
+    c_part, nc_part = m.args_cnc()
+    n_nc = len(nc_part)
+    if n_nc in (0, 1):
+        return m
+    else:
+        last = nc_part[-1]
+        next_to_last = nc_part[-2]
+        if isinstance(last, FockStateKet):
+            if isinstance(next_to_last, SqOperator):
+                if next_to_last.is_symbolic:
+                    return m
+                else:
+                    result = next_to_last.apply_operator(last)
+                    if result == 0:
+                        return S.Zero
+                    else:
+                        return _apply_Mul(Mul(*(c_part + nc_part[:-2] + [result])))
+            elif isinstance(next_to_last, Pow):
+                if isinstance(next_to_last.base, SqOperator) and \
+                        next_to_last.exp.is_Integer:
+                    if next_to_last.base.is_symbolic:
+                        return m
+                    else:
+                        result = last
+                        for i in range(next_to_last.exp):
+                            result = next_to_last.base.apply_operator(result)
+                            if result == 0:
+                                break
+                        if result == 0:
+                            return S.Zero
+                        else:
+                            return _apply_Mul(Mul(*(c_part + nc_part[:-2] + [result])))
+                else:
+                    return m
+            elif isinstance(next_to_last, FockStateBra):
+                result = InnerProduct(next_to_last, last)
+                if result == 0:
+                    return S.Zero
+                else:
+                    return _apply_Mul(Mul(*(c_part + nc_part[:-2] + [result])))
+            else:
+                return m
+        else:
+            return m
+
+
+def apply_operators(e):
+    """
+    Take a SymPy expression with operators and states and apply the operators.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import apply_operators
+    >>> from sympy import sympify
+    >>> apply_operators(sympify(3)+4)
+    7
+    """
+    e = e.expand()
+    muls = e.atoms(Mul)
+    subs_list = [(m, _apply_Mul(m)) for m in iter(muls)]
+    return e.subs(subs_list)
+
+
+class InnerProduct(Basic):
+    """
+    An unevaluated inner product between a bra and ket.
+
+    Explanation
+    ===========
+
+    Currently this class just reduces things to a product of
+    Kronecker Deltas.  In the future, we could introduce abstract
+    states like ``|a>`` and ``|b>``, and leave the inner product unevaluated as
+    ````.
+
+    """
+    is_commutative = True
+
+    def __new__(cls, bra, ket):
+        if not isinstance(bra, FockStateBra):
+            raise TypeError("must be a bra")
+        if not isinstance(ket, FockStateKet):
+            raise TypeError("must be a ket")
+        return cls.eval(bra, ket)
+
+    @classmethod
+    def eval(cls, bra, ket):
+        result = S.One
+        for i, j in zip(bra.args[0], ket.args[0]):
+            result *= KroneckerDelta(i, j)
+            if result == 0:
+                break
+        return result
+
+    @property
+    def bra(self):
+        """Returns the bra part of the state"""
+        return self.args[0]
+
+    @property
+    def ket(self):
+        """Returns the ket part of the state"""
+        return self.args[1]
+
+    def __repr__(self):
+        sbra = repr(self.bra)
+        sket = repr(self.ket)
+        return "%s|%s" % (sbra[:-1], sket[1:])
+
+    def __str__(self):
+        return self.__repr__()
+
+
+def matrix_rep(op, basis):
+    """
+    Find the representation of an operator in a basis.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import VarBosonicBasis, B, matrix_rep
+    >>> b = VarBosonicBasis(5)
+    >>> o = B(0)
+    >>> matrix_rep(o, b)
+    Matrix([
+    [0, 1,       0,       0, 0],
+    [0, 0, sqrt(2),       0, 0],
+    [0, 0,       0, sqrt(3), 0],
+    [0, 0,       0,       0, 2],
+    [0, 0,       0,       0, 0]])
+    """
+    a = zeros(len(basis))
+    for i in range(len(basis)):
+        for j in range(len(basis)):
+            a[i, j] = apply_operators(Dagger(basis[i])*op*basis[j])
+    return a
+
+
+class BosonicBasis:
+    """
+    Base class for a basis set of bosonic Fock states.
+    """
+    pass
+
+
+class VarBosonicBasis:
+    """
+    A single state, variable particle number basis set.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import VarBosonicBasis
+    >>> b = VarBosonicBasis(5)
+    >>> b
+    [FockState((0,)), FockState((1,)), FockState((2,)),
+     FockState((3,)), FockState((4,))]
+    """
+
+    def __init__(self, n_max):
+        self.n_max = n_max
+        self._build_states()
+
+    def _build_states(self):
+        self.basis = []
+        for i in range(self.n_max):
+            self.basis.append(FockStateBosonKet([i]))
+        self.n_basis = len(self.basis)
+
+    def index(self, state):
+        """
+        Returns the index of state in basis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import VarBosonicBasis
+        >>> b = VarBosonicBasis(3)
+        >>> state = b.state(1)
+        >>> b
+        [FockState((0,)), FockState((1,)), FockState((2,))]
+        >>> state
+        FockStateBosonKet((1,))
+        >>> b.index(state)
+        1
+        """
+        return self.basis.index(state)
+
+    def state(self, i):
+        """
+        The state of a single basis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import VarBosonicBasis
+        >>> b = VarBosonicBasis(5)
+        >>> b.state(3)
+        FockStateBosonKet((3,))
+        """
+        return self.basis[i]
+
+    def __getitem__(self, i):
+        return self.state(i)
+
+    def __len__(self):
+        return len(self.basis)
+
+    def __repr__(self):
+        return repr(self.basis)
+
+
+class FixedBosonicBasis(BosonicBasis):
+    """
+    Fixed particle number basis set.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import FixedBosonicBasis
+    >>> b = FixedBosonicBasis(2, 2)
+    >>> state = b.state(1)
+    >>> b
+    [FockState((2, 0)), FockState((1, 1)), FockState((0, 2))]
+    >>> state
+    FockStateBosonKet((1, 1))
+    >>> b.index(state)
+    1
+    """
+    def __init__(self, n_particles, n_levels):
+        self.n_particles = n_particles
+        self.n_levels = n_levels
+        self._build_particle_locations()
+        self._build_states()
+
+    def _build_particle_locations(self):
+        tup = ["i%i" % i for i in range(self.n_particles)]
+        first_loop = "for i0 in range(%i)" % self.n_levels
+        other_loops = ''
+        for cur, prev in zip(tup[1:], tup):
+            temp = "for %s in range(%s + 1) " % (cur, prev)
+            other_loops = other_loops + temp
+        tup_string = "(%s)" % ", ".join(tup)
+        list_comp = "[%s %s %s]" % (tup_string, first_loop, other_loops)
+        result = eval(list_comp)
+        if self.n_particles == 1:
+            result = [(item,) for item in result]
+        self.particle_locations = result
+
+    def _build_states(self):
+        self.basis = []
+        for tuple_of_indices in self.particle_locations:
+            occ_numbers = self.n_levels*[0]
+            for level in tuple_of_indices:
+                occ_numbers[level] += 1
+            self.basis.append(FockStateBosonKet(occ_numbers))
+        self.n_basis = len(self.basis)
+
+    def index(self, state):
+        """Returns the index of state in basis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import FixedBosonicBasis
+        >>> b = FixedBosonicBasis(2, 3)
+        >>> b.index(b.state(3))
+        3
+        """
+        return self.basis.index(state)
+
+    def state(self, i):
+        """Returns the state that lies at index i of the basis
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import FixedBosonicBasis
+        >>> b = FixedBosonicBasis(2, 3)
+        >>> b.state(3)
+        FockStateBosonKet((1, 0, 1))
+        """
+        return self.basis[i]
+
+    def __getitem__(self, i):
+        return self.state(i)
+
+    def __len__(self):
+        return len(self.basis)
+
+    def __repr__(self):
+        return repr(self.basis)
+
+
+class Commutator(Function):
+    """
+    The Commutator:  [A, B] = A*B - B*A
+
+    The arguments are ordered according to .__cmp__()
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import Commutator
+    >>> A, B = symbols('A,B', commutative=False)
+    >>> Commutator(B, A)
+    -Commutator(A, B)
+
+    Evaluate the commutator with .doit()
+
+    >>> comm = Commutator(A,B); comm
+    Commutator(A, B)
+    >>> comm.doit()
+    A*B - B*A
+
+
+    For two second quantization operators the commutator is evaluated
+    immediately:
+
+    >>> from sympy.physics.secondquant import Fd, F
+    >>> a = symbols('a', above_fermi=True)
+    >>> i = symbols('i', below_fermi=True)
+    >>> p,q = symbols('p,q')
+
+    >>> Commutator(Fd(a),Fd(i))
+    2*NO(CreateFermion(a)*CreateFermion(i))
+
+    But for more complicated expressions, the evaluation is triggered by
+    a call to .doit()
+
+    >>> comm = Commutator(Fd(p)*Fd(q),F(i)); comm
+    Commutator(CreateFermion(p)*CreateFermion(q), AnnihilateFermion(i))
+    >>> comm.doit(wicks=True)
+    -KroneckerDelta(i, p)*CreateFermion(q) +
+     KroneckerDelta(i, q)*CreateFermion(p)
+
+    """
+
+    is_commutative = False
+
+    @classmethod
+    def eval(cls, a, b):
+        """
+        The Commutator [A,B] is on canonical form if A < B.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import Commutator, F, Fd
+        >>> from sympy.abc import x
+        >>> c1 = Commutator(F(x), Fd(x))
+        >>> c2 = Commutator(Fd(x), F(x))
+        >>> Commutator.eval(c1, c2)
+        0
+        """
+        if not (a and b):
+            return S.Zero
+        if a == b:
+            return S.Zero
+        if a.is_commutative or b.is_commutative:
+            return S.Zero
+
+        #
+        # [A+B,C]  ->  [A,C] + [B,C]
+        #
+        a = a.expand()
+        if isinstance(a, Add):
+            return Add(*[cls(term, b) for term in a.args])
+        b = b.expand()
+        if isinstance(b, Add):
+            return Add(*[cls(a, term) for term in b.args])
+
+        #
+        # [xA,yB]  ->  xy*[A,B]
+        #
+        ca, nca = a.args_cnc()
+        cb, ncb = b.args_cnc()
+        c_part = list(ca) + list(cb)
+        if c_part:
+            return Mul(Mul(*c_part), cls(Mul._from_args(nca), Mul._from_args(ncb)))
+
+        #
+        # single second quantization operators
+        #
+        if isinstance(a, BosonicOperator) and isinstance(b, BosonicOperator):
+            if isinstance(b, CreateBoson) and isinstance(a, AnnihilateBoson):
+                return KroneckerDelta(a.state, b.state)
+            if isinstance(a, CreateBoson) and isinstance(b, AnnihilateBoson):
+                return S.NegativeOne*KroneckerDelta(a.state, b.state)
+            else:
+                return S.Zero
+        if isinstance(a, FermionicOperator) and isinstance(b, FermionicOperator):
+            return wicks(a*b) - wicks(b*a)
+
+        #
+        # Canonical ordering of arguments
+        #
+        if a.sort_key() > b.sort_key():
+            return S.NegativeOne*cls(b, a)
+
+    def doit(self, **hints):
+        """
+        Enables the computation of complex expressions.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import Commutator, F, Fd
+        >>> from sympy import symbols
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> c = Commutator(Fd(a)*F(i),Fd(b)*F(j))
+        >>> c.doit(wicks=True)
+        0
+        """
+        a = self.args[0]
+        b = self.args[1]
+
+        if hints.get("wicks"):
+            a = a.doit(**hints)
+            b = b.doit(**hints)
+            try:
+                return wicks(a*b) - wicks(b*a)
+            except ContractionAppliesOnlyToFermions:
+                pass
+            except WicksTheoremDoesNotApply:
+                pass
+
+        return (a*b - b*a).doit(**hints)
+
+    def __repr__(self):
+        return "Commutator(%s,%s)" % (self.args[0], self.args[1])
+
+    def __str__(self):
+        return "[%s,%s]" % (self.args[0], self.args[1])
+
+    def _latex(self, printer):
+        return "\\left[%s,%s\\right]" % tuple([
+            printer._print(arg) for arg in self.args])
+
+
+class NO(Expr):
+    """
+    This Object is used to represent normal ordering brackets.
+
+    i.e.  {abcd}  sometimes written  :abcd:
+
+    Explanation
+    ===========
+
+    Applying the function NO(arg) to an argument means that all operators in
+    the argument will be assumed to anticommute, and have vanishing
+    contractions.  This allows an immediate reordering to canonical form
+    upon object creation.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import NO, F, Fd
+    >>> p,q = symbols('p,q')
+    >>> NO(Fd(p)*F(q))
+    NO(CreateFermion(p)*AnnihilateFermion(q))
+    >>> NO(F(q)*Fd(p))
+    -NO(CreateFermion(p)*AnnihilateFermion(q))
+
+
+    Note
+    ====
+
+    If you want to generate a normal ordered equivalent of an expression, you
+    should use the function wicks().  This class only indicates that all
+    operators inside the brackets anticommute, and have vanishing contractions.
+    Nothing more, nothing less.
+
+    """
+    is_commutative = False
+
+    def __new__(cls, arg):
+        """
+        Use anticommutation to get canonical form of operators.
+
+        Explanation
+        ===========
+
+        Employ associativity of normal ordered product: {ab{cd}} = {abcd}
+        but note that {ab}{cd} /= {abcd}.
+
+        We also employ distributivity: {ab + cd} = {ab} + {cd}.
+
+        Canonical form also implies expand() {ab(c+d)} = {abc} + {abd}.
+
+        """
+
+        # {ab + cd} = {ab} + {cd}
+        arg = sympify(arg)
+        arg = arg.expand()
+        if arg.is_Add:
+            return Add(*[ cls(term) for term in arg.args])
+
+        if arg.is_Mul:
+
+            # take coefficient outside of normal ordering brackets
+            c_part, seq = arg.args_cnc()
+            if c_part:
+                coeff = Mul(*c_part)
+                if not seq:
+                    return coeff
+            else:
+                coeff = S.One
+
+            # {ab{cd}} = {abcd}
+            newseq = []
+            foundit = False
+            for fac in seq:
+                if isinstance(fac, NO):
+                    newseq.extend(fac.args)
+                    foundit = True
+                else:
+                    newseq.append(fac)
+            if foundit:
+                return coeff*cls(Mul(*newseq))
+
+            # We assume that the user don't mix B and F operators
+            if isinstance(seq[0], BosonicOperator):
+                raise NotImplementedError
+
+            try:
+                newseq, sign = _sort_anticommuting_fermions(seq)
+            except ViolationOfPauliPrinciple:
+                return S.Zero
+
+            if sign % 2:
+                return (S.NegativeOne*coeff)*cls(Mul(*newseq))
+            elif sign:
+                return coeff*cls(Mul(*newseq))
+            else:
+                pass  # since sign==0, no permutations was necessary
+
+            # if we couldn't do anything with Mul object, we just
+            # mark it as normal ordered
+            if coeff != S.One:
+                return coeff*cls(Mul(*newseq))
+            return Expr.__new__(cls, Mul(*newseq))
+
+        if isinstance(arg, NO):
+            return arg
+
+        # if object was not Mul or Add, normal ordering does not apply
+        return arg
+
+    @property
+    def has_q_creators(self):
+        """
+        Return 0 if the leftmost argument of the first argument is a not a
+        q_creator, else 1 if it is above fermi or -1 if it is below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import NO, F, Fd
+
+        >>> a = symbols('a', above_fermi=True)
+        >>> i = symbols('i', below_fermi=True)
+        >>> NO(Fd(a)*Fd(i)).has_q_creators
+        1
+        >>> NO(F(i)*F(a)).has_q_creators
+        -1
+        >>> NO(Fd(i)*F(a)).has_q_creators           #doctest: +SKIP
+        0
+
+        """
+        return self.args[0].args[0].is_q_creator
+
+    @property
+    def has_q_annihilators(self):
+        """
+        Return 0 if the rightmost argument of the first argument is a not a
+        q_annihilator, else 1 if it is above fermi or -1 if it is below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import NO, F, Fd
+
+        >>> a = symbols('a', above_fermi=True)
+        >>> i = symbols('i', below_fermi=True)
+        >>> NO(Fd(a)*Fd(i)).has_q_annihilators
+        -1
+        >>> NO(F(i)*F(a)).has_q_annihilators
+        1
+        >>> NO(Fd(a)*F(i)).has_q_annihilators
+        0
+
+        """
+        return self.args[0].args[-1].is_q_annihilator
+
+    def doit(self, **hints):
+        """
+        Either removes the brackets or enables complex computations
+        in its arguments.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import NO, Fd, F
+        >>> from textwrap import fill
+        >>> from sympy import symbols, Dummy
+        >>> p,q = symbols('p,q', cls=Dummy)
+        >>> print(fill(str(NO(Fd(p)*F(q)).doit())))
+        KroneckerDelta(_a, _p)*KroneckerDelta(_a,
+        _q)*CreateFermion(_a)*AnnihilateFermion(_a) + KroneckerDelta(_a,
+        _p)*KroneckerDelta(_i, _q)*CreateFermion(_a)*AnnihilateFermion(_i) -
+        KroneckerDelta(_a, _q)*KroneckerDelta(_i,
+        _p)*AnnihilateFermion(_a)*CreateFermion(_i) - KroneckerDelta(_i,
+        _p)*KroneckerDelta(_i, _q)*AnnihilateFermion(_i)*CreateFermion(_i)
+        """
+        if hints.get("remove_brackets", True):
+            return self._remove_brackets()
+        else:
+            return self.__new__(type(self), self.args[0].doit(**hints))
+
+    def _remove_brackets(self):
+        """
+        Returns the sorted string without normal order brackets.
+
+        The returned string have the property that no nonzero
+        contractions exist.
+        """
+
+        # check if any creator is also an annihilator
+        subslist = []
+        for i in self.iter_q_creators():
+            if self[i].is_q_annihilator:
+                assume = self[i].state.assumptions0
+
+                # only operators with a dummy index can be split in two terms
+                if isinstance(self[i].state, Dummy):
+
+                    # create indices with fermi restriction
+                    assume.pop("above_fermi", None)
+                    assume["below_fermi"] = True
+                    below = Dummy('i', **assume)
+                    assume.pop("below_fermi", None)
+                    assume["above_fermi"] = True
+                    above = Dummy('a', **assume)
+
+                    cls = type(self[i])
+                    split = (
+                        self[i].__new__(cls, below)
+                        * KroneckerDelta(below, self[i].state)
+                        + self[i].__new__(cls, above)
+                        * KroneckerDelta(above, self[i].state)
+                    )
+                    subslist.append((self[i], split))
+                else:
+                    raise SubstitutionOfAmbigousOperatorFailed(self[i])
+        if subslist:
+            result = NO(self.subs(subslist))
+            if isinstance(result, Add):
+                return Add(*[term.doit() for term in result.args])
+        else:
+            return self.args[0]
+
+    def _expand_operators(self):
+        """
+        Returns a sum of NO objects that contain no ambiguous q-operators.
+
+        Explanation
+        ===========
+
+        If an index q has range both above and below fermi, the operator F(q)
+        is ambiguous in the sense that it can be both a q-creator and a q-annihilator.
+        If q is dummy, it is assumed to be a summation variable and this method
+        rewrites it into a sum of NO terms with unambiguous operators:
+
+        {Fd(p)*F(q)} = {Fd(a)*F(b)} + {Fd(a)*F(i)} + {Fd(j)*F(b)} -{F(i)*Fd(j)}
+
+        where a,b are above and i,j are below fermi level.
+        """
+        return NO(self._remove_brackets)
+
+    def __getitem__(self, i):
+        if isinstance(i, slice):
+            indices = i.indices(len(self))
+            return [self.args[0].args[i] for i in range(*indices)]
+        else:
+            return self.args[0].args[i]
+
+    def __len__(self):
+        return len(self.args[0].args)
+
+    def iter_q_annihilators(self):
+        """
+        Iterates over the annihilation operators.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> i, j = symbols('i j', below_fermi=True)
+        >>> a, b = symbols('a b', above_fermi=True)
+        >>> from sympy.physics.secondquant import NO, F, Fd
+        >>> no = NO(Fd(a)*F(i)*F(b)*Fd(j))
+
+        >>> no.iter_q_creators()
+        
+        >>> list(no.iter_q_creators())
+        [0, 1]
+        >>> list(no.iter_q_annihilators())
+        [3, 2]
+
+        """
+        ops = self.args[0].args
+        iter = range(len(ops) - 1, -1, -1)
+        for i in iter:
+            if ops[i].is_q_annihilator:
+                yield i
+            else:
+                break
+
+    def iter_q_creators(self):
+        """
+        Iterates over the creation operators.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> i, j = symbols('i j', below_fermi=True)
+        >>> a, b = symbols('a b', above_fermi=True)
+        >>> from sympy.physics.secondquant import NO, F, Fd
+        >>> no = NO(Fd(a)*F(i)*F(b)*Fd(j))
+
+        >>> no.iter_q_creators()
+        
+        >>> list(no.iter_q_creators())
+        [0, 1]
+        >>> list(no.iter_q_annihilators())
+        [3, 2]
+
+        """
+
+        ops = self.args[0].args
+        iter = range(0, len(ops))
+        for i in iter:
+            if ops[i].is_q_creator:
+                yield i
+            else:
+                break
+
+    def get_subNO(self, i):
+        """
+        Returns a NO() without FermionicOperator at index i.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import F, NO
+        >>> p, q, r = symbols('p,q,r')
+
+        >>> NO(F(p)*F(q)*F(r)).get_subNO(1)
+        NO(AnnihilateFermion(p)*AnnihilateFermion(r))
+
+        """
+        arg0 = self.args[0]  # it's a Mul by definition of how it's created
+        mul = arg0._new_rawargs(*(arg0.args[:i] + arg0.args[i + 1:]))
+        return NO(mul)
+
+    def _latex(self, printer):
+        return "\\left\\{%s\\right\\}" % printer._print(self.args[0])
+
+    def __repr__(self):
+        return "NO(%s)" % self.args[0]
+
+    def __str__(self):
+        return ":%s:" % self.args[0]
+
+
+def contraction(a, b):
+    """
+    Calculates contraction of Fermionic operators a and b.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import F, Fd, contraction
+    >>> p, q = symbols('p,q')
+    >>> a, b = symbols('a,b', above_fermi=True)
+    >>> i, j = symbols('i,j', below_fermi=True)
+
+    A contraction is non-zero only if a quasi-creator is to the right of a
+    quasi-annihilator:
+
+    >>> contraction(F(a),Fd(b))
+    KroneckerDelta(a, b)
+    >>> contraction(Fd(i),F(j))
+    KroneckerDelta(i, j)
+
+    For general indices a non-zero result restricts the indices to below/above
+    the fermi surface:
+
+    >>> contraction(Fd(p),F(q))
+    KroneckerDelta(_i, q)*KroneckerDelta(p, q)
+    >>> contraction(F(p),Fd(q))
+    KroneckerDelta(_a, q)*KroneckerDelta(p, q)
+
+    Two creators or two annihilators always vanishes:
+
+    >>> contraction(F(p),F(q))
+    0
+    >>> contraction(Fd(p),Fd(q))
+    0
+
+    """
+    if isinstance(b, FermionicOperator) and isinstance(a, FermionicOperator):
+        if isinstance(a, AnnihilateFermion) and isinstance(b, CreateFermion):
+            if b.state.assumptions0.get("below_fermi"):
+                return S.Zero
+            if a.state.assumptions0.get("below_fermi"):
+                return S.Zero
+            if b.state.assumptions0.get("above_fermi"):
+                return KroneckerDelta(a.state, b.state)
+            if a.state.assumptions0.get("above_fermi"):
+                return KroneckerDelta(a.state, b.state)
+
+            return (KroneckerDelta(a.state, b.state)*
+                    KroneckerDelta(b.state, Dummy('a', above_fermi=True)))
+        if isinstance(b, AnnihilateFermion) and isinstance(a, CreateFermion):
+            if b.state.assumptions0.get("above_fermi"):
+                return S.Zero
+            if a.state.assumptions0.get("above_fermi"):
+                return S.Zero
+            if b.state.assumptions0.get("below_fermi"):
+                return KroneckerDelta(a.state, b.state)
+            if a.state.assumptions0.get("below_fermi"):
+                return KroneckerDelta(a.state, b.state)
+
+            return (KroneckerDelta(a.state, b.state)*
+                    KroneckerDelta(b.state, Dummy('i', below_fermi=True)))
+
+        # vanish if 2xAnnihilator or 2xCreator
+        return S.Zero
+
+    else:
+        #not fermion operators
+        t = ( isinstance(i, FermionicOperator) for i in (a, b) )
+        raise ContractionAppliesOnlyToFermions(*t)
+
+
+def _sqkey_operator(sq_operator):
+    """Generates key for canonical sorting of SQ operators."""
+    return sq_operator._sortkey()
+
+def _sqkey_index(index):
+    """Key for sorting of indices.
+
+    particle < hole < general
+
+    FIXME: This is a bottle-neck, can we do it faster?
+    """
+    h = hash(index)
+    label = str(index)
+    if isinstance(index, Dummy):
+        if index.assumptions0.get('above_fermi'):
+            return (20, label, h)
+        elif index.assumptions0.get('below_fermi'):
+            return (21, label, h)
+        else:
+            return (22, label, h)
+
+    if index.assumptions0.get('above_fermi'):
+        return (10, label, h)
+    elif index.assumptions0.get('below_fermi'):
+        return (11, label, h)
+    else:
+        return (12, label, h)
+
+
+
+def _sort_anticommuting_fermions(string1, key=_sqkey_operator):
+    """Sort fermionic operators to canonical order, assuming all pairs anticommute.
+
+    Explanation
+    ===========
+
+    Uses a bidirectional bubble sort.  Items in string1 are not referenced
+    so in principle they may be any comparable objects.   The sorting depends on the
+    operators '>' and '=='.
+
+    If the Pauli principle is violated, an exception is raised.
+
+    Returns
+    =======
+
+    tuple (sorted_str, sign)
+
+    sorted_str: list containing the sorted operators
+    sign: int telling how many times the sign should be changed
+          (if sign==0 the string was already sorted)
+    """
+
+    verified = False
+    sign = 0
+    rng = list(range(len(string1) - 1))
+    rev = list(range(len(string1) - 3, -1, -1))
+
+    keys = list(map(key, string1))
+    key_val = dict(list(zip(keys, string1)))
+
+    while not verified:
+        verified = True
+        for i in rng:
+            left = keys[i]
+            right = keys[i + 1]
+            if left == right:
+                raise ViolationOfPauliPrinciple([left, right])
+            if left > right:
+                verified = False
+                keys[i:i + 2] = [right, left]
+                sign = sign + 1
+        if verified:
+            break
+        for i in rev:
+            left = keys[i]
+            right = keys[i + 1]
+            if left == right:
+                raise ViolationOfPauliPrinciple([left, right])
+            if left > right:
+                verified = False
+                keys[i:i + 2] = [right, left]
+                sign = sign + 1
+    string1 = [ key_val[k] for k in keys ]
+    return (string1, sign)
+
+
+def evaluate_deltas(e):
+    """
+    We evaluate KroneckerDelta symbols in the expression assuming Einstein summation.
+
+    Explanation
+    ===========
+
+    If one index is repeated it is summed over and in effect substituted with
+    the other one. If both indices are repeated we substitute according to what
+    is the preferred index.  this is determined by
+    KroneckerDelta.preferred_index and KroneckerDelta.killable_index.
+
+    In case there are no possible substitutions or if a substitution would
+    imply a loss of information, nothing is done.
+
+    In case an index appears in more than one KroneckerDelta, the resulting
+    substitution depends on the order of the factors.  Since the ordering is platform
+    dependent, the literal expression resulting from this function may be hard to
+    predict.
+
+    Examples
+    ========
+
+    We assume the following:
+
+    >>> from sympy import symbols, Function, Dummy, KroneckerDelta
+    >>> from sympy.physics.secondquant import evaluate_deltas
+    >>> i,j = symbols('i j', below_fermi=True, cls=Dummy)
+    >>> a,b = symbols('a b', above_fermi=True, cls=Dummy)
+    >>> p,q = symbols('p q', cls=Dummy)
+    >>> f = Function('f')
+    >>> t = Function('t')
+
+    The order of preference for these indices according to KroneckerDelta is
+    (a, b, i, j, p, q).
+
+    Trivial cases:
+
+    >>> evaluate_deltas(KroneckerDelta(i,j)*f(i))       # d_ij f(i) -> f(j)
+    f(_j)
+    >>> evaluate_deltas(KroneckerDelta(i,j)*f(j))       # d_ij f(j) -> f(i)
+    f(_i)
+    >>> evaluate_deltas(KroneckerDelta(i,p)*f(p))       # d_ip f(p) -> f(i)
+    f(_i)
+    >>> evaluate_deltas(KroneckerDelta(q,p)*f(p))       # d_qp f(p) -> f(q)
+    f(_q)
+    >>> evaluate_deltas(KroneckerDelta(q,p)*f(q))       # d_qp f(q) -> f(p)
+    f(_p)
+
+    More interesting cases:
+
+    >>> evaluate_deltas(KroneckerDelta(i,p)*t(a,i)*f(p,q))
+    f(_i, _q)*t(_a, _i)
+    >>> evaluate_deltas(KroneckerDelta(a,p)*t(a,i)*f(p,q))
+    f(_a, _q)*t(_a, _i)
+    >>> evaluate_deltas(KroneckerDelta(p,q)*f(p,q))
+    f(_p, _p)
+
+    Finally, here are some cases where nothing is done, because that would
+    imply a loss of information:
+
+    >>> evaluate_deltas(KroneckerDelta(i,p)*f(q))
+    f(_q)*KroneckerDelta(_i, _p)
+    >>> evaluate_deltas(KroneckerDelta(i,p)*f(i))
+    f(_i)*KroneckerDelta(_i, _p)
+    """
+
+    # We treat Deltas only in mul objects
+    # for general function objects we don't evaluate KroneckerDeltas in arguments,
+    # but here we hard code exceptions to this rule
+    accepted_functions = (
+        Add,
+    )
+    if isinstance(e, accepted_functions):
+        return e.func(*[evaluate_deltas(arg) for arg in e.args])
+
+    elif isinstance(e, Mul):
+        # find all occurrences of delta function and count each index present in
+        # expression.
+        deltas = []
+        indices = {}
+        for i in e.args:
+            for s in i.free_symbols:
+                if s in indices:
+                    indices[s] += 1
+                else:
+                    indices[s] = 0  # geek counting simplifies logic below
+            if isinstance(i, KroneckerDelta):
+                deltas.append(i)
+
+        for d in deltas:
+            # If we do something, and there are more deltas, we should recurse
+            # to treat the resulting expression properly
+            if d.killable_index.is_Symbol and indices[d.killable_index]:
+                e = e.subs(d.killable_index, d.preferred_index)
+                if len(deltas) > 1:
+                    return evaluate_deltas(e)
+            elif (d.preferred_index.is_Symbol and indices[d.preferred_index]
+                  and d.indices_contain_equal_information):
+                e = e.subs(d.preferred_index, d.killable_index)
+                if len(deltas) > 1:
+                    return evaluate_deltas(e)
+            else:
+                pass
+
+        return e
+    # nothing to do, maybe we hit a Symbol or a number
+    else:
+        return e
+
+
+def substitute_dummies(expr, new_indices=False, pretty_indices={}):
+    """
+    Collect terms by substitution of dummy variables.
+
+    Explanation
+    ===========
+
+    This routine allows simplification of Add expressions containing terms
+    which differ only due to dummy variables.
+
+    The idea is to substitute all dummy variables consistently depending on
+    the structure of the term.  For each term, we obtain a sequence of all
+    dummy variables, where the order is determined by the index range, what
+    factors the index belongs to and its position in each factor.  See
+    _get_ordered_dummies() for more information about the sorting of dummies.
+    The index sequence is then substituted consistently in each term.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Function, Dummy
+    >>> from sympy.physics.secondquant import substitute_dummies
+    >>> a,b,c,d = symbols('a b c d', above_fermi=True, cls=Dummy)
+    >>> i,j = symbols('i j', below_fermi=True, cls=Dummy)
+    >>> f = Function('f')
+
+    >>> expr = f(a,b) + f(c,d); expr
+    f(_a, _b) + f(_c, _d)
+
+    Since a, b, c and d are equivalent summation indices, the expression can be
+    simplified to a single term (for which the dummy indices are still summed over)
+
+    >>> substitute_dummies(expr)
+    2*f(_a, _b)
+
+
+    Controlling output:
+
+    By default the dummy symbols that are already present in the expression
+    will be reused in a different permutation.  However, if new_indices=True,
+    new dummies will be generated and inserted.  The keyword 'pretty_indices'
+    can be used to control this generation of new symbols.
+
+    By default the new dummies will be generated on the form i_1, i_2, a_1,
+    etc.  If you supply a dictionary with key:value pairs in the form:
+
+        { index_group: string_of_letters }
+
+    The letters will be used as labels for the new dummy symbols.  The
+    index_groups must be one of 'above', 'below' or 'general'.
+
+    >>> expr = f(a,b,i,j)
+    >>> my_dummies = { 'above':'st', 'below':'uv' }
+    >>> substitute_dummies(expr, new_indices=True, pretty_indices=my_dummies)
+    f(_s, _t, _u, _v)
+
+    If we run out of letters, or if there is no keyword for some index_group
+    the default dummy generator will be used as a fallback:
+
+    >>> p,q = symbols('p q', cls=Dummy)  # general indices
+    >>> expr = f(p,q)
+    >>> substitute_dummies(expr, new_indices=True, pretty_indices=my_dummies)
+    f(_p_0, _p_1)
+
+    """
+
+    # setup the replacing dummies
+    if new_indices:
+        letters_above = pretty_indices.get('above', "")
+        letters_below = pretty_indices.get('below', "")
+        letters_general = pretty_indices.get('general', "")
+        len_above = len(letters_above)
+        len_below = len(letters_below)
+        len_general = len(letters_general)
+
+        def _i(number):
+            try:
+                return letters_below[number]
+            except IndexError:
+                return 'i_' + str(number - len_below)
+
+        def _a(number):
+            try:
+                return letters_above[number]
+            except IndexError:
+                return 'a_' + str(number - len_above)
+
+        def _p(number):
+            try:
+                return letters_general[number]
+            except IndexError:
+                return 'p_' + str(number - len_general)
+
+    aboves = []
+    belows = []
+    generals = []
+
+    dummies = expr.atoms(Dummy)
+    if not new_indices:
+        dummies = sorted(dummies, key=default_sort_key)
+
+    # generate lists with the dummies we will insert
+    a = i = p = 0
+    for d in dummies:
+        assum = d.assumptions0
+
+        if assum.get("above_fermi"):
+            if new_indices:
+                sym = _a(a)
+                a += 1
+            l1 = aboves
+        elif assum.get("below_fermi"):
+            if new_indices:
+                sym = _i(i)
+                i += 1
+            l1 = belows
+        else:
+            if new_indices:
+                sym = _p(p)
+                p += 1
+            l1 = generals
+
+        if new_indices:
+            l1.append(Dummy(sym, **assum))
+        else:
+            l1.append(d)
+
+    expr = expr.expand()
+    terms = Add.make_args(expr)
+    new_terms = []
+    for term in terms:
+        i = iter(belows)
+        a = iter(aboves)
+        p = iter(generals)
+        ordered = _get_ordered_dummies(term)
+        subsdict = {}
+        for d in ordered:
+            if d.assumptions0.get('below_fermi'):
+                subsdict[d] = next(i)
+            elif d.assumptions0.get('above_fermi'):
+                subsdict[d] = next(a)
+            else:
+                subsdict[d] = next(p)
+        subslist = []
+        final_subs = []
+        for k, v in subsdict.items():
+            if k == v:
+                continue
+            if v in subsdict:
+                # We check if the sequence of substitutions end quickly.  In
+                # that case, we can avoid temporary symbols if we ensure the
+                # correct substitution order.
+                if subsdict[v] in subsdict:
+                    # (x, y) -> (y, x),  we need a temporary variable
+                    x = Dummy('x')
+                    subslist.append((k, x))
+                    final_subs.append((x, v))
+                else:
+                    # (x, y) -> (y, a),  x->y must be done last
+                    # but before temporary variables are resolved
+                    final_subs.insert(0, (k, v))
+            else:
+                subslist.append((k, v))
+        subslist.extend(final_subs)
+        new_terms.append(term.subs(subslist))
+    return Add(*new_terms)
+
+
+class KeyPrinter(StrPrinter):
+    """Printer for which only equal objects are equal in print"""
+    def _print_Dummy(self, expr):
+        return "(%s_%i)" % (expr.name, expr.dummy_index)
+
+
+def __kprint(expr):
+    p = KeyPrinter()
+    return p.doprint(expr)
+
+
+def _get_ordered_dummies(mul, verbose=False):
+    """Returns all dummies in the mul sorted in canonical order.
+
+    Explanation
+    ===========
+
+    The purpose of the canonical ordering is that dummies can be substituted
+    consistently across terms with the result that equivalent terms can be
+    simplified.
+
+    It is not possible to determine if two terms are equivalent based solely on
+    the dummy order.  However, a consistent substitution guided by the ordered
+    dummies should lead to trivially (non-)equivalent terms, thereby revealing
+    the equivalence.  This also means that if two terms have identical sequences of
+    dummies, the (non-)equivalence should already be apparent.
+
+    Strategy
+    --------
+
+    The canonical order is given by an arbitrary sorting rule.  A sort key
+    is determined for each dummy as a tuple that depends on all factors where
+    the index is present.  The dummies are thereby sorted according to the
+    contraction structure of the term, instead of sorting based solely on the
+    dummy symbol itself.
+
+    After all dummies in the term has been assigned a key, we check for identical
+    keys, i.e. unorderable dummies.  If any are found, we call a specialized
+    method, _determine_ambiguous(), that will determine a unique order based
+    on recursive calls to _get_ordered_dummies().
+
+    Key description
+    ---------------
+
+    A high level description of the sort key:
+
+        1. Range of the dummy index
+        2. Relation to external (non-dummy) indices
+        3. Position of the index in the first factor
+        4. Position of the index in the second factor
+
+    The sort key is a tuple with the following components:
+
+        1. A single character indicating the range of the dummy (above, below
+           or general.)
+        2. A list of strings with fully masked string representations of all
+           factors where the dummy is present.  By masked, we mean that dummies
+           are represented by a symbol to indicate either below fermi, above or
+           general.  No other information is displayed about the dummies at
+           this point.  The list is sorted stringwise.
+        3. An integer number indicating the position of the index, in the first
+           factor as sorted in 2.
+        4. An integer number indicating the position of the index, in the second
+           factor as sorted in 2.
+
+    If a factor is either of type AntiSymmetricTensor or SqOperator, the index
+    position in items 3 and 4 is indicated as 'upper' or 'lower' only.
+    (Creation operators are considered upper and annihilation operators lower.)
+
+    If the masked factors are identical, the two factors cannot be ordered
+    unambiguously in item 2.  In this case, items 3, 4 are left out.  If several
+    indices are contracted between the unorderable factors, it will be handled by
+    _determine_ambiguous()
+
+
+    """
+    # setup dicts to avoid repeated calculations in key()
+    args = Mul.make_args(mul)
+    fac_dum = { fac: fac.atoms(Dummy) for fac in args }
+    fac_repr = { fac: __kprint(fac) for fac in args }
+    all_dums = set().union(*fac_dum.values())
+    mask = {}
+    for d in all_dums:
+        if d.assumptions0.get('below_fermi'):
+            mask[d] = '0'
+        elif d.assumptions0.get('above_fermi'):
+            mask[d] = '1'
+        else:
+            mask[d] = '2'
+    dum_repr = {d: __kprint(d) for d in all_dums}
+
+    def _key(d):
+        dumstruct = [ fac for fac in fac_dum if d in fac_dum[fac] ]
+        other_dums = set().union(*[fac_dum[fac] for fac in dumstruct])
+        fac = dumstruct[-1]
+        if other_dums is fac_dum[fac]:
+            other_dums = fac_dum[fac].copy()
+        other_dums.remove(d)
+        masked_facs = [ fac_repr[fac] for fac in dumstruct ]
+        for d2 in other_dums:
+            masked_facs = [ fac.replace(dum_repr[d2], mask[d2])
+                    for fac in masked_facs ]
+        all_masked = [ fac.replace(dum_repr[d], mask[d])
+                       for fac in masked_facs ]
+        masked_facs = dict(list(zip(dumstruct, masked_facs)))
+
+        # dummies for which the ordering cannot be determined
+        if has_dups(all_masked):
+            all_masked.sort()
+            return mask[d], tuple(all_masked)  # positions are ambiguous
+
+        # sort factors according to fully masked strings
+        keydict = dict(list(zip(dumstruct, all_masked)))
+        dumstruct.sort(key=lambda x: keydict[x])
+        all_masked.sort()
+
+        pos_val = []
+        for fac in dumstruct:
+            if isinstance(fac, AntiSymmetricTensor):
+                if d in fac.upper:
+                    pos_val.append('u')
+                if d in fac.lower:
+                    pos_val.append('l')
+            elif isinstance(fac, Creator):
+                pos_val.append('u')
+            elif isinstance(fac, Annihilator):
+                pos_val.append('l')
+            elif isinstance(fac, NO):
+                ops = [ op for op in fac if op.has(d) ]
+                for op in ops:
+                    if isinstance(op, Creator):
+                        pos_val.append('u')
+                    else:
+                        pos_val.append('l')
+            else:
+                # fallback to position in string representation
+                facpos = -1
+                while 1:
+                    facpos = masked_facs[fac].find(dum_repr[d], facpos + 1)
+                    if facpos == -1:
+                        break
+                    pos_val.append(facpos)
+        return (mask[d], tuple(all_masked), pos_val[0], pos_val[-1])
+    dumkey = dict(list(zip(all_dums, list(map(_key, all_dums)))))
+    result = sorted(all_dums, key=lambda x: dumkey[x])
+    if has_dups(iter(dumkey.values())):
+        # We have ambiguities
+        unordered = defaultdict(set)
+        for d, k in dumkey.items():
+            unordered[k].add(d)
+        for k in [ k for k in unordered if len(unordered[k]) < 2 ]:
+            del unordered[k]
+
+        unordered = [ unordered[k] for k in sorted(unordered) ]
+        result = _determine_ambiguous(mul, result, unordered)
+    return result
+
+
+def _determine_ambiguous(term, ordered, ambiguous_groups):
+    # We encountered a term for which the dummy substitution is ambiguous.
+    # This happens for terms with 2 or more contractions between factors that
+    # cannot be uniquely ordered independent of summation indices.  For
+    # example:
+    #
+    # Sum(p, q) v^{p, .}_{q, .}v^{q, .}_{p, .}
+    #
+    # Assuming that the indices represented by . are dummies with the
+    # same range, the factors cannot be ordered, and there is no
+    # way to determine a consistent ordering of p and q.
+    #
+    # The strategy employed here, is to relabel all unambiguous dummies with
+    # non-dummy symbols and call _get_ordered_dummies again.  This procedure is
+    # applied to the entire term so there is a possibility that
+    # _determine_ambiguous() is called again from a deeper recursion level.
+
+    # break recursion if there are no ordered dummies
+    all_ambiguous = set()
+    for dummies in ambiguous_groups:
+        all_ambiguous |= dummies
+    all_ordered = set(ordered) - all_ambiguous
+    if not all_ordered:
+        # FIXME: If we arrive here, there are no ordered dummies. A method to
+        # handle this needs to be implemented.  In order to return something
+        # useful nevertheless, we choose arbitrarily the first dummy and
+        # determine the rest from this one.  This method is dependent on the
+        # actual dummy labels which violates an assumption for the
+        # canonicalization procedure.  A better implementation is needed.
+        group = [ d for d in ordered if d in ambiguous_groups[0] ]
+        d = group[0]
+        all_ordered.add(d)
+        ambiguous_groups[0].remove(d)
+
+    stored_counter = _symbol_factory._counter
+    subslist = []
+    for d in [ d for d in ordered if d in all_ordered ]:
+        nondum = _symbol_factory._next()
+        subslist.append((d, nondum))
+    newterm = term.subs(subslist)
+    neworder = _get_ordered_dummies(newterm)
+    _symbol_factory._set_counter(stored_counter)
+
+    # update ordered list with new information
+    for group in ambiguous_groups:
+        ordered_group = [ d for d in neworder if d in group ]
+        ordered_group.reverse()
+        result = []
+        for d in ordered:
+            if d in group:
+                result.append(ordered_group.pop())
+            else:
+                result.append(d)
+        ordered = result
+    return ordered
+
+
+class _SymbolFactory:
+    def __init__(self, label):
+        self._counterVar = 0
+        self._label = label
+
+    def _set_counter(self, value):
+        """
+        Sets counter to value.
+        """
+        self._counterVar = value
+
+    @property
+    def _counter(self):
+        """
+        What counter is currently at.
+        """
+        return self._counterVar
+
+    def _next(self):
+        """
+        Generates the next symbols and increments counter by 1.
+        """
+        s = Symbol("%s%i" % (self._label, self._counterVar))
+        self._counterVar += 1
+        return s
+_symbol_factory = _SymbolFactory('_]"]_')  # most certainly a unique label
+
+
+@cacheit
+def _get_contractions(string1, keep_only_fully_contracted=False):
+    """
+    Returns Add-object with contracted terms.
+
+    Uses recursion to find all contractions. -- Internal helper function --
+
+    Will find nonzero contractions in string1 between indices given in
+    leftrange and rightrange.
+
+    """
+
+    # Should we store current level of contraction?
+    if keep_only_fully_contracted and string1:
+        result = []
+    else:
+        result = [NO(Mul(*string1))]
+
+    for i in range(len(string1) - 1):
+        for j in range(i + 1, len(string1)):
+
+            c = contraction(string1[i], string1[j])
+
+            if c:
+                sign = (j - i + 1) % 2
+                if sign:
+                    coeff = S.NegativeOne*c
+                else:
+                    coeff = c
+
+                #
+                #  Call next level of recursion
+                #  ============================
+                #
+                # We now need to find more contractions among operators
+                #
+                # oplist = string1[:i]+ string1[i+1:j] + string1[j+1:]
+                #
+                # To prevent overcounting, we don't allow contractions
+                # we have already encountered. i.e. contractions between
+                #       string1[:i] <---> string1[i+1:j]
+                # and   string1[:i] <---> string1[j+1:].
+                #
+                # This leaves the case:
+                oplist = string1[i + 1:j] + string1[j + 1:]
+
+                if oplist:
+
+                    result.append(coeff*NO(
+                        Mul(*string1[:i])*_get_contractions( oplist,
+                            keep_only_fully_contracted=keep_only_fully_contracted)))
+
+                else:
+                    result.append(coeff*NO( Mul(*string1[:i])))
+
+        if keep_only_fully_contracted:
+            break   # next iteration over i leaves leftmost operator string1[0] uncontracted
+
+    return Add(*result)
+
+
+def wicks(e, **kw_args):
+    """
+    Returns the normal ordered equivalent of an expression using Wicks Theorem.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Dummy
+    >>> from sympy.physics.secondquant import wicks, F, Fd
+    >>> p, q, r = symbols('p,q,r')
+    >>> wicks(Fd(p)*F(q))
+    KroneckerDelta(_i, q)*KroneckerDelta(p, q) + NO(CreateFermion(p)*AnnihilateFermion(q))
+
+    By default, the expression is expanded:
+
+    >>> wicks(F(p)*(F(q)+F(r)))
+    NO(AnnihilateFermion(p)*AnnihilateFermion(q)) + NO(AnnihilateFermion(p)*AnnihilateFermion(r))
+
+    With the keyword 'keep_only_fully_contracted=True', only fully contracted
+    terms are returned.
+
+    By request, the result can be simplified in the following order:
+     -- KroneckerDelta functions are evaluated
+     -- Dummy variables are substituted consistently across terms
+
+    >>> p, q, r = symbols('p q r', cls=Dummy)
+    >>> wicks(Fd(p)*(F(q)+F(r)), keep_only_fully_contracted=True)
+    KroneckerDelta(_i, _q)*KroneckerDelta(_p, _q) + KroneckerDelta(_i, _r)*KroneckerDelta(_p, _r)
+
+    """
+
+    if not e:
+        return S.Zero
+
+    opts = {
+        'simplify_kronecker_deltas': False,
+        'expand': True,
+        'simplify_dummies': False,
+        'keep_only_fully_contracted': False
+    }
+    opts.update(kw_args)
+
+    # check if we are already normally ordered
+    if isinstance(e, NO):
+        if opts['keep_only_fully_contracted']:
+            return S.Zero
+        else:
+            return e
+    elif isinstance(e, FermionicOperator):
+        if opts['keep_only_fully_contracted']:
+            return S.Zero
+        else:
+            return e
+
+    # break up any NO-objects, and evaluate commutators
+    e = e.doit(wicks=True)
+
+    # make sure we have only one term to consider
+    e = e.expand()
+    if isinstance(e, Add):
+        if opts['simplify_dummies']:
+            return substitute_dummies(Add(*[ wicks(term, **kw_args) for term in e.args]))
+        else:
+            return Add(*[ wicks(term, **kw_args) for term in e.args])
+
+    # For Mul-objects we can actually do something
+    if isinstance(e, Mul):
+
+        # we don't want to mess around with commuting part of Mul
+        # so we factorize it out before starting recursion
+        c_part = []
+        string1 = []
+        for factor in e.args:
+            if factor.is_commutative:
+                c_part.append(factor)
+            else:
+                string1.append(factor)
+        n = len(string1)
+
+        # catch trivial cases
+        if n == 0:
+            result = e
+        elif n == 1:
+            if opts['keep_only_fully_contracted']:
+                return S.Zero
+            else:
+                result = e
+
+        else:  # non-trivial
+
+            if isinstance(string1[0], BosonicOperator):
+                raise NotImplementedError
+
+            string1 = tuple(string1)
+
+            # recursion over higher order contractions
+            result = _get_contractions(string1,
+                keep_only_fully_contracted=opts['keep_only_fully_contracted'] )
+            result = Mul(*c_part)*result
+
+        if opts['expand']:
+            result = result.expand()
+        if opts['simplify_kronecker_deltas']:
+            result = evaluate_deltas(result)
+
+        return result
+
+    # there was nothing to do
+    return e
+
+
+class PermutationOperator(Expr):
+    """
+    Represents the index permutation operator P(ij).
+
+    P(ij)*f(i)*g(j) = f(i)*g(j) - f(j)*g(i)
+    """
+    is_commutative = True
+
+    def __new__(cls, i, j):
+        i, j = sorted(map(sympify, (i, j)), key=default_sort_key)
+        obj = Basic.__new__(cls, i, j)
+        return obj
+
+    def get_permuted(self, expr):
+        """
+        Returns -expr with permuted indices.
+
+        Explanation
+        ===========
+
+        >>> from sympy import symbols, Function
+        >>> from sympy.physics.secondquant import PermutationOperator
+        >>> p,q = symbols('p,q')
+        >>> f = Function('f')
+        >>> PermutationOperator(p,q).get_permuted(f(p,q))
+        -f(q, p)
+
+        """
+        i = self.args[0]
+        j = self.args[1]
+        if expr.has(i) and expr.has(j):
+            tmp = Dummy()
+            expr = expr.subs(i, tmp)
+            expr = expr.subs(j, i)
+            expr = expr.subs(tmp, j)
+            return S.NegativeOne*expr
+        else:
+            return expr
+
+    def _latex(self, printer):
+        return "P(%s%s)" % tuple(printer._print(i) for i in self.args)
+
+
+def simplify_index_permutations(expr, permutation_operators):
+    """
+    Performs simplification by introducing PermutationOperators where appropriate.
+
+    Explanation
+    ===========
+
+    Schematically:
+        [abij] - [abji] - [baij] + [baji] ->  P(ab)*P(ij)*[abij]
+
+    permutation_operators is a list of PermutationOperators to consider.
+
+    If permutation_operators=[P(ab),P(ij)] we will try to introduce the
+    permutation operators P(ij) and P(ab) in the expression.  If there are other
+    possible simplifications, we ignore them.
+
+    >>> from sympy import symbols, Function
+    >>> from sympy.physics.secondquant import simplify_index_permutations
+    >>> from sympy.physics.secondquant import PermutationOperator
+    >>> p,q,r,s = symbols('p,q,r,s')
+    >>> f = Function('f')
+    >>> g = Function('g')
+
+    >>> expr = f(p)*g(q) - f(q)*g(p); expr
+    f(p)*g(q) - f(q)*g(p)
+    >>> simplify_index_permutations(expr,[PermutationOperator(p,q)])
+    f(p)*g(q)*PermutationOperator(p, q)
+
+    >>> PermutList = [PermutationOperator(p,q),PermutationOperator(r,s)]
+    >>> expr = f(p,r)*g(q,s) - f(q,r)*g(p,s) + f(q,s)*g(p,r) - f(p,s)*g(q,r)
+    >>> simplify_index_permutations(expr,PermutList)
+    f(p, r)*g(q, s)*PermutationOperator(p, q)*PermutationOperator(r, s)
+
+    """
+
+    def _get_indices(expr, ind):
+        """
+        Collects indices recursively in predictable order.
+        """
+        result = []
+        for arg in expr.args:
+            if arg in ind:
+                result.append(arg)
+            else:
+                if arg.args:
+                    result.extend(_get_indices(arg, ind))
+        return result
+
+    def _choose_one_to_keep(a, b, ind):
+        # we keep the one where indices in ind are in order ind[0] < ind[1]
+        return min(a, b, key=lambda x: default_sort_key(_get_indices(x, ind)))
+
+    expr = expr.expand()
+    if isinstance(expr, Add):
+        terms = set(expr.args)
+
+        for P in permutation_operators:
+            new_terms = set()
+            on_hold = set()
+            while terms:
+                term = terms.pop()
+                permuted = P.get_permuted(term)
+                if permuted in terms | on_hold:
+                    try:
+                        terms.remove(permuted)
+                    except KeyError:
+                        on_hold.remove(permuted)
+                    keep = _choose_one_to_keep(term, permuted, P.args)
+                    new_terms.add(P*keep)
+                else:
+
+                    # Some terms must get a second chance because the permuted
+                    # term may already have canonical dummy ordering.  Then
+                    # substitute_dummies() does nothing.  However, the other
+                    # term, if it exists, will be able to match with us.
+                    permuted1 = permuted
+                    permuted = substitute_dummies(permuted)
+                    if permuted1 == permuted:
+                        on_hold.add(term)
+                    elif permuted in terms | on_hold:
+                        try:
+                            terms.remove(permuted)
+                        except KeyError:
+                            on_hold.remove(permuted)
+                        keep = _choose_one_to_keep(term, permuted, P.args)
+                        new_terms.add(P*keep)
+                    else:
+                        new_terms.add(term)
+            terms = new_terms | on_hold
+        return Add(*terms)
+    return expr
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/sho.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/sho.py
new file mode 100644
index 0000000000000000000000000000000000000000..c55b31b3fa9fca4fa33a9f8e91c90c2174fe81a5
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/sho.py
@@ -0,0 +1,95 @@
+from sympy.core import S, pi, Rational
+from sympy.functions import assoc_laguerre, sqrt, exp, factorial, factorial2
+
+
+def R_nl(n, l, nu, r):
+    """
+    Returns the radial wavefunction R_{nl} for a 3d isotropic harmonic
+    oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.  Corresponds to the number of nodes in
+        the wavefunction.  ``n >= 0``
+    l :
+        The quantum number for orbital angular momentum.
+    nu :
+        mass-scaled frequency: nu = m*omega/(2*hbar) where `m` is the mass
+        and `omega` the frequency of the oscillator.
+        (in atomic units ``nu == omega/2``)
+    r :
+        Radial coordinate.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.sho import R_nl
+    >>> from sympy.abc import r, nu, l
+    >>> R_nl(0, 0, 1, r)
+    2*2**(3/4)*exp(-r**2)/pi**(1/4)
+    >>> R_nl(1, 0, 1, r)
+    4*2**(1/4)*sqrt(3)*(3/2 - 2*r**2)*exp(-r**2)/(3*pi**(1/4))
+
+    l, nu and r may be symbolic:
+
+    >>> R_nl(0, 0, nu, r)
+    2*2**(3/4)*sqrt(nu**(3/2))*exp(-nu*r**2)/pi**(1/4)
+    >>> R_nl(0, l, 1, r)
+    r**l*sqrt(2**(l + 3/2)*2**(l + 2)/factorial2(2*l + 1))*exp(-r**2)/pi**(1/4)
+
+    The normalization of the radial wavefunction is:
+
+    >>> from sympy import Integral, oo
+    >>> Integral(R_nl(0, 0, 1, r)**2*r**2, (r, 0, oo)).n()
+    1.00000000000000
+    >>> Integral(R_nl(1, 0, 1, r)**2*r**2, (r, 0, oo)).n()
+    1.00000000000000
+    >>> Integral(R_nl(1, 1, 1, r)**2*r**2, (r, 0, oo)).n()
+    1.00000000000000
+
+    """
+    n, l, nu, r = map(S, [n, l, nu, r])
+
+    # formula uses n >= 1 (instead of nodal n >= 0)
+    n = n + 1
+    C = sqrt(
+            ((2*nu)**(l + Rational(3, 2))*2**(n + l + 1)*factorial(n - 1))/
+            (sqrt(pi)*(factorial2(2*n + 2*l - 1)))
+    )
+    return C*r**(l)*exp(-nu*r**2)*assoc_laguerre(n - 1, l + S.Half, 2*nu*r**2)
+
+
+def E_nl(n, l, hw):
+    """
+    Returns the Energy of an isotropic harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    l :
+        The orbital angular momentum.
+    hw :
+        The harmonic oscillator parameter.
+
+    Notes
+    =====
+
+    The unit of the returned value matches the unit of hw, since the energy is
+    calculated as:
+
+        E_nl = (2*n + l + 3/2)*hw
+
+    Examples
+    ========
+
+    >>> from sympy.physics.sho import E_nl
+    >>> from sympy import symbols
+    >>> x, y, z = symbols('x, y, z')
+    >>> E_nl(x, y, z)
+    z*(2*x + y + 3/2)
+    """
+    return (2*n + l + Rational(3, 2))*hw
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/wigner.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/wigner.py
new file mode 100644
index 0000000000000000000000000000000000000000..e08f3fb4a480439fd2bb1f8ff8c305bf69d7abae
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/physics/wigner.py
@@ -0,0 +1,1213 @@
+# -*- coding: utf-8 -*-
+r"""
+Wigner, Clebsch-Gordan, Racah, and Gaunt coefficients
+
+Collection of functions for calculating Wigner 3j, 6j, 9j,
+Clebsch-Gordan, Racah as well as Gaunt coefficients exactly, all
+evaluating to a rational number times the square root of a rational
+number [Rasch03]_.
+
+Please see the description of the individual functions for further
+details and examples.
+
+References
+==========
+
+.. [Regge58] 'Symmetry Properties of Clebsch-Gordan Coefficients',
+  T. Regge, Nuovo Cimento, Volume 10, pp. 544 (1958)
+.. [Regge59] 'Symmetry Properties of Racah Coefficients',
+  T. Regge, Nuovo Cimento, Volume 11, pp. 116 (1959)
+.. [Edmonds74] A. R. Edmonds. Angular momentum in quantum mechanics.
+  Investigations in physics, 4.; Investigations in physics, no. 4.
+  Princeton, N.J., Princeton University Press, 1957.
+.. [Rasch03] J. Rasch and A. C. H. Yu, 'Efficient Storage Scheme for
+  Pre-calculated Wigner 3j, 6j and Gaunt Coefficients', SIAM
+  J. Sci. Comput. Volume 25, Issue 4, pp. 1416-1428 (2003)
+.. [Liberatodebrito82] 'FORTRAN program for the integral of three
+  spherical harmonics', A. Liberato de Brito,
+  Comput. Phys. Commun., Volume 25, pp. 81-85 (1982)
+.. [Homeier96] 'Some Properties of the Coupling Coefficients of Real
+  Spherical Harmonics and Their Relation to Gaunt Coefficients',
+  H. H. H. Homeier and E. O. Steinborn J. Mol. Struct., Volume 368,
+  pp. 31-37 (1996)
+
+Credits and Copyright
+=====================
+
+This code was taken from Sage with the permission of all authors:
+
+https://groups.google.com/forum/#!topic/sage-devel/M4NZdu-7O38
+
+Authors
+=======
+
+- Jens Rasch (2009-03-24): initial version for Sage
+
+- Jens Rasch (2009-05-31): updated to sage-4.0
+
+- Oscar Gerardo Lazo Arjona (2017-06-18): added Wigner D matrices
+
+- Phil Adam LeMaitre (2022-09-19): added real Gaunt coefficient
+
+Copyright (C) 2008 Jens Rasch 
+
+"""
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.numbers import int_valued
+from sympy.core.function import Function
+from sympy.core.numbers import (Float, I, Integer, pi, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import (binomial, factorial)
+from sympy.functions.elementary.complexes import re
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.spherical_harmonics import Ynm
+from sympy.matrices.dense import zeros
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.utilities.misc import as_int
+
+# This list of precomputed factorials is needed to massively
+# accelerate future calculations of the various coefficients
+_Factlist = [1]
+
+
+def _calc_factlist(nn):
+    r"""
+    Function calculates a list of precomputed factorials in order to
+    massively accelerate future calculations of the various
+    coefficients.
+
+    Parameters
+    ==========
+
+    nn : integer
+        Highest factorial to be computed.
+
+    Returns
+    =======
+
+    list of integers :
+        The list of precomputed factorials.
+
+    Examples
+    ========
+
+    Calculate list of factorials::
+
+        sage: from sage.functions.wigner import _calc_factlist
+        sage: _calc_factlist(10)
+        [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
+    """
+    if nn >= len(_Factlist):
+        for ii in range(len(_Factlist), int(nn + 1)):
+            _Factlist.append(_Factlist[ii - 1] * ii)
+    return _Factlist[:int(nn) + 1]
+
+
+def _int_or_halfint(value):
+    """return Python int unless value is half-int (then return float)"""
+    if isinstance(value, int):
+        return value
+    elif type(value) is float:
+        if value.is_integer():
+            return int(value)  # an int
+        if (2*value).is_integer():
+            return value  # a float
+    elif isinstance(value, Rational):
+        if value.q == 2:
+            return value.p/value.q  # a float
+        elif value.q == 1:
+            return value.p  # an int
+    elif isinstance(value, Float):
+        return _int_or_halfint(float(value))
+    raise ValueError("expecting integer or half-integer, got %s" % value)
+
+
+def wigner_3j(j_1, j_2, j_3, m_1, m_2, m_3):
+    r"""
+    Calculate the Wigner 3j symbol `\operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,m_3)`.
+
+    Parameters
+    ==========
+
+    j_1, j_2, j_3, m_1, m_2, m_3 :
+        Integer or half integer.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import wigner_3j
+    >>> wigner_3j(2, 6, 4, 0, 0, 0)
+    sqrt(715)/143
+    >>> wigner_3j(2, 6, 4, 0, 0, 1)
+    0
+
+    It is an error to have arguments that are not integer or half
+    integer values::
+
+        sage: wigner_3j(2.1, 6, 4, 0, 0, 0)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer
+        sage: wigner_3j(2, 6, 4, 1, 0, -1.1)
+        Traceback (most recent call last):
+        ...
+        ValueError: m values must be integer or half integer
+
+    Notes
+    =====
+
+    The Wigner 3j symbol obeys the following symmetry rules:
+
+    - invariant under any permutation of the columns (with the
+      exception of a sign change where `J:=j_1+j_2+j_3`):
+
+      .. math::
+
+         \begin{aligned}
+         \operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,m_3)
+          &=\operatorname{Wigner3j}(j_3,j_1,j_2,m_3,m_1,m_2) \\
+          &=\operatorname{Wigner3j}(j_2,j_3,j_1,m_2,m_3,m_1) \\
+          &=(-1)^J \operatorname{Wigner3j}(j_3,j_2,j_1,m_3,m_2,m_1) \\
+          &=(-1)^J \operatorname{Wigner3j}(j_1,j_3,j_2,m_1,m_3,m_2) \\
+          &=(-1)^J \operatorname{Wigner3j}(j_2,j_1,j_3,m_2,m_1,m_3)
+         \end{aligned}
+
+    - invariant under space inflection, i.e.
+
+      .. math::
+
+         \operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,m_3)
+         =(-1)^J \operatorname{Wigner3j}(j_1,j_2,j_3,-m_1,-m_2,-m_3)
+
+    - symmetric with respect to the 72 additional symmetries based on
+      the work by [Regge58]_
+
+    - zero for `j_1`, `j_2`, `j_3` not fulfilling triangle relation
+
+    - zero for `m_1 + m_2 + m_3 \neq 0`
+
+    - zero for violating any one of the conditions
+         `m_1  \in \{-|j_1|, \ldots, |j_1|\}`,
+         `m_2  \in \{-|j_2|, \ldots, |j_2|\}`,
+         `m_3  \in \{-|j_3|, \ldots, |j_3|\}`
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 3j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+
+    Authors
+    =======
+
+    - Jens Rasch (2009-03-24): initial version
+    """
+
+    j_1, j_2, j_3, m_1, m_2, m_3 = \
+        map(_int_or_halfint, map(sympify,
+            [j_1, j_2, j_3, m_1, m_2, m_3]))
+
+    if m_1 + m_2 + m_3 != 0:
+        return S.Zero
+    a1 = j_1 + j_2 - j_3
+    if a1 < 0:
+        return S.Zero
+    a2 = j_1 - j_2 + j_3
+    if a2 < 0:
+        return S.Zero
+    a3 = -j_1 + j_2 + j_3
+    if a3 < 0:
+        return S.Zero
+    if (abs(m_1) > j_1) or (abs(m_2) > j_2) or (abs(m_3) > j_3):
+        return S.Zero
+    if not (int_valued(j_1 - m_1) and \
+            int_valued(j_2 - m_2) and \
+            int_valued(j_3 - m_3)):
+        return S.Zero
+
+    maxfact = max(j_1 + j_2 + j_3 + 1, j_1 + abs(m_1), j_2 + abs(m_2),
+                  j_3 + abs(m_3))
+    _calc_factlist(int(maxfact))
+
+    argsqrt = Integer(_Factlist[int(j_1 + j_2 - j_3)] *
+                     _Factlist[int(j_1 - j_2 + j_3)] *
+                     _Factlist[int(-j_1 + j_2 + j_3)] *
+                     _Factlist[int(j_1 - m_1)] *
+                     _Factlist[int(j_1 + m_1)] *
+                     _Factlist[int(j_2 - m_2)] *
+                     _Factlist[int(j_2 + m_2)] *
+                     _Factlist[int(j_3 - m_3)] *
+                     _Factlist[int(j_3 + m_3)]) / \
+        _Factlist[int(j_1 + j_2 + j_3 + 1)]
+
+    ressqrt = sqrt(argsqrt)
+    if ressqrt.is_complex or ressqrt.is_infinite:
+        ressqrt = ressqrt.as_real_imag()[0]
+
+    imin = max(-j_3 + j_1 + m_2, -j_3 + j_2 - m_1, 0)
+    imax = min(j_2 + m_2, j_1 - m_1, j_1 + j_2 - j_3)
+    sumres = 0
+    for ii in range(int(imin), int(imax) + 1):
+        den = _Factlist[ii] * \
+            _Factlist[int(ii + j_3 - j_1 - m_2)] * \
+            _Factlist[int(j_2 + m_2 - ii)] * \
+            _Factlist[int(j_1 - ii - m_1)] * \
+            _Factlist[int(ii + j_3 - j_2 + m_1)] * \
+            _Factlist[int(j_1 + j_2 - j_3 - ii)]
+        sumres = sumres + Integer((-1) ** ii) / den
+
+    prefid = Integer((-1) ** int(j_1 - j_2 - m_3))
+    res = ressqrt * sumres * prefid
+    return res
+
+
+def clebsch_gordan(j_1, j_2, j_3, m_1, m_2, m_3):
+    r"""
+    Calculates the Clebsch-Gordan coefficient.
+    `\left\langle j_1 m_1 \; j_2 m_2 | j_3 m_3 \right\rangle`.
+
+    The reference for this function is [Edmonds74]_.
+
+    Parameters
+    ==========
+
+    j_1, j_2, j_3, m_1, m_2, m_3 :
+        Integer or half integer.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> from sympy.physics.wigner import clebsch_gordan
+    >>> clebsch_gordan(S(3)/2, S(1)/2, 2, S(3)/2, S(1)/2, 2)
+    1
+    >>> clebsch_gordan(S(3)/2, S(1)/2, 1, S(3)/2, -S(1)/2, 1)
+    sqrt(3)/2
+    >>> clebsch_gordan(S(3)/2, S(1)/2, 1, -S(1)/2, S(1)/2, 0)
+    -sqrt(2)/2
+
+    Notes
+    =====
+
+    The Clebsch-Gordan coefficient will be evaluated via its relation
+    to Wigner 3j symbols:
+
+    .. math::
+
+        \left\langle j_1 m_1 \; j_2 m_2 | j_3 m_3 \right\rangle
+        =(-1)^{j_1-j_2+m_3} \sqrt{2j_3+1}
+        \operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,-m_3)
+
+    See also the documentation on Wigner 3j symbols which exhibit much
+    higher symmetry relations than the Clebsch-Gordan coefficient.
+
+    Authors
+    =======
+
+    - Jens Rasch (2009-03-24): initial version
+    """
+    j_1 = sympify(j_1)
+    j_2 = sympify(j_2)
+    j_3 = sympify(j_3)
+    m_1 = sympify(m_1)
+    m_2 = sympify(m_2)
+    m_3 = sympify(m_3)
+
+    w = wigner_3j(j_1, j_2, j_3, m_1, m_2, -m_3)
+
+    return (-1) ** (j_1 - j_2 + m_3) * sqrt(2 * j_3 + 1) * w
+
+
+def _big_delta_coeff(aa, bb, cc, prec=None):
+    r"""
+    Calculates the Delta coefficient of the 3 angular momenta for
+    Racah symbols. Also checks that the differences are of integer
+    value.
+
+    Parameters
+    ==========
+
+    aa :
+        First angular momentum, integer or half integer.
+    bb :
+        Second angular momentum, integer or half integer.
+    cc :
+        Third angular momentum, integer or half integer.
+    prec :
+        Precision of the ``sqrt()`` calculation.
+
+    Returns
+    =======
+
+    double : Value of the Delta coefficient.
+
+    Examples
+    ========
+
+        sage: from sage.functions.wigner import _big_delta_coeff
+        sage: _big_delta_coeff(1,1,1)
+        1/2*sqrt(1/6)
+    """
+
+    # the triangle test will only pass if a) all 3 values are ints or
+    # b) 1 is an int and the other two are half-ints
+    if not int_valued(aa + bb - cc):
+        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
+    if not int_valued(aa + cc - bb):
+        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
+    if not int_valued(bb + cc - aa):
+        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
+    if (aa + bb - cc) < 0:
+        return S.Zero
+    if (aa + cc - bb) < 0:
+        return S.Zero
+    if (bb + cc - aa) < 0:
+        return S.Zero
+
+    maxfact = max(aa + bb - cc, aa + cc - bb, bb + cc - aa, aa + bb + cc + 1)
+    _calc_factlist(maxfact)
+
+    argsqrt = Integer(_Factlist[int(aa + bb - cc)] *
+                     _Factlist[int(aa + cc - bb)] *
+                     _Factlist[int(bb + cc - aa)]) / \
+        Integer(_Factlist[int(aa + bb + cc + 1)])
+
+    ressqrt = sqrt(argsqrt)
+    if prec:
+        ressqrt = ressqrt.evalf(prec).as_real_imag()[0]
+    return ressqrt
+
+
+def racah(aa, bb, cc, dd, ee, ff, prec=None):
+    r"""
+    Calculate the Racah symbol `W(a,b,c,d;e,f)`.
+
+    Parameters
+    ==========
+
+    a, ..., f :
+        Integer or half integer.
+    prec :
+        Precision, default: ``None``. Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import racah
+    >>> racah(3,3,3,3,3,3)
+    -1/14
+
+    Notes
+    =====
+
+    The Racah symbol is related to the Wigner 6j symbol:
+
+    .. math::
+
+       \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+       =(-1)^{j_1+j_2+j_4+j_5} W(j_1,j_2,j_5,j_4,j_3,j_6)
+
+    Please see the 6j symbol for its much richer symmetries and for
+    additional properties.
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 6j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+
+    Authors
+    =======
+
+    - Jens Rasch (2009-03-24): initial version
+    """
+    prefac = _big_delta_coeff(aa, bb, ee, prec) * \
+        _big_delta_coeff(cc, dd, ee, prec) * \
+        _big_delta_coeff(aa, cc, ff, prec) * \
+        _big_delta_coeff(bb, dd, ff, prec)
+    if prefac == 0:
+        return S.Zero
+    imin = max(aa + bb + ee, cc + dd + ee, aa + cc + ff, bb + dd + ff)
+    imax = min(aa + bb + cc + dd, aa + dd + ee + ff, bb + cc + ee + ff)
+
+    maxfact = max(imax + 1, aa + bb + cc + dd, aa + dd + ee + ff,
+                 bb + cc + ee + ff)
+    _calc_factlist(maxfact)
+
+    sumres = 0
+    for kk in range(int(imin), int(imax) + 1):
+        den = _Factlist[int(kk - aa - bb - ee)] * \
+            _Factlist[int(kk - cc - dd - ee)] * \
+            _Factlist[int(kk - aa - cc - ff)] * \
+            _Factlist[int(kk - bb - dd - ff)] * \
+            _Factlist[int(aa + bb + cc + dd - kk)] * \
+            _Factlist[int(aa + dd + ee + ff - kk)] * \
+            _Factlist[int(bb + cc + ee + ff - kk)]
+        sumres = sumres + Integer((-1) ** kk * _Factlist[kk + 1]) / den
+
+    res = prefac * sumres * (-1) ** int(aa + bb + cc + dd)
+    return res
+
+
+def wigner_6j(j_1, j_2, j_3, j_4, j_5, j_6, prec=None):
+    r"""
+    Calculate the Wigner 6j symbol `\operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)`.
+
+    Parameters
+    ==========
+
+    j_1, ..., j_6 :
+        Integer or half integer.
+    prec :
+        Precision, default: ``None``. Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import wigner_6j
+    >>> wigner_6j(3,3,3,3,3,3)
+    -1/14
+    >>> wigner_6j(5,5,5,5,5,5)
+    1/52
+
+    It is an error to have arguments that are not integer or half
+    integer values or do not fulfill the triangle relation::
+
+        sage: wigner_6j(2.5,2.5,2.5,2.5,2.5,2.5)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+        sage: wigner_6j(0.5,0.5,1.1,0.5,0.5,1.1)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+
+    Notes
+    =====
+
+    The Wigner 6j symbol is related to the Racah symbol but exhibits
+    more symmetries as detailed below.
+
+    .. math::
+
+       \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+        =(-1)^{j_1+j_2+j_4+j_5} W(j_1,j_2,j_5,j_4,j_3,j_6)
+
+    The Wigner 6j symbol obeys the following symmetry rules:
+
+    - Wigner 6j symbols are left invariant under any permutation of
+      the columns:
+
+      .. math::
+
+         \begin{aligned}
+         \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+          &=\operatorname{Wigner6j}(j_3,j_1,j_2,j_6,j_4,j_5) \\
+          &=\operatorname{Wigner6j}(j_2,j_3,j_1,j_5,j_6,j_4) \\
+          &=\operatorname{Wigner6j}(j_3,j_2,j_1,j_6,j_5,j_4) \\
+          &=\operatorname{Wigner6j}(j_1,j_3,j_2,j_4,j_6,j_5) \\
+          &=\operatorname{Wigner6j}(j_2,j_1,j_3,j_5,j_4,j_6)
+         \end{aligned}
+
+    - They are invariant under the exchange of the upper and lower
+      arguments in each of any two columns, i.e.
+
+      .. math::
+
+         \begin{aligned}
+         \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+          &=\operatorname{Wigner6j}(j_1,j_5,j_6,j_4,j_2,j_3)\\
+          &=\operatorname{Wigner6j}(j_4,j_2,j_6,j_1,j_5,j_3)\\
+          &=\operatorname{Wigner6j}(j_4,j_5,j_3,j_1,j_2,j_6)
+         \end{aligned}
+
+    - additional 6 symmetries [Regge59]_ giving rise to 144 symmetries
+      in total
+
+    - only non-zero if any triple of `j`'s fulfill a triangle relation
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 6j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+
+    """
+    j_1, j_2, j_3, j_4, j_5, j_6 = map(sympify, \
+                [j_1, j_2, j_3, j_4, j_5, j_6])
+    res = (-1) ** int(j_1 + j_2 + j_4 + j_5) * \
+        racah(j_1, j_2, j_5, j_4, j_3, j_6, prec)
+    return res
+
+
+def wigner_9j(j_1, j_2, j_3, j_4, j_5, j_6, j_7, j_8, j_9, prec=None):
+    r"""
+    Calculate the Wigner 9j symbol
+    `\operatorname{Wigner9j}(j_1,j_2,j_3,j_4,j_5,j_6,j_7,j_8,j_9)`.
+
+    Parameters
+    ==========
+
+    j_1, ..., j_9 :
+        Integer or half integer.
+    prec : precision, default
+        ``None``. Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import wigner_9j
+    >>> wigner_9j(1,1,1, 1,1,1, 1,1,0, prec=64)
+    0.05555555555555555555555555555555555555555555555555555555555555555
+
+    >>> wigner_9j(1/2,1/2,0, 1/2,3/2,1, 0,1,1, prec=64)
+    0.1666666666666666666666666666666666666666666666666666666666666667
+
+    It is an error to have arguments that are not integer or half
+    integer values or do not fulfill the triangle relation::
+
+        sage: wigner_9j(0.5,0.5,0.5, 0.5,0.5,0.5, 0.5,0.5,0.5,prec=64)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+        sage: wigner_9j(1,1,1, 0.5,1,1.5, 0.5,1,2.5,prec=64)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 3j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+    """
+    j_1, j_2, j_3, j_4, j_5, j_6, j_7, j_8, j_9 = map(sympify, \
+                [j_1, j_2, j_3, j_4, j_5, j_6, j_7, j_8, j_9])
+    imax = int(min(j_1 + j_9, j_2 + j_6, j_4 + j_8) * 2)
+    imin = imax % 2
+    sumres = 0
+    for kk in range(imin, int(imax) + 1, 2):
+        sumres = sumres + (kk + 1) * \
+            racah(j_1, j_2, j_9, j_6, j_3, kk / 2, prec) * \
+            racah(j_4, j_6, j_8, j_2, j_5, kk / 2, prec) * \
+            racah(j_1, j_4, j_9, j_8, j_7, kk / 2, prec)
+    return sumres
+
+
+def gaunt(l_1, l_2, l_3, m_1, m_2, m_3, prec=None):
+    r"""
+    Calculate the Gaunt coefficient.
+
+    Explanation
+    ===========
+
+    The Gaunt coefficient is defined as the integral over three
+    spherical harmonics:
+
+    .. math::
+
+        \begin{aligned}
+        \operatorname{Gaunt}(l_1,l_2,l_3,m_1,m_2,m_3)
+        &=\int Y_{l_1,m_1}(\Omega)
+         Y_{l_2,m_2}(\Omega) Y_{l_3,m_3}(\Omega) \,d\Omega \\
+        &=\sqrt{\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4\pi}}
+         \operatorname{Wigner3j}(l_1,l_2,l_3,0,0,0)
+         \operatorname{Wigner3j}(l_1,l_2,l_3,m_1,m_2,m_3)
+        \end{aligned}
+
+    Parameters
+    ==========
+
+    l_1, l_2, l_3, m_1, m_2, m_3 :
+        Integer.
+    prec - precision, default: ``None``.
+        Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import gaunt
+    >>> gaunt(1,0,1,1,0,-1)
+    -1/(2*sqrt(pi))
+    >>> gaunt(1000,1000,1200,9,3,-12).n(64)
+    0.006895004219221134484332976156744208248842039317638217822322799675
+
+    It is an error to use non-integer values for `l` and `m`::
+
+        sage: gaunt(1.2,0,1.2,0,0,0)
+        Traceback (most recent call last):
+        ...
+        ValueError: l values must be integer
+        sage: gaunt(1,0,1,1.1,0,-1.1)
+        Traceback (most recent call last):
+        ...
+        ValueError: m values must be integer
+
+    Notes
+    =====
+
+    The Gaunt coefficient obeys the following symmetry rules:
+
+    - invariant under any permutation of the columns
+
+      .. math::
+        \begin{aligned}
+          Y(l_1,l_2,l_3,m_1,m_2,m_3)
+          &=Y(l_3,l_1,l_2,m_3,m_1,m_2) \\
+          &=Y(l_2,l_3,l_1,m_2,m_3,m_1) \\
+          &=Y(l_3,l_2,l_1,m_3,m_2,m_1) \\
+          &=Y(l_1,l_3,l_2,m_1,m_3,m_2) \\
+          &=Y(l_2,l_1,l_3,m_2,m_1,m_3)
+        \end{aligned}
+
+    - invariant under space inflection, i.e.
+
+      .. math::
+          Y(l_1,l_2,l_3,m_1,m_2,m_3)
+          =Y(l_1,l_2,l_3,-m_1,-m_2,-m_3)
+
+    - symmetric with respect to the 72 Regge symmetries as inherited
+      for the `3j` symbols [Regge58]_
+
+    - zero for `l_1`, `l_2`, `l_3` not fulfilling triangle relation
+
+    - zero for violating any one of the conditions: `l_1 \ge |m_1|`,
+      `l_2 \ge |m_2|`, `l_3 \ge |m_3|`
+
+    - non-zero only for an even sum of the `l_i`, i.e.
+      `L = l_1 + l_2 + l_3 = 2n` for `n` in `\mathbb{N}`
+
+    Algorithms
+    ==========
+
+    This function uses the algorithm of [Liberatodebrito82]_ to
+    calculate the value of the Gaunt coefficient exactly. Note that
+    the formula contains alternating sums over large factorials and is
+    therefore unsuitable for finite precision arithmetic and only
+    useful for a computer algebra system [Rasch03]_.
+
+    Authors
+    =======
+
+    Jens Rasch (2009-03-24): initial version for Sage.
+    """
+    l_1, l_2, l_3, m_1, m_2, m_3 = [
+        as_int(i) for i in (l_1, l_2, l_3, m_1, m_2, m_3)]
+
+    if l_1 + l_2 - l_3 < 0:
+        return S.Zero
+    if l_1 - l_2 + l_3 < 0:
+        return S.Zero
+    if -l_1 + l_2 + l_3 < 0:
+        return S.Zero
+    if (m_1 + m_2 + m_3) != 0:
+        return S.Zero
+    if (abs(m_1) > l_1) or (abs(m_2) > l_2) or (abs(m_3) > l_3):
+        return S.Zero
+    bigL, remL = divmod(l_1 + l_2 + l_3, 2)
+    if remL % 2:
+        return S.Zero
+
+    imin = max(-l_3 + l_1 + m_2, -l_3 + l_2 - m_1, 0)
+    imax = min(l_2 + m_2, l_1 - m_1, l_1 + l_2 - l_3)
+
+    _calc_factlist(max(l_1 + l_2 + l_3 + 1, imax + 1))
+
+    ressqrt = sqrt((2 * l_1 + 1) * (2 * l_2 + 1) * (2 * l_3 + 1) * \
+        _Factlist[l_1 - m_1] * _Factlist[l_1 + m_1] * _Factlist[l_2 - m_2] * \
+        _Factlist[l_2 + m_2] * _Factlist[l_3 - m_3] * _Factlist[l_3 + m_3] / \
+        (4*pi))
+
+    prefac = Integer(_Factlist[bigL] * _Factlist[l_2 - l_1 + l_3] *
+                     _Factlist[l_1 - l_2 + l_3] * _Factlist[l_1 + l_2 - l_3])/ \
+        _Factlist[2 * bigL + 1]/ \
+        (_Factlist[bigL - l_1] *
+         _Factlist[bigL - l_2] * _Factlist[bigL - l_3])
+
+    sumres = 0
+    for ii in range(int(imin), int(imax) + 1):
+        den = _Factlist[ii] * _Factlist[ii + l_3 - l_1 - m_2] * \
+            _Factlist[l_2 + m_2 - ii] * _Factlist[l_1 - ii - m_1] * \
+            _Factlist[ii + l_3 - l_2 + m_1] * _Factlist[l_1 + l_2 - l_3 - ii]
+        sumres = sumres + Integer((-1) ** ii) / den
+
+    res = ressqrt * prefac * sumres * Integer((-1) ** (bigL + l_3 + m_1 - m_2))
+    if prec is not None:
+        res = res.n(prec)
+    return res
+
+
+def real_gaunt(l_1, l_2, l_3, mu_1, mu_2, mu_3, prec=None):
+    r"""
+    Calculate the real Gaunt coefficient.
+
+    Explanation
+    ===========
+
+    The real Gaunt coefficient is defined as the integral over three
+    real spherical harmonics:
+
+    .. math::
+        \begin{aligned}
+        \operatorname{RealGaunt}(l_1,l_2,l_3,\mu_1,\mu_2,\mu_3)
+        &=\int Z^{\mu_1}_{l_1}(\Omega)
+         Z^{\mu_2}_{l_2}(\Omega) Z^{\mu_3}_{l_3}(\Omega) \,d\Omega \\
+        \end{aligned}
+
+    Alternatively, it can be defined in terms of the standard Gaunt
+    coefficient by relating the real spherical harmonics to the standard
+    spherical harmonics via a unitary transformation `U`, i.e.
+    `Z^{\mu}_{l}(\Omega)=\sum_{m'}U^{\mu}_{m'}Y^{m'}_{l}(\Omega)` [Homeier96]_.
+    The real Gaunt coefficient is then defined as
+
+    .. math::
+        \begin{aligned}
+        \operatorname{RealGaunt}(l_1,l_2,l_3,\mu_1,\mu_2,\mu_3)
+        &=\int Z^{\mu_1}_{l_1}(\Omega)
+         Z^{\mu_2}_{l_2}(\Omega) Z^{\mu_3}_{l_3}(\Omega) \,d\Omega \\
+        &=\sum_{m'_1 m'_2 m'_3} U^{\mu_1}_{m'_1}U^{\mu_2}_{m'_2}U^{\mu_3}_{m'_3}
+         \operatorname{Gaunt}(l_1,l_2,l_3,m'_1,m'_2,m'_3)
+        \end{aligned}
+
+    The unitary matrix `U` has components
+
+    .. math::
+        \begin{aligned}
+        U^\mu_{m} = \delta_{|\mu||m|}*(\delta_{m0}\delta_{\mu 0} + \frac{1}{\sqrt{2}}\big[\Theta(\mu)\big(\delta_{m\mu}+(-1)^{m}\delta_{m-\mu}\big)
+        +i \Theta(-\mu)\big((-1)^{m}\delta_{m\mu}-\delta_{m-\mu}\big)\big])
+        \end{aligned}
+
+
+    where `\delta_{ij}` is the Kronecker delta symbol and `\Theta` is a step
+    function defined as
+
+    .. math::
+        \begin{aligned}
+        \Theta(x) = \begin{cases} 1 \,\text{for}\, x > 0 \\ 0 \,\text{for}\, x \leq 0 \end{cases}
+        \end{aligned}
+
+    Parameters
+    ==========
+
+    l_1, l_2, l_3, mu_1, mu_2, mu_3 :
+        Integer degree and order
+
+    prec - precision, default: ``None``.
+        Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number.
+
+    Examples
+    ========
+    >>> from sympy.physics.wigner import real_gaunt
+    >>> real_gaunt(1,1,2,-1,1,-2)
+    sqrt(15)/(10*sqrt(pi))
+    >>> real_gaunt(10,10,20,-9,-9,0,prec=64)
+    -0.00002480019791932209313156167176797577821140084216297395518482071448
+
+    It is an error to use non-integer values for `l` and `\mu`::
+        real_gaunt(2.8,0.5,1.3,0,0,0)
+        Traceback (most recent call last):
+        ...
+        ValueError: l values must be integer
+
+        real_gaunt(2,2,4,0.7,1,-3.4)
+        Traceback (most recent call last):
+        ...
+        ValueError: mu values must be integer
+
+    Notes
+    =====
+
+    The real Gaunt coefficient inherits from the standard Gaunt coefficient,
+    the invariance under any permutation of the pairs `(l_i, \mu_i)` and the
+    requirement that the sum of the `l_i` be even to yield a non-zero value.
+    It also obeys the following symmetry rules:
+
+    - zero for `l_1`, `l_2`, `l_3` not fulfilling the condition
+      `l_1 \in \{l_{\text{max}}, l_{\text{max}}-2, \ldots, l_{\text{min}}\}`,
+      where `l_{\text{max}} = l_2+l_3`,
+
+      .. math::
+          \begin{aligned}
+          l_{\text{min}} = \begin{cases} \kappa(l_2, l_3, \mu_2, \mu_3) & \text{if}\,
+          \kappa(l_2, l_3, \mu_2, \mu_3) + l_{\text{max}}\, \text{is even} \\
+          \kappa(l_2, l_3, \mu_2, \mu_3)+1 & \text{if}\, \kappa(l_2, l_3, \mu_2, \mu_3) +
+          l_{\text{max}}\, \text{is odd}\end{cases}
+          \end{aligned}
+
+      and `\kappa(l_2, l_3, \mu_2, \mu_3) = \max{\big(|l_2-l_3|, \min{\big(|\mu_2+\mu_3|,
+      |\mu_2-\mu_3|\big)}\big)}`
+
+    - zero for an odd number of negative `\mu_i`
+
+    Algorithms
+    ==========
+
+    This function uses the algorithms of [Homeier96]_ and [Rasch03]_ to
+    calculate the value of the real Gaunt coefficient exactly. Note that
+    the formula used in [Rasch03]_ contains alternating sums over large
+    factorials and is therefore unsuitable for finite precision arithmetic
+    and only useful for a computer algebra system [Rasch03]_. However, this
+    function can in principle use any algorithm that computes the Gaunt
+    coefficient, so it is suitable for finite precision arithmetic in so far
+    as the algorithm which computes the Gaunt coefficient is.
+    """
+    l_1, l_2, l_3, mu_1, mu_2, mu_3 = [
+        as_int(i) for i in (l_1, l_2, l_3, mu_1, mu_2, mu_3)]
+
+    # check for quick exits
+    if sum(1 for i in (mu_1, mu_2, mu_3) if i < 0) % 2:
+        return S.Zero  # odd number of negative m
+    if (l_1 + l_2 + l_3) % 2:
+        return S.Zero  # sum of l is odd
+    lmax = l_2 + l_3
+    lmin = max(abs(l_2 - l_3), min(abs(mu_2 + mu_3), abs(mu_2 - mu_3)))
+    if (lmin + lmax) % 2:
+        lmin += 1
+    if lmin not in range(lmax, lmin - 2, -2):
+        return S.Zero
+
+    kron_del = lambda i, j: 1 if i == j else 0
+    s = lambda e: -1 if e % 2 else 1  #  (-1)**e to give +/-1, avoiding float when e<0
+
+    t = lambda x: 1 if x > 0 else 0
+    A = lambda mu, m: t(-mu) * (s(m) * kron_del(m, mu) - kron_del(m, -mu))
+    B = lambda mu, m: t(mu) * (kron_del(m, mu) + s(m) * kron_del(m, -mu))
+    U = lambda mu, m: kron_del(abs(mu), abs(m)) * (kron_del(mu, 0) * kron_del(m, 0) + (B(mu, m) + I * A(mu, m))/sqrt(2))
+
+    ugnt = 0
+    for m1 in range(-l_1, l_1+1):
+        U1 = U(mu_1, m1)
+        for m2 in range(-l_2, l_2+1):
+            U2 = U(mu_2, m2)
+            U3 = U(mu_3,-m1-m2)
+            ugnt = ugnt + re(U1*U2*U3)*gaunt(l_1, l_2, l_3, m1, m2, -m1 - m2, prec=prec)
+
+    return ugnt
+
+
+class Wigner3j(Function):
+
+    def doit(self, **hints):
+        if all(obj.is_number for obj in self.args):
+            return wigner_3j(*self.args)
+        else:
+            return self
+
+def dot_rot_grad_Ynm(j, p, l, m, theta, phi):
+    r"""
+    Returns dot product of rotational gradients of spherical harmonics.
+
+    Explanation
+    ===========
+
+    This function returns the right hand side of the following expression:
+
+    .. math ::
+        \vec{R}Y{_j^{p}} \cdot \vec{R}Y{_l^{m}} = (-1)^{m+p}
+        \sum\limits_{k=|l-j|}^{l+j}Y{_k^{m+p}}  * \alpha_{l,m,j,p,k} *
+        \frac{1}{2} (k^2-j^2-l^2+k-j-l)
+
+
+    Arguments
+    =========
+
+    j, p, l, m .... indices in spherical harmonics (expressions or integers)
+    theta, phi .... angle arguments in spherical harmonics
+
+    Example
+    =======
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.wigner import dot_rot_grad_Ynm
+    >>> theta, phi = symbols("theta phi")
+    >>> dot_rot_grad_Ynm(3, 2, 2, 0, theta, phi).doit()
+    3*sqrt(55)*Ynm(5, 2, theta, phi)/(11*sqrt(pi))
+
+    """
+    j = sympify(j)
+    p = sympify(p)
+    l = sympify(l)
+    m = sympify(m)
+    theta = sympify(theta)
+    phi = sympify(phi)
+    k = Dummy("k")
+
+    def alpha(l,m,j,p,k):
+        return sqrt((2*l+1)*(2*j+1)*(2*k+1)/(4*pi)) * \
+                Wigner3j(j, l, k, S.Zero, S.Zero, S.Zero) * \
+                Wigner3j(j, l, k, p, m, -m-p)
+
+    return (S.NegativeOne)**(m+p) * Sum(Ynm(k, m+p, theta, phi) * alpha(l,m,j,p,k) / 2 \
+        *(k**2-j**2-l**2+k-j-l), (k, abs(l-j), l+j))
+
+
+def wigner_d_small(J, beta):
+    """Return the small Wigner d matrix for angular momentum J.
+
+    Explanation
+    ===========
+
+    J : An integer, half-integer, or SymPy symbol for the total angular
+        momentum of the angular momentum space being rotated.
+    beta : A real number representing the Euler angle of rotation about
+        the so-called line of nodes. See [Edmonds74]_.
+
+    Returns
+    =======
+
+    A matrix representing the corresponding Euler angle rotation( in the basis
+    of eigenvectors of `J_z`).
+
+    .. math ::
+        \\mathcal{d}_{\\beta} = \\exp\\big( \\frac{i\\beta}{\\hbar} J_y\\big)
+
+    such that
+
+    .. math ::
+        d^{(J)}_{m',m}(\\beta) = \\mathtt{wigner\\_d\\_small(J,beta)[J-mprime,J-m]}
+
+    The components are calculated using the general form [Edmonds74]_,
+    equation 4.1.15.
+
+    Examples
+    ========
+
+    >>> from sympy import Integer, symbols, pi, pprint
+    >>> from sympy.physics.wigner import wigner_d_small
+    >>> half = 1/Integer(2)
+    >>> beta = symbols("beta", real=True)
+    >>> pprint(wigner_d_small(half, beta), use_unicode=True)
+    ⎡   ⎛β⎞      ⎛β⎞⎤
+    ⎢cos⎜─⎟   sin⎜─⎟⎥
+    ⎢   ⎝2⎠      ⎝2⎠⎥
+    ⎢               ⎥
+    ⎢    ⎛β⎞     ⎛β⎞⎥
+    ⎢-sin⎜─⎟  cos⎜─⎟⎥
+    ⎣    ⎝2⎠     ⎝2⎠⎦
+
+    >>> pprint(wigner_d_small(2*half, beta), use_unicode=True)
+    ⎡        2⎛β⎞              ⎛β⎞    ⎛β⎞           2⎛β⎞     ⎤
+    ⎢     cos ⎜─⎟        √2⋅sin⎜─⎟⋅cos⎜─⎟        sin ⎜─⎟     ⎥
+    ⎢         ⎝2⎠              ⎝2⎠    ⎝2⎠            ⎝2⎠     ⎥
+    ⎢                                                        ⎥
+    ⎢       ⎛β⎞    ⎛β⎞       2⎛β⎞      2⎛β⎞        ⎛β⎞    ⎛β⎞⎥
+    ⎢-√2⋅sin⎜─⎟⋅cos⎜─⎟  - sin ⎜─⎟ + cos ⎜─⎟  √2⋅sin⎜─⎟⋅cos⎜─⎟⎥
+    ⎢       ⎝2⎠    ⎝2⎠        ⎝2⎠       ⎝2⎠        ⎝2⎠    ⎝2⎠⎥
+    ⎢                                                        ⎥
+    ⎢        2⎛β⎞               ⎛β⎞    ⎛β⎞          2⎛β⎞     ⎥
+    ⎢     sin ⎜─⎟        -√2⋅sin⎜─⎟⋅cos⎜─⎟       cos ⎜─⎟     ⎥
+    ⎣         ⎝2⎠               ⎝2⎠    ⎝2⎠           ⎝2⎠     ⎦
+
+    From table 4 in [Edmonds74]_
+
+    >>> pprint(wigner_d_small(half, beta).subs({beta:pi/2}), use_unicode=True)
+    ⎡ √2   √2⎤
+    ⎢ ──   ──⎥
+    ⎢ 2    2 ⎥
+    ⎢        ⎥
+    ⎢-√2   √2⎥
+    ⎢────  ──⎥
+    ⎣ 2    2 ⎦
+
+    >>> pprint(wigner_d_small(2*half, beta).subs({beta:pi/2}),
+    ... use_unicode=True)
+    ⎡       √2      ⎤
+    ⎢1/2    ──   1/2⎥
+    ⎢       2       ⎥
+    ⎢               ⎥
+    ⎢-√2         √2 ⎥
+    ⎢────   0    ── ⎥
+    ⎢ 2          2  ⎥
+    ⎢               ⎥
+    ⎢      -√2      ⎥
+    ⎢1/2   ────  1/2⎥
+    ⎣       2       ⎦
+
+    >>> pprint(wigner_d_small(3*half, beta).subs({beta:pi/2}),
+    ... use_unicode=True)
+    ⎡ √2    √6    √6   √2⎤
+    ⎢ ──    ──    ──   ──⎥
+    ⎢ 4     4     4    4 ⎥
+    ⎢                    ⎥
+    ⎢-√6   -√2    √2   √6⎥
+    ⎢────  ────   ──   ──⎥
+    ⎢ 4     4     4    4 ⎥
+    ⎢                    ⎥
+    ⎢ √6   -√2   -√2   √6⎥
+    ⎢ ──   ────  ────  ──⎥
+    ⎢ 4     4     4    4 ⎥
+    ⎢                    ⎥
+    ⎢-√2    √6   -√6   √2⎥
+    ⎢────   ──   ────  ──⎥
+    ⎣ 4     4     4    4 ⎦
+
+    >>> pprint(wigner_d_small(4*half, beta).subs({beta:pi/2}),
+    ... use_unicode=True)
+    ⎡             √6            ⎤
+    ⎢1/4   1/2    ──   1/2   1/4⎥
+    ⎢             4             ⎥
+    ⎢                           ⎥
+    ⎢-1/2  -1/2   0    1/2   1/2⎥
+    ⎢                           ⎥
+    ⎢ √6                     √6 ⎥
+    ⎢ ──    0    -1/2   0    ── ⎥
+    ⎢ 4                      4  ⎥
+    ⎢                           ⎥
+    ⎢-1/2  1/2    0    -1/2  1/2⎥
+    ⎢                           ⎥
+    ⎢             √6            ⎥
+    ⎢1/4   -1/2   ──   -1/2  1/4⎥
+    ⎣             4             ⎦
+
+    """
+    M = [J-i for i in range(2*J+1)]
+    d = zeros(2*J+1)
+
+    # Mi corresponds to Edmonds' $m'$, and Mj to $m$.
+    for i, Mi in enumerate(M):
+        for j, Mj in enumerate(M):
+
+            # We get the maximum and minimum value of sigma.
+            sigmamax = min([J-Mi, J-Mj])
+            sigmamin = max([0, -Mi-Mj])
+
+            dij = sqrt(factorial(J+Mi)*factorial(J-Mi) /
+                       factorial(J+Mj)/factorial(J-Mj))
+            terms = [(-1)**(J-Mi-s) *
+                     binomial(J+Mj, J-Mi-s) *
+                     binomial(J-Mj, s) *
+                     cos(beta/2)**(2*s+Mi+Mj) *
+                     sin(beta/2)**(2*J-2*s-Mj-Mi)
+                     for s in range(sigmamin, sigmamax+1)]
+
+            d[i, j] = dij*Add(*terms)
+
+    return ImmutableMatrix(d)
+
+
+def wigner_d(J, alpha, beta, gamma):
+    """Return the Wigner D matrix for angular momentum J.
+
+    Explanation
+    ===========
+
+    J :
+        An integer, half-integer, or SymPy symbol for the total angular
+        momentum of the angular momentum space being rotated.
+    alpha, beta, gamma - Real numbers representing the Euler.
+        Angles of rotation about the so-called figure axis, line of nodes,
+        and vertical. See [Edmonds74]_, however note that the symbols alpha
+        and gamma are swapped in this implementation.
+
+    Returns
+    =======
+
+    A matrix representing the corresponding Euler angle rotation (in the basis
+    of eigenvectors of `J_z`).
+
+    .. math ::
+        \\mathcal{D}_{\\alpha \\beta \\gamma} =
+        \\exp\\big( \\frac{i\\alpha}{\\hbar} J_z\\big)
+        \\exp\\big( \\frac{i\\beta}{\\hbar} J_y\\big)
+        \\exp\\big( \\frac{i\\gamma}{\\hbar} J_z\\big)
+
+    such that
+
+    .. math ::
+        \\mathcal{D}^{(J)}_{m',m}(\\alpha, \\beta, \\gamma) =
+        \\mathtt{wigner_d(J, alpha, beta, gamma)[J-mprime,J-m]}
+
+    The components are calculated using the general form [Edmonds74]_,
+    equation 4.1.12, however note that the angles alpha and gamma are swapped
+    in this implementation.
+
+    Examples
+    ========
+
+    The simplest possible example:
+
+    >>> from sympy.physics.wigner import wigner_d
+    >>> from sympy import Integer, symbols, pprint
+    >>> half = 1/Integer(2)
+    >>> alpha, beta, gamma = symbols("alpha, beta, gamma", real=True)
+    >>> pprint(wigner_d(half, alpha, beta, gamma), use_unicode=True)
+    ⎡  ⅈ⋅α  ⅈ⋅γ             ⅈ⋅α  -ⅈ⋅γ         ⎤
+    ⎢  ───  ───             ───  ─────        ⎥
+    ⎢   2    2     ⎛β⎞       2     2      ⎛β⎞ ⎥
+    ⎢ ℯ   ⋅ℯ   ⋅cos⎜─⎟     ℯ   ⋅ℯ     ⋅sin⎜─⎟ ⎥
+    ⎢              ⎝2⎠                    ⎝2⎠ ⎥
+    ⎢                                         ⎥
+    ⎢  -ⅈ⋅α   ⅈ⋅γ          -ⅈ⋅α   -ⅈ⋅γ        ⎥
+    ⎢  ─────  ───          ─────  ─────       ⎥
+    ⎢    2     2     ⎛β⎞     2      2      ⎛β⎞⎥
+    ⎢-ℯ     ⋅ℯ   ⋅sin⎜─⎟  ℯ     ⋅ℯ     ⋅cos⎜─⎟⎥
+    ⎣                ⎝2⎠                   ⎝2⎠⎦
+
+    """
+    d = wigner_d_small(J, beta)
+    M = [J-i for i in range(2*J+1)]
+    # Mi corresponds to Edmonds' $m'$, and Mj to $m$.
+    D = [[exp(I*Mi*alpha)*d[i, j]*exp(I*Mj*gamma)
+          for j, Mj in enumerate(M)] for i, Mi in enumerate(M)]
+    return ImmutableMatrix(D)
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/release.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/release.py
new file mode 100644
index 0000000000000000000000000000000000000000..b9f68edb2f571e7bfaad9472d36a2d357b5574b2
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/release.py
@@ -0,0 +1 @@
+__version__ = "1.14.0"
diff --git a/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/this.py b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/this.py
new file mode 100644
index 0000000000000000000000000000000000000000..c2a5504ac42c7d57790d65524b066a6df86ab539
--- /dev/null
+++ b/code/LaDi-RL-old-qwen-cod/LaDi-RL-old-qwen-cod/venv/lib64/python3.10/site-packages/sympy/this.py
@@ -0,0 +1,21 @@
+"""
+The Zen of SymPy.
+"""
+
+s = """The Zen of SymPy
+
+Unevaluated is better than evaluated.
+The user interface matters.
+Printing matters.
+Pure Python can be fast enough.
+If it's too slow, it's (probably) your fault.
+Documentation matters.
+Correctness is more important than speed.
+Push it in now and improve upon it later.
+Coverage by testing matters.
+Smart tests are better than random tests.
+But random tests sometimes find what your smartest test missed.
+The Python way is probably the right way.
+Community is more important than code."""
+
+print(s)